Quantum_Phase_Estimatoin.ipynb

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        "<a href=\"https://colab.research.google.com/github/MonitSharma/Learn-Quantum-Computing-with-Qiskit/blob/main/Quantum_Phase_Estimatoin.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      ],
      "source": [
        "%pip install qiskit\n",
        "%pip install qiskit-aer\n",
        "%pip install qiskit-ibmq-provider\n",
        "%pip install pylatexenc"
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    {
      "cell_type": "markdown",
      "source": [
        "## Quantum Phase Estimation\n",
        "\n",
        "Quantum phase estimation is one of the most important subroutines in quantum computation. It serves as a central building block for many quantum algorithms. The objective of the algorithm is the following:\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "Given a unitary operator $U$, the algorithm estimates $\\theta$ in $U|\\psi⟩ = e^{2 \\pi \\iota \\theta} |\\psi⟩$. Here $|\\psi\\rangle$ is an eigenvector and $e^{2 \\pi \\iota \\theta}$ is the corresponding eigenvalue. Since $U$ is unitary, all of its eigenvalues have a norm of 1."
      ],
      "metadata": {
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    {
      "cell_type": "markdown",
      "source": [
        "## Overview\n",
        "\n",
        "The general quantum circuit for phase estimation is shown below. The top register contains $t$ 'counting' qubits, and the bottom contains qubits in the state : $|\\psi⟩$\n",
        "\n",
        "\n",
        "\n",
        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)\n",
        "\n"
      ],
      "metadata": {
        "id": "4zgZdq4CFs6S"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Intuition\n",
        "\n",
        "The quantum phase estimation algorithm uses phase kickback to write the phase of $U$(in the Fourier basis) to the $t$ qubits in the counting register. We then use the inverse QFT to translate this from the Fourier basis into the computational basis, which we can measure.\n",
        "\n",
        "We remember (from the QFT chapter) that in the Fourier basis the topmost qubit completes one full rotation when counting between $0$ and $2^t$\n",
        ". To count to a number,$x$ between $0$ and $2^t$\n",
        ", we rotate this qubit by $x/2^t$\n",
        "around the z-axis. For the next qubit we rotate by\n",
        "$2x/2^t$, then $4x/2^t$\n",
        "for the third qubit."
      ],
      "metadata": {
        "id": "ti0ifD0uF3UR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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YCSkjo6NNKijoayqLOEEZ3GlGKEA692rukCBmnTSEczkrSAvLKMsCCfsThRR5Z9tkZLsjn2nlaPiCCKP5clbVXYV2erh3aX+oVB4UpcJReeL+ow0BIXjJrK1UHIb/ACC9oRK38DNi5rbLooq0N17WsGr33U3W9tpPsc1d0KSMTELwG1/F0uHhtLtsuyESy2hxrwpTbVTalWhWYzYVQlOK1CK91c3jgUeWibUyvCZXPNNUmLWkwdUKHyFTbeArs9XDu0HbklzGADQ2lNKToepK3R8B+U1juYTjx+ko2iBM7SAIbF26J8/3YGrHTOJraNj9fchE1FNVeB3j9kMkRrTNq8f/AHGnFzTNRRj88ykbDD0TJoDFYFntyBLlFoeQCTWbJNG7l5JJTHIXdE5W0ctM1wFsLyGQM5PZ6uG9ob2sBhveVSba8SBAwlLJ2+yw5sxSWeJC2JGwHXKjLyuThDYFtkvOAQ1Im4t7j0Ncb2LUxlAqP2npvFMnjIhQDU0KUOt75Ge2Ok2akt6Q5Sj64SF4QufSpUlpC3JQtmhrQzEMxJ1//Y1L2xK5gescBOuXI5JFKaZSgdy+tzQFuiXGa4bUcX2/5u6uZDMkDk10UWTZBeTjf4Mmfy4y3wmclTIP8GDzX2zBrzHJJUSWNq4Dok/rD7bwTJy8saIU38i2UYYEoMiySYaoZMZGuA0aEhuK0HJcW2JcbJS1vRK2012bo+iE3N8mRGtTgnPApL2nLAe1k2hqyPqoTLSpYi+NK2NvX2W40j6yyzC9gXLapzFaSZbVIBtE8ZHmnh7SsZCdMunBqRGShKo0u18j7RBsOz9j5A7BC4yaC0wS1vkIerIHjjsjTDsaV/m+VfxqDfYP4Tg3p3UhljrdHQfwcHfI13iJNMgNJKAnB/WKOyVKguzmENgWdndMypzTnbJ943EkEYJ0smqRmpGNuC0IOlejA4J4oqu3n7TbFFy4QbDtJGlbjd1YH1NIkfQrQp14J1Do83h8gk6EuNZOa3AJZgTQ0htY7IfTcNhWdoOkVGI5g5Rs5GuIcCujKTR5mx40d7uzF/mzo6zgpXNXKYKGiOOk3KbEzvPhG1JpMkiyQpZOpIBQ6TaKgj0hSSVJSGXLFMqo8dyi8eStXLUdGPGQLCQzeSEvjnMVxx5bxkC4qkTjLkyxXI56hIgMkUyls2S+cExm9k+QnO3tk/RM5OoLVlLBHAI85yHUZmz2sfFcyd3O7W6zg1X1YtfAMiM9NPnGrTd/iShOeWqLvfw0onLo/q/LshEVFZ4a4LKvfdR87dH9Z5XkLeCeu0cOTqC1ZSm5gSvOch06z6XR8zYpUFpCipnIJYbZsyERdvyKrbFFr+L+nU/oXDA+cyJ/f0sdTJI+45FHZFMYyBHkY0imqYtLxa19+jZWe/TDrmbWMNNyyy9PsGkLtKqcEBLoni6g7Hsl6H6aEoT2GE8upp+hjW/lmo5JjccanbbJKiN+POutc3p3ItfGXeHHMMnTvXQ4khUJ8VGGNy3WmLkc0MzUTPnhH5NkOmZsmhC3/JcrfjUG+wbD90rnexjtaKzamj9xKWfIwl9s2ToBxs1RoyW8jbLPsmG/sNGmWKBjIj2gcKd2sh6R4hcjbpdhyMTjkAAAl268IIyhXqRs5b83YddBrWc4kCgtlZEkfTVlQFkLxUlCaJpw2enEy0tQp3Eq1vDtzP8AP2ZKCcKN41PTnR6laBMu/qJSv8saoKoIYI+0oFmSlxRQCAUpSErAOOPGhddVFJE3DOlz6x0jmzaqEnVEqwdD2vs1oMTox8n1jBYwLQqPZ3HZdXcUs2TWDky8KFNyaer3sGpBI1TneNRJMxA23t4qluME7hWNH4ttfLX36L9EbKTI1NeaM2KvlrDLMMz1sqj8MaiBXBY/8nyt+NQb7Bsgvi9uNkh3+8Gmj9xKWfIwl9s2Sf8APuiWfZMN/Yaft/lmPW+Uqm/ybIdeTZDqAw1zjSvY3fuPoYO+Rswvv4ytUUiJJmkilhnk2Q6mqOQpFex2xgWJUFrn6AdsgvceGkVFLidmZ/n7DCwnBUYvMQKQoshN1JsjrmlSEVhW/pspLuWagFXl7knTgSl9N7b6XRptcKPx3YsZqqWsVNGSi1A0UjbXC9ZTV/8AHR1u8qbdCVNPOEsLoF1SUWG95t0KVJaMtwWqptdlY0zGT0qjOETAooTMU0Rka2KrLX36MriYH8qGyFWPYr+VlpOMolvVBXJtXMB3DYFMzRsBYsorklR2VN0oK/yXK341BvsGw+9opO9jHe0rm1cTyfIlO6otEiwl9s2Sf8+6JZ9kw39ho0uxwMXqPIV1KFBaQuLSgiVptjd+4+hhBYUG9SN4LYW7DrWNEz5Q4ns1jrheztZdOCNfTw8pGFKiWkOJNZBuRaPYvAaXG9mZ/n7HuRII6WUaA4NZf4HkETAaWy/02ZHC4D8dRvyFt0lCBOqpyxo2qhIo8/xq72/rVz+kmzUooo4B4eu9rCsQC0XeKKS29qNrq6kNBBRLjPjkiMlCX1SpTyjPhcjwNM2iJUqRYwlBp9tGXR0bqRCZZdzsq+Xktv56N47Wc7H9WTxdLLEzSzpWUm9t9TBIGASAN7Ct/kb22TM9c6xCbvaZDGZ42p2JsmRC6pNGUkpSEo51GwKGybyoEejySMo6msKKlhJR2QmqyFhe3YWPIoriSOjGfIFxKoHMVi/ybIdRVFJEg6kTdLlKxXHJ6uIZoXNWAhpa5sSsqXQcqRisoyE22Pi0omF21tTtCZYE4ZHk2Q6LgcxKcfJsh1F0r2lI6ovjJS2JT1M+bqtCH+WqE5BaUtWkKXEExSTw0ZJ0+c6fse+YtsXQydKerRkuBN4E8Ro27rkIuhQh9lB5BBaUtTYwRXk2Q6eYDMJDfybIdRZI+pS3ZoSPiYmGySKiC65CMpHAXF7Wf079vlk1JtuBqGDsUDHpRju4usMaXe14Ke1288lzEJFlFAISVzSLep/bvME0acrL0pK7iyTY+PhLKQyx5dIlRZQSQ9eSDwksGMU9iI/WTWUxnVsroW9ItGeMgkgml7Kf257KCaz4eV2Oaf4GbDLDJTguUV/CkmRm2LK/fUyVHJEmlCPZJMjNsWV++pkqOSJNKEfpcMXgDi4u6p9D8NSduXlbJjtrE1su1wjzc6054tSHXs2TOOWRZIVJRIpW1rgWva+10BeKujcqMNmdSiaAbBxeOKSwaOaFFgtUXTcm0U8toHdFiQ85NpDAE0KRSOHSGweInwufcI9XIMfc3UpnywkAFZlmOpy2Jkcpm8aObvoCMMsppfuVZK9yrJRBNk5fVLPsmH/x/bLPsmH/AMf0H/8AcH0leFQUKHFp4Visvt1MvqhiTNqblEnUoSkqwr4I1LQjgzyz0KYySPCbMosy8SwKSQpIyHhSR9lZ7mOPRUho08tb1zyG3htsZeK1z7Syey883RB084acX34Ej1laBMvClYmxALSzd9Aj+Rtmst9j0hBnGLpdM+TkOyWfZMP/AI/tln2TD/4/1OqwxAk9473ThJ3FRKfeO90zzl2cllOEy5GQbIvM/aRdRmRHoAmzJipW6Pk7TNagvIj0MVKJ0BNIj5hIHWhZEe4+YjWEuBHopMQcRkw4X/4SezUkpXnE00r2sKnCItDnddBEjOmRnuahWxzdCyWSvyBZbSNbbvk123HdZkLSciAqk2ND+WOgt7FTLTV5HjqE/wB6MYr3oxivejGK96MYr3oxivejGK96MYpKqKXE9WbvoCMzMpRfvqZKacrtLwsrNn2lD9NT5+4eyWfZMP8A4/tln2TD/wCP6D5+4e2QfuDsxd972ToZ4Jq1NKdmI2OiItwyJa26nlrJekWF1phrb/YyyVmNhjKkWpE38B1eETISpzGwkiY8gMj+P+DjmYrJeX05FnCqIVE3wcja9ixWU3kNLukfE3WMPiD7RuURcrX3/wBQ6JudR4aUWDRXZqQm43SY6bw8pmNPwHLIyiOprIZQrbUq+ztjxvdFCmOSNlonJD0z01ZBaHMJRxagPSMViw4tPUObxtgxfnst0lFt4GhOJtmcOLvacaZsZZzx+ybJXsmyV7JsleybJXsmyV7JsleybJRRQCAdWbvoEfyNubPtKH6anz9w9ks+yYf/AB/bLPsmH/x/QfP3D2yD9wdmLvveyT/n2079y9mGv7F/eSmBvx0xmWK/gqIGqf39MlJRgyBC0bwhxnIjZCz/AMDB3yOla3JXIJZYCQ7Jl9ixP+N6D6yp5Aixy7qPB/T3qIr/ACSUFdum5qbIkeHkFgJ9KSSlNHi2tgVSVQSSBOBpF/3DaYWE2zjCWhxCbjZU23PfpYwWaMpI1Y0L83OV9k4W8gx4ha7oWfZNH20fasVJLlNGkffwgG7GincHL8Ux1RjCUFyytH266TMDApEiXp3IrRzd9Aj+RtzQQIxlZFQFrfTyYEeQ9ks+yYf/AB/bLPsmH/x/QfP3D2y4XITjZiowJzxsk/59tO/cvZhr+xyZcTqsACxYdkxl5MUTFRyXyEChjmEXBEZYnliSnWaLmuYHR+UyKzmjlkELjj6RJEGhKXIppasOtxqRm6pJNHJwcioFIxXcHp8iyDHrurfGU6/hBi6QuEiQ1kJ3VsbLF1hzi0Vi54Ob058LkrnSpzlGPRt68lzTUc0T+5knXTiJpWc8apBUkb5YpVyRnm1myENsvUNPk2Q6jpDomRjGEoJUjkE8U+71/wB579KIKJMoCrJ2Sf8A6/L/AOodEZ11kRegv7XpzpSFKx44KsBi0ZJMimwTBCfGbsajixynrWsTe43csToDr3Z5hHCi8lqmusizZA/tUXRAb2nZIlQp/IiSQJy9JT8tkEBzm+LzeYe9XJi5S7ubFGG6OlL2xI6Ft4BY+l2jlKOuEjSJg3AVteWoh8RNtpXj4KeUyh8r2KXpJTUkcJYmVuCufuSWOJpzF0aB2nRimpI4SxMrcFc/ckscTTmLo0DtOjFPXMow6DdvOch0zuk1OWVOoeGXI0srlrCBKqkUsvj+LrmByox4yBYS5pmzg7+c5DqKrZIrHRsachTjZjSOOMf/ALFzFxci7Ut7SKf7En/XJ9SkFjMlUoJCpLwqMQU3UbcVgec5Do5QJctTcHhdL4u8rbsON1i2ypuUE5gxL+OKPlYS+21lj8bhP2GsHkg8NO7aW7osMOAj2vZmr7JH/teybfYcT/jeyRJTVrXh93SibaEGwrbczjuSgALx2/p0LeAMuizmZAnvTy8qMIaI6Ry7Z13vYNn2aGr1MeiadpttaQXFJ9JQlJVhlTGicZYLHryyXvL5AwglWVwuDdi9gSs6HTdVIUaTFJFjawwTcwzVn5d2OSlGgOBTmEMrnf8AkrsDl8h7YMC5c42SC3iyDR37l7MNaLw1EPaPDzoeInpm9t7BiX8cqZfYsS/jij5WEvttZY/G4T9hrB3yNmF94jdmavskf+17Jt9hxP8Aje2QY1aH84OPH5CNS/S+E2a3Ih4S7MyA5lIG3ht/TupfJTeexP2jb8dTW7kDSywYE1UWHwA6lSopEWve101VMMeSsBHQw7/avSMMCUDGwRSCR1OsgEsQIbjMtQQ5YrDar+28cLQZXAWNBKWpyq17C0MsvPItTc1+ysOwynuWzasyd2drQMrBKbU7MM8NKx86MgQ/5LlEkaC6c8CorY939jZkEVh2NNAQCJb5bK6O/cvZhrqPN4BcSm6OWhp6eE7Cjw22ncHpXpAuCbFLn5UbWQXIpvY8S/jgg+O2JVHlKusvLyymSE/Yawq5lJzamEgKjbZiVmG2MuzNX2SP/a9k2+w4n/G9khfCo6hZX1FIE1ZDWkImDGSQ1JHNjx/2Waf1GTv9i4FX3gyNDThjhM4TSgrRmt+alvU7u6dlTgKdMkKmxrTM5HSwCsKWaWR3byhhxU32Z2KU5IPXKITjkDLfarbUq+z3jJsdA+x8njpqefPLKJryYyOQiFJSoO1WqKREsgjsgv8AkNTYiPY/QeWsOql8Mln2zLRPlCskzjA/yR1bSXhJAXQ5pO2PDMkfkwIPJGEI4FIJBZrbEzMmocK8cl2Q2G+yPXIsbJHZTdhnpFy8aqHU5OnLSF9UugCWTjJj06Iu5RbytmxL+OVLMfEyFQVH53a6rHYVbWyNvk6CmDGCZqRnxyZo6Q4yPWqghsG1H48ejTFuKHFyADGryUGLRdewnUqTFrSQ4vXI693D3UdalDMjGAJoV2MSyVF2SfgpLjQSxUENg2qVyQiLt+PY8e1pf6jJzX5g1RZdZyaam8CPSnwiekSIrQWnCUT3pkkqSRwtpYFktOJJAnB1RkfjlWlmN7IWGt7S/wA6TMEZQx0rrEAJlnSAsrpZTipYhua7zeL0yZPSLqQvre5VN3ZXK1jDHSIy25YWcayQiyUnVUG2hc4CKwrVktX7UOhYLFA/yWVxQqRlstnIKb+ZMvsWJfxz+SPxWCiiCtxdf6mQkCUtuKnCypp2TTHfPDi2Sb8UAwmB6m0Rqqf9EjlfJ2j0QPWnWtu0I1YPtL1jGEuz/khoY6Pd5dNb4/j5bvIghsC2o6R9teAShI1o3KIxoEdQKflqW5Y7TLWfY+ikiYEFkbFa8VmbmGLwltigfQQ4ktQBIiToC/8ABFF9wIoATFJdsphSCUlkrpHjQ6NyxvlBPTDACOmey9/DT9MjXEyLQ4hhtoxm4jJP0GnFkBdciMTTYeT17zSaHSGXgZsZMzXUyei440YhZ7IWnUNNAQCWTxVIjITBU8ZKp0U2SJMSAUrzfVxR2TsobS5EmhPBtMLCaF3xjyx7Tk5c1Km5zSuxW2BCsdK6PUFpS3B7XThVH40lj5ex2mLcyqS5g0GUB+bjKAsINvxi64oKEsIBRjoiKqNvyFJIFuSGBFSnMjSXf3oOLimTqZ++D91K90MbcXsTcIhMUltsyiMb65t6IDcm05FKUMZTqVb/AJOPjMSQxUnZlNwEkZcctV2li9XFXy5U3XdGbHL7Z4a+l3Y0L6U4Y4c2ITTlJahVNj4heQ1j0djZM6OqZnIEFfkBQ2tidqJ2qW1KtubDWc2j8asp1g4uQlGuOMilw74oDcYsPph1bDbfeo5AG5S6Ax8whCli7QiuAsJVulSoAkKxuQbI37ScnZGzlPeU1zubHsXnKTk6ctKXtlqm8plqT5Xq4o7C+xq3RiVdbg0pHULxic9MYGaSqIGxGaJmZza2FbPVCdOWlL1Iur5mQ6GW3qyJqgTHZhZ9B8lDbHQuOTXF3GkxksezWaPN7AX0PrqWxoMVNZh9iN3g9XFHYX2zpq5gpmdCndPoDLCaFJCG9/fx44kMdpPkCTMV2zKjOsuheELnbShRnGkmgAz28l3U5SBuZwu+XkRFWVTaY03YrKNGgbUrWX1ZVcBuJjW1gZW1L8v1cU/LK7DyAKS4qL2SdtGMmCLndCDYdnWEM7zZxw2ENzG6fMVw5ZeG0aHMjOopHOGJfYlWQo6oWWUB9657IC4+1YtYgNbRRp5ZFls3Ym+luYGgir5Ff3c4LFN5FdFiFvCJrjDWzB0HNwKakuNkJ8hdT+xJ8v1cUdhX6hrJsfEsTRd588btC3hSZD6RlgNsrhTGtpdiBkU0owwaXcUKmzdcK7IbbQcgS9JROWlxQrZrJDeL5ARs7hbM7L4r5hYwiBmBiHQswMlr++hqvc7NKUNKMvqqkMkdZ2rTOE/VF+yk6crjxEscaRYeZU92eLNbDawbB1MpPB7kewNBbEgO7Evy/VxT8srsowsJoUohQGQWvv0JTbkJzqXDYVHtiNTUPZWxU6ChTEO4oMwDoEHYS6DEGQNFxZnJopqREVPX4qLtWJo75Y3/AMCTvpUcb8YMJqoyj/lo/l+rijsK7dkrYAP6LHMpG5FdeVyblKyxeMOrjuxw3jpvfdSz/wBjSkAAlB173sGzqIzJj6QQBMXR3Yk+X6uKLbwFdm2dsB6A+PPhT+j6stt4VTLFl/mbTq4/Ucd46coSa7M345ifs03fwMjy0+xkLjAIyg2HdiL5fq4q+WX27RWsKykszGTsjWFLyemYo7rmXEjlzjLq43F43XoXriW0hgN95Dp/AmsxIiqbH0PGUPaf8tJ8v1cU9hXZ0PLQnfEjA4KccuQRWHboGGxgcdiGxyDVxyEXmHROnMyZuTEyp4+i15LISI2jiLCqmLh8Og3sR/L9XFHYV29MjjyeRpI9JFsMWAHYy3RNv+tSkIrDtqY/KNsp25Bllo+jxrEPJEuvIJAkjaVkZl+RXEkkCcHQd2JLbi/VxT2F9vVII6lkSdlkauBryTgKAbcosgXZmx89hemXUiy9OoXbJA+p46jhjCZMV+vJZMki6VmZHHJCokkCcHSbfcFKLxg9XFPYV2dckjKOTpm1ydMYrEC9O5k7DSgnAhykULkumL4YpsK6mnFwIakyYK7KryQQWlL1pVKCIylYIwqmZxJIE4Oo3sRfL9XFXyyuzQcmxM7kK2x3x6cwShFICtmWmI0RcOkhcnbdIXwxinsUctWktxK5Yuys4MrMmYUmre+6pVkvwHROHKxk2t4dA3sR33g9XD+0vt0RBsO0kx1cJkcyIaQcWaE4JpQTgJVAsXPxZgTQ6JnbAHQ5uJXr3HLC9jYkceTark7pGkEsUvErPisHQRcOib2I+z1cU/oArs03yNIZAALRIIGbHp43vgZhFypWggEmUsSn46Mml7fFymxE8ZOVoG8htK1FawhCXIMqcamCAOTioKKASHSM/UKPs9XFXyyuygG2M0/jUhgLe+gKPlEDMkRrFPiIzN1kUGjWkOBXStXp20p/yuYsMjuMTVhxJIE4NNYuTt5brlgoRpEHkMzPYos2xwGob+oEVtxfq4p7AXtYAxCUXACwLal7WFZ7x80vVPGO3tEW3rneMqG3MoiLIsnx9bY3IceJpbmBjTUPJj9IRJ8avkkMYIo2RoGkMwJVnbIjG00HITxJqR4xcnkxnjDaw21jexHfcWAYxj9W1Xy7CEosWXYu38BY2pl9nzEiJzG6Yrd26ggSM5rI+QQBbZJGI4sBgDbdahwTJLCmjJYx0zE3pR2mkse6T47fH2zNjZmaAEJikoP4Bt9wEoRG2CHw29Wj7CuDcYOgJTbVy59cA+uAdu5Y+uAbXLnVwDd3BN3cudV0x1csfViDq5c6uXOrgmbuXPrgHbuXOqxBtcudRiIRoVsAaV1HYjax0LFasgFoNK0gCGefJ6NLyEWHwZFrlsjColgnauvdxJDxE4Z8VN+LWlBZLGUiMXLG1wDqEQbXLn1Yg61cudViDaEUZu5c2uAdXLnVdObeuXNrgHVy51csdViDa4BtcA2rkm2twzTbEEGCCSEQLerN77qEMSq5hfgLL7f7S97Br9VNxW3ARdnq0O4jxALsXZR2F9v9oMIjxBDYFjO1F2erii+4Bfb/AGxnai7PVxR2F9v9sPtRdnq4ptvAV2/2w+1F2erij9QF9v8AbC+CLs9XFHYX2/2wvgkvvD6uKewvt/thfBL/AKQln2MF6tqewF9wC7iOH/EPcEyWlE2Z09XyAhEX7eCMoMsczij5E9lmkvz2OnmaPLSD30LSLps3JRXT5cj59kErZ3OrXsL+KZ+gSfEbRRVirerR4TBUYBQG1gnGVYlRawSlFcNTXCU1wlNXKU1wlNcJTXCU1wlNcNRVy1G8RaiuGprhqK4airlKKNGYnstmKVCLz6RuJo41InUKfGhILEQhARclqsltwD64SiuEorhqLU/zZKxBOnz+/iMhT84IVGKJCK6+DPrVSB4XNpiKcSxEBszAkUU1vaZ6twzr2uUfXCUVwz71wlFcM+rlKK4SirFH1wj64R9cI+uEfVyz64R9cJRXDPtX/lPogozwl77B9W1hm6ycHgBrusvbWm58jfn2kUGVqbpmNCkF1yCaomKkaaUywxviba30AAS7bXmLtj+FyhDvCTY+5x/IIXfDlrC8+mcOCw5UaHaxRoDw6nwq4xKheCwAoxeIPq2cbYq3Dv4C+3VeZq3NFWBIpiFugzYhEENgW6zjgJwPModZAphbOFM+aE9gYlVY8nHtCTe2+n3HbO+BOjkogImHLaFZcswJwdI0vihLLsVYXwRX3h9WzCgm0p/QBXZpu8iQslvMnmXmNEOb2rSXLiG0kpaunihsakzQVHhWFJtHJMUObj4fJipS37JHA2qRgVN8mxxeLZEbJNqC+CD9A+riq+4BXZojHYFn+bjue1QIswwALF20VaspCVYhbkhwRoyW8mo4VcEn0TSgHgShvjiT/Hbe2+pPi5K4Cap+5xE5EuIcSdG/wRfD1cVdhXZoLlxLcU4FvE5PZY+kYy9I88CYs4S6fuTegIayNkYMMHINLIseC+tOM5JZ8bOh9j6KRp1ra+YyUxiXoJSVoXpF8PVxR2F9vXI5OkjZLe0HykZRQSQ6ciXjlqtsbSmojbFzhjkOle2+mskuCy/pMLCaGXwBTHjoTkNPJtC9Iu31cVdhXZ1SmUExxPH4iY9qbW3ak+khjeVC4taNI+iNFjJe9PL7IE5LHHOzw2dU6xzdUZAMgeddd6Q/D1cU9hXZ0yqUExtPFmM9zFqP70UwooJHzFyjpjth+d6cpa/OmnDbhxG/ryDAvNrY+n/ntum9Ir7/AFdU9hfb0Pr0SxJImwqZKs1L38NKwDnz4WWEkPTFbbnTUihdo1NtDIcLGG8EmZcoTdF6Q/D1cU9hfbtWKykBLYkVzl0AAJYdTJEiMbksOZLsbb1Qnw3c9Se28ml2jOIyoiS2LSNPJ0O29IPV1T2Fdmz4U+mHzRWgRFNxGorVFoiYogMkrx1wpLwnLUzQl/27UpstRaBxIFAFFlOMJClUlLStl6Qi3+rqrsL7dk/fjECSIx+zCi1clOhis1lay2ZF1wcQBvGpldJZSwQFTzTBoyWPp5IhxxIDWVVsvSD1dV23lldlOjiU0pYISe/KtVesA3p4Mg81UCMCCjnhAno6Vs5FCn7AGrZEj9wCyGxBLIyGxqAnT5iIqMS6PtysubMRtFSFsOEA8szSnJNz2HEJ9jGHSylGb1DJOXKm7Yh9XVPYX21M1Pnrg3ICmtPomnlpwqZ0wpKU5gbA0HJL04XljzI3U4GPZQYT7o1am5eGkFqtipj3e6+Pbg41jwbexTJ4AwZjDQoUzCDEIY0Oa1TjBhU0PELVcwzGhQzzIG7ozDWqboqOk80R2T5UUJ7pcnMp1J5G2KhWFYW2Skcy0YTF/wAdpHEgUltXixvJtiP1dVdgO17crNCHH7OZu63SStjLZzy6iLsN3m8lovGq90Jb8RMaSkUZam6lB4ERMGQikbvowS3hXdRhBZ1l0SZ3G7lilpW0Xjt+Z6vIJnH6R5abxCvI2t2S4SNtcOnk6N+eNeN5B560Uk9XVFt4C+2ZKbv7omIAlK6Fi5O3lvOVm5JRdpvL6QYjbCxNzE3tIejKL5ZGijLSFkbtGBCsJw03JkbnML/F0Difj8p6SmtuQtwm59QOukINh2Q/+vpVSS271dVdihUBCmx8nE7rNq5wTtpTnlQxacTjd2kahkiLXHwdbfumUu0b1jksYVWkccAgLi5uMsVtDEmYUuFxf7hUhTrgrsaoRmqF8piI2bITY6XtewrdeW2HzBthzxZ8aEfq6qvuLn7jw0jE1lsyGr33VJcmkIhIoK8S0TPH0DCXoS1y8ra8dMBbO3aN6hXhsdoubonaSQBcJsehQktxR3ZhcIgqtnxp5hja804oJNFzGHJCByFa9hW6VSYtYTjVXdnd0Px9XFXYEJUgk1ObqmZ07m7Ps9Oi0HQRkOlP+I/u5BAExejf4Y9SWTGaEgkiVgJbo+qligsoJIaVX3E4VBbd0vkObH6rJ3iChYJagkNunIIRRiRtwrDt6uPiuyBFixHfln5/Sx1K6Jn+XgaMjIWum6TtjoG19+iYOxQYMqBInTSF8IEkNTn9b9J7JKjcOMNM+G18N4DdhUvc39V7WFZ+gBKoTDOViFQWYE4O3KLZ5gyY7X8+zermTXKyJob1SWHR5nbFeQ3EooBAFbalX2dscNbnYmMSBhNKnLs3Gt09aXC5R5Z9umfvAmZnx+2BbmbSF8IOcWcZ0/CpJKVChRF4cSxdMzP5djw2XYLLoOjQmdiyjV0ENbnNM7E7FieytPiVRyovVzIfgcXRNYzI7skSFISegQbCpdEmtwGogh6auflTXdPlFv3IHpE5h2ZH8bs7FFBIBpD7cYiuPpOPAnA6ObjJ1DKwp2QvpyafwI5i0sAI7oqUpSwtxRrMfqWl1IeU2xrHdjnXq5kBwNUyCHMAY826K9mQugT8dILWsxy1gujnJ6MqLPqJ6kwR2HbSH2wBNy4drk6JmkkAl88UoEBLaV1ZhUcNig6ayRh0jiQKAOZqiAKUK4lxIrIW9ufrX36kgkKONJXicyzl0Jgjk1XvYNj5Y8zFd7ASG126YO8YcPUcYrFhhRPtLJCuzUlS0tua4PDkjggOgTkhOOkT8wFNuUGtVZE6o3K3WO+4MPOAcDY/vxLCnamddMREkgTg68zf+YlsIslR6a5CS5EMpw4I8VldGAbawqedbtJ/d/IkEdjC+cq80hsBqa/o6yc7iaGHHzOFmYqya0AdWHHrsJ5YfUacrboGLECOxTSX26mV3G5KBlRBbkOxdHG1xo/F5Sc04M1YRJ8qcsJrljW726Dr7i8XqLKE9SiZFM9NceE5Wtbdo5H8ThJ9WZR8t9Q4+kXnCLJJFjWHHKmymPaQg2Fas2/bGv6Os3G7kSK3hTgmDOavfi7GtmFDL3afUbIxhAGTG5YQR4vt1JSfdxmXUpQp1oV+OWpXdRF5A2D9tX1lu15IZ3GkywhYE++4vGAOEmfZaM8+NQ0loFpJr3d8h6y8q8KlMzKsewYhN4jBqZt+2Nf0dZvBe6VH9ORipMS9vV9zfhMP/F+o2ad/lePA/wDXAdupDbCeZZo3tYVOkHZnahYvMbROS2TxpExSsvhRHyRMXpCF4LYxR3XvOtkdos5NYF3m8Uw3+jNqZt+2Nf0dZebrrWKJuNnVnqeLwtzBipuugj/Utc0jYH2sZK9rGSvaxkoIrDt0yWXuTIrNyY8EAiEl9q2/ZJZe5Mis3JjwQCISX2rb9AxzSFKPSXMCe5zDADbHRsvt03hXyCHDoBGo9Nyc07SSoMcp+fEkHMJwtjUJe3jfAKBZIWsgWvIrG50WaA23VL192xmxYeNa06zqm5xFCVBg49hW3/F6TiuA2JffUyVkOfN8tRo8yMqciN5GbZSrWJCl5DYuXYrUe9SNeFUevywsIJAmL6s3fQJsYxowr3XRivddGKKLCSDqln2TD/4/tln2TD/4/oP/AO4PpLkImx0fxC52ObAdunklTdOwY3b7tzBpPkjRsQELArmgxpi0yTGQ96Iwgs2joggMErjbkUFeyFWEU0mJySJVI2ikuUmoVN7ujdgbcwrxp2iEN/ljHrX+ERcwqkuGgCC0/wAAQbDtaNtNjAhsG3Xm76BH8jbkOVK4mhTGXOKpxl6xHKdks+yYf/H9ss+yYf8Ax/qdTFZSTznIdL1kmvKvOch0zuk1OWU6S5YhlGyGy9ZIXGjHjIFhIZvJCXxzmK448t4yBcVL54e3Sg9TM3+yyQTCF00Oqd8Seiky32ZIS6XYHMv9Q6eWxgEjbU9kiTRkssLabR2HKD1NrbqWW3kY6LKLR7b2sKlkeQLg3gwkZjoyuIa8tQgGhWSdqoGUBoRoZizuFZHHd7kIbeG2spMsUVDyykzNiYAQsWm4ZcZ21V76mSvfUyV76mSvfUyV76mSvfUyV76mSm9aByS9WbvoCMiPQC/eO900zp2cFlZs+0ofpqfP3D2Sz7Jh/wDH9ss+yYf/AB/QfP3D2yD9wdmLvveydAONmqNGS3kbF6YtVkilyMtwT4WUGcl6KPxF1La1sV32MY6kwJA2aeQTQuEj+Ghe+6nuYCVHRyGktA9i36fG5YSkfWYlJOu4wRAtGrjLsnp8YERA25ErLc0s8fWmkuRmU6ky1OttqT5xs1sSBMJqhGKiblRz+Vm76BH8jbmz7Sh+mp8/cPZLPsmH/wAf2yz7Jh/8f0Hz9w9sg/cHZi773sk/59tO/cvZhr0VMD4w428Rd35GZjp4a3Mh4S6Sj/kp91nHATgcpAtmB8diiKOA2uH6JcbnGHN+gIVg2cJY0tlKcqNqwrGcZLem5RA1KITmxqgUna05FFyGUtN02WEwLtklbHe2jltwMXHT8mzHG4YRyzHqrVpDaSblclSP3pnoqZJAgkRGjm76BH8jbmRIM9jjq8t0bKdVRanImyWfZMP/AI/tln2TD/4/oPn7h7ZwZ5PMaGKxdsTHhVO2yT/n2079y9mGvRZo/wCNly5tTu6RpUrMZPSdQWrL0YpbnZp1ObqmZyOK6ZJUNTOlZiehx/VLjH9W3QmMaMlCWRpmyJgEDk08ObfKWbYraki6lMGRDu5Rd1KAoYkCERa55SnJcmOLYJqnzO6FqHMklKwyNM/g2uzkSzpIClHK3jLHiUiTE2Tk6uRjDX6QN7emaiBgCYEwkMHm+jkSJLJcmIBcovauREuSdPFpVCxJ7Th5r2AOTSCpI3yxSrVxyeriGiGTZhToGmdFqakjfLFKtXHJ6uIaIZNmFOgaZ0Wp65dDFbqu8myHTO1zUlZUsiyaWIkqeexwCJokT+KGRBZHXGjGfIFxKoHMVi/ybIdRVFJEg6HDlopfsgERWRX0WlJF2yWF9sijqSSpGd5c8ZrkqktYVoYyuSqdel+kaSPlIGNfNjUyUpGX0ul/Cjxha3lfX8Km+RRF3g2PLNNmlhVL5P1GklnWWQ5rWVaELG8TzGR+KyPy0SRY8IT2/KSK1kDsjcwfCpi6Kp45sbOQwonIfm841sipTWV4b3BM6kDGEuwLBnMz9SssF2s2th/NJKfGFHIUxJzritayvqOQJ+pSLwE4eHc8HRKJoRHqj0OPcj7WsG3U728SHGhXCa+p4fETCQ4Sh7yGph8GSRMDmtC2pMPpjnBZpODY3qAOTUzoLqm9W4HJ8dHrEih4fCFEfjSWPhvfw2xt/wAzI9aYy5FHSkGOHdWa54velAIfJ05J/qVNW+zmz4ycLq2jYrRkrynuDOkROimUEbxf49L+ZwWzDVv+M2X/AEqRzERxsWiflRWg7buSxkLxNfQrWkIC3jKFjDG3HThJDkSEhuKrLTqBGzQJl8jZdJ2iondYREGsi9glJgTGfnuiiDwMiLAqZvPkTRjS41KDWZr+cZA2ZlJskuQZxivUlYHxFw4y7LIeiVY9bpGBK7P2OhR2YtknBtlArBaMQ7/JaONAnA6SFdMTY1F08dJ0Xz7fjUQbtGx3k7Wx2dMrKV402O3eSmskZbo+Da+lGzWY2tu1HZ7RMZThIHjJh8ShiOKkbMwuIx0xIrNxGs+XFBJelVkrihCsG0xXhyE9BDYFvUlRfcGfA8nWplAFZXQcQWoA+4pKuIqcPsSMYJo1SO1Szw+TYjDYLGuXkNpJprlPlDOypWMg40KctBLG1fRZoDbdcjVFp26EyprjrQuysI8fgm8nKR4hRCMbGdEzl9EldrMbZiJvGcVpHqC0pcgy4UWNogDnKjULenbCtm/dTAo9sJim+brODcmdSDcUlpRe61Qtsxx1vjhPqUrvuBJWcD61Y2cQqWzqUpSVhbritHRcilsHpXk5tkLPA5Qhj8bbWlznipKlKRF1e2+lMbb1N1mPxguBskyO9jpQSec+yZPZrfno8RkjmIzfFN1NeyUwXiNxcWQTAogzrEKZEnR268uOBqw1jawMqDQWL07eB3ysmsZeJSacGRuDtcYD0T988iZsTsnlrQn+d6uK+wrsITCjEk0L2sKpZAWZwTMsEdnBMDIr/Gaa8pMbhZMtIWh0pAOxbbjDf5P1qDwJS4Qn9rZD1DGEuz1kZkZb+896dzk+NHZ/OZoi1MXXORmSyRkEgTFkfO9XFfYX2zpoNdG2HOvmTfoPQvC34dViUNRpQDwrsfsS6luJlSW4Vk7jQ0eZblGIcpR9bZE9IHG3VJC+K142I5dn68rO90rbC4+GNtewZgSrLJmyILrMwNpYS5nK5EIWOZA/3bcYMiG5CYpIDrlT6CONmJmkZpdEfO9XFW7wF9tXGfBpPv36C0vjJ8MiuVboWNyVwCuxdHltKcKpqvBZg1X8yyC00DK78huRmxLSfMTGbRGS48eF8njGrbcdyJsStJcnaDqtI2q9WfW69GSZpKq8yY7UPIceBc7KseJpzlyZ3kQ8zDNomfy5zEcjyC8GAxI7uNNmKmRCWgjLU2WtbdpzpeZL35GkKQk0Rfed6uK77gF/qGplH/PkOPpENzT9d7b6xYGyB70b2telDOgV0bC2I65uOY8dT/itjTI41i1ueEFsKNtrjwmgvcGF20Ne5lq8JWHWUuicVx8m+SWljjqSEwVCgay0pJP8CcSUMZbcXRq6JLsT/O9XFfYX27JajFEF7Y5EO6brZQ+VzrVlRvBZ8Xi8TD0nGhIAwJTMiyP+AaaAgBBR2SJGENgW2EfP9XFXYDt2OTeS6po8vHBHfrlHjZ5lqyvw+UY6N4zL05WkZgC4VHbRls/gZBlZjkpi7AXGm/aR9R6uKuwHbtl8etIEMClAzrdWYyfAU3qwL0upL/s2MN3kHQ6OiZmTRBoDIXv+BOZYGPJcbw0xnB0E33qPVxX2F9vRkCIHKBQeWhk6PpyI2eZsWMHSzkw6kz3eSY6D4WPolCxVkF7bG4lpS68nkyeMpYPGzpKu6SfqPVxV+oC+3pl0ZPYFURlqeUpeg4kKgvGR4mh11JaLws8AtazLtybKhNaXH0UvGW/XkD+mjiRgaF2Rl5RYCAdJXz/VxZ2F9vTe2+pNED2NTEJgnlBHRNCBxiUhFYdtN7SWXIo0aUch2SeRERlFA40pelevJJKjjCZnZl+R3BOnLSl9RPz/AFcV/LB29V7b6l0GVNaiEzsmSl7ckMXnbNjB/s8NGnNzxJmTG1r2YKdXROzJWkpXlF4JJAnBrSiVJYwnaYmtnCsooJAOsr6j1cW/LK7NCV49LcDY5kDwG/HZe3ismM93cttfxW0p0DiMePQCLYlaspCU4nOOVHJoaU7Il1pdkshoE2Q+8gOCGwLaBX1Pq4r7C+3RkUVRyIsDw+47NZH9FICKyDFbSZuxlKQOKTSnqkCVjiLwmSxxxWuOU3NhY00dR6ppwCakkmdZQuhuP0kXDpBva6j1cV9hfbpKUpSwt2gCtlMj+RhbyTgKAz+PqY04ReSppOj0Ze7tTWgaES3IhzKyJGBLqCFYFpNlFG1ijTO+P6lA2pmwGmX9T6uLewvt1HqNoH8C2PSGIXYsjonmnlpcoAsjEtRygjqMMCUGS5VTJLsmOnCSnpUpSIrTEKxdn/JzS0BAnlWRxxuAtkc1i/qfVxX2cWxZae4x31XmItj3S6Ev7KJxsoSKmDMJ6Sm+cMjlQDQGWEMIKWy5mbqdcxow1dol8/FF4A2Ri2m6PiBmA7ZUJtVmCWTSo9jxpj9vhrgt/uBj41AD4LerN1RdqVHgGAJgDK5squaKrmyq5squbKrmyq5kuuZLrmi65kuuaKrmyq5ouuaLtXMl1ZQXelhCJyAvxy0iC6Y3dkQwgUNxqBpa3W7ZiyPmU1MTOyh5kuuOCuZLtXMl3rmC65kuuZLrmC65guhLCQWW5DYENOGYU/hOUTSShR4rQm01NTWyl8wXXMl1xwWrjgvXHLrmC645dccuuYLrjgrjl3rjgrjgqx4L1xwVxwVzBdCH4zQCLJta+/1aMKJBQif9IUxdw8qVXKlVyhVcoVXKlVypVcsXXLF1yxdcqVXKFVypdcsXXKlVy5dcuCuWLrlS65Uqj2xKqsvxcwLqVYbtYXsZLG2j1M2Q0dNZEgLDktWAJuWwl3Fl7fYOXTh3tN39dV3WcLgii03dLocWG+BBihhRUlY0CGuVLrlS65QquVLrlS65YuuWLrli7VyxdcsXXLgrli65YuuVLrlS6umLvVkxdq5UuuXL3CAEwRZIePwAVa271asTcward4C+3+TcNr1wS6snKtVigB/kmiGaIsuxdi/qfVxb2F9v9uH6r1cWW3gL7f7cNg8f1cV9hfb/AG9i9xvq4r7Adv8Ab2uLmfVxb2F9v9uH6r1cW9hfb/b2+q9XFIrhCDt/t7fU+ri3sK7f7e31Xq4s7AdtlFxmf23/ANIx+CxIxDt6siGENKzAXAI3i0Xcsu3FBXEDXFBXFBXFDXGBXGBXFBXFBXFDXFBXjDXEDXEDXEDXjDXEDXjDXEDXjDXEBaj3pAmoczaA2HPW21Fz9IcE6e8Gi51xKcMhlNgAZsb96fMTEbdNkGPKrJXJIut4rV4rVvtW+1b7V4rVvtW+1b7Vvrfat9b7VvrfW+t9b631vrfsFfwKAA4t/Vo1OA2jiw7y0QN3JF1yIK5QFckCuRLq6MF65AuuQLrkQVZEC1ckCuRBXJhoKQAaujBe/IgqyIFq5EFODk2t9lMxBY/dJHUBUBcVdE4ybQ0mhjUlsCPoSq8qItXIF3ry8unZQ1tJT3No8aJJGVL0iVwN8sJQzujLTfL3dHdPkx0QU05MYV10o0jiASMIqEksKroQ3qyENqEjsKuStVkVqEjsKrIrWrkrVyf68larJLWrkg1ydq5OuTtRqcJdgFeM0krhW9WfhQz7niPDwywduuvc0rYByn36kNsmfbp4U3gsSmKTW6nZ7RMhd5g+yY9LBE590DE3tW29rXp6gbM+WWw98go2QiKz6y/E7i1DInkli9mHIzM+1a+/WMMsXYJfGvutzPq0eXc0JBFiLK/1CDt1XB4RtQTZg5yK6bHtld0Tcmbw6EpndmwxtbFjg/EkFpgdc3x9Yy2PZ1eQgNKAeF7xYzulhJpbjuzBlNqdqCKw7aY04TBV/wDV6uKuwHw01SslEBxmh645BAyzhkJykoNC9/DTrKjnhXHounZAnXB7YaOSokajHCZUXKkFfGpHjdpf6uOUY1DGJ22ScOpf6r1cV3vYAO3SkcxRsISI04zETe2JmorRvfdUlel0pWR2OJo4nowIrTPRGCxljkw8byUAwmh2CBYy0mxUSeYy5GWR81GsJXk6V93M+riztB26Ax2LtIpKvdDGCFEoL6cmkSl6WxqNJ44n2cxe8w0pvHS5G2Yrkfmbf0SCNoZKnUJn3Fh0blaGUEaN/qfVxX2g7ete4ENZF1SubCbWwlrK05m/jJBF46FiT7QqLe2GmrSXhMw6TSgHhlkDWRk+E5CSycOhe3+49XFfaH4dTo5p2hOBCtySoRoiW8nTlMgLjqKAR5T4ugoN/azTyuwebNkFdBPDJ1TnHAjhwHIPnehfdzPq4r7AdvS5uZDSQ3Fn5CNIILTA01CgtIU2JDsgu9reHpsIYpTpuiLzFHh481GZ1z+A+aWx9PfO7dQvqvVxZ2A7ehSpLRlW5vJDqmTFIytScL1L4taGwpnS9KXiCk2oIn2Zn2hkOEeK8BmgJOm6R/VerivsB27b38NOzopmbo2NhDQn1JbIAxxvxs0GhS9TeG5ss1MwJxI1xBtjy9CdxdRGVcTkxEpQdA/qfVxb2F9u2ZvJxtRtjCwo9S991LiTJzIAhsC3U3Jb+12pl9FzLJClQVjHoGFhOC5kn4vfkaspeRtGH/cerivsB27JO+lx5Bj5oP4WrkSQ+St0FYLMbb1t47+2GpPkllrBidTx4/oyBiTyJFj56MjC/aZ9T6uLOwHbQhWBZCpFOXy1rBtqfCkJJc2favfdQlJQKE9N4KtIWsVe0jXuLlDSda763Bs2rmkqRgdUZtWNALTdSrnosKnf7PSypFLuBEGlRUoQbDPqfVxX2l9tZAd+WSxWPFxxDpKHBMkpZkdgRXUZgQhvJ8jupqNnb5qlQ+ys3XWti55PoGICxEhw820Xh5oLCTi9lJAVixlJq+NWgV0WO29Y+qMQtptx4gOCIyFPZd1LNLm8R7vNUN75Oc0oUeXm4yyacMimilZJ3QaHxgwv4ilukMNjLWJFjKS2vYVqN+p9XFvYDtONCQCNJzpQ8dZygpMFzyKyNtKMpuLpYlpmMgLR4XsMSHGTAipM0oUNhE+3Mp0WYO6V9N7b6VMqBaFwxyxuFl+KCh0SwTZlF7wn5lpvygyLaSuCZcHGIuFJdPIMb9o2rFkhE7tdG/U+rizsB2z54GQXHGkLI3dHwp3mzQz0PIkgkV7Y0c3y7VjljaqJIKTB2zR7AxNeNmfy1q0We++WaQgWHZ0hjO71J4ghYxRE14aHhryKkVXTLSFltJYG+PZTa/isd9R6uK+wN9wW21pZKNt77qkOTmplEcnl08Gw4ramqxCcpKDqml/amRFlhJBox+wxS3SvfdUqnFktQ9gJRlQi/wD3VexoXOluN+Aepk7/ABMTNOGp5toZQYPOWjHLz5wyGh/8/q4t7Je7WZ2qCMYGZu2SSaN0ZDxpPka0cx21R/RXqwoE+OGUYlGkyhAGQ6MrflrVTo/OThSWMKzhIEgUCeDWFabbBBsOzzj9sdbrTZLD7R/ILa99YwWMDDh2isoO+o9XFnZLgecuQAWLCMVgWk8+VHji+NrEGgAEsOjlJzNJRR9pCxt+lHCTLSTQWrSW8mRSNRJbxKHXShsu56UVj+3El3TIIE1v1EjfIVTJJUL+HpysmMaV6daBw9XVwrALg4bvD6pUloy5RKHGWhh8ojjCWhd0bmHSLPIkkq02AB95L1urwQ0lqVLhMVUcjBbUXSNiRoVNYmvdS7dQg2Ms+Y+DcbJkAaU8ArGW2z9ss6seM3Dm2z1cmC6zc1Y6SAa2R1cVmRXBoaE7IlcYy1u1L8aJhBKRSyO3DkmyVQgljU41a+/qfHGzSgxc32un02QwA37qlUtJj4CWp4eVzKxkM5e1SPhFYVBYd9B3YUb0ElU4Qg5GuIcCtgg2HaCBuzPvq5lMfGRuyw54Nj0eSxtJ0HpSVVnCAtS4wyKvLXXtQ/N5iTIrOoskXpl4NmV1phbfH20LQ3acSH45J0yqYDQ1GWoT7dA3ktpXRJTrJ2nCxAAtmiqSlrClqFXj5S0O6d7TbJDcLHOfVzK7pch0xjHhIEWh8acYk0ugbY6sgEI6YR8xpyAUdZY5JJZK9SLJLlvu0wwJIZHNbrTI9F1DndIkKRF9OQlHLx7EaaxEf0jiQKALQix4c3uBLonrMpQixIVFlab1beAWlU0KD4AajmmSGEQ2Jo5IepjsmahAmLi2Wa8hsznYk8tQHQYhFDdNixWUgKe5UdJajcLAOghsC3VlkwfkUDS8mwaa1GU4Etwj4A72v4qyki5xoganmmHSUKC0hSZwfcmKvc01XusXPeMVRB4FRZpoCAFOLzktX7nGy1y3d5xwvCKwreoziq5JLihPzKwHw1MgONm5kgCHk2ahlhNs4QVmcLG44Wtp58hlrAJuyu2H03PaB2t0wxSE56p7fkrCSuehykuMQ+yDq+FJVyddszQrHYpsTWRI9SVx0qRIseyATgnnpHMtOIlHFYtJ0bSXhKwsieOoqyuWEcbxyaM6OZXdLtzDCWsLOyVkVsA5x/GTmJzj/qNI7BG24pIAWgD8NTLCywjSCrEF9LiwNztZbjFHejkcqZqLySegu2TdmdbhFYdqhJXDfJHKiGOwUCqQL2CNEs4OkQrF2fpYrezoC5LGw1ucCHQifmXd5drSYi8Rkj/4FiLCZv8As9XKroJwEzNoGdDm8zckRfTlZIZznV8DYbdhMd/KvUbKQxBj2Jfs4fhqLxXfJ1onJylFnXHDO5UXAXthHeSyFhTMk0AnVNbMY7ntDKQzl9Lo6pmVOpc3WcKEDIjjiLDqQteU0tblE3lvTGvc81py0ectESXhdGjCgbl6szmoI9aDw0xoFWby96RF9OVjdnJdXwVgN2EwX8q9RsjkXUR3FV7GMQPhpiFYNsbqPOn7TGMJQX2UK5CphkRa16pVjEvjGHSxuXEZNLIC2S9oeK+O1ybE7sQgQJ2wiXrQt7Lh9r5NnVH2Sk4pVFOg9YYfGHHpwyFeGPq9OaTryQULhPk19mV2u7iwwp0C7slZFcgNjBjJsE2R/qe5G3xwv3oxivejGK96MYoowJwOmSOEsTK1cjnqEiByJTKGvZJHCWJlauRz1CRA5EplDXoHyNvSuHpLISbKWzELj4Ag7dORKroWzDqIRLbpLFpDeWsOcJ6YzMaViIgfhs5bF7UjdAuOKGdXXsvJWAomeuzWNDkFlWWTKyVgKy+6CAljrb5O25CchNbDiNv5Ri12dcnvLcPeK6rSlahalaYiocowP3jvde8d7qKSNbIKNKAeApuecaK/fG2XuW0POR1wQ2Dbqzd9AlirKIn2TZK9k2SghsC3VLPsmH/x/bLPsmH/AMf0H/8AcH0lcbb0sbc/JnQkVhg08lG+BihKSyNl0Xh5IZSEzW5zlWkSEoS6hCaxLh0jLCZZ1gbM7VbG6toMG9zGLBbJSnd5EhfEDmHMi4QUzKi8tQa8bLt7TYaL3Efys3fQI/kbcoSBfHW5IO5hNOskcU0x2Sz7Jh/8f2yz7Jh/8f6nUtWak8myHS9vkhUq8myHTO1zUlZTxI3FLMNkDkji8ulGM+QLiTvcpaJGre39/GWz5AsKnWaLmuYHR+UyKzmjlkELjj6RJEHooYHxgaGITugxlI7Ozdp5dWBsnbU/JpNCRytOx2aokod1IQ2BbZBS+G49d7+GprIVMxXN0IakaB1xWiV3dG50s+pMnLEN0UxaVwQjCO2o5LAt6SElDJbMKlXs26bhPnhGq9473XvHe69473XvHe69473XvHe69473TeoGsS9WbvoCHjIFi/Och00uk2OWVmz7Sh+mp8/cPZLPsmH/AMf2yz7Jh/8AH9B8/cPbIP3B2Yu+97JymEsmpZYSg7FILGZKpQSFSXhUYgpvRWLW5aTy1tOgju0uqd6S6WQg+ZSLQkkyuSOMwcKE3ogKjiqupWrJQlP0zWzA6KRUiMp6NNCSDGAPOn5SkIWBdccszpVsfPbFc+YSWM3Q5TZ1FInNI4h0csPHIM56McbhWJk9iY9/Kzd9Aj+RtzZ9pQ/TU+fuHsln2TD/AOP7ZZ9kw/8Aj+g+fuHtkH7g7MXfe9kn/Ptp37l7MNeizgGzbNl7andkiJQsxe9EHgUg0XD/AJCfdQxhLC9y5XI1MaiKdhD0XrHv1fQIVg2keT2pmCBkkuRzY/GUEZI2ZKdfK2DEzbyLDtvbfTnFGp4CoxSWnMWCmUcG35WCA1plbW9htff03vYNvGHJEly8bw2qGo+RY9V6e0cfTFT5/kFhyyZNQYtMUEtK0c3fQI/kbcvt41jFE3Yt6aaXLy3DIOyWfZMP/j+2WfZMP/j+g+fuHtyELyOTgGE0KlSUjKxMbzDrsk/59tO/cvZhr0WySSNK7F3sIMijyWSpGd7csaL0isleToNAS1k66Vi0lAUrWOE/NYo+kjxGww4smrGBFsvWOP1U3MCGlT+2orLcmMSOlWV3JyGRFJTL7sOOGdi6cvKTXBegShQp+tY2JHCzjjBqV17HSiNV7yHxlE3ZSYl10yslYCsmyoZYYFFLRZuykddU6El2JBqz4N32WFFAJBT0WCMTzRm8O9sSCS+EDacSBQAeN3NjOTxSUOVDgRVnupLEHJ7Vm4zeDwJMVuTeWggLwkU1JYg5Pas3GbweBJityby0EBeEinrlcILkZ3u4e6Z4M7Nqyn5hSSRGRCZWw2a4g4qDovDPZtdRmO3oYjcSrzj/AHcPdRaMr2AdDhXjkuyGw32R9FsmJgHMkUVc60U/MCORpU6t2xctaXhI9kdcDMLVyrofJAjjxBLevyCrRISG4na8MRD2E3He8RsFcbD9jX+14bGFywarFfOGEYcag0ggTG3hITlJQ9O/dUWOHLJnpiAEdnfHzG8Uox24NVL5nJIneHw4KMyhiDIJ5rZGaFSRcxyZtkRS9ySNZbSSOdyj1KkSMLi34pcLjRbF6BO5ku0QdoMfE8lIZB1CvutiUfMOG2SyshhAwxxa93LLCSHrF8McmbztGZuflTNiBl5Bq1ZzkEiNAhcEUKlVOK0Dclx+cS8Ha0wmt2I0OJ/OBn4YQApjl6trcfUpZ2NxnkUu6JPjVufrtcifIGaxyZukYNp19wMPW3X2SebcsOMQnlxaI/0DjPd4dHLC053cG1CBsS6ZhgCQyjJBqw2F43C332ZWd/LWWFtnlbNrRwXO5A2ZrLsWQmHc0r1JV9uR0XAC3LQOKXoVJSlpb1iwxGaiyO5MBjNJW1/DSjdwsNl8MAr2DZ9lKt3URaIJ44XpD7cXFjtonngTF4/EZKpBpyXIrVHK4cgykKORFujINsrOtKpYpBYAtaWp1MKkbRIW59LWuCVtLdVN8pvdreH1KWdry1AeW/GKq5KbqXNyZzKWYnLRnp57IYiJsyKzP5WI1ydCiWPDnPVTIwJWEnTH24/4d9HKz2JsacdsfkbLofCn2ftLJS16lc1Mi+JkTVcILF22u7iW0IsRtglx6zv1jSgHBccUx9wukw+wJhIW9M2FepSv9Qh+C9IKOyi1/FoHEFqQP2KmdzpDF3pRZjyXeOEtU+Y3ewRhMtpGfoHF19+i429upba27rc35vZwuGYkBBpyKXTy7Nixpb6AAJdunLrqMYI40AYW5Ze3j9XFt9wQfCVoDFqCAOglrboX+GKFvFVLm5K5Fr8UMaqj8fyFjv7by2NiQ5kazjEM4YnGxZoDrdSj9SsVpxJyOuaPF2RoxVHLtaDaesIS0tyOwIqPy/zJpxc7k1keIizxNEWamO3WsVloCIOWZMX6ltv9Xq4s/QIf1tT2pOhMmCKw7aGNQCQyTbu304xVodaXYcZ1Fe6N1bhctkFmr3iypspPm4NqTZfYjqT5Ljqmk8sZlVjH5uGDFquwyLGAvXitW+1XMDarqiQ0Y9t5NKJixpqyHKkkkdA5aYkRJuafGJTN5e4meRz56pvxBxgIMbMSC6JtStwdLLMhuAEUYC4220t7/Vxd2A7alrFaQt2P5ENYDQjhfl880VDSiWUpgrAqo3FccMo3ELIOluF0dgxfGg30oOGFhYx4dct5OInIuvc6pFSfCvDuVhVBa0ugjHHG/HOPELq3p4WxpaJRJ02u8OhTMjgDWZKXPYtt/r9XFvYDt2TNsGwL2h1JeUnW7bmue6qu+4jFCi6hL1Sg43IMiSJS0RP8CbuR0veWxuJaUuxd3eriztB8Ni1GUvIZDx46drX39eTeI3OoRWHbUWfT4ssWFF05Bk/s02Yrjo25F/AyDMi44mxzFxMSLau7vVxb2g7dspjpMhSQCSni68upeMyxZbZwaNRf9LiQNgIugY7F2Vt4Z7JrW3fwH17TsCSER5RKHPoX93q4u7AdvRkKImragswDJ03TLW3zdoxC4BPatRx+kxOG1m7oyfI1Jw4bGQRZu1168hsIJKU5SeSSQJy+hf8AH1cWB8QLfDpl8YPZVUSlieUpui9vFUN/65LNRf8ATYv3eXbZhJS4w34xjZw766lSUjKcHNbk5xZ2hOyJeld+l/VxWLwht8Om9t9SaHnsCqJy0iTE9GUEpzO6JzwqStNaXc1PEExSJPsWKykBKNMsya8FlhKDrLFhKAlzdnDJi5jYkkeTdS236+ri7tB8Oq9t9TCFq2hVCp0TJy9s2ZPP2jEr7z7ZpuxvARYqUmLEFCFYFpC/KMhurIzJ2FHrOTmnaE6/zPJytkZUzAk613x9XF3aDt0JbjznDY3PreLfv2uVvd/LgDCZbSereJvxOEQWn4VPJaokB8LiBETR60omKCLFARK8mBbW1O0p9Bf6ure0Hw0ZLDkMkCRJHuBnM72jfSKnUXBJ23F0huam0nsYSm/GKopQ1TeaqXlRCIaCJptX4VNZ6JoNi2NjTzgFhKDouFW9XFl9wQ/DSWoSHApfBXCNqI1ksleIIrDtkaOnsiyKSYiUItF35XkwOHnNRGEIokDVkkybouW2vr3O1bbGUTcfpr7b6t6uLt/hB26j7FED+BQgkUFAxZCbJDZ7aF2OnCLytHKU3XJpy2RgIUshyidHo4jjKbUeZO2sIVs/fZedHsVFEDLLASHUX1b1cX33BB21xt4tR7gbW9XXMkqj9KlvIHx/L/Dptf253DsNPLIs7ZMYmqlc3ksyHF8TEohgAEsOkMYSrPGQWhpCKVyiY3YcSkkjRIE7cXrOFW+Hq2rBYdrW3WMN8Vyy7F67ixoXWl+IkdrPcHeWo1JIXlvGiHIHyisQLnC7Ni9jarEkFpw6Kx3RN9OOUGJDYzIUgfQ2gUhkgGHHTOyBCGwLfwHGhHbrEl3D6tCNAClJwBBGosKieGC3GBXGBXGBXFBXGBXGBXGBXEDXFBauICuMCuMCuKCuKCuKCuIGuIGuIGnJja3anHEjKquLHD622CKeNdjJ/IEIfe/coojMbaZYeYmYNr5mZ9181NVCzElHV8ruaihSSdOlNzBMFV0uHE1xoIGwt9ACAq1b631vrfW+t9b637N9b9BaO24gq1vVsaUBlzyyw0BGXu5Muroy71yZdcoCroy71yZdckXV0Rd6sjBauSLrki65EuuSLqyIu1ciXVkQLX5IFckCrIgWrkgVyIK5IFcoG1coCjGwg2vZ5BehQ9oHXsWzVaGs4aKZkpFcgXauUDXKhrkw3qyMNquhDegJbAuNLYdcpVkdq5O1clauStXJWqyW1rXS773R2vXJ1ZJ+ok++uRrlK5KrpN9HEeChprlhCl9WxneMSoHgLD8P7VSo8FJiOHS/sK7PVlRYYrElWKsrLuYAu17B/tBW32JShL2Hk8ewA+C3/wCMH//EAD8RAAAEAwQGBwYEBQUAAAAAAAECAwQABREGEiExIkFRYXGAExSBkbHR4TIzQlKh8BAjYsEVJDSC0ENywMLg/9oACAEDAQE/Af8AkwMsaA7XIkPxGAItNZAZcIGR0ij3gMCFORSQh/Mkgs1O/voB7RMv1bIvsJuIgt+Up/2CH1nF2xelAKlHWH7hyJ2SRMq9IBd/0CHkwPK5qKg6hxprAQi2EvC91xINA/jt7Ya2ldIJikBqgOGPInZaZEl7oFFMsQ7wifvQeOjqlyEYsy9JMGp2K+zQ8cO2HCAoHEhsw5FWDwzNUqpfhi1TUHiZHyQYGDSpkHItY2aFG8yX9g/0GJiz6oqKezw1cipDiQahE2apTJoDpHMtAN97uRay016sp0RvYPnxifSwWC4k1Zhw5FQGmMLH/jrC9/qJ+G7jyLSGY9TWxyHAYtJLeqLVAKAbHbnyLSw4T5kLYfeE9kdoBl5QcgkGg8isqmBmKoKh28ItTLRC67L7Knj68izOf1ZmaK5fDu/8TromKUwCbEIXCVPShd/LHXv3bIc2LHo+lRUKYNg594Q9kjhp7wg+OHZFORRNcyfsjSEbXOiFumG94474SnjF1gunTfn4UGvGBswxe/0q2OoB+8PvCHdl3Lc12l7hjXhCqBkhoYKceRQo0yhnaBy1GpTVpt0vGAtwDgtxymA7w8hgjOUTHEDdGYdWWPbhs1w5sIoBb6JymDu9IeSVw094QQ35h3hyKpulEwoURDtiXW5cti3DUMG/On3ugk7lr0KOE6D8wekIWVQmWk1UpjgU2I02jsh7ZB22EaBep8uPkMKoHSGhwpx5FCHEg1DCGNqnbPADXg2G0vWELcouwuPU67wx+nrASmUzL3Klw2wcMeA4dgDD6wa6fuhA4DljQfL6w6lizUaKEEKfefIq0mq7X3ZxDw7ob24cFC6oAGAYJMZVMREXBOjEaZZbNXlBrFpvNJipeDfq++EPrIvGmIkqH6cfWDkEmA/gxaC7VKkGF4aRPbOqyk1D4gORgy5EU1jJDUoiHCGdr3jb4q/7sfrCtsW0wLddJY0peChqd8JyWWvygVA4gbIa4aqiag/tC1gnZNJIQNsoOO4cfOGkzVTL1WZkNd1GN3Z+ET+zxpea+TFMch8+RSXzN0kYARMbDIM/pEumj93g5QvlH+0M86DX9oAzNNG4e6UusoiETtBFBwYqA1Jq5E5VakJchcTTC/8AP6Qva16rhfpwhRUyg1MNf8sgS+x7x4S+UKBvwh02O2OKZ8BDPkTsvJWz0DKOT0AuqtBGJMm0Oe4zTqFcVDYh/bXERhzaRBIpuiEDXM9nANvZhD92LtUypviGvfyJ2ds0Z8a+rop69VQ+9cWitKmUOrsdEoYCIYV4eecCy6pJ758zGqHbh4cicns2VEoOX2BNm3j5ZxPrRi7Ho0dFMMA1CIbOH4PJ4u7RKgcdEuXrw5ESEE40CJTKmkuT6y8NUdRA1DsHf4ROZ2pMT4+zqDkTZsjuz9GmFRGHUvTs9QTYqZ7uzzh/MFHp+kU5E5VJ1Zie4n2jqCHD5rZ5LoW+moOY08fKHTo7o/SKDUR5E5JZ1SZjX2S/MMTK0JZal1Rlh8xt8GMJsR5E5JZszgOnWwSDPfFoLUgsHQNNEgYcfTkTpErkRGROtPMtRd/6vKJ9aM8xG6XRJ8ofvyJppicbpYaS9GRF6Z0FT/CX78Ym85UmJ6ny1BqDkUQWMia8WHj1R2a+oNf8PP8A/8QAMREAAQMCBQIEBQMFAAAAAAAAAQACAwQRBRMhMYASQSIyUYEQFCNxkTNh0EOxwODh/9oACAECAQE/Af8AJgZ5Mtpd6KjxHN0dwVrP0yjDldLuxVpaby+IKKtY8278E8QNojdRRCansFhs2mW7cJ9Exx6uCdfCZWWCpI8tgBVcwwvErfdMf1i44KzRiRvSVQSZbjE724LYlDb6jdwoJMxt+CpbdU8hgky3d9uC1fB1jqG4VHPnNvwWaPlJbdjwWrIcxqoZ8xv24LTj5SXr7FA34K1EOa2yoJv6Z3HBaWl+pmN9/wDSddwuNEDPEfVMxTWzgoqtkux4KuYHbp2GsOyNLLH5Cvn5Yv1GqPEGP/ZNcHbcFZKNj+yOFdBuwrMqIe10zFRs4EKOqZJseCpYDupsLY/UaI0s8XkKdiD4dJAo8Rjdvp901wdtwUIupaCOT/idhbmaxlfMTweYXCixdh82ijna/Y8FZKdkm4T8JYfLojDPD5TdDEjHpILKLEY5O/5QN/hLJlt6lS1gnGnBFzA7dS4bG/shhz4tWO9kameLVw0TMWYfNopIGu8cBVLViXQ78FJYI3auAU0UUerHa/lDrLri91TOc5oLt+Cc9BnPuTp6JuHRt7JrQNv5ZAlxCOM2THh4uOCddUvjsGDdVGYNZD7BNpXG1+6hZltDeCdbXCIWG/8AZUlDfxy7rMzKnTtwTqa0u+nFuqSiy9Xb/COlaxxcN+CJNlPUSTHoj/KpqUQj9+CcsojF3JsxrNOyhhEQsOCdRUtgF3JkL613U/QeijjEYsOCdXWiD7+igpDOcyT8IC3BOrrQzwt3VJQW8b9TwUqKwynLi/KpKEQ6nU8EybKWZ1Uelm3qqalEA04KPb1aFRxiMWH8PP8A/8QAXBAAAQIDAwQLCQoLBgYCAwEBAQIDAAQRBRIhEzFBUQYQFCAiMDJhcYGRI0JScHKhscHRFSQzYnN0gpKy4RY1QENQU6KzwtLTJTRgo8PwNmOTlMTxg+IHRFSggP/aAAgBAQAGPwL/APxm8H9L3dPjcKovmLjfJig/StU64AHKMVOc+NwwEJ5MXU/kueM8Z4zxnEZ4ziM4jOIziM4jlCOUIziOUI5QjlCOUIzxyo5UcqMTGeM8Z4zxnjPGeMDFCYzxdTF5WeOD4271/CDwqgQFJVAoqkcuOXHLjlxy45ccuOXHLjlRy45ccqOVHKjlRyo5UcowVzTwQkZ7xpBSmYLqhobFYuSEq85j0e2DkrPuJAwvAxdKUt84uwpT76Kd6K5oupnaPa7xglc7jo4RitnzlV0OCzpi+26p3yXEH0x74ZcVTE1aSrzpgptOQbrowW36axdtGTdaOtCgseqEhE2G1HQ7VP3RlJZYcSdKVV280ZorGaM0ZoxEZozRmjERgIzRyY5McmLqE8KK6awMI4Ip427ieRBCIH5FdmX03/BBqYvWJKqeqaJJ+6ELdf3I3gVJrT0Qr3RfcevdUXmJVFdZx9MXWkJSOYb3KvqCE61GkblsZlU2+ocEjkwULVuNk8+SHm4UOOWzNmYmHRQ0rQDTnzwDux4YUzCK2bPAr1OIoPNWC5MywfZ0ra4VPWOyAmzJwyE3WndFEJP00+sDpgqnWzNyqacMpygp5ScYDNtS7ksvwk8JPtjL2W+h5PxTj2cfdTni8c8dcDxtVMZNHJ1xdG0OPLjqglI0mCizEmbdzC7yax3VW4mFAHwT7YD82VzD2tRoOwRkpdAQgaEinECzrLAmJ1daCuA9sC0tlj5bb0Mo1eqNz2e2EDXpO+LpTkJv9a1gT5WuPc220resjMk8rDWg+qEzi2W3kODB1OCu0YwZjYxPuNKGKULw/aHsjc+yOXVMyya8NQ9Cx64DaXNzzH6t7DsOY8YQjPFXOVtdcDxtXa0i6NowONvLNBBk7JaVNP5qjkg+uDNbI31MME1QyjRAbk2hUd8cTxJefUEoGcmDZGx0liWCqOOYio6Ys2UaBeUtYUtxeu9o4ldnWgm80vtHOIMpP3nLIfzEaecfGGmETUqoLacF5KhpEFDgCknODCnrN95zB8HFH1fZAZmkmckQM5qtAA1KzpwhKUryE1pZWfQdPG9cDxumBxl105SYPJbHr1QHZgmTs86MxP8AvngIlk1VTlqxVxS56dVcaQMYqgFmxUHTnP3wJeVTRPnPTFmNg0xT9ril2bM4Kztr8FWgw5sHtvg8I5GuhWroOjbuqFQYU9Y3vSa5WHIJ9XVCbF2Vsl6WGCVnPTWlXfQJuznAtGnWOnjB43TSBxRfmFBDacSTAszYgjKrczujvcY3TafviaVwjf4QB68/FqmppV1tAqSYzutWSxn0A/fCZWVSENoFABtWYoZwQT1Hi29k0iPfMqRfpnu1wPVDdoIPdBwHBqUN4ZO0WkutHQoeiFW9sPdWtCcVN98E9HfCBJWndl7Q1Zkr6Ofm4seN0wOJy8+4EDMOcwMqsy9mg4pHNAlbPbCE6TpPTxZdcNEpFSYbZk13LKZXVXPQ6enRCZSTQENJ0Dbs5Xeinp4stOYpUKGH9i8yfesyuieYnFB682+3ZZtJafGNRyVdPPzwNjezJKqI4Ie0pGjpHPCZiXUFtLFUqSagjiMdcDo8bpgcRlH+FMKHc29ce6+yUdycoWmzhTo5oDbYokZgOM/BCxlcKoDqx5x1aYTJywzZzrO8s+4rgcGqfpcZLbKJdBMwytLZNcAM4PbDFqs5nUV6DpHbvtzTouuj4N0cpJ9nNCbKtlJesxSjdpq8JB9UIn7PWHGHBUEb/rhPR43TA35d5b5wQga493NlwC3iq+2g+v2RQcZuOW4U8/ghIz0Mbsmqqn5gXnCrEiuje2fMAi9gm7p048Y/ZzyQoOIOB16ImrDVW+w5lAPiqw9I8+/VZ9povtnMdKTrEG/efsZ5XUfYoeeG7Rs9d9hwVB346PEE5atoEhlulboqTU0AEOLszKJUzS+h0AEVzZiR+RTOxuXQ8JmVCytSgm4bqgnDGunV/ggwN9lF0VMLwbb1wrZFshJUt1V5ts+YkejjXLQnDRCB2nVDmy+2UhQr3Af71b6QUFcJPejPjr41ySSkoamSUpxw7qLw8/ELs+0EX2XBT7xBYcvv2S+cPjDm+MIROSirzSxUHfDo/wAb2RZazQPzJGGenBT/ABR8POfXb/kj4ec+u3/JDztmuPLLwAVlSk5tVEjiHLKtAEsuUrdNCKGoIhxFmZRSnqX1ukEmmbMAOO2QfLn94veWz5Ex++R/ggwN6ZucUAMyRrMHZPsjHcUHuDRzGnqig41FgSprJS6u6kHvtJ6s0IlZcXW0CgG+kwpN51SRjXNn42zdkTIOVSaE6OAbw9cImEclaQodfEOWbPDgrGB0pOsR+Ddu4yDpqlegVzKHNrgONmqTiCN6Oj/G+x2WH6+91ZRHs4pUjI2JMTzQSk5Zu/Q10YNq9MKff2NzaG0AqUpRWAAM5JyUG1Mhuejim7l+/mppoNe3+CbzASi4VqmS5gAGi5ybvNrgu7DrJykr3j80bgWNaUlSMDoxhCdm1l5JlxVMswcB51An6Q80NzsmoLZdSFJUNIO+bfs6z3bQWtd0oarVIpnwSqMNjM5/mf0otKbl7LenX5hdXW27wLZvE40SrXH/AAxOf5n9KHWrSsp+zktpBSp29wubFCdq3bQnl3GGmphSlH5VEZfY9YoRLnMZtQCiPJvop54bs/ZzZ+48pmeb5GfVjhroo9GMBxBqkioI2kyhSqZn3ORLt58c1dVes80bolLGYQycbrquH53E/Zj3C2TSqrNnlHgXzVCq5sefRoOvR/gIbxT7xohIqTG73V/2TLmgb1wGmxRKRQDjSGDSaf4DdM454MzNf3ua4aq6BoG/lUrRVRbSEqrm43dGmXeSvt4PriRexFGgjH4nB4kyj1EzCcWXPBV7NcHYTskqhxKrjCla/Brq8HeYQOj/ABvZK51VxmXYLqj9fz4QXrGaYsuWPI3Ti8RrIooDoIqOyDOz257Sl04ruJxCdOYIPmMbrk6odRg60rOk+sajxFpfM5j92YV85c9CdtuUmMW1BJUNd1itDzGlCNIwigh6zJtIU26gpx16D1GJmznf/wBd7gg6AsZu0HiLe+V/1F7y08uKhkvugaKhxIFeitekA6NqcQ8m8tlpTzesKQK4eiGQ6alhS2eoZvMYftJ7kMNqcP0RExs2tXuk7NOrCCe9GmnXhzAbT3B99S6S8yrTVIzdcMvzBvTDJLDh1lOY9lP8AEiBvPwWs5262n4RQ0kaIRIyibqE+c6+NLjholIqTBtRV/cUlyRTgnm4iUytMoUYefjZ9pQr3BSx0pxgsH8y+tI6DQ+vik23Ztd2SwxA75Axw5xGQmT7+lgEuV74aFe3eDo/xuiemJdpcy3yHFISVp6Dn212fJi7KzgPBGai03/ModnEWl8zmP3ZhXzlz0J22vI/8Y7drfLI/i4i3vlf9Re8tnyJj98janvmz32DCvnLnoTE+U/qwO1QiXa2P2fLPSHdMm44oXjwzX86nTXRH4pk/rj+tCmlWVJ0UCOWnT/80TMrbLORUt6+kX0qwu070n/ABgbeSlv74/wGx06Yy89RU89wlq1DVxwsezz77m+DQZ7n3w1Jq+FPDc8o8RJNBHJRW928a4x4aFJ7RFpWas8JtaD6Rxbeyeyq7mmF8JAwTzo69ENWjKGrTyQpO2P8bqsZt9Cp1CbymgcQNszErizIpN5Q+Ii79o04i0vmcx+7MK+cuehO215H/jHbtb5ZH8XEW98r/qL3ls+RMfvkbU982e+wYV85c9CYm7Nb5brK0p8qmHnj3LOD8m4tKkHPRRvA+kdW05OzSrrLSStR5hCLSs1V9heY0IzZ8/8AgAwNpUw8aIQKkw7slmKplpY3Wk+rjlPPKCUJFSTzRMW9aky0mSZPcQ7QdFKxfVPNkfFqr0RdS6tZ5kH1wp9tmYUEmmYe2AGpJ0p13hFPc9d3WF19UXkWY4EXVGuJxAzZoUHbMWimnhEeiBds5xSjmAVTHrhNoO2fdcaFwpvY+iEmZkHkBSbwxhKltPi8aZk+2EvuOLbQrFJWgivRri6mcaCs1FG76Yo3MNHoWIqnEcRalnozHK0+g5xbtlzY4LgwPgq0GHdhNsmiQohmuhQ0fSzj79sdH+N07ItjTolbWRQ6krppqMx8xzGEs2xYS5lzNflyaGmu4F+qNx2TZnuYhyoU8+o3k9FQk9iSdUFpo5WadxedOnmHNv1NbG5CXmJK6mi3FAGun84n0Q/Zz9lSgbfbW0opWmtFihp3aPcyz7Ml1t3y5V1xBNT0OjVDLdr2bKtSZV3VaFCoTzd1Po2m9kgZ/s4JoXb6f1BTya3s/Nt2h7rs5LLupU3wkqqBe8EniJ20NicuxOMTyr/dVUKMa0xUjXzx+KZP64/rQ6NlcmxLNhIyZaINTp79e1aVtzjNySmEvBty+k1vOJIwBrmGrampVgVccYcQkayUkCDI2u1kn8utd28lWBA8EnaVsp2DrS3Nr+Hl1YJc182Oo011EZGc2OTC3RnU0V3fMhXphMvbiBZdkghSm0mq1/756AaiRDdnyKbjDSbqR/gAwNprY9Z+MzMEXh8WG5JkAXQL1NJ0niaqwEHLzTVUit1Krx7BBRJMPP8APgke2CNj9m9z0EoWs+oR3R7cyTTSlP2cYabtacMxOTC+SkqIApTzwgWm+6XlgKUEYXeaLqmVueW4fVSKIkWj5XC9MZFiUZSitaBApWOA0gdCRFEoSOqMBtZol0KFU5OtKcxjhNpPUI7tJS6v/jTFxyTbpSmGEDKM3FJ5KmzdIj3q+63hTQYyFm2upLQN4DEY9RhW55sTFMQCoKr9aMtatmlxOGYEdOasIVaMq80VDGmNDFG5tKFanOD6YvMLSsfFNducZzXzMU6+FxiNltnYTUsU3yNQOCuqGbTa5ZF1xOpYz7Q6PG6aQIVMOmiECpiY2WzVSb6kN1zHnHQN/lHlBKRpJpBQ24Zl0d60PXmjJ7G7NomnKNVefARS37QyLZVW5eveZOEByZU5MrHh4J7IvSckyhWu4Ce0xQRUw5PP8KRkDVrwcPvx23pxIqW0FVOiFNToDbyMajkkRUb2VJzlNP2d4ZOyAJmerdoMUpPP7IM3sh4Kl4pQRQjeZObZbcSfCSDGVSwWlfEVh2QZjY5Prac0BVR5x7IGXbTOsprjyj5sYydsSbrLmm7j6aR7oSZG531Koo4Z2+MXKTAvNOJKVA6jE1sTnCQw+ujdfCHJPWNodHjeES1iS2K5lYKhXOAc3XDcjLpupQMw597lLUfSg6EZ1HoEbk2JyC3TXFRxIx1DAdcGc2Uzqmk1wbrfPYMBCUBgPLSOU6AoxdQKDm3rjrXw73ckdemEOPju8z3VVefN5tt7nFPPEvaDlQw/gog8mEOSB3XJnHqMGUKrj6cClWvmO8lmhTk3v2TtGYnVhCfOeiNzWC0GZVQxcWdFdNM3RG6CkOzh5TpHo1cQVrNEjOYVsfsllpwY333E5vJ9sDYspxWIHDT3qrl6FGQXuuWHJRerQdCoEnbMs6wrAXqYRekXkOcwOPFNbKJMUfY4ClDRjwVdUMWonlLSL/lDBUJ6PG9e0Uh+1nB71k8EV15h7d4X7TeS3qTXhHoEGzth8upprS733WcyYTPbKH1TExnUhJw6znPmjIWcyhlGpCacRLbGm67nlzVzVrV7ICE4AYDbfW9yeCMOcwiUT3yDcroIMGw51XvljXq1dUJnFNAOpNajeIe1Nj7MLsywW1TM2klBwwB9ce62yhanXTw9zg6dUKZmbIQ3LNmgAStNOvNHv6SdbxxuKCvTSA3llNKP6xBHorH9nzLT3kLB3qpmYN1tAqTCZGyVZOz6AuK6dBgS8sKkChWc5hISKcIV5+5bWRtBpLqfjCN02DMKlXkYoT3tYSzb8vupnNlAfX7YQ405cUvvF4GvEPWfMCrbqCkxO7EZzguIcKmwebBXtgf44dtSeNGWU3lf754y8hsdnHpdWKHBf4Q14Nkecw2y5sbm0JWoJKjlMKnP8F+RO2w+guBugCE6So0EPXWDLusXbyb14UVWmNBq1fkUw5ubc2QKB8Jfrer8UavyBuzNyqmFlAcWb9wAE6MDXNzQzaTFQ2+2lxNc9FCv6NIhy4qjrvckHnVDSlpuuvd0VtF10hKRnJj3E2Ioyr6jdy1Kj6I09MG0tmrheeUeQFH9o+yEyki2lppOZKRxLs/MGiG01MTOyRTfdnllN7XjU03i5OW5ZKT2GGJN3loTjDOyKzxQEgPff1Ql9o1SoVG8blb3CyeanxdcL2Z7GHFAheUdQM6a5zzp1xl8EzTfBeR6+gxQwUzsqy5XPeQIpuXJHW0SkwXLGn1tnQHE/wASaeiFbhWZtmuHCyg+qrGMhsnkFN/GTVJ+qYSmXmUodV+bd4CvPG655dBoAznogTk0VMWaCeD4Q5vXCZaVSENpzAbSbhrwrx/6O8urFQdBi9KEyr6cUlvNXogItJG7pAd+MaDp0dcDcjl16lS0vBW/ktkLdMk7Sp504K8xhDiMUqAI/wAcTXlM/vBFnfN0fka5C0Gw7LuYKSqFM2MwGUrNVYkk9aqn8itHy2vQr8gRNWvLJedbFEqqoGmo3SK9cJYYSEtoASlIzAD9GmJLYulN7MtXNX7oCE5hhCp20F3Gx2nmEFqVvSlmJVp6/rQGpFFXacJ1XKPFtWHKkhyZXj5I1wxZzf5psA016d85JvclwUh7Y5NrJW2at3s53jZXi4tvDm4MFCxUHAiE7IrCH9nOHFOgVzoPNqMItOQPAVnGlKtIO9yM60h1GpaawoyqnGZxfCS23wx16h1w1asywuakmgCELNeD5Nb0CWngJFxNEgK5HVAcaIUg4gjNtPFsDgXqn/4qb66rERu6zve02O+RAs7ZW0pTIwDwz/fAmZNYcbOkb1x1I7rLEOp9fmhjKGrsvVlX0c3mp/jd5uyrNlXJMLIaWpQqU6Ce6j0Q81shs+WYkSUX1tqF4cIU/Oq080Srdk2bKuyYaTklqUKlOivdR6IbTM2XKJZKhfIUME1x/PbW75+pqbrbaeUtWoRuuQTLWXLqxRlRVRHPVK/siN2Ws2xakonFws4KA6kp7bp54TaVmq4GZSTykK1Hamdii0NbkZReSoBV/kpOetNOraW4nOlJMPzlooaQtt24MkCBS6DpJ2jk7KkymuHCGb/rRKbHdkUpKsGYoTcqTdNcQQ4oaIcs/YfIKn1tEpcfUq4ylWqppeppxEDKWVJhNceEM3/W2lNbG5CXmJK6mi3FAGun84n0Q5OzVlyaWWUKcWbwNEpFTmeg2naCW0O5ZSKNAgUAGsnXtokZZozdpvfBy6PSaV6hpgTImJOQr+aoD/A56YQzs3lkOSblEibl9B5/ZRJz0rCJmWUFtOAKSpOYgw6uSSFTAQotpOYqpgNGmPxTJ/XH9aF7G9kjEtLqabUteTrUYAjG+oZjCxsLswzTCcBMvKuNqPxQSmo64ZbtWzZVuTKwHVpUKhOkjup9G/nlBtb8y86y2ww3ynFUV5hnJ0CA+y/IyA/Vco9ZKF5uYw3K7OZdK5Rw3RNMjz4YHookwiZllBbTiQpKhmIMVOaF2bsDlUPNtGjk298H1ZvXXVpjdG75N6mOSujHm+DT9qFbHNksvuO1U5h3q+j/ANkHRtVMOWXsElUOttGi5p7kdWbqzk6oyvulJa8ndHZ8F6+uEyuzyRybK1UTNMYp9dfMad7CJmWUFtOAKSpOYgw4qWAU8Em4DpVTCPxTJ/XH9aJdu3JGTZEwohGdVaUryXTr21zUyoIabSVKUcwAhY2GSjbckgkbpmdP+9XC56RlTaEk9T83dGP+Un0wiydnkpuJ1fJfT8GfT2gkdEVGb9DmJ22nAaMi6nrw9Agzs8eZCdKjDlsWyssS4JSw3Q4f70whmQDcxLN6ECvm9kUt+SWwPCHsMVlZgA6l8E+eMOJVJ0rJyox+jj9riG7fs/CaYIrTSIRNDC8MRz7aZkKOUIzfQ2nLPnE3mXUlKh0w5sdn1HcMyq6knNj8Gv1H7t6LJs3u06rDg40++F2vbbhmJhSryQrEJ2lImWEpdJvZVAoqsKfkPfdmfSKEDnToPPmgS7K8nN0rk1YV8k6fTFpOk4gv0+tTiNzTzaXG9SoNo7FXC5JYFTJxP3iDL1CJtHKbr6N44w5yVpunri0Njr5xRw+sGh9XHzloyarj7bdUKoDQk001hm1Ja1JVLT6AtIWhNaHXRkx+NpP6g/ow07bdoyr0kD3VCEipFPkh6f8AE015TX7wRZ3zdG3uKZ4UpZjd4I0Ein8Sh2bczYTHBkp9N9CBmBu3h/ENqf8Akf4EbTvkK9ETfzn+AbdmsyZuurZaQFeDeWsE9QxhElJoDbLYupSNA3lpfM5j92YV85c9CdpTq+SkEnqi0dms+Lzyncm1XvMP5aDaesucFWnk3ejUerPE3semzVyRdoPJVXDtB7dubkPzLqAl/wCTyKSR9Lk9BgNtgJSkUAGjiJ+fUKvJybaTqBqT20G1MWW+K5RBu8yhyT2wuRdNTKO3U+SrEeesKl3hebWClQ1gwLOstFxkEq1mp1nasS1WMHy4QT8mtBH2jtTyZP4Yyztymu6YVLskboQ8oujTjmPZtGUn2kPMqpVCxUYRQZtuxvLf9Le3PCWz3UVp4N8XvNEmmTI4CSlwDQuuNfTtI3Y0h3JLDiL4rdUNI/RE1O6UN4dJwhdu2gbodUpZ1mmAAhVp2zebsxlfBb100D1wlhkXUJFABtZGbbS4g6FCsJcZQZdac2SNB2QHrCn76QOSvCvVmge7UjlGyaBSB7MIyS1Ftd29ws1M2cQHZZaXEHMUmu9mJ9X5tskdOiJi15ipW+6QCrPQffxBbXmOELsefNWniS0abYlaYBvPj4O2yvKZCYZOC6Vqk6IalLxXk0BF5Wc02qnNHuRsV4TqjdW5qHNAeUlK5w8pz2byhzRu/Y7SUnUcK6nBKv5TDq7ZWQqYSpu+rwyoZ4qM3EptOyTkZpBKqDvo9xrbRkJ1FBeOZR9R2zEs6kEbsCbx8rg+rj5pPhKZH+YDFnNnPuVk9qQf8UTXlNfvBFnfN0bdtZTPSa7Mumm3Z1P1aP49qf8Akf4EbTvkK9ETfzn+Abdk/It/ac3tpfM5j92YV85c9Cdqdu59zu/YMOObFZ2XlpXLqCkupBN+6nH4NWimmPxtJ/UH9GPxtJ/UH9GJyeth1h0zQB7kVcqpJzpTr25z5H/SRxNo+W16Fbdr05F9n0uQ5OTSrjLSStSjoAhY2GybbUkgkbomNP8AvUArnj8bSf1B/Riy/wALZtmavOqyOSAF3FF6vARza9s2vsYnHLNmlZwjk89KEEecc0Van5WabFeCsDHp4APYqEI2b2Zk2VmmXYzelQJ6x0QiclFBbLiQpChpB27G8t/0t7amXQFIUKKBzEGFT+xC0XZAqNS3iU+nNzGsFQmpScATgk09N1GPSaQiz9nUhuMuZn28UZ+vDoUeiLycQf0OiX/XOhJ6BEtsalfxVZ6eFdzKVpMJYYFEJ31DFX5dN7wk8E+aEuWZOOtJbHBbqaeaHBkhNsIHBPKPthMra8suXfUaUGMXJaZQV+CTQ9h2kWW3eLr6r1EjQjXEtIaUNi906eJE6z/eGMQcc0ImAarHBV0jaUrGmT1/F3qpiYUEtpzkx7n2SS3JYhxR/wB1gMSiRepwl6Vb5x3wUKPYItJub4DqVIU26NCjer1R+CWyrBqtGnVHBOrHwT5oqOJykucnNoxSdBPPC7F2QJKZphV0LOnp2jFn2w0fgVKT20I9EMzjeKXW0rHWOOufrJhtPpPqiXsWWaenZ9DLYMvLJvKSLo5Wr0xlrXsCblpcZ18L+JCR54y9lOVUml9tWC09I9Yw/wATTXlNfvBFnfN0be7Zngylpt3QvQCafxpHbtzNuscKSkE3ELGYml0dvCO0pU1gidbAQfKQAP2k02pibmTdbbaWonqib+c/wDbsn5Fv7Tm9tL5nMfuzCvnLnoTtKaXyVAg9cWhsKnuC+h3KN17/AAofNdPRtLmZlQQ02CpSjmAELn5NtxtCHC3wxnpq25z5H/SRxM/IKNHlZNxI1gVB7KjamLUfNMmg3edR5I7YXPOihm3byfJTgPPWJzI1/N3qasoKxIbmpS4a08K8b3n2rHYTym3FlXNeUino2lWjaa7jKe0nUOeETsi4HGHBVKk7U/uul3JcGvh9754lA/XHKFNfBKzTbsby3/S3toftZ3JpcWEJ01/9aYDzKgpChUKGII2jl6ZXLN5KueumnVWJBuZrlBLNA18n9Dyck2eEEldOnCA69jMzPdF82ocX74aQvnIjdEiVyzwFAUmohRs6Y3Wzd5DijWvQYlk25KmkqUm6ObGAh13IOUrddw+6A4yoKQcxBrxF05oyIwkpoYU0HaXMFJPcuVSl3DNz7xU3NHBIrQZzCZp0mWsxs4Ad9AYlkhKRq389MVpRhzHpFImH/DmCK9CRBbAAnWxVhw69R5jDmxe2FUnJUlLd7OUp73q9HFGZs7gzzeKfjU0eyDY9q8C0WcKHvqeuDDi08qXUh0dRofMYk16UJLZ+iaccmz7RU4htDgcBaIBqARpB1xuaRTSuK1nFa1eEpWkxQ5ok9klkDJyswTlW0jDAi+OsGo54vJzH/EjrthWhLMyJpk0LSLwwx/NK088Ks607Sk3JddLyaUzGoxDIMNyElacmhhpN1CaVoB0sw07b1oSz0iL2UbbSLx4Jp+aTppp2twT9RQ3m3E8pCtYjckgqWtSXTgjKmiwOtSPtKjcdquS9mSqsHA1iojqKuy8OeE2bZyeCMVKPKWrWdpCkLyE8xi076jzeiBKbnlZ8JHwqlD+dv0RuvZe+1RGLMox8GF6FLOc00DHXD8naK2lrcdvjJEkUugaQNo5O1ZMJrhwRm/6MNW9Mz8mqeYAS25jgBXRkqaToj8bSf1B/Rh47LJtiZQQMkGgBQ6a8BG0p3Y3Py8vJXU0Q4kE10/m1emHJKatSTUy8hTaxdAqlQoczMbhsi0ZNpi8V3eVifKaMMuWvaUq7JhXdUISKlPN3IenaRaEo6ZS1Gfg30eg+o6IEsJeTn6fnagfxN+iEtbLJluTs/BSpeXzk+fzqV0Q3Z1noDbDQolIh1EkoJmChQbUcwVTA6dMfjaT+oP6ML2RIn5MWg4LqnMc1KZslTMNUfjaT+oP6MOJ2VTLUy+V8AtCgCaeSjfvs2jMIbm8oh2WflVEqbUkEd8Bga0I0iAwyxIz4/W8k9YK0Z+YQ3M7OZlKJRshQlWT5sMB01UdUIlpZIQ02kJSkZgBDklNJvsupKFp1gw4NiD7c3IKN4S7+Br5h1hQrqzRkH2ZKzk6XeUacwvrzc9IalZKY/tFl3dG6Hsco4c9/zU1AAUhxeyqdYmZcoohLQAIVXP8ABo0QuTnUBxlwUUlWYwZjYLP3GFKvKlpjFPoPRoNO+gt+5kkumF+8Mef4UeiEu7N5xG42zVMtLZj05u3hHohEtLJCGm0hKUjMAM0OJliEvFJuE6FUwj8bSf1B/RhldsT8m6ZepbzppepXktDUI/G0n9Qf0YdGyuaamXCoZMtClBp7xEKs+02w4yrRqOsajFzYhPodkak7nmtFer0XYDZs2SRXC/eGHP8ACn0Qm1tns0mYyZ7nKtfB9ebspjpV+iE2fypeXWE/RbFVeeEgauNU6rMkExO27O450hJ0XlZuwRSYYCVVreb4JhStj00pB0JWT6oWu0pbdMuknMK8HpTGQtVpyVd098I96vIX0HfEJHdUcJMBKlXnG+CdGaFySibzYqMdBTpFNtT7uK+9SNJj3e2RrOQPwbJ1dGqA00AlCcABxEyHTRK7iD1qES5SKZQrX+1tS+zayAUuJcAfu69B68xhq0mKUcTjQ1odI4pGy2yRdmpcgru6RrhM+xnOC0+CrSIm21CqTLufZh6WH5p85/jD8hs+RRi+t1ZSnqA9cIbVnSkD8j9zLQamFu3AurSUEUPSoR8BOfUb/nj3UkEuJavFFHAAcOgnb9zLQamFu3AurSUEUPSoR8BOfUb/AJ491JBLiWrxRRwAHDoJ8V5VqETloujhXXK9KlDjpp5JotacknpXhDKXhR1yriueubzbz3/LoWrwqY9sZayph2XcGapvD2x7yeTOsJPJreNPpYxkdksipg6VJr6D7YQ42+lF/MHOCfPFRtptZuu4pg0WkaCYfSg9xLVebkjaFlWX3afXhhiE9MLnNkSg6+8vKZM43TxUvK3qFx+t3WEpPtiRlzgUy7demm0/Zr3JeQU+yJ6wn0lKGnMoiuivBUPNxRbcFUnAiHbIfruOdNUeDieD7IKNaSItGQPelCvSOOYtDY8+tE3KKvhoKolfPqvDnjceyxp2RnkYLq2q6erlDopBcl31zC9CENLB/bAEI2YbJGjLybFNyy6s+GbDVprp6OKkvl1fZhDin5yqkg8tv+SPh5z67f8AJHw859dv+SEMI5KEhIrzb+0vmcx+7MD5dz1by0vmcx+7MD5dz1cTZnyA/wBTxTTE46KobaWojoEWlOISAFUI14qgcbKWQxTKPO3qacMPXDEr+rbSnsG/yU02lxB0KFYohvIKzgtnNF/Y5aCj8VxRH3Rd2QSYdYFKrSKecYRkXyuWc/5gw7RC5dhbboOahrQwvLm4ttpSFVzcER7j7Fu6OKN1Tqc3P/7jdTwvzis6s93orxdmWYkjQKc610i6NG3MyuZuYDnWCL48/Fi1Wzdekjfr8WJedV8IU0X0iLVlMczn7LnH5GeZbeR4LiAoeeMrIycuyvW20lJ8w4uS+XV9mGvIT6N41P7n3RlHcndv3KYE1zHVCHs15IVTp2pfYlua9l0hWWymbA97Tm17dpfM5j92YHy7nq3lpfM5j92YHy7nq3707LMqmHW0FSWk51nUMD6I/wCGJz/M/pRLW3MWW8iaaSA3J8K+oUV8Wuk97H/DE5/mf0oZkZqwJqVacVRTy79E85q2PTtS2xPc17dCArLZSlK3u9pza9ufs3c+R3Eq7eyl69wiM1BTNz7RQNjU4QDSvdP6US9g2jZDkm5MH864QQNd0tjVCrLs+XftCeQOE1LJvXfKP/uAg7GpwAmle6f0tr8E3mAlFwrVMlzAANFzk3ebXBd2HWTlJXvH5o3Asa0pKkYHRjCE7NrLyTLiqZZg4DzqBP0h5obnZNQWy6kKSoaQfErPpH6hZ7BE+6eT3MemBxslJq+DZCPNVXF0ViIvzMqi/wCEkXT5oempCbVKqz5VZzdkOolwubdHfgE3k+mAi0bPMq85ylIGPWMIbLT6avCqArgk9R4sTjzSjLSpADgHBvNprTt3gSn8yfNkseLclnReQtN0jpiesM0AZcqkddDFpsmt5W6P3g4xySmpy68ytTaxknTRSTQ5kx/fv8l7+SP79/kvfyR/fv8AJe/kj+/f5L38kf37/Je/kj+/f5L38kf37/Je/khudlTeZeQlxBzVSoVGffyXy6vswhtTE5VKQOQ3/PHwE59Rv+eGbLlmZoOvquJK0op10WdqV+dD7CoZ+TT6Nqzvkk+he3aXzOY/dmB8u56t5aXzOY/dmB8u56uJs75JPoXvLM+RT/qbdvfK/wCovbs3cXw5ZbSiugqWsV6s8CTkk0TnUo8patKlHSTttykxi2oJKhrusVoeY0oRpGEUEPWZNpCm3UFOOvQeoxM2c7/+u9wQdAWM3aD+km7BsJGXtmZ+DRoQPCVCUWxNGbmjitdxKR0AJAw6fyHdlqvIYa1q08wGcnmEXG0zLw8JDYp+0pJhMtJzFyYVmadF1XRqJ6D+RTTlpIZQWFICckFDlVz1J1b6Wbs5lta375Kna0ATTQCNeuGLYdbyS3b1UjNwVEYbbk9NqusNJK1qoTQDPmhNo2W5lZdRICqFObDMqh4gpBKSdI0dse5+y53dFmTSve87cSi4fBcugDr681btR+iJiTP51paO0RaEkr4TgK85EDjbStSvAQHBpzFQAz9HGGdn1XUDtJhLz1ZayWzhTvvviYkmEkS7TVxPmi7OMoc8pNYTPBbrK04AIIu06Dmh6ZsSbU+bwLTVcLumoMXNk1nGgzqSCj2iKlwsKFLwdFKV580ZRhQWk6Umu+K1ZgKxaU+46tTAKlXa1TecV7BvJ/ZA3XItFwpVrvcEebiyBDvgTCFYdIrFpKP/AD/OscYp9+z5RbiyVKUphBJJzkmkfi2T/wC3b9kfi2T/AO3b9kfi2T/7dv2R+LZP/t2/ZH4tk/8At2/ZH4tk/wDt2/ZH4tk/+3b9kJYYSENoASlKRQADMAN/JfLq+zDXkJ9G8lfnQ+wqGfk0+jas75JPoXt2l8zmP3ZgfLuereWl8zmP3ZgfLueribO+ST6F7yzPkU/6m3b3yv8AqL27J+Rb+05vGvI/8Y7drfLI/i/SL9rTHJZTUDWrQOsw5sttjh2naPdKnvWzmA6fRQaPyJ21NlLges5qm5mknAjwSNFNPha9EBiUbS02MyUAAeaHrSlWw3aMuguIcQKFV3Gh182qAqcN6Yl15FavCoKg9n5DaPltehW+DVosNvoBqEuoCxXrgNMpCUJwAGAG3aXzV37MS/lu/bPEu2VOjubgz6UnQR0RMbE7YPv+zVXK+E3o7PRT9EqZeFxD7i2T9I4eekDjH5teZttauwROWppeWEjoGPr4vh90mVchoevVCrZ2RXky6wLjBOiAywkJQkUAETiG8RcJVj0by46kKTqMLSuXDZcIJLXBxEB7Y7PKQUqvBK6jqwgqn5XdSL2dIrwelMCXtVlco4dJxT7YKJGZacUM4CsduderQlooH0+DC5teeZdKh5KcPTXbenfzihk2/KVG7DepMLJSFah9/FkwxJBQDaeD2tVpFqvVOGWBr8oOOLjhCUjEk5hBbQ6uZUP1Ca+c0Hni69uiXGtxuv2CqBN2e6h5lWZaDUcVJfLq+zDXkJ9G8ZdQKhuZSVdBSoemJWbZxQ4y2odadqRSg1KG0hXTdWfXt2l8zmP3ZgfLuereWl8zmP3ZgfLueribO+ST6F7yyZ9/BlaEICue8pPrG3bjrZqlTlQeYrXt2T8i39pzeNeR/wCMdu1vlkfxfpGyNiSOTNP5R2h71OH83ZAbQKJAoBtpVdy048brDI746+iN1Wxaxs69wksy4xT03Sn7Rjdlk2kbUQjFTL6SVHoqSexQOqN1sDJvt8F5o50K9h0bXuQ68fcwIrkQhNVKLJIANL1SulMc+Ebon7U9y0KxTLywvFA1KWCmp140j3Wl7QVaki2avIeBJp1lRp0Kwz5qw1a0pgF8pPgqGccTNzswQAlpYHOoigHWYXNPCgmXitHkgAV7a787EthCQqaTg8/gQimfPgKaTrwGMCamNkb6X+UUpClIr0XwKfRiZZt5aHTkV7ln20j4QJqEuJOAOrQc2eGrRtRzKzCluAqoE5lak0EKUM4BiZmbZeyziHrqTdSnC6PBA2nrRstzJTCVNgKoFZ1UzKqIkp+cVffdYQtaqAVJHNtTklZTW6LSmHGw02TRIABvLWdCU+c0GmMvaGyBxhzwJZBSgV6FIr1iG3rZd907IJCVL74decHpqD0w1aEmq8y8kLSeY7SyxakoG7xugpGbR+ZhFo2jacuttbgaAabQTUgnS0NUSs0+auOMNrUdZKQTtZTYzPS8vJ3BwHUgm9p/Nq9MTS7XtKWck0tlTqEChKRowaHphp3Y7PyzEjeXdQ4kXq3sfzatPPH42k/qD+jAa2SPNzE7eVVbeApo71PoguOGiUipMOt7E1JkbKZVdMysVUr/AHnoOsxlhslmspnpRd2v/UzdXVGV2ShNpWUVUy7eC01zavP0XoRMthQS4kKAUkpOOsHNt2XbqOC3PDcz3P3uPan6v6JtKYQo3pR4qOu7fp7IYtAcu7dcGpQz8ZOLczFF3H42ES60pu5QqXTr4r3Ms/u0+rAJTogW3shUp6aPCCF6Onbm2QOGhJx7OIvTks2tVKXinHtgu2S85LOH6Q9sUsyZE02k4IPCNPpQGNk0ipt3HFGHmMMyNlOEqcdCloIoQAPbEpJtZkMpr0nE+fbY2PyCqyEtwlnQrwleoQlhkBKECgA1cWYdeu13OF0V5KbsWq6RQ1Uesrx9HHSOweSXcbmLq3TrvKoOylYDFlsJSRncIqtXSrP/ALwgy9osoebOhaawiwpVZ9zLQuUQr49QnrCsOjPxUqxYzOWW26VKF5KcKfGIhtCs4SAezePWVOirTyaHm1HqMGzkSfupZiTVstVvCp0Uqoc4unpjc9nWNuCpop+bUaJ57pSgnzxI2uwgvSjaKzEypSLynCFXiRWunVgKAYDayexmRl5iTuDhuqAN7T+cT6Ifs5+ypQNvtraUUrTWixQ07tHuXIWZLqavFdXHEE49Dohlu0LMlESpcSHVJUKhFeER3Y6ObayexmRl5iTuDhuqAN7T+cT6Ifs5+ypQNvtraUUrTWixQ07tHuXIWZLqavFdXHEE49Dohlu0LMlESpcSHVJUKhFeER3Y6ObiJbZfsZS29NMJuFl00Bz45xr1iPxTJ/XH9aGWrZs6Vakiruq0KFQObup9G0G21BudYJUws5ucHmMJkbZsZyeUnBLrNcaaygLHojIzkp7k2Yr4WqqvrHgpzXa6TQHVjFqPzsuGZZ9fcKKQRdvK0JOGG0cnZUmU1w4Qzf8AWiX2TvWawJqWSEoSlxFzCufutdOuPxTJ/XH9aHhsslGJZAAyRaINTprw17TeyQM/2cE0Lt9P6gp5Nb2fm27Q912cll3Uqb4SVVAveCT+kbPQrMiXI/y3Fbx3L8JqzWzk086KD7Sq7bkmxwZe0W7xSM1Sm99oHt2mQvEXa9kuTtLl3cUOJKT0GLQklZm30nrIofRv1FrFdDdHPH4pk/rj+tDQ/wDysqaYQFVZZDQTK151JJJ9WukI3HdyF0XLnJu6KU301aIzsMuODpCcIfth3hPzTxqs57qPvrtWil0VAl1q60iohj5R37UL8kxN/OP4BtTHltfbEWd82b9G1aExTh1aTXm4W0/ZkwKoeQU+zsiYs5w/3Z7gjUF4+mu2x88R+7XEj82Z+wNu0fmznoiX8t37Z252TlfhnZd1COkpMKsQqCJ1p1ai2cCQdI9B1bV1QqN5IzLfwiJqqT9EwFDTj+iLTs2ZTeYm23QR5VFQ9satRR3G+QW1qzDUr1HjGm2T8JMJB5wAYlGqBPcUVAwGIrxF5WaPcDYyCt0m6t0eenthMzMJSud0r1dG8m3ruASpNeLyU02lxGpYrDOx6y2si3wA5k9BPCJpzCFTOx6fUtQNUtlRR26I/t2RLtLvCSMOfhDCDZ9kNOMzb3BcKu9Tpp0wZgOtuz0xQuXVA3B4Pt4x6bc5LaCs9UWlslc+FN5Pbwj6otOfVjeUhNdecnjrL2WPj3nVLbh8EpJ9R8xgPMkKQoVBGYjalhIcNmzkt5Zac1WlFf2iE/4ms59fJclzQ/QcTvLZSvPSaPa+kjbs4J/Vo/j2mvI/8Y7drfLI/i4l2zJ5N5p1NOg6COcRObH5o3txrBb5gqoI6Kjz760fm6/RDPyjv2tq0vmrv2YY+Ud+1C/JMTfzj+AbUx5bX2xFnfNm/RtWj5bXoVt2s8Pg1LZofr7bHzxH7tcSPzZn7A27R+bOeiJfy3ftneGeouWmialxk0qecHD0GMpZeyB+grRLgVTsvEHshMzsjSzaFn1AW43gU156J86evNDVpyJvMvJvJ/3zbdnyCPhHpqieynri6NH6IZfVmfQKUHNdjKyY9/sJJb+MNKfZH4PWz3O0WBdTXC+lP8Q4uypFWNXCbuupAhKBoAG/VMzSwhtOcmPcexApFnfnHaemAxKpqunCcPKO9n+HUUVh2cWp1zBKQSeqJ/ZM5yE3iOlw4ebaVZdmd1tFfBwxCPv5oVauyxBXMzHCDZJBTXSec+aEubH5xyXWgGl72iLxInWmx5ZP8Ubk2Qybku8KVu8/MY96zTdToUbp88VTiOI9zW8XJtV0j4oh5HJfUwtxdfDWKfdDswr87MKp1ADjlI2SgOMO4BmlVLpqHNrwprgvbEyuy7NXi2zOuhzXiE3Ddrqp1mKTk4maY79qUcSytSa4gKyafX0HNC7DsuXVIzyMXmH/AIQkab3ferV/iazdlkuCTITAv08FRHsp9KETLBvNuJCknWDttbIX8LPtBOTcXoSaUPnAV2wFoNQcQRBeeUEoSKknMBE5suSPeMt3JgnXduinVU9Y2mvI/wDGO3a3yyP4t8t4gquJKqJFSaaocSwMjMtqNWVnhXdCvbqO07ak8qjbYr5R0Ac5idt+ZFBNrCUc90m8e006t89IO8h5tTZ6FCkTmwu1O5zbTyltg99oUB2VGsGu1Noc+EfaW02kZySMewYnmhj5R37UFJ0xaWxScN2ZQ5eTXvrvBV6j0bRkM7zy0G6NCUqxUeatB0kRZ3zZv0bU3Zr/AAVv3C0TmUU1qnppjTp2np50jKlJQynwlnN7TzQJp8UXOLy1Pi5k9ufr22PniP3a4kfmzP2Bt2j82c9ES/lu/bO25asyhbiG+9bFT9w54E/ZbgcbOcaUnUoaDtTu6lAZVstoGtSs3tiTTMYFd9wD4q1EjzY7clZqKKl7KRl3eZef03PP+ibLtdPerpXoIMJPNA2WWBeE4zRS0ozmnfDnEbnWbs+2BfQcL3OOKsuVPCQjJ4aiVfdv1Ts8qiBo0nojKP1lrGQeTr++EyUgi40nfWiMxCTTzcXMrSaOPDII+nn81YM/OFKBMLLtThRIwEHY5sQQpbqzky+Bj9D2x7qW2cvPk3gM6Ue1XPvLs4y275SQYQJUrlS3ycnm7IS/YM5uhkcpq9drjqNRCm9lklwRyVIFK+qMkXFML/5icO2MrLLS4g6Umu8XNzKrrTYvKPNDtrTSf7PlTeSCPqJ9Zhxn9cUt+esSkurlFJWfpGvHPJn+GzIJVk0HN3Og+0a7dnbKpDgTaF3VEd9dxTXzg80JdGZQB7f8SvWZNirTyCg+3qhzYHbhpNytTLKOZxrm/wB5sO921WdabeUZV2g6wdcZDYpbA3NXgtzKeSObgrHYBAa2YWvel68JqWTQK1aEjtSYRZ1nNhthsYAf7z7Sdme6eSKZDJ/8so5V7rzbc1743RupYX8Hcu0rznXv/deynl2faNb2UazE66CmPOD2xkpW2JZbQzFxAvdfclemEzezO0nJ67mZTwUf76AITLSyQhpAupSkUAG/TPtLMraKKXX0c2ao5tBzwJdu2WDLjC+pF5dOts4/S64tO07UmVz9pqk3U5dzvRdzIT3ohj5R37W0m2JB9UlaaPzqNNM1aUNecHtjILtmXDGIvXApdOtv+KH7NfnFuT80UF6cdTfUbhrQJrgnUKxL2Xfym520t36UrTmx2pmzJ98zKX1tuJWlGSU2pFaFJvHHGMjY1ttusaN0oF+mjG4usItTZpPKn3EUo0K3OjHRzAJi6nADaW4jZJNpSpRISMphzfCwGLRt+YfbBvBLqFLFddC7Aaa2SzaUJFAAHAAB/wDLDr1pWs/aKVpuhDt7g458Vq2nJSZTeadSUKB0gwWLHt6blZStUNC9hXyXEjzR/wATzn+Z/VgSM/NuTzoUo5ZytcdGJV6YLbgCknAg5jHulsTnHbMfJqUoqUHqqOzEaKRcateUKBgCpArT/on0wLS2YT7lpKRyGyLqB583MKc9YupwA2nLSmKFfJaR4a9A9vNDtrWvU2naCsq9XOBoHrPZo/RImBX3q4HTTPd0xKTg75oV6RhtfhTsUqh9BvrbRnr4SfWITJz6ktWknAozX6aR7OJl2gjgNopWnxK+bfVfN+YVyGxnMe7myJS0S5oW2AcCOjVAZZSEoTmA39pk40vJqRmx4uWsaWdC8jeW4E48I4AdMMSaFbksZpKUhOiiftnzQGZFHDpQuq5Z6+IuuAEc8ELl8io43meB90ZTY7aC0U0LJSe1Psgbta3YwNN2/wCdOPbARazRlHCK1J4Me8Zltw0rQKx7Ia2KWBUy6llLrnelSc+OpMCzJTGnCWvwlaTFnWIyKqcXlKfsiG5ZHJbQlI6hxyrQtDgSM+k0c0C/n7FjHmNYvJxB2pHYfZBDjqVkukY3Sf5RUmEtpzJFP8TIeaXue0Zc3peYTnSdR5oSi38iZpOBUwolKuehSKfltpfNXfswx8o79r8qOTAKtAJpH4RbMHGnlsn3pLNVLTY18ICp6ufUB+iZlhsVWptVBzwZUmrjLiqima9t+7mxujNopN8pGAX0aj6Y9xNlydzTacMooUHXqgLbNUnMRv5g3yptoLwrmomnp3qrPsS6/aWYIryY/CHZZw5tVClk8lPV6ooOItEoNOVVOvhcRfWQEjSYLSV7pmPAa185hKbMa3HIq5RBoKHWvP2QUugPSkoVLUSOCqmCc/PjF1IoONydpS7bg10oe2E2PsMSt2aVebXwryQVYUTzwxLuAKm0o4a/KNSIVEq842oyDGZWjgCv2uP3Dard9GdJGCknWDGS2LWz3DvWphOCR2LHYkQZe17bbaaP/wDOnHzJb9MEyKSuYVgp5zl01cw/2fEKpiYSlbaxRSVCoI5xG5pFpDLQzIbSEp7B/gUxN2YSMhM1IA18oeau898pyc0OS8nldesQmUnxumy7xoc4pzHOD0xl7OXwxymlYLT1evfWpMUwTlvtjbqc0GxNiiS88eCtxGjo9sGbe7pOuYqUrGnMOKtJQpk03h9Ko3uUfUlCdajSOHMh5fgscP7oWzsXkSVAYFfCNa+CIU5swm1y7XeMppn5wMIDkwgzj479/EfVzemHpy6MwbQjMCVaMIVaRHDm11+inAevjS88oJQkVJOYR+DWwtKl5SqHHUjE9Goc8JmZgJXaKhwl+DzJ2nppeZtBV2RPW3OElKlXEdJxV6vG6Ys3ZJL8kKDbmrD7qwl5vFKgCOveZN0BSToMN2vsRc3NMtqKrhOHVHuRszlylQ/OJFCOkaR0QJuznUutHSneWq6MD3Wv/UG0p+YUENpFSow5Ylg1akUcp3w8dcUYF58jhuaTtiQn1KSsitbuEYTSBhXGOBNMn6YgobcQpQzgKEUvJ7Y5Q7Y4bqB0qEd1mGk9KxFpKffaS2u8Qu9n4UcOav8AyaSqLsqxMOmtBgAPTC5mxLNKlJNKcJf2RAVdMs1zpS2PPwoExsgtIrxqUiqvTmjKFtb6wa1dX6hSLkshLadSRTbkNjEsunCx8tWvoEMyDHwbKEoHUOMM1aC8e9bTiomNzyKTK2PrOanP4R5oLMgmriuW4rlHbVKM/CzS0tADPrMS7Tgo65V1fSr7vG6YfYR8IEX09I9sBhWDsqcmRzd7vtzWoyl1OiucdBjduwyaUKY5MmijzVzHrj3I2USa8peuXkDhdY09UFdnPJcpygDiOkbVsLCaHh/vIM5PrCEDz9EVSVy9lo6q+0+aBKSSbqB595em2UOEaVJBgjcyU18HCKIQts1rVK/bG6JeZmEHUDBcE46ivNF/3QdpdApd++OHOu4nHg54q9NPnooPbE5ITeUU2zyMaHBUXFSoWM/CJi9KyTCVDTkxWLraQkc2+XNPmjbaSpR5hE7sqmuQgkp8tebsTxZmrSeS02PC9Ue5WwthVSaZW7eWehOjrj3V2au7odV+avV+sqEy8skIbSKJSnADeStisC8xJkBerwln1QAM3jdMDoh2yikJYngVIOjWPPhxGStBlLo0VGI6DCp7YlOKZWTXJrUR2KHrgN7JpcvSxNKkehY9cWhaj4VdfvZFvnUuueBbuyQ3JIfBNJMJl5dIQ2kUAHG2klYAKapFOZXE+5SFUem1Up8ROeGWLtHXe6uVz1V93E3rVfCFHMgYqPVG4dikmvhd+U3l05hmEItHZZNuKJSCW61VjnGoRkbJYS0DnPfHpOfev2o9maRUc50Dtid2Uzo7o+SlBPTVRgXc3jeEMWuySl+UWCCNRMbol1Bd1RbURrTxJbdAUk5wYtKznrzCW7yk3CkUN7QNUKf2L2hf+JW4SPsxkNkcgp0DvrhT5xhAbncpKOUxyg4I6xF6z5hp7yFA8Xarh+MMRTv+JwqZCT7ClB09Kt/ftKZba5iceyA3YjKppxVaE8FOHngLlgqSY0EdyT28owZ/ZVMuTs0s3lAGiPb6I3PZ7SGmxoSN/LbEbPN551YUtI8w9cNWY1mabCTznSYHjdMCFy7wq2sFKhzGF7FZlXAf4bZ0V0do4q0Gl99lR6DtXVCogiblwCe+QSk4dEZWwJxTJGhz+ZPsgGVeM00hOhQX5lYwWrcs2h0YKbPnrFJxp5g9AUPNFWJ5rVRZufapFZd1C/JUDvrTyfKqqv1+IcWs0df7k2Bnxz9ghM+U93nO6EnPd0D19e1efWlA1qNI98TzVRhRBvn9msUkW3pnnAujzxkLCs8JSeSpQUuoOOfACAu0JkyjWIIvXcPJRGWtV92YUdFbo9sJRZ8q2gpzKpVXaceJdtGZwbaSVGJnZlaiNJyZIwvHV5IhUDxu4wNpFvyZuTMlwifi/dDM6r4a6A4PjcTwK3nCb2GGLW+uupChziKvyDNfipu+iKyxel/JVUeeCqzbRI1BaaecGKyM8Vj4kwr+KO6sqfCfioXX6uMDd1lXk1/UOJi7aVlKSKVqm8PMRAS9Z6xr7p90TtpTTLpE0okAEYY1i6WZmmu6n+aLpTMdNwe2BhMDpQPbFEJfV0IHtgJRLzGemN32wcjIuq6Vge2AZSzOUARVyvoENhMsTucGjLSVK6SYSmWYLDYACBkkJpTRwsY9+T5aHy1PMiEKti0yopGhJV6TF+ZW++fjKoPNBFlyyGyrOc57TFE4DjGNiFjVU6pQywTrPJHthiy2czScTrVpPbCoHjdMCm0WnRVChQiNxqJ9zZzXmGo9UVHEWdNI/PZKvaU8bwhWKTMu055SAYtFh6XaXk1fBqRWnCzxeVZ8vXyBFDZ7HUmkUTZ7H1Y4MhL/APTEdykJYf8AxJjuMuynTghIhbzCUiZe7m1SgxOnqhVsTI7vOYiuhAzduf8AIXbSe5QFEDWo5od2ZWuKvP1yNc/xlbSuiB43TA21NADdLdVMk6/vhVh2nVM7LYcLvk/dxFm2i3dC0k8I/FIMBY0ivHWvMOjglZAOvhnfVOaNx3r1mSngnC6M/wBYwG2xRKRQD8gvHNAs2TVdsyRPD58cT6hCWGEhLaBRIGgbSujxvGB0bxrZXYCAH2l3naZzz+2ETzOCsziPBVpG/wB2E0VLOJUOvCJOd8NpNekYcda1e9VT9o773Nlf71OAo6EaYykwPfszRbnMNCf96fyFOxCwKqnH6BwpzivejnhLCsZtzhPL1nV1baujxvjeXVYiBON312XOKN7UPvEInJVV5pwXknfTrCBVWSKhX4uMbkUKKlnCnqVwuOtZSeTez9CjvVzs2q602KkwLbnGiiSkFdzScyjoHrP5DTlTrvwSPWYOyu2uHOzHDQFDFF7T07xXR43xvXLNnk1acHYdYhywbbUTZjmLS9FTpHrEBacQd6UKzEUMWjsbUClpVSgK+IfYeOtQvHh3+TzXjvUbDrEVVtpQLpGYq09SYbsuRHAbGJ0qOkn8gVPTGKszaPCVB2W7IqKl0q7kkjldWpPp3qujxvjfGSmhRWdtelKoOx3ZXe3KT3J44gdfg+iAtBqk4gjeyWyJNQ29S/z04KvNAUnMceNtGYcHAcc4KtHKO8MrKq9/viiAM4Gkx7rzw9/zQqa96n79P5AZ+0VUHep0qOoR7vW9VFmoPBQMxp3o9ZhLLKQltIokDMBvVdHjfG/3PNpF8VuL0pMfg3sjKlSJ+DdPe11fFhL7CgptQqCNO8XM45WU7qmg0aRDCq1dYAZc6U/dxs7JSFMmwEVKdKjUnbXaM4c3JTpUrUIXsx2QAqQF9xQoYGnqH5AZ2dNVZkNjOox7vbIDk7OCu5tjTTQPXCWGEhLaBRKRmA3xMV8bw6OIMnPpxHIcHKSY9y7YCn7KWeAoZulPrEJnJFYcaXmI21MuCqVAgjpiY2MTZO55ldGydfeHrzcYYtN1ZzrGHWdpy0J5YQy0KqJjdD1W7IllZtSdXlGEy7CQltAoAOPL7vCfUDkkazA2R7KL6Wr1UNHMoDVqEBlhIShOAAzb89EY6/G8OjiTJWg2HGlaDG6bDBmbMXnT4PT7YSqWWA/dqponhJ22dlFnVy8qQHKeDoV1GG59PwyeA8nUse3izFpOA8pxOimGMLnJ1YbZbFVKMe51mKLNksUKifSefUIRZtnputIHWTrPHVMe4WxRO6J1RuZQYgH4us+aN0bMlbpdK8olpzhFJ5z6s0UGbiFdEdfjdxFYHFXVioOiDbGxNZl5yt+4DQE83sgWJswRkZmt0O0pj8YeuA60QpBzEQplwVSoUIhUm8lSrOmu/wDi66a0wHWjeQoVBHFGmqLStTZDeYYSoUvimauAECzbOSqXstk1UT9pXPqEJkLNQEpHKOlR1njg5POpRXkgnE9Ahuwtjt5qVIC33eSMdBPqjKMjKTZHCeVn6tXFGuqOvxvDo4y5PI4Y5LicFjrgvyDu6bMBJuHEU6NHTCUKO55gm7cXr5jBk1G6+nhMr1K9hj8CtkiVIWk0ZUrRzdGo8UXJ5YL5HAZTylf71x7pWkchZSDQDvehI0nWYEtJoCECmbTTDHjTMzjiWmk51KNBHudsQbU9ML4KXbv2U6YFs7MplSl5w0Dj1nR0CLjQoOLI5opz+N0wOja4PF0hZQMg+rEKRmvaDSAxM1nbNHfHEDrziGnBMJlLUA7kVn9lUe4GzEKySfg3sVEDp0pgTUk4l1pWZSTUb4zU+6hpod8s0g2VsOZU46rAPFNfqp9vZHuzs0cL0wo3sle+0fVAZYSENpFAlIoBxhmJ51LTY0qNI9z9jLCpp8m6FkcGvMM580C0NlT6peXrW4c9PipzCMnZjISrS4cVnr41XRHX43cYB0Ui63yYoONuqxEF0t5F89+3h5o3JJLE5JaicR0DR1QsWSp5lbfLbOIP0YDeyCTN/SWsD03Ve2BWYLSjocSRHDnkZ6YBR9UXZcPvn4qKD9qkGX2KyF0eHQuEeoQJ3ZdOFAz3K31fyiLllshK++cVis9fF33CEp1mCFTAedHeM8Lz5vPBY2LyKkJzFw8IjrzRu3ZdPKKvASbxp05h1RSzZdKFaV51Hr489EEnXHxPG4YDSc0XU/kN2bbCufT254MzKTDjTx8Pug8+MByXbbnEDOEGh7MI3PsisVVeZxxHprF5clkVVxy6Mp7YSizZmXSjMEghHmwi82oKHMeIvTTzbY+MoCBLicbUs+Dws3RCmLOYcmVJNArkpPRp80f2HZwQ0pJoSk4HyjQRf2VT6hgaJvXiD6ICVt7pXUG87rEBmVQltsZkpFB+QmuqLvexQeNvgGkHGoiqVYRy45ccvGOXHLjlxQqgi9HLjBccvzxy45ccuKXsY5ccvGOXGK45cFDpChzx3aVaHOjg+iL0upbR5jUeeLln2mtvRpGHUYUiVtS94PdViBWaCulaT6RFEcIg5wW8e2LvC6e5Ryl/Wagbpnsjh+sH8Ig7ptaqFcqq3D5o9/z6l+Sn2xmU6vWtXspGUl2Wkq1hOMYLil+MFxy45ccuMVwAFRy45ccuOXHLjlxy45cYrjlxy4xXGfARVCqCKLNfG1UxcbwTF1ED9K1MYYIggaoPT428kBwdMXU7Q/St04IEXUweiOvxvD9Lnojr8bw6P0ueiD0+N4dH6XMdfjeH6XMHp8bw/S5g9PjeHR+lzBrF1PjdBOqL/ej8l98PIR5ShFDMXj8UExlpdt1wVoMKR71k1qzxlGrPUHDmSawkIkbzZ1JVhAvyVK8ysIJ9zb6qgVAUU+aCibs1IPlqT6RHvuRcQnWhYV7ISXFutE6FtnDsrHvKdZVzXqHsMVTiPyU9EZNvAaYup8bdGjSKrOEZMGKBVI4So5UcqOVGCo5UcqOVHKjlRgqMFRyowVHKjlRlJh1KE6yYDeULq1ZruaFN2bK3G9Cle3NCfdCdyQ0hKvZhHvp5bx6aRfSwgn42MBMshtHQkRnEcqOVHKghbmWeT3jWPaYyVg2deTmrky5580BU23KicUbxSWmhTHNgOuCoNsnVdWkRWYkXFJ1t8P7NYpLTb0quuPCVTsjLrRu6V/WBN4fWR64CLSQ5Lq0qHCT7YvWZONu8wVj2Z45WMYKjlRyo5cYKjBUcqMVRyo5UcuOXGCo5UcqKleEFNagR3Ixw8/jcyYzwPyANPOhbpNLiMYyex6XyTR4N9WcdZwgvbIZxTqlUJSnm5/ugOMsIvjMoip4gsCr81+rbx7Y3ROOmRkDiE5jToz9sXsilx08paxWvVFxsBKRoG8u2nLpWrwxgv6wxhVr7Eni5Lp4SkHFV3URmUI3JbMm01aCa4Dg3tZSRj1GDNbG5pTS84Q56lDGALVY3TKppwlcPAfGGPbF2dO43sB3Tk4/G9tIDrKgtBzFJqOOuIwQIITBrr8bldOiC85nMDo45Td7LPjvG8YCnPeMirRiDAfdRl3hpcx80XUig4gvPKCUJxJMe4uxJspaI4UwfboETUtOry7zaaqqODeGkcT7vbGxkp5rhqSjC9zjn9Me51qEC0WsMcL4GmmvXFDmhRLIl31Y5RrDHozRumwnVTckk1UhOIpzo9kCTt1JlJmtCr83X0iA60QpBzEcXci4mDB6fG5wtG0OjjPfrgCzyUDOYydmo3PIVxWrSOnTAcyYceHfqHFKm51YbaTpMKRLXmLMbNDXv6+uBLySAkaTpPTFoXU0wOPWOKTsy2P8AAW2q88E6D4fthM8jgvJ4LqNSvv21F5oNTKvzzYoqvPrgTFnOGbs4coUqOsd71QJeu55z9UvT5J0+njDCunxu154HRxV9ZoBpMe4extJcnSSkquk3eqBauyJRmJs4lJPB64CECiRmA4pU1MqCW0CpJi8+QixmFaK4/fCZSUQENIzAbVpK0XfXxSmXgFIUKEHSDBlySLMnM2qhzfVOEVG3Q5oNo2F71nM9382r2QLF2aNLUkZnNIH8QhM5JLDjKxUKHFq6fG8OjiTMzarqBAlmKytloPCOuLkomrh5Th5SuLVMPqCW0CpJhUpRTFjsec88IkpJIQ0gYDbtO9W4CfTxbriUVmZYFxs6eeBKOn31J0bXXV3p3pkrUbvp0HvknWDBnLIKpiySaqGjoUNB54vSSrswBw2Tyh93FK6fG8OIys2auqwQ2M5hFt2sVtoxozXCmikBpoUSOMTsasrhSoVV9Y+L6oTKS2YZzpJ3looUi6Be6+FxdDBkluAS87yRjQJWeDWvPvi24ApKsCDH4S7DStIQbymkZ0eTrGsQJCdAYtEDk6F86fZxJ8bw6N/fPDmV/BtwnZPslvKWqiksr9mrmig4wWLZR/tCZ4KeYHDtij3CnHcXVere2il3TVSa6r3GNbIGyUvyxu1GonDzxK2jUKLjSb1PC0+ffnZDsa7lOI4am04XiNKdRj3FtzudpIwBOGUp/FxCunxvDo3xVyppQ7m3DeyPZEKzGdtJ59JHGuT72cYIT4StAhezC2aqfdJySVDNz+zfWiV5jyanGleMm7NBopxs3TzjERMWUpYUph28BzL+/iPduwhctFrhEJwv0/ij3ItkhFpIwGjKU9e/V43cYFNW9XPTGN0YJ1wdluyH4NRqw0c3N1DjanNAZbWfcyUONNPP1wGmhRCRQDfWgFOlawTwSM1Tr42bsevcpi+EU5+Gkerifwq2NpuzjZvOpRp+MOfXGRfIFoMgZVOv4w3yvG8OjeKmpk3W0DGFWraiFN2aye5oV33+9cBtAokYADjRY9nf3yawwzhP3w0xMf3lQq4efV1b+03L95wuKqDnAvcbZ1tAhDa8kVE8yqK83FDZnsYqhF6ryE5kk/wnTCLRlqBeZxGlKtXs3qvG8OjeJsWzzSzUK7q4NJEIkpYUbbFBxq5p80QgVMPbLLQuqZbUQwK1ofu4i03q1q5q+NxsjaOlt1SO0V9US84nM60hfaOJUw+kKbWClQOkGN0Nj+yZk5hmuavKTCJuWUFtOJCkqGkHeK8buEDb9y7NBVPTPBATnCTAS5jMucJw8+rjpfYjIC85MEFfqEM2dLgBLaQDTSdJ4i1S2qvC/iPGuOFNSy4hfq9cSLhzhu59U04pdnTaa6UHUrRCtg1tcFaScidSs9z2bxXjeT0bTloTRo22msP7KrVFbyqMc1OOdnXuS2kqh7ZbOtkPOKIRU1HSI4ZA6Yq/MspprWIGVnWBXNwxCvfqDdz0CvZBdE4Low5KvZCpjdHAQoJPBOc80ZRt808kwcrNCo0UNYnXN03cu5UEpOMcGea1YmkZJqcYUvUHExVtaT0Hip9tOfIk9mMBmuLTzie3H18WjZfZuEzLFJdp4IzK6oTPpF15JuOo1K+/bV43htS+xFit0m87d/3oENyEqKNtig4q++tKE61GkXXJ5oq1IN70RckWH3VaKgJSf99ED3KspV06aKVDOxyawdfuKyKAE4nNDUru8MNJzoS4qg+rAXaFqKUvySfSY7rNvmuelBDYcDqsmKculemLqpdR58oqLu5P21e2MjuNu4YomSQKGumC2ZYFKhSlTE8mbYqmXXRCbxoMTzwo5FSCo14KzGWbfmE81QfVAmd2OBFSbiUhI6qZoyljWotLWhC1K4PRHvWZDtDhwgftRedswKCRjwa1OvgmG0W1Zq2rxulYJpXoIhImFrYWvCi0+uMmxNtFeq8IqnEbc8wM6pZ0fsmJxGp8fZ4tUu+kKbWClSTpBj3OeUfc6dwB0UJ4J6s22rxvCHrRV+bSSOmHdkVoKyj8wTcV8U6eI/tKZbbOqtT2CFIsZlyYdGYqFEn1wn3PlzJMKHKpd86seyFI2R2gpS1Y0SSun1ovTOVmFfHVQfs0gbik2UU03BXthcy5g22kqPVExs0m08AEpaTqV9w4q0x8cHznf3XkJUOcVjKTUm0VjSBQ+aMpKqcl3NaTX0wV2NaZPgipT5sRAFpSu62/Cu186IyNqMOyq9NcYdbkptpSltKoK45tRi0Wsb15tX2uMM00PfMpVxPk98IbS+qs1Ldyc14ck9Y2lHxvCGdiDCylFLzlB32enZCJZkUQgBIHRvTMTzqGmx3yzSFMWRWZmAMMCE1gKV7yk3KfEw+1GWtNbkwutSL1B7YydnS7bQ5k49u9TYjOMxNmlB4MMSAACgmq6eEc/FWmU1reSDXXU8YfdOXbcGtQ9cGW2Gtu30K4ah8GOgxMzFgKBydBMNihrnp64TLW9LmXeOoH0GKSD6HFeDXHs4opViDBkyfeU6oJ5ghXJPUcO3aV43lTb5ohtF4xObK5kGq1lDernpvDNT7iWmhpUY9ztiMqp9w4BxSa9ifbG7tl82oNnENg1V/KmAiz2E3x+cVis9fELn+VJyOb6Obz8Xaa16XfWeLyjpoINkWQnJySDRxZ08xhUtJjQSVRaSRiOBj1mMnNtpcT8YRuuylrlXNSc3tjKPN7tkK00qIGuueBLvqMtM5ihzX0xVOI4gWs18NJmv0DniWniauXLrnlJwhXjeYshOeaUAung/8AuGbPYFAhOPSc+1Uwqz9jyN2TYzlOKU+2EWpstm3ENHhBnTTozJjIWWylsaT3x6TxMxMVurKbiSNasI3Qk3lzRyhVzd7xc+hApRzXXXxRmp1YSkdp6Iq73CzG1BQpp6IEtKJuoEKpqMWmFaA36VbwuON5N8/nEYHrgztkL3XJ6Wubo9kCTtL3pN5qL5NemLycRvlykwLzbiSlQOoxaGxV6oF5RSDrRq6RC/G8haVXkSacU6OD/wDb0bSp60XA20nSfVG4djwyFnZlKOrWT6oyjQys3TF1Xq1cXIbGGMW7wU7Q5q/dCJdkUQgBIHMOLtDHhlwVTqz8SXHjee71sHEwm3NkNUMfm2c0BpoXUjMBtOHNwT6ItFwY8JvH62+vzbID2hxOBhS2VGcs8EGhzpHNFJZdx8Z21Z+rXvpLZSxXJu0ylNNzA9qYLiTUKoR43XptXeJJiatdeeYdwPRn88GenleSnSowLfnGFrkai5Lo1c3thNlTEiuTbbFBQeqL8rMJ6FcE+eKjiS4rkpFTE5boSRcUR03s3YOMn1zJqtakmvbxCpGyqPWhQ3U56GPdzZPRybVwgg406d5NveCw6f2TE26e+fHmTv7qs0e6Fhq3LOJxF3kwmwtljKkOjDLa6a/bAcaIUk5iN4t5Karl1JcHRmMMVztDJH6OHjdLHfzCwgCGH543UIbBprUrGkDZDaouWa3glGe9zD1wllkBKEigAi5OsodHxkgx3K/Lkfqzh2GL9kzQflRmaUaemNz29ZyrmbKJFPugNFwsunvXBSLzKgocxrvnXWCA85RtPXnhghNFv91V9L7uMnizXBwDHr31TCdj+x1Ki+5S88nEJHNG7HyXZ1fKWrRrpvbQdP8A/OsdopDrgHKmFeZI4nJzSeF3qtIgomLztlEpoc9KnHo6IE3Z7gcaOkbbsqvM4hSe0RPWAtQKmVXuvMrxuyFjuGgQC6ejT6IIXhYspwUp8LRWESkqkIabFEpG9ooVEbocYCXqUvt8E+aFKsSdW1eXforXpxELenWkPMJrgkVwHRjA90WnWDUg4VpSL8k8leFaaezbs7Y8ggoUoXk6aqPshLLYolIAA6OLPRFoE0+G0de9Lz6glCc5Me5Vh1bkwqjjo0jp0RcY4TnfOHOd9OfHuI7VCJZTYpfLhPTepxSpaZSFtqzgx7p2YC5ZZ5aBX9qET0maoWOzbdlwLjU4T13k3vteN19iUqXqBlu6eahhqU/PEXnT8bisnPsIcHOIX7nKWwtdMeVm6YV7mTImmicAo1oOgxd2SSy2ngoiqUkJIGnGJi2pl1LbeJbDlBjyRj0ReQajm4s9ETlTwsrinPTr3hmZ5d1PnPRHDTkrGTWhzV++BLSwokdp34ZH519A7KmJBofqUq+tjxamHgFIUKEGEPSyCuzFmmAzcx9UInJRV5tYqDtWbbJNG7ycRrQuvoMVHGKtC010TmSkcpZ1JEDZI0sSdnPu5NhvJoJzVrwkknp7IZdcxUptJPSRtXlYAQ5ZOwe6xJsmjs4sV7M/VpPNG6BskmcrW9dou5XoylKdXVDex7Z4ErbewZnEZj05qjRmBGc56+MgrVmArE1bxHcWyp3rUeDA6ONmZ11IVcRwQRXhHAQ5aE61k3nXVXbmFAMM3TGX2P2ittFb1xVc8X7Xl90AAkqSnVziAJ8LlVnwsR5ovSL7bvkq4gnmh9bASGyoGiQRjprXbMw7wnO8RrMe6eyUFuWCrzTQww9kBllIShOAA4iRlLwSLy1nzD1wxLJzNtIT2DjFyU2m80sUIg2FPL/s+aNWSdB0fftImTS82+P2gYlZoGt9lBr1cW/axaW8GU3riM//AK1wNlezL+6Z5eW0EdGhPnVpwzyaECiRMUAHkGJf5JH2dp/JG67MES6fpcr9kGJVoCjjyA+55S8fMKDq2phZHdZXu6D5PK81YlZl81dQC0s86DTzinjHnZhBorJXAfL4PriZmu/cep1AffA6ONZsxgBTsy5m5kwxJo7xAz69O3Wal0FWsCh80brsOaWw5jQKxAr0UirRE6wM1OF/9oyGyCRdl16x7DSKykwmua6vgnz71R+KYm6Jp3bnx7doyUj3aeOF1ON3phi1dkaazQT8Gc1dZig4my7KPwXctPhrx45XBrMMgraIz1pmjccwqs1K8BXONBibWrO242sdN6nriSUO9SUfVURxd1WIO1KfOf4DEv8AJI+ztSLHhPLV9VP3w0B+rT6I9wW5tBngopuUPKGi9S7XmrE40vkql3QfqGJprQmaJ7UJ8Y77c2oJSvAc5zgQ2RXhOKgdHG2bZyASlm7Wubwj5t/cnGkOp+OkGMpLBUuseBm7DGXsGdymFLjhoOzNGTt6QLg8NAI+6Lry1Sy9Tow7Yyso4hxGtBrCyc10xOZrmWzg80Cw9j9VvrqkuJFaf71wbRne7T68So406OLUp2pRLqVSujJop6ePTaiU3bPncFU1qz+fGLSwr3KvYawEeA+4n0H18bKfOf4DEv8AJI+ztSDmgOODtA9kNeQn0R+EW6llsP7oDNzv717lVzV5omyc2Qd+yYm1aN0/wDxjy3g5f+ExL85Wf2oHG2jbC6lDRWE1HPdHm4qhzRemJZKV+E3wT5oL+xyeW0rQF+0eyL7oE4gA5RStA6sYXZUwpyXl3l1cU2cebqi5Zcwh2YVylLNHD1cWVHMMYtHZIpd4YpGuqzX1ceZnM5KnKjCvTE3MKxJlHAa60giHkYYTKs3kp42U+c/wGJf5JH2drdLeeVeS4fJPBPpiSnkmpUykK8pOCvPtTzyzS+yppPS5wfXDK1iipha3j14DzAb8OWi+1LpVgC6sIr2x+MpP/uG/bH4yk/8AuG/bH4yk/wDuG/bAWg1BxBG+3FIWNMT7VwKyrV+lTowQr0wp9/Y3NobQCpSlFYAAzknJR7rZHIcNSLl+/m56Db3FIWNMT7VwKyrV+lTowQr0wp9/Y3NobQCpSlFYAAzknJR7rZHIcNSLl+/m56DiU2c7MNJml4paKxfPQnP4pssPzT6FHrqPXEopJ8IdijA6OMmZ3HuTS1YcwictJ8d0dfpf1gD7+MM3OruoHaeiFuNjI2MzUi931PXDuRkmpli/d4ScUnXrir8u/Lvp8E1T58YmJyz7QamWcaN3qY6BdUIa/CWSoXBXueBHTWAN0ZFZ717g+fNF9pQUNYO/nZxHKSyoJ6VYCDOutNtVXcGTTS9cGc89a8fMSv6xpae0Ra8m7WrTbtB0oMTROfdP8I4t60nwS2w2p1QTnokVwj4Cc+o3/PDEnZzb6Ftu3zlUpApdI0KMNMLYm7yEJSaIb0Dy49zLPamEO3CurqUAUHQow5JTQvMupKFDmMOWXa7Tj9hurvNPoxu1/wB4jrEX91mvg5Fyv2aQzLyrLktseYVfU4sYrPt0ACtM5hMuwLraEhKQNAG/kvl1fZhtapLEpBPdndXlR/cf857+eP7j/nPfzwllvBKQAOgb+0vmcx+7MD5dz1by0vmcx+7MD5dz1cTZnyA/1PFNPIX4APYRExZRPDYdvgcy/vEDjJkJNFOXWx1mJZCxRTl5w/SPFjdaxlV8hGuG7Y2RVQwlRKGxhVOr74XLyyQhCW1AAZs0TCMKpdoaDmjuqQrpgutJLaiamhwqOaFJlXkvN4nJqA9BqISu2rJySf1kvVOPRiIS9sctJTGSBqHuCak6SMIvWtLialrvLaxxprT7ISm0AuXWRU1F4DsjLWc+h1PxTvG5FkkKmXaGmlKRX2RJSt26rJBahzr4R/INkKpdFxORUoEnmVD5VpmDjr4I/IbqxUHQY3SJCVytb1/IovV11pF1OAHESXy6vsw15CfRvGZ6zkNLW49kzlQSKXSdBGqG3VZ1JB7RtSuxZtDW5X0BSlEKv5lZjWmjVt2l8zmP3ZgfLuereWl8zmP3ZgfLuerfvOWShLs4EHJIVmKtFcR6Y/FMn9cf1olpqclWfdkJGRYqMndor4/T30fimT+uP60MtWzZ0q1JFXdVoUKgc3dT6NqT2LtIaMrMIClKIVfxvZjWmjVt2lZ06hpLcmu62WwoE8JQxqTq2jk7KkymuHCGb/rRKbHdkUpKsGYoTcqTdNcQQ4oaIcs/YfIKn1tEpcfUq4ylWqppeppxEDKWVJhNceEM3/W2vwdmQymzUtlxblFZQUZLmumcao3RY6Jey5Y4t7oxeI+MLqwK6qYQmb2RpZtCQvUW42KEV5wE06082qGrUkFXmXRUc2sHnHiVnlJFSGSaHmiXnXODLzVWlnpPqNIB5uMlJVxRF569hzD74Ylk5kNpT5uK3JI3XZ9WARXN0+yPd7ZOrKPnFLZ0dPsigh0fEV6If3MaoL3q3lFQpt1oC9nucH0QX7Jmloz8BXtEUtKz2pxA/OAcLtFDCm5VU3ITLmbvk9GFDGTsucRPtJUcCbyui6rhdkIl9kFnuMqIrVPsMBLE0gLPer4J88WbYLSuBwa//Ir2CLo0cet1eZKSTFv2klVELZyfRWvtgLT3zqvNQcY/Zz7M2XGHFtKKUIpVBoacOPgJz6jf88fATn1G/wCePgJz6jf88fATn1G/54+AnPqN/wA8fATn1G/54+AnPqN/zwxaLAIbfbQ6kKz0WKiu/kvl1fZhCE7GpxQCQK90x/yo/wCGJz/M/pQzJTNgTUs04q6p5d+iOc1bHp2pX50PsKhn5NPo2rO+ST6F7dpfM5j92YHy7nq3lpfM5j92YHy7nq4mzvkk+he8sz5FP+pt298r/qL27NZkzddWy0gK8G8tYJ6hjCJKTQG2WxdSkaBtstPgKTwV0OtDF4ecbTsjMCrbqFIUDzxOyDtaMvggarwx9HiVm5dOdbDg/Zh5bA99yEypaRrSpIqPNWEMuK9+S4uODm0HjLLsN0Eo4JwOlSvu4mpj3E2OVcfOCnU4010gz82ovzi8aqxu9G275CvREwlrkZc07OIC3W0qIxBIgzDJU04dWase83kPtZsm6Lw/aj+1ZVxldAVOS5om90Kr6oM3ZLyQtqpaU6QDqGeo88I/CGUDza8ApsesVEJEw9kFK8PppGUlHUOJ1oUDxs49WiloySeleETrqgL80R2EgRLlXfqcV+1+VyXy6vsw15CfRvJX50PsKhn5NPo2rO+ST6F7dpfM5j92YHy7nq3lpfM5j92YHy7nq4mzvkk+he8sz5FP+pt298r/AKi9uyfkW/tObxryP/GO3a3yyP4vEqUaxSLTk16HRh0VEM7I7OSdwTCuGlPPykesQ3aMiq8y4Kj2Hi0odPBlkC4OhNfXxBeeUEoTnJhVibHKol0mjrhwqNMe9U3n1cpxWfePEfq1eiHMuACl0jDo4mqsBFJqZRe1DH0RNsNNrC22llJWBSujzw9aFp3+E7daUlVDQDGMtYE1dPgrhSrYstDzdfhGuVT6OfrEFyzZx+SdGcOCtPpJx80Xpe5aEoeTThmn2u2Ai2JR2WqaVzj1QFSEy2uuitD2HipPYrInuriwsjWTgmGrHRjwm2vqitYs9qlPe6DTpFeOXOz7iWmEYqUrNCmdjdnTVoKTTFKSB5go9ojKW/Yk5KM+FiftJRG7LJdDiBgoZlJPONHFSXy6vsw15CfRvETCMzEwhSuggp9JESk+yapcZR20xHUdqTSya5JIbV5VxR9e3aXzOY/dmB8u56t5aXzOY/dmB8u56uJs75JPoXvLItqZwllJSi9qoohXYFA7RWs0SMSTFtTLXIcWFp6CtR27J+Rb+05vGvI/8Y7drfLI/i8S1oyAwS8CoeZUGQn0BbK04iDZU/wrKmVVB0U0KHONMJmZZQW0sVSoZjxVpzasC3lBTru79U5aDgQ2PP0RRq9K2S2c/he0wJWQQEjSdJ6d68DmyavRDi9bx9A4lMi1MFgBVTqMJ2PyH9o2oo0UVZm66ABpMPS60ndLiwjqGJHbSJOSpdUGgpQ+MrE7fvplCq6aYxlZVS2ljNjDbaQ3Ptorg6AT+1FLRYes944jJqvYdB9sFWx60AuX71pxVD2Lw7DC2Nk0ieDmW2CL3qgO5bIE969gYXaLRDrSE3uAawVS9ULTnQrPvHrSmzRtpJUfZD2zSfTwWjdb8r7hEpZrB4S1qNBz4Q3LpzISE9g46zth98olVXFrppKifQkYdMJkbPbS0wjMlIgtuAKScCDEvLWZ3OTn8nVoZu6qKadShUauKl5azVtIU04VnKkjRTQDCG1Z0pA3jkhOJvsupKVDmhaNibzU5IFV4MPUB89B2KFdUZC0Ny2WzXhra4TlPi8JY9ESNtSCmxIyrd1QWpWVUeFVWahJKqk117WU2Mz0vLydwcB1IJvafzavTDklNWpJqZeQptYugVSoUOZmNwWTaMm0xUqu8rE+U0YZctC05RcqHEl1KUipRXhAdxGjn2spsZnpeXk7g4DqQTe0/m1emHJKatSTUy8hTaxdAqlQoczMbgsm0ZNpipVd5WJ8powy5aFpyi5UOJLqUpFSivCA7iNHPxDGyPY7MIlrTYTcBcFUkditZ0GPxtJ/UH9GGXbZtGVdkgruqEJFSObuQ9O0ZCaNxxPCadAqUK9msQJCURLWkwnBClqFQBmzqbPp9EA7MHGWJHAqk5b85zLOPB1gKNYtK0JxbSm5xd5sNlRI4SjjUDXtHJ2rJhNcOCM3/Rhq3pmfk1TzACW3McAK6MlTSdEfjaT+oP6MPHZZNsTKCBkg0AKHTXgI2kbLwtncaU0u1VlPgSjNSmfn2533QW0vdLiVJyRUc1c9QNfiWlLXNEsuoSkk6+TA6IVIT6fIXpSdYj3EtwFyzFHgnm8JHrEImpZV9pYCkkajxNrTbWJCqAnUpRO+yk2ruh5KBnMItbZHREkPg201BIhMtLJCG0igA30wf+UvP0Q4oV4T6jTR1cT7h7E+7TS+Cp1HCu8yeeBbdt91tVQvJCsQ2T6VQizJwUWmYvO01JN47+68kKHOKxUtXDWvANIvWZNX2r14tOYBXTDj1qSCUNGqklioIxzYYeaP7Bnly6qcJLqVDzivojdrbQUU0q5LgEdd2Et2y2tlWYuAXke0RlpB5DqeY7Sdilg4yzSuGvQdajzCGrKkxwGhn1nSeuJezwaoZpew8HhEcfZ2zhtBXLslLb9NFDn6wadNNcInrPcS6wvMpJgrcICRiSYbtOQ4dnWaEAvd6ooJUKfSPYK+Mtibu1U2+KHUSIYmPDbSfNtGQtJF5J5J0pOsRkpq/M2Q6cCM33GBO2a4Fo0jSDz79xepJPmi0ZothF5xGbr3qZdCFPzK+9Roj8IdlfDeWbyGtXT7Iupzb+ZSf1S/RCkXaAOq6T078zlqOhtA7T0CDY2xttTFnnBaub46tHQPPClNkvTbnLcV6BD9oO8lltS+wRP7I5vEngBWtSjeVxazPtt0UOEo4eeL1k2hkH0muHCObNURihUypXfBOeETklMuyEyvFbXe+0eeHNhspPqm33XA2VJ4QAPKFc/TCzKjurl28rmSKARU5otK3XE0u3qdK1ewceJWYb3VNTAutyoxv1wxz4dRrqhVqNPosLK45CULhI8rhjHHQacwgFVsKtC6QchNl0IVQ5qhaj6OkZ4/BCfkk2XPt8lpPwa+dJ19tdfjLmZQipKbw6U4wJRwUclllFDqOI21Ss4hLjSs6VCFW3sLcWpnlKZGKh1d8I3Fa43JNDSo8A9eg76cdHesOH9mJleuY/hG3Ux7g7GlBc2vglwaOiA/ait0TquEoq4QB5uJmL2bJL9ELIFE5ZQHYN7uidcS02O+WaCDZuxRndUwRg5o6k5zAtjZq+vhY5IHhdB0AdEJlZJAbaTgANo2dfuvTRASBpCSCYlpVQo6sZVzyl4+jDixMTMwrcmloe2ArI3iBThYxhRDaR0CPwW2I3lOLVcW6jOeZPrMbrfOVn1jhK0J5htTE+nl0uI6VYQbUfQlLswSTQAVANBm4+cem+FuVLmSB0XKI9ZO3ZtuS3Bm2nCkKHNwh2H0wh7wkg9vjKpE7seewSsXm+jOPTvXHkIDE8rM6nWNYhcpbKFTtloSMmvV0K9UXrPdo7paXgsdWneTyl5tzueiFg4jdCqHqG0p54hKEipJj3J2NJIkSShb2a9rx0CLiO6PnlOHP0cVNU/Ur9EXUd66obZNpzKG1DG5WqvqjGBJbEJRTi14BxQqfq+2Ez+zGaUE6Wq1V1UwEBqzWQk+GcVHr3jdnAXpKUISryU4q7ThFBxm6bTeS0nRXOeiDY9goLFnV4ajq+OfVASyA5Nkd0eIxPRqG3J7H5bFTyr6h5kw3JJ/NNpR2ceNkj6SbNnqhagM14cIdIIvdEJmpNxLrSxVKkmoMXlYARJ7GLDVlJZglTzyOTjS8QfijMdJMBCcww8ZXXEjsmaFKKCHFDmxA64RNMG824kKSeY70svpC0HOFCogz2xd0yr9b1ypu15jnEJktlUsXGNDpzmmojAwBIPAPfql4L/30bU9lOTudz0QSnEF9fqgzU4sIbTrgy7VWLKQqhIOf7+aBJ2egJTpOknWYU+5yUipjgO3CNC8Iq2oKHMeImso4lCiyulTTGkZO0JjupdUbqeEYMrsek1PO6CuuPUmAhykim9nxbqPTG6rbmXZpzCoBuj2xuezGEMo+KN7M2mc7aDd8o4DzxM7JZzF59WSSo6k5/8AfNxapiZWENpFSpRoBG4Ni7RmnzhlKG79EZzCLb2bOqT4LXfEZ8dXpgSkg2lppPepG3UxM2gvhysoO5YYUQrg+fGF48eqRtFpLzC86VQpzY5aU3Z5Ua0SokeYpPngtW9bc7Ns+BUj7Sl+iNy2SyG0nlHOpXST4y+uHZFYqq7eR5QzR7nXrzkobmOehzb9UvNoS40oUKVCohx/Y8vcr600oeEnq0iEy9tMGZk0V7oar/bHricknQqWm1MLAQvFJNMwMZecVRWWcuNjEqzQLYtpRZswHubOv/euEy0qgIbTmA2qHNF4spSo6U4RlrGnXWHQKC8SYQlqYC273CxBw5r0XFIZcYJz6umkYyLa1Vpwb0P7uk7qGkqKLqFC+dFKwMhZwDVfBxp01hSuA0O9AuCL07aWTSdGUP8ADDs/bs87MZNsmiRq6axu59gOryquXXRzRclGkNj4qQOIk9i8mcXDfWOfMmJey2szKAnpOnicvPOoaRrWaRuDY43umYUaBS+Cipww0nzRl9kT+5pWtUp/lR6zAVJt35nS+5ivq1dW9feSaPOjIt9KvYI3e6O7TZv/AERmhfjeHRDrqABJTyStWOYjEnq4mhzRMT4YDMyltSgtvg4gaRmg2vYqm3Mm4U3K4m704QiX2T2fVPhUuHtHBgZdxUs4dDgw7RGUk3UOp1oUDxc2tWYMr9EEq/XL4hcy+braElSjzCJnZVMCrLKipuuvMkdQ395whI1mC049lnh3jQvefNBa2OWblGyCBnUa6CSMBAtLZdOUUcS2jhH+UdUXpCXTlf1isVdu/lNjMriyyaOdeKuwQiXZFEISEpHMIX43h0QtchUTTWa7nKTyk9cIQ4avy/cnOkcTNKGJDDn2YfbWonJvmnNUQWnkhaDnChURe3Ihtetvg+aMpsan8ic9DeT50xcebXOy6TnIDlR0jhQWbckFNUzlBxHUqE33ywo6HUkU6xURWRmWnfJWDv5tsaWV+iAj/mr4gWTLrAfmiBT4tYZkfzyhfdPxj7M23ecISOeCh+davp71JvHzQpVny7z9MyiLqYU1YkjkGTyXCg4dasIy2yS0btTyASr2CMo82qZXh8KcMOYRkZZCW0DvUig4h6018pIoga1HND+ymeJW9MqIQVatJ2l+N3GB0bRKq+5c+odHC9YPmio4h1rwm1DtEWjIqpVKm1YGueu9yU8y28nUtIMG7LlhR0tKI8xqIKrOnnWzovpB9FIpZVo3208kZZQ8xwiswyt5I+Ilz7OMXbVs5OGfgLQY99yTifJUD6aRR1L7fSgH0GC4Jq7TQpCgfRE2xJzqC8plQSKKGPZCWJucZQ9fUSFKp6Yo1PSxI/5qYru6W/6qfbGE2wf/AJEx3SelxT/mpj+/y+GOCwYu7uQegKPqigeWvyW1euBsgn21uSTShk2tNEZvPiY94WaVE4CrmnoAgbgsyiDqaX6ThCry9zNHReQgebGMpblpgq+k56aQgTKFTDyDXKKUU+YRdkZRpFc/Br6YoOLl9h0j8C2vhqGunCP0RCJOWSEtNi6kDaX43euB0bV1r+9MHKNHn1Qqyp8+/ZTgnnTr9XEUi1rL0iv7C6evisY99SrLnlNpMVXZ8vXmQB6Ixk0iprwVKHrh+dlMq2ttskcOor1wmdmnH0OKJHBIpTzxUTkx+z7IqmdfHSExjNzHPyfZFzdEx+z7IxcmTUU5Y9kBeScUpNKEuHR0QmUkGB7oTB4JJJKUjOdXNDJtWVadnHO6LLiAoiuYY6oqy2hPQkD8gVMpPvhzgNDn19UG359Pvya5N7Olv/7Z9tfjeHRtp2X2cDklq7qkZqnP2+mG7RklXmnBUcRNMorcmb9a84v8dOu0rRlUNn/mOZ+nfKfcwQgFR6BDlvTv9wlSLqDqHJT6z+QqeeIShIqSdEbpeCvcaU5OogfzHzRdTgBtr8bw23LPnE3mnRQwrYxaKlbgepklqGAUdPXxEhaijSXmLoPTyfZx05lcU5JVYbWml2+ulOnfN7FrLKjNzJF+5nu6E9cNyKsX1d0ePxz7M35CNhdgd0ecVceI+z7YbsxnFQxWrWo594vxvDeLbZA3YhJyKzoMHY5bav7Ql8BXvh7Rv5G0se5ulNR2+qGZ1nkOtpWOscbOaskYZu+G56d6u0bQWEMo0mH9m7o97Xve+nhUpXq9P5DueWNbQfFGk6q6YVbdrj+0JjQrOke071XjeHRvU7J7Aqi0GaFYT3wGnpEAzFETrfBcTrp3w30ygcpqjwr8X7oZR38uSyrqxHm42dvioyRwhgkUqVkY1071vY5ZC/7OaJC1A4G7yldWYQ1ZsmKMspCU/kG6n+E6rBpsZ1GFbNNkAUQVVZSvSfYNG+X43cNcDo334X7GE0Uipdb0Y99T0xlW6JmUYOt6jzc29Uw5ilYKT1xaGxiZVpKkaKlBofNxs4c/cjDFNa/tbz3Fs4+/ZrDg50p9pgbqxnHuGv4vxfb+QKtCeOA5KRnUdQg29sgqiz2+ClAwvY1u9GswllkBKEigA0DfK8bvXA6N9Q5o/CjYpVLgNVNJzc/VFRRucRg61Xzjm3snsnbwl31Jv9OZXmgLRiDiOMdlFGgWAPPCVSuLV5YBpStDn21T8xQrzNorylR+GmyE3r5vsoOvX0avyAztoKx7xscpR5oTb9vgosxHIRXA8yebWYTLy6QhtAolI0b9Y8bw39DH4T7DiUOJ4S2U+lPsgSs5Rq0U50eFTSPZvHcmmr8v3ZHVn80IlXFVmJTua+jvTxk48gkEI0Z88S18UPDP7W05aNoLuMtip9ghVo2iFJsiXzIrh5PSdMJYYSEtoFEpGYDj8vM8J1WCEDP/AOoTsg2UK960q2lJz9GoQGWhdQkUAHEK8bvXCejifdmwjuefTjROAX7DAsPZOCzOINwrVr5/bFRtUOaFsvcGz5vTouLOH1TFRm4ucQPAHpiVDmfhfahU1NrCGkCpJhMnIhTVjMK5ejyjrOoQ3ZtnputNjt5zx5s2wwJqfrTWlJ6s5hrZHsnSsPlKay6jwajXzc0BKRQDRxKvG71wOjiiHxcmAOA8kcIQJa10qnLOUeX7D6o3VZrl4d8nvk9I2jkEAzrHCaPpHXAsKadvTsqKYilUD2ZuLmnnheSAnD6Qhm1J1SWJdIVWpzcIx7m2ZeasZlWKv4lc+oQizJAcBGcnOo6zx1XVAdMObFdiqSGBwXnhn58dA9Mboe7vPq5ThzDmTxZpq8bvXA6OLMvNIC21Z0qhdr7DHShymLVTXXhr643Fsra3K8nDKUITXnGiA6woLQcxGMI2a7HhRN6rwGhXsVphM7KkZQYOo8FXFL/CCjjK8AznKzzQhDjW5rBl18FtOCegazzwmz7MRcaT2k6zxt5ZoBpMbisVO7Zo4cHkj29Ue7myclprvGjWv1e99MZGSbDaSammk8/GKHjd64HRxuTtBup0KGBgTmxl3Ly6aJU1TQNJB9UGzbca3M/ihQVig64Xsh2LFLllumq0DEJ5jzajAelTdfpw2jnB9e/LjhCUDEk5o3BsaTuybOF4cgfzeiPd3Zs6uisQzXh9HxRzQmVlUBtpAolKcw4y+s0AzkwpEmrdcwMLrfJrzn2R76JlLMPMUopzDOqA+2nLTf65z1DRxyvG8FK1RlF8nRx16aZCXf1iOCqFzNgTiphKuUhw1qOcHAxlmmF2fOtq4SkBSU9I1eiEy2yJrLI/XNcrszHzQMjONoWe8cNw+eKtqChzGKrIA54O655gEaAsKPYIyVhS7ky54ShdT2Z/RANpqMpIHQrgJ+pnPX2wHWk5eb/XOZ/ojRxmWtOYQyn4xx6hBZ2OMKm3q0qcB1UxMBduu7kk143OTh5A9cX0t7of0rdx7Bm/IFGMm1F3xtUJiiTFXjmjPHKjPGeM8Z4zxnjPGeKVjlRnjlRnjPBYnUJcQcKKEf2ZcQR3roK0+msFTSBMN1wLR9UGXmnJiWwzXcadFRFZm3S2vAEPNKzdN6kJcXPLmdPAUkA9lYAs2XbRTvqVV2nGOVGeM8Z4zxyozxnjPBUtYAGJrF1c4latTdV+iFM2LKOOzF66nKcnzYxebUJFlRpd+Dw6eVAdtubcedPLodPSYDFmtIbCdNMe2M8UvRiYzxnjPGeM8cqM8Z4zxnjAxnjPHKg3TRJjP1xUeNq+oRlSKCASI5MZo5MZozRyYzRmjNFaRmjNGaOTGaM0ZozRmi7MsocHxhWDdYLCjpaUR5jhAVZtoLQBmC0184IislP5ami/6lRRMoh0Z60B6sDCXZqya+FwHIVumx1VTzq9kAIstRqK4uEeqL6LKJHyp/lgBNlZz4aj6oV7n2PzVUFwUsyOSUNIbp9sxWamgwk6MpT7ELTas+tzK0vgV9JMXnW1vq/5i/ZSKScuhvyRSM0ZozRmjNGaM0ZorSK0jNGaM0ZozRmjARWkUphGTZGGuMmc0UphFB42r72jNGMDo/KsRFbqeyMEJ7I4KQOr8pySM2mKJhQ8bvXA6P0wfG71wOj9ME9943euB0fpgr8bw6P0wRo8bvXA6P0wfG7hrgdH6Y/3q8bvBgfpg+N3rgdH/wDwr1wOiLjY4Ov9MViqvG1wjSMCIDacBFARHKEZxHKEZxGcRyhHKEcoRnEZxHKEZ4ziM4jOIzxnEZxGcRnEYqEd3mWk9KxBUJgKu57oJjud9XVmhTjTLnB14Vhte5F3V005oruRdK0GMKcmpR0UFaRR6TfT0FJ9kUdEw1zlAPoMX0T7Yxpw6p9MXpN9p0fEWD6Iz73P+Q34yjnV426rijebXAOMaYzmNMaY0xXGNMaY0xpjTGmKVMVisaYzmM5is3MJHNWpgSdmSrjytZj3s2JWpzqwoOuK2vaCjpomsAzDjzh6aRdaZzmuJrHc2UD6IjgpA6htVhTtrOISimZWJPVFyQslM0vwnEJT6ATDtoCxmmVH4JFHElVMfCGfRByVmuBI8HH1xlJuWfYrheoRHveec0US5iPPCfdiUS62rMtuqa9eIMATK3JZepxOHaIy0i+l1GeqFAxnMZ4zmM5jPHKMZ4xMcoxnMVvRWpit4xnjPHKjlGKlRi4YpWvjarGSZza4wgfkGWn3UtJ+MYyFhSy5hytK0OfogrtR0SzChS6MD2CEbrBfUjwsxPRF1hCUD4opv8vaLoQNA0noEGW2Ly+Tla0yyx6zhG67fUZmYUOEKm7H9nyzTR1pSK9u3Q5oJmJZLbv6xrgq9h64VO7H1mbkc6kH+NGnpEGWelRJWlylBo3b3knN1RuzYnOm8MySbiu0YQJfZNIreQnAuK4J+sMDFxLu53vAe4PnzRUcdjGVczaPG5cSaRQZ464HHZSfdS3zE49kGW2LSykt1KS8r0wmZ2RTC33c6kg4V6Yycm0lA5hxKbKsVvdM84buGZMNM7KVBbriLy2TqpWAywkIQMwHEG3Ni6MlPNnKFCML1NI54Nl2rRNos9V8e3XGTeSFIOhQqIWuSTuR9Wlvk/Vi9Lq3XZ6TmxWinpTAZnzuOYOhfJP0vbF5BqDpHGX1eOAcZl5taW2xpUaR7m7GGVOuaV0zRu63lqefON28T1QGZZIQgaBxNTmg2Bsb4RHwq+bTSA4eHMmtVnn1Q3TlZP8Ah4obL9jwLbzarz4bz+X7e2BMZppvgvp+Nr6DtrfSjc82ofCN6+dOaBepN2cnDSUAelMJbYcyU3TFlefq1+OrDXA6OLyVQ7NnANA6eeE2lsicLLOhlOr/AHpgS8i2EJ856eKqY/BfY+k7nr3V4Kphp6oErKiq+/Wc6tpBrgWjh9HiihYqk4EQiYl6+5U3gRounR0pPmgONmqVCoO3cWKpOcGDamxlW5pocLJd6ejV6I9x9mrS00wS5ThdevphM3JLDjKxVKk5vHQK64HRxJWs0SMSTHuLsUQq8o0W9zc0Jn7WO6p8AcNWIT0cYnYpserRWDz2PZGQY4Ty8XHNZ9m3kqYBrV8Xi3Jcju7QLjRGe8B649x5pVZuTwxzlGjszb0ydpIr4Kxyk9BjKyajNWUvPXk9fgmMvILo537SuUnih43RXXA6OIVOzyw20jOTH9nLUxItqosEUvjX90BiXHSrSeM9w7Lqqcf4BuZ0VhIcN+ZKQFKPo3hZSk1uYnRyOMbtG8ESU6ojPoXnHUd8WnkhSFYEHNH4T7D1LCUG8ptOdHRrTzQmSmu42kBig5l0zlPs4mvjd64G/VPTqrrae09EJnZhZaspB5HR6zrhMpKICGkCgA4xU2aF4ghpJNKmF7J7cxmpjhISdFdO9XfGGT4J+jxgtBBAekze+ic4iUm3cXAjJr6UYb8W9sVGSm2+EppGFTnvJ1GPcW2u52kjAE4ZSn8Xjl64G+VOzirqE+fmECetFJbs9pdUp0K5vbAYl0hDacABxi5l83W0C8owq150/wBlyyuA3jjq++KDNvbqgS2lo3ToBIx4yYkP1zS0doi0LAmSLzar9K6RwVeriDblgjJ2k3wyE4X6euPcS2e52k1wQThlKfxa9+PG71wOjeqmZg3W0CpMXuE3YsuadP3mEy0skIaQKADjWtiVjnvgX/8AfNDchL5kDE6zpO+dLi0XQk3R3wFONSs8GXnSSP8A5R/PxJ2VWCmk40co4hPfU74c4jc80Qm0Ghw0+EPC3w8bw3lTmj3BsgqTIs/Cr0HX90JkZJN1tPGrnM7x4LSdavuj3dtMe+pklQJGN06evfzTylJNxFwDTm42zbbZGIqCedBBEIeTmWkK7eJGzbYxwAlVXkDvSdNPBOmE2gxwXBwXUeCrejxu9cDo3n4O2OCqYe4Lih3gMIlL2UdzrXrPG1MIlylXuXKZzoNPbAQgUSMAN/NTFRS56hxomB+YeSfrcGJB5s1GRSnrThxJadAUhQoQdIhE9Z6T7lzHe1wKdI6RohE7KqvtOC8kjeBXjeHRtuTy/hKUbTrVB2QWmol+a4QB1a+O3MyTuma7mimemkwjKA7qf7o6VZ8cw4iYQlfByZqmvRo42eaIrRu+PoG9Dbf6lxxA7a+vinLMncyuSrSlWgw5sKtmqUqcOQKtCtX0tHPvE+N3rgbRWvADEwtxYJsyTrcpmJ5+mLqc3G1MKtF68ZSTNEoUODhmoefaxiq1pHSYouaZB+UTBKZxg3cT3RMKXutmiBVRvjAReanGSM1QqL6ppkAa1iJq092M90Tgq+KR3OYaPQsRwVDt4uYZSKlTSwB1ROyijih5KqdI+7ixsis/CbleXTOUa+lMB2vvlmiHgdfhde2nxugDXA6NpNjsH3xOcDDPdhMkjhOHhLVrPF++Xm2/KUBBQZrKLGhtJV580XZSVecxpjQe2MixLCXTMhSUnG9TWISzZDZYSs3jW6FY6eFA3VaIbI/5p/hEXpy1jXHDhqz9JhtiZnnCpBJJAglcy/eOkUEFBemTXPwh7ILVHTeTdJK4IbywJ034qsLV0n/ZiYsW+8llkE1qK+iCpl95uoA0aIQuVtJQKM1UffCBI2lk2xdrivHWcSc8XrLncuzjwHCmtevRCr0sHgNSAfRAE9ZDl9NcoeEkegwnd8u+wSaaFCDSbQihpw+DHcnEq6DvFJ1gxaUq5nCUeZRHFlC8QcCICgSLKnDd+gf5D5ovJzHaT43R0wOiFPOYJSKmHdkk+PezR7gM45uziMrMLShA0qNBChugPODvWsfPmgNbGbOWVq75QK/MIWi1H9yIUMBUDH6OiMta8+tatOTT6zWOEwXjrdUT90e9JdpvyUAQl5AJs6QNCdFUH1nip1WtB9W+xgtzcs0tJz1SIuqYLXyaiIDllzrrK05q4+iPes2JhoZheveZUXdkVm1TmvJBT7RAS8tUuvU4MO0RlJN5DiT4KgYtSXrocwGbgucYttoe+WO6NdWcdce580qs1Jm4a5yjvfZtJ8bo6YENWFJrCZmdN2p0J/8AcMWenOlPC8o598UPzCFvfq0EEwWdi0gUt5r928e3kiA/sltBzGhLdb1NdNEYS+XX4T3C82aA1LoShAzBIoN49MFV11Yybeu8YTOOju833RWnDRxU3jiELw6xxd1YqOePfcqi/wCGjgnzRk7Am3d24UZzkc9Rmh6ZkmspNJvJfSvE0JxOuMjaKDLOXruOI9sXpVxLg+Ka8Xu9OFnzXe/FWcfqnGKjNCPG8CdUO2hnlpGgGqoze3eVOaDLSx3VM6m+SOlXsgBXvKzV/RFPtK9EBy0Pfr40ucn6vtgMSyEttjMlIoN/J7GmMWmTV2mjSrzQlpsUQkUA4q0XDyaEeji6mDZ1jmr3fOaE9Ee6xcLzsyL1VY0rzxaQOJO6MR5ce/WELPhUx7YFobHppcu6DWiiT54/tiXM1JpwLn3iAG3g06cMm5geJVMNfDyvdE9GkQwpw1eY7iv6ObzQlXjd64W937lG0/SgKGLkwcoo+jbIml35mmDKMVdeqDuVSZSy1HoB9Z9EB+5uia/WOY06BxLs47gltJVE3spm1BbkwSEkc+J9nFzxFb5FcekcU2xZrV5S87hFQmLkw8SLo+DwHmhozgUjL8nX0mGpNvktpCYtG8Kf3n94Nu4sVB0GMuync8xoU3m7IQtlO7JFtNFafvgMuK3PMnvHPUd+W14pUKGJrYxeIl3qhCTr5SfNCerxu9cSFjNrwTQuJ8r7oDaMEpFBBWs0SMSTHuTsNbyzyjdLoFfq+2BbOyVeXnVcLJ5wCdZ0wG2wEpGYDimbKkr2Wml04Or74Ys1vHJp4R1nTxdovLWbuNAeniVTc2q62mAmVvNyYNEo0rMbrthIK8ChvwemNzsGrbTd1X0cfTtWq8s1V3b94N8XVIyEx+sbwhQmaztnAYa005494ud0HKQc430hsslMFJIbVTWnEeuJefYxbeQhaeg+N28rNE/byxVCeCjmrh6IVMzKghtAqSYeasZtabIa+EUAaroc/wB0Is9CXGnjy3Fp0+qL8g+h0fFPFlLZvbi7KJ/+3GTz8xybqgnovDiL7xq4eSjSYJdTwgeAzeNAIS7NAKmcCfBB5tp20ZZFHnuUdq1p099p8pZO/KFiqTnBj3S2Nr3NNJqq7oJ9Ue4eytstTSVXcpTDmr7YC0GqTmI3k01Sqm05VPSjH0QzKk8KWWWzXVnHp8bsxMq8Gg6TG75iiA8pTyifBhFlWNVNmNK7oo8kjX90Is6RTRpPnj39KtrPhUoe0R/Y765VevleyEoYXu2VSMam8rz4xuK2JN1k15QHqi6xMJC811fBPnjDfP2ifzSCR06ImNkDqaPzbh7B9/GTqErvFKTh17/IN90nXPg0e2N0OXlvucK+cEJGgiKIAyx5a9e8cdPepJ80WjMiudseniQJxAK04pXpEZCdvPWaoFV6mA6DAmZNxLjZ0pO2UKzHCJ2wXdKypIroScPN43ZayUnhzD2H0f8A3Et/+P7E/u7CEJmljTTOIEhIjnUo51He3JhCVj4wrCZhtBYdRiC3m7IWuxJy/eAolWFKatEZK0pC80gUU5rwz4YR3dwsKrdIWNMZaSdQ6g6UGu2zZzI/vDnC6B98S1nIFMm2K9OnjLUwzXvtb4yNjgLmO+Wcya+uFTL5yuJqtVdMCWlhRI3s88rMmXd+zEzMI5a37qvop+/ilS0ym82sUIj3Qsy85Zziquj1U9cIn5FVUK7Rtys8gYTOSvV+NwD43ZVCc8ui+nyiY92J4e+5vhY57v38TjBTMyyKqzqQLp80KesWbcbVcKUJUcB2QorTu6WHJpj98Kbttoyj6KYZ6xLMtLQuVYpyvi8LDpOHG2lMayc/Kz7wuOkJSMSTBsyya7mzOPJOfmEJem6tyycb1eEuBLSqQhtOYDfTyvCbufWNIQ5pddcX6vVxZZeSFIUKEGBMSqL1nurx5ub2Qiek1Xmlio2pG0EYBKimvPnHrhqaSahxCVdo8bhlWsWm3LquhrlQlAzADjXHbQbQttCSo1GqJy07qmGgRcCThU4mL1hTgdb8BWimoGKbIZS7jdvIqPbA7rkFHQ6KefNGUl1pWk6UmvEzjjAxVW8q9U1CqUpo21TUybrac8LlkpUzJAi74SiITPWinuY+DaPpMXU4Ab8sNcpx1A6hUn0RIs/8q99Y14xcnNpvNLFCI9zZtZNkzR4C1Zgf954qM0Oq/VXF+ekSSyalLdz6uHFrmphQQ02kqUo5gBnh4WY+qz7EZVdvo5auvSebMOfTllTc6Zit6/fRytfJr54Z3bMKtGxHlUq5y081TmPmPNCJlg3m3EhSSNIMKfeN1tAKlE6AIdRZMwqz7DYVdLiKha/v5sw01jdCZydEzW9lL6OVr5NfPDNn7In1T1jP8FEwrlI7anDUScOTqgKTiD4x3pw/mm1L7BWJ+15jFzAV8s1PogcbMqpVToyQGu990S6lct4ZQ9eYdQ2rjgCk6jFFSyWzrb4Mbs2OTxRjeCFVHnHsj3/JiYY8JIvedPsgN2khyWc01FU+3zRes6Ybd5gcezfWq2K1C1acOVtGYnFY96gZzDTUzeQ4tSrrIBood7AnLTouYzpGhO/UZRxLl00N05jtSMg3Wi1rWac1B64YlBmbaQjsHGmWcwdRwm1ajC7Inj77lcOFnKfuicaP6gq+rjGS0tvLHbjxbtmTl7IvC6q6aGnTDdkyFck3XFXKNTWp2plSs6FtFPTfA9cSCnuVcUnqSsgeaHGmzRc0tLPVnPmFIkpQCii0HF+UvhHanEr5TKMuk6i3j6KiJYumrjF5g/Qzfs08Y8y2s0StspJ6cImXEmtXQOysDjbNsgYlbt8p8whLKBRKQABvrtoSzbnORj2xlLIeXLL7RCFSTgm2095nr9bGMlsjkFsq03fYfbGTYmQlzwXOCfPF5BqObatZQTwVKJB+lAZSQuaXglOrpgvTSi5OHMO9SIDjndJnSs+rfFazRIzkwqwtiYvYHKvc3ND0/lEhhpYS8FZjerpFYROySwtpekRZ1iKxZQWQR5SqnzU4+W2SS6aSkwe7UzfG9sOoTwkOMLpTUUxPS/gvJV2j7uOlthNl90m5lxKlgaB3oPp5gIl7LaxSw2lFddNMSDOgurV2D74a8hPoj8HEl3L5TIhwpGTK60pWtc+GakTiFZjLuj9kxNN6BM17UJ8Y8xd0qbB+tDqjpmP4RA41qUPCZk7uHki96eKuTCErTqUKwVtoVLrJrVo+qC7sftArRnyajd9ogzFtymXoe8FD1kYRNuS5Mu5NqzqFblTng7meD7vfTCh/vGLjGKzylnOd8qftFeTZTpjc1i9xssYKcUMFDn19EOplk5kKUtWk0EWozNJvsryQNfpRuGTBfsuY4WPe/ePPDs/ymJQq6roujz8e8wk0WjuiSfiw025itlORVTmi0UKwxa/i41NnWcndFrv4NMjGldKvUNMLt+3VZa2ZnFajjcro6dfYMM8SD2gOrT2j7oa8hPoj8I0h3L5TLBsqGTC61rSlc+OekTi1ZhLun9kxNOaDM07EJ8Y86lOdKUr+qoGFUphMKr2CBxhUcwi1LYVo5BGailfdxhccNEjOTH4P7FAVN/nH04eeJ+UnW8opkhN69jWuNIRM2ZNuMXdH3ikXW2g/IAADEKzaTprGUtyUcl0Xy3eGsfFzwNxTTZUe9Ubquw7wyc8m+0rOITJSDYbZRmSInplZp3BaR0qFBCp5WeacJ6k4e2HJleZtJUeoROWiJbJP5nHbxN8rUTx5QdIpE9Yrv5peHbQxadM3A9KuMFi2KndFsPUSlAxuVzV59Q6zBtu21botl/Fa1Y3K6Bz6z1DDbcdbFVyq0vdWY+Y1iSmwaqyQbX5SOCfRtTil8p5GQSNZcw9FTEsHRRx+8+fp5v2ab9D9svZFDhupN1Ssfogx/fv8l7+SP79/kvfyR/fv8l7+SEvN4pUAR0HfZPYzIy8xJ3Bw3VAG9p/OJ9EOTs1ZcmlllCnFm8DRKRU5noFqT6W0O5RaKNggYdJO3k9jMjLzEncHDdUAb2n84n0Q5OzVlyaWWUKcWbwNEpFTmegWpPpbQ7lFoo2CBh0k8S3YD71J94XkN3VYjHTSmg6fFNOMLzKYcH7MTlkE6Uup6sD6oHRxk3NIwUhlZHTSJidcGL7+HQkcWZmcWltsaVGkOSUjelpBpyhX4VM9fVG5pFNPCVpUeeLTSUgOXzp+MdvJWgwh5Pxk1isnlJZVa8E1HniliTeXovMT3tMBdOENs7JZApSeU4kEfdCSp7IlRoMqKRlpRxLiDpSa7UtYDCby5tdT9HN2mJWzaAKabSFXc17T54m3m+WtOST9PD0QJkg35l1azXm4Pq/IJ+Xl61ouvSlWMWotaaGqPSri5p+xUqVOhHcwhN9VSaYCHJ5/Y9OzloOE1fWHARXV3M4nSa4x/wAMTn+Z/Sj/AIYnP8z+lD/ulZj1nZK5dyt7h3q1pVCc1PPCmHhebWClQOkGHXLJl1WhYb6rxbRUrR9/PmOmkbnTJzpma3cncRytXKr5oZtDZEwqRsVjhIlzyl9tDjrIGHJ0mAlOAG/kvl1fZhsqs6TJKE//AK7eroj8Wyf/AG7fsj8Wyf8A27fsgIQKAYADf2l8zmP3ZgfLuereWl8zmP3ZgfLueribM+QH+p4pnxSvc14dUM2sgXWS4ULGi6c/thK04ggHjHmgq5lFITXrrEo2Maov/Wx4ozExirvUDlKPNAn7YGRsxPJRr6PbAlpRAQ2nQNq0nAq9eVjrGJ31xwBQ1GKuy4bX4TXB+6FzWxufU0aYIVh2n7oWq1GhNsA8ulRTpT64GyLZNeSwj4NATeCackdWeA5IzDbgVqVj2RJ2Uzy3nb/1cPXEtIfqmkJNNYH5BatptrqynLk/Widd1uJGGbT+VyXy6vsw15CfRvGJux3ci6t8IJupVhdJ74GG3F8pSEk9m1JbH2XqSDrYK27qcTRWmldGvbtL5nMfuzA+Xc9W8tL5nMfuzA+Xc9W/ebslaWpwoOSWrMFaK4H0R+NpP6g/oxLS8zOMqtpaQW3+8AorRc6e9j8bSf1B/Rhl22bRlXZIK7qhCRUjm7kPTtSNgMPUkXm0qW3dTieHppXRr27WkrSeyjMs5RoXUi6L6hoA1ado5O1ZMJrhwRm/6MSOx7ZBPNvIfotQaQil03tNxJ0QpOw1plqRFQJyZzOHW2McOehBgZS1ZMprjwRm/wCjte5Drx9zAiuRCE1UoskgA0vVK6Uxz4RuiftT3LQrFMvLC8UDUpYKanXjSPdaXtBVqSLZq8h4EmnWVGnQrDPmrDVrSmAXyk+CoZx4lVI1giLUs9A98yzqHUDXS8CI9zpg++5TgEKz3RmPq4yTspainLukkj4v/uGJUfm20p7BxO50d0nFclA0dMe7eyZzKA4pZph/6gIQKJGYbdp0VUFYPnPEVOaBsM2OYtV7ovQr/wCqfPDNlzEu29kxispxKtJjK2Y+uVVq5Q9RhFjZQz78pS6K3s3CzGAnZNIFlOIvpqP2T7YC0TCUVw7pwYvINRzca/POclptS+wRatvTQrlG1Ur32BJiadOZUxQdSRxj8oxsem3m2nFoS6m/RYSaBQ7kc+eP+GJz/M/pR/wxOf5n9KP+GJz/ADP6Uf8ADE5/mf0o/wCGJz/M/pR/wxOf5n9KP+GJz/M/pQxNvtllx1tC1NKzoKhUpObNm38l8ur7MIDdlSZRdFOEM3/Wj8Uyf1x/Whlu17NlWpMq7qtChUJ5u6n0bUr86H2FQz8mn0bVnfJJ9C9u0vmcx+7MD5dz1by0vmcx+7MD5dz1cTZ3ySfQveWZ8in/AFNu3vlf9Re3Zso2q7lGWkqIz3Std7zVgNNAJQkUAGgDbZC8Rdr2S5O0uXdxQ4kpPQYtCSVmbfSesih9HiWtSWpQEq+1DeyyyQRKvK4aRmvHlDoVDdpWeq+y4MOLsmyDS4KL7VfdxKrG2PDL2hmNMQn7492LYWX55XCorMk+s720EFF265n14nfqmpxxLTSMVKUaCPwe2HhQZUbjjtOUD9kRcTRc2oDKu66eraU85glIKj1RaOyR0Vpeoedw+yMlNtpcRqUKwVZIsrOls+rNBd2OWheAxCFkp6tUBFtSe6GQBVwCnnThAE5lJZWm+mor1RlJF5DqfiKrxW4GyMrNqu4+CMTGSmcH3Gqkai4r2Qy4M7rjiz209X5XJfLq+zDXkJ9G8lfnQ+wqGfk0+jas75JPoXt2l8zmP3ZgfLuereWl8zmP3ZgfLueribO+ST6F7yzPkU/6m3b3yv8AqL27J+Rb+05vGvI/8Y7drfLI/i8SySM00gecfdCrOn0BbLiaEQZCZvLsiZVh0eEOcaYS+wQpCsQRxTLWNJdKajoTe9e/K3DRIzkwdj2xGupb+jt0CN0L7rPKHDcPq31p417oB2E72qsBBRJK3ZMYijZ4IPOfZCX7cO5LOSahJBSPop09Jjc1lt0ry1nlKPOduZINHH6MJ+ln81YRMEcOZWpw9GYejeUMXJ2WQcb1U8E16oMzYM45LrrVKTiB1iEplRu2WA4Rpex+1G49kMouWcCa1HRqMZSQmEmmFFcE+eKje3lZhCFIqbPkjU6ilJ/iMJaRnWtI6hEhLEUIYST0qx45Vo2o5caGHOTqA1wXNiVj3mK8F2YVgfOkdijSDM21YrbjI/8A51YjsU56ILlnkpdR8I0vlJ9o4qS+XV9mGvIT6N5l2v8A9Z5DqvJoU+uJWeZNatpSsalpFFDak1y+LbYyd7QopSutOg1HSDt2l8zmP3ZgfLuereWl8zmP3ZgfLueribO+ST6F7yydkzv92oltZ1XVG9+yrzQHGzVKhUEaRC5uaUENNgqUo5gBFtPlJRfWFXVYEVWrA7dk/It/ac3jXkf+Mdu1vlkfxeJay7YQOCk0UfINYCk5iIVZ8+OdChnSdYg2HbgLtmrVVKv4k+sQiblFhxpYqlQ08TNuFV5TKVEdgTTq3ypqcWENpzkwZCQQWbLSvhO15QjcsgnylaVbdXVBPSaRwSDt2moVAyo4B0Z44RAgmam2UU1rEGjxdoPzaa164yGxizyrUpQUs9ghLmyqZMtK/qxnP0R64S7k90TCcco7j2DNvZDY5K4k8PmvLN1MNSbXJaQlA6uIuzzDbo+OkGCZIrlFf8s4V6DF/Y/N7oTU8C/T9lWHngM7IbOzDFVCj2iMm84qWX/zU4dogPSjiXEHSk12vwUseqpyYwcu6EnvekwGnf749w3jz6E9UWZYzRF5ZzeUqkJZRyUgJHVx1mbHJk+9AEKKdd4m95hSAyyAlCRQAZgNqSds4XETuSyiE4Duyi2fRe6eKZld0bnyKyuuTv1wprEJaz3QB2bxTD6QptYKVJOYgwuZ2D2kZZCzXIPYp7eFXmqmvPGS2UWx72rwm5RISVjVeCUU88SeyCUeDLMm0lpMuG9CQRyr3Pq2t2yFszEg1cCck1fpUacFp9EKYf2STa21gpUlQWQQc4IysbnkNkEww1Wt1tC0jsDsMzT2yKbebbcStTar9FgGt091Ofa3bIWzMSDVwJyTV+lRpwWn0Qph/ZJNrbWClSVBZBBzgjKxueQ2QTDDVa3W0LSOwOwzNPbIpt5ttxK1Nqv0WAa3T3U5+IatKVmXJK0WRdQ+1np2g69Izx/xPOf5n9WGZ6at+ammm1VUyu/RXMauH0bS7MtJNW1YgjlJVrHPG5djVsI3LjRL45PQClz1Q3PbMbQM6WyFIl0C6yFjSQKXqaMBE/aW6Mtu1V67k7t3hE56mufm2isbJZwAmtO6f1YTaD1vPrmkYIdU2orHQrK1j/iec/zP6sPOWlar9ohwAJDt7g01VWraTsz3TyRTIZP/AJZRyr3Xm25r3xujdSwv4O5dpXnOvxLOOOfm1JVXVjEm+c+RSD1YbRkLSRVPeqHKSdYhMnaBL9juHgnRTm1HmgTtnOBbZ7R08RaswhBCk5QVJr+c3u6rRXTwUjEmN3ThUzZCD3MeEOaEykmgIaTmA3iW5pSwEmvBMFTE+8kVrSMpK2o6PKrBUbVJrnFVUibRLzqmriqFQrQ1jKO2g7TPrisy++4ekCMm3KpXp7pwvTGSlkJbRqSKDfVh+1V8JiXvrT0J4KPbxl1YBHPBW9Lhtw9+1wT7ILmxKeydQBcc9o9kLkLZW05MKQMkKBRz00euEbIrT4doONAm9nClYqPTjTo2ic6JM/uvv4+S2b2U2XVyRAfQM9wGtfOQfZAfsx9Kyc7daLT0pz/7wgzNovIZbGlaqQNlaG1JsmSAQytYplCitKfSJPN0+Mt+RczOoKeuH7IdJykqvTqP3jbVJT7YcZXnSqF23sQWpcocVtZyBzjSITJTnvaePeq5KjzH276sWrMqxJKcelR3mSRRycVyG6+mDamzDh3jwGSMwgNNAJQnAAcQYtFoGt1wV8/FTcwFhtwtqQ2T4RGELtN0Udm14eQnN568cZGRIdtJWZOcI51eyPwr2VKLkws30Nr16Cro0Daen3uQyhSz1CH9kG50NOleSKk14Wk8e1YtkM7qteZ+Db0JrmKv99JEG0tlEz76cxUiTbQ2lPNW7j00rAdsuaeQ+khScult1FRrTdFRCdiGy5ptqYNBLvtYNuVzYaK+nCnjL64ckXOC1NpqgnTexp271c3K+9pwpPCRgkn4whuydlSFPyFw3XBwimmo6euMpZTwWRykZlDpG8UTqMWkKDloIUPpbfuRYIy86TdUpOIR98e6myD3xOKN4X8bvTz8UeiJ4V4WVqeuvFSexSRxxClU8NeA7B6YZs9jkMoSgdXGZR1QSkZycIOx/YakuTK1XMsB9n2wLX2Sd3tCt4JUbwR7TtmWTy5pWT6s5iQbKQFuJyq+lePo4+0HpjFTSXbnNduoHm27Pn0YPodUEqHRX1Q26rOpIJ7PGUOmJTZCxg9LrCL2oHXDU8yapcSFb1UtNoDjShQpVCrU2Hvll7PkiaU8lXthFm7L5VRVmygF0+wxfsyYS4dKcyh1bS72a6YtCigRlEZuuLysBHuDsZSrHBb49UFfwk05i4s6+biz0RPuu51Oj18SuZeNG20lSjzCJnZNM8hit2maqzh5uMLJXuib/VNY9p0emKr96WUlVQcQkj+IiKSDfdiOE6rlHeSuxnBUtL1C+ki8rshtCcEjAcejZvLNqdkH+DMAaCRdI68COfCA/Zcwh2veg8IdKc4gzFoPIZbHfOKCfTEvIWYlfuPJmrjpBANaXu2lE6dMUGbxlDph6zHszqKV1HQYfsN9VXJZwkDUDnHbv9zWg0l1vUsVj3S2OPKQ4mt1twnPzKGMCR2WSqnUXqZVWGHMoYGFsMu5GYKVANvYVw0HNFoTEyvJtIWglSs2Yx7nWB3Ky0nujpwr/vVGQlE8I8pZznjDXNSJ7c5q0HaA6+fidwy57tOKyf0dPshltwd3f7s59LN5uKLRdy8x+qaxPWcwhUjZDCpKVzE4p+sv1CEzttK3XNA3gPzYPr6+yLiBRIzAbx+0n+Qygqic2WTuLriyhB5ziowjjyy8kLQoUKVCoMFaGlyyj+oXTzKqPNF57dEwNTjlPsBMCUs9pDLI71AoPGX17TdsMIUZadFxy6Mx/wB0MVGbiCzMIStBzpUKiDMSYMm9T81yfq+ykTCbMbLzbC+6ISoY/R0wizbZswy6U4VbFw9is/bHcZpLavBd4B88XkEEHSOLUeaLQpW7lU0r18SJJJKpCUNDQ4URyu04RQZt/ftOZbZ5lHHszwluzpZ2Zbrivk9g/wDUZR6tnyCsyFEpFOjlHrgPWgN1vfG5HZ7YuNgBI0DfSuxqTqXJhYUsDVmA7YYstofBp4XlHPCPG6OmBCnJL+9sd1ZwrwhCJWaruiX4Kq56aPZxVqy4oEhwKFOk6YyFoMoeb1LSDBVKoXLr+KokdhhTuxWcwJ5OUIw1UOEZK3pPLoFKqKKftJwjIzzLsvovYKEVl55roWbh/apF5lQUNYNd+sfFMTl7S6OImJtn4YpKG+kwq15oe+ZzHTUI69efee+XUN+UoCLu6g4r/lAq8+aNy2FILeUeSVH+Ee2DmkWdVcn7VQJnZBOOPuXQFBP8xilmyyEK8OlVdp4hycmTdaaSVqPMImNlU9iwwe5imnvewbSD43RXXA2k2qB/Z06KOevszwFpxBxHE2pJOCl4LI6A5vKGFbuk2VqVnVdortGMFUm49Lk5hW8kdvtjKWLaYBGblI9FYDbS1TLY01Qv04x/a1ncEHhFTS0xSds8jyHPaI7tlmvKRX0RQTgSfjpUPVBUxPMEDE8MCFhqbYKrpwyqYm1vrTeU6KcIaowUO2M+1iRHCcQPpCO6zbCelxMUen2OpYPohiSYfPuYzS8tIOc8ojqhLEm1MLaaSECiAMwwzmLkjZyldLnsEXLGs4oRrySj51YR78mVS6PlAj93GV2RTrjk1raObrVCl5EulVa5RVRjzRkpFlDSR4CacW1sVkql+auldNVcB1mGrObADlLzpGlZz7SPG6OmB0bTkiPheU30j2wuwbS4M3Lcka0fdxM8wv8AO5Wn0qL4r31LNOeUgGO6yDP0Rd9FIqJZSPJcX7YJaL6K6l/dCnZWddTQE0UkK9kOPCbLNxV3kVB84jKN2mAddw19MVRaacc/BUPXFfdWiuYK9sEOWmVV+If5oCnbRJI1NffHd5x5R+KAPbDtqPLcU9yWkVABWeqDatvsleVV3IXingjThrgZGQYqNaa+mKS7TaPJSBx7tpTXIaTXp5of2Z2sLyUOHI18L2J0c+2g+N3rgbaNmln4AEZYf70GG7RkzVDg7Dq4iWm64TFwU8pNzjnCc1xXoicNSU5fCujDftbH7P8A7lKqotX21eoQ3KSwutNJCEjmH5CzsMso+90L7ssZq6fq+mGrOlBRppN0baPG6OmBtuSU0LzTqSlQ5jHuBPLrZ8yapVjgdB9sVG/su2UfBXghZ8lVYCk5jjxrtc1xXoiZQwAEh7Prw3ylsKpOPcBn1nqhVtz499zvCFc4R9+fs/IdxS5vT74olI70HvoM3PYzk0b5rnSNW8QR43R0wN4WXEgvIBU0fjUj8G7e4E6zg3XvgNHVvw9WmSeSe3CJOaSq9VlAJ5wKHjXvk1eiJwJ//o9W9K1miRiSYbmGSXLLlUpvKrwcDmHTFBm/IF2hOHBPJGs6oc2ZbIU1bvdyQoYE6Kcyd6jxujpgdG9GyOw+DaLHKCe/SPWILczwJ5jB1OvnG+m5AcpTZKa6xiIcs3M5KumqeZWPt41/5JfoiYUitwvYE6cN6jYhYgvvP8F678bMj1mEWeOE8eG8rWo+z8gXOzqghpAqTG6HFKRZEt3vq6TCWGRdQgXQOYb1Hjd69+Nl2xy8CleUfaRp5/bGVb4Eyj4RrV929oc0TtgkBLT965Tm4SfNxr1c2TV6IeUjkl4kDq3i5w4vqqlpOtX3Q5sstrhPzCr7V7PjnX1/kC5qZUENIF5SjoEe5NlAt2Yyo3nNFNZ59UIs+SFEJ0nOo6zvkeN0Hn39Dmj8KdipyVzhONJ/3mg4ZKcawdaOcfdvZHZZKDgJKQs6ik4V6RCJhrkLSFDr4x1pOdSFDzQ7KMXSpCwFqTpVdG2ucmlXWmxeUYNoTQKLHYVgDzaBznTAabFEpFABx65ucWG2UCqlGE2RYt9qy0K4a+bwj6hAkbPTROlRzqOs79HjdFNcDf0MfhVsQqlxJvONJ9I5uaNzTIyNoI5SPC50+zeTEkkVdAyjflJxg2TMH3xKKpQ57hzdnGTDw71pZ7BE1MvkqWuZUSo6cBtFajQDOYRsWsOvuck90Xrp33RqhuzJEUbR2k6SePVPz67jKM5hMqwCxZCFE3tB5+c80Is6QTRCRidKjrPEI8bo6YHRxPu5sbO57QSb5AwCjr5jHuNsl7hPINyqsK6qxUbabQAKZCaxwzXV8rsOMBaDVJxBHFzSRnyLn2YcC82XVToptfgbsXBcKzddWjvvi9GsxkE0XNOYvOazqHMOPvzar0wRwGU8o+wQxaMwVykkmoW3TA496dPTCJGQQG2UZgOJR43R0wOKvvpCJkCiXRn69cCS2SIMxInBK06APBgTlmOhxGnWOkbSmQPfTVVsEeFq64/Bu01gTcvUNpJ4VwaPo8XNOOGiQysk9UOLl6hsPK5R5hA2J7EKuFzguut6eYHVrMEOqys67i456hx2MJsOw28vaLunPcrzaTBt3ZkrLzC8Q0rH63sgNtgJSMABxSfG6OmBxZlZ1sONKzhUG2NhziiMas10euNw263uSaHfHkH2RfQag6RCNm9ggpUlQL13Qrwug6YTOsYOjB1vSlXFPptVQTKFBDhJpwTCthmwdtbdnqVVxzG8rWTqEKMv3WZXynVZ6ahx16eXeePJaRio+yAuUbVL2Sg4nMD16T0Qu0UovzjnKdVn6tXGJ8boprgdHGlMym46fziM/wB8ZayjuuSbreQaqqCcMNFINnWinc8woXVNO8lVdFfbB2R7G0ZSzXRRSa1Ca6DzajAmZM3Xad0aJ4STxBTMrykzoYbxV16oy0wrctkVw8Hs74wJGzUU8NZ5SjrPGldpPpSod4MVdkGytiEupps4ZQcqnOrMmE2jsld3VM57gPBrznOYDTSQlAzAZuNT43R0wOjauDjS/k8hMn863h5oUqz3ROyYTdyRTWqedMbrssOWdaCTUtpUbnVq6DAk9lDVFDDLtY9o9kBdnTLbtdAOPZn27760oTrUaQUiY3Q74LPC8+aDI7F5ZTDBwK05+tZwEC0Nkjm6Zmt64CboPOc6oDbYCUjMBxd9whKRnJhVx3dLoFbjOPnzRktj0sZaUUaZXm51H1RuzZG8Zp450Y3cdZzmBLSLSWmh3qBTj0+N0VikZNuOfj/fzCFnNepj2wTZyirEnJuKp2KA9UFZlXMgnklvhgDpEBhE+6zTQ4pVPXADNvs1zBJmFIPoEZe1bTCifBvOeckRV1szTvhOn1DCA1LpCEDMEig4qs9MNNeWsCF5N4vuIGCUJOPWcIP4L2fdThwiL5x7BAd2Sz6mwrO1np1DCB3PdDw793HzZouIFEjQPyFPXASnlReXyj42qKMYGuMXEGOCRHKEcoRyhGcRyhHKEcoRWojEiM4jlCOUI5QjlCM4jOIziM4j+0pdp0jSRj2wpyTccl1K0BV5Pn9sJRYlqi6n4ym/RWMVJmEp8hdfXA3ZZRWSNCVDp1xlZuzlpINCL/tEVcln04fFMA5OYNdSR7YqGJn6qf5owlpj9n2xSTknnD0iFNSdlkO6K3leYAQNxSeQBH6sD7cZa05/J300pf5PRdwrGWtSecdJNSE4ec1gXJVDix3zvDPnwjJtAJSNA/JLmmAtXK8bd9WeLrdawCdvTFYrjtaY0xpjTGmNMadrTFQTGmNO1pjOY0xpjTFHBUc4EYsN/VEC9KM4f8tMYSbIr8QRhJs/9NMdxQlPQkCMI0xnMZzGeM5itTGeOUYzmM8coxyozxSsVrFKxyjFb0cqOUY5UcqOVF1JJVF5RxMA3vG3kmu2B0wP0tk2+XF5zFRgdMJ6PG1cb0xTTFE56wAc9P0rQRfOKtq6YCRo/wD8YX//xAAtEAEAAQMDAgYCAgMBAQEAAAABEQAhMUFRYXGBECAwkaGxcPDB0UDh8VBgoP/aAAgBAQABPyH/APGYuTipvZ/68zB6Py5DOlQ9m0tSzjU17o3/ANUzbWFQYvqLnzflzXU7Z6n0jk1NTU1JUlSVDeob1DcqG5XMVwvehcD3rje9cL3r/tVwPev+1Uf91f8AeqfHvV/3qis+5X/YpO771f8AUr/sV/1K06NCNOYKQyKGwKwTWnG1cWks1SzXWrcGv7zwESyK0/pRC8zNFGmO1SJp/LbkRnOUoECyrsUHAm16fVtkvT/0tFufm0E5x3pTX80b2kpmVuutSVGuqU5dCLqpSzL2qHLpyLmgmuowErUoRKptVYDkq81lDTc0gz6OKmXTAlu7BR5aTd3OCWMZeKy1AZuVol4o0x2EZa4vFCoIziXcWKtclgQlulZRUkRZaGO9FYiODvxGaiwBschuH00AqtlInWT6Io/qsYdkf3WVSwl7qfatrGkfcoC0PvQF4feldXvQOr3oFgM9a3vlSv8AvWApcqM1t6A8Jug+CjlGl9FGAKuzCrfJfFCCz9lOkLYq6FLb8tKXOKUqszRtxXwf8JiJu2DmxUovECzGbdmtTpABmNzf3bVP5/eHdq3X/tPdAs6EBLAR9eV+O5APmiSiQXvkzfakI8aHzfzU4JXIqYC5TZmBIp4I01+eWoTThXvL6Ub0EWcb29xpj68fOMXYUT4geXCRD3UpsZ+aLD2aCa+4HVXO568XK7Wo5XHUAcK+IfloDLAVgYc00E1lrTbeveTMrAV/2JFmXsUJUNImTUSZHWjpvWTa/wCxaI4EEHx51i7UGrh3R0y4KsDU53CG3zaGhJfLqL5rGKQIkaDA+eaDyk+zdBy/bWps3bX9oJs0vQFhQ8R/rND9cAKGMN97QUiwTDV/YzxQzc9NIYjass2+GDor4B+WovUTRnGeGkqwOPVbkPKsFGwDatpa8ZcUCdjMI6ad70V3LBl3N/69EkDyuA96kJIsm4iYOMtuakXEBPRYjPoxb/GyaJolSjBN2HQtMA/iKAqXCJigLhAJHs0GGfJke63s6UqKDsUEWGG3FAWXBTJ2B88erj6K+MeIz+WhCrrvUzxGT9v+qbnyZiJMBZetm1R1EC8kc6dD0j5yifoNWpjpCGFMPMvaoElddTdatReB6zN3pRyrj3P4NE1KamAT3soe7y6+KAwoRJGiOGUE+tP9BtTSIkpv8EGzfSSljLDC7DT9j0zNhLNWhwfl1qMq1W3pFdCXgCmhgiUWwZkgE1nFW9OkuK7Dk5e1ACCx6QfawGBNQgt7Mcr48W2QDKCkLpL6aLyfGUZdz8PFAK6zyvch7+Q9e6iOVkeS9Ta2TCK8aA6TxrSPgtJsLXuP+HpKJSl9KUpwfl1yKUtx6MhhYXOwFAU4YLOo5fgoGw6jutfTO04rAGal9sUONf8AYFEmWwfLz4mtAL01n6ZGSgbjV7N1cStlYy6m3muDlhRLmBjg71Jno4nAT9a/Wjh4IIaiegg6Svhvy9tLt6EzpqFu+dilFvCpRZnYvdoc54sA9STAdwz+obs2oNwEtw6y+TBPI+bJl9TcQFEHG+EztWNXI1G3YD5mcFsf/a3auKipHLi6+izd67Zr+Gahk0TUbnn45srWbPy6oo0u3ngFuiVYU2p9m7KCNGI2oBLAYPUIK5NwsTOjtWdRCg3X/e75SMSsciV2Hf1DF8GGN1a9na9OQGORC4Dpc84itz2q+if6bVEhoxsOHhfDajwRT9kTRGyeZRLmvjvwEJ68ggA3V4NVC9T6AQWnK4DDh6/4Rt3JgYmNXMSLT/8AEQBq2LbzStk5V1v0KuajTEdA6NKx6h9Z6NdAcrUmJxZQRs30xOfNAnEGCxN9UaHq2DzrQLG2Jt6AvEEOTk0TRoKwlmJM6DXNeiUDQo387JqeXM71o8Q/+3VYlchEs/rD4/fsSS+wGp1Xn0BPXkECG4nJoiWqfQGC04WAJcHX/wCaxQZBSluPLnGoZ2inGWobCtZ0fLQBgD1WqQohZoakIc0fcc2x5iGwwISWSDcnGk+qCtv4jHrfsr4MFhJ6EkVlvg8xT5XMmKyXq06dqMAcQkRwj5J47lOX4f8A276Ck7h+PSiGsrKEtktQmJTbpQiAXVxXwCIKn4aPEXakGoF0MJ6+KJuHZdys3GjIMgCzO1akA18pJGDViDsZ+jt5tfcj4M8fTB1qFl9a4YytmeAouiEMV/1abNkCbWEaXOXwH1p1AxhdXAF1sUMLqdN+zT3Wa0xZSumRlJmBJIM7AQikJEcI+EL3/mzeCsQJoimOKgB0XmT2gmLtEB0BwEYRKyuxab/8CMsiaMFx5BQPO0CiRSPJHg6S6ulHaMBgD1eq+pJmPGnNHHeNc9/5Hnp54KThCUud7bd/V5TkbBR8Kt6jM5ZV08xPomcC6+DXlo75Kl03hT7TK5jU8l5zKUrw/wDtwiqDywA1SQC6oEtXWXvTjBnS2tL5VMD9uhaDv1nKRSMFRqXYvqdzUET1HKo3bqNivO2ARUi0AwBUAwRo0HMCOiUqrBoNYfcOq+h8r5BEmwcooYZQTjIB8DCoeLvLyQeQpTLjRd+T2A6FYqTN5GO+KSELqYFvniZG9kFl8JbmGt0ekyRiYdCt+CRQZOVp3Z/+AbMKcrx5LjQm91szAfdGyHoRuLl9URijNAu037YIgw23M5bVjzyGAI2ZUIRp6tvbE4Y/JURAbygu916R9at52B1jc6FWFCfLAPX2PU8csE3KEHh/9vBlyzoySkIdnwzUIl+TDBGLoNrD1HKr570+/wAr6BB0KkWheyG/DQg9IBLfjgiLbBnLQsi5bEkCKxpmunAmwMa//AGaHK8eLTA8iH+H7pRILuBk/t60gxjdTDHVb3rIM5eG52x29BEbAwxaMvVJzHuAUuHKaWn+vSzRx6BILTAQZK06lSC9XDo8mHnw+0r4n/29w3KNpnm5bMMxHicUMXhkfux6jlV896ff5X0CDoVfyyYn1U50vYFwM5eovA1zd6DLSp5MiZUBNQ2/+A3kV8DwG867QKv7gFy4h2F3r6z9jOQAJagDbtaLS+5jWKCKTH+oaLujBbdZhaiyUMj7zZU4oy7B2GnSMj8AV0wyHLDBnf4oS4ZhYG+n2zExmoIFLouxZLZMFLwZWxROXZ0oKZnBZO4U698XooRN0HAkXYESSbkVdVRciuItmmpTA3NnvRkwmp6F0eGmz0e/piqW2rhh5GtDZXy8OB3MeAy7xcvW/my//wBulVUZWWSBs2bI8jV/r5dYXAzPBvBZCaiM0CNkdeEQtS/QFQswGhvBO6+caNR4sshxv/VGUOQLWSiYbSPSkaLbAoNzx0UMY4r1zq+7p4XQb1D7lY92L+Pvok0OBkzHoOY6oLjMapwjICYfAW55xsnsY0uDwznVJbuplG45v4X9XWEOJYCV1tU5yBgJGQaOs+EqEFZLvCcnlBNrVYncmjk0h/OMN6s1ryGG91U0gyGoNaUfQN3Vcrlbv/wM+N4SSt9byYDu/FXR4giz8nomLAZWhM1AIe40gCMIX7r8KLw4XMayf0URIKRLTewaW1sChwTGTe16gdRgUkomeBnbStKjnJ5oKIJiD9jSBFDtZhiM1MX/ADC/ihYBsAosgDpXEUvke1HIhSCBGqwRW7V1iL/1URj8AGBxDRPTmDtH81HMPAOXfS9A9n441HULplgjP1SWCcumDIjMuMVgUEgbF4/dKhkbff8AD5rn0ID48S8gYFlf2Xp6gjxHO+ZKDp0pYCwWkt/k4ShLFi5Wl2fl1I2VOVxR2kWdigH6wMTa2QWOvnZXHIgd2tPUpg9/0mmrHVtDmcPeaZSETSjsdJNaAlkXc26cK1HtP+wGjIQDQoCtAXWp4MShdOAeviRLv9yJq/vZ3BxQCWR1PLsRo7r+SGKikSxZl4VhQIHtjHTyJstD7ikbmzePckrVsgSzpSgsaQDvMPvVpWmQhBliTterS7fcOdZt6hi7koQhpCIlxgnY0+sFT4sUYHh+XctaTahujxgjR3PqiXcYTc558trBSD2Tf+KsIUDQMJgZLXUGpSENO0R2Q+fpSOtE4TE6Rp201o4Y8Ag8v1Nii/YfNM8EZ02w/bv4xLYuYyKfhDYmcMabcdqhQYDi9jJUxPFoHZgemfJIXhbacXXwEGBQXsDWm+t6huFdHKrZF1qeD/t6A8iSlgKGUATVpwnihsWJdhm5p3q1EANg6ydlackVC0LuMOdpo1JtHhxn0kYwk4Q+4Unc2pjSGO1s9z2r4T8uuHNGlYSqW+EJnNht18gg8CoOjkambOEJg6rY+eamneYzdn+CnEz1PrGe/oSrJSZQHxe6jphgGgeMgDgZWaD1CUzUh96mlEsZXx+miUc5GLKM38nP+kcXF6Q+si0eM3dqh3JFgZE9tIPem4lHkT1K2sbUSNsCgJ4H3qcfwC+PMHzQywF0QOoMnlByg7YrFhXt+yuahSTALjFu7bFRXBnC9328NnGkkdHJQYCQFhvkv90HJ8DEhRtNc0JBOBCBkN/QGuUnk/hqY3VszsdbdFa/b/7h1D0BK6AcqA5aJ3BpBcau4Dml4dlAwKtsZyf4UlroAmBLglu3g0W1X3bJOuBzUny/wtl7dGXDHV/gPUiEpQalc6MXzByhtiAB5/8ANgilcBSZG4z0mkNhG7ctOuL9/AMJyuAOWrXmu1L+pW4anCEHpP0tCPiioHEQHomAfZ+PmoqAvF1FluoaY8kIsVHW9RXRB61WrfwVjbsf1ioUzJ5ITzJta05dKVFjUxIRkcHHSjKl4OjoT9GTSkBkKLC6zWOYoOQUwUfZ8Vv/AM9bZSiDAwEMXsO0UYTYhscz/afzWNNDKbaHstPJDa+XYVC6ELqW6nU9qJOEA8LqCHDGPkfktkJGpGMdWmb/ANIqcawuQNsqLvCLAdtTk84LBD15InqXzSxyINRx/wDc0f1e3+GN6NGYZMXEbiXG5ejO6hWmJZIlgm2n/hBJpZJek4AmbSLu7QnEhgCADYP/ADXEVLgcWJG7fMF95mrZAA6FBFDY1djVoXoHMgYyUyxbT5rFAxx7+hwemFE1uJI7FfihlAgyJjd3b+aVCa0sk4afGWTYcx9nkaofCbcu96KgNRcR0pBTB353btdS8n8YfC90fOfKkQ9IfmnDOh3XY3T/AEKMTu1bRtOx1qd6gQTjo741aDKMmKNxPDMUObEnefMyATI3K3VwkB4tjtUcES54M4EZ1rEDlZ9/KE9LWsFvm+K/RJN7/wD7cA3dc7yNOHSplTaELUMkDLtmh+SF492r7OlAyjlaXC64cPTwTun6ADdwHMCdcAdhbXS850bWzJdKBjt4BwwnCETgpt4DJ6Pwly3gbquarkbp6dPCMqBziQmoqw95kM++/gFgVNnZWq55QCzoAbvPtQMXIA6WCWBsTqBaETJyV/CNGo8WWQ43/qrkjBgEhVgMAu1ChF2KhZs9XjDMi4mFghK+gLwL1EdEzYS6z+m95pStgLGJSWd9wHAaP00gSI1ioJC1NexhNzqeAsSKSJJpW3H+KSuCOCbvWkGdrXQbuu95GHLp57zFoptBsF1a5sM0LlDbGICK4SAs6RQicAMxf5bWEEgpWpHyNIjslAF4F1aMcNh9iRGzKExjT2RV7n8TrV6o4pISWCsMXLBdaeAFSAurR4lrPtSIdUgmNdIXQnS97/b/ANqPgoa8MgjdZHUZpo/TSBIjT8w8bANyy8nXwFxEVCQMaTEc7638VzkbAUq9CknPZL4tBg3gItLCiBV5Ad4nxpmdtf34luIxIxyCgA8q4n/jqS4p5IJnnD2SoSosXJwH8ulN/lcFmha0xK81M0q2kbKh+29SAloJHWH4Wrl0jXvt2oBKk9FqE9WTEPVR29B+WQ5C09MURkrhoLJ7+MxwZ0weELTybbNk0dGoBuZJ+yLnyrwRIWEuJ/RrVwVjOwWcvaDwgbaBA7pEjqa9b1HQpcsBlZJi5Qd8XaOafkkiHtDIUbMijgHoE61oT3Ka8GzCC8nyF6kjJL5bz68lxt3QsalPOQvrruOr19NuQCBgBzqUcAAM4IA9l8BbyTo2ciE1Y0f/AE4X9Xt4kAjCLhpU7zMh8EmziiRN/gulCHwnavnvD/VbvIju4bEBPLI5CzigEHHgD9vu3fO5VWM+gQlozRfZGTGlkbmJvd8DRsqSZaPKgclcnp2ECHYd4vnBp8VhcsXuAQINACwAYD0BKyZCbOvcdPCHomIvfByQ+qlZBMyxxdoDiiVpjgEI9SrF/wCVRZVLuxOgGngAcYtlAK/pPhJ9F6mNHO3NQ6pvbJuEQPCaeCOiQbykkdmgAcCwHmgzAxTWiv2TxNb/AC2ZbFuz1CPhovAulTYTf/yIkyLOg+6vWzH2gW8UEe3M3L70aEbHAYPBtmccezSFJVwC34Z2ioC7XmwQXSqVsmaHuy+lZ/WgkSU3CJKEOMiB9vKsEe1kfKrALCuut8pJ9vQPCTUdag54sA2vyfPjHvPUXaumvjjRQd9Mk1ubX3rsz6nEvL4GLgLq0wcicSJZljhdNKFEWCUUJk38hhMUQjrQs0wLiyRGphLU/do1pi/mG+9AR5VxPQzQA4NIEkZyO2k6VdwFV23HQ8XHboLsyeBDbHDL1/1oP4VMEiUG11Pv/wCpC/q9vH5oP1ojx5H8MS8PnvD/AFW71EcDlUwk8eN6AMhmGc3WZDkNtXwFi1XmFjdCCJ2e3rhBOxZtOh2oWOAIOVre4FVFtQnkC0g8BfGRDjFZpjwca+CuMWbOWRCrlJ0IUcQDLAiC424QCXYzk3bJFjIZoocVl8E1SASPmgvTMXIEImolS4nOXqEgkOjnRSSdVZ0T/ZezbUJJlsxMxaVBmxsCQFIlxH/x9SI7uSv8Uu8RJrDNpmxx1ooJIA8wGGTmrIt9nLzQDxJoCM2URO8TQ1xCeSHiMaTA29NtUQT5o26/82NDNyorDVOmJeiUqbiD+qT8n0Yt7uHLFbDAsf8AbwTCjtQdOfKdZZoIyLAJRi8WRkNe1WaoIrxqvm/7cI0gGo0nhGqtPxV/QXIF3c6H8MAcg4fR0pf2OF/mkIRkWF4FvazqeH1PujtCna6uB0lSly04J9YnbcvlClFwEHQDDote4tCNCwql1R+thTuCIO/63uK0f/pwv6vbxKLPIsGEXuMQF8Fi7iuuDcH1pJ8B3pDqd/H2hTzHgDlAth/p6iOByqGOTrgQ1MWXxoAg6kd0unglVr4GlV4pCYCIFdKMkJtDb1AhKyZSbOncdfCHoiJvbByw+6lZBMQxzd5Div7gn1W/HFEf7jQc3T4TOqAYsqd72Nr+FhfyYlGAMr9tQ8MNSJ/e5kbPhrBh1RbzbFGKJH3H2OTjzQQH2oqS3YNBdaHMFA4c6IYRMnggN11J/suKNcGORZA9D/x7CiTJJcHqRagxxrsfrPl9PJxCQ1vzmsHuFPMN571oGtkguWJjmgBobwo5pNrv0TScrSFMOW/yoOmyMEeT0HQyiErKiGC0lp6LHShmpAG4tIQujKd3yXf0F6DYq53zPju84K2w7Il3efPsQ7YqPuhiTrBP7lN81IEZWuhxmoSwPZCt2PXs9JmQkmA3S53aVm5CsI/g196Az8VBKf0MslDbwINFvoettX4IyFiFpVk8pnclXfd6EFqEpirI102NCjMQQNCpYsKSQkev/wBI0359GNy7hy/iknY8qluIN6EDKJ0IlF7tJv8AhCUIJgmxsa48E5p+gA3MJzCA4SPYO0zLRjUtbEpzqOH3yPDScIGKNveMvv8AAQFvCTaoZPNuG64l1cm4nUYCbbuVReXbeZrIcy0iM5dd5gISmpqw85kM+23gloVFnJWrZMxBMRaXyLPgLEi+mEsoZiN/BaNA4kulzv8AxVyRgwASKSORHalbMiGECyrQ1ihjHReuNX2dfCDdl1KDJCjbQZ5FqhQjNjC5n/XibzUqKQNIzDgxuAQRN6+fuSFXVW6t1vWagkLU1rCE2ej4C90nUoe3hbwC59yDoFZi9M6PXzvsTkkU3YZEkGLNRQuQN8IhIjlCAzpFBMwBmL/LawIIaFqR8DQAbBRIEY0cJU/KkAJJLs0dRSGjywwBBrKQroAFS+UmGExJGhQGBgQG9AVZ5RWFdFi7V6U1Xh0h++2lCeDu70YG0SjlIpgJNAO3RObNx0KF0PNC6yiHUwqDUygGwPADYKPmHjZBs2Hh6eAtynNyeQp1px18BbbvShHYxqcNZB7qzoIXDRKnFUA9iEZurviRvSMqxJ79UYs2XA1cntgDMWCNwkhNcoIsY/8AHUlHnaw+8ygxos9XODHoE1lCmMN1Q4QN7NXe41A7xZ70oSxEuG/9MxUVaMQsYj+YoNDgyIZ6X+KEnjzn2z5hOm7pqZO9Z2r4k4Yq8YJlqTsHDOvivFtL50CrIWY0StHR8mi9hBQBwegnh6jMSPior+Gmcome3gpJUUaJ+Pp704iMgINpDZ9JwIrERt1Hs7lQxAEmUMlYGA86qBBOsQLP36z42PqQlQ+Qjr2rOcfqEf4e+ZGCxd8228PpBavlc7Fi+/jvmRgsXfNtvD6QWr5XOxYvv+L5Dwj7UipUx0mqx+rlkAMiXHQlqYqWay5c2eS9w6MB6C9CkuJxeNvlQ6cl9g4h2DQg+sEX069GQnPG3+lCyibnjkuFORB80ymASbi0x4Ahg4zWxZrxRsARAbrzjgrFj0VxHd6QeyKUHZDkV+XwD6ehlLuzUFYhU3HoBPz6RiDqMI0JQKkQG8PvUgGmdSpXSzujLfx61zHPsyAdBbBFOoEhkoTeI7slwtA0Bck9fkv6pCmKQKctRMG9BOIqelDNUDiCUnx/frVKpZQIJ/xnLzl79Tt+Jj2AkyiWKWY8q4Gg+L05bj1UVzXdYo70knK/UDzrciBj5qecUg0i5ZkpVJ5Lw5yvarCKlUztP8aIbMfyj5ijkpKA6MxQzAJIkEZ4pAPSANg6W/pUKYktIlkvR19OZ5JuYV3sUIYAHiA7JEWDDmsCPf0xtcsF3UW5hpbFgXPD75p5SFwwSJ/Prp1vKtDOAmQepU5OjS65cH1If1WzyaetvS9X+Ed6s5qpMQmPDoUaXrF+e3n/AAHLzl6TypcTaSXhdK/6tK3QqEtwWa6SYEc1/wBWmSkaI8aD+Hh/HzIl2e3njx/mm9vqnOXgttADBBzUTnwUpMTVJRk62qVoxmWLADC7AjU0RtoSYAufCLtSDUC6GE9fFE3Dsu5WbjRkGQBZnatSAa+UkjBqxB2M/R2/Cr5Z9w/im1Ay9FV8H1Vhy8kuWuO3pmRCZGkEvnfPMKjHy4KdQYZxianRSr6LLaQ896hzYHqTckHvRnqH4ZmIG2tDNz0nozJlAJmLT8gUS5pwf5H0x9pK1LKeb8G3ssumK59Jxm39TIJg4ASowmRTb0JJJJJJJLRnDYAkQSRwg7+hDNUDiCQjw/SxJAyu5EdB8Vf7Hb/ly3Lzl6XV8r4iKRf8Dt7k5GoRJmoLZqCOTddX68Tduo2K87YBFSLQDAFQDBGjQcwI6JSqsGg1h9w6r/6R2LfI/wCMug7K2Lh0AgO9E28lzbH+CpGbC3UTCmFoLxVluzG9H8RVtBZNlMF7ROLf4UMtkxAn6dHmPjHC4lAqrqw2ZsbsAYspGWjEn8+OO1cByoCtthayACvLlYyceghGEEU8iCe40ggjOkCB7OqxQBkH/wAgcJ9wyoCgDmgQdmPetDt6sE2AEHgNaX1b1NCeDOgAovB9eM83zonBSBz3Ziyl63qALMRUDS5Yw0CYdIoxhMCHQs5xhNaSdX1PmT3Kg0hZZQSJu60YwaAPjzKEDktrFEKHy6n2mzbSPFYu0c6PzEsfyfTSsHQgxdez9yoHEvtpIPUdiUy6UJqt1c+g5cuXLly5NhUwdAFgCwGPQh/VbPKr/Y7f8uW5ecvS6vlfOYPnv/U73lkyYmt3wPmrkJsr322hD/hIRS08MeVYneTAaAesB2BFiBVg7zI5RxcEJuohiRQUszIBfMod0XX/ABwkFTgJuApNGQSHAGgGPH93v9KZM+hhwfdK/wANmpxGETN2Gb6J3f8AkTInFLfrvMFz46WdP1H3h73Whxq5OFy6+m6rQ3XloobhbirCFom+JbNqCY4eADar6uygYGPIvYciI9mruahrgYLfFJDo0DMXOZbUo92BBgzqT1Kw7L+ysPbvWFu7w7Z8Yf7mf+yoobG7Efh4pPYj2h6Ge1Lo/SJZ7yJ1A9OUSTai4OEjJNsN3WoduCCL/wAHrGHNTgDKrTGfBIfZ3jhcU8gEW4Z623TpWL6BtGSTU1Mnpw/qtnk6OR5JPcHekWkR0PA/ACNLJ7B7/wCM5ecvS89SjElHaZ6+GKIscbCkPnwfPf8Aqd1JY4wMx7IV1FBiCBgDB4ku/qvuIvCTF1QMyHjbkoEWJfXDy3xPc6eGCbujMWTKUpvKQtPUWnUdTIngCUnH7weIwZIwYp5Is/0RH4CTjYtVhg3AqEnfeCmdg6Lmyfo4dSHX0QPFKxND5QKZ0TUiTvcOyHzs2lTcEEuDFhcCyZieA92CVLSBxpVm+WhIGpCXwpClVnZAOGCxg4pbdSOoVGgK00yIBl18MBAzwasYOK10BAEWAB2PARPWrAqInVBvSJuS48rC4GBki+VoemZ3Tu+lnjSKtDNpzuGiYTRt4Ol6TMnY36ctRlCgW6hYh67Wq3q6wlxBASulvC3/AJ1Byvbbfwouu4zkoV32gOtJnUvAFeuaWrt4CzMhDitsgwlDOOOwBdaiixCovhG6RCIIyxTqBd9Ii27ojsoBLjECsrQ6FFYY0QwgRBOErh8b4y0RZSBXe/R/5M5gANlnDwtFtJjoWP56PqQtY/VIhRdLScsPg9KDmhhm4nd4qV5tEeib34wUEWMeB+RvSo/L0Ls3QFrsL0MxYidWePlUJzSB9hHA1rFg+Br/ALaZhYtCQdMjDpUWpkQ2rkcnwWLtY4pDgchpEf7KIOU6AFgA9OdvNO60C0iU92s9uCZj7b1jVGFbgHcKjhY1KD5xEKvdrstsEoAtQN+hN7Zx1L03vcaYn2bQ671/Sx1ErKMyDO1C3B5yeRhRJZQyHICclSTblAaC4ZQBZEDLYi6hO0i0GIBPA0GjoK3ZVQAI2AVf/wA6g4Xtlv5UZQ5AtZKJhtI9KOD18jnc8W2pLCrbjuAkl3Rx4X/86g4Xtlv5UZQ5AtZKJhtI9KOD18jnc8W2pLCrbjuAkl3Rx6GGy9ogCRw5NIiceAuDmpTHyDX5eEh4C7mLK5CXJRBhiEuXrbTAFkeYbtI0UjYk7ebTikQg3QotjL4BgEIEWQ28AsCps7K1SRgxobIK1cDTwFqRfTGWEMRG3hdBvUPuVj3Yv4++iTQ4GTMf+jniE4j7T5FfNZg+TH7DbxRstjDpRvZdfgEUAu3G9k8BrhPuMPxTczZTaX9Hzl2CyYYWNNfAWZg2gDu1cuyZmiva0WDgRGI8z4PRupHdq0E+QrcXdt3tPgeQmHkXZBr9Tvr9LtXx/lJnP9TLFHv4Fafx0Uu6qE5KkxMqZHZ7X6f3RzMwMkGpwd21PRg0h9rWOpAnJ4QZJoknksIC2CJ9hQYUD3f+RtdhBKCEtvKT4n3Dis3PTAkIGSUEQ5vE1J7BgwMgDq+g4QBdWrRxxmLwOkv8Kg6/HMnMm/fyCgHPLI+m/dslPs1kWjMFgsCxUQEEh4Eq+Cj4+JR1M7BHShCKxl7BmXCbQcxRZ2sbMGFx7np6iGxopjNEtW5OjqtaMTvLdOZ29Z3DFpqCes4a1Apc/KLiJkfBdZ8qTBp/2k7P/wBM4SNtFtvePc8ma0Tp8EfFMsF9hPx4fPep3HIg5JfYSXHeo05BMyA+Eh1Y8zBCb/tRCJp93w/d76/U76/S7V8f6BM5CG54Ggsv6fn1PujmYwYO1yhMuS5laISY1pkglPRqm9w2tPnWKAEGL4Wls3UisqznkeVImiPiqEih3/c0IYBB2/8AIvZNPl2petKRZx1TV5+XWjWkjUCLz3Ny5r6eY/eMP7KjxL2w840vl8BU44ImEnLQ4LtGshBCXl28uCSvtER7+myUsnQEtTSZbwB2L4OAEwX+ro7fdtUwbhR3TidL7YIAYKXpiT2aCcGUE14iyogHLC31WkO7UJIgiQTsQmjBhMJ6BnMICd5xuwc3oLU0UERguLW7K1NV0ffT6wjNbtbtKGxukhgxTWj5kZSYUspTdsJf1xaCJgZSc/YJS9C3yS8NrOyf/TRTD+ti/E1hiifgcj7eISffQRN0S4YYsfA4hIjhGmFOfgGVXSgokYOJ/kF1PC+e9HuZrYDJMDVdCnoFRVlsbyYE4pSFoiD4Fhh6pLFFwQTBKhx7heb5bd2vukZyQrQCRDZvAWHwY+boTuQbTNoFa/U76LCgj3oDaDbMsB0A3U4J8E0wjcRnYZF0Wvjywkm2A4zi5CUoKIHwO6QLCOAdOwGkYMBaRPYEOPTfdHMwFsFyi4lxuKx1gYl4G152h/skv4HTCPm2AcZbAtElCW/2Wju8bFoUvcgm36MR/wCTO1JmOMPlqKdQ1IS2CGMPcNSuwLYFz65NPSbVgkum/IPPoZKLpsK0LHX7nlgoi+kMruur5nJECapPHf07JjdSz2TUnRG4BEi9F71ImcJk2YGm7xk3qNOaLI3v/Q038kEYkXj3akwNBTfuv7omp9yw0bZrNOFLEr3Myu21A3lAGFPCT3ij+GBx8eQFzKdBTutO6Bi5q/ZQbsm98nFqXYgkXX6etoUpbGJbq9ceLvxm0YbTjkKMFCPgadE//S8hJiTgcq5yVOuAKMsm5jJ/I8TfXOwsaIb9sTUE7Aycx9g894hvISBFzfzfBi12SGUz5yuVZVu+GNs+8/m3w8+P/JiFr+zz/avBrRC2GZRU41QYd32aOVRZJMXvOOtczeALfxgWADz2I+hM80TsEHIRSsaILTyjHg1SwSrI7m+E1i7xiv1O/wAAgYBPGsCAFgjGSBFxwwcihss/DRtTZI4WLYYrwWTrXsWI+Juh0l8E1uIs8ig1W2RFqEIJlHCCTV7qkt4u1OmJlJqYTPctcpQIAUAWAPAAuEQKyC3FAzaFpEAomFJ5aN9I+BAARAMFDkOLFEoZumDr4DExthwntUIZQcczdKW8x/mv+LS/kjdRWu1qCDNGkHIjkpwNil2mLgJ1MOjTyxkRehdTu6tNYcXIW5K6CQK7lAgBQBYA8EQhy2FD2NVoGr7RbNKvs3Q0X/yTKgoM2Ej99q0UTLqvkrNOdPnwZE/TG1TIiRghm13y7ejN2lNRHOezzWGA/LHYp+70EBjgvdoJSQOAPPchGCpssDgPl9NxQl4CBSaCbc1LN5pIgTgdS+U4oXyYIPVB8ehMC9BJROFkiUmGC7LkorPCl4KjsE8NpB0u+g1r4S7xlhKgRLZlu+qowzsYRHCRd3tV70LK75Po2IpZb1d0HdWhvgC4i9aO1KswxksdwsCgtQJAUiXEfA7ejOjl0dHsTI1jCh6BH/0yjtEKs2Mt9smowBQQadUq3CTaMf5v7vfX6nf/AJSQgOALygx7PSkkCic6nJl9xdb/AMowLpb0LHvSEZIQgltvefGbvgaYa6Ph1UaYs0jdi5bOGgCElEicPnYESkkAwDS58pNmYBlyavFG9CAsFl0PsoBgD0NBlEm6F2bW/n0EOUiQHeraZJMIDdsdpeKgJvI+sl0m2nsY5ZGKVmwOQoIIcAQHqqooQUHWxhPepkQqwN1lG8wc6PAgW1mCO0tfCqNeTHbKpfXPL4kvg0/DhEpzHCXrAgX2AdiKNcQTfk3mb/K42yaRrMpMwgDgMwXR+BVasLPWRLI7NAV8oaW7ABf/AOFmRQcIaE/l6HkSWjb2Rg+g9oqdwhAx7rpLSzteugHVHOo4W7+bSgqjuB4mFwF1aS4kkaoeFMc5hN2Trr6USo7S5TPldBOQD3aYGg7yepZ3aRyIHZDZM6v1UMLt5ucqAFsyvFWngbEkRYeye6pjrk1gaDES2SxamHDxO+/J6pBTn4Ayq0vBpAjwj93btWBinkllH2XXwyYS7JohgpMTPsWfl361AEsiKQUi91Efl1uCTyLrEEJGhc01Eplh/ENotSX7bNYeT5UNvZEmOpkeHyCfijfUPbwbOZWACo8Kk5MREMEMxrHaojxhw/0njZ54U9M0nCEspYqHvkRGp3rMTACdSrzdGSFW5t9FdCKw/moW7Yj/AM03cmQjhAJm21B2UafwUU4ukJ73T8UhlBqUXWAtV+lzEC2yo2OvdfcFnCxRyOAhj2XvNcfsY+PEqAbWcNwaYerQdR0Li9SbFjcEMEaTGWCkcuAym9M9hb7p4UPO/pODxYt15Bg7xHerBorlk+n5d0nFT1rYSVGYOiTvRAZBda6Rbt5lOoAd8LlIHjwsxD+E96CCRCCdJsnXDgpge4unstzwDoSV31Vh1tLdbDVoKg5hIIf00UDnM3W67+QpZ8KDu0BBkrJy6datY1KT9qQt8yOGdG00qUBYCTic6lO4zScoImklIJLVnvZ5+KZZLBbixkouLz0IyEP+6vLzL3gN+KAYOFR3Sa45iQPjzH8YTQJaMsdbAsAn9I9PWJcrvRlehT9NxsHE4jzLtSpt1FStZ1uh70GHwEA2PI1Q1zkPsCOoogLAsBp+XTPao2U6KRBQsEGfYkT0IKJl/MB2qS9brGe7wDvQZUDTHNF7qecN6jYHEgzTqHrnCccFruWgzmHgA9VQgwTiInXLafRDQ2gzIPvYPelnDd4gekD0QpMn2jFDZ/XJuo+4rThcFBRMsoDtM5tS7HzJ6rd7+VwSYDq270Cpj2apmG6sHv8Al5rJ2r49QY72LBzMWG/BNbMoRmhThycJ6JQSgIj1GgKix0lN48dyiUoshXSFV3ir1YCk21jX7d6yJhPf7LSQqJ85Q6gyemjJnBoIkb2M7+gsXcVLphQTUnVpcefEgKBnGYF32osHLmXcSp9TszYN5fBJU/pfZvt2hFooZZpCPdy9/Pm1FlmYb3s6NZgUOD5GjBdfy7b2K0O1E2bDUIaGRZl2yw6hHY9LO8ZpdEPjwSCTIklRwSOEmz4oWGmJVnsU0+BLtpab0KOXLIhDtl1tUazxf5JT8U0LhyKen0ULEd/oHzZVpIY/T6CyROohcfZparsqhuNrts6PBx6Ej5oxvyVydKJ6DZhve/4qSfBgwQkYDN6Zr5GeXud4pbl8LjW97utAAGE+1fL0UM6moLHVbVOaArweMuhUrWYq/vfl1g9NqUs28L6pAmXKbXl3O9EwLNaRv759GPFYqGqIZv7eZww5CT5qTVWsi/bT840C9or81fxko+7+FTzOUA+IlCjmI0yh9okGZHRGKFX2EgDK4ZrSgu1gtPDV+DGkVwZiagDezfarcqJgpWGMljRVYPyeg66qlhzcBzrnUYjpBCk6FIEwK2lJOKUEtlzc3l4DTajW1IYtEWiP460sztHPLNiLUwa0ctrCfvF6HiWQW7EfmssgOX7q0REbBb1Ho32UMrsZ7JqJuCbxfvSpw3Fazn8uuOxUdlHgDxh2EbJTbdCUK+5i8XoAXBx6BhoQL8yn49W3B1E0LEs/3xRLpYOJqBNja2lTS6R1nP1RRTGu8/uoWHEPR7Vnhzb+it/11Y5bFSKnIIBft/MUqqORL8pu9kf4Kkl1+mfy8VN8w2T9uDifBQhur5T+XddWj28VBw0HHFtMKEezsEGPfHpHoRDLkw2Unu0OPEO56ylBwkSPo8wFeBdWhHNMhzMlO9jpEWvRDDAYAsH+A4WASrTWwJvQ67HQoJySoAweGq3VGMbv5dgTXwXkKuEyyMFmES1nNQYa8FPJ/HHnvM+t858lEJnshL5PWcwRyPNTtYhBMln1ZgoCFeP7Ua8uP8G+U67OPI12KBACZzytsPd8dNurD1fy7k6lTv5jyKgEsjUTKQWZIY9xHUtRWiQbPmKJHu7/AE1LWF/aPuvqtFlYBqYHlA9MBjoHK2OaRw8QlN03iPY/wb9AEHP8QfL3pGrrlgS6tNjr5JWMypSLRf8ALplxuV8HyimiJ10uQqEOESQsfsb0xIKRNR8oxy4NxpqROLjYjrNyA+q0GGQRCCcLzz5ZZUiL4NRIt+Z2moRmI3Pul/r/AAI81zIkwTobtEjKGIRglb7qACCweS8Ji69Y5Zu/l2UozWrzHmHUNqWWE/muv/TDk1KgdiiEiPliEkMHsnWUhUgB4fUbFXyYQzMPCamyPkuMhdJcdW9vfSikDzR3Drl2H+AMk5D7c/YpcwW+NMLp7nWgrKLgGAPL8pUMO7+XRLDijB8HnaLnKJQfXFKISxO4td21AQUvIHUfIJrlvEwhuIv2otxU6gQPeD6ji9DFHETJkaSNnptHiN+Ck4aKbL/FDOuwDYRvbjRZrHrzHj4XnG7pU6t2Ngse2ibzQcEEwDAHmk/QaxqLv5daOOKu6L0MhSSdUP2a1hEupA5bRP1zQnalf7fxkTO2oIaFcwr3do93qfAaB6p4aRc7+D5m/VG64DVomU6FibHRhvscBRjkW4A9eDAbLjJvsf8AKWhBtAFk5X5vG9BIaHgHB5xI8ql3H5dQKdyrodno59TaDuOjTdkCt1E2ILH6abPgc7h4mQELO6f2rPFMzAGoBftkdfT1GzWFAAcBvpKlGYAP2xrTFrySGXEZ3Db3oN9we6bVfWAqQGVrUFwNGj7GHNDSaFlRd+llAA4FgPQcJyq4xF35dQOw2r4Z6T8goUSJQTBMzkmnwqO5ykDo2J2W+6LmsrkThqbMztRs0kUTPM7AWkYd6DyApIjhPSSOJZW7UDKY0yTyF+Wsog1nEFlbrF+WhYsWcfLq/XrSonAk+2RoH5rLBPcY0Z1qBeOJ3B0fLr6UdlKvvfl1qpuU5Xh6loziZ2/hSPGCTgurwtNZMYOB24H4aK9/Es+w++lSZIwWye/+DFCCTHoqzAsltLaHK1XeiEJD/YHpxQf5FgMBLcwZ9XA6gg7tTpLqUk+4utuGpJ3LvRiKwoEFPQ9M9WVZxL8uiZK0uyli7U1s9NASuU0C6hIyFNpKOQQsP9S6NqSG+NMOhg1MJktRmb4XQJZPEzY9qwS6JPbzZIChHzrxV2P8FO8avWiFbAkZ/bDvtQb5CAGgHqZcEHHzTdtnQtMORo2oQNbs+Vb8NHf74Mf0QceqYBu/L0IT6KYFqO6a1Cv1XQCWRuNNRMj9Ap+4m+8yn29bUucAMohuohO1BYY4Ja7cow2Nng9ST5qOu1RUE3izrTP6CUpfFXj9EyTYWx3pp2PTAeAn7elTukj3Vf0Qcem1GMqB7tAGpYZvZ96ZfAFctmUG17zUgXT2Ql8Bqaq5Dunf11Cm6pt2lVlHX+XPqVgLhLQfF/g6fukIKYQQE4aKFl5yRiZdGWtddi9xL2WuszPYySD70AOAJD6zNvakB/4YT/hRhRwknx6HJa/vWpEPQN3GUJU9+sTm5e4UtICKrkTLKdKEmFBbW5b21GBbHWSSACsWUDLsf4JJ3KgJgt6DSz8tqiXvTALHWWKJBivZazTf1asQYctT3ZN2oMfNqH/anS+bRqj1aYpe4u1FEfNqT/K1+1UEj7NGV+bUsL1XaDa42WlOfVq4PkaP+9qHqdWt/wCbS4lpeezUrILMC59tOOghDdg/dBHBItc6UPLTkqI6jU9ztoWN8k04ay3Qb0mVoS5gaJJFphqzYMluDyfRSAYVmVyYFQRSJtEX5TRJSZvdaLg/mL8omnZDq0qQ+TSsmN6/StZ75NKs/ZoBk7tLg+7X61pkX7Nb3zakkhPLWrl1abUfJqxH2aNT5tf7Q02w+1W4+zSptmstKCzKsiZvV2N+WgOAKxnG7R9G70IPj/1TJ4Km9Q/NHvFWs/LZVAGTUUYKzV8M/wDVUy0DAQFfLUYfV+XZ5zWvzB/6+j3VY/y6vhyZrX7P/X+aoR+XRJjuV8N/6+o2aF/V+XTIO5Wj2/8AX+M/l4M81INzB/6/wmiafl04byVr9n/r6bMNHB5mzS66Gv5cy0WIFIRY0v8AFv2bwMU/C2pzTaKnjmBk666a04bl12ZJgiNd+a0DS+PLFRZ2yoUb0IxW8oRN6m6MEgOaRdVsSDeZKhv/ADhk+9Zoeod1r2mhJZYuN7otGTCan+KpLurdSzT3OP5bHOXq9P1VBoTrao8gFgaJ/ZTp/Kgf96dE+9StHrShv61HP86Nj704DXvTpm1MCEdak2o61+1pyh71rxrR/OnYxeGVoriDqjKfVMcaMJRTlF1EyzKpN+3/AErqRr/soqE6p+9EVjaR8UHcJ4o1fnV/+9JFT71h3zMl7B+2q7KZUnLAPegxDGQsUreMh1iiF02Ip0sUdrinAjmxW5N8D1H9UasqY8PsD7t6mfOgL6+DWHXxo9XZ7UiFg5zWCPvX7WlkoDhr9jUd+xNMiA70Ab+tf77ViKwyB96dKkeKQCCZqXT71xfemzUOa1zlbVPIl96BBzr/AC4eqK5kk+usXaj4iXc8uDvTFylRSGuB7UqOULbQTpDsYQBBGWgix52sKAFi4lp0zUmxwgSey7qqM1MBS30HYoXbgBAdjyNEQgKLpB2Y4rLNIBGR9xE9M0Ht+avkgsXkjmp6LUWDixdxqOEIeATPCf8AihDpoFLdg/hQSVyIhwnqqXNcnFQWtGm2D+H5clLLCmYOtV7mz1Vi7QAdfkxYXBUGGhMOc7v1Uek2aA6xh7zQAQYAg9AJzS0AVL0qFFtzDkytqmiFcpAXNpff0QL5wco7ODt9s6xXWL4g0d6MpirI03gLMfJyc/dBYsAknh5b6uO9al0Owc/aW3oaYyuROE9MESk6lHcJXwGtAnD8uQiZopYJuWpSvD1AHOYbS2nVtSomMSg1tD2HE183OHBftMvNRFj0RBxK8dutD5kwAauRkJtrQlCBBdNVrQnuNwXs+kXqJYYmQcOPfvRr9hv+MjxuSMDcjRyn3pU5zMjNb7ZqoN6gBwXXL2ei3D1PhNCA/l1YGYV8F6ScV8pAVKkYyM2hfrg1qIVcslHu+qCkSAQB6TPmIRUoz4L3DMPLSjFJAvCdCpTa1yx6ThTHSAhGjjtlqtF7+woQZB8QKcqyNJeS2mE6Az6W41qIaEZ27gOL81Prwsn+nj0snSn+XY4bE3K+C9EbnuXgrUJQ3v13eMFWMVr23X+PTfEh6AChpCGYJsM8kxsVCXMH28vifWBm0WMenHA0tlydQxTFrfyeZwQ8nlCplO3sE/DrQtV3rHDcdD/qoRQlvV68j0cXpUbT+XRlU5fg9AZJspf/AIOatfskG6i6zmh4HgD08U39wLdfsfdo/rZJeBlfJidYzcwh9MC3Bs0XxkyEJWoETfzBvJGkRyJV2JWPM/yS25g2QTNtheTXXVtJ6GD0pqqQT+XZTjcr4rzx4jQDdd3g+aWc0ZAPPwe6gIEBg9QTNkAVThGrTappEAmnHg+XymSk7BK8t4n1A/LY5nSckYPPcIDMeMSD2l5s1wwJlyR+zh4cwBCznmW0GprkPPg0lTT8usvWvgvM5Ya5nd4PmrIPhWxqFuhWPUvAnuEwH7apUg4iE/8APDzAFxSkA26C39TtgyP54vxQZBJxOtpB9/QX5ZCUkY2OuKK+TVLXDbqa5NfNg1idz8uxmKCSiB4Q8u2kLK/rehvXNmA3Q40N80EWPUILwLq0EAqCYIwhxKscUdwg2AMHmmXabg2S7GxGPUzSYMBsC3tD3ejNzHRcF49uzJfNR8KYdvQ32evlwaxNZ/LpFzuVafDyCNkE/XVqPKwVhoRjloCIpYAD1WKkXedrG+BV2Iuddfsl7z5xbOQmBZxG3TT1X0lAV7FfTQzc9DNYpXK4XY7I0etlcgEuR5XGq1PJg0Pmfl0yw3K1OzxXJxS0It/Ijg03qF8u9bV5fVmDezUbHktuPZfq+gJzlGgyfVK9j4Dayyxacwb6IfEjkBCJUvWYDNv9k36NKTIyQEj44NJftc/LsuaSlL8Hj2yMFFticHep1ximf+HrP/hexaY/ke1cOUYPyPoMetCIkNzj1YCk+5ecdqM9n5aPwekDhJfwnkN42eKjImcu4u3zy6+ODNbeJPy7Ida+I8JZ1Pl0DlbVDp3NxTIGxi+vrMQDyWJgx3xUKWIZznVLW96+SQFCpUSx4N81LITNxJxFXdnZCNNKTpKJ1Hikp7Ec8CmExbMRQJbFcfUycd6BQ0RL2cBjmliC+fyugxxMVKQYZajvFB3C5MPzQ0BzZazj0ez6/Nngo2SSEYs9OhGcQarPUdnjpQqIrMxfwLntp4OKEd5+Xdjcr4Z4TfQ10a9NS+tQWH/ueX0mhjkA92nEGnI276Umtv72StJUB6uXsyAU3JrjkwWZxEy6VELMAeiWO7i7QAsIUWnWkJnwEJfI1MCXfuIGekHFHUhUj7JQcmDeVpCzbJIdMXmaHLKEXT1mpBdaQDiW3araVV95LGs1n5Ykh4GSjCAgkaNtVCwZkSowCACdDoFYSsQsTOpPcod3ETjs120qOy5FMG/I4KCkxCDV/sUGxAHxPRJatPbWz7NEzCal/FrXFdanUzCja5/r0zlPBICEaCTGlNl5cu7hWhm5TiuOL/l3f3Kt6BV/WMOuioYl5TEkokIn69CeaIvPuNPzROsQifgVCTA2s9XC6MUnKAS7N75TUGAv+Z/JRITwCe5L81ith7CaJ8MJlSz+mvotTg5jdbnn4sGQ+aE4CfNoU1YS0H7f2piDBlF3oJjS44jJ9ClROxCCJJlwntVvQCy97DSqVLLqMPUDPy94fRfqU9lDNkC79m401FA1fy6UDvXwyrt1OacCxYy64oUB5aAjy58zBHzUdFG4URMS/XNArlLQ37XfezUw4EkrF5S699Nq5lwUuqu+/laxGuLF1jdtzQkjwokpXouKmQSFaPUz4KSlE+D80sgCbLQxJfe8xUrFglJoub5DJTK1IowjcJ+elWdwlFnqr+kAcJEdRp2TCjJqBiX7OVNSBI30/LoW3cqQ0yuwVcDPHudBB7+TJ32Mf7anuqSScWNOUdK08wH8R9E0ckSJkzMu+mCDzrF3FEbGXMLYe8nt6WDSDzmHI+mQBzhLu2A5dKYTd3CLDBeOC9K0JRMqx9UE3EOZC8NcQcFqxikllzfo96c2QzEahZ3tS3CoSAHGj3ijDCYT0DPJMIZTLo3qy1m9kT1z3pjaRf8ALsw81f6iAVDbTdFRkY6ry9/ACrAXZpBFkKVxF30tzS2GFna/qLGlWv1Ak9Vu+iZjSuCZHbNM9M4xk+F+/pYVaBj1FTf0h/IoahoNaHTqnOJaWrzo4oZPvV3XVoKeX8VRpyFjE8XigIcVFef+sYf29Rc6LEoP3egAswrS4aO9GEEuJjzApwykIa2C8eNDoyj0KQwbn5dEuogWE06l9MjXkeGbB+o7DVdqIufRhkkOZEMOnNCpBDPJyHR88+mJRFO8HeTi+omnloEHpZulTtBaTC4+/REG5bJumhWHONyzpofLRcRxgHggKoeTSgpuQ7XzLFvfJeYz3pfrCdkXBNqYzgiwt12OTzE1JjUSgPsVESajCOH8u2ezvIWq0Fca0XfJUUoCz2gfsUAcNba8MuLwoseoQXDV37yrQyRxPD2hQGWR1PRW+ENwE1BLZX9MDbk9PJGYaIY+y3V6Bc6AFg6MaxeOKLilqzkZ6mhgoMDHig+TezUsfkh0/wBnncAKsjWkzGxszpjtapUPlG5fcRooKpyiRPJ8/Hp9bPap/K1XMv7EP5dkSSK1C7RMG0ZxzlWtWEPAzg05UaVx0AGAr9mLF6KkcsXDpMnxFW0xHIGtpHzTcEqEYXmbrtFf9nipcrkF5fTzPIGX73tNQNN13D6enYl2asfrAvsvL5lBgCrATDkc/wC2lT5XlEyf5NfKGEH6pzUUZnO8H0XRUCDnSLNALcjcYzWHVbWu180dk0fE85cnaqFQsQhu+Jj8uufeNxJfpWTvV0we4/FjeijtJgA8o8bYSacuanML7Pip5qWkN08J2SKw5UucF5UJN/ahilwet2vxNHJsLkAcSrnilERMOoJmAtEWHbACD0/mqM0ceULY0qgKnb7gzfoDNDSnLE/1HHmOZeFCmK+VyS+PSJmMYVY7RQonNy32SoIoMarUenjAF3fGlfrb8uh1qGrx+8p0mkOEcuq07Y9LVB1uR65rJeqUAUwZHvW1li188bTUqJgoB+m1AAIFw7LPbOaiw3lPp3nyqIzuM10m1hNvIaQ8GpsNaeSoyFo7/AqE2AlvBquvnTMkOg+wKIdJbNr3/v00JmOkRqUy5euZlzJKrXFAkjh9PPgXhgjAl8HtQEwN/Uh6WraHWPwZUKHeOixKBIQXkC4Rhw5b4kK48HCAJVwFPLEqSvmYAYYA5JNEn2YzEx8BbpZUZiAYZYuASInR1KM/kdR4cngqd8hri2H29q1Oz1ZWyQHBHlopEny2UratLUcgAlHKYkZ2iK6HpxOiTbTeoUIYX3m73KiOOJfbPocFpolGVAIsgJZ1PGKtLSQ/1VqLFA7N5fNHuYGgA9BwFwvs21vTCsHtnqECaR9nJSSXMKRhWxOPdUzcpDRDrgJH0UMPOfMZ9MpyAC7l2GVoS1I+DVmefpW9A+BYEAEIFfr9ngxTlNc2EUJ9aCCUcvABpILHGh396NqWY6jKwqu8h5fyPe9DYSJUShZ9jj7Vabs9ULhbwXWgdZSpREGohUSnlfBBs4qBHmS8ojMKgm6sSIQZL96XFhRDXNxjDF6OJ0JFvPXfLWT5NRukQntQjc8k14E+KcgZcyrjXwAFjQzDhH8Uq0uVmDAYnjFAMAejx5IgXXqwFBFj1UGVmhBqc1JiUXZf1h5o+JVdsr2VIxM9G/pgiAFCNxGgixjwR/X7PB9J+AKlhwJ7KaoAmHUzAxkm0TQbSHcIUqcA/Zt+R7ZMVcYg5kntU8YQ2jEFvb3r4L1cRdFN82Oy/wDXn4hB9jRW/YnOc3kpgKESAva6cLaUAHLD3LJP1rswC2WMnvFA1rBT8UF9hH2q7l3SYf8AFTkBc5Mhg6ytUPEiWDc3Szz6YWQl0ISfP18zpQsJb29ijggsyyW5fFY0tEc5PWI/r9nhrjf1UUvQ/cUFdi+EsN4ab4suVJxAmamNSgdv7fyOohy9bH80hHm6dVGB4PVYld7F7Hs9IyMVo0nljkvY9ykEXLSP11oOhZYekoWW7ihXANlxAnJugqGGgAbAlD8emeFiu1TuqMx3O2CB641WXTBgdNe1T80P8kfaaQApkHL1pH9fs8I5LExOT6q9KHJBxm1F2L4TSe4m1j9b1Gx5bjn7u87S6hcthZL5HLlyfA4hIjhHzZO47KTbpI92KJiU26UIgF1cVEZfSDfczt45O47KTbpI92KJiU26UIgF1cVEZfSDfczt6ISKh873RkWcGjt+JtEPSg+0VM4iWbQgitXmHqZUYVLdbFS57i0BiMWV78eoP73xsNWnnZAFjKGV7FO+eWDb5OiNmpp9teU4EDvgqSdVKZCzGHo3dVqStfLCYsslzZxQYDTGW3+ypGLok+PPEReDEX3NIBrURAO8lL1/+8ilE6p62sDuUhkHpo/XqC1IChMFpTr4fZw09pgM2+1IUrUCQGK7ZkYLN3zfahWt3qMNKISNdsvoLa6XGWWUYnjPwX+yiAJhQpG5IxlATVuFDNtzgUAdD0IZK75qviySCDDvMBBn/GcvOXv1O34mYuDvVFTVgca/s96UpweoadswmYZI6DXz7kiPiPTXD2tRcxMHLalQkB9hDb3N+KBLw8C6pJLuQTSw2aLBo7ggmWBVTUKhDM6IwdIqNBWXgXc+3ekGyZzSMz3FIx+bRIXZiP1vVpf5kGFu+K3qvGp1MnfyDjCKyiHiaS1ygax7+val2pNwpiCQCWMUL5hjZ/gr4lshI1D1xmdnUTOuaBACgCwB6MP6rZ5ARFCSLKfM7qgLH8YmTwY/ijqpYOjl6/4Dl5y8j0xsadoezr4CyVIpnWVyG+5Z7HgLg5qUx8g1+Xg4ev4uiHRytfGJT8JZsTYYDwCwKmzsrVc8oBZ0AN3n2oGLkAdLBLA2J1AtCJk5K/hkl1ERbE2iL4tm9JEPBxlkEag4S5Z4aRwYAatwuK3Sw6pJxYBolnn8KoxRUSOVFjG0iIbdx0pcsPUEs4wZsBQ84Ndh6TNoDCT15e5pJuS3V/HRQCCA0qTdS+VG0qMOjCfIZEJs0TNtVxpZAMEYl/TFNZOpZhGruZnmh10DQcOTzQRMALAYUI91S4PH03ImO9Wm5hM2CIUJ+F+ZJufprQhgEeunkN3ATSAorJMYsOaRB37G4/gn1FInItrJDElpDp6H379+/fv0IlyASkBSYbwvX0IS4CiwAZ66/wCrSWeaEZ2FHUdfFX+x2/5cty85el1fK+Ju4bEBPLI5CzigEHHgD9vu3fEEJICSavYHwIwciSDFMekMZFGDv0/hXG4DqqhAP9yFWDk5oREOXdFr+5nn1NqLGw8YjVQQgwegBwBTmY0kEUBzJu4Kv7APBP258Y38fzKlI1ucQx6DgLAKiazVwp188kZ+aSsMACD9b0Yn7fR2tAY4aT/EfQdQXw91RuAoMzOs7a9i9ZGGAbWyJMX3iuMpB+PVU855f6atLqI47X4FrIt2eYfX+ZD+q2eVX+x2/wCXLcvOXpdXyvnMHz34Y7y/hvcU7NrcZJJIdqv0dwCHSv8ADxRYS01N9hMJ6Yue7lJldLy9AJTSqAKJXKeY+QfLWAg1z4NjyJyQ+/TSAU4Da3oonAytioANYebRD4qCBFnZV91MwMJxLrtUqEWZBtDckZ5K1spOAnePdUVktQyzhFo4UFnYkvhwOYUl6iHSzIyt3pGRKNJ6DQzcx6KOY16mK3d70w0BzvMu5Kz7y+Uz5fWOgMnA/dDK2Kd7oVIZZseLQzDtUdtNEcjGl2i9+KmXawdge/DRySenD+q2eQlZ4rn3sO9GSQdBBuQR5PAJriugWdgT/jOXnL0vIA9YS54SVmhqFUIAMrSTywbjvjz4Pnvwz3jEQtESv8C0ZxQm+iclLOpb+1GMB27UdkDMg+kQphKdhI9vOWRdcrYatCPZahv/AMCtJC4u7rXygSwp3urU8Pvn0azwBi9UImPapERbj8zqxLGW9FOz03i2OctS/vev7d8RmREKNnXNCTPDGh+lqV1ry+4ETvhqWGmeDK8fr71EheO40cmaBAHnCMTLteRiov5eK1rNyO9LdVMphslTvHESHJGTyCVv4iUwOVsc1e0DDEyPn+qM8EjRZAmraB/pF62Z4GwZevcFRm0iOOV3XVbrdoUJwEiOiNT6jGJLC24QsW9Jylycjiz6jKkcYkI8hiVn1X87Ojep7ikAqZETGXMMGKaAbARjzC/cSsLu1Qu3aIM6+RAVVeFv/OoOV7bb+FXJGDABIpI5EdqJF9o5DKvmgsKtmO4GQWdTPhb/AM6g5Xttv4VckYMAEikjkR2okX2jkMq+aCwq2Y7gZBZ1M+hrXTDaHQQ3K2InwFyc1CY+Ea/DwdozqAI1WJCTUQQrxttGAuJxNtyYoHt7oWZ70gXjaKgHXCWLEWGF8EtCos5K1bJmIJiLS+RZ8BYkX0wllDMRv4ToSec9y08ebeOwaGhd1ezE/hZi9yWKz2TtV3TVOmygcdPs1qdm6Nwlm/XrQ9sGJCT0FgmhOZHrrT5P4080f6H9a25q9SLdAtZ05y1EzM8AeaJYsl0GeatGMmwkNyx19BQS4qes7XxtbzzwdcSHJJ3Jr7jppvRbVwuDQO4fNBFjzcb/ACHzSJHskZ6YrEqJYQ3ITktioAaQxEA3z6vlpgxbcGZhhu2JWUKyYywmE6yFapDiHmPoetAlnrdzJSglxQAX82WGEHb3ajdRXU+XlXo7NkIXgsf2PXMh+mYrHCaHEBkSJdZnjkdkwjcbNAUVQgAyrQDwYDc5aza3TCPyWkBuGQi+1vqoV1GGbt3gTm6Hpl0fvWup8ivGY9TWmhq03RDTzxx/XURFitQwovLad/K+4MHzV34qe0A1Y2QcfpowAAgDziggTnvpIoSGIsF+WnnM51hu+2Za1kCElahhtkpDxCFiNHQ+XesuO/eipmb4f6YI9/TGftqK2HoowxYxb2woe9LrIMtNV7fdTaUYLMxaSSJvRwTYxhJJCHRYB1mreFFqYHYb5W7RpbBLQJkWrkUfYeuj94UXQYJtkVhXi2BcEl4wCEE1ESJRCtGA4zCDxLbAursw8Mu4F7sFxtvyXicC5wI9qQU0hDte147eJVXiYGgxxlP4CDuc0KGYIA+Mo6D70IJMeV2SMsZsqkbqExmP7PFAwBU2xtwHty50qSNMnsV2pv19GY7LhiddSUBMaxc7+VpY0h+ambXKFnwYO3tVugAIZT9Cu6NAXkDjHhKOOiY0tyDm+0XkAxlQy6jpDs9MGaGUMxEXYagnOC2wxTJM4WwBvRKxrstnbOjxa9KrBlwP26vbGatMiQSb0LfNOiHr6QwNn1zEWS5LdH6FnPiwUTa+M/SY6qnAi19E/kqTdxzV3EjBhDm3heUdBkboRWZw60Xakm18AhNsTxpFRADpv4hySeRMEMiZzqFYCGC54ah3PQAZWnFxM7WjQCO7QDIkc3aHMekk19v31OlZFdwPEWsah6SfCpcrq5Jix95XUp7hNGMfp9yiZEh9xK/kVTssHlfaOpFAQoCwepJF5C7oTAytAByuAeDvofmoMIuyH0NdfHT8gussUcs1hAwESiF9/XGXUjzAsaFyUEo0SAgYDyUiQFKtgCpBe4nkIJYwQibUTUCA4PyVdnEKK5XBkvBqXdIo/wCAmEJPKCu4EQ5Gh5MS2Bn/ALp0o6+IEmohOjnu0mcktu7a9z4SnnBdr705KjlI0oQwMrPBzU1SkWGqjf2Cgou/vI3q2K/pFCrIoRneuXaA+hFRDHknES08BJgdAwYKsDSThLYmY6lMEum+X0QVm1poAqylGDC3XuUDIdIl5XK9fL38+z/Mij1d6TMOrb0zYPCAGqtSUpBfyF9jrQUsjCT2EMb4iy1qxWygH+3nxQMAUTkR1IAcuJ+zSms6btu/r4MAeThNk0S5pQQwQT06XiXrmph3EQFmbxdCNCa0oVs3Ud88aGgfkv2lUik54c/06NTg5EYpmXS5287tRCEHrSCawTi5uZ64tJQ6IATS9b5cVwbHgo9XkKVGvjlBgZCdWujHkDY25X2o6XwOA8AKErI0ozGMX9UMWGJInFmhqqUW8IZ+6BwBDD5g9UppDRAIzdnal3FBKwWEu4MVNwcHrLoT27U2NoEnuzajRhoSA8AKFP2v4TlJ+KmvcCkBCC6OWda4SH9R6GK19N0w27vtVwlo+47svotzPSjtOaCwMz0QJRc6OaUKuyWDgf5etRS4iAk52DiHM+UurtMcKdxqPgvSkOI/b3pWwgv9/l0uJN6+CrCaNugS6peBoZuY9ARMVkadIwcWQRXG7E809fwekGQMzq0dbsCdjiRdAKPoUHOPWPeKbAGQPx6etXd4tPWt4NNEtGEz19AKKQ4Ala1t5GR9FakjXzxqnUA+aXfZs4OzYPegtpBh0YBE3htzrVsdvaK/wkqABF4yfqx2jzqffAuTBXoR1mjIHBgCCsbr9/l37a+Op4gFxWbpDTWKA1hHMsMC8pnmfRY/IISZu0qFYoOgWAoacwInUaUWkjHo4WjtU8pLdqza8zGklWii/RBd6mlVEpAwka81rwzNHP2FDJ9ga9pnzplhMTS8M3PeNNPQVh8TdIn3YJxmoyWDAGOUtPBfTxjjOrA+acVBXDuJ0YCFgZ2m6dyjgZIIR+0LUOsysDDYEbVLkVLPIZtHvNFMOhl2PQvD9r2P5eCrhA+mD7y27eEwtL/f5d6DNfHVmrfXFixWer91AGQfQnf+7CmRVnQsGTp5dXs/y0o2dM2p0+gojoAfIqgSFIGAaWaW4GbX3VqHtCify0nxUFl4Ivr2UZk2lw9yoWKE3AYx1U+GEoUQFxSLsdWS62U05KBL90EiAYd+k3biWGt71JOpp/sqZvQlhO1BpdY/qKPdTfwhT04zQWCywTQDiQBnTlLiKiNXlGt79JSVIAo99VLIgQvHV1IZy8Cc8RwzSsuAsJjEsloDBAYD07lZhUk5dCQ6zQOkhQAeAQsk/f5dvLspy3Z4TVnoNL9x8xV19XbOMhuZehBVhtSozxYyL6RZSJzVk/Si5SCcEf6VTy3U5Dt8MURhzlqxIF+aPuGuwbMJ9qgW7RUuEO6/qhAS7ITuUvlGmZnM5qWkiJRz0qSkDkI68KPjNI5YFhOFt4xRP41gOycPmafkv7Ef4BqDnksw4X6xTdrrFeM53Xsjx3O/3+Xftr47xjImGtsS4qIwexpuPI2fQUdmYsJi/X1poErD0rNfInzH9kTsEtEHervJ7z1L/wCC6dz8AMq1cXCaVbHW40AECgDAHjILS/3+XRPcVb0DxGYqb8JyNypASsTSGbYOzeKzc851WHab/h9YjGwziiwwYQANh5lRIF5NAvL+DmoXuqI3On0Tr/ggNFz9l0Jtq0xT3XvXZdNuPIsGL/f5d03cq0ODyHIocAUnmPe9F1CGVwizPS5842+6QCgbb6KdKVHib1RIsZE4jWgLiNTyzcLLqOgbrpQ7XAVTcXfro/wXwUCXcEzrjmmct2yvZZ21eLb+XkIJ+Xftr47yzsjlOKP0StcgTtWNnU0fNNIDThLl+1FOwp+jI9XOl8GW5TiANGBcX338mLtWgoGZhPv7nTLUXuVrbV5W7z/gM8ua6PpUApVQBrHb6PNfNz+XSwbFavZ5hdo/mDkBps70EbLG+5uWns+UhAUJIghtR0JCIyAjdXx6tiWFgJmsRZRDRVJGkOnkBIQmq9YYjoHF9qBIJ6JwOny6f4GhKO2597F6CJa6RkA4dTbgQJjoAwHmdt5/LqS3ZXx3mApyrI0vgbZiOw16mldTogPyL48tmJ8UmFuHRvmn4BCGEfUm9cPZTnQXMBSXLldc+K2pl8HSDjfYpXNrdNvaizXP+BdoZO0Q+3BU0zYUCNi3aGd5oO5CYAedBqL/AJd1tkr4h5wGQdKaqbCxqhqOvt2qHLM8GtL85Hklxde2295d4q1UZLf/AFLdvUNkSFwJJarlAwdUz4DkkByum4uAp8bF9HYb5lt2KCggmAWAPXlzIyaYy7D/AJVxJKYjNj5mtDLAsgB6Bv8AX8umexVnQejGk6dzDOkdTXWrKjIgQoTgL6atqEGQfA0OUQjWxiF8Ji+F4HejB5RInprnD8BqWuY77SipbiHgKXKnBtwyWU6U9WgoxhutU1XX1sVdKRiZzH0CkvpyiDI0u/nmhDCgBAB6Mvc/Lv1K+G9IiMYBKXOoOlNyRE1buVw8qNEsSWR0/QdPB5BmVC8/A11qxE1IrQzlzenB/RzUCklIqxCwTl2DOlCnAWrRtarte7Szwt1Mpu/GD1ggC2JZqYitoV42dLelmhLHsn85ePTxAZT+XfrVd03phI6ASNSltUmQ2adke6lNKi/GxLrnFBUuVge5UYWJOayptW5daNuAm3iudNnX0ojF4GUAds2CnT6BENT3+WlEluFyrKar6r0hpUgCgY3Sm++TLj3Ucfi+F22GjJKkKoRrpdVlfUfYP5dwxsr4b1XI4Ys3uZ6NOpJd0zMxnRYUeYvQ7yxOz70SxAEWZt34Dw8xfYT8a8bOfOGcZOAGqtJZkY6rxH07qA5PiEZlpwr9KCVYqANvUeiNKIA5a1BtNixox3VLr6XSl1HrbkpiNwkJRjOL7c+t9/wzj8tuJwN9adc4tS5LsPWkVC/2iZ70sP8AKNuXy70ecxYTsN+cXbFFQFYiEYlcUDyQiZTi0fiakUmoP1RqFXVRRzBZfmFfipPTjpjU703OwUM6C/s2UjEt0hD7B+efUyNSC4juPYqKQQAr0S+Cp8RdQ0yVOWBZmqdhfvzQAgx65HFaea4btRspjX8tJt6cVfARHFNFtgVHYt6NDYp+8a/aNQMfWpLfVq2OutWqLD8aHmMaSdXo1+gawmvhpyqCTGPDSkFQKaqRao1ekS6s2YD3TisV6kmNL4aTe2ISupSYeYD2aSVkGsUeLxIJuxR3p7n3/vN8qEwK496c6pjVTYTetOFI5qNeupiUMDVFEBq09Z5QcHIie9aYFAFzDV0+a5MwAhM5LanT/saGUzFPFWUeQk+qu+9QaaRbE01kwjWlGa0I0lk1pRrThWrGjENS6aTJjWDauxGa4dcSiv0ZqKn9lAcw/lqUuX5opXBYrPhDVpamt92pL/Zr9K1pfev2NQ4r+9aXz82r38rX6V8Hg20pnwGHGua06/vatR9649gf2op7d09z4UESckP0MUGgCES4OCPmtAGYjkbD94qe2lLaNri0kBvIHGt52zVhISQ+9Qm4DQNktqJnSo6cSAnD8VKvmJPSLh7V0YIfsKgFbFSwcjPFNALqke1Ql55jT1Sv3rX72sm/loP/AHpXNVujmv2NGB8qkdXrVwyla/kcsG586ylf71q5q9abxuZrqv6GRSSlgdjSgOgflpZgwVHDCSK+G/ysAPUqZlN0VhnPGviCH+TC9DlUGutK4/bfl3H0V8F/60eDYP3H5dgjhQg+H/sQquVu35d7dlfHf+xvK/l0Twm9fFf+xeD9n5dwxsrV7P8A2LP00/LsowmytXs/9iU9vy6kahmvgH/sfG/j8u2neEVd03/sImfuPy7HOjh21lX9Bn/11rxv/qimZ0KgfG35asoLlqEKZ3pSshBZrudpoTHuUjZ96tz3K1LXWof7q/6lf9Sv+hUl/mqX+6tL5K1oR1r/AL1I596v+9QmB71/1qi/uofHvV/2qcQdypkZMkj7oPeJ/oFIBnwwDRdltmlMzAglx7UQk4TrbuA1gepFvG1KyI4S97XjWpoRGb73fdQyaZGHvPxUJXgmz0JbnFct7+7VxveuQ965iuYqLKVwPeuY965iuYqG5XMVAy1zFQ3qG9Q3qFQ3qG9Q3qG9SUarQ/im0LR+W3b0m1ZDhqqZWSTmlCPtX/VoO+XWldfdSn+1PYKm199Ba+6uf3UNE+6g7jS7M0DOpzShNYvem1965/BrDf5KTOW0BJ0KbP8ACAOzANuZqfgDsD9wvW1ZarduHulQQLMkLrg1peGJE0ne9XpZzH9dGEHH9FN8/wAVey+KIoZJHQRV9qeThELekh8UItmGMDBsSuC6NZ7ULuy6WrBuUnz6M4iF+/eFTa/j4O58NT1KxdfPt1ipUI2J+KhJqGBRGwViC8AtSlT5oHl1Ay2qzUB3qQ3U0qympTIq5M62nSG0rVvUQTtqiJgf6qWkl+WlBLBXcxpGm8FrQbH+BB/dYF6GWkmZyqAWLLvxUcJJIJ1vfKVDbRdxuEVx3kPp51MbOr8w0FsLlxu2HQFq2Uz6K3+jiv3tV3fPiLGK0aaEZgybmD2DWlFRpGslhFsnSiarVRqwSL6J65p+ZFL9u87xU/gAZIchtrrO9AFgyx8LZveeKAiyOE9aXO+hT9lKyTMfx+W7/SsllloAyxTQbHrMQwTkOmVW9VCk2E2N6tKNcDllHtVnpBqMbuX0UARjNm3d496ua5gxoIwyY2krEClwefNmiaa6tdCY44euY1GhYstY0GjvSzOwidmkCktqecPaKuaAoBalPqg61euwDzNiBY9lHCCkSRPUISW0rFNrTP8AX5dxda+EeotyQIPml2sLuZ2DljpUjwyRCbybWnQiraXw4PRELwLq0aeMIQzgJx1rKxmkcoaddagwXM6DP+PSJoa0SGwjn9ppDpDxYhh7h7aeCAhxWjDFo2OR8PNNbSFqiwYT460MJLvE9Z4PTuHq4LuP4/LpDXT4r00QfRkRFnaVo2/YGU2HHyaON8xk3WV6+kBwBmo1EJeA/TmpLQGqv648I1pDot9IKhVFxHJUWhZEoS6eoM+6jGGEwjcfFqIkAkTkqRLLFm56/wBRV+dyUkGJvt4fNS7dFKPTtZbx/H5dQNjTS7PRDsVQgAqTUwJY1S0OXtUB/GiCADtu+odFyEgRNiYLXdagYXGL/wAQ0PEVYsJlyz6aonAIwPpGtqnk4VzJu/TTymTtxh9/4sOtSNAWFs2bGpZ5oJECUHeNTk9Igmqfx+XY7Wml2egUkp+kbtb7A2N5WvS7AAGCzvHqArJpcHThT2zWv0IwGB08kb23jRd39SEpoJvCRGBxJ2L0M3PKJxIeUO40yeK+b6PeUwblMYaHFH9lyOS/o2/D+Py7hnZXxjzwqitsmw1aQ18jJMsE5DOiinI9RtFXgjpEipdmOfFTGx5UtIZINtQPqGvImjeMtYuD20zSkXQmbl7ygPfzZs1NgkxnXJq6a6Q5KEBW0MGNNxrk29C1nMfx+XVYb0EBweYPQu60DVafSeVgxBL8qByEPAHT1CBppwBTNIgzBZEY5VEA4Fg8uNJYgblraNvUJVC4pILgxxUBLSQo+L0FxNZHvCYMW3rCINhMMjgRZrk188+CD6/Ls4xT4rynPSdoFFh1G1mYdfgKNeA6AD1dVCg51jpk80BHeGsdXzBjJ7tA2LXuzOnqqtLi8jCP609GcMyVNS1DrMZ65H9AfLQPvZ81/Z+vy7cDmvgHkILwLq0fcGuQsSTTTdQWz4NXVeX1YZX+8DPTJpHNJR1DP9OvnO6FJIiXGX6Jzp6tzP4QuW92kLEgjJAnPoZrDyF2yD7Dp0xEplG557OR28pJ+n1+XQoigg+HkKsHxOhndpmrK8p/B6oFsBmkoHmWLBff8UfQICwBp5yqgOxMw+qPDpX6S+yUFAGxpdnZPRa+I6RLIlNz22R+F5eMbtHqHwSPkSEaZ/Lu9vXxHiw0yaxse2aGe7Dwry5dOPWmL56F+o701CHITuTofM+hcpUXqDL1TtrONw/hWYYlG3pIWrdgsMPT5qHF9R8ixlycz5AzcH5dwUuTg8H4BKOAKibkepndZjajAACANPVUGgVlXu9Lu5F08AuUHNFwfcSmUsJRsHvRpcLLQbt6sZjGQZgVMXq/C7DE9aUwylHkky7VPpjGK4JBbTbetKfd/wA1DSZxA9OdZ+aq4p75kGZLePTHehEYpnDqdJ2oWLGqbLdH3k8Xa6fl2bmE1q9nhIlJA1Fn3xTISbeFf6LemFN8jXO7Rz7K8nYh9qmjpLF7FCTHDNhC5ATc1ayhxmQy0dOMUqdpgs8RVkYAZDuwVY4xDRwArHzNXS5jSkjZ709EtUMnSpe1oxJnQjTahrXZEWNsRH9VCFgkE76x9opVHjJeIvZrtTz6EFFmcTWsnQ/ZWyTM3wReRMJiYvBBagsOlkI3LlpP91l3gSHpPHzQPJQAEak2OrTtKIgF6yPxQCWRDyOtqsbWYFb+SAdF7lJ8zBy19+mNQNRhHJWa01c5OUznuowkhIm3gL3T8u6D2V8VSly7cBNHxh3joUm4u8+gzykP7jQwh51v6b1LsAtXsh3WpPX3EdF/czUlSZECvX+lAEPZyToR8KjAJ/0ood8gJgH7R6SRx7rPmBaJOaiULC+iiaAvPvJc+K6YTbNrwbVkGKsDxDN+Gp+Vat9foqQehNiViLlHsLH6ipzNyghQnx6hasVF1HwvmK1Aik6h2+nh9f8ALs7GaWSbFIe5KetaW9mKPMDLNbi9/KoJbFQriYlkJ3g7tNZ0mYndcdyrXYAupsuhaIfi1zpDcf2dqttmGDseSdqUOQ6dC9SgCTLL/jfv6QgvDQQGH+fTgybIJKDUCIg+ehPOATebP4a1FN4Jg6wbguTnmovblSPwOkV0Y4+kzU9JwQez/wDABrRg8okShNja/wCXYQXepl2uWkbZBgUmvlnyAK8C6tMmORa77HyphUw69t9l3FFOqnELRAGE7qIgMBB0DzozQkuJZOgijDFGwAQHpEkez3h9emBwhrTJGJ77xueajCbOsXRYTeo1R3AI2v2xRcaRsHoL0qnRCGdhf3mhoEkMHhP5KTIVyTRpo0M3PQhoTrasfqv2pI9k0yybnrCs2NLfl0SOipTQF1F7F7E0zLI3UbdkX7+OetL052OWldERbkHExP0ikgQLogXtny81j0EoF5eCjJHYxfOTz8H0zMk0wxBBuelaTKoi7W97UTOyJcixwamYqZXYk8RO980RH04rKql2/k8X4jQhI1atiBRwnH2ihLmQy7aujqW3rlu1AvsUM3PMe8gTqNmjui0ISSeWlW3/ANP5dsC0a40JEpCebFvpJvR7QAGgYoexVCADVo+hxBswwl+H3TpkLTqz9p1oUIwCAOD0rGSrVG0b3PxTxWPK3Xv6bnLCqbRwaBHoigLKv0c0pUMSk+0/1QlgVYiGvLioSU8GjcD2eEY+358sk2auoOLqeTDTKUzeo9CcaUsSRGzmNte3mvliRqX+pDtWSKrhn8u6I7L7VlNNmZYDoPmkvkfgAqTrBDKBSaXt3NGaO7KvIuegI5re0kMnUz6b6sLJOCx3f16hcI9lgGPQeCAxpKGL0kK09sFjqtKRJcyIizfnw3GmJLssGk60sXaItu938B5zpEgEiVcOYheIP/FD0Yx3u6tlqGsSUSJ5Ftj/AJyI6yKlSdcgn6odvy7FTZzbMFJkUHsCxL0KJFk22FKM8UggXW6tVohmOj6o1E9f7Huj3q45a9Hb+isfQchtK/ulBcdwTFAEqTjzCrMO30PeomAJTCSxxL49S+SbJtJcRvz5wYwIAkHE8aSLDe5k6Wi1nTWgKw4Lpu3bxPkOyCX6Sq5Yci11+/ou1OGE5s/xTPexjOCwxeEDatLEAezGvibUkodRp4jfILBHXPT8u2aAo3oXyWlsgXeNd3pVpfy11fLwFsPtTTQkYly5GitZKziLL3xe1FqiXJO6CEYx81NTBsgXJNuaJYABHx4zoAZmmH3RVtkPVv8AJfUQbEQmZ8rFTIQLhKy0d16kswDyNaaTavmPpd/LOkJW6q/iOAJ6QNjitmovSQMhfQLQYpF09zU1HxRFDsJbF2B/LrjIV4kvS3Ymkaexnc75dI9FCy4oB5BuCc0FJUNM8xas4UCDe5b3qAeJuKdraVqEUkveyDUWcUM49RhABIAXTGzcdHPkCqchAFM1sEdyGPto7HwQWbafdB5KAebcuF2P5UabrOyenJecNIjTJltTdr0Ii7WikFIfTyeF70jWf6NCEA6axP5cT1vjcAj3JHeiEwEBweqkEjngMzOaJJDmL2xmMalFrMzYNAkkd6KnWkDzobS5q/nYL9vlQ68YAPj0Sk2EUFboanHjCfMr+DmoW6IZy9pv9FJQdzUfy0MMFAGDzkRuy8WJXFJbZbr1P5+oNBpVEI6LBWHiMe6iA8q4lWglQ9v4lqwRLZnN/j6aAgNgOU9Cs5VtOFCKl2QaDK9JBoWUunnTfVzUqc7x1UIolwm22VwqeEcOR7lGZwIgSr0K5p1YGJEZF7gUuZI9nUl08qermkCOCMmt0F1yM1I0RIAImEfyOGPe/wDRkEvVqv3p8I9VWwiWklDiHVipNSd+gOwB4NVjIifNL1FHrpwW+KSRIp3Rw2E4aEAk9ox1NWjPDsXcoxuEo4dcjzOW8oLbLBjHhjANR29ua6xjnAdTvnSgRyiDoffmUEuCjAxr5Bo+BPSRGwTvOu2OjGercWEQuGnfFJBe6OB+jQqUCz/XSi3jzaz+Xp65Cu0piHzuWbVn50UVZKALfYNgPAUx4G/hlRXwCfs8Cmqk6b57avdXKWSx3eix0PAkLqNe4+/YNXWkPCz7vyPE+xjFr1+lEWVnLwFf3r4Xqo7jzZuTPdoLxaYAI82E5ixHQQ046LEse2R+WoBbRlKy08mzio9nZTzQ/Q71oezRwCYVJ4Wws1yF0/YjNE4Y37ZaP6Bq8GwHSLa3q+h7qJ08w6RJRAFODBphCJnte77VdW6nRLCMMaUPYJEmHUeTWkSSl3qzFvWdE0XILYMbyDms2XLUqIqaJ/VfrA0yvviEt7uGzSAdRQX7m9P/AFisoIE/cVGQlAg2eosN5wxDQEywOGpmqI6/0PyOTYuOIP2VA2w6RR8Y9VugSbt93n8elM4tAPmp0GKMK8pPaKwh6XLsy/FDWtIQC7MiFvmobILUUURlvF8URyicQdJaRez8x8xQ4QqW7gAy0JnZdKLPYoSOFIyj2OKJisV80v7WLoU8WA9nwKUXrCXZdc/XUOjzEa0Y3JpcZMuCx7MVC6Ut3p9WwUR920IvHc4EouuS7ZvS4lqLGw8D/wBYraKVP3FTkJUJNnoLBacEQUhMMHgqJqiOv9j8j34cImynxR1eJAvzVotj1LCYK9qMDOAYaszeYEd/UMOeUQBU6DtM6o0Bq61kI0QJixpbWvdzi3CL3oKsquoXvBWxbrmrbSV6c90DTeitGX1BaEElzx3l6IoVHRin99ajzRDpo7pWl7vt/mnwQXTUGcXRBGHEAd76+ueKN7qwnzjkf8VDbAIRB6kUnYLHXHVf6SJe/qe56+z+weDVScNs9sXsqJv7pHd7y6M+CkQvXXH2kcDVlpDws+zz5oC3XBMQjG/kkkkUGXeJCTPmv/51BwvbLfyq5IwYBIVYDALtSAxaKxizZvv43/8AOoOF7Zb+VXJGDAJCrAYBdqQGLRWMWbN9/RimTL5Mow8wx0/E2W73dVAfKFT/AAHqKcK1YyBfrUL5kr35HK+noEQgnQvS5ACOFnLwMa5o4FOe+8VQeJlLk2PHhuhQ6OlBSQHw6P7VFDEk4thdeqGaMEiQCzGLqepTt2A0PNz5oJgcc+54b+ASYRG258VhVNoUJfeTSpgSQm6lbuoCZwEcP8AiO0gImnnE0FQ3zJHplw8MwFIjKCpZxMUpe4eLmC4moeBX/Vp/6tP63fUtqYnDGpmcCIEI9SrmqsDiYJYFrEQuYJ9nUl0cqerikIIKsmtgm4jES0AkAADAHoQtdAVkWHjcuT4HAIAMAf4zl5y9+p2/EzUwvNb7UDrOhZjvSYdKRwBE1E9RhtTKcRWOCmeyzvL0jT2H2wFKITO22H37KExkBweE5ed2TF5myzkJPmh3RBJnMH8KcgImQvBI0OPJmC1Yk7KnzAvD7yFdz1o7cSAfJf4q7OpG4IfNbYAxJBAn5/wC677srO+LWY+6EdlTlKScnZP8yH9Vs8mZWJ63QDIc0v0oG6hfC4TreRc4cMaP8By85eB6YWde0Pd08BZp3sTGgUQsWDJZzfwFyc1CY+Ea/DwvutPkuZo4YGPHvO+/AxsMnwS0KizkrVvNPp4kMKzp96kyitgSQSRcPpGUsCIk7K/hBKTj94PEYMkYMU8kWf6Ij8BJxsWqwwbgVCTvvBTOwdFzZP0cOpDr+Ff+4QUj1xWflM+YoG8v9f8AUfT1DkBIGABc1vQ8D9nT0ZAAdVhmODjLQ9hx8OE3two+AICwB4NFranRfQDC4AlXSgMYprRCs6bmrGkuUJCpZnyT9U1geAAJM2wX5pENnKsEwQ7lShcsjJt/pVNXkBZRMS2xzRID4VJ6rJAqljM1aNlc/sslfs8Ke/qMVaydYAIJCFzlr/q0/wDVp/6tP/Vp/wCrT/1af+rTPV6yKyApbKQxg9CEiQls7C3hFjGOK9c6vu6eKv8AY7f8uW5ecvS6vlfEXxjKhMXRYhyNy9B5AdACADY8QigF243sngNcJ9xh+KbmbKbS/o/hZy81xGJn3QhB6SkvwSmzjBV7CCwjqJoj6bRFIKXW+D0x9GckXBcfrgoAibyUfROfI4pvPTGHMUGA6tO4szsS8O+WhkC0N4ogmU4b38GYlzsCWnvGK/A2x2xwUpTtGfmr+uVeEvKfhUh5aMsZLzrSU2XcWb4UbYQwHUTP6rkTwekmDhR3Z/Ce9X1Om4I7I70BEciP9f8AmIf1Wzyq/wBjt/y5bl5y9Lq+V85g+e/DPeIInrxdT7pMoQvhORuNG0Wmsmj6NqdqCi+jJ6RJ64wtcs9nnFIWUQAbtHmiURcYY+RrpRayWVeLk8Hz5cGrnskm3s/KiYDKsFCmtp4H75U0sliB1a6jg50q/Jjlm1/gIDQ8QiIUaNkJeND7US7+QDDI6NPZ5MFhrMalE5fTxAx70pw1UPda1NV0mhy00nQlmn8tCtK8QntQGSR1PK6SAlXQKCJckOAD/RMdKfRbImZNPamiZM7E/l9YCjwavxrl/tgFqPdQhI5nd2jqGQo3Ki4TVZvwjLaoJv2ZNhtImiPWG3pw/qtnkj8sYCbk+yXoNH/QgzEI6PxDh8GvtE4gb1JVNBp/jOXnL0tTrgB1R8oay7EMMWkS4js0zFp4uCtOqSAXbgcJhPPg+e/DPe46GEAN/ZavmATpFWaPwX/S9Z3MQwOvt8nOTDWZkHouMXmg/YvvzFweaUP5RWhua9DvQUot3zbr4mw91L7V8UieGD0q6it4UyZg9tK+bxCpc0hu52iZq5fkJwomBQT+tOJafwLQ92hQWGwa22ZzdxTQzkBIO+B8vNBFjyFowEar86A+9D8BAcI9D9UEt6ISspcm1yeyUlmncKQluLf2UIW4JTfIwvajbrox8g94q7g4OPjwggYXM6FHd2OtHmMY7xoHY/MtOaTFTpG3MUPsDHAg9ZB0Ulud7j4XoFLj4BYAMB4Xx9XJhvLJ3Z9L3f0ixFv5q52S7wjyF8aGQIRNkrIdEBvrAQNTCypWmAPFDbmpa2straXMY4QWx38Zv4YO47KTbpZ9maJiU26EIolkc1f3i7tywiWhvClEakCAQyOcPhg7jspNuln2ZomJTboQiiWRzV/eLu3LCJaG8KURqQIBDI5w+hAsUU3cIWUwSKUyWr/i0wUjRHjQfy8GDQl4Fh7wO4lkRShDp2etAA9oahdoafs4ghhkMom95iv4pvb6Jxh4LbQAQBcVD2IEkmBIMuHV3r/i020BZmmXVZ4x4Y2z7z+bfDz4/wDJiFr+z8LFjjA3wW64pZfOU3P9PCcRXsN27/DrUPGoCmWfduqs7pIbmw0fQC+jZBAuDMdi3PltiFgMvgpO9sTicjd1WYxRJnjyIgDIwDG9TgOCJa+CIrGG4SHPPSor4sAcINP0pLEV8qdLXt801xzIiU8Xq6PZ/wBNoaHkk2aa6PijoZg/tHmQJWCr5STFj+7+XqcSaElbqbPxF3cq6BQGMESTfrNMf/vg3JY4l3vegE1KJdjLsI0b+BcG6zvZ9/XGKicpYgaXEuCOChvqJgq9msw3wwqS9CT6Ux7Tl4LtXdziSUD/AAIBhfks4xBcIs9mmSgwSxxryeI+Mgkn+nZKtd0RB3j5IufNLWqjAQv/AFUz5ZLaLTshZDm69PJMO17pw7D7p1gsjRoNsca2vmjtgDQAbeh8JqaG+pUlYxxHpHMsw5wCBZ25yhepxZZPT+57esWa4xN+Tb3Wo1ERksryvgEdDwZKPcioDwMWoMyvEuvr2oy2ZRAiZvaSwoMlCOQnXyJk5yGVzR7IgyQQjdBGR1EkQ1aBjWHAksJBlLn8lSAlHgKamhEW0CHlIOMEKdxDnKXqcKS3WjRG1wRCFqclsU92X7458gLIC92qDEHVAXxS+rIA7aPGr1ghgSjsfpWPRUjlTtBi4JZekJ6w3oF9yn1XVYnv6jjKZgO7UzTmVeYQ/wDJk3odhrkLRZ/lDTx0ymHG79HetLxhdSE+w9eCkFluwvf7+Msb+oQR8UJtfevlJuZfkozMxRJWtEkTM8LJ3o1Q5DOS528q0JCSI1drUcstY6e6tMNUyRLMb0iVyFV7p3748Jjsu+kUI4F9hRUgF1aSSD4h6UDde1TzkmIhOGkS39NwvKsF7LH619GZlCaDK+1B5Ak6gj2n8epaMsMQfb6PZUJelF5EAbTOJqF5gGHv6HB5I8kXCzpTUAdRmrU8ANAx68RotxhWtYtblkEUDqAoScmGudSjAdKA2+0dbU1kw6qS0hAJ3wCYABwLB+SoxNNLKhoX7DFFV1CkR2Pt52zPeKJ3NnmosiUKEWtRHM8tWv8Ai4eIft3rVW/C7h7jxRfHSxwH+M0vJjpkM6uomBfetIIzHN3bY9SPKJpYHMp3asTtx6IaFq8ISffbupyI0C8ix6Q9FcnFQ7HMKWs/yDPFam5JDeQH5NxqCkVyC4z8VCoiQCAODyKnc/KFju2oLJid37we9a/9v66OqCAORGyU9ORWB2I54HFPJBFuCOtv16VNzFDzOW2rv+SxCGaYJ2rJmGgubdTkvQAeVcfQtwnCTqNQVZMwm7q/lQ43hxKGG66NrlWksFpFlczdoJWP7lj2aIXzCSPpuU0X1VkgkQQoiGOfRivXbMi3321EQ4BAHngwtjPpk9qSsoanrCr1oeJO4mepuRwHgpBUYcwJtO/c0BwECA827Qw0vdXdihkEMjW4/egS5n+fy7IqfCKh0L84FtDmSY5hpOoYWZ3ft8PRza2qKRDC5Zvk0iZtM/NLOLERe5906NsGmJaDOteyK2axf/NE58itLzEIdmiBqsZZ0o45eh8ecwWv10IxiDGMO/oNIE8MW89iXrV4kZgE2Hk9keS9ftTdplRU2Ek0gXd6sWslpldRW1Am5sAy1mShSTsDc6rxgoQGESl+8+hwRxgJaL7M9g8Ot53Y8O5v5/LrFUOVuHhIqFCMFwHXFxJT8gxDCPopFv8AkTDE9/IgZCpViFDR0vlUdVWCzoJpq2SU899GWj6q98dSwNgeyqW70hOpu4OwfdYVblYHS9poQif5VhQAN0IcjEVYo5EuNpouI4MzGyasrHgVxveuYrBLqlW/qn9ldKiy/mlUNMn8iqyNZwLWWWLDvpUY+nIIDZzFXZ8prey/dTH8ITL7wCpcXFE53F3vU02Ikk6hV9ijbaKnZIOm1D7fgD6emFTXK49fQqKWOgYn/BweDj9dfy6ZofFeFk4Q3fjphRWa80mPd2e3ozbvLfkgeik2a1q/30oVBTq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)"
      ],
      "metadata": {
        "id": "nv76Egb0F3RR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "When we use a qubit to control the $U$-gate, the qubit will turn (due to kickback) proportionally to the phase $e^{2 \\iota \\pi \\theta}$. We can use successive $CU$-gates to repeat this rotation an appropriate number of times until we have encoded the phase theta as a number between $0$ and $2^t$\n",
        "in the Fourier basis.\n",
        "\n",
        "Then we simply use $QFT^{\\dagger}$\n",
        "to convert this into the computational basis."
      ],
      "metadata": {
        "id": "utquAqlnF3O5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##  Mathematical Foundation\n",
        "\n",
        "As mentioned above, this circuit estimates the phase of a unitary operator $U$. It estimates $\\theta$ in $U|\\psi⟩ = e^{2 \\pi \\iota \\theta}$, where$ |\\psi⟩$ is an eigenvector and $e^{2 \\pi \\iota \\theta}$ is the corresponding eigenvalue. The circuit operates in the following steps:"
      ],
      "metadata": {
        "id": "M0C9ipYkF3Mq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Setup:$|\\psi⟩$ is in one set of qubit registers. An additional set of n qubits form the counting register on which we will store the value $2^n Θ$\n",
        ":\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-17-59 Quantum Phase Estimation.png](data:image/png;base64,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)\n"
      ],
      "metadata": {
        "id": "oxP4Z31VF3J5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Superposition: Apply a n-bit Hadamard gate operation on the counting register:\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-18-31 Quantum Phase Estimation.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "bGILv25bG71i"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        " Controlled Unitary Operations: We need to introduce the controlled unitary CUthat applies the unitary operator U on the target register only if its corresponding control bit is $|1⟩$. Since U is a unitary operator with eigenvector $|\\psi⟩$ such that $U|\\psi⟩ = e^{2 \\pi \\iota \\theta}|\\psi⟩$, this means:\n",
        "\n",
        "\n",
        " ![Screenshot 2023-08-02 at 15-20-06 Quantum Phase Estimation.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgoAAAAtCAYAAADP90PyAAAQ2UlEQVR4Xu1dZ7CWxRVe/zG0zJhJgoApogQ0ERBFDdK8gCBSVRBhKEIoFoo0g5S5gITepBcpcxEheEGUgAoGQozSlYgiiClyKZo4E4rDv+R7Njnf7N27b+/3nu+Pct9999332bNnn3P2nPPe8J/cT/CPEWAEGAFGgBFgBBgBAwI3MFFguWAEGAFGgBFgBBgBKwSYKLBsMAKMACPACDACjIAlAkwUWDgYAUaAEWAEGAFGgIkCywAjwAgwAowAI8AIeEegwngU3tmzV6xYvVa8/lqRd5Qq4B3TZsyWbz3hhTEV8O2z88pfnSsRvx76nFi17GVxc+1a2Rk4j5QRcInAo0/0FoMH9hdtWxe4vIObhY1AhSEKYQPH/TECjAAjwAgwAhUBgXJDFP59+bIYP7FQXLx0SXz9zT/FxN+MkQyU/n72y7+K54c/w6z0/1J98rNTYtac+eLS19/Iv5BFir8vXb5KnPjkpHh1/RrPVios3MXLVoqCVs0Z65A0CLw7Z858IT499bno3bOHGP7sUNkz/n78o49Fo4YNfHl+fle8Xezbf0AsWTjX80itxuSmow8OHhL339sk35RkEX+4q1HD/Pu56YvbJIOAlb51OxpVBiCHb+3cJb7829/FLT/9iVi/ZoXshv5+9dq1Up5glhe3KIfXrtwQhXEvThZ3N24kHu/WRTwzfJQ4dOSoWDRvlqhevbq4nCMRhdNmiAH9+8jr/BMC7rwpkyeI2rVqih69+olr330n3tq2RRw8dFhUq1ZNDHt+rCjevNETUeg7YLCEFhva0EEDxVN9ezPUARGAsjxy9LiY+VKheGV9kVi2crUkC/369BLv7HlPXsMP193+SAGDJGLeD+zd7fbWvAI3jYkIjF1nePaiJcvzRB5Kf9TY8ZLEk9zt2bVDfC+3bvmXXgSs9K1KAK1Gr8pA/Xr1xIjR48QrK5eKcyXnRb+BQ8Tt9X4uyQLkvVq1qmLN2g1i95vFsjuWl2RkotwQhXuathTfv/FGKVBgq9joOnfsIC0tWLndevTyvPElMyXRP5XwebBlC7nBLFy8TBRt2ixeKpwovQBYyOri9DIi6puJghfUrNuCfIF4EWmDnP/45tp5C6tdx26+CTD6hhXnlSg4jcnLmxO5xMaAOKIXJ08V61YvF3fUr+elG24bMwJ2+tbLUEj3jB01QhpxJFtEFkFIVCLM8uIF3fDalhuigM3typWr0orViYLVxgfFBEbrNwgMjDerVjMWaP16dSUx0ImCvji9iFsURAFuTljPfr1BsELgVXJj7Xh51zjaAs9Dh49KDwKsbJUoBCXAfomC3ZggO+/t218GGpBS/D4+8RdR55afyeMOzAssSNokIIdbt70hli9ekCcKQddY0PvjmOMsPsNK3/bt/aSYMHmKJLf6D/MMT5QqA5Dh4u07ROuCVnLOSSbp2FMlwlHLS1A9k8V5dDvmVBEFYpPq4CtVqpQ/K9evq9fUe3D0gJiEzRvXSXfWhqJNpVgptUV/j3Ro72oDgqt+9MhhpTYbPKfxXY0SIwvYNPSfam3q19VrdB8WB44eoLynT52c21CvyCh6v8c0VkSB/q6Pl7w+puvqNRwdkfvRTrhB/jZu2pI/50RbKJghz47wbDm7XURO7YiI6e3Ig2O6TtfUe7Dprd1QJGZNnyKP1D7NvZdfzw/69UsUrMa09w//IwhdO3cUkwqniSe6PybOn78gYw4wL2+8+XtRtWpV8cXZs9IjQsQA59L4wbtRpXLlUvMMGXZ7BJbGNeokG+Xhuqpvh40cI3UqjLbzFy7I/3bp1EHqTZMMqO9PRADeyDY54nD5yhVJJGn+w5QX0nt6tlCzgnaliGp5mJ8w3iFVRIGUOoTDigRA2Kb+drZUliYLkbwHc2dNFyUlJdKViQ0S5/G6O9MtUYBQPdK1e5ngPjrrpeCbMCbEax90bm0iAeiLAt4WzJlp9JzAArx48aJYNH+2eHnpipwy3yma3N1YkgZYsHj3dRs22g6LrF00cvIoUPwIkQC9Yyj7W+vUEePHjcqfU6NPt0TBKq0TlsnkCS8k6lWAErp+/Xr+iEd9d+Dcun0ny9gOOpsFgbuvyT3iyb4D5KaqEjqsjc9OnbacK/IgUYOgREEdk+rtoTmoliMFiDuA1w2WI34Y92NdO0vyAFlA0CyOPuj9dblwSxTSvEa9rukstVf1rapfKaURpH3s6JFS95pkgN4V8/fUoKfzgbm4H0HpD7UpyAfqhikvVuny0Ic1b6rBAbWaEKaOKEDwZs1dUOocVrdgdu7abayHQNbktMJJOU9CibS67M463RIFK6Ei5aS6SuNe5OTqtdp4sbhuygm+qR4CKfTnnh4sXfttWz8YOIjMiShgw/7Xt98aN0tgh82UMlYISy9EwSrnGtbI6VzmgJ8I/zDmlI4JrAgweT1MmSa4FwFf8GjVrlUrRwZOhZJREoQo2I2J5hCbRIvmzfIeN5Xk357bOGB9wsOAOaEAN90AcEsU0rxGw5CfNPZhpW9VWUZsmBpzossABa1CFklWrI6L0CYsebEyKKBrxo6flJj3MY3zjDGljij43fj0aNjlK9eIXj272ypUt0TBrvhQ0gzUz8aLiYdifm3LVrn54AeLPYyiPXZEwe9m6ZYoWFmVeD969uH39yWyFv0SYLK0OrRvJ2NKyL0fRiEsv0TBbky04SODBkQAP/K4gbQifRkeI6TPHjpyTFy4cFESBchx+4falLHk3BKFNK/RRAQu4ofa6VvyUmLeMX9qSq8uA4iRopgoHFHgqBh6yVQYD3MclrzYFXFKg/cx4unz3H3qiAJtfEhtNB0twFoxHTuQW1dFwCl62i1RQDsr0pEkA6XND9kepk2eFrN+jc4CVaxg6XqNfteljY45/vHVOZmBQkFr1I42S0p/0u+HJbH/jwdKxRegjVuigHZz5i+yrL6pWi2eV0rAG4gAq0pT7RIKtO5tt5bZKOmoRm0bNKOE8tARE4CjEMyHE6nWx4r0Y9OY1A1br9OAa2+/u1fc+Ys78sGMiB3Bv628Xm6JQlrXaECxSe3tdvpW1auYcxxBqbU/VBmgo1P1RXH0afL8kaciDHnB+K3qxCTtfUzjpKeKKPi1OP0CqxMFijlAxC5FYqNvUlY4zoBb6lf33Vsqbz0pBurXSvWLV9D7/HqLdKKgFtHCmCjIEQv8fM5CRconbbBqIFySMSV+PT9BMQ9yP/A8dvwj2QVIRf8+vWMP3NWJQtbWaBD8k74X62z6zLkyholkwCo2LOmx0vN1eSHjBfEOdESs6hMiKqq+T9r7mBYs1XGkiijEvfGpRIGsURT+QFCZWpOBAumI0eqR2RC2z0+fcSx6Q9Xs3AqCU0aG343X7fPDbud3s9SJAs0bIupR/0HNwSbMCBtVAeB97CwJel+18psbDHBuSsGfpvZxE2A3Y7ZrQ0cLaENBwFTjwG0GQtAxmBR/FtdoWDg49RO2blGtd5JtPONP73/gKvvIabxRXVeJAhkOONJAXR21bgwZFLTn0DUaFwyNli2aucqIi+pd0tRvqohC3BufShQo1RGVwBBMaRIqTJx6TkYTmRQD9bvxJiGAQTZLlSjQcQpSX5HWicBItRgR/T9F0evHT0nElMRNgIPOr4lk4W+U1hi0fy/3q4o/i2uUPFumdFfgQBatVTCy03UvWHppC92Cqp1khetZCV76irOtKi+U6oj0eNT2MBkUGBviFRADpNbESdL7GCdebp+VKqIQ98ZnilHQF7Z+9qmfuRHQaDdk0IDY0u+CbLxuhSPMdkE2S1OMAsVZUFqoHp9glSeNdgh0jTOlNW4CHGTeiGChD2BbtUoVGWmOGAIU0/FbnMzvmEwxCllZo3hn0mlWsSkkG1ZxO07X/eJqdx95j9AG48L8X716VWYlPNq1U+DMqCjGTH2a5AWEAT+KSdC9iqb6G2iPdgjK5XLiKct6oAJBJvcmRenjaCCsidOJAilJNThQFSrafFCjQU27TOJTv5RdQEck+uILUl0xioVMRYV0Fx89y64UsYkogLCh5gMpYPR/JafMKBtAjVdQ3ycJjwIVCtOPQTAuyA5qCySZYqviQ3JltXFFIRt2feqKP0trFO+F8aIwll1VUGCOdFErveZ0Pew5obVqRW7Cfl6Y/enyQqSH5Fk3KNTjLBV/9iiUnpVUeRTA7BAxrxMFSnvT8+uDCpjJo6DXMFej6K1qEsA9ePTYccccfa/niHZf0lMVpl6xkDZWndAExSvI/bRgTUSBguZQ9MmkLE1EwVQjniL36XjC9P5uKq95jVEALqjdYWVtE6kxEQXI4G25bIcw0h2DzA/dS54a0zzhWtzfYDBZiFlZo2HMh9s+wtQtpgA/VT7ilgG3GKCdLi9EfNWjZDIoyPAzfVU46aq7Xt45jrapIgo6+wMA+Nu8hUuMOdZBAbI7ekB6JmrsQ6hQkAg54TVq1ChVMVC1hpOo+qdb1RD817ftEFu2Fqfyk9pEBCn1Fdb0+qJX5aeSTZUzCV+7oweyFMjz82Hu65fIwx48sH+ZGhpJWQnkNcD7kCuTyIhTIGRQGfdzP7w7VapUzqeZQq5QtROfurYjRH6e5XSP3dFDFtao0/ul8Toda6pxE/gbvuEAHejlS6Vxv5/d0QPV9oBBUStXuAxlxps/0LRMSnISHuK4cfL6vFQRBSIGK1avlZ4F/JBT27njw6FUotPBMREFUoqI7kWgHFz7P/rhDyy/CUGbGILrwjoS8TKJsKx3vf2uHCtqISB1s0/vnrFbfm7GTOlWf/7woMzfB7YPNL1fEjE77KzqKFC8AX2ABmfqjRo2sDxLT7KOAojB0uWr5OfP8cNY9QAqNxjG0YZIDD5DDdnHL6nzaZPiz9oajWPOwn4GGWggjBSnkoUsAJO8YOOfMXueLBdOeqfBnb/Mf4NCx47rKJSVptQRhbAF3q4/p4JLblLpkjjzjhOjNDzLqeCSHp9gGjNbCWmYSe9jcCq4xGvUO6bl+Q47eXEqyEa4JFUXJ83zwkTB4uuRboQqDd96SLNwhTU2J6JgV5WPxsBWQlizEW8/QRU/r9F45yvpp9nJixuDImkPcdL4WT2fiYIFUXAjVEmdeadVmKIalxNRcGNVspUQ1exE229Qxc9rNNr5SVvvdvLixqBgD7F5RpkoWBAFKJjatWrapjVxZGw8asKOKOBIoXj7DtvPwqpFmpKII4kHpfL5FDvFz2u0fM55kLdyIpbdunSyrQXiJisqyPiyem+FJgpuFI3dxCKNqE1Bq9iL0GRV2PyO2w0ZsOsbRAG57I936+J3CHxfQgjAs+ek3HmNJjQ5KXxsEHnBMdW6DRttjY4UvnIsQ6rQRCEWhPkhjAAjwAgwAoxAhhFgopDhyeOhMwKMACPACDACUSPARCFqhLl/RoARYAQYAUYgwwgwUcjw5PHQGQFGgBFgBBiBqBFgohA1wtw/I8AIMAKMACOQYQSYKGR48njojAAjwAgwAoxA1AgwUYgaYe6fEWAEGAFGgBHIMAJMFDI8eTx0RoARYAQYAUYgagSYKESNMPfPCDACjAAjwAhkGAEmChmePB46I8AIMAKMACMQNQJMFKJGmPtnBBgBRoARYAQyjAAThQxPHg+dEWAEGAFGgBGIGgEmClEjzP0zAowAI8AIMAIZRoCJQoYnj4fOCDACjAAjwAhEjQAThagR5v4TQQCfm61fr65o27ogkefzQxkBRoARKC8IMFEoLzPJ7yERwDflx08sFCc+OSkO7N3NqDACjAAjwAgEROC/6wQ7PflCfAMAAAAASUVORK5CYII=)"
      ],
      "metadata": {
        "id": "zcSUK1QPG7yb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Applying all the n controlled operations $CU^{2^j}$\n",
        "with $ 0 \\le j \\le n-1$ , and using the relation:\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-21-12 Quantum Phase Estimation.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "YoLVfpH7G7vq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![Screenshot 2023-08-02 at 15-21-19 Quantum Phase Estimation.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "yL-6S3j6HoLr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "where $k$ denotes the integer representation of n-bit binary numbers."
      ],
      "metadata": {
        "id": "2c1hmBL1HoJS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Inverse Fourier Transform: Notice that the above expression is exactly the result of applying a quantum Fourier transform as we derived in the  article on [Quantum Fourier Transform and its Qiskit Implementation](https://medium.com/@_monitsharma/learn-quantum-computing-with-qiskit-quantum-fourier-transform-e27176c8f378). Recall that QFT maps an n-qubit input state$|x⟩$ into an output as:\n",
        "\n",
        "\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-22-44 Quantum Phase Estimation.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "z1Y_tyDgHoHB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Replacing $x$ by $2^n \\theta$\n",
        "in the above expression gives exactly the expression derived in step 2 above. Therefore, to recover the state $|2^n \\theta⟩$\n",
        ", apply an inverse Fourier transform on the auxiliary register. Doing so, we find\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-23-40 Quantum Phase Estimation.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "nygMsVXCIOcT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Measurement: The above expression peaks near $x = 2^n \\theta$\n",
        ". For the case when $2^n \\theta$\n",
        "is an integer, measuring in the computational basis gives the phase in the auxiliary register with high probability:\n",
        "\n",
        "\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-24-17 Quantum Phase Estimation.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "N3N6AppOIOZs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For the case when $2^n \\theta$\n",
        "is not an integer, it can be shown that the above expression still peaks near $ x = 2^n \\theta$\n",
        "with probability better than $4/\\pi^2 = 40\\%$"
      ],
      "metadata": {
        "id": "L-FcyRdDIOXE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##  Example: T-gate\n",
        "\n",
        "Let’s take a gate we know well, the T-gate, and use Quantum Phase Estimation to estimate its phase. You will remember that the T-gate adds a phase of $e^{\\iota \\pi/4}$\n",
        "to the state $|1⟩$:\n",
        "\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-26-01 Quantum Phase Estimation.png](data:image/png;base64,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)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "Since QPE will give us $theta$ where\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-26-25 Quantum Phase Estimation.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "2lY4G1H0HoEq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We expect to find:\n",
        "![Screenshot 2023-08-02 at 15-26-42 Quantum Phase Estimation.png](data:image/png;base64,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)\n",
        "\n",
        "In this example we will use three qubits and obtain an exact result (not an estimation!)"
      ],
      "metadata": {
        "id": "VzOKGc_jIxiK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Creating the Circuit\n",
        "\n",
        "Let's first prepare our environment:"
      ],
      "metadata": {
        "id": "ggQa7XoYIxfa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#initialization\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import math\n",
        "\n",
        "# importing Qiskit\n",
        "from qiskit import IBMQ, Aer, transpile, assemble\n",
        "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
        "\n",
        "# import basic plot tools and circuits\n",
        "from qiskit.visualization import plot_histogram\n",
        "from qiskit.circuit.library import QFT"
      ],
      "metadata": {
        "id": "8M5Wb_gSDxRq"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, set up the quantum circuit. We will use four qubits -- qubits 0 to 2 as counting qubits, and qubit 3 as the eigenstate of the unitary operator (T).\n",
        "\n",
        "We initialize $|\\psi⟩ = |1⟩$ by applying an X gate:"
      ],
      "metadata": {
        "id": "eLpXSVj3JMoL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "qpe = QuantumCircuit(4, 3)\n",
        "qpe.x(3)\n",
        "qpe.draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "KeGvo52XEeWK",
        "outputId": "5e0d212f-9fc8-4e96-eb61-381e9d21d098"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 203.885x451.5 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we apply Hadamard gates to the counting qubits:"
      ],
      "metadata": {
        "id": "jQN1XmlrJT6S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for qubit in range(3):\n",
        "    qpe.h(qubit)\n",
        "qpe.draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "VidOe6UZEf_i",
        "outputId": "6fae919b-86fe-4636-edda-e4613b4cefd8"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 203.885x451.5 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next we perform the controlled unitary operations.\n",
        "\n",
        "\n",
        "\n",
        "We'll use Qiskit's `PhaseGate` to create the T operation. The phase gate does the transformation\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-28-22 Quantum Phase Estimation.png](data:image/png;base64,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)\n",
        "\n",
        "\n",
        " , where $\\lambda$ is the angle we provide. Since we want to implement T, which performs ,\n",
        "\n",
        "\n",
        " ![Screenshot 2023-08-02 at 15-28-50 Quantum Phase Estimation.png](data:image/png;base64,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)\n",
        "\n",
        "\n",
        "  we need to set\n",
        "$\\lambda = \\pi/4$.\n",
        "\n",
        "\n",
        "\n",
        "Also remember that Qiskit orders its qubits the opposite way round to the circuit diagram in the overview."
      ],
      "metadata": {
        "id": "3jA_YruQJV6q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "repetitions = 1\n",
        "for counting_qubit in range(3):\n",
        "    for i in range(repetitions):\n",
        "        qpe.cp(math.pi/4, counting_qubit, 3); # controlled-T\n",
        "    repetitions *= 2\n",
        "qpe.draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "CMjYHmXwEifj",
        "outputId": "c6890864-ccbd-4dd5-d546-98b74373ae5e"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1374.44x451.5 with 1 Axes>"
            ],
            "image/png": 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/TZJyUldff3CNF2rPSy3Jj2/o+hMuxk1N1j77RO8URZ964Znkkdu63u9tF81J4zLnBgCArqjZp6IsXbo0xx13XDZs2JC5c+dm/vz5mTlzZs4888xMnz495557bpJD19cA6AlDRyYnzOp6v4ZFPV4KVTJ+ejJsdNf6lOqSSfN7px4AgFpWs8FGQ0NDVq5cmQsvvDDDhg3LunXrMm7cuNxwww254447snbt2iSCDaB3nHxWUj+48+2PmZiM9zSMmlGqS055c9f6THljMrTjp5MDAHAENX3zwOzZs3P77bcf9vPdu3dn3bp1qaury7x586pQGVDrRh2fLLgoefS2pO3AkduOPiFZeFHSCw9loopOmpO8tDt55u6jt50wJ5nxlt6vCQCgFtV0sPFaHn/88ZTL5cyaNSsjRhz+9JGbbropSfLEE08c8v20adNyxhln9F2hPaBhztty5b+Vj9jmaNuB7jluanLGbyY/+8/khWeT/NJ/tcHDkonzkpPPSQYNqUqJ9LJpZyYjxiXr7kt2bj58+/CxyZTTK7ch9fI61gAANWtABhurV69O8tq3oVx88cUdfv/bv/3b+drXvtartQG15ZXZGPt2JlvWJk//8Bfb3vTfuna7CsV0wozK186m5MV1ybM//sW2cy4TaAAAvF6CjQ6Uy2YwAD1r2Jhk6hnJ0z9KZeZGSagx0IyZUPl69p4cHANCDQCA129A3tF9tGADAAAAKIYBOWNjxYoV1S4BAAAA6AEDcsYGAAAAUBsEGwAAAEBhCTYAAACAwhJsAAAAAIUl2AAAAAAKS7ABAAAAFJZgAwAAACgswQYAAABQWIINAAAAoLAEGwAAAEBhCTYAAACAwhpU7QLo2JD6ZNkl1a6i84bUV7sCAAAABiLBRj9VKiVDHR0AAAA4IreiAAAAAIUl2AAAAAAKS7ABAAAAFJZgAwAAACgswQYAAABQWIINAAAAoLAEGwAAAEBhCTYAAACAwhJsAAAAAIUl2AAAAAAKS7ABAAAAFJZgAwAAACgswQYAAABQWIINAAAAoLAEGwAAAEBhCTYAAACAwhJsAAAAAIUl2AAAAAAKa1C1C6Bj5XKyv63aVXTekPqkVKp2FQAAAAw0go1+an9b8snl1a6i85Zdkgw1mgAAAOhjbkUBAAAACkuwAQAAABSWYAMAAAAoLMEGAAAAUFiCDQAAAKCwBBsAAABAYQk2AAAAgMISbAAAAACFJdgAAAAACkuwAQAAABSWYAMAAAAoLMEGAAAAUFiCDQAAAKCwBkSw0dzcnKVLl2bGjBkZNmxYJk+enCuvvDItLS257LLLUiqVcv3111e7zF7R+MQP83cfLuXBO657zTZ/9+FSvnHdO/uwKgAYWPbvSdb9NFn9rWTVrclj306ankza26pdGX2lZWvy9I+SR76RPHJbsuZ7ybYNSblc7croC+Vy5Xiv+V7l+D/6jcp4aNla7croK+1tlfP+Y9+uvA6s/lbldWH/3mpXVhsGVbuA3rZq1apccMEFaWpqysiRIzNnzpxs2rQpX/ziF/Pss89m69bK2WTRokXVLRQAqDmt+5O1K5KmNYeHGE1PJENGJtPOSiaflpRK1amR3rVnW/Lk95Ot6w/ftvGRZOT4ZNbbkuOm9XVl9JUXn0vW/jBpefHwbevvT8ZNTd5wXjLi2D4vjT5QLicbHkrW3VcJuV9ty1PJz+5JJsxJZi1JBg2pTo21oKZnbDQ3N+dd73pXmpqactVVV2Xz5s156KGH0tTUlGXLluWOO+7I/fffn1KplAULFlS7XACghrS+lDy4PNn02GvPzNjfUgk+1t7lk/tatOuF5P7/3XGo8YqW5uThmyuf5FJ7mtYkD9/Scajxiq3rk/v/T7L7hb6ri75RLidPvXyO/+VQ4xXtbcmm1ZXXi9aX+ra+WlLTwcYVV1yRxsbGXH755bnuuusyevTog9uWLl2ahQsXprW1NdOmTcuYMWOqWCkAUGtW357s2tK5thseShpX9Wo59LED+5JVN1f+PKpy8vi3kx2be70s+tCOzcnjdybpRGh5YG8lAPHGtrZseDhpfLhzbXdtSR67o3frqWU1G2ysWbMmy5cvz/jx43Pttdd22Ob0009PkixcuPDgz2666aa8733vy9SpUzNixIi84Q1vyJ/92Z9l9+7dfVJ3b2ndvyd7dzV3+AUA9KydTZXp512x7qdJe3vv1EPf2/x48lIXLh/L7ZXbEqgd639aOa6d9dKuyrihNrS3VW4/6YrmnyW7nu+dempdza6xceONN6a9vT2XXnppRo0a1WGb4cOHJzk02LjuuusyZcqU/PVf/3UaGhqyatWq/OVf/mV+9KMf5e67705dXTGzoJ/cfE1+cvM11S4DAAaExke63uelXUnzs8kJM3u+HvpWudy9GTgvPFMJQ4Z2fOlKgezbVTmeXdW4Kmmw5k5NeOGZyu2GXdW4Kpn9az1eTs2r2WBjxYoVSZIlS5a8ZpvGxsYkhwYb3/rWt3L88ccf/P6tb31rjj/++Fx66aX58Y9/nLe85S29VHHvmrfkY5l51sUdbrv1M+f3cTUAUNu6Olvj1f0EG8W3d0dl0dCuKrdX1ls4aW7P10Tf2rq+e+vmtGxN9u1Mhh/T8zXRt15c171+zd18/RjoajbYWL++skrT1KlTO9ze2tqae+65J8mhwcarQ41XnHHGGUmSjRs3dquWM844I01NTV3qUz94eN77V0936/d1ZOyEmZky77we298vmzVzZtoOeFbR0Xz1ivWpq6tPe1tbGho6HpvUNmMAY2Bg+Kc/eDLDh3T9Y/dbbvpm/ul3/6AXKqIvTTl+bv7Hpd/pVt9PLf3v+cEjX+vZguhz5y363Xz4bf+jW33Pfev52dC8pocroq994tf/Z35l1ju73G978640NMzuhYr6vwkTJuSBBx7oVt+aDTZaWirzfvbu7fjN9vLly9Pc3JzRo0fn5JNPPuK+7rrrriTJ7NndG2BNTU1dDkUGDR3Rrd9VLZs2b0rrS6+x1C8HlV9ePaqccreDMorNGMAYGBj2vdTSrWBj2/Zm46IWvNT967gtz280BmrAlondP4brG3+WzS8aA0W3becRHoVzBHv27XIO6IaaDTYmTJiQbdu25aGHHsrixYsP2bZ58+ZcffXVSZIFCxakdISb2DZu3Jg///M/zzve8Y4sWrSo27V0Vf3g4d36XdUy8aSJZmx0Qimlg39OmjSpytVQDcYAxsDAsP6FR3Ps6K7f6rll11rjogbU1x3Izj3NGTNifKf7lMvllEqlbNv/c2OgBmx7qTJ7/JXj2lk7Wp7P4BHtmTTMGCi6LTvXdqvf+uZHB+w5oDvvm19Rs8HGeeedlzVr1mTZsmU5//zzM2vWrCTJ/fffn4985CNpbq48DeRIYcXu3bvznve8J0OGDMlXv/rVbtfSnek0L7Umn1ze7V/Z59Y+/XSG1uxo6jnf/5sk5aSuvv7gGi8MLMYAxsDA0PyzZNUtXetTPyT5l298JoOGfKZ3iqJPPXN35Uk3nVUqlTK2IbnvkR/0XlH0qftvTHZs7NoqoAv/ywlZf41FFmpB60vJyv+ZtB3oWr/Llr4jS//J9UFXFfMRH52wdOnSHHfccdmwYUPmzp2b+fPnZ+bMmTnzzDMzffr0nHvuuUkOXV/j1fbu3Zt3vetdee655/Ld7343J510Ul+WDwAU2HHTkhHjutZn0vxk0JBeKYcqmLQwqavvWp8pp/dOLVTHlDd2rX1dfdKwoHdqoe8NGppMnN+1PiPHJeOm9Uo5Na9mg42GhoasXLkyF154YYYNG5Z169Zl3LhxueGGG3LHHXdk7drK1KCOgo0DBw7k/e9/fx544IHceeedmTNnTl+XDwAUWKkuWXhRMnhY59qPbUhmvLlXS6KPDT8mmXthkk5+YD/1VzwRp9aceGoXwqpSMu+dybAxvVoSfWzGWyrn984YPDxZcJFH/XZXTd88MHv27Nx+++2H/Xz37t1Zt25d6urqMm/evEO2tbe359JLL80PfvCDfPvb386ZZ57ZV+X2ioY5b8uV/3bkZ00dbTsA0HUjxyVnfCh59BtJyxHWkDvxDcmctyd1NX1VNjCdOCupuyh54v8lr7UUWV19cvLiZNpZfVoafWTm25JBw5LnfpKU2zpuM3h4MveCZPz0Pi2NPlA/KDntN5InvpNseeq1240cnyx8TzLi2L6rrdYMyJfQxx9/POVyObNmzcqIEYeuWv2JT3wi//Ef/5FPfepTGTFiRH7yk58c3HbKKad0+DhYAICOjByXnP1fk20/TzasSl541ZPcp5xeuV1hZBdvWaFYjj8ledN/S55/Ktm4Otn+qlvnZ7wlmTgvGVKsh+HRBaVSMn1x0rAw2fRY0rQm2f3CL7bP/fWXA7AB+a5sYKgfksx/VzL9V5PGR5IXf5bs2faL7W/8QHLsZDM1Xq+avRXlSFavXp2k49tQ7rzzziTJZz7zmSxevPiQrzvuuKNP6wQAiq9USsZNrXwad/C2hFIya4lQY6CoH5ScNDc544M5ZAxMO1OoMVAMGVE53mf/dg4ZAyfNEWoMFCPHJacuSc65LIeMgXFThBo9YUD+NzpSsLFu3bo+rgYAAADoLjM2AAAAgMIakDM2VqxYUe0SAAAAgB4wIGdsAAAAALVBsAEAAAAUlmADAAAAKCzBBgAAAFBYgg0AAACgsAQbAAAAQGEJNgAAAIDCEmwAAAAAhSXYAAAAAApLsAEAAAAUlmADAAAAKKxB1S6Ajg2pT5ZdUu0qOm9IfbUrAAAAYCASbPRTpVIy1NEBAACAI3IrCgAAAFBYgg3op6ZNm5ZTTz01ixYtypw5c/IP//APr9n24osvzr333tup/d500035+Mc/fsjP/uVf/iWlUim33XbbwZ+9+c1vznPPPdet2nn9HH+MAYwBjIGBzfHHGOg8wQb0Y8uXL8+qVaty55135tOf/nQeffTRw9r89Kc/zdatW7N48eJO7fPWW2/NRRdddPD7devW5Z//+Z9z9tlnH9LuqquuyjXXXPO66uf1cfwxBjAGMAYGNscfY6BzBBtQAFOnTs2pp56atWvXHrbthhtuyIc+9KEkyfbt29PQ0JDjjjsuixYtyuzZszN06NB89KMfTZIcOHAg99xzT84999wkSXt7ez760Y/m7//+7zN06NBD9nvhhRfmzjvvzI4dO3r5b8fROP4YAxgDGAMDm+OPMXBkgg0ogNWrV+fJJ5/MwoULD9v2wx/+MGeddVaSZOzYsfnQhz6UP/qjP8qqVavyt3/7tzn77LPz5S9/OUly11135ZxzzsngwYOTJJ///Ofzq7/6qzn99NMP2+/gwYMzf/78rFy5shf/ZnSG448xgDGAMTCwOf4YA0fmuRvQj11yySUZPnx4RowYka9+9auZOXPmYW0aGxtz4oknHvx+1apVueKKK5IkDz74YE477bSD22677ba8973vTZI89thjufnmm3P33Xe/5u+fMGFCGhsbe+qvQxc5/hgDGAMYAwOb448x0DmCDejHli9fnkWLFh2xzYgRI7Jv376D369atergyevBBx/Mu9/97iRJuVzOd77znXz2s59NkqxcuTLr1q07eHJsamrKxz72sWzevPngYkL79u3L8OHDe/qvRSc5/hgDGAMYAwOb448x0DluRYGCW7BgQZ566qkkycaNG1MqlTJp0qQkyaOPPpr58+cnqSwqNHv27IwaNSpJ8vGPfzybN2/OunXrsm7dupx99tn50pe+dMgKyWvWrOlwuhv9h+OPMYAxgDEwsDn+GAOCDSi897///fnOd76TJHn44YcPmWo2duzY/OM//mOSw1c/Ppp169alra2tECeygczxxxjAGMAYGNgcf4yBpFQul8vVLgIGiu//TZJyklJy3lU9s8/du3fnnHPOyb333puRI0e+Zru5c+fmrrvuygknnNCp/X7qU5/KjBkzDq6gTM/o6THg+BePMTCweR3AGMDrAMZAzzNjAwpu1KhR+cIXvpDnnnvuiO0ef/zxTp/EkmTixIn53d/93ddbHr3M8ccYwBjAGBjYHH+MATM2oE/1xqc0FIsxgDEwsDn+GAMYAxgDPc+MDQAAAKCwBBsAAABAYQk2AAAAgMISbAAAAACFJdgAAAAACmtQtQugY+VyOXva26pdRqeNqKtPqVSqdhkAAAAMMIKNfmpPe1uOXfG9apfRadvOPT8j6w0nAAAA+pZbUQAAAIDCEmwAAAAAhSXYAAAAAApLsAEAAAAUlmADAAAAKCzBBgAAAFBYgg0AAACgsAQbAAAAQGEJNgAAAIDCEmwAAAAAhSXYAAAAAApLsAEAAAAUlmADAAAAKKwBEWw0Nzdn6dKlmTFjRoYNG5bJkyfnyiuvTEtLSy677LKUSqVcf/311S6TGre7OUn55W/KSbl8pNbUmnJ7sn1TDhkDDCxt+5OtP48xMIC9tDuHHP+2A9WshmpoeTGuBQawcjnZsTleBwawtgOuBXpLqVyu7VPqqlWrcsEFF6SpqSkjR47MrFmzsmnTpmzZsiUXXnhhtm7dmnvvvTcrV67Mm970pmqXe1BLW2uOXfG9172ftq9+Le3//n9T/8d/lLp3/Noh28rlctqu/lTKa9Zk0PVfTOnkad3+PdvOPT8j6we9zmprT3t70rQmaVyV7Nx86LaR45JJi5JJ85L6IdWojr5wYF+y8ZGk8ZFk385Dtx07OWlYlJwwKymVqlIefWDPtmTDw8nmx5PWlw7dNmF2MvmNyTEnVac2+sa2xmTDQ8kLz1RCzlcMHpZMnJc0nJYMP6Z69dG7yu3Jlqcq1wLbNx66bfjYyuvApAXJINcCNav1pWTjo5Vrgb3bD902tqEyBk481bVALdu7o3ItsOmxpHXfodtOPDWZfFplLNB9NR1sNDc357TTTktjY2OuuuqqXHPNNRk9enSS5LOf/Ww++clPZtCgQWlra8v27dszZsyYKlf8Cz0VbJQPHEjrJ65IXmjOoC/9U0rHjz+4re3mW9N+wz+n7nf/a+o/+IHX9XsEG4dr2588+q3kxeeO3G70icmi30iGjuybuug7e7YnD990+EXML5swJ5nz9qSuvi+qoi+9uC559BtH/2T+1HMrAQe1Z919yTMrj9xm0NBk4XuTY13U1py21uSxO5IXnj5yu5Hjk9Pelwwb3Td10Xf27Uwevvnl2TpHcMKsZN6vJ3Uup2vOtg3JI7cd/uHGL5vxlmTamX1SUk2q6VtRrrjiijQ2Nubyyy/PdddddzDUSJKlS5dm4cKFaW1tzbRp0/pVqNGTSoMHZ9DVVyX79qXt83978OflDY1p/9rXU3rDqam7+H3VK7BGlduT1bcfPdRIkl1bklU3J637e78u+s7+luTh/zh6qJEkTU8kT37flORas31T8sitnbvd4KkVlU9xqC0/f+jooUZSudhddXOy6/ner4m+Uy4nT9x59FAjSVqaK0H4gX1Hb0txHNiXPHTT0UONJHl+bfL4/3MtUGt2bklW3XL0UCNJnrm7MquD7qnZYGPNmjVZvnx5xo8fn2uvvbbDNqeffnqSZOHChQd/tnLlypx33nk56aSTMnTo0DQ0NOSSSy7JmjVr+qTu3lCaOSN1H/xAyg8+lPY77ky5rS1tn70uKZdTf/VVKdX7mLinvfBM0vyzzrff9Xxliiq147mfVqYddtam1YffrkRxlcvJUz9I2ts63+epFZWZXtSG/XuTZ37U+fZtB5K1d/VePfS9resqt6B0VsuLyc8f7LVyqIL1DyR7tna+/ZYnX15/gZqx9q6uraf09A8FnN1Vs8HGjTfemPb29lx66aUZNWpUh22GDx+e5NBgY9u2bZk/f36++MUv5rvf/W6WLVuWxx9/PIsXL05jY2Of1N4b6i79zWT69LT985fT/g//M+Wn1qbuv/5WSpPNe+0N3QkpNj4ipa8VbfuTzd349H3Dqh4vhSrZ2VSZjdUVbfuTpid7px763ubHuhZsJZXpyp35ZJdi6M45feOjXR839E/tbcmmR7vezwddtWP3C8n2Lr59bG8zg7O7ajbYWLFiRZJkyZIlr9nmlaDi1cHGu9/97nzhC1/IxRdfnLe+9a259NJLc8stt2THjh25+eabe7foXlQaNCiDrv7jZP+BtN9+R0rz5qbuNy6qdlk1ad/O7qXte3d0/eRH//TCs52bcvjLtjzlKQm1ojvBVuJippZserxv+9G/7N/btZmbB/u1VGZ6UHwvrkv27+l6v+ZnkgN7e7wcqmBzN8/n3e030NXs8jTr169PkkydOrXD7a2trbnnnnuSHBpsdOS4445Lkgwa1L1/rjPOOCNNTU1d6lMeMiS54R+69fte08iRyeDBSWtrSr9yRkp1PZdrzZo5K6X95lAnySknvTF/fsk3u9X3Y79zRe598pYeroi+dsHpH88lb/6zLvcrtyVvXHBWXty18eiN6df+6N3/kkXTz+9yv589uTHvbTirFyqir/3jxx/PiKFdf9TJv3/91tzwoT/shYroSw3HvSF/9ZHvd6vv/3f5p3LX6n/r4Yroa+cu+K381rl/3eV+5XLyq2edm01b1/ZCVfSlj1/wDznr1Pd0uV/Thu1paJjXCxX1fxMmTMgDDzzQrb41G2y0tLQkSfbu7TjyXL58eZqbmzN69OicfPLJh21va2tLe3t71q9fnz/90z/NhAkT8oEPdO/JIU1NTdm4sYtvVIYNzeBu/baOlcvltP3NF5LWA8mUyWn/P/+eure+JaWJPfOMwU2bNyX7uvERdQ0aU9/923u2bn2x62OFfmfHjO3d7ru5aXNe+OXnAVI4r/XaczStba3OATWira396I060LKnxRioAYPbju12323btxkDNWD7lO3d7rtlS1M2Pm8MFN2ePd2YspOkva3NOaAbajbYmDBhQrZt25aHHnooixcvPmTb5s2bc/XVVydJFixYkFIHD41+61vfenBGx4wZM7JixYocf/zx3a6lq8pDhuSFbv22jrXf9s2UH3k0db/z26lbfHZaP/GHafubL6T+umUd/v27auJJE83YeFn98MrNseVyucv/tuXB+zJp0qTeKIs+1FbX0q1+B1r3ZdQxQzJkpDFQdHtau7Ba3Kvs2LPFOaBGbG9pyugRXX9zu69tuzFQA4YMK6e9vS113XiOd3v9XmOgBrTVd+9aoK29NUNHlTJpsDFQdHvbtner3/Y9TQP2HNCd982vKJXLtblc4RVXXJG///u/z+TJk/P9738/s2bNSpLcf//9+chHPpKf/exnOXDgQD7xiU/k+uuvP6z/U089le3bt+e5557L5z73uTz//PO55557MmXKlD6pv6WtNceu+F6P7Ku8cWNaf//ylKZNTf3f/k1K9fVpu3F52v/lf6Xu4/8t9e/t+hSpX7bt3PMzsr5mc7Iue+g/kq3ru9Zn+DHJOR9NeiBnosraDiQrb0hau7iq9Ulzk7kX9E5N9K2dTclPuzGTfPbbk0nze74e+t76Byqr23fV4t9NRo7r8XKogkduqzwlrSuGjkp+9feSbuQh9DPtbcmPv1RZN6UrTpiZLHj9l+b0A7ubk598rev9Zi1Jppze4+XUvJpdPHTp0qU57rjjsmHDhsydOzfz58/PzJkzc+aZZ2b69Ok599xzk7z2+hqnnnpqzjrrrHzwgx/MD37wg+zatSuf/exn+/Kv0CPK7e1p+9znk/b21F/9xwcf7Vr3gfenNGtm2r/6tZQ3ecZkT2tY1L0+Qo3aUD84mTi36/26M27on8ZMqHx1xaChyYQ39E499L2Jc7v+5nTcFKFGLenOOX3SAqFGrair715Q3XBaz9dCdYwanxw7uWt96gZVPuii62o22GhoaMjKlStz4YUXZtiwYVm3bl3GjRuXG264IXfccUfWrq0syHO0hUOTZOzYsZkxY0aeeaaLsXs/0H7TLSk/sSZ1v/3hlF4126RUX5/6P/njpL0tbX/zhdToxJ2qOf6U5PgZnW8/5sSk4ehDkQKZdlbSlVnokxZ2/Y0w/dup/6VygdKV9vU9ubgSVTV4eOVTt86qH9K19vR/46YmE2Z3vv2o8T6lrTVTfyUZeVzn20+Y0/U3wvRvs86tnN873X5JMnhY79VTy2o22EiS2bNn5/bbb8+uXbuya9eu3HffffnYxz6WlpaWrFu3LnV1dZk37+grzj7//PN56qmncsopp/RB1T2n/POfp/1//WtKs9+Quvf9xmHbS9Ompu7Dl6a8+rG039a9p3jQsVJdMu/CzoUbYyYki97XtZMe/d+QEclp709GdOLT14nzKm9qzdipLceclCx6byf+b5eSN5yfnDSnT8qiDzUsSma+7ejtBg9LTntfMqp7S3nRT5VKyZy3JyeeevS2o46vvGYMGtr7ddF3Bg2tHNfO/N8+8Q2V8eJaoLaMPr5yfh/UibBi5tt80Pl61OwaG0dy33335eyzz86pp56aJ5988pBtH/7whzNjxowsWrQoY8eOzdNPP50vfOEL2bx5c+6///7MmNGFj+Ffh55cY6MvWGOjY+X2ZMtTSeOq5JcfdDFqfOWi96S5PqWtZa0vJRtXV8bA3u2HbjtuWmUMjD/FhUwt27sjaXw42fRYcuBV667U1VcuZCe/sTJri9q1Y1Oy4eHK60H5VQ9LGTy8cutBw6Jk2OiqlUcvK5eT59dWXge2bTh028hxL18LzEsG+YCjZrXur7wGNK5K9vzS2tLHTqmMgRNmuhaoZft2Va4FNq5ODrzqwWml+uTEWZVrgWN65mGVA9aADDa+/OUv5/d+7/fygQ98IMuXLz9k2/XXX5+vf/3refrpp7Nv375Mnjw5S5Ysyac//elMnTq1z2oUbNSelq3Jvp2Vi9qhoyrpvRewgaNcTnZtSfbvqczoGTE2GT622lXRl9oOJDu3VMKu+sGVc8CQ4dWuir60vyXZ/WJlLAweWpmx15XblSi+PdsqYWe5PRkyMhl9gmuBgaRcTnY9XzkXlOoq1wEjxla7KvpSe2tlgfEDr1wLjK/M8uX1G5Avp6tXr07S8foal19+eS6//PK+LokBYOQ4i8INZKWSNTQGuvrBybEN1a6CahoyMhk3stpVUE0jju3a+kvUllLJDL2Brm5QMta1QK+o6TU2XsuRgg0AAACgOAbkjI0VK1ZUuwQAAACgBwzIGRsAAABAbRBsAAAAAIUl2AAAAAAKS7ABAAAAFJZgAwAAACgswQYAAABQWIINAAAAoLAEGwAAAEBhCTYAAACAwhJsAAAAAIUl2AAAAAAKq1Qul8vVLoLDlcvl7Glvq3YZnTairj6lUqnaZQAAADDACDYAAACAwnIrCgAAAFBYgg0AAACgsAQbAAAAQGEJNgAAAIDCEmwAAAAAhSXYAAAAAApLsAEAAAAUlmADAAAAKCzBBgAAAFBYgg0AAACgsAQbAAAAQGEJNgAAAIDCEmwAAAAAhSXYAAAAAApLsAEAAAAUlmADAAAAKCzBBgAAAFBYgg0AAACgsAQbAAAAQGEJNgAAAIDCEmwAAAAAhSXYAAAAAApLsNEP/Ou//mtOP/30HHvssRk+fHhmz56dz3/+8ymXy9UuDQAAAPq1QdUugOSEE07In//5n+fUU0/N0KFDs3LlyvzBH/xB6uvrc+WVV1a7PAAAAOi3SmXTAvql9773vUmSW2+9tcqVAAAAQP/lVpR+plwu56c//WnuueeeLFmypNrlAAAAQL/mVpR+YseOHZk0aVL279+f9vb2XHPNNbniiiuqXRYAAAD0a4KNfmL06NFZtWpV9uzZk//8z//Mn/7pn2bixIm57LLLql0aAAAA9FvW2Oinrr322vzd3/1dmpqaql0KAAAA9FvW2Oin2tvbs2/fvmqXAQAAAP2aW1H6gWuuuSZvfvObM3369Bw4cCB33313li1blt/5nd+pdmkAAADQrwk2+oGdO3fm93//97Nx48YMGzYs06dPz7XXXpvf//3fr3ZpAAAA0K9ZY6NgNmx+Pscde0xGDBta7VIAAACg6szYKJDWtrb8263fy76X9ueyD/x6pkw6sdolAQAAQFVZPLRAHlz9VHbsasmQIYNz0gnHVbscAAAAqDrBxi9pa2vLv/7rv+bXfu3Xcvzxx2fo0KGZMmVK3vGOd+TLX/5y2traqlJXa1tbVvznw0mSt521KIMHm2wDAAAA1th4lZ07d+aiiy7KXXfdlSSZOHFiJk2alE2bNmXTpk0pl8vZtm1bxo4d2+e13bfqidz6nR9n9KgRWfqxDwo2AAAAINbYOMRll12Wu+66Kw0NDfn617+eJUuWHNy2ZcuWfOUrX8ngwYO7vN+//1+3ZNfuva+jsnJ2tVT6HzjQms99afnr2BcAAAD0L6NHDc8f/vZvdKuvYONlDz74YG666aYMGjQod955Z+bNm3fI9hNPPDGf/vSnu7XvXbv3Zufulp4oM/te2p99L+3vkX0BAABA0Qk2XnbbbbclSS688MLDQo3Xa/So4a+jd2W2RrlczrChQzKkGzNGAAAAoD97Pe+bBRsve+KJJ5Ikixcv7vF9d3c6TZLct2pNbv3OSmtrAAAAQAe8S37Zzp07kyTHHHNMj++7+2tsWFsDAACA2meNjR4wZsyYJMmOHTt6fN89scaGtTUAAADgcIKNl82dOze33HJL7r333h7fd/fuFbK2BgAAAAPD61ljo1Qul8s9WEthPfzww3njG9+YwYMHZ9WqVZkzZ05V67G2BgAAABxdXbUL6C9OO+20fOADH8iBAwdywQUX5Ec/+tEh27ds2ZJrr702LS0989jWI2lta8td9z6cJHnbWYuEGgAAAPAazNh4lZ07d+Y973lPfvjDHyZJJk2alIkTJ2bz5s3ZuHFjyuVytm3blrFjx/ZqHWZrAAAAQOeYsfEqY8aMyfe///185Stfydve9rbs2bMnjzzySOrq6vL2t789X/nKVzJ69Oher2PI4EEZM2qk2RoAAABwFGZs9FMHWltTSimDBtVXuxQAAADotwQbAAAAQGG5FQUAAAAoLMEGAAAAUFiCDQAAAKCwBBsAAABAYQk2AAAAgMISbAAAAACFJdgAAAAACkuwAQAAABSWYAMAAAAoLMEGAAAAUFiCDQAAAKCwBBsAAABAYQk2AAAAgMISbAAAAACFJdgAAAAACkuwAQAAABSWYAMAAAAoLMEGAAAAUFiCDQAAAKCwBBsAAABAYQk2AAAAgMISbAAAAACFJdgAAAAACkuwAQAAABSWYAMAAAAoLMEGAAAAUFiCDQAAAKCwBBsAAABAYQk2AAAAgMISbAAAAACFJdgAAAAACkuwAQAAABSWYAMAAAAoLMEGAAAAUFiCDQAAAKCwBBsAAABAYQk2AAAAgMISbAAAAACFJdgAAAAACuv/B75xWjKJ58z6AAAAAElFTkSuQmCC\n"
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We apply the inverse quantum Fourier transformation to convert the state of the counting register, then measure the counting register:"
      ],
      "metadata": {
        "id": "kTi5AQE6Jsdy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "qpe.barrier()\n",
        "# Apply inverse QFT\n",
        "qpe = qpe.compose(QFT(3, inverse=True), [0,1,2])\n",
        "# Measure\n",
        "qpe.barrier()\n",
        "for n in range(3):\n",
        "    qpe.measure(n,n)\n",
        "\n",
        "qpe.draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "bPx8KNvqEnEU",
        "outputId": "99386c1c-a2f2-40ed-9820-250b51d5df7f"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1959.72x451.5 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        " Results"
      ],
      "metadata": {
        "id": "gj_68XF-JuEj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "aer_sim = Aer.get_backend('aer_simulator')\n",
        "shots = 2048\n",
        "t_qpe = transpile(qpe, aer_sim)\n",
        "results = aer_sim.run(t_qpe, shots=shots).result()\n",
        "answer = results.get_counts()\n",
        "\n",
        "plot_histogram(answer)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "at3kSBRGEpEi",
        "outputId": "f165da93-b841-48a8-fd44-abc4d0621534"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We see we get one result (001) with certainty, which translates to the decimal: 1. We now need to divide our result by $2^n$ to get $\\theta$\n",
        "to get :\n",
        "\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-30-03 Quantum Phase Estimation.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAArgAAAAlCAYAAACpp5qbAAAHbklEQVR4Xu3dW2wUVRzH8T9vpC0lKQJNBN8UxAfBC8b4IBG8EECgCmjatBQaWi4WQkNBKW7KpbFcBCqXIkTAbIUiVAkxcg9eUEHRJy4GCiqYICgJrRjelP8kZyxlS6bL7uyZ2e+8kCy7M//zOfPwy/Q/53T599YhHAgggAACCCCAAAIIhESgCwE3JDPJMBBAwBqBk6fPyLr6jdJ8/oLs3dNkTV13K+R6S4vsP3hY6tbWS/n0MhmXNyYQdVMkAgggEEuAgMt9gQACCCRI4Ntjx6V8dqUM6N9PTp35WXrk5AQi4BZNLpU/rlx1FP66dk0qK2YRcBN0T3AaBBBIjQABNzXuXBUBBEIu8OQzQwITcM1UrF6zXqLbGgm4Ib83GR4C6SBAwE2HWWaMCCDguwAB13dyLogAAgi4AgRcbgYEEEAgCQIE3CSgckoEEEDAowAB1yMUX0MAAQQ6I0DA7YwW30UAAQQSK0DATawnZ0MAAQQcAQIuNwICCCCQOgECbursuTICCIRYgIAb4sllaAggYL0AAdf6KaJABBAIogABN4izRs0IIBAWAQJuWGaScSCAgFUCBFyrpoNiEEAgzQQIuGk24QwXAQT8ESDg+uPMVRBAAIFYAgRc7gsEEAicgG5I8OXXR+XK1T+luLBAJhUVWDEGs5NZrGKaGhukb5/7raizfRG6k5nuvNb+eG7Is1K7pNrKmikKAQQQuJsAAZf7AwEEAiUwd35EzjU3y8JIlZw6fUaWrlglWzbVyyMP9w/UOCgWAQQQQCB5AgTc5NlyZgQQSLDA/oOHZH5kkbuVrHliOnVKiTVPcRM8ZE6HAAIIIBCHAAE3DjR+ggAC/gtcb2mRkWPHS2ZGhjQ2bJHu2dliAi5/Svd/PrgiAgggYLMAAdfm2aE2BBBwBT7YGpX172+S0aNGSNW8Oc7n2osb3dYoBFxuFAQQQACBtgIEXO4HBBAIhMArrxXIbxcvSd27S+XppwY7NWs/7uEjX7gtC4EYCEUigAACCCRdgICbdGIugAAC9yqg7QnDhr/c4Wk6esnspL6Etnyl58tnZWVJzaKI0/5g07H4nWVy9uw5zyWNHDFcxuWN8fx9vogAAgiETYCAG7YZZTwIhFDA9No+0LeP7NoedUZ48dLvkjchX3rk5Lg9uSEcOkNCAAEEEIhDgIAbBxo/QQABfwVi9drG6sn1qyrdxCGRx/dHjyTydJ7OFc8YUlGnp8HwJQQQQKCdAAGXWwIBBKwXMAG3smKW+6d37cnVjR7q16xiDVzrZ5ACEUAAAX8FCLj+enM1BBCIQ6Cj9W/brqgQ67Sd7cHVcyyuftu6Hcc624P72KCBMnPG1Dik+QkCCCAQDgECbjjmkVEgEGoB85JZwesTZGJhvkyaMk1ye/e28oWwUE8Eg0MAAQQCIkDADchEUSYC6S7wcdOnzra8+qLZoIGPyhvTSq1b7aCjOdInsK2tfztbDGswX7t6RbpPJ+NHAAEEkipAwE0qLydHAIF0F9CX4TZ/GJWlNQsdivLZlbdtVpHuPowfAQQQSIYAATcZqpwTAQTSRkD7gzds2uxsQqGHPmFetbzW7ePV/2/YtkPyXx8v3bp1szLgagtITe0K5wmzHjdu/CORqnnuhhppM5kMFAEEQiNAwA3NVDIQBBDwW0DX512+sk4WRqqclRxMG4XW0dTYcMfLarrz2jffHXOe5prd2PyuOdb1iiaXStsX08y6w213jbOhTmpAAAEEvAoQcL1K8T0EEECgnYDZKnjqlBKZVFTg/K/5bPATj7u9tropxdboR7LvwCF5dexoq1Y40JUmJpaU3RHINfTm5uZK7ZJq5h0BBBAInAABN3BTRsEIIGCLgAmzbZcrM2v26g5re/c03VaqeTKqq0HYsoyXCbgD+veTupXL3Bf3XhqVJ5OLC9ny15abjToQQKBTAgTcTnHxZQQQQOB/Ae1dPXXrCeiAW+0J3bOzYz7B1ZfMWltb3UCrO4h17dpVvjq01xpK3TTD9BDr0+gTP/7k1FazKBKYlSqswaQQBBCwQoCAa8U0UAQCCIRBQAPvyLHjpVfP+9y+XH0SmpmZ4bx4pkfehHxp275gw7i1bl1b2IRcrSlWD7ENtVIDAggg4EWAgOtFie8ggAACHgTMS2QL3pwjLwwb6vxCWwDW1W+UrKwsuXz5stPX+tbcCquejGpbxc5Pdjv9wfrvzZs3ndp5yczDpPMVBBCwUoCAa+W0UBQCCARNQFdQ2L5jp5SWFLvhNghjMNsgL6le4NStT3PfW7dBdu/5zFnybNf2aBCGQY0IIIDAbQIEXG4IBBBA4B4FTLg1y4Xpy2R62LQUWEdDnD6zQprPX7jjhTj9/PgPJ2hVuMd7g58jgEBqBAi4qXHnqgggEBKB9mvh6rC0VaHfQw+6S4fZPFTTVtH+pTdtW/h83wFpbNhiVTuFzZbUhgAC9ggQcO2ZCypBAIGACWh/bdmMWZKZkSG9e/V0qz//y69SPr0sEEtsmTG8+PxQqZo3xxmD+ay4sCAQIT1gtw3lIoCADwL/AQXT4rCUMOTIAAAAAElFTkSuQmCC)\n",
        "\n",
        "\n",
        "\n",
        "This is exactly the result we expected!"
      ],
      "metadata": {
        "id": "IEgUIuyIJwUy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Example: Getting More Precision\n",
        "\n",
        "### The Problem\n",
        "\n",
        "Instead of a T-gate, let’s use a gate with $\\theta= 1/3$\n",
        ".\n",
        "\n",
        "In the cell below, we set up our circuit as we did with the last example.\n",
        "\n",
        "We'll use Qiskit's `PhaseGate` again, which does\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-28-22 Quantum Phase Estimation.png](data:image/png;base64,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)\n",
        "\n",
        " . Since we want to implement\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-31-15 Quantum Phase Estimation.png](data:image/png;base64,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)\n",
        "\n",
        ", we need to set\n",
        "$\\lambda = 2\\pi/3$\n",
        "."
      ],
      "metadata": {
        "id": "OZqZizsnJ6lD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create and set up circuit\n",
        "qpe2 = QuantumCircuit(4, 3)\n",
        "\n",
        "# Apply H-Gates to counting qubits:\n",
        "for qubit in range(3):\n",
        "    qpe2.h(qubit)\n",
        "\n",
        "# Prepare our eigenstate |psi>:\n",
        "qpe2.x(3)\n",
        "\n",
        "# Do the controlled-U operations:\n",
        "angle = 2*math.pi/3\n",
        "repetitions = 1\n",
        "for counting_qubit in range(3):\n",
        "    for i in range(repetitions):\n",
        "        qpe2.cp(angle, counting_qubit, 3);\n",
        "    repetitions *= 2\n",
        "\n",
        "# Do the inverse QFT:\n",
        "qpe2 = qpe2.compose(QFT(3, inverse=True), [0,1,2])\n",
        "\n",
        "# Measure of course!\n",
        "for n in range(3):\n",
        "    qpe2.measure(n,n)\n",
        "\n",
        "qpe2.draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "_L0IAP4bEqcj",
        "outputId": "6fc5816d-11d5-40b2-9433-bae7885f734b"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1792.5x451.5 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Let's see the results!\n",
        "aer_sim = Aer.get_backend('aer_simulator')\n",
        "shots = 4096\n",
        "t_qpe2 = transpile(qpe2, aer_sim)\n",
        "results = aer_sim.run(t_qpe2, shots=shots).result()\n",
        "answer = results.get_counts()\n",
        "\n",
        "plot_histogram(answer)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 473
        },
        "id": "tA9u3FoUEsQq",
        "outputId": "ad85aa70-5d27-45b1-a0b1-a997b50e68e6"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We are expecting the result $\\theta = 0.33333$ , and we see our most likely results are 010(bin) = 2(dec) and 011(bin) = 3(dec). These two results would tell us that $\\theta = 0.25$ (off by 25%) and $\\theta = 0.375$ (off by 13%) respectively. The true value of $\\theta$ lies between the values we can get from our counting bits, and this gives us uncertainty and imprecision."
      ],
      "metadata": {
        "id": "JMZDxOo5KO-r"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The Solution\n",
        "\n",
        "To get more precision we simply add more counting qubits. We are going to add two more counting qubits:"
      ],
      "metadata": {
        "id": "kbcOZtVFKchb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create and set up circuit\n",
        "qpe3 = QuantumCircuit(6, 5)\n",
        "\n",
        "# Apply H-Gates to counting qubits:\n",
        "for qubit in range(5):\n",
        "    qpe3.h(qubit)\n",
        "\n",
        "# Prepare our eigenstate |psi>:\n",
        "qpe3.x(5)\n",
        "\n",
        "# Do the controlled-U operations:\n",
        "angle = 2*math.pi/3\n",
        "repetitions = 1\n",
        "for counting_qubit in range(5):\n",
        "    for i in range(repetitions):\n",
        "        qpe3.cp(angle, counting_qubit, 5);\n",
        "    repetitions *= 2\n",
        "\n",
        "# Do the inverse QFT:\n",
        "qpe3 = qpe3.compose(QFT(5, inverse=True), range(5))\n",
        "\n",
        "# Measure of course!\n",
        "qpe3.barrier()\n",
        "for n in range(5):\n",
        "    qpe3.measure(n,n)\n",
        "\n",
        "qpe3.draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "C2tHH05UEtm7",
        "outputId": "51d79dad-9310-4aa4-eb62-262b1f44ad9c"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 2210.55x1956.5 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Let's see the results!\n",
        "aer_sim = Aer.get_backend('aer_simulator')\n",
        "shots = 4096\n",
        "t_qpe3 = transpile(qpe3, aer_sim)\n",
        "results = aer_sim.run(t_qpe3, shots=shots).result()\n",
        "answer = results.get_counts()\n",
        "\n",
        "plot_histogram(answer)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 496
        },
        "id": "D9uKyLOnEv6C",
        "outputId": "5cfcf671-e425-4c7f-b27a-60fdca3c31c2"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The two most likely measurements are now 01011 (decimal 11) and 01010 (decimal 10). Measuring these results would tell us $\\theta$ is:\n",
        "\n",
        "\n",
        "\n",
        "![Screenshot 2023-08-02 at 15-33-04 Quantum Phase Estimation.png](data:image/png;base64,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)\n",
        "\n",
        "\n",
        "\n",
        "These two results differ from $\\frac{1}{3}$\n",
        "by 3% and 6% respectively. A much better precision!"
      ],
      "metadata": {
        "id": "fhZU3v16KfQ8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Experiment with Real Devices\n",
        "\n",
        "\n",
        "\n",
        "We can run the circuit in previous section on a real device, let's remind ourselves of the circuit:"
      ],
      "metadata": {
        "id": "fFLcAkY1KqZO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "qpe.draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "lkr1CydwExfq",
        "outputId": "a4544b10-c158-4fc3-aff8-eb85f36524c2"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1959.72x451.5 with 1 Axes>"
            ],
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          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit import IBMQ\n",
        "IBMQ.save_account('ENTER API TOKEN HERE')"
      ],
      "metadata": {
        "id": "yulwThSjE2zq"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.providers.ibmq import least_busy\n",
        "IBMQ.load_account()\n",
        "from qiskit.tools.monitor import job_monitor\n",
        "provider = IBMQ.get_provider(hub='ibm-q')\n",
        "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= (n+1) and\n",
        "                                   not x.configuration().simulator and x.status().operational==True))\n",
        "print(\"least busy backend: \", backend)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8zYJOTTFEyv0",
        "outputId": "dbb2e30e-09f3-4792-cbda-4a5daf941e7a"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "least busy backend:  ibm_perth\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Run with 2048 shots\n",
        "shots = 2048\n",
        "t_qpe = transpile(qpe, backend, optimization_level=3)\n",
        "job = backend.run(t_qpe, shots=shots)\n",
        "job_monitor(job)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ShKvS_5KE1qr",
        "outputId": "a04c1d3d-6ab5-409b-cdf8-d44304386d91"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Job Status: job has successfully run\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# get the results from the computation\n",
        "results = job.result()\n",
        "answer = results.get_counts(qpe)\n",
        "\n",
        "plot_histogram(answer)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 473
        },
        "id": "55Qs_IgeFiVS",
        "outputId": "cb9ba95c-6142-4193-9c91-1fb7940ed76c"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can hopefully see that the most likely result is 001 which is the result we would expect from the simulator. Unlike the simulator, there is a probability of measuring something other than 001, this is due to noise and gate errors in the quantum computer."
      ],
      "metadata": {
        "id": "mgmikQBuK-Dq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The quantum phase estimation algorithm may seem pointless, since we have to know $\\theta$ to perform the controlled-U operations on our quantum computer. We will see in later chapters that it is possible to create circuits for which we don’t know $\\theta$, and for which learning theta can tell us something very useful (most famously how to factor a number!)"
      ],
      "metadata": {
        "id": "qGU7BMOXLClM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "Check the entire blog series : [Learn Quantum Computing with Qiskit](https://medium.com/@_monitsharma/list/introduction-to-quantum-computing-with-qiskit-6caba64cc007)\n",
        "\n",
        "or visit my website for more such learning resources :\n",
        "\n",
        "[The Quantum Classroom](https://monitsharma.github.io/)\n"
      ],
      "metadata": {
        "id": "QWjow8k4LYyF"
      }
    }
  ]
}