jupyter/00-spatial-genome-alignment-walk-thru.ipynb

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   "source": [
    "import ipywidgets as wg\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import igraph\n",
    "import copy\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from IPython.display import Image\n",
    "\n",
    "from jie.demo import mock_experiment, error_types, polymer_model, polymer_skip, find_polymer\n",
    "\n",
    "from jie.aligner import (log_bond,\n",
    "                         find_chr,\n",
    "                         edge_weights,\n",
    "                         boundary_init)\n",
    "\n",
    "from jie.utilities import (cartesian_esqsum, \n",
    "                           cartesian_sqdiff, \n",
    "                           cartesian_diff, \n",
    "                           check_lp_wgaps,\n",
    "                           find_loci_dist)"
   ]
  },
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   "source": [
    "## Demo\n",
    "- Say we put a haploid cell under the microscope, and perform multiplexed DNA-FISH\n",
    "    - Within one nucleus, we image 4 genes each separated by `5 kb`, all lying on the same chromosome\n",
    "    - We excite each labeled gene sequentially, quenching its signal before imaging the next gene:"
   ]
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    "wg.interact(mock_experiment, Slides=wg.IntSlider(min=1,max=6,step=1, description=\"Slides : {} /\".format(6)));"
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    "- `5kb` in the scope of the entire genome is fairly small. We'd expect the spatial coordinates of genes lying on the same contiguous fiber to be spatially proximal.\n",
    "    - Yet, we see multiple spots for every gene (in a haploid genome, where we'd expect to see `n=1` spot per locus) and they appear all over the place. What's happening here?\n",
    "---\n",
    "- We might be tempted to find __the closest series of spots__ belonging to each locus. Here's why this is a __pitfall__:\n",
    "    - What we think might be happening is a collection of errors that disguise detection of the true loci belonging to the contiguous chromatin fiber:\n",
    "        - The true chromatin fiber `DNA (unobserved)` is not imaged.\n",
    "        - Instead, we intend to discern discrete locations `True Pos (Ground Truth); Red cross` with FISH probes, to gain a coarse-grain view of chromatin structure.\n",
    "        - In practice, the signal emitted from these FISH probes (`True Pos (Observed) ; Green circles`) may be displaced from its true location.\n",
    "        - Some signals may not emit at all, as FISH probes fail to label an intended locus (`False Neg ; Yellow triangles`)\n",
    "        - Still other signals (ie. off-target hybridization, background fluorescence, hot-pixels) have high signal intensity and may be mistaken as a real signal (`False Pos; Purple diamonds`)\n"
   ]
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    "wg.interact(error_types, Slides=wg.IntSlider(min=1,max=6,step=1, description=\"Slides : {} /\".format(6)));"
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   "source": [
    "---\n",
    "##### Load example data\n",
    "\n",
    "- To figure out which spots belong the true chromatin fiber, we can perform a type of inference.\n",
    "    - We load the data from our mock experiment:"
   ]
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     "text": [
      "/home/b2jia/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:1773: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self._setitem_single_column(ilocs[0], value, pi)\n"
     ]
    }
   ],
   "source": [
    "# load data\n",
    "df = pd.read_csv(\"../data/df_spalign_demo.csv\")\n",
    "df.columns = ['x_hat', 'y_hat', 'z_hat', 'Annot', 't', 'bp']\n",
    "df.reset_index(drop = True, inplace = True)\n",
    "\n",
    "# subset data\n",
    "df_fiber = df[df['Annot'] == 'Fiber']\n",
    "df_data = df[(df['Annot'] != 'Fiber') & (df['Annot'] != 'FN')].sort_values(by='t')\n",
    "\n",
    "# add indexing\n",
    "df_list = []\n",
    "for hyb, group in df_data.groupby(by='t'):\n",
    "    _df = copy.deepcopy(group)\n",
    "    _df['i'] = list(range(_df.shape[0]))\n",
    "    df_list.append(_df)\n",
    "df_data = pd.concat(df_list)\n",
    "\n",
    "df_data = df_data[['x_hat', 'y_hat', 'z_hat', 'Annot', 't', 'i', 'bp']]\n",
    "    \n",
    "# add localization err\n",
    "df_data.loc[:, 'sig_x'] = 1\n",
    "df_data.loc[:, 'sig_y'] = 1\n",
    "df_data.loc[:, 'sig_z'] = 1  \n",
    "\n",
    "# make all positions positive\n",
    "xmin = np.min(df_data['x_hat'].values)\n",
    "ymin = np.min(df_data['y_hat'].values)\n",
    "zmin = np.min(df_data['z_hat'].values)\n",
    "\n",
    "df_data.loc[:, 'x_hat'] = df_data['x_hat'].values - xmin\n",
    "df_data.loc[:, 'y_hat'] = df_data['y_hat'].values - ymin\n",
    "df_data.loc[:, 'z_hat'] = df_data['z_hat'].values - zmin\n",
    "\n",
    "# translate fiber accordingly (for visualization)\n",
    "df_fiber.loc[:, 'x_hat'] = df_fiber['x_hat'].values - xmin\n",
    "df_fiber.loc[:, 'y_hat'] = df_fiber['y_hat'].values - ymin\n",
    "df_fiber.loc[:, 'z_hat'] = df_fiber['z_hat'].values - zmin\n"
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       "           x_hat     y_hat     z_hat Annot  t  i     bp  sig_x  sig_y  sig_z\n",
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       "5000    8.345561  8.037631  5.236670    TP  1  0   5000      1      1      1\n",
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    "- Above, we have a series of `4-D` spatial coordinates, acquired by sequentially imaging 4 loci inside one nucleus. \n",
    "    - We know the coordinates in Euclidean space (`x_hat`, `y_hat`, `z_hat`).\n",
    "    - We also know the order of these loci (`t`).and the genomic distance relative to the first locus imaged (`bp`)\n",
    "        - __Q__: When discrete genes are imaged and __the fiber connecting them is not visualized__, how can we __infer__ which signals lie on the __same contiguous chromatin fiber__?"
   ]
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\n",
      "text/plain": [
       "<Figure size 1296x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize = (18, 9))\n",
    "ax1 = fig.add_subplot(1, 2, 1, projection='3d')\n",
    "ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
    "\n",
    "# Draw imaged loci\n",
    "cdict = {0:'Red', 1:'Green', 2:'Blue', 3:'Purple'}\n",
    "ax1.scatter(df_data.loc[:, 'z_hat'],\n",
    "           df_data.loc[:, 'y_hat'],\n",
    "           df_data.loc[:, 'x_hat'],\n",
    "           c=[cdict[elem] for elem in df_data.t], alpha = 1, marker='^', s = 100)\n",
    "\n",
    "ax1.set_title(\"Input\", fontsize = 20);\n",
    "\n",
    "# Draw imaged loci\n",
    "cdict = {0:'Red', 1:'Green', 2:'Blue', 3:'Purple'}\n",
    "ax2.scatter(df_data.loc[:, 'z_hat'],\n",
    "           df_data.loc[:, 'y_hat'],\n",
    "           df_data.loc[:, 'x_hat'],\n",
    "           c=[cdict[elem] for elem in df_data.t], alpha = 1, marker='^', s = 100)\n",
    "\n",
    "# Draw fiber\n",
    "ax2.plot(df_fiber.loc[:, 'z_hat'], df_fiber.loc[:, 'y_hat'], df_fiber.loc[:, 'x_hat'], c='Blue', alpha = 0.3, label = 'DNA (unobserved)')\n",
    "\n",
    "# Draw true positive (true location)\n",
    "ax2.scatter(df_data.loc[[0, 5000, 15000], 'z_hat'],\n",
    "            df_data.loc[[0, 5000, 15000], 'y_hat'],\n",
    "            df_data.loc[[0, 5000, 15000], 'x_hat'],\n",
    "            alpha = 1, marker='o', s = 300, facecolors='none', edgecolors='r')\n",
    "\n",
    "ax2.set_title(\"Output\", fontsize = 20);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "310d255d",
   "metadata": {},
   "source": [
    "---\n",
    "##### The key insight here is recognizing that true loci lie on the same contiguous fiber and are physically linked.\n",
    "---\n",
    "- What if we can examine the probability two loci are connected?\n",
    "    - Take the first locus `t = 0; Red` and second locus `t = 1; Green` for example. \n",
    "    - If we didn't have the annotation (provided for this dummy example), it's hard to tell which of the three spots belonging to first locus (`t = 0`; `Red`) is connected to which of the three spots belonging to the second locus (`t = 1`; `Green`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7b326ba4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_hat</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>z_hat</th>\n",
       "      <th>Annot</th>\n",
       "      <th>t</th>\n",
       "      <th>i</th>\n",
       "      <th>bp</th>\n",
       "      <th>sig_x</th>\n",
       "      <th>sig_y</th>\n",
       "      <th>sig_z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.121910</td>\n",
       "      <td>7.182445</td>\n",
       "      <td>6.081194</td>\n",
       "      <td>TP</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15001</th>\n",
       "      <td>8.508098</td>\n",
       "      <td>9.697731</td>\n",
       "      <td>9.965565</td>\n",
       "      <td>FP</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15002</th>\n",
       "      <td>10.631071</td>\n",
       "      <td>7.161015</td>\n",
       "      <td>9.452167</td>\n",
       "      <td>FP</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5000</th>\n",
       "      <td>8.345561</td>\n",
       "      <td>8.037631</td>\n",
       "      <td>5.236670</td>\n",
       "      <td>TP</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15003</th>\n",
       "      <td>12.077955</td>\n",
       "      <td>9.836819</td>\n",
       "      <td>8.411960</td>\n",
       "      <td>FP</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15004</th>\n",
       "      <td>8.011521</td>\n",
       "      <td>5.150124</td>\n",
       "      <td>2.489517</td>\n",
       "      <td>FP</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           x_hat     y_hat     z_hat Annot  t  i    bp  sig_x  sig_y  sig_z\n",
       "0       7.121910  7.182445  6.081194    TP  0  0     0      1      1      1\n",
       "15001   8.508098  9.697731  9.965565    FP  0  1     0      1      1      1\n",
       "15002  10.631071  7.161015  9.452167    FP  0  2     0      1      1      1\n",
       "5000    8.345561  8.037631  5.236670    TP  1  0  5000      1      1      1\n",
       "15003  12.077955  9.836819  8.411960    FP  1  1  5000      1      1      1\n",
       "15004   8.011521  5.150124  2.489517    FP  1  2  5000      1      1      1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_data[df_data['t'] <= 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a8f40e6",
   "metadata": {},
   "source": [
    "---\n",
    "- If we use a __polymer model__ to draw bonds between these candidate spots, we might be able to figure out which pair is most probably physically linked.\n",
    "<br></br>\n",
    "- Say we draw a polymer bond between `t=0; i=0 (True Positive)` --> `t=1; i=1 (False Positive)`. \n",
    "- We also draw a polymer bond between `t=0; i=0 (True Positive)` --> `t=1; i=0 (True Positive)`\n",
    "<br></br>\n",
    "    - We evaluate the bond probability using the following formula:\n",
    "$$\n",
    "w_{t ; i}^{t+c ; j}=4\\pi(R_{t ; i}^{t+c ; j})^{2}\\frac{1}{\\left(2 \\pi\\left(s^{t+c;j}_{t;i}\\right)^{2}\\right)^{3 / 2}} e^{-\\frac{(R_{t ; i}^{t+c_{j} ; j})^{2}}{2(s_{t ; i}^{t+c ; j})^{2}}}\n",
    "$$\n",
    "<br></br>\n",
    "    - We note that the additional term $4\\pi(R_{t ; i}^{t+c ; j})^{2}$ comes from integrating the probability density over a sphere. \n",
    "        - In practice, this additional distance term is outweighted by the exponential term (in our illustrations and in our implementations, this term is removed but can be toggled on/off by the user ie. `log_bond(svt=True)`). A derivation of this term can be found in the **Appendix** (below).\n",
    "    - Without this term, our bond probability is:\n",
    "$$\n",
    "w_{t ; i}^{t+c ; j}=\\frac{1}{\\left(2 \\pi\\left(s^{t+c;j}_{t;i}\\right)^{2}\\right)^{3 / 2}} e^{-\\frac{(R_{t ; i}^{t+c_{j} ; j})^{2}}{2(s_{t ; i}^{t+c ; j})^{2}}}\n",
    "$$\n",
    "<br></br>\n",
    "\n",
    "- $R_{t;i}^{t+c;j}$ is the Euclidean distance, or observed spatial distance, between two imaged loci.\n",
    "- $s^{t+c;j}_{t;i}$ is a function of the expected polymer contour length:\n",
    "\n",
    "$$\n",
    "\\frac{2}{3}l_{p}\\tau L^{t+c;j}_{t;i}\n",
    "$$\n",
    "<br></br>\n",
    "- $l_{p}$ is the persistence length of DNA. We fix this as `150bp`, a value derived from studying DNA in free solution (the true persistence length _in situ_ is likely different)\n",
    "- $\\tau$ is the distance parameter that converts base pairs to nanometers. We fix this as `0.34nm/bp`; the lengthscale of DNA _in situ_ is also likely different.\n",
    "- $L^{t+c;j}_{t;i}$ is the genomic distance separating locus `t;i` and locus `t+c;j`\n",
    "    - The length of the expected distance is based on the genomic separation between these two spots, `5000 bp`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3078a3e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "951efe3b961c4ec9a5a525c43bd08675",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='Slides : 6 /', max=6, min=1), Output()), _dom_classes=('…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wg.interact(polymer_model, Slides=wg.IntSlider(min=1,max=6,step=1, description=\"Slides : {} /\".format(6)));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53972ca2",
   "metadata": {},
   "source": [
    "---\n",
    "Note: we take the **negative log bond probability below**.\n",
    "\n",
    "Explicitly, it is:\n",
    "\n",
    "$$\n",
    "w_{t ; i}^{t+c ; j^{\\prime}}=\\left(\\frac{\\left(R_{t ; i}^{t+c ; j}\\right)^{2}}{2\\left(S_{t ; i}^{t+c ; j}\\right)^{2}}\\right)-\\ln \\left(\\frac{1}{\\left(2 \\pi\\left(S_{t ; i}^{t+c ; j}\\right)^{2}\\right)^{3 / 2}}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d0e370f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is the bond probability between spot 1, hyb 0 - spot 1, hyb 1:  8.592620998568247\n",
      "This is the bond probability between spot 1, hyb 0 - spot 2, hyb 1:  5.642909529063303\n"
     ]
    }
   ],
   "source": [
    "# parms\n",
    "nm_per_bp = 0.34\n",
    "pixel_dist = 100\n",
    "l_p_bp = 150\n",
    "l_p = l_p_bp*nm_per_bp/pixel_dist\n",
    "L = 5000\n",
    "\n",
    "# calculate expected contour length\n",
    "s = L*nm_per_bp/pixel_dist\n",
    "\n",
    "# calculate Euclidean distance between observed spots\n",
    "r_fp = np.linalg.norm(df_data.iloc[0, :3]- df_data.iloc[4, :3])\n",
    "r_tp = np.linalg.norm(df_data.iloc[0, :3]- df_data.iloc[3, :3])\n",
    "\n",
    "print(\"This is the bond probability between spot 1, hyb 0 - spot 1, hyb 1: \", \n",
    "      log_bond(l_p, s, r_fp))\n",
    "\n",
    "print(\"This is the bond probability between spot 1, hyb 0 - spot 2, hyb 1: \",\n",
    "      log_bond(l_p, s, r_tp))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af59c919",
   "metadata": {},
   "source": [
    "- We see that the bond probability (negative log probability) is less probable (greater negative log probability) for `t=0; i=0 (True Positive) --> t=1; i=1 (False Positive)`, than for `t=0; i=0 (True Positive) --> t=1; i=0 (True Positive)`\n",
    "    - In this manner, we can evaluate the probability two discrete signals are linked on the same polymer fiber using this function.\n",
    "    \n",
    "---\n",
    "- It turns out the multiplicative product of each of these bond probabilities, spanning from beginning to end of a chromatin fiber, reflects its __physical likelihood__ (Conformational Distribution Function; CDF):\n",
    "\n",
    "$$\n",
    "C D F=\\prod_{h=1}^{H} w_{v_{h}}^{v_{h+1}}, p=\\left\\langle v_{1}, v_{2} \\ldots v_{H}\\right\\rangle\n",
    "$$\n",
    "\n",
    "- We strive to seek the series of bond probabilities that allow us to connect the start of the chromatin to the end, such that we can __maximize__ the bond probabilities between every pair of imaged locus.\n",
    "    - If we use negative log probabilities:\n",
    "$$\n",
    "w' = ln(w)\n",
    "$$\n",
    "    - ...this is reframed as the __sum__ of negative log probabilities, and a value we strive to __minimize__:\n",
    "    \n",
    "$$\n",
    "CDF^{*} = \\min \\sum_{h=1}^{H} w_{v_{h}}^{'v_{h+1}}, p^{*}=\\left\\langle v_{1}, v_{2} \\ldots v_{H}\\right\\rangle\n",
    "$$\n",
    "\n",
    "where $p^{*}$ is the series of most optimal bonds (shortest path)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "489145ae",
   "metadata": {},
   "source": [
    "#### Spatial genome alignment\n",
    "\n",
    "- Let's apply spatial genome alignment to this demo dataset. What's the most likely fiber we find among these spatial locations?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "232d446f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/b2jia/projects/jie/jie/aligner.py:576: FutureWarning: Boolean inputs to the `inclusive` argument are deprecated infavour of `both` or `neither`.\n",
      "  pts_clr_next = cell_pts.loc[cell_pts['hyb'].between(i, i+num_skip, inclusive = False)]\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_hat</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>z_hat</th>\n",
       "      <th>Annot</th>\n",
       "      <th>t</th>\n",
       "      <th>i</th>\n",
       "      <th>bp</th>\n",
       "      <th>sig_x</th>\n",
       "      <th>sig_y</th>\n",
       "      <th>sig_z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.121910</td>\n",
       "      <td>7.182445</td>\n",
       "      <td>6.081194</td>\n",
       "      <td>TP</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>5000</th>\n",
       "      <td>8.345561</td>\n",
       "      <td>8.037631</td>\n",
       "      <td>5.236670</td>\n",
       "      <td>TP</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15000</th>\n",
       "      <td>5.277496</td>\n",
       "      <td>6.326657</td>\n",
       "      <td>5.903535</td>\n",
       "      <td>TP</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>15000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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      "text/plain": [
       "          x_hat     y_hat     z_hat Annot  t  i     bp  sig_x  sig_y  sig_z\n",
       "0      7.121910  7.182445  6.081194    TP  0  0      0      1      1      1\n",
       "5000   8.345561  8.037631  5.236670    TP  1  0   5000      1      1      1\n",
       "15000  5.277496  6.326657  5.903535    TP  3  0  15000      1      1      1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cell_pts_input = copy.deepcopy(df_data)\n",
    "cell_pts_input.rename(columns = {'t':'hyb'}, inplace = True)\n",
    "\n",
    "mat, path, _ = find_chr(cell_pts_input = cell_pts_input, \n",
    "                        gene_dist = [0, 5000, 10000, 15000], \n",
    "                        bin_size = 5000,\n",
    "                        nm_per_bp = 0.34,\n",
    "                        num_skip = 3,\n",
    "                        total_num_skip_frac = 1,\n",
    "                        norm_skip_penalty = False,\n",
    "                        stretch_factor = 1.01,\n",
    "                        init_skip_frac = 0,\n",
    "                        lim_init_skip = False,\n",
    "                        lim_min_dist=False)\n",
    "\n",
    "df_data.iloc[path]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35aa2945",
   "metadata": {},
   "source": [
    "- It looks like the most likely fiber is one that traverses `t=0`, `t=1` and `t=3` loci, as any connection to `t=2; (Blue)` is deemed physically unlikely\n",
    "    - What's happening behind the scenes of this function, `jie.aligner.find_chr`?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e5a9184",
   "metadata": {},
   "source": [
    "---\n",
    "##### Under the hood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ea91fdb9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_221512/1976230745.py:49: FutureWarning: Boolean inputs to the `inclusive` argument are deprecated infavour of `both` or `neither`.\n",
      "  pts_clr_next = cell_pts.loc[cell_pts['hyb'].between(i, i+num_skip, inclusive = False)]\n"
     ]
    }
   ],
   "source": [
    "cell_pts_input = copy.deepcopy(df_data)\n",
    "cell_pts_input.rename(columns={'t':'hyb'}, inplace = True)\n",
    "gene_dist = [0, 5000, 10000, 15000]\n",
    "bin_size = 5000\n",
    "nm_per_bp = 0.34\n",
    "num_skip = 3\n",
    "stretch_factor=1.2\n",
    "exp_stretch = 1\n",
    "total_num_skip_frac = 1\n",
    "norm_skip_penalty = False\n",
    "stretch_factor = 1.01\n",
    "init_skip_frac = 0\n",
    "theta = np.pi/20\n",
    "lim_init_skip = False\n",
    "lim_min_dist=False\n",
    "\n",
    "############################################\n",
    "\n",
    "## Define constants ##\n",
    "n_colours = len(gene_dist)\n",
    "init_skip = int(init_skip_frac*n_colours)\n",
    "end_skip = int((1-init_skip_frac)*n_colours)-1\n",
    "total_num_skip = int(total_num_skip_frac*len(gene_dist)) \n",
    "corr_fac = nm_per_bp / pixel_dist\n",
    "l_p = l_p_bp * nm_per_bp / pixel_dist # persistence length in pixels\n",
    "\n",
    "loci_dist = find_loci_dist(gene_dist = gene_dist,\n",
    "                           nm_per_bp = nm_per_bp,\n",
    "                           pixel_dist = pixel_dist)\n",
    "\n",
    "# make copy of input dataframe\n",
    "cell_pts = copy.deepcopy(cell_pts_input)\n",
    "\n",
    "# add current index\n",
    "cell_pts.reset_index(inplace=True, drop = True)\n",
    "cell_pts['CurrIndex'] = cell_pts.index\n",
    "\n",
    "# create transition matrix\n",
    "n_states =  cell_pts.shape[0]  \n",
    "trans_mat = np.zeros((n_states, n_states))\n",
    "\n",
    "trans_mat_prog = {}\n",
    "trans_mat_prog[-1] = copy.deepcopy(trans_mat)\n",
    "\n",
    "for i in set(cell_pts['hyb']):\n",
    "    \n",
    "    # grab nodes of curr hyb and reachable hyb\n",
    "    pts_clr_curr = cell_pts.loc[cell_pts['hyb']==i]\n",
    "    pts_clr_next = cell_pts.loc[cell_pts['hyb'].between(i, i+num_skip, inclusive = False)]\n",
    "\n",
    "    # grab node indeces in adjacency matrix\n",
    "    ## NB: rows --> starting vertices | cols --> ending vertices\n",
    "    rows = pts_clr_curr['CurrIndex'].values\n",
    "    cols = pts_clr_next['CurrIndex'].values\n",
    "\n",
    "    # convert node indeces to position in transition matrix\n",
    "    trans_idx = (np.array([n_states*rows, ] * len(cols)).T + np.array(cols)).flatten().astype(int)\n",
    "\n",
    "    # find degrees of separation between nodes\n",
    "    next_hyb = i+1\n",
    "    skips = np.array([pts_clr_next['hyb'].values,] * pts_clr_curr.shape[0] ) - np.min([next_hyb, n_colours-1])\n",
    "\n",
    "    # calculate edge weights\n",
    "    trans_prob = edge_weights(pts_clr_curr, pts_clr_next, \n",
    "                              bin_size, l_p_bp, \n",
    "                              nm_per_bp, pixel_dist, \n",
    "                              theta, loci_dist, lim_min_dist)\n",
    "\n",
    "    # update transition matrix\n",
    "    np.put(trans_mat, trans_idx, trans_prob)\n",
    "    \n",
    "    # save state\n",
    "    trans_mat_prog[i] = copy.deepcopy(trans_mat)\n",
    "    \n",
    "    # save intermediate data\n",
    "    if i == 0:\n",
    "        ex_pts_clr_curr = copy.deepcopy(pts_clr_curr)\n",
    "        ex_pts_clr_next = copy.deepcopy(pts_clr_next)\n",
    "        ex_trans_prob = copy.deepcopy(trans_prob)\n",
    "    if i == 1:\n",
    "        ex_trans_prob_skip = copy.deepcopy(trans_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c3c8248",
   "metadata": {},
   "source": [
    "- We star with spatial coordinates of a given locus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "07e26673",
   "metadata": {},
   "outputs": [
    {
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       "      <td>7.121910</td>\n",
       "      <td>7.182445</td>\n",
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       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x_hat     y_hat     z_hat Annot  t  i  bp  sig_x  sig_y  sig_z  \\\n",
       "0   7.121910  7.182445  6.081194    TP  0  0   0      1      1      1   \n",
       "1   8.508098  9.697731  9.965565    FP  0  1   0      1      1      1   \n",
       "2  10.631071  7.161015  9.452167    FP  0  2   0      1      1      1   \n",
       "\n",
       "   CurrIndex  \n",
       "0          0  \n",
       "1          1  \n",
       "2          2  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex_pts_clr_curr.rename(columns={'hyb':'t'}, inplace = True)\n",
    "ex_pts_clr_curr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49ba3267",
   "metadata": {},
   "source": [
    "- We consider all spatial coordinates belonging to loci `num_skip=3` bonds away (non-inclusive):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a2523885",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_hat</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>z_hat</th>\n",
       "      <th>Annot</th>\n",
       "      <th>t</th>\n",
       "      <th>i</th>\n",
       "      <th>bp</th>\n",
       "      <th>sig_x</th>\n",
       "      <th>sig_y</th>\n",
       "      <th>sig_z</th>\n",
       "      <th>CurrIndex</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.345561</td>\n",
       "      <td>8.037631</td>\n",
       "      <td>5.236670</td>\n",
       "      <td>TP</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12.077955</td>\n",
       "      <td>9.836819</td>\n",
       "      <td>8.411960</td>\n",
       "      <td>FP</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.011521</td>\n",
       "      <td>5.150124</td>\n",
       "      <td>2.489517</td>\n",
       "      <td>FP</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.237000</td>\n",
       "      <td>FP</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>10000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.511619</td>\n",
       "      <td>0.446863</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>FP</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>10000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x_hat     y_hat     z_hat Annot  t  i     bp  sig_x  sig_y  sig_z  \\\n",
       "3   8.345561  8.037631  5.236670    TP  1  0   5000      1      1      1   \n",
       "4  12.077955  9.836819  8.411960    FP  1  1   5000      1      1      1   \n",
       "5   8.011521  5.150124  2.489517    FP  1  2   5000      1      1      1   \n",
       "6   0.000000  0.000000  1.237000    FP  2  0  10000      1      1      1   \n",
       "7   0.511619  0.446863  0.000000    FP  2  1  10000      1      1      1   \n",
       "\n",
       "   CurrIndex  \n",
       "3          3  \n",
       "4          4  \n",
       "5          5  \n",
       "6          6  \n",
       "7          7  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex_pts_clr_next.rename(columns={'hyb':'t'}, inplace = True)\n",
    "ex_pts_clr_next"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "99fa199f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, 1, 1],\n",
       "       [0, 0, 0, 1, 1],\n",
       "       [0, 0, 0, 1, 1]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next_hyb = 1\n",
    "n_colours = 4\n",
    "skips = np.array([ex_pts_clr_next['t'].values,] * ex_pts_clr_curr.shape[0] ) - np.min([next_hyb, n_colours-1])\n",
    "\n",
    "skips"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3902669d",
   "metadata": {},
   "source": [
    "- We calculate the bond probability between every pair of starting coordinates (`pts_clr_curr`) to end coordinates (`pts_clr_next`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b7569bc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize = (5, 3))\n",
    "axs.imshow(ex_trans_prob, cmap = 'plasma')\n",
    "plt.yticks(np.arange(3),[\"t=0;\\ni=0\", \"t=0;\\ni=1\", \"t=0;\\ni=2\"], fontsize = 18);\n",
    "plt.xticks(np.arange(5),[\"t=1;\\ni=0\", \"t=1;\\ni=1\", \"t=1;\\ni=2\", \"t=2;\\ni=0\", \"t=2;\\ni=1\"], fontsize = 18);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc11cc83",
   "metadata": {},
   "source": [
    "- We do so for all subsequent spatial coordinates, building directed edges from all coordinates of a given locus to all coordinates of successive loci (defined up to `num_skip` bonds away).\n",
    "    - Slowly, our adjacency matrix populates with directed edges and weighted accordingly by the bond probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1ad9e9e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 5, figsize = (20, 5))\n",
    "for (t, mat), ax in zip(trans_mat_prog.items(), axs.flatten()):\n",
    "    ax.imshow(mat, cmap = 'plasma')\n",
    "    if t == -1:\n",
    "        ax.set_title(\"Adjacency matrix :\\nInitial\", fontsize = 18)\n",
    "    else:\n",
    "        ax.set_title(\"Adjacency matrix: \\nt={}\".format(t), fontsize = 18)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e97c8f83",
   "metadata": {},
   "source": [
    "- The reason we consider bond probabilities between non-successive loci (and up to `num_skip` bonds away) is __to acknowledge error__:\n",
    "    - For instance, it is possible that some spatial coordinates are __inadvertently detected__ for a particular locus (__False Positive__ signal ; ie. off-target hybridization, background fluorescence)\n",
    "    - At the same time, it is also possible that some spatial coordinates are __never detected__ for a particular locus (__False Negative__ signal ; poor probe hybridization)\n",
    "        - __THEREFORE__, we must permit the possibility that ___all spatial coordinates___ detected for a particular locus are __noise__ and allowed to be __skipped__:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5416c3b4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4bf65f20d90346a982150ec2d089e92e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='Slides : 4 /', max=4, min=1), Output()), _dom_classes=('…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wg.interact(polymer_skip, Slides=wg.IntSlider(min=1,max=4,step=1, description=\"Slides : {} /\".format(4)));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f9d0268",
   "metadata": {},
   "source": [
    "---\n",
    "- In the demo dataset, we illustrate an example where signals belonging to __t=2__ are seemingly out of place and not congruent with the expected spatial distance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d7be6976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fd1038cc160>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/U0+h53ke8/Pz0uy+xWI5k11gGAZutxtutztvDCwUCmFnZwccx+XtcKfUlnK77u12Ozo7OyXXPiL8m5ubiMVicDqdUsTvdDobThQLCX82mz0j/PIFPY32O1JKQ4Weci6CIODo6Agul0uTDl+ycc7j8ZTcOKd2H321EKGXp+rls/vlLOEhY2CkGzwSiUhWr2RsKhwOG2aVKyUfhmEku96urq48177V1VUkEgm43W5J+O12e8OJonwlL1BY+JU+/Y32O1LyoUJPKQlpuFtYWMDdu3elcZ9KCQaDmJ+fx9WrV6WaaTHqEdGn02m8+eabuHXrVtVRuHKH+8nJCZaXl3F4eIilpSVYLBYpzd+ItWGjo8UcfSHXvng8jnA4jKWlJaRSqTPC32gUEv5MJlNwQQ/x6afXamNBhZ5SEGWqvtqRJJ7nsbKygkgkgtHR0bJuiLUUep7nsbi4iEwmg7e//e2S6YqWWCwW2Gw2XLt2DcCT2vD29jai0WjDp4iNhiAImmdN5OWa3t5eCIIgufbNz88jk8nA6/VK51Evu2Y9KSX8ROQtFouU6qfCb3yo0FPOUGg2vpo0eiqVwuTkJJqbmzE2Nlb2TaFWqXuyEa+trQ0Oh0MXkS+EsjasTBHL/d0bMVKsN7V4SGQYBl6vF16vF/39/Xmufbu7u8jlcgVd+86DbMAzAnLhJ8eUyWSQyWQAiN9TZY2fYiyo0FMklLPx8if18za7FYOkqW/cuCEZmpRLLSJ6cnxkI97e3p5u71Xq9ymUIlZGikQwmpqaavYw0ujUOtKUu/YBYumLCD/xhZALf7FSmB7ZCC0gnycV/saCCj0FwPmz8Wqja57nsbCwgGQyWfHGOT0jepKqj8fjum7Eq5RCkSKxed3a2pJsXolgNJLbW60wgte9yWSSHs4A0bWPnMf19XUwDCOdR5/Plyeg9T72cigk/CTVv76+Do/HA5/PR4W/zlChp5Q1G69GdOPxOKamptDR0YHr169XfMPSK6InqfrW1lZcu3atZjfUan4flmXPCEYkEkEoFMLq6mqeoOjh9tYIoqPEiGJpNpvzGjSz2SwikQiCwSBWVlak8+jxeOp8pJUhv38kk0m43W5J+OURv7Krn6IvVOifYpSe2aW+cOUK/e7uLtbX13Hr1i34fL6qjk8PoT86OsLi4qKUqq8lWooOsXltaWkBcNbtzWazScLfiKYvWmBEoVdSyLUvEong8PAQsVgMb775Zp5rXyOJIs/zZ4ScRPzpdFrq6ieb+Uwmk9TVT9EWKvRPKWr3xp+38IXjOMzNzYHjODx8+LDqMTzynlql7nmex9LSEqLRaF1T9Xr1HCjd3pLJZJ7pi8vlkgTD4XA8FTdTozSzqcFqtaKtrQ0+nw/ZbBbXr1+XGvui0WhDPcDxPH/mwaTYSt5UKiU9mNGVvNpDhf4ppBIb21LNeGTjXF9fH7q7uzX7YmoV0cu7/kdHR+t246jl+ypNX8js9/LyMlKpVF5Hv81mq9lx1ZpGFQkikjabDR0dHZI9NHmA29rayhvJ9Pv9qpcs6U0hoVdSSvgJVPirhwr9U0Q1NraFomtBELC9vY3t7W3cvn1b87qiFkJ/fHyMhYWFirr+ix1TNdQjylTOfhOr3nA4jNnZ2bwRsKamJk2yMUagEVL3xSh27MoHOCL88iVLRsnclCP0Sqjw68PF+EZTzqXavfFKoc9ms5iZmYHZbM7bOKcl1aTuBUHA8vIyIpEIxsbGDBG1GmWpjdyqd2BgABzHSZ3gGxsbZzrBGxUjfNaVQr6npWAYBk6nE06nM2/JkjxzU0/XvkqEXkkx4U8mk3kd/1T4S0OF/oJTajZeDXLRPTk5wczMDC5duoTOzk5Nj1dOpcKYSqUwNTWFpqYmVQY9TysmkwmBQEDKeJBO8OPjY6ysrCCRSGB9fR2BQKDhrHob6VjlVDJHX8i1LxaLIRwOY2FhQdquWKuSjRZCr0Ru4AVQ4S8XKvQXGGWqvpoLnuyGX1tbw8HBAUZGRgpunNOSSiJ64qV//fp1aYTJKBgloj8PZSf4a6+9BrvdfmaNa1NTk+HqwnIuYupeDQzDwOPxwOPx5G1XlJds5Ha9Wpsw6SH0SsoRfvkM/9Mq/FToLyjVpuqVcByHra0ttLS04OHDhzUZ81EjjIIgYGVlBeFwWNdUfSOLR6WwLCs1hBWqC8vTww6Ho96HK9HI50oPkVSWbOQmTNvb22fWKlfbq1EPd79Cws9xHHK5nPQzRPjNZvNTs5mPCv0FQ81sfLmEQiFsbm6ipaUF169f1+Aoy6NcoU+n05icnITf79c9VV/NazdKRF+KQnVhkh5eXFxEOp02zFKXRv6sa/GQojRhUvZqXAT3xUI1frnwMwwjbeW7yMJPhf4CcZ6NbSWvt7KyglAohEuXLtV0NzxQXuqepOqvXbsmmcfoxUW8AVRLofQw8Xbf2dnRPEqs5PgakVqkvZUoezXk7otra2uSjz9xX7wowp/L5fJ6mC6i8FOhvyBUMhtfCtLQ5vf78eDBAxwcHCAej2t0tOVRKgIWBAGrq6sIBoNlr72tNxchoj8P+VKXS5cugeM4RCKRPG93EkX6fD5dxayRU/dGOHal+yJp0jw6OsLy8jLMZjP8fr/UpNlIrn2EQsKfzWYl4U+lUrBYLHC73Q0t/FToG5xqZuOLQWxi5Q1ttVoZK6fYFyqTyWBychJerxdjY2MNeYN5WjCZTGe83cPhsLQ10Gq1oqmpCYFAQHOnNyOIZaUY8diVTZrpdBqRSAR7e3tYWFiQzmWje/XLMxXBYFDq3id/r/TpN9p5KgQV+gZGrY3teZTa6HaeBW6tCIVCmJubw9WrV6UbjtbodZN9GiL687BYLGhra0NbWxsAMWKSW/USp7dAIFC14YsRxbJc6pG6V4vNZsuzXSbncnt7G7FYDKlUCltbW4afzigFz/N5Qk/uuel0WrrnEuEnPv1G/D2p0DcoyrpStRdXIpHA5OQk2tvbC250K2WBWwsEQcDa2hqOjo50TdUTMTbil7Ve6PlwYrfb0dnZic7OTgiCgEQiIRm+JJNJae47EAgYwvSoVjTiNSg/lzzP4/XXX4fJZMLGxgbi8TicTqdU43c6nQ3x+3EclxfhKyN+ufADTzbzkXE+owg/FfoGQ8vZeML+/j5WV1dx8+ZN+P3+gj9Tj9Q9IZPJYGpqCm63Gw8ePNA10tEz6jbCF97IMAwDl8sFl8uFnp4eCIKAaDSKUCiE2dlZZLNZ+Hw+BAIB+P3+c+e+G1EsCY0Q0ZdCEASYzWZ0dXVJdr3kIW51dRWJRMKwY5lylEKvRC785L6hXMkbjUaxtbWFt73tbfofcBGo0DcQPM9jd3cXPp8PFotFk9n4+fl5ZLNZPHjwoOSNs15Cn8vl8Prrr+PKlStSuldPaHr9LPVcAuT1euH1eiWr3tPTU2nck4x/BQIB+Hy+MzfkRhb6Rj524OyDSqGHOOVYphEXLZ0n9HLkznzAE+GfmZnBn/7pn1Khp5RGPhu/vb0Nl8tV9XxyLBbD1NQUenp60NPTc+5NpdZCLwgC1tfXkU6n8fzzz9fsib+Rb64XHZPJlDf3Tca/iFUv+XvSBd7ID2z1MJvREp7nkUMOf7bwZ3jPtfec+ftCY5lE+Ofm5pDJZODz+aRUf738GDiOq/g8kHtJMpmE2+3W8rBUQ4Xe4Chn400mEziOq+r1dnZ2sLm5qWrjXC2FPpPJYHp6WjJmqWVa77xeBI7jLsx2t0ZHOf6VyWQQCoWk3e2ZTAb7+/tob29vuGYw0gTWqPA8j8/vfh6fWPgEej29eNj1sOTPsywrZW/6+/sL+jGQDYvllG20/D2q9QsgWwXrSeNeSU8BhWbjqxHcXC6HmZkZmEwmPHz4UNWNpFZd95FIBDMzM7h8+TLa29vx8ssv6/6ecoqJAcdxmJ2dRTgchtlsliJLv9/f0JHXRcJqtebtbh8fH4fJZMpb4RoIBAxdEyY0euo+kUngUyufAgB8+B8/jL/7Z3+n6t8X8mMgrn3ysg3xY9DroUhN6r4YsViMRvSUs5Saja9U6MnGuYGBAXR1dan+93p33QuCgI2NDezv7+PevXu6L8wpRqHfM5FIYGJiAt3d3bhy5Qp4nkc4HJZSxhaLRRIQrWfBKZVDPPrtdru0wjUUCuXVhMl5q6dVbyEavRnvs7OfRU4QbWbHD8bxaPfRuVF9KQq59hHhX1tbO7NaWSvXPi2EnuyDqCdU6A3GebPxalP3cgG9e/duxSkkPVP32WwW09PTsNvtNVuYUwzl502MXYaHh+H1epHJZGA2m/OMQ5Sz4I0UOV5k5FGxfIWrfJNbKBQyhFVvqWNvNFK5FH7tjV9DkktK/11JVF8Ks9l8xoipUL8Gseut9J5C7sPVEI/H0dvbW9VrVAsVegNBGu5K2diqEVxS63Y4HFULqF5CTzINg4ODUspVSS1veqTrnud5LC0tIRaLSeZBxUoXyllwZeQoHwmjGAP5Jrd6W/UWQguBqRd/OPWHyPJZ6b8FCJpE9aVQuvZlMhlEIhEcHBxgaWkJFotFmtBwu92qzqcWHiX1ylASqNAbADU2tuUKLtk5rdVYmtZCLwgCNjc3sbe3V3K3fa0NbBiGQTqdxvT0NAKBAO7fv6/qvQtFjvLaYjwex8rKijQS1sjpWaOj5ro5z6pXXp7xeDy6X4+N2nWfyqXwqy//KhK5xJk/1zqqL4XVas1zYEyn01JjXzQahc1mkx7kSpXbtDjPsVis7pbAVOjrjNq98SaTqaTgype93L9/X7PUsZbz5SRVb7PZzs00kAeMWt30iDnPjRs3NNmGp1wF+ujRI3i93jyvd1J7bLTOcKNTzQNiMave7e1tRKNRyapXL5e3Rk3dK6N5Qi2i+lLYbLa8Rs1kMpn38O1wOHQ7n8QcqJ5Qoa8T8tl4oHwbW5Zli9bo5RvntF72otWFT1L1ly5dQmdnZ1nvW4tufzK3H4vFcPfuXSmy0xqGYc7U90OhEDY2NqTuXDIL3ggb+YyMltdNMate4vImN3vR4rw1YjMeiebj2cJbLmsd1ZfC4XDA4XBIrn1E+NfW1qTmOb/fD47jqn7oouN1TynV7I0vJvSFNs4ZCUEQsLW1hZ2dHVVNgbWY35c3AzY3N9e0A9tut+fZhBLTkPn5eck0hKSM690g1ojotZyokFWv8rwR4a9k5rsRI/pi0Tyh3lF9MRiGkTw7uru7pT6bYDCITCaD119/Pc+uV+2DXDwep6n7p41q98azLCtlAcjrLS0tIRqNYmxszDDWkXJyuRymp6dhsVjw8OFDVeMqekf0p6enmJ6eljIMU1NTdXNUK+QWdnJyIkX89W4QazRqJZZyq15i9kL6Mra2tvJmvv1+f1nXf6M14+X4HD76ykcRz8bBoPhxp3Ip/PLXfxl//QN/XcOjUwfps7HZbAiFQhgZGZEe5BYWFpBOp+H1eqXv4nmBAR2ve4qQp+qr2RsvH69LJBKYmppCa2srRkdHDXljIEJa6fy+nkY929vb2NzcxJ07d6QvopG87pX1fWWDGGkoovX9wtQrKlaeN2LVGwqFsLq6WtboV6M14zFg8HPP/BwSWbEJ7+TkBCaTqaDADfgGanx0lUFm6As9yBHh393dRS6XyxN+ZQaHRvRPCVrujSep7P39faysrODWrVuGHNsSBAHb29vY3t7OE1K16GHUw3Ec5ubmwHHcGYdAIwm9EmWDGKkrEuc3t9stNfYZMbNTa4xyHgtZ9YbDYezv72NxcbFgB3ijpe5NrAk/PfrT0n+vr6/D6XTWZBGVXhQzy5GPZsqXLZFmTZ7nYbPZMDs7ixdeeAHJZLKivo0f//Efxxe+8AW0tbVhenoaAPBzP/dz+PznPw+r1YqhoSH8xV/8hV8QhMh5r0WFXmeqTdUX4ujoCPF4HA8fPqyZ57MalFa71ThLaS28cpe73t7eM+fjvPcz0s1X2VAUi8Wkla65XC6vTvy01veNdL4IVqsV7e3taG9vB5DfAU4MlxKJBNLpNOx2uyF/h/NoxGZCJeUutFEuW+I4Duvr63jppZfwiU98AsfHx/h3/+7f4Z3vfCeee+65svuT3ve+9+Gnf/qn8d73vlf6sxdeeAEf/ehHYTab8Qu/8AsA8IsAfuG813o6v/01QM1sfLnEYjEsLCzAYrFgZGTEkDeAaDSKqakp9Pf3o7u7u+rX01LoScq7VBbEyBF9KeT1/f7+/jxvcHl9PxAIVOUU1mgY8TuiRPnAFo/HMT09jfX1dWQyGUOubz2PiyD0lS60MZlMGBoawm//9m9DEAQ899xzeP755/G3f/u3+PCHPwy73Y5f+IVfwHd+53eWfJ1v+ZZvwfr6et6fvetd75L+/7fW3vaUc0xU6HVA7Wx8Oezs7GBjYwNDQ0M4Pj6u2w2sVEpxe3sbW1tbVaXqlWjRdS9vWCQud8VoVKFXovQGJ/V9ebqYdPPT+r5xII1gVqsVw8PDYFlWqgc3UqZGi61v9UYLn3tA/C5+13d9F77ru74LABAMBpFOp6t+3U9/+tMA8Dfl/Kwxr5IGpdLZ+FLkcjnMzs4CAB4+fIhUKoXDw8Oqj7USiOgqL375MT548EDTm0+1wptOpzE5OYmmpqayGhYvitArKVTfD4VCUn2fRI20vm8MyAN1oXqwMlOjxzKXaqlmj7tR0ELoCwUpWow//5f/8l/Iffb/KefnqdBrhDJVr0WERDrW5WnwWu6FV1JI6GOxGCYnJ9HX14eenrKySBW9ZyWQKOjatWtlu9xdVKFX4nA40N3dLc0NF4oaqT9//SiWOSuUqZEvcyErlAOBQE2seotxEVL3Wgh9MpnU3Of+M5/5DL7whS/gy1/+MpxOZ1k3Kyr0GqB1qp74wO/u7p5Jg6vdXqclylE3Uk64ffu2buMjlQgvcbk7PDxUbQN83vs1Wjd0OSjHh0jUSCL+RCKBtbU1STwa/QbeCJR7nSmXuRBP9+3tbcRiMdjtdkn49bDqLcZFEfpqfwetXfH+9m//Fh/72Mfw1a9+VdUDBBX6KtBqNl6O0gde+URphIie4zjMzs6C5/kz42lao1bo5Z/fgwcPVJ+TiybilaCMGl977TU4nU7s7e1hYWGhbuLxtFHJ5yr3dC9m7VoLi+WLIPQ8z1ftklmN0P/gD/4gvvKVr+D4+Bg9PT34yEc+go9+9KNIp9N44YUXAAATExP/H0EQ/tV5r0WFvkKqsbEtBkmdXr58WRq9UXLeUhs9YRgGsVgMS0tL6OnpQU9Pj+43eTUPNqTjv1wf/ULoMbff6LAsK42DycVD7vNOGvtofd84FLJ2JRbLcoc3UqLR0vr5Igi9Fql7Mi5ZCZ/73OfO/NlP/MRPKP/oXJEHqNBXhNaz8YIgYG1tDUdHR+emmuspROl0GnNzcxgZGamZ01O5ET0pI1Tb8V/qXJK/u4jp+3IpJB7RaDRvfl9u92rUrvCnkUIWy0qjF9Kb4fP5qjp3VOhFjLC5DqBCrwrScDc/P4/29nb4fL6qXzOdTmNqagoej6esVHM9BIY4yaXTady5c6emdo7nCX0plzs93k+LZr2L9KAgr++TrvBIJCI59hE7WFrfNx4sy8Lv98Pv9+PSpUvI5XJSR//a2pr095V4L1ChFyEbKesNFfoykdvYchyHXC5X9WseHx9jYWFBVVd4rYnH45icnMzr+q8lpVL3iUQCk5OT6OzsRF9fnybi+bR03euFyWRCc3OzNEJE7F53d3cRjUZht9ulND+t7xsLs9mcd+6I98LBwQEWFxdhtVqlc0esekvR6OdWi4cVI6yoBajQl0Uul8ubjTebzVWlz3mex/LyMk5OTgy7cQ4A9vb2sLa2huHhYXi9XszNzdW8bFBMeMtxuasUPYW+EX3Mq0Fu90rq+2S5SyKRkJaBBAKBmq4HppyP0nshlUrlWfU6nU5J+B0Ox4W7pmlE/5RQbDa+2E74ckgmk5icnERLSwvGxsYM+eXgOE5q1nnw4IHkp1+Pjn/lewqCgKWlJZyenp7rclcJNKLXD3l9v6enBzzPS/7809PT4DhOShWXu86VUjvsdjs6OzvR2dkJQRCQSCQQDoexvLyMVColLVUinu+NDq3RPwWUmo2vdJb94OAAy8vLuHnzpmG/DPJ0+I0bN/J+73o0AsqFV63LXbXvpwf0QeIJLMsWrO/L17kS4fB6vYZ8KH5aYRgGLpcLLpcLPT09Z5oy4/E4FhcXpaZMIy7fOg8thD4ejxuiLEuFXoHSxrZQjUat0PM8j/n5eaRSKc2iUD3Sv2T17fDwcMFGw3pE9OThgoweXr16VTIH0ev9qBDXh0L1/VAohN3dXczPz8PpdEpp/ouYKiY04vWnbMp89OgRWltbEQqFsLm5CUEQpGyNkax6S2FEw5xKoUIvo9zZeJPJhEwmU9ZrxuNxTE1NFYyQK4U41Gl1o+N5HgsLC0ilUiVX39ZL6I+Pj7G/v6/a5a7S99Pzd6QPEuVjtVrzzF+UqWL5/P5Fqu9fhB4Osi2RZC5zuVyeVa88W2PUaQxBEDQR+lpOKRWDCv1bqJmNL7dGv7u7i/X1ddy6dUuTUTzl+2vx5SCp+o6ODly/fv3c37uWIpXL5bC5uQmGYfDw4cOa3AyoEBsTZaqY53kpVbyzswOe5/Pm9xshYixGows9KXfKMZvNaGlpkdLY8mwNmcYgDwZG2aaoxTEQN8J689QLfSV7489L3edyOalDXQ+LWK0ia9IzUG7nei0jeuJyR6K1Wj3xlxL6TCaDubk52Gw2NDc3VxSJ0AcJbZBvdSMz4PL6vtlsRjqdxunpaV2Xu1RCo8+gl3P88mwNcHabIrHqJR39jQpN3RsA+Wy8Goe7UkJPBKqvrw/d3d263GCqtcElqfpkMqmqZ6BWzXhyl7tEIoGTkxPd35NQTIhPTk6kTYKCIEi+7w6HI28unFIflBFjKpXC48ePsb29jWg02lCjYBcholf7oKLcphiPxxEKhbC4uIh0Ol2XMo0WD+Q0dV9nSMNdJTa2hYReEARsbW1hZ2enahvW89BivK+tre3cVH2h9yVNinrAcRzm5+eRzWalTEgymaxpBFxI6Le2trC9vY179+7BbDZDEIQzc+Gkbuzz+aRIpFCvA43oa4PVaoXFYsHNmzel+r78PJH5fSPW97WoDdeTajMSDMPA7XbD7XZLVr3yMg0Zw9TTZlmrhy06XlcnKknVK1GmsLPZLGZmZmCxWApunNOaSlPoxGSm0vE+PVP3xVzuat0AKBdiYq9LSjAmk0l6OCQ/q5wLPz09RSgUwtbWFgCgqakpL83fyJFao0E+a3l9v7e3t2h93ygd4YVq3I2E1qUHZZlGabMsb/zz+XyavLdWv0MsFqMRfa3Ram+8PKKPRCKYmZnB0NCQVG/SG7Xix/M8lpaWEIvFqhrv00t0j46OsLi4WLBXoNYRMHm/ZDKJiYkJdHV1obe3t6xrRe4dDjyxEJWvd02lUkgkEoaLIi8apSKyYvV90hFuNpvzOsJrLbpPY+peDcoxTPI9I4GMxWKp+vxpMUMPiN4fRviuPxVCr5yNr3bjnMlkQi6Xw9raGg4PD3Hv3r2a1mfVzPGnUilMTEygtbUV9+/fr+r31rrrvhyXu3oIfTwex+PHj6s2NpJbiJKHh6mpKayvryOTyUgrQoul+SmVo0YslfX9dDqNUCgk1fddLlfe/L7ePA3NeFpSzKpX3p9BIv5y9ytoJfRA7feDFOLCC70ee+M5jsPJyQm8Xm9ZG+e0ptzImkTKWjnxaRnRE5c7v99f0uWulql7QRCwv7+PSCSCZ599VtMdBCTN73A4cPXqVVit1oJp/ko2hVG0xWaznbF6lTeG6f2ARiP66ihm1Uv2K3g8Hkn47XZ7wdfQYnzZSOfxQgu91nvjASAYDGJ+fh5WqxXXrl3T4CjVc574kaU5WvvBa9V1r8blrlYRfS6Xw9TUFACgvb1dt0VD5Pcplubf39/H4uKitOXtorvA6YVWN9lC9X35A5ogCHn1YS2iwKe9GU9Liln1hsNhzM/PI5PJFGyg5Xles3NphO/uhRR6eaq+0oY7JTzPY2VlBZFIBKOjo3j8+LEGR1oZpcbrUqkUJicn0dzcrLkffLXRtSAI2NjYUOVyVwuhj8VimJycxKVLl2Cz2XBwcKDr+xWiUJpf2SVO0/zlo9cNVvmAVqy+HwgEylrlWgjajKcfcqve/v5+8DyPk5MThMNh6cGNePNXew6M9DlcOKGvdDa+FEQ8A4GAITbOFRuvI/vtr1+/LjWqaP2+lQp9LpfD9PQ0rFarKpc7vVP3+/v7WF1dxe3bt+HxeBAOh3V7L6C8B5dyu/lpmr84tYqkCs3vy1e5ulyuvPn9cjBKFFgpRhK482BZtqBV7+7uLk5PTxGPx6W/V/tdSyQShjDLAS6Y0OuRqiednDdu3EAgENDgKKun0OrW5eVlRCIRXffbVyq6xERoYGAAXV1dqv6tXhE9mUSIx+N5q3iNOOdO0/yNg7I+rDR+Oc9nAWgsoSyElo1stYY8uHEcB6/Xi66urrzvms1mk87feRkb8qBnBC6E0GsxG6+EuMclEgld9p5Xg9y4Rr66Ve9sQyVd98Tvv1ITIT0ievKZBQIB3Lt378wqXqOvqa11mt9oDz7lYISouJDxizJNTDIz8vlvIxx7NTT6gwrwpEZvtVrR3t6O9vZ2AKLhmDJjI7fqlZ83o9jfAhdA6LWajZejZtFLPTCZTEilUlJjoF6peiVqRJfneczNzeW53FWC1sJLfA9KNQI2krDRNH9hjCiWhdLE8vlvq9WKQCDQUNdfIXie18WtrpYUy0o4HA44HA50dXVJGRvlRsVkMomWlhbEYrGKXfF+/Md/HF/4whfQ1taG6elpAEAoFMI/+2f/DOvr6xgYGMD/+B//o+xpqoY9G1rPxhP29vawtrZ27sY50oFejxsnWd0aCoUwOjpadEREj/ctR+iJ2YzS5a7S99Tqxkcsikv5HpyXtaj2GtM7Y6BHmt9oglkORhR6JWazGa2trdIDZyqVQigUwt7eHpLJJJLJpPSQVqvvuBZchIie47hzs2HyjI3ccfGv/uqv8KlPfQonJyfweDz4q7/6K7z97W9XtcH0fe97H376p38a733ve6U/e/HFF/HOd74TH/rQh/Diiy/ixRdfxMc+9rGyXq8hhV6ZqtdqNn5ubg65XC6vZlsMYlpT6ws6nU5jZWUFLMvWvDGwnIjeiLP75NwKgoAHDx6cWz/UU+hrDe3mbxzsdju6urrAMAwymQyam5sRCoXyxsACgYDUFW5ULorQq+0zII6LP/qjP4of/dEfxec//3n8xV/8BV599VVJkN/xjnfgF3/xF8+N9L/lW74F6+vreX/2l3/5l/jKV74CAPgX/+Jf4B3veMfFFXqe57G7uwubzaaZPWU0GsX09DR6enrQ09NT1msSoa/lFy4UCmFubg5dXV1IpVI1F51SoksaAk9OTjSf3a8mAlZrZXve+1Ubjdez2e9pSvM3QkRfDEEQYDKZCtb3Q6EQNjc3AUBzf3etuAhCr8XvkMvlcOvWLfzH//gfAYhlw6997WsVuyseHBygs7MTANDZ2YnDw8Oy/23DCL08VU9SIl6vt+rX3N7exvb2NoaHh1UtH6h2VawaBEHA6uoqgsEgRkdHkU6npRtzLSmW1s5kMpicnITP59Nldr9SYSTjhoU89IthxK57vSg3zc/zfMMJZ6Mdr5xCx66s72ezWUQiEam+T7rBA4EAXC5XXX/3iyD0WkwOKMfr/H4/vvu7v7vaQ6uIhhB6pY2t2WxGLper6jXJXLfZbK5o41w1q2LVQETU6/VibGxM6riv5UY3QiERVONyVylqhVcQBKytrSEYDKoeN2yErnu9KJbmT6fTeP311xsqzW/Uz7gcymlms1gsefV90g2+vr6OeDwOt9stnata1/ep0ItU04xXiPb2duzt7aGzsxN7e3uSt385GF7oC83Gq1nqUoiTkxPMzMzg0qVLUipELdUeQzkUE9Far24tRCUud5WgNjIhVrYOhwOjo6OqbzjlCHE10WKjRJnyNP/e3h5GR0cbLs3fKJ+1kkquL2U3eCwWy7N5Jfvbm5qadO+Ip0IvEo/HNd1o+t3f/d34zGc+gw996EP4zGc+g+/5nu8p+98aVuhLzcabzWakUqmKXpOI08jISFUb5/QUehKRHh0dFRTRWjxklKJSlzu9kVvZVvoAV4uIuxGjzUYz7Wnk1H21QskwDDweDzweD/r6+qQlXOFwGBsbG9L+dr0e0qjQi5DMSiX84A/+IL7yla/g+PgYPT09+MhHPoIPfehD+IEf+AF86lOfQl9fH/70T/+07NczpNCfZ2NL1sSqIZPJYGpqCk6nUxNx0qtGT47T7XYX3YxXz4ie4zg8evSoIpc7PVFa2VZKLVL3FwHlalCy4c0o3fyNLPRaH7vJZJIewoAnD2kHBweS2xs5V1rU9y+C0GvxOyQSiYqF/nOf+1zBP//yl79c0esZTuhzudy5s/FqI1rSrX7lyhVVdY1S6FGjJ6n6846zXkK/u7uLZDKJZ599tiox1RKe57G4uIhkMlnWWOR50Ii+MpTd/NFoFMFgUHKAI0JTqzQ/FfriKB/SSC+Gsr4fCAQqstPWavNbPTFijb4aDCP0ambjzWZzWSIrCAJWVlZ0MZbRMn0uCALW19dxeHhYVr271kLP87xU63O5XIYRebmV7bVr1zRbS/q0NuNpBZknJgYhygiyFmn+Rv6Max0ROxwOdHd3o7u7W6rvh0IhzM7OIpfL5c3vl1Pfr4e/iB5Ue11SC1wFajfOlSOyqVQKU1NT8Pv9Ure6lmgl9NlsVmoeK5aqV1LNyJlayBx6R0cHbty4gVdeeaUm73sexMr22rVr0uYwLXgahLjW1CvNTyN69cjr+/39/VJ9n0T85dT3L0LqXot7QCKRMExQZAihJxd1uRfHeTV64s6mpwe8yWRCOp2u6jWIWF2+fFlammAkirnc1fNGJAgCtra2sLu7q0u3/3lCb3QLXD3Q+njLSfMTIxhAvCcobw2JBLC7yyCXY+ByCejtzT/GRk/dG0UolfX9TCaDSCSS14RJhN/pdErXd6N+9lpSTTOe1hhC6AF16ehi0TSp18bjcV3XtQLVpc/l3f+lfNfrRam1t/X8InMch9nZWQAoy8q2EhpRiBuZQml+YgQzObmC5eVWOJ1e3LnjhNdrQybDYHFRKYIMbDYebW1Pzlsjiw3JbBoRq9VasL6/uroqRbDZbBaZTEbX+6/eaPH5U6GvkkI1+kQigampKbS1tWlWry1Fpan7bDaL6elp2Gw2Q42mEeQud4W89MkDTq2Pm2wULNfKtlJojf4stRQdYgTT3NyKoyMT2tvT4LhTfO1rR8hkMnA4HPB4PHC73TCbnzzo/fevP8bfxz+B/+vbPoNSo8upFHB8zODoiEE4zCCXA5xOwOEQ4PMJ6OgQUO97cyM9pCjr+9FoNK++T+b3y63vGwGtvp9GethpjE9egXKL2v7+PlZWVlRZnVZLJUJ/cnKC6elpDA0NaWqkoBXlrHCtR8d/LpfDm2++WdPzS6kvy8ssolHgwQML2tsDWFhowfIywDAJdHUdIpdbwOamHZFIGzweD/745Gcxe/oGPvvKV3HX/W04PbUjHvdhZcUEiwWw2QCOA2Ix8fVtNqC5WYDFIpYB4nEGh4cMlpYAjwfo6ODrJvqNWuNmGAZerxc2mw337t07U98nNr6BQAAej8ewv6MWHfeAsXpEGlboAfGEzM/PSzvPazmvq0boBUHA5uYm9vb2DJuqL/f4atkISDz+0+k0nn/+ed3c9+SU+nKSzykej6OlpQU+n0/1DaERI/pas7XFYGWFgccDtLYKWF1lsLrKoLNTwMiIHSzbB6AP169n8Xd/l8bkyd9jOTYJATz+e+hn8e2XvgavN4N0OoOODgGZDJBOA1Yr0NUloLVVQKE1GakUsL/PYH+fxdISi6UlIBAQMDzMo5bN040U0ZeiUH0/HA5jd3cX0WhUmr5oamqS6vtGQAuhN9p33DBCr/YkE+OW7u5uXVO5xSjXMCebzWJmZgZWq1XTujLJamixYWl6ehoWi6WsUkKtInoyjeB0OuF2uzXbhlcp8s+pqakJx8fHWFlZgcViQXNzc14zEqVykklgdpaFyQREo8Df/Z34fensFHD3Lg/5x+t2W/DOd1rwq5/7LaR5sTF2J7mJiejncN16HS6XGYGAKDblBAF2OzAwIGBggEMqJTb7LS+z+NrXTPD5xAyA1yvAbhfgdIpZAT1oCKEPhwG3G1ARXFmtVrS3t6O9vV3apRAOh/Pq++TBoJ7fd60yKkY6j4YR+nIRBAE7Ozt1N24pxzDn9PQU09PTVVmylnr/ai9IYhmrxuVOWTbRg2g0iqmpKQwODqKjowOPHj2qqwlHIpHAxMQEent70dnZiWw2m7dMhDQjJZPJc0fFnuaIfmeHweQki7e/nUMmAyirMNksMDkpXs/PPsvh618vLvKEufgr2M5MS/+d5JL4/a3fx5+/8OeIRCJIJBLY3t6GIAhS2ricta52OzA4KKC7m8PmJoNgkMXqKgMg/yAYRpwIMJkAj0dAc7P4P58PBY83kRB7BFhWfI+mJgHKy9rwqXtBgPPd7wb33HNI/8ZvKP6qvGtbvktBWd+fmZmR6vtkfr+W330tInqt0v9a0VBCn8vlMDMzA5Zl4XK56trRWCp1T0bAdnZ2cPfuXV1ME6qNrHd3d7G+vq7aMlbviH5vbw9ra2u4c+eOdH7rKY5k1e3w8DB8Pt+Zcy5vRiq03z0QCKC5uRkej8cwT/f1gnTLf/Wr4g3w0iUB16/z4Dgxel5dZZFIALdv88hkxH/jdKKoyAPAL331l5DkEnl/thpZxcv7L2O0aRT9/f24dOkScrkcwuFw3lpXEj2WysTYbMCVKwKuXOGQy4lCnUoxSCTEBxOeZ8DzQC4HRCIMFhfJqLAo5CTqFwTxZ0iPgJy2NgGXLvF4K8NtqEiwEKYvfhHs+jrYtTVkfuEXIMhGgys9dlLf93q9GBgYAMdxiEQiCIfDWFtbq2l9v94+93pgGKE/7+IgG+dI9Pnaa6+B47i6dXIWE/pq19+WS6WCS1zu0uk0Hj58qPrz00vo5Va2yuOqZV8AgbgVHh0dlT2qWWjxSygUwvb2NqLRKFwuFwRBqHsZol44nQJSKQY9PQKiUQZ7ewysVjE9znFiE9zDhzycTgEvvWSCyyVG9sVuDa/svIKZ45kzf57IJvDi4xfxp+98svTDbDafWesqz8TI08bF0vxmM+D1Al6v/FrMvy7TaSAYZBCJMEingUzmSWRvsYjZic5OAQwDJBIMjo8ZbG8zODwUf9/eXh6ZjIEjekGA7Zd+CUwyCcFqhfVjH8uL6rXKRphMJjQ3N0s+KJlMBqFQ6Ex9Xw93Ra3sb43iigcYSOiLQWbO9/b28qJjMmJXL6EvlLonKedaLHyppOs/mUxicnIS7e3tuHHjRkVfDj2EPp1OY2JiAi0tLQVHI2tRLpAjCAImJydhsViqclW0WCx5Ncl4PI7l5WVsb29jd3c3L5VspDSfXiSTDFpbBdy+zeONN1icnDBYWBA/2ytXePT3i13wMzMscjngbW/jSpaAf+mrv4RELlHw7zZiG3jt6DX09/cX/HtlJoakjStJ88ux2cSGv66u8x9MnU4BLS0CrlwRyxq7uyzm51msrTXB6TRhaAiQ959ms+JDhM0mNhPW45IxffGLYLe3AQBMJgPLZz+bF9XrVWKzWq3o6OhAR0eHVN+Xuyt6PB7pnFX7IK3Fw4qR7G8Bgwt9JpPB9PQ0HA4HnnnmmbwPv96rWuXHIggCtre3sb29nZdy1vv91YhfMZc7tWidRi/HyraWqftEIoFEIoH+/n709PQUPJZKYBgGbrcbTU1NsNvtaGlpQTgclpr6rFZrWankRoXjxEa77m4BuZwYFR8ePvkdSZe73w+cnop/VuprVCyaJyRzSfzXif+K7x/9/nM/S7lpTzVp/koxmYC+PgF9fRwiESAUSmFry4ytLaClRZztj0QY7OwwIF8DhgHa20VHwJaWGmW7SDQfjz/5M57Pi+pr4XMvr+/L3RVDoRCmp6fBcVxV9X2autcR5ZeHbHIrZg9byapaPcjlcpidnQXDMLqm6pWUK/SlXO70fN9yjqtcK9taRfTBYBDz8/Ow2+0FRV4LyEOLyWRCS0uL9HBTrKkvEAg0jNFIKcjp29lhsbEhRqdybDago0NAMCjWvM/7lUtF84TN2Ca+svkVfGv/t6o61lJp/kQikXdutB7p9fuBq1djGB7msLnJYneXwfS0eG/s6xPQ2ckjk2EQConCv78vjiEOD3Nnmhu1Rh7NE5RRfT0aCQs9qJH5/dXVVZjNZnRtbsJ5/z7cPT3nPqjR1H0NILPTx8fHJQWg3hE98GTEr7+/H93d3TV973LG+4jLndfrLehyVwlaCD3HcVJTZTkjh3rX6JX1+DfeeEO39ypGsaa+zc1NMAzT8E19Fgtw/z6PpSUWPA9cv87j8FAUrJYWUeBDIQZvexuHaPSst72czdNNvL7/Ohzm/Nosz73VCGcSIPACsnwWnxz/pGqhV6JXmr/0ewLXrvG4dk1s4DObxeY+ETHKv35dbGJcXGTxyiuiMZDbLZZBmps1/r4UiuYJsqjeCBMDZrM5v75/dISm7/gOHP2Tf4JH/8f/AafTKU3GFKrva1ESpqn7EpC1oz6f79xNbvUW+u3tbSSTSXzTN31TXVI05433kZT4ebvtK3nfaoSeWNkS/4Ny0DN1z3GcNB+vx5ZDJeX8LvKmvsHBQcloRN7UR2b3jWKxWQ7t7QLa259cs01NAl55xYTeXgGDgwJef53FG2+YcPcuh1LeSH3ePsz/5DxyQn5GTzTaYTF8i0c2twuGYXBz4Kamv0M90vzFbi8sC/T0iJ/p5iaDZFJs7nv0iEVvr4Br13g1Y+4lKRTNE+RRPW+3113olbg/+UkwgoC2v/kbPPPii4h7vQiHw3n1fSL8VqsVHMdV/b2Kx+OG2VwHGEjoE4kEvvGNb5S9dtRsNtcldU9S9QDgcrnq9tRWTHD1duGrRujJqJpaK1u9Ov3l8/F6peq1QGk0Eo/HEQwGJT/xRm3qI3owNcXimWc43LnDY2qKxde/bsKzz3Ila/RdnrPNrp1XASFswsEi4Pdb0d/PwW3V9yG83G5+IiJ6YLEAQ0MCAAEcJ/Y7rK0x2NszoblZwNWrfHVWvqWiecJbUT3/4Q8bS+hPTmD93d8Fk05DsFph+9jHgE98Ai6X60x9f2dnR7rPNDc3V5XCTyQSNKIvhNPpxIMHD8r+MtQjoicGM319feju7sarr75at5nXQuJHfAbMZrOhtruRckwoFFJ1jqt5z/Mg9fha++dX+7uQpj632y3tCydNfcvLy7o3jmmJ0wk0NQGRCPDaaya0tgqw28VZ9VdeMeGd7+RKpvCVWCziON7EBIvpaSuyWR46D7+coR5pfjkmk1gW6ewENjZYHBwwePllE27f5tHZWdl1Z/riF8Gurpb8GSaTgeUznwHzgQ+AraEV+XlYf/d3pQYRJpOB5Y//GJkPfQjCW7tGCmVoZmdnEYvF8PjxY5jN5rz5/XK/T7FYzFB7OQwj9AzDqBKAWgv9zs4ONjY28gxmyDHU4wlW+fuThxC9+wXURtfEytblcmF0dLSiz0pLoSfjmgcHB7qvMq4FjdzUZzaLI3TxODA9zSIcZqRUc1eXoErkCSYTcO8ej3A4g+1tJzY3GfT11cdsqZ7d/D4fcOcOj2QSePzYhPFxFuPj4ufzrnepu28yh4fgBwfP/0GTCczODthyfrYWkGg+mXzyZzwP64svIv2JTxT8J2azGVarFV1dXfB6vUin03llM1LfJ/P7xYjH44bKEhrmm6/2IjebzUilUjodzRM4jsPc3Bw4jjtj5ELEtpbLdAhywSVucmpd7ip933IfsJRWttW8pxape1KPJxmPejyg6T0qWMqpj2EYNDU1Ga6pz+UCnnlGu9IMwwBDQynkclbMzrLw+7mCS2xqTbnd/FqWqRwOcRPf6al4rTc1qb/2cj/6o8j96I+W9bOpgwOwNbgvl4M8micUiuqVyFP2Npstb34/kUggFAphaWkJqVSqqOU1Ha/TiFqM18ViMUxNTaGnpwc9BcYyyl1sowcsy0pppkpd7ip936xyNqoAhaxsK0ULcUwmkxgfHy+7Hm90G9JyUDr1EXexRm/qKw8Bly9nsbgIhEKMws3OGBRL86dSKXzjG9+oOs0vCMD4OIv9fQbt7QLu3OHPHVusFiN03QMoHM0Tzonqi/0ODMNIfVm9vb3Sg3Q4HMbW1hYEQcCXvvQl3Lp1C7FYTBOh/83f/E38/u//PhiGwe3bt/EHf/AHsD8ZvygbQwm9mhu63ql74gU/PDwMb5FwQE10qzUcx2FjYwP9/f0Vu9xVwnnRNc/zWFhYQCqV0uzho1qhV1uPJ++nx2daa5c/OUp3sWJNfX6/3xg36wpYXxc7z09ObEgm7TCZxFWzRkee5j8+PsbIyEjZaf7TU2B+nkUmI3oQCALg84n9Dvv7DIaGBFy5UnxfgJYYRegLRfOE86L6cpvw5A/SpDSzsbGBz3/+83jppZfw5ptv4j3veQ++/du/HSMjI6o/l52dHfz2b/82Zmdn4XA48AM/8AP4kz/5E7zvfe9T9TqAwYReDcQCV2uUO+5LCVW9RvyOj4+xtraG5uZmDAwM1PS9Swm93Mr2+vXrmgllpan7Suvx5x13o0f6gLqmvkbZtpfNioInCMDhoQVNTQzu3+cNkbYvF/JZl5vmb2pqwtGRDcEgA7NZdNITf39G2h9w+XJtRB4Qhb7uvSClonlCiai+0m57s9mM97znPXjPe96D973vffipn/opbG9v4xOf+ATGx8fx/d///fjwhz+s6jVzuRySySQsFgsSiUTF1uoNK/R6pO7j8XjejPd5N/RaC70gCFhZWUE4HMbVq1cRK7QKS2eKRddkbv/69euSUYXe71kKYspjMplU1+P1rKMbdU1tqaa+RCKB+fl5NDc3o6mpqf43chk8L+6tD4UYHB6KFrHPPsshFDqF1+utnT2sRhTLJMnT/IIgSL0XOzs7yGYFhMM98Ps9uH3bDrNZNCWKx8X+h1oG2FrMoFeL9fd+DzinT4DJZGD5b/8NmV/8xbzte4A2WYlEIoHLly/j277t2/De974XgiAgHA6reo3u7m787M/+LPr6+uBwOPCud70L73rXuyo6HuN8Y1Hf1P3+/j5WV1dx69Yt+Hy+uhxDKZQud6FQCCcnJzV5bznK6FqNla1W73keyWQSExMTqkx5lMivw3Qujf/zS/8nPv7Oj8NuUl8fa0TkwvLo0SN0dHQgGAxiY2NDWhlaz6a+XA7Y2BANcshX0OEQo1e/HwiFan5ImlBOyYhhmDPd/C7XKV555RRf/vIiOjoYKRvDME4AtTs/Rkjd87duIfve957/g2ZzwacgLcp2ymY84m6phnA4jL/8y7/E2toa/H4/vv/7vx+f/exn8SM/8iOqj8dQQq8GrURWvrb1wYMHqjro9d7NTijkclevRkD576zWyrZS1DwAajEfr7Tc/fTEp/H747+Py02X8TMPfqai1yQYNaIvBcMwRZv6iKc3ERY9orlEAjg+ZsAw4qz86SmDjQ0GuRzQ2ipuimtqEvLc9Bq1mbISoTSbzbh5M4C9PRPa27tw5Uq8aJpf7xXJRhD63Pd8D3Lf8z11PQYtuu6/9KUv4dKlS1L55nu/93vx8ssvP11Cr0WNntixdnZ2VtTQpndEL4+WlS53tXrIUELel7jK9fT0VBw1l0s54iivx4+OjlbUmap8PUCM5v/TP/4nAMCvvvyreP/I+2EWzA0pIlqhbOqLxWIIhUKaN/XxPLC8zGJl5exn3dYmYHCQR7FFjI0q9JUeN8uKGY1YjIHZXDzNz/O8rqY9RhD6atHiutFi7Lqvrw+vvvoqEokEHA4HvvzlL2NsbKyi1zKU0Kv5gKsVuv39faysrGB4eLjsVL0SPYWeuNyRGrMyWq6n0CcSCbz55ps1c5U7b7qhmnp8IeQPFp+e+DQyXAYAkONz+OSbn8RP3fspTV77IsAwDDweDzweT8mmvubm5oILRIpxegq8+aYJiYTo5z44KDaU5XLicpfzAtNG/YyrEcrubh7z8yy+/GXRZXB4mIfNdjbNr6dpz0UQ+mrR6tp75pln8H3f9324f/8+zGYz7t27hw984AMVvZahhL4WkPGvZDKJhw8fVvXUZTKZkE6nNTw6ETK/T6x2i713rYVeEAQpXfv888/rngYklBJHLerxxd6PRPPxrOjxncgm8OIrL+LHhn8MLmtlPtYXTeiVFGvqIwtEvF7vuU19sRjw6JEJLAuMjfFoba3s83qaInoAuHRJQCDAYW+PxcYGg5deMuHBAw5yD61yuvlJxF/J97vRhZ7nec2uGy1e5yMf+Qg+8pGPVP06T5XQk1R9R0eHJuNfeohtuS53tZ7hJ1a2VqsVfr+/ZiIPFF9TGwqFMDc3h5s3b6KpWA63AogY/8HEH0jRPCHH5/CpiU9VXat/Wijk1Cdv6iPRJGnqi0ZFkWcY4JlnOFS6F6RRU/fVCqXPB/h8osf/N75hwptvmvD888V3Bii7+aPRKILBIKanpytK818EoW/k4y/GUyP0BwcHWF5e1jTdrKXYyo1mymkKrGXqXm5l6/f7MTMzU5P3JShNZsiGvv39fU3q8YXeL5VN5UXzhEQ2gY+/9nG8f+T9cFrUbwa86BF9Kc5z6nO73djc7ALgwzd/M1uxyAONK/RaHbfXCwwP83jjDRZ7ewy6u8+/5hiGgdfrhdfrldL8kUgER0dHeWn+pqYmuFyugsfZ6EJZzcY6QjabNdQIKmAwoa/kAj/vi8HzPBYXFxGPxyvanFYKrWr0qVQKExMTaGtrKzvTUKvRPqWVbSaTqXnJQC6Oyk5/PW4qDMPgM9OfORPNE3J8Dr8/8fv4mTEa1VdDoaa+mZk0OG4Fc3ORqpv6nmahBwCrlZjvVPbvzWbzmTJMOBzG+vq6tG+dZGTIfZUKvdhxb6QVtYDBhF4tROyKPT0lk0lMTk6ira0N165d0/yLr4XYkh3tN27cUDVnqXdkWMzKth5NgOQ99ajHFyLLZ/Hiay+eieYJiVwCH3/143j/XfVR/dMc0ZeCNPV1dvrhdLbh7t0MIpFIxU19jfoZaymUkYj4GTkc2nwWDocDDocDXV1dBdP8fr9fl56lWqKF0JORUyPR0EJPRuwKCT3pKtW6fiunGqGXu9xVsi5Vz2illJVtPYSeYRgkEgk8fvxY1/NJ+MvtvywazROepqi+lqKZSgGBQOFoUt7U5/P5pDRyoe//0566B554/O/vs/B6tf3OFkvz7+3tYXx8HDabTcrIFEvzGxEthD6RSBhqcx1gMKGvZI49l8vliSTP81haWkIsFtM8Va+kUtHLZDKYmpqCx+OpeEe7XoTDYczOzha1sq11RCoIAg4PDxEOh/Hss89qXo8vxGdWPgNe4OGznR275DkevMAjx+fwG6/9Bv7VnX+l6hqjEX1xOE4cn7PZzn4+DocDXm83WLbnrc7oE5ycBLG6ugmLhTnT1NeoQq9lRO/1Al1dAlZWGLS2oqjngBaQBzO73Y4HDx6UleY3Ilp8/jR1rzHKiJrUultbW3H//n3dv+iVRPQnJyeYnp7Oc7kzAqTBbW9vr6SVbS1vnhzHYXZ2FplMBm1tbTUReQD4zYe/CZvflvdl5TgOa2trsNlsaG9rRyqdApLI605ubm6G1+s11IObFtTqnEej4v9VBkOJBDA1xSIUIsfBAmh+63/AyEgKDBPMa+pLJpPIZEpnZYyI1g8o167x2N01IRxmKtpFXymF0vyhUCgvzU+6+fVy1KwErVL3NKLXELnQHh0dYXFxUXWtW6v3Pw/icrezs3PG5a7e1MrKVg2pVArj4+Po6uqCx+PB7u5uzd77hv8Guru7pe5w4gL4v93439DV1YVMJpN3M87lcgiFQtjf38fi4iKcTqdUT1aWZGhEX5x0WvxMbTYB2SwQDjMIh0W7WwC4fp1Hc7O4ne30lMH0tPhAJQhWdHbmN/XNzc1hdXUVq6urkqg0wvpdrYWeDO/UaZs2gPw0/8DAgJTmJ/0XVqtVivbrneanNfoaoPYEm81mZLNZLC4u4vT0tKJadzWUK/S5XA6zs7NgWRYPHz40hJASiIj19vaip6en3ocD4Ox8/OnpaU3FUS7G5FjIWGah4zCbzWhra0NbW5u0511pCdvc3FyxA+PTgs8nfravvirO0ZOPurlZdHmTPxv7fAK6ujj8v/+vCaurLFpaOFitT5r6nE4nBgcHYbVapRGxw89/Htnr19HU3Y1AIKDKqa9WaJm65zjgjTfE16pR7FMWlXTz1wpaozcggiBgcXERnZ2dGB0drfmXtpz3Iy53eglpNREAyYJUYwOsJcXm45Vz9HpDhJ6UMtTM6sv3vPf19UnRC2kONZlMYFkWqVSqZqWIRkGeaRcE4OFDDn4/UOy+azIBIyM8vvENFm++yeLhwyd718n3gohKKwDXz/4s4v/7/46tD3yg7Ka+WlNtRJ/Lid32oRCD/X0G8Thw+7aYCTEqRkrz8zxf9XWgxUIbran/lV0hx8fH2N3dRVdXF4aGhup9OAUhq2+Hh4fh9Xo1f33SDKj24pd3/OvdsFgupB7PMMyZ+fh6pLvX1tZgsVgwNjZW1c1FHr0IgoD9/X3s7e1hfn4e2WwWfr8fzc3NDZFW1otgkMHaGoOjIwYWC5DNiiLuchUXeUJLi4Dr13nMzbHY2RGNYcRsQP71Yvn1Xwd4Hq5PfhI9//bfoqdHbOo7OTlBKBQq6tRXa6qJ6Pf3GUxMiLvoAdEl7/59Hu3txhV5JfVO83McV3VWOBaLSRbDRsFQQl/OSRMEAcvLy4hEIrh06ZIhb45qXe4qpRKhJ1a2LpcLY2Njhkhdyuvxvb29Z46pliN96XQaBwcHaGlpwa1btzT9fBiGgcPhgNvtxtWrV8Fx3JlZ8ebmZmlW/CITjwO7uwx2d1kkEuKSmsuXefT3i/X5f/xHE5aWWNy+ff55b20VMDcnNuzNzgK9vQJyOUY6d8zxMayf+hSYbBaCyQTr7/wOMh/+MFiWRVNTkzSuWcipT8/1u4WoNKKPx4GJCRYeD3D1Kg+/X6jYKKdS9HgYV6b5U6kUQqGQbml+rQxzBgYGqj4WLTGU0J9HOp3G5OQk/H4/xsbGsL+/j1QqVe/DyqMSl7tKUSuAxMp2aGgI7e3tuh2XGsg4X6n5+FpF9Kenp5iamoLP50N7e7su507+miaTSRJ2QKzthUIhLC4uIp1O50X7RurrqIZUClhaYrG9LX4OgYCAy5cFdHYKkh+71Qr09wtYX2fQ0cGcu9TG5QLe8Q4O4bCYFVhfZ7C15UVrK4ve3rei+beuHyaVgvl3fg+L3/UzsLX7YbMJaGoCGKb4+t2ZmRkphUx6LfQKMCoV+rU1MZIfGeFQrz7fWrji2e12dHV1FUzzcxyX581fyXeG1uhrRLGbejAYxPz8PK5duyY93ZE5+npDvpyVutxVipqu/93dXayvr0tWttVSbS2RTCGUUwOvhdCTMsvIyIjuHf7Ffhen0wmn04menh5wHIeTkxMEg0Gsrq7CYrGgublZs3Wi9eDggMH4OAtBAAYGBFy6xKPYab9yhcfRkQnf+AYLmw1wuQR4vUBnJ49CqyocDtEBrqtLwKVLwJ//OYeJCQv82WN0fupTYGSObQLPw/Sbv4Pxf/4fAQAeD3D/fr5AKtfvKnstSPaFnA+tUFsjJg13wSCDQECom8gDtbe/LZXmX1lZgcViUZ3m1yqip0KvElJPDoVCZwShVn7vpSCNYuvr6wgGgzXt/C8noidlhHQ6nWdlq8X7VvqF4Hkes7OzEAShrBq4nql7Ugo6PT3NK7Po9WBRrkCbTCbpJgWImSIi+slkEj6fT4r2jdBEdh6xGDA+LqaWy4k6zWbguec4bG0xODlhEI8z2NgA1tdN8HqB3l4eXV2F09NeL3Dz5ikiESDzn37jSfs+ee1MCjf+7nfR9F9+GidME2ZnWbz6qgnPPceh2Fe3UKd4MBjUvKlPzQN0OAyMj5uQSomjhwMD9a3F19vnXos0PzXMqQMkVe/z+TA2NnbmBBAL3HrCMAweP34Mr9db8Bj15DwBJFa2ra2tmpYRiq2NLQdS2ujs7CxYjy+EXhF9LpfD5OQkXC5XnsGS3hmESl7bbrfnrXsl0f76+rpUAjDCHHIxZmZYmExi5FzusIHJhLfES/y8slmxrr+1xWJmhsX8vJjiHxrizwi+xSJgyHuIni98CkymgP86zyPwB78D94c/DI+Hw8svmzAzw+L+/fIeKB0OB3p6eko29TU3N8Ptdqs6H+UKTTYrrqG1WICHD43RVV9voVdSSZqfRvQ1gtxkyfzy1atXi3Yw1jt1f3JyglgshuvXr9dlBt1kMhUV+vOsbKuh0gibHJPa0kY1DxbFIP4B/f396Orqyvs7PYVei9dWNpGl02lJ9OPxOLxeryT8Roj2T06AUIjB0JBQtsgXwmIRhb2/n0M4DGxssFhdZbC/b8Lt21zerLggCOj6zG+eieYJTCoF6+/9HjL/+l/D6/djYEDA2hqDXE79trdiTX2bm5uSSxoR/vMaxpQRPceJ2RCeF3sXUinxs9zbY5HLAc88w0GHgZ6KqCbLpzfldvNnMhlNInqPx6PRkWtD/e8CCkiqPhgMnlu7rVfqXu5y5/f7dV+yUgyWZc/8/uVa2VaD2rl28nnt7u5WtD9e6zl60u9RzD+g0dzrbDabFLnwPI/T01NJaKqJLgnVfBahEPD4sQk2G9Dfr905bGoCmpp49PYCk5MmvPaaCb29orEOAJjDYbT8z0+DzZZo1uV5qQPf7RYAMMhkKl/rSijU1Kfc8lasqU8QBAiCOG64u8vi9LT473/9Om8YkQeMF9GXoliaP5FI4M0336yqm58KfRnMzMzAZDKVlQavR+pe6XJHOnLrgTKyllvZPnz4ULcvnZqIXl6Pr9ReVyvhFQQBGxsbODg4KNlLYfSIvhQsy8Lv98Pv92NwcBCZTAbBYFCKLj0ejxTt6zX2SYhEgEePTHA4gLGx4vXvamhuBr7lWzgsLLDY2GDg84mz9IH/+7+L+e0SMKmUKPQ/8zNIJv3aHxzym/rkkSRp6rPb7ZKgOJ1OxOPA/LwDDMPC7weGhgR4vQJMJiCdBux2wOsVYADrizM0ktArIWn+7e1tjI2NSRMXlXTzJxIJQ1mcAwYU+hs3bqhqWKpl6j4ej2NycjLP5a6eDYFywa2llW25Qk/q8R0dHejr66u4dqxFzZnneczMzBQ05Cn0fqXE2Ig18GJYrVZ0dnais7Mzb4f49vY2AEjRfimDmEp/3/V1FmYz8OyznK7CZDIBN27wiEbF2v3GBpCz34D9uR8AwwBmE9DcIsBc4P4s2GzIpHisr7NobdW/a10ZSZKRyoWFZayustjZsSMQSOJbv9WO7m5jpsGLwXFcwwo9gWEYsCxbVTe/Fu56WmOso4G6KF2P2m0xirnc1VPoyXvX2sq2HKGvtB6vB+l0GuPj42U/cDRyRH/ee8t3iGez2TMGMSTa18J8JBRi0Nxcm+iTYYB793jMz7PY3WWw9sx3Y+xH/w2yWQZeP5BjgGIhwcaSWJu/dq32mTmn04lUyolwuB92u4DOziUMDR1hb28dBwfVl11qSSNH9KUop5vf4/FAEAT09vZq9r6RSATvf//7MT09DYZh8OlPfxrPPvtsZb+DZkd1QSHjaclksqDLXT2FnmEY7O/vg+f5mlrZnveAtbm5id3dXd16BNRA1gKraUpstBp9pVgsFrS3t6O9vb1gLZmITDWfxdGRaGJznumNFlitwJ07PG7eBN54IwS3uzxr7HicgdksGu/Umt1dBpOTLBwO4NlneRweZtHV1Q2v11tVU189uKhCr6RQN//s7Cw+9KEPIR6PAwC+9KUv4fnnn6/q/vfBD34Q7373u/E//+f/RCaTQSKRqPi1DCf0RnpqLcflrlTnu55ks1lsb2/DZrPV3Mq2WERP6vHkwaPeHbi7u7vY2NhQvRb4okb0pVDWkrPZLMLhMHZ3d5FIJDA9PS1F++X6RDx8yOHNN0XTm85OATdu8LrU6ZWYzYAavensFLC3Jz6Q1MIXPhYTnewSCTHr0dQEjI5ysFiA/f0nYnleU5+8bmwEgW10oRcbIdWdf5Ile9vb3oavfOUriEQieNe73oW//uu/xi/+4i+iubkZ73rXu/BDP/RD6OzsLPt1T09P8bWvfQ1/+Id/CEC8Fqp5uDOc0BsF0pl9Xuq5UOe73hArW+KJXo+tfUqh16oerwVkq2E8HseDBw9U18tqvS3PiFgsFmn1bjQaxcDAAILBIGZnZ880JxW7ubvdounNygqDlRUWyaQJzz5bX9+LQjQ1iTf39XUx86CnVnGc6ONPGBoScPkyL71nMcOcQk194XC4aFNfPbgIQl/t8TscDng8Hvzmb/4mAGB7ext///d/j2g0qkroV1dX0draih/7sR/DxMQERkdH8Vu/9VsVG/E0vNCTCEkrYREEAaurq2WN9wG1T93LrWxjsZiUKqolyojeSPX4bDaLyclJeL1e3Lt3r6Lr4ryou5rrzagRfSnkq3eJHWw4HMbBwQGWlpbgcDikaF/5fWFZ4MoVAVYrj9lZFo8fs7h2ja9LmrwYVqu4ynVqisXUFIu7d/V7yCODAG1tAkZHz75PudeW2WxGa2ur5DFCmvrquX630YVeC7OcWCyWJ8Y9PT34sR/7MdWvk8vl8PjxY/zO7/wOnnnmGXzwgx/Eiy++iP/8n/9zRcfV8EJPImotLmYiEm63u2yXO5PJhHS6gPOWxhSysk0kEnWJPOVCT/wEjFCPj8fjmJiYwODgIDo6Oip+nUYU41oiFxlBEJBIJKQMWDablaJ9+erdvj4B2SyP5WUWBwcm+P1AS4voW9/crG8UXQ49PQKiUXGRzpUr0K37npQuihmnVSqW8j0JWjr1qcGI3eZq0EPoK4W4Lj7zzDMAgO/7vu/Diy++WPHrGe6sqL0IzWYzcrlc1RcYadq6fPmyqs1utajRp1IpTE5OnrGyreX6VjksyyKXy0m1QiPU48nkwe3bt/OmIirhaazRVwrDMHC5XHC5XOjr6wPHcQiHw5LjGEkpNzc34/JlB3p7OWxvMzg4YLG8LAqaxSI+CAwN8efun9eTVErs3tezjyAaFf9vsalgLbKT5Tj1aTldQaARvXab6zo6OtDb24uFhQVcu3YNX/7yl3Hz5s2KX89wQq+WalPngiBge3sb29vbqpu2AP1r9KWsbOvV8c/zPFZXV9Hb24v+/v661+PX19dxdHSk2eRBKTEmv2ulN2QjNZvqgclkOjMnHgwGpdW7JNofGPBDEEwIhxlsbjJYWWGQTpe3f14Pjo8Z7O8zuHxZn4cNQQA2NhjMz4vb+Hp7C/+eeohlrZr6Gl3ojbbQ5nd+53fwwz/8w8hkMhgcHMQf/MEfVPxaT7XQEyc5hmHw8OHDip7m9BJbYmW7v79ftFegHhF9OBzG1tYWOjs7MTAwUNP3VkLOX7lOiuVSjmFONVH5RYroz4OklHt7e8FxHCKRCEKhEFZXVyV/8Rs3mmGxuLG9zeD6dTHCrzW7uwwsFrE5TmsyGeDNN1mEQgxaWgTcvcsX9RbQst+oEHo29RnZ674ctErda7XQZmRkBN/4xjc0eS3DCX0lqftKhLaQy10l6CH0HMdhenoaZrO5pItbrYWe1OP7+vp0t08thPwmKN+C19fXp+n76J26f1ohW/ZIZiqZTOL4OIT5+RW89podbrcLkYgVgUBTzQUjGmXg9WrXK5DJAMEgg2CQwd4eA44Dhod59PaWvq70Fnol5TT1lbsOudEjeq021xltRS1gQKFXSyU2uMVc7ip9fy2FXo2Vba1m+Hmex9zcHDiOw4MHD7C/v4/sOT7iWkMeakwmEyKRCGZmZnTr8tf7Rvs0RfSlOD11YnraDaAPAwMCrl8P4uQkiPX1NZjNZumhwOl06npOTk6A01NgcLD619rfF0sRwaB4vCYT0NoqYHCQRzmmlfUWy0JNfWQz4nlNfY1ugXtRV9QCF0ToyxVanuexuLiIRCJR0OWuErSMqkn6rFwr21rM8JPIub29XarH16NkQKLsnZ0dbG5uVtRPoQa9fr+L1oxXDT7fk89B3KneBEBsICM2o6urq0gmk9LqXT3GxWZmxO16g4OVn3NBAGZmWGxtMbDbxRJAa6so7mq1zyhZn0LrkEs19dX7IaVaqNDXELUXeblCTzrXW1pacO3aNc2+TFpE9IIgYHl5GScnJ6oayvQWXBI5KxsB6yX0i4uLyGQyFZngqKHUzSqXy2F1dVWaHTeiFWmjYLeL6ezpadECNv/v7GdW7waDQWlcjET7LpcLqRQDQRA75hlGXY0/kxEj+suX+ap6A4jIDw4KuHqVh0G0WlNsNtuZBUlkwxvP88hms4hGo3A4HA0p+Fo8qMRisapGe/XCcEKvlnJq9GTGV43feblUK/Rkdt/j8WB0dFTVA4iegksmEQrNx9dymRAA6Qbi8/lw9+7dmkQ8hX6/VCqF8fFxtLa2IpVKYXp6GoIglLUBjkAj+nxIAFXqMpav3gWeRJaTk9sYHzfBbHbD4/HA7XbD/NaKur09HwYHxaU6pbBaxQeDgwMWAwOcarHPZkWR39tjMDQkivzTgHxBEmnqe/PNN6WIXz5WWW9/jXLhOK7qB3etxuu0xpBCr+ZmaDKZkMlkCv6dWpe7SqhG6ImV7dDQkKrZfS3euxjKenyhVFYtLWJjsRgmJyfhcDhqNspX6Poj2Y2bN2/C5XJBEISCG+Bque/9IuB0ip/z3ByLGzd4OBw4d7yNRJabm924cgXo7DzF6WkYkcg6BIGB09mEVAp49IjF2Bh/7kKdu3d5fOMbLB49MuHBg/JW6nKc2Km/sMAimwWuXOFx+fLT+wBnNpthNptx5coVWCwWqamPjFWqaeqrFzR1b2CKiV0lLneVUKnwkIUrd+/erbhLU2vRI+tc5fX4QtQqdX94eIjl5WXcvn0by8vLNXu4UAo9OVckuyF/sFRugJPve2cY5kzzEo3o8/H7gZs3RXtc4gFvtwN373Io1WfJcUAkwqCnR8CtW24AbgC9kjmMIBxgeVnAzo4b73iHGf39xR+8WltFO9rHj1m8/LIJ3d083G7AZhNgt4tRfzwubrlLJoFkUuykz+UAnw8YHuZQZU/vhUCe+q6mqa9eUKE3MIVS95W63NUCnucxPz9fk1qzGorV4wuht9ALgoC1tTUEg0GMjY3BarXWVCDJewmCgKWlJcRisbLOlXLfu9KRzOv1oqmpqaGEvhbH2t8voLmZw8mJKKSbmywWF01429uKZ6uOjxnwPM5smyPmMFtbW/jhH76Kf/iHDF599RRbW7PwenPSjLjX680TmLY2AQ8ecFhcNEmOfcVgGKCjQ0BvLw+NK4ENTbEa93lNfR6PRzov9ex50aJGn0gk6HhduahN3ZPxOrnL3cjIiOE+cPna2xs3bhjmSXZ7extbW1tld7LrKfTEQ8BqtWJ0dFT64tVa6DmOw/j4OFwuV8XLcZSOZKenpzjYPsD2329LM+WBQAAul8sw10K9cLsBt1s8v4IgeuKHQiga1e/vizvkA4Hi14TTyeDbvs2G11/vQCrVgY6ONMzmIHZ3dzE/P39mv3tzM/DssxyyWSCZBNJpBqkUkE6Lu+rdbgEOh7gGl1KYcq7j85r66rV+V6uI3uPxaHRE2tHwlyxJ3XMch9nZWQCo2OVOT0pZ2dYLkl3IZrOqPjO9hD6ZTGJiYkJa6FCL9yxEJpPB0dERbty4ga6urjN/X8lDB8Mw8Pl8mP/0PFY/uooH3/EAjJnB2toaksmkVMNsaqq9WYzRuHRJwM4OMDlpwvPPcwWF9fSUgcdTeHRNfm6cTuBtb+PwxhsmTE7aMDjYiatX28Gyha1gm5ub38rKsAAaJ/PSqBRq6ivk1FeLpj6jOeNpScMLvdlsRjqdxqNHjySBqEd0VMzRShAEbGxs4ODgQLeGwEpIp9OYmJhAa2ur6uyCHl335EHo5s2bUopPTq0i+nA4jPn5efh8voIiXw3ZeBav/9rrAAO89iuv4Xv//Hul8TFSw1xbW4PFYpHGxxwOx1MX7ZvNwI0bYs08GGTOpOe3txnEYuLPlIPNBjx8yGF2lsXqKoO9PRNu3ODR3n7WCnZ/fx+Li4twOp2SwNj03HJDyUO5GTGZTNasqY9G9DVGzY0tGAzi5OQEDx8+LMtkRg+ICCmPO5fLYWZm5lwr21qjph5fCK277kuN8hFqMdJHzHhu3LiBnZ0dzV9//P8eB8/xgABsv7SNo+kjtA63nqlhplIpBINByYbU7/dLN7enJdo3m4W3/m/+n8fjwOwsi0BAQH9/4euh0HfRbAbu3OHR3Q3Mzprw+HF+R75SYOLxOEKhEGZnZ5HL5aRoX890ciP1btQChmHONPWRXQnr6+swmUxSbV+Lpj4thD6ZTBpynNCQQl8OxOWOeAvXS+SBJ+UD+Q1AKy/98yCiW+7NR209vhBapdHlpYPzVt3qOdInCEKeY2I6ndb8ppuNZ/Haf30NuYTYT8KlOfzjf/hHfO+ff++Zn7Xb7eju7kZ3d7d0cwsGg9IiGHm0f1HJ5YiFrIBgEAiFGKRSDI6OGDAMcPt2cVOaUn7xzc3Ac89x+NKXTDg8ZAqO3jEMA7fbDbfbjb6+PuRyOUQikbx0MjkHWmboau1z32iQbn1ie611U58WzXiCIBjyYbwhhV7pcvfKK6/U9XiI0JPxHbVWttVARPe8C7TSenyp96yGTCaDiYkJNDc3l1U60Ct1n8vlJMOikZERMAyDTCaj+XtJ0fxbCLyQF9UXQ3lzSyaT0trXTCaTF+0bJWOkBRaL+Pm/8sqT69RqFRvirl3jUY37MfmYyv24zGaztHqXpJOJCVc2m9XsHDS6hWyt0bqpTxCEqj5/I2dkDCn0pW76errcVQoR+kqtbKuhHNGtph5f6XuWghgFXb58GW1tbTV5z0Ikk0mMj4+jv78/rx6v9UOFMponlIrqi+FwOKReFLL29fj4GMvLy7pEmvW4ee3uMpiefnLDHRgQcOUKX3a3ezmRMcuK9rdqkaeT5at3yTmw2WwVZ1waOaLneb6ux15OUx+ZctE7E2bEc2hIoS8Ema0+Pj42VFMbIAp9Op3G/Px8RVa21b53KQEkngLXrl1DS0uLJu9ZTb384OAAKysruHPnjqruVK3FlzT/3bp1S7JWLee9BEEAx3HI5XIwmUzSkp9SKKN56bXKjOqLoVz7mkgk8iJNrerKel3LggDEYkA4zODggEE4LK5zldPcLODyZVHkDycO0XyjGSZr6WxUOYLZ2irg8PCJR36lFFq9SzIu6XRaVX9FtRFlPTFaNqJQU5/yvAQCgbymvmrvLzSir5JsNoupqSk4nU5dXe4qJZfLSWJaa4OeUhvstKjHF6IS0RUEASsrK4hEIhVtDtRS6Hd2drC1tVX0gbHYexGRZxgm7wGL/BnLsmeuzWLRPKGSqL4YykhTHtGQJTxG6SLf3hbtY0lU7XCI2+xCIVF1L10S0NbGS3P08YM4/vjb/hjP//LzGPvXYyVfu5zrpK1NwO6u+IDR0aHdDVqecVH2V5BpikAgUHD1br2j4mowmtDLUWZh5E19a2viSuRAICBlZSs9B+l02lABqBxDCr38gz49PcX09DQGBwdLbgWqV9prZ2cH4XC4LiIPFE5pG819L5fLYWpqCg6HA/fv36/ohqBF6l7edDc2Nlb0cykk9IIgSMZM8n/H87x0gyCRPgAp2i8WzUuvW2VUXwyTyZRXVybR/uzsLDiOQ1NTE1paWs44xNWCeByYmmLR1ARcu8bD7xfgdosp+1CIwfPPc1BOKL368VchCAJe+/hruPv+u7A4Sj8onvc7tbcL8HiA8XEWIyO8pmJPUPZXkGkKsnpXOSrW6Kl7owq9kkJNfcFgENlsFo8ePaq4qS8WixnOpI1gSKEnkIj0PD94YoNbS0GTi2l3d3fdFpgoBVDreny1JBIJTExMoK+vD93d3RW/TrURfS6Xw8TEBLxer9R0V+q95HAcJ0Vbyr+TR/E8z0uCz/M8uDSHVz/+atFoXjq2VA5f/8jX8U//9J9W+NuVhmEYuFwuuFwuqYs8HA4XdYjTm2RS/AwvX+bR0lIoc5L/3/GDOGb+aAZCTgCX5TDx+xMlo/pya/TPPMPhpZdMWFpi0dGh7XKoQiinKeTeCWazGR6PR7qG6v29VUsjCb0Sm82G9vZ27O3t4f79+wWb+oiRUqnfkUyAGRFDCj3HcZiamoIgCGV1iBMb3FoJPbGybW9vx40bN7C2tlbz/ewE+VIfPerx1RAKhTA3N1ewDq6WasbryMPGwMAAOjs7y34vQRDA83xRkVdCbgLkes0yWTzzc88gm8hCkLms7e/to6urK+/1mq6cNQnSC2X9UukQR1L8ehl/+HziZxGJAPLLlFjgxmIMvN4nn9erH38VAi/+dy6Ry4vqEwng4EAcvbPZBDid4va7bPZ80bFYAL//SbmglhTyf9/d3UU8HsejR4/g9XqlNH+9M3Ll0MhCDzyZoS/W1EeMlEo19Rl1oQ1gUKEnJiHlutzpsa61GES8bty4IaV+StXJ9YZE9MTsRet6fKVsbm5ib29Ps8bJShsAyflSM+pIsgckLc+ybEURlsVmwbM/+yyAJ9H+zs4OXIcuDA8PA4D02vW6STIMA4/niUOccu2u2+1GNptFNpvVLGtlsQBeL7C7y2JwkJPG3Mg9MhZjQOxnSTTPZZ58v3JpHl/9tUm0fc8D7OyI54VlAZ4X//902oy9vSZEoyZ0d4vNfMU+3pYWAXt7DLa3xU149cJms6GlpQWpVArXrl3D6empNCNu1G1vci6K0Cspp6mP53l0dXVpGtFzHIexsTF0d3fjC1/4QtWvZ0ihd7vdqlKIhTbYaU0pK9taPmgoYRgGGxsbMJlMhqjHy/fZj42NaWYeUUnqnjjuVfKwkU6nEQ6H4fP5NLmxMgyDlZUVJBIJaUkOSfGTBwrgSTagXjdN5drdk5MTRCIRTE5OAoAU7VcrOJcvixa3y8ssrl4VMzUsKz4AhMNPfk4ezRO4VBbTv/cqrt69h0tXzOjvF+fqs1kgkQBCoRzs9gS8XgErKwwiERb37xcez+vuFrC+DmxssOjpqc93mEDEkmVZ+P1++P1+DA4OIpPJIBgM5hnDkKiyXiVDJTzPG9IoplzKeVAp1tT3Z3/2Z/jkJz8Jm80Gv9+PiYkJ3Llzp6rvx2/91m/hxo0bOD09rfg15BhS6NWit9ASK1uLxVLQypaM19WadDqN/f19+Hy+qi8sLchkMhgfH0draysGBgY0PR6WZZHNZsv6WUEQsLCwgFQqda7jXqF/KwgCrly5gp2dHWlksrW1teIbK9nI53Q6886TvLavFHx5JqGe0b7X64XNZsPo6GjBtbuVppfb2wX09IhCDDwR+0BAwMaGuII2eRTH9B9N50XzBBYcmlcf48Z3P6nVWyzifniLhUM8nsHwMI/tbQZTUyzW1hhcuVLIBQ+wWgVks/WPkovV5q1W6xljmGAwiO3tbQCQon2Px1O3e8BFjehLQTItP/mTP4mf/MmfxB/90R/hb/7mb/Diiy9ienoa9+/fx3d8x3fgB3/wB1Wdl+3tbfyv//W/8O///b/Hb/zGb6j9VQpyYYSedDtrDbGyLdVMVo+IntTjSdduvRf5nJ6eYmpqClevXkVrq3bd44RyI3rSdOfz+XD37l1Vn4u86U4e1Z6enuL4+BgbGxtgWVbqZi9nvSxpjuzp6Sm6JKdQQ59S9IuN79WSQmt3SaTJsqwU7Ze7dnd4mAfA5ol9ICBgfZ1BJAI8/tirEIq0ZeQSOXzj11/D/X95tgNffl329AjY2RGwv8/iypXC39F0moHDUf8Z6HKjSlJDvnTpUsFSC3n4quVu96dR6JVYLBY899xz+NCHPgSO4/D48WO88sorqu/N/+bf/Bt8/OMfRzQarep45BhS6NV+MHoJLZlBvn37Nrxeb9Gfq3WNXl6PPz4+rksjoHyRz/7+PlZXVzEyMqJb12k5NXrSdHfp0qWSo5hKSjXdkfWyPp8PQ0NDSKfTOD4+ltLwpCM3EAicuVFEo1GpOZL0c5TzewLiNW2xWM6M75HrzAjRPvlcBgcHJd/x9fV1JBIJKdpvamoqMcaYL/a5HIuBAfFafvmLSSz9txkIBaJ5QrEOfGVkHAgIWF5mkMudXZJzfCxuwuvurr/QV9Jtryy1KBsrSbSv9xglFfr8FbWklPrgwQNVr/GFL3wBbW1tGB0dxVe+8pWqjkeOIYUeUFeT1Vro1VrZnudOpxU8z2NhYQHpdFqqx7Msq1s2oxTk4WZlZQWnp6cVmeCo4byu+0qa7oDSIl8Im812ZuEMEX7SUNXS0oJYLCY5AFbz8FNqfA/QP9ov9zso9x3neV6K9tfX12E2m6VoX2kUwzDArVs8TCYWGxsMNjbEm+3Rn70KIVf6O51L5PDqx149d64+k2FgMond+Erm5lg4naLNbr2p1hmvUGOlfIzS5XJJD6VamyYpl3o1Glo8qCQSiapGiAHgpZdewl/91V/hr//6r5FKpXB6eoof+ZEfwWc/+9mqXtewQq8Gs9msmdhlMhlMTk7C5/OVbWVbi9S9fAnM9evXpeMymUzIVGLaXSUMw2BiYgIejwf379/XvXRQ6sFva2sLOzs7qpvuiGiSSErt76A03kgkEjg6OsLjx4+RTqfR1dWFTCYDh8OhyU1QOb5XKNon27O0jPYr+VxIM9nQ0JBkFLOyslJw7S7LAjdv8ujoAObnTXC7BZx0+5Eduwy/D7Dbn5z3VIpB5ATSn5udZvBZHpBNOikj45MTBj6fUNDqlmEgjeh1dtZX7LV2xrNYLGhra0NbW5u0eldpmqRm6UspaEQvfv+rzWh+9KMfxUc/+lEAwFe+8hX82q/9WtUiD1wQoddK7IgLn5plK+T99RR6Uo8vVP/WY9nLeSQSCZyenuLq1avo6+uryXsWiuhJhoM4AKptuqtG5Atht9sRj8fh9/tx9epVRCIR7O3tSdEUifa1qp2eF+3ncjnpZ+p5Ey537W4g4MA3fZP4PRr+jXv4+tfHwPNiet/vF2A2AxwH/P3fm9DWJuD+/cLXvVLoTSZBWnurZGSEwz/+owlHR/UXej297uWrd/v7+6X58IODgzyL5EAgUNE4LM/zdZ/4qQatUvd6eU9Ui2HPTK1T96TufZ4LX7H310tsd3d3sbGxUXQ+vtZCT5amkE70WqGs0WezWUxMTKCpqSkvw1EOcjHU6sZK9jEEAgH09/eDYZgzpjTHx8eYmJgAII6ptbS0aNYpXSzaJ//XKLX9Umt30+m01PPg9/tx6xaDN99k8frr4rHabGK3fn+/2LC3v1/Yp14p9M3NApaWGCSToqe+nHRa/Dk9LHDVUkuve+V8eKGFSGTpSznXykWI6KstPWptmPOOd7wD73jHOzR5LcMKvRqqSd3L97RXOoeuR0RfqB5fq/cuhCAI2NzcxP7+PsbGxjA3N1fTBwz5g188HsfExMS5+w+UqK3Hl0sikcDU1BQuXbpUMBMkr52STmnSxU/G1FpaWtDc3KxZVFRObb/eog+cv3b32rVm8HwLslk7YjEGm5sMSEJkfp5Fezt37va5zk4BS0uil/7QUL6gkzFl4tZXT+plfau0SCYLkeTngTT1FVvxehGE3gipe724EEJfqdjJrWxJFFYJWnfdF6vHF3tvvQWX53nMzs4CgOQjUOtMAonoSdRx3iSEEr1EPhKJSDa/5R6PxWLJm4s+OTnB8fGx1LhGUvyFNpxVgjzalwt9IbOeet6si63dDYfnpCjz5s0WrK42AWCRTALLywwGBgTIgzGlYLpcYlS/usqiv5+TOu95HtjeZuFyidmCemMUsZQvRALE8xAKhfKyLiTal2eQjHDslaLF8cfjcZq615NKhL6QlW0t378YperxhdBbcNPpNMbHx9HR0YG+vr48s5daR/Snp6eIRqMYGxtT1TWsRz0eAPb29qQ1wJXa/DIMIzWuXb58GalUCsfHx1haWpIa11pbW9HU1KRpQ5/SrIek95Upfr3hebzlXiea5Dgcov98W5tQcO1uMHgAq3UJKyvtsNt9yGa9WFkxo6NDwMAAD7+/cGQ8OCjg9dcZBIMM2tsFcBzw+DGLWAwYHa3PngolRl1mQ86DPOsSCoWkHotAIIB0Ot3QQq9FRE+97itAzQWvxgK3lJVtpWj15ST1eDXz6HrO8JOHjuvXr0tRlvx9ayX0PM9jfX0d6XQazz//fN2b7gRBwOrqKqLRKO7fv69pE5Ldbs/bZ05SqEtLS7Db7VKkpdXea5KdMZvNRc16yJ/pcSNfWWGwvMzC4xFn3I+PgZ0dBjMzostdWxuP7m4BDseTKPPqVQF+fxpvvJGAzTaH01MGBwfNWFryYmDAgc7O/O9kNgtpcc3jxyyee47D7KwJ4bDY6NfWVv+0PWBcoZejzLokk0mEQiFEIhGcnJxIKf6mpqaGssSlQt8AlOuMl8vlMD09DavVWtDKtl6QejyxbFUjHHo1Ap7XBFjt2thyIU13LpcLPp9PtciT60Krc81xHGZmZmC321U776lF7jYHiDeS4+NjzMzMIJfLSQ19WvnxK816stks5ubm0Nraqtv43vY2i9ZWAWNjT67haBTY2RFta09OWCwtiU14t27xsNnEa+/KFTs2N13o7W3B1asZHB2FMT29h1df5cCyZly/nkFfXwaxmBWPH5sgd09+6SXxGhoZ4eveaS+nEdPfDocD3d3dOD09RXd3NziOy1u9W8w/wWhoIfTJZLJoD0O9uTBCf15UW46VbT0g9fhAIKC6exzQPrIWBAGLi4uIx+MlHzpqEdGTpruhoSG43W4sLS2V9e/0qsen02lMTk6is7MTPT09mrymGkjDFBmPCoVC2N3dxdzcHNxutxTxamFcRK7L7u5udHV16WLWE4sBqRTONMh5POJsO8OI2+WOjhgcHDA4ODDB5RLT/amU+LM+nwCz2YzOzlZ0drbi+ecFfPGLIczNMVhZ2UEqBbS1ufDN3+yA2+3Gyy8/uZ739hi0tOTX9+tJI0T0xSDjdV6vV1q9m0qlpBR/Mpksyy2xXmj1kGXUBzVjfdoy1Fzw59mjHh4eYnl5GcPDw6oauPRGC394LQU3m81icnISXq9X2rBWi/ctxPHxMRYWFqSmu0QiUVYGQS+Rj8VimJ6expUrV86UMeqB2WzOM0OJRqM4Pj7G+Pg4AEiiX8mWuXg8jqmpqbzftRyzHvJz5Ub7R0fMW8eaf16Jgc3goIBr13gcHjJ44w32rWMD2toEeL2i493xMQOWhRSZOxwMhocZhEIudHS0I5fjkE5H8Q//cIJg8BB2ux1erxf9/W4cHJgRDpswOMijr08o6JxXSxoxoicUOna73Y6uri7pQZG4JZKdEWp3I+hJtRF9LbKb1WBYodcCYmV7enqKsbEx3Zc8qHkir6QeXwitGgHVjqzpKfRkl7286a6c99NL5MmY0fDwsCFrcPJFJ/K1pmtra4jH4/D5fNL43nk3MzJFMDw8XLKDWAuznoMDsTYvrwyl08CjRyaYTEB/v/habW0CvvVbOczNsdjfZ3B4+OS8np4y2N1lsLIirrlNpYDDQxsYJoHWVgEWC4tMxgeW9cHrFeD1nuDLX05hcfEAly7FEYl04vFjP9bX7bh7l0eVfblV0egRfamHFLlbIoC83QjxeDwv2q/H6l0tUveAdv1aWnNhhV5uZVsLi1aSVTjvfXiex+LiIpLJpCb747WolR8dHWFxcVHVyJoeQk88DXK53JkeivN+T70667e2tnBwcID79+/XdBtYNcjXmvI8L43vra2twWKx5I3vyTk4OMD6+rrqKYJKzXpYVkAqxeBv/kb8dxYLIAhALgc8fMhDfgh2O3DvHo9QCDg+ZmGxkM58YGNDTO0zDNDcDAQCGTidcWn1bT5efOu3Mhgf70BbWxrXrx9jdXUNExMslpbcaG0V/+fzmdDeLqClRUCtguxGFnq1Xvfy3QjyTYhbW1sAILn01XL1bjXvQyP6CqnmQycp8StXrqiysq0G0v1e6mKX1+OvXbumyQVc7cW5vr6Oo6Ojspb3KN9Xy4s7m81ifHwczc3NuHTp0pnfq1R5Ro+mO7LTPpfL4f79+w2bUmVZFk1NTVLdNJlMSmURMhPd0tKCaDSKUCiE+/fvVx1RKaN9+f+ImLEsi8FBARMTT25B2aw47z40JKC5ufC5DgSAQCBfwAcGhLylNIeHWSQSxY+vs1PAxgYQDNpw86a4dvfBAwGzs3Fsb0exvLyHZNICp9OHpiYPenut6OtD0WPSiouWui8X+SZEQLxPhkIhbG1tSbayxE3RqA/byWSyYNOyUTCs0KuFCM/u7i42Nzd1XZlaCJJCL3aT1Htfu1pI97jJZMLY2JjqL6mWEX0sFsPk5GTJHQOFvO71StXncjlMTU3B5/Np9kBmFBwOB3p7e6XZdGKEkkql0NTUhMPDQ7S0tGi23axQip+cM58vh+efz4LnWdhs2vnxlxMZOxwCTk8ZpFJitsBiYXD3rht377oBdCKVymB5OYKlpS289BKPb3zDhZ4eF557zgmvV5/bZiNH9Foeu9VqRUeH+ABG+k+CwSCmpqYAQLJJ1nv1rhri8bhhXfGACyT0LMtiZmYGHMdpkhJXS6la+e7uLtbX12v+8FGMVCqF8fFxdHV1VbyURqv5fRJd3rlz59yasDyi10vkk8kkJicn0d/fr8pet1HZ3d1FW1sbLl26hEQigePjY0xPT4PjOGl8T6sbaqEUfymznkqFvxzRuXSJx8GBCa+8YsKNGzza2/O329ntVgwPt2F4uA25HI/5+TgeP07ij//4CCMjMXR1NWk+NtbIET2gT31a3n9C7KPJtMn8/Dzcbrc0u1/PaD8Wixni3l4Mwwq9mosmlUohFouhubkZQ0NDdXnKKzTPLq/HP3z40BAjJZFIBDMzM1U7ArIsi6x8OFklxDv/4OCgrLKBPKLXS+RPTk4wOzuLGzduSE1DFxVSRurq6pLGTcl2M7LLPBQKYXt7G6enp/B4PFJDn1bNUuWY9VQzvlcKrxd45hkOExMmvPmmuJO+q4uHwyEuuJF/Vc1mFsPDHvT2evDyy53welMwm4+ksTGfz6eJSUwjR/S1wmKxoL29He3t7dKyqGAwiOnpafA8nxftl3vNaFGCpBG9zhArW4/Hg87Ozrp9UZQRvR71+GohG/qKmeCooZrUPc/z0lKccssG5PPTq+mONKKNjIwY1vRCKxKJhFQqIX7mSpQ31NPTUxwfH2NzcxMsy0oNfVqNRinNepTje6QHoxyznnIF0+cDvvmbOezvM1hbY7G8LL7m3BzQ3y9gaIjPG7lLJMTX9HiseWNjJycn0pSDxWLJM4lRg55rai8i8mVRAwMD0urd/f19LCwswOl0SueiVCnqorviAQ0s9KSR7PDwEKOjo1heXq7JFrdiyFPZle61r4ZSNzetO/2ByoWePAC1tLRgYGBAtUjo0XS3vr6OSCSC0dFRQ2Rd9KTc8Tk58mapoaEhpNNpBINBrKysIJFIwO/3o6WlBYFAQDPb03K27xWL9tVExgwjNud1dnLI5cRtdhsbLFZWGKTTLPr6eKytsTg+ZpDNigty2tufRICFmh2DwSCWl5elvgeydve8a7aWa2ovIsrVu/F4HKFQCLOzs8jlctK58Pl8eedCq4U2NKLXmEJWtuXa4OoFiej39vawtrZW0V77SiGiW+gmSyxk/X4/RkZGNLuRVNJ1X07TXTHIQ9T09DRaW1s1cYAjW/nMZjPu3r174aOpw8NDrK2tVZ21sNlseREtWS27srICm80mRftaZUbUju9VmgI3m5909T9+zGJ7m8H2tglmsyjuzc0COjpKG+uct3aXjI0V+mxoRK8dDMNIpai+vj7kcjlEIhEcHh5KeyNItE9snauBRvQVUuyLSqxs+/v70dXVJf15rfayF4NlWWxtbYFl2ZrX44sJPRHWoaEhtLe36/Ke5XJ0dISlpSXcvn1b1SpHeT3+wYMHiMfjODo6wvj4OBiGqTiFTHwW2traKm5IbCQ2NzdxdHSkyficHJZlpdEn4Mn43tzcHDKZDAKBAFpaWsqKaNW8ZzlmPdVEateuic16AHDzprhYRy3F1u4uLCxIa3flEWajRvRGnyEHkLf+WRAEKfMyPz+P1Ft+yqFQqOLrNBaLUaGvFGXUeHBwgJWVlYJWtvUU+kwmg93dXbhcLk2j5nIp1AhIbH/VCmu5lCv0ZFvg4eGhandCeXMWidZITW5wcBDpdFqKJJPJpDQTft5KV2LxWqpGfVEguwuy2Szu3bune8RYaHzv4OAACwsLcLlc0s1Wqw5pZbR/cnKC/f193LhxIy/aJ39fye+/ucmiu7v6e0uhtbskwnQ4HEilUshkMnVxhquGRstEMAyTdy7C4TA2NzelzIvNZpMyL+X2WdCIXgMEQcDS0hKi0SgePHhQ8ItgNpvrkrqPRqOYmppCc3NzRb7iWiDvDxAEAWtrawgGg7ra/pYj9CQ1DkD1rL686a7YbnSbzYbu7m50d3dLK12Jy5/T6ZRS/PLPgMyNG9XOVkuIV4LT6cTVq1fr8gCqrJkeHR1hcnISPM+jubkZra2tmrmfkXM7MjICp9OZZ9Qj7+QvZ3xPnpDLZKo+tDOYTKa8CDORSGB8fBwLCwvgOE4aGVPTPV4vGn0sUBAEuFwuXL58GcDZPgu/3y/1WRRL8ScSCUMHDYYX+nKtbOsR0ZN6/J07d3B6eop0Ol3T9ycQ0eU4DtPT07BYLBgdHdX1y3ee0GcyGYyPj6OtrQ39/f2qbuRKkS/3eOQ1NyIqExMTAMQlLyTCvHfvnmaGMEaFfG86OjrqsmlPibxmSuahg8EgNjc3EY1G4fV6pfG9Sspe+/v70kSJfD9CMbMe8n0p1tBns4ke/IkEoPd4NsMwcLlcsFqtuHfvnhTtk+5xl8slXdtGdIZrdKFXHr+8z4L0oASDQayurkpTFSTaJ/c12oxXBaenp5icnCzLytZkMiGjx6N3AeSrXEk9Ph6P1610wLIskskkpqenpQtUbwo51RFIluPKlSuqXQBJrbUawxSlqKTTaczMzCAWi8FisWB1dRWtra1Vzz0bFTI+NzQ0ZAgXxkJYLJY89zPix7+xsZEX7RYzpBEEsUN+c5PB8vIRgsEYbt58gN1dFm1tApT33Er8+Eni0O+vXQ2aYZiC3ePyWXF5tG+Emr5an3ujUWq8TtmDkkqlJNFPJpP44he/iMHBQZycnFRdIt3a2sJ73/te7O/vg2VZfOADH8AHP/jBql6TYGih39vbK9tNzmw210RoSaTk9/vzVrnWs0cgl8thbm4Ot2/flsZ89KaY9zxpurtz546q1LheJjgcx2F+fl5avSsIAiKRCI6OjqRO6JaWFrS2tl6IKJ+Y/ty6dctQK5lLwTBM3mYzcjNdXl5GMpmUxvdMpiZsbJgRjTKIxwGOAw4P92CzxXH37mWkUizm5hjMzQGdnTw6OwVwnLjG1u0W4HZDcr87r6EvGuUQConXYVtb/ZrN5A+t/f39yGazCIfDec5wJNqvV22/0SN6NXP0drs9r1x4cnKCL3zhC/iHf/gHPHr0CBMTE3j3u9+N4eFh1fcws9mMX//1X8f9+/cRjUYxOjqKF154ATdv3qzk18p/7apfQUeuX79edmd3LcbrSKRaaDysUENcLdje3kYkEsG1a9dqJvLA2dQ9mUc/Pj6uuOlOa5FPpVKYnJxET0+PNKHBMEzeE3o8Hj9j+6pl3biWaDU+V2+UN9NwOIylpTBefTUMu92C3l43uro8CIc3MTbGYXj42lsCziORALa3GayuMtjbyxcft1vA1as8lM7Gymg/k+Hx+LH4dzzPIxTi4PFwZZn16I3FYkFbWxva2tokZ7jj42NMTk4CgDTlUMt+oYsg9JWUi1iWxQsvvIAXXngBP/mTP4n3v//92N7exq/8yq9gbm4O//Jf/kv81E/9VNmvR7b5AYDH48GNGzews7Nz8YVeDXpH1PJ6fKFIVSvv93IhK10zmQw6Oztr/jQvF3qe5zEzMwOGYVT3BujldHd6eoqZmRlcv3695AOQy+WCy+WSoiV53VjNHvd6s7W1hcPDQ83H5+qNmDptRirVipERYGQkhkjkEBsbMzCbGdjtnTg5OZGa1pxO4OpVcZtdIiGuvuU44OREFP/Hj01wOMTUfkeHgL6+s9H64aEJmQyLb/omDnNzQDBowuBg5sz4nh7WvGqQT6Eo+x7I1jcyhaLnNXERhL7a3od4PI7BwUF8+7d/O973vvdJLn2Vsr6+jjfffBPPPPNMVcdFMLTQq7np6yX08np8sY5/Pd+/EMRdrrm5GTdu3MDq6mrNswlE6LVqutNS5Elke/fuXVU2pPK6sXyP++rqqmQE09raqmpXu94IgiB1B9difI4Q3Y3ia//xa/jO/+93gmH1jRxDIdF+tq+Ph8tlwfLyMYaGhtDR0SEtOJmbm4Pb7ZYezKxWa14TndcroKdHwM4Og8NDBrEYMD0tXsPyFbcAQBKDNhuQzbJwOCAJQTm1/Xqh7HsgO96JbTFJ8WtlW0xodKEvZjamBuV4HemzqIRYLIb3vOc9+MQnPqFZ+c3QQq8GPcbritXjC1Gr1H2h8kGtswnkPbPZLF5//XVcu3ZN9WiJFk13SsjMfjAYrDqylVubXrlyRdrsNjs7i2w2K6X469kQRcbnHA5HRTXBanjpV17C7OdmMfTuIVx/z3Vd38vrBZxOAcvLObzxxhLe/e4+tLeL174yja2ctJCnsRkG6OkRBV8QgDfeYDE/z8DvFyDfYdTZKWB+XsCbb7JIpxn09Dz5bpVjzWsE0ZfbFg8ODiKTySAYDGJ9fR3xeDxvEU+15l6NLvRG8rrPZrN4z3vegx/+4R/G937v91b9eoQLI/RaR9REUMt1latFRE8Mg5TlAy13w5fL0dEREokEvumbvskQTXeklAFAl8jW6XSir69PstMMBoPSZrdqR8MqgVgbt7e3o7e3tybvSYjuRDH732cBAfjqv/8qrv3Ta7pG9RYLcP9+FH/3d8twOK7i8NCJ1lYB8lOsNFOSC1ssFpPKMIFAAGazGQwD3LnD4+tfZ/HoEYtv/VZe6rK32cQd9fE4A7tdQLGvv7y2Lxd65ey+yWSquxBarVapBszzvBTtkykH+SIetd9JKvRAOp2uuplXEAT8xE/8BG7cuIF/+2//bVWvpcTQQl+v1P3+/j5WV1dVdY7rGVULgoCVlRVEIpGC5YNaCr286c7lchlC5LPZLCYnJ9HS0oK+vj7dI1uz2Xxms9vR0RHW19ellB0ZDdODZDKJiYmJuo3PvfRfXoLAienuZCiJhf/fgq5RPZkkePe7h7G15cT6OotQSMDYGH9mjI6gFDZShiEb5ki0PzrqxEsvmbC1xWBw8EkKn0zq9vTkP1AUgwidPNqXp/eNlOJnWTZvyoEsKap07a4Wqe96ooXQA9Uv2nrppZfwR3/0R7h9+zZGRkYAAL/6q7+K7/zO76z62Awt9GooNu6lhnIc+IqhV0Sfy+UwNTUFh8OB+/fvF7yYTCZTTcx6eJ7H9PQ0TCYTRkdH8eqrr5b9b/Wqx5OZ8cHBwZptCpQjT5FevnwZqVQKR0dHWFhYQDqdRnNzM1paWs5szKoU0mR48+ZN+Hw+DX4DdZBons+KD5bZeFbXqJ7YkpJJgps3BbS2cnj9dRO++lXx5tzSIsDrFdDUJKCt7ckIHUG5YS6VSuH4+Fg6R6enPZif92FgwAWWZZFKAbkcWUlb2T2FpPjNZnOeWY/coa+YWU+tUS4pUrt2t9Ej+mqPv9IlSkqef/553fYGXBihrxYSFXq93pIOfMXQI4pMJpMYHx9HX18furu7i/5cLSL6dDqN8fFxdHR0oL+/X9W/1Uvkw+EwFhYWcPPmTcPMjNvt9jNe73t7e9LMc2tra8Uzz0dHR1hZWanr+Jw8mifoFdXv7e1he3sb9+/fz+uKPjnJv36OjxkcH4t/5nQKGBoS0N1dPBK32+2SsVQ0ymF9PYXj4zAePRL7HazWNmSz7bBYLEXT9mqQp/gtFosk+OR7Ia/x11s0C63dDYVCJe1g633M1aJFRK+V2OuFoYW+Vh+c2np8LQiFQpibm8OtW7ekFFsx9Bb6aDSKycnJipru5FGMljeD3d1dbG9vY2RkxFBd8HKUXu/RaBRHR0dSFzTp4i/HEGp7exv7+/sYHR2t2/icMpon6BHVk6bKe/fu5fU9ZLPA0hKD9nYBt26Jc/OTk2IUfuuWgM1NBlNTLJaWBDzzTPHUfi4HRCLAo0dWeL1WAF50dvbA4YhjYeEEGxsb4HkeV68KUkZGq/uRsqGP53msra3B5XJJwm+UaN/hcEieBhzHSdE+WUnc3NyMTCajW5mqFlQr9I2wddDQQl8LKqnH683m5ib29vYwOjpalojp2fFPGgDLdSgk6FWPJ/0K8Xgco6OjDVMbZBgGXq8XXq8XQ0ND0ua9paUlpFIpNDU1obW19cyaTDI+l0wmce/evbr+voWieYJWUT35fdPpNEZGRs4IXTIJCAKDri4edrvYNHfvHo+XXjIhnRbw3HM8Dg+B8XEWMzMsHj4kTXKikc7JCbC3x4Dj8q9Hs1nAzIwJgBeAF5cviwLw6NEpbt3aRiIxJ82la+lCxzAMVldXkc1mcevWrbeONT/aJ/vS613bN5lMeWZTZO3uwcGB9CBLov16P6CoodqMRCKRMLTPPXDBhJ74r5dz0qqpx+sFz/OYm5sDx3EYGxsr+6auRyOgfAue2s9HTztbMk52584dwz9Fl0K+eY8sMZGvc21tbUUgEMDi4iJsNhtu375d19+3WDRP0CKqJ9e/2WzGrVu3Cv6+5HlWXsr0+YDWVgFrawwGBsQ6/cCAgOVlFl//OotsFkgmCx9TZyeP27cFmM2id/7pKQOzWcDjxyaYTCb4/U3Y2WnCO96RQy6Xn5EhI5aVzqULgoC5uTmYTCbcvHlTeo1S43tGMesBnqzdzWazcLvdYFlWspZ2OBxSbb8RrKWr+W7F43HDZzQMLfRqP3zSEHfeF6DaenwpKq3VEOOZ1tZWDAwMqHoNrVP3RFDNZnNFTnd6iHw6ncbk5CS6urpK9is0IsqVpbFYDAcHB5ifn4fFYkF3d7e0HateYl8qmidUE9VzHIfJyUk0NTVhYGCg6M/5fIDVKmBlhUFHx5M6/OXLPF55xYTFRQZ9faLIA6Jwy7l8WUznW60CAgFA/izt9YrGOgDQ389ja4sBz4v//itfMeP+fS/6+sSMTCaTkcyU4vG45McfCATK7lSfnp6Gy+XC4OBgwfNaySKeesDzPMxms2S/S9buBoNBzM7OIpfLNdTaXbUYfRc9YHChVwsR+lLRp571eNL5r/ZmfHp6iqmpKVy9erWicSkthZ403XV2dqKvr+/cn5f/vno13UWjUczMzODq1atS2vCiQraXBYNBqT/j+PgYKysrSCQSUoq/qampZjfMbDKLmf9nBiarCWZH8VsGl+bw6DcfqRb6bDaL8fFxdHd3SzsJisEwwM2bAsbHWRweQvKtb2oCurp4rK+zWF9/8vPf/M0cpqdZcBzw/PPlf0fcboDnGTzzDIfXXhOF9vFjExhGgM8HNDfb0Nn5pFM9EolI58lqtUojloWaJslDTSAQUNXYWqi2T/5HvnP1EH1lFpWs3XW5XJLvBFm7u7i4CKfTaei1u2qJxWJU6GvJeSNuetfjy80oFDomtTXwQu9bLeSB4/r162hubj7358kDhslkgiAIkjOhljcZ0ml++/Ztw9fBtKDQ+Jx89CkcDuP4+Fi6YZJMgJ7pUYvDgn/x6r9ALnm+86SzVV0KM5VKYWJiAoODg2U/5HZ0CLDbBaytsejoeCLeIyMCAgEe09NPrr+DA3F7XTZb/jEJArC/z4BlBXi9wAsvcPja11hkMsDQkICjI9E3f2WFRUeHgGvXkFe7TiaTOD4+xvz8PNLptBTp+v1+8DyPiYkJdHR0VJWZKuTQJxf+XC4HhmFqYtZzXrm00dbuqsXou+gBgwt9JWv+Ctng1qoeT2rl5bw+aTo6PT2t+pi0iOgrabpTLrbRMooHxKbEo6OjM+NVFxUyM17Mo1/uV07So0dHR5iamgLP81IXvx6by1puqJu2KIdYLIbp6Wlcv3793MkSOSwL9PcLWFhgkUwC8qC5r09ANMpjb49BLgcsLj4RoG98g8X9+3xJA5x0WrTGjUQY3L79xC2vtVXAwQGDq1cFXL0qIJsF1tYYrK0xOD5m8c3fzEvH4XA4zoxYklJMJpNBe3u76umV0p/H2RR/Lc161DSzKdfu5nI5aV+BfO1uIBCoyXdei455KvQ1plBkq2c9vpz3L0Qul8Pk5CRcLpcmx1SN0AuCgNXVVYTDYdUPHAzDIJfLvWUpqq2d7eLiIjiOq+milnpCxufKfaiRp0cHBgaQzWZxfHwsWb6qrRnXmkgkgrm5Ody+fbui7Bp5Dspm84UeEMfsbt0S/eynphhsb4vXz+Ehg/19Bl1dxXsNVlfFzvx798R99gST6UkjICDa8oqjdwJefdWEYJBBT8/Z1yUjlh6PBycnJxgaGgLHcdLDGTFU0jKarbVZTzVd62az+cy+gmAwiKmpKQCQon291kZr4QEQj8fh8Xg0OiJ9MLzQMwxTtluQUmhjsZjkmtahXEKtA+UIfSKRwMTEBPr7+8+tR6p530qEnuM4TE9Pw2q1FnXdK4YgCDCbzdjY2EBHR4dmpZBsNoupqSmpKasRU3lqkI8LVjM+Z7FY8ixf5TVjm80m1YyN4DlwdHSE1dVV3Lt3r+LjIV+zUqsFGAa4fVtAe7v4w4IAlDJPjMWAzU0GgQDyRB4QHyY4jkEqJY70EZqaAJYVcHIC9PQUfl1iWXzt2jXJiIY8nAWDQWxtbSEajUo7EwKBgGZZx3LMeqod39PKAle+r4B8PqFQCNvb24hGo/B4PFK0r9Xno9VCGxrR1xCz2SwJLUlF3759u2ZPW+cJfTAYxPz8PIaHhzW1L61kvI7URru6ulQvRSE3iWvXrkke2YlEAoFAoOAseLkkk0lMTk5iYGDAMMZFesLzPGZnZ2GxWDQdFxR3uOfPOx8dHWFmZgYcx+kSRZbL7u4udnd3q94uaDaLQpxIPInuC8EwKNvdbnubAc8Dw8NnH5rb2wXMzwPLywyGh588BORyYtPe1hZw/boApWbEYjFMTU3h1q1bZ9wbC62VPTo6yls009LSoum0RTnb99RG+3o544nOhE92SkSjURwfH2Nra0u6xqv9fIy0uU5PLpTQm0wmZLNZLC0taVL7VkuxFLogCNjc3MT+/j7GxsY0b5xSe5GfnJxItdFymu7kyJvulB7ZpBa5sLAg7QZvaWkp6xyQVG69PNxrDSkptba2ljXdUA1OpxP9/f3o7++XoiR5FElm9vXcvEdWCIfDYU2Mf8jwRSTCoKVFG39wQRAfDAq5C7tcwMCA2NXf28uBXKImk/jQwfNial/+a5HGynLKE/KdCQAkQyX5tEVLS0vZi2bKQavxvVpY4MoNpwqt3SXZELVrd7USeqMHJoYXejWpe0C0zmxra9O9Hl+IQhE9idoEQcCDBw/qXm+upstfvkNe+dkSS1f5LPjh4SHefPNNqU5ZbKPb/v4+Njc36+rhXktINqUemQtllHRycoKjoyNpgUmpsbBKEQQBi4uLyOVyuHv3ribfgWRS/L9aZkybm8VO/oMD5kzqHgCuXBGwsSFgdZXByIjYA/D66yxyufzGPeDJHoZKr2m5oZJ82mJ5eRk2m01qvNSyFHNetJ/L5Qqm+OthAavV2l2tavQ0oq8RsVgM6+vr8Pv9uHr1al2OQSn08kUwtVifWgpSCz45OdHd6U5eaxsaGpI2us3PzyObzealjtfW1nB6eor79+/XbJd7PYlGo5iensaNGzdUdZrrAcMweetKyVjY3NwcstmsVIqpxued53nMzMzAbrfnub9VCwnCUilNXg4A0NoKuN0CFhZEL33l/d9iEcfrlpdZHB+LUTzHMbhzh89rxJP3IGiRvZNPWwBiKeb4+Bizs7PSedJyQyJ5T6BwtC9v7CP9QfVexFPp2l0tIvpEIkGFvhaQevylS5dqsq61GHKhryY9rjWky9dms6nOdGjhdCff6EbGaba2tnB8fAybzYbLly9f+KY7QOzRWFpawp07dwzZvCMfCyPnaWdnB3Nzos87SfGX+5BIpkuam5tVbzw8D7cbCAQELC4yCAQEaFHtYRjg6lUejx+bsLfHoLv7bFR/9aoAp5NHMCj+fGurkBf97+/vY2trC/fu3dNtPMzpdKKvrw99fX3gOA7BYFDakEjsk7U2oylm1pNKpcBxHLLZbN0d+ghq1u5qIfSxWMyQ32c5hhf6UgKgnEWPRqOIx+M1PLp8yNPt7u4uNjY2cO/evbp7IKdSKYyPj0trOdWgh9Od2WyG3+/H5uYmhoaG4PV6pQiIdIe3trY2hD+2GnZ2dqQmtEbwBFCOPZ2enuL4+FhKjZLUcbHrO5PJYGJiAj09Pejs7NTlGEdGeLz8MotHj1i87W08tOi5JZnwUkMsPT1CwQ777e1tHBwcnNm4pycmk+nMeNrx8TEmJiYAQMqeaTmeRkQ/k8lgdnYWV65cke59JNo3yvY95drdVCqFYDAord21Wq2w2WxVCT5N3esIaWbyeDxSlKqVQ1ylMAyD/f19mM1mPHjwoO6paJJVuHHjhmrrWL2c7ohJypUrV6RMh9/vx5UrVxCPx2tmAFMriE9BLBbD/fv3DTnTfh7yRjFSijk+PsbCwsIZ5zeWZaVxMvk51gO7HXjmGR6vvCKK/d27PCr1oREE4PAQmJtjYTIJ6OhQ1+BHGg1HRkbqdo7lJbNLly5JDWsbGxuIxWLw+XzS+F619yZSlrx8+XLeOTaqHz/Bbrfn9T4sLy8jHo/jjTfekNbuNjc3q+qroHP0OlFsPl4+XldrstmsFO3cu3ev5sKk3Ny3t7eHtbW1irIKpZruqoGkroeHhws+AcsNYMhNam1tDfF4vC4e79VCtrGZTKaG37Ynx263SxkiufPbwsICbDYbYrEYbt26VZOSlcsFPHzI4/FjFo8emTA4KO6QL/cSiUaBnR3RSCeRYGC3C3jwIL+xrhTkQS6RSODOnTuGujblDWuk8fL4+Bhra2swm81S86zatDNpJr1y5cqZAEKP8T29YFkWDocDHo8HnZ2dSCQSCIVCWFxcRCaTgd/vL2vtbiPU6JlzOtq1mVupglwulyfeh4eHWF5eLjgfn0qlMDMzg9HR0ZoeYzwex8TEhNRxfu3atZq+PwC89tpr0n52Us64e/euqid3vTbPAWJac29vD3fv3lWduiZdx0dHRwiHw1IdstzRvXqgZ33aqIRCIczNzaG5uRmnp6d5kxh6b97jOGB2lsHWFgubTcDgoFg7VzalJxJAPA5EowzCYeYtL3wBfr9onyvfiHcegiBgYWEBgiDg+vXrDfUgR7Iyx8fHSKVSeeN7pUSNlALl5j/lIjfrIQ8BAKoy66mW9fV1OJ1OtCmclDiOQyQSQTAYRCQSgd1ul6J95aTDO9/5Tnzta1+rlxlVWRed4SN6+Wa05eXlkl3j9UjdkxTm7du3wXEc9vf3a/r+BJZlkc1mMT09DbvdXnHTHVnKo9VNi4xWZTKZilPXSo/3WCyGo6MjaXTvvHpxrUmlUpicnER/f7/h52u14vDwEGtraxgdHZVueMpZcJLi1yMrYzKJLnidnRwWF1nMzbGYnxfQ1AT4fKI3/fExg1TqyXVtswkYGuIxOCiUHcETSLbGarU2ZDOpPCsjf5BeWlqC3W6XHtDk4kVKMmp3ExDKGd8jP1Mr0S9Wm5eP6JG9EuRBNpfLwe/3Y21tDW9/+9uRyWSq7in627/9W3zwgx8Ex3F4//vfjw996ENVvZ4Sw0f0HMchmUxiamoKLpcLV69eLfql4nker732Gp599lndj0sQBKyvr+Po6AgjIyOwWq04OTnB1tYWhoeHdX9/Ja+//jqy2Sz6+voM0XQHiF/c6elpeDyeoju3q4VEJkdHR0in02hubq56JKwajDQ+VyuIT//du3eLZliUWRmn0yllZfRoTozFgN1dMWKPx8VFOM3NQEuLALdbgMcDVPq2PM9jamoKXq8Xly5d0vbA6wwRNRLt53I5NDc3w+12Y21tTTdDK3ltX65Jetf2FxcX0dbWpuq7msvlsL29jV/+5V/G+Pg4eJ7Hf/gP/wH/5J/8k4qs1jmOw9WrV/H3f//36OnpwYMHD/C5z30ON2/eLOefX4yIPhaL4fHjx2X51ZN98HrDcRxmZmZgMpkwNjaWN3Najx6Bk5MTnJyc4ObNm6r98/USeRLV9vb26tZ1DeRHJsqRMOL61tzcXJMGKaOPz2mNIAhYW1tDNBo91+1OmZUhjZekO5xEkFo1XrrdkDbNaQnHcZiYmEBra6tq6+hGQL4siWyX293dlbIXW1tbSCQSmpfNyqnt6yH6ateKA2Iv2MDAAP7wD/8QHMfh+eefx9HREX7oh34IiUQCL7zwAj7wgQ+UfX08evQIly9fxuDgIADgn//zf46//Mu/LFfoyztmzV5JJ1iWralf/XmQRpTOzs4z1qX1EPq9vT2sr68jEAio/ozkTXdafnlOTk4wOztb86hWORJGXN9qMbq3u7uLnZ2dhhmfqxZSn+Z5XnWjoXxVqbw7nDRe+v1+qfHSSFMK2WwWExMT6O7u1vXh1UikUins7OzgwYMHcLlckt/8+Pg4AO0f0IB8sx650Bcy66k2OKl2IQ/ZEvjzP//z+Pmf/3mcnJzgS1/6kqolYzs7O3kPBT09PXjttdcqPqZCGF7oXS6XYW6ckUgEMzMzRcfVain0pGchGo3iwYMH0k233H+rV9PdwcEB1tfX625nK3d9u3Llim6720lUS9z9jCRMesHzPKanp+FyuTQpySjtTCORCI6OjrC8vCzVi+vtrZDJZDA+Po6BgYEzjVsXFVKGkmeolH7zpIs/Ho/D5/NJpkpa+/EXMuuR32srjfarNcxRZgR8Ph/e8573qHqNQllorcuOhhd6o7Czs4PNzc2S42rV7IVXQy6Xw9TUFJxOpzTKV+4GO71EnvQshMPhqjeT6YFysYv8BlXp6B7P85ifnwfLsrh7927DNWRVQi6Xw8TEBNra2nRJXSs37ym9FUgPhl77yQtBOs319gUwEmQhT6kylNVqPeNAd3x8jNXVVVgsFina17JJtlCKXy76asf3qhV6LUbrenp6sLW1Jf339va2ZivMCYYXerVfZuU8ebXwPI/FxUUkk8lzTXBqEdEnk0mMj4+jr68P3d3d0p+X85ChVz2edCCzLIuRkZG6z8eeh3J3O2kSW1xcLHt0j4zPBQIB9Pf3PxUin06nMTExUdNpArm3AtnfrjSA0bMHIx6PY2pqquJO80bk5OQEc3NzqrJySgc6sjehmKmSFshT/BaLJW98j5j1CIJQcnyvWqGPxWJVP8g8ePAAS0tLWFtbQ3d3N/7kT/4Ef/zHf1zVayoxvNCrhYitFhcTqcn5/X6MjIyUtcxFT0jp4ObNm2dmWM8Ter1EXr5utbe3t+EEr9ToHsuyUl1f/mUmjYZ9fX0Vddk2IolEApOTk7h69apql0WtkO9vV0aQemx0I6nr4eFhw/QI6U0kEsH8/Dzu3r1bVelNvjeBmCodHh5iYWEBTqdTiva1LMdUYtZD7oeVooX9rdlsxu/+7u/iO77jO8BxHH78x38ct27dquo1z7yHpq9mAIjQV5s6Ju57Q0NDhpiFJv759+/fL/gFLJVNkF/sWkbbJNoZGhpCa2urZq9bL+QWooODg2esXsmY0f+/vfeOj6rM+/4/M+mkt0kgIZX0DiK4SFPB2whkqKLrAg8qPqv+bnT3tq3rs/rY196eXcuqu7iLShKKCSjKLSoqlhvSEwikt2mZZNKmnXN+f7jXMQkpM8mZmTMz1/v18g9Jcuaadj5X+X4/n5aWFqSnp1ttGOKskG3crKwsBAUFOXo4AMauIEkNhlqtRm1tLd8SFhkZiaCgoBndyInguUsHBQDeFS4/P19Q8xcSUx0ZGcl3XKjV6jHHMSTN0hYFfQAmXe2T/2b6uIODg4K44hUWFqKwsHDW15kM0Qu9tW+Ap6cn79E+U4hxhBiq/TmOQ2NjIwYHB6c8OphoRW/LojtyU8jKynL4a2Qrxlu9tra24ty5c/D09ERXVxcfuevKBXjkfc7LyxONIdFEjE50M5vN0Gg06OjogE6nQ1BQEL/Fb4lTJGmTFFrwxAwJehEqWncyRndckOMYkmY5MDAwo5RES5hota9SqfgF0kzNeoaGhpxiIih6obeW2ZyTkwpqjUaDyy67zOHV/qTozt/ff1r//PFCb0uRJ0lstr4piAmlUgm1Wo0rrriCN0ca37o33knM2VEoFHwKozO9z56enoiKikJUVNQYj/eWlhZ4enryq8uJdsaUSiVaWlrcpk0SAH/8Ycto3cnw8vIa816NTkm0lYWyVCrlaz1I0uBMg3io0AuIRCKx2AhnpkLPMAxqamrg5eWFRYsWzWqLe7bnPsAvRXfx8fEWVWB6eHjAZDLxj2+L83jS0jc8POw2rWSkm6Cvrw8LFy7kV4QTte7V1taCYRiXSN1rb2+HUqkc85ydkdFtlgsWLOCLxBoaGvjjmIiICAQHB0OhUKCjowMFBQWi6xqxFWRiQ9w9Hcn4lMTxFsqj/fhnc+/p7e3ldy/Ic56ofY+s/InYTyT6zpBcBziJ0FvDTBLsZpPZPh6ysp7NB1Gr1aKurg5ZWVkWV/qSx7WVyJOJ0Jw5c1wqiW0qSPscAOTl5U06+bNF656j4DiOv7EWFBQ4xZitYXyRmEajQXd3N6qrq8FxHFJSUhw9RLuhUCj4lmExTmx8fHzGRMr29fVBrVbjwoULfPFlRESEVUWDWq2WP5aZaGIzWfse+c9sNvOR6FKpFMPDw3RF7wisXdETUZ2okn2mjz8boSf9+pMV3U0G6aO3RYY8aauKjY0VvL9TrJBjk5CQECQkJFg8sRGidc9RjPYFyMnJcfnJnIeHB2QyGYaGhhAUFISEhARoNJoxHRcziXF1Bnp6evjdC2fYsRnvr0CKL+vr62Eymfj2veDg4EnvfVqtFufOnbP4KGqigr7R2/sMw6ClpQURERECPUvbIf53GNZv3VtajNfR0YGOjg6rRXUqiOBaeyMnKW/Dw8PT9utP9LceHh5QqVR864pQQk9ajNLS0hzWVmVvyMRmtj79M2ndcxRkxyYwMBCJiYkuL/LAL0dRBoOBz5IPCQlBcnIy33HR2NjIx7hGRkYK2gfuKLq6utDd3Y38/HynEPmJGF18Sdr3uru70dDQAH9/f361T1btfX19OHfuHPLz82dcb0JW+56enmBZFi0tLSguLsaTTz4p5FOzCaJPrwN+7tW21HGuo6MDDMNMmQHOsizfMpWTkyPoWTNx0LJmFUDMVwIDA62OvBztDEWERKPRwMvLCzKZbFbWoSqVChcvXkROTo5LrmomYnBwEDU1NTbvFzcYDFCpVKJI3SN+EdHR0bM+unIWOI5DQ0MDJBIJ0tLSpnzNGYbhd2b6+vr4nZnw8HCHn2tbS2dnJxQKBfLy8lyyxoZMqNVqNTQaDTiOg7+/P+/YKdSCrqOjA9u2bcMbb7yBJUuWCHLNGWLRzcLlhL6npwfDw8N8EtB4jEYjKisrER4ebpOVS3V1NeLj4y3uN7a26G40U1XWkwIxlUoFjuMQEREBmUxmkWBzHIe2tjao1Wrk5uaKcpvZFpCtvezsbEF6Yy2FnBWrVCq+HYy0GNl6xUVCmhITE93Gw51lWdTW1sLPzw/JyclWT6yJkKjVagDgiy+FrAy3Be3t7fx32hVFfiI0Gg3q6uoQGBiIkZERq1stJ6K7uxtbtmzBK6+8guXLlws8YqtxHaE3m80Wn7uTvOvU1NRLfjYwMIDq6mosWLDAZje1uro6zJ0716Lz/pkU3RGsKboj4RNKpRJ6vX7K1SM5p+U4DhkZGU6/TWkpPT09aGtrQ25urkNb5Ean7mk0Gpu27hHDo7S0NLcx/2EYZkztxWwh3y2VSsVXhoux+LKtrQ29vb38EYU7QKx8icvf6FbL3t5eeHh4jGnfswSFQoEtW7bg2WefxVVXXWXjZ2AR7in0vb29UCgUyMjIGPPvCoUCFy9eRG5urk1Xa+fOneNnjFNB6gNmYsrBcdyMi+7Grx5HJ06xLIvq6mq38m/nOA6tra3QarXIyckR3ZklKTpSqVRgGAbh4eGQyWSzbt0jUcLuZO9KAnmioqJsckRBii+JkNjK6tVaWlpa0N/fj5ycHLcReZ1Oh7q6uimtfEkdhlqthl6vHxOPPNHrpFKpsHnzZjz55JNYu3atrZ+Cpbin0Pf396O9vR3Z2dkAfr6RNzU1QavVIi8vz+bb0I2NjQgODp50x4DkeI+MjFgtLEKb4HAcx0eCqtVqGAwGzJ07F8nJyW6xXU9qNTiOQ3p6uuhvgqR1T6VSzap1jzi/zdbP3JkwmUyoqKjA/Pnz7ZJPMNrqVa1WCxqNbA1NTU0YGhpCVlaW6D/fQjEwMIDa2lqrPt+jJ2larRa+vr4ICAiAVCpFUlISent7sWnTJvzpT3/C9ddfb+NnYBWuI/Sj28amY2hoiO+TNJvNqKmpga+vL1JTU+3yQW9qaoKfn9+E1dpkRREUFDTjojtbON319fWhrq4OSUlJGBkZ4a0hp3IQc3bIFm5QUJBTVpmPbt3TarUWF4h1d3ejo6MDeXl5TldINlMMBgMqKiqQlJTksEyG8ZO0kJAQRERECJrdPhrih6DX65GVleV0n++ZQkQ+Nzd3Vt0sQ0NDOHPmDP74xz9icHAQALBz507ce++9YqtvcE+h1+v1fMLbRHGutqa1tRUeHh6XbA0ODw+jsrISCQkJVrds2VLku7u70d7efsnZtF6v54v5TCYTvxqxZw64rTAYDKiqqkJMTIxL+AKQ1SN5v4h1KCkQI7S2tkKj0SA3N1d0RxS2YmRkBJWVlQ5N3RvPaPOX3t5eweswSNugyWRCRkaG039fLWVwcBDV1dWCBhHpdDps3boVS5cuRV9fH3744Qfk5OSgsLAQcrlcDK2x7in0JpMJP/zwAwDMqMhttnR0dIBlWcTFxfH/1tvbi/r6emRnZyM4ONiq69nSzrapqQkDAwPIzs6e8sZPcsCVSiW/ZSyTyZyyp5gUoKWkpExbR+GsjG/dCwsLg8FgAMdxyM7Odrr3bKYMDQ2hqqoKmZmZVn/v7MnoLX5ShzHTNDfix8GyLNLT06nIz/Ka27Ztw549e3DTTTcB+Pn1raioQHl5Oe68804xFLG6jtCzLMv7uE9Ha2srzp8/j+XLlzukerqrqwsGgwGJiYkAHFd0NxUMw6C2tha+vr5ISUmx6mZAtoyVSiX6+vr4tKnZtKvYC61Wi4aGBuTk5Ni1fc6RmEwmVFVVwWAw8DG8zvJ+zQYSrets7zVJc1OpVBgYGLCq1ZJ4A0ilUqSmprqNyJMJnZAiPzw8jG3btmHHjh3YtWuXINe0Ee4l9CzLor6+HgzDYGBgAMuWLbPT6MaiUCgwMDCA5ORknDt3Dnq9fkamPCRNSeiterJtPXfu3FlXHpO0KdIK5u3tzZ/riy3tjCSxObp9zp4wDIOqqiqEhobyBlLk/VKr1WPeL1d6TYgfwmzPaR3N6FbL3t5eeHl58Vv84+tmOI5DfX09vLy8rK7/cWaIyAs5odPr9di+fTu2bNmCPXv2CHJNG+I+Qm80GlFRUYHIyEgkJCTgu+++w69+9Ss7jvAXRvfUkhQmsRTdEdc3W21bz8akx1aQ9jnSQ+zKq9jRkCrzqeoQJmrdc/Y6DJJ2lpeX51KTFwB8oaxareb93SMjIxEUFIS6ujr4+vpafb9xZmwh8gaDATfffDOuu+463Hnnnc7wWrqH0Ot0OlRXVyM1NZWvqP32228dJvTd3d2or69HZmam1W08thR5kvpkL9c3o9HIi/50Jj22grQyMgzjVuY/xO3OmipzUoehUqkwODjI9xSHhYU5zetG0tjcoaPAbDajt7cXSqUSKpUKvr6+SEpKcvkjGcLw8DCqqqqQlZUlmA+E0WjEzp07sXLlStxzzz3OIPKAKwk9x3EwGo2X/HtPTw+ampqQl5c3ZtXoKKHXaDSora1FQEAAFi5caNXf2qroDvjZ+lKhUCA3N9chN8CpTHps1apCQloCAgKQlJTkLF/aWUOKkjIyMmZciEqqwsmW8Zw5c/gtY7EKaGdnJ3p6epCXl+cWQgeAN7gKCgpCWFgYf4Tm6enJd10489HFZNhC5E0mE2655RZcdtlluP/++53pfuG6Qk/aR3Q63YRe7N999x2WLFli15VIe3s7Ojs7kZqaivb2duTl5Vn8t6NFXsgxkxWt2WxGZmamKFZmLMuiv78fSqWSFxGZTCZodCvJM3CV9jlL6evrQ0NDg6C7NqNb99RqNSQSyYSte45k9NGMyHqcbQbLsqiqqkJYWNiYDh/gF8e30V0XERERTtklMx7SLpmZmWlxnsh0mM1m3H777cjIyMDDDz/sTCIPuKrQk5zwOXPmTFpZ+sMPP6CgoMAu7m7EXc1oNCI7OxtGoxH19fUWr+htVXRHXqfg4GDRGsIQEVEqlVCr1YKY9LhD+9xEqFQqfnfLlmfTBoOBFxG9Xs+fE4eEhNj9M0ZaRIeGhtyqbZAUWUZERGD+/PnT/i6p4u/v70dAQABvy+ts7pe2EHmGYXDXXXchNjYWjz/+uCjvk9PgOkIP/HyDIaYz0yW9nTlzBpmZmTYvxiHxnqGhofz2MFlNLl68eMq/teV5/MjICKqqqhAfH28Xu0+hmMikxxpf976+Pt6vwF3824GfWzo7OzuRn59v15v3eBGxZ+se6Rcn9RdOeIOeEQzD8H791hqBcRyHgYEBvmefGCuRUBcxv4Z6vR4VFRXIyMgQzBOBZVncfffdCA0NxTPPPOOsE0XXEnpS5GaJ6UxlZSWSk5NtWnQ2NDTEFzyNFlOGYfDTTz9NmVFsS5EnYSViNwmZjvGWoaNXjhN9IRUKBVpaWlyy2noyRgfyOHrbenyrJWkFs0XrHsdxqKurg5eXl9U+EM4MsdCeO3euIEdSZHdGrVZjeHiY3+IXW/KerUT+vvvug6enJ1566SVRPV8rcR2hZ1kWZ86cQWpqqkX92TU1NZg/f77wQsdxQGcn+i9eREtrK5JWrEDguKhLjuOmbO+zZdEdEbvc3FyX8qdnWZZfOY426YmIiICHhwfa2tqgVquRk5PjdNuRM4WsaM1msyg7CkgrmNCteyzL8kWWYj2SsgVmsxkVFRWIjY21yS4d+Y6RUBexFGASkU9PTxfM5ZRlWfzxj3+EXq/H//t//0903x0rcR2hB34usJpmrDz19fWIiooSxtuaYSA9dgzS996D9PRpMBwHfUgI/Hx9IW1vB0JCwK5YAea228BdfjkgkUxa9W9LO9uWlhb09fWJMmpVSEavHEk/sY+PD3JyclxqcjMVLMvyzobOYI4iVOseOZsODw+/pADNlSGeCHFxcYiKirL5440vwATAb/HbM3nPYDDg7NmzSEtLE8xqluM4PProo1Cr1XjrrbdcoXjTfYW+sbGRv5nMBskXX8DrzjvBRUTAfMstOB8fj+GQEGQTpzuWheTiRUg//hgeb70Fbt48mP/6V3yjUl0i9LYqumNZFnV1dfD09LRbQp8YIO1zPj4+8PX1hVqtBsdx/HaxWCrChcZsNvNiR9zunImZtu6Reph58+a5VScFMQNLSEiYNPraHmMgW/wkeY/EI9tKKEniYGpqqqAi/9RTT6G1tRXvvfeeYGPfvXs3ysrKIJPJUFNTA+DnfJMbbrgBLS0tSEhIwEcffWQrX3zXEnqTyQSWZS363amiYi2CZeHxwAPwKCmB+fXXYbj6alRWViIsLGzy7UKWhfSvf4XnE0+gYfduJD32GADbnscbjUZUVVVBJpO51QqHFDzOmzdvTEHSRCY9MplsRuEgYoQ879jY2Jl/tkXERCvHiSZqYhA7R0Ced1JSEiIiIhw9HABjJ2okt520Wwple200GnH27FmkpKQIljjIcRxeeOEF1NbW4v333xd01/Orr75CQEAAduzYwQv9fffdh7CwMDzwwAN4+umnodVq8cwzzwj2mKNwX6GfLCrWIlgWnv/7f0PS3AzTgQMY8vLii/ss2TaTnD8PZu1aeD74IJg9e2wm8qSNbMGCBaK5CdgDYpYx3fMmJj1KpRIDAwMIDg6GTCZzKqe30ZDWIlduG5yodS84OBjNzc0u/bwngqxoFyxYIOrnPXqixrLsrGsxiMgL+bw5jsNrr72G77//Hh9++KFN6nhaWlqwbt06XujT0tJw8uRJzJ07F93d3Vi1ahXOnTsn+OPCQqF3ycNcDw8PMAwzs7999VVIGhpgOnYM6pERnPt3ApalfZtcaioqnn8eS3//e5jT0sAuWya4yPf29uL8+fN2s7MVC6SjICsra9r3w8PDAzKZDDKZbMwqpLGxEf7+/vx2sTMU7w0MDKCmpsbpOymmw8fHBzExMYiJiQHDMHynjaenJ7q7u2E2m93C4pUUoKWmpgq2orUV/v7+8Pf3R0JCAl+L0draisHBQasdMMkOhtAi/+abb+LUqVMoKSmx2/ddoVDwu25z586FUqm0y+NOhtN8Y6wRSk9PTxgMBusf4/x5ePz5zzB+/TXaNBp0d3fjsssuu2RLiuOAqYZjjInByIsvwve3v8XI6dOQCCjGHR0d6O7uRkFBgegS4myJUqlEc3Mz8vPzrS66k0qlCAsLQ1hYGDiOw+DgIFQqFc6ePcub9MhkMlG25Y1OYnPVuoOJGB4eRnt7OxYtWoSAgAC+ALOlpcWmrXuOhuzcCFllbi+8vLwQHR2N6Oho3gGThAz5+PjwW/wTvWek4JD49QsBx3F49913cfz4cRw8eFC09s32wGmE3hpmuqL3ePxxmO+5B7UjI2AYBosXL55wm3f7dk/86lcc9u699DFYlkVwcDC+Z1ksSk6G5M034fG7383oeYyG4zg0NjZCr9dj4cKFrlAtajFtbW1QqVRYuHDhrGfkJJM9MDAQSUlJvElPbW0tGIbhb0b2rC6ejNGTG1cTtKkgOzejJzfBwcEIDg7GggUL+Na92tpamM1m/j1z5tQ94BeRF7Jf3FFIpVKEhoYiNDQUKSkpfFIiec/IFn9QUBDMZjPOnj0reC3Cvn37cPjwYRw5csTu35+oqCh0d3fzW/eOri1xmjN6s9lssXj39vZCoVAgIyPD8gdQKOCdl4fT//oXQhISJi26q66WYNkyL/j4AM3NRpDF+viiO7PZjIFjxxB+//347p13EP5vl7eZFIaRCnN/f3+3iqEkkxuDwYCsrCybn61ba9JjSzo6OviQFmc4XhAKciyVl5dn0c7NZK17tqwItwWk5kZIe1exYjabodFooFar0d/fD6PRiJiYGCQmJgp2LPPBBx9g3759KCsrs8tO2Pgz+nvvvRfh4eF8MV5vby/+/Oc/2+KhXasYj2EYmM1mi35Xp9Ohra0N2dnZFl/f9Ne/YujIERjfe2/K2deGDZ74/HMpfHyABx9kcN99zOSV9RwH35wcjOzfD1VUFF8YFhoaCplMZpGA6PV6VFVVITY21q3aihiGQW1tLebMmeOQyQ0xEFEqlby9q0wmQ3h4uE0FhOM4NDc3Y2BgANnZ2U4lVrNFpVKhubkZeXl5MzqWcsbUPeCXxEF3s242mUw4e/YsIiMj+eJZLy8vfodmpr4YpaWleOutt1BWVmaX1/PGG2/EyZMnoVarERUVhUcffRRyuRzbtm1DW1sb4uLicODAAVvVW7iv0A8NDaGxsRH5+fkW/b5arQZ3xx0IufxyeP3Xf036e9XVEqxY4YWRkZ9f28BADk1NBsyZM3llvfeuXWCuuQbMzTcD+PlmpNVqoVQqeZe3yQREp9OhtrYW6enpturBFCWkbTA6OnpmnRMCQ0x6lEolNBoNfHx8IJPJEBkZKaiAkLRBlmXdyr8d+NniuqOjQzC//qla9+bMmSOa15aIfE5OjlsV1pLt+vj4+DELq5GREb5n32AwIDw8HBEREQgODrZoV+3jjz/GK6+8gvLycqercZghtOp+OjiOQ1tbG3p6evCr3l6wBQVTzmweesgDo2v8zGbg9del+P3vzZNW1rNZWZA2NICMRiqVIjw8HOHh4eA4Dv39/XzymJ+fHx/ZqtVq+dWNK2ZKTwZpn0tOTp614ZFQSCQS/ow4JSWFF5DKykoAE/d+WwuxdnXUDoYjaW9vh0qlQkFBgWBbtxKJBAEBAbxVLvFYIHUu5FjGUgGxBaSbwt0KLYmdb1xc3CW7p35+fpg/fz7mz5/Pr/K7u7vR0NCAgIAAPjRposngJ598ghdffBFHjx51F5G3GKcRemur7qcTepZlUV9fD5Zlfy66MxrBTvFlq66W4OuvpWDZX8YxMiLBc8954be/NWPSybifH6BQTPgjiUSCkJAQhISEYMGCBRgaGoJCocDp06fBMAwSExPdauvWmvY5RzK6pYj0fp8/fx4Gg4HfdrSmFoOElchksmljR12N5uZm6HQ65OXl2fSz7u3tPaZ1r7e3lxcQe6buEfr7+1FfX+92E/nRnv3T+ZKMbpElyXsqlQptbW3w8PDAwMAAwsPDkZOTgxMnTuDpp59GeXm56FsSHYHTCL01TLeiJw5jERERSEhI+PmG7OcHDA5O+jfjV/MEhgH++ldP/Nd/TXKsMDz887WnQSKRYM6cOfx2VXx8PNRqNaqrq3lrV5lM5rI3BZVKhYsXL86ofc6RjO79JkVG7e3tGBgYsMjT3WAw8NHL9vAxFwscx+HChQswGAzIycmx66qatFRGRkaOyU4Y3boXERFhs89hX18fGhoaLC44dBVIxO5MgnkkEgmCgoIQFBSE5ORk6PV6lJeX4+mnn0ZnZycMBgNeeeUVupKfBKc5o2dZFiaTyeLfnyxYZnBwkHdWG71t5Hn33eCSksD8539e8jfjz+bHExjI4cKFkQlX9d47d4K59lowN9005XhNJhOqqqoQERGBuLi4MatBo9EIpVIJlUoFo9FodU672Glvb4dSqURubq7LVJiPLwybyKSHHFM4gzGKkHAch4aGBkgkEqSlpYnqM0xa90hgktCte8QXwd1aJhmGQUVFBebNmyeoffM333yDBx98EHv37sXp06dx6tQpZGRkYN26dfj1r38tqs+WjXCtM3oh3jCVSoXz588jNzf3kmpMduFCSI8fn/DvJlvNE8zmSVb1HAfpjz/C9MADU46L3PCTkpImrPj39vZGbGwsYmNjYTaboVar0dzczLeAkQp+Z/tQk1WdXq9HQUGBU1rTTsZEJj1KpRJnz56Fp6cnAgMDoVQqrXJddAVICJOvr68oaxH8/PwQFxeHuLg4foemra2Nt1G2xultPKR10B1FvrKyEnPnzhVU5H/44Qfce++9+PjjjzF//nz85je/AcdxqK6uxrfffiu6z5YjcZoVPcdxMBqNFv/+6BU9x3FobW2FUqlEfn7+xJXSajW8s7NhrKsDRq2uqqslWL7cC3r91B+aiVb10q++gvfvfgf9jz9OaqVHZvgz6Z8lZ41KpRI6nc6p/NxJ8Zmfn59TRK0KSXd3NxobG/mbvZhMemwJwzCorq5GSEgIEhISHD0cqxgf5uLn52dV655Go8GFCxeQn5/vVo6WROSjoqLGBFDNljNnzuDOO+/E4cOHne6zJDCutaKfKWQFAQCXXXbZ5AIYEQG2sBAeb74JZtQK/NgxCYxGQCqdes4zNAT8+KMUq1f/Erzj+dprMN9666Qi39XVxbcUzWSGP/6ssa+vD0qlEo2NjQgICODb9sTmDU6OKdyx+EyhUKC9vR1LliyBj48Pb9LT1NSE4eFhp96hmQpScBgVFSWKlklrGb9DMzw8PKbzgkzW/P39L3nfiD9AQUGBqPv5hYZhGFRVVQku8lVVVbjzzjtRUlLi7iJvMS67ov/uu+9QUFDAC0p8fPz0N86LF+G9YgVMX3wBLjV1VhnyHgcPwuvRR6H/7rtLivE4jsPFixcxNDRkE1MUUqFK+r69vb1t0vc9E0ZGRvhjCrG0z9kLUouQl5c34eSL7NCoVCr09/cjKCiIrwZ35u4L4mPuKvG64yF57SqVCiMjIwgNDeUdFdVqNVpaWlBQUOAy9SeWwLIsKisrERkZKejErq6uDrt378ZHH32E9PR0wa7rxLiWYQ4Aq4JqvvvuO7Asi9TUVKsERfqXv8Dj73+H/tgxsP/eSrVW5CWNjfBduxaGDz4Au2TJmJ8Rxzd7blkPDQ1BqVRCrVZDKpU6LMSFGAC5egrbeMjEbnh4GNnZ2RYdq4z2WNBoNPD19eV3bxw9WbMGErfqLhM7Mlkjpi8MwyAlJQVRUVGi21mzFSzLoqqqCuHh4YLu2DU0NGDXrl3Yv38/srKyBLuuk+N6Qm80GjHNeAH8HAZSVVWFgoICq5OQOJaFx969kFZUQP/RR5BYGUYgqamBz6ZNMD30EJidO8f8zGAwoKqqCvPmzRN0K8saSIiLUqkEwzC8eNjalYu0z7lbSxHLsmhoaIBUKp1VhTkx6VGpVJBIJGNc3sQKCWlxt64C4BenvwULFvDC7+npyb9vrvodYFkW1dXVCA0NRVxcnGDXvXDhAm6++Wbs27cPeXl5gl3XBXA/oec4Di0tLfyXKiUlxSoB4zgODMOAY1l4/9//C699+2B8/nkwcvnUubQAYDLB85VX4PXKKzD++c9gbrhhzI8HBgZQW1srqpueyWTiRV+v1yM8PHzGwTtTQQJacnNznWo1OltIGFFgYOCkIUkzwWAw8KJvNBrHJIGJ5VyfhLS4QhKbtXR1daG7uxv5+fljjlyIvatKpYLJZBLl+zYbbCXyra2t2L59O9555x0sWrRIsOu6CO4l9CzLora2FhKJBJmZmairq8P8+fMtvslwHMd76ZOtVenp0/C+6y5AKoX5ttvArF4NLikJIFuvJhMkdXXwOHoUnu+8Ay4jA8ZXXwUXHz/m2mQ1m5OTI1qrS2I3OZPgnckYvWWdlZXl1OfM1mIymVBZWWlzv37SAqZSqXiTHplMhtDQUId1XpAjGnfzbwd+ntSSOoypPu/j37fZtu45GtJFExwcjPhx97/Z0NHRgW3btuGNN97AknHHoBQArij0JpMJLMte8u9GoxEVFRVjiu7q6+sRFRVl0ep5yqI7loX05El4/v3vkH7/PSQ6HbiICIDjIOnpARcXB2bFCph37waXk3PJtUmWek5OzqWrWZ0OHgcPwuO77yCtrAQ0GkAiARcTA7agAOyKFWAKCwE7F/GMD96ZSVEYmXj5+PggJSXFJVYslqLX61FZWYnExES75lCTFjClUgmtVgt/f38+O8Fe58PE9S03N1fUxwq2oK2tDRqNBrm5uVaJNcuyfD1Gb2+v09VjEJEPCgoStAq+u7sbW7ZswSuvvILly5cLdl0Xwz2EfmBggHcXG13s09jYyPeVT8ak8bJTodFAotEAUim46GhMZnLPsizOnz8PhmGQkZExdnXV1wevxx+H5/79YFauBHvVVWDz88FFRQEsC0lbG6RnzsCjvBySpiaY77wT5v/v/wMcUMxDisKUSiV6e3vHBO9MVkVM2uciIyMF3cJzBsiWdVpamkMTB0eb9KjVat7aNTIy0mZFmKRXPC8vz60MYYCft5f7+voEsfMdXY8BTN2652g4jkNNTQ0fHiQUPT092Lp1K5577jmsXr1asOu6IK4v9EqlEhcuXEBubu4lW4QkDW6ydh4i8gzDQCqVCvoFMplM/FkV76X/b6QnTsD7t78Fc911MD/wALhp2o0ktbXwfuABQKuF8W9/A5eWJtg4rYVEfxLx8PT05Nv2iAkIaZ+z92pWDJBQHjHmihNrV5VKBYZheBtlocRDoVCgtbV1ckMqF6a5uRkDAwMWd1RYw+jWPeKzQFr3HG2KxXEcamtrMWfOHCQlJQl2XZVKhc2bN+PJJ5/E2rVrBbuui+K6Qj+66C4vL2/CG0trays8PDwmPB/li+44bkbtc1NBhC4hIeGSkBKPAwfgfd99MPztb2Cvusryi3IcPN9+G15PPgn9wYPg8vMFG+9sGBkZ4T34OY5DUFAQ1Go1srOz3a4AS6PRoLGx0Sm6CkgRJhEPUhQ2U5Oerq4udHV1IS8vz616xTmOQ1NTE0ZGRpCZmWlz4WUYBlqtFiqVCn19fdPGttoSIvJ+fn5ITk4W7LoajQabN2/Gn/70J1x//fWCXdeFcT2hN5vNMJlMqKmpgYeHx6Vb4qPo7OyEyWS65MzIliLf19eH+vr6CfvEpV9/DZ8dO6AvKwM3wx5Qj8OH4fW738Hw9dfg5s0TYsiCQWxd58yZM2bF6Oq2rsAvrVSTTTrFzGxNemZ6Lu3skEJTg8GAzMxMu3/GR8e2ajSaMS6Ztp5ochw3Jq9AKPr6+rB582bcf//9kMvlgl13PC+++CLefvttSCQS5OTk4N1333XmoybXE/qhoSH8z//8D6Kjo6et7Ozp6cHQ0NCYD+JsnO6mo6enB21tbcjNzb30QzM4CN8lS2B8/nmw//Efs3ocryeegPTMGRiKi6dv+bMTnZ2d/IrO29ubD95RKpUYGhri2/aCg4NdTvTb2tqgVquRm5vr9IYoE5n0kHqM8RMYjuPQ3NyMwcFBm2xZixmO49DY2Aiz2YyMjAxRfKaJP4atW/c4jkN9fT28vb0FDSXS6XTYsmUL9u7di61btwpyzYno7OzElVdeibq6Ovj5+WHbtm0oLCzErl27bPaYNsb1vO57enqQnJyMiIiIaX93dCb9jIruLIRs3+l0OixcuHDCm73XCy+AveKKaUX+3Xc9kJrKYdmySzsLCKZ774XvsmXwOHoUjIO3tkZb+S5cuJBf0Xl6eiI6OhrR0dH8irGzsxP19fVOFbwzFaOT9/Lz8536uRAkEglCQkIQEhKClJQUvh6jsrJyjEmPn58fL3Q5OTmiEDp7wXEczp07BwCiEXkA8PX1xfz58zF//ny+da+9vV3Q1j0SL+zl5SWoyA8ODuKGG27AHXfcYVORJ5jNZoyMjMDLywvDw8OYJ7LdUVvgVCt6hmH4Xvfp0Gq16OnpQXp6us1EnmEY1NXVwdvbG6mpqRNf22CAX3o69J9+Ci41ddJrqdVAaqofYmI4VFXpp1yse+zfD89//QuGjz8W4FnMDBIW5OXlNflzn+BvRme0k+CdiIgIp9r2ZVkW9fX18PT0tPi5OzvEpIckJfr5+SE9Pd1lzF4sgaxmiRmXMzzvyVr3IiIirErRIyLv4eEh6HMfHh7Gtm3bsGPHDrutql9++WU89NBD8PPzw9q1a/HPf/7TLo9rI1xvRW8NHh4eMJvNNjuPNxqNfDLTVH7OHp99BjYtbUqRB4AXXvi5mEahkKCszAPr1zOT/i6zcSO877sPkq4uh5zVk/a5iIgIq8wxxieAkeCd5ubmKbeJxQRJ5AoNDbUsKMlF8PHxwbx589Db24vY2FgEBASgra0Ng4ODfIiLI016bA05l/bx8RF0NWtrpFIpQkND+VZP0rpXXV0NjuMsat0juxhSqVRQkR8ZGcFNN92E7du3203ktVotDh8+jObmZoSEhGDr1q14//33cfPNN9vl8R2FSwv9wMAAdDodAgMDBf1iDg4OoqamBikpKdN66Ut/+AHMihVT/o5aDbz5picMBgkMBuAPf/DCunXM5Kt6X1+wixdD+tNPYDZsmOGzmBnEDGairgJrkEgkCAoKQlBQEBYsWMBvE1dUVPCFRY4I3pkKksIWExPjFtt9oyETnPDwcN4bITo6mjdXUqlUOH/+PF8Jbk+THltDzJ9IG5mziPxE+Pv7w9/fHwkJCXzrHnGvnKh1j+M4nD9/HhKJRNDdK4PBgN/85jcoKirCbbfdJsg1LeHzzz9HYmIi77myadMmfPvtt1ToxYSlHzKGYeDl5YWEhAS0trbyH+KoqKhZbzWSNqrs7GyL7D2lVVUwT/NBfuEFL4w+QbFkVc/m50NaVWVXoR8YGEBNTQ0yMjIQEhIi6LX9/f2RmJiIxMREvrCotraWD94hPd+Ogkxw3CWFbTRmsxkVFRWYN2/eJRMcqVSK8PBwhIeHj6kEb21ttYtJj60hrm8kr8CV8Pb25t9T0rqnUChw7tw5BAQEICIiAv39/QAwq0Cm8RiNRuzatQtr1qzBHXfcYdeJU1xcHE6fPo3h4WH4+fnhxIkTuOyyy+z2+I7Cqc7oWZaFyWSa9OeTFd1N5uMeGhpq1YdsJuEsPqtXw/TUU2CXLp3w52o1kJ7uh5GRseNISmKnPKv3fP11SJqbYXruOYvHPxvIBMfefv1k1UGCd8hWoz3PhgcHB/mAFqEnOGKH2EvHx8dbvYMz2meBZVle9MXo8DYRJKQlJCREUP92scNxHHQ6Hc6fP4/h4WF+l0aI1j2TyYTdu3fj8ssvx3333eeQz8Gf/vQnfPjhh/D09ERBQQHefvttq+oVRIbrtddNJfSWVtazLIve3l4olUr09/cjODgYUVFRU54vku0ro9GIzMxMqwrHfNasgelPfwJ75ZUT/vwPf/DCG294Qq8fO15/fw5/+5tx0lW958svQ9LVBdMzz1g8lpnS1dWFzs5Oh/eJMwzDu4QJFbwzHcQbwR0DWsguhqWdLlMx2uFtZGQEYWFhom65nOiowl0g3TRGoxEZGRlj0hJn07pnNptx++23IyMjAw8//LAo33cnxPWEnuM4GI3GCf99JkV3HMfx4S1arRaBgYF8EA4Rc7PZzG/dzeR8znv3bjArV16STQ9MvponTLWq9/rP/wSXng7zHXdYNR5rIK2DAwMDyMnJEVVl/ETBO6RtT6hxqlQqNDU1uaV3+/DwMKqqqpCeni74LgZpuSQV/LZ472Y7vsrKSshkMpsmD4qVCxcuTGoENNPUPYZhcOeddyIuLg6PPfYYFXnhcA+hF8rpbnR4i0ajgb+/P0JDQ9HV1YW4uLhJPfOnw/PVVyG5eBGml1665GeTreYJU63qfa68EqZnnwV7xRUzGtd0kBYyDw8PQc/nbMFMgnemg+xi5Ofnu5WtK/DLUUVWVhaCgoJs+lgTvXekmM8Ru0cMw6CiogLR0dGIiYmx++M7mosXL0Kv11vk9sdx3Jh22cla91iWxd13343Q0FA888wzLtuZ4SBcX+gnypAX6nG6u7tx/vx5eHl5jen3tvamL6mrg8+GDdDX14+Jm51uNU+YaFUvaWqC76pVGDl/HrDBStNsNo/ZthSzyI9notS28cE70/19a2srtFqt29m6Ar8E8+Tm5tq9+JGEJpFtYqlUyhdi2iM/gBQdxsTEzHhi78w0NTVheHgYWVlZM/rOk/dOrVbjk08+wdDQEDZu3IgPPvgA3t7eeOmll6jIC4/rCT3wc1uGLZ3ugJ+TuFpaWpCbmws/Pz9eOFQqFby9vXnhsLggb+1amG+/Hczmzfy//fnPnnjiCS9MF9mt00lQVqbH6tW/uOV5/eEPAMfB9NRTM3p+U6HX61FVVTWj4isxMj54RyaTTSocpBaDWJu6202pt7cX58+fF00wz3hbV1KIKXS7LPBL6+T8+fMRHR0t6LWdgdF2xkK8tj09PSgtLcUHH3yA1tZW3HTTTSgqKsLy5cvdbofMxrim0Ov1epva2ba0tECr1SInJ2fCD+Tw8DCUSiWUSiU8PDx44ZhqtSg9fhze99wD/fff8/n13d0SVFVZNvZly1g+9l7S0ADftWuh/+YbcFMY9cwE0j6Xnp7u0Cx1WzHa3Y0IBwneIWlcvr6+WLBggVPtYggBqUfIz88XZQUyyU9QqVSCm/SYTCacPXsWCQkJbhetDAAtLS3Q6XSCZhZwHIdHHnkEGo0Gr732Gk6dOoUjR47g66+/Rm5uLv7+97+73UTaRrie0Pf19aGtrQ2JiYmCZ8iTM2mpVIq0tDSLPoR6vZ4XfQBTbjN679kDeHnB+NprMw+j0evhc+21YH79a5j37JnZNSaBrObs3T7nKEwmEy8cQ0NDMJvNiIyMFH09gi3o6elBe3u709QjjDbp0Wq1/NFaeHi41SY9pH1wtImKO9Ha2or+/n7BRf6pp55Ca2sr3nvvvTHHXyQQKHUap1CKxbie0J87dw579+6FWq1GYWEhNmzYIEiwBLF0jYyMxPz582d0PYPBwIv+hCYv/f3wvfZaMGvXwvToo9aL/cgIfH79a3CBgTC++y4g4GyYFJ7l5uaKcjVnS8iNPjg4GGazGTqdDiEhIbzPgquvOjo6OqBQKJCXl+eUTnajrZQ1Go1VNRkGgwEVFRVYsGDBtA6Xrkhrayv6+vqQk5MjqMg///zzqKurw/vvv++Unyknw/WEntDb24sjR46gpKQEHR0duPbaa7Fx40ZkZWVZ/YEdGhpCdXU1kpOTBZvRG41GfovYaDQiIiICUVFR8B8Zge+mTeDmzoXx5ZcBCwt+JFVV8Ln9drDp6TC++eaYor7ZQKJGdTqd6Nrn7MHIyAgqKyvHWBmT4B3ScumswTuW0NLSwt/oXeW5DQ8P8+f6xMt9IldFIvIpKSkICwtz0GgdR1tbG39EKaTIv/rqq/jxxx/xwQcfOMXukAvgukI/mv7+fpSVlaGkpAQXL17EmjVrUFRUhIKCgmk/wGS7OisrC4GBgTYZn9ls5kV/ZGQEEYGBSPrnP+H/z3/C/L/+F8y33DLpWbukogJeb70Fj7IyGB9/HMzNNwuWQc+yLBoaGiCRSJCenu5229WkHiEzMxPBwcET/g5xCCOVxCR4JzIy0qlvYsQQZWRkZEaTY2dhvKsiMXrx8fFBZWUl0tLSXLIWZTra29uh0WiQm5srqMi/8cYbOHnyJIqLi0UdTOViuIfQj2ZwcBBHjx5FcXExGhoasHr1ahQVFWHx4sWXrFiam5uhVqvtul1NnN2USiXY+nokHz+OiGPHgMhIsAUF4KKiAJaFpK0N0jNnAIkE5ltugXnXLkDAIiGz2Yzq6mq3S2AjaLVanDt3zup6BBK8o1Kp+EJMZ/NxJ0lkHMe51QSP2GB3d3dDrVYjLCwMsbGxojHpsRcdHR1QqVTIy8sTVOTfeecdHD16FAcPHnSq74ML4H5CP5qRkRF8+umnKCkpwdmzZ7F8+XLI5XJcfvnl+P3vfw9PT088//zzDvuSsyz7s/9+VxfYmhpEdXYixGyGn78/EBMDduFCcImJgq3gCQaDAZWVlYiLi3PLNiISiztbtztSiKlSqUQTvDMdLMvyUavu2Fkw2u2P4zje6IWY9Dj7Ts102ELkAeAf//gHSkpKcOTIEVG0ZboZ7i30ozEYDPj888/xwQcf4Pjx48jOzsbevXuxcuVKUXyxx9u5BgcH85agQn4hSbyuu25ZklCivLw8Qd/3iYJ3ZDKZTfq9ZwoJaAkKCnK5FDZLGBoaQlVVFbKzs8cc04036SERyUIEuIiJzs5OvuhSyMXNBx98gH379qGsrEzUk1wXhgr9aLq6urB161bs3r0bcXFxKC4uxqlTp7B48WIUFRVh1apVoqg4J7aSxBI0MDCQbx2azReU1CNYGq/rSpCiw4GBAWRnZ9t0F2f08Qzp97Z18I4lY6qsrOS7StwNYulrSTDRRCY9xGtBLJM2a+nq6uInuEJ+9ktKSvD222+jrKzMZjVOlGmhQk+oqqrCjh078PLLL2PlypX8v5vNZpw6dQoHDhzAl19+iby8PBQVFeHqq68WxWyeFIOR1qE5c+bwFeDWtK10d3ejvb0deXl5opjM2BNyJs2yLNLT0+0qtuOTEh0R3kIc32JjY93S1pUUXc7E0tdkMvHx1kNDQ6KYtFlLd3c3urq6kJ+fL+hn7siRI3j11VdRXl7udtHNIoMKPaGurg5eXl5ISUmZ9HcYhsF3332H4uJinDhxAhkZGSgqKsLatWtFsSVFPNwVCoXFFeDE6Y+0ULlbTyvLsqipqcGcOXOQnJzs0BXZRKFJM5m0WQOpx3BXMxidToe6ujpBTKDGH68FBgYiMjJyRiY99sJWIn/s2DE8++yzOHr0qFu2JooMKvQzhWVZ/PTTTzhw4ACOHz+O5ORkbNiwAdddd51otqhGV4B7enryVrykrYW0zwGw+0pWDJjNZj5qVGzb1ZMF74x+/2YL8QhITU11y5txf38/6uvrbeLbP77t0sfHhz/XF8uOWU9PDzo6OlBQUCCoyH/++ed4/PHHcfToUURERAh2XcqMoUIvBCzLorKyEsXFxTh27BjmzZuHoqIiXH/99aLZshoZGYFCoeATv8LDw6FWqxEeHo6EhASnPVucKWQl6yzBPMTkhVgpTxW8YwnEBCojI2NSjwBXpq+vDw0NDXYL5yH5F2q1GhzH8aLvqJ1AhULBWxoLudvw1Vdf4Y9//CPKy8ud4nvlJlChFxoSfFJcXIzy8nKEhYVBLpfj+uuvF83sVqfTobKyEh4eHvDy8kJkZCSioqJEUXNgD0gLlbOuZEcH75jNZoSHh1tVDEbOpMdXl7sLpOg0Pz/fIf3cxBVTpVKNMekJDg62y4RbqVSitbUVBQUFgor8N998g/vvvx9lZWWYN2+eYNcdT19fH2699VbU1NRAIpHgnXfewRVXXGGzx3MBqNDbEhJpWlxcjI8//hhz5sxBUVERNmzYAJlM5pBVNGmfIyJnNBp5/30S2iL2Xu/ZoNPpUFtbi6ysLAQFBTl6OLOGBO8QV8WwsDDIZLJJRYOsZHNzczFnuvxjF0Sj0eDChQuiSeAjJj0qlQo6nQ7BwcGIjIy0WTEmEXmhw4m+//57/O53v8ORI0dsfgy2c+dOLF++HLfeeiuMRiOGh4dFs3MqUqjQ2wuO49DU1ISSkhIcPnwYnp6eWL9+PeRyOebOnWsX0ddqtWhoaJi0hchkMvErRYPB4BJtQ6MhKzlXFTmGYfgK/omCd4jIzdYIyFlRq9W4ePEiCgoKRGm/yrIsX4zZ29s7poNGCFFWqVRoaWkRXOTPnDmDO++8E4cPH0ZCQoJg150InU6HvLw8NDU1ucQ9yU5QoXcEHMeho6MDxcXFOHToEMxmM9atW4eNGzfOOBlvOnp6etDW1obc3FyLbvIk21upVGJ4eJjfHg4KCnLKL5hCoUBra6vbtA+OD97x8vKCwWDAwoUL3eaIZjQqlQrNzc3Iz88XpciPh5j0kHP92Zr0kOdfUFAgqMhXVlbi9ttvR2lpKRYsWCDYdSejoqICe/bsQWZmJiorK7Fo0SK8/PLLLrsDKRBU6B0Nx3Ho7u5GaWkpDh48iMHBQaxbtw5FRUWCtHtxHIfW1lb09vYiNzd3RmdyZHtRqVRiYGCA3x4OCQlxCtFvb2+HUql02pjV2dLZ2Yn29naEhoZCq9W6TPCOpSgUCrS1tQm+krUno016rK3LUKvVaGpqElzka2trccstt+Cjjz5Cenq6YNedip9++glLly7FN998gyVLlmDv3r0ICgrCY489ZpfHd1Ko0IsNpVKJQ4cOoaSkBL29vSgsLMSGDRtmFC7CcRwaGhrAsiwyMjIEaZ8jBi8KhUL0uewkgW14eBjZ2dmiG589aGtrg1qtHuN45grBO5ZCWsiEri53JKQuQ6VSYWhoCGFhYYiMjJzQpEej0eDixYuC72Q0NDRg165d2L9/P7KysgS77nT09PRg6dKlaGlpAQB8/fXXePrpp1FeXm63MTghVOjFTG9vLw4fPoySkhJ0dXXh2muvhVwutyg2lGGYMb7ltlh5j98eJq5u4eHhDhdVjuNQX18PqVSKtLQ0p9h5EJLRlr5T5YmPDt5hWXbSbHZnpKurC93d3S69k0Mm3iqVaoxJT0REBPr6+nDhwgXBaxIaGxvxm9/8Bvv27UNeXp5g17WU5cuX4+2330ZaWhoeeeQRDA0N4dlnn7X7OJwIKvTOQn9/Pz7++GOUlpaiqakJ11xzDeRyOfLz8y+5iev1elRXVyMmJsambS6jIa5uCoUCvb29CAgI4AuJ7J3+xzAMampqEBgYaLNJjpjhOA6NjY0wmUxW7eSQ4B2FQjGmGFNMwTuWYquAFjEz2qRHoVDAaDQiKSkJ0dHRgtWltLS0YPv27Xj33XexaNEiQa5pLRUVFXzFfVJSEt599123DOCyAir0zsjAwACOHj2KkpISNDQ0YPXq1ZDL5Vi8eDGqq6uxd+9efPjhhw4zrOA4DgMDA1AoFNBoNPDz8+O3h229sjKZTKisrER0dDRiY2Nt+lhihOxkeHh4IDU1dcYCbTab+bqMwcFBfns4NDRU9KLf3t4OtVqN3NxctxH50fT29qKxsRFpaWno6+uDSqUCgFmb9LS3t+OGG27AG2+8gSVLlgg5ZIptoULv7IyMjOCTTz5BSUkJvv32W5jNZjz44IO4+eabRXGTI9XDxH/f29sbUVFRNikE0+v1vG+7TCYT9NrOAPHt9/f3R1JSkmCCLIbgHUtpa2vjC08dfXzkCLRaLc6dO4eCgoIxq3hi0kNaZ63toiHJnq+++iquvPJKWz4FivBQoXcViouL8eyzz+K3v/0tTp48iR9//BG/+tWvsHHjRixbtkw01cYT+e8L4f9NLF3T0tLcchuPYRhUVVUhLCwM8fHxNnscRwTvWEpLSwv6+/unrElwZYgZ0nSOf+O7aIKDg/mJ20SvW09PD7Zu3YrnnnsOq1evtuVToNgG9xT6Tz75BHv37gXDMLj11lvxwAMPOHpIM4bjOLz44os4fvw4PvroI97tzWQy4YsvvkBxcTG++eYbXH755SgqKsKqVatE00c8MjLCu/JJJBLev93a6u/+/n7U1dW5raUrCeeJjo5GTEyM3R53fPCOt7c376xo789YU1MThoaGLCpUdUUsFfnxkIJalUqF3t5e+Pv7w9PTk9/mV6lU2LRpE5566imsXbvWhs+AYkPcT+gZhkFqaio+++wzxMbGYvHixdi/fz8yMzMdPbQZYTAY8Oyzz+L++++fdNVuNpvx9ddf48CBA/jqq6+Qn5+PoqIiXH311aJpqTIYDLzoMwzDi/50DnYajQaNjY12CycRG0ajEZWVlYiLi3N4iAgJblGpVJBIJLzo2/J9IS2Uer0eWVlZoq8fsAUkhW+23v1k4kYiZn19faHX63Hvvfdi165dwg2YYm/cT+i/++47PPLII/j0008BAE899RQA4MEHH3TksOwGwzD49ttvUVJSghMnTiAjIwNyuRxr164VjS3s6PNEo9HIC8Z4297u7m4+gUssuxT2hNQkJCcniyYwiTA+eGd0255QYsxxHC5cuMB3F7izyAs90e3r68P27duRnp6OlpYWDAwM4LrrroNcLkdOTo5bvtZOjEVvlks1oHZ2do4JXYiNjcX333/vwBHZFw8PDyxfvhzLly8Hy7L48ccfUVxcjGeeeQbJyckoKirCf/zHfzh0C9zb2xsxMTGIiYnhzUEuXryIkZERXjC0Wi00Gg0WLlzo8LNhR0Cy5MVak+Dj44PY2FjExsZe8h4KkdZGAqOIGZQ7Co9Op7OJyOt0OmzduhV33303tm7dCuBn4T969CieeOIJPPHEE3axu6XYF5da0R84cACffvop3n77bQDAvn378MMPP+DVV1918MgcC8uyqKioQHFxMY4dO4bY2FgUFRWhsLBQNMlQDMNApVKhqakJBoMB8+bNQ1RUlN3iPcXC4OAgqqurnTKBb3xa20ycFYnjo1QqnVULoTMzMDCA2tpawUV+cHAQW7duxe23346bbrpJsOtSHIr7rehjY2PR3t7O/39HR4fdTGXEjFQqxcKFC7Fw4UI88cQTqKmpQXFxMTZs2ICIiAjI5XJcf/31CA8Pd9gYJRIJNBoNwsPDkZycDK1Wi46ODtTX1yM0NJQXDFe+8ZOY3ckSCMUOsdyVyWRjnBXPnz+PwMBA3llxsrY94hPg5eWFBQsWuPR7PRlE5HNzcwUV+eHhYWzfvh27d++mIu+GuNSK3mw2IzU1FSdOnEBMTAwWL16Mf/3rX3b1a3YmOI7DuXPnUFxcjLKyMgQEBGDDhg1Yv349ZDKZ3W60pH0sJCQECQkJYx6XZVlotVooFAr09/cjODgYUVFRovTfnw2kR9oVCw+Jqxtp25soeIfjONTW1sLX11eQwCdnhOzm5OXlCVpTMzIygu3bt2Pbtm247bbbBLsuRRS4XzEeABw9ehR33303GIbB7t278dBDDzl6SE4Bx3FoampCcXExDh8+DG9vb6xfvx5FRUWYO3euzW68JpMJFRUVFln6chwHrVbL++8HBgYiKipKlOYu1kCOLPLz890iZndwcJBPayMRrb29vQgKCkJSUpKjh+cQiMjn5uYKmkVgMBjw61//Gtdffz3uuOMOt5xAuTjuKfSU2cNxHNra2vh4XZZlsW7dOsjlcsyfP1+wmwWpLE9KSkJkZKTVYxxv7hIVFYXw8HCnKuDr6enhuwvEYnxkT4aHh1FZWQmGYeDj4zNrK1dnZGhoCFVVVYKLvNFoxM6dO7Fq1SrcfffdVORdEyr0lNnDcRy6u7tRWlqK0tJSDA8PY926dSgqKpqVFStZwWRkZMy6IJD47xNzF19fX0RFRSEiIkLU4tnR0cGHszjT5EQoWJZFVVUVQkNDER8ff0nrJbFydcbgHUshIi90XYbJZMLu3btx+eWX47777nPZ149ChZ5iA5RKJQ4ePIiSkhJotVoUFhaiqKjIqrjYvr4+1NfX26zobLSjm6enJ++/L6Z+/NbWVmi1WuTk5Dj1scNMIXUZERERY1piCRMF78hkMoSEhLiMaNlK5M1mM/bs2YPMzEw8/PDDLvN6USaECj3Ftmg0Ghw+fBglJSXo6enBtddeC7lcjszMzEkL5ch5dF5enl2c+0Y7ukmlUr4q3FFn4cTtbWRkxG0tXRmGQWVlJaKioiyy9Z0seCc8PNxpX7/h4WFUVVUhKytLUF8LhmFw5513Ii4uDo899hgVedeHCj3FfvT19eHjjz9GaWkpmpubsWbNGsjlcuTl5fE343fffRfx8fFYvny5Q7bU9Xo9b8XLcRwv+vaqciddDhzHIT093S1vwsS7f+7cuTNqfeU4jm/bI/7tYgnesRRbiTzLsrj77rsRGhqKZ555xmknQRSroEJPcQwDAwMoLy9HSUkJzp07h9WrV2NoaAj19fUoLS0VRTjNeBtXYsVrqyIwlmVRX18Pb29vt+0RN5vNqKioQGxsLKKjo2d9vYmCd0jbnpiOaUZDXA8zMzMFNURiWRb33nsvvL298eKLL1KRdx+o0FMcz9DQEG688UY0NjbC09MTK1asgFwux9KlS0VzNm0ymaBSqaBQKGA0Gnkr3oCAAEEEmWVZVFdXIygoCImJiQKM2PkgbZS2DOhxRPCONdhS5B966CEYjUa8/vrrVOTdCyr0zkJ7ezt27NiBnp4eSKVS7NmzB3v37nX0sGaN0WjE7t27ERsbi6eeegpGoxGfffYZDhw4gJ9++gnLli3Dxo0bsWzZMtFsu5rNZn6lT7zbZTIZgoKCZiT65Dw6MjJywqIzd8BoNKKiogIJCQmQyWR2eUySmKhSqWwWvGMNer0eFRUVyMjIQHBwsGDXZVkWjz76KHp7e/Hmm2+KZvJMsRtU6J2F7u5udHd3Y+HChRgYGMCiRYtw6NAhp43XJdx2223IzMzEPffcc8nPjEYjvvjiCxQXF+Pbb7/FkiVLUFRUhJUrV4pm25VhGKjV6jGV39b475tMJlRWViImJgZz5861w4jFBxH5pKQkh6XwkeAdoSZv1mIrkec4Dk8++STa2trw3nvv2VzkGYbBZZddhpiYGJSVldn0sSgWQ4XeWSkqKsJdd92FNWvWOHoos2JwcNCitiGz2YyvvvoKBw4cwNdff42CggIUFRXhqquusktlviWwLMu3e5HAlqioKISEhEy4VeqIVazYMBgMqKiowIIFCxyaozAaEryjVCoxMDAwo+AdayAin56eLmiAFMdxeO6559DQ0IB9+/bZZUfshRdewE8//QSdTkeFXjxQoXdGWlpasGLFCtTU1DhdepkQMAyDb775BiUlJfjv//5vZGZmQi6XY82aNYL6f88G4r+vVCrR19eHoKAg3opXKpXyN/eUlBTRCJy9Ia9BamoqwsLCHD2cCSHvo0ql4i2VpwvesQaDwYCzZ88KHjfMcRxeffVV/Pjjj/jggw/s0sHS0dGBnTt34qGHHsILL7xAhV48UKF3NgYHB7Fy5Uo89NBD2LRpk6OH43BYlsUPP/yA4uJiHD9+HCkpKZDL5Vi7dq0oKveBS9u9/Pz8MDAwgKysLNEKnK0hRWdCr2JtyfjgHT8/P96OdyZCSnYzUlNTBRf5N954AydPnkRxcbHdjrm2bNmCBx98EAMDA3juueeo0IsH94updWZMJhM2b96MX//611Tk/41UKsXSpUuxdOlSsCyLiooKHDhwAM8//zzi4uJQVFSEwsJCQc89rUUikSA0NBShoaHQ6XSoqqpCWFgYzp8/jzlz5jhdj/dsISIv9Hm0rZFIJAgODkZwcDBSUlL4tr2zZ8/C09OTF31LjpLIsU1KSorgIv/OO+/gs88+w8GDB+0m8mVlZZDJZFi0aBFOnjxpl8ekCAtd0YsAjuOwc+dOhIWF4aWXXnL0cEQPx3GoqanBgQMHUF5eDplMhqKiIqxbt85hq+i+vj40NDQgJycH/v7+Y3q8VSoVfHx8eCteMfvvz4ahoSFUV1cL3j7maEZGRvhODI7jpgzeMRqNOHv2rE3qEv7xj3+gpKQER44csWvL4IMPPsjXAej1euh0OmzatAnvv/++3cZAmRS6de8snDp1CsuXL0dOTg5fEPTkk0+isLDQwSMTPxzHoaGhAcXFxSgrK0NQUBA2bNiA9evXIzIy0i5V1RqNBo2NjcjPz590xTc0NMSLvqenJ+/KJ5YOg9lCfNuzs7NFc6xiC6YK3iFeAcnJyYKL/P79+/H++++jrKzMocl+J0+epFv34oIKPcW9ID7yxcXFOHLkCHx8fLB+/XoUFRUhOjraJqKvVCrR0tKC/Px8i0V7ZGQECoWCN3Yhoi+WDgNrIUmEtgopEitms3lM+6XJZEJ8fDzi4+MF/ayVlJTgrbfeQnl5ucMnUVToRQcVeor7wnEcWltbUVpaioMHD4LjOKxfvx5yuRyxsbGC3Ii7u7vR2dmJvLy8GW/HE/99lUoFlmURGRmJqKgo0bi5TcfAwABqamoEz1J3JkwmE86cOYOIiAgYDAb09/cjODgYkZGRsw7eOXLkCF577TWUlZU5TWEjxa5QoadQgJ9Fv7u7GyUlJSgtLYVer8e6detQVFSExMTEGYl+e3s7VCoV8vLyBDMqMRqNfOgOcXOLiooSrYD29/ejvr4eubm5oml9tDcmkwlnz55FYmIiIiMjAQgXvHPs2DE8++yzOHr0qNt2cFCmhQo9hTIejuOgVCpx8OBBlJaWQqvVorCwEHK5HKmpqRaJfnNzM3Q63ZiaCqEh/vtKpRJ6vZ4XfaH892cLKT7My8tzmt0HoSFn8vHx8ZOaIs00eOfzzz/H448/jqNHjzrMUZDiFFChp1CmQ6PR4NChQygtLUVPTw+uvfZabNy4ERkZGZeIOMdxuHDhAoxG44Q/txWjz4KHh4ftbuE6Hq1Wi3Pnzk1ZfOjqmM1mnD17dkqRn4jxwTtE9EdPlr788ks8/PDDKC8vt1kAEMVloEJPoVhDX18fjhw5gtLSUrS2tuKaa67Bxo0bkZubC47jcNttt2Hz5s0oLCx02Kp6vIVraGgob8VrjzH19vaisbEReXl5bi3yFRUVmD9//qyEWK/XQ6VSoaWlBb///e9x1VVXITs7G3/5y19QXl6OefPmCThqiotChZ5CmSk6nQ7l5eUoLS1FQ0MDfHx8kJaWhr/85S+iMb9hWRa9vb1QKpV8AVhUVJTNfNs1Gg0uXLiA/Px8+Pj4CH59Z4CIfGxsLKKjowW7rkqlwuuvv44PP/wQQUFBuP7667Fp0yZcdtllNHaWMhVU6CmU2aLX67FlyxZERETAaDSiqqoKq1atglwux5IlS0QTC8qyLF8AptVqERQUxPu2CyEUKpUKzc3NVrURuhoMw6CiogIxMTGCijwA/M///A/uuusuHD58GDKZDMePH8fBgwdx9uxZ3H333di9e7egj0dxGajQU+yHK0ZYDgwMYNOmTbjhhhtw6623AvhZ+D/77DMcOHAAZ86cwbJlyyCXy7Fs2TLRrPQ5jkN/fz/v2x4QEMBXfc9kYqJUKtHa2or8/HyXdfWbDiLy8+bNEzxyuLKyErfffjtKS0uxYMGCMT8zmUzQarVum4BImRYq9BT74YoRls899xzi4uKwbdu2CX9uNBrx3//93yguLsZ3332HJUuWQC6XY8WKFaJZ9XIch4GBAb7q28/Pjy8As2RiolAo0NbWRkW+ogJz584V/Ny8trYWt9xyCw4cOIC0tDRBr01xC6jQU+wDjbD8+ez2yy+/RHFxMb7++msUFBRALpfjqquuEs15NsdxGBoagkKhsKjVixgC5efni2a3wt4wDIPKykpER0cLLvINDQ3YtWsX9u/fj6ysLEGvTXEbqNBT7AONsBwLwzA4deoUSkpK8MUXXyArKwtyuRzXXHONqIxlhoeHeSteDw8P3orXx8cHXV1d6O7uRn5+vmjqEOwNEfmoqCjExMQIeu3Gxkb85je/wb59+5CXlyfotSluBY2ppdgeGmF5KR4eHli5ciVWrlwJlmXx/fffo7i4GE8++SRSUlKwceNGrF271uG+8HPmzEFiYiISExMxMjICpVKJ6upqGAwGAHBrkWdZFlVVVZDJZIKLfEtLC3bs2IF3332XijzFLtAVPWVW0AhLy2FZFmfPnsWBAwfwySefID4+Hhs2bEBhYaFostvb2tqgUqkQEREBtVoNhmF4/30x7UbYEiLy4eHhmD9/vqDXbm9vx7Zt2/Dmm29iyZIlgl6b4pbQrXuKfaHJVpbDsixqampw4MABHD16FFFRUdiwYQPWrVvnMF/z1tZW9PX1jbH2HR/LOtp/XwxWvEJjS5Hv6urC1q1b8eqrr+LKK68U9NoUt4UKPcW+UKGfGRzHob6+HsXFxSgrK0NwcDCKioqwfv16RERE2EVQm5ubMTAwgOzs7En77k0mE2/FOzIygoiICD6L3RVEn2VZVFdXIzQ0FHFxcYJeu6enB1u2bMHzzz+P1atXC3ptiltDhZ5CcTaIn35JSQmOHDkCHx8fbNiwAUVFRYiKihJcUDmOQ1NTE4aHh5GVlWWxuQ7DMGOy2In/fnBwsFOKPhH5kJAQxMfHC3ptlUqFTZs24amnnsLatWsFvTbF7aFCT6E4MxzHobW1FSUlJTh48CAkEgnWr18PuVyOmJiYWQsqx3G4ePEiDAYDMjMzZ3w9hmF4K16dTofQ0FDIZDKEhoY6heiTY5SgoCAkJCQIem2NRoPNmzfjkUceQWFhoaDXplBAhZ5CcR04jkNXVxcv+gaDAevWrUNRURESEhKsFlSO49DY2Aiz2YyMjAzBBJllWWi1WigUCt5/XyaTISwsTJSe7RzHoaamBgEBAUhMTBT02n19fdi0aRMefPBBFBUVCXptCuXfUKGnUFwRjuOgVCpRWlqK0tJS9Pf3o7CwEHK5HCkpKdOKNsdxOHfuHAAgLS3NZqtujuPQ19cHhUIBrVaLwMBA3n9fDG17HMehtrYWc+bMQVJSkqDX1ul02Lx5M+655x5s2bJF0GtTKKOgQk+huANqtRqHDh1CaWkplEolrr32WmzcuHHClTop/PP09LRoUiAUHMdBp9NBoVBAo9HA39+f9993hOseEXk/Pz8kJycLeu3BwUFs2bIFv/3tb3HjjTcKeu3RtLe3Y8eOHejp6YFUKsWePXuwd+9emz0eRZRQoadQ3A2tVouPP/4YJSUlaGtrw5o1a7Bx40bk5OSAZVns2rULO3fuxDXXXOOw83OO4zA4OMhb8fr6+vJWvPbw0+c4DnV1dfD19RVc5IeGhnDDDTdg586d2Llzp6DXHk93dze6u7uxcOFCDAwMYNGiRTh06BAyMzNt+rgUUUGFnkJxZ3Q6HcrLy1FSUoJz587Bx8cHGRkZeP3110XlXT84OMiH7nh6evJWvLYIBiI7Gt7e3khOThZ0sjMyMoLt27dj27ZtuO222wS7rqUUFRXhrrvuwpo1a+z+2BSHQYWeQqH83P9+0003wdvbm68wX7VqFYqKirBkyRJRnJcThoeHoVQqoVKpIJVK+ZW+r6/vrK9NRN7LywsLFiwQVOQNBgNuuukmrFu3DnfccYfdd0taWlqwYsUKvnuA4jZQoadQLKWvrw+33norampqIJFI8M477+CKK65w9LBmjdFoxPbt23HllVfid7/7HQBAr9fj+PHjOHDgAM6ePYsrr7wScrkcv/rVr0S10tfr9VAqlVAqleA4jl/p+/n5WX0tjuPQ0NAADw8PwWsTjEYjduzYgdWrV+Puu++2u8gPDg5i5cqVeOihh7Bp0ya7PjbF4VChp1AsZefOnVi+fDluvfVWGI1GDA8PIyQkxNHDmjWvvfYaAOCuu+6a8OdGoxEnTpxAcXExTp8+jaVLl0Iul2PFihWiyp83Go286JvNZkRGRkImk8Hf33/avyVdBhKJBKmpqYIKsclkwu7du3H55Zfjvvvus7vIm0wmrFu3Dtdeey0/kaO4FVToKRRL0Ol0yMvLQ1NTk1MYvFgDx3EWPyeTyYQvv/wSxcXFOHXqFBYuXAi5XI7Vq1fDx8fHxiO1HJPJBJVKBYVCwfvvy2QyBAQETNhlcP78eQAQXOTNZjP27NmDrKws/PGPf7T7Z4fjOOzcuRNhYWF46aWX7PrYFNFAhZ5CsYSKigrs2bMHmZmZqKysxKJFi/Dyyy9btFp0VRiGwalTp1BcXIwvvvgCOTk5kMvluOaaa2a0dW4rzGYz1Go1FAoFRkZGeCteck7d2NgIlmUF9wtgGAZ33HEH4uPj8dhjjzlkgnjq1CksX758TAjRk08+SR343Asq9BSKJfz0009YunQpvvnmGyxZsgR79+5FUFAQHnvsMUcPTRSwLIvTp0+juLgYn332GdLS0rBx40asWbMGAQEBjh4eD8Mw0Gg0UCgUGBwchFQqhY+PD3JzcwV15WNZFnv37kV4eDiefvppUTr+UdwGKvQUiiX09PRg6dKlaGlpAQB8/fXXePrpp1FeXu7YgYkQlmVx5swZHDhwAJ988gkSExOxYcMGFBYWiqbam9j7Dg4OwsfHBzqdDiEhIbz//myEmWVZ/Nd//Rd8fHzw4osvUpGnOBoq9BSKpSxfvhxvv/020tLS8Mgjj2BoaAjPPvuso4clakji24EDB3Ds2DFER0djw4YNWLduHUJDQx02rgsXLowJ6mFZlrfi7evrQ1BQEG/Fa41QsyyLP/zhDzCZTHj99depyFPEABV6CsVSKioq+Ir7pKQkvPvuuw4VK2eD9KgXFxejrKwMISEhKCoqwrp16xAZGWm3cVy8eBF6vX7SND6O49Df3w+FQoHe3l4EBAQgKipqWv99lmXx6KOPore3F2+99RYVeYpYoEJPoVDsD8dxuHDhAoqLi3HkyBH4+flhw4YN2LBhA6KiomxWuNbU1ITh4WFkZWVZ9BjEf1+pVEKj0cDPzw9RUVGX+O9zHIcnn3wSbW1teO+990RlMERxe6jQUygUx8JxHFpaWlBSUoJDhw5BKpVi/fr1kMvlmDdvnmCi39zcjMHBQWRnZ8/omsR/n1jxfvrppwgNDcW2bdvwj3/8Aw0NDdi3b5+oDIUoFFChp1AoYoLjOHR2dqKkpAQHDx6E0WjE+vXrUVRUhPj4+BmLfktLCwYGBpCVlSXYlnp1dTX279+P8vJyDA4O4uGHH8bmzZsRFRUlyPUpFIGgQk+hUMQJx3FQKBQoLS1FaWkpdDodrr/+esjlcqt86FtaWqDT6ZCdnS3ouTnHcfjrX/+KL7/8Es899xzKyspw6NAheHh4YOPGjbj11lsxZ84cwR6PQpkhVOgpFIpzoFKpcOjQIZSWlkKlUuG6665DUVERMjIyJhX91tZW9PX1jTGMEQKO4/C3v/0Nn3zyCUpLS8cE6nR1deHw4cO45ZZbbJKuR6FYCRV6CoXifGi1Whw5cgQlJSVob2/H2rVrsXHjxjGr9tdffx05OTm48sorBa+A/8c//oGSkhK+kJBCETFU6CkUinOj0+lQVlaGkpISXLhwAddccw2MRiMqKytx6NAhQeJrR7N//37885//xMcff+zWFsgUp4EKPYVCcR2GhoZwzz334Pjx4wgKCsKqVatQVFSEyy+/XJCWt+LiYvztb39DWVkZAgMDBRgxhWJzLBJ66vpAobgIL774IrKyspCdnY0bb7wRer3e0UMSlH/961/o7OxEQ0MDfvjhB1x99dV47733cMUVV+D3v/89vvrqK5jN5hld+8iRI3jjjTdwrqf4gAAABJtJREFU+PBhKvIUl4Ou6CkUF6CzsxNXXnkl6urq4Ofnh23btqGwsBC7du1y9NAE4V//+hf27duHgwcPXrJdbzAYcOLECRQXF+P777/HFVdcAblcjuXLl8PLy2vaax87dgzPPvssjh49irCwMFs9BQrFFli0oqfuDxSKi2A2mzEyMgIvLy8MDw9j3rx5jh6SYCxfvhwbN26c8Ezex8cHhYWFKCwshMlkwsmTJ1FSUoL7778fl112GeRyOVatWgUfH59L/vazzz7DM888Q0We4tLQFT2F4iK8/PLLeOihh+Dn54e1a9fin//8p6OH5FDMZjNOnTqF4uJinDx5Erm5uZDL5bj66qvh5+eHkydP4v/8n/+D8vJyaoRDcVZoMR6F4i5otVps3rwZH374IUJCQrB161Zs2bIFN998s6OHJgoYhsHp06dRXFyMEydOIDw8HD09PThx4oRL7XxQ3A66dU+huAuff/45EhMT+aS4TZs24dtvv6VC/288PDywbNkyLFu2DCzL4tChQ5g3bx4VeYpbQIWeQnEB4uLicPr0aQwPD8PPzw8nTpzAZZdd5uhhiRKpVIpNmzY5ehgUit2g7XUUiguwZMkSbNmyBQsXLkROTg5YlsWePXscPSwKhSIC6Bk9hUKhUCjOCTXMoVAoFHvyySefIC0tDQsWLMDTTz/t6OFQKADoip5CoVAEgWEYpKam4rPPPkNsbCwWL16M/fv3IzMz09FDo7gudEVPoVAo9uKHH37AggULkJSUBG9vb2zfvh2HDx929LAoFCr0FAqFIgSdnZ2YP38+//+xsbHo7Ox04IgolJ+hQk+hUCgCMNExqERi0c4qhWJTqNBTKBSKAMTGxqK9vZ3//46ODmrIQxEFVOgpFApFABYvXozGxkY0NzfDaDTigw8+wIYNGxw9LAqFCj2FQnEsu3fvhkwmQ3Z2Nv9vvb29WLNmDVJSUrBmzRpotVoHjtAyPD098dprr+Haa69FRkYGtm3bhqysLEcPi0Kh7XUUCsWxfPXVVwgICMCOHTtQU1MDALjvvvsQFhaGBx54AE8//TS0Wi2eeeYZB4+UQhEdNL2OQqE4By0tLVi3bh0v9GlpaTh58iTmzp2L7u5urFq1CufOnXPwKCkU0UH76CkUinOiUCgwd+5cAMDcuXOhVCodPCIKxXmhQk+hUCgUigtDhZ5CoYiOqKgodHd3AwC6u7shk8kcPCIKxXmhQk+hUETHhg0b8Pe//x0A8Pe//x1FRUUOHhGF4rzQYjwKheJQbrzxRpw8eRJqtRpRUVF49NFHIZfLsW3bNrS1tSEuLg4HDhxAWFiYo4dKoYgNWnVPoVAoFIoLQ6vuKRQKhUJxd6jQUygUCoXiwlChp1AoFArFhaFCT6FQKBSKC0OFnkKhUCgUF4YKPYVCoVAoLgwVegqFQqFQXBgq9BQKhUKhuDBU6CkUCoVCcWGo0FMoFAqF4sJQoadQKBQKxYXxnObnFvnoUigUCoVCESd0RU+hUCgUigtDhZ5CoVAoFBeGCj2FQqFQKC4MFXoKhUKhUFwYKvQUCoVCobgwVOgpFAqFQnFh/n9K6OVcGvfsuwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1296x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize = (18, 9))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# Draw imaged loci\n",
    "cdict = {0:'Red', 1:'Green', 2:'Blue', 3:'Purple'}\n",
    "ax.scatter(df_data.loc[:, 'z_hat'],\n",
    "           df_data.loc[:, 'y_hat'],\n",
    "           df_data.loc[:, 'x_hat'],\n",
    "           c=[cdict[elem] for elem in df_data.t], alpha = 1, marker='^', s = 100)\n",
    "\n",
    "# Draw fiber\n",
    "ax.plot(df_fiber.loc[:, 'z_hat'], df_fiber.loc[:, 'y_hat'], df_fiber.loc[:, 'x_hat'], c='Blue', alpha = 0.3, label = 'DNA (unobserved)')\n",
    "\n",
    "# Draw true positive (true location)\n",
    "ax.scatter(df_data.loc[[15005, 15006], 'z_hat'],\n",
    "            df_data.loc[[15005, 15006], 'y_hat'],\n",
    "            df_data.loc[[15005, 15006], 'x_hat'],\n",
    "            alpha = 1, marker='o', s = 500, facecolors='none', edgecolors='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41be8eb0",
   "metadata": {},
   "source": [
    "- In fact, this is reflected in the bond probabilities. If we evaluate the bond probabilities between every spatial candidate for `t=1` to `t=2` and `t=3`, we see that it would be more favourable for us to skip `t=2` and connect directly between `t=1` to `t=3`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "61241e9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize = (5, 3))\n",
    "axs.imshow(ex_trans_prob_skip, cmap = 'plasma')\n",
    "plt.yticks(np.arange(3),[\"t=1;\\ni=0\", \"t=1;\\ni=1\", \"t=1;\\ni=2\"], fontsize = 18);\n",
    "plt.xticks(np.arange(5),[\"t=2;\\ni=0\", \"t=2;\\ni=1\", \"t=3;\\ni=0\", \"t=3;\\ni=1\", \"t=3;\\ni=2\"], fontsize = 18);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1855eb7",
   "metadata": {},
   "source": [
    "- The bond probabilities skipping `t=2` (`t=1` --> `t-3`) will incur a penalty, but this is still more favourable than linking any coordinate between `t=1`--> `t=2`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d2b88a1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[15.5, 15.2,  7.1,  7.4,  8.1],\n",
       "       [24.7, 24.6,  9.1,  9.8,  9.9],\n",
       "       [11.8, 11.3,  7.4,  6.9,  7.8]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.around(ex_trans_prob_skip, decimals = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51736dce",
   "metadata": {},
   "source": [
    "- So what if the starting locus is error prone (ie. all of the spatial coordinates belonging to the starting locus `t=0` are noise and need to be skipped)? \n",
    "- Likewise, what if the ending locus is error prone?\n",
    "    - We create a __single source__ that connects to spatial coordinates belonging to the first `num_skip` loci.\n",
    "    - We create a __single sink__ that connects to spatial coordinates belonging to the last `num_skip` loci.\n",
    "        - We create a \"pseudo\"-bond that incurs a cost of traveling a bond commensurate wtih the number of bonds skipped.\n",
    "            - This allows us to accomodate skipping the first and last few loci.\n",
    "            - We achieve this by \"padding\" the adjacency matrix to create an extra row for the source, and extra column for the sink.\n",
    "                - We populate \"pseudo\" bond probabilities using the function `jie.aligner.boundary_init`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f83791ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate initial and terminal gap penalties\n",
    "trans_mat_pad = boundary_init(trans_mat=trans_mat,\n",
    "                              loci_dist=loci_dist, \n",
    "                              l_p_bp=l_p_bp,\n",
    "                              corr_fac=corr_fac,\n",
    "                              n_colours=n_colours,\n",
    "                              cell_pts=cell_pts,\n",
    "                              exp_stretch=exp_stretch,\n",
    "                              stretch_factor=stretch_factor,\n",
    "                              lim_init_skip=lim_init_skip,\n",
    "                              init_skip=init_skip,\n",
    "                              end_skip=end_skip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f690de1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'After adding source, sink : \\nadj matrix shape (13, 13)')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize = (10, 5))\n",
    "\n",
    "axs[0].imshow(trans_mat, cmap = 'plasma')\n",
    "axs[0].set_title(\"Before adding source, sink : \\nadj matrix shape {}\".format(trans_mat.shape))\n",
    "axs[1].imshow(trans_mat_pad, cmap = 'plasma')\n",
    "axs[1].set_title(\"After adding source, sink : \\nadj matrix shape {}\".format(trans_mat_pad.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55a990ab",
   "metadata": {},
   "source": [
    "- There is no penalty incurred by entering from source to any of the spatial coordinates belonging to the first locus `t=0`.\n",
    "- Similarly, there is no penalty incurred by exiting from any of the spatial coordinates belonging to the last locus `t=3` to the sink.\n",
    "\n",
    "---\n",
    "\n",
    "- With this adjacency matrix, we create a graph. \n",
    "    - We initialize the source and the sink (aka target). We seek to find the shortest graph traversal from source to sink."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a48559eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a9a4a93aec9b4507bded2e624fb7ab75",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='Slides : 4 /', max=4, min=1), Output()), _dom_classes=('…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wg.interact(find_polymer, Slides=wg.IntSlider(min=1,max=4,step=1, description=\"Slides : {} /\".format(4)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f92acb3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create discrete state space model\n",
    "G = igraph.Graph.Adjacency((trans_mat_pad > 0).tolist())\n",
    "\n",
    "# add edge weights\n",
    "G.es['weight'] = trans_mat_pad[trans_mat_pad.nonzero()]\n",
    "\n",
    "\n",
    "# find shortest path (Dijkstra)\n",
    "shortest_path_length = G.shortest_paths(source = 0, \n",
    "                                        target = trans_mat_pad.shape[0]-1, \n",
    "                                        weights = 'weight')[0][0]\n",
    "## NB: path is written in index of FUTURE cell_pts dataframe (subsetted after iterative subtraction)\n",
    "shortest_path = [elem-1 for elem in G.get_shortest_paths(0, to = trans_mat_pad.shape[0]-1, \n",
    "                                                         weights = 'weight')[0][1:-1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ff2f929",
   "metadata": {},
   "source": [
    "- The path reflects the selected coordinates from the input that belong to the most likely polymer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b150af03",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_hat</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>z_hat</th>\n",
       "      <th>Annot</th>\n",
       "      <th>hyb</th>\n",
       "      <th>i</th>\n",
       "      <th>bp</th>\n",
       "      <th>sig_x</th>\n",
       "      <th>sig_y</th>\n",
       "      <th>sig_z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.121910</td>\n",
       "      <td>7.182445</td>\n",
       "      <td>6.081194</td>\n",
       "      <td>TP</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5000</th>\n",
       "      <td>8.345561</td>\n",
       "      <td>8.037631</td>\n",
       "      <td>5.236670</td>\n",
       "      <td>TP</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15000</th>\n",
       "      <td>5.277496</td>\n",
       "      <td>6.326657</td>\n",
       "      <td>5.903535</td>\n",
       "      <td>TP</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>15000</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x_hat     y_hat     z_hat Annot  hyb  i     bp  sig_x  sig_y  sig_z\n",
       "0      7.121910  7.182445  6.081194    TP    0  0      0      1      1      1\n",
       "5000   8.345561  8.037631  5.236670    TP    1  0   5000      1      1      1\n",
       "15000  5.277496  6.326657  5.903535    TP    3  0  15000      1      1      1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cell_pts_input.iloc[shortest_path]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f9ab870",
   "metadata": {},
   "source": [
    "#### Appendix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f3c0fb7",
   "metadata": {},
   "source": [
    "##### Q: Where does the extra $4 \\pi r^{2}$ term come from? It no longer looks Gaussian?\n",
    "The basis of the freely jointed chain (Gaussian chain) is that in each bond of the molecular chain, if we fix one end of the a bond to a coordinate origin (0, 0, 0) and allow the other end of the bond to freely rotate, we can model the probability the other end of the bond lies at coordinate (x, y, z) distance $d$ away using a Gaussian:\n",
    "\n",
    "$$p(x, y, z)=\\int_{-d}^{d} \\int_{-\\sqrt{d^{2}-x^{2}}}^{\\sqrt{d^{2}-x^{2}}} \\int_{-\\sqrt{d^{2}-y^{2}-x^{2}}}^{\\sqrt{d^{2}-y^{2}-x^{2}}} \\frac{1}{\\left(\\frac{2 \\pi}{3} n b^{2}\\right)^{\\frac{3}{2}}} e^{-\\frac{3\\left(x^{2}+y^{2}+z^{2}\\right)}{2 n b^{2}}} d z d y d x$$\n",
    "\n",
    "where $n$ is the number of bonds, each of bond length $b$.\n",
    "\n",
    "If we rewrite this in spherical coordinates, where $r^{2}=x^{2}+y^{2}+z^{2}$, $x = r \\cos{\\phi}\\sin(\\theta)$, $x = r \\sin{\\phi}\\sin(\\theta)$ and $z = r \\cos(\\theta)$, then the differential volume element $dx dy dz$ can also be re-written in spherical coordinates:\n",
    "\n",
    "$$\n",
    "p(r, \\phi, \\theta)=\\int_{0}^{2 \\pi} \\int_{0}^{\\pi} \\int_{0}^{d} \\frac{r^{2} \\sin \\phi}{\\left(\\frac{2 \\pi}{3} n b^{2}\\right)^{3 / 2}} e^{-\\frac{3 r^{2}}{2 n b^{2}}} d r d \\phi d \\theta\n",
    "$$\n",
    "\n",
    "It's evident that:\n",
    "\n",
    "$$\n",
    "\\int_{0}^{\\pi} \\sin \\phi d \\phi=-\\left.\\cos \\phi\\right|_{0} ^{\\pi}=2\n",
    "$$\n",
    "\n",
    "and \n",
    "\n",
    "$$\n",
    "\\int_{0}^{2 \\pi} d \\theta=2 \\pi\n",
    "$$\n",
    "\n",
    "Thus,\n",
    "\n",
    "$$\n",
    "p(r, \\phi, \\theta)=\\int_{0}^{d} \\frac{4 \\pi r^{2}}{\\left(\\frac{2 \\pi}{3} n b^{2}\\right)^{3 / 2}} e^{-\\frac{3 r^{2}}{2 n b^{2}}} d r d \\phi d \\theta\n",
    "$$\n",
    "\n",
    "This is the origin of the \"additional\" term."
   ]
  },
  {
   "attachments": {
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"
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    "##### Q: The bond probability gets maximized at the expected distance, right? Shorter or longer distances get penalized?\n",
    "\n",
    "The Gaussian chain, in its most familiar form is given by:\n",
    "\n",
    "$$\n",
    "P\\left(R_{i j}, n\\right)=\\frac{1}{\\left(\\frac{2 \\pi}{3} n b^{2}\\right)^{3 / 2}} e^{-\\left(\\frac{3 R_{i j}^{2}}{2 n b^{2}}\\right)}\n",
    "$$\n",
    "\n",
    "where $b$ is the bond length, $n$ is the number of bonds, $R$ the spatial distance separating two monomers. \n",
    "\n",
    "Our hypothesis is that the bond length $b$ can be esimated from the genomic distance separating two loci $L$, as well as a distance parameter $\\tau$ and persistence length $l_{p}$:\n",
    "\n",
    "$$\n",
    "n b^{2}=2 l_{p} \\tau L\n",
    "$$\n",
    "\n",
    "To find the maxima of the bond probability, we take the derivative of the bond probability with respect to $r$:\n",
    "\n",
    "$$\n",
    "\\frac{d w_{t_{i j}}^{t_+c; j}}{d r}=\\frac{d}{d r}\\left(\\frac{4 \\pi}{\\left(\\frac{2 \\pi}{3} n b^{2}\\right)^{\\frac{3}{2}}} r^{2} e^{-\\frac{3 r^{2}}{2 n b^{2}}}\\right)\n",
    "$$\n",
    "\n",
    "If we let $\\frac{d w_{t; i}^{t+c;j}}{d r}=0$, we see that the maxima can be found at:\n",
    "$$\n",
    "\\frac{4 n b^{2}}{6}=r^{2}\n",
    "$$\n",
    "\n",
    "Substituting $n b^{2}=2 l_{p} \\tau L$, we see that:\n",
    "\n",
    "$$\\frac{4}{3} l_{p} \\tau L=r^{2}$$\n",
    "\n",
    "The maxima of the bond probability can be found at $\\sqrt{\\frac{4}{3} l_{p} \\tau L}$. \n",
    "\n",
    "As an example, if we plot the bond probability for a range of $r$, assuming a fixed persistence length of $l_{p}$ = 150 bp and a fixed genomic distance of $L$ = 1 Mb:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "So a common pitfall is thinking any distance less than the contour length $\\tau L$ is also penalized. We see that the maxima is less than the contour length - which allows the Gaussian chain to model DNA behavior. For instance, it is quite probable that a two loci separated by 1 Mb long might \"loop\" back such that, while genomically distant, they are spatially proximal. This bond probability accounts for such behavior.\n",
    "\n",
    "#### Works Cited\n",
    "\n",
    "- Bower, D. An introduction to polymer physics. 74-75 (Cambridge Univ. Press, 2002)."
   ]
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