From 16e9030ffb8837c48fac59330f046ca6644e4959 Mon Sep 17 00:00:00 2001 From: "Kevin J. Sung" Date: Fri, 31 May 2024 09:26:21 -0400 Subject: [PATCH] Add spin-balanced UCJ operator and refactor spin-unbalanced UCJ (#208) * add closed-shell UCJ operator * rename open/closed to spin unbalanced/balanced * update docs * rename files * use single interaction_pairs tuple * rename file * rename file * allow specifying different reps for ab and aabb * delete beh test * fix test * update docs and rename files * add ucj spin balanced qiskit gate * reorder classes in file * handle None * docs * fix sampler * fix deprecations --- docs/explanations/index.md | 1 + docs/explanations/lucj.ipynb | 82 +++ .../qiskit-gate-decompositions.ipynb | 108 ++-- docs/how-to-guides/lucj.ipynb | 193 +++---- docs/how-to-guides/qiskit-circuits.ipynb | 58 ++- docs/how-to-guides/qiskit-sampler.ipynb | 115 +++-- python/ffsim/__init__.py | 6 +- python/ffsim/qiskit/__init__.py | 6 +- python/ffsim/qiskit/gates/__init__.py | 7 +- python/ffsim/qiskit/gates/ucj.py | 98 +++- .../{ucj_open_shell.py => ucj_operator.py} | 23 +- python/ffsim/qiskit/sim.py | 16 +- python/ffsim/qiskit/transpiler_stages.py | 8 +- python/ffsim/random/__init__.py | 6 +- python/ffsim/random/random.py | 58 ++- python/ffsim/variational/__init__.py | 6 +- python/ffsim/variational/ucj.py | 3 + python/ffsim/variational/ucj_spin_balanced.py | 485 ++++++++++++++++++ ...j_open_shell.py => ucj_spin_unbalanced.py} | 355 ++++++++----- .../double_factorized_decomposition_test.py | 48 +- tests/python/optimize/linear_method_test.py | 4 +- .../qiskit/merge_orbital_rotations_test.py | 39 +- tests/python/qiskit/sampler_test.py | 18 +- ...pen_shell_test.py => ucj_operator_test.py} | 5 +- tests/python/qiskit/ucj_test.py | 35 +- ...hell_test.py => ucj_spin_balanced_test.py} | 104 ++-- .../variational/ucj_spin_unbalanced_test.py | 170 ++++++ tests/python/variational/ucj_test.py | 11 + 28 files changed, 1521 insertions(+), 547 deletions(-) create mode 100644 docs/explanations/lucj.ipynb rename python/ffsim/qiskit/gates/{ucj_open_shell.py => ucj_operator.py} (73%) create mode 100644 python/ffsim/variational/ucj_spin_balanced.py rename python/ffsim/variational/{ucj_open_shell.py => ucj_spin_unbalanced.py} (59%) rename tests/python/qiskit/{ucj_open_shell_test.py => ucj_operator_test.py} (90%) rename tests/python/variational/{ucj_open_shell_test.py => ucj_spin_balanced_test.py} (57%) create mode 100644 tests/python/variational/ucj_spin_unbalanced_test.py diff --git a/docs/explanations/index.md b/docs/explanations/index.md index c7f713323..93f8bbd04 100644 --- a/docs/explanations/index.md +++ b/docs/explanations/index.md @@ -7,5 +7,6 @@ state-vectors-and-gates hamiltonians orbital-rotation double-factorized +lucj qiskit-gate-decompositions ``` diff --git a/docs/explanations/lucj.ipynb b/docs/explanations/lucj.ipynb new file mode 100644 index 000000000..ed72090d7 --- /dev/null +++ b/docs/explanations/lucj.ipynb @@ -0,0 +1,82 @@ +{ + "cells": [ + { + "attachments": { + 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The local unitary cluster Jastrow (LUCJ) ansatz\n", + "\n", + "This page explains the local unitary cluster Jastrow (LUCJ) ansatz, which was originally introduced in [this paper](https://pubs.rsc.org/en/content/articlelanding/2023/sc/d3sc02516k). For a guide on simulating the LUCJ ansatz using ffsim, see [How to simulate the local unitary cluster Jastrow (LUCJ) ansatz](../how-to-guides/lucj.ipynb).\n", + "\n", + "## The general unitary cluster Jastrow (UCJ) ansatz\n", + "\n", + "The LUCJ ansatz is a specialized form of the general unitary cluster Jastrow (UCJ) ansatz, which has the form\n", + "\n", + "$$\n", + " \\lvert \\Psi \\rangle = \\prod_{k = 1}^L \\mathcal{U}_k e^{i \\mathcal{J}_k} \\mathcal{U}_k^\\dagger \\lvert \\Phi_0 \\rangle\n", + "$$\n", + "\n", + "where $\\lvert \\Phi_0 \\rangle$ is a reference state, often taken as the Hartree-Fock state, each $\\mathcal{U}_k$ is an [orbital rotation](orbital-rotation.ipynb), and each $\\mathcal{J}_k$ is a diagonal Coulomb operator of the form\n", + "\n", + "$$\n", + " \\mathcal{J} = \\frac12\\sum_{ij,\\sigma \\tau} \\mathbf{J}^{\\sigma \\tau}_{ij} n_{i,\\sigma} n_{j,\\tau}.\n", + "$$\n", + "\n", + "In ffsim, the UCJ ansatz is represented using classes that store the diagonal Coulomb matrices and orbital rotations as Numpy arrays. To facilitate variational optimization of the ansatzes, these classes implement methods for conversion to and from a vector of real-valued parameters. The parameter vector stores the entries of the UCJ matrices in a non-redundant way (for the orbital rotations, the parameter vector actually stores the entries of their logarithm).\n", + "\n", + "### Spin-balanced and spin-unbalanced ansatzes\n", + "\n", + "ffsim implements two variants of the UCJ ansatz, a \"spin-balanced\" ansatz, which is appropriate to apply to a closed-shell reference state, and a \"spin-unbalanced\" ansatz, which is appropriate to apply to an open-shell initial reference state.\n", + "\n", + "In the spin-balanced ansatz, $\\mathbf{J}^{\\alpha\\alpha} = \\mathbf{J}^{\\beta\\beta}$ and $\\mathbf{J}^{\\alpha\\beta} = \\mathbf{J}^{\\beta\\alpha}$. As a result, each diagonal Coulomb operator is described by 2 matrices, $\\mathbf{J}^{\\alpha\\alpha}$ and $\\mathbf{J}^{\\alpha\\beta}$, and both of these matrices are symmetric. The spin-balanced UCJ ansatz is represented by the [UCJOpSpinBalanced](../api/ffsim.rst#ffsim.UCJOpSpinBalanced) class.\n", + "\n", + "In the spin-unbalanced ansatz, $\\mathbf{J}^{\\alpha\\alpha}$ and $\\mathbf{J}^{\\beta\\beta}$ are allowed to differ, and $\\mathbf{J}^{\\alpha\\beta}$ is no longer required to be symmetric. Since $\\mathbf{J}^{\\alpha\\beta}_{ij} = \\mathbf{J}^{\\beta\\alpha}_{ji}$, we don't need to store $\\mathbf{J}^{\\beta\\alpha}$ separately. Therefore, each diagonal Coulomb operator is described by 3 matrices, $\\mathbf{J}^{\\alpha\\alpha}$, $\\mathbf{J}^{\\alpha\\beta}$, and $\\mathbf{J}^{\\beta\\beta}$, and of these matrices, $\\mathbf{J}^{\\alpha\\alpha}$ and $\\mathbf{J}^{\\beta\\beta}$ are symmetric. The spin-unbalanced UCJ ansatz is represented by the [UCJOpSpinUnbalanced](../api/ffsim.rst#ffsim.UCJOpSpinUnbalanced) class.\n", + "\n", + "## The local UCJ (LUCJ) ansatz\n", + "\n", + "Implementing the $e^{i \\mathcal{J}_k}$ term of the UCJ ansatz requires either all-to-all connectivity or the use of a fermionic swap network, making it challenging for noisy pre-fault-tolerant quantum processors that have limited connectivity. The idea of the *local* UCJ ansatz is to impose sparsity constraints on the $\\mathbf{J}^{\\alpha\\alpha}$ and $\\mathbf{J}^{\\alpha\\beta}$ matrices which allow them to be implemented in constant depth on qubit topologies with limited connectivity. The constraints are specified by a list of indices indicating which matrix entries in the upper triangle are allowed to be nonzero (since the matrices are symmetric, only the upper triangle needs to be specified). These indices can be interpreted as pairs of orbitals that are allowed to interact.\n", + "\n", + "As an example, consider a square lattice qubit topology. We can place the $\\alpha$ and $\\beta$ orbitals in parallel lines on the lattice, with connections between these lines forming \"rungs\" of a ladder shape, like this:\n", + "\n", + "![square_lattice_gray_150dpi.png](attachment:653ac304-dbd2-4aea-9880-4898b4136750.png)\n", + "\n", + "With this setup, orbitals with the same spin are connected with a line topology, while orbitals with different spins are connected when they share the same spatial orbital. This yields the following index constraints on the $\\mathbf{J}$ matrices:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "\\mathbf{J}^{\\alpha\\alpha} &: \\set{(p, p+1) \\; , \\; p = 0, \\ldots, N-2} \\\\\n", + "\\mathbf{J}^{\\alpha\\beta} &: \\set{(p, p) \\;, \\; p = 0, \\ldots, N-1}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "In other words, if the $\\mathbf{J}$ matrices are nonzero only at the specified indices in the upper triangle, then the $e^{i \\mathcal{J}_k}$ term can be implemented on a square topology without using any swap gates, in constant depth. Of course, imposing such constraints on the ansatz makes it less expressive, so more ansatz repetitions may be required." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/docs/explanations/qiskit-gate-decompositions.ipynb b/docs/explanations/qiskit-gate-decompositions.ipynb index 642607a8b..bc14fc854 100644 --- a/docs/explanations/qiskit-gate-decompositions.ipynb +++ b/docs/explanations/qiskit-gate-decompositions.ipynb @@ -252,7 +252,7 @@ "outputs": [ { "data": { - "image/png": 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kKW6Y7JIkSZIkSVLcMNklSZIkSZKkuOEC9Udg2y4oq4jOvnPbQFpydPYtSZIkSZIUK0x2HYGyCrhyQXT2/fAoGNI+OvuWJEmSJEmKFU5jlCRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGC9Q3sZKfFFC5ophAUjKBxCRSup5El4nTaDP4zGiHJkmSJEmSFHcc2RUBXSZOI/+pbQx6fAOt+45g1V1fp6ZyS7TDkiRJkiRJijsmuyIoIbklHc6aTHD7Nrb/uyza4UiSJEmSJMUdk10RFNxRzWcvPUxCahtSuvSOdjiSJEmSJElxJ2aSXTt37mTKlCl0796dVq1aMW7cOBYuXEggEODZZ5+NdngN+njmFJZc1pal3+5J1ep3yL31/0hMbRPtsKJi++5oRyA1npoQrKsM/+wORjsa6dh9uh0+3AbVflZLOkxVu8OfG59tj3Yk0rHbHYSPKuHjqnA/T1LsiokF6kOhEBMmTGDhwoXcfvvt5ObmMnPmTMaPHw9Afn5+lCNsWJfL7qTz+B9FO4yo+qQaHlkJ/7d2b9llRXB5LpzTLWphSUdlVxBmlMHTq+HTHeGy9i1hQk/4j1xomRjV8KQjNvdjeLwUln+xnGSLBPhyN7iyD3ROjW5skpqnjyrDfbsX1oX/LgIMbAff6g1jO0c3NulIbd8NfyyDv62Bz3eGyzq3gkty4NJekBQzQ0Qk7RETya6HHnqI2bNns2TJEvr37w9AQUEBOTk5ZGZm0qNHjyhHqIb8uwqueBU27YB9B7+UVcCti6B8G3z3pKiFJx2RXUH4wRvw+qd1yzfugN+XwJufwf2nQQsTXooRj5XCb5fXHeq9MwjPfQjz18NjY6Bb66iFJ6kZWr0VJv8Ltu2q27d773P44UL44YBwgkCKBdt3w/eKw9fvvoO51lfDr9+HJRth+ikmvKRYExP/y06fPp2JEyfWJroAEhMTycnJqR3V9aMf/YicnBwCgQDLli2LVqg6gGnv1E90wd7Xf1gJyz6PdFTS0Xnqg/qJrn29vRH+tCpy8UjHomRLONEFB/6M3rITfrokwkFJavZuWwTbdh+8b3fvsvDNTCkWPFJaP9G1r/kb4H8/jGhIkhpBs092lZaWsnr1ai688MJ6dWvXrq1Ndn3961/nlVdeITs7O9IhqgEfVYYTAw0tZ5RAeDqY1NwFQ/DUaggcot3Ta1znQbHhmTUNdwSCwKKN4VEckgSwfHN4ynPwEH/nnlkTiWikY7MrCLPWHDzRBeF+318/gJB9OymmNPtpjOvWrQOgU6dOdcpXrFhBeXl5bbJr9OjRR72P9PR0du7cech2qX1HcOLUoiPadt9pR9b+YM44o4CqkuJG2VYkZYy6mB43zGiwTRCY9dYq7h7RLzJBHScG/DW8UmzLlilRjiR+JLbpQL9H1h2y3afboU2XXuzedOi2Ojxez02j972LSOne/5DtTrvoSjYXNfxZrsPn9axYlvml79H1yl832CYEPPLCG9wy9PTIBHWc8LOj8bXo0oe+v17aYJsQ8ME2aNWmLaGd1ZEJTBIAweDRPwWs2Y/sat++PQBlZWW1ZaFQiJtuuolgMNjsF6c/7oUO8+L0VoliwRF92HpNq/kLHe417We0pD0Os28X8u+gYoF9OyluNfuRXXl5eeTm5nLLLbeQnJxMWloaDzzwAIsXLyY1NZW+ffse8z62bj28+RlLNsKVC455d0dl3rwihrSPzr6Pxfpq+OpLDf9pSAC+cVouP9mxI1JhHReGPRf+d4fntdGEQnDRvPAj1g92TQcIP71n4cerSTjUfEcdNq/npnHP0vA08kN19d/++yN0a/1IRGI6Hng9K5aVVcA3ihpuEwCu+fJpXPsjr/HG5GdH49sdhPNeCj9o6GASgN4Z8NbWLRGLS1LYggULjnoWX7Mf2ZWUlMQzzzxDVlYWkyZN4oYbbuDcc89l7NixDBo0iISEZn8Ix7XOrcKPnz7UmjATekYoIOkYBALwjZyGk7ch4Bu9MNGlmHBRz0PfjBjZyacxStortw0MyWy4bxcALugZoYCkY5CUABNyGm4TBC49RBtJzU9MZIoGDx5McXExVVVVlJSUcNVVV7F48WKnMMaIHw+Crq3rL+q95+L7r/7QJyPSUUlH54KeUNgl/Pu+1/Se38eeAJfYIVKMyEmHmwaGf9+/QxAATmgFU4ZEOChJzd6dJ0P7lAP37QKEPze6pEY+LuloTMqF0zqGfz9Q3+4r3eG87pGOStKxiolk1/6qq6spKSmpk+y6/vrr6datGx999BGFhYX073/oBXcVGe1T4I9j4IrekJG8t/yUjnD/aXDZidGLTTpSiQGYNjScxM1J21veIw3+eyBMPyV8l1CKFRflwO9GwPCOe8vaJMPlufDE6dDRdZAl7ScrFWacDt88EVrvsyjKqBPgwVHw1R7Ri006UskJ8Kvh4RvwXfdJ0ua2CSdubxsSHt0vKbY0+zW7DuTdd9+lpqamTrLrvvvu47777otiVHtVrlzI2kd+AKEQ6YPG0XXi1AbrQrt3sfreb7JryydkDD2PzhfcGMXom0ZGC7g6D757EmzbBS0TICUmrz4pnPC6sCdckA2nPB8ue+YMO0KKXad2DP/sWQ/mpXPC17kkHUyHFLihP1zXD4Z/8bfwl8OjG5N0tJISwjfgL+21t283c6x9OymWxWS6Yfjw4YSa8ZOhUnvlc9L08Er2K6ecSU1VBYmpbQ5at+Xtf9D6pJGccP4NfHDPN9i15VOSMzoedPuxLDEQTnxJ8WDfDpCdIcUTE12SDpefF4on9u2k+OFkmyYQSArP1QvV1JCc2YWElqkN1u3csJpW2eFFU1K651FV+mbkg5YkSZIkSYoDJruayKb5M3nv2jwSW7clkJjUYF3Lrn3Ztmw+oVCIbe+9Sk2Vj7WVJEmSJEk6GjE5jbG5qP7wfT588Oo6ZRn559D5opvJHHsZ7cZ8gw9+PoHqNUtp1XNgbZv969qeej4VS+ZQettZJGV0JCmjU6QPRZIkSZIkKS6Y7DoGrXr0o++0onrlwV07SEhuSSAhgcRW6QRapDRYF0hMJPuqBwiFQqz51STSThoRwaOQJEmSJEmKHya7msCWhc/xyezfQjBIWv/TSenSm12fr2fjvBm0PKFnvbqdn37I6l9dTiCQQKev3lBnjS9JkiRJkiQdPpNdTaDdqAm0GzWhTllyu850vuDG2vp9tejY44AjxCRJkiRJknRkXKBekiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDdfsOgK5beDhUdHbt6TYU1RUxBVXXEF2djbZ2dk8/vjjdepnzJhBVlYWhYWF3HXXXfzjH/9gyJAh3H///XXavfDCC9xxxx2kp6fzxz/+kS5duvDVr36ViooKkpKSeOqpp+jQoQN33nknL730Ejk5OTzyyCNUVFQwdepU7r333kgetiRJkiRFjcmuI5CWDEPaRzsKSbFm8uTJ3HrrrVx//fUUFxczYsSI2rrnn3+ep556ig0bNrBo0SJeffVVfvCDH/DWW28xbNiw2nbTp09n3rx5lJWVMX36dH79618za9YskpOTmTFjBjNnzmTChAksXryYV155hd/85jc8//zzjB8/ns2bN7Nt2zbS0tKicfiSJEmSFFFOY5SOU0VFReTk5FBQUMCkSZPq1U+bNo3S0tKDvn/Tpk0MHTr0gAmU6upqvvzlLzN27FiuuOIKABYuXMioUaMYOXIkt956KwDLly9n+vTpjXREzd+AAQNYt25d7etNmzaRkpJCIBDgrbfeYuzYsQCMGzeOhQsX1nlvUlISKSkp9O/fv7YuOTkZgO3bt5OXl0d5eTn9+/cHYODAgRQXFwMwfPhwioqKmvrwJEmSJKlZMNklHccmT55MUVERGRkZtYkRgGAwyLvvvkvv3r0P+t709HReeuklTjvttHp1c+bMYfTo0cyfP5/k5GSWLVtGfn4+CxYs4LXXXqO4uJiKigry8vJYtGgRoVCoSY6vuSkuLiY3N7f2dVlZGdnZ2QBs3ryZNm3C85XT09PZvHlznffu2rWLjRs38q9//YtNmzYB4WTZyJEjue+++8jLy6NXr168/vrrBINBXnnlFbZs2QJAdnY2K1eujMARSpIkSVL0meySVG/E0TvvvEOfPn0afE9ycjKZmZkHrMvJyaGyshKAbdu2kZGRUTsKqaamhi5dupCamgpAr169eO+99xrjMJqtRx55hIKCArp27cqQIUMO2KZt27ZUVFQAsHXrVtq2bVunfurUqVx00UU8+eST9OvXD4DMzExee+01pk6dyi9/+Us6derE+PHjGTduHBs2bKBTp05NeViSJEmS1CyZ7JJUb8RRaWkpPXv2POrt5ebm8uqrr5KXl0cgEKB79+4AzJw5k7y8PNq2bUtSUnjJwONh1NGeEXRTp06tU56bm0t5eTkAQ4cO5ZVXXgFg3rx5nHrqqXXajh49mnnz5vGtb32L4cOHEwwG2b17NwAZGRmkpKQAcPXVV1NUVER2djZf/vKXASgvL29wlJ4kSZIkxROTXdJx7HBGHL3//vsUFBTU+bn77rsb3O7jjz/OJZdcwvLly+nQoQOvvfYaAJdddhkrVqzg448/ZunSpY19ODEnMzOTqqoqADp37sygQYMYM2YMO3bsYNiwYaxfv5577rkHgJ/+9KeMGzeO+++/n+uvv57KykrOPPNMzjjjDO6++26uu+46AC644AIKCwupqqqqXQj/9ddfp6CgICrHKEmSJEmR5tMYpePYnqcE7q93797MmjULgH79+h3x4ubBYLB2imNmZiabN29mx44dtGzZkoSEBNLT02tHIpWXlzNq1KhjO5BmbE+C8GDOP/985s6dS2FhIVOmTGHKlCm1dZ07d+bGG28E4LbbbuO2226r89758+fX296e/257bNq0ibZt25Kenn4MRyFJkiRJscORXZLqGTx4MCUlJYdsV1hYyOLFiyksLGTZsmW1I5Euu+wyHnvsMQoKCliyZAlnnXUWzz33HAUFBZx++ul069atdlpdWVkZAwYMaOpDarYuv/xyCgsLm2z7mZmZ/PKXv2yy7UuSJElSc+PILuk41dCIo4SEBAYNGkRpaWmDaz3NnTu3XtmekUhz5sypUz5hwgQmTJhQp2z58uUMHTqUQCBwhNFLkiRJknRgJrskHdCBpjc2try8PPLy8pp8P5IkSZKk44fTGCVJkiRJkhQ3THZJkiRJkiQpbjiN8TBt2wVlFdGNIbcNpCVHNwZJkiRJkqTmzGTXYSqrgCsXRDeGh0fBkPbRjUGSJEmSJKk5cxqjJEmSJEmS4obJLkmSJEmSJMUNk12SJEmSJEmKGya7JEmSJEmSFDdcoL6JlfykgMoVxQSSkgkkJpHS9SS6TJxGm8FnRjs0SZIkSZKkuOPIrgjoMnEa+U9tY9DjG2jddwSr7vo6NZVboh2WJEmSJElS3DHZFUEJyS3pcNZkgtu3sf3fZdEOR5IkSZIkKe6Y7Iqg4I5qPnvpYRJS25DSpXe0w5EkSZIkSYo7MZPs2rlzJ1OmTKF79+60atWKcePGsXDhQgKBAM8++2y0w2vQxzOnsOSytiz9dk+qVr9D7q3/R2Jqm2iHpTgWDEU7guNDKHTg3yVJ0bcrCJt3wM6aaEciSdpXKATbdkHFTvvQajoxsUB9KBRiwoQJLFy4kNtvv53c3FxmzpzJ+PHjAcjPz49yhA3rctmddB7/o2iHoePA9hr4ywfw19V7y/5jPlx2IpzTFQKB6MUWT2pC8Pc18Jd9zvOF/4RLesGF2ZAUM7cRJCn+lG+DJ8rgHx/BziAkBqCwC1yeC30zoh2dJB2/QiF4fm34+8rKinBZViu4OAcuyYEWidGNT/ElJpJdDz30ELNnz2bJkiX0798fgIKCAnJycsjMzKRHjx5RjlCKvurdcHUxLP28bnnJFpiyCJZ9Dj8aYMLrWNWE4Ja34OV/w76ncm0l3LMU3vgEfn6KCS9Jiob3PoerXgvf/Al+UVYTgpfWwT//Db88FU7rFNUQJem4FArB1Hfg2Q/r9qHXV8Ov34cFG+DXp0FLE15qJDHxdWz69OlMnDixNtEFkJiYSE5ODvn5+WzcuJEvf/nL9O3bl4EDB3LBBRfw6aefRjFiKfIeLAkntPa3p7P/1GqYvz6iIcWlWWvCiS6AfUdd7/n9lQ11R3xJkiKjJgQ3vlk30bVHENgdhJvegqrd0YhOko5vL64LJ7rgwH3otzbCY6WRjkrxrNknu0pLS1m9ejUXXnhhvbq1a9eSn59PIBDgv//7vykpKWHp0qWceOKJ3HzzzVGIVoqO7bvh7+V1/3DsLwGTMMcqFIInP6h7N2p/AeCpD1w3TZIi7V8b4JPt9RNde4SAyt3wwkeRjEqSBOGpi4dKPjyzJrzeotQYmv00xnXr1gHQqVPdMecrVqygvLyc/Px8MjMzKSgoqK077bTTeOCBBw57H+np6ezcubPBNql9R3Di1KLD3uYefacd+XsO5owzCqgqKW607Sl+tModRu7PFjTYJgi8uX4nLVumRyaoOJSY3p5+j37cYJsQ8O9qSO+Sw+5NDbfV4Rvw1+0AtGyZEuVI4pvnOTI8z02j83/cTYfzriOQePDubahmNzf+5ikuvf8/IxhZ/POajgzPc2R4nptAYhID/1J5yGabd0L73kPY8dHyCASlWBAMHn32s9mP7Grfvj0AZWVltWWhUIibbrqJYDBYb3H6YDDIAw88wPnnnx/ROKXoOtyFuFyw65gc0YJnnmtJiqjD/oz281mSmi0XGFYjafYju/Ly8sjNzeWWW24hOTmZtLQ0HnjgARYvXkxqaip9+/at0/66664jLS2Na6+99rD3sXXr1kO2WbIRrmx44EyTmzeviCHtoxuDmqfK3fClF8PrlBxMAjCwUzJv79gRsbjiTTAEX5sbXkizoVmKHVPgjY8/ING/1Y1m2HPhf3d4/TYpz3NkeJ6bxtyP4ea3Gm4TSEzirmsu45L/d1lkgjpOeE1Hhuc5MjzPTeOyIiitaLgPnZYEn5YsdpF61VqwYAGjR48+qvc2+5FdSUlJPPPMM2RlZTFp0iRuuOEGzj33XMaOHcugQYNISNh7CD/60Y8oLS3lqaeeqlMuxbvWSfDV7g3fqw4Sfqyvjl5CAC7p1fAfaYAJPTHRJUkRVtAZMlsevHMbAFIS4bxukYxKkgSH7kMHgPHZPo1RjScmMkKDBw+muLiYqqoqSkpKuOqqq1i8eHGdKYy33HILb7/9Nv/7v/9Ly5YtoxitFB3X5MGJ6fUTXnten9cNzu4S6ajizzdyYETHg9cPaw8TT4xcPJKksKQE+NnQ8L/7d3ATCM+MufNkSEuORnSSdHz7Snco/OK7yIG+r+S1he/0RWo0MZHs2l91dTUlJSW1ya733nuPn/3sZ3z88ceMHDmSIUOGMH78+ChHKUVWWjI8PBouz4U2+3Tku7WG/x4I/5PvFPjGkJQA9w6Ha/PC0xX36NASvncS3HcatPCOlCRFxdAO8NgYKMiq28k9rRM8NBLOyIpaaJJ0XEsMwLSh8F/9ISt1b3nbFvCffeDBkdCq2S+ypFgSk5fTu+++S01NTW2yq3///oRCh5pY1PQ+fOg6qlcvoc3J55I14Zba8uCOalZNv5Dg9kpantCLnt9/jB0b1rDiphGkdO1Liw49yPnBEwcsk45EWjJc1y+cdPmkGhIT4IQUk1yNLTkBvtUb/iM3fJ5DQKeUcCJMkhRdfTPg56fA1l1wxj/CZfedFt2YJEnhhNdlJ8I3esGpz4fLXjjbPrSaRkwmu4YPH94sklv7qix9i0BCEn1/9iqr7r6IXZs3kNz2BAAqlswhLW80WRNuofy336G6fBkJKWlkDD2Pntc9XGc7ByqTjlRyAnRtHe0o4l9ioO6dKUlS85HudEVJapYS9rkRb6JLTcVLq5FUrnyD9EHjAEgfMJaqsrdr61qckENweyUANdu3kZiaAUDF4hcp+fEYNhb9ubbtgcokSZIkSZJ0eGJyZFdzVFO5mcTsAQAktEqnpnJzbV1KVi7b3n+V967JI7XXybTo2J3grh0MeKAECFB6+5fIOPkckjOz6pUltWkfleORJEmSJEmKRSa7jlD1h+/z4YNX1ynLyD+HxNZtqamqACBYvZXkznsfx7bxn4/TbvQldDrvGtb+4ftsW/4aaXkja+vT+o1hx/pVtO5zar0yk12SJEmSJEmHz2TXEWrVox99pxXVK68sfZNNrzxJ21O/ytb3XqHd6Itr60LBIEnpmQAkpmdSU7mZmuptJLZKIxQKUVX2Fp3Ou/aAZZIkSZIkSTp8JrsaSevep7Dx5T9S8uMxtMn/EsltT2DX5+vZOG8GHc6+kg/uuYRPX3yQpNbtyLroFrYunce6GbcQSEqm3ciLSM7MomLxnHplkiRJkiRJOnwmuxpRj+/9ts7r5Had6XzBjQD0uWNOnbo2+WfTJv/sQ5ZJkiRJkiTp8Pk0RkmSJEmSJMUNk12SJEmSJEmKGya7JEmSJEmSFDdcs+sw5baBh0dFPwZJkqKhqKiIK664guzsbLKzs3n88cfr1M+YMYOsrCwKCwt57rnn+NWvfkUwGOSJJ56gR48ete2+/e1vs3LlSmpqanj00Ufp06cPX/3qV6moqCApKYmnnnqKtm3b8r3vfY+HH3440ocpSZKkOGCy6zClJcOQ9tGOQpKk6Jk8eTK33nor119/PcXFxYwYMaK27vnnn+epp56isrKSv/zlL7z88ssEAoF62/jd735HcnIyr776Kr///e+59957mTVrFsnJycyYMYOZM2dy/fXX07FjR1atWsWJJ54YyUOUJElSHHAaoyQp5hUVFZGTk0NBQQGTJk2qVz9t2jRKS0sP+v5NmzYxdOhQ0tLSDqv+QO2XL1/O9OnTj/FIYsOAAQNYt25d7etNmzaRkpJCIBCguLiYYDDIWWedxTXXXEMwGKzz3uTkZAC2bdvGgAED6pRt376dvLw8AAoKCvjHP/4RicPRcaypPzvWrFlDVlYWBQUFXH755ezatYuLL76YgoIC7rnnHuD4+uyQJClSTHZJkuLC5MmTKSoqIiMjg+Li4tryYDDIu+++S+/evQ/63vT0dF566SVOO+20w6o/UPu8vDwWLVpEKBRqpCNqvoqLi8nNza19XVZWRnZ2NgCffPIJn332GXPmzKFDhw4899xz9d5/5plncu2113LKKacA4YTByJEjue+++2qTXdnZ2axcuTICR6PjXVN+dgCcd955FBUV8cQTTzBr1ixGjhxJUVERb7/9Np9++ulx9dkhSVKkmOySJMWV/UcdvfPOO/Tp06fB9yQnJ5OZmXnY9Qdr36tXL957772jiDo2PPLIIxQUFNC1a1eGDBlywDYZGRmMGTOGhIQETj/9dEpKSuq1efnll5k1axa33347AJmZmbz22mtMnTqVX/7yl014BNLBNcVnB8CLL77ImDFj+POf/8zq1asZOHAgEE6Qv/nmm0D8f3ZIkhRpJrskSXFl/1FHpaWl9OzZMyL7jvfRSHtGwEydOrVOeW5uLuXl5QCccsopvP/++wAsXbq03rnfsWMHEE6KtWrVimAwyO7du2vLUlJSACgvL29wRI3U2JrisyMrK4uSkhLmzJnDgw8+SO/evZk/fz6hUIhXX32VLVu2APH/2SFJUqS5QL0kKS488sgjzJ07l9GjRx901NH777/P1VdfXafsnHPO4eabb45AhPErMzOTqqoqADp16sTJJ5/M2LFj6dixIzNnzmT9+vXMmDGDG2+8kfHjx1NdXU0gEOC3v/0tlZWVfOUrXyEhIYGWLVvyxz/+EQivpTR58uQoHpWOF0352dGyZcva38eMGUO3bt2YO3cuZ511Fh07dqRTp07HHL8kSarPZJckKS7seVLg/nr37s2sWbMA6NevH0VFRU0WQ3l5OaNGjWqy7UdTQUEBBQUFB60///zzmTt3LoWFhdx0003cdNNNtXWdO3fmxhtvBGD27Nn13jt//vw6r3fv3s0nn3xSZ5SN1FSa8rNj27ZtpKWlEQqFeOutt7j22mt54IEHCIVCTJo0qfaJpvH82SFJUjQ4jVGSFNcGDx58wHWj9ldYWMjixYspLCxk2bJlrF+/vvZpaQeq3/81hBdq3/OEwePN5ZdfTmFhYaNsKykpiUceeaRRtiUdrcb47HjttdcYNmwYI0eO5Oyzz2bXrl0UFBRw5plnctFFF5Gamgoc358dkiQ1BUd2SZJiXkOjjhISEhg0aBClpaUNrgE1d+7cemV7RiMdqH7/18uXL2fo0KEEAoEjiFxSNDX1Z8fZZ5/N2WefXadu/xFifnZIktT4THZJkuLegaYoNba8vDzy8vKafD+SIsfPDkmSYpPTGCVJkiRJkhQ3THZJkiRJkiQpbjiN8Qhs2wVlFdHZd24bSEuOzr4lSZIkSZJihcmuI1BWAVcuiM6+Hx4FQ9pHZ9+SJEmSJEmxwmmMkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtxwgfomVvKTAipXFBNISiaQmERK15PoMnEabQafGe3QJEmSJEmS4o4juyKgy8Rp5D+1jUGPb6B13xGsuuvr1FRuiXZYkiRJkiRJccdkVwQlJLekw1mTCW7fxvZ/l0U7HEmSJEmSpLhjsiuCgjuq+eylh0lIbUNKl97RDkeSJEmSJCnuxEyya+fOnUyZMoXu3bvTqlUrxo0bx8KFCwkEAjz77LPRDq9BH8+cwpLL2rL02z2pWv0Oubf+H4mpbaIdliRJkiRJilOhENSEoh1FdMTEAvWhUIgJEyawcOFCbr/9dnJzc5k5cybjx48HID8/P8oRNqzLZXfSefyPoh2GJMWc1z+BmR/sfT3hnzAhB77eA1okRi+ueLPsc5i5au/rr7wEF/aECT0hLTlaUUlHZ0M1/OUDePbDvWXT34XLekH3tOjFJUlSpCzaGO7bvbohnOzq1jrcr7swG1JiIgt07GLiMB966CFmz57NkiVL6N+/PwAFBQXk5OSQmZlJjx49ohyhJKmxPboSfrcCEgJ7y9Zsg58vhZc/hl+fBikmvI7Z7LVw+2Jgn/O8vhp+uzxc94dR0LZl1MKTjsiqCvjOAqjYBfveyP7bGvi/tfCbETA4M1rRSZLU9P66OtxfTghA8Is/husq4ZfvwYvr4IGR0DomMkHHJiamMU6fPp2JEyfWJroAEhMTycnJqR3V9fWvf53BgweTn5/PmDFjWLJkSZSilSQdq7c+Cye6YO8fadj75XXRRnhwRcTDijsfVcLtSyBI3fO8R/k2mPpOpKOSjk4wBD96E7bul+iC8DW+owb+6w3YXhON6CRJanorNsM9S8O/H6gPvXwz/HJZhIOKkmaf7CotLWX16tVceOGF9erWrl1bm+x6/PHHeeedd1i8eDE/+tGP+M///M9IhypJaiRPfdDwH6gQMKsctu+OVETx6W9rwms5HEwQmL8e1ldFKiLp6L3xKaytDF+3BxIEtuyCuR9HMipJkiLnr2vqDNavJwT8fx/Blp0RCiiKmv3gtXXr1gHQqVOnOuUrVqygvLy8NtmVkZFRW7dlyxYSEg4/j5eens7OnYf+r53adwQnTi067O0C9J12ZO0P5owzCqgqKW6UbUlSc9fvic9IbJXeYJvK3ZA19AyqVrwWoajiT+49b9Kq56AG24SAwV/7Tza/8ufIBHUcGPDX7QC0bJkS5UjiS+eJd9HhKzcQSDz4/OZQzW6+/6u/cOFvJkcwsvjnNR0ZnufI8DxHhue5aZz0+w9Ibt+1wTa7gnDi2PFsXTQ7QlEdvWDwYLewDq3ZJ7vat28PQFlZGaeeeioQXrD+pptuIhgM1lmc/sorr2TOnDmEQiFeeOGFqMQrSTp2gYTDW4zrcNvpwAKJh9cN8DwrFoSv50M9cirk9SxJil+H2bfjOPhbGAiFGprAEH27d+8mLy+PXbt2cc8995CWlsYDDzzA4sWL2bRpE1u3bq03imvGjBk8+eSTzJ7duJnKJRvhygWNusnD9vAoGNI+OvuWpEi78l/w7qaDT0cCSArAC2e7ePqxuGMx/H9rGz7PADPHQp+MQzTSYRv2XPjft86Pbhzx5h8fwZRFh253Qz+YmNv08RxPvKYjw/McGZ7nyPA8N40fvAELNjTctwsAzxVCVmqkojp6CxYsYPTo0fzrX/9i1KhRR/TeZr9mV1JSEs888wxZWVlMmjSJG264gXPPPZexY8cyaNCgA05X/I//+A/mzZvHxo0boxCxJOlYTchp+I90AnBWVxNdx+rCnoc+zwPbmehSbBiXBW2SG16rJDkBvuJDvCVJceqQfegAjOwUG4muY9Xsk10AgwcPpri4mKqqKkpKSrjqqqtYvHhx7RTGbdu2sXbt2tr2zz//PJmZmWRm+mxpSYpFZ3UJ/xxIAnBCK/h+v4iGFJcGtINJX4xw2T9BkACkJsGtgyMdlXR0WibCT08Od+T37+AmEL7GfzIY2raIQnCSJEXAiI4wPvvAdQmE/wbe1PByrXGj2a/ZdSDV1dWUlJRwww03AFBZWcmECROorKwkMTGRzMxMnn/+eQKBhu7tSZKaq4QATB0KfTPgLx/AZzvC5S0S4NxucNVJ0MH1TBvFtXnQvTU8XhZ+kh2Ez/+4znBVHmSnRTc+6UiMPgEeHAm/XwFv7TPAv19b+HZfGHVC1EKTJKnJBQLw40FwYjr8aRWsrw6XJwXg7K5w9UnQ+TgY1QUxmux69913qampqR3ZdcIJJ/D6669HOSpJUmNKDMC3esPEE2HNtvCTY7q3hrTkaEcWXwIB+Ho2fK1H+DxX10BWK2jnFFHFqCHt4fejwh38jdvDd7G7to52VJIkRUZCAL7RCy7OgVOfD5e9+CXIOM5GNsdksmv48OE083X1Adjw3K/Y8ub/0efOuXXKP3zoOqpXL6HNyeeSNeEWAD594UE+X/BXQsEa+tzxEoEkv81JEkBSAuS2iXYU8S8QgJz0aEchNZ7OrcI/kiQdjxL2meh2vCW6IEaTXbEgtHsX1auX1CuvLH2LQEISfX/2KqvuvohdmzcQ2rWD6vKl9Lnz5cgHKkmSJEmSFEdiYoH6WLSxaAbtxlxar7xy5RukDxoHQPqAsVSVvU3F4jkEt1ey8tZxfPzk7RGOVJIkSZIkKX6Y7GoCoWCQikUvknHyl+rV1VRuJjE1PB8noVU6NZWb2bXlEwgE6DP1n+zYsJqqD5ZEOGJJkiRJkqT44DTGY1D94ft8+ODVdcoy8s+hZVYuGaeef8D3JLZuS01VBQDB6q0kdz6RxNQM0geMBSC9/+lsX1dCaq8hTRq7JEmSJElSPDLZdQxa9ehH32lF9cr//ddpbF1WxKaiGVStXsJncx6mw9lXAtC6z6lseuVJ2p76Vba+9wrtRl9McrvObHplJgDV5UvJPMD0R0mSJEmSJB2a0xibQNbFP6HPT1+i9+0vkJozhA5nX8muz9ezftY9tO59CqFdOyj58RhScwaT3PYEUk88mVDNbkp+UkBwRxWt+w6P9iFIkiRJkiTFJEd2NbE+d84FILldZzpfcCMAPb7323rtul/5q0iGJUmSJEmSFJcc2SVJkiRJkqS4YbJLkiRJkiRJccNpjEcgtw08PCp6+5YkSZIkRUdRURFXXHEF2dnZZGdn8/jjj9epnzFjBllZWRQWFjJmzBgWL17MihUr6NatW512P/7xj5k/fz6JiYn87ne/Y+DAgXzrW9+ipKSEli1bcttttzFu3DiuuOIKHn30UQKBQCQPU4oLJruOQFoyDGkf7SgkSZIkSdEwefJkbr31Vq6//nqKi4sZMWJEbd3zzz/PU089BcDTTz/NzTfffMBtfPe73+VnP/sZq1atYsqUKcycObP2PfsmxoYPH868efMYN25cEx6RFJ+cxihJktSMFBUVkZOTQ0FBAZMmTapXP23aNEpLSw/6/oULFzJq1ChGjhzJrbfeWq9+06ZNDB06lLS0NADWrFlDVlYWBQUFXH755QAsX76c6dOnN9IRSVL8GTBgAOvWrat9vWnTJlJSUmpHYXXu3Pmg7+3ZsycAiYmJte0DgQCXXHIJF198MZs2bQLgjDPOYPbs2U10BFJ8M9klSZLUzEyePJmioiIyMjIoLi6uLQ8Gg7z77rv07t37oO/Nz89nwYIFvPbaaxQXF1NRUVGnPj09nZdeeonTTjuttuy8886jqKiIJ554AoC8vDwWLVpEKBRq5COTpPhQXFxMbm5u7euysjKys7OPaBtTpkzh6quvBuDee+9lwYIFXHLJJfzsZz8DIDs7m5UrVzZe0NJxxGSXJElSM7X/yIF33nmHPn36NPie5ORkAGpqaujSpQupqan16jMzM+uUvfjii4wZM4Y///nPtWW9evXivffeO9ZDkKS48sgjj1BQUEDXrl0ZMmTIUW/nD3/4Azk5OYwaFV4Uul27dgCcf/75fvZKjcBklyRJUjO1/8iB0tLS2ukvDZk5cyZ5eXm0bduWpKSGl2jNysqipKSEOXPm8OCDD7Jx40bAEQWSdCB7Rt5OnTq1Tnlubi7l5eWHtY3i4mJmz57N7bffXlu2devW2rqcnBwAysvLGxzJK+ngTHZJkiQ1M4czcuD999+noKCgzs/dd98NwGWXXcaKFSv4+OOPWbp0aYP7atmyJampqbRq1YoxY8awatWqxj4cSYp7mZmZVFVV1b6eOHEic+bM4dJLL+Xll18G4Ic//CEAN998M+Xl5YwbN47rrrsOgMsvv5zRo0dzxx131C5sP2/ePM4999wIH4kUH3waoyRJUjOz52lf++vduzezZs0CoF+/fhQVFdVrs2PHDlq2bElCQgLp6emkpKQ0uK9t27aRlpZGKBTirbfe4tprrwXCIwr2TK+RJFF7Y+Fgzj//fObOnUthYSF/+tOf6tX/4he/AGD+/Pn16v7+97/XK3vjjTf4zne+c/QBS8cxR3ZJkiTFiMGDB1NSUtJgm+eee46CggJOP/10unXrRu/evVm/fj333HNPbZvCwkIWL15MYWEhjz76KMOGDWPkyJGcffbZZGVlAeHFlgcMGNCkxyNJ8eTyyy+nsLCw0bb32GOPkZDgV3bpaDiyS5IkqRlpaORAQkICgwYNorS09KDruEyYMIEJEybUKevcuTM33nhj7eu5c+fWqb/++uvrvF6+fDlDhw4lEAgcxRFIkiRFl8kuSZKkGHKg6Y2NLS8vj7y8vCbfjyRJUlNwTKQkSZIkSZLihskuSZIkSZIkxQ2TXZIkSZIkSYobrtl1BLbtgrKK6Ow7tw2kJUdn35IkSZIkSbHCZNcRKKuAKxdEZ98Pj4Ih7aOzb0mSJEmSpFjhNEZJkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3XLOriZX8pIDKFcUEkpIJJCaR0vUkukycRpvBZ0Y7NEmSJEmSpLjjyK4I6DJxGvlPbWPQ4xto3XcEq+76OjWVW6IdliRJkiRJUtwx2RVBCckt6XDWZILbt7H932XRDkeSJEmSJCnumOyKoOCOaj576WESUtuQ0qV3tMORJEmSJEmKOzGR7Nq5cydTpkyhe/futGrVinHjxrFw4UICgQDPPvtstMM7pI9nTmHJZW1Z+u2eVK1+h9xb/4/E1DbRDkuSJEmSJCnuNPsF6kOhEBMmTGDhwoXcfvvt5ObmMnPmTMaPHw9Afn5+lCM8tC6X3Unn8T+KdhhRtaMG/vERPLMGyrdBy0Q4IwsuyYFc836NJhiClz+Gv66Gki2QGIARneCSXjA4M9rRSUdu2efwlw9gwSdQE4TeGTChJ5zVNXx9S7FkfTU8vXrv6wtehq/1gPHZ0KZF9OKSpONdKATz18PTa/aW/Whh+LvKKR2jFpakY9Dsk10PPfQQs2fPZsmSJfTv3x+AgoICcnJyyMzMpEePHlGOUIdStRuuLYZ3Pw8PJQwC1TXwbDk89yFMGwqFXaIdZezbHYRbF8Hcj/eeZ4C5/4Y5H8MP+sM3T4xmhNKReXo1/HwpBALhRC7A0k3wziZ4aR1MPwWSYmJ8shRO3F5THP6buMeHlXD/cvhbOTw0Cjq3il58knS8CoZg2jvw7IeQsM+NtFc2QNF6+HYf+O5J0YtP0tFp9l8Tpk+fzsSJE2sTXQCJiYnk5OTUG9V1xx13EAgEWLZsWaTDVAP+3zJY+nn49+A+5UHCf1xufRs+qoxGZPHl8bJwogv2O89fJAl++R68/VnEw5KOyrubYPpSCLH3Goa91/b8DfDwymhEJh257bvh+69D9e7wNb2/9VVw05sRD0uSRHjmybMfhn+v0+f44vc/rAyP+pIUW5p1squ0tJTVq1dz4YUX1qtbu3ZtnWTXokWLeP3118nOzo5kiDqEzTtg9toDd+4hXF4Tgr+tiWBQcWh3MDzVqyEJHLqN1Fw8tfrQf6D+uhp21kQkHOmYvPgxbNlV90bEvoLAe5vhvc8jGJQkiWAI/rwKGloZIQGYuSpSEUlqLM16GuO6desA6NSpU53yFStWUF5eXpvs2rFjB9dccw1PPvkkBQUFR7yf9PR0du7cech2qX1HcOLUoiPadt9pR9b+YM44o4CqkuJG2VYktTntArJ/+GSDbULAH15ZwX+fPDgyQcWhlF759J7+eoNtgsDLH26n5ZiMyAQlHYN+j396yAd5VOyCE4aMpWplw9e+FG09/msmbU79GoHEg3e7QsEg51x7J588c1cEI5Max4C/bgegZcuUKEcS3zzPja/FCb3o+5vlDbYJAm9vhJTW6YR2H/o7ow6P13NkxPp5DgYPdqvw0Jr1yK727dsDUFZWVlsWCoW46aabCAaDtcmu2267jYkTJ9KzZ89ohKkGBJKSD6tdQlLLJo4kvgUSD+88H247KdoaSgrUaZfkqt6KAYnJ4cXnGhTyepakCDuSvvHhfq+R1Dw065FdeXl55Obmcsstt5CcnExaWhoPPPAAixcvJjU1lb59+1JcXMxbb73F3XfffdT72bp162G1W7IRrlxw1Ls5JvPmFTGkfXT2fSzKKuAbRQ23SQjAlwbn8O6OHRGJKR5t3gnnvAi7DzZflPDw7Ny2ibzteVYMmPQKLN988GlfEP7sWFn8Eh1i80aVjiMPrIBHVx58Sj9AICGRh+/6MWc//uOIxSU1lmHPhf/dYR+jSXmeG9/23VD4Imw/xLIInVvBm5s3Hfq+hQ6b13NkxPp5XrBgAaNHjz6q9zbrkV1JSUk888wzZGVlMWnSJG644QbOPfdcxo4dy6BBg0hISGD+/PksX76cnJwcevbsyUcffcSXvvQl5syZE+3wBeS2gYHtGr7QgiG4KCdiIcWlti3grK4Nn+cQcLHnWTFiQs9DJ7rO6IyJLsWErx/iwdEBICMZzsiKSDiSpC+kJMH5PRpeswvC/RITXVJsadbJLoDBgwdTXFxMVVUVJSUlXHXVVSxevLh2CuPNN9/Mxx9/zJo1a1izZg3dunXjxRdf5Oyzz45y5Nrjx4OgZWLdR/nu6yvd4dQOkY0pHl2bB+1TDv4/9bD28NVDfOGSmotzusHITgeuSwDaJsP3+x+4XmpuslLhun7h3/f/Uxj44ue2fEhu9r0ySYo/3+kDXVIP3IcOAP3bwiXeMJZiTsx1q6qrqykpKanzJEY1b30y4LEx9RNa7VrANXlw2xDvlDSGE1qFz/O4rLqJxdRE+GYv+PVpfpFS7EhKgP93ClyeC633mXCfAIztDH88PdwxlWLF5blw+5D61+1JGXD/iPB1LUmKvLYtw33oL3WDpH360CmJcFFPeGBkeASYpNgSc//bvvvuu9TU1Bw02bVmzZrIBqTDktsGfjMCPq6C8+eGy2afbfKlsXVuBXefAp9th3O+mMn74pegVcz9ny5Bi0S4vl/4juvo2eGy/+9s6OjURcWor/SAL3eHFVugYid0agW90qMdlSQpsyXceTL8sD+UVoRvxJ+UAWmuSS/FrJj7Cjx8+HBCoYaWeI2+3Vs3Ufo/Z7F9XQn5T22rU7djwxpW3DSClK59adGhBzk/eILgjmpWTb+Q4PZKWp7Qi57ffyxKkTe9fe9om+hqOvuuY2SiS7Fu37upJroU6xIC0K9ttKOQJB1I25ZwSsdoRyGpMZhuaAKJrdLpfcdLtO5z2gHrM4aeR99pReT84AkAKpbMIS1vNH3vmk8gKZnq8mWRDFeSJEmSJClumOxqAoGkZJLSMw9aX7H4RUp+PIaNRX8GoMUJOQS3VwJQs30biakZEYlTkiRJkiQp3pjsirDkzCwGPFBC79vn8NmLD7K7YiMpWblse/9V3rsmjwABWnTsHu0wJUmSJEmSYpKr+RyD6g/f58MHr65TlpF/Dp0vuvmg70lIbln7e1q/MexYv4qqVW/TbvQldDrvGtb+4ftsW/4aaXkjmyxuSZIkSZKkeGWy6xi06tGPvtOKjug9NdXbSGyVRigUoqrsLTqddy2VpW/WTntMTM+kpnJz4wcrSZIkSZJ0HHAaYxNZOaWQqtWLWTmlkOryZez6fD3rZ91D5YrXWP5fwyi5aSRt8s8mOTOLzLGX8dnLj1HykwKqP1hCmyFnRTt8SZIkSZKkmOTIribS58659co6X3AjAG3yz65TnpTWjj53zIlIXJIkSZIkSfHMkV2SJEmSJEmKGya7JEmSJEmSFDecxngEctvAw6Oit+/jQVFREVdccQXZ2dlkZ2fz+OOP16mfMWMGWVlZFBYWMmbMGBYvXsyKFSvo1q1bnXY//vGPmT9/PomJifzud79j4MCBfOtb36KkpISWLVty2223MW7cOK644goeffRRAoFAJA9TkiRJajT2oSWpLkd2HYG0ZBjSPjo/acnRPvrImTx5MkVFRWRkZFBcXFyn7vnnn+fMM88E4Omnn+aiiy464Da++93v8tprr/HHP/6Rn/3sZ7XlTz/9NEVFRYwbNw6A4cOHM2/evCY6EkmSJCky7ENL0l4mu9RsDRgwgHXr1tW+3rRpEykpKbV3kDp37nzQ9/bs2ROAxMTE2vaBQIBLLrmEiy++mE2bNgFwxhlnMHv27CY6AkmSJBUVFZGTk0NBQQGTJk2qVz9t2jRKS0sb3MaDDz7ImWeeSUFBAbt27aotf+GFFygoKKCgoID27duzZMkSdu3axcUXX0xBQQH33HMPAMuXL2f69OmNe2DNlH1oSTLZpWasuLiY3Nzc2tdlZWVkZ2cf0TamTJnC1VdfDcC9997LggULuOSSS2rvVGVnZ7Ny5crGC1qSJEn1HGzUUTAY5N1336V3794Hfe+HH37I0qVLefnllykqKiI5ee+Uh3POOYeioiLmzZtHr169GDx4MLNmzWLkyJEUFRXx9ttv8+mnn5KXl8eiRYsIhUJNepzNgX1oSTLZpWbokUceoaCggK5duzJkyJCj3s4f/vAHcnJyGDUqvNBau3btADj//PN57733GiNUSZIkHYH9Rx2988479OnTp8H3zJkzh8rKSsaNG8ftt99+wDZvvvkmw4YNIxAIsHr1agYOHAhAXl4eb775JgC9evWK6z6gfWhJ2stkl5qdPXf+pk6dWqc8NzeX8vLyw9pGcXExs2fPrtMh2rp1a21dTk4OAOXl5Q3eSZQkSVLj2X/UUWlpae3UuYP55JNPCAQC/POf/2T16tUsWbKkXptnn32Wr33tawD07duX+fPnEwqFePXVV9myZQsQ/6OR7ENL0l4muxQzMjMzqaqqqn09ceJE5syZw6WXXsrLL78MwA9/+EMAbr75ZsrLyxk3bhzXXXcdAJdffjmjR4/mjjvu4OabbwZg3rx5nHvuuRE+EkmSpOPL4Yw6ev/992vX39rzc/fdd5ORkcHYsWMBOP300ykpKan33nnz5tUunn7++efz6aefctZZZ9GxY0c6derUZMcVC+xDSzoeJUU7AGlfezo2B3P++eczd+5cCgsL+dOf/lSv/he/+AUA8+fPr1f397//vV7ZG2+8wXe+852jD1iSJEmHNHnyZG699dZ65b1792bWrFkA9OvXj6KionptFi1axMyZMwFYunQpl156aZ36Dz74gG7dutGiRQsgvLj6Aw88QCgUYtKkSYwYMQIIj0baMzUv3tiHlqS6HNmlmHL55ZdTWFjYaNt77LHHSEjwfwNJkqRoGDx48AFHau3r5JNPZvfu3RQUFFBVVcXw4cNZv3597ZMW953CCOEF7QsKCjjzzDO56KKLSE1NBcILtQ8YMKDpDqYZsw8t6XjjyC5JkiRJTaahUUcJCQkMGjSI0tLSBteA+tWvflXndefOnbnxxhsB+MEPflCnrkePHvVGiC1fvpyhQ4cSCASOOH5JUuwx2SVJkiQpag40vbGx5eXlkZeX1+T7kSQ1D449lSRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccM1u47Atl1QVhGdfee2gbTk6OxbkiRJkiQpVpjsOgJlFXDlgujs++FRMKR9dPYtSZIkSZIUK5zGKEmSJEmSpLhhskuSJEmSJElxw2SXJEmSJEmS4oZrdjWxkp8UULmimEBSMoHEJFK6nkSXidNoM/jMaIcmSZIkSZIUdxzZFQFdJk4j/6ltDHp8A637jmDVXV+npnJLtMOSJEmSJEmKOya7IighuSUdzppMcPs2tv+7LNrhSJIkSZIkxR2TXREU3FHNZy89TEJqG1K69I52OJIkSZIkSXEnZpJdO3fuZMqUKXTv3p1WrVoxbtw4Fi5cSCAQ4Nlnn412eA36eOYUllzWlqXf7knV6nfIvfX/SExtE+2wJEmSJEmS4k5MLFAfCoWYMGECCxcu5Pbbbyc3N5eZM2cyfvx4APLz86McYcO6XHYnncf/KNphRNXuIMxfD7PK95bd/z5c2BO6pEYtLOmoLfscnl4Nb28Mvx6SCRNyYHBmdOOSjsb6KvhbObz8MVTthp5pcEFPGJcFSTFzW0xSJO0KwtyPYdaavWUPrgh/dnRMiVZU8ScYgn9tgL+t2Vv2i2UwoSf0SItWVJLU/MVEsuuhhx5i9uzZLFmyhP79+wNQUFBATk4OmZmZ9OjRI8oRqiE7auDGN+G1T+oOJXyiDJ78AH5xKozoFLXwpCP2WCn8dnn4eg5+UTbnY3hhHXy7D3z3pGhGJx2ZNz+FHywMf1aHvijbtAPe2gindIBfngopMdFbkBQplbvh+tfhnU11+3YPr4Q/r4L7ToMh7aMWXtzYHYRbF4WTivue5798EL7hNm0onNklauFJUrMWE/drp0+fzsSJE2sTXQCJiYnk5OTUjurq2bMnJ510EkOGDGHIkCG8+OKL0QpX+/n1++FEF+xNDED4S9WuIPxwYXhUgRQLiv4dTnRB3es5+EWW4A8r4aV1EQ9LOiqfbQ8nunbuk+iCvdf2W5/BL96LRmSSmrO73oF3N4V/379vt70Gvv8GbNkZjcjiyx9WhhNdUP8814Tglrdh9dZoRCZJzV+zT3aVlpayevVqLrzwwnp1a9eurTOF8ZlnnmHJkiUsWbKEL33pS5EMUwexdRf8b/nB6/ckvGY10EZqTv60quEPzgRgxqpIRSMdm/8tD38xDR6kPgQ8/yFs3hHJqCQ1Zxuqwzd1QgepDxIe+fX82khGFX+218BTHxy8PgSEQvDX1RELSZJiSrOfmLBuXXiIRKdOdee5rVixgvLy8kZZrys9PZ2dOw99+ym17whOnFp0RNvuO+3I2h/MGWcUUFVS3CjbiqQ2p36N7Bv/2mCbYCjE7/65nB8Mad5rr8WaAX/dDkDLli6c0VgSUtvQ//FPG2wTBN7fDKkdu1FT0XBbHT6v56Zx4t3FtOqVTyAQOGib3SHo8+XL2fKvpyIYmaTmqt24K+h21e8bbBMKBZn29AIm/09hhKKKP60HFNDrfxqeqRIEZi76mNtOyYlMUFIjsm8XGbF+noPBg92SPbRmP7KrffvwhP+ysrLaslAoxE033UQwGKyT7PrmN7/JoEGDuPrqq9m8eXOkQ9UBJLRodcg2gUCAhJauUq/mLyH58P9IHM61L0VbQsvUBhNdte28niV94fD6dgkE7Nsdk8P93A34+SxJB9TsR3bl5eWRm5vLLbfcQnJyMmlpaTzwwAMsXryY1NRU+vbtC8Crr75K9+7d2bFjBzfccAPXXnstf/rTnw5rH1u3Ht5k9yUb4coFR30ox2TevKKYXOhz+Wb4j1cabpMAjBvYk3d3OE+mMQ17LvzvDs9ro9kdhLNfhIpdDbdLTYRNH5bSIjEycR0PvJ6bxn+/CUXr9645dzAv/vlBBmc+GJmgJDVrr38C177ecJsE4OKCodzuZ/ZRW7sNxv+z4TYJwNDu7VjieVYMsm8XGbF+nhcsWMDo0aOP6r3NfmRXUlISzzzzDFlZWUyaNIkbbriBc889l7FjxzJo0CASEsKH0L17dwBatmzJ1VdfzYIFUcpKqY6TMqBPm4YvtCBwUc8IBSQdg6QEGJ8NDY2DCQBfy8ZEl2LChT0bTnQlADlpMKhdpCKS1Nyd2hGyWjX8tzAIXJAdqYjiU/c0GNb+MPrQzmCUpANq9skugMGDB1NcXExVVRUlJSVcddVVLF68uHYKY2VlJVu2bAHCUxz/8pe/MGTIkChGrD0CAbh5ECQmHPxiK+gMIzsdpFJqZv4jF7qmHvh6TgA6t4Irekc6KunonNoBzu564LoEICEAPx4c/iyXJAh/Lvzki8+Fg300nN8DBpokP2Y/HAAtEw/ehz61A5zVJaIhSVLMiIlk1/6qq6spKSmpTXZt2LCBgoICBg0axIABA1i5ciW/+93vohyl9hiUCQ+NhJPa1i1PSYT/OBHuHhbuOEmxoG0LeGQ0FGTV/QANAGM6w6NjILNltKKTjkwgAD/NDydoU/cbjdi7DTwwEk6OwSn0kprWaZ3gN6dBr/S65a2T4Dt99ybDdGx6Z4T7HAMz65a3SIAJPeHe4eFR55Kk+pr9ml0H8u6771JTU1Ob7OrVqxeLFy+OclRqyMBMeOJ0WLkFyreFE11DO0BqTF6BOt61T4GfnwKfVMOXXwqXPX9WeFSXFGuSEuCaPPjP3jBmdrjsT2PD09Al6WBO7Qh/KYDlW2BdZbhPN7RDuI+nxtPni4TXB1vDP8kJMLQ9pCVHOzJJat5iMtUwfPhwQqFDrKYbRZUrF7L2kR9AKET6oHF0nTi1wbrQ7l2svveb7NryCRlDz6PzBTdGMfqm1Scj/CPFg077JLdMdCnWtdqnR2CiS9LhCASgX9vwj5pWr/T6I+kkSQcXk8mu5i61Vz4nTQ8vkL9yypnUVFWQmNrmoHVb3v4HrU8ayQnn38AH93yDXVs+JTmjY9TilyRJkiRJilXO8m4CgaTwuOJQTQ3JmV1IaJnaYN3ODatplT0QgJTueVSVvhn5oCVJkiRJkuKAya4msmn+TN67No/E1m0JJCY1WNeya1+2LZtPKBRi23uvUlO1JUpRS5IkSZIkxTanMR6D6g/f58MHr65TlpF/Dp0vupnMsZfRbsw3+ODnE6hes5RWPQfWttm/ru2p51OxZA6lt51FUkZHkjI6RfpQJEmSJEmS4oLJrmPQqkc/+k4rqlce3LWDhOSWBBISSGyVTqBFSoN1gcREsq96gFAoxJpfTSLtpBERPApJkiRJkqT4YbKrCWxZ+ByfzP4tBIOk9T+dlC692fX5ejbOm0HLE3rWq9v56Yes/tXlBAIJdPrqDXXW+JIkSZIkSdLhM9nVBNqNmkC7URPqlCW360znC26srd9Xi449DjhCTJIkSZIkSUfGBeolSZIkSZIUN0x2SZIkSZIkKW44jfEI5LaBh0dFb9+SYk9RURFXXHEF2dnZZGdn8/jjj9epnzFjBllZWRQWFnLXXXfxj3/8gyFDhnD//ffXaffCCy9wxx13kJ6ezh//+Ee6dOnCV7/6VSoqKkhKSuKpp56iQ4cO3Hnnnbz00kvk5OTwyCOPUFFRwdSpU7n33nsjediSJEmSFDUmu45AWjIMaR/tKCTFmsmTJ3Prrbdy/fXXU1xczIgRe5+4+vzzz/PUU0+xYcMGFi1axKuvvsoPfvAD3nrrLYYNG1bbbvr06cybN4+ysjKmT5/Or3/9a2bNmkVycjIzZsxg5syZTJgwgcWLF/PKK6/wm9/8hueff57x48ezefNmtm3bRlpaWjQOX5IkSZIiymmM0nGqqKiInJwcCgoKmDRpUr36adOmUVpaetD3b9q0iaFDhx4wgVJdXc2Xv/xlxo4dyxVXXAHAwoULGTVqFCNHjuTWW28FYPny5UyfPr2Rjqj5GzBgAOvWrat9vWnTJlJSUggEArz11luMHTsWgHHjxrFw4cI6701KSiIlJYX+/fvX1iUnJwOwfft28vLyKC8vp3///gAMHDiQ4uJiAIYPH05RUVFTH54kSZLUKJryu8oLL7xAQUEBBQUFtG/fniVLlhyw/fH2XSXemOySjmOTJ0+mqKiIjIyM2sQIQDAY5N1336V3794HfW96ejovvfQSp512Wr26OXPmMHr0aObPn09ycjLLli0jPz+fBQsW8Nprr1FcXExFRQV5eXksWrSIUCjUJMfX3BQXF5Obm1v7uqysjOzsbAA2b95Mmzbh+crp6els3ry5znt37drFxo0b+de//sWmTZuA8B/xkSNHct9995GXl0evXr14/fXXCQaDvPLKK2zZsgWA7OxsVq5cGYEjlCRJkhpHU31XOeeccygqKmLevHn06tWLwYMHH7D98fZdJd6Y7JJUb8TRO++8Q58+fRp8T3JyMpmZmQesy8nJobKyEoBt27aRkZFROwqppqaGLl26kJqaCkCvXr147733GuMwmq1HHnmEgoICunbtypAhQw7Ypm3btlRUVACwdetW2rZtW6d+6tSpXHTRRTz55JP069cPgMzMTF577TWmTp3KL3/5Szp16sT48eMZN24cGzZsoFOnTk15WJIkSVKTa+zvKnu8+eabDBs2jEAgcND2x8N3lXhlsktSvRFHpaWl9OzZ86i3l5uby6uvvkpeXh6BQIDu3bsDMHPmTPLy8mjbti1JSeElA4+HUUd77kpNnTq1Tnlubi7l5eUADB06lFdeeQWAefPmceqpp9ZpO3r0aObNm8e3vvUthg8fTjAYZPfu3QBkZGSQkpICwNVXX01RURHZ2dl8+ctfBqC8vLzBO1+SJElSc9XY31X2ePbZZ/na177WYJvj4btKvDLZJR3HDmfE0fvvv187p33Pz913393gdh9//HEuueQSli9fTocOHXjttdcAuOyyy1ixYgUff/wxS5cubezDiTmZmZlUVVUB0LlzZwYNGsSYMWPYsWMHw4YNY/369dxzzz0A/PSnP2XcuHHcf//9XH/99VRWVnLmmWdyxhlncPfdd3PdddcBcMEFF1BYWEhVVVXtQvivv/46BQUFUTlGSZIk6Wg01XeVPebNm8e4ceMaMWI1Jz6NUTqO7XlK4P569+7NrFmzAOjXr98RL24eDAZrhwFnZmayefNmduzYQcuWLUlISCA9Pb12JFJ5eTmjRo06tgNpxvb80T2Y888/n7lz51JYWMiUKVOYMmVKbV3nzp258cYbAbjtttu47bbb6rx3/vz59ba357/bHps2baJt27akp6cfw1FIkiRJkdVU31UAPvjgA7p160aLFi0abBfv31XimSO7JNUzePBgSkpKDtmusLCQxYsXU1hYyLJly2pHIl122WU89thjFBQUsGTJEs466yyee+45CgoKOP300+nWrVvttLqysjIGDBjQ1IfUbF1++eUUFhY22fYzMzP55S9/2WTblyRJkiLpWL+rwIGnMO7fHvyuEssc2SUdpxoacZSQkMCgQYMoLS1tcK2nuXPn1ivbMxJpzpw5dconTJjAhAkT6pQtX76coUOHEggEjjB6SZIkSfGqqb+r/OAHPzhke7+rxDaTXZIO6EBDhhtbXl4eeXl5Tb4fSZIkSfHD7yo6FKcxSpIkSZIkKW6Y7JIkSZIkSVLcMNklSZIkSZKkuOGaXYdp2y4oq4huDLltIC05ujFIkiRJkiQ1Zya7DlNZBVy5ILoxPDwKhrSPbgySJEmSJEnNmdMYJUmSJEmSFDdMdkmSJEmSJClumOySJEmSJElS3DDZJUmSJEmSpLjhAvVNrOQnBVSuKCaQlEwgMYmUrifRZeI02gw+M9qhSZIkSZIkxR1HdkVAl4nTyH9qG4Me30DrviNYddfXqancEu2wJEmSJEmS4o7JrghKSG5Jh7MmE9y+je3/Lot2OJIkSZIkSXEnZpJdO3fuZMqUKXTv3p1WrVoxbtw4Fi5cSCAQ4Nlnn412eIcluKOaz156mITUNqR06R3tcCRJkiRJkuJOTKzZFQqFmDBhAgsXLuT2228nNzeXmTNnMn78eADy8/OjHGHDPp45hfVPTyWQ1JKU7v3IvfX/SExtE+2wFKfe3wzPrNn7+rfL4YJsyEqNVkTxac02+Nuava9/vhQu6gm90qMVkaTmrmo3vPARvLgONu+Ezq3gqz2goDMkxcztR0mSjt5HlTCrfO/rae+E+9B9M6IWkuJUTCS7HnroIWbPns2SJUvo378/AAUFBeTk5JCZmUmPHj2iHGHDulx2J53H/yjaYSjOhUJw/3J4oqzukM0/lsKMMpg6FAq7RC28uPL06nBya1/PrIa/rob/6g+XnRiduCQ1Xx9Vwvdeg/XVEABCwOqtsOATGNgO7jsN0pOjHaUkSU1n9lq4fUn4e8sez5bD38vhO33DP1JjiYn7iNOnT2fixIm1iS6AxMREcnJyakd1bd++nauuuorevXszcOBAvvOd70QrXCkq/l4eTnQBBPcpDwE1IfjJ21DicxGO2eufwPSl4fO6z9/p2nN+73vwyvooBCap2dodhGuK4ZPt4dd7Pjv2fG4s+xymLIpGZJIkRcbSTfA/iyEYOnAf+qGScDJMaizNPtlVWlrK6tWrufDCC+vVrV27tjbZ9d///d+kpKSwcuVKli5dyp133hnpUKWoCYbgj2Xh0QIHEiJ8B+UvH0Qyqvi0/8i5/SWwN+koSQBF62FdVfiz+kBCwL82hEd6SZIUj/60CgIH+7JC+HvMH8vqjvqSjkWzn8a4bt06ADp16lSnfMWKFZSXl5Ofn8+2bdt44okn+Oijjwh88X/QCSeccNj7SE9PZ+fOnQ22Se07ghOnFh1Z8I3sjDMKqCopjmoMap5Segyg9y/ebrBNEPjfldu467T2kQkqDiWkpNF/xsYG2wSBJZsgtUMXarY23FaHb8Bfw0NiWrZMiXIk8c3z3DS6f/9xMkZcRCDx4N2uUCjImCtv49P/vSeCkUmSFAGBAANmbiWQdPD5+iHgg63QJjuPnRu8Q99YYr1vFwwGD93oIJr9yK727cNfzMvK9g6VCIVC3HTTTQSDQfLz81m1ahXt27fnjjvuYNiwYRQUFPCvf/0rWiHX0Xdaket1qcklpKQdXruWrZo4kviWkNL68Nu2PPy2kuJbQkpaw7ezAYIhElod3me5JEmxJJDUosFE176OpL8tNaTZj+zKy8sjNzeXW265heTkZNLS0njggQdYvHgxqamp9O3blyVLlvDBBx+Qn5/PPffcwxtvvMFXv/pVysrKaNPm0E893Lr10PMGlmyEKxc0xhEdvXnzihjioBwdwGfb4dw5dee/7y8AdE1L5O0dOyIVVtzZHYQzX4DK3Q23S0mEzz4sJSUxMnEdD4Y9F/53h9dvk/I8N417l4WnkTd0bzKQmMj9P72Zr/3x5ojFJUlSpHzpRdh4iO5FYgA+XPYWGS0iE9PxINb7dgsWLGD06NFH9d5mP7IrKSmJZ555hqysLCZNmsQNN9zAueeey9ixYxk0aBAJCQn06NGDpKQkLr30UgCGDx9Ohw4dWLlyZZSjlyKjQwqMPgESGhg4ECL8WF8dvaQEOL/HwddGg/CH6le6Y6JLUq2vZzec6AJolQhn+cRcSVKcurBnw/UJhJ8cb6JLjaXZJ7sABg8eTHFxMVVVVZSUlHDVVVexePHi2sXpO3TowBlnnMFLL70EwMqVK/nkk0/Izc2NZthSRF2bBy0TDvw/dQDolQ7jsyMdVfyZlBtOLh7oPCcAbVvCFb0jHZWk5qxXOlyc03CbG/pDarMfby9J0tH5Rg50b33wPnRqEny3b6SjUjyLiWTX/qqrqykpKalNdgH8/ve/56677mLgwIF84xvfYMaMGbRt2zZ6QUoRdmIbeHg09N5v5m4AOP0EeGgkpB3eVHk1oEMKPDoaTj7AlOLBmeG6E1waTdJ+fjQAvt2n/qjPdi1gypBD3/GWJCmWtWkBfxgFIzrVr8trC4+OgR4uXalGFJP3EN99911qamrqJLt69epFUVFR9IKSmoG+GfDnAnjvc1hZEZ73PqwDdEmNdmTxJSsVfj8KVm+FdzaFywa2CyccJelAEgLw3ZPgP3Lh9Nnhsl+eGu70J8XkrUdJko5MhxT49WnwUSW8vRGCoXCi66SMaEemeBSTya7hw4cTCjW0FHd0fPjQdVSvXkKbk88la8ItteXBHdWsmn4hwe2VtDyhFz2//xg7NqxhxU0jSOnalxYdepDzgycOWCYdjf7twj9qWjnp4R9JOlz7TlUc0zl6cUiSFC3dWod/pKYUk8mu5qiy9C0CCUn0/dmrrLr7InZt3kBy2xMAqFgyh7S80WRNuIXy336H6vJlJKSkkTH0PHpe93Cd7RyoTJIkSZIkSYfHgfONpHLlG6QPGgdA+oCxVJW9XVvX4oQcgtsrAajZvo3E1PA4zYrFL1Ly4zFsLPpzbdsDlUmSJEmSJOnwOLKrkdRUbiYxewAACa3SqancXFuXkpXLtvdf5b1r8kjtdTItOnYnuGsHAx4oAQKU3v4lMk4+h+TMrHplSW0OsAq2JEmSJEmSDshk1xGq/vB9Pnzw6jplGfnnkNi6LTVVFQAEq7eS3PnE2vqN/3ycdqMvodN517D2D99n2/LXSMsbWVuf1m8MO9avonWfU+uVmeySJEmSJEk6fCa7jlCrHv3oO62oXnll6ZtseuVJ2p76Vba+9wrtRl9cWxcKBklKzwQgMT2TmsrN1FRvI7FVGqFQiKqyt+h03rUHLJMkSZIkSdLhM9nVSFr3PoWNL/+Rkh+PoU3+l0huewK7Pl/Pxnkz6HD2lXxwzyV8+uKDJLVuR9ZFt7B16TzWzbiFQFIy7UZeRHJmFhWL59QrkyRJkiRJ0uEz2dWIenzvt3VeJ7frTOcLbgSgzx1z6tS1yT+bNvlnH7JMkiRJkiRJh8+nMUqSJEmSJClumOySJEmSJElS3HAa42HKbQMPj4p+DJIkRUNRURFXXHEF2dnZZGdn8/jjj9epnzFjBllZWRQWFvLcc8/xq1/9imAwyBNPPEGPHj1q2337299m5cqV1NTU8Oijj9KnTx+++tWvUlFRQVJSEk899RRt27ble9/7Hg8//HCkD1OSJElxwGTXYUpLhiHtox2FJEnRM3nyZG699Vauv/56iouLGTFiRG3d888/z1NPPUVlZSV/+ctfePnllwkEAvW28bvf/Y7k5GReffVVfv/733Pvvfcya9YskpOTmTFjBjNnzuT666+nY8eOrFq1ihNPPDGShyhJkqQ44DRGSVLMKyoqIicnh4KCAiZNmlSvftq0aZSWlh70/Zs2bWLo0KGkpaUdVv2B2i9fvpzp06cf45HEhgEDBrBu3bra15s2bSIlJYVAIEBxcTHBYJCzzjqLa665hmAwWOe9ycnJAGzbto0BAwbUKdu+fTt5eXkAFBQU8I9//CMSh9PsNPX1vGbNGrKysigoKODyyy9n165dXHzxxRQUFHDPPfcAx9f1LEnS8epY+xzV1dV8+ctfZuzYsVxxxRX16vfvkyxcuJBRo0YxcuRIbr31VqDp+hwmuyRJcWHy5MkUFRWRkZFBcXFxbXkwGOTdd9+ld+/eB31veno6L730Eqeddtph1R+ofV5eHosWLSIUCjXSETVfxcXF5Obm1r4uKysjOzsbgE8++YTPPvuMOXPm0KFDB5577rl67z/zzDO59tprOeWUU4BwR2jkyJHcd999tcmu7OxsVq5cGYGjaZ6a8noGOO+88ygqKuKJJ55g1qxZjBw5kqKiIt5++20+/fTT4+p6liTpeHYsfY45c+YwevRo5s+fT3JyMsuWLatTv3+fJD8/nwULFvDaa69RXFxMRUVFk/U5THZJkuLK/qOO3nnnHfr06dPge5KTk8nMzDzs+oO179WrF++9995RRB0bHnnkEQoKCujatStDhgw5YJuMjAzGjBlDQkICp59+OiUlJfXavPzyy8yaNYvbb78dgMzMTF577TWmTp3KL3/5yyY8gtjTFNczwIsvvsiYMWP485//zOrVqxk4cCAQTtq++eabQPxfz5Ikaa+j6XPk5ORQWVkJhEftZ2Rk1Kk/UB8aoKamhi5dupCamgo0TZ/DZJckKa7sP+qotLSUnj17RmTf8T4aac+dv6lTp9Ypz83Npby8HIBTTjmF999/H4ClS5fWO/c7duwAwkmxVq1aEQwG2b17d21ZSkoKAOXl5Q3eSTxeNMX1nJWVRUlJCXPmzOHBBx+kd+/ezJ8/n1AoxKuvvsqWLVuA+L+eJUnSXkfT58jNzeXVV18lLy+PQCBA9+7dD7mfmTNnkpeXR9u2bUlKCi8j3xR9DheolyTFhUceeYS5c+cyevTog446ev/997n66qvrlJ1zzjncfPPNEYgwfmVmZlJVVQVAp06dOPnkkxk7diwdO3Zk5syZrF+/nhkzZnDjjTcyfvx4qqurCQQC/Pa3v6WyspKvfOUrJCQk0LJlS/74xz8C4TUkJk+eHMWjiq6mvJ5btmxZ+/uYMWPo1q0bc+fO5ayzzqJjx4506tTpmOOXJEmx4Vj6HBkZGVxyySVcc801fP/73+e1115j5MiRDe7vsssu4xvf+AYTJkxg6dKltaPLG5vJLklSXNjzpMD99e7dm1mzZgHQr18/ioqKmiyG8vJyRo0a1WTbj6aCggIKCgoOWn/++eczd+5cCgsLuemmm7jppptq6zp37syNN94IwOzZs+u9d/78+XVe7969m08++aTO3cXjTVNez9u2bSMtLY1QKMRbb73FtddeywMPPEAoFGLSpEm1T9mM5+tZkiSFHUuf47e//W3tNMXMzEw2b97c4L527NhBy5YtSUhIID09vc6I/sbucziNUZIU1wYPHnzAdaP2V1hYyOLFiyksLGTZsmWsX7++9sl0B6rf/zWEF2rf84TB483ll19OYWFho2wrKSmJRx55pFG2FW8a43p+7bXXGDZsGCNHjuTss89m165dFBQUcOaZZ3LRRRfVrp9xPF/PkiQd7w6nz3HZZZfx2GOPUVBQwJIlSzjrrLMa7EP//Oc/p6CggNNPP51u3brVLlnRFH2OQMjH7EiSmrlhXzzQ763zj+79U6dO5ZJLLmnSNaCWL1/Os88+G9NTIo/1POvweD1LkqRIiPU+x4IFCxg9ejT/+te/jnjkl8kuSVKzZxImMjzPkeF5liRJkRDrfY5jSXY5jVGSJEmSJElxw2SXJEmSJEmS4obJLkmSJEmSJMWNpGgHEEu27YKyiujsO7cNpCVHZ9+SJEmSJEmxwmTXESirgCsXRGffD4+CIe2js29JkiRJkqRY4TRGSZIkSZIkxQ2TXZIkSZIkSYobJrskSZIkSZIUN0x2SZIkSZIkKW64QH0TK/lJAZUrigkkJRNITCKl60l0mTiNNoPPjHZokiRJkiRJcceRXRHQZeI08p/axqDHN9C67whW3fV1aiq3RDssSZIkSZKkuGOyK4ISklvS4azJBLdvY/u/y6IdjiRJkiRJUtwx2RVBwR3VfPbSwySktiGlS+9ohyNJkiRJkhR3YibZtXPnTqZMmUL37t1p1aoV48aNY+HChQQCAZ599tloh9egj2dOYcllbVn67Z5UrX6H3Fv/j8TUNtEOS5KavYqd8OdVe1//Yhms2Rq9eOLV9t3wv+V7X097B977PHrxxKvdQZj78d7XUxbBwk8hFIpeTJIkKf5s2wV/Xb339fR3oawievFEQ0wsUB8KhZgwYQILFy7k9ttvJzc3l5kzZzJ+/HgA8vPzoxxhw7pcdiedx/8o2mFIUkx581P4r4VQXbO37C8fwJMfwHf6hn907Moq4Jpi2Lhjb9mz5fD3cji/O/xkCCQGohZe3PikOnyeV2/bW/biOvjHR3BaR7jnFGgVE70ySZLUnC37HK5/HSp27S372xp4eg18sxfc0B8Cx0HfLia6VQ899BCzZ89myZIl9O/fH4CCggJycnLIzMykR48eUY5QktSY1m6DG96AXcG65XsGwDxUAp1S4OvZEQ8trmzdBVe/Bpt31i3fc9qfWwvtU+CavIiHFldqQnDt61C+rW558IsL+o1P4adL4GfDIh6aJEmKI59uD99cq95dt3xP3+7PH0DHFJiYG/HQIi4mpjFOnz6diRMn1ia6ABITE8nJySE/P581a9YwZMiQ2p+ePXuSmZkZxYglScfiqdWwM7j3D/P+AsCjpXuTBTo6/7cWNu08+HmG8Ei6yt0NNNAhLdgAH2w9+HkOEZ7e+FFlJKOSJEnxZtYaqNrdcN/u8bL6N5TjUbMf2VVaWsrq1au577776tWtXbuWCy+8kJ49e7JkyZLa8htuuIHduw+/Z56ens7OnTsP2S617whOnFp02NttTGecUUBVSXFU9i1JkZb38EckZXQ8aH0I+LgK2uUNZ/vqJRGLK970mjaf1NxTCSQc/N7X9hroeeY3qHj97xGMLL50u+5R2o66hEDiwbtdwVCI4d/6CZ8994sIRiZJkuJJn/uW0aJzLoEG5il+vhNOOOVLVC4rilxgRykYPPqsXLNPdq1btw6ATp061SlfsWIF5eXl9dbr2rlzJ3/+85958cUXIxZjQ/pOK4p2CJIUcxJapR9Wu8TUjCaOJL4ltm7XYKKrtp3n+ZgkpmYcenGMYA2JrX14jSRJOnqJqRkNJrr2tov/PkezT3a1b98egLKyMk499VQgvGD9TTfdRDAYrJfseu655+jatSsnn3zyYe9j69bDe7TXko1w5YLD3myjmjeviCHto7NvSYq08S+Hp3Qdapbiu6/OoVvriIQUl65/HV7/pOGh7gDPPvEgwzs+GJGY4tHPl8Izqxs+z4HEJH51+81c8MebIxaXJEmKL5Negfc3H7oP/erzT3NS2wgEdIwqKipYunQpAwcOPOL3Nvs1u/Ly8sjNzeWWW27h6aef5h//+Adf+9rXWLRoEampqfTtW/dxXI8++ij/+Z//GaVoJUmN4YLshv9IJwD5mZjoOkZf73GIBAxwQgoM6xCpiOLT1w5xngFaJMDZXSMSjiRJilPjD9GHDgC56dA3Rgbtt2nThlGjRtGmzZGPRGv2ya6kpCSeeeYZsrKymDRpEjfccAPnnnsuY8eOZdCgQSTsM/1i3bp1zJ8/n29+85tRjFiSdKzGZ0OP1gf+I5UAJATgun6Rjir+nN45nDQ80GD3AOHO0g8GQOJx8HjqptQ3A87r1nCb750EacmRiUeSJMWnc7pB3zYH79sFgBv6H3p1hXjQ7JNdAIMHD6a4uJiqqipKSkq46qqrWLx4cb0pjI8//jjnnXde7dRHSVJsSkuGh0bByQcYUdSpFfxmBAzyobvHLCkBfnUanNmlfqeoTTJMPRkKu0QltLgzZQhckgNJ+53oVonhTud/nBiVsCRJUhxJSYTfjYRRJ9Sva98SfnEqnNapfl08CoRCoZh7cHt1dTXp6ek88MADfPvb364t79OnD/fddx/nnHNOk+w3mmt2PTwK1+ySdFxaVQGvfxp+RHKfDDitY3hklxrXx1Xwyvrw0xe7tw6P+kqOiVtisWXTDpj3b6jYBZ1S4IwsSG32K6hKkqRY8+E2+NcG2BmEXukwslP4RufxIia7V++++y41NTX1RnatXLkyShEd2IbnfsWWN/+PPnfOrVP+4UPXUb16CW1OPpesCbcA8OkLD/L5gr8SCtbQ546XCCQ5l0GSAE5sE/5R0+qSCt/oFe0o4l9mS7iwZ7SjkCRJ8a5HGlyWFu0ooicmk13Dhw+nuQ9IC+3eRfXqJfXKK0vfIpCQRN+fvcqquy9i1+YNhHbtoLp8KX3ufDnygUqSJEmSJMWR42gQW2RtLJpBuzGX1iuvXPkG6YPGAZA+YCxVZW9TsXgOwe2VrLx1HB8/eXuEI5UkSZIkSYofJruaQCgYpGLRi2Sc/KV6dTWVm0lMDc/HSWiVTk3lZnZt+QQCAfpM/Sc7Nqym6oMlEY5YkiRJkiQpPsTkNMbmovrD9/nwwavrlGXkn0PLrFwyTj3/gO9JbN2WmqoKAILVW0nufCKJqRmkDxgLQHr/09m+roTUXkOaNHZJkiRJkqR4ZLLrGLTq0Y++04rqlf/7r9PYuqyITUUzqFq9hM/mPEyHs68EoHWfU9n0ypO0PfWrbH3vFdqNvpjkdp3Z9MpMAKrLl5J5gOmPkiRJkiRJOjSnMTaBrIt/Qp+fvkTv218gNWcIHc6+kl2fr2f9rHto3fsUQrt2UPLjMaTmDCa57QmknngyoZrdlPykgOCOKlr3HR7tQ5AkSZIkSYpJgVBzf6xhM7JkI1y5IDr7fngUDGkfnX1LkiRJkiTFCkd2SZIkSZIkKW6Y7JIkSZIkSVLccBrjEdi2C8oqorPv3DaQlhydfUuSJEmSJMUKk12SJEmSJEmKG05jlCRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJccNklyRJkiRJkuKGyS5JkiRJkiTFDZNdkiRJkiRJihsmuyRJkiRJkhQ3THZJkiRJkiQpbpjskiRJkiRJUtww2SVJkiRJkqS4YbJLkiRJkiRJcSNmkl07d+5kypQpdO/enVatWjFu3DgWLlxIIBDg2WefjXZ4EfdJNTyyEn66BH6xDBZvhFAo2lFJas52BeGldXDXOzB1CfxtDVTtjnZUkiRJktS4AqFQ80+RhEIhvv71r7Nw4UJuv/12cnNzmTlzJi+88AIff/wx5eXl9OjRI9phRkQoBL8vgcdWQghICITLgkD/tnDvqdA+JcpBSmp23vsc/mshbNwBiYFwWU0IWiXCHfkwrkt045MkSZKkxhITya4HH3yQa6+9liVLltC/f38AampqyMnJobKyko0bN0Y5wsj5Yyn8ZvmB6xKAXukwYywkx8yYPUlN7aNK+OZ8qN4dTozvK/DFz+9GwrAOUQhOkiRJkhpZTKREpk+fzsSJE2sTXQCJiYnk5OSQn58PwMqVKxkxYgR9+vRhxIgRlJaWRivcJlO9Gx5defD6IFC2Feb9O2IhSYoBf1514EQXhEeIAvyhJJIRSZIkSVLTSYp2AIdSWlrK6tWrue++++rVrV27lgsvvBCA733ve1xzzTVMnDiRP/3pT3z3u9/ln//85yG3X1FRQefOndm9ezeBQKDR429MGSMvoscP/txgm1DNbq79w0uU/+zrkQlKUrPX74nPSGyVftD6IPD2Rmid1Yvdm9ZFLjBJkiRJakCLFi3YunXrEb+v2Y/sWrcu/MWrU6dOdcpXrFhBeXk5+fn5fPLJJyxatIhLL70UgEsvvZRFixbx6aefHnL7S5cupbq6mhiYzUlSm06HbBNITCK5becIRCMpFgSSWjSY6NpXUhvnMUqSJEmKfc1+ZFf79u0BKCsr49RTTwXCC9bfdNNNBINB8vPzWbt2LV27diUxMREIT3Hs0qULa9eupWPHjoe1n6KiIkaNGtU0B9FI5qyDW95uuE0CUHhaPu/t2BGRmCQ1b6EQjJ0NVTWHblu6ZCGdWjV9TJIkSZLUlJp9sisvL4/c3FxuueUWkpOTSUtL44EHHmDx4sWkpqbSt29fFi9eHO0wI+L0EyA1seEvrUHgK90jFpKkZi4QgK/0gGdWH3jNLggnyU9uj4kuSZIkSXGh2U9jTEpK4plnniErK4tJ/397dx8eVX3n//85uSGAIDRgKnIbGsAIBiIoyo2ZAlKx1Z+ItFtrxRbbLmr9sd1aWr7StRVvWL9X7aot1urWmxbbLksLuFQR1wBKlKJBQCAECxFBvKPcBgLJzPePKYGQEO6SmczJ83FdMTOf85nJ+xwP58x5zeecM2ECkydPZsyYMRQUFJCXl0dKSgpdu3Zl69atVFXFUqCqqiq2bdtG167BSn1apsEtfY4/PQXodTaEO8WtJElJ4Iae0Cqt7g1+6B//+fb5cS5KkiRJkhpJkw+7APr3709RURHl5eWUlJQwadIkiouLq+/EmJWVxYABA3juuecAeO6558jPzz/pUxiTydc/B9/qDSl1XEu/72fgF5dBelL8X5UUL13OgplDoEPL2tNapcK/D4qN7JIkSZKkIEjKWGT//v2UlJRUh10Ajz32GI888gi9e/fmkUce4bHHHktghY0nFILvnA8LroDbc4+0PzkM/nMYZGYkrjZJTdcF7WH+KJgx6EjbXf3hxS84GlSSJElSsDT5a3bVZdWqVVRVVdUIu84//3zeeOONBFYVXx1bws294NF1sef9MxNbj6SmLy0FRp535Pm13RNXiyRJkiQ1lqQMuwYPHkw0Gk10GZIkSZIkSWpikvI0RkmSJEmSJKkuhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSJEmSJCkwDLskSZIkSZIUGIZdkiRJkiRJCgzDLkmSJEmSJAWGYZckSZIkSZICw7BLkiRJkiRJgWHYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSJEmSJCkwkibsOnjwINOmTaNr1660atWKESNGsHz5ckKhEHPnzk10eZLOQGUEXt4GD6+FR9fCso8gEk10VZIkgO3l8FQp/PwdeHYjfLQ/0RVJkiTVLy3RBZyMaDTK+PHjWb58OXfffTc5OTnMmjWLsWPHApCfn5/gCiWdrjc/galvwqcVR9L3pzZC59bw4MXQu11Cy5OkZutQBP59Ffz5PYgCqSGoisIja2F8NvxLX0hLmq9NJUlSc5IUYdfjjz/OggULWLlyJX379gUgHA6TnZ1NZmYm3bp1S3CFkk7H+p3w3ddjI7sAIkdN+6AcvrMMfns5dD4rEdVJUvN279vw/JYjz6v+MeI2AvxhU2wE7pS8hJQmSZJUr6T4Pm7GjBnceOON1UEXQGpqKtnZ2dWjur7//e+TnZ1NKBRizZo1iSpV0in49YZY0BWpY1oE2HcIfvtuvKuSJG3aUzPoqsvszbCtPC7lSJIknZImH3aVlpayadMmxo0bV2vali1bqsOua6+9liVLltC9e/d4lyjpNOw8CEu21x10HRYB5m85MppAkhQf/7MFQifRb8EJAjFJkqREaPKnMW7duhWArKysGu3r16+nrKysOuwaNmzYGf2dcDhMSkqTz/5q6ffHAwBkZLRMcCXSqcnofD69f/72CfsdqII2mecQKd8dh6qaB7cbkk6ky21P0H74PxFKTT9un0jlIe595Dfc9uvvxrEySZLUnLRo0YI9e/ac8uuafLrToUMHADZu3FjdFo1GmTJlCpFIxIvTS0mqau+Ok+oXOVRB5MC+Rq5GknS02Db6BGO7UlKo2vNpXOqRJEk6FU1+ZFdubi45OTlMnTqV9PR02rRpw8yZMykuLqZ169b06dOnQf5OYWEhQ4cObZD3iqdB82K/KyoqEluIdBr++TV469Pjn8qYAnwxO4O39ntRmIbkdkPSiazdCTctqb9PKCWVwkd/RM+nfxSXmiRJkk5Wkx/ZlZaWxuzZs+nUqRMTJkxg8uTJjBkzhoKCAvLy8pLy1ENJMbf0id3Ovq6xAyFit7T/ek6ci5IkcUF7GJJ1/LFdIWBEJ+jZNo5FSZIknaSkSIr69+9PUVER5eXllJSUMGnSJIqLiz2FUUpygzrC9IGxUOtYrdLgZ5dAztnxr0uSBPcNhEvOqdl2eHM99LPwEz+GSZKkJiopwq5j7d+/n5KSkhph1x133EGXLl14//33GTVqFH379k1ghZJO1hc6wwujYfJR/2R/lAd/GQ2XZh3/dZKkxtUmHR69FJ486h5A43rAU8PhoUtiX0pIkiQ1RUkZdq1atYqqqqoaYdfDDz/M+++/T2VlJdu3b+edd95JYIWSTkW7FnDj5448H9cDzvIgSpISLhSC/plHnk/Jg36fibVLkiQ1VUl5ODl48GCi0Wiiy5AkSZIkSVITk5QjuyRJkiRJkqS6GHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSJEmSJCkwDLskSZIkSZIUGIZdkiRJkiRJCgzDLkmSJEmSJAWGYZckSZIkSZICw7BLkiRJkiRJgWHYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTASJqw6+DBg0ybNo2uXbvSqlUrRowYwfLlywmFQsydOzfR5SmgKiOweDv85wb47Ub4255EVyRJOuzD/fD7v8GTG+Av78OBykRXJKmpOxSBRdti241Z78L7+xJdkSSpMaQluoCTEY1GGT9+PMuXL+fuu+8mJyeHWbNmMXbsWADy8/MTXKGC6LUP4Z6V8EnFkbafr4VLOsL0gZCZkbDSJKlZO1AFD6yCBVsgclT7WWlwxwUwrkeiKpPUlL20Nbbt2HXoSNvP3oGCc+En+dAmPXG1SZIaVlKEXY8//jgLFixg5cqV9O3bF4BwOEx2djaZmZl069YtwRUqaFZ8Av+yHKLRuqf982vw1OXQOin+BUlScESjMOWv8NpHtaftq4T7V0EIuK5HvCuT1JQVfgBT36x72pLtcHsR/HoYpCfNeS+SpPokxeZ8xowZ3HjjjdVBF0BqairZ2dnk5+fz6aefctVVV9GnTx8uvPBCrrvuOj7++OMEVqxk9/N3gCjUkXURAf62F57fEueiJEms+KTuoOtoj6yDiqr41COp6YtEYyO4oO7PdlFgzU54eVsci5IkNaomH3aVlpayadMmxo0bV2vali1byM/PJxQK8YMf/ICSkhJWr17N5z73OX74wx8moFoFwcbdsH5XzVNjjhUC/lQWr4okSYfNfQ9SQvX32XMoNlJDkgCKP4Vt5XUHXYelAH/2s50kBUaTPwlr69atAGRlZdVoX79+PWVlZeTn55OZmUk4HK6edumllzJz5sxT+jvhcJiUlCaf/dXS748HAMjIaJngSoKj7UVj6PGjP9fbJwqs/2AXGRlZ9fbTqXF9jg+Xs5JZz3te4azzh5yw382Tf8Qn834Wh4qaB7cbSmbtL7+Brt/9Tb19IsCydZvJGNEnPkVJkk5KixYt2LPn1O8U1+TTnQ4dOgCwcePG6rZoNMqUKVOIRCK1Lk4fiUSYOXMm11xzTVzrVHBUle86YZ9oNEpV+c7GL0aSVEPVvp1EIyc+R7Fq387GL0ZSUqgq333CPtFIhKq9f49DNZKkeGjyI7tyc3PJyclh6tSppKen06ZNG2bOnElxcTGtW7emT5+a375897vfpU2bNtx+++2n9HcKCwsZOnRoQ5YeF4PmxX5XVFTU31EnrTICV78EH9ezSFNCIb4zpDu3udwblOtzfLiclcz+Zwv8W3H9fdJCsPZPM8nMOLVR3jo+txtKZgcq4QsLYzexOJ5QSgo//FI+X5/sOi5JQdDkR3alpaUxe/ZsOnXqxIQJE5g8eTJjxoyhoKCAvLy8Gqcefv/736e0tJQ//OEPSXlKopqGtBT4Ru/jT08BWqV6a3tJSoRR58F5rev/ADO2O2RmxK0kSU1cyzT4+ueOPz0FaN8CrvYG75IUGE1+ZBdA//79KSoqqtH26KOPUlBQUP186tSpvPnmm/zP//wPGRl+wtWZGd8DPj4AvymNXYz+6Auatk6D/7gUzm2VoOIkqRnLSIVfXga3FsUuOH1YCrFr7ow6D77XL1HVSWqqvtkbPq2A/9p8ZHtxWPsW8Ohlsd+SpGBIyuFP+/fvp6SkpPp6Xe+88w73338/27ZtY8iQIQwYMICxY8cmuEols1AIbsuF//o8/FPPI+1TLoTnr4D+mYmrTZKauy5nwezPw/SLjrRd3Q3+cxjcPxDSk/LTjaTGlBKCKXnwuwK4rseR9rv6w9xR0LtdwkqTJDWCpBjZdaxVq1ZRVVVVHXb17duXaLS+mwlLpye7LfxrP3jub7Hn47MTW48kKaZFKlzZBe56K/Z82oCEliMpSfRpBz/Mg9mbY8+v7Z7QciRJjSQpw67BgwcbbkmSJEmSJKkWB/pLkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSJEmSJCkwDLskSZIkSZIUGIZdkiRJkiRJCgzDLkmSJEmSJAWGYZckSZIkSZICw7BLkiRJkiRJgWHYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYCRN2HXw4EGmTZtG165dadWqFSNGjGD58uWEQiHmzp2b6PIkSar28QGY9x7M3gRvfgLRaKIrktTUVUZgyXb4r03wwvuw91CiK5JOXzQKq3fA7M3w5zLYui/RFUlqbtISXcDJiEajjB8/nuXLl3P33XeTk5PDrFmzGDt2LAD5+fkJrlCSJNhXCQ+8DS9uhchR7V3Pgv/THwZ1TFhpkpqw59+D/1gLfz94pC0jBf6pJ9yaC6mhxNUmnap1O+EnxbBxz5G2EDD8szBtAHwmI0GFSWpWkiLsevzxx1mwYAErV66kb9++AITDYbKzs8nMzKRbt24JrlCS1NwdrII7XodVO+DYgVxb98HtRfDLIXBRh4SUJ6mJ+nMZTH+7dntFBJ7eCDsPxgICKRls3A3fei22TzxaFHj1Q/j2a/Cb4dAmPSHlSWpGkuI0xhkzZnDjjTdWB10AqampZGdnV4/quvbaa+nfvz/5+fkMHz6clStXJqhaSVJz9NI2eLuOoAtio7wiUfjZmnhXJakpO1AJD71Tf5+578H6XfGpRzpTj6yNBV2ROqZFgE174U9l8a5KUnPU5MOu0tJSNm3axLhx42pN27JlS3XY9fTTT/P2229TXFzM97//fb75zW/Gu1RJUjM2Z3P9O9UIsQPWDR60SvqH//0gdvpzfVKAuYYDSgIf7YdlH9UddB0WAv57c5wKktSsNfnTGLdu3QpAVlZWjfb169dTVlZWHXa1a9euetquXbtISTm1HC8cDp/ya5qCfn88AEBGRssEVxJsLuf4cDnHh8u5ceT+egtp7bNO2G/ol77M7uXeWKWhuD7Hh8u5cWRd/3/IGn8XoXo+g1ZFI/znnxfx44uvjmNlwec63fBa97mMz00vrLdPFNiyp4qMjNZxqUlS8mvRogV79uw5ccdjNPmwq0OH2MVNNm7cyCWXXALELlg/ZcoUIpFIjYvT33LLLSxcuJBoNMoLL7yQkHolSc1T1f7dpLY7h1Co/itJRw54SypJMZEDe+sNumKdIkQO7I1PQdIZiOw/uYPRyMHyRq5EkpIg7MrNzSUnJ4epU6eSnp5OmzZtmDlzJsXFxbRu3Zo+ffpU933iiScAePbZZ7nzzjtZsGDBSf+dwsJChg4d2uD1N7ZB82K/KyoqEltIwLmc48PlHB8u58bxi3XwVGnd1+w6rG06bHv9f8hIjVtZgef6HB8u58bx/j4Y+3L9241QahqP3HodV97nsm9IrtMNLxKFa1+GD8qPv06nANf0aUuxy11SI2vy5+2lpaUxe/ZsOnXqxIQJE5g8eTJjxoyhoKCAvLy8Ok89/PrXv84rr7zCp59+moCKJUnN0bjukJFa/471az0x6JJUrctZMKJT7DpGdUkBOrWK9ZGaupQQ3Jxz/KAr9I8+X82OZ1WSmqsmH3YB9O/fn6KiIsrLyykpKWHSpEkUFxdXn8K4d+9etmzZUt1//vz5ZGZmkpmZmaiSJUnNzLmt4eeDa4dZh3e013SDb/aOe1mSmrgf58OAf3xkTTkm9erYEh69DFoYkitJjO0eC7yg5oFmCEgNwf2DoFe7ul4pSQ2ryZ/GWJf9+/dTUlLC5MmTAdi3bx/jx49n3759pKamkpmZyfz580943RRJkhrSoI4wdxTMew8eXRdr+0KX2Kiv/pngbknSsc5Kg8eGwqsfxu66uOTDWPvUPLiyC7ROyk/raq5CIbj9Ahh1HszeDH9+L9Y+sTdc2x3ObZXQ8iQ1I0m5+1y1ahVVVVXVI7s++9nP8vrrrye4KkmSIDMDbu51JOy656LE1iOp6UsNQcG5sZ/D15K6rkdCS5LOyPnt4a4BR8Kufz4/kdVIao6SMuwaPHgw0Wh9l/KUJEmSJElSc5QU1+ySJEmSJEmSToZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSJEmSJCkwDLskSZIkSZIUGIZdkiRJkiRJCgzDLkmSJEmSJAWGYZckSZIkSZICw7BLkiRJkiRJgWHYJTWAwsJCsrOzCYfDTJgwodb0e++9l9LS0uO+fseOHQwcOJA2bdrUmrZ//36uuuoqCgoK+MY3vgHA8uXLGTp0KEOGDOGuu+4CYN26dcyYMaOB5khSY2vM7UZd0+vq73ZDkiRJQWTYJTWQiRMnUlhYSLt27SgqKqpuj0QirFq1il69eh33tW3btuWll17i0ksvrTVt4cKFDBs2jMWLF5Oens6aNWvIz8/ntddeY9myZRQVFbF7925yc3N56623iEajjTJ/khpeY2036ppeV3+3G5IkSQoiwy6pgfXr14+tW7dWP3/77bfp3bt3va9JT08nMzOzzmnZ2dns27cPgL1799KuXTvS09MBqKqq4rzzzqN169YA9OzZk3feeachZkNSHDX0dqOu6cfr73ZDkiRJQWPYJTWwoqIicnJyqp+XlpbSo0eP036/nJwcli5dSm5uLqFQiK5duwIwa9YscnNzad++PWlpaQB0796dDRs2nFH9kuKvobcbp8LthiRJkoLGsEtqIE8++SThcJjOnTszYMCAOvusXbuWcDhc4+eBBx6o932ffvppvvKVr7Bu3To6duzIsmXLALjhhhtYv34927ZtY/Xq1Q09O5LioLG2G5IkSVJzlpboAqSgmDhxYvXF4o/Wq1cv5syZA8AFF1xAYWHhKb1vJBKpPvUoMzOTnTt3UlFRQUZGBikpKbRt25aWLVsCUFZWxtChQ89sRiTFTWNtN06F2w1JkiQFjSO7pEbWv39/SkpKTthv1KhRFBcXM2rUKNasWcP27dt58MEHueGGG/jNb35DOBxm5cqVXHHFFcybN49wOMzll19Oly5dqi9ivXHjRvr169fYsySpkZ3pduN40499Dm43JEmSFDyO7JIawOFTi+qSkpJCXl4epaWl9d5ZbdGiRbXa7rzzTiB2R8ajjR8/nvHjx9doW7duHQMHDiQUCp1i9ZISobG3G3VNP/a52w1JkiQFkWGXFAd1nabU0HJzc8nNzW30vyMpPtxuSJIkSafH0xglSZIkSZIUGIZdkiRJkiRJCgzDLkmSJEmSJAWGYZckSZIkSZICw7BLkiRJkiRJgWHYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAiMpwq6DBw8ybdo0unbtSqtWrRgxYgTLly8nFAoxd+7cRJengNu4+8jj3QcTV4ek5LHn0JHHpbsSV4ckSZLUHKUluoATiUajjB8/nuXLl3P33XeTk5PDrFmzGDt2LAD5+fkJrlBBVbILHlgFq/9+pO3KhXB1V/iXvtCyyf/rkRRvFVXw8Fr4U9mRtq8uhgvaw5QLoe9nElaaJEmS1Gw0+cP1xx9/nAULFrBy5Ur69u0LQDgcJjs7m8zMTLp165bgChVEG3bBxFfhYFXN9oMRmFMGm/fCo5dBelKMjZQUD5UR+P5yKPq49rT1O+Hbr8Gvh8WCL0mSJEmNp8kfqs+YMYMbb7yxOugCSE1NJTs7u9aorp/85CeEQiHWrFkT7zIVMD9bEwu6InVMiwJvfgoLt8a7KklN2Ssf1B10QWxbcigC/3d1XEuSJEmSmqUmHXaVlpayadMmxo0bV2vali1baoRdb731Fq+//jrdu3ePZ4kKoC17YcWndQddh6UAszfHqSBJSWH25vp3qhFg1d/hb3viVJAkSZLUTDXp0xi3bo0NncnKyqrRvn79esrKyqrDroqKCm677Taee+45wuHwaf2tcDhMSkqTzv7q1O+PBwDIyGiZ4EqCo23+lfSYWv+NDyLAyvd3kpHx2fgU1Uy4PseHy7lxnP/r90hvf+JtwuCrvszu5d5cpaG4PseHyzl+XNbx4XKOD5ezpDPVokUL9uw59W+Lm3S606FDBwA2btxY3RaNRpkyZQqRSKQ67Prxj3/MjTfeSI8ePRJRpgImcnD/yfWrKG/kSiQlk+hJbhNOdhsjSZIk6fQ06ZFdubm55OTkMHXqVNLT02nTpg0zZ86kuLiY1q1b06dPH4qKilixYgUPPPDAGf2twsJChg4d2kCVx8+gebHfFRUViS0kQCqqYndd3HPo+H1SgBsuOo8pLvcG5focHy7nxvHQGpj1t9h1/Y6ndSq8/9p8WjXpvW9ycX2OD5dz/Lis48PlHB8uZ0mJ0qRHdqWlpTF79mw6derEhAkTmDx5MmPGjKGgoIC8vDxSUlJYvHgx69atIzs7mx49evD+++/zhS98gYULFya6fCWpjFT4p+zjTw8BKSH4cj19JDU/47MhLSW2jaivj0GXJEmS1LiadNgF0L9/f4qKiigvL6ekpIRJkyZRXFxcfQrjD3/4Q7Zt28bmzZvZvHkzXbp04cUXX2T06NEJrlzJbGJvGN059jjlqCPXEJAagvsGQnbbhJQmqYnqchb8+6DagdfhHe3nO8Gk8xNRmSRJktS8JN33y/v376ekpITJkycnuhQFWFoKTL8Ivtgldoe10t3QIgUuPxfGdYeubRJdoaSmaPi5MPvz8N9lUPhB7LTonLNhXA8Y9tma4bkkSZKkxpF0YdeqVauoqqqqHtl1rM2bN8e3IAVWSgiGfjb2I0knq/NZcMcFsR9JkiRJ8Zd0YdfgwYOJRuu7/K8kSZIkSZKaqyZ/zS5JkiRJkiTpZBl2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSpMAqLCwkOzubcDjMhAkTak1/9tlnWbRoEQD33Xcfw4cP57vf/W6tfi+88AKXXXYZo0ePZtu2bQBcffXVFBQUMHLkSD755BMA7rnnHi6//HImTJhAZWUlO3bs4Hvf+14jzqGak1NZn+fNm8eIESMIh8O89957Nfp961vfoqCggGHDhrFhwwag9vpcWVnJLbfc0vgzJUlSIzDskiRJgTZx4kQKCwtp164dRUVFNabNnz+fkSNH8uGHH/LWW2+xdOlS0tLSWLFiRY1+M2bM4JVXXuFnP/sZM2bMAGDOnDksXryYm2++mVmzZvHBBx9QXFzMkiVLuPjii5k/fz6ZmZns3LmTvXv3xm1+FWwnsz7v27eP3//+97z88ssUFhbSrVu3Gv1++ctfsnjxYu6//34ee+wxoPb6nJaWxjnnnMO7774bt3mTJKmhGHZJkqRmoV+/fmzdurX6+Y4dO2jZsiWhUIgVK1ZQUFAAwIgRI1i+fHmN16alpdGyZUv69u1bPS09PR2AAwcOkJubS1lZGX379gXgwgsvrA4iBg8eTGFhYWPPnpqZ+tbnoqIiIpEIV1xxBbfddhuRSKTGaw+vu3v37qVfv3412g6vzwDhcJi//OUv8ZgdSZIalGGXJElqFoqKisjJyal+vnHjRrp37w7Azp07OfvsswFo27YtO3furPHaQ4cO8emnn/Lqq6+yY8cOIBYuDBkyhIcffpjc3Fx69uzJ66+/TiQSYcmSJezatQuA7t27V58qJjWU+tbnjz76iE8++YSFCxfSsWNH5s2bV+v1I0eO5Pbbb+fiiy8Gaq/P4LorSUpehl2SJCnQnnzyScLhMJ07d2bAgAF19mnfvj27d+8GYM+ePbRv377G9OnTp3P99dfz3HPPccEFFwCQmZnJsmXLmD59Og899BBZWVmMHTuWESNG8OGHH5KVldWYs6Vm6mTW53bt2jF8+HBSUlK4/PLLKSkpqdXn5ZdfZs6cOdx9991A7fVZkqRkZtglSZIC7fA1jqZPn16jPScnh7KyMgAGDhzIkiVLAHjllVe45JJLavQdNmwYr7zyCjfffDODBw8mEolQWVkJxIKFli1bAnDrrbdSWFhI9+7dueqqqwAoKyujV69ejTqPaj5OZn2++OKLWbt2LQCrV6+mR48eNfpWVFQAsXW3VatWx12fXXclSckqLdEFSJIkJUJmZibl5eUAnHvuueTl5TF8+HDy8vIYNGgQ27dv59lnn+XOO+/kpz/9KYWFhXTu3Jlf/epX7Nu3jy996UukpKSQkZHBU089BcB1113H7t27GT58OJdddhkAr7/+Og8//HCiZlPNxNHrc1ZWFhdddBEFBQWcc845zJo1q8b6PHbsWPbv308oFOIXv/jFcdfnwsJCJk6cmMC5kiTp9ISi0Wg00UUk0muvvcawYcN49dVXGTp0aKLLOWWD/nEJhhXXJLYOqSG4PseHy1lBcqbr8zPPPMN5553HqFGjGq6oo+zYsYN77rkn6U8Lc7sRP2eyrBtyfa6srOQ73/kOTz755Bm/V1PkOh0fLmdJieLILkmS1GzddNNNjfr+mZmZSR90KXk05PqclpYW2KBLkhR8XrNLkiRJkiRJgWHYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKjKQJuw4ePMi0adPo2rUrrVq1YsSIESxfvpxQKMTcuXMTXZ4kSYqzysiRx5v3JK4OqaG8u/vI46po4uqQJCnZJUXYFY1GGT9+PE888QR33XUXzz//PNnZ2YwdOxaA/Pz8BFcoSZLiJRqFP2yCq1860nb9K/CNpbDy08TVJZ2uv34MX18MXyk80nbNSzBnc2x9lyRJpyYt0QWcjMcff5wFCxawcuVK+vbtC0A4HCY7O5vMzEy6deuW4AolSVK8PLIOntlYu/2dv8M/L4NHLoWLz4l/XdLpePVD+N5y4JhQ68MDcN8q+KQCvt0nIaVJkpS0kmJk14wZM7jxxhurgy6A1NRUsrOzq0d19ejRg/PPP58BAwYwYMAAXnzxxUSVK0mSGknprrqDLoAIEInCT1fGfktNXWUktr5Go7H1ty6Pl8CWvfGsSpKk5Nfkw67S0lI2bdrEuHHjak3bsmVLjVMYZ8+ezcqVK1m5ciVf+MIX4lmmJEmKgzll9X94iQAf7Ic3Po5XRdLpW/oh7KioNairhhCx9V6SJJ28Jn8a49atWwHIysqq0b5+/XrKysoa7Hpd4XCYlJQmn/3V0u+PBwDIyGiZ4EqkM+f6HB8uZyWznj/9X87KHXrCftdPmsInz/+88QtqJtxuNI6s66eS9eVphELH/wwaiUb45eyX+MFF18SxsuBznY4Pl7OkM9WiRQv27Dn1OxE1+XSnQ4cOAGzceOSchWg0ypQpU4hEIjXCrq997Wvk5eVx6623snPnzniXKkmSGlnk0AGikeOd8HVEtPJgHKqRzkzkUAWxsVv1iEZdnyVJOkVNfmRXbm4uOTk5TJ06lfT0dNq0acPMmTMpLi6mdevW9OkTu2Ln0qVL6dq1KxUVFUyePJnbb7+d3/72tyf9dwoLCxk69MTfFDc1g+bFfldUVCS2EKkBuD7Hh8tZyey378LP3zlxv9d/9xDd2jzU+AU1E243GseGXXDD4vr7hFJSuX/i1Yy7x2XfkFyn48PlLClRmvzIrrS0NGbPnk2nTp2YMGECkydPZsyYMRQUFJCXl1d96mHXrl0ByMjI4NZbb+W1115LZNmSJKkRXN0VWqce/wNMCjA0C7q1iWdV0unp3Q4u6lD/+nx2OozpEs+qJElKfk0+7ALo378/RUVFlJeXU1JSwqRJkyguLq4+hXHfvn3s2rULiJ3i+Pvf/54BAwYksGJJktQY2rWAnw2GFqk1T/46/Di7LfykYS7nKcXFfQOhy1mxx8eu063S4OeDoXWTPxdDkqSmJSl3nfv376ekpITJkycD8OGHHzJu3Diqqqqoqqriggsu4Je//GVii5QkSY1iUEf4Qxj+azO8uBX2VcJ5rWBsj3+M/ErKTzdqrjq2hGcuh3nvwZ/K4MP90DYdruwC43vAua0TXaEkScknKT8Orlq1iqqqquqRXT179qS4uDjBVUmSpHjpfBZM7hv7kZJdm3S44XOxH0mSdOaSMuwaPHgw0Wg00WVIkiRJkiSpiUmKa3ZJkiRJkiRJJ8OwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEtSUigsLCQ7O5twOMyECRNqTX/22WdZtGgRAPfddx/Dhw/nu9/9bq1+L7zwApdddhmjR49m27ZtAFx99dUUFBQwcuRIPvnkEwDuueceLr/8ciZMmEBlZSU7duzge9/7XiPOoSRJkiSpIRh2SUoaEydOpLCwkHbt2lFUVFRj2vz58xk5ciQffvghb731FkuXLiUtLY0VK1bU6DdjxgxeeeUVfvaznzFjxgwA5syZw+LFi7n55puZNWsWH3zwAcXFxSxZsoSLL76Y+fPnk5mZyc6dO9m7d2/c5leSJEmSdOoMuwLuRKNh7r33XkpLS4/7+h07djBw4EDatGlTa9r+/fu56qqrKCgo4Bvf+AYAy5cvZ+jQoQwZMoS77roLgHXr1lWHClJD6NevH1u3bq1+vmPHDlq2bEkoFGLFihUUFBQAMGLECJYvX17jtWlpabRs2ZK+fftWT0tPTwfgwIED5ObmUlZWRt++fQG48MILq4O1wYMHU1hY2NizJ0mS1Cw05rEKwObNm+nUqRPhcJibbrqJQ4cO8eUvf5lwOMyDDz4IeKwiBZVhVzNwvNEwkUiEVatW0atXr+O+tm3btrz00ktceumltaYtXLiQYcOGsXjxYtLT01mzZg35+fm89tprLFu2jKKiInbv3k1ubi5vvfUW0Wi0UeZPzU9RURE5OTnVzzdu3Ej37t0B2LlzJ2effTYQW3937txZ47WHDh3i008/5dVXX2XHjh1A7IPSkCFDePjhh8nNzaVnz568/vrrRCIRlixZwq5duwDo3r07GzZsiMMcSpIkNQ+Ndaxy2Be/+EUKCwt55plnmDNnDkOGDKGwsJA333yTjz/+2GMVKaAMu5qRY0fDvP322/Tu3bve16Snp5OZmVnntOzsbPbt2wfA3r17adeuXfUImaqqKs477zxat24NQM+ePXnnnXcaYjbUjD355JOEw2E6d+7MgAED6uzTvn17du/eDcCePXto3759jenTp0/n+uuv57nnnuOCCy4AIDMzk2XLljF9+nQeeughsrKyGDt2LCNGjODDDz8kKyurMWdLkiSp2WvoY5XDXnzxRYYPH87vfvc7Nm3axIUXXghAbm4uf/3rXwGPVaQgMuxqRo4dDVNaWkqPHj1O+/1ycnJYunQpubm5hEIhunbtCsCsWbPIzc2lffv2pKWlAY6IUcM4/M3f9OnTa7Tn5ORQVlYGwMCBA1myZAkAr7zyCpdcckmNvsOGDeOVV17h5ptvZvDgwUQiESorKwFo164dLVu2BODWW2+lsLCQ7t27c9VVVwFQVlZW77eLkiRJOj0NfawC0KlTJ0pKSli4cCG/+tWv6NWrF4sXLyYajbJ06VJH70sBZtjVDJzMaJi1a9cSDodr/DzwwAP1vu/TTz/NV77yFdatW0fHjh1ZtmwZADfccAPr169n27ZtrF69uqFnR6olMzOT8vJyAM4991zy8vIYPnw4FRUVDBo0iO3bt1dfl+GnP/0pI0aM4JFHHuGOO+5g3759jBw5ks9//vM88MAD1XdwvO666xg1ahTl5eVcdtllALz++uuEw+GEzKMkSVIQNdaxCkBGRgatW7emVatWDB8+nC5duvDxxx9zxRVXcM455zh6XwqwtEQXoMY3ceLE6ovFH61Xr17MmTMHgAsuuOCUL7wdiUSqhw0fvlNdRUUFGRkZpKSk0LZt2+pRMmVlZQwdOvTMZkTN2uEPNsdzzTXXsGjRIkaNGsW0adOYNm1a9bRzzz2XO++8E4Af//jH/PjHP67x2sWLF9d6v8P/Ng7bsWMH7du3p23btmcwF5IkSTpaYx2rQOxSK23atCEajbJixQpuv/12Zs6cSTQaZcKECdVfaHqsIgWPI7uasf79+1NSUnLCfqNGjaK4uJhRo0axZs2a6lEyN9xwA7/5zW8Ih8OsXLmSK664gnnz5hEOh7n88svp0qVL9SlfGzdupF+/fo09S2rGbrrpJkaNGtVo75+ZmclDDz3UaO8vSZKkI870WAVg2bJlDBo0iCFDhjB69GgOHTpEOBxm5MiRXH/99dXXF/ZYRQoeR3YFXH2jYVJSUsjLy6O0tLTe6xAtWrSoVtvhUTILFy6s0T5+/HjGjx9fo23dunUMHDiQUCh0itVLkiRJCqrGPlYZPXo0o0ePrjHt2BFiHqtIwWTY1czVNWS4oeXm5pKbm9vof0eSJElScHisIul0eRqjJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAkTdh18OBBpk2bRteuXWnVqhUjRoxg+fLlhEIh5s6dm+jyEuKTA0ceR6OJq0NqCOWVRx5XVCWuDkmSJJ25vYeOPK6MJK4OSc1TUoRd0WiU8ePH88QTT3DXXXfx/PPPk52dzdixYwHIz89PcIXxtXE3fO8NGLPwSNu4/4X57yWuJul07TkEM1bB6BePtF25EB5da+glSZKUbHZUwD0ra362G7MQnigx9JIUP2mJLuBkPP744yxYsICVK1fSt29fAMLhMNnZ2WRmZtKtW7cEVxg/63fCt16DiggcPZhryz74yUrYVg7fOT9BxUmnaO8huOVV+NuemuvznkPw9EZY9Xd49FJokZqwEiVJknSSdlTAzUthezkcnWv9/SA8VgJrd8KDl0BqKFEVSmoukmJk14wZM7jxxhurgy6A1NRUsrOzq0d1HThwgEmTJtGrVy8uvPBCvv3tbyeq3EYTjcK/FcdGu0SOOW3x8NNfb4DSXXEvTTotT2yoHXQdFgXe+hT+uDnORUmSJOm0PLK2dtB1tCUfwoItcS1JUjPV5MOu0tJSNm3axLhx42pN27JlS3XY9YMf/ICWLVuyYcMGVq9ezT333BPvUhvd6r/Du3uOv/OA2P/Q2ZvjVJB0Biqq4E9ldQddh4WA/9rkNekkSZKaut0H4YWtJz5W+eOmeFUkqTlr8qcxbt26FYCsrKwa7evXr6esrIz8/Hz27t3LM888w/vvv08oFBsT+9nPfvaU/k44HCYlpWlnf5lf+Gc63/If9faJAM++vIK7Lxkan6Kk09TivN70+Y/V9faJAlvLoXX7TCIH9sWnsGag3x9jd7fIyGiZ4EokJQu3Gwoa1+mG17r3YD5375J6+0SAtZ8eIiOjTXyKkpT0WrRowZ49e075dU073QE6dOgAwMaNG6vbotEoU6ZMIRKJkJ+fz7vvvkuHDh34yU9+wqBBgwiHw7z66quJKrnxVFWesEs0GiV6Ev2khDuF9TQa8Ur1kiRJTdnJHoNEo16lXlLja/Iju3Jzc8nJyWHq1Kmkp6fTpk0bZs6cSXFxMa1bt6ZPnz6sXLmSv/3tb+Tn5/Pggw/yxhtvcPXVV7Nx40bOPvvsk/o7hYWFDB3atEdDvbcXrvvf+vukhEJMvvpSvnNnRXyKkk5TJArXLILt+4/fJwXo+xlYsccL0TWkQfNivysq3E5IOjluNxQ0rtMN72BV7I7auw8dv08KMLxLBm+53CU1siY/sistLY3Zs2fTqVMnJkyYwOTJkxkzZgwFBQXk5eWRkpJCt27dSEtL46tf/SoAgwcPpmPHjmzYsCHB1Tesbm1gSNbx/6eFiN3ZZGz3eFYlnZ6UEHy1Z/19Ipy4jyRJkhKvRSqMz66/TwT4ygn6SFJDaPJhF0D//v0pKiqivLyckpISJk2aRHFxcfXF6Tt27MjnP/95XnrpJQA2bNjARx99RE5OTiLLbhT/NgC6nFW7PYVYeHDfQMhqFe+qpNPzTz1h9Hmxx0dvjA4//mpPuOK8eFclSZKk03FLb7jsnNjjuj7b/XMfuDTr2FdJUsNr8qcx1mX//v2UlJQwefLk6rbHHnuMb37zm/zrv/4r6enpPPvss7Rv3z5hNTaWDi3h6ctjd1z8782xU8AyUuCKzrFgoE+7RFconbzUEEwfCEM/G7szz9qdEArBRZnwlZ4QPjf2XJIkSU1fego8NBjmb4l9ttu4O/aF/OBzYscqlxl0SYqTpAy7Vq1aRVVVVfXILoCePXtSWFiYuKLiqG06fKNX7CcSje1ApGSVEoIvdo39RKOxNgMuSZKk5JSWErusytjusWOVEH62kxR/SRl2DR48mOjho+JmzqBLQeIHIUmSpODwWEVSoiTFNbskSZIkSZKkk2HYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkqQzUlhYSHZ2NuFwmAkTJtSa/uyzz7Jo0SIA5s2bx4gRIwiHw7z33ns1+n3rW9+ioKCAYcOGsWHDBgCuvvpqCgoKGDlyJJ988gmVlZXccsstjT9TkiQpaRl2SZIk6YxNnDiRwsJC2rVrR1FRUY1p8+fPZ+TIkezbt4/f//73vPzyyxQWFtKtW7ca/X75y1+yePFi7r//fh577DEA5syZw+LFi7n55puZNWsWaWlpnHPOObz77rtxmzdJkpRcDLskSTWcaITGvffeS2lp6XFfv2PHDgYOHEibNm1Oanpd/detW8eMGTPOcE4kJUK/fv3YunVr9fMdO3bQsmVLQqEQRUVFRCIRrrjiCm677TYikUiN16anpwOwd+9e+vXrV6PtwIED5ObmAhAOh/nLX/4Sj9lRM9XY+8LNmzfTqVMnwuEwN910E4cOHeLLX/4y4XCYBx98EHBfKElnwrBLklTL8UZoRCIRVq1aRa9evY772rZt2/LSSy9x6aWXntT0uvrn5uby1ltvEY1GG2iOJMVLUVEROTk51c83btxI9+7dAfjoo4/45JNPWLhwIR07dmTevHm1Xj9y5Ehuv/12Lr74YiAWGgwZMoSHH364Ouzq3r179WmOUmNpzH0hwBe/+EUKCwt55plnmDNnDkOGDKGwsJA333yTjz/+2H2hJJ0Bwy5J0nEdO0Lj7bffpnfv3vW+Jj09nczMzJOefrz+PXv25J133jmNqiUlwpNPPkk4HKZz584MGDCgzj7t2rVj+PDhpKSkcPnll1NSUlKrz8svv8ycOXO4++67AcjMzGTZsmVMnz6dhx56qBHnQKpbY+wLAV588UWGDx/O7373OzZt2sSFF14IxL7w+etf/wq4L5Sk02XYJUk6rmNHaJSWltKjR4+4/G1HbkjJ5fAomOnTp9doz8nJoaysDICLL76YtWvXArB69epa25OKigogFoq1atWKSCRCZWVldVvLli0BKCsrq3dUjdSQGmNf2KlTJ0pKSli4cCG/+tWv6NWrF4sXLyYajbJ06VJ27doFuC+UpNOVlugCJElNz5NPPsmiRYsYNmzYcUdorF27lltvvbVG25VXXskPf/jDOFQoKVlkZmZSXl4OQFZWFhdddBEFBQWcc845zJo1i+3bt/Pss89y5513MnbsWPbv308oFOIXv/gF+/bt40tf+hIpKSlkZGTw1FNPAbHrKU2cODGBc6XmoDH3hRkZGdWPhw8fTpcuXVi0aBFXXHEF55xzDllZWWdcvyQ1Z4ZdkqRaJk6cyF133VWrvVevXsyZMweACy64gMLCwkaroaysjKFDhzba+0tqOOFwmHA4fNzp11xzDYsWLWLUqFFMmTKFKVOmVE8799xzufPOOwFYsGBBrdcuXry4xvPKyko++uijGiNtpMbQmPvCvXv30qZNG6LRKCtWrOD2229n5syZRKNRJkyYwGWXXQa4L5Sk0+VpjJKkk9a/f/86r7FzrFGjRlFcXMyoUaNYs2YN27dvr767VF3Tj30OsYtaH74bm6TkdtNNNzFq1KgGea+0tDSefPLJBnkv6XQ0xL5w2bJlDBo0iCFDhjB69GgOHTpEOBxm5MiRXH/99bRu3RpwXyhJp8uRXZKkGuoboZGSkkJeXh6lpaX1Xi9n0aJFtdoOj9yoa/qxz9etW8fAgQMJhUKnULkkSQ2jsfeFo0ePZvTo0TWmHTtCzH2hJJ0+wy5J0imp65SOhpabm0tubm6j/x1Jkk6H+0JJato8jVGSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSJEmSJCkwDLskSZIkSZIUGIZdkiRJkiRJCgzDLkmSJEmSJAWGYZckSZIkSZICw7BLkiRJkiRJgWHYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMJIm7Dp48CDTpk2ja9eutGrVihEjRrB8+XJCoRBz585NdHmSlBQi0SOPD0USV4ek5LTrYKIrkM7c/sojj6PR4/eTJCWvpAi7otEo48eP54knnuCuu+7i+eefJzs7m7FjxwKQn5+f4AolqWmrisJv34X/b9GRti+8CL9YB+WVx3+dpObt7R1wx+tHno96Af7lDXjn74mrSTpdH+2He9+OrceHfW0xvPB+4mqSJDWOtEQXcDIef/xxFixYwMqVK+nbty8A4XCY7OxsMjMz6datW4IrlKSmqyoKU1fAyx/UbN99CJ4qhaKP4PGh0Dop9giS4mXJdrjzr3D0wJco8NpHse3GzwfDpVmJqk46NdvK4RtL4e8VcPTA5o274a63oGwvfOf8hJUnSWpgSTGya8aMGdx4443VQRdAamoq2dnZ5Ofns3nzZgYMGFD906NHDzIzMxNYsSQ1Hc9vqR10HRYFSnbB4yVxLUlSE1deCf/nzdipz5FjTvOKRP8Ror8JFVWJqU86Vfe+XTvogiPPf70B1jhiUZICo8mHXaWlpWzatIlx48bVmrZlyxby8/Pp0aMHK1eurP659tprueGGGxJQrSQ1PX/4G4TqmR4F/lQGBzxolfQPf3kf9lfVHNV1tCix0aEvb4tnVdLp2bIX3vi4dtB1tBRg9uY4FSRJanRN/qSVrVu3ApCVVXOc/Pr16ykrK6t1va6DBw/yu9/9jhdffPGU/k44HCYlpclnf5J0alLTuPD3+07YbV8lZJ1/ERXvvROHoiQ1dZ0n/YrPFHyNUGr6cftEqw5x632/5oP//Jc4ViadunbDvkK3//+ZevtEgP9evpH7L+1bbz9JUny1aNGCPXv2nPLrmny606FDBwA2btxY3RaNRpkyZQqRSKRW2DVv3jw6d+7MRRddFNc6JalJOpXbTHlLKkmHRSPUPyaU2HS3G0oGkZO8/bDrsyQFRigabdpb9crKSnJzczl06BAPPvggbdq0YebMmRQXF7Njxw727NlTY0TWVVddxZVXXskdd9xxUu+/e/duVq9ezYUXXsjZZ5/dWLMhSQnzjaWxO6fV91G/fQv4y2hIb/JfgUiKh+e3wN3FJ+43YxCMPK/x65HOxPZyuHrR8U/LhdgIgLHd4Uf941WVJKkxNfnDmrS0NGbPnk2nTp2YMGECkydPZsyYMRQUFJCXl1cj6Nq6dSuLFy/ma1/72km//9lnn83QoUMNuiQF1j/1rD/oAri+h0GXpCOuOA/apR//g2IK0DEDCs6NZ1XS6Tm3dWxdrW83FyW2L5QkBUNSHNr079+foqIiysvLKSkpYdKkSRQXF9c6hfHpp5/mi1/8YvWpj5IkGH0eXNc99vjojf7hE5Qu7gjf7BXvqiQ1ZRmp8OAlsRD82A+LKf+Y/n8vgbSk+CQpwY/yoPNZtU/OTflHw7/2g17t4l6WJKmRJOVHlP3791NSUlIr7Hrqqaf45je/maCqJKlpCoViH/LvzofeR32QP681TO4LD18KLVITV5+kpumiDvDM5XBVV0j7RyDQIgWu7gbPFkC/zyS2PulUdGgJTw2Hb/SKnbp/2CUd4dFLY6OgJUnB0eSv2VWXN954g0svvZS//vWvDBo0KNHlSFJSKa+ESBTOSosFYZJ0IpWR2F1bz0pzNJeSXyQKew/Fvuhp6Zc9khRISRl2SZIkSZIkSXXxuzlJkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTAMuyRJkiRJkhQYhl2SJEmSJEkKDMMuSZIkSZIkBYZhlyRJkiRJkgLDsEuSJEmSJEmBYdglSZIkSZKkwDDskiRJkiRJUmAYdkmSJEmSJCkwDLskSZIkSZIUGIZdkiRJkiRJCgzDLkmSJEmSJAWGYZckSZIkSZICw7BLkiRJkiRJgWHYJUmSJEmSpMAw7JIkSZIkSVJgGHZJkiRJkiQpMAy7JEmSJEmSFBiGXZIkSZIkSQoMwy5JkiRJkiQFhmGXJEmSJEmSAsOwS5IkSZIkSYFh2CVJkiRJkqTAMOySJEmSJElSYBh2SZIkSZIkKTD+H8hGbNeIQXviAAAAAElFTkSuQmCC", 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", 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" ] @@ -279,7 +279,12 @@ "source": [ "## Unitary cluster Jastrow (UCJ) operator\n", "\n", - "A UCJ operator is implemented by the [UCJOperatorJW](../api/ffsim.qiskit.rst#ffsim.qiskit.UCJOperatorJW) gate. This gate decomposes into a sequence of diagonal Coulomb evolutions sandwiched by orbital rotations. The number of diagonal Coulomb evolutions is equal to the number of ansatz repetitions (in this example, two)." + "There are several gate variants for the UCJ operator:\n", + "\n", + "- [UCJOpSpinBalancedJW](../api/ffsim.qiskit.rst#ffsim.qiskit.UCJOpSpinBalancedJW)\n", + "- [UCJOpSpinUnbalancedJW](../api/ffsim.qiskit.rst#ffsim.qiskit.UCJOpSpinUnbalancedJW)\n", + "\n", + "All variants decompose into a sequence of diagonal Coulomb evolutions sandwiched by orbital rotations. The number of diagonal Coulomb evolutions is equal to the number of ansatz repetitions (in this example, two)." ] }, { @@ -300,10 +305,10 @@ } ], "source": [ - "ucj_op = ffsim.random.random_ucj_operator(norb=norb, n_reps=2)\n", + "ucj_op = ffsim.random.random_ucj_op_spin_balanced(norb=norb, n_reps=2)\n", "\n", "circuit = QuantumCircuit(qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n", "\n", "circuit.decompose().draw(\"mpl\", scale=0.7)" ] @@ -326,9 +331,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 9, @@ -339,7 +344,7 @@ "source": [ "circuit = QuantumCircuit(qubits)\n", "circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n", "\n", "circuit.draw(\"mpl\", scale=0.7)" ] @@ -424,9 +429,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" + "
" ] }, "execution_count": 12, @@ -469,7 +474,7 @@ "\n", "pass_manager = PassManager(\n", " [\n", - " Decompose([\"hartree_fock_jw\", \"ucj_jw\"]),\n", + " Decompose([\"hartree_fock_jw\", \"ucj_balanced_jw\"]),\n", " ffsim.qiskit.MergeOrbitalRotations(),\n", " ]\n", ")\n", @@ -482,38 +487,24 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The [pre_init_passes](../api/ffsim.qiskit.rst#ffsim.qiskit.pre_init_passes) function returns a generator that yields these transpiler passes. The function is so named because we recommend using these passes for the `pre_init` stage of Qiskit's transpiler pipeline. You can construct a pass manager using this function as follows:" + "The [ffsim.qiskit.PRE_INIT](../api/ffsim.qiskit.rst#ffsim.qiskit.PRE_INIT) constant stores a pass manager with transpiler passes that decompose gates into orbital rotations and then merges them. The constant is so named because we recommend using it for the `pre_init` stage of Qiskit's transpiler pipeline.\n", + "\n", + "Let's do a full transpilation of the circuit with and without the `PRE_INIT` pass manager, and then print the final gate counts." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, - "outputs": [], - "source": [ - "pre_init = PassManager(list(ffsim.qiskit.pre_init_passes()))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's do a full transpilation of the circuit with and without the `pre_init` passes, and then print the final gate counts." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Gate counts without pre_init passes:\n", + "Gate counts without PRE_INIT passes:\n", "OrderedDict({'cp': 56, 'xx_plus_yy': 48, 'p': 32, 'x': 4})\n", "\n", - "Gate counts with pre_init passes:\n", + "Gate counts with PRE_INIT passes:\n", "OrderedDict({'cp': 56, 'xx_plus_yy': 32, 'p': 24, 'x': 4})\n" ] } @@ -532,13 +523,13 @@ "transpiled = pass_manager.run(circuit)\n", "\n", "# Transpile the circuit with pre_init passes\n", - "pass_manager.pre_init = pre_init\n", + "pass_manager.pre_init = ffsim.qiskit.PRE_INIT\n", "transpiled_opt = pass_manager.run(circuit)\n", "\n", - "print(\"Gate counts without pre_init passes:\")\n", + "print(\"Gate counts without PRE_INIT passes:\")\n", "print(transpiled.count_ops())\n", "print()\n", - "print(\"Gate counts with pre_init passes:\")\n", + "print(\"Gate counts with PRE_INIT passes:\")\n", "print(transpiled_opt.count_ops())" ] }, @@ -546,88 +537,81 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The XXPlusYYGate count is significantly reduced when the `pre_init` passes are used.\n", + "The XXPlusYYGate count is significantly reduced when the `PRE_INIT` pass manager is used.\n", "\n", "### Locality in the UCJ operator\n", "\n", - "Recall that the UCJ operator decomposes into orbital rotations and diagonal Coulomb evolutions. As explained [previously](#Orbital-rotation), orbital rotations decompose into a pattern of XXPlusYYGates that can be implemented using only linear qubit connectivity. However, the diagonal Coulomb evolutions decompose into a pattern of controlled phase gates which in general require all-to-all connectivity, and their implementation on a limited connectivity qubit device would involve the insertion of swap gates. The following code cell decomposes the diagonal Coulomb evolution in a UCJ operator and draws the resulting circuit." + "Recall that the UCJ operator decomposes into orbital rotations and diagonal Coulomb evolutions. As explained [previously](#Orbital-rotation), orbital rotations decompose into a pattern of XXPlusYYGates that can be implemented using only linear qubit connectivity. However, the diagonal Coulomb evolutions decompose into a pattern of controlled phase gates which in general require all-to-all connectivity, and their implementation on a limited connectivity qubit device would involve the insertion of swap gates. The following code cell constructs a UCJ operator with a single ansatz repetition, decomposes its diagonal Coulomb evolution, and draws the resulting circuit, showing the high number of controlled phase gates." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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6RE2YMIGcnBxatWpFr1699lpv48aNXH/99Tz66KORC06SJEmSpB/JObukQ9SuObt+KDs7m+XLlwMQCoW4/PLLufPOO2nZsuV+rbekpIRGjRpVZ6iSJEmSJO03k12SKklPT6ekpAQIP7XxjTfeYO3atQCMHz+eVq1aMXHiREaOHMlTTz3Fgw8+yIYNG9i4cSP33nsvb731FieeeGI0P4IkSZIk6RBmsks6BOXk5JCTk7PX5aeddhrTp08nNzeX4uLi3ZaPHDkSgKFDhzJ06NBKy6ZMmcK4ceOqNV5JkiRJkvaXyS5Ju/lhAutAPPzww9UYiSRJkiRJB8YJ6iVJkiRJkhQzTHZJkiRJkiQpZpjskiRJkiRJUsww2SVJkiRJkqSY4QT1qnU274CijdFpOzsNUhKi07YkSZIkSTp4JrtU6xRthCtmRqftx/pDrybRaVuSJEmSJB08hzFKkiRJkiQpZpjskiRJkiRJUsww2SVJkiRJkqSYYbJLkiRJkiRJMcMJ6hUTFt6Ww5YFBQTiEwjExZPU6ghaDrmbtJ7HRzs0SZIkSZIUQfbsUsxoOeRuek/eTI8nV9OgUz+W/PZ0yrZsiHZYkiRJkiQpgkx2KeYEExJpesIwyrdtZttXRdEOR5IkSZIkRZDJLsWc8tKtrH39MYLJaSS17BDtcCRJkiRJUgTVmWTX9u3bGT16NG3atKF+/foMGjSIwsJCAoEAL730UrTDUy3w5aTRzL6wEXOvzKRk6cdkj/oXcclp0Q4rKraXffd7KBS9OKTqEArBqhL4YguUlu27vlTbfVMKn2+GzTuiHYmkumJbGazYDKu2em6nuq88BF9+e263ozza0ShW1YkJ6kOhEOeccw6FhYWMGTOG7OxsJk2axBlnnAFA7969IxZL5qn96HzFf5HeNZPS4k08f9S1EWtbVWt54V00P+PGaIcRVZt3wOOL4cXl35Wd8R+4oD2ckwnBQNRCkw5YKAT/WA6TlsDnW8JlDeLh9LYwrCOk1YtufNKBen9N+Bj9/trw62AABrWAKzpC9qF5b0bSPnxTChMWwcufQ8m3N3yyUmBINpzWBgKe26kOKQvBs5+Ff77aGi5rmABnZsLlHaB+nchOqK6oE7vTo48+ytSpU5k9ezZdu3YFICcnh6ysLNLT02nbtm3EYindsIUFj79K0mEN6XrVLyLWrrQvm3bAFTPgs03w/Rt+K0vgvrnw6Tfwm94mvFQ3hEJw98fwz8/h+7vslp0w6TOY+TVMGAANTXipjnj1Cxj9UeX9uTwEb3wJM1bDI/2ge3rUwpNUC63bBpfPCPeA+f653bLNcNdsKNoI/93VhJfqhrIQ3PoB/Oeryt+FG3bAE4vh3a/hz/0huU5kKFQX1IlhjOPGjWPIkCEViS6AuLg4srKyKnp13XjjjWRlZREIBPjkk09qLJav3prD0pdmsuWLNTXWhvRj/HH+7oku+O71v7+A17+MdFTSj5O/Kpzogj3v059vhoc+jXRU0o/zTSmMmRXed384WqOc8NDz//kwfCEgSbuM/wS+Ktn7ud0zn8F7XpKojpjyeTjRBXvepxdsgL8sjHRUimW1Ptm1ePFili5dyllnnbXbshUrVlQku04//XTeeustMjIyIh2iFHVbdsKUFbt/cXxfEJj8WaQikg7O35dW/QVVDrzyBWzcHqmIpB/vpc9hZxUH6HLC8/AUfB2xkCTVcuu2hRMDVU1nFAzA5KURC0k6KH9fWrlH1w+FCE/F4vysqi61vpPgypUrAWjWrFml8gULFrB8+fKKZNeAAQN+dBupqals3777FVP7+MbclPbj16vKBg7MYcnOb/ZZL7lTP9qPzT+gdXe6+8Dq783AgTmULCyolnVFUv3sn5J9z4wq65QDH6/ZQWJiSmSCOkR0+/s2ABITk6IcSWzp+rdvCCYmV1lnezlkHHU8JfOr3ve1/9yfa0bbkX8n7chfEIiL22udUHkZF4z8X76efGcEI4t97tOqq1J6/Zys216usk55CPIWryXxZ60iFNWhweNGDYiLp/uzW/ZZbfNOOKxTb0pX2H1fYeXlP/4JBrW+Z1eTJk0AKCoqqigLhULcfPPNlJeXR3RyeqnWCu3vQcAxMqobQvu7T/tIKtUF5eXs1/HX/VnSLp7bKZYcyPeb34WqJrW+Z1fnzp3Jzs7m1ltvJSEhgZSUFB555BFmzZpFcnIynTp1Oug2Nm3atMfy1YULeGXwqINev8Ly8vI5/Kgj9llv9jq4YmYEAtqDvLx8ejWJTtsHY9tO+Plr4eGMexMEjmxejw9LSyMW16Ggz7c3XUvdrtXq/70LBWvCd633JikOvvjwDRrU+m+yusP9uWZMWgL3z6u6TiAYxz/uH8VREz3vqE7u06qr1m+Hk6ZVPQQ6CJx0xGHMdv+uVh43asalb8Gn66semtuoHqxbPJuEWt8lR5Eyc+bMHz2Kr9bvRvHx8Tz//PO0aNGCSy65hBEjRnDyySdz3HHH0aNHD4LByH6EQDBIXGICgfh4CASIS0wgWM8rLUVXUjyckVH1OPhy4LysSEUkHZzz2lWd6AoAp7XFRJfqhF+0gcTg3o/RQaBtA/hp00hGJak2a1QPTm6973O7cz23Ux1xfruqE10A52RiokvVpk7sSj179qSgoICSkhIWLlzINddcw6xZs6IyhLH92T/j4mXPMPAvN5DS+jAuXvYMZ854KOJxSD90dSfo3nj38l1/5Be0g+OaRzQk6Uc7phkMzQ7/vqcvqiMawvWdIxqS9KOl1YP/7QNxgd335yDQIAHu/SkEqrqqlXTI+e9u0D5194TXruPIVZ3gJ3VwRIIOTT9vBae3Df/+/e/CXfv3T5vCZR0iHZViWZ28J75161YWLlzIiBEjKsqGDx/OCy+8wKpVq8jNzaVJkybMm7ePMQM/QtHf8yn6e361r1f7Z8uiQlZM+DWEQqT2GESrIWMrlm34aBpfPXsHcSmNaXfDJOIaNASg5LPZzL/xpxz5wo5ohR0RSfHwx2Pg2c/guaWwOjy3Jp0bhRNdP2/lhZTqll91hi6N4OklMPfbZ1sclhS+63dBO6hfJ7/BdKg6tjn89Vh4qghe/zJclhQX7vV1cXto1SC68UmqfVIT4LEB8Mxn8NwyKP52VF3PdLioPeS0iGp40gEJBOC2ntArHSZ9Bos2hstbJId7KJ6XZa8uVa86eakwZ84cysrKKvXseuihh3joIXtYxbrkdr05Ylx4Qq9Fo4+nrGQjcclpAKx+aTwd7/oPG2e/xprX/kLzM24EYM2rj5Dc7idRizmSkuLg0g7hHjFbdoZ7ESTXyb9yKXxSlNsy/LNr/ox/nxB+1LpUF3VuBPf0gde/3Z/zT4Z4T+wlVSElAa7sBMM6wlFTwmV/8WHxqqMCAfhF2/DPrnO7l473hrxqRp28DO7bty8hn9JwSArEJwAQKisjIb0lwcRkAMq2bSGufirBxPqkdh9E8ZtPA7Dty8XEpx1GXP3UqMUcDcFA+G6gFGtMdCmWmOiStL/8/lOsMtGlmuJpluqc4jcnMe/6zsQ1aEQgLpyvLduynrj64R5ewfoplG3ZAMDXUx6k2SnXRy1WSZIkSZIUWSa7VOekH3chXR9ewI7iL9m6bC4AcQ0aUbY1PPC7fOtm4ho0ZPu68KQoCY2dlV2SJEmSpEOFyS7VKeU7wjNzBoJB4uqnEqiXBEBcUgPKtm6ifPs2Ns3NI7nDUWxb8SklS2ezeMxJlCydzeePDo9m6JIkSZIkKQLq5JxdOnRtKHyZr6c+DOXlpHT9GeXbtrAubyJNBl7M4YP/m0WjBhKX0pis/55EfEoj0nrlArBodC5tr/IBBpIkSZIkxTqTXapTGvc/h8b9z6lUltyuFwANf3ISDX9y0h7f1/Gu6TUdmiRJkiRJqgUcxihJkiRJkqSYYbJLkiRJkiRJMcNklyRJkiRJkmKGyS5JkiRJkiTFDCeoV62TnQaP9Y9e21J1yc/P57LLLiMjI4OMjAyefPLJSssnTpxIixYtyM3N5be//S2vvPIKvXr14ve//32lepdeeikLFy4kMTGR22+/nUGDBnHqqaeyceNG4uPjmTx5Mk2bNuX8889n2rRpTJkyhQEDBrBz506uvvpqHnvssUh+bEmSJEmKKpNdqnVSEqBXk2hHIVWPYcOGMWrUKIYPH05BQQH9+vWrWDZlyhQmT57M6tWr+eijj3j77bf59a9/zQcffECfPn0qree5556jdevWFa9feOEFEhISmDhxIpMmTWL48OH87ne/409/+lNFnfj4eA477DCWLFlC+/bta/7DSpIkSVIt4DBGSYqAbt26sXLlyorXxcXFJCUlEQgE+OCDDzjuuOMAGDRoEIWFhZXeGwgEOO+88zj33HMpLi4GICEhAYBt27bRuXNnAJo3b75buzk5Obzyyis18plqk/z8fLKyssjJyeGSSy7Zbfndd9/N4sWL9/r+4uJijjzySFJSUva4fNmyZbRo0YKcnByGDh3Kjh07OPfcc8nJyeG+++4DYP78+YwbN656PpAkSZKkH81klyRFQEFBAdnZ2RWvi4qKyMjIAGD9+vWkpYXH0KamprJ+/fpK773//vuZOXMm5513Hvfccw8QTs4cc8wxPPTQQxXJrj3JyMhg0aJF1fxpaqdhw4aRn59Pw4YNKSgoqCgvLy9nzpw5dOjQYa/vTU1N5fXXX+foo4/ea51TTjmF/Px8nnrqKV544QWOOeYY8vPz+fDDD1mzZg2dO3fmo48+IhQKVevnkiRJknRgTHZJUg2aMGECOTk5tGrVil69eu2xTqNGjdi4cSMAmzZtolGjRpWWN27cGIDTTjuNefPmAZCens4777zD2LFjeeCBB2os/rroh73oPv74Yzp27FjlexISEkhPT6+yzrRp0zj22GN5+umnWbp0Kd27dwegc+fOvP/++wC0a9eu4v9IkiRJUnSY7JKkGrSrt9HYsWMrlWdnZ7N8+XIAjjzySN566y0A8vLyOOqooyrV3bRpExDuHZaVlUV5eTk7d+4EoGHDhiQlJe21/eXLl1fZoykW/bAX3eLFi8nMzDyodbZo0YKFCxfy2muv8ec//5kOHTrw5ptvEgqFePvtt9mwYQNwaPWkkyRJkmorJ6iXpChIT0+npKQECM+11aNHD4499lh69OhBnz59WLVqFRMnTmTkyJEMHTqUNWvWkJiYyBNPPMGWLVv4xS9+QTAYrCgDuOGGG3jxxRf597//zYgRI7jooovIz89n2LBhUfykkTNhwgSmT5/OgAED9tqL7tNPP+Xaa6+tVHbSSSdxyy23VLnuxMTEit+PPfZYWrduzfTp0znhhBM47LDDaNas2UHHL0mSJKl6mOySpBqSk5NDTk7OXpefdtppTJ8+ndzcXEaPHs3o0aMrljVv3pyRI0cC8OKLL+723jfffHO3svHjxzN+/PiK1zt37uTrr7+u1Msplu168uUPdejQgRdeeAGALl26kJ+ff8Dr3rx5MykpKYRCIT744AOuv/56HnnkEUKhEJdccknFUzaXL19O//79D+pzSJIkSTo4DmOUpCgZOnQoubm5Nbb++Ph4JkyYUGPrryt69uzJwoUL91kvNzeXWbNmkZubyyeffMKqVasqnrT4zjvv0KdPH4455hhOPPFEduzYQU5ODscffzxnn302ycnJQPjBA926davRzyNJkiSpavbskiTVeVX1ogsGg/To0YPFixdXOX/Z9OnTdyvb1bvuxBNP5MQTT6y07Ic9xObPn8+RRx5JIBA4sOAlSZIkVSuTXZKkmLen4Y3VrXPnznTu3LnG25EkSZJUNYcxSpIkSZIkKWaY7JIkSZIkSVLMcBijap3NO6BoY3Tazk6DlITotC1JkiRJkg6eyS7VOkUb4YqZ0Wn7sf7Qq0l02pYkSZIkSQfPYYySJEmSJEmKGSa7JEmSJEmSFDNMdkmSJEmSJClmmOySJEmSJElSzHCCesWEhbflsGVBAYH4BAJx8SS1OoKWQ+4mrefx0Q5NkiRJkiRFkD27FDNaDrmb3pM30+PJ1TTo1I8lvz2dsi0boh2WJEmSJEmKIJNdijnBhESanjCM8m2b2fZVUbTDkSRJkiRJEWSySzGnvHQra19/jGByGkktO0Q7HEmSJEmSFEF1Jtm1fft2Ro8eTZs2bahfvz6DBg2isLCQQCDASy+9FO3wVAt8OWk0sy9sxNwrMylZ+jHZo/5FXHJatMNSDAuF9vy7ak6521mSapWd5bC+FLbtjHYkkqQfKtkJ67dD2SF4Dl0nJqgPhUKcc845FBYWMmbMGLKzs5k0aRJnnHEGAL17945YLMF68Rz92ytoMaA7SU3SKFn9DfMff4UFj78SsRi0Zy0vvIvmZ9wY7TB0CCgLwYvL4Nml35Wd9Qac1w7OyoD4OnMboXYLheD1L2HSku/KTnkdzsqEi9pB/TrxDSZJsWntNniqCF76HLbshABwTDO4OBv6NI12dJJ0aHtzFfytCGYVh183rhc+hx7SHlISohpaxNSJS4VHH32UqVOnMnv2bLp27QpATk4OWVlZpKen07Zt24jFEoyLY+vX63nt/LvYtHw16V0yOOGZUWxbs55lUwoiFoek6CgLwa0fwH++Cp/Y77JiC9w3F977Gu79qQmv6vDQpzBxSeUuyGu2wZ8WwJtfwZ/6Q4M68S0mSbHlyxIYNiOc8NrVWSAEFKyBd76G0b3gtMidnkuSvufxRfDHBRD83sXKN9thwiL4z5fwlwHQqF704ouUOnE5Nm7cOIYMGVKR6AKIi4sjKyuL3r17s27dOv7rv/6LTp060b17d84880zWrFlTI7Hs3FrKrHufZdOyVRAKUTxvGSte+4BmR3WukfYk1S4vLAsnuuC7E/zv//7W6so9vvTjzFwdTnQBlO9h+YIN8IdPIxqSJOlbt38E67ZV/h6E8FDzEDB2NqzcEoXAJOkQN6c4nOiC3af/CAHLN8P/zY14WFFR65NdixcvZunSpZx11lm7LVuxYgW9e/cmEAhw0003sXDhQubOnUv79u255ZZbIhJfID6Ow/t25pv5yyPSnqToCYXgmc8q9+j6oQAw+TPnljpYf19a+W7UD4WAKSvCQ2ckSZFTtBFmF+/5RsQuIeAFT40lKeL+vrTqJE854WlC1m2LVETRU+sHgKxcuRKAZs2aVSpfsGABy5cvp3fv3qSnp5OTk1Ox7Oijj+aRRx7Z7zZSU1PZvn37buXt4xtzU9qAKt979G+HsWPzVpY89+Z+t3eoGjgwhyU7v9lnveRO/Wg/Nv+A1t3p7gOrvzcDB+ZQstDhqNqzuNQmdHn8yyrrhICvtkJqyyx2FlddV3vXdWIxwaQGVdbZVgatjxxEyYKZEYoq9nX7e/jMJzExKcqRxDa3c+S4ratf+om/pNWVD1VZJwT8ceq73Nj7uMgEdYhwf44Mt3NkuJ1rxhF/XkZCeosq65SFoNOgM9n04b8jFNWPV15e1a2VqtX6nl1NmjQBoKioqKIsFApx8803U15evtvk9OXl5TzyyCOcdtppNR7bT8dcwmFHduL1i+6mfIfdC6SYF6iqT9dulWssjEPC/m7rA/o/kSQdtP087gb8HpSkyPMcukKt79nVuXNnsrOzufXWW0lISCAlJYVHHnmEWbNmkZycTKdOnSrV/9WvfkVKSgrXX3/9frexadOmPZavLlzAK4NH7XHZUXdeSosB3Xn1nDsoLd7z+1VZXl4+hx91xD7rzV4HV0Spo0ZeXj69mkSnbdV+5SEYPB1Wbd19npLvOywJ3vvyM+Ji/zukxlzzDny4tuphMvWCsLzwP6QdAhNsRkqfl8P/lpaWRjeQGOd2jhy3dfWbvx4ufqvqOgHgipP68t83ut2rk/tzZLidI8PtXDNueh/yV1U9pUoQ+HT6P2hWP2Jh/WgzZ85kwICqR9vtTa3v2RUfH8/zzz9PixYtuOSSSxgxYgQnn3wyxx13HD169CAY/O4j3HjjjSxevJjJkydXKq9uR911OS2O7RFOdK3bWGPtSKpdggE4r13ViS6AczIx0XWQzsuqOtEVAE5ujYkuSYqwzo2gS6Oq51WE8CPuJUmRdW7WvhNdOS2oE4mug1Xre3YB9OzZk4KCyvMo/eEPf+C4476bB+DWW2/lww8/5N///jeJiYk1FkuD1k3pcsV/UbZtO2e/93BF+er3FjD9ortrrF1JtcP5WfDe1+HHq+9JnyYwpH1kY4pFxzWHMzLgxeXhxNb3v7MDQEYKDO8SpeAk6RB3Z2+4fAZs3lH5xkSQ8OsbuoWP05KkyOrTFC5uH36q+Z7OoQ+vDzd1j1JwEVYnkl0/tHXrVhYuXMiIESMAmDdvHvfccw8dO3bkmGOOASArK4sXX3yx2tve8sVanmhxdrWvV/tn56ZiFv/mBLatXEjvyZsrLVv+hyvZ9uUiQuVlZP7qcZJadQRgxzermHtVFt0eWUy9pq2jEbZiSHwQ7u8LTy+ByUthzbdPMmmaCGdnwdD2UC8uujHGgkAAbu0BRzSESZ+FH5MMkBIfToJd1sFeXZIULZmpMPFnMGExvPIF7Pg249WtMVzaAX7WPLrxSdKhbHgXyE6DiUVQ9O2MS/XjYHBbuLwjpNdc36BapU4mu+bMmUNZWVnF5PRdu3YlFNrXwCLFgrj6qXS443U+u/fc3Za1vfqPBOIT2DTvbda8+ifaDLsfgK//9XsadOwb6VAVwxKC4ZP5i7Ph62/n72qWFE6EqfoEAuFhMGdmwNfbwhdTzZJMJkpSbdCqAdzeC27sBj+bGi57/NiohiRJInwOfUob+K/W8NMp4bLXT4KkQ+wcuk4mu/r27Wty6xAViE8gPjV9r8sAyrdtpn5GNwB2bl7Pzk1rSWyWGakQdQiJC0CL5GhHEfsCgXCXa0lS7ZNcJ68mJCn2ff+Bi4daogvqwAT10oFYNPp4Pn/0ehpk/xSANVMf5rCTro5yVJIkSZIkKVJMdimmdLzrP7S/5QW+fHYM5aVb2bbiU5Lb9Y52WJIkSZIkKULseKyYUb6jlGBCInHJDQnWq0/p18soXbWExWNOYuvyuezc/A3Zt70U7TAlSZIkSVINMtmlOmfR6FxKls5i0ehcWl4whs0LCmh+5kiW3HMG5aVbCQQCtPnlw9Rv05kj7nsXgGUPXkrLi8ZGOXJJkiRJklTTTHapzul41/RKr1O6DACgw+1T9/qezP/3RE2GJEmSJEmSagnn7JIkSZIkSVLMMNklSZIkSZKkmGGyS5IkSZIkSTHDZJckSZIkSZJihhPUq9bJToPH+kevbUnSnuXn53PZZZeRkZFBRkYGTz75ZKXlEydOpEWLFrRp04bLL7+cYDBInz59eOCBByrVu//++xk/fjzXXHMNo0aNAuDVV1/ljjvuIDU1lSeeeIKWLVty2WWX8fjjjxMIBCL2GSVVr/09buTm5nLssccya9YsFixYQOvWrSvVe+uttxg5ciQAt956K4MHD2bNmjVcddVVrF+/ngsuuICrrrrK44YkCTDZpVooJQF6NYl2FJKkPRk2bBijRo1i+PDhFBQU0K9fv4plU6ZMYfLkyRQXFzNt2jRSUlK4+OKLWbRoER07dqyoN2TIEHr16sU777xTUTZu3Djy8vIoKipi3LhxPPjgg/Tt25e8vDwGDRoU0c8oqXrtz3ED4LnnnuOWW27Z4zoeeOABXnzxRdLT0znllFMYPHgwd955J7/73e/IyMioqOdxQ5IEDmOUJEk/Qrdu3Vi5cmXF6+LiYpKSkggEAjRp0oSUlBQA4uLiduth0axZM4LByqcg8fHxJCUl0bVrVwoLCwEYOHAgU6dOreFPUvvk5+eTlZVFTk4Ol1xyyW7L7777bhYvXrzX9xcXF3PkkUdW/B/sa3lhYSH9+/fnmGOOqehpN3/+fMaNG1cNn0b6TlXHDYDmzZvv9b0dOnRgw4YNbNmyhdTUVAAWLVrELbfcwoknnsjChQuBQ/e4IUmqzGSXJEk6YAUFBWRnZ1e8LioqqtS7AmDevHmsXbuWDh067HN9O3bsYN26dcyYMYPi4mIAMjIyWLRoUfUGXkcMGzaM/Px8GjZsSEFBQUV5eXk5c+bMqXKbpqam8vrrr3P00Ufv1/LevXszc+ZM3nnnHQoKCti4cSOdO3fmo48+IhQKVe8H0yFtf44bezN48GB+/vOf07NnT66++moAZsyYwdixY3n44Ye57bbbgEP7uCFJ+o7JLkmStN8mTJhATk4OrVq1olevXnutt3HjRq6//noeffTR/Vrv2LFjOfvss3nmmWfo0qVLNUVb9/2wJ8zHH39caUjoniQkJJCenr7fyxMSEgAoKyujZcuWJCcnA9CuXTvmzZt3MOFLwP4fN6oyevRo3n///Uq9Drt27Ur79u0ren1JkrSLyS5JkrTfdvU4Gjt2bKXy7Oxsli9fDkAoFOLyyy/nzjvvpGXLlvu13gEDBpCXl8ell15K3759AVi+fPl+9QqLZT/sCbN48WIyMzOrvZ1JkybRuXNnGjVqRHx8eEpXe8iouuzPcWNf4uLiSEtLIzk5mdLSUgAyMzNZu3Ytq1evrkjSetyQJIET1EuSpGqQnp5OSUkJEJ5z6o033mDt2rUAjB8/nlatWjFx4kRGjhzJU089xYMPPsiGDRvYuHEj9957L3feeSf5+fm0atWKP//5zwDk5eVx8sknR+0zRdOECROYPn06AwYM2GtPmE8//ZRrr722UtlJJ5201wm+q3LhhRdy/vnnc8455zB37ly6d+/+Y8KWDsj3jxsQfnjFG2+8wZIlSxgzZgzHH388N9xwA+PHj2fEiBEMHDiQUCjElVdeCcCoUaM488wz2blzJw899BBwaB83JEnfMdklSZL2S05ODjk5OXtdftpppzF9+nRyc3Mr5t36vpEjRwIwdOhQhg4dWmnZ7bffzu23316p7L333uOqq646+MDroF1Pr/uhDh068MILLwDQpUsX8vPzD7qt0tJSEhMTCQaDpKamkpSUBIR7yPTv3/+g169D24EcN/72t7/ttnz8+PEAnHLKKZxyyimVlvXo0YO33nqrUtmhfNyQJH3HYYySJKlaDB06lNzc3Gpb31//+tfdntp4qOvZs2fFU+eqkpuby6xZs8jNzeWTTz5h1apV3HfffXtcfu+995KTk8PPfvYzWrduXTEErKioiG7dutXYZ5HA44YkqWbYs0uSJKkWqaonTDAYpEePHixevLjKeYmmT5++W9munnV7Wj569OhKr+fPn8+RRx5JIBA4gMglSZJqB5NdkiRJdciehjdWt86dO9O5c+cab0eSJKkm2MdXkiRJkiRJMcNklyRJkiRJkmKGwxhV62zeAUUbo9N2dhqkJESnbUmSJEmSdPBMdqnWKdoIV8yMTtuP9YdeTaLTtiRJkiRJOngOY5QkSZIkSVLMMNklSZIkSZKkmGGyS5IkSZIkSTHDZJckSZIkSZJihhPUKyYsvC2HLQsKCMQnEIiLJ6nVEbQccjdpPY+PdmiSJEmSJCmC7NmlmNFyyN30nryZHk+upkGnfiz57emUbdkQ7bAkSZIkSVIEmexSzAkmJNL0hGGUb9vMtq+Koh2OJEmSJEmKIJNdijnlpVtZ+/pjBJPTSGrZIdrhSJIkSZKkCKozya7t27czevRo2rRpQ/369Rk0aBCFhYUEAgFeeumlaIenWuDLSaOZfWEj5l6ZScnSj8ke9S/iktOiHZYkSZIkSYqgOjFBfSgU4pxzzqGwsJAxY8aQnZ3NpEmTOOOMMwDo3bt3ROM5+p4raHNCHxLSktmxeSvL/1XAB3f9jfIdOyMahypreeFdND/jxmiHIUl1ziffwKQl373+xetwViackwkpCdGKKvYs2wRPf/bd6xNehcFt4fx20DQpenFJP8bG7fD3pfCP5d+Vjf4ILmoHRzSKWliSJAF1JNn16KOPMnXqVGbPnk3Xrl0ByMnJISsri/T0dNq2bRvReOb/9VU+uHMiO7eWkpieSs6jN9Bj+JnMHv/3iMYhSdLBmroCxswCAt+VrdoKD88PL/tLf2iUGLXwYsYHa2H4u7Cz/Luyb7bDk0Uw5dvt3DYlevFJB2LtNrhiBnxRUrl82hfw2kr47ZFwfMvoxCZJEtSRYYzjxo1jyJAhFYkugLi4OLKysip6dZ1++un07NmT3r17c+yxxzJ79uwai2fDoi/YubU0/CIQIFQeIrVdixprT5KkmvDFFhgzG8qB8tDuy5dvhrEfRzqq2LNlJ9xQGE50lf9gWYhw0uum9yG0h/8DqTb6zSz4smT38l3Hkts+hK+3RjwsSZIq1Ppk1+LFi1m6dClnnXXWbstWrFhRkex68skn+fjjj5k1axY33ngjl19+eY3G1f3607moaCIXfPI46V0z+PTRf9Voe5IkVbd/LKs6wVIOvLkKVu3holb775UV4YTXDxNdu5SHoGgTfFwc0bCkH2XZZnhvzd735xBQFoIXl++lgiRJEVDrhzGuXLkSgGbNmlUqX7BgAcuXL69IdjVs2LBi2YYNGwgG9z+Pl5qayvbt23crbx/fmJvSBuzxPXP/8E/m/uGfNOzQinZnHsvWr7/Z7/YOVQMH5rBk5763U3KnfrQfm39A6+5094HV35uBA3MoWVhQLeuSpNou+773qZ/Zo8o6IaDn4MtZ/9bTkQkqBrW94RnSfnoagbi9n3aFyss59f/dzdfPjY1gZLGv29+3AZCY6KRo1SX9hCtpddUfqqxTHgrxuynvMrxnTmSCOkS4P0eG2zky3M6RUde3c3n53m6t7Fut79nVpEkTAIqKiirKQqEQN998M+Xl5ZUmp7/iiito27Ytt912G08++WRE4tuweCXF85Zz7O+HR6Q9SZKqS1XJl0r1gnE1HEmMC8ZDILCPSiG3s+qE/TluBAIB92dJUlTV+p5dnTt3Jjs7m1tvvZWEhARSUlJ45JFHmDVrFsnJyXTq1Kmi7mOPPQbAxIkTGTlyJFOnTt2vNjZt2rTH8tWFC3hl8Kh9vj+YEEeac3btU15ePocfdcQ+681eB1fMjEBAe5CXl0+vJtFpW5Ii7Y5Z8O8Vex+OtMtbf/8LHRv+JSIxxaLHFsKfFlZdJxCM48lxtzLwqVsjE9Qhos/L4X9LS0ujG0gMmVMMl8+ouk4QuOSEo7j5Brd7dXJ/jgy3c2S4nSOjrm/nmTNnMmDAnkfb7Uut79kVHx/P888/T4sWLbjkkksYMWIEJ598Mscddxw9evTY43DFiy++mLy8PNatW1ft8SSkJpN9bg710pIBaNw5g54jzuLLfGfwlSTVLWdlVp3oCgLdG0PHhlVU0j6dngHBKjp2BYEmiXDs4RELSfrRujeG9qlVX0SUEz6+SJIULbW+ZxdAz549KSioPI/SH/7wB4477jgANm/ezDfffEObNm0AmDJlCunp6aSnp1d/MKEQ7c76GT8dcwnBevFsW7uR5VPfY/Z9k6u/LUmSalC3xnBJNjxZBAHC83PtEgSS42FUzygFF0OaJsHN3eGeOeHt+v0EY5BwImzsTyC+1t+ClMIjcu/4CVw5A0rLKu/Pu44jV3eC7LQoBShJEnUk2fVDW7duZeHChYwYMQKALVu2cM4557Blyxbi4uJIT09nypQpBPY5P8aB27F5K6+dd2e1r1eSpGi4vjO0aRBOeK3YEi4LBmBQc7imM2SkRDe+WHFWZrj31mOLYMGG78qPOgyuPiKceJTqiiMawhPHwiMLwk9s3ZUoz0iByzrAKW2iGp4kSXUz2TVnzhzKysoqJqc//PDDeffdd6MclSJt56ZiFv/mBLatXEjvyZsrLVv24KVsW7mQQEIiLc67nbQeg6IUpSTVboFAeJjd4LawbDNsLYMW9aFxYrQjiz05LcI/X2yBDdvhsCRoVj/aUUk/Tvs0+L+jYN02WL0t3BM0o8F+PItBkqQIqJPJrr59+xIKhfZdUTEtrn4qHe54nc/uPXePy9vd9Bz1mraOcFSSVDcFApCVGu0oDg2tG4R/pFjQJCn8I0lSbeLsEKqzAvEJxKfubV62AJ/ddx6f3XsuOzcVRzQuSZIkSZIUPSa7FJNaD7ufI8bNpPGA81j1/D3RDkeSJEmSJEWIyS7FpPiU8Ey/jY46ja0r5kU5GkmSJEmSFCkmuxSTyko2AbB5YQGJzbKiHI0kSZIkSYqUOjlBvbTLotG5lCydxaLRubS8YAybFxTQ/MyRLPvdUHZsXEMwIZHM4U9EO0xJkiRJkhQhJrtUp3W8a3ql1yldBgDQ/tYXoxGOJEmSJEmKMocxSpIkSZIkKWaY7JIkSZIkSVLMMNklSZIkSZKkmOGcXbXMgN9dx44t23jvtgnRDmU3FxVN5JXTb6f4k6U12k52GjzWv0abqLJtSZIU+/Lz87nsssvIyMggIyODJ598stLyiRMn0qJFC9q0acPll19OMBikT58+PPDAA5XqXXrppSxcuJDExERuv/12Bg0aBMCqVavIyspi8eLFtG7dmssuu4zHH3+cQCAQsc8oSXXR/h6fc3NzOfbYY5k1axYLFiygdevWler9z//8D2+++SZxcXH88Y9/pHv37rz66qvccccdpKam8sQTT9CyZUuPzzHKZFcNan5MV3rdcC5NerQDYN2cz5j9f39nVcG8KEcW1uuGc2nSsz3/GXrPftV/OvviGo4oLCUBejWJSFOSJOkQNmzYMEaNGsXw4cMpKCigX79+FcumTJnC5MmTKS4uZtq0aaSkpHDxxRezaNEiOnbsWGk9zz333G4XWb///e/p27dvxeu+ffuSl5dXkQyTJO3d/hyfIXz8veWWW/a4jl/+8pfcc889LFmyhNGjRzNp0iTGjRtHXl4eRUVFjBs3jgcffNDjc4xyGGMNaZ17JCdMGsWK6R/y95/8kr//5JesmP4hJzwzitbH/2SP7wnEVd9/RyA+rtrWJUmSFMu6devGypUrK14XFxeTlJREIBCgSZMmpKSkABAXF7fbnf9AIMB5553HueeeS3FxMQDr169n7dq1ZGZmVtQbOHAgU6dOrfkPI0kxpKrjM0Dz5s33+t5dx+DvH7vj4+NJSkqia9euFBYWAh6fY5XJrhrSd+zlFD2Xz7xHXmbHphJ2bCph3iMvs+T5Nzlq7OUAnF34R3qMOIv/evluhnz2NE17tgcgoUESOY/ewEWLJ3L6mw/QMqfnPttr3q8rFxVNpOOQXM5+/xFOm/5/ALT4WQ9+MW0cFy58ktP+M562J/0UgLYn/ZTuw8+g1cBeXFQ0kYuKJhKsV3VHv0u/ep4mPdsTiAty4aKnaNSpTbjtY7py6VfPk/GLcLa9frNGDP38WRJS6v+4jSdJkhRBBQUFZGdnV7wuKioiIyOjUp158+axdu1aOnToUKn8/vvvZ+bMmZx33nncc0+4t/zDDz/M1VdfXaleRkYGixYtqqFPIEmxaX+Oz/syevRorr32WgB27NjBunXrmDFjRsUNCo/PsclkVw1Ia9+S1IzDWfrPmbst++zFGaRlNietXQsAss/JYeYNf+Tp7ItZ9+1cWFmnD+CzF99m0hGXMOf3LzLo8ZtIbp6+z3bj6yfStFc2//zZCP518s2kZjYn98lb+OQP/+SZLpfx4d1/47hHfk1610w+f/V95j70IivzZvN09sU8nX0x5dt37tfnC5WVs/q9+bQY0B2AFsd2Z+PSr2gxoFv49YDurJvzGTs2b92v9UmSJEXDhAkTyMnJoVWrVvTq1Wuv9TZu3Mj111/Po48+utuyxo0bA3Daaacxb948tm7dyqeffkrv3r1rKmxJinn7e3zel7/85S9kZWXRv394UuixY8dy9tln88wzz9ClS5dqila1kcmuGpCUngrA1tXFuy3b+vU34TpNwjOhL5z4OhsWryRUXl6RbFr17qd8/kohobJyPnv+Lb75dDmZp/bbbV0/FAgG+fC3T7NzayllW7eTNfgYVr83n2VTCgiVlbPyjVl8/toHtD/nuIP+jKtmfFIpuTX7//5ekfxq3r8bX8385KDbkCRJqknDhg0jPz+fsWPHVirPzs5m+fLlAIRCIS6//HLuvPNOWrZsuds6Nm3aBIR7H2RlZbFs2TKWLFnCSSedxOuvv851110HwPLly3frFSZJ2rP9OT7vS0FBAVOnTmXMmDEVZQMGDCAvL49LL720Yl5Fj8+xyWRXDdhWHD7pqX/47r2x6jcL3/3btm4jAFtWrtmtzpYvKpdtXrFmv3p27dxaSum3bQMkt2jC5h+ua/lqklsc/OzvX82Yy+FHd6FeWjJp7Vqy9J8ziasXT3KLdFoM6MZXb8896DYkSZKiIT09nZKSEiD8VLA33niD0aNHk5OTw4cffsiqVau47777ABg6dCgDBgzgjjvu4JZbbqFz5868++67vPrqq5xwwgk8/PDDAOTl5XHyySdH7TNJUiz4/vEZYMiQIbz22mtccMEF/Oc//wHghhtuAOCWW25h+fLlDBo0iF/96lcA3HnnnQwaNIjf//73DB8+HPD4HKt8GmMN2LjkSzZ9vpqs045h1Q96OGUNPoZNn69m42dfARAqD+32/gatD6v0OqXNYaz5aN9jiEPl5ZVel3y1jub9uv5gXc0o+WrdHusfiOJ5ywiVl9Plyl/w9fsLCJWX89WMT+h4YS7JzRrz9fsLfvS6JUmSalpOTg45OTl7XX7aaacxffp0cnNzK+Z1+b6RI0cC8OKLL+51HU888UTF7++99x5XXXXVj45Xkg4VB3J8/tvf/rbb8vHjxwPw5ptv7rbs9ttv5/bbb69U5vE5Ntmzq4YU3v4E2ecNpOsvTyUhpT4Jqcl0+eUvyD53IIWj/1rle5sf3YU2J/YhEBek3ZnH0rhLBsv+/e4Bx7D0pXc4vG9nMk7pSyAYpNXAXrT5eR+WPP8WAFvXbqBBq6Y/+imQq96ZR5erTuGrGeFeXF/NnEuXq07h6w8XUVa640etU5IkqTYYOnQoubm51ba+v/71rwSDnnpL0sHy+Kz9Yc+uGrJi2vtMH/Jbev732fQaeS4A6+Z8xvQhv61IDu3N0n/OoP05x/Gzh/8fW75aR94V/0fJl+sOOIZNy1bxxuX38pP/uYj+D1zHli/W8Nb1D1H87UT4y6YU0O70AZz/yeMEAgGe7TFsvyepB/jq7blk/qIfX80I9177asYn1Etr4HxdkiRJkiQpakx21aCvZsytMrH1/FHX7lY2Y8TDP6qtVQXzeDr74t3KV+bNZmXe7D2+Z/v6zbx61m/2a/2BbzPd30+GLXzqNRY+9VrF662rv+GJFmcfQNSSJEmSJEnVy7562i+Nu2ZQvmPnHifUlyRJkiRJqi3s2VWHDM5/gJTWTXcrX/Hah7x17e8Oev25T9/G4X2P2K18x+ZtBBPi+PC3k9i+sWQP75QkSZIkSaodTHbVIS/l/LpG1z/9ortrdP2SJEmSJEk1zWSXap3NO6BoY3Tazk6DlITotC1JkiRJkg6eyS7VOkUb4YqZ0Wn7sf7Qq0l02pYkSZIkSQfPCeolSZIkSZIUM0x2SZIkSZIkKWaY7JIkSZIkSVLMcM4uxYSFt+WwZUEBgfgEAnHxJLU6gpZD7iat5/HRDk2SJEmSJEWQPbsUM1oOuZvekzfT48nVNOjUjyW/PZ2yLRuiHZYkSZIkSYogk12KOcGERJqeMIzybZvZ9lVRtMORJEmSJEkRZLJLMae8dCtrX3+MYHIaSS07RDscSZIkSZIUQXUi2bV9+3ZGjx5NmzZtqF+/PoMGDaKwsJBAIMBLL70U7fBUS3w5aTSzL2zE3CszKVn6Mdmj/kVcclq0w5IkSZIkSRFU6yeoD4VCnHPOORQWFjJmzBiys7OZNGkSZ5xxBgC9e/eOSlxxSfUY/MZ46jdrxNPZF0clBlXW8sK7aH7GjdEOI6rKQ/CfL+HvS2HhBogLQL9mcF476Jke7ehiS8HX4e380brw657pcG4W9G8GgUB0Y5MO1NJNMHkpTP8StpVB2wZwZib8og0kxUU7OunArN8OLyyDlz7/ruyP8+GcLDgsKWphSZKAD9eGzzl2ueYdOCcTBrbwHFrVq9Ynux599FGmTp3K7Nmz6dq1KwA5OTlkZWWRnp5O27ZtoxJX75HnsfmLtdRv1igq7Us/tLMcRn0UvlgNAuXflk//Cl77En7dFS5qH80IY0MoBA99ChOXVN7O766Bd76G87Pghm5+WavueHMV3Px+OFm+a39evBH+dw68/Dn8sR+kJEQ1RGm/fbEFrpoJX2+rXP7XxfD8MnjkGOjUMCqhSdIhb8IieGQBBL93nvzhWnh/LZzSGn7Tu/Iy6WDU+mGM48aNY8iQIRWJLoC4uDiysrJ269V1xx13EAgE+OSTT2o0piY92tFqYC8+efifNdqOdCCeLAonuuC7C1YIX8ACPDAv/GWigzNtZTjRBXvezs8uhX+tiHhY0o+yqgRu+QDKQpX35293Z+avDye9pLogFIIbCmHttj0sAzbvgP/3Luwo3325JKlmzVwdTnTBd+fN8N35x7+/gGc/i3hYimG1Otm1ePFili5dyllnnbXbshUrVlRKdn300Ue8++67ZGRk1GhMgbggx/zf1bx762OUb99Zo21J+2tn+b6/HIL4BVIdJn1W9YEzADy9JHzRJdV2LywPHz/2truGCPcM3VPyQKptPlwHSzZVTtx+XzmwthTyvopkVJIkgGc+23evrUmfVU6ESQejVg9jXLlyJQDNmjWrVL5gwQKWL19ekewqLS3luuuu45lnniEnJ+eA20lNTWX79u27lbePb8xNaQMqlXW7djDr5i5l9bvzad6v627v0d4NHJjDkp3f7LNecqd+tB+bf0Dr7nT3gdXfm4EDcyhZWFAt64qkpHa96TDu3SrrlAP/+Xwbicc6fuPHCjZoRNcnVldZJwQUbYKU5m3Zub7qulK0Zd9XSFJGDwJVjLstD0HXX1zK+refiWBk0oFrftHdND3t1wSCe59oLlS2k2vGT+KLh6+MYGRS9ej29/Cdh8REJ5+rSW7nGhAM0u3ZLQQCVfe1WbUVGrXrQemXCyMUWOyr6/tzefmP745dq3t2NWnSBICioqKKslAoxM0330x5eXlFsuv2229nyJAhZGZm1mg8qZnN6TT0RD64a2KNtiMdqEDc/k2os7/1tGcHsv0C8fVqMBKpegTi6lWZ6Kqo5/6sOiAQnwChfZ8Uuz9LUmQFgvH7THRV1I33ekXVo1b37OrcuTPZ2dnceuutJCQkkJKSwiOPPMKsWbNITk6mU6dOFBQU8MEHH/C///u/P7qdTZs27bF8deECXhk8quL14UcdQf2mDTlz5kMABOPjSGhQn/PnPU7esPtY/e78Hx3DoSAvL5/Djzpin/Vmr4MrZkYgoD3Iy8unV5PotH0w1m+Hk6bBziq6/QaA7EZxfFhaGrG4Yk1ZKLydv9m9I2glaQnwzYoiEmr17QQJbvsQXv9y30MG/vPMo3Rt/GhkgpJ+pJc/hztnV10nEBfPbVeez2X3nh+RmKTq1Ofl8L+lnsvVKLdzzTh9Oqws2fvUCQCJQfhy/oc0qNVZirqlru/PM2fOZMCAAfuuuAe1+lIsPj6e559/nhYtWnDJJZcwYsQITj75ZI477jh69OhBMBjkzTffZP78+WRlZZGZmckXX3zBz3/+c1577bVqj2fplHf4xzHX83LujbyceyMzb/gTO0q28XLujaz5aHG1tyftr0b14IRWVf9Bh4BzsyIVUWyKC8DZmeHE4d4EgDMyMNGlOuHszKoTXUGgYxp0aRShgKSDcGJLSI6r+hgdF4DT2kQsJEnSt87JqjrRFQROaYOJLlWbWn851rNnTwoKCigpKWHhwoVcc801zJo1q2II4y233MKXX37JsmXLWLZsGa1bt2batGmceOKJ1R5L2dbtlHxVXPFTum4jhEKUfFXsZPWKuus7Q5Okvf9R92kCp7aNaEgxaUg2tE/d88VUEMhIgUs7RDoq6cfplQ5n7eW5LkHCSdtRvWA/RjpKUZcUD6N7hX//4S676/V/dwt/V0qSIuvsTOjReO/n0IfXh192inBQimm1Ptn1Q1u3bmXhwoWVnsQYLasK5vF09sXRDkMCwl8Qfz0WBrWo/KST5Di4qB08eLS9japDg3j4ywA4PQPqfW97JgTDd6MmDIBUpxpQHREIwM09YHgXSE+svOzIpjDhWHt1qW45oRU80Bey0yqXt2kAdx8J59nDWZKiIjEOHu4XHmmS9L3niMQFwsfuvx7rzQhVrzrXSXDOnDmUlZXtNdm1bNmyyAakiNu5qZjFvzmBbSsX0nvy5krLNnz0Kl89ewfB+qlkDn+Cek1asug3JxLavpVg/TTajZxMXP2UKEVe85rXh//9KazdBid9O5J32s+hfp37S6/dUhPgtp7hBMHAV8Jlr54IDZ3zWHVQMABDs+HCdnD0v8Jl/zweWjeIblzSjzXgcOjfDJZsCn8fNqoHnRraQ1GSoq1+PIzsDtd2hvnrw1MpZKftfsNNqg517hK4b9++hEL7mElXMS2ufiod7nidz+49d7dlq/4xjo5j8yj9qojVL4yjzZUPknHtoyQensna1ydQ/NYkDvv5VVGIOrKafu+uiImumvP9HlwmulTXxX+vp6KJLtV1gUD4AuqHPbwkSdHXIB76NI12FIp1DmpSnROITyA+NX3Py+LiCdZLIqltV7YsLgQg8fDM8MJgnLd1JUmSJEmKcSa7FFNCZTvYuXEdmz+dwc5NxRXl5aUlrH3tL6T33703mCRJkiRJih0OcFJMaXXRWJaMO5v6bTpTv02XivLlf7yalheMIa5BwyhGJ0mSJEmSaprJLsWUlC4D6HR3HlsWFbJpzhsArH7pfuq36UJarxOiHJ0kSZIkSappDmNUnbRodC4lS2exaHQumz+dwaoX7gPgy2fvZNGoQXz979/T7NThlO/Yzsqn/ocNs15l4W05rH19QpQjlyRJkiRJNcmeXaqTOt41vdLrlC4DAGh5/u3A7ZWW/eQfpZEKS5IkSZIkRZk9uyRJkiRJkhQzTHZJkiRJkiQpZpjskiRJkiRJUsxwzi7VOtlp8Fj/6LV9KMjPz+eyyy4jIyODjIwMnnzyyUrLJ06cSIsWLWjTpg2XX345wWCQPn368MADD1Sqd//99zN+/HiuueYaRo0aBcB1113HvffeS4MGDSL2eSRJkg5l+3tul5uby7HHHsusWbNYsGABrVu3rlTv9ttv580336S0tJT777+fY445hldffZU77riD1NRUnnjiCVq2bMlll13G448/TiAQiOTHjLrq2s7/8z//w5tvvklcXBx//OMf6d69u9tZqmb27FKtk5IAvZpE5yclIdqfPnKGDRtGfn4+DRs2pKCgoNKyKVOmcPzxx9O0aVOmTZvG22+/zdq1a1m0aFGlekOGDGHixImVyk499VQmT55c4/FLkiTpO/tzbgfw3HPPcfbZZ+9xHaNHj+bNN9/kueee4//+7/8AGDduHHl5edx///2MGzcOgL59+5KXl1eDn6b2qo7t/Mtf/pJ33nmHJ554gnvuuQdwO0vVzWSXdIjr1q0bK1eurHhdXFxMUlISgUCAJk2akJKSAkBcXNxud5WaNWtGMFj5MPKzn/2MadOm1XzgkiRJ2k1V53YAzZs33+t7ExLCd343b95M9+7dAYiPjycpKYmuXbtSWFgIwMCBA5k6dWpNfYQ64WC2c2ZmJlD5/NrtLFUvk13SIa6goIDs7OyK10VFRWRkZFSqM2/ePNauXUuHDh32ub7k5GS++eabao9TkiRJ+7Y/53ZVufjiiznhhBMYOHAgADt27GDdunXMmDGD4uJiADIyMnbr8X+oOdjtDOGedNdeey3gdpaqm8ku6RA1YcIEcnJyaNWqFb169dprvY0bN3L99dfz6KOPRi44SZIkHZD9Pbfbl4kTJ1JYWMjtt98OwNixYzn77LN55pln6NKlSzVFW3dV13b+y1/+QlZWFv37hycrdjtL1csJ6qVD1LBhwyomlf++7Oxsli9fDkAoFOLyyy/nzjvvpGXLlvu13pKSEho1alSdoUqSJGkf9ufcbl9KS0tJTEwkJSWl4mFDAwYMIC8vj8LCQt544w0Ali9fvl89/mNRdWzngoICpk6dyj/+8Y+KMrezVL3s2SWpkvT0dEpKSoDwE2feeOMNRo8eTU5ODh9++CGrVq3ivvvuA+Cpp57ihhtu4IknnuCmm24C4K233uLEE0+MWvySJEn6zvfP7SD8gKHXXnuNCy64gP/85z8A3HDDDQBcc8015OTkcMopp3DbbbcBcOeddzJo0CB+//vfM3z4cADy8vI4+eSTI/xJarcD2c633HILy5cvZ9CgQfzqV78C3M5SdQuEQqFQtIOorVYXLuCVwbtn7fXjnPzSWA4/6ohoh3HI6PNy+N8PTjvw9z711FO0bNmS3NzcA37vddddx7hx4yomto91B7OdpdrG/VmSaq9ondvtyWWXXcaECRN2e1BRLHA7K5bU9XO7mTNnMmDAAGbMmFEx5Hd/OYxR0m6GDh36o9/78MMPV2MkkiRJOlgHc263J3/961+rdX2xwu0s1R6miCVJkiRJkhQzTHZJkiRJkiQpZpjskiRJkiRJUsww2SVJkiRJkqSYYbJLkiRJkiRJMcOnMarW2bwDijZGp+3sNEhJiE7bkiRJkiTp4JnsUq1TtBGumBmdth/rD72aRKdtSZIkSZJ08BzGKEmSJEmSpJhhskuSJEmSJEkxw2SXJEmSJEmSYoZzdikmLLwthy0LCgjEJxCIiyep1RG0HHI3aT2Pj3ZokiRJkiQpguzZpZjRcsjd9J68mR5PrqZBp34s+e3plG3ZEO2wJEmSJElSBJnsUswJJiTS9IRhlG/bzLaviqIdjiRJkiRJiiCTXYo55aVbWfv6YwST00hq2SHa4UiSJEmSpAiqM8mu7du3M3r0aNq0aUP9+vUZNGgQhYWFBAIBXnrppWiHp1rgy0mjmX1hI+ZemUnJ0o/JHvUv4pLToh2WJEmSJEmKoDoxQX0oFOKcc86hsLCQMWPGkJ2dzaRJkzjjjDMA6N27d8RiGfC768g6YwDlO3ZWlOVfOZ6VebMjFoP2rOWFd9H8jBujHUZUhULw3hp4ftl3Zf87B87OhGzzfqqDlm6C55bBjNWwsxw6NQzvz8c0g0Ag2tFJB2Z9Kfzzc3j1C1i/HZonw+C2cHIrSKoTZ2SSIq08FP4O/Mey78rGfwLnZELblGhFFZs+WgfPLf3u9Z2z4dxMOKJRlAKSdFDqxKnVo48+ytSpU5k9ezZdu3YFICcnh6ysLNLT02nbtm1E41n0t+m8d9uEiLYp7Ut5CO6ZAy8uh+D3kgAvLAufII3qFb6okuqKqStgzGwgBOXflq3dBm+vhlNaw+29Ic6El+qIoo1wzTvwzfbvytaVwiffwDOfwZ+OgfTE6MUnqfbZWQ6jPoLpX1YejvPsZ+GkzN1HwvEtoxZezAiF4KFPYeKSytv5X5/Dy5/Df3eFC9tHLTxJP1KdGMY4btw4hgwZUpHoAoiLiyMrK6uiV1dmZiZHHHEEvXr1olevXkybNi1a4UpR8cxn4UQXhBNfu5QDIWDsbJhbHIXApB9hwQYYMyu8L5d/r3zX7//+Aib6/AnVEdvL4Ffvwobtlct3HaqXbYL/+SDiYUmq5f6yKJzogsrfhSGgLAS3fhjuAa2DM2VFONEFez7nuH8evPt1pKOSdLBqfbJr8eLFLF26lLPOOmu3ZStWrKg0hPH5559n9uzZzJ49m5///Oc1FlO7M4/lgk//yulv/Y4e/+9MAnG1fjMqxpWF4G9Lqq4TAJ5dWnUdqbaY/Nm+6zy9JHzXW6rt/vMVrNlW+SLq+8qBD9fBog2RjEpSbbatrOrvwhDhHkl/99zuoIRC4ZtnVXUUDxI+55BUt9T6YYwrV64EoFmzZpXKFyxYwPLly6tlvq7U1FS2b9++W3n7+MbclDagUtmnE6bywV0T2Va8iSY92nHcH0cQl1iPWfc+e9BxxLqBA3NYsvObfdZL7tSP9mPzD2jdne4+sPp7M3BgDiULC6plXZGUlNmDDve9X2WdcuCVz0r4v2MaRyaoQ0S3v28DIDExKcqRxJYuf11FXErV++o326Fpj2PZurgwQlHFPvfnmtFmxEQaHn0mgbi9n3aFQuUMuvoO1rzwvxGMTFJt1aBbDu1+U/VIlXJg0kdfcvtPsyITVAxKOCyDI/64qMo65cA7X5eT1CCN0M4dkQlMqiZ1/dyuvPzH39mu9V2SmjRpAkBR0XfjVUKhEDfffDPl5eWVkl0XXXQRPXr04Nprr2X9+vU1Ek/x3KVsW7cRQiHWfbyEWf83mazB/WukLWl/BevV3696gQQnhFHdEKi3f1/I+7vvS9EUrFd/309UKA8RTHR/lhS23+d2fg8elP3ezoEggXjPo6W6pNb37OrcuTPZ2dnceuutJCQkkJKSwiOPPMKsWbNITk6mU6dOALz99tu0adOG0tJSRowYwfXXX8/f/va3/Wpj06Y9D3ZfXbiAVwaPqvrN5aGq+72qQl5ePocfdcQ+681eB1fMjEBAe5CXl0+vJtFp+2AUl8JJr1Weq+uHAkBmWhwflpZGLK5DQZ+Xw/+Wul2r1YX5sHjjd3Ma7UkAmD/zNQ73PL/auD/XjIc+DQ+TqXJ/jovjT3fdwn89cUvE4pJUe63YDGe8UXWdIHBkm8bM9pj9o5XshNxXYfs+Oo80SYSS9et8ErTqnLp+bjdz5kwGDBiw74p7UOt7dsXHx/P888/TokULLrnkEkaMGMHJJ5/McccdR48ePQgGwx+hTZs2ACQmJnLttdcyc2bNZEsyTzuGhNRkABp3zqDnDeew7F91b9ibYkt6IgxsXvUfdAg4OzNCAUkH6ezMqhMDQWDA4ZjoUp1wRtt9J25T4mGQT1WT9K02KdCnSdXnduXA2Y5gPCjJ8XBKm6q3cwA4J3PfHXQl1S61vmcXQM+ePSkoqJxQ+sMf/sBxxx0HwJYtW9i5cycNGzYkFArx7LPP0qtXrxqJ5YhLf06/cVcRTIhj6+r1LHn+Teb8/sUaaUs6EL/qAu+vhc07d+/hFQC6NILT20YjMunA/aJN+ImLc4p3TxIEA5AcB/+vS1RCkw5YmxS4rAP8dfHuywKE9/FbekBSXKQjk1Sb3dANLp8BpWV7fsDFUU3hBJPkB+3KjjBjNazbw4NEgkBmCpzfLhqRSToYdSLZ9UNbt25l4cKFjBgxAoDVq1dz1llnUVZWRllZGV26dOGPf/xjjbT96pm/qZH1SgerdQP467Hwv3PCSa9d4gNwcmu4sTsk1cm/eB2K6sXBH44OP+77Xytgx/fOPnulhxMDmanRi086UNceAY3rhRNe33zvmTitkmF4F3t1Sdpdh4YwYQCMmwsfF39XXi8Ig9vC/+sK8bV+nE7t16w+/HUA3DMH3vn6u5tswUA4mXhTd0hJiGqIkn6EOnnpO2fOHMrKyiomp2/Xrh2zZs2KclSKhC2LClkx4dcQCpHaYxCthoytWLbho2l89ewdxKU0pt0Nk4hr0BCAks9mM//Gn3LkC7H/9JSMFHjkGPh8MyzaGE509UqHRs6nqTqofjzc1hOu7wzHvxoue35Q+A6rVNcEAnBhezg3C47+V7jssf7QM92hMZL2ruO3Ca/PNoV/EoJwZBOTL9WteTI8eDR8WQLz14d73fZIh6Z18wF2kqijya6+ffsSClU1+4ViVXK73hwxLjwf26LRx1NWspG45DQAVr80no53/YeNs19jzWt/ofkZNwKw5tVHSG73k6jFHA1tU8I/UixoWO+73010qa77fi+MuvhAFEnR0S41/KOa1TI5/COp7rPjq+qUQHz4NlaorIyE9JYEE8PfRmXbthBXP5VgYn1Suw+iZHEhANu+XEx82mHE1ffsQJIkSZKkQ4HJLtU5xW9OYt71nYlr0IhAXLhzYtmW9cTVD/fwCtZPoWzLBgC+nvIgzU65PmqxSpIkSZKkyDLZpTon/bgL6frwAnYUf8nWZXMBiGvQiLKtGwEo37qZuAYN2b7uSwASGjePWqySJEmSJCmyTHapTinfUQpAIBgkrn4qgXrhWSPjkhpQtnUT5du3sWluHskdjmLbik8pWTqbxWNOomTpbD5/dHg0Q5ckSZIkSRFQJyeo16FrQ+HLfD31YSgvJ6XrzyjftoV1eRNpMvBiDh/83ywaNZC4lMZk/fck4lMakdYrF4BFo3Npe9VDUY5ekiRJkiTVNJNdqlMa9z+Hxv3PqVSW3K4XAA1/chINf3LSHt/X8a7pNR2aJEmSJEmqBRzGKEmSJEmSpJhhskuSJEmSJEkxw2SXJEmSJEmSYoZzdqnWyU6Dx/pHr22puuTn53PZZZeRkZFBRkYGTz75ZKXlEydOpEWLFuTm5vLb3/6WV155hV69evH73/++Ur1LL72UhQsXkpiYyO23386gQYM49dRT2bhxI/Hx8UyePJmmTZty/vnnM23aNKZMmcKAAQPYuXMnV199NY899lgkP7YkSZKkOuBArleuueYaFixYQO/evbn//vsr1Tv//PNZtWoVmzZtok2bNvzzn/+kqKiI66+/ntLSUn7961/zX//1XxG9NjHZpVonJQF6NYl2FFL1GDZsGKNGjWL48OEUFBTQr1+/imVTpkxh8uTJrF69mo8++oi3336bX//613zwwQf06dOn0nqee+45WrduXfH6hRdeICEhgYkTJzJp0iSGDx/O7373O/70pz9V1ImPj+ewww5jyZIltG/fvuY/rCRJkqQ6ZX+uV9577z0SExPJy8vjxhtvZNasWfTu3bui3rPPPgvAn//8ZwKBAAB33HEHzz77LI0aNaqoF8lrE4cxSlIEdOvWjZUrV1a8Li4uJikpiUAgwAcffMBxxx0HwKBBgygsLKz03kAgwHnnnce5555LcXExAAkJCQBs27aNzp07A9C8efPd2s3JyeGVV16pkc9Um+Tn55OVlUVOTg6XXHLJbsvvvvtuFi9evNf3FxcXc+SRR5KSkrLH5cuWLaNFixbk5OQwdOhQduzYwbnnnktOTg733XcfAPPnz2fcuHHV84EkSZKkCKrqemXp0qV0794dgO7du1NQULDHdUyZMoVTTz2V7du3s2LFCoYOHcrgwYNZvXo1ENlrE5NdkhQBBQUFZGdnV7wuKioiIyMDgPXr15OWFh5Dm5qayvr16yu99/7772fmzJmcd9553HPPPUD4y+eYY47hoYceqkh27UlGRgaLFi2q5k9TOw0bNoz8/HwaNmxY6Qu4vLycOXPm0KFDh72+NzU1lddff52jjz56r3VOOeUU8vPzeeqpp3jhhRc45phjyM/P58MPP2TNmjV07tyZjz76iFAoVK2fS5IkSappVV2vdOrUiTfffBOAt956iw0bNuz2/s2bN7Np0yZatGjB2rVr+eSTT3jyyScZMWJExTVMJK9NTHZJUg2aMGECOTk5tGrVil69eu2xTqNGjdi4cSMAmzZtqtTVF6Bx48YAnHbaacybNw+A9PR03nnnHcaOHcsDDzxQY/HXRT+8K/Xxxx/TsWPHKt+TkJBAenp6lXWmTZvGsccey9NPP13p7lbnzp15//33AWjXrl3F/5EkSZJU2+3P9Urv3r3JzMxk0KBBADRr1my3OtOmTeOkk04CoGHDhnTv3p3GjRtz7LHHsnDhwhqLf29MdklSDdrV22js2LGVyrOzs1m+fDkARx55JG+99RYAeXl5HHXUUZXqbtq0CQjfbcnKyqK8vJydO3cC4S+SpKSkvba/fPnyKns0xaIf3pVavHgxmZmZB7XOFi1asHDhQl577TX+/Oc/06FDB958801CoRBvv/12xd2tQ6knnSRJkuq+/bleAbjzzjt54403SElJ4cQTT9xtPS+99BKDBw8GoEGDBiQlJVFaWsonn3xScS4eyWsTJ6iXpChIT0+npKQECM+11aNHD4499lh69OhBnz59WLVqFRMnTmTkyJEMHTqUNWvWkJiYyBNPPMGWLVv4xS9+QTAYrCgDuOGGG3jxxRf597//zYgRI7jooovIz89n2LBhUfykkTNhwgSmT5/OgAED9npX6tNPP+Xaa6+tVHbSSSdxyy23VLnuxMTEit+PPfZYWrduzfTp0znhhBM47LDD9nh3S5IkSaqrvn+9smPHDk444QTi4uI499xzadOmTaXrlbKyMhYtWkSXLl0q3n/DDTdw/PHHExcXV3G9EslrE5NdklRDcnJyyMnJ2evy0047jenTp5Obm8vo0aMZPXp0xbLmzZszcuRIAF588cXd3rtrzPz3jR8/nvHjx1e83rlzJ19//XWlXk6xbNeTZH6oQ4cOvPDCCwB06dKF/Pz8A1735s2bSUlJIRQK8cEHH3D99dfzyCOPEAqFuOSSSyqeWrN8+XL69+9/UJ9DkiRJioQDuV754Tn0969X4uLiePfddystz83NJTc3t+J1pK9NHMYoSVEydOjQSl8A1S0+Pp4JEybU2Prrip49e+7XPAG5ubnMmjWL3NxcPvnkE1atWlXxpMV33nmHPn36cMwxx3DiiSeyY8cOcnJyOP744zn77LNJTk4GwhN5duvWrUY/jyRJkhQJ1Xm9EulrE3t2SZLqvKruSgWDQXr06MHixYurnCNg+vTpu5Xtult14okn7jY3wQ/vbs2fP58jjzySQCBwYMFLkiRJqlYmuyRJMW9PwxurW+fOnencuXONtyNJkiSpag5jlCRJkiRJUsww2SVJkiRJkqSYYbJLkiRJkiRJMcM5u1TrbN4BRRuj03Z2GqQkRKdtSZIkSZJ08Ex2qdYp2ghXzIxO24/1h15NotO2JEmSJEk6eA5jlCRJkiRJUsww2SVJkiRJkqSYYbJLkiRJkiRJMcNklyRJkiRJkmKGE9QrJiy8LYctCwoIxCcQiIsnqdURtBxyN2k9j492aJIkSZIkKYLs2aWY0XLI3fSevJkeT66mQad+LPnt6ZRt2RDtsCRJkiRJUgSZ7FLMCSYk0vSEYZRv28y2r4qiHY4kSZIkSYqgOpPs2r59O6NHj6ZNmzbUr1+fQYMGUVhYSCAQ4KWXXop2eKpFyku3svb1xwgmp5HUskO0w5EkSZIkSRFUJ+bsCoVCnHPOORQWFjJmzBiys7OZNGkSZ5xxBgC9e/eOeEytj/8JvW8+n7T2Ldm5eSuf/GkK8x55OeJx6DtfThrNqufGEohPJKlNF7JH/Yu45LRoh6UYtWwz/GPZd6/vnQtnZ0K71GhFFJtWb4UXl3/3eswsOCsDujWGQCB6cUmqvXaUwxtfwZTPYc02aFQP/qsN/LwlJNWJM19Jkg7O2m3w0uffvb7tQzgrE3qnHzrn0HXiK//RRx9l6tSpzJ49m65duwKQk5NDVlYW6enptG3bNqLxtDyuJ/3u+yUzhv+BVQXziK+fSINWTSMag3bX8sK7aH7GjdEOQ4eA55aGk1vf9/xS+PtS+O+ucGH76MQVa95cBbd8ADvLvyubugL+tQIuaBfe1ofKl7Wk/bO+FK4rgIUbw8MXygn/++E6+Osi+NMx0Dw5ykFKklSDCtfAfxfCtrLvyl7/EqathFPbwKheEHcInEPXiWGM48aNY8iQIRWJLoC4uDiysrIqenVt27aNa665hg4dOtC9e3euuuqqGoun903nM+d3/+CrGXMJlZWzY/NW1i9cUWPtSao93v0axs2FEOGfXXblY+6fB2+tikJgMWbJRrj5/XCia0/b+ZnPYPLSaEQmqTa7+QNYvDH8+67jxa5/vyyB4e9CeWhP75Qkqe77qgR+/R6UllUu3/XdN2UFPL4o8nFFQ61Pdi1evJilS5dy1lln7bZsxYoVFcmum266iaSkJBYtWsTcuXO56667aiSe+PqJNO3VnvqHNeKMtx/kvDmPMeiJm0lp06xG2pNUuzxVVPWBM/htHR2cyUvDX8pVXZM+WQRlXrRK+tb89eEeXOV7WV4OfLYZCr6OYFCSJEXQ88tge3nV59CTPts9GRaLav0wxpUrVwLQrFnlZNKCBQtYvnw5vXv3ZvPmzTz11FN88cUXBL4d03L44Yfvdxupqals3759t/L28Y25KW1ApbJ6jRoQCAbJOKUvr18wlq3rNnDUnZcxcMJIppw48kA/3iFl4MAcluz8Zp/1kjv1o/3Y/JoOZ48GDsyhZGFBVNpW7RdMSqHrxHVV1ikHZhdDctOWlG2quq72rvPjXxGfml5lnTXboEnXY9i65MMIRRX7uv19GwCJiUlRjiS2uZ1rxuHnj+GwM24iEIzba51Q2U4uvvtJVv752ghGJklSZHT8w3wSD29XZZ1NO6Dl0f/F5jn/iVBUP155+d5uYe1bre/Z1aRJEwCKir7rKhEKhbj55pspLy+nd+/eLFmyhCZNmnDHHXfQp08fcnJymDFjRo3Es2Nz+AT108emsvmLNZRt3c5H90yiSfcs5+2Kok535ztfl2pcMKnB/tdN3P+62l0wcf8m1QkmpdRwJJLqimBSCoT2fVLscUOSFKvi9vM77kCua+qqWt+zq3PnzmRnZ3PrrbeSkJBASkoKjzzyCLNmzSI5OZlOnToxe/ZsPvvsM3r37s19993He++9x6mnnkpRURFpaft+Gt+mTZv2WL66cAGvDB5VqWzHphI2r/gaQo6dOVB5efkcftQR+6w3ex1cMTMCAe1BXl4+vZpEp23VfjvL4fhXYcvOquslxcHazxeTtPfOBdqHc94IP/FyX0faeTNeo4WTTVebPt8+VLi0tDS6gcQ4t3PNmLwU7ptbdZ1gXDz/fdl5XHvveZEJSpKkCBr2Nsz9Zu9D+nd551/P0aFhREI6KDNnzmTAgAH7rrgHtb5nV3x8PM8//zwtWrTgkksuYcSIEZx88skcd9xx9OjRg2AwSNu2bYmPj+eCCy4AoG/fvjRt2pRFi2pm5rWFT71G5ytOIbllE+ISE+h90/ms/XgJW1aurZH2JNUO8UE4rS1U9fCSIPCLNpjoOkhnZVad6AoCRx+GiS5JFU5uBfX248x2cGQf4i1JUsScmVl1oisIdGlEnUh0Haxan+wC6NmzJwUFBZSUlLBw4UKuueYaZs2aVTE5fdOmTRk4cCCvv/46AIsWLeLrr78mOzu7RuKZ+/BLrHxjFqe9di/nfPQoyYenkzfsvhppS1Ltckk2NE3a88EzCDRKhMs6RDqq2DO4LXRM23NiMQjUi4NfdYl0VJJqs7R6cF3nqutcnA2tYn/khiTpEHViK+iVvudz6AAQDMB/d410VNFRJ5JdP7R161YWLlxYkewC+NOf/sRvf/tbunfvzvnnn8/EiRNp1KhRzQQQCvHh3X/j2W7DeLbrZbxx2Th7dUmHiKZJ8PgA+Mkehrv2TA8vO7x+5OOKNfXj4U/HwMAWu39Zt0uFPx8DnQ6BO1KSDsxF7eGW7pCWULk8OQ6uPQJ+tY9kmCRJdVlCEB46Gk5uHU5sfV/bFPjjMRwy0/bU+jm79mTOnDmUlZVVSna1a9eO/Pz86AWliNi5qZjFvzmBbSsX0nvy5krLlv/hSrZ9uYhQeRmZv3qcpFYdAdjxzSrmXpVFt0cWU69p62iErRjTIhn+1B+WboKPi8Nl3RtD+31PEagDkFYP7v0prNoK76+BHeXQsSF0bQSBqsaSSjqknZ0VHnL+ztdw4/vhstd+Dkl18qxXkqQDkxwPd/4EhneBd7+G0nJonxq+MX8onUPXya/9vn37EnKC+ENSXP1UOtzxOp/de+5uy9pe/UcC8Qlsmvc2a179E22G3Q/A1//6PQ069o10qDoEZKWGf1SzmteHU51jR9IBqBcHOS2+e22iS5J0qGmaBL84hM+h6+QwRh26AvEJxKem73UZQPm2zdTP6AbAzs3r2blpLYnNMiMVoiRJkiRJiiKTXYopi0Yfz+ePXk+D7J8CsGbqwxx20tVRjkqSJEmSJEWKyS7FlI53/Yf2t7zAl8+Oobx0K9tWfEpyu977fqMkSZIkSYoJzmCgmFG+o5RgQiJxyQ0J1qtP6dfLKF21hMVjTmLr8rns3PwN2be9FO0wJUmSJElSDTLZpTpn0ehcSpbOYtHoXFpeMIbNCwpofuZIltxzBuWlWwkEArT55cPUb9OZI+57F4BlD15Ky4vGRjlySZIkSZJU00x2qc7peNf0Sq9TugwAoMPtU/f6nsz/90RNhiRJkiRJkmoJ5+ySJEmSJElSzDDZJUmSJEmSpJhhskuSJEmSJEkxwzm7VOtkp8Fj/aPXtiRpz/Lz87nsssvIyMggIyODJ598stLyiRMn0qJFC9q0acPll19OMBikT58+PPDAA5Xq3X///YwfP55rrrmGUaNGAfDqq69yxx13kJqayhNPPEHLli257LLLePzxxwkEAhH7jDp07O/+nJuby7HHHsusWbNYsGABrVu3rlTvrbfeYuTIkQDceuutDB48mDVr1nDVVVexfv16LrjgAq666ir3Z0mSIshkl2qdlATo1STaUUiS9mTYsGGMGjWK4cOHU1BQQL9+/SqWTZkyhcmTJ1NcXMy0adNISUnh4osvZtGiRXTs2LGi3pAhQ+jVqxfvvPNORdm4cePIy8ujqKiIcePG8eCDD9K3b1/y8vIYNGhQRD+jDh37sz8DPPfcc9xyyy17XMcDDzzAiy++SHp6OqeccgqDBw/mzjvv5He/+x0ZGRkV9dyfJUmKHIcxSpKkA9atWzdWrlxZ8bq4uJikpCQCgQBNmjQhJSUFgLi4uN16sjRr1oxgsPIpSHx8PElJSXTt2pXCwkIABg4cyNSpe3/SbqzKz88nKyuLnJwcLrnkkt2W33333SxevHiv7y8uLubII4+s+D/Y1/LCwkL69+/PMcccU9HTbv78+YwbN64aPk3dUNX+DNC8efO9vrdDhw5s2LCBLVu2kJqaCsCiRYu45ZZbOPHEE1m4cCFw6O7PkiRFg8kuSZJ0wAoKCsjOzq54XVRUVKkXC8C8efNYu3YtHTp02Of6duzYwbp165gxYwbFxcUAZGRksGjRouoNvI4YNmwY+fn5NGzYkIKCgory8vJy5syZU+U2TU1N5fXXX+foo4/er+W9e/dm5syZvPPOOxQUFLBx40Y6d+7MRx99RCgUqt4PVkvtz/68N4MHD+bnP/85PXv25OqrrwZgxowZjB07locffpjbbrsNOLT3Z0mSIs1klyRJ2m8TJkwgJyeHVq1a0atXr73W27hxI9dffz2PPvrofq137NixnH322TzzzDN06dKlmqKt+37Y4+jjjz+uNCR0TxISEkhPT9/v5QkJCQCUlZXRsmVLkpOTAWjXrh3z5s07mPBrvf3dn6syevRo3n///Uq94bp27Ur79u0ren1JkqTIMtklSZL2264eR2PHjq1Unp2dzfLlywEIhUJcfvnl3HnnnbRs2XK/1jtgwADy8vK49NJL6du3LwDLly/fr15hseyHPY4WL15MZmZmtbczadIkOnfuTKNGjYiPD0/peij0RNqf/Xlf4uLiSEtLIzk5mdLSUgAyMzNZu3Ytq1evrkgeuj9LkhQ5TlAvSZIOWnp6OiUlJUB4zqk33niDtWvXAjB+/HhatWrFxIkTGTlyJE899RQPPvggGzZsYOPGjdx7773ceeed5Ofn06pVK/785z8DkJeXx8knnxy1zxRNEyZMYPr06QwYMGCvPY4+/fRTrr322kplJ5100l4nUq/KhRdeyPnnn88555zD3Llz6d69+48JO2Z8f3+G8EMV3njjDZYsWcKYMWM4/vjjueGGGxg/fjwjRoxg4MCBhEIhrrzySgBGjRrFmWeeyc6dO3nooYeAQ3t/liQp0kx2SZKk/ZKTk0NOTs5el5922mlMnz6d3Nzcinm3vm/kyJEADB06lKFDh1Zadvvtt3P77bdXKnvvvfe46qqrDj7wOmjXUwJ/qEOHDrzwwgsAdOnShfz8/INuq7S0lMTERILBIKmpqSQlJQHhnkj9+/c/6PXXVgeyP//tb3/bbfn48eMBOOWUUzjllFMqLevRowdvvfVWpbJDeX+WJCnSHMYoSZKqxdChQ8nNza229f31r3/d7amNh7qePXtWPN2vKrm5ucyaNYvc3Fw++eQTVq1axX333bfH5ffeey85OTn87Gc/o3Xr1hVD7YqKiujWrVuNfZbazv1ZkqS6y55dkiRJtUhVPY6CwSA9evRg8eLFVc7/NH369N3KdvWs29Py0aNHV3o9f/58jjzySAKBwAFELkmSVDuY7JIkSapD9jS8sbp17tyZzp0713g7kiRJNcG+1JIkSZIkSYoZJrskSZIkSZIUM0x2SZIkSZIkKWY4Z5dqnc07oGhjdNrOToOUhOi0LUmSJEmSDp7JLtU6RRvhipnRafux/tCrSXTaliRJkiRJB89hjJIkSZIkSYoZJrskSZIkSZIUM0x2SZIkSZIkKWaY7JIkSZIkSVLMcIJ6xYSFt+WwZUEBgfgEAnHxJLU6gpZD7iat5/HRDk2SJEmSJEWQPbsUM1oOuZvekzfT48nVNOjUjyW/PZ2yLRuiHZYkSZIkSYogk12KOcGERJqeMIzybZvZ9lVRtMORJEmSJEkRZLJLMae8dCtrX3+MYHIaSS07RDscSZIkSZIUQXUm2bV9+3ZGjx5NmzZtqF+/PoMGDaKwsJBAIMBLL70UsTguKppY6Wfo589y2n/GR6x97d2Xk0Yz+8JGzL0yk5KlH5M96l/EJadFOyxJqvW27YR/Lv/u9d0fw7xvohdPrNpZDtO//O716I+gcA2EQtGLKRaVh6Dga7jtw+/K8r4Kb39JknRoqBMT1IdCIc455xwKCwsZM2YM2dnZTJo0iTPOOAOA3r17RyyWp7MvrvT6tP+MZ+lLMyPWvvau5YV30fyMG6MdhiTVKUUb4boCWFf6XdlLy+HF5XBaG7itF8QFohZezPh6a3g7L938Xdm0lfDKF3D0YXDfT6F+nTgrq90274BfvweziiH4vf125PvQIQ3+cDQ0SYpefJIkKTLqxGnVo48+ytSpU5k9ezZdu3YFICcnh6ysLNLT02nbtm1U4mraK5tGHVtTNDkvKu1LknQwNu2Aa9+B9dsrl+/qAPPyinBi4LrOEQ8tppSF4Pp3YfnmyuXl3/boem8N3Dkb7ukT8dBizqiPYHZx+PfyH/SYW7IRfl0ITx4LARO4kiTFtDqR7Bo3bhxDhgypSHQBxMXFkZWVRUJCAsuWLeP000+vWLZ+/Xo2btxIcXFxjcbV4cJBrHxjFltXO9ZDklT3/GsFFG+vus4zn8GlHaBBnThjqJ1mrobPNu19eYjw8MbrtkDrBhELK+YUbYQZq/e+vBz4dD18sBZ+elikopIkSdFQ609dFy9ezNKlS3nooYd2W7ZixQrOOussMjMzmT17dkX5iBEj2Llz5363kZqayvbtu5/tt49vzE1pA/b4nvj6iWQN7s/bw/+w3+0c6gYOzGHJzn0nBpM79aP92PyaDmePBg7MoWRhQVTalqRIa3f3myRnH0UguPcpPLeVQebx57Px3RcjGFlsaf2rx2nU/zwCcXs/7SoPheh76W2sfdl5QH+sZueOptlZt1a5P4fKdnLuHX/ly79cH8HIJEnSj1Fe/uMn3Kz1ya6VK1cC0KxZs0rlCxYsYPny5bvN17V9+3aefvpppk2bVqNxZZ7aj51bt/PF9A/3XVk1rtPd+dEOQZLqnLgGjatMDFTUS24YgWhiV1xyw32PmysvI66BD1U5GHHJDSFURtXPXwr58BpJkg4BtT7Z1aRJEwCKioo46qijgPCE9TfffDPl5eW7JbtefvllWrVqxU9+8pP9bmPTpj2PLVhduIBXBo/a47IOFx3Pkr/nEyrz0T77Ky8vn8OPOmKf9WavgyuiNOd/Xl4+vZpEp21JirTh78K7X383R9fevPTUn+l72J8jElMsuncuPL+06u0ciIvnd2Nu4cwnbolYXLHm6SXwwLyq6wTjEvh/l57Hr+49LzJBSZKkH23jxo3MnTuX7t27H/B79307N8o6d+5MdnY2t956K8899xyvvPIKgwcP5qOPPiI5OZlOnTpVqv/4449z+eWX12hMae1b0qxPJxY9858abUeSpJp0ett9JGCAw5OgT9NIRRSbBu9jOwPUC8KJrSISTsw6uTXE76MDXQg4NTrPNZIkSQcoLS2N/v37k5Z24L2ya32yKz4+nueff54WLVpwySWXMGLECE4++WSOO+44evToQfB7wy9WrlzJm2++yUUXXVSjMXW4YBCr35vPpqWrarQdSZJq0s+aQ+/0cFLrhwKEEwO/7gZxPrnuoHRqCKe0rrrO1UdASkJk4olV6Ylweceq65yVAZkpkYlHkiRFT60fxgjQs2dPCgoqTxr+hz/8geOOO65S2ZNPPskpp5xSMfSxpnw49m81un5JkiIhPgi/Oxrumg3/+TKc3NolLQFGdofcltGKLraM7hVOZv1jGez83oauHwe/PAIuahetyGLLlR3DvbseXxx+uMIu8QG4oB1c3yV6sUmSpMipE8muH9q6dSsLFy5kxIgRlcqfeOKJPT61UbFp56ZiFv/mBLatXEjvyZsrLVv24KVsW7mQQEIiLc67nbQeg6IUpSTVbg3i4X/7wJcl8NaqcIKgTYNwr6+EWt//u+6ID4aTh8M6Qt5XsHEHNEuCgS0guU6ejdVOgUC4d9e5WeHtvLYUGtULb+dG9aIdnSRJipQ6eXo1Z84cysrKdpucftGiRVGKSNEQVz+VDne8zmf3nrvH5e1ueo56TfcxbkSSBEDLZDjf3kU1Lj0RzsqMdhSxLyXBubkkSTqU1clkV9++fQmFQvuuqJgWiE8gPjV9b0v57L7zqNekFW2v+VMV9SRJkiRJUixxgIJiUuth93PEuJk0HnAeq56/J9rhSJIkSZKkCDHZpZgUn9IYgEZHncbWFfOiHI0kSZIkSYoUk12KSWUlmwDYvLCAxGZZUY5GkiRJkiRFSp2cs0vaZdHoXEqWzmLR6FxaXjCGzQsKaH7mSJb9big7Nq4hmJBI5vAnoh2mJEmSJEmKEJNdqtM63jW90uuULgMAaH/ri9EIR5IkSZIkRZnDGCVJkiRJkhQzTHZJkiRJkiQpZpjskiRJkiRJUswIhEKhULSDqK22byrhm/mfRzuMmNG4c1vqpSbvs97mHVC0MQIB7UF2GqQkRKdtSZIkSZJ08Ex2SZIkSZIkKWY4jFGSJEmSJEkxw2SXJEmSJEmSYobJLkmSJEmSJMUMk12SJEmSJEmKGSa7JEmSJEmSFDNMdkmSJEmSJClmmOySJEmSJElSzDDZJUmSJEmSpJhhskuSJEmSJEkxw2SXJEmSJEmSYobJLkmSJEmSJMUMk12SJEmSJEmKGSa7JEmSJEmSFDNMdkmSJEmSJClmmOySJEmSJElSzDDZJUmSJEmSpJhhskuSJEmSJEkxw2SXJEmSJEmSYobJLkmSJEmSJMUMk12SJEmSJEmKGSa7JEmSJEmSFDNMdkmSJEmSJClmmOySJEmSJElSzDDZJUmSJEmSpJhhskuSJEmSJEkxw2SXJEmSJEmSYobJLkmSJEmSJMUMk12SJEn6/+3deXhU9aH/8fckYTUgBAQUAgSCGEAgdUEFJKClWiuKSlsVxYpXrVvxutCfgpfi0lKr9rrRctVaUWgVtUiLomiiomhAQBYFwiqLoLIvIZBkfn+MBmMgBAgzmZP363nykPmeM5PPjMeZM5/5njOSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAWGZZckSZIkSZICw7JLkiRJkiRJgWHZJUmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYll2SJEmSJEkKDMsuSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCoykWAeQJEmSJEnV1+5tO9n0+RexjhEYDTNaUrNe3VjHiCnLLkmSJEmSFDObPv+C1y8YFusYgXHuxPtoeuoJsY4RUx7GKEmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYERN2XX7t27GT58OKmpqdSpU4c+ffqQm5tLKBRi4sSJsY6ngNqyG8YthXvnwKi5MG09FIVjnUqSFA7Dpxvhofkwcg48tQjW5cc6lSRJqkyhxAROvfdXXPrZ37hs4d8546Ffk1irRqxjKQ4kxTpARYTDYQYMGEBubi4jRowgPT2dcePG0b9/fwAyMzNjnFBB9MoKeHA+7CmGxBCEgZdWQOpR8Eg3aJ0c44CSVE1tLoDbZ8CcjZFP7UIhKA7DXxfBFelwUwYkhGKdUpIkHa7Ot1xEszM6MbHPbRTtKeSsZ4dy0rAryB3+TKyjqYqLi5ldY8aMYfLkyUydOpXrrruOs846izFjxpCYmEhKSgotW7aMdUQFzFtr4IG5kaILIrO5ir+d0bVmJ1z/QeTNliQpugqL4aaPYO7GyOViIs/RYSI/zy2BpxbHMKAkSao07S4/i3mPvsLOdRsp2LCVOQ+9SPovsgglxEWVoRiKiy1k1KhRDBw4kI4dO5aMJSYmkpaWVjKra/HixZx++ukcf/zxnH766eTl5cUqruJcOAxPLoT9TQooDsM3BfDqF1GNJUkicjj5wi2Rkmt//p4H2/dELZIkSToCatavS3LzY9i4YHnJ2IZ5y6lZry7JqcfEMJniQZU/jDEvL4/ly5fz6KOPllm2atUqLr74YgCuv/56brzxRgYOHMjzzz/PddddxzvvvHPA29+6dSvNmjWjsLCQUMhjHgR12p5E+h8+LHedcLiYh99eyvWdOkUplSQJoOVt/6D+KecTStz/LkxBMbQ9bzCb330+iskkSdKhapvUkDvr9yg1lpRcB4DdW3aWjO3esgOAGt8u07717p3F0sJNsY5RKWrWrMm2bdsO+npVfmbXmjVrAGjSpEmp8YULF7Jy5UoyMzP56quvmDVrFpdeeikAl156KbNmzeLrr78+4O3PmzeP/Px8wmHPOq6IpKObHHCdUCihQutJkipXUoOm5RZdJev5HC1JUlwr3B755pka9euWjNU8+igA9mz3W2lUvio/s6tRo0YALFmyhFNPPRWInLB+6NChFBcXk5mZyapVq2jevDmJiYlA5BDH4447jlWrVnHMMRWb3piTk0P37t2PzJ1QXFmwCQa9f+D10poczewCT9wlSdF0xwx498vyD2ME+OvDv+dnL/0+KpkkSdLhWZ+7kNcvGFZqbPfWnWxf8zUpHVuzdelaABp1SmP3tp1sX3XgiS3VWXZ2Dk1PPSHWMWKqypddGRkZpKenc9ddd1GjRg2Sk5MZPXo0s2fPpm7durRv357Zs2fHOqYCpEMDaHkUrNoROdnx/vTzexEkKerOawHZX5a/Tu1EyGoWnTySJOnIyXvhbTrf3J/1H39OcWERXW/7OUv+mUO4+EAfe6m6q/JlV1JSEhMmTOD6669n0KBBpKamMmTIEOrXr8/SpUtJSEggNTWVNWvWUFRURGJiIkVFRaxdu5bU1NRYx1ccCoXghgz47cx9L08AGtWGC1tFNZYkCejRNPKhxMLN+5/ddVU6JNeIYihJknREzH30FWql1OfCnEcIJYRY8e+P+OR+z8mpA6vyZRdAly5dmD59eqmxxx9/nF69egGR83l17dqV8ePHM3DgQMaPH09mZmaFD2GUfujs42BYF/jjPNj9g3dTLY6CP3eDBjVjk02SqrOkBHj0NLgjF2Zv3Dse+vbnynQYfHys0kmSpMoULiomd/gz5A5/JtZRFGfiouz6ofz8fBYtWsSQIUNKxv7yl78waNAgRo4cScOGDXnuuediF1CBcGEr6HMsTF4Nf5ofGXv0NDjtGEjwizslKWYa1IQx3WHBZrjq23Ms/voE+FkqNPHLmSRJkqq9uCy75s6dS1FREZmZmSVjJ5xwAh9//HEMUymI6teEX7bZW3ad4Zd7SVKVEApBp4Z7L1/tbC5JkiR9Ky7Lrm7duhEOl3fqcEmSJEmSJFVHCbEOIEmSJEmSJFUWyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYll2SJEmSJEkKDMsuSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAWGZZckSZIkSZICw7JLkiRJkiRJgWHZJUmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYcVN27d69m+HDh5OamkqdOnXo06cPubm5hEIhJk6cGOt4klTlFYfho6/g8c/gfxfAW2tgT3GsU0mSADYVwPhl8OcF8NRiWLk91okkKfZan3865068l8uXjOWS3CdjHUdxJCnWASoiHA4zYMAAcnNzGTFiBOnp6YwbN47+/fsDkJmZGeOEklS1Ld0Kd8yAL3bs/ZSjGGhYE+47CbodE8t0klR9hcMwZhH8LQ8Kw5AYinw48ZeFcNaxMCIT6sTFHrskVb6CLTtY+Mwb1D7maDpe+7NYx1EciYuXzjFjxjB58mTmzJlDx44dAcjKyiItLY2UlBRatmwZ44SSVHWty4drP4BteyKXvz+Za8tu+M1H8FQP6NQwJvEkqVp7ejH83+K9l4vCe39/50vYWQiPngahUPSzSVKsffneXABannNKjJMo3sTFYYyjRo1i4MCBJUUXQGJiImlpaSWzum6//XbS0tIIhULMnz8/VlElqcoZvxS27ildcn2nmMgMgr8ujHYqSdK2PfBM3v6Xh4HpX8PsjVGLJElSIFT5sisvL4/ly5dz8cUXl1m2atWqkrLrwgsv5L333qNVq1bRjihJVVY4DBO/iLxh2p9i4KOv4Ztd0UolSQKYuhZ2H+DciQkhmPRFdPJIkhQUVf4wxjVr1gDQpEmTUuMLFy5k5cqVJWVXjx49DuvvZGVlkZBQ5bs/xUinFyMtQK1atWOcRDo4oaSadBq/7YDrhYG2XU5l14pPj3woqRL5/Kx41uSSu2kyYBihcvZBi4rDjJs0lQdO81w1koKrbVJD7qx/eO/ptVfv3lksLdwU6xiVombNmmzbduD3Mz9U5dudRo0aAbBkyZKSsXA4zNChQykuLvbk9JJUjnDhbooLdlZo3aLtHicjSdFUtH1juUUXAMVFFG3fEJ1AkiQFRJWf2ZWRkUF6ejp33XUXNWrUIDk5mdGjRzN79mzq1q1L+/btK+Xv5OTk0L1790q5LQXPya9F/i0oKIhtEOkQ3P8pTFy573N2QeRTj04NYeaaJftZQ6q6fH5WPPtmF/z0rci5E/cnlJjEs7f9kh5//GX0gklSlK3PXcjrFwwrMx5KSCChRiKhpCQIhUisVYNwOEzx7sIYpIwf2dk5ND31hFjHiKkqX3YlJSUxYcIErr/+egYNGkRqaipDhgyhfv36LF261EMPJekALm8Dk1fBnuJ9F15h4L8q53MDSdJBaFwbLmkNLy7f9/IEoN3RcHqTfS+XpKBre8mZ9Pjfm0ouX7FiPNtXfcWEU2+IYSrFgypfdgF06dKF6dOnlxp7/PHH6dWrV4wSSVL8aF0v8rX1t+XC9h98CJYUgmFdfSMlSbHy3x1hxx74z+pIufX9DyVOaAB/7gaJoRiFk6QYW/JiDktezIl1DMWhuJwWlZ+fz6JFi0qdr+uWW26hRYsWrF69mrPPPpuOHTvGMKEkVS0nNYbX+8KwLnvHbukAb/SFn6XGLpckVXdJCfC7H8E/suCXbfaOP3E6PNsTUmrFLJokSXErLsuuuXPnUlRUVKrsevTRR1m9ejWFhYWsW7eOBQsWxDChJFU9dZLgwlZ7L1+ZDg18EyVJVUJ6ffjvTnsvdzsGEpzRJUnSIYmLwxh/qFu3boTD5ZzJU5IkSZIkSdVSXM7skiRJkiRJkvbFskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAWGZZckSZIkSZICw7JLkiRJkiRJgWHZJUmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYll2SJEmSJEkKDMsuSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAVG3JRdu3fvZvjw4aSmplKnTh369OlDbm4uoVCIiRMnxjqepMMQDsOMr+HZPPh7HszfFBmT4tWK7fD8UnhmMeR8CYXFsU4kSVL0FIXhg/XwtzwYuwQWbYl1IsWjhJpJnPGn67n4oye4PG8s/ac9yglXnxvrWIoTSbEOUBHhcJgBAwaQm5vLiBEjSE9PZ9y4cfTv3x+AzMzMGCeUdKg+3wx3fwJf7Cg93v5o+P1J0DI5JrGkQ7J5N9wzCz78qvR4Sk24uyv0ahaTWJIkRc2sDZHXwnX5pce7psD9J0HTOrHJpfiTkJhI/lebefOX97Jt5XpSOrTix+OHsevrzayYND3W8VTFxcXMrjFjxjB58mSmTp3Kddddx1lnncWYMWNITEwkJSWFli1bxjqipEOwbBtc+wGs3lF2Wd5WuGYafJVfdplUFe0qghs+hI++Krts0264PbdsCSZJUpDM3wQ3Tt/3/tvcjZF9uy27o59L8akwv4DZf/wH21asg3CYjQtWsOrNmTQ5NSPW0RQH4qLsGjVqFAMHDqRjx44lY4mJiaSlpZGZmcmGDRv46U9/Svv27TnxxBO56KKL+Prrr2OYWFJF/N8iKCiCfR3hVRyOFAQvLI16LOmQvLEaFm/d9/b83VG5f17gIbqSpOB68nMoKt7Pvh3wZT5MWBHlUAqMUFIiTbtlsOnzlbGOojhQ5cuuvLw8li9fzsUXX1xm2apVq8jMzCQUCnHnnXeyaNEi5s2bR9u2bfntb38bg7SSKmrrbnj7y33vDH0nDPzri0jxJVV1r66EUDnLw0RmM37ueUskSQG0bifkflP+vh1EXi+lQ3HaA4PZsz2fpS+9G+soigNV/pxda9asAaBJkyalxhcuXMjKlSvJzMwkJSWFrKyskmWnnXYao0ePPqi/k5WVRUJCle/+FCOdXtwFQK1atWOcJDhqNT+B4//86QHX21EIR6UcQ/HOrVFIVT24PR8ZGf+3iqQGTQ64Xq9+v2Drx/868oGqCbdnBY3btOJV3fan0/a+nAOu9+WOImrVqnvkAymutE1qyJ31e+x3+SkjBnHMSe2ZMmAExXsKo5gsPvXuncXSwk2xjlEpatasybZt2w76elW+3WnUqBEAS5YsKRkLh8MMHTqU4uLiMienLy4uZvTo0fTr1y+qOSUdnKKdFZveEi4qpLhg5xFOIx2+op2bCVfgGMWiHU7tkiQFT0X37YrzD/5Nq6q3U0dexXFndmbKz39HwUa3H1VMlZ/ZlZGRQXp6OnfddRc1atQgOTmZ0aNHM3v2bOrWrUv79u1LrX/zzTeTnJzMTTfddFB/Jycnh+7du1dmdAXIya9F/i0oKIhtkIC5+v3IiUz3N909ATgrNYlPdu7jDPY6ZG7PR8aYRZGf8jSsCetnvEGNKv9RU/xwe1bQuE0rXoXDcEk2fLF977kqfygBuKRjA37r9q0fWJ+7kNcvGFZm/NR7r+bYHp1445IRFGzwSI+Kys7OoempJ8Q6RkxV+bIrKSmJCRMmcP311zNo0CBSU1MZMmQI9evXZ+nSpaUOPbz99tvJy8tj0qRJHpIoxYGrj4chH+97WQgIhWBg26hGkg7ZRa1g/DLYsWf/Be6gdlh0SZICKRSCa46H4bP2sxxISoBfpkU1luLYUS0a0+Gan1K0azeXfPxEyfj6jxcy9fL7Y5hM8aDKl10AXbp0Yfr06aXGHn/8cXr16lVy+a677uKTTz7hP//5D7Vq1Yp2REmHoEdT+H+dYdTcyCeA3/8UMCkB7v8RdGwYq3TSwWlcGx4/DW75CLbs2TueQKT8GtgWLm8Tq3SSJB1557aA9fnw+OeRcuv7+3a1E+HBU6B1vVilU7zZsfobnj32kljHUJyKy8+X8/PzWbRoUcn5uhYsWMDvf/971q5dyxlnnEHXrl3p379/jFNKqoiLW8NrZ0dmeX3npgz4z4+hz3ExiyUdko4N4bUfR0rc7wxIg39kwZCOkU+9JUkKsqvawat9Ss/O/++OkX270w78PS6SVCniYmbXD82dO5eioqKSsqtjx44VOimwpKqpWV349Qnw9OLI5avaxTaPdDiOSoqUuL+fG7l8x4kxjSNJUtSlJsNvOsLYpZHLl3laCklRFpdlV7du3Sy3JEmSJEmSVEZcHsYoSZIkSZIk7YtllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAWGZZckSZIkSZICw7JLkiRJkiRJgWHZJUmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYll2SJEmSJEkKDMsuSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCoy4Kbt2797N8OHDSU1NpU6dOvTp04fc3FxCoRATJ06MdbyoKwrDh1/BS8vhP6tg8+5YJ5IkSUG0qxCmro3sc7yzFgqKYp1IOnTFYcj9OrI9//sL2LAr1omkw7N0K7yyIvKzZGus01S+035/DQNm/oXLFj/HgFl/5dSRV5FQIynWsRQH4mIrCYfDDBgwgNzcXEaMGEF6ejrjxo2jf//+AGRmZsY4YXS9sxYenA9ff+/FOSkEF7WGWztCjbipMCVJUlUVDsPfl8Df8mBH4d7x5CS4tj1c2gZCodjlkw7Wh1/B7z+FL/P3jiWG4LwWcOeJUDsu3hlJEWt2wIjZMHtj6fGuKTAiE1ocFZtcle3zv73BzJFjKcwvoFZKPbLG3EbnWy5izkMvxjqaqri4eEofM2YMkydPZs6cOXTs2BGArKws0tLSSElJoWXLljFOGD1vr4Xfziw7XhiGF5fDV/nw4CnufEqSpMMzeiE8k1d2fHshPLwAdhXB1cdHP5d0KD76CoZ8HClxv68oDJNWRQqwx06DJD80Vhz4ehcMngYbC8oum7sRfvU+jO0FzepEP1tl27J49d4LoRDh4jD12hwbu0CKG3HxdD5q1CgGDhxYUnQBJCYmkpaWVjKr68ILL6RLly5kZmbSs2dP5syZE6O0R05hMfxpXuT38H7WyVkHM7+JWiRJkhRA6/IjM7rKM2bRvt9oSVVNOBw5KiIc3vc+dBiY8Q28ty7ayaRD8/e8yPNv8T6WFQNbdsOzB3gOjycn3nQhly8Zy6XznyGlYys+G/PvWEdSHKjyZVdeXh7Lly/n4osvLrNs1apVJWXX3//+dz799FNmz57N7bffztVXXx3tqEfcR1/D1wX7L7oAEkLw6sqoRZIkSQE06YsDr1MYhsmrjnwW6XDN3QQrtx9gHxp4xX1oxYE9xfDaF/suur5TDPx7VWQGbhDMe/xfvJB+Ba+e+RsWPfcm+V9tinUkxYEqfxjjmjVrAGjSpEmp8YULF7Jy5cqSsuvoo48uWbZlyxYSEg6ux8vKyjro60Rbo3Nu4LjBj5S7TnEY/vX+LB7qfnqUUlUPnV6MnCCtVq3aMU4SbD7O0eHjHB0+ztHh43xktLjxKRr0/CWhxBr7XSdcuIfhjzzD4KduiWKy4HObrnwNzryM1Jv/Vu46xcB785dTK+uE6ISqJtyeK19Sg2Zk/N+Bm9ldRdC4ZTp7vomPTyXaJjXkzvo9yl1nS94aNi5YSc/HbmHKJSOiEyxO9e6dxdLCYJSCNWvWZNu2bQd9vSpfdjVq1AiAJUuWcOqppwKRE9YPHTqU4uLiUienv+aaa3jzzTcJh8O88cYbMcl7JBXtOvB/4HBxEcX5B78hSJIkfad413bgACcATUj4dj2paivOP/B2Gg4XU+Q+tOJAccGOiq+7q+LrxouEGonU95xdqoAqX3ZlZGSQnp7OXXfdRY0aNUhOTmb06NHMnj2bunXr0r59+5J1n3rqKQDGjh3LHXfcweTJkyv8d3JycujevXul569MGwvgp29GDhvYn1BCIiMv7cXP7/IkGpXp5Nci/xYU+LgeST7O0eHjHB0+ztHh43xkzPgafj29/HVCCYn850+30enp26ITqppwm658OwrhJ1PKP6QrFErgv8/pzOBbfNwrk9vzkXHDh5HzNO/vUMaEEHRpCDM3fBnVXIdjfe5CXr9gWKmxGvXq0urcU/nijVx2b91Jw4xWdBlyMWtzPo1RyviRnZ1D01Or90zVqn3cHpCUlMSECRM49thjGTRoEEOGDOHcc8+lV69edO7ceZ+HHl5xxRVkZ2ezYcOGGCQ+clJqQb9yvngyIQQNa8JPW0QvkyRJCp6TG0P7o/e/o5hA5OvtOzaIYijpEB2VBL9I2//yhG/XubD6fMG74tyV6Qc4Z1cYBrWLWpwjJxymzcVncvFHT3D5krH0+dudrH57Nh/f/XSskykOVPmZXQBdunRh+vTSHy8+/vjj9OrVC4Dt27ezadMmUlNTAZg0aRIpKSmkpKREPeuRdlsn+GoXTFsfKbeKvzfLq34NePx0SN7/6TUkSZIOKBSCP3eDX38IK753BFgCkTdYbevDH0+JrCfFg1+fAF/mw5tryu5D10mCR0+DRp5WSnHitCbw284wam7k8neb83dPybd1gh5NY5Gscu3Zns+bvxgZ6xiKU3FRdv1Qfn4+ixYtYsiQIQDs2LGDAQMGsGPHDhITE0lJSWHSpEmEArgHVisRHj4Vcr+OfGPMO9/OTL29E5yXCvUsuiRJUiU4pja80AveXgv3zI6MdTsGftYS+hwLNar88QHSXkkJcP+P4KJWkW8unxL5Dix+0wHObwkNasY2n3SwLmkNpzSGl1fAuGWRsV+2gYtbQet6sUwmVQ1xWXbNnTuXoqKikpPTN23alI8++ijGqaInIRRp809rsvc4+F+2iW0mSZIUPLUS4aepe8uux/yyZ8WxUChyiO7JjfeWXVekxzaTdDhaJcN/d9pbdt3WKbZ5pKokLsuubt26EQ6Xc5Z2SZIkSZIkVUtOQJckSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIk6bDk5OSQlpZGVlYWgwYNKrN87NixTJ06lUWLFtG9e3d69uzJrbfeWma9N954g9NPP52+ffuydu1aAHr37k1WVhZZWVl89tlnFBYWcs011xzx+yRJCrYef76RbvcPjnWMfbp8yVhSOqXFOkZcs+ySJEnSYRs8eDA5OTkcffTRTJ8+vdSySZMmcdZZZ9G4cWOmTJnC+++/zzfffMPixYtLrTdq1Ciys7N5+OGHGTVqFACJiYnk5OSQk5NDhw4dSEpK4phjjmHp0qVRu2+SpKqt2RkdOefl33F53lguzxvLOS//jmand4x1rBJdb/s5Zz33/yq8/gvpV7Bx/vIjmCj4LLskxY0DzRy4//77ycvLK/c2br75Znr27MkDDzxQavyNN94omTnQqFEj5syZs8+x3NxcunfvzhlnnMGwYcMA+Pzzz0velElSddepUyfWrFlTcnnjxo3Url2bUChEo0aNSE5OBiIlVigUKnXdpKQkateuTceOHcnNzQUgHA6TlZXFNddcw65duwDIysri9ddfj9I9kiRVZS3OPokfjxvGqqmf8OKPruPFH13Hqqmf8OPxw2hx1o/2eZ1QYuVVIaGkxEq7LVUeyy5JcWV/MweKi4uZO3cu7dq12+91Z86cSVJSEu+//z6zZs1i/fr1JcvOOecccnJyyM7Opk2bNnTp0mWfY5mZmXzwwQd8+OGHTJ8+na1bt5KRkcGsWbMIh8NH9L5LUjyYPn066enpJZeXLFlCq1atSq2zYMECvvnmmzLP2Xv27GHDhg1MmzaNjRs3AjBhwgRycnLIyMjg6aefBqBVq1ZlZoVJkqqnbvddzZKXclgw+jX2bNvJnm07WTD6NZZOeJdT77sagEtyn6TzkIv56Wv3M3DZCzTu0haAGkfVJmvMbVyeN5YL332E47K6HPDvNTu9I5cvGcvxA8/mkhmj6Tf1TwAce2ZnfjZlFJct+jv93n6IluecAkDLc07hxFv607x3Vy5fMpbLl4wloWZSuX/jqi8n0KhLW0KJCVy2+DkatE+N/O0zOnLVlxNo9bPTAajTpAFXfvEPaiTXObQHL8AsuyTFpR/OHPj00085/vjjy73Oxx9/TJ8+fQDo1asXn3zySZl1ZsyYwcknn1xqtsH3x2rUqAFAUVERxx13HHXr1gWgTZs2LFiw4LDvlyTFq6effpqsrCyaN29O165d97ve1q1buemmmxgzZkyZZffddx+XXHIJ48ePp0OHDgA0bNgQgH79+vk8K0kqpX7b46jXqinL//VBmWXLXp1G/dbNqN/mWADSB2TxwW1P8kL6FWz49hDBtAt7sOzV9xl3wiDmPvYqfZ65k7rNUg74d5Pq1KJx13T+deYQ/n3uUOq1bsbZf/8t8x//F+M7/IpP7n+eXqNvJaVja754YwbzHn2VNdlzeCH9Cl5Iv4Li3YUVun/homLWf/w5x/Y4EYBje57I1uVfcmyPTpHLPU5kw9xl7NmeX6Hbq04suyTFpR/OHMjLy6N169blXmfz5s3Ur18fgHr16rF58+Yy60ycOJELLrig3LFx48aRkZFBgwYNSEqKfCrjLANJ1d13M2/vu+++UuPp6emsXLkSiBySePXVVzNy5EiOO+64MrfRo0cPsrOzueqqq+jWrRsA27ZtAyLP+2lpkZP1rly5styZvJKk6qF2Sj0A8tdvLLMs/6tNkXUaRfb/F419iy15awgXF5eUTes++owvXs8lXFTMsgnvsemzlbQ+//QD/t1QQgKfPPAChfkFFOXvJu2CM1j/8eesmDSdcFExa96ZzRdvzqTtgF6HfR/XTZtfqtya86cXS8qvZt078eUH8w/7bwSRZZekuFKRmQOfffZZybm2vvv5wx/+QIMGDdi6dSsQefPUoEGDMtfNzs4umf21v7HLLruMhQsXsnbtWubNm1dp902SgiglJYWdO3cCkXMvvvPOOwwfPpysrCw++eQT1q1bx4MPPgjAyJEj6dOnD4899hi33HILAGeffTY9e/bkpZde4tprry25nXPPPTc2d0iSVGXs2hj5QKRO07Kzseo0icwM3rUhsv+/Y83XZdbZsbr02PZVX1doZldhfgEF3/5tgLrHNmL7D29r5XrqHtvogLd1IF9Om0fT0zpQs35d6rc5juX/+oDEmknUPTaFY3t04sv3fT+yL+UfKCpJVczgwYNLTgz/fe3ateOVV14BoEOHDuTk5JRZZ8aMGYwfP57zzz+f9957j5///Oelli9btowWLVpQs2bN/Y4VFBRQq1YtEhISqFevHrVr1wYiswy6d+9eWXdTkuLKdx8s7E+/fv2YOnUqZ599dsm5uL7vjjvuAOCee+7hnnvuKbXs448/LnW5sLCQr776qtTsXklS9bR16Vq2fbGetH5nsO4HM5zSLjiDbV+sZ+uyLwEIF5c9v+5RLY4pdTk59Ri+nnXgozXCxcWlLu/8ckOZb39MTm3Czi837HP9g7FxwQrCxcV0+K+f8dWMhYSLi/ly2nyOv+xs6jZpyFczFh7ybQeZM7skBUKXLl1YtGhRueuccsopFBQU0LNnT7p06ULTpk1LzSioyCGMr732GllZWZx55pm0aNGi5DCaJUuW0KlTp0q+V5IUDFdeeSVnn312pdxWUlJSyYnqJUnKvedZ0n/Rm47XnU+N5DrUqFeXDtf9jPSf9yZ3+N/KvW6z0zqQ2vdkQokJtLmoJw07tGLFfz466AzLJ35I024ZtDqvG6GEBJr37krqT05m6YT3AMj/ZgtHNW98yN8Cue7DBXS49jy+nBaZxfXlB/PocO15fPXJYooK9hzSbQadM7skxY3yZg4kJCTQuXNn8vLyyj2PyxNPPFHqcrNmzUpmFNx6661l1v/h2IABAxgwYECpsc8//5yTTjqp1EntJUmSJB15q6bMYOrAB+jy35fQ9Y7IkRsb5i5j6sAHSsqh/Vn+r2m0HdCLM5/4DTu+3ED2NX9i59oNB51h24p1vHP1H/nR/7uc7o/cyI7VX/PeTY+y8dsT4a+YNJ02F/bgl/OfIRQK8Y/Ogyt8knqAL9+fR+ufnc6X0yKz176cNp+a9Y/yfF3lsOySFBj7OrwxGjIyMsjIyIjJ35YkSZKquy+nzSu32Jpw6g1lxqYNeWIfax7YuukLeCH9ijLja7LnsCZ7zj6vs3vzdt64+H8qdPuhhMjsr++XYYuee5NFz71Zcjl//SaePfaSg0hd/XgYoyRJkiRJUhXQsGMrivcU7vOE+qo4Z3ZJkiRJkiR964KcR0hu0bjM+Ko3P+G9G/582Ld/9gt307TbCWXG92zfRUKNRD55YBy7t+487L9TnVl2SZIkSZIkfWtiVtlz+VamqZfff0RvXx7GKEmSJEmSpACx7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAiIuya/fu3QwfPpzU1FTq1KlDnz59yM3NJRQKMXHixFjHk1QJVu/Y+/vXu2KXQ5JUWmHx3t9nfgNF4dhlkSRVT4m1a3LRh49x+ZKxsY6iOFHly65wOMyAAQN46qmnGDZsGP/+979JS0ujf//+AGRmZsY4oaTD8eVOuHk69H9779h5b8JvZ8LmgtjlkiTBKyvgvLf2Xr7+Q/jZW/DvL2IWSZJUDWXe8Qu2r/4m1jEUR5JiHeBAxowZw+TJk5kzZw4dO3YEICsri7S0NFJSUmjZsmWME0o6VF/lw6/eh40F8P2JAsXAO2thyVb4W0+oVyNWCSWp+vp7Hjz2ednxr3fBiDmwowh+kRb1WJKkaqZR5zY0792VGb97jt5P3x7rOIoTVX5m16hRoxg4cGBJ0QWQmJhIWlpamVldv/vd7wiFQsyfPz/aMSUdgv9bHCm6ivexrBhYsR3GL4t2KknSN7vgiYXlr/PnBbB1d3TySJKqp1BiAmf86Xo+uuspincXxjqO4kiVLrvy8vJYvnw5F198cZllq1atKlV2zZo1i48++ohWrVpFM6KkQ7SzEP6zat9F1/dNWAFhzw8jSVE1aRUUH+C5d08xTF4dnTySpOqp0w0XsGHectZ/tI+pxlI5qvRhjGvWrAGgSZMmpcYXLlzIypUrS8qugoICbrzxRsaPH09WVtYh/a2srCwSEqp097dPnV6MnMm7Vq3aMU4SbD7Ola/Wce05/n/nHnC9jQVQt2FjivO3RSFV9eD2HB0+ztHh43xktLjx/2jQ41JCSfs/jjxcuIf/99AzDHrqligmCz636ejwcY4OH+foCMLj3DapIXfW71FqrF7rZrS/si+v/fiOGKWKX717Z7G0cFOsY1SKmjVrsm3bwb8XrNJlV6NGjQBYsmQJp556KhA5Yf3QoUMpLi4uKbvuueceBg4cSOvWrWMVVdJBKt6dX6H1wuFiwnv8ekZJiqbi3bsgFCp/pVCI4oKd0QkkSap2mp56AnUaH81FHzwKQEJSIjWOqsMvFzxD9uAHne2lclXpsisjI4P09HTuuusuatSoQXJyMqNHj2b27NnUrVuX9u3bM336dGbOnMkf/vCHw/pbOTk5dO/evZKSR8/Jr0X+LSjwa+uOJB/nyhcOwy9yYPm20ien/74EoFuTBD7ZsT2KyYLP7Tk6fJyjw8f5yPhgPfzm4/LXCSUm8eqoW/nRU7dGJ1Q14TYdHT7O0eHjHB1BeJzX5y7k9QuGlRpbPulD1r6/90iQY05qT4//vZHXzr6dXRu2RjtiXMnOzqHpqSfEOkZMVenj9pKSkpgwYQLHHnssgwYNYsiQIZx77rn06tWLzp07k5CQwLvvvsvnn39OWloarVu3ZvXq1fzkJz/hzTffjHV8SeUIheDK9P0XXRA5n9flbaOVSJL0ndObQOvk/e8oJgDtj4bMlGimkiRVJ0X5u9n55caSn4INWyEcZueXGz1ZvQ6oSpddAF26dGH69Ons3LmTRYsW8etf/5rZs2eXHML429/+lrVr17JixQpWrFhBixYtmDJlCn379o1xckkHcl4L+FW7yO/ffzL67vfbO8FpTX54LUnSkZYQgv/tBk3qRC5/d0Djd/82PwoePvXARzpKklRZ1k1fwAvpV8Q6huJElT6McV/y8/NZtGgRQ4YMiXUUSYcpFIIbM6B7E3hpBczdGBnrdgxc0joya0CSFBvNj4J/ZMG/V0W+PXdDARxTG85PhXNT4ai424uUJEnVRdztpsydO5eioqKSmV0/tGLFiugGknTYujaK/EiSqpbkGvDLNpEfSZKkeBF3ZVe3bt0Ih8s7y48kSZIkSZKqqyp/zi5JkiRJkiSpoiy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJirKcnBzS0tLIyspi0KBBZZaPHTuWqVOnAtCzZ0+Sk5NZvXp1mfVGjBhBZmYmWVlZjBs3DoAbb7yRHTt2HNk7IEkBVlnP0bNmzaJ79+706tWL+fPnA/Dwww/TvHlz7rvvvpL1fN6WpMpn2SVJUgwMHjyYnJwcjj76aKZPn15q2aRJkzjrrLMAeOmll7jkkkv2ezuPPfYYOTk5XHbZZQCcf/75/POf/zxywSWpGqiM5+iRI0fyyiuv8PLLL3PvvfcCMHDgQMaOHVtqPZ+3JanyWXZJkhRDnTp1Ys2aNSWXN27cSO3atQmFQgA0a9as3OsPGTKE8847jxUrVgBw5plnMmXKlCOWV5Kqk8N5jt6xYwdNmzalcePGJc/RTZo0ISGh9Fswn7clqfJZdkmSFEPTp08nPT295PKSJUto1apVha77m9/8hpkzZzJixAiGDh0KQN26ddm0adMRySpJ1c3hPEfXq1ePvLw8li1bxoIFC/a7ns/bklT5kmIdQJKk6ujpp59m6tSp9OjRg65dux7SbTRs2BCAU045hQ0bNlRiOkmq3irjOfr+++/nhhtuoEmTJvTs2bNyA0qSymXZJUlSDAwePJhhw4aVGU9PT2flypUVuo1t27ZRr149li1bxlFHHQXAzp07adCgQWVGlaRqpzKeozMyMnjrrbf44osvePjhh/e7ns/bklT5PIxRkqQqJCUlhZ07d5ZcHjhwIG+++SaXXnopb7/9NgC33XYbAEOHDqV79+4MGjSo5OTH7733Hn379o1+cEmqBg7mOXrMmDH07t2b3/zmN9x9990APPfcc9x22208++yz3HnnnYDP25J0JDizS5KkKMvKyiIrK2u/y/v168fUqVM5++yzef7558ssf+ihhwB48sknyyybNGkSo0aNqrSsklTdVNZz9LXXXsu1115batmVV17JlVdeWWrM521JqnyWXZIkVTE/fCN0MJ544olKTCJJ+qHDeY7eF5+3JanyeRijJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYll2SJEmSJEkKDMsuSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGHFTdu3evZvhw4eTmppKnTp16NOnD7m5uYRCISZOnBjreJIklSgo2vv7lztjl0OSVNbqHXt/31McuxySytfjzzdyxcrxXL5kbMlP895dYx1LcSIp1gEqIhwOM2DAAHJzcxkxYgTp6emMGzeO/v37A5CZmRnjhJIkQWExPL0Y/rF871i/qdDtGPjvTtCmXuyySVJ1t3gLPLIAZnyzd+ycKXBZW7iqHSSGYpdN0r4tfn4qH9/9dKxjKA7FRdk1ZswYJk+ezJw5c+jYsSMAWVlZpKWlkZKSQsuWLWOcUJJU3RWHYdgsmLq29HgYyP0afvU+PNMD2taPSTxJqtYWboFrpsHuotLjW/bA6IXwxXYYkQkhCy9JCoS4OIxx1KhRDBw4sKToAkhMTCQtLa1kVlfr1q054YQT6Nq1K127dmXKlCmxiitJqobeW1e26PpOMZBfBA/Oi2okSdK3fv9ppOja31GL/1kNud/sZ6GkmGlzUU8u/exvXPjen+n8m4sIJcZFhaEqoMrP7MrLy2P58uU8+uijZZatWrWKiy++uOTyhAkT6NSpUzTjSZIEwIQVkBCKzPDal+IwzNwAK7dDq+SoRpOkam3xFliwufx1EkIwYXnksHNJVcNnT09m5r1j2bVxG406t6HXk0NIrFWT2X/8R6yjKQ5U+bJrzZo1ADRp0qTU+MKFC1m5cmWlna8rKyuLhIT4a4k7vbgLgFq1asc4SbD5OCtI3J6PjBP+7wtqNGh6wPVOPncAW3Nfi0Ki6sHtWUHjNl35GvS8lNRbni13neIwvDFnGY/2zIhOqGrC7Tk6gvA4t01qyJ31e5Qa2zhv70lQN3y6lNl/+ieZt//CsqsCevfOYmnhpljHqBQ1a9Zk27ZtB329Kt/uNGrUCIAlS5aUjIXDYYYOHUpxcXGpsuvyyy+nc+fO3HDDDWzevDnaUSVJ1Vh4T0HF1ivcc4STSJK+r7jCz88VW09SjBSHwfPqqYKq/MyujIwM0tPTueuuu6hRowbJycmMHj2a2bNnU7duXdq3bw/A+++/T2pqKgUFBQwZMoSbbrqJ559/vsJ/Jycnh+7dux+pu3HEnPzt5ICCAl+cjyQfZwWJ2/ORMWouvLxi/+eDAaiVACve+xfJNaKVKvjcnhU0btOVb3MBnPMmFO7nMHOIvH++NiuDW3zcK5Xbc3QE4XFen7uQ1y8YVmqsdb8zWJM9hz3bdtIwoxVdbhvAin9Pj1HC+JKdnUPTU0+IdYyYqvJlV1JSEhMmTOD6669n0KBBpKamMmTIEOrXr8/SpUtLDj1MTU0FoFatWtxwww3069cvlrElSdXMgDR4eSWRr1/chxDQvxUWXZIUZQ1qwXmp8NoX+36KDgGJIbioVbSTSSrPCVf9hNNHXUtCjUTy129m6YR3mfvYq7GOpThR5csugC5dujB9eukG9/HHH6dXr14A7Nixg8LCQo4++mjC4TD/+Mc/6Nq1awySSpKqqzb1YGQm3DMbCO+d4ZVA5PdTGsPNHWKXT5Kqs9s7Rb4gZM7Gvc/LEPk9IQS/PxlaHBXDgJLKeOOi/4l1BMWxuCi7fig/P59FixYxZMgQANavX8/FF19MUVERRUVFdOjQgSeffDK2ISVJ1c45LaBtPXhxBWR/CbuLIyXYJa3hnOaQVOXPlClJwVQnCZ48HV5fEznkfMV2qJ0AfY6Dn6dFnqslScERl2XX3LlzKSoqKjk5fZs2bZg9e3aMU0mSBO2Ohru7RH4kSVVHzUS4oGXkR5IUbHFZdnXr1o1wuJwzTEqSJEmSJKla8oAKSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAWGZZckqUROTg5paWlkZWUxaNCgMsvHjh3L1KlTAejZsyfJycmsXr26zHojRowgMzOTrKwsxo0bB8CNN97Ijh07juwdkCRJUomD2bcD+Ne//kW7du3KrPfee+/RrVs3unXrxsSJEwF44403OP300+nbty9r164F4Fe/+hXhcPgI3Rup4iy7JEmlDB48mJycHI4++mimT59eatmkSZM466yzAHjppZe45JJL9ns7jz32GDk5OVx22WUAnH/++fzzn/88csElSZJURkX37QBefvllUlNTy9zGI488wquvvsq7777Lo48+CsCoUaPIzs7m4YcfZtSoUQB069aN7OzsI3hvpIqx7JIqwYE+Mbn//vvJy8sr9zZuvvlmevbsyQMPPFBq/I033iArK4usrCwaNWrEnDlz9jmWm5tL9+7dOeOMMxg2bBgAn3/+eckLj3SwOnXqxJo1a0oub9y4kdq1axMKhQBo1qxZudcfMmQI5513HitWrADgzDPPZMqUKUcsryRJkvbvQPt277zzDj169CAhoWxN0K5dO7Zs2cKOHTuoV68eAElJSdSuXZuOHTuSm5sLQO/evZk8eXIU7o1UPssuqZLs7xOT4uJi5s6du8/pwN+ZOXMmSUlJvP/++8yaNYv169eXLDvnnHPIyckhOzubNm3a0KVLl32OZWZm8sEHH/Dhhx8yffp0tm7dSkZGBrNmzXIqsQ7J9OnTSU9PL7m8ZMkSWrVqVaHr/uY3v2HmzJmMGDGCoUOHAlC3bl02bdp0RLJKkiSpfAfat3vmmWf2+cE9wAUXXMBPfvITunTpwvXXXw/Anj172LBhA9OmTWPjxo0AtGrVisWLFx/BeyFVjGWXVMl++InJp59+yvHHH1/udT7++GP69OkDQK9evfjkk0/KrDNjxgxOPvnkkk9efjhWo0YNAIqKijjuuOOoW7cuAG3atGHBggWHfb9UfTz99NNkZWXRvHlzunbteki30bBhQwBOOeUUNmzYUInpJEmSdDAqsm83c+ZMOnToQO3atfe5fPjw4cyYMaPUkSP33Xcfl1xyCePHj6dDhw5HKr50SCy7pEr2w09M8vLyaN26dbnX2bx5M/Xr1wegXr16bN68ucw6EydO5IILLih3bNy4cWRkZNCgQQOSkpIAP13RwftuluJ9991Xajw9PZ2VK1dW6Da2bdsGwLJlyzjqqKMA2LlzJw0aNKjUrJIkSSpfRfbt5s+fz1tvvcU555zDnDlzuP/++0utm5iYSP369albty4FBQUA9OjRg+zsbK666iq6desGwMqVK8s9okWKFssuqZJU5BOTzz77rORcW9/9/OEPf6BBgwZs3boViJQE+yoEsrOzS2Z/7W/ssssuY+HChaxdu5Z58+ZV2n2TAFJSUti5c2fJ5YEDB/Lmm29y6aWX8vbbbwNw2223ATB06FC6d+/OoEGDuPfee4HIt/j07ds3+sElSZJUxvf37a666iqys7N544036Nq1K3fffTewd99uyJAh9O7dmzPOOIOrr74agJEjR9KnTx8ee+wxbrnlFiDy/uTcc8+Nwb2RSkuKdQApKAYPHlxyYvjva9euHa+88goAHTp0ICcnp8w6M2bMYPz48Zx//vm89957/PznPy+1fNmyZbRo0YKaNWvud6ygoIBatWqRkJBAvXr1SqYgr1y5ku7du1fW3VTAfVfC7k+/fv2YOnUqZ599Ns8//3yZ5Q899BAATz75ZJllkyZN8gsTJEmSouhg9u2+M3Xq1JLfv9u3O++88zjvvPNKXfeee+7hnnvuKTX28ccfc+2111ZCcunwOLNLOsK6dOnCokWLyl3nlFNOoaCggJ49e9KlSxeaNm3KunXrePDBB4GKHcL42muvkZWVxZlnnkmLFi1Kpg8vWbKETp06VfK9UnV15ZVXltoZOhhPPPEEycnJlZxIkiRJh+pw9u325W9/+9s+v81RijZndkmVoLxPTBISEujcuTN5eXnlHr/+xBNPlLrcrFkz7rjjDgBuvfXWMuv/cGzAgAEMGDCg1Njnn3/OSSedVOqk9pIkSZIkBZlllxQF+zq8MRoyMjLIyMiIyd+WJEmSJCkWnF8oSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAWGZZckSZIkSZICw7JLkiRJkiRJgWHZJUmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBhxU3bt3r2b4cOHk5qaSp06dejTpw+5ubmEQiEmTpwY63gKsC279/5eWBy7HFJl2F209/cdhbHLIUmSpMO363v7drvct5NKJMU6QEWEw2EGDBhAbm4uI0aMID09nXHjxtG/f38AMjMzY5xQQbQuH578HN5cs3fs/Lfg0rYwsC0khGKXTTpYu4vg6Tx4afnesb5vwM9S4YYMOLpm7LJJkiTp4OQXwl8Xwasr9471nQIXtIJfnwB14+KdfsW0OOtHZA79JfXbHkfh9nzm/2USC0a/FutYquLi4n+BMWPGMHnyZObMmUPHjh0ByMrKIi0tjZSUFFq2bBnjhAqadTth0PuwqQC+P5nr6wJ49DNYshV+lwkhCy/FgcJiuDUXPv669HhBMbyyEmZugGd6WHhJkiTFg12F8OsPYcFmCH9vfGcR/GMZzNkAf+0ejMLruF5dOP3B65h2y+Osm76ApDq1OKp541jHUhyIi8MYR40axcCBA0uKLoDExETS0tJKZnXt2rWLX//617Rr144TTzyRa6+9NlZxFQB/ml+26Pq+yavh3XVRjSQdsldXli26vhMGvtgOf1kY1UiSJEk6RM8vg/mbSxdd3wkDC7fAc0uiHOoIybzzl8z988t8OW0e4aJi9mzPZ/OiVbGOpThQ5cuuvLw8li9fzsUXX1xm2apVq0rKrjvvvJPatWuzePFi5s2bx7333hvtqAqIr/IjRVZ5p+dKCMFLK6KVSDo8Ly6H8iYhhoFJqyLT4SVJklR1FYVhwvLy1wkDL6+I//MNJ9WpReOubalzTAP6v/+//GLuU/R5dijJqU1iHU1xoMpPbFyzJnLCpCZNSm/QCxcuZOXKlWRmZrJ9+3aee+45Vq9eTejb48qaNm16UH8nKyuLhIQq3/2V0enFXQDUqlU7xkmCI7nrT0i7u/xjwIvD8MGyjdTKOjZKqaRDlJjEif/YccDVdhVBs4yT2PXF/CiEkiqPr4MKGrdpBYnbc+VLOroJGU8deGbTpt1wdPM2FG5cc8B1q4K2SQ25s36PUmM1GxxFKCGBVud1461L7yN/wxZOHfkrej99B5P63hGjpPGhd+8slhZuinWMSlGzZk22bdt20Ner8u1Oo0aNAFiyZO88zHA4zNChQykuLiYzM5OlS5fSqFEjfve733HyySeTlZXFtGnTYhVZ8a64gtNbiosOvI4Ua+FiwuGKfawXdpuWJEmq0sJFBzEVP8737fZsj5Slnz01me2rv6Yofzezfj+ORiemed4uHVCVn9mVkZFBeno6d911FzVq1CA5OZnRo0cze/Zs6tatS/v27ZkzZw7Lli0jMzOTBx98kI8//pjzzz+fJUuWUL9+/Qr9nZycHLp3736E703lO/nbCUgFBQWxDRIg2/fAT6ZETt69PwlAv47HMMfHXXHgug9g9obyD81tXAs+yptDUpX/CEQqzddBBY3btILE7bnyhcNwaQ4s3bbvc3ZB5PQVrZJhxrqVcfOFWutzF/L6BcNKje3ZtpPtq76K3GkdlOzsHJqeekKsY8RUlX9bk5SUxIQJEzj22GMZNGgQQ4YM4dxzz6VXr1507tyZhIQEWrZsSVJSEpdeeikA3bp1o3HjxixevDjG6RWPkmtEvrK3vNeFYuDnadFKJB2eS9uUX3QB/KINFl2SJElVXCgEl7Xdf9EFkWWXtgnGN8cveu5NMq45j7rHNSKxVg0y7/wl33y6lB1rvol1NFVxVX5mF0CXLl2YPn16qbHHH3+cXr16AdC4cWN69+7NW2+9Rd++fVm8eDFfffUV6enpsYirALglAxZvgTkbI6XXdy8mCaHI+bpu7wSdGsYyoVRxWcfCVenw7JLIJxzfFV/f/Z7VDK5oG7t8kiRJqrjzU2Hepsg3bu9r3+78VOjfKnb5KtO8JyZS8+hk+r35Rwgl8FXuQrIHPxjrWIoDcVF2/VB+fj6LFi1iyJAhJWN/+ctfuPrqq7ntttuoUaMGY8eOpUGDBjHLqPhWOwmeOB0mfhH5JruV2yExBD2awi/bwMkeIq44c1MH6JwC/1wOM7+JlLbHHx2ZoXheamT7liRJUtUXCsFdneHUxpF9u7kbI+OdGkZm6/c9LhizugAIh/nk/uf55P7nY51EcSYuy665c+dSVFREZmZmyVibNm3IycmJXSgFTq3ESBHw87RIMRAiQC8aqpbObBb5CYcjsxUT3J4lSZLiUigEP24e+fnulFa+V5H2isuyq1u3boQ9SZ2iyFJAQRIKlX9OOkmSJMUPSy6pLE9HLEmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOwKsJycHNLS0sjKymLQoEFllo8dO5apU6cC0LNnT5KTk1m9enXJ8gceeICePXty8803l7nu119/Tf/+/enduzdjxowB4Fe/+hXhcPgI3RtJkg5eRV8LFy1aRPfu3enZsye33nprmfXeeOMNTj/9dPr27cvatWsB6N27N1lZWWRlZfHZZ59RWFjINddcc8Tvk6qvw923+86sWbPo3r07vXr1Yv78+QA8/PDDNG/enPvuu69kvRtvvJEdO3YcoXuj6u5gtmeAf/3rX7Rr167Meu+99x7dunWjW7duTJw4Edj3c7bvVaTqxbIr4AYPHkxOTg5HH30006dPL7Vs0qRJnHXWWQC89NJLXHLJJSXL1q9fz6xZs3j//fdJSkpi5syZpa47cuRI/vznP5Odnc21114LQLdu3cjOzj7C90iSpINTkdfCxo0bM2XKFN5//32++eYbFi9eXGq9UaNGkZ2dzcMPP8yoUaMASExMJCcnh5ycHDp06EBSUhLHHHMMS5cujdp9U/VzqPt23zdy5EheeeUVXn75Ze69914ABg4cyNixY0utd/755/PPf/7zCNwLKaKi2zPAyy+/TGpqapnbeOSRR3j11Vd59913efTRR4F9P2f7XkWqXiy7qolOnTqxZs2akssbN26kdu3ahEIhAJo1a1Zq/ZkzZ9KrVy8A+vTpQ25ubqnlixcv5re//S19+/Zl0aJFQOQT7smTJx/JuyFJ0iEr77WwUaNGJCcnA5ES67vXx+8kJSVRu3ZtOnbsWPKaGA6HycrK4pprrmHXrl0AZGVl8frrr0fpHqk6O9h9u+/bsWMHTZs2pXHjxqxYsQKAJk2akJBQ+q3BmWeeyZQpUyo/vPQDB9qe33nnHXr06FFmGwVo164dW7ZsYceOHdSrVw/Y93O271Wk6sWyq5qYPn066enpJZeXLFlCq1at9rv+5s2bqV+/PgD16tVj8+bNpZZPmzaN++67jyeeeIK7774bgFatWpX5JFySpKqiIq+FCxYs4JtvvilzqMyePXvYsGED06ZNY+PGjQBMmDCBnJwcMjIyePrppwFfCxU9B7tv93316tUjLy+PZcuWsWDBgv2uV7duXTZt2nTYWaUDOdD2/Mwzz+zzUEeACy64gJ/85Cd06dKF66+/Htj3c7bPz1L1khTrADqynn76aaZOnUqPHj3o2rVrha/XoEEDli1bBsC2bdto0KBBqeUdO3akbdu2AGzZsqWy4kqSVOkq+lq4detWbrrpJl544YUyy+677z4uueQSMjIy6NChAwANGzYEoF+/fjzyyCNHJLv0Q4e6b/d9999/PzfccANNmjShZ8+elRtQOggV2Z5nzpxJhw4dqF279j6XDx8+nBkzZlC3bl369evHOeecs8/nbEnVi2VXwA0ePJhhw4aVGU9PT2flypX7vd5JJ53Es88+y80330x2djaXXXZZqeWtW7fmm2++oaioiLp16wKwcuXKfZ40UpKkWKrIa2E4HObqq69m5MiRHHfccWXW7dGjB9nZ2eTm5vLOO+8AkQ+D6tWrx/Tp00lLSwN8LdSRd6j7dt+XkZHBW2+9xRdffMHDDz+83/V27txZ5gNPqTJVZHueP38+b731Fu+99x5z5szh/vvvLzmyBCKHntevX5+aNWtSUFAA7Ps52+dnqXqx7KqmUlJS2LlzZ8nlgQMH8s4777B06VJGjBjBWWedRefOnenZsyedO3fm5JNPZt26dYwdO5Y77riDYcOGcdFFF1FYWFhyIsjs7GzOPffcWN0lSZIOyvdfC3NycnjnnXf45ptvAHjooYdo3rx5yeveyJEjycnJoXnz5vz1r38F4Oyzz6ZmzZo0aNCA559/vuR2Bg8eHJs7pGqtIvt2t912Gw899BBjxoxh/PjxNGjQoORbtZ977jn+93//ly1btrB161b++Mc/8t5779G3b99Y3SVVY9/fnq+66iquuuoqIPK8+13R9d32PGTIEHr37k04HOa//uu/APb5nO17Fal6CYWr+fevfvDBB/To0YNp06bRvXv3WMc5aCe/Fvl3Zr+Dv+5zzz3Hcccdx9lnn10pWX71q1/x9NNP7/PEkZIkHQmH8zoIlftaWFhYyHXXXVdy/i7pUFSlfbsbb7yRUaNGlXx5g3SwqtL27HuVqm197kJev6DsLD8dmnMn3kfTU0+IdYyYcmZXNXbllVdW6u397W9/q9TbkyTpSKvM18KkpCSLLsVUZe/bPfHEE5V6e9LB8L2KpMNhrS1JkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYll2SJEmSJEkKDMsuSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAVG3JRdu3fvZvjw4aSmplKnTh369OlDbm4uoVCIiRMnxjpeTOwojHUCSZKqhu17Yp1AOnxuxwqS3UV7fy8Oxy6HpOopKdYBKiIcDjNgwAByc3MZMWIE6enpjBs3jv79+wOQmZkZ44TRtXoHPL0Y3lizd+yq9+CqdpB1bOxySZIULe+vg7/l7b189hvw4+bwX8dDy+TY5ZIOxbJt8NQiePvLvWPXToOrj4fTmsQul3Qotu+JvFd5deXesf5vw2VtYUBrSAjFLJrizOVLxpa6nFizBpvz1vDaWbfFKJHiSVyUXWPGjGHy5MnMmTOHjh07ApCVlUVaWhopKSm0bNkyxgmjZ/k2GDwt8iJS/L3xzzbD7TPg1o5wedtYpZMk6ch7aTmMmld6enphGKasiZRgT/WA9PoxiycdlM82w3UfQEFR6X27ORvh5o/gnq5wfvXZ1VWc27Yn8l5l+Tb4/mSutTvhwXnw2Sb4n0wLL1XMC+lXlLrc7+2HWD7xgxilUbyJi8MYR40axcCBA0uKLoDExETS0tLIzMxkxYoVdO3ateSndevWpKSkxDDxkfM/s2F7YemdIdh7+ZEFsGJbtFNJkhQdq3fAH+dFfi/zWhiGnYVw9ycQ9pAZxYHiMNw1s2zRBZHLYeDeT+HrXTEIJx2CJz4vW3TB3sv/WQ1vrY12KgVB467pNDi+BUv+mR3rKIoTVb7sysvLY/ny5Vx88cVllq1atYrMzExat27NnDlzSn4uvPBCLrvsshikPbI+3xz59K+8Y95DwMsr979ckqR49soBXuOKgaXbYO6mqMSRDkvu17B6Z9mi6/uKw/Av9+0UB7bvgUlflC26vi8BeHF5tBIpSNpd1oc178wmf70v8KqYKn8Y45o1kRNTNWlS+oQFCxcuZOXKlWXO17V7925eeOEFpkyZclB/Jysri4SEqt39pfS9jub/9Wi564SBp6fkctdJPaMTSpKkKEob8RbJHc884HrnXnMHG/5T/mumFGvHXPRbmv7yfwiF9r8PGi4u5sHxU7jp9xdGL5h0COq0O5X0B94vd51iYM5Xu6lVq150QilutE1qyJ31e+xzWVKdWqRd0J33b3k8yqniV+/eWSwtDEYxWLNmTbZtO/jD16p2uwM0atQIgCVLlpSMhcNhhg4dSnFxcZmy67XXXqN58+b86Ec/imrOqAiX97nf99fz2A1JUkCFiwlX5HXO10LFA/ftFCQV3J7dnHWwWp9/OoX5u1k99ZNYR1EcCYUrtMcYO4WFhWRkZLBnzx4efPBBkpOTGT16NLNnz2bjxo1s27at1Iysn/70p5xzzjnccsstFbr9rVu3Mm/ePE488UTq16/aZ7NduhV+kVP+OiFgUDrc1CEaiSRJiq6/LoSnFpd/mAzA82fCCQ2ikUg6dHM2wDUVONfyLR3gyvQjn0c6HLsK4Sdvwo7C/a+TEIJTGsMTp0cvl+LD+tyFvH7BsH0uO3fivXz18UI+eeCFKKeKX+dOvI+mp54Q6xgxVeVndiUlJTFhwgSOPfZYBg0axJAhQzj33HPp1asXnTt3LlV0rVmzhnfffZfLL7+8wrdfv359unfvXuWLLoC29eFHjcr/jxYC+reKViJJkqKrf6vyv8UrAejUwKJL8aFLCrStt/9tOgTUTIB+qVGNJR2S2kmR5+jyvmixOAw/T4taJAVA/bbH0eTk9iwe/3asoyjOVPmyC6BLly5Mnz6dnTt3smjRIn79618ze/bsMocw/v3vf+e8884rOfQxiEZmQuPaZV9EEoiM3dMVmh8V/VySJEVDkzrwu8zI694PC4IQ0LAW3HdSLJJJBy8UglEnQ/0a+9i3C0V+HjgJGtSKSTzpoF3fHk5sWHb8uzedl7eBM5tGNZLiXLtL+7D+48/ZtnxdrKMozlT5E9TvS35+PosWLWLIkCGlxp999lkefTTYJ6NtVhfGngnPL4VXV8L2wsjOUfemcEV6ZOaXJElBdk4LOLYujF0C766LHNJ4VBJc0DLyWnhM7VgnlCqudb3IYbdjl8JrX0B+UaTk6tMMBqZDp30UB1JVVTsJnjwD/rkMXloB6/Ij4x0awmVt4MfHRUpeqaI+ue/5WEdQnKry5+zal48//pjTTjuNGTNmcPLJJ8c6TswUhWHHHqiVGPmRJKm62V0Eu4rgqBqQ6BsoxbnC4sj5juokQk337RTnwuHI9pwYgjpxOcVC0VTeObt08DxnV5zO7OrWrVvFvokp4BJDUL9mrFNIkhQ7NS0FFCBJCXC0+3YKiFAIkmvEOoWk6iouztklSZIkSZIkVYRllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkwLLskSZIkSZIUGJZdkiRJkiRJCgzLLkmSJEmSJAVGKBwOh2MdQpIkSZIkVU+7t+1k0+dfxDpGYDTMaEnNenVjHSOmLLskSZIkSZIUGB7GKEmSJEmSpMCw7JIkSZIkSVJgWHZJkiRJkiQpMCy7JEmSJEmSFBiWXZIkSZIkSQoMyy5JkiRJkiQFhmWXJEmSJEmSAsOyS5IkSZIkSYFh2SVJkiRJkqTAsOySJEmSJElSYFh2SZIkSZIkKTAsuyRJkiRJkhQYll2SJEmSJEkKDMsuSZIkSZIkBYZllyRJkiRJkgLDskuSJEmSJEmBYdklSZIkSZKkwLDskiRJkiRJUmBYdkmSJEmSJCkw/j9LifqWWSxP3wAAAABJRU5ErkJggg==", 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" ] }, - "execution_count": 16, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "ucj_op = ffsim.random.random_ucj_operator(norb=norb, n_reps=1)\n", + "ucj_op = ffsim.random.random_ucj_op_spin_balanced(norb=norb, n_reps=1)\n", "\n", "circuit = QuantumCircuit(qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n", "\n", - "circuit.decompose([\"ucj_jw\", \"diag_coulomb_jw\"], reps=2).draw(\"mpl\", scale=0.7)" + "circuit.decompose([\"ucj_balanced_jw\", \"diag_coulomb_jw\"], reps=2).draw(\"mpl\", scale=0.7)" ] }, { - "attachments": { - "779ec75b-28ff-47e5-b7c0-609fe7e8c53b.png": { - "image/png": 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qJ4iMjMSUKVNw/fp1Q91+BdDFFLlhOVZKCCF++gFxs1w1Gg169+6N/v37Z3sTjI6OxsmTJ3H16tUM9oCHDx8ajCl3d3eXsf/UrFkT1apVy7aV98SJEwgNDTXkmkwF0JdS+n22bpxHQAh5C8A+SFW7GdjZ2aFTp04YOXIknJ2zxz4ZExODyMhIXL16NYPB5cGDBwbD5woVKpTBEuPn54fq1avj/fffz7YSeunSJUyaNMmQVYcC+IpSOitbN84j0Id/bAfQnHddpVIhMDAQ48ePR5Ei2SvknZ48d+XKlQy53rt3z2CugEajga+vbwajiL+/P2rXrp1tZeXOnTuYPHky/vzToOF8MYBh+ZHcQB/+sQFAe1GfJk2aYMqUKShZMsscSxliY2MRGRmJixcvZjC43LlzB8nJ4vOig4MDfHx8Mth/qlSpgjp16mT7YPXkyRPMnj0bO3bsMNQtHJLXJFtUfHkB+giEOQBGivoEBARgypQp2SaaiI+Px8mTJ3H+/HkZS5ohUgk7Ozt4e3tnsP9UrFgRAQEB2bbev3r1CosWLcKmTZsMrft/AGiTX+n5CSFDAcyHwDBUqVIlTJ06Ff7+2SItRVJSEs6cOYNz585lrMM3b940mAOiVqvh5eWVIdcKFSogICAg26F/SUlJ+O6777BixQpD68NFAC3ya9FqQkhnSIom98Dr6+uL0NBQfPDBB9m6b0pKCqKionD69GkZ+92rV68MjQUlS5ZE2bJl4evriwoVKqB27drZXit0Oh02btyI+fPnG3qP7gD4OKc07jlSSgghtSFR+3EL5TVo0ACzZs0yWhNMj2c7cOAAIiMj8eTJkzceW2ZoNBrUrFkTjRo1QuvWrVG8uHF1/ZKTk7F48WKsXLlSZF2nkNi5FphkoFYCfVLWrwDK8K5XqVIF3377LcqWLWvU/XQ6Hf7880/8+uuv2WV6MAgHBwdUq1YNDRs2RGBgILy8vIwez4YNGzB79mxD1vU5kFhh8o0FNitF09fXF/PmzUPVqsbVW6OU4vTp09izZw8iIyOzCsswGmq1GlWqVEGDBg3w6aefZmsB3blzJ0JDQw3lm/wAKR8h3+QP6T2a4QC47koPDw/MmTMHDRoYz9x94cIF7NmzB8ePH8fVq1eNZSs0CJVKhQoVKqB+/fpo3bo1KlcWRiExOHLkCMaMGYNnz4RpJL8BaJufLLB6RXMdpKrdDFxdXTFlyhQEBgYafc/o6Gjs2rULx44dw8WLF7PKozQafn5+qFu3Llq1aoWaNWsaTVhz7tw5jBgxAnfv3hV1OQOgJaXUNIcBK4Be0ZwLYATvuoODA8aMGYMuXboY7b24f/8+du3ahaNHjyIqKsqgwSA7SGdE/eSTT1C/fn2jre7R0dEYMWIELl26JOpyE9IBNsuElLwEQsgISLJlJoBarUb//v0xcOBAow30z549w+7du3HkyBGcOXPGGNIIo5DOiNq8eXM0adLEaLa2hw8fYvTo0YiIiBB1eQppvr5xHaI3VkoIIU0gbYRM1qtarcbAgQMxcOBAo17iCxcuYOvWrdi7d69Brc8UUKvVaNSoEdq2bYvmzZsbNb7IyEiMGDHCkJK0CJIFNs8fYAkhNSAVuOKavjp06IBJkyYZ9RJHR0djy5Yt2L17d3Z57LMNlUqF2rVro23btmjVqhUcHbOm67906RKGDBliiLN7E4Ae+eEAq09o/xWCyt0ff/wxvvnmG6OS2O/fv4+ff/4Z4eHhJlMwDcHf3x/BwcEIDg42yoMSExODoUOHGvKG/Q4gOD/QyxJCikIyDHEL0gYEBGDevHlGWbKfP3+eIVcjkldzjHfeeQdBQUFGswc9f/4cI0eOxLFjx0RdTgNolR8OsHoGy60QEBVUqlQJixYtgo+PT5b3io+PR3h4OMLDw3H+vPlTq7y9vTNYoYwxFMXHx2PChAnYs2ePqMstAB/lhwOsnu53JYCevOtvv/02Fi1aZJR35PXr19izZw+2b9+OU6dOmcRwYAienp749NNP8fnnnxtlKEpOTsasWbOwfv16UZfHkA6wf5tynLkBvaIZqv/HoGjRovj222+N8o7odDocOHAA27dvx9GjR01mOBDB3d0drVq1wmeffWaUoYhSiu+++w7z5s0TjS0BQLs3Zb98I6WEEPIRgN3gsAl4enpi4cKFRuWOREZGYvny5fjrrzdLzVCpVLCzs3tjq0Dp0qXRr18/BAcHZ6m5PnnyBMOHD8eJEydEXeZRSoUu9rwAQkh1SC5z5mTq6uqKWbNm4aOPsmS0w8WLF7F8+XL89ttvb7xQphdjexN4enqiV69e6NixY5bx1XFxcfjqq6+wf79w/myBFBqSZ0N+9MXVjoET3+ro6IiJEyeiQwdh2lAGbt68iZUrV2Lnzp3ZLUaagZzItXDhwggJCUHXrl2zDAN6/fo1ZsyYgR9++EHU5QikEII8G/KjV0j+BPCe8ppKpcKQIUMwYMCALK2tjx49wqpVq/DTTz+9sSUuJ3LVaDTo0KEDevXqlaVXXafTYenSpViyZIlobbkIoBGlNEteS2sFIUQDYD+AhrzrISEhGDt2bJaGoZcvX2LdunXYuHEj/v33zSKgciJXe3t7BAUFoW/fvkYl8W7atAkzZswQ7ecxABrkZWYufc5XGKTipQxatmyJGTNmZEnbnJiYiB9//BFr1qx5Y2NfTuSqUqnw0UcfYcCAAXjvPWbpYbB//36MHTtW5L1+BaAxpfTcGw3GSkAImQdgOO9a3bp1MX/+/CwjdNJJPlauXIl79+690TgcHByQmpr6xueuBg0aYODAgUaf34cPHy56B18DaE0pPZjdMWRbKSGE1AJwCJw6FaVLl8a6detQunRpg/e4dOkSpk6dalQtiVKlSmXEwKXHJxcrViyjijDwX/L7q1evcO/ePdy+fRvR0dE4d+4cLl26lKWmWbJkSXz55ZcIDAw06HbW6XQYP348fv75Z1GXMZTS2Vn+UVYIfW7QMQBvKa95eHjg+++/R8WKhinxb9++ja+//hqHDx/O8vc8PT1Rp06djMruvr6+8PDwyKhMCvyX/B4fH4+YmJiM2Njz588jKirKUOgVAImJZtCgQejcubNBjxilFHPmzMF3330n6rKcUjogyz/KCqFnAPkTHCpnZ2dnLFu2LMuwnidPnmDWrFnYvXt3lotdkSJFULt27YyKwmXKlIGnp2dGQmU60pPf79+/nxHPfunSJfz9999ZHoydnZ3Rq1cv9O3bN0uP2IYNGzB9+nTRuHcB+B+l9M00rFyE/uD6GziFae3t7TF37ly0atXK4D3+/fdfzJ8/H2FhYVnOpUKFCmXINT1fr2TJkkxSe3ry+8OHD3Hz5k3cvHkTV69eNapQooODA7744gsMHTo0y0T5X3/9FSNGjBAxJZ4A0DQvUkHrLek/AWjLuYaxY8eiZ0+ukT0DSUlJWLFiBdasWZPlXNJoNKhRowYqVaqUkYvp5eXFJLWnE5A8efIkY76myzWrQolqtRpt2rTBqFGjsqSdjoyMRL9+/UQH2BsA6udVTxghZCEkhlIGXbt2xYQJE7I8f2zYsAFLly7N8pnb29ujWrVqqFq1akYupre3N5PUrtVqkZiYiKdPn2bkFF27dg0nT57MMnyeEIImTZpg/PjxWZ75rl27hu7du+PxYy5p6VNICuc1gzexUhBCvoJUtJdBmzZtMGvWLIM5zZRShIeH49tvvxU9nwyo1WpUrlwZ/v7+8PPzg6+vL0qXLg03NzdZUntSUhK0Wi2eP3+eMV9v3LiBU6dOGRXdULt2bUycODHLM19MTAx69OiBmzdv8i4nAmhGKRXGevGQLaWEEFIO0sGVMWdVqVIFa9asQdGiRYXfj4uLw7x58/Djjz8KFQW1Wo169eqhZcuWJqn+HRcXh5MnT+LgwYPYt2+fwdoGderUwdSpUw26JimlmD17NlatWsW9DKBXXkt+J4R4Qjq4llde8/b2xrp16wyGCbx+/RorVqzAd999J6RTJoTg/fffx6effoq6devmuPq3VqvF6dOncfjwYezevdsQkwsqVqyIadOmoVo1bipFBtatW4cZM2aIDrATKaXTczRoC4MQ4gyJwrqu8lrx4sXx/fffG7R0pSe3LViwwOC8ee+99xAYGIj69evnuPp3cnIyzp07hyNHjmDnzp149OiRsK+Pjw9CQ0PRsCHXoJyBnTt3YsyYMSLvzgZIjGt5JvRSX8R0BzhUkxqNBsuWLTMYJkApxc6dOzFz5kxDORooU6YMAgMD0bBhwxxX/9bpdLhw4QKOHj2KXbt24fbt28K+np6eGDt2bJa5EhEREejfv7/o3dwLICgvKZz6EJBV4IT22NvbY/bs2fj0008N3uPw4cOYMmWKwYNHyZIl0aZNGzRq1AjVqlXLEQtbWloarl69imPHjmHXrl0GixG7ublh+PDh+OKLLwy+SxcvXkTPnj1F9WpOAWiS13KHCCGTwQntIYRg1KhR6NOnj8Hv//3335g0aRKuXLki7FO0aFF8+umn+PDDD01S/Ts6OhrHjx/Hnj178PfffwsJhhwdHdGvXz/06dPHoJEoJiYG3bt3x61bXNb9aEiKiXjBt0IQQrpAov1ltMmQkBBMmDDB4H547do1hIaG4tSpU8I+rq6uaNGiBZo3b45atWrlmNkwJiYGERER2Lt3LyIiIgyexbt06YJhw4YZ9N7Fxsaid+/eOHv2LO/yM0hyNTr53WilRE/7ewIAczqtW7cuVq5caZCF6fjx4/jyyy+F2nfJkiXRpUsXBAUFmY2HOykpCb/99ht++OEHnD7Nz8Oxs7PD8OHD0adPH4NWi2XLlmHevHm8S6mQ3Fa/mmTQZoY+dvkYOMnPFStWxLp16wzGe1++fBlDhw4VLTQoUqQIOnXqhLZt22ZpTXlTpKam4siRI9i8eTOOHDnCXTxVKhW6du2K0aNHG9yEt23bhq+++kqkmPSglK413cjNB73F9RdwKsi+/fbb2Lhxo0F53L17F0OHDsWFC/x6Vy4uLvj888/Rrl07VKhQwVTDliEtLQ2RkZHYsmUL9u/fL1w8g4KCMHXqVIPrz9GjR9G/f3+R0hxKKZ1qmlGbH4SQtQC6Kdvd3d2xdu1ag8W3nj17hi+//FKYl+Hg4IDg4GB89tlnWSrxOcHZs2exdetW7NixQxh+26hRI8yZM8egoev8+fPo0aOHyHK8mlLa2zQjNj8IIVMhFeiVwcnJCcuXLzeoaCYkJGDChAnYvZvPZq5Wq/HJJ5+gffv2qFOnTo7pX0W4cuUKtm3bhi1btgipnP39/bFw4UKDBsfbt28jJCQEDx484F3eB2mPzRMhtXo6Z8YNr1KpMGvWLAQHBwu/m5KSkpGXwdvXCCFo3LgxOnbsiIYNG5qtltSdO3cQHh6OH374QWgALFu2LBYuXGjQuv7s2TN069ZNpFz9DekAa5psbjODENISwE5w6NdHjhyJ/v37C7+blpaGFStWYNGiRcJQ6Fq1aqFTp05o1qxZjktdiPD48WPs2LEDGzduFBoAPT09MX/+fNSpI66vnJCQgL59+yIyMpJ3+RaAOsbSBRullOhjIfeBc8CpWrUqNm3aJDwQpMcAL126lHuo8PHxQb9+/RAUFGTRyu4nT57EsmXLhJtzo0aNMHfuXIO0qLNnzxaF/LwA8H5eiH8VHXBKly6NLVu2GHS3//DDD5gxYwb3oJedvA5T4vLly1i2bBkOHDjAVSyM2RB//PFHTJo0iXcpCUA9SinXJGBNIIRMgVTDQYYiRYogLCzMoKdq3759GDduHLfYpLu7O0JCQhASEpJj3vzs4Pbt21ixYgV27NjBXcT9/PywcOFCvPsuE6WWgUOHDqF///68dSgNwCeU0gMmHbQZIDrgODk5Yf369ahRo4bwu4YIO9LzOnr37m3R4myPHz/G6tWrERYWxg01KlGiBBYsWGAwxjkqKgqdO3cWhSp1p5SuM9mAzQRCSAtI3h2ZtqBWq7Fo0SJ8/PHHwu/+888/GDx4MNf7lJ7X0a9fP6OS4k2F2NhYrFu3Dhs2bODms7i5uWHmzJkGcxTv3LkH5Kr6AAAgAElEQVSDzz//XOQxmUQpnWa6EZsHhJAqkIy5zCY4ceJEdO3aVfjde/fuYciQIVzDkEqlwscff4wBAwZkGWJjSiQmJmLz5s1Ys2YNdx1xdHTEhAkT0LEjlzAOAPDixQu0b99eZMjME4YEQkgpAOcAMBbbfv364csvvxR+NyvCjg8++AADBgzIcU2/7CAlJQXbt2/HihUruPksarUagwcPNpijqNVqERISIvKY7IdEQpKlIcFYpWQ8pKqNMvj4+GDLli3CBJ74+HgMHDiQm8ju7OyMIUOGoFu3brlaKfrPP//E5MmTuQxMb731FlatWiWc9JRSjBs3Dlu3covPRgJoaM3MTYSQDpAK/MhQrFgxhIWFoUwZLiMwUlJSMGbMGOzatYu5Zm9vj549e2LgwIG5Wik6KioKEydOxOXLl5lrhQsXxuLFi1GvnrCALubPn4+lS5fyLl0HUNOaufMJIY0hhW3JYiQ0Gg02bNiA6tWrc7+XlpaGmTNn4vvv2ehDlUqF9u3bY+TIkRZVRpSIjo5GaGgo1yLj5OSEmTNnonXr1sLvh4eHY/To0Tyr4xMA1SmlXNOsNYAQUgnASQAyC5CdnR1WrFiBxo0bC7+7Zs0azJ49m2sYatGiBSZMmIC33mLSySyGhw8fYvr06fj1V9bBrFarMXbsWHTv3l34/cOHD6Nfv368vy8BQG1KKbsQWAn0VN1nocjnI4RgxowZ+Owzbl40ACk0cdy4cVzDUL169TB58mSjqdvNgdjYWMyaNQs///wzM+cIIejduzdGjRoljEo4f/48OnfuzPO6pEFi5PrdLAM3AfQ1oU6Bk883ZMgQDBnCTS8BABw7dgxDhgzhKnSVK1fG1KlTjaZuNwe0Wi0WL16M77//nmskCgoKwjfffCM0NN+9exft27cXJUmHUEo3mnbEpgMhxA4SIRCTzxcUFIQ5c+YI3+dLly6hd+/eXIWuTJkyCA0NzRZ1u6mRmpqK1atXY+nSpVwjT8OGDbF48WIhC+bLly/Rvn17UY7JWGPqv2WplOgrUx6CwkXl6emJrVu34u23+QUrnz17hh49enAPhU2bNsWUKVNydRPMjNevX2PlypVcb46rqytWrFghdF3pdDr07dsXf/zxB+/yDErpeJMP2AQghLwLiUJT9na5uLggLCxMqIglJiaif//+XEWzZs2a+Prrr3OcL2Iq6HQ6bNq0CXPnzmUmmIODA+bOnYuWLZmw/AyMGzcOP/30E+/SJkppF9OO1jTQh1meg+KAo1arsWbNGuGCl5qaitGjR3MVzQoVKmDGjBnZLuJlLlBKsWvXLkybNo0J21GpVBg/frxBC+TixYuxcOFC3qXDAJpTSs3LwfgG0IdZngLATMy5c+ciKCiI+z1KKWbNmoXVq1cz195++21Mnz4920W8zIkjR45g4sSJ3LCdPn36GDzA/vzzzxg7dizv0iVIiomwNHxuQR9meQgcpq2sQkDWrl2LGTNmMIf9IkWKIDQ01KBybmmcPXsWX331FZdqOigoCDNnzhQaJ48ePYrevXvzFM4HkAwJVpn4Tgj5EZwaMx07dsS0aWInz549ezBq1CiGfEKj0WDMmDHo2LFjjqt0mwrXr1/HuHHjuNbxBg0aYNmyZcIomkuXLqFjx448hTMOkuHPKhPfCSGzAIxWtjdp0gTLly8XyiYiIgL9+vVjCD/s7OwwaNAg9OnTx+h6IebG/fv3ERoayj3XVq5cGWvWrBGG9cfExOCzzz7jKZypkJjWDNLtGlRK9Jr+ZQDemdvVajU2btyI2rVrCwcVEhLCFESyt7fH2LFjERISYnRxJUvizJkzGDZsGB4+fChrd3BwwIIFC4Su5levXqFNmza85MI0SPSUQmL93IB+IzwFgDGZz58/X5hM+fLlS/To0YNxJ6tUKvTr1w9Dhw61msUyM65fv47BgwczG6JKpUJoaCg6derE/V5ycjLat28vyqvoSCkNM/1ocwZCyG4AzGlk9OjRwmRKrVaLAQMGcKuht2/fHhMnTjRbTGtO8ODBAwwbNgx//83S3A8YMAAjRnBrk4FSir59++LQoUO8y1bJoEcIWQaAOaF26dIFoaFcanzodDqMHTsW4eHhzLVmzZph1qxZMoYla0FsbCxGjx7Nlc///vc/zJgxQ7jOTJo0CT/++CPv0hJK6WDTjjTnEDH3NGvWDMuXLxfuk3PnzsWKFSuY9lq1amH+/PlWY/DLDK1WiylTpnDZKxs1aoSlS5cK15nly5fj22+/5V3aSSnla+S5CEJIJ0h1rmTw9/dHWFiY0IOwadMmTJ06lQk9Ll++PBYvXmw1Br/M0Ol0mDdvHr777jtGQa5atSq+//57oXd9586dGDmSW0nhNIAAazMQEUIaQTJeySamt7c3du3aJUxC379/P0aMGMHkz7399ttYuHChWfP33hSUUqxduxazZ89mvGG+vr5Yt26dMAw+IiIC3bp14xkS7gCoZIgZMSulZA4AJjhu+PDhGDhwIPc7z549w+eff84oJCVKlMCKFSsMJmFaA2JjYzF06FDGE2Bvb49Vq1YJLc3nz59H+/btedSalyBZc6wmjIsQMhQAU4W+Q4cOmD6dTzCVmJiILl26MAXp3NzcsHDhQquytvKg1Woxfvx4xhNACMHs2bOFyYb37t1DYGAgL7/iEYB3KaXmrfaZDRBCggFsV7Y3atQIq1at4saC6nQ69OvXj6FxdnBwwDfffIM2bdqYbbymgE6nw8yZM7F2Lcs/MGLECAwYwGdyNmBISIS0aN429VjfFISQmpDCQWUn8XfffRc///yz8CA3fvx4bNmyRdamUqkwZswY9OjRwyoNQ+mglGLVqlWYO3cuc0AzZGlOTk5Gu3bteB76NAB1KaUnzTLgNwAhpDQko5/MW12yZEns3r1beJBbsmQJFixglm/06tULo0aNskrDUGZs374dEyZMYA5ohizNaWlp6NmzJ9dwAiCQUsrP8M8FEELcAFwBUDJzu5ubG3bt2iU8yG3btg1jx45lDvZt2rTB9OnTczUc2hgcOXIEw4YNY/ZKf39/bNq0STj+r776ShQCP5BSusz0I30z6MO2zgCQxc3Z2dkhLCxMqFgcPXoUffr0YQ72DRs2xLx583I1HNoYREVFoX///kzIma+vL7Zs2SL0mCxatAiLFi3iXZpJKf1K9HtCpUQfv3wWgEylDwgIwPr167kLR3x8PDp16oRLly7J2o2tX2ItSElJwejRoxkmk6xi8r///nvMmMGlqx5JKeVSdVka+vCeKwBkM6F8+fLYtm0bd+FITU1Fnz59cPToUVm7sfVLrAWieiRqtRpLlixB8+bNud/bv38/Bg0axLu0gFLKLZhkaejpfy8B8M3cXqJECezZs4dL2CDKiTK2fok1Yf369fj6669lB1hCCL7++mt8/vnn3O9ERUWhffv2vJjo7ZTS/5lvtMZDTzISAUDmlnZ2dsaOHTuE+QLz5s3DsmXy/dze3h5z5syxqrCerCCqR2IoJv/OnTto06YNjyr4NCQWGKtgbSKE7AIgc0ur1Wps3rwZ77//Pvc7YWFhmDBhgvI+GDNmDHr16mW2sZoaonokbdq0wdy5c7kK84sXL9C6dWtePP5dAO9ZS10aQsgSAIzVdunSpULCAhEJR9euXTF+/HizsaWZGqJ6JPXq1cOaNWu4HqLXr1+jXbt2PDrpfyEZ/h4yX8oFEEJGA2ByIgwRFohyooypX2JNENUjqVy5Mn744QdujklaWhq6d+/OC/VPBlCNUsrlD+e+6Xq+9MVQKCQuLi6YO3cuVyHR6XQYOHAgo5BUrlwZP//8c55RSABp8/7222/RpYs8bUCr1aJv3764f/8+93vdu3cX5Z5MJoTwk28sj3lQKCRqtRpz584VWjLGjRvHKCTe3t746aef8oxCAkib9+jRozFq1ChZu06nw4gRI7j5T4CUCCwIaRtMCLEWv+tEKBQSAJg2bZqQQW7BggWMQlK0aFGEhYXlKYUEkDbv2bNny9YmSikmTpzIvLvp8Pf3FxWia0sIMVx50HLoD4VCAkjWRZFCsmXLFkYh0Wg0WLVqVZ5SSADg448/xsqVK5m1adGiRcIitj4+PiL2m5oArOLkTgj5BAqFBJCYe0QKyeHDh5lQvfS1Oy8pJIBk3Ny0aROzNu3cuROLFy/mfqdo0aIiD1lpANxkIkuDEPI+gH7K9uDgYKFCcuHCBQwZMoRRSMaMGYOJEyfmGYUEkIybYWFhjDfo+PHjIkZLODo6YubMmbxzpRuAmWYZaDZBCPEGh667Vq1aCAkJ4X4nJiYGPXv2ZBSSrl27Yu7cuXlGIQGkIuabN29m6ppdvHgRgwcP5jKdqlQqzJw5k5dT5ABgBRG46kVve1sAHyobhwwZIoxVXbJkCaMR+fj4YPXq1QZ55q0VKpUKkyZNYphPXrx4gSFDhnArIBNCMGnSJN7kcgWHvczSIITUASfxrkuXLsIielu3bsX27fKIoKJFi+L777+Ht7c39zvWjr59+zKeD61Wi8GDBwuLBH711Ve8AkJqANxAZ0uCEOIDgEmg+Oijj9CkSRPudyIiIrB8+XJZm0ajwcqVKw0WVLRmpNcryYx0hVNQ7wCDBg2Cl5cX79K3+tyrXIM+DISpn+Lv74/27dtzv3P16lXm4GZnZ4fFixfnOUUzHQ0aNMCiRYuYdTU0NFRYrK9jx46oXLky79LX+lzJXIP+vWLiGkqVKiVMbH/06BFGjx4tO7gSQjBt2jSrD7EUIT1hVnloWbJkiZAutWnTpqI1bZSepjW3MQ+KMEs3NzeMGTOG2zkuLg5DhgxBUlKSrH3IkCHo3dvqmXG58Pb2xsaNG5lyAryzRDoqVaokohHuog9fzW18DUC2btjZ2WHatGlcr15qaiqGDx/O1HQJCgrChAkTrDp0VoRixYph/fr1jDHs6NGj3Pw2QApFFaR6NATAXbhESgkT7/XOO+8IXVQnTpxgLHOenp5Yv369kC44L4AQgunTpzMJ7lFRUaLCiahQoYLoOXUihPA5di2H8VAkaHl4eGDo0KHcztevX2cOeYUKFcK6deuEdMF5BcOGDWM8YXfu3MG4ceO4/T09PTFs2DDepSaEEIYa0MIYBcn6kAGNRiP8W549e4YRI0bIrBt2dnZYtmyZMDQxr6B9+/bM+xwbG4uRI0dy6XA1Gg0TDqNHBQDtzDJI49EfgMyik24s4VlPExMTmQNO+hpmiC44L+DDDz/E7NmzZZv569evMXjwYIbNBpA8CNOmTeM9p+LgWLItjPYAyikbJ02axM0P0ul0GDp0KHPAGTlypDA0Ma+gatWqWLFihYx1KC0tDSNHjhQWWp48eTLPq+8ITv6rJUEIqQugkbJ95MiRwnPQpEmTmLoQHTt2NEgXnBfg7e2NtWvXws3NTdYeGhrKZWADgC+//JJXI4kA4G9kFgIhpCw4xtyePXuiXDlmGgMAZs2axTCSNWnSBLNmzcqTCkk6ihQpgvXr16NkSVm6FBYsWICIiAjud3r06CEiaJjE85YwK7a+SiVTgWvKlClcd1NcXByGDx8u2/AdHBywcuVKgwXq8grS3ePKh7p69WqhEIYOHcorOmgP6fCYKyCEVAWHlWns2LFcxojU1FQMHTpURqVLCMG8efPyrCVdiQkTJjAFin755RcuWxEgeZQE1cuFSVvmhr7GQQ9l+4ABA4Tz78svv2To+iZNmmT1ZAXGYvDgwUyY0qlTp4TWnI8++kj0t48TuZjNDUKIBgCTr9ShQwchNfO0adMQHR0ta+vbty/atctt3co0aNOmDROmdPv2bXzzzTfc/lWqVBH97SMIIblCJ6d/n5j14sMPPxR6NZcuXYozZ87I2tq0aYN+/XJbtzIN6tWrx1A5P3/+HF99xV9Wvby8REyCvQkhlqv8yYKJT6pYsSI6dOjA7bx161YmbzUgIACTJ082y+AsjXfffZc5hGu1Wua8mI5ChQqJmLiCCCFct6eFMAaKkhglSpQQ5Zni2LFjWLdunaztnXfewcKFC62ehMIYlCxZEosXL5bpA2lpaRg1ahTXQGRvby9iiKwOTkF2nqeEWQkCAgKE9L/z5s1jLBpjx461epat7MDZ2RmLFy+WWWfS49WVDCKAlHsjiFXvQQjhxopYAOOg8JL4+PgIY8zXrl2La9fkNOE9e/YUbpx5EWq1GgsWLGDCC7/++mum/kV6f4ErshUhRFxK27wYAUW14PSq6zzs2bOHCY345JNP8MUXX5htgLmBGTNmMIaE5cuXc6vVAhB5wbiKvIXQC0CJzA12dnbo27cvt/OZM2eYHItq1aqJ/q48iy+//JKpWv/TTz+Jqghj0KBBvOTakuAo8hZCGwDMAWvwYD5b8Z07d7By5UpZm6+vL+PBzusICQlBixYtZG1HjhzB/v37uf27d+/Oo7N2BkeRtwT0uYVM0sjgwYO5B9HY2FjMmTNH1lasWDHMmzcvXxxc09G8eXMmcuSff/7Bhg0buP2DgoLg6+urbOYq8pYAIaQkAGYz7d27NzcHNyUlBVOnTpUxqGk0Gub8mNdRrVo1Jm/v0aNHovpfqFevnqhCPaOtyJQSfRgKE3gsinO9fPkywwnftGlTJiwmP6B8+fJMOMzt27e51a8B4IsvvuBRvTkCsLhfVh82xpgM+/fvz10AHz16xCQbVq1aVZQ8mqdRokQJzJ4tL0sRGxuL+fPnc/u3aNFC5IrkmnjMCUKIKzihKCEhIVw2jPj4eIYdrlSpUkJLc16Gs7Mz5s+fL7PmJCUlCQ9z/v7+qFevHu8SPxjcjNAzbjHvU3BwMLdYrU6nQ2hoqGwjLFy4MJYsWZKnkimNgVqtxvz582Xe3bS0NISGhnKtr15eXggMDOTdapT+OVsaTNG1Bg0aCKtzT548WcY8Zm9vjyVLlggrKudlzJgxg3m/p0+fziuuh0KFConOGQNyKWdoLBRGv3LlyqFZs2bcznPmzMGLFy8yPhNC8O233/LCl/I8xowZg0qVKsnaFi5cyA3PU6vVIi9Ye33upKUxHIDMq1q0aFFhTt/KlSsZhqpJkyYJw7zyMnr27MmEBa9fvx5Xr17l9hfQ89fVhz1mQLkod1N+w9/fH/Xr80Pmp06dKtsInJ2dMWXKlDwdM2cIHTp0QM2a8pyrpUuXcieXs7MzunXrxrtNl1xIoA2BIvmuZMmSwgTJ2bNnyzYCtVqN6dOn57sDTjoaN26MVq3kZEubN2/GlStXmL4qlUpkrQ4mhFiacLwdJBKFDGg0GqFRYPny5cy7Ghoaykvgzxd477330L17d1nb4cOHceTIEW5/waJZnxDCjdkzI5oAkG3ABjZrhIWFMe/qiBEjrLKAning5eWF4cPlBvHLly+Lah1gwIABPOOLLzjx/+YEIeQdAAHKdlHNr0OHDjF1OXr27Il3333XLOPLbbi5uWHiRDnB0aNHj4Rhl926deMpZ26QiHosBkJIYQCM5tu/f39u7hfvXQ0MDMyzRBRZwd7eHtOnT5c9i/j4eMZTlI62bdvyjC9qABa1duvPaZ2V7d27d+d6PR4/fsy8q7Vr18434bNKEEIwZcoU2bPQ6XTCGlIffPCByPgic6VlvCX6GObPlL1FVIMnTpzA6dOnZW2G2LnyAwghmDp1quxwrtVqhd6SLl268BIXvQA0NdsgFdDHMDMTq0ePHlzO8Lt372Lv3r2ytk6dOuWbPBIRJkyYwFhflexU6QgMDORZtJxg+cRoZpHu0KEDlwI4NjYWmzbJCww3b94cH37IkOzlKwwZMoTZ4AQFnRAQECAKO+1k+pEZBCPX5s2bc8klUlNTmbo7lStXFsax5xfw1qRly5bxas7Ax8cHTZtyl1x+jKP50BUKa7q/v78orIFZf7y8vIQKTH5Bs2bNmBDhDRs24NUrtkatu7u76MBnabm2hyKE9q233hKGRi9btkxGMlKoUCEhO1d+QZUqVZg1adeuXbh9+zbT187OTmRYs3QIzkdQFMDUaDTo1Im/HaxevVpGMqJWqzFp0qR8a6QHpIr0SmNeZGQkoxukQ5DW0D5zjl9mNb4NAFmQZuHChUWLOcO25ePjI/IM5CuUL1+ecd39+OOP3BwEA8/PkpOrHhRML2q1WlR3A8uXL5d5vwoXLpzv4tJ58PDwYDwg+/fvZ1yxgLRoCrxMFpOrvho0Y+lt25ZvJNywYYMsCc3Ozg7jx4832/isBRqNhkmejIqKEpJUBAcH85pDLJXwTghxAcfSK5JreHg4UzdJQEuer6BWqxmr+oMHD7Br1y5uf4Fc21kq1Ef//jCJWyK5Hjt2jMmTGTt2bL6KSxdh/Pjxsvc3Pj4eGzdu5PYVyPVDfV0JS4FRgoKCgrhzMDo6GgcOHJC1DRo0KF+GbSkxYsQImeFPp9Nh1apV3L6C51eeEMJ4Gs0IrnFIySgGSKUiwsLCZG2dO3fOt17NzOjVqxdDqqPUD9LRrFkz3vNzR6aaTZmVEkYArVu3llH1peP8+fNMTZK+ffvm2/AeJfr27SvzMiQmJhpM3OIg2IJxr4xcGzVqxKUofPToEcM8FRISwp2E+RFdunSR5QFltWhy8IEFaZ87QxF++e6773KLWWq1Wub9DAoKyhfseMagVatWjJdBFBLy6aef8tYxHwCWoiZrCwUffrFixdCwYUOmI6WU8ZLUq1dPWHwvv6FWrVpMsdqVK1fKcmvS0bhxY54HsRA4YTdmQiMAspfQ3t6eCRtNh/L99PPzYxLB8yt8fHyYPKB169bJmCDTUblyZbzzzjvKZhU4CqA5QAjxg2T4k0GwP2DlypUyL4m7u7vQ8p7f4O7uznhAtm/fzg1/L168uCiczSKGP32NKEaIIrmuX79e9n46ODjk2Toz2YW9vT1j0D169Ci3GLWjoyNatmzJu02GXFUAoHedMLRKIgEo4yHfeustkcUiX8LLy4t5Nlu2bOEmWjZs2JBHD+wCTnFKM4HZ9URy3b59uyz8QaPRCFmc8iNcXFyYv3fPnj1cmrsKFSrwFAACgDvjzAAmNkAk1/3798s8eYbyE/IjeH/v8ePHuUxcRYoUQaNG3FSDXJOrQFHCyZMncevWLVmbIC8m30JJwhIdHc3Q5wIGFQC+VmB6MHJt0qQJjwwFMTExOHHihKytX79+eaqyd06h/HtjY2Px22+/cfsKvNaWlKvMi1qlShVuYnN8fDz27dsnaxPlJ+RX9OjRQ1YsMyUlRUjBL5CrpdgQm0IRkle8eHFufnVaWhq2bdsma2vbtm2+TmVQ4n//+x9KlJCRRQpz/ARybZ4ewpU+6+tDwTDw9ttvo1q1asw3k5OT8csvv8jaQkJCuPkJ+RnKXJvHjx/j1KlTTD+1Ws0UX9TD7Ny6hJDyAGTmcI1GIwzJ27lzp+xzu3btuPkJ+RkhISEy76BWq2Xc7ekQxAxbQq6uAJgqtyKrq1KuH374IVOVNb8jODhY5h2klApDfQRyNXsemD7Ep7GyXSTXHTt2yD6/9957CAiwZHRD7qNBgwaMcUD5XNIhmq8WCs1jjFAiuW7fvl3m7fHw8BCG2+ZX+Pn5Mcw+2ZRrHX0opLlhtFz37dsns6Y7OjrajJckHe7u7owBWyTX5s2bw9HRUdlcmhBiCSorRq4tW7bkhuQdP34cjx49krX16JFbjOO5AwcHB8YLtmfPHqSkpDB9a9asyVPYnKAnAUlXSpiDVL169bgJOr///rss6UylUokoF/M1/Pz8GCYB0eSqW7cur9kSnhJGrjVq1OBNdERFRTGF10TxzvkZ7u7uTPJ3NuXa2AJUox9AKsaZgbJlyzJVVgFJWVbmT9iiXO3s7JiDXXh4ODfUR7D2VSeEmFtDrwxAFlzu4uLCTb5PSkpiajjYolwB1kO4d+9eWcJpOqpXr85ja3oLABvzaEIQQooCqKZo4yqQlFJmvQkMDLSZ0OjMUB5e//rrL6boKyDRmpcuXVrZ7ABOeQNTQs/OxMRVCqjFGY+AyFOW36GU6/Xr17mhPhqNBtWrV+fdIlfOTsbKtVq1ajZn9AMkuWZW2l6+fImjR48y/QghBs/EqswfMkNkcVO6UOvXr29TbqrMUE6ugwcPyuJF0xEQEMBzvVclhDBxXSbGG8vVz88vXxXAzA6Uh5zIyEj8+++/TL9KlSrxCngVBcAvuW06MHIVTHIcPHhQFlbIU7psBUq53r59Gzdu3GD6FStWjBd+wT2AmBjMRlinTh3ugfT48eOIi4vL+MxTumwFgYGBss0wLi4OJ0+eZPqp1Wqm8KIe5vZuNgYn/0tZtBUArly5grt378raRGGZ+R1NmjSRra86nQ6///47t28uGf6qA5AZKtzd3bnJzbGxsQwjkS2FvGdGtWrVmBy/X3/9ldtXcF4xq1wJIZ4AZNR+arWay5Kn0+lw6NAhWZutyrVEiRJMjl825doEAFR6KmDmaYsOr5GRkbLPIlelLeCTTz6RWVRjY2O5Gr9goSIwf/Isc4gSyVVpTbdluTZu3FhmUdXpdMJDjoDO09yHV+b+ysUgHUq5Nm/e3OZCLdNRqVIlplqwiIVLcMgxt1yZ9cBYuQYEBKBYsWLmGZWVw8PDA7Vr15a15VW5KvdXPz8/LnmFLcDR0ZEJNc6mXM1dh4YrV17uT2RkpMxg6erqyiWvsBUok51FchV4J8wt14ZQ5Am99957PAMkLl68KDMOqVQqUSK3TSCHcq1DCHFSASgPQGaKK126NJO0AkhJhEqmBJGF1hZQvHhxhvlDuamkQ7lp6mG23UYfMiBzYWk0Gq73IyEhARcvXpS1iVyVtgB7e3umSGY25Wq2oi76+HfmveEpR5RSJmHWluUKsOuVtchVdH9RDQvluG15HQZYY0telatyE7d1ufLmKy/k0lrkqtw30qF8H2vVqmWTIXnpUMo1KiqKSyhTtWpVbq03MxcqNlquyvlaoUIFm8vDzQylXB8+fIg7d+4w/UqWLMlj/3wrBDQAACAASURBVLQH8I4KAFOtmMccAYA54Hh7e/Mqb9oUjD3kCJ6pOStFM/f29fXlJmqdOnVKFuKj0Wjg72/uCCTrhhXL1QuKKu7u7u48hjdcu3YNL1++lLWJLLS2AqVcT5w4wT3kWFquhBA7AH6KNu44Xr16hatXr8rabC3BXQmlsn358mVuyGW5cuV4+ULl9PkB5gLjJufQ2CItLY0hS7F1uSrn6/Pnz7khl56enjzqejdCiDljy42SK8CenWxdru+//75M2dDpdFzWPDs7O/j4+PBuUd58o2PX+fLl+T+njKCwdbn6+PjAy8tL1pbNs1N5rlIiStJRboQia48tQfkMrl27xu0neKYWVUqMlWu1atVsNsQnHUq53rhxg0v5bA1y5VX6Bli5+vr62kSRLkNQyvXVq1cMcwogLa4cBd4nc+VZE6MMpOTcDJQoUUJGn5mO69evy0JBNBoNKleubKZh5Q1UqVKFOeTwDq8uLi48Bd4RUi0ak0MfHi0zCarVal5iNh4+fCgLBQEK9ti33nqLeVbKdS0dgnUw1/fY1NRUpgivrcvVwcGBIQqyZrmK9ljlec/W5QqwzyC7cs2WUqLkxBdZBWwJymfw8OFDbpEna5hYxspV5CmzJSgtqqmpqdy6Fl5eXjz38luEEDYA1TQokGsO4OHhwTDeKJ8TIIXwcdzLKgDmeohvLNcyZcrk+wruWcHOzo7JF+LJFbC4IaE8FEnupUuX5obuKMdbpEgRm80TygzlumUNctUz8cm0WycnJy7pz507d2QGLUII/Pz8mH62BuXZSSRXwbMyp6eEOdjy3i2tVovHjx/Lv1hwJjZaroL5Wl4FjoVIpBUqtX1bpD1TonTp0rIDAaUUt2/fZvp5eHjA1dVV2VzYjLGRjFyVm3Y6CuTKgmdRVT4nQEpsE7iXzWJ55d23YL5mDzk8vPryGk0A5r4Fcs0elM+rQK75A8bKVfBcfU0+IMF9fX19uUnuyvG+9dZbXA+orSGHcuVPohyCEFIMgCwO0M3NjcuUd/PmTVnor52dHby9vc0xrDyFHK7DZeygEAAAbqJOSkoKoxWKDrm2hHSLauZknrt373IZU4oUKcK45wE8IoSwQe05h4OygTexAKmCcGYUyFVC2bJlZcQOSqrOdAgS204RQlh+6JyDiasTJdYp5So6DNkaypYti3PnzmV85iXiAcLnup0Qwsbx5RyM6Vw0X5UeuwK5SlBuctmcr4sIIfNMPyowLqwCuWYPOZTraELIcNOPCoz2USDX7CGHcu1ICPmf6UclZ90CjJert7e3TZMXpEP5fj948AA6nY7x5gvk6moHRdIsAF6BKSQkJDAJoQWuZQlFixaVHWzi4+O5/XjPFVI8s0Ug+H1GUSqQqwTlYiSSq8DqxSiF5oKxchUtrraGHMrVHhzF0BwQWVOV4y2QqwTlJscxAAEQPlc7cBRDc6BArtmDsXIVrINqcBRDc0Ak14J1mI8cylUFqQq42VEg1+xB+RzS0tKQkJDAEFEI5OqqAkcp4QmBt3GLDkO2BuVz4FHb8fpZGjy56nQ6pvpxbo/TWmCsXAsVKmSJ4Qhh7CGnQK4SCuSaP6GUl7XKVSSvArnykdflqhxvgVwlKOWl1Wq5xadz+3kVyDV74M1D3pwVPC83FQDmDiJPSWbY29vbPENTOoxdNHP7peW9LImJiYwHLLfHaS3Iy3IFJNlmRm6P01pQINf8ibwiV9HvF8iVj7xi9CuQa/agfA6UUi5JUIGymbfg5OTEhLHx5qxArq4qKFzWhBBuspZSgy2InfsPSuUsJSWF2y+3nxmPoYdHc5vb47QW5GW5Aqxsc3uc1gKlXFNTU7n9cvt5Fcg1eyiQa/6Eg4M8EjavyVU53twep7VAKVeAv8fm9vMqmK/Zh/JZ8OSqUql4NaPsVQBkPmNKKRPOA0hc+JmRlJTEPdDaIpRaoEizF1l4LAWlxQbgh4jk9jitBXlZrgAr29wep7VAGSZTINf8gbwiV541GCiQqwh5Xa7GenpsDcamBOT28yqYr9kDLyWAN2e1Wi2vcHGcCgCTXWRM/JfI1WaLUCY8Weuiyft9BwcHxsKY2+O0FuSVzVD0+wWLJh/Gxu7n9vMqkGv2UCDX/IkCueZPKOXq6OjITQnI7edlbLhgbo/TWsBTNo3NMwHwL+MpAfgWOt5N//33X6MGmd+hFIIoQTW3X1qR5VU5uQrkKkGpbFrrZiiSq3LOFshVgrFyFbFyWQoF8zV7yCtyNfaQUyBXCflNriKWKVtDgVzzJ3jPwVjyLABxdgCYlY+3GGo0GhQqVEh2o3v37sHLyytbA86PUPJVlyhRgttPIIR+4MjABBgKoE7mBtEm5+HhgdjY2IzP9+7dQ82aNc0wpLwFZf0KT09Pbj/BYjQBAFttMefoDKClEb8PDw8P/PPPPxmfeRXpbRFKPnyRXAXzdT6AUyYfFPAJgC6ZG0RyVY63QK4ScijXDQD2m3xQ0ho8NHNDgVyzB6Vcs7m/7gXwg8kHBfgBmJa5wVi5iupx2BpyKNdIAItMPijAHcCyzA0F8zV7UMrV3d0djo5s5QtDSsljZeu9e/dQpUoVpneZMmVw4cKFjM83b95EnTp1mH62hMePHzMPl1epUqvV4unTp8rmFABrKKX8zL0cgBBSHwqlRDRpypYti+vXr2d85lUutzXodDrmeYkqLAue6wZKqclXKUKINxRKiSG5Hj16NONzgVwlKCvMZlOu2yilf5l6TPqEP5lSYkiumVEgVwk5lOsvlNItph4TISQGCqWkQK7Zg1KuouKDguf6B6V0s6nHRAjxgUIpMVaud+7c4RaTszUYK1eBEnfKTHK1h6TsZGRqP336FElJSXBykpdFUco1Li4OT58+hYeHh6mHlaegXLeyKdfHKgDXlK3GloUvWDTZZ+Dm5sYtPnj79m1eUk+0ORQSPd5YrqJ+toR79+4hOTlZ1sardB8bG4sXL14omxMAxDCdTQNGrqJ5WCBXFklJSXjw4IGsjbdoUkpFz+uKeUZWINecwtjNUPBcr5p+RPz7GivXBw8e4PXr1+YZVR6Clcr1HgBZfOWzZ8+40QjK8SYnJ+P+/ftmGlbegTXKlVKaAkC2oKalpTFRE4DkKVGGSBeciY1XNkVyVSEbi6afn5/sc1RUlFGDzM9QPgNrmFiiexsr13PnzplnRHkISrnyFiBAeCC8RjkaqInwxnK9cuWKzR9yLly4IKM3V6vV8PHxYfo9efKEF0v8glL63ExDuwZA9s7cvn2by3ColOvTp09t/pATExOD58/louF5SnQ6Hc9CRwHcMMe4KKVPALzM3BYfH8/zmsPHx0dmPdfpdLh48aI5hpVnoNVqcfWqfMlTvv/psPDhNQ2cd4a3H7i5uTHW84KzE3vOEHk2BXusRc9Oxhp0C+Sac7lmSyl5//33ZZ+joqJyPck3txEZGSn7LMrFEDxTxjpqQryxXB89esS1DNgSrFiu0QBk3rUHDx5wabyrVq0qYzN5/fo1zp49a8ahWT8iIiJkn6tUqcLlyxfI1VxeElBK4wDIXDgpKSmIiWEdbt7e3kw884kTJ8w1tDwBpVw9PT1RqlQppt/du3d5nPkxlFJzZtMatRY7OTnhvffek7Up1yFbw5kzZ2Qea3t7e1SuXJnpp9Vq8ejRI2UzY/U2Md54j7V1uUZHR+PJkyeytho1anD7WsPZKTo6mtuxQK5yJCQkMIaU7MqVq5RcvXqVS/dbvXp1WVydTqfD33//na1B5yekpKTgzJkzsraAgABuX4EGbU5t/y4AmRCfPXvGPeSULl0ab7/9tqzN1ieX8pBjLXKllCaD417OnOuVDo1Gg6pVq8raCuQql2vdunW5/QTeQnNuhNz7iyxvylw+W5er8u+vV68et5/geVpcriJvtPJ9LJCr/O+vXr06UzMNAM6fP88UeAZwUx+OYy4w67xIrsr9o0Cu8r/f29uba0S4d+8eLzw6EeYLjwY4chWtw0q5nj59Wljc0xZw4sQJmXdfo9HA39+f6afVanHtGnfZvarSu5dvZ25NTk7mKhuOjo6oXr26rO3gwYNvMvZ8gb/++kumvKnVatSuXZvpp9PpcPr0ad4tzGbe1LuXmR8VLYbKyfX777+bZVx5AVevXmWUN9HhVXnI1cPcZuuTRo6DGbcty/Xly5eMp0ikbArmibnlytxfNF+Vcj1y5IjNboYpKSk4cuSIrC2bcjX3CZGZr8bK9cyZMzJmRFvDoUOHZJ+tbL6+sVzv3LkjtL7bApT7kEiugn3tpP58Yy4wclUettNRu3ZtWchlYmKiTSucSrnWrFmTG4lw+vRpnsc6mlL6TKX/cEh5VfRgGzZsKPu8d+9ebgl5W8COHTtkn2vUqMHl2o6KiuLRnz0BcMlsg5PwxnI9evQoE6NtK1DK1dvbm5sr9OTJE15cZCqAY2YbnITDygZj5frPP//gyhWzRSFZNfbs2SM7uLu4uHBdy8nJyYwHVA9mPpkYjFxFymaDBg2gUqkyPj9//lzGtGZLOHLkiOzgrlKp8MEHH3D7CuYJ89xNDOa9OX36NEOkAUibeGZPQHJyMvbu3Wve0VkpLl++zFhTGzVqxO0rmCfmlusfUITSRkdH4/FjhtAUfn5+TDRCeHi4OcdmtXj69Cn++ktOYCiSay7N1/MAZElfvLAkQMoXqlatmqzNVuX6+vVr7Nu3T9amPH+kQyDXQwCQvqsZvRm2adNGphnGxsbi8GFzvyPWh/j4eEYrDAoK4vYVPMtDZkyGTgcjmOPHj3M7NmvWDG5ubhmfU1NTsXv3bvONzEqRlpbG/N0iuSoXVj1OUkrNXfWMcU+ePXtWGHJZunRpWZtS6bIVKDeLFi1aMDSPgPQsOTk6Dyil5g7zOQZAxkRw7949bsill5cXatWqJWsrkKuEgIAAbs2Du3fv8p7lawD8RdFEoJT+A0DGRKDVanH+/Hmmr0ajwccffyxrK5CrBB8fHyYcFZCepSC8xqwHE30eGGO94OV3EULQpk0bWVt4eDjX+p7fsXv3btnf7erqisaNGzP9KKUGD6/mgv5c9oey3dCZODMOHDhgk7nWhw4dkrHPqdVqtG7dmtvXkBEhXSlhYjrOnz/P1fg9PT0ZV+SPP/5o5LDzD7Zt2yY7BDo6OqJFixbcvoIQN0tochGQ6Gkz8OTJE67G7+joyGyGmzdv5sXp5mscPHhQljDJ20wy9+XA3NZ0UErvQJFXkpKSgj///JPpSwhhlKrt27dzFZj8jIsXLzKHQJGyKZCr2eNUKaWJ4ISciELugoODZZ8PHjzIJI/mdzx69IgJ8cmmXI9TSi0xGf5QNohCn5VyPXv2LC5fvmyWQVkrEhMTGaUkODg4vZ6PDH/88QcvWuOGfp00N5j1XiRX5Xv5+PFj/PHHH2YZlLUiLS0NYWFhsraWLVtyjUPnz5/nrWeJ4IRXmQHM+Uwk11atWslClLRarU16S5R6QP369bk1Wx4/foxLl5ggIYrMSgml9CEUoUQ8i3E6lIvmsWPHbIoKLSUlBatXr5a1KT0N6YiOjuYlIVMAv5ltgOk/IiVFMydV0YRp27at7HN0dDQOHDhglrFZK5YvXy77XL16dW59klevXok8hGaXq+h3RHINDg6Whfq8ePGC2RjyO5YtkxXphZeXF7fwq06nE617VifXFi1aMKE+q1atMt/IrBCrVq2SHUidnZ0Z40o6BM8x1+S6a9curqW8bt26KFmypKxN+f7md2zevJkJyRMpm9Ym199//51br6Rs2bJMqI+tyXX//v0M65LyPJkOgVwP68815gYj13PnznFpbAsXLoymTZvK2latWmVTOX5nz55lvB8iue7YsYO37l2glD4C/vOUAABTHXPbtm3cm7Zq1YqJj1Qe5vIztm3bhocPH8raevbsye0rmFgRlFJLVTxj5Lp7927uhKlVqxbjHl+6dCmv6GO+xJEjRxgFUiTXvXv38mLC7wMwebVvARi5/vHHH3j58iXT0dvbG82aNZO1rVq1ymZqlty4cYOxcnXv3l2mqKXjzz//xLNnz5TNiQB2mm2AcmyGol7JxYsXuUwlhQoVQvv27WVtYWFhPLaafIlnz57hp59+krV17NiRm9d3/fp1/PPPP8pmCsDkVdwFCIei2N6TJ0+44bQqlQrdunWTtR04cADXr1835/isBq9fv8aaNWtkbR9//DGXnenFixeiXCpLhW8cgYIJihdbnw7lfhIVFSUKA853oJRi5cqVsjZ/f38u3X5qaqool8oicqWU3gDHI7NzJ38b6NWrl+zz/fv3bSrscunSpbLPXl5ewsghwTPMkGvmXXkjAFmsjmAhx//ZO+/oKKo2Dj+X0FIgFClCKCGCoDRBShCUoqggEFABQaR3CCBNUQiEoiBIB4n0pogKKFJEiqImGvCjKTWEklAFAiFZIGzu98fsRjYzsyUkm8I853A8zt7ZvcnNzr1v+725c+emR48eNtd27tzJn3+6I6qWuZhMJpUB1qhRI81cVyklmzdv1nqbVRkzO02+AWyq7O08yOnfv7/N/x89evSRKLQ0m83MmDHD5lpAQAAvvfSS5nidB85KKaW7koR/RiOFS2+tBg0aZJP6cOXKFVauXJmhE8wqTJs2zSYNsXDhwqrDvBWddd1gyR/PcKSUUWjUOHz33Xea43v16qVKHZg7d26GzS8rMXv2bJs0xLx58+o6Eb799luty3ullG5pwWypM1Mtot7BpVOnThQpUiTl/5OTk1XPp5zK0qVLVWk7ffv21RybWrzCwhnc5ByyqECpDsp66/ryyy9TsWJFm2uffPLJI1FbsmnTJlXazsCBAzXH6jjYbuM+5xBonNM2bNigmdJeo0YNVVlD6udTTiUyMlKlfti3b1+bHmlW/v77by0Hm813KMUokVKeQzno2LBqlfb5uWPHjjYNvKSUjB8/PseHrGbPnq3qnjxgwADNsT/99JNWYeU9YH2GTE4DKWUCoNqR9db1xRdf5Mknn7S5NnnyZOLj3XImyzRWr16tytseOHCgpjf96NGjek0I3VZcZSnGW5P6+qpVqzQfmk899RQNGza0uTZnzpwc3wl8x44dqpqDnj174uXlpRp75coVduzQzPpwpxNB8/O+/PJLzQ2uZMmSqjD5mjVrcnw67ZEjR1RRkvbt26uaSoJiqOlE/TN9Xbdu3apZB+Tp6ck777xjc+2nn35S/S3nNC5cuKBKaWratKlmw8Tk5GS++EIVMAZY4QYRGZvPS30hMjJSK2+eXLly0bt3b5trR44cyfHptLdv32batGk216pUqUKTJk00x+ucT9ZbzjPuYi2phEdiY2N164BSnwMvXryoiiDkNMxmM+PHj7fJpilWrBivv/665niddd0lpTxv/Z/UJy5NyzB1qhIohdGDBg2yuXbixIkc7X09ceIEy5cvt7nWtGlTlQqOFZ2Uts1SSndr7arWde/evZoN94QQjBw50uba1atXmT17dsbNLpO5cuUKs2bNsrlWtWpVWrZsqTl+3rx5Wilt+6SUagWBjEW1rlFRUXoHa0aNGmWjnGcymZgyZUrGzS6TMZlMTJo0yeba448/TteuXTXH66S0XcANRe6p+Aqwkf+Ki4tj3TrtTKPBgwfbGFnJycmEhobmWO+r2Wxm7NixNj+fj4+PrnPoiy++0EppM+FG55CFHwGbtuP37t1TpSpZ6d69u0pFbOLEiTna+zphwgRV76/hw4drjt2+fbtWSpsEVmfYBDWQUv4DqBq7ffbZZ5rj27RpQ5UqVWyuffrpp1ppozmG6dOnq4zv0aNHawoX2Elpc6sTQUp5HVDl4enVAQUGBqokcJcsWZKj+9EsXryY48dte02+++67msIFdlLabNY1tVHyBWBjgWgVdVvp2LGjqlvjjBkzcqRSyN27dxk+fLhNJCh//vyMHTtWc/zevXs1JR+BORkzQ7vsBFQHZr06oMaNG6vSllauXKmp7pTdSU5OZtSoUTaRoFy5cjF+/HibA7wVO4d+t6+rRaJ2e+rrenVAVapUoXPnzjbXtm/fztdff51hc8xMQkJCVJGgDz/8ULMjtJ1D/wI3puQBIKW8gcbBavHixZo9oUqWLElwcLDNtYMHD+ZYL93s2bNVDpWhQ4dqRknsHPpXSClvZswMtZFS3gdUD921a9dq1oJ5e3szZswYm2vnz58nNDQ0w+aYmXzxxRcqpbmuXbuqIvdWUtcnWNhiqQdwN6qcye3bt3PqlHoqHh4eTJgwweZAfvPmTYYNG5YjHQk///wza9bYBvVfffVVVeTeis5z6280MnncgGpdDxw4oCsPPH78ePLly5fy/0lJSQQHB2tJzGd7jh49ypw5tsee6tWr60ZJwsLCtDKpLpPKOWRjlEgp7wAql/i6des0rfhcuXIxYcIEm8Pb3bt3GTx4sFazwGzN+PHjVfU1/fv3p0yZMprjdazpX6WUbv9iWULZH6W+vmPHDs0CWoBx48bZHN6Sk5MZPny4pkx0dmbevHn8+qttr8P27durVFKsLFiwQCs96jQaheduYlLqC//8849uzdC7776rOryFhIRo1o5lZ77++mtVHUHDhg11lZkWL15MYmJi6ss3gXkZMkHHfEyqxmyXLl3Sq42ge/fuVK5c2eaa1t92diciIkJ1GK1UqRJvv/225vj169drPbPuA9M0hruDuYCNNJPJZGLFClUGEKCIyqT2vq5fvz7HSY6eOHGCyZMn21wrVqwYgwcP1hy/a9cuTWl7ILNCv2tQallSSE5OJiwsTHNwrVq1VIe38PBw3fHZlUuXLjFixAgbJ5mnpyfvvfee5vijR4/qqVpOyuAu7ppIKXehtFawQc/hU7ZsWfr06WNz7fjx43z0ker4la1JSEggODjYJrPAw8ODSZMmaaa8X7lyRc/5OSO1JLv6bsWTY+O2uXPnDtOnT9ecXNWqVVU5kmfPnuW9997LMT0uvvrqK9avt430a/3cVrZu3UpkZKTWS5O1LrqJdYBNrFtKqdoIrDz++OOqB8f169dzlNW/Z88e1cPFz8+PUaNGaY4/dOiQnlzsVIsX1O1IKX8FVBbIRx99pFnf5ePjw6RJk2y8dHfv3mXo0KE2EpzZmcOHDzNhwgSba76+vrp/67GxsXqHwrnu9qZbsRS8q0I3M2fO1JQb9fDwYMqUKTbFhcnJyYwcOVKz+WJ25Pz58wwZMsTGm5w3b14++eQTcufOrRp/8+ZNlSfPwho3qh/aYImCqTxWS5Ys0V2n0NBQldx8SEhIjslIuHHjBgMGDLDZV4QQfPTRRxQoUEA1PikpialTp2q91S4pZYY2wtRDSpkEfJL6+saNG3Xru9577z1KlSplc23WrFk5JiPBZDIxaNAgVRTwgw8+UKm3Wpk8ebJWlP8U7k+1fBCVoRsREaGbJt2vXz+eeuopm2tr1qzRVbPNbpjNZt59912VPLLWz21l6tSpWqnR1wFVjqPKKLGohKhCVt98842uutawYcNUsm7btm1j/PjxmuOzE7t27VKlaHl7ezNz5kwb1RsrJpOJjz/+WOut/odGqo27sKSgqLyDv/32m65iU+fOnWndurXNtf379xMcHJztw8yHDh1S/Ry5c+dm5syZmv1mzGYzH374oZahHYNGoaObUZ22T506xbJlyzQHN23alO7du9tci4qKomfPntk+X/3cuXP07t3b5uewHnD0NsLUeewWEsicVMsHmUwqRcR///1XVf9kpXr16iqD+urVq3Tt2jXb56vfuHGDnj17cu2abTnemDFjePrppzXvmTFjhmo8yu9TdXh0MzNJJQ9sMpl0jWY/Pz+mT59u40hITEykW7dumn0TshMmk4m+ffty5swZm+u9e/fW7PINSlRTJ08/M51+AEtQatBSSE5OJiQkRHO/LFSoEHPnzrVxJJjNZgYMGMBff6lKVLIVZrOZ4cOHc+DAAZvrLVq0oGPHjpr3bNq0Sa+D+2R3p9A+iJRyM7A/9fXQ0FDN/TJfvnzMnTsXHx8fm+tjxozJEX3fJk2apEqzrFOnjiqF2EpkZKSeeuQsLVVLrUgJwCzApipJSqlbPOnh4cGsWbMoXLiwzfW1a9fqeaqyBZGRkZoH8KlTp+Lv7695jx1Fo/fcrAiixUrgWOqLkydP1k23Cw0NpVy5cjbXdu3apXdAzxacOnWKnj17qtJ1Ro8ezTPPPKN5z9q1a/U8kxOklJna8ENK+SMaHaPnzp2rKVIBStF76nqwgwcPEhwcrNV/JVtw+fJlzQN4t27daN68ueY9O3fu1FM0+lRKeTX9Z+k8UsqjaCisrVmzRtdLrvWznj17lj59+mRbBb34+Hh69Oiharr2yiuv6KZtHT58WE/RaKWUUi2L5EaklFdQ9lgbduzYoZe6QtOmTenSpYvNtevXr9OzZ09N9a7swL179xg0aJDqAF6rVi3effddzXtiY2P1UqN/sqTaZBqWfUBV8GNPXatGjRqqQn6TyUS/fv2ybYF0cnIyH3zwgeoA7u/vr5vGFB8fr+fM/QeNZ2AmoCoetqeuVa5cOZXIitVQ27dvX8bM0A3MnDlTpaBVtGhRZs+erVmDe//+fcaNG6cV/bqEjtNP0yixhJhVOSzHjh3T7RhcsmRJPv/8c1UR6Zw5c5g4cWK2O8Du2rWLHj16qFKVgoODdZvCHDlyRM87/bXl4JipWDqhDkp9/cqVK3zyibbz0MfHhyVLllC0aFGb6+vXr2fw4MHZ7gB76NAhOnXqpAopBwUFqRqWWYmNjeXTTz/VeikCWJrec0wjAwGbKujExERCQkI0i95z585NWFiYqlv97t276dGjR7arCTt37hydOnXi/PnzNtcbN27M6NGjNe+5deuWXtHwaTRqsDKJkYBNXp3ZbOaDDz7QLHoXQvDJJ5+oJFQPHTpEhw4dsl1N2NWrV+ncubOqsL1atWoqiVEr9+7d03Oa3AC0/xjcz2TgkTKebAAAIABJREFUbOqLEyZM0DUex4wZwwsvvGBz7dy5c7Rv3z7bRUwSExPp06ePqr9BmTJlmD9/vmY6npSScePGaXmnNfe1TOJzQJW7/emnn+o6iHr27Mmbb75pc+369et06NAh20VMkpKSGD58uKp+oHDhwnz22WeajU1BcfRevaryAUlgoCU1LlORUm5FaYBqw5IlS3TrMV977TWVQq3JZKJ79+66ssJZFSklU6dOVRlh+fPnZ/78+ZoiI6CIUeg0fR2plxqtFykBxau+J/XFmTNn6lp6NWvWZNasWSqLacWKFYwaNSrb9DD5+uuv6d+/v+rh16lTJ90QVWJiIu+++67Wz5gIjMiQiaYBKeVOQOW2WbNmjV69BOXLl2fRokUqg3P79u307dtXq0A4S7Jnzx46d+6skgdt1qwZU6dO1ZQnNJvNDBs2TOugYAYGZEbxnRYWWcqZqa/v2rVLJWNtpWjRonz++ec2TdpAyZft0qWLVupLluTgwYO8/vrrnD1re8arWbMmc+fO1TzgALz//vt6Uc0hqYvvMgsp5WU0vHSHDx/WPZR7e3uzZMkSVYTzxIkTvPXWW5w7dy5D5preREdH8+abb6qiQuXLl2fJkiWavWYAPv74Y80eEcAYS5Qi05FSJgJDUl+PiYnh/fff17wnd+7czJ07VxXhjImJoWPHjpoS71mRq1ev0rFjR5UIQ9GiRVm+fDnFihXTvG/x4sUqI8bCdCnlca0X3I1lP+iPsj+kcPPmTQYNGqR5BhJCMGnSJJo2bWpzPS4ujm7dumWbGpPbt2/Tq1cv1TnC09OTxYsXExAQoHnf1q1b9SJJa6SUe9J9omlnCKkaUSclJTFo0CBdJ97QoUNV6WrWSFh26fhuNTRTByQ8PDyYM2eOqnTDSmRkpF6m1F7sRL90jRJLqtEgUnlfzWYzQ4cO1ZQwBOWAN3nyZFUF/saNG+nQoUOWbtZ29+5dQkJCeO+991QpWy1atCAkJET33g8//FCVXmAhREqp8ohlMsNQlIVsGDdunMrTbKVmzZrMmzdPVUezd+9egoKCOHZMlRWWZTCbzcyZM4e+ffuqDM26devqhh5B6Qau461aIKXU7KCYiUwglQIMKF4onWaP+Pv7s2TJElUdzeHDh2ndurWeYEOWYc2aNbz11luq51GlSpVYvHixpvwvwPLly9m+XbPEa5MlhzgrsQBQFfQtX75ct9jSesArWbKkzfVz584RFBSU5XObt23bRrt27VTF3yVLlmT58uUqQ9rKrl279Bp07UfxYmcZpJSbANXf2rZt21QSqla8vLxYvHixqiv4tWvX6NixY5ZvwhcREUGbNm1Uhqavr6+mIW3l4MGDetHqc2Se4pYmUsr9gEpG6+DBg8ycqfIbAcoBb/bs2aqeZ4mJifTq1Yt58+Zl6WyTo0ePEhQUpOovki9fPubPn68ypK2cPXtWJXtt4RZZJ6oJgKXBn6puyc7PACjRz9TZNffv32fEiBGEhoZm6WyT8+fP0759e1VNiFVYJbUhbSUuLo7hw4drlXvcBwbZK2UQjsochBAhwPjU15s0acKiRYs05b8AtmzZwogRI1S/cF9fX6ZMmaIrzZlZREVFMXToUM1Q3FtvvaXbtwKULpWp1X4shAMvZIXwY2qEED1QCvNsqFatGl988YVm8xuAP/74g379+qkiB/nz5+eDDz6gY8eOmhGHzOLy5csMHz5cs4DuxRdfZNasWbo/608//UT//v311EBqW0QhshRCiOYoDZ9svph+fn5s3LiRQoUKad537NgxevToocpP9/DwIDg4mH79+un+/WcGN2/e5MMPP2TrVlVvK2rXrs2iRYt0f9aDBw/SsWNHrfSnf4FnpJRZTq5KCFET5Xli88daqFAhNm7ciJ+fn+Z9sbGx9OjRQ5WfLoTgnXfeYeTIkbp//5mByWRi6tSprF6t7n8XEBDAsmXLVIpFVqwGl4Y6mQmoJ6XMcqEEIUQZ4ABgY2Xly5ePdevWaXYyB2XT79Wrl6qQGJS0ES3Frszk/v37LFiwgPnz56sOKiVKlGDp0qW6/Uhu3LhBmzZtuHDhQuqXkoGXpZTubm7qECGEL0pDxQqprhMWFqbbyfzOnTsEBwdr1rk999xzfPLJJ7qpMpmBlJK1a9cyZcoUlbpSgQIFWLRoEXXr1tW812Qy0aFDB736uG5SyswWkFEhhMgD/AqofqjQ0FA6deqkeZ+14etXX32leq1q1arMmjVLlUqd2WzdupUxY8aoznp58+bl008/1S1jMJvN9O7dW68twVgppaqNwYM4Y5TkQlGNejH1a2+99RYTJ07UvTciIoJ+/fpphraaNm3KuHHjdDdTd3Hnzh3CwsJYtGiRlmQZffv2VXU4f5Bdu3bRv39/LYvwBlBLSnkmPeebngghVgJdUl9v2rQpCxcu1D2Enjhxgu7du2vmp9epU4fx48frbjDuwmw2s2rVKmbNmqX599euXTs++ugj3Z/x4MGDdOnSRSs17S7QQEqZZZN9hRBTAFUOSI0aNVi1apVu2ktMTIxmQTFA5cqVmTBhArVr1073+bqClJKNGzfy8ccfa6aXNW3alNmzZ+tGSKw5+BpqVBIIklJqyoRkBYQQ/dGQky1Xrhzr1q3jscce07wvLi6OPn36aEb8SpYsyYcffqi7wbiTXbt2ERoaqimNW716dRYvXqwbIbl+/TodO3bUi1b3kVJmqSjJgwghWqBETGy8OUWKFGHdunW6oiomk4ng4GDN4vhChQoxYsQIOnTokOlOosjISMaPH6/q/AxKX4fly5dTtmxZzXtNJhNdu3bVi1ZPlFKOS9/Zph9CiGdRDrD5Hrzu6enJihUrqFWrluZ9ZrOZcePGaTZz9fT0pHfv3vTv399GtSszOHbsGCEhIezfrxKmolixYixdulTVud6K2Wxm8ODBehHbL6SU2qf7LIAQoiyKmqrNw8jDw4O5c+fqiqqAUmOhVb+bO3duOnfuzIgRI3T3LndhbdCq9Vzx8vJiwYIFuo0vQYkM6USrdwMvOVJSc2iUAAghSqB4c0qmfi04OFi3zgLg5MmTDB48WLOzqaenJz179qRbt266Xs2Mwmw2s3nzZmbOnKm5CXp7ezNp0iRatWql+x4HDhygS5cuWoV3EmgnpczSSYNCCG9gH1A59WtBQUF88sknuhvaxYsXGTJkiOZm4eHhQefOnenbty8lSpRI72nbRUrJ7t27mTFjhuYmmCdPHkaPHk3Xrl11f7YzZ87QoUMHvZqKQVLKLN0qWwiRG+UBoHpyPPfccyxevFh3Q4uLi2PUqFGanjohBG3atGHQoEGZ4tX5888/mTFjhuYmmCtXLvr168eQIUN0Dc1r167RoUMHlfyohWlSyiyVLqCFEGINoNqwq1Wrxpo1a3QNTpPJxIQJE/QaWNG0aVOGDRume4jISP755x9mzpypqzzVvn17xo0bpxvRSUhIoHPnznrN9L6SUnZIv9lmDEKIGYBKcqpMmTJ89dVXunUWZrOZTz/9lLCwME1Bizp16vDuu++q0oLcQXR0NPPmzeO7777TnNuLL77I1KlT8fX11bz//v379O3bV6+O5BegaWZKxTqDEGIoGrV+hQsX5ssvv9Sts5BSsmzZMqZNm6ZZh1KlShWGDRtGkyZN3G50Xr58mc8++4y1a9dqqrE+++yzzJo1S5U6akVKyZgxY1S93yycAJ7VkorNSgghXgO+I5UjIX/+/Cxfvly3zgIU6eOxY8dq1uKWKVOGYcOG0bJlS7dnJsTFxbF06VKWLl2q2YuuUqVKzJ07V/dvFpSacx1FsssoWQjaag8P4JRRAiCEeAklLUT1m5owYQKdO3fWvddkMhESEqLbjdjb25vOnTvTrVu3DA9N3r17l++++46FCxfqFnxWqVKFOXPm6HqoQOnS2alTJ27e1BQQmCml1NY0zGIIIWqgpIWozPN+/foxYoR+jb7ZbGb69OksXrxYc9PJmzcvb7zxBj179tTNFU4v7t+/z48//sjChQt11TD8/PyYM2cO1atX132fixcv0qFDB61UAVBU1N7UeiGrIYTwQ/HmqNznQUFBTJs2TTf1UkrJkiVLmD59uuaG6OHhQcuWLendu3eGH2KTk5P59ddfWbBgga7ARtGiRZkxY4Zd783Nmzd5++239f42fgcaZ8U0y9RY0kL2AU+kfq1hw4aEhYVp9k+ysmHDBj0FI4QQNG7cmL59+9rdVNOLffv2sWjRIvbs2aP5/PDy8mLixIm0adNG9z3u3r1L7969+f13zZ552eKAAyCEyIty0K6X+rWnnnqK1atX203H+vnnnxkxYoRurWedOnXo378/DRs21P3epxdHjx4lLCyMLVu2aB5a8+TJw6hRo+jWrZvugdpsNjNq1Cg2bdqk9fIVlAOO5kM6KyGUH/BbICj1a35+fnz55Ze6h3dQIvZDhgzRbaxZpUoVBgwYQPPmzTP8EHv27FkWL17MN998o1kHIYSgb9++DBs2zO5cpk2bpte5PhElzVLTu5DVEELMAQanvl6oUCHWrl1LpUqVdO+NiooiODhY03EKSvS7X79+tG7dmnz58mmOSS+uXLnCsmXLWLNmja5o0Ztvvsm4cePsRnHslDGYgebOSnY7bZQACCH6otGBUQjB4MGD7UZMQKkzmTRpkq6uuoeHB8899xxt2rShefPm6RbGSk5OZv/+/Xz77bds27ZNV3Ixb9689O7dmwEDBtj9Qzh48CC9evXS2wA2A20zq8N3WhBCtEJ5cKpkirp06cLYsWPtbmS///47ISEhurKUQghq165NUFAQr776qq5nLC0cOnSITZs2sXnzZl21KA8PDzp27MiIESM0OwRbiYqKonv37noGyZ9AMyllttHKFULUBXYCPqlfa968OTNnzrT7d3748GHGjh2r54EG4OmnnyYoKIjXXntN15ubFk6dOsXGjRv57rvv9NYDUPLnx4wZY9eZceXKFXr27KlnkEQBz1lUrrIFQognUNJCVGHIevXq8dlnn9n9O4+OjiYkJETvIA9AhQoVCAoKonXr1umaYhsTE8OmTZvYtGmTXqoVoBhYEyZMsOvMSExMZMCAASoVJwtXgUZZRZXJGYQQxVDWVXWaqVixIsuWLbN7gL1y5QoTJ07UrLOyUqpUKdq0aUNQUJBdj6erXLlyhR9++IENGzbY7TRfo0YNJk6cqNv5Gf5T+9myZYvWy4koKSCZ0rk9LQghvIAdQIPUr5UuXZqlS5faXYtbt27xySefsG7dOt1i96JFi/Laa68RFBREtWrV0mvqxMXFsW3bNjZu3Mj+/fs1nQeg1HtNmDCB+vXr676XlJKPP/6YJUtUpaygHFzflFKqZHezKkIID5RO821Tv+br60tYWJjddOc7d+4wb948lixZoinvDkpdzquvvkrbtm2pXbt2ujkUEhMT2bFjBxs3buT333/XbYZdsmRJxo4d67AGfPny5UyePFnv72OwlHKes3NzySgBEEKMBzRlqLp27coHH3xg9xeXkJDArFmzWLlypd2u4Hny5KFmzZoEBgZSp04dnnjiCacPPQkJCURHR/O///2PiIgI/vjjD+Li4uze07BhQ0JCQuxGR0DJex4yZIhe5+s/UA6uCU5NNAshhOiC0plc5bp6+eWXdTvYW7l37x6ff/45Cxcu1Az9WfHw8KBq1aoEBgZSt25dKlasyOOPP+7UHO/cuUN0dDSHDx8mPDyciIgILW1zG2rUqMGECRN0C0atHDp0iF69eqnkgi2cBBpmFTlRVxBCvAj8AKgWr379+nz22WeqzrMPYjab+fLLL5kxY4ZWAfGDn0PlypWpX78+gYGBVKpUiVKlSjn1EE1KSuLs2bMcOXKEiIgIwsPDHar0BQQEEBISQoMGqn3ehnPnztGtWze9qOgVlHXVFFLPyljy1XcBKuujUqVKLFu2zGHq5ObNm5kyZYrD5nsVKlQgMDCQ+vXrU6VKFcqUKeOUV9ZsNnP+/Hn++ecfIiIiiIiIsGuIgLIJfvDBB7z66qt2x129epUePXroGZrxQBOLClK2QghRAfgNjVRpPz8/li1b5nCP+vXXXxk/frxemqLN+1m/r08//TTlypVzqk4hOTmZCxcucPz48ZTv6/Hjx3UPrPBfjUv79u3tPhMcGJpJQBtLz4hshRDiMRQpVFWqdKFChQgLC9OtMbFy8OBBQkJC7DqJQKnnCAwMJDAwkKpVq+Lv7++0mMXFixc5efIkf/75J+Hh4Rw5csTuOc3T05OBAwfSs2dPu387SUlJjBw5ks2bNYUNJdBbSqlprWRlhBCewI9opEp7enoyd+5cGjdubPc9oqKiGD9+POHh4XbHFSpUiHr16hEYGEjNmjXx9/fX7fuSmqtXr3Lq1CkiIyMJDw/nwIEDuoYQKDUuPXr0YNCgQbopwfBf/5LFixfrDRknpdQvPNfAZaMEQAixEOin9Vrr1q2ZPHmywyjH6dOnWbRoEZs2bXK6f0mBAgXw9/encOHCeHl5pXjcExMTSUhI4NatW5w7d86lBmHPPvssAwcOpFGjRg7HfvHFF4wfP17vS/o3imdOO36eDRBCfABoKiM0bNiQWbNmOaz9uXTpEp9//jlfffWVnuGmwtPTE39/f4oWLYqPjw8FChQgV65cmEwmEhMTuXXrFjExMVy4cMHuxvcg1rD2yy+/7PBg/OOPPzJ8+HC9+caieNKzmqyz0wgh3gGWo2FwVq1alYULFzo0DOPi4li2bBmrVq2ya5w8SN68efH396dYsWIUKFAAHx8fPDw8uHv3bsq6xsbGEhsba3fje5CyZcvSv39/goKCHB6g9u3bR//+/fUimjdRUrbU8kXZBIvS2vdoGJxly5YlLCyMJ55QZXnZkJiYyNq1a1myZIlDA99K7ty5KVeuHCVLlqRAgQJ4e3uTJ08ekpKSSEhIID4+nosXL3Lu3Dmnn+3FixenV69evPXWWw73jhMnTtCnTx+9lJZ7QMusqMjkLEKIZ1B6hKnytYoWLcrChQsdHmCTkpL4+uuvCQsL05V5T42Hhwd+fn6UKlWKggUL4uXlRb58+TCbzdy+fZv4+HiuXr1KdHS00zKmvr6+dO3ala5duzqMkMfGxtKvXz89Q1MC70gp1bJs2QQhRHkUg1MlH+fl5cXMmTNp1qyZ3fdITk5my5YtLFy4UDf1R+NzKV26NKVLl05ZV09PT5KTk4mPj+f27dtcu3aN6Ohol/bsjh070rt3b4cp93FxcQQHB9uLzI6RUmaVZrUuI4QogpJ6+XTq13Lnzk1oaCjt27d3+D579uxhwYIFLjXMLFGiBGXLlqVgwYJ4e3unGBA3b94kMTGRGzduEB0drZsdlJo8efIQFBRE//79dcUnrJhMJt577z1++OEHvSELpZQDnP5hLKTVKPEAFgPdtF53piDGSkxMDIsXL+a7775z+rDzsHh4ePD888/Tu3dvXbm6B0lMTGTs2LF6+a0A/6DkzGXdJixOIoSYDGiKbpcqVYrZs2fzzDPPOHyfa9eusWzZMr7++mstpaMMIVeuXNSpU4eePXs6VQCYlJTEtGnTWL58uZ6xE4MiOamfj5BNsCg3zUOjN1HhwoWZNm2arkzlg8THx7N69Wq+/PJLt/Ycql69Ol27duW1115z6KWXUrJo0SJmzpypZ+zEAa2klJru2OyEEKIt8AWpFH5AOTiMHz+e119/3eH73Llzh/Xr17N69WqVfHBG8sQTT/D222/z5ptvOpU7vX79ekJDQ/UOT3eAt7K6wIgzCCEaoRTSqrxAuXPnZvjw4fTq1cvhM85sNvPdd9+xYsUKhx729MTPz4+OHTvSpUsXp7y5O3fuZPTo0XoZDckonb1VqePZDSHEUyie9dIar9GjRw9Gjhyp2/DVipSSnTt3snTpUiIjI5121j0sxYoV44033qB79+66SngPsn//foYOHarbzR6YJKVUNYfNbgghSqOsq2ZeYtu2bQkNDXWqJCEiIoLFixezd+9ep511D4uvry9t2rShV69eupLrD2JPwMrCMpTol8s/QJqMEkgp4ApBJ5Urf/78jB07lg4dnBM+uXv3Lrt27WLDhg3s3bvXbmgprVjz31u1aqUrn5maU6dOMXjwYE6e1M3w+BPFM+eek7cbEEIMAmajcYD18PBg4MCBDBo0yKnUHLPZzN69e9m4cSM7d+502hPjCgEBAbRu3ZqgoCBKl1Y96zW5cOECQ4YM0W0qCBxDMUiyR/trJ7AcYNeSqteF5TXeeecd3nvvPadTOPbt28eGDRvYvn17hjgUSpcuTatWrWjbtq3T+e83btxg5MiR7NmzR2/IJeDV7BwhSY0QojGwEdB0RQcFBTFx4kSna/QOHTrExo0b+eGHH3TrtB6Gxx57jJYtW7qU/37nzh1CQ0M1df4t3EZRPNTuJpkNEUI8DWwDNIt6nnvuOWbMmOHSXuZMnVZa8fX15eWXX6Zt27Y8++yzTqlCmc1m5s+fb6854D2UCIlaHzebIoQoh7KuqlQuUJT05syZQ5kyZZx6v5iYmJR1dZQemRY8PT158cUXCQoKomHDhk6lbkopWbFiBR9//LFetFQCI6WUM9J7vpmFEKIwSuT6Oa3XK1SowJw5c6hcWXPZVVy9epXNmzc7rNNKK3nz5qVRo0a0bduWpk2b2k3PfxB7YikW5gBD7TVItEeajZKUNxAiGEXyTvOEmpZ+JCaTif3796fUg5w4cYKEBNfKNKwpBs8++yz169enfv36LhXiOupfYmEz0EFKqS1ZkI0RQrRDOcBqui/r1KnDhAkT7CpMpCYpKYkDBw6k1IMcP35cT71MFw8PD0qXLk2tWrVS8madseytOOpfYiESxdB0Lp8lGyGEaIJygNWU8qlcuTKhoaEO00MexGw2c+TIEcLDw/njjz/4+++/9Wpz7M2LUqVKUaNGjZQ8d0e586nZunUrEyZMsBeZiwJekVLquneyK0KIqigHHU2rvEyZMowbN86paJgVKSXHjx8nPDw8Jb/cUf2JFiVKlEipI7PWG7kiY2qvf4mFS0ALKaWuhyG7Ykn52Y5G8TsoBt7o0aMJCgpy6Xd6+vTplOfwoUOHXEqNtVKkSBGqVq2akuf+9NNPu6QAtW/fPkJCQuylId0GXpdSajazyM5YUn6+R6P4HRRDYNCgQfTq1cul32lsbGzKuv71118upcZa8fX1pXLlytSrV48GDRpQo0YNl3qinD59mvHjx9tL17oHdJVSfunSxLIBFlGD9UALrddz585Nz549CQ4OdklV6+rVqynrun//fs6ePet0aqwVHx8fKlasmPJ9rVWrlktiUpcuXWLSpEls27ZNb4gERksp1Y1YXOChjRIAIURH4HM0VH7A+WIoe1y+fJnTp08TExNDfHw8CQkJJCYmkpSUlJJL5+vrS/HixfH396ds2bJplsjbvXs3oaGhjnJx5wHDspPKlqtYiqTXAprWXO7cuenevTvBwcFpVkq7fv06UVFRnDt3jlu3bpGYmEhiYiImkwlvb++UGpOiRYsSEBDgdDGmFvv37yckJIRjx47ZG7Ye6J4dxQqcRQhRC/gGKK/zOm+88QajR49Oc/+gmzdvEh0dTXR0dMq63r59G5PJhJeXV0qNSeHChfH393epGDM1J06cICQkhMjISHvDdgPtc1JEMzVCiACUda2hN6Z58+aMHTvWaXGJ1CQkJHD69Gmio6O5efNmSg2JyWTC09MzpcbE19eXChUquFSMmZqYmBgmTpzIzp077Q37H8rBVVv6LwcghCgOfAW8oDemXr16hIaGpllRy2QycebMGaKjo7lx40ZKDUliYiKenp74+Pjg5eVFwYIFqVChAuXLl0+ziuK1a9eYNm0a3377rT1D6DRK5Otgmj4kGyCE8EGp9dPNr3zqqacIDQ2lZs2aafqMe/fucfbsWU6fPs21a9dSakgSEhLw9PTEy8srZV3Lli1LQECAU2lZWiQkJDB79mxWrFhhzxC6AnSUUmo3JcoBWLq+zwb6640pV64cISEhPP/882n6jPv373P+/HlOnz7N1atXU2pIEhISyJMnD15eXnh7e1OgQAHKlClDhQoV0txuw0kRo3igp5RSs/mMK6SLUQIghKgMrAN0m0D4+/vTv39/Wrdu7TBnMjPYv38/8+fP55dffrE37CbQS0qp3YUsh2HJlVwL6H57SpQoQd++fWnfvn2aD5YZybFjx1iwYAFbt261twneAYZLKVUds3MillDzUjT0860UKlSIHj160KVLF7sSs5nF+fPn+eyzz/jmm2/seY3MKOINE7N6o7X0wKIGMwvoozfG09OTLl260KNHD6dTf9zJlStXWLJkCWvXrnWU7rkQeFdKqS/3l0Ow1HGOR6n308xKyJ07N+3bt6dPnz7pKuOcXty8eZOVK1eyfPlyRxHyr1H2WNfC6NkUIcRg4BN0shJy5cpFy5Yt6d+/v0uZCe7CZDKxbt06wsLCHEVS9wCdnGmglxMQQnQAwtDJSgBo0qQJAwYMcKpO193cv3+fjRs3snDhQs6etavzcwAlY+hEenxuuhklAEKI/MBUwG7DktKlS9O9e3c6duyYJQ6x+/btIywsTLOLdSr+Qvnl57j0D3tYNsSxln+6hSRFihTh7bffplu3bnYbfbmLo0ePsmDBArZt2+YoNeEMivfmD/fMLOsghOgDzEVDwcmKt7c3b7zxBn379s3w5qbOcO7cOcLCwli/fr2j1ISrQBcp5XY3TS3LYEm/XIJGobSVvHnz0qJFC4KDgx0qrbiDCxcusGTJEtatW2dXVhzFK9cnJ6Z/OMKSfrkG0A115cqVi5dffpmhQ4emay+StHLjxg1WrVrF8uXLHdWe3UVJ/5jtpqllGSzR63VoNEV9YAxNmjRh4MCB1KihGwx1G4mJiXz11VfOGCMSZY8ZnpMzS7SwpF9+iUZT1AepXbs2ffv2pWnTpu6Yll3TIZD0AAAgAElEQVSSkpLYvHkz8+bNc2SMAKwC+qVnCUO6GiUpbypEG5Twld023oUKFaJVq1YEBQW5/Ut26dIlNm3axIYNG+wpCFgxAR8DU6WUugUmOR0hxPPAAjSk7x7E29s7peFPnTp1MryD8IPcuHGD77//no0bN3Lo0CFHw++jpOGNyw5dnzMKIUQNFK9zoL1x+fLlo1mzZrRt25bnn38+wzsIP8jt27fZtm0bGzZsIDIyUreJmAUJrAZGZMfeMumFpefFXHTym61Y1Qjbtm1Ls2bNMryD8IPcvXuXn376iY0bN/LLL784k/++GQjOyelajhBClABmAJ3QkPm2YlUjbNeuHa+88kqa0+jSwv379/nll1/YsGEDu3btsleXaeU3oL+U8rAbppclEUIURInqDgDsPlxr1KiRItqT1hTbtJCcnMyff/7Jhg0b2LZtmzO1voeBATlB6TCtWJz17wGj0RCZeZCKFSvStm1b2rRp47DPVHpz8OBBNmzYwObNmx329UNx5AZLKb9P73lkiFECIITwBj4E3sWOF9ZKQEAALVq0oEGDBtSsWTPNdQP2OHXqFBEREezYsYPw8HBHBxsrW1A6Uqa/rEU2xJIvORRFdc3hLle6dGlee+01AgMDqV27dpprT+xx/vx5wsPD2blzJz///LOzBWC/ozwsc2zOsisIIXIBPVCM76KOxj/22GO0aNGChg0bUrduXbsNGNPKlStXCA8PZ8+ePezYscOR99zK3yjrajcH81HCoro2G3Ao51OwYEFeeeUVnn/+eerVq0fhwoXTfT43btzgjz/+4Oeff2bbtm3OauifBYZIKXV12R81LKprC4AqjsZ6enry0ksv8cILLxAYGJghEc/4+HgiIyPZu3cvW7ZscVa57SowCliRVrWenIalT80CQL89uoU8efLwwgsv0KxZMwIDAzMkbc8qPPT777+zefNmZ5Xb4oEJwOxHLTqihxDiCRQn0SuOxnp4eBAYGMiLL75IYGBghkQ8rcJDv//+Oz/88IOzym13genAlIwSeMowoyTlA4SoAkwDWmLHq/Mgnp6e1K5dm7p16xIQEECFChUoV66c05JlUkouXLhAdHQ0p0+f5sCBA0RERLiqHHMU+EBKucGVmx4VhBBlUA6wHXDg1bGSN2/eFHWlihUr4u/vT/ny5V0yVKyCB9HR0Rw6dIiIiAh7qjxanEN5WC4zNkE1QoiiQCjQE50c59R4eHhQtWpV6tevz5NPPom/vz8VKlRwyTN77dq1lHX9+++/iYiIcLVfxlWU1NE5Usr01xPP5licRGOAwWh0gdciV65cPPnkk9SvX5/KlSsTEBCAv7+/SwXOcXFxnDlzhqioKI4dO0ZERATHjh1zRekpHsWg+ignqhw+LA84iUYBThcIBQQEUL9+fZ5++mn8/f1dLnC+fft2ipDFsWPH+OOPPxx2/07FHZReZyFSStek+h4BHnASjcMJZ4IVPz8/AgMDqVatWspz2BWP+4OCBydPniQiIsJh9+9UmFH6Jr2XE/q2ZQRCiNeBycCTzt5TvHhxAgMDqVGjRoqASKlSpZxW3HtQ8MDa2X3//v2utGiQKFHqkVJK57p2ppEMN0pSPkix/j8A2mKnLkEPqxSsr6+vTffKPHnypCiFJCQkkJCQwLlz55z1qmpxEOUP5hsppVOhlEcZIURF4H3gbcDl8JZVCrZw4cIp3Wa9vb3Jly9filKIVVXi/PnzLktDP8ApFCNqlZTSuXbEjzAWgYORQG/AKy3vUbx4cYoXL56i3OPt7Y23t3eKUohVkevChQsuS0M/wEUUz82inKyYll5YpEiHoBgnaQqDFClShMcffzxlPa1qala1Jutz+MKFC9y4cSOtU72Bonc/xzi0Osai5NQXGI6dehN7+Pr6UqpUqZTvq1XR0rqe1u/rlStX0iQNbSEBpfh3upQy/Zul5DCEEHmBriipP2lyl3t7e1OmTJmU76pV0fLu3bsp63rr1i2uX7/OxYsX09qI8R5KfcHHj1rNbVqwGJ1vojiKdMWh7JE/f37Kli2b8hy2KlomJSWlPIdv3bpFXFwcFy5cSGsjxmQURcfJ7soqcZtRkvKBSkfTESgLkv45H2kjGUUydDaw2fCgu46lIdS7KMZJ2jQFM4YIlLqRLx8F9aX0xiJHOgToBjjfECbjOYxSB7PsUVBfSm8s+esDUIzOCpk8nQeJQpGXX/Ao13mlFUv+eg8UOdKqmTydB4lFkb+dnRP7P2U0QojcQEdgIE6kdbmRayj1e5/mpEbD7sLShLwVyh7bmDQ47DOIeJT2CNOllEfd+cFuN0pSPlhJJ2iLcoh9ESdTgNKZf1Cs+zVSSrtNSQycw+LZaQm8g1Jg61zOXfoSjfKgXJ1eMnWPOhYFthdRvq9tcaKeKAO4hCJPvSondWTPTCybYgOU7+ubpDF68pDcQOnDsQr43XAKpQ+W7IQuwFtAyUyYQgLwLcq67jKcQumDEKISyrq+jU6vqQzmLkqt7Upgi5F5kD5YUuLfRllbh3ViGYAZ2IFydtqQWemymWaU2ExCiMeBV4EmQFMyziObAOxFiYr8aBxsMhZLqsiD6+pai27nuQuEA7uAn4AI42CTcVhSRV7mv3XNqAfofSAS5fu6E/jZONhkHEKIfCiGZ1PLv+pkjOcuGSVNdpfl385HWdUwo7F42V/gv3V9FsioRmH/oKypdY+9nUGf88hjcSjUB15CWdf6OFkHmAZO89+6bjNSKjMWi0PBuq4NyTgn4AX+ew5vywo9ZLKEUZIaSyPG51EOO5WBSigeAVc2yKvAMeA4cALl0PqHUQSbeQgh/FE2x6dRirwqoxgqrmyQN1DW9BjKukYCv0kpna7YMkhfLE6FJkA1lO9qZRS9fVeiZPH89109htKp+2cjhSfzsIgevAA8g7KuT1r+64qEnon/1vUESq+nX6SUTkkzGaQ/ltS951HWtTL/rasrHVLvotTpHbf8OwzsyQqHmkcVS+PU54A6/Le/VsK16GcSSqaBdY/9G+U5fCZdJ2vgNJbsk7ookv3W53BloJgLb2NGUTC07q//AHullMfSd7YPT5Y0SrSwePH8UB6E9hgErJVSprnC0sB9WNRjSqPUftiTCZkCzDLykbMHlnSv0sAmoKadocuBMcZhJntg8c6WRqn7sCdtuQ2lXiXWiFpmDyzOhSko9WN6HADaoKyrEbXMBgghiqEotI2xM+wySqQl1nDcZg8smShvodTM2uMJICa7RKMzKoSb7lh+oVFOSKDFGAZJ9sHyADwjhHCUl3rRMEiyD5YDyzkhhCNFrKuGQZJ9sBgYMUIIR9214qSULml1G2QuUsqLQghHz9gEo6A5eyGlvCqEcPSMvWdEQ7IXUsrrQgiHz1gppUva+plNVqn0NzAwMDAwMDAwMDB4RDGMEgMDAwMDAwMDAwODTMUwSgwMDAwMDAwMDAwMMhXDKDEwMDAwMDAwMDAwyFQMo8TAwMDAwMDAwMDAIFMxjBIDAwMDAwMDAwMDg0zFMEoMDAwMDAwMDAwMDDIVwygxMDAwMDAwMDAwMMhUDKPEwMDAwMDAwMDAwCBTMYwSAwMDAwMDAwMDA4NMxTBKDAwMDAwMDAwMDAwyFcMoMTAwMDAwMDAwMDDIVAyjxMDAwMDAwMDAwMAgUzGMEgMDAwMDAwMDAwODTMUwSgwMDAwMDAwMDAwMMhXDKDEwMDAwMDAwMDAwyFQMo8TAwMDAwMDAwMDAIFMxjBIDAwMDAwMDAwMDg0zFMEoMDAwMDAwMDAwMDDIVwygxMDAwMDAwMDAwMMhUhJQys+egixDCAygPVAKqAOWAYAe3bQN+A04Ax4ETUkpTBk7TwEWEELmA+kAjoDbwBFANyG3ntkso63kY+APYKaW8mMFTNXARIcQzQFP+W9enAS87t1wDjgLHgHBgt5QyOqPnaeAaQojKQDOgLsrz+CmgoJ1bbgH/oHxn/wR2SSmPZfQ8DVxDCOGPsq71gcqWf0Xt3JII/I2yv+4H9kgp/5fR8zRwDSHE48CLQD2gKvAkUNLOLfdR9taTwF/AXiBCSpmcwVM1cAEhhCfKWlay/HsOeMXBbXOAMyh77AngjJTSnIHTfCiylFEihCgKvIByqGmE8svP95BvK4FzQASwC+XQc/Ih39PABSwPyL7Aayibnnc6vbUZuAr8DqwCvjMeou5DCFEE6AG0RTEqfQCRDm+djGKs/AmsA9ZJKe+lw/saOIEQwgvoBrwBPAP4kj7rKoE44H/AemCllDIxHd7XwAmEEHmBDkBHFOOyCOmTLSGB28AhYCOwVEp5PR3e18AJLE6+1kAXoAFQDPBIp7dPQHEa/QAsMhyB7kUIURHlPNwExXFQlod/Ft9FcRb9AuxGcSxkme9rphslQohKKF+mlkAN3JNSdh74EViLsiDGQTadEULUA0JRHpI+bvrYZBQDdDXwkXHgSX8sHvPJKA/KQm76WAlcBL4BxmelB2hOQQhRBpiI8hx+zE0fK1GMz++BsVLKWDd97iODxXEwAXgdxVOeHsalM9wAdgIfSClPuOkzHxksjoMxwNtAGdyXih+P4gQcK6WMdNNnPjJYDMwmQCegOeDnho9NBg6gGJ6rMttpnylGiRCiEP9Z9s1w34NSi1iUw84yKeWBTJxHtseyAX6I8oUqkcnTkSjhynlSygWZPJdsjRCiIDASxXvujoekPSQQDSwCphsOhbQjhMgNvIsSxayQydMBuIziKPrQcCg8HEKIt4ERQHUyd38FuA58jWKg/JvJc8nWCCHaAO+hRLoyuyb4FvAdMMqIoDwcFmdfR+AdwD+Tp7MfJfNkrZTyqrs/3K1GiRCiLDAc6IX9PPPM4jdgqpTy+8yeSHbCEu0KA54n8zdALUzAZ8AI4xDrPEKIEsBCFAdCeqUDpCd3gRXAECnlncyeTHZBCOEDzAC6A3kyeTpa3EeJnvQyomLOYzEyQ1AMzay4vyaj1Cp0lVKezezJZCeEEKOAsbgv68AVJErqXjfDsesaQoiGwGiUCHVWOztZ99dJUsrz7vpQtxgllry491AiIy5tgsWLF6dChQr4+/vj7+9P4cKF8fT0pECBAvj4+ODh4cGtW7cwmUwkJiZy69Ytzp8/z+nTpzl9+jTnz5/HbHa5pmcvMFlKud3VGx8lhBC1gc9R8s5dwrdwUUqXr4hf+ScoXf4JfAsXJb+nFz4FC5Hf04vcefKSmBDPHVMid00J3L51kysXzhN7NoqY6JNcOB/N/SSXywysxskoKeV9V29+VLB8Xxej1HW59KD0KViI0uUC8PNX1rZQ0WJ4evngXaAg+Ty9yJs3P3cSE7hjSuSOZV3/vRxL7JkoYs6eJPZMFPfuumxfJKF42AdJKW+7evOjgsXI/BxlA3TJy+rp7UPpcgEpa1ukWEm8fQri6e1Dfk9v8uX35O4dE3dMCZgSbpNw+xbXr14iJvoksWejiD0bhSnB5aUxA5uBPlLKK67e/KhgMTIXoHhaXdpf8+bLT+nyAfiVq0jp8gE8VqI0PgV9ye/pTX5PL/J7eXPv3h3umhJJiL+FKfE2cdeuEnPmVMra3r4V5+qUJfAzitEZ5erNjwoWI3M6SiQzvyv35s6Tl1Jl/PHzr0jpcgEUL1UGn4K+5LOsq5d3Ae4n3eOOKZHbt+K4Y0rk5o1rxJ45RcyZU8SeOcnNG9fSMu2/UNbVED+wgxDiVeADlEJ1p/Hw8KBMmTJUqFCBChUqUKZMGQoWLIiXlxeenp4ULFgQs9nM7du3iY+Px2QycePGDaKjo4mOjub06dNcueLyo/QeSuTkYynlKVdvdpUMNUqEEL4odQUDccLTmitXLp588knq169PYGAgzz77LAUL2hN4ccz9+/c5fPgw4eHhRERE8Ndff3HnjtOHnt3AQCnl0YeaRA7Dkn63AWjs7D1+/hWpXqchNeo24unaDShU5OHS1pOTzUQf/5tDkb9y6M+9HPkr3JVDTyIwWEq59KEmkcOwFMJ+gVK47pQxUqJUWarVaUiNeo2oXqchRYs//lBzkFJyPvoEh/7Yy6HIXzm87zfib95w9vYklJqTKQ81iRyGJU95PtAHJ42RIo+VoHrdhlSv24hqzzbk8TLlH3oeF89Fc2jfrxyO/JWDf+7lxr9Ob45mYKGUcvBDTyKHIYQIQTncOGWMFChUhGq1G1C9biOq121IGf9KCPFwDtp/L1+wPIeVZ/GVi047VSXwFfCOIWRhixCiNzAb8HRmvKe3D1VrBVKjXiOq1WmEf6WnyJXr4YLbcdf/5ci+31L22JgzLp1HdwLtpJS3HmoSOQwhxNMoz+IXnBmfP39+atWqRWBgIPXr16datWrkzm1PpNQxt27dYt++fYSHhxMeHs7x48dx0g64D8wFQqSU8Q81CTtkmFEihOiEYuU7PKXUqFGDtm3b0qJFC4oUKZIh87Fy79499u7dy4YNG9i1axf37jl8Ft4DPkUJYSVk6OSyAUKID4FxOLEJlnuiCk1bdeCFV9ryWMnSGTovs/k+hyN/Y9f36/h952bumJxKST8KtDK8dSCE6IUiHehwEyzpV46mr3Wgccs3KFU2Y0sRZHIyxw7tY/cP6/ll2wZnvbIxKBviI1+IKYRoBazECVGCIo+VoHHLN2jS8k38n6ya4XM7ffwIuzd/xc9bvuH6v5edueU60EVKuSWDp5blEULUR6mFLOVobAHfwjz/SluatHyTJ6vVRuTK2FKE2LNR7Pnha3Zt/orLsU5laSUCA6SUKzJ0YtkASyr09yhyr3bJ7+VNg2av0axVB6o+2wAPj4c7rDri30ux/Lz1W3Z+v45zUU6pe98Dxkkpp2boxLIBlmjmOGAoDs5OefPmpWnTprRr146GDRuSN2/eDJ3btWvX2LJlCxs3buTgwYPO3HIBeFdKuS4j5pPuRokQwg9YjlLArouvry9vvfUWbdu2JSAgIF3n4CxxcXH88MMPrF69mpMnHQoOnAN6SCl3umFqWQ4hRACwBweFzvk9vXgxqBMvtelEQJXqbplbau4kJvD7zs38sG4pxw/vdzQ8GZgjpRzmhqllOSziBHtR+k7okjtPXhq3eJ3mbTtTpWa9h/aupoWke/f485ftbPt6Bf8L3+NouATWSyk7ZPzMsh5CiPwoCoON7I7LlYsGTVvSvN3bPBPY+KG9q2khOdnMX7/v5sdvVxO+ewsy2WHZ189A80fRu26Jeq0H2jka+0xgE159syt1GjUnTwYfbLSQUvL3XxH8uGE1v2z9lvv3kxzdcgh4QUrpcj5YTkAIMRclq8Tuw7Vy9Wdp0aEHDZq9Rn7PzCkdOvXPQX7atJYdG9dy947DNnDngOcf1ToiIURzlHToMvbGVaxYkS5dutCyZUt8fX3dM7lUREVF8e233/Lll19y8+ZNR8N3AN3TWzUxXY0SIcSLKHKsuspLRYoU4e2336Zbt24PnZqVXkgp2b17N/Pnz3dkKUqU8NXwR6kmQQjRBViCHQvf09uHl9p04o2eQyjyWGYLb/3HP/+L4Oulc/jzlx8dDT0N1HuU1GGEEK+gpOHp5ivnyZuXRs2DeKvfqHRJ4UkvTh8/wsaVC9i95WtHh9hLQINHqSGjpdZrJ0p/Ee0xuXLx3Iut6Nx/NGUqOHTKuo2L58/wzfI57NiwFrPZ7iP2JtDkUcpdF0KURum3pesYEkJQp9FLdOgznCer1Xbf5Bxw9WIMG1YuYNs3Kx3VjN0FOkgpN7lpapmOJR16D0pLBF2eqlmPN3oEU/eFl90yL2e4FXeNzV8sYdOaRSTE2z3E3keJhn3upqllOpbm32Mt/3TDk1WqVKFHjx60bt0aD4+soSeTmJjIV199RVhYmKMalH9R0i+3ptdnp4tRYinImowiG6pp5fv4+BAcHEynTp3In9+lmi23smfPHj766COiouxm9OwBOuV0GTyLV24j0EpvTN58+WjXdTBtuw7A2ydrGJla/HPgDxZ/MpYTR/6yN8wEBEkpHVow2R0hxCKUGgNNcuXyoEWH7nTsPZxCRYu5cWaucebE3yz5dDz/C99tb9h9lOLLHJ8eIoQYC4xHZxMUQvDCq+3oMmgMJUqXc+vcXOFSzFlWzp3EL9s22BuWjCIf/JGbppVpCCF6oMhg6+boPNvwRboPC6HcE1XcNzEXuf7vZb5cNJ2tX6+w50yQwAIp5SA3Ti1TcMYxVLlGHXoND6VyjTrum5iLJMTf5Jvl89iwcj5J9lPiN6Gk1uZoFUyLA2EtiiKpJk888QRjxozh+ed1h2Q6JpOJ1atXM2/ePBISdKsXkoGpKKl6D+2sf2ijxFLMvhE7Rc+tWrXi/fffp3jx4i69t9ls5ujRo5w4cYLTp09z5swZYmJiuHnzJgkJCZhMJu7du4ePjw8FChTAy8srRa0rICAAf39/atasiZeXayHOpKQklixZwvz58zGZdEOTl4GWUkqH+UHZEUtvir+x45Wr1aAp/d+fyuNlXZPVllJy9tRRzpw8qii4nDnF5QvnuBV3zaLKlMjdOya8fQri5V2A/J5eFH6sOKXLP4Ff+Sfw869Ipaq18CnoWu8+mZzMtm9XsXLOJHvF0xJ4P6fmwVocCPuw45V7slptBnw4nYDK1Vx+/9izUZw+flhR04o+waWYs9yMu8bdRGVdExPiFYU1L0UFplCRxyhd/glKl1PWtlLVWmkygn79cROLp4/l38sX7A37TErZ3+U3zyYIIbYBum7UMhUq0X/MNKrXaejye1+9GMPJfw4oSlpnThF7NopbNyzf18QEEm7fwruAr6LY5OlFwcJFKV3uCUqXVxS7Kj39TJrqyg5E/MxnH412VGT7g5TyNZffPJsghPgcRUZfk8dKlqbPqMk0aOb6ryDu2lVOHPnLorh0itizp4i7/m/Kut6+FZfyDM7n5YVv4cco6VcOP4tyYoXK1dJUV3by7wMsmDyCk3/bVZD9CyV6nSOzEiz1maHoOHILFCpCtyFjaR7U2eU6oNu34jh+eD8x0SeJOXOKC2ejuPHvlZRncMLtW+TL75nyffUt/BjFS5VN2V/LV6xC2YDKLqfpxp6NYuGUURyI+NnesHPA0zlVKVEIUQdFNVDzwOvp6cngwYPp0aOHy0XriYmJHDhwgOjoaKKiolLUtBITE4mPj+f27dvkzZsXT09PvL298fX1xc/Pj/Lly1OhQgWefPJJKleu7HJE5vLly0yePJktW+yW8+0C2j6suMFDGSVCiJLANnQOOH5+fkyZMoUGDRo4/Z4xMTHs2LGD8PBwIiMjiY9/uCJ/Dw8PatSoQWBgIC+88ALPPPOM01+02NhYxo4dyy+//KI3JB5lEXJUnYnFyj8MFNZ63bdwUfqPmUbD5m2cfs8b/14hYvcWDv65l8ORv6ZVbjCFXLk8qFC5KtXrNKRWg6ZUr9vQ6Xz4mzeu8fm0MezZ8o29YXOllMEPNckshqXY7m+grNbr+b286Tk8lFfadXF6E7x9K46I3Vs59OdeDv65l2tXHi54KISgTIUnqVG3Ec8ENqZWgybkzuNcPvydxARWzpvC92vD7KmJbJJSBj3UJLMYlojmPnSkuXPnzkOn/qNo13Wg879LUyKRv2znQMQvHIrcy8XzZx56no+X9ad6nYbUrPc8dV94hXz5nRIW4n7SPb5eNocvPptuL6VrH8oBNkd5YIUQ3wOa1oYQgjZv9+Ptge87XVuQdO8ef/2+i/9F7OHQH3s5d/r4Q8/xsRKlqF63ETXqNqJ+k1fxLuBcPrxMTmbL+uUs/TTEXl3CGZQDbI5qpimEWADoOkiavtaeXiMnUrBQUafeLznZzME/9vLX77s4FPkrp48fcaY2yy6FijxGtWcbUr1eIwKbtHDJWbR3+wYWTBlNfJxum6HrQNWclm1iKWHYgE4/mcaNGzNx4kQef9w5lUopJX/99Rc///wzERERHDx4MC0tLmwoWLAgderUITAwkJdeeonSpZ13Fv3666+MGTOGCxd0nX//A16VUjqlXKJFmo0SIYQ/sB2oqPV6s2bNmDp1KoUKOfZm3759m61bt/Ltt9+yb98+Z+XJ0kTZsmUJCgqiXbt2+Pk5bk4tpWTFihV8/PHH3L+vuSHeQ8mpyxAlAncjhKgK/IFO862qtQMZ+XGYU9Kv9+7eJWL3FnZtXsdfv+0mOfnhvkz2+D97Vx0WVfa/3zN0KQIGigomFmKLiahri6iLnRjY2F1rYbHm2rF2F+paX7tz7UZABEFAlK65vz9mQO495wC6cwfQ3/s8+zw7Z84wx3vmnvvJ97UsZA3nNp3RtF0XlChtn63PnPfdi7/mjc+MqctXEIT2GltkDoIQUggqh4TJxVy8VDlMWrwpW6UfqakpuHf1f/if717cvnQqq3T9f4KZuQUat3SDS7suKFe5erY+c/vyGfw5fXhmD8SHAKr/DAasuqH9IThsPVZFimHiwg2o4Fg7y78lKJV4dFfFYHftnC8S4uQjGzQyMUW9pm3h0q4LHGrWz5YT/PrpA3iPH5AZo9M7qAydPG/Aqh3N8+BQh+Yzt8SYuatRs2GzbP29l4/v4bzvXlw+dfh7KLa/G/oGBqjTuBWatHNHjfou2WKECnr3Gt7jPeD/+hlvyk9lwBJC9gH4nfWevoEhBk9cgBademXrbwW8eY7zvntx4cQBRH76qMlliqCjo4vq9ZrApZ076ji3hr6BQZafCQ8NxqKJg/DswU3elDgAtQRB4G58XgIhxA2qki2qFE9HRwfDhg3D8OHDocjGWff+/XscPnwYhw8fxvv38ukWKhQK1KpVC25ubmjVqhVMTEyy/Ex0dDQmT56MU6dO8aa8A9BCEIQs2aNY+CGnRE1bdwlAEel7enp6mDhxIvr06ZNlRuLz58/Yvn07tm7diq9ftUtnrVAo4OzsjOHDh8PBIWuWqHv37sHLywshIcxzUQkVC8E2Ta9Tm1A7JPcAUOFUolDA3cML3YdMyPJBkxAXizaJTg8AACAASURBVDOHd+DAlpWyHpQ8fE9DYODbF/Ae55FZxPCMIAi5p7PwB6AWzXsDTvSmRadeGDxxAfQNMu/1SklOwuVTh7F7/RKEBGq/b7y0fRX87uGF+s3bZ3m2hH/8gIUTB+L5v7d5U54KgiA/762MUDsk78A4hwGgbpNW8PpjZZZljoJSiWvnfLFrzSKNRM6/FyVK26NzvxFo3LpTlmdLdFQk/pw+PDPiio8A7ARB+G4FztwCtUPyGBxGvErV62K893pYFc6SDRj/3ryEHasX4MWjuxpeZdYoZF0cHXp5omXnPlmeLYkJ8VgzfyLOHd3FmxINoExeF9EkhJwFwPQkS5apgEmLN2WLeCKNwOXOlbOyBnFZyF/AEm26eMC15+Ass2KpqSnYvmo+Dm5ZyVtnEoBqed0xIYT0AbAZjF6+YsWKYfny5XB0dMzy77x48QIbN26Er6/vf86IfC9MTEzQuXNneHp6omDBzLNigiBgy5YtWLRoES9Y/xEqxrXvdky+2ykhhBQFcA2ArfQ9MzMzrFu3DrVrZx6V+/LlC1atWoU9e/Zk1rOR9n0oXbo0ypQpk67qbmFhARMTExgZGUFXVzddzf3z588ICgpKr7d7/vw5EhMTs/z7zs7OGD9+PMqVy/wwiIiIgIeHB548ecJ6OwWqJukTmf6RXAp1ydZrMHQq9PT1MW7+WtRvnnnSICkxAQe2rMDRHVkycQBQlXOULFNBpRJtWwbmloVgaGQMI2NT6OrqIjExAfGxMYj5GoXQ4PcIDniLIP/XePvicbaiuJWq10XfUTOyjBInxMVi3pg+mdHMbhcEoXeWX5gLoS7Z8gdA1QEQhQKDJ8xH227ccnUAqgfLiT2bsH/z8mwJ3hW0tkHJMvawsS0HG9sysChYGAZGxjAxzQddXV0kJyelq0OHBb9Pr3n2e/kkW1HcUuUro/eIaVlGiVNSkrF8xkhcOLGfN+WKIAi5t8swE6gN11cAmHzqv/cfhd4jp2XqvAmCgAvH92HX2kX4GJQ1W2cBq0KwLVspve7cspA1DI2MYZrPHLq6ukhJSUlXhw4PDUaQ/2t88H+Ld6+eICriU5Z/37qEHXp4TkTj1p2yXPfWZbNxcOsq3pTXAOzzaiaMEHINALPmuWn7rhg5a1mWztuti6ewffUC+L96muX3meUvgFLlK6Oo+hwuVLQ4jIxNYWKWD3p6+khJSUFszFckxMUiMjxU1S/m/wr+r58j/GPWbKAWBYvA3cMLrbv0y7LE9uiOtdi4dAav9CgcQMm8mgkjhOwA0IP1Xo36TTF56ZYsy/Ce3r+Jv5fPwbN/b2X5fYbGJihTwUHd21UGhaxtYJrPHEYmpjAwMERKSgri42IQHxeLqIiw9H6xgDfPs1WuaZa/AFx7eqJjn+FZZk6unD6MpVOHISWZmVWPg8rhzJOZMLUW1CEwSCgcHBywcePGLPX3Xrx4gcWLF+PSpUx7cQCoBBXt7e3T+6ZtbGxQoECBdFX3lJQUxMXFIS4uDpGRkelq7m/evMHbt2+zdGKNjIzQo0cPDBs2DGZmZpnOvXnzJjw9PRETw2wPegeg/vfu63c5Jeqm9osAKJfPysoKmzdvRsWKfLkDQRBw5MgReHt7IyKC31NgaWmJFi1awMnJCXXq1PlhQcXExEQ8ePAAN27cwLlz5/DyJT8KqKuri759+2LkyJGZNsbHxcVh6NChuHr1KuvteKj485lv5lZkZrgaGptgqs9WVHNqkunfuH35DNZ5T85ULMvENB/qurRG1TqNULV2wx9W/05NTcGrx/fx8PYV3L1yNtMoICEEzVy7o9/oGZnW56YkJ8Fn2rDM2H6WCoIw7ocWnEPIzHDV1dPHmLmr0ailW6Z/49mDm/hr/sRMjRt9A0PUadwSjk6NUbV2IxSx+TFWJ0GphN/LJ3h4+wruXT2HR3evZVoX7eTSBoMmzENBa34ZZjYM2COCIGR+EXIhCCG3AVB0PIQQ9PWaiU59Mycu8n/9DGvmT8DT+9zSCujq6qF6vSaqnq06DVGiVPkfXm/g2xd4ePsKHly/gPvXL2SqWVG5Zj0Mnbo4y+87tnMdNiyZzvuN3BQEwemHF5xDIITsAcDU1mnffRAGjp+baalbaHAg1nlPxu1Lp/nfoVDAoVYD1GzQDA61G6JUuUo/LKgY8t4fj25fwYObF3H70ulM6X5Lla+MoVMXZ8kidfHkQSybPpz3GwmAyoDNU83vhJD5ACaz3nNu3Qlec1ZBV5evqRcVGY4tf87Ced+9mRqV9lVroVbD5qhauyHKVq72w4KKEWEheHj7Cv69eQm3LvyD2Bh+JYt1cVsMnuidZZDo0Z2rmDuqF+JimX3CnwHY5jUFeLWI6TkAVN1T3bp1sXbtWpiaMgsUAACxsbFYtmwZtm3blmlmxN7eHs2aNYOTkxMcHR1hkI3yORYiIyNx8+ZN3LhxA6dPn0ZkJLfEGQULFsSkSZPQvn3mlQkvX75Ev379eNTBT6DKmGS7ZjTbTom6VOAsAIq6pUSJEvj7779RvDhfGyY4OBjjxo3D7dvscgodHR00b94cHTt2ROPGjWXha37+/DkOHTqEw4cPIyqKrc9kbW0Nb29v1K9fn/t3kpKSMGbMGF5NXSSABoIgPNfIomWGmo3JHwDV7WRuYYXZf+3LVAQxOioSK/8Yg+v/O877+6hRvymatu+S7VrU78WHgLe4cHwfzh7ZxW20NstfAJ6TF6JxK77mmKBUYt2iKTi+eyNvynBBEFb/9xVrB4SQB2AEEAyNjDH1z78zdTQTE+KxftEUnDm0g/sQrFitLn7r0B31mreDsUnmEZUfQfjHD7hw8gDOHt6J4EA/5hxDI2P0GTUdbbsOyPTgPLB5BbYu/4P39p+CIIz57yvWDgghx8Cg6dbR0YXXnJVo0oZZrg5A5dDv/GshDm1dxXUMSpWvjOZuPdC4VcdsN9p+D758jsClfw7i3JFd8HvJzDpDV1cPnfuPQjfPcZkaVud992L5zFG8BvjDgiBkKTKYW0AIWQFgBGM8S0dTEAQc3bEW21fN5zaNFytZGs079IBzm87ZKv36XsTFRuPqmaM4d2Q3N5JPFAq07NQbA8fPzbSk6961/2HB2H68fr+7giDkXn5cCQghXgD+ZL2XHUfz4okDWOs9CTFf2TaLVeGiaObaHS7t3H+ICS0rJCUm4OaFf/C/Y3tw//p57vOgfvP2GD59KczyM/lxAKhY12YN68IjunkPlWOSJzKchJBKUAkPU//gVq1awcfHB3p6fEfz8uXLmDx5MkJD2T3hBQoUgJubG9zc3FChguZpvlNSUnD58mUcOnQIZ8+e5TpFTk5OWLx4MYoUYVYJAwACAgLQt29fXv/LJah6TDIvW1Lje5wSJltEoUKFsG/fvkybxs+fP48JEyYwHQE9PT20adMGw4cPh62tbbbW8l8RHx+PvXv3YsOGDcwfBCEEvXv3xuTJk7mUbampqRgxYgTOnGHWNr8CUFMQhP9GHaYFEEJOA/hNOm5sYoYFm45m6pBk1nhKFArUatAM3YdMRJmKmWpCaQxpPQ97N/jgQwBbZ8alrTuGTV+aKfPPWu9JPMdECaCGIAiZ8ljmBhBClgEYJR3X1dXD9BU7UKN+U+5ns2o8dazbGD2HTtIab76gVOLOlbPYtXYR3jxji5vWcW4Jrz9WZvpA3LN+CXas9ua93TYvlF4SQkYCWM4Yx8hZy9C8A7M6BEDWjadpvVi1Gv323VSgP4pnD25i55pFeHiLzXCYHWKNCyf2w2fqUJ6xNE4QhKWaWa18IIS4QkWtT6H3iKlwHzCa+9nYmK9YMcsL184eY75vW7YiOvYZBuc2nbPNUPhf8ezfWziwaTm35yE7xBoPb13GrOFdeUQaawRBGKq5FcsDdZ/mQzB6DVp17oNh0/k/zaTERGxdNhvHdq1nvl+4WEm49hiElp37yhLsYyHgzXMc3LISl/45xAwEZIdYw//VU0zs355X4n1cEASuLlpuASHEBMAdANQP2MXFBWvWrOEG1lNTU7F69WqsWrUKSkaW19LSEj169ED//v0zzbJoEkFBQdiyZQv27NnDbHkwNzfHkiVL4OzsnOnfcHd352VMVgiCQNkjLGTLKSGEdAZAFWabmZlh165dXC9OqVRiyZIl2LBhA/Ngat26NaZMmZKpByYnEhMTsXHjRqxZswYJCXTauU6dOli1ahUKFGAbOgkJCejbty/u3mWWD20VBKGfZlesWagFuTZJx3X19DFz5S5Uc3LmfvbojrXY7DOLeTA51m0Mz0nesLFjErPJjtTUFJw6sA3bVs5jHny25Sph+rJtXPE4pTIVCycM5D3kPwMoIgiCfJRT/xGEkKZQZTWJZByj56yCSztmdQgA4NI/h7BythczQlm2kiOGTFmUbRYsTUMQBFw+dRibls5gEigULlYS0/78G3bl+f3rGxZPw9Eda1lvJQAoLghCuMYWrGEQQuyhSodTT7v+Y2ajY59h3M/+e/MSFk4cyGQkK1ayNDwne2dZoikn7l8/j7ULJjEzYvkLWGLCoo2oWrsh9/OZZMJSAVQUBOGVxharYagVvUPAYO1p06U/hkxZxP3s2+ePMHd0b3wKCaLesyxkjQHj56BBc1etOZlSvHh0F2vmT8Db54+o9wyNTTBq9nI0/I3P0H3pn0NYMsWTVaInAGgtCAKXAiinoa5CCAVA1Z/XbdIKU3y2cp3Ej0EBmDOqJwLe0AUXpvnM0WfkNLTo1EtrTqYUgX4vsXb+RDy6Q1eq6+rqwWPcH2jXbSD384/uXMXMoe48h3OIIAjMQzq3gBCyDQBFkebo6Ijt27fDyIgd9IyIiMCwYcOYNqORkRGGDh0KDw8P6Otnj7pd0wgODsa8efNw+jRd/kkIgaenJ8aMGcM9T169eoVu3brhyxemw9lJEIRDWa0hS6eEEFIKKhEjEc2CoaEhtm7dipo1azI/l5ycjAkTJsDX15d6r2TJkpg9ezYaNPh+ES85EBQUhFmzZuHixYvUe6VLl8bmzZu5XM5RUVHo2rUr3rxhinv1za0q0oSQsgCeQ2LgKBQ6mLRkE1eISxAEbPaZicPb/qLes7AqjAHj52bZp6AtREV8wmafmTh/fB/1noVVYfyxZh9sy1VifjYpMREzhnTGk3s3WG+fFwSBn2rIQagNnGAwCAsGTZyP9t25Iu44sv0vbFo6kwogmJjlR5+R09Cqc58frj3XJOJio7FjtTeO795I0UybmObDtOXbUaUmu/xSUCqxaOIgXDnDDEq/FAQhe3zSWobawPkIRt9Xxz7D0H/MbO5nL586DJ9pdJOpvoEBugwci459hkMvhx6CGZGclIQDW5Zj/6ZlSJJE6/T09TFm3l+ZGrAbl0zHke1rWG99giqQkCvLQgghr8Cg1m/cqiPGzV/Lvece3rqMuaN7Iz5W3GSqUOigfY/B6DFkAoxMtBNpzQxKZSpO7N2M7SvnU/0ERKHAwPFzsziX1mDjkumst+IAWOfWPgRCyEUwKJ0dajXA7L/2ce85v5dPMHOoO5NUpJlrN/QbPQv5C2i+rPJHcPHEAWxcOp1JZNGp3wj0HTWDa8BeOXMEiyYOYjmcKVARVbDLHXIYvGBuuXLlsHv3buTPz2YkCwoKQr9+/fDuHc1c6eLigpkzZ36XZoicuHTpEmbNmsUsx+rQoQO8vb25VUS3b99Gv379WBmXKKiY1vwz++5MnRJCiA6A6wCoXNyCBQvw++/s2uW4uDgMGzYMV65cod5zdXXFnDlzvltlXRvYvn07FixYgCSJ9164cGFs2bKFy87l7++PDh06sBgIYgE4CoKQqRxxToAQEgyAqonoPmQCuntOYH4mJSUZK2aOYhr51eu5YOz8NbnmsMyIK2eOYOWs0dQD0cQsP6Yv34HKNdj9sF8+R2CkuzOvT8VTEIR1ml/tfwMh5F8wxEybd+iBUbOpqh8Aai2eFXNwYPMK6r1ylatj4uKNKFyUqbeYo3h4+wqWTB5MPbz19PUxbsE61G/GrgJISkzAmB6/8crTciWhAU9Er3o9F8xevYdruPru3oD1i6ZSD/5iJUtj0uJNmWaVcgpvXzzGwvEeVNYkK7Y4QanE9CG/89Skc6VoJq/MslT5yliy/TS3LOfqmaNYOnUIFWm2KFgEE7zXo3LN7AsWawsh7/2xcIIHswTzdw8v9B4xlWvA+kwbhvO+TCmw+4Ig1NDsSv87CCFDAVD9h1ZFimHl3gswM2eT9zy5ex1zRvWkGstNTPNh5Ozl3DMtJxEV8QlLpngy77us2OJ2rF6APeuZJWwfBEHIWkhOy1DLYTyARMfNzMwMR48eRYkS7OckrxncwMAAU6dORffu3eVa8g8jJiYG06ZNw/HjdL9w48aNsWrVKm5GaM+ePZg2bRrrrZtQMXJxA0RZOSXDAayUjrdp0wbLl7MNnKSkJAwYMADXr18XjRsYGGDWrFlcRya34OnTpxg2bBiCgsTpcAsLC+zduxd2dnbMz508eRIjRzIFwHOdzgWPCaRyzXqYv+EwMyUsCAJ8pg6l6FWJQoFewybj9/6jckUUnYeQwHdYMK4f1VhrYGiEeRsOw96BnfF7ev8mpgzowCpTSwBgmZvoKQkhPQFsl46XKG2PP3ed5fbRbF3+B9Mhad9jMPqPnpltFfCcQFTEJyyaOJAqI9DR0cUUn62o49yS+bngQD+M6upCRZmh6huyFQRBPsWq7wQhpA6AG5CU45lbFsTKfZdQwKoQ83Mn9m7Gmvl0gKFRSzeMmPFnroii8xAXG40Vs7xw9cxR6r2hUxejtTu7MjYqMhwjf2+MyHBm82h9QRCus97ICahp2AMgyVYbGptg2a5z3PLXm+dPYv7YflSW0LFuY4xbsA7mFkx91FyB5KQkbFo6Hcf3UIFm/O7hhT4jmYYMEuLjMKZ7c56OTndBEHZrdqU/DjUpUCQk2WodHV0s2HQEFavVZX7uxcM7mDqoI0VUULqCAyYv2fLDrIbagKBUYu9GH+xcs4gKgLi0dcfouauZDqegVGKaZ2deT9kfgiDMlGfFPwZCyEkAraTjPj4+aN+eLZng5+eHrl27UkxXJUuWxKpVq2RpYtckdu/ejTlz5lDB+gYNGmDDhg3cZv6xY8fi6FH6/EYW5Xlcp0QtuPYCgEh5y9bWFkeOHGE24CiVSnh5eeHkyZOicWNjY/z111+5plwrK4SHh8PDwwNPn4ppUK2trbFv3z5YW7ObLqdNm4Y9e/aw3spWLZ02QAixgKrOVRS6MLewwop9F2FRkN3fs3HJDBzZLi7Z0tXTx9h5q9GwRe4o18oKCfFxWDC2H+5d+59o3MzcAou2HOeKVu3d4IPtq+az3so1dLLq8p7PkAgkGhoZw2fXWS696vE9m7B2wUTp30L/MbPh1jvX95ECUBEcLJsxAhdPHhSN6xsYYM7ag6hUnW0EXD51GIsmMuuec1X0lZXVJAoF5q49gKp12DIrPMO1ffdBGDhhXo71GHwPeBk8olBg4sINaPCbK/Nzj+9ew9SBHal/O4AgQRD4FJFaBi+rOXb+Gi6D2pO71zFj6O9UeZtzm87w+mNlprSyuQnHdq3HhsXTKAN2wLg56NCL4tMBoKKVHt29OYtdLBaAeW6hCSaEHAfQRjred9QMdO7PDFwi0O8lJvZtS+k0Va3dENOWbc/VAYSMuP6/41gyeTD1+2zbbQA8J7FJRqIiPmGEe2NWuVoKVOV5uaLPjxDSBQBl4PXo0QOzZ7PLZ8PCwuDu7k4FuStXroxNmzbB0jL3VZawwNMjadu2LXx8fJgq9XFxcXBzc8Pbt1QV3meoyvOYHfGZhbYXQ+KQ6OjoYNmyZVxGgLlz51IOiZWVFfbs2ZNnHBJAteadO3eibl2xMRMSEoKBAwciLo4dHJ82bRpKlmRGM5aptUByA3zBEPkZOWs51yE59PdqyiExNDbBrFW784xDAqgM9OnLt1Nrjo6KxIyh7rzoKtw9vHjRLVdCSDXNr/SHsBUMxfa+XjO5DsnlU4exznuSaExXVw9j56/NMw4JkOYcr0H7HoNF40mJiZgzqidXpbxRSzde/1N1NblHjoMQMguMMsvOfUdwHZLHd69h4cQBIqOcEAKPsX9g0MT5ecIhAdRUuKNmoN/oWaI1C0olfKYN5WqsVKlZHx16ebLesiGETJFntd8HQkg3MBwS5zaduQ5JwJvnmDOqJ2Xwdeg1BGPnrckzDgmgco7HzF1NrXmTz0xevxdKlLZHn1HM3hITMGr8cwKEkFoAWkvHK9dw4lI6R4SFYIbn75RD0qilG2b/tTfPOCQAUK9pW0xfvhOGxmLZjuO7N/IIRmBuWRDDpi5hvaULlShhjoMQYgaAqjMrVaoUpkxhHykxMTHo27cv5ZA4OTlh586decYhAVSaK6w1Hz9+HN7ebGfT2NgYixcvZjksBQAs5H0X0ykhhDgB6Ckd7969OypXZtcgnzx5Etu2bRONmZmZYcuWLZkKKuZWmJqaYuPGjVQj/4sXLzB5MlMDCYaGhpg5k5ltLA5gEusNbYIQ0hgMpeC6TVqhdmN2hdmTezfw9/I5ojFdPX1M9dkKx7pUD1+uh66ePsZ7r6Vqcz+FBGHRxIGs6CqIQoGhUxay6mIJgAOyLTabIISUBEAVpZat5IjW7n2Zn/kQ8BYr/xgtamonhGDEzD/h3LqTXEuVDUShwKAJ8yjHJOZrFLzH9udqNwwYN4ensbJB86v8PqjLQKgnXiHr4ug6mN32EhXxCYsnDqJ6Dfp6zcxTjmZGdOo7HL0lZT1JiYlYMK4fsxkYALp7ToBVEWbT6Ez1dc1pUBaaiWk+eIxha+kkxMfBe7wH1WvQ2r0fBoybk2cczYxo0uZ3eM1ZJSr7FZRKLJ8xEu/92GRpbbt6oLR9FdZbPdXlcDmNfZCUWerq6mHo1MXM8malMhU+U4ciPDRYNF7HuSXGzl+Tq0tneajm5IwZK3ZSjfybfWZx6cjrurRG7UaUMgEANCSE5IaI9hQwtNxmzpzJFTKcOXMmXr0S/46rVq2K9evXw8SE0lrM9ahUqRK2bdtGNfJv3rwZx46x6cgdHBzQrVs31lt9CCFM3mhepmQ6JDeWlZUVRo9mc6UHBARQ3qKhoSHWr1+f6+vlMoOhoSE2bNgAe3sxIc+JEyewfz/FkAwAaNSoEVq0YBr4IwghfBEF7YCipjEwNMLA8XOZk798jsDiSYNE/RREocC4+WtylD70v0Kh0MHY+WupBvcnd69jzzo2b7xtuUq8BttShJDmml/ld2ETpPS/CgU8Jy9k9gclJSbCe3x/qp/CY+wfaNq+q6wLlRsDx82hynoC/V5izfyJzPkWBYug+xAmsYM5IYTPsasdrARAhb8HTZzP7A8SlEosnTqEyvi17TYgS4X33I7f+49Ch15ipyoq4hMWTxrEDCQYGptg4Lg51DgAfQDMsKy2QAgZCyCfdLzX8Cnc/qC/5o2nDPVGLd0wZDI34Jgn4Ny6EwZPXCAaS3PAWOrwCoUOhs/wYRn4CuRwIIEQ0gSArXTctZcnSpRmk/rtWO2Nh7fFhEBVatbHxEWbfliNPTfAoVYDTFy4UfT8SU1NwaKJg/A1iimcCM8pC3l9j0xKPW1BXfJOPQvatm3LFdnetWsX1U9RtmxZbNq0idscnhdQvnx5rFmzhnLEpk+fzmQVA4AxY8awskIEALOBjLqzCSHVAVDdoZMnT0a+fNQ5mi4iKK01W7RoEWrVyjOiq1yYmZlh3bp1MDcXVbJh9uzZrFo5AKoyLsYPLx+AHLMMCCE1wBD66TpoLFevY9n04RTzVD+vmdxa7rwEfQMDTFu2nWoe3L1+CbcspMfQibCwKsx6iyKD0BYIIYUAUB5iy069Ub4Kuy1iw6IpePdS3C/Vvvsgbi13XgJRKDB23hpKS+Xc0V249A+7EqBd94E8amg+z67MUPcIUTz4tRo2R90mVJ8lAGD/5uV4cOOiaMzJpQ1l9OVVeIyZRREXPLpzFYf/punJAZXCdPV6Lqy3Bqivb06Byn6Vtq+C1l3Yzfvnj++jmKfsq9bCmLmrczW5SHbRtqsHRVwQ8OY5Nvuwe5zLVqqG5q5MtqIWhJCc7PKn2BitChdFt0HsrOajO1exf7OYMKhoiVKYtny71sQQ5URdl9boNUL8Uw8PDcbymWwNvULWxXk9N5UJIY6aX2G2MRKAKJ1uYmLCLdt68+YN5s2bJxqzsLDAli1bKDsyL6J27dqYP1/cYxsbG4uxY8cyVeHz58+P8ePHs/5UW0IIVcLKOtGmQBJ1LV26NNq1Y1PRbd26Fc+eiak1e/TogdatqbLKPItixYphyZIlohR5QkICpk2bxhSFtLa25qWsvNS1iTkBKopkZm7BFTi6euYo7lw5Kxqr2bBZni0BYcE0nzkmLtokSjMLSiVWzxmLlJRkar6xiRnv0CxPCMkpDs71kNzHevr66DpoLHPy66cPcOqQmKCrbCVH9B8zS671aR16+vqYvGQzpe6+YfFUppimjo4uerCzJZaEkD7yrDJLeAOgLJMeQ9lVoGEh77F3g49orKC1DUbOWpYnS3tYIAoFRs9ZRdFT71yzEKEfApif6TNqOuvfbwCAnR6WGYSQfmCI6fUYNpmZ1Yz5GoVNEo0O03zmGO+9Lk+W9vAwcPw8lK7gIBo7sW8LXjxiChOj+5AJrH+/AgzHQBtQM+RRdGm/e3hR/RWAipzjr3njRY3+evr6mLhoI0xM6eBvXkXnfiOpQMKti6dw8/xJ5ny33sOQz5zZa5EjWTC1cjuVJenZsycKFaKzmoIgYNasWSKNDkIIvL29c0wkXA64urrC3d1dNPbo0SPs3LmTOd/NzQ2lSpWSDhMwAjQiY4YQUh4A1fk5ZMgQZnd9aGgoVqwQM6NUqFCB60HmZTg7O6N///6isTt37jA5nAFgwIABrFpDCwB8mVOZoBZKpBqy3XoNYR6YWb0PWgAAIABJREFUCXGxlFiVVZFiGDtvzU9j4KShbCVH9PMSR+QC/V7i6HZ2U16LTr15lJsUJ73cIIQYg6Fd0ax9N1gWohnilMpUrJw9WvQgNDHNh0mLN/1UBg7wzSDPiKiITzwWNdRt0holyzBLTdkfkB9U2qpWw+YoU5EKLAFQlfdk7JvR1dVjOmZ5HWkGecbSlqTEBKxfNJU5v7R9FV6paU5lredJB+zKV0KthuwK0L+Xz8GXz+JyF5Zjltehp6+PSYs2ifq7BKUSaxdMZJbnWRUuiqbturD+lGsO9QxRzlABq0Jo3qEHc/Khv1cj6N1r0ZjH2DmUY5bXQQjBqNnLqefRukVTkBBPEwYZGhmjfQ+miVSTEFJanlVmiiEARA98Q0ND9OvHzmoePXoUN2+KKy0GDRoEFxdmxjZPY8aMGShfXkyi8+eff+LTJ1pIU0dHB4MHD6bGAXRW26fpkHoa/aRjNjY23CyJt7c3YmNjRV+8YMECbuNPXseYMWMocZwFCxYgPp5uoi1UqBA6d2YS+HjIs7pMQT0IjU3M0KZLf9Zc7NmwlGq8GzJ54U9n4KShXbeBsK8qLjXcvW4xIj99pOYaGBrBtSeT2acqIUTbIa4pkGgcKBQ66NiHbW+d3LeV0mnpNWIqt3wvr8PJpQ1Vanhy31a8k1wDQPXw/L0/s6ygKCFEqwqDamYmSl329wFezPm3L53G3SvnRGOuvTypErafBfZVa6GdRAH81sVTuHv1HHN+NzYpgIm2GdYIIRXBYFJz9/BiBnvePHtIZTUbt+rI1d7J67AuYYeew8SZwDfPHuL0oR3M+Z37j2L1XehAy6QyamZNypvo0Gsoswwr/OMHKqtZsVpd7vM4ryOfuSUGTxKXkH4KCcL+TcuY89t1HwQTM6Yqek5kNyl7zd3dHVZWdGAyNjaWYqKys7PDqFHscrW8DkNDQ8yfP1+UsIiOjsaiRYuY811dXWFjQ+lhKgD0lQ4AAAghCgCUWz9w4EDo6NBp5bdv3+LEiROisW7dunHZuX4GGBgYUHzUYWFh2L2brds0cOBAVoaporq/Q5ugaunadOnPvPGjoyIpYasa9Zv+tA9CQFUWMnz6UtEDLiE+Dof+Zic/2nT1YDE2MVORMoMqLWrUsgOsS9ACn8lJSdRDoHQFBy4718+CQRPni/ZKqUzlKQijUSs3noPGpkSSD5QVXal6XVR0rMOcvHvdYtFrqyLFuHXsPwt6DJlARV93rWE/DCs41uZdOzb7gXygsm7WxW1RvzlbdG33usWirKaRiSk8xmr7p6hdtO02AKXKi22IvRt8kJKcRM1VXTtmwFTb1v1MSEreTUzzofXvfZmTD2xdKcpq6ujoYshk75+uCiEj6jVtS2UDj+5Yy2x6NzHNh5ade7P+DFUVICfU7FAihgIdHR14eLDjyjt37kR4uFhSZdq0adDX/7mqEDKiatWqlCD6sWPHmE3vurq6vGvXS+1/ABBnRZoCELkxBgYG3CzJ2rVrocxwYJqbm2PMmDFZ/yvyOBo2bIimTZuKxjZu3CiqIUyDjY0NnJycqHEwGljlAiHkN6h43EVo6srsecHRneuQEPct+6Wrp4+hU9kP+58JtmUrUgfhP/u3UqUTgCrLxDEktLmvdpDcrwC45QLnju2mSAuGTFnErGP/mWBhVRjuA8SsgdfPn2BqlygUOrySEDZftgxQl55QTZ28fb179RxeP/1XNOYxdjazLPNngpGJKfqNniUae/XkPh7cuMCc36wD87yrruVSH4rztGn7rsx70P/1M9y+dFo01t1zAldL6meBQqEDz8niaHP4xw84f3wfc37zDsyG9+JqmnRtgZJPaNDClakvEhXxCWckmZ82XfrDrvzPG8xNw6AJ80W6NAnxcTi+my0v85sbdUkBwJQQos3oKPU8r1evHooVo5mnExISsGXLFtFYixYt0Lhx3pNN+F6MHz9eRBOcmpqK9evXM+e2b9+e5aQVB+Cc9iKjU0JtQNOmTZmMW0FBQRQvcd++fZlzf0aMHDlSFNUICwvDgQNsuYoOHTqwhrsTQrSldEVRmNhXrQUb2zLUxLjYaPju3igaa9quy09b3iOF+4DRoqb3xIR4HNnOZiN0aefOGi5KCGHLwmseVEmeZSFrVKlFUxSmpqbg4BZx71f1ei6wd6hJzf0Z0bbbAFHzpKBUYv9GdulAU9eurIilMSGEeSPLgEmQlNAaGBpRujpp2Cf5d5QobY8GzdiR958NjVu6wcZO3Fu8d+OfzLkNfnNl0Y0qAGglkkYIcQVgJBmDc2u2UOL+TctEJCrmFlYUQ9XPiorV6lIaWPs3L2f2ljjWaQyrwkVZf0YrKSV1PTzlKbq0ZQY3cGTHGhHVsb6BATp75Hx5T2hwIALePJf1O6xL2MFZIgx6bNd6ipoeAIqVLI2ylZi6xFqpRlDbZxQ/Pseew4EDB0S9FIQQDB+et2nYswtzc3P07i0O6B4+fBjBwcHU3Pz586NJE2aPX7r/oQAAQogOAOpJxtuAffv2iai/TE1N0auX1oLEOY5KlSqhUSOxmvKePXuYc1u0aMGiBy4IgE1wrXlQpWIubZkGNS79c0jETqRQ6KBTvxHyrSwDkpOScO7ILiycMBBje7bA4PZ1MMmjPfasX4KQQDb/taZhWcia0uk4e3gHk4mrcnUnFLIuzvozbNorzYPqjHVp686Muj64fhEfg8TsRF0G5kxW89+blzDUrT7CQt5r7TsNjYzh2lPcZHflzFFER0VScwsXLYEKVZmaTtp6wlAPQqembZhR10C/l5QYmbuHl1ZoYsM/fsCBzSsw3bMzhrrVx9CODTBlQAdsWTYbT+5el/37AVXZpbuHuM/myd3rCHz7gpprbGLGK0FlhmRlANUQVKmGE0VJDqhKaK+dExOouPYawtNw0Chio7/gxN7NWDCuP0a6O2NAmxoY1dUFSyYPxumD2ynxRrkgPZ9CAt/h4a3L1DyiUKBxq46sP8HmzdY8qP6VIjYlUbEaXS6YkpKMs4fF7ETNO/Tg0cxrDbExXzGxb1v8vUL+lo0uA8eInlExX6Nw5cwR5lxO1pp5OMuARpA0uJuYmOC335gCj1QJf5MmTfK0Rt/3ok+fPiJByJSUFG6g3s2N4tICVAQVOsC3iFwNAKIGA3Nzc8rwBgClUkmJwnTt2pVSefzZ4ekpbnZ+/vw5XrxgPAyNjdG8OZNZRXY6BjW3t6jTTkdHFw1bsJ3NC77iFHn9Zu1QtARF46ZxPLx9BYPa18a2VfPhUKs+xi1YB+/Nvug2aBzePHuIQa518Ne88ZRKtRzo1FecBYuKDKe0H4BMH4ZNWYOahLqxkuq0c27D7ts9f5zWOKhUva4sa+Phc3gY1i+aihlD3BHo9xJfIsOz/pAG0bbbABgafesdT0lOwpUzR5lzOddRW13j1A3n3Jq9r/87Jg6EFLIujoYt5U3oCEoldq9bjEHt6+DmhZMoVb4yWrn3RR3nloiKDMfBLSsxyaM9RndvhtdPH8i6FgBo3LoTpdx+4QT7YSiN0qpBp4zlAVWS59yKva+X/jkk6qEwNDbRShO07+4N6NfCEf/evIQa9V0wdNoSTPH5G536jsDHD4FY+cdo9P3NAQe3rhL1usiBKjXrUzpL/5NotaSBc39YqdkJ5YazdKBxq07M/pB7V/8nKgcmCgU69slpfVZg05IZCA8N1srz1bq4LZyathGNSTV40tColRsryGagJeIRKpzfvHlzpvDhs2fP8PKluBx44ECtk6zmKMzNzSmK4MOHDzMlMxo3bszyFwpAfUamOSWUgezk5ARdXVpf6vbt2/jw4YNorGNHpnH2U6NmzZoUE9eRI2yPn6P6qQ1J9EHSgbKVHJksWiHv/fH84W3RGKcOW6O4fek0Zg7tAh0dHSzbfQ6tfu8L6+K2KGBVCFXrNMK0ZdvR3XM8Tu7bgplD3ZkNj5qEdXFbymA/78uuZ3Z0cmYN22p6TQxQDe4WVoWZlLZxsdG4dfGUaIwjPKYxfI2KwL83L+HK6cPYs34JZg7tgn4tHXFs5zpmCYY2YGKaD04ukochp069Wl1n1nABtbKvbCCE1IVEwV1XTx+Va9ASOIJSiUsnD4rGXNp1kVUFWhAELJ06BCf2bsbUP//Gku2n0G/0LLTrNhB9Rk7D6oNXMHTqYigUOnj99F+M79MGF07sl209gCrI0kTibFw8eYBpNDvUrC+qaVdDT26NIbWgH6WaVq2eM3O+1Phu0Lw9i1hDo9i4ZAbOHN6BhVt8MfXPv/GbW0/YO9REqfKV0ailGxZu8UWN+k0RHxuDLX/OwpIpnkyDQ5NoJul7vPG/E8xSH9tylVDAitKMINBOjx+V6uJQUFPGt0PN+jleGv3w9hWcPcLWlpAL0n19ev8mU2con7klSleowvoTlF0jAyibuGHDhsyJhw8fFr0uWbIkatb8NUqjM0LqlLx//x7379+n5unp6aFOHSbxiAvwzSmh7qK6ddmR1JMnxaI3VapUQbly2iqjzz0ghFDlbdJrk4Z69ZjPvDrqiLecoKL2VWo1YE68euaI6CFjYVUY1dhGt8YQGhyIpVOGICU5CaNmr+A2cXYdNA4OtRrg0Z2r2LSUrfKrSbhI0sa3Lv6DJAaRQYWqtaFvQPXJ6hBC5M6WUKFBhzrsA/PWxVMiphd9AwM0+E3enoNXjx9g2uBO8Jk2DFdOH4VVkaKYu+5gjj+Apfv68tFdhH/8QM2zLmHHK82Tu6ifetjaO9QQZXjS8PTBLYq2u0lbdn+CpnBo6yrcv34R89YfQo369E+cEILW7v0wYJyqnD8lOQnLZ4zEoztXZV2XtMzjU0gQU3TP0NiER5Ms975SlDOFi5Vkao2EfgigMkxNOOW2msKDGxdxct8m9B89CyXLsktOdHR0MXD8t/KeS/8cwvE9G5lzNYWGLTpQPX5SQV9A9burUpMZ+JP1hlA3XYtC+QaGRlSGB1Ct/fZlMXGB3PuaFRLi47Dqj9GyO5dSVK/XBOaWBdNfC4KAq2d9mXMdajOfa83kWZkKaoFryqvg2cRSFlo3N7efmkmNh7Jly1IlazybmHMtmwCAQt3QQ93RvA24ceOG6HX79r9GUyULUmay4OBg+Pv7U/Osra1RsiRlkDGvu4ZBccM6cJySh7eviF43bMlMnWoU21fNR2zMV5St5Mh7qABQPXTSlNRP7N0M/1dPZV1X/ebtRWKCSYkJVBYJUBn4FST6Jmow+Qw1CEpBj7uvt8T7WqvhbzwOeI3B0akxDt0OwuE7wVh98ApGzPgTlWs4IafP6ap1GooiqoIg4F9GnToAONRmXk9X1qAGQdXLOtRiO5uPJPdr2UrVUKykfNpiXz5HYPf6JegxdCJPZDId7boNRInSKibNlJRkrJk/gdmXpSnY2JWlROce3ubtK/N6Omt8UWJQLAXZPYctChaBQyZnoybwz/6tSEpMxHTP3zG+d2tRECMjbOzKihypIxyBWU3BNJ85ajQQ25+8fa1amy41B0MwWMOgKPEqONYWOVJpePbglqg8Sk9fn0teoS38vXwOLNkkAbJCR0cXDX8TB3Sl51kaOPeJ3CWXDSDJWNvZ2aFwYbr35+3btwgLCxON/b9N/A3Xr7P7CzmstA0JIboKqGqYRfyRBQsWROnS9AMuLCyM4h/mlCb9ErCzs6PEYKROWxo46SrZaiMJIYUgLQXR1WM34CUn4fm/YqObU8KiMUSEheDyP6q0JyvqKoVDrQYwNDaBUpmK43vZNIKagolpPiqi+pgT7WWxXYHhNGgYlFdRpSbbyJGum1NyplHo6uqxMkg5DoVCB1UlRikvis9xkuV+GFIWAuf3RRlncmc1r5w+gtSUZOjq6TGzSxlBFAr85vatRPC93yv8e/OSrOuT/vsf3f6u+1Vuy4x6mPL2VWqcOdZpJDtxwft3r9L//+XjexR5QkZYFPqWzQ79ECB747tjHTELF8945VxPqmROw6AEE3nBNem6yzvUZJJXaAsvHt7B3atn0XOIVnUm0yFlV3ty7zqzNLtSdSdWSaqeuiRSLlA1Yxz7jVJvL168OFXW/yuhQQOxHfLmzRumwnuZMmVgaWkpHTYFYKcAUF76jlQ6Pg1Sg9vS0hJly5Zlzv1VIM0oSX+kaeBcU/aF1gwoS79IcVsmg8uLR/coMaeK1dk3oaZw4fj+9P6CMhWpHlAKunr6KGJjCwC4cvqoiFZRDkgjNNIIZhpsy1RkDdNE5hoCIaQ0JJSxhkbGTBaf0A8BCA0OFI3xIrS/CqTlizwjx7Ysc19l6ylRi0dRnpwtIyuRmBCPV0/Etbpy7+vTezeQnJSElbNHY0jH+njv9yrT+ZWqiyNhPLV1TUH673/x6A7zjODsq1FG8S4ZQP1u7NjrwKM710SvtXG/ZhShJIRkGj1PkmRRdGTOpkuDCCHv/ZnMfdY2zGebQq3nJBconSi7cpWYEx/f1f6+8pCclIQVs7wwbNpSGDBKQ7WByjXriSoxWGcaoHq2FS7GNPKdZVscwy6zt7dnzaNsYl6F0a8Ce3t7mJt/iwUIgsC0iQkhvLaPckynxM6OfR8/e/ZM9LpWrVq/ZO1cRkg9aOk1SkOpUkwWKzmdEio/xtImAQC/F49Er0tXcJC9sfLauW81pBnrSzODuYUqOBIb/QVP7slLOyot3/F78ZhZe1uMfU3ljNBR9bTFSpZm3odvXzwWvbYoWETWEp+8AAdJRik8NJgpkFnMtgzrmhrIKLZXCxJV6HzmljAzp/2gwLcvRaUgurp6qOAoL1Pm58hvJQrxsTG4fOpwJrOBQpJ+ibAPgZyZmkHFanVFEdWkxESm45S/gCWL6INApuymmgFKXzKGooz7MCriEyI/fRSN8TIqmsSAcXNg71AThayLo6/XTJQoxX8sfQ7/9jsoYlNSdpFOG7uyVBO73/PH1DyiUMCazRQpJ6EMlbFmPQ8EpRJ+L5+IxqTnkDaxfdU8VKrhRGUrtAkT03xUE7v0eZUGjt0iJzlFtm3i58/F2i6/ulOiUChQu7b4WSS9Rmng2cRMp4QzGX5+fqLXPO/xV4I0AxIYGIiUlBRqHudHLadTQqUgOQY0gvzfiF7zoj2aQkpyEvxff+sLMbfIplOSwXlhRVU0CVtJw2diQjwiQmkxIOvitqz0sq6MTE2U9cnb1w+SfeVEiX8pFCluSxlSHwLeUPMMjYxFEeQMkMtKpCwEXhBBuq/WJexk17CQNv4XKkoFiUWQMjcmxMdpfE0ZwcoWfgh4y5zLuV+cNb4oFahmB6sixZj7JT2HjUxMKedODtiWrYgl209h86kH6NSXL8cTERaCyPDQ9NcNWzD1BjQKQgjVw8Tb1+K2zKoNWVL+6vJoUZpIV1ePGdUP+xhEZe14hAJy49WT+7hy5ij6jpqeI9+fESUlVQa8fZUKpKpBlc5pENmyiZOTkxEUFCT+IKfK6FeC9BpI/YY08GxiBRj1rjyvUPrHec7LrwQ7OztRRDU1NRWBgXRUsGjRojA0pIKshWVk4KJOR16UXGrk8IxcTSHgzQtRpDdfgezZ7/kLfCsjfcuIlmkSrCi11GgAVGVlnPSyXMYrderZsB/G1Hp5Ru6vBEIIihYXn2/S338aOPcBs0NPA6AestkNIsh9vwJA7+FTUL2eC8wtrNCmS3+KyUyKyE+hotfZzYb+F0ivQ5D/a+Y8zn2QdQ3pj4EyirPrbPIyoDmFG//7xjKUz9wSHXoN0cr3Sq8X6xwGuPeBXJFTKlJfxKYki3Ka2ldOtk52pCQnYfnMUfCc5C072Ul2IN3X7zyHZaFyJITkg0QDzMjICEWK0MygAQEBIhFxhULBIjT65SD1H6R96Glg9a0DKK0LRqlJoUIU5zdSU1Mpr5DnvPxKSPvBhoSEpI/5+/tTDptCoYCVlRV1DQH8jxAih/gGxWnKo9wNfi/+0chd4vNJ0ihrZJS9EoCMzdNSOlQ5YGNbRkQAEBzox0x5WxQsjOBAKhrgQwiZIMOyKEaZAgXZisAhgeJ9ZZWM/IooZltWVE4RHMCO5HCUlocQQlrIsCwqPWnB29f34vVqoyTPqkgx/LGGrevCgjSTWdFR3h41QHW/3r70jXaVcU8CAAqw97UtIYTdYPTfQG0O5/sRnAP7ml0kJsTj6K51AFQZgTFzVyN/AapRVRZIjdLgQHZEnXO/1JBpX6k0KndfJedwMU4QSW7sWe+D0vZVUMe5ZY58vxRSp4R7DrPtlhIy7auBdMDKyooZHAgIEGurWFtbM8UVfzVIbd+AgAAolUooJIQdBQsyA1XmulB1vItgbEw3P8XExIi8QgBMirRfEYUKFRI5JV+/shlJTEyYxre8xeAZYGTMTsrEfI0SveaUrWgMURHf2BgIIdlml9HR+ZYt/xwRlslMzUBqlEqvUxo417UMtKQWzXPqpOu1knlf8wosC4kfctx9ZbPjFIX8bE0AwK3Xj/n6RfRa7vv1R5BRNNHA0AgNWsirNA/QxgtvX43Z+2oBFRWo7OB8v9bP4ewiOSkJS6cMQUjgOxibmGHs/DWo2VBWqQgR6H39wpzHuV9NoKV95bFpxXz9LHptyQkOygn/V09x5vAOrNwvLwve98Aiu+cw+/mqDy3tq6kpe1+josTrZQXzf0VIr0NKSgri4+Mp+5dzXc10AVAdzazJcXF0TTDLefkVIb1esbGxzHkcp0RrYB2agiBQ9d5yNy/GxUan///3kN5kZOuIj4nOZKZmYCRp9mepCavm5Ry1Y2bfHxcnXq/c+5pXICVxiI/LpfvKCSJIf4dGuWxfQ97742EG/Re33sPSSSrkhHS/uPcr57pqC7z7ULrenLpfoyI+ITjwLaIiwxES+A7nju1GSOA7OLfuhD4jp6Ogdeb9RJqG1InLrfvKuw/j48T2gLbPldTUFCyfNQqDJ87XWnYrO5DuV3xcLARBoLISOX0O8+xcqU2c0/ZdbgHLf4iNjaWuD+d6sZ0S1mSpoa2jo8PqkfglIb1eMTHsQzOnf7SsQzsxPg6CUika40XyNIXUDEJqCp3sU0oqdL45MMkMTnNNg3oY5lbjlfP9lPGaw+vMLZBehziukZOz9yvvPpQ6mzltjEmxZ/2SdKa6spWqoevgsVr5XmPT7AURcto5z66zKfc5zMOeDUvx4uEdAEBcTDTCgt+jiE1J2NiVk10zhQUqOMQ7h3N6X7N5Dmv793dwy0oUsCqM+s1zl6if9H5VKlORlJhAkUDk9L7y7DapTZzT9l1ugZGREXR0dESVVTExMVQGhePsmelCUkNHCKGYUwAgMTFR9NrAgCq9+2Uhdc6k1yoNOX3NWEqzSUk0l7+evrzrFJUBMmh2+chAKMBgONM09KX7msDWRtHXz1nnXE+P3lcASE4S/w71Zd7XvAKpsCNP80bfIGfrg1n3KwCkSPc1FwlVPr1/E+d99wIAChcriRkrdjKbf+WAgWS/ePtqkMPBNN75Kg206OXQueI5yVv0OvrLZxze9hd2rVmEPeuXol23Aeg1fIrWfncGBtJzmK04n9P3gZ4eZ1+TxPuqr0U7IMj/DXx3b8Cy3f/T2ndmF6z9SkqIp5ySnN5Xfc45nCTZ15y273ILCCHQ19dHfPy3+5RlE+vr64MQIpVaMFIAEOWgBEFg/gFpA09CQgJTt+FXhNRj5qX7Mm5SToB1mBsy+hF4h76mkLE3JFWZmslMMZQZnBkdhuOsaSRI0+6ciI3cdKdZgbdfUmEsufc1r0C6r7zIZUI8uwxTW0jknBfSh3ZiQs7+/tIQFxuNlbO9IAgCClrbYO66g5TGhJyQlsnw9zWn71f299P7mjvuV7P8BdB7xFT09ZqBlOQkHN72FyZ7uHJ7ADSN+Pi8fg5L9lVLdoCgVGLFLC/0HTUj1/QnZYT0HAYAQ0YWMaf3NYETjJQGo3PavsstUCqV1DVj2cQcHyJGAYAqzmf1REhTU6wv/lWR3TQer6xLW2CVM+gbGFI6G7yyB00hYwRYUCqz7dwqM5SZ8bIDmoS0rIebnueUE2gLvO83pmp2c3aduQXS6yC9TunzZL4PsoK0TCsN2S0/0yYEQYDPtGEI8n+DIjYl4b3pKKyL22p1DXSvTe7cV5YxBmS/Jyan0KGXZ7pmxMvH97BwwgCq9FcOZLcMNafPN6lTnAa6d0I76zy6cx309PWzpO/OKUivg66uHjM7nNP3QXZ7hHnzfjXExcVRNl12WkLUiGY6JaymdtYfjY6Wv9k4LyC7TklO/2h5D0NpRDE2hs0epimYmolZqAUhew+21NRvJVva4FnPK0YO92EoeXjHRsu7r3kFecXZ5BqvUiMnNufP4V1rFuHm+ZMobV8Fi//+B4WLaZ+vX7pfXAKI3Hq/GkudzZzf14xQKHTQpM3v6a8f3LiIi/8clP17pdchu70b2kYCLzgkDSJogaQl9EMADmxZgREz/sxVWjcZIb0OufUcZtnDQPZ7iX81sK7D9zglumA4Jaw/amxsDENDQ1F25MOHD/9PgwbVdcgICwu2GCBnE9YBkMNbGQwVHWI6eJHX/AUsERv9jWbx08cg2DvUlGFJKphLSjqSk5KypUidkqHmOr+F/CwiYSHvRa9538l5GJ4B8IT1xn9ETwCiC8h7GEuZVqT6ML8qwoLF4qYZRTkzgnNd7wGQg1fTFRJNC+6+SpiswoIp7SOt4vSh7di9bjEcajXA1GXbYGKaL0fWEZrdfWWfg28BHNX4olRK8dUzDvCcDen9Ghb8njkvJ2FftZbo9bGd60WOihyQ/r6/834NBbBT44sCqgBonnGAt6/5zCX7GiLvvgqCgJV/jEG3weNRxCb3ivmFhUj39buerzEA1mt8USqJjEGiL+I4G1I7T2oH/qqQXgcjIyMmKVZmTkmEdDQ4OBgVKlQQjSkUCpQoUQKvXr1KH3v37h2qVaO03H4pREVFITIyUjTGUrpPSUlBWBilraEE4CUIgsbr4AghbSBR/+ZPEfR1AAAgAElEQVQ95IqWLCUSGuMpq2oKBYsUE72Oj43JllPy5fO3n6pV4WKZzPzvEAQBHwLEIl085eywj0yj0FsQhAuaXhchxBGAi+j7OQ+5oiVK4eHtb/pSPIXrXw3ZVUT/FMJ8yOwUBOFPTa+JEJIfEqfkE/t3haIlxOcLT+FaG7hz5Sz+mjse9Zq2xbgF67TaxCuF9NziKad/CmFe1/8JgqBxmjBCyDhInBLO91PipnKfw2mIigxHVHgobOzKQjeLstgixUqIXr95/hBxsdEUzbYmkd195ZyDj2Xa1+aQOCWc84ISwfwQ8JZJfaspXDp5EG+ePUT9Zu1w6sC2TOdmvGYRocGi+UYmpmjcqqMsawSAoHfi5xH3+cre1/cy7asRgIHIwKoTGhqK1NRUUS8sQIuHR0RE4MuXL8ifX/4qjtwMPz+xCKadnR3zt85x4iJ0AbwGIFIo5snClypVSuSUSL/8V4T0GhgaGqJIEVocKSAggBKfBBAoh0OixltInJLgALYSro1tWdy9ci79tdxGTvFS5WBobJJenhIT/QXmlkx1TxE+h39z6kpXqCLb+gDVAS0tn2E9DBPi4xDBVpe/Ic/K8BQSp0TqPKVBeshry8jJzUhNTcHH9/6iMZ6R857txF1mDWoAdwF4ZBzg3Ye5ZV9fPLoL73H90bJzb3hO8ubSxQa9ew2/l0/QqKWbrOt5n00jR2oMqXFH8ysCAFyVDvD2i1K4fv8OqakpVM+fJnHedy9WzB6NlOQkFC1RCt5bfCnR2IyQltgISiUiP4XK6pRk13jl3C+PNb8iAMA16cCn0A9IZLBHSdcbHxuDz+GhPKXy/4w0YeG/V8zNcm5GhrrgQD9sXf5H+uuC1sXkdUok5yvvHObcL7IceoIgxBNCggAUTxtLSUnB+/fvYWtrK5pbrFgxGBgYiIih/P39UbVqVTmWlmcgtYlZQXrWPDVe6QJ4mc3J1B9/+vRpthb5M+PZs2ei17a2tlAwHs6ca0pdew3iIYDWGQd4Ro6NbVnR67fPH8m2KEBVm1y2oiMe31Wd6xFhIdwDKSOiIr85JWUryZuhe/tC/Cwzy1+ASsMDqgOT0aifKKOzeQPACOkaWEhrSk3Du5dPoVSmikQofzX4v36OlAw6OYQQKvMAANFRkYiOiqTGATyQaWnnpQNB6t+WNMpUXLKvYR+DEB0VCTNzdtmoHAgJfIe5o3rCpV0XeE5emGnU98b5EwgOfCerU/LlcwQVHJBGqAFVBjT4PTPopvGsphq3pQNRkeGI/vIZZvkLiMalxmtKchLev30J23KVZFoasGO1d3pZbHCgH07s2YRew6dw57OYo+Qs10tNTYH/a/EzlrWvAPccvK75VQGCIMQRQpKgUhZXjSmVCA54C7vylUVzC1gVgolZflGJ9Jvnj1BbJqfErfdQuPUemq25h7f9hU1LZwAAqtRqgDlr98uyJhb8JM9YaaYwDRy7Ra5zGFDZZcUzDvj5+VFOiUKhQMmSJUWB+idPnvzyTonUJpZmlNLASX68VOA7nBLpxb579y6Sk5OZc38V3LghDog7Ojoy5+WAU0JF6DgRQpSrUp2alzErIQfqOH9LzoV+CMjWZyJCPwIATPOZw6FWQ1nWlYaMZU8AUL5KDeY8zoHJtGY1BIpwPuS9v4gEIA3lK1cXRa9jY77i7XO5Aod5A48k+1q8VHlmgyUnSxInZJeV4TshCMIrACLvNiEuFpGfPlJzi9mWEUWmBaUSj+/JYnsxERkeimmDO8GlXRcMm7YkyzKUd6+eUg6ypvHozhVRcMDELD+K2dJGTvjHDywCAaUgCOx043+E+vdCWfKs7KaJaT4qOPPoDnWMaxRfo8TV2zxtlzRkLKEFAHPLgtnKcv8oXj/9V9SrQRQKlKlIG30pKckI/RBIjQO4KNvigM/SgaAAdoCoXGVxEO2xzPua2xH56SP17OQ+Y9l2i5wX8Idt4lu3bsmzojyC5ORk3L9/XzTGc9LevmUeuWyn5MWLF6xSI9SuXVtUVxcfH4/Hj39dI0epVOL2bXEgrG7dusy5Uu9RjVesQQ3honTg08cg6iEEAHZlK4qyAIIgpGcx5ELTdl3T689fPrqX5fyPQQHpa6/fvB1XWE5TkBqvVWo1YM7ze8HMKjGfjpqAIAhhAEQ3Z0pyEgLevKDmmplboGQZcW+Y3EZObod0X6vWZju3fmznLVzzKxKB6qhkZS11dHRRuYaTaExb+xofG4PZw7qiQQtX9B8zO8v5SmUq/r15GSVKl89y7n/Bo9vif3+VWvWZGUFpBlQNuWlzqN8NLxvtIPk9yr2vGbMOhsYmaObaLdP5b549FL1u8JurrOxO0vu1VPnKzIx1gCQDqkaKIAhy3rPUOc/dV8nzQ/rv+tXw7y1xFay5hRX1rAJUWcWIsBDWn5DzAlI2Ma8qSGrv3bx585fW77t//75Ir0VHRwc1a9KkSSkpKaIMUwa8UgB4D+BTxtGYmBg8eUITB5mZmaFSJXEq+dIlOYho8gYePXqEz5+/BUsIIUynRBAE3Lx5k/Un7rMGNQFBEOIgidAJgoDHd2hngygUqFKznmjs7tVz1DxNwszcAs6tVawtty+fplRvpbh29hgAQFdPH537jpR1beGhwQh481w0xjNepRkVNZibrUF8kg48us1udZA+DO/JvK+ZQZn6Lcmg1IK+gRSJCfF4cl+c2XSozXY2OfsqdwTGP5vroNZ979r/ZH8YpiQnYe7o3khNTYW1jR1OHdjG/e+f/Vuxd4MPFk4YiK9REShuV062dQmCgPvXxdVX0t99GjjGILuJUnOgHqY8Z0O67sd3riGJIWasKTRp6w6iUGDwpAXY4HuHaRhmxM2LJ9P/39DYBO4eXrKtDQDuXxdXNfL2lXOfUOekhkGFxaXOcRqkzqbfq6eIDA+VZ1XfgYxnhkxJYCbuXxMn/KvUbMB0bh/fvco61+JkLI8GGHYZz9lwchIHhyIjI5m286+Cy5fFdoiDgwNMTelKhMePH7PYt8IAfFAIqit9UfqutCwpDfXqiY3Xo0eP/rKe4ZEjR0Sv7e3tYWVF0xW+evUKERFUhiIaquZWOUGlZ3gZEMe6jUWvb5w/IbuSap9R02FuWRCfw8Nwct9m7rzY6C84smMNAKDroLGwLsGuUdQULp44IPpN5zO3RCn7ytS82Ogv8HvBPIA2yrc6AAyn5xHD2QSAak7OoteP711HeA5QA8d8jRL1BH0Myl7JniZx88I/InpJXV09VKlZn5onKJWU86LGHvlWBwA4LR3glXk41nUWvQ4JfIeXj+Q7TgRBwIrZo/Hw1mX4v36GVXPGZPrf6rnjsH3VfFw7ewwGhkYoXLR41l/yg3j+7y2qBLSa5PqkgWO8/qPxRYlBFeo/unOVKTzoULuBqLE9NuYrbl2Sb3ltu3qgVLlKuHjiAHT19DKd++LhHdy7qjImCSEYMeNP2Zq1ARXF89P74qNOep6lgeNsypvuV9H5i/Dm2UNR70gaylSsKuohEpRKXDxxQN7VZQMhGfqrwoLfa0UMMyEuFjcviH/Tjk6NmXMf3WLuq9xW/21IsqefPn1ilnAVKlQIZcuKS1OlduGvAqVSiWPHjonGGjRgBxGuX2eWG58XBEFIKzinmvw4kX106NBB9DooKAh378ptW+c+pKSk4MSJE6Kxtm3bMudyHLzLgiDI3ZBzQjrAi7w2+M1VVBIVHxuDG+epj2sU+QtYYubKXTDLXwB/r5iDe9eodgkkxMXCe/wAfA4PQ9P2XdFlwGhZ1wQAF06IbYhGrdyYpSCP7lyFUkmVOSYIgiD3oUnx7j++e43ZV1LNyVnE/y4oldS/T9NISUnGgc0rsGvtImz2mYklUzzh6VpXFPFdPnMk/hjRHRuXTMe2lfNwYPMK+L+SlzjjvO9e0esaDZrCNJ85Ne/ti8esJncBwD7ZFqfCWunAu1dPmSWXtmUrUg3Q54/Lt7y9G3yo65dd2NiW4TJzaQL/k6yrtH0VFC9FZ2aiIsMR+JYuc4Q8egcZsROSfqHoqEiqgRtQBUCq1XMWjV3wlW9fdfX0MfuvfUhOSsSQDk44fWi7SA8qDX4vn8B7vAcEQYCevj6Gz/CRlZkJAC4c3y8KDplbWFEZB0DVDP/0AdNe2SHf6gD1OS9KYymVqZQjBahKLhv85ioaO3d0t5zLY+LZg5vYvW4xNi2dgVnDu+LMoW+XKDjQD17dm2H9winYsXqBbOfJtXO+ooCnrp4+6rm0Yc7l2CvHZVmYGmq7jIoG8QL17dq1E7329fVFSgr9LP7ZcevWLYSEiEvteDYxx7+4AABpIRmK+eXu3buIiYmhUi9lypRBpUqVRDV2e/fuRa1ataR/4qfGmTNnRKVbCoUCrq6uzLmcEje52F4yYj2AGRkH3vu9wsegAEpUySx/AdRo0Aw3z39Lz58+tF12YayylarBZ8cZrJ43DrOGd0OT1p1Rq1FzmJjlx7uXT3Fy3xZEf/mMAePmwLWnp+zqtC8e3qFKt3jXgFPiJid5QRoOQaVxk27pxcfG4PmD26gsKcPT1dVDo5Yd4bt7Q/rY2SO70KnfCNlYuJSpqbh77Rz09PRhYqbibK+szkjo6OiI+tXCQ4OREB+LlORkFC9VTjamobCQ9/j3pvg+/M59/SgIQuY1hv8RgiC8JYTEAzDKMIZ7184z1+rS1h2bfWamv7586jD6ec3kKiP/F3wKCWI2GGcHvKyFJhAXG42rp8Wah03asvf13tVzvFIQWcu3BEFIIoSEAhClFe5ePUcxNQFA03ZdRBTt966dR/jHD7AqIo82k7llQSzdcQYHt67A1uVzsHHJdFSt0wjFSpSCkYkp3jx/hDuXziA1NQXV67mgr9cMlGKsW5NQKlPxv2Nio71Rq07Q1aWzOU/u3WAJ7CkB+Mq2wG94CcAh48CdK2dRu3ELaqJLW3f8s39r+uvAty/w8vE9boO3HAjyf4On92/CyNgUhkYmcGqqcgYUCkV6SW1keCjev3uFL58j4NLWXeNrOH1I7CvWbvQbkzkwONBPpJ+WAXIHEQCVfdYy48DFixfRs2dPamKHDh2wbNmyb9cvMhLnzp1Dy5Ytqbk/M/btEzuxDg4OKF2aJhuJjo6mmuHVOA+onRJBEF6quZlt0t5NSEjAqVOn0LlzZ+qTbm5uIqfE19cXXl5esLGxoeb+jBAEAWvWrBGN1a1bl6lPEhYWxktV0WkBDUMQhA+EkGgAIhL5Cyf2odvg8dT8pu26iJySJ3ev4/m/t1HBsbas67QuYYe56w4iyP8Nrp/zxZ0r55AYHwfLQtbo5jkeTk3baE0let9GsS5esZKlmQ+NpMREXD1zjBqHzFEcQMXoo75fRUpm54/vo5wSAHBp5y5ySoID/XDt7DE0bCEPRau+gSG8NzGvTY7h4JaVokySiVl+1G7MfmhcZGeStMUQ8ASAKMJz3ncf0ylxbt0JW5f9kZ6ti/kahZP7t6JT3+EaX9SImRrXi9QITuzdjNiYr+mvdXR00ahVJ+ZcTuRXW0wtNwD8H3tnGR7F9fbh+4QAUax4cCku7R9t8QIVoLi3uBSnFC8UKe7FrXhxt0JxadG2uBMIJGiAhHhIct4Ps+FlMzObTZrdCHNfFx84c2bmJJudOY/9HrMv3JHdm2iuUZNRscaXuLqle/tzRUZGsGXFXLoPnWizxaVOk4ZW3QbSpH0fLpw+yrULZ/B9+oiwByFkyJSZTgNGU65qHV053oTm+L7tPI7RT0hvg3xE+3N9aCulvBj8Tgyj5OQfO+g2eIJKjKVomfLkzGPeqHjTr7MYMWu1HZapULfxN9RtrN5Y24ur/5zmWoyolv7nqvkcfi2ltEcxjmp/duLECXx9fVUp+jlz5qRChQpm3v+FCxe+V0aJl5cXe/fuNRuLmVUVze+//27W2yX6ElLKO/COpxWN1AS93LimTZuSLt3/bxIjIyNZvNgexmvS4MiRI1y/bu5Nb9++vebcXbt2aSmZ3UbpI2IPVFGww7s3atYBla9Wl2we5hGUDUtn2G5lMciVrxAtunzPgHHzGDZ9Od2GTKB2w9Z2M0ju3bzCuRMHzMYatOmmOffssX1aucMSsNcvTPV9PfnHDsJC1X0ECpf4iOJlK5qNrVs03S75w0mBV77POLB9rdnYl83ba3Yfv3n5bz2Z58m2WZ2KBTEHLpw5hq9Gg85MWbLzaW3z1IFtq+bFKuuaUggLDWHHavNfV9XPG2o2/3vx7LGmyAcw2zarU/FzzIEHnje5ffWCamKatE7UbWK+cdy/dZVdCqPTpE1Lheqf06HfTwycsJAfZ66k98gZNPzmO7sZJFJKNv06y2ysaJnympG68LBQTh3STDNeqzVoAyYRMzXP/xXnTvyhmiiEoH7rLmZjZ47u00zjS6msXzzd7P/Zc+WlfPW6qnlSSo7u1TRK1L9YGyCl/JsY6qiRkZHs2qUdfGvXrp3Z/69cuaIq+k7JLFy40Gyf6+7urmuUbNu2TWv47X7mXaNEZa6fOXMGb29v1dnu7u60adPGbGzz5s14edm/eNXeREZGMmtWjAdm0aLUqlVLc76OYbdK2k8dQNUJS68o1tExNc06mvXl4++Th7h24f3Q3l41Z7yZsZYxc1Zdr5KO1/WGlNKWPUreZQwxXobBQQGcPbZPc3Kzzv3M/v/g7g1OHtihOTelsW7RVLONepq0TjT6pofmXB2vq6/pJWVzpJTLAbM0MRkVxfF9mg9yWnTpb5bS6PfiObvW2VpnIWmw87dF+L38f8VXIYRm5AEUr6tG/VeYlNIum1cp5b+AqjhI5++Nxu17mRnN4WFhbFo6S3NuSuPY3i2qFNpW3X7QnPvXoT1mkTITEsVYsDlSSj8UJ6MZevUYXzRtZ9bXRUrJmnm2i4AlJa78fYp/T5lnrTfv1N9M2CGa6xfOqCJlJmLXIU84VM8GPUd9nTp1VAXvM2fOTBSVSXvj6emp+r20b9/eLHARjY+Pj14N+tucvrdGiZTyAmAmsi2lZNMm7aLYzp074+z8NvWZ8PBwRo0apTk3JbF27VpVz5GePXtq1jpcvHhRFVFBeWDatADP7GZSXkORWjPj980rNefXbtjGTFFFSsm8nwdqacCnKE4f+V0VJWnSvremN/35Y2/++VMVgAKYa5vVqZFSBgKqP67fN2l/rhWq1aVgMbMsAxZP+VHrhZ6iuHPtIvs2rzIbi7kxiCYkKJBjv2/Vukz8Krzjj6oI7Y+tqzUjW/mLlKR81TpmY2sXTObZ44e2W10SwPeJDxuWmAclK9X8SlPSNioqkj+2aT5yNb/ENkQlt3Rk72ZNlcNMmbNRu6G542/PhmV6fVZSDMFBASybOdpsrGDRUvzv08805+/bovm8uyKltOeDbV7MgfMnDmpGN9OkdaLhN9+ZjZ0+8jtnj9slAJBoREZGsHDSULOxzNly8tnXLTXnx3xmm3hqBxGZd1lNDMff1atXNXvzCSH47jvzz/Xy5cts2GDvV4f9GTdunFkTdWdnZ93MofXr12tl6VyQUr61PWJKoqie3KtWreL1a/X3O2PGjKobnzx5kj/+SLlfLl9fX2bONM+tLl68OJ9/ri5qA5g/f77W8HEp5f0EX5xlVN+MY3u38PSRusefklts7pXyunOdvRv0JXuTO2GhISyZ8qPZWOZsOfmyeQfN+VtWztVs1IWGepKNUaWeXDp3Ujey1ban+Uvhle8z1i+aZpuVJQFkVBTzxw8y85A7u7rRrJN2n5toUYWYlwHG2myR2vwUc8D7/h3+PKidOtC21zAz0YKw0BCWzRhts8UlBRZNHm62mU+VypG2PYdozj2xf4dewaw9va6gfK4qFa59m1doTm7R5XucnF3e/j8qKpKFE4ekaAn+NfMm8fL5E7Ox9v1Gajr9blw8x5XzmvWa9i6Amovy/H9LxJtwtq5U2SoA1G/ZWSWlvGTKcJv2o0lsdqxZpFJXbP3dIBxTq5sgP/H20nMO2c2ZCyCl9ERDVjpmPXE09evXp0gR8yax06dP5+VLeyVP2J89e/ao0tS6dOlCxowZVXMDAgL47TeVcCiAmQUa0yhZCZi5bQICAli7VjvC3atXL1Vx+8iRI3n2TOWYT/ZIKRkxYoSZgebg4MCYMWPMutxHc+PGDQ4f1nTE2XvjCsrL0MzNGhHxhq0rtB37XzZrryruXjVnPA887SEsZX+WTh2hMtC6Dh5vtiGI5pXvMzMZxXf4w06Fle+yhBgNMgE2//qL5uQK1epSsYZ58d32NQt1ZaKTOxt/ncWtK+YqH217DNHsrRAeFvq2F04Mrkgp7fpAk1KeBlQFBBuXztTckBYsWoqvWnY0Gzv5xw6bSz8nFsf3bVPJlTdo05V8hYur5mrVJ5h4IqW0a16q6e9IVUCwdeV8zQ1p5mw5adVtoNnY9QtndTe7yZ3L5/9kd4zUw09rN+DjT7RTo2PWJ5gIMaVA2g3Tc19VGL1/yyqz9MJonF3d6PyDuZ/j8cP7LJuZMjNNHty9wW/zzbPpCpf4iLqN2mrO37z8Fy15+0js7xwCjf3awYMHuX1blbFHqlSpGDNmjHk6rZ8fQ4cOTZGOhOfPnzNu3DizMQ8PD7p1067D1QlwBBGjdMTMKDE9NFUJycuXLzdrHR+Ns7Mzw4eblyy8ePGC77//Xqu4O1mzdOlSDh40lwpt1qwZH330keb8BQsWaP0h3kUjhG9rTHmve2OO/7FtjcorBUqH9x7Dp5h5X0NDgpk0sLNmIXVy5sQf21WpbB9VrqEqII5m++r5WoXEEuiiMd2mmF6GqgZeZ4//wd3rlzTOgO+GTjIztmRUFNOGdeeVb8pyJFz95zRrF0wxG8tTsKiq0DSa/VtX6/0Oeib86qxCVQvmefOKnlwx7fr8qCrwnjduIN731C/P5MyjB57MGWveqyhj5qy0/k6tJghw5sjveoXEoxN8cdah+gN8+fyJSv42msbte6qMrVWzx6W4Oj+/l75MHdLNLKqZ1smZTj9oB7Pu3ris2dcKjVQqO9GZGFGwsNAQdv6mejwDUP3LJpSpWM1sbPe6pXoRgmSL1r5B2V9M1uxd5Pv0EYd2avao3W3nlLxo1hOjZigqKoqFC7V9y+XKlaNxY3NVy8OHD7NixQpbrS9RiIqKYsCAATx//txsfNSoUWZlHdGEhISwcqVmquUiKaWZ5a7V0WoqMQotX7x4wdKl2sWTdevWVaUvnTlzhtmz7SVqYnvOnTvH9OnmXpls2bIxePBgzfmXL1/m9981u/COl1ImVledzsSIlrwJD+e3+dqiQoWKl6FBm65mYw/u3mD++EEpxup/4HmT2aPNC2NdXN3p+aN2StPzx97s0U5jOyalfKx1wA4MIkYDL4AVv2g7lbLkyMU3vdRpXDNG9NJsvpgceen7lClDupr9PI6Oqek7epZmn4PgoAC9IuJbUkp7SQGbIaVcBqhyyZbPHKNZ3+Xi6q6SjA0NDmLykC6EBgfZbJ32JDgogPHft1f1pOj541RNhb7IyAjWzNesd34hpdTeLdoYUxTsbszxtQunaNZ3pUrlSM8RU82KgSMjI5g6tDt+L56r5idHIiLeMHVIV5W6WPt+I8mWM4/mOcum/6T1HgoDhtlkkbEgpfRBI9Vnx5qFmmnSAL1GTMPJxdVsbP64gXrqf8kOKSVzx36vyrBo/G0PPiz5seY5q+aM5024qh2UBLrbZJGxIKWMRNkTm7Fr1y4uXtQWUB06dChZs2Y1G5syZYpeb45kybRp01TNJOvVq6cr+LRgwQKtNLYwNNRKVUaJlNKbGDle0Re9d0+7x9TEiRNVaVzz5s1j1SrNYqVkxe3bt+nRo4dZh04HBwemTZtGhgzqbtBRUVGMHj1aS3XhIRqduO2FKQqmLqDd/hs3Lp7TPKfj96MoWsa8KeahnetThFrIy+dPGN2zleYGJ0fufJrnLJg4RKsoNdEemAAmI1eVT/bvqaOc/ENbXavhNz2oVPPLGPOPMHNk72RvcAYHBTCmVytePDO3Eb/t8yNFS5fTPGfV7HF6cqt9tAbtyISYAw/u3mD3Oz1n3uXTOl/zVQvzNK57N6/yc79vtF70yYqIiDdM/KGTSpWpQeuuVNbpBr1t5Xy9KElipIG8i6qo6ZXvM9YtVO19AChetqKqXub5Y29GdG+qJUuerFA2rgNUKaQVqtWlQeuumucc3btFL+V0eSI6/QA6oREtWTZdOy0rZ54C9Btt7gwJCnzNiG5N8H3iY7NF2ouVs3/m6N4tZmOFS3xEuz4/as6/9u9pPTW6g3bqTaLHCsDMsrSwzyNTpkzMmjXLLK3/zZs3dO7cmRs3bth6rTZn7dq1qhYgefLkUaVyRePl5cWvv/6qdWiZyZg3QytSAsrL0CxHJTw8nPHjx2tOTpcuHbNnzyZ1anMv5Pjx49m/f7/OLZI+jx49okOHDvj5+ZmN9+/fn8qVK2ues27dOj0LeqytO0JbQUdiREu0ioGjcXRMzaCJC9925Y5mw5IZZs34khuBr/0Y+V1zlULRl83aU6OeulkoKClRZ49p/i2flFLe0jpgR/oSI7oJsGTqCK1Oxwgh6DdmNllymDsSju7ZzIpZ9q79TTjCw8L4ue83KoWi8lXr0KR9L81z7l6/xN6NKzQPSSkTVbVDSjkN8Is5/tuCKSqjK5ouA8dRsGgps7GLZ08w66feybYvjYyKYsaPPVVyooWKl6HTAO2/V98nPqxfrBnxfCWlTNQwvpRyL6Dy8O1au4R7N7XFhZp36qdSoLp/+xoTBnRI1gbnshmjOLjDPHUtW848DBg/X7O4PTgogGXTVToQoHhdv9c6YC+klLeB0zHH/zy4Szftsurnjfm8ybdmY75PHzG6d2sCX6u++smGnb8tYvMy86+ZW7oMDJu+TLO4PTIygvnjB2s5xaJQsjwSDSnlG0DlibWkrlWhQgV69zZvYhsQEEDXrl15/Dixkir+Owp7HM4AACAASURBVPv27WP06NFmY2nSpGHOnDm4u7trnjNq1CitZokh6PT+0jRKpJT30ND5Pnr0qF5aEqVLl2bs2LFmD5LIyEj69evHzp1Jq7uzNdy9e5fWrVvz9Km5gf7FF1+opN+iefbsGTNmaPbOOwskunyVlNILRczADM+bV3RzX7N55GXQpEWqtJfFk4cny4LLl75PGdq5ocrjWuLjSnQdrHJMA4pU7KJJmlkBEUCTBF9kHJFSBqOh2PTi2WNW60S13NNnZPj0FTi7upmNb1kxl6XTRia7iElQ4GtG92rJ5fPmGRS5C3you8GJjIxg3riBWga5BLQ7P9mfjjEHLPw9kiZtWobPWEHGzObpA8d+38rUYd2JeJO8NrBvwsOZMqSbqk9LpszZGDZ9uaprdjQLJw3VlNoFtLUq7U8TYnjVIyMjmDd+kGYapXBw4IcJ88mVr5DZ+MWzJxjdq6Wm8yEpI6OiWDx5ONtWmStUOru6MXzGCtzSqbMQQEnv0Ylq/iilTApdQxsRQ4kLYNGkobpplN2HTlQ1t71/+xrDujRMlrV+W1bMZcnUEWZjjo6pGTJlCVlz5NY8Z/vqhXpRzWVSyqSgb74EUDXYmD59uqquIppevXpRt655Y8jHjx/TunVr3ayjpMyOHTvo37+/WXRICMG4ceMoUaKE5jm7d+/m5EnNDOgJpv2oCr1ICShGicoD/OOPP2o2VARo3rw5AwYMMBuLiIjghx9+0K1JSYpcunSJ1q1b4+NjHlmqWLEi06dPx0GjQCsqKoqBAwfi768Kp0cBfRJBmUmPLkBAzMGVs8dx55p2jmS5KrXp//Ncs8I0KSXLZoxi8eThycYD+8TbiyEd66ukCfMULMrIX9Zo9iQBWDBhME99NL8/k2IWaSUWUsrJKCmCZuxau5jTR7QdCYVLlGXErNWqjd321QuY/mOPZNOb5pXvM4Z3bsilc+YPvw+y5mDM/A24p1fLEwKsmTtRpc5lYpOd9fB1kVJuR+Nl+Neh3Xpa/mTzyMvPCzerNnbH921jVM+WBAepvv5JktDgIH7u9w0n/jBvzOXi6s7o+Rt06w12r/9V72/+tJRSW1fZzpj6gqnyK29cPKebxpUuwweMW7xVFeG8ePYEw7o01FR6SopEvAln2vDv2LnWPAXEMXUahk9fruqnFM25EwfYs14zDeS+lFJTisvemNKkVZLEjx/eZ/YY7caeadI6MWreOvIXMd/Y3bt5lYHffoGPl6oEKUkipWT5rDEsnznazKklhKDPqJl8VLmm5nm3r/7L6rmaDsHXJGJq9LuYakt6oKiAvcXPz4/+/ftrCjs5ODjwyy+/8Omnn5qNe3t707x5c/79919bLjlBWbFiBYMGDTIrYwAYNGgQTZpo+2V9fHxUURUTdwDdXgS6RomUMgyNnOrXr1/Tt29fs2Yp79KjRw9V/xIpJZMmTWLEiBGEhiYFZ4Y+mzZtom3btqqinGLFirFw4ULS6mxcf/nlF/76S1MzfYGU8mzCrzR+mIyjDjHH34SHM3lwZ91mejW+akqn70erxneuXcz4Hzok+VDz2WP7+b5NbR4/MPdQZM2Rm58XbtL1zO3bvEqvO6+vlHJkwq/0P1GfGN5XKSWzfuqj20yvTIWq9B87V6WEcnTPZn7s2lg3TSipcO3CGb5vW0eVsuWePiM/L9yk65k7f/Igm1fM0ToUDHyrdSAR+ZoYL0OAxVOG6TbTy1e4OD/OXKkytC+ePcHg9vWSvCrXA8+bDGhbl3/+MpdVT5M2LT/N/o0CRUpqnnf/1lWWzdDM4Y8k6US/ommJhqT3hqUzValq0WTOlpNRc9aqnld3rl1kQJs63Lz8t00WmlD4PvFhWJdGKpUpB4dU/DB+nu7G1feJDzNG9NKK4EqSQLT6XaSUg9FoWHx83zYObtdur+Dqlo5Rc9apDM6njx4wqN1XnD+hnf6VVAjwf8XP/b5hy3L1M7XzD2P47OtWmucFBfgzaVAXvQhulyTkzEVKeR4NddozZ84wb5521kjq1KmZM2cOxYqZN3X18/OjXbt2bNu2TfO8pEJISAjDhg1j3LhxqvqZjh076sr/RkRE0K9fP1Xpg4m+lqKaliIlmHKqVd+iS5cuMWXKFI0zFEaMGEH37moDd/369TRr1gxPT81GVolKcHAwAwcOZNiwYSr543LlyrFmzRrdnLmTJ0/qNdR5AIzQOpCYSCm3opH7+vjhfeaM+V43dadxu550HzpRtYE9fXgv/VrW0vM6JyoREW/4dfpP/NzvG1VjvDwFijBlxW4+yJpD89z7t66yeIpKmRWUF2HDBF/sf8TUFVVlQQW+9mPa0O90Ix/Vv2zCkMlLVBGTq/+cpm+LGnrSm4mKlJIty+cwrFNDVVHoB1lzMGnZTvIULKp5ru/TR8wc0Usvwtc9CdR+mWFSdlOl04aHhTF1SFfd1J1S5T5l7PxNKmWq+7ev0b9NbT1jO9E5tHM9A9rUUan2uLqnZ+yCzZQs94nmecFBAYz/oYOWZDfAuEQullVh+jtTFTvJqCimD++hKdcOisE5adlOVb+dZ48fMqRDfbavnp8k0y/PnThAn5Y1uX7B3EeXJm1ahk77laqfN9Y8LyLiDZMGdSbAT7MJ3VopZVJ0OTcnhoMIFLGUB3e1i50zZ8vJlOW7yV3gQ7Px134vGNOnNctnjUmSCok3Lp2nb8uaqppL4eDAd8Mm0+hbbVV1xWHWVy8L4S8pZVJstDQMjYyEefPmqdSookmXLh2rV6/m44/NFcdCQkIYNGgQQ4cO1Wy5kdjcvXuXpk2bsmmT+mPo0aOHqh3Iu0yYMIELFy5oHVotpdRO3TAhYnt4CSHcUNIHisQ8NnLkSN128qA0S9GysJycnOjWrRvdu3fXjTzYk8OHDzN27FjNtLRatWoxe/ZsnJycNM+9ffs2rVq10krbigBqSClVMoFJASGEE0qDNpWWZsuuA/i2t/4f3KnDe5g6tJuq4VeqVI7Ua9mJb3oPw8VV24CzJ1f/Oc2CCYM1c1U/LPkxo+etI12GDzTPffHsMYPafaUXYZhq8oYlSYQQPkDOmOM16jXjh3HzNfXhQWle9nPfb1TpPUIIatZrTqcBY8jwQRabrDku3L91lfnjB2v2asiVvzA/L9ik8jhGExwUwLBOX+tFGLZJKZOU1/VdhBAXgDIxx8tUqMroeRt06yu87lznpx4tNKNeFarVpfvQiWTzyJvg640rT7y9WDRpKOdOHFAdy5g5K2Pmb9SNkES8CWdMn7Z6EYbzUsryWgeSAkKIXShRTjPyFS7O5OW7VEIj0Tx7/JCfvmuuKSFb4uNK9Bg+RbOhpL0J8HvJyjnj2L9ltcpYcnJx5ccZK/mocg3Nc6MjvTq9K7yllNqh0CSAEGIGGsX3mbPlZNqq38mc3UPzvMDXfozp00ZlvAHk+7AEPYdPpvhHlRJ8vXElNCSY9YunsW3lfJWx5Jg6DT+Mn6draIIiWx+zGN5EIJDNVCuZ5BBCVAKOA2aFtu7u7qxdu1YVFYkmJCSEvn37cuSI+hmVPXt2RowYwRdffKFxpn2JiIhgzZo1TJ8+XWUsCSEYOnQonTvraw+sXbuWn37SFKO4DZSLrd9MrEaJaSGlUTzrZl1RonPmvvzyS+0TUar1hw4dSmCg2puXP39+hg0bRs2aNTULUW3N3bt3mTx5smbndSEEnTp1YvDgwZod2wGePHlC8+bN9dQUBpnUc5IsQoiKwClA9cvvOmgcDb/RLugHZQM7dUg3zaLDTFmy06H/T9T4qqlZA0Z78fyxN6vnTeTI7o2aHsOa9ZrT+6cZpHVSN/kBpWh6aKcG3Lt5VevwRSll2YRdccIihMiLkrfpGPNY0w696aiRhhfNvZtXmDiwE48eqKOZbuky0LbnEL5o2l53A2xL/F+9YMOSGexZ/6umx/B/n37GwAkLcM+QSfP8iDfhjO7dmgunVcrYoBjoOZNSukBMhBAuKOt0i3ms2heNGTRxka7B+fTRAyYN7MTtq2rvVZq0TrTo0p+Gbb9TCR/Yg5CgQLatns/mZbM1oxwflvyYYdOW6RqaMiqKKUO6qWpPTAQB2aWUSbYSXAjhAPgA2WMeK1XuU8bM36hb7/ba7wVTh3bn31NHVcdSpXKkQZuutOjSX9f5YkvCw8LYt3kFvy2YoildnCtfIYZNX07eQtqbOICl035i++r5WofeAAWTSBG0LkKIq4DKMsxTsChTVuzWTRsODQlm7tjvVZK6pmvy2det+KbnUF3DxpZERUVyZPcmVv7ys+77f8iUpZT4WN9w2rNhGQsmaPr1JFBFSqmZC59UEEIMQ0OyPVu2bGzcuBEPD+3PJTIykokTJ7Jy5UrNvclnn33G4MGDKViwYIKvOTaklBw6dIiJEyfi5aWOXqVLl47JkydTp04d3WscOHCA3r17a9XYhAKfWBPVtMooARBC9ESjW2ratGlZtmwZFStW1DhLwcfHh759++o2mylSpAhdunTh66+/1jUAEpKbN2+yZMkSdu3apVmg5O7uzsSJEy1ara9evaJVq1bcvatZhLYHaCCTYgw9BkKIcYBKOFw4ODB40iKLng7/Vy+YPryHKu87mmweeWnYthtfNOug+1JNSJ76eLFjzSL2bVmpiuKAkibQod9PfN1Wv3YuLDSEkd2b6XVMDgZyJFJn2TghhGiPoq+uovMPY2ncTr9ReUhQIHN/HqDbXThDpsx81aITjdr1sEtEzO+lL3s3LGP76gWaRdqpUjnSsusAWncfqLspj4qKZNLAzvx1aLfW4QjgQ5PqYJJGCFEdOIKGI+Hrtt3pNlhbth2UNJg18yayZfkczReii6s7X7XsSNMOfXTFARKS4KAA9m5YzpYVc1SpldF80awd3w2dpCkjGs3CSUPZvU5TSEUC1RKrAWZcEEIUBq4DqhdglboNGTJ5ie7ftpSSXWsXs2zGaM0UTSdnF+o2/oamHfvopqomJKEhwfyxdTVbVszVrUn7tHYD+o75RbPpZTRbls9hub5E+bdSSlV/pqSGECID8IgYDl1Qolk/L9xMmrTaWRgAh3dtYN64gWYd0aNxdExNtS8a06LrAJUqmy2IiHjD8d+3snHpTN0Gj2UqVGXgxEUq9b93Obp3C9N/7KGXPjtGSjk6QRZsQ0yOhD2AapNYsGBBNmzYoNnHLppDhw4xZMgQzZoLBwcHatSoQZ8+fShVqpTG2QlLVFQUR48eZc6cOVy+rF2jWLJkSWbPnk2ePNriIgCnTp2ic+fOhGtLlHeXUi7WOhATq40SACHEQjTUEJydnZk/fz5Vq1bVPTc8PJwZM2awYsUKVQV/NLly5aJhw4Y0atSI/PnzW70ua/D392fv3r1s376df/75RzfntmrVqowfP56cOVXZL295+vQpHTt25NYtzfYUV1BehNpv2SSIEOIAUDvmeHQX7FoNWuqeK6Oi2LJiLusWTdV8cIKSelH9y6bUrN9C1UPhvxIaEsxfh3ZzZPcmLp45rtlvBaBIqf/Rd/Qsi165oAB/xvZty9V/VOU2oBTKVjF1ZE4WCCEWAapKNCEE7fuOpFknVQ83M/ZvXc3ymWN0RQzc0mWgat2G1GzQgmJlKiRotPNNeDjnTx7g0K4NnD9xUFfKNneBD+kzaqZKUjPmtaYN686fBzWFlyTQMonmL2ui56UDpZlgt8HjdTewoNSALZg4RHfD6OTsQuVa9ajVoAVlKlZL0GhnVFQkF04f48juTZw6vEdPtpfM2T3oOXwKFap/rnstGRXFosnD2K2tyATJIFr9LkKI1igNdlVfpCp1G/LD+AUWI5RX/j7FnDH9ddWaHFOnoXzVOnzWoCXlqta2aOjFFSkl1y+c4fDujZzYv0O3qaN7hkx0HjCG2g1bW7zehiUzWDNvot57eoGUUt+rksQQQlQBjqJhcJYq9ykjfllt0Ti7f+sqv4zupxnlBEUkoEzFatRq0ILKterh5OySQCtXuHvjMod3beD4vq26EsVOzi606TGExt/2sPjsObhjHXPGfK9XG7NfSpn4+UtWIoTIBJxAIxJWpEgRli9frurs/i7e3t78+OOP/Pmndoa/EIL//e9/NGrUiC+//JL06bXTOOOLp6cnO3bsYPv27Sql2WgcHR3p0qUL/fr1U/UhfJejR4/Sp08fvdqYeVLK3loHtIirUeIArEcp4jIjVapUjBs3jubNVYfMuHXrFqNGjeLcOe0u4tEUK1aMTz75hEqVKlGhQgVcXV2tXicoYbIrV65w6tQpTp8+zdmzZ/UsOMD6nL4HDx7QoUMHHjx4oHXYGyVElaRDyloIIf4BPtIYt2oD++zxQxZPHq4rPxtNrnyFKFupOqUrVKXU/z7RTbXRQ0ZFcf/2NS6ePcGlsye4dO6k7sYGlJdgh74jqdu4rcWH5SvfZ4zq2QJP7eZlyW7jGo0QYjeg2fLamg2s/6sXLJ85mkM711ssns2aIzcfVa5BqfJVKF2hCpkyZ4vzWr3v3ebSuZNcPHuCi2eOW1R0c3J2oVW3gTRq10PVQ+ddQoODGD+gvWZ6i4khUkp91Y4kihBiNjod5z/5rD4DJy6yGJ0MCQrktwVT2LV2scXi2QwfZOGjSjUoU6EqpSpU0ZXhtcRTH6+3n+uF08fwe6Gt6w+KI6Tht9/Ruvsgi5uriDfhTP+xFyf266rXzJJSJmozvfgghOiPhqQsQOnyVRjxy2qL0ck34eFsXTmXjUtn6jqJQFGnK12hKmUqVKV0+Srkyl84zmt96fuUS2eUZ/C/p4/y/LF2qwBQIu91G7WlQ7+RFp/50VLzMfuXvMNOKWWSExmJDSFEQ2AbGgZn3kLFGLtgo8UoloyK4vfNK1k1Z7zl56KLK6XLV6GM6bPNW6iYxee7FgF+L7l0/k8unzvJv6eOxipJ/Mln9ek2eHysqWQ7f1vEkqkj9N4jV6SUtg8LJDBCCA/gT0BVlOfh4cHy5cspUKCAxWvs3r2bCRMm8OyZfk+atGnTUr58eSpVqkTlypUpWbJknLOKAgMDOXfuHKdOneLUqVNcv37d4vxKlSoxZsyYWFPJduzYwZAhQ/SCDduBZiZJZauIk1ECbwukfwdqaBxj2LBhdOrUyeI1pJTs3buXefPm6UUbVOTIkYMCBQqQL18+MmXKhIuLy1s1rJCQEIKDg/H39+fhw4d4enry4MEDXdnid8mQIQMdO3akY8eOuLhY9jD8+++/dOvWjVevNIMgL1A86drSGkkcIYQjcBfQ3HU0bteTTt+PjvUB989fh1m3aJpmkZ4WGTNnJVe+wnjkK0iGTFlwcnZ9m2cbHh5KaHAQga/9eProIT5ed/G5f9uqDsZOLq7Ua9GRZh37xmr4PPS8xeherXj6SNPQBOglpdR9SyZ1hBDngHJax2rUa0a/0bNjrRG5cfEc6xZNs1qJK12GD/DIV5Bc+QqTMXNWXFzdcXVPhxAORLwJJyRE+VyfP/Y2fa53LBqX0aROk4baX7emZdcBsb4EXz5/wuherfQMTYBpUspBVv1ASRAhxFZAM7/yo8o1GDptmUUPLMCDuzdYt3AaJw/utKrfkKt7ejzyFiRXvkJ8kDUHru7pcXZ1I1UqRyIjIwgJCiQowJ8Xzx7jff8OPvfv6MqMv4uDQyqq1P2a1t0HqdSHYhIU4M+EAR24ePaE3pTNUkrL3rEkjBBiGvCD1rGCxUozau66WI3+p48esHHJTA7t2mBVw0wnF1c88hbEI29BsuTIhVu6DDg7u+KYOg1SRhEU8JrgoABe+T7D+/5tvO/f0VPDivmzUK5Kbdr0GEzhEiqflxnhYWHMHNnbkqF5VkqpHxJN4gghegFztY5lz5WXMfM34pHX8gbQ76Uvm5fNZt/mFVY9L9OkTUvOvIXwyFuQbDlz45YuA04urqRJo6SMBb72IzQkCL+Xz/G5fxfv+7etbthY/KNKtPluEGUrVbc4Lyoqkl+nj2LHmoV6U7yAQlLKpCctZgVCiGIoERNV4VamTJlYsmQJZcqo9EnMCAwMZNmyZaxatUpPRteM1KlTkydPHgoUKEDu3LlJnz49Li4uODsrWYIBAQEEBwfz8uVL7t27x71796zuJF+sWDF69eplVdH94sWLmTp1qp6heQT40tRexGribJQACCHSA/sBzQfEV199xYQJE3Bzs1w0KaXk4MGDLFy4ULfexFZkzZqVTp060aZNm1iNESklK1asYMqUKXqGziuUX75mIUJywaS0dhfQjDmWqViNgRMWWswXjebSuZNsWDKDS2dP2FWe0j19Ruq17EzDtt2sisIc3bOZueN+0O22SzLJcbWEKcJ5DQ0FPVA2OkOn/EqOPLGnTN6+eoGNS2dy5ug+3VQ5W+Dk4krdRm1p0qE3mbPpp1ZG8++pI0wf3sNSQ7lVUsqk0t073gghjqDhIALIkTsfQ6b8SqHill+IoESpNi37hWO/b7Vr1/fUadJQ/cumNO/cP9YNGSiN1iYN6qInIwpwREpZK0EXmQgIIVah0y8nwwdZGDhhYaybQVD6e2xZMZcD23+zahObUDg4pKJyra9o0XWAVSm7Pl53mTSok564CMANoERSFqKwBiHEGEBTmsjZ1Y0+P82k2hf6dZzRvPZ7wY41i9izYZlde4QJIShbqTotuwzQleZ+l5e+T5k6pBuXz+uKkD5FMUiSrBCFNZhEg/YBqkKSNGnSMGTIENq1axdrinNQUBC//fYbK1assBg5sQVly5alZ8+eVglPBQQEMGzYMPbt26c35TTweXzqb+NllAAIIVyBTYCm9JaHhwezZ8+O1UKM5tatW2zbto2dO3fy9Klt5OSdnZ2pU6cOjRo14tNPP7Uq/BUQEMDw4cP5/XfdtKTHKAaJfa0qGyGESANcBjTdlekzfsAPExbw8SfWvfefeHtxePcGjuzZpGpcmFA4pk5DuSqfUatBS8pXrWuVMlR4WBgrZo1RdRV+Bwn0k1JqdthLbpgMk8OA5k7G2dWN3iNnUP1L6xRxXz5/wtG9Wzi8a4Om5HJCIBwcKFOhKrXqt+CTz+rj5BJ7CmdUVCTrF01n3eJpljz/yTK1Rw8hxAaghdax1GnS0LH/KBq06WZVzU+A/yuO79vGkT2buHHRcortf6FY2QrUrNecqp83srqoft/mVSycNNSS0ZQsU3v0EEJMBIbqHKNB6650+mGMxfTFaEKDg/jz4C4O797IpXMnrYqKxYf8RUrwWYOWVPuyqdUpnH8e3MXsUf0sRdQuAh8nd4MkGiFEX2AWGqlcALXqt6DXyOm66pDv8iY8nLPH9nF490b+PnlItxfVfyVnngLUrN+cWvVbWC0ffuncSaYN7a6p0GXCEyiVVKV/44oQogSKYaIpE1i7dm0mT55sVW1IZGQkJ06cYMeOHRw4cMBmTcezZ8/+to67cGHrUjivXr1Knz599EoYAA4CTaSUalUaK4i3UQIghEgNLAfaah1PkyYNPXv2pFu3bqSxUkI0MjKSS5cucfr0aU6fPs3ff/8d7w/EwcGBIkWKvM3Dq1SpUqxRkXc5dOgQY8aM4dGjR3pTbgBfSCl13XbJEdMG9gw6KT/CwYGGbbvTtscQqyVEpZR43rzC5XMnuHT2JJf//ku36Zs15C7wIaXLV6G0KSc6LmpBV/4+xfxxA1XN2d4hEmglpdwc7wUmUYQQ27HQ+LFWg5ZKP5JMma2+pve921w4c5zL505y6fyfVqV16JHNI+//50RXrGZVVC6a+7euMnfcQEubaQn8IKXUzNlPzliqMQEoX7UO3w2fHKeakKePHnDxzHEunTvJpTMnLG0uYiVT5myUrlj17eeaNYf17SWeeHuxcOIQzp+02NU6RRma0QghBgJT0NnAFi9bkZ4jpsapH8lL36fK53r2JJfOnrCUthor6TJ8QKlynyj1KRWrxUkFyu/Fc5ZOH8nRPRYfs1ullE3jvcAkihCiJUpjas186LyFitFrxNQ49SMJ8HupfFdN9Vve927He30uru6U/F9l5f1aoapufyAtgoMCWDN3IrvWL7Vk/J5Bqb9NEYZmNEKIfChZRJpOXQ8PD0aNGkWtWtYHc4OCgjhz5szb+uibN2+qev9Zi7OzMx9//PHb/XDp0qVxsLLmKCwsjEWLFrFgwQJLpRGrgc5Synhbx//JKAEQivttMjAQnQdn/vz5GTVqFFWqVInz9SMiIvDy8sLT05N79+7h4+ODv78/wcHBBAYGEhER8ba+xN3dnaxZs1KgQAHy589PgQIF4lwgD4oqwtixYzX7l7zDSaCxlFI3PyS5I4TYAXytd/yDrDnoMuhnqtZtFOdrR0VF8tT7AT5ed/G+f4sn3l4EvvYjOCiQ0OAgwsNCcXJR6kucXdzI8EEWJZc9f2Fy5Sukq+9uCb+XviybMUq3f4mJMKB2cpARjS9CiLlodJKOxi1dBtr3HcEXTdvFuUhSSsmzxw955HUX7/t3eOTlSeBrP0KCAwkJDiIkKBAXN3dc3dLh7OpG+owfkDOvUnuSK39h0meMez+F4KAAfps/md3rlloq2o4E2kopN8T5BskEIcQQYCI6z+G0Ts607DqAJu17xUt5KbpOJPqzDfB/RUhQICHBgQQFvMbVPR0uru44ubiSLkMmPPIWNH22heIlRfsmPJwtK2azceksvS7toBiag6SU0+N8g2SCEKINsAoN9SZQxAEatOlK2x5DrIomxsTvpS/e927jc/8OPl538H/1gtDgIIICXxMcGICzq5vyz1Tv55G3IB75CuGRryBZsueKs+peVFQkezcsZ/W8iboqXSZ+kVL2j/MPlEwwyXvvBzQVKZR+JK3p+P2oeD0XA/xfKe9Xz1v4eN3l1YvnhJpq+UKDg0iT1kn5XE3v2ey58pIr34d45CtENo/c8VLdO/b7Vn6dNjI2B0aSblL7XxFCZEEp8NbNb6tduzYjR47U7WdiicDAQO7du4enpyeenp48e/aMwMDAt3Ukjo6OuLm56vM9+gAAIABJREFU4eLiQvr06fHw8KBAgQIUKFCAPHny4Oioal8WK8ePH2fMmDGa/UtMSBQ7YPh/bYXxn42StxcSohGwDNB1WX/xxRf06dOHIkU0U9sTHT8/P5YtW8ayZcssRWckiudqRHItzIoLpuK8X9B5IQKUrVSdb3oOpWiZpNk0OTQ4iD0bl7Nx6czYXoK3Ubw3KdbQjEYI0QRYB+juTguX+Ihvew+zOlXP3kS8CefgjvWsXTiFl8+fWJr6FKgqpYy/6zCZIIT4BGWjoxvCzJWvEG17DaVK7a/jbHTag6ioSE7+sZM18yZqNvF8hwCgbnKS6Y4vQogPURxhWfTmZM6WkzY9BlOrfosElftNKKSU/H3yEKvnTeDu9UuWpoahqB3usNPSEg0hRFbgL0C3oMo9fUZadv2eL5p1SHC534Ti2r+nWTNvEpfOWfTlRQK9pZS6Fe8pBVMW0QQUwQpNq93Z2ZkuXbrQvn17iz1NEpPr168ze/ZsDhw4YGnaS6CDlFJTcz+uJJhRAiCEyIOy0dG1EIUQ1KxZk169elldb2JrXr58yZo1a1i+fDkBARbT4HyB9lLKvXZaWpLAmhciKKkEzTr1tdhbwJ6EBAVyYPtvbPx1lkUZUhOrpZTt7LGupIJJZ/0vdArgo8lfpASNv+1JjXrNErRnRXx5Ex7OoZ3rWb94Gr5PdVMrozmGEvlK8Q6EaEwKifvQqR+KJnuuvDTr2I/ajVpbVZdga942Z/t1ljWpJxdR1A6TdYFsXDCl1W5GR3EtmoyZs9Kw7Xc0aNPVqroEWyOl5NzxP1i3aBq3r8ba0NkTqCyltG+VbyKj11PqXdJl+ID6rTrzddtu8coUsAXX/j3N5mWzOXv8j9imvgSqSyl1pRBTIkKI+ihNjHVDXS4uLjRv3pzu3btb7GtiT65fv878+fPZt29fbEJF51AcCAlWMJygRgm8LZQeCQxCJywZTcWKFWnatCmff/55vNKs/gtRUVGcPn2abdu2sXfvXsI0OoDHYBfQU0qpL8aegjG9ELeg1CNYjNcXLlGWz75uTfUvm9ilM3RMblw8x+HdGzm6Z7NmB/AY+ANt3jdD811MTVG7opPfHE3uAh9Su2EbatZrRqYs2e2zuHe4f/sah3au58jujZZUtaIJRZFyXmaHpSVJhBCjgBGAxXh91hy5qd2wNTXrtyBH7nx2Wdu7PH5wj8O7N3Jw5zqLvS5MRACjpJSazSPfB4QQXYHZgH4rcBSVrlr1W1CrQcs41ZwkFC+ePebons0c2LHWGiMzCqUpotVN1lIaQogGwBrAoo63q1s6atRrRs36LShaWrPs06YE+L3k2L5tHNyxljvXYtX3kSj9WZqntPoRaxFC5AYWoNMvLBonJye++uorGjduTMWKFa2u9UgogoKC2LdvH1u2bOHs2VhbOoSipGuN/y/1I1okuFHy9sKKd30eGp3CY+Ls7EzdunWpV68eFStWtJmBEt1Q8cCBA2zfvp0nTyymfERzH0WFaadNFpXMEEL8D+UhE2ulanQH4epfNqFMhapxbpRoLTIqinu3rykqJLs2xpbyEU0USrph9/f1YfkuQoiCwE40utPGxMEhFWUrVafGV00pW7lGvBolWov3vducP3mAw7s2Wuo38i4S5edoJaW0jWRJMkIIkRnYgYXo9TtzKVamAjXrN+fjT2vFq1GitTz18eKfv45wZPcmrl88a61s+EmgoZQy/koKKQQhhAuwAWWjE2tRR8GipahZvwXlqtSOV6NEa3np+5R//zrC0b2buXjmhLWy4ZeBBilNMCY+mJx/S4H2xOIkAvDIW5Ca9VtQsfrn5Ctc3GbpmAF+L7lw9jjHft/K+RMHrZUN90Kpu401PPY+YCpxmIVGo8WY5MiRg4YNG1KnTp14NUq0lsDAQM6cOcPevXv5448/9Dqyx2Q/0MdW6dA2M0re3kBRmZiCTlO+mKRKlYpSpUpRuXJlKlSoQMGCBcmRI0eci+lAqRG5d+8eFy5c4NSpU5w9e5bAQKuj/SHADGBCSpGsS0hMRbVjiCUa9na+gwMFPixBqfJVKV3+U/IULErWnLnilQ4UHBSAz/273LryD5fOneTyuT957fciLpe4AnydkCHHlIIQoiMwB7DaM5CnQBFKV6hCqXKfku/DEmTzyBOvdKCw0BB8vO5y9/pFLp1VFGRiqRWJiRfQVEr5d5xvnsIRQnyFUixtdcVs9lx5KV1eUbcrULQkOXIXsEpuOyZvwsN59OAu925efasMZKHPiBa+KCIFseaIvG8IIcqjRLCtljPLlCX7247fBYqVxiNvwXileUVEvOGJtxf3b13l8vk/uXTuJA89rWuGbCIAJftgTZxvnsKJi5MomnQZPqBU+U8pU6EqhUt8hEe+gri4usf53lFRkTz1eciDuze4fP4vLp09zr3b1+IiIx2GUnM7Lc43T+GYWmmMAPoBVn3p3NzcqFChApUrV6Zs2bLkz58/XjUoUkoePXrE3bt3OXv2LKdPn+by5ctERlrdb8wLGGhrVVKbGyXwNqWrHYrmeuwdsmLg7OxMvnz53n4Y7u7ub9UFHB0dzZQHgoKCuH//Pp6ennqd12MjACXUNkNKaZuGKSkEUxf4qUB3rPyCvUvqNGnIkbsAufIVIl3GTEq3WWdXnF1cSePkTNBr/7eqTcGBATz18cLn/p3/Ik16DSUykmKVtRIKIcQIlBRMyy3BNXB0TE02jzzkyq90c3d1S4eTi/K5Ojm7ERTgT0hwEKEhyuf67PFDfLzu4vvEJ76NNu8D/d+Hwtj/ihCiO/AzsdSHaeHgkIqsOXPhkbcQWXJ44OzihrOLG04urri4uhMcFEBocBAhwYEEBwXg++QRPl53ePbIO76NNp+ibG6Wxufk9wmTcMVMrHT+xTiXzNk9yJWvEFlz5MbZ1e3tc9jVPT2hIcozOFqR6+Xzp/jcv8NTnwfx7YvhD0yWUk6Mz8nvE0KIaij7kXjl32XKnI1c+QuTzSPvW6UtZxc3XNOlJzw05O1zOPC1H69fvcT7/h0eP/TkTXi8GqiGAPOBoe9TDV98EEJkRymC/w4LoiR6ZMyYkYIFC5I3b15cXV3fKtC6ubkRERHxVp02ICDgrXP+/v371kZCYnIHRdVxdUKnamlhF6Pk7c2UTWwrlM1Oabvd2Dp8Ub5QvxjpAXHDFHIeg2L9x901Y1skcAHoanjQ446p0ddPxMHDbkduoai5WJQGMVAjhGiN4lCIuyal7fFG8cilWPlmWyGEqAvMBWyXoxV/fIGxKaUhrT0xpU0vBcpgRbqenXmNkpY0xkiFjhtCiA9Q9k09AOubg9mHSyh1IxuklPHyKsUHuxolZjdWul9+i5I7af+qWYUw4ABKWsMOKWW83AMG/48Q4guUiNgnQGJK+rxEUar5yYh4/XdMaSLDgC+IR1QsAQlGyWkd8j5I/NoaU5rIaJR+RHGOiiUgYcBhYPD7ptBjC0zFtSOAZoBtivmsIxw4hSJOcCwR15EiEEJkQHEStQFsV8wXO5EoadDjpZSbEnEdKQIhRCqgJkpGUVMgsbSfo/dNqxMroyTRjJK3C1CiJ3VRCvZqAUVtfMvnwBEUY2SLlDJeOV4GljF9rr1RDM9i2H4jK1HSPU4A46SUFoXwDeKPqe6kG1CSeISe44EvcBaYaKTe2Q4hREMUr93HQHo73NIP+BeYmVAa9wZqTClAQ4EK2CfiGYhSvL5ASrnaDvd7LxFClAV+BKoCWbF9BCUEuA6sBOYaURHbIITIiOJMqAPUIB6ptnHkOsqeeDdwILFT7xLdKImJECIninFSFSWPsijxD2sFo6R43AROo3jiLv/XjpMGccekxvYDsWixx4PHKA/m34xIl/0RQnig5MWOSOBL+6N8rivfp14USQWTaldn4iBmYSVhwCjg1/ehSWlSQwjhBnQExpHwkbGxwGIppU8CX9cgFkx1u22B8UCOBL78YmC6lDJOKgYG/x2hKDyVQtkTVwY+NP2LbyTlOcp++BqKA/ewlDLWZl/2JMkZJVqYmrwVQZFSWxfL9FnAXhRj5IFhgCQdhBC5gIcJfNl1Uso2CXxNgzgihIgiYT11f0opqyTg9QzigRDCi3gUT1vggZQyVklMA9sihDgJfJqAl5RSSvs2VjBQIYRYC7RO4Mvmfl/7syVFTIZKHhTj5CugfyyntEYRg7mVHOqlLTbVSiqYfpGngFNCiNiMkqNG4auBgYGBgYGBgUFKwuRo9wK8TP2KLBolUsr1dllYAmF4NgwMDAwMDAwMDAwMEhXDKDEwMDAwMDAwMDAwSFQMo8TAwMDAwMDAwMDAIFExjBIDAwMDAwMDAwMDg0TFMEoMDAwMDAwMDAwMDBIVwygxMDAwMDAwMDAwMEhUDKPEwMDAwMDAwMDAwCBRMYwSAwMDAwMDAwMDA4NExTBKDAwMDAwMDAwMDAwSFcMoMTAwMDAwMDAwMDBIVAyjxMDAwMDAwMDAwMAgUTGMEgMDAwMDAwMDAwODRMUwSgwMDAwMDAwMDAwMEhXDKDEwMDAwMDAwMDAwSFQMo8TAwMDAwMDAwMDAIFExjBIDAwMDAwMDAwMDg0TFMEoMDAwMDAwMDAwMDBIVwygxMDAwMDAwMDAwMEhUDKPEwMDAwMDAwMDAwCBRMYwSAwMDAwMDAwMDA4NExTGxF2ANQogsQBEgnxXTPxNChAK3AC8pZZQt12ZgYGBgYGBgYGBga4QQDkBelD3xZ1bMbwt4ATeklL42Xt5/JskZJUKI3EAtoCpQAvgQyBSHS/Qx/QMIE0LcRDFQTgOHgYuGoWJ/hBAlge9tcOmaQoiuwGopZagNrm9gASFEfqAbIBL40qWEEP2BFVJKvwS+tkEsCCGyoXyu2RP40tmFECOAxVLKZwl8bYNYEEJkADoCpRL+0mICsEhK6ZXA1zaIBSGEE9AeqGmDy48WQsyQUl6zwbUNLGAyQMqifK6VUAyRD4G0cbjMmneu9xJlP3wVOA4ckVI+TLAFJwBCSpm4CxAiNfAlUA/FGClk41u+BI4CB4BNUsoXNr7fe4kQwhEYALQBihK3L1F8kMBz4C9gnJTybxvf771FCNEd6IziNHCxwy1fAn8DE6WUR+xwv/cSIUQzoB9QGkhnh1u+Bi4Cs6SUW+1wv/cSIcRnwBCgHJDRDrcMQtn0LJFSLrXD/d5LhBD/A0YCnwCZSXjHUExCgZsom9xZUsoIG9/vvUQIkRloDtQBqhM3p3x8uA0cAXYD+6SUb2x8P4skmlEihCgBfIvitcmaKIuASJQPYzWKgRKSSOtIMQgh6gGDgE9J3Ejca2AnMFBK+TQR15EiEEJUBEahhIvTJOJSgoH9wFAp5a1EXEeKQAhRGPgJ+Br7GCJ6hKFEsodKKS8l4jpSBEKIvMBwoBm239RYIgI4Dww3HAr/HVOk6ycUZ1+2RFxKJHAFxVG0IRHXkSIQQqQF6qLsiRuSeO/YV8AmlMyTk4mxALsaJaaoSBuUTWsJu93YOl4CC1A8AEk+7y4pYYqKjAN6AW6JvJyYSOAS0F1KeSaxF5PcEEIMBIaRuBsbPe4CfaWUexN7IckNIUR7YAKQM7HXosEjYIiUck2sMw3MMDmFfgEKJvZaNHgBjJdSzkzshSQ3hBCVgEUoaXe2jojElUBgDjDCSI2PG6Z66f7AdyS9d+wVYAqwzp5RMbsYJSYrsBMwGOuK1c1wcXGhQIEC5M+fn/Tp0+Pq6kq6dOlwcXHB0dGR169fExwcTHBwMAEBATx48ABPT098feNlWwShfPmnSykfxecC7wtCiDTALJTPNs7pWc5p0lAoZ04K58xB5vTpcHN2Jr2LCy5OaXFKnQb/oCCCQkMJCgvDPygIr2fPufPoEd6+8c64uwn0MDx2ljHlsY5BeVjG2chM4+hIgRzZ+dAjJ1nTZyCdqwvuzs64pE2LS9q0BAQHExQWRlBoKP5BwTz09eXOo0c8ePacqPg9jx4CP0gpN8Xn5PcJIUQflIjXB3E91zFVKvJlzUphj5zkyJSRDG5uuKZNi4uTE25OTgSGhhJs+r76BQby+OUrbvs84v6zZ0RERsZnub7AKCnl/Pic/D4hhGiNsoHIFddzHYQgT9YsFMqZk9yZM5Pe1QVXJydc06bF3cWF4LAwgsPCCAgJ4XVQMM/8/bjp7cO9J08Jj4jXXiUAmA78bGxiLSOEqAPMRakjiDO5Mn9AoZw5yZs1C+ldXXFNmxZXJyfSu7oS+iac4NAw/IODCQwJwdf/NbcfPea2jw+hb+KVwRMKLEV5FofH5wLvC0IID2AgSt1enFOgM2fOTIECBciTJw/u7u64uLjg4uJCunTpiIiIIDg4mNevXxMUFIS/vz/37t3D09OT4ODg+Cz3HjAZpb4zLD4XiAs2NUqEEAJoi/IDWeWRc3R0pGzZslSqVIly5cpRuHBhsmWLX5QyICAAT09PLly4wKlTpzh37hz+/v7Wnh6G4nEaK6UMitcCUjBCiFHAj0Bqa+ancnCgTIH8VC9VkqolilM0d25yZ8mMg4i70ycoNIzbj3z4+/Zdjl+5wrHLV3lu/ecKcAP4Wkp5O843T+GY6kVmYOWDUghB8Ty5qV6yJNVKlaB4njzky5aVVA5xVxsPe/OG2z6PuHjvHkcvX+H45StxNUC9gWZGREyNEKIRsIw41BQUypGD6qVLUrVkCcrkz0f+7NlJnSpVnO8dHhHB/adPueB5jxNXrnL88lXuPH4cl0u8BNpJKffE+eYpHCHEJyjpFlZHvHJnyUy1kiWpUaokZQrkp1DOHKRNbdVj3IyIyEi8nj3nqtcDTly5ytHLV7j+8CFx2FMEoUQ6l8X55ikcIURRYAdxMEayZkhveg6X5H+FClIoZ05cneJeyhklJQ+f+3L94UPl+3rlKhc97xEZZbX9GI5icI6L881TOEIIdxSnUG+sdOSmT5+eChUqUKlSJT766CPy58+Pu7t7vO7/5MkT7ty5w/nz5zl16hQXL14kwnrHgjcwWEq5Ll43txKbGSVCiOLAPKBGbHNdXV35/PPPqV+/PuXLl8fZ2dkma4qMjOT69escOHCA7du34+PjY81pD4H+RiGmgimMvAUrXoJOqVPzVflyNK9aheqlSpDe1dUma5JScv3hQ/ae+5u1R49x09uqz1Wi1BJ1Ngr2QAjxIbALK16CjqlS8VnZMrSqVpWaZUqRJX16m63r7uMn7P/nH9YdPc4/d+5ae9peoLmUMl5uoZSESUVrF1DeirlUKV6MVtWrUefjsnh8EOdgitV4+77gwL//sv7YCf68dt3ajexpoKGh2gVCCDeU53Bda+b/r1AhWteoRt2PP6JgjoQWVPt/nvv7c/jiJdYfO8GhCxet3cheBxpIKa3+gqdUTKnQK1DS3GP12BXNnYs2NarzVbn/UTR3LkQ8nHzW4B8UxNHLV9h04iR7z/1NmHWRFB+gsZTynE0WlcwQQjQHZgIesc3NlSsXjRo1onbt2hQvXhyHeDj5rCEkJISzZ8+ye/du9u/fb20k5TDQS0p5wxZrSnCjxJSqNQZFeUnX/SKEoHLlyjRt2pS6devazBDRIyoqivPnz7N161b27NlDSEisNe77UOoSHthheUkO08NyO4pKmkXKf1iYb2vVpFmVT2xmiFji7zt3WHvkGOuOncA/KNYgVyDwjZRyhx2WliQRQiwDOhDLS7B4njy0+6wmLapVIVuGDHZZ27vceOjNb0eP8dvhozz1i1UlOAzFmbDQDktLkgghxgFDAYvhjfzZsvFNrRq0rlGdvFmz2GVt7+L17Dnrjh5j9eEj3H8aq70RAUyQUo6yw9KSJEKIXijRTIvFsNkzZqRtzeq0rVmDIrli3QclOE/9/Nhw/CSrDh3m+oNYVUejgKVSyu52WFqSRAjRBFgFWHxpZnBzpXX1arSpUZ2PC9m/dMgvMIjNf/7JmsNHOXcr1mQDieIUafq+Ov+EEPlQSgIsOhCcnZ2pX78+TZo0oVy5cjYzMPUICQlh//79bN26lb/++iu26eHANGBMQqfqJahRYlL8WI+ip6yJg4MDNWrUoHfv3pQuXTrB7v1fePXqFatXr2bFihW8fv3a0lR/oIuUcrOdlpYkMIWST6DIDupSuWhRBjRpyFfly9lnYbEQGBrKyoOHmbF1O09evYpt+jYpZRN7rCupIITIAZxCacSkS5kC+RnYtDGNK1ey+4NSi/CICDaf+JNJmzZz9/GT2KYfA2q/Ty9EU8+CI1h4DgMUy5ObAY0a0qJaFRzjkZaV0ERJyfZTpxm/fiM3HnrHNv0iUEVKGWiHpSUJTLVem4HGlublyZKF3l/Xp1Pd2jinSUyhvP/nyMVLjF27gbO3YhXM8wEqJ7XeCbZGCLEIpb5Al8zp0tHty8/p3aBeojj7tPjr+g1mbN3O7+djVeB/BdR435T1hBBfA8uxUMTu6upKs2bN6N69O1mzJpYQrTk3btxg6dKl7Nq1i0jL9YB/Ay0TMsqZYEaJSeN+KaCZyyGEoF69evTp04eCBZOiMAj4+/uzcuVKlixZYilyIlFCcEMTW8/ZHgghvkexiHXjh3U+KsvINi35XyFbt5iJH8FhYSz74yCTN23hZUCApan3UF6IKV5C2FQYuxIL0cyKRT7kpzatqFE6ofusJQxvIiNZf/Q449ZviK32xBeoaqtwc1JCCFEd2IMFb2uxPLn5qXUr6lcsH6+aLlsTJSU7T59h7Nr1saViBgFfJJZ0pT0xpUMfx4JAQZ4sWRjRugUtqlWNV+2PPTh04SJj167n/O07lqaFA23fB+efyTH0FxYEgD5I587QFs3oWCfpGJkxOXfrNmPXrufwRYs2RyQwQEo5207LSjRMIkBTgL7oZCC4uLjQvXt3vv32W9KlS0w1dn1u377NnDlz/o+9qw6LYvvf7yGkFQVFShEFC9RrJ9jdrdfu7m7F7u68ttfurwnqtRsTFDBAEUGkkZjfH7twmTnnLAt3Zwl/7/P4PO6Z2d3DnJ0zn3xfnD+vkuAyHIoyeI20OPxnp0QZvVkBBVMPE8WLF8e8efNQrVq1DH9+QkICPnz4gPfv38Pf3x9BQUEIDw9PZdtKTEyEsbExzMzMYGpqioIFC6YydTk6OmaqIejLly/w8PDApUuXVJ2W6+ubCSHnADTnHbeztMCy/v3QunrVDH92YlISAr59g8/nwFSGnh+RUYhSsvfExf+CiZEhzJVMMIXMzeFkYw1nW1s429qgQCbWNTQiEjP37sNfV6+rqmH/BYWhk2sZutKLylnkNYNHzx7o1aBehjMjyYKAj99C4BsUBJ/AIPh9+YKwqCgFi1pcPKJiY2FmbIy8RkYwMTKEZd68cLKxgZOtDZxtbTJVFhYdF4+Fh49gw5lzSOBHdZIA9MnNNLNKpfR54DwETQwNMK1LZwxv1SJTRuvn76HwDQyEb9AXvAsKQmikYl2j4uIQER2DvCbGMDU0hImhISzMTFHCRrGmJWxsYGeZ8f6UX4mJWHf6LJb8fRTRcVzSFwHAdEEQFmX4C3IIlPTNO8EJDOXR08PI1i0xpXNHGBtkvLE5ODxcsQ8rmZdCIiIQExePiNhYRMbEwNTICCaGCtamAqamcLS2RknluhYpVDDDjm2yIGDXpSuYve8AfkSpTHRtEgRhWIb/oBwCpajleXDK8HQIQZ9GDTCv55/Ib5pxpv2wyEj4BAbBJzAQPoFB+Bb+EzHxcQiPjkF0bBwMDfLAxMAApoaGyG9mCodCheBsZwsnWxs4FCqUqezpidt3MXnnbgSGqgwSnREEoXWGPzyHQNnHdxoA1zBq2rQpZsyYgcKFM97fFRERAX9/f/j7++P9+/cICQlBdHQ0IiMjERMTAz09PZiYmMDIyAjm5uawsbGBo6MjHB0dUbRoUehngtTi9u3bmDNnDvz8/FSdtgKKRvj/xKj3n5wSpTf4F4AurOOGhoYYMWIEBgwYAD099XT0kpKS8OTJE9y9exd3797FkydPEB+fORYyQgicnZ1Ro0YNVK9eHdWrV4dpBm5uT09PzJkzB58/c0sJfAE0EQTBP1MTzKZQ9o88AFCBdVxXRwcjW7fEtC6d1Wb3EAQBT9774caLl/DyfoHbr14jKi4u03N0srGGm6sL3FxcUK+cKyzyqu+k3Hvrg5GbtuDlB257UDKA7rlRFIoQchacviBCCHo1qIf5vXpkyOl79fGjki3rJW6+fInwqMyT1aVlBqpbzhU2FupTt7/++Amjt2zDP69e804RoNg0l2d6gtkUhJCNAIbyjreqVhXLB/TLkHPw/stXeClZ0LxevMC38Awx3IlgZW4ON5eycC+nWNdiGWBU/BgSgvHbduL8g4eqTlsvCMLITE8wm4IQMhnAInAczTply2DNkEEZ6hkJDA2F53NveHq/wM0XL/EpJPOyXPlNTVHHpUzqPlzKXn1G4u8REZi+Zy/2XfNUddopQRDaZnqC2RSEkO5QEK0wHU1XBwesGzoIVZyd1P7M7xERuP7cGzeU6+oblCGGOxFMDQ1Rq2wZuLuUhZurCyo4FlM7QBUVF4cFhxRBIhVEB48AVM1tlNCEEEcoxH2ZZSP29vaYN28e6tSpo/ZnRkZGptrDd+7cga+vb0YY7kQwMDBAxYoVU+3hChUqQFdN5zMhIQHbt2/H+vXrVdnkBwD0/S99Jpl2SgghJlDUtzZlHS9WrBjWrl2L0qVLq/V5b968wfHjx3HmzBmEhIRkak7pwcDAAA0bNkTbtm3h5uam1mJERUVh+vTpOHeOy0b5FUAzQRCeanKuWQVlPfozcFiYCubLh51jR6F+efX6gd5/+YqDnl444OmFD9/kWVd9XV00/KMCutdzR/MqlWGoRiQgPiEBM/bsw8Zz3LSkAGCqIAhLNDnXrIIyo/kPOH0GZsZG2DBsCDrUqqnW5wWGhuKw103s9/RSp/4/U9AhBLVdyuLPuu5oW6MaTNUgwxAEAatOnMKc/Qd88DtpAAAgAElEQVRVPRDXCILAzezmNBBC/oZCuZuCob4+5vXqgeEtuQlPEUIjIvH3rX9w4LoXHr1TWWLzn1DF2Qld3d3QuU4ttR3gA9e9MGrzVsT+4j7vclUElhCyGMBk1jFdHR1M7tQBUzp3VIt+OzImFifv3MX+6564pT7bWYZRpkgR/FnPHV3c6sC6gHrs02fu3ceQ9RtVBTOeAaiYWwxYQsgYKIgKmFZ+t7puWDd0sFqlWnEJCTh77wEOenrhytNnmdUDShfFrKzQra4butV1h2Nh9QIKN1++Qt+Vq/EljNvP6Q/AJbewJBJCykLhkDAjBI0bN8bixYvVKtVKSkqCl5cXTpw4gWvXrmU6MJ8eChUqhNatW6Ndu3YoWbKkWu959eoVRo0ahYCAAN4pV6FgXVNZK89DppwSQkg+AJfBoZls06YNPDw8YGysWuogOTkZly9fxubNm+Ht7Z3hefwXFCxYEH369EGPHj1gokbT2N69e7Fo0SL8Yj8Qw6FwTO5qep7aBCEkL4B3AJgUPA3/qIAdY0bCUo2b6vqz51h27AS8vF9oeJaqYW5qgkFNm2B4qxZqzfPYP7cxfONmRMZwe4jm5XSmH6VD8hocR7OyUwnsGT8WDlbpN9k99H2HZUeP4/yDh5kVOswUjA0M0KtBPYxp2wb2BVXyLQAAvLxfoO/KNapYuvYKgtBLo5PMAhBCbgBght2cbKyxd+I4uDo4pPs5bz59xvLjJ3Ds1u3MCuJlCnn09NChdk1M7NBerWj/Mz9/9Fy+UhXBgacgCPU0OsksACFkHxQaXxSsC+THrrGjUcelbLqf8zEkBKtPnMbea9cRI5Nhw4Kujg5aVK2MiR3aq8UQ5fc1GL2Wr8ST99zykLcAyuR0x0TJiDeddSyvsTE2jRiKtjVU8lMAUFAvrz9zDtsuXlKHYVJjIITA3dUFkzq2h7urS7rnfwv/iX6r1+I6v9fkG4DiOZ2wghBSA4pSPKr+2MDAANOnT0f37t3T/ZyoqCjs27cPe/bskS04z0P58uUxZMgQNGzYMN2sWHR0NKZPn46zZ8/yTrkHRRVRhtPrGXZKlJH0/wFwkx7T0dHBjBkz0KuX6me9IAg4ffo0Nm3ahHdqROMIIbCxsUGxYsVQrFgx5M+fH8bGxqmlWHFxcYiNjUV4eDg+f/4MPz8/BAQEIEENLm1zc3P06tUL/fr1S7e06/nz5xg4cCBC2fWSoQDcBEF4le6XZkMoS7b8wVEEHt++Leb06J5u/fDFR4+x6PDf6TUypsLGooCip8DGBgXz5U1VmwUU2YyY+HiERUbiU8h3+AYFwTcwSFWkNBUmhgbo17gRxrdvm66OxrsvX9B27gL4B3P720cIgrBBrT8oG4IQ8ghARdaxHvXrYt3QwciTTnnl7ddvsPDw36oeLiJY5s2Lksr6ZCtzc5gq15UQgoSkRETHxiE8Olqp5v4FPoFBiEqflht59PTQra4bJnfqmC59bXB4ODrMX6TK0FkhCMIEtf6gbAhCyEkAbVjHGlf8A3snjE03u/Qi4AMWHv4bZ+7dV8vJNDc1gbONLZztbGBdoADyGhnBzNgYujo6SEpORmRMDCJiYxEUGgafwED4BgWpVc6nQwja1KiGaV06oUyRIirPjYyJxZ/LVuDq02e8U3I0kx4hZDWA0axjlUqUwLEZU9Ld0/yDg7H4yFEc9rqpqs8qFWbGRnCysUEJG2vYW1rC3MQEJkaG0NfVgyAI+Bkdjai4OASHh8M3MAhvPwfiu2qmylQ0/KMCpnXphGolVUsgxSckYNiGzTjkdYN3ykNBENLV28muIISMgkKQmUJx68I4OWtGulmI4PBwrDh2ArsuX1XLyTQ2MEAJG2s42djAvqAlCpiZwdjAIFUs82d0NKLj4hDyMwI+QUHwDQxUldkQoVpJZ0zt0gmN/mBWeaciWRAw8699WH3yNO+Uj1A4JjmSIVGZIbkBBsOWpaUltm/fDhcX1Q5cZGQkduzYgb/++is9BlgAQJ48eVC0aFE4OjrCzs4O5ubmMDIygqGhIQCFcxMTE4OwsDAEBASk9mOrY+87Oztj+PDhaN68ebrOya5du7Bo0SIks6sSPKEI1meoTj9DTgkhRBfAYQAdpMf09fWxbNkytGzZUuVnvHnzBrNmzcLjx49VfQ9cXFxSe0EqV66cbtZFiqSkJLx69Sq1Fu/evXuIU9HDUKhQIUyfPh0tWqiW4fj06RP69OmDDx8+sA4HAqglCALzYHYGIeQpgPKMcSzo1QOj26quiggI/obx23bg4iP+ugIK5p96rq5wL+eC2mXKwNw0Y9SGKUKJKT0Mnt7eqrIcMDc1wZw/u6N/k0YqHapv4T/R1mMBnvkx24MEAN1yYo8JIeR/4PCjD2vRHEv690n3ukzb8xcOed1UuaE5FrZCvfLl4ObiAjeXsihknnFBRd+gL0rF7xe49vw5QiP42V9jAwNM7NgeY9q2VulQRcXF4c+lK3DlCbe6clpObJImhKwHMJx1rLNbbWwdNUJlM3tkTCw8Dh7Clgv/U1nyYWNRAPXKlUNdV4VSdGYa1j+FfMeNFy/g5f0S1549U2n06OnqYliLZpjetbNKh+pXYiIGr92AIze5xFvbBUEYmOHJZjEIIeOhYDuk4O7qgsNTJsHMmH9d4hISsOrEKSw/ehxxKoJyFnnNUL9cOUVfnmtZlLC2zvBcv4X/hNcLRc/R9WfeqoI6IITgz3ruWNC7p8oMtiAImKHagD0nCIJqIyMbQqlBchSMkq2yRYvg1KwZKsvdkpKTse3iJczdfxARKgTuzIyNUNfVFW6uZVHX1QWl7e0zTFYSHhWNmy9f4ob3S1x7/jzd8twWVStjWf9+6QaJNp47j8k7dvOCHy8FQUg/9ZLNQAixg6Ismoqk2NnZYffu3XBIJ1N96tQpLF68WGVmxNDQENWqVUvtBSlTpozavSApiImJwYMHD1J7U16+fKnymV6lShXMnTsXzs6qgwmnT5/GpEmTeMrwp5FBjRq1nRKi+GVvA9BfeszY2BgbN25E7dq1ue+Pj4/HihUrsGfPHi7vsb29Pdq1a4e2bduiSDrRsowiMjISFy9exPHjx/Hw4UPuYtSuXRvz58+HnR2/Ye/bt2/o168f3rxhMoy+goJ+NEwjE9cCCCHXAdSVjuvr6mLLqOHo4sZvykpKTsaqE6ew+MhRbgajcP786OJeB3/WdUfZoppd19hfv3Dm3n0c9LyhUkG4Yoni2DR8KFwc+JIcETEx6LxoKW6+eMk6nAQFz3qOoR9ViiL2ZYxjfq8eGJOOo7nz0hXM+Gsftzwgv6kpOtWphW513VA1nY0ro0hISsKlR09wwNMLFx7yFYSdbG2wYdgQ1CrD712LT0jAwDXrcewfpiCUAIV45gGNTFwLIITMhIJli8KIVi2wuG9vlYbIqbv3MH7bDq5zYGpoiNY1quHPuu5wc3XRKG1wsiDghvcL7Pf0wuk797hkFzYWBbBq0AC0rMoPjCcLAibv2K2qLyxHOZyEkJ5Q0HRTF7xj7ZrYNnqkSgf85ouXGLFxC959YTc4G+jro3mVSuhe1x2NKv6hcdrge299cNDTC0dv3eayauU3NcWC3j3Ru2F9lZ+18vhJzNp3gPeczlEOp5Km+xoYTe1uri44ko6j+dw/AEPXb8JTDvORro4OGlQoj2513dCqWlWN0wa//PAR+6574siNW1y9L2MDA0zt3BFj2rVRuV8c9LyBoes38rJ3VwRBaKSZWcsPQoglFPptpaTHSpUqhZ07d6rUHfn06ROmTp2Ku3fZVf+EEFSuXBnt27dHs2bNMkTSpA4+fPiAkydP4sSJE1wyJz09PfTt2xdjx45FHhW/q5s3b2LYsGE8KY0tgiAMUXdeGXFKmKlHAwMD7N69G1Wq8B8eAQEBGDlyJF6/ZrPilC5dGv369UPr1q0z7P1lBj4+Pti6dStXGMbU1BSLFi1Cs2bNuJ8RHh6Orl278srPLgJokRPqX3nNlDqEYM+EsWhfswb3vSE/f6L/6nXcMopiVlYY2rI5BjRplJoulhMfvoVg/emz2HnpMjNKqE7Tb+yvX2gzdz6PwSkWgI0gCOnKiWc1CCEDoAgiUFjctzdGtuYHG6NiYzFi4xb8fesf5nErc3OMaNUCQ1o0yxQFaUbxPSICW85fxPoz55hRwpSm36ldOnEfiEnJyeizYjWO377DPAygtCAI6coTZzWUNKKXwTBcR7ZuicV9e3Pfmx65g0VeMwxu1hTDW7bIcAYzM4iKjcWeq9ex4tgJbu9Pv8YNsXxAP5X7x6Qdu7DhLPNvEgDUEwTBSyMTlhFKgdoXAKgHYMfaNbFr3Bjubzs9cgdTQ0P0alAf49q3Vbv5/L8gPiEB+697YfGRo1xq2DbVq2HTiKEqRQDXnjqDqbv/4h3uIwjCnv8+W3lBCCkARQWFofRYnbJlcHL2DJXELAeue2H0lm3MUq2UfqwpnTtmKtOVUSQkJeHvG7ew7NgJ+ASy9YPcXF2wa+woFM7P/50dvXUbfVeu5mVMFgiCMEMzM5YPyj7NiwAoJ8rJyQkHDx6EuQp6+ytXrmDy5Mn4+ZNuuUgRGB89ejTKlk2/b+y/QhAEXL9+HevXr8fz5+zy7LJly2Lt2rUoWpQf1L137x769evHa8ofLgjCRnXmo5ZTQgipBEWKSmSB6OrqYs2aNWjalEnABQA4f/48pk6dimhGtLV48eKYNm0a3N3d1ZmrxuHv748lS5bgypUr1DFCCPr06YMpU6ZwHaXg4GB07twZgewbdEp2Z24ihFSHQriJetotG9AXw1rwjXcv7xfos3I1kybU1sIC83v3QMfatbJEnC0wNBQeBw9j3zVPZqSts1ttrB86hEtnHBkTi8YzZuG5fwDr8AtBELKnmqAShJCiUBAWUGHVCR3aYW4PfsPdMz9/9Fi2An5f6VKM/KammP1nN/RuWD/dHhQ5EBYZiWXHTmDT2fPMSFuDCuWxa+xoLj30r8REdFywmOdEhwAonJ0DCUoiii8AqFrWzm61sWPMKO795h8cjB5LVzKjrSaGBpjUsQOGtmiuNsW3JhEVF4eNZ89j2dHjTOOrYoni2DdxPLc8RBAEDF63Efuve7IOR0Oxrtm2kVZp4AQCoEQL3F1dcGLmNK5TFvLzJ/qsXAPP5zRRjL6uLoa3aoEJHdplSufivyI+IQG7Ll+Fx8FDzL6iEtbW2D9pvMrs9fQ9e3mlXIkASmlSSVoOEEJegxFJL1u0CC7Nn8d1/qPi4jB8wyYcvUVnd1Oo22d07ZIhynRNISk5GUdv/YMZf+1DUChdEFI4f37sHj8GdcqW4X7GtouXMGYLM2YmQNGbm60rEpSaUB7S8cKFC+PIkSOwsbFhvi8xMRELFizA3r17mcebNGmCiRMnplvyJQdSnJNFixbB358uYzczM8PixYvRpEkT7mdcvXoVw4YNYwX74wHUFARBdX0/1HBKCCFmAB5CwtxDCMGCBQvQuXNn7nt3796NhQsXUk0whoaGGDRoEIYMGaIyJaQtXLt2DfPmzWOmsOrXr481a9bAiFPfHBAQgC5durCa3xOhiNJly5uLEGIMBZ0xZcFN79oZ07p04r73yI1bGLR2PWUY6unqYlDTJpj9Z1e16FvlxuN37zF6yzY8fkc/tyqVKIHjM6dy65u/hP1Aw2kzEBDM1MbcIAjCCM3OVjNQGjifAFC7Yre6btg2agS3tOeG9wt0XryU6tEhhKCrex0s6tMr3QZbbcA3MAhjt+1gNt07FrbCqdkzuQ2jUbGxaDpzDq/5PVtTyhJCngOgHOJ65cvh+IypXEfx1cePaD13PrNcq1nlSlgxsH+69eDaQFBoGGbt24+DnnSjs5W5OU7MnIbyjsWY701ISkLnhUtw6fET1uEngiAwiR6yAwgh5wFQafmKJYrjwrzZ3L30w7cQtJnrwdSjqFWmNFYPHpAuaYA28CMqCgsP/Y3N5y9Q0XFTQ0McmDwBDSpQ7YwAFIbSsA2b8dfVa6zDwVBkrrNlIIEQsgoMUeliVla4ssiDm034ERWFDvMX4d5bH+qYq4MDVg8egOql1KNvlRPRcfFYffIUlh87QTH25dHTw9bRI9Cpdi3u++cdOIQlfx9jfjSycSCBEOIGBe2taMM1NzfH4cOHUbw4m20uNjYWI0eOhKenJ3XM3t4es2fPRt26dTU/4QwiMTER+/btw8qVKxEjqUwghGDSpEkYOJBfPXno0CHMmMFMdr0DUEkQBJWd/Oo4JYfAEEccOHAgJk9mUqhDEAQsXboU27bRnnDp0qWxbt26LPEEVSE2NhazZ8/G8ePHqWMVK1bE1q1buem4O3fuoE+fPizv8BOA8oIgqEdnoUUQQu6DQencqXYt7B7Pl3DYcPY8puykm9WKWVlhz4QxqFSCqRmUZUhISsKcfQew5tQZKmvibGuL07NncClmX3/8BLdJU1nRWwGK/hIuTUxWgadZUbtsGZybO4ur0nv01m0MXLOOergUzJcPO8aM5BoNWQVBELDu9FnM2rufco6tC+THqVkzuP1LX8J+oMa4iQhhpM6RTctCeGWWJe1scWPZYpgaUtUhAPiOpqmREdYNGYTObvw+wKzCQc8bGLNlG9VvktfYGEemTuJS4UbFxqL2hMk80bhsWRbCK7O0MjfHnVXLYMV55ngHBKDtvIVUjX8ePT14KEtUM9rgLDf+9+gxBq5dTxFYGOjrY8eYUWhXk02Fm5CUhGYz5uAOu4fzsCAIXTU/2/8GQkg9KAxX0SKYGBrg5rIlXPrrjyEhaD13PnwDg0TjOoRgXPu2mNmtS6aU1uXEAx9f9Fq+Ch8ljdo6hGBp/74Y2oJdBi8IAnotX8Urqb0rCAK/djyLQAixgEI3R7SAurq62Lt3L6pWZYu4h4eHY8CAAXj6lCZc6dSpE2bPnp3KnJVd8P79e4waNQpv376ljg0ZMgTjx4/n7jELFizArl27WIcOCILApDpPgUqnhBDSFMAF6Xj58uVx6NAhrlz93LlzmempP//8E9OmTYOBFurQM4vjx49j9uzZVMNO6dKlsX//fq7wzdq1a7F27VrWoU2CIAzT/EwzD0JIRwB/S8eLWxfGP8uXcpvuVp88jel76HVVpz44q8F7INoXtMTVRfNha8FmFfrr6jUMXb+Jdei7IAhZH15OA0JIFSj4wUU7hWXevLizchk31X/kxi30X72WcjTruJTFrrGjtVKHnlnc9/FB7+WrqQeiuakJLs2fx3VMbni/QMs5Hqwa/DgA+TNKYygnCCHWUAQ4RNaIob4+PJcu5OqQeHm/QHuPhVR/lauDA/ZOGAsnW3aJQXaAT2AgeixbiZcfPorGDfX1cWLmNLhxNBJefvgI90lTWaQbSQBsBUHgU0RpGUp6/TAAog1XhxCcmj2DK1D7IuADmsycTZVEOVgVwp7xY1HZKXsFhtIiMDQUfVeuoXr2dAjBjrGj0LkO20kODA1FjXETWYx8AoAqgiA8kmXCmQQh5BsYel/bRo1A93rscvXP30PRYOp0fP4urrqwzJsX28eMTJd6NysRHhWNIes34sy9+9Sxhb17ctk70wkkdM1ujJeEkK0AqDTBuHHjMGwY28yLiIhA9+7dKWIkY2NjeHh4oE0bJqt7tkBcXBw8PDxw+DC9DL1798bMmTOZ70tMTES3bt3w5Akzc91SEASuGjlXCpYQYgSA0mbIly8f1qxZw3VI1q1bRzkkhBBMmzYNc+fOzdYOCQC0b98eBw4cgIXESH39+jX69+/PYxfAiBEjeOxjgwkh1TQ/08xBqUeyUzpuoK+PvyaM5Tokh7xuYMZf+6jxYS2aY/+k8dnaIQGAJpUq4sbSxVRD4KeQ72g9dz6XLaZXg/q8h4glISS7MfucgMQhIYRg04ihXIfE87k3hqzfSDkkXd3dcGbOzGztkABAVWdneC1dhAqOjqLx8KhotJk3Hx++sWkW3VxdML59W9YhQwD7NT7R/4ZzYDRArxw0gOuQvAj4gG5LllMOSd1yrriycF62dkgARRbz+uKFlCEWl5CAzouXcpmIyhYtgsX9mM3+ugDOaHyi/w2HIXFIAGBK545ch+Tz91B0WLCIckj+KO4IzyULs7VDAij6Dc/Pm41eDcTsW8mCgEFr1uMyh7rb1sKCV3pKANDlDVkIQshyMBySng3qcR2SsMhItJ7rQTkkDlaFcHXx/GztkACKINDByROYZd/T/9qHvVevM99namSEvRPH8Zr9tynLkbMFlEE/in22evXqGDx4MPM9cXFxGDx4MOWQWFpa4uDBg9naIQEUrRYLFizArFmzoKMjXoo9e/Zg0yZmwBZ6enpYs2YNr7pojTIgw4SqBZ8KwFE6uHDhQi5d7uHDh7FmjZigS19fH6tWrUK/fv1UfFX2gqurKw4dOkT9nU+ePMH48eOZQjE6OjpYtmwZaxF0AKxXarxkB+wEo4/Eo1cPyrBLwcVHjzF43UZR+RMhBIv79sayAX2zXZkADw5WhXBp4TyUK+YgGn/z6TM6LVjCpTReNWgAr0dhAiEkfRl0LYAQMg2SlDIAjGzVAs2rVGa+56HvO3RetISi2x3VphW2j1atc5GdUMg8Hy56zKEUhr+E/UCbefO5eifTu3bmCbq1I4RkCytAmdX8QzrevmYNLq2q39dgtJrrQVE5d3arjRMzp2WLfi91YGJogCPTJlN16ZExsWjvsYjX74UBTRqjTXVmHKgKIYTpiWobSvKYVtLxGqVKYUpnqvoSgIKFrsWsuZThWq98OVz0mJMt+r3UgZ6uLjYOH0IxACYkJaHH0hXMHkBAEVgaxi4FKkIImaT5mWYchBArMPpISlhbY+VAyp4FAMTEx6PD/MV4+1lMmFPesRiuL16oFWYtTYAQguldO2NRn14im0AQBIzctIXX7wVXBwfMZpOvmAHYLstkMwil/bYFEpvZ3Nwcq1evZpIhJSUlYfTo0Xjw4IFo3M7ODocOHdIKs5am0KtXLyxfvhx6kr7FlStX4ujRo8z32NjYwMOD4gIAgOJglCKngOmUEEKKA6Bu8vr163M7758+fYrZs2eLxnR1dbF27dp0BRWzI4oVK4aDBw+icGExIcqlS5ewYQNb3LtgwYIYN24c61BlAAM0PskMQrmuPaTjFRwdMaQ5m0HN72sw+q5cQwmsrRjYTyWtbHaFlbk5LnrMocp67rx5g4nbmTWQMDU0xPIBTKdaD4rsRJZCSVowRzpuZ2mB6d2odjAAQGhEJLovWY7oOHG/zLj2bamHSk6AmbERs6zHNzCIWZoGKIyjNUMGsmq0s1P0dYd0wMzYCEv7U/IzABSZhO5LllOseF3c6mDHmFFZwpr2X5BHTw87x42mel+Cw8Px59IVXP2aZQP68pwv9k2ufRyDJKuZ8nvU1aEfy8mCgL4r11AaJHXLueLY9Ck5xtFMQUpQS6qVFBUXh+5Ll3Mz17O6d+VlfT1URV+1iJNgZjX7c+nTx23bgfs+4qZ2F4eiuDBvdqZEaLMao9q0op6XCUlJ6LNyDTeQMKxFM17Wt7eSTTKrMRiM4NCkSZNgacnuSV2/fj2uXr0qGrOxscGhQ4eyXU+1OmjdujXWrFkjcsAEQcCsWbPg7U2z/wFAs2bNeOy6UwghTNYSXqZkGiT0v4aGhtz6sYiICIwZM0ak6EgIgYeHBxo1yjFaOBSsra2xe/duKvuxbt063L7NFGJD165dUb48syl4BiEkq6nGdkDyINQhBKsG92c+COMTEtBr+UpKG2Jal04Y3IxPA53dkc/EBKdmzaAYh3ZdvoJDXuze9SaVKqJVNWYTW01CiGaVAzOO9QCo/PfS/n2ZDdCCIGDoho2UhkC3um6Yp4IuOLvDQF8ff0+dRGX8Lj95itUnTjHf4+rggEFNmYGWYsqeuiwDIWQyAKqJbWa3rtyyuonbd8I7IEA0Vq98OWweOSxL6Lk1AR1CsHXUCKqE5amfH6buYutY2FpYYBo742BOCBmr+VmqD0JICwCUoTWsZXNuD9Syo8dxTcI2V7FEcRyeMlErGlByYX6vHlQp16eQ7xiweh2Tzt3UyAiL+jDL8/KAoaOmTRBCnABQKbr2NWtwiUL+vvUPVdrkYFUIp2ZNz/Yl0aowpHlTTO7UQTT2MzoavZavoshUAIVDvn7YYNYepQNGYEabIIQYQGETi1CuXDl07MjOat67dw8bN4plOczNzbFr1y4q0J2T0KRJE8ydO1c09uvXL4wYMQLhHK2p2bNns9o2DAFMYZ1PWaKEEHswoulDhw6Fvb0980snT55M0emOHDlSJV1wTkGJEiWwZcsWUdoqOTkZEyZMwA+GuqmOjg7mzp3LSufZAegp62RVQFlmREmz923ckKvGPWPPPoo6tVeD+pjeNeevawpDU15jseTD6C3b8f7LV+Z7lg/ox2M5YhKuawNKR5dis2hQoTyvhAVrT53BufsPRWON/qiAzSOG5bgMiRSmRkY4PnMq7CzFPWFzDxxiUmwCiugrx8hfp/kZZgjUpl22aBEMasbOVh/75zZ2XhJrLpV3LIbDUybluAyJFPq6utg3aTwVTd1y4SJO3b3HfM/wVi140desZuGifleF8+fHVE7Z1j+vXmPBoSOisSIFC+L4jKk5LkMiBSEEa4cOQj1JD83FR495gpjoWLsmGlekgtYA0EfZM5lV2A1J0M/UyIjX4wTfwCAM3yCuyc9nYoJTs2eoFB/MKZjZrQvVQ/Po3TvM3stu2avsVAI96tdjHaqvLIvLKvQBg21r/vz5VJ8FAISGhmLMmDEiNtY8efJg+/btXLrgnISuXbti6NChorHAwEBu0qJIkSK8npu+hBAqCsPKlEyCIuqQCktLS/Tvz66HvHjxIi5fviwaq169OoYPH848PyeiUqVKmDhxomjs27dvWLp0KfN8FxcXNG/OFB6cmoWb5i5I1ttQX5+rR/L43XtsPi8mXitTpAhWDHVXg4oAACAASURBVMw5vUHpwcnWBhuHi2+uqNhYjGaLOsHO0gKD2GVudZTOfFZgOST3KyEEi/r0Yp78KeQ7FhwWGzi2FhbYMWZUtqOazCyszM2xd+I4UU9MYlIShm/czBRdNDM2wqSOHahxACUIIVnCmaukiqUa1Bb07sns9YmMicWkHbtFY6aGhtgzbkyWCCLKAVNDQ+yfNJ4i4xizZRvVPwMooq+zujPLFwsQQtidqTKDEOIOgCpbmNGtMxUgARSCnyM3bRGxxOnp6mLXuNE5pockPejr6mLX2FFUYGDu/oNcoop5PbuzAih5ACyWZZLpgBBiC4CisB3esjmX2XH0lm1U+eymEUNzTA9JeiCEYN3QwVRgYP2Zc3jo+475njk9usGI1q4jALbKMcf0oOwlmSAdb926NcqUYYtDLlq0CCESNsgpU6agQoVs0aaoEYwdOxa1aol7/S5cuIBr15h6Qhg4cCBFHgVFdQeVtRYZqUpvlPI++vXrx+RQjo2NxeLF4j3A0tISK1eu5Kqg51T069ePKkU7evQo7t+nKfAARWaJsWkWB6D1NAMhxBwAZU33adSAGZFJFgSM3bpdVIdvYmiAfRPHceticyra1axORZ6vP3uOY/+wy/NGtmrJ2zS1ni1RMpNQ9ITNq1TiloGM27ZD9CBMMXB4Kug5FVWdnTGzu1i+4PXHT9h4hs1E2KthfV50crPmZ6cWFkoHKjg6oiGnDGTWvv2UZsXaoYOyPctWRlHcujDWDx0iGvsW/pPKJKSgWeVKvGzJXNagFrBROmBjUQDd67JZmdaeOkM1QHv0/DNbiOdpEgXz5cOucWNEZcQx8fGYsms383xXBwc0YWdLsop+fxcYmiTDW7Zgnnz4xk14eb8QjQ1v2Zyb3c6pMNTXx96J40QZvRT7gkHHDitzc/xZry7ro1oSQth6DPKiGwARpZ2Ojg6GDBnCPPnhw4c4dUpcKly/fn307JllRTKyQEdHBytWrEChQmKenzlz5jAZao2MjNCnTx/WRw0ihIjq6KWZkt6QUBSamZmhW7duzImtW7eOKtuaP38+NdHcAEII5s+fj3xpolOCIMDDw4MlmghnZ2c0aNCA9VFZEaHzgGSt9XV1udzh2y7+j4pkzO3xJ1fwKadjYZ9ecLAS/2an7NpDibcBCqanPo2Y69ogC+gLB0FRmynCuHZsgqFz9x/i/ANx2daIVi1Qq0xpWSaX1Rjbrg1Vmrjw8N8ICg2jzjXU18coNnFDWW2XDhBCaoJBKTqxYztmed2T937Y8T9xtrpj7Zro4kZVa+YKdKxdE21riIX2Np+/SPXSAIp9e0KHdqyPsdI2VbuyhJa62Ua3ac3sC/kU8h1Lj4oVr2uUKpUjCUbUQZ2yZTCspbjC4PTd+/jfo8fM8yd3ZmY3jZRZRq1Bue9TdUf9GjdiBnsiY2IxbbdYNqG4dWHM60VVzecKONlYY4ak5Pvxu/fYffkq8/wJHdqxssE6yJpAAuV9NG7cmFmGlZSUhFmzZol6oczNzbFkyZIcXxbNgqWlJWbNmiUaCwoK4tIE9+zZk6XzZwxAVNYhNaKou6J3794wM6NvrO/fv+Ovv8RNhnXq1EHDhg3Zf0EugIWFBcWu9fr1a5w/z6595Yjp1OGxDsgIqoahi3sdFClIa//FJSRg2VEx8VDZokUwsGlj+WaXxTDKkwerB4sTDkGhYdh24X/M88e0bcPaNPUAaLtmcaR0oG45V2YUVRAEzDt4SDRma2GBqZzyvdwAFolDVFwcVhxnE6b1b9oY+U1NWYfmyDJBPqiHr7OtLVpzoqgeBw+Loo4qmoFzDZb06yPq70pKTsb8g+xsSbua1eFkwyyJmSfP7LjwgCSabpHXDH0bsZ+Zy44dF2U1dXV0sHJQ/1xp4KRgRtfOFLvWnP0HmU3vVZ2dUceFSatKUfLKjFFQ7P+pyKOnh1GtKcZnAMDm8xeorObS/n15Wh25AkMZ7FoLD/9N6SgBCkHjTm7Mqll2dFwmKNlKa0rHeVmSM2fOwEfCojZx4kTkzwX9QTw0bdqUYtfatWsXwsLowJ+pqSl69GA63qI0UurTmhBSEYCr6KCODrp0YVOK7tq1C3FpIskGBgaYN0/be7z20a1bN7i4iGlHN23axNw0y5Urx6o7JGA4f3KBEOICRtS1fxM2K9qeK1fxJezfDTOlLjS39Bvw0OiPCpSex9rTZ5jaJXaWFmhSqSLrY7RWOkAIMQUj6tqvMdvAOf/gEV4EfBCNLe7Xm9e4n2tQwdERA5qIHerdl68imMEUYmpoiK7uzOwCuwNZPrhJB/o2asBkz3ruH0Dx/0/v0okrlplbYGdpQbH7nHvwkPqNAwpjvndDZnaTXTMlH6jfUTd3N2bPz5ewH9h3zVM0NqR5U0pjKbfB1MgIC3qLS12e+wfgfxyNC85+V0bLpT7Uvt+sciXmPRgTH4/1khLS1tWroin7eZJroKeri5WDxJ0BX3/8wH7JbzwFnHW1Utoz2kJPSIIIrq6ulP0HKMiPNm8WV/qWL18enTrl3qBfCmbOnCkSU4+NjcXu3buZ53bp0oVFDlCeEJLKdJH2KFX0Vr16dVgzmq7Cw8Oxb59Y3btjx45cdq7cBB0dHYwePVo05uPjgytXrjDPb9eOWTrQi2gv3EXVppewtkYVJyfqxISkJKw5eVo01rRSRZ7AXK7DrO5dRFHIb+E/uSnmbnUpuxEAShJCtGUNzoNkw8xrbMwVSlx54qTotauDA9pJSmByK6Z07ijqA4pLSMDaU2xxb866WirVfGWHsvRE1LSkq6ND6XSkYOnRY6KAiJW5OQZy2LlyG4a1aiHqAxIEAcuPsbNgXd3dWLTnBoQQrRR7K8USqb2B83vDmlOnRRoshvr6GM8uQ8t16FS7FtUTt+TIMea5ratXYxEEEDAoXOWAcr8vIR3nrevOS1fwPSIi7fsxk6MlpU38Skykmu41jZqlS1G03suOHWeSj9QoVSpLs5tK+4wKHrdtyy6NvnTpEt69E5e8jx07lsnOldvg4OCA9u3bi8b++usvRKT5nafA1tYWlSszbZTUfTjtFaNcOt4CnDhxAtFp2E709PQwcCDVb5trUbduXSoDIi1lS0GrVq1YTf8lwBDikQlUrWv3eu7MEoBz9x9QbCcTO7anzpMLrz5+xNrTZzFh+070W7UW0/fsxeUnTynhRrng6uCA5lUqicY2n7vAPLdZ5UowN6V45AkYTB0ygbpfO9SqyWrCx0Pfd7j75q1ojNefIDc+fAvBoLUbRA9muVHIPB+lfr7z0hVm6UClEiXgbMvsndKWYjRVG1C/fDlmE35QaBhO3xUTbYxu04r5G9A0kpKT4eX9AnP3H8SgtRsweN0GzNy7Hyfv3OUK32kahvr6GC7pQTh++w5VGgMoKMDdXZlB1hHyzI4CRUNcuog9pakDKKLpu6+IgyH9GjeClTlFxiYLHr97j9UnT2Pkpi3otXwVRm3eivVnzjF7duQAqw/ovo8PU+ndUF+f6i9SQlulPlMgCQ4VMDNjZtIFQcAWCaNly6pVUKYIm5REW0hMSkKT6bMxaO162b9rkiS7+SnkOy48eMQ8tzO7J05b/QGVoCAmSoWenh5atWKX5EntP1dXV9SunSXEjVmCwYMHi+zcqKgonDjBDhBxAvWpnrkOABBCSkHCw2xkZMRVbz9+XNxz0LJlS9jZ2ak1+dwAQgjF03zv3j18kajtAopmIM6Psz5rUJNQ0tSaSsbQ1Z0dxTng6SV6XcelrFayJJ+/h6LjgsWoOW4SXn/8hKolndGxdk3kNzXF2C3b4TRgMFXKIBekD8N3X75QaruAQqivQy2q3BQAmFzQmoSSVpqiVeJF5w5cF69rCWtr3oNcNiQLAo7cuAW3iVOw/7onPnKoPuXCmLZtRCWIETExOHf/AfPc7uzrqK0nDFXvyWNmOnzjpqiXxNzUBP210Pv1v0ePUXHEGHRbshx33/ogWUhGYGgYNpw5hz+XroBT/8EYu3U7QiMiZZ/LoGZNRCJzScnJOHLjFvPcbux9T1vlIBRdbHfOPnz2/gNExvzLYKOKlESTuPPmDWqNn4zuS5fj/ZcvKFOkCNxdXWBsYIBlR4+j+tiJqDNxCm6+eCn7XDrUqoni1mKRuYOebGHbbuySSzstEY80kw50rF2TqQt09+1b+H0NFo1xSBi0itUnT+O+jw8iGaxJmkbN0qVQu6x4izvo5cU8l2OnmBFCtMGZTNV7urm5oUABuhDi8+fPePBA/Czh6HLkWhQpUgQtW4oJOE6ePMk8t1mzZiwxRXul+GhqpoQykCtXrgwThqKor68vXr9+LRrj9Z3kZjRq1EjUwJScnExRwaXAzY15czFVgjSMQdKBkna2lJI5AIRFRuLy46eisb5slimN4tXHj6g9YTJuvXqFi/PnYtOIoehcpzaaV6mMCR3a4eG6VahVpjQGr9uASTt2yT6fqs7OVOkA72EoTUUroQ2uznaQkFTkNTZmNrj/SkzE0X/+EY31alifVcqiMSQLAsKjouEfHIzLT55i/sHDqDhiNPquWpOaIRFA92DJCfuClqgvEWjjrmtF5rpaKYUqZYNyUxaxH+oQwlWDPuglnn/nOrVl7xFae/osui1Zjm513eCzfTMuzJuN7aNH4uycmXi/cyt6NqiH2F+/sPXC/1B93AQ8esfWI9AUTI2M0KGW2N4/oGJdGdlB45SHoVxQ/m4oSkqOACAVRGhU8Q9KDFTTOOh5A90WL8egZk3wcvMGrBs6GENbNEP/Jo2wuG9vPFy7EqXs7fD43Xs0mzWXW/6oKejq6FBCekdu3mKW+tQsU5rSroFif5TfkwOoqJ2661qmSBFUdqIqv7QK38AgLDr8t1a/s3cDsbl58eFjhEXSAQzHwla8Ei7KrpEBlE0sbehOwcmTJ0UltBYWFrma8IkHaf+Mt7c3fH19qfNMTU1RqVIlahzKa55imVAGcvXq7Eiq1PC2t7fn1Yjlaujp6VGe4Zkz7I26Rg0qSAYAboQQuek2qKh9XXYJA479cwe/EhNTX5saGaFVtaryzQyKaHXnhUsR8vMnVgzoxzSqDfX1sX3MKJS0s8WGs+exiVNOpUlII6pHb91mcqq7uZRlGfeGaZu2ZAKl4F7HpQzT0bj69JkoYq1DCK+ZW2O4/PgJbHv2gcuQEegwfxHOPXiIfo0b8VTTtQapuvCVJ0+ZpUblihVjUXkSMFjsNAwqvOZazIFJK/oi4ANefvgoGuNlyjSF03fvY/be/dgzfgymdO5IOUD5TU2xecSwVBKNoNAwtJ23EO8YGWRNQrqu3gEBePPpM3VewXz5UKYIs++RrQysOfQAo8SnDENL6HtEBK49ey4ak3tdX338iLHbtuPMnBnozQlYFMyXD2uUDIWCIGDanr248JBddqMpdHWvIyJ3+B4RAc/n3tR5erq6qFmaSWsua78QIaQCJP1ferq6qM0Q1UtMSsLx23fEk6tfV8bZpY9kQcCwDZuYZaxyonWNaiJyh1+JiTh19x7zXHdXV9YwW/xFQ1AGEWpJx3k2sdTua9WqFfQYmbLcjqpVq8LGRlzAce4cWxeMcy3rAYCOsqGnrppvwq1b4tR4mzZtcjVFoSpIe258fHwoJU8AcHJygqWlpXTYFIDczbPUTs2hUMS1Z89Er9tUrya7UOLSo8fhHxyMYlZW3JIyQOGYTFL2tszZd0DEDiYHurjVEf2mwyIj8czPnzovn4kJyjsy2Z3l5smnbs46ZTnr+lRs4NRxKctVGNYUKjs54dKCebi3ajmC9u/BnZXLMKpNKxjqy9/roAotq1YRiXglJCXhBqMURYcQpmEBoCtrUIOg6mXduPereF1LWFtTmiyaRFxCAsZv34HRbVunG6xY1Kd3ag9MWGQkRm+WV1e0esmSKGYllpK5Krk+KeAEZagSHA2DEsyt6+rCZFPz8n4hCoCoIq/QFNadPofImFjUnTSNEs1Ni1plSqeqyAuCwBWs1BSKFCxIaShde/qMeS5nXZn1tRoEtc//UdyRlbXB4/fvER71bx+uDiFc8gptYdO5C0wWQrlhamiIVtXE9ObS51QK3Msx11XuksuqAERlQoUKFWJqkwQHB+P9e3GvE68XO7dDR0cHrVuLk5NSfyEFNWsyb816RFlzWQSAyGI2MzNj0p5FRERQpVu8lNbvgHLlyolKuARBwN27d6nzCCE8J0+2ZnclZSxVCsIycpIFAbdeiteVl4LWFCJjYrH1wkUAQIuqldMtJ2pRpQr0dXURFReHLcr3yQUbiwJUCZdUfTcFnOZZeVNMkvsVAOqyN294SubNUUHWKCzymqFWmdJwcSiarSiHjfLkQR1JPfMN3rpmzcOwKDUPTmZTuq6ckjON4fSdewiLiESzypXSJZ4wMTRArwb/Jt89n3sz+7I0BUIIGv4hLnHjris78uqg8UmJQXm4bpx1le4z7q4usutXpJTYxSUkYOuF/+HO6zfM8wghIpHZp37+iImXl7GpkWS/8uL0s3DuE2qf1DCofZ4XRPB6Ll7XcsWKMckrtIWA4G9YdeIkRb+sLTSW7Fee3i+YzrCbS1lW0NuIEEJRrmkQFEsBL0h/5444+2VhYYGynADh7wCpP+Dt7Y0oRjWCq6srqz2kEAA7HTBq4EuVKsVijML9+/dF6uXGxsZwZW/yvwUIIagm8fhZTgkAll4JIG//AeUt2he0RAGGEKa3f4CoppMQgjouzPlqDMdv30mlIKyiRoTXzNgIjsrGx4OeXtxonqYgjbzxnBJOpoQyLjUFpSq06ObMo6eH0gw67u8REXj96ZNojGcM/S6Q/v1S4z4F5Ysx15VuxtIsKOVGFjtTYlISbkuCQ26MIJImceXpM8QlJKD+lOmoOmZ8uuxp0v6ds/fYpAKagnRdb7x4ySy55NyvTMVMDYL63VRgz4Nyptxc5TdwpGxtqjSp0tbOC4KAXwmJ3HM1AamR7+0fwCRQKFO0CFPQlhAip2NC1d9VKE7frwDtTGljXXkQBAEjNm3BrO5dZc+a8yB1IsMiI/FKUo4KAJZ588KWrbkkZ5qJsst4jobU3qtWrdpvWzkEABUqVIBRmmqEpKQkigQAAHR1dVGyJNP8dWY6JcXYD2Q8fy5OsVWuXPm3rJ1LC2m/yLNn7PSyI8O4gLxOCXXTOrGpTvHQV9yMWtLOVnb6ySM3/03rqdtrUEg5p8/fQ3H/rXyRV4A28h4wGrYAwNmGIsECGHoEGgTVQVessBXTkHjk+05kROQzMcn14mvpQepsvv0cKGI6SkFJO+a9YiQXo4+SAVH0NDM1MkLh/PR96BMonrOOFoIIn75/T/3/28+BXP2eFDjZiu8L36AgWeaVAncXF5ExEBETA99A+jttLQqwsnc6cjW7K5nyqC8swWjgjYiJgW+QuP/GXWZnE1Do+KTU+LevWQNVnfmX4lv4z9T/W+bNi3wmcgasFeVQaXVIkgUBj9/T1MD6urqiLE4ayEkoQ+3znOcBHkmesbwMqDaw49JlJCcno2d9bXDtsFE4f36Kep33jOXYLXI2RmbaJuZlVH4X6OvrU03s0muUAp5NzHRKOCfDz89P9Pp3TlOlQJoBCQgIQDIjQsf5UcvplFCUPbwNU2owsKKzmkSyIIgcoUJqOkCFlPXMAPDAh72BaQoViovXKzwqmhkdLmFjw4qM5CGEyFW3RLEmcHQ14CMxyso5FJWVdSsnoEwRexFdpyAIzEbs/KamzKwiFPz1coBie3GysWZG3aTrWqRQQeQ3lTfYn08iUGeQTkmRiYH45/8jTT29HLDIa0YxVLEcIUJIasZVgrqyTIxR4lMwXz7meknXNY+eHkrZy0+136xyJXzYsxMBu7dj78Rx3Ejvz+hofE7jnDavUln2qLCeri5cJKW0PAeXY7zK0leiLB8S3QQ6nN9WcHg4ImJiRGO8TJncCAoNw+IjR7Fh+JAsj+hLr4HUIU8Bx26Rs15VLZs4OTkZHz58EI39v01M28RSvyEFPJtYBwAVFuF5hdIP5zkvvxOk1youLo6pV1K0aFFWVsleRuOV6soqYcum95Y+DJ1t2c6LpuAbGISoNJzoFmbqGVQF8+VN/T8rWqZJ2BSgI6rS6wQo6uc56WWKvUNDoHY9aVQ6BdKHN++83wl6urpwkDRFsyLqAFCSbeTIRYVEOTvcdZXM14kTbNAkxrdvm9rkXNmpRLpR1u+RYgc+Py00qnFIr0MG11WuPjAqosvbX6XzLW5jrbUgglGePKnry8OVp89Sy2bz6OlhbDttMO4ysm6cdeVcV7lSEtQ+YGdpySSHkT43TI2MtCaEKcXwjZsxoUN7ihgiK6D2urKz1nTXuQagdDZFX6inpwd7Rnl0YGAg4iU9VTzb+XeC9BrwnBIWcQAAJz0AVFGhlNYLYHuF/78AgLm5OQoUKICwsLDUMT8/P9hKHnx6enooVKgQgsSGog6ANYQQOcKI1J1sTzOAAQDeSYxXVmmBJvHh2zfR67zG6pUApGVOklt8jxCCEjY2eJrmhvINDELN0qWoc+0tC+Lz91Dp8CRCiBzUhdRDlqdhII08acN4zQlwtrWBT2Bg6uu0/08L+4KWuEP3/HYnhLBTU/8NdaUDdpz7NSvWtYqzE97t2IKvP8Jha1Eg3Sirt7/4WVGR/QDSKJxtbUSsZD6ciLpdQeZ1rUcIWSnDtOpS389dV6mzqQ2NOPUgCAI2nj2f+npuzz+5GVpNQ/o9rOAQANgXZLZ8lZNpXalmWnv274p6vjrbMrPrsmPfNU/8jI7GoGZsUWxtg3ZKOPsw+36xl2ldTSEpo7WysmL2WPv7ixk5LS0tkTdvXuq83w3SZEVAQAAEQaB+8yw/A4CFHgCqRsGUkVqOiYmhvELOh/52sLGxETklaf+fFsZs41sbQkAAADOO8f9d0jhYhL25awzBP8Q0hKoaK9MibdRQ+hlywL6gpcgp4TX3mhoxk12Nlf9kR14j9rqGSubLeWj/dpD+vjO4rhXBYGeRA3mNaGpRgLGuDDFUOaCnq6u2iN+JNKw0OoSgbQ35a62pdf3JXlcz9nUtDmCsxiel/vdTDdxy78MZwcLDf+Pum7cghGBal04Y1bpl+m/SEKTGPu9+NWPfr4WgpXU15ayr9HfICw7KieDwcMzedwDn5s5iUlFnBaS/75CMrasptLSuLBFxgLbz/t8eVkAakI+NjUVcXJyoAR7gXlczPTCYR1jGc3Q0Hcw3Y9dc/3aQOnGsawXwf9zaAo+eNTouTvRa3cxFZvEjWszXri7SOiU/ommaOU1DyjcfGUs3RAN8I0NbMOGsa5RkvnkZ/Pm/I+h1jWOexzMytAUT9sMYUdL7NYvnKUVYZCRO3flXDK2Lex2tlA5K10v6++edp21wnF1qf8nKfSU+IQEhPyMQEByM7Rcv4e9b/8DJ1gbL+vdFoz/kpZ+WQnodsuu6coxn6n5l6ZjIjbFbtmN4y+Za6VFSF9LrFZVd92GO3Sa181jB/N8RrOsVFRWVIaeE8ixYJ0sXQEdHB4bZSIMgKyG9XjynJKt/tKybO/bXL0p3gPfQ1BQS0ijHZ6RmOu25aT9DLpgZ5uyHodTYzup5Zheoa+RktbMp/f2lQGq8Zrd13Xj2POKVKtHWBfJjab8+WvledZ1N3v2iLfDWKyouezglPZetpNTHyxQpggW9e1BUz9pAbgsOaXueR2/dhn9wMPZM0EpiQW2YSTL8iUlJiEtIoHR5snxd1XRKsjronF1gYmICQoiI+TM6OhoFJZkxVU6J6JdBCIEBo1krVnJjGRoaZjl7Q3aB9OJKr1UKpJ6itmFsQCtqx8TR4ldyK7mndYIy8htKe67c/PgAHamOZlwrAKl0mlkFI856xUrKLVnr/ztCajxEcwTgTGS+D9IDb12lgnXZaV3ff/mKVSdOAVDsIwcmT+CxmGkc0kxwdDzbKTE2yFqnxDgPe71i4n+JXvPWX27snTgOe5X//xEVhWd+/lhx/CTaeSyEY2ErzOnRHR1qyS2W/i+k68p6ZgHyP7fSA+/7s3JdwyIjMXX3Hvw9bTJLxyVLwQp+RsfGUU6JcRY/X3nB9zhJBiyr7bvsgpSERVo7mGUTp/gQglhzzlQHgOjKCoKAREYUWuqoSPtLfmdIf5wsp451nrYRzzDkDfLQ1J5xvxJknUfaki2WwBkPac/VBitNnPRhwjEmYn/9Yo5rC78S2OslXVu51zWnIO5Xzl5XQ33xfOM452kbyYKAkZu2IC4hAUZ58uDI1EmoqoYwqqYgXS/eukrXX9uI52R5pcZYdljX/KamqFvOFadnz0DPBvXg9zUYvZavwvCNmzO0d/8XSNfVMLuuK+9+lezD8Vqc5/htO9GrQX3Zaf4zg9h4+joYMQIsWb4Pc74/j+R3+P82sQKCIFDXjGUT//r1S+qQAECsDgCqOJ9VfiTNBiQlJWW5kZ1doG5tYYyEq1zbYJWpmBgYUH0dvHIWTSGtTkRmnRJ9fflFOyPjpGUynJ4cTpmItsDtiTCU1uzKu645BXT5k3q14NqG9PeXguy6rvMOHIKX9wuYGBrg2IypqKflUh9pTTqv7INX/qMtcMtAs+m6Aoos9fIB/VDIXEEbvPvyVUzasUsr351j1pWzX0gzs7z9WtO4+Ogxnvr5Y2LH9lr5voxCWq6oq6PDDCRk9X3As9vULdv/3RAXF4ckaUsAwybmXK9IHQCR0lHWyeo2v/+OiIoS+3Xq1iBqG6xNkxACY2rTlHcTkLKASXtaeEjrlEjF2eSAurXAWf0wlBIVpEBau66th2F2B0UAwGEvy+qHIc/ZlTpR2WFdT9y+i+XHTsAirxnOzZ2dJYrVUoE63v3Ku1+0BXUberN6X5HC1NAQXd3/lefYfP4ibr54Kfv3UuvKaRTPtuuaBc5mREwMxmzZho0jhlAZuOyCiBi6N45Vzs27rtoCz26T2sRSO/B3RWQk5VIwbWKOsxepbDFEhgAAIABJREFUBzWdElNTU+jq6oo8oG/fvsHCQj2KyNyMb1LdDQ5XNefHfQ+AHPnJagBEYQfeZpjf1ER07EvYDxmm8y+kwlGJyclq0QKndV5SInZyQnod8nNEHjkRsncA2BK1/w0VAYjucJ7xkt9EPN8vP9hU1b8bpOtqzhH24xj7QQDkUO4sC0CkwsmLvErVwL9wKMi1hfs+Phi0dj2KFLTEqVkzskyk88sP6bqy71fO/RIGQA4LuzgA0QXhrav0d/hV5n04M3B3dcHaU2dSX684fhJ1XORVsab2Ye66Mq9rFIAnGp8UYA2ghOiLePermfR+lX9dJ+/cg3Y1a6BGKVpXK7tAum/xBFY51/UXFLaTpmEAiZAqzykxl9gxUjvwd4X0Oujr6zP7bThOXIQeAErw4du3b3CW1ALr6urCzs5OJKDo5+eH0qVLZ2riuQWxsbH4+vWraIwlKpmcnIzv37+zPqKhIAgad7EJIe8gUT3lbYaOhQvjU8i/c5OKeGka1gXyi16zmttYCEvjgRfOn1/FmZqBVKSrhDVbzIxjPIwRBOGcpudECLkJoLbo+39w1tW6MO68+Vf9j6eY+7vhrUSki7uu7Ou6QRCEhZqeEyFkL4Aeace496t1YdHrrFzXN58+o73HIjhYWeHkrGmwzcIglfQ68ERgOet6VhCE3pqeEyFkJoB5acd4TmRxybryRAKzEtJreuPFS8T++sXt39EEKKV7yXVKAWddHwuC4K7pORFC2gA4mXaMu66FJesaxBYJ1BQ8n3vj9L17ODJ1Mp68Z6tpp84lzV4YGRMrOj+Pnh7KFi0i2zzpdWXfr5zr+lEQBDfWgf8CQogZAJFgSkhICFP8r2jRoqLXX758QWxs7G/f8C5VcC9SpAh0GD3AHCfupx4UUb96aUf9/f1Ru3Zt6mxHR0fKKfnd4efnJ2rW0dPTg729PXVeUFAQqwfnqxwOiRIfIXFKeM6Gs60NvLxfpL7mKVxrCqWL2ENfVxcJyszHz5gYWORNn6EnrWCiq0NRFWf+d3yPiBA5QQCtQAsAvxITEcC+uf6RZ2Z4C4lTwjNKnSXzzY5GjrYhCAL8voiDCLzIPuc+uMMa1ACeQeKUZPd1DQwNRZt581G2aBH8PW0yV98o5OdPfP4eij+Ky9tsK1WE5ind+3xmXi85oukAI5rL24el8/UNCmQaQ5rEvbc+GLx2PT58C0HLqlWwdfQIlQ5GPskaxyckICg0jOsoaAI+lCI6W0ne5zPzfn2t+RkBAG5KBwK+BiMhKYliuXKSzDc0IhJhkZGysdLde+uD8KhoNJ4+K0Pvu+/jg9oTJqe+LlqoIF5t2ajp6aWCXlfePsy8XwI0PiEAgiBEEkJCAKTy16YEnq0lTlPRokVF1UOCICAgIOC3D9RLle6lCu8p4PgP7/SgMHLUORmOjo64fv166uu3b6m3/naQXgN7e3vo6dFN2NKFSnm7PLMCADyHxNnkGjl24k3z5YePsk0KULDiuBZzwON3iiqY4PAfcCxsle77vv38mfr/P4oXV3Hmf4f0GpgYGsCmQAHqPP+vwayemERBEOSSnL8HoH/aAenmngLpw1vudc0J8PsaTJUDsIzX6Lh4XqZCLqfESzrAi6hK19X/61fExMdrlRI1MiYWHeYvhoOVFY7NmMoVZgWAIzf/wUMfX+waN1q2+UTHxcM/WBwccOJkSjhOgafGJ6XADenA5++hiI6Lp6jEpesaHRePgG/fUMwq/b0xsxi5aQt8gxRVpsdv30FlpxIY3bY19/zEJJqYJA/jeacpCIKAl2kCoQA/A8bZB+Uo8YEgCGGEkEQAqX98QlISAoK/Ub87+4KWMMqTR8Qi9fLDR9nK3oY0b4rObnRQmYU9V65h2dHjAICapUth6+gRqcf0dOSlEJY+j0pwgggcu+WZ5meUirdI45QACptY6pTo6+tT1UNv37797Z2SN2mqMwB25RDAt4l1wDCMOSejTJkyotf3799nUXr9Vrh3T7znSa9RCt6/Z5ahy+mUUMYTL6JaXvKjeernj8gYeZvx0opwffwWotZ7UjIlhvr6qF/eVZZ5peCGpIGznEMxZsTyLTs6J5dDAgDXpAPvgoKY92F5R/G6fv3x47cv4ZI25tpZWjCzdD6BgaxrGi8Iglxdl48AiL4wJaIqRSl7OxikKXdMSErC3TfaCxDFJSSg08LFKGSeDydnTVfpkADAyw8fUNKOHd3WFG6/fi0KDhjq66MkQ7065OdP/KBrmQUogjgah/L38ksyhvdf6HazQub5YGMhDnzI3UguzRp+DFG9F0t/j6aGhlQ5ribx9nMgvoX/FI1Jn1eAgo5a+rcoQe2XGsRP6QArW6NDCFwdHERj0ueLJpHPxATFrKzU+lcgTX+OkYGB6Jh9QUvZ5vgzOhrP/MR2ZnlHB+a5nGfWbY1P6l+oHaiX2ntSe/B3Q3JyMh48eCAa49nEnGvKdkrevHnDNHJq1Kgheh0WFgZfX1+1J5wbcffuXdFr6TVKgY+PD3NY8zNKxXXpgP/Xr0wBwCrOTqKoXWJSEm6/livrrUCfRg1SqYif+rGd4LT4HhGBIGVtaZNKFZFPZvVUr+cvRK/dy7HZhF5+ZGYfZKt/EwThPQBRuDI6Lh5+X4Opc4sWKoiihcQqqnI+DHMC0pYpAoC7K9u55WSVZOsoFwQhGQAVCXgR8IE61yhPHlRxdhKNaWtdkwUBA1evg5GBAY5Mm6xWL4GX9wuUtKMdBE1Cuq7VSpVk9qlx1jVGef3lAvW7Ya0rANQpK46ey72uaXuACCFoUbWKyvOl169Z5UpqkZRkFp6SdS1uXZhpLL//8pUSFQWQLAgC+0JrBtQ+/+ID++vcXMXrqg3WsuyMmy9fidg0TQ0NUdnJiTovKi6OVx7tKdvkGDYxryqoevXqotdSe/B3w+vXrxEe/m9MlhCCatWqUecJgsC1iXUA+AEQ0Qt8//6d6cUUKlSIqg+7detWZuaeK+Dn54dASR0zzynh/Fi9NT8rBQRB+AZApOakiKi+oc7No6eHaiVLisauPpUzOwoUs7JCwz8qAAAuPHyUbsbtwoN/zxnRuqWsc4uIicFDibPtzkm1c4wGeS8eI0LHe8hJjW6511UVhDSJgKxIsCYlJ8PTW3zLubtmaF3ljsBQ4XOeUSql3L32VJZAP4VJO3bhzedATOncEa8/fsKT937cf9eePceyo8cREPwNpWTOlFx7Jv77eZTEnOspd/rwHTWPl+x1rSsJfng+90ayjDdL6xrVQAjBsBbNcXbOTFEGm4XLT5+m/l9XRwfj2reVbW4AcF2yrm4u7HXl7H9yZqwBRnaNd7/Wlfwe7/v4ZjnluBTarHqRrmuN0qWYivO3X71mlUf/EgRBTspByi7jORtSe+/Tp0/4yA5U/haQ+gNOTk4oWLAgdZ6vry9CQ0Olw5EAAnQEQUgEQHkWd+6wS6eli3D69OmMzDlX4cyZM6LXtra2FCMDoGhyZ/xQf0G+ZugUUJ6lNKKYgnrlxMbrsX/uqK0fklks6tMLBvr68A0Mwtn7D7jnJSYlYd2ZswCA7vXcUbO0vDSHx/+5k9qEDwDGBgaoWqokdV5cQgLus8tmdss2OQWeSge8XrDXVWrk/O/RY/zMAr2cxKQkfI/4t/SDVZYkNzyfe4tKQQgh3EwJx8g5yRrUIKi+EnWdkkfv3qX2BsiFFcdPYtO5C3j18SPqT5mO2hMmq/zXao4H5uw/CH1dXRTn9AFoAm8/B1KlIHXLsdeVs/9RWWUN44x0wPM5Ox4l/T1+CfuBG5w9WxMY06Y1rMzN8SM6Kt0eh48hITh269+qmfHt26JcMQfZ5vYjKgqXn4i3Ov66Mq/nY83PSoS90oG7r98gjqHsLs3cxSck4OSdrC/1+R7xL9EUo6xRFiQkJeHYP2L7Ump/pIBzv1JOvoZxC5KAbkBAAMWyCij6rK0kPV//bxP/C16QnuNf3BQEITGFp4valHmeYfPmzUWvX7x4wUvD5GoIgoCTJ8U2ivTapOD2bWb54z1BEOS2Dq9IB3hOSYfatUQ9E19//MB1zoNTUyhlb4fNI4ZBV0cHY7ZsZ5YgAcD0PXvx8sNHVHYqgdWDBso6JwA44Cm2DVtUqcwsBeE8gBIFQZDbyDkqHbjh/ZIZ6WpeubKoATouIQHHb8vVq61AUnIyrj97jv89eoxj/9zG+jPn0HL2PFFkcOzW7Vh05CiO3Pw/9s4zPIqqDcP3IQRIofciJfQuKr1jAQUUlC5FCKIIftKbKII06YIoVXovAZHektBBpHcIGJKA1CSkQcr5fswmZndmNhvIbhKY+7r4wdkzuyc52Znztuc9yJ/HT7D/zFm76/ev2G++rzXLlqFIHrWE7fU7d/Ry65fYZ2UJzLccOHH1mmbKZe3y5VRrX+2jqqlOMTYcOsyo5Suf69oSBQrYtRh6xX5vs/+/ljePKr0NlFSQk9c0zzML7LKw/5hnOXD7/gNu/atOSymWLy9vlTZrf8EqO+5r7mxZWTtiCDtPnqLZyFGc1smdfxwWRtcp03lqut/1bPoe33fqYLd1Aaw/eDjh80ARG2n21huqeVJKPeN9rf1WB1LKXUBM4rGo6GhOXFUHVF0zZ+b96m+ajVk+ZxzBzX//Zdffp1h/8DBjV61hwc7dCa+duuFHn1/nsNrHl63H/+Lkdfuc/fecOs39EHPn0Ee1a2nO1Tmv7NYaTClMiqgqL6mtZ2IvL69Xstb60qVLqiL35s2ba87V+V3uB4g3SvZqXRQTE2M5TI0aNShikR+8ceNGG5b8cnHixAlu375tNtaqlXYo+9AhzYCIvQ+uoPEwPHXDT9NLXSxfXmpbRAOW7bX/Ets1qMe6EYoMYcMhw5m7fQc3//2XkPBwfM+d55OxE/hly1baNajH1tHfqxRrUpobd+5y+JL5F6tjI2059D3aqVC3UnxRahZjURR99/FjzXz5rK4utLDIE7f3vkY9i+aTcRPpMWMm3y5Zxpyt2wl48NCsiFIgWLHPmzErVtP7l9/o8NMUdp+ylyqrkpL35/HjZmN6+6qT4vbIzikDSCmPYuGhexYTwwGNVJ8MQtCuQX2zsZX7fewW3Zy3fedzP2jLaxScpxQxsbGs8TVXZ+3QsEFCvVpifM6eN4uAmngmpdQP06YAJiU+VSqRXiplp8bmbTU2HT5qV+GRN0uV4uCUn8jh7k79QcN4d8R3TF6/Ea/DR9l96jRTNnhRo99ATly9RsFcOZn/v778/OXndpUqBli+z/w+1bJmTU1RhbM3b6mK4VHuj6pIhh1QFZHo7msj8309cP4CN//VdsTZi5X7ffhs2s8MW7SY1T4HyOXubnZf9jl7ntErVtNr1i8MX7TULmtYvs/b7P/1KpSneP58qnn3Q0I4e/OW1luozjV2QCWQcOCASgUagI8//tjs///88w9//fWXfVaVhrG0A4oWLUq1atVU86Kjo/UEAfbBf3J2p1BumgktKoODg/Hx8eHtt982u0oIwUcffcTs2bMTxlavXk3v3r3Jnt3+XbbTCnPmzDH7f/ny5SlbVp3iEx4ezp49qoAF2FcVBAAp5VkhxFOULqWA4sVef/Awvd5vqprfsVFDswP5piNHuX7njm5zuZSi6ZtvcPbXWWw5doxNR44xb/tOwiIjKZInD1VKFMd38gTeLFUqyfdJCaZ7bTY7fOXNnp0mr1dVzYuTkvUHNY1NlYGf0kgpI4QQDwGzis81Bw5SSaN/S8dGDVh74L8MzWNXrnLo4iXqVrCPdKFblsw8Wvt8XnV78dvW7WYRh0wZM/JxHe3Q8lpfzTo5e6eCxHMDMMtPXON7gGZvqj3EnzZqyLSN/0Vr/e/fZ8Ohw7S3MFZSgp1jR6f4e6YEa3wPEPDAPDe5fX1tOdS12ocKe6eCxPM30CTxwBrfA3g2fVc1sV39egxftDQhShAWFcW8HTsZaMf6jWL58rJuxFAu+d9m/aHDeJ87z4r93oQ/fUqebNmoX7EiTd+sxoe1atq1UWI8vufO85dFVKuTjhNhzQHN7+t9OyrlJWY/Fv3A1voeYFSnDiqj7b03qpEvR/YEAypOSn7e9AczvrB/9D+ebzu049sO7Rz2eZbcuHOXLccsnUPavS3XHzxsVgxvIkpKedE+qzNjHzAy8cDu3bs1myOWL1+ecuXKmUUJ5s+fT/Xq1kUjXiaCg4NZu9Y8MNmqVStNx8X+/fsJDQ21HH6EKS09A4CUMhbYbDnLMj0pnrZt25r14ggLC2PpUvtY1WmR8+fP4+trHlLv2LGj5tydO3cSqS5ou4d9Je0So/ICrvLWTgdoW68uOdz/U7WKjYszO/TYE7csmenQsAGrhw3m5MzpXJk/h70TxjK9V0+HGSSBDx+qQuqfvfu2ZgHewfMXuH3/gdbbTLXP6lTssBxY7eOrdRPn7derqvrA/LRug/1WlsYIj3rK7D+3mo19Uq+OZvMyv7v/cuyKZjrqbK1BO6Cy5rYcPU5oRIRqYrnXilCvornc4qT1G+1aGJ2WiJOSKRvM70/1K1WkfFF189onEZFsPa7pvVxun9WpmGE5cPjSZU1PeU53d1pZpLPM+uNPLXWpFKd80df4rmN7to7+ntOzZ3JtwVyOTJvM7/3/R/sG9R1ikAD8tN7c61qqYEHNepI4KVmnbZRst8/KVEy0HPjn3n0OXVSrV2Z0cqLr22Z2Kcv27rd72mpaYtL6DWbPqJzu7nxSV9s5pJPe5qhCnAOA2ZczIiKCXbt2aU62PP/t37+fS3ZWME1LLF68mPBEtarOzs60adNGc66OXbEpXgExce93Vahzz549ZvJe8RQpUoQPPzRvsLRkyRJCQlQh1JeSmTNnmv0/f/78yd2AFVJKdTWcfRhjOXD86lXNbtVZXV348oP3zcZWefs6PMScWkxev1GVw9y3pXZO5ErtPO9AKaWjNLJHWA4EPXykWRSrpZKz9/QZh/a2SE3mbNvOw0RF9hmEYPAnH2vOXeXto5WmFC6ldIx1Dj9hIfkc+ewZm3WKYgd/0trs/5dvB7DxkH1rhtIK6w4cVN3HhrbR3tcNhw6bNa8zEYuDnAhSyi1YSD5LKVnto50SMugTcy/j/ZAQ5m/fadc1phUOXbykEgIY+EkrnDJkUM3dd/oMQQ81sypH2Wd15pgk2lUV0Hp1QH1bNlfV+E3d6GW39aUlrt+5wxqLv/evWnyAu0XkARTxivjmyhaMt8/qzDEJQKlqkry8tPeqTZs25Mv3XwqalFJ1TnxZCQ4OVgUlWrVqRSGNZpjBwcF4e3trvU2C/ZH4W74fMCuSiI6OVlXTx/Pll1+SIdFNIjg4mGnTpiX5A6R3fH192bfPPPOqZ8+eZNLwIAUEBOgV9DjKO4eUcjegktVYqlNX0Ldlc7ObxLOYGPrNtXcdaOpz2s+P33eZp9l5Nn2PPNmyqeaGRkTgdVhzXx2RwwyAlPI2EGA5vmSPdlZg5yaNVfr+/5szz+4Ka6lN4MOHTLKICrWqXUuzmV9MbKyqaNqEw06DUspnKOm0Zujt6zvVXldFEkcsXqrqWv+yERYZycil5rfR6mVK01hH0nbZPs373d+m37ejUP0drdjnrRndrFC0qKoWbPza9XoH8JeGmNhYBi343WysSJ7cdGionbql8xzzt3N/EktU9/0Nhw5r1gHlzZ6dz94xT4mft32nXu3ES8WQhYvNarqyurrwVXNtcaAlezXvd09M4gKOQpX+c+TIEQICVI9dMmfOTI8ePczGdu/erXcAf6mYNGmSWTqWk5MTX3zxhebczZs380ztHPIHEqz4BKvCFDpZYTl7/vz5mgXvHh4etGzZ0mxs1apVnNOW5nspiIqKYtQocwdM/vz56dBBW4Vk7ty5xKkfOBellI7KT49nm+XAgp27NKVhc7q78+UHzczG9pw6bVWyN70TJyX95y5UNXP65qOWmvPnbtuhpTEvgQl2W6Q2iy0HNh4+wnWNbtHOTk4MaG0eLbnwj7+Z+srLyNDfF5sd0J0yZGBo2080564/eIh/7mmqbjnE65qIyZYDRy5fVgkwxDO8vXmUNvDhQyasWWeflaURxq5eqzqgj9TJlT9w4aJeVHBSyq/MKt9aDtz89182HNLO5B3ero1ZwX5YZCQjFr/cadJztu1QHdCHtWujqd7md/dfNh/VjCD+rjVoR8ZgITzyJCKS+Tu0fRn9Wn9oJtgSGxfHgHkLX2rFJq/DR9l50vzY06dFc7N08XhCIyJYtEuzDvdP+6xOGynlX4BZ6kFsbCwLFmg7aTt16qTqyTF27FitQ/hLw+nTp1m/3lwMtFWrVhQvXlw1NyYmht9/1/xqLkvcvNYyHroIi9SBoKAgXd3loUOH4paos3ZcXBwjRozgqQNyX1ODqVOnqhS3RowYoSp8Avj333/ZsEEzb18l++kAVKk+TyIimbNNVZYAwOA2H6vkRgfMW5gqvSUcwewtWzluIWs9on1bCuTMqZobHvWUX7ZsVY0Dp6SUquotOzMBJQUlgdi4OGZ4aX9fPZu+S1WPEmZjo1esemnT8zYdOaqKaPV6v6mmGECclEzeoBmaD5RS2q9RhAZSyjVYNLQFJb1Qi/ffepP33zKXG529ZaumNOnLwNHLV/htq3nJQMuaNRKasVpiGSkzES6lVElr2xNTga6qUeOUDdoSolU9SqgK4dcdPPTSOoiu37nDj6vWmI29Uaok3SwiC/FMXr9RK9Ibi5IC6TBMErIqya1ZW/7UShmkcO7cDG1r7kg4cvmy7vM4vfMgNJTBC80Po0Xz5tUVbvhly1atGjqJhlHvABZZDqxbt477GpLxrq6uDBs2zGzs1q1bzJihKid7KYiMjGT48OFmjvds2bIxePBgzfleXl6qZuMo39fFiQfMjBIp5VVA9eTT8fiTL18+vvnmG7OxS5cuMW7cOCs/Svpk//79LF682GysTp06ujrMCxYs0LKQH2J/TXwVprxXVXTmly1bNdM83LNkYWL3z8zGAh8+xHPGrJfOm3Py+nW+X2YeICz3WhG+0qkl+X3XbrOGU4nok/Krs46UMgKNxmzL9+3XLMJ3ypCBWb17mXlfQyMi6DJ5mlktzcuA//379P11rtlYvhzZ+a5je835fxw9xuXb6rA8MDzlV2cTv1kO7Pr7lF6eNdN6eZp5X6NjY+k8eepL50gIDgunx/SfzQ6jLpkyMbF7N835f127rur2biK1Er5HWg5c+MefbSdOak7+4dNO5LVQtew1c7Zmj5P0zNPoaLpNmWEWgc4gBNM+99SUdw548FCvL89GB6luWfKl5cC94BDdtMuvP2yhSiH9dskyTt3Q7hOTXomTEs8Zs1TF/JN7djerrYknPOopc7ZpahSckFLe1HrBzswFzB6mT58+1fP489FHH6kaBs6fP5+9e+0uyulwxowZw7Vr5o6v/v37kydPHtXc2NhY5s3TVHJeJ6U0k9lTV47BOCxCkTdu3NBV4urWrRsVK5p3gl25cqVuLUp6JCAggMGDB5sdyF1cXPjhhx805wcGBrJ69Wqtl6abvCqpQU/LgUdPnjBb2+tP6zq1VN7XXX+fYsaml6db6eOwMLpMnsazROmJThkyMPPLXpqKW6EREUz3UonUAVwy9ZhIDT7HIroZHRurq671ZqlSKu/rqRt+L1VaSFR0NJ9OmqrqUDzJszvZ3dTpAtGxsYxbrZnu9EBK6bA6IQuGA6qQ85iVmvcViubNq/K+Bjx4SO9ffntp1LiUA85MVYrdyI7tNfscAPywYpXWcBQaxoEjkFIuQnFOmfHjqjWa9V053N2Y2L2r2VhIeDjdp/38UjkSBi9cpGrc2Ov9pppNMAHGrl5jdt82EYeGceAIpJTHAJVs35QNG7VSfcmUMSM/f/G5mcH1NDqarlOmaaZVp1embPBiz6nTZmMta9ZQ1UvFM2PTZjNRkkQ4Tjc5EaYG17Msx1esWKHZ4R1g1KhRZEnUT0dKybBhwwgKUgVJ0y1eXl6sW2f+zKxatSqdOnXSnL9x40Zu3lTZlJop7yqjREp5Go0ahJ9++klTXcvJyYmZM2fi7u5uNj5kyBC9poHpiuDgYDw9PVUqZN9//z0eHh6a14wdO1ZLBjgUx8mKqpBSngJU+t6T12/UTd+Z/01fVXH098tWsP6go9SM7Ufks2e0G/+T6oAzrF0b3f4dP65cw78aanTA1ym/QtuQUj4AVAm4S/bs1ZO2ZWKPz6hSorjZ2JxtO5i5Of07EuKkpOeMmaqIQrd3mtC2Xl3Na37dspWL/urGkzi+liQBk/qLKnVg96nTenn09G/9EU0sCr3/PH6CgfMX2mWNjmb4oiXssMhLb1i5El9/2EJz/vqDh9mvHSWZnziHORVQKSKeu3WLuTrqWh0aNuDTxo3Mxo5fvUq3qTM0i+TTG9O9NrPQoratYrGijO3WRXP+kcuXVQ34TGy3d4PTJFAZRHcePWacTn1X/UoVGWyhFud3919ajRnvEPlne7Pu4CF+tHCiFM6dm9lfaduNfnf/1WtBcFZKqflFdhA/A2aH34iICN2MoFKlSjFypLnP4/Hjx/To0UNTzTa9cezYMb791jyTLlu2bMyYMQMnDWducHAwkyeryiQB/tDaV61ICcCPWERLHj58qKuuVaxYMcaPN1dqi46Opk+fPly86Ig+N/YhMjKSXr16ceOG+QGnRYsWtG3bVvMab29vdu/WLB6eYersm5qoJBEinz1jyMLFmpNzuruzdFB/s6hB/KHP0vuRnoiNi8Nz+kxV4XD9ShV1i6DP3rzF3O2aOb/XpZSpHZvtgcX3NU5KBsxbqHloyeLszLLBA1RSjCOWLNN72KcbhixcpKojKV/0Nab07KE5P+jhI8av1SwteCyl/DXlV5gs+mPR4R2UnzFxI8h4MgjB7/3/R8Fc5rVQ87bvZKqD+g3Zi0nrN6pqufLlyM6iAd9oSsWGRUYyfPESrbd6BgyyyyJtRErXnDypAAAgAElEQVQ5E40O7z+uWs3dx9o9K6b36km514qYjW05dpwB89K3wbnG9wDfWaTPumfJwvLBAzR7osTExtJ/rmZReByp5E2PR0q5H1C5g3/9cxsX/tF0ejCyY3tV/5V4gzM9KyP6nDvPFzNnm0VpMzo5sWRQP3JnU/eHAhg4fyFR2tE/bSknByGlDEHDobx9+3bdLu8dOnTgo48+Mhu7fv06np6eWg7rdMOVK1fo3bu3qjRh9OjRvPaauj8UwJQpU3j0SOUriAPGas3XNEpMoUjVHX316tWcPattsH7wwQd0797dbCwsLIwePXpw4cIFzWvSMk+ePKFnz578/be5Z658+fIqAyyeqKgoxoxROcEA/sHBxXdaSCkPojQFMmPbib90iydrlCnDj107m41Fx8by6aSpernaaZqn0dF0n/azyttcNG9elgzsp3nAiZOSfnPnax3wJaBtxTgQKWUgGrKUp/38mKfjfS1VsCC/9vnSLH1ASknfX+ewxlf7RpuWiZOSwQsWqQqgc7i7sXLIQM38ZTCpc2k/JLStGAdiyo1X3VACHjxk/BqVhD6gSI4uHtCPzM7OZuOjlq/k53Saejnda7MqbS2LszMrhgwif44cmteM01DnMvG9g2WA9ehlOfAkIpJhv2saUrhlycyKwQNV6YcLdu5i6O+L02Wt3ypvX76YOdts7RmEYM7XfShTWC3ZDUpE99ytW1ovLZZSqmUHHc8nWDiIYmJj6Td3vmYaZQYhWNjva5WwzLYTf+E5Y6ZWilqaZ+/pM7Qb/5MqvXD8Z12pXa6c5jWbjx5j198qJXQA71RMjU7MBCxaZoByGI/SkV8fM2YM5Sx+3jNnzvD5558TFpZaWfzPz/nz5+natauqG3vPnj1VSrzxnDlzRtXp3cQik7qZCr1ICSjeJLPc19jYWPr376/7Cx0xYgStW5s383rw4AEdO3bk4EHNrqtpkvv37/Ppp59y7Jj5wbVIkSIsXLgQV1dXzetGjx6Nv3YayDemouS0QCs0vK99Zs/R1cD/+sMWfNPKvFlmWFQUn4ydwLqD6SdFLywqinYTJqkkOHNlzcrmUd/qHnB+WrdBLxVqQyqHlRPjCaiScUcuWab3EOeTunWY+rmn2Vh0bCyeM2alqwPss5gYPKfP5Net5lmnLpkysW7EMN0DzvJ93mw8rNlo8IQDmyVaRUo5FlBJlszcvEXXKVCvYgWWDupvZmBLKRmxZBmDFyxKNzUmUkpGLl3OyKXLVQfXBf3+R53y2gcc33Pnmf2nKgMZlP4Vqe4cApBSrkOjH826g4dYuV+zkzXlXivCpu9HmAkagCJY0mPGTLMeEGmd2X9uo9fMX1RrntC9G63r1NK85qK/Pz8sX6n1UiipHCWJx5QmrcqDPXzpMlO11f0okDMnW8eMUgkarD94mI/GjNPsd5JW2XTkKG3H/6QS0Onf+iP6tNDuSRL48CFf/zZX66VooLXWC47GVAs8wHL81q1bumlcbm5u/P777xQpYh7hPHr0KO3bt+fevfQjVnH06FE6d+7Mw4fm5XAtWrRgyJAhmtdEREQwePBgLZGsR1gRkNE1SqSUD4HvLMf/+ecfRoxQKcwCIIRg/Pjx1K1rnrsdERFBr1699CymNMW5c+do27atKu0sd+7cLF682KxrZ2K2bt2qKvwxsVNKqVkdnRqYcm5V3tcHoaF0n/6zbo7yuK6d6djIvIHVs5gYekz7mUnrN6b5g871O3d4Z/h3qrQztyyZ2ThyuO7B9cCFi3o9H6IA7aTnVMBUg/CZ5XhUdDRdJk/TiwbQ6/2mKmnG+APsoAW/p3lP3d3Hj/lw9FjWHjB3emR0cmLpoP66B9drQXcYuEBTQSWONPIgTERrNNLzPGfM1E33aVGjusrgBPh16zY+mzpD9+8hrfAkIpLOk6dpCktM/6Kn7sH1XnAI3afP1Itqard7Tz2aYyHpDdBv3nyuBKjsUECJXP/eX52yttb3IK3GjOO+Rt1nWuJpdDT95s5nyEK1cTy4zcf01VE9DIuKovPkaZoSu0CvVK4RsqQ9oPqC/bhqDT7ntNXFSxUsyNoRQ1QRXd9z52n63Sj87qZt2fY4KZmwdr2mkmOnxg35scunmtfFxMbSfdrPesXt49NAynsCJglxlbdj1apVbN6sfcTLly8fixYtIleuXGbjV65coUOHDumivGHFihV0795dFYyoV68ekydPNmuinpiRI0fi56epJjdMSqnZEAysR0pAkUNThc62bdumpy6Fs7Mzc+bMoUEDiwPss2eMGDGCgQMHEqHWoE4TLF26lPbt26s6dhYoUIDly5drNoQB8PPzY/hwTcMvDPgqpdf5ouh5Xw9euMi41dqGoxCCOX2/UhVcxknJ6BWr0vQDcf3Bw9QbNFQVMcju5sbGkSN0FV7uBYfwmX4x6depJD2pi5RyIxrSz9eC7tDfSrHz6M6dNDXjf9u6nXeGf5dm5Ue9z56j9oDBHDhvnh6axdmZpYP680H1tzSvi3j6lI4/TdY7mE81pcOlGaSUJwBV6OpecAg9f/5F1yHwebP3mKohqbrh0GHqDhyaZrtIn/bzo+6gIWw6Yv7oySAE03p50rPpe5rXxcbF0XXqdD1DzUtKqa27m0qY0o1U0sThUU/pOnW63gGcFjWqs2Rgf1WKnvfZc9Tqr/4+pBVu3LlLk2Ejmb9D3ZR7cJuPGdVJuwkxwNe/zdUz1E6Y+vqkGUzPhf6W47FxcfT8eZaepDw1ypRh43cjyGaRiXHG7yZ1Bw5R1cqlFe4Fh9Dyhx8Zu2qN6l7UuUkjfuvTG6Eh6wyKmuChi5e0XrotpfwhpdeaAnyDRg+pUaNGcUsnI6FEiRIsW7ZM5dD29/enbdu2rFih6lmeJggLC+Obb75h1KhRRFsYmo0aNeK3337D2eIeFM+KFSv0+hseAqwWwomkclGFEMVRwsxmuS2ZM2dm0aJF1KhRQ/O6mJgYhg4dqmlBFitWjB9++IH69etb/WxHcfv2bUaPHo23t7fqtZIlS7Jo0SIKFSqkee3jx4/p0KGDqhjeRBcp5fIUXWwKIYQoCVwGzFrlZhCCxQP78UndOprXSSn5dulyzfSe/DlyMLFHN9rVr2ePJSebe8EhDF+8VFPPvmCunGz+fiQVixXVvDby2TNajvqRI5c1u2jvklI2TdnVpgxCiGzAHUCVYzihezf+p6NUBEoayLBFS1T56dlcXfmhc0d6Nn1Ps+bG0YRGRPDjyjXM2bZd9RDM5urK2hFDqV+xgua1sXFxdJk8TU/B6qKUsqLWC6mNECIDcBfIa/la35bN+anHZ7rXrj94mM9/nqWKemVxdmZwm4/p3/oj1QE3NYiKjmbaxk1M2eCl8rZmdnZmQb+v+bhObZ2rYdCC31U1RSb+BQqlMW96AkKIy0BZy/FP6tZh8cB+mn06QCkmbj9xkiq9xylDBr5q8QHftm9HVld1Y19HExsXx7ztOxm9cpVqrRmEYJJnd3o3f1/3+ulemxm5VPMxGg4USEWZfasIIfYCTSzH61WswOZRI8mi8507d+sWrcaM1zSuOzVuyPhuXVSpXqmBlJK1Bw4ybNES7gWrHZIDPm7FmM6ddA2StQcO4jl9ppZTJQYoJaX8J8UXnQIIIbph0fAPFNWt1atXk0MnDTwgIIAePXpoRg+aNGnC999/r0r1Si28vb0ZPXq0qlk4QOvWrZkwYQIZM2bUuBKOHDmCp6enVp++R8AbSe1rkkYJgBCiBYqnzuyvy93dnZUrV1KhgvYBQErJ1KlTmTt3rmYhXrNmzRgxYoTugd/eREVFMX/+fObOnatZrFSrVi1++eUX3T+yyMhIunXrpiqGN7FQSqnqDZKWEEJ0B1Q5LJkyZmTdiKG6HZJBSQMZsWipZh5zw8qVmPa5p0otxlFEx8aycOduxqxcran5XqVEcVYPG0KxfKrzHZDkwfUxyoMwLRTLaiKEaAzsxeL7Gh/t6tykke616w4eos/s3zTVnV738GD6F57UKFMmZRdsI/EPwRGLl2k+sEvkz8/qYYM1O7bHY+XgGgUUTmVJUavoORIAfuzyKQN0OiSD4kXvOnW6ZppEqYIFmfJ5D9618n23NztP/s3ghYu4cUet/Z83e3aWDepP/Ur69uJP6zbo9XCJBSqYGgOnSYQQOVA6vassiJ5N3+PnL/XLJc743aTDxMn4a3SYLpgrJ+M/60rbenV1D4b25ujlKwyYv5Azfuq+d+4uLszp+5VuKh4o6lw6TXsl0FhKqV2AkwYQQmREcSTktnztg+pvsWroIDJqSKgC3Pr3Hu0nTuL8LfX5LbubG6M+7YDne+/qXm9vLvr7M2D+75pRuUwZMzKxRze+eL+Z7vU+587T+sfxer12ekkp56fcalMeIcRiQNWxtWrVqixfvhwXF21nwKNHj+jTpw8nTqiFhbJkyULv3r3x9PQ063PiSAICAhg/fjy7dqmjmUIIvvrqK/r166d7P7ly5QodO3ZUFcNjSp+1pVbTJqPEtKCZaPRjyJ07N2vWrNFNbQI4dOgQAwcO5MEDdZfpjBkz0qJFC/r06UOJEiVsWsuLEhERwdq1a5k3b55msZEQgl69ejFgwABN3WVQIkFffPEFPj6a98QLQI00VNyuixDiT5TcZjPcXVzY8eMPVCup3YsF4O/rN+gyZZpmek8GIWj65huMaN+WN0qVTNE16/EsJob1Bw7x07oNXL+jLcTSsVEDZn7ZS1eNSUpJn1/n6HXijQOqpaHidl2EENPQSCFwdnJi7YihvPdGNd1rrwUG0XnKNM0HIkDtcuUY2bGdSsrSXsRJyY6/TjJu9TpVg7V4WtSoztyv+5DDXd0cMZ6xq9YwQVv+VwItpJSa1dFpCSFEH+AXjXFmf/Ul3d5ROWYTCHr4iM+mzdBLl6BWubIM/LgV77/1psMOsfvPnOXHVWt0e+rUq1iBRf2/oVDuXJqvA6zc70OvWbP1FKj6pAFp5yQRQrwL7MTCkQDwXcf2DGvXRn2RiScRkXw1+zc90QYqFC1K/1Yf0q5BPYcdYo9cvszUDZvYcfJvzX0p91oRlg8aQPmi2jKiADtO/k37CZP0pHF/kVKmWn8oWxFCVADOoZEq36lxQ+Z93Uf3uxYVHc13S5arBDziKZo3L30/bIFn03d1oy4pzYV//Jm+aTNrfQ9qpjW/ljcPiwf0o1Y5VeAvgb+v3+D9735QFcOb2Cyl1PeupBGEEG7AcUDlkW/cuDG//fabbiQhNjaW2bNn88svv2gVgZMrVy46d+5M9+7dyZpVWz45pQkICGDRokWsXr2apxo9cnLmzMnkyZNp1KiR7nvcvn2bdu3acV/DQQJMk1IOtGUtyTFKMqPcNBtavlakSBGWLFlCsWL6Hso7d+4waNAglaJVPE5OTrz77ru0bt2ahg0b6m7oi3DhwgU2bdqEl5eXbhObggULMnHiRFWxfmKePn3KgAED2LlTU271AVA3LXvmEmNKC7kFqJ4OebJlw+u7EVaNisdhYfT9da4q/zvR+/P261X5tFFDWtaqoak9/6JcDQxklbcvy/bt584j7cLfXFmzMr1XT9rU005Lg/jeHgs0c55NfCml1JQJSYsIIU4AqsIKtyyZWTFkkFXPeMTTpwz9fTGLdu/VlRutXa4cXd5uTOs6tVR50CnB7fsPWO2j7KuWBx2Un2VMl858+YG+Vw6UJqE63b0BfpJSDnux1ToOIcRGNIrxMzo58Vuf3nRqrLpFJxATG8u41WuZ7rVZV62pcvHidHm7Me3q17VLmsj9kBDWHjjEsr37dZXhnJ2cGPRJa4a3b2s1ZXDZ3v30+XWOXt3XWill+xRZtAMQQkwBNB/cSUXCpJTM/nMbo1es0m28V6pgQbq83Zj2DeqrmuKmBCHh4XgdPsqyffs5evmK5pwMQtCz2XuM/6yr1WfBzpN/03nyNL2f5aiUUj+PL42h50gA+PKDZkzu2UM3RQ8UEYMB8xfyWEf1tFDuXHRu3IhOjRpSunDKZ51EPH3Kn8dOsMLbh72nz+g+Dz6pW4eZX/ay6hj669p1Ph47Xq+w/RZQMq2mWVoihCgPHARUHpNmzZoxbdo0Mln5Gz9w4ADDhg3jX53m1Tly5KB169a0bt1aNxvpRYiOjsbHxwcvLy/27NlDrM7zoG7dukyaNIn8+fPrvtfNmzfp3r27qh7bxD7gfVuzS2w2SiAhX90bULlZ8+TJw8KFC6lYUT/ELqXkjz/+YMKECZpRk3hy5szJe++9R506dahZsyZ58jzfDTQqKoqTJ09y5MgR9u7dy7Vr13TnZsyYEU9PT/r27asbegMlyvLVV1/pSRxHAO9KKdNVy3MhhCtKLxXVL9qWAywoD5GB83/X7Q4PkNXVhebVq9OkamUaVq6s0ma3lejYWE5cvYbPufNsP3GSk9ev687NIATd3nmbMV06kcuK1+FZTAyf/zzLWrf6yVJKbe27NIrJ4LwClLJ8LaOTE7N696Lr2/qedVDSL/rNXaB7eASlNqHZW2/SpGoVGlapRKmCBZ9rvbFxcZz288P33AV2nvybQxcvWVV1a1W7Fj/1+Mzq35G1GigT66WU2p1Q0zBCiCOAKu9FCMHwdm34tkM7q9df8r9Nv3kLOHhBX/0lo5MTTapW4d03XqdR5UqUf+2154qgSCm56H8b73Pn2XPqNPvOnLXaGK5B5UrM6NWTskW0FfHimf3nNms9Og5KKdNG0WIyEEKsBDpqvda7+ftM8uxu9QDrf/8+gxcs0u07Bco9sW7FCjR9oxoNK1eiqkeJ564VuxZ0B59z59h3+iw7T/6t1/wOUNI/Z3zRU1dYJJ7VPr58OetXPaP5Funo4BqPEOJHYKTWax/WqsGiAf2sRjsehIYyculylu/zttqT5q3SpWj21ps0rFyJ6mVKmzU+Tg637z/A59x59p05y9YTf1lV6ytVsCBTP+9hNd0blBTS9hN1BUYeA8WllNoqAGkUIUQNlEO3yhKrWbMmc+bMsRrtCA8PZ+bMmSxZsoQYK0qXZcqU4e2336Z27dq88cYbz53e9eDBA44ePcrhw4fZtWuX1Q7z+fLlY8SIEbRooV+HCkr/Ek9PT5VcsIlzQIPkqKglyygBEEIURKmgV+Vaubu789tvv1G7tnUnRmhoKLNnz2blypVJdrcUQuDh4UGpUqUoUaIExYsXJ1euXLi5ueHm5oaTkxORkZFERETw+PFjAgICuHHjBjdv3uTSpUtaxTaq92/SpAlDhgyhZEnraUb37t3D09OTS5c00x+igVbpIQVEC9O+XkejQDpTxozM+6YvbevpR49AKQ6fuXkLs/74U9erk5gS+fNTvuhrlC5ciDKFCpE3e3bcXbKQzdWVjE4ZiHz2jLDIKB49CeP2/ftcDQziWmAQZ2/d1Kx5sKR+pYr82OXTJB+CTyIiaT9xkq5cI7BESvlZkh+YBrFmcAohmNi9m64MZzwxsbEs2LmbKRs26kaiElM4d24qFH2NskUKU7pwIfLnyIF7lizkcHcno1MGnkbH8CQiguDwCG4/eMC1wECuBd3h7M1bmjVAlrzu4cHozh2TfAg+i4mh18+/WOul4yOlbJTkB6ZBTAbnZUDzj/ubVh8yrmtnq0ZEfI3OuNVrdSNRicmbPTuVihejdKGClClcmEK5c5HNxYXsbm44Z3TiWUwMoeERhEZGEvTwEVdN+3r+1j82KfOVLlSQbzu2T/I+EyclwxctUXV4T8RVoHx6O7jGI4TwBTQNqvYN6jP3f32SPGzuOPk3o1essklhLbubG1VKFKdM4UKUKlSI1/LkIYebK1ldXcnsnJGY2DiCw8IIi4ri7uNgrgUGcjUwiAv+/rq9rRJTOHduhrT9mO7vvpOk8TNj0x+qvjSJuI9ycE3zadFaCCGWoiMj37hqFVYPHYS7FYcoKGlxo5at1E3BTIxblsxUKV6CMkUKUbpQIV7Lm5dcWd1xd8mCS6ZMxMTGERoRQVhkFPdCgrkWdIdrgUFc9Pe3SXExV9asfPNRS77+sEWSQhlrfA/wxczZeoZmOFA6jTS/TDZCiOaAF6D6JVSsWJGFCxcm6Vi/cuUKU6ZMwdvbutEJishUuXLl8PDwwMPDgyJFipAzZ05cXV1xcXEhNjaW8PBwwsPDefToEbdu3eLmzZtcv34dPz+/JN/f1dWVLl260Lt3b9zd3a3OPXjwIF999ZWeoq4fStZQ0g+XRCTbKAEQQpQGfACVSzRjxowMGjQIT0/PJL1qjx8/ZtmyZSxZsoQQB8vJZsiQgUaNGvG///2PSpUqJTn/+PHj9OvXT6/hTSzQXUqp6qqdnjDlv54CVDFHIQTffNSSHzp3SvKBGBYVxZI9+5jutcmmQ2xKU7tcOb7r1J6GlZPe13O3btFlynSuBQbpTdkppbSeG5TGEULkQzE4NV02nzZuxPRePVVN2SyxpWbHniSn5uGfe/fpOmUaf13TjaKdl1I6pijGTgghsgA3gQJarzd98w3m/68vubNZz0u2pWbHnpQv+hoDWn1kU83Dg9BQes6YxW6LfkOJuAN4pDW57uQihDgPaKYd1CxbhsUD+1E0r7ZQR2KSqtmxJ8Xy5aVPS9tqHsKiovhmznxNpUQTT1AUmdKmPrmNCCF2Apqa1mWLFGbZoAG6ipCJOXzpMtM26tfs2JM82bLR6/2mfP1hiyTTdqNjY/l+6XJmbdmqt85nKHWaab9hhxWEEF2ARYDqBlagQAGmT59O9erVk3yfK1euMH/+fLZs2aKbTmUv3NzcaNOmDb17907SiJJSMm/ePKZNm6a3zjsoERL9NBYdnssogQSp4J2AphRP3bp1mTp1qk2pV2FhYezYsQMvLy9OnDihWfyTUhQvXpxWrVrRqlUrm+TXpJQsWbKEiRMn6oXXnqFI/6b9zpA2YFL4OYXOAfbNUqVYOqg/xfNrN5FMTFR0NH8eO8Eqbx/2nD5jNWXjRSmcOzcdGtanU6OGNqt+rdzvwzdz5+vmYAN/SCk/SrFFpiImw+Q8GpKyAGUKF2bZoP5WlaviiYmNZfep06zy9mXr8RNWUzZelNzZstKufj06NmrAm6VUWWiabD3+F1/Mmm0tWncGRZowXXrSEyOEyIQSIte8DxfOnZvFA/vpNpFMTJyUHDx/gZU+vmw6ctSunaSzurrQqnYtPm3UkHoVK9iUFnbwwkW6T//ZmnfeD6icXj3piTFFwvahUcMJivT1r316W1WuSsxf166zytuHdQcP6eXzpwgumTLRokZ1OjZqwNuvV7WpsP5KQCCdJ0/jor+/3pRHQKX06km3RAixBtDMr8zi7MyYrp11u59bcsn/Niu8fVjre5BA7fSZFMHZyYl336hGx0YN+KD6WzYV1gc8eEi3qdN164tQIiQ10rtBEo8QohWwClDlVjk5OdGnTx/69u2r22wwMQEBAXh5ebFp0yb++cd+ysgZMmSgZs2atG7dmqZNm+Lmpl8PFM/jx48ZPHiwZgsNE35A0+cxSOAFjBIAIUR+lA6Xb2i9XrBgQcaNG6dqpGiNoKAg9uzZw5EjRzh+/PgLR1CcnZ2pWrUqderUoUGDBrz+uu2yl7dv3+bbb7/l8GHdOoMQlJQt7xdaZBrDtK8X0JAyBMjp7s60zz1p18D2fiT3Q0L48/gJfM6ex+f8eU1d8+TglCEDr3t40LBKJd59vSr1KlW0mmudmH+Dgxm8YBEbDlkt/ZkupRzwQotMY5hSuS4AxbVed82cmR+7dubzZrb3IwkJD2fbiZPsP3sO3/PnuX1fv1bMxjVSoehrNKpcibdfr0qT16vanBcdGhHBqOUrmb9jlzXv4UYp5ScvtMg0hukAexTQdMVldHJiaNtPGPhxK5v7kUQ8fcqOk3/jffYcvufOcy3oxc+DpQsVpGHlyjSqUplmb71hs+hFVHQ0k9dvZMoGL2uOjaMoqQLp3tBMjBBiE6DpGBFC8OUHzRjVqaPN/UiexcSw78xZ9p46g8/581z0v/3CnvaiefPSoHJFGlepzAfV37JZ9CI2Lo4523YwatkK3UaRvESGZmKEEDNQGvFp0rZeXSb37G6z0ESclBw4f4Hdp07je+4Cp/389MQfbCZ/jhw0rFyJBpUr0rJmDfJky2bTdVJK1vgeYOCC3wkO003HfYBiaKbtVvXJRAjRBCWVS/OXVa9ePcaOHZusfiSnTp3C19eXI0eOcPr0aau1J7aQI0cOatSoQe3atXnnnXcomIwaUG9vb7799lvd4nzgL6D5i0Q0X8gogYTi9w3AO3pzmjVrxsiRIylQQDPLQJe4uDguX77M1atXE+pEgoKCePz4MREREURERBAdHY2bmxvZsmXDzc2NfPnyUbJkSUqUKIGHhwdVq1a1WriuxbNnz5g7d65u/xITQSi/fN08gvSMEMIdxbOu6zpvWLkSM77oSZnC1gtStbjkf5vz/v5cDQjkWmAQt+7d49GTJ4RFRhEeFUXks2dkdXUhu6srbllcyJ8zR0Iue5nChahepnSyFZ9i4+KYv2OXbv8SExIYLKWcmuwfKh1gOsCeQMeRAFCtpAc/f/m5zZGJxNy4c5ezN29xLSiIq4GB+N25q+xrVJTyLzKK7G6uZHVxwS1LFvJmz07pQgUpXbgwZQsX4s3SpWx++CVmre9Bhi9eqtfNO55ZUsr/JfvN0wlCiC2AblViqYIFmf5FT5pUrZLs9w58+JC/r9/gWmAQ14LucD0oiAehTwg37WtIeDjZ3dxwz5IFd5cs5M6aldKFlVz2UoUK8mapUlZlffXYfeo0A+cvTKrmZZOUUqVG9rIghPgV6K33esFcOZnY/TOryoJ63A8J4eT1G8p9OEip2bsfGkp4VBRPIiMJCY/A3SWLaV9dyOXuTslCBSlTSKk/qepRAo8C+qo8ehy/epVv5sxPqublOFD7ZTM04xFCDAUmoCEDDZDD3Y0fPu2EZ9N3bXa4xRMSHs5f165zNVC5D18NDHWmMTwAACAASURBVOJecAjhUZGERETwJCISl0yZcMuShawuLuTM6k6J/PmV72zhQlQuVuy5+oxdvh1Av3kLNPuXJOImikHyUhma8Qgh3gC2opNW6+LiQu/evfn88891O6LrERkZyZkzZxLOwzdu3OD+/fuEh4cTGhpKeHg4zs7OuLq64ubmRo4cOShcuDAlSpSgZMmSlClThrJly9oUrUlMUFAQY8eO1exfkohdwCcv2sz0hY0SSGgS9AMwHA09blCKZ/r27UuXLl2SbSQ4Cikle/fuZeLEidyyojYE7AE6v2xWviWmA+x6NORH48mUMSNff9iC/q0/ImcSRVGpyYHzFxi2aGlSOfMRKP0q9jtoWamGEGIW0AedB2IGIejx3rsMa9eGgrlyOnZxyeC0nx/DFy/DV1+kABQRim5SSl1N4JcF00FnPDr3YVCkO0d92pGSBZPnJHIk14Lu8MPylbpS4ybigCEvqwMhMaac9YVoFNPG06RqFcZ/1oXKVnqGpTaBDx8yfs06lu7ZZ01ZTwIzXrZItRam/jSb0WicGc+bpUoxoXtX6lYo77iFJZNHT54wdeMmZm/Zqis1bmKdlNK6NOBLgBCiALAC0JW39PDwYNiwYTRu3DjVmpsmRUREBEuWLOHXX3+1JkoVB4wFxkgpXzhHP0WMkoQ3U0JXy9EogI8nZ86cdOnShW7dupHdDhr4z0NcXBze3t7MmjWLc+fOWZsai/LL/zElfvnpBSFEZ5TO77oPRPcsWej6dhMGfNwqTR1iD1+6zLjVa/E+a3VfAS4BtdKbJOGLIIR4D9iElQdipowZ+aReHYa1a/PcUr/24OjlK0zZ4GVLoWcQUEdKab/E3DSGSbDCF530S/ivuenIju143UO/QaqjuejvzzSvzaw7cCipGrTHQJOXNVKthRCiMHAYsFoJ3bhqFb7r2J6aZTXLjFKFf+7d55c//uT3XbuTqkGLAD6UUu510NJSHVO2iS9Q1dq82uXKMeDjjxza3DQpHoSGMnfbDn7ZspVQbQWmeGKA3lLKBQ5aWqojlE0aAoxDowA+nrJly9KzZ08+/PBD3WbdjiY8PJx169Yxd+5cvWaI8dxHqanWbNr3PKSoUQIghCiEcoBtam1e1qxZ6dChAx9//DGlS1uXbLUXjx8/5s8//2T58uXcuHEjqel+QA8ppWYL95cdIUQxlB41xa3Nc8mUic5NGtG5SWPeKp389J+U4ElEJJuOHGXu9h2cupGkmlAcMDW99SBJKYQQOVD21eoD0dnJiU/q1eWzd5pQt2KFZKcTpATxwgkLd+1OKjICird1pZSyswOWluYwFcBvx4qnzjSP5tXfovt77/COjYXJKU28cMKi3XvYduKkLTUOe1Cacb1YcnU6RQixCmiPTpQznoaVK+HZ9F2a16jusI7fiYkXTli8Zx8bDh22Rejkb6Dxq+QYSoypeWZ/rEQ5Ad4oVZIv3m9Gq9o1k5QQthcnrl5j+T5vVuz3tlYPFI8fihJToAOWluYwOesXksTZqWTJknTu3JmWLVuSI0cOh6zNkqtXr7Jx40bWrFnDkydJCmJsAzyTK/mbFClulCS8sRBtgOlAkomJlSpVolWrVjRv3py8NsgcvghRUVEJXSx9fHyITlo56CkwCZggpbSfHE06QQgxCMXyT7JKtUzhwnzauCFt69ejWD777uuzmBh8zp1npbcPW44et+VGCYpqUctXyYuuhyk95Dc0mkBZUjRvXjo2akD7BvWTbHD3osTGxXH08hVWefuy4dDhpLxx8fyDIkDxynjR9TBFw1ZiJWoST74c2WlXvx4dGjbgdY8SdvXGSik5dcOP1T6+rD1wyKY+JijFsR1eJS+6HkKIN1EKal9Lam52Nzc+qVubjo0aUrNsmedulGgrl/xvs+bAQVb7+NoqfBEG9HoV0iuTQghRAtiCjhx0YlwzZ6ZlzRp0atSAhlUqP3ejRFu59e891h04yEpvX64G2mRfPAWGSymn23Vh6QCTyMy3wCCSODs5OzvTqFEjWrduTYMGDZ67UaKt3Lt3j23btuHl5cWFC1ZrgeK5DfSTUm60x3rsZpRAQrH0D8D/sJL6k2g+pUqVonbt2tSuXZvq1au/sMX47Nkzzp49y5EjRxLUC5JqqJiIXUBfKaV+K/hXENO+bgTetfWakgULmJQ8KtGgUkXyv+C+RsfGcvbmTZOa1wWOXLpkU0NFE+HAl1LK5S+0iJcMU23YMmzwwsZTOHduGlapRKPKlahfqaJNvROsERsXx+XbAXifO4/PuXMcvHDJpoaKJp4BI16FGoPkIoSYDnyNlTSCxOTNnp2GlSvSoJLynS1VsMALGSlSSq4H3cHn/Hl8z13A59x5HoTa7BCPRakxGPTcC3hJMdUQjcEGJxEoBkr9ihUSvrNlixR5YSPln3v3OXD+At7nzuFz7rxNDRVNSJR07x6vatRLDyFEN2A2NjiJQGmUWLt8eRpVrkTDypWoXKL4Cxspdx8/5sCFi8oz9tw5/O4mq4R2O9DmZS1mf16EEGVR9vVtW+ZnypSJatWqUatWLWrXrk2VKlXIZKNqoR7BwcEcP36co0ePcuTIEa5ds/l4G40SaBgjpbT5oZxc7GqUJHyIEB7AUKAbYL1DmwW5c+dO6FxZokQJsmfPjru7O1mzZsXNzQ1nZ2dCQkIS1LhCQ0Px9/fHz8+PmzdvEhgY+DxNaPYDY6WU+5J74auEEKIKsAB4CxsPsfHkdHenTOFClClSmNKFCpEnWzayurqQzcUFN5csZHHOREh4OOFRTwmPiiI4PJx/7t1TVJ0CArn1772kCuq0CAdmAd++rIouKYEpVe93oDHJ3Nesri6UKVSYUoUKUrZIYfLlyJ6gyuSWJQuumTPzJCKCsKgowp8+JSQ8nNv3H3A96A5XA4O4cecOT5Pf9+QZsBT4Or03zbMnQog8wFwUidlknVhcM2c2qWkVpFShQhTOnZvsbq64mfbVPUsWZU9NCmuhEREEPnzI9aAgrgYGcT3ojrV+QHrEokQDvpBS2nzSfdUweWFnonQLT9aJJbOzMyULFjR1cy/Ia3nz/Pd9zZyZrK6uRDx9mqCyFhwWzv2QEC4HBHA96A7XgoKep59NHEoPlh5SytvJvfhVweQkGo8iSJIsqUlnJyeKF8hP2cLKvbhYvnzkcHMzfV8zk93NjajoZ4RHRhEaGUloeAQPnzxRlLoCgrgWFGStz5MeEkUxraeUMsn82lcZIcQ7KJGTRsm5zsnJKUFNy8PDg6JFi5ItWzZcXV1xdXUle/bsREdHEx4ezpMnTwgLCyMkJCThPOzn58fD5PezeYrSGPInKeWt5F6cXBxilCR8mNL/oj+Kxy55eq6O4RDwvWGMJA8hRGlgPtCAZB5iHUQoykN7lGGM2I6p4eIc4EOSeYh1EFH8Z4zYHP581TFFOqcCn5HMQ6yDiEFJYekhpQxO7cWkF0yH2FHAANLm8zUOOAB8+qrWFzwvQoivUER20o6KzH9I4BiKImmSxbkG/yGEqAsMA5qT9s5OT4ElKMJOAY76UIcaJQkfKkR2FG9dF5QwVmpuRgCKdNsiKaVu61GDpDEVTX8PdAKSL16fskjgMvCLlPLXVF5LusZ0iB2KcohNvnh9yiJRdO7nAlMMI/P5MR1iewF9gXKk/kMxAFgMjDMiXi+GSTFxEFCZJAqnHcC/KLK3w42I14shhPgI5RBbg9Tf11DgD2DQy94ewd6Y0ro6Ap2Bkqm8nJMoadwrpJQv1g35OUgVo8RsAUKURNmI5igN3Rzhkb0J7EYxRg7I1P4lvIQIIaqh5Do3QKe7qR2IQ9nbJSihRsN7nsKYomJjUZqlJr8b3vMhgUBgDUo+6yupzmNPhBAFUb6vLYF8OMZAkcA9lAPr98bBJuVJ5ChqCxTGcYbnQ5Rn7EjDe57yCCGyoDiKuqKoOjnKQAlBkS8eJaU85aDPfGUw9YarD3yKUrNb3AEfG4uifPcnsFxKmaRkqT1JdaMkMaYbaEMUGcv6QHngRaUHYlHUeI6i5LHuk1LefMH3NEgGpjSgXijdpiuiFO+lxMMxBsULdwhYKqXcmgLvaWAjJn39HsDHKJLCWUmZfY1DUVo6iqIctcEohHUcpgNPF5SD7JtADlLm0BOH0l/kb2AtygPQiIg4CFNkrC3QAagF5CFl9lWieM3PABuAxYbjwLEIIZqjGCj1UJwKGVPgbSVKHeYFlIjIAinlvRR4XwMbMdVjN0Y5E9ciZQzQKJS+bL4oZ2IfKaVN8oeOIE0ZJZaYrMaiQFnTv2Io+bLW2IrSYOqK6d81KWWyKywN7IsQojqKAfom4AFUw7pCWxBKOtY5lPzV3akRWjSwjhCiEsoN9C2gFIqxYi2//QFwEeXBdwzYY+Sbpz1MEe34B2MZlLQga91vQ1C+q1cxOYQMj3naQwjxGv/tawXTvzxWLolAMT6uAyeAvVLKi/Zep0HyMDkC3wZqAlVQzk+FrFwSDZxC6SlyEuWgesLe6zRIHkKIzCj33zIoe1oHJcvIGtOAWyjn4auAf1pOe07TRokWQoikFtxKSrnZIYsxSDGEEP5Y19z/Wkr5i6PWY5AyCCEOAnWtTJn8qjauTM+YGvh1sDJltZSyo6PWY5AyCCEmAYOtTDkkpaznqPUYpAxCiL4oypN63JZSFnXUegxSBlON0SZrc6SUqV0rmCxSu1DKwMDAwMDAwMDAwOAVxzBKDAwMDAwMDAwMDAxSFcMoMTAwMDAwMDAwMDBIVQyjxMDAwMDAwMDAwMAgVTGMEgMDAwMDAwMDAwODVMUwSgwMDAwMDAwMDAwMUhXDKDEwMDAwMDAwMDAwSFUMo8TAwMDAwMDAwMDAIFUxjBIDAwMDAwMDAwMDg1TFMEoMDAwMDAwMDAwMDFIVwygxMDAwMDAwMDAwMEhVDKPEwMDAwMDAwMDAwCBVMYwSAwMDAwMDAwMDA4NUxTBKDAwMDAwMDAwMDAxSFcMoMTAwMDAwMDAwMDBIVQyjxMDAwMDAwMDAwMAgVTGMEgMDAwMDAwMDAwODVMUwSgwMDAwMDAwMDAwMUhXDKDEwMDAwMDAwMDAwSFUMo8TAwMDAwMDAwMDAIFVJN0aJEMJFCFHGhqlFhRC57b4ggxRBCJFJCFESyJTE1EJCiPyOWJPBiyOEyCiEKAa4JzE1nxCisCPWZPDiCCEyCCFeA3ImMTWnEKKIECLdPGNedUzfw3xJTHMXQhQVQmR0xJoMXhzTc7NQEtMyCSE8hBBJPYcN0gimc25RG+aVEUJkccCSUgQhpUztNagQQlQAGgAVgLJAGZRffnIecA+AK4n+HQWOSimfpexqDWzFZHw0RNnX8ij7WhxIzgMuGLiKsqeXgb+Ag1LKiBRdrIHNmA4zjYHKKHtaDigJOCfjbcJQ9vUqyr7+DfhKKUNSdrUGtiKEyIvyfa2Gsq9lUO7HmZPxNlH8t69XgNOAj5Tyfsqu1sBWhBDZUfb1Df57vpYF3JLxNs+AGyjf1avAeWCflDIoZVdrYCtCCDegLlAdZT/j/2VPxtvEALf47/l6AeX76peiizWwGSFEZqCW6V/887UskBznexzgz3/n4YvAASnlxZRd7YuTJowSIUQR4H2Ug01joICdPioCOATsA3ZLKU/a6XMMACFEHpR9bYKyr8Xs9FHPgGOY9hU4IqWMs9NnvfIIIbIBzVD2tAnKjdIexAInUfZ1H7BfShljp8965RFCuADvAG/zn5Ep7PBREjjHf/u6W0oZZYfPMQCEEM78911tgmKMONnp465g+q4CO6SUT+z0Oa88pihkHZTvbBOgJklnHDwv//Dfvm6TUj600+cYAEKIt4B3Ufa1DuBqp4+6y3/7ul1KGWinz7GZVDNKhBDuwMdAF5RffGqE+S8Dy4DlUkr/VPj8lw6TVd8C6IpikCTHW55S+PPfvl5Ohc9/6RBCOAHvoXxfWwEuqbCMe8AqYKmU8u9U+PyXDiGEAOqhfF/bkjyvakoRDKxD+c4elGnBU/YSIIR4E2VfO5B0WpY9iAC8gOUohmdsKqzhpUMIUQ7lPtwZG9J37MAzYDuwFNgqpXyaCmt46TClO3dG2duyqbCEOGAvyn14o5QyPBXW4HijRAhRERiE8gBMTrjYnsQBPsDPwB/GQzH5CCGKAwOBT0k639yRHAd+AVYZXvbkY8pH7gd8hv0imM/DBeA3YKHhZU8+phSer4DPgRKpvJzE+AELgNlSytDUXkx6wxTt8gR6o6TJphXuAIuAn6WU91J7MekNUw1PJ6APUCOVl5OYR8AKYJqU8lYqryXdYXIKfQR8g1KykFZq8MJQHEVTHJ3i5TCjxBSOGoGyAcn+xTs5OVGkSBFy5MiBu7s77u7uuLi44OzsTFhYGE+ePCEyMpKwsDD8/f2JjIx83qWeA8YD6wzPTtKYvDbDUG6YyY6KZMiQgUKFCpEzZ06yZcuGq6srrq6uZM6cmSdPnhAeHp6wrwEBATx58tzZAH7AT8ASw7OTNEKIoijOg548Z1SkQIEC5MmTh2zZsuHi4oKrqytubm6EhIQQGRlJREQEYWFhBAUFERwc/LxLvQtMBeZIKcOe901eFUwplf2AvjxnVCRPnjwUKFAAd3d3XF1dcXFxIWvWrAn34Ph9vXv3Lg8ePHjepQYDs1AOsUaqSBIIIbKiGCIDgOcSBMmRIweFChUy29fs2bMTHh5OREQEkZGRhIaG8uDBA+7evfu8S40A5qMcdgKe901eFUyZB92BITyn8yBr1qwUKVIk4czk5uZG1qxZefr0KREREURERBAaGsrjx48JCgoiLu65Mp+jUYyTCVLKq8/zBq8SpsyD9sBwoNLzvIeLiwtFixZN2NesWbPi7u5OdHR0wpkpLCyM4OBgAgICiI19ruNsHLAJGOeo7AS7GyVCiErAZJQcdJtwdXWlevXqVK9enZIlS+Lh4UHRokVxdrb9zBsUFMTNmze5efMmp0+f5vDhw9y7lywHzTXgWynluuRc9Kpgioz8BLTBRiMzc+bMVKtWjRo1alCmTBmKFy9OiRIlyJzZ9rrZ+/fv4+fnx82bNzl79ixHjhzh9u3byVl6IDAGWGDUnagxFTePA7phY36yk5MTVatWpUaNGpQrV44SJUpQokQJXF1tT4N9/Pgxfn5++Pn5cfHiRY4cOcL169eTs/SHKPeZ6YaYhRrToXUkiqfVpgh1hgwZKF++PDVr1qRChQoJ+5otWzabPzc0NDThPnzx4kWOHj3K5cuXk3PwCUOJdI4zjE41pkPrABQHQi5brytVqhS1a9emQoUKeHh44OHhQc6ctge4IyIiEvb18uXLHDt2jLNnzybn4PMMWAh8L6V8bsv1ZcVUL9IL+I6klbMSKFq0KLVq1aJKlSqUKFECDw8P8ubNa/PnPn36lJs3b3Lr1i2uXr3KsWPHOH36NE+f2uzHiwPWAMOMlHhthBDtgbFAKVuvyZ8/P7Vr16ZatWoUL14cDw8PChYsaPNnRkdH4+/vz40bN7hx4wYnTpzgxIkTyXXebwMG2ztyYjejxFQzMgolLJWkNVG6dGk++OAD6tSpQ9WqVcmYMeUVB/38/Dh69Ci7d+/m8OHDtt5AdwF9pZTXUnxB6RCTZOAg4FtsKL4qUqQILVq0oG7durzxxhvJMkBsJTAwkCNHjrBv3z72799PdHS0LZcdA74yahMUEj0Ex2ND+l2+fPlo3rw5devWpUaNGskyQGzl/v37HD16FG9vb3bt2mXrDfQy0EdKuS/FF5ROEUK0A6YBSUovZ8+enQ8++ID69etTo0YNcuTIkeLrCQ4O5tixYxw4cIDt27cTEmKTwNrt/7N3nWFRHW30zC4oYMNeAopBjcaImoglGk2w1wgxEqOxo2LDnkSRYo2FWLChImpQYwVbNNGgJraoUcGWGBs2FBsWisIy34+78HHvzCwL7i6wy3kefuzc2d3hvntn3npeAGMppdsNvqACCkJIGwBLoQfRhJ2dHdq1a4dWrVqhadOmOVJU9UViYiJOnTqFY8eOYe/evXj0SC+CtSeQvMWhhU4iCdqskuUAGmU3t0iRIvjss8/g5uaGpk2b4p13DM+unpKSgrNnz+L48ePYs2cP7t7VK8CVCGA6pLQuvQ5kcwch5D1IDpY22c1Vq9Vo3rw52rRpg2bNmqF6dcNn2KalpSE6OhrHjx/H3r179XUCpkI6S6Ybq+bEKEYJIeQLAAsBOOiaV6ZMGXTt2hXu7u744INcRbByjfj4eOzatQsRERH4999/s5v+GsBcALMsOX+dEPIZgGWQKOmEKFGiBDp06AAPDw80atQIUtqkaZCQkIC9e/ciIiIC58+fz266BtLm72vJ1LOEkA8BrIBEJSmEjY0N2rZti+7du6NFixZQq41F4MMiKSkJ+/fvR0REBP766y99PO0bAYynlOY6z6SggxBSE5LS2lbXPCsrK7Rq1Qru7u5wc3NDkSKma1Xw5s0bREVFYceOHfjjjz+QlpZt2dd+SE6i6yZYXr4EIaQygAWQ0j+EUKlUaNq0Kdzd3dG+fXujOA5E0Gg0+PPPPxEZGYmDBw8iJSXbY/MkAG9KababtrmCEGIPySk0FNlkHzRs2BDdu3dH586djeI4EIFSijNnzmDHjh3Yt28fXr3KNnh5GZLz74gJlpcvoa3zmgJgIrLJPnjvvffg4eGBrl27okIF03JTXLhwAREREdizZw+ePn2a3fTbAHwopZGGXodBjRJtg5Y5AEbrmufg4ID+/fujV69eRvGc5xRnzpzBypUrERWVrXP1EgBPSuklEywr30BbZOcLKZQs3CzLli2L3r17Y8CAAShRooTJ1ifClStXEBoait27d2cXFYsF8BWl9KSJlpYvoC2yGw3J4BZulsWKFUOPHj0wbNgwo3hYc4o7d+5g7dq12LRpE9680Zmp9QhAP0rpPhMtLd+AENIHksEtbF5ZpEgReHh4YMSIETlKBTAWHj9+jLCwMKxfvz67qNhLSArsBhMtLd+AENIaEpuVkHTCysoKXbp0gbe3N5ydnU23OAESEhKwfv16rFu3LruoWBqkc2aupZHNaJnSNkPq78SFSqXCp59+ihEjRqB+/fqmW5wASUlJ2LJlC1auXJldajyFVB82wdKiJtqG31sA6BTYRx99hKFDh8LNzc00C9OB1NRU7NmzB0uXLsWtW7eym/4TpL3YYFETgxkl2oaHWwDUFc1xdnbG8OHD0aVLF5N6WfXF+fPnsWzZsuyMk5cAhlBKfzbRsvIU2u7NmyA1ZeKicuXKGDZsGHr06JEvjEwl/vvvPyxfvhx79uzR5WF/DamYMNgSDkRCSBkAawF0Fc0pXbo0Bg0ahD59+qB48ewas5sed+/exapVq7BlyxZdKXvpAGYDCLAE9jVCiB0kBWCgaI6dnR369u2LAQMGoGzZnPTfMg1yYJysguStyzWrSUGB1jE0HcC3EPSOsba2hqenJ7y8vIySxvO2ePnyJcLDwxEaGpodsUUkgIGU0mcmWlqeQesY8oHkzOU6hlQqFbp164Zhw4ahRg29yxBMhpSUFGzduhUhISHZESD8CaBXfuiFYQoQQnpDykAQHp6tW7fG8OHD84WRqYRGo8GuXbuwbNky3Lx5U9fUCwB6Gqr9gkGMEu3ND4GggNLOzg6jR49G//79c1UrQilFXFwcbt68mcnUk8EakZaWJmMeKF++PJydnXNcGJ8Vf/75JwICAhAbG6tr2goAo83Z8ieEtIfEqMHVXKytrTFo0CCMGDECtra5a1sRHx+Pmzdv4vbt23jx4kUm21ZKSgrs7OxQsmRJFCtWDOXKlctVYXxWREdHY+rUqbh8WWed1g5I3nWzLaolhLgC2AYBx71KpYKnpyfGjx+f69SAjML1W7duyeT66tUrFC9eHCVKlICdnR3KlCmTq8L4rLh+/Tr8/f1x8qTOQNcfAL40ZzpSbbrWDuhgc+nYsSN8fX1RsWKuCJpkhesZ+3BiYmKmXIsVKwY7OzuULl0683nNSWF8VsTFxWHGjBn49ddfdU2LAeBhzulchJBKkOg5W4jmNG/eHP7+/nj33Xdz9R0Zhes3btzAs2fPkJSUhJcvX2bKNYO1qVSpUqhWrVqOC+OzIiEhAXPmzMH27dt1OYluAfjCnGv+tOQTP0FiJOWiXr16CAwMhIuLS66+I6Nw/ebNm3jy5AkSExPx4sULJCUlwcbGRiZXR0fHHBfGZ0VycjKCg4OxZs0aXWmYjyEZJgdz9SUFANq62yWQ6Na5qF69OgICAtC8udDXqxNZC9cfPXokY6C1srJCsWLFYGtrm8mol9PC+KxIS0vD6tWrsXTpUl1OolcAvAzhrH9ro4QQ4gOp8IWb1uPm5gZ/f/8ceW6SkpJw+vRpnDx5EqdOncLVq1dzTPGrVqtRtWpVfPTRR2jatCmaNWuWo4M4LS0N4eHhCAoK0vXdByEdiGbXtVZraIZBQFLQuHFjBAYGombNmnp/5uvXr3Hu3DmcPHkyk4VHj5xUGTIohD/88MNMuTo6Our9/vT0dOzcuRMzZ87U5a07A6ATpVSvSs2CBEKIGyRPJDe/rk6dOpg2bRoaNmyo92dqNBpER0dnyvXy5cu5ovitXLkyXFxcMuWaU69gVFQU/Pz8dHnrbgBoTynNEa1XQYA2/eMXCJrkVa1aFf7+/mjVqpXen5meno4rV65kyjUmJgZPnuScnbdcuXKoV68emjVrhqZNm6J27dpQqfRnhT9x4gQCAgJw/brQ7ngIoCOl9FyOF5fPQQipDuBXANyNtkKFCpg4cSK6d++eo9q9//77L1Ou0dHRuaL4tbe3R926ddG0adNMxqecZEBcvHgRfn5+iImJEU15BaAHpVSnVVoQoY1U7wXQlHe9ZMmSGD16NL755psc3dPbt29nyvXs2bO5ovgtUaIE3nvvvczntUGDBjlyBN68eROBgYE4evSoaMobAP0ppZtytLACAEJIlQTpMgAAIABJREFUMUgOhI686zY2NhgyZAiGDh2ao3v68OFDnDhxAidPnsSZM2dw586dHFP82traolatWmjSpAmaNm0KV1fXHDmTHz58iHnz5iEyUlhGQiGxrs3N0cIUyLVRog07zoYUTmZgZ2eH6dOn4/PPhU4AGVJSUnDw4EFERkbi6NGj+hQ85hi1a9dG9+7d0a1bN72LiK5fv47Ro0frKoY/DUmBNRtaQ0LIKEhEBYzmoFarMW7cOAwZMkSvQzAtLQ1//PEHduzYgUOHDuWEWlBvODk5oVu3bnB3d9fbQImLi8OYMWPw999/i6Zch6TAmo0HlhDiDqkA3IZzDX379sX333+vVzQzPT0df/31FyIiIvDrr78iMdHwRByVKlVC165d4eHhobfxm5CQgIkTJ+LQoUOiKQ8gKbBmU1BLCPkUwE4A3JBE9+7dMX36dL0PoPPnzyMiIgJ79+59m/4xQpQuXRqdO3eGu7u73mkLKSkpmDdvHtatWyea8gqSg+iAodaZ19DS6e+HgDXNzc0Nc+fO1TuaefXqVezYsQO7d+/Gw4cPDbhSCcWLF0f79u3h7u6Oxo0b62V4ajQaLF26FEuWLBEpz28A9KWUbjb0evMK2s7dv0LQtbt+/fpYtGgRHBx08gRl4s6dO4iIiMDOnTuzy+7IFWxsbPDZZ5/B3d0drVq10stIopRi3bp1mDNnjii1lgKYRCmdb+j15hUIIaUB7AHwMe+6s7MzFi9ejPfe069Ze3x8PHbu3InIyEh9yJhyDCsrK3zyySfo3r072rRpo7eRFBkZCT8/PyQlJYmmLAYwJrdp8LkySrSNX0Ih9TJgUKdOHSxatEivUPKdO3ewevVq7Nq1620a4+UIarUaLVq0wODBg9GsWbNs5ycnJ8Pf3x87duwQTbkMoJ055EoSQmZBomhk4ODggMWLF+sVSn706BHCwsKwffv2XHlXcwNCCBo1aoSBAweiTZs22RpNaWlpmD9/PkJDQyF4Du5BkqtJO5oaA4SQ4ZBqDRhNoUyZMggKCsInn3yS7ee8ePEC4eHh2LRpE+Li4oywUj7q1q2L/v37o1u3btkeipRShIaGYv78+SLnRgKArpRSoSuvoIAQ4gHJ0GROlJw4hlJSUrBlyxaEh4fjxo0bRlgpH++++y769OmDnj17wsaGsZUZ7NixA/7+/qLo9WtIqSERhl6nqUEI+QTAbnAaXFpbW2PSpEno37+/Xnvcrl27sHbt2uzSVg2KKlWqoFevXujTp49epCeHDx/GxIkT8ewZt4wkHRLN9wpDr9PUIITUhdRmgOk9QgjB0KFDMXbs2Gz3uPT0dBw8eBBhYWE4c+aM6PwyOMqWLYsePXpgwIABKFeuXLbzz58/Dx8fH9y7J1SNZlJKfQ26yDwAIcQBklzr8K5/+eWX8PPz08sxdPz4caxevRrHjh3LbcPDHKNkyZLo1q0bBg8erJcxrIezPgxSOleO/4HcGiUhkHoaMHB3d8eMGTOytbquXbuGFStW6MOMlAl7e3s4OTmhTJkymXUkgGQ0JCcnZ3aujIuL0/shbdiwIYYPH47PPvss27lbt27F1KlTRYrOJQAtKaXZcqnlVxBCfCEVUzJo1aoVFixYkG1++P3797Fy5Ups3bpV76hI8eLFUb16dZQtWzazizAgpXtlyPXevXu4f/++3r+VWrVqwdvbG506dcp2g4+KisKYMWNElv89AM0ppYZ3QZkIhJB+kDYJRoOpX78+li9fnm3k8OnTp1izZg3Cw8P1TrmztbWFk5MTypcvn9lFWKVSITU1FUlJSXj+/Dni4uJw584dvSOjDg4OGDJkCHr06JEtde25c+cwbNgwkVH8AkCrghwx0dZ87QKnQNbJyQkrV67M1jGUmJiIn376CWFhYXo7D4oUKQInJydUqFAhs5ZPrVZDo9Fk5jY/fPgQsbGx2bGjZaJcuXIYOHAg+vTpk21t0fXr1+Hl5YXbt7m92d4A6FKQIyZaiu5D4ES+ypcvjxUrVmQbYXr9+jW2bduGVatW6dtXAlZWVnB0dESVKlVQsmRJ2NnZwdraGunp6Xj58iUSExPx6NEj3Lp1S+906pIlS+Kbb77BgAEDso3oPHjwAMOGDcPFixd5lymkWr+f9PrifAhtw+Fj4BgkxYoVw6JFi/Dpp5/q/AyNRoM9e/ZgxYoV+O8//VqnqdVqVKlSBQ4ODihVqhRsbW0z9bPnz58jOTkZT548wc2bN/Xe221sbNCzZ08MGTIElSoJieAASNHrMWPG6ErnmkIpnaXXF+dDEELKQqpZfF95zdraGjNmzMAXX3yh8zMopYiKisKyZcsQHR2t7/cycs0wejLqS54+fYqbN2/q2wsKVlZWmaQK2Z0dKSkpmDJlCnbu3CmaspxSOlyvL86CHBslhJDpkGj7GPTr1w9TpkzRGbZ9+fIlFi5ciPDwcJ0KZkb372bNmqFx48aoUaOG3oV1ycnJuHXrFs6dO4cTJ07gr7/+ypZ3uVmzZggICMiWQvHYsWMYPny4KF3lLwCtjdVUxpgghAyBRFbA4PPPP8ecOXN0pvW8fv0aISEhCAkJ0WmMZHT/btasGVxdXVGrVi29U+nevHmDW7duISYmBidPnsSJEyeyTUOoW7cupk2blu0hfuHCBQwaNEj0O7kGoAWl1PA5D0YGIaQLgAgAjPCaNWuGFStWoFgxcYNvjUaDDRs2YMGCBTojmRndv5s1a4YmTZrgvffeQ+XKlfVO8bt9+zYuXryYmQ8tUDgz4eTkhICAALRoIaz9BSBFYvv37y9Ka3gESa5Xs11kPoOWrCAKHGaXDz74AKGhoTqZtSil2LVrF3744Ydsm9zVrFkzM7+8Tp06qFKlil4pHBqNBvfu3cusSzlx4kS2DboqVKiAyZMno0uXLjrnPX78GAMHDhR5/5MAtKGUnsh2kfkMhBBnAEfBofx1cHDA2rVr4eTkpPMzDh8+jGnTpmX7DFWtWjVTrh988AEcHR31St2klOL+/fu4evVq5vN65coVnbULpUqVwrhx49CrVy+d+kFSUhJGjBiBP//8k3c5FUB3Sukv2S4yn4EQUg6SXJncHXt7e6xevRoNGjTQ+Rnnzp2Dn58frly5onNeRvfvZs2aoV69enByctK791B8fDyuXr2KU6dOZdYb6dLTbGxs4O3tDS8vL53fkZqaikmTJmH37t28yxQSo+lqvRaZj6BlO/wNHHZSW1tbLFmyJNs6vv/++w/+/v44deqUznllypTJrN/K6Oyub0ru06dPce3atUy5njt3Lls9rV+/fvDx8dGpH1BKMW/ePKxcuVI0JZBSGqDXIrXIkVFCCPGG1DxPOY4JEyZg6NChOt+/Z88ezJo1S8hprVar8cknn8Dd3R2tW7fWK5yvDyilOHv2LCIiIvDLL7/gxYsX3HnW1tYYPHgwRowYofO7Y2JiMGjQIFGoeS+kjbPA0I8SQroB2A6O4tq3b1/4+vrqPEiOHj0Kf39/YT4rIQSurq5wd3dHx44dDUove/nyZURERGD37t14/Jhf1pPBJjVx4kSdkZ7bt2+jf//+osP8NAC3gsTKRQhpAuB3cFjx2rVrhwULFuiMaOrDVubi4oLu3bujS5cuKFOmjCGWDQC4ceNGZj6tjtA/OnXqBF9fX52G7aNHjzBw4EDRYX4DUiSswDRZ1LJsHQWnqL1JkyYICQnR+YzduHEDfn5+OtnKatSoge7du+Pzzz83aA+TuLg47Ny5ExEREboK19G8eXMEBgbqVMCTkpIwfPhwkQf2MYBPDEVTaQoQQipAkitTQFWrVi2EhYXpJGt5+PAhpk2bppOtzMHBIVOuhuwS/eTJE+zZsweRkZG4cOGCcF69evUwffp0nc2SU1NTMWHCBOzdu5d3ORlAW0rpsbdetImgZdk6BOAj5bV33nkHYWFhOr3Sz58/x5w5c7Bt2zah4Ve+fHl06dIFHh4eqFOHm0GUK7x8+RL79+/Hjh07dKaJVa9eHYGBgfj4Y245BQBJD5szZw5Wr+baHhpIPeC2G2ThJgAhxBpSLR9T1F6qVCmsWrUKH374ofD9+rCVlSpVCp06dYK7uzsaNmxosEbUKSkpOHDgQGYNt8jwrFixInx9fdGxI7duPxNr167FzJkzRb8PH0rpYn3XprdRQgjpAEnhZrTTadOm4euvvxa+NykpCX5+fsKq/eLFi6NPnz7o16+f0ZuzvX79Grt370ZISIiQe1mfmpirV6/i66+/FhWCLqaU+hhmxcYFIaQhgOPgFD97e3tj/PjxwvempaVh3rx5WLNmDffHWLRoUXz55Zd65ym+DTQaDQ4cOIBly5YJlWgHBwcsWrRIZ9TkwYMH8PT0FCnCEZBoKvN9HxNCSFUAZ8Ghc/bw8MAPP/wgNDQppVi1ahWCgoK4m5VarUbXrl0xZMgQ1KpVy9BLZ9Zy7NgxLFu2TOhJKlOmDObPn4+WLVsKP+fFixfo3bu3yDA5CSn1Mt/Te2u7Pp8FwGiUn3zyCUJCQnR6LHXVZBBC4ObmhmHDhuWIfS23OHv2LFasWIFDhw5x9w99amLevHmDIUOGiAyTawA+opTyvVD5CFoa0aMAXJXX6tati/DwcJ21GYcOHcLEiROFxARNmjSBt7c3mjdvbjDFRoR///0XK1euxJ49e7j7h5WVFSZOnIiBAwcK15Keno5JkyaJdIZHAD6klOqXl5aH0BIC7QSnH5SDgwM2b96s09A8f/48Ro8ejfv373Ov161bF97e3mjbtq3Re79l1P9u27aN62UnhMDLywvjx4/XuZb58+djxQpueVAygKaUUiEdW34CIWQpACY9yd7eHps2bdJJznL9+nWMGjUKV6/yg/Tvvvsuhg4diq5du+od5cot4uPjsW7dOoSHhwsJa7744gsEBATojMxs2LAB/v7+vEsaSOQyeqXU6mWUEEIqAjgPTkh57NixGDFihPC9V69exahRo7heMVtbWwwZMgT9+vXLNZd9bqHRaLBv3z78+OOPXM94sWLFMH36dHTr1k34GdHR0ejTp48ov/YLSqmwMj4/gBBSHBL9LRNS/uqrrzBjxgzhe+/fv4/Ro0fj/Hk2Jd/KygrffPMNhgwZYvIO4JRSHDlyBEFBQVwFVJ8i0djYWHh6eooiLzmy+vMC2kZrh8EJKbu5uWH58uXCQ+PZs2eYOHEiDh8+zFxTqVSZHcBzQsNsKJw5cwY//vgj1zhRqVQYMmSIziLRp0+fwtPTU+SMCKKUTjDsig0PQsh2AB7KcRcXF4SHhwvrMbIj62jXrh18fHz0ZoYxJK5cuYJFixbh4EF+64LsikSTk5PRt29fnDvHZQTeSintabjVGgeEkIWQmujJULVqVWzevFm4j6alpSEoKAirV6/mGnZNmzbFuHHjdHpsjYXbt28jODgYkZGR3LVlxx6WlpaGYcOGcfciFBBHAiFkPACGYap06dLYvHmz0PFJKcWaNWswb948rhe9bt26GDduXI4ovg2F+Ph4rFy5EuHh4dy1ffTRR1i4cKEwwkopxZQpU7Blyxbe5f8ANMrvjgRCSA9I1L8y2NraYu3atfjoIyYolomIiAj4+flx9UYnJyeMHTsWHTt2zBFtuiHw/PlzrFu3DqtWreKurWbNmggODtZJ1b948WIsXsxVj+IBNKSU8q3rLMjWKCGEqCDlzLVWXuvduzcCAwOF7z1x4gS8vb25xVO56V9iDGRXCzF06FBMmDBBqMAeOnQIw4YN43mEEiB5c3S2wsxLEEJ+AtBHOd66dWssW7ZMqNz9+++/GDBgADcNz9XVFYGBgUb3oGeH9PR0bNmyBT/88AP39+fu7o7Zs2cLc6gvXLiA3r1784rfUyEdhjo79eUlCCFzIHWnl6F+/foIDw8XKnd3797FgAEDuEp7nTp1EBgYmCfKjRL79u1DYGAg12hs0aIFli1bJlTO79y5g549e/LqKCgAd0qpsGovr0EIGQmJQU0GJycnbN68WVhDkpCQAC8vL67S7ujoCH9//2wLbE2B48ePIyAggMv+5eLigtWrVwtTBJ89e4avvvpKlBLmnZ+Zm7R1X7ugIKIoW7YsNm/eLExhS05OxsiRI3HkyBHmWvny5TFp0qQc9y8xBi5cuAA/Pz9uWpejoyPWrl2LatWqcd+bkpKCfv36iajbZ1FKpxh2tYaDtu7rKBREFMWKFcOGDRuEKWwajQZTp07lKu0lSpSAj49PjvuXGAM3b95EQEAAjh1jM+nKly+P0NBQvP8+U/sNQPoffXx8sH//ft7lzZTSrwy7WsOBEPIupGi1jBnPysoKISEhQkORUorg4GCu0l60aFEMHTo0x/1LjAFd/Ujs7OywbNkynbWc06dPF1G3H4FUc62TrUgfo2QagKnK8datW2P58uVCa27v3r2YMGECw1Ftb2+P2bNno23btjq/19S4efMmxowZg0uXLjHXPD09MW3aNOEmsHHjRvj5+fEunYJUSJvvvDmEEC8ATHVS/fr1sXHjRuGDcfLkSQwbNoxR9G1sbDB16lT07Nkzzw/BrIiPj8eECRNw/Phx5lrr1q2xaNEiYf1QVFQUhg4dyvPy3YBkcOpHaWFCEEI6QkqzlAnB0dERkZGRmcxmSly5cgWDBg1iDE21Wo2xY8fCy8srzw/BrHjx4gWmTp3KzTv/8MMPsXLlSqEH9sKFC/D09OQxQz2B5M25Y/AFvyW0jEzHoaD+tbe3x86dO4XOnXv37mHAgAGMok8IQf/+/TFhwoQ8PwSzIiUlBXPnzsX69euZa87OzggLC0OVKgx5EQDJqP788895TDMpAJrlR6Y1bc+KcwBkLC5FixbF1q1bhUpdQkICBg0axGXq6datGwIDA/Wi4jUVNBoNli1bhiVLljAOvAoVKiAsLEwYpUtISED37t15LGLpkNJCfjPKot8C2jTLcwCcso6rVCqsWrVKqLgmJyfDx8cHUVFRzLUWLVpg3rx5Js8+0AVKKTZt2oSZM2cyTt0SJUpgxYoVaNKkCfe9KSkp6NWrl6gGaRCldI3hV/x20KZZHgPQSHlt5syZ8PT05L5Po9HA19cXW7cywRW4uLhgwYIFQsM8r7B//35MnjyZqcEuUqQIgoKChHUmGo0Gw4YNE/UKC6CUiiMZyMYoIYTUA/A3FF29K1eujN27dwsP/a1bt2LKlClMUVbDhg2xaNEi4aGS13jz5g1mzZqF8PBw5lrHjh2xcOFCoWI2fvx4ETXat2/b4dLQIIRUBnAFCku/ZMmS2LVrl7D+4/Dhwxg+fDijzDk7OyM4ODjPoyMipKenZzboUh6Irq6uWLNmjTB6MHfuXBGzxFJK6UjDrzb30DKBXAYg292srKzw888/C9ldYmJi0K9fP4Zdq1KlSli4cCEaNWL233yDjRs3cg/EmjVrYuPGjULGvvDwcAQEBPAu7aeU6q7qMzG0faFOA2ioGMfy5cvRpk0b7vtu376NXr16MQx1pUqVwg8//JDvHENZ8euvv+L7779nDsRKlSph06ZNwvTBQ4cOYciQITxHwlkAjXPDm29MEEL2AOisHJ8+fTp69erFfc/Tp0/x9ddfM0xmNjY28PPzQ8+e+Tdb7a+//sLYsWMZ50fJkiWxfv16YfQgJiYGnp6evEZ8dwC8n98ISAghKwAwzD+66jSTk5MxcOBAnD59WjauVqvh4+ODYcOGmTylR19cuXIFPj4+jPOjSJEiWL58udAIu3PnDrp168ZjdnwJoLY+6T6mBCFkCgAmr71z585YtGgR9z2iqBAhBP369cO3334La2tr7nvzGnfv3oWPjw/j/FCpVJg9e7aQ6vj58+fo1q0brzY3DVJ6npD3WGiUaAu0DgOQVY+q1Wps3LhRmDN34MABjBw5klH+PDw8MGvWLL0oB/MaO3bswPfff8/8D7169cL06dw2HkhKSoK7uzsvfSAJQF1K6S1jrDU3IIRsAfClcnzp0qVo37499z3nzp1D3759mVzDli1bYsmSJdn2FsgP+OOPPzBixAjmf9BVZ6HRaPD111/z0gfSIXlfdfP4mRCEkPkAmBNv6tSp6NeP2+cUN27cwFdffcVQIWeXLpOfEBMTg8GDBzP/Q3bpamPHjhVRVH5OKd1l+JXmDoQQHwALleODBw/Gd999x33P48eP0bNnT6Zerlq1ali7dm2e1ATlFLGxsejfvz/u3JEHrqpVq4YtW7YI09VmzpyJsLAw3qWRlNKlhl9p7qBtfMmwDXXs2BHBwUyWHgDpnOnTpw9iYuS1wOXKlUNoaCjq1q1rlLUaEo8fP8agQYOYrITs0tXWrFmDWbO47Sx+oJRyG/7mBQghjSC1B5BZEA0aNMDPP//M1YFE3mV90mXyCxITEzFixAiGdMLW1hbh4eFCgpn9+/dj5Eiuf28jpbS34VeaO2jJYy5DwWbp5OSEyMhILuOhqH7GysoKc+bM0auxbV4jNTUV3333HeN0V6vVWL58Odzc3Ljvi46OhqenJ6/u6CikFHiu8aHL7B4AhUECSBEBkUFy+vRpjBkzhlHm+/Xrhx9++KFAGCSAZECtWbOG4WfetGmT0Bq2s7PDwoULeRavHYAgoyw0FyCEtAXHIPnmm2+EBsm1a9fg5eXFKPPdunXDypUrC4RBAkgG1IYNGxhFOyoqCpMmTeIWY6rVaixcuJCX9qQCEKytucpzEEI+ADBaOd66dWv07duX+574+HgMHDiQUeabNm2K9evXFwiDBJAMqO3btzPh7+joaAwdOlTYwG/atGmiqOAibdQpz6GNak5TjtevXx8TJvDr8l+9eoVBgwYxBkmtWrV0RhnyG6pVq8ZNYYqNjUW/fv2E1O6TJk1CvXr1eJdmaElb8hyEkGIAFijHHR0dMXv2bO570tLSMHLkSMYgcXBwwKZNmwqEQQJIBtSmTZvwySefyMafPHmCb775BnFxcdz3DRgwQKQAjSOE8PPcTAxtVHMFFLqVvb09lixZwtWBKKXw9fVlDBJ7e3usW7euQBgkgFQrs2rVKnTtKicaS05OxqBBg4QU4B06dEDv3lzb42tCCF/jzRsEQ2GQFClSBEuWLBFSsP/444+MQWJra4uQkJACYZAAEjnQ/PnzMWSIvF+6RqPB6NGjmcheBurXr48xY8bwLrUAwFdKIDBKCCFlAMxRjtepUweDBg3iflBcXBy8vb2ZNIrRo0dj6tSp+TbsKELz5s0RGhrKeFmDg4Pxyy/83k116tTBwIEDeZc8tLn+eQptPuQS5XilSpWECs7Lly/h5eXFUE327NkT8+fPLzCGZgZcXFywadMmJq1n586dWLOGn8JauXJljBs3jnepMQAvgy8yd1gKRZplsWLFMG3aNG6NT2pqKry9vZk8bTc3N4SFhRm0l4wp4OjoyFW4jx8/jjlzmK0MgJTzLKgFcwKQXwpo50PR2VutVmPGjBlCBWfChAmMF7p+/frYsmWL3o1K8wvKlSuHDRs2MEbGP//8g++/5zvHM7oocyKf9gDmGWWhOcdUAFWVgwEBAcJnb8aMGfjjjz9kYxlRI0P2HDEF7OzsEBISwhAsxMXFYdSoUVxWJ0IIAgMDeZFP7rmWRxgKTj+SCRMmCDufr1q1iqk1KFOmDDZv3mwSam5DwtraGkFBQfjyS7nfMyEhAUOHDhV2jJ84caJob1qq1VvyFFoyCoaKdfDgwahduzb3Pbt27cLy5ctlYxnsXHnBmvY2IIRg0qRJGDVqlGw8JSUFI0aMEDax9vLyEtWKzdXWXTEQWQrjAJRTLkpU7K3RaDBmzBhGce3duzdGj2actwUGjRo1wuLFi5n/+bvvvuMyxADAyJEjRd7XWSTvK8AHAGAKP3x9fYVdO/38/Jj0idatW2P69OkFztDMgLOzM0JDQ5kIz7x583D27Fnue3r16iUKPwcQQgzT5TOX0Bq8TFTTx8dHyIE/d+5cJk+0fv36WLRoUb7Nb80OFSpUwLp165hC0HXr1gkbyrm5uaF1a4ZYEADGaJvZ5Rm03l+GhaZv377CBmlr165lqHWrVauWbUPF/IwSJUpgzZo1cHZ2lo3/+uuv+Omnn7jvqVu3rqgmo482qphn0EZrmIOxQ4cOQmVl//79TK1j2bJlsXr16gJnaGYgw8uszLw4f/485s9nWHQBSA4iQarPZ4QQfnGViaA9B3yV4/Xq1RPW+URHR+PHH3+UjWV40pW/94IClUqFGTNmoEOHDrLxW7duYfLkydz3FC9eXORkqA0OQ6gpodXbmGh1lSpV4O3tzX1PbGws4/CysrJCcHCwTrrg/A4fHx8mFfzp06fcDClAcqAFBgbyHKMVwKFABzhGCSGkJACm8ciXX34ptNqDgoKYnPuOHTuKGqkUKHz22WdMv46kpCSMHTuWmxZia2srergagNP501TQhpWZcEiLFi2YzSMD4eHhTM69q6sr11AraHBxccGSJUtk/0daWhrGjh3LY++BSqVCQEAAzxCrBKC/MdeqB5idvmbNmsK0rYMHD2Lt2rWyMWdnZ50F/wUFVatWxerVq5n/Y/LkyTz2HgCAv78/7/+2g2DTNCF8odijy5cvL3T0REdHY+5cOadGhQoVsH79epQrV477noKC0qVLIzQ0lPk/Zs+ejYsXL3LfM2HCBJ7CTsChyzYxxgGQ/eBsbW2F9UF37txhzpRixYph7dq1BS5CooSNjQ1CQkKYfh2hoaEi9h4MHjxY5H3N6+jmYACy5hw6zg0kJCRg5MiRsqhQRp5+QYuQKKFWqzF//nyGQv6XX37Bpk2buO/p2rUrmjVrxrs0Wdt7K6/QFQqSEQDCZoKvX7/GyJEjmajQ7Nmz8wX1+tti8uTJaNeunWzs9OnTwtKGRo0aoXv37rxLowkhDEUgz9U9AlKYOxO2trZCxoiLFy8iNDRUNubk5ITZs2cXWE+6El9++SVD9Xbp0iURKxPat2+Pxo0b8y7l5abZC4Cs641KpYKvL+PYASA1R1SmvZS+5bkoAAAgAElEQVQtWxaLFi3KVxSib4OWLVsy4ch79+4xil0G6tWrJ2qmOYkQkifhBUJIS0g5mjJMmTKFm97z6tUr+Pn5yepnbG1tsXTpUiFdcEFD3bp1mYLY58+fC3/rVapUwYABA3iXRopCzMYGIaQGAMa9Om7cOC7Vq0ajwZQpU2TsRCqVCvPmzcvzXlCGgoODA8OA+ObNG0yaNImb7lO8eHHm+dail7bXgMmhTY1m3KteXl5C1sMpU6Yw7ESBgYHCaFlBQ0a9RVYFj1KKyZMn81iZoFarMXHiRN5HfUoIyZMCDO3+zzj9PDw8hAXes2fPZupnxo4dW2BqSLKDjY0NgoODmdrEWbNm8ViZAEi/dY5X3RmcOlgTgvEyf/zxx8IC7+XLlzONm/v06QN3d3fjrM7EyDA4lY6EkJAQXL58mfueSZMm8VovcPdCmdWgLe5kKlO++uorLtNJeno6/P39ZWGbokWLIjg4uMCmCojg5+fHFFyuWLGCSW3KwPDhw3nDHxNCPjX44rKBNvz4rXK8Xbt2wu6c06ZNkxW2q1QqBAUFFdhUARGGDx/OHAJbt24VdYeGt7c3z9iuDsnoywswhm7dunXRvDnTzB2AFNVU0nEGBgbq7NJaENG1a1eGrvDo0aOiZl0YOHAgj7ChJIC8on3+DoAsHFm5cmWRxwmhoaH4559/ZGOjR48W/g4KKpo2bcqkTFy9elWYxvXFF1/wUhitwNkPTYRRAGRWpa2tLb755hvu5N27dzM9ljw9PYW/g4KKWrVqMU6DR48eibpD49NPPxXRB/Pzg4yPPlBQsavVagwdyrACAwD+/vtv7NixQzbWsmVLppi4oKNixYqYP3++7MxMTk4WkjnUrl1bpOz75gWpDCGkNYCmyvERI5hkIgBS2taqVatkY7Vr1xZGQQsq7OzssHjxYpmhkdGLRdkKBJAi/D169OB91DhCiCzcpBSyJ6Rcr0xYW1sLi9s3bdrE5KVPmDDBbDw4WVG0aFEEBQXJvM8pKSmYNo1JNQQgpUUJPCR5UWTTBgCzgw8bNow7OSoqislL79evn9l4cLIiw5uc1fvMM7Yz4OzszIQutTC5XAkh7wFgFjNy5EhucfulS5ewceNG2ViHDh3g4eFhtDXmJQICAhjv84wZM5CUlMTMtbe3x1dfcZsIDzd16gAhpDQ4edReXl7cep+4uDgsWSKv823QoIHIMVLgMWrUKLi4uMjGFi5cyBjbgFS3MHjwYN7H9DV1FEz7O2I8g3369OH203n16hWjvDk6OmLqVKaXsVnA09OT6Z2zfv16xuucAcH51YEQUtPwq8sWTEiuQ4cO3PQ6jUYDf39/WbS6VKlSmDdvntlkl2RFy5Yt0aePfDvbv38/Q9qQAYHC/z6Azwy+uOzByLVhw4bChpABAQEysidra2udDZoLMmrXrg0fH3mGc0xMDLZt28adP2TIEN75VRGKjADlE8AkoXt4eHBZI5KTkxkvRq1atYQeH3NAzZo1mTSPQ4cO4dQpfqsKgVLQmRBi6gRvRigtW7bkepoopUyRoa48dnNA+fLlMXbsWNnY5cuXsWfPHu78ESNG8JT+j/KggJaRq7Ozs6hwG/PmzZMZWjrqn8wCtra2jPf1wYMHWLduHXe+l5cX7/CoDMmoNyU8oejcXrZsWYbRJgPBwcEyQ0utVmPatGlmqeAA////sqZxJSYmYulSfgsSQaTfBqZPCWkP6RDORNGiRUWpgwgLC2MMralTp5qlgpMBPz8/WRqXRqNhCsEz0L59e17DXgITF0YTQuqC09hUFPWIjIxkoprjx48X9t0xB4wbN47Jspg3bx6Xht/FxUXkADW1XMuCUwcscvYcP34cf/75p2xs8ODBBZawQB8MHDiQYR9bsGABUlJSmLlVqlQRRXhlekzmqUUIqQYOg4/IyNi8eTOePHmS+ZoQgunTpxc4iticYtSoUahcWVbLJjwM3dzceHnCRcDJFTcWtHz4TDKjSK4HDhzA1atXZWO+vr7cPHZzQu/evZn0vOXLl3NDkXXq1GEK+DI+xjirY6FNyftaOd63b1+uMhoTE8M0tfLx8TGbegMR2rRpw6QDhIWFMT13AMk4FXQ5N7Wnhfm+nj17cosq4+LiEBERIRvj/ZbNDR988AET2dq6dSs3WmJrayvqPJzncu3YsSM3JTYpKYkxntu2bSvMYzcXVK5cmfGUHz58mKG4BiSdQ8Cw1s/ETJdMZ1pXV1du3xiNRoOQkBDZmIuLiyhKazYoXrw4vv1WnjF55coVREVFcecL9JMvCSGmrAv4GpK+lgkHBwdhsfqyZctkr9955x2zjVZnQK1Ww8/PT+akffTokTBaIpDrZ4SQTC7/rNrLN4rXqFOnDpeDOS0tjenp0KZNmwJNdaYv7OzsGErCY8eOcalkCSGiwmhTHoY9AMge5LJlyzKNqzKg5NWuU6cOOnXqZLTF5Reo1WqmV8u1a9fw22+/ceeLLH4ty5kp8CmkWpZMWFtbo3PnztzJyg2zUqVKQnYuc8O3334rM9SePn2Kn3/+mTtXIFd3QohJWAC0Be4MBY1gH8GqVatkxe22trYiylSzw5gxY2SG2ps3b5h87gwIUhRbEEJM4sbUsloyQhTVhmzYsEFGsa9SqUS9kswOAwcOlBlqlFLmXMpA165deSkh1QDwDzgDQ1vnwFhGoqLm/fv3M+0EJkyYYLZRzazo1q0bY6gpz6UMtGrVite8txgAUxZTMXqau7s7NzX6/PnzOHnypGxs9OjRBZ7NUh80btyYMdRCQkJk51IG3n//fR5zngpZomBZnwTmwRJtmHv27MH9+/dlYyK+ZnOEh4cHEy1RUqxmQHAPm5qQ/YWRa9euXbkRrVOnTuHChQuyMUGqklmiZcuWTK66klkuA506deKxkL0DEx2G4MjVzc0N9vZsmnxsbCx+//132djgwYNRpEie96QyCZydnZkIyJo1a7hRsBYtWvA817YATNV+txekFJRMuLi4oGZNNk3+1atXTNO1Xr168Q5zs0Tp0qUZVsSff/4ZiYmJzNwaNWrwPNcEUqqcKeABBQ1wxYoVuRSoGo2GOU/at2/P/Q2YI3h1QL/99huX0tve3l7U28VUxCOfApClQ9jY2Ahp9pXO3Pr16+Pjjz821tryFQghTB1QdHQ0zpw5w8y1srJCly5deB9jErlq65JcFWPCLuyrV6+WvX7nnXcKTMd2Q0AZ3YyLixOSygh04ky5qgCAEPIOpEKiTKjVanTt2pX7ocp0gRYtWjDKnDnD2toaXl7yRt6///47Xrx4wcx99913RQXv3DwRQ4IQUhSclDyRF0fJBqKjqNtsoTSuz507h1u3bjHzSpUqhc8+49bdmar+gPn9iJwIkZGRstzdMmXKMMqcuUMZRo+Li2M8W4C07wkOw3wn13379snS0HQUdZstlMZ1cnJyTg9Do+/Dou/p1q0bt9/TiRMnmA7J5p4GokSvXr1kxf/p6emM3pGB/CbX1q1bc9Odr1+/zhADWZpc27dvz9RYKPWODAjk2spEHd6Z/b5hw4ZwcnJiJiYkJDBpaF5eXmZfypAVDRo0YIxr0fMq2Pc+IIRUBv4fKWESVV1cXLi5rg8fPmQO8969TZZKn2/g4eEhC829fv0a+/bt484VFB5/apSFydEMCu9chQoVuLmuKSkpTNfrr7/+2iLCylnRunVrhthh586d3Llt2nD1VKMzhGijbE5Zx4oUKcJNyaOUIjIyUjam/O1aAurWrcs4B3IoVz57gAGhpWRnGhyJiAuUh3mbNm3MjrI7O1SqVImps8ihXJspKSmNhE+VA4L1MId5w4YNzZLRUhdsbW0ZpVTpXMlAq1ateFFfZ22drLHB6E76yrVixYpm0UwvJ1CpVEz9zL59+7iF0S4uLjw672Lg7JFGACNX0T68d+9eWSNtW1tbs+lJkhN8/bW8xPXYsWPcGr+KFSvySJYItHtkhsbJKFKCzprYuXOnjMHH3t7e4h4sQCrcUm4+SuUvA4J76WaCYjxGrqK+BQcPHpQ1qtIRPjVrqFQqJn9fJFdB2L2xNn/cmGA2zIYNG3JZec6ePcv00jG3Hgf6QnlQ7N+/n3sYNmzYkGe0VSGEMFQ/BsYnULBuVa1alUtGcO/ePSbtoVCuEk6ePMlEGgCJTpdDPFIUgFHzZwgh7wOoknXM1taWm12QnJzM1LFZooIDsHVAsbGxiImJYeaJ7iWM7CDS1pkxhbQ8ulhKKXbt2iUbc3d350bKzB1du3aV/d8vX77E4cOHuXMF1LtGZXvQ6mWfKsebNmXalQBgnSDt2rVDsWLFjLG0fA03NzdZA2aNRoO9e/dy5wru5WeADqNEJAAlt3SXLl243PmWAKUScPbsWbx69YqZ5+LiwmsmWQEAG7IwLJiHV1+5tmzZ0qwpCnVBKdc7d+4wxYmAFHXi8NBbgdNh3cDI9fMqIq+wBHTu3Fm2VyUmJnLzma2trUXsasamPtLbOXT06FGZ17hcuXKi3HqzR6tWrZhUH1EPBF2HoRHBfL6rqyv33Dx16hSTkmcJRCM81KlThymKPXLkCHeu4DkxtlxbQtHgtEaNGtxo5bVr15g6XEs1NsuVK8dQ/orkmkfPqwsAWduGEiVKcFsoPH/+nEnJs1S5FilSBB07yhmUcyhXNwBQEUIqgpMKwjuUX79+zXS6FoW0LAEff/wxw6nO61miVqvh6urKjAPgd+AxALSsIIwXR6S8/vXXX7LXlizXWrVqMR7VEydOcOcKDkOjyVULJnwtkqty3aLUAktA6dKl0bChrJ0At64EyD9yFTXpUsq1VatWFul1BaSobsuW8tK5HMqV//AYDno/r8p1N2rUiEteYSlQpublcB/Ot3J1cnIy6/4V2UEp1+PHj3Pn6chGMGZeOSNXV1dX7v56+vRpWeaQnZ2d8DdgCVDK9e+//5altmWgUaNGPKeMMyGkvAoAw8/13nvvCVNBsnartLKyQqNGjXK1eHOAtbU1Q4MsOgwF4WXm3hsQ1aCoJylfvjw3FSQ2Nhb37t2TjYk8tJYC5f8vkquAxMBoctUW+TllHVOpVKhXrx4zNykpiUl3sOQNE2D/f5GSY2q5ij6/QYMGzCRKKeNEKJRrwZKrYB3MPlMoV/n/f/78eW6PoXr16vHqH98lhBgzjaNQrrmE8ny9d+8el13NwcGBl7FhB8CRmWw45Fqurq6uFlXgrkSTJk1kxltycjITSQKklEsONTAAvMc1St59l89Wq+zFUb9+fYsrmFVCubn8/fff3HmCe2rMw5D5bE6qEQBWrpUrV0bVqlWNs6oCgnws1xqQUsQyUaVKFa4TISYmBmlpaZmvixYtylVyLQnKw/DixYsyR0sGTC1XQkgJSN3jM2Ftbc11Ity5cwePHj2SjYkiKpYCpVzj4+O5So6joyPPQ/eOkZuy6XXGpqSk4PLly7IxS5frRx99JCtiT01NZWjrAUnJURKUQNonjUm9z+TB6qs7Wbpc3333XaaIXXTGCvQWY9b3MXIVRbUK5SpHsWLFmDS3nMo1R0aJMq/ekmiARVAqebzaA0B4T435YOVariKvgCVBKdf4+HhuvZDgwappRBIDveV6/fp12evatWvzeqtYFJQeVY1Gg9jYWGZehQoVeMWKZQgh5ZjJhsF7UPQncXJy4qYMKOVaoUIFVKlShZlnSXBwcEC5cnLRKO8TIKXSchwuBIBRmoBo06Nl+VfFixdH+fLlmbm3bt2SpYKo1WpuBNSSYGNjw3hUeXIFTOtI0KYP1VCO886DFy9eME4ES3cOAayeIdKdBGdsnjt0KaXMb7FQrvrrxLqMEkYxFnnUlR9uyTmRGVBuhC9fvsTjx4+ZeU5OTrzwsjMhxFixvlzLVaTkWhIcHBwYmsmbN28y8+zt7UWdZxmaHwNBb7kq11soV0nJUSrwPLkSQkx9GOZarqJ5lgblfeDJFTB5FExvJ4Jyve+8847FNDjVBeX9yidyrQpFenS5cuVQsiRLvKhcb5EiRSzeiQCw8hIprwI901jGJjc9ulo1ll360aNHTKPWwjP27eVqBYAhgnZ05KfrFSo5LCpUqIDixYvLvOg3b95kvHa2trYoV66ckrfZGsAgQgjbdfHtwRT7iORaaJSwUKvVcHR0lHlCbty4wfVcOjo64unTp8rhvoQQ/tP4dmCaYRbKNWeoXr26LLVHpOQ4Ojri4sWLyuEvCCHGyG3sqBwolGvOUL16dZw+fTrztS65ctDRSNFNJp+DQ0sMoFCuIuhrbArk2ooQwubxvT2YKIm+z6soAmppeEu5uhJCjNHd3R6K9Ojy5ctz06OVci1RogSj91kilHIVGSUCuVa0AsC0HuV1I01OTmbSV0Sbq6XB0dERV65cyXzN48gHpLA9p5nMCuOtTA6eXAEwoeVCuUqoVq2azCjhNQIChPd1hnFWpff3F8pVAGX6jq7nlYOxhl8RHyK5Kn+HImXI0vCWcu2r/TM6CuWaM7ylXDtr/4wOwfcXylWAt5RrEwAbDb4o/b+/UK4CKOX64sULpKSkMIad4L6WUIFjlPAav/Dy6XmhSkuE8uYqQ3oZyOuGOqLvV663UK4SlMpDQZOr8pktlKsEfeUqOoxMBX2fV5GSa2kolKt5olCu5omCIlfR9xfKlQ/efUhKSmLGdBklzBXew6UUACHE4pm3MlCQldc3b94gNTU123mWiIJubCo3grxeZ35BoVzNEwVFriIlp1CufBTK1TyhvF88XQTI+/ulr7GZ1+vML+A9B7xnVnC/SjJGCSGEmz+n5Aa3sbEpzIvUQnlzeVEl3jxTw87OjhnjWbB5vc78goIsV6DwMBShoCg5hXLNGQqKXEXOvEK58lHQ5VqovPKhj/NbNM+UKHxecwa1Ws3YEDzdydbWFpwyvhIqAGlZRyilSE9PZz5AyRyVtf+BpUNp3XN48AHk/T3LSjeZAZ5hmdfrzC8oyHIFWNnm9TrzC5RyFTW7yuv7VSjXnKFQruaJgiJXnt4EsOvN63XmF/DuA++Mzev7JZJr4fMqhvJe8OSanp4OSqlyOFUF4KVyVB/veWpqKjfUZonQ1xMi8vCYCrzvt7OzY6zVvF5nfoHyPuibW2pqiL5f6WnP63XmFyi9NoVyNQ8UytU8UVDkKoqkF8qVD+X9UqlU3KiE6L6aCvpmSBTKVUJKSgpjlOhbpw7gJdco4d1cffPELBEFZdPkfT8v1JbX68wvUMpV34JyU0PfAsFCuUrQ14lQKNeChYIiV57TDyiUqwgFXa6Fyisfyvtga2vL6+WW5/erUK45w1vaDy+sADBPsihSQgiRhVuePHkCe3t7Zq6lQdmjQmSUCDbN1wCYGJYBUASA7AkXPVwlSpSQ1Qw9efLECMspeNBXroKH6w0Aftz37WANQBY31iXXrCiUq4S3lGsqAH7+zdvBCgp+fH2V10K5SlDKVcSGI5BrGhSpzAaCGtIzm933F8pVgLeUqwbSM2toqCCdsdl9P7NeTk8ri8RbyjUd0hlraBAARfX4/kK5CqC8DyqVilsfKbivL1UAnmf3oYCUE1axorzPoqjZjSUhNTVV1ogNYHmaM5CQkMAbrkQptTX0H4CflV8kOuSU/SsK5SpB2fRHJNdnz57xhl2NJNd5yi8SbYaFcuXjLeXqYSS5jlF+kUiuSj78QrlKUMpV1DdAINfRRpJrD+UXFco1Z3jL53WukeTKNMXUV66iZnKWhrd8XjcaSa5V9Px+Zr23b98urCsBK9cqVapwa5cF9/WFCkCsclS0GerbPt6SEBsbKytcVKlUqFatGjPv0aNHePmSyZRLoJRyLRVDLE05cOvWLe7EQrmySExMZJoP8josp6enIzaWudUAcMsoCyt8Xt8ayudA1DlbcL+MpSneYr6oUK45gvJ+FcrVPKC8X8qO0RnIa7neunWLWxStXO/Dhw+FUVBLwls+r7cMviAAlNKnAF5kHXv+/DnX4Hz33Xdl9bgajQa3b982xrIKFJTyyqlcVQD+1XMy8+HXrl3Ta5HmDOU9qFSpErdYS3AQMffegCiU61vg2rVrslRFa2trbkf0+/fv4/Xr18rhOErpC2ayYVAo17dAfHw8E7HkKTmpqam4d++ecjgdwHUjLS3Xcr1165aQ0clSkJaWxhibIuXVxHvxf1CkcYo8qkq5JiQk4PHjx0ZaVsHBf//9J3udH+SqdSbKWnqnpKTgwYMHzNxq1arJGLgopYV7MfSXq2AfNKbudFWfNdja2jLZQ8r/yRKh/G3nVK45Mkree+892etTp07ptUhzhvIeKO9RBvLgwdJbrrVq1ZK9jo6Oxps3xkjXLDhQytXZ2ZkbgswPchV5XpVyjY2NRXx8PHeupeD06dOy16VKlWIOFoCNgGpxi1KaYqSl3YRUX5YJkUe1Ro0asoLQ5ORkXLx40UjLKhiIiYlBSsr/RaNWq1GjRg1mHi8CCum+G8XFSSlNBnAn65jIo1qpUiWULFlSNnbmzBljLKvA4MGDB7hzR3b7mH0tA/nV8WdlZcUYnJYu19evXyMmJkY2JtKd8oNcRWescs2WLleAPWNzKleuUSKy9ho3bix7fffuXaaewtJw4sQJ2esmTZhUUwBCLzVjkRsQjFxFHlVXV1eZJyc5ORnR0dFGXFr+h1KuTZs25c7LA7nGQcGYl5CQwDU2atWqhTJlysjGTp48acSl5X/wnldOAyeTy5VSqgFwQzHG3YtLlSqF2rVry8aU/5elQfn/v//++9zC2f/++4/HjX9Ne/+NBb3OWJVKBVdXV9lYoVzl/3/ZsmW5xubDhw/x4gUTnH5OKX1ovNXprzsp9QJL34fPnTvHOBE+/PBDZh4vAqqFMUMSjFyvXuVv/Uqd2NLlGhsbi/v378vGcqoTqyAJV8ZOcefOHW4Y0tnZGRUqVJCNWfKm+ejRI+bGNmvWjDtXEFW6bPhVSaCUPoOkwGYiOTmZ8U4AErPaBx98IBuzZLmmpqYyHg+RUfLXX3/xho0pV8r7fKV3AgAIIcymaclyBfQ3Nk0tV9HnizxvynVb+mGolGt+2YdFn897XoFCuSrBkyvPiVDQ5Hr69GmLLopWyrVBgwZcqufo6GheevQ9I9biAjmQq3Kf+ffffy2ahev48eOy11WqVOHWWN+/f58X0HgD4JpKG15mTj7RZqgUwt69e3OyZrPCL7/8IvO62dvbo06dOsy8hIQE/PPPP8phCuBPoy6Q8/kiuSo3TUuW66FDh2RpM2q1mlHuASkNQ7BZHTHe6gBw5CpQopnn9cCBAxabmnfx4kWGlECkvAqMN2PL9Q/lgL778IkTJyy2/iA+Pp55DkXGZkGT6/Xr13HlyhXjrCqf4/Xr1zh48KBsLL8/r6dOneIWuzdp0kSWcvny5Uv88QfzdouBUr8QyVWp5GphivNVFk69cuUKnj9niGpRt25dWcpleno69u3bZ+Tl5V/88ssvstc5lOtflNKUjKckSnlVtGm2bduW+XBeVMUSEBkZKXvdtm1bbvOfkydP8jaqaEqpsbWIQ7y18NCuXTvZ6+vXr3OjKpYApVybNWvG5HoDkpLLSRl4AsDYN46RqygC0rZtW1ktTEJCAg4dYt5uEVDK1cnJCTVr1mTmPX78GNevM/XsGnCUEAODEcypU6e4HtWPP/5Y9pvUaDTYvXu3cVeXT7Fr1y5ZWmqpUqW4RgkvAqoFc/4ZGIeg6G3z77//co3I2rVrM4Whyt+tpeD333+X7a9qtRpubm7cuYL9z9gb3XkAMl7ThIQErhFpb2/POLYiIiKMurj8inPnzjEpWe3bt+fOFegrRpUrpTQewKWsYxqNhhuNU6vVaN26tWzMUuX68OFD5h7lUK5RwP+b6zGb8vHjx3m5t3Bzc5M1TExPT8euXbv0XLb54Nq1a7hw4YJs7PPPP+fOzaMNEwB+Vw78/fffslzODLi4uMDZ2Vk2tmPHDuOtLJ+Cp7TnUK6HKaXGaJqYFX9AkXJ58+ZNJpcTACpUqMB4KyxRrmlpaYzS7uHhwZ177Ngx3t531sgpAwBwEYAsBz4xMZHrHChatCg6dOggG7PUw1CptHfq1AlFihRh5p0/f17WJFaLOABMGNuQ0P5uzivGhNHNbt26yV7v2rXLIlN9lHJt0aIFypcvz8y7e/cuUwwPKRXkmNEWh8w6MMZrL/ACw93dXfY6KipK1LvMrKGUa61atbgZJsnJyTh//jwzDtPoTlydmAelXM+fP2+RdN47duyQOYdKly6Nli1bMvMopULdCfi/UXIcgExTvX//Ps6dO8e8q0iRIujcubNsbP369UhNNUbT1PyL0NBQ2esqVaoIU3x+/fVX3kcY2zsHSul/ULDKpKSk4PffGVsFAPtwbd++3eLyI5W/ZVtbW6G1L0hxM4VcXwFg8sZEKXdKuR4+fNjiNs2IiAhZ81BCCKP8ZUBwH/kPjQGhrRc6rOd6GLlevnzZ4mqGjh49yqTGdu/enTt3z549vOEoyvO+GR6MIqVLrlnrJh49emRxjr/r16/j8OHDsrEcyvUkpZTfituw0FuuHTt2lHW2fv36NcLDw423snyIhIQExnkikutvv/3Gqye5TSk1Fi17VjBy3bdvH5coqGnTpqhcubJsbM2aNcZbWT7EmzdvmN9yly5dZARKGThz5gwePmT4J5IAnAC0RomW5vKgcpbI8/bll1/KXj948MCivHT3799n/t8ePXpwU7eOHDnCC9MngqN8GAnMDimSlbu7O6ytrTNfJycnY/369cZbWT5DYmIi8/926dJFdpBk4J9//uGF6SmAX5jJxgGTqyOSa7t27WTRTY1Gg5CQEOOtLJ+B9/82b96c23fm6dOnolxvUxVZMRrW7t27uZ7yRo0aMVSjy5YtM97K8iGU/6+zszOXxSc1NVWkLOaZXA8dOsT1lDs4ODDRzZCQEG6tgrli+fLlsv+3dOnSaNOmDXeuIL3NlHKVGbUXL17ksnDZ2epJIPgAACAASURBVNmhU6dOsrG1a9daVCPF0NBQ2f9bpEgRoVGyc+dO3rCpclR/h6QoZ+Lx48c4evQoM1GlUqFHjx6yse3bt1tUWcO2bdtkhgYhhLETMiB4Xg9SSl8D/4+UAABjsv/yyy/cotgPPvgALVq0kI2tWLHCYkLMISEhsv/Vzs4Offv25c4VCGCH1tttCjBy/fPPP3lc/ahYsSLjfV2/fj2vbsIs8dNPP8mUBLVajSFDhnDnCuT6B6X0llEWx+InKPLUr169isuXWcIZW1tb9OvXTza2c+dOXsqDWWLPnj1MDvOwYcOEczn72C0YORUkCyKgoHx++vQpjhxhazsJIRg6dKhs7MSJE/j777+NusD8gtOnTzM5zMOGDeOyMx0+fJhnALwAwNV8jIA/oOgunpqaKvLyM3K9fv06U0RqroiNjWVSLfv3789tSnzx4kUetWg6gI1GW2AWUEpvgLM3iOqAvLy8ZM7LhIQEi4mW8P5XDw8PhtEVkAyAY8e4W65JvKSU0pcAGCGK5Nq3b1/Z7zM1NdViHH9v3rzBypUrZWOtWrXC+++/z8x9/fq1iAggU65ZjZKdAGT0As+fP2fYLzIwfPhw2evbt29bRMjq33//xebNm2Vjffr0kXmiM/D8+XNRqtRPxlkdFyeg4PTWVRQ7bNgwWWH0ixcv8OOPPxp1gfkB8fHxzCbSqVMnbjfStLQ0UTqFyeRKKb0HTj6zqF6kf//+sr4NaWlpmDFjhtHWl1+QnJzM/H4bNGggZGcS3L/1JkrxgTblhFmESK6ff/45E/GZNm2a2Xd412g0mD59umzM0dFRmJInuH/bKaUmcVNrfz8blOMiuTZv3pyJ+MyZM8civOozZ86U/X6LFy+Ob775hjtXcP+iKKWmbKDGKMqRkZHcZ9DZ2ZkhlVm6dKlFNLUNCgrCy5f/97eo1Wp4eXlx5wru37+UUlN27GbO8wMHDnCdtKVLl8ZXX30lG9u4caNFMOetWrWKofcVOf0E9+8ZskSSM40SbQrXVuXskJAQbsF748aNmUZPwcHBiIuLY+aaCyilmDp1qsyTamtri4EDB3Lnr1u3jpcTeR8mqDvIgOgwDAsL49YBVa1aFV26dJGNbdq0CZcuXWLmmhNmzJjBbJje3t7cuZGRkbxDJAXAdqMtkA/GxbZ582Y8e/aMmViiRAn07t1bNvb7778jKspkP8U8waJFi3Dv3j3ZmI+PD3fu8ePHRZ3RmefHyGDkevDgQW4HXCsrKyaad+nSJfz888/GW10+QHh4OBMV9Pb2ljlUMnD9+nWRc8jUuanroUj1iYmJEfXYYPafuLg4s0/PO3DgALMn9e/fn8t+mJCQgG3btvE+xtRy3QJAxqDw8OFDoeNvxIgRsmhJYmIifvjhB6MuMK8RHR3NOHO7d+/O7WGRlpYmShs3pTMXAA5A0estJSVFGNny8vKCjY1N5muNRoNp06Zx9Wdzwd27d7FixQrZ2Mcff4xGjRpx5ytrsbXYkpG6BcgjJQAQppx96dIlURgNfn5+skMgOTkZ/v7+ZiuETZs24ezZs7KxkSNHoly5csxcXn2CFuuN3D2Yh3VQpPrExcUJQ5GTJk2SNTLSaDTw9fU1WzKDqKgoJjWiV69eqFWrFjNXRz3GDhOwMymxDYpUn+TkZPz0E3/v9vb2RsWKFWVj06ZNkxlj5oRLly5h7dq1sjE3Nzd88skn3PnLly/nDR+llBqtk7sAUQBkDVU0Gg0TIs+Ap6cnw14TFBRktg6ie/fuYeHChbKxDz74AF988QV3vqAe4yaMT/Esg5Z4hGEiEBkan332GVq1aiUbCw0NNVvv6/Pnz5noV+XKlZlUtgysWbOGFzl6ASkF0mSglD4HJw1QWReTgTp16sDT01M2tnv3brPtW/LmzRtMnTpVdi+KFy+O8ePHc+dv27aNxySpAcdZY0xo9TTmMA0LC+Ox+KFChQpMBtHp06exdSvj6zcLUErh5+cnuxdWVlbw9fXlzj9y5AjDWKvF2qwvZEYJpfQ4AKaSR7Rp1qlTB3369JGNRUVFYd26ddz5BRlXr17F7NmzZWPVq1fHgAEDuPM3bNjAy2FOARBslAXqgLbOgXkyli9fzg0xV6xYEaNGjZKNXbhwAfPmzTPWEvMMDx48wLfffisbK1u2LMaOHcudv2/fPp7HmgIIMsoCdUCb98po0uvXr0diIks8U6xYMUyePFk2dvfuXXz//fdGW2NeISkpCWPHjpVFNW1sbDB16lTu/PPnz4uYq+YYZ4ViaCml5yvHIyIimKgPIEX1ZsyYIfO+vnjxAiNHjjS7Or+0tDSMHTtWZkirVCoEBARwoyT3798XpVrOMwF1Nw9zlQNHjx7lMl0CgL+/P4oWLZr5OjU1FSNHjsSrV6YqSTQNKKWYPHkyo4z6+vpya0levXol8lgvMWG9ZlbMgSIKdv36dfz222/cyePHj0eZMmUyX1NKMWHCBLNM4/rhhx+YqOaYMWO4tSQajQarV6/mfcwmSmks74KRsQAKZtpnz54JI9FeXl5Ma4XAwECzdCSsWrWKMaT79evHdeYCQqffEUqprGkJSxcFzFIOnDp1Sth0j/fjmjNnDqKjo7nzCyKSkpIwcuRImUVICMH06dO5fPivXr0S1desoZSyzSRMg1lQbJq3b98WUk32798ftWvXlo2FhYUJ6YQLIjQaDcaMGcOkO33//fcoVaoUd/7SpUt5H7WXUnqWd8EE+BGK1IGEhAQmQpCBzp07MyQV+/fvx4YNps5QMi6+++47hvZ4+PDhcHR05M5Xet61iIbpWHyUCAUgo29JS0sTbeyoX78+wwATHR2NBQsWGG2BeYG5c+cy0WpPT080aNCAOz84OJhnmMWBkxVgIuwCwLgLlyxZwp1ctWpVJj87NjYWfn5+RllcXmHdunUMdf6nn34qpGNfs2YNLzc9CQD3QTY2KKXnATAVvEuXLuU6/uzt7Rln2NOnTzFmzBizqgfbv38/kzFSp04dnTVCSlISSMQFeZLfRil9AIUnH5AUcl59l7W1Nfz8/GRkG69fv8bYsWO50ZWCirNnzzK1mpUrV8bo0aO5848ePSpqXMvYG4xRQindB4B5d0BAANfrVqJECSxcuFDmpUpNTYW3tzdT/FIQkZaWhlGjRjEKjpeXl7BYdtGiRTwa4FQAeRZqoJReAIdOb86cOdzCLSsrKyxYsEDmpaKUYty4cWZRX0Ipha+vL/OgdOrUSUhRuH79ei7VI4DZvEFTgFL6EJICK8Py5cuFz9/8+fOZJmTTp083m/SBRYsWMel4rq6uwjSQ/fv3c6keAcw0VYG7EpTSZEheOhm2bNkidPj4+voyXrqVK1eaTfpAZGQkwsLktkT16tXx3XffcefHxMRg+3Zumdd8bQ2lyaH9PTH7xZEjR3SSyihztHft2iVykBQ4HD58mMlCKFu2LGbNYvQVAFL63qpVq3iXQiilLK2k6TBdOXDlyhWhw+eLL75giBlOnTplNgbnhQsXMGnSJNmYra0toy9m4Pnz55g/nwkQA0AEpTQvlY65AGTKb3x8PIKD+UkvzZs3ZzJorl27htGjR5uFwXnnzh2MGDFCZg+o1WrMnTtXlvafgdTUVCYtU4uzkOp2ZOBFSgDOpnnt2jXmQMhA48aNMWLECNlYfHw8+vXrx1POCwwyFFclHWf9+vWF6T3//POPsEjLhHSxIsyAIlry+PFjkZcYNWvWhL+/v2wsMTERAwYMKPDN94KCghhlrVq1asKDMD4+HosWLeJdOqhNe8xLzAUgY1RISUkRsmuVK1cOCxYskB0MaWlpGDFiBOOFLmjYtGkTc1iUKVNGeBAmJydj5syZvI+6AtMTFyixHMCTrAPp6ekICAjg5qrb2dkhODhYVmyZsYeJ0kgKCqKiovDtt9/K6hWLFi2KxYsXcw9CjUbD5LFr8QhAXnN1bgHA1ClNnz6d601Vq9VYuHAhSpcuLRtfsGCBsH6soCA6OppR1lQqFYKCgrjpPYDkIOXcpxTkQQptVmjTUJimewsWLOBS8AMSwYqy19DmzZuFZ3JBwe3bt+Hl5cVEE6b9r70zD4/p3v/465tFJLHTalNtJZTSWnspqqUbrTVJ7TsRy02FhqCoiD22kqAqQkRVLbex9mqvqi7EUlv5NbUmiCqlQjYRyff3x5kZSc45MxPZJng9j8fzzJkzOcl3zvd81vdn6lRV4MTIggULcgy4NSDRiKYXJVLKOHTEgnSClIwdO1alnvfDDz8wduzYEt1z/c8//zBo0CDV93nUqFGq2UpGIiIiOHdOc95lsFbQT88piUZjuJ85da0PP/xQVRZy4cIFfHx8SuRU8KysLIKDg1XqHpUrVyYsLCzHkEEjUkqCgoK0vOHbgHYxexEipTyERrPY2rVrNedbgDIUMvcQHOMXs6TOuVi2bJlKMcLZ2ZnFixdTpkwZzXNmzpypVcd9D9Du1itCpJSX0Hgg79q1S1ddq1mzZqqmvLS0NIYOHVpiM2HR0dFMmTIlx2v29vYsWLBA1eBvxMyeFlBMPQcmDD1Dqq7BEydOsG7dOs1zatWqpQokZGZmMnr0aL1skM3z888/a0YZp06dqmrwN/Lll1/qfY8nFNGkb10MDbQBuV+/fPmybvbjqaeeYt68eSrHevr06XpD5myeEydO4OPjozJc/f39VbaEkV27dvHDDyq7H2COQSa9uAkgl6hMUlKSrrqWi4uLqiIBlHK+kjrn4uLFi/Tr108VkO7evbtqDpoRM3va6mIsjc7OJHKJyty7d4/JkydrOhkODg4sWLAgR98QKPPBpk2bViIHod64cYMBAwaoempbt26tW4VgZk/7Xkqp2Tug6ZQYvBc/lJIjE6mpqYwZM0YzBWVnZ8eSJUt4+eWXc7z+f//3f3zwwQdcvHhR86JtkYyMDAICAlSNdK6urkRERODm5qZ53ooVK/QGlwUVYy9JbgKBHB34RqNFr+Zx2rRpKhWYhIQEunbtquvM2CJSSkJCQlQpYgcHBxYvXqxr4Pz3v//VG3IWKqX8reCv9IGYTq7hbAATJkzQjdL5+/urHM6bN2/Ss2fPEmfARkZGMm7cuBx7kxCC6dOn6xo4x44d0+v92iSl3Fk4V5pnlgOqhr6QkBC96BNdu3ZVCVWkpaXh6+urO6zPVtm6dSu+vr7cuZOz2mrkyJG6alvx8fHMn68ZND8E2MQwLSnlDjSGs4WHh+sOv2zVqhWzZ8/OUa+emZnJmDFj9MqZbJaYmBj69u2rEoPx9PRUVV0YuXHjhl5p0wWKQZBCC0NvicoK27Jli65E8EsvvURoaCgODg45Xp87d26JM2BPnTpFjx49VKXDrVu3ZurUqZrnpKWlERgYqPV73gTGaZxS5Bjm3qh+gUOHDun2b1arVo2IiAhcXFxyvB4VFcWYMWNKlAhJQkICPXr0UNl79erVIzQ0NIfIipGsrCw+/vhjLbvyLjBCdYIBvUwJUsrf0ahpPnDggK4al9Foz609fenSJXr06FEimt9v3ryJj4+P6uHt6Oio6XQZOX78uN6QwZNobFLFhaEHQZW1OXPmjF7dn8lob9CgQY7Xr1+/Tu/evUtEL0JaWhofffSR6uEthGDWrFkqp8vIxYsXVYpVBv5CY5MqLgw9CKNyv379+nUCAgI0H2xGo/2tt97K8XpqaipDhgzRlYy2Je7du8e0adOYPn266ncMCAhQOV1GEhMTGTlypNaDIRUYUygX+wAYsjUfkiv6mpqair+/v8pYNzJy5Eh69uyZ4zVjsCU8PNzmSwiklCxbtozRo0er1qhXr14qp8tIeno6I0aM0MpqZgJDizv7lQt/IEfWxii+oaHcCICXlxejRuW8zY3BlpkzZ5aImvVNmzYxaNAg1Rq9/fbbhISE5HC6jGRlZTF69Gg9daoPi2oIppV8gjKPLAdBQUG61QVvvvkmM2fOVP3uq1evJjAwsEQ0Sf/www90795dtUYNGzYkLCxMs3wWlL/L2bNntQ5NkFLakhzZQhTxkxyEhIToqufVq1ePJUuWqCprtm7dyuDBg3Xvc1vi6NGjdO3aVZUhqV69uqbTZWTRokXs26dZ2T5PSqkrR6brlBiYSi69fFBSi3pqXJUrV2b16tUqx+TatWv06NGDVatW2ewD8dChQ3To0EH1hzTWLutFXBMTExkxYoTWHI8sYJiU0tYGfHwGqMJxGzZs0C0FcHZ2JiIigvr16+d4PSkpCR8fH+bNm2ezD8TTp0/j6empcjSNUqJ6KeW7d+8yYsQIvTkeIw369DaDIR2qSonGxMTozriwt7dn0aJFvPHGGzlev3v3LmPGjNGLdNgEly9fpkePHpoS5H5+frrDL43ym1ryuihZzeKQntRFSnkYWJb79VOnTqkahLMzZcoUvL29c7yWlZVFSEgIQ4cOtdkHYmJiIkOGDGHevHmqZ0WXLl1U5WnZmTp1qp785hIppbblUEwYyi5VkaArV66YrT338/PTnJi8cuVKevXqZbPzadLS0hg7dizjx49XPStbt27NokWLdA3XpUuX6mVvo6WUNpX+k1LeRiOwcfv2bUaOHKk778vb25spU6aoos5btmzB29tbz3AvdjIzMwkJCWHIkCEqR7NBgwasWLFCU9YZFLWtr7/+WuvQIZQssc0gpbyHEuHPEdgwypRrCQYBvP766yxcuFCl1PrLL7/QqVMnm+3jlFKyYsUKevbsqaq2cHd3Z/Xq1aryNCN79+7VU4qMBzSbOI2YdUoMtbd9yKU8kJmZyUcffaSr7lOtWjXWr1/PSy+9lOP1jIwMZsyYwdChQ7WG4xQbd+7c4dNPP6VPnz5cvXo1x7GyZcuyatUq3n33Xc1zjV9Ind9nppRSe/JkMWKoae4NqMKJn3zyiW5JVoUKFfjiiy9UzpkxqtmzZ0/dxq/iIDMzk8jISLy9vVWlLqVKlSI0NFQ15dyIcTCQTl16lJRyQ8FfcYHgS64ptKA0W/7888+aJzg7O7N8+XI6d+6sOrZx40a8vb11I0HFgZSSzZs307lzZ44dO5bjmJ2dHUFBQbpCFAChoaHs2bNH69D3KBLLtshYQPVlXLt2rZ7CFPb29oSEhODr66s6tnv3bjp16qQS8ShufvjhBzp27KjZNzBs2DBmzZqla7hu2LBBNTXawAlAW6Kr+JmHRv/m7t27zaprjRkzhkmTJqkM2MOHD9OxY0e2bNliU8G/w4cP4+npqWmAenl5sWzZshwCDdnZs2ePntLRZUC7mL2YkVKuQ6M5+rffflP1vWWnd+/eLFy4UBVZP3PmDF5eXkRFRdlU8O/06dN0795dM/v6xhtvsGbNGipUqKB57okTJ/QCDElAbxvLagIgpfwZjVLBhIQEAgICdNembdu2rFy5UtWz+ueff9KzZ09CQ0NJT0/XPLc4SEhIYPDgwcyePVuVqa5Xrx7r16/nmWee0Tz34sWLetUZGUAvS1lNYc3GJYT4GA0FhOeee44NGzZoTjQHRanJz89PM8Lh7OyMn58fPj4+mk3jRcWePXsIDg7WTKs+/fTThIeHq+Z1GJFSMn78eD2j4CfgrWKY3m41QojugGoKUKVKlfjqq69UqiBGMjIyGD9+vGZWxcHBgYEDBzJixAjdtF5RcOTIEYKCgjSjphUqVGDx4sW6ks6gyObmboY3cBr4l6EJ2SYRQrRCMbBzWG/Ozs6sXr1apQpixFgGojW8ys7Oji5duhAYGKhSASpKzpw5w+TJkzl06JDqWOnSpZkzZw7t2rXTPX/dunV6AxSvAQ2llLYZZgaEEC8BB4EcN5a9vT1hYWG0adNG99xVq1Yxe/ZszYdmmzZtmDRpkm6vXFFw+fJlpk+fzv/+p1KIxN7engkTJtC/f3/d83fv3s3w4cO1fr8UoIm5coHiRghRFTgGPJX7WFBQkO5MB1AmgY8fP17ToHn11VcJDg6mZs2aBXm5eeKff/5hzpw5/Oc//1EZrUIIhg4dyujRozVLtkApi+7Tp49WtjYTaCOl1FbysAGEEGVQIv4qA+LDDz9UleFlZ+/evYwYMUIz+l63bl2mTp2qO5unKEhNTWXRokWsXr1aszfC29ubmTNnqvpkjFy8eJFu3brpqbP2kVLa7OAsIYQDisqaqnSmc+fOzJs3T/f7/Pvvv+Pr66sKfoOi/hkUFKSqWihKMjIyWLFiBUuXLtWskGjVqhVhYWG6tt0///xD9+7dtQZMAwRKKTU1n7NjrVMigC1Ax9zH6tWrxxdffKEpywiKobN8+XIWLFig+UB85plnGDhwID179swxubaw+fXXX1m+fLmuOtFrr73G/PnzdR0ugFmzZhERoRoRAYrsZCMbUQMxixAiAhiU+/Vnn32WDRs2qOZZZCc6OprJkydrfnkrVapEnz59GDhwIGXLli3QazZHbGwsERERbN26VbOPwtiYpTdED5Tos04E5w7QTEpp881RQoggYEru1ytUqMD69et1ZRlBUbgZN24ct26pq9NcXV3p0qULw4YNM/vdKGguXbrE559/zsaNGzX3EQ8PD0JDQ3UDCKD8Xn5+flrnZwHvSSnVFrGNIYQYhMZcmtKlSxMZGamaZ5GdQ4cOMXLkSM26/FKlSuHt7Y2fnx9PP/10gV6zOa5fv86qVauIiorS3EeqVq3KwoULadKkie5nHDt2jL59++qVGfaXUmpqtNsSQoi3gO/IFUgwlle+9957uueePXuWESNGaGap7ezsaNu2LaNGjTJ7zxc0N2/eZM2aNURGRmoa1mXKlGHWrFm8//77up8RHx9P9+7dtWRiASZKKYtVKtYahBD1gAOAqn5p0qRJDBgwQPfcP//8k5EjR2pmqYUQvPnmm/j5+al6PQuT1NRUNmzYwPLlyzX3EScnJwIDA83+XteuXaNbt256lTafSynVtYk2hhCiGnAUUBmIQ4cOJTAwUPfcmzdvMmbMGN0s9SuvvMLQoUNVvZ6FSUZGBtu3b2fx4sVcuKCuXra3t8fPz48PP/xQs6kdlCREr1699KpL/gu0t2bul1VOCYAQ4gmUm8s997FmzZqxfPlys5Hx/fv3ExAQoNeoRtWqVenbty+enp489ZQqYFQgpKWl8d1337F27VrdOj5HR0cCAgIYPHiwrrcLSl+NjpZ4Bsof3+YNHAAhhAvwM6AKn9epU4dVq1aZdcxiY2MZOXKk7tySChUq0KtXL7y8vHB3V311CoSMjAz27NnDl19+qVuiZGdnx6BBgxgzZoxu9AaUcqWJEydqOTQSGFASDBwAIYQdsB1QPfWfeeYZoqKiVH1f2bl06RKjRo3SFadwcXGhW7dufPDBB7qqZfklMzOTmJgY1q9fz7fffqurQuPt7U1wcLBu3TIoGVE/Pz+9FPkkKaXZOldbQgixAvDJ/XqFChVYuXKlqu8rOzdu3CAwMFBXnMLR0RFPT0+6dOlC48aNze6BD4qUkiNHjrBp0yY2b96sW2PfunVr5s6dazYzd/z4cQYNGqTpQFNCDBwjeoEEJycnPvvsM7MR1JSUFCZPnqzbE2hnZ8d7771Ht27daN68uW4JXH6JjY1l06ZNbNiwQbcXrWHDhixcuJBq1arpfk5cXBz9+vXT64/ZDnS2xfIeLYQQA9FQfbOzs2PWrFm6KnKgPNvmzJnD6tWrdfe/N954g549e9K6detCqzqJi4sjOjqaL7/8UrcXrUaNGixatMhsYOjvv/9mwIABnDp1Suvwr8AbBtEWm0cI0Rblu6gyKAICAlSS+9nJyspi+fLlLFy4UFeF65VXXqFXr160adPG7LMtP1y5coUtW7awZs0azewNKHLkn376qdnAUEpKCr6+vhw8eFDr8DngVSmlZnQhN1Y7JQBCiBrAXkAl+v/yyy8TERFB5cqVdc9PTk5m4cKFrFmzRrf2zs7OjmbNmtGuXTuaN29u1nCyhsTERA4cOMCuXbv49ttvVZro2WnRogVBQUFmI0pSSmbPnq2XIZHAICllZL4uuogxOJw/A7VzH6tWrRqRkZFUr15d9/z09HSWL1/O559/rqsGBMrDqH379rRs2ZIXXnghX9eckpLCwYMH2bNnDzt27DDbtPvyyy8THBxsMaIUGRnJjBkz9GqxJ0gpi21y+4NgcDj/B7TIfaxKlSpERESo+r6yk5mZydq1a/n000/1mv0BqF27Nh07dqRly5bUrVtXN5JiDXfu3OHIkSP8+OOPbNu2TTeIAUqzXVBQkK4AhZEtW7Ywbtw4vc2/RBmuAEIIe2AjoFJocHZ2ZsmSJRZLALZu3crs2bPN/n2fe+45OnXqxOuvv07Dhg3zZcjeu3eP48eP89NPP7Ft2zazEvFPPvkkEyZMoEOHDmY/c9++fQwfPpyUFM2xI9sBL0NzaolBCBGGoraWA3t7e6ZPn66rJmfkxx9/JDg42Ozft2rVqnTs2JFWrVrRuHHjfFUoZGZm8vvvv7N37162bt3K6dOqmZAmypcvT0BAAD179jS7R5w4cYLBgwfrZUgOopRFF+usmbwihPgEDbVGIQQjRozA39/f7PnHjh1j8uTJZiX4K1SoQPv27XnzzTdp2rRpvsqnpZScOXOGvXv3sn37drPKqc7OzgwfPpzBgwermrmzk5CQwIABA4iPj9c6fA54zaAOWmIQQvQBogBV9KZv37588sknZr/rZ8+eJSgoiAMHDui+x9XVlbZt2/LOO+/QtGlT3R4da4mPjycmJoYdO3Zw8OBBXWfXwcGB/v374+/vr1sJBUq228fHRy9D8jfQUkqpvzHkIk9OCYAQ4l/AbkBVk/Pss88SGRlp0ZGIjY1l2rRpel5VDtzc3GjSpAkvvPAC1atXx93dnUqVKuHq6mq66TIyMkhJSeHmzZskJCRw/vx5zp8/z7Fjx4iNjbWo812tWjXGjBlj8SGYkZFBYGCgOa1/q2rmbBEhhAfwC6Cq3XjiiSeIiIigbt26Zj/j0qVLzJgxg++//95ik2WV9Ka+UwAAF3tJREFUKlVo0qQJtWrVwsPDA3d3d6pUqYKLi4upGSwzM5Pk5GQSExO5fPkycXFxxMXF8dtvv3H8+HGLDX+VK1fG39+fHj16mDWopJTMmTPHnNb/Z1JK/bCHDSOEqIzicKrSGS4uLixdutSiUf/3338zd+5ctmzZYvFvXr58eZo2bZpjXZ988klcXFwoV64coESJkpKSSEpK4s8//zSt68mTJzl69KjFhr8yZcowZMgQiw9BUBzNmTNn6u0BWwFvW+770kMI4YxS7qNaPEdHR+bMmUPHjqpq2xwkJSURGhrK2rVruXv3rtn3uri40KRJE+rUqUP16tWpUaMGVatWxdXVlfLly5ved+vWLVJSUrh69Srnzp0jPj6e2NhYDh06ZDYgBEpGoE+fPhYfgmDR0TwAvF3SDFcwOZxfAV00jjF27FhN4YLspKen8/nnnxMREaHnsJlwcnKiUaNGvPzyy7i7u+Ph4YGbmxtlypShbNmyJoPq9u3bpKamcu3aNeLi4jh37hynT5/m0KFDelkqE/b29nh7exMYGKir1mMkJiaG4cOHa0k6A5xBMXBsSSbWaoQQn6Ih2w7Qv39/Jk6caNaANQaJFi9ebHEgtb29PQ0aNKB+/fq4u7vj7u5OtWrVKF++PGXKlDE9D5OTk0lNTeX69evExcVx/vx507rq9Htk/31o27Yt48ePN5v1AkUpcODAgXpBkGso62o7Kjl5QAgxFp05OZ06dWLOnDlmqzOklGzdupV58+ZZVM6zs7OjTp06NGzYkBo1auDh4cEzzzxDxYoVcXV1NWXKUlNTSUlJ4Z9//jE9X8+ePcvBgwetUudr0aIFkyZNolatWmbfl5CQwMCBA/V6SJKA1nkdfplnpwRACPEuSiRKZRE88cQTLFiwQHfkfHYOHTrE0qVLdUturLgOHBwcdNP/lqhevTrDhg3D09PT7JcG4OrVq4waNUqzwdbAAillsU/3zg9CiIYoSjDlcx+zpgbYSGxsLEuXLjVbcmMJR0fHB17XqlWr4uvrS/fu3S2mPW/dusW4cePYtWuX3lvWoyhGlIhSAS2EEM+jZDhVchmlSpViwoQJ9OnTx+LnXLhwgWXLlpktubFEfta1QoUK9O/fn/79+5scHD3u3LnDtGnT9NSYAH5E6SPRT+3ZOEKISiiCGqp0l52dnakG2FKG49q1a4SHh/PVV189sPxzftbV2dmZXr164ePjw5NPPmn2vZmZmSxatIjPPvtML/BxEqUE5OYDXYwNIIQoDXwLaKa7evXqxcSJEy1mOBITE4mKimL16tUWHQc98rOujo6OeHt7M2zYMLM9fKAYZlFRUcyePVvv5yWgRNJLzhTmXBhKatcB3bSOt23bllmzZlnc29LS0vjqq68IDw83m+k0R37W1c7Ojvfff5/hw4ebLdUysn37diZOnKjnIN8CWpWEPk1zCCHmAwFax5o2bcrChQst7m0ZGRls3ryZZcuWafZ1WIOjoyP37t17YOW9Vq1a4efnpyuGk529e/cSEBCgl9FMBzpIKXUNKz0eyCkBU2NeNKC6g4QQDBkyhICAAKtS/idPnmTjxo0Wy3AKAgcHB1q1aoW3tzfvvPOOVde3b98+Ro8erTsZGwgFRlnTxGPrGBrzdgKaUjyenp5MmzbNqhrH8+fPs3HjRrZs2fLAm6e12NnZ0bx5czw9PWnfvr3FCDooZQL+/v66A62ANYCPDc6ZyTNCiOooho5m6OPdd99l9uzZOaLeely5coWNGzeyefNms2UiBUWjRo3w9PTE09PTYgQdlPpnf39/vXkVALtQMiQ2q6BmLQbHZDugGQWy9oEIinLK119/TXR0tF7Nd4Hy4osv4uXlhbe3t1WKbtevX2f06NHs3aursv4r0E5KqbtRlxSEEK4oJXqaUaCaNWsSFhZmVRlsSkoKmzdvJjo6WiWhXRg8//zzeHp60rVrV6v6Q5OTk5kwYQLffPON3lvOA22llLY5qCMPGDJhy4DBWsfd3NxYtGgRjRo1svhZd+/eZfv27URHR3PgwIFCn/xetWpVOnfuTNeuXa3qD01PTzf1w+hwFeV+tc1BHXnAIAYVZPinomLFisybN093SHN2MjMz+d///sfXX3/NTz/9VOiT3ytWrEiHDh3o2rWrxWoY4/UtWbKEJUuW6FVOJANdpJTfPsj1PLBTAqZSrm8ATRmeZs2aMWfOHKulJo0Ny9999x0xMTH89ddfD3xt2XF1daVp06a0atWK9u3bWy1pmp6ezqJFi8xNQM4CPpJShhbIhdoIQoiaKAaspiZw3bp1WbBggdVSk8aG5Z07dxITE/PAUYDclC5dmsaNG/P666/TsWNHqwUSMjMzWblyJfPnzzd3w4cAHz8MjqYRg/ToN2iIGoDSQzB//nyrHohwv2H5m2++Yd++fZw9e7ZAZiM4ODjQoEEDWrZsSceOHc32M+W+nq+//prg4GBzpUIPjaNpxCA9+jWgOUypcuXKhISE0Lp1a6s/MzY2lu3bt7N3715iY2MLZDaCvb09devWpUWLFnTo0CFPAgm7d+9m/Pjx5spWvkV5EGrW/ZREhBCOwCqUmVIqXF1dzQ5/1SIuLo5t27axd+9ejh8/XiAGjxCCF154gddee43333/fqiirkcOHDzN69GjdmWcojmb7klqypYXBgA0BNCWaHB0dCQwMpH///lb3cV25coVt27bx888/c/ToUbO9nXmhevXqNG/enLZt29KiRQur+wVPnz7N6NGjzQWGzqE4muf03lASEUKMRJl1pfpD2dnZMWTIEPz9/a0KmoISKNqxYwc//vgjBw8etFgCay1PP/00zZs3p02bNrRq1cpqgYTLly8TGBhorvXiGoqjqRrObS35ckrA1IvwLaBpoTo7O+Pr68uwYcOsXggj8fHxHDhwgNOnT3P+/Hni4uL4888/zUYEKlasSI0aNUz1sf/617+oX79+nps0Y2JimDJlimroXjbuoqgxrcvTB5cQhBBPoRiwmhaqg4MDvXv3JiAgwKrodXauXLlCTEwMp06dMvX/JCQkmDV8ypUrZ1pTDw8PGjduTKNGjfL8nTp58iSTJ0/mt99+03uLBMZJKefm6YNLCAYD9j+A5lALIQSdO3dmwoQJFuu/c3P9+nX2799PbGysqe784sWLZssEXFxcTL0nHh4eNGjQgCZNmuRZbSQuLo7g4GC9qc9GQlGCCCW2FE8PIUQpIBLoqfeet956i6CgIN2hV3rcunWLgwcPcuLECVN9clxcnNneHycnJzw8PEx9gPXr16dp06YWS1Nyc/XqVebOncvmzZvNvW0tMPBhcjSNWDJgQcmGBQcH51k8JDU1lUOHDnH8+HFTP0FcXJxZw8fR0ZHnn3/etA/XqVOHZs2amRW40SIxMZGwsDDWrFlj7nm+G0WsQHtUdgnHnAELivrl1KlTrQ4SGUlPT+fo0aMcPXrU9HyNi4vTnTgOSsDg2WefNa1r7dq1adasWZ7lwdPS0ggPD+ezzz4zt++fQCmdtZ0J2gWIEKIXyl6saek/99xzBAUFWZU1yU5mZibHjx/n8OHDpnU9f/48N2/qV6ra2dnh5uaGu7s7NWrUoFatWrz66qt5FpC6d+8eX3zxBQsWLDC3P8ShrKvVTe1a5NspAZN6UxSgK6Zes2ZNgoKCrOo1MYeUktu3b5OSkkJqaioZGRmmprzsjT4PyuXLl5k5cybffms283QB6CGl3J+vH2bjGAzYzwDdhgM3NzcmTpxImzZt8i0famymTElJIT09nbJly1KmTBlcXFzyPcPmxo0bzJ8/n02bNpl7CF5HmWugW0fwMGAwYGejNF1qLlrFihUZO3Ys3t7e+ZYPNTZTpqSkkJKSQvny5XFxccHFxSXfUocpKSksWbKElStXmov6pgB+UkrdOoKHAYMBOxaYjoZMJShOoL+/P/369cuzQ58b45qmpqaSlJRE2bJlTUIV+V3X9PR0Vq1axZIlS8z1uWQAE4D5D1NGUwvDfJowcg3ONOLo6MjgwYMZPnx4vofWpqWlkZqaSmpqKrdu3cLV1TXHv/yQmZnJxo0bmTdvnrlSbYky6X7iw+hoZkcI0RElG6bp1dnZ2dG9e3cCAgLyPbQ2PT2d1NRUkpOTSUpKwsnJybSm+Z0lJqVk586dzJgxw1KFy2qUvbjEiVDkBSFECxTBCt1mqnbt2vHxxx/ney6UUegpKSmJ5ORkHB0dcXFxUYmQPCi//PIL06ZNMxegByWA3V9KaV4dwQoKxCkB0wPRH5iLjocI9wfDvPnmm4Wigf+gJCQksGrVKtatW2dJiWYbSobEvPzFQ4QQoh+wFNB9Ir344ov4+PjQqVOnQtPAfxBu3LjBypUrdYezZeMg0F1KGV80V1b8GB6IkYBuSqRatWoMGDCgyIebWiI5OZm1a9cSHh5uqQ/tD6CblPJEEV1asSOEaIryQNQt/K5SpQoDBw6kX79+haaB/yCkpaWxfv16wsPDdXXzDVwCekopdRtMHjaEEC8CG4B6eu8pU6YMvXv3xtfXN9/SoQXJvXv32LZtG0uXLtVT6jFyA8W42VFEl1bsCCGeRWmAf03vPc7OznTr1o0hQ4ZQtapqIkOxkZWVxZ49ewgLC+PECbNbbBpKOfSiIrq0YkcIUR5l0K3uIBoHBwc6dOjAv//9bzw8NKvli41ff/2V0NBQ9u3bZ+5t94AZwNSCqkAoMKfE9IFCtERJpz9n7n3169fH19eXt99+O98Ru/xw7NgxoqKi2LFjh6W66TsoUbmFD3tUTgshxMsoho7+YAuUAUq+vr60a9cu3xG7/HD69Gm++OILNm3aZMnJzATmAJNL2kyDgsCgzPUlGrNMsuPm5oaPjw+dO3cuVmPn0qVLrFu3jrVr11qSO5UoD4SRUsqCKcQtQQghqqAMbDOrC1ypUiUGDBhAly5drGqGLyyuXbvGxo0biYyMNFuOYGALyjyoRyYwZMTQAB8GDDT3PqNz0qNHD4vKV4VJYmIimzdvJiIiwhop0p+B3lJKXeWRhxVD/9B0YDSgG9VzcnKiS5cu9O7d26Jca2GSmprKjh07WLFihaUIOijlWj2klPpDVh5SDMH60ShrqxvVs7e3p0OHDvTr18/iPLXCJD09ne+//57w8HBLTiZAPMr9atZrySsF7pSAaWjbWGA8ZhYClF6Bt956Cy8vL1q0aFEk2ZO//vqLnTt3smnTJv744w9rTtmNknK06s0PK4aN89/ANDTm1GTHycnJtK6tWrUqkuxJYmIiO3fuJDo6msOHreqzOgz8W0ppeWDOQ4xh4+yLUjKhKVphpFSpUrRs2RIvLy/eeeedQpsgnJ2kpCR27drF5s2b2bdvnzXN9GeAD6WU3xX6xdk4hmxYGGC2iNjOzo5GjRrh5eVFp06diiSgkJ6ezu7du4mOjubHH3+0ppn+T5Roa1ShX5yNI4RoBSzBQpAIlOGxRvW6oggoZGZmsn//fqKjo9m5c6c1Tdc3gWAg7GHs98oLBln+peio6WWnZs2aeHl58cEHH1ClSpVCv7asrCyOHDnC5s2b2bp1qzVN16kolTMzpZTmByE95BjEg8Iw0+JgxMPDgw4dOuDl5VVkAYWTJ08SHR3N1q1brQkKZaCU9U8sDGGRQnFKTB8uRF2UG8yqjh43NzeaN29u+ldQaUpjQ19MTAwxMTFWDVQ0cAmlMfY/BXIhDwlCiOeARYCnNe+vUqUKzZs3p1mzZjRv3pznnjObRLOa9PR0jhw5wv79+4mJibFqoKKBG8DHQMSj/hDMjiG6HoIShbUYHShfvjyvvvqq6X61Vo3NEsaGPuP9euTIEYvD/QykoDjMCx72WvS8YOgNCwJGYqa01oiLiwtNmzY13a916tSxWnXHHFlZWfz++++m+/XgwYPWzkXJQGkInvaw16LnBUNv2BhgIjq9JtlxcnKicePGpr24QYMGBRYsOnPmjOl+PXDggNmm6mxkoWQzP5ZSag47eBQxzDPxBWZiprTWiL29PQ0bNjTdr40aNSqwUtsLFy6Y7teYmBi9mRRa/AfFdnrksl7mEEJ0Q9nLLKqN2NnZUbduXdP92qRJkwILFv3111+mNY2JibFqoKKBQg/QF6pTAqYorBfKxmm9ViDKhPiaNWua1Hnc3d2pWLEiLi4upiZoe3t7kpKSTE2Xt2/f5tKlSzlUJ06dOpVXSctrKF+cJQ+TxGRBI4R4G/gEK51OI0899RQvvPCCSenD3d2dSpUq4erqSrly5XB1dcXBwcHUGG1suDROdc++rpamf+fiNrAYxWh9/BDUQQjRBGVdO2CFc2KkcuXK1K5d23Sv1qhRgypVqpiEKFxcXChVqhRpaWk51tU41T0+Pp5z585x6tSpvEof3gFWACFSSl1t0UcdQ0/CRKAHOo3wWpQrV44XX3zRtK4eHh5UrVrVdK+6uLhQunRp7ty5k2Mfvnr1qulejYuL448//rDWWDVyD6XWfoaUsvAHp5RQDD0J44FBQGlrz3NxcaF27domtUp3d3eefvppkxCFq6srzs7O3L171yRmkJyczN9//51jXU+dOpUXYxWU0sqtKE7mA0uHPuwYgkSjUaoTrJatc3JyMu3DxrV1c3PLsa6urq7cu3fPdK+mpKRw48YN4uPjTbbTmTNnHmQsww8o6/pDXk98VDAEiUYAH2GhMiE7Dg4O1KpVK4cK6bPPPptjHy5btiyZmZkmMYPU1FRu3rxpulfPnz/P2bNnzc1m0+MwMF1KaVYGsSAodKckxw9T+k2CgbeK7IfmjavApyhp5EeuDv1BEUK8hvJQbE8ejNgi5AaKM7KoJE96LmoMfURjgV6YqXMuRlJQIq1zpJSXi/tiSgqGQZofAUPIgxFbhNwF1qM8BPMlL/koIYR4EsWA/Yg8GLFFSBaKSs+Ux86I9QghyqKs61isyJwUE3tR+jJ3F/eFlBSEEE5Af5QAYLVivhw99qEodW4vql7qInVKTD9UcU4GAF2A/GuW5Y9MlAnPa4BNUso8hd4fcx9DPexAlFkJVkcACgmJslFGAeseZ7weHCFELZT7tQ9mJA6LkKMo67rmccbrwRFCVOP+utYu3qsB4BTKPhz52Ml8cAwR9r5AP6BhMV8OwEXgC5R1PVPcF1NSMTgnPVHW9jWKPwB4DSWTuUpKebyYr6XEYnBOuqKs69sUfwDwFrAR5X4tcnXDYnFKTD9cCGegE/cXo6iidhI4hqIS9qWU0uqCusdYxtAQ/x7Kur4PlCnCHx+LohK2RkppVnvyMXnDUOvcGmVdOwP5E87PG/EocqhRUsr/K8Kf+0gghHgVZV27AEWpOfoXsAnlfn2kBScKA0O2sx/QDQtiBwXMPygqaVHAT4979woWw9DqviilmC8W4Y9OBnagOJk7H0XFysJECOGGUpnQCyWgUFSO5x3uB+e3SiktqlMUFsXqlGRHCOEANADeMfx7AyhIreDzKH/0vcD3jyNxRYMQwh7l5jKua0sK1vn8C0VKchfwrZTyQgF+9mN0MDgodVAidu+gTIgvyKzn38AelPv1l8flHkWHweAx3q9vU7AlI8nAfpT7dRdw5FGUWC8ODOvaEuWebUfBloykopR6GJ+x+x8brEWDEOIp4HXu78PVC/Dj7wHHuX+//vSoK2kVFYah5K25f8++UoAfn4kSmDeu6y/F6Yhkx2acktwIIUqjlBTUMvx7EeVmc0UxfsqhROAdURqYb6E88FJQpCNPo5QD/AGcflzmYRsYFGNqoKxnLZQ19kBZy4qG/8sAzkAikMT9df2L++t6GvhDSml2wtpjigZDUMEdZT2N/zyACij3a5ls/xJR1tS4rleBsxjuVeDU44Z128DgfD7P/Xv1RZR1rYIiC25c03Io+7BxXZOA6yjBoD9Q7tlTwMXHUXPbwNAgb1zX2kBNlCyZK/fXtQL31zQZ5TmbCJzDsAejrGv8YyfENhBCVEW5T7PbT09xf13LoqxrGvfX9abhf+O6Gtf23GMnxDYQQlTm/h5sXFc3lDXNbhdnoKxldrv4Atmeryg2sU04Ibn5f48YODHxhJaHAAAAAElFTkSuQmCC" - } - }, "cell_type": "markdown", "metadata": {}, "source": [ - "The [local UCJ](../how-to-guides/lucj.ipynb) ansatz is more amenable to qubit hardware with limited connectivity. It works by allowing only certain entries of the diagonal Coulomb matrix to be nonzero. The pattern of nonzero entries is motivated by the connectivity of the target hardware. For example, if the connectivity is that of a square lattice, we can map the spin $\\alpha$ orbitals and spin $\\beta$ orbitals onto adjacent lines:\n", - "\n", - "![square_lattice.png](attachment:779ec75b-28ff-47e5-b7c0-609fe7e8c53b.png)\n", - "\n", - "The available connections between orbitals with the same spin are referred to as the `alpha_alpha` connections, and those between orbitals of different spin are referred to as the `alpha_beta` connections. The following code cell initializes a local UCJ operator specifying these connections." + "The local UCJ (LUCJ) ansatz is more amenable to qubit hardware with limited connectivity. It works by allowing diagonal Coulomb interactions only between certain pairs of orbitals, with the choice of interactions motivated by the connectivity of the target hardware. As explained in [The local unitary cluster Jastrow (LUCJ) ansatz](lucj.ipynb#The-local-UCJ-(LUCJ)-ansatz), if interactions between orbitals of the same spin are restricted to a line topology and interactions between orbitals of opposing spins allowed only within the same spatial orbital, then the diagonal Coulomb interactions can be implemented directly on a square lattice topology without swap gates by mapping the $\\alpha$ and $\\beta$ orbitals onto adjacent parallel lines. The following code cell shows how to add these restrictions." ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { - "image/png": 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OsiP4LJekRBT3VwCzsrLIzMzk9ttvJzU1lYYNGzJx4kQWLVpEgwYN6Nq163Hv42DJeWPeCt648M7j3r4iZs/OoeWZp8S6jMMKheHCWbBh98GHgQYCAW46pxPXFRdHtbba5qdvw8KvDz4MNAn4fkZdFu7eFc2yar3TX4v8W+z7VzXQzCL4zUEm6dqnThKsem0SjepMik5RkiqwD121qroPHfdXAFNSUnjllVdo3bo1Y8aMYdy4cQwbNozs7Gx69OhBUlJ0DyGQlERy3VQCKSkQCJBcN5WkOnGfo3UUkgKRacQPFv6SgMapcLG3mx63a//9Oh9otvYAkJIEP3ImP0nfEGwNnRoeugNzWSdoVCdqJUk6Avah40eNeNV79uxJbm5uhbZHH32U7OzsqNfS+ZJzGPA/Pyt//KO1L7Bj3Rd+l0kt84P2sLkE/vfjbwSUQOTqYHpdeOQsaObtU8ft9GZwTx+4a1Fk+vZvqp8C/306ZDaKTW2S4lNqEjzWD37+LuR/49bgJCKjCS7uADdmxao6SQdjHzp+1IgA+G27d+9m5cqVjBs3rrzt5z//OVOnTmXDhg0MHTqUpk2bsmzZsirfd8FLORS8lFPl21X8+VEmnNc28nUPq7dHOh39W8Dg1lAnOdbV1R7ntYWzmkdm+3z43//J/qYHnH8SnFAjP6EkVbfm9SLfxfrul5EgCHBlZxjeHjLSYlubpAOzDx0/amT3asmSJZSVlVWYAOaRRx7hkUceiWFVqo1a1IefHP9tpjqMxnVgdOf9AXBkx5iWI6kGSApAv29MxPyLbgdfV5K0X40MgH379iUc9ovBJEmSJOloxP0kMJIkSZKkqmEAlCRJkqQEYQCUJEmSpARhAJQkSZKkBGEAlCRJkqQEYQCUJEmSpARhAJQkSZKkBGEAlCRJkqQEYQCUJEmSpARhAJQkSZKkBGEAlCRJkqQEYQCUVGPk5OSQkZFBMBhkzJgxlZbfe++95OfnH3IbN910EwMHDuS+++6r0D5//nzOOuss+vXrx4MPPlhh2cMPP8zQoUMB2Lt3L5deeinBYJAHHngAgOXLlzNhwoTjOTRJkqSoMABKqlHGjh1LTk4OjRs3Jjc3t7w9FAqxZMkSunTpctDnLliwgJSUFObNm8fChQvZuHFj+bJOnToxd+5c3nnnHf7xj3+wa9cuIBL4Fi9eXL7e1KlT6devHzk5OXzwwQd8+eWXZGVlsXDhQsLhcNUfsCRJUhUyAEqqkbp3705RUVH54w8//JCTTz75kM957733GDx4MADZ2dl88MEH5cvatGlDnTp1AEhOTiYpKfLxOHnyZC6//PLy9dasWcNpp50GQFZWFu+//z4QCZDLli2rgiOTJEmqPgZASTVSbm4umZmZ5Y/z8/Pp2LHjIZ+zZcsWGjVqBEBaWhpbtmyptM7MmTPp3Lkz9erVIxQK8eabb3LeeeeVL+/atStz5swhHA4zb948tm7dCkCHDh1YtWrV8R+YJElSNUqJdQGSdDSefPJJZs2axYABA+jVq9cB1/n444+54YYbKrSdf/75NGnShG3btgGwfft2OnfuXGGd9evXc//99/Paa68BkeGew4cPr7DO8OHDmTFjBueeey7NmzenRYsWVXRkkiRJ1c8AKKlGGTt2LHfeeWel9i5dujB16lQATj31VHJyciqt8/777/PCCy9wwQUXMHfuXC699NLyZcXFxfz4xz9m4sSJNGzYEICVK1eSk5PD5MmTWbx4MU888QTXXnstEydOJBwOM2bMGM4++2wACgsL6d+/fzUcsSRJUtVxCKikWqFnz56sXLnykOucccYZFBcXM3DgQHr27EnLli3ZsGEDDzzwAFOmTOHjjz/m+uuvJxgMUlRUxB133MHMmTP55z//Sa9evbj22mv59NNPCQaDDBkyhEsuuYQGDRoAUFBQQPfu3aNxqJIkScfMK4CSaoxgMEgwGDzgsqSkJHr06EF+fv4hZwJ97LHHKjxu1aoVt9xyCwBXX331QZ83a9YsANq3b1/p6uLy5cvp06cPgUDgCI5CkiQpdgyAkmqNAw0NjYasrCyysrJism9JkqSj4RBQSZIkSUoQBkBJkiRJShAGQEmSJElKEAZASZIkSUoQBkBJkiRJShAGQEmSJElKEAZASZIkSUoQBkBJkiRJShAGQEmSJElKEAZASZIkSUoQBkBJkiRJShAGQEmSJElKEDUmAJaUlDB+/HjatWtH/fr1GTx4MHl5eQQCAaZNmxbr8iQdh3AY3v9y/+OlmyNtUk21dgc8txr+sgpyPofSUKwrko7dlhKYuhaeXAWvFsL2vbGuSNLxSIl1AUciHA4zatQo8vLyuOuuu8jMzGTKlCmMGDECgN69e0etlqQ6KZx137W0HnAa9Zo2YtfGzSz/yxus+MsbUatBqk2Wb4E7PoBPd+5v+/E86NoY7u8D7RvGrDTpqG0pgf9aCO98UbE9vQ7c0QuyW8WkLOmYlIXh8eXw/Goo/cZJuf/+CMZkwk+6QlIgdvWpZrEPHT9qRACcNGkS06dPZ/HixXTr1g2AYDBIRkYG6enptG/fPmq1JCUns/uLLcy47G62F24k/dQOnPvCnez5cgtrX8+NWh1SbfDJdrjubSguq7wsfxtcOx+ey4YW9aNfm3S09pTBDe9AwbbKyzaXwH/mwf+cBf1aRL826Vg8tBReXFO5vSQEf14V+femU6Nfl2om+9Dxo0YMAZ0wYQKjR48uD38AycnJZGRk0Lt3b77++mu+973v0bVrV0477TQuvvhivvzyy0Ns8diV7i5m0X//le1rN0A4zKZla1k3YwEtzsyqlv1JtdmfV0bC34FGx4XCkU7z86ujXpZ0TP65HlZtO/D7ed/Fk4eXObxZNcP6nfDSAcLfN00ugC/3RKce1Xz2oeNH3AfA/Px81qxZw8iRIystW7duHb179yYQCHDrrbeycuVKPvroIzp37syvf/3rqNQXSEmmZd8sNi8vjMr+pNpiWwm89fmBO8v7hIFXP42EQSne/b0QDjUaLkzkqvfyrdGqSDp2r687/Doh4P+OYD3pQOxDx07cDwEtKioCoEWLimNmVqxYQWFhIb179yY9PZ1gMFi+7KyzzmLixIlHvI+0tDRKSkoqtXdOOZFbGw045HPPum8se3fsZvXLc454f4lq0KAgq0s3x7oMxYm6bU/h5Ic/POx6O0vhhPTmhHYdYFydjkn3lyKn7OvWrRfjSmqXrD+vI6XJ4cd3Zg//Idvee7X6C0oQvp+rx0k3PkGTgZcRSE496Drh0r389n+e4vo/3xTFylQT2IeuWoMGHbgPXadOHbZv337U24v7K4BNmzYFoKCgoLwtHA5z2223EQqFKk0AEwqFmDhxIsOHD6/22s64awzN+3Rl5pX3EtpbWu37k2qTsl1HdhkkXFZKqHhXNVcjHb+yXVsIH8H4zrKdXgJU/CvbtY1DX9MGkpIo27klGuWolrEPHVuB8JH8tYqh0tJSsrKy2Lt3Lw888AANGzZk4sSJLFq0iE2bNrF9+3aSkvbn2BtvvJGioiKmTp1aof1YbMxbwRsX3nnAZWf+7se0HnAa/xz1W4q/9srEkRg27R5annlKrMtQHLlmXuQrHw42DDQJGNIG7j89mlXVfqe/Fvl3QfWfJ0sok1ZGfg7lxDow/buQGvenX2sO38/VY/HXcO3bh1/v+ezIrM3SN9mHrlpV3YeO+z9BKSkpvPLKK7Ru3ZoxY8Ywbtw4hg0bRnZ2Nj169KgQ8v7zP/+T/Px8XnzxxeMOf4dy5t3X0HpgD9+40nG65uSDh78AEAjA6M7RrEg6dhd3gLTUQ/9hHdPF8KeaoWc69Eo/+Ps5AJzd3PCno2MfOj7E/T2AAD179iQ3t+L0sI8++ijZ2dnlj2+//XY++OAD/u///o+6detWWy0nnNSMU6/9HmV7SrjkvcfK2ze+t4JZV95bbfuVaqMBLeE3PWDCksgEGd8cjpCSBPd+B7qdGKvqpKPTrB48ehb8/F3Y+o0vyk4icqJjdGe4slOsqpOOTiAAfzgz8n7+eMv+9qRAZGKunulwn6MzdBTsQ8ePGhEAv2337t2sXLmScePGAbBs2TLuv/9+Tj75ZPr16wdARkYGf//736t83zvXf8XTrS+p8u1KiWpkR+jfAv7+KSzbHDmr3KcZDG8P6dV3LkeqFt1OhNfOjXwlxP1LIm2jMmBEB8hsFNvapKPVpA48NRByv4Bx70XavtsGvt8O+jb3S+B1dOxDx48aGQCXLFlCWVlZ+QQw3bp1O6Ib7yXFp1YN4D+8PVS1xAkpkRMb+wLgLafFtBzpuCQHIqM19rmnT+xqkVQ1amQA7Nu3r4FPkiRJko6St6JLkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkhRlOTk5ZGRkEAwGGTNmTKXlkydPZtasWQAMHDiQhg0bsn79+krrLVy4kP79+5Odnc3SpUsBeOihh2jbti333HNP+Xo33ngjO3furKajkSTVJAZASZJiYOzYseTk5NC4cWNyc3MrLHv99dcZMmQIAC+//DKXXHLJAbfxu9/9jqlTp/K3v/2Nu+++G4DRo0czefLkCutdcMEFvPjii9VwFJKkmsYAKElSDHXv3p2ioqLyx5s2baJevXoEAgEAWrVqddDn7ty5k5YtW9KsWTPWrl0LQIsWLUhKqvjn/ZxzzuHNN9+s+uIlSTWOAVCSpBjKzc0lMzOz/HFBQQEdOnQ4ouempaWRn5/PJ598wrJlyw66XoMGDdi8efNx1ypJqvlSYl2AJEmJ6Mknn2TWrFkMGDCAXr16HdM27r33Xm644QZatGjBwIEDq7ZASVKtZACUJCkGxo4dy5133lmpPTMzk8LCwiPaRlZWFjNnzuTTTz/loYceOuh6u3btokmTJsdaqiSpFnEIqCRJcSQ9PZ1du3aVPx49ejQzZszg8ssv56233gLg5ptvBmDSpEkMGjSIX/ziF9xxxx0APPvss9x88808/fTT3HrrrQDMnTuX7373u1E+EklSPPIKoCRJURYMBgkGgwddPnz4cGbNmsXQoUN57rnnKi1/8MEHAbjuuuu47rrrKiy76qqruOqqqyq0vf7660yYMOH4C5ck1XgGQEmS4sy3A9zxeuyxx6p0e5KkmsshoJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgakwALCkpYfz48bRr14769eszePBg8vLyCAQCTJs2LdblSZJU7ss9+3//4CsIh2NXi6SaoTQEczfAy2vgn+thx95YV6TaKiXWBRyJcDjMqFGjyMvL46677iIzM5MpU6YwYsQIAHr37h3Ves66/1ranXs6qY0asHfHbgr/kcuCu58jtLc0qnVIkuLLzlL4/YfwZtH+tuvfgXYnwB094fRmsatNUvz6x6fwPx/D5pL9bXWT4LJOcEMWJAdiV1tVsg8dH2pEAJw0aRLTp09n8eLFdOvWDYBgMEhGRgbp6em0b98+qvUsf+qfLPjdZEp3F1M3PY3gpJvp8fOLWfzgS1GtQ5IUP0rK4OfvwpJN8O0LfkU74We58Hg/+E7TmJQnKU69Wgj3fFi5vTgEzxTAlhIY3yvqZVUL+9DxoUYMAZ0wYQKjR48uD38AycnJZGRklF/9u+iii+jZsye9e/dm4MCBLF68uNrq2bpqPaW7iyMPAgHCoTBpnVpX2/4kSfFv5mfw4QHCH0AICIXhoaXRrkpSPNtTCn9cduh1pn0KK7ZGp57qZh86PsT9FcD8/HzWrFnDI488UmnZunXrGDlyJADPPPMMjRs3BmDatGlcc801LFy4sNrqOu1nF9Fj3EhST6jPnk3bmHnFc9W2L0lS/Ju6NnJWNXSQ5SEinbhVW+HkxtGrS1L8+tfnkaHjh5IETCuEU3pEpaRqZx869uI+ABYVRW6kaNGiRYX2FStWUFhYWH4FcF/4A9i6dStJSUd+cTMtLY2SkpJK7Z1TTuTWRgMO+JyPHn2Vjx59lcZd2tLp4oHs/mLzEe8vUQ0aFGR1qa+TFGvdX4rMUFK3br0YV1K7ZP15HSlNWhx2vf4/uJRteU5eVlV8P0eHr3P1aHHJHbQYdSeBQ/Rby8Ih/vLqLP7rjAuiWNnxsQ9dtQYNOnAfuk6dOmzfvv2otxf3Q0CbNo3cLFFQUFDeFg6Hue222wiFQhUmgLn22mtp3749d9xxB88880xU6tuaX8SmZYUM/N+fR2V/kqT4VLZ7G+EjmO4ztGdnFKqRVBOE9uw4ZPiLrBQitGdHdAqKIvvQsRP3VwCzsrLIzMzk9ttvJzU1lYYNGzJx4kQWLVpEgwYN6Nq1a/m6TzzxBACTJ0/mlltuYfr06Ue0j4Ml5415K3jjwjsP+/yk1GQaOX75sGbPzqHlmafEugwp4Z3+WuTf4uLi2BZSyzy2HJ7OP/A9gPukpcJn7/4fdZOjVlat5/s5Onydq8f6nTDirUN/bgSSU/jfGy7m/PtqzmtvH7pqVXUfOu6vAKakpPDKK6/QunVrxowZw7hx4xg2bBjZ2dn06NHjgEM9f/SjHzF79my+/vrrKq8nNa0BmZcGqdOoAQAnZnWg57iRfJZzgOmbJEkJY2QHqJt86D+sV3bC8Cep3EknwODWcLBveUgCWtePrFPT2YeOH3F/BRCgZ8+e5ObmVmh79NFHyc7OBmDHjh1s3ryZdu3aAfD666+Tnp5Oenp61RcTDtNp5DmccdcYkuqksOerbRROf4/FD7xY9fuSJNUYrRrAw33hl+/B7rL97fsmhhneHq45OVbVSYpX/9UbNhXDok2QFIjMGLxPs3rw6NlQpzacOLIPHTdqRAD8tt27d7Ny5UrGjRsHwM6dOxk1ahQ7d+4kOTmZ9PR0Xn/9dQKBqv/WzL07djPjh7+r8u1Kkmq+05vBtKHw2qcwZwPsKYPMRpGrgz3ToRr+LEmq4U5IgT/1h/kbI7N9zt0Yab+9B5x/EjSokb31yuxDx48a+ZZasmQJZWVl5RPAtGzZknfffTfGVUmSBOl14cddIj+SdCSSA5DdKvKz737LizvGtCTVYjUyAPbt2/eIZlqTJEmSJO0X95PASJIkSZKqhgFQkiRJkhKEAVCSJEmSEoQBUJIkSZIShAFQkiRJkhKEAVCSJEmSEoQBUJIkSZIShAFQkiRJkhKEAVCSJEmSEoQBMM4MePhG+t47NtZlHNCVBZNJ754R6zIkVaOcnBwyMjIIBoOMGTOm0vLJkycza9YsAO677z4GDhzITTfdVGm9n/zkJ2RnZzNgwABWrVoFwF/+8hf69evHRRddxPbt2wG47LLLOPHEE5k/fz4ApaWlXHvttdV1eJKkWso+9JEzAFajVv26cf7ffsuV+ZO5Mn8y5//tt7Q6u1usyyrX6+ZLGfLsb454/eczf8SmpWuqsSJJ8WDs2LHk5OTQuHFjcnNzKyx7/fXXGTJkCBs3bmThwoXMmzePlJQUFixYUGG9xx9/nDlz5nD//ffzpz/9idLSUp555hnmz5/PtddeyxNPPAHAww8/zC9+8Yvy56WkpNC8eXNWr15d/QcqSYpL9qGrlwGwmpw0tA/nTrmTdbM+4KXvXM9L37medbM+4NwX7uSkId854HMCyVX3f0cgJbnKtiUpMXXv3p2ioqLyx5s2baJevXoEAgEWLFhAdnY2AIMHDyYvL6/Cc1NTUwHYsWMH3bt356uvvqJ9+/YkJSVx2mmnlQfLVq1aVdpvMBjkjTfeqK7DkiTFMfvQ1c8AWE363nMNBS/nsGzia+zdvou923exbOJrrH5lDmfecw0Al+Q9To9xI/nea/cy+pPnadazMwCpJ9QjOOlmrsyfzEVz/kibYM/D7q/V2d24smAyJ48eyiXvT2T4rD8A0PqcHvzgzQlcsfIZhr/1IO3PPwOA9uefwWk/H0HbQb24smAyVxZMJqlOyiH38ePPX6Fpz84EkpO4YtWzNOnaLrLvft348eev0OEHZwNQv0UTrvr0r6Q2rH9sL56kuJCbm0tmZmb544KCAjp06ADAli1baNSoEQBpaWls2bKl0vOHDBnCz372M8444wyaN29OQUEBe/bsYe7cuWzduvWg++3QoUP5sFFJUmKxD139fWgDYDVo1LkNaR1asubVtyst++Tv82nUsRWNOrUGIHNUkLdvfpznM3/E1/++NJxx0QA++fs8ppwyhiX/+3cG/+VWGrRKP+x+U+rXpVmvTF49Zxz/GHYbaR1bMfSZX7P00Vd54dSr+eDe58ie+EvSu3Xk03++z0eP/J2i2Yt5PvNHPJ/5I0IlpUd0fOGyEBvfW07rAacB0HrgaWxb8zmtB3SPPB5wGl8v+YS9O3Yf0fYkxZcnn3ySYDBI27Zt6dWr1wHXadKkCdu2bQNg+/btNGnSpNI6b731FlOnTuWuu+4iOTmZW265hfPPP58PP/yQli1bVuMRSJJqIvvQ0elDGwCrQb30NAB2b9xUadnuLzZH1mkaOXO+cvJMtuYXEQ6Fyt88G979mE/fyCNcFuKTV+ay+eNCOl5w9mH3G0hK4oP7nqd0dzFlu0vIuLAfG99bztrXcwmXhSj61yI+nbGAzqOyj/sYN8xfWuHNuvgPL5W/mVv1787nby897n1Iio199wDec889FdozMzMpLCwEoE+fPsydOxeA2bNnc+aZZ1ZYt7i4GIDGjRtTv37kTObFF19MTk4Offv2ZdiwYQfdf2FhIV26dKmy45Ek1Qz2oaPThzYAVoM9myKz29VvWfmMQ/0WJ0bW+Tpy5nxn0ZeV1tm5vmLbjnVfHtHZi9LdxRT/e98ADVo3Zce3t1W4kQatmx52W4fz+fyPaHnWqdRp1IBGndqw5tW3Sa6TQoPW6bQe0J3P53103PuQFF/S09PZtWsXELl3r0ePHgwcOJDi4mJOP/10NmzYwAMPPADAiBEjGDRoENdccw133HEHADfccANDhgxh7ty5XHrppQDcfPPNPPvss/zyl7/k+eefByIzkR4qIEqSaif70NHpQx96wKqOybbVn7H9041kDO/Hhm+l+IwL+7H9041s++RzAMKhcKXnn3BS8wqPG7ZrzpcLD38/TDgUqvB41+dfV5oxqWG7Fuz6/OsDrn80Ni1bSzgU4tSf/IAv3l9BOBTi8/lLOfmKoTRocSJfvL/imLctKXaCwSDBYPCgy4cPH86sWbMYOnQo48ePZ/z48eXLWrVqxS233ALA9OnTKz338ccfr9T24IMP8uCDD5Y/Li0t5Ysvvqhw76EkKTHYh45OH9orgNUk77+eJvOHg+h2/QWkNqxPaloDTr3+B2ReOoi88U8d8rmtzjqVdt89nUByEp0uHsiJp3Zg7f+9e9Q1rJn2Di37ZtHh+30JJCXRdlAv2p13OqtfiQzb2v3VVk5o2+yYZ07a8M4yTr3u+3w+P3Km4vO3P+LU677PFx+soqx47zFtU1J8u+qqqxg6dGi1bT8lJYUnn3yy2rYvSYpv9qGrvw/tFcBqsu7N95k1+j56/uoSet0SGer09ZJPmDX6vvL/sw9mzavz6Twqm3Me+wU7P/+a2df+gV2ffX3UNWxfu4F/XfPffOc3V9L/jzeyc/2XzP3ZI+XfQ7L29Vw6XTSAy5b+hUAgwF97jD3im1gBPp/3ER1/cDafz4+cofl8/lLqNDrB+/8kSZJ0TOxDV79AOByufP1UAGzMW8EbF94Z6zLiQiApiTFFLzFt8M1sXl54TNsYNu0eWp55ShVXJulonf5a5N8Fw2Nbh1QVfD9Hh69z9NSG19o+9H7x2Id2CKiOyIndOhDaW3rAG24lSZIkVRaPfWiHgNYgF+b8kYYnNavUvm7GB8y94eHj3v7Q5++gZd/KZxf27thDUmoyH9w3hZJtu457P5IkSVK02IeuyABYg0wL/rJatz/rynurdfuSJElStNmHrsghoJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCBqRAAsKSlh/PjxtGvXjvr16zN48GDy8vIIBAJMmzYt1uWplivYBm8WwezPYVtJrKuRjs9Xe/b/vm5H7OqQJEmxkRLrAg4nHA4zatQo8vLyuOuuu8jMzGTKlCmMGDECgN69e8ekruR6dbjwXw9Sv0UTns/8UUxqUPVauRV+vwQ+2ry/rU4SXNAOftkN6sX9fz3SfttKYMJHMPOz/W0j/gV9m8NvesBJJ8SuNklS4rAPHXtx34WdNGkS06dPZ/HixXTr1g2AYDBIRkYG6enptG/fPiZ19b7lh+xY/xX1WzSJyf5VvVZthbHzoaSsYntJCKYWwtod8OjZkFojrqEr0e0shevehk+2Q+hby97/Cq6eB8+eA60bxKQ8SVICsQ8de3HffZ0wYQKjR48uD38AycnJZGRkVLr699vf/pZAIMDSpUurtaamPTrRdlAvlj72arXuR7Hz0NJI+Pt2ZxkgDHzwNcwoinZV0rF5eQ0UHCD8AYTCsLUE/rQi6mVJkhKMfej4ENcBMD8/nzVr1jBy5MhKy9atW1chAC5cuJB3332XDh06VGtNgeQk+v3hp7x7+xOESkqrdV+KjXU7YMHXB+4s75MEvLI2SgVJx+nlNYdeHiJyn+v2vVEpR5KUgOxDx4+4HgJaVBS5xNKiRYsK7StWrKCwsLA8ABYXF3PjjTfywgsvEAwGj3o/aWlplJRUnt2jc8qJ3NpoQIW27jdcyNcfrWHju8tpdXa3Ss/RwQ0aFGR16ebDrRZzab3Pp+Pth55cKAQsXr+FunVbRqco6RgFUlLp/sLhZ3spDcNJ3c9gz9olUahKqjrdX4rMbFS3br0YV1K7+TpHT214re1DV61Bgw7ch65Tpw7bt28/6u3F9RXApk2bAlBQUFDeFg6Hue222wiFQuUB8L/+678YPXo0HTt2rNZ60jq2outV32XB3ZOrdT+KrVDJ7iNbr3hXNVciHb9wWSnhsrLDrwiEio/svS9J0tGwDx1f4voKYFZWFpmZmdx+++2kpqbSsGFDJk6cyKJFi2jQoAFdu3YlNzeXBQsW8Pvf//6Y93Ow5LwxbwVvXHhn+eOWZ55C/WaNufjtRwBISkkm9YT6XLbsL8we+wAb311+zDUkgtmzc2h55imxLuOwisvg/BmHHg6XBFzxnTbcVlwctbqkY3VzHszbGLnf70ACRGYBfX/NUgKBqJYmHbfTX4v8W+zncbXydY6e2vBa24euWlXdh47rAJiSksIrr7zCT3/6U8aMGUO7du0YN24cjRo1YvXq1SQlJTFnzhyWL19ORkYGAOvXr+e8887jqaee4rvf/W6V1rPm9Xf4bN7+4VHN+3RlwP/cyGtD/5M9X2+r0n0pduomw2UZ8OdVB14eAJICcGlGVMuSjtmVnWHuhoMvDwM/6ozhT5JULexDx5e4DoAAPXv2JDc3t0Lbo48+SnZ2NgC//vWv+fWvf12+rGPHjvzjH/+ge/fuVV5L2e4Sdu3eVP64+OttEA6z6/NNh3iWaqKxJ0PhzshMn0mB/VdOAkByAO7rAxlpMS1ROmLfaQq/7hH5XssA+yc4Svr371d0ghHVO3+WJCmB2YeOL3EfAL9t9+7drFy5knHjxsW6FDbkLvMLLGuplCS45zvw/ZMis33O2xhpv7IzjOwA7RrGtDzpqI3sCD3TIzOCvvsllIXhtBPhko7Qp1msq5MkJRL70LFV4wLgkiVLKCsrq/QdgPusXbs2ugWp1koKQP+WkZ994/HHOWmVarDMRvCbnrGuQpIkxVKNC4B9+/YlHD7ITAaSJEmSpIOK66+BkCRJkiRVHQOgJEmSJCUIA6AkSZIkJQgDoCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJqrVycnLIyMggGAwyZsyYSssnT57MrFmzABg4cCANGzZk/fr1ldZbt24dgwYNon///nz44YcAjBkzhgEDBjBkyBCKiooAuPrqqwmHw9V4RJJ0fAyAkiSpVhs7diw5OTk0btyY3NzcCstef/11hgwZAsDLL7/MJZdccsBtTJgwgYcffphXX32V3/3udwD89re/Zf78+dx+++089thjAPTt25fZs2dX49FI0vExAEpV4HBnmO+9917y8/MP+vxNmzbRp08fGjZsWGnZ7t27+d73vkd2djZXX301AHl5efTv359+/fpx5513ArB8+XImTJhQRUckSbVP9+7dy6/UQeSzt169egQCAQBatWp10OcWFBTQs2dPmjdvzs6dOwHo2LEjAMnJyeXbGDRoENOnT6+mI5Ck42cAlKrIwc4wh0IhlixZQpcuXQ763LS0NGbOnMlZZ51VadmMGTMYMGAAc+bMITU1laVLl9K7d2/efvtt3nnnHXJzc9m2bRtZWVksXLjQoUeSdBC5ublkZmaWPy4oKKBDhw5H9NxQKHTQ3++77z7Gjh0LQIcOHVi1alUVVSxJVc8AKFWxb59h/vDDDzn55JMP+ZzU1FTS09MPuCwjI6P8bPOOHTto3LgxqampAJSVldGmTRsaNGgAQKdOnVi2bFlVHIYk1RpPPvkkwWCQtm3b0qtXr2PaRlJS0gF/Hz9+PJdddhmdOnU63jIlKSoMgFIV+/YZ5vz8/PJhQsciMzOTefPmkZWVRSAQoF27dgBMmTKFrKwsmjRpQkpKCuCZZ0k6kH0jNO65554K7ZmZmRQWFh7RNjp37sySJUv46quvOOGEEwD429/+xqZNm7jmmmvK1yssLDzkiA9JijUDoFRFjuQM88cff0wwGKzw8/vf//6Q233mmWf44Q9/yPLly2nWrBnvvPMOAFdccQUrVqzgs88+46OPPqrqw5GkWi89PZ1du3aVPx49ejQzZszg8ssv56233gLg5ptvBuC2227j5z//ORdeeGH5vde/+tWv+PDDDwkGg9x7770AzJ49m2HDhkX5SCTpyKXEugCpthg7dmx5p+CbunTpwtSpUwE49dRTycnJOarthkKh8uGh6enpbNmyheLiYurWrUtSUhJpaWnUq1cPiJx57t+///EdiCTVIvtOth3M8OHDmTVrFkOHDuW5556rtPzBBx8EoH379pU+vw909fC9997juuuuO66aJak6eQVQqmY9e/Zk5cqVh11v6NChLFq0iKFDh7J06VI2bNjAAw88wBVXXMFTTz1FMBhk8eLFnHvuubz22msEg0HOOeccTjrppPLhRgUFBXTv3r26D0mSao2rrrqKoUOHVtn2nnrqqQr3CEpSvPEKoFQFDnWGOSkpiR49epCfn3/I+0L2fRHxN91yyy1AZCbQbxo1ahSjRo2q0LZ8+XL69OlTPhW5JEmS9G0GQCkKDjQ0tKplZWWRlZVV7fuRJElSzeUYBUmSJElKEAZASZIkSUoQBkBJkiRJShAGQEmSJElKEAZASZIkSUoQBkBJkiRJShAGQEmSJElKEAZASZIkSUoQBkBJkiRJShAGQEmSJElKEAZASZIkSUoQBkBJkiRJShA1JgCWlJQwfvx42rVrR/369Rk8eDB5eXkEAgGmTZsW6/JUi23Ytf/3PWWxq6O221QM734BeV/C9r2xrkZSTVAa2v/72u2xq0OSapKUWBdwJMLhMKNGjSIvL4+77rqLzMxMpkyZwogRIwDo3bt31GoZ8PCNZIwYQGhvaXlbzk8epGj24qjVoOgo3AEPLYV3vtjfdt6bcGkGXN8VUmrM6ZP49vUeeGgZzPoMysKRtjpJ8IN28PNToWFqbOuTFH/CYXhpLTy9an/bJbPhtBPhF6dCr6YxK03SQdiHjh81IgBOmjSJ6dOns3jxYrp16wZAMBgkIyOD9PR02rdvH9V6Vj03i/fueDKq+1R0Fe6Aq+fBjr0Q/kb7zlJ4Kh9Wb4MHzoTkQMxKrBU2F8M18+HzXfCNE/mUhODvhfDxFvhzf6hfIz6pJEXL/y6HZwsqty/bDD99B/73LDijefTrknRo9qHjQ424hjFhwgRGjx5dHv4AkpOTycjIKL/617FjR0455RR69epFr169ePPNN2NVrmqBB5dGwl/oIMvnboR/fRbVkmqlP6+Cz3Yd+HUOAyu2wotrol2VpHiWv/XA4Q8inyWhMPxuceRfSVJlcX9ePT8/nzVr1vDII49UWrZu3TpGjhxZ/viVV16he/fu1V5Tp4sH0mnEAHZ/tZVP/jaXjx59lXDZwaKCaprPd0HuFxWv/H1bEvDSGji3bbSqqn32lMJrnx76dYbI6zwmEwJebZUETC2MfAYf7K9uCPh8N7z3JZzdIoqFSTos+9DxIe4DYFFREQAtWlT8FF+xYgWFhYVVcv9fWloaJSUlldo7p5zIrY0GVGj7+MnpLLh7Mns2badpj05kPz6O5Lp1WPTffz3uOmq7QYOCrC7dHOsyDiut9/l0vP3QEwuFgPc/3Uzduq2iU1QtVLdNV07+nyWHXe+LPdCgSVNCe3ZEoSpJ8a7T7/7FCVn9D7veJf9xG1/94+HqLyhBdH9pDwB169aLcSW1X214re1DV61Bgw7ch65Tpw7btx/9DFhxPwS0adPIndwFBfvHe4TDYW677TZCoVCFAHjllVfSo0cPbrjhBrZs2VIt9Wz6aA17vt4G4TBff7iaRX94kYwLD/+HSDVHaG/xEa0XLq180kBHLlR6ZK8zQLjMaUElRYT27iEcOvwVAz+jpfhiHzp+xP0VwKysLDIzM7n99ttJTU2lYcOGTJw4kUWLFtGgQQO6du0KwLx582jXrh3FxcWMGzeOn/3sZzz33HNHtI+DJeeNeSt448I7D/3kUBgcmnZEZs/OoeWZp8S6jMPaXRqZ7XPXIb7yIQkY1aMldxYfeYhRReEwXPwvWL/z4MNAk4DeTWHBjm3RLE1SHHtuNTy87PDrvfv8H2nf8I/VX1CCOP21yL/F/t2rdrXhtbYPXbWqug8d91cAU1JSeOWVV2jdujVjxoxh3LhxDBs2jOzsbHr06EFSUuQQ2rVrB0DdunW54YYbePvtt6ulno7D+5Ga1gCAE7M60PPmUaz9R2617EuxUT8FRnY8/HqjMqq9lFotEIArOx/6HsAQcEXnaFUkqSa4oB00SD54ByYJ6N8C2jeMZlWSDsc+dPyI+yuAAD179iQ3t+Ib5NFHHyU7OxuAnTt3UlpaSuPGjQmHw/z1r3+lV69e1VLLKT8+j7MnXEdSajK7N25h9StzWPK/f6+WfSl2bsiCT7bD219UnGxgX4fjv3pB18axqa02GdkhMqPf3741qUNSIHJi8PqukO1tlpK+oXEdeKgvjHsPisv2n0QKEPk9Iw1+G72vB5Z0hOxDx48aEQC/bffu3axcuZJx48YBsHHjRkaOHElZWRllZWWceuqpPP7449Wy739e/P+qZbuKL6lJ8OCZkS8nf3kNFGyPtJ3TKvJF8KcY/qpEIAC/7gEDWkZm+8z9MtIe/PfrfHqz2NYnKT6d3gxeDMLLa+HNosh3tLapDyM6/vsKYY3s3Ui1m33o+FEjPyKXLFlCWVlZ+QQwnTp1YtGiRTGuSrVNShKcf1LkR9UnEICBrSI/++57+O8zYluTpPjX9gQY1y3yI0k6cjUyAPbt25dw2G94lSRJkqSjEfeTwEiSJEmSqoYBUJIkSZIShAFQkiRJkhKEAVCSJEmSEoQBUJIkSZIShAFQkiRJkhKEAVCSJEmSEoQBUJIkSZIShAFQkiRJkhKEAVCSJEnHJScnh4yMDILBIGPGjKm0fPLkycyaNQuA++67j4EDB3LTTTdVWu8nP/kJ2dnZDBgwgFWrVgHwl7/8hX79+nHRRRexfft29u7dS//+/cnOzmb48OHs2bOHTZs28atf/ap6D1KqJQyAkiRJOm5jx44lJyeHxo0bk5ubW2HZ66+/zpAhQ9i4cSMLFy5k3rx5pKSksGDBggrrPf7448yZM4f777+fP/3pT5SWlvLMM88wf/58rr32Wp544glSU1OZM2cOc+bM4YwzzmDGjBmkp6ezZcsWduzYEc1DlmokA6CkGuNwZ5jvvfde8vPzD7mNm266iYEDB3LfffdVaJ8/fz5nnXUW/fr148EHH6yw7OGHH2bo0KEA7N27l0svvZRgMMgDDzwAwPLly5kwYcLxHJok1Rrdu3enqKio/PGmTZuoV68egUCABQsWkJ2dDcDgwYPJy8ur8NzU1FQAduzYQffu3fnqq69o3749SUlJnHbaaeXBMiUlBYBQKETnzp0B6Nu3Lzk5OdV9eFKNZwCUVKMc7AxzKBRiyZIldOnS5aDPXbBgASkpKcybN4+FCxeycePG8mWdOnVi7ty5vPPOO/zjH/9g165dQCTwLV68uHy9qVOn0q9fP3Jycvjggw/48ssvycrKYuHChYTD4ao/YEmqYXJzc8nMzCx/XFBQQIcOHQDYsmULjRo1AiAtLY0tW7ZUev6QIUP42c9+xhlnnEHz5s0pKChgz549zJ07l61btwLw8ccfc8YZZzBz5kzatWsHQIcOHcqHjUo6OAOgpBrp22eYP/zwQ04++eRDPue9995j8ODBAGRnZ/PBBx+UL2vTpg116tQBIDk5maSkyMfj5MmTufzyy8vXW7NmDaeddhoAWVlZvP/++0AkQC5btqwKjkySaqYnn3ySYDBI27Zt6dWr1wHXadKkCdu2bQNg+/btNGnSpNI6b731FlOnTuWuu+4iOTmZW265hfPPP58PP/yQli1bAnDqqafy/vvvM2rUKJ555pnqOiSpVjIASqqRvn2GOT8/n44dOx7yOUdy5nnmzJl07tyZevXqEQqFePPNNznvvPPKl3ft2pU5c+YQDoeZN29e+dlozzxLSnT7Rmjcc889FdozMzMpLCwEoE+fPsydOxeA2bNnc+aZZ1ZYt7i4GIDGjRtTv359AC6++GJycnLo27cvw4YNY+/eveUjLho3bky9evUAKCwsPOQoEEkRKbEuQJKOxpNPPsmsWbMYMGDAQc8wf/zxx9xwww0V2s4///xKZ5733Teyz/r167n//vt57bXXgMhwz+HDh1dYZ/jw4cyYMYNzzz2X5s2b06JFiyo6MkmqndLT08uH1bdq1YoePXowcOBAevTowemnn86GDRuYPHkyt9xyCyNGjGD37t0EAgEee+wxAG644QZWrlzJqaeeysMPP8yaNWsYO3YsSUlJnHjiiTz33HMAvPvuuzzyyCMxO06ppjAASqpRxo4dy5133lmpvUuXLkydOhWIDA060EQA77//Pi+88AIXXHABc+fO5dJLLy1fVlxczI9//GMmTpxIw4YNAVi5ciU5OTlMnjyZxYsX88QTT3DttdcyceJEwuEwY8aM4eyzzwYiZ5779+9fDUcsSfEvGAwSDAYPunz48OHMmjWLoUOHMn78eMaPH1++rFWrVtxyyy0ATJ8+vdJzH3/88QqPMzMzmTNnToW2TZs20aRJE9LS0o7jKKTE4BBQSbVCz549Wbly5SHXOeOMMyguLmbgwIH07NmTli1bsmHDBh544AGmTJnCxx9/zPXXX08wGKSoqIg77riDmTNn8s9//pNevXpx7bXX8umnnxIMBhkyZAiXXHIJDRo0ACKTHHTv3j0ahypJNc5VV11VPptydUhPT+ePf/xjtW1fqk28AiipxjjUGeakpCR69OhBfn7+Ie8B2TekaJ9vnnm++uqrD/q8fV9g3L59+0pXF5cvX06fPn0IBAJHcBSSJEmxYwCUVGscaGhoNGRlZZGVlRWTfUuSJB0Nh4BKkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkiRJUoIwAEqSJElSgjAASpIkSVKCqDEBsKSkhPHjx9OuXTvq16/P4MGDycvLIxAIMG3atFiXJ+k47Srd/3txWezqqO1KymDFFli2GXaWHnZ1Sargs12xrkDS8UqJdQFHIhwOM2rUKPLy8rjrrrvIzMxkypQpjBgxAoDevXtHvaaThnyH3rddRqPObSjdsZulf3qdZRNfi3odUk23fS88vhxeX7e/7fwZMLID/KQr1E2OXW21SUkZPJkPL6+BbXsjbXWT4Aft4IYsaFwntvVJik+5X8D/t2L/4+GzoGc6/LQrnNE8dnWp5rIPHXs1IgBOmjSJ6dOns3jxYrp16wZAMBgkIyOD9PR02rdvH9V62mT35OwHrmf+zx9lQ+4yUurX5YS2zaJag1Qb7NgL186HT7ZD+Bvt2/fCMwWwZDM8ehbUMQQel9IQ/DIP3vuyYntxCKYWwoKv4S8DDIGSKvrnehi/EALfav9oE9yYCxPOgEGtY1Kaaij70PGhRgwBnTBhAqNHjy4PfwDJyclkZGSUX/3bs2cP//Ef/0GXLl047bTTuO6666qtnt63XsaSh//G5/M/IlwWYu+O3WxZue7wT5RUwROrKoe/fcLAwq/hpbVRLqoW+nth5fC3Txj4dAf8acWBl0tKTNv3wu8WRz4jQt9aFiLS/v8Wwm6Hkuso2IeOD3EfAPPz81mzZg0jR46stGzdunXlAfDWW2+lXr16rFq1io8++oi77767WupJqV+XZr06U795E0bM+x9+uOQJBj99Gw3btaiW/Um1VXFZJJgcKPztEyAyZDF8qJV0WC+tqXwG/5vCRIbg2pGTtM//rYOSbye/bwgDu8rgzaKolaQazj50/Ij7IaBFRZFPlhYtKr45VqxYQWFhIb1792bHjh08++yzrF+/nkAg0s1p2bLlEe8jLS2NkpKSSu2dU07k1kYDKrTVaXICgaQkOny/LzMvv4fdX2/lzN9dzaAnb+H1795ytIeXUAYNCrK6dHOsy1CcqNPmZLr+z0eHXCcMFO2CBk3SCe3ZGZ3CapvkFE776+Ffuz1l0CqrD3s+XRqFoiTFu7Y3TOLEc64gkJx60HXCZXv55YQn+OGT46JXWALo/tIeAOrWrRfjSo6dfeiqNWjQgfvQderUYfv27Ue9vbi/Ati0aVMACgoKytvC4TC33XYboVCI3r17s3r1apo2bcpvf/tbTj/9dILBIPPnz6+WevbuiPxH+fET09mx/kvKdpew8P4pND0twzHM0tEoO/LLTeGQ04Ies3CIcPgQp/ErrOrrLOnfyko59NgBgICfGzpi9qHjR9xfAczKyiIzM5Pbb7+d1NRUGjZsyMSJE1m0aBENGjSga9euLF68mE8++YTevXvzwAMP8N5773HBBRdQUFBAo0aNDruPgyXnjXkreOPCOyu07d2+ix3rvnBM2jGYPTuHlmeeEusyFCdC4chscht2H3ydJKDbibBg+9ao1VUbXf82LPq68n0839SsLrybv5iUuD8tKCkaZhTB7R8cep1AcgqT7/oZA//0s+gUlSBO//eEmMXFxbEt5DjYh65aVd2Hjvs/9SkpKbzyyiu0bt2aMWPGMG7cOIYNG0Z2djY9evQgKSmJ9u3bk5KSwuWXXw5A3759adasGatWraqWmlY+O4Osa79PgzZNSa6bSu9bL+OrD1ezs+iratmfVBslBeDyTodeJ8Th19HhXd7p0OEP4IedMPxJKjeoNTSte/COYhLQuj70O/I7biT70HEi7q8AAvTs2ZPc3NwKbY8++ijZ2dkANGvWjEGDBjFz5ky++93vsmrVKr744gsyMzOrpZ6PHptGncYNGT7jvyGQxBd5K5g99oFq2ZdUm13WKfKF5DM+i3Qm9oWUfb9f3gnObRO7+mqLYGv4cSY8XXDg1znYCn7UOXb1SYo/qUnwx77wH+/ArtKKE3YFgIapkeXJhxslKn2Dfej4UCMC4Lft3r2blStXMm7cuPK2P/3pT1xzzTXcfPPNpKamMnnyZJo0aVI9BYTDfHDvc3xw73PVs30pQSQH4J4+0L9lZKbKj7dAIADfSY9ckQq2ijzW8fvZqdAjHV5cs/8rIU5uDJdmwPfb2YmTVNmpTeCFILzwSWRW0G17oXEqDG8f+YxuVT/WFarGsQ8dF2pkAFyyZAllZWXlXwEB0KlTJ3JycmJXlKRjkhSIBJDvt9t/W4Chr3qc0yrys+/+kueyY1uPpPjXpgHc3D3yEwpHPrMl1Ww1MgD27duXsDeQSrWOwU+S4pfhT6odvOVfkiRJkhKEAVCSJEmSEoQBUJIkSZIShAFQkiRJkhKEAVCSJEmSEoQBUJIkSZIShAFQkiRJkhKEAVCSJEmSEoQBUJIkSZIShAFQklQuJyeHjIwMgsEgY8aMqbR88uTJzJo1C4CBAwfSsGFD1q9fX2m9hQsX0r9/f7Kzs1m6dCkADz30EG3btuWee+4pX+/GG29k586d1XQ0klS7VNVn9Ny5c+nbty99+/Zl2rRpALz88suceeaZnHXWWbz77rsAXH311YTD4Wo8IsWCAVCSVMHYsWPJycmhcePG5ObmVlj2+uuvM2TIECDSWbjkkksOuI3f/e53TJ06lb/97W/cfffdAIwePZrJkydXWO+CCy7gxRdfrIajkKTaqSo+o//4xz/y97//nTlz5vDII48A8NhjjzF37lymTp3KH/7wBwD69u3L7Nmzq/FoFAsGQEnSAXXv3p2ioqLyx5s2baJevXoEAgEAWrVqddDn7ty5k5YtW9KsWTPWrl0LQIsWLUhKqvhn55xzzuHNN9+s+uIlqZY7ns/oLl26sHXrVnbu3ElaWhoAHTt2ZOfOnWzdupX09HQABg0axPTp06vxKBQLKbEuQJIUn3Jzc/nFL35R/rigoIAOHToc0XPT0tLIz88nOTmZZcuWHXS9Bg0asHnz5uOuVZISzfF8Rl944YWcd955hEIhnnjiCSAyIqN3796UlZWVh74OHTqwatWqqi9eMWUAlCRV8OSTTzJr1iwGDBhAr169jmkb9957LzfccAMtWrRg4MCBVVugJCWwqviMHj9+PO+//z4NGjRg+PDhnH/++UyYMIHly5ezdetWfvrTn/Laa69VbeGKGwZASVIFY8eO5c4776zUnpmZSWFh4RFtIysri5kzZ/Lpp5/y0EMPHXS9Xbt20aRJk2MtVZISTlV8RicnJ9OoUSPq1KlDcXExAPXq1aN+/fqEw+HyybkKCwvp0qVL1RWvuOA9gJKkI5Kens6uXbvKH48ePZoZM2Zw+eWX89ZbbwFw8803AzBp0iQGDRrEL37xC+644w4Ann32WW6++Waefvppbr31ViAyE913v/vdKB+JJNU+R/MZPW7cOAYNGkS/fv245pprALjqqqvo168fgwcP5le/+hUAs2fPZtiwYVE+ElW3QNi5XQ9qY94K3riw8hkWHZth0+6h5ZmnxLoMKeGd/u9RPQuGH/1zn332Wdq0acPQoUOrpJYbb7yRCRMm0LBhwyrZniTVdPH0GX311Vfz5JNPVprA63DsQ1etqu5DOwRUknTErrrqqird3mOPPVal25OkRFbVn9FPPfVUlW5P8cEhoJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSJEmSlCAMgJIkSZKUIAyAkiRJkpQgDICSlEBC4f2/7w3Frg5JUmU79sa6AiWClFgXcKRKSkq4++67efrpp/nqq684++yz+f3vf0/fvn159dVXufDCC6NSx5UFkys8Tq6Typb8Il4bcnNU9i9Jx6IsDC98Ai9+sr/tvDdhZEe4ugs0qDF/DSSp9vlkOzyxEt76fH/bdfPhmpPhrBaxq6sq2YeOHzXiT344HGbUqFHk5eVx1113kZmZyZQpUxgxYgQAvXv3jlotz2f+qMLj4W89yJppb0dt/5J0tMrCcPuCih0LgG174el8yP0CJvU3BEpSLHy8Ba5/G4rL4JsDMxZvgpvehf/qBRe0j1FxVcg+dPyoEX/uJ02axPTp01m8eDHdunUDIBgMkpGRQXp6Ou3bx+a/ima9Mmly8kkUvDg7JvuXpCPxj3WVw98+YWDlVpi0EsZ1i2pZkpTwQv8+Qfft8Af7H9/9YeQqYPN60a6u+tiHjq0aEQAnTJjA6NGjy8MfQHJyMhkZGaSmprJ27Vouuuii8mVbtmxh27ZtbNq0qVrr6nLFYIr+tYjdGzdX634k6Xi8+AkEiIS9AwkDfy+En54C9ZKjWJgkJbi8L2H9rkOvEwrDq4Xwk67RqSka7EPHVtwHwPz8fNasWcMjjzxSadm6desYOXIkHTt2ZPHixeXt48aNo7S09Ij3kZaWRklJSaX2zikncmujAQd8Tkr9umRc2J95P3/0iPeT6AYNCrK61P/QpahKTuG0v+487Go7S6HFKd+h+NNlUShKkgTQ/OJf0/Ky/0cgcPB5GcOhEA+88CY/u/+i6BV2nOxDV61Bgw7ch65Tpw7bt28/6u3FfQAsKioCoEWLinfArlixgsLCwkr3/5WUlPD888/z5ptvVmtdHS84m9LdJayf9UG17keSjkv4YNf9jnNdSdLxCx/hdMy16PPZPnTsxX0AbNq0KQAFBQWceeaZQGRSmNtuu41QKFQpAL722mu0bduW73znO0e8j4Ml5415K3jjwjsPuKzLlUNY/VIO4TLnUT9Ss2fn0PLMU2JdhpRwrp4HyzZXvr/km5rUga9XLSLVLweSpKhZ/DVce5h5UAJJSdz5o+9x1W+Lo1NUFbAPXbWqug8d93/qs7KyyMzM5Pbbb+fll1/mjTfe4MILL2ThwoU0aNCArl0rDoj+y1/+wjXXXFOtNTXq3IYWp3dl1QtvVet+JKkqXNbp0OEP4JKOGP4kKcp6pkPnNEgKHHh5AKiTBMPbRbWsamMfOj7E/Z/7lJQUXnnlFVq3bs2YMWMYN24cw4YNIzs7mx49epCUtP8QioqKmDNnDldeeWW11tTl8sFsfG8529dsqNb9SFJV+G4buLhD5Pdvfujv62+c0Qyu6RLtqiRJgQBMOB0ape7/TN4nKRD5ua8PNKkbk/KqnH3o+BD3Q0ABevbsSW5uboW2Rx99lOzs7AptzzzzDN///vfLh41Wlw/uea5aty9JVSkQgN/0gB7p8NdPYMXWSHubBjAqA36Y4dU/SYqVjmnw3DkweTW89insLosEv8GtYHQmdD8x1hVWHfvQ8aFGBMBv2717NytXrmTcuHEV2p9++ukDzhYqSYkuEIAftIv87CqNTCt+QkqkXZIUW60awC2nwS+7RWZlrp8MdfxaHlWTGhkAlyxZQllZWaUJYFatWhWjiiSp5mhQIz/5Jan2S0mCxnViXYVquxrZDejbty/hWjQdriRJkiRFg3d9SJIkSVKCMABKkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkiRJUoIwAEqSJElSgjAASpIkSVKCMABKkiRJUoIIhP1G9YMq2b6Lzcs/jXUZtcaJWe2pk9Yg1mVIkiSpGtmHrlpV3Yc2AEqSJElSgnAIqCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJkiQlCAOgJEmSJCUIA6AkSZIkJQgDoCRJkiQliP8fyIGsUZC/3fsAAAAASUVORK5CYII=", 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" ] }, - "execution_count": 17, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "alpha_alpha_indices = [(p, p + 1) for p in range(norb - 1)]\n", - "alpha_beta_indices = [(p, p) for p in range(norb)]\n", + "pairs_aa = [(p, p + 1) for p in range(norb - 1)]\n", + "pairs_ab = [(p, p) for p in range(norb)]\n", "\n", - "ucj_op = ffsim.UCJOperator.from_parameters(\n", - " ucj_op.to_parameters(),\n", + "n_params = ffsim.UCJOpSpinBalanced.n_params(\n", + " norb=norb, n_reps=1, interaction_pairs=(pairs_aa, pairs_ab)\n", + ")\n", + "ucj_op = ffsim.UCJOpSpinBalanced.from_parameters(\n", + " rng.standard_normal(n_params),\n", " norb=norb,\n", - " n_reps=ucj_op.n_reps,\n", - " alpha_alpha_indices=alpha_alpha_indices,\n", - " alpha_beta_indices=alpha_beta_indices,\n", + " n_reps=1,\n", + " interaction_pairs=(pairs_aa, pairs_ab),\n", ")\n", "\n", "circuit = QuantumCircuit(qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n", "\n", - "circuit.decompose([\"ucj_jw\", \"diag_coulomb_jw\"], reps=2).draw(\"mpl\", scale=0.7)" + "circuit.decompose([\"ucj_balanced_jw\", \"diag_coulomb_jw\"], reps=2).draw(\"mpl\", scale=0.7)" ] }, { diff --git a/docs/how-to-guides/lucj.ipynb b/docs/how-to-guides/lucj.ipynb index 56caf3604..ff81b68d0 100644 --- a/docs/how-to-guides/lucj.ipynb +++ b/docs/how-to-guides/lucj.ipynb @@ -6,7 +6,9 @@ "source": [ "# How to simulate the local unitary cluster Jastrow (LUCJ) ansatz\n", "\n", - "In this guide, we show how to use ffsim to simulate the local unitary cluster Jastrow (LUCJ) ansatz. We'll use it to calculate the ground state energy of an ethene molecule at a stretched bond length." + "In this guide, we show how to use ffsim to simulate the [local unitary cluster Jastrow (LUCJ) ansatz](../explanations/lucj.ipynb). We'll use it to calculate an approximation to the ground state energy of an ethene molecule.\n", + "\n", + "First, let's build the molecule." ] }, { @@ -18,8 +20,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "converged SCF energy = -77.4456267643962\n", - "CASCI E = -77.6290254326716 E(CI) = -3.57322412553862 S^2 = 0.0000000\n" + "converged SCF energy = -77.8266321248744\n", + "CASCI E = -77.8742165643863 E(CI) = -4.02122442107773 S^2 = 0.0000000\n", + "norb = 4\n", + "nelec = (2, 2)\n" ] } ], @@ -29,8 +33,8 @@ "\n", "import ffsim\n", "\n", - "# Build a stretched ethene molecule\n", - "bond_distance = 2.678\n", + "# Build an ethene molecule\n", + "bond_distance = 1.339\n", "a = 0.5 * bond_distance\n", "b = a + 0.5626\n", "c = 0.9289\n", @@ -59,33 +63,21 @@ "mol_hamiltonian = mol_data.hamiltonian\n", "\n", "# Compute FCI energy\n", - "mol_data.run_fci()" + "mol_data.run_fci()\n", + "\n", + "print(f\"norb = {norb}\")\n", + "print(f\"nelec = {nelec}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## General UCJ ansatz\n", "\n", - "## The unitary cluster Jastrow (UCJ) ansatz\n", - "\n", - "Before describing the LUCJ, we first introduce the general unitary cluster ansatz (UCJ), which has the form\n", - "\n", - "$$\n", - " \\lvert \\Psi \\rangle = \\prod_{k = 1}^L \\mathcal{W}_k e^{i \\mathcal{J}_k} \\mathcal{W}_k^\\dagger \\lvert \\Phi_0 \\rangle\n", - "$$\n", - "\n", - "where $\\lvert \\Phi_0 \\rangle$ is a reference state, often taken as the Hartree-Fock state, each $\\mathcal{W_k}$ is an [orbital rotation](../explanations/orbital-rotation.ipynb), and each $\\mathcal{J}_k$ is a diagonal Coulomb operator of the form\n", - "\n", - "$$\n", - " \\mathcal{J} = \\frac12\\sum_{ij,\\sigma \\tau} \\mathbf{J}^{\\sigma \\tau}_{ij} n_{i,\\sigma} n_{j,\\tau}.\n", - "$$\n", + "Since our molecule has a closed-shell Hartree-Fock state, we'll use the spin-balanced variant of the UCJ ansatz, [UCJOpSpinBalanced](../api/ffsim.rst#ffsim.UCJOpSpinBalanced). We'll initialize the ansatz from t2 amplitudes obtained from a CCSD calculations. We'll first demonstrate the general UCJ ansatz, without adding the locality constraints of the LUCJ ansatz just yet.\n", "\n", - "In order that the operator commutes with the total spin Z operator, we enforce that $\\mathbf{J}^{\\alpha\\alpha} = \\mathbf{J}^{\\beta\\beta}$ and $\\mathbf{J}^{\\alpha\\beta} = \\mathbf{J}^{\\beta\\alpha}$. As a result, we have two sets of matrices for describing the diagonal Coulomb operators: \"alpha-alpha\" matrices containing coefficients for terms involving the same spin, and \"alpha-beta\" matrices containing coefficients for terms involving different spins.\n", - "\n", - "In ffsim, the UCJ ansatz operator $\\prod_{k = 1}^L \\mathcal{W_k} e^{i \\mathcal{J}_k} \\mathcal{W_k^\\dagger}$ is represented by the `UCJOperator` class, which is just a dataclass that stores the diagonal Coulomb matrices and orbital rotations. A constructor method is provided to initialize the operator from a truncated double factorization of t2 amplitudes (e.g. from CCSD or MP2).\n", - "\n", - "In the code cell below, we run CCSD to get the t2 amplitudes for initializing the ansatz. We'll create an ansatz operator with 2 repetitions ($L = 2$). For our reference state, we'll use the Hartree-Fock state. Since `UCJOperator` defines a unitary effect, we can use the function `apply_unitary` to apply the ansatz operator to the reference state to obtain the ansatz state. Finally, we compute the energy of the ansatz state." + "The following code cell initializes the ansatz operator, applies it to the Hartree-Fock state, and computes the energy of the resulting state." ] }, { @@ -97,14 +89,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "E(CCSD) = -77.49387212754468 E_corr = -0.04824536314851528\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Energy at initialization: -77.46975600021695\n" + "E(CCSD) = -77.87421536374032 E_corr = -0.04758323886585128\n", + "Energy at initialization: -77.87160024816264\n" ] } ], @@ -114,14 +100,12 @@ "\n", "# Get CCSD t2 amplitudes for initializing the ansatz\n", "ccsd = cc.CCSD(\n", - " scf,\n", - " frozen=[i for i in range(mol.nao_nr()) if i not in active_space],\n", - ")\n", - "_, t1, t2 = ccsd.kernel()\n", + " scf, frozen=[i for i in range(mol.nao_nr()) if i not in active_space]\n", + ").run()\n", "\n", "# Construct UCJ operator\n", "n_reps = 2\n", - "operator = ffsim.UCJOperator.from_t_amplitudes(t2, n_reps=n_reps)\n", + "operator = ffsim.UCJOpSpinBalanced.from_t_amplitudes(ccsd.t2, n_reps=n_reps)\n", "\n", "# Construct the Hartree-Fock state to use as the reference state\n", "reference_state = ffsim.hartree_fock_state(norb, nelec)\n", @@ -139,9 +123,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To facilitate variational optimization of the ansatz, `UCJOperator` implements methods for conversion to and from a vector of real-valued parameters. The precise relation between a parameter vector and the matrices of the UCJ operator is somewhat complicated. In short, the parameter vector stores the entries of the UCJ matrices in a non-redundant way (for the orbital rotations, the parameter vector actually stores the entries of their generators.)\n", - "\n", - "The following code cell shows how one can define an objective function that takes as input a parameter vector and outputs the energy of the associated ansatz state, and then optimize this objective function using `scipy.optimize.minimize`. Here, we set a small limit on the number of iterations; increase the value if you would like to run it to convergence." + "To variationally optimize the ansatz, we'll take advantage of methods for conversion to and from real-valued parameter vectors. In the following code cell, we define an objective function that takes a parameter vector as input and outputs the energy of the associated ansatz state. We then optimize this objective function using `scipy.optimize.minimize`, with an initial guess obtained from the operator we initialized previously from t2 amplitudes." ] }, { @@ -157,12 +139,12 @@ " message: STOP: TOTAL NO. of ITERATIONS REACHED LIMIT\n", " success: False\n", " status: 1\n", - " fun: -77.50963778067545\n", - " x: [ 1.263e+00 -4.692e-01 ... 8.693e-02 1.366e-01]\n", - " nit: 5\n", - " jac: [-4.974e-05 6.295e-04 ... -3.588e-03 -4.502e-03]\n", - " nfev: 584\n", - " njev: 8\n", + " fun: -77.87387390686946\n", + " x: [-1.153e+00 6.076e-05 ... 2.465e-04 1.287e-01]\n", + " nit: 10\n", + " jac: [ 2.558e-05 -1.990e-05 ... 4.263e-06 2.274e-05]\n", + " nfev: 949\n", + " njev: 13\n", " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n" ] } @@ -173,7 +155,7 @@ "\n", "def fun(x):\n", " # Initialize the ansatz operator from the parameter vector\n", - " operator = ffsim.UCJOperator.from_parameters(x, norb=norb, n_reps=n_reps)\n", + " operator = ffsim.UCJOpSpinBalanced.from_parameters(x, norb=norb, n_reps=n_reps)\n", " # Apply the ansatz operator to the reference state\n", " final_state = ffsim.apply_unitary(reference_state, operator, norb=norb, nelec=nelec)\n", " # Return the energy ⟨ψ|H|ψ⟩ of the ansatz state\n", @@ -181,7 +163,7 @@ "\n", "\n", "result = scipy.optimize.minimize(\n", - " fun, x0=operator.to_parameters(), method=\"L-BFGS-B\", options=dict(maxiter=5)\n", + " fun, x0=operator.to_parameters(), method=\"L-BFGS-B\", options=dict(maxiter=10)\n", ")\n", "\n", "print(f\"Number of parameters: {len(result.x)}\")\n", @@ -192,22 +174,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## The local unitary cluster Jastrow (LUCJ) ansatz\n", - "\n", - "Implementing the $e^{i \\mathcal{J}_k}$ term of the UCJ ansatz requires either all-to-all connectivity or the use of a fermionic swap network, making it challenging for noisy pre-fault-tolerant quantum processors that have limited connectivity. The idea of the *local* UCJ ansatz is to impose sparsity constraints on the $\\mathbf{J}^{\\alpha\\alpha}$ and $\\mathbf{J}^{\\alpha\\beta}$ matrices which allow them to be implemented in constant depth on qubit topologies with limited connectivity. The constraints are specified by a list of indices indicating which matrix entries in the upper triangle are allowed to be nonzero (since the matrices are symmetric, only the upper triangle needs to be specified).\n", + "## LUCJ ansatz\n", "\n", - "As an example, consider a square lattice qubit topology. We can place the $\\alpha$ and $\\beta$ orbitals in parallel lines on the lattice, with connections between these lines forming \"rungs\" of a ladder shape. With this setup, orbitals with the same spin are connected with a line topology, while orbitals with different spins are connected when they share the same spatial orbital. This yields the following index constraints on the $\\mathbf{J}$ matrices:\n", + "Now, let's add locality constraints to simulate the LUCJ ansatz. We'll restrict same-spin interactions to a line topology, and opposite-spin interactions to those within the same spatial orbital. As explained in [The local unitary cluster Jastrow (LUCJ) ansatz](../explanations/lucj.ipynb#The-local-UCJ-(LUCJ)-ansatz), these constraints allow the ansatz to be simulated directly on a square lattice.\n", "\n", - "$$\n", - "\\begin{align*}\n", - "\\mathbf{J}^{\\alpha\\alpha} &: \\set{(p, p+1) \\; , \\; p = 0, \\ldots, N-2} \\\\\n", - "\\mathbf{J}^{\\alpha\\beta} &: \\set{(p, p) \\;, \\; p = 0, \\ldots, N-1}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "In other words, if the $\\mathbf{J}$ matrices are nonzero only at the specified indices in the upper triangle, then the $e^{i \\mathcal{J}_k}$ term can be implemented on a square topology without using any swap gates, in constant depth. Of course, imposing such constraints on the ansatz makes it less expressive, so more ansatz repetitions may be required.\n", - "\n", - "In the following code cell, we demonstrate the optimization of the ansatz with these constraints imposed. We still choose to use 2 repetitions, so notice that the number of parameters in the optimization has decreased from 72 to 46." + "In the following code cell, we demonstrate the optimization of the ansatz with these constraints imposed. Notice that with the same number of ansatz repetitions, the number of parameters of the ansatz has decreased from 72 to 46." ] }, { @@ -220,31 +191,28 @@ "output_type": "stream", "text": [ "Number of parameters: 46\n", - " message: STOP: TOTAL NO. of ITERATIONS REACHED LIMIT\n", - " success: False\n", - " status: 1\n", - " fun: -77.45741377950904\n", - " x: [ 1.264e+00 -4.835e-01 ... 8.482e-03 8.513e-03]\n", + " message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n", + " success: True\n", + " status: 0\n", + " fun: -77.87363426546702\n", + " x: [-1.152e+00 -2.540e-04 ... 3.519e-02 2.561e-01]\n", " nit: 5\n", - " jac: [ 1.464e-04 -1.009e-04 ... -1.330e-03 -3.375e-03]\n", - " nfev: 423\n", - " njev: 9\n", + " jac: [ 1.847e-05 0.000e+00 ... 4.263e-06 4.263e-06]\n", + " nfev: 329\n", + " njev: 7\n", " hess_inv: <46x46 LbfgsInvHessProduct with dtype=float64>\n" ] } ], "source": [ - "alpha_alpha_indices = [(p, p + 1) for p in range(norb - 1)]\n", - "alpha_beta_indices = [(p, p) for p in range(norb)]\n", + "pairs_aa = [(p, p + 1) for p in range(norb - 1)]\n", + "pairs_ab = [(p, p) for p in range(norb)]\n", + "interaction_pairs = (pairs_aa, pairs_ab)\n", "\n", "\n", "def fun(x):\n", - " operator = ffsim.UCJOperator.from_parameters(\n", - " x,\n", - " norb=norb,\n", - " n_reps=n_reps,\n", - " alpha_alpha_indices=alpha_alpha_indices,\n", - " alpha_beta_indices=alpha_beta_indices,\n", + " operator = ffsim.UCJOpSpinBalanced.from_parameters(\n", + " x, norb=norb, n_reps=n_reps, interaction_pairs=interaction_pairs\n", " )\n", " final_state = ffsim.apply_unitary(reference_state, operator, norb=norb, nelec=nelec)\n", " return np.real(np.vdot(final_state, hamiltonian @ final_state))\n", @@ -252,11 +220,9 @@ "\n", "result = scipy.optimize.minimize(\n", " fun,\n", - " x0=operator.to_parameters(\n", - " alpha_alpha_indices=alpha_alpha_indices, alpha_beta_indices=alpha_beta_indices\n", - " ),\n", + " x0=operator.to_parameters(interaction_pairs=interaction_pairs),\n", " method=\"L-BFGS-B\",\n", - " options=dict(maxiter=5),\n", + " options=dict(maxiter=10),\n", ")\n", "print(f\"Number of parameters: {len(result.x)}\")\n", "print(result)" @@ -281,36 +247,31 @@ "output_type": "stream", "text": [ "Number of parameters: 46\n", - " message: Stop: Total number of iterations reached limit.\n", - " success: False\n", - " fun: -77.4700926744293\n", - " x: [ 1.407e+00 -4.288e-01 ... 1.441e-01 -3.911e-01]\n", - " nit: 5\n", - " jac: [-5.345e-03 1.154e-03 ... 9.218e-04 1.695e-03]\n", - " nfev: 733\n", - " njev: 5\n", - " nlinop: 503\n", + " message: Convergence: Norm of projected gradient <= gtol.\n", + " success: True\n", + " fun: -77.87363432133785\n", + " x: [-1.152e+00 -5.961e-05 ... 3.502e-02 2.559e-01]\n", + " nit: 3\n", + " jac: [ 6.165e-07 -7.634e-08 ... -1.103e-07 -1.696e-07]\n", + " nfev: 523\n", + " njev: 4\n", + " nlinop: 339\n", "\n", "Iteration 1\n", - " Energy: -77.45703391925728\n", - " Norm of gradient: 0.013052588959043813\n", - " Regularization hyperparameter: 0.02551810621378698\n", - " Variation hyperparameter: 0.7000448555166967\n", + " Energy: -77.87363008607939\n", + " Norm of gradient: 0.0017644518359106424\n", + " Regularization hyperparameter: 0.0031063730910734907\n", + " Variation hyperparameter: 0.9971884634671736\n", "Iteration 2\n", - " Energy: -77.45820771708807\n", - " Norm of gradient: 0.00834757840661909\n", - " Regularization hyperparameter: 0.0003721662094729132\n", - " Variation hyperparameter: 0.7036683998701272\n", + " Energy: -77.8736343159954\n", + " Norm of gradient: 4.409978218198142e-05\n", + " Regularization hyperparameter: 0.003106389097943625\n", + " Variation hyperparameter: 0.9971884640463475\n", "Iteration 3\n", - " Energy: -77.45823388646428\n", - " Norm of gradient: 0.00819459947388564\n", - " Regularization hyperparameter: 1.0388352484646413\n", - " Variation hyperparameter: 0.6991628670959933\n", - "Iteration 4\n", - " Energy: -77.46334910906903\n", - " Norm of gradient: 0.024356204901877048\n", - " Regularization hyperparameter: 0.003183073141343953\n", - " Variation hyperparameter: 0.6994537036015821\n" + " Energy: -77.87363432133785\n", + " Norm of gradient: 4.178532608295441e-06\n", + " Regularization hyperparameter: 0.0031071089983360466\n", + " Variation hyperparameter: 0.9971884650809466\n" ] } ], @@ -322,12 +283,8 @@ "\n", "# Define function that converts a list of parameters to the corresponding state vector\n", "def params_to_vec(x: np.ndarray) -> np.ndarray:\n", - " operator = ffsim.UCJOperator.from_parameters(\n", - " x,\n", - " norb=norb,\n", - " n_reps=n_reps,\n", - " alpha_alpha_indices=alpha_alpha_indices,\n", - " alpha_beta_indices=alpha_beta_indices,\n", + " operator = ffsim.UCJOpSpinBalanced.from_parameters(\n", + " x, norb=norb, n_reps=n_reps, interaction_pairs=interaction_pairs\n", " )\n", " return ffsim.apply_unitary(reference_state, operator, norb=norb, nelec=nelec)\n", "\n", @@ -354,10 +311,8 @@ "result = minimize_linear_method(\n", " params_to_vec,\n", " hamiltonian,\n", - " x0=operator.to_parameters(\n", - " alpha_alpha_indices=alpha_alpha_indices, alpha_beta_indices=alpha_beta_indices\n", - " ),\n", - " maxiter=5,\n", + " x0=operator.to_parameters(interaction_pairs=interaction_pairs),\n", + " maxiter=10,\n", " callback=callback,\n", ")\n", "\n", @@ -392,7 +347,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.1" + "version": "3.12.3" } }, "nbformat": 4, diff --git a/docs/how-to-guides/qiskit-circuits.ipynb b/docs/how-to-guides/qiskit-circuits.ipynb index b648d38fa..68fe7d682 100644 --- a/docs/how-to-guides/qiskit-circuits.ipynb +++ b/docs/how-to-guides/qiskit-circuits.ipynb @@ -39,7 +39,7 @@ "source": [ "## Circuit transpilation\n", "\n", - "In this section, we show how to use transpiler passes included in ffsim to optimize quantum circuits built from fermionic gates. As a representative example circuit, we construct a circuit that prepares the Hartree-Fock state and then applies a [unitary cluster Jastrow (UCJ)](../api/ffsim.rst#ffsim.UCJOperator) ansatz operator to it." + "In this section, we show how to use transpiler passes included in ffsim to optimize quantum circuits built from fermionic gates. As a representative example circuit, we construct a circuit that prepares the Hartree-Fock state and then applies a [unitary cluster Jastrow (UCJ)](../explanations/lucj.ipynb) ansatz operator to it." ] }, { @@ -49,9 +49,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 2, @@ -61,12 +61,12 @@ ], "source": [ "# Construct a random UCJ operator\n", - "ucj_op = ffsim.random.random_ucj_operator(norb=norb, n_reps=2, seed=rng)\n", + "ucj_op = ffsim.random.random_ucj_op_spin_balanced(norb=norb, n_reps=2, seed=rng)\n", "\n", "# Construct circuit\n", "circuit = QuantumCircuit(qubits)\n", "circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n", "\n", "circuit.draw(\"mpl\", scale=0.7)" ] @@ -142,7 +142,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 4, @@ -170,7 +170,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 5, @@ -210,7 +210,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 6, @@ -240,7 +240,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -261,7 +261,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Unitary cluster Jastrow (UCJ) operator" + "#### Spin-balanced unitary cluster Jastrow (UCJ) operator" ] }, { @@ -272,7 +272,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 8, @@ -281,10 +281,40 @@ } ], "source": [ - "ucj_op = ffsim.random.random_ucj_operator(norb=norb, n_reps=2)\n", + "ucj_op = ffsim.random.random_ucj_op_spin_balanced(norb=norb, n_reps=2)\n", "\n", "circuit = QuantumCircuit(qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits)" + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Spin-unbalanced unitary cluster Jastrow (UCJ) operator" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ucj_op = ffsim.random.random_ucj_op_spin_unbalanced(norb=norb, n_reps=2)\n", + "\n", + "circuit = QuantumCircuit(qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinUnbalancedJW(ucj_op), qubits)" ] } ], @@ -304,7 +334,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.1" + "version": "3.12.3" } }, "nbformat": 4, diff --git a/docs/how-to-guides/qiskit-sampler.ipynb b/docs/how-to-guides/qiskit-sampler.ipynb index d9643d905..0f9dedd95 100644 --- a/docs/how-to-guides/qiskit-sampler.ipynb +++ b/docs/how-to-guides/qiskit-sampler.ipynb @@ -134,7 +134,7 @@ "\n", "### Sampling from an LUCJ circuit for a closed-shell molecule\n", "\n", - "The following code cell demonstrates a possible workflow for sampling from an LUCJ circuit for a nitrogen molecule in the 6-31g basis.\n" + "The following code cell demonstrates a possible workflow for sampling from a [spin-balanced LUCJ](../explanations/lucj.ipynb) circuit for a nitrogen molecule in the 6-31g basis.\n" ] }, { @@ -146,25 +146,25 @@ "name": "stdout", "output_type": "stream", "text": [ - "converged SCF energy = -108.835236570775\n", - "norb = 16\n", - "nelec = (5, 5)\n", - "E(CCSD) = -109.0398256929734 E_corr = -0.204589122198831\n" + "converged SCF energy = -108.835236570774\n", + "norb = 14\n", + "nelec = (3, 3)\n", + "E(CCSD) = -108.9630419334855 E_corr = -0.1278053627110058\n" ] }, { "data": { "text/plain": [ - "{'00000000000111110000000000011111': 9897,\n", - " '00000000001101110000000000011111': 27,\n", - " '00000000000111110000000000110111': 21,\n", - " '10000000000011110000000000011111': 7,\n", - " '00010000000101110000000000011111': 5,\n", - " '00000000000111110000000001011011': 5,\n", - " '00000000000111110001000000010111': 5,\n", - " '00000000010110110000000001011011': 3,\n", - " '01000000000011110000000000011111': 3,\n", - " '00000000000111111000000000001111': 3}" + "{'0000000000011100000000000111': 9924,\n", + " '0000000000110100000000001101': 16,\n", + " '0000000001011000000000010110': 10,\n", + " '0000000001110000000000000111': 10,\n", + " '0000000000011100000000011100': 10,\n", + " '0001000001010000000000000111': 5,\n", + " '0000000001011000100000000110': 4,\n", + " '0000000000011100100000001100': 3,\n", + " '0010000000011000000000010110': 3,\n", + " '0000000000110100010000000101': 3}" ] }, "execution_count": 3, @@ -173,11 +173,12 @@ } ], "source": [ + "import pyscf\n", + "import pyscf.cc\n", "import pyscf.data.elements\n", - "from pyscf import cc, gto\n", "\n", "# Build N2 molecule\n", - "mol = gto.Mole()\n", + "mol = pyscf.gto.Mole()\n", "mol.build(\n", " atom=[[\"N\", (0, 0, 0)], [\"N\", (1.0, 0, 0)]],\n", " basis=\"6-31g\",\n", @@ -185,7 +186,7 @@ ")\n", "\n", "# Define active space\n", - "n_frozen = pyscf.data.elements.chemcore(mol)\n", + "n_frozen = 4\n", "active_space = range(n_frozen, mol.nao_nr())\n", "\n", "# Get molecular data and Hamiltonian\n", @@ -197,26 +198,24 @@ "print(f\"nelec = {nelec}\")\n", "\n", "# Get CCSD t2 amplitudes for initializing the ansatz\n", - "ccsd = cc.CCSD(scf, frozen=[i for i in range(mol.nao_nr()) if i not in active_space])\n", - "_, _, t2 = ccsd.kernel()\n", - "\n", - "# Construct LUCJ operator using indices for a square lattice mapping\n", - "n_reps = 1\n", - "alpha_alpha_indices = [(p, p + 1) for p in range(norb - 1)]\n", - "alpha_beta_indices = [(p, p) for p in range(norb)]\n", - "ucj_op = ffsim.UCJOperator.from_parameters(\n", - " ffsim.UCJOperator.from_t_amplitudes(t2).to_parameters(),\n", - " norb=norb,\n", - " n_reps=n_reps,\n", - " alpha_alpha_indices=alpha_alpha_indices,\n", - " alpha_beta_indices=alpha_beta_indices,\n", + "ccsd = pyscf.cc.CCSD(\n", + " scf, frozen=[i for i in range(mol.nao_nr()) if i not in active_space]\n", + ").run()\n", + "\n", + "# Use 2 ansatz layers\n", + "n_reps = 2\n", + "# Use interactions implementable on a square lattice\n", + "pairs_aa = [(p, p + 1) for p in range(norb - 1)]\n", + "pairs_ab = [(p, p) for p in range(norb)]\n", + "ucj_op = ffsim.UCJOpSpinBalanced.from_t_amplitudes(\n", + " ccsd.t2, n_reps=n_reps, interaction_pairs=(pairs_aa, pairs_ab)\n", ")\n", "\n", "# Construct circuit\n", "qubits = QuantumRegister(2 * norb)\n", "circuit = QuantumCircuit(qubits)\n", "circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n", "circuit.measure_all()\n", "\n", "# Sample 10,000 shots from the circuit using FfsimSampler\n", @@ -237,7 +236,7 @@ "source": [ "### Sampling from an LUCJ circuit for an open-shell molecule\n", "\n", - "The following code cell demonstrates a possible workflow for sampling from an LUCJ circuit for a beryllium monohydride molecule in the 6-31g basis." + "The following code cell demonstrates a possible workflow for sampling from a [spin-unbalanced LUCJ](../explanations/lucj.ipynb) circuit for a hydroxyl radical in the 6-31g basis." ] }, { @@ -249,21 +248,28 @@ "name": "stdout", "output_type": "stream", "text": [ - "converged SCF energy = -15.1172960668632\n", + "SCF not converged.\n", + "SCF energy = -75.3484557094412\n", "norb = 11\n", - "nelec = (3, 2)\n", + "nelec = (5, 4)\n", "\n", "WARN: RCCSD method does not support ROHF method. ROHF object is converted to UHF object and UCCSD method is called.\n", "\n", - "E(UCCSD) = -15.1402344412343 E_corr = -0.02293837437111472\n" + "E(UCCSD) = -75.45619739083253 E_corr = -0.1077416813913165\n" ] }, { "data": { "text/plain": [ - "{'0000000001100000000111': 9998,\n", - " '1000000000100000100101': 1,\n", - " '0000000010100000100101': 1}" + "{'0000000111100000011111': 9991,\n", + " '0000100101100000111011': 2,\n", + " '0000100110100000111011': 1,\n", + " '0000000111100110000111': 1,\n", + " '0000010101100001011011': 1,\n", + " '1000000101100000111011': 1,\n", + " '0101000001100000011111': 1,\n", + " '0000010110100001011011': 1,\n", + " '0100000110100100001111': 1}" ] }, "execution_count": 4, @@ -275,12 +281,13 @@ "import pyscf.data.elements\n", "from pyscf import cc, gto\n", "\n", - "# Build BeH molecule\n", + "# Build HO molecule\n", "mol = gto.Mole()\n", "mol.build(\n", - " atom=[[\"H\", (0, 0, 0)], [\"Be\", (0, 0, 1.1)]],\n", + " atom=[[\"H\", (0, 0, 0)], [\"O\", (0, 0, 1.1)]],\n", " basis=\"6-31g\",\n", " spin=1,\n", + " symmetry=\"Coov\",\n", ")\n", "\n", "# Get molecular data and Hamiltonian\n", @@ -292,27 +299,23 @@ "print(f\"nelec = {nelec}\")\n", "\n", "# Get CCSD t2 amplitudes for initializing the ansatz\n", - "ccsd = cc.CCSD(scf)\n", - "_, _, t2 = ccsd.kernel()\n", - "\n", - "# Construct LUCJ operator using indices for a square lattice mapping\n", - "n_reps = 4\n", - "alpha_alpha_indices = [(p, p + 1) for p in range(norb - 1)]\n", - "alpha_beta_indices = [(p, p) for p in range(norb)]\n", - "beta_beta_indices = [(p, p + 1) for p in range(norb - 1)]\n", - "ucj_op = ffsim.UCJOperatorOpenShell.from_t_amplitudes(\n", - " t2,\n", - " n_reps=n_reps,\n", - " alpha_alpha_indices=alpha_alpha_indices,\n", - " alpha_beta_indices=alpha_beta_indices,\n", - " beta_beta_indices=beta_beta_indices,\n", + "ccsd = cc.CCSD(scf).run()\n", + "\n", + "# Use 4 layers from opposite-spin amplitudes and 2 layers from same-spin amplitudes\n", + "n_reps = (4, 2)\n", + "# Use interactions implementable on a square lattice\n", + "pairs_aa = [(p, p + 1) for p in range(norb - 1)]\n", + "pairs_ab = [(p, p) for p in range(norb)]\n", + "pairs_bb = [(p, p + 1) for p in range(norb - 1)]\n", + "ucj_op = ffsim.UCJOpSpinUnbalanced.from_t_amplitudes(\n", + " ccsd.t2, n_reps=n_reps, interaction_pairs=(pairs_aa, pairs_ab, pairs_bb)\n", ")\n", "\n", "# Construct circuit\n", "qubits = QuantumRegister(2 * norb)\n", "circuit = QuantumCircuit(qubits)\n", "circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)\n", - "circuit.append(ffsim.qiskit.UCJOperatorOpenShellJW(ucj_op), qubits)\n", + "circuit.append(ffsim.qiskit.UCJOpSpinUnbalancedJW(ucj_op), qubits)\n", "circuit.measure_all()\n", "\n", "# Sample 10,000 shots from the circuit using FfsimSampler\n", diff --git a/python/ffsim/__init__.py b/python/ffsim/__init__.py index 936e893b7..e4fb9be4f 100644 --- a/python/ffsim/__init__.py +++ b/python/ffsim/__init__.py @@ -83,7 +83,8 @@ HopGateAnsatzOperator, RealUCJOperator, UCJOperator, - UCJOperatorOpenShell, + UCJOpSpinBalanced, + UCJOpSpinUnbalanced, multireference_state, multireference_state_prod, ) @@ -107,7 +108,8 @@ "SupportsLinearOperator", "SupportsTrace", "UCJOperator", - "UCJOperatorOpenShell", + "UCJOpSpinBalanced", + "UCJOpSpinUnbalanced", "apply_diag_coulomb_evolution", "apply_fsim_gate", "apply_givens_rotation", diff --git a/python/ffsim/qiskit/__init__.py b/python/ffsim/qiskit/__init__.py index 6b23aa34f..be41021f3 100644 --- a/python/ffsim/qiskit/__init__.py +++ b/python/ffsim/qiskit/__init__.py @@ -23,7 +23,8 @@ PrepareSlaterDeterminantJW, PrepareSlaterDeterminantSpinlessJW, UCJOperatorJW, - UCJOperatorOpenShellJW, + UCJOpSpinBalancedJW, + UCJOpSpinUnbalancedJW, ) from ffsim.qiskit.sampler import FfsimSampler from ffsim.qiskit.transpiler_passes import DropNegligible, MergeOrbitalRotations @@ -53,7 +54,8 @@ "PrepareSlaterDeterminantJW", "PrepareSlaterDeterminantSpinlessJW", "UCJOperatorJW", - "UCJOperatorOpenShellJW", + "UCJOpSpinBalancedJW", + "UCJOpSpinUnbalancedJW", "ffsim_vec_to_qiskit_vec", "pre_init_passes", "qiskit_vec_to_ffsim_vec", diff --git a/python/ffsim/qiskit/gates/__init__.py b/python/ffsim/qiskit/gates/__init__.py index a2f23a9d3..967a66e32 100644 --- a/python/ffsim/qiskit/gates/__init__.py +++ b/python/ffsim/qiskit/gates/__init__.py @@ -25,8 +25,8 @@ PrepareSlaterDeterminantJW, PrepareSlaterDeterminantSpinlessJW, ) -from ffsim.qiskit.gates.ucj import UCJOperatorJW -from ffsim.qiskit.gates.ucj_open_shell import UCJOperatorOpenShellJW +from ffsim.qiskit.gates.ucj import UCJOpSpinBalancedJW, UCJOpSpinUnbalancedJW +from ffsim.qiskit.gates.ucj_operator import UCJOperatorJW __all__ = [ "DiagCoulombEvolutionJW", @@ -39,5 +39,6 @@ "PrepareSlaterDeterminantJW", "PrepareSlaterDeterminantSpinlessJW", "UCJOperatorJW", - "UCJOperatorOpenShellJW", + "UCJOpSpinBalancedJW", + "UCJOpSpinUnbalancedJW", ] diff --git a/python/ffsim/qiskit/gates/ucj.py b/python/ffsim/qiskit/gates/ucj.py index 2860be265..bf0ab9460 100644 --- a/python/ffsim/qiskit/gates/ucj.py +++ b/python/ffsim/qiskit/gates/ucj.py @@ -22,52 +22,114 @@ Qubit, ) +from ffsim import variational from ffsim.qiskit.gates.diag_coulomb import DiagCoulombEvolutionJW from ffsim.qiskit.gates.orbital_rotation import OrbitalRotationJW -from ffsim.variational import UCJOperator -class UCJOperatorJW(Gate): - """Unitary cluster Jastrow operator under the Jordan-Wigner transformation. +class UCJOpSpinBalancedJW(Gate): + """Spin-balanced UCJ operator under the Jordan-Wigner transformation. - See :class:`ffsim.UCJOperator` for a description of this gate's unitary. + See :class:`ffsim.UCJOpSpinBalanced` for a description of this gate's unitary. This gate assumes that qubits are ordered such that the first `norb` qubits correspond to the alpha orbitals and the last `norb` qubits correspond to the beta orbitals. """ - def __init__(self, ucj_operator: UCJOperator, *, label: str | None = None): - """Create a new unitary cluster Jastrow (UCJ) gate. + def __init__( + self, ucj_op: variational.UCJOpSpinBalanced, *, label: str | None = None + ): + """Create a new spin-balanced unitary cluster Jastrow (UCJ) gate. Args: - ucj_operator: The UCJ operator. + ucj_op: The UCJ operator. label: The label of the gate. """ - self.ucj_operator = ucj_operator - super().__init__("ucj_jw", 2 * ucj_operator.norb, [], label=label) + self.ucj_op = ucj_op + super().__init__("ucj_balanced_jw", 2 * ucj_op.norb, [], label=label) def _define(self): """Gate decomposition.""" qubits = QuantumRegister(self.num_qubits) self.definition = QuantumCircuit.from_instructions( - _ucj_jw(qubits, self.ucj_operator), qubits=qubits, name=self.name + _ucj_op_spin_balanced_jw(qubits, self.ucj_op), + qubits=qubits, + name=self.name, ) -def _ucj_jw( - qubits: Sequence[Qubit], ucj_op: UCJOperator +def _ucj_op_spin_balanced_jw( + qubits: Sequence[Qubit], ucj_op: variational.UCJOpSpinBalanced ) -> Iterator[CircuitInstruction]: - for mat, mat_alpha_beta, orbital_rotation in zip( - ucj_op.diag_coulomb_mats_alpha_alpha, - ucj_op.diag_coulomb_mats_alpha_beta, - ucj_op.orbital_rotations, + for (diag_coulomb_mat_aa, diag_coulomb_mat_ab), orbital_rotation in zip( + ucj_op.diag_coulomb_mats, ucj_op.orbital_rotations ): yield CircuitInstruction( - OrbitalRotationJW(ucj_op.norb, orbital_rotation.T.conj()), qubits + OrbitalRotationJW(ucj_op.norb, orbital_rotation.T.conj()), + qubits, + ) + yield CircuitInstruction( + DiagCoulombEvolutionJW( + ucj_op.norb, + (diag_coulomb_mat_aa, diag_coulomb_mat_ab, diag_coulomb_mat_aa), + -1.0, + ), + qubits, + ) + yield CircuitInstruction( + OrbitalRotationJW(ucj_op.norb, orbital_rotation), qubits + ) + if ucj_op.final_orbital_rotation is not None: + yield CircuitInstruction( + OrbitalRotationJW(ucj_op.norb, ucj_op.final_orbital_rotation), qubits + ) + + +class UCJOpSpinUnbalancedJW(Gate): + """Spin-unbalanced UCJ operator under the Jordan-Wigner transformation. + + See :class:`ffsim.UCJOpSpinUnbalanced` for a description of this gate's unitary. + + This gate assumes that qubits are ordered such that the first `norb` qubits + correspond to the alpha orbitals and the last `norb` qubits correspond to the + beta orbitals. + """ + + def __init__( + self, ucj_op: variational.UCJOpSpinUnbalanced, *, label: str | None = None + ): + """Create a new spin-unbalanced unitary cluster Jastrow (UCJ) gate. + + Args: + ucj_op: The UCJ operator. + label: The label of the gate. + """ + self.ucj_op = ucj_op + super().__init__("ucj_unbalanced_jw", 2 * ucj_op.norb, [], label=label) + + def _define(self): + """Gate decomposition.""" + qubits = QuantumRegister(self.num_qubits) + self.definition = QuantumCircuit.from_instructions( + _ucj_op_spin_unbalanced_jw(qubits, self.ucj_op), + qubits=qubits, + name=self.name, + ) + + +def _ucj_op_spin_unbalanced_jw( + qubits: Sequence[Qubit], ucj_op: variational.UCJOpSpinUnbalanced +) -> Iterator[CircuitInstruction]: + for diag_colomb_mat, orbital_rotation in zip( + ucj_op.diag_coulomb_mats, ucj_op.orbital_rotations + ): + yield CircuitInstruction( + OrbitalRotationJW(ucj_op.norb, orbital_rotation.transpose(0, 2, 1).conj()), + qubits, ) yield CircuitInstruction( - DiagCoulombEvolutionJW(ucj_op.norb, (mat, mat_alpha_beta, mat), -1.0), + DiagCoulombEvolutionJW(ucj_op.norb, diag_colomb_mat, -1.0), qubits, ) yield CircuitInstruction( diff --git a/python/ffsim/qiskit/gates/ucj_open_shell.py b/python/ffsim/qiskit/gates/ucj_operator.py similarity index 73% rename from python/ffsim/qiskit/gates/ucj_open_shell.py rename to python/ffsim/qiskit/gates/ucj_operator.py index 31cc3d552..c5d066be6 100644 --- a/python/ffsim/qiskit/gates/ucj_open_shell.py +++ b/python/ffsim/qiskit/gates/ucj_operator.py @@ -21,13 +21,15 @@ QuantumRegister, Qubit, ) +from typing_extensions import deprecated from ffsim.qiskit.gates.diag_coulomb import DiagCoulombEvolutionJW from ffsim.qiskit.gates.orbital_rotation import OrbitalRotationJW -from ffsim.variational import UCJOperatorOpenShell +from ffsim.variational import UCJOperator -class UCJOperatorOpenShellJW(Gate): +@deprecated("The UCJOperatorJW class is deprecated. Use UCJOpSpinBalancedJW instead.") +class UCJOperatorJW(Gate): """Unitary cluster Jastrow operator under the Jordan-Wigner transformation. See :class:`ffsim.UCJOperator` for a description of this gate's unitary. @@ -37,7 +39,7 @@ class UCJOperatorOpenShellJW(Gate): beta orbitals. """ - def __init__(self, ucj_operator: UCJOperatorOpenShell, *, label: str | None = None): + def __init__(self, ucj_operator: UCJOperator, *, label: str | None = None): """Create a new unitary cluster Jastrow (UCJ) gate. Args: @@ -45,7 +47,7 @@ def __init__(self, ucj_operator: UCJOperatorOpenShell, *, label: str | None = No label: The label of the gate. """ self.ucj_operator = ucj_operator - super().__init__("ucj_open_jw", 2 * ucj_operator.norb, [], label=label) + super().__init__("ucj_jw", 2 * ucj_operator.norb, [], label=label) def _define(self): """Gate decomposition.""" @@ -56,17 +58,18 @@ def _define(self): def _ucj_jw( - qubits: Sequence[Qubit], ucj_op: UCJOperatorOpenShell + qubits: Sequence[Qubit], ucj_op: UCJOperator ) -> Iterator[CircuitInstruction]: - for diag_colomb_mat, orbital_rotation in zip( - ucj_op.diag_coulomb_mats, ucj_op.orbital_rotations + for mat, mat_alpha_beta, orbital_rotation in zip( + ucj_op.diag_coulomb_mats_alpha_alpha, + ucj_op.diag_coulomb_mats_alpha_beta, + ucj_op.orbital_rotations, ): yield CircuitInstruction( - OrbitalRotationJW(ucj_op.norb, orbital_rotation.transpose(0, 2, 1).conj()), - qubits, + OrbitalRotationJW(ucj_op.norb, orbital_rotation.T.conj()), qubits ) yield CircuitInstruction( - DiagCoulombEvolutionJW(ucj_op.norb, diag_colomb_mat, -1.0), + DiagCoulombEvolutionJW(ucj_op.norb, (mat, mat_alpha_beta, mat), -1.0), qubits, ) yield CircuitInstruction( diff --git a/python/ffsim/qiskit/sim.py b/python/ffsim/qiskit/sim.py index 71d4520d3..a86d1bb5c 100644 --- a/python/ffsim/qiskit/sim.py +++ b/python/ffsim/qiskit/sim.py @@ -30,7 +30,8 @@ PrepareSlaterDeterminantJW, PrepareSlaterDeterminantSpinlessJW, UCJOperatorJW, - UCJOperatorOpenShellJW, + UCJOpSpinBalancedJW, + UCJOpSpinUnbalancedJW, ) @@ -202,7 +203,18 @@ def _evolve_statevector( ) return Statevector(vec=vec, norb=norb, nelec=nelec) - if isinstance(op, (UCJOperatorJW, UCJOperatorOpenShellJW)): + if isinstance(op, (UCJOpSpinBalancedJW, UCJOpSpinUnbalancedJW)): + if not consecutive_sorted: + raise ValueError( + f"Gate of type '{op.__class__.__name__}' must be applied to " + "consecutive qubits, in ascending order." + ) + vec = protocols.apply_unitary( + vec, op.ucj_op, norb=norb, nelec=nelec, copy=False + ) + return Statevector(vec=vec, norb=norb, nelec=nelec) + + if isinstance(op, UCJOperatorJW): if not consecutive_sorted: raise ValueError( f"Gate of type '{op.__class__.__name__}' must be applied to " diff --git a/python/ffsim/qiskit/transpiler_stages.py b/python/ffsim/qiskit/transpiler_stages.py index 183e717fa..63860a845 100644 --- a/python/ffsim/qiskit/transpiler_stages.py +++ b/python/ffsim/qiskit/transpiler_stages.py @@ -34,6 +34,12 @@ def pre_init_passes() -> Iterator[BasePass]: .. _Decompose: https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.Decompose#decompose """ yield Decompose( - ["hartree_fock_jw", "hartree_fock_spinless_jw", "ucj_jw", "ucj_open_jw"] + [ + "hartree_fock_jw", + "hartree_fock_spinless_jw", + "ucj_jw", + "ucj_balanced_jw", + "ucj_unbalanced_jw", + ] ) yield MergeOrbitalRotations() diff --git a/python/ffsim/random/__init__.py b/python/ffsim/random/__init__.py index d056ccd69..a0d898da3 100644 --- a/python/ffsim/random/__init__.py +++ b/python/ffsim/random/__init__.py @@ -20,8 +20,9 @@ random_statevector, random_t2_amplitudes, random_two_body_tensor, + random_ucj_op_spin_balanced, + random_ucj_op_spin_unbalanced, random_ucj_operator, - random_ucj_operator_open_shell, random_unitary, ) @@ -36,6 +37,7 @@ "random_t2_amplitudes", "random_two_body_tensor", "random_ucj_operator", - "random_ucj_operator_open_shell", + "random_ucj_op_spin_balanced", + "random_ucj_op_spin_unbalanced", "random_unitary", ] diff --git a/python/ffsim/random/random.py b/python/ffsim/random/random.py index 2fb4a5638..1291abfb0 100644 --- a/python/ffsim/random/random.py +++ b/python/ffsim/random/random.py @@ -13,6 +13,7 @@ import itertools import numpy as np +from typing_extensions import deprecated from ffsim import hamiltonians, variational @@ -269,6 +270,10 @@ def random_molecular_hamiltonian( ) +@deprecated( + "The random_ucj_operator function is deprecated. Use " + "random_ucj_operator_closed_shell or random_ucj_operator_open_shell instead." +) def random_ucj_operator( norb: int, *, @@ -310,14 +315,59 @@ def random_ucj_operator( ) -def random_ucj_operator_open_shell( +def random_ucj_op_spin_balanced( norb: int, *, n_reps: int = 1, with_final_orbital_rotation: bool = False, seed=None, -) -> variational.UCJOperatorOpenShell: - """Sample a random open-shell unitary cluster Jastrow (UCJ) operator. +) -> variational.UCJOpSpinBalanced: + """Sample a random spin-balanced unitary cluster Jastrow (UCJ) operator. + + Args: + norb: The number of orbitals. + n_reps: The number of ansatz repetitions. + with_final_orbital_rotation: Whether to include a final orbital rotation + in the operator. + seed: A seed to initialize the pseudorandom number generator. + Should be a valid input to ``np.random.default_rng``. + + Returns: + The sampled UCJ operator. + """ + rng = np.random.default_rng(seed) + diag_coulomb_mats = np.stack( + [ + np.stack( + [ + random_real_symmetric_matrix(norb, seed=rng), + random_real_symmetric_matrix(norb, seed=rng), + ] + ) + for _ in range(n_reps) + ] + ) + orbital_rotations = np.stack( + [random_unitary(norb, seed=rng) for _ in range(n_reps)] + ) + final_orbital_rotation = None + if with_final_orbital_rotation: + final_orbital_rotation = random_unitary(norb, seed=rng) + return variational.UCJOpSpinBalanced( + diag_coulomb_mats=diag_coulomb_mats, + orbital_rotations=orbital_rotations, + final_orbital_rotation=final_orbital_rotation, + ) + + +def random_ucj_op_spin_unbalanced( + norb: int, + *, + n_reps: int = 1, + with_final_orbital_rotation: bool = False, + seed=None, +) -> variational.UCJOpSpinUnbalanced: + """Sample a random spin-unbalanced unitary cluster Jastrow (UCJ) operator. Args: norb: The number of orbitals. @@ -354,7 +404,7 @@ def random_ucj_operator_open_shell( final_orbital_rotation = np.stack( [random_unitary(norb, seed=rng), random_unitary(norb, seed=rng)] ) - return variational.UCJOperatorOpenShell( + return variational.UCJOpSpinUnbalanced( diag_coulomb_mats=diag_coulomb_mats, orbital_rotations=orbital_rotations, final_orbital_rotation=final_orbital_rotation, diff --git a/python/ffsim/variational/__init__.py b/python/ffsim/variational/__init__.py index b99018d75..720c13a5e 100644 --- a/python/ffsim/variational/__init__.py +++ b/python/ffsim/variational/__init__.py @@ -17,14 +17,16 @@ multireference_state_prod, ) from ffsim.variational.ucj import RealUCJOperator, UCJOperator -from ffsim.variational.ucj_open_shell import UCJOperatorOpenShell +from ffsim.variational.ucj_spin_balanced import UCJOpSpinBalanced +from ffsim.variational.ucj_spin_unbalanced import UCJOpSpinUnbalanced __all__ = [ "GivensAnsatzOperator", "HopGateAnsatzOperator", "RealUCJOperator", "UCJOperator", - "UCJOperatorOpenShell", + "UCJOpSpinBalanced", + "UCJOpSpinUnbalanced", "multireference_state", "multireference_state_prod", ] diff --git a/python/ffsim/variational/ucj.py b/python/ffsim/variational/ucj.py index 44d476165..b9fd2c12f 100644 --- a/python/ffsim/variational/ucj.py +++ b/python/ffsim/variational/ucj.py @@ -19,6 +19,7 @@ import numpy as np import scipy.linalg from opt_einsum import contract +from typing_extensions import deprecated from ffsim.gates import apply_diag_coulomb_evolution, apply_orbital_rotation from ffsim.linalg import double_factorized_t2 @@ -40,6 +41,7 @@ def _validate_diag_coulomb_indices(indices: list[tuple[int, int]] | None): @dataclass(frozen=True) +@deprecated("The UCJOperator class is deprecated. Use UCJOpSpinBalanced instead.") class UCJOperator: r"""A unitary cluster Jastrow operator. @@ -303,6 +305,7 @@ def _apply_unitary_( @dataclass +@deprecated("The RealUCJOperator class is deprecated. Use UCJOpSpinBalanced instead.") class RealUCJOperator: r"""Real-valued unitary cluster Jastrow operator. diff --git a/python/ffsim/variational/ucj_spin_balanced.py b/python/ffsim/variational/ucj_spin_balanced.py new file mode 100644 index 000000000..23a512276 --- /dev/null +++ b/python/ffsim/variational/ucj_spin_balanced.py @@ -0,0 +1,485 @@ +# (C) Copyright IBM 2024. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Spin-balanced (local) unitary cluster Jastrow ansatz.""" + +from __future__ import annotations + +import itertools +from dataclasses import dataclass +from typing import List, Tuple, cast + +import numpy as np +import scipy.linalg + +from ffsim import gates, linalg +from ffsim.variational.util import ( + orbital_rotation_from_parameters, + orbital_rotation_to_parameters, +) + + +def _validate_interaction_pairs( + interaction_pairs: list[tuple[int, int]] | None, ordered: bool +) -> None: + if interaction_pairs is None: + return + if len(set(interaction_pairs)) != len(interaction_pairs): + raise ValueError( + f"Duplicate interaction pairs encountered: {interaction_pairs}." + ) + if not ordered: + for i, j in interaction_pairs: + if i > j: + raise ValueError( + "When specifying alpha-alpha or beta-beta interaction pairs, " + "you must provide only upper triangular pairs. " + f"Got {(i, j)}, which is a lower triangular pair." + ) + + +@dataclass(frozen=True) +class UCJOpSpinBalanced: + r"""A spin-balanced unitary cluster Jastrow operator. + + A unitary cluster Jastrow (UCJ) operator has the form + + .. math:: + + \prod_{k = 1}^L \mathcal{U}_k e^{i \mathcal{J}_k} \mathcal{U}_k^\dagger + + where each :math:`\mathcal{U_k}` is an orbital rotation and each :math:`\mathcal{J}` + is a diagonal Coulomb operator of the form + + .. math:: + + \mathcal{J} = \frac12\sum_{\sigma \tau, ij} + \mathbf{J}^{(\sigma \tau)}_{ij} n_{\sigma, i} n_{\tau, j}. + + For the spin-balanced operator, we require that + :math:`\mathbf{J}^{(\alpha \alpha)} = \mathbf{J}^{(\beta \beta)}` and + :math:`\mathbf{J}^{(\alpha \beta)} = \mathbf{J}^{(\beta \alpha)}`. + Therefore, each diagonal Coulomb operator is described by 2 matrices, + :math:`\mathbf{J}^{(\alpha \alpha)}` and :math:`\mathbf{J}^{(\alpha \beta)}`, and + both of these matrices are symmetric. + Furthermore, each orbital rotation is described by a single matrix because the + same orbital rotation is applied to both spin alpha and spin beta. + The number of terms :math:`L` is referred to as the + number of ansatz repetitions and is accessible via the `n_reps` attribute. + + To support variational optimization of the orbital basis, an optional final + orbital rotation can be included in the operator, to be performed at the end. + + Attributes: + diag_coulomb_mats (np.ndarray): The diagonal Coulomb matrices, as a Numpy array + of shape `(n_reps, 2, norb, norb)` + The last two axes index the rows and columns of + the matrices, and the third from last axis, which has 2 dimensions, indexes + the spin interaction type of the matrix: alpha-alpha, and then alpha-beta. + The first axis indexes the ansatz repetitions. + orbital_rotations (np.ndarray): The orbital rotations, as a Numpy array + of shape `(n_reps, norb, norb)`. + final_orbital_rotation (np.ndarray): The optional final orbital rotation, as + a Numpy array of shape `(norb, norb)`. + """ + + diag_coulomb_mats: np.ndarray # shape: (n_reps, 2, norb, norb) + orbital_rotations: np.ndarray # shape: (n_reps, norb, norb) + final_orbital_rotation: np.ndarray | None = None # shape: (norb, norb) + + @property + def norb(self): + """The number of spatial orbitals.""" + return self.diag_coulomb_mats.shape[-1] + + @property + def n_reps(self): + """The number of ansatz repetitions.""" + return self.diag_coulomb_mats.shape[0] + + @staticmethod + def n_params( + norb: int, + n_reps: int, + *, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, list[tuple[int, int]] | None + ] + | None = None, + with_final_orbital_rotation: bool = False, + ) -> int: + r"""Return the number of parameters of an ansatz with given settings. + + Args: + n_reps: The number of ansatz repetitions. + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a pair of lists, + for alpha-alpha and alpha-beta interactions, in that order. + Either list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + Each integer pair must be upper triangular, that is, of the form + :math:`(i, j)` where :math:`i \leq j`. + with_final_orbital_rotation: Whether to include a final orbital rotation + in the operator. + + Returns: + The number of parameters of the ansatz. + + Raises: + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list contained lower triangular pairs. + """ + if interaction_pairs is None: + interaction_pairs = (None, None) + pairs_aa, pairs_ab = interaction_pairs + _validate_interaction_pairs(pairs_aa, ordered=False) + _validate_interaction_pairs(pairs_ab, ordered=False) + # Each diagonal Coulomb matrix has one parameter per upper triangular + # entry unless indices are passed explicitly + n_triu_indices = norb * (norb + 1) // 2 + n_params_aa = n_triu_indices if pairs_aa is None else len(pairs_aa) + n_params_ab = n_triu_indices if pairs_ab is None else len(pairs_ab) + # Each orbital rotation has norb**2 parameters + return ( + n_reps * (n_params_aa + n_params_ab + norb**2) + + with_final_orbital_rotation * norb**2 + ) + + @staticmethod + def from_parameters( + params: np.ndarray, + *, + norb: int, + n_reps: int, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, list[tuple[int, int]] | None + ] + | None = None, + with_final_orbital_rotation: bool = False, + ) -> UCJOpSpinBalanced: + r"""Initialize the UCJ operator from a real-valued parameter vector. + + Args: + params: The real-valued parameter vector. + norb: The number of spatial orbitals. + n_reps: The number of ansatz repetitions. + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a pair of lists, + for alpha-alpha and alpha-beta interactions, in that order. + Either list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + Each integer pair must be upper triangular, that is, of the form + :math:`(i, j)` where :math:`i \leq j`. + with_final_orbital_rotation: Whether to include a final orbital rotation + in the operator. + + Returns: + The UCJ operator constructed from the given parameters. + + Raises: + ValueError: The number of parameters passed did not match the number + expected based on the function inputs. + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list contained lower triangular pairs. + """ + n_params = UCJOpSpinBalanced.n_params( + norb, + n_reps, + interaction_pairs=interaction_pairs, + with_final_orbital_rotation=with_final_orbital_rotation, + ) + if len(params) != n_params: + raise ValueError( + "The number of parameters passed did not match the number expected " + "based on the function inputs. " + f"Expected {n_params} but got {len(params)}." + ) + if interaction_pairs is None: + interaction_pairs = (None, None) + pairs_aa, pairs_ab = interaction_pairs + triu_indices = cast( + List[Tuple[int, int]], + list(itertools.combinations_with_replacement(range(norb), 2)), + ) + if pairs_aa is None: + pairs_aa = triu_indices + if pairs_ab is None: + pairs_ab = triu_indices + diag_coulomb_mats = np.zeros((n_reps, 2, norb, norb)) + orbital_rotations = np.zeros((n_reps, norb, norb), dtype=complex) + index = 0 + for orbital_rotation, diag_coulomb_mat in zip( + orbital_rotations, diag_coulomb_mats + ): + # Orbital rotations + n_params = norb**2 + orbital_rotation[:] = orbital_rotation_from_parameters( + params[index : index + n_params], norb + ) + index += n_params + # Diag Coulomb matrices + for indices, this_diag_coulomb_mat in zip( + (pairs_aa, pairs_ab), diag_coulomb_mat + ): + if indices: + n_params = len(indices) + rows, cols = zip(*indices) + vals = params[index : index + n_params] + this_diag_coulomb_mat[cols, rows] = vals + this_diag_coulomb_mat[rows, cols] = vals + index += n_params + # Final orbital rotation + final_orbital_rotation = None + if with_final_orbital_rotation: + final_orbital_rotation = orbital_rotation_from_parameters( + params[index:], norb + ) + return UCJOpSpinBalanced( + diag_coulomb_mats=diag_coulomb_mats, + orbital_rotations=orbital_rotations, + final_orbital_rotation=final_orbital_rotation, + ) + + def to_parameters( + self, + *, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, list[tuple[int, int]] | None + ] + | None = None, + ) -> np.ndarray: + r"""Convert the UCJ operator to a real-valued parameter vector. + + Note: + If `interaction_pairs` is specified, the returned parameter vector will + incorporate only the diagonal Coulomb matrix entries corresponding to the + specified interactions, so the original operator will not be recoverable + from the parameter vector. + + Args: + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a pair of lists, + for alpha-alpha and alpha-beta interactions, in that order. + Either list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + Each integer pair must be upper triangular, that is, of the form + :math:`(i, j)` where :math:`i \leq j`. + + Returns: + The real-valued parameter vector. + + Raises: + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list contained lower triangular pairs. + """ + n_reps, _, norb, _ = self.diag_coulomb_mats.shape + n_params = UCJOpSpinBalanced.n_params( + norb, + n_reps, + interaction_pairs=interaction_pairs, + with_final_orbital_rotation=self.final_orbital_rotation is not None, + ) + + if interaction_pairs is None: + interaction_pairs = (None, None) + pairs_aa, pairs_ab = interaction_pairs + triu_indices = cast( + List[Tuple[int, int]], + list(itertools.combinations_with_replacement(range(norb), 2)), + ) + if pairs_aa is None: + pairs_aa = triu_indices + if pairs_ab is None: + pairs_ab = triu_indices + + params = np.zeros(n_params) + index = 0 + for orbital_rotation, diag_coulomb_mat in zip( + self.orbital_rotations, self.diag_coulomb_mats + ): + # Orbital rotations + n_params = norb**2 + params[index : index + n_params] = orbital_rotation_to_parameters( + orbital_rotation + ) + index += n_params + # Diag Coulomb matrices + for indices, this_diag_coulomb_mat in zip( + (pairs_aa, pairs_ab), diag_coulomb_mat + ): + if indices: + n_params = len(indices) + params[index : index + n_params] = this_diag_coulomb_mat[ + tuple(zip(*indices)) + ] + index += n_params + # Final orbital rotation + if self.final_orbital_rotation is not None: + params[index:] = orbital_rotation_to_parameters(self.final_orbital_rotation) + return params + + @staticmethod + def from_t_amplitudes( + t2: np.ndarray, + *, + t1: np.ndarray | None = None, + n_reps: int | None = None, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, list[tuple[int, int]] | None + ] + | None = None, + tol: float = 1e-8, + ) -> UCJOpSpinBalanced: + r"""Initialize the UCJ operator from t2 (and optionally t1) amplitudes. + + Performs a double-factorization of the t2 amplitudes and constructs the + ansatz repetitions from the terms of the decomposition, up to an optionally + specified number of ansatz repetitions. Terms are included in decreasing order + of the absolute value of the corresponding eigenvalue in the factorization. + + Args: + t2: The t2 amplitudes. + t1: The t1 amplitudes. + n_reps: The number of ansatz repetitions. + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a pair of lists, + for alpha-alpha and alpha-beta interactions, in that order. + Either list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + Each integer pair must be upper triangular, that is, of the form + :math:`(i, j)` where :math:`i \leq j`. + tol: Tolerance for error in the double-factorized decomposition of the + t2 amplitudes. + The error is defined as the maximum absolute difference between + an element of the original tensor and the corresponding element of + the reconstructed tensor. + + Returns: + The UCJ operator with parameters initialized from the t2 amplitudes. + + Raises: + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list contained lower triangular pairs. + """ + if interaction_pairs is None: + interaction_pairs = (None, None) + pairs_aa, pairs_ab = interaction_pairs + _validate_interaction_pairs(pairs_aa, ordered=False) + _validate_interaction_pairs(pairs_ab, ordered=False) + + nocc, _, nvrt, _ = t2.shape + norb = nocc + nvrt + + diag_coulomb_mats, orbital_rotations = linalg.double_factorized_t2(t2, tol=tol) + diag_coulomb_mats = diag_coulomb_mats.reshape(-1, norb, norb)[:n_reps] + diag_coulomb_mats = np.stack([diag_coulomb_mats, diag_coulomb_mats], axis=1) + orbital_rotations = orbital_rotations.reshape(-1, norb, norb)[:n_reps] + + final_orbital_rotation = None + if t1 is not None: + final_orbital_rotation_generator = np.zeros((norb, norb), dtype=complex) + final_orbital_rotation_generator[:nocc, nocc:] = t1 + final_orbital_rotation_generator[nocc:, :nocc] = -t1.T + final_orbital_rotation = scipy.linalg.expm(final_orbital_rotation_generator) + + # Zero out diagonal coulomb matrix entries if requested + if pairs_aa is not None: + mask = np.zeros((norb, norb), dtype=bool) + rows, cols = zip(*pairs_aa) + mask[rows, cols] = True + mask[cols, rows] = True + diag_coulomb_mats[:, 0] *= mask + if pairs_ab is not None: + mask = np.zeros((norb, norb), dtype=bool) + rows, cols = zip(*pairs_ab) + mask[rows, cols] = True + mask[cols, rows] = True + diag_coulomb_mats[:, 1] *= mask + + return UCJOpSpinBalanced( + diag_coulomb_mats=diag_coulomb_mats, + orbital_rotations=orbital_rotations, + final_orbital_rotation=final_orbital_rotation, + ) + + def _apply_unitary_( + self, vec: np.ndarray, norb: int, nelec: tuple[int, int], copy: bool + ) -> np.ndarray: + if copy: + vec = vec.copy() + for (diag_coulomb_mat_aa, diag_coulomb_mat_ab), orbital_rotation in zip( + self.diag_coulomb_mats, self.orbital_rotations + ): + vec = gates.apply_diag_coulomb_evolution( + vec, + (diag_coulomb_mat_aa, diag_coulomb_mat_ab, diag_coulomb_mat_aa), + time=-1.0, + norb=norb, + nelec=nelec, + orbital_rotation=orbital_rotation, + copy=False, + ) + if self.final_orbital_rotation is not None: + vec = gates.apply_orbital_rotation( + vec, + mat=self.final_orbital_rotation, + norb=norb, + nelec=nelec, + copy=False, + ) + return vec + + def _approx_eq_(self, other, rtol: float, atol: float) -> bool: + if isinstance(other, UCJOpSpinBalanced): + if not np.allclose( + self.diag_coulomb_mats, other.diag_coulomb_mats, rtol=rtol, atol=atol + ): + return False + if not np.allclose( + self.orbital_rotations, other.orbital_rotations, rtol=rtol, atol=atol + ): + return False + if ( + self.final_orbital_rotation is None + and other.final_orbital_rotation is not None + ) or ( + self.final_orbital_rotation is not None + and other.final_orbital_rotation is None + ): + return False + if self.final_orbital_rotation is not None: + return np.allclose( + cast(np.ndarray, self.final_orbital_rotation), + cast(np.ndarray, other.final_orbital_rotation), + rtol=rtol, + atol=atol, + ) + return True + return NotImplemented diff --git a/python/ffsim/variational/ucj_open_shell.py b/python/ffsim/variational/ucj_spin_unbalanced.py similarity index 59% rename from python/ffsim/variational/ucj_open_shell.py rename to python/ffsim/variational/ucj_spin_unbalanced.py index 15f654954..f92bad994 100644 --- a/python/ffsim/variational/ucj_open_shell.py +++ b/python/ffsim/variational/ucj_spin_unbalanced.py @@ -8,7 +8,7 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -"""Open-shell (local) unitary cluster Jastrow ansatz.""" +"""Spin-unbalanced (local) unitary cluster Jastrow ansatz.""" from __future__ import annotations @@ -26,20 +26,28 @@ ) -def _validate_diag_coulomb_indices(indices: list[tuple[int, int]] | None): - if indices is not None: - for i, j in indices: +def _validate_interaction_pairs( + interaction_pairs: list[tuple[int, int]] | None, ordered: bool +) -> None: + if interaction_pairs is None: + return + if len(set(interaction_pairs)) != len(interaction_pairs): + raise ValueError( + f"Duplicate interaction pairs encountered: {interaction_pairs}." + ) + if not ordered: + for i, j in interaction_pairs: if i > j: raise ValueError( - "When specifying alpha-alpha or beta-beta diagonal Coulomb " - "indices, you must provide only upper trianglular indices. " - f"Got {(i, j)}, which is a lower triangular index." + "When specifying alpha-alpha or beta-beta interaction pairs, " + "you must provide only upper triangular pairs. " + f"Got {(i, j)}, which is a lower triangular pair." ) @dataclass(frozen=True) -class UCJOperatorOpenShell: - r"""An open-shell unitary cluster Jastrow operator. +class UCJOpSpinUnbalanced: + r"""A spin-unbalanced unitary cluster Jastrow operator. A unitary cluster Jastrow (UCJ) operator has the form @@ -103,26 +111,56 @@ def n_params( norb: int, n_reps: int, *, - alpha_alpha_indices: list[tuple[int, int]] | None = None, - alpha_beta_indices: list[tuple[int, int]] | None = None, - beta_beta_indices: list[tuple[int, int]] | None = None, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + ] + | None = None, with_final_orbital_rotation: bool = False, ) -> int: - """Return the number of parameters of an ansatz with given settings.""" - _validate_diag_coulomb_indices(alpha_alpha_indices) - _validate_diag_coulomb_indices(beta_beta_indices) + r"""Return the number of parameters of an ansatz with given settings. + + Args: + n_reps: The number of ansatz repetitions. + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a tuple of 3 lists, + for alpha-alpha, alpha-beta, and beta-beta interactions, in that order. + Any list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + For the alpha-alpha and beta-beta interactions, each integer + pair must be upper triangular, that is, of the form :math:`(i, j)` where + :math:`i \leq j`. + with_final_orbital_rotation: Whether to include a final orbital rotation + in the operator. + + Returns: + The number of parameters of the ansatz. + + Raises: + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list for alpha-alpha or beta-beta interactions + contained lower triangular pairs. + """ + if interaction_pairs is None: + interaction_pairs = (None, None, None) + pairs_aa, pairs_ab, pairs_bb = interaction_pairs + _validate_interaction_pairs(pairs_aa, ordered=False) + _validate_interaction_pairs(pairs_ab, ordered=True) + _validate_interaction_pairs(pairs_bb, ordered=False) # Each same-spin diagonal Coulomb matrix has one parameter per upper triangular # entry unless indices are passed explicitly n_triu_indices = norb * (norb + 1) // 2 - n_params_aa = ( - n_triu_indices if alpha_alpha_indices is None else len(alpha_alpha_indices) - ) - n_params_bb = ( - n_triu_indices if beta_beta_indices is None else len(beta_beta_indices) - ) + n_params_aa = n_triu_indices if pairs_aa is None else len(pairs_aa) + n_params_bb = n_triu_indices if pairs_bb is None else len(pairs_bb) # The diffent-spin diagonal Coulomb matrix has norb**2 parameters unless indices # are passed explicitly - n_params_ab = norb**2 if alpha_beta_indices is None else len(alpha_beta_indices) + n_params_ab = norb**2 if pairs_ab is None else len(pairs_ab) # Each orbital rotation has norb**2 parameters per spin return ( n_reps * (n_params_aa + n_params_ab + n_params_bb + 2 * norb**2) @@ -135,32 +173,33 @@ def from_parameters( *, norb: int, n_reps: int, - alpha_alpha_indices: list[tuple[int, int]] | None = None, - alpha_beta_indices: list[tuple[int, int]] | None = None, - beta_beta_indices: list[tuple[int, int]] | None = None, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + ] + | None = None, with_final_orbital_rotation: bool = False, - ) -> UCJOperatorOpenShell: + ) -> UCJOpSpinUnbalanced: r"""Initialize the UCJ operator from a real-valued parameter vector. Args: params: The real-valued parameter vector. norb: The number of spatial orbitals. n_reps: The number of ansatz repetitions. - alpha_alpha_indices: Allowed indices for nonzero values of the "alpha-alpha" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - This list should contain only upper trianglular indices, i.e., - pairs :math:`(i, j)` where :math:`i \leq j`. Passing a list with - lower triangular indices will raise an error. - alpha_beta_indices: Allowed indices for nonzero values of the "alpha-beta" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - beta_beta_indices: Allowed indices for nonzero values of the "beta-beta" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - This list should contain only upper trianglular indices, i.e., - pairs :math:`(i, j)` where :math:`i \leq j`. Passing a list with - lower triangular indices will raise an error. + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a tuple of 3 lists, + for alpha-alpha, alpha-beta, and beta-beta interactions, in that order. + Any list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + For the alpha-alpha and beta-beta interactions, each integer + pair must be upper triangular, that is, of the form :math:`(i, j)` where + :math:`i \leq j`. with_final_orbital_rotation: Whether to include a final orbital rotation in the operator. @@ -170,17 +209,14 @@ def from_parameters( Raises: ValueError: The number of parameters passed did not match the number expected based on the function inputs. - ValueError: alpha_alpha_indices contains lower triangular indices. - ValueError: beta_beta_indices contains lower triangular indices. + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list for alpha-alpha or beta-beta interactions + contained lower triangular pairs. """ - _validate_diag_coulomb_indices(alpha_alpha_indices) - _validate_diag_coulomb_indices(beta_beta_indices) - n_params = UCJOperatorOpenShell.n_params( + n_params = UCJOpSpinUnbalanced.n_params( norb, n_reps, - alpha_alpha_indices=alpha_alpha_indices, - alpha_beta_indices=alpha_beta_indices, - beta_beta_indices=beta_beta_indices, + interaction_pairs=interaction_pairs, with_final_orbital_rotation=with_final_orbital_rotation, ) if len(params) != n_params: @@ -189,6 +225,9 @@ def from_parameters( "based on the function inputs. " f"Expected {n_params} but got {len(params)}." ) + if interaction_pairs is None: + interaction_pairs = (None, None, None) + pairs_aa, pairs_ab, pairs_bb = interaction_pairs mat_indices = cast( List[Tuple[int, int]], list(itertools.product(range(norb), repeat=2)) ) @@ -196,12 +235,12 @@ def from_parameters( List[Tuple[int, int]], list(itertools.combinations_with_replacement(range(norb), 2)), ) - if alpha_alpha_indices is None: - alpha_alpha_indices = triu_indices - if alpha_beta_indices is None: - alpha_beta_indices = mat_indices - if beta_beta_indices is None: - beta_beta_indices = triu_indices + if pairs_aa is None: + pairs_aa = triu_indices + if pairs_ab is None: + pairs_ab = mat_indices + if pairs_bb is None: + pairs_bb = triu_indices diag_coulomb_mats = np.zeros((n_reps, 3, norb, norb)) orbital_rotations = np.zeros((n_reps, 2, norb, norb), dtype=complex) index = 0 @@ -217,7 +256,7 @@ def from_parameters( index += n_params # Diag Coulomb matrices for indices, this_diag_coulomb_mat in zip( - (alpha_alpha_indices, alpha_beta_indices, beta_beta_indices), + (pairs_aa, pairs_ab, pairs_bb), diag_coulomb_mat, ): if indices: @@ -237,7 +276,7 @@ def from_parameters( params[index : index + n_params], norb ) index += n_params - return UCJOperatorOpenShell( + return UCJOpSpinUnbalanced( diag_coulomb_mats=diag_coulomb_mats, orbital_rotations=orbital_rotations, final_orbital_rotation=final_orbital_rotation, @@ -245,45 +284,55 @@ def from_parameters( def to_parameters( self, - *, - alpha_alpha_indices: list[tuple[int, int]] | None = None, - alpha_beta_indices: list[tuple[int, int]] | None = None, - beta_beta_indices: list[tuple[int, int]] | None = None, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + ] + | None = None, ) -> np.ndarray: r"""Convert the UCJ operator to a real-valued parameter vector. - If `alpha_alpha_indices`, `alpha_beta_indices`, or `beta_beta_indices` is - specified, the returned parameter vector will incorporate only the diagonal - Coulomb matrix entries corresponding to the given indices, so the original - operator will not be recoverable from the parameter vector. + Note: + If `interaction_pairs` is specified, the returned parameter vector will + incorporate only the diagonal Coulomb matrix entries corresponding to the + specified interactions, so the original operator will not be recoverable + from the parameter vector. Args: - alpha_alpha_indices: Allowed indices for nonzero values of the "alpha-alpha" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - This list should contain only upper trianglular indices, i.e., - pairs :math:`(i, j)` where :math:`i \leq j`. Passing a list with - lower triangular indices will raise an error. - alpha_beta_indices: Allowed indices for nonzero values of the "alpha-beta" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - beta_beta_indices: Allowed indices for nonzero values of the "beta-beta" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - This list should contain only upper trianglular indices, i.e., - pairs :math:`(i, j)` where :math:`i \leq j`. Passing a list with - lower triangular indices will raise an error. + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a tuple of 3 lists, + for alpha-alpha, alpha-beta, and beta-beta interactions, in that order. + Any list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + For the alpha-alpha and beta-beta interactions, each integer + pair must be upper triangular, that is, of the form :math:`(i, j)` where + :math:`i \leq j`. Returns: The real-valued parameter vector. Raises: - ValueError: alpha_alpha_indices contains lower triangular indices. - ValueError: beta_beta_indices contains lower triangular indices. + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list for alpha-alpha or beta-beta interactions + contained lower triangular pairs. """ - _validate_diag_coulomb_indices(alpha_alpha_indices) - _validate_diag_coulomb_indices(beta_beta_indices) n_reps, _, norb, _ = self.diag_coulomb_mats.shape + n_params = UCJOpSpinUnbalanced.n_params( + norb, + n_reps, + interaction_pairs=interaction_pairs, + with_final_orbital_rotation=self.final_orbital_rotation is not None, + ) + + if interaction_pairs is None: + interaction_pairs = (None, None, None) + pairs_aa, pairs_ab, pairs_bb = interaction_pairs mat_indices = cast( List[Tuple[int, int]], list(itertools.product(range(norb), repeat=2)) ) @@ -291,20 +340,13 @@ def to_parameters( List[Tuple[int, int]], list(itertools.combinations_with_replacement(range(norb), 2)), ) - if alpha_alpha_indices is None: - alpha_alpha_indices = triu_indices - if alpha_beta_indices is None: - alpha_beta_indices = mat_indices - if beta_beta_indices is None: - beta_beta_indices = triu_indices - n_params = UCJOperatorOpenShell.n_params( - norb, - n_reps, - alpha_alpha_indices=alpha_alpha_indices, - alpha_beta_indices=alpha_beta_indices, - beta_beta_indices=beta_beta_indices, - with_final_orbital_rotation=self.final_orbital_rotation is not None, - ) + if pairs_aa is None: + pairs_aa = triu_indices + if pairs_ab is None: + pairs_ab = mat_indices + if pairs_bb is None: + pairs_bb = triu_indices + params = np.zeros(n_params) index = 0 for orbital_rotation, diag_coulomb_mat in zip( @@ -319,7 +361,7 @@ def to_parameters( index += n_params # Diag Coulomb matrices for indices, this_diag_coulomb_mat in zip( - (alpha_alpha_indices, alpha_beta_indices, beta_beta_indices), + (pairs_aa, pairs_ab, pairs_bb), diag_coulomb_mat, ): if indices: @@ -343,20 +385,21 @@ def from_t_amplitudes( t2: tuple[np.ndarray, np.ndarray, np.ndarray], *, t1: tuple[np.ndarray, np.ndarray] | None = None, - n_reps: int | None = None, - alpha_alpha_indices: list[tuple[int, int]] | None = None, - alpha_beta_indices: list[tuple[int, int]] | None = None, - beta_beta_indices: list[tuple[int, int]] | None = None, + n_reps: int | tuple[int, int] | None = None, + interaction_pairs: tuple[ + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + list[tuple[int, int]] | None, + ] + | None = None, tol: float = 1e-8, - ) -> UCJOperatorOpenShell: - """Initialize the UCJ operator from t2 (and optionally t1) amplitudes. + ) -> UCJOpSpinUnbalanced: + r"""Initialize the UCJ operator from t2 (and optionally t1) amplitudes. Performs a double-factorization of the t2 amplitudes and constructs the ansatz repetitions from the terms of the decomposition, up to an optionally - specified number of ansatz repetitions. Terms are included in decreasing order - of the absolute value of the corresponding singular value in the factorization. - The terms from the alpha-beta t2 amplitudes are used before including any - terms from the alpha-alpha and beta-beta t2 amplitudes. + specified number of repetitions. Terms are included in decreasing order + of the magnitude of the corresponding singular value in the factorization. Args: t2: The t2 amplitudes. This should be a tuple of 3 Numpy arrays, @@ -365,27 +408,47 @@ def from_t_amplitudes( t1: The t1 amplitudes. This should be a pair of Numpy arrays, `(t1a, t1b)`, containing the alpha and beta t1 amplitudes. n_reps: The number of ansatz repetitions. - alpha_alpha_indices: Allowed indices for nonzero values of the "alpha-alpha" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - This list should contain only upper trianglular indices, i.e., - pairs :math:`(i, j)` where :math:`i \leq j`. Passing a list with - lower triangular indices will raise an error. - alpha_beta_indices: Allowed indices for nonzero values of the "alpha-beta" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - beta_beta_indices: Allowed indices for nonzero values of the "beta-beta" - diagonal Coulomb matrices (see the docstring of this class). - If not specified, all matrix entries are allowed to be nonzero. - This list should contain only upper trianglular indices, i.e., - pairs :math:`(i, j)` where :math:`i \leq j`. Passing a list with - lower triangular indices will raise an error. + You can pass a single integer or a pair of integers. + If a single integer, terms from the alpha-beta t2 amplitudes are + used before including any terms from the alpha-alpha and beta-beta + t2 amplitudes. If a pair of integers, then the first integer specifies + the number of terms to use from the alpha-beta t2 amplitudes, + and the second integer specifies the number of terms to use from the + alpha-alpha and beta-beta t2 amplitudes. + interaction_pairs: Optional restrictions on allowed orbital interactions + for the diagonal Coulomb operators. + If specified, `interaction_pairs` should be a tuple of 3 lists, + for alpha-alpha, alpha-beta, and beta-beta interactions, in that order. + Any list can be substituted with ``None`` to indicate no restrictions + on interactions. + Each list should contain pairs of integers representing the orbitals + that are allowed to interact. These pairs can also be interpreted as + indices of diagonal Coulomb matrix entries that are allowed to be + nonzero. + For the alpha-alpha and beta-beta interactions, each integer + pair must be upper triangular, that is, of the form :math:`(i, j)` where + :math:`i \leq j`. tol: Tolerance for error in the double-factorized decomposition of the t2 amplitudes. The error is defined as the maximum absolute difference between an element of the original tensor and the corresponding element of the reconstructed tensor. + + Returns: + The UCJ operator with parameters initialized from the t2 amplitudes. + + Raises: + ValueError: Interaction pairs list contained duplicate interactions. + ValueError: Interaction pairs list for alpha-alpha or beta-beta interactions + contained lower triangular pairs. """ + if interaction_pairs is None: + interaction_pairs = (None, None, None) + pairs_aa, pairs_ab, pairs_bb = interaction_pairs + _validate_interaction_pairs(pairs_aa, ordered=False) + _validate_interaction_pairs(pairs_bb, ordered=True) + _validate_interaction_pairs(pairs_bb, ordered=False) + t2aa, t2ab, t2bb = t2 nocc_a, nocc_b, nvrt_a, _ = t2ab.shape norb = nocc_a + nvrt_a @@ -426,13 +489,27 @@ def from_t_amplitudes( ] ) # concatenate - # TODO might need to scale by a factor of 2 - diag_coulomb_mats = np.concatenate( - [diag_coulomb_mats_ab, diag_coulomb_mats_same_spin] - )[:n_reps] - orbital_rotations = np.concatenate( - [orbital_rotations_ab, orbital_rotations_same_spin] - )[:n_reps] + if n_reps is None or isinstance(n_reps, int): + diag_coulomb_mats = np.concatenate( + [diag_coulomb_mats_ab, diag_coulomb_mats_same_spin] + )[:n_reps] + orbital_rotations = np.concatenate( + [orbital_rotations_ab, orbital_rotations_same_spin] + )[:n_reps] + else: + n_reps_ab, n_reps_same_spin = n_reps + diag_coulomb_mats = np.concatenate( + [ + diag_coulomb_mats_ab[:n_reps_ab], + diag_coulomb_mats_same_spin[:n_reps_same_spin], + ] + ) + orbital_rotations = np.concatenate( + [ + orbital_rotations_ab[:n_reps_ab], + orbital_rotations_same_spin[:n_reps_same_spin], + ] + ) final_orbital_rotation = None if t1 is not None: @@ -456,26 +533,26 @@ def from_t_amplitudes( ) # Zero out diagonal coulomb matrix entries if requested - if alpha_alpha_indices is not None: + if pairs_aa is not None: mask = np.zeros((norb, norb), dtype=bool) - rows, cols = zip(*alpha_alpha_indices) + rows, cols = zip(*pairs_aa) mask[rows, cols] = True mask[cols, rows] = True diag_coulomb_mats[:, 0] *= mask - if alpha_beta_indices is not None: + if pairs_ab is not None: mask = np.zeros((norb, norb), dtype=bool) - rows, cols = zip(*alpha_beta_indices) + rows, cols = zip(*pairs_ab) mask[rows, cols] = True mask[cols, rows] = True diag_coulomb_mats[:, 1] *= mask - if beta_beta_indices is not None: + if pairs_bb is not None: mask = np.zeros((norb, norb), dtype=bool) - rows, cols = zip(*beta_beta_indices) + rows, cols = zip(*pairs_bb) mask[rows, cols] = True mask[cols, rows] = True diag_coulomb_mats[:, 2] *= mask - return UCJOperatorOpenShell( + return UCJOpSpinUnbalanced( diag_coulomb_mats=diag_coulomb_mats, orbital_rotations=orbital_rotations, final_orbital_rotation=final_orbital_rotation, @@ -509,7 +586,7 @@ def _apply_unitary_( return vec def _approx_eq_(self, other, rtol: float, atol: float) -> bool: - if isinstance(other, UCJOperatorOpenShell): + if isinstance(other, UCJOpSpinUnbalanced): if not np.allclose( self.diag_coulomb_mats, other.diag_coulomb_mats, rtol=rtol, atol=atol ): diff --git a/tests/python/linalg/double_factorized_decomposition_test.py b/tests/python/linalg/double_factorized_decomposition_test.py index 6565551bb..06f1c2007 100644 --- a/tests/python/linalg/double_factorized_decomposition_test.py +++ b/tests/python/linalg/double_factorized_decomposition_test.py @@ -15,7 +15,6 @@ import itertools import numpy as np -import pyscf import pytest import scipy.linalg from opt_einsum import contract @@ -71,7 +70,6 @@ def reconstruct_t2_alpha_beta( orbital_rotation_a, orbital_rotation_b ) return ( - # TODO maybe don't have this factor of 2 2j * contract( "mkpq,mkap,mkip,mkbq,mkjq->ijab", @@ -363,30 +361,6 @@ def test_double_factorized_t2_tol_max_vecs(): np.testing.assert_allclose(reconstructed, t2, atol=tol) -def test_double_factorized_t2_alpha_beta_beh(): - """Test double factorization of opposite-spin t2 amplitudes with BeH.""" - mol = pyscf.gto.Mole() - mol.build( - atom=[["H", (0, 0, 0)], ["Be", (0, 0, 1.1)]], - basis="6-31g", - spin=1, - symmetry="Coov", - ) - scf = pyscf.scf.ROHF(mol).run() - ccsd = cc.CCSD(scf).run() - _, t2ab, _ = ccsd.t2 - diag_coulomb_mats, orbital_rotations = ffsim.linalg.double_factorized_t2_alpha_beta( - t2ab - ) - # TODO how are the 4 terms from each singular vector related to each other? - nocc_a, nocc_b, nvrt_a, _ = t2ab.shape - norb = nocc_a + nvrt_a - reconstructed = reconstruct_t2_alpha_beta( - diag_coulomb_mats, orbital_rotations, norb=norb, nocc_a=nocc_a, nocc_b=nocc_b - ) - np.testing.assert_allclose(reconstructed, t2ab, atol=1e-8) - - def test_double_factorized_t2_alpha_beta_random(): """Test double factorization of opposite-spin t2 amplitudes with random tensor.""" rng = np.random.default_rng() @@ -395,10 +369,30 @@ def test_double_factorized_t2_alpha_beta_random(): diag_coulomb_mats, orbital_rotations = ffsim.linalg.double_factorized_t2_alpha_beta( t2ab ) - # TODO how are the 4 terms from each singular vector related to each other? nocc_a, nocc_b, nvrt_a, _ = t2ab.shape norb = nocc_a + nvrt_a reconstructed = reconstruct_t2_alpha_beta( diag_coulomb_mats, orbital_rotations, norb=norb, nocc_a=nocc_a, nocc_b=nocc_b ) np.testing.assert_allclose(reconstructed, t2ab, atol=1e-8) + + np.testing.assert_allclose( + diag_coulomb_mats[:, 0], -diag_coulomb_mats[:, 1], atol=1e-8 + ) + np.testing.assert_allclose( + diag_coulomb_mats[:, 0], -diag_coulomb_mats[:, 2], atol=1e-8 + ) + np.testing.assert_allclose( + diag_coulomb_mats[:, 0], diag_coulomb_mats[:, 3], atol=1e-8 + ) + + np.testing.assert_allclose( + orbital_rotations[:, 0, 0], orbital_rotations[:, 1, 0], atol=1e-8 + ) + np.testing.assert_allclose( + orbital_rotations[:, 0, 0], orbital_rotations[:, 2, 0].conj(), atol=1e-8 + ) + np.testing.assert_allclose( + orbital_rotations[:, 0, 0], orbital_rotations[:, 3, 0].conj(), atol=1e-8 + ) + # TODO add the rest of the relations diff --git a/tests/python/optimize/linear_method_test.py b/tests/python/optimize/linear_method_test.py index 08faf3c39..340863cdf 100644 --- a/tests/python/optimize/linear_method_test.py +++ b/tests/python/optimize/linear_method_test.py @@ -33,7 +33,7 @@ def test_minimize_linear_method(): # Initialize parameters n_reps = 2 - n_params = ffsim.UCJOperator.n_params(hartree_fock.mol.nao_nr(), n_reps) + n_params = ffsim.UCJOpSpinBalanced.n_params(hartree_fock.mol.nao_nr(), n_reps) rng = np.random.default_rng(1804) x0 = rng.uniform(-10, 10, size=n_params) @@ -46,7 +46,7 @@ def test_minimize_linear_method(): reference_state = ffsim.hartree_fock_state(norb, nelec) def params_to_vec(x: np.ndarray): - operator = ffsim.UCJOperator.from_parameters(x, norb=norb, n_reps=n_reps) + operator = ffsim.UCJOpSpinBalanced.from_parameters(x, norb=norb, n_reps=n_reps) return ffsim.apply_unitary(reference_state, operator, norb=norb, nelec=nelec) def energy(x: np.ndarray): diff --git a/tests/python/qiskit/merge_orbital_rotations_test.py b/tests/python/qiskit/merge_orbital_rotations_test.py index 73f0aa224..d50965abb 100644 --- a/tests/python/qiskit/merge_orbital_rotations_test.py +++ b/tests/python/qiskit/merge_orbital_rotations_test.py @@ -222,20 +222,39 @@ def test_merge_ucj(norb: int, nelec: tuple[int, int]): """Test merging orbital rotations in UCJ operator.""" rng = np.random.default_rng() qubits = QuantumRegister(2 * norb) + n_reps = 3 + + with pytest.deprecated_call(): + circuit = QuantumCircuit(qubits) + circuit.append( + ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), + qubits, + ) + ucj_op = ffsim.random.random_ucj_operator( + norb, n_reps=n_reps, with_final_orbital_rotation=True, seed=rng + ) + circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits) + transpiled = ffsim.qiskit.PRE_INIT.run(circuit) + assert circuit.count_ops() == {"hartree_fock_jw": 1, "ucj_jw": 1} + assert transpiled.count_ops()["slater_jw"] == 1 + assert transpiled.count_ops()["orb_rot_jw"] == n_reps + ffsim.testing.assert_allclose_up_to_global_phase( + np.array(Statevector(circuit)), np.array(Statevector(transpiled)) + ) circuit = QuantumCircuit(qubits) circuit.append( ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits, ) - ucj_op = ffsim.random.random_ucj_operator( - norb, n_reps=3, with_final_orbital_rotation=True, seed=rng + ucj_op_unbalanced = ffsim.random.random_ucj_op_spin_unbalanced( + norb, n_reps=n_reps, with_final_orbital_rotation=True, seed=rng ) - circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits) + circuit.append(ffsim.qiskit.UCJOpSpinUnbalancedJW(ucj_op_unbalanced), qubits) transpiled = ffsim.qiskit.PRE_INIT.run(circuit) - assert circuit.count_ops() == {"hartree_fock_jw": 1, "ucj_jw": 1} + assert circuit.count_ops() == {"hartree_fock_jw": 1, "ucj_unbalanced_jw": 1} assert transpiled.count_ops()["slater_jw"] == 1 - + assert transpiled.count_ops()["orb_rot_jw"] == n_reps ffsim.testing.assert_allclose_up_to_global_phase( np.array(Statevector(circuit)), np.array(Statevector(transpiled)) ) @@ -245,14 +264,14 @@ def test_merge_ucj(norb: int, nelec: tuple[int, int]): ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits, ) - ucj_op_open = ffsim.random.random_ucj_operator_open_shell( - norb, n_reps=3, with_final_orbital_rotation=True, seed=rng + ucj_op_balanced = ffsim.random.random_ucj_op_spin_balanced( + norb, n_reps=n_reps, with_final_orbital_rotation=True, seed=rng ) - circuit.append(ffsim.qiskit.UCJOperatorOpenShellJW(ucj_op_open), qubits) + circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op_balanced), qubits) transpiled = ffsim.qiskit.PRE_INIT.run(circuit) - assert circuit.count_ops() == {"hartree_fock_jw": 1, "ucj_open_jw": 1} + assert circuit.count_ops() == {"hartree_fock_jw": 1, "ucj_balanced_jw": 1} assert transpiled.count_ops()["slater_jw"] == 1 - + assert transpiled.count_ops()["orb_rot_jw"] == n_reps ffsim.testing.assert_allclose_up_to_global_phase( np.array(Statevector(circuit)), np.array(Statevector(transpiled)) ) diff --git a/tests/python/qiskit/sampler_test.py b/tests/python/qiskit/sampler_test.py index 8870a98f6..585df6531 100644 --- a/tests/python/qiskit/sampler_test.py +++ b/tests/python/qiskit/sampler_test.py @@ -38,6 +38,8 @@ def _brickwork(norb: int, n_layers: int): yield (j, j + 1) +# TODO remove after removing UCJOperatorJW +@pytest.mark.filterwarnings("ignore::DeprecationWarning") @pytest.mark.parametrize("norb, nelec", ffsim.testing.generate_norb_nelec(range(1, 5))) def test_random_gates_spinful(norb: int, nelec: tuple[int, int]): """Test sampler with random gates.""" @@ -50,7 +52,10 @@ def test_random_gates_spinful(norb: int, nelec: tuple[int, int]): ucj_op = ffsim.random.random_ucj_operator( norb, n_reps=2, with_final_orbital_rotation=True, seed=rng ) - ucj_op_open_shell = ffsim.random.random_ucj_operator_open_shell( + ucj_op_balanced = ffsim.random.random_ucj_op_spin_balanced( + norb, n_reps=2, with_final_orbital_rotation=True, seed=rng + ) + ucj_op_unbalanced = ffsim.random.random_ucj_op_spin_unbalanced( norb, n_reps=2, with_final_orbital_rotation=True, seed=rng ) interaction_pairs = list(_brickwork(norb, norb)) @@ -65,7 +70,8 @@ def test_random_gates_spinful(norb: int, nelec: tuple[int, int]): ) circuit.append(ffsim.qiskit.GivensAnsatzOperatorJW(givens_ansatz_op), qubits) circuit.append(ffsim.qiskit.UCJOperatorJW(ucj_op), qubits) - circuit.append(ffsim.qiskit.UCJOperatorOpenShellJW(ucj_op_open_shell), qubits) + circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op_balanced), qubits) + circuit.append(ffsim.qiskit.UCJOpSpinUnbalancedJW(ucj_op_unbalanced), qubits) circuit.measure_all() shots = 3000 @@ -91,6 +97,8 @@ def test_random_gates_spinful(norb: int, nelec: tuple[int, int]): assert _fidelity(ffsim_probs, qiskit_probs) > 0.99 +# TODO remove after removing UCJOperatorJW +@pytest.mark.filterwarnings("ignore::DeprecationWarning") @pytest.mark.parametrize("norb, nocc", ffsim.testing.generate_norb_nocc(range(1, 5))) def test_random_gates_spinless(norb: int, nocc: int): """Test sampler with random spinless gates.""" @@ -136,6 +144,8 @@ def test_random_gates_spinless(norb: int, nocc: int): assert _fidelity(ffsim_probs, qiskit_probs) > 0.99 +# TODO remove after removing UCJOperatorJW +@pytest.mark.filterwarnings("ignore::DeprecationWarning") @pytest.mark.parametrize("norb, nelec", ffsim.testing.generate_norb_nelec(range(1, 5))) def test_measure_subset_spinful(norb: int, nelec: tuple[int, int]): """Test measuring a subset of qubits.""" @@ -181,6 +191,8 @@ def test_measure_subset_spinful(norb: int, nelec: tuple[int, int]): assert _fidelity(ffsim_probs, qiskit_probs) > 0.99 +# TODO remove after removing UCJOperatorJW +@pytest.mark.filterwarnings("ignore::DeprecationWarning") @pytest.mark.parametrize("norb, nocc", ffsim.testing.generate_norb_nocc(range(1, 5))) def test_measure_subset_spinless(norb: int, nocc: int): """Test measuring a subset of qubits, spinless.""" @@ -228,6 +240,8 @@ def test_measure_subset_spinless(norb: int, nocc: int): assert _fidelity(ffsim_probs, qiskit_probs) > 0.99 +# TODO remove after removing UCJOperatorJW +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_reproducible_with_seed(): """Test sampler with random gates.""" rng = np.random.default_rng(14062) diff --git a/tests/python/qiskit/ucj_open_shell_test.py b/tests/python/qiskit/ucj_operator_test.py similarity index 90% rename from tests/python/qiskit/ucj_open_shell_test.py rename to tests/python/qiskit/ucj_operator_test.py index 53aed174b..e84916118 100644 --- a/tests/python/qiskit/ucj_open_shell_test.py +++ b/tests/python/qiskit/ucj_operator_test.py @@ -19,6 +19,7 @@ import ffsim +@pytest.mark.filterwarnings("ignore::DeprecationWarning") @pytest.mark.parametrize("norb, nelec", ffsim.testing.generate_norb_nelec(range(5))) def test_random_ucj_operator(norb: int, nelec: tuple[int, int]): """Test random UCJ gate gives correct output state.""" @@ -26,10 +27,10 @@ def test_random_ucj_operator(norb: int, nelec: tuple[int, int]): n_reps = 3 dim = ffsim.dim(norb, nelec) for _ in range(3): - ucj_op = ffsim.random.random_ucj_operator_open_shell( + ucj_op = ffsim.random.random_ucj_operator( norb, n_reps=n_reps, with_final_orbital_rotation=True, seed=rng ) - gate = ffsim.qiskit.UCJOperatorOpenShellJW(ucj_op) + gate = ffsim.qiskit.UCJOperatorJW(ucj_op) small_vec = ffsim.random.random_statevector(dim, seed=rng) big_vec = ffsim.qiskit.ffsim_vec_to_qiskit_vec( diff --git a/tests/python/qiskit/ucj_test.py b/tests/python/qiskit/ucj_test.py index 3a2d70d7e..c5a8b32d7 100644 --- a/tests/python/qiskit/ucj_test.py +++ b/tests/python/qiskit/ucj_test.py @@ -20,16 +20,43 @@ @pytest.mark.parametrize("norb, nelec", ffsim.testing.generate_norb_nelec(range(5))) -def test_random_ucj_operator(norb: int, nelec: tuple[int, int]): - """Test random UCJ gate gives correct output state.""" +def test_random_ucj_op_spin_unbalanced(norb: int, nelec: tuple[int, int]): + """Test random spin-unbalanced UCJ gate gives correct output state.""" rng = np.random.default_rng() n_reps = 3 dim = ffsim.dim(norb, nelec) for _ in range(3): - ucj_op = ffsim.random.random_ucj_operator( + ucj_op = ffsim.random.random_ucj_op_spin_unbalanced( norb, n_reps=n_reps, with_final_orbital_rotation=True, seed=rng ) - gate = ffsim.qiskit.UCJOperatorJW(ucj_op) + gate = ffsim.qiskit.UCJOpSpinUnbalancedJW(ucj_op) + + small_vec = ffsim.random.random_statevector(dim, seed=rng) + big_vec = ffsim.qiskit.ffsim_vec_to_qiskit_vec( + small_vec, norb=norb, nelec=nelec + ) + + statevec = Statevector(big_vec).evolve(gate) + result = ffsim.qiskit.qiskit_vec_to_ffsim_vec( + np.array(statevec), norb=norb, nelec=nelec + ) + + expected = ffsim.apply_unitary(small_vec, ucj_op, norb=norb, nelec=nelec) + + np.testing.assert_allclose(result, expected) + + +@pytest.mark.parametrize("norb, nelec", ffsim.testing.generate_norb_nelec(range(5))) +def test_random_ucj_op_spin_balanced(norb: int, nelec: tuple[int, int]): + """Test random spin-balanced UCJ gate gives correct output state.""" + rng = np.random.default_rng() + n_reps = 3 + dim = ffsim.dim(norb, nelec) + for _ in range(3): + ucj_op = ffsim.random.random_ucj_op_spin_balanced( + norb, n_reps=n_reps, with_final_orbital_rotation=True, seed=rng + ) + gate = ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op) small_vec = ffsim.random.random_statevector(dim, seed=rng) big_vec = ffsim.qiskit.ffsim_vec_to_qiskit_vec( diff --git a/tests/python/variational/ucj_open_shell_test.py b/tests/python/variational/ucj_spin_balanced_test.py similarity index 57% rename from tests/python/variational/ucj_open_shell_test.py rename to tests/python/variational/ucj_spin_balanced_test.py index c7df2ce5f..03ac7fee8 100644 --- a/tests/python/variational/ucj_open_shell_test.py +++ b/tests/python/variational/ucj_spin_balanced_test.py @@ -8,7 +8,7 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -"""Tests for open-shell unitary cluster Jastrow ansatz.""" +"""Tests for spin-balanced unitary cluster Jastrow ansatz.""" import itertools @@ -24,55 +24,44 @@ def test_n_params(): for norb, n_reps, with_final_orbital_rotation in itertools.product( [1, 2, 3], [1, 2, 3], [False, True] ): - operator = ffsim.random.random_ucj_operator_open_shell( + operator = ffsim.random.random_ucj_op_spin_balanced( norb, n_reps=n_reps, with_final_orbital_rotation=with_final_orbital_rotation ) - actual = ffsim.UCJOperatorOpenShell.n_params( + actual = ffsim.UCJOpSpinBalanced.n_params( norb, n_reps, with_final_orbital_rotation=with_final_orbital_rotation ) expected = len(operator.to_parameters()) assert actual == expected - alpha_alpha_indices = list( - itertools.combinations_with_replacement(range(norb), 2) - )[:norb] - alpha_beta_indices = list( - itertools.combinations_with_replacement(range(norb), 2) - )[:norb] - beta_beta_indices = list( - itertools.combinations_with_replacement(range(norb), 2) - )[:norb] - - actual = ffsim.UCJOperatorOpenShell.n_params( + pairs_aa = list(itertools.combinations_with_replacement(range(norb), 2))[:norb] + pairs_ab = list(itertools.combinations_with_replacement(range(norb), 2))[:norb] + + actual = ffsim.UCJOpSpinBalanced.n_params( norb, n_reps, - alpha_alpha_indices=alpha_alpha_indices, - alpha_beta_indices=alpha_beta_indices, - beta_beta_indices=beta_beta_indices, + interaction_pairs=(pairs_aa, pairs_ab), with_final_orbital_rotation=with_final_orbital_rotation, ) - expected = len( - operator.to_parameters( - alpha_alpha_indices=alpha_alpha_indices, - alpha_beta_indices=alpha_beta_indices, - beta_beta_indices=beta_beta_indices, - ) - ) + expected = len(operator.to_parameters(interaction_pairs=(pairs_aa, pairs_ab))) assert actual == expected with pytest.raises(ValueError, match="triangular"): - actual = ffsim.UCJOperatorOpenShell.n_params( + actual = ffsim.UCJOpSpinBalanced.n_params( norb, n_reps, - alpha_alpha_indices=[(1, 0)], - beta_beta_indices=beta_beta_indices, + interaction_pairs=([(1, 0)], pairs_ab), ) with pytest.raises(ValueError, match="triangular"): - actual = ffsim.UCJOperatorOpenShell.n_params( + actual = ffsim.UCJOpSpinBalanced.n_params( norb, n_reps, - alpha_alpha_indices=alpha_alpha_indices, - beta_beta_indices=[(1, 0)], + interaction_pairs=(pairs_aa, [(1, 0)]), + ) + with pytest.raises(ValueError, match="Duplicate"): + actual = ffsim.UCJOpSpinBalanced.n_params( + norb, + n_reps, + interaction_pairs=(pairs_aa, [(1, 0), (1, 0)]), ) @@ -82,13 +71,13 @@ def test_parameters_roundtrip(): n_reps = 2 for with_final_orbital_rotation in [False, True]: - operator = ffsim.random.random_ucj_operator_open_shell( + operator = ffsim.random.random_ucj_op_spin_balanced( norb, n_reps=n_reps, with_final_orbital_rotation=with_final_orbital_rotation, seed=rng, ) - roundtripped = ffsim.UCJOperatorOpenShell.from_parameters( + roundtripped = ffsim.UCJOpSpinBalanced.from_parameters( operator.to_parameters(), norb=norb, n_reps=n_reps, @@ -107,15 +96,14 @@ def test_parameters_roundtrip(): def test_t_amplitudes_energy(): - # Build a BeH molecule + # Build an H2 molecule mol = pyscf.gto.Mole() mol.build( - atom=[["H", (0, 0, 0)], ["Be", (0, 0, 1.1)]], - basis="6-31g", - spin=1, - symmetry="Coov", + atom=[["H", (0, 0, 0)], ["H", (0, 0, 1.8)]], + basis="sto-6g", + symmetry="Dooh", ) - scf = pyscf.scf.ROHF(mol).run() + scf = pyscf.scf.RHF(mol).run() ccsd = pyscf.cc.CCSD(scf).run() # Get molecular data and molecular Hamiltonian (one- and two-body tensors) @@ -126,7 +114,7 @@ def test_t_amplitudes_energy(): # Construct UCJ operator n_reps = 2 - operator = ffsim.UCJOperatorOpenShell.from_t_amplitudes(ccsd.t2, n_reps=n_reps) + operator = ffsim.UCJOpSpinBalanced.from_t_amplitudes(ccsd.t2, n_reps=n_reps) # Construct the Hartree-Fock state to use as the reference state n_alpha, n_beta = nelec @@ -142,19 +130,18 @@ def test_t_amplitudes_energy(): # Compute the energy ⟨ψ|H|ψ⟩ of the ansatz state hamiltonian = ffsim.linear_operator(mol_hamiltonian, norb=norb, nelec=nelec) energy = np.real(np.vdot(ansatz_state, hamiltonian @ ansatz_state)) - np.testing.assert_allclose(energy, -15.122153) + np.testing.assert_allclose(energy, -0.96962461) def test_t_amplitudes_restrict_indices(): - # Build a BeH molecule + # Build an H2 molecule mol = pyscf.gto.Mole() mol.build( - atom=[["H", (0, 0, 0)], ["Be", (0, 0, 1.1)]], - basis="6-31g", - spin=1, - symmetry="Coov", + atom=[["H", (0, 0, 0)], ["H", (0, 0, 1.8)]], + basis="sto-6g", + symmetry="Dooh", ) - scf = pyscf.scf.ROHF(mol).run() + scf = pyscf.scf.RHF(mol).run() ccsd = pyscf.cc.CCSD(scf).run() # Get molecular data and molecular Hamiltonian (one- and two-body tensors) @@ -163,28 +150,17 @@ def test_t_amplitudes_restrict_indices(): # Construct UCJ operator n_reps = 2 - alpha_alpha_indices = [(p, p + 1) for p in range(norb - 1)] - alpha_beta_indices = [(p, p) for p in range(norb)] - beta_beta_indices = [(p, p + 1) for p in range(norb - 1)] + pairs_aa = [(p, p + 1) for p in range(norb - 1)] + pairs_ab = [(p, p) for p in range(norb)] - operator = ffsim.UCJOperatorOpenShell.from_t_amplitudes( - ccsd.t2, - n_reps=n_reps, - alpha_alpha_indices=alpha_alpha_indices, - alpha_beta_indices=alpha_beta_indices, - beta_beta_indices=beta_beta_indices, + operator = ffsim.UCJOpSpinBalanced.from_t_amplitudes( + ccsd.t2, n_reps=n_reps, interaction_pairs=(pairs_aa, pairs_ab) ) - other_operator = ffsim.UCJOperatorOpenShell.from_parameters( - operator.to_parameters( - alpha_alpha_indices=alpha_alpha_indices, - alpha_beta_indices=alpha_beta_indices, - beta_beta_indices=beta_beta_indices, - ), + other_operator = ffsim.UCJOpSpinBalanced.from_parameters( + operator.to_parameters(interaction_pairs=(pairs_aa, pairs_ab)), norb=norb, n_reps=n_reps, - alpha_alpha_indices=alpha_alpha_indices, - alpha_beta_indices=alpha_beta_indices, - beta_beta_indices=beta_beta_indices, + interaction_pairs=(pairs_aa, pairs_ab), ) assert ffsim.approx_eq(operator, other_operator, rtol=1e-12) diff --git a/tests/python/variational/ucj_spin_unbalanced_test.py b/tests/python/variational/ucj_spin_unbalanced_test.py new file mode 100644 index 000000000..b32ca2255 --- /dev/null +++ b/tests/python/variational/ucj_spin_unbalanced_test.py @@ -0,0 +1,170 @@ +# (C) Copyright IBM 2024. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for spin-unbalanced unitary cluster Jastrow ansatz.""" + +import itertools + +import numpy as np +import pyscf +import pyscf.cc +import pytest + +import ffsim + + +def test_n_params(): + for norb, n_reps, with_final_orbital_rotation in itertools.product( + [1, 2, 3], [1, 2, 3], [False, True] + ): + operator = ffsim.random.random_ucj_op_spin_unbalanced( + norb, n_reps=n_reps, with_final_orbital_rotation=with_final_orbital_rotation + ) + actual = ffsim.UCJOpSpinUnbalanced.n_params( + norb, n_reps, with_final_orbital_rotation=with_final_orbital_rotation + ) + expected = len(operator.to_parameters()) + assert actual == expected + + pairs_aa = list(itertools.combinations_with_replacement(range(norb), 2))[:norb] + pairs_ab = list(itertools.combinations_with_replacement(range(norb), 2))[:norb] + pairs_bb = list(itertools.combinations_with_replacement(range(norb), 2))[:norb] + + actual = ffsim.UCJOpSpinUnbalanced.n_params( + norb, + n_reps, + interaction_pairs=(pairs_aa, pairs_ab, pairs_bb), + with_final_orbital_rotation=with_final_orbital_rotation, + ) + expected = len( + operator.to_parameters(interaction_pairs=(pairs_aa, pairs_ab, pairs_bb)) + ) + assert actual == expected + + with pytest.raises(ValueError, match="triangular"): + actual = ffsim.UCJOpSpinUnbalanced.n_params( + norb, + n_reps, + interaction_pairs=([(1, 0)], pairs_ab, pairs_bb), + ) + with pytest.raises(ValueError, match="triangular"): + actual = ffsim.UCJOpSpinUnbalanced.n_params( + norb, + n_reps, + interaction_pairs=(pairs_aa, pairs_ab, [(1, 0)]), + ) + with pytest.raises(ValueError, match="Duplicate"): + actual = ffsim.UCJOpSpinUnbalanced.n_params( + norb, + n_reps, + interaction_pairs=(pairs_aa, [(1, 0), (1, 0)], pairs_bb), + ) + + +def test_parameters_roundtrip(): + rng = np.random.default_rng() + norb = 5 + n_reps = 2 + + for with_final_orbital_rotation in [False, True]: + operator = ffsim.random.random_ucj_op_spin_unbalanced( + norb, + n_reps=n_reps, + with_final_orbital_rotation=with_final_orbital_rotation, + seed=rng, + ) + roundtripped = ffsim.UCJOpSpinUnbalanced.from_parameters( + operator.to_parameters(), + norb=norb, + n_reps=n_reps, + with_final_orbital_rotation=with_final_orbital_rotation, + ) + np.testing.assert_allclose( + roundtripped.diag_coulomb_mats, operator.diag_coulomb_mats + ) + np.testing.assert_allclose( + roundtripped.orbital_rotations, operator.orbital_rotations + ) + if with_final_orbital_rotation: + np.testing.assert_allclose( + roundtripped.final_orbital_rotation, operator.final_orbital_rotation + ) + + +def test_t_amplitudes_energy(): + mol = pyscf.gto.Mole() + mol.build( + atom=[["H", (0, 0, 0)], ["Be", (0, 0, 1.1)]], + basis="6-31g", + spin=1, + symmetry="Coov", + ) + scf = pyscf.scf.ROHF(mol).run() + ccsd = pyscf.cc.CCSD(scf).run() + + mol_data = ffsim.MolecularData.from_scf(scf) + norb = mol_data.norb + nelec = mol_data.nelec + mol_hamiltonian = mol_data.hamiltonian + linop = ffsim.linear_operator(mol_hamiltonian, norb=norb, nelec=nelec) + + n_alpha, n_beta = nelec + reference_state = ffsim.slater_determinant( + norb=norb, occupied_orbitals=(range(n_alpha), range(n_beta)) + ) + + operator = ffsim.UCJOpSpinUnbalanced.from_t_amplitudes(ccsd.t2, n_reps=4) + ansatz_state = ffsim.apply_unitary( + reference_state, operator, norb=norb, nelec=nelec + ) + energy = np.real(np.vdot(ansatz_state, linop @ ansatz_state)) + np.testing.assert_allclose(energy, -15.125629) + + operator = ffsim.UCJOpSpinUnbalanced.from_t_amplitudes(ccsd.t2, n_reps=(4, 2)) + ansatz_state = ffsim.apply_unitary( + reference_state, operator, norb=norb, nelec=nelec + ) + energy = np.real(np.vdot(ansatz_state, linop @ ansatz_state)) + np.testing.assert_allclose(energy, -15.126083) + + +def test_t_amplitudes_restrict_indices(): + # Build a BeH molecule + mol = pyscf.gto.Mole() + mol.build( + atom=[["H", (0, 0, 0)], ["Be", (0, 0, 1.1)]], + basis="6-31g", + spin=1, + symmetry="Coov", + ) + scf = pyscf.scf.ROHF(mol).run() + ccsd = pyscf.cc.CCSD(scf).run() + + # Get molecular data and molecular Hamiltonian (one- and two-body tensors) + mol_data = ffsim.MolecularData.from_scf(scf) + norb = mol_data.norb + + # Construct UCJ operator + n_reps = 2 + pairs_aa = [(p, p + 1) for p in range(norb - 1)] + pairs_ab = [(p, p) for p in range(norb)] + pairs_bb = [(p, p + 1) for p in range(norb - 1)] + + operator = ffsim.UCJOpSpinUnbalanced.from_t_amplitudes( + ccsd.t2, n_reps=n_reps, interaction_pairs=(pairs_aa, pairs_ab, pairs_bb) + ) + other_operator = ffsim.UCJOpSpinUnbalanced.from_parameters( + operator.to_parameters(interaction_pairs=(pairs_aa, pairs_ab, pairs_bb)), + norb=norb, + n_reps=n_reps, + interaction_pairs=(pairs_aa, pairs_ab, pairs_bb), + ) + + assert ffsim.approx_eq(operator, other_operator, rtol=1e-12) diff --git a/tests/python/variational/ucj_test.py b/tests/python/variational/ucj_test.py index 538b3a4f2..2c3de272b 100644 --- a/tests/python/variational/ucj_test.py +++ b/tests/python/variational/ucj_test.py @@ -28,6 +28,7 @@ def _exponentiate_t1(t1: np.ndarray, norb: int, nocc: int) -> np.ndarray: return scipy.linalg.expm(generator) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_n_params(): for norb, n_reps, with_final_orbital_rotation in itertools.product( [1, 2, 3], [1, 2, 3], [False, True] @@ -90,6 +91,7 @@ def test_n_params(): ) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_parameters_roundtrip(): norb = 5 n_reps = 2 @@ -133,6 +135,7 @@ def test_parameters_roundtrip(): ) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_t_amplitudes_roundtrip(): norb = 5 nocc = 3 @@ -153,6 +156,7 @@ def test_t_amplitudes_roundtrip(): ) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_t_amplitudes(): # Build an H2 molecule mol = pyscf.gto.Mole() @@ -194,6 +198,7 @@ def test_t_amplitudes(): np.testing.assert_allclose(energy, -0.96962461) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_t_amplitudes_spin(): """Test that initialization from CCSD amplitudes gives a singlet.""" # Build an N2 molecule @@ -242,6 +247,7 @@ def test_t_amplitudes_spin(): np.testing.assert_allclose(spin_squared, 0, atol=1e-12) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_real_ucj_n_params(): for norb, n_reps, with_final_orbital_rotation in itertools.product( [1, 2, 3], [1, 2, 3], [False, True] @@ -289,6 +295,7 @@ def test_real_ucj_n_params(): assert actual == expected +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_real_ucj_parameters_roundtrip(): norb = 5 n_reps = 2 @@ -332,6 +339,7 @@ def test_real_ucj_parameters_roundtrip(): ) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_real_ucj_t_amplitudes_roundtrip(): norb = 5 nocc = 3 @@ -352,6 +360,7 @@ def test_real_ucj_t_amplitudes_roundtrip(): ) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_real_ucj_t_amplitudes(): # Build an H2 molecule mol = pyscf.gto.Mole() @@ -393,6 +402,7 @@ def test_real_ucj_t_amplitudes(): np.testing.assert_allclose(energy, -0.96962461) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_real_ucj_t_amplitudes_spin(): """Test that initialization from CCSD amplitudes gives a singlet.""" # Build an N2 molecule @@ -441,6 +451,7 @@ def test_real_ucj_t_amplitudes_spin(): np.testing.assert_allclose(spin_squared, 0, atol=1e-12) +@pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_real_ucj_preserves_real(): """Test that the real-valued UCJ ansatz preserves reality of t2 amplitudes.""" norb = 5