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@tillahoffmann
Created December 25, 2017 08:11
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt, rcParams\n",
"from tqdm import tqdm_notebook\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"rcParams['figure.dpi'] = 144"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Individual examples"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def plot_matrix(x, **kwargs):\n",
" vmax = max([np.max(_x) for _x in [x.real, x.imag]])\n",
" \n",
" fig, axes = plt.subplots(1, 2)\n",
" \n",
" for ax, part in zip(axes, ['real', 'imag']):\n",
" ax.set_title(part)\n",
" _x = getattr(x, part)\n",
" mappable = ax.imshow(_x, cmap='coolwarm', vmax=vmax, vmin=-vmax)\n",
" plt.colorbar(mappable, ax=ax, orientation='horizontal')\n",
" \n",
" return fig, axes"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def generate_matrix(num_blocks, block_size):\n",
" matrix = np.asarray([\n",
" [np.diag(np.random.normal(0, 1, size=block_size)) \n",
" for _ in range(num_blocks)] for _ in range(num_blocks)])\n",
" matrix = np.rollaxis(matrix, 2, 1)\n",
" matrix = np.reshape(matrix, (num_blocks * block_size,) * 2)\n",
" return matrix"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5,0.98,'matrix $M$')"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f2aef1ba8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(0)\n",
"num_blocks = 3\n",
"block_size = 10\n",
"matrix = generate_matrix(num_blocks, block_size)\n",
"\n",
"fig, _ = plot_matrix(matrix)\n",
"fig.suptitle('matrix $M$')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5,0.98,'eigenvectors')"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f2ad6b860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"evals, evecs = np.linalg.eig(matrix)\n",
"\n",
"fig, _ = plot_matrix(evecs)\n",
"fig.suptitle('eigenvectors')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x7f9f282e9cf8>,\n",
" array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f9f2ac822b0>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7f9f2ac37cc0>], dtype=object))"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f282e9cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_matrix(np.linalg.inv(evecs).dot(matrix).dot(evecs))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"real 90\n",
"imag 28\n",
"both 28\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f280a62e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"threshold = 1e-8\n",
"\n",
"fig, axes = plt.subplots(1, 2, True, True)\n",
"fig.suptitle('eigenvector elements')\n",
"\n",
"for ax, part in zip(axes, ['real', 'imag']):\n",
" x = np.sort(getattr(evecs, part).ravel())\n",
" neg = x[x < 0]\n",
" pos = x[x >= 0]\n",
" ax.plot(np.arange(neg.size), - neg, color='C3')\n",
" ax.plot(np.arange(pos.size) + neg.size, pos, color='C0')\n",
" ax.set_yscale('log')\n",
" ax.axhline(threshold, color='k', ls='--')\n",
" ax.set_title(part)\n",
" \n",
" print(part, np.sum(np.abs(x) > threshold))\n",
" \n",
"print('both', np.sum((np.abs(evecs.real) > threshold) & (np.abs(evecs.imag) > threshold)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Block diagonalisation \n",
"\n",
"Suggested by [`kimchi lover`](https://math.stackexchange.com/users/457779/kimchi-lover)."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x7f9f23fae710>,\n",
" array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f9f2ac199e8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7f9f23ee5160>], dtype=object))"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f23fae710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"idx = (np.arange(num_blocks)[None, :] * block_size + np.arange(block_size)[:, None]).ravel()\n",
"\n",
"block_matrix = matrix[:, idx][idx]\n",
"\n",
"plot_matrix(block_matrix)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5,0.98,'eigenvectors')"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f23eda5f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"evals, evecs = np.linalg.eig(block_matrix)\n",
"\n",
"fig, _ = plot_matrix(evecs)\n",
"fig.suptitle('eigenvectors')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Ensemble properties"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "21d843b1493b4028bb9eadd4d43e2d2e",
"version_major": 2,
"version_minor": 0
},
"text/html": [
"<p>Failed to display Jupyter Widget of type <code>HBox</code>.</p>\n",
"<p>\n",
" If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
" that the widgets JavaScript is still loading. If this message persists, it\n",
" likely means that the widgets JavaScript library is either not installed or\n",
" not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
" Widgets Documentation</a> for setup instructions.\n",
"</p>\n",
"<p>\n",
" If you're reading this message in another frontend (for example, a static\n",
" rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
" it may mean that your frontend doesn't currently support widgets.\n",
"</p>\n"
],
"text/plain": [
"HBox(children=(IntProgress(value=0, max=600), HTML(value='')))"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"num_runs = 20\n",
"list_num_blocks = np.asarray([1, 2, 3, 4, 5, 6])\n",
"list_block_size = np.asarray([10, 20, 30, 40, 50])\n",
"\n",
"shape = (len(list_num_blocks), len(list_block_size), num_runs)\n",
"total = np.prod(shape)\n",
"\n",
"reals = []\n",
"imags = []\n",
"\n",
"with tqdm_notebook(total=total) as progress:\n",
" for num_blocks in list_num_blocks:\n",
" for block_size in list_block_size:\n",
" for run in range(num_runs):\n",
" matrix = generate_matrix(num_blocks, block_size)\n",
" _, evecs = np.linalg.eig(matrix)\n",
" reals.append(np.sum(np.abs(evecs.real) > threshold))\n",
" imags.append(np.sum(np.abs(evecs.imag) > threshold))\n",
" progress.update()\n",
" \n",
"reals = np.asarray(reals).reshape(shape)\n",
"imags = np.asarray(imags).reshape(shape)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f9f234234e0>,\n",
" <matplotlib.lines.Line2D at 0x7f9f2342bcf8>,\n",
" <matplotlib.lines.Line2D at 0x7f9f2342be48>,\n",
" <matplotlib.lines.Line2D at 0x7f9f2342bf98>,\n",
" <matplotlib.lines.Line2D at 0x7f9f23434128>,\n",
" <matplotlib.lines.Line2D at 0x7f9f23434278>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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w8MP3nLhT/4H0GflrDzOqvFT8i4icYfu3Z7FvWxYAYeGGrgOaepyRiEj1kbJuNV+9+rwTN+vclUG33aUFFY5Bxb+IyBm2osyof9tzkomvFe1hNiIi1cfB3SlMe+av+H0lANRt0oyr7n+E8IhIjzOrvFT8i4icQYfS8ti+8oATd79Em3qJiFSE3EOZTB7/OIW5uQDE16rNiDFjiYnXrunHo+JfROQMWvVNCtjA78061aVuY70piYicruKCAqZMeJLsA2kAREbHMHz04yTU1xLKP0fFv4jIGZJ/uIgN3+1z4h6XatRfROR0+f0+Pn9hIqnbtwBgTBhX3jua5JatPc6salDxLyJyhqyZtwdfsR+A+s1q0rhtLY8zEhGp2qy1zHnnDbYv+8Fpu/iWO2h5dm8Ps6paVPyLiJwBxUU+1szd7cQ9BjXTyhMiIqdp+ZfTWPnV507c66oRdL/0Cg8zqnpU/IuInAGbvttHQU4xADXrxNDq7PoeZyQiUrVtXryQuf96y4nbnncB/X59k3cJVVEq/kVEKpjfb1n5TYoTdxvYlLBwXW5FRE7V3s0bmP7iM2ADKyg0atuBwX+4HxOma+vJ0j8xEZEKtmPVAbIO5AMQHRdBh/MbepyRiEjVlbl/L1Mn/oWS4iIAajdsxNAHHyUiKsrjzKomFf8iIhVsZZlNvTr1a0xUTISH2YiIVF35h7OZMn4s+YezAYipmcDwMWOJS0j0OLOqS8W/iEgF2rf1EPu3B96kwiIMXQc08TgjEZGqqaSoiKmTniJz314AwiMjGfbgY9Ru0MjjzKq2Cin+jTEjjTEvGmMWGGOyjTHWGPPeMZ7bIvj4sX7eP04/NxpjfjDG5Bhjsowxc40xVx7n+eHGmPuMMauNMfnGmAxjzJfGmL4V8XeLiBxtRZlR/3bnNiA+MdrDbEREqibr9zP9lefYu2l9oMEYrrhrFI3bdfA2sWqgor6LfhToBuQAu4H2J3DOKmBqOe1ry3uyMeZpYFTw9d8AooDrgM+MMXdba1866vkGeB8YCWwCXgLqANcC840x11hrp51AniIiJyRzfy47Vqc7cfdLtKmXiMipWPD+u2z+boET97/+Ztqed4GHGVUfFVX830egKN8K9AfmnMA5K621Y0/kxYMj9aOAbUBva21msH0SsAx42hjzubV2Z5nTriNQ+C8CBlprC4LnvAZ8C7xhjJltrT18IjmIiPyclbNSILAQBS261KVOw3hvExIRqYJWzZzOkmkfO3H3y4bQ88rhHmZUvVTItB9r7Rxr7RZrg+svVbw7gse/Hin8g/3uBF4GooGbjzrnzuDx0SOFf/CcJcAHQH0CHw5ERE5bXnYRm77b78TdB2nUX0TkZG1fsYRZb73qxC3P7s2AG2/TJokVyMsbfhsZY243xjwSPHY9znMvDh5nlPPY9KOegzEmBugL5AELTuQcEZHTsWbubnwlfgCSmtekUZtaHmckIlK1pG7fyufPTcDawLU0uWVrrrxnNGHh4R5nVr14uf7coOCPwxgzF7jRWvtjmbZ4oDGQY63dV87rbAke25ZpawWEA9uttSUneI6IyCkpLvSxZt5uJ+5xaXONUomInITs9DSmTHyS4sLAZI2E+kkMH/04kTExHmdW/XhR/OcBfyFws+/2YFtXYCwwAJhljOlurc0NPnZkIdesY7zekfayw2yncs4xGWOWHeOhE7mxWUSquY3f7aMwNzDOkFAvhpbd63mcUWjTNVukainMy2XK+CfIzcwAIDounuGjHye+Vm2PM6ueXJ/2Y61Ns9b+2Vq73Fp7KPgzH7gUWAy0Bn7rdl4iIqfC77es/KZ0ec9uA5sRFq4tVEREToSvpJhPn/lf0lN2ARAWHsHVo/5EvabNPc6s+qo0205aa0uMMW8C5wL9gOeDDx0ZpT/WVm5H2g+VaTuVc46XW8/y2oOjS2efyGuISPW0fcUBstMDX1NHx0fQoW9DjzMSXbNFqgZrLTP//hI/rl3ltF12xx9p1vl4t4HK6apsw1MHgkdnfbzg9J89QA1jTHnvqm2Cx81l2rYBPqClMaa8DzjlnSMiclKstaz4epcTd+nfhMho3ZgmInIivv/kfdbNm+XEfX95PR37aS2WM62yFf/nBY/bj2qfHTxeXs45g496DsGlPRcBccCFJ3KOiMjJ2rf1EGm7AluFhEeE0eWiJh5nJCJSNaybN4tFH/3biTv1v4TzRlznYUahw/Xi3xhztjHmv/o1xgwksFkYwHtHPfxa8PgnY0ztMue0AP4AFAL/OOqcI4vEPhVc+vPIOb0J7PJ7APjk1P4KERFY8XXpXP925zUgLiHKw2xERKqGH9eu4uvXX3DiZl26M+i2u7RKmksqZM6/MWYYMCwYNgge+xhj3gn+nm6tfSD4+7NAG2PMIgK7AkNgtZ8j3/M8Zq1dVPb1rbWLjDHPAvcDq40xHwNRBIr4OsDdR+3uC/A+MILARl4rjDGfAXWD54QDv7PWZp/6Xy0ioSxjXy471xwMBAa6X9LU24RERKqA9JRdfPrM/+L3+QCo17Q5V9//MOERleY21Gqvov5JdwduPKqtZfAHYBdwpPj/FzAc6E1g+k0kkAp8CLxkrS1vUy6staOMMWsIjPTfBviB5cAka+3n5TzfGmN+RWD6zy3A3UABMB946ugPGCIiJ6PsCj9nda1H7Qbxx3m2iIjkZGYwefxYCvMCq7nH167D8DFjiY7T9dNNFVL8W2vHElin/0Se+xbw1in28w7wzkk8vwR4LvgjIlIhcrMK2bR4vxN3H9TMw2xERCq/ooJ8pkx4gsPpgbVdImNiGT76cRLq1fc4s9BT2W74FRGp9NbM2Y2/xAKQfFYCDVsda1VhERHx+3x88fxE0nZsA8CEhXHVvaNJPquVx5mFJhX/IiInoaighLXz9zhxj0HNdJOaiMgxWGuZ/Y/X2b58idM28JY7OatHLw+zCm0q/kVETsKGRfsozCsBILF+LGd19/Yra2utp/2LiBzP0s+nsGrml07ce+hIug0afJwz5EzTrdUiIifI7/OzalaKE3e/pClhYd6O+qeOG4c/J5f6995DZFKSp7mIiJS16btvmf/e207crm8/LrzuNx5mJKCRfxGRE7Zt+QEOHywAIKZGJO36lLfpuHsKt20j89//IWvyZLZdPpiinTs9zUdE5Ig9G9cz/eVnnLhx+45cfue9mDCVnl7TvwERkRNgrWXFzNLlPbv0b0xkVLiHGUHqhAkQXCs7tnNnIps39zQfERGAzH17mPr0U/iKiwGo3bAxQx94lIgobYRYGaj4FxE5AXs2H+LAj4cBCI8Mo8tFTTzNJ2fBAnLnB7dFMYbkh8foxmMR8VxedhaTx4+l4HBgH9XYhERGjBlLbM0EjzOTI1T8i4icgJVlRv3b92lIbE3vRrBsSQmp4yc4ca2R1xDToYNn+YiIABQXFTJ10l84tH8fABGRUQx78DFqNfB2iqT8lIp/EZGfcXBvDrvWHgwEBroPbOppPpkffEDRtsB62WHx8dS/5x5P8xERsX4/M156ln2bNwYajOGKux+gUdv23iYm/0XFv4jIzyg76t+yW31qJcd5losvK4v0F1504rq3305EvXqe5SMiAjD/P++wefFCJ77ohltpc25fDzOSY1HxLyJyHLmHCtn8Q6oT97i0mYfZQPorr+DLygIgsnFj6tyoZfNExFsrv/qCpZ9NduIel1/F2VcM9TAjOR4V/yIix7F6Tgp+X2AjrYatEmnQMtGzXAq37yDj3/9x4qQHHyQsOtqzfEREti1bzOx/vO7ErXqdy0U3/lYLEFRiKv5FRI6hqKCEtfP3OnH3Qd6O+qdNmgQlgd2FY3v1pOZll3qaj4iEttTtW/n8+YlY6wcguWUbhtz9IGFh3i6DLMen4l9E5BjWf7uXovxAsZ2YFMtZXb2bW5+zcCE5c+YEAmNIHvOwRtZExDPZB9KYMuEJSgoLAUion8zw0X8mMibG48zk56j4FxEph8/nZ9WsFCfufkkzTJg3xbYtKSGtzNKeicOGEdu5kye5iIgU5OYwefxYcg9lAhAdH8+IMWOJr1Xb48zkRKj4FxEpx7ZlaeRkBka0YmtG0v68Bp7lcujjjyncsgUAExdH/Xvv9SwXEQltvpJiPn3mfzm4O7AKWlh4BEMfeJS6TbxdAllOnIp/EZGjWGtZUWZ5zy4XNSEiyps5rL7Dhznw/AtOXO+23xGZnORJLiIS2qy1fP3aC6SsW+20XX7nPTTt2MXDrORkqfgXETnK7o2ZpKfkABARGUbn/o09yyX91dfwZQa+Wo9o1JA6N93kWS4iEtoWffQf1i+Y48TnX3sDHS4c4GFGcipU/IuIHKXspl4d+jYktkaUJ3kU7dpFxr/+5cRJo0YRppvpRMQDa+fM5PtP/s+Ju1x8KecO/6WHGcmpUvEvIlJG+u4cflyfAYAx0O0S7+axpk6aBMXFAMR2707CFVd4louIhK5dq1cy842XnLh51x4MvPX3WnGsilLxLyJSRtlR/5Y96pNYP86TPHK/X0zON7OcOPkRLe0pIu478ONOPn32f/H7fADUb9aCq+57mPCICI8zk1Ol4l9EJCgns4AtS1Kd2KtNvazPR+r48U6cOPRqYrt29SQXEQldORkHmTL+CYry8wCoUacuw8eMJTrOm0ERqRgq/kVEglbN3o3fbwFo2DqRBmclepLHocmTKdy4EQATG0v9++7zJA8RCV1F+XlMnvAEhw8eACAyJpbhox+nZl3vNjuUiqHiX0QEKMwvYd2CPU7c49LmnuThy8nhwN+ed+K6t95KZAPv9hgQkdDj9/n4/PmJHNi5HQATFsbV940hqUVLjzOTiqDiX0QEWL9gL8UFgTmttRvE0aJzXU/yOPj66/gOHgQgokED6t56iyd5iEhostYy6+1X2bFiqdN2yW//QIvuPT3MSiqSin8RCXm+Ej+rZqc4cfdLmmHC3L+5tiglhYx3/unESaPuJyw21vU8RCR0Lfn0E1Z/M8OJzx3+S7oOvMzDjKSiqfgXkZC3dWkquYcKAYhNiKLtucme5JH29DPY4NKeMd26kjBkiCd5iEho2rhoPgv+844Ttz+/P+dfe4N3CckZoeJfREKatZYVZZb37HpREyIiw13PI2/JEg5/9ZUTJ48ZgwnTJVpE3LF74zpmvPysEzfp0JnL7rxXSwxXQ3pnEZGQlrI+g4N7cgGIiA6nc//GrudgfT72jxvnxAlDhhDXo4freYhIaMrYu5tpk57CV1ICQO1GTbj6gT8RERnpcWZyJqj4F5GQVnbUv2PfhsTEu/9mlzV1GoXrNwBgoqNJGnW/6zmISGjKy85i8vixFOQcBiAusRbXPDyW2Bo1Pc5MzhQV/yISsg78eJjdGzMBMAa6DWzqeg7+3FzS/vacE9e99RYiGzVyPQ8RCT3FRYVMnfgkWan7AYiIimbYQ4+RmKTlhaszFf8iErJWflM66t+qZxIJ9dxfWSf9jTfwHUgHICIpibq33up6DiISevx+H9NffIZ9WzYFGoxhyB8fpGHrdt4mJmecin8RCUmHMwrYsjTNiXsMauZ6DsV79pDx9j+cuP599xEWH+96HiISeua/9w+2/LDIiQfc+Dta9z7Pw4zELSr+RSQkrZqVgvVbABq3rUVS8wTXc0h75hlsUREAMZ06kTj0atdzEJHQs2LGZyz7YqoTn33FUM4erOtPqFDxLyIhpzCvmPXf7nXi7h6M+uctX072l9OdOPmRh7W0p4iccVuXLmbOO284cevefeh/g3YSDyV6pxGRkLNuwV6KC30A1G4YT/NOdV3t3/r9pI4b78Q1B19OXM+eruYgIqFn/9bNfPH8RKz1A9CwdTuuuHsUYWHu720i3lHxLyIhxVfsZ9XsFCfuMagpJszdTWyyP/uMgjVrADBRUSSNesDV/kUk9GSl7WfKxCcpKQrsZp6Y3IBhDz1GZHSMx5mJ21T8i0hI2bwklbyswDz7uMQo2vZ2d0k7f14eac+U7qJZ56abiGri/sZiIhI6CnJymDz+CfKyDgEQE1+DEWPGEpdYy+PMxAsq/kUkZFhrf7K8Z9cBTQiPdPcyePDNtyhJC6wyFF6vHnVvu83V/kUktJQUFzPtmafI2BP4xjN4yLlpAAAgAElEQVQ8IoKhDz5KnUZNPM5MvKLiX0RCxo/rMsjYmwtAZHQ4nfu5O+JevG8fB99+24mT7ruX8Bpa2lNEzgxrLV+/9jy716912i7//X006dDZw6zEayr+RSRkrJi5y/m94/mNiI6LdLX/tGefwxYUABDdsQOJw4a52r+IhJZFH77Hhm/nOvEFv7qR9uf39y4hqRQqpPg3xow0xrxojFlgjMk2xlhjzHvHeG4bY8xoY8xsY0yKMabIGJNqjJlmjBlwjHNuCr7msX7uOMZ5scaYJ4wxm4wxBcaYNGPMh8aYDhXxd4tI1ZG2K5s9mwLzXU2YoetAd7/yzl+5kuzPPnPi5DFjMOFaYUNEzow1c77m+8kfOHHXgZdzztCRHmYklUVEBb3Oo0A3IAfYDbQ/znP/AlwLrAe+BDKAdsDVwNXGmHustS8c49xpwMpy2pce3WCMiQZmAucHH38eaAr8AhhijLnYWrv45/80EakOVs4snevfumcSCXVjXevbWsv+ceOcuOagQcSfc45r/YtIaNm5ajkz//6SE7fo3pOBt96JMe6ubCaVU0UV//cRKPq3Av2BOcd57gxggrV2RdlGY0x/AsX6JGPMR9bafeWcO9Va+84J5nQ/gcL/Y+BaG1zU1hjzATAVeNsY0+VIu4hUX9np+WxdfsCJe7i8qVf2519QsGo1ACYykqQHtbSniJwZB3bt4LPnxmH9gfKmfouWXHXvaML0TaMEVci0H2vtHGvtFmutPYHnvnN04R9snwfMBaKAvqeTjwl8tD0yFeihsgW+tXYasADoSOCDiohUc6tmpWD9gctTk/a1qd+spmt9+/PzSXu2zNKeN/6GqGbu7ygsItXf4Yx0Jo8fS1F+PgA16tZjxOjHiYqN8zgzKctX4u24c2W74bc4eCw5xuPdjTH3GmPGGGNuMMYca9JuK6AZsNlau6Ocx6cHjxefRq4iUgUU5BazflHpF4luj/of/Mc/KNkX6D+8Th3q3lHuLUoiIqelMC+PKeOfICfjIABRsbGMGDOWGnXc3cFcju/gnhz+74nF7Fyd7lkOFTXt57QZY5oDA4E8YP4xnnbPUbHPGPMmcK+1tqBMe7vgcfMxXmdL8Nj2BHNbdoyHjndvg4hUAqtnp1BS6AOgbuN4mnas41rfxampHHzjTSeuf889hNeo4Vr/oUrXbAk1vpISPv/beA7sCox3hoWHc9X9j1C/WQtvE5Of2LI0ldnvbqCkyM/Mt9cxckwvajdwf7nnSjHyH7w5999ANDDWWpt51FN2AHcTKOrjgUbAL4GdwO3A20c9PzF4zDpGl0fatbWdSDWWe6iQFWVu9O0xqJmrN7wdePY5bPDr9+h27ag18hrX+haR0GCtZdbbr7Jz1XKnbdDv7qJF1x4eZiVl+f2W76Zs5es311FSFJjy47eQfbDgZ848Mzwf+TfGhAP/InBz7gfA00c/J3g/wLwyTXnAR8aY74FVwK+MMROstavORI7W2p7ltQdHl84+E32KyOlb/Nl250Jbt3EN2pzTwLW+89esJWvaNCdOflhLe7pF12wJJT9M/Yg1s75y4vOuuY7OAwZ5mJGUVZBbzNdvrSNlfYbTlpgUy+A7ulC3kTffBHta/AcL//cILL/5IfA/J3LT8BHW2hRjzJfA9UA/Ah8EoHRkP7HcE0vbD5100iJSJaTvzmFDmbn+51/TmrAwd0b9rbWkllnas8bAgcSfd54rfYtI6Njw7Vy+ff9dJ+5w4QD6/uJ6DzOSstJ3H2b6a2vITi8d4W/epS6Dbu7o+iaTZXlW/BtjIglM9fkF8B/gN9Za3ym81JH1+8pOmtoUPB5rTn+b4PFY9wSISBVmrWXRJ1sgOJTQrFNdV+f6H54xg/zlwa/gIyNJ1tKeIlLBdq9fy1ev/s2Jm3bswmV3/FFr+VcSW5YE5/cXl67s0+uKFpxz5VkYlwaijsWT4t8YE0VgpH8o8C5w82mst39u8Li9TNs24EegrTHmrHJW/BkcPM4+xT5FpBL7cX0GKRsCtw4ZA32vaeVa3/6CAtImlc5erHP99US1aOFa/yJS/R3ck8K0p5/CVxJYHLFO46ZcPepPhEd4N5osAX6fn++mbv/JxpKR0eFcclNHWvao72FmpVy/4Td4c+8UAoX/W5xA4W+M6VVOW5gx5mGgD5BOYPMwAIJTh14LhhONMWFlzhsKXEhgh+Gy9xGISDXg9/lZ9MlWJ+5wQSNX51VmvPNPivfuBSC8Vi3q/f5O1/oWkeov91AmU8aPpSA3B4C4xFqMGDOWGK0k5rmCnGI+e3HVTwr/WslxjBzTq9IU/lBBI//GmGHAsGB45I66PsaYd4K/p1trj3zv/RpwBYGCfQ/w53K+opprrZ1bJl5ijFlLYE7/HgJz9s8HOhO4+fd6a232Ua/xLHAlMBJYbIyZRWDt/18Ez7lFu/uKVD8bFu0jY28uEBhtOefKs1zruzgtjYN//7sT17/nj4QnJLjWv4hUb8WFBUyd9Bey0lIBiIiOZvjox0lMSvY4MzmQEpjff7jMCj4tutbjkps7Eh3r+fo6P1FR2XQHbjyqrWXwB2AXcKT4P/JOXA/483Fec26Z358GziGwKVcdwE9gWs/LwLPW2u1Hn2ytLTTGDALGAL8C7gOyganA49ba9Sfyh4lI1VFUUMLiz0pn+Z19WTPiE6Nd6//A88/jz8sDILpNa2r94heu9S0i1Zvf7+PLF59m/9bA7YrGhHHlPQ/RoFWbnzlTzrTNP+xnzr82/mR+f+8hLeg9xPv5/eWpkOLfWjsWGHuCz73oFF7/wZM9J3heHoEPGMf7kCEi1cSKr38kP7sIgPha0XS7xL3dfPPXrSNr8hQnTho9BhNRuUZ7RKTqmvfuW2xd8r0TD7j5Nlr1PPc4Z8iZ5vf5WTRlG6u+SXHaImPCGXRzR87qVnmm+RxN70wiUi3kZBb8ZJ7leUNbEhnlzrr61lrSxo2H4ErFNfr3p8YF57vSt4hUf8u/nMby6Z86cc8rh9Pjsis9zEjyDxfx1Zvr2LOpdF/a2g3iGHxHF0927T0ZKv5FpFpY/Ol25yvXek1r0O5c9zb0OjxzJnlLlwaCiAiSRj/kWt8iUr1tWfIdc95904nbnNuX/tff7GFGcuDHw3z52mpyMgqdthZd6zHo5o5EVbL5/eWp/BmKiPyMAymH2fj9fic+/5rWrs2z9BcVkTZxkhPX/vWviG7Z8jhniIicmH1bN/HlC0873yo2bNuewXeNwoS5vlijBG1avJ85723EV2Z+/zlXnUWvwS0q5fz+8qj4F5EqzVrLwo+3Oht6tehSlybt3dvQK/PddynevRuAsMRE6v/+9671LSLV16HU/UyZ8CQlRYHR5VrJDRn24GNERrm3iIGU8vn8fPfJNlbNLp3fHxUTzqBbOtGiaz0PMzt5Kv5FpErbtfagM+fShBn6jGjtWt8l6emkv/qaE9e/6y7Ca9VyrX8RqZ7ycw4zefxY8rOzAIipmcCIh8cSl5DocWahKS+7iK/fXMuezYecttoN4rjizq7USo7zMLNTo+JfRKqsozf06nRBI+o0dO9GqwPPv4A/N7CnQFTLltS+7lrX+haR6qmkuJhPn/4rmXsD3yiGR0Yy7IFHqd2wsceZhaa0XdlMf20NOZml8/tbdq/PwJs6EBVTNcvoqpm1iAiwfuE+MvcH1tWPjAmnt4sbehVs3MihTz5x4uQxozGRka71LyLVj/X7+erVv7F7w1qnbfAfRtG4fUcPswpdG7/fx9z3NuErCc7vN3DuVS3peXnzKjO/vzwq/kWkSirKL+GHz0r39+t5eXPiEqJc6dtaS+q48eAPvCHEX3ABNfr1c6VvEam+Fn74HhsXznPiftffTLs+F3iYUWjy+fws/Hgra+bsdtqiYiMYdEtHWnSpWvP7y6PiX0SqpOVf7SL/cDEANWpH0+3ipq71nTN7NnmLFweC8HCStbSniJym1bNmsHjKh07cbdBgel01wsOMQlNedhFfvbGWvVvKzO9vGM8Vd3SpkvP7y6PiX0SqnMMZBaycVbriwnnDWhHh0oZe/qIiUidMdOLa115LdJs2rvQtItXTjpXL+ObNV5y45dm9ufjmOzCm6k4tqYpSd2Yz4/Wfzu9v1aM+F99Ydef3l6f6/CUiEjIWT9vurLFcv1lN2vZOdq3vzPf+TfGPgZ2EwxISqHf3Xa71LSLVT9rO7Xz23HhscBph0lmtGHLPQ4SFuzOgIQEbFu1j3n9+Or//vKEtOfuy5tXuQ5iKfxGpUtJ2ZbNpsTcbepVkZJD+6qtOXP8Pvyeidm1X+haR6ufwwXSmjB9LcUE+ADXr1mf46MeJion1OLPQ4Svxs/CjLayZt8dpi46LYNCtnWjeqa6HmZ05Kv5FpMqw1v5kac8WXevRuJ17xfeBF1/Ef/gwAFHNm1P7V79yrW8RqV4K8/KYMn4sOZkZAETFxjFizOPUqO3eJoWhLjerkK/eWMu+rVlOW51G8Qy+owu1kqrH/P7yqPgXkSpj5+p0Z5OVsDBD3xGtXOu7YPNmDn1QejNe0ujRmCh3VhcSkerFV1LCZ8+N48CPOwEICw/n6lGPUK9ZC0/zCiX7d2Qx4/W15B4qM7//7CQu/k37ajW/vzzV+68TkWrD5/OzaPI2J+7UrzG1G7izoZe1lrTxE0qX9uzbhxoDLnKlbxGpXqy1fPPmK+xavcJpu/T2P9K8S3cPswot6xfuZd7/bcJfYgEwJrBwRI9Lm1W7+f3lUfEvIlXC+gV7OZQa2NArKiac3kNauNZ3zrx55C5aFAjCwkgaPSYk3iBEpOItnvIha+d87cR9Rv6aTv0HephR6PCV+Fnw4RbWzf/p/P5Lf9uJZh2r5/z+8qj4F5FKrzC/hB8+3+HEPQe3ILamSxt6FRcHRv2Dav3yF8S0a+tK3yJSvWxYMIeFH/zLiTv1H0ifkbp3yA25WYXMeH0t+7eXzu+v2ziewXd0JbF+aN1greJfRCq95TN2UpAT2NCrZp0Yul7cxLW+M//v/yjauROAsBo1qP/HP7rWt4hUHynrVjPj1eeduFnnrgy67S59i+iC/duzmP76GvKyipy21r2SuPiGDkRGh96Sqir+RaRSy07PZ9Ws0i3WzxvekohIdy7WJZmZHHjpZSeud+edRNTRShwicnIO7k5h2jN/xe8rAaBuk2Zcdf8jhEdEepxZ9bduwR7mv78Zv690fn+f4a3pPqhpyH7wUvEvIpXa99O2O5uuJDWvSZue7m3olf7Sy/izswGIbNaM2jf8j2t9i0j1kHsok8njx1KYmwtAfK3ajHh4LDHxNTzOrHrzFfuZ/+Fm1i/Y67RFx0dw2a2dadoxtAdxVPyLSKWVuiObLUtSnfj8kW1c29CrcNs2Mt9/34mTH3qQMC3tKSInobiggCkTniT7QOA6Fhkdw/DRj5NQL8njzKq33EOFTH99Dak7sp22uk1qcMUdXUioF1rz+8uj4l9EKiVrLQs/2eLELbvXp1GbWq71nzphAvh8AMSdcw41Bmo1DhE5cX6/jy9enETq9sB1zJgwrrxvNMktW3ucWfW2b1sWM15fQ1526fz+Nr2TGXBDeyKjQm9+f3lU/ItIpbRjZbqz62JYmKHPcPc29MqZP5/c+QsCgTEkP6ylPUXkxFlrmfvPN9m2dLHTNvDWO2jZo7eHWVVv1lrWLdjLgg9+Or+/7zWt6TYwdOf3l0fFv4hUOr4SP4smb3Xizv0bUyvZna3WbXExqRMmOnGtkdcQ06GDK32LSPWw/MtprJjxmRP3umoE3QZd4WFG1Zuv2M/89zexfuE+py0mPpLLfteJJu1De35/eVT8i0ils3b+HrIO5AMQFRtB7yFnudZ35ocfUrQtsJNwWHw89e+5x7W+RaTq27x4IXP/9ZYTt+1zIf1+fZN3CVVzOZmFzPj7T+f312tag8G3a37/saj4F5FKpTCvmCVflG7o1WtwC2JquLMcni8ri/QXXnTiunfcTkS9eq70LSJV397NG5n+4jNgA9NOGrXryODf34cJC/M4s+pp79ZDzPj7WvLLzO9ve04yF/2P5vcfj4p/EalUlk7fRWFuYC3smnVj6DrAvQ290l95BV9W4D6DyMaNqfOb37jW96nafXg3+3P306tBL69TEQlph/bvY+rEJykpDhSitRs2YugDfyJCq4RVOGsta+ft4dsPt+D3B+f3hxnOv6Y1XS9uovn9P0PFv4hUGtnp+ayek+LEfYa3IjzSnRGzwu07yPj3f5w46cEHCYuOdqXvU1XkK+KBeQ+wIWMDd/e4m1s630KY0QijiNvyD2czefxY8g8Hpp7E1kxg+JixxCUkepxZ9VNS7GPe/21m46Iy8/trRHLZ7zrTpF1tDzOrOlT8i0il8d3UbfhLAqM4yWcl0Lqne2thp02cCCWBbxxie/Wk5mWXutb3qZq0ZBLrDq4D4OUVL3NRk4toXVvLCIq4qaSoiGlPP0Xmvj0ARERGMeyhx6jdoJHHmVU/OZkFTH9tDWm7Djtt9ZvVZPAdXahZJ8bDzKoWFf8iUins357F1qVpTnz+yDaufXWbs3AhOXPnBgJjSB7zcKX/2njGjhm8v6l0E7JRvUap8BdxmfX7mfHKc+zZuD7QYAyD7x5Fo7ZaIayi7d2SGZjff7jYaWt3XgMu+nU7IjS//6So+BcRz1lrWfhx6dKerc6uT8NW7nxdbktKSBs/wYkThw0jtnMnV/o+VTuzdvL4osed+JJml3B9h+s9zEgkNC14/102fbfAifv/zy20Pfd8DzOqfqy1rJm7h4UfHTW/f2Rrug7Q/P5ToeJfRDy3bfkB9m8PbugV7u6GXoc+/pjCLcEdOOPiqH/vva71fSryS/K5f9795JXkAdC0ZlOePP9JvQGKuGzVzOksmfaxE3e/bAg9hwzzMKPqp6TIx7z/bGLj9/udttiagfn9jdtqfv+pUvEvIp7ylfj5bkrpqH+Xi5qQWN+dDb182dkceP4FJ6532++ITHbvPoNTMW7xOLZkBj6sRIVF8Uz/Z6gZVdPjrERCy/YVS5j11qtO3LLnOQy46TZ9CK9AhzMC8/sP/Fg6vz+peU0uv13z+0+Xin8R8dSaubvJTi8AIDougl5XtHCt7/TXXseXmQlARKOG1LnpJtf6PhVTt05lytYpTjzm3DF0qKu5xSJuSt2xjc+fm4C1fgCSW7bmyj8+RFiY5p1XlD2bMvnqzZ/O72/fpwH9f92OiEj9cz5dKv5FxDMFucUs/XKnE/e6ogUx8e5s6FW0axcZ//qXEyc/8ABhMZV3NGlz5mb++v1fnXhIyyGMbDPSw4xEQk92ehpTJjxBcWFgwCKhfhLDRz9OZCW+dlQl1lpWz97Nwk+2YoPz+8PCDBf8sg2d+zfWNysVRMW/iHhm6Zc7KcwLLK+ZUD+WLhe5t6FX6qRJUBwYVYrt0YOagwe71vfJyi3OZdTcURT4AgVHy8SW/Pm8P+uNUMRFhXm5TBn/BLmZGQBEx8UzYsxY4mtp7nlFKCnyMfffm9i0+Kfz+y+/rQuN2tTyMLPqR8W/iHgi60Aea+buduI+w1oRHuHOBlW5339PzjeznDj54TGVtpC21vLEoifYmb0TgNiIWJ696FniIt25L0JEwFdSwqfPjiM9ZRcAYeERXD3qT9Rt0szjzKqH7IP5TH9tDekpOU5bUosEBt/emRq19a1KRVPxLyKe+G7KNvy+wNe6DVom0urs+q70a30+UseNd+LEoVcT27WrK32fig83fcj0ndOd+LHzHqNVLfdWQxIJddZaZv79JX5cs9Jpu+zOe2jWufJeN6qS3Zsy+eqNtRTklM7v79C3If1+1Vbz+88QFf8i4rp927LYtvyAE58/srVrI++HJk+mcNMmAExsLPXvu8+Vfk/FuoPrmLCkdA+Ca9pcw1WtrvIwI5HQ8/0n77Nu3jdO3PeX19PxwgEeZlQ9WGtZNSuFRZO3/WR+/4XXtqFTP83vP5NU/IuIqwIbem1x4ta9kmjQ0p0NvXw5ORz42/NOXPfWW4ls0MCVvk9WVmEWo+aOotgfGA1rX6c9Y84Z43FWIqFl3bxZLPro307cecAgzhtxnYcZVQ/FRT7m/GsjW5akOm2xCVFcfltnGrXW/P4zrUIm2BpjRhpjXjTGLDDGZBtjrDHmvZ85p68x5ktjTIYxJt8Ys9oYc68x5pjf8RhjrjTGzDXGZBljcowxi40xN/5MPzcaY34IPj8reP6Vp/q3isjp2bosjdQd2QCERRj6DHNvCsvB11/Hd/AgABENGlD31ltc6/tkWGt5bOFj7MnZA0B8ZDzP9H+GmAjNfRVxy49rV/H16y86cbMu3bnkt3/QiPRpyk7PZ/KkZT8p/JPPSuCXD/dW4e+Sihr5fxToBuQAu4H2x3uyMWYo8AlQAHwAZABXAc8B5wO/KOecu4AXgYPAe0ARMBJ4xxjTxVr7QDnnPA2MCub0BhAFXAd8Zoy521r70qn8sSJyanzFfr6bss2Juw5oSkK9WFf6LkpJIeOdfzpx0qj7CYt1p++T9e76d5mTMseJn+z7JM0SdGOhiFvSU3bx6TP/i98XWI2sXrMWXH3/w4RHaMLE6UjZkMHXb66jILd0fn/H8xvS77p2hEe6s+CDVFzxfx+BAnsr0B+Yc6wnGmMSCBTiPuAia+3SYPtjwGxgpDHmOmvt+2XOaQE8TeBDQi9r7c5g+5PAEmCUMeYTa+13Zc7pS6Dw3wb0ttZmBtsnAcuAp40xnx95LRE581bP2c3hg8ENveIj6DW4uWt9pz39DDa4tGdMt64kDBniWt8nY2XaSv627G9OfH2H67m0xaUeZiQSWnIPZTJ5/FgK83IBqFG7DsNHP050XLzHmVVd1lpWfpPCd5O3YgPT+wkLN/S7ri2dLmzsbXIhqEI+Zllr51hrt1h75F/pcY0E6gPvHyn8g69RQOAbBIA7jzrnFiAaeKlssR4s6P83GN5x1DlH4r8eKfyD5+wEXg6+3s0nkK+IVICCnGKWTt/pxL2HnEV0nDsbeuUtWcLhr75y4gYPP4wJq3yjTBkFGYyaN4oSGxht7FKvC6N6jvI4K5HQUVSQz5QJT3A4PbAgQWRMLMPHjCWhnjurkVVHxYU+Zr61jkWflBb+cQlRDLv/bBX+HvHi3e/i4HFGOY/NB/KAvsaY6BM8Z/pRzzmdc0TkDFnyxQ6K8gNFbWJSLJ37uXPRtz4f+8eNc+KEIUOI7d7dlb5Pht/6eWTBI6TlpQGQEJXA0/2fJjLcnQ9IIqHO7/PxxfMTSd2+FQATFsZV944mqUVLjzOrurLT8/lk4jK2LE1z2hq0TOCXj/SmYSt3FnqQ/+bF5LV2wePmox+w1pYYY3YAnYCWwIYTOGefMSYXaGKMibPW5hlj4oHGQI61dl85ORxZaqTtiSRsjFl2jIeOe2+DiAQcSs1j7bw9Ttx3eGvXNvQ69NHHFK4PXEpMdDRJo+53pd+T9cbqN1i4d6ETj7twHI1qNPIwo6pL12w5WdZaZr/zd7YvX+K0XXLr7zmrRy8Ps6raUtZn8NVbaynMLXHaOl3YiAt/2Vbz+z3mRfF/5KNe1jEeP9Je9pbvEzknPvi8vFPsQ0TOkO+mbMMfXMe5YetEzupez5V+i3btInXiRCeuc8vNRDaqfAX14n2LeWXVK058a+db6dekn4cZiYSWZZ9PYdXXXzjxOUNH0vWSyz3MqOqy1rLi6x/5fuq20vn9EYZ+12p+f2Wh29ZPgLW2Z3ntwdGls11OR6RK2bvlENtXlt3Qq40rS+XZkhL2jh6DzcsDIKplS+rdfvsZ7/dkHcg7wOj5o/FbPwA9k3tyV4+7PM6qatM1W07G5u+/Zd57bztxu779uOC633iYUdVVXOhj9rsb2LqsdJpPXGIUg2/v4tp+LvLzvCj+j4y6H+u/giPth446p17wsYPHOSfrqOPJ9CEiFcz6f7qhV5veySS3SHCl74Nvvkn+ypWBICKCRpMmEhZTudbJL/GX8ND8hzhYELis1Ympw8R+E4kI07iMiBv2bNrAly8948SN23fk8jvvrZQLAlR2WQfymP7aGg7uyXXaGrZK5LLbOhOfGH2cM8VtXvzXvSl4/K/59saYCOAsoATYfoLnNCQw5We3tTYPwFqbC+wBagQfP1qb4PG/7iEQkYqzZVkqabsOAxAeEcZ5w9y5cS5/7ToOvPSyE9e/6y5iO3Vype+T8crKV1iaGlj0zGCY0G8CSXFJHmclEhoy9+1h6qS/4AsuAVy7YWOGPvAoEVFRHmdW9fy47iAfjVv6k8K/c7/GDL2vhwr/SsiL4n928FjeZLp+QBywyFpbeILnDD7qOadzjohUkJJiH99PKf0M321gExLqnvlNtfz5+ex96CEoCdxkFtujB3V/e+sZ7/dkLdi9gDfWvOHEd3a/k/ManudhRiKhIy87i8njx1JwOLDbeGxCIiMefoLYmu58M1ldWGtZNmMnn720isK8wDU3LMIw4Ib29P91O9cWdpCT48W/lY+BdOA6Y4xzG70xJgZ4Khi+etQ5/wAKgbuCG34dOac28EgwfO2oc47Efwo+78g5LYA/BF/vH6f+Z4jI8ayevZvDGYENvWJqRHL25S1c6TftmWcp2h740GHi4mg0YTymku3KuS9nHw9/+7AT923Ul9u7Vr77EUSqo+KiQqZNeopD+wOLAUZERjHswceoldzA48yqlqKCEr56Yy3fT90OwRt742tFM2JUTzqeX/kWVpBSFfKOaIwZBgwLhkf+7+ljjHkn+Hu6tfYBAGtttjHmdwQ+BMw1xrxPYOfeqwks6fkx8EHZ17fW7jDGPAi8ACw1xnwAFBHYMKwJ8EzZ3X2D5ywyxjwL3A+sNsZ8DEQB1wJ1gLu1u6/ImZF/uIhlZTb0OufKs4iOPfMFeM63C8l87z0nTn54DFHNmp3xfk9Gsa+YB+Y/QFZh4NakpLgkxl04jlnlO9IAACAASURBVDCjETKRM836/cx4+Tn2bg6uJG4MV/zxARq11SqwJ+NQWmB+f8beMvP7Wydy2e80v78qqKh34+7AjUe1tQz+AOwCHjjygLV2qjGmP/An4BogBthKoFB/obydgq21LxpjdgZf5zcEvrVYDzxqrf1neUlZa0cZY9YQGOm/DfADy4FJ1trPT+1PFZGfs+TzHRQV+AColRxHxwvP/CiQ79Ah9j3yiBPXGDCAWiNHnvF+T9azy55l9YHVAISbcJ7u/zR1Yup4nJVIaJj/n3fY/P23TnzRDb+lzTl9Pcyo6tm19iAz317nTPMB6HJRE84f6d7+LXJ6KqT4t9aOBcae5DkLgStO8pzPgM9O8px3gHdO5hwROXWZ+3NZu2CvE/cd0Yrw8DP7hmCtZd8TT1CSFlheLrxOHRr+5UlXlhQ9Gd/s+ob3NpR+M3Hv2ffSI6mHhxmJhI6VX3/J0s8mO3GPwVfRc8hQDzOqWgLz+3ex+NPSaT7hEWH0/3U7OvQtb20Vqawq10RYEanyFk3ehg1u6NW4bS1adD3zG3plf/4Fh6fPcOKGT/2FiHrubCR2olKyU3hs4WNOfFHTi7ix09FfmIrImbBt2Q/Mfrv01sBWvc7jot/81sOMqpaighJm/XMD21eU7tlSo3Y0l9/e5f/Zu+/4pqr+geOfmzTde0AZLVB2WQIiyJA9FRFRURy42EN/oICiAooKAvpIUTYojwsHiCB7iiwBGWXPMlpG9x5pcn5/pNy0PChQkt40Pe/X63n1+Z6b5HyrNTm593u/p8TaN0u2Ixf/kiTZTOzJZGIOJ6hxyz417H723RgXx9X331dj/yefwKdDB7vOebdyTbmM3jaaDGMGAJW8KzG51WSHuzIhSc7o2rkzrPp8KqJgI73Q6jV5eOQb6HR6jTMrHVKuZbF6TjTJV6z1/RVr+tN1QH08fWVb1NJILv4lSbIJYRbs+OWMGtduHkq5KvY9IyTMZuLeehtzumUvAUNYGOXGjrPrnMUx9a+pHE+y3GBo0BmY0XYGfm5yt0tJsre0+OssnzqJ/FxL93DfkPI8NuY9DG6OteGfo4qJTmDDomPkZVvr+xu2r0zLJ2rYvZxTsh+5+JckySZO7b1G/MWCDb0MOpr3sv+GXklLlpC1Z48l0OmoOHUKem8vu897N1adW8VPp35S4zebvUm9YMfbcEySnE1OZgbLpkwkMyUZADcvLx4fNxEv/4DbPFMSZkv//j0rzxep72/3XG3qtJD1/aWdXPxLknTP8vNM7P71rBrf1zEMn0D7nlnLOXWK+E8/U+OgAQPwbNLErnPerXMp53h/l7UkqVvVbjxd+2kNM5KkssGUb+S3GR+RePkiAHoXF3q98Q5BlcM0zszx5WXns/GrY5w/ZC3h9A5wo/vgBna/miuVDLn4lyTpnh3afImMZMtldQ8fA026VrHrfOa8POLGjEXk5QHgHhlJyLChdp3zbmUZsxi1dRTZ+dkAVPWtysSWE2WdvyTZmRCC9XOjuHT0sDrWdcjrhEU20DCr0iH5aiZr5kSTfDVLHatUy1Lf7+Ej6/udhVz8S5J0T7LS8ti/9oIaP9AzAlc7b+iVEDWL3BMnAFDc3Kj4yVQUV8f5YBJCMHn3ZM6mWq6GuOndmNFuBl4GxypJkiRntOvn7zj2x2Y1bv30C9Rt3U67hEqJ84cT2LjoqLpHC0CjDmG07FMdnazvdypy8S9J0j3Zu+o8xoIPi4BQTyJb2bceNGvfPhIXLFDjcqNH41ajhl3nvFvLTi9j5TnrliTjm4+nVkAtDTOSpLLhyNaN7Pr5ezVu0KELDzz2pIYZOT5hFuxdHcPeVefVMb1BR/vn6lC7eaiGmUn2Ihf/kiQVW9KVTI7+WWhDrz417HqGyJSRQdzYcVCwCbhXywcJeO5Zu81XHCeSTvDRno/UuFf1XvSu2VvDjCSpbLhw+CAb5kWpcdVGTej4ylBZavcv8rLz2bD4WJEWzT6B7nQf3ICQcB8NM5PsSS7+JUkqtp3Lzlg39KodQJX6QXad79pHH2OMjQVA5+tLhY8+QtE5zuXojLwMRm8dTZ7Zci9CDf8ajG8xXuOsJMn5JVyM4bdPP8JsslyFDAmvyiOvj0PvIpc5/yT5aiarZ0eTcq1QfX/tALoOqIeHt+OUUUq2J/+rkCSpWC6dSOJCdKIlUKDVE/bd0CttwwZSly1T49AJ72EIdZxL0kII3tv5HhfTLd1FPF08+bTdp3i4eGicmSQ5t4ykRJZNmURetmUR6x0YRO9xE3Hz9NQ4M8d17mA8G786ppZsAjTqFEbL3rK+vyyQi39Jku6a2SzYWWhDrzrNQwkJs98l4vz4eK6+N0GNfR95BL+HH7bbfMXx3Ynv2HBhgxpPajmJan7VNMxIkpxfXk42y6e+T3piPACuHh70HjsBn6BgjTNzTMIs+Ov38+z7PUYdczHoaP98HWo94DgnUyT7kot/SZLu2qk9V0m4lAFYPjjsuaGXEIIr77yLKdmyUY9LaCih775jt/mK43D8Yabvm67GfWv3pVu1bhpmJEnOz2wyseo/U7keY+mqpeh09Hx9HOWq2n+DwdIoNzufjYuOEnPjii3gE1RQ32/HkzeS45GLf0mS7ooxz8TuFefU+L7O4XgH2G9Dr5SlP5KxbZsaV/z4I/R+fnab726l5qbyxrY3yDfnAxAZFMmYZmM0zkqSnJsQgs2L53D+wD51rNOrw6h6X1MNs3JcSXGZrJlbtL6/cp0Aur5aH3dvg4aZSVqQi39Jku7KoY0XyUwp2NDL15XGXcLtNldeTAzXpk5V48D+L+D14IN2m+9umYWZ8X+O50rmFQB8DD7MaDsDV728WU6S7Gnvb79waMMaNW7e+ykaduyqYUaO69zBeDYuPoYx11rf37hzOC0ei5D1/WWUXPxLknTHMlNz2b/uoho371kNV3f7vI2I/Hxix45FZFt2yHWtUZ2Q//s/u8xVXIuPLGbbZetVicmtJ1PZp7KGGUmS8zux8w+2f/eVGtdp1ZZWfZ/XLiEHJcyCv1adZ9/qGHXMxaCjwwt1qdmsvHaJSZqTi39Jku7YX6vOk19w9iiwohd1W9pvQ6+EefPIOXTYEhgMVPrkE3Tu9isvulv7ru4j6oC1p3j/yP50CO+gYUaS5PwunzjK2i8/U+PKdevTdcjrspf/TXKzjGxYdIwLR6z1/b7Blvr+4Mqyvr+sk4t/SZLuSGJsBsdLaEOv7OhoEr74Uo1DRozAPTLSLnMVR2J2ImP+GINJWL4I3RdyH681fU3jrCTJuSXFxbJi2mRMRiMAARUr8+gb43ExyJr1whLjMlgzO5rU+Gx1LCwykC6v1MPdS/6zkuTiX5KkO7Rz2dkbG+sSVjeA8MhAu8xjzs4mbsxYKNisx6NJE4JeedkucxWHyWxi7PaxxGdbWgsGuAUwre00DDr5oSpJ9pKVlsqyKRPIyUgHwNPPnz5vTcTDW57FLuzs39fZ+PVx9QotQJOu4TTvVR2dTl4dkSzk4l+SpNu6dCyJi0etG3q17FPTbpfZr0+bTt758wDoPD2pOHUKil5vl7mKY+7huey5sgcABYUpbaYQ6iX7Y0uSvRjzcvn1k/dJvXYVABdXN3qPeQ+/cvK/uxvMZsFfv51j/9oL6piLa0F9//2yvl8qSi7+JUn6V2azYEehDb3qPliB4MredpkrY/t2kr/7To3Lj38b17Awu8xVHDvjdjLn0Bw1HthwIC0rtdQwI0lybsJsZk3UDK6cPmkZUBQeHvkmoTVqaZuYA8nJNLJh0VEuHk1Sx3yD3ekxpCFBlezzXi2VbnLxL0nSvzqx6wqJsQUbernqaP6ofTbQyU9O5srb49XYu2NH/B5/3C5zFce1zGu8tf0tBJbap+ahzRnSaIjGWUmSc9v2zSJO/7VTjdv3H0CNZi00zMixJMZmsHpONGmF6vvDIwPpLOv7pX8hF/+SJP2jvJx89vxm3dCrcedwvPzdbD6PEIKrEyeRH2+po9cHBVHh/UkO08HDaDYy5o8xJOVYzqwFewQz5aEp6HWOU44kSc7mwNqV7P/9VzVu0qMXTbo/qmFGjuXM/utsWnJTfX+3KjR/NELW90v/Si7+JUn6Rwc3XiIrNQ8ATz9XGnepYpd50lauJH3dOjWuMPkDXIKC7DJXcUQdiOLv638DoFN0fPLQJwR7BGuclSQ5rzP79rDlq/lqXKPZg7R93nFu/NeS2SzYs+Icf68rVN/vpqfjC3Wp0bSchplJpYVc/EuSdEuZKbkcWG/9cGn+aAQGN9uf6TbGxXH1/Q/U2P+pp/Bp397m8xTXlotbWHxksRqPaDyCZqHNNMxIkpzb1bOn+X3mJwhhBqBCjdr0GDEanbzSZqnvX3iUi8cK1feHeNBjcANZ3y/dMbn4lyTplvasPEd+nuXDN6iSF3UetP2GXsJsJm7cW5gzLPcUGMLDKT92jM3nKa7YjFjG77Deh9CmUhteri/PPkqSvaRev8byqZPIz80FwK98KI+NeReDm+Ns8KeVhMsZrJlzmLSEHHUsvF4QnV+OlPX90l2Ri39Jkv5HwuUMju+8osYt+9SwSw1p0ldfk/XXX5ZAp6Pi1CnovLxsPk9x5JnyGL11NOl5lr7iFbwq8FHrj9Ap9tnYTJLKupyMDJZNmUhWagoA7l7ePD5uIp5+/hpnpr3T+66xeclx9YQMwP09qtLskWqyvl+6a3LxL0nS/9i57AwFTW0IrxdIeKTt6+9zTp4i/rPP1Dho0EA8Gze2+TzFNX3fdI4mHgXARefC9LbT8XeXixBJsod8o5HfZnxIUuwlAPQuLvR68x0CK1bWODNtmc2C3cvPcmDDRXXM4Kan44t1qd5Y1vdLxSMX/5IkFXHhaCKXCupJFQVaPl7D5nOY8/KIGzMGYTQC4F6vHiFDh9p8nuJaG7OW7098r8ajm46mYUhDDTOSJOclhGD93JlcOhatjnUb+n9Urltfw6y0l5NhZP3CI1w6nqyO+ZXzoMfghgRWdIwrpFLpJBf/kiSpzCYzOwtv6NWqol1uIkuYOZPck5ZNexQ3NypO+wTF4Bg1qzGpMUzcOVGNO1fpzLN1n9UuIUlycjt//Ibj27eocetn+lOnVVsNM9JewuV01syJLlLfX7VBEJ1eisTN0zHeK6XSSy7+JUlSHd95haS4TMDSOu6BntVsPkfW3r0kLlykxuXefBO3CPtsHHa3cvJzGLVtFJlGyz+DMJ8wJrV0nP0GJMnZRG9Zz+5lS9W4YcduPNDrCQ0z0t7pvQX1/cai9f0PPFINRdb3SzYgF/+SJAEFG3qtPK/GTbqE4+Vn2w29TBkZxI0dB8JyQ4FXq1YE9HvGpnPci4//+pjTyacBcNW5MqPtDHxcfTTOSpKcU8yhv9kwb5YaV72vKR1fGVJmv2ybTWZ2/XqOg4Xr+931dHoxkoj7QjTMTHI2cvEvSRIAB9ZfJDvNsqGXl58r93UOt/kc1yZ/iDEuDgCdnx8VPvoQRecY3XNWnFnBstPL1Hhc83HUDaqrYUaS5LziL5xn5WcfI8yWs9shVSPo+fpYdPqy2cs/OyOP9QuOcvmEtb7fv7wn3Qc3ILCCrO+XbEsu/iVJIiM5p8jZpua9qmNwte2HcNq69aT++qsaV5g4AUP58jado7hOJ59m8u7JavxIxCM8UbNslx5Ikr2kJyWwbMpE8rKzAfAOCqb32Pdw9fDUODNtxF+01PenJxWq728YbKnv95DLNGcjhCB940ZcAgLwvP9+TXKQf1WSJLHr17NqfWlwmDe1W4Ta9PWN169zdcIENfZ9tCe+3bvbdI7iyjJmMWrrKHJMlg/eCL8I3m3xbpktPZAke8rLzmL5lElkJCUC4OrhweNjJ+ATGKxxZto49ddVtvz3RJH6/maPVKNZj6qyvt/JCCHI2LqV+Kgoco8dx71BA6r+uFSTzxq5+JekMu7M/uuc2nNNjW29oZcQgivvvIMpxbJxj0uFCoS+847NXv9eCCGYuGsiMWkxAHi4ePBpu0/xNJTNM5CSZE+m/HxW/mcq8Rcs9xbp9Hp6jnqbkCq2byzg6MwmMzuXneXQpkvqmKu7nk4vRVKtkazvdyZCCDJ37CQ+aiY5hw6r4znR0WRs2YpPh/YlnpNc/EtSGZaelMPWb0+occ1m5QmrE2jTOVKWLiXzj+1qXPHjj9H7+tp0juL66dRPrDm/Ro3fbfEu1f2ra5iRJDknIQSbFs0m5uB+dazzgOFUbeg4G/uVlOz0PNYtOELsyRR1LCDUUt8fECrr+51J5u49xEdFkb1/f5Fxxd2dgH798LivkSZ5ycW/JJVRZrNg4+Jj5GblA+AT6E7bfrVtOkfu+fNcm/qJGge++CJeLZrbdI7iOpZ4jCl/TVHjPjX70LN6Tw0zkiTn9devPxG9aZ0at+jzNPXbd9YwI23EX0xn9ZzDZCTlqmPVGgXT6cVIXGV9v9PI+vtv4j+fSdaePUXGFVdX/Pv2JXjgAFxCtLvCI//SJKmM+nvdBeJOW848KQp0ftm2N5cJo5G4seMQBTf1udWsQcj/vW6z178XaXlpjNo6CqPZssNwncA6vNX8LY2zkiTndHzHNv78YYka123TnpZPlr2N807uvsKWb09iulHfr8ADj1Tj/u6yvt9ZZB8+TPzMKDL//LPoAYMB/yf6EDxoEIZQ295TVxxy8S9JZdDV86n8Vain//09qlKhhr9N50iYO4+cwwX1jQYDFadNQ+dm230DikMIwbt/vktsRiwAXgYvZrSdgZte+9wkydlcPnaEdV9+psZhkQ3oOnhkmbqh3lSwc/rhzZfVMVd3PZ1frkfVhmXzRmdnk3PsGPEzo8jYurXoAb0ev96PETx4CK6VK2mS261osvhXFOVFYPFtHmYWQugLHl8VOP8vj10qhHj6H+bqDwwDIgETcACYLoRYdXdZS5JzyMvJZ8PCowizZaOt0Ag/7u9R1aZzZB8+TMLs2Wpc7rWRuNepY9M5imvJsSVsvrRZjT9o9QHhvrbf00CSyrrE2EusmD4ZU76ltDCwUhiPjh6P3sWgcWYlJystj3Xzj6hXWQECKnjRY3AD/MvLxgKlXc6pUyREzSJ9w4aiB3Q6/Hr2JHjoEFyrVNEmuX+h1Zn/g8CkfzjWBugArLnFsUPAr7cYP3KrF1IUZTowGrgMzAdcgaeBlYqijBBCzLrV8yTJmW3/4RRpCZa2lpazT5Ho9LbbaMuclUXcm2PAZALA4/6mBL70ks1e/14cvH6Q/+z/jxo/V/c5Olcpe3XHkmRvWakpLJ8ykZzMDAA8/fx5fNxE3L29Nc6s5Fy/kMaaOdFkJFvr+yPuC6Hji3VxdZeFF6VZ7rlzJMz6grQ1a9Qd6wFQFHy7dyd4+DDcIiK0S/A2NPnrE0IcxPIF4H8oirKr4P/Ou8Xhg0KIiXcyh6IoLbEs/M8CzYQQyQXj04D9wHRFUVYJIWLuLntJKr1O773Gid1X1bhtv9r4BnvYdI7r06eTd+ECADovLypOmYriALt2Juck88a2N8gXlrOQDYMbMqrpKI2zkiTnY8zNYfkn75N63dJC2MXNjd5jJ+BXzjE29SsJJ3ZdYeu3JzHlW+v7mz8aQdOuVWR9fymWd+ECCV9+SerKVWA2Fznm07kzwSOG416rlkbZ3TmH+uqpKEoDoAUQC/x+jy83uODnhzcW/gBCiBhFUb4A3gVeAibc6smS5GzSErPZ+t1JNa7VvDy1HrDtjUcZf/xB8nffq3H58eMdos7RLMy8tf0trmVZFiN+bn5Mbzsdg77slB9IUkkwm02sjprO1TOnAFAUHY+8NobQ6jU1zqxkmExmdvx8hugther7PVzo/HIkVRvI+v7SKu9yLAmzvyT11xXqVe0bvNu3J2TEcNwjIzXK7u451OIfGFjwc6EQwnSL4xUVRRkEBAGJwC4hxOFbPA4spUMAa29xbA2WxX8H5OJfKgPMJjMbFx8jL9ty1ts32J22T9u2rWd+cjJx48ersU/nTvj1fsymcxTXgugF7IjbocYftf6ICt4VNMxIkpzTtiULObN3txq3f2kg1Zs6Rntfe7tVfX9gRS+6D26AfzlZ318aGa9eJWHOHFJ+WQZGY5FjXm3aEDJiOB4NG2qUXfE5zOJfURQP4DksN+Uu+IeHdS74X+HnbQX6CyEuFhrzAioBGUKIK7d4ndMFP+/o2oyiKPv/4ZBj3MEoSbexf+0FrpxJBUDRKXR+uZ5Ne0oLIbj63gRM8QkA6IODCX3/fYfo6PFn7J98cfALNX6l/is8VPkhDTOS7E2+Z2vj79Ur+HvNb2rc9OHHaNz1EQ0zKjnXYtJYO7dofX/1xiF06C/r+0sj4/XrJM6bT8rSpYibFv2eLVoQMnIEnk2aaJTdvXOkv8inAH/gdyHEpZuOZQEfYLnZ91zBWENgItAe2KQoyn1CiMyCY34FP1P/Ya4b47btbShJDujquVT2/h6jxs0erkpohN8/P6EYUlesKNLtoOKHk3EJCLDpHMVx8PpBRm0dhVlYajOblm/K8MbDNc5KkpzP6b272LLEet6uZvOWtH3uZQ0zKjnHd8ax7btTRer7W/SKoEnXKg5xAkS6c/lJSSTOX0Dy998jcnKKHPNo2pSQkSPxav6ARtnZjiMt/m+U/My9+YAQ4jrw3k3DfyiK0gX4E2gOvAp8bo/EhBBNbzVecHap9H71k5xeXnY+GxZZ23pWqOFH0+5VbTvH5ViufTBZjf2f7ot327Y2naM4TiadZOimoWTnWzYZq+BVgWkPTcNF50hve5I9yPfsknXlzElWz5yudj2pULM23YePRtHZrouYIzLlm/nzp9Mc2Rarjrl5utD5lXpUqRekYWbS3TKlpJC4aDFJ33yDyMoqcsy9UUPLor9lS6f5MucQn4KKotQDWmJpybn6Tp8nhMhXFGUBlsX/Q1gX/zfO7P/T6c0b4yn/cFySnMK2H05a23p6uNDppUh0Nuw0IUwmrowbhznTctHNUCWc8mPG2Oz1i+tS2iUGbxxMel46AIHugczrPI8QT+22U5ckZ5Ry7SrLp75Pfp6l3MW/fAUeG/MeBlfn3jQvMzWXdfOPqOWUYKnv7zGkAX4hsr6/tDClpZH01dckff21+jl2g3tkJMEjR+Ddtq3TLPpvcIjFP7e/0fffxBf89LoxIITIVBQlFqikKEqFW9T932g7cOruU5Wk0uHUX1c5teeaGrfrVxvfINu29Uz66muy9u2zBHo9lT75BJ2nth9817OuM2DDABKyLfcfeBu8mdNpDlX9qmqalyQ5m+yMdJZNmUh2mmUB7O7tQ+9xE/H0tW1ZoaO5ej6VtXOiyUzNU8dqNC1H++fryPr+UsKUkUnyN/8lcdFizGlpRY651apF8Ijh+HTq5HSL/hs0/ytVFMUdeB7Ljb4Li/ESLQp+nrtpfHPB63bjf3cT7l7oMZLkdNISstlWqK1nnRah1Gxm2x7bOSdPEv8f64ZZwYMG4dGokU3nuFupuakM2jCI2AzLZXg3vRuzOs6iblBdTfOyO7MJdNrvpSCVHflGI79N/5DkOEtLS73BwGNvvktgRe1b+9rTsR1xbPv+JOZ8S4mTokCLx6rTuEu40y4UnYk5K4vk774jccFCTClFiz9cIyIIGTEcn65dnb5kTfPFP/AkEACsusWNvgAoitIEywZf5pvGOwL/VxB+c9PT5mBZ/I9XFOXXQpt8VQWGAbn875cCSSr1zCYzGxYdJS/HchHNN8SDNk/bdtMRc24ucW+OUbsguDdoQPCQwbd5ln1lGbMYumkoZ1LOAOCiuPBpu09pWv6W5d/O49Q62DABXlgBPmVnEyVJO8JsZt3s/3D5+BF1rPuwUVSqU3r6nN8tU76Z7T+e5ugfRev7u7xaj/BIWd/v6Mw5OaQsXUrCvPmYEhOLHDNUCSdk2DB8H37YITakLAmOsPi/UfJzqx19b/gUqKkoyk4s9wWApdvPjV7+7wohdhZ+ghBip6IonwKjgMOKovwMuAJ9gUBghNzdV3JG+1bHcPWc5TKmpa1npM0vRcd/PpPcUwWb+Li7U3HqVBSDdhtm5ZnyeH3L6xyOt2z7oaAwufVk52/puW8x/D4KhBm+exJeXA1u3lpnJTm5HT9+w4kd29S4Tb8Xqf1gGw0zsq/M1FzWzj3C1XPW+v6gSt50H9wAvxDbllJKtmXOyyPlp59InDuP/OvXixwzVKpE8NCh+PV6FMXFEZbDJUfT31ZRlLpAa25/o+9/gd5AMywlOwbgGvAjMEsIsf1WTxJCjFYUJRrLmf6BgBn4G5gmhFhlq99DkhzFlTMp7Fsdo8YPPFKN0Gq2rb/N3PMXSYutF83KjXkTt4hqNp3jbpjMJsZtH8euK7vUsbeav8XDEQ9rlpPdCQGbP4DtM6xj2cmQGS8X/5JdHd60lj3Lf1TjRp270+zRPhpmZF9Xz6WyZm40WYXq+2veX472z9fF4FY2zhKXRsJoJGX5chLmzCE/ruhtny6hoQQPHoz/471RXF01ylBbmi7+hRDHgdsWyQkhFlK8+wEQQnwFfFWc50pSaZKbnc+GRcdudNujYk1/mnSrYtM5TOnpxL01Tm3p59W6NQHPPGPTOe6GEIIPdn/AhgvWPQaG3TeMZ+pol5Pd5efBimEQbV2AUeE+6PejLPuR7Or8wf1sXPClGldrfD8dXhrstLXuR7fH8scPpzCbrPX9Dz5eg/s6hTnt71zaifx8UleuIuHLLzFeKlpJ7hISQtCgQfg/9SS6Mrrov6FsXeeQJCclhGDbdydJT7K09XTztH1bT4Brkz9Uz6Lo/fyo8OGHmn4I/ufv//DL6V/U+Lm6zzGo4SDN8rG77BRY+hzEFLrYWbMLPLFYnvGX7Op6zDlWfjYFYbbceleuanUeeX0sOieskTYZzfzx4ymObY9Tx9y8XOj6an3C6gZqmJn0T4TJRNrqNSR88QV5MTFFjukDmHVd9gAAIABJREFUAwkaMICAZ55G5+6uTYIORi7+JckJnNpzldN7C7X1fLYOPoG2fZNLW7uO1BUr1Dh00iQM5cvZdI67sejIIhYdWaTGj1Z/lDebvem8Z+RSL8M3T0D8cetY0xehxwzQy7dyyX7SExNYPmUixhzLhnk+QSH0Hvseru7OV++emZLLmrnRXDtvbf8YHOZN90EN8A12vt+3tBNmM+nrNxA/K4q8M2eLHNP7+RH46isE9uuHzsvrH16hbJKfGJJUyqXGZ7PtB+uWFXVaVqBGU9suyo3XrnN1wgQ19uvVC99uXW06x934+dTPfLb/MzVuF9aOSS0noVOctD3b1Wj49klIL1S72uFdaDPaUosgSXaSm5XF8ikTyUhOAsDVw5PHx03AO9D5OtxcOZPC2nlHyEorVN/frDztn6+DwdX5rnCUZkIIMjZvJj5qFrknThQ5pvPxIfClFwl84QX03vKK6K3Ixb8klWKmgraexoK2nn7lPGjzVM3bPOvuCCG4Mn48plRLpwuXihUo/854m85xN9bFrOP9Xe+rcbPQZkxvOx0XnZO+nZ3dDEtfgILditEZoNcX0KivtnlJTs+Un8/Kzz4m/mIMADq9nkdHv01weFVN87I1IQRHt8exfWnR+v6WfWrQqKOs73ckQggyt28nfmYUOUeOFDmm8/QkoP8LBL34Ino/595o7l456aelJJUN+36PUS9P63QKnV+uZ/O2nsnff0/mn39aAkWh4pQp6H18bDrHndoZu5Nx28chsHxARwZFMrP9TNz0bprkY3cHvoWVI8Gcb4ndfKHvNxDRVtu8JKcnhGDjgi+5cPiAOtZl0EiqNLhPw6xsz2Q088cPJzm2w3pVzd3LQNcB9ahcR9b3OwohBFm7dhE/M4rsgweLHFM8PAh87lkCX34Zl4AAjTIsXeTiX5JKqbjTKexfE6PGDzxajfJVfW06R+6581z/ZJoaB770El4PPGDTOe7UwesHeX3r6+QXLISr+lZldqfZeLs64WVdIWDbVNj6sXXMtxI8+zOUd96NlCTHsWf5jxzZsl6NH3ziGeq17ahhRraXkZzL2nm3qO8f3ADfIFnf7yiy9u4l/vOZZO3bV2RccXMj4OmnCRrwKi7BwRplVzrJxb8klUK5WUY2LD6qtvWsVNufxl1s29ZTGI3EjR2LyCnoIFSrFiGvv2bTOe7U6eTTDNs0jOx8yw2HoV6hzO8yn0B3JzwzZzLCytfhYKFNy8vXh2d/At+K2uUllRnHt29hx9L/qnHkQx148Il+GmZke3EF9f3Zher7azUvT/tn6+Ai6/sdQtaBAyRERZG5c1eRccVgwP+ppwgaOFDTphOlmVz8S1IpI4Rg67cnyUjKBQraer5o+7aeCbPnkBMdDVjebCtO+0ST3siX0i8xaMMg0vIsZ+cC3QOZ13keoV6hJZ6L3eWkwU/9LXX+N0S0h6eWgLttr+pI0q1cOnqYtbM/V+Pw+g3pMmiE09S9CyE4si2WP388jdlcUN+vU2jVpwYNO1R2mt+zNMuOPkJ81Ewy/7hp/1YXF/wff5zgwYMwVJQnQu6FXPxLUilzYtdVzuy3blPe/vk6eAfYtq1n9sGDJMydq8Yhr7+Oe+3aNp3jTsRnxTNw/UDis+MB8DJ4MbvTbKr5abejsN2kXbF09LkWbR2771no+TnoDdrlJZUZiZcvsWLGh5hNltK6oMrh9Bz1NnoX5/j7yzea2Pb9KU7sLFTf722g24D6VKota8W1lnPiBPFRs8jYtKnoAb0ev169CB46BNfKlbVJzsnIxb8klSIp17P4Y6m1rWdkqwpUb2zby57mrCxix44Fk6WDkGezZgS+2N+mc9yJ1NxUBm0cxOWMywC46d2I6hBFZJAT1rxfP27p4Z922TrWdhy0GydbeUolIjMlmWVTJpKbmQmAl38Aj4+biLuXc9xTk56Uw9q50Vy/kK6OhYT70H1wA5vviSLdndzTp4mf9QXp69YVPaAo+D7yCCHDhuJataomuTkrufiXpFLCZDKzYeFR8nMti3L/8p60fqqWzee59sknGC9cBEDn5UXFKR+jlPAunlnGLIZtGsbp5NMA6BU909tOp1losxLNo0Sc/wN+eA5yLa1UUfSWs/1Nntc2L6nMMObksHzq+6TFWzYKNLi503vsBHxDnKOeOu50sqW+P92ojtVuEUq7frVlfb+Gcs+fJ+GLL0n7/XfUG9gK+HTrRsjwYbjVqKFRds5NLv4lqZTYu/K8etZKp1fo8ko9DG62/eDK2LaNlB+WqnH5d9/BUKmSTee4HaPJyP9t/T8OxR9Sxz5o9QHtwtqVaB4l4vBP8OsQMBcsSly94amvoUYnbfOSygyz2cTvUdO4ds7yRVtRdDz82hjKR5T+RZcQguitsez4qWh9f+sna9Cgnazv10repUskfPElqb/9BmZzkWPenToSMmKEJmWmZYlc/EtSKRB7Mpn96y6ocfNeEYSE27bXfn5yMnHj31Fjny5d8OvVy6Zz3I7JbOKtP99iZ9xOdWzcA+PoWb1nieZhd0LAn5/CJutmZXiHWjr6VGioXV5SmSKEYOvXCzi7b4861uHlwVRvqk07X1vKzzOx7buTnNh9VR3z8DHQdUB9KtWS9f1aMMbFkTB7DinLl0N+fpFjXm0fImTESDzq19Mou7JFLv4lycHlZBrZ+NUxCva1onKdABp3CrfpHEIIrr73HqaEBABcQkIInTSxRM+MCSGYvGcy62KsdZ9DGw3l2brPllgOJcKUD2vehH2LrGMhdS0Lf/8w7fKSypy/V6/gwNqVanx/z8e5r0sPDTOyjfSkHNbMiSb+orW+v1wVH7oNkvX9WjBeu0bi3Lkk//QzGI1Fjnm1bEnwiOF4Nm6sUXZlk1z8S5IDs7T1PEFGsqWtp7uXgY79I1Fs3NYzddly0jdsVOMKH31Y4jslzjwwk59P/azG/er0Y3CjwSWag93lZcLPL8Optdaxqm0su/Z6+GuXl1TmnNqzg63/XajGtVq05qF+L2qXkI3Enkxm3YKi9f11Hgylbb/auBhkfX9Jyk9IIHH+fJK//wGRl1fkmGezZoSMHIFnMye8j6sUkIt/SXJgx3de4ezf8WpsaevpZtM5Mvf8xdWJE9U4oN8zeLdpY9M5bmfxkcUsiF6gxo9EPMLYB8Y6V01uxnX47imIO2Ada/Ak9PoCXGz771SS/k3cqROsiZqh3mRZsVZdug8bhaLTaZxZ8QkhOLz5Mjt+OYMoqO/X6RRaP1WT+m0rOdd7iYPLT04maeFCkr79DpGdXeSYR+PGhLw2Es/mzeW/Ew3Jxb8kOaiUa1lsL9TWs16bikTcF2LTOXJOnuLy8OGIgkuxrjWqU+6NN2w6x+0sO72MT/d/qsbtKrfj/Vbvo1NK70Lkf8Sfgm/7QMpF61jrUdDhXSjFCy6p9Em5eoVfP3mffKPlTGxAhYr0evMdXDTYwM9W8vNMbP32JCf3FK3v7zawARVryitqJcWUmkri4sUkL/kv5qysIsfc69cn5LWReLVuLRf9DkAu/iXJAZnyzaxfeJT8PEsnhIBQT1o9WdOmcxjj4rg0YADmdEtdrEu5coTPnYvO09Om8/ybDRc2MGnXJDVuWr4p09pOw6Bzjk2FALiwC75/GnJSLLGig4dnwP0va5uXVOZkp6exbMoEstMtu2W7+/jSe9xEPH39NM6s+NISs1kzJ5qESxnqWLmqvnQfVN/mmx9Kt2ZKTyfp6yUkffUV5oyMIsfc6tQhZOQIvNu3l4t+ByIX/5LkgP5aeU69WU3notD55XoYbNiP2pSSwsUBA8m/btkpWOftTdj8eSXa1nNX3C7G/jEWs7B8wakbWJeoDlG4uzjRB/bR5bBsEJgs92xg8IQnFkPtbtrmJZU5+Xl5rJg+meQrcQDoDQYee/NdAkIrapxZ8V0+mcy6+UfIybDW99dtWYGHnqkl6/tLgDkzk6RvviVx0SLMqalFjrnVrEHw8BH4dO5UqsvJnJVc/EuSg7l8Iom/11vLQx58rLpN23qac3K4NHQYeWfPAqAYDFSeNatE+yofjj/Ma1tew1jQ376qb1Vmd5qNj6tt25dqRgjY9QWsH28d8wqBfj9CpSba5SWVScJsZu2XnxF74phlQFHoMXw0lWrX1TaxYhJCcGjTJXYuO2ut79crtOlbi3ptKsozzHZmzs4m+fsfSFywAFNSUpFjrlWrEjx8OL7du5X45pDSnZOLf0lyIDkZRjYutrb1DIsMpFEH27V/FCYTsW+8Qfbff6tjFadOwatFc5vNcTtnks8wZOMQsvMtN4KV9yzPvM7zCPIIKrEc7MpsgnVvw5451rGgmvDczxBQVbO0pLJr+w9LOLlruxq3ffYlarVorWFGxWfMM7Hlvyc4vfeaOubh60r3gfWpUEPW99uTOTeXlKU/kjB/Hqb4hCLHDGFhBA8bit8jj6C4yKWlo5P/hiTJQQgh2PLNCTJTLTfiuXsb6Ni/rs3aegohuPrBB2Rs3KSOlX9rHL49Sq6v9+X0ywzaMIi0PEvNcYBbAPO6zKOCd4USy8GujNnwy6twYpV1LKwFPPM9eAZql5dUZh3asIa9K6wtdBt1eZimj/TWMKPiS0vIZs3covX95av50m1gA5t3QZOsRF4eKcuWkTBnLvlXrxY55lKxAsFDhuD/2GMoBie6V8vJycW/JDmIY3/Gce6gta1nhxfq4uVnuw+0xDlzSPlhqRoHvvwygf372+z1bychO4GBGwZyPdtyn4GXwYvZnWcT4RdRYjnYVWaC5cbey3utY5GPQe+5YHCi+xikUuPcgb1sWjhbjSOaNKPDiwNLZVnMpeNJrF9wlJxMa31/ZOuKPNS3FnqDrCm3B2E0krpiBQlfzsYYF1fkmEu5cgQNHoT/E0+gK8WdosoqufiXJAeQfDWTP388rcb121aiWsNgm71+yi+/EP/5TDX27dmTcm+Mttnr305aXhqDNgziUvolAFx1rkR1iKJekJNs5Z54Fr59ApLOWcceHA6dP5CtPCVNXDt/llWfTUUU3FBfPqIGj7w2Fl0pq8MWQnBw4yV2LTtzY1sCdHqFh56uRb02JdegoCwRJhNpq1YR/8WXGC9eLHJMHxxM8MAB+Pfti85NXm0preTiX5I0ZjIWtPU0FrT1rOBFqz41bPb66Vu3cuW9CWrs1bIlFT+cXGIdGLKMWQzbOIxTyZY9C/SKnmltp9Es1El2dry8z7J5V1ZiwYAC3aZACyfbnVgqNdISrrN86iSMuTkA+IaUo/fYCRjcS9cVKGOuiS3/Pc7pfdfVMU8/V7oPakBoROltT+qohNlM+tq1xM/6grxz54oc0/v7EzTgVQKeeaZE20FL9iEX/5Kksd2/nVNrWHUuCl1eqYeLjdp6Zh8+TOz/jQKTCQC3yLpUmjkTpYQu0xpNRkZtG8XB+IPq2Put3qdDeIcSmd/ujq+y1PgX3LyMizv0WQB1e2qbl1Rm5WZlsnzKJDKTLV1Y3Dy96D12Al7+ARpndnfSErJZPTuaxFhrfX9ohKW+38tfnnG2JSEE6Rs2kBA1i9zTp4sc0/n5EfTSSwQ89xx6by+NMpRsTS7+JUlDl44ncXCD9bJqy941CK7sbZPXzj1/nkuDBqvbqxsqVyZ87twSewM3mU28/efb7IjdoY6NbTaWR6s/WiLz292eebBmDGprJo9A6LcUwh7QNC2p7DLl5/Pbpx+TcOkCADq9C4+OHk9wWBWNM7s7l44lsW7hEXIz89Wxeg9Vos1TNdG7yDI6WxFCkLF1K/FRUeQeO17kmM7bm8D+/Ql8sT96HydpwSyp5OJfkjSSnZHHxq+OqXF4vUAadqhsk9fOj4/n0oCBmJKTAdAHBBA2fx4uISE2ef3bEULw0Z6PWBuzVh0b3Ggwz0U+VyLz25XZDBvfg51R1rGAavDcLxBUXbu8pDJNCMGGebO4GG29ytZ18EjC6zfUMKu7I4TgwPqL7P71rLW+30Wh7dO1iWxdejcjczRCCDJ37CQ+aiY5hw4XOaZ4ehL4/PMEvfQien/ZOtVZycW/JGlACMHmJSfIKmjr6eFjoGP/SJt04TBlZHJp0GCMly8DoHh4EDZnNm7Vqt3za9+pqANR/HjqRzV+ps4zDG00tMTmtxtjDvw62LJz7w2V7rec8fey3Q3aknS3dv/yA0e3bVTjlk8+S+RDpae8zphrYvOS45zZb63v9/JzpZus77epzN17iI+KInv//iLjirs7Af36EfTqK7gEyrbEzk4u/iVJA0e3xxFz2LpJSocX6uLpe+91+CIvj9iRI8k5VnBFQa+n0mef4tGo0T2/9p36+ujXzI+er8Y9qvVg3APjSmV7wSKykuCHZ+HiTutY7YctNf6u8gY4STtHt21i50/fqnG9tp1o0edpDTO6O6nxWayZE01ibKY6VqG6H10H1rdpu+OyLGv/fuJnRpG1Z0+RccXVFf++fQkeOKDErgxL2pOLf0kqYUlxmez4yXpTVYP2lana4N7PGguzmbh33iFzp3VxWuH9Sfi0a3fPr32nlp9ezvR909X4ocoPMbn1ZHRKKa/TTb5gaeWZcMo69sBAS1cfXelqnSg5l4tHDrF+rrUELbzBfXQeOLzUfNm+eDSR9QuPkptlre+v37YSrZ+U9f22kH34MPGfzyRzx46iBwwG/J/oQ/CgQRhCQ7VJTtKMXPxLUgkyGc2sX2Rt6xlY0YuWj9umTjz+009J+22lGgePHIF/nz42ee07senCJibumqjGTco1YXrb6Rh0pXzXx7gD8O1TkGktR6DLZEsf/1KywJKcU8KlC/w24yPMJsvCOTisCo+Oegu9i+N/tAsh+HvdBXavOKfeM69zUWj7TG0iW8n6/nuVc+wY8TOjyNi6tegBvR6/3o8RPHgIrpXlPgllleO/Q0iSE9n161kSL1ta1+lddJa2noZ7P3OctGQJiQsWqrF/374EDxlyz697p3Zf2c2bf7yJuWBDoTqBdZjVcRYeLh4lloNdnFoPP/UHY5Yl1rtC7zlQv+S+VEnSrWSmJLNsykRysyylMl4BgfQeNxE3T8dvx5iXk8/mJcc5+7d1R3Mvfze6D2pA+Wq+GmZW+uWcPEXCrCjSN2wsekCnw69nT4KHDsG1Sunq/iTZnlz8S1IJuXgskUObLqlxyz41CKp0720909as4drHU9TYu2NHQt97t8Qu+0fHRzNy80iMZiMAVXyrMKfTHHxcS3l7uH2L4ffRICx7JODuD898D1VaapuXVObl5WSzfOok0hMsi2eDuwe9x07AN9jxa7ZTrlvq+5PiCtX31/Cj28AGNrnvqazKPXeOhFmzSFuzFrVVEoCi4Nu9O8HDh+EWEaFdgpJDkYt/SSoBWWl5bPzK2ke5SoMgGrS790uumbv3EDdmrPpm79G4MZVmTEfRl0wd+tmUswzZNITsgk2uynmWY17neQR5BJXI/HYhBGz+ALbPsI75h8OzP0NIbe3ykiTAbDLx++efcO3cGQAUnY6er4+lfDXHbzN74UgiGxYVre9v0K4yrZ6sgV4v6/uLI+/CBRK+/JLUlassbYgL8enSheDhw3CvVUuj7CRHJRf/kmRnQgi2/Pc42WkFbT19XenwfN17PjOfc/Ikl4cPRxgtZ9xdIyIIm/0lOnf3e875TsRmxDJw/UBSc1MB8HfzZ37n+VT0LsX1uvl5sGIYRFvblFLhPuj3I/iU1y4vSaKgRfBX8zj39151rOPLQ6jW+H4Ns7o9IQT711xgz0prfb/eRUfbfrWp27KCtsmVUnmXY0mY/SWpv65Qd3C/wbt9e0JGDMc9MlKj7CRHJxf/kmRnR7bFEhOdqMYd+997W09jXByXBgzEnGG5f8ClXDnC588rsU1ZErITGLh+INezLTfBerp4MrvTbCL8S/Fl5ewUWPocxGy3jtXsAk8sBjfb7LosSfdi/6rlHFr/uxo36/UEjTp31zCj28vLyWfT18c5d8Ba3+8d4Eb3wQ0oV0XW998t49WrJMyZQ8ovy6DgxM8NXm3aEDJiOB4NS8/GbpI25OJfkuwoMS6DHb+cUeNGHcKoUu/eSmJMKSlcHDCQ/OuWhbfO25uw+fMwVCqZzg1peWkM3jCYi+kXATDoDMzsMJP6wfVLZH67SL0M3zwB8YW2uG/6IvSYAXr5Nilp79TuP9n2zSI1rt3yIdo8/YKGGd1eyrUsVs+JJvmKtb6/Yk1/ug6oL+v775Lx+nUS580nZelS9WrvDZ4tWhAycgSeTZpolJ1U2shPNUmyk3yjiQ0Lj2IqaOsZVMmbFr3v7cy4OSeHS0OGknf2LACKwUDlWbNwr10ytejZ+dmM2DSCk8knAdApOqa1nUbzCs1LZH67uBoN3z4J6VesYx3ehTajZStPySHEnjzO6lnWe1Aq1Ymk25DXUXSOWycfE53AhkXHyMu21vc3bF+Zlk/I+v67kZ+UROL8BSR//z0iJ6fIMY+mTQkZORKv5g9olJ1UWsnFvyTZya5lZ9UdK/WGe2/rKUwmYt94g+wDB9SxilOn4NWiZBbeRpORUVtH8ff1v9WxSS0n0TG8Y4nMbxdnN8PSFyAv3RLrDNDrC2jUV9u8JKlA8tU4fp32AaaCs70BFSrR6413cHF1zDPnwizYtyaGv1adt9b3G3S0e7Y2dVrI+v47ZUpJIXHRYpK++QaRlVXkmHujhpZFf8uWpWYzN8mxaLb4VxQlBvinZrPXhBD/s+WcoigtgXeAFoAHcBpYBEQJIUw3P77gOY8AbwCNAT1wFPhSCPH1vf4OkvRPLhxJ5PCWy2rcqk8NAisWv/+2EIKrH3xAxsZN6lj5t9/Ct0ePe8rzTpmFmfE7xvNn7J/q2Jv3v8ljNR4rkfnt4sC3sHIkmAvOTLr5Qt9vIKKttnlJUoGstFSWfTyBnPQ0ADx8/Xh83EQ8fByzVj4vO5+NXx3j/KEEdcw70NK/X9b33xlTWhpJX31N0tdfY87MLHLMPTKS4JEj8G7bVi76pXui9Zn/VOA/txjPuHlAUZRewC9ADrAUSAJ6Ap8BrYAnb/Gc4UAUkAh8A+QBTwBfKYrSQAjxhm1+DUmyykrLY9PXx9S4asNg6re9t3r8xDlzSPlhqRoHvvIygS+UTL2vEIKP9nzEmvNr1LGBDQfyQj3Hrjf+R0LAtqmw9WPrmG8lSyvP8rI7huQYjHm5rJg2mZSrlnI0F4Mrj735Lv6hjnn2PPlqJmvmRJN81XqWulItS32/h49jXqVwJKaMTJK/+S+JixZjTksrcsytVi2CRwzHp1MnueiXbELrxX+KEGLi7R6kKIovMB8wAe2EEPsKxt8FNgNPKIrytBDih0LPqQpMx/Il4X4hREzB+PvAXmC0oii/CCF22fIXkso2IQSbvj5OdrrlEr2nrysdnq9zT2/YKb/8QvznM9XYt2dPyo0efc+53qlZB2ex9KT1i0ff2n0Zft/wEpvfpkxGWPU6HPjGOla+Pjz7E/iW4halklMRZjNrv/iMuFMFN6ArCj1GvEHFWnW0TewfnD8Uz8bFx8jLsV6Ab9QxjJaPV0cn6/v/lTkri+TvviNxwUJMKSlFjrlWr07I8GH4dO3q0Pd3SKWP1ov/O/UEEAIsubHwBxBC5CiK8g6wCRgC/FDoOS8DbsDUGwv/guckK4ryEbAQGAzIxb9kM4e3XObiUWtbz04vRt7TWa/0rVu58t4ENfZq2ZKKH04usQ+CJUeXMO/wPDXuXq07bzd/u3SefcpJg5/6W+r8b4hoD08tAXdZkiA5jj+++4pTu60ldu2ef4WazR1vZ2lhFuxdHcPeVefVMb1BR/vn6lC7+f9U7kqFmHNySFm6lIR58zElJhY5ZqgSTsjw4fj26FFiGzZKZYvWi383RVGeA8KBTOAw8Mct6vc7FPxce4vX+APIAloqiuImhMi9g+esuekxknTPEmMz2LXsrBo36hRGWGRgsV8v+9AhYv9vlLqBi1tkXSrNnIlSQjf6rTizgmn7pqlx60qt+bD1h+iUUngGKu2KpaPPtWjr2H3PQs/PQW/QLi9JusnB9avZt3KZGjfu1pMmPXppmNGt5Wbns3HxMWIOW+v7fQLd6T64ASHhPhpm5tjMeXmk/PQTiXPnqe2abzBUqkTw0KH49XoUxUXr5ZnkzLT+6woF/nvT2HlFUV4SQmwrNHajj+Gpm19ACJGvKMp5oB4QARy/g+dcURQlE6isKIqnECLr5sdI0t3IzzOxfuFRTPmWtp7BYd482Kt6sV8v9/x5Lg0ajMjOBsBQuTLhc+ei9y7+TcN3Y9PFTUzYab3i0LhcYz5t9ykGXSlcKF/eDz++AGnWG7BpOw7ajZOtPCWHcnb/X2xeNEeNq9/fnHb9X3W4K23JVzNZPTualGuF6vtrB9B1QD08vGV9/60Io5GU5ctJmDOH/LgrRY65hIYSPHgw/o/3LrGTO1LZpuXifzGwHUv3nXQsC/fhwEBgjaIoDwohDhU81q/gZ+o/vNaN8cLbm97Jc7wKHvevi39FUfb/wyHHLMCUStzOZWdJirN0ZnApaOupNxTvDHl+fDyXXh2g1n/qAwIImz8Pl5AQm+X7b/Zc2cOb297EVHABrnZAbWZ1nIWHi0eJzG8zZhPs+By2fGjt6KPoLWf7mzyvbW6SXZXG9+xr586w6vOpCGE5gVA+oiYPj3gTnc6xyj7OHYxn41fHMBaq77+vUxgP9pb1/bci8vNJXbmKhC+/xHjpUpFjLiEhBA0ahP9TT6KTi36pBGm2+BdCTLpp6AgwWFGUDGA0MBHoXdJ5SdLdijmcQPTWQm09n6xJQGjxztCbMjK4OGgQxthYABQPD8LmzMatWjWb5Ho7RxKOMHLzSIxmyw3L4T7hzOk8B1/XUlYTnxoLywdBzHbrmJsvPLkYanTSLi9JuoW0+OssnzqJ/FxL1apvSHl6j30Pg7u7xplZCbPgr1Xn2bc6Rh1zMeho/3wdaj3bUJEyAAAgAElEQVQg6/tvJkwm0lavIeGLL8iLiSlyTB8YSNCAAQQ88zQ6B/p3LJUdWpf93MocLIv/hwqN3Th77/e/Dy8yXvhW+VQguOBY4v884/ZXBlRCiKa3Gi84uyT30y7DMlNz2bTkuBpXaxRMvTbF6xoj8vKIHTmS3GMFr6fXU+mzT/Fo1MgWqd7WuZRzDNk4hKx8y4Wwch7lmNdlHsEewSUyv80cXwm/jYDsZOtY5WbQZwEEVNUsLanklKb37JzMDJZNmUhmiuXv1c3Li8fHTcTLP0DjzKxys4yW+v5o60epT1BBfX+YrO8vTJjNpK/fQPysKPLOnC1yTO/nR+CrrxDYrx86r5Ip4ZSkW3HExX98wc/C/2WcBO4HagFFLucqiuICVAPygXM3PSe44Dm7bnpOhYLXvyzr/aXiEmbB5q+Pk5NhOUvu5edKh+frFqs+V5jNxI1/h8yd1j/VCu9PwqddO1ul+6/iMuIYsGEAKbmW789+bn7M6zKPSt73tj9BicrLhHVvw/6vrGOKDtq8AW3Hgt4R3+6kssyUb+S3GR+RePkiADq9C73eeIegymEaZ2aVFJfJ6jmHSb2erY5VrhNA11fr4+5dCu8BshMhBBlbthA/M4rcEyeKHNP5+BD40osEvvACem9vjTKUJCtH/DRsUfCz8EJ+M/As0A34/qbHPwR4YukSlHvTc1oVPOfmdp7dCz1Gkorl8JbLXDyWZAkU6PhSZLE/DK/PmEHaypVqHDxyBP59+tgizds6lniMEZtGcD3b0nnCw8WD2R1nU92/+Dcsl7grh+GXVyCh0P39vpWhz3yo4ngtEiVJCMH6uVFcOnpYHes25DXCIhtomFVR5w4U1PfnWuv7G3cOp8VjEbK+v4AQgszt24mfGUXOkSNFjuk8PQno/wJBL76I3u+fChckqeRpsvhXFKUucFEIkXnTeFVgVkFYaBcefgamAk8rihJVaJMvd2BywWNm3zTNYmAMMFxRlMWFNvkKAN4ueMwcJKkY4i+ls3P5GTVu3CmcsDrFa+uZtGQJSQsXqbF/374EDxlyzzneiY0XNvLW9rfIMeUAYNAZmNlhJg1CHGcB8q/MZtgzGzZOBFOedTzyMej5H/BwnNIJSSps18/fcewP6/mnVn2fp26b9hpmZGU2C/beXN/vqqPDC3WpeX957RJzIEIIsnbvJv7zmWQfPFjkmOLhQeBzzxL48su4BMj3IMnxaHXmvy+WHXb/AC5g6fZTHXgYcAdWY9mdFwAhRJqiKAOwfAnYqijKD1h27n0US0vPn4GlhScQQpxXFOVNYCawT1GUpUAelg3DKgMz5O6+UnEY80xsWHgUc74AICTch+a9Ior1Wmlr1nDt4ylq7N2xI6HvvWv31n5CCBZEL2DmAevOwT4GH2a0m0GLCi3+5ZkOJP0a/DoEzm6yjhm8oMcnlh7+DtYeUZJuOLJ1I7t+tl7Ert++C817P6VhRla5WUY2LDrGhSPW+n7fYHe6D25IcGVZsgKQtXcv8Z/PJGvfviLjipsbAU8/TdCAV3EJLmX3SkllilaL/y1YFu2NsZTmeGG5WfdPLH3//yuEEIWfIIT4VVGUtsB4oA+WLwlngFHAzJsfX/CcKEVRYoA3gBcAHXAMeEcI8bV9fjXJ2e38+QzJVy23iri46uj8ciR6l7u/BJ65ew9xY8ZCwZ+uR+PGVJox3e47Ouaacpm4cyKrzq1Sx8J9wonqGEWEX/G+xJS4U+stC/8s6wZDVLgP+iyE4Bra5SVJt3Hh8EE2zItS4yoNG9Pp1aEO0cs/MS6DNbOjSY231veHRQbS5ZV6uHvJ+v6sAwdIiIoqcm8WgGIw4P/UUwQNHIihfDmNspOkO6fJ4r9gA69tt33g/z5vB9DjLp+zElh52wdK0h04fyieI3/EqnGbp2oVq61nzsmTXB4+HGG03CzsGhFB2Owv7d72LSE7gde3vM6h+EPqWLPQZnza9lP83f3/5ZkOwpgDGyfAnpsq9lq9Bu3fARfZK1tyXAkXY/jt048wF+zaHRJelZ7/9xZ6B9jN9ezf19n49XHyC9X3N+lahea9ItDptP9ioqXs6CPER80k84/tRQ+4uOD/+OMEDx6EoWLxurxJkha0f8eRpFIiMyWXzUusXRwiGodQt1WFu34dY2wslwYMxJyRAYBLuXKEz5+H3t++i+9TyacYvmk4VzKtu0v2qdmH8c3HY9CXgrN614/Dz6/A9aPWMe9Q6D0HqjtGrbQk/ZOMpESWTZlEXrblqqF3YBC9x03EzdNT07zMZsGe387x99oL6piLq46O/SOp0bRsn8XOOXGC+KhZZGzaVPSAXo9fr14EDx2Ca+XK2iQnlWpCCFJyUwhw1+aeELn4l6Q7YDKZ2fjVMXIyC9p6+rvR/rk6d32pPj85mYsDBpJ/3dJZR/f/7J13eFTV1offM8mk955MAqHXQBJ6SEApKohKsV69dq8NUK73u0XsXWxXwEIRsXdFRcGGQAr9Bgi9JSSZ9N4z7Xx/TJjJkAkQMslMkv0+jw8za+85Z0fIOb9Z57fX8vIiatVKlKqOLam5JWcL/9z6T1MNf4Wk4B+j/8EtQ25xCLvBOZFl2LUafn0MdA3m+KCZcPVy8Ay039oEggtA01DPdy8/Q3WpsZK10s2dOf96Eu9A+/rCG2q1/LbmINkHy0wxn2B3Zt4XQ6Cq5/r7G0+coHjZcqp/+cVyQJLwmTWL4AcfwCU62i5rE3RdqjXVbM/fTnJuMqnqVFTeKj6c8aFd1iLEv0BwHvR6A7+9d5DcI01NoySYfsfQNntgDQ0N5D7wIJpTxiq2klJJ5Ftv4TZokK2XbEKWZT489CGv7X4NGePeAk+lJ0smLWFS5KTzfNoBqC2FH+bD0Z/NMWc3uPx5GH2X2NQrcHgMej3r//syRVnGhk+SQsHVi/5NSLR999eUqmv4+Z39VJWYv1D3GhbA9Dt7rr+/MTOTkrfepuqnn0x7sc7gfcUVBM9/ENf+Yk+R4MKQZZnjFcdJzk0mRZ3C3qK96GSdabykoYTKxkp8XTu/DKwQ/wLBOdDrDfy2+iAn04tNsdEzolENatujOlmnQ/3IP6hPTzcGJImIJS/jOW6sLZdrgVav5bkdz/Ht8W9NMZWXimVTljHAf0CHnddmnPwTvrsPagrMsdDhxk69IUPsty6B4AKRZZlN779LZrq5Ksy0ux8kOtZqA+JO48SeIv740NLfP+qK3oy9umf6+zU5OZS8/Q6V339vLB/cDK9pUwlesKBDkzSC7kOtttaU3U9Rp1BYV9jqXG8XbzIrM4kNie3EFRoR4l8gaAVrwn/klCjGXtWnTceRZZmCZ5+z8I2G/uff+MyYcY5PtY+KhgoWbV7E7kKz6IgLieONS94g0N3BbTI6DWx6FtKWWsbH3Q/TngJlx26KFghsxa4fvmHfbxtM78fNuZ4RUy+323oMBpkd35/kf79km2LOrk5Mu20I/eJ7nr9fm5dHyTvvUvHdd6DTWYx5TZ5M0IIFuA8fZqfVCboCsixzqvKUSezvKdqDzqBrdf7QwKEkqZJIVCUSExSDk6Jjq/u1hhD/AoEVrAr/qVFMvLZ/mz3yJe+8Q8UX5jYUAXfdScCtt9psrWdzqvIU8/+YT051jil2db+reXLCk7g4OXg1nJITxk69+c2a5ngGwzVvw8DL7LcugaCNHEnbSvKna03vB0+czMTrb7Hbehpqtfz63kFyDpn9/b7B7sy4P4bAiJ7l79cWFlK6YgXlX30NTRXXzuCZkEDwwgW4x3Z+NlbQNajT1rGzYKdJ8OfV5rU619vFm4SIBJJUSUxUTSTI3TH6PwjxLxCchV5v4NfVBzllA+Ff8fXXlCw11/T2ueoqQh55xGZrPZs0dRr/2PIPqrXVpthD8Q9x1/C7HHtjryxD+sew4Z+grTPH+0+D2e+AV8/LSgq6LrlHDrLx7TdM7yOHDOfy+x9GUrS9H4gtKMmtYcO7lv7+3sMDmX7nUFw9eo6/X1dSQumqVZR/9jmyRmMx5jFmDMEPLcRj9Gg7rU7gqMiyTFZVFinqFJJzk9lduButQdvq/MEBg0lUJZKkSmJE8AicFY4ntR1vRQKBHdHrDfy66iCn9jYT/tOimDiv7cK/evNm8p98yvTeMyGBiOef6zAB8OnhT1myawl62ejjdXd258XEF5nae2qHnM9m1JfDjw/DoXXmmJMLTHsaxt0HdhJMAsHFUJan5vtXnkPflFH2j4jk6n8sxllpH5F9fFchmz46jE5j9rKPnhnN2Fl9kHqIv19XXk7Ze+9R9smnyPX1FmPucXFG0T9unGMnSASdSr2unl0Fu0zZ/dya3Fbneim9mBAxwZTdD/Fw/GSVEP8CQRN6XVPGv5nwj50WRcJFCP/6fftQP7wImpr5uA4dgmrpUiQX29tudAYdL+18iS+Omq1FoR6hLJuyjCGBDr4xNisVvv0bVDW7sAYNMm7qDR9hv3UJBBdBXVUl3770JA01xidvHr5+zPvPU7h7eXf6Wgx6A9vXnSL9N7O/X+nqxLTbh9I3LrjT12MP9JWVlL7/PuUffoShrs5izG34cIIfWohnYqIQ/QIAsquySVYnk6xOZnfBbhr1ja3OHeA/wOTdjw2JRanoWk/QhPgXCLCt8G/MzCTn3vuQG4yP2JWRkfRasQInr7Z3Aj4fVZoqHtn8CNvzt5tiwwOHs3TKUoI9HPgGr9fClpch+TWQm1XXGH0nXPY8uNi38ZFA0Fa0mkbWLXmGykJjdSpnF1dm//NxfEPCOn0tDTVafll9wFyeGPAL9WDGvTEERNj+OuRo6KurKfvwQ8rWfoChutpizHXwYIIXLsDr0kuF6O/hNOob2V2w2yj4c5PJrs5uda6Hswfjw8eTFGkU/GGenf97bUuE+Bf0ePQ6A7+sOkDmvhJTLHZ6LxLm9mt7E6/iYnLuvgd9RQUATv7+RK1aiXOw7YV4dlU2D/7xIFlVWabYFdFX8OzEZ3FzduCKOGWZ8O09kLvLHHP3NzbsGjLLfusSCC4S2WBgw/LXyD9+1BiQJK5c+H+E9+/88pDFOdVseDeD6lKzvz86JpBpdw7D1b173/INtbWUffwJpWvWYKistBhzHdCfoPkL8J4+zW57LwT2J7c6l2S10cqzM38nDfqGVuf28+1nEvvxIfEonbpWdv9cdO8rgUBwHmwp/PU1NWTfey9atRoAyd2dqHffwbVP20qDXgi7CnaxaPMiKhvNN7j7R97P/SPvd+xs1v4vYf3fQdMsGxedBHNXgk+E/dYlELSDLR+v4fiONNP7S2+7h/5jxnf6Oo7tLODPj46g0zbz918Zzdgru7e/31BfT/lnn1O6ejX6sjKLMZfoaILmz8dnxhVITvYpqyiwHxq9hj2Fe0yCP7Mys9W57s7ujAsbZxL8EV7d954kxL+gx2JN+MdN78WEixD+skaDeuFCGg8dNgacnFC98TruI0facskAfHPsG57b/pypU6CrkyvPTnyWGX06rm9Au2mogp//AfvN+xJQOMOUxyBhIdip1rFA0F7SN/7Inp/Mm9XjZ1xN/IyrO3UNBr2BtO9Osu93c3lfpVuTvz/Wge1/7cTQ2EjFF19Ssmol+uISizFlVBRBDz6A76xZSM5C6vQk8mryjJV51MnsyN9Bva6+1bnRPtHGyjyRSYwKHYWrk2snrtR+iN8IQY/EpsLfYCDv0cXUpm0zxcKfeRrvSy6x1XIB0Bv0vL7ndT489KEpFuQexNJLlxITHGPTc9mUnF3G2v0Vp82xgL7GTb0q+3Y6FQjaw4ndO/hz7SrT+/5jJjD51rs6dQ31NRp+WXUQ9VFLf//M+2PwD+ue/n5Zo6Hi228peXcFuoICizHniHCC7r8fv9mzkexUYUnQuWj1WtKL0k3Z/RMVJ1qd6+bkxpiwMabsfpR3VCeu1HEQ4l/Q49DrDGxceYCs/c2E/2W9mDCn7cIfoOjV16hav970PmjhAvzmzbPJWs9Qo6nhX8n/YmvuVlNscMBglk1Z5rgbjwx6SHkd/nwRmsqPAhB7M8x4GVw7vwKKQGArCk4e56elS5CbNqyH9x/EzAWPoOjEp1jF2U3+/rJm/v4RQUy7Y2i39PfLWi2V339PydvvoM2zbKzkHBpK0H334jdvXodUVRM4FgW1BaSoU0hRp7Atbxt1urpW5/by7mUS+6NDRzv2nrhOovtdHQSCc2BN+Mdf3ovxsy9O+Jd98AFla9aY3vvdcANB999vk7WeQV2jZv4f8y2yGVOipvBi0ot4KB20Kk5lrrGE5+lUc8zVF2a9DjHX2m9dAoENqCwq5LuXn0bXaCwF6BsSyux/Po7StfNExdEdBfz58RH0zfz9Y6/qw+gZ0d3O3y/r9VStX0/xW2+jzbasyOIUFETQ3+7B74YbULj2DMtGT0Rr0LKvaJ+pFOfx8uOtznVRuFhk93v79O7ElXYNhPgX9BhsLfyrfv6ZwhdfMr33mjqVsCcet+mG2/SidB7+82HKGsyb2O6OuZsFcQtQSA5aseLgOvhxITQ0q7YRNR7mrQK/XvZbl0BgAxpqavj2paeoqzRW9HLz9GLuf57Gw9evU85v0BtI++Yk+zaZ/f0ubk5Mu3MYfUYEdcoaOgvZYKBqwwZKlr+FJtNyo6aTvz+Bd9+N/19uQuHubqcVCjqS4rpik3d/W942arQ1rc5VealIVCUyKXISY8LG4O4s/k2cCyH+BT0CvdbAxlVnC//ejJ/d96LEeu32HeT969+m9+5xcahee9Wm1SR+PPkjT6Y9aWojrlQoeSrhKa7u17mbCS8YTS1s+Bekf2SOSQqY/G9IegScxOVG0LXRabX88NrzlKmNwtvJ2Zlr/u8xAiIiO+X89dUafll1APWxClPMP8yDGfd1L3+/LMtU//YbJcuW03jcMsOr8PUl8I478L/llg7pnSKwHzqDjoySDFNX3cNlh1udq1QoGRU6ythoKzKRPj59HLvSnYMh7saCbo9ea2DjygyyMkpNsfYI/4YjR8idPx9ZaxTlLv36EfXO2yjcbPPI3yAbWJa+jNUZq00xf1d//nvpf4kPjbfJOWxO3l7jpt7SZhutfHsZs/29Or/koUBga2RZ5tcVS8k5lGGKXf7AIiKHDO+U8xedrmLDuxnUlJu7jvYZGcS024fi0k38/bIsU/PnZoqXLzNXTmtC4eVFwG23EXD7bTh5i/1C3YWS+hJS1amkqFNIzUulWlPd6txwz3BTV91x4eMc1/baBegeVwyBoBWsCv8rejP+mosT/lq1mpx7/oahxvj40TkkhF6rVuLkZ5tH/nXaOh5NeZQ/sv8wxfr79WfZlGVEendOdrFNGAywbTn88Qw0PaEAYPg8uPJ1cO8cK4RA0NGkffkxh5P/NL1PvPFWhkyc3CnnPro9nz8/OWr290sw7qo+jLqie/j7ZVmmNiWV4mXLaNi/32JM8vAg4K9/JfCO2212nRXYD71Bz4HSAyTnGr37h0oPtTrXWXImPjTeJPj7+V2cRVfQEiH+Bd0WvdbAhpUZnG4m/Edd0ZtxFyn8deXlZN/zN3TFxYAxExW1ahXKCNs0AimoLWDhpoUWjzqTVEksmbQELxcvm5zDplQXwHf3wSmzIMLFC2a+CiNvBHGR7jQOqCuJ8HMnwFNUOekIMv78le3fmntUxEy9nLGzr+vw8+r1BtK+PsH+P3NNMRd3Z6bfOZTomO7h76/dvoPipUup/9//LOKSmxv+N/+FwLvuwjkgwE6rE9iCsoYyU3Y/LS+NisaKVueGeISQpEoiSZXEuPBxjnnv6wYI8S/olthc+JeWkvPAA2hOnQJAUiqJfOst3AYNtMl6D5QcYMGmBZTUm/ck/HXoX3lk1CM4OWIDrKMb4PsHoc78/5eIeGPt/sB+9ltXD0JvkPntUAFrUrLYmVXG36cPZOHUAfZeVrcja386v696y/Q+OnYU0+56oMMzkHVVRn9/3vFm/v5wT2beF4NfaNe3O9Tt2UPx0mXU7dhhEZdcXPC78QaC7rkH5+Du26CsO2OQDRwqPWTy7meUZCAjW53rJDkRGxJryu4P9B8osvudgBD/gm6HVeE/ozfjrr444V+fcYDchQvR5ecbA5JExJKX8Rw31ibr3Zi1kcdSHqNRb/TyOkvOLB6/mGsHOmBJTG09/Po47FrVLChB4iK49FFwEk11OprqBi1f7MphbVoWueXmzpUfbjvNvZP74ursgF8Wuyj11VX8+PqLGPTGPhXBvftw1cP/QmHDjf3WsObv7xsXzNTbhuDi1rVv2/X79lG8dBm1qamWA0olftfOI+jee1GGOWjvEkGrVDRUkJaXZvLuN69QdzZB7kEmsT8+Yjw+Lj6duFIBCPEv6GbotQY2rMjg9AHbCP+KdesoeOJJZI3GGJAkQh9bjM+MGe1eqyzLvLvvXd7e97Yp5uPiwxuXvMHYcNt8sbAphQfh67uguNlGPO8ImLsS+iTZb109hNOltaxNy+Kr3bnUNOosxpwVEon9A6lp0OHqJcS/rXD39mHa3Q+w8e3/4uHnx5x/P4mLe8dm3Q+n5bPl06Podc38/Vf3ZdQVvbt0RrT+4EFKli6jZssWywEnJ/zmziHovvtQqlT2WZygzRhkA0fKjpi8+xklGRhkg9W5CknByOCRJsE/OGBwl/633B0Q4l/QbdBp9WxcccBC+I+eGc3Yq9peAkzWail8eQnlH39siim8vVG9+gpek9u/ya9B18ATqU+wIWuDKRbtE83yqcsdryGJLMPOVfDrY6A3ZyIZchVctRQ8hB+3o5BlmR2ZZaxJyeS3w4XIZz059/NQcvO4Xvx1fDRhvqJrZUcwJPESvPwDcPPyxjug43z2er2B1K9OkLHZ7O939XBm+p3D6D08sMPO29E0HD1GyfJlVP/2u+WAQoHvVVcR9OADuPQS/T+6ApWNlWzL30ZKrrGzbmlDaatzA9wCSFQlkqRKYkLEBHxdfTtxpYLzIcS/oFug0+rZ8O4Bsg+2X/jrSkpQP7yIut27TTGX/v2IWr4cl+jodq+1uK6Yh/58iIwSc8nA8eHjeXXyq453gawtgXUPwPFfzDFnd5jxEsTfJjb1dhCNOj3r9+WzJjWTg3lVLcb7h3hx58Q+zIlT4e4iMv0dTdSwER16/LoqDRtXZpB/wtwYLyDCkxn3xeAX0jX9/Y0nT1K8fDnVGzZaDkgSPjNnEvTgA7j27WufxQkuCFmWOVp+1NhoKzeZfcX70Mt6q3MlJGKCY4ybdSOTGBIwxHEbUQqE+Bd0fWwp/OszMshdsBBdQYEp5n3ZZYS/8IJNGsocKTvC/D/mU1hXaIrdMOgG/jX2XygVDuaXP/EHrLsfasxrJSwG5q2BYNtsdBZYUlLTyKc7svlo+2mKqxtbjE8eGMxdiX1IGhAkHpt3Ewozq9iwIoPaCvPfd7/4YKbc2jX9/ZrTpyl+6y2q1v9kLAXcDO/LLiNo/oO4DRTXD0elWlPN9vztpKhTSMlNoai+qNW5/q7+TFRNJFGVSEJEAv5u/p24UkF76HpXFoGgGUbhn0H2QfPmotFXRjN2VtuFf8U331Lw9NMW/v7gRYsIvOdumwitP7L/4D/J/6FeZ9ykqZAU/GvMv/jLkL+0+9g2RddorNu/bbllfMJ8mPoEOLvaZ13dmCMFVaxJyWTd3jw0OkvB5KZUMDc+kjsnRtM/RDQ36k4cSs1jy2dHMeia/FwSTJjdj7jLenW5L3eaXDUl77xN5brvQW+ZHfaaMoXg+Q/iNnSonVYnaA1ZljlecdyU3d9btBedrLM6V0JieNBwk51naOBQx6xGJzgvQvwLuiy2Ev6yRkPhSy9T/umnppjCxwfVa6/ildT+jayyLLPmwBre/N+bpnJnXkovXp38KhNVE9t9fJtSfAy+uRMKzJYkPENgzjvQf5r91tUNMRhkNh8r4r2UTFJPtPTOhvm4cWtCb24a0wt/Ub+/W6HXGUj58jgHtqpNMVcPZy67axi9hnUtf782P5+Sd1dQ8c03oLMUjZ5JSQQvXIB7TIydViewRq221pTdT85NtngSfTa+rr4kRCSQpEoiISKBQPeu9e9TYB0h/gVdEmvCf8yV0Yy9qm0eUl1xMbkPL6J+zx5TzHXAACLfWm6TTWgavYantz3NDyd/MMUivSJ5a+pb9PVzIL+rLMP/PoAN/waduXwkAy6Da94GL1Fv21bUNur45n+5vJ+aRWZJbYvxkZG+3JnYh5kx4SidhGe2u1Fb2cgvKw+Qf9Ls7w9UGf39vsFdx9+vLSqidMVKKr78ElmrtRjzmDCe4AUL8YiPs9PqBM2RZZlTladMYn9P0R50BuvZfYChgUNN2f2YoBiR3e+GCPEv6HLotHo2vJNB9qH2Cf/6ffvIXfgQukJz1sN7xhVEPPccCs/2+/vLGsp4+M+HSS9KN8VGhY7ijUvecCxvZMEBYyWf5p16nVzhsmdh7N/Epl4boa6o58O0LD7bmU1Vg+WNVyHBFcPDuCuxD/G9/Luc5UNwYRScqmTjigxqKzWmWP9RIUy5dQhK164hsHSlpZSuWk35Z58hN1ruS3EfPYrghQvxHOuApYp7GHXaOnYW7DQJ/rzavFbneiu9SVAZs/sTVRMJcu8e3aMFrSPEv6BLYSvhX/H11xQ8/Yw5Y6VQEPL3RQTcdZdNhNfx8uMs2LQAdY35sf6c/nN4fPzjKB2lEVZ1AWx6DtI/hubdF4OHwLXvQegwuy2tO7HndDlrUjPZeKAAvcGyVqe3mzM3je3FrRN6E+nfdbK+grZzKCWPLZ+b/f2SBOPn9CNuetfw9+vKyylb8z5ln3yCXFdnMeY2coRR9CckdImfpTsiyzJZVVkmsb+7cDdag7bV+YMDBpuy+yOCR+CsEHKwJyH+tgVdBp1Gz8/vZpDTDuEvazQUvPACFZ9/YYopfH1RvfYaXom28d9vzd3KP7f+k1qt0dIhIfHI6Ee4deitjh0Ae3oAACAASURBVHFj1NRC2nJIfRO0zWwnkgLG3APTnwalu/3W1w3Q6g1sOFDAmpRM9uZUtBiPDvTgjol9mDcqEi9XcRnuzuh1BpK/OMbBZHPm1dXDmcvvHk7UUMfvkaGvqqJs7VrKPvgQQ62lTc1t6FCCFi7Aa/Jkx7i29TDqdfXsKthFcm4yKeoUcmtyW53rpfRiQsQEU3Y/xCOkE1cqcDTEXUfQJbAq/Gf1YeysPhd8DG1REeqHHqY+3WzDcR00iMjly3CJimr3GmVZ5uPDH/Pq7ldNnQ49nD14edLLXBJ1SbuP324MBtj3GWx6FqrzLcf6T4Ppz0KoqMbRHirqNHy2M4cPt2WRX9nQYjyhXyB3TuzDlMEhKBRCLHV3aisb2bjiAAWnmvv7vZr8/Y79BVtfU0v5Rx9S+v5aDFWWvSZcBw4keOECvKZOFaK/k8muyiZZbeyqu7tgN436liWBzzDAf4Cpq25sSKzjlZMW2A0h/gUOj06j5+d39pNzuNwUG3tVH8ZceeHCvy49HfXCh9AVF5tiPjNnEv7csyg82m+30Bq0vLDjBb4+9rUpFu4ZzrIpyxgUMKjdx283p7bAr4stq/gAhAwzevv7T7XPuroJJ4pqWJuWyTd71NRrLcscujgpuCY2gjsT+zAk3MdOKxR0NvknK9m4MoO6Zv7+AWNCufSWwQ7t7zfU1VH+6aeUrn4PfYXlUyuXfv0Inv8g3pdfjqQQm9E7g0Z9I7sLdpOsNmb3T1edbnWuh7MH48PHkxRpFPxhnmGduFJBV0KIf4FDYwvhX/7llxQ8+xw09/c/8ggBd95hk6xVZWMlf9/8d3YW7DTFRgaP5L+X/tf+G6eKj8Fvj8Oxs7pseoXCpYsh7hYQlRwuClmWSTlRwnspmWw+WtxiPMjLhVvG9+bmcb0J9ha9EXoSB5PVbP38GAa92d8/YW5/YqdFOWym3NDQQPnnn1O6ajX6UsvSs8revQiePx+fmTORnMT1oqPJrc41evfVyezM30mDvuVTxDP08+1nEvvxIfGOs6dM4NAI8S9wWNor/A0aDYXPPU/Fl1+aYk6+vqjeeB3PhASbrDGzMpMFmxZYZGOu7HslTyc8jauTHQVfbQlsfhF2vw/N27E7u0PCApj4ELh62W99XZgGrZ7v0tWsScnkeFFNi/Eh4T7cldiHq0aG4+oshFJPQq81sPWLYxxKMfv73TyVXHb3MKKGOKa/36DRUPHVV5SuWImuyLKbq1KlIuiBB/C95mokZyEXOgqNXsOewj2m7H5mZWarc92d3RkXNs64WTcyiQiviE5cqaC7IH6bBQ6JVqPn57f3k3vk4oS/trAI9UMPUb93rynmOmQIkcuW4hIZaZM1bsvbxiNbHqFaU22KLYhbwD0x99gvu6dtgB3vQPLr0NjcpyvByJtgymPgq7LP2ro4hVUNfLTtNJ/sOE15nWUVDUmCqYNDuSuxD+P7BjhsdlfQcdRWNLJhRQaFmebfu6AoL2bcG4NPkOP5+2Wtlopvv6Pk3XfR5VvuAXIODyfovvvwmzMbyUU0mOsI8mvyTd79Hfk7TJ3frRHtE23K7o8OHY2Lk/g7EbQPIf4FDoc14T/u6j6Mnnlhwr/uf+nkPrQQfXGJKeYzaxbhzz6Dwt02N+Evj37JCzteQN+UVXdzcuOFpBeY3nu6TY7fZmQZDnwDvz8NldmWY9FJcPnzED7SPmvr4mTkVrImNZP1+/PQ6i1LdXq6OHHd6ChuT4gmOqj9vSEEXZP8ExVsXHmAuiqzv3/g2FAuuWUwShfHevoj63RU/vAjJW+/jTbXsjqMc3Awgffei9/116EQot+maPVa0ovSTdn9ExUnWp3r5uTGmLAxJsEf5d3+ghQCQXOE+Bc4FNaFf19Gz4w+72dlWabiiy8peP55S3////0fAbffZpNsrM6g45Vdr/DpkU9NsRD3EJZOXcqwQDvVxc/eDr88Cuo9lvHAAcbNvAOvEI262ojeIPPboQLWpGSxM6usxbjKz507JkZz/ZgofNyEx7anIssyB5PzSP6imb9fIZEwtx8jpzqWv1/W66n6eQMlb72FJivLYswpMJDAe+7G/8YbUbi52WeB3ZDC2kKTd397/nZT+Wdr9PLuZZHdd3MWfw+CjkOIf4HD0B7hb9BoKHz2WSq+MlfbcfLzQ/XfN/AcP94m66vWVPN/W/6P1LxUU2xo4FCWTVlmn5rJZafgtyfh8A+WcY9AuOQ/MOp2EJu/2kRVg5Yvd+WwNi2L3PKWj+HHRPtz58Q+TB8airOTqHbSk9Fp9Wz9/BiHU82WGTcvJZffPYzIwY7j75cNBqp//ZXi5cvRnDhpMebk60vA3XcRcPPNNql61tPRGrTsK9pnyu4fKz/W6lwXhYtFdr+3T+9OXKmgp2MX8S9JUiAwB7gSiAFUgAbIAN4H3pflpkLpxvnRQOs7YOALWZZvbOVctwEPAkMBPZAOvCrL8vp2/yACm6HV6Pnprf2ojzYT/tf0ZfSM6PN/trCQ3IULadi33xRzHTqEqGXLUKps429PU6fx/I7nya42W2qm957O84nP4+7cyX7e+nLY8grsXAnNOzg6ucD4+yHpEXDz7dw1dXFOl9ayNi2Lr3bnUtOosxhzVkjMGhHOnYl9GBHpZ6cVChyJmvIGNqw4QFGW2d8f3MubK+4djk+gY/j7ZVmmZtMmipctp/HIEYsxhbc3AXfcTsCtt+LkJTb+t4fiumJTdn9b3jZqtC2LAJxB5aUiUZXIpMhJjAkb0/n3DoGgCXtl/q8D3gHygT+BbCAUmAusBmZIknSdLMvyWZ/bB6yzcrwD1k4iSdKrwCNALrAKcAFuBH6UJGmBLMvLbfCzCNpJe4R/3Z495D70MPqSZv7+q68i/JlnbPL4Or8mnyW7lvB79u8W8XtH3MsDsQ+gkDox+6vTwK7VsOVlaDira+zweTD1SfAX2aMLRZZldmSW8V5KJr8fLuTsq42fh5Kbx/Xi1gnRhPqIR/ACI3nHK9i4MoP6avMX74HjQrn05sE4O4C/X5ZlardupXjpMhoOHrQYU3h6EnDbrQTcfjtOPqLnxMWgM+jIKMkwddU9XHa41blKhZJRoaOMjbYiE+nj08ehrGCCnou9xP8x4Grgp7My/I8CO4F5GL8IfHPW5/bKsvzUhZxAkqQEjML/JDBGluXypvgrwB7gVUmS1suynNW+H0XQHozCfx/qo2YxO352X0ZdEX3Oz8myTPlnn1H4wouga8rUOjkR+q9/4v/Xv7b7AqvRa/jg4Aes3L/Sosayl9KLx8c/zsy+M9t1/DYhy3BkPfz2hNHq05yocXD5CxA5uvPW08Vp1On5cV8+a1IyOZRf1WK8f4gXd07sw5w4Fe4OIOYEjoEsyxzYoibly+MYDGZ//8Rr+zPi0ki7izpZlqnbto3iN5dSv2+fxZjk7k7ALTcTcOedOPv722mFXZeS+hLS8tJIzk0mNS/VosLb2YR7hhvLcKqSGBc+Dg+lsFMJHA+7iH9Zlje1Ei+QJOld4HngElqK/7ZwX9Ofz58R/k3nyJIk6S3gceAO4Ml2nEPQDrSNen56u+3C39DYSMHTz1D57bemmJO/P6r//hfPcWPbva4UdQov7XypRSfFq/tdzaJRizq3cZf6f/DLYshOs4z7R8O0p2HoNWIz7wVSUtPIJ9uz+Wj7aUpqGluMTx4YzF2JfUgaEGR3ISdwLHRaPVs+O8aRNLO/391byeV3D0c1yP5iunbnTkqWLqNu926LuOTqiv9NNxF49104B9m54WAXQm/Qc6D0gCm7f7D0YKtznSVn4kPjjdl9VSL9/PqJ64fA4XHEDb9nnqXqrIxFSJJ0LxAIlALbZFneb2UewJSmPzdaGduAUfxPQYh/u3Cxwl9bUEDugoU0ZGSYYm7DhhG5bCnKiPY1O8mryWPJriX8kf2HRXyQ/yAWj19MXEhcu47fJipy4I9nIONLy7ibL0z6J4y9B5xF19jzYTDI7Mwq4+s9ufywLw+NzmAx7qZUMC8+kjsmRtM/xNtOqxQ4MtVlDWxckUHRaXO2N7iXNzPui8E7wL52sLr0dIqXLqVu23aLuKRU4nf99QT+7W8oQ+1QjKALUtZQRqo6lRR1Cml5aVQ0VrQ6N8QjhCRVkim77+Ui9k0IuhYOJf4lSXIGbm16a020T2/6r/lnNgO3ybKc3SzmiXETcY0sy5bdS4wcb/pz4AWua08rQ4Mv5PMCS7SNTVafY+aL64Q5/Yi//Nx+9bpdu8h9eJFF63nfa64h7Omn2uXvb9Q3svbAWlZnrLaw+HgrvZkfN5/rB12Ps6KTflUaqiDlDdj+NuiatXRXOMOYe2DyP8HDcSqJOCrHCqv5Ll3N9+lq8iobWoyH+bhxa0JvbhrTC39PUc+8u2Gra3ZDjZavXtxl4e8fPD6MyX8ZZFd/f33GAYqXLaV2a7LlgLMzfnPnEnTfve1OhnR3DLKBQ6WHTNn9jJIMZM7eZmjESXIiNiTWlN0f6D9QZPcFXRqHEv/AS8Bw4GdZln9pFq8DnsW42feM6XkE8BRwKfCHJEmxsiyfKaJ7ptRJZSvnORMXpTs6mYsR/rIsU/7JpxS+9JKlv//f/8b/lpvbdRFOzk3mxZ0vklOdYxG/pt81LBq1iED3wIs+dpvQ6+B/H8DmF6G22HJs8CyY/gwE9uuctXRRCqsa+GFvHt+lq616+QFGRvpyZ2IfZsaEoxSlOgXnwc1LyeDx4aT/lo1CITHxugHEXKKym/BrOHKE4qXLqNl0lnPWyQnfa64h6IH7bdbBvDtS0VBBWl4aKeoUUvNSKWto2cPjDEHuQSbv/viI8fi4iA3Sgu6Dw4h/SZIWYtygewT4a/MxWZaLgCfO+shWSZIuA1KAccDdwJsdsTZZlkdZizdll+I74pzdkYsR/obGRgqefIrKdeYiT04BAcb6/WMv3t+vrlHz8s6X+TPnT4v44IDBLB63mNiQ2Is+dpuQZTj+G/z2OBRbluMjPNa4mTd6YuespQtS3aDll4OFrEtXk3qypEXFHgB/DyWzRkQwN15FbJSfyNj1AGx5zR4/px+1lY0MS4ogYoB9/P2Nx49TvPwtqn/5xXJAkvC5ahbBDzyAS3S0XdbmyBhkA0fKjpCcm0yyOpmMkgwMssHqXIWkYGTwSFN2f1DAoM6t5iYQdCIOIf4lSZqPUbgfAqbKstz61/FmyLKskyRpNUbxPwmz+D+T2W+t2PmZeOumPoFN0TbqWb98H3nHL1z4a/Pzjf7+A+ZKrm4xMUQufRNlePhFraNR38iaA2t4L+M9GvXmTZ/eLt4sjFvIdQOvw0nRSY/zCzLg18fg1GbLuE8kTHsShl8LCnHzORut3kDy8WK+S8/jt0MFNGhb3sxdnRVMGxrKnFgVkwYG4+Is/j8KLg6FQmL6nfbp3t2YmUnJW29T9dNPnP3N1nvGFQTPn49rP/FEsDmVjZVsy99GSm4KKeoUShtKW50b4BZgyu5PiJiAr6vojyLoGdhd/EuS9DDwBsZa/VObsvxt4YxHwvNMQJblWkmS1IBKkqRwK77/AU1/tt5+T2AzrAr/uf2Iv6x14V+7YyfqRYvQl5m/B/rOmUPYU0+icL24ja5bc7fy4o4Xya3JtYjP6T+Hh0c9TIBbJ3npq/Lhz+cg/RNo7jF18YakRTD+AVCK5i/NkWWZvTkVrEtX8+P+fMpqNS3mSBJM6BvI7DgVVwwPw8dNdDcWdE00OTmUvPU2lT/8AAbLL7de06YSvGABboMG2Wl1joUsyxwtP2pstJWbzL7ifehlvdW5EhIxwTGmzbpDAoeI7L6gR2JX8S9J0r8w+vz3AtNlWS45z0esMb7pz7MKoLMJo33oCoxdg5szo9kcQQeiadDx01v7L1j4y7JM+UcfUfjyEtA3XcCdnQl99D/433TTRVk2cqpzWLJzCZtzN1vEhwQMYfH4xYwMHtnmY14UmlpIWwapb4K2zhyXFDDqdrjkP+AlKnM0J7OklnXpatbtVXO6tM7qnMFh3syJU3F1bAThvuJLk6Dros3Lo+Sdd6n47jvz/qYmvCZPJmjBAtyH2+cphCNRralme/52UtQppOSmUFTfes7Q39WfiaqJJKoSSYhIwN/N/qVZBQJ7YzfxL0nS48AzGBtuXXYuq48kSfEYG3wZzopPBRY1vf34rI+9i1H8L5YkaV2zJl/RwINAIy2/FAhsiDXhnzC3P3GX9bI639DQQMGTT1L5/Q+mmFNgIJFv/heP0W1vYtWga+D9A++zOmM1GoM5U+zj4sPCuIVcO/DazrH4GPSw7zPY9BxUn/UQqv90uOxZCBnS8evoIpTWNLJ+fz7fpavZm2PdmRfm48Y1cRHMjlUxJFxsxBN0bbSFhZSuWEH5V1+DVmsx5pmQQPDCBbjHdtI+JAdElmWOVxw3Zff3Fu1FJ1urBm7M7g8LHEZSpNG7PyxwWOdZOQWCLoJdxL8kSbdhFP56IBlYaCWjmyXL8tqm168DAyRJSgPOeDZGYK7l/7gsyxZdkGRZTpMk6XXg78B+SZK+BlyAG4AAYIHo7ttxaBp0rF++j/wT5oJLCfP6EzfduvDXqtVGf/+hQ6aY24gRRn9/WFibz785ZzMv7XwJdY3aIj5vwDwWxi/sPIvPqc1GX39BhmU8dLhR9PebYvVjPY16jZ7fDhs37m49VozO0HLnrrerMzNjwrkmLoLxfQJRKMTGXUHXRldSQumqVZR/9jmyxtLK5jFmDMEPLbyoxEd3oFZba8ruJ+cmU1hX2OpcHxcfJqomkqRKIiEiofOqtAkEXRR7Zf77NP3pBDzcypwtwNqm1x8Bc4AxGC07SqAQ+BJYLstysrUDyLL8iCRJGRgz/X8DDMD/gFdkWV7f/h9DYI22Cv/a7TuM/v5yUyNmfOfNJeyJJ9rs78+pyuGlXS+xNXerRXxo4FAWj1vMiOARbTreRVN8FH59HI6fVZ3DKwymPAaxf4Eeno3SG2S2nSzlu3Q1Gw/kU6tp6dNVOklcMiiEOXEqpgwOwU3Zs/+fCboHuvJyyt57j7JPPkWur7cYc4+LM4r+ceN6VGUqWZY5VXnKJPb3FO1BZ7Ce3QejbTMp0ujdjwmKEdl9gaAN2EX8y7L8FMYa/Rc6/z3gvYs811rMXyIEHYw14T/x2v7ETmsp/GVZpuyDDyh65VWzv1+pJGzxo/jdcEObbnwNugbeO/AeazLWWFh8fF19WRi3kHkD5nXOzaGm2Firf89aaL7pzNkdJi6EhIXg2nO7QcqyzKH8Ktalq/l+bx5F1Y1W543u7c/sOBVXxoSLJlyCboO+spLS99+n/MOPMNRZ7mFxGz6c4IcW4pmY2GNEf522jp0FO02CP682r9W53kpvJkRMMNl5gtyDOnGlAkH3wu7VfgTdh7oqDRtXZlyQ8DfU15P/xJNU/fijKeYUHETkm2/iEX/hZbhlWebPnD9ZsmuJhcVHQmLugLk8FP9Q52zw0jbAjndg62ugqW42IBmz/FMeA5+e23FTXVHP93vVrEtXc6ywxuqcvkGezIlTcU2sil6BHp28QoGg49DX1FD2wQeUrf0AQ3W1xZjr4MEEL1yA16WXdnvRL8syWVVZJrG/u3A3WoO21fmD/AeZxP7I4JGd12ldILAlei1UqaH8NFSchops42ttHdz4iV2WJH6TBO3GYJA5uFXNjh9O0VhnfkzbmvDX5KrJXbCAxsOHTTH3kSNRLV2KMvTCq91kV2Xz0s6XSFZbur6GBw5n8fjFDA8afhE/TRuRZTjwDfz+NFRmW471mQSXPQ/hnWQ1cjAq67VsyDBu3N2RaX0/f5CXC1eNjGBOnIoYlW+3Fz+CnoWhtpayjz+hbM0a9JWWDeddB/QnaP4CvKdPQ+rG/TzqdfXsKthFcm4yKeqUFqWWm+Op9CQhIoFEVSITIyYS6hnaiSsVCC4Sg8FYzKO5sG/+ukpt6QQ4g6QwfjFw6vyy1EL8C9pF/slKtn5+lJIcy2xua8K/Ni0N9d8fQV9hruLid911hD7+GAqXC7N31OvqWZ2xmvcPvG+RNfJ19eXh+IeZO2Bu59Ruzt4OvzwK6j2W8aCBMP1ZGHi5sfh8D6JRp2fz0WLWpav543ARGn3LBlzuSicuHxbK7DgVif2DcHbqvsJH0DMx1NdT/tnnlK5ebdGrBMAlOpqg+fPxmXEFklP39KlnV2WTrDZ21d1dsNuioeLZ9Pfrb/Lux4bEolSI/hwCB0OWobbEKOjLs4yivuJ0k8jPhsoc0LfsPXP+4xqgMhcC+px/ro0R4l9wUdRVadj23QmObCuwiPsEuzPphoH0Hm5ZbUGWZcreX0vRq6+am9YolYQ99hj+N1x/QeeUZZlNOZtYsnOJhTdUQuLagdeyMG4hfm5+7fvBLoSyU/Dbk3D4B8u4R6CxVv+o2+3yTd5eGAwyu0+Xs26vmp/251NZ3/IxvkKCxAHBzImL4LKhYXi6ikuPoPthaGyk4osvKVm1En2xZdsaZVQUQQ8+gO+sWUjO3evff6O+kd0Fu0lWG7P7p6tOtzrXw9mD8eHjSYw0dtYN82x7NTeBwObUl1tm7c8I+zMZfK31PjMXjFcY+PcGv97g18v82ss+T7e61xVI0OEY9AYObFWz44dMNPVmi4+zUsGoGb2Jnd4L57Mqshjq68l/7HFji/oz84ODUS19E4+4uAs67+mq07y480VS1akW8ZigGBaPW8ywoE5ofFNXBltfhZ0roblP1ckVxt8PSX8Ht57THv5EUTXr0vNYt1dNbnm91TkxKl9mx6m4amQ4Id5unbxCgaBzkDUaKr79lpJ3V6ArsEyIOEeEE3T//fjNno2k7D5JgdzqXKN3X53MzvydNOgbWp3bz7cfiapEkiKTiA+JR9mDkiMCB6GxxlLMm6w5p6E8Gxorz3+Mc+ERaBT1fr2bhH0v8Is2vvaNAqVj3f+E+BdcMHknKtj62TFK1ZYWn76xwUy8rj8+gS27q2pyc8mdv4DGI0dMMfe4OFRv/hdlyPn9/XXaOlZnrGbtwbUWFh8/Vz8WjVrE7P6zO9biI8uQu9tYvefAN6A7S+QOvxamPmH8Be8BFFU18MO+PL7fm0eG2vrFMtLfndmxKmbHRdA/xLuTVygQdB6yVkvl999T8vY7aPMsK9U4h4YSdN+9+M2bh3SBlkZHRqPXsKdwjym7n1mZ2epcd2d3xoWNI1GVSGJkIiovVSeuVNAj0TYYLTQVWS099xWnoa60fcd39TlL2Dd/3Qtcu9a9Toh/wXmpq9KQ9u0Jjm63zGj5BruTdONAeg+z3lClJjWVvL8/YrHRze/GGwh79NHz3gxlWeaP7D9YsmsJ+bXmrrgSEtcPup4FcQvwde3ALHt9Bez/0ij6iw62HI8aD5c/D5HdvwFPbaOOXw4W8F26mtQTJVjpv4Wvu5JZI8KZHadiVC9/0YBL0K2R9Xqq1q+n+K230WZbbvR3Cgoi6G/34HfDDW3uU+Jo5NXkmbL7O/J3UH928qMZ0T7Rpuz+qNBRuDp17Z9d4GDodVCVa2nHaf66Ov/8xzgXzu6Wdpzmr/17g5tft9rDJ8S/oFUMegMZm9Xs/PEUmgbzTnVnpYJRM6OJm9YLJ2XLrLssy5StWUPRa6+b/P2SUknoE4/jf9115z1vVmUWL+58kbQ8i6bNjAgawaPjH2VYYAdZfGQZcnfB7vfh4Hcts/xg7Mw7+Z8w5OpudSE4G53eQPKJEtalq/n1YCH12paVClycFUwbEsLsWBWTBwXj6tw9Ny8KBGeQDQaqN26kePlbaE6dshhz8vcn8O678f/LTSjcWz4F7Qpo9VrSi9JN2f0TFSdanevq5MrYsLFGwa9KIsonqhNXKuh2GAxQU2A9a3+uijkXikIJflFnZe2biXvP4G59Tz8bIf4FVsk7XsHWz49Sqq61iPeLC2bidQPwDrDuXzPU1ZG3eDHVGzaaYs4hIUQufRP32NhznrNOW8eqjFWsPbjWorOjv6s/i0Yt4pr+13SMxae+vFmW/1DLcaUHDJ8Lo+4A1ahue4GQZZn9uZV8l65m/f48SmqsVy8Y3zeAOXEqrhgejq+78O4Kuj+yLFP922+ULFtO4/HjFmMKX18C77gD/1tuwcnL004rvHgKagtIUaeQok5hW9426nStb2yM8o4iSZVEUmQSo0NH4+bsWD5mgQPTvGKOKWvfTORfbMWcM0gK8FG1bs3xDgfRBdqEEP8CC2orG0n79gTHdhRaxP1CPUi6YQC9hlq3+MiyTG1aGkUvvWxxc3SPjyfyzf/iHBzc6jllWeb37N9ZsmsJBbVma5FCUnD9wOuZHzff9hYfWYacHUbBf/A70FnZrBYaA6Nvh5jruu1G3kadnt1Z5Ww5Vszvhwo5VVJrdd7AUC/mxEVydWwEKr+umdUUCNqKLMvUbN5M8bJlNB46bDGm8PIi4LbbCLj9Npy8u47fV2vQsq9on6kU5/Hy463OdVG4MCZsjMnO09unZ+xtElwk9RUt7TjNX9uiYs7ZdpwzIt83skdV2WsvQvwLALPFZ8ePp9A2t/i4KBg9M5rYqa1YfAwGajZtomTFShoyMizG/P9yE6H//vc5/f2ZlZm8uONFtuVvs4iPDB7J4nGLGRI4pJ0/2VnUl8O+L4yiv/hwy3GlBwyf15Tlj+92WX5ZlskqrWPL0SK2Hi9h28lSq5YegFAfV66JVTE7VsWQcG/RgEvQ45AbG8l//An0JeaynZKHBwF//SuBd9yOk18nlBa2AUV1RaSqU0lWJ7Mtbxs1WutdtgFUXioSVYlMipzE6NDReChFt21BE5paK02ssmxXMcc9wIrnPrpJ4EeBUiSebIUQ/wLyjpez5bNjlOWdZfGJD2bitdYtPrJOR9WGDZSuXEnjcUtfqOTiQtiTT+A3b16r56zT1rFi/wo+PPShhcUnwC2ARaMWcXW/q21n8ZFlY0OuPWvh0DrrWf6wGKPgj7kOfUzD2AAAIABJREFU3Hxsc14HoaZRR9qJErYeL2bLsWJyylrftOfl6swVw8OYE6difN9AnMTGXUEPRuHmRtA9d1P44ktIbm74/+UvBN59F84BAfZe2jnRGXTsL95v2qx7pOxIq3OdFc6MDh1tyu738ekjvuj3VHSNUJHTujWnruT8xzgXLt7Ws/ZnXnexijldGSH+ezC1FY2kfnOC47taWnwm3TCQqKEtb3AGjYbK79ZRuno12pwcizHJxQW/a68l8K47Uaqsl3aTZZlfT//KK7teobDOfF6FpODGQTfyYNyD+LjYSHzXlcH+M1l+Kzc/pSfENGX5I+K6TZbfYJA5lF9lFPtHi9lzuhydtRI9TfQJ8mTSgCAmDwpmQt8g3F2EL1IgOIPfjTeiKysn4Jabz2lftDcl9SWkqlNJUaeQmpdKtaa61bnhnuGmjbrjwseJ7H5PQa8zbpxtzZpTnQ+0fq84L2cq5rRmzXH37zb32a6OEP89EL3eQMafuez8MRNtYzOLj6sTY2ZGM3JqFE7Olll3Q10dFV99Rema99EVWn5ZUHh44P+Xmwi47bZz3hxPVZzihZ0vsCN/h0U8LiSOR8c9yuCAwe3/4WQZsrc1efnXgbW28mEjYPQdxhr93STLX1rTSMqJErYcLWbr8RJKaqz83E14ujgxoZ9R7E8eEEyvQHHjFwhaQ+HqSsiih+29jBboDXoOlB4gOdfo3T9UaqVYQRPOkjPxofEkqZJIVCXSz6+fyO53R85UzGnRxKrpz0obVMzxjTzLmhNtfu0VIsR9F0GI/x6G+mg5W79oafHpPyqEidf2x8vf0uKjr6qi/NNPKfvgQ/Tl5RZjCl9fAv76VwJuufmc3tc6bR3v7n+Xjw5+hE62tPg8MvoRrup7VftvRHVlsO8zo+gvOdZy3MULYq6FUbcbs/xdHJ3eQHpORZPYLyZDXYl8joTN0HAfJg0MZvLAYEb19sfFuQMbowkEgg6hrKHMlN1Py0ujorGi1bkhHiHGyjxN2X0vF69OXKmgQ5BlY7OqFsL+TOfaHOsJrwvFVDHn7CZWTa9FxZxugxD/PYSa8kbSvjnO8d1FFnH/MA+SbhxI1GBLi4+utJSyDz6k/NNPMdRYbg5zCg4i8PY78LvhhnOWtpNlmV+yfuGV3a9QVGc+r0JScNPgm3gg9oH2WXxkGU6nNXn5v7d+0QuPNQr+mGu7vJ8wt7yOrcdK2HqsmNSTJVQ36Fqd6++hJGmAUewnDQwixFuU5BMIuhoG2cDBkoMm7/6BkgPIrdgynCQnYkNiTdn9gf4DRXa/K9JQ2Xqt+4ps0FqvyHbBeIW2bGJ15rVPJDh3/W7UgvMjxH83R683sP+PXHb9ZMXic2U0I6dYWny0BQWUvreGiq++Qm6w3BirjIgg8J678Z0797ydK09WnOTFHS+yo8DS4hMfEs+j4x5lUMCgi/+hakvNWf5SK2XqXLyMG3dH3dals/wNWj07MsvYcrSYLceKOFnc+kXfSSERF+XH5IHBTBoYzHCVr9isKxB0QSoaKkjLSzN598saylqdG+QeZPLuj48Yb7v9UoKOQ1Nr3lRrzZrT0N6KOf5nNbFqbs0RFXMERoT478bkHilj6+fHKC+wrK07YHQICfMG4OVvFvCa06cpXb2ainXfg1ZrMd+lb18C/3YPvldeiaQ8dx3dWm0t7+57l48PfWxh8Ql0C+SR0Y8wq++si8tGyTKcTjV23z38g/VmIBFxxiz/8GvBtes94pZlmRNFNWw5ZvTt7zhVSqPO0Or8CF83Jg8KZtKAYBL6B4mGWwJBF8QgGzhcdpiUXGN2P6MkA4Ns/fdeISkYGTzSlN0fFDCoYxofCi4eXSNU5jaVwLRS6762uH3HN1XMsWLN8evVbfaxCToWIf67ITXlDaR+c4ITZ1t8wj2ZdONAIgf5m2INR49RunIlVRs2GDcLNcN16BCC7r0P72lTkZzO7fM7WnaUn079xA8nf6C0odQUd5KcTBYfb5eLsN3UlsK+T5uy/FZazbt4w4jrIP42iDh3B2FHpLJeay7DebSYvEorZUibcHFWML5vIJMGBHHJoGD6BXuJx/oCQReksrGSbfnbSM5NJlWdanHNPJsAtwBTdn9CxATbNzwUtA29DqrzrFtzKrKhKo/2VcxxsxTzZ2fwRcUcgQ0Q4r8bodcZ2PdHDrt+zkLXzOKjdHVizKw+jJgSiZOTMUtUv28fJStWUrNpU4vjuMfHE3TfvXgmJZ1TXBbUFvBz5s+sP7XeapfI+JB4Fo9fzED/gW37QWQZspKNgv/wj61k+eONFXuGze1SWX6DQSZDXcnWY8aa++k5FejPUYazX7AnkweGMGlgEOP6BIoynAJBF0SWZY6WHzV693OT2Ve8D30rVVckJGKCY0ybdYcEDhHZ/c7EYICawrOEfZb5dZUaDK3vtzovCmdjxRyLrH20+bVnCCjE37egYxHiv5uQc6SMZGsWnzGhTJzXH08/V2RZpnb7DkpWvEvdtu0tjuGZmEjQvX/DY8yYVs9Tranm99O/s/7UenYV7LK6+SzEPYRFoxdxZZ8r25aZri2BvU1Z/rKTLcddvGHE9UYvf/jICz+unSmqbiD5WAlbjhWTcqKEslorX2aa8HZ1ZmL/ICYNDGbSwCAi/UUZToGgK1KtqWZ7/nZS1Cmk5KZQVF/U6lx/V38mqiaSqEokISIBfzf/VucK2oksG6vDVWRZr3Vfkd2+ijlI5oo51mrd+0SIijkCuyPEfxenpryBlK9OcPJ/ljeWgAhPJt0wENUgf2RZpvrPPyl9dwX1+/a1OIb39GkE/u1e3GOGWz2HVq8lRZ3C+lPr2ZyzGY2hpXh1c3Lj0l6XMqvvLCZETECpuED/uSxD5lZzlt+gbTlHNcrYiGv4XHBpvbqQo6DRGdhzutzo3T9WzKH8qnPOHxHpy6QBwUweFExslB9KJ5H1EQi6GrIsc7ziuCm7v7dor8W+p+ZISAwLHEZSpNG7PyxwGE5CENoOU8UcK577imzQ1Jz/GOfCM6RlpZwzr32jRMUcgcMjxH8XpVWLj5sTY2f1IebSSBTIVP38MyUrVtJ49KjlAZyc8LlyJkH33IPrgAEtji/LMvuK97H+1Ho2Zm2ksrFlBQKFpGBc2Dhm9ZvF1F5T8VS2QZjXFJu9/GWnWo67+hiz/PG3QfiICz+uncgurWPLsSK2HCth28kSajWtN1IJ8nIxif3E/kEEep27cpJAIHBMarW1bM/fTnJuMinqFIuu5Wfj4+LDRNVEklRJJEQkEOge2Ikr7WZo6izFfHmWpchvaL3/wQXh7n/WhtpmGXzfKHART2QFXRsh/rsgOYfK2PrFMSoKLS0+A8eGkjCvPx7uEpXrvqN05So0p09bzJGUSnznziXw7rtwiYpqcezMykx+OvUT60+tR12jtnr+IQFDuLLvlczoM4MQj5ALX7jBAFlnsvzrrWf5I8cYK/YMm+PQWf46jY5tJ0tN3v2s0rpW5zorJEb19jdV5hka7oNClOEUCLocsixzqvKUKbu/p2gPunP4v4cEDCEp0ujdjwmKEdn9C0Wngcqzy2E221jb7oo5XtabWJ15LSrmCLo5Qvx3IarLGkj96jgn0y0vfIEqYxWfsCh3Kr7+mrz33kOXn28xR3J3x/+GGwi443aUoaEWYyX1JfyS9QvrT67nQOkBq+cO9wznyr5XcmWfK+nv379tC68phr0fw54PoDyz5birL4y8wZjlD7NuPbI3DVo9h/Or2JlZxpZjxezOKkejb70MZ6S/O5ObOupO6BeIt5sowykQdEXqtHXsLNhpyu7n1ea1Otdb6U2CKoFEVSKJqkSC3IM6caVdCIPeuHG2hTXH1hVzrHWqjRYVcwQ9HiH+uwB6rYG9f2Sz++csdBqz4HRxc2LsVX0ZOtqPyi8/58TaD9CXWpaMU3h743/LzQTceivO/uZNZHXaOjblbGL9qfVsz9tutfKEt9Kby6IvY1bfWcSHxret4oTBAJlbjFn+Iz+1kuUf2yzL7ziPUc8I/QPqSjLUlWSoqzhWWH3OqjzuSifG9w0wNdnqE+QpynAKBF0cWZaZ8/2ccwr+Qf6DTN79kcEjcVaI26q5Ys7Zwv607SvmmDz30ebXomKOQHBOxFXKwck+WMrWL45RWVRvER80LoyxU4NoXPc5p/7zCYYqy02lTgEBBNx+O/5/uQknL2MpTJ1Bx478Haw/tZ4/sv+gXmd5TABnhTOTIyczq+8skiKTcHVqox+9uhD2fgL/+8DowzybM1n+UbdD6LC2HbsDaNDqOXRG6Ocaxf7xoppzCv0zDAr1Nll5Rkf746YUj/QFgu6EJEmMCRvD9ye/N8U8lZ4kRBiz+xMjJhLqGXqOI3RTmlfMaW7H6ciKOc1fe4eDk5AvAsHFIn57HJTqsgZSvjrOKSsWn4TLQ3Dd9CV5s79ErrP0mjuHhRF41134XTsPhbs7sixzsPQg60+uZ0PmhlabycSHxDOr3ywu631Z25rIVKohe5ux++7pbVB82Pq8qHFGwT90tt2y/GeE/hmRf6ANQh+gT5AnMSpfEvsHkTQwiHBf0SZdIOjuJEUmcbD0oMm7HxsSe+HVzLoyDZUtG1g1f22zijlWrDmiYo5A0KEI8e9g6LUG0n/LZs+GLHRaS4vPqP9v786D4yjvNI5/fzO6ZUvCNraxhCXLYDBgzOEY2+yCgcUYLBI2IbUXSTYbrk1SbBLIHjmWJFU5NgeVhE32zC4s2doAIZAiIYTiSLAxGwowgSyXDT7wBb5kybZuvfvH2yPNjGYkjY5pzfTzqZpqqWc0euedVvejd3799gUzmPPCfbR/5Ccc7UktoylrbGTm9ddRe+WVWFkZO9t38tCL/gJcWw9nqLMHmmubaWlu4YrmK6ifVj9y45zzV9ndvtHfdmz0B4FsKmph6Z/4Wv45p43q9U+Uju6kEf0xBP3mWdWcUV/Lkvpazqiv5fT6GmpUty8SOWsa13BZ02VhN2PiDcyYkyjN2ZZapjPeGXMq6oZenVYz5ohMCQr/U8j23x1g/d2vc3hfajnOyadXc9KOn9H1+ftp60utzS9ftIiZN1xPzdq1tPUe4d6tD/DzN3/O8+88n/F3zKqcxeULLqeluYXFMxYPX5fe3wd7XwpG9jf65UizLMRK/Cj/2R+A096Tlx28D/qJsh0f+Lfsyz3on9kQBP15NTpBV0QACvfcneQZczKN4B/NftGxUSmblmE6zPmDI/gVOXyCLCJ5pfA/BbTt72DDvZvZ+tv9KetnzCrhtEOPU/a9u0mvnqxYeiazbriR0gtWsn7Xen7260/x5K4nM047V1lSyaWNl7JuwTqWn7A8+wlpvV2w63lfwrPjaXjrGega/gJVlFRCwzJoPB8aV/qpOidxis5MQX/zO+2MJuebDZbuDIzoK+iLSCHq7/Oz4qRfxCoR8sc7Y068PDXMp895XzVDM+aIFCiF/xD19vSx6ZEdPPfwdvqSS3zKYFHHs8y6705iLnU6yaoVK5hxw3W82lTCnVsf4pF7Pkt7T/uQ545bnFXzVtHS3MLqE1dTVZphBL6rHd76TVDG8zTsem7kk7QqamH+SmhcBfNXwQlLJ60281h3Ly/vbgtm3PGlO1veOTLqoN8cBP1E+c7p9bVMK9cmLyIFwLnBGXMObfcn1yaH/MM7xzdjjsX9jDnpF7FKLDVjjkjRUhIKybaX9rP+ns20pZX4NPS8TtNTP6CsJ/VkqmkXXUTHn17B/VVb+PnWW9n7+t6Mz7tk1hLWNa9jbdPaoVeQPLp/sHxn+1O+pMdln6se8LMqJMJ+4yo4fvGkHBASQf/FnYcH6vTf2Jd70F/SUMeS+lpOm1ejoC8iU5dz0HFoaK19a9KMOb2d4/gFBjXzspfmTJ+nGXNEIkp/+XnWtr+D9fdsZtuLqSU+NT37OPmlO6ltSzo5Nxaj7NLVPLemiXv7n+HVN/8u43M2TGugZWEL6xaso6m2afCO1h1JJ+c+DftfH7mBMxb68p35q/zyuAUT/tHu0a7egVl3xhL0Fx4/LWVEX0FfRKakrvbMs+UkRvC7h35qm5Pq47NcqbbRj+qX5DhVs4iMinOO7r5+unr76erpp6u3j67efjp7+oasS10/uK6rt4+/XXtqKOcVKTHl0d6th3ngtk0pJT4l/Z00b3mA+t0bsER9ZkkJrRefxX3L+3mkbz1u/5NDnquuvI7Lmi6jpbmFpccvxQD2vQbP/sdgGU/bzhFaZDDnjGBUf6Uf4Z8+d8JeL/ig/39B6U5y0HejDPonJQf9hlpOO6GGagV9EZkKejqg9a2k2XLSQn7HofE9f0Vd2lz3ySP4J07q+VUiU11/fxDAe/rp7O1LC9x9aevTAnrauszP4b/u7Bl8vuSfGU2OGcnNl55CWYnCf1E7fv50amdVcHCPn5v/hD0bWfjmTwdKfFxZKS+fX8+/nvE2e6a9AGkX3S2Pl7P6xNW0NLdw/pzzKN33MmzZAI9/wwf+joPDNyBWCvXnBGU858OJy6GybkJeW3dvP3sOd7DrUAev7G3POejH0kf0FfRFZCpo3QEH38xwIavtviZ/PEqrs891Xzd/wvbPIpOlr98NjmonBeRM61KCdLYR86TR8c60UfKB5wnWd/eNULZcALp6+ygryf+5NUpWedSzZQvNG79Hz6yLWbT5Hmrbtvn1FaU8uqyE+87ppq06dbTeMJbPXc66xjX8QbyO6btfgCe+7Wfi6Tk6/C8srfYBv3GVD/wNy6B0bBemauvsYXerD/e7WoNb8PXu1g7eae8a9X/BMYOTZk8bKNtJlO5UlWlzFJEp5ifX+7LJsYiXpYb59BH8qpmaMUfGxTlHT58bWmKSPoLd00dnhrKTbKPaXRnKVzIF9N5RTqldjErjRnlJnPKSmL+VxlOXJTHKS+JUlPpleenguvKSGBWlcUrj4ZxUr7SVR2ULmpjR+RbLnvs6BhytivHgMnj43H6OVfQAgweBRbULaaldzOVdvczd+Vv4zUehvyfbU3uVMwaDfuNKmLt0VCd09fc79h/pYmcQ6HenhftdrR20d45tVomYwcmzpwdBv4YlDbUsPkFBX0QKRF1j9vBvcaitHzoNZuLraXM0Y04EOOeGhOLBYJ0crlMDdWeGgJ5txDtT+UrieSKcvykLQnZFWuBOBO3B9YlgHqNi4P7U4F6Rsi6e9tjU5ygviROPFe4/7kpgebS76x0eWlHKssfgwfNiPHqW0VU2uPHMLq1hXclM1h3cxylbfwU8MfwT1jT4kJ+YdnPWoowHmq7ePva0dmYcsd/V2sGe1s5xf3wWM5hTU8G8ukqaZlYr6ItIcTjhTF/PP+RCVo1QU68Zc6aIvn6Xe4nJKEfBM53Emfzc3b2FX34yVmZkDMgDobs0Rll88PuKDKPjKQG9ND3AJ35u6LqyeIxYAQfwMGmvlUezq2bzkzOOcseiOL3BCR7TiHNpdz8tB/ayrHMHw44RzVqUOu1m3XwADnf0+BH7V/cNBvykkL+vfYS5+0ehvCRGfV0l9cdVUl9Xyby6ypTv59ZWhPbxlYjIpFn5MX+TYWUqP8k4kt2TVp6SQ1141zDPE+Xyk5KYpY58Z/w6NVinjHKXZgjt2QJ62gh7adwK9yrYEVb04d/MGoAvAWuBmcAe4AHgi865cU7FkJuyriNcEqvg/ngbq48eo+XIUS7s6KQiU7G8xWDumbj5K2k9/l3smHYm27uqfcjf2sGuTW+z69A2drd20N41jgu9BOqqSn2YD4J9Q3LIP66SmdVl+gMXEZnCUspPkkpNRio/yTWgp6xT+QkwWH4yGKxHLj8ZEsKTwnW20fD00F4Wj1GigTfJUVGHfzNbCGwEZgM/BV4FlgN/Baw1s/Odcwfy1qDyGm7Y8To39Rylrj/1Y8L+WBn7687gzaqzeDF2Gk93L+CNw3H2bOigp88Bo5ijP4uYwdyaitRR++OCkB98r1l1RETGL1P5SfapBINgnkONd6bpCBNhXOUnmeuzM9V4ZxvJznhyZqbyk6SfVfmJFJpiT3zfxwf/m5xztydWmtltwCeBLwM35qsxvcQ4Wr6YOV3PcMwq2cSpPNV9Ms/0n8pLrpmuY2VJjx59qU5FaaIkp4r6uoqBcpx5tX45t6ZCIwMiImPwgw1b2bTjUMaTM7sznJzpB2uiqSRmo6vnzmEUvCJDQC8vHXqCp8pPREavaMN/MOq/BtgGfC/t7luB64EPmNnNzrkR5sycGPGY8ZnDV9HefRWvuPn0D1/hP2BGdVkwYl9BfV1VMII/+PVxVaXa6YmITILnth/koZf2ht2MUUsuPxkarIeOWudSYpJeF16WViOuQSaRwlC04R+4KFg+4pxL+SzUOdduZk/h/zlYATyWjwaZGYfqlvDa24OXdI/HzJfkpJ9MO/B1hWbLEREJSXlJPKfHm5FbjXeWkezcasXjA/XfKj8RkZEUc6o8JVhmK5bfjA//ixgh/JvZc1nuOjXXRn384pPo63cDNfdzppdrtEREZAJN5D77mhXzuejU2So/EZGiUczhvzZYHs5yf2J9Xq+ffuXSefn8dSIiMg7nNs7g3MawWyEiMnGKOfxPGOfcuZnWB6NL5+S5OSIiMgzts0VEsivmepPEyH5tlvsT61vz0BYRERERkdAVc/h/LVguynL/ycFy7BPoi4iIiIgUkGIO/08EyzVmlvI6zWw6cD5wDPjffDdMRERERCQMRRv+nXNvAI8ATcDH0u7+IlAN3JWvOf5FRERERMJW7Cf8fhTYCHzXzC4BXgHOw18D4HXgsyG2TUREREQkr4p25B8GRv+XAXfgQ//NwELgO8AK59yB8FonIiIiIpJfxT7yj3PuLeDDYbdDRERERCRsRT3yLyIiIiIigxT+RUREREQiQuFfRERERCQiFP5FRERERCJC4V9EREREJCIU/kVEREREIkLhX0REREQkIhT+RUREREQiwpxzYbehYJnZgcrKyhmLFy8OuykiIjl55ZVX6OjoOOicmxl2W/JF+2wRKVQTuc9W+B8HM9sK1ADbQm7KVHJqsHw11FbIWOi9K0xjfd+agDbn3IKJbc7UNY59tv42hlKfDKU+GUp9ktlY+qWJCdpnK/zLhDKz5wCcc+eG3RbJjd67wqT3bfKpj4dSnwylPhlKfZJZ2P2imn8RERERkYhQ+BcRERERiQiFfxERERGRiFD4FxERERGJCIV/EREREZGI0Gw/IiIiIiIRoZF/EREREZGIUPgXEREREYkIhX8RERERkYhQ+BcRERERiQiFfxERERGRiFD4FxERERGJCIV/EREREZGIUPiXcTGzmWZ2rZndb2ZbzKzDzA6b2QYz+4iZaRsrIGZ2jZm54HZt2O2R4ZnZJcHf3l4z6zKz3Wb2SzO7Iuy2FQIzu9rMbjez9WbWFmz3PxzhZ1aZ2UNmdjDY371oZp8ws3i+2j2ZxrpPj0C//IOZPWZmbwWv76CZbTKzW81sZpafKeo+yWQ0xxAzazGzXwXb1REz+42ZfSjfbZ0MZrYt6fWn3/Zm+Zm8bye6yJeMi5ndCPwTsAd4AtgBzAHeC9QC9wHvd9rQpjwzOxF4CYgD04DrnHP/Hm6rJBsz+zrwaWAn8AtgP3A8cC7wqHPur0NsXkEwsxeApcARfD+eCvy3c+6aLI9/D36f1gncDRwErgROAX7snHt/Pto9mcayT49Iv3QDzwMvA+8A1cAKYBmwG1jhnHsr6fFF3yfpRnMMMbOPA7cDB/D90g1cDTQA33LO3ZLXRk8wM9sG1AHfznD3EefcN9MeH8524pzTTbcx34CLgw01lrZ+Lv6g4YD3hd1O3UZ8Hw14FHgD+Ebwvl0bdrt0y/p+XRe8R3cAZRnuLw27jYVwAy4CTg62/9VBn/4wy2Nr8KGvC1iWtL4C2Bj87B+H/ZomoE9y2qdHqF8qsqz/cvAavx+1PknrhxGPIUATPuQeAJqS1h8HbAl+ZmXYr2Wc/bAN2DbKx4a2nagkQ8bFOfe4c+5B51x/2vq9wD8H367Oe8MkVzfhD/ofBo6G3BYZhpmV4wPHDuB651x3+mOccz15b1gBcs494Zzb7IIj7giuxn+y8iPn3LNJz9EJfC749i8noZl5NYZ9elT6pTPLXfcEy5OT1kWiT9KM5hjyF0A58I/OuW2Jlc65Q8BXgm9vnMQ2TjWhbSclk/GkIoFEAOkNtRUyLDNbDHwN+I5z7kkzuzjsNsmwLsUfML4N9JvZOuAM/IjaM865p8NsXBFL/F08nOG+J4FjwCozK3fOdeWvWXmVaZ8e9X65Mli+mLQuUn2SwzFkuH75RdpjClm5mV0DzMf/I/Qi8KRzri/tcaFtJwr/MinMrAT4YPBtpg1bpoDgfboLP4r8mZCbI6PzrmDZCWzCB/8BZvYkcLVzbl++G1bkTgmWr6ff4ZzrNbOtwOlAM/BKPhuWD8Ps0yPVL2Z2C76evRZf7/97+HD3taSHRaZPcjyGDNcve8zsKNBgZlXOuWMT29K8movvk2RbzezDzrlfJ60LbTtR2Y9Mlq/hQ8lDzrlfht0YyervgbOBP3fOdYTdGBmV2cHy0/ia0N8HpgNnAo8AFwD3htO0olYbLA9nuT+xvi4PbQlDtn161PrlFuBW4BP44P8wsCbtn+0o9Ukux5DR9kttlvsLwX8Cl+D/AagGlgD/gj/f4RdmtjTpsaFtJwr/MuHM7CbgZuBV4AMhN0eyMLPz8CM131KpSEFJ7Ld7gXc75zY45444514C/hA/a82FZrYytBZKUdE+fZBzbq5zzvDh7r34UdlNZnZOuC3LPx1DhnLOfTE4b+Zt59wx59zvnHM3ArcBlcAXwm2hp/AvEyqYxus7+OnQLnLOHQy5SZJB8FHtf+E/bvx8yM2R3LQGy03JJ80BBB+VJ0Zll+ezUREw0qhkYn1rlvsL0ij26ZHslyDc3Q+sAWbi96cJRd8nYzyGjLZfso3rV7gQAAADZklEQVSEF7LEyfIXJK0LbTtR+JcJY2afwM/f+zv8QSLjBS1kSpgGLAIWA53JFyLBf6QN8G/BukzzFUt4XguW2Q4Ih4JlZR7aEiWJfl+UfkcQhBbgP415M5+Nmkyj3KdHrl+SOee24/8xOt3MZgWro9AnYzmGDNcvJ+DLZHYWeL1/NomysOqkdaFtJzrhVyaEmf0Nvib0BeBS59z+kJskw+sCfpDlvnPwNZwb8DsnfZw7tTyGr/U/zcxi6VMyMngC8Nb8NqvoPQ78GbAW+J+0+y4AqvAzehT87C2Q0z49Uv2SxbxgmZjNJQp9MpZjyOPA+fh+ST+uXJ70mGK0IlgmB/nwtpPJuHiAbtG64T/yc8CzwIyw26PbuN/PL6CLfE3pG/DT4D36ZNr6NUA/fvS/Nux2FtKN0V3kax8RuHBTLvv0KPQLfmR2yN8TvnoicZGvp6LUJyP0V8ZjCH4ku2gv8oX/FKQ6w/omYHPw+j4zFbYTjfzLuJjZh4Av4Uc81gM3mVn6w7Y55+7Ic9NEitnH8CNrtwXz/G/CH1ivwv8tXuucK8a62QllZlfh+wz8CZwAK83sjuDr/c65WwCcc21mdh3wY+BXZvYj4CDwbvyUfT8G7s5X2ydLrvv0iPTLFcBXzWwD/hO1A8Ac4EL8Cb978VfdBiLTJzlzzm01s08D3wWeNbO7gW78xa4aKPwTh/8IuDmYbnk70A4sBNbhA/1DwDcTDw5zO1H4l/FaECzj+KnPMvk1cEdeWiMSAc65nWZ2Ln6avXfjPyJuAx4EvuqceybM9hWQs4APpa1rDm7gD+C3JO5wzj1gZhcCnwXehz+gbwE+BXzXBcN2BS7nfXoE+uVR4CT81J5n46dePIo/2fUu/GtMORE6An0yJs65281sG/7v6oP4T09eBj7nnLszzLZNgCfwof1sfHlTNf7crA347eSu9Pc9rO3EIrr9iYiIiIhEjmb7ERERERGJCIV/EREREZGIUPgXEREREYkIhX8RERERkYhQ+BcRERERiQiFfxERERGRiFD4FxERERGJCIV/EREREZGIUPgXEREREYkIhX8RERERkYhQ+BcRERERiQiFfxERERGRiFD4FxERERGJCIV/EREREZGIUPgXEREREYkIhX8RERERkYhQ+BcRERERiYj/B55b8B9l6JWaAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f23d2cac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1, ax2) = plt.subplots(1, 2, False, True)\n",
"ax1.plot(list_num_blocks, reals.mean(axis=2))\n",
"ax2.plot(list_block_size, reals.mean(axis=2).T)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f9f21b67dd8>,\n",
" <matplotlib.lines.Line2D at 0x7f9f21b7b668>,\n",
" <matplotlib.lines.Line2D at 0x7f9f21b7b7b8>,\n",
" <matplotlib.lines.Line2D at 0x7f9f21b7b908>,\n",
" <matplotlib.lines.Line2D at 0x7f9f21b7ba58>,\n",
" <matplotlib.lines.Line2D at 0x7f9f21b7bba8>]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9f233daa20>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1, ax2) = plt.subplots(1, 2, False, True)\n",
"ax1.plot(list_num_blocks, imags.mean(axis=2))\n",
"ax2.plot(list_block_size, imags.mean(axis=2).T)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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