diff --git a/Assignment_0/Assignment_0.ipynb b/Assignment_0/Assignment_0.ipynb new file mode 100644 index 0000000..aad75e2 --- /dev/null +++ b/Assignment_0/Assignment_0.ipynb @@ -0,0 +1,1132 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 13, + "id": "fd8e810f", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "0e99f9ac", + "metadata": {}, + "source": [ + "## Question 1" + ] + }, + { + "cell_type": "markdown", + "id": "0e7e3ef3", + "metadata": {}, + "source": [ + "### 1.1 Find number of corners of an n dimensional cube" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "de131010", + "metadata": {}, + "outputs": [], + "source": [ + "def cube_corners(dim):\n", + " return 2**dim" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "63cee73f", + "metadata": {}, + "outputs": [], + "source": [ + "Corners = []\n", + "for i in range(100):\n", + " Dim = i+1\n", + " corners = 2**Dim\n", + " Corners.append(corners)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "be9ee752", + "metadata": {}, + "outputs": [], + "source": [ + "dimension = np.arange(1,101,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "17ebaaf2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dimension, Corners)" + ] + }, + { + "cell_type": "markdown", + "id": "e2e7ac3b", + "metadata": {}, + "source": [ + "### 1.2 Calculate length of the longest diagonal" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "4f2c6091", + "metadata": {}, + "outputs": [], + "source": [ + "Max_Diag = []\n", + "for i in range(100):\n", + " Dim = i+1\n", + " max_diag = np.sqrt(Dim)\n", + " Max_Diag.append(max_diag)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "e896b4f8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dimension, Max_Diag)" + ] + }, + { + "cell_type": "markdown", + "id": "5563f71a", + "metadata": {}, + "source": [ + "### 1.3 Calculate volume of B_n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "65f11faa", + "metadata": {}, + "outputs": [], + "source": [ + "Volume = []\n", + "for i in range(10):\n", + " Dim = i+1\n", + " points = 0\n", + " for j in range(10**6):\n", + " point = np.random.uniform(size=Dim)\n", + " condition = np.sum((point-0.5)**2)\n", + " if condition < 0.5**2:\n", + " points = points+1\n", + " volume = points/10**6\n", + " Volume.append(volume)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "24a0862d", + "metadata": {}, + "outputs": [], + "source": [ + "dim_circ = np.arange(1,11,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "23dcb521", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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9JUMZktmR7z21iHVlFV5HEpEQUaFHoLjoKGZcPQK/z5j8aAH7q+u8jiQiIaBCj1BZqQlMvzKP4tL93Dp7Mc7pIKlIe6dCj2Bj+qZz27iBvLx0GzPeWet1HBE5SUEVupmdb2arzazIzG47ynKnmlm9mV0WuojSkm44vTdfye3GH15bxbuflHodR0ROwjEL3cyigOnAOGAQMMnMBn3OcncBr4U6pLQcM+Puy3Lp36UDNz/xMZt2VXodSUROUDBb6COBIufcWudcDfAkMKGZ5W4GngV2hDCftIKEGD8PXDMC5xyTZxVyoKbe60gicgKCKfRMYFOT5yWBaZ8ys0zgEmDG0d7IzCabWYGZFZSW6s/7tqRXWiL3TBrOqm17uW3OEh0kFWmHgil0a2ba4f/b/wL8xDl31E0759xM51y+cy4/IyMjyIjSWs4a0Jkf/k9/Xli0hb/PW+91HBE5TsGMKVoC9GjyPAvYctgy+cCTZgaQDlxgZnXOuedDEVJaz9Qz+7KkpJzfv7ySQd06MrpPmteRRCRIwWyhfwT0M7McM4sBrgBebLqAcy7HOZftnMsGZgNTVebtk89n/Omrw8hOS+Cmfy5ky54DXkcSkSAds9Cdc3XATTSevbISeNo5t9zMppjZlJYOKK2vQ1w0M6/Np7qugSmPFVJVq4OkIu2BeXXwKz8/3xUUFHiybgnO68u3MXlWIZePyOLuy3IJ7FITEQ+ZWaFzLr+5ebpSVD7Xlwd35Zaz+/JMYQmPfbjR6zgicgwqdDmq753bn7MGZPCbfy2ncMMur+OIyFGo0OWofD7jL18bTveUeKY8tpDte6u8jiQin0OFLseUnBDNzGvyqaiuY+rjC6mpa/A6kog0Q4UuQRnQtQN3X5ZL4Ybd/Oal5V7HEZFmBHNhkQgAX8ntztKSch54dy25mSl89dQex36RiLQabaHLcfnxeQP4Yt90fvH8MhZv2uN1HBFpQoUux8Uf5WPapOFkdIhlymOFlO2v9jqSiASo0OW4pSbG8MA1I9hVUcONjy+ktl4HSUXaAhW6nJAhmcncMXEoH67bxR0vr/I6joigg6JyEibmZbGkpJy/z1tHblYyFw/PPPaLRKTFaAtdTsrPx5/CyJxO3DZnCcs2l3sdRySiqdDlpERH+Zh+ZR6pCTFMevAD3lujkahEvKJCl5OW0SGWZ6aMJjMlnm88/BGzFqz3OpJIRFKhS0hkpSYw+ztjOLN/Br98YTm3v7CMOp39ItKqVOgSMkmxfmZem88Np+fwjwUb+OY/CthbVet1LJGIoUKXkIryGT8fP4i7Lh3K/KIyJt43n407K72OJRIRVOjSIr52ak9mXT+Ksv3VTJj+Pv9dp3upi7Q0Fbq0mNF90nhu6lhSE2K46qEPeKZgk9eRRMKaCl1aVE56Is9NHcuonDR+PHsJd76yioYGb8axFQl3KnRpcckJ0Tx83alcNaonM94pZspjhVRU13kdSyTsqNClVURH+fjdxUO4/cJBzF25nctnLGDLngNexxIJKyp0aTVmxnVjc/jbN05l465KJkyfp3uqi4SQCl1a3VkDOjNn6hjion189YEFvLRki9eRRMKCCl080b9LB56fOpahmcnc9M+PuWfuGpzTwVKRk6FCF8+kJcXy+A2jmJiXyZ/nfsJ3n1xEVW2917FE2i3dD108FeuP4k+XD6Nv5yTufnU1G3dVMvPaEXTuEOd1NJF2R1vo4jkzY+qZfZlx9QhWb9vHxffOY+XWvV7HEml3VOjSZpw/pCvPTBlNg4NL75/P3BXbvY4k0q6o0KVNGZKZzAs3jaVv5yRumFXAzHeLdbBUJEgqdGlzunSM46nJo7lgSDd+//Iqbnt2KTV1ure6yLEEVehmdr6ZrTazIjO7rZn5V5nZksDPfDMbFvqoEkniY6KYNmk4t5zdl6cKNnHN3z5kd0WN17FE2rRjFrqZRQHTgXHAIGCSmQ06bLF1wJecc7nAb4GZoQ4qkcfnM37w5QH85Wtf4ONNe7j4vnkU7djvdSyRNiuYLfSRQJFzbq1zrgZ4EpjQdAHn3Hzn3O7A0w+ArNDGlEh28fBMnrjhNCqq67jkvnm8v6bM60gibVIwhZ4JNL2RdUlg2ue5HniluRlmNtnMCsysoLRUo8NL8Eb0SuX5G8fSPTmerz/8X2Z9sMHrSCJtTjCFbs1Ma/a0AzM7i8ZC/0lz851zM51z+c65/IyMjOBTitA4EPWzU8fwpf4Z/PL5ZfzqxeUaiFqkiWAKvQTo0eR5FnDE3ZTMLBd4CJjgnNsZmngih0qK9fPgtfl864s5PDJ/vQaiFmkimEL/COhnZjlmFgNcAbzYdAEz6wnMAa5xzn0S+pgin4nyGb/4yiDunNg4EPWlGohaBAii0J1zdcBNwGvASuBp59xyM5tiZlMCi/0vkAbcZ2aLzKygxRKLBFwxsiePXj+SHfuqufi+eRqIWiKeeXUVXn5+visoUO/LyVtXVsH1j3zEpt2V3DExl8tG6CQrCV9mVuicy29unq4UlXbv4EDUI3M68aNnFvOdxwpZsUU395LIo0KXsJCcEM0j143ke+f24/01ZVzw1/e44dEClpaUex1NpNVol4uEnfIDtTwybz1/e38te6vqOGtABjef04+8nqleRxM5aUfb5aJCl7C1r6qWRxds4KH31rK7spbT+6Vzyzn9ODW7k9fRRE6YCl0iWkV1HY99sIEH31tL2f4aRvdO45Zz+nFa706YNXfdnEjbpUIXAQ7U1PPP/25kxjvFlO6r5tTsVG45px9f7JuuYpd2Q4Uu0kRVbT1PfbSJGe8Us7W8iuE9U7jl7H6cOSBDxS5tngpdpBnVdfXMLizhvreK2bznAEMzk7nlnH6ce0pnFbu0WSp0kaOorW/guYWbufetIjbuquSUbh255ey+nDe4Kz6fil3aFhW6SBDq6ht4cfEW7n2ziLVlFfTvksRNZ/dj/NBuRKnYpY1QoYsch/oGx0tLtjDtzSKKduynd0YiN5/dlwtzu+OP0rV44i0VusgJaGhwvLJsG9PeXMOqbfvolZbAjWf15ZLhmUSr2MUjKnSRk9DQ4PjPyu1Me3MNyzbvJSs1nqln9uWyEVnE+FXs0rpU6CIh4JzjrdU7uOeNIhZv2kP35Di+c2YfLs/vQVx0lNfxJEKo0EVCyDnHu2vK+OsbayjcsJsuHWP59hl9mDSyJ/ExKnZpWSp0kRbgnGNB8U7ueWMNH67bRXpSLJPPyOHq03qREOP3Op6EKRW6SAv7cO1Opr1ZxPtFZXRKjOH6L+YwbkhXctITdZGShJQKXaSVFG7YzbQ31/D26lIAuiXHMbpPGmP6pDOmTxrdU+I9TijtnQpdpJWtL6tgXnEZ84t3sqB4J7sqagDITktgTN/Gch/dO420pFiPk0p7o0IX8VBDg2P19n3ML97J/KIyPly3i/3VdQAM7Nrh0633Ub070SEu2uO00tap0EXakLr6BpZuLm8s+OIyCtbvprqugSifMTQzmTF90hjbN50RvVJ1OqQcQYUu0oZV1dazcONuFhTvZH7xThZt2kN9gyMmykderxTG9klnTN80crNSdIWqqNBF2pP91XV8tG4X8wP74Fds3YtzkBgTxcicTozpk87oPmkM6tZRd4OMQEcrdJ0sK9LGJMX6OWtgZ84a2BmA3RU1fLC2cet9XnEZb61eCUBKQjSje6cxpk8aY/qm01unSEY8FbpIG5eaGMO4od0YN7QbANvKq1iwtox5RY0HWV9Ztg2ALh1jPz3AOqZvOpk6RTLiaJeLSDvmnGPjrsrGci8uY0HxTnYGTpHslZbAqdmdyE5LIDM1nsyUBLJS4+nSMU73d2/HtMtFJEyZGb3SEumVlsiVo3riXOAUyaLGXTRvr95B2f6aQ17j9xldk+PICpR8Zmo8WanxZKXEk5kaT7fkeN1Fsp1SoYuEETNjYNeODOzakW9+MQeAAzX1bN5zgM17DlCyu5LNuw8+PsC8ojK276ui6R/qZtClQ6DwU+PJTIknKzWhyeN4nU7ZRqnQRcJcfEwUfTsn0bdzUrPza+oa2Fp+gM27D1ASKPrG0q+kcMNuXlqylfqGQ3fNpifFNFv0Bx/rAilvqNBFIlyM3/fpbpvm1Dc4tu+taiz6PZWU7Drw6Rb/iq17+c/K7dTUNRzymuT46ENKvkvHOJJi/XSI85MU2/iT2PR5nJ9Yv7b6T1ZQhW5m5wP3AFHAQ865Ow+bb4H5FwCVwDeccwtDnFVEPBDlM7qnxAduLNbpiPkNDY6yiuomW/af7dpZv7OC94vKqKypP+Z6YqJ8JMZGkRTnJyk2mg6Bok8MfAE0/TI4+CVwyO+Dy8f4I/ag7zEL3cyigOnA/wAlwEdm9qJzbkWTxcYB/QI/o4D7A79FJMz5fEbnDnF07hBHXs/UI+Y756isqaeiuo591XXsr6pjf3Xgp8njfVV1VDR5vL+6lh37qqgoq//0eVVtQzMJjpQYE9X4RRDn//SLISnWT3x0FNFRPqL9PmKifERHGTF+X+O0qM+mHZzfdN7BZWOimizvN2Kiooj22yHvEeP3efKlEswW+kigyDm3FsDMngQmAE0LfQLwqGs8B/IDM0sxs27Oua0hTywi7YqZkRjYxdL5JN+rtr7h09I/+IVw8Evi0C+DuiO+QMr2VVJVV09tXQM19Y6aunpq6x219Q3UNYT+9G2f8dmXxMEvgkDxXzmyJ986vXfI1xlMoWcCm5o8L+HIre/mlskEDil0M5sMTAbo2bPn8WYVkQgXHeUjJSGGlISYkL5vQ4OjtqGBmrqGT0u+8XEDNfUN1Na5xt+Bn8/mOWrrPpte3eT1B197cNnaOvfptIwOLXPb5GAKvbm/Gw7/OgtmGZxzM4GZ0HhhURDrFhFpcT6fEeuLavcHZoO5eqAE6NHkeRaw5QSWERGRFhRMoX8E9DOzHDOLAa4AXjxsmReBa63RaUC59p+LiLSuY+5ycc7VmdlNwGs0nrb4d+fccjObEpg/A3iZxlMWi2g8bfG6lossIiLNCeo8dOfcyzSWdtNpM5o8dsCNoY0mIiLHQ3fgEREJEyp0EZEwoUIXEQkTKnQRkTDh2YhFZlYKbPBk5aGTDpR5HaIN0edxKH0en9FncaiT+Tx6OecympvhWaGHAzMr+LyhoCKRPo9D6fP4jD6LQ7XU56FdLiIiYUKFLiISJlToJ2em1wHaGH0eh9Ln8Rl9Fodqkc9D+9BFRMKEttBFRMKECl1EJEyo0E+AmfUws7fMbKWZLTez73qdyWtmFmVmH5vZS15n8VpgCMbZZrYq8G9ktNeZvGRm3w/8P1lmZk+YWZzXmVqTmf3dzHaY2bIm0zqZ2X/MbE3g95GDsZ4AFfqJqQN+6Jw7BTgNuNHMBnmcyWvfBVZ6HaKNuAd41Tk3EBhGBH8uZpYJ3ALkO+eG0HgL7iu8TdXqHgHOP2zabcAbzrl+wBuB5ydNhX4CnHNbnXMLA4/30fgfNtPbVN4xsyxgPPCQ11m8ZmYdgTOAvwE452qcc3s8DeU9PxBvZn4ggQgbzcw59y6w67DJE4B/BB7/A7g4FOtSoZ8kM8sGhgMfehzFS38BbgUaPM7RFvQGSoGHA7ugHjKzRK9DecU5txn4I7CRxkHjy51zr3ubqk3ocnBUt8DvzqF4UxX6STCzJOBZ4HvOub1e5/GCmX0F2OGcK/Q6SxvhB/KA+51zw4EKQvTndHsU2Dc8AcgBugOJZna1t6nClwr9BJlZNI1l/rhzbo7XeTw0FrjIzNYDTwJnm9lj3kbyVAlQ4pw7+BfbbBoLPlKdC6xzzpU652qBOcAYjzO1BdvNrBtA4PeOULypCv0EmJnRuI90pXPu/3udx0vOuZ8657Kcc9k0Hux60zkXsVtgzrltwCYzGxCYdA6wwsNIXtsInGZmCYH/N+cQwQeJm3gR+Hrg8deBF0LxpkGNKSpHGAtcAyw1s0WBaT8LjL0qcjPwuJnFAGuJ4EHTnXMfmtlsYCGNZ4d9TITdBsDMngDOBNLNrAS4HbgTeNrMrqfxS+/ykKxLl/6LiIQH7XIREQkTKnQRkTChQhcRCRMqdBGRMKFCFxEJEyp0EZEwoUIXEQkT/wel0B9T7dYIPwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dim_circ, Volume)" + ] + }, + { + "cell_type": "markdown", + "id": "f81d60f3", + "metadata": {}, + "source": [ + "### 1.4 Volume of the skin" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "82f6ec7c", + "metadata": {}, + "outputs": [], + "source": [ + "def skin(dim):\n", + " return 1**dim-(1-2*0.01)**dim" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "a30893bb", + "metadata": {}, + "outputs": [], + "source": [ + "Skins = []\n", + "for i in range(100):\n", + " Dim = i+1\n", + " skins = skin(Dim)\n", + " Skins.append(skins)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "c1492574", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dimension, Skins)" + ] + }, + { + "cell_type": "markdown", + "id": "b50b74a5", + "metadata": {}, + "source": [ + "### 1.5 Distances between points" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "edfc8fd0", + "metadata": {}, + "outputs": [], + "source": [ + "Hist = []\n", + "for i in range(10):\n", + " Dim = i+1\n", + " points = []\n", + " Distances = []\n", + " for j in range(1000):\n", + " point = np.random.uniform(size=Dim)\n", + " if len(points) > 0:\n", + " ps = np.array(points)\n", + " distances = np.sqrt(np.sum((ps-point)**2, axis=1))\n", + " length = len(distances)\n", + " for k in distances:\n", + " Distances.append(k)\n", + " points.append(point)\n", + " Hist.append(Distances) \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "id": "b6b1b79e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "\" \\nfig, ax = plt.subplots(10, figsize=(12, 80))\\nwidth = Bins[0][1] - Bins[0][0]\\nax[0].bar(Bins[0], N[0], align='center', width=width)\\nwidth = Bins[1][1] - Bins[1][0]\\nax[1].bar(Bins[1], N[1], align='center', width=width)\\nwidth = Bins[2][1] - Bins[2][0]\\nax[2].bar(Bins[2], N[2], align='center', width=width)\\nwidth = Bins[3][1] - Bins[3][0]\\nax[3].bar(Bins[3], N[3], align='center', width=width)\\nwidth = Bins[4][1] - Bins[4][0]\\nax[4].bar(Bins[4], N[4], align='center', width=width)\\nwidth = Bins[5][1] - Bins[5][0]\\nax[5].bar(Bins[5], N[5], align='center', width=width)\\nwidth = Bins[6][1] - Bins[6][0]\\nax[6].bar(Bins[6], N[6], align='center', width=width)\\nwidth = Bins[7][1] - Bins[7][0]\\nax[7].bar(Bins[7], N[7], align='center', width=width)\\nwidth = Bins[8][1] - Bins[8][0]\\nax[8].bar(Bins[8], N[8], align='center', width=width)\\nwidth = Bins[9][1] - Bins[9][0]\\nax[9].bar(Bins[9], N[9], align='center', width=width)\\n\"" + ] + }, + "execution_count": 146, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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kvZVe7yyos0lSr6QTkh4piC+UdCTteyYtpUlabnN3ih+UNGsMztXMzEaQp4dwDfhnEfEJYAGwXNJiYCPQHRFtQHd6j6R5ZEtgzgeWA89JmpCOtRXoJFtnuS3tB+gALkXEHOBp4MmbPzUzM6tE2fsQ0mL3P05vb0s/AawAlqb4drKlNR9P8V0RcQ04mdZJXiTpFDA5Ig4ASNoBrCRbV3kFHzwQeg/wx5KUfreNgf1Ln611E8yszuS6MS39hf8GMAd4NiIOSpoaEf0AEdEv6d5UfDrwnYLqfSn2Xtoujg/WOZOONSDpMnA38E5ROzrJehjMnOmbtprZ859ZWTpO6biZlZdrUjkirkfEAqCV7K/9B0YorlKHGCE+Up3idmyLiPaIaG9paSnTajMzq0RFVxlFxA/JhoaWA+ckTQNIr+dTsT5gRkG1VuBsireWiA+pI2kiMAW4WEnbzMzs5pQdMpLUArwXET+UNAn4ebJJ373AOmBLen0lVdkLvCzpKeB+ssnjQxFxXdKVNCF9EFgLfLmgzjrgALAK2O/5A3toyc5h93loyGz05ZlDmAZsT/MIHwK6IuJbkg4AXZI6gNPAowARcVRSF3AMGAA2RMT1dKz1wEvAJLLJ5H0p/iKwM01AXyS7SqnuDbtespnZLSjPVUZ/DXyyRPxdYNkwdTYDm0vEe4Ab5h8i4iopoZiZWW348de3qK4vDdS6CdbE7nv9cMV13n54wai3w0aXH11hZmaAE4KZmSVOCGZmBngOwUq4eumpWjfBzGrAPQQzMwOcEMzMLPGQkY25K3PbAXiB7hq3xMxG4h6CmZkBTghmZpZ4yKgGHpzttRzMrP64h2BmZoB7CFal1bMfz13Wk8lmtwb3EMzMDHBCMDOzxAnBzMyAHAlB0gxJr0s6LumopMdS/C5Jr0l6K73eWVBnk6ReSSckPVIQXyjpSNr3jCSl+O2Sdqf4QUmzxuBczcxsBHl6CAPA70TEXGAxsEHSPGAj0B0RbUB3ek/atwaYDywHnkvLbwJsBTrJ1lluS/sBOoBLETEHeJpszWYzMxtHZRNCRPRHxJtp+wpwHJgOrAC2p2Lb4f1Vz1cAuyLiWkScBHqBRZKmAZMj4kBEBLCjqM7gsfYAywZ7D2ZmNj4qmkNIQzmfBA4CUyOiH7KkAdybik0HzhRU60ux6Wm7OD6kTkQMAJeBu0v8/k5JPZJ6Lly4UEnTzcysjNwJQdJHga8DX4yIH41UtEQsRoiPVGdoIGJbRLRHRHtLS0u5JpuZWQVyJQRJt5Elg69GxDdS+FwaBiK9nk/xPmBGQfVW4GyKt5aID6kjaSIwBbhY6cmYmVn1yt6pnMbyXwSOR0ThUlp7gXXAlvT6SkH8ZUlPAfeTTR4fiojrkq5IWkw25LQW+HLRsQ4Aq4D9aZ6hZk7d8bla/nozs3GX59EVnwZ+Azgi6XCK/T5ZIuiS1AGcBh4FiIijkrqAY2RXKG2IiOup3nrgJWASsC/9QJZwdkrqJesZrLm502o++5c+W+smmNktrmxCiIi/pPQYP8CyYepsBjaXiPcAD5SIXyUlFDMzqw3fqWxmZoATgpmZJU4IZmYGeD2EutL1pYFaN8HMmpgTgo2bh5bsrHUTzGwEHjIyMzPAPQSrsV/T12vdBDNL3EMwMzPACcHMzBIPGY2iB2fPrHUTzMyq5oTQ4K5eeqp8ITMznBCsQlfmtgPwAt01bomZjTYnBDMbF/e9friqem8/vGBU22HD86SymZkB7iFYsnr247nKeajIrHG5h2BmZkCOhCDpK5LOS/p+QewuSa9Jeiu93lmwb5OkXkknJD1SEF8o6Uja90xamhNJt0vaneIHJc0a5XM0M7Mc8vQQXgKWF8U2At0R0QZ0p/dImke2/OX8VOc5SRNSna1AJ9kay20Fx+wALkXEHOBp4MlqT8bMzKpXNiFExF+QrXNcaAWwPW1vB1YWxHdFxLWIOAn0AoskTQMmR8SBiAhgR1GdwWPtAZYN9h7MzGz8VDuHMDUi+gHS670pPh04U1CuL8Wmp+3i+JA6ETEAXAburrJdZmZWpdGeVC71l32MEB+pzo0Hlzol9UjquXDhQpVNNDOzUqpNCOfSMBDp9XyK9wEzCsq1AmdTvLVEfEgdSROBKdw4RAVARGyLiPaIaG9paamy6WZmVkq19yHsBdYBW9LrKwXxlyU9BdxPNnl8KCKuS7oiaTFwEFgLfLnoWAeAVcD+NM/Q1PYvfbbWTTCzJlM2IUj6GrAUuEdSH/CHZImgS1IHcBp4FCAijkrqAo4BA8CGiLieDrWe7IqlScC+9APwIrBTUi9Zz2DNqJyZmZlVpGxCiIhfHWbXsmHKbwY2l4j3AA+UiF8lJZRG1PWlgVo3wcwsFz+6wqry0JKdtW6CmY0yP7rCzMyAJu0hnLrjc7VugplZ3WnKhGBj49f09Vo3wcxughNCGfW0TrKXwzSzseSE0MQGl8MEr3NgZk4IDcmL3ZhZNXyVkZmZAe4hmFmdu+/1w1XVe/vhBaPajmbgHoKZmQFOCGZmlnjIaBz5CaZmVs+cEMzPJTIzwAmhYn56qZk1KicEu4EfQWHWnJwQaijvoyjev9HsY8PfcPbCHR/cZOYbzsysGk4IZtaQfP9C5eomIUhaDvwRMAF4ISK2jOXvq6eH1o02TxKbWTXqIiFImgA8C/wC0Ad8V9LeiDhW25aNrN4vI/VcgJlVoi4SArAI6I2IHwBI2gWsAMYlIYzGlUMVzwfAsHMChfMBDy3ZyQl+s+xxH8r1282snGqGmhplmKleEsJ04EzB+z7g54oLSeoEOtPbH0s6UeXvuwe+/87gm3lVHoQTyyqu8rv8SbW/rQqfLFfgHuCdcoWagD+HjD+HTMWfg8aoIWPkp4fbUS8JodTnGTcEIrYB2276l0k9EdFevmRj8+eQ8eeQ8eeQaebPoV6eZdQHzCh43wqcrVFbzMyaUr0khO8CbZJmS/owsAbYW+M2mZk1lboYMoqIAUn/Bvg22WWnX4mIo2P4K2962KlB+HPI+HPI+HPINO3noIgbhurNzKwJ1cuQkZmZ1ZgTgpmZAQ2eECQtl3RCUq+kjSX2S9Izaf9fS/pULdo51nJ8DkslXZZ0OP38QS3aOZYkfUXSeUnfH2Z/s3wXyn0ODf9dAJA0Q9Lrko5LOirpsRJlmuI7MURENOQP2eT03wI/A3wY+B4wr6jMZ4F9ZPdBLAYO1rrdNfoclgLfqnVbx/hzWAJ8Cvj+MPsb/ruQ83No+O9COs9pwKfS9j8C/ncz/v9Q/NPIPYT3H4cREf8ADD4Oo9AKYEdkvgN8TNK08W7oGMvzOTS8iPgL4OIIRZrhu5Dnc2gKEdEfEW+m7SvAcbInJhRqiu9EoUZOCKUeh1H8D56nzK0u7zn+E0nfk7RP0vzxaVpdaYbvQl5N9V2QNIvsOS8Hi3Y13XeiLu5DGCN5HoeR65EZt7g85/gm8NMR8WNJnwX+B9A21g2rM83wXcijqb4Lkj4KfB34YkT8qHh3iSoN/Z1o5B5CnsdhNMMjM8qeY0T8KCJ+nLZfBW6TdM/4NbEuNMN3oaxm+i5Iuo0sGXw1Ir5RokjTfScaOSHkeRzGXmBtuppgMXA5IvrHu6FjrOznIOk+SUrbi8i+F++Oe0trqxm+C2U1y3chneOLwPGIGO7Z9U33nWjYIaMY5nEYkn4r7X8eeJXsSoJe4CfA52vV3rGS83NYBayXNAD8PbAm0mUWjULS18iuoLlHUh/wh8Bt0DzfBcj1OTT8dyH5NPAbwBFJh1Ps94GZ0FzfiUJ+dIWZmQGNPWRkZmYVcEIwMzPACcHMzBInBDMzA5wQzMwscUIwMzPACcHMzJL/D1PC90xzffUoAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Bins = []\n", + "N = []\n", + "for i in range(10):\n", + " D = Hist[i]\n", + " n, bins, _ = plt.hist(x=D, bins=20)\n", + " bins = (bins[1:]-bins[:-1])/2\n", + " Bins.append(bins)\n", + " N.append(n)\n", + "\n", + "''' \n", + "fig, ax = plt.subplots(10, figsize=(12, 80))\n", + "width = Bins[0][1] - Bins[0][0]\n", + "ax[0].bar(Bins[0], N[0], align='center', width=width)\n", + "width = Bins[1][1] - Bins[1][0]\n", + "ax[1].bar(Bins[1], N[1], align='center', width=width)\n", + "width = Bins[2][1] - Bins[2][0]\n", + "ax[2].bar(Bins[2], N[2], align='center', width=width)\n", + "width = Bins[3][1] - Bins[3][0]\n", + "ax[3].bar(Bins[3], N[3], align='center', width=width)\n", + "width = Bins[4][1] - Bins[4][0]\n", + "ax[4].bar(Bins[4], N[4], align='center', width=width)\n", + "width = Bins[5][1] - Bins[5][0]\n", + "ax[5].bar(Bins[5], N[5], align='center', width=width)\n", + "width = Bins[6][1] - Bins[6][0]\n", + "ax[6].bar(Bins[6], N[6], align='center', width=width)\n", + "width = Bins[7][1] - Bins[7][0]\n", + "ax[7].bar(Bins[7], N[7], align='center', width=width)\n", + "width = Bins[8][1] - Bins[8][0]\n", + "ax[8].bar(Bins[8], N[8], align='center', width=width)\n", + "width = Bins[9][1] - Bins[9][0]\n", + "ax[9].bar(Bins[9], N[9], align='center', width=width)\n", + "'''" + ] + }, + { + "cell_type": "markdown", + "id": "ff36631f", + "metadata": {}, + "source": [ + "## Question 2" + ] + }, + { + "cell_type": "markdown", + "id": "01c0bc8b", + "metadata": {}, + "source": [ + "### 2.1 General Dataset based on function" + ] + }, + { + "cell_type": "code", + "execution_count": 117, + "id": "17fd48db", + "metadata": {}, + "outputs": [], + "source": [ + "def func(x):\n", + " return 0.5+0.4*np.sin(2*np.pi*x)\n", + "\n", + "# for size=9\n", + "x9 = np.random.uniform(size=9)\n", + "y_err9 = np.random.normal(loc=0, scale=0.05, size=9)\n", + "y9 = func(x9)+y_err9" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "id": "f9efc782", + "metadata": {}, + "outputs": [], + "source": [ + "# for size=15\n", + "x15 = np.random.uniform(size=15)\n", + "y_err15 = np.random.normal(loc=0, scale=0.05, size=15)\n", + "y15 = func(x15)+y_err15" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "id": "28d8a110", + "metadata": {}, + "outputs": [], + "source": [ + "# for size=100\n", + "x100 = np.random.uniform(size=100)\n", + "y_err100 = np.random.normal(loc=0, scale=0.05, size=100)\n", + "y100 = func(x100)+y_err100" + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "id": "838d32b1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 120, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x9, y9)\n", + "plt.scatter(x15, y15)\n", + "plt.scatter(x100, y100)" + ] + }, + { + "cell_type": "markdown", + "id": "ca47ecd4", + "metadata": {}, + "source": [ + "### 2.2 Find the best polynomial approximation" + ] + }, + { + "cell_type": "code", + "execution_count": 143, + "id": "34519675", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/yuzezhang/opt/anaconda3/lib/python3.8/site-packages/IPython/core/interactiveshell.py:3437: RankWarning: Polyfit may be poorly conditioned\n", + " exec(code_obj, self.user_global_ns, self.user_ns)\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 143, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# for size=9\n", + "Z9 = []\n", + "for i in range(10):\n", + " degree = i\n", + " z9 = np.polyfit(x9,y9,degree)\n", + " Z9.append(z9)\n", + " \n", + "def poly(x, coeffs):\n", + " o = len(coeffs)\n", + " y = 0\n", + " for i in range(o):\n", + " y += coeffs[i]*x**(o-1-i)\n", + " return y\n", + "\n", + "plt.figure(figsize=(24,16))\n", + "plt.scatter(x9,y9)\n", + "for i in range(10):\n", + " coeffs = Z9[i]\n", + " x = np.arange(0,1.001,0.001)\n", + " y9_p = poly(x, coeffs)\n", + " deg = str(i)\n", + " plt.plot(x, y9_p, label=deg)\n", + "plt.ylim(-2,2)\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 144, + "id": "2636e202", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 144, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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at2A1DHIcNo04EBERERERERFJArFYjJUrV3LBBRdMei0FtJJwpaWl9PT04Pf7E11KUstz2ukMKaAVEREREREREUm0n/70pyxcuHBK1lJAKwm3fw5tS0tLgitJbnkOuzpoRUREREREREQSrLW1lYceeoiPfexjU7KeAlpJuKKiIqxWq+bQvoV8p53OkGbQioiIiIiIiIgk0uc+9zn+53/+B4tlaqJV25SsIjIJdrudoqIiGhsbE11KUstz2OmLRAnH4zim6BeAiIiIiIiIiMhs9Oydu+ltGZ3SNeeVpHDa5QuOeM66devIzc3lpJNO4umnn56S6yrlkaRQXl5OR0cHwWAw0aUkrTzn2OspPWF10YqIiIiIiIiIJMLzzz/PAw88QHl5OVdeeSVPPfUUV1999aTWVAetJIXy8nKeeeYZmpubWbDgyK9UnKjyHHYAukIRilyOBFcjIiIiIiIiIpI4b9XpOl2++93v8t3vfheAp59+mh/+8If88Y9/nNSa6qCVpFBcXIzVatWYgyPId44FtJ3aKExEREREREREZM5QB60kBYfDoTm0b2Gig1YjDkREREREREREEu6MM87gjDPOmPQ66qCVpKE5tEc2z2HDwtiIAxERERERERERmRsU0ErSKC8vxzRNWlpaEl1KUrIaBrkOO10acSAiIiIiIiIiMmcooJWkUVxcjMVi0ZiDI8h12uhUB62IiIiIiIiIyJyhgFaShsPhoLi4WAHtEeQ77BpxICIiIiIiIiIyhyiglaRSXl5Oe3u75tC+iXynXZuEiYiIiIiIiIjMIQpoJaloDu2R5Trs9EWihOPxRJciIiIiIiIiIiJTwJboAkQOdvAc2vnz5ye6nKST77QD0B2OUuxyJLgaEREREREREZETT3l5OampqVitVmw2G+vXr5/UegpoJaloDu2R5TnGfmS7QxEFtCIiIiIiIiIiCfL3v/+defPmTclaGnEgSUdzaN9c3ngHbWdYG4WJiIiIiIiIiMwFCmgl6eyfQ9vc3JzoUpJOvmMsoNVGYSIiIiIiIiIiiWEYBmeffTYnnXQSv/nNbya9nkYcSNIpKSnBZrOxb98+FixYkOhykkq2w4bVgK6QOmhFRERERERE5MT191t/Q3fTvildM7eskjM/fMNbnvf8889TWFhId3c3733ve6mtreX0008/7uuqg1aSjt1up7S0lH37pvaHbC6wGgY5djudCmhFRERERERERBKisLAQgNzcXC655BJeeeWVSa2nDlpJSpWVlTzxxBOMjIyQmpqa6HKSSp7TRpdm0IqIiIiIiIjICexoOl2ng8/nIx6Pk5qais/n47HHHuOrX/3qpNZUQCtJqbKyEoCGhgaWLVuW4GqSS77TTksgnOgyREREREREREROOF1dXVxyySUARKNRPvShD/G+971vUmsqoJWklJ+fj9vtZt++fQpoXyfPYefVIV+iyxAREREREREROeFUVlayefPmKV1TM2glKVksFioqKti3bx+maSa6nKSS77TTH4kRiscTXYqIiIiIiIiIiEySAlpJWpWVlQwPD9PX15foUpJKgdMOoI3CRERERERERETmAAW0krT2z6Hdt29fgitJLoVOBwDtCmhFRERERERERGY9BbSStDIzM8nIyFBA+zr7O2g7FNCKiIiIiIiIiMx6CmglaRmGQWVlJQ0NDcRisUSXkzQKxwPa9mA4wZWIiIiIiIiIiMhkKaCVpFZZWUkoFKKjoyPRpSSNFJuVNJtFHbQiIiIiIiIiInOAAlpJahUVFYDm0L5egdOhGbQiIiIiIiIiIgkwODjI+9//fmpra1m4cCEvvvjipNZTQCtJzev1kp+fr4D2dQqddtpDGnEgIiIiIiIiIjLTPvvZz/K+972PXbt2sXnzZhYuXDip9RTQStKrrKykubmZUCiU6FKSRoHTrhEHIiIiIiIiIiIzbHh4mGeeeYaPfvSjADgcDjIyMia1pgJaSXrz588nHo/T0NCQ6FKSRqHTQU84SjgeT3QpIiIiIiIiIiInjH379pGTk8P111/PypUr+djHPobP55vUmrYpqk1k2pSUlGC329mzZw+1tbWJLicpFDrtmEBnKEKp25nockREREREREREZtTgg3sJt08uGH09R6GXjAurjnhONBplw4YN/PznP+eUU07hs5/9LN/73vf41re+ddzXVQetJD2bzUZlZSV79uzBNM1El5MUCpx2AI05EBERERERERGZQcXFxRQXF3PKKacA8P73v58NGzZMas0p6aA1DONm4AKg2zTNJYf5/BnA/cD+96jfY5rmN6fi2nJiqK6upq6ujr6+PubNm5fochKuwKWAVkREREREREROXG/V6Tpd8vPzKSkpoa6ujpqaGp588kkWLVo0qTWnasTBrcD/An84wjnPmqZ5wRRdT04wVVVjP3R79uxRQAsUOR0AtCmgFRERERERERGZUT//+c+56qqrCIfDVFZWcsstt0xqvSkJaE3TfMYwjPKpWEvkcLKyssjOzmbPnj287W1vS3Q5CZdqs5JitdARCie6FBERERERERGRE8qKFStYv379lK03kzNo324YxmbDMB4xDGPxDF5X5ojq6moaGxuJRNQ1CmNzaDXiQERERERERERkdpupgHYDUGaa5nLg58B9b3aiYRg3GIax3jCM9T09PTNUnswG1dXVRKNRmpqaEl1KUih0OmgLKqAVEREREREREZnNZiSgNU1z2DTN0fHjhwG7YRiHHSRqmuZvTNNcbZrm6pycnJkoT2aJsrIyrFYre/bsSXQpSaHQZdeIAxERERERERGRWW5GAlrDMPINwzDGj08ev27fTFxb5g6Hw0F5ebkC2nEFTjvd4SiRuJnoUkRERERERERE5DhNSUBrGMbtwItAjWEYrYZhfNQwjI8bhvHx8VPeD2wzDGMz8DPgStM0lSrJMauurqa3t5eBgYFEl5JwhU4HJtAV1pgDEREREREREZHZyjYVi5im+cG3+Pz/Av87FdeSE1t1dTV/+9vf2LNnD2vWrEl0OQlV6LQD0B4MU+xyJLgaERERERERERE5HjO1SZjIlJg3bx4ZGRnU19cnupSEK9gf0IbUQSsiIiIiIiIiMhPq6upYsWLFxC0tLY0bb7xxUmsqoE0SwWiQP2z/A5GYwrYjMQyDBQsWsG/fPsLhE3uDrP0dtG0KaEVEREREREREZkRNTQ2bNm1i06ZNvPbaa3g8Hi655JJJramANkk81fwUP1j/A6586Ep29O1IdDlJraamhmg0SkNDQ6JLSah0u400m4XW4IkdVIuIiIiIiIiIJMKTTz5JVVUVZWVlk1pHAW2SOK/yPH525s8YCA7woYc+xM82/IxwTMHb4ZSVleFwONi9e3eiS0m4YqdDAa2IiIiIiIiISALccccdfPCDR9ya66hMySZhMjXOLD2TVXmr+MGrP+C3W3/Lk81P8q13fotlOcsSXVpSsdlsVFVVsXv3bkzTxDCMRJeUMMUuBy0KaEVERERERETkBPPII4/Q2dk5pWvm5+dz7rnnHtW54XCYBx54gO9+97uTvq46aJNMujOdb5/6bX757l/ii/i45pFr+NH6HxGMBhNdWlKpqalhZGSEjo6ORJeSUMWusQ5a0zQTXYqIiIiIiIiIyAnjkUceYdWqVeTl5U16LXXQJqnTik/j3ovv5cev/Zhbt9/K0y1P8813fpOVuSsTXVpSmD9/PgC7d++msLAwwdUkTonLwUgszlA0RoZdP84iIiIiIiIicmI42k7X6XL77bdPyXgDUAdtUkt1pPK1t3+N3579WyLxCNc9ch3ff+X7+CP+RJeWcF6vl+LiYurq6hJdSkIVuxwAmkMrIiIiIiIiIjJD/H4/jz/+OJdeeumUrKeAdhZ4W8HbuOeie7ii5gr+uPOPXPbAZbza+Wqiy0q4mpoaOjo6GB4eTnQpCXMgoI0kuBIRERERERERkRODx+Ohr6+P9PT0KVlPAe0s4bF7+I+3/Qc3n3MzhmHwkb99hG+/9G18EV+iS0uYBQsWAFBfX5/gShKnZDyg1UZhIiIiIiIiIiKzkwLaWWZN/hr+etFfuWbRNdxZdyeX3n8pL7a/mOiyEiI3N5f09PQTesxBtt2K22JoxIGIiIiIiIiIyCylgHYWctvcfGnNl/jDuX/AYXVww+M38PUXvs5IeCTRpc0owzCoqalh3759RCIn5lv8DcOg2OWgNaSAVkRERERERERkNlJAO4utyF3BXRfexfVLrufePfey9v61PNP6TKLLmlE1NTVEo1H27t2b6FISptjloCWggFZEREREREREZDZSQDvLuWwuPn/S5/nTeX8izZHGp578FP/x3H8wFBpKdGkzory8HJfLxc6dOxNdSsKUqINWRERERERERGTWUkA7RyyZt4S/XPAXblh2Aw/te4iL77uYxxofwzTNRJc2raxWKwsWLKCuro5YLJbochKi2OWgPxLDd4J+/SIiIiIiIiIis5kC2jnEYXXwmZWf4Y4L7iDXk8sX/vEFPvf3z9Ht7050adNq4cKFBINBmpqaEl1KQpS4HAC0Bk/MObwiIiIiIiIiIjPpJz/5CYsXL2bJkiV88IMfJBgMTmo9BbRzUG1WLX8+/898/qTP83z786y9by137757znbTVlVVYbPZTtgxB8XjAW1LUGMORERERERERESmU1tbGz/72c9Yv34927ZtIxaLcccdd0xqTQW0c5TNYuP6Jddzz0X3UJtdyzde/AYfe+xjNA83J7q0KedwOJg/fz67du0iHo8nupwZV+yyA9CqgFZEREREREREZNpFo1ECgQDRaBS/309hYeGk1lNAO8eVppVy09k38bW3f42dfTu59IFLuWXbLUTj0USXNqVqa2sZGRmhra0t0aXMuDyHHbthKKAVEREREREREZlmRUVFfPGLX6S0tJSCggLS09M5++yzJ7WmbYpqkyRmGAbvX/B+Ti8+nf9+6b/58Ws/5tHGR/nGO75BbVZtosubEgsWLMBisbBz505KSkoSXc6MshgGRS67RhyIiIiIiIiIyAlj9+5vMTI6teMuU1MWsmDBfx3xnIGBAe6//34aGhrIyMjgAx/4AH/84x+5+uqrj/u66qA9geR6crnxzBv50bt+RJeviyvXXclPN/yUUCyU6NImze12U1FRwa5du+bsrN0jKXY61EErIiIiIiIiIjLNnnjiCSoqKsjJycFut3PppZfywgsvTGpNddCeYAzD4Ozyszml4BR+8OoP+N3W3/FE0xN8/R1f56S8kxJd3qQsXLiQdevW0d3dTV5eXqLLmVElbgdP9A0nugwRERERERERkRnxVp2u06W0tJSXXnoJv9+P2+3mySefZPXq1ZNaUx20J6h0ZzrfPvXb/N97/49IPMKHH/0w33rxW4yGRxNd2nGrqakBYOfOqW1vnw3KXU56wlF8sViiSxERERERERERmbNOOeUU3v/+97Nq1SqWLl1KPB7nhhtumNSaCmhPcO8ofAf3XHQP1yy6hrvr72bt/Wv5R8s/El3WcUlNTaW0tJQdO3YkupQZV+Z2ANAc0JgDEREREREREZHp9I1vfINdu3axbds2brvtNpxO56TWU0AreOwevrTmS/zx3D+S6kjl0099mi/940v0BfoSXdoxW7RoEd3d3fT09CS6lBlV5h77RdAYmP3zhEVERERERERETiQKaGXC0pyl3HnBnXxqxad4ovkJLr7/Yh7Y+8Cs2nRr0aJFAGzbti3Blcys8vEO2kZ10IqIiIiIiIiIzCoKaOUQdqudjy//OHddeBcVaRX8x3P/wT89/k80DzcnurSjkpaWRllZGdu3b59VwfJkZdptpNusNAUV0IqIiIiIiIiIzCYKaOWwqjKq+P25v+c/T/lPtvdu59IHLuV3W39HJB5JdGlvacmSJfT29tLV1ZXoUmZUmdtBk0YciIiIiIiIiIjMKgpo5U1ZDAtX1F7B/Wvv5/Ti0/nphp9y+YOXs6l7U6JLO6KFCxdiGAbbt29PdCkzqtzt1AxaEREREREREZFZRgGtvKVcTy4/PuPH/OzMnzESHuHaR67l2y99m5HwSKJLO6yUlBQqKirYtm3bCTXmoMzloCUYJho/cb5mEREREREREZHZTgGtHLUzS8/k/rX3c9XCq7iz7k7W3reWJ5qeSMoQdPHixQwMDNDR0ZHoUmZMudtJ1IT2kObQioiIiIiIiIhMl5/+9KcsWbKExYsXc+ONN056PQW0cky8di9fPvnL/Pn8P5PpyuRfnv4X/vnv/0ynrzPRpR1i4cKFWCwWtm3bluhSZkyZ2wFAU0ABrYiIiIiIiIjIdNi2bRu//e1veeWVV9i8eTPr1q2jvr5+UmsqoJXjsmTeEu644A6+cNIXeKn9JS6+72L+tPNPxOKxRJcGgMfjobKyku3btydlh+90KHc7AWgMag6tiIiIiIiIiMh02LlzJ29729vweDzYbDbe9a53ce+9905qTQW0ctxsFhsfXvJh7r34XlbmreR7r3yPqx++mrr+ukSXBsCSJUsYGhqitbU10aXMiAKnHbth0KgOWhERERERERGRabFkyRKeeeYZ+vr68Pv9PPzww7S0tExqTdsU1SYnsOLUYn717l/xSMMjfP/V73PFuiu4dtG1fGLFJ3Db3Amrq7a2FqvVytatWykpKUlYHTPFahiUuhw0BdRBKyIiIiIiIiJz23/Vt7JtNDClay5JcfOt+cVHPGfhwoV8+ctf5r3vfS8pKSksX74cm21yEas6aGVKGIbBeZXn8cDaB1hbvZZbtt/CJfdfwvNtzyesJpfLRU1NDdu2bSMWS47RC9OtzO3QDFoRERERERERkWn00Y9+lA0bNvDMM8+QlZXF/PnzJ7WeOmhlSqU70/n6O77OBZUX8I0Xv8HHn/g451acy5fWfIl57nkzXs+yZcvYsWMHe/bsoaamZsavP9PK3U5eHfJhmiaGYSS6HBERERERERGRafFWna7Tqbu7m9zcXJqbm7nnnnt48cUXJ7WeOmhlWqzOX81fL/orn1z+SZ5oeoKL7ruIu3bfRdyMz2gd1dXVuN1utmzZMqPXTZQyt4ORWJz+yInRMSwiIiIiIiIiMtMuu+wyFi1axIUXXsgvfvELMjMzJ7WeOmhl2jisDj6x4hOcU3EO337p23zzxW9y3577+OrbvkpN1sx0s9psNpYsWcLGjRsJBoO4XK4ZuW6ilLudADQFQ2Q79OMtIiIiIiIiIjLVnn322SldTx20Mu0q0yu56eyb+M6p36F1pJUr1l3BD179Ab6Ib0auv3z5cqLRKDt27JiR6yXS/oC2wa+NwkREREREREREZgMFtDIjDMPgwqoLeWDtA1wy/xL+sOMPXHzfxTzR9ASmaU7rtYuKisjKyjohxhyUux1YgD0KaEVEREREREREZgUFtDKj0p3pfO3tX+O2c28j3ZnOvzz9L3z6qU/TOtI6bdc0DIPly5fT2NjI4ODgtF0nGTgtFkpcDvYGFNCKiIiIiIiIiMwGCmglIVbkruAvF/yFL67+Iq92vsol91/C77b+jkgsMi3XW7ZsGQBbt26dlvWTSZXHyT510IqIiIiIiIjIHDTd78SeCsdaowJaSRibxcZ1i6/jgbUPcGrRqfx0w095/4Pv59XOV6f8WpmZmZSWlrJ58+ZZ8YM8GdUeF3v9IeJz/OsUERERERERkROLy+Wir68vqbMd0zTp6+s7po3qtc27JFy+N5+fnPkTnml9hu+8/B0+8rePcFHVRXxh9RfIcmVN2XWWL1/Ogw8+SFtbG8XFxVO2brKp8jgJxON0hCIUuRyJLkdEREREREREZEoUFxfT2tpKT09Poks5IpfLdUzZkwJaSRqnF5/Omvw1/GbLb7h1+6083fI0/3LSv3Dp/EuxGJNv9l68eDGPPvooGzdunPMBLcBef0gBrYiIiIiIiIjMGXa7nYqKikSXMeU04kCSitvm5rOrPsvdF97N/Mz5fOPFb3DtI9dS11836bVdLheLFi1i69athMPhKag2OU0EtNooTEREREREREQk6SmglaRUlVHFLefcwrff+W2ah5u5Yt0V/PDVH+KP+Ce17qpVqwiHw+zYsWOKKk0++Q47XquFvf5goksREREREREREZG3oIBWkpZhGFxcfTEPXvIga6vX8vsdv+ei+y7i8abHj3sYdGlpKdnZ2WzYsGGKq00ehmFQ5Xay168OWhERERERERGRZKeAVpJeujOdr7/j69x27m2kO9P5/NOf5+NPfJzGocZjXsswDFauXElzczO9vb1TX2ySqPI42aOAVkREREREREQk6SmglVljRe4K/nLBX/jKyV9hS88WLn3gUn624WfHPPZg+fLlGIbBxo0bp6nSxKv0OGkNhgnG4okuRUREREREREREjkABrcwqNouNqxZexYOXPMj7yt/Hb7f+lrX3r+XJpiePeuxBamoqCxYsYNOmTcRisWmuODGqPS5MoEEbhYmIiIiIiIiIJDUFtDIrzXPP4zunfYdbzrmFFEcKn3v6c3ziyU/QNNx0VM9ftWoVPp+P3bt3T3OliVHlcQJoDq2IiIiIiIiISJJTQCuz2ur81dx5wZ18ec2X2dS9iUvuv4Sfb/w5gWjgiM+rrq4mJSVlzm4WVuVWQCsiIiIiIiIiMhsooJVZz2axcfWiq3lw7YOcU34Ov9nyG9bet5anmp9607EHVquVVatWUV9fz8DAwAxXPP28Niv5Djt7A8FElyIiIiIiIiIiIkeggFbmjBxPDt897bvcfM7NeOwePvv3z/KpJz9Fy3DLYc8/6aSTMAyD9evXz3ClM6Pa46Tepw5aEREREREREZFkpoBW5pw1+Wu488I7+dfV/8qG7g2svX8tv9j0C4LRQ7tJ09PTqampYcOGDUQikQRVO31qvC52+4NHvXmaiIiIiIiIiIjMPAW0MifZLXauXXwtD6x9gPeUvYdfb/41a+9fy9MtTx9y3sknn0wgEGDHjh0JqXM61aa48MXitIbmXvgsIiIiIiIiIjJXKKCVOS3Xk8v3T/8+N59zMy6ri8889Rk+/eSnaRkZG3tQUVFBdnY2r7zySoIrnXo1HhcAu0aPvGGaiIiIiIiIiIgkjgJaOSGsyV/DXRfdxRdXf5FXO19l7X3jYw9iQdasWUNbWxvt7e2JLnNK1XjHAto6nzYKExERERERERFJVgpo5YRht9i5bvF1PLD2Ad5d+m5+vfnXXHzfxfRn9mO323n11VcTXeKUSrfbKHDaqfMroBURERERERERSVYKaOWEk+fN43/e9T/ccs4tpDpS+fJLX2Ygc4AtW7cQCMytcQA1Hhd1owpoRURERERERESSlQJaOWGtzl/NXy74C/95yn+yzbONWDTGj+7/EUOhoUSXNmVqUlzU+4PETTPRpYiIiIiIiIiIyGEooJUTms1i44raK7jjyjswsgyG64e56J6LuHv33cTisUSXN2k1XheBuElzMJzoUkRERERERERE5DAU0IoAGa4MrjznSjwxD4tji/nGi9/gQw9/iE3dmxJd2qTUesY2CtulMQciIiIiIiIiIklJAa3IuPnz55OVlcUK/wq+f9r36Q30cs0j1/Dvz/47Pf6eRJd3XBZ4xwLaOp8CWhERERERERGRZKSAVmScxWLh7W9/O+3t7Sy2LubBtQ/yT0v/iUcbH+WCey/g5m03E47NrlEBKTYrxS47u3xza/MzEREREREREZG5QgGtyEGWL1+O2+3mxRdfxGP38M+r/pn7L76fk/NP5iev/YRLH7iUZ1ufTXSZx6TW61YHrYiIiIiIiIhIklJAK3IQh8PB6tWr2bVrF/39/QCUpJXw83f/nF+++5cYGHzyyU/y6Sc/TfNwc4KrPTo1Xhd7/CGicTPRpYiIiIiIiIiIyOsooBV5nTVr1mCxWHjppZcOefy04tO456J7+MJJX+DVzldZe/9abnztRvwRf4IqPTq1Xhdh02RfIJToUkRERERERERE5HUU0Iq8TlpaGkuXLmXjxo34/YeGr3arnQ8v+TDrLlnHuRXnctO2m7jg3gu4f8/9xM14gio+ssUpbgC2j2oOrYiIiIiIiIhIslFAK3IY73jHO4hEIrz88suH/XyOJ4f/PvW/+eN5fyTfm89/Pv+ffOihD7Gxe+MMV/rW5ntcOAyDbQpoRURERERERESSjgJakcPIy8ujpqaGl19+mVDozUcDLM9Zzh/P+yPfOfU79Ph7uPaRa/nSP75Ex2jHDFZ7ZHaLQa3XxbYRBbQiIiIiIiIiIslGAa3ImzjttNMIBoOsX7/+iOdZDAsXVl3Ig5c8yP9b9v94quUpLrzvQv534/8mzXzaJaluto76MU1tFCYiIiIiIiIikkwU0Iq8ieLiYiorK3nhhReIRCJveb7H7uHTKz/Ng2sf5KySs/i/Lf/HhfdeyIN7H0z4fNolKW76IzE6Qm/9dYiIiIiIiIiIyMxRQCtyBKeddho+n4+NG49+tmxBSgH/867/4bZzbyPHk8O/P/fvXP3w1Wzq3jR9hb6FpakeAM2hFRERERERERFJMgpoRY6gvLyc4uJinn/+eWKx2DE9d0XuCv58/p/571P/m05fJ9c8cg1ffubLdPo6p6naN7fI68IAtmoOrYiIiIiIiIhIUlFAK3IEhmFw+umnMzQ0xJYtW475+RbDwkVVF7HuknXcsOwGnmx+kgvvvZBfbvolgejMhaVem5VKt5Pt6qAVEREREREREUkqCmhF3sL8+fPJz8/n2WefPeYu2v08dg+fWfkZHlj7AGeUnMGvNv+KC++9kHX71s3Yxl1jG4UpoBURERERERERSSYKaEXegmEYnHHGGfT397N58+ZJrVWYUsgP3vUDfv++35Ptzubfnv03rn7karb0HHt37rFakuKmJRhmMBKd9muJiIiIiIiIiMjRUUArchRqamooKiriH//4B9Ho5APOVXmruP382/nWO79F+2g7Vz18FV959ivTOp92aaob0EZhIiIiIiIiIiLJRAGtyFEwDIOzzjqLoaEhNmzYMCVrWgwLa6vXsu6SdfzT0n/i8cbHueDeC/jZhp/hi/im5BoHW5wyHtBqozARERERERERkaShgFbkKFVWVlJWVsYzzzxDOByesnW9di//vOqfefCSB3lP2Xv47dbfct4953Fn3Z1E41M3jiDHYafAaWeLOmhFRERERERERJKGAlqRo2QYBmeeeSajo6O8+uqrU75+YUoh3zvte9x+/u2Up5XzrZe+xfsfeD/PtD4zZRuJrUz1sGF46rtzRURERERERETk+CigFTkG5eXlVFVV8dxzzxEKhablGkvmLeHW993KjWfcSCQe4VNPfoobHr+Buv66Sa+9Ks1DYyBMX1gbhYmIiIiIiIiIJAMFtCLH6KyzziIQCPD8889P2zUMw+DdZe/mvovv4ysnf4Wd/Tv5wIMf4L+e/y+6/d3Hve6qNC8AG0f8U1WqiIiIiIiIiIhMggJakWNUVFTE4sWLeeGFFxgeHp7Wa9mtdq5aeBUPXfIQ1y66lof2PcQF917ALzf9En/k2EPW5aluLKAxByIiIiIiIiIiSUIBrchxeM973oNpmjz11FMzcr10ZzpfXPNF7l97P6cXn86vNv+KC+69gHvr7yUWjx31Ol6blVqvi43D6qAVEREREREREUkGCmhFjkNmZiYnn3wymzZtoqOjY8auW5Jawg/f9UNuO/c2ClIK+OoLX+XydZfzYvuLR73GqjQvG4b9xKdo4zERERERERERETl+CmhFjtPpp5+O2+3msccew5zhsHNF7gr+eO4f+cG7foAv4uOGx2/gE098gj0De97yuavSPAxFY+wLTM8mZyIiIiIiIiIicvQU0IocJ7fbzbve9S4aGhqor6+f8esbhsH7yt/HA2sf4Iurv8jm7s1c9uBlfPPFb9Ib6H3T561K9wCwQWMOREREREREREQSTgGtyCSsXr2arKwsHnvsMWKxo58FO5UcVgfXLb6Ohy99mA/WfpB76+/lvHvO4xebfoEv8sbNwOZ7XKRYLQpoRURERERERESSgAJakUmw2WycffbZ9Pb28vLLLye0lgxXBl85+Svct/Y+Tis6jV9v/jXn3XMed+y6g0g8MnGe1TBYkephw/Abw1sREREREREREZlZCmhFJqmmpob58+fz9NNPMzw8nOhyKEsr40dn/Ig/n/dnKtMr+e+X/5tL7r+ExxoPzMo9Kd3LjtEA/lg8wdWKiIiIiIiIiJzYFNCKTJJhGJx77rnEYjEee+yxRJczYWnOUm4+52Z+8e5fYLfY+cI/vsDVD1/N+s71nJzuJWqiLloRERERERERkQRTQCsyBbKysjj11FPZtm0bDQ0NiS5ngmEYnF58OndfeDfffMc36fR3cv3frufOTV/DArwwOJroEkVERERERERETmgKaEWmyKmnnkpGRgYPPfRQwjYMezNWi5VL5l/CQ5c8xGdXfZatXS9jCTdwe9M2On2diS5PREREREREROSEpYBWZIrY7XbOPfdcent7efHFFxNdzmG5bC4+tvRjPHzpwyz3GnTEMzj/3rXc+NqNjIRHEl2eiIiIiIiIiMgJx5boAkTmkpqaGmpqanj66adZuHAh2dnZiS7psDJcGfxz7Zlct7WBpaUf4KZtN3F3/d3csPQGrqy9EofVkegSRUREZlzMNNnjD9HgD9EcDNESDNMeijAUiTEcizEajROKx7EZBjbDwGoYpNus5DhszHPYyHHYqPK4qPY4qfI48Vqtif6SRERERGQWMPbv6p6MVq9eba5fvz7RZYgck+HhYX7xi1+Qn5/Pddddh8WSnI3qg5EoC5/bxr9W5HNu6gA/ee0nvNjxIkUpRXx65ac5r+I8LEZy1i4iIjIV+iNRnh0Y4ZVBH1tGAmwbDRCIxyc+77VaKHI6yLRbSbFaSbVZcFgM4iZETZOIaTIUidETidIbjtIfiXLwf1mXuRysSfeyOt3LmnQvC70uLIYx81+oiIiIiCQFwzBeM01z9Rsen4qA1jCMm4ELgG7TNJcc5vMG8FPgPMAPfNg0zQ1vta4CWpmtNmzYwAMPPMD555/PmjVrEl3Om3r3q7vIstu4a0U1AC+0v8BPXvsJu/p3sTBrIZ9b9TneXvh2DP1jUkRE5gDTNNk6GmBd9yBPD4ywdSSACXisFpamuFma6mZZqof5HhelLgdZdusx/R0YisdpCITY4wtR7w+ybTTAq0M+usNRALLtNs7KTuU92WmckZlKul1vZhMRERE5kUx3QHs6MAr84U0C2vOAzzAW0J4C/NQ0zVPeal0FtDJbmabJbbfdRmtrK5/85CfJyMhIdEmH9R+7W/lzRx91py3FMd7pGzfjPNzwMD/f8HPafe2cnH8yn131WZblLEtwtSIiIsdnty/IvV0D3Nc9QEMgjNWA1WleTs9M5YysVJanerBZpufFSNM0aQ6GeWXIx9/7R/h73zAD0Rh2w+Dd2alclpfFe7PTcFn1rhURERGRuW5aA9rxC5QD694koP0/4GnTNG8f/7gOOMM0zY4jramAVmazgYEBfvnLX1JWVsZVV12VlF2o67oH+dj2Rtatms/qdO8hnwvHwty1+y5+s+U39Af7OavkLD6z8jNUZ1YnqFoREZGjF47HeaR3iFvbenlx0IcFeGdmCmtzMzk3J52sBHWvRuMmG4Z9PNQ7xH1dA3SFo6TZLKzNzeQjxfOo9boTUpeIiIiITL9EB7TrgO+Zpvnc+MdPAl82TfMN6athGDcANwCUlpae1NTUNCX1iSTCyy+/zCOPPMJFF13EqlWrEl3OG/SGoyx5fhv/VlHAZ8vzDnuOP+Lnth23cev2W/FFfFxYdSGfXPFJilKKZrhaERGRtzYcjXFzaw83t/XSHY5S4nJwbWE2V+Rnkeu0J7q8Q8RMk+cGRrmrs591PYME4ybvzEjho8XzOGdeOtYkfHFXRERERI5fogPah4Dvvi6g/ZJpmq8daU110MpsF4/HJ0YdfPzjHyc7OzvRJb3Be1+tw2u1cN+q+Uc8bzA4yE3bbuL2XbcTM2NcvuBy/mnZPzHPPW+GKhUREXlzfeEov2vt4aa2Hoajcc7MSuWjxTmcmZU6K4LOvnCUP3f0cWtbL22hCNUeJ58ty+OS3MxpG78gIiIiIjPrzQLamRp21QqUHPRxMdA+Q9cWSRiLxcLatWuxWq389a9/JRaLJbqkNzgzK5X1wz6Go0euLcOVwRdWf4F1l6zj4qqL+UvdXzjvnvP4+cafMxIemaFqRUREDuWLxfhRQydrXtrBT5q6OC0zlcdXL+D25VW8JzttVoSzANkOG58py+Plty3iN4vLcRgGn9nZzKmv7OTPHX1E41PTVCEiIiIiyWemAtoHgGuNMW8Dht5q/qzIXJGens5FF11Ee3s7Tz/9dKLLeYMzs9OImvDcwNGFrPnefL7+jq9z38X3cXrx6fxmy284955zuWXbLQSjwWmuVkREZEzMNPlzex/veGknP2js5MysVJ4+uYabllSwNNWT6PKOm81icFFuBk+sqeHWJRWkWa18flcLZ71ax+O9Q0zVu99EREREJHlMSUBrGMbtwItAjWEYrYZhfNQwjI8bhvHx8VMeBvYBe4DfAp+ciuuKzBaLFi1i5cqVPPvsszQ2Nia6nEOsTvOSYrXw9/5j64ItTy/nh+/6IX+54C8smbeEH7/2Y86/93zu2n0XkXhkmqoVERGBDUM+zl5fx+frWih2OXhw1XxuWlIxpzbYshgG78tJ52+rF/C7xeVEzDjXbG3g/Zv2snXEn+jyRERERGQKTdkM2umgGbQyl4RCIf7v//6PaDTKxz/+cTye5Onu+cjWBjaP+Fn/9kUYx/lW0Fc7X+WnG37K5p7NlKWV8ekVn+bs8rOxGDPVqC8iInPdUCTKd/Z18If2PvKddr5eXchFORnH/XfXbBKOx/lDex8/buxkMBLjI8Xz+HJFAak2a6JLExEREZGjlOgZtCInPKfTyWWXXYbP5+Ovf/0r8Xg80SVNODM7lbZQhHp/6LjXWJO/htvOvY2fnfkz7BY7//rMv3Lluit5ru05vR1TREQm7eGeQU57ZRe3tffxT8U5PHtyLRfnZp4Q4SyAw2LhY8U5vHDKQq4pzOam1l5OfXkn93UN6O9ZERERkVlOAa3IDCoqKuLcc89l7969/OMf/0h0ORPOyEoD4O/9w5NaxzAMziw9k7svvJvvnPodhsPDfOKJT3D9365nfae64UVE5NgNR2N8ZmcTH9nWSJ7DzqOrF/DN+UWknKCdoxl2G9+vKeGhk+aT57Dz8R1NXLu1gc6QxguJiIiIzFYKaEVm2EknncTy5cv5xz/+QX19faLLAaDE5WC+x8nf+45tDu2bsVqsXFh1IQ+ufZB/P+XfaRpu4vq/Xc8Nj93Alp4tU3INERGZ+54bGOHMV3ZxT9cA/1KWx8MnLWDZLN4AbCqtSvPyyOoFfKO6kGcHRjjjlV38tbNf3bQiIiIis5ACWpEZZhgG559/Pnl5efz1r39lYGAg0SUBcFZ2Gi8MjjIcjU3ZmnarnQ/WfpCHL32YL67+Irv6d3HVw1fx6Sc/zc6+nVN2HRERmVuicZPv7evg/Zv24rJYeHDlfL5cWYDdcmKMMzhaVsPg/5Xk8uSaGqo9Tj61s5mPbGukPxJNdGkiIiIicgwU0IokgMPh4PLLL8c0Te644w5CoeOf/TpVLsjJIGyaPNE3uTEHh+O2ublu8XU8ctkjfGblZ9jQvYHL113O55/+PHsH90759UREZPbqCkW4fPNebmzq4oMFWTy+poZV6d5El5XUqjwu7l81n69WFfJk3zDvfrWOFwdHE12WiIiIiBwlBbQiCZKdnc0HPvABuru7ufvuuxO+adhJaR7yHXYe6hmctmt47V5uWHYDj172KP9v2f/j+bbnueT+S/jKs1+habhp2q4rIiKzw3MDI7xnfR0bh338tLaUn9SW4rHqP1ePhtUw+GRpLutOmo/LYnDZxj38qKGTmEYeiIiIiCQ9/RevSAJVV1dz7rnnUl9fz2OPPZbQWiyGwbk56TzVN4wvNnVjDg4nzZHGp1d+mkcve5QPL/kwTzY9ycX3XcxXn/8qbaNt03ptERFJPqZp8rvWHq7YvJcMm5VHVi/gioKsRJc1Ky1L9fD46houycvkB42dXL5przYQExEREUlyCmhFEuzkk0/mlFNO4aWXXuLVV19NaC3n56QTiJs8NUWbhb2VTFcmnz/p8zxy2SNcWXsl6/at44J7L+DbL32bLl/XjNQgIiKJFYrH+UJdC/9Z38Z7stN45KQF1HrdiS5rVkuxWfnfhaXcWFvChmE/7361jpc08kBEREQkaRnJvNPr6tWrzfXr1ye6DJFpF4/Huf3229mzZw9XXnklNTU1CakjGjdZ9sI2Ts9M5deLy2f8+p2+Tn6z5TfcW38vFsPCFbVX8NElHyXbnT3jtUhyC4fD+P1+fD4fgUCAUCj0prdYLEY0GiUWi73h+OC/Aw3DOOTYMAxsNtthb3a7HafTidPpxOVy4XK5Jo6dTicejwev14vNZkvEt0dk1ugJR/jotkZeGfLxubI8vlSRj8XQRmBTabcvyPVbG2gKhvj2/GKuK8w+5PediIiIiMwcwzBeM01z9RseV0ArkhxCoRC33norPT09XH311ZSXlyekji/uauHe7gG2v3MJrgTN/WsZaeH/Nv8fD+57EKfVyYdqP8T1S64n3ZmekHpkZpimSTAYZHh4+A230dFRfD4fPp8Pv99PJHLkt+vuD1AdDsdEqGq1WrFarYccWyyWQ0Lag4/j8TjRaPSwt0gkQigUIho98k7pLpcLr9c7cUtJSSElJYX09HTS0tIm7u12++S+eSKzUIM/xAe3jL39/sbaUtbmZSa6pDlrKBLlkzuaebJ/mKsLsvnOgiIcFr2RTkRERGSmKaAVmQV8Ph+33HILIyMjXHfddRQWFs54DX/vG+aDW/Zx65IK3peT2EC0YaiBX23+FY82PIrX7uWaRddw9aKrSXOkJbQuOX7RaJTBwUH6+/vp7+9nYGBg4n5oaOiwwWtqaiopKSkTXamvv3e73ROdq/tDWavVOmNfTygUIhgMTtwHg8GJ7l6fz3dIuDw6OkowGHzDOl6vl7S0NDIyMsjKyjrklpqaikVBiswxG4f9XL1lHyYmty2t5KR0b6JLmvNipsn393Xws+Zu1qR5uWlJOblOvTgkIiIiMpMU0IrMEkNDQ9x8881EIhGuv/56cnJyZvT6kbjJyhe2c3K6l5uXVszotd9M/UA9v9j0C55sfpJUeyrXLLqGqxZdpaA2ifl8Prq7u+np6aGnp4fe3l76+/sZHh4+pEvV4XCQlZVFZmbmRDfpwZ2lKSkpMxa2zpRIJMLw8DBDQ0MMDQ0dcjw0NMTAwACxgzbqs9lsZGZmkpWVRU5ODrm5ueTm5pKdna3OW5mVnuwb5mPbGpnnsHH78kqqPa5El3RCub97gM/tbCHLbuWPyypZmKJ5vyIiIiIzRQGtyCzS29vLLbfcgsVi4cMf/jDZ2TM7g/Xre9r4XWsPm96xhHmO5JmhubNvJ7/e/GueanlKQW2SCAaDdHZ20tPTMxHIdnd34/f7J85xOp3MmzfvkK7Q/YGj1+vVLMTXicfjDA8PT3QZ9/X1HXIcj8eBsTm5WVlZ5ObmTgS3eXl5ZGdnq+NWktYdHX18oa6FhV43f1pWSZ46OBNi68hYB7M/FueWpRWcmpma6JJERERETggKaEVmmc7OTv7whz9gsVi47rrrZrSTdpcvwBmv1PHN6kJuKMmdseseLQW1ieHz+ejo6Ji4dXZ20t/fP/F5h8NxSFi4/z41NVUh7BSJRqP09/fT3d19SCDe398/0Zlst9vJz8+nsLCQgoICCgsLmTdvnkJbSbhfN3fz9b3tnJ6Zwk1LKki1za3u+NmmNRjmqi372OcP8ePaEj6Qn5XokkRERETmPAW0IrNQd3c3v//97zFNk+uuu468vLwZu/b71u8mFI/z1JqapA3XFNROn2AwSFtbG62trbS1tdHZ2cnw8PDE5zMyMigoKKCgoID8/Hzy8vJIS0t7yz8rZtwkFo0Tj5sw9j/M/cemiWke2KjLYjEwLAYW6/ht/ONk/fOYSJFIhN7eXrq6umhvb58I0PfP9LXb7eTl5VFYWEhxcTElJSVkZGToeykz5qeNXXy3oYMLctL55aIybVCVJIYiUT6yrZHnB0f5ckU+nyvL0+8FERERkWmkgFZklurt7eX3v/890WiUa665ZsY2Dru1rZev7G7lb6sXsDzVMyPXPF4KaicnHo/T09NDa2vrxK2np2fi89nZ2eRk55GRkkmaxYsn5sT0RwkNBwn5QoT9EcKBKJGwSSQKkahBLA7xuEHMtBAzDeJYx27G5DvmDDOOgYmFGDYjhtWIY7XEsVlMbFaw2sBuM7C5bNhdNhweO65UF640N65MD66sVNyZXpwpDlweO3aXdU4GEvF4nN7eXjo6OiZC246OjonQNiUlhZKSkolbQUEBNlvyjDSRucE0TX7Y2MmPGru4LC+Tn9aWYrPMvZ+32Swcj/P5XS3c3TXANYXZfG9BMdY5+DtRREREJBkooBWZxfr7+/n9739PIBDgAx/4APPnz5/2aw5Goix/YTsfKsjmuwuKp/16U0FB7dEJhUI0NTaxt76BlsYmuvu7icajAFhNK+6oF0fYgzWYBpEM4Agb+JhxbNEg1lgQWzSALR7GRgSLEcdqmFgtJlYrEzeLAVaLicUADuqINSwGhsUCmBhmHEyTeBziJpj7702Ix8GMxYhHTWJxiMYMYqZB1LQSM63EDBsxbMStDmIWBzGrk6jNBcYRuvXMOA4jgtMSxeWM43ZbcKfa8GS48WZ58ealk1KUjTfbiyfNgdU2ezv/4vE43d3dtLS0TNwGBgYAsFqtFBYWUlJSQnl5OaWlpbhc2rxJjp9pmnxnXwc/b+7mivwsflxbouAvSR38/9XFuRn8fGGpupxFREREpoEC2mQXDQMm2JyJrkSS1PDwMH/+85/p6uriwgsvZNWqVdN+zU/taOJvvUNseMdi0mbRrEAFtRANxxjsGGZgVytdDR20dXfTGxxi2BglZAuAwdivnGgKtnAq9kgajqALdyCMM+obCyxtMVxOE5fHhjvFjjvFgSvNgSvDgzPDiysrDUdGCrb0dCwpqVg87vGQNbFM08QMhYiPjBAbGSU2PESwf5TgwCjBIT/B4SCh0TAhX5igL0I4ECMYMglFrYRwEbalEHakErMdfmdzJ0HctgheL6SkOUjJ8ZBWmEFaWS7pRZl40x1YrIn/PhytkZERWltbJwLbtrY24vE4hmFQWFhIeXk5FRUVlJSU4HTq7yg5OqZp8vW97fxfSw/XjndlWhTOJr3/beri2/s6eHdWGr9bUo57Fv0uExEREZkNFNAmu/on4E/vh7QiyKqAzPKxW1YFZFaM3bszE12lJFgoFOLOO+9k7969nH766Zx55pnT+tbszSN+zlm/m69XFfLx0uTbLOyt7Orfxa83/5onm5+ck0FtLBqnv7GP3u0t9DX2MtgVYGQ4xnDUwOcME3YMEXEMEbP7xp4QN/CE7KSFbczDQb43hYycVFILMkkrzsZTmI1t3jwsXu+k/1zFolHCwQCRQIBQwE84ECC8/z7oJ+wPEA2HiEYixCJhopEwsUiEWCRCNBwmFo2MfS4cJhqNEI/GMM342HzaeHx8Xq2JOXE8dj/WjWvFYrFgjN8sr//YasVmt2NzOLHa7dgcDmwOB1a7A5vdgdU0MSIRCEWJ+yPEfFGio2O3kM8kHLYTiroJ2TIIOjPeGOSacdxGkBRXlLQMO+l5XtJLs8laUEBGYToub3LvWh8Oh2ltbaWhoYHGxsaJwNZisVBYWEhFRQWVlZWUlJRoJIIclmmafGtvB79s6eZjxfP4VnXRnBwjMlfd1t7Ll+paOSXdy23LKrWZm4iIiMgUUkCb7HrrYdtfob8BBhpgoBFGuw49x5XxxtA2czzMTSuCJOhck+kXi8VYt24dGzduZOHChVx88cXT+jbkSzbW0xwI8/LbFs3auYGvD2qvXnQ1Vy28inRneqJLOyrRcIye+m56tjXRt6+Pwe4gQ34rflIwDQtxI0LEMUjM2kXYNUzEMT6uAINcdyplRQVUL6qhbNEi7Mf4ZyUWjeAfHiI4MkJgZITg6DCBkeGDjkcIjo4QGBkmODpC0OcjEggQjYSP+hpWu30sGLXbJ45t48fW/Y/bbOPhq2Xs3hi7Z+LjsZtpmsTjccx4DDMeHz+OE4+NfWzG48RisfEwOEw0PBYOH3zPUf69aLHacDidOOxObBY7lrgVohbMiIV41EHUTCHqyCJqz8Iw3BgWDxhu7ERIsYdITbWQme8lqyqHnIXFZBSl4XAlX+AZDodpbm6msbFxIrA1TRO73U5FRQVVVVVUV1eTlZWlEE4A+FFDJz9o7OTDRfP47nyFs7PRfV0DfHpnE4tS3Ny+rIpsR/L9bhIRERGZjRTQzkZh31hQe3Bou/94sBnGZ0YCYHVARtlB3bcHB7hlYD/8W3VldjJNk5deeonHHnuM7OxsrrjiCnJycqblWn/rHeK6rQ38elEZa/Nmdxf3wUFtij2FD9Z+kKsXXU2WKyvRpU3wDQbofG0vXVtb6W0ZYWDEyqiRNjFD1YhHcYW6sboHCKeHGPVEGDJDADjsdsrKyykvL6esrIyCggKs1jd2PpmmScjnwzfYj29wYOw20I9vaHDsfv9jgwMER0fetFa704UrNRV3Str4fSpOrxeH24PT7cHhdmN3u8eOXW7sbg9OtxuH24Pd7cY+3sGaTOGNaZrEY1Gi4QiRYIBwMDDR/RsK+An7/WOP+f1jj/n9hPy+8dB6eDysHiESDLzJFQyshgOL6cS0pGLaMsCSgmF4MCxenIaVNI+L7Jx0ssuyyVlcSvb8XDxpjqT5PoVCIRoaGti7dy979uyZmGGbkZFBdXU1VVVVVFRUaH7tCepXzd18Y287l+dncmNtqcYazGKP9w7xT9sbqXA7uWtFNfMU0oqIiIhMmgLauSYWheHWQ0Pb/vEQd6ARQsOHnp9acGhoe3CQ68kC/QNqVmpoaOCuu+4iGo2ydu1aFi1aNOXXiJsmp768izSblUdOmp80IdFk1PXX8dutv+Wxxsdw2Vx8YMEH+PDiD5PjefOQ2xeNsXU0wLbRALt9QVqCYVqDYQYiMXyxGMG4ic0wsFsMMmxWchw2Cp0OFnhd1HpdrErzUOo6NGTz9ftoe6GOju0d9LYHGAg4CVm8E593BvuxhvtIS4mSXenGl2WlhxCt3d1Eo1EsFgvFxcVUVlZSWVlJUVERVquVaDjMSF8Pw709jPSO3/f1jj/WS6BvECNqYrM4sBkObBY7dsOBw+7Bm5KB252G25WKw+nB6XBht7uwWe1YrXashg2LYcNiWDBiYMZMzOjYpl6YgDkWcgKHPIZpYjJ2bFiMsRm445uEMX4bO2bse2Qd/9hqwbBbMGxvcn/wscOK4bRicY7fu2wYTuvY52b4z200EiE4MkxgdGTsfmR4PADfH3734+vrZbS/D//o6Pg36WDGWHBrScOwpGIz3HicbjKzM8mtLKH0lCUULCzB7kj8W4/7+vomwtrGxkbC4TAWi4WysjJqamqoqakhM3N2v7gjR+f3bb18eXcrF+Zk8KtFZbP2XRdywLP9I1y7dR9lbid3ragix5HcI1pEREREkp0C2hOJaYK//3WhbcOBIHek49DznWmHn3mbWTE2OsGqjolkNjQ0xJ133klbWxurVq3inHPOmfKNfG5t6+Uru1u5a3kVp2WlTunaibRvcB+/2/o7Hm54GKth5dL5l/KRJR+hIKWAaNzk1WEfzw6M8Gz/KBtHfETHf11m2qyUuh0Uuxxk2214rRZcFgsx0yRsmgxEYnSHI7QEwzQEQsTGn5dnGCzu91Nb309+Q4QI47NwzTgpgS7S7aOYbpPnR0LsSnETTbORZxuh0DKC0xjrmM/NzaWiooKCedmkAIGuAXydfYR6hokMBYj5wxACh9WFw+LCYXHjtLpw2rw4rC5s2DE4ytDEYmDYDAybZSwoHT82rBbYf2yzYFjHQ1YYe7HHGH/NZ/x4/wtA+zNS0wTiJsRNzPhYiGuOfzzx2P77aBwzamJGYpjROGbExIzGIH4M/0cbHBLcGk4bFqcVi9uGxWPD4rEfeuyxjX889rhhm97xMfF4jMDw8EQn83BvN4ONDfQ1NDPY3YPfP0IoFuQNIa7hwmZJxeVMJS1zHrnV5RSvXExhTTkpmYkZNxCNRmltbaW+vp66ujp6e3sByMnJmQhri4qKsGgkz5xzV2c//7yzmXdnp3HzknIc+v94znhuYIRrtuyj1O3kboW0IiIiIpOigFYOiARgoOnQ0HZ/J+5gE8QOmh1psUFG6Rtn3u7vwHV43+QiMpOi0ShPP/00zz33HJmZmVx66aWUlJRM2frBWJx3vryTHId9znTRHqxluIWbtt3EfXsfIGKvJq/gSjosVQxETSzA8lQPp2WmsCbdy5IUF/OskTc0nRuGBYvFhTE+iiAw4KP56W00bGlna9DKjqxMGnMdNOTbCTosOCIx3tE9xOX2OGevqMAoyqOhsZEb732O9MgAqZaxsQVm3IYr4iI35mGxIwNPyI41ZsNl9eK0Hn50iYmJaQfDZcXqdWBLdWHz2rF47BhuGxbXeIepw3po16njoBDTbh0LXpPU/s7dseB2PMANxYiHxu4PHEcnHosHY5jh8ceDUeKBKHF/lHggcsTA13BYx0Jbrx1rqgNLih1ryvh9qh1LigNryti9xWOblp8PMx5ntL+Pvm3b6Ni8g66GNgYGBvGH/IQJEDf9HBzgGoYNpyudjNx88msWkD+/gnnFpWQWFuFwzdzIm76+Pnbv3k1dXR1NTU2YponH42HBggUsWLCAqqqqKX9BSWbe471DfHhbA29PT+G2ZZW4rQpn55r9IW2Jy8lfVyqkFRERETleCmjl6MRjMNz+xpm3+ztxg4OHnp+S98aZt/vDW2+ORifMsMbGRu69916Gh4d55zvfyemnn47D4ZiStW/v6ONfdrXw28XlXJibMSVrJovecJQ/tfdwS2snnREDqxmmLPoap9l3cpa7gzSGicVGiUZHicVGj7iWGXUQjzqIRV3EIx5iwRQsfhvOuJsUbzbppdXsyV/B34bSeGgEgoZBnm+EpU27qOxpx2laKIhnUhzPojCeRbrpwcAgEg8TsYSJ2+MYbgvWNCeOrBQ8uRm48zOxpTmx7g9hndax8QByVEzTHAtw/VHi/sh4cBsZ//jAccwXIT4aJjY6dn/YUNdijAe4dqxpTqxpDqzpTqzp++/HHrNM4WZg8VCIoc3baXxhM+17WukdHGE0FiVsiWDGBzHjgxwc3rq86WSXlpNbVkp2cQlZRSVkFRbjSc+Y1hdfAoEAe/bsoa6ujj179hAMBrHZbFRXV7No0SIWLFigubWz0IYhH5dt2sN8r4t7VlSTYkv82A2ZHgppRURERCZPAa1MjcDA4Wfe9jfAcBuHvAXXkfK60QnlBwLc9BKw6j/sp0MwGOTRRx9l06ZNZGRkcP755zN//vxJrxszTc58pY6YafKPk2tn9WxB04zj8+3hxa4d/L7b5OlgCVFsLDa3cDp/5yRewUGUvqjJYNQk1ZVPVdZisr3F2KwpWK1uoqE4A7vb6W8bYnQUQhYXFlsIi9WP2zKEJyWCK8PE8ISJMkjEHMA0wofUEcDFc9Ez+ZvlfDqsBeSFB7isbRO1TX10jGbTFE2l0epkr9VLSlY6z//buxP0HZPXM+PmWJA7GiY2cmhwO/HxcJjYcIi4L/qG5xtO64HQNm08wM1wYst0Yc10YctwTmq0ghmJ4Nu9l85XdtOxq5POrkEGIjECtjjx+CBmrB8z1gccqM2VmkZuWQU5ZeXMK60gp7Sc7OJSbFP0Is/BYrEYzc3N7Ny5k507dzIyMoLVaqWyspJFixZRU1ODx+OZ8uvK1NrrD3LhhnpSrVbWnTRfgd0J4PmBEa7e0kC528E9K6vJtGsMloiIiMixUEAr0y8ShKGW1wW4B4W40eCBcw0rpBcfftOyrApwzp05p4nS0NDAunXr6OvrY/Hixbz3ve8lIyNjUms+2jP2Ntb/WVDMtUXzpqbQGRIO99PX9w96ev/O8/3d/DX2PrYZK3AT4L3O3VyeOcLijEK83mrc7nJstlQGQ4PctuM2bt91O6OhUS4Lnc3JHcsY7nTQb2ZjWmw44mEKzQHys51k52bhcqcQ7QthjsYYMvy0W/ppswzQbukjbgthtwdJtQZwWX2YTj+5+SaZ82K8ahTxl9h7aKKccnMvV3MrpZFGOn259ATyWFmxnNXzV+D1zMfjKcMw1KU2W5iROLHhELGh8IH7odDYbXj8eCR86IhZA6ypjrGwNtOJNcs1Ht6Oh7gZzrFZwMdSRyyGv34fHS/uonNnBz2dEfpMF36HBTPWhxnrxYh1EosPYJqxsTIsFrIKi5lXWk7OeHibU1pBSlb2lHXbxuNx2tra2LFjBzt27GBoaAiLxUJ5eTmLFi2itraWlJSUKbmWTJ3uUIQLNtQzGouxbtUCKj0aVXGieKZ/hKu37GNxipu7VlSpa1pERETkGCiglcSKx2G0840zb/cHuYH+Q8/3zHtjaLv/PiVPoxOOUjQa5bnnnuPZZ58F4G1vexunnnoqbvfxzaA0TZNLNu5hly/IMyfXkutMrm6p+za28YO/1dE+GKAww82/nl3EmvxNdHbcy+DQeraxhHss11BnVpFtjfKxwhQ+WlZN2pt0AI129FO/7jUat3XT7UvF5Ugh3WqQbfrIcltIcXiwxg78w3TE9LPPbKHN0kevPUB4/FNOq4WegJWGcAr7jHyGrAfCpqIMN89/5SwAYvEof2ndx7f3DdFv2lkwuo3L4vezKK0Ji9k38RyLxYnXU403ZQEpKTWkeGtISanB4cidc/OBTxRmzCQ2EiLWHyI6ECQ2ECQ6ECLaP3YcGwq9McBNd2LLdmGb58aW7R67n+fGluU66u7beCDA4GtbaX15L537hugdtjPkzCdqBDFjPRjRDmxGDzFzkFBoeOJ57rR08iuryauaT17lfPIrq0nJyp7898E0aW9vZ+fOnezYsYP+/n4Mw6C8vJylS5eycOHC4/79JVNnNBrj0o17qPeH+OvKKlalaR79iebRniE+ur2BU9JT+JPmDouIiIgcNQW0ktyCQ4efeTvQAEOtYB407NHmPmhsQsWhxxmlYJv6t+POdoODg/z9739n8+bNuN1uTj31VFavXn1cm/PU+4K8Z30d781O43dLKqah2uNz38Y2/u2erQQiURZk7uHM4udZkbsVhzVCu+td3Glcw6vBTAqddj5dmssHC7Lf8A/KeDxO9/rd7HlkKwOdBoYti3SbhQxLnDSbBet412rMjDEU7qE/0k2b0UevI4jfayM0vmu5w26nrLSUBbW1VFVVkZmZSeW/PczhftsaQMP3zj/kMX8szo2NnfyypZs0m5Uf1pRwdqYVv78Bn6+e0dE6Rn27GR2tIxzunniezZZBSsoCUrw1B4W3C7DZ1JE+25mxOLGh8IHwtj9IrD9ItC9ItC9A3H/QGIX94e3+wDbbjW2e60B4+xZBSqi9i47nt9C+uZXu9hD9sQwC7lxMM4QR6cRtacPqGiJiDjLc14U5/vvZm5lFXmU1+ZXzyasau/ekZxz/12yadHV1sWPHDrZt20Z/fz9Wq5Xq6mqWLl3KggULpmzGthy9aNzkmq37eGZghN8vreQ92WmJLkkS5J6uAT61o4kzs1K5dWkFDotCWhEREZG3ooBWZq9o+NDRCQcHuQONEPEfONewQFoxZJa9bnzCeJDrzkjM15AkOjs7efzxx9m7dy9ut5uTTz6ZU0455ZhnPf6sqYvv7OvgpiXlnJ+TMT3FHqPTvvc4+c6XOKf8KSrSmxkNe3is9z38I+UietMzybJb+VxZHtcWzsN1UEAVDUVofuA1etZ3EQu6SLU7SbdasIx3okbMEAOhLgZCXfRFuulzB4lkpzBsNYjELBgYxI04mQWZrF64mqqqKvLz87G87h+q7/zeU7QNBt5Q98EdtK9X5wvymR1NbBkN8KGCLL5VXYT3dW8ljUQGGB3dzaivjtHROnyjdYz66g/ZzMzlKsLrPbTb1uOpwGJRuDVXxP0RIr2BscC2NzB26wsQ7Q1iBg8Kb60Gtmw39lw3tlwP9lzP2H2OG8N++Lcpx4NB+l/eRMuLe+jYN0JPMJVRd/7Y79tYgBSjCbd3ELxBRn3dDHS0wfh/W6Rm51Awv4bCBbUULlhIbkUlVtuxd97v76zdunUr27dvZ2RkBLvdTm1tLUuXLqWqqgqrVW+znm6mafKV3a38vr2PH9eU8KHCyXdNy+x2W3sv/1rXygU56fx6Ufmsnk8vIiIiMhMU0MrcZJow2v3Gmbf7j309h57vzjz8zNvMCkgtgBOk+6O1tZVnn32Wuro67HY7K1asYPXq1eTl5R3V8yNxk3Nf201XOMKTq2sSOurANGN0dt7PPzZ8lxx3P52+XB5oO48XvGcQKUyBuMkXqgv4eEkuqTYr8VAU/64eup6sI9gewmVx4LSMjTiIxiP0hdrpC7XTH+rE5wpiKcohnprBaCzOwPAIAFarlaKiIopLi+l0dnJ39900jDZQmlrK9Uuu56Kqi3BYDw0/D3T4xiYec9utfPfSpaxdWfSmX184HueHDZ38vLmbMreDXy0qZ2XakQN10zQJBtvxjYe2+8Nbv38fpjkW1hmGHY+n4pDQ1uutweUq1JiEOcQ0TeL+6IHQtsdPpMtPtGcswJ1o6zbAmunCnuPGlufBnjMe3OZ5sLgOHQFiRqMMb9lF8zM7aa8foGfEybC7ENOwYphxUi19ZGQP48w1CcUG6Ny7m+GeLgCsdjt5lfPHA9ux0NabkXlMX1M8HqepqYmtW7eyY8cOgsEgbrebRYsWsXTpUkpLS9/wAolMjd+19vCf9W18qjSX/6oqTHQ5kiR+3dzN1/e2c0V+Fj+pLZl4gVNERERE3kgBrZyYQiMHNil7/fiEwWYwD4RlWJ1jnbevn3mbWQ4ZZWB3JeZrmEZdXV08//zzbN++nVgsRmlpKatXr6a2tvYt3zq8YzTA+a/tZmmqh7tXVM34WxtN06Sv/x/s3fsDRkd30eYr4y97z2dz2hqipaljgVOLjwXdER6+YBn+ul6GNrRgC9uxGBZM02Qo0kt/qJ2+YDt+px9b2Txs2fMI2Rz0j/jo7Rub+2qz2SguLqa8vJyysjKKi4ux2w+E0rF4jCebn+R3W3/Hzv6d5LpzuXbxtbx/wfvx2g/MZnzDjNxzao4Yzh7sxcFRPr2jid5IlP9ZUMIVBVnH/D2Lx8P4/Q2HhLa+0TqCofaJc6zWlIPGJBwIb+329GO+niQ3Mxon2hsg0u0n2u0fvw8Q6fVD9MB/G1gzndjzvdgLvGP3+V5s2W4M61gIY5om/voGmp/cTOv2brqHHAy5izEtVizxKNmOYXKKwV1mJRjpo6O+jq599cSiYy8WpOfmUTC/lsKahRTVLCKntBzjKH+fRKNR9u7dy9atW6mrqyMSiZCens7y5ctZvnw52dnq8JwqT/YNc82WfZw9L42bl1QohJND/LChkx82dvJPxfP4ZnWRXugTEREReRMKaEVeLxYdG53w+pm3/eP34dGDTjYgrfCgmbflhwa57sxZvXGZz+dj06ZNrF+/noGBAex2OzU1NSxZsoTq6mpstsNvonVf1wAf39HE1QXZ/KCmeMb+QRYItLCr7r/o738Wt6uUwoov8v3G+dw3MoppMyhoD3LZ7hHeHTQpNtwYhkHMjNIX6qAn0EJvqJ1YqkH60gWYqekMhyN0dHYRCIyNIHA4HIcEskVFRW/6PTiYaZq82PEiN2+9mZc7XybNkcYHaz/IVQuvItN1bF2Ch9MXjnLD9kaeHxzlhuIcvlpVOCVvJ41GRw6Za+sbD3Cj0QObQjmd+aR4F+BNqcHrqcbjrcDrqcRun/zXJcnFjJvEBoJEuvxEunxEOv1EOnxEe/2wfxy4zYI9zzMe2HomAlxrigPTNBndWU/TE1to3dVPl8/LqLtg7GnxIDnuUQoXpJK2MB2/v4v23Ttp370L38DYZpEubwpFCxdTvHAJJYuWklNegcXy1uMLwuEwu3btYvPmzezbtw/TNCkpKWH58uUsXrxYm4tNws7RABduqKfc7eT+ldVvGLUiYpomX93Txm9be/mvqkI+VZqb6JJEREREkpICWpFjYZrg73td1+1B4xNGOw8935n+xtB2/+ZlaUVwFOFCMojH4zQ3N0+8dTgQCGC326msrGT+/PlUV1eTkZFxyHO+s7ednzV389WqQj45zf8gi8ejtLb+nr37foJhWCmt+BzPcy4/bOimKx7nlN4Qn9sVYb7PHB9X0EZ3sI3O6DABRwxPcQ7WwnkMjAzT398/se68efMoKSmhuLiY4uJicnJyJv0W6S09W7hp60081fIULquLyxZcxnWLrqMgpWBS60biJt/cO/aP4NMyU/jt4nIy7G8dHh8r0zQJhToZ9Y0HtuNzbn2+vZhmeOI8uz0Tj6cCj6cSj6cS7/ix212qGbdzjBmJE+kZC2sjnQdu8ZHIxDmWVDuOwhTsRSkT95Y0O0Mbd9D49E5a64fpCaUTcI11tjrjPvKzIpStKiTnpEL6Wutp3bmN1h3bGOzqAMDh9lBUu2gisM2tqML6Fi+YDA8Ps2XLFjZv3kxPTw82m42amhpWrFhBZWWl5tUeg55whPNeqyccj/PISQsodOnnWg4vbpp8YkcT93cP8vOFpXwg/9jf6SEiIiIy1ymgFZlKYf+B0QkHB7j9DWOjE+IHAgusDsgofePM28zysZvj2DbomimxWIx9+/ZRV1dHfX09Q0NDAGRmZlJSUkJpaSklJSVkZmfzqV2tPNgzyL9VFPDZ8qObY3usRn317Njxr4yMbCXV9U42dV3D7xwZNHvsLBuI8cndfgq6GmmOdtBlhBm1GlhdEPNAMHbg/4/MzEzy8/PJz8+nqKiIoqKiae2s2ze4j5u23cTD+x4G4PzK8/nIko9QmVE5qXXv6OjjS3WtVHqc3LG8ivwZmgMcj0cJBlvx+xvw+/fh8+8bP95LONw7cZ5hWHG5inG7S3G7S3C7inG5S3G7inG7S7DZ0vUW2DkiNhoeC2s7/EQ6Rgm3jRLt9k/Mt7V4bNgPDm3znPTt2EnjM3W0NwXpteQTsaeAGSfDMkRxuZOqsxaRVpFGW912WndspXXHNvrbWwGwO10U1iykdMlyypauOGKH7f7NxTZv3szWrVsJBAKkpKSwbNkyVqxYQW6uuvyOJByP84FNe9ky4ufelfNZ8Rbzr0VC8ThXbd7HS0Oj3La0kjOz0xJdkoiIiEhSUUArMlPiMRhue+PM2/3jE0JDh56fkv/Grtv9Qa4nOylGJ5imSU9PD3v27KG5uZnm5mb8fj8wtmFWVk4Of6tYwiuOFK50G3yuMJPszEy8Xu+kO1HjsRi7t/2Gtt6fEY84WN/xCe6Zt4qWFAd5o37O2FNHYXcLQbuJaTnw+8xms5GdnT0RxhYUFJCXl5ewtzm3j7bz++2/5576ewjFQpxVehYfW/oxlsxbctxrPjcwwnVbG8i0W7ljeRXVnsTOSY5GR8YCW98+/OPBbSDYQiDQQjR66J97qzVlLLh1l+ByFeNy5uN05uGcuM/FYnEm6CuRyYqHY2OhbfsokTYf4fZRIp0+iI39jBpOK/ZCL46iVCyZBr2762jc0kp7n50hdxEYFuyxAHmpPsqW5lB93ioMZ5zWndtp3bmVlu1b6WttBsCVkkrp4mWULVtJ6dIVZOTlH7amaDRKfX09mzZtor6+nng8TlFREatWrWLJkiU4nfrz9npf2d3KrW29/HpRGWvzNM5Ejs5INMbajfU0BMLcs6Jawb6IiIjIQRTQiiQD04TAwOu6bhsPjE8Ybjv0fEfqYWbejh+nl4B16t/afjRM06S/v5/W1la6urro6uqio6uLRwqq2FlYQeFAD2fteo30WASv14vb7cblck3c22w2LBYLFosFwzCwWCzEYjGi0SihYJCRwQF8A4OE/T4Kq17CW9jCE/4LeNRyPoPuNDJ9w6xqqqOqux1bzIkjaiXb46LqpFpKayqYN28eaWlpSbmTe3+wnz/t/BO377qdkfAIpxScwkeWfIS3F7z9uDpKt4z4+dDmfcQx+dOyKlYm6T+Eo9ERAoEWAsEWgoHW8eC2lWCwlUCghXg8+Ibn2O1Z42Ht+M2Rh92RhcOeid2ehcORjd2ehd2eicWSmJ8FOXpmND4217Z9rMs20jZKuGN0YkMyi9eOoySFuD1Ed1MLjU39dESyCDvGOvDSzAGKS+1UnbWQ4pOrCIwM0bx1E01bN9O0bROjfWMd3Om5eZQuXUHZ0hWULF6GJ+2NG9z5fD62bNnChg0b6OnpwW63s2TJElatWkVx8czN005mf+7o4/O7WvhkSS5frS5MdDkyy3SFIlywoR5/LM66VfOp8OgFEBERERFQQCsyO0SCMNj0xpm3Aw0w0ASx0IFzLbaxkPbg0PbgTlxnyoyXHwwG+UNTJ9/tGMRmmlwSG2XNaD/RgJ9AIEAwGCQQCBCLxTBNk3g8TjwWIxaPY2BCLI4lBg7DToo7jHXZFp71nMKz5lkELU6Kh0d427YuqjrsOCNQkRFgyQVLKT510awLVHwRH3fV3cUfdvyBnkAPtVm1XLf4Os4pPwe75djGFTT4Q1yxeS99kSh3LK9iTbp3mqqeHqZpEo0OEwp1Egp1jd8OPu4iGOokEul70zVstnQcjqyxwNaWjs2Wis2Whs2Wgs2WitWWOv7Y+M2aitXqwWp1YbG4sVpdGIbmks40Mxon0ukj3DpCuHmEcOsI0e7AxOet2S4iliB93T209oVos84jZlixx4MUpPupWFNE9bkrcaY4Gehoo2nrJpq3bqJl+1ZCfh8AueVVlC9fScWK1RQsqD1kfq1pmrS1tbFhwwa2bt1KJBIhJyeHVatWsXz5cjye5HzBY7ptGPaxdsMe3pbh5c/LqqZkM0I58ez1B7lwQz1pNisPrppPjmNmRvGIiIiIJDMFtCKzXTwOIx1vnHm7f3xCYODQ8705h9+0LLMCUnKndXTCPn+Iz+9q5qUhHwVOOx8tmsf5ORlUeJz4Bgdo27V97K3KO7Yy2NZJkbuakpSFZLnLqE+383jxIM8UmbQaxdjNGKsaBli8x6BwwCDb0s+iU3JYePnbcbhn/2Y14ViYh/Y9xK3bb2Xf0D4KvAVcs+gaLpt/GR770YdDnaEIl27cQ3c4wh3Lq1g9y0LaoxGPR4lGBwmH+4lE+glH+omED77vIxLuJxIdJhodIRodIRYbwTRjR7W+xeLAYnFhtbixWF1Yre7xj10YFjsWw45hsWEYtvFj+0HH+x+3YVgcGBhgWMbusYBhjD9mYGCBiWNj/Ngy8Rxg7JyDzh17AcIYP37d88c/HnsOBz1n/Dw46DmWg665/zmW8brHvkaLxYFhOLBY7FgsdgzjwL1hTH9XejwYHQtsW0YIt4wSbhk+sBGZBSKWMP0jo7SFHXTjJByPMc82QFlNGgvOX0lmVR7xWIyufXto2rqJpi0bad+9k3gshtPjpXTpcipWrKZ8xSpSs+ZNXDcUCrFt2zY2bNhAW1sbVquVhQsXsmrVKsrLy5OyI3869IQjnL1+NzbD4G+rF5A1DZsQyoljw5CPyzbtpcbr4p6V1XisJ8bPkYiIiMibUUArMtcFBt/Ydbs/wB1qZWLHHgC798AmZVmvC28zSsE6+S4X0zR5bmCU79e3sN4fBiBnpJ+srjayhwfJs6SR7S3GsKTQ4bKwz2OwO81K1GpgmHEWxHZTu81BdUMmaYEAFQVBVlx5MrmLiiddWzKKm3GebX2Wm7fdzIbuDaQ6Urmi5gquWngV89zz3noBoCMU5tKNe+gJR/nL8ipOmoMh7bEyTZNYzE80Nh7Yjge3Y+FtkFg8QDwWIBYPEp/4+OD7ILFYANOMYMajxM0Iphk99NiMEo/vP44cdSA8GxmG7UCQbXWPdSFb3Fj2H0/cDnzOZkvFZk8/0Nk8cZyO1frWb3s2TZPYUJhwy/BYYNs8TLh1FKJxAMLxML2hKN2mg/6oiRkZoKQIqt+9iOJ31mKxGIT8Ppq3bmbfxvU0bn6N0f6xbuyc0nLKV66mYsVJFC5YONFd29XVxYYNG9i8eTPBYJCMjAxWrVrFihUrSEubu5seReImH9i0h80jfh5cNZ8lqSdmB7FMrb/1DvHhrQ2cl5PObxeXY5ll73gRERERmUoKaEVOZNEQDLYc2n07EeQ2QvTAW4oxLJBe/MaZt/sDXNebhxOmaTLQ0U7rzm207dxG667tDPd0M5iaSdP85XRXr6THk06nw0rsoLfMOkNxIr4IS4O7eFfe45T3jzL03Ecwhkd5+1nFLLr87dhdJ85bI7f0bOHW7bfyRNMT2Cw2Lqy6kOsWX0dleuVbPrc9GObSTXvoC0f5y4oqVqUppJ1pY3+vxifuwRw/NjHN+PhjjB+bB+4xx+ZUE5947HDnHbIe8fHn7H/+m6154NxDrjP+nP0hc9yMYMYjxM0w8Xh4/Dhy0P3Y47F4iHjMTzTmJx7zE4sFiMXH72P+8dtYsH0kFosD23hY63Bkj9/mvfFmH7vfH+ia0Tjh9lHCjcOEGocJNw0R90UBiMRj9EWhPwZD4QCeVB9V7yyn6pzl2F12TNOkt7mRhk2v0bBpPe11Y921DreHsqUrqDzpZCpXrcGTlk4kEmHXrl1s2LCBhoYGDMOgtraWNWvWUFFRMetGq7yV/6xv5XetvfxyURmXalMwmUK/aenmq3vaNdNYRERETngKaEXk8EwTRjoPjEp4ffetv/fQ8z3ZE6GtmVnOkCWXlt4Yzc29tOzeg2+wf+y09AyKaxdTWrKMnGghNISJD4cxXFYcy+ZhXZGDszQNY2SE73zyt6xcWkfG2/7OaPsidj95IY+mZLDP66Xhe+fP9HckaTQPN/OHHX/gvj33EYqFOKPkDK5ffD0rc1ceMRhqD4a5ZOMehqMx7l81nwVe1wxWLXJAPB4mGh0lGh0aGz0RGSIaHZ44jkSHJu7D4T7C4V7C4V5isdHDrmezpeFyFuB0FeByFY4dj99sgSyMdg+RJj/BPX3EB8cC27hpMhgz6Y9EiVtHmbc8kwWXrMGV5gaY6K5t2LSeho3rGR3oB8OgcMFCqlefQtXqU8gqLKavr4/XXnuNjRs3EggEyM7OZvXq1XNmVu2dnf38885m/l9xDt+YX5TocmSOMU2Tf69v45a2Xn5QU8w1hUf3zhARERGRuUYBrYgcn+DwgfB2oJGRlnqa9zXR0j5Cy6CN4chY+OexhilNGaEk10FRUQkO+zvw91QTGXKDBVwLMvCclI+7NhvDbmFk11423fw09d1puJevJ3f53XQ0LuL7uz7CiGVstmxRhpvnv3JWAr/45NAf7Of2Xbdzx647GAwNsixnGdcvvp4zS87Eajn8xlZNgRAXbKjHYRg8sGo+Ra7ZP69XThyxWGgsrI30ToS2kXAfoVA3wVAHoWAHwVA7kcjrZm9j4HTm43aX4raXYg/kYulKI7bLgWMgH1vcjTke2AbiftzFdsovW0lqWTYwFiJ1N+xlz/qX2fvay/Q07gMgs6CIqtWnUHXSyeRWzmfnrl2sX7+elpYWbDYbS5YsYfXq1RQVFc3KrtodowHOe203q9K83Llcm4LJ9IjGTa7duo9/DIzwp2WVnJE1d8eFiIiIiLwZBbQiclx8gwO0bN9Cy/atNG/fzGBnBwCulFRKFi2hpKKI0nwPmdYhIk0D+BozCQxUYpoO7MZevNbHcVufwWqMYKYW0jVQw4amNTS7VhKzOimafz+pK9fxWtdJ/HrL1cTNscDRbbfy3UuXsnalOrn2C0QD3LfnPv6w/Q+0jrZSllbGtYuu5aKqi3DZ3tglu23EzyUb95DvtHP/qvna7EfmnFgsQDDYQSjUQTDYQTDYRiDYQiDQhN/fRCTSd8j5dksW1pFsrP15eEZLcfqKcIwUEgh4MNJM5r2rkuxTyrC4xn5Whnu72fvaK+xd/zIt27cSj0VxpaZRuXI1VatPwZNfxKat29iyZQvhcJj8/HzWrFnD0qVLcThmx4sio9EY56zfzUgsxpNrashxnDjjZGTmjUZjXLShnpZgmAdWzWdhijvRJYmIiIjMKAW0InJUAiPDtO7YRvP2LbRs30JfazMADreH4kVLKF28jJLFy8gpLcewWIgHovg3duN7pYNIpx/DYcGzIhfvmjzsGQGMgUbMnj00PLiRTXUFdKYtA9OkNPwSlSvupGNZgJyeEAv2GjREctkbnUe/o4ilS1ewcvnKsXEKaUVwguygfjRi8RhPND/BrdtuZVvfNrJcWVxZeyVX1FxBlivrkHNfGBjlg1v2sjjFzV0rqvBaD99xKzIXRaMjBAIt+ANNBPxNBAJN+Pz78Pn2EI0OTpxnhD04fUU4fYU4RgqxBIrIKFhB9kk1OCvSsTithPx+Gje/xt71L7Nv46uEfD6sNhtly1ZSvupkAu4UNm3ZSnd3N06nk+XLl7N69Wpyc3MT9w14C6Zp8okdTTzQPcjdK6p5R2ZKokuSE0BbMMx5r+3GbjF4eNUCcp16UUBEREROHApoReSwQn4frTu307J9M83bt9LT1ACmic3ppLh2MSWLl1G6eBm5FVVYDgr3Ip0+Rl9ox7+xGzMSx16UgvfkfDwrcrA4x7rPYj4fdTevY8srw/R5q7DGwyyoNFl9/amEzWfZsuOzZDlrWMZ7sAy2HJh/O9gM8eiBIq0OyCg7sFFZZvlBx2VgPzE7cEzTZH3Xem7dfivPtD6Dw+LgwqoLuWbRNVRlVE2c93DPIB/d1qgdtEXGmaZJONKHb3Q3Pv8efKP1DLRvwh9uBId/4jy7PwfnSBnueBUZ+SvILF9NSnkFcTNGe90O9qx/mfpXXmCktwfDYqFk8XKyFy6lJxJjd/0eYrEYZWVlnHzyydTW1mJNshdIbm3r5Su7W/n3ygL+uSwv0eXICWTziJ+1G/ZQ43Vxz8pqPFa9CCsiIiInBgW0IgJAJBikrW7HRIds1949mGYcq91O4YKFEx2y+dXzsdoO7Wox4ybBXf2MvtBOaM8g2Cx4V+bifVsBjqIDnVfhvn62/Xod23fBsLcYZ9zP4pUprLjmHbhTHAwNbWTDxqvxeuezauWfsNm8hxYZi8Jw69js20M2LWuA/kYIjxx6fmrhoaFtVsXERmZ4suAECCT3De3jjzv+yAN7HyAUC/HOondy7aJreXvB2zEMY2IH7U+X5vKfVdpBW+RwTNMkHO6lfcOjNG97jpC9C2tWF6R0T5xjDaXjic8nPXUFmSUnk1G0mv7mLna/8gL1Lz/PYGcHhmEhr3YRtpIq2oaGGR4eIS0tjTVr1rBq1Sq8Xu8RqpgZW0b8XPBaPadmpvDHZZV64UZm3KM9Q1y/rUEvHoqIiMgJRQGtyAkqGg7TvnsXLTvGAtmO+t3EY1EsViv51TWULllGyaJlFC6oxfYmMxPjwSi+9V2MvthOrC+INd2B9+2FeNfkY/UeCHFDbe1s+dU6trWk4nfn4WWU5aflsvTyNdjsY51jgUArr66/BJsthdUn3YXDcYw7OZsm+PsPCm0bDw1wRzoOPd+ZdlB4W35QgFsB6cXwJptszVYDwQHurLuTO+ruoDfQS3VGNdcuupZzK87lq3t7+EN7Hz+uKeFDhdmJLlUk6ZmmSd/6Hex4+CV6Al248n14MpuxZjQSSW0fP8nAFSsjzbuczII1mLFCmjY2s+flF+lrbcYE0hYsIpSRS9/IKFarlaVLl3LKKadQUFCQkK9rOBrjva/WETFNHl9dQ7ZD86klMX7d3M3X97bz+fI8vlSRmJ8HERERkZmkgFbkBBGLRujcU0/L9i00b99C++6dxCKRsY6uyipKliyndNFSCmsX4XAdeTRAbCjEyLNt+F7txAzFcJSlkfLOQtyLszEOejtisKmZTT+/n509OfjduaRZRjjp3HJqz1+G5aDdwKNRH69tuJxgsI01q+/F46mY+m9A2D82IuGQrtvxIHewCWLhA+dabPD/2bvr8LjOM+/j32EWM7MssmVJZkwcx47tgINtymm2lG03pbew2y3Dlpk2m7Zp06Thhhy2YwbJIMtiSyNmaUbDdM77h0yKnCZOZI/g+VxXLo3tR6P7KII597nP74nKmNy0vbCZqw3/lNs75Q/52dG+gwfqH6B5rJkYfQy3FbyX1+R1HB738fCiXFZHW8JdpiDMGrIsM1zdQOMzx7F2Q8gSQUKclai4ZhSxHXgj25A0E/EIKtlChLEcg6mEMauK0/vbGWxvJ6TVo87Kx6UxEJIk0tPTWbZsGUVFRVcs/kCWZe4+ZeXFYTtPLs5nSeTs/TknzH6yLPPZxi4e7h/ljyVZ3JAQFe6SBEEQBEEQLivRoBWEOUqSQgy2t9FZd4Ku+pP0NJwi4PMCEJ+VQ0ZJGekli0grKkFnfHsn4oEhN87dPbiODoAsY1gYj2V1Ktq0yQ09b0c3R880Zr2GOCI1LpbemE/+1YUolJNvVZRliZN19zA09Arli+4nNnbN9HwCLoUUgvHeiabtxeITvPbJ682JUzNvz741xc2K6ARZljnUf4i/1v+V3d27Uasi8aZ9j6AygleWFJFp0IW7REGYlQYP19P47Ams3Qoc2gSiVDLpUVYi0noJmttxRzURMPUDoMKESV+GbzyWnmPjdJ0cJRAZj5SQSkChxGwysWTpUiorKzGbL+9GXf/bNcTXWnv4em4Kn8yYuRuYCfOHT5K49dhp6pxunq7Ip8xiDHdJgiAIgiAIl41o0ArCHCFLEsPdnRMTsnW1dNefxOd2ARCTmk56yUIySxeRVlyKwRJxSc/t73Hi2NWFp24YVApMVUlY1qahjtFPWuft7ObYL5+mfjgerz6WKI2TpbcWk7c2F8WbNC2t1t9xuu3H5Of9JxkZd72zg7/cPGNTm7ZjHROPx3uAC35eas1nIhOypsYnRKaDaubtSn02p/YJ6wEGEv4Li8LD7/ONXJW24k3/vwmC8K/JsszAvloan6vF2q/FpYtHLYXI0ztJzVQgm9tx6evwRDfhN09EsCgxovCnM9yqoOe0jnFVJiFzJEqFgqKiIlauWkVqauq013riTO7s1bEW/lyaLb7vhRljyB9gc3UzAC9UFRCvnXm/QwVBEARBEKaDaNAKwiwlyzK2/l4662rPbezlGZ+Y9IxMTJrY1Kt0EenFZZijY97Rx/C12xnf2YWveQyFToV5RTLmVamoLJMzaf09PZz4xZPUDcThNiQQrXGw7PYScla/eWMWYGzsEEePvZ/EhC2UlPx8djYFAt4z0QnWi8cnhHzn1ypUEJU+NfP2bCNXF95ogTHvGN+re4m/juejcx9kcehlPlj8AbbmbEWnEhO1gvBOSaEQvS8fof7lJjrHLPi0UahCPnJMDnLzUtDrg9hdNXiiGnHH1uM3TkzYKoKR2HrMDAzEMuIvICgZiI2wsHrdOhaWL56W+ANXMMTG6ma8ksSrSwqJ1ojcWWFmOelwc8PRVkrMeh5fnIdOqXzrdxIEQRAEQZhlRINWEGaR8eFBOutq6ao7QeepWpyjIwCYY2LPNWQzShYSEf/ubk/1dYwz/nIHvlYbSrMG8+pUzMuTUeonn7j7+/up+/kjnOyOxmlOJULtYvmtC8hbl/eWzVaff5jDh69HrTaxpOop1OrLe/tuWEgSOPsvmLq1Tm7gekYnrzfGXSTz9kwD15x4xaITftreyw+tg2R7X8I5+Fdi9DHcWnArtxfcTqIp8YrUIAhzleTz0/b0AZr2WOl2xxJUG9EEXWRGOVmwOAeLIRqHtQWH5iiuuJO44+qRVB6QFbhskYyMpjBiz8TniqW0sJANW7dhvsS7Ii50b0Mn/+gf5fHyPFZGz8Gfw8Kc8MygjX87ZeWOpBh+viB9dl7QFQRBEARB+BdEg1YQZjCXbWxiOrbuBF2nTmIbmLgN1hARSXrJQjJKFpJRupCopJRpOVnxdzmwv9yBr3kMpVmDZV06pmVJKLWTp7RCdjsNv3iIY01axi1ZmFQelt2YS+E1hZM2/3ozsixx/MRd2GyHWVL1JGZz4buufVby2i+SeWudeGzvBlk6v1ZtuEjmbdbE46gMUGsv/jHegbObBb0wZOcb6X5qO//K612vo1Ko2Ji5kTuL7mRR/CJxgiwI71LA6ab50T00Hx6gP5iApNJiCNjISgpQfM1CTCoLnsYhbGPHcMecxJVwCq+5DRQyfp+ekdE0RodT0QdzWb1uI0WVSy7p+/KpgTE+Ud/BZzMT+VJO8mU8UkF4937U3sdPrAN8My+Fj6eLnGRBEARBEOYW0aAVhBnE43TQferkuciCke5OAHRGE2nFZWSULiS9ZCFxaRkopvEWP3+Pk/GXO/A2jqI0qicasyuSpzRmJY+H0398hOpDXkYj8tErvFRdl0np1iJUqrdfT1fXn2lu+TaFhd8mLfXOaTuOOSXoB3vXxadvx6wQcJ9fq1BCRBrEZE2NT4jOAkPUJX94ZzDEdTXN2IIhXq0qxOfv5+HGh3my5UkcAQelsaXcWXQnm7I2oVVNX3NYEOYrz5CNhof30nrSxpAiCRRKIoLD5BbqKLlpGRqXEk/9CK62ThyW47gSjuGMO4ms8hIKqRgbS8YxmEiiZSWrrr2NmOR/nVXb6fGx4UgThSY9Ty3OR/02Lq4JQjhJssy/nbKyY8jOgwtzuCr2nU+OC4IgCIIgzDSiQSsIYeR1OelprKer/iRddbUMdrSBLKPR6UktKpmILShZSEJ2Dkrlu88afKPgiAf7Sx14TgyhMKixrE3DvDIZpW5ylIEcDNL796c4/HwHvZGL0BBg8bp4Ft+2GLXm0upyulo4cuRGYqJXsXDhH8UU5jshy+AcfMOmZdbzj11Dk9cboqc2bc8+tiTDmzT7G5wettQ0Uxlh4h/luagUCtwBN0+ffpoHGx7EOm4lVh/L7YW3c3vh7cQZ4i77oQvCfGBv6ab+kf2cPh3Erk1CIYdIUA5RsDSBBbesRBr0420Ywd04iEM+ji2hmvGEYyj1dmQZHPYYfMOp5KTfROmq7RgjIic9f1CS2X6slUaXh1eWFJJpEBnTwuzgCoW44WgLXV4/OyoLyDXq3/qdBEEQBEEQZgHRoBWEK8jjdNDdUEd3/cR/Qx3tyLKESqMhpaCI9JIyMkoWkZSXj0p9+XYqDrkCOF7rxHmwD4VSgXl1KpZ1aVMyZmVZZmTHKxz56xGs5gpQqiheaGDZh5ehN116fZLkp7r6Vry+PpYt24FOKxp6l4XPcSYqwfqG+IR2sHWBHDq/VqU7M3WbNTU+ISqTh4ZdfLaxiy9kJfGF7KRz7ybJEgd7D/Jg44Ps7t6NWqlmc9Zm3lf0PkrjSq/s8QrCHCXLMgP766j75wmsIyZ8mkjUQQ9pETaKNxaQcW0F0rAXT8MonvphbGN1dCfsxZNwHINlGADXWAQKVz45ue+hSVvBT15toyNWTTAvgo8aLXx3WW6Yj1IQLk2X18+m6ibiNBqer8zHrJ7+C9iCIAiCIAhXmmjQCsJl5B63X9CQPclQVwfIMmqNluT8QtKKS0krKiO5oBCN9vJPMEn+EM59PTh2dSP7Q5iqkoi4JgNV5NSP7aqto/pn/6RJUUpAayE7Q2bVx1YQGWd8xx+/vf1XtLX/nIVlvyM+/tp3cyjCOxUKTkQnvDHzdvTMW7/zgsUK5IgUPpP/BR4zLeZRVQ2rY6LON3KNMQB0jHfwUONDPNX6FK6Ai4XxC3nfgvexMWsjGuXlu9AgCPNJyB+g7Z/7aXi9gx5fPJJKhzEwSnZqiLLblhBblkPI6cfbOIb71DCt3YfoTngdTXwDloiJDSVdIyZeG13Hw/l3oex1E9nk4Ps3l3HT4n8dhyAIM83eMQd3nDjN5rhI7ivJEnfjCIIgCIIw64kGrSBMI5dtjK76kxMN2Ya6cxmyap1uYkK2qJS04lKS8gpRa65c40qWZTzHh7DvaCc07kdfFEPk5iw0iaYpawMDg5z80V85MZiM25hEQqSftR9bRmJu9Luqwelq4fDhG0iIv5bS0l+8q+cSLhNZBtfwBU3bialb11g3m5M+gU1l4NXqu0kIjE6s10dOyrx1RqTwT18fDw3sp8PVS4IhgdsLb+fWgluJNcSG88gEYU7xDNupf2gPLbXjjKgmJttjgn3kl5opef96DHGRSP4Q3qYxeo62cbxnN+PxR9DFD/L9iK+iJshXRr9BU2c2RwNb+eeXPhDmIxKES/eHrkG+3trLV3OS+UxmYrjLEQRBEARBeFdEg1YQ3gXHyDDd9SfpOjMlO9bXA4BGbyB1QTFpRaWkF5eSmJOPSq1+i2e7PPzdDmzPtOHvGEeTaiZqaw66nMgp6ySPB+vv/srhQ35Goosxa7ysfl8pOcvS3/VkiiyHqKm5A5e7nRXLX0Qrog1mnbN5tFUGeNjSjcpmnRyfYOsEKQCABOwzmXkwJpZ9ahkNCq6LyOc96ddSlrEWojJB+84nsQVBOG+03srJR4/Q1qnErYlGGfKRoh+m+Koccm5YjkqtQg5KvPe/nqe33ExrfAT/1vNnqiIOY4wYQpZBGk8mPn4rxVUfR6ePCfchCcLbIssy9zR08uTAGA8uzOFqsWmYIAiCIAizmGjQCsLbJEkhhjs76Gmqp7epgZ6mehzDE5sx6YymiYZscRnpRaUkZOeiVIU3Ey3k8GN/0Yq7ZgClSUPkpiyMlYko3rBTtyzLDD/5LIcfOkFH9FJUSpnKDcks3l6KSn3xzaMuVVfXX2hu+RbFxT8hOemmaXlO4cp7qG+EzzZ28eXsJO7NSpr8j1IIxnumZN622U7zUHCIpw0a3EolJT4f7xl3shkL+jdm3p59bIwFcbuqIFwSSZLofPkop15ootsRRVBtQB8YJzvFT9ltS7j6cA9DuWY0TTY2dHaTo+5HZ+olOb6D5IROlMZR5JAKpSeP9Nz3kFt0B0ql2DxMmNncIYnrjzbT7Q3wYlUBWWLDO0EQBEEQZinRoBWEN+H3euhraTrXjO1racTv8QBgjo4hZUEJqYVFpC4oIT4zC6VyZmxSIYcknPt7GX+lEzkgYV6VQsSGjCkbgAF46uup/p9HaFQuwq+LJL9Aw6qPLsV0kUzad8rnG+LAwWuIjCinvPzPIiduFpNlmU/Wd/DskI1nKgpYHPE2p2BlGed4N8/U/51/dL7Iae8QkQo12yUDt9tspNt6Jq/XWiAma3LTNvpMEzcyHVThmUYXhNnCP+6i4aHdNNcMM6hIZsys5o+bLMQMO/HXjOLWaAGZDLWbWxLGGRvtItIySl7cAKaEZmSdAzmgQy9XUbDok8QnLRc/u4UZq8PjY3N1M4k6Dc9V5GMSm4YJgiAIgjALiQatIJzhGB0+14ztbWpg0NqGLEmgUBCXnklqYTGphUWkFBYTEZ8wI09WfR3j2J5sIdDvRl8YTeS2HDTxU5toIbud5h/dT3VbJOMRWcRGBFn/iaUk5URNe02n6r/AwMCzLF+2A6Mxe9qfX7iy7IEgVx9pQqdU8nJVwSWfCMuyTPVANQ81PsRrna8hyRKrU1bynpR1rFZForR1TGTgnp3EHeuAkO/8EyjVE03aC5u2Fz7WmafzcAVh1htusHJrYy/tRh0ff9FBzLgLv7uT+ngzmz64nu2V6QwNDXHgwAFOnDhBKBQgP9pFelwXwYRaZFUAhTuemOgtFFV+Ep0+PtyHJAhTvD7q4L0nTrMtIYo/FGfOyNdogiAIgiAI/4po0Arzkt/rYaCtlb6WJvpPN9PX2oxzZBgAtVZHcl4BqQuKSSksJjm/EL1pZjd9JHcA+wtWXIf7UUVqibohF31x7JQTFFmSGPrHkxx8vImu2KXoVUFW3FpA0frsKdEH08Fmq6bm6B1kZn6SvNwvTPvzC+Gxf8zJLcdbeV9yLD9ekP6On2fANcBjLY/xWPNjDHuGSTWnckfhHWzP206UPmpikSSBo3dy03a0/fxGZp6xyU9qip88dXthfII5QUQnCPPOrzsG+E5bH78sSKOiupn6V9ro8cUjKTWY/UPk5ygoe/9qLFkpOJ1Ojhw5wuHDh/F4PCSaDBSYB9AnnsQb1QaSEq27hIzCD5CefwNK5ZXb7FIQ3srZr/Wv5aZwT0ZCuMsRBEEQBEG4JKJBK8x5khRipLvrXDO2v6WJ4a5OZFkCIDIxiaTcApLzCkktLCI+KydsG3pdKlmW8RwfwvZcG5I7gHllKhEbM1Hqpk41umtPcvSHD9OgXYJfY6a43MzKD1ehM1yeY5XlEIeP3EggYGPF8pdQqcSmUHPJd0738uvOQf5UmsV18VHv6rkCUoBXO1/l4caHqRmoQafSsTlrM+9Z8B5K40r/9Tt7bFObtmcf27uBC36XaUwXTNxmTZ6+jcoAlWg2CXPLKaeHzdXNXBsXwX0lWecu2rmH7NQ9uJvmU27sqngUUpBkRR9Fq1PIv30dIQWcOHGCAwcOMDo6SqQ5gkKjghh9Pd7kakK6cZQ+CxZ5LflLP0FkXHGYj1QQJl4TfexUB88N2XhoUS7rYizhLkkQBEEQBOFtEw1aYU6RZRn7QD8D7acZaGuhv7WZ/rZWAt6J7Fi9yUxSXgFJeYUk5xWQlFeAMSIyzFW/M8ERD2NPtuJrtaFJtxC9PQ9tytRJ35DDQduP/sCRJiNj0QuIjQxx1SeXkZh1eXc77un9B42NX6W09FckJmy5rB9LuPL8ksS2mha6fX52LllAom56mpvNY8080vQIT59+Gk/QQ2lsKe9Z8B42Z29Gp7rEbOSgD2xdkzYtOz+Ja4Wg5/xahRIi06Zm3p59rBe7gwuzi0+S2FzdzHAgyK4lC4jVXvxiXO+hJuqePI512ERAbUTvt5GT5KHsjmXElOXQ1NTE/v376erqQq/XU5KRTayjCdlyDG/CKVCG0I3nkRR9G1nL3odab7jCRyoI57mCIbYebWHAF+CFqgIyxaZhgiAIgiDMEqJBK8xaUijEaG83g+2nGbSeZqD9NIPtbfg9bgCUKjUJWdkTzdj8QpJyC4hOTpn1uWSyJOM60Iv9BSsoFURuzsK0LHlKRIEsy4w9/xKH7t9Pe+xK1CoFy27KpWxjDsrLEGdwoWDQxYGDGzAY0qmseGTWf86Fi2txebm2uonlUWYeXJiDchr/Pzv9Tp4+/TT/aPoHbfY2onRRbM/bzq0Ft5IRkfHuP4Asg6P/DU3bCxq57pHJ642xUzctOzuJa04CpfLd1yQI0+hbrb38tmuQvy3M4ZrYt77AEPT4aXh0Hw37+xmS40GhJC7US2FlLMXvX8/A2DD79++noaEBlUpFaUkJKXKQwMhrhJKPETQNo/SbiXCsJbvoo0QXLUKhEj/7hSuv3e1jc00zaXoNz1QUYFSJn8+CIAiCIMx8okErzAp+r4eR7k6GOqznGrJDHVaC/onNg9RaHfGZWSRk5ZKQnUtidi6x6ZmoNXPrluXAsIexx5rxW8fRF0YTtT0fddTU6ZBATw913/4Dx9zFeIwJ5BboWPPRKkyRV2aS5HTbz7Baf01V5WNERi6+Ih9TCI8/9wzz5eZuvpefyl1p0795kCzLHOk/wsNND/Na52uE5BDLkpdxe8HtXJVxFZrLlYHpHZ8amXD2sb0b5ND5tWr9G5q3FzyOygC1mOASrqyzOdEfSInlh4WXnhM91tRN7UMHON2lwqOJQhN0kxltZ9HN5WgLkzlw4ADHjh0jGAySl5dHWWE+7sZX8Cr3IiW2glLCMFpMnGob6YtvRZ8ZIy7UCVfUqyPjvL+2jZsSovit2DRMEARBEIRZQDRohRklFAww2tvDcFcHI10dDHVaGenqwD44cG6N1mAkITuHxOzccw3ZmJQ0lKpL201+NpElGee+XsZfsoJKQdS2XIyVCVM3AQsG6b//bxx8oZfehOWYdAE2fKyC9JIrt+u219fPgQMbiIvbQFnpL6/YxxXCQ5Zl7qxt46DNxa6lhZf1dtJB9yBPtjzJ4y2P0+fqI1Yfy/b87dySfwtplrTL9nGnCAXA1jm1gXv2bcB1wWIFRKSeb9y+MT7BEH3l6hbmBUcwxFVHGlErFLxaVYhJ/c5/N0rBEKefPsCpV630BhKQlWpiAn0sWBxB9i3LONHcwOHDh3G5XCQlJbFi+XK0rm76mv8B8XXIxnFU3igih9aSmvgeoheXokk0TePRCsKb+7m1nx+09/Od/FTuvgwXEAVBEARBEKaTaNAKYeFzuxjr7WGsr4fRvh5Ge3sY6epgrK8HKTQxmaZQKolJSSMuPZO49ExiMybeRiUkoZhHtxMHhj2MPdqMv2Mc/YIYom/OQxUxtQnmqTvF8e/cT51hFX5dJAtXxLD8vQvRaK9s47qh8av09T3BiuUvYzBc+uSWMPv0ev2sP9JIscnAE4vzpjXq4GJCUoh9vft4tOlRdvfsRpZlVqau5LaC21iXtg61Moyb/MkyuIYuknl7ppHrGpy8Xh918czbmGywpIjoBOGS3dvQySP9ozxdkU9V5PQ1Qx1dg5z46x5aToNbE4066CbLMkrR9SUMRcKBAwcYHh4mIiKC5cuXk5eZRvOh/8Pt3YUqsRtkJZbBSmIcW0goXI+xPAF1lH7a6hOEN5JkmQ+fbOe10XGeKM9jadTUnH5BEARBEISZQjRohcsm4PUyPjzIWH8fY73dE83YM01Zt912bp1CoSQiIYHYtIxzzdi4jCyik1PnXETBpZBlGfeRAWzPngalkqgbczGWx0+ZmpV8Prp//gcOHg4wFL+Y6AiZDZ+qIjHrym9+5nZbOXjoWlJT76Sw4BtX/OML4fNw3wj3NnZd8Umlflc/T7Q8weMtjzPoHiTBkHBuqjbZnHzF6njbfE6wdbwh89Y68djWCVLw/FqVFqIyp2beRmdDdCZoxGZMwmQ7hmx8pM7KvZmJfDnn8nz9SyGJtuerqXuplV5fHLJSTbS/l4JSA4a1ORypO4HVakWn01FRUcGSqir6m/dgbbkfbXwLCp0f3XgG0Z0bidVvxFKRjqE0DqU+jBdWhDnLHgiyqaYZT0ji5apCEqZpQ0tBEARBEITpJhq0wjsiyzI+twvn6Ajjw4OMDw5iHxpgfGiQ8aEB7EODeMbtk97HGBlFdHIK0clpE29TUolJTiMyMWleN2IvJuT0M/ZEK976EXS5kUTfXoj6IvmxrqNHqfn+QzRErEXSGKjanE7F9fmowrQhxqlTn2Nw6EVWrtiJTpcQlhqE8JBlmQ+cbGffmINXlywgx3hlc1eDUpDd3bt5tPlR9vXsQ6FQsCZ1DbcV3Mbq1NWolLMgAiUUhPHuqZm3Y+0wagW/Y/J6S8rUqduzk7jGGBCZi/PKkD/AusONpOq0PFeZj/YKTF87+0Y58de9NDcHcaujUAfdZBqHSN6QQUtgjFOnTqFQKCgtLWXlypWog05qD/4Mn3IP2igXSr+JqO6riOq7msj8QowViejyoqZseikI70a908PWmmYWWYw8Wp6HRnx9CYIgCMKMJkvSvLpr+izRoBXOkWUZv8eN1+nA63TicYzjtttwjo3iGhudeGs783Zs7NwGXWepNBoi4hKIiE8gMj6RiPgEIhISiUpMIjo5Fb1J3Fr2dnibRhl9rBnJHSRycxbmValTTlYlj4fOH/+Wg7VqRmLLSIhXcM09S4lOCl+2n9PZzKHDW8jIuJv8vC+HrQ4hfPp9Ew2iQpOeJxfnoQpTg7DH2cPjzY/zZOuTDHuGSTIlcUv+LdycfzMJxll64UCWwT06uWl7YXyCo2/yel3EBc3brMkN3Mg0mA0Na+Ftk2WZD51s5/UxBy9VFVJourLRAbIs0/7ScU7uaKLHHXNuqjajRIM918DxUycJBALk5OSwcuVK0lNTOHXgfvoGHkIX348CBeahSqI7rsUklWBanIipIkHk1QrT5rH+Uf69oZNPpMfzjbzUcJcjCIIgCMKbkINB9nz2t8SkR1H6/z4Y7nKuKNGgneHGhwfpOHkcpVKFUnXmP6UKhUqFUqVEqVSBLCNJElIohCSFkM8+DoUIBQMEvD4CPu/5/87+2euZaMQ6HWeasg5kSbpoHRq9AXN0DKboaMzRsZiiYzBHRWOKiSUyPoGI+ERMkVHz8irHdJEDIWzPt+M60Ic60UjMHYVoU6Y2tZ2HDnHsBw9RH7MBSaNn+Q3ZlG/ODfvEUe3Jexgd3cuqlbvQaMTGR/PV2ZPgr+em8MmM8DZDA1KAXV27eLTpUQ70HUClULEubR23FNzCypSV4c2qnW5+90R0whszb8esE38f8p9fq9RAVPrkpu25Rm4WaEVTbLZ5pH+UzzR08o3cFD4R5u87Z7+N2r/uoakpcG6qNtUyhLLCRP1AJ06nk8TERFauXElJSQm9rQdoqvslsukEKl0I1XgKcZ3XEdm3Am1KFMaKBIyL4lGZtWE9LmH2+0pzN3/qGeZ/S7K4PiEq3OUIgiAIgvAGE83Z33EyUEJmjJNt37sh3CVdUaJBO8O1Vh/inz/69rQ8l0KpRKPTo9Hr0eh0aPQGDGYzenMEerMZgyUCvcmM3mxBb4lAbzJhjIzGHB2N1mCclhqEiwsMuRl9sJFAvwvzqhQiN2ej0ExudktuN10//CWHatUMJVQQH69k4z1Lwjo1e5bT2cShw1vIyvp3cnM+G+5yhDCSZZmP1LWzc9TBK1WF5F/hSb430zneyWMtj/HP1n8y6h0lwZjATXk3sT1vO2mWtHCXd3lJIRjvnZp5e7aR650cR4M58eKblkVngylORCfMMH0+P+sON1J0ZpO+cE2uv5EkSVhfPMrJHc30eCeyaiMDPZiLgnTrnAyPjGCxWFi+fDmVlZWEfOOcOPAT7N4daCNcyB4jMX2biLVeg0oyoy+MxliRiKEoBoVaXAwWLp1fkth+rJVGl5cdlQUUzJDfT4IgCIIggBwKsfezv6XWX0JalItt390atujGcBEN2hku4PfhGbcjhSamYmUpdG46VpJCSMEQCqViYqpWqTw3ZatQqlAqlag0mjNNWR1KlXrKBlNC+LmPDzL2RCsKtYLo2wsxLIiZssZz4gTHvnEfddHXENKaWLo1k8Vb81DOkBy1ulP3Mjz8GqtWvi6mZ4VzWZiZeh3PVOSjniFfpzAxVbu7azePtzzOvt59SLLE8uTl3Jx/M1dnXI1OdWWzc2cE9+jUpu3YmY3MxnuAC14PaM3nJ20vzLyNyYbIdFCJPPErSZZl3l/bzn6bg9eWLCD7Cmc/v13O3hFOPLCb5hYJtyYadcBBdHwf9lSJnpFBtFotVVVVLFu2DIvFQtOxv9DVfT8qSy9SQIl+YCmpvbeitcWhMKgxLorHVJmIJs0sXtcIl6TX62djdTMxGhU7Kgswq0XciyAIgiCEmxwKsffzv6XWW0JqpIvrv7sV1Ty8IC8atIIQJnIghO2ZNlyH+9FmRhDz3gWooyafXMt+Pz2//gMH97gYSFxKTIySa++pIjZ15uT5ut3tHDh4LRkZHxXZs8I5Tw2M8Yn6Dr6Wm8I9Yb7l+s30u/p5qvUpnmx5kl5XL5G6SK7PuZ7t+dspiC4Id3kzQ8ALts6pmbdnJ3FDF2SRK1RnohOyLh6foLOE5xjmsIf6RvhsYxffyU/l7rT4cJfzlqSQxOlnDnPy5Tb6ghM/F8zKNoJZXrq9Y5M2FEtKSqK/ez8NJ35ESHcSkAn2Z5LufB+R3YUQlNEkGTFWJWFcnIDKJC4OCG/P3jEHtx8/zdb4KP5Ykima/IIgCIIQRnIoxJ7P/4GT3gWkRji5/nvb5mVzFkSDVhDC4sJIA8v6NCI2ZqJ4w/i+r7WVk//5C44b1uHXR1F5bTpVN+bPuDH/+oYvMzDwNCtXvI5ON/MbBMKVIcsyd9VZ2Tk6zs4ZPNkHIMkSB/sO8mTLk7za+SoBKcDCuIXcnH8zm7M3Y9KEP0ZkRpIkcPZPbdqefewZnbzeGHeRzNszj82JIjrhEvV4/aw/3EiJeSLaQDnLPn826wDHH9hHa6cKn9qCOjSAKqmfAZ2LQDBITk4Oq1atIicnB7ezi5PVP8DhfxWlJoh7wEK8+ybSxzcjDwRApcBQHIuxKhF9fnTYM9mFme/XHQN8p62Pb+al8PH0mXkRURAEQRDmOlmS2P35P1LnKSA1wsH137t+3jZnQTRoBeGKc9cOMfZYy5tGGsiSxNCfH+DwE010pG7AYlGw6d+XkJgVEaaK35zX28v+A1eRmnonhQVfD3c5wgzT7wuw9nADZWYjj5XnzooppTHvGM+2PcsTLU/QamvFoDawOWszN+ffzKL4RbPiGGYMr/3imbejVhjvBvmCTSnVhotn3kZnQVQGqMUGUReSZZk7a9s4aHOxa2khmYaZewHkrQQDQZoeO0Dd7l6G5Xhk2Yva2IQtxo03FDi3oVhpaSmS5Kap9jf0Dz2EQuvEa9OiHl5OofrDaLu1SO4gqggtxspETFWJqGMN4T48YYaSZZmP1ll5ccTOY+V5rIiaOXcmCYIgCMJ8IEsSr3/hfznlzictYpxt379hxg2jXWmiQSsIV4gsydhftOJ8vRtthoWY9xWhjpx8Uh3o66P5y9+jJliBw5LJgqoY1ry/FK1+Zu4239LyPbq6/8zKFbvQ61PCXY4wA/2td4QvNHXxk8J03pcSG+5y3jZZljk5fJInWp7g+fbn8QQ95EbmcnP+zVyfez3RepG1/K4E/WDvuiDz1jr5ccB9fq1CCRFpEJN18fgEfWR4jiGMHuwd4fNNXXwvP5W7ZkG0wds1dKqL4w8dom3ASEClRVa34o0bxYWfiIgIli1bRmVlJVqtmi7r45xu/TWyupeAS43Tmk1h5MdI9OfiPz0OMuhyIjFWJWIojUOpFVmjwmTjwRDXVTfjCIV4uaqQRJ2IyRAEQRCEK0EOBtn1+fuo9xWQHmFn2/dvRDnPm7MgGrSCcEVI7gAjDzXia7FhWp5M1LacKbtQ2198iZpfPE1T6jbUejVX37WQ3MUz97a7YNDB3n2riYu7itKSn4e7HGGGkmWZW46fps7pZvfSIpJm4QmwK+DiReuLPN7yOLVDtaiVatanrefGvBtZlboKjXL2HdOMJsvgHHzD1O0Fk7iuocnrDdFTp27PPrYkg3Juvdjr8vq56nAjiyxGHi3PnXXRBm+H3+On7u97qT88ik0RTUg9SDDCikPrQ6fTUVlZybJly4iIiGBkeA8NdT/ELzcQ9CkZa4wn0XwHRfFXI7d4CY14UehUGMvjMVUliY3FhEkaXR6uq26hzGLg8fI8NCIeQxAEQRAuKzkQ4LXP3UdjoJDMaDtbvjO1OStJIWRJRqWemYNql4to0ArCZebvdTLytwZCdh/RN+VhWpI06d8lj4fO7/6YQw0mhuPLSc0ysPETFZiiZvYtq51df6Kl5TssqXqSiIiF4S5HmMHa3T6uOtLI1TER3F+WHe5y3pXWsVaean2KZ9qeYdQ7Sqw+lm0527gx70byo/PDXd784HNcMHFrndzItXWBHDq/Vq2HqMyLxydEZYBGH6aDeGdkWeaOE6epGXezc0khGbM42uDt6jnYzPHHjtM5HolP6yVoaMFlcqJQKidtKDY+XktT/U+wu/YihxSMNEah8aymfOEdRI1H460bQQ5IqBONmKqSMFaIjcWECU8OjPHJ+g4+lhbPt/JTw12OIAiCIMxZks/Ha5+9jyapiKxYB9d9+waUb7g46hwb5flf/oiE7FzWf/DuMFUaHqJBKwiXkfvEIGOPtaA0qIl5fxG6jMk5st7GRk5+5aeciNpEQB/J8htzKb82a8ZvcCLLIfYfuBqdLomqyn+EuxxhFji7Ict9JVlsS4gKdznvWkAKsK9nH0+1PsXrXa8TlIMUxxZzU95NbMneQqRu/t12PyOEghPRCRc2bcesE7m3Y+3gd16wWAERKWeatllT4xOMMRf9EOH0QM8w/6+5m/8pSONDqXHhLueKco84OPHAbppO+RjX6fHp2/GYh5EUMrm5uaxcuXJiQzF3G6dbf83Q8LPIssRYaySerkLKlr+XnOhFeE+MEehygFqBsTQO09JktNkRYqp2nvuvlm7u6x7m98WZ3JQoImwEQRAEYbqFvF5evfc+WigmJ8HF5m9sm9L3sNYeY8evf4Lf6+Gaj36KknUbwlRteIgGrSBcBrIkM/6iFcfr3WizIoh9XxEqy/lNbmRZZuSBv3Lk4RO0ZVyHJULFdZ+uIj7DEsaq377BwRc4WXcPZaW/JSFhU7jLEWaBoCSzpaaZPn+A3UsXEK2ZO7erjHpH2dG+g6dan6JxtBGNUsP69PXclHcTK1NWolbOnWOd1WQZXMNTM2/PTuI6+yev10dePPM2OgsiUkF5ZTNNOzw+rjrSRFWEkX8smh2b7l0OsizTtuMotTua6QlE4TH24zN1E1SFSExIYOWqVZSWlhIIDNDR8X/09PwdGT92q5nR+lTyFm5nYeW1KFoDuI8NIntDqOMNmJYmYaxIFFO185Rfkrj1+GnqnB6er8xngUlsMCcIgiAI0yXkdvPyf9zPaVUxuckeNn1ty6TmrCSFOPDYQxx84h/EpqZz/We/TGxaRhgrDg/RoBWEaSb5Q4z+ownvqZGJvNnrc1BckKkSHB2l7SvfpNpWyFj0AvIWRXPVR8pm7EZgF1Ndczs+3yArV7yKQiE2XhHenjqHm001zdyWGMPPi+bmL9zG0Ub+2fpPnmt7jjHfGHGGOK7PuZ4b824kNyo33OUJ/4rfBWMdUzNvR9vB1glS4PxalXYiIuGNmbdnG7ia6W3uSLLMbcdPc8LhZufSBaTrtW/9TvOA3TrAsQf20typwmFx4zV0END6sBhNLF+1ksrKSlQqD11dD9DZ+SdCkgNnr4mBo3EkpW6g4tobiPLF4z4ygL9jHFQKDGVxmJcmoc2OnLdN8Pmq3xdgY3UTESoVL1QVYFGL1zeCIAiC8G6FnC523PsAHepC8tN8bPzq5knN2bORBl31JylZfw0bPvIJNPrZFUM2XUSDVhCmUWjcx/Bf6gn0OoncloN5ZcqkEzx3dTW1X/s1tcnbkfRm1ty5gOJVKbPqJNA+foLq6pvJz/8vMtI/Eu5yhFnmu6d7+VXnII8symVtzOyYGH8nAqEAu3t281TrU+zp3kNIDlEWV8aNuTeyOXuziECYbaQQ2LunZt6ejU/w2SevNydNzbw928g1xsIl/sz/U88wX2nu5seF6bw/JXaaDmruCPoC1D+8l5P7BxjQqfGaOvDrHGhUaqqWLmH58uWYTGp6e/+B1foHAsFh3ENm+o5EY1AvpHLLTeTkVOI9Oozr6MDEVG3cmanaSjFVO5/sH3Ny24lWNsdFcl9J1qx6fSYIgiAIM03A7uC5zz1EjyaP4hw/67+4adLv1o7a4zz/6x/P20iDNxINWkGYJv4eJyN/OYXkDRFz5wIMC87nF8qSxND//h+H/9lKR/q1RMVq2HxPBbGp5jBW/M7U1f0HwyO7WL1qH2r17KtfCC9PSGLDkSaCsszOpYWYVHN/QmnYM8xzbc/xVOtTtNpa0Sq1XJVxFdfnXM/K1JVolKL5M6vJMnjGLmjatp/PvB1tB0fv5PVay8Uzb2OyISINVJPvpujw+Fh/uIllkSYeWpQjGkZvofdwM8cePc5ptwqXuR+ffgiFAkqKili9bh3x8dH09T2K1fo7fP5+fDYLvYciCdrSKb92G2XrN4HVj+tw//mp2tI4TEuT0OWIqdr54Hedg3zzdC9fy03hnoyEcJcjCIIgCLOSf9TG0194nAFtNuXFQVZ95tpz/zYRafAwB594eF5HGryRaNAKwjTw1I8w+lAjSqOG2A+XoE02nfu34NgYbV/+Bkfsxdii8ilcEse695eg0c2+xpTPN8i+/atJT/sw+flfDXc5wix1wOZk+7FWPp4ezzfz5s+O2bIs0zDawFOtT/F8+/PYfXZi9DFsztrM9bnXUxJbIpo/c1HAMxGR8MbM27H2iUiFkO/8WqUaItPPNW2lqCxuZimnQnp2Lc4kNUJsXvR2uUccHP/zbupanIxZxvEa+pCVEhnxSazbvJGsrDQGBv5Ju/W3eL1dhNxRdO0z4eiOoWjV1VRsuYEobTyuw/24jg4ie4Pnp2orElCZRczEXCXLMv92ysrzQ3YeKc9ldfTcvdtDEARBEC4HT+8g//zP5xnRZbB0scySj5+fjHWMDPP8r35Md0MdJes2sOGuT87bSIM3Eg1aQXiXHHt7sD/XhibNQtwHiydtBuY+eoy6//wZJ5K3E9JHsP6DxSxYnhzGat+ddutvaGv7KSuWv4LRmB3ucoRZ7ItNXTzYO8KLVQWUWYzhLueKC4QC7OnZw7Ntz7KraxcBKUBWRBbX517P1pytpJrnT+N6XpOkiQnbN2benolPuC/6Kv4r/z/4adP/cGf/82BKuHjmbXQ2mBMuOTphPpAkmZZnqzn6civdWh8eYw+SKkC01si6zddQsrCE4aHnsXb8Fre7DdkfQ89BM8ONRjJKF1O55UaySsrxnBrFdej8VK2xLA7TihS0GRZxYWUOcgZDXFfTzFggxMtLCkjWiYa8IAiCILwdztOd/PPbu7DpUli1Ukv5h9ae+7fTNYd54Xc/J+T3c83dn6J47dXhK3QGEg1aQXiHZEnG/kI7zt09GEpjibmjEIVmYipWlmVG7v8zNf84yunsG7FEadjymcpZGWlwlixL7D+wHoMhg4rFfwt3OcIsZwsEWXO4kRSdhucrC1DN4wbHuH+cl6wv8czpZzg6eBSAysRKrs+5no1ZG4nQRoS5QiEc2t0+rj7SyAqDxIOGdhS2s5m3Z97au4ELXqtpTBc0b7MmN3KjMkAlojSGm/uo+dt+6u1OnJYBQmo3etSsWL6UpetWMT6+C6v1NzhdTSikWPprouk/riYqMZXF191AyboNKOwSzoN9uI8OIvtCaJJNmJYnYyxPQDkL74wR3lyzy8t1Nc0UmfQ8sTgPrVL51u8kCIIgCPOYrbaZp396BKc2nvWbIim+ZRkAwUCAPQ/+iaM7niYhK5et//H/iEm5+ECKLMl4G0ZQaFXo8+fX3WOiQSsI74AclBh7rBn38SFMK5KJuj733E6EIYeDzi99jSP9aQwlVJBdGsWGjy5EZ1C/xbPObCMjr3P8xF2UlvyCxMRt4S5HmAOeGhjjE/UdfCc/lbvT4sNdzozQ7ejmubbneLbtWazjVrRKLevS13F9zvWsTl2NRjTZ5gVJltl+rJUGl4fXly64+PRe0Ae2rslTt+cmca0Q9Jxfq1BCZNrFNy2Lzgb9/LoI4Hf5OfHgHmrquhgxjRHQ2VFJCsqyc1m/fSuBQDXt1l/jcNShIpbRhhSs+/xo9RbKrt5ExXU3YDJH4z4+iOtgH4E+FwqdCmNFAublyWgSTW9dhDArPD1o42OnrHw4NY4fFKSFuxxBEARBmLGGD5zgmT804tVGsvGWZPI2LQJgrK+HZ3/xQwbbT7P4uutZ+767UGumntNI/hDumgGce3sIjnjRF8cS98HiK30YYSUatIJwiSRfkJG/NeBrsRGxKRPL+vRztzf6Wlpo/Ow3OBqzDY8xgeU357F4Y8acuP2xtvYT2Ow1rF61D6VS3OonvHuyLHNnbRuH7S52L11Aql58XZ0lyzJ1w3U82/YsO9p3MOYbI0oXdS6vtiyubE78XBEu7o9dg/x3ay+/LMrg9qSYt36HN5JlcPRPzbw928h1j0xeb4yd2rQ9+9acCHN0clCWZayvN3Dg2Wo6VOP49MMAZJpiufaOG9GZ27C2/xr7+DHUyhjcXYU0vmADWUXhijVUbttOQlYO/k4HroN9uGuHICSjzY7EvCIZQ3EsCvXc/NzNJ99s7eF3XUP8YkEGdyS/g+9HQRAEQZjj+l46yPMPdRNUG9n8oRwyVy8AoH7PTl6577eo1Go2ffJe8qqWTXnfkNOPc38vzgN9yJ4g2nQL5jWpGEriUKjm1/mOaNAKwiUIOfwM//kUgT4n0TfnY6pKOvdv4zt2cOwnj9KQfRtas55NnywntWBujOT7fAPs27+GjPSPkpf3pXCXI8whEzvUN7IuxsKfy3LCXc6MFJAC7O/ZzzNtz7Czcyd+yU9WRBZbc7ayJXsLGRFix9O55LTby4YjTayJtvBAWfblacR7xy+aectoO9i7QJbOr1Xrz+fcXph5G3MmOkGtm/76wsDePcr+P79CnW0Yl3EYlBKxsoGrNq0neUEIq/XX2GyH0KjjCA6Vc+rZYfxuH+klC6natp3s8kokd3Bi8uNQP6FRL0qLBtOSJExLk1FHzY3P03wUlGTuOHGamnEXT1fks3Ae5qYLgiAIwptpf+w1Xt7hAKWabZ8qIWVxFn6vh9fu/z2nXn+V1AUlbP3MF7HExk16v6DNh3N3N64j/chBCX1xLJa1afM63180aAXhbQqOeBi6vw5p3E/M+4owLJiYopCDQQZ+8jOOvD5GZ8Y1JGYYue5TizHNoZOx9vZf09b+M1YsfxWjMSvc5QhzzK87BvhOWx9/Ks3iuviocJczozn8Dl7ueJlnTj9D9cDE78HS2FKuy76OzdmbSTAmhLlC4d0IyTI3HW2l2e3l9aULSNKFIdIiFABb5+Sm7YVvA64LFivORCdkXXzzMsPsu0gZ9AU5/tDrHDzZxKjRhqTyYwhqWFZUTOmmBDo6fzPRqNXEo3Ku5NSzQziGx4hJSaNy200Ur7kalVqDt3kM18E+vE2jAOiLYjEvT0aXF3UuEkmYPYb8ATZVN6NUwEtVhcRoZndslSAIgiBMh4b7nuX1Qyq0+Ljhi8uIK0hm0NrGsz//H8b6e1lxy3tYfvN7UKrO5/QHhtw4dnXjPjYIgLE8Hsv6dDQJ4gKoaNAKwtsQ6HcxdN9JkGRiP1yCLmMiry84MkL7575CtWchozHFlK5JZvV7ClGp5s4tjbIcYv/+9RiMWVQs/mu4yxHmoIAks6m6ibFgiN1LF2BRi4123o5+Vz8vtL/A8+3P0zDagAIFS5KWcF32dWzM3EikLjLcJQqX6Pedg3zjdC+/KsrgtncSbXC5yTK4hi6SeXvmsWtw8np91MUzb2OywZIy46MTOvc38trTr9OlshHSeFAHVRRFJbLithz6Ru7HZjuEVpuAPriBxhdtDLZZMUREUn7tVsqv3YIxMorgqBfX4T5cRwaQXAHUsXpMy5MxVSaiNIpM6dnk6LiLm462sjLKzIOLcub15paCIAiCcPQnj3OwKQIzdm76xgYsyVEcf/FZXv/b/RjMFrZ8+guklyw8t97f7cCxqwvPqREUaiWmJUmY16SijtaH8ShmFtGgFYS34O92MHx/HaiUxN9dem7zD8+JEzR+8bscS7kVnyGWde8vonhVSpirnX7Dwzs5UXs3paW/IjFhS7jLEeaoo3YXW4+28NG0OL6TLzZiuVTt9nZ2tO9gR/sOrONW1Eo1q1NWsyVnC+vS1mHUiCvSM12r28s1R5pYG23hL5cr2uBy8znPb1L2xvgEWydIwfNrVVqIypyaeRudBdGZoDGE5xguwjlg45X7n6XB3o9P70QhKUmXI1hzYzLjyqew2Q6j1SYSqb2e07s8tNUcRaXRULz2aiq33kRsajpyUMJTN4zzYB9+6ziolRjL4zGvTEGbYg73IQpv04O9I3y+qYv/yEzkKznJ4S5HEARBEK44WZbZ999/48RQKrGKIW78/jZQS7z0+1/QeuQgORVL2PTJezFGTAyL+DrGGX+lA1+LDYVehXlFCuZVKajMYv+RNxINWkH4F3xWO8N/OoXSoCb+38pQx06cMNqefIqTP3+UU4XvR2s2sOXfF5OUMzen1WpPfgqb7YjYHEy47L7S3M2fe4Z5vrKAxRGiofhOyLJM/Wg9O9p2sMO6g0H3IAa1gfXp69mavZWVKSvRqMTU3kwTkmVuPNpCq9vH60sXkBiOaIPLLRSE8e6pmbdj7TBqBb9j8npLytTM27NvDdEQhgZ2KBjiwIMvcbihgXHdOKAgxmtgxXIDyox92OxH0GkTiYu6g64DMvWv7yYY8JNTsYTKrdtJL5nY3M/f58J1oBf3sUHkgIQ2KwLzyhQMJbEo5tAdOHPV5xs7ebBvVMTyCIIgCPOO5PPzyhf/Sos/m1TtIFv/52Z6W+t54Tc/xT0+ztr3fZiKLTeiUCjwdY4z/konvuYxlCYN5jWpmJcno9SLmKA3Ixq0gvAmvK1jjPylHlWkjri7y1BH6ZBDIQZ+9BOO7hygPXsr8WlGttyzGHP03MmbvVAgYGPP3hWkpb2Pgvz/Cnc5whw3Hgyx5lAD8VoNL1QWoBY5je+KJEvUDNSwo30HL3W8hN1nJ1IXycbMjWzJ3kJlYiVKhWgGzQS/6xzkm6d7+XVRBrfOxGiDy02WwT3yhqbtBfEJjr7J63URkyMTLnwcmQbKyx+T0rL/JK88v5NBpQ1ZKWH0GCjP9hFdcZJx51F02kSSkz5E/zE9J156Cc+4nYSsXKq23UTBijWo1GokdwBX9QDOg32ERr2oIrQT8QdLk8RUyQzmDUncdKyVVreXF6oKyDOKWzMFQRCEuS8w7uD5LzxCtzKb3Ngxrv7vbRx49EGqn32S6ORUtn76CyTm5OHvcmB/ueNMY1aNZW0aphUpKLUixu6tiAatIFyEp3GUkb/Vo441EH93GSqLlpDDQcfnv8SRkTyG48spXJrA+g8UodbM3R803T1/p6npayxZ8k8iLKXhLkeYB54dtHH3KStfz03hkxliw6vpEggFONB3gOfanmNn1048QQ8JhgQ2ZW9ic9ZmyuLKZuct9XPA2WiDdTEW/lw6S6MNLje/G2wdUzNvx9phrAOkwPm1Sg1EZVx807LoLNCaprW00b5hdvz5SU67B5BUQTR+HYXRNtKWN+EKnESnTSQt7W7sp+M5+uxzjPZ2Y46No2Lz9ZRt2ITeZEaWZLyNozgP9OJrsYFKgXHhmfiDdMu01itMjx6vn43VTcRpNDxfmY9ZZKcLgiAIc5inZ4BnvvY8Q9pMFua4Kb5zIc//6icMWk+zaON1rPvAR5EHA4y/0oG3aQylUY15bRrmFSkodeJ35Nt1WRu0CoViM/ALQAXcJ8vyD97w7+uBfwLtZ/7qCVmWv/VWzysatMLl5D45xOhDTWiSTcTdVYrKpMFvtdL86S9THbUNtymZVbcVsPDqtDl/Il1dcxvBoINlS3fM+WMVZgZZlvngyXb2jjnZvWwB6XoxRTbd3AE3u7t381z7c+zt2UtQCpJiSuHarGvZlLWJktgS8f1+hcyLaIPLTQrBeO/UzNuzj732yevNiW9o2l4Qn2CKe8fRCX6fn1cffIbjbU341H6UIQ1Z+jGyq+rwa1rQaRPJzPg4vqE8jj73HF2natHoDZRdfS0V191AZEIiAIFBN84DvbhrBpH9IbTplon4g7I4FGox8T6T7B1zcPvx02yJj+R/S7LEz01BEARhTrKdOs0zPzrAuC6J5UuUqDN97HrgPtQ6HZs+/hkyUkoZf7kDb+PoRGN2TRrmlckodVOjDEKhEKOjowwPDzM+Po7dbmd8fByXy4XX68Xn8+H1egmFQhQVFXHTTTdd+QMOo8vWoFUoFCqgGdgIdANHgPfKslx/wZr1wBdkWd52Kc8tGrTC5TLRnG1Emx5B3EdKUOrVuPbv59R//pQTOR9ANlrY/MlFZBTHhrvUy87t7uDAwavJzfkiWVmfCHc5wjzS7fWz9nAjK6PM/HW2bpY0S4z7x9nVtYsXrS+yv3c/QSlIqjn1XLO2OKZYfP4vo7PRBr8pyuCW+RhtcCW4R6dO3Y5aJ/5uvAe44PWu1nx+0vaN8QmR6fA28pslSeLozgPsfn0f40o3SAqSdQ7ySo+CpQOdLonMzE+g9lVxbMfzNO3fjSzJ5C9bSdW27STnF048jzeIu2YA54E+gsMelGYNpmXJmJcloYqYm7FKs9FvOgf59ulevpabwj3irg9BEARhjunddZQdD7TjV5lYtUFPW9ceTlcfInPhYja+51MED9nw1A6jMKixrE3FvDLlXGM2EAjQ29tLT08P3d3dDA4OMjo6iiRJ555fpVIRGRmJyWRCr9ej1+vR6XSo1WqSk5NZtGhRuA49LC5ng3YF8A1Zljed+fNXAGRZ/v4Fa9YjGrTCDOGpG2bk741o0y3E3VWCQqti7G8PUnvfizQs+ACmaD3bPlNJTMr03h45U7W1/5L29l+yauVu9PqUcJcjzDN/6Brk6629/LEkixsSosJdzrxg99nZ2bWTF60vcrD3IEE5SJo5jU1Zm9iUtYkFMQtEs3YanY02WB9j4U8i2iA8Al6wdU7NvD37OOQ7v1ahgqj0qZm3ZydxdVOjCDpb23nx0efo8Y4AEvFGJ7m51Whius81aiN0V3PipZeofeUFfG4XKYXFVG27idyqZSiVKmRJxtdqw7m/F2/TKCgUGEpjJ+IPMiPE102YybLMv52y8vyQnUfKc1kdLSIpBEEQhLmh+eHX2PmKByUhFl8jU73zMbxOB+tuuYtMeQHumgEUKiXmNalY1qYRUISwWq20tbXR2dnJwMDAuWZsVFQUSUlJxMfHExcXR1xcHFFRURiNRvFa5gKXs0F7K7BZluW7z/z5A8AyWZb//YI164HHmZiw7WWiWXvqrZ5bNGiF6eY5NcLIgw1o08zE3VWKQinR963vcPyIg/bs60nKNrPlU+UYLPPjdmtZljlw8Gr0+lQqFv8t3OUI81BQktlS00y/P8DeZUVEiHy/K8rus/Na52sTzdq+g4TkEBmWDDZlbeLarGspjC4UL6beBRFtMAtIEjj737Bp2QXxCZ7RyeuNcRfJvJ14PC4ZePmR56jvOk1IGSTGbCcn4yiGuJ6J6IOsTxIfvY3613dT8/zTjA8NEJWUTOWWmyhZvwGNbmITquCIB+eBPlzV/cjeEJoUE+aVKRgXxaOYw3n4M50zGGJLTQvDgQAvVRWSJqJ5BEEQhFmu+kePc7glAmNohKSFfZza/yqJaXlcveRDSHVukGWMSxJxl+po67Vy+vRpurq6kCQJtVpNeno6aWlppKWlkZqaitlsDvchzQqXs0F7G7DpDQ3apbIsf/qCNRGAJMuyU6FQbAF+Icty/ps838eAjwFkZGRUdnR0vKv6BOEsT8MII39rQJNiJv6jpcg+Fx2f+SxHxwsYSFxKwdJErv5AESrN/Ml+s9lrqKm5naKi/yEl+dZwlyPMUyccbq6rbuYDKbH8T2F6uMuZt8a8Y+eatYf7DxOSQ2RGZHJt5kQMQkF0gWjWXqLfdg7yLRFtMLt57RfPvB21wng3yOdv30NjhOgsApHZHLTlcKBfh1sVJNoyQnZGLabYHrTqBLJyPkVS4i20VR+l+tkn6G9tRm+2sGjjFhZv3oYpKhoAyR/CfWwQ5/5eggNulEb1RPzB8mRUkSL+IBxa3V42VzeTZ9Tz1OI89Kr585pREARBmDukYJCdX/k7jY40okJNBCwnsfX2sa7yfSS4UpB8QcYLVXTF2Glsa8ZmswGQlJREbm4uubm5ZGRkoFZPzZ8V3lpYIw4u8j5WoEqW5eF/9dxiglaYLp7GUUb+Wo8m2UT8R8sIjvTT+ol7ORqxGXtEDstuzKFyc+a8az40Nn2Nvr4nWLP6EGq1uNolhM/XWrq5r3uYZyryqYqcH/EiM9mod5RXO1/lReuLHOk/giRLZEVksTFzIxsyN4jM2rehxeXlmuomrhLRBnNX0A/2rjdM31rPPZaDHppCubwWuIpBvZnIyEGy0+uwxPSiDhrJjd5EctLt9I1BzUsv0Vp9CJVKRdGaq6nadhOxaRnAxN0uvjY7zn29eBtGJuIPyuKwrE5Fmy5utb/SdgzZ+Eidlfclx/CTBRnhLkcQBEEQLonf5uD5Lz9Ot5xOFHsZcZ0kP7qCstg1jPoctMfbOB3qxeFyolQqycnJobi4mIKCAjEhO00uZ4NWzcQmYRuAHiY2CbvzwggDhUKRBAzIsiwrFIqlwGNApvwWH1w0aIXp4G0eY/iBU2gSTcR/tBRfSz2N9/43x7I+gN8YwzV3lZJXOf82fJAkH3v2riA2di2lJT8PdznCPOcMhlh7uJEItYqXqwrRKEUza6YY8YzwauervGR9ieqBakJyiBRTChsyN7AxcyOL4hehVIgpsguFZJkbjrbQdibaIEFEG8w/sgzOgXNN28GuNl457qQloCUipp+s9HoiontRutTkddtIdRixa7OpGYzllNVHMCSRXZhD1dYbSa9aj0I1EW0QHPXi3N+L60g/si+ENsOCeVUqhtJYFGKa84r5flsfv+gY4MeF6bw/Ze5vKCsIgiDMPiFZ5vi4m52jDhpcHqweH/1uHwGnH6UEke5hskbsbPDGkjQ6RId+gJGgHaVSSX5+/rmmrMFgCPehzDmXrUF75sm3AD8HVMD9six/V6FQfAJAluXfKxSKfwc+CQQBD/A5WZb3v9Xzigat8G752uwM3V+HJt5A/L+V4dy7k/pv/Zbaon9DZTGx7dMVJGZHhLvMsBgaeoXakx9n0aL/Iy52fbjLEQReGLLz4bp2/jMnmU9nJoa7HOEixrxj7OraxSudr3Cg9wABKUCcIY4NGRvYkLGBqqQqNErRjDwbbfDb4kxuTowOdznCDOJyudj36m6qj1ZjjOomM6OOiKh+cBvJsseQPTKGd6ifE6MJHB9LwR3SEq93sSQzSEFBMqrYifxbyZKNuzsR5wk/wVEfqkgtphUpmJYkoTKJ78HLLSTLvO9EG/ttTp5anEeFuPNDEARBmCFa3V4e6BnhsYFRRgMhFECeUUeS14e30UYADwq1E2dUMtZIAwGVCl3Ax3LnAKsVPl5pC9Bhh1hLBJ/eUM5NFWnhPqQ557I2aC8X0aAV3g1/j5OhP9aiitAS97GF2B/7O3X3v0R98YexxBm5/t4KIuON4S4zbE6d+jzDI7tYs/ogStFQEWaIu062s3N0nJ1LF5BlEBmLM5nT72R3925e6XyFvT178QQ9ROoiuSr9Kq7JuIYVKSvQqubfJjpnow2ujong/tIsEW0gXFQwGKT2+Alef+lVFMbTZGTWEhk5iOSxkGK4naKFNyMNd9Kwfw/Vh+oZtfkw6yQqYvpYaOlApwoBIMtKvPprcQa24XNnoVCGMOb4MC+LQZObC0aRfXy5jAaCbK5uxidJvFhVSJKYlBcEQRDCqM7h5gft/bwyMo5GoWBzXCRb4yNZG2Nh6LHd7HxlEK1lJ1GZIQKxQygMY2j0ftqMuexSrKGapRhwczt/ZwMvoUQmIKlRqWKIiczGZMrHYl5AVNQSjMZc8Rr3XRANWmFeCQy5Gfp9LQqNkri7Sxj57U84sbuf1rxbSMyKYOu/L8Jgnn+Ng7MkycfuPUtJSLiO4qIfhLscQTinz+dnzaFGKiNMPLwoR/zinyU8QQ/7e/bzSucrvN71Oo6AA5PGxNrUtVyTeQ2rU1dj1Mz9C2Ii2kC4VLIsY7Va2fX8S9j9R8nIOkFk5BBBt4Uo53Usvv6raAwm2k/UUP3Mk3SdqkWr11O2dBEVC1OJCA2dy7wNDPlxOlbhCq0HdOiURzEbXkEf70ARkwkxE9O3E2+zICIVlKowfwZmtwanh61HW1hg0vNEudg0TBAEQZh+Tx3r4UcvNtFr85ASZeCLmwq5aXHquX/v8/n5VmsvTw7aiFKr+Fh6PB9IiSVOo2J8vI7jT/wem74eY1wvyjMXeKWQGo0mjaiobPSGVPS6RL6118HByHJGzYnEOvpY0rebWPUoyRYX63K8uFwthEJOADSaGOJi1xOfsJmY6NWoVGKw5lKIBq0wbwRtXoZ+V4sckoj7YD593/1PjvfE0Z12NTnlcWy8qwS1dn6fkAwNv0pt7cdEvIEwI/2pZ5ivNHfz66IMbhU73886gVCAQ/2HeKXjFV7rfI0x3xg6lY5VKau4JvMa1qatJVIXGe4yL4vfdA7y7dO9/K44k+0i2kC4RCMjI+zb9TrWrpdIyzxOZOQQAXcEuu51LN54L1G5WQy0tVL97JM0HdgDQMHy1VRt205Sbv7Ek/hdhHrbcR3uw1mvQvJqUGtHMRtexeh/AqXsOP8BVVqIypjctL3wsUZkzr0dzw7auPuUlTuSYvj5gnRxYVEQBEGYNk8d6+ErT5zEEwid+zuDRsX3by7j+vIU/tQzzA/a+gjJMh9PT+DjaTHIzmoGBp5lcOhlgsExAJzOaBy2JEz+fBYuu4mc0tUoFJN7Itlffg4JCKUZCRZFofCG0NQMo3KHaP/BVmRZxuOxYrNVMzZ2gOGR1wgGHajVkaQk30pq6nsxGrOv5Kdn1hINWmFeCDn9DP2+lpDTT/StafT89+c5pljBUHw5i65OZ+WteSjF5kOcqv8Cw8Ovsmb1IZTK+TtJLMxM0tkpRI+PPUuLiNWqw12S8A4FpSDHBo/xSscrvNL5CoPuQVQKFZWJlVyVfhVXZVxFqjn1rZ9oFmh2edkoog2EaeDxeKg+Uk3diYdJSqshInIIvyeCUONKSkvvJPPalThGhji64xlOvvoCfo+HtOJSqrZtJ2fxEhTKiSlOOSjhqRvGsbeHQLcThV6FaaERc64ddbD9zAZm7ec2MsM3PrkQS/IbmrZnGrcx2WCMBfE1fs4P2/v4qXWA7+SncndafLjLEQRBEOaIVT94jR6bZ8rfJySYSF6fyiG7i/XRFr6W5kU18giDg88TCIwCekb6UhiyJ+MdzSQ3mM3aWzcRU/rmr7sv/FhSpAZ/RSzIkN7k4Mh/rJ+yXpL8jI0doLfvMYaGXkKWgyQkbCE769OYzQXT9SmYk0SDVpjzJG+QoT/UEhz2ELkljs7//jxHE27Gbsli1a15lF+TEe4SZwRJ8rFn7zLi466luPiH4S5HEC6qwelhY3UTNydG88uizHCXI0wDSZY4NXyKnV072dm1k1ZbKwAF0QXnmrXFMcWzsrEZkmWuP9pCu4g2EKZRKBSisbGRmoN/wRKzm4jIIXweC85Tq8kzbaDsQ5uQlHDytRc5+vzTOEaGiE5Jo2rrTRStvQqNduJ2Q1mW8Xc6cO7rwVM3DDIYSmIxr05Fmxkx8T0ny+AZm9q0PfvY0Tu5OK0FYrImN23PNnIj0kA1vy6sSbLMXXXtvDwyzsMLc1kTYwl3SYIgCMIckP3l53hjxy6UZCBQHIVeo2ThYA3Xa/9GTmQnMlo06gqaT1noG4rDEoxgQSCJohVFZG6rQvEWg2pvnNaVTGoCS+KI0Gt4aVkhmf9ifxCfb5Du7gfo6n6AUMhNUuKN5OV9CZ0u4d1+CuYk0aAV5jQ5IDH0fyfxdzmwrDXR8d2vcDT7Q3hMiWz8aCl5leIHw1nDwzs5UXs3ixbeR1zcVeEuRxDe1Pfb+vhFxwCPLhInu3NR13gXr3W9xs6unRwbPIYkSyQaE1mfvp6r069mSdISNKrZ0ej8dccA32nrE9EGwmXT29vLkUN/RuLpM41aMyMN60gZq6DyA1dhyUul+dA+qp95gsH20xgiIim/divlm7ZijDgfKRK0+XAd6MV5uB/ZE0STasa8KgXjwngU6n+RnxrwgK3zDQ3cs01cK4T859cq1RCZPjXz9mwzV2e+TJ+l8HIGQ2w92sKgL8ALVQX/8kRWEARBEN6OC6daZQUECyIIZVmI9w1wr+J/yNJ00ONIpqG3DOVwPJqQkvhQBGXBNLQqL+VfvBl95Nv/vfvGvNs7r8nlV55x4rVqnqssIEL9r6MiA4ExOjr+l86uP6FUasnJuZf0tA9OiVOY70SDVpizZElm9KFGPCeHMVYosP782xwr+gQhUxRb7iknrVCcLF+ovv6LDA2/zJrVh0W8gTCjeUISVx9pRAZ2LlmAQWy+MmeNecfY3b2bnV072d+7H0/Qg1ljZnXqaq5Kv4rVaauJ0EaEu8yLanB62FTdzMa4CO4rEdEGwuXldDqprn4Au/2vmC2D+LwmBprXYWlZRMW1RWRuW05v4ymqn32StqNHUGu0FK+7msqtNxGTknbueSR/CPexQZz7eggOelCaNZiXJ2NanozqUjdRlaSJCdsLm7YXNnK9tsnrTQkXybw982dzwqyOTrB6fGyubiZJp+G5inxMb3EiKwiCIAj/ytmpVjcyisVmvNEWrpF28D7+TN1gMY1d5cS6VBgVQeJDFqpCeQTGB4nekE3J9mumpYZ9Yw7uOHGaq2IieKAs+2291nW722lu+TYjI68TFbmE4uIfYzCkveX7zReiQSvMWbZn23Du7UGX5aHtzz/nRNk9qCLM3PAfFcRniKm7C0mSnz17lxEXt4GS4h+HuxxBeEt7xxzcevw0n8lI4Ku5KeEuR7gCvEEvh/oOsbNrJ7u6djHiHUGtUFOVVDURhZB+Fcnm5HCXCYBfkthS00K/L8CupQuIE3nJwhUSDAaprX2Yvt7fozf24fWa6D+9CvnUEsoLY1j4kWtwOMeoef4p6ne/RigQILdqGVVbt5NaVHLu5EqWZXwtNpz7evA2jYFagbE8AfOqVLTJpukp1jM2tWl7dvLW3g0X3rypMV0QmZA1OT4hKgNmwVT966MO3nviNJvjIrmvNAvlLG44C4IgCOH320MH+YXDi0tp4kPyfazSGvjb66mkBvyYFAGiQhGsDOWidXs4MXaKW358L+b42Gmt4b7uIf6rpYcfFKTx4dS4t/U+sizT3/8UTc3fAKBowXdJTNw2rXXNVqJBK8xJjr092J9tQx1t5/ST93Fy0ScxxJi48d4KohKN4S5vxhke2cWJEx9l0cL/JS7u6nCXIwhvy380dPL4wCgvVRVSbBa7is8nkixRO1R7Lre23d4OTOTWrktbx9q0tZTFlaFShmdK7X/a+vhZxwB/Ls1mc3zkW7+DIEwzWZZpbf0nbW0/R63pwus10du2FG/TKgoNaio/sBJDRizHXnyO4y89h9cxTmJOPlXXb6dg2SqUqvPfO4FBN879vbhrBpADErrcSMyrU9EXxrxlbt07FvRdEJ1gnRqfEPSeX6tQQmTa5KnbCydx9TNnyv4PXYN8vbWXL2Ql8YXspHCXIwiCIMxCHk83TzT9g/8aXYFe4eP78U2kuPPYs+cEDocDfSiCq0O5RPhV1I0dos6r4eWSVez76oZpr0WSZd5X28ZBm5OXqgrJN+kv4Th6OFX/Wez2GjIzPkZu7hcY8oywu3s3r3e9zoLYBdxTfs+01zyTiQatMOe4Tw4x+vdGFJpRWnc+Qn3Jh4lMsnDDfyzGHC1yvy6mvuFLDA6+wNo1h1EqxedImB1GA0FWH2ogy6DjmYp8VGIaad6y2q3s6trF7p7dHB04SkgOEaWLYnXqatalrWNl6sorFoVwdNzF9UdbuEVsZCfMALIs09v7Mo1NPwLa8HpNdFsX4zi9jgyXksUbssnYuoTGfbuoee4pxvp6iYhPoOK6Gym7eiNaw/mL2pI7gPNwP64DvYTsftRxhomc2opElLoreDFEksA5MLVpe/axe2TyemPs1Kbt2UauORGUVy4mR5ZlPtPYyaP9Y9xfmsWW+Kgr9rEFQRCE2c3nH6a9/Zc80dvJb7mHNLWX75iV1O+pYXR0lGRzPOWjaSQGLTTYD3LaZeOgIY+apAy+f3MZNy1OvSx1DfgCXHWkkTSdlmcr89Fewu/VYMjL4ZOfxzP6Ap3BCH7dH8AvK0gxpXBb4W3cXXb3Zal5phINWmFO8VntDN13EoKjNB1+jsaC20nKiWTrPYvQm2b+7W/hIEnBiXiD2PWUlPwk3OUIwiV5vH+Uexo6+W5+Kh9Niw93OcIMMO4fZ3/PfnZ372ZPzx5sPhsqhYrFCYvPTddmR769nKxL5Q5JXFvdhCcksXPpgrfcMEEQrhRZlhka3kVjww8JBJvxek10dSzE3r6SaJuFRbkmyj5yFb0dTVQ/+yQ9jafQGU0svGYzizdfjyX2/G2LckjCUzeMY28vgS4HCr0K09IkzCtTUEe9/cmZy8Y7PnXq9uwkrr0LZOn8WrUBojOnZt7GnIlOUE//RWtvSGL7sVaa3F6eXpxHqUXc2SUIgiC8uVDIR1f3n7Faf8tz0lX8jQ9RqpXZWn8UW083seZoqtxZpLmjsTrqOGk7ikJRyN9iMyA5ni9uKrxszdmznhuy8dE6K9/MS+Hj6f96I3Z3wM2BvgPs7t7N7u7dDHuGWWUOcUuUj4AmhdyiX1AQt3he7t8gGrTCnBEYcjP42+NIzjEa6l6nJXMzGaUxbP5YGRqtOEl+M2Njhzl67L2Ulv6axITrwl2OIFwSWZZ574k2joy72L10Aal6scGdcF5ICnFy+OS5F4BNY00ApJnTWJu2lnVp66hKqkKrmp6vm/9q6ea+7mEeK89ldbTIOhdmHlmWGR3dTWPTj/B6GyYatZ2ljHZWYRxPpFAnUfmeJYSiFVQ/+xQtB/ehUCooXLmWqm3bScjKmfR8vs5xnHt78NQNA2AoicO8OhVthmVmnliFAhPRCZOmbq3nG7kB9wWLFWeiE7ImZ96encQ1vPPNZgd8Aa6raUYBPF9ZQKJODBEIgiAIk8myzNDQi7S0/gCPt4sXjF/mb54llLhtrKjZTYzBRJWcR9ZoNPbQIEf6X2CcePLiC9n83feiNly5O2NlWebO2jZqxl3sX1Y8af8FWZZpt7ezp2cPe3r2UDNQQ1AKYtFYWJW6irVpa1mdupqg4wh1p/4DvT6DxYv/gl43/6KARIN2hvvmM6eo7x0Pdxkznikkc29PEIvXTePpGtqSVjAQraI5U4M8E08QZpBlcX+nNPIlHmj7HQFZ5HgKs49Ho6A6U0e0W6Kk14/4jhfeTIBRHKqTOJUncSkbkBUBFLIOs1SEWSrDHCpDQ9Q7eu4xg5LadB2pY0HyhgLTW7ggTDuZdGMtlTGPkWBox+c10tVdwlB3CTpXOpEjQQajNTSnxZLYW0N833FUoQD26Cz6M5Zjj8mBC15fRQVlVo9LLHPIGCXo0MGeCCUnTAqk2fI6TJaJlGwkhvpIDPZOvA31kRjsJzHUR5Q0Nmm5U2FmQJ3MgCqFflUyg+okBlTJDKhTGFXGIiv+9S2eDp2C4+k6TD6ZRd0+VDP31EsQBEG4wmJ1VlbE/Y0UYyMjvjT+4PsCpyLTKezrYE1LHblkc7UnFZfs5+Tgi/R4utAaNuAxaakuKwxLzS7txDlZsj1E3qATl7IJp/IkTmUdAeVE/JBOSsEslWKWSjFKeSiYvJFusqGeTck/xR2Kojn4fb6ybW04DiVsRIN2hhMN2remkmU+1RMgwxeiwXqC1phF9MSrOJ2qmXTyIFzc7ZlfwBGIZ0fvl8JdiiC8Y13RatriNRT3+oh3Sm/9DsK8J+E/88KxFqfqJAHFKAB6KR2TVII5VIJRzp3ywvFigkqoztShlKGyQzRahNlEJs1YS0XMUyQZWvD5DfR0F9HXU4jGnUKEzUxQ9lKXl4LR1kxS12G0fiduUzz96csYSSpBVp7/HtFKMlVOmbV2ifgg2FSwL0LJAYsCj2p2vybTSR4SQ30khPpJCvZNauTGhQZREzq31o+GIVUSAxc0bQdUyQyokhhUJxFQTEw1DZuUnErREu8MUdQXEBcYBUEQ5jmt0sWS2EcojnwNb8hM9fDNvKpcTktiAkW9Vm46bWeLOwMlSk6NH+b06F4UmmJMyhKaM/V0pl7eKIN/xacYoCVeYiQyi+i+b6AOtp8ZhFgw0ZQNlaIh9i2fJ1HfzHWpP8QpFXPbtY9egcpnDtGgFWY1WZYZffAknjo7LX1N1BtyqNicyfIbc2bmrXUzjMvVxsFDGyko+DrpaR8MdzmC8I4FJZnNNc0M+QPsWVYksj+FSyLLMi22FnZ372Zfzz6ODx4nKAcxaUwsS1rGqtRVrEpdRar54i96723o5JH+UZ6pyKcy0nSFqxeEd0+WZWy2w1itv2F0bB+ybKSro4DunkIU3hiMzgTyFTLlNy/CwSjVzzzBUKcVU1Q0izdfz8KN12Ewn4/1kCUZb/MYzr09+FptKDRKjBUJmFelokmYg5mroSCMd0/NvB1rh1Er+B2T11tSzkUm/CZqHd+WC/hcjMT/y8+aiE4Qr2EFQRDmFVmWGRh4muaW7xIIjJGa+gHs9nX8d/s4JxLSWTc2wrdOKjB5NIyaBtnT8AhBWYXSuJk0LWz+1g0YrvDGk96glyP9R9jbs5c9PXvocnQhKYzYU39KusbDz/LNVCRUvKMoMbv9KDpdEnp9ymWofOYSDVphVrM9V49zzwjdo73UKONZdkMOVVuywl3WrNHR+b+0tv6AlSt2YzCE72qbIEyHY+NuttY08/6UWH5YmB7ucoRZzOl3cqj/EPt69rG3Zy99rj4AsiOzWZWyitWpq6lMrESv1vPSsJ0Pnmzn3sxEvpyTHObKBeHds9uPYbX+luGR1wADg33FnG7PIeQ3ofckk+RQsbgqBcviWI6++DTWE0dR63SUrr+Gyi03EZU0+fsg0O/CsbcH9/FBCMroC6Mxr0pFlx81Py6myzK4RyZn3Z59O2ZFdvTx2YIv8XDyFn7b8G1uth+Z2LjsjZm30dkTmbhKcQFSEARhLnG722ls+m/GxvYTEbEIk/FjvLarjUejUmlKzuSOPg9fqA0SipXZ2/oog/YOtOqFKAwrqcrzsOSL21Eq/3WsznSQZZkuRxd7e/ayt2cvh/sP4wv50Kv0LEtexurU1axOXc0Toxq+19bHS1UFLBQbYV4S0aAVZi3H7kZszw0y4razL2Bi1a15lF+TEe6yZpWao+8lGBxn2dLnwl2KIEyLr7f28IeuIbFJkzBtZFmmfbydfT372NezjyP9R/BLfnQqHWVJq9mjeT/JOi2vLClBpxKNE2HucDhOYbX+jsGhF1AodDjti6mrT8HvM6L1R2MZj2JhvJ6szXk0HNtDw55dSFKI/CUrqNy2ndTCoknPF3L6cR3qx3mgF8kZQJ1gxLw6BdPiBBSaefy943fjH7Vy+2kHx/waHve9TNXwkTMN3A6QLsi0VmogKuMim5ZlTzR1tWKCXxAEYbYIhXx0dPwea8fvUal0JMR/gpoaIy2tbRwoWUZtXDJ3t/r4xIhMs7+aY6dewGyKJ6C4FgM6rr0jg/Rrp/TyptW4f5zDfYfZ37uf/b376XH2AJAZkcma1DWsTl1NVVIVOtX5DcnGgyGqDpxiTbSF/yvNvqz1zTWiQSvMSs5D9Yw92oNLgl1uFavvLKR0rZgAvRSBwBh79i4jM/MT5OZ8LtzlCMK0cIckrj7SiCzDa0sLMYmGmTDNPEEPNQM17O3ex19saYxpCoju/28ydTKrUiaiEJYmLcWsNYe7VEGYFk5XCx3W39M/8DQKhRpZWsmJ6kTGPVqUQT0GVyK5ASi+Kp0hfw+1L+/A63KSXLCAqm3byVuyHOUFU59yUMJ9Ygjn3h4CfS6URjWmZcmYVySjirhyO07PNKOBIFtqmnEGJXZUFZCu14IUgvHeyVO3F8YneO2Tn8Sc+Iambdb5x6Y4EZ0gCIIwQ4yP11Lf8P9wuVqIi91Cd/dKqqub0Wi11C9YzStRFj5qDfD+wCiv7r2fkBwkQl2KS7uGZPrY/PXNmFLip72uoBSkbrjuXEP25PBJJFk6F/u1MmUlK1JWkBHxrwfj/qetj591DLBraSELTGIj8rdLNGiFWcd15AQjf7MS0Ebwuktm5QeKWLBC3FZ6qfr6n6K+/vNUVT1BZMSicJcjCNNm/5iTm4+38vG0eL6ZLy7cCJfHI/2jfKahk39PNZIvHWNv714O9R3CE/SgUqgoiytjecpyViSvoCy+DI1SE+6SBeFdcbutdHT8gb7+JwEZnW49TbXpdPYHQVag8yQQP65lUYEFspWc2PkC9oF+IhOTqNxyI6XrN6LR6889nyzL+NvtOPb24m0YAYUC48I4zKtT0abNzzsgWlxeth5tJkWn5ZmKfCxvlafuHr145u1Y+0RjlwvO57TmM1EJWVPjEyIzQPXWGyIKgiAI744k+bFaf4u147doNXGoVB9h9+5RvF4vC1OL2KXL5B9pOj7okKk8+A+6T9eRmJqH21ZJUJ1IeYad5V+5GeU0DqF0O7rPNWQP9x3GEXCgVCgpjS1lRcoKVqasvOTXsqOBIFUH6rkuLpLfFGdOW61znWjQCrOK60gNQ/fVoYzKZq87xJIPFZNflRjusmalk3WfxmY7wupV+1EoLn9mjSBcSV9u7uYvPcM8U5FPldi0SZhmVo+PDUeaKDMbeHxxHqozU2mBUIBjg8c42HeQA70HODVyChkZo9rIkqQlrEhZwfLk5eREio0shdnL6+2lo/OP9Pb+A0kKEhl5DX2dpRw/MUIICbXfgtkRTZEW4qtMNNYfoa+5Eb3JzKJrt1C+aRvm6JhJzxkc8eDc34vryACyP4Q2KwLL6lT0xbEolPPre2X3qIM7a0+zKsrC3xbmoHmnxx/wgq1zSubtuWZuyHd+rUIFUelTM2/PPtbNz4a5IAjCdHI6mzhV/wWcznoslms5fqyQ3l4bGfGpLHPm8tc4E3/O0bHVPkLJI79EbzSRaCmnz7UYU9DGhvdkknHt0ndfh9/J4f6J2IIDvQfodHQCkGxKZmXKSlamrGRZ8jIidZHv6uN880z03OEVxaTpL32jsPlINGiFWcNdXU3vz15Fn76So54QZR8tJXthXLjLmpUkyc/uPUtITNhCUdH3w12OIEw7ZzDEusONGFVKXq4qRK8SFyGE6RGUZG481kKL28trSxb8yxecdp+dw/2HOdB7gIN9B+lydAGQYExgefJylicvZ0XKCuIM4neZMPv4fIN0dt5HT+9DhEJuoqPX4XGv49CeQca9LhSSCr07gXSnTG6xjn5fN601h1GpVCxYvZ6qrTcRl5E16TklbxDXkQGc+3sIjflQReswr0zBtCQJpX7+THg+3DfCvY1d3J4UzS8WZEz/BR1JAkffBVO3b4hP8IxOXm+Mu0jmbdbEY3OiiE4QBEH4FyQpSGfn/9LW/gtUKgvj9huoqQlhMVlYoSsivdfM/WUmfpeioqqtjvUvPUx++XIcp9OwqzNIV3Vy7TduRB8f/Y4+fiAU4OTwSQ71HeJg30FODJ0gJIcwqA0sTVp6bko2KyJrWn/fdHn9LD1Qz72ZiXxJbKT7togGrTAruA4dpus7D2AuuYM2v0TW3aVkFMeGu6xZa3R0H8eOf5CFZX8gPv6acJcjCJfFzpFx3lvbxmcyEvhqbkq4yxHmiB+19/ET6wC/L87kpsRLe6Hc7eg+N117qP8Qdt9EfmR+dP5EszZ5BZWJlRg1YsdbYfYIBGx0d/+Vru4HCARGiYyoQG/YzonDQVqt7cgKGY0/kiibgaLoEIEED401Bwj6fGSVV1K1dTsZZYsmnRTKkoy3fgTH3h781nEUWhWmqkTMq1JQx86PLLuftPfzI2s/n8tK5P9lX+ETW6/9IlO3Z+ITxrtBls6v1RjPT9y+MT4hMh3UYmpKEIT5y+Vqo77hi4yPH0elXMrhw/n4fBoWxy6gpCsOrV7PX1dZ+LkqSGnjUe5srSY3bTmN9bHIKFi2KEj5PddfUuNUkiUaRxs53HeYg/0HOTpwFE/QgwIFRbFFrEpZxYqUFZTHl6NRXd4IrvfXtlHrcFOzouSd3xEyj4gGrTDjuQ4exPrlH2Ne9mlskoKYD5eQXiKas+9Gc/O36el9iLVralCp5seJjjA/3dvQyaMDo+yoLGChRTS9hHfniN3FjUdbuCUpml8Vvbs8rZAUonGs8dx07bGBY/glP2qlmvL4cpYmL2Vp0lIWxi287C+eBWE6hEIeevsepbPzPrzeHkymfBITP0RHWwKH9x3BHfKikDQYnTHk+LxEZgRoOV2L224jPjObqm3bKVy5BpV68te7v9uBc18v7tohkGT0RbFYVqegzY6c01Ehsizz+aYu/t43yk8L07kzZYa89g36wd71hqnbCxq5Qc/5tQolRKRBTNbF4xP07+72WUEQhJlKliW6uv/C6dM/ArR0dq6hvS2W7Jh0loxkEBHQY1yWxM/UnfyvMZaitjq+ZVZiPyjR4UkhMtDPpnsqia8ofBsfS8Y6buVQ3yEO9x/mcP/hc0MAOZE5LE1ayvLk5VQlVb3r2IJL9fKwnQ+cbOePJVnckBB1RT/2bCQatMKM5tq/n7bP/jf6tf+JQqFC954FpFckhLusWe/AwWvR61NYXP7ncJciCJeVLRBk3eFGYjVqXqgqQKsUUQfCO+MIhrj6SBMK4NUlhW+9ec8l8gQ9E/m1vQc50HeAptEmZGT0Kj2LExazNHkpS5KWUBJbglo5f271FmYfSQowOPg81o7f43I1o9elkJ5+F17vEva9coiOgS5QgMYXReKYRGqMi353N6N9PZijYyjffD0LN2zCYImY9LyhcR/Og324DvYhuYNokk2YV6diXBSPQj03f7YHJJkPnmxj95iDv5blcHVsxFu/UzjJMjgH3rBp2QWNXPfw5PWGmItk3p75syUZxO9sQRBmIY+ni/qGL2GzHcLvW8DRYyWYNEksDxaQZo9EXxiNt0jiu4d382TZaspHe/mh2kT1M6N4VBYKI/tY983b0Bj0b/ox+l39HOo7NPFf/yEG3YPARI7ssuRlLE1ayrLkZSQYw9s7Cckyyw7Wk6nX8fjivLDWMhuIBq0wYzn37KXt3i8jrf06MVodii05pK9LC3dZs57X28u+/WvIz/tPMjLuCnc5gnDZvThs50Mn2/l/2Ul8Lisp3OUIs9S/13fwxMAY/6zIZ8kV2HjO7rNT3V99bhKi1dYKgFFtpCKxgqVJExO2C2IWoFJOb7NYEKaDLMuMjOyio+MP2OxH0GiiSUv7IFGRN1F9sJGaI9X4ZD/KkBazw0J6yEbQMEJvRytqrY6iNeupuO4G4tInT6vLgRDuY0M49vUQHHCjNGswL0/GtDwZlXnu3U7vDIbYfqyVNo+PpxbnUTab7wbxOd4QmXBBI9fWBXLo/Fq1HqIyp2beRmdDdCaodWE6CEEQhIuTZZme3odoafk+kiTT2lLJ0GAeFYZCiocT0CdYMFydyMGDT/CP7kF2XH0Ly1UhPrmrg5beSAwBG+u2xJF76/opzz3qHaW6v/pcQ7ZjvAOAaF00S5MnmrHLkpaRbkmfcXeX/LJjgO+19bFn6QLyTW/edBZEg1aYoZy7d9N275exr/ovsk0WpGVJZGzPD3dZc0JPz8M0Nv0ny5a9gNkkPqfC/PCJU1aeG7LzUlUBRWYR6yFcmqcGxvhEfQefz0rki1c6C/KMEc8I1QPVHO6baNhax60AWDQWKpMqzzVs86PzUSrE1Jkws9hs1XR0/pHh4VdRKg2kptxBWtqH6bS6eP2FnfTZBwDQ+qJIsHuJMI7QO3CaUMBPRlk5FdfdQM7iKhQXTFTKsoyv1YZzbw/epjFQKzCWJ2BZnYom6fJfRLmSBnwBttQ0E5BlnqssIH0u7oYdCkxEJ1ysgTvaDgHXBYsVEJFyZuo2a2p8gjEmLIcgCML85fX20dDwZUbH9uJ0pFNfv4R03QKqhjKIMJixXJNBu/Mkex55gNqEDJ6+5g6qVEq2/70FjyKGDGUHG/77eoxJExvHDnuGqR6oprq/mpqBmkkX6quSqliWtIxlyctmxeu+IX+Aiv313J0Wx9fzUsNdzowmGrTCjOPYuRPr575C5/KvsCgyBjk3krS7y2bclaDZ6uTJf8c+foxVK/eKz6kwbwz7g6w93EC6XstzFQWoRUi98DZ1e/1cfaSRfKOefy7OnzFfO4PuQY70H+FI/xEO9x+my9EFQJQuiqrEKpYkLaEqqYq8qLwZ/8JdmD+czmY6Ov/IwMAzgEx8/GYyM+5GkjLY+8oeTtTVEiCAMqTFMm4kPtiH09eNy2EnOjmF8k3XU7p+A1rD5CnSwKAb5/5e3DUDyAEJXV4U5lUp6AtjUMyQ79l3q8nl5YajLSRo1TxTkU+UZh5FncgyuIYvnnk71j4Rq3AhfeTFNy2Lzp5o7Iq7DgRBmCayLNPf/ySNTd8kGPTRdnoxPvtSljvzSAlFY16ZgivDw86//y8Dba3YV23k/rJ15Dl9bH/ehsHvY+UyJfHvW0LNQA3VA9Uc6T9y7kK8UW1kccJiqpKqqEqsoiSuBI1y9u1N8MHaNk46PdSsKEYpehBvSjRohRnF8dpO2j//FRqXfJGq6Hg0sQbSPluBQiNeSE0HSQqyZ+8S4uM3UVz0g3CXIwhX1NODNj52yiqiDoS3LSTL3HKslZNOD68tKSTTMHNvqe139U/EIZyZsO1z9QEQoY2gIrGCyoRKKhMrWRC7YFa+sBfmFq+3l67uv9DT8zChkJOoyCVkZHyU6Oj1NNQ3sWfHawx6RkEGrTeKOPsoKnqwjQ2gNRgpu3oj5ZuuJypx8s9yyR3Aebgf1/5eQuN+1HEGzKtSMFYkotTN/teS+8ecvOfEacojjDy8KBejSlx8AcDvgrGOqZm3Y1awdYIUOL9WpYWojKmZt2cncDXiLhtBEN4en3+Y+vqvMDr6GnZ7Au2tayn1VVDkTMJYHI92dQz7dvyd+t2vYY6JxXznv/GVoJnEUQ/v2eUl2dVK95Z2XleeoNPRCYBZY2ZxwuKJC+2JVRTFFs2JvQfO3o32RHkeK6PN4S5nxhINWmHGcO7eTdt//D9OVH6OxdFJRBpUJN9biTpG5JRMF7v9KNU1t1Fa8ksSE7eGuxxBuOI+Vd/B04NjPFdZwKLZnOMnXBE/s/bzP+39/GJBBnckz55bZmVZptvZzdGBo9QM1HB08Oi5rDKD2sCi+EVUJk40bMviytCrxe9ZITyCQQe9vY/S1fUnvL5eDIYsMtLvIjn5Zux2D7t37KSuuYGgIjiRVWtXEuHrwjHehSTL5FYuo3LLDaQVT77TSg5JeOqGceztJdDlQKFXY1qahHllMuqo2f31/uyZi41XxUTw57JsNHNkQviykUJg7546dXu2gesbn7zekjx107KzzVtjLIjJL0EQgIGB5zhV/5+EQm6s7eWYhzdSac8mMjkGy+ZM6ptf58DjDxEKBKjcup2RFcv4zGkXUQ6JD788jEt+nEeXHsSsj6AyoXJiQjapigXRc3NvAVcoRNm+U9ySGM2PCtPDXc6MJRq0wozgOnCAtk/dy/GKz5IZmUyOVkns+4swlMaFu7Q5pa39l7S3/5K1ayY26xCE+cYWCLL+cBMRahUvVRWgF9NHwps4YHNyy7FWbkyI4rfFmbM+EmbIPUTNYM25pm3LWAsyMmqlmrK4MioSKqhMrKQ8oRyL1hLucoV5RpKCDA29QGfn/zHuqEWjiSY19U7S0j6IShnFqdp69r60iyHPKABar4kI+yCSy0rA7yE+I4vFW26gaNV61NrJ+ay+jnGc+3rw1A0DYCiNw7wqFV1mxBU/zunyt94RvtDUxc2J0fy6KEPcLvpOyTJ4xi6+adloOzh6J6/XWi6eeRuTDRFpoJr9U26CIPxrgcAYx098ifHxV3GMxzLUfh0Vg1UkmxOI3JTJkLqX1/7yR8Z6u9Hlp9CzxMDJ0SAnUz6Cyavg48/WML68juwVS6lKqiI/Kn9ONmQv5p76Dl4dGad2VQlapTgHuxjRoBXCzn3kCG0f/3dOlH8agzmNpUYV5pUpRN2QG+7S5pzq6luRkVhS9US4SxGEsNk5Ms57a9v4RHo83xBB9cJFDPuDXHOkCYNKwctVhZjVc++Fs91n5/jgcWoGaqgZrKF+uJ6gHESpUFIYXUhlYiUViRUsTlhMnEFcLBWuDFmWsdmO0Nn1fwwPv4pCoSEp6UYy0u/CbC7AZrPx+nM7OdVcj18RQBFSYxoPonNa8TuHMUREsuiazSzauAVzTOyk5w7avDj39+E63IfsDaFNt2BenYKhNA7FLLxY96uOAb7b1sddqXF8Nz911l9EmpECnjPRCdap8Qm2Dgj5z69VqiEyfWrm7dn4BO3c2rhOEOajnp4dNDR+FVl20ttVQUr7DSyQMzGsSqIhsY2aJx4h1NyP0xTi4IIRuuM9bOi4lX8uvx5dQOLbdXVs//x7UWtnbmTW5fTKyDjvr23jL2XZbIqLDHc5M5Jo0Aph5T52DOvdn+BE2SfxmjK4JlaHNt5IwicXoVDPvhfLM1kgYGf3niqysj5Fbs5nw12OIITVl5q6eKB3hMdFDpLwBpIs8/7aNvaOOXmuMp+yeRKF4Q64qR2uPTdhWztUizfkBSDNnMbihMWUJ5SzKH4ReVF582baQwgft7udzq4/0df3OJLkJSZmDelpHyI2dh2yDA11jex5/jX6PcOgALVXg8nWT8jWgUqpoHDFGiquu4GkvIJJzyv5QriPDuDc10tw2IMqQotpZQrmpUkojbMnn1mWZb55upffdw3xxawkPp8tstWvKEmamLC92KZlo+3gtU1eb0q4SObtmUauKV5EJwjCDOb32zl0+HP4/btwOaPxN22nfGQFvRljPByzA09tC0XtZiSFTG+phvg1FSzyL6Bth5pfXZ2NWgrySLKFRZVF4T6UsApIMov217Em2sIfSrLCXc6MJBq0Qth4TtZhvetuaos+yogpl63ZFtSuAImfXow6TgT0T7fBwRc4WXcPlRX/ICpqyve8IMwrrlCIDUeaCMnw2pJCLHNwQlJ4Z37TOci3T/fy/YI0PpI6fydHA6EAp0ZOcWLoBMcHj3Ns8Bgj3hFgYgOLhfELKY8vZ1HCIhbGLcSsFRc6hMvD7x+lp+fvdPc8iN8/iMGQSXraB0lOvgW12oLD4WD3szupbTiFT+lDISnRj3tQ2azgcZCcV0D5tVspXLFmUvyBLMl4m0Zx7uvF12pDoVFirEjAvCoVTcLsuDAjyzL3Nnbxj/5Rvpefyl1p8eEuSTjLM3bxzNsx60QmLheca2tMkzcquzA+ISoDVLPnwoEgzDVNTU/Sbv0marWT4a4KCpvfT79+mPviH0c9Os7i5ig0XpnYyhKu/cDHSYzP5NAvX+T1Lg1/2hCNQgtPLy+iMEJM0cPEkMwj/aPUry7DMAvvXrncRINWCAtvYyPtH7qLuvz3M2hewKbKOPSn7cS8txDjooRwlzcnNTR+lYGB51i7phql2MFbEDhid3Hj0RbekxzDTxdkhLscYQaotru46VgLm+Iiua8kS9wyfIGzG48dHzzOiaETHBs8di7HVoGC/Oh8FicsZlH8IsoTykkzp4nPnzCtJMnP4NCLdHf9Bfv4MVQqE8nJt5Ce9kGMxmxkWab5VDOvP/sqfZ4hZIWMyqdAb+tDYevDaDJRtmETizZeR0Tc5NeagX4Xjr09uI8PQlBGXxg9kVObHzXjv46DksxHT7Xz0vA4vy7K4Jak2bOh4bwV9IGtc2rm7dlJ3KD3/FqFCiLTpmbenp3E1c/eLGVBmIkcfgd1w3Uc6zqIsft50qPbcLsjMdW9D4s7h4NFTeiMCuRdzTh7B0hdUMz6D9xNUl4BPQebee1PtXQbY3nwKiP+CB1PVRVSbBbDZ2ftGh3nPSfaeKAsm2tFzMEUokErXHG+1lasH/gQp7Jvpy+ijKuuSiXi2CCmpUlE35wf7vLmJFmW2b9/LZaIUhaW/S7c5QjCjPHd0738qnNQvEgQsAWCbDjShFKh4JWqAiI1YrOXt+L0O6kdruXE4ETDtna4FlfABUCcIY7y+HLKE8opiyujKLYIg1qcoAjTY3y8lq7uvzAw8ByyHCA2dh3paR8iJmYNCoUSj8fD6/98jRP1J/EovSAp0DpcqGxdqD1O8qqWU75pKxmliyY1YENOP65D/TgP9CI5A6gTjJhXp2BanIBCM3PvtPCGJO6sbeOQ3ckfirPYlhAV7pKEd0qSwDkwNfP2bCPXPTJ5vTH24puWRWeDJUlEJ/x/9u47PrK7PPv/50yv6l1arbRabe+77r1hG3DBmGYHAglJnkBCSSAkT/JLSEICCSGEVEKSB0IILaGDwbjg3u3tVXXV+4ym13N+f0ir3fWuvU3SSKvrbc9rzkhnNPesdqWZ69zn/oq8DtMy6Qx3Tr2WGd3NntE9dIY6uSpXzRtrh/B44qR7L6Ol+914r6rHt6qYp775FTpfeZHiqmquvf99tF52FZlYisf/+qe0jRSRcib42ptriPk8fGtLC9vUOXuStGmy/ql93FVVwufUIHMKBbQyr9JdXXS/5z0cqr2DvrIdXHHbcmr2jmAPuqj64JYF/eJ3MYvHO3nu+VtYvfrPaai/r9DliCwYadPk9peOMJrN8eglq6l0qbt8KbIsi1/Z183D4xF+sG2lXkyfp7yZpz3cftJYhL5YHwB2w86q0lVsrNjIhooNbKrcRHNxMzZDp7fJ+UunR+kf+Cb9/f9NJjOKz7eChob3UFvzFhyOqbEbXW1d/OJ7P6cvNoxpM7FlLZzhYRyTI1RUVrLltjtYd82NuH3HxxpYOZPE7lFiT/WTHYxj8znwX1ZL4Ipa7EULc3GXeC7PO3d3sjMa5/9t0EHHi1YqcvqZt6GuqdEJlnl8X4cXSpefHNoeC3JLGsGxMP8ui8yVcCrMnrE97BmdCmT3je0jlo0BUOwu5hLHFrbleqit3E8uVUzVvl9hxdrbcVxawvMP/A+7H3oAp9vD5W99J1tvuwOH08nh77/AUz8eJGX3U+zv5x/eso1xy+Jbm1vYXqzXk6fz6/u7eTYcY/eV67HpINJJFNDKvMn09dF9/y9xuPJmeiquZPutjbRMJMl0R6j67a2LZt7XYtTX998cPvLHXHH5I/h8TYUuR2RBORhLctvLR7iqJMDXNq3QC4Ul6N96R/n/2vv505V1/MYyjdmZTWPJMfaO7mXv2NTlxDdDAWeA9RXr2VixkY0VG9lUuYkK79Kd+yvnzzQzjIz8lN6+/yQS2Y3dHqC29q001N+H378SgEwmwzM/fZJXXt5JxDb1d9ART+IID+JJxdl4w81secObKW9YNvN1Lcsi0zVJ9KkBUgfHwWbg21RJ4Ko6XA3BgjzX1xPJ5Xn7rg4OxJJ8dVMz15fp9PclJZ+dGp3w6pm3xwLcbOKEnY2p0QmlTacuWlbaDN6SQjwDkVmTzWc5Ej7CvtF9Mx2yRyNHgeMHjTdVbmJT5SZaPC0cfv5nOF1fw+eLYOu9grXGRyi5qZW9rzzC89/7Fplkkk03386Vb7sPX1Exkf4JHv3sw/SnKvCnRlj7pio+sqyG0UxO4ewZfGdogg8e7OEn21r15/QqCmhlXmRHRjj6S+/msO9SumtuYNONDWyp8zP5405K3rKSwGW1hS7xorZ3328zOfkKV1351IKfpSZSCP+vb5T/29bPn62s49cV0C0pL4Rj3LOrnZvLi/jyhmb9jJxjpmXSPdnNnrE97Bvbx57RPbSF2shZOQBq/DVTYW3FJjZUbGBd+Tp8Th3AlbM3ObmL3r7/ZGTkp1hWlpKSy2iov4/Kyjdgs00tEjY6OMoj3/4pHWO9ZO1ZMC2ck+M4J0dpbGxi+5vvomX7Zdjsx8/syo0niT0zQPzFYaxMHldTEcGr6/GsK8ewLZyfG+Fsjnt3ddCeSPG1TSu4unThBclSAJYFsZHTz7yd6IL4yMn7e0pODW2PBbnBOrDp7AdZOPJmnq7JLvaN72P/2H72j+/n8MRhMmYGgHJPOZsrN88EsuvL1+Nz+sjlcjz99BN0d/8D9Q17sdJBmoY/RMP1d9PR/RJP/89/Exsfo3nLdq57969S3tBILpfnpS8+yq7dOSzDxtqSQVZ87E7e0TmkcPYshbI5Njy9jw8uq+L/ttQVupwFRQGtzLn85CRH3/0e2nIttDe+mXVX13HVTQ2M/NMuPCtLKf/ldXpDPIcsy+LJpy6lvPxa1q/7XKHLEVmQLMvivfu6+MV4lJ9sb2VjUIHQUjCSznLLS4fx2W08uGM1RQ6N2SmEVC7FoYlD7BndM9Np2x/rB6a6XFaWrGR9xXrWl69nXfk6VpWuwmV3FbhqWegymTEGBr9Df/83SKV6cTrLqat7O/V178TrbQDANE32PL2LZx55ilEzhGWzsKXTOCZHKcpl2HHbm9h00634iktmvq6ZyhF/cZjYM/3kQ2nspW4CV9Th31GNzbcwxuSMZ3Lcs6udnmSGb25ewWUlgUKXJAtdOnY8vH31+ITJXjBzx/e1u6dHJzSdOj6hZDk4PQV6ErIUWJZFX7SPfeP72De2j/3j+zk4fpBEbqpD3O/0s658HRvKN7CuYh0bKzZS5687JW84cuQIjz78FWobfk4gEMI/djXr1nySkfQwT33zq4z39VCzchXX3vdelq3fBED3Ywd44uuHiNpKqEx3c92vbMW8dD1v3dnBSCbLNze3sEPh7Fl56852xrI5Hr90TaFLWVAU0MqcMhMJen7lV+kc9XOw9T5W7qji5vesZeyfd5OPZaj+yDbsAb3Jmkux2GGef+GNrF3zV9TV3VvockQWrPHM1CJRAYeNB3eswm9XWHcxy5oWb9vVzu5ogp9sX6UVdheY8eQ4+8b2zQS2+8f3M5meBMBhOGgtbWVd+TrWla9jffl6WktbFdrKaVmWycTEk/T1f52xsUcBi/Ly62iov5/y8uswjKmf9fFYgl9860H2d7aRdCbAsrDHI7gmx1m9ooUdd72V+rXrZ97kW6ZF6sA40af6yXRHwGHDt6WSwBV1uOoLH4iOZrK8ZWc7Q+ks397cwjaFBnK+8jmI9J1+0bKJbshET94/WHdCaNs03X07HeB6S7VwmZyT4fjwTGfssUA2kokA4LK5WFO+hvXl69lQsYEN5RtoKm563fn24+Pj/PSHPyJj/YDGxn3YcgFag3+IUbqWJ7/5nwwcPkBpbT1Xv+s9tF56JYZhEB0M8djfPkJPtAxPeoJLNlts+ODdDJsWb93ZwfB0OHuJfs6etS/1jvDH7QM8d/lamryah32MAlqZM2YmQ9//+U262+Ls2/BrNKwt500f2ET0593Enuin/L3r8a4pK3SZF73evq9y5MifcuUVj890jIjI6T0VivK2XR28q7aMv9XKohe1T7b388XeUf5xbSP31uh30UJnWRYD8QEOjB9g/9h+Dowf4MDEgeOhrc1Ba4lCW3l9qdQA/QPfYmDgW2Qyo3jcddTVv5O62rfjdlfO7Ne1v4vHvv8wfckh8o485HM4Jycozma47Lbb2HjTbXgCx0PYzGCc+LMDJHaOYGVNXI1BAlfW4d1QgeEo3Kngg+kMb9nZzngmx9cVHshcsCxIjL8qtD0hyI0Nnby/u3iq+/Z04xOKG8Cmg+NLlWVZDMYHOTh+kIMTBzk0cYgD4wcYTY4CU2fUtJa2sr58Pesr1rOhfAMrS1fitJ3dmQvpdJonHn2cPfsfoLX1afzBCcrMm6hd/ls89/0f0PHS8/hLy7jy3vtYf/3N2B0O8rk8L33xEXbuzmMaNlZ5e7nqE3firaviaDLN23Z1MJHN8Q39fD1n3ck0lz93kE+11vP+hsoz32GJUEArc8LK5ej/nd+l5/lOdm//CJXLi7nzw1sw+2KM/cde/JfVUnr3ykKXuSTs2fsBotF9XHXlE4UuRWRR+MuOAf6+Z4QvrW/izqqSQpcjc+BHI2F+bX83762v4DOrdOBqsbIsi/5Y/1RYO36A/eNTwe2xzppXh7brytexsmQlHodOv13qTDPL6NjD9Pd/nVDoGQzDQWXFLdTVvZ2ysqtmumpzuTzP/uBxXn5lF2F7BGxgSyVwRiZYVVPPFe98F7Wtq2e6as1kjvjLw8SfGyQ3lsQWcOK/pAb/ZbU4SgrTITSQynDvrg6GMlm+tnEFV5YWvrtXlpBMAsJHT515G+qC0FEws8f3tTmhpPHUmbfHtl0aP3WxyJt5jkaOzgSxx0LZY7+/bYaN5qJm1pavZUPFBtaXr2dN2Zrz+v1tmia7Xt7FIw89SFnNiyxv3IuDIprqfo/DTwyx/7FHcHo8XHrXvWy7/U6cnqnH6HhkH09/6zBRWykV6aNc+56N1N4wlZsdiad4+64O0qbJ1ze3sLVIfzfPx2XPHmC138NXN60odCkLhgJamXWWZTH4R39E34MvsOuyTxCoDHDPx7bjssHwF17BcNmp+u2t2Fw6QjrXLMvkiScvobLiJtat++tClyOyKGRNi7t2ttEWT/HQJat12s1Fpi2e4raXj7DG7+F7W1fi0kInF5UTQ9tjge2Joa3NsNFU1MTqstWsKVvDmtI1rCpbRYW3osCVS6HE4530D3yDwcHvksuFcbtrqat9G7W19+L11s/sFxoJ8ejXH+DwSDcZV3ZmBEIgleLK669j65vuxOWdepNumRbp9jCxZwdIHZoAA7xry/FfWYd7RfG8r70wnM7ytl0d9KbS/OfGFVxbpoXDZAEw8xDpP3Xm7bHRCdNnSMwIVJ868/bYHFx/hUYnLFCZfIb2cPtMR+yhiUMcCR0hmUsC4LQ5aS1tZW3ZWtaWrWVN+RpWla7C67jw0VNHO7t54Hs/JppvY/3q5/EERynz3cz4wdXsfegJDAO23PpmLnvL2/EGiwAYbxvi8X96isFUGd70BNu3wMYP3o3N4QBgXzTB23d3YDcMvr25hbUakXXefu9wL98dDnHw6o04F9Bim4WkgFZmlWVZjPz1Z+n75o/ZeeUf4Szyc8/HtxModTPxjUMk941T9YHNuBr0wnA+RKMHeeHFN7Nu7Weprb2n0OWILBq9qQy3vHiYBo+LH21rxWtXiHcxCGdzvPHlNiZzeR7asYo6j05/Xwosy6Iv1sfhf1XjQgAAfLFJREFUicMcmjjE4dBhDk8cZjA+OLNPhbdiKrQtXcOasjWsLltNY7ARu063XTJMM83o6MMMDP4PExNPAVBWehV1dW+jsvIWbLbjB+uOvHiQJ37yKAPZMUynBWYeZyTMMl+QW3753dSuXjuzb24iRez5QRIvDmEmcjiqfASuqMW3rQqb2zFvz280k+XtuzroTKb5jw3N3FxeNG+PLXJeEhOnn3kb6oLIAHBCXuEKTHfanmZ8QvEysM/fv7WlLJwK0xZu40joCIcmDnFo4hDt4XZy04vM+Rw+1pStYW352qnrsrWsKFlx1mMKzlZoPMTP/vfHHB5sY8WyQ9Qv34XDXkR+5Hr2/KgDyzTZcMMtXPaWd1BUMXV6fWoyyVN/93OODPiw5TOsLRnkso/dhafm+On3L0/GuW9PJwG7jW9vaaHFpzNyLsSxM9p+uHUll2oxS0ABrcyysS9+kb5//jI7r/kTTE+Qez6+jdIaP4ldI0x88zBFtzZRdMOyQpe5ZPT0fpm2tk9x1ZVP4vHUFbockUXlobFJ3r23i/try/ic5tEuejnT4v49nTwTjvG/W1q0qrkwmZ48JbTtCHeQs6beSHodXlpLWme6bVeVrmJV6Sp8Tp3KeLFLJvsZHPoOgwP/Qyo9gMNRQm3N3dTVvZ1AYPXMfvlcnme/+zgvvvIik84E2A2MbAZfPM7Wteu49pffg8sz1V1lZfMk9owRe3aAbF8Mw23Ht62KwBV1OKvm5+/URDbHO3d1cDCe4t/WN3FbZfG8PK7IrMumINxz6szbUPfUJZ8+vq9hh5Jlp3bdHgtw3Xo9cK6y+SxdkS6OhI7MXNpCbYwkRmb2KfOUTZ2pMh3Iri1by7LgstddwOtCpVNpfvHdn/PikZ34vCE2rXsJm38AI7mOA9+zkYlbrL/uJi6/5x0UV9UAUz/Hd375cV55IUHW5qHR7ODq37yW0m1rT/ravxiP8Kv7u6l2Ofj2lpUs00H+CxbK5lj31D5+p6majzfXFrqcBUEBrcya0De+Qe9ffJbd1/4JCWcxd390G9VNReSjGYY//zKOCi+V/2czhtrX583uPb9BPH6EK6/4RaFLEVmUPt05yBeODvOFNY28o1YLSS1mf9LWz7/2jfK3q5dxX115ocuRBSqTz9A52XlScHto4hDRE1Yprw/U01rSysrSlTPXzUXNOO2z2wEkhWdZeSYmnmFg8NuMjj6MZWUoCm6itu5tVFe9CafzeMAZGYvy8Fd/yOGhdtJeEwwDWypJeR5uevMbWX3ttTOjDTK9UWLPDJDYMwp5C3dLMf7L6/CuK8OY4zM2JrM53rm7k72xBP+0bjl3VZXO6eOJzDvThOjgqTNvj10nQyfv7688NbQ9FuQGqpf06ATLshhNjp4Uwh4JHaFzsnOmK9Zhc9BS3MKq0lW0lrbOHMys8FbM2zgX0zR56WfP8NiLT5IkwZamowSWPQ+mi94nqhk/4mXt1ddzxVvfSWlt/cxza/vZHp77XgdRWwllyR6uvKuRxrfccErd3x6a4HcO9bDK5+Ebm1uoduv3/Wy57aUjuGwGP9zWWuhSFgQFtDIrIg/+nJ7f+Th7r/lDwo5K3vzBzSxbW4ZlWYz/10FSR0JUf3grzkp1ncwXy8rzxJM7qKq8jbVrP13ockQWpZxp8Y7dHbwSifPA9lWaM7VIfWNwnI8e6uX9DRV8qlWLgsm5Obay9LFTNdtCbbSH2+me7J7ptnUYDpYXLae1tJWVJStpLW2ltaSV+mD9nHYLyfzJZkMMDn2fwYH/IRY/jGG4qKy4iZrat1Bedi22E07R7Xqlg4e/8wOG8iHyHjtYFs5EgqZACW/8tfdSWjcVEORjGeIvDhN/fpB8OI0t6MS/owb/pTU4Sufu1NloLs/9ezp5cTLOX69u4N11msEsS0gyfMLIhFeNT4j0gWUe39fpOx7enrhoWdn06ATHxdNFGclE6Ax30hHuoD3cPhPKhtPhmX2qfdUzAeyxQLapuGnWRxSci/Zn9/PgIw8xmgvTWJykZdOz5Ix+wp1l9D5ZTsvWG7jy3vsobzh+Fm//S5089ZWdjOVK8abG2L55es6s6+Tvp2VZ/EPPCH/ZOcg1pQH+Y0MzRQ6NPppNn+4c5B97hjl09UaC+rNVQCsXLvHSS3T/yq+x/5IPMeJazq3v38DK7VVTn5sebVD8xmaC1+pN8XyKRPfx4ot3sX7d31JTc1ehyxFZtEbSWW556TB+u50Hd6zSi4dF5qXJOPfsbOeyEj/f2NSCQ2dxyCw5dopne6h9JrhtC7fRH+uf2cfr8NJS3MLK0pVTwW1JKy0lLVT5quZ9oSiZHZZlEYsdYHDoewwN/YBsdgKns4zq6juorbmbYHDjzPfWzJu8+L0nePa5x5l0Z7GcDsjn8SXSbG5p5aZffQ8OtxvLtEgdniD+/BCpwxMAeFaV4r+sFs+asjk5+yyRN/m1fd08MhHh95tr+PDyav2dFMllpkcndJ/cdXusE3d6YSsADBsUNUBZ08ndt8eCXM/CHCEymZ6kc7KT9nD7TCDbEe5gJHl8PMGxET8ndsS2lrZS7F44z2lgbzcPPfBzupIDBO0G27f1kPc8RiY+1TVbXXMLV779fiobm2buM94+zJP/8hT98VJcmQjrqsfZ8btvwV1x6llyecviD9v6+Ur/GPdUl/J3a5ZpYdk58FQoyr27OvjqxmbeULFw/n4VigJauSDptja67v8lDre+k77gZq595yo2Xj8VxGq0QWEd7fl32ts/zdVXPYPbXV3ockQWtWfDMe7d1c5tFcX82/ombHoTuyj0pTLc/vIR/HYbD2xfRZlTi4TI3EtkE7SHTw5t20PtjKfGZ/bxO/00FzWzomQFzcXNrChewYriFTQEG3DY9Pd0sTDNLBMTTzE49F3Gxh7GNDP4fCuprXkLNTV3njT/PxVL8dC/fYsDfUdI+mxgt2PkcpRk4Nqrr2Tzm2/DZrORC6eIvzBE/MVhzGgGe7EL/yU1+C+pwV7sfp1qzl3WtPjooR7+dzjErzVU8Kcr6/X7TeS1WBbEhk8NbY8FuYmxk/f3lp1+5m1ZMwRqYI7Dvsn0JO3h9pkAtmOyg85wJ6PJ0eMlOrysKF5BS0nL1KW4hRUlK6gPLNyzPyYOD/Lojx5if7QLh2FjxyoDR8X/YtmjjO0rI2DcxWV33U/l8uaZ+0SHIzzzj4/SMeLHls+yyt/HZR++Hf+K06+NE8/n+e0DPTwwNskHllXxRy21+tk4R9KmyZon93FfbRl/sUoNfQpo5bxlBwfpftd9dJZeQXv1zWy7dTlXvKUF4ITRBhNUf3ibRhsUwK7d7yeZ7OaKyx8udCkiF4Uv9ozwyY4BPt5Uw+821xS6HDmDSC7Pna+00Z/K8KPtrazxazyFFNZEaoL2UDsdkx10TXbROdlJV7jrpK4lp83J8qLlNBc3nxTcNhU34XXo7/BCls1GGBl5gMGh7zE5+RJgUFp6BTU1d1FVeSsOR3Bm35GuQX765f+mLzFK1ucGmw1bJkutzcstb72Dpq2bsfImqYMTxJ4fJN0WBht41pQTuLwW98qSWWt8MC2LT7YP8KW+Ue6tLuXzaxpxqqlC5Nylo6eZeds9tR3uBSt/fF+HB0qWnzrztrQZSpeD4+wOxpiWyWB8kO7Jbroj3XRNdtE12UVHuOOkg4I+h4+WkpaTw9iSFmr9tQs2iH21WOcET/zgYXaGD5MzTDbUVBOs/gH24iMkJ9w4I3dyyW2/RVnd8ZAvOZnk+X95lIOddizsLDc6ufI3rqF027rXfJy+VIb37u1ifyzJn62s59eWVc7H01vS3rW7g4F0lscvXVPoUgpOAa2cl/zkJN33309Ptp4Dze9g1aXV3PzedTMvFjXaoLCm5s9up6rqjaxd85eFLkfkomBZFh861MP/DIX4jw1NvKmypNAlyWvImhb37+ngmXCMr29q4dqy4JnvJFIg0Ux0JrA9Ftp2RbrojfZiTs9CNDCoC9TNBLfNxc0sDy5nedFyjUtYgJLJHgaHfsDQ0HdJJnuw2VyUl19PddWbqai4Ebv9eNh+4LEXeexHP2LcliDv84Nh4EznWBEs55ZfupeKxmXkxpNTXbUvDWPGs9jLPPgvrcG/vRp78MJnYJ44Z/GGsiBfWt+kcT4isymfhcneV828PaELNxs/YWcDiuqnRyU0QWkz0eJaup0uuo0cXclRuiNTgWxPpId0Pj1zz4AzcFIIu6J4BStLVlLjr1m0vydSRyd5/geP89z4PpJGhubiOirKnsNR+RQ2p4kxeQXbr/40pTXHM4dUNM0LX3qMA4dN8oaT2kwnV9y3idpbLn/dx3pxMs779naRNk3+ZX0TN5cXzfXTE+AL3cN8umuQA1dvWPJnuymglXNmptP0/Oqv0t+dYvfGD1C3qpQ7fnszdsfU0TeNNii8aOwQL7zwJtat/Rtqa99S6HJELhqpvMk9u9o5FE/x422trNOiYQuOZVl89FAv3xya4O/WLOOdteWFLknkvGTyGY5Gjp4U3HZOdtId6T7pDbnX4WVZcBnLi5afdGkMNlLmKVu0b8ovBpZlEYnsZnj4RwyPPEAmM4Ld7qey4maqq99MWdnV2GxTAWsul+Opr36XV3a9QMwDpi8AgCdlsq6+kevvv4dgUQnJ/ePEnx8k3TkJdgPv+nL8l9bibim+4O/11wfH+fjhXlb7PHxt0wrqPBfPAkgiC5ZlQXyM7Hgb/UO76B4/QHfkKN3JEbpyMY7aLMZPOGBitywaLDtNjiBNviqaipppqlhHU+0llFeuw7BfHAFXuifCnh89x9PDuwnb4lR5S6n09uCufBB/dRLSDWza/Dkq645nWel4hhf//TH278+Rs3moTrZxyZubabz3ljP+fPzm4Di/d7iPeo+T/9y4glX+uVuoUU72bDjGW3a2aw4tCmjlHFn5PP0f+SgDzxxg1xV/QFF1gLd8bDtu79QvgpNGG3xoG84qjTYohL6+/+bwkT/myit+gdfbWOhyRC4qw+kst750BKfN4GfbV1HuujheCF8sPt89xF91DfE7TdX8XnNtocsRmXWmZTIUH+Jo5OjMpSfaw9HIUfqj/eSs3My+QWeQxqLG46FtUSNNRU00FjVS5FJn0HyyrDyh8AsMD/+YkZGfkcuFcTiKqaq8lerqOygtvQzDmAphJkfHeeTfv0bbQAdpvxfT4wXLIpA22NzSytXvuANHyjHVVfvyMFYyh73cg39H9VRXbdH5z6p9fCLK+/d14bfb+dqmZjYE9VpeZLakcin6on30RnvpifbQG+2duQzEBsifMAah1F1KU3ETTYGGqTDWstOUSbMsNoEzdHR6dEIPmMd/5mN3QUnj6RctK20C58JvLEh3T3L4pzt5ZnAXQ7YwRU4fJbkxvCWPUrk+hIGPlhWfYHnz/TOhayaZ5aX/eJx9e9JkbV6qEu1c8sZGlr/9DRhnmPWbNS0+1THAv/aNcm1pgH9d30TpEu/inG+pvMmqJ/fy/oZK/nhl3ZnvcBFTQCtnzbIshv/8Uwx+56fsvPaT2Px+7v3EdgKlx48uJXaPMPENjTYotH37P0oo9BxXX/WMOmdE5sDOSIK7d7axvcjPtza3aF7fAvG/QxP81sEe7q0u5R/WNurnnyw5WTPLYGxw5tTXEwPcgdgAFsdf35e4S2gINNAQnL6csF3tq9ZiZXPINDNMTDzN8PCPGR17iHw+jstVSVXVbVRV3k5JyY6ZsLb/0BF+8dVv0BsdIRMswnK5wbQoyTrYtn4tl95xK/mOBPEXh8l0TYIBntVl+C+pxrOmDMN+7vMlD8aS/NKeTsK5PP+q03xFzkkkEzkevEZ6TwpjRxIjJ+0bdAVpDDayLLiMZcFlMwfRmoubKXafRSehmYfJvlNn3h7bTkdO3j9Y+6rQ9oQg11cGBXrdZFkW6bYwHT/fw3PDe+i1j+OxOfHHJ/DaX2TZVaM4PFlqa95O66pP4HRO/dlkklle+fKT7N2VIGPzUZnoYMct9TTfdyuG/cxjWvpSGf7P/m5eiiR4f0MFn2ypx6HX9AVxx8ttmFj8ZPuqQpdSUApo5ayNffFfGfjHf2X3DX9Oyh7gno9vp7w+MPN5M5Fl6HMvYy/zUPWbGm1QSE8/cy1FwU1s3PiPhS5F5KL1naEJPniwh1+qLeezqxsUBhbYYxMR3r2ni0uL/Xxj8wpcc7w6sshik86n6Yv2zYS2fdE++mJ99EX7GIgNnNR56zAc1AZqTwlw64P1NAQazi44kLOSzycZG3+M4eEfMT7+GKaZxuksp7LyFqqqbqe05DJsNidmPs/hZ57lqe/9gJFcglxRMZbDBaZFed7N9s3r2Hz1deT2TBJ/eRgzmsEWcOLbVo1/R/U5n9U2lM7ynj2d7Isl+bPWen61vkK/50SY+lk6GBtkIDZAf7x/6jrWT3+0n55oD+F0+KT9K7wVNAYbaQg2zISxjUVT13P6s9SyIDHxqtD2hPA2OnDy/u6iqQXKXr1oWVkzFDXAHIxOsEyL1IFxjj58gOfH99FlH8Fp2PFMjuKKH2bFzSE85eMEAutZu+ZTFBVtAiAZSfHSvz/OwUM5sjYv5YkudtxQRcu7b8dwnF2dD41N8qGDPWQti79ZvYy7q0tn/fnJ2ftUxwD/2jvK4Ws24juPA4sXCwW0clYmf/hD+j7xh+y94Y8JGRXc8dubaVhTdtI+E/97hMQrw1T99jZctf4CVSqp1CBPP3M1ra1/ROOy9xW6HJGL2qc7B/nC0WH+74paPrS8utDlLFkvTcZ5264OVvhcfHfLSop1aprIOcmZOUYSIyeFtiduh9Khk/YPuoJTgW2gntpALbX+Wur8ddQEaqjz11HiLlGYdx5yuTjjE48zMvIzxsd/QT6fwOEoobLiJqqqbqes7EpsNjfpRJxdP3uIFx95mEm7Sa6oFMvhxDCh0vSwbesG1rbuILtrgtShCTAtXMuL8F9SjXdjJTb32S0AFs/l+eDBo/xsLMK7asv4zKoG3Dr4JRe51wpgB2IDDMQGGE2OnrS/w3BQ7a8+3gV7rCO2aBkNgQZ8zgU6JiSbhGOjEo4tVnYswA0fhXzm+L42x/TohKaTu26PBbmuc3vvb+VNErtGGfjFYV4MH6TNMYgNA1doBFf4KKvfYOKubcfh8NGy4mPU178Lw7ATG43ywr8/yZEuG3mbi6pEO1tvrKXl/tswnM6ze9qmxWe6BvmnnhE2BLx8aX0TK3znPxZGZsdDY5O8e28X39nSwlWlS3dxXwW0ckbxF17g6K/+Gocv+xADjmZu+ZV1rLq05qR9Uh1hxv5tL8HrGii+vblAlQrA8PCP2bf/w1yy43szRxlFZG5YlsUHD/bw3eEQ/7S2kbfWlJ35TjKrDsSSvGVnO+VOBz/YtpJK19m9QBeRsxfLxOiP9c+Etr3RXvpiU523Q/EhkrnkSft7HV5q/DXU+mtnLnWBOmr8NdQF6qjyVeG06d/q68nnU0xMPMnI6M8YG3uEXC6K3R6gouJGqqpuo7zsWux2L+HhIV7+4Y/Y/eJzJL1ucsETwlrLx9aN61lVsY7sznFyo0kMlx3f5kp8l1TjWhY8Y5BuWhaf7Rri80eH2V7k4/9taKbare+dLE6WZTGRmmA4McxQfGjmejA2OBPGjiXHTrqPw3BQ46+hPlBPXaCOukDdzHZ9oJ5KbyV229kd9Fg0zDxEB0/tuj22nQqfvL+/6jQzb6cDXH/lzOgEK2sSf2mIocfaeSV+hEOOfiwsnOPDeCIjbLi1GFfdTvJmlLq6t9Oy4ndwuSoI94V5/t+epGPQjWXYqEu3se1NLTS+9eYzzpg9UWcizW8fPMrLkQTvqSvnz1bW41nC3ZoLSTibY+1T+/i95ho+2lRz5jtcpBTQyutKd3bR/a530bniTjqLL+fyu1ew/bamk/axsibDX3gFy7So/sg2bK6L7BfUInP4yCcZHPwO116zE5vmx4nMubRp8q7dnbw4Gecbm1dw9RI+6jvfuhJp7tzZhtMw+MG2VpZpxXGReWdZFuF0mMH44NQlNnjS9kB8gInUxEn3sRk2Kr2V1PprqfHXUOWrospXRbWvema7yleFy65/0zA9szb0DKMjDzI69hDZbAibzUNZ2dVUVtxEecWNuJzlDLYd5pUfP8ChA3tI+33kgmVYDsd0WOtnS8sqVnpWkt0fxsqaOKq8UyMQtlZhL379DrIfj4T50KEeiux2/t/GJrYV6Ww5WVgsyyKUDjEcPzl8PXY9FB9iJDFCxsycdL8lGcBeqGTo9DNvQ91TM3FPmHeO00++aD3x/O0Mj69mpzXIIUc/pmXiDI9Rkk2w5daVGJWPk0x1UFJyGata/4hgcB3DB/p54asv0BMKYlh5luXa2XHvRmpuv+acztIwLYuv9I/x5x2DuG0Gn1nVoJEGC9ANLxyi2uXkm1taCl1KwSigldeUm5ig+x3vpM/Vyv5lb2XdVbVc/0trTvlhOPnQUaKP9FDxKxvwrNIPukJ74YU7cTiL2Lb1a4UuRWTJCGdz3PlKO0OZDN/f2sq6wMJfJXexG0xnuOOVNhJ5kx9sbaXV7znznUSkIFK5FMOJ4ZmO24H4wEyQO5wYZjg+TCqfOuV+pe7SkwLbVwe41b5qit3FS2qcgmnmCIefZ3TsYcbGHiGV6gcMioq2UFlxMxWVN+F1N9O7fw87H3iA9vbDZAJF052102Ft3semupU004jVmwQD3CtL8G+rxrO+/DWbLQ7Ekvzy3i5GMln+orWB+2vLltSfvRROPBtnJDHCWHKM0cQoo8nRqe3kKCOJkakgNj582vC1yldFjb+Gal/11LW/mhrf9LW/hjJPGTZDXZSzJpeGcA9MdJHt6Se238XwUBm77X0ctvdjYuGcHKM+1sb2mi7MbQZjJXk8ppdW1/VUlN1M+0Evu56IMpotw55P02TrZMd9l1Bx3aXnXE5fKsPvHurl8VCUG8qC/O2aZdS6dfBvIfrE4V7+dzjE4as3LtnF2hTQymmZqRQ9730fg31pdm36LWpbS7njQ5uxv+oUgOxwnOG/34lvUyVl71hdoGrlmFwuxuNPbKW56YOsWPGRQpcjsqT0pjLc+UobOcvih1tbadY8qzkzmslyz852BtNZvrN1JZuDC3S+m4icFcuyiGQijCRGZi7DieFTbr+6ExfAbXdT4a2gwltBuad86tpbfvL29O0FOwvyPFmWRSx+mLHRhxgde4RodC8AXm8jFRU3U1lxE37fRrp37WL3gz+nq7udbLBkurPWjmFCRd7HurImmjP1OCZNDJcd78YKfNuqcDcXn7Lo70Q2x2/uP8rjoSj3VpfyV6sa8DvUXSjnzrIsJtOTjCZPCFwTx4PXE7dfPUYFwGVzUemrnApgTwhcZ4JYXzXl3nKFr/PMsiwyXRGiT/Yxeqif3Y6jHLZNjTJwTY6zdlkVOy5pJGF/iP70C9gsaJoooqYjxv7uHezNvIm4qwZ3OkRr+hdsXX+EojWNp45PCNbMjE44nZxp8R/9o/xV1xCWBX+6so5315XroNIC9r3hEL954Cg/37GKTUv0tb0CWjmFZZr0/+7vMvzYy7xy9Z/gK/Pz1t/bjsfvfNV+FqP/uofcaILq39mOPaAjUYU2PvEUu3b9Mls2f4Xy8msKXY7IknMknuLunW347DZ+uLWVOp1yP+tGM1neurOD3lSGr29ewRUlgUKXJCLzJJvPznTMvTrAHU+NM56curx6UbNjfA4f5d7ymTD3WHhb4a2gzFNGmaeMEncJpe5SitxFiy7YSaWHGBt7lLGxh5mYeBbLyuBwFFNefh3l5dcR8Gzj6M7D7Hn0YXr7eskFi8kFy7GcDrCgLOdjta+BFekavBkn9lI3vq1V+LZV46w4fmZI3rL4wtFhPts1xEqfm3/b0MQav84cWeosyyKRSzCRnGAiPcFEcoJQOsREamLm3+XMx6b3yZm5U76Oz+Gj0ldJhbeCSu/0ta+SSm/lzHWFt4IiV5HCtgXEylsk940RfbKPif5Rdjq7aDMGsbDwpWJcsmUL2265gYno9zja8+/k8wnq6t5GVfD97P36EY60mWRtHoriPayrHWLDteC2TpiDO9kHlnn8AR3e6UXLmk5ZtGy3vZKPtw+zJ5bk5vIiPr2qQWOwFoGjyTSXPXeQv1rVwC/XVxS6nIJQQCunGPnc3zL05f9m181/Qdbu597f305x5alHMGLPDxL+Xjul967Cv0Orly8EnZ1/R1f3P3Hdta/gcGgOpkgh7I4meOvOdmrdTr6/tZVyl2ZBz5aRdJa37mqnL5Xlvzet4MpShbMicqqsmSWUCjGeHGcsOcZ4avp6OsCduZ0aZzI9edqvYTNsFLuKKfFMBbYl7hJKPadel7pLZ/bxO/0LJjDK5eJMTDzF6NhDjI8/TjY7ARgUBTdSXn4dPvc2BvaFOfjEk/T39ZALlpArKsd0ucCC4pyXVmctLekagpYX1/IifFur8G6swO538v2d/fzpsx0MrvBjOGy8J1jEX122dOcGXmyOha2T6cmpS2ZyZjuSiRBOhWfC12OXUCpEOp8+7dfzOXyUekop95RT6imlzFNGqaf0tCHsxdbpfrEzE1niLw0Te2aAkckxdjo66baNgmVR7rRx/Y03svaySxka+l+6uv+BTGaMyspb8cffwYHvTdAbDmBhUJ1sY9M11bT80u3Yvac54JPLwGTvqTNvjwW42QSjzlI+0/x+vl7zRipzET4V/il3eBIYpU0nBLjN4C2Z3z8kOSuWZbH+6X28obyYv1vbWOhyCkIBrZwk9D//w8Af/yn7b/4zxq1S7vrwVupaS07ZLx/JMPS3L+GqC1DxaxsXzIvRpe6Vne8mmw1z2aU/KnQpIkvaM6EY9+3pYJXPw7e2tFDqVEh7oRTOishcyOazU923qXEmU5OE0iHC6TCh1MnXE6kJwukw4VSYnHVq1x9MzbsMuoIUuYsIOqevXUGKXEUUuYqOf+6Ejx37eNAVxDFHi7talkk0uo/x8ccZH3+cychuwMTpLKWs7BoCnh1MtNs5/PROers7p8LaYAWmZ2pUTzDnoYVqWvI1lBgBJqt9/PPIBL/IZ0i4bGQ2l2GVubnE6eZrl7VSrN95C0LezBPPxYln4kSzUeLZONFMlFgmRiQTOSV4PfF2JB15zb/nAF6Hl1J36Ulha7mnfGb7WEf6sdseh+bEX2wyg3HizwwQ2znEUD7ES/bDDDviGKZJY0UZb7jzTuqWNzEy8lM6Oj9HMnmUouAOzLbbOfxkCVGrCEcuQaOth813rqX2jddh2M7vrIVULs+/dXbzhYEIKQt+lW5+J/wIxeOHp8Lb+OjJd/CWTnffnhDaHuvEDdbBedYhF+7+3Z30pTM8fumaQpdSEApoZUbs6afp+fXfoP2qD9Nra+Hm961j9WU1p913/BuHSO4fo/rD23CeprtW5p9p5njiya3U1r6V1as+WehyRJa8R8YjvG9vF6v9UyFtmd6wnrfeVIZ37OpgMK1wVkQKy7IsYtnYTAfhiSFuOB0mko4QzUSJZI5fRzKRMwZeAH6nn4AzgN/pP+Xic/iObzt9M/v5nNMfd/hPuv16YW82G2J84inGxx9jfPyJk7prg/5LiPX76Xh2gJ62dnKBEnJFFeSnO9p8OTfLzQparGqCZhHPGiYPGlmebvaSWRmk3uPiC2sbubr07M/k+v7Ofj774GEGwknqSrx8/NbV3L21/qzvf7GwLIusmSWZS5LIJkjmklPbuePbyVySWCZGLBs7fj29Hc1GTwpj49n4GR/T7/RT7Cqm2F1MkbtoZrvYXUyJu4QiV9HM7RP3c9s1Z38psvImyf3jRJ/qI9MTpcs2zEvGYSLOHHYsNrS2csudd+EP+Bkd/TldXX9PLH4Yt6OFxM6b6Ny/ibzNTTDRx6rGHBvfeyP+lU3nXU/WtPjW0ASf7x6iP53l1ooi/riljhbfqw4IpGPTHbcndt9Ob0/2womjNuxuKF1+6szbsmYoWQ5OHWyYS3/TNcTnuodou2YjgSU431wBrQCQOnKEo/fdT++qOzhcdDU73tjEZXeuOP2+HWHG/m0vwZsaKb5l+TxXKq8lEtnLiy/dzfr1f0dN9R2FLkdEgEfHI7xvXxcrfW6+vXmlxh2ch7Z4infs7iCWz/O1jSu4VDNnRWQRsiyLZC55Umh7UpCbPv6xRC4xE7DFs3ES2QSxbIxENnHGkPcYh82Bx+7B4/Cccu12uPHavbgdbjw2N+W2OOXmAEX5Xjy5QQwsLMNJ3rGC5EQ54QMwui9KLlBKPlhOzu8Hw8BpOliWL6PZqqI4X8K3iw0euaaK7lye32io5A9aanGfoRPt+zv7+YPv7iWZzc98zOu08+l7Ns57SGtaJnkzT9bMkrfy5M08OSs3c53Op8nms6Tz6ZO3zdf4eD5NJp8hY2bI5DOk8+mTgtZXB7HJXJK8lT9zodM8dg8BV4CAc/riChB0BWeC/mPbQVfwpH0CzsBUGOsuxmlznvmBZMnLxzLEXxgi8lQvuUSWA3Szx95Nyglel5Mrr7iSy6++GofDflIwa8/XMfHK9Qx2X4ctl6Mu28mG6xpoftcbsHnOP+jMmRbfGQ7xt91DHE1l2Fbk4/+uqD2nA0PHn1xuenRC9wkBbhdMTN/OxE7eP1h3QmjbNB3kTge43tLXXbhMzuyR8Qj37+nku1tWLsmGDAW0Qm58nO63vZ0hTwu7G9/Jyh1VvOFX1p+yaitMHTUb/sJOrJxJzUe3YTiX3lGNhaqn98u0tX2Kq658Co+nttDliMi0xyYivHdvFyu8br69ZSUVCmnP2u5ognft7sCGwbe2tLA+oEVoRGTpsiyLjJk5KbidCXJzJ99O59OkcilS+dTU9Wtt51Okc2mS+SQ5M4fHsFjpzrPKY7Lak6faOfWeMJozGAy5iPcGsB8pI21WTge2pVh2A8MyqDVLqKGK77XW8dNlxfjTwwTC/4Yn34vdsGMYBnbDjs2wzVxGIlnyJoCBZdkAAywDp93B6uqphdosrJnnD2Bhnbx9wu1j+83cZ/pzM4GrmZsKXadv563pQNbMz9xnttgMG267G6fNidvuxmV34XV48Tl8eB3e4xfn8e1TPnfC5499LuAM4Hf5Fa7KnLJMi3RnmPAT3WTboiStDC9Y++hyhcjbDcpLSrj+pptYt24dNpvByOiDdHX9PfH4EaxEFcO7byfcdyW+xBgtZSE23XclJZdsvqCa4rk8Xx+c4F/7RuhLZdkU8PLx5hpuLp+jBeMsCxLjx0PbE2feTnRBbOjk/d3F06Ft08njE8qaoagebMpOzmQ8k2P90/v4/1rq+GBjVaHLmXevFdDq3eMSYWYy9H3ow0ykvOxb906qlxVx03vWnjacBYg9M0BuJEH5e9YpnF1gIpO7cLtrFM6KLDDXlxXx1Y0reM/eTu7e2cY3NrdoJdmz8MRElF/Z10WJ0863N69khU+nU4rI0mYYBm67G7fdTZmnbNa/fs7MzXR5HusETaYGiEdexh3dSZFnN1blOGwbZyI+yMRgkHy3k+RoGSlnFUPBLAOuEMs7D/O2ieX8fPV6Rqv+kFtD41zibyNcEsLExLSmLnkrz/8M9IBhAeb09dR2xjCp8lWRt/IYGDPhizH939T/J3zMMI7fPmHfY7cdNgd2w/761zY7DmPq+tjHTrx97M/eaXeevG07/ccdhkPrdMiik49mCD9zlNhzA9iTNvqtEV7iEGOeLJYBK1tWcsWVV7JixQosK8/I6AN0dvwjyVQ72UgVI/vfT/zoZmoyR9l2aZjW+27DUVJyQTX1JNP818A4Xx0YZzKX57JiP3/R2sAb5iqYPcYwwF8xdVl2yamfzyQgfPTk0DbUDcP74dADYGaP72tzQknjqTNvj227NDYSoNzlYLnHxc7ImUe0LCUKaJcAy7IY+uSfEt7bxr4b/xKfz8Mbf3MTDtfpg9d8JE3k4R48q0vxrJ39F4VyYSYjuykq2lLoMkTkNK4tC/LNzS28Z28nd77Sxjc2r2CNX92gr+Xrg+P83uFeVvo8fH3TCuoUaIuIzDmHzYHD5sDv9B//YHETVF8JTL13iMfbmAg9zcHuR/F7Xsa9Mg30kEmWkhr0MN7jIhytw5lIc0+kn+db1vPTumaeTwb4zafHuLuskqob1+JaFsSwGTz65KP0h5On1FJf4uUfb7pxfp64yBJnmRaxA8OMPXwE+9BUJ/me3EEOe0eI2U1cTieXbruMSy+9lPLycvL5BD09X6Wr/YvkjRHSkRrG9r8f26EqVi2zWPdbzRRteuMF1ZQ1LR4an+S/BsZ5bCKKAdxeWcwHllWxvdh/xvvPC5cPqtZOXV7NzEOk/9SZt6Eu6H0R0pMn7x+oOXXm7bHw1l+xpEYnbCny8dKkAtoTacTBEjD+5a8w+NnPsffWTxMxg7z149upaHjtOR/j3zxEcu8YNR/djqNCwcJCksmM8+RTl7Ky5RMsX/7rhS5HRF7DwViSd+7uIGVa/NfGZs1TfRXTsvhM5yB/3zPC9aVBvrShiaIluECAiMhiYJpZotG9hEIvEA4/T3jyZfL5qTfVubifcK+LSKiC/a4r+dm6Gwn7Aqwa6uHO9l5WpQLUF5URam3kw68MEs8VfgatyFKTGo4w+OBezMMJ3HkPYTPMK7ZDDPjTpPI5SktLueyyy9iyZQsej4dUapwDL/wDE8nvYjjjJMZaiOy9moqRUtbdspqGO6/HcJ3/QXXTsnhxMs73RsL8aCTMeDZHrdvJfbVl3FdbTv3FdMA+MXFyaBvqPj73NtJ/8r6uwAkzb5tODnCLl4H94uqv/GLPCJ/sGGDvVeupdC2tUS6aQbtExR5/nJ7f/ADt13+cXrOR235jAy1bX3vGR7ozzOiX9hK8cRnFb2iav0LlrIyN/YLde97Ptq1fp7T0skKXIyKvoyeZ5l27O+lPZ/jC2kbuqiotdEkLQjyf56OHevnhSJhfqi3n06sacL7GuB0REVl4TDNHLHaAUPh5wqEXCIVfIJ+fWmAnHvXzP7l38mjJG7CbJtuPHmZDfydB00VdrhR30s3elI0na2v58JvXK5wVmSPpyTh9P3uF7P5JApliTMvkoNlGV3GI4XwCy7Jobm7m8ssvp7W1FcMw6N79DJ0HvoRZ8Tw2R5ZY30aMvRtYUbue1nfdgLu25vzrMU2eDcd4aCzCz8Ym6U9n8doMbqko5t7qUm4sK8Kx1F4PZlNToxNePfM21D11yaeP72vYoWTZqV23x7bdi68Z5PlwjLt2tvPVjc28oaK40OXMKwW0S1C6vZ3ud76LvtVv5lDwGi55UxOX3rHiNfe38ibDf78TK52n+ne2Y3uNEQhSOB2dn6e7+5+57tpdOBwL5JQPEXlNY5kcv7Kvixcm43x0eTUfb67BtoROXXq1rkSa9+3r4nA8xR+11PGBZZWa2ycisshZVp5Y7BCh8AuEJp5jYuJ5+q0AX+N97DK2U50d4o6hR6kcjTMZL8XKO6kyi6nIBqgLBFl983rKL1uv3wcF8v2d/Xz2wcMMhJPUlXj5+K2rF21wbloWkVyeWN4kmTdJmCaJY9t5k6RpkjEt8pZFfnp/02LmNoDDALth4Jy+2A0Dp83AYRh4bQZ+ux2f3Ybfbpu59tvtC+Jgczoep+ehl0juHKMoWYrD5mQsP8rh4iH6nDGiyQRer5ctW7awfft2KioqGGkfZv9j/0XC/zCe6jbMvINsx1oqY1ez9s13E1iz8rxqyZkW+2JJnp+M8Uw4xpOhGIm8iddmcE1pkLuqSri1opiAzqA6PdOE6OCrQtsTOnGToZP391eeGtqWTd8OVC/I0QnxfJ5VT+7lQ43VfGLF0lpfRwHtEpMLheh+xzsZtdWys/k9NG+u5LZf3/Cai4IBRJ/qZ/LHnZS/ey3e9RXzWK2crZ273ksmM8pll/6k0KWIyFlKmyafONzHN4cmeFNlMX+/phH/Enwx+vOxSX7r4FHsGPzL+uVcX1ZU6JJERGQOWJZJPN7O5OQr/KS/h3+ObWbIqGaL9RJvy3+DqkiEWLSWsVg5kUglznQJFdkSSvJultWWser2rRStWq7Adh58f2c/f/DdvSSzC3f0RDJvMpzJMpjOMjR9Gc5kmcjmCGXzhI5d53KEs3nMAtXpNAyCDhvFDjslDgclTjslDjslTsf0tZ1ih53SmdsOSqc/7rLZzvtxoxPj9DzxMoldIxTHyvA5gqTMFN3Fg/SXpDg6PoRpmjQ2NrJjxw7Wrl3L2JExDj34LBM8iW/lM7gCY+RjQbxD21iz5b1UXHLNOf37syyL3lSGA7EU+2NJXorEeWEyTjw/9d1Y7nFxXVmQN1QUc1VJAK/9/J+vTEuGTw1tj41PiPSBdcK/BKfvVSMTTtguXgaOwo2UuOnFQ6zyefiX9U0Fq6EQFNAuIVY2S8+vvp/xQ328fPkfEaz0cc/Ht+PyvPbMknw0w9DfvIRreREV79MR7IXIsiyeeHI7VVW3sXbNXxa6HBE5B5Zl8aW+Uf60fYBVfg9fWt/EKr+n0GXNi4xp8jddQ/x9zwibAl7+fUMTjV53ocsSEZF5kjZNvth9lH/oDRE3Da7Iv8JbrS9TYx8EIJMIEIlWMRktIxqtwB5pIJgqoTjnYEVzJSvfsJVga6Pen8yBqz7z2ou3Pf3787N4WzJv0pPKcDSZ5mgyw9FUmu5khr5UhqF0lvAJc4uP8doMypwOSp0OSp1ToWfpdPhZ6rQTmO5y9dlteG22k7ZdtqmuWLsBNgxs0x2zxw6d55lauCpnHb9kLYusaZGc7shN5E3iM9f5mdvRvMlkNkc4lyeczROeDo0nc68fHPvttqnn4Ziqv+RVz6fEcfx5ljhs5Ab7mHx2F7n9IcoyVRS5yjEtkyH/GH01Sboiw0RjUTweD5s3b2bb1m2kepIceXAfw+l2fCteJNjwMjZHlvxoPc91XcJ/ha+hqqToNTuoLctiIpuf+V71pjL0pDIciac4EEsSnQ5jDaDV5+GKEj9XlAS4rMRPrfsimim7GOQyEO45IbR91fiE3An/5g0bFDecOvP2WCeuZ25HD8Ry+SXZRa2AdomwLIuhT/4pY//7A3bd9tdk8PC2P9hB0RkW+5r49mESu0ep/uh2nFoYbEFKJLp49rmbWbPmL6mve0ehyxGR8/DYRIQPHDhKMm/xl6vqeWdN2UX9hrM9keIDB46yJ5rk/toyPtXaoK4JEZElKpzN8U89I/x73yhZy+Ke4ixviv0ce+hJ8vajOLwZACzTRjxeQjRaQSxSAZPLcYzVUWLaaV1Zw/IbN1G8pumi/v05X5p//yecLg0wgK7PvGnWHsec7rA8HE9xJJ6iLZHmaHIqiB3KZE/a12+30eR1sczjosbtotblpMZ9/FLrdhK02xbV99+0LKK5/FRwOx3ehqaD3FB2KsSdmA5zj318InvmjuBA1iKYz+M18thyScxEHIdpUh7wU1tWjjdukewOk0pk8Jb14Ctvw+GJgmkn6FjFhHMb392TI4MFdgPLZuBw2rl0ZTmVpV7GMznGs9OXTI7Mq7KjMqedFq+HdQEP6wNe1ge8rPF7luSZYouGZUFs+DQzb6e3E2Mn7+8tO/3M27JmCNTABXR/L2UKaJeIif/+b4b+/C849Ma/YDhVwp0f3kL96tdfmCbTG2Xkn3YRvK6B4tub56lSOVeDg9/jwMGPcdmlDxAIrC50OSJynobSWT5w4CjPhGO8tbqUz6xqIHiRvZC1LIuvDY7zx20DeGwGf7NmGW+qLCl0WSIisgAMp7N8/ugwXxsYw4bB22pK+WBjNYGJIxw99ADjo8+TtXrwlMewOafCu1zOQSxWTiJaST7USG6kkWCsmOZl5Sy7fCXVl6/D5lxaq4DPhtnuoM2ZFkdTaY7EUxyJpzmSmApk2xMpkubx3KHa5aDZ62a5102T1zV17XHR6HVT7rQvqvB1LliWxejRLrr27KR7bwfJCQe+ohYMXyWTLoOxoMlQJfSTYjiRJGl3kPf5MdxeMjmDlGmRttvIOgysc/mztCzIW9gsaAh6KHc6qHA5KHc6KHc5qHY5aPS4afS6aPS4lmTn40UvFTm+SNmrxyeEe8E6oaPd4YGS5afOvC1thtLl4NAZc69FAe0SEH/uOXp+9f30XPMB2lnDte9cxcbrG173PpZlMfrFPeTGk9R8bAe21xmDIIV1+MgnGRz8LtdduxPD0C9DkcUsb1n8Xfcwn+seotbt5K9XL+Om8otjJmtnIs0njvTyZCjGtaUBvrC2Uae2iYjIKY4m0/xL7yjfGBwnY1q8ubKE315exaagD8s0Gevt5uihXzAy8Ay5bA/O8gjO4gkM21RPYTbrJh4tJxOpJT3egGu0knpPA8u2LKfhhs24SpfWquDn40Jm0KbyJgfjKfbFEuyNJtkbTXIwniR1QhBb73ayyu9hld/Dat/UdavPTbFT7zlfLR4OcXTvLo7ueoXwgT7KrVrqfa0Uu6bWhsmVwESLRXt2kLaudrLZLIFAgPriOtz9DkJDHlL48Fa0U17/C/zNe8GVxmaroKT2rZRX343P14xlgcXU5fK/fBjLgumV0sCa6p6e7Q5quUjkszDZ+6qZtydcZ+Mn7GxAUf10aLv85PEJZc3gff0mwoudAtqLXKavn+5772V42ZXsKX8T666p4/r7Vp/x6GNizygTXz9EyT0rCVy6tFbOW2xefPEt2Oxetm/7eqFLEZFZ8tJknI8e6qEtkebe6lL+rLWeskX6piVjmvxzzwifPzqMyzD4w5Y63lNXjm2Jd8GIiMjrG81k+bfeUb7cP0Y0b3JlSYD31ldwe0UxzukFji3LYmKgj94DOxnueJZs6ii2kii2kjHsgTFs06FtPu8gGa0kFaqH0SqKU/XUVK+l/rK1lG9uwWZXk8OrfX9nP5998DAD4SR1Jd7TziCN5PLsiyanwthYkn3RJEcSKfLTUUKRw8aGgI+NAS9rAx5W+720+tzqsHwdyWiEvoP76D2wl/79+zFGTOr9rTT4V+G1B7AMCxo8hBpM2tP9HO44QjqdxuPyUE4x9lE/yUQ1GA58RW1U1j2Or/UQljeCzealqvJWamrupLT0Kmy207+2XAgziOUiYVkQHzu56/bE8Qmx4ZP39xQfD2tbboRt7ylI2YWigPYiZiaTdN93P+PjJi9v+jBVTUXc9ZGt2B2vPw/EypoM/e1L2NwOqj60FcOmN9ELVT6f5vEnNtO47H2sXPmJQpcjIrMobZr8Xfcw/9AzTLHDwSeaa7ivthzHIvmZbFkWPx+P8KmOAdoSae6oLOFTrfVUu3WqqYiInL1ILs9/DYzzlf4xelMZqlwO7q8t59115dR5Tj4Tw7IswsOD9O3bx/j+DlKTfeSLQpilo5jBATyBMRyOHACmaSMVrSI9UYdjvIoio46qunUsv/wSAivql/zp9K82msmyN5pkXyzJnmiCfbEk3cnMzOerXY6pMDboZWPQy4aAl0aPS3+OZ5CYDE8HsvvoO7CX+MAEtb4V1PlbqPY24cAJDgNjZYCBsihd8QHauzrIZDI4DDuBVBFGrAZ7tgLDylMeeJGylbtxNXeQd4UxDDulpVdSW/MWKipuxuHwn7GmC+mgFjknmfjJHbcnBrkrroc3f77ABc4vBbQXKcuyGPi9TzD+s1/wyhv+CsPl5m1/cAm+ojOfThp5rJfIz7qpeP8GPCuXdov5Qjc5uYuXXn4rGzf8M1VVtxa6HBGZA/tjSf7gSB8vTMZZ7ffwxy113FgWXNBveF6ZjPNnHQM8NxmnxevmkyvruKVCp5SKiMj5y1sWv5iI8pX+MR4Zj2AA15UFube6lNsqil9zAaJkNMLgoUNM7DpKrGeShH2cVNkQ6aIenIFh/IEJXK70zP7ZVJBsqApHpBKfUUd59UYaL7mRoobXHxF3sbCmF+461hF77PrERbuWe1xsCHrZFPCxIehlY8BLlQ7AnpFlmkwM9jN45BADbYcYOHyQUF8/FZ4G6oMraShag88MAGArcpFb4aHXN0H7eA/dPd1YloXDdOBKluFMV+HMlBBM91HVsJ/gul7M6nayhDAMJ2VlV1FVeRuVlTfjdJ77e/qz6aAWkdmlgPYiNf6VrzD8mb/mwB1/xWgywD0f205105nnGOajGYb+5iXcK4qp+OX181CpXIje3q9wpO3Pueqqp/G4awpdjojMEcuyeGBskj/vGKA7meGqkgAfWl7NtaWBBRPUWpbF85Nx/qlnhIfGI1S6HHysaarr17lIun5FRGRxOJpM8/XBCf53aIL+dBavzcbtlcXcU13KtaUBXK+zgriZzzPa1sn4S13EOieIJjNEvGEiwS6ygQG8/hB+fwi/bxKbfaqD0LIMctFyrEgl7mwNxcGV1K6+gqr1l+NYxAve5EyLtkSK/bGpzti90ST7Y0nCuannbTeg1edhQ+B4V+yGgFezYs9SKh5jqP0IA0cOMdh+mMG2Q6TjcYqdFdQVt7KsdC3FZjk20wZ2A0dTgPHKDJ3pYdq725hMRgCw5zy4UpW40+UEI0mqgkcp29iLc+UQcfshTDOFzeahvPxaqipvo6LiRhyOYIGfvYicKwW0F6Fji4L1XvdB2szV3PBLa1h3dd1Z3Tf03TbiLw1T/dFtOCt9c1ypXKh9+z9KOPQ8V1/9TKFLEZF5kDFN/rN/nH/qGWEok2VjwMsHG6t4c2VJwUYfZE2LB8cm+efeEV6JJChz2vm1hkp+vaHyNbuZREREZoNpWbwwGec7wyF+NBImnMsTsNu4oayIN1QUcVN50VnNcE+NRxh7sZ3IkRHCo1HCZooRW5iwvw97YAS/L4zfH8bvC+PxRTGMqffKVt5OPlaGPVmB115PSeVaqtddSUnFOhyOwFw//XMSz+Vngthj14fiKdLTi3e5bQZr/VNB7MaAlw1BL2v9Xrz21x+PJ1NS8Rij3Z0Md3Uw0t3JcGc7EwN9YFkUuSport1CXbCFQKYYW3bqNZu9zEOiwU5bvJeO0aOMp8OYhgmWgTNTjDtdRHkoS10gQenGCTyrQiQ8bcQT7QB4PMuoqLieivIbKCm5HLt98R4sEBEFtBedbH8/Xfe+jbH6S9hZcRfrrqrlhnevPav7ZgbjjPz9KwSurKPkjpY5rlRmwzPP3kggsJpNG/+l0KWIyDxKmybfGQrxz70jtCfSVLoc3FNdyjtqylgX8M5LDftjSb49OMF3hkOMZXMs97j4zcYq3l5Thk9v5kREZJ6lTZPHJ6L8fCzCz8cnGcnksAGXFPu5ujTAlSUBthf58bzG76hjp3T3h5MEMNho5rnBbrLJZZDMJhmzxRi1RQjZJ3D7w/j8YfyeSXyeSby+KB5/FGN6UTIAM1GELVWJ22iguHw1Va2XUFKxHperak7PfslbFt3JNEfiKQ7HU+yPTXXIdiXTHHuHX+qwsyHoZX1gKoxdH/Sy0utZNHPuC8myLOLhEGM93VNh7PQlPDwIgIFBTcVKGqvXUeVpxJvwY6Sm/uRtRS7CgQwdsX56EiOEiJFzTM3xteU8eBM+yhMWy/0mVVuzOFdPEuUg0dg+LCuPzeampHgHZeXXUlF+Az7figVzJpWIXDgFtBcRM5mk+/77CY+keGnbxymtDfCWj23D4TxzB5NlWYz9xz6yAzFqPrYDm08zhBa6bDbEE0/uoKXl92ha/huFLkdECsC0LB4ej/DNwQl+Pj5JzoJ1fg83lxdxQ3kRO4r8szZeIG2avBCO8+hEhEfGoxxJpHAaBm+oKOLtNWXcXF6EXW8SRERkATAti93RJD8fm+SRiQj7oklMwGUYbCvycUVJgM1BH5uCXmrdTn6wa+CURZGO8TrtfOauDdxeU0yyO0z08CCj/aOMp6OMGpGp0NaIgc3E44kScIfwu0N4vVG8/jieogh25/HFtKysC1JlOK1q/L5llNSup7RuPX5/M253NYZxdmefZEyTo8kMRxKpmTD2SDxFRzI90xUL0OhxTY0mmB5RsD7gpc7tVLB3FhKTYcZ6exjvO8p4X8/Udu9RUvHYzD4V1ctpqt1Ipb+RQK4YWxjITAX1eafFMFG6MmP0EyXmjGE6UgDY8nYCKQeVOGlZ7qJqY55cxRiR+F6isYOAiWHYKSraTGnpFZSVXklx8VZsNnXJilysFNBeJI4tCjbx04fY/cbPkTadvP3/XkKwzHNW908eGGf8qwcouWMFgas0/HsxGB9/kl2738vWLf9FWdmVhS5HRApsPJPjeyNTp3i+FImTtyBgt3FJsZ/NwalVlVd43Sz3ul+3w9WyLCK5PL2pDPtjKfbFEuyNJtkdTZI0TVyGweUlfm6rKObu6tKzOnVURESkkCK5PM+HYzwzfdk7HdgCVDgdJEYTpCfS2OI5jHgOI5HDyB7vhq0v8fL079940tc0E1kyfTEyPRGinWMM9g8yloswZoswbkQJG3EsA8DC7Ujgd45OBbeeBB5/CncggSsQnZlzC1MjE4zp8NbrbcSo2kS8bA0jVDGQC9CTznM0maE7lWYglcU8oZ5lHherfB5W+d2s9ntY5ffQ6vMQ1Lih15VNpQgPDxIaGiA8NEh4aIDQ0ADjvT0ko5GZ/dx+P5X1K6ivbKXcV4/fLMY+YWCFp8J3C4uIlaY7P0m/ESfkiJByRLDsU4ur2fMGpaabZWV2mtY5CbYYxNKHmZzcSSYzMrWP3U9R0WaKi7dRXLyVkuIdC25UhojMHQW0F4mJ//xPhj79Gdru+gz9kSB3fngLDWvKzuq+Vt5i+O9eBqD6I9swdGrqotDd/S90dP4N116zE6fzzAvAicjSEcnleSoU5bGJKC9OxjmSSJE/4dd6scNOicNOkcOOzQC7YZDKm0TzJqFsjlj++Fs+r81gXcDL5qCP68uCXFUS0GxZERFZ1BJ5kwOxJLujCfZEk3y7bRjL74ATzzrJmBjJHEY6j5HK87HrVlLtdlLhdBCc/h0atNsocthx22w4AMJpcoNxMgMxUv0RhvqHGE6FGLUlGLXHGXUkiTsg7XCRdjjJGgamM0vebZL2ukh4fUTdQSadxUzaiskZJ5/VWGRNUpUPUWtFqbfnaQn62FBVybrSGsr9DVoY6jRy2Syx8TEiY6NEx0eJjo0yOTpMeGgqlI2HJk7a31dcQklNHZU1y6kqWo4vX4ojZMMI5bClLQym/o7EzSw9VpxBokzYosQcEXKOONOfxo+dhmpoWGGnqDqDSQ+x2MGZMBbA62mcCWOLi7fh96/CZtOBb5Gl6rUCWv1UWETizz3P8F9/luEbf5O+ySBX3NNy1uEsQPzlIXKjScrfvU7h7CISje7H62lUOCsipyhy2HljZQlvrCwBpt6IHomn6E6m6U6mGc3kCOXyRHJ5TMvCtKDK5SBgt1PitFPvdlHncbLW76XF59boAhERuaj47DZ2FPvZUewH4KUftNM3mcTy2rF8Diy/E8vvmLrtdUCpm7/qGjqrr+00DBxuyDdDpqkKqDqr+7lyWXzpFP5kivJQnOWJIYrS45Rnh6jJ91PDAMWeOK6iPK5AGmcggS1mYsZg3/TXMDNuSJVgz5fhNMrxeqrxlzRQVNNCsKIJj6cap7MMw1j87/nyuRyJSJhEOExiMkx8Mkw8HCIxGZ4JYqPjY8TDoVPueyyErV+zCb+jFF+2CFfSizPlwpG2407ZcfVMHYy2yBMyE/QTY5gok0aIhD1G2p0FA+z2DEWBGKuqLMprTLzeCBhDpFK9WFaWDDAesuP3raSs7CqCgXUEg+sIBNbpfZyInBUFtItEdmiI/o9+lOjqazhobaBlWyVbb2k86/ubmTyRh3pwLS/Cs+7sQ10pvEh0H0VFGwtdhogsAj67jS1FPrYU+QpdioiIyILz8VtXT82gTeQhkYex9MznvE47n75nI7dtqmU4k2Uimyc6fZAzkp/azpgWWcsia1rkraltp2HgtBm4DNvUtc3AYRgE7TaK7Xb8iRyBUAbfeBr3cJzkYJTR0BghK07YFidsTF2yhps8K+hnBQNRcA2DLZMmn5zEZUTwuCK43XHc3iSuQAZXMI4rEMHhayfjyTKZgoFuoHvq+Vh5G/mkFzPlh3QQW64YByW4XOV4vRX4ihvwlzUQLF+Gt6wat8+NbZYXD7Msi1wmTTadPn6dTpNNp0gn4qTjcVLxGKlYjHQ8Rjpx/HYqFiUeDpGKRU/7tR1ONx5/EW53kKCvnhL/SpxWELdZjNMM4rYFcNvceBMOAikDz/RzM7GYJEm/NcG4NUnEihFzJkm7o9g8cTzuGB5PjKpghqLiLB5PHMOYwLKOz6M1DAeGbTl+XwtVVW/A71uB39+K378au12zY0Xk/CigXQSsTIb+j3yUpOVl7/J3UFLi5cb3rD2nge+xpwcwoxmK71+jQfGLSDY7SSrVS33dOwtdioiIiIjIonb31qk1OD774GH6w0nshkHesqgv8fLxW1fPfH65181y7yw+8PKTb67MW+RDKXLjSXLjKbJjCSLDISYmJghFJ5kkQcRIEHElibh9xIwqZuLBDLjCDjwRB04sjHQaMx3BZk5gt03icEZxupO4/FmcvhwOXxynfxKbrws8JpmpL8EkQGjqYpmQSznIpZzkU05yKQf5lJN8xoF57JJ1YGUdmFknZsZOPmMnnzGw8gYYU2GsZVlgmZhWHtPMYZq5s/4jshlObDYXNsOFYbgwDA9Qj9ftwzL8WLYgbmcpXrsfn92Hz+7Aa0yNaPLapq49NgMLi6SRIOoKMekcY9QZIuWeJOuKkXMmMB0xnK4kLlcStzNJgyeF05nEMMyT67F58Hga8Hqb8Xiuweupx+drxudrwettxGbTYtsiMrsU0C4Cw3/zN8R37+PgXZ8nnzK4/Tc24PKc/bcuH88SfawXz9oy3E3Fc1ipzLZodOpEpmDRhgJXIiIiIiKy+N29tX4miC0Uw27gqPDiqDieApcyleNaeYv8ZJrcWJJ8OE02lCQ+HmUiNEEoEiKSiBHLpYgbKWJGmrgtT8ZXBJxwGr0JnoQbX9aNJ+HGM+nCZdiwmylsVgQbEQwrjEkUw5bAZk+AM4XhTmN3ZXCVpbB5othdOQzb669ZY5kGZs6Ombdj5eyYOcf0thMz78TKOzBzLizTAZYDy5q6tlkObDiwW05spgM7NhyGid1m4jAs7LYsNlsGm20Smw1MwyRvy5K3p8jbM+RtaTL2NCl7hgl7FsuexbBlsdnT2E9YkM0/fZmp1zKw2YpwOsvxepfj81bjclfhclXgdlXh8Tbg9dTjdJarsUlE5pUC2gUu8sADhL76X/S++Y8YD9u47TfWUlrjP/MdTxD9RS9WJk/xrU1zU6TMmWh0PwBFwfUFrkREREREROaaYTdwlHlwlHlmPlYCHIuULcvCjGfJh9PkJ9PkY1lS4QThUIhIJEIkHiWajBHPJElm0iSNDGPESBoZssax4NINVE9fpjiw4zKcuG3TF7sLp82Ow2nhdORwOrM4HBkcjgw2exa7PYVhS2HZkjjIYhlZMDJgZMGZAVcWbBksI4NljwE5MEwsw4QTL0xdGzYLyzIwLYM0BlgGFgaWNRWqgoFp2jBN+9Ql78A07VimCzs+7HhxGD5sRhFOZyk+bwXBYDVFRTX4fJU4HEU4nUU4HCVaoEtEFiT9ZFrA0p2dDP7R/0f4knvoiNWy+aZltGw9u+Hzx+RCKWLPDuDbVo3zHINdKbxIdB8eTz1OZ2mhSxERERERkVnw/Z39fPbBwwyEk9S9arzCmRiGgT3gwh5wQUMQgABQcZp9rZyJmcxhpnJYqTzpaJLoZJRYJEoyniSVSJJMJUln0qRyadK5DOlchlQ+QyKXJGfmySbz5K08OaYux/tpPdOXkgv948Bhd+ByuXC5XLjdblzu49terxefzzdzfeJ2IBDA7dbMVxG5OCigXaDMeJy+D32IRFEde8tuobouwBVvaTnnrxN56CgYUHTL8jPvLAtONLqfoLpnRUREREQuCt/f2T+1UFl2qpu1P5zkD767F2DWRy8YDhv2oAt70AWAiyBBzq3h50SWZZHP58lms2SzWUzTxDTNmfmzxy4nfsxms2G321/z2uFwYLPZZuspi4gsWgpoFyDLshj84z8h2d3HwTs+jy1j49Zf24DdcW6/uLJDcRI7Rwhc04CjREcWF5tcLkoy2U1t7T2FLkVERERERGbBZx88PBPOHpPM5vnsg4cLPhv3TAzDwOFw4HA48HpncxU1ERHRoaoFKPT1rxP5yU/ovfNPCIUsbnnfeoInzCA6W5M/68ZwOyi6vmEOqpS5Fo0eAFAHrYiIiIjIRWIgnDynj4uIyNKggHaBSe7ezfBn/orQ9b9M50Qx229bzvIN5ef8ddKdYVKHJghe34DN55yDSmWuHVsgLBjcUOBKRERERERkNtSVnL7z9LU+LiIiS4MC2gUkFwrR95GPkm5Yx17n5dS1lnDpHc3n/HUsy2LyZ93Yi1wEr6qbg0plPkSj+3C7a3C7TjfyX0REREREFpuP37oar9N+0se8Tjsfv3V1gSoSEZGFQAHtAmHl8wx87OOkQ1H2b/lNnF4Hb3j/emz2c/8WpQ6HyPRECd7UiPGqX/6yeESi+9U9KyIiIiJyEbl7az2fvmcj9SVeDKC+xMun79m44OfPiojI3NIiYQvE5I9+ROzppzn6js8xOZLnzo9swl987gt7WZZF5Ofd2Ms8+HdUz0GlMh9yuTiJRAfV1W8qdCkiIiIiIjKL7t5ar0BWREROooB2gSi+8046RgJ0v2LjsjubaVhdel5fJ7V/nOxAnNK3rcI4j+5bWRhisYOARZE6aEVERERERERELmoKaBeIsb44L+5x0LiuhO23NZ3X17BMi8mHjuKo9OLbWjW7Bcq8ikb3ARAMri9wJSIiIiIiIiIiMpfUYrmAVDcXcfOvrMOwGed1/+SeUXLDCYpubjzvryELQzS6H5erErdbYypERERERERERC5msxLQGoZxm2EYhw3DaDcM4/dP83nDMIy/n/78HsMwts3G415MKhuDvOV3t+ENuM7r/lbeIvJwD45qH96NlbNcncy3aHS/umdFRERERERERJaACw5oDcOwA/8E3A6sA95lGMa6V+12O9A6ffl14F8u9HHlZImdI+TGkhTfslzds4ucaaaJJzoIBtYWuhQREREREREREZljs9FBeynQbllWp2VZGeCbwF2v2ucu4KvWlOeAEsMwamfhsQWwciaRR3tw1gfwrC8vdDlygeLxDiwrRyCwptCliIiIiIiIiIjIHJuNgLYe6D3hdt/0x851HzlP8ZeHyU+kKLplOYah7tnFLhY7BEBAHbQiIiIiIiIiIhe92QhoT5cIWuexz9SOhvHrhmG8ZBjGS6Ojoxdc3MXOyplEH+3F1RjEs7q00OXILIjFDmGzufF6lxe6FBERERERERERmWOzEdD2ActOuN0ADJzHPgBYlvUly7J2WJa1o7JSi12dSfyVYfKTaYpuVvfsxSIWO4TfvwqbzVHoUkREREREREREZI7NRkD7ItBqGEazYRgu4J3AD1+1zw+B9xhTLgcmLcsanIXHXtKsvEn0F704lwVxt5YUuhyZBZZlEY0d1PxZEREREREREZEl4oJb9CzLyhmG8VvAg4Ad+H+WZe03DOP/TH/+i8ADwBuBdiABvO9CH1cgsXOEfChNyV0r1T17kchkRslmJwgqoBURERERERERWRJm5Rxqy7IeYCqEPfFjXzxh2wI+OBuPJVOsvEXkF7046wOaPXsROb5AmAJaEREREREREZGlYDZGHEgBJHaNkB9PUXRjo7pnLyKx2EEAAoG1Ba5ERERERERERETmgwLaRcgyranZs7V+POvKCl2OzKJY7DBudy1OZ3GhSxERERERERERkXmggHYRSu4ZJTeWJKju2YuOFggTEREREREREVlaFNAuMpZpEXm0B0e1D+/68kKXI7PINNMkEp1aIExEREREREREZAlRQLvIJPeNkRtJUnRTI4ZN3bMXk3i8A8vKqYNWRERERERERGQJUUC7iFjW1OxZR6UX74aKQpcjsywWOwRogTARERERERERkaVEAe0ikjocIjsYJ3jdMnXPXoRisUPYbG683uWFLkVEREREREREROaJAtpFJPpYL/ZiN74tlYUuReZANHYQv38VNpuj0KWIiIiIiIiIiMg8UUC7SKS7J8l0RwhcW4/h0LftYmNZFrHYIYIabyAiIiIiIiIisqQo6Vskor/oxeZ34L+kptClyBzIZEbJZicIBFYXuhQREREREREREZlHCmgXgcxAjNThEIEr67G57IUuR+aAFggTEREREREREVmaFNAuAtHHejFcdgJX1Ba6FJkjxwNaddCKiIiIiIiIiCwlCmgXuNxYkuTeMfyX12LzOQtdjsyRWPwIblc1TmdJoUsREREREREREZF5pIB2gYs+0Qd2g+DV9YUuReZQPN6G399a6DJERERERERERGSeKaBdwPKRNPGXh/Fvr8Ze5Cp0OTJHLMskHu/AH1BAKyIiIiIiIiKy1CigXcCiTw2AaRG8tqHQpcgcSqX6MM2kOmhFRERERERERJYgBbQLlJnKEX9+EO/GChzl3kKXI3MoFm8DIKCAVkRERERERERkyVFAu0DFXxzCSucJXqPu2YtdPHYEQB20IiIiIiIiIiJLkALaBcjKm8SeGsDVXIxrWbDQ5cgci8fbcLtrcTj0vRYRERERERERWWoU0C5AyT1j5CfTBK+tL3QpMg9i8TaNNxARERERERERWaIU0C4wlmURfaIPR6UXz+qyQpcjc8yy8iQSHRpvICIiIiIiIiKyRCmgXWDSHWGyg3GC1zZg2IxClyNzLJnswTTT+P2rCl2KiIiIiIiIiIgUgALaBSb6RD+2gBPflqpClyLzIB5vA8AfUAetiIiIiIiIiMhSpIB2AckOxUkfCRG4sg7DqW/NUhA7FtD6Vha4EhERERERERERKQSlgAtI9Ik+DKcN/2W1hS5F5kk83obHU4/D4S90KSIiIiIiIiIiUgAKaBeI/GSaxO5R/JfUYPc7C12OzJN4vE0LhImIiIiIiIiILGEKaBeIzEAMw2kjcFVdoUuReWKaOeLxTgW0IiIiIiIiIiJLmKPQBcgU79py6v7wMgynvdClyDxJJo9iWRkCCmhFRERERERERJYsddAuIApnl5b4sQXC/KsKXImIiIiIiIiIiBSKAlqRAonF2wADv39loUsREREREREREZECUUArUiDx+BG8nmXY7d5ClyIiIiIiIiIiIgWigFakQOLxNvwBzZ8VEREREREREVnKFNCKFIBpZkkkuvFrgTARERERERERkSVNAa1IASSTR7GsLH6f5s+KiIiIiIiIiCxlCmhFCiCe6ADA728pcCUiIiIiIiIiIlJICmhFCiAR7wTA51tR4EpERERERERERKSQFNCKFEA80YHbXYPDESh0KSIiIiIiIiIiUkAKaEUKIJHoUvesiIiIiIiIiIgooBWZb5ZlkUh04Pdp/qyIiIiIiIiIyFKngFZknmUyY+RyUXx+ddCKiIiIiIiIiCx1CmhF5lki0QFogTAREREREREREVFAKzLv4olOAPwKaEVEREREREREljwFtCLzLBHvwG734XbXFLoUEREREREREREpMAW0IvMsnujA52vGMPTPT0RERERERERkqVNCJDLPEolOfL6WQpchIiIiIiIiIiILgAJakXmUzydJpfo1f1ZERERERERERAAFtCLzKpHoBsDnVwetiIiIiIiIiIgooBWZV4lEBwA+ddCKiIiIiIiIiAgKaEXmVTzRCRj4vE2FLkVERERERERERBYABbQi8ygR78DjacBu9xS6FBERERERERERWQAU0IrMo3iiE79f4w1ERERERERERGSKAlqReWJZJolEJz6fFggTEREREREREZEpCmhF5kkqNYhppvBrgTAREREREREREZmmgFZkniQSHQDqoBURERERERERkRkKaEXmSXw6oNUMWhEREREREREROUYBrcg8SSS6cDiKcDrLC12KiIiIiIiIiIgsEApoReZJIt6Bz7cCwzAKXYqIiIiIiIiIiCwQCmhF5kki2Y3P11zoMkREREREREREZAFRQCsyD/L5JOn0ED5vU6FLERERERERERGRBUQBrcg8SCSPAuDzNRW2EBERERERERERWVAU0IrMg2SiGwCvAloRERERERERETmBAlqReZCYDmg14kBERERERERERE6kgFZkHiSS3bhcFTgcgUKXIiIiIiIiIiIiC4gCWpF5kEx041X3rIiIiIiIiIiIvIoCWpF5kEh2a4EwERERERERERE5hQJakTmWy8XIZEY1f1ZERERERERERE6hgFZkjiWTRwHwqoNWREREREREREReRQGtyBxLJLoB1EErIiIiIiIiIiKnUEArMscSyW4AfL7lhS1EREREREREREQWHAW0InMsmejG7arGbvcVuhQREREREREREVlgFNCKzLFEslvzZ0VERERERERE5LQU0IrMsUSiG59X4w1ERERERERERORUCmhF5lAuFyWbncCnDloRERERERERETkNBbQicyiR6ALQiAMRERERERERETktBbQicyiR6AbA520qaB0iIiIiIiIiIrIwKaAVmUOJ5FEAvJpBKyIiIiIiIiIip6GAVmQOJRPduN212O2eQpciIiIiIiIiIiILkAJakTmUSHZrgTAREREREREREXlNCmhF5lAi0a35syIiIiIiIiIi8poU0IrMkWw2TC4XxqsOWhEREREREREReQ0KaEXmSCLRDaAOWhEREREREREReU0KaEXmSCLZDaAZtCIiIiIiIiIi8poU0IrMkWSyBzDwepcVuhQREREREREREVmgFNCKzJFk8ihudw02m7vQpYiIiIiIiIiIyAKlgFZkjiSTvXi9jYUuQ0REREREREREFjAFtCJzJJnsUUArIiIiIiIiIiKvSwGtyBzI55NkMqOaPysiIiIiIiIiIq9LAa3IHEgmewHUQSsiIiIiIiIiIq9LAa3IHEgmewAFtCIiIiIiIiIi8voU0IrMgWRquoPWoxEHIiIiIiIiIiLy2hTQisyBZLIHuz2A01la6FJERERERERERGQBU0ArMgeSyR683kYMwyh0KSIiIiIiIiIisoApoBWZA8lkr+bPioiIiIiIiIjIGSmgFZlllmWSSvXi9Wr+rIiIiIiIiIiIvD4FtCKzLJ0exjQz6qAVEREREREREZEzUkArMsuSyV4ABbQiIiIiIiIiInJGCmhFZlky2QOA16MRByIiIiIiIiIi8voU0IrMsmSqB8Ow4/HUFboUERERERERERFZ4BTQisyyZLIHt7sOm81Z6FJERERERERERGSBU0ArMsuSyV68Xo03EBERERERERGRM7uggNYwjDLDMB4yDKNt+rr0NfbrNgxjr2EYuwzDeOlCHlNkoUsme7RAmIiIiIiIiIiInJUL7aD9feARy7JagUemb7+WGyzL2mJZ1o4LfEyRBSuXi5HNTiigFRERERERERGRs3KhAe1dwH9Ob/8ncPcFfj2RRS2Z7AXQiAMRERERERERETkrFxrQVluWNQgwfV31GvtZwM8Nw3jZMIxfv8DHFFmwkskeAHXQioiIiIiIiIjIWXGcaQfDMB4Gak7zqT88h8e5yrKsAcMwqoCHDMM4ZFnWE6/xeL8O/DpAY6NCLllckqnpgNajv7siIiIiIiIiInJmZwxoLcu6+bU+ZxjGsGEYtZZlDRqGUQuMvMbXGJi+HjEM43vApcBpA1rLsr4EfAlgx44d1pmfgsjCkUz24nCU4HQWFboUERERERERERFZBC50xMEPgV+e3v5l4Aev3sEwDL9hGMFj28AbgH0X+LgiC1Iy2aP5syIiIiIiIiIictYuNKD9DHCLYRhtwC3TtzEMo84wjAem96kGnjIMYzfwAvATy7J+doGPK7IgKaAVEREREREREZFzccYRB6/Hsqxx4KbTfHwAeOP0diew+UIeR2QxMM0cqVQ/VVVvLHQpIiIiIiIiIiKySFxoB62ITEunh7GsHF5PQ6FLERERERERERGRRUIBrcgsSaX6ADTiQEREREREREREzpoCWpFZciyg9XjqC1yJiIiIiIiIiIgsFgpoRWZJMtUPGHg8tYUuRUREREREREREFgkFtCKzJJXsw+2uxmZzF7oUERERERERERFZJBTQisySZKpP4w1EREREREREROScKKAVmSWpVD9eT0OhyxARERERERERkUVEAa3ILDDNHOn0oDpoRURERERERETknCigFZkF6fQwlpXH41UHrYiIiIiIiIiInD0FtCKzIJXqA9CIAxEREREREREROScKaEVmwbGAViMORERERERERETkXCigFZkFyVQ/YODx1Ba6FBERERERERERWUQU0IrMglSqH7erCpvNXehSRERERERERERkEVFAKzILUsk+PF6NNxARERERERERkXOjgFZkFiRT/Xi0QJiIiIiIiIiIiJwjBbQiF8g0c6TTg3i1QJiIiIiIiIiIiJwjBbQiFyiTGcGycuqgFRERERERERGRc6aAVuQCJZN9AHi8CmhFREREREREROTcKKAVuUCp1FRAqxEHIiIiIiIiIiJyrhTQilygZKofAI+nrsCViIiIiIiIiIjIYqOAVuQCpVJ9uF3V2GzuQpciIiIiIiIiIiKLjAJakQuUSvbh8Wq8gYiIiIiIiIiInDsFtCIXKJnqx+PRAmEiIiIiIiIiInLuFNCKXADTzJFOD2qBMBEREREREREROS8KaEUuQCYzgmXl1EErIiIiIiIiIiLnRQGtyAVIJvsA8HgV0IqIiIiIiIiIyLlTQCtyAVKpqYBWIw5EREREREREROR8KKAVuQDJVD8AHk9dgSsREREREREREZHFSAGtyAVIpfpwu6qx2dyFLkVERERERERERBYhBbQiFyCV7FP3rIiIiIiIiIiInDcFtCIXIJUexKP5syIiIiIiIiIicp4U0IqcJ8sySacH1UErIiIiIiIiIiLnTQGtyHnKZCcwzQxuT22hSxERERERERERkUVKAa3IeUqnBgDwuNVBKyIiIiIiIiIi50cBrch5SqUGATTiQEREREREREREzpsCWpHzlEpPd9BqxIGIiIiIiIiIiJwnBbQi5ymVGsBm8+JwlBS6FBERERERERERWaQU0Iqcp1RqAI+nDsMwCl2KiIiIiIiIiIgsUgpoRc5TOj2o+bMiIiIiIiIiInJBFNCKnKdUagCPW/NnRURERERERETk/CmgFTkPppkmkxnFrQ5aERERERERERG5AApoRc5DKjUEgMejDloRERERERERETl/CmhFzkM6PQiAx60OWhEREREREREROX8KaEXOQyo1AKiDVkRERERERERELowCWpHzcCygdWuRMBERERERERERuQAKaEXOQyo9gNNZjt3uKXQpIiIiIiIiIiKyiCmgFTkPqdQAHo/mz4qIiIiIiIiIyIVRQCtyHtLpIc2fFRERERERERGRC6aAVuQcWZY11UHrVgetiIiIiIiIiIhcGAW0Iucol4uQz8c14kBERERERERERC6YAlqRc5RKDQDgVkArIiIiIiIiIiIXSAGtyDlKpwcB8Lg1g1ZERERERERERC6MAlqRc3Ssg1YjDkRERERERERE5EIpoBU5R6nUAIbhxOWqKHQpIiIiIiIiIiKyyCmgFTlHqfQAHncthqF/PiIiIiIiIiIicmGUMImco1RqELdH82dFREREREREROTCKaAVOUfp1AAeBbQiIiIiIiIiIjILFNCKnAPTzJHODONxa4EwERERERERERG5cApoRc5BJjOCZeU14kBERERERERERGaFAlqRc5BKDwLg8aiDVkRERERERERELpwCWpFzkEoNAOBxq4NWREREREREREQunAJakXOQTg8B6qAVEREREREREZHZoYBW5BykU0PY7X4cjmChSxERERERERERkYuAAlqRc5BKD+F21xS6DBERERERERERuUgooBU5B+n0EB4FtCIiIiIiIiIiMksU0Iqcg7Q6aEVEREREREREZBYpoBU5S6aZI5MZxe2uLnQpIiIiIiIiIiJykVBAK3KWMtkxLCuP21Nb6FJEREREREREROQioYBW5CylU0MAmkErIiIiIiIiIiKzRgGtyFlKp4cBNINWRERERERERERmjQJakbOUTg8CaAatiIiIiIiIiIjMGgW0ImcplR7CMFw4nWWFLkVERERERERERC4SCmhFzlI6PYTHXYNhGIUuRURERERERERELhIKaEXOUjo9jNuj+bMiIiIiIiIiIjJ7FNCKnKV0akjzZ0VEREREREREZFYpoBU5C5ZlkUoP4Xarg1ZERERERERERGaPAlqRs5DNTmBZGTwKaEVEREREREREZBYpoBU5C+n0MABud22BKxERERERERERkYuJAlqRs5BODwFoBq2IiIiIiIiIiMwqBbQiZyF1LKD1aMSBiIiIiIiIiIjMHgW0ImchnRrEMOy4XZWFLkVERERERERERC4iCmhFzkI6PYzLVYlh2AtdioiIiIiIiIiIXEQU0IqchXR6CLdb4w1ERERERERERGR2KaAVOQspBbQiIiIiIiIiIjIHFNCKnIV0egiPAloREREREREREZllCmhFziCXi5LPx3F7FNCKiIiIiIiIiMjsUkArcgap9BAAbld1gSsREREREREREZGLjQJakTNIp6YDWk9tgSsREREREREREZGLjQJakTNIT3fQagatiIiIiIiIiIjMNgW0ImdwLKB1u6sKXImIiIiIiIiIiFxsFNCKnEEqPYTTWYbN5i50KSIiIiIiIiIicpFRQCtyBun0EB635s+KiIiIiIiIiMjsU0Arcgbp9BBuj+bPioiIiIiIiIjI7FNAK3IG6fQwbi0QJiIiIiIiIiIic0ABrcjryOdTZLMh3O7qQpciIiIiIiIiIiL/f3t3F2Pbfd51/PfMzN7TNHbtxK4b8kYjCC+mSiQ4BCpApDSCJKoapSJSAqKoIFkIgrhMUCS46A0IISHUlGBVVYWEiCqoSVDcpskFpKhETSqlSYybykpRYxl5zrwcGzvRXmtm/lzMtj09mTMzyXj2Wtnr85Ese+9ZPuu5WTpHX//9rDUk0MI5um4nSQRaAAAAAK6FQAvnWCyWgXYu0AIAAADw8hNo4RyLxdNJku3tBwaeBAAAAIB1JNDCORZWHAAAAABwjQRaOMdi8XQ2NubZ2rpn6FEAAAAAWENXCrRV9b6qeqyqjqvqxjnXvbOqvlZVT1TVh69yT1ilbnEz8/kDqaqhRwEAAABgDV31BO1Xk/xUks/d6YKq2kzy0STvSvJgkg9U1YNXvC+sxKJ72v5ZAAAAAK7NlQJta+3x1trXLrjsbUmeaK19vbXWJfl4kvdc5b6wKovFTrbn9s8CAAAAcD1WsYP2dUm+cerzk8vvzlRVD1XVF6vqizdv3rz24eA8i8XTmTtBCwAAAMA12brogqr6bJLXnPGjj7TWPnGJe5y1vLPd6eLW2sNJHk6SGzdu3PE6uG6Hh8/n6Oi5bG87QQsAAADA9bgw0LbW3nHFezyZ5A2nPr8+yVNX/DXh2nXdTpJke+4ELQAAAADXYxUrDr6Q5M1V9aaqmid5f5JPruC+cCWLxTLQWnEAAAAAwDW5UqCtqvdW1ZNJfjTJp6rq08vvX1tVjyZJa+0wyQeTfDrJ40l+ubX22NXGhuu3WDydJFYcAAAAAHBtLlxxcJ7W2iNJHjnj+6eSvPvU50eTPHqVe8GqLV5YcSDQAgAAAHBNVrHiAL4ndYudbGx8XzY37xp6FAAAAADWlEALd7DodrK9/UCqauhRAAAAAFhTAi3cwWKxk+259QYAAAAAXB+BFu5gsXg68+0Hhh4DAAAAgDUm0MIZWmvpuh0vCAMAAADgWgm0cIajo+dydPTNbDtBCwAAAMA1EmjhDIvFTpLYQQsAAADAtRJo4QyLxdNJ4gQtAAAAANdKoIUzLLrlCVo7aAEAAAC4RgItnKFbrjiYz39w4EkAAAAAWGcCLZxh0e1kc/OV2dq6a+hRAAAAAFhjAi2cYbF42v5ZAAAAAK6dQAtnWCx2Mp8LtAAAAABcL4EWztAtdrwgDAAAAIBrJ9DCbVprWXRWHAAAAABw/QRauM3h4bM5Pl5ke+4ELQAAAADXS6CF2ywWTyeJE7QAAAAAXDuBFm6z6HaSJHM7aAEAAAC4ZgIt3KZ74QTt3AlaAAAAAK6XQAu3WSxuJrHiAAAAAIDrJ9DCbRbd09naujubm68YehQAAAAA1pxAC7dZLHYyt94AAAAAgBUQaOE2XbdjvQEAAAAAKyHQwm26xW7m8x8cegwAAAAAJkCghVNaa1l0N7Mt0AIAAACwAgItnHJ09HyOj7+V+bZACwAAAMD1E2jhlK67mSRWHAAAAACwEgItnLJYnARaKw4AAAAAWAWBFk556QTt/QNPAgAAAMAUCLRwihUHAAAAAKySQAunLLrdVM0ym9079CgAAAAATIBAC6d03c3M5/elyqMBAAAAwPVToeCUbrFjvQEAAAAAKyPQwimLbjfbAi0AAAAAKyLQwiknKw7uH3oMAAAAACZCoIWl1o7SdXuZbz8w9CgAAAAATIRAC0tdf5Dk2IoDAAAAAFZGoIWlbrGTJF4SBgAAAMDKCLSw1HU3kyTzbTtoAQAAAFgNgRaWFstAa8UBAAAAAKsi0MJSt9hNYsUBAAAAAKsj0MJS193M5uZd2dx8xdCjAAAAADARAi0sLbqdbG87PQsAAADA6gi0sNR1u9YbAAAAALBSAi0sdd3NzOf3Dz0GAAAAABMi0MLSYnEz2/MHhh4DAAAAgAkRaCHJ0dG3cnT0nBUHAAAAAKyUQAs5WW+QJPNtKw4AAAAAWB2BFpIsloF22wlaAAAAAFZIoIUk3WI3Saw4AAAAAGClBFrI6RUHXhIGAAAAwOoItJAXVhxsZD571dCjAAAAADAhAi0k6RY7mc/vS9Xm0KMAAAAAMCECLSTpul37ZwEAAABYOYEWcrLiYHt+/9BjAAAAADAxAi3k5CVhXhAGAAAAwKoJtExea8fpuj0rDgAAAABYOYGWyTs8fCat9VYcAAAAALByAi2Tt1jsJIkTtAAAAACsnEDL5HXdbhKBFgAAAIDVE2iZvEV3M0myvS3QAgAAALBaAi2T99IJWjtoAQAAAFgtgZbJ67u9VM2zuXnX0KMAAAAAMDECLZPXdbuZz+9LVQ09CgAAAAATI9AyeSeB1noDAAAAAFZPoGXyun4v8/l9Q48BAAAAwAQJtExe1+05QQsAAADAIARaJq21JtACAAAAMBiBlkk7PHw2rfWZz6w4AAAAAGD1BFomret2k8QJWgAAAAAGIdAyaS8FWidoAQAAAFg9gZZJ6/q9JE7QAgAAADAMgZZJc4IWAAAAgCEJtExa1+0l2chs9qqhRwEAAABgggRaJq3rdjObvSpVm0OPAgAAAMAECbRMWtftZtv+WQAAAAAGItAyaX23l5n9swAAAAAMRKBl0rpuL3MnaAEAAAAYiEDLpHX9rkALAAAAwGAEWibr6OibOTr6ZuYzKw4AAAAAGIZAy2R13V6SOEELAAAAwGAEWiar63aTJHMvCQMAAABgIAItk/XSCVqBFgAAAIBhCLRM1ksnaK04AAAAAGAYAi2T9UKgnXlJGAAAAAADEWiZrK7fy9bW3dnc3B56FAAAAAAmSqBlsrpu13oDAAAAAAYl0DJZXbdnvQEAAAAAgxJomayu23OCFgAAAIBBCbRMlhUHAAAAAAxNoGWSjo/7HB7eynxuxQEAAAAAwxFomaS+308SJ2gBAAAAGJRAyyR13W6SOEELAAAAwKAEWibpxUA7E2gBAAAAGI5AyyR13V4SKw4AAAAAGJZAyyRZcQAAAADAGAi0TFLX7WZjYzubm3cNPQoAAAAAEybQMkldv5f5/P5U1dCjAAAAADBhAi2T1HV7XhAGAAAAwOCuFGir6n1V9VhVHVfVjXOu+z9V9ZWq+lJVffEq94SXQ9fteUEYAAAAAIPbuuK//9UkP5Xk31/i2h9rre1e8X7wsui63fzA3T8y9BgAAAAATNyVAm1r7fEk9njyPaW14/T9fmZzKw4AAAAAGNaqdtC2JL9eVb9dVQ+t6J5wpsPDZ9PaYeYCLQAAAAADu/AEbVV9NslrzvjRR1prn7jkff5Sa+2pqnogyWeq6ndba5+7w/0eSvJQkrzxjW+85C8Pl9d1+0mS+ezVA08CAAAAwNRdGGhba++46k1aa08t/75TVY8keVuSMwNta+3hJA8nyY0bN9pV7w236/q9JMlMoAUAAABgYNe+4qCqXllVd7/wz0n+ek5eLgaD6F84QTsXaAEAAAAY1pUCbVW9t6qeTPKjST5VVZ9efv/aqnp0edkPJfmfVfU7SX4ryadaa792lfvCVThBCwAAAMBYXLji4DyttUeSPHLG908leffyn7+e5K1XuQ+8nJygBQAAAGAsrn3FAYxN1+9nc/OubGxsDz0KAAAAABMn0DI5fbfn9CwAAAAAoyDQMjldv5/Z7L6hxwAAAAAAgZbp6ft9J2gBAAAAGAWBlsnpuv3MnaAFAAAAYAQEWialtZa+P8jMCVoAAAAARkCgZVIOD/9fWusznwm0AAAAAAxPoGVS+n4vSTITaAEAAAAYAYGWSem6k0DrJWEAAAAAjIFAy6T0/X6SZDb3kjAAAAAAhifQMilddxJo7aAFAAAAYAwEWiblxRO0MydoAQAAABieQMukdN1eNjdfmc3N7aFHAQAAAACBlmnp+v3MrDcAAAAAYCQEWial7/Yz94IwAAAAAEZCoGVSun7fC8IAAAAAGA2Blknp+/3M5gItAAAAAOMg0DIZrbV03Z4TtAAAAACMhkDLZBwdPZfWeidoAQAAABgNgZbJ6Lq9JHGCFgAAAIDREGiZjL7fT5LM5vcNPAkAAAAAnBBomYyuOwm0TtACAAAAMBYCLZPR9ScrDmYzJ2gBAAAAGAeBlsnoXzhB6yVhAAAAAIyEQMtkdP1+NjZekc3NVww9CgAAAAAkEWiZkL7bz9wLwgAAAAAYEYGWyej6PS8IAwAAAGBUBFomo+/3M7N/FgAAAIAREWiZjK5zghYAAACAcRFomYTWmhO0AAAAAIyOQMskHB09n+PjLvOZl4QBAAAAMB4CLZPQ9/tJ4gQtAAAAAKMi0DIJXXcSaJ2gBQAAAGBMBFomoev3kjhBCwAAAMC4CLRMQv/iCVqBFgAAAIDxEGiZhG65g3Y+t+IAAAAAgPEQaJmEvtvLxsb3ZXPz+4ceBQAAAABeJNAyCV2/b70BAAAAAKMj0DIJfX/gBWEAAAAAjI5AyyT0/UFms1cNPQYAAAAA/CECLZPQdwItAAAAAOMj0DIJXb8v0AIAAAAwOgIta+/4uMvR0XOZC7QAAAAAjIxAy9rr+2eSJLOZl4QBAAAAMC4CLWuv7/eTJLO5E7QAAAAAjItAy9rr+4MksYMWAAAAgNERaFl73TLQzq04AAAAAGBkBFrW3ksnaO8ddhAAAAAAuI1Ay9rru+UOWoEWAAAAgJERaFl7fX+Qzc27srGxPfQoAAAAAPCHCLSsvb6/5QVhAAAAAIySQMva6/v9zAVaAAAAAEZIoGXtdf1BZnOBFgAAAIDxEWhZe31/YMUBAAAAAKMk0LL2BFoAAAAAxkqgZa0dHS1ydPS8QAsAAADAKAm0rLX+8CBJBFoAAAAARkmgZa31/a0kyXz26mEHAQAAAIAzCLSstb7bT+IELQAAAADjJNCy1vreigMAAAAAxkugZa29GGjnVhwAAAAAMD4CLWuteyHQbt0z8CQAAAAA8O0EWtZa3+9na+vubGzMhh4FAAAAAL6NQMta6/sD+2cBAAAAGC2BlrXW97cym9k/CwAAAMA4CbSstb7fd4IWAAAAgNESaFlrfXeQuUALAAAAwEgJtKy1zg5aAAAAAEZMoGVtHR19K8fH3xJoAQAAABgtgZa11fcHSSLQAgAAADBaAi1r68VAOxdoAQAAABgngZa11fe3kiSz2auHHQQAAAAA7kCgZW11/X6SZG7FAQAAAAAjJdCytuygBQAAAGDsBFrWVt8dJKlsbd0z9CgAAAAAcCaBlrXV9wfZ2vqBbGxsDT0KAAAAAJxJoGVtdf2+9QYAAAAAjJpAy9rq+wMvCAMAAABg1ARa1lbf38ps/uqhxwAAAACAOxJoWVu9FQcAAAAAjJxAy1pqraXvDwRaAAAAAEZNoGUtHR9/K8fHCztoAQAAABg1gZa11HUHSeIELQAAAACjJtCylvp+P4lACwAAAMC4CbSspb53ghYAAACA8RNoWUt9fyuJQAsAAADAuAm0rKWXTtDeO+wgAAAAAHAOgZa11B8+kyTZ2rpn4EkAAAAA4M4EWtZS3x9ka+vubGxsDT0KAAAAANyRQMtaOuyfyWzL/lkAAAAAxk2gZS31/UG2ZtYbAAAAADBuAi1rqe9veUEYAAAAAKMn0LKW+sNbmc2sOAAAAABg3ARa1tLJCVorDgAAAAAYN4GWtXN8fJjDw2e9JAwAAACA0RNoWTuHh88miR20AAAAAIyeQMva6ftbSQRaAAAAAMZPoGXt9IcHSQRaAAAAAMZPoGXtHPbPJElmMztoAQAAABg3gZa10/cnJ2i3tu4ZeBIAAAAAON+VAm1V/auq+t2q+nJVPVJV997hundW1deq6omq+vBV7gkXeWkHrRO0AAAAAIzbVU/QfibJj7TW3pLk95L809svqKrNJB9N8q4kDyb5QFU9eMX7wh31/a1UbWZr6+6hRwEAAACAc10p0LbWfr21drj8+Pkkrz/jsrcleaK19vXWWpfk40nec5X7wnn6w1vZ2ronVTX0KAAAAABwrpdzB+3fS/KrZ3z/uiTfOPX5yeV3cC36/lZms3uHHgMAAAAALrR10QVV9dkkrznjRx9prX1iec1Hkhwm+Y9n/RJnfNfOud9DSR5afnyuqr520Yxr5P4ku0MPsT6coGVQnmdYD55lWB+eZ1gPnmVYH1N8nv/oWV9eGGhba+847+dV9XeT/ESSH2+tnRVen0zyhlOfX5/kqXPu93CShy+aax1V1RdbazeGngO4Os8zrAfPMqwPzzOsB88yrA/P80uutOKgqt6Z5ENJfrK19s07XPaFJG+uqjdV1TzJ+5N88ir3BQAAAABYB1fdQftzSe5O8pmq+lJVfSxJquq1VfVokixfIvbBJJ9O8niSX26tPXbF+wIAAAAAfM+7cMXBeVprf/wO3z+V5N2nPj+a5NGr3GsiJrnaAdaU5xnWg2cZ1ofnGdaDZxnWh+d5qc5eGwsAAAAAwHW76ooDAAAAAAC+SwLtAKrqnVX1tap6oqo+fMbPq6r+7fLnX66qPzvEnMDFLvE8/+3lc/zlqvrNqnrrEHMC57voWT513Z+vqqOq+purnA+4vMs8z1X19uU7NB6rqv+x6hmBi13iz9n3VNV/q6rfWT7LPzPEnMD5quoXq2qnqr56h59rYBFoV66qNpN8NMm7kjyY5ANV9eBtl70ryZuXfz2U5N+tdEjgUi75PP9+kr/aWntLkp+NHTswOpd8ll+47l/m5MWnwAhd5nmuqnuT/HySn2yt/Zkk71v1nMD5Lvl78z9K8r9ba29N8vYk/7qq5isdFLiMX0ryznN+roFFoB3C25I80Vr7emutS/LxJO+57Zr3JPkP7cTnk9xbVX9k1YMCF7rweW6t/WZr7WD58fNJXr/iGYGLXeb35iT5x0n+S5KdVQ4HfEcu8zz/rSS/0lr7gyRprXmmYXwu8yy3JHdXVSW5K8l+ksPVjglcpLX2uZw8n3eigUWgHcLrknzj1Ocnl999p9cAw/tOn9W/n+RXr3Ui4Ltx4bNcVa9L8t4kH1vhXMB37jK/N/+JJK+qqv9eVb9dVT+9sumAy7rMs/xzSf50kqeSfCXJP2mtHa9mPOBlpIEl2Rp6gAmqM75r38U1wPAu/axW1Y/lJND+5WudCPhuXOZZ/jdJPtRaOzo5qAOM1GWe560kfy7Jjyd5RZL/VVWfb6393nUPB1zaZZ7lv5HkS0n+WpI/luQzVfUbrbVnr3k24OWlgUWgHcKTSd5w6vPrc/Jf/L7Ta4DhXepZraq3JPmFJO9qre2taDbg8i7zLN9I8vFlnL0/ybur6rC19l9XMiFwWZf9s/Zua+35JM9X1eeSvDWJQAvjcZln+WeS/IvWWkvyRFX9fpI/leS3VjMi8DLRwGLFwRC+kOTNVfWm5QLz9yf55G3XfDLJTy/fZPcXkzzTWvu/qx4UuNCFz3NVvTHJryT5O07mwGhd+Cy31t7UWvvh1toPJ/nPSf6hOAujdJk/a38iyV+pqq2q+v4kfyHJ4yueEzjfZZ7lP8jJSfhU1Q8l+ZNJvr7SKYGXgwYWJ2hXrrV2WFUfzMkboDeT/GJr7bGq+gfLn38syaNJ3p3kiSTfzMl/GQRG5pLP8z9Lcl+Sn1+evDtsrd0Yambg213yWQa+B1zmeW6tPV5Vv5bky0mOk/xCa+2rw00N3O6Svzf/bJJfqqqv5OR/kf5Qa213sKGBM1XVf0ry9iT3V9WTSf55klmigZ1WJ/83AAAAAAAAq2bFAQAAAADAQARaAAAAAICBCLQAAAAAAAMRaAEAAAAABiLQAgAAAAAMRKAFAAAAABiIQAsAAAAAMBCBFgAAAABgIP8fBonS+oZ/LTgAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# for size=15\n", + "Z15 = []\n", + "for i in range(10):\n", + " degree = i\n", + " z15 = np.polyfit(x15,y15,degree)\n", + " Z15.append(z15)\n", + " \n", + "plt.figure(figsize=(24,16))\n", + "plt.scatter(x15,y15)\n", + "for i in range(10):\n", + " coeffs = Z15[i]\n", + " x = np.arange(0,1.001,0.001)\n", + " y15_p = poly(x, coeffs)\n", + " deg = str(i)\n", + " plt.plot(x, y15_p, label=deg)\n", + "plt.ylim(-2,2)\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "id": "80fabc47", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 145, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# for size=100\n", + "Z100 = []\n", + "for i in range(10):\n", + " degree = i\n", + " z100 = np.polyfit(x100,y100,degree)\n", + " Z100.append(z100)\n", + " \n", + "plt.figure(figsize=(24,16))\n", + "plt.scatter(x100,y100)\n", + "for i in range(10):\n", + " coeffs = Z100[i]\n", + " x = np.arange(0,1.001,0.001)\n", + " y100_p = poly(x, coeffs)\n", + " deg = str(i)\n", + " plt.plot(x, y100_p, label=deg)\n", + "plt.ylim(-2,2)\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 186, + "id": "fdf8a0b7", + "metadata": {}, + "outputs": [], + "source": [ + "# Note that to find the best model, we simply find the derivative of error function and equate it to zero\n", + "# this gives the minimized error\n", + "# However, the minimized error on the raining set is not valid due to over-fitting\n", + "# the minimized error on the testing set is valid given the model is not biased by the data itself" + ] + }, + { + "cell_type": "markdown", + "id": "bb606836", + "metadata": {}, + "source": [ + "### 2.3 Find MSE" + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "id": "3a623f72", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 187, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# generate test data:\n", + "\n", + "# for size=9\n", + "x9_test = np.random.uniform(size=9)\n", + "y_err9_test = np.random.normal(loc=0, scale=0.05, size=9)\n", + "y9_t = func(x9_test)+y_err9_test\n", + "\n", + "# for size=15\n", + "x15_test = np.random.uniform(size=15)\n", + "y_err15_test = np.random.normal(loc=0, scale=0.05, size=15)\n", + "y15_t = func(x15_test)+y_err15_test\n", + "\n", + "# for size=100\n", + "x100_test = np.random.uniform(size=100)\n", + "y_err100_test = np.random.normal(loc=0, scale=0.05, size=100)\n", + "y100_t = func(x100_test)+y_err100_test\n", + "\n", + "plt.scatter(x9_test, y9_t)\n", + "plt.scatter(x15_test, y15_t)\n", + "plt.scatter(x100_test, y100_t)" + ] + }, + { + "cell_type": "code", + "execution_count": 188, + "id": "a8fd777f", + "metadata": {}, + "outputs": [], + "source": [ + "# training MSE for size=9\n", + "\n", + "MSE_TEST9 = []\n", + "MSE_TRAIN9 = []\n", + "for i in range(10):\n", + " coeffs = Z9[i]\n", + " y9_train = poly(x9, coeffs)\n", + " y9_test = poly(x9_test, coeffs)\n", + " dy_train = np.abs(y9_train-y9)\n", + " dy_test = np.abs(y9_test-y9_t)\n", + " MSE_train = 1/len(dy_train)*np.sum(dy_train**2)\n", + " MSE_test = 1/len(dy_test)*np.sum(dy_test**2)\n", + " MSE_TRAIN9.append(MSE_train)\n", + " MSE_TEST9.append(MSE_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 189, + "id": "b3034e43", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 189, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "poly_deg = np.arange(0,10,1)\n", + "\n", + "plt.plot(poly_deg, MSE_TRAIN9, label='train')\n", + "plt.plot(poly_deg, MSE_TEST9, label='test')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 190, + "id": "8630044c", + "metadata": {}, + "outputs": [], + "source": [ + "# training MSE for size=15\n", + "\n", + "MSE_TEST15 = []\n", + "MSE_TRAIN15 = []\n", + "for i in range(10):\n", + " coeffs = Z15[i]\n", + " y15_train = poly(x15, coeffs)\n", + " y15_test = poly(x15_test, coeffs)\n", + " dy_train = np.abs(y15_train-y15)\n", + " dy_test = np.abs(y15_test-y15_t)\n", + " MSE_train = 1/len(dy_train)*np.sum(dy_train**2)\n", + " MSE_test = 1/len(dy_test)*np.sum(dy_test**2)\n", + " MSE_TRAIN15.append(MSE_train)\n", + " MSE_TEST15.append(MSE_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 191, + "id": "78c80dd2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 191, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(poly_deg, MSE_TRAIN15, label='train')\n", + "plt.plot(poly_deg, MSE_TEST15, label='test')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "id": "807b26c4", + "metadata": {}, + "outputs": [], + "source": [ + "# training MSE for size=100\n", + "\n", + "MSE_TEST100 = []\n", + "MSE_TRAIN100 = []\n", + "for i in range(10):\n", + " coeffs = Z100[i]\n", + " y100_train = poly(x100, coeffs)\n", + " y100_test = poly(x100_test, coeffs)\n", + " dy_train = np.abs(y100_train-y100)\n", + " dy_test = np.abs(y100_test-y100_t)\n", + " MSE_train = 1/len(dy_train)*np.sum(dy_train**2)\n", + " MSE_test = 1/len(dy_test)*np.sum(dy_test**2)\n", + " MSE_TRAIN100.append(MSE_train)\n", + " MSE_TEST100.append(MSE_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 193, + "id": "999b9dcb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 193, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(poly_deg, MSE_TRAIN100, label='train')\n", + "plt.plot(poly_deg, MSE_TEST100, label='test')\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "d3e41e2c", + "metadata": {}, + "source": [ + "### 2.4 Minimize Error Function" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "06faaeb6", + "metadata": {}, + "outputs": [], + "source": [ + "# the plan is to minimize the error function with the w^2 parameters\n", + "# once it's minimized," + ] + }, + { + "cell_type": "markdown", + "id": "32bcfd86", + "metadata": {}, + "source": [ + "### 2.5 Test Minimization" + ] + }, + { + "cell_type": "code", + "execution_count": 194, + "id": "3142b2fd", + "metadata": {}, + "outputs": [], + "source": [ + "def regularization(model, data, coeff, l):\n", + " error = 1/len(model)*np.sum((np.abs(model-data))**2)\n", + " add = l*1/len(coeff)*np.sum(coeff**2)\n", + " return error+add" + ] + }, + { + "cell_type": "code", + "execution_count": 202, + "id": "a1d394e2", + "metadata": {}, + "outputs": [], + "source": [ + "ERROR = []\n", + "for i in range(10):\n", + " coeffs = Z9[i]\n", + " error = regularization(poly(x9_test, coeffs), y9_t, coeffs, 0.5)\n", + " ERROR.append(error)" + ] + }, + { + "cell_type": "code", + "execution_count": 203, + "id": "3642e711", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.2032167737983944,\n", + " 0.29805174754080993,\n", + " 0.1878489319208772,\n", + " 46.016260266826976,\n", + " 40.21844354660332,\n", + " 288.2098494269156,\n", + " 1505.9115197163387,\n", + " 1728796.9819142863,\n", + " 8728997349.059772,\n", + " 1183123626.2022896]" + ] + }, + "execution_count": 203, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ERROR" + ] + }, + { + "cell_type": "code", + "execution_count": 233, + "id": "29f53ea4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " fun: 0.00021126522683696\n", + " hess_inv: array([[ 3.87296683e+04, -1.14279620e+04, -3.42184350e+04,\n", + " -2.77204872e+04, 2.35688573e+03, 3.49780329e+04,\n", + " 2.89254233e+04, -4.16018321e+04, 1.05970097e+04,\n", + " -3.86039147e+02],\n", + " [-1.14279620e+04, 3.64429117e+03, 1.03678376e+04,\n", + " 8.19538105e+03, -1.07032453e+03, -1.09223562e+04,\n", + " -8.71670798e+03, 1.32156017e+04, -3.46895414e+03,\n", + " 1.33100733e+02],\n", + " [-3.42184350e+04, 1.03678376e+04, 3.05063642e+04,\n", + " 2.45119205e+04, -2.45115415e+03, -3.15018991e+04,\n", + " -2.57454610e+04, 3.76759025e+04, -9.68904112e+03,\n", + " 3.58327447e+02],\n", + " [-2.77204872e+04, 8.19538105e+03, 2.45119205e+04,\n", + " 1.98534072e+04, -1.69450869e+03, -2.50632586e+04,\n", + " -2.07329921e+04, 2.97817679e+04, -7.56603068e+03,\n", + " 2.72663694e+02],\n", + " [ 2.35688573e+03, -1.07032453e+03, -2.45115415e+03,\n", + " -1.69450869e+03, 6.82241294e+02, 2.97012379e+03,\n", + " 1.98559939e+03, -3.89918929e+03, 1.16964162e+03,\n", + " -5.62023519e+01],\n", + " [ 3.49780329e+04, -1.09223562e+04, -3.15018991e+04,\n", + " -2.50632586e+04, 2.97012379e+03, 3.29303325e+04,\n", + " 2.65142142e+04, -3.96914130e+04, 1.03515763e+04,\n", + " -3.93223133e+02],\n", + " [ 2.89254233e+04, -8.71670798e+03, -2.57454610e+04,\n", + " -2.07329921e+04, 1.98559939e+03, 2.65142142e+04,\n", + " 2.17634866e+04, -3.16071109e+04, 8.06085206e+03,\n", + " -2.89430902e+02],\n", + " [-4.16018321e+04, 1.32156017e+04, 3.76759025e+04,\n", + " 2.97817679e+04, -3.89918929e+03, -3.96914130e+04,\n", + " -3.16071109e+04, 4.81880521e+04, -1.27660347e+04,\n", + " 5.06644906e+02],\n", + " [ 1.05970097e+04, -3.46895414e+03, -9.68904112e+03,\n", + " -7.56603068e+03, 1.16964162e+03, 1.03515763e+04,\n", + " 8.06085206e+03, -1.27660347e+04, 3.51723250e+03,\n", + " -1.58851227e+02],\n", + " [-3.86039147e+02, 1.33100733e+02, 3.58327447e+02,\n", + " 2.72663694e+02, -5.62023519e+01, -3.93223133e+02,\n", + " -2.89430902e+02, 5.06644906e+02, -1.58851227e+02,\n", + " 1.13590741e+01]])\n", + " jac: array([ 2.36222513e-06, 1.34862421e-06, 9.55962605e-07, 1.22810343e-06,\n", + " 1.53023575e-06, 8.23942173e-07, -6.84643965e-07, 6.70155714e-07,\n", + " 2.18027344e-06, -7.62444506e-06])\n", + " message: 'Optimization terminated successfully.'\n", + " nfev: 638\n", + " nit: 57\n", + " njev: 58\n", + " status: 0\n", + " success: True\n", + " x: array([ 4.30235586, -2.37869899, -4.52176676, -2.14840648,\n", + " 3.19970191, 7.17795115, 2.35545956, -13.13932295,\n", + " 5.32432463, 0.35892596])\n" + ] + } + ], + "source": [ + "import scipy.optimize as o\n", + "\n", + "def eq_m(x, a, b, c, d, e, f, g, h, i, j): # assumed signature of eq_m\n", + " return a*x**9+b*x**8+c*x**7+d*x**6+e*x**5+f*x**4+g*x**3+h*x**2+i*x+j\n", + "\n", + "def regularization(params):\n", + " a, b, c, d, e, f, g, h, i, j = params\n", + " model = eq_m(x9, a, b, c, d, e, f, g, h, i, j)\n", + " error = 1/len(model)*np.sum((np.abs(model-y9))**2)\n", + " add = 1/len(params)*np.sum(params**2)*0\n", + " return error+add\n", + "\n", + "p0 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] # initial guess for lambda, mu, and sigma\n", + "res = o.minimize(regularization, p0)\n", + "print(res) # see if minimization succeeded.\n", + "a, b, c, d, e, f, g, h, i, j = res.x" + ] + }, + { + "cell_type": "code", + "execution_count": 234, + "id": "5aca8306", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 234, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x9, y9)\n", + "plt.plot(x, poly(x, res.x))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fd660da8", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Assignment_0/Assignment_0_Yuze.ipynb b/Assignment_0/Assignment_0_Yuze.ipynb new file mode 100644 index 0000000..aad75e2 --- /dev/null +++ b/Assignment_0/Assignment_0_Yuze.ipynb @@ -0,0 +1,1132 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 13, + "id": "fd8e810f", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "0e99f9ac", + "metadata": {}, + "source": [ + "## Question 1" + ] + }, + { + "cell_type": "markdown", + "id": "0e7e3ef3", + "metadata": {}, + "source": [ + "### 1.1 Find number of corners of an n dimensional cube" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "de131010", + "metadata": {}, + "outputs": [], + "source": [ + "def cube_corners(dim):\n", + " return 2**dim" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "63cee73f", + "metadata": {}, + "outputs": [], + "source": [ + "Corners = []\n", + "for i in range(100):\n", + " Dim = i+1\n", + " corners = 2**Dim\n", + " Corners.append(corners)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "be9ee752", + "metadata": {}, + "outputs": [], + "source": [ + "dimension = np.arange(1,101,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "17ebaaf2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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vtL9MSep/vbyoCFoI9MysAncBjwPPAX+Umbsi4o6IuKNx2u8AFwH3RcTTETHSsYolqQ9N15JXXu/Ngy1mtNJyITN3ADtm7dva9PozwGfaW5okFceBw0ep9ug+6DO8UlSS2uD7+w8DcMWKZT2rwUCXpDbYuec1hgYW8b7Ll/esBgNdktpg50sHuXrN8p4tWQQDXZLO2OGjUzy77w1uuOLCntZhoEvSGRr54SGma8n1V1zU0zoMdEk6Q9/dc5DFA8E1l1/Q0zoMdEk6Qzv3vMbVa5azdKh3/XMw0CXpjLxZqfK9fW9w/bretlvAQJekMzLyg4NM15Ibetw/BwNdks7Id19q9M/ftbzXpRjoknQmdu55jatWL+fsoZbupNJRBroknaa3KlWeGXuD63u8/nyGgS5Jp+kvnz/QN/1zMNAl6bTUask93x7lipXn8P6fWtHrcgADXZJOyzd2/4jv/+gwv/HB9QwsmutJnd1noEvSKarVki9/a5QrVpzDP7nqsl6Xc5yBLkmn6Bu7f8xz+ye464Pv7pvZORjoknRKMpPf/9aLrFtxDh/ro9k5GOiSdEr+4H//gN37J7jrA+9mcKC/IrS/qpGkPvbV//MDfvex3dx05SVsvrq/ZudgoEtSS76684f89td2cdOVl3Dfbdf03ewcoPfXqkpSH9v3+iT3fHuUh//mZW668mLuu+0ahgb7L8yhxUCPiI3Al4EB4IHM/A+zjkfj+M3AEeCTmfm3ba5VkrqiOl3j2Vcm+OORvfzRyF6C4JPvX8vnb35P34Y5tBDoETEA3Av8EjAGPBkR2zNzd9Npm4D1jZ/rgfsbf0pS35muJW8dqzIxOcXEZJVX36yw99ARxg5N8tz+CZ586SBvHZtm8UDwz39uDb9+47u5bPnSXpc9r1Zm6NcBo5m5ByAiHgE2A82Bvhn4SmYmsDMilkfEpZm5v90F//UL4/z7x3bPf6Kkvpenen6e+I2f+N2sb2cmCdQyqdXq29OZTNeSai2ZqtaoVGtUa3N/8uKBYO1F5/Ar16zihisu4uevuIiLli05xSp7p5VAXwXsbdoe4+2z77nOWQX8RKBHxBZgC8Dll19+qrUCsGzJIOsvWXZavyup/wSneGFOvP1lRP1dIur7FkXU9wUMLgoGGj9DA4tYsngRSwYHWLp4gPOXLua8pYNceM4S1ly4lIvPPauvLhQ6Va0E+lyjm/3XWyvnkJnbgG0Aw8PDp/qXMwDXvusCrn3Xtafzq5JUaq1098eANU3bq4FXTuMcSVIHtRLoTwLrI2JdRAwBtwDbZ52zHfhE1N0AvNGJ/rkk6eTmbblkZjUi7gIep75s8cHM3BURdzSObwV2UF+yOEp92eKnOleyJGkuLa1Dz8wd1EO7ed/WptcJ3Nne0iRJp6J/V8hLkk6JgS5JJWGgS1JJGOiSVBLRfCltVz84Yhz44Sn8ygrg1Q6V088W4rgX4phhYY57IY4Zzmzc78rMlXMd6Fmgn6qIGMnM4V7X0W0LcdwLccywMMe9EMcMnRu3LRdJKgkDXZJKokiBvq3XBfTIQhz3QhwzLMxxL8QxQ4fGXZgeuiTpnRVphi5JegcGuiSVRCECPSI2RsTzETEaEXf3up5OiIg1EfGXEfFcROyKiM829l8YEd+MiBcbf17Q61rbLSIGIuL/RsRjje2FMOblEfEnEfH9xj/zn18g4/5XjX+/n42IhyPirLKNOyIejIgDEfFs076TjjEiPt/Itucj4iNn8tl9H+hND6neBGwAbo2IDb2tqiOqwL/JzCuBG4A7G+O8G/hWZq4HvtXYLpvPAs81bS+EMX8Z+Hpmvge4ivr4Sz3uiFgF/AYwnJk/S/123LdQvnE/BGyctW/OMTb+G78F+PuN37mvkXmnpe8DnaaHVGfmMWDmIdWlkpn7M/NvG68PU/8PfBX1sf5h47Q/BH65JwV2SESsBj4KPNC0u+xjPg/4BeC/AmTmscx8nZKPu2EQWBoRg8DZ1J9sVqpxZ+YTwMFZu082xs3AI5lZycyXqD9T4rrT/ewiBPrJHkBdWhGxFngf8F3gkpmnPzX+vLiHpXXCl4B/C9Sa9pV9zFcA48AfNFpND0TEOZR83Jm5D/hPwMvUHyD/RmZ+g5KPu+FkY2xrvhUh0Ft6AHVZRMQy4E+Bf5mZE72up5Mi4h8DBzLzqV7X0mWDwDXA/Zn5PuAtit9mmFejb7wZWAdcBpwTEb/a26p6rq35VoRAXzAPoI6IxdTD/L9n5qON3T+OiEsbxy8FDvSqvg74B8DHIuIH1FtpH4yI/0a5xwz1f6fHMvO7je0/oR7wZR/3TcBLmTmemVPAo8D7Kf+44eRjbGu+FSHQW3lIdeFFRFDvqT6Xmf+l6dB24PbG69uBr3W7tk7JzM9n5urMXEv9n+u3M/NXKfGYATLzR8DeiPiZxq4PAbsp+bipt1puiIizG/++f4j6d0VlHzecfIzbgVsiYklErAPWA39z2p+SmX3/Q/0B1C8A/w/4zV7X06Ex/kPq/6v1DPB04+dm4CLq34q/2Pjzwl7X2qHx3wg81nhd+jEDVwMjjX/efwZcsEDG/e+A7wPPAl8FlpRt3MDD1L8jmKI+A//0O40R+M1Gtj0PbDqTz/bSf0kqiSK0XCRJLTDQJakkDHRJKgkDXZJKwkCXpJIw0CWpJAx0SSqJ/w9ltgMmdFYCGAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dimension, Corners)" + ] + }, + { + "cell_type": "markdown", + "id": "e2e7ac3b", + "metadata": {}, + "source": [ + "### 1.2 Calculate length of the longest diagonal" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "4f2c6091", + "metadata": {}, + "outputs": [], + "source": [ + "Max_Diag = []\n", + "for i in range(100):\n", + " Dim = i+1\n", + " max_diag = np.sqrt(Dim)\n", + " Max_Diag.append(max_diag)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "e896b4f8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dimension, Max_Diag)" + ] + }, + { + "cell_type": "markdown", + "id": "5563f71a", + "metadata": {}, + "source": [ + "### 1.3 Calculate volume of B_n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "65f11faa", + "metadata": {}, + "outputs": [], + "source": [ + "Volume = []\n", + "for i in range(10):\n", + " Dim = i+1\n", + " points = 0\n", + " for j in range(10**6):\n", + " point = np.random.uniform(size=Dim)\n", + " condition = np.sum((point-0.5)**2)\n", + " if condition < 0.5**2:\n", + " points = points+1\n", + " volume = points/10**6\n", + " Volume.append(volume)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "24a0862d", + "metadata": {}, + "outputs": [], + "source": [ + "dim_circ = np.arange(1,11,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "23dcb521", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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9JUMZktmR7z21iHVlFV5HEpEQUaFHoLjoKGZcPQK/z5j8aAH7q+u8jiQiIaBCj1BZqQlMvzKP4tL93Dp7Mc7pIKlIe6dCj2Bj+qZz27iBvLx0GzPeWet1HBE5SUEVupmdb2arzazIzG47ynKnmlm9mV0WuojSkm44vTdfye3GH15bxbuflHodR0ROwjEL3cyigOnAOGAQMMnMBn3OcncBr4U6pLQcM+Puy3Lp36UDNz/xMZt2VXodSUROUDBb6COBIufcWudcDfAkMKGZ5W4GngV2hDCftIKEGD8PXDMC5xyTZxVyoKbe60gicgKCKfRMYFOT5yWBaZ8ys0zgEmDG0d7IzCabWYGZFZSW6s/7tqRXWiL3TBrOqm17uW3OEh0kFWmHgil0a2ba4f/b/wL8xDl31E0759xM51y+cy4/IyMjyIjSWs4a0Jkf/k9/Xli0hb/PW+91HBE5TsGMKVoC9GjyPAvYctgy+cCTZgaQDlxgZnXOuedDEVJaz9Qz+7KkpJzfv7ySQd06MrpPmteRRCRIwWyhfwT0M7McM4sBrgBebLqAcy7HOZftnMsGZgNTVebtk89n/Omrw8hOS+Cmfy5ky54DXkcSkSAds9Cdc3XATTSevbISeNo5t9zMppjZlJYOKK2vQ1w0M6/Np7qugSmPFVJVq4OkIu2BeXXwKz8/3xUUFHiybgnO68u3MXlWIZePyOLuy3IJ7FITEQ+ZWaFzLr+5ebpSVD7Xlwd35Zaz+/JMYQmPfbjR6zgicgwqdDmq753bn7MGZPCbfy2ncMMur+OIyFGo0OWofD7jL18bTveUeKY8tpDte6u8jiQin0OFLseUnBDNzGvyqaiuY+rjC6mpa/A6kog0Q4UuQRnQtQN3X5ZL4Ybd/Oal5V7HEZFmBHNhkQgAX8ntztKSch54dy25mSl89dQex36RiLQabaHLcfnxeQP4Yt90fvH8MhZv2uN1HBFpQoUux8Uf5WPapOFkdIhlymOFlO2v9jqSiASo0OW4pSbG8MA1I9hVUcONjy+ktl4HSUXaAhW6nJAhmcncMXEoH67bxR0vr/I6joigg6JyEibmZbGkpJy/z1tHblYyFw/PPPaLRKTFaAtdTsrPx5/CyJxO3DZnCcs2l3sdRySiqdDlpERH+Zh+ZR6pCTFMevAD3lujkahEvKJCl5OW0SGWZ6aMJjMlnm88/BGzFqz3OpJIRFKhS0hkpSYw+ztjOLN/Br98YTm3v7CMOp39ItKqVOgSMkmxfmZem88Np+fwjwUb+OY/CthbVet1LJGIoUKXkIryGT8fP4i7Lh3K/KIyJt43n407K72OJRIRVOjSIr52ak9mXT+Ksv3VTJj+Pv9dp3upi7Q0Fbq0mNF90nhu6lhSE2K46qEPeKZgk9eRRMKaCl1aVE56Is9NHcuonDR+PHsJd76yioYGb8axFQl3KnRpcckJ0Tx83alcNaonM94pZspjhVRU13kdSyTsqNClVURH+fjdxUO4/cJBzF25nctnLGDLngNexxIJKyp0aTVmxnVjc/jbN05l465KJkyfp3uqi4SQCl1a3VkDOjNn6hjion189YEFvLRki9eRRMKCCl080b9LB56fOpahmcnc9M+PuWfuGpzTwVKRk6FCF8+kJcXy+A2jmJiXyZ/nfsJ3n1xEVW2917FE2i3dD108FeuP4k+XD6Nv5yTufnU1G3dVMvPaEXTuEOd1NJF2R1vo4jkzY+qZfZlx9QhWb9vHxffOY+XWvV7HEml3VOjSZpw/pCvPTBlNg4NL75/P3BXbvY4k0q6o0KVNGZKZzAs3jaVv5yRumFXAzHeLdbBUJEgqdGlzunSM46nJo7lgSDd+//Iqbnt2KTV1ure6yLEEVehmdr6ZrTazIjO7rZn5V5nZksDPfDMbFvqoEkniY6KYNmk4t5zdl6cKNnHN3z5kd0WN17FE2rRjFrqZRQHTgXHAIGCSmQ06bLF1wJecc7nAb4GZoQ4qkcfnM37w5QH85Wtf4ONNe7j4vnkU7djvdSyRNiuYLfSRQJFzbq1zrgZ4EpjQdAHn3Hzn3O7A0w+ArNDGlEh28fBMnrjhNCqq67jkvnm8v6bM60gibVIwhZ4JNL2RdUlg2ue5HniluRlmNtnMCsysoLRUo8NL8Eb0SuX5G8fSPTmerz/8X2Z9sMHrSCJtTjCFbs1Ma/a0AzM7i8ZC/0lz851zM51z+c65/IyMjOBTitA4EPWzU8fwpf4Z/PL5ZfzqxeUaiFqkiWAKvQTo0eR5FnDE3ZTMLBd4CJjgnNsZmngih0qK9fPgtfl864s5PDJ/vQaiFmkimEL/COhnZjlmFgNcAbzYdAEz6wnMAa5xzn0S+pgin4nyGb/4yiDunNg4EPWlGohaBAii0J1zdcBNwGvASuBp59xyM5tiZlMCi/0vkAbcZ2aLzKygxRKLBFwxsiePXj+SHfuqufi+eRqIWiKeeXUVXn5+visoUO/LyVtXVsH1j3zEpt2V3DExl8tG6CQrCV9mVuicy29unq4UlXbv4EDUI3M68aNnFvOdxwpZsUU395LIo0KXsJCcEM0j143ke+f24/01ZVzw1/e44dEClpaUex1NpNVol4uEnfIDtTwybz1/e38te6vqOGtABjef04+8nqleRxM5aUfb5aJCl7C1r6qWRxds4KH31rK7spbT+6Vzyzn9ODW7k9fRRE6YCl0iWkV1HY99sIEH31tL2f4aRvdO45Zz+nFa706YNXfdnEjbpUIXAQ7U1PPP/25kxjvFlO6r5tTsVG45px9f7JuuYpd2Q4Uu0kRVbT1PfbSJGe8Us7W8iuE9U7jl7H6cOSBDxS5tngpdpBnVdfXMLizhvreK2bznAEMzk7nlnH6ce0pnFbu0WSp0kaOorW/guYWbufetIjbuquSUbh255ey+nDe4Kz6fil3aFhW6SBDq6ht4cfEW7n2ziLVlFfTvksRNZ/dj/NBuRKnYpY1QoYsch/oGx0tLtjDtzSKKduynd0YiN5/dlwtzu+OP0rV44i0VusgJaGhwvLJsG9PeXMOqbfvolZbAjWf15ZLhmUSr2MUjKnSRk9DQ4PjPyu1Me3MNyzbvJSs1nqln9uWyEVnE+FXs0rpU6CIh4JzjrdU7uOeNIhZv2kP35Di+c2YfLs/vQVx0lNfxJEKo0EVCyDnHu2vK+OsbayjcsJsuHWP59hl9mDSyJ/ExKnZpWSp0kRbgnGNB8U7ueWMNH67bRXpSLJPPyOHq03qREOP3Op6EKRW6SAv7cO1Opr1ZxPtFZXRKjOH6L+YwbkhXctITdZGShJQKXaSVFG7YzbQ31/D26lIAuiXHMbpPGmP6pDOmTxrdU+I9TijtnQpdpJWtL6tgXnEZ84t3sqB4J7sqagDITktgTN/Gch/dO420pFiPk0p7o0IX8VBDg2P19n3ML97J/KIyPly3i/3VdQAM7Nrh0633Ub070SEu2uO00tap0EXakLr6BpZuLm8s+OIyCtbvprqugSifMTQzmTF90hjbN50RvVJ1OqQcQYUu0oZV1dazcONuFhTvZH7xThZt2kN9gyMmykderxTG9klnTN80crNSdIWqqNBF2pP91XV8tG4X8wP74Fds3YtzkBgTxcicTozpk87oPmkM6tZRd4OMQEcrdJ0sK9LGJMX6OWtgZ84a2BmA3RU1fLC2cet9XnEZb61eCUBKQjSje6cxpk8aY/qm01unSEY8FbpIG5eaGMO4od0YN7QbANvKq1iwtox5RY0HWV9Ztg2ALh1jPz3AOqZvOpk6RTLiaJeLSDvmnGPjrsrGci8uY0HxTnYGTpHslZbAqdmdyE5LIDM1nsyUBLJS4+nSMU73d2/HtMtFJEyZGb3SEumVlsiVo3riXOAUyaLGXTRvr95B2f6aQ17j9xldk+PICpR8Zmo8WanxZKXEk5kaT7fkeN1Fsp1SoYuEETNjYNeODOzakW9+MQeAAzX1bN5zgM17DlCyu5LNuw8+PsC8ojK276ui6R/qZtClQ6DwU+PJTIknKzWhyeN4nU7ZRqnQRcJcfEwUfTsn0bdzUrPza+oa2Fp+gM27D1ASKPrG0q+kcMNuXlqylfqGQ3fNpifFNFv0Bx/rAilvqNBFIlyM3/fpbpvm1Dc4tu+taiz6PZWU7Drw6Rb/iq17+c/K7dTUNRzymuT46ENKvkvHOJJi/XSI85MU2/iT2PR5nJ9Yv7b6T1ZQhW5m5wP3AFHAQ865Ow+bb4H5FwCVwDeccwtDnFVEPBDlM7qnxAduLNbpiPkNDY6yiuomW/af7dpZv7OC94vKqKypP+Z6YqJ8JMZGkRTnJyk2mg6Bok8MfAE0/TI4+CVwyO+Dy8f4I/ag7zEL3cyigOnA/wAlwEdm9qJzbkWTxcYB/QI/o4D7A79FJMz5fEbnDnF07hBHXs/UI+Y756isqaeiuo591XXsr6pjf3Xgp8njfVV1VDR5vL+6lh37qqgoq//0eVVtQzMJjpQYE9X4RRDn//SLISnWT3x0FNFRPqL9PmKifERHGTF+X+O0qM+mHZzfdN7BZWOimizvN2Kiooj22yHvEeP3efKlEswW+kigyDm3FsDMngQmAE0LfQLwqGs8B/IDM0sxs27Oua0hTywi7YqZkRjYxdL5JN+rtr7h09I/+IVw8Evi0C+DuiO+QMr2VVJVV09tXQM19Y6aunpq6x219Q3UNYT+9G2f8dmXxMEvgkDxXzmyJ986vXfI1xlMoWcCm5o8L+HIre/mlskEDil0M5sMTAbo2bPn8WYVkQgXHeUjJSGGlISYkL5vQ4OjtqGBmrqGT0u+8XEDNfUN1Na5xt+Bn8/mOWrrPpte3eT1B197cNnaOvfptIwOLXPb5GAKvbm/Gw7/OgtmGZxzM4GZ0HhhURDrFhFpcT6fEeuLavcHZoO5eqAE6NHkeRaw5QSWERGRFhRMoX8E9DOzHDOLAa4AXjxsmReBa63RaUC59p+LiLSuY+5ycc7VmdlNwGs0nrb4d+fccjObEpg/A3iZxlMWi2g8bfG6lossIiLNCeo8dOfcyzSWdtNpM5o8dsCNoY0mIiLHQ3fgEREJEyp0EZEwoUIXEQkTKnQRkTDh2YhFZlYKbPBk5aGTDpR5HaIN0edxKH0en9FncaiT+Tx6OecympvhWaGHAzMr+LyhoCKRPo9D6fP4jD6LQ7XU56FdLiIiYUKFLiISJlToJ2em1wHaGH0eh9Ln8Rl9Fodqkc9D+9BFRMKEttBFRMKECl1EJEyo0E+AmfUws7fMbKWZLTez73qdyWtmFmVmH5vZS15n8VpgCMbZZrYq8G9ktNeZvGRm3w/8P1lmZk+YWZzXmVqTmf3dzHaY2bIm0zqZ2X/MbE3g95GDsZ4AFfqJqQN+6Jw7BTgNuNHMBnmcyWvfBVZ6HaKNuAd41Tk3EBhGBH8uZpYJ3ALkO+eG0HgL7iu8TdXqHgHOP2zabcAbzrl+wBuB5ydNhX4CnHNbnXMLA4/30fgfNtPbVN4xsyxgPPCQ11m8ZmYdgTOAvwE452qcc3s8DeU9PxBvZn4ggQgbzcw59y6w67DJE4B/BB7/A7g4FOtSoZ8kM8sGhgMfehzFS38BbgUaPM7RFvQGSoGHA7ugHjKzRK9DecU5txn4I7CRxkHjy51zr3ubqk3ocnBUt8DvzqF4UxX6STCzJOBZ4HvOub1e5/GCmX0F2OGcK/Q6SxvhB/KA+51zw4EKQvTndHsU2Dc8AcgBugOJZna1t6nClwr9BJlZNI1l/rhzbo7XeTw0FrjIzNYDTwJnm9lj3kbyVAlQ4pw7+BfbbBoLPlKdC6xzzpU652qBOcAYjzO1BdvNrBtA4PeOULypCv0EmJnRuI90pXPu/3udx0vOuZ8657Kcc9k0Hux60zkXsVtgzrltwCYzGxCYdA6wwsNIXtsInGZmCYH/N+cQwQeJm3gR+Hrg8deBF0LxpkGNKSpHGAtcAyw1s0WBaT8LjL0qcjPwuJnFAGuJ4EHTnXMfmtlsYCGNZ4d9TITdBsDMngDOBNLNrAS4HbgTeNrMrqfxS+/ykKxLl/6LiIQH7XIREQkTKnQRkTChQhcRCRMqdBGRMKFCFxEJEyp0EZEwoUIXEQkT/wel0B9T7dYIPwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dim_circ, Volume)" + ] + }, + { + "cell_type": "markdown", + "id": "f81d60f3", + "metadata": {}, + "source": [ + "### 1.4 Volume of the skin" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "82f6ec7c", + "metadata": {}, + "outputs": [], + "source": [ + "def skin(dim):\n", + " return 1**dim-(1-2*0.01)**dim" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "a30893bb", + "metadata": {}, + "outputs": [], + "source": [ + "Skins = []\n", + "for i in range(100):\n", + " Dim = i+1\n", + " skins = skin(Dim)\n", + " Skins.append(skins)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "c1492574", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(dimension, Skins)" + ] + }, + { + "cell_type": "markdown", + "id": "b50b74a5", + "metadata": {}, + "source": [ + "### 1.5 Distances between points" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "edfc8fd0", + "metadata": {}, + "outputs": [], + "source": [ + "Hist = []\n", + "for i in range(10):\n", + " Dim = i+1\n", + " points = []\n", + " Distances = []\n", + " for j in range(1000):\n", + " point = np.random.uniform(size=Dim)\n", + " if len(points) > 0:\n", + " ps = np.array(points)\n", + " distances = np.sqrt(np.sum((ps-point)**2, axis=1))\n", + " length = len(distances)\n", + " for k in distances:\n", + " Distances.append(k)\n", + " points.append(point)\n", + " Hist.append(Distances) \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "id": "b6b1b79e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "\" \\nfig, ax = plt.subplots(10, figsize=(12, 80))\\nwidth = Bins[0][1] - Bins[0][0]\\nax[0].bar(Bins[0], N[0], align='center', width=width)\\nwidth = Bins[1][1] - Bins[1][0]\\nax[1].bar(Bins[1], N[1], align='center', width=width)\\nwidth = Bins[2][1] - Bins[2][0]\\nax[2].bar(Bins[2], N[2], align='center', width=width)\\nwidth = Bins[3][1] - Bins[3][0]\\nax[3].bar(Bins[3], N[3], align='center', width=width)\\nwidth = Bins[4][1] - Bins[4][0]\\nax[4].bar(Bins[4], N[4], align='center', width=width)\\nwidth = Bins[5][1] - Bins[5][0]\\nax[5].bar(Bins[5], N[5], align='center', width=width)\\nwidth = Bins[6][1] - Bins[6][0]\\nax[6].bar(Bins[6], N[6], align='center', width=width)\\nwidth = Bins[7][1] - Bins[7][0]\\nax[7].bar(Bins[7], N[7], align='center', width=width)\\nwidth = Bins[8][1] - Bins[8][0]\\nax[8].bar(Bins[8], N[8], align='center', width=width)\\nwidth = Bins[9][1] - Bins[9][0]\\nax[9].bar(Bins[9], N[9], align='center', width=width)\\n\"" + ] + }, + "execution_count": 146, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Bins = []\n", + "N = []\n", + "for i in range(10):\n", + " D = Hist[i]\n", + " n, bins, _ = plt.hist(x=D, bins=20)\n", + " bins = (bins[1:]-bins[:-1])/2\n", + " Bins.append(bins)\n", + " N.append(n)\n", + "\n", + "''' \n", + "fig, ax = plt.subplots(10, figsize=(12, 80))\n", + "width = Bins[0][1] - Bins[0][0]\n", + "ax[0].bar(Bins[0], N[0], align='center', width=width)\n", + "width = Bins[1][1] - Bins[1][0]\n", + "ax[1].bar(Bins[1], N[1], align='center', width=width)\n", + "width = Bins[2][1] - Bins[2][0]\n", + "ax[2].bar(Bins[2], N[2], align='center', width=width)\n", + "width = Bins[3][1] - Bins[3][0]\n", + "ax[3].bar(Bins[3], N[3], align='center', width=width)\n", + "width = Bins[4][1] - Bins[4][0]\n", + "ax[4].bar(Bins[4], N[4], align='center', width=width)\n", + "width = Bins[5][1] - Bins[5][0]\n", + "ax[5].bar(Bins[5], N[5], align='center', width=width)\n", + "width = Bins[6][1] - Bins[6][0]\n", + "ax[6].bar(Bins[6], N[6], align='center', width=width)\n", + "width = Bins[7][1] - Bins[7][0]\n", + "ax[7].bar(Bins[7], N[7], align='center', width=width)\n", + "width = Bins[8][1] - Bins[8][0]\n", + "ax[8].bar(Bins[8], N[8], align='center', width=width)\n", + "width = Bins[9][1] - Bins[9][0]\n", + "ax[9].bar(Bins[9], N[9], align='center', width=width)\n", + "'''" + ] + }, + { + "cell_type": "markdown", + "id": "ff36631f", + "metadata": {}, + "source": [ + "## Question 2" + ] + }, + { + "cell_type": "markdown", + "id": "01c0bc8b", + "metadata": {}, + "source": [ + "### 2.1 General Dataset based on function" + ] + }, + { + "cell_type": "code", + "execution_count": 117, + "id": "17fd48db", + "metadata": {}, + "outputs": [], + "source": [ + "def func(x):\n", + " return 0.5+0.4*np.sin(2*np.pi*x)\n", + "\n", + "# for size=9\n", + "x9 = np.random.uniform(size=9)\n", + "y_err9 = np.random.normal(loc=0, scale=0.05, size=9)\n", + "y9 = func(x9)+y_err9" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "id": "f9efc782", + "metadata": {}, + "outputs": [], + "source": [ + "# for size=15\n", + "x15 = np.random.uniform(size=15)\n", + "y_err15 = np.random.normal(loc=0, scale=0.05, size=15)\n", + "y15 = func(x15)+y_err15" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "id": "28d8a110", + "metadata": {}, + "outputs": [], + "source": [ + "# for size=100\n", + "x100 = np.random.uniform(size=100)\n", + "y_err100 = np.random.normal(loc=0, scale=0.05, size=100)\n", + "y100 = func(x100)+y_err100" + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "id": "838d32b1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 120, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x9, y9)\n", + "plt.scatter(x15, y15)\n", + "plt.scatter(x100, y100)" + ] + }, + { + "cell_type": "markdown", + "id": "ca47ecd4", + "metadata": {}, + "source": [ + "### 2.2 Find the best polynomial approximation" + ] + }, + { + "cell_type": "code", + "execution_count": 143, + "id": "34519675", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/yuzezhang/opt/anaconda3/lib/python3.8/site-packages/IPython/core/interactiveshell.py:3437: RankWarning: Polyfit may be poorly conditioned\n", + " exec(code_obj, self.user_global_ns, self.user_ns)\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 143, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# for size=9\n", + "Z9 = []\n", + "for i in range(10):\n", + " degree = i\n", + " z9 = np.polyfit(x9,y9,degree)\n", + " Z9.append(z9)\n", + " \n", + "def poly(x, coeffs):\n", + " o = len(coeffs)\n", + " y = 0\n", + " for i in range(o):\n", + " y += coeffs[i]*x**(o-1-i)\n", + " return y\n", + "\n", + "plt.figure(figsize=(24,16))\n", + "plt.scatter(x9,y9)\n", + "for i in range(10):\n", + " coeffs = Z9[i]\n", + " x = np.arange(0,1.001,0.001)\n", + " y9_p = poly(x, coeffs)\n", + " deg = str(i)\n", + " plt.plot(x, y9_p, label=deg)\n", + "plt.ylim(-2,2)\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 144, + "id": "2636e202", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 144, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# for size=15\n", + "Z15 = []\n", + "for i in range(10):\n", + " degree = i\n", + " z15 = np.polyfit(x15,y15,degree)\n", + " Z15.append(z15)\n", + " \n", + "plt.figure(figsize=(24,16))\n", + "plt.scatter(x15,y15)\n", + "for i in range(10):\n", + " coeffs = Z15[i]\n", + " x = np.arange(0,1.001,0.001)\n", + " y15_p = poly(x, coeffs)\n", + " deg = str(i)\n", + " plt.plot(x, y15_p, label=deg)\n", + "plt.ylim(-2,2)\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "id": "80fabc47", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 145, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# for size=100\n", + "Z100 = []\n", + "for i in range(10):\n", + " degree = i\n", + " z100 = np.polyfit(x100,y100,degree)\n", + " Z100.append(z100)\n", + " \n", + "plt.figure(figsize=(24,16))\n", + "plt.scatter(x100,y100)\n", + "for i in range(10):\n", + " coeffs = Z100[i]\n", + " x = np.arange(0,1.001,0.001)\n", + " y100_p = poly(x, coeffs)\n", + " deg = str(i)\n", + " plt.plot(x, y100_p, label=deg)\n", + "plt.ylim(-2,2)\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 186, + "id": "fdf8a0b7", + "metadata": {}, + "outputs": [], + "source": [ + "# Note that to find the best model, we simply find the derivative of error function and equate it to zero\n", + "# this gives the minimized error\n", + "# However, the minimized error on the raining set is not valid due to over-fitting\n", + "# the minimized error on the testing set is valid given the model is not biased by the data itself" + ] + }, + { + "cell_type": "markdown", + "id": "bb606836", + "metadata": {}, + "source": [ + "### 2.3 Find MSE" + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "id": "3a623f72", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 187, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# generate test data:\n", + "\n", + "# for size=9\n", + "x9_test = np.random.uniform(size=9)\n", + "y_err9_test = np.random.normal(loc=0, scale=0.05, size=9)\n", + "y9_t = func(x9_test)+y_err9_test\n", + "\n", + "# for size=15\n", + "x15_test = np.random.uniform(size=15)\n", + "y_err15_test = np.random.normal(loc=0, scale=0.05, size=15)\n", + "y15_t = func(x15_test)+y_err15_test\n", + "\n", + "# for size=100\n", + "x100_test = np.random.uniform(size=100)\n", + "y_err100_test = np.random.normal(loc=0, scale=0.05, size=100)\n", + "y100_t = func(x100_test)+y_err100_test\n", + "\n", + "plt.scatter(x9_test, y9_t)\n", + "plt.scatter(x15_test, y15_t)\n", + "plt.scatter(x100_test, y100_t)" + ] + }, + { + "cell_type": "code", + "execution_count": 188, + "id": "a8fd777f", + "metadata": {}, + "outputs": [], + "source": [ + "# training MSE for size=9\n", + "\n", + "MSE_TEST9 = []\n", + "MSE_TRAIN9 = []\n", + "for i in range(10):\n", + " coeffs = Z9[i]\n", + " y9_train = poly(x9, coeffs)\n", + " y9_test = poly(x9_test, coeffs)\n", + " dy_train = np.abs(y9_train-y9)\n", + " dy_test = np.abs(y9_test-y9_t)\n", + " MSE_train = 1/len(dy_train)*np.sum(dy_train**2)\n", + " MSE_test = 1/len(dy_test)*np.sum(dy_test**2)\n", + " MSE_TRAIN9.append(MSE_train)\n", + " MSE_TEST9.append(MSE_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 189, + "id": "b3034e43", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 189, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "poly_deg = np.arange(0,10,1)\n", + "\n", + "plt.plot(poly_deg, MSE_TRAIN9, label='train')\n", + "plt.plot(poly_deg, MSE_TEST9, label='test')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 190, + "id": "8630044c", + "metadata": {}, + "outputs": [], + "source": [ + "# training MSE for size=15\n", + "\n", + "MSE_TEST15 = []\n", + "MSE_TRAIN15 = []\n", + "for i in range(10):\n", + " coeffs = Z15[i]\n", + " y15_train = poly(x15, coeffs)\n", + " y15_test = poly(x15_test, coeffs)\n", + " dy_train = np.abs(y15_train-y15)\n", + " dy_test = np.abs(y15_test-y15_t)\n", + " MSE_train = 1/len(dy_train)*np.sum(dy_train**2)\n", + " MSE_test = 1/len(dy_test)*np.sum(dy_test**2)\n", + " MSE_TRAIN15.append(MSE_train)\n", + " MSE_TEST15.append(MSE_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 191, + "id": "78c80dd2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 191, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(poly_deg, MSE_TRAIN15, label='train')\n", + "plt.plot(poly_deg, MSE_TEST15, label='test')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "id": "807b26c4", + "metadata": {}, + "outputs": [], + "source": [ + "# training MSE for size=100\n", + "\n", + "MSE_TEST100 = []\n", + "MSE_TRAIN100 = []\n", + "for i in range(10):\n", + " coeffs = Z100[i]\n", + " y100_train = poly(x100, coeffs)\n", + " y100_test = poly(x100_test, coeffs)\n", + " dy_train = np.abs(y100_train-y100)\n", + " dy_test = np.abs(y100_test-y100_t)\n", + " MSE_train = 1/len(dy_train)*np.sum(dy_train**2)\n", + " MSE_test = 1/len(dy_test)*np.sum(dy_test**2)\n", + " MSE_TRAIN100.append(MSE_train)\n", + " MSE_TEST100.append(MSE_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 193, + "id": "999b9dcb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 193, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(poly_deg, MSE_TRAIN100, label='train')\n", + "plt.plot(poly_deg, MSE_TEST100, label='test')\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "d3e41e2c", + "metadata": {}, + "source": [ + "### 2.4 Minimize Error Function" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "06faaeb6", + "metadata": {}, + "outputs": [], + "source": [ + "# the plan is to minimize the error function with the w^2 parameters\n", + "# once it's minimized," + ] + }, + { + "cell_type": "markdown", + "id": "32bcfd86", + "metadata": {}, + "source": [ + "### 2.5 Test Minimization" + ] + }, + { + "cell_type": "code", + "execution_count": 194, + "id": "3142b2fd", + "metadata": {}, + "outputs": [], + "source": [ + "def regularization(model, data, coeff, l):\n", + " error = 1/len(model)*np.sum((np.abs(model-data))**2)\n", + " add = l*1/len(coeff)*np.sum(coeff**2)\n", + " return error+add" + ] + }, + { + "cell_type": "code", + "execution_count": 202, + "id": "a1d394e2", + "metadata": {}, + "outputs": [], + "source": [ + "ERROR = []\n", + "for i in range(10):\n", + " coeffs = Z9[i]\n", + " error = regularization(poly(x9_test, coeffs), y9_t, coeffs, 0.5)\n", + " ERROR.append(error)" + ] + }, + { + "cell_type": "code", + "execution_count": 203, + "id": "3642e711", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.2032167737983944,\n", + " 0.29805174754080993,\n", + " 0.1878489319208772,\n", + " 46.016260266826976,\n", + " 40.21844354660332,\n", + " 288.2098494269156,\n", + " 1505.9115197163387,\n", + " 1728796.9819142863,\n", + " 8728997349.059772,\n", + " 1183123626.2022896]" + ] + }, + "execution_count": 203, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ERROR" + ] + }, + { + "cell_type": "code", + "execution_count": 233, + "id": "29f53ea4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " fun: 0.00021126522683696\n", + " hess_inv: array([[ 3.87296683e+04, -1.14279620e+04, -3.42184350e+04,\n", + " -2.77204872e+04, 2.35688573e+03, 3.49780329e+04,\n", + " 2.89254233e+04, -4.16018321e+04, 1.05970097e+04,\n", + " -3.86039147e+02],\n", + " [-1.14279620e+04, 3.64429117e+03, 1.03678376e+04,\n", + " 8.19538105e+03, -1.07032453e+03, -1.09223562e+04,\n", + " -8.71670798e+03, 1.32156017e+04, -3.46895414e+03,\n", + " 1.33100733e+02],\n", + " [-3.42184350e+04, 1.03678376e+04, 3.05063642e+04,\n", + " 2.45119205e+04, -2.45115415e+03, -3.15018991e+04,\n", + " -2.57454610e+04, 3.76759025e+04, -9.68904112e+03,\n", + " 3.58327447e+02],\n", + " [-2.77204872e+04, 8.19538105e+03, 2.45119205e+04,\n", + " 1.98534072e+04, -1.69450869e+03, -2.50632586e+04,\n", + " -2.07329921e+04, 2.97817679e+04, -7.56603068e+03,\n", + " 2.72663694e+02],\n", + " [ 2.35688573e+03, -1.07032453e+03, -2.45115415e+03,\n", + " -1.69450869e+03, 6.82241294e+02, 2.97012379e+03,\n", + " 1.98559939e+03, -3.89918929e+03, 1.16964162e+03,\n", + " -5.62023519e+01],\n", + " [ 3.49780329e+04, -1.09223562e+04, -3.15018991e+04,\n", + " -2.50632586e+04, 2.97012379e+03, 3.29303325e+04,\n", + " 2.65142142e+04, -3.96914130e+04, 1.03515763e+04,\n", + " -3.93223133e+02],\n", + " [ 2.89254233e+04, -8.71670798e+03, -2.57454610e+04,\n", + " -2.07329921e+04, 1.98559939e+03, 2.65142142e+04,\n", + " 2.17634866e+04, -3.16071109e+04, 8.06085206e+03,\n", + " -2.89430902e+02],\n", + " [-4.16018321e+04, 1.32156017e+04, 3.76759025e+04,\n", + " 2.97817679e+04, -3.89918929e+03, -3.96914130e+04,\n", + " -3.16071109e+04, 4.81880521e+04, -1.27660347e+04,\n", + " 5.06644906e+02],\n", + " [ 1.05970097e+04, -3.46895414e+03, -9.68904112e+03,\n", + " -7.56603068e+03, 1.16964162e+03, 1.03515763e+04,\n", + " 8.06085206e+03, -1.27660347e+04, 3.51723250e+03,\n", + " -1.58851227e+02],\n", + " [-3.86039147e+02, 1.33100733e+02, 3.58327447e+02,\n", + " 2.72663694e+02, -5.62023519e+01, -3.93223133e+02,\n", + " -2.89430902e+02, 5.06644906e+02, -1.58851227e+02,\n", + " 1.13590741e+01]])\n", + " jac: array([ 2.36222513e-06, 1.34862421e-06, 9.55962605e-07, 1.22810343e-06,\n", + " 1.53023575e-06, 8.23942173e-07, -6.84643965e-07, 6.70155714e-07,\n", + " 2.18027344e-06, -7.62444506e-06])\n", + " message: 'Optimization terminated successfully.'\n", + " nfev: 638\n", + " nit: 57\n", + " njev: 58\n", + " status: 0\n", + " success: True\n", + " x: array([ 4.30235586, -2.37869899, -4.52176676, -2.14840648,\n", + " 3.19970191, 7.17795115, 2.35545956, -13.13932295,\n", + " 5.32432463, 0.35892596])\n" + ] + } + ], + "source": [ + "import scipy.optimize as o\n", + "\n", + "def eq_m(x, a, b, c, d, e, f, g, h, i, j): # assumed signature of eq_m\n", + " return a*x**9+b*x**8+c*x**7+d*x**6+e*x**5+f*x**4+g*x**3+h*x**2+i*x+j\n", + "\n", + "def regularization(params):\n", + " a, b, c, d, e, f, g, h, i, j = params\n", + " model = eq_m(x9, a, b, c, d, e, f, g, h, i, j)\n", + " error = 1/len(model)*np.sum((np.abs(model-y9))**2)\n", + " add = 1/len(params)*np.sum(params**2)*0\n", + " return error+add\n", + "\n", + "p0 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] # initial guess for lambda, mu, and sigma\n", + "res = o.minimize(regularization, p0)\n", + "print(res) # see if minimization succeeded.\n", + "a, b, c, d, e, f, g, h, i, j = res.x" + ] + }, + { + "cell_type": "code", + "execution_count": 234, + "id": "5aca8306", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 234, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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j4lm6+xSHCyqMjiOE03ltoe/LKye3tJqbZZlcj/LzCQl0Cvbnd6uOyh6kwut4baEvTysgwNeHGwd0MTqKsKOwID8en5TErpNlrD502ug4QjiVVxa62WJlzaHT3JAcQ6ise+5xfjQ8juSuHXl+zXFq6mUjDOE9vLLQd+aUUVpVz7RBXY2OIhzA5KNYOD2FgvIalmzKNjqOEE5jU6ErpW5USqUrpTKVUk+0csx4pdR+pdQRpdQ39o1pX58dPE2wv4nr+kUbHUU4yMjeEUwd2JU3vsmkUDbCEF6izUJXSpmA14CbgBRgrlIqpdkx4cDrwA+01v2BH9o/qn00WKx8cbhxuCXQz2R0HOFAT9zUD63hhc+PGx1FCKew5Qp9BJCptc7WWtcDS4EZzY65DVimtc4D0FoX2Tem/WzPKuVcdQNTZbjF48V1Dua+sb1ZeaCQ3SfLjI4jhMPZUuixwKkmH+dffKypRKCTUmqjUmqvUurOlr6QUupepdQepdSe4mJjdppZffA0IQG+jEuUlRW9wf3j+9ClYyC/XXUEq1WmMQrPZkuht3RPfPO/Gb7AVcBUYDLwtFIq8TufpPUSrXWq1jo1Ksr5hdpgsfLFkTNMTJHhFm8R7O/Lk1P6cbjgPB/vzTc6jhAOZUuh5wNNd37oDhS2cMwXWusqrXUJsAkYbJ+I9rM1s4SKmgamDpThFm/yg8HduKpnJ15ce5wLtQ1GxxHCYWwp9N1AglKql1LKH5gDrGx2zApgjFLKVykVDFwNuNyOA58dPE1ogC9jEiONjiKcSCnFgmkplFTW8+r6TKPjCOEwbRa61toMPASspbGkP9JaH1FK3a+Uuv/iMceAL4CDwC7gLa31YcfFbr96s5Uvj5xhYv8YAnxluMXbDI4LZ/ZV3Xlnaw4nS6qMjiOEQ9g0D11rvUZrnai17qO1/v3Fx97UWr/Z5JjFWusUrfUArfVLDsr7ve3ILuV8rZkpA2S4xVvNn5yEn8mHRWtc7h+PQtiFr9EBHG15WgGL16ZTUF6DAsqq6o2OJAwS0zGQn13Xl8Vr09mWWcKovjL0JjyLR9/6vzytgCeXHaLg4p2CGli48gjL0wqMDSYMc8+1vejeKYjffXYUs0W2qxOexaMLffHadGoavr04U02DhcVrZQMEbxXoZ+LXU5I5fuYCS3efavsThHAjHl3ora3hIWt7eLebBnRhRK/O/PmrE1TUyDRG4Tk8utC7hbe8E1FrjwvvcGka47nqel5Zl2F0HCHsxqMLff7kJAJ8v32KQX4m5k9OMiiRcBUDYsO49ao43t12kuziSqPjCGEXHl3oM4fGMiH5/5bIjQ0P4vlZA5kp284J4PHJSQT6mfj9apnGKDyDx09bzD9Xw5C4cJb/bLTRUYSLiQoN4KHr+/LC58fZdKKYsbJgm3BzHn2FXlhew8H8Cib1jzE6inBRd4+Op0fnYJ5bLdMYhfvz6EL/+thZACalyEbQomUBvo3TGE+creQ/u/KMjiO8wPNrjrHhuGO2jPDoQl93rIj4iGD6RocYHUW4sMn9Y7imdwR//uoE5dVyJ7FwnPLqev62KZsjhRUO+foeW+jV9Wa2Z5fKvqGiTUopFkxP4XxNAy99LdMYheOk5ZUDcFXPzg75+h5b6NsyS6k3W5nQT8bPRduSu3Zkzoge/HtHLplFF4yOIzzUntwyfH0UQ+LCHfL1PbbQ1x0vooO/iRG9HPObUHie/zcxkWA/E8/JNEbhIHtOnqN/t44E+TtmCW+PLHStNRvTi7g2IRJ/X488ReEAESEBPDwhgY3pxWxId9l9zoWbarBYOZBfzrCenRz2Gh7ZdsdOX+B0Ra0Mt4h2u2tUPL0iO/DcZ0dpkGmMwk6WpxUw6vn11DZYWZFW6LAVXz2y0Ncfb5yuOL6f3Cgi2sff14ffTEkmq7iK93bkGh1HeIBLy3gXV9YBUFZdz5PLDjmk1D200IsYGBtGdGig0VGEG5qQHM2YhEhe+jqDc7IhirhCzlzG2+MKvayqnrRT5Vwv0xXF96SU4qmpKVyobeAvX58wOo5wc85cxtvjCn1jehFaI4UurkhSl1DmXd2T93fmceKsTGMU358zl/H2uEJff7yIyJAABsaGGR1FuLlHJybSwd/Es58dRWttdBzhpuZPTsLPR33rMUct4+1RhW62WNl0opjrkqLwafY/UIj26tzBn1/ckMjmjBLWO2jtDeH5Zg6NpX9sGCbV2EmOXMbbo5bP3X+qnPO1ZsYnyXCLsI87runJeztzeW71McYkRMl9DaLdtNbkn6th+uCuvDRnqENfy6N+OjdllOCjYHTfCKOjCA/hZ/Lh6akp5JRU8a/tJ42OI9xQdkkVJZV1XN3b8b3kUYW+OaOYQd3DCQ/2NzqK8CDX9YtmXGIUf12XQenFucRC2GpndhkAVzthGRKPKfSK6gYOnCqXXWeEQzw9LZnqegt//kqmMYr22ZlTSlRoAL0iOzj8tTym0LdmlWDVMDYh0ugowgP1jQ7ljpE9+WBXHsdOnzc6jnATWmt2ZpcxoldnlHL8RA2PKfRNJ4oJDfB12LKUQvzihgQ6BvnJNEZhs+ySKs6cr2VUH+e8r+cRha61ZnNGCaP6RuBr8ohTEi4oPNifR29IZFtWKV8ePWt0HOEGtmaWADCmr3OGgj2i/bKKqygor5Hxc+Fw867uQUJ0CIvWHKPObGn7E4RX25JRQlznIHpEBDvl9Tyi0DdnFAMwNkEKXTiWr8mHp6elkFtazbtbTxodR7gws8XK9uxSru3rvPf1PKTQS+gV2YG4zs75LSi829jEKCb0i+aV9ZkUX5BpjKJlhwoquFBrZrQUuu3qzBa2Z5UyRma3CCf6zdRkahss/OlL+y+BKjzDpfHzUX2k0G22N/ccNQ0WGW4RTtU7KoS7RsXz4Z5THCmsMDqOcEGbM0ro360jnTs470ZHty/0TSdK8PVRjHTStCAhLnl4QgKdgv353SqZxii+rbrezL68c04dPwcPKPStmSUM69GJkACPWmdMuIGwID8em5jIzpwyvjh8xug4woXsyimjwaKdOn4Obl7oFdUNHC6sYJQsxiUMMmd4HP26hPL7NceobZBpjKLRNyeKCfD1YXi849dvacqmQldK3aiUSldKZSqlnrjMccOVUhal1Gz7RWzdjpxStHbumw5CNHVpGmP+uRre3pJjdBzhIjamFzOqTwRB/ianvm6bha6UMgGvATcBKcBcpVRKK8f9AVhr75Ct2ZZZQpCfSW73F4Ya3TeSiSkxvL4hk6LztUbHEQbLKakip6SK6wzYBtOWK/QRQKbWOltrXQ8sBWa0cNzPgU8Ap23tsi2rlOG9OsumA8Jwv5mSTINF8/znx42OIgy2Mb2xAscnumahxwKnmnycf/Gx/1JKxQI3A29e7gsppe5VSu1RSu0pLi5ub9ZvKbpQS0ZRpdMWvRHicuIjO3DfuN58mlbAjuxSo+MIA21IL6ZPVAen3e7flC2F3tKaj83naL0E/Eprfdl3hbTWS7TWqVrr1KioK5s3vj2r8S/NaBk/Fy7iwfF96d4piAUrDtNgsRodRxigut7MjuxSrjNoG0xbCj0fiGvycXegsNkxqcBSpdRJYDbwulJqpj0CtmZbZikdA31J6dbRkS8jhM2C/E08M70/J85W8o+t8gapN9qeVUq92WrI+DnYVui7gQSlVC+llD8wB1jZ9ACtdS+tdbzWOh74GHhQa73c3mGb2pZdwsjeEZh8HL9ovBC2uiElhgn9onnp6wxOV9QYHUc42Yb0Ijr4m0iN72TI67dZ6FprM/AQjbNXjgEfaa2PKKXuV0rd7+iALTlVVs2pshoZPxcu6Zkf9Mdi1Ty3+pjRUYQTaa1Zf6yI0X0jCfB17nTFS2y6vVJrvQZY0+yxFt8A1Vr/+MpjXd62rMZFb5x9F5YQtojrHMzPruvLn786wdzhJVwrC8d5hUMFFRRW1PLYpCTDMrjl/fLbskqJDAmgb3SI0VGEaNG9Y3uzbF8+C1Yc5sHxffjL1xkUltfQLTyI+ZOTmDk0tu0vItzKl0fOYvJRTDBo/Bzc8NZ/rTXbskoZ1SfCKZuuCvF9BPqZeOYH/ckuqeKJZYcoKK9BAwXlNTy57BDL0wqMjijsaHlaAW9+k4XFqpn2yhbDvr9uV+hZxZUUX6iT8XPh8sYnRRPo54PZ+u1ZvjUNFhavlXXUPcXytAJ+9cnB/36fjfyl7XaFfqTwPErJ+LlwD7UNLc9HLyyXGTCeYvHadOrM3/4+G/VL2+3G0GcMiWV8YjRhwX5GRxGiTbHhQRS0UN7dwoMMSCMcobVfzkb80na7K3RAyly4jfmTkwhsttZQkJ+J+ZONmwkh7CumY2CLjxvxS9stC10IdzFzaCwv3DKIqJAAADr4m3h+1kCZ5eJBRrewH4NRv7Sl0IVwsJlDY9n91A3cdU1PqhssxEd2MDqSsKPc0mq6hgUSGx6EonGYzahf2m43hi6Eu3p8chJrj5zliU8Osurn1+Jnkuspd1dYXsOe3HM8PimRh65PMDqOXKEL4SyhgX78dkZ/jp+5wFubZfEuT7D64GkApg3qZnCSRlLoQjjR5P5dmNw/hpe+PkFuaZXRccQVWnWwkIGxYS4zjCaFLoST/fYHA/Az+fCbTw+jdfOtBYS7yC2t4mB+BdMHdzU6yn9JoQvhZF3CAvnljUlsySxh+X5ZAsBdfXZxuGWqiwy3gBS6EIaYd3VPhvYI53erjlJ8oc7oOKKdtNZ8mlbAVT07EetCN4lJoQthAJOP4sVbBlFVZ+Hp5TL04m4O5FeQWVTJ7Ku6Gx3lW6TQhTBIQkwov5iYwBdHzrD60Gmj44h2+GRvPgG+Pkwd5Drj5yCFLoSh7h3Tm0Hdw1iw4ggllTL04g7qzBZWHihkcv8udAx0rWVIpNCFMJCvyYfFswdTWWtm4YojRscRNlh3rIiKmgaXG24BKXQhDJfUJZRHbkhg9aHT/71RRbiuj/fm06VjoEsu4S2FLoQLuG9sbwbGhrFgxWFKZejFZRWdr+WbE8XcPCwWk4/r7ZgmhS6EC/A1+bD4h4M4X9vAgpUy9OKqPtx9CotV86PUOKOjtEgKXQgX0a9LRx6+PoHVB0+zQm44cjkWq+aDXXmMSYh0mVv9m5NCF8KFPDC+D0N7hPPU8sMt7nQkjLPheBGFFbXMu7qH0VFaJYUuhAvxNfnw0o+GYLFqHv/oAFar3HDkKt7fmUt0aAATkmOMjtIqKXQhXEzPiA4snJ7C9uxS3t4iy+y6glNl1Ww8Ucyc4XEuvY696yYTwovdmhrHpJQYFq9N59jp80bH8Xrv78xDAXNGuO5wC0ihC+GSlFK8cMsgwoL9+MXS/dQ2WIyO5LWq6sz8Z2cuk/t3MWTj5/aQQhfCRXXu4M+LsweRfvYCL36RbnQcr/XJvnzO15r5nzG9jI7SJil0IVzYdUnR3HVNT97ZmsP642eNjuN1LFbNO1tyGBIXzrAenYyO0yYpdCFc3JNTkknp2pHHPjpAoUxldKp1x85ysrSan47pjVKud2doc1LoQri4QD8Tr80bRoPZysMfpNFgsRodyWu8tTmH2PAgJvd33amKTUmhC+EGekV2YNGsgezJPcdfvjphdByvsPtkGbtOlvGTa3vh68JTFZtyj5RCCGYMiWXuiDhe35jFNyeKjY7j8V5el0FEB39uc/Gpik1JoQvhRhZO70+/LqE8+uF+zlTUGh3HY+0/Vc7mjBJ+OrY3Qf4mo+PYTApdCDcS6Gfi1duGUdtg4cH391JvlvF0R3hlXQbhwX7cPrKn0VHaRQpdCDfTNzqExbMHsy+vnN+ukqV27e1wQQXrjhdxz+hehAT4Gh2nXWwqdKXUjUqpdKVUplLqiRaen6eUOnjxv21KqcH2jyqEuGTqoK7cP64P7+/MY+muPKPjeJQ/fplOWJAfd42ONzpKu7VZ6EopE/AacBOQAsxVSqU0OywHGKe1HgQ8Cyyxd1AhxLfNn5zEmIRIFqw4QlreOaPjeITtWaVsTC/mZ9f1cbkNoG1hyxX6CCBTa52tta4HlgIzmh6gtd6mtb70E7UDcL3dU4XwMCYfxStzhxITFsAD7+2j6IK8SXoltNa88MVxuoYFcuc18UbH+V5sKfRY4FSTj/MvPtaae4DPW3pCKXWvUmqPUmpPcbFMuxLiSoUH+/O321Mpr6nngff2ySJeV+CLw2c4cKqcRycmEujnPjNbmrKl0Fu637XFVfeVUtfRWOi/aul5rfUSrXWq1jo1KirK9pRCiFaldOvIn28dwt7cc/zy44NoLZtitFed2cKLa9NJjAnhlmHuO8BgS6HnA013RO0OFDY/SCk1CHgLmKG1LrVPPCGELaYM7Movb0xi5YFC/vJ1htFx3M7bW3LIKaniN1NTMPm4/potrbFlTs5uIEEp1QsoAOYAtzU9QCnVA1gG3KG1lvuShTDAA+P6cLKkipfXZRAfEcwsN77SdKbTFTW8uj6TSSkxjEt075GDNgtda21WSj0ErAVMwDta6yNKqfsvPv8msACIAF6/uCKZWWud6rjYQojmlFI8N3Mgp8pq+NUnB4kND+Lq3hFGx3J5i9Ycx2LVPD2t+eQ996OMGm9LTU3Ve/bsMeS1hfBkFdUNzHpjK0UX6vjw3mtI6dbR6Egua2tmCfPe2skjExJ4dGKi0XFsopTa29oFs9wpKoSHCQv241/3XE1IgC93vrOL3NIqoyO5pKo6M08sO0h8RDAPjO9jdBy7kEIXwgPFhgfx73tGYLFauf3tnRSdlznqzS1em07+uRpenD3YbacpNieFLoSH6hsdyrt3j6C0sp4739lFRXWD0ZEMszytgNEvrKfXE6sZ/cJ6/vxlOv/cfpK7rolnRK/ORsezGyl0ITzY4Lhw/n5nKtnFVdz5j12cr/W+Ul+eVsCTyw5RUF6DBgrKa3hlfSadgv2ZPznJ6Hh2JYUuhIcb3TeS1+YN42hhBXe8vYuKGu8q9cVr06lpdgetBnwUdHCz1RTbIoUuhBeYmBLDG/Ou4mhhBXe+vdOrSr21jbVLK+udnMTxpNCF8BI3XCr10+e58+2dlFd7XqG1pFt4ULsed2dS6EJ4kRtSYnjz9qs4dvoCt/5tO6crWr569STzJycR6PvtqgvyM3nc+DlIoQvhdSYkx/DuT4ZTWF7LLa9vI7PogtGRHGraoK70iAj+78ex4UE8P2sgM4debtFY9ySFLoQXGtUnkqX3jqTeopn95nb2eegGGVprnll1hBNnK1k8exAnX5jK1ieu98gyByl0IbzWgNgwPnngGsKC/Ji7ZAcrD3xnEVW395evM3hvRx73jevND1Pj2v4ENyeFLoQX6xnRgU8eGMWg7mE8/EEai9cex2r1jPXU/7ntJC+vy+DW1O48cWM/o+M4hRS6EF4uMiSA9/9nJD9KjeO1DVnc+++9bn8D0r+2n2ThyiNMTIlh0c0DubgKrMeTQhdC4O/rwwu3DOSZ6SlsSC9i6sub2X+q3OhY38uSTVksWNFY5q/eNhRfk/fUnPecqRDispRS/Hh0Lz66byRWK8x+YxtLNmW5zRCM1ap54fPjLFpznGmDuvL6vGEE+HrGolu2kkIXQnzLVT07s+bhMdyQHMOiNce5/e2d5JVWGx3rsqrqzNz/3l7e/CaLeVf34K9zhuLnRVfml3jfGQsh2hQW7Mcbtw/j+VkDOZhfweSXNvHW5mwsLni1nnH2Are8sY2vj53lmekpPDdzgFvvC3olpNCFEC1SSjF3RA8en5SIVWueW32Mfk9/zh/XphsdDWicY/7+zlymv7qF4gt1vHv3CH48upfXvAHaEs9aakwIYVfL0wr4wxfp1JmtADRYNK9uyGTTiWJemjOE3lEhhuTKLKpkwYrDbMsqZUxCJH+6dTDRoYGGZHElUuhCiFa1tPQswKGCCm748zdMHdSNB8f3Ibmrc/YtLauq52/fZPHO1hwC/Uw8O3MA80b0wMdLh1iak0IXQrSqtaVnNXDf2D68tyOXVQcKGZMQyW0jejAhOQZ/X/uP5J6uqOHf23P557aTVDdYuHloLE/elExUaIDdX8udSaELIVrVLTyIghZKPTY8iCdu6scD4/rwr+0n+c+uPB54fx8RHfy5aWAXJqV0YWTviCsq98o6M5tOFLNsXwHrj59FA1MHduWRCQkkxIRewVl5LqW1Me9ap6am6j179hjy2kII21zavq3psEuQn+k7qxVarJpNJ4r5aM8pNqYXU9NgoYO/iWE9OzG0RycGxYYRHxlM907BLW7IXG+2cqailqziSvafKmdf3jl2ZpdRb7ESGRLArandmTuiB3Gdg7/zud5GKbVXa53a4nNS6EKIy1meVsDitekUltfQLTyI+ZOTLrtaYW2Dha2ZJWxIL2JvbjnpZ85zabajUtAx0I8O/iYC/UzUma3UNlgoq67nUhX5KEiIDmVMQiQ3pMSQ2rOTV93t2RYpdCGEYSrrzKSfOU9eWTW5pdWcq6qnss5CrdlCgK8PgX4mIkMC6N4piJ6dgxkQG+Zxe33a0+UKXf6vCSEcKiTAl6t6duaqnp2NjuLx5N8xQgjhIaTQhRDCQ0ihCyGEh5BCF0IIDyGFLoQQHkIKXQghPIQUuhBCeAgpdCGE8BCG3SmqlCoGcr/np0cCJXaM4w7knL2DnLN3uJJz7qm1jmrpCcMK/Uoopfa0duurp5Jz9g5yzt7BUecsQy5CCOEhpNCFEMJDuGuhLzE6gAHknL2DnLN3cMg5u+UYuhBCiO9y1yt0IYQQzUihCyGEh3DpQldK3aiUSldKZSqlnmjheaWUevni8weVUsOMyGlPNpzzvIvnelAptU0pNdiInPbU1jk3OW64UsqilJrtzHyOYMs5K6XGK6X2K6WOKKW+cXZGe7PhZztMKbVKKXXg4jnfbUROe1FKvaOUKlJKHW7lefv3l9baJf8DTEAW0BvwBw4AKc2OmQJ8DihgJLDT6NxOOOdRQKeLf77JG865yXHrgTXAbKNzO+H7HA4cBXpc/Dja6NxOOOdfA3+4+OcooAzwNzr7FZzzWGAYcLiV5+3eX658hT4CyNRaZ2ut64GlwIxmx8wA/qUb7QDClVJdnR3Ujto8Z631Nq31uYsf7gC6OzmjvdnyfQb4OfAJUOTMcA5iyznfBizTWucBaK3d/bxtOWcNhCqlFBBCY6GbnRvTfrTWm2g8h9bYvb9cudBjgVNNPs6/+Fh7j3En7T2fe2j8De/O2jxnpVQscDPwphNzOZIt3+dEoJNSaqNSaq9S6k6npXMMW875VSAZKAQOAY9ora3OiWcIu/eXK28SrVp4rPkcS1uOcSc2n49S6joaC/1ahyZyPFvO+SXgV1prS+PFm9uz5Zx9gauACUAQsF0ptUNrfcLR4RzElnOeDOwHrgf6AF8ppTZrrc87OJtR7N5frlzo+UBck4+70/ibu73HuBObzkcpNQh4C7hJa13qpGyOYss5pwJLL5Z5JDBFKWXWWi93SkL7s/Vnu0RrXQVUKaU2AYMBdy10W875buAF3TjAnKmUygH6AbucE9Hp7N5frjzkshtIUEr1Ukr5A3OAlc2OWQncefHd4pFAhdb6tLOD2lGb56yU6gEsA+5w46u1pto8Z611L611vNY6HvgYeNCNyxxs+9leAYxRSvkqpYKBq4FjTs5pT7accx6N/yJBKRUDJAHZTk3pXHbvL5e9Qtdam5VSDwFraXyH/B2t9RGl1P0Xn3+TxhkPU4BMoJrG3/Buy8ZzXgBEAK9fvGI1azdeqc7Gc/Yotpyz1vqYUuoL4CBgBd7SWrc4/c0d2Ph9fhZ4Vyl1iMbhiF9prd12WV2l1AfAeCBSKZUPLAT8wHH9Jbf+CyGEh3DlIRchhBDtIIUuhBAeQgpdCCE8hBS6EEJ4CCl0IYTwEFLoQgjhIaTQhRDCQ/x/hFaATo8ywBgAAAAASUVORK5CYII=\n", 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