{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 03wk-2: 깊은 신경망 (1) – 로지스틱의 한계 극복\n",
"\n",
"최규빈 \n",
"2024-03-20\n",
"\n",
"
\n",
"\n",
"# 1. 강의영상\n",
"\n",
"\n",
"\n",
"# 2. Imports"
],
"id": "fa9a5b8c-9821-4db7-b89a-842e9a0b0a44"
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import torch\n",
"import matplotlib.pyplot as plt \n",
"import pandas as pd"
],
"id": "dd3e2acd-7950-4fb9-96cd-3a598686b677"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. 꺽인그래프를 만드는 방법\n",
"\n",
"`-` 로지스틱의 한계를 극복하기 위해서는 시그모이드를 취하기 전에 꺽인\n",
"그래프 모양을 만드는 기술이 있어야겠음.\n",
"\n",
"`-` 아래와 같은 벡터 ${\\boldsymbol x}$를 가정하자."
],
"id": "c03cb1dd-d5b3-4d9d-8eb5-38346b8cf47e"
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"x = torch.linspace(-1,1,1001).reshape(-1,1)\n",
"x"
],
"id": "b7342520-6750-4952-a629-44a0d0fdec7f"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 목표: 아래와 같은 벡터 ${\\boldsymbol y}$를 만들어보자.\n",
"\n",
"$${\\boldsymbol y} = [y_1,y_2,\\dots,y_{n}], \\quad y_i = \\begin{cases} 9x_i +4.5& x_i <0 \\\\ -4.5x_i + 4.5& x_i >0 \\end{cases}$$\n",
"\n",
"## A. 방법1"
],
"id": "0399d996-7da0-4ae5-a766-8ded38efe3fd"
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"y = x*0 \n",
"y[x<0] = (9*x+4.5)[x<0]\n",
"y[x>0] = (-4.5*x+4.5)[x>0]"
],
"id": "da54ec95-ed9f-4205-b4af-02f769e7d196"
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\nbGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9h\nAAAPYQGoP6dpAAA9+UlEQVR4nO3deVyU1eIG8OedGRj2UUBEBARxF8Hd3FLLzNSsNCszy7r1y9LU\nFjNbrrZiad3S0tK61r1mlkumZotezVDcFURxFwQFRBBmWAdm5vz+sEhyA5mZM8vz/Xz4fGJ4YR6O\nxDy85z3nVYQQAkREREQSqGQHICIiIvfFIkJERETSsIgQERGRNCwiREREJA2LCBEREUnDIkJERETS\nsIgQERGRNCwiREREJI1GdoBrsVgsyM7Ohr+/PxRFkR2HiIiIakEIgeLiYoSFhUGluvY5D4cuItnZ\n2YiIiJAdg4iIiG5AVlYWwsPDr3mMQxcRf39/ABe/kYCAAMlpiIiIqDYMBgMiIiKqX8evxaGLyJ/T\nMQEBASwiRERETqY2l1XwYlUiIiKShkWEiIiIpGERISIiImlYRIiIiEgaFhEiIiKShkWEiIiIpGER\nISIiImlYRIiIiEgaFhEiIiKShkWEiIiIpGERISIiImlYRIiIiEgaFhEikiIlqwhfbE1HWaVJdhQi\nkohFhIjsLruoHA99vhNfJqXDZBGy4xCRRCwiRGRXQgi8tCoVxUYTfDw08PPUVD8uBEsJkbthESEi\nu/p2dxZ+P3YeWo0K8x/qDJVKAQAs2ZmJ579LQamRUzVE7kQjOwARuY8zhWV468fDAICpt7dGTCM/\nAEBhaSUS1h9GWaUZyWeK8MmDndG2SYDMqERkJzwjQkR2IYTAtJUHUGI0oWuzhni0d3T1xxr6euLL\nR7sjNMALp86X4u5PtmHpzkxO1RC5ARYRIrKLlfvOYtuJAnh5qPDevXFQ/zEl86fu0YFYP7kvBrRu\nBKPJgpe/T8WkZckorqiSlJiI7IFTM0RkF0M6hOLgWT2aBfmg+R9TMn8X6OuJLx7phkWJpzD7l6NY\nm5KNtGw91k/uC61GbefERGQPLCJEZBc+nhrMHN7+usepVAqe7BeDrlGBmPTNftzTqSlLCJELYxEh\nIps6nGNA68b+1atjaqtLs4ZYP7kv/LR//ZrKulCGAG8P6Lw9rB2TiCThNSJEZDOnC0oxYn4SHli4\nA/qyul/rofP2qL6WpKLKjCf+swfD5iUiJavIykmJSBYWESKyCYtFYOqKAyivMkOlAvy96ncCNkdf\ngdJKE7IulOPeT5PwxdZ0rqohcgEsIkRkE19tz8Cu9Avw8VRj9r3xdZ6a+bvoYF+se6Yv7ogNRZVZ\n4M11aXjiP3tRVFZppcREJAOLCBFZXXp+Kd79+QgA4OUhbRER6GOVr6vz9sD8MZ3xxl3t4alWYePh\ncxg6dyv2ni60ytcnIvtjESEiqzJbBKYuT0FFlQW9WwRhTI9Iq359RVHwcM8orHq6F6KCfHC2qBxz\nfjnKaRoiJ8UiQkRWtXhbOvacLoSvpxrvjoyDotRvSuZqYpvqsPaZPhjdPRIf3B9vs+chItuyWxFJ\nSEiAoiiYMmWKvZ6SiCS4qXkQ2oT649Vh7RDe0DpTMlfj7+WBhBEd0ETnXf3YJ5tPYFf6BZs+LxFZ\nj132Edm9ezcWLlyIuLg4ezwdEUkU21SHNRP7wENt/zMUvx3Nw+xfjkKtUvDcba3wVL+Yel8kS0S2\nZfMzIiUlJRgzZgwWLVqEhg0b2vrpiEiSS/cJ8dSopEyVdIsKxIhOTWG2CMz+5SgeWbwL+SVGu+cg\notqzeRGZMGEChg4dioEDB173WKPRCIPBUOONiBzf8XPF6DXrf/hw4zGYLfIuGvXVavDB/R0x+944\neHmokHg8H3d8lIikk/nSMhHRtdm0iCxbtgz79u1DQkJCrY5PSEiATqerfouIiLBlPCKyApPZgheW\np6C00ozkrCI4wkzIqK4RWDuxD1o19sP5YiMe+nwnPttyUnYsIroCmxWRrKwsTJ48GUuWLIGXl1et\nPmf69OnQ6/XVb1lZWbaKR0RWsjDxFFLO6OHvpcGsEbZbJVNXLRv744cJfXBf13BYBNC0off1P4mI\n7E4RNlp8v3r1atxzzz1Qq/+6a6bZbIaiKFCpVDAajTU+diUGgwE6nQ56vR4BAQG2iElE9XA0txh3\nztuKSrMF74+Kx8gu4bIjXVFyVhE6RjSofr+4ogr+XrxxHpGt1OX122arZm699VakpqbWeOzRRx9F\nmzZtMG3atOuWECJybFV/TMlUmi0Y2DYEIzo3lR3pqi4tIXmGCgydtxX3d43AlIEtoVFzOyUimWxW\nRPz9/REbG1vjMV9fXwQFBV32OBE5n09/O4nUs3rovD3wzj0dHGZK5nrWp+bgfLERH/+x38jc0Z0Q\nqqvd9DERWR//FCCiGxLg7QGtRoXXh7dHSIDzvJCP6x2NeaM7wU+rwa6MCxgyNxGbj+bJjkXktmx2\njYg18BoRIseWoy9HaICX05wNuVRGfikmfrMPB89e3CbgyX7N8cKg1vDgVA1RvdXl9Zv/xxFRnVgu\n2Sekic7bKUsIAEQF+2LlU70wrlcUAOCzLafw6W9c4ktkbywiRFRrh7L1uP3D37EnwzXu5aLVqDFz\neHt8+lBndIpsgMf6RMuOROR2WESIqFYqTRY8/10KjueV4N/b0mXHsarBsU2w6qle8NVevH5fCIFl\nuzJRabJITkbk+lhEiKhWPt50HEdyixHo64k37nK9lW+XTjF9npiOl1alYtRn25F1oUxiKiLXxyJC\nRNeVekaPT/64fuLNu2IR7KeVnMi2ooN9ofP2QEpWEYbMTcTPB3NkRyJyWSwiRHRNRpMZzy9Phtki\nMDSuCYbGNZEdyeYGtmuM9ZP7onNkAxRXmDB+yT7M+OEgjCaz7GhELodFhIiu6aONx3HsXAmC/Tzx\npgtOyVxN0wbe+PbJnniyX3MAwFfbT2PkgiRk5JdKTkbkWlhEiOiqLBaBY+eKAQBv3d0Bgb6ekhPZ\nl4dahel3tMXicd3Q0McDR3OLUVReJTsWkUvhhmZEdE1CCGw/VYBeMcGyo0iVoy/H/swiDOnw19SU\nEMJp91EhsiVuaEZEVqMoituXEODi5m2XlpC0bAPumZ+Ek+dLJKYicn4sIkR0mX2ZhZi6PAV6TkNc\n1cw1h5CcVYQ7523F6v1nZcchclosIkRUQ0WVGS8sT8HyvWfwrw3HZMdxWB8/2Ak9mwehrNKMKd8m\nY9qKAyiv5KoaorpiESGiGt7/9ShOnS9FiL8Wzw5sJTuOwwoJ8MKSx3tgysCWUBTg2z1ZuOuTrTj+\nx8W9RFQ7LCJEVG1PxgV8vvXi9u0JIzpA5+MhOZFjU6sUTBnYCl8/3gON/LU4dq4Ewz/ehrRsg+xo\nRE6DRYSIAADllRenZIQA7u0SjlvbNpYdyWn0ignGT5P7om/LYHRp1hCtQ/1lRyJyGhrZAYjIMbz3\nyxFkFJQhNMALrw1rJzuO0wn20+KrR7ujtNIEterikt6KKjOyLpShZWMWE6Kr4RkRIoKhogrrDly8\nn8qskR2g8+aUzI1QqRT4e/01dm+sS8OweVvxza5MOPCWTURSsYgQEQK8PPDLlJsxa0QH9G8dIjuO\nS6g0WZBTVA6jyYLpq1IxaVkyiiu4HJro77izKhGRjVgsAosST+G9X47CbBGICvLBxw92RmxTnexo\nRDbFnVWJqFZ2nirAD8lnOW1gIyqVgif7xeC7J3uiaQNvZBSUYcT8JPx3ewbHnOgPLCJEbqrUaMLz\ny1MweVkylu7KlB3HpXVp1hA/TuqDgW0bo9JswfsbjqGgtFJ2LCKHwFUzRG4q4afDOFNYjqYNvHFX\nx6ay47i8Bj6eWPRwF/x7WwaignwQ7KeVHYnIIbCIELmhrcfzsWTHxbMgs++Ng5+WvwrsQVEU/KNP\ndI3H/nf4HE4XlOHR3lG8ky+5Jf72IXIzxRVVmLbyAABg7E3N0KsF76wrS36JEc99d/HmgttPFWD2\nvXFo4OMpOxaRXfEaESI38876wzhbVI6IQG+8dEcb2XHcWpCvJ54f1AqeahU2pJ3D0LlbsS+zUHYs\nIrtiESFyIyfySrBsdxYAYPa98fDllIxUiqLg4Z5RWPV0LzQL8sHZonLc9+l2LPz9JCwWrqoh98B9\nRIjcTNKJfOzPKsKEAS1kR6FLFFdUYfqq1Oodbm9pE4JPH+oCTw3/XiTnw31EiOiqerUIZglxQP5e\nHpg3uhPeuacDPDUqhOq8WELILfC8LJEb2Hv6AkL8vRAR6CM7Cl2Doih4sEckukY1ROQl/1bFFVXw\n9dRApeKqGnI9rNtELk5fVoWnv96H2z/8HXsyLsiOQ7XQqrE/vDzUAACzRWD8kr14ZPEu5JcYJScj\nsj4WESIX98a6NJwzGBEa4IX2YbzHibM5nGPA3tOFSDyejyEfJWL7yQLZkYisikWEyIVtTDuHlfvO\nQKUAs0fFw9tTLTsS1VFsUx3WTOyDliF+yCs2YsznO/DRxuMwc1UNuQgWESIXVVRWienfpwIAHu/b\nHF2aNZSciG5Uq8b++GFib4zqEg6LAP618RjGfrETecUVsqMR1RuLCJGLmrnmEM4XGxHTyBfP3dZK\ndhyqJx9PDWaPiscH98XDx1ONpJMFmLh0v+xYRPXGVTNELui3o3lYnZwNlQLMGRVffeEjOb8RncMR\nF94Azy9PwevD28uOQ1RvLCJELqhnTBCe7h8DlaKgUySnZFxNixA/rH66V42b5K1PzUHnyIYI1XlJ\nTEZUdywiRC5Iq1HjxcG8j4wru7SEJGcVYdI3+xHg7YEP7otH/9YhEpMR1Q2vESFyIcfPFcNktsiO\nQXbWwNsDrUP9caG0EuMW78a7Px9BFX8OyEmwiBC5iIISIx5YuAMjFiQhV8/VFO4kKtgXK5/qhYd7\nNgMALPjtJB5YuAPZReWSkxFdH4sIkYv45w+HUFBaCWOVBQ19PWTHITvz8lDjjbtisWBMZ/h7abD3\ndCGGzE3ExrRzsqMRXROLCJELWHcgGz+m5kCtUvD+ffHQarhKxl3d0aEJfnymL+LDdSgqq0J6fqns\nSETXxItViZzc+WIjXlt9EAAwYUALxDblNu7uLjLIB8vH98LKfWfwQLeI6seFEDUuciVyBDwjQuTE\nhBB4dXUqCsuq0LZJACYOaCE7EjkIT40Ko7tHVhePUqMJ98xPws8HcyQnI6qJRYTIia1JycYvh85B\no1Lw/qh4eGr4vzRd2Rdb05GcVYTxS/Zhxg8HYTSZZUciAsAiQuTU2ofpEB/RAJNubYl2YQGy45AD\ne6p/DJ68uTkA4Kvtp3Hvgu04XcDrR0g+RQjhsLdwNBgM0Ol00Ov1CAjgL1miK/lz3xCNmn9X0PVt\nOnIOz3+XgsKyKvhrNZg1Mg5D45rIjkUupi6v3/zNReSEDBVV1f+tUatYQqjWbmnTGOsn90W3qIYo\nNpowYek+/Gd7huxY5Mb424vIyZwzVKDfe5uR8NNhzvPTDWmi88Y3T9yECQNiEOKvxeDYUNmRyI2x\niBA5ESEEpq+6uEpm+8kCqLkUk26QRq3C1NvbYOPz/RDi/9eN8pKziuSFIrfEIkLkRFbsPYNNR/Lg\nqVbh/VHxnJKhegvw+msX3nUHsnH3J9vw4ooUlFfybBvZB3+LETmJHH053liXBgB49rZWaNnYX3Ii\ncjVnCsuhKMB3e87grk+24vi5YtmRyA2wiBA5ASEEXlqZiuIKEzpGNMATfaNlRyIXNL5fDL7+Rw80\n8tfi2LkSDP94G5bvyZIdi1wciwiRE/huTxa2HDsPT40KczglQzbUq0Uw1k/qiz4tglFeZcbUFQfw\n3HfJKDWaZEcjF8XfZkROwEOtgp9Wg6mDWqNFiJ/sOOTiGvlr8Z/HuuOFQa2gUoBV+85iz+lC2bHI\nRfGmd0ROYETncPSMCaqxuoHIllQqBRNvaYluUYHYc7oQ/Vo1kh2JXBTPiBA5MIvlr42Pm+i8oVZx\nuS7ZV4/mQZhwyc0Us4vKMX1VKoov2VSPqD5YRIgcVNaFMgz+6HckHj8vOwoRgIsXTT/7bTK+2ZWJ\nO+dtxcGzetmRyAWwiBA5IItFYNrKAzh2rgTz/ncCDnxLKHIjiqLgxcGtEabzQkZBGUYsSMJ/d5zm\nzyfVC4sIkQP6eudpJJ0sgJeHCu/dGweFO6iSg+jSLBA/TuqLgW1DUGmy4LXVBzFx6f4a9z8iqgsW\nESIHk1lQhoSfjgAAXhrcBlHBvpITEdXU0NcTix7uileHtoVGpeDH1BwMm7sVGfmlsqORE2IRIXIg\nFovA1BUpKKs0o0d0IB7uGSU7EtEVKYqCx/s2x4qneiG8oTd8PNUI1XFVF9Udl+8SOZD/bM/AzvQL\n8PFUY/a98VBxlQw5uI4RDfDjpL4wlFfBy0MNADBbBEqMJui8Pa7z2UQ8I0LkUFLPGgAA04e0RWSQ\nj+Q0RLWj8/ZAROBfP6/zN5/AkI8SsS+Tm6DR9bGIEDmQ9++Lx5J/9MCY7pGyoxDdkIoqM77ffxZn\ni8px36fbsfD3kzX2wyH6O5sWkYSEBHTr1g3+/v4ICQnB3XffjaNHj9ryKYmcXp+WwZySIafl5aHG\n6om9MTSuCUwWgXfWH8Hj/9mDwtJK2dHIQdm0iGzZsgUTJkzAjh07sGHDBphMJgwaNAilpbyymuhP\np86XYMqy/SgoMcqOQmQVAV4e+Hh0J7x1dyw8NSpsOpKHIXMTsSfjguxo5IAUYcedaM6fP4+QkBBs\n2bIFN99883WPNxgM0Ol00Ov1CAgIsENCIvsyWwRGfZqEfZlFuDM+DPNGd5Idiciq0rINmLh0H07l\nl8LHU41t025BQ19P2bHIxury+m3XVTN6/cXtgAMDA6/4caPRCKPxr78KDQaDXXIRyfLF1lPYl1kE\nP60GL93RRnYcIqtrFxaANc/0wavfp6JrVCBLCF3GbmdEhBC46667UFhYiMTExCseM3PmTLz++uuX\nPc4zIuSKTuSVYMjcRFSaLHh3ZAfc340XqJLr+vOl5s9dgg+cKUKp0YyeMUEyY5GN1OWMiN1WzUyc\nOBEHDhzAN998c9Vjpk+fDr1eX/2WlZVlr3hEdmUyW/D88hRUmizo16oR7usaITsSkU0pilJdQvTl\nVXj6630Y8/kOfLTxOMxcVePW7FJEnnnmGaxZswabN29GeHj4VY/TarUICAio8UbkihYlpiMlqwj+\nXhrMGtmB95Iht+KhVtCzeRAsAvjXxmMY+8VO5BVXyI5Fkti0iAghMHHiRKxatQqbNm1CdHS0LZ+O\nyClUmiz4bs/Fs30z7myPJjpvyYmI7MvHU4PZo+LxwX3x8PZQI+lkAYZ8lIitx/NlRyMJbHqNyNNP\nP42lS5fihx9+QOvWrasf1+l08Pa+/i9frpohV2WoqMKqvWfwSK8ong0ht3YirwQTl+7DkdxiKAow\ncUALTBnYCmrupePU6vL6bdMicrVfsIsXL8a4ceOu+/ksIkRErq+iyozX1x7CN7uycEubEHz+cFdu\n6ufkHGb5rh23KCFyeEdyDdifWYQHukXwLAjRJbw81EgYEYc+LRqhV0xQdQkRQvD/FTfAu+8S2UGV\n2YLnv0vBoWwDzhcbMenWlrIjETmcoXFNarz/wvIDaOSvxfODWsFDzVujuSoWESI7mL/5JA5lG9DA\nxwMPdOdSXaLr2ZdZiJX7zgAAdmdcwLzRnRDWgBd2uyJWTCIbO5Stx7xNxwEArw9vjxB/L8mJiBxf\n58iG+OTBzvDXarD3dCGGzE3ExrRzsmORDbCIENlQpcmCF5YfgMkiMLh9KIbHh8mOROQ0hsY1wY+T\n+iIuXIeisio8/p89eGtdGipNFtnRyIpYRIhs6OPNJ3A4x4BAX0+8dU8sL7wjqqPIIB8sH98Tj/W+\nuA/V51vT8fTX+ySnImtiESGykbziCny65SQA4M27YhHsp5WciMg5aTVq/PPOdlg4tgsa+nhgXK8o\n2ZHIinixKpGNhPh7Ydn/3YRfDuVethqAiOpuUPtQ9GoRDD/tXy9dqWf0aBXqB61GLTEZ1QeLCJEN\ndY5siM6RDWXHIHIZl5aQ0wWleHDRDkQF++LjBzuhWZCvxGR0ozg1Q2Rlh3MMOJFXIjsGkcvL0VdA\no1aQelaPoXO3Yt2BbNmR6AawiBBZUUWVGZO+2Y8hcxOx6QiXGhLZ0k3Ng7B+cl90bdYQJUYTJi7d\nj1e+T0VFlVl2NKoDFhEiK/pw43EczytBgJcHOkVwSobI1provLHs/27C0/1jAABf78zEPfOTcOo8\nz0o6CxYRIivZn1mIhb9fXCXzzj2xaOjrKTkRkXvQqFV4cXAbfPVYdwT5euJwjgHf7s6SHYtqiUWE\nyAoqqsx4YXkKLAK4p1NTDGofKjsSkdvp16oR1k/ui0d6NsPzg1rLjkO1xCJCZAUfbDiGk+dLEeKv\nxYw728mOQ+S2Ggd44fW7YuGpufjyZjJb8NLKAziRVyw5GV0NiwhRPaWe0WNR4ikAQMKIDmjgwykZ\nIkex4LeTWLY7C3fO24YVe8/IjkNXwCJCVE9tm/jjhUGtMbp7JG5t21h2HCK6xP3dI9C7RRDK/5g+\nfe67ZJRVmmTHoksoQgghO8TVGAwG6HQ66PV6BAQEyI5DdE1CCN5LhsgBmS0C8zefwL82HoNFADGN\nfPHJmM5oE8rXFVupy+s3z4gQ3aCM/FIYTX/tV8ASQuSY1CoFz9zaEkufuAmNA7Q4eb4Ud328DT8f\nzJEdjcAiQnRDyipNeGTxLgyftw3p+aWy4xBRLdzUPAjrJ/VFv1aNoFIUtAjxlx2JwHvNEN2Q934+\nitMFZWii80KQHy9OJXIWQX5aLB7XDcfyitEixK/68cLSSu79IwnPiBDV0Y5TBfgyKQMA8O7IOAR4\necgNRER1olIpNa4P2ZV+Ab3f3YT/7jgNB75s0mWxiBDVQanRhKkrUgAAo7tH4OZWjSQnIqL6+n7/\nGZRVmvHa6oOYuHQ/DBVVsiO5FRYRojqY9dMRZF0oR9MG3nh5SFvZcYjICt65pwNeHdoWGpWCH1Nz\nMGzuVhw4UyQ7lttgESGqpaQT+fjvjtMALk7J+HNKhsglKIqCx/s2x/LxPdG0gTcyL5Rh5IIkLN6W\nzqkaO2ARIaqliEAf9GwehDE9ItGnZbDsOERkZZ0iG2L9pL4Y1K4xqswCr69Nw+ajebJjuTxuaEZU\nBxaLQKXZAi8PtewoRGQjQgh8mZSBlKwi/Ov+jtwj6AbU5fWby3eJrqO4oqp6GkalUuClYgkhcmWK\nouDR3tE1dkvWl1dhbUo2xvSIZDGxMk7NEF2DoaIKgz9MxGurD/L+FERu5s/CIYTA9FUH8Orqg3j8\nqz0oLK2UnMy1sIgQXcPb6w7jbFE5fj9+XnYUIpKoV0wwPDUq/O9IHobMTcSejAuyI7kMFhGiq/jt\naB6+3ZMFRQFm3xsPH0/OZBK5I0VR8NBNzfD9070QHeyLHH0F7l+4A/N/OwGLxWEvs3QaLCJEV6Av\nr8JLK1MBAI/2ikb36EDJiYhItvZhOqx9pg/u6hgGs0XgvZ+PYtyXu1FQYpQdzamxiBBdwZvr0pBr\nqEB0sC+m3t5adhwichB+Wg0+vL8j3h3ZAVqNCsdyi3nxaj3xXDPR32w6cg4r9p75Y0omDt6eXCVD\nRH9RFAX3d4tEx4iGKK00IfCSm+VZLAIqFYtJXfCMCNHfVJkFdN4e+EfvaHSN4pQMEV1Z61B/dI5s\nWP3+ir1nMPbfO5FXXCExlfPhhmZEV5BnqECAtwc3LiOiWimvNKPPu5tQUFqJYD8tPnqgI3q3cN8d\nmOvy+s0zIkR/uLSThwR4sYQQUa15e6qx7P9uQuvG/sgvMeKhL3big1+PwsxVNdfFIkIEoLC0EkPm\nbsUvh3JlRyEiJ9WysT9WT+iNB7pFQAhg7qYTeHDRDpwzcKrmWlhEiADMWHMIh3MMmP3LUVSZLbLj\nEJGT8vZUY9bIOHz0QEf4eqqxM/0Chs5NhL68SnY0h8VVM+T2fj6YgzUp2VCrFLw/Kh4eavZzIqqf\nuzo2RYemOkxYuh+3tGkEnbeH7EgOi0WE3FpBiRGvfH8QADC+X3PERzSQG4iIXEbzRn74/ule0Fyy\nnDfrQhnUKgVhDbwlJnMs/NOP3No/1xxCQWklWjf2x6RbW8qOQ0QuxstDDc0fZ1mNJjMmLN2HIXMT\nsenIOcnJHAeLCLmtHw/k4McDOVCrFMwZFQ+thqtkiMh29OVVEAIoKqvCY1/uwds/pvGaNLCIkBtL\nzioEAEzoH4MO4TrJaYjI1YX4e2HFUz0xrlcUAGBRYjpGfbodWRfK5AaTjBuakVvbdiIf3aIC4alh\nJyci+/nlUC6mLk+BocKEAC8NZo+Kx+3tQ2XHshpuaEZUS71bBLOEEJHd3d4+FD9O6ouOEQ1gqDDh\nk80n3HbzM/4GJreSV1yBycv2I1fPDYaISK6IQB9892RPPN0/BvNGd4LaTW+WxyJCbkMIgVe+P4gf\nkrPx7LfJsuMQEcFTo8KLg9ugWZBv9WOfbD6BHw/kSExlX9xHhNzGD8nZ2JB2Dh5qBf+8s53sOERE\nl9l7+gLm/HoUQgDbT0Xi1aHtXP6+VzwjQm7hnKECM9YcAgBMuqUl2jbhxc9E5HjiwhtgfL8YAMCS\nHZkYMT8J6fmlklPZFosIuTwhBF5elQp9eRU6NNVhfP8Y2ZGIiK7IQ63CtMFt8OWj3RDo64m0HAOG\nzU3ED8lnZUezGRYRcnkr953F/47kwVOtwhzeS4aInED/1iFYP6kvukcHorTSjMnLkvH62kOyY9kE\nfyOTSxNC4L/bMwAAU25ridah/nIDERHVUqjOC0sf74FJt7SAogDtw1xz40VuaEYur7zSjCU7TuPR\n3lHV93wgInImR3OLa/whVVBiRJCfVmKia+OGZkSX8PZU44mbm7OEEJHTurSEFJZWYti8rXj+uxSU\nVZokprIO/mYml5RdVI7F29JhcdOdConIdW07mY9zhgqs3HcGwz/ehqO5xbIj1QuLCLkcIQSmrTyA\n19em4Y11abLjEBFZ1bC4MHz9+E0I8dfiRF4Jhn+8Fd/uzoQDX2lxTSwi5HKW7c5C4vF8aDUqjO3Z\nTHYcIiKr6xkThPWT+6Jvy2AYTRZMW5mKZ79NRonR+aZqWETIpZwpLMNbf5wFmXp7a8Q08pOciIjI\nNoL9tPjq0e54cXBrqFUKVidn4/1fj8qOVWfc4p1chsUi8OKKAyitNKNrs4Z4tHe07EhERDalUil4\nun8LdIsKxOxfjmLKwFayI9UZz4iQy/h6VyaSThbAy0OF2aPi3fZOlkTkfrpFBeK7J3tC5+0B4OK1\ncou3pcNQUSU52fWxiJBLKDWaMOeXi6ckX7y9DaKDfa/zGUREruvrnZl4fW0a7py3Faln9LLjXBOL\nCLkEX60GS5/ogQd7RGJcryjZcYiIpGoXFoCmDbxxuqAMIxck4ctt6Q67qoY7qxIREbkgfVkVpq5I\nwa9p5wAAt7dvjPdGxkPn42Hz53a4nVXnz5+P6OhoeHl5oUuXLkhMTLTH05IbyCwow8Gzjn3akYhI\nBp2PBz4b2wUz7mwHD7WCXw6dw9B5iUjJKpIdrQabF5Fvv/0WU6ZMwSuvvIL9+/ejb9++uOOOO5CZ\nmWnrpyYXZ7EIvLA8BXd/sg3f7z8jOw4RkcNRFAWP9o7Gyqd6ITLQB9lF5aioMsuOVYPNp2Z69OiB\nzp07Y8GCBdWPtW3bFnfffTcSEhKu+bmcmqFr+ffWdLyxLg2+nmr8POVmRAT6yI5EROSwDBVVSDpR\ngMGxodWPWSwCKhusMHSYqZnKykrs3bsXgwYNqvH4oEGDkJSUdNnxRqMRBoOhxhvRlZw6X4L3fjkC\nAHh5aFuWECKi6wjw8qhRQk7kleC2f21BXnGFxFQ2LiL5+fkwm81o3LhxjccbN26M3Nzcy45PSEiA\nTqerfouIiLBlPHJSZovA1BUHUFFlQZ8WwXiwe6TsSERETmf2L0fQpkkAGvlppeawy8WqilLztI8Q\n4rLHAGD69OnQ6/XVb1lZWfaIR05m8bZ07D1dCD+tBrNGdrjizxIREV3b+/d1xKwR8n+H2nSL9+Dg\nYKjV6svOfuTl5V12lgQAtFottFq5zYwcW2ZBGWb/sXHZK0PbIrwhp2SIiG6En9Yx7vJi0zMinp6e\n6NKlCzZs2FDj8Q0bNqBXr162fGpyUeENvTFtcBsMatcYD3Tj1B0RkbOzeR167rnnMHbsWHTt2hU9\ne/bEwoULkZmZifHjx9v6qckFqVQKHusTjUd7R0k/nUhERPVn8yJy//33o6CgAG+88QZycnIQGxuL\n9evXo1mzZrZ+anIh2UXlaODjAR/Piz+yLCFERK6BW7yTwzOZLRixIAn68irMH9MZ7cN0siMREdE1\n1OX12zGuVCG6hs9+P4UDZ/QI8NIgyJcXMxMRuRLefZcc2pFcAz7ceAwAMHN4e4TqvCQnIiIia2IR\nIYdVZbbgheUpqDILDGwbgns6NZUdiYiIrIxFhBzWp7+dxMGzBui8PfDOPfI33SEiIutjESGHlJZt\nwNxNxwEAb9zVHiEBnJIhInJFvFiVHFKQnyf6tmwEjUrB8Pgw2XGIiMhGWETIITUO8MIXj3RFRZWF\nUzJERC6MUzPkUEqNpur/VhQF3p5qiWmIiMjWWETIYRhNZoxckITnv0uBvrxKdhwiIrIDFhFyGPP+\ndwJHcovx29E8mMwW2XGIiMgOWETIIRw4U4QFW04CAN68OxZBftxBlYjIHbCIkHRGkxnPf5cCs0Vg\nWFwTDOnQRHYkIiKyExYRku7DjcdxPK8EwX6eeOOuWNlxiIjIjlhESKrkrCJ89seUzFt3d0Cgr6fk\nREREZE/cR4SkKqkwIchPi14xQRgcGyo7DhER2RmLCEnVp2UwNjx7MxRw0zIiInfEIkJSCCGqd0xt\n4MPpGCIid8VrRMjuKqrMGLEgCav3n4UQQnYcIiKSiGdEyO7m/HIU+zOLkF10GAPbNYaflj+GRETu\nimdEyK52Z1zAF9vSAQCzRsSxhBARuTkWEbKbskoTpi5PgRDAqC7hGNAmRHYkIiKSjEWE7Oa9n48i\no6AMTXReeHVYO9lxiIjIAbCIkF3sOFWAL5MyAACzRsZB5+0hNxARETkEFhGyi72nCwEAo7tHoF+r\nRpLTEBGRo+CVgmQXEwa0QJdmDdE+LEB2FCIiciAsImQ3NzUPkh2BiIgcDKdmyGZKjCY8+20yMgvK\nZEchIiIHxSJCNpOw/jC+338WT/xnD3dQJSKiK2IRIZtIPH4eX+/MBADMGN6u+r4yREREl2IRIasr\nrqjCtBUHAAAP92yGXjHBkhMREZGjYhEhq3tn/WFk6ysQGeiDaYPbyI5DREQOjEWErGrLsfP4ZlcW\nAOC9e+Pgy3vJEBHRNbCIkFUt/uOGduN6RXG5LhERXRf/XCWr+mxsF3y5LQNjezaTHYWIiJwAiwhZ\nlVajxpP9YmTHICIiJ8GpGao3fVkVFv5+ElVmi+woRETkZFhEqN5eX3sI76w/gue+S5EdhYiInAyL\nCNXLhrRzWLX/LFQK8GjvKNlxiIjIybCI0A0rKqvEy9+nAgCe6NscnSMbSk5ERETOhkWEbtjMNYdw\nvtiImEa+ePa2VrLjEBGRE2IRoRvy88FcrE7OhkoB3r+vI7w81LIjERGRE2IRoTozmS14c10aAODJ\nfjHoGNFAbiAiInJaLCJUZxq1Cv/5R3eM7ByOKQNbyo5DREROjBua0Q2JaeSH9++Llx2DiIicHM+I\nUK3llxix93Sh7BhERORCWESoVoQQeG31QYz6NAlf/nFjOyIiovpiEaFaWXcgBz8dzIVKUdA1KlB2\nHCIichEsInRdecUVeO2HgwCACQNaILapTnIiIiJyFSwidE1CCLz6/UEUlVWhXZMATBjQQnYkIiJy\nISwidE1rUrLxa9o5eKgVzBkVD08Nf2SIiMh6+KpCV3WhtBL//OEQAOCZW1qiXViA5ERERORqWETo\nqhr6eODlIW3Qs3kQnuofIzsOERG5IG5oRlelKAru7xaJ+7pGQFEU2XGIiMgF8YwIXSa/xAhDRVX1\n+ywhRERkKywiVIMQAlOXp+D2f/2OPRkXZMchIiIXx6kZqmH53jPYfPQ8PNUq6Lw9ZMchIiIXxzMi\nVC27qBxvrk0DADw3qBVaNvaXnIiIiFwdiwgBuDgl89KqVBQbTegU2QBP9G0uOxIREbkBFhECAHy7\nOwu/HzsPrUaFOaPioVbxAlUiIrI9FhHCmcIyvPXjYQDA1NtbI6aRn+RERETkLnixKsHHU4P+rRsh\nV1+BR3tHy45DRERuhEWEEOjriY8f7IxSo4lTMkREZFecmnFjZZUmCCGq3/fVspcSEZF9sYi4KYtF\n4B9f7sHTX+9DfolRdhwiInJTNisiGRkZ+Mc//oHo6Gh4e3sjJiYGM2bMQGVlpa2ekupgyc7T2H6q\nAL8dPY9So0l2HCIiclM2Oxd/5MgRWCwWfPbZZ2jRogUOHjyIJ554AqWlpZgzZ46tnpZq4XRBKRLW\nHwEAvHRHGzQL8pWciIiI3JUiLr1IwMZmz56NBQsW4NSpU7U63mAwQKfTQa/XIyAgwMbp3IPFIvDA\noh3YlX4BNzUPxNLHb4KKF6gSEZEV1eX1265XJ+r1egQGBl7140ajEUbjX9crGAwGe8RyK19tz8Cu\n9Avw8VRj9r3xLCFERCSV3S5WPXnyJObNm4fx48df9ZiEhATodLrqt4iICHvFcwvp+aV49+eLUzLT\nh7RFRKCP5EREROTu6lxEZs6cCUVRrvm2Z8+eGp+TnZ2NwYMHY9SoUXj88cev+rWnT58OvV5f/ZaV\nlVX374iuqrCsEkG+WvRuEYQx3SNlxyEiIqr7NSL5+fnIz8+/5jFRUVHw8vICcLGEDBgwAD169MCX\nX34Jlar23YfXiFhfcUUVyivNCAnwkh2FiIhclE2vEQkODkZwcHCtjj179iwGDBiALl26YPHixXUq\nIWQ9QggoysVrQfy9PODv5SE5ERER0UU2awbZ2dno378/IiIiMGfOHJw/fx65ubnIzc211VPSFZgt\nAg//exeW7syEHRdIERER1YrNVs38+uuvOHHiBE6cOIHw8PAaH+MLov18nngKicfzkZxZhIHtQhDi\nzykZIiJyHDY7IzJu3DgIIa74RvZxIq8Y7284BgB4bVg7lhAiInI4vGjDRZnMFjy//AAqTRb0b90I\no7qGX/+TiIiI7IxFxEUtTDyFlKwi+HtpMGtEXPXFqkRERI6ERcQFHc0txocbjgMAZtzZHqE6TskQ\nEZFjYhFxQbszLsBkseDWNiEY2bmp7DhERERXZdd7zZB9PHRTM7QPC0BYA29OyRARkUNjEXFRnSIb\nyo5ARER0XZyacRFVZgumLk/Bibxi2VGIiIhqjUXERXyy+QSW7z2Dhz7fhUqTRXYcIiKiWmERcQEH\nz+rx8aYTAIBXhraFp4b/rERE5Bz4iuXkKk0WvLA8BSaLwB2xoRgW10R2JCIiolpjEXFyH286jiO5\nxQj09cSbd8dylQwRETkVFhEnlnpGj09+OwkAePOuWAT7aSUnIiIiqhsWESe2OCkdZovA0LgmGMop\nGSIickLcR8SJvTcyDm1DAzCCu6cSEZGTYhFxYhq1Ck/c3Fx2DCIiohvGqRknU1FlxmdbTsJoMsuO\nQkREVG8sIk7mXxuOIeGnI3jsy92yoxAREdUbi4gT2Xu6EIsSTwEAHukZJTcMERGRFbCIOImKKjOm\nLk+BRQAjOjXFoPahsiMRERHVG4uIk3j/16M4lV+KEH8tZtzZXnYcIiIiq2ARcQJ7Mi7g863pAIBZ\nIztA5+MhOREREZF1sIg4OCEEZq49BCGAe7uE45Y2jWVHIiIishoWEQenKAoWjOmCuzqG4bVh7WTH\nISIisipuaOYEIgJ98NEDnWTHICIisjqeEXFQZZUm7DhVIDsGERGRTbGIOKh3fzqCBxbuwEcbj8uO\nQkREZDMsIg4o6WQ+vtp+GgDQuVkDuWGIiIhsiEXEwZQaTXhxxQEAwIM9ItG3ZSPJiYiIiGyHRcTB\nJPx0GGcKy9G0gTdeHtJWdhwiIiKbYhFxIFuP52PJjkwAwHv3xsFPy0VNRETk2lhEHER5pRnTVl6c\nkhl7UzP0bhEsOREREZHtsYg4CC8PFabd0QZx4Tq8dEcb2XGIiIjsguf+HYSiKBgeH4Y745pAURTZ\ncYiIiOyCZ0QkK66owoXSyur3WUKIiMidsIhI9ta6wxj0ry3Ycuy87ChERER2x6kZiTYfzcO3e7Kg\nKICPp1p2HCIiIrvjGRFJ9GVVeOmPVTKP9Y5Gt6hAyYmIiIjsj0VEkjfWpeGcwYjmwb54YVBr2XGI\niIikYBGR4H+Hz2HlvjNQFGD2qDh4c1qGiIjcFIuInRWVVWL6qlQAwBN9m6NLM07JEBGR+2IRsTOV\nSkH/1o0Q08gXz93WSnYcIiIiqbhqxs4CvDzw3r3xKDGa4OXBKRkiInJvPCNiJxVVZgghqt/nDe2I\niIhYROzmxRUHMG7xbuToy2VHISIichj8s9wOfkrNwZqUbKhVCs4XG9FE5y07EhERkUPgGREbKygx\n4tXVBwEAT/WLQVx4A7mBiIiIHAiLiI3984dDKCitRJtQfzxzawvZcYiIiBwKi4gNrTuQjR9Tc6BW\nKZgzKh5aDVfJEBERXYpFxEbOFxvx2h9TMhMGtEBsU53kRERERI6HF6vaSEGpEQ18PBGq88bEAZyS\nISIiuhIWERtpExqA9ZP6Ir/ECE8NTzwRERFdCV8hrezSTcu8PdWICPSRmIaIiMixsYhYkRACz3yz\nH58nnoLZIq7/CURERG6ORcSKViefxboDOXj35yPIKCiVHYeIiMjhsYhYyTlDBWb8cAgAMGVgK8Q0\n8pOciIiIyPGxiFiBEALTV6XCUGFCXLgOT97cXHYkIiIip8AiYgUr9p7BpiN58FSr8P6oeGjUHFYi\nIqLa4CtmPeXoy/HG2jQAwLO3tULLxv6SExERETkPFpF62pNRiAqTGR0jGuCJvtGy4xARETkVbmhW\nT3fGh6FFiB+0GhWnZIiIiOqIRcQK2jYJkB2BiIjIKfFP+BsghMDMNYdw8KxedhQiIiKnxiJyA77Z\nlYUvkzIweuEOGCqqZMchIiJyWiwidZR1oQxv/3hxlcyU21ohwMtDciIiIiLnZZciYjQa0bFjRyiK\nguTkZHs8pU1YLALTVh5AaaUZ3aMC8WivKNmRiIiInJpdisiLL76IsLAwezyVTX298zSSThbA20ON\n9+6Ng0qlyI5ERETk1GxeRH766Sf8+uuvmDNnjq2fyqYyC8rwzvojAIBpg1sjKthXciIiIiLnZ9Pl\nu+fOncMTTzyB1atXw8fH57rHG41GGI3G6vcNBoMt49XJf3dkoLzKjB7RgXi4Z5TsOERERC7BZkVE\nCIFx48Zh/Pjx6Nq1KzIyMq77OQkJCXj99ddtFalept/RFuENfTCgdQinZIiIiKykzlMzM2fOhKIo\n13zbs2cP5s2bB4PBgOnTp9f6a0+fPh16vb76LSsrq67xbEalUvBIryhEBl3/zA4RERHVjiKEEHX5\nhPz8fOTn51/zmKioKDzwwANYu3YtFOWvswdmsxlqtRpjxozBV199dd3nMhgM0Ol00Ov1CAiw/+6l\nFovAv7el48EekfDx5Ca0REREtVGX1+86F5HayszMrHGNR3Z2Nm6//XasWLECPXr0QHh4+HW/huwi\n8sXWdLy5Lg3tmgRg3TN9OCVDRERUC3V5/bbZn/mRkZE13vfz8wMAxMTE1KqEyHbqfAne+/niKpmH\nbmrGEkJERGQD3Fn1CswWgReWp8BosqBvy2CM7h4hOxIREZFLstuFD1FRUbDRLJDVfbH1FPZlFsFP\nq8GskXE1rnMhIiIi6+EZkb85kVeMOb8eAwC8NqwtmjbwlpyIiIjIdbGI/M2b6w6j0mRBv1aNcF9X\nTskQERHZEovI38y+Nw7D48Mwa2QHTskQERHZGDfH+JuQAC/MHd1JdgwiIiK3wDMiAExmC7aduPYm\nbURERGR9LCIAPvv9FMZ8vhMz1xySHYWIiMituH0ROZJrwIcbL66SiY/QSU5DRETkXty6iFSZLXj+\nuxRUmQVua9cYd3dsKjsSERGRW3HrIjJ/80kcyjaggY8H3r4nlqtkiIiI7Mxti8ihbD3mbToOAHh9\neHuE+HtJTkREROR+3LKIXLyXzAGYLAKD24dieHyY7EhERERuyS2LiFql4PnbWqFNqD/evJtTMkRE\nRLK47YZmA9s1xq1tQ1hCiIiIJHLLMyJ/YgkhIiKSy62LCBEREcnFIkJERETSsIgQERGRNCwiRERE\nJA2LCBEREUnDIkJERETSsIgQERGRNCwiREREJA2LCBEREUnDIkJERETSsIgQERGRNCwiREREJA2L\nCBEREUmjkR3gWoQQAACDwSA5CREREdXWn6/bf76OX4tDF5Hi4mIAQEREhOQkREREVFfFxcXQ6XTX\nPEYRtakrklgsFmRnZ8Pf3x+Kolj1axsMBkRERCArKwsBAQFW/dr0F46zfXCc7YPjbB8cZ/ux1VgL\nIVBcXIywsDCoVNe+CsShz4ioVCqEh4fb9DkCAgL4g24HHGf74DjbB8fZPjjO9mOLsb7emZA/8WJV\nIiIikoZFhIiIiKRx2yKi1WoxY8YMaLVa2VFcGsfZPjjO9sFxtg+Os/04wlg79MWqRERE5Nrc9owI\nERERycciQkRERNKwiBAREZE0LCJEREQkjVsWkfnz5yM6OhpeXl7o0qULEhMTZUdyKgkJCejWrRv8\n/f0REhKCu+++G0ePHq1xjBACM2fORFhYGLy9vdG/f38cOnSoxjFGoxHPPPMMgoOD4evri+HDh+PM\nmTP2/FacSkJCAhRFwZQpU6of4zhbx9mzZ/HQQw8hKCgIPj4+6NixI/bu3Vv9cY5z/ZlMJrz66quI\njo6Gt7c3mjdvjjfeeAMWi6X6GI5z3f3++++48847ERYWBkVRsHr16hoft9aYFhYWYuzYsdDpdNDp\ndBg7diyKioqs800IN7Ns2TLh4eEhFi1aJNLS0sTkyZOFr6+vOH36tOxoTuP2228XixcvFgcPHhTJ\nycli6NChIjIyUpSUlFQfM2vWLOHv7y9WrlwpUlNTxf333y+aNGkiDAZD9THjx48XTZs2FRs2bBD7\n9u0TAwYMEPHx8cJkMsn4thzarl27RFRUlIiLixOTJ0+ufpzjXH8XLlwQzZo1E+PGjRM7d+4U6enp\nYuPGjeLEiRPVx3Cc6++tt94SQUFBYt26dSI9PV0sX75c+Pn5iQ8//LD6GI5z3a1fv1688sorYuXK\nlQKA+P7772t83FpjOnjwYBEbGyuSkpJEUlKSiI2NFcOGDbPK9+B2RaR79+5i/PjxNR5r06aNeOml\nlyQlcn55eXkCgNiyZYsQQgiLxSJCQ0PFrFmzqo+pqKgQOp1OfPrpp0IIIYqKioSHh4dYtmxZ9TFn\nz54VKpVK/Pzzz/b9BhxccXGxaNmypdiwYYPo169fdRHhOFvHtGnTRJ8+fa76cY6zdQwdOlQ89thj\nNR4bMWKEeOihh4QQHGdr+HsRsdaYpqWlCQBix44d1cds375dABBHjhypd263mpqprKzE3r17MWjQ\noBqPDxo0CElJSZJSOT+9Xg8ACAwMBACkp6cjNze3xjhrtVr069evepz37t2LqqqqGseEhYUhNjaW\n/xZ/M2HCBAwdOhQDBw6s8TjH2TrWrFmDrl27YtSoUQgJCUGnTp2waNGi6o9znK2jT58++N///odj\nx44BAFJSUrB161YMGTIEAMfZFqw1ptu3b4dOp0OPHj2qj7npppug0+msMu4OfdM7a8vPz4fZbEbj\nxo1rPN64cWPk5uZKSuXchBB47rnn0KdPH8TGxgJA9VheaZxPnz5dfYynpycaNmx42TH8t/jLsmXL\nsG/fPuzevfuyj3GcrePUqVNYsGABnnvuObz88svYtWsXJk2aBK1Wi4cffpjjbCXTpk2DXq9HmzZt\noFarYTab8fbbb2P06NEA+PNsC9Ya09zcXISEhFz29UNCQqwy7m5VRP6kKEqN94UQlz1GtTNx4kQc\nOHAAW7duvexjNzLO/Lf4S1ZWFiZPnoxff/0VXl5eVz2O41w/FosFXbt2xTvvvAMA6NSpEw4dOoQF\nCxbg4Ycfrj6O41w/3377LZYsWYKlS5eiffv2SE5OxpQpUxAWFoZHHnmk+jiOs/VZY0yvdLy1xt2t\npmaCg4OhVqsva3B5eXmXNUa6vmeeeQZr1qzB5s2bER4eXv14aGgoAFxznENDQ1FZWYnCwsKrHuPu\n9u7di7y8PHTp0gUajQYajQZbtmzB3LlzodFoqseJ41w/TZo0Qbt27Wo81rZtW2RmZgLgz7O1TJ06\nFS+99BIeeOABdOjQAWPHjsWzzz6LhIQEABxnW7DWmIaGhuLcuXOXff3z589bZdzdqoh4enqiS5cu\n2LBhQ43HN2zYgF69eklK5XyEEJg4cSJWrVqFTZs2ITo6usbHo6OjERoaWmOcKysrsWXLlupx7tKl\nCzw8PGock5OTg4MHD/Lf4g+33norUlNTkZycXP3WtWtXjBkzBsnJyWjevDnH2Qp69+592fLzY8eO\noVmzZgD482wtZWVlUKlqvuSo1erq5bscZ+uz1pj27NkTer0eu3btqj5m586d0Ov11hn3el/u6mT+\nXL77xRdfiLS0NDFlyhTh6+srMjIyZEdzGk899ZTQ6XTit99+Ezk5OdVvZWVl1cfMmjVL6HQ6sWrV\nKpGamipGjx59xSVj4eHhYuPGjWLfvn3illtucetleLVx6aoZITjO1rBr1y6h0WjE22+/LY4fPy6+\n/vpr4ePjI5YsWVJ9DMe5/h555BHRtGnT6uW7q1atEsHBweLFF1+sPobjXHfFxcVi//79Yv/+/QKA\n+OCDD8T+/furt6Sw1pgOHjxYxMXFie3bt4vt27eLDh06cPlufXzyySeiWbNmwtPTU3Tu3Ll62SnV\nDoArvi1evLj6GIvFImbMmCFCQ0OFVqsVN998s0hNTa3xdcrLy8XEiRNFYGCg8Pb2FsOGDROZmZl2\n/m6cy9+LCMfZOtauXStiY2OFVqsVbdq0EQsXLqzxcY5z/RkMBjF58mQRGRkpvLy8RPPmzcUrr7wi\njEZj9TEc57rbvHnzFX8fP/LII0II641pQUGBGDNmjPD39xf+/v5izJgxorCw0CrfgyKEEPU/r0JE\nRERUd251jQgRERE5FhYRIiIikoZFhIiIiKRhESEiIiJpWESIiIhIGhYRIiIikoZFhIiIiKRhESEi\nIiJpWESIiIhIGhYRIiIikoZFhIiIiKRhESEiIiJp/h+u10qeQCCYsAAAAABJRU5ErkJggg==\n"
}
}
],
"source": [
"plt.plot(y,'--')"
],
"id": "19605fdc-b9b0-4b7e-8db7-b1f51be238ca"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> **Note**\n",
">\n",
"> 강의영상에 보셨듯이 아래의 코드실행결과는 다르게 나옵니다.\n",
">\n",
"> ``` python\n",
"> ## 아래를 실행하면 꺽인선이 나오는데용...\n",
"> x = torch.linspace(-1,1,1001).reshape(-1,1)\n",
"> y = x*0 + x \n",
"> y[x<0] = (9*x+4.5)[x<0]\n",
"> y[x>0] = (-4.5*x+4.5)[x>0]\n",
"> plt.plot(x,y)\n",
"> ```\n",
">\n",
"> ``` python\n",
"> ## 이걸 실행하면 그냥 직선이 나옵니다...\n",
"> x = torch.linspace(-1,1,1001).reshape(-1,1)\n",
"> y = x \n",
"> y[x<0] = (9*x+4.5)[x<0]\n",
"> y[x>0] = (-4.5*x+4.5)[x>0]\n",
"> plt.plot(x,y)\n",
"> ```\n",
">\n",
"> 다르게 나오는 이유가 너무 궁금하시다면 아래의 링크로 가셔서\n",
"> 깊은복사/얕은복사에 대한 개념을 이해하시면 됩니다. (그렇지만\n",
"> 가능하다면 궁금해하지 마세요…..)\n",
">\n",
"> - [깊은복사 얕은복사 강의들으러\n",
"> 가기](https://guebin.github.io/PP2023/posts/2023-06-21-13wk-1.html)\n",
"\n",
"## B. 방법2 – 렐루이용"
],
"id": "22a22db0-307d-492d-a82f-814fc44933c5"
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"relu = torch.nn.ReLU()"
],
"id": "8771d2bb-4dda-4c11-8479-0191a6582079"
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\n"
}
}
],
"source": [
"plt.plot(relu(x),'--',label=r'$relu(x)$')\n",
"plt.plot(relu(-x),'--',label=r'$relu(-x)$')\n",
"plt.legend()"
],
"id": "15dfca77-f1ea-4ecc-bfe3-12199323e2fe"
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\n"
}
}
],
"source": [
"plt.plot(-4.5*relu(x),'--',label=r'$-4.5\\times relu(x) + 4.5$')\n",
"plt.plot(-9*relu(-x),'--',label=r'$-9\\times relu(-x) + 4.5$')\n",
"plt.legend()"
],
"id": "74392d57-82a2-4ca8-a216-d6e5bdf5dad4"
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\niBTDIEJERESK+T/CzbvzdWuYtAAAAABJRU5ErkJggg==\n"
}
}
],
"source": [
"plt.plot(-4.5*relu(x)-9*relu(-x),'--',label=r'$-4.5\\times relu(x) -9 \\times relu(-x)$')\n",
"plt.plot(y,'--',label=r'$y$')\n",
"plt.plot(-4.5*relu(x)-9*relu(-x)+4.5,'--',label=r'$-4.5\\times relu(x) -9 \\times relu(-x)+4.5$')\n",
"plt.legend()"
],
"id": "e22e7d43-df43-40e1-ac0d-3e4841e8ccc4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 우리의 목표: 저 초록선에서 시그모이드를 태우면된다. 즉 아래의 느낌임"
],
"id": "17770da2-b0cf-42a1-991b-e36caeb15a33"
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"sig = torch.nn.Sigmoid()"
],
"id": "ad85c852-0782-4548-a215-ce1730cd8885"
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAxYAAAGGCAYAAADmRxfNAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\n+wAAAABJRU5ErkJggg==\n"
}
}
],
"source": [
"fig = plt.figure(figsize=(8, 4))\n",
"spec = fig.add_gridspec(4, 4)\n",
"ax1 = fig.add_subplot(spec[:2,0]); ax1.set_title(r'$x$'); ax1.set_ylim(-1,1)\n",
"ax2 = fig.add_subplot(spec[2:,0]); ax2.set_title(r'$-x$'); ax2.set_ylim(-1,1)\n",
"ax3 = fig.add_subplot(spec[:2,1]); ax3.set_title(r'$relu(x)$'); ax3.set_ylim(-1,1)\n",
"ax4 = fig.add_subplot(spec[2:,1]); ax4.set_title(r'$relu(-x)$'); ax4.set_ylim(-1,1)\n",
"ax5 = fig.add_subplot(spec[1:3,2]); ax5.set_title(r'$-4.5 relu(x)-9 relu(-x)+4.5$')\n",
"ax6 = fig.add_subplot(spec[1:3,3]); ax6.set_title('sig(...)');\n",
"#---#\n",
"ax1.plot(x,'--',color='C0')\n",
"ax2.plot(-x,'--',color='C1')\n",
"ax3.plot(relu(x),'--',color='C0')\n",
"ax4.plot(relu(-x),'--',color='C1')\n",
"ax5.plot(-4.5*relu(x)-9*relu(-x)+4.5,'--',color='C2')\n",
"ax6.plot(sig(-4.5*relu(x)-9*relu(-x)+4.5),'--',color='C2')\n",
"fig.tight_layout()"
],
"id": "f2c297fd"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## C. 방법2의 다른구현\n",
"\n",
"`-` 렐루이용하여 만드는 방법 정리\n",
"\n",
"1. 벡터 x와 relu함수를 준비한다.\n",
"2. u = \\[x,-x\\] 를 계산한다.\n",
"3. v = \\[relu(x), relu(-x)\\] 를 계산한다.\n",
"4. y = -4.5 \\* relu(x) + 9 \\* relu(-x) +4.5 를 계산한다.\n",
"\n",
"`-` 1단계"
],
"id": "442fc35d-c7e1-4909-a5bb-336b56ad050a"
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"x,relu"
],
"id": "034b25f9-ac00-4489-ad2d-2ddcc4867657"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 2단계"
],
"id": "1a832fae-3a7c-47a4-99ef-f55437a90156"
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"u = torch.concat([x,-x],axis=1) # u = [x, -x] 같은것\n",
"u"
],
"id": "11ece33a-b1dd-4a87-ad89-3f844a7fac7a"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 3단계"
],
"id": "2ee4d36c-ea27-4832-a679-9667f52dba9b"
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"v = relu(u) # 각각의 column에 렐루취함\n",
"v"
],
"id": "f9f574aa-a216-4051-86f2-67ff3c3a4de5"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 4단계"
],
"id": "21424b19-bda5-46da-8d04-4e9e7f50afcd"
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"-4.5 * v[:,[0]] - 9.0 * v[:,[1]] +4.5"
],
"id": "64d7ec7b-cc5c-41e8-9af9-8d44c491867d"
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"y"
],
"id": "95af1027-0139-4a03-b345-8e8384d7e208"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 그런데, 4단계는 아래와 같이 볼 수 있다.\n",
"\n",
"- ${\\boldsymbol v}\\begin{bmatrix} -4.5 \\\\ -9.0 \\end{bmatrix} + 4.5 = \\begin{bmatrix} v_{11} & v_{12} \\\\ v_{21} & v_{22} \\\\ \\dots & \\dots \\\\ v_{n1} & v_{n2} \\\\ \\end{bmatrix}\\begin{bmatrix} -4.5 \\\\ -9.0 \\end{bmatrix} + 4.5 = \\begin{bmatrix} -4.5 v_{11} - 9.0 v_{12} + 4.5 \\\\ -4.5 v_{21} - 9.0 v_{22} + 4.5 \\\\ \\dots \\\\ -4.5 v_{n1} - 9.0 v_{n2} + 4.5 \\\\ \\end{bmatrix}$\n",
"\n",
"위의 수식을 참고하여 매트릭스의 곱 형태로 다시 포현하면 아래와 같다."
],
"id": "420b16e8-1016-4f20-a6d4-b1dd8747d826"
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"#-4.5 * v[:,[0]] - 9.0 * v[:,[1]] +4.5\n",
"What = torch.tensor([[-4.5],[-9.0]]) \n",
"v @ What + 4.5 "
],
"id": "f1d597b6-709f-4cc9-8e59-731cc924015d"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이제 매트릭스의 곱 대신에 `torch.nn.Linear()`를 이용하면 아래의 코드와\n",
"같아진다."
],
"id": "a107cc5a-6f60-4f92-ac6f-4c721f647101"
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"l2 = torch.nn.Linear(\n",
" in_features=2,\n",
" out_features=1 \n",
")"
],
"id": "543f25db-81d4-4662-a708-0183d86764e8"
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"l2.weight.data = torch.tensor([[-4.5,-9.0]])\n",
"l2.bias.data = torch.tensor([4.5])"
],
"id": "22965f65-445b-4763-a436-22f9fb71cfbd"
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"l2(v)"
],
"id": "dc9dfde0-707c-4f99-8151-b895729a0d9a"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 사실 2단계도 아래와 같이 볼 수 있다.\n",
"\n",
"$$\\begin{bmatrix}\n",
"x_1 \\\\\n",
"x_2 \\\\\n",
"\\dots \\\\ \n",
"x_n \n",
"\\end{bmatrix}\\begin{bmatrix} 1 & -1 \\end{bmatrix} = \\begin{bmatrix} x_1 & -x_1 \\\\ x_2 & -x_2 \\\\ \\dots & \\dots \\\\ x_n & -x_n \\end{bmatrix}$$"
],
"id": "b802e8a4-a145-45af-8779-413637b648b4"
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"#u = torch.concat([x,-x],axis=1) # u1 = [x, -x] 같은것"
],
"id": "c3679474-9661-4415-aa2f-eb9bff07ffe7"
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"l1 = torch.nn.Linear(1,2)\n",
"l1.weight.data = torch.tensor([[1.0],[-1.0]])\n",
"l1.bias.data = torch.tensor([0.0,0.0])"
],
"id": "416a91c3"
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"l1(x)"
],
"id": "5741e0e4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 따라서 `torch.nn` 에 포함된 레이어를 이용하면 아래와 같이 표현할 할\n",
"수 있다."
],
"id": "23c40eda-84ec-48f6-a0b6-746812e21ebf"
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"l1 = torch.nn.Linear(1,2)\n",
"l1.weight.data = torch.tensor([[1.0],[-1.0]])\n",
"l1.bias.data = torch.tensor([0.0,0.0])\n",
"a1 = torch.nn.ReLU()\n",
"l2 = torch.nn.Linear(2,1)\n",
"l2.weight.data = torch.tensor([[-4.5,-9.0]])\n",
"l2.bias.data = torch.tensor([4.5])"
],
"id": "5e0f02d7"
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"l2(a1(l1(x))), y"
],
"id": "86d2a237"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 각각의 layer를 `torch.nn.Sequential()` 로 묶으면 아래와 같이 정리할\n",
"수 있다."
],
"id": "7c08c347-d8ac-487e-89df-04cb81e6d36b"
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"net = torch.nn.Sequential(\n",
" torch.nn.Linear(1,2),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(2,1)\n",
")\n",
"l1,a1,l2 = net\n",
"l1.weight.data = torch.tensor([[1.0],[-1.0]])\n",
"l1.bias.data = torch.tensor([0.0,0.0])\n",
"l2.weight.data = torch.tensor([[-4.5,-9.0]])\n",
"l2.bias.data = torch.tensor([4.5])"
],
"id": "19054fca"
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"net(x),y"
],
"id": "d203e846"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## D. 수식표현\n",
"\n",
"`(1)` ${\\bf X}=\\begin{bmatrix} x_1 \\\\ \\dots \\\\ x_n \\end{bmatrix}$\n",
"\n",
"`(2)`\n",
"$l_1({\\bf X})={\\bf X}{\\bf W}^{(1)}\\overset{bc}{+} {\\boldsymbol b}^{(1)}=\\begin{bmatrix} x_1 & -x_1 \\\\ x_2 & -x_2 \\\\ \\dots & \\dots \\\\ x_n & -x_n\\end{bmatrix}$\n",
"\n",
"- ${\\bf W}^{(1)}=\\begin{bmatrix} 1 & -1 \\end{bmatrix}$\n",
"- ${\\boldsymbol b}^{(1)}=\\begin{bmatrix} 0 & 0 \\end{bmatrix}$\n",
"\n",
"`(3)`\n",
"$(a_1\\circ l_1)({\\bf X})=\\text{relu}\\big({\\bf X}{\\bf W}^{(1)}\\overset{bc}{+}{\\boldsymbol b}^{(1)}\\big)=\\begin{bmatrix} \\text{relu}(x_1) & \\text{relu}(-x_1) \\\\ \\text{relu}(x_2) & \\text{relu}(-x_2) \\\\ \\dots & \\dots \\\\ \\text{relu}(x_n) & \\text{relu}(-x_n)\\end{bmatrix}$\n",
"\n",
"`(4)`\n",
"$(l_2 \\circ a_1\\circ l_1)({\\bf X})=\\text{relu}\\big({\\bf X}{\\bf W}^{(1)}\\overset{bc}{+}{\\boldsymbol b}^{(1)}\\big){\\bf W}^{(2)}\\overset{bc}{+}b^{(2)}$\n",
"\n",
"$\\quad=\\begin{bmatrix} -4.5\\times\\text{relu}(x_1) -9.0 \\times \\text{relu}(-x_1) +4.5 \\\\ -4.5\\times\\text{relu}(x_2) -9.0 \\times\\text{relu}(-x_2) + 4.5 \\\\ \\dots \\\\ -4.5\\times \\text{relu}(x_n) -9.0 \\times\\text{relu}(-x_n)+4.5 \\end{bmatrix}$\n",
"\n",
"- ${\\bf W}^{(2)}=\\begin{bmatrix} -4.5 \\\\ -9 \\end{bmatrix}$\n",
"- $b^{(2)}=4.5$\n",
"\n",
"`(5)`\n",
"$net({\\bf X})=(l_2 \\circ a_1\\circ l_1)({\\bf X})=\\text{relu}\\big({\\bf X}{\\bf W}^{(1)}\\overset{bc}{+}{\\boldsymbol b}^{(1)}\\big){\\bf W}^{(2)}\\overset{bc}{+}b^{(2)}$\n",
"\n",
"$\\quad =\\begin{bmatrix} -4.5\\times\\text{relu}(x_1) -9.0 \\times \\text{relu}(-x_1) +4.5 \\\\ -4.5\\times\\text{relu}(x_2) -9.0 \\times\\text{relu}(-x_2) + 4.5 \\\\ \\dots \\\\ -4.5\\times \\text{relu}(x_n) -9.0 \\times\\text{relu}(-x_n)+4.5 \\end{bmatrix}$\n",
"\n",
"# 4. 로지스틱의 한계 극복\n",
"\n",
"## A. 데이터"
],
"id": "4af3f17f-31a2-46c4-84d1-129bfadf7fcd"
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"df = pd.read_csv(\"https://raw.githubusercontent.com/guebin/DL2024/main/posts/dnnex.csv\")\n",
"df"
],
"id": "9eef0054-a918-43dc-8c63-827c57b589dc"
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"x = torch.tensor(df.x).float().reshape(-1,1)\n",
"y = torch.tensor(df.y).float().reshape(-1,1)\n",
"prob = torch.tensor(df.prob).float().reshape(-1,1)"
],
"id": "f9c64252-10e4-436f-a33d-60232b7812b5"
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\nAElFTkSuQmCC\n"
}
}
],
"source": [
"plt.plot(x,y,'o',alpha=0.02)\n",
"plt.plot(x[0],y[0],'o',label= r\"observed data = $(x_i,y_i)$\",color=\"C0\")\n",
"plt.plot(x,prob,'--b',label= r\"prob (true, unknown)\")\n",
"plt.legend()"
],
"id": "625869c1-cdf7-46d1-84c0-a942b9b15ce6"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## B. Step 1~4\n",
"\n",
"`-` Step1에 대한 생각: 네트워크를 어떻게 만들까? = 아키텍처를 어떻게\n",
"만들까? = 모델링\n",
"\n",
"$$\\underset{(n,1)}{\\bf X} \\overset{l_1}{\\to} \\underset{(n,2)}{\\boldsymbol u^{(1)}} \\overset{a_1}{\\to} \\underset{(n,2)}{\\boldsymbol v^{(1)}} \\overset{l_1}{\\to} \\underset{(n,1)}{\\boldsymbol u^{(2)}} \\overset{a_2}{\\to} \\underset{(n,1)}{\\boldsymbol v^{(2)}}=\\underset{(n,1)}{\\hat{\\boldsymbol y}}$$\n",
"\n",
"`-` Step2,3,4 는 너무 뻔해서.."
],
"id": "dbf528f9-3bce-4418-990b-70683dc0ca00"
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"torch.manual_seed(43052)\n",
"net = torch.nn.Sequential(\n",
" torch.nn.Linear(1,2),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(2,1),\n",
" torch.nn.Sigmoid()\n",
")\n",
"loss_fn = torch.nn.BCELoss()\n",
"optimizr = torch.optim.Adam(net.parameters())\n",
"#---#\n",
"for epoc in range(3000):\n",
" ## \n",
" yhat = net(x)\n",
" ## \n",
" loss = loss_fn(yhat,y)\n",
" ## \n",
" loss.backward()\n",
" ## \n",
" optimizr.step()\n",
" optimizr.zero_grad()"
],
"id": "e3d05bed-d4d5-4266-b069-dba1f85d4d78"
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\nbGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9h\nAAAPYQGoP6dpAACnQElEQVR4nOzdd3wUZf7A8c+U3U0jgdCRqrQAghQRUAQR8ey9oSIWFD0r6p38\n7Hp3ePYK6umJBZGzcJZTioUmKtKUJl0pBumhpOzOzPP749ndZFMgCUk2Cd/3i2U3U787uzvznWee\n5xlDKaUQQgghhIgTM94BCCGEEOLwJsmIEEIIIeJKkhEhhBBCxJUkI0IIIYSIK0lGhBBCCBFXkowI\nIYQQIq4kGRFCCCFEXEkyIoQQQoi4suMdQGl4nsfvv/9OnTp1MAwj3uEIIYQQohSUUuzdu5dmzZph\nmiWXf9SIZOT333+nRYsW8Q5DCCGEEOWwceNGmjdvXuL4GpGM1KlTB9BvJjU1Nc7RCCGEEKI09uzZ\nQ4sWLaLH8ZLUiGQkcmkmNTVVkhEhhBCihjlYFQupwCqEEEKIuJJkRAghhBBxJcmIEEIIIeJKkhEh\nhBBCxJUkI0IIIYSIK0lGhBBCCBFXkowIIYQQIq4kGRFCCCFEXNWITs9E9aKUQimI9GETeV1SpzYF\npy88jed5eB6Yph53oGWVtJzIcNd1cF0D2wbbtkuMFfQwpf+ITud5+m/DIGa8aZqYJngeOI6D54Fh\nKCzLxrJAKQPHcXBdBSgsy8K2TUzTRCmF47g4jofnuWCaWAaAget50XUopVDhdRsYmKaJbZkYhoHr\netFpVfjNGCgUhl6faWGgcD3AUJgYYBgoz0MZBigvOm34n34dHmYYJmY4psg6Ck5j5M8aM1/B50jc\nBd9LaeYv77iKXrZhmNFtahhgKPAApbxKWW/BzzCyjoLzRbZnwW0Z+ZyUAk+pItMUt94DfS6FP/vo\n/+HvDqaJiQJMlPLwIuspELdhmFimAQpcpYpsr+LeLyhMw8QM/ygVFPtdjUyjlIouu+DnhP60Yt5b\nwfer34reYF54TZZpYRr6t4wBlqn3OY7rotB/Gxh4SuF5XnR7maaFbRoYhqn3WeHfbWR7RdaoPxcj\n/DmFt5Gpt1Hkt+zpnQuGGX4vyiiyb1AQ85s0whtS73vAsnQ5QsHlYRiYhoFpGvnbHj3KNPXfkfmV\n8nA9A9sCy7LwPL2OyH4rHsqcjMyaNYsnnniCBQsWkJmZyeTJkzn33HMPOM/MmTMZNWoUy5Yto1mz\nZvzlL39h5MiR5Y1ZxInnKVzPw1X5rwEs08Q0DSwj/3Xh6SMi03ieIug4BD39A3Y9Dwvw2za2bcYs\nq6TlRHZv+/Mc9uXlkZ2novMlBSDR9uPz29H5vXDCEfQ8Qo6L4ypCrkcwpJOFkOvhuB6O4+IpvTM0\nTLBNA8fzcByPfUEPVx/1CfjDRYtKsS9PL8vAICFgkhywSLBNHAd25uSxZ3+IoOPieS6eq3dyygXH\ncwm6Lg75iU+C7SPRb2NZ4R2tqwiFXPIch5Dn4SkPD7BNCyu8ky94UFDhZEvvvBRO+EDiegovPM4L\n78hN08QX2YkR/ixUeB70QTnmO1AgoYnsiK0C80em8cIHgJLmp8D0ZRlXcL3lmb/wOEMfvTAVGKaJ\nHT14hRNc5eEqhacqZr1GwW0dHhc5UOrjiRE+SBdIHI3wdlYFYiacQEczbf06kl8rA0yK/1xcFfvZ\nW6aJz9QHfiMyr2lgKJ2VKaXwXPDwCLkujhc+8JsmdjhUA/3dCXkeTjihKPx+lQGWYYbXZ+hkwwTl\n6e+mG55XH1T1slX4++wpheMpvPCyrejJSPjEosC5i4l+Tzoh0LGaphn+rYBlWvj9lt72nhs+iQgn\nPeGkX6/PwwUMyyTRtLCtyG9M73dc18MwDAyT8FmOiWkBHuF1GliWhRV+IwYGrqdQHvp9eAqFh/IM\nDDOcASuwfBYWJoaB/i5E3ocieoKiDD2/44Lr6N+3Xp9BwLbx+Qwsw8RnmRim3v6WaeCiUI7CRS/L\nNAwSfAYpgQCpyQGS/BZ1En0kBfzYdtUmJWVORvbv30+3bt24+uqrueCCCw46/fr16zn99NMZMWIE\n77zzDt9++y033XQTDRs2LNX8onrwPH2w1cc4FT1LAr0TMhW4GHiuhy+8+4tMbxqRUg+FqyCY5xBy\nPTANTCJnW+AoUI6rzwgsE8/1sDxDnxUVWk7IVTiui+N57MnJw/UMEn1gWjahUIhd+2GflUt6UgDb\nZ+EqRZ7jEnI8PM8j5CmCIYfcoENO0NWlD+Fp8kIehoKAbaIM2B/U0yllELAM/LZFruuwPcslFAxi\nYuKzTRL9NsowyMp12bY/B+UAeHrnZEBuKMTeHIfs3FxcF1R4Rx8KJzqmaeKzLAJWUO/0IlvG1IlX\nyHXJC4UIugoDhWVYGHio8Nmi37YxDXBdhYMXPg2ycFxdmuMoF+XlnyWahoWJCpfghE8VjfCBBQPP\ndfGU3nFGDsSEz+QiZ3wmekcfOQpGz+gME+V5xc4PJoQPOkqpUo8ruF4jfBAuy/yFx+mzSL3tCG9L\nyzB1IuKp6Jm6pwxcz9VnwIewXn0mTPjAbISnt8JbW3/PIwdwnVzo35dtWRjh344Kx2iEi0gcD71s\nI3w2X+DM3CDyueZ/Lip6pq1LPSxLlxTYpoVpRs6sLUxDfz8cN4Sr9DcCBY7SiTyGhRmOO+S6epmW\niakUDgau40RLDEyInvXblg/L1ElJpHzD0BkJLgau62KFt4nn6YRAlwRY4HkEFbiOg2WG9xzhZM4y\nwDDMaCmCUeD9mqaBz7L1viZcEhSwLAwTQo4XTpJ0iUhuKEhuyEWh9MHatDHDy/Q8V5d6Wvp3qoxw\nIuAplAl2pLTH0PtE27JJ9OnEKug6uJ5OAPy2SchxyQ25hBwXy7KxDf0dVLiYysT2mbokJnwyZpqm\n3m6WhfI8go6H47k68bIsXXLl6e+OzzSwbJ1w+X2W/g5h4uDiepBgmjpBckxsBXmujUeQBFtvG8fT\nj9TEqk1IypyMnHbaaZx22mmlnv7ll1+mZcuWPPvsswBkZGQwf/58nnzySUlGahA3XGRpmYb+AaN/\nWHqc3gn6LDN6hgNEp48wDF16kh3+YSb7fYQcXTzqs/WPJujos68kn4UbLj0xLavIcvR5GuzL1YlI\nckL+VzlkWiT49I56b14udX3J0WJUN3yGYZmmPrh54LMs8PSZjqUMAqaJaekdG56H4SoMFT6QWDZ+\nn4mLgeG5eErv1Azbxu+zMS0L8hxy81xcz8VzFT6fhW1ZWC7YfkAloFyXYMjDMMHymbim3tH5fTaG\nCUE3f4foeh4+y8L22eQZFobjYYd3QHmOS8Bn64MCKro85XgEHQe/beGZlj7bcxTKVpFjJpZl6RIj\nQ5+dRkrXDdPANk0cx9WfY7S4usD2jxQdG0b4ckb+/F744OZFvgeF5rctC8d1o3+XdlzB9UaKycsy\nf+FxmPoihIsiYPtwXZdg+ABn2Pq74eHpA5Wnl3Yo67XCxd9OgSIe29Tj9Nmrqc+Yw9vSCJdsKMPQ\nCVJ4wW748zIs/TnlhZzo9NHLBejvuOu6MZ+LES010JcJDcvUiVD4rNnvs7FsE8fT3yXH0fM44UuQ\nngLTUtimRW4wBCZ4pg9P6WTFsAx8poVjONHLBA5KJx+WiWXber22Lh1VSmFZBRIkW+8z8kIurukR\nvepjGihTYRsmnunhoEsGItvNwcMOb18z/N0NofBZFpZtgwkhzyPgs7EMkzzPQaHwJfixTUvvZwzA\nDIARThJ8PgJ+ny4h8Txc1wLLBNPA8ln4bQvlhKc1LSwLXKUvsvgsW+8PldKfnOnH8FyUZeEBps/C\nIASWjc82ccK/ccvw4yoXRxn4fBYWEMQl0bbx2xau6+EohWlbGK6Jozx9EoKBE/1uKpRpYlpW+JKT\n3ieE8nTiZfttfKZB0FGYPpO0JB+uMshxQ6TYAUwDckMOCT4T2/ZTVSq9zsh3333HkCFDYoadeuqp\nvP7664RCIXw+X5F58vLyyMvLi/69Z8+eyg5THECkRCNS7Bl5HWEa+kdoKxXOrPWPomACEeF5Ho4u\nFMELX3opOJltQtCDBE+fTQc9SLSihfMx8eA57Mv1qJNgxowjXJLiMz325irqJIRw0Ts/Q0Uupygc\nxyHoulgogpFLNJ6Hh4GJR57jhafxcPFQhoVPuezPUyjPIeS5uJ5D0DUJ2C65jkkiipDrEPIccvNC\nuBgkos9ichxdwhLKC5EbcnSy4hn4bBNP6e2W5+rDjue5uEphG+AZBiFD7wRDji6tyAs5OulTHrmO\ni2UZeK6CyFmnoQgFHZyg3m6up6+5e64KFysbegcfLbYvULfGMPFMQ3+Okctb4c/WU0SL891wcumF\nj5LR+YkcQImWokXmV5FxRZZ54HEF1+voNRQaV7ZlW6ahz+vD8YZCjr4cEz4Tj9Qd8VyFG77erovz\nvXKtV89J+Lq9it1OSn+/LcvAdcNF9+GEGcMgpL/Z0WQj8nlFPifX1aV9pmHkX8IJry+/tIT8ZZom\nbuRylGHghetNmJaBclxc28JTitzwgTRyWcFxVfiSg4GLQyjk6PWa4Lj5MSnL1JdeXC98mQewTJRp\nkefoC5KhPF0opFyFiiRJtj54Bj2F6znh0kJdgBQKl4oapi5xC4Vc/Q7Dlyc9DzxTl4446Hg9T2H4\nbHBdIjmN4arowdYwFK7tw2e65DpO+HPQl0T1JSdFbvhEK+S6oDyc8OfkBG08n0VeuM6Gi0vQMLBQ\neIZJgg2epZMivS+CkAc+0yUHA8tQ5Dl6f7Q/T1+icU0P2zIJuR6WAaGgi9/Wl3YIl4DlOR5Bx41+\nDzwPDA9MS58seZ7eNyb6FHmAYxn4bZO8oEuupwiE9yGuYUTrywRdRYIF+4NQNxQi4PfhKch1PBI8\nr8rqkFR6MrJlyxYaN24cM6xx48Y4jsP27dtp2rRpkXnGjBnDww8/XNmhiVKKJNy6qFJFX0dEzliV\n0tdJI5Uyi6uEGilKNMM7kMLTmeGaorr+XGR47HIi8Xjhy0GWlf81VgWWZ5o2EMJxDbDQxcamCUa4\nCNw0MQwzfOalzyZ04baBYRmokMIzLFS46BplYFoWjuuhTAvT8vBjEnTBMH0oDDxMPNPEtmxsWx+V\nLMsOV3gFn8/A7xqEPBOMcMlIuHjcKlBhD9PG8FS4+Dlcj0DpSzGOUuApPNfFMiLbwMQ0IwdaXYRt\n+2wilR0MU5+FuqbKP2hFsodw4hdN+cL1QDD1QdFQShdVo4vcjfDn5CmlSw2UKjJ/ZDqInb/guMLL\nPNC4gut1w/EWHleWZRfcBka4PoFSKua9mIaBZ+nk1rJMDFOXWpRnvSqcSKEUplX8drJNE0wvmkyb\nRrgI3nWj711/8b0in5PnFbjkAbFxFnpPulhfRX8nVjhZMk1DV/A0DSx0SYK+xAKO52EZKlzBU2cI\nlm1ieOFtaeZXrjYNQyfFlk7uMHQJjhEukVHhbM009XRu+IBnheuRuLgow8RGhS9HEU56dD0KZYDC\nja7PDn8XI+/fCG8jM1w507YsHBVeh6UvTVp2fkmnZRpYSic5BuDzefq3Z1oY4borXnhrGuHtZYbf\nj42+jGcCTjjJjeyTLNPAs3TJhG2buK7CtvSlbMs0sG297YIhV18es8J178hfjmGA369LrwzDxLJc\nrHApra60rvelZrg00/U8lKv3OZH9p2nZuMrDcD38fr8+2QF8phX+LkTq8YHrGBgBM7yvJ9q4oCpU\nSWuawgelAx2sAEaPHs2oUaOif+/Zs4cWLVpUXoDigCIfk1Kq0Gsj+joyXUnTROjqBbpipemzwI2d\nLlK0r38A+cWOBROSyCLNcO0H13UwTV3CZhSIxwsXm9uWwiWcMHl6Z2/qPZy+ph4+uBvhX5+HgXJ1\nxVBTuRhKn3kqw8JzFRYmynPxXJdgyMFVpr70gQ8TD9PzcFwHxwmFr4N7WJaJ6+qzyWAopFv+hEtG\nzHDJiGfoioQFS0YIl4wYhUpGlKffi97JWuH6OrpkxFW6ZMQJOdHtWrBkxAuXjFgHKBnhICUjHuF6\nDyWUjFgHKBmxiilFyNmdwN5dCSQkutgJIeyAQyDBiRTgxKxXn+UWXzJS3LKLG2cVbHHg6iQ10oIi\nUjLihUtGjHDifKCSkYOtN/JNLlwyEpkPDCiuZMQ1onV8PLdoyQimgVNCyYiihJIRXYSQn4yGz5CV\nZWAqC8OwwpVhwxV5wyUjrqsgXDJioOtueJ6HKlQyYoQv13qFSkZM09KXPz0dnCK/ZER5BtiWrqvk\nKbxCJSP655tfMuIUKBkh/PmYJhheuIQgXDJiYmNgRQoWcLHDdT10yYhleLhK/zZVuCQoFNK/PcO0\nsE0frlL6cpfSdWSwDAxslKdPTCKJEIb+/DzDDH9XTLxwKx3HCbfGU/o74XoKJ1wyopSBa6hweayp\nS5Q8/Tu0DINg0MFnWyilx7lubMmIZ1hgmIQ8V287pb+rlmGFS0wdXfqLIhjM05eTDSNceRcMvxm+\ntG5g2fktokzTqrJEBKogGWnSpAlbtmyJGbZ161Zs26Z+/frFzhMIBAgEApUdmiilSF0PV+mz+Ojr\ncFLgKaJn8K6nsMMZecFpIkzTxDbB9cI13D03ZjrHA78ZOQNW+E3C1dyKice0SUkIEXQNIlf7IvUY\nDKUIeSZ1Ejws24fheTimLha3Lb0ztm2F39XFmn7LCRe5hItFMQnYBn7TAOXgOSYoMA2LJL9JTsjA\nZ3q4po4XS7eeMSwLn6UvEZkBI6bOiPIMXD8EFRi2qeuMGPq9BkMutmUR8NnhYu+idUYMYH+eQ8jx\nsP26zkiwQJ0RInVGTDNcMc/Eb1uEXA9bKUKOwvTn1xnxheuMWEbxdUYI1xmJtHSCSAFTfgVQw9Bn\n0QXrjGDouhCRukOu52Eq2LM1kT/WprH91zR2bEqm/7BfqNskGwtYtfwIvnuvQ6EvnsKf4OBPcjjx\nqhUckZGFUorta9NY/UNj/IkO/kSHhJQQCSkhAskhktNcEtOy8SV40XgjonU3Iu8lfBbtofDZPkzX\njbZwMczYOiOuB6YvnMgU2BYlLru4cQXWV1KdEaOYOiO2oVtvhHO+6OcV+ZxUyIm2LivIMk293gKf\nS+E6I5ZlYhFpDqrrjPjDdUZsE/Icl0idEX84AVRK1xlRhqnrjHhgROqMmLrOSG7IwfYRfb+WYWJZ\nJoFwnRG7hDojSunWa3khC8uXX2ckkjibhknQ8fDZsXVGvAJ1RqxwnREPhW1Zuk5FuATGH64zYvkt\nXWfEsrBMCxxdeTPkeijTRTkuPr+PhHCdEcvT9TUiLWoC4TojpuOSF64z4i9QZ8QO1xkJ+HVJjIuB\n7bmYloWP8EW3UIigB8kxdUZMbOWilEFiuM5IjptfZ8QyPXyWLs0NuQpXeST6fPl1Rix0pXTLJBDQ\ndUM8BQGfhcpzcA1dPy9SZ8QwwG8ZhJRBasAIV5vQ37uEKm7mW+nJSN++ffn0009jhk2bNo1evXoV\nW19EVE+WqVu3uOFiWU8pHDdcihEumnXDRcWRinr50+cfwDwFAcsmhK4RHilKjpzxW4YRPkjqZflt\nW5+ZFFqOvpyiSEkIsCcnj/25Dn5LYVo2eC65DvgsgzqBhOgxEvTyPUO3YDEMffAOBcOlEKbeQed5\nukgzYOuzLmUZKFfvIDzXIRiydAsCE0zDxVAmynEImoDjEvIUpq0wnHCxe7gEw3VDOEEH8nIxXPAb\nutVGKOShHA/XNAk6FgHL0kkQClwPywTDC1+3DoVQrsIJ6TOfAB4q6ALh1jQK3KC+YBTwPAh5mOHW\nNGah1jSuU0JrGk+37zDDrWmMYlrToDxUpHVICa1pcnb6WLe4ERuXN2DLunrk7Y+tDLd7Q4B69Xdi\nAAF/LqkN9xPMsQnm+PBcE5RBMMdHMMeH6QUhmAvKY8evjVkxo3mJ39VTRiygTfetKKXYuKwhi6Ye\nRUJySD9S8khKyyMpLZfktCANmu8nIUmXVBl4+COtaRzdmsYMt6ZR4dY0Zrg0oXCLGc8xMUtoTRMd\nF/5d2JDfp4ZhYeFhuMW3plGAYVmYqpjWNI6upG2V0JoGTKxiWtN4KtyqBIXpWboyc/jyjBF0cR0L\ny1AYhoUdbk1jF2pNEzQsbDwMT7emMVS4NY2jW9MY4dY0kfeLaWK44Lq6NY3p6VZMBmCo/NY0nuvi\nhpdtltCaRjmOTsJQ4OpCBNsg2prGCyfIPgOU5+C6QUzLxocu4VBGgdY0uUFCBtiGrpETCgUh5OJD\nYYRc8lwHM3I50nOxlG5NY6IIOQ6e42F5CmU6uAVa04SCDqpAaxrXDemTAE9hhlvTqJCr9xeObk3j\nObruSaQ1jQp5uKaB7SlcxyHoOfqyk6EIOh7Kc7HRLZecAq1pon2KuC7K1J+v63gYlsLwwAk6KNsA\nw8QLuWRlh6iTYJNoJeCEK8cnB2z8dtV2Q1bmte3bt481a9ZE/16/fj2LFy8mPT2dli1bMnr0aDZv\n3sxbb70FwMiRI3nxxRcZNWoUI0aM4LvvvuP1119n4sSJFfcuRKUzTX0RwvX0TiNSmRUI/wCL9jMS\nnV4RPVhZBvgDNoFoPyP5Z322gT7bsGL7GTEL9jMSXo7PMvBbNgqdHOl+RsByHCzTol5ybD8jlmGQ\nYFv4TZOg52E6LpbhC5855fczkmB7OHZsPyN1E/1F+hlJsHykpfkwSQBVoJ8RZZCWYJIcSCjSzwg+\nA79lUS/RFy6iLk8/IwGqaz8jhoq0JtYHxZ9W1GfOpPzSDtvn0ezIfTRvt5emR+7nyE4Oqel1AWhx\n5n5OOnNxeNkGXsgkN9siN9siL9smvRkkJKbq9XZ1sJ2N5GVb5O63yd5nk73XR/Ye/dyiuZ8WDdIA\nyMytzx9r00v8Xl9250qO7LsTU8Hqn+sxa3IzUusFqVMvSFqDPNIa5JLaIJe0BnkkJbvReh7FbZPS\njJN+Rqp7PyOB6HY9vPoZ8eMP+Ejw1aB+RubPn89JJ50U/TtSt+Oqq65i/PjxZGZmsmHDhuj4Nm3a\n8Pnnn3PHHXfw0ksv0axZM55//nlp1lsD6YpSFraK7Dh1YXRkf1i0fkjh6fOnMU0D2/aTEK2sGin1\nKLqsAy0HIM0ySU30H6QH1vxYozuwyJ6b/HoskH85XXpg1dMUODbGzBd53rHDZMI7Pt6b6OPyK0Lc\nfHMQBezsAb//6HDyYJf+/R26HO3h9wOkAnWApgdcdonjhpQ0TQjd1qZVdNxZHQwuGJDDzh2wY4fJ\ntm3wxx8mf/xh8McWk6tPa07Pnk0xDJNX19q8sTSh+C8/8MabOZx9dggwWL7M5OuvLVq1VrQ9yqV1\nG0Vi4sG3lxF9KT2wSg+s0gNrQYYquEeupvbs2UNaWhpZWVmkpqbGOxwhBLBkCTz7LEyYAJGW+Mcd\nB99/H9ewym3NGvjhB8jMhN9/h99+y39s367H9e6tp33uObj99vx5DQNatID27fXjllugY8e4vA0h\nqpXSHr/l3jRCiDJZvhweegjefz9/WM+ecNNNUJMLPNu21Y/i7NsHBevUt20Ll14Ka9fCqlWQlQUb\nNujHl1/CsGH50775Jrz4Ihx9dOyjUI8HQhzWJBkRQpTJX/4C//uffn3hhTBqFPTpE62vWCulpMT+\nfcYZ+gG6GHz7dp2URB4FS0V+/BHmz9ePgho2hK5dYdw4aNeucuMXorqTyzRCiANSClwXIpXrFyyA\nv/0NHn5YH0zFgf32m05ElizJf6xZE62LzfbtEOnl4J//hJkzoVcvOPZYneQ1bBi/2IU4VKU9fksy\nIoQo0datcPXV0KWLPlCKipGdrS93rVoFQ4fmDx88GL76KnbajAzo318/LrkEpEcEUZNIMiKEOCTT\npsGVV+qEJDFR148o5u4NogItXAjffacv7cybBytW5I+rWxd27MjvnnvuXGjZEpqX3OWKEHEnFViF\nEOWilG4tcueduilgly4wcaIkIlWhRw/9iNi+Hb79FmbPJtxbrx6uFFx+Ofz6K3TqBKeeCkOGwIkn\nQlJSXEIX4pBIyYgQIioU0q1iXntN/33NNfDSS5BQcvcbIg6ysnQC8uOPRG84CeD364Tkqqvgiivi\nF58QEaU9fsendxMhRLWjlK6/8Npr+gz86af1a0lEqp+0NN2fy7Ztuon1iBH6kk0wqJsWF+zrxXVh\n6dL8CrNCVEdymUYIAejLAOecA59/Du+9B2edFe+IxMGkp+vm1RdeqJONVat0s+v+/fOnmTtXl5Yc\ndZTuG+Xyy3WlWCGqE7lMI4SIsWULNGkS7yhERXntNbj55vxecgGOOUaXgl16qe45VojKIpdphBAH\n5XnwyCM6AYmQRKR2ue46XRF24kRd2mXbsHix7ryuZUv46ad4RyiEJCNCHNbuvRcefBAGDtT1DUTt\nlJKiS0E++UQnnq+8AgMGQOvWumv6iP/+F37+OV5RisOZXKYR4jD13ntw2WX69fjxugWGOLxkZ+c3\nBc7LgyOO0H2ZHHcc3HijTmAK3pNHiLKSyzRCiBL99JNutgtwzz2SiByuCvZJsmsXnHSSvozzww8w\nfLi+jPPww7rjOyEqkyQjQhxm9uyB88+HnBzdUdbf/hbviER10KSJbia8eTOMGaN7dt26Vd+huUUL\neOuteEcoajNJRoQ4zNx2G6xbB61awbvvgmXFOyJRnTRqpEvL1q3TlV5799b1iXr3zp9G6heJiibJ\niBCHkd2787sWf/vt/LvFClGYz6frjPzwg76pX8eO+eOuvVb3ADt7dvziE7WLJCNCHEbq1oVFi+CD\nD2I7xhLiQAp2krZjh76cM22a7kxtwABJSsShk2REiMNMnTq6zogQ5VG/PvzyC9xwg74XzqxZOik5\n6yxYsiTe0YmaSpIRIQ4D33yj+5YoeFM1IcqrdWt4+WVYu1YnJZYFn30G3brpUjchykqSESFqudxc\nfcAYORKeeire0YjapHlznZQsXw4XXaTvlXPKKfGOStREkowIUcs9/TSsXq2bbl5/fbyjEbVR+/bw\nn//AypX6jsKQfxfod9+VOwaLg5NkRIhabNs2eOwx/frJJ/MPFEJUhoKtsyZP1k2DL79c1ylZvDhu\nYYkaQJIRIWqxv/0N9u6FHj3yu34Xoiqcfrr+/iUlwZw50LMnjBoF+/fHOzJRHUkyIkQttW4djBun\nX//zn2BWxq89lAOrp8PeArf99VwplxckJOgbMf7yC1xyia48/cwz0KULTJ0a7+hEdWPHOwAhROW4\n/34IhXSX74MHV8IKgtnw9rmw8Qe4/EOo00QP/2kifHIrJNbTj6T0/NeJ6dD9CmjcSU+7bxtkbcyf\nJpCqe2QTtUaLFvqmjFddpStR//or3HGHvjuwLUcgESZfBSFqqeuvj60zUqHcELx/lU5EMCC1af64\nnF2gXMjerh87Cs171KD8ZGT1VPj4z/njDKtA4lIPTn4A2oR7Z9u+GtbNKCbBkSSmJjjtNFi2DO67\nT7e8iSQiSslHJyQZEaLWGjBAPyqcUvDJLbB6GtgJMOxjaNw5f3zv66HLBTopydkF2TvzX+fshAZt\n86c1TKjTTI9zcmKTGAAnL3/ajT/A53cVH5NhwUVvQKdzwtP+CPNfL1Q6kw5J9fWjXisI1KnY7SIO\nKiUFnn02dtgzz8CKFfo5JSUuYYlqQJIRIUTZfPN3fSnGsOCiN6Fln9jxdgBSm+nHwRwzVD9A1z+J\nJi3hR9Nu+dPWaQoZZ0HO7tgkJ5LE+JPzp932i46xJOe/Bl0v0q/XfgNfPRybrCSlhx/1ofmxkNZc\nTyun8RVq61ZdUpKTA19/De+8A337xjsqEQ+SjAhRy4weDa4Ld94JjRtX8MJ//g/MekK/Pus56PCn\nilu2L1E/Skpi2p6sH4WFcnSCklg3f1iz7jD44fzSmOzwI2cnZO+A5Ab502ZthN8XlRzXBa/D0Rfq\n17/8DybfEE5cCiYv4QSm45n5l6CC+yE3S4+zA2XZEoeNRo3g889h2DBd4fqEE3Rdp/vvl7tJH24k\nGRGiFtm2TReD5+bqa/QVnoxsXa6fj78delxZwQsvp0gSU1CTLvpRGm0Hw9D/6CQl+tiZ/5zWIn/a\nnJ0Q3KcfWRuKLiv9yPxkZO3XMOkK/dqfkp+8REpgel0Nrfrp8ft3wLYVkNRAJ0qJ9cA8PI7GAwfq\nyqy33qrvJP3ww/rGexMm6I76xOFBkhEhapF//UsnIsceq3fyFW7wQ9DqBF0JtbYo7SUlgC4XQqvj\n85OVSElL5NGwQ/60wf36UpZy8xOY3QUSmPan5r/eMDc/cQFdlyYxXScmSQ3ghDugXbhJ1J5M2PBd\n/rjkBnpaq+buzuvWhbfegj/9SVe8/vpr/R1euVL3UyJqv5r77RVCxAiFYOxY/frWWyuwaoMT1AfH\nyMGuXWW0E64h/ElQ/yj9OJhul8LRF0PenvxSloLJS7Pu+dMaJtRvC/u3Q+5uUF5sRd5jr82fdtOP\n8MHVhVZm6MtUSQ10C6ROZ+vBu36DVVN0SUzB5CWpPli+Q9gQlWPoUN1B34UX6qbAkogcPiQZEaKW\n+O9/YfNmfR3+oosqcMFT/qqb1V7wOtSp6Os+tZxp6iQhse6BE5iOZ+gH6GbT2Tt0YpK9XT+36J0/\nbSBFl87s36bH5ewCVH6lX+XmT5u5GL74S/HrTEiD05+Erhfrv7ev0ZV+o0lLff2c0kg/V1HJS8eO\n8OOPEChQzea336BePUhNrZIQRBxIMiJELfH88/p55MjYHfkh+WkSzP83YMAfSyUZqQqWT3cgV6eE\nChNHDYq9TOY64dZF23WC0jAjf1xyQ+h0bji5iSQvO3XJS25WbOnIH0th9pMlx3XW89DzKv1620r9\nvUhuAMmNdMKS3FA/UhoVrcNTRokFZt+zR9d/Mgz45BM4qhSFUqLmkWREiFpg8WJ9/w/bhhtuqKCF\nbl0Bn92uXw/4S/EtWUT8WTakNNQPMmLHteqXX0k2wnN166Ps7ZBSILms21L3EVOwRCbyWnm6JCVi\n6wr44eWSYzrzWV1BF+CP5TDv1fxEpWDSktxQL/cA1xQ3boSsLPj9d12P5P334WT5KtY6kowIUQvU\nravriQSD0KyUdTEPKJQD7w+HUDYcORAG/LUCFiqqBdPSl2CS68cOP6KHfhTmubrkxVegAkf9o+CE\nUbB/q+7Sf/9Wnbjs2wpunq6TErHtF1jwRsnxnPkM9LpGv96yFL4fG1Pi0jm5AYumNOKqmxox7dv6\nnHqqxTPPwC23lH8TiOpHkhEhaoHWreG55ypwgdMf1AeRlMa6g7DDpJmpKIZpxfbLAtDkaP0oTCnI\n2wuWP39Yww4w4J7wZaJI8hJ+5O3RpSMR21fC4glFFtsI+OJkeKPbM1zz0jXceivk/LqUu49/ASOl\nkf6epjTWpS0pjfXlxIS60kFdDSLJiBAi1uovYd4r+vW5Y8PF/0KUgmFAQqFapo07x94uoKBQrm5J\nFNGok24NFE1YCpS4ZO9g+E0N2dYS/vpXWDB1JUad90qOpWCJyx/L9KWiaNJSKHnxJRza+xaHTJIR\nIWq4xx+H446DE0+soBPBlEbQoIO+PNP2MG7GKypf4SSgUYZ+FMd1MFD8pRO0bAlvPtmFPcc9TKqx\nFfb9EX6EX+fujq0Ps3UFLBhfchxnv5jfid8fy2HR28WUtjTR/bmYZsnLEeVmKKVUvIM4mD179pCW\nlkZWVhap0rZLiKjffoM2bXTp+Pr1+nJNhQjl6OdDbBUhRGUJBsFf4GpQdnaBfkkiJS52eIItS+GX\nz3SisrdQ4uLmwaUToePpetqf34ePrit+pYalSwu7Xar/3voLLHk/P2mJtIJKaSKlLWGlPX5LyYgQ\nNdhbb+lEZNCgCkhEQrn5O1BJQkQ1VzARefdduOcemDoVMjIomgiUdHsApXQpil1g+gZt4fjbiiYt\n2dt1Hy4FWxVt+bnk5tAJdeGsZ6Hzefrvnetg9fRwwtI0v7RF7lsESDIiRI2llN4Jg+6t8pBk74SX\n++vmmMffVi175xSiOI6jL1Vu3KgvVU6dqntxLRXD0PcBKqhZ99jecSPckK7HUjAZqddGN4fe9wfs\n3ZL/cPPCSU6BpH7T/OI7oEtM18nJKQ9Du1P0sKxNsHmhHl6nsS5psf1F561FJBkRooZasgR++UV3\ncHbuuYe4sCmjYc8mWPoh9Lu1IsITokrYNnz5pb6vzYIFcNJJ+k7Axx9fwSuyfEXvYdTiWP0oKFLa\nsncLpB6RPzylEXQ6J5ywZOqSFzdPd0KXs1PPF/HrtzD5+tjlJtXXSUmdJtD/TmgdfoP7tsHu38KX\nhxrX2BMJSUaEqKHeCzckOOOMQ+wme/WX8PN7gAFnv1Drz8BE7dOggb653pln6jv+Dhmib49wyilx\nCCZS2lK4xOXIgfoRocJd+O/dAvu2QNNj8sf5k6D5sTph2ZsJXij/nkZbl8FxI/OnXfsVTC7Q02FS\ng3CJSjhxOfba/JKevH2676CkBtWuIq4kI0LUQErlJyOXXHIIC8rbm9/Lap+boHmvQw1NiLhITYUp\nU+D88/WlmjPP1N3Hn3rqweeNC8OApHT9aNwpdlzGWfoB+seevVMnLHszdfLStGv+tEpBWgs93Avl\n32DxjyV6fKdz8qdd8Sn8dySYBW45UKepLvE5Zig07Va57/kAJBkRogbaskXvy5KTdclIuc38J2Rt\nhLqtYNC9FRafEPGQlAQffwyXXqpLRr76qhonI6VlGPk95hbXX8sxl+mH5+nLPdG6K7/r54JNpXN3\nA4ZOWrI26kdEmxPjmoxI014haqhIc94jjyznArathHH9wHNg6PvQfkiFxidEvASDunL3VVdJJ6xF\nuCFd4XZPZn7Csud3fRPE9PLuTEomTXuFqOUM4xASEYDfF+t+EzoMkURE1Cp+Pwwfnv93Xh4sXw7d\ni2kkc9ixfJDWXD+qEUlGhKhh9u6FhATwHWql+W6X6JYAZs2sfS9EaeTmwoUXwjff6Dol/fvHOyJR\nnOpVnVYIcVCPPw6NGsELL1TAwtKPhLotKmBBQlRfoZDuofXMM2Hx4nhHI4ojyYgQNcx//wu7d0O9\negebsgQLxsPGHysuICGqsYQE/Zvp3x/27NEVWlevjndUojBJRoSoQdauhaVLwbLK2YomaxN88Vd4\nfbCuMyLEYSAxET79FLp1g61bdT8kmzfHOypRkCQjQtQgH3+snwcMKGfJyNd/BycXWp0Q12Z8QlS1\ntDTd/0jbtvDrr7qEZOfOeEclIiQZEaIGiSQj5er+fcsS+Gmifj3kEWnzKA47jRvD9OnQrJm+4/Wq\nVfGOSERIaxohaogdO2DOHP367LPLsYBp9wMKulwAR/SsyNCEqDFat4Zp0yAnB3pJh8PVhiQjQtQQ\n06bpThaPPhpatSrjzGu+hHXf6Ga8Jz9QKfEJUVN0LtSR6fbt+v42In7KdZlm7NixtGnThoSEBHr2\n7Mns2bMPOP2ECRPo1q0bSUlJNG3alKuvvpodO3aUK2AhDlc9e8KDD8KNN5ZxRs+F6Q/q172vh3qt\nKzo0IWqsuXOhY0d48cV4R3J4K3MyMmnSJG6//XbuvfdeFi1aRP/+/TnttNPYsGFDsdPPmTOHYcOG\nce2117Js2TLef/99fvzxR6677rpDDl6Iw0n79vDQQ+VIRpSCY6+Dxl3gxLsqIzQhaqzZs/Ul0Ntu\n0y1uRHyU+d40xx13HD169GDcuHHRYRkZGZx77rmMGTOmyPRPPvkk48aNY+3atdFhL7zwAo8//jgb\nN24sMn1x5N40QlQApaTSqhCFKAXXXw+vvaZvtDdzptQlqUilPX6XqWQkGAyyYMEChgyJvY/FkCFD\nmDt3brHz9OvXj02bNvH555+jlOKPP/7ggw8+4IwDdJKQl5fHnj17Yh5CHM6++AI++giysg5hIZKI\nCFGEYcDYsbrvkexsOOccyMyMd1SHnzIlI9u3b8d1XRo3bhwzvHHjxmzZsqXYefr168eECRO45JJL\n8Pv9NGnShLp16/LCAfqyHjNmDGlpadFHixbSXbU4vD32GFxwgb4Taam5IXjrXFj8LrhOZYUmRI3n\n88H770NGBvz+u/6t5eXFO6rDS7kqsBqFzrCUUkWGRSxfvpxbb72VBx54gAULFjBlyhTWr1/PyJEj\nS1z+6NGjycrKij5KezlHiNooK0tXsgPdUVOpLX5Xt6CZ/gC4smcV4kBSU3U/PnXrwnff6XtAiapT\npqa9DRo0wLKsIqUgW7duLVJaEjFmzBiOP/547r77bgC6du1KcnIy/fv3529/+xtNmzYtMk8gECAQ\nCJQlNCFqra+/BsfRFViPPLKUMzlBmPWEfn3CHeBPrrT4hKgt2rWDSZPg7bfhzjvjHc3hpUwlI36/\nn549ezJ9+vSY4dOnT6dfv37FzpOdnY1pxq7GsixAl6gIIQ5s2jT9XLZSkXcgayOkNIFe11RKXELU\nRkOG6GQkKSnekRxeynyZZtSoUbz22mv8+9//ZsWKFdxxxx1s2LAhetll9OjRDBs2LDr9WWedxUcf\nfcS4ceNYt24d3377Lbfeeiu9e/emWbNmFfdOhKilvv5aPw8eXMoZXAfmPKtfn3AH+BIrIywhaj3P\n0/W11q2LdyS1X5l7YL3kkkvYsWMHjzzyCJmZmXTp0oXPP/+cVuEuITMzM2P6HBk+fDh79+7lxRdf\n5M4776Ru3boMGjSIf/7znxX3LoSopTZt0vfPME048cRSzrTsI9j9GyQ1gB7DDj69EKJYDz0Ejz4K\n//mPrreVkBDviGqvMvczEg/Sz4g4XL3/Plx8se734McfSzGD58G4frBtBQy6D068u9JjFKK22rQJ\nunfX3cWPGAGvvhrviGqeSulnRAhRtS66SBcRjx1byhkMA05/HDqcAceOqNTYhKjtmjfXzekNA/71\nL3jzzXhHVHtJyYgQQghxAI88ou8LlZgI338PXbvGO6KaQ0pGhBBCiApw3326NVtODlx44SH2hCyK\nJcmIENXUxIm6a+oPPijlDJOu1Hfn3S93xBaiIpkmvPMOtGgBv/2mS0dExZJkRIhq6rPP4JNP4Kef\nSjFx5k+w4hOY+wIE91V6bEIcbho0gA8/hDlzytjnjyiVMjftFUJUPqXgm2/060GDSjHDd+Earp3P\ng3qtKi0uIQ5nxx4b7whqLykZEaIaWrtW3znU74e+fQ8y8Z5MWBq+ltP3z5UemxACFi6E887T9UjE\noZNkRIhqaM4c/dy7dyk6WvrxX+A50LIvHNGj0mMT4nAXCsH558N//yv3sKkokowIUQ1FkpETTjjI\nhMFsmP9v/VpKRYSoEj4fvPaa7n9k3DiYPDneEdV8kowIUQ2VOhn5aSLk7IJ6raHD6ZUdlhAibPBg\nCN+MnmuvhY0b4xtPTSfJiBDVTF4eNGyoL8+UcDPsfEcNguNG6hvimVaVxCeE0B59VFdq3bULLr8c\nXDfeEdVc0gOrENVUMKgrsAohqq+1a+GYY2DfPvjnP+Evf4l3RNWL9MAqRA0niYgQ1d9RR8Fzz+nX\nM2fqZvmi7CQZEaKa2b+/FBNtXwPvD4dfv63scIQQB3H11bplzaef6kqtouwkGRGiGsnOhvr1dbHv\n7t0HmHD+v2HZZJj7fBVFJoQoiWHoWzeYckQtN9l0QlQj8+bpCqzbt0NaWgkTBbNh8Tv69bHXVVls\nQoiD27cPbroJ5s6NdyQ1iyQjQlQjBZv0lljcu/QDyM3SzXmPOrmqQhNClMJDD+m+R4YN04mJKB1J\nRoSoRg7av4hSMO9f+nWva6VcWIhq5r77oHlz3com0g+JODjZkwlRTXge/PCDfl1i/yKb5sOWn8FO\ngO5XVFlsQojSqVsX3nhDv375Zfj667iGU2NIMiJENbF6ta60mpAARx9dwkQ/vqafu1wASelVFZoQ\nogwGD4Ybb9Svr7uulC3kDnOSjAhRTURKRXr21Pe+KFbzXpB+JBx7bZXFJYQou3/+E1q2hPXr4d57\n4x1N9SfJiBDVRKtWcMUVuolgiXqPgJsXwBE9qywuIUTZ1akDr76qX0+YcJCm+kK6gxdCCCEqy7hx\ncN550KRJvCOJj9Iev+0qjEkIUV6/L4ZtK6HT2eBLjHc0QohSitQdEQcml2mEqAa2bIElSw5w18/v\nx8Lk62Ha/VUalxCi4vz3v7BoUbyjqJ4kGRGiGnj3XejaFS69tJiRObtg+cf69TGXVWlcQoiK8cIL\n+nLN1VdDKBTvaKofSUaEqAYiLWm6dy9m5JIPwMmFxl2gWY8qjUsIUTEuuUTfd+qnn+Dpp+MdTfUj\nyYgQ1UAkGTnuuEIjlIIFb+rXPYbJLUGFqKEaNcpPQh5+WDf5FfkkGREizrZsgd9+03nGsccWGpm5\nGP5YAlYAjr4oHuEJISrIlVfCSSdBTo6+mV71b8tadSQZESLOIqUiGRlQpOXbwrf0c6ezpcdVIWo4\nw9BNff1+mDIF3n8/3hFVH5KMCBFnJV6iAdj7h37uMazK4hFCVJ4OHWD0aP36ttsgOzu+8VQX0s+I\nEHH244/6udhk5LJ3Yec6qNu6KkMSQlSie+6B776DW2+FpKR4R1M9SDIiRJzdcw/07w+DBpUwQfqR\nVRqPEKJyJSTA1KnxjqJ6kWREiDg7+WT9iJG9E5QHyQ3iEpMQoups2aKb/ZZ4g8zDgNQZEaI6mvcv\neKoDfDMm3pEIISrRW29Bx47w3HPxjiS+JBkRIo6mT4ePP4Zt2woMVAp+mgieA+lt4habEKLyOQ5k\nZcFDD8GmTfGOJn4kGREijh5/HM49FyZPLjBw4w+waz34kiHjrHiFJoSoAsOHQ79+sH8/3HVXvKOJ\nH0lGhIgTpWDBAv26Z88CI36aqJ87nQP+5CqPSwhRdUwTXnpJP0+aBN98E++I4kOSESHi5NdfYdcu\nXWmtS5fwwFAOLA0Xk8hN8YQ4LBxzDNx4o359882H5430JBkRIk4ipSJHHw2BQHjgys8hLwvSWkCr\nE+IWmxCiaj36KDRoAMuX6zv8Hm4kGREiToq9RPPzf/Rz10t0ua0Q4rBQrx489pj+2cdUaD9MSD8j\nQsRJscnIOWNh6YfQbnBcYhJCxM/VV0PfvtCpU7wjqXqSjAgRByVWXk2uD8ddH5eYhBDxZZqHZyIC\ncplGiLiZOxfeeUfXGRFCiIKWL4eRI3U/JIcDKRkRIg4MQ9+9s0OH8IAtS+F/o6DHVdD98rjGJoSI\nr7w8fa+qP/7QJSW33hrviCqflIwIUR0seV93drbqi3hHIoSIs0AAHn5Yv37wQdi+Pb7xVAVJRoSI\ng8ceg6eegs2bAc/TlVYBjr4ornEJIaqH666Dbt1g926dkNR2kowIUcWUgief1F0/Z2aiS0SyNoK/\nDrQbEu/whBDVgGXBs8/q1y+/DEuXxjWcSifJiBBVbONG2LEDbDtceXXJ+3pExlngS4xrbEKI6mPg\nQDj/fF14escd+kSmtpJkRIgq9tNP+jkjAwJ2CJaFu38/+sL4BSWEqJaeeAL8fvjyS5gyJd7RVB5p\nTSNEFYskI926AWu/gZydkNwQ2gyIa1xCiOrnyCN1nZGEBDj55HhHU3kkGRGiiv38s37u2hUI1IG2\np0CD9mDJz1EIUdT//V+8I6h8svcToorFlIy06gutPqjdF4OFEBUmFIKcHEhNjXckFUvqjAhRhXJz\nYf16/bpbtwIjDCMu8Qghao7Zs3Wl97vuinckFU+SESGqUEICZGXp+9I03vEx7N4Y75CEEDXIypXw\n2muweHG8I6lYkowIUcUSE6FHx53wwbXwbBfYuT7eIQkhaoD+/eHii/VV3drW1LdcycjYsWNp06YN\nCQkJ9OzZk9mzZx9w+ry8PO69915atWpFIBDgqKOO4t///ne5AhaiVljxKXghaNwF0tvEOxohRA3x\n+OO6hHXGDPjvf+MdTcUpcwXWSZMmcfvttzN27FiOP/54XnnlFU477TSWL19Oy5Yti53n4osv5o8/\n/uD111+nbdu2bN26FedwuRWhEAXccotHYmKQ0RnfkJjSArpeqSuSCCFEKTRuDA89BOPGwXPPweDB\n4PPFLx6fz4dlWYe8HEOpshX0HHfccfTo0YNx48ZFh2VkZHDuuecyZsyYItNPmTKFSy+9lHXr1pGe\nnl6uIPfs2UNaWhpZWVmk1rYqxOKwkZcX5MMP19MgPUiLtN/1wNRmYEqjNiFE6Xmevq+V50F6OtSp\nE9946tatS5MmTTCKqYhf2uN3mfaCwWCQBQsWcM8998QMHzJkCHPnzi12nk8++YRevXrx+OOP8/bb\nb5OcnMzZZ5/No48+SmJi8V1f5+XlkZeXF/NmhKjJlFKsXp1Jy5YWzerVo1mdkO76vZ5cohFClF29\nevD777qJbwkXJSqdUors7Gy2bt0KQNOmTcu9rDIlI9u3b8d1XRo3bhwzvHHjxmzZsqXYedatW8ec\nOXNISEhg8uTJbN++nZtuuomdO3eWWG9kzJgxPBy5f7IQtYDjOOTmZpOQ0IwmdbaQYBuQ2kBf/BVC\niDJq2hRSUnSpSDx7BogUKmzdupVGjRqV+5JNuSqwFi6KUUoVWzwD4HkehmEwYcIEevfuzemnn87T\nTz/N+PHjycnJKXae0aNHk5WVFX1s3CjNH0XN5rouoRBYhkWCFa4jklA3rjEJIWouw9ClItWhi6Kk\npCQAQqFQuZdRppKRBg0aYFlWkVKQrVu3FiktiWjatClHHHEEaWlp0WEZGRkopdi0aRPt2rUrMk8g\nECAQCJQlNCGqvVAIfD6bbVYXGtfdD1Yca50JIWoNx9H9F9WvH5/1l1QYURZlKhnx+/307NmT6dOn\nxwyfPn06/fr1K3ae448/nt9//519+/ZFh61atQrTNGnevHk5QhaiZgoG9XNikgUJUhFbCHHoHAeW\nLtU9O+/fH+9oyq/Ml2lGjRrFa6+9xr///W9WrFjBHXfcwYYNGxg5ciSgL7EMGzYsOv3QoUOpX78+\nV199NcuXL2fWrFncfffdXHPNNSVWYBWittGll7rhmnzthRAVxbYhcuFh06aa2xFamdsUXnLJJezY\nsYNHHnmEzMxMunTpwueff06rVq0AyMzMZMOGDdHpU1JSmD59Orfccgu9evWifv36XHzxxfztb3+r\nuHchRDXn88ER9ffSutE6fE5T8NWLd0hCiFqiWTPYuRP27tWXa+rWjXdEZVfmfkbiQfoZETVdbm4u\n63/+jjZN0kio3xKSG8Q7pAozcOBAjjnmGJ599tl4h1IhyvN+avo22LFjBxkZGcybN4/WrVvHLY4L\nL7yQfv36MWrUqLjFUFNt2gRbtugGep06gVmFN3vJzc1l/fr10Z7ZCyrt8VvuTSNEVdi1AdxwpZGE\ntANPewCup/hu7Q4+XryZ79buwPWq/bmEKMHAgQO5/fbb4x0GoLtTOOuss+KaiAA88MAD/P3vf5e+\npcqhaVN9ySY3F7Zvj3c0ZSddPwpRBT555kuOPu8oXCu53K1opizN5OFPl5OZld99fNO0BB48qxN/\n6lL+zoZqomAwiN/vj3cYtUJOTg6vv/46n3/+ebxDoWvXrrRu3ZoJEyZw4403xjucGsWy9OWaDRt0\nZ2jp6To5qSmkZESISqYUdLC+BMD1le8y45Slmdz4zsKYRARgS1YuN76zkClLMw85zpLk5eVx6623\n0qhRIxISEjjhhBP48ccfY6ZxHIebb76ZunXrUr9+fe677z4KXgH+4IMPOProo0lMTKR+/foMHjyY\n/eGq/0opHn/8cY488kgSExPp1q0bH3zwQczyBw4cyM0338yoUaNo0KABrVq14ogjjsDzvJjpzj77\nbK666qro3wdb9v79+xk2bBgpKSk0bdqUp5566qDbozTzTJkyhRNOOCG6Pc4880zWrl0bHT98+HBm\nzpzJc889h2EYGIbBr7/+etD5KsMXX3yBbdv07ds3OmzixIkkJCSwefPm6LDrrruOrl27kpWVVabl\nN2/enLFjx8YMmzt3LklJSfz2229Fpj/77LOZOHFiGd+FAGjQQFeQr1cDq6RJMiJEJdv802o61F+F\nwsBOKvtNJFxP8fCnyynugkxk2MOfLq+0SzZ/+ctf+PDDD3nzzTdZuHAhbdu25dRTT2Xnzp3Rad58\n801s2+aHH37g+eef55lnnuG1114DdKX2yy67jGuuuYYVK1YwY8YMzj///Giyct999/HGG28wbtw4\nli1bxh133MEVV1zBzJkzY+KIrOPbb7/lww8/ZPv27XzzzTfR8bt27WLq1Klcfvnl0WEHW/bdd9/N\nN998w+TJk5k2bRozZsxgwYIFB9wepZln//79jBo1ih9//JGvvvoK0zQ577zzosnTc889R9++fRkx\nYgSZmZlkZmbSokWLg85XnH/84x+kpKQc8HGgO6vPmjWLXr16xQy79NJL6dChQ/R+Yw8//DBTp07l\niy++iOkzqjT69OkTk7wqpbj99tu5/fbbow0fCurduzfz5s2LuSWIKB3ThIwMaNWqZpWKAKBqgKys\nLAWorKyseIciRJktG/e4ynmis1o0e6bKyckp8/xz12xXrf762UEfc9dsr/DY9+3bp3w+n5owYUJ0\nWDAYVM2aNVOPP/64UkqpAQMGqIyMDOV5XnSav/71ryojI0MppdSCBQsUoH799ddil5+QkKDmzp0b\nM/zaa69Vl112WfTvAQMGqGOOOSZmmrPPPltdc8010b9feeUV1aRJE+U4TqmWvXfvXuX3+9V7770X\nHbdjxw6VmJiobrvttmK3R3nmUUqprVu3KkAtWbIk5j0daJ6S5itsx44davXq1Qd8ZGdnlzj/Oeec\nE7MdIz799FMVCATU3//+d1WvXj21dOnSmPHTp09XTz/99AHjV0qpJ554QnXu3Dn695tvvqkaN26s\n9uzZU+xyfvrppxK/L6J6ysnJUcuXLy92/1ba43dNy52EqHHm/3EcyzdvoWWf5HLNv3Vv7sEnKsN0\nZbF27VpCoRDHH398dJjP56N3796sWLEiOqxPnz4xvTD27duXp556Ctd16datGyeffDJHH300p556\nKkOGDOHCCy+kXr16LF++nNzcXE455ZSY9QaDQbp37x4zrPDZ++WXX87111/P2LFjCQQCTJgwgUsv\nvTR6b4yDLXvt2rUEg8GYyxPp6el06NDhgNujNPOsXbuW+++/n++//57t27dHSzY2bNhAly5dDrj8\nss6Xnp5e7juig64zUrgFBMCZZ55Jp06dePjhh5k2bRqdO3eOGT948GAGDx580OX36dOHv/71r+zb\ntw/TNPm///s//va3v1EnfKvZwsuJ9D+VnZ1d7vckICdH39n3iCNqRt9GkowIUck+/vlEFizozaRr\n15dr/kZ1SnczvdJOVxYqfCmlLPejKsyyLKZPn87cuXOZNm0aL7zwAvfeey8//PBD9GD7v//9jyOO\nOCJmvsK3hEhOjk3mzjrrLDzP43//+x/HHnsss2fP5umnn46OP9iyd+zYUar4C1Kl7AnhrLPOokWL\nFvzrX/+iWbNmeJ5Hly5dCEa64a3A+f7xj3/wj3/844DL/eKLL+jfv3+x4xo0aMCuXbuKDJ86dSq/\n/PJLsTdHBTjttNN4+umnycjIOOC6e/XqhWVZLFy4kC+//JL69etzzTXXlLicyOW/hg0bHnC54sB+\n/x1279Z11oq560q1I8mIEJXsp5/0c3kbf/Ruk07TtAS2ZOUWW2/EAJqkJdC7TfnPjkvStm1b/H4/\nc+bMYejQoYC+Gdb8+fNjmqV+//33MfN9//33tGvXLlpKYRgGxx9/PMcffzwPPPAArVq1YvLkyYwY\nMYJAIMCGDRsYMGBAmWJLTEzk/PPPZ8KECaxZs4b27dvTs2fP6PhOnTodcNn16tXD5/Px/fff0zJ8\nD/Zdu3axatWqEmNp27btQefZsWMHK1as4JVXXokmAHPmzCmyLL/fj+u60b9LO19hI0eO5OKLLz7g\nNIWTsYK6d+/OO++8EzNs4cKFXHTRRbzyyiu899573H///bz//vsx06xevbrYe4sVlpCQQLdu3fjo\no4949dVX+fTTTzELdIJReDlLly6lefPmNGhQe/riiYcjjoBdu3QnaHv36rv7VmeSjAhRiby54xjY\naSALNrbBV8774lmmwYNndeLGdxZiQExCEimbePCsTlhmxd++Mzk5mRtvvJG7776b9PR0WrZsyeOP\nP052djbXXnttdLqNGzcyatQobrjhBhYuXMgLL7wQbWXyww8/8NVXXzFkyBAaNWrEDz/8wLZt28jI\nyKBOnTrcdddd3HHHHXiexwknnMCePXuYO3cuKSkpMS1jinP55Zdz1llnsWzZMq644oqYcaVZ9rXX\nXsvdd99N/fr1ady4Mffee2/MgbKwlJSUg85Tr1496tevz6uvvkrTpk3ZsGED99xzT5FltW7dmh9+\n+IFff/2VlJQU0tPTSzVfYYd6mebUU09l9OjR7Nq1i3r16vHrr79yxhlncM8993DllVfSqVMnjj32\nWBYsWBBN9rKyskhJScEuZS3JPn368Pzzz3PmmWdy8sknR4cXt5zZs2czZMiQcr8foSUkQMOGsG2b\n7hCtY8fqcYffElVKbZYKJhVYRY30x3KlHkxV6uH6KnvX1hIreJXWF0t+V33+8WVMpdU+//hSfbHk\n9woMuqicnBx1yy23qAYNGqhAIKCOP/54NW/evOj4AQMGqJtuukmNHDlSpaamqnr16ql77rknWqF1\n+fLl6tRTT1UNGzZUgUBAtW/fXr3wwgvR+T3PU88995zq0KGD8vl8qmHDhurUU09VM2fOjFlHcZU9\nHcdRTZs2VYBau3ZtkfEHW/bevXvVFVdcoZKSklTjxo3V448/ftCKpaWZZ/r06SojI0MFAgHVtWtX\nNWPGDAWoyZMnR6dZuXKl6tOnj0pMTFSAWr9+fanmqwx9+vRRL7/8stqxY4fq2LGjuv7662PGn332\n2erUU0+N/j1nzhw1dOjQ6N9vvPGGOtDh5LXXXlM+n0/98ssvMcMLLycnJ0elpqaq77777lDfklBK\n5eUptWCBUj/+qNTOnZW3noqowCrdwQtRWb4ZAzMfg/Z/Ivf8N0vsLrksXE8xb/1Otu7NpVEdfWmm\nMkpExOHl888/56677mLp0qUHLBmKeOWVV9i5cyejR48G4KGHHmLGjBnMmDGj2OkHDRpE165di3SX\nX3g5L730Eh9//DHTpk07pPcj8m3eDJmZuqSkc+fKKR2piO7g5TKNEJVBKVg2Wb/ufF6FLdYyDfoe\nVb/ClicEwOmnn87q1avZvHkzLVq0OOj0y5Yti2mlNHXqVJ577rmYaTzPY9u2bbz++uusXLmSyZMn\nH3Q5Pp+PF1544RDeiSisSRN9qSY3F3bs0B2jVUdSMiJEZfhjGYzrR9Dz03PiGl56PUDDhodeMiJE\nTTFjxgwGDRpEx44deeONNzjuuOPiHdJha/t2cF1dh6QybqAnJSNCVFfhUpFp605h6Zo06tWr+D5A\nhKjOBg4ceMCeY0XVqa6lIQVJd/BCVLQCl2je/ek8/H6I881QhRAC0LunAi3Kqw1JRoSoaHu3wL5t\nuEaAz1adSufOlLtZrxBCVJQ9e2DZMl2ptbqRZESIipbaFO5ew+tqCnuDqXTrFu+AhBBCy83VFVqr\n230IJRkRojLYfqb83AOArl3jHIsQQgCpqfqhVPUrHZFkRIiK5OTpXzr53cBLyYgQorqI3Blg506o\nTvcilGREiIo0+yl4/hi8RRM55RQ47jgpGRFCVB/JyRC5e8CmTfGNpSBp2itERVr+Mez6FdOAl1/O\nH5wrLXuFENVE5CZ6e/boR3XovktKRoSoKFt/gW2/gOmDDqfFOxohhChWIKA7QAOdlFQHkowIUVGW\n/1c/HzWIjdvrSmnIQbRu3brIvUpKIxgM0rZtW7799tuKD6qaGT9+PHXr1o13GGV27LHH8tFHH8U7\nDHEATZtC27bQsmW8I9EkGRGioiz7r37udA4XXwwpKfDpp3GNqFZ69dVXadWqFccffzwAv/76K4Zh\nsHjx4vgGJqLuv/9+7rnnHumBtRrz+aBu3cq5cV55SDIiREXYthK2rQDTh9f+dJYs0b0cHnVUvAOr\nesFgsFKX/8ILL3DdddeVeb7KjkvkO+OMM8jKymLq1KnxDkWUguPAvn3xjUGSESEqwvKP9fORA1mX\nWY/9+/V12fbt4xvWoRo4cCA333wzN998M3Xr1qV+/frcd999FLy/ZuvWrfnb3/7G8OHDSUtLY8SI\nEQB8+OGHdO7cmUAgQOvWrXnqqaeKLH/v3r0MHTqUlJQUmjVrdtA7ti5cuJA1a9ZwxhlnRIe1adMG\ngO7du2MYBgMHDgRg+PDhnHvuuYwZM4ZmzZrRPvxhGIbBf//735jl1q1bl/Hjx0f/3rx5M5dccgn1\n6tWjfv36nHPOOfz666+l3WylWk+kROejjz7ipJNOIikpiW7duvHdd9+VuMwdO3bQu3dvzj77bHJz\nc5kxYwaGYfDVV1/Rq1cvkpKS6NevHytXroyZb9y4cRx11FH4/X46dOjA22+/HR135513ctZZZ0X/\nfvbZZzEMg//973/RYR06dOCVV14B8rfrk08+SdOmTalfvz5//vOfCYVC0ekty+L0009n4sSJZdpm\nouplZ8OSJbBmTXy7iZdkRIiKcORJ0PNq6H55tH+Rzp3BPkh7tf37S34UrnNyoGlzcko3bXm8+eab\n2LbNDz/8wPPPP88zzzzDa6+9FjPNE088QZcuXViwYAH3338/CxYs4OKLL+bSSy9lyZIlPPTQQ9x/\n//0xB/zIfF27dmXhwoWMHj2aO+64g+nTp5cYy6xZs2jfvn3M3T/nzZsHwJdffklmZmZMXYWvvvqK\nFStWMH36dD777LNSvd/s7GxOOukkUlJSmDVrFnPmzCElJYU//elPlVK6cu+993LXXXexePFi2rdv\nz2WXXYbjOEWm27RpE/3796djx4589NFHMXdHvffee3nqqaeYP38+tm1zzTXXRMdNnjyZ2267jTvv\nvJOlS5dyww03cPXVV/PNN98AOuGcPXt29JLKzJkzadCgATNnzgRgy5YtrFq1igEDBkSX+c0337B2\n7Vq++eYb3nzzTcaPH1/ks+3duzezZ8+usO0kKkdCgm7u27x55dzRt9RUDZCVlaUAlZWVFe9QhDio\nBx5QCpS6+ur8YTk5OWr58uUqJycnZlrdQ1rxj9NPj11uUlLJ0w4YEDttgwbFT1dWAwYMUBkZGcrz\nvOiwv/71ryojIyP6d6tWrdS5554bM9/QoUPVKaecEjPs7rvvVp06dYqZ709/+lPMNJdccok67bTT\nSozntttuU4MGDYoZtn79egWoRYsWxQy/6qqrVOPGjVVeXl7McEBNnjw5ZlhaWpp64403lFJKvf76\n66pDhw4x7zkvL08lJiaqqVOnlhhbYQdbTyTu1157LTp+2bJlClArVqxQSin1xhtvqLS0NLVy5UrV\nsmVLdcstt8TE9c033yhAffnll9Fh//vf/xQQ/a7169dPjRgxIiaOiy66SJ0e/oLt3r1bmaap5s+f\nrzzPU/Xr11djxoxRxx57rFJKqXfffVc1btw4Ou9VV12lWrVqpRzHiVneJZdcErOOjz/+WJmmqVzX\nLfU2EzVTSfs3pUp//JaSESEqWG3rebVPnz4YBWq59e3bl9WrV+MWKNPt1atXzDwrVqyIVjCNOP74\n44vM17dv35hp+vbty4oVK0qMJScnJ6ZE4GCOPvpo/H5/qacHWLBgAWvWrKFOnTqkpKSQkpJCeno6\nubm5rF27tkzLKo2uBXrFa9q0KQBbt26NDsvJyeGEE07g3HPP5fnnn4/5LEqzjJI+i8h2TktL45hj\njmHGjBksWbIE0zS54YYb+Omnn9i7dy8zZsyIKRUB6Ny5M5ZlxayzYMwAiYmJeJ5HXnW7CYqolqTT\nMyEO1ZxnoGU/aH4smGaZkpEDVRorsK8HoNC+Pkbh4tUyVm84ZMnJyTF/K6WKHDRVgXomB1LcwTai\nQYMGLFmypNxxRZZfOJaC9R08z6Nnz55MmDChyLwNI50zlMLB1hPhK3BL58h7L9gKJRAIMHjwYP73\nv/9x991307x58zIvo7jPouCwgQMHMmPGDPx+PwMGDKBevXp07tyZb7/9lhkzZnD77beXuL7I8gu3\nnNm5cydJSUkkJiYWiVeIwiQZEeJQ7FgLXz4EhgV3r0ElpvPnP+vSkdJ0A1/MsbLKpz2Y77//vsjf\n7dq1izkzLqxTp07MmTMnZtjcuXNp3759zHzFLbtjx44lLrd79+6MGzcu5mAaKflwS1n7rmHDhmRm\nZkb/Xr16NdkFbtLRo0cPJk2aRKNGjWLqppTVwdZTWqZp8vbbbzN06FAGDRrEjBkzaNasWannz8jI\nYM6cOQwbNiw6bO7cuWRkZET/HjhwIK+//jq2bTN48GAABgwYwHvvvVekvkhpLV26lB49epR5PnF4\nkss0QhyKSEdnbU6EpHQMA+66C95+O//+DzXdxo0bGTVqFCtXrmTixIm88MIL3HbbbQec58477+Sr\nr77i0UcfZdWqVbz55pu8+OKL3HXXXTHTffvttzz++OOsWrWKl156iffff/+Ayz7ppJPYv38/y5Yt\niw5r1KgRiYmJTJkyhT/++IOsrKwDxjZo0CBefPFFFi5cyPz58xk5cmTMmf7ll19OgwYNOOecc5g9\nezbr169n5syZ3HbbbWwqw808DraesrAsiwkTJtCtWzcGDRrEli1bSj3v3Xffzfjx43n55ZdZvXo1\nTz/9NB999FHMZ3HiiSeyd+9ePv3002hrpIEDB/LOO+/QsGFDOnXqVOaYZ8+ezZAhQ8o8nzg8STIi\nxKGIdHTW+dx4RlGphg0bRk5ODr179+bPf/4zt9xyC9dff/0B5+nRowf/+c9/eO+99+jSpQsPPPAA\njzzyCMOHD4+Z7s4772TBggV0796dRx99lKeeeopTTz21xOXWr1+f888/P+YSim3bPP/887zyyis0\na9aMc84554CxPfXUU7Ro0YITTzyRoUOHctddd5GUlBQdn5SUxKxZs2jZsiXnn38+GRkZXHPNNeTk\n5ERLSiJNag/U3Pdg6ykr27aZOHEinTt3ZtCgQUXqaJTk3HPP5bnnnuOJJ56gc+fOvPLKK7zxxhvR\npAN0vZHu3buTnp4eTTz69++P53nlKhXZvHkzc+fO5eqrry7zvOLwZKjSXsiNoz179pCWlkZWVtYh\nFZsKUaF2roPnu+tLNHethuT6zJ+ve15t1y62zkdubi7r16+nTZs2ZaqAGW8DBw7kmGOOKVe37ZVl\nyZIlDB48OFrJNB7Gjx/P3//+d5YvX17u0o7a7O677yYrK4tXX3013qGIKnCg/Vtpj99SMiJEeUU6\nOmt9AiTXB+DmmyEjAz74II5x1XJHH300jz/+eJk7IatIU6ZM4R//+IckIiVo1KgRjz76aLzDEDWI\nVGAVorwKXaJxXd2TIdSeZr3V1VVXXRXX9b/33ntxXX91d/fdd8c7BFHDSDIiRHnkZsG+P8AwoaPu\nSnvdOt21cmKivkxTG8yYMSPeIQghDgOSjAhRHglpcMdy2LocUnTfE5H+Rbp0KdpHiBBCiJJJnREh\nyss0oUmX6J+1redVIYSoKpKMCFFWoRzwinaw9fPP+rk0nZ0JIYTIJ8mIEGU171/wVAf4/uWYwVIy\nIoQQ5SN1RoQoq+Ufw/5tYOZXDFEKnn1WJySSjAghRNlIMiJEWezeCJvnAwZknB0dbBhw7rn6IYQQ\nomzkMo0QZbHiE/3cqh/UaRzfWGq41q1bl6tn12AwSNu2bfn2228rPqgCDMPgv//9b6Wuo6IVjHnr\n1q00bNiQzZs3xzWmhx56iMaNG9fI7VlbjR8/nrp168Y7jBiSjAhRFpGOzjqdGzP4s8/0Y+fOKo/o\nsPPqq6/SqlUrjj/++ApZ3kMPPcQxxxxTZHhmZiannXZahazjQCrrIN2oUSOuvPJKHnzwwQpfdmmt\nWLGChx9+mFdeeSW6PcubhJbWuHHj6Nq1K6mpqaSmptK3b1+++OKLmGmUUjz00EM0a9aMxMREBg4c\nGHPzRYC8vDxuueUWGjRoQHJyMmeffXaRGyXu2rWLK6+8krS0NNLS0rjyyivZvXt3pb232kySESFK\nK2szbJqHvkRzVsyohx+Gs86Cr7+OT2jVSTAYrNTlv/DCC1x33XWVug6AJk2aEAgEKn09lenqq69m\nwoQJ7Nq1Ky7rX7t2LQDnnHNOhW/Pkr5nzZs357HHHmP+/PnMnz+fQYMGcc4558QkG48//jhPP/00\nL774Ij/++CNNmjThlFNOYe/evdFpbr/9diZPnsx7773HnDlz2LdvH2eeeSaum9+SbujQoSxevJgp\nU6YwZcoUFi9ezJVXXllh7/GwomqArKwsBaisrKx4hyIOZ9+NVerBVKVePzVmcCikVEKCUqDU6tXF\nz5qTk6OWL1+ucnJyqiDQijNgwAD15z//Wf35z39WaWlpKj09Xd17773K87zoNK1atVKPPvqouuqq\nq1RqaqoaNmyYUkqpDz74QHXq1En5/X7VqlUr9eSTT8Ysu1WrVuqRRx5Rl112mUpOTlZNmzZVzz//\n/AHjWbBggTJNs8i+YNOmTeriiy9WdevWVenp6erss89W69evj47/5ptv1LHHHquSkpJUWlqa6tev\nn/r111/VG2+8oYCYxxtvvKGUUgpQkydPVkoptX79egWoSZMmqRNOOEElJCSoXr16qZUrV6p58+ap\nnj17quTkZHXqqaeqrVu3Rtc7b948NXjwYFW/fn2VmpqqTjzxRLVgwYKYbVBw3a1atYqO++STT1SP\nHj1UIBBQbdq0UQ899JAKhULR8atWrVL9+/dXgUBAZWRkqGnTpsXEHNG6dWv1+uuvH3C7lofjOOqa\na65RrVu3VgkJCap9+/bq2WefjY5/8MEHi2zbAQMGFBkW8e2336r+/furhIQE1bx5c3XLLbeoffv2\nxWyr4r5npVGvXj312muvKaWU8jxPNWnSRD322GPR8bm5uSotLU29/PLLSimldu/erXw+n3rvvfei\n02zevFmZpqmmTJmilFJq+fLlClDff/99dJrvvvtOAeqXX34pMZa8vDx19913q2bNmqmkpCTVu3dv\n9c0330THv/HGGyotLU1NnjxZtWvXTgUCATV48GC1YcOGmOWMHTtWHXnkkcrn86n27durt956K2b8\nrl271IgRI1SjRo1UIBBQnTt3Vp9++mnMOqZMmaI6duwY/e7+/vvv0flL+s0U50D7t9IevyUZEaK0\n/liu1NT7lFr8XszgZct0IpKSopTrFj9riT/WvH0lP4JlmTa7dNOW0YABA1RKSoq67bbb1C+//KLe\neecdlZSUpF599dXoNK1atVKpqanqiSeeUKtXr1arV69W8+fPV6ZpqkceeUStXLlSvfHGGyoxMTF6\noI/MV6dOHTVmzBi1cuVK9fzzzyvLstS0adNKjOeZZ55RHTt2jBm2f/9+1a5dO3XNNdeon3/+WS1f\nvlwNHTpUdejQQeXl5alQKKTS0tLUXXfdpdasWaOWL1+uxo8fr3777TeVnZ2t7rzzTtW5c2eVmZmp\nMjMzVXa23pbFJSMdO3ZUU6ZMUcuXL1d9+vRRPXr0UAMHDlRz5sxRCxcuVG3btlUjR46MxvbVV1+p\nt99+Wy1fvlwtX75cXXvttapx48Zqz549Simltm7dGk2AMjMzo4nMlClTVGpqqho/frxau3atmjZt\nmmrdurV66KGHlFJKua6runTpogYOHKgWLVqkZs6cqbp3715sMnLxxRer4cOHl+2DL4VgMKgeeOAB\nNW/ePLVu3brod2PSpElKKaX27t0bTfYi23bHjh2qefPm6pFHHokOU0qpn3/+WaWkpKhnnnlGrVq1\nSn377beqe/fuMXEX9z07GMdx1MSJE5Xf71fLli1TSim1du1aBaiFCxfGTHv22WdHE5yvvvpKAWrn\nzp0x03Tt2lU98MADSimlXn/9dZWWllZknWlpaerf//53iTENHTpU9evXT82aNUutWbNGPfHEEyoQ\nCKhVq1YppXSi4PP5VK9evdTcuXPV/PnzVe/evVW/fv2iy/joo4+Uz+dTL730klq5cqV66qmnlGVZ\n6uuvv1ZK6e9Hnz59VOfOndW0adPU2rVr1aeffqo+//zzmHUMHjxY/fjjj2rBggUqIyNDDR06VCml\nDvibKY4kI0JUA+++q5ORvn1LnqbEH+uDqSU/3rkwdtq/NSl52n+fHjvtP9sUP10ZDRgwQGVkZMSU\nhPz1r39VGRkZ0b9btWqlzj333Jj5hg4dqk455ZSYYXfffbfq1KlTzHx/+tOfYqa55JJL1GmnnVZi\nPLfddpsaNGhQzLDXX39ddejQISbGvLw8lZiYqKZOnap27NihADVjxoxil/nggw+qbt26FRleXDIS\nObtWSqmJEycqQH311VfRYWPGjFEdOnQoMX7HcVSdOnWiZ6iF1xPRv39/9Y9//CNm2Ntvv62aNm2q\nlFJq6tSpyrIstXHjxuj4L774othl3XHHHWrgwIElxlSRbrrpJnXBBRdE/548eXJM6YdS+nN/5pln\nYoZdeeWV6vrrr48ZNnv2bGWaZvQ3U9z3rCQ///yzSk5OVpZlqbS0NPW///0vOu7bb79VgNq8eXPM\nPCNGjFBDhgxRSik1YcIE5ff7iyz3lFNOicb597//XbVr167INO3atSvy2UWsWbNGGYZRZN0nn3yy\nGj16tFJKRRO4giUuK1asUID64YcflFJK9evXT40YMSJmGRdddJE6/XS9H5g6daoyTVOtXLmy2Dgi\n61izZk102EsvvaQaN26slFIH/c0UVhHJiNQZEeIQ1fbOzvr06YNhGNG/+/bty+rVq2Ounffq1Stm\nnhUrVhSpYHr88ccXma9v374x0/Tt25cVK1aUGEtOTg4JCQkxwxYsWMCaNWuoU6cOKSkppKSkkJ6e\nTm5uLmvXriU9PZ3hw4dz6qmnctZZZ/Hcc8+RmZlZ+g1QQNcC3es2bqxbUx199NExw7Zu3Rr9e+vW\nrYwcOZL27dtHKznu27ePDRs2HHA9CxYs4JFHHom+n5SUFEaMGEFmZibZ2dmsWLGCli1b0rx58+g8\nhbdlRGJiItnZ2SWuq+A6Ro4cyYYNG2KG/eMf/yhx3pdffplevXrRsGFDUlJS+Ne//nXQ91bS+x0/\nfnzMek899VQ8z2P9+vXR6Qp/z0rSoUMHFi9ezPfff8+NN97IVVddxfLly2OmKfidBl2ptfCwwgpP\nU9z0B1rOwoULUUrRvn37mPc6c+bMaP0aANu2Y95rx44dqVu3bvS3UdLvKzJ+8eLFNG/enPbt25f4\nXpKSkjjqqKOifzdt2jT63a3I30xpST8jQpTGN2Og+bFw5ACwfDGjIslIMQ0yDu7/fi95nFHobnt3\nrznAtIXOK25fUo5gyi85OTnm7+J2yEqpUi3rQAeEBg0asGRJ7HvzPI+ePXsyYcKEItM3bKhvYvjG\nG29w6623MmXKFCZNmsR9993H9OnT6dOnT6liivD58j/7SJyFh3meF/17+PDhbNu2jWeffZZWrVoR\nCATo27fvQSv5ep7Hww8/zPnnn19kXEJCQrHbsqTttnPnzuh2KM7ixYujr1NTU0lPT48Zlp6eXux8\n//nPf7jjjjt46qmn6Nu3L3Xq1OGJJ57ghx9+KHFdJfE8jxtuuIFbb721yLiWLVtGXxf+npXE7/fT\ntm1bQCcwP/74I8899xyvvPIKTZo0AWDLli00bdo0Os/WrVujCWaTJk0IBoPs2rWLevXqxUzTr1+/\n6DR//PFHkXVv27Ytupzi3qdlWSxYsACr0N00U1JSYv4u7vM8UCJU8DeXmJhY7PoLKvi9jSyv4Peq\non4zpSXJiBAHs2MtzHxMJwd3rYLkBjGjD6lkxF+6nWulTnsQ33//fZG/27VrV2RnWlCnTp2YM2dO\nzLC5c+fSvn37mPmKW3bHjh1LXG737t0ZN25czI63R48eTJo0iUaNGpGamnrAebt3787o0aPp27cv\n7777Ln369MHv98eU1lSk2bNnM3bsWE4//XQANm7cyPbt22Om8fl8Rdbfo0cPVq5cGT2gFtapUyc2\nbNjA77//TrNmzQD47rvvip126dKlDBw4sMQYi1tHSestaPbs2fTr14+bbropOqzg2X1JitvePXr0\nYNmyZaVab3kopcjLywOgTZs2NGnShOnTp9O9e3dAt8yZOXMm//znPwHo2bMnPp+P6dOnc/HFFwO6\nqffSpUt5/PHHAV0SlZWVxbx58+jduzcAP/zwA1lZWdGEpbDu3bvjui5bt26lf//+JcbrOA7z58+P\nLnflypXs3r07+tvIyMhgzpw5DBs2LDrP3LlzycjIAHQJ3qZNm1i1atUBS0cOpqTfTKUo1QWhOJM6\nIyKuZj6h61u8eU6RUZ6n1M8/K/X220rt31/yImpya5qUlBR1xx13qF9++UW9++67Kjk5OdrqQKni\n6wBEWr1EKrCOHz++2Aqsqamp6p///KdauXKlevHFF5VlWdHWCsXZvn278vv9asmSJdFhkQqsAwcO\nVLNmzVLr1q1TM2bMULfeeqvauHGjWrdunbrnnnvU3Llz1a+//qqmTp2q0tPT1dixY5VSun5AcnKy\nWrRokdq2bZvKzc1VShVfZ2TRokXR9X7zzTcKULt27YoOi7RSiDjmmGPUKaecopYvX66+//571b9/\nf5WYmBizvdq1a6duvPFGlZmZGa0wOWXKFGXbtnrwwQfV0qVL1fLly9V7772n7r33XqWUrqDYqVMn\ndfLJJ6vFixerWbNmqZ49exapM7J//36VmJioZs2aVeI2La9nn31WpaamqilTpqiVK1eq++67T6Wm\npsbUvymuzsgpp5yizj77bLVp0ya1bds2pZRSP/30k0pMTFQ33XSTWrRokVq1apX6+OOP1c033xyd\nr7jvWXFGjx6tZs2apdavX69+/vln9X//93/KNM2YitGPPfaYSktLUx999JFasmSJuuyyy1TTpk2j\nFYuVUmrkyJGqefPm6ssvv1QLFy5UgwYNUt26dVOO40Sn+dOf/qS6du2qvvvuO/Xdd9+po48+Wp15\n5pkHjO/yyy9XrVu3Vh9++KFat26dmjdvnnrsscei9VoilUt79+6tvv/+e7VgwQLVt29f1adPn5jt\n6vP51Lhx49SqVauiFVgLtsoZOHCg6tKli5o2bZpat26d+vzzz9UXX3wRXUfhyrcFP6uD/WYKkwqs\nQlSFsf10MrLgzXIvoiYnIzfddJMaOXKkSk1NVfXq1VP33HNPkaa9xR0kIk17fT6fatmypXriiSdi\nxrdq1Uo9/PDD6uKLL1ZJSUmqcePGMU1DS3LppZeqe+65J2ZYZmamGjZsmGrQoIEKBALqyCOPVCNG\njFBZWVlqy5Yt6txzz1VNmzaNNjN+4IEHlBtu+pSbm6suuOACVbdu3YM27S1rMrJw4ULVq1cvFQgE\nVLt27dT7779fZHt98sknqm3btsq27ZimvVOmTFH9+vVTiYmJKjU1VfXu3TumFdPKlSvVCSecoPx+\nv2rfvr2aMmVKkWTk3XffPWCF2kORm5urhg8frtLS0lTdunXVjTfeqO65556DJiPfffed6tq1qwoE\nAjHj5s2bp0455RSVkpKikpOTVdeuXdXf//736PjSJiPXXHONatWqlfL7/aphw4bq5JNPLtJCy/M8\n9eCDD6omTZqoQCCgTjzxxJgEVyn9m7355ptVenq6SkxMVGeeeWaR5rU7duxQl19+uapTp46qU6eO\nuvzyy2O+D8WJtEJq3bq18vl8qkmTJuq8885TP//8s1Iq/zv04YcfqiOPPFL5/X41aNCgIs1qD9a0\nd8eOHerqq69W9evXVwkJCapLly7qs88+i1lHQQU/q4P9ZgqriGTEUKqUF3LjaM+ePaSlpZGVlXXA\nYlghKty2VfDSsWDacNdqSCr++vnB5Obmsn79etq0aVOkAmZ1NnDgQI455phK7TGzrJYsWcLgwYOj\nlVZFyXr37s3tt9/O0KFD4x2KKKXx48dz++2316ieXA+0fyvt8Vta0whxIMs+0s9HDSo2EXn1VX23\n3gIV/kUlO/roo3n88cf59ddf4x1KtbZ161YuvPBCLrvssniHIsRBlSsZGTt2bDQD6tmzJ7Nnzy7V\nfN9++y22bRd7Hwghqh2lYGk4GelyQbGTvPAC3HEHLF1ahXEJrrrqqpgmtaKoRo0a8Ze//OWgzVWF\nqA7KnIxMmjSJ22+/nXvvvZdFixbRv39/TjvttIO2Lc/KymLYsGGcfPLJ5Q5WiCqVswuUB1YAOpxe\nZHReHvzyi35dW/PrGTNmVKtLNELUdsOHD69Rl2gqSpmTkaeffpprr72W6667joyMDJ599llatGjB\nuHHjDjjfDTfcwNChQ0vsmEeIaicpHW7+EW6ZDwlFr3UuXw6OA/XqQYG+p4QQQpRRmZKRYDDIggUL\nGDJkSMzwIUOGMHfu3BLne+ONN1i7dm2pb2Wdl5fHnj17Yh5CxIVhQN2WxY4q2L9IaUvCa0B9cSGE\nKJOK2K+VKRnZvn07rusW6V2ucePGbNmypdh5Vq9ezT333MOECROw7dL1sTZmzJho18lpaWm0aNGi\nLGEKcehydkEo54CTRDqpLM0lmkhHXwfreVMIIWqayO0GCvfqWhbl6oG1tH36u67L0KFDefjhh8vU\nC9zo0aMZNWpU9O89e/ZIQiKq1uynYf6/4eQH4bjri52kLD2v2rZNUlIS27Ztw+fzYZrSkE0IUbMp\npcjOzmbr1q3UrVv3gL0yH0yZkpEGDRpgWVaRUpCCffoXtHfvXubPn8+iRYu4+eabAd03v1IK27aZ\nNm0agwYNKjJfIBAgEAiUJTQhKo5SsOy/ENwHKY1KnCTSgqY0JSOGYdC0aVPWr1/Pb7/9VmGhCiFE\nvNWtWzd6z5/yKlMy4vf76dmzJ9OnT+e8886LDp8+fTrnnHNOkelTU1OL3NRq7NixfP3113zwwQe0\nadOmnGELUYk2zYesDeBPgXZDip3EMHTfIkuXQqdOpVus3++nXbt2cqlGCFFr+Hy+QyoRiSjzZZpR\no0Zx5ZVX0qtXL/r27curr77Khg0bGDlyJKAvsWzevJm33noL0zTp0qVLzPyNGjUiISGhyHAhqo2l\nH+jnDqeBP6nEyVJSoKz3jDJNs0b1wCqEEFWhzMnIJZdcwo4dO3jkkUfIzMykS5cufP7557Rq1QrQ\ndzY8WJ8jQlRbrgNLP9Svj74ovrEIIcRhQu5NI0RBa76Edy6ApPpw50qwiq8d/sADsGMH3HADdO1a\nxTEKIUQNUdrjd7la0whRay0JX6LpfF6JiQjAO+/oOiMXFN9LvBBCiDKQZESIggb8Beq1gfanljjJ\nrl35N8br3r2K4hJCiFpMkhEhCko/Egb+9YCTLFqkn9u00V3BCyGEODTS85IQZbRwoX7u0SO+cQgh\nRG0hyYgQANk7YdIVurOzg9TplmRECCEqllymEQJg2WRY8Sns+hU6n3vASSUZEUKIiiUlI0IALHlf\nPx998QEnCwYhJ3z/PKm8KoQQFUNKRoTYvQE2fAcY0OXAbXX9fvjtN9i2DRo2rJrwhBCitpOSESEi\nfYu0PgHSjijVLJKICCFExZFkRIjoJRrp/l0IIeJBkhFxeNuyBLYuB8sPnYreebqwk0+GP/0Jfvml\nCmITQojDhNQZEYe3vH3QrAekNYfEugecNCcHZs4E14U6daomPCGEOBxIMiIOb636wvXfQCj3oJP+\n/LNORBo1gmbNqiA2IYQ4TMhlGiEAfAkHnaRg/yKGUcnxCCHEYUSSEXH4WvMl5Owu9eTS2ZkQQlQO\nSUbE4Sl7J7x7KTzZHrI2lWoWSUaEEKJySDIiDk9LPgAvBA3b68qrBxEMwpIl+rX0vCqEEBVLkhFx\nePrpXf18zOWlmnz7dujfH1q3hjZtKi8sIYQ4HElrGnH42boCfl8Epl3qjs6aNYOvvtI39JXKq0II\nUbGkZEQcfhaHS0XanQrJDco0qyQiQghR8SQZEYcX14Gf/6NfH3NZqWfbs6eS4hFCCCHJiDjMbPkJ\n9m+FxHRdMlIKe/ZAvXrQrh3s21fJ8QkhxGFI6oyIw8sRPWHUCtj2C9j+Us2yYAF4HoRCkJJSyfEJ\nIcRhSJIRcfip00Q/SmnePP187LGVFI8QQhzm5DKNOHwEs8s1248/6ufevSswFiGEEFGSjIjDg1Lw\nyonw5tmwc12ZZo2UjEgyIoQQlUMu04jDw2/fwo7VsDcTkhuVerYtW2DjRjBN6NmzEuMTQojDmJSM\niMPDgjf1c5cLIFD6WqiRSzQZGVJ5VQghKouUjIjaL3snLP9Yv+55VZlmbdoUrrsOmh/89jVCCCHK\nSZIRUfv9/B9w86Dx0dCsbLfc7dVLP4QQQlQeuUwjajelYGH4Ek3Pq6Q/dyGEqIYkGRG12+YFsHU5\n2Alw9IVlmnXbNl1nJBSqpNiEEEIAkoyI2q5RJzh3HAz4KyTWK9Osn3yim/OefnolxSaEEAKQOiOi\ntvMnwTFDyzXr3Ln6WXpeFUKIyiUlI0KUIJKM9OsX3ziEEKK2k2RE1E6eC2+fB9+NLVc38Dt2wC+/\n6Nd9+lRwbEIIIWJIMiJqp9XTYe3XMOvxcrWg+f57/dyhAzRoUMGxCSGEiCHJiKidfvyXfu5+BfgS\nyzy7XKIRQoiqI8mIqH12rIU1XwIG9Lq2XIuQZEQIIaqOtKYRtc+Pr+vndqdAeptyLeLvf4eZM2Hw\n4AqMSwghRLEkGRG1S3A/LHpHvz52RLkX06+flIoIIURVkcs0onb5eRLkZUG91tBWijWEEKImkJIR\nUbs06w4ZZ0PrE8AsX679xhuQlASnnALp6RUcnxBCiCIMpZSKdxAHs2fPHtLS0sjKyiI1NTXe4Yha\nTClo2hT++EPXGTnxxHhHJIQQNVdpj99ymUaIAlat0olIIKDvSyOEEKLySTIiaofMn+Dzu2HnukNa\nzMyZ+rlvX0hIqIC4hBBCHJTUGRG1w9wXYcl/IGcXXPBauRczY4Z+HjCgYsISQghxcFIyImq+rM2w\n7CP9uu/N5V6MUvklI5KMCCFE1ZFkRNR8814Bz4HW/aHZMeVezNq18Pvv4PfLzfGEEKIqSTIiarbc\nLJg/Xr/u++dDWtS8efr5uOMgsey3sxFCCFFOUmdE1Gw/vq47OWvQAdqdekiLGjoU+veHnTsrKDYh\nhBClIsmIqLmC2fDdS/p1/1Hl7uSsoBYt9EMIIUTVkcs0oubyHOgxDBofDV0ujHc0QgghykmSEVFz\nJaTC4AfhhllgHVoh35tvwumnw4cfVlBsQgghSk2SEVHzVcDlmU8+gS++gBUrKiAeIYQQZSLJiKh5\nXAcmj4R1M3TnIIfIceCrr/TrU0455MUJIYQoo3IlI2PHjqVNmzYkJCTQs2dPZs+eXeK0H330Eaec\ncgoNGzYkNTWVvn37MnXq1HIHLATLJsNPE+H94RDKOeTFzZ8PWVlQty706nXIixNCCFFGZU5GJk2a\nxO233869997LokWL6N+/P6eddhobNmwodvpZs2Zxyimn8Pnnn7NgwQJOOukkzjrrLBYtWnTIwYvD\nkOvAjDH6dd8/gz/pkBc5fbp+PvlksKxDXpwQQogyMpQqWzn3cccdR48ePRg3blx0WEZGBueeey5j\nxowp1TI6d+7MJZdcwgMPPFCq6Ut7C2JxGFj0Dnz8Z0iqD7f9BIE6h7zI/v1hzhx4+WW44YYKiFEI\nIQRQ+uN3mUpGgsEgCxYsYMiQITHDhwwZwty5c0u1DM/z2Lt3L+np6SVOk5eXx549e2IeQuAEYeY/\n9evjb6+QRGTvXvj+e/260NdaCCFEFSlTMrJ9+3Zc16Vx48Yxwxs3bsyWLVtKtYynnnqK/fv3c/HF\nF5c4zZgxY0hLS4s+WkgvVAJg0duwewOkNIZjr6uQRW7dCieeCJ07Q5s2FbJIIYQQZVSuCqyGYcT8\nrZQqMqw4EydO5KGHHmLSpEk0atSoxOlGjx5NVlZW9LFx48byhClqk1AuzHpSv+5/V4XUFQE46ijd\nkuannypkcUIIIcqhTD1FNWjQAMuyipSCbN26tUhpSWGTJk3i2muv5f3332fw4MEHnDYQCBAIBMoS\nmqjtLB8MfkiXjvS8quIXLxVXhRAibspUMuL3++nZsyfTI80PwqZPn06/fv1KnG/ixIkMHz6cd999\nlzPOOKN8kYrDm2lBt0tg+GdgV0yiun07ZGZWyKKEEEIcgjJfphk1ahSvvfYa//73v1mxYgV33HEH\nGzZsYOTIkYC+xDJs2LDo9BMnTmTYsGE89dRT9OnThy1btrBlyxaysrIq7l2I2s1zK2Wxr78OzZrB\nbbdVyuKFEEKUUpmTkUsuuYRnn32WRx55hGOOOYZZs2bx+eef06pVKwAyMzNj+hx55ZVXcByHP//5\nzzRt2jT6uE2OAKI0dm+A54+BBePB8yp00Z99pp87dKjQxQohhCijMvczEg/Sz8hh7MMRsOQ/0Lo/\nXPUplKKidGns2AGNGun85rffoGXLClmsEEKIAiqlnxEhqtTvi3QiAjDk0QpLREDfFM/zoGtXSUSE\nECLeJBkR1ZNSMO1+/brrJdCse4UuPnKJ5swzK3SxQgghykGSEVE9Lf8Yfp0NVgAG3V+hi87L0yUj\nIMmIEEJUB5KMiOonuB+m/p9+fcLtULdie+D98kvYs0e3pDnuuApdtBBCiHIoU6dnQlSJNV/Cns1Q\ntyWccEeFL75/f3j7bcjNBVPScSGEiDtJRkT10+kcuPZLcHLAl1jhi09NhSuuqPDFCiGEKCdJRkT1\n1OLYeEcghBCiikgyIqqPdTMgrQXUP6rSVvHYY7qF8JVX6jojQggh4k+SEVE9ZO+ED66F4D4Y9jG0\n7FPhqwiF4IknYOdO6N1bkhEhhKgupPqeqB6mjIbs7ZB+JDTrUSmrmD5dJyING+pKrEIIIaoHSUZE\n/K2eDj+/Bxhw9gtg+ytlNW+9pZ+HDgVbygSFEKLakGRExFfeXvj0dv26z03QvFelrCYrCz7+WL++\n8spKWYUQQohykmRExNfUe2HPJqjbCgbdW2mr+eAD3a9Ip07Qo3KuAgkhhCgnSUZE/KybCQvfBAw4\n5yXwJ1faqt5+Wz9feWWF3m9PCCFEBZAr5yJ+Wh0PA/8PnFxoU3k1Sh0HjjgCkpPh8ssrbTVCCCHK\nyVBKqXgHcTB79uwhLS2NrKwsUlNT4x2OqKFyciCx4jt0FUIIUYLSHr/lMo2oeutnQSi3ylcriYgQ\nQlRPkoyIqrVpAbx9Prw+WHd0VskWLYKff6701QghhDgEkoyIqpO9E96/CrwQ1GsNifUqfZWjR0O3\nbvDii5W+KiGEEOUkyYioGp4Hk2+ArI26l9VzXqr0Zi1r18LUqXo1p59eqasSQghxCCQZEVVj9lOw\nehrYCXDRm5CQVumrfOUV/XzqqXDkkZW+OiGEEOUkyYiofCs+hW/+pl+f/gQ07Vrpq9y7F159Vb++\n8cZKX50QQohDIMmIqFxuSPeyCnDsCOgxrEpW+9prugv4Dh3gzDOrZJVCCCHKSZIRUbksHwz/DHpf\nD396rEpWGQrBs8/q13feCaZ8y4UQolqTHlhF5VAqv4Jq3Zb68kwVWbtW97raqJHcFE8IIWoCOWcU\nFc8JwqQrYMVncVl9x46wfj1Mnw4JCXEJQQghRBlIyYioWJ4HH98Ev3ymb4TX6mdISq/yMPx+6Fr5\n9WSFEEJUACkZERVHKZg6Gpa8D6YNF71RpYmI68IHH+hLNEIIIWoOSUZExVAKpt8PP7ys/z53HLQ7\npUpDeP99uOgiOP54HY4QQoiaQZIRcegiicjcF/Tfpz8JXS+u0hDy8uC++/TrM86o9M5dhRBCVCBJ\nRsShW/FJbCLSe0SVh/DSS7oVTZMmMGpUla9eCCHEIZAKrOLQdTwLel4NjTvHJRHZvh0eeUS//tvf\nICWlykMQQghxCCQZEeUTygUU+BJ1r2JnPhO3ayMPPqh7W+3WDYYPj0sIQgghDoFcphFll7Mb3j4P\nPrwO3HDTlTglIj/8AOPG6ddPPw2WFZcwhBBCHAIpGRFls301TLwUdqyBQCrsXAsNO8QtnLp1deuZ\nNm1g0KC4hSGEEOIQSDIiSm/1dPjgWsjLgtTmMHRSXBMR0DfCmzkTcnLiGoYQQohDIMmIODjPg7nP\nw1cPg/KgRR+45G1IaRS3kLKzISlJvzZNSE6OWyhCCCEOkdQZEQf3+V3w5YM6EelxFVz1adwTkWOP\nhTvugNzcuIUhhBCigkgyIg6u+xW6fsiZz8BZz4Htj2s4d94Jy5fDpEmwb19cQxFCCFEB5DKNKCqY\nDRu/h6PCNUKP6AG3L4HEunENC2D8eHg53OP8W29BgwZxDUcIIUQFkJIREevXOTCuH0y4GP5Ylj+8\nGiQi338PN9ygX99/PwweHN94hBBCVAwpGRFa9k74+m8w/3X9d51muj+RamLDBjj/fAgG4dxz4aGH\n4h2REEKIiiLJyOHOc2HBePj6UcjZpYf1uAqGPAoJaXENLcJx4PTTITMTOnfWl2dMKdMTQohaQ5KR\nw5lS8OZZ8Nu3+u9GneC0f0KbE+MbVyG2DX//O/zlL/DFF1CnTrwjEkIIUZEkGTmcGQa0/xP8sRRO\nug96XQNW9fxKnHOOLh3x+eIdiRBCiIomhd2Hkw0/wISL4Jf/5Q87biTcshCOu75aJSK//w5DhsC6\ndfnDJBERQojaqfocfUTl8FydfMx9ATbN08P2boEOp+uSEdsPdvVqHzt/Ppx3HmzaBFdfDTNmxO0+\nfEIIIaqAJCO11f4d8NO7MP/fsDNcvGD5odulcPzt1fboPmECXHed7lm1Qwd4881qG6oQQogKIslI\nbfXRCFj7lX6dUBeOvQ56Xw91Gsc1rJLs3Qu33w7//rf++4wzdGKSVj0a9AghhKhEkozUdErB74tg\n2Udw7Aio10oP734FZO+AnlfB0RdDICW+cR7A77/DCSfA+vW6FOT//g8efhgsK96RCSGEqAqSjNRE\nngub5sOqL2DZf2HXej08qT6ccId+3fk86HJ+3EIsiyZNoFEjfXPgt9+G/v3jHZEQQoiqJMlITbL3\nD5h2L6z5Mr+DMgA7ETr8CY7omT+sGle02L4dnnsORo2CevV0B2bvvKMTktTUeEcnhBCiqkkyUl3t\n/SPcGZmCLhfoYQmpsOIzcHJ076htB+tWMe3/VK0vw0Rs3AgvvggvvQT79+vLMJFu3du2jWtoQggh\n4kiSkeogbx9s+VnX/fh9MWxeADvX6nENM/KTEV8inPEUpB8JzY+tVv2ClMRxYPp0fafdzz7Tl2IA\nevSA446Lb2xCCCGqh+p/NKtNXAd2/Qp7NsGRA/OHv3YybPul0MQGNO4CrU/QR/DIzVi6X15FwR46\npSAjA9asyR920kn68swZZ1TrK0lCCCGq0GGbjLieYt76HWTuyiYtYNH1iDpYJoABKMDQB0ul/4oM\nK804UFhbFmNvW4aZtREz6zesnauxdq/HcIMoK8Dum1eBYaGA5Aad8eXsxmnUFadxV9zGR+M26YmX\nUFcvc8/+Uq/3UOIu7TjDAAMDpRQYBspTrFptMmumxcIFFi+Ny8Uw9HzHdA+wY4ePSy8LMXx4iLbt\nPECxK0sv0DQtLEPnWx4KA6X/V94B11swRtM0MBSYto1leDiOgeOFYsZ54ekNdAZkGAZmOBuKvFPT\nNAGFUgamqadRCjzPxVMGpqGwbR+WBUoZOI6D6yrdd5xtYekvEK7r4boenueBYWBbJrZtRZevS4cU\npmmGEzL9Po1IPErhuh6O46IUWJaBZVn6vRjh96/ykznX9aLTGYaB5ymUUhiGUezyC4ssr+BnXdK0\nB1IwrvLMH0+Ft2llv4+DbavixhceVprtXdr16O+9/hsi08Z+V00zEkdsDJ6n54l8Pw8WBxD9jkYU\n/q4WnMYwjGK/+wf7O7KMSGyQ/1sxTf0+XNfDMAxs28QwjJjfklngbpye5+E4HkopLEtvi4LbSz8b\nWJYR/v2CYXgYhoVSLq6rt6NlmcV+noX3DQVjN4zINtf7Jc8D13Wj69P7Ef15ua7S+50CMel5VPic\nVu/fDMPAssBxFK7nYZkGtm1j22bM+65Khir4jSilsWPH8sQTT5CZmUnnzp159tln6X+AJhAzZ85k\n1KhRLFu2jGbNmvGXv/yFkSNHlnp9e/bsIS0tjaysLFIroIbj5z9n8vCny/hjb150WIrfpG+LRFqk\n+cAwivST76HwO9mkujtIDe0kxYk8dpHs7CAltIu3Wv0DwzDBMLhw4z/otGd2kXUHjQDbAy15r9Uj\nZNt1wwsP4hklrzdyJC5pXORgWt75SzsucgDP2uFj46o6bF6bwqa1yWxem0xudn5ee/NTi2jYIhsD\ng5x9flKSXCw7/ANTCjf8C7QtC384bit8EA0pF9dT0eQh+iMskJUoPQZlGFgY+G2bBL+NrcBTHq6n\ncDwDRznRnU10fsPANi1sUw+zLBPbMsPv08DnM7HDP27P8FCOwlUGtmFg+yySAia2oROT7CC4SmFi\nEAgYJNgGJiY5IZd9uQ6Oq/BZJskBm9RkH3UT/di2Hd0h2Sb4LYvEgI3P1kmZ43jsDQXZnR1if46D\n53r4TIO0ZB8pCQES/RZmuM1znuMQdBw8z0QZOmkylE7wlGGA8rAMkwSfhc+28FkGVoGDiufpHVHI\n1c+uAssAyzSLTHsgkeW4BfYkkeWUZv54Khh75DXkx17R7+Ng26q48UbkgGfkf24oD4z8uArHWdr1\nhFxFyHXJdVxCjqtPCpQe53no34hp4rPAZ5kEfPq7CuC5Lq7Kj8sywG+Z+Gyr2Dg8T69LPxRB18Nz\nFQZgWwY+y8JvhxN65eF6+vTBMsA2DXymgRlOygtvg4J/A4RcN/xZmmCA4+p9gadMgp5Lbp6DcjwM\n08K2DQwUtmXis2ws28QyINE2sU2LoOuwJxgiN6hwXA9TeZimjtcNJwAovWqlFMrTv8Fc18V1QgSD\nYBgKTxnYlsI2TWxLn4ia+gwLK5yIKQNCjkcopPcfrlLgKUzLwDZNQq6L5ymc8MmRzzRJSrCwLRtX\nKYIhl/15DnnBEI6n94eeq/T+wdX7U9NnYIQ/F6UMLNMm4Depm+SjUWoi6XUSSAr4se2KSUpKe/wu\nc8nIpEmTuP322xk7dizHH388r7zyCqeddhrLly+nZcuWRaZfv349p59+OiNGjOCdd97h22+/5aab\nbqJhw4ZccMEFZV39Ifv850z+/O5CIr/RdsYmWhtbqOvuo+6v++iYkk0DYy/Jaj/J3j5erPsXHNMP\nKK7NepHeud+WuOx9f/xKlq8BhlIs9drg+Pexw2rIdqsxmXYzttjN2Wmko0wLtUthsJvoqT9m+Mek\nM+tIcnGwcUrpUgTDNPVOq4zzFx6nXIPsvQlk7/azf3cS+3f72bsziaMH/Upaeh6GYTD/8yOZ90m7\nmPdu+VyaHLWL5h13sDu0m9COXEzDwlAeWUEDT3m6VMLUiYdhWBieC6aJCh80sQyUq3dcrudiYIQP\n9gXO1MJnI5ZlYQKWZeOzTGwUnmHieSEsO4Bt6J3Z/lAIz3GxrHACYloYgGXqMwqfZeH3WViGgWlb\n+Azw+WwMPPIchWmB37QIJPox8kLszjEIOkF8po/kgEWi3yakYPdeB8dxdQmNYeCzTSzLIITBnmCQ\nvSGHXftDpCf5SEtOwG8bhJSF5zlgGHhK4XiKvXlBsnNDuJ7CbykMy8R1PXbvD5ETdElNTCA5UZcM\n5YQcPA8s0wMFeSGXYMjDb3kk+C0wTVzPI8+JHEgtPOXhI7LD1ombGynBMXSpVGQnHpn2QAdifYDx\nwjvW/LNTV6ETqYPMH08FY0cpvGiJmz4gmwpcjAp7HwfbVpanv+8Fx7uuR66jE6RA5Ow9mjh6WKaF\nYRCzvYFSrccNJwd5jkfI0QmC5+nXeSEPQykS/D4sQ5HnGOSF9G8qEf0bDHr6t5ng0wmC6ylyHQ9P\nQcBnxcSB0gfyXMclL+TiuF603FWXIpp4nl5PpDTEtkwCtoEHZAcdTMMkyQ9+24rZBgZm9G8DXZoY\n8sIlIIaH43pk5+lSTNNwyHM9cnJDoAwSfYqQY5Cd52BiUi9FUccXAAOy8hyCodxo6YXP0knL/lyX\n3KCDaRj4LRO/z0bhkZvr4rgKw1BYpkXICbE3pMB1SbBtDEORE1LkuR4BU5+k+GwLx3UJeUT3w56n\n9wVBxwVlYBrgBHXi6Lh6X5nkN/HbFjmhELvzggDYGHhGOBFzFfuDIfJCCqU8XKWwDQufCTm5+jO2\nFPgCNvUSDSzDZG/QxdudjeNCeiqkJlZcQlIaZU5Gnn76aa699lquu+46AJ599lmmTp3KuHHjGDNm\nTJHpX375ZVq2bMmzzz4LQEZGBvPnz+fJJ5+s8mTE9RSPfLYsusMBGGl/wgXWnPwBebHzJFohsix9\nz/o9vgZk5yWRZdUjy6xHlpXO7shruz45gXQMKwFPKaanncd0zotZlm1Z4eI1TRUa55RjnBEpw8Mg\nGDQwTYVp6x1a9h4fe7YmoUI+8nLBCVqEci3ysn3k7bfpeOLv1G8axHFdVn/fmB8/bEvOHj9KFd3p\nHtF5L3Ua70QpRXqrPBq22kuD1ntp1GYvjVvvpW6zbDBcDNNAeQYYiViWRdBxilxJsv0+fKZJdl5Q\nlxIoCIbfle0zsQyTYDCIYeqSBk954UtCBS4Phc8s/AkBDOWR4zg6UCuA7feR63hYfvDZfnLygoCB\nYZn4/TaOq3BQBPw2pm3hGQrTMgnYPn0mYRh4roFpm5iY2AGbgGUTxEC5Dp5ngW1g2La+PINBbsgj\npBQh18Hvswn4ffjCZ3FBR392LvpMRykPD5sknxk++LsEXX2gygt6KA8SfPqnaYV38sGgQ9DxcJVD\n0DUIuR6maZEYMMkNOTiOh2VZBAwT19E7++SADzdc1O0qhY+CyUaBy3GGgWUa4Q8I3HBRcWRa0yy5\n9znX0wcbq8CB2jD02Wwk0TnQ/PFUMPaQo1/bkUttnk5OfJZZYe/jYNsq6DiYlhUz3lMqv5RBXxcA\nw8BvGdG4IqVq0cQSSrUeIt/H8HfAb5vkBHVxvs+2QCksy8BR+kBsmvq3mBf+rflsOxqXZZjY4Zgc\nz8P2jJg4Qo6Ho3RspmmgXB2PGU7YLUNfSnX1l48En4llmfmXZ00T09AlkZH4I9ug4N+5IYeQ4+Kz\nbSxT/50TdLAtC9NU/9/e2QdXddT//72755x7b0IIzyThIcWKPIX2W0AeWgdaikC/g6XqT0ARY6fD\nFGeqtNVRGEcBZ6wwah3rUBGGPvjQlqmAjgNWcYTan0kfhNjSUtqKERAIKQgkheTec3Y/3z9270lu\n7k3IDUnuJe5rJgN372fP2c/Zh/PZz352L640JRBIhVjEg+AMiUQA5UtEPBcO08ZTICViUQ/NQYAr\nzQFcwVBYENHjkNTeIaWApuYEBGOIegIfxAlSAZ7DoQgIAol4QqEo4qI5AQAKnDtwVADFBIhUuEys\nSNdnwif4voTjCEQEM32aweEMQVxB+gqew+G5Aoq0p0pwjviVhJ60CeOhIo6ICzTFJQTTLhsZSAhP\ntxPmKxA43AhHQSQC4hwRT3trAqWQkAk0+w6iLofjeNfU5rMhK2MkkUjg4MGDWLNmTUr6/PnzUVVV\nlTFPdXU15s+fn5K2YMECbN++Hb7vw83wU6zxeBzxeItV0NDQkE0x2+XV2vOoa0i1Nt6uG4/XYpfw\nH78Y/0kMwIVEf8TVAHwQ9MdFfwD+E3XB+jWDwPDdNx7Cybe/h+TCln4/Mij9nsTMT7+NSP9mMBD+\n8WoZjr9eojsTmWgFYnqJgYCZ/+8tFA5uAmfAsb+V4dgrI0HQ55mR5FCKQUkOJRlur3wDA8quQBHh\n3b+Oxt9//2H9ndKdWiktB2JY8JVqlI29AEXAsZeH45VfT2r3eQwb8z76D7ik3bKJAFcuRQAAjCsU\nFMf134BmFA5oQqywEX5zMxgDRo4/hVETTiPpqWAMUH7LGigXuizE9ACsiMJ1TyE4AqkgBYMMJFRC\nPzyltIzkAkIwSD8AlF67lZJASM509PKKz/QaZ9BE8EEIfN+sG3NQIEHQblHPYZCJQOfnAiQlzAoG\noBSUDg5BxBFgEfOCVgoBgAhncFwHfkIizoAgCNDkS5AiNCWAAleiiQEuCIGSCKSPJl8PMr5UEMZb\nJZWOhVGKoSmQiCYCuA5HoAiugHbHJgLEfQnf1wO9Uix8MTLoFyNnhOaEMWyIoTDKQ7dwIPW6r2CA\nb7wsSumySELoeYlwgplom8Fd/9uaZLqAWaIyM9W2JGfb7TkMktdpL38uaV32THq0Lnt36HG1Z8VA\nSCggJsJF17Q8gYkhSBoZbcvFWbpMe/eJcmXaiIn50A0fQSDDGAIdf6Q9HYJrz1kgCcqX4JzDc/R9\n25ZBkn6pM2PkUtge9R8pAk96OSXgcGNISRV6RRRxMLS0VYcDivR4EoChwDyn1s+NwqU2wDNLvFIq\n+AHB9bSHJO4HkIoQcTkYgEBKNAeEAa4CYxyKCPFAwQ0C+L6CUhI+OEhJvWykTCwYSQQEECnEEz7i\nCQnBFOIB4DLClYREoBRcJcEZoSkgFMBHswQ8rtCsmJ6oSW1kBWbZylcKTBLipJdvJCn4vi6nTwqM\nAKEYiDHEAwkigm/K5AemnhyGy3EykziFhFn2piBAoyRI0mNYs89Q6Omlmis+YaAgBACaEhL9ggDN\ngYOoUr0WQ5KVMXLu3DlIKTF8eOrvmwwfPhx1dXUZ89TV1WWUD4IA586dQ2lpaVqe733ve9iwYUM2\nResUZ9sYIgCw6dXV+NYb6ctLSZZN///o5yQAxvD+yaE49tqIdmWnf/IkhHMZDMCl+gE48UZJu7Ly\nnn/BcfWSyeUL/XHqaPu/nCuDGITrgxOBpIemhmi7slAxCKcJHEDhAEL/YVfgehLCU3BcCTcq4RX4\niBYGKB6mIJwIGIDRNzXgnjWvITYgjlhRAlzoWBEzFuiYDoqAs5ZAMm6WARhgBhA9Cxcm5oKUAgTA\nzdKQniVxCB0BCsd1kLTOuGgV92KCqYj0+iq4Aoz7mgF6VkcELgRc14Uf+BCOCI0RhzNIE1ziCA7H\n1d4XzrleIhJ6kVZwDm5mX9xxzPotA5iCUhTGdwghQArgwgGXgHA4FDGACSgwSDBACDgOIJSCEI5Z\nu9bLUowROOPgTIDATTAbN04JDpglJQkGZtzuOpDPvFAYAzNlV8QQKGYC/nTZkSw3GBhnYFw/KaWg\n18OT69GU/JfC6wLpL9jW3jagJWCxLS2XaefFZ67TXv5c0rrsLYGCqZ6EZNk5v3Y9rvasks+65d/0\nPKnBpenPN9kvO3MfvbwbZtQGus6ol3xNP6QwFwvbqiJAv8pZxjIw1rIBsCWgGi3tlCW9LMnJC4ck\nHb4OM74wc30C6b4rOEhROJlLf14svAdjybw6noVp1wpIDwJ6PGI6loQ4ByD1sjHXD4EUECidlzuO\nDoAnFnqQwBiY8bRwJvQSC7QsEhLEOSgZvAoG4QhASijodAgBAYKCvp8wzwLJOmR66V1w7bVVUgJC\ngEs9PsBMyJTRkTsCJPVYzBk3S7sBGBfam5cI4HAO7nCQTIBzR0/ylFm2Ztx4Q7UXhoibZbPUjZw9\nTZd207Rt6ElrNhv5TOlJ1q5di4cffjj83NDQgFGjRnWlqCkM7x9JS4t9+CxEUbMpqC5XWT+GqNAz\ndS4uQwYSBIbRFacRK/4AegDXjmzTfsEZ4HgNkEEABsLIiadRWPyBcTOSaUCACb1EtOgSAt8HZ8DI\nSadQOEBfl5iCIwjgCkIQmAD6D70E6ftQRLhhygkMvfFsKxlACAKEgusF4K6EDPQsovzmExh980nz\nEkvOrvV3utwMMtDfuVHCwBGNUGFnZGE+glZQEaBYcmBiULLFMwJq8YyQ8YzwDJ4REhxMOWCCmRiL\nVM+IjunQO1WgAGTwjJA0AwIc+JAACDJo8YwwIULPSMAYAj8AN54R5ggwqXXkrgCH9oyoQEEJRw9o\nSkFBB5OCOZAguI6ADAIoJXUdcwEQB4ceWCAlgsA3O2kIIA5AT+eI9CxF6fHP/OaOAoy7FkQQjCBA\nSCipjTZHtPQrIpBSkNAGnMP1jFm7es22APMcSZExArnZMUAtS1ym/bV0O93e2/bflph2M/tsbzbP\nWuTb85y0lssnUsve+v9tX/zdo8fVnlXL4muLEdg6T6ZrZE7v3H0YM7Km7ehYMgrbGnGmvXPGICFQ\n2FaT4xiQ3ImTWgY9IWHhswtt5WQ7pZYdH0nvC8z99U45Bh2Nkoxv07tZKOklSg444RRHl6fFMCKT\nl4ElP5OOgYEZj8jEsLFw54kElPFEcgGHA4wIKgj0TiKmx7rweUkZeo1czhEHQZnlWKaUua8yY5l5\nbtAxZZCBNgTM2KPldBmJFBhpY0wqPbZx7cLRng5FANeTIA6ux7lAgpQCJ4BxAkkFQQRSEkrqewdK\nwTEmnlQmfkY4UEqCc20QAdqD5ToA5wqc954hAmRpjAwZMgRCiDQvSH19fZr3I0lJSUlGecdxMHjw\n4Ix5IpEIIpF0w+FamT5mMEr6R1KWagrG1qNgbH34OeYw3Do60qoju+YPKP+fJoyY/EHGa+vBQYAz\nB4oIZROaUTahOUUmNfZDmD9g6BgfpR++kBIXkprPRSA5BAA3CvQb4re5r555K2opq0jJr++bTMv2\nO8B4NKAHFyE4OJhu4JylBKLpmBE9XrgmZkS0GTuSMSOqVcyISsaMcA7GOAK0xIywDDEjjtCBqE40\nApcU4k5LyWMRF36gDbVAMQilZ3KO4IiZmBGYmBHPEXrLruCImZgRwR3dic39XU8g4jjhjCvuK0Q8\nAe4IxFw9+3F8giOAGAI4joAreOhFEsZTwTlDzNFBrzAeHEV6V43jCHDBEZA20vTMUUfZE/RMSCog\n6glEI64OPiUTDMxZuCNIKgJnzATrcrNEhDCNoO8HmKUYRuEumiSt7ytYx54PwZCWv+118m2JBmhT\ndp6uR+uyS0XXrMfVnhWBwePh6zctD6B3lAAt12j7fBWly7R3H93+FALOwEkHtAJ6C7oyM4yk9zPZ\nflraKg+vRRnKwKDjGcJycBP3YO7FSMdkOczEjASk27EjIJNbcVmrtsqAREDhbqBk22z73Ljx5ohW\nn4XgcB0GBQ4uGCKuo5eJTd9xhEABUwiIw4Eua8ThcBwHrivBud6FxrjQxwYoDt2dBRwmwRhHxHPh\nE0NzPNABtwQUeEwHuXIBFRBijvasRilAQnG4TMEzntdEoJfFPKWNFSF0IP3leADBOSKu9i65EnCY\njhMhAiKOiR3hCpIxuCJZBwyFEaDZ10tlEQHEAwnmOChygctNgOKEqMtATHvBClzj4QUh5gk4joNo\nL2/zzcoY8TwPU6dOxb59+/DJT34yTN+3bx8WL16cMc+sWbPwu9/9LiXtj3/8I6ZNm5YxXqQnEZzh\n24smpeymacuEwRwiiIedUVvmupJUwME72NUCUiDjBsw2f1e/67X7AmYXDANLuvTMYEWk9DkcUGBB\ny5keMhBwkhHirXbTUNyHzwQ8JQHS+b3kbhrfRMkrCSYz76bRi8PaGEmoAK7giKFlNw0lgChTkAnA\n931ws5tGEEOgAu2d4AwUl1CBgOMKMKkQVwSXAdx1ILheO4aQCOIKcQ4wJY37Ws+iKAgQcD3gSigw\npuAJXQ/xhI9ABGBMGzuMcQgkdxLpOU3cVxAMcD1X52McCU9BKolmPwA3szu9JZEh4nII5sATAq4Q\naPIDNMUVBIcJPgzMbhq9XTnua8+TI/RuIZiZkTADjJL6LBeYbZTJM160l4WnyLbfpziU2ZXTeudG\n8qV0tfy5JLXsZkeTCaBMxiYljbnu0ONqz8pznHCXS/L7ZPwRALjJ3TSBbHk5C5HxeXfmPjDtMTB1\nnpB6hs45WtoO5zruShGklIh5DiJmCTUhFTgA19VlkGY5xjOBlanlYHAYhw+9BMpMX5YB6XZoAmC5\n4OG1mFRwTEAoKQXFOITD4Dkm0NI8A89xWn3WyyW+UgikHrNinhPupom4HOA6+FTvpuEQrsCVuA8f\nHAP7eXCEgB9IMHAURLW3NOEH+qwT6LiTRBDAdXWwcXNCB4oKDiQCBcZIB6FCoTERAFJCONoLEQDw\nSSJilmYEAM4ICUkAI7ieNgbjkqBAUFLH04ADwuVISD2uFXjc7IZTgKOPOODQu2mklEj4BMVUGDAP\nRpC+9oIQ194bP65wBUCEe4gnOOICKHQ4POEh6jrwnN49hizrc0Z27NiBFStWYMuWLZg1axa2bt2K\nbdu24a233kJ5eTnWrl2LU6dO4ec//zkAvbW3oqIC999/P1auXInq6mqsWrUKzz77bKd30/TGOSNF\nHsfMq5wzYtZccn7eR67u2/q8juRSDYMOjtLrqroDESUPMNOz89ZN2p4zYs8ZySfsOSP2nBF7zsh1\nes7I0qVLcf78eXznO9/BmTNnUFFRgb1796K8vBwAcObMGZw4cSKUHzNmDPbu3YuHHnoImzdvRllZ\nGR577LGcnDGS5H9vKsWCipIePYH1WvLn+311/2kJgAtn1K2Mhdb5GeNm14LZntjqO3sCK0I9GWOI\neEABuRhSePUTWGOeABDp8gms3Jy74ggCkUip62yWJMLr0PV3Amt62fWLtqf0uNqz6uj78MROB2DM\nafncUd1e7T6CECWBInTlBFZdho5OYG1bDt1mu+EE1rbPoM3n1vfR5dBbVLtyAmsUDvrFPHsCaw/T\npRNYe5vu9oxYLBaLxWLpeTr7/s7fBV2LxWKxWCz/FVhjxGKxWCwWS06xxojFYrFYLJacYo0Ri8Vi\nsVgsOcUaIxaLxWKxWHKKNUYsFovFYrHkFGuMWCwWi8ViySnWGLFYLBaLxZJTrDFisVgsFoslp/Tu\nL+F0keQhsQ0NDTkuicVisVgsls6SfG9f7bD368IYaWxsBACMGjUqxyWxWCwWi8WSLY2NjSguLm73\n++vit2mUUjh9+jSKioq69YerGhoaMGrUKJw8ebLP/uZNX9fR6nf909d17Ov6AX1fR6tf1yEiNDY2\noqysrMMf4bsuPCOcc4wcObLHrt+/f/8+2cBa09d1tPpd//R1Hfu6fkDf19Hq1zU68ogksQGsFovF\nYrFYcoo1RiwWi8ViseSU/2pjJBKJYN26dYhEIrkuSo/R13W0+l3/9HUd+7p+QN/X0erX81wXAawW\ni8VisVj6Lv/VnhGLxWKxWCy5xxojFovFYrFYcoo1RiwWi8ViseQUa4xYLBaLxWLJKX3eGPnud7+L\nW2+9FQUFBRgwYECn8hAR1q9fj7KyMsRiMdx+++146623UmTi8Ti+/OUvY8iQISgsLMTdd9+Nf//7\n3z2gQcdcuHABK1asQHFxMYqLi7FixQpcvHixwzyMsYx/3//+90OZ22+/Pe37ZcuW9bA26XRFvy9+\n8YtpZZ85c2aKTL7UH5C9jr7v4xvf+AYmT56MwsJClJWV4Qtf+AJOnz6dIperOnz88ccxZswYRKNR\nTJ06FS+99FKH8i+++CKmTp2KaDSKD33oQ9iyZUuazM6dOzFx4kREIhFMnDgRu3fv7qnid4psdNy1\naxc+/vGPY+jQoejfvz9mzZqFP/zhDykyTz31VMY+2dzc3NOqZCQb/Q4cOJCx7EePHk2Ry6c6zEa/\nTOMJYwyTJk0KZfKp/v7yl7/gE5/4BMrKysAYw29+85ur5smLPkh9nG9/+9v06KOP0sMPP0zFxcWd\nyrNx40YqKiqinTt30uHDh2np0qVUWlpKDQ0NocyqVatoxIgRtG/fPjp06BDdcccddPPNN1MQBD2k\nSWYWLlxIFRUVVFVVRVVVVVRRUUGLFi3qMM+ZM2dS/p544glijNGxY8dCmTlz5tDKlStT5C5evNjT\n6qTRFf0qKytp4cKFKWU/f/58iky+1B9R9jpevHiR5s2bRzt27KCjR49SdXU1zZgxg6ZOnZoil4s6\nfO6558h1Xdq2bRsdOXKEVq9eTYWFhXT8+PGM8v/85z+poKCAVq9eTUeOHKFt27aR67r061//OpSp\nqqoiIQQ98sgj9Pbbb9MjjzxCjuPQyy+/3KO6tEe2Oq5evZo2bdpEr776Kr377ru0du1acl2XDh06\nFMo8+eST1L9//7S+mQuy1W///v0EgN55552UsrfuS/lUh9nqd/HixRS9Tp48SYMGDaJ169aFMvlU\nf3v37qVvfvObtHPnTgJAu3fv7lA+X/pgnzdGkjz55JOdMkaUUlRSUkIbN24M05qbm6m4uJi2bNlC\nRLpxuq5Lzz33XChz6tQp4pzTCy+80O1lb48jR44QgJQGUV1dTQDo6NGjnb7O4sWLae7cuSlpc+bM\nodWrV3dXUbtEV/WrrKykxYsXt/t9vtQfUffV4auvvkoAUgbUXNTh9OnTadWqVSlp48ePpzVr1mSU\n//rXv07jx49PSbv//vtp5syZ4eclS5bQwoULU2QWLFhAy5Yt66ZSZ0e2OmZi4sSJtGHDhvBzZ8en\n3iBb/ZLGyIULF9q9Zj7V4bXW3+7du4kxRv/617/CtHyqv9Z0xhjJlz7Y55dpsqW2thZ1dXWYP39+\nmBaJRDBnzhxUVVUBAA4ePAjf91NkysrKUFFREcr0BtXV1SguLsaMGTPCtJkzZ6K4uLjT5Th79iz2\n7NmD++67L+27X/3qVxgyZAgmTZqEr33ta+GvJ/cW16LfgQMHMGzYMHzkIx/BypUrUV9fH36XL/UH\ndE8dAsClS5fAGEtbiuzNOkwkEjh48GDKcwWA+fPnt6tLdXV1mvyCBQvwt7/9Db7vdyjT23UFdE3H\ntiil0NjYiEGDBqWkf/DBBygvL8fIkSOxaNEi1NTUdFu5O8u16HfLLbegtLQUd955J/bv35/yXb7U\nYXfU3/bt2zFv3jyUl5enpOdD/XWFfOmD18UP5fUmdXV1AIDhw4enpA8fPhzHjx8PZTzPw8CBA9Nk\nkvl7g7q6OgwbNiwtfdiwYZ0ux9NPP42ioiJ86lOfSklfvnw5xowZg5KSErz55ptYu3YtXn/9dezb\nt69byt4ZuqrfXXfdhc985jMoLy9HbW0tvvWtb2Hu3Lk4ePAgIpFI3tQf0D112NzcjDVr1uBzn/tc\nyo9c9XYdnjt3DlLKjH2nPV3q6uoyygdBgHPnzqG0tLRdmd6uK6BrOrblhz/8IS5fvowlS5aEaePH\nj8dTTz2FyZMno6GhAT/+8Y9x22234fXXX8fYsWO7VYeO6Ip+paWl2Lp1K6ZOnYp4PI5f/OIXuPPO\nO3HgwAHMnj0bQPv13Nt1eK31d+bMGfz+97/HM888k5KeL/XXFfKlD16Xxsj69euxYcOGDmVee+01\nTJs2rcv3YIylfCaitLS2dEamM3RWPyC9nNmW44knnsDy5csRjUZT0leuXBn+v6KiAmPHjsW0adNw\n6NAhTJkypVPXbo+e1m/p0qXh/ysqKjBt2jSUl5djz549aUZXNtfNht6qQ9/3sWzZMiil8Pjjj6d8\n15N12BHZ9p1M8m3Tu9Ife5KulufZZ5/F+vXr8dvf/jbFCJ05c2ZKkPVtt92GKVOm4Cc/+Qkee+yx\n7it4J8lGv3HjxmHcuHHh51mzZuHkyZP4wQ9+EBoj2V6zp+lqWZ566ikMGDAA99xzT0p6vtVftuRD\nH7wujZEHHnjgqrsCbrjhhi5du6SkBIC2FktLS8P0+vr60DIsKSlBIpHAhQsXUmbX9fX1uPXWW7t0\n39Z0Vr833ngDZ8+eTfvu/fffT7NiM/HSSy/hnXfewY4dO64qO2XKFLiui/fee++aX2S9pV+S0tJS\nlJeX47333gPQ8/UH9I6Ovu9jyZIlqK2txZ///Oer/vR3d9ZhJoYMGQIhRNpsqXXfaUtJSUlGecdx\nMHjw4A5lsmkD3UVXdEyyY8cO3HfffXj++ecxb968DmU55/joRz8attne4lr0a83MmTPxy1/+Mvyc\nL3V4LfoREZ544gmsWLECnud1KJur+usKedMHuy36JM/JNoB106ZNYVo8Hs8YwLpjx45Q5vTp0zkL\nYH3llVfCtJdffrnTwY+VlZVpOzDa4/DhwwSAXnzxxS6XN1uuVb8k586do0gkQk8//TQR5U/9EXVd\nx0QiQffccw9NmjSJ6uvrO3Wv3qjD6dOn05e+9KWUtAkTJnQYwDphwoSUtFWrVqUFz911110pMgsX\nLsxpAGs2OhIRPfPMMxSNRq8aTJhEKUXTpk2je++991qK2iW6ol9bPv3pT9Mdd9wRfs6nOuyqfslA\n3cOHD1/1Hrmsv9agkwGs+dAH+7wxcvz4caqpqaENGzZQv379qKamhmpqaqixsTGUGTduHO3atSv8\nvHHjRiouLqZdu3bR4cOH6bOf/WzGrb0jR46kP/3pT3To0CGaO3duzrb23nTTTVRdXU3V1dU0efLk\ntG2hbfUjIrp06RIVFBTQT3/607Rr/uMf/6ANGzbQa6+9RrW1tbRnzx4aP3483XLLLXmvX2NjI331\nq1+lqqoqqq2tpf3799OsWbNoxIgReVl/RNnr6Ps+3X333TRy5Ej6+9//nrKVMB6PE1Hu6jC5bXL7\n9u105MgRevDBB6mwsDDcebBmzRpasWJFKJ/cVvjQQw/RkSNHaPv27WnbCv/617+SEII2btxIb7/9\nNm3cuDEvtvZ2VsdnnnmGHMehzZs3t7vNev369fTCCy/QsWPHqKamhu69915yHCfFSM1X/X70ox/R\n7t276d1336U333yT1qxZQwBo586doUw+1WG2+iX5/Oc/TzNmzMh4zXyqv8bGxvA9B4AeffRRqqmp\nCXfa5Wsf7PPGSGVlJQFI+9u/f38oA4CefPLJ8LNSitatW0clJSUUiURo9uzZadZwU1MTPfDAAzRo\n0CCKxWK0aNEiOnHiRC9p1cL58+dp+fLlVFRUREVFRbR8+fK0LXZt9SMi+tnPfkaxWCzjuRMnTpyg\n2bNn06BBg8jzPLrxxhvpK1/5StpZHb1BtvpduXKF5s+fT0OHDiXXdWn06NFUWVmZVjf5Un9E2etY\nW1ubsU23bte5rMPNmzdTeXk5eZ5HU6ZMSfHEVFZW0pw5c1LkDxw4QLfccgt5nkc33HBDRgP5+eef\np3HjxpHrujR+/PiUF10uyEbHOXPmZKyrysrKUObBBx+k0aNHk+d5NHToUJo/fz5VVVX1okapZKPf\npk2b6MYbb6RoNEoDBw6kj33sY7Rnz560a+ZTHWbbRi9evEixWIy2bt2a8Xr5VH9JD0577S1f+yAj\nMpEqFovFYrFYLDnAnjNisVgsFoslp1hjxGKxWCwWS06xxojFYrFYLJacYo0Ri8VisVgsOcUaIxaL\nxWKxWHKKNUYsFovFYrHkFGuMWCwWi8ViySnWGLFYLBaLxZJTrDFisVgsFoslp1hjxGKxWCwWS06x\nxojFYrFYLJacYo0Ri8VisVgsOeX/AFwvu+5UTVzSAAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"plt.plot(x,y,'o',alpha=0.02)\n",
"plt.plot(x[0],y[0],'o',label= r\"observed data = $(x_i,y_i)$\",color=\"C0\")\n",
"plt.plot(x,prob,'--b',label= r\"prob (true, unknown)\")\n",
"plt.plot(x,net(x).data,'--',label=\"prob (estimated) -- after 3000 epochs\")\n",
"plt.legend()"
],
"id": "ba69a29c-39b6-4714-920f-791956adf2a5"
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"for epoc in range(3000):\n",
" ## \n",
" yhat = net(x)\n",
" ## \n",
" loss = loss_fn(yhat,y)\n",
" ## \n",
" loss.backward()\n",
" ## \n",
" optimizr.step()\n",
" optimizr.zero_grad()"
],
"id": "05f6f9a4-c15b-4c52-854a-515f30375865"
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\nouKUEYfD4XA4HEXFKSMOh8PhcDiKyv8HV7PJ4RzromIAAAAASUVORK5CYII=\n"
}
}
],
"source": [
"plt.plot(x,y,'o',alpha=0.02)\n",
"plt.plot(x[0],y[0],'o',label= r\"observed data = $(x_i,y_i)$\",color=\"C0\")\n",
"plt.plot(x,prob,'--b',label= r\"prob (true, unknown)\")\n",
"plt.plot(x,net(x).data,'--',label=\"prob (estimated) -- after 6000 epochs\")\n",
"plt.legend()"
],
"id": "72bfb73b-928a-4ac9-83ba-4fd790579516"
}
],
"nbformat": 4,
"nbformat_minor": 5,
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3 (ipykernel)",
"language": "python"
},
"language_info": {
"name": "python",
"codemirror_mode": {
"name": "ipython",
"version": "3"
},
"file_extension": ".py",
"mimetype": "text/x-python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.8"
}
}
}