{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a1c5908",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "7301dad1",
   "metadata": {},
   "source": [
    "梯度下降与牛顿法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "53538b5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "真值 x* = 3\n",
      "步数           梯度下降          牛顿法\n",
      "1      0.90000000   3.00000000\n",
      "2      1.53000000   3.00000000\n",
      "3      1.97100000   3.00000000\n",
      "4      2.27970000   3.00000000\n",
      "5      2.49579000   3.00000000\n",
      "6      2.64705300   3.00000000\n",
      "7      2.75293710   3.00000000\n",
      "8      2.82705597   3.00000000\n"
     ]
    }
   ],
   "source": [
    "def f(x):\n",
    "    return (x - 3.0) ** 2 + 1.0\n",
    "\n",
    "def fp(x):\n",
    "    return 2.0 * (x - 3.0)\n",
    "\n",
    "def fpp(x):\n",
    "    return 2.0\n",
    "\n",
    "x0 = 0.0\n",
    "x_gd, x_nt = x0, x0\n",
    "eta = 0.15\n",
    "\n",
    "print('真值 x* = 3')\n",
    "print(f'{\"步数\":<4} {\"梯度下降\":>12} {\"牛顿法\":>12}')\n",
    "for i in range(8):\n",
    "    x_gd = x_gd - eta * fp(x_gd)\n",
    "    x_nt = x_nt - fp(x_nt) / fpp(x_nt)\n",
    "    print(f'{i+1:<4d} {x_gd:>12.8f} {x_nt:>12.8f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ffcb3a1f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "24f56b35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdUAAAHpCAYAAADUAaYhAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjEsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvc2/+5QAAAAlwSFlzAAAPYQAAD2EBqD+naQAAvx9JREFUeJztnQd8W+XVxo/33nsltuPsvSeBDDZhj7BHoay2UChtKS2jA2gpfG2BFsosZYQyQ4BAIAMIGWTv6b33HrJl6fs95+rKsiPbsn1lrfNvX+6VrMiydPU+7znvGV5Go9FIgiAIgiAMGe+hP4UgCIIgCEBEVRAEQRA0QkRVEARBEDRCRFUQBEEQNEJEVRAEQRA0QkRVEARBEDRCRFUQBEEQNEJEVRAEQRA0QkRVEARBEDRCRNWNkWJZ7kddXR21t7eTp6DX6wd0v9CFvEeOQUTVTXnzzTcpMjKSmpqaBvxv9+zZQ6+++irV1NQM+vc3NDTQH//4Rzpx4sSA/t13331HDz74IJWWlna7/9e//jW/Lkfwt7/9jX7+85/b/PjNmzfT119/PajfBcHs6z2Li4uj1157jRxBZ2cnvfzyy1RUVKT5c8+aNYuvuZ688sordMYZZ9DJkyfN91VXV9P48ePpww8/JHdk3bp1dNFFF1FHR8egn2Pbtm00ZswYKiwstOnxbW1tVhfhBoOBWltbT/mOfvXVV4N+be6OiKobgC9OXl5etxESEsLCtmbNmm73Hz16lFpaWvp8vu+//57uuOOOIb0miPnvfvc7m7/UAEJ63XXX0aefftrtNdbX1/NEM3/+fHruuefI3tx666302GOPmW9jQt+7d6/N//7tt9+ml156yXwb/xavG/dBlCzHCy+8QIcPHzY/9plnnqGpU6d2+/eWBAQEUGBgIDkCTLq33XZbvwslXDuxsbGUmpp6ykhKSqK77rrrlH+TnZ1t1bLCtXD8+HEaMWKE+b6YmBiaNGkS/fKXv3RLqz0+Pp5F65577hn0c+Aawmdwww032OSxSkxMJG9vb/Ly8uo2fHx8KDg42Lw4x/uN78e99947qAW7J+Dr6BcgDJ25c+fy6t3Pz6/b/RBWTII9V6SbNm2iRYsWsVjB+oNFazlRYyU6YcIEqqio4NHz3+NLOn369D5fEyZ/0PM19QYm1QsvvJAnTFh50dHRVFlZyV/cjIwMXnljEv3pT39Ka9euZUHCBK01WJljIv/tb39rvs/X15cnl75obm7mof69sDJycnL4/crPz+fFDCanH374gf/Wa6+9lh8HIZk2bZr5eX7xi19QbW0t/fjHP6bi4mK22i3fT7wO9bXgc8Dz43fiNdqDlJQUevTRR/k6Un9HeXm52XKE9YrXMHnyZJ6UAUTz8ssv52sKHgZYlTfeeCP/DI+FaOzevZsefvhheuONN/izxt/k7+/f7Xfjmsa1AC8Bfo5rAe8hfg8WbC+++CK7w/F86nsOIdDyvfjkk0/4b8BnOXv2bF7sjBs3jn8GC/qbb77h15aQkEBnnnkmL8ZGjhw5pN+J6wHeEVzrGHj/+gILszvvvLPXn6ufS08gkOr1ioXLt99+S/fddx/t37+f74uKiuIFdmZmJs8lAO97WVkZ7dq1i0JDQ4fwV7ox6FIjuB5VVVXGN998k8+zsrKMf/vb32z+twaDgY87d+40+vr6GkNCQowRERE8wsPDsaw1BgcH8/04V3+GgfuWLl1qfi69Xm9cu3atMS8vr9vvqK2t5X/73XffnXL/1q1bjc3Nzeb73nvvPf6906ZNM1ZXV5vvv+GGG4xeXl7GTZs2me/75JNPjFFRUcarr77aaA82bNjAvxOv8cSJEzxuuukm44IFC8y3jx07Zjxw4ICxqKjI/O9eeOEFY2BgoDE0NNTo7+9v9PPz4/OAgADjF198YX7cHXfcYbz11lv7fR2vvPKKMScnx3j33Xfz+9jXwPtnL0aMGGF8/fXXzbe9vb35OoiJieGBc1xDjY2Np/xbvH68D/h7cZ38+9//NjY0NPDP8Jnitbe2tvJtPNdrr73W7d//+c9/5sfs3r3buGfPnn7fB4w1a9Zo9rdv376d/7aHH37Y+PXXXxtPP/104+jRo/lvAbiNgWsFn1d6eroxMTHRWFpaOqDfg/euo6PjlPuPHDli079/9dVXjRkZGfzdsmXgPcLn2BN8j0eOHGm+jfcT17kKrjP8O3teb+6AiKqL8s033/DkvXnzZuPUqVONTzzxhHHfvn3Go0ePmif/nuP48ePGXbt28STVG08//TRPlBUVFSzcEApMKL3R3t7OX75//vOfNonqV199xfcfPnzYfN8777xjPPPMM401NTXm+zBRQdzU12IJBLy+vt5oDy666CKbJm+M+++/3+pz4P4bb7zR6s/mzJljfOmll6z+rKWlxbht27ZT3sfKykrzhIjFx4svvsjneL9KSkq6LVC0BpPsf//7X/NtTKo9P1NrQCSw+Fq2bBmLEIQmMjLSvKDAc+A9VBd4PUUV1xV+Nx5TWFhobGtrM2ZnZxuLi4v5uayNgoICY1NTk2Z/+4UXXsivXwXfIbye1atX820IKq4Xy+sSi9Gf/exnA/o9tl5vGI888ohVUZ09eza/z6rg9wWuMSzEewp5X6L62Wef8VzwwAMPDOhv80REVF0YTN5nnHGGcebMmcabb76ZrYKwsDBjdHQ0T1KwKiFMqlWh3mdpaVoCwcWk8Oyzz5rve+ihh4xjxozpZkH2BF++l19+2SZRxWIA92OC7A1MTklJSbxYwMSGv6+8vNxob/D34/369NNPu91/zz33dJtcMXHBulCtLPW+q666ihcuqqhCGHAfRGHJkiUsSD4+PuaB37VixQrzc/z973/nx+Df63Q6q68RiwxLkdMaiBxEWp2ce4oqXnfPzxT/Bq9Xfc0Qn/POO4//LRYEeJ8g/r/97W/5s8fkrYqqSk9Rff755/n9UUUV4P3cuHHjKa/5+uuvN77xxhuavg8QnKCgIONTTz11yvv/pz/9yaqogiuvvJKtxoFw8uRJ9nr0tlj4+c9/zu/Dddddx+9nb+D960+U586d2+u/701U8flecsklxmuuuYbPcW385Cc/6eapEboQUXVhsHqHtQLRsRRClWeeecYYGxtrs9sTVhBEDJOFuhrHRAZBgcBBMKyBiban6643UVUn09zcXKvPhfvHjx/PQg4hhUU6Y8YMY3Jycjc3sNZAEKZMmWKcP3/+KT/rKaq9oVrgqqhiAsJ9mDTPPvts9iZYAtfu5Zdf3u0+uJHhgTjrrLNYjDBUa86aqOLzsbTOIPa4Ljo7O236u/HceA5Yyer7PxDLyXKof9+vfvUrvg3XNxZ66s9hqeJ6hEsZ11tvogohwcIQImIpqh9//DHfzs/PN/87/Az3/eY3vzFqiWqVfvDBB93uh+tfde9aE1W8B1gMWC64hgIWtVho/eMf/+j3sZgL8B3FZ2g5YGVmZmaydap+r3t+V/Hv4OZPSUkx/zv8/di6wN+M60O1bPH54jsPD5NwKhL968IgeAXBBAgWQTBCVVUVpzuoA0FGCESwvA8DwSIqSJtBMMTy5cvpqquuovfee48WL15Ml1xyCb311lv87xFBPHr0aA5GQQANAoUaGxs1/3sQNYuoRQSbrF+/ngNQwsPDOVgFv3/JkiV06aWX9ppag8ArBAQVFBQM+HcjuAUpQAh+GSwIWAkKCjLfVqMnLYOLEPiBoBYEI6n/xpLbb7+d//YnnniCg6XwfJZRmfgbr7/+evNtBPcgYARBPAjaCQsL4wAhPG/PSE5rA8+N5zj33HP59ycnJ3OgCiLFEY1tORDJ/atf/YpThizvR0AVgrHw2sEtt9zCKV34O3AE+MzwNyNI7oMPPugzgA0BM7i2EZhmyTnnnEMRERH08ccfm+87cOAAH1esWEFagu8SwPVnCdJUECnbGwi6wvoKn8VQwHPge/nXv/6Vv5M47w/MBfiepKen88B7hahzfK9vvvlmOnToEAcD9gSBefi7brrpJv4sERiIob7nY8eOpWPHjvF3BEFRf/nLX+jf//43rVy5ckh/o7si0b8uCoQUkYn40iFlA5MUIkqRetKTtLS0brfxGEQqIhJ16dKlPHFDQNUvye9//3v+NxAxgJ/ji/3RRx9xdCMi/zBhagEiNvHcf//73/n1XHHFFRxhiQnBcrJAigFEBn8vXgcmD0wUanQswP24b+HChTzxDwSIwsSJE/l9hFBAcFSQ3oNISUQ9qhHCeP9xH87xWtT7VfAzy1xb9fkwWUJcEHHdG4jMBoi6vP/++1kk8e/x3mARZPne4/dgIDoTwoqobfwNGP1FLKuvGRHI6iQKgcXiSeXgwYMs8P/4xz84MvvPf/4zL7oshWXHjh00ZcoUc4QyJmgMsHPnTj6q0eV4j0Ffn8+VV17JEbZYIFiC54f443P+2c9+xvchihjXCiJztUTNEVUjZ+fNm0fbt2/n80ceeYQjoq1h+TkPFnweuI6xePj888/5O9oX+NzxufWMnsb3/Omnn+bIeWQIWIJrBr8H0dQQXSxW//Of/3A09tatW81/CxZYEFVcS3/60584+hfXAhZOgnVEVF0UTGQQQYTAl5SU8KSKLxVuY+IDZ511Fqc/bNmyxRwSj8lWnfzmzJnDlgRSA3pO8llZWSzalvmqsAbOP/980ul0p0x4gwXWD3Le8OXG64XAYvQGLGpMMv/617+6Tf5DBX8bVvJ9YS2FB1YnxNa0lcKipqYdYVKE+GKokyyO+DeWom0NWAJY2KgWJCzHDRs20H//+99eBRmfSX9/w0CtNRQhQMEJWCm4diAylulXWIzAmsHAwgzgeoMQYzEGyxpgcYDXB7H6zW9+0+/vhkjjb+4Jrj9M6BASWOgQ1dNOO82mBcRAUNNFkCYF8L7jHDmafYFFDz7bvhZNfYFCC1g8QdiweMJ3tD8g+H197vi5NbAIx/dfXYRhrkBuqyX4W5DaBpGHlwGWKrxVuKZxf19Wu6ci7l8XBV8UFA3A5IWJC2471U2ICRBfEHwxsRqFCCHnT83fs8xbg0WBSQ7CgMdDYOE+xXNCoC2LN8C6feCBBzQTVNUaQ14s3Etnn30250Xm5uZaHRAYfIlhneI2JlhL4L6CaA3USgVYzeNvxmSNRYMqkhhIwl+2bJn5NiYUiAMsWMtKPxATrOyRM4i8TPwcAorPQLVi8bngPhVL61YF7znyVS1F5fHHH2cL/JprruHb+B2fffYZ2QtcD7hu4IKHxaN6DlSXMcCkCjGF6CKv0tKzAGsW19LMmTP5PogD7psxYwa7VPEe9vb39wWeE+89rhn1czv99NNJa0aNGsVH5BQDeCOQP9qfBbpv3z6+pi23AWwF31FcZ/AEQcBsEVQAyx3fn57fl9dff51/joWH5f3IuYUHAha3JSjqYS3HFp8XxBbbMBBUAE8BXh8W9EJ3xFJ1YfDFh6UAdyIqzKjWDyYs7G/B0sEXCtYdJiNYOj3BFwXl4TBpQ1CQzI6J4+KLL2aXGpLCVfcxxAVuInzxLfdmBjox9gTuJQBrA8KP/SBrwJpVLRJrlglEES5XPM6yAo8t9JXI3vPvg6hgWBYZwHuPik8AE6pq4aguY9WdiIWLWjzA8n5LIJiw1FQvAfYjsd9suZcM4UK1HHy+Qy020BNcU7hm8Du++OKLU/YVVbHBIgdeD7jmIawqKFagFiyA+xcLP7gYLf9uTO4AVj0+L1tBVSaIFvam8TswqUOse/s74NEAWDha+zt6A4+FyxSCBU8KwGfaVzUp7Eci/sBaxaj+WL16NX+/UAUNbmZ1S8EWenss4gsAvr89LVBrwDKGi7cnWETj+lO/C3fffTdv0Tz77LO8mBe6I5aqi4OgIUxW+NKoq2gEsuB+uGrg9l21ahW7Ja2tslE/FQIKd5UaPKIKFgQWAgqXFKraIIgIEzlcQZhAAKwwPC9chZblENVgIYiK5f09RcaWyi+W9GUpYALERKtac1ox2P0xvDewOAACfLBHDXcbXKqwprFAgXVtCSYrfHbPP/88CzWsF/w92MOznDwRVIX9SWwBaF04HYsyeEKw4LLc21bB3husNlx3EDdbXICwjN555x2uooSgG7j68b7aKqjwHqiLG7w/2NuHCODfw/oFeD7LsoWw+LEVggGxGih/+MMf+HOCyxfvBa77ngF6CEiCCMIqhMUML4TlPr8tPPTQQ3wtLFiwgP9GiDKs1eEEiycENsLz0Bu4FuEdgpsfW0N9VXHyaKxEBAsuAvLFJk6cyPl/4Pzzz+d0DuR59sxlRF4ocknxkaOSEtiyZQvfVlNVkBSO2wiVRzUXdSAvD/evX7/eWFZWZvzFL37BaRgAofaDSb84ePDgKX8PqkL19++uvfbafvP0Fi5cqOn7fNddd9mUUqOCnGHkA06fPp3TndTcvssuu4wrMyHXEOklyP2zrES0Y8cOzhO+/fbb+Tb+zahRozhFY/ny5cZ58+YZJ0yYwGkPauUmVPx58MEHjfYEaU1IgVHzJZES89Zbb/X6+Ntuu41Tk/DakeuJf4O0EKR1IH/1r3/96ynPj7+j5zWrprUgbQafqS3XFdJceqZvWablDJT333+f/w4UPrj44ou5SIlagAG/C8+N9JLU1FROkeorj9QaKASC50AqFUDuJ9Ks8JnHx8fzNYMUlieffJLfN6TsIM0Gn4X6HewJUtHwvX388cf5uevq6vp8DbjOcL3ielRBShb+7f79+/k2UovS0tI4LefQoUMD+hs9DRFVF+bzzz/nXEA1bw8Tb29VftSiC5iYkceofoEt81vx5cOkjwnfsjQhvtzqRD9U1InOWlUn5NVa5sn1HOeee+4peZ3DAUQCxRtsAbl8SP6HiGAyRL4iJrjFixcbx44da85xxH2YoCZPnmwu8YhFD8rcWVaQ+uUvf2n86U9/yoUhMLF9//33nPeqlvtD/iKEVv1MteC+++4znnPOObwgiIuLM+eYYoL/8MMP+63ag9cL8YHYY4GGSl/WXh8WFBAsLCTwO1AW0BLk/OJ+vD84x0LMcrHXc2Cy71naDyIHwbZn1amhgAXXRx99dMr9KLrwhz/8gRchWDjje4HcXRR3wcA12Rvqdx0DOd79gYpMWBhYfifxfuG+H374gcsS4rlQ2AI5rULfeOE/jraWhcGDvS01qKI/EESDvTpn5cknn2SXtbWoT0eCaNMjR46YUw36A3tjiCbGviTA/jNcuWhjZrm3hf1fuOrhTkWAFoCbciB7f3D9wuU5kH1JW1yB2BvEvjRcztivx7G/iOXBABcr3M0IUlP3pFUQhIT7EISjpugMBNWViufvreuPO4LrAUFsmBew7WNLgwG8x2psgzXg4u6ZliNYR0RVEIZhkuuZQyjYH4gpes9i4aKmkQmCvRFRFQRBEASNkOhfQRAEQdAIt8lTxf4JctaQU2WPvR9BEATBczEajZxSpRbacXtRhaD2rHErCIIgCFqC/GcUIXF7UVVL5+EPHkj0pCAIgiD0ByLzYbj1V6bVbURVdflCUEVUBUEQBHvQ3/aiBCoJgiAIgkaIqAqCIAiCRoioCoIgCIJGuM2eqiAIno3a51YQBgO6dGnR7F5EVRAEl88fREtBtGEThKGAFphoZTiUWgciqoIguDSqoMbHx3NjASn+IgxmYdbS0sI9ZUFSUhINFhFVQRBc2uWrCmpMTIyjX47gwgQFBfERworrabCuYAlUEgTBZVH3ULVsfSd4LsGm62goe/MiqoIguDzi8hWc5TryePdvUXMF1bQ1kNFoIF3xHupsqSaf4BgKSJlOXl7eFB0YTqkh8Y5+mYIgCIIL4Ovpgrpg9Y9JZ7Bi6h94gw8B3n605aJ/i7AKgqA5tbW1vHenllatqqriMW7cOGpra6Pt27fT4sWL+7WgDh48SDU1NfzY4eKvf/0rrVy5ss/i8p6IR7t/YaFaFVQL8HM8ThAE98Zo6KSW7G+oYe+7fMRte/PrX/+aXnnlFfPtL7/8km688UY+/+677+iuu+5ice2PDRs20G233dbrz9GyLDc3l0pLSzlauq9RUFBAxcXF/O+++uor8vX15VQTf39/euCBB/h+iP2jjz7KP3M2vvnmG/57wSWXXEL/+te/hvX3O987MozA5avl4wRBcE0aD35MlWvuI329IibANyKF4lY8Q2GTLrbb74VQRURE8Ller6fLLruMjh49Sjqdjt5++236y1/+Yo5KVdm6dStdcMEF3bqlIAoaQpKenm5+rqamJvrkk0/YesXx5ptvpsDAQHMvUDwGaSQ9G5Dg/oULF7LA4/UtWrSINm3aRPPmzWPLFDz88MP8upcvX863Idg/+tGP6B//+Ee/fzNe1y233EKffvopi/LPfvYz+uMf/2j++UMPPUT//Oc/uSPMm2++SVOmTBnQe4rXiMXApEmT+PnxN6vgfcXfj0IP9sKjLVXsoWr5OEEQXFNQS99c2U1Qgb6+hO/Hz+0FJngIF3j99ddp6tSp9NFHH1FKSgp9/fXX9Ktf/YrF84svvuj2b/DzvLw8HhAyCC1Si3D7ySefpM2bN/Nt1R187bXXUnt7O7cvw/0YH3/8MY0YMcJ8Wx0QPQgqUF8b3NSVlZU0c+ZMevnll+nw4cMUGxvLv+ff//43p6D84Q9/sOlv/vnPf06tra106NAhWr16NT399NMsguDFF1/kgUUAhBYCidc9EOBOV4UU7xWsayw2MDIyMuh///sf2ROPtlQRlKTl4wRBcI5EfmNHi22PNXRSxSc/x5m1nyIelCo/uY+Cs5aSl3f/eYtefrYVn9izZw/94he/oP3799O3335Ln332Gb3zzjt066238s/vvfdes2V4zjnnmMXN/Hu8vNjqgoBAfCCk6t7mM888w/clJyezqAzFRav+LbAqzz//fD7fsmULi+C6devYoq2vr6c1a9aYLe6+MBgMnK7y1ltvsYUMkZszZw6/H2eeeSa7avG+nHbaafz41157jd8f1SLuDTwn/k5r7z32fm+66aZTrHF7ua49WlQR5avl4wRBcDwQ1JMPR2v1bKRvKKbsR+NsenTW72vIyz+k38dNnz6drcGEhAS6//776brrrmNhgUUJIcTe5gcffMDiWFRUxAJqfkVGI4sprFhYs3C9/vjHP6bQ0FD++YkTJ+jOO++kgIAA+vvf/85i1R8lJSUswr2B13rGGWfw+e9+9zu2jGE9w6qFoMF6PfvssykzM5Pdrr2Bvw0WuaXb+uTJkzR69Gj+uw4cOMCWrwoEd9euXf2K6k9/+lN+3pCQEBZuLEgAzvEeQahV8F7C/Yz3xh54tKgibUaN8u33cYIgCBoC0YS7FUdYTRBBuFf/+9//drNUe4LAJewJ/u1vfzMLzz333ENz587l21dccQW7VJcuXWrT64CAI9r4T3/6E4uTNR555BHexx07dixdeeWVtGzZMn7s3r172ZULQYXQZmdn9ymqPXnjjTd4gXDeeeexQEMEYb2qwJo9fvx4v8/z3HPP0QsvvMDncBdDrLEX/ec//5ld6rD2hwuPFlXkodpCm0Fv99ciCII2wAULi9EWWnI3U8lrF/b7uOSbP6HgjEU2/W5bgPvxscceo3PPPZeysrLoJz/5CVtTn3/+OYuSpaUKzjrrLHbrgubm5m4lGS+99FIWNAwAlywsYFtBAfn333+fI2Wrq6s5qrcnsCQhfD/88AM9++yzvC+K/VTs0cLChDjCYs3JybH59yISGX8zxBALCggqwLkK9kYRTNUflq5cLEhg3WNfdseOHd3eK7xmuJ7xN4j71w6gsAPyUPtLq3l010v0/plPUIhvVxSZIAjOCfbVbHHBgpDRyznKF0FJ1vdVvfjneJwte6q2AlclrL6RI0eyJbV27VqaPXs2i8yMGTPYWoNbGJYq9jMtg2sguHDVYh8TkbMQNexnqvuJsGSPHDnC7llbo1wh2ngNEHk8HwTfEjXVBsKH4CdEKMPVCmsZP8OeLizWAAtB7As8z/XXX08rVqxgyxrAssRAQJQakYyI5p77yX2B171x40ZOMQIQTlU8IfiXX345u37tmQrk0dG/KOiAwg5fnft3WnfO/9H7iXPp5ZPb6fWyPL79j/k/ZyHdXX2crt3wCDXr+88XEwTBdYBQIm3GdKvnT/m/cSue1lRQwVVXXUVPPfWU+TYEFUBUx4wZY3blqqhpMAB7kAhKgiBhP/Wiiy7iICK4YiEmqhU80LQRiCUsVmvCePvtt/O+KqxivDa4V3sCQey0cn9v+bkoXI/UGUtmzZpltrgB9pkR6dwfWAhggYE0JLwHPbvM4HkQ/IS0n8cff5zsiUdbqqqwqtWS2qdcSXlf/4m8yZuyYsfQ1NgxlBWRSlet/x1trTjIwvrW0sfEYhUEN4LzUK9b1Uue6tN2yVNFmkzPPNNf/vKXbH3CxYo9TAAhQ4qJ5T4jRMPSRfvEE0/Q6aefztYXrNP77ruPc0sHAyxVDBXVJYu0Hbxe7AHDtazmjsL9i9e+atUq3sucMWMGW9Z9AVcx/iZE9eL5sZeKBQDEHJYk9kEvvPBCtoAh8nicLeA9wmN7ur4RQYz0HWtRwPbA40XVEp9wZXVjaKsnQ3szefuH0MzYcfTusj+IsAqCGwPhDJ2wglpzN5O+sYx8wxIpKGOR5hZqTyBIiEaFKCI1BdWAsAcIaxMDQTzYz1QrGe3bt4+OHTvGj1ctNNyeNm0a779CUOAGhtUKaxbP1VuKDwQN/74v8BoA3NQgOjqa90JVLN2/tvJ///d/LMZ4zSqoIgWXOCxi5K7iteN9QYoRgrf6A8IMix2VoLZt28bvCSpSff/99+wVgAVri8WrBSKqFngHhHOgAULy9Q2l5B+bxfeLsAqC+wMBDR6liNVwgX1ICBsqJ2FvFfuUAEE/2BtFKollOglEA5YojkjDgcAhchcRuXgOiCmKOiDFBfWAJ0yYwCkplu5jFYhWfyUQLVN5rIEgov4e0xO4YnsD1ipyYCGGOEdksy3g/YBbGm5fBH4h2AuCjNxfNdVouPAy9rdUcRGw8sFmPVZ7PctuDYTcp8ZTR3UOpd6+/pRov11VR1lYGztaaH78JBFWQXAwEAXsK8L1Z1mOzhPIz8/niki9WaKwMhHoExUVNeyvzR2vJ1s1xqMDlazhG6YkQHc2dLk4VFSLNcwv2GyxSvCSIAiOAC7Zvqo3YY9VBHX4EVHtga9pX1XfeKqoAhFWQRAEoTdEVHvgE5bIR+yp9oYIqyAIguASoorIL9SPhOsC0WFIYnaIpdqHqAIRVkEQBMGpRRV1I9HzD+HZiOZCErTatcFZ3L+WiLAKgiAITiuqsEohqAgPR74VOi30FX5tD3zDknoNVLKGCKsgCILglHmq6IJgCRJ4kfhsDeRGWeZHIdxZW0u1zOZ/I3msguC6FDVXUE1bQ581wtWqa4LgUqJqCUpeoX0REp2tgdJcPYs+26uqki2IsAqCawrqgtU/7rOpBppuoEa4vYQVxgPyH9EtBsUcUCwfnWiCg4P7rMSEYhHowoKau8ivRPUly3q/KEGAeVSt5Ys+q1VVVTR//vxuz4Vau6hGhFq8w83+/fspMjKS823R3xQN0N99911yZZzK/WsJal+iukhve6oPPvggJ+Gqo7CwUNOqSrYEK/VEXMGC4FrAQu2vSxV+3pclO1RQ61Ytrg+BBP11ZoGAolMM8lRRlQnzJYrRo5IQRBTnGBBLFbX4/h133MFl/VTw+IEW37cE9XmXLFkyqH/7xBNPcIs2gOBUy4ILKF7RX8UnZ8QpLVUUjH7++ee5hmNvHzYuBFvbDA0EXKS+4YlcVQkuYLVUoa2IxSoIjgUWWkunbaXzWjvbbX6cLQvkYJ+APgsy9ATCgQL069ev79UihbCo5Qs/++wz7geqzn033HADlzSEOEGc0YMVP//www+ttndDGUOUMEQN4csuu4yfB/8eVmp6erryt7a2ciF/y9q8vYHHoW6v2mVnoGBxoAopSini9aP+sfq3o7A+tMCVcDpRxWrq6quv5jcSdSsdVVUJomprsFJPRFgFwXFAUDNXXabpc164Tilo3x85Kz8Y0PcctWnhaVMtPbVqLFzBljWAETMCAUSjcHSggbsY/xZ9VtVG4bBS0YsU4FwteI/awfDkwa2K9mgPP/wwF9NHI29YhxBaxLPk5eXxv0Gsii2WK1rQobn63XffzZ11bKXT1B4OgtoTdKlBYX1L8B4MxZL2aPcvVkj4cOGiQBd6uCgwhrs88UDSanpDXMGCIPRXjB5xIbAcsdeJgbRCgM4vuA3Bhciplmltba25Y4wKmp2jJRtEsby8nAeK6cfGxnYL5vz8889ZbLGHCquwt0bd+F3WCvD3BB1wsKc7UOPnvffeY+sUJRTxmn71q1/xa/3tb3/LrmCcqwM1dm0tqu8sOJWlum7dOjp8+DCPl156qZv1qromnKWqki2IxSoIww9csLAYbeFgTY5NVugnZz1Fk6IzbfrdtrJp0ybOxb/22mtt/jcQQgT29BRBdS8WIB1x9+7d3azBtLQ0djFDwGEFo3MLrF1YgDBcIL6W7l9kXWzevLnP1zLYusJXXHEFrVy50nwbCwe8FrjBEbR1//33kyvjVJYqLFRYpT3HcArqQKoq2YJYrIIwvGBPEwtXW0aQT98BQSp4nC3PZ+t+KuY1uHxhmfX1b/A4NWAH5+pj1QAeWLZwj1o+BzrTxMXFWX1fbrvtNhZVCCkK7MCFC6vx2WefZUtXtXb7E9Sh4GPh9oVLeuLEifya8bst6xJUV1ezAFv2b3UFnEpUnQUt3L+WiLAKgmBJTk4OuzYRgASrEdYnhurahesTt2HBqcfjx4+zgEL0YEkiXQaBSjU1NXw/wBHPp0YPY+/UEjwWUcGwDgFEHRbn9ddfz0KNdnLDxRdffEE//elPuYF4WFgYW+GqSxqv5dJLL+XX62qddkRUNaiqZAsirILgfKCwA/JQ+wI/x+O0ZNSoUSyAcLsiJxV7ouq+KMB+Km4jCEl1z2LvNDo6mt2zCDyCcKKZN9IL1biTAwcOcO10FVVsVR544AGaN28eizQChpCK8+KLL7L1iKhhBEJhr9fevP322xyQiv3VxYsXd/sZLNQzzzyT3dpr1qxxuT65TrWn6iwMpqqSLcgeqyA4FyjogMIOzlJRqacI9gdEF8UisI+6du1aeu655zjI89VXX2XBHDdunPmxX3/9NX300Uds8QJEAcMFvWDBAr59yy23cCrOPffc0y2mxR6EhIRwepD6u1WwFzx58mR2+6L4T2/BVM6M673iYWCwVZVsQYRVEJwLCKazlCHE/qktIAoY1iuieRHoBPFBNSLkn6IyEdzCJSUlLKIA+6e4DxG2cC3jMY8//jidc845nL+qFtGBhYznPvfcc9n9ag/a29s5Bxb7qHABY18YKTmqyELQ586dS66KiGofVZWMHS0crDTQAhD9IcIqCEJfogrh6ctKQ24pXMirVq2iGTNmsAhCZGGNYn8SFieiaFGY4auvvmK3MtzHyCsFSFOBJYu9WVi68fHxPOBeRp7od999Z7Oo3nTTTTxsxWAw8OuFGzsjI4NTcpYuXcrNVJKSFIPGlfEyDncSqJ2AGwT7BFhtIQBgqOQ+NZ4LQKTevp6CMxaRPdhVdZSFtbGjhebHTxJhFYQBgoAWpNxhcna1vbehAuFVA5Lg0oVA9owkxr5szxQcYXDXk60aI4FKfVRV0jpYqScSvCQIwmCxrA+MfFdrqTkiqMOPiOowpdX0hgirIAwdN3G4CW5wHYmo2rmqki2IsArC4FBrwg5HGojg/rSYrqOh1BqWQKVhqKpkCxK8JAgDB/mVcHGqvUDRg3QgXWIEwdzZqKWFryNcT9aK/duKiKqD3b+WiLAKwsBRO7o4osm24F5ERkaar6fBIqI6jFWVbEGEVRAGBixTpGIgJWSgxRMEQQUu36FYqCoiqsNcVckWRFgFYeBgQtRiUhSEoSCBSjZWVRpuJHhJEATB9RBR7aeq0nAGK/VEhFUQBMG1EFHtBezT+IYnOswFrCLCKgiC4DqIqDq4qpItiLAKgiC4BiKqTpZW0xsirIIgCM6PiKqTVFWyBRFWQRAE50ZE1YmqKtmCCKsgCILzIqLqIu5fS0RYBUEQnBMRVSesqmQLIqyCIAjOh4iqk1ZVsgURVkEQBOdCRNWJqyrZggirIAiC8yCi6uRVlWxBhFUQBME5EFF1gapKtiDCKgiC4HhEVF2kqpItiLAKgiA4FhFVF02r6Q0RVkEQBMchoupiVZVsQYRVEATBMYioumBVJVsQYRUEQRh+RFTdzP1riQirIAjC8CKi6sJVlWxBhFUQBGH4EFF18apKtiDCKgiCMDyIqLpBVSVbEGEVBEGwPyKqblJVyRZEWAVBEOyLiKobVVWyBRFWQRAE+yGi6mZVlWxBhFUQBME+iKi6eVpNb4iwCoIgaI+IqptWVbIFEVZBEARtEVF146pKtiDCKgiCoB0iqh7q/rVEhFUQBEEbRFQ9oKqSLYiwCoIgDB1fDZ7D7XGHqkoDEdar1v/OLKxvLX2MQnwDHf3SXAqDwUgdej11dOhNx07q0HfwUa/Hud507KTOzq6jvhNHA/8M5waDgW/zwLnBQIZOg3I/zg1GMhiNZMS50ci3jbiNc9PRiPvwooxdx17x8iIvi6OXtxenlHnjtml4e5tue3uTD869vXl0O/fB8OH7cPQ13fbFfb7KbV8++vDRz9fXfPTzMx35vOs2frcguAIiqoOoquTtH0LuiicJK8Stra2d2nTt1NrWTrp25RxDp+sgXXuHct7eQe2m8/YOPZ+r9/HtDpybjh2KYAraAmH19/clfz8/Flt/P18K8Pcjf3+/riPuC/Dn2zwCcPSnQNwX4MdHdQQF4j5/FnZB0BIR1QFUVTJ2tHCwkn9sFrkzriCssMIgci2tbdTcoqPm1jZqaWmjljYdtbbqqLWtjVpadTxa29TRTm04Qjjb2tkatDc+3t7k6+dD/myNKZaXYqHBGlMsNVhxOIeFx9acxVGx+BTrT7UCFYsQFqPpiNtsPXZZkWxpsnVpOuIe03lf7ynMWdi0isVLXZavyQo2GA18v0G1lE1WMixt3GaL2mRxqxY2Fhl8v8kC1/c4wlI3W/Adnbw4wX38ekywxa/XUzO1aS7WgYGKyAYFBlgMfwoOCuTz4KAA8zEkOJDvxwgJDmCRFytasEREdQBVlTqqc9gF7O6iOtzCiom1ubmNGptbqKm5lZpbWqmRj218m++DeKpHiGdrG0/iWgCrhy2YwC5LppvF469YOapVpFpGZmvJD7cVdyWfs9tScWFCBIXBwYILFzp7AxRPAM51qldA9RSYPAeWHgX1tuptwCJKZ/JCtOkg2vousW7SU2NTy6BeIxY/qtiGBAfxMTTEdAwOMp0rx7AQ9XYgL4QE90REdQBVlSCq7hyspJWwQuyaW1upobGFGppaqKGxmSctHs2tFueKiMKaHCyw9ELYcoAloRyDcIRlAavCZIEEmqyPoAD8HMKp3IZ7UITPOWGL3seHPz97CLbq+scRHo42neLNUDwdymg2nateECzm+LxVp1jhnZ3KNT4AUYZhGxIURKGhQRQeGsxCqxyD+RgWGkzhYTgPofCwEL5OxRp2HURUbcTd02psFdYr1z1Efx73E2pv7qD6hmaqa2xm0ay3ODY2tvCEMxAwaYRitc8r+uBTVvy4Hz+HcIaGqO63QLYMBWGgQKxxfWEMBrimYQWrXpMmHFvgVcG54m3BOY54jLKAVB4LrzYeg1FWUdPv74LHg0U2LIQiwkLMx8jwEIoIDzWdh7IYywLR8YioenhVJXWCwBe/tr6RR119E9XWN1FdQxPV4XZDM83XTaMNydtpZ81RFta5uVPJ19B3kAdET11544sfihV4SDCv0CGcYaYjbmPljv1BQXAFsAhUtwpiosJt/nfYZ1a2N+CtUY5NTa1s6TY1t3R5d5oU7w4sZ7ioq2sbePT3miC+EFgMCG4URiRuh/ExOiKctzkE+yGi6gFVlRDVWlPbSNV1DVRT10g1tcoRAoojhBN7U30RSAE0v20qbc3cR9Wh9bRv3FG6wft8iguLpIjw7ito1XUF16wgCF3AksT3BMMWYA1DXOEBgmcIYstHk1cIC1/1fmy74Bwjn8p7fU64kyMjwigaIxJii2M4Lw5whPjCOhYGh7xzbuD+hUupqqaeqmoglg18jlUtziGmcDPZAlxh+JLxSjcijFe5kRHKqhdHiOfxlgK6asPvqJgqaFP8DqeLChYEd4ID46IjKDY6os/HIQobFi5vybCHCZ4mLJzV8yZeQKtR8K1t1VRaXt3r82FxHB2lCG0MBDfadB6F1xLOsQiCdURUXaCqEtINIJAV1XVUVV1PlTXqEUJaz1+U/kCwBwQTXxReoZqOWKVG4RgRyhGr/TEzxPnTbQTB00A0ser2HUkJvT4OgVm8zQOPlWmoHivFg9XAXiu2jBubKbfA+nyHSObYmEgW+ziMmEiKi4HgRvJc4snRzV5Gy2QwF6ahoYEiIiKovr6ewsNt3+OwlfaKo5T3zFTyDoygrEcr7OKirayqp4rqWqqoqqPK6joWURxxwff3MWHfEitJXOS8soRoRnW5dBAVqyW7qo6ysDZ2tND8+EkirILgBmCegWcLAqt4uxrNni8cIbr9Rev7+viwZasIbSTFq8fYSIqLjnTZbSFbNUZE1UY62+op+9F4Ps/6fc2gqirB4oSVWV5Zq4wqHGtYROGe6QvkPsapK0PTsWs4xh0jwioIngeCGqtr66myWvGUVcFzVtPlOevsNPQZTIWFfnxsFCXERVGCeoyLYmPAmS1cEVWNwdt08uForqqU/otDvRaA4JVecyuVVlRTWWUtlZmOEE9ccH0VLECaSAJWc7FRFB8D8Ywyr/IQ/OOMuWoirIIgWO7t1tY3mb1s6oARgSMCr3oDFizmu8S4aEqIj+ZjUnw0JcRFa+5pGwwiqnYg96nxXAAi9fb1FJS+kPciSsqrOdcMR2z8Q0yxkusN1CBNiI1m8cTqTFmxKbdRecUVEWEVBKE/jEYj79NWwENXVcdHzJ04wlvXV9lQ7BVDYBMTYig5PoaScEyI4W2v4UJEVSPw9mDlVVJeRYaPr6LA2n20LeoO2tE4ijf9rQGDEvuY6iqra+UVxReHM1qcQ0WEVRCEoVi42Lctq6xhqxZii3MMRDT3lbEAcU1OiKXkxK4j8t+1RkR1ECCKtrisiopKK6m4tIqKyiqppKzKvDF/gdcqGu99gDYYzqNdxoVc6DwuNpI/1CTT6gnHxPgoj6z0I8IqCILWYP6FuJZaeAPhGcS+bm/qhZSg5MRYSk2KpZTEOEpNiuN52pYMh94QUe0D7Gtic72wpJIFVB3Y87QGKv1gQ32x8VMaUfMZ6cbdRNHn/Invc9VINnshwioIwnCAjAl1641HWRUf+5vHU5PjWWTTkuIoNTnOZu+hiKpFxC1ctwXFFVRQUkGFxRVUWFrB/TKtgSIHqYmxlII3PDGOUpJiKTE+miuM1HzzNFWt/Q2FTbuakla+Pox/nWshwioIgqNAg4Ti8ioWWdXziNFbrAtcyGnJ8TQiOZ7SUuJpREo8i2/PSGSPFdW9B49RbX0LFRSXU35xOb+p1kK8YWGmsHsgjt9Q1U3QV4Hthj1vU9m7N1PQqDMo7bYv7fwXuTYirIIgOFWQVEMzG1SKyFZRUUkFu5WtZWSgkhULLYtsAo1MSaCQID+Kjo7qV1TdrqLSMy/+j/wDuk/eCMc2v0HJCbwaQfDQQDs6OLKqkqvhCo3OBUHwDLy8vJSSqxGhNHlcpvl+9OeF4aV4McvZownRRerPybxiHiqTx4yw6Xe5najC0hwzaiSNSE1kc35kagInG2sRcdtV/7dMg1fq/oiwCoLgzCBwKT0tkYdlJDIikPOLyqmgpFw5FldQanKsTc/pdu7furo6PtoDLaoqeSLiChYEwZWBi7i2tpZiY2P6df86b02oQWLPHFDvgHDy8gt22RZwjrZYw/yCzRZrs773AhmCIAjOBCKHbU3HcTtRtbdg+4abmpWLC3hAiLAKguAJiKgOEN+wZD5KsNLAEWEVBMHdEVF1o2blroAIqyAI7oyI6gDxCTO5f8VSHTQirIIguCtul1IzbJaqiOqQ8OR0G0QSduj1nCPX3qEnPc75dicfUQUMo0PfSZ2dndy9Q99poE7c34n7DNRpMJBBPRq6jnhug9FIRoORE97VgftAX8H+apCft5cXn6sDQRo4ota1l7dyRLUZHJHrrQwfPqJBNYaPr+ncF8OX/Hx9eCjnvtwf2M/Ph2tk4zHu2GRC8ExEVAeIuH89S1ghQuhGhGYLrW3tXAKtVaczHdtJp2vnnyNZHPehHilKYOK2rqOD2tsx9Hy7nW8rAip0AT1lofX3Y7HFMcA0LM8DA/wpAMN0jhEUqBwDAwMoiG8HUFCQP4u1CLXgCERUB4hUVXJNYYWooXl8cwtGGzWZjhgtOLaazlsxIKA6PrbpdL12wtACWHcQFITrd1lyJgvPZOnBCvQ1WYPqka1Dthi9+LZqSbJViaMXxApH3O6yQIn/f6rYGMmI/3RZtKrFa+yyfs2WsNk6NrIljftUC9p81Ov5CGtbtb4tj7DS1fJw+JWw2DE0e1+9vSkw0J+CWWQDuapaSDCOgXwMUY/qCAqikJBALh6Dz0MQBotcPQNEqio5h7DCOmxobKHGJmU0NHedNza3UlNTCwsnhBRjqBO2OknDElIsJBz92EIKhCXFlpNiQVlaVwH+XbcVK0wRUFhSmLwHWirTnYAAswu8XU/tepMV32Gy6mH5t7fzka1+3IYHwOQZYO8AHzt4AWTpTYB3Ae5wddFEZL1rSW8EBPhRaHAQCyyaYIfhGBJMoaFBFI7bpoHz8NCQIbUTE9wPt6uopHWT8p5IVSX7savyKF25/rfUpG+lKaFZ9MvEG0jX2E71jc08GkwD54MRSQgYJkvFOlGPgV0WDCwanAcG8BGuxeDAQHYnQgDFnej8YDqDAKueBhbaVh17ItgL0aKcK4Jr8lbgNrwYrW1Wi6v3BxZY4WHB3MMzPCyEjzzCQ7mtWGRECB/xOLmG3F9jZIk1yKpKxo4WDlbyj81y9EtyCeAurGtoptq6RqqttxxNfF9dQxN3kZgeMJ62Zu6j/U0n6Z69T9Pc3Knka7DesxaWn2oxqNaDYlkEm6yMIMXiMB1hRcqk5t7g81X3W6Miwgb0byGoEGGIbWNTq8nTAe9Hq8kDYvKKNLVSQ1Mzn8PFrVjIOq4X2xe4Xrmoe3gov7aoyDCKilDOo/k8jEJDgtmFL7guTimqVVVVNHv2bNq4cSOlp6eTM1ZV6qjOYRewiKoCgnCqaxuouqaBqmrrqQbntQ1UU9dINXUNLJq2WAFRLRG0rHQubUzeQdWh9XRkykm6N/pqSgiPoojwEHa3wRqAZYCJUxC0AmKmei7iY6NssophDUNgFS9Ki9mrUm9aJNaajrCS4V2pqKrj0RvYR4fYRptGTFQENwSJiY6g2Khw/hkeIzgvvs4oqBdccAHl5eWRM1dVgqh6UrASLE1YlZXVdVRZU09VGNV1fIR4YiKxZV8SwhgdGa6s0E2rc5xHhofxKh5uMwTnqEX4cztKaJXPl/TWXOeKChYELLBVEU6Kj+l30VlX30x1DYp3ps7CSwOPTU19Iwsz9pn5O1Zd1+vvxPclNhpiG0FxMREUFx1JsaYjFpvijXEsTieqK1eupGuuuYa2b99Ozoq7ptXAlVVdW0/lVbWmFXUtVVQrK2vcb63ZuyWwHJUvezhFY3UdiWMYRUeE8334wiO/0V3SbQTBVhCYFh8byaM3EBkNjw57d+DpqWvgIzw9VTWK5weR04r3p5GIiqz8Hl+Ki4nkEY9jbCQlxEZRQlwUL1zFteyBgUq5ubmUkZHBqy2c9+b+1el0PCw3kdPS0uweqAQq1vyC6r5/lqIW30dx5z1BrgQ+buwNlVXUUFllLZVX1LCIYj8Iq2NETfYV6IPVMYQzPkY5Wg4E+2i9Spa2cYLQ9d2Fi5m9RLUmb1FNPX9vcYTQ9jWdQ3DjTQKrCG00JcZHU2JcFH93BTcNVIKg2sITTzxBjz32GDkCV6iqhP1LWJcl5dVUilFRbRLSGt4H6g1EuSor6ijzUVn1RrCr1lZLUyvEYhUEBSxYsX2CMSpdaezR09KFNQuRrajGIrnevGCurqnnPd2i0koePcG2iyKwitAmJ8RQckIs/y5xJ7u4parizJZqw563qezdmylo1BmUdtuX5Ejw8WGFWlJWRcVlVVRSjiMEtLrXtBN8R2BxYoWK1SpWrvgyQUAV4XS+L5FYrIIweLBXiyBCbOlgYQ2hVY9wOfcGimZgvzg5MZZSEmNNxxgOGPQ0GlzVUrWVgIAAHp5UVQlh++pKs6i0iopLK1lEkfBu9XX6+PCqMwkjIcZ0HsMWKPZ4XAmxWAVh8GAuYLdvXBRNHp/Z7WdqOhC8WaUVNezZglcL1i68Wtn5JTwsQUGMlKQ4FtrUpDgeyYkxLjev2AOXtVQdVfwBtFccpbxnppJ3YARlPVqh+fPjI0FkYGFJBRUWVyjHkgqOuu0tqtbsssFqMgEryhiOBnS3ij1isQrC8ICgqPKKWiouhwesmr1hWMTDvWxNNeDhSoiLprTkeBqRHEdpyQk0IiWec8bdAVs1RkTVwVWV8PYjyCCvqIwKiiuooKicCkoquLSeNZB2gos2FW4Y00oRrlukoXgKIqyC4DjQNAIiWwxvWVmV4jkrqeRiGdZAvi0LbUoCjUxVBgpguBoiqnYEb9nJh6O5qlL6Lw4NqAAEctLyCsvMI7+43FSf9NRVH1y1uBiVgZWf+6z6hooIqyA4D6p3ragUXrVKs3ett0IXMA7SUxNZYNPTEikjLZFLhzozLi+qA2U4RRXkPjWeC0Ck3r6egjMWWX0MWoHlFpVRbkEpD4iotaAA7HekJMXSSFxkKcqKDhaoFOruGxFWQXBuWtt0LLIFxeU88orKeb/Wmuwg1iM9LYkFNmNEEruOnaljkIiqnSl8YRm15m2mpKvfpLCpV/BFglVZdn4xZeeXUk5+CbtGer69sECx54nVGVZq6WkQ0DiPct9qiQirILie+7iguKLLY1dUZtWihbEBYc0cmUxZ6ck0amQKW7iOQkTVzhS/dS01H3ifqsb+lPZ4LaLsvGJuOWZtPwGrrswRSebVF9qBCdohwioIrk1zSyvlFZazRy+nUPHsWYsrQWW2UekplAWhzUhhg2S4UgBFVO2wusrJL6XjOUV0IreIUvP+TTNoM/1gOI2+MZ5jXllhj2DUyGReXeHoyJWVJyHCKgjug9Fo5ChjpPLA63cyz7rnD3m0ENkxGak0OjOV5197NRwQUR0iaHp8MreYjucU0rHsQsovKu9Wwm+213d0hvcXVBq+iNoWPMkVTvCBOtMegKchwioI7ktbWzvlFJTyFhvm5uyCEtLpOk4pxcgim5lKY0elUUZakmZbayKqg8jJworo6MkCOnqykN0PPevgwpU7OiOVxoxKo/TWbdT2xU+doqqS0IUIqyB4Bp2dBo4whudQ9SD2zKSAyGLOHpc1gsaPHsEZFIMttSqiakNtXIR/HzmRT0dOFPAH0rOsH/z3WO1gwLUQGxVhroPZcnIjFb18DvnHjaX0+/eTM2M0dFJr7mbu/+oblkhBGYvIy9t9A6NEWAXB8zAYjFRaUUXHs4vomMnD2HNfFo0DxmWl0fjRI2nC6JE29c1VEVG19pimZjp8LJ8OHc/j0djU0u3n4aHBNG70SF7VjBuVxoXkHVVVSSsaD35MlWvuI319sfk+34gUilvxDIVNupjcFRFWQfBsDAYjV4E6mg3vYwFv5fUs6RoXHUETx6bTxLEZNG7UCAoM7D2IVETV5B6AG/fAsVw6dCyX90UtCfD3Y1cuVixwDSDVxdaODFpWVbKnoJa+uRK2ao+fKH9j0nWrRFgFQfAIOjsNnL4DgT18PI+y80q6bfGh3CsiiiGyk8dmcu0ASz3wWFEtKS2ngtJq2n8kh4W0p48dPnW8aZPGpnPe02A3sYdSVWm4XL65fx7dzULtjhdbrBm/Oi6uYEEQPDLw6VhOIesEPJc9c2URQzN5XCZNmZDJ3su21lbPFNWb7vkj+foFdPOhKyKaQRPHpHN/wOGsquQoWrK/oaKXzur3cam3raPgUaeTOyPCKghCf6At3qFjeezZPHayoFuMDQKeZk/NoptXrnDf1m99+dHRrWXKhFG8ykCuqL06tfiGJbOoDncLOFtAUJKWj3Nl3KFtHNa+6InZ0dFJ+k49N6TW6w3U2Ynbneza4mEwkME8jGQwKkf8e2Xws1n5DV7s6oK3C9GRfPTy5nMfHy8+Yvj6eJOPtw/5+OLchz096hHpZPiuSVNrwRVB0BLGkoXTqb2jg46dLGSP5/4j2dyz2t/XtrZ2bieqj9x3A2WmjxiW3+UbrvRV1Tc6n6giylfLx7k6wymsEC/kOaMXJWqfdo12djm16XTUpuvgx+jaO0inHts7qB2jQ89f6vZ2HPXUgaG33nDe2YCg+kFg/Xy5t6a/v+mI2/5+HMfAI8CfAtUjRqA/BQX4U1BggHIeGMCJ/Rj49yLUwnCCaw59ZzGuMS7jTjydHdb7Vru9qMZG9x6xqzU+JkHSO6GlirQZ7Jnq60t6tUzwczzOUxiMsMLiQ1h+Y3MLNTYpR9zGwH49SlO2tCjnza1tfISAwjq0J7AIYR3CaoSI4TYCLbzVIw/F+vRmC1SxNhGj5mUKVLOky5JVhgEDli4sXqORrWCcKxZxl3UMi9ky2AP/VlkU6KmZ2jT7W4MDA7iLSUhwIAUHB1JocCDfRtem0OAgCgvFeTAfw0KCedtnuMrXCe6Nl5cXx+Jgi9EjRXU4MVuqTiiqCD5C2owS/YvJxXKSVyabuBVPu3WQUq/CurRLWC/+7Ff0m+SbSNfUQfWNzdTQ1EINODY2c8oVekQONuoAbtGgoAAKMllesMjUo2qdWVpufPTzYysP52zt+fuyWxWWXpeL1cepBAPiC0saAosjD5OFrWu3sLpN1jhKfuIIS91ssevaeTGC81a28JXbEGyINxYv1mpr9wYWFqEmgQ0PC6GIMPUYQhHhoXxET8/IiBCpxS1oioiqm7p/AafLXLeKyj+8iwwt1eb7fUJiKP6S5902nQYu1uq6eqqpbeS9kJq6Bj6ily1a79XWNdI0v3G0NXMf7W88SXfveorm5k4lX4P1BQY8j6pVhElaOQZRCFtJXRaT4q4MpJAgWFOK29ITgMCriwMtgdUL8W1pbaOWFp3ZE4Di6ziyx6BF8Roo3gQcW9jtDjGub2jmQaWVff4eLHSiIiCwYXxE1Gd0ZLgyonAe5jGfpTB0RFSHgG+YIqrOGKikAuHUNxRT5Sf3me+LXPQzlxZUWDpVNfVUWV3Px+raBvMRA5Nwf0R1RNCS4jn0TeoOqg6tp8OTT9LPIq6kuPAoCodVExrCxUBwDtG0V7Cb0LfbTbXqB7KrA4sZbvqGxhYu+KIeIbDwQMAjUQfBbWzi2rHqnndJedfCsye4FlBhLToqnGKjI7i6Gh9jIvh+qfktqMiVoIml6twRtB3VuXz08gsiY0cr6Ur2kSsIZ3llHZVX1XD+GMLdK6rrqLKqjifF/oDFqFgcqtURRlEYEaEUFRHGLkBYVmq6TV5HCb0X8DW9tdC1ooKFU4GbHJ8xRn9ATOvqm6iWRyN7MWrqG6mmtsF8hLXM2wJNLZRbWGbVk4HfxdGjMZF8TMCIi2LRFcH1LOTTHgI+JlE1tNWTob3ZKasqgY6aHD6GjDuXmg58SLri3eQMwL2HiaysooZKK2r4WFapDEx0fQFXK4LSYqMVywHWgnqMiYzos9yYu6XbCIMHrl+MpISYXq9ReD6qahrMHhFsJ+CoDoiuss3QyNV6elrbsVHhlBAfTYlx0ZSEo2lgK0Gimt0PEdUh4B0QTl5+wVxVCcFKzlZVSaWjOpuPYZMvY1HtqMmlzpZa8gm2vZj0UMDEBNcb+iFilJQrx9KK6lNaN1mCfUqs+ONju1b/qMeMgShQrRBhFXoDoqdEHQdxa0dr1zYC2tibUm3yqFTVUnmV4mXB9V2JrYqaejp4VPEYqSBqGWKekhhDyYmxlGIa+F2C6yKiOsQvnG94IheAgAvYGUUV5Qrx+kBg6kzyjRpJ+tp80pXuo+BRZ2j++xDpWVJWzXldlqNnuUjLKM242EhlFZ8QQ4lxcJtFs4BCVIcLEVZhsHMAoooxUDf2lMVkYzOVV9Z2eWEqqtkrA2sXQVbojoVhSWREKKVCYJPiOJUjNSmOvx+yr+8aiKi6cVUlgCAlY2c7kY8f+UakUWDydGqqzae24j1DFlWkPxQUV1BBcTk3K8ARE4e1HE1MPthjwkocjQt4dZ4Qy4KK1BNnQIRV0BJc85y2Ex7K7SMtgcu4vLKGF6Cq5wYDLmZsfWAcPJbXbZ8Y352RKQk0IiWB0tMS2LqV/VrnQz4RN0+r6ahSXL9+Uenk5eNLAakzqOnQx6Qr2Tuw5+nQU2FpJXf9yS8qo7yicl51W8vhhIWZlhRnWmnH8Uo7KT6G8y6dHRFWYThAkBzEEaNn4BTEFd6d4tJKKiyp5NtYwGLhatlpC4tRdFJJT02kkWmJlJGaSMmJMYNuwi1og/PPck6OM1dVAu2m/VT/mFF8DEyexkdd8Z5e/w3cVlgxZ+eX8MjJL1HKdHV2Vc6xdFVh9Yz9JmWSiOeVuSsHYIiwCo4CQVNZ6Sk8VOD5qaqpY69QfnE5FUBci8t5S8UstNv2mcUa38WMEUlc93xUejKnhwnDh4iqG1dVsoz89TOJaoBJVNurjpNB10jeAWEsloUlFXQyr5gH+gyiSEJPUPAgPS3RPEamJGra9ceZEGEVnKm4hlrsfdbUseaFb1VtPQss0nzyMIrKODDqeE4RDxUE+qHNJfZ8R6encOSxKy96nR0RVU9x/5pE1TcsgXzCk6mzoYQ2rHmb9tdEsyWKPZ6eAUSpyXG8Ys4cmUyZI5I4XcWTvowirIKzgu9hXHQkj5lTFKFFbWYEQWGLBt/pk/klVFpebcrzrqOtuw6Zo44hsNjnHZOZxtszzlT20tURUXXzqkqq+7faEEVbN2znPLoJDRGUSSV04ocv6YhxgTnvE+6irIxUPsIS1brsnCsiwiq4CthLVdNyFs2ZzPfBRZxTUEIn80roZG4RW7SIOt576CQPtVDKmMxUbsSNgdaZnrR41hq3a1LeXwNZrWmvOEp5z0wl78AIynq0gpwBfKRYmR46lkNJny0hH6OOXu78OdVSLP98gdd6Wui9gUojTyfDaX+m0ZmpHIkrq9XekUbngjuAEo7Yjz2RU0THcgrpZG4xB0H1LMk4bvRImjhmJE0Yk84xEgLZrDEiqkOks62esh+N5/Os39c4rKoSvhiwQg8dy+VQfFR6CaEGusvnz2QwetGL/k/S6KwMGpeVRqO8jpLuk5vJP3ESpd+7yyGv1xURYRXcDcRTQGSPnSzg+QMxFWjbZwncwxPHptOksRm8HYT0Hk+kQUR1eMDbd/LhaK6qlP6LQ8NaAKKyuo72Hc7m7vRYeaLHpQoSxeckNtGisj8RhadR1q+Pm0PtO+qLKfeJTCJvH8p6rJq8/aSCi62IsAruDNr2YT/28AllgY7cc0uFCAjwowmj02nK+EweKHrhKTTYqDGyp+pCVZUQWo8cUXU/pGdXDdS+xWpy0rgMDkLQHVhF5e8TBSeM6Za75hueTD6h8dTZVEG60gMUNGKO3V6zu+GKe6xK43GLRuTordujvS4al3uZm5nLNoCngmISY0eN4HHJOYu428/h4/lcYhEii/Z6ew6e4IFt18wRyTR14iiaPnE0RxULIqpOX1UJEX0Ij9+1/zgLqWWqCya/0RmpNGX8KF41omKRZYBBU3X3yF8VPAapNS3H15GuZI+IqgOFFQulNp3SKxTNudELVG3Wjb6wrdzIW2nijQhtNPqGew6DG4FbNAfHkUengToNnezaw/VjrcJVfyD6GwsxeDwwUGiAj75omu7DhTwwAXMjddOwbLZu2YhdKVrvT8GBgdy0Hf1mYfFIMIzzg6L/c6eP54HrCJbr/iOKdwz5sWou+4eff8eiOn3SaJo1ZQyXV/TUz1dE1QnTajARnsgtpp37jtKuAye4YLcKJiNYo9MmZtHkcZl9FpZXC+n7RWee8rPAlOksqm3FA6usJPQtrAHkp7QJa2zmHp747BqbWpWjRVNttdE2RNQZd2DQ5Bujx/aaZkC0EXGuNHpXmryrA/nQYaHBPFC4ICIshMJCg6RSkIPBIl7NUb/wrIXclWf/4Wxe7B/NLuD6xms3bOeBphfIqZ01ZSxXVfMkgRVRdZKqSphYEe6+bfdhtkote4ZCOLECnDFpNI0bPcLmep89qylZEpAyg4+wVAXbgOVYXVdPNbVKmy+0rbvecB69YlzNwjrv1dtoVvYk8jUMPJADlh5bdEFKKzKMwAA/PqqWn7/pyNahyUr084PV6Ed+Pj4cQKJalObh7cOToerWVSY3HLt+t+oahk8Y1ggPo2Ll6vVdVq9iEXdaWMZdFjOsaMuB9wrWNazuFm4C3k6trW18jueCYGORgWELeN0QW1TwQi9cRKSqvXG5X26U0jvX30/SwIYLvN9nLJjGA4vDA0dz2C184EgOx3uoAgsP2uypY2nujAncGMDdEVF1cFWlypo62r7rCG3bc5i7WahgFc+ulKljOXdsoEXnMUmaLVUr+7zmcoVlB8mobycvX9v6j7ozEIrqmgb+TKqq0a6rztRHE30zG7ivpjXmBE+mrZn7qCK4hrZn7KMFedMpKjSMrazwsGDF8goJptBQWGLBFBocaGonFshWWnBwgMcURsd1iU5GzS06amlpo+ZWWO5tbLmzyKoWvakpOCx+7Ovh36mNwqm499Q1pIPEREdwD1PEGMSiVSAfIygmMlysXTuB+Up1E+va29k9vHPvMTpwNJfntU+/3sYjIy2R5s2cQLOnjePvhDviGd9kJ3P/4qLbue84bdl5sFs5MVgr0yaNprnTx3GE3VBC1w0t1dw8HfhFZ5z6mqNGkndQFBlaa0lXfojdwZ4ArDC03UIvV3zZ0SkEvS/RAxP39+eJRaI8VujqiIwIo8jwEFrpvZR+efx5qg6tp8qlVfT3pT916uAlR8H7+f7Yd/Xn988WYNnCZY54gvrGJqpraDZ1clE8BvjccISFrAovqgr1BJY7hDY+RunPC6sJ+4Bo9oDFjye5KO1JgL8/zZ46jgc8FnsPn6Qf9hyhQ8fzuKQixv8+2USTx2fSwtmTeBvLndraiagOY1UlbPJ/u20/bd9zxJxwje/xuFEjePU2Y9IYDuzQgnZTD1XfiFSrKTOYQAJTplHLyY1cXN/dRBWWDSba4rJKc3stREujbFvPPDxL4GrFxIs9IeUYQTFREXwOS6evzydjZBLvsW5zkahgVwETLmpMK3WmT20Urn7e8CSgEQRytOFZQBF6nFdW43Y9p5wpCyl4hHJPWSyhkpDSNBztCWO4A4wUox8agYH+NG/GBB7wOvyw9yht3XWY50I1iwGf68JZk2jR3MlcdtHVEVHV1FItO+VnWD3jQvpm695ubZvgklo4ZzJfbKipqzVm16+V/VSVgOTpLKptJXsoglzbbVtcWkUFJRVUWFxBRWVom1XF+3m9TdJogg4rRW2IjgEhHYrF4orpNu4CPjPFpR50Sjs1gP3h2vomqqiuo4rKWvZMlHLT8BoWXAiy2lDCEgRLofhBalIsjUhOoLSUeEqKjxY38iAIDwuh5afN5IHF7pYdh7gecX1DM32O/deN29lDd/r8qTR1wiiXfY9FVDXAxySqcLca2pu5qhL24TZu2UvfbT9g3ovDZI5go9PmTaWxmWl2zQe0SVRN1qnOhSKA4QqE1QkXUj535ijnL6i1tnSIMLVsjJ5sskAgnvZyN4mwOieYoLF4xRifNaLbzxBoBeu12OTNKDE1DIeliz3eIyfyeVhu00C40WINkbAZaUncCUbcx7aTkhhHV6w4gy459zS2Vr/dvp/fY7iIMfA5LVkwjRbNmdJnhoMzIhWVNK6q5HX1Bvp6XxXtOXjSnCqBC+SM+dN4/wAr3+Gg9N2bqXHP2xR7zh8p+owHrD6mveoE5f11Enn5BnJlJTQxdzawioX1gCovOYWl3OrKmvsWXzxMdAjfR45camIcW6KOKqkmlZdcH8Q+YOsAvYQLMYoruEViz45OqvsYAps5IpHbrKGzE4J3BNtBvfJvt++j7384yKln6gJm/syJbN06uriElCkc5uCX40+MJu/GQnq78zYqpnS+HyvipYtmcGGG4XZlFPxzMbUVbKeka9+hsMmXWn2M0WCg7Mfiua/qyHt3U0DixGF9jae8HlOPSJRcRADXidwi/qL1BIUERqaa+rqmJrLF4Ixt6URY3Q+4kWHVoncptnMQEIVtB6QZWYJLMTUpnkZnpHAHGBRp8aSSfkMB0eE/7DlK6zfv5gWN+n5OnZBF5yyZw120HIGI6jAAl+OOvUd5L2Bx5ZOU5pVHn9HVFD3zalp+2gx2cTiK7D+kUGdzFY342Q8UmDy118cVvricWnO/o4QrXqaImdfTcIPAkqMn8+noyUI6nlPIwUWW4MuE9xFfpMyRSexqwz6oq5TSE2F1fxAAhT18CKxaYQh5mj3BXizKh6IEINLkUOhC6B1IExbXX327k2ucq2CRct7SeTRhzMhhXUiLqNp5tYoI3k+/3mq2pC7y/R+NMe6j0OV/ouTlvyBH0q1zzmNV5B3Qe+pCxZpfUN33z1Lkgrsp/sJn7P7a4Do7nl2o7J0cy6OyyppT9kFhgaId3Rj0dk2HG821RUiE1fNA+g/aqh3PLWLPi2pxqUALsF0xcWwGTRyTzotGd0or0RpE7X/5zQ7atuswFw4BmSOS6KKzF9L40cMjriKqdnLz7tx/jNas22IWAyTvL188k6Y3vEtN2/9JUYvvo7jzniBH0la8hwqenUc+oQk06rcFfT62YfdbVPa/WygofSGl3bHBLq8HkZZIBkciOKxRS1cZvgxICMfKHSv4UelJnOfmboiwejbIs8V2xrHsQm6xhkAoS1A5C5bX5HEZnLcprmLrICd53Tc7OTURUf8gKyOFLj57Ic8f9kREVWMQmfb+Z99QgamaCwJjzj59Ni1ZOJ1Lx9V88zRVrf0NhU27mpJWvk6OpHH/+1T69rUUOHIBjbhzY5+P1ZUfofz/m0Ze/iGU9WgVeWmw94tLCu+T2s2iZzcdJP2rK/Txo0e4vCVqKyKsggqKVxw+kce9jw8fz+M60Cpq95fpk7Jo+qQxHFksnOoJ+GLjD/TNtn3mRTq6c11+/mK7bbuJqGoEVpQQU7Q+AhBQiOmy02bw6tL8+/e8TWXv3kxBo86gtNu+JEdSvfHPVP3lwxQ+4zpKvPKVPh9rNHTSyUdiyNjRSun37yf/uLGD+p24jHLyS2nXgWO0+8AJ3is9tZtOJl/4qGDjbEFFw4UIq2BtOwmpYQeP5pi7v1iCPNkZk9H9ZSwXpxC6L04+W7+Nvtu+n93CmFeQZQG3MOpDa4mI6hBBbukn67bQxi172O2LvT4kJV+wfL7VtBgUUSh6+RwWJYiTIyl778fUsOs/FHPmIxSz7Df9Pr7gn6dTW8E2Slz5HwqftnJAvws5o9t2H+EyZJZCilB47qYzKYtb07larpk9EWEV+gLBevsOnWQvz7Gcwm6t+yCw82aMp9nTxttc5tETKK+spQ/XfssLerWb14rl82nZopmapdWJqA4SvB0oowXrVG25hsL2l523mAsJ9EZ7xVHKe2YqeQdGUNajvRf8Hg4KX1hGrXmbKXHlGxQ+7ap+H1+++h6q3/oCRZ12L8Wd/+d+H49yYwjUgpii3JgKLuRpE7JoxuQxNHFsOpf8E6wjwirYAhoN7D2UTbsOHGc3sVrkBI4e7CHOR3nTyWPYgyYQ57T/b80mc+1n5LZec/EyDmYaKiKqgwCRvG+8/yUHEwAU3L764qU0YYySd2pzxO3va7iqkqPIfjyDOhtKaMTd31Ng2qx+H1+/43Uq/+B2Cso8g9J+bN11jdUyUl+wh7HvULY5Ag8WPFy6c2eM59Ji0nrLdkRYhYEGO6EtJBa0CHqyXMzOnTaeFs+bwvnbno7BAMPoIH3w2bfm1oILZk2kK1ecwWUsB4uI6gD3NDZ8v4c+WvsdV+uB6xJu3jMXz7LZdWBZVSn9F4fI30q7teEAZRLxOsCoh8vIJ7h361qlrWQfFfxjDlvZox4p77bfibZbqHDy7bZ9VFmjdL0BiNhFpZNZ08YOqYUT9nRbczdz3WTfsEQKylhEXt6OqYLkCERYhcGAesUQ1y07D3F0vQoKoZw+fxrNmTbO4z1FzS1ttPrLzbRp617uPoW2gNdeupwt+8EgomojqNH76qq15hZsSM6+4fKzBxVxl/vUeOqozqHU29dTcMYicgToj5r/t5nkHRxNWQ/b1orO2NmhLAg62yn9gSPkH5PJrdG++nYX54WpoesIzEI3ncVzplBq8tAj7BoPfkyVa+4jfX1XEXPfiBSKW/EMhU26mDwFLYQVBQh0OqVBOGrZ8tArQ200jhU83IdqQ3IVLKKUJubeHFTmqzY89/XhPq9YZMIDgSbpmKgln9L5CiRg0Yv9RFwHADEMp8+bytkJWgfsuBrZeSX0n/e+oNIKJQ0STUyuvnjZgMtIiqjaALrHvPnBV9zNBC6UKy84g06bO2XQkanqXmbS1W9S2NQryBE0HlxNpW9eSQGps2jkT763+d/lP7eAdEW7iJY/S18WxHIUogqS1M9YgNXvWM1ySCGopW8iKKrn5ae890nXrfJYYZ0TM4H+b8q91NGi596gauPuZoxWNPRu40C6llYdtbXpqFXXfkqZPHsCkcUeXlBQAAUHBnBKFCZxbrpu0ZAdbdMiwpSWbZaR8oJ9wHXy/Y6DvEUDSxZggYStGWQseHLkcEeHnov1rN34Ay9EUNb01mvOp6z0FM01xvkqqA8DWL2v+ngDd0ZQK3PgDUb3kuFsVm4POqpP8tG/j+40PcFF1hqaRd60i7ate4/2G88219qECxz1S7VMgYHLFxbqqYLKP2VhrVxzP4VOWOF2rmBYi8ixQwcU9PmEpwS9P5HUfkbLbFob8z39UH2YLlzzAM3NnUq+hoH9/djj9vf3ZQvTz89XsTh9fNi6xM9gjXp5exH+B4x4v43KFojBaOQjrNkOfSfp9arF28kWsLr+xhYJBgTfVrBojY4Io6hIpVMMBnrUqk3DIcaemmalFchKQG3cs06fxZ1fUCQBJRMhtBgzp4yhFWfOd2j5VEeB7wI64iAT4eV3PuNFx1P/WkWXnnsanXX6bE2vPY8TVUxe/3rjE8orLGPhQA3JFWcu0MSl5ROmBAno+2lWbk9saflmCVxH2HcIym2js7yJEr1LafGsKXTm6bM4UMse8B6qhcv3VIykry/ixwWPOp1ckba2dnahY6BnZxk3x65hIVXd6T3xIm+aXz+Ftmbuo+rQetoz9jBd2X4mxYRGUFiI0isU4gOLEK6r4MBAbgINKzAwAK5Zf7t15YGgwhpua2+nNl07/33w8MBahtXc1NzGVjSCaZqaYV23UkNTM0eKt7a1s2sa7jfVBWetSUJcTBRH2CdixMdwrVxcg5gQBdvBwgn7hhhwfaK8395DJzjIafeB45zvuuKsBZwv7mmMSk+mh39+A7354decBvj+Z99STkEp3Xzlufxd0gKPulqxanv+tY/YlYaJCdYpcim1wmypOlJUa3JsslQx2b/36Td0wOTmTfFJ5WNGUA2dedmZdrUarDVzH8rjnKE9XX5xGRUUVVB+cTnXeVXdb9bAvmVMlGKloVl9tMlyQ95hVGQY5XQU07WbHqVSqqIfUg84RfASrgeIG8ZAA9PQQq22rolq6xt5UYt8Zgy8Rxi4H8KL9CzLFC31vUIDebTzwzbEiNQEGpkS7zFVuLQQkbvSL+Kew2u+2srCumPfMdq5/zgtmjOZy/t5WknEoMAAuvXq82h0egqt+mQD70Vj4fuzH13K38uh4jF7qriYXnnnc7YS8AW968aLeFLT9DU4QVWlnCfHkL4un9Lu3ERBI+dbzXvDl8uyqMXCOZPpvNOnUvUzGUQGPWX8+iT5RabZ7TW2ZH9DRS+d1e/jUm9b53SWKgQir7CccgpKKLegjD0eEAVrYC8R1gAsL3TWgdUVHxtF0VFh7JLtC0+KCoaLubKmjioq67imNgaS+VHeElawNWDRou1fxogk7l6UlhTvsN65rgT6waKoDdzDAHvj5y+bxxXisGXgaWTnl9ALb3zCWzKIDv7pLZdyQw9rSKCSBRu/30PvrF7PYdUolXfbtRfYJVna0VWVDHodnfxdBHx1lPnbQvINVfJmAT7mbbsP0/8+2WRuAIy80ssvON3s5s3/+2zSle6n5Ovfo9CJF9rtdWJPNffPo0lfX9LLvqoXRwFn/Oq4w/dUsZeYnVfMRdCPZhdSflFZtwo3AEY93JUjYUmlxFNqcjylJcUNubWXJwmrNXDNYrIrKqnknqUQBJTws+YFQPAUOr2MzRpB40aN4IlRopR7B3mu736y0VwSEdkO1192Fje28MQKVs+++iF7mHAd3X3TxVZrE4iomvhy0w/sNwdLFkyjlRcttVvDcEdXVVJ/v5d/KLd8U124mIT++8FXXJEFJCfE0FUXoqjFSKvlDaOX/oZiz3rErq+19+hf4OWw6F98HfDlQls6vF8n8opPiayNiggz93bNGJHIbkl7VbTxdGG1BnKn8wvLKbewlCvnYE/MsiC9ukeLikNo2jBxXDrFRUtR+p5gcbht9yH6cO13vIUBTpszmRfanuZeb23T0Qv/XcPfeXiR7rjhQjY6LBFRJeLm4R9+/h2fn7dsHu8f2HOv0NFVlZqOfEYl/7mUApKm0sh7lNDxzT8c4BUpLC64xy48cwEHIVlzP9Zu+SdVfvJzChl3LqXc9LHdX2/Dvveo7B00Rre8BL1M5RWvpOECEa8I2EIQx55DJ7lId08RxQp+XBYaTKdpsu8yEERY+wbXOVzF6NOrehR6uo1Rrm7GpNEcvANvgkQad4Fgs4/Wfkubtu7j28hrvfmqc09ZdLs7en0nvfTWp7T74AneFoOwTpvYVcTH40UVydCwzsDF5yzifQN74+iqSrWb/0GVnz5AoZMvpchLX6f/frCOdu47xj9Dl5gbrjirz4je1vytVPivM8gnLIlGPaRYtfakJXsTFb10NnkHRnGD9IrPfkWG5gpKvPq/FD71Sruv0uEC27nvKO06cMJc5xnABQQ3IqwcTCx4zxw9CYuwDmyRhICxw8fz2fJABKxaVhMgdW7W1LE0e+pYLlDv6M/WWcDCEmVasZ+Nt+ScJXPpwrMW9Lv/7050dhro1VWfcw0DGCH33nqZuU+rR4tqdkE5/euN1byHet7SuZyfNFw4sqpSxep7qW7rv8hv1t307xPj2e2LFRcWFcjFQiRlvyUOH4nFpidl/ibPHM1sLyq/+C3VbnqKwqZfQ0lXvUZVX/2eatb/iYJHL6PUH31ul9+JvNDvth+g73ce7GaRIhocq9KZk8ewVeqMaRwirIO3xA4czaHd+4/TwWO5nGOrgoIIi+dO4cL0Q6kL6y7Ao/W/Tzaac/hRHOHOGy70qAjhzk4DvfDfTziYC9s6v7rraq4g57GievhoNj3/xhq+OPBluc7O6SHOVFWp6NUV1HJ8HX3tfTnt6ZjOaRo/vm4FF7ewlbxnplF7xRFKvuljCh13rl1fb/6z80hXvIcSr3yVwmdcSx01uZT7l3Ec+ZPxy2PkFzVSM6v00LFcrgGKyVW94hFaz30qp45lIXWFFbkI69BAji3SyJBWgmtB3S9H5CuuA8RdIKLY04GH64331/FeI1K9fnrzpZqUJnWliPS/vfw+W++YRx+65zoyduo9s6LSv99SBBWtfq65ZPmwu3YcWVWpofgwf6CVHZG894cV5kBX3wEp01lUdcV77Sqq+qZKFlQAyxT4RWdQcNYSjqJu2PVfiln+26H9Dn0nbdl5kL7YtIMqq+vM90NA0dEDlqmrpRHMjB1H7y77Awvr1oqDdO2GR/oUVrVoQ3tHB1dG6uzEMJLB2OUOVSstYVHh5+fDdX7dNT0FlsfsaeN4wIL9Ye8R+nbbfo4s3rrrEA80i0BRmKkTR3msaxgLDIjos69+xAX7n/zn23TXDRfZ1LHLHYCnCmmXf/r7m9xI5MX/rqFbV55t0791rRnFxvDolKQEuv26CxwSUu+oqkrrNm6jtKYSLp07ZtpCumLl5YOyvAKTp1HjnreprXg32ZOWkxv4GJA0hbvTqITPuolFtX7nGxyF7DWISG2ICMqyfb5hG18PABWIFsyaxI3m7VUpariYGJZJz0//Bd256y8srOd8+HO6xe8iam/u4IpGiIRFPjIKKsAyG4wzCkKrVmviur5BgRQaGsy5fOFhwRzMEhkRxqUHYck4o7u8P3BNnDF/GheeRwTxpi172ULLLSyj5//zMeezI7DPU8UV35Pf/PRadoUiAOzZ1z7ihTpK/XkCIcFBdPfNl9ATz73F7UC//s62OdH1vgn9gH1D5KE6an/EEVWV1n2zg776fDXd5mMgg7c/XbXyKvIepCsTlirQlewle9JyXAkiCx69vNv9oRMv4pQkFLBoyd5IISYr1hYgHijygQbzqNijFmA454w5dNrcyZo1AxjO1BHkaMKKQnRraXk1VVTXsXCCGcETuKTh8fYCeqrmjX5rBUMY1DrASmcaTmlmqxX7SLBiVf1FYI8izm19VodSgcgi1xHpWsmJsVyMAUFAWpV+syd4L5DjinHFitPp62930YYte/h9h7iinRpS8QZSfN1dwILqnh9dRi++uYb3GP/5n9V0940X0+TxmeQJpCTG0tUXLaPX//cFfb5+m2eK6vnL5jt0T2S43b/oqYhyg+mk1FQNjMsatKCCgOSpfNTXFVBncxX5hMSS1kD8mk98bVVUvf2CKGzaSqrf9iI17PyPzaKKiMW3P/qaDp/I59vojoLi4nDzWjZOd9b+rXDPojpTTr6Se5lXVGa2sq0BCzIlfBRl6pNplc86rhWcM6uAfp95G9cKhmWp1AT255ZtKLLfn+eCXcWdndTeructlDadjlpb25Xavi2t3er5Isirtr6Jyw4i8AdFGjDUFooAop0QG82ihLzezBHJbP05c1EGdNa59LzFHNi37tudtGHzbi6Q8Ofn3+Gyfpedt3jIRT1cDWwF3H79Cq5IB0selusv71rpMQ3RF8yaSMdzCikiNJBe+3v/j3e7QKXBNCl31apKJ/OK6ekX/scT4cqsEkrLfZ5CJqyglBveH9Lz5v51InVUnaSUH31GIT1ETwt0ZYco/28zyMsviBupe/t13w9sK9pNBc/NJy/fAMr8TX6fjdYRhARLffW679ntiwng3CVz6Owz5pzSpNmZ+rfia1dQXEH7Dmdz2gdEFNZiT2D9weLDihmRqqiDi/Kalsn5jgxewt8BixqddtAwABZ1cWklFZZWnpLvC/CZZI5MpsnjMji5HmUbnRksIj5au5nzvUFocBA3usaeo6eBeQZ7rLhesWj9zc+uY9e/p9Agrd8cbanatxg83HJIVMaFPn3SaJoUXU71uQNr+dYbgcnTWVQRrGQPUW05obh+gzJOO0VQVRe0f+Jkai87QI37VlHk/DutPg/2DbF6PnA0l29PGD2SJzxrE3VvFZxQKpHvH4YKThAgWKI79x/jQhM9LVG4quGCRLQ2yuylJSfY1Eh5oMFLWrtOYd1h9IwyhyAplY/KuPpRTn4JBwcdOZHP439rNvFiAQUZkDPqjP0+8XfdeMXZtHDWJHrzw6+ouKyKXaHHc4u4/7K7BnRZgysNXb+C/vLPVVx17JV3PqP7b7/SbhXqXBURVY3xMYmqoa2e8z7tVVXprQ+/4kkZiey3XHUuVb/7nwG1fOuLgJRp1Lj/PbsFKzWb9lN7E2xM1BGzb+KeqvU7/2NVVNF1A6tm7J1iYrv64mVcYs1aQImj+7fCXYoGBlt2HuompCgygWjKKRNGcbWm2KiIQQfEOFJY+xIk7L2p+2/wKpSUV7Gg7j+Swy41iBTGmq+2sMCeNncKLZw9yW5lHwdLVkYK/fbe62n1l9/TFxt/4Hri+YVldPfNF/Pf6SlgSwHBSr//2xvs6v9y0w46d+lcR78sp0JEVWO8A8LJyy+YqyohWMkeVZXgfkGeHQdlXXM+B4MMtI9qXwQkq8FKSsqLlhg6WnlPEwSPObPXx4VPu5qqPn+Q027aSvZRoGmvF6A92P/9+33e58Oi4o7rL+TSc87Wv7Wiqo5rT2/ZdcicD4lm3dMmZHFPy/FjRp7ioh4KziisluB6hSsb48zFs9jTAPc3gssOHc9jcV21egN9su57WrpwOi1dNGPAbebsbalhT3V0Rgp7SBAx/Nd/vUv3334Vexk8BXiC1OCdT77aQnOmjxv20p3OjNjtGsMRluGJdnMBowQb3GZgyYLpHJQFSwxVnIB/zNCj8pBWA/Ccna1d+Z1a0Jr3PRn1beQbnkL+8eN7fZxPSAzvD4OGna+b70dE5tMvvseCinzCh352bZ+Cas/+rXjf0cauYe+7fMRtgOLkmHR/+5dXuDINBBWu0R9fewE988hd3Md32qQsTQW1p7CG+QWbhbVZb719mqNBhD7SnNBu6+mH76JrLlnGEzZcxJ9+vY1+/ad/0weff8vt9pwJpJQ8+NNruSY0mq7/9YV32dXtSSB4B7nwuLbV+uqCgoiqHfANS+Zjpx3SavYeyuYVPQJVVpyp9EvVNxSTsbOdyMePfCOG3gcVguYbqVQz0pUoRba1osUi6rc/VydcwKBhzztk6GjjKFSE9OMIkbr3titsSp2yzIPV4nHqHi3a16EvbNmqG/iI23vWPEePPP0at9nDHuqkcRn0wJ0reRJGwQHLSGR74UrCapm6gUXiHx64mT0PiBhGVDFcrY898wYH5TlbDucDd17FgTro//ry25/zgtdTwHf3yhVn8Dnq5CL6XlAQUXWxtJoN3yv7nChioAqKaqX6RaWTl482Hv3AFPu4gNX91OAx/QdABWctI9+IVDK01lLT4U+4bBpyJlE27Gc/usymIB6AtBmfcGWhYx30b03lx9mCGvTU06XcUV9MwZvvp+SWXWw9/+Zn13KO35jMVJssXE8XVoCgl5lTxtBDP7uO+1rCGkQ1LATHYD/TmZIVsPVw762X89449ok/X7+dPAm0PEQUN0AJUEFBRNWFqiohyAWVPWDgoQqMSrtpP1WLyN+eRSDairX7suD9aC87yAmMIVlL+308gobCZ6I1HFHpty/y3hsq/SBnDpaNreB5gjP72is1Utz5T9kUpNRX0JNqd58f/BX9+u6V3G/VVgsX99sqvLaKsqsKq2oJoYzko/ffxMXuIaaffr2V3cHOBCKWr71UiQ34bH1XBS9PAd4FAM+MJ1nqfSGBSi5UVQlF4UF6WhJbaypaBimpBKYo+6o6DSOAW06sNwdC2VpUInzmDVSz4Qmi4u8pjObT7PlLrIpVX3S21FDzUaXrjXdQFFu+PemoPmnTc/UX9IQFj5+ukjoKtpJfj6CnvtN6riLd8oc5sA3pTPU/vMJufRVY2hFzbuXX3rj3HS7MoeIdEkthU1dyAwKf4BjSN1eSobWGf016UCS9GDKCflx/goX1oi8foD/NvpOCfE6Nro0ODKfUkL73p4cbeCNuWXkeVzNCK0dEmyJHEoFOzrS/+P2OAxwNi5xpVF/yFBBsh4bwqPKFdnsZA/xuuiNOJ6oHDx6km2++mU6ePEm33nor/eUvf3G5upv2cv+q1Wom9mge3FGlvaiqEcDtVcfJoGsi74DQIT+nWkUppI+o354g8MonbSF1Fn5PU3z20Nln/GrAv7dm0184xQl1htPu3kJt+VvMFZXaq09SxYd3UdW6RygwfUG/7fpsDWbqqC9hK1L9PYEj5/eT1kNU8/Xve32+zoaSXn9uaK6i+i3P9fpvscv+m7BY+s2IqXSgNocuXPeA1ccFePvRlov+7XTCChbPm8oBTLBUUYYSua2WC0tHg37Nx3Pep807DtDlF5zuEh2PtAB/J/qNooThiZwiEVVnc//qdDpasWIFzZw5k3bu3EmHDx+m11/vivx0FXzDkuwSqIRuEQApCZao7l8/DSJ/VXzDEpR9SKORdKVDrwxlNBi6BSkNhOr4s/g41XcvRQ0wdaGjroDqtvyTz2PP+QN5+/px2kz4tKv4GDH7Fgqbfi33kC1953rSN1VoEsxU9dkvurl4c57I6Cetx77Ed+gUM7oPdIYOqmlTaiY7I2efMZsjTpHvun7zLnImxmWN5OBBna6DK2V5EsgvBuVV2mYKeIyoHj9+3D6vhIjWrl3LJaCeeeYZGjVqFD3++OP0yiuvkKthr6pK1XXKhGeZE4a9po4aNZ1G2+4RampNm6lF21CAMHc2V5KXfwgFjZg3oH97zDiR2oyBFKKvotacbwb0b6u/+iMZ9ToKyjydgsec2roJXpCES54l//hxbA2WvXszLwB6I3DEPC6v2B+W7lnVmhSGBj6r5Ytm8jn2150J5OCOSleC4VAUwpNA2UxQU9t/4wVPYMCiOm3aNJo+fTo9+eSTlJur7PFpxb59+2jevHkUHKwkfE+ZMoWt1d6sWtRitBzOWlVJKwym2rDoeanS2VRORvwOL2+O/tWSgJQZmnWsMVupmaeTl+/AquV0GHzpqHEKn9db5KzaUmO4Yfd/+Tz23D/1uo2AqldJ177DYonXCXexNQx6HZW+cx0ZO5QuMcLwEx8XyUek2zgbwYFKNDpKh3oSatu/ToPzRGa7lKhWVlbSQw89xHufM2bMoDlz5rBlWVhYOOQXA2HMyFBCtAEmQR8fH6qtPTWw5IknnuDixupISxt6fqbWVZU0D1YyiQKaTJ8SpBQ1YsBiZWuwkhaWarOp3m9fVZT6sgIOGBULpengR9TZYltOXNWXv2O3bujkSykobXafjw1ImEDxF/2Dz6u/eoyaT2zoFmHb2dZAJf+5hJoPf8KF/qNOf4C8TfnI5tdph44+QncaGlv4iChwZ6PDJPSuFgMyVNRGEJ71V/fOgK/MkJAQuvzyy+nNN99kgb3tttvoD3/4A6Wnp9Npp51GmzcrJegGg6+vLwUEdM89DAwMpJYW5YtkyYMPPsiuYnVoIerOXlUJOXsA7bZU2u0QpNQzraa94jCXFxwssNbb8rbw+WAK9GPPpoxSqNE/jV25jfvetalyU/ORz4i8fSj2rMds+j0Rs27gaGMIcfGr53fbE83+QwpHL2OxlHLTxxR37h8p89cnaEPUL2iN4UoqnvV3ir/grwP+24SB8c02pRjJhB7Beo6GmyUUKgvolB4xD+5Ojal3cZQHdazpi0Et906cOMHu3wULFtC9995Ly5Yto1WrVnG07hVXXEGDJTo6moXaksbGRvK30lwa4ov2O5bD3asqoQ0YKK2otms6jQpKCfqExMHvTDrklw6SlpxvueITqjT5xY4e8L9Xiid40R69YjmjyH5/E1zl2of4PGL2zeQfN8bm32UOojL22FdFxSpco0t/TcGmHFtvH1+auvwaOmqcSh/ta6eaDtvq1NqjR60nsPvACdq1/xifO1NKjVo+E63u0Cu2Z7ced6e0ssZcDEMYhKhOmjSJpk6dStu3b6ef//znVFFRQe+//z6L6eLFiyk2dvATxuzZs2nr1q3m29izxd4pxNbVsEdajfplPXKi4FRRjdYu8tfS4kbHGoDC9kPdTw0Zs2xQrjG0QEtOiKH9HZPJ6OXLubO6kt4jkpsPr6G2/K1sVcYs+63NvwdFFKrWPtjnY+q3/btbsQWUHhydkUqtbe30/Noi8grFZ+TVZ+WmjAdzKfW2dZS48g2KWf6w6fHiPOsLFD156e1PEYzO6TVodu5MfL5BqaaEVB971HR2VhCJffREPp+jT64wCFH99a9/TeXl5fTRRx/R1Vdfze5gFeyHHjigNPMdDBBl7Ku+9tprfBvRv8uXL+d9VVfDHlWVJo1V9puRD4Z+qvaqpmRJoDlYaeiiGjxaSY0ZzJ7qecvmUSuFUDZN6DNgydipp6ovIVREUYt+al7c2EL/3WzI3M3GMk/vJzdfzC7quqZWWtt2linrtKdIKrfjVjxN3r7+5rSemOUPUdJ1q8g3ovuE5BOeQtHLHzYLL7wG3d6TkFgKHneezVZvZGc7+fdTDhF5qigA4WyTNgo+/O2l97l4O6osXXPxMnI2wUd/XHD+Ms9qg4Y+uQ1NLbyQyDJFP3s6Ay7+cN1119nnlZj2VF9++WUW6wceeIDrgG7apHRkcTXsUVUpMT6ac1TRIPj7HQfpzMUzuyxVO7SYsywCMdhyhR11hdRecZSjk4NHKQW4BwOaWK/fvJv2FkyjLJ/9XGQ/9rwnyNu3+x58w+43qb3iCHkHR1PU6fcP6HcMtpsN8hPvve1y7u96oJioja6mcwK/pMCOLje9b0QKC6q1Rui4D71cWdRNxSJQh9iybCLcztZ+DqsZ96PYBFKWelZU8g6KJENbHUWTN61PnU6tCePJy8v6WtrZKiqhUP1/3vuSTuYqCx0IKjr9wMXqLKA7jWpBow9sSqJn7adu2qLMC9MnjSY/X6erJeQQnO5duPDCCyk7O5t27drF6TUxMTHkitjD/QvX6ZKF0+m/76/jwvqLp6Vx2g7wi+6KmrZHBDBq9hr17QOOMFat1MC02eQTHDXo14EF1m3Xnk9/+r8qamwPp7DWGmo69AmFT+3aw0cwVfVXStWhmCW/Jp/AgfV4HEo3m8jwUHrwJ9dws+21G73oubbxlOFXRLNHR9PUWfMpduLyPmsLc33iPnq59vbz/v6dJa6yk4uYAXSn2b77CHUaDNyD9qoVS2hRL03oHQUqPD332sfc6g81gK++2HPKE4Lq2gbauU/Z40b/W8FJRRUkJibS+eefT66MvaoqzZ0+ntas28IX9NYNnxOcgtin87ahIMFg8I1KJ+9AxdrRlR82i+xASxMOtIqSNeKiI+mWay6gva+vpXm0kQ6v+SvNnnSZ2XKp2/I818v1jRxBEfNuH/Dzw/qDRYlavNbLCWJPNKXXbja+vj50ybmnsUWFOrU5Jd6Uc5jog+OHaf5MLzrztJk8+QrWg8vQ3m3dNztp3+GTbPkBtM679pLl5gIDzgK2X/7+8vuUW1jGnoo7rl9BAVYCKt2ZD9d+xzm5qHKFvs6CE4uqO2CvqkrYu7jk3EX02rtf0MEd37Co2iPyt2ewUmv2Jt5XHYiocjeVkxsGnUrTW4PozoseIPpkI0U17qMXX3iRrr/xRgr21lHNxqf4MbFnPkLefrZ3sbG0+uJWPGMqeu/VQ1i79kT762aDCea391xPB47m0NoN2yk7v4S+276fB9plzZo6hmZNGevx0ZIQUkTN7tx/nHbuPUqVNV0VebAwOXfpXKeMpIUl/a//rOYG5eiWdN+Pr6DkBFfxA2jD0ZMF9MOeI5w6f8UFg9/WcUdEVIepqhKq9mjFvBkT6dtt+ym0YD2HmvnaIfK3Z29ViCqKQCBFxVYQMWxoqeFiGIFpczR7PdMXLKMj22eTT/kOis9/g956ajctTa0haqsj/8RJFDb96kE/N+95XreKi99bBi31tSfaW3DV1AmjaMr4TDqRW0xffbuT9h/JpoLich4ffv4d749DPKZMyKSRKQns4nZ3OvR6OplXQvsPZ9OegyfY46KCvqTwxCBdxlkt+u17jvD2i669g13+6JebmuxZ+6joSPPKKqXr02lzp3JDeaELEVU7V1UydrRwsBJaemn23N5e9KNrzqOtTz3LxtTxKi+y53p+sOUKzQ3Js5Zo1jxdJSZzNtWV76Ap3ruJdLuJlHgtChx9jk19UfvClsChgVj6yLPFaGxq4VzLnfuP0fGcQg44w0Cf0MAAfxo1MpnTEjJHJlFGWqK5Cb0rW6J1DU2UW1BGOQUlbLHnFZZxFK+lkE4cm8GBaFhcOKsLFTmo767ZaN5DhMsTQVPhYdotll2letKrqz7n9yMxLpquXGHbfr4nIaJq56pKHdU5PDFrKarq/mJWtJ6omuiH7Fby2raP8/fsgVpYH0XxkbJiq0AOtitNf6Avad3Wf51yP/bh6r/7K5VTCk05784hBbUMJADIVsJCg+n0+VN5YLUPy3Xf4Ww6fDyf2nTtdOh4Hg8VtDaDuxgWLVJ2khNj2GXsjG3F2js6qKyill2j6mKhoKic0y16Eh4aTJPHZ7Irf+LYdKfO64SIbNq6lz7+YjN/RrimkDaz4swFHuFZ6LlIWrV6Ax04msuRvrdec77TLoIciduJKiyBMxYqdWKdoaoSRFXrYCWVgLZSwpofCRNvffQ17+/MnDJW89/jF5NFXv6hZGxvovbKYxSQOLHff4Naua0F2zQXVezT9taXFBoKYe349lH6S14EXXT2aTQuawQ5I6EhQbRg1iQeBoOBikqr6GRekdmqq6iqY9coBtykKpjUoyJCuVMRysLhHG5INO6GaIeFBlFIUBAFBwfwxDeUhQUmUbg5W1rbqKkZo4Vr79Y3NrMFWlvfSDV1jVRdU29VPFWvCvYbsTcKCzwrPZUrgzlTFK818JlgrxdBgUjtUffKr7v0TBqR4jxpR8PJmq+28gIDH92t15znUW7fdd/spIjQ7ul7HiOqq1avp0njs5wiWtBezcpBZ1s95yWCsTMWUcXuHPr3W5/SLZ0G3pfSEi9vb7ZWW/M28z6pLaLKLdoMeg6iQqNxreivQAO+8OFUT7q87+npF0vZ7XrBmQto3Kg0p53IYfFgoubJeqFyH4Qsv7iCikoqqLCkkkrKq6isooZFDkKG0R+IioZbGZagv78fW7h+vj78+zDURQgEBKkrcMtizxO/o729gy0zFF+wFUTBwpqGiKYlxXHVI+w3OrMl2puYfvrVFg5EAqHBQRwcuGjOFF4keBpYXH385ff0+XplkXzliiVcOcpTOHKygN7/bBPp2pSCOx4nqigX9/Lbn9Ev7riKUxzcraqSCixg/h2hCXTdVRdTp/eXtGXnIXrlnc/YtbhskbIPqhUcAZy3mdpK9lD4zOts30/V2PVrazT1nDHRVJrtQ8dziuiZF//HbtSlC6fRrKnjXGKSh0CNzxrBw3Jyg6VYVVPPTRUgrLAYMRoam9labGpqpebWNn4sXJdI/VCrbw0WiHNIUKDJEg5mqzgiPIQbPERHhrGbGotYvGZnXbj0B74zKKgCSwzvLwgOCqAzT5tFy06bQUGmtm6eBq4huHzxvoArLjidlp/mHJ7A4SrugT1kLD4XzJpIb3iiqAYF+nNAxDsfr6frLjvToV9ye1RVslZIH1bHjVecw+4+dPHAlwBWzVUXLdFs/81crtDGykrmer8ai6qtBRoWLz2T5lwxg77YuJ2+++EAR9y+/r8v6X9rNrHLdfHcKU4bYdobuJYhZhijqPeScLAude3t1Nqm40Um9jvb2/VmSxQ/N1o0DFAtV1ixWIiqlm1QQAAFBfmTv5+fy4plX2DhkZ1Xwt8ZBI+pAVTYRkEz9KWLZrCweirwlrz45qd0+HgeezVWXrSUli7UdrHuzOB6+Ncbn5iDsi497zS6wxNF9cYrzqbX3vuKvt2+nydNR66q7On+7ar5q7hW4Za69tLlFBcTQR98/i2vLBE0cuvV51NkRKhmbeDaSvaS0WBgl3Dvry1HEX1vXwoaQmnCoRZoCPb2oWsuWU4rzlpAm384QN9s3cd7lF9/t4sHImxREH/W1LHmtnruAK4FWFaeal31R2l5Nf2w9yjt2HeUyiu7evPC/X7G/Gk0Z/p4l/Bm2BPkD7/45hp+fxCh/aOrz6cZkwfeYcqVF1xvfvgVl8iEoXbXTRfZfE24nagiPP+y8xbT+599S+9+spH3Q+bNVIqwu0tVJdBhpY8qrImzz5hDCbHR9PI7n3Gh78f+7z90y1XncrTlUPCPHUNefkEcrNRRfYL843oPiGo5uZ6PQSPmkY/GBdoHU6AhLCSYzl0yl84+fTYdOpbHCy5E3qIaDgas16z0FJo5ZQxPHNGRzlVUXhj6BFlSXs1F73ftP07FZVXmn0EwsLBC5DwWWe5okQ/0vUI93/99uoktNSw20TAC2yeexAeff8vbAbgebrvmAkqKj+FmLx4pquCs02dTXUMzWyOv/W8t+fv7OmRj3V5VlUBHjbKnaq2a0rRJWVzRB4FLWHH+49UP6Yz5U+nS8xYP2npBGk1A0hRqK9jOxfX7FFU77acOtUADXJxYXGCgXuuuA8fohz1HebsAJfIwsBCDxTJxTDqne4wameLwvXlh4LS1tdOxnEI6dCyX05QQTW25Rzxh9EiaM208TZ04Six6E9ijh3V24Igyt6BwyU1XncOLUk/i06+3cmckcMPlZw3YIPEyYmniBmAVERERQfX19dywHPtGr/9vLW3ddZjdYbesPE/zqFhbInSzH1XC77N+X6NpVaXsxzOos6GERtz9PQWmWW/Y3NGh5xUXursABJXARYz8wMFQ/vHPqH7bixS1+OcUd96TVh+DPNbs3yeRQddAaXdvpqC02WQv1A4tQy3QgMkEVgzSsZDWYvmNgCUzZlQaBwwhPQc5o56Wn+gKYK8Y6UhHT+ZztGZufilHNKsgtmDCmJG8uEYVK+ybCgqYK7/dto/nCkR847267PzFHOzoSZa70Wik1V9+T5+ZopwvP/90OvuM2b1qjEdZqgBCetOV57BLcOsuJSoWq1ck3rt6VSWUPYSgUj91f/38fDm4AOXy3nh/HUc1oj0Z3Jy4YAaadoRyhYiLRLnC3mgr2sGCitZranCTvdCqQAMWG9h7x0C03+Fj+XTwWC4dPpHPVZAOHs3lARC4wlWPkHc5IpnS0xJcvvKRK4IcWVRnyikopZz8EhZUCKslcdERNGFMOvchxoIoMFAKFfQE7yECG+GtUXNxb7rybI+rZWwwGHgbSDVALj9/cTdBHQhuK6oAFgWEFeKClRhcG1W19XTJOacNS76ZvaoqddQoEzyEy5Z2auNHj6RH77+RPlm3hb76dhfvK6GSD9zk5y6Zw7mMAypXWLyXV3XWVrHNx01VlLKWDrlcoCMIDw3hPXgMrOCLyyrpyIkCtoBQwxftvixFFqDKUXpqAifDpyUnsPsYxR2EoYPrrLa+ibcxEMGdX6QMpBH1BOk+yEeGgI7LGslFJgTrIKL1oy++4zS8rkYdp9GSBdM8zhOja++gV9753FxkBYbIUFIS3VpUAcTzukuXc24del2iT2NldR2Lra1i4mxVldrVIKUBFNJHOTF0k5g3YwLvGyKICcnc3/9wgM5fPo97VfbXZDggfjx5+fhzGzh9bZ7VHq4tJ76ySyqNo64dFDDAOOv0WZyzh8ldqWNbSnmFpbxXh+sJY4epLixAlaPkxFhKio/mIIeEuCgeuN+TXGoDsRQQmY1oU1QwQkoYotcRVGQtzxbvYXJCDHsNYF1ljUymxPhoeW9tSJNBcwcsriEmAHMCBBUeG0/0ePzzP6vZYofb++aV59KcaeOG9JxuL6oAX7QLz1rA7s433v+SLTWE1d9540Wcf+RqaTUd1Sf56D+Ilm8QiPtvv5L2HDxJ73/2DYvB2x+t58XG+cvn04KZE3sNzEGDcnSB0RXvZhdwT1HtbKmltkJlgz949DJyNxDgkp6WyGOpqfJRc0sr5RUqnWfyuQNNBb+nalEG5PhZgj1aWLbKiOBrEiUHYyLDuewg3MvuKAywOBubW6imttFcfhFeo6rqOqqoruOtCSxaelvcYGGCaxfeAAx4A6TurO0gZ3n9d7tp3bc7+RxgC+PKC5dwIwdP5Fh2AefhYosHe+x33XgxV2AbKh4hqiqoiBEfE0kvvPkJh9g//o836YbLz+Y8RVeqqtRX5K8tYNJG6sjk8Rm0efsB+nzDdg7WQUsrWK9IPVkwe5LVvCz0U4Woolxh2ORLu/2sJXsTooc4Mtgv0jlr7moN9lMRJYyhgkkLFhYWbqrFVV5Vy8LR3qHnn1mmdViC9xxpDCjwgA4oKD4PVzIiMLmub3CgubYvolbhbXGECMOyRGEJ/K2wfmBNNrW0cmWixiaMFt6fRpWn+vomqm1o6tadxhpYzOH7mRAXbbbwkWsOixRbOMLAweewccseWr95D39OAO/nhWct5DnAHRdw/YFtnS+/+YGbJOAcwYd33XiRZv2NPe5KzcpIUdJN3vyUTuQWcYIzglLgR7eHO9geVZXUakqDsVQtgbt3ycLptHDOJO7PiobasCDe/ng977+esWAqLVkwvVt7q4BktQjEnl5dv8FjziRPBmKHvFcMSyAqeH8rTAILC63GZLFhUQNBgkuO3Z+mIu79gTmR6/uaavzCeoM1jAEhglDBrQUr2wf1flE9ycuL/51a/BdWpEGtAdyp1gE2VWDq0PNCAANVmnQ6pSaw6jocCFyXOSyE84Bjo8IpJjqCJ7LYqAhKiIvkxYSn7efZC1w/X3+7i/dM1QAuuMfRXWfWlLEeWcNYdfe+umotN1lXXd+ovKdlsQ+PE1WAfa37br+Cuy6s3bCNk3whsDdfeS6LrrO7f9urTJZq7NBEVQVl6BD5etrcKbRlx0Hec6msqadPv95GX2zcQXOmj6MzFkyjjLSkbuUKLYOVcG4OUnKD/VR7AIFT91atAaFCAAm++OgEg3q+jc2tfITgYjSbrMLWVh3pOzs5/UexGNvJEWBhBqsZdX/DQoK42Apb1lbqBON7Jzm/9gNWF7YbYJkeOJpjTg2DuxyRrDMnj/HYRYvRaOSYh7c/+pq/P1h0rrx4GS2aPUlza90jRRVg9X7JOYto4piRHPmFgJO//Osdtsywaa+V1ap1VSWDXkf6+oIhuX97A6s1WK5IO0LOJvZfcgtKebWLgaoqp88eS4lePtwhR99QTH4Ryh5ER9UJ0tflE/n4UXDmYk1fl6eA978v0e05ScACaTMJaptOx6KMwdZlu55/jgHrEwKMSVfZt1SsUxUvL6VjDSZcWLMQPhxVSxeLLkxCAQGwhP0oEDWBA/3ZIheRdDwoZLJl50GuFKY2A1CLNyDCH/uEnujmVcFCFa0x9x46aV5koBesveJpPFZUVcZkptEj993IOUqwWDd8v4fTTa69ZPmQS/vZo6qSHuk0sBD9Q8knJI7sASZX7DNjoOA4Vr67DhznYJz/FpfTTT7xFEellLvra8o640Z2JTWbCugHjVyoaZELwTqYJBWx8+vmnhc8A7jmsW21dechnq/UQhcIdJs/cyLXMIa715MxGIy0+Yf9XLIWe/9YKJ63bB6dt3SuXReDHi+qAK4rpNjMnjqO/vvBOt73Qmk/VF656sIlQ+rN6mMSVUNbPRdtGKrgdBXSHzUsq89R6ck8rmpewl9grIbLqpIozruUtnyxil7d1k5zZ0ygKQWf8+NDPHw/VRDsBbwLOfmltG33Ydq57xgHhqkgghfbN1gIe3ozAJBbWMpZDUiVAYjYR7MVBCXZGxFVCxDB+ej9N9GadVu4sgbcBSjAfs6S2bwnMZgQfq2rKql9VLXaT7UVRJ/ClXTm4ll0/JMyoq27KcmnjL6vbaAv1m+m0d7fkL8X0Z76BJpcVUvxsf27MAVB6F9I4SHadeAE7dh7tJt7F5Hhc2eM51aGwyEWruIKX/3lZtq84wDvKWObApHOSxdOH7b9ZBHVHmAv9YoVZ3BELFY6KJKAgCZYaBedtZAWzp40oA9H66pKln1UHQH+nhFTl1Dh1t9TVmgd/fj8C+jY5vfJv6idmo0htGpzKa3a/Ap/yadPGk0zJo2mlKRYj97TEYSBgCjsk3klXOEHA54zFexrT584mqNWUTkKUd0CcWT6um92ciF8y6IWqGGMALnhRES1F1D7EkUSUCgChaaxQkT93K++20WXnnMad7ewVSi0rKpk6f51FAHJUzk/orOxlKaPiqSM8naqKSLyTltE4/0zOKm6qLSSB6pYxUSFsysdgROjM1P7rdwkCJ4G9vyOnMin/UdyaP/hbI76VkGQ2KRxGTRzyliu4y3u3e57y4iFWfP1FrZSAVr4XbliieaZHLYis1sfQDSxRwEBRYNrtARCQv/z//mYI8hQpWnyuMx+xVXLtBpHW6oA+8Io8NBecZR0JXvNQUoZ86+k+2ZewVWGEDyBCOLDx/N5pQ13OgYmCKywUeQcxc5Rn1WsWMETg2hQ8hIpMAg4QkCgZVcdxHlgEYoCDfieiJB2B9Hs6ED22ddbzZY8Yl8uPfc0nrMdOaeIqNoALCvkcaIi0xebdtCGzbu5qDc6vmBVhPJ++AL09kFqVVXJ2NlBHbX5DhdVtQgERBW5qaiwZFmaEFWGsM+DAbcM9qWxAkcReuRf8mrc1LMRViwmDbRWQyQ2choFwR33RuHtOppdSEdP5LNVammNAsQhTB6XwdYoPDpI+xNOtUwRqIXKb8ilB8iFPnfpXFo8b4pTeMEc/wpcCKwesRI687SZ7LtHqkluYRk999pHlJIYS+csmcMRxD33ObSqqtRRV4BEVfLyDTTnvzoKlCts3PsO1W1/iVN8fKPSySdU6R1rCYK70MMSAxMLXMJYmUNo0RQcq8zvtu/nAZAGMCYjlXuYjs5I4eo7guBq4FpHVSN0NjqeXUjHc4q4qIcl2B8dN2qEUuZyTIZ01ekDVPHCHIFGAOr7iGIj5yyZy3n1zmTJi6gOAlSKufyC07lzCTbHN23by7VcUUQC9SQRIbtw1iRz/0at3L/myN+YTC4350gMOmX/gvRKPVF0rcn982iKW/EMhU262Oq/gSWvdn05d8lc/qIczynk1moICCsqreBauRgIDFMtWbXkH7qRIOhJVvCCs4HgGETpIuUFi8XsvOJTLFEstnENj81M44bp6McrxTP6BvukMF42btlrrl0Mb9aZp83iMqrO2FTBy2hZWsWFsbUruz1A2atNW/fS+u92mb9ICOVeOHsyV2gKrdtDRS+fw/uQ6fcrYjEY6ra+QBWr76GQCSso5Yb3yVE0HvyYSt9cyZV5uqO4v5OuW9WrsPYF9mJP5BTTsZxCLhuJPSfsPVkC9w46lKjdYjDiY6I8tpap4Jj9PMRWIAcSA94q9N21dq1mjEjkikajM9I439uZLCpnJq+wjGMwduw7au5eBPc4Uhvnz5jgkAYLtmqMWKoagM4h5y+bR2cunsnl/NBiiQtaf7eL1m/eRXMzA+g0DaoqOUPkr9HQSZVr7rMiqPxTFtbKNfdT6IQVA25Sjr3YaZOyeACU4MspwMq/yNy/FE3Cs/PRz7TE/O+wgEEJRYjtiOQESk2O4xJkYgUIQwUxASVl1bxtobT3q6CikkpzkXpLsLfHvV25YEoKBzM6wx6fq9Ch13O2xcbv9/D33rKwBeZWpOi5Qu1i+cQ1BCXjUB5s8dypHNUHQT14LI92Z9fTaT5KVaXP122kBXNnU2REqEtG/rbmbiZ9fXEfjzCSvr6IHxc86vQh/S64z+EmwwCwBNDhRbEOILJlVFBSwbVv4T7GsHS1QVix141m4XxMiKXY6HCX+GIKwx8Ag/Z8JeVVVMKt+dAgvZJ741rz5WEhNzLV5C0xHdHkWyLZBw5aI2K/dOvOw+YqUfj+Ij5l2aIZ/N66EiKqdgCuSOSVYcBi3fT9HurY5kd+1EEbv1pHq9fvpinjR9GiOZM5tcTWBG5nEFVbrW2tah33fF8RyIQxb+YE5fd0dlJZeQ3lFZWxJVFYWknFpVXmnqY9+5bCckDBevTphOjiuRJiI9m1hALxgvuCnS50+oF4YnFWVllr7nlbUV17ivvWsnIRipnAAwIhHZmSwC3rZMthaB6AXftP0Hc/7KeTuV2LdHQzWjx3CkfyumpNaxFVO4OJGy2Gco6nkb4mh8YmBdD2UiOXQMTAF3bO9PE0f+YEDuDpbaVrNBioA8X02f079EL/g8XXlB6k1eOGCoKWMNlhEE02T541dQ2KqJZWcUN6nGPyhItJLUzRE0QTQly5x2d0RLeBqixSvcb5wedbW9fI6SvqQN/ayup6tjqx2OqrmhoWW/BqWA5XndydDYPByIGJW3cd4gYd6M0LMOchJRG1i5FS5OqeJBHVYcIvPJlF9aplE+m8xCW0+YcDtG33EWpoauG9V4zkhBi2wOZMG0cxUd2L+KPNmlGv49ZqvhFpDvs7gjIWkW9ECunrsadpbWXvxT/H4xwFvqR4/zDgEbAs/4ZJtrSiRrFQKmuovLKWLZfGphYOMsOw3K9VQYcLuOwRjYw0n6jIMIqOCOMjBBcRiVggufqE4MzAK4HesnUNzVRX30i19U28eIKIosk70rPqG5usumstgZsWi6dEbrMXTUnxMZSUEM1WkrhvtcVoNPLCdvveI7R995FuaUVYvCL3H6Vf8d67CyKqw4RlWk3y1Fguo3XpeYs5XxPJzLBaYVF9+Pl3PLA5j8ogM6eM4QvO7PqNSicvH8d9bAg+QtqMEv2LCchyBlMmpLgVTw84SGk4gOBhMsVAgr0lsGBgyVRaWDVs6dTW82SNCEQcLeuw9gQTMoQVlk1EGJp0h1A4jiE4D+IjGngjICs0JJDdzZ48iWORg8Az7KM1N7dRY7OysGniBU4LNTS28KITQoqiIXDd2gKqdsWYPAxxGCbPA/JAcUTsg2BfSsuruSn4zn1HeRGrgtZ0s6aMZeMBaXLueP2LqA4T1qoqwXWJyR0DOVjoRLFt1yFOJ1EjXN/9ZCNffIsjj1CMgyN/VThd5rpVHAVsGbQECxWCOph0GkcDgVMiiBOsuq1gAamiamkd1TU0cRNkTP5YlWPyx+gKmeod7MmhoAhGSFAAH4OC0ABcaQIOd6Q6AjD8lSbhSCcI8FOOyvAhPx9f8vH15mvKHhOV0uC8k61Fbn7e0ak0Q+/Qm45Kg3QeOjRNVwaCyLBgUUY7X+ctLW3U3NrG9w00oQ8ueETZwjsAzwF7DSLCFA9CVBjFRkXwwsUdJ2tnBtc+jILdB45zBK9lLAOuScSXoMA93LyOSIcZTtz7r3Mi+quqhAn1tDmTeWCSxp4DeiYikRwj2WsLxXgT7SnsoD1fbeW0E+z3OGrygHAibYajgRvLeA8VLl9ntFCHCsQPEzcGFji9WV2KZdXMCes4qpaW2bXc1MK5uLC4IEYQKpzbaoHZClzVEB8MWOfeXl7k7ePN1wr/z3TJ4Laapo4DzjHwt3QalCMGhLS3IB4twKJBseAD2dIPDQnmI4qswNIPDw1h9zrEFFa+BAg5B7g2sPBX40MqqurMP8O1h/KjsErRTAMWqqcgojpMDKSqElbgCCXHgDWE9k/e6z8kaiUqaAqiPeu+p9Xrvrfo/jKKE8yHOy8TAjrUtBl3AeKFz41TpWxojgHrDm5PWG7NLTrFgmPrrZ1aW3XUqlMsO9XqgwWII8S4vb2jy0rU683J8SoozM7F2ZU4ELsA6wMWh79psPUMS9pkUasWNixvHIPZ+g6g4GDFIoeAhsBKDw6UClkuBHLHD5/I44YZqN9tuSDE/DN+9EiaNWUMTZ2QxZ+xJyKiOkyotXoH2v4NQRUQ17yd7dTeSjRz0XIyVCee0v0FdUTHZ43kOqKIoOsZ6CQ4FxAh1fodKrAi9Z160uthVSoiy9Zlp8naNBqosxOWpmKJqlapCluwXurRiy1Bb68uSxeih3NMmsq5j1iLHuXWreJmGAeO5rLXzHIRBwsUnbqwuEd6YKCpNKsnI6I67JZq2aAu7I4ape7v9PnLaG7cGM7zOnK8gPYePkkHjuSwm1F1w6ipPEqh7nQaMyrVKWtkCtoAgfP39iOlAp7nuNkE+wDrE110Dh3P44HtKEsQ+KXGgqBnqXgauiOiOkz4mEQVVZUM7c3ck9RWOpvKydjeDH8rR/8CiKRa0k/tzYjuL1hR5hSUcLoIBqxYtZA3OmKgl2nmyCQpnyYIAoOAMQRHHjtZSEdOFnBjC8sAMrj3sb00aVwmW6MoniL0jsysw4R3QDh5+QWTsaOFg5X8Y5X6trbQlU4zgrx8/a1aKqgzioEaxNibQ+eXw6aVJtzEqFqCgUbrEFQU90a3DLRYQ9FvEVlB8Jx9Ubhx0bji2MkCyi8uPyUQDUGQ8HIh2AiC6u4Ru1oi79Qwgb0q3/BEbt8GF/BARLW9amDlCREIgvxWDLU5Mlag+AIdPVnArmIcMQD2yjLSktiVw8XARyZzlKUgCK4PCi4o7ehKuL8rvFo9m5PBpTtuVBqNGz2Sj1JFavCIqA4jvmHJLKoDDVYaSs1fiDm+MBioqcnNkytq6Gi20sMUzZOR6gH3D4ZKUnw0d9rIHAmRTaLEuBgJThEEF2gMUFhawX1dc0y57tYKlqAIBizQsaNG0NhRaZxJIGiDiOowMthm5WZRjR56zV+ILOqbYqDXK0QWZfrQVBmrWKxmsRfLpfwqaricIpCuHILgXFh2bUJDidyCUu7aBGG1BN9R1BXHls/o9BReLOO7K9gHEVUHV1WyhXZT5K89qinhC8fdWuKiuak6QIk4rHQhtFjp4kuLnElLlzFAcj7v5aYo+7moRiRCKwj2E1DsfxYUoa9rOXdlwvfS2vYPghFHjUimURkplJGWyLnCwvAgoupEVZV6TaepUtJk/AawDzsUUKNWDZkHyEtDrlouVsSmgZ6TcBsj2hhDBQnfaJOFlTG3y0qK40YBEuggCLahti1EM3S1oxIGCoD0BJG5+K6xByktkWMjUONYFraOQ2Y6J3f/GlpqOA0H+EVnkCNASg6+uBjYlwWo9VpUWkX5RWWUX4RVcwULbXNL2ykNw7EXiyL2iChMTYzjpuHJiTEUFx0p7dQEjwXVsMoraqnY3Bi9isWzt6YNqoCOSIk3eYgSeRtHvkPOhYiqk1dVajftp/pGpJK3n/NE5KLTR+aIJB6WkwS6UyC6EIKrHCtZaBEchYFi2ypIGkfOGxqFo/0WNyCPi+b7xF0luAuo91xWUWvOHcd3BPEKVTV1vdZURrlL9vhwc/R4PmJhKgLq/IioOnlVpaFE/g43yHXt2emFO7c0NFNRWaWpYbiyIsfEgtq13EjcoqOF5aSSEBvFI149xkWydSuuZMEZcz8rqpXevCgsjz692APF7b4aJqDMX3KC0gwd3puURGyZxEpKmwsjs5OTV1VyJVG1BvZ21ELzqMaighV6dS0ahldTaTmahddQKZqGV9RwRxeURsOwdCOr4LniYyK5vjFSA9SBtICoiFBpFC5oDrwwaPcH1yz32bUY6L2La7YvUOPZ3BQ9ocszgxZ2sv/pXoioOnlVpfZqNfJ36Ok0zgT2WdX8WXTZsYTdxZU1ykrfvOKv4yM6taiCS1Rk9XnN/TUjMcIoKjKMj9ER4RQVGcrRkTKRCSpKC74WLpKArlAYSr9ctX9uI/fT7a/3K9rXKZ6VSMW7AhE1HaX2tucgourkVZVc3VIdDIggRlUnDEvgSka6T1VNA1sHqqVQbTrW1DdypLLaTLw3EPDB1nN4KPfojDAflZ6d6N+JPp6YJMXqdV2Qr6n2s20wNY/n0dDEWxI45ybzDU2ntM/r7bqJjgpXPCPqkYeyOPSknqFC74ioOnlVJU8U1b4WJSx4oSHdAqRU0OasrqHZwsJooJraRrMFgqPaIBz7XpZNla3/PqLQ4CDOx1WHcjvI1FQ7iG+HhqA/qNJkGwFWYgVrDz5bpJrAi4GBXrTNzcoRrldu9m7RDB5iihrYtoKPDKX54OWIRku+SNXbEcZCinOkmslnK/SHiKoTp9V0ttVTZ3OlW7p/7QGsSp4EI8MoK916p3CkAtXVw0JpZGulzsJqwWgwDUzWcPfxJI39svJqG1+DFwUHovm2qSm3qTm32qwblakCAwK4/y038vb353N/NPi2GIiuRkCWq0Z7wqsA64+bqnd0cGN1nWngvE2Hc6UBuzI6qK0NjdmV5uzKEc3blQbuOO/P/drb54HFEHsg4I0wDUVA4aFQ9vvhpZAWZoIWiKg6cVUlWLT8b0ITyDtAyoppAcRK2fOK7PNxEARYPw1NzdTYBGFV3IhNJpFFmgRbR3zexhM/BIT35/Czlr4DV2zFx9ubxdXP14ePvr7KudowHEc8BuKL5uFqY3FvbjbubWo47kVe3t4EG0sxtBRrC+ddQtXVvBzDYDQ1ODcox06MTotjZye7V9EMvUPfybc7OnCupw4WUv0pRdu1AAuQkCDFMxAaHMgeA2UEU1iI6lUwHUOC+XFSs1oYTtxOVPEld5eqSuL6dRwQJ95jDbe9WwcsspYWHTW3tposLJPl1apjawznyrGdLTac60yWmmrB8bFDb35OFjF+DLksEG+2xP1MVri/YqUHwFIPwH2qBY9jAAUG+nMwWZDpCGsfrnWcYxEhCMMNvCr4/nqkqP7myZdoxpQJXGJv0th0p8v3Goj7V7VUxfXrOlawf4QfuxOHAqxDfaee2tv1ZssPR4gtrENYhJ0WFqJiQZqOnQa2MnE0GnG/yfI04HaXRYpjF14sfNgv5P+ZrFtYeF5eihWMc7aEzVaxN/n5KO5pX1jSPrCkYTn7ckAPcpZhWfv7+7JFLXuRgquBmIz9R3Jo/+FsOnqykJYtVKrJeZyotra20469R3ngi4zODMiPnDwug1KT4h3uChpIVSW1mpJYqp4FrlF/b2VfVRCE4fNyol0eapkfOJrL1eAsQQcgjxTVe2+7nHILK3iFgUo9J3OLeXz8xWYKDw2miWPTaeLYDJowZiTvuThzVSVx/wqCINgPFKA5dCyPDh7Lo6Mn87t1/WGjbGQyTR6fSVMnZFJokD/dd7sHiirehOmTx9Gl5y3mN+zAkVw6eCyXW5YhzH7rrsM84I1COb0JY9Jp/OiRlDUyeVjK3w2kqpJqqdqj5ZsgCIKn0dKqo+M5hXT4RD4dPp7HxWUsQdAbNGHy2AyaOC69m+HV0NB77rtbi6olKGN3xoJpPLAnBYsVq5JDx/PYtEd3FYy1G7bzHlBWRgqNzxpB47JGsODaI53B1qpKENzOhhI+F0tVEARh4CAe4WR+idIL+kQ+t6+0jErHVkvmiGSaOAYezHQamZo45C1CtxZVSyCasEgxLqfTOT/x8PF8OnIin46czOdcRT4/kc+PR+ThmMw0HmNHpVFacpwm1XVsrarUUaP0KPUOjiaf4Kgh/15BEAR3p0Ovp9yCUjqeXURHswsoO7+Eg/ssQQnJCaNHsBbAgEJUuZZ4jKj2BCXqFsyayAMrFxR2P3KigFc0KOKO8Ol9h7N5qCKLggKjM1NZaEemJAw6vN+Wqkrm/dRoifwVBEHoLdUlO6+UTuQW0vGcIsopKD1FRJEWNz4LAppG47JGcnUse+KxotrTekT7JYxli2Zw+gGabh/LLqBjOUV0MreIN7AREYYBkDaQMSKJRmekUFZ6KmWOTOIcO63SamQ/VRAEoTsoxnIyt4Sy84rpRG4Rz9PI5bYEAaljRqXRWHgZs9K4R/NwpnSJqFoBbt70tEQeZ58xh0UWDbePZRfxB4mBKjqwaNXWZPjM0AsRgVKZpmLwqNpj7cO0paqSRP4KguDJdHYaOIMDaS7ZpoFGGj1BWdLRGfAgKl5EdAVyZF60iKqNIosNbIyzTp/FyfllldV0IqeYTuYpA11SEPyE8c22feZIMhR+h8hmpCVRelqCUhXGhqpKqqiKpSoIgidQ19BEeYVlvCcKN25uYSnpdB2nPC45IUbZistIpdGZKRyQ6kyIqA4CRIep7uLT5081XxDZeSXmVRWiilEXlityHFEqIwGsouaElNM4ImqszKPo9g4u3daT9irl3/jFiqgKguBetLS2UV4hsi/KOCIXYoouUj1B6Upss40amUSj0lPYSNE6sEhrRFQ1DHyaOWUMDzUKrbCkkkUWKy+Mypp6zovaV9lI43yIqotO0tO/+weL88jUBB5I5UmJCyd9fQE/j7h/BUFwZZpb2nj7jFMYixUhtdZ2UYltieFtN2ULLYmS4mNcrqexiKodU3jY9WvR9xOdTvILy6n46Haiba9SqFcjGTqNZrfx9zsO8uOivaroR95G0nsH0voduZSW0kJpyfHceUMQBMEZQRZFTV0jz2WFxRVc1q+guJx7G1sjLjqCRiJ2JVWJX4FRAcvU1RFRHUZQnWPSuAwanx5N2duIAqiNnnzgOiqsaKLcojIq5FVcOUU2VfHjqzuj6P3Pv+sWGg5xTUuKo5SkOEpNimN3svSBFARhOEE3pdLyaiouq2SPHAtpSWWvjeFjoyNoRHI8jUhNYBGFgCLmxB0RUXUAllWVwrybaNqkLB4qJV8/TU1fEwUnjKGZcWP4Yq2oqlWaaTfkcsFnFVR9Qsh4SmIsJSfGUgr2ehNj+CJ2NbeJIAjOBXI+y6tqqKSsmkrKq6i4TBFSROFaa5fr7e3FLlss/kekxFMqjsnx3LrPU3A6Ua2qqqLZs2fTxo0bKT09ndyR/qoq+TYraTojJsyhmedcyOdtbe1UVFZJRSWVVFhaScUYZVXcixNHjJ7u56SEaN6vTUqIoaT4aL7YY2MixLIVBOGUXsCI9yirqKGS8mouhlNSVsV7nz3zQFVgaWIxDwFNTYrlLmDJCTHDUkPdmfF1NkG94IILKC8vj9ydvqoqWSv8gMbNCCPHsNzDwH4FryBLFWFVvxAIlEJiNIYl6IcZFxPJbmNYuAnx0ZQQG0WJ8VHsnpa+l4LgniAVsK6hkcoqatn6VEW0rLKGe4daszwB9jkhluwJsxjhYb03A/FknEpUV65cSddccw1t376d3J2+qirZWvgBAgg3L8aU8V2PRbGKyup6Zc+jvIqP+OLgC4S9ED6vrKF9pPweFVSEQsEKiCzqY0J4IcDxMZG8KhXBFQTnF876xiZ2z8LKxLZReVWt+RyN7nsDqSrs0WLPFkQ0hsU0KiJMvvuuKqovvfQSZWRk0D333NPvY3U6HY+BtuVxFnqrqmTs1FNHbf6Q0mmwlwpBxLDcq4Vli1wwXqmahLWsUjnHShX1jtXOPdZWqxDYuJgIiouONIs53MmopQl3syAIw1PvFsVmsHDGUR0V1XVUVV3PXqregKcK31n2UqneqjhsDUXLwlkjhn0mvPjii2nTpk2n3P/HP/6RfvKTn9j8PE888QQ99thj5Kr0VlWpo66AyKAnL99A8g3rSsfRAnxhoiPDeaBJe7ff26GnimoIrLKiVVe4+OJCiLF3i1wzjFOfF5HJoRQbpQgsj+gIiuHfFUbRUWEU4O/6ofKCYG+w8MXitqa2karrGqimtoG3eKpq6/lYXVNPjc2tfT4HgoXw3WMvk8njpHqfsBC2R0tLwYGi+uKLL1Jr66kXRXR09ICe58EHH6T77ruvm6WalpZGru7+7XL9ZpLXMEbvIrgAtYsxrAUxVNc0KCthXiErR3XApVxX38QDJRutgeg/uJFYZCPDKDIijG9HRYTyMTIi1C1y1AShL8FEk2zsa9bWNymjDueNnN9ZCxGtb7Rams+aqxYCCc8RFrMQUOV2JC9iJRjRg0Q1ISFBk+cJCAjg4aqoVmjPQCVnLKTv7+en7LMkxFidKFCOEStpCCxW1lU1DbzKxqoakwWsXFRVwUA+W2+gvR4qU2HA8kVeLp+HhSi3w0IoPCyYxVfcVIJziWUb1Tc2U31jC9U3NCnpb41NVMdpcDgqi86+9jQtCQ0OYnGMsfT+RIWzcOLo7KX6PBnZCHO4pVrm0i3fIG6o9ISBpgHWwOq8th6uLItVeb2yWq8zHSG8aK/X2lZDpRU1ff5OtN3D70P0Ido8YYRZjpAgCg0J5j2isNAg2e8VBrVvicViY1MrV0LjY1OL6VwZDRiNODZzRxVbgdcGi8WoyDCKMh3hvYmKULZLoiJDZbvEhZHZxkH4mETV0FZPhvZm8vYPcVpLdagEBwVQcJB117IK8nCxmq/FKh9usYZGXu3jPkxcfGxqZtcYVvu8v9RL+bOeBAT48cofIhuCY3AgheA8KJAnuGDTEbeDgwMoODCQgoICWLzFInZtCxLXS0tbGy/s4CmBRYnR3KKjZhybW81H7FXiMRDTvoJ9egPXETwpqmclMjyEIsKwvaF4XpRjCHt+BPdFRNUJqiohWEktAIHcVXcTVVtAHm5iYDQlxkf3a0GwdWCyEHCE9QCroclkPSgWRgs1tbRyigEmVgxbRdgyUhLiilQjZfiz6xnnOOI185GHHx9hYUDE0XkI5/7+vnzu7+8n+1w2iKC+s5Pa2zt4n769Xc+fdxsWUu0d1GY61+naeREG7wZ7OPi2js8hngj0UbweOn7OwYLPKzQ0iPO34f1QPSHwjISajqqI4n7xiAjAKa+CoXwRXLmqktFgoI4aRVT9YzId/RKdEghVXIyS3mNrJGVTcxsLb3NLK5/zEVaL+djG1gomZMWSUSZjVJKBQGNoAUQaIovJF4FhsIT9/PzIz9eHz319ffhnOCrDl3x9vJVzHx/y4eHN9+EcUZ4+3j7kjdveXuTt5U1eOPK5F19j6n0ARrcX8X+U2+RFRjJ914z4v9FcAAC5zngPMLAwMfDRoJwbDPze8LHTNPi8k/Q413dSR2enctTjvk6OLjcf9Z3sbcA5guDwGBwhovb47uM9Cw4MoGALrwSOoeqRPRi4HUQhIYEsojjH4kg8FYJbiKqn0LOqkr6hmIx6HZGPH/lGuE4ks7OCCRGTJgaKWtgKJnZlj9dk9bQq5y1tyI1WztU9YNVagmWFI1tUJssKVhbuhxABCA9bUNRux7/aPYAQqtY+H1XrH14Bfz8KZG8BvAOK14C9CIGKFwEDIsrn4sYXhhkRVSdKqzHvp0alk5ePfDSOAhOwOjlr59KEK7Ojm3XWAevMZLEptxUrji06vXpuIL1ez9YgbqsWYZd1qFiUuK+bRQmLz2iyOE2vw9IKtDQILfUGfzsPUxERtna9TVavt7fJOlbuh/Cx9ezdZT37WFjWPExWt2qBw0L3Mx9Vax1HPz6HmxzWvLjKBVdFZm4nqqrkapG/Qv9AfNjd6+vrUZ06BMFTkdIaTlRVyR0jfwVBEDwJEVWncv96ZuSvIAiCuyCi6kRVlSxLFAqCIAiuh4iqk1RVQhCJ7KkKgiC4NiKqTlJVCfmpxvZmIi9vjv4VBEEQXA+3i/597tUPaUxWBo1MTaARKQlcJABpAM5eVak193u+zy9qBHn5St1PQRAER4G0trLyGsovLudRUFRO0yake6aoHsspotziKvNtJIaPSImntGRl4BzdVpwhD86yqlJrnklUxfUrCIIwbCB/HN2zuF90cQUVlFTwbeSFWxIeEuCZonr1xUupqrZZeWNKKrnKzfGcIh4qENTkxBhKTYpjocURA+XKHFVVqTVvM98WURUEQdAexK2gMQd0gUW0tJKKSiqorLLWanlMVOmCtxMaAc9nXFSoZ4rqglmTKDw8nM9Rbaasspryiyp4FVJQXE6FJZVcZq4AK5LiCiI6ZP63aMeUmhRLKRDZREVoUeAdlWDsHazUUXWSj37REvkrCIIwFFAitKSsmsWzuKyKjxjoQmQNNEdgTya2DdmjmcC9ay23DhsaGjxTVC1ByTS0G1Najk3k+7AiQTNtiCuEVn2zcR83Em5oooPH8rqew9ub4uOiKCUxlpITYig5IZat3PiYKH5+raoqqUjkryAIgm2gtCf6L5dWVFNJWRULKI6VNfVWHw+RTIiNolRsB8J4Sla8lTCotMKtRbW3fUwEL2HMmDzafD9aSRWVVVJxaVW31Q2s2tLyah6WQFAT46J5fzYpHmIbQ0kJ0RQfGzWgFlCqpariZ2oBJwiCIHRZnmUVNVSCuRgiWl5NJeVVVFld32tnI1if8DamJMUqx8Q4nqdRa9qeeJyo9gY6XGSlp/BQwYdVW99ExaWV/AEWlykfJD5QFEKH8GL0XAnFRkdSUrzSGxTCyyM+2uqe7SmiGp1hx79SEATBufc8yyprqbyihsoqa1hIYYXW1DX2+u/QhQrew2QYN4mx7FXEQI9bRyCi2o9VGx0ZxmPy+K69TnQDqalrMAms8qGzNVtRza29Kqpqeew7rBRzUEFBdQgsrNmEuCh2Q8TouiLKvENiyctH0mkEQXBfWlrbqBzCWVXb41hDOl1Hr/8OIgljBdZmotk7GMNN4p2ptZ+X0U06gmMTOSIigurr682BSsMN3sr6hmZ2UZRX1lCpaaWFc2srrdF0iJZ7f0KhXk3m+3R+MVQ74V4KmXiR2U2tRQsyQRCE4ZoHm1paqaKqjiqrlaGeQ0Cbmlt7/beKpy+CErC1pnr64nEe45DsjMFojIjqMOZCwXqFSwOrMv2Jz2l8/l/4Z5ZrLPXTWG24hk6YgqtwMbHARkdQrHqMjqC4mAiKigjjPpeCIAjDBXI4q2sbqLKmjoM8q6rr+byyup6qaurYY9cXEeEh7KnjERetHOOjKC460q7ZFsOhMeL+HSYC/P3MBSiMhk7K3XEt6a08Dl4M6OpZ/l9Que8MamjR8coOI7dAKbxvCaKT4Z6GyMZgRIV3G5HhYZpEKQuC4Dl06PVUW9fIwllV20A1tRDLBuU2Z0o0dmt0b42oiDBe+GO7S/G6RVBCLLa/Irkoj7siouoAWnM3k76+uNefw3IN7qyhP9wyhbxS5vHqD66TKvNKUFkV4gJHLi7Cx/sKIUe4eHRUOEVHhlNMZBhF8T5xuHm/GBv9zrQnIQiC/UBMSGNTC9XUN7BwYmuKBbSugc9rahuovrG53+fx9/M1ecwiux3jTUd7R9k6K575VzsYdKWx9XHhgQFcWhGjJwaDgaPlsIKE0FbXYjSYB74oqGHJXxTe0y3u9csBocXKMioilI+ROIYrR4gyggTE4hUE53fL1jc2UV19M1uTyF6oq2+i2nrlHEfcxrzQH5gXVI9XdFQExeLctPWEc8wJshg/FRFVB+Dbo+DDYB+HvVTF4gynMZmpVlekDY3NygoULhx1JWpenTZQY3Mrpwdx9F1lba+/C1+e8LBgFlhE20WYjyEUGRbKx/AwjOAB5ekKgmBbnmZDYwsHQkI0YUkq5ziiaA1EtKnPICBLoIURYaEmr5U6TN6sqDD2bIUGB4loDgKZ/RxAUMYi8o1IIX19CUKTrDzCi3+Oxw0Fdv3C0owIpVEjk3utSKKsYk1Cyytb09FUYQrCDIHmL3FD/26h4KAACg9VBBZCixVthOkYFhJEYSHBfI4ALDxWvriCp4HvU3NrKzU1tVJjcwu7YxubWqmhqYW/b7iNc4hmQ1Nzn6kmPUFtc17shivfffY8hZsEFN6oSCyCQ52iqYg7IqLqALy8fShuxTNU+uZK0w6qpbAqAhO34ml+nL3BvgcCCTB6A25mfOHhTsKKWF0Zq6tk/uLjvLGZ93hbWnU8EOncHwi0grhiqEKLFXJoSCCF4BgcRCEhgcqRRyCnGDlrOz/B8+Brvq2NmpvbOJUE9WVhMTa3tFJTC+5XAg3xM3iGmppa+P6BJl7AHYvFKRaqEE1LjxELqElE8R2RharjkJQaB9J48GOqXHNft6Al34hUFtSwSReTq4FLCYndisgqK22ILY6NFoNvN7cMaPVtCSYMWLgIsMIxBMdgnAdSSFAABeFngcrPIMA8gvyVY0AA+fv7iSgL3RaNbboOatPpuCxpa2s7iyTSQnA9Y4HYygvFNmo23ebzFtPP2nSD/t24RhUPjuK9wQgPDerm6VHPETErYuk4JE/VRUB6DUcDN5bxHipcvsNhoToD7R0d1ITVfXMLr+Sxiofo8gq/2WKVj6PJAkC+71DBvBQYEMCTFMpTBuFoGgGm+wL9/fg8wPLo78eCrJz7kr+fnzJM5xLIZV8wVcEqRAxAe3sHXz/t7Xq+JjBwn65DOdfp2nnR1taOY7tJNJXzVr7dzvW+W3W6QS/urLUKU70piocFnpbALu9LKDwwyhaI6p0RF6zrIHmqLgIENHjU6eSJQIiiIzHCBpQ/14Lc3ZZWC2uhy3pQXc84Z6sDEycflYG9LCwj1dtkPRNpUEBU4aJDoBbc6nxucdvP14d8fdVj1zn+HSZXvs8Ht5X74BrnIw8ftq59vJWfeXt5kZe3F3l7efP9PLy8Tfd5sUWjDLwy5eiFrQX832zsdG098NLaiP8r7w+f4bYRRyMZcDTgaOD30GA+V28bqBOj0zT4vJN/hqO+08CRqYg67TQdcbsD53q9cuzs5D1+HvgZxLOjQzniMR16fj57gfcewhhk6eEIhEdEOcIjgp9BNNk7wh6SABZM3C8CKQARVcGlgEBFhGOEDPjfQhwwSbe1dbCgtpmsFp3JYmHrRbVwdO1s+fBtkyVkaRGxVdTewSKv+nogJq2d7dRKfVeTEYYOFgzwEASwp6DLiwAPg7+FdyEwQPmZpWdC8Up03cdbAwEBHptXKWiLXEWCR03EAf6YbP0HJcq9CXWHyYrSteu7rCu2tOCi7LK8zBYZW2h6k+UGC07PgoyfsVWHo0Gx7NgC7FQsQtynWn6wHFULkYdqUbIlrg5ia5ItUJPym+08y10fk+mqGrCwdvl/JktXtXphDStHxVKGxYzbsKhxH1vQqnVtus/XZGXDCsd9qjXe7ejrw4slPposetXCV6199QiBxBH/VvYXBWdERFUQhmoxmfZWQxzTaUoQBCdCIisEQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEATBHUV19erVlJmZSb6+vjRt2jQ6cuSIo1+SIAiCILieqGZnZ9PNN99MTz75JBUXF9OYMWPo1ltvdfTLEgRBEATXE1VYpRDUK6+8khISEujOO++kPXv2OPplCYIgCILN+JKTcMEFF3S7fezYMRo9enSvj9fpdDxUGhoa7Pr6BEEQBMHpLNWLL76YIiMjTxnPPfec+THt7e309NNP0x133NHr8zzxxBMUERFhHmlpacP0FwiCIAiCdbyMRqORhpHy8nJqbW095f7o6GgKDw/n8wcffJDWrl1LO3bsID8/P5stVQhrfX29+XkEQRAEQQugMTDg+tOYYXf/Yr+0LzZs2EDPP/88bdu2rVdBBQEBATwEQRAEwVlwmkAlkJubS1dffTWL6oQJExz9cgRBEATBNQOV4BJGsNJFF11El1xyCTU1NfH9ISEh5OXl5eiXJwiCIAiuY6muW7eODh8+TC+99BKFhYWZR35+vqNfmiAIgiC4lqUKC3WYY6YEQRAEwT0tVUEQBEFwdURUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjRFQFQRAEQSNEVAVBEARBI0RUBUEQBEEjfMlNMBqNfGxoaHD0SxEEQRDcDFVbVK1xe1FtbGzkY1pamqNfiiAIguCmQGsiIiJ6/bmXsT/ZdREMBgOVlJRQWFgYeXl5OXQ1A2EvLCyk8PBwh70Od0LeU+2R91R75D21D87yvkIqIajJycnk7e3t/pYq/sjU1FRyFvDhyxdLW+Q91R55T7VH3lP3fV/7slBVJFBJEARBEDRCRFUQBEEQNEJEVWMCAgLokUce4aOgDfKeao+8p9oj76l9cLX31W0ClQRBEATB0YilKgiCIAgaIaIqCIIgCBohoioIgiAIGiGiaidWr15NmZmZ5OvrS9OmTaMjR444+iW5BVVVVZSRkUF5eXmOfimC0A25NrXFVedQEVU7kJ2dTTfffDM9+eSTVFxcTGPGjKFbb73V0S/LLSatCy64QCatIXLw4EGaPXs2RUVF0QMPPNBvLVOhf+Ta1JZsF55DRVTtAFZUuBiuvPJKSkhIoDvvvJP27Nnj6Jfl8qxcuZKuueYaR78Ml0an09GKFSto5syZtHPnTjp8+DC9/vrrjn5ZLo9cm9pyxIXnUEmpGQZeeOEF+te//kX79u1z9EtxaXJzc9m9htrOOE9PT3f0S3I5Pv74Y7rllluoqKiIgoOD+Zq8++67afPmzY5+aS6NXJv25QUXmkPFUh0CF198MUVGRp4ynnvuOfNj2tvb6emnn6Y77rjDoa/VHd5TTFrC0MCkNG/ePBZUMGXKFLZWhaEh16b9aHexOdRtCuo7ghdffJFaW1tPuT86Otp8jkogISEhLrMf4ArvqTC0jh+WAgDLysfHh2pra3mPVRCcjUdcbA4VUR0C8PX3xYYNG+j555+nbdu2kZ+f37C9Lnd+T4WhgUjKnuXeAgMDqaWlRURVcDo2uOAcKu5fO4F9lauvvpoviAkTJjj65QiC2eKvrKzsdh96RPr7+zvsNQmCO82hIqp2AO5LhNdfdNFFdMkll1BTUxMPiQkTHA1SabZu3dpt4kJEsLjXBWei1YXnUBFVO7Bu3ToO/njppZcoLCzMPPLz8x390gQPZ/Hixbyv+tprr/Htxx9/nJYvX877qoLgLKxz4TlUUmoEwcP45JNP2K0WFBRE3t7etGnTJpdyrwmCMyOiKggeSFlZGe3atYvTa2JiYhz9cgTBbRBRFQRBEASNkD1VQRAEQdAIEVVBEARB0AgRVUEQBEHQCBFVQRAEQdAIEVVBEARB0AgRVUEQBEHQCBFVQRAEQdAIEVVBEARB0AgRVUHwIEpLSykiIoJbaam9KhcuXOgShcoFwRWQikqC4GE888wztHr1anrvvfdozJgxXPt32rRpjn5ZguAWiKgKgoeh1+tZRIODg2nu3Ln07LPPOvolCYLbIO5fQfAwfH196dZbb6UdO3bQHXfc4eiXIwhuhViqguBhoJ8qWr1NnDiRQkND6YMPPnD0SxIEt0EsVUHwMB566CFasGABiykClj799FNHvyRBcBvEUhUED+KHH36gpUuX0qFDh2jkyJH01ltvscjidkhIiKNfniC4PCKqgiAIgqAR4v4VBEEQBI0QURUEQRAEjRBRFQRBEASNEFEVBEEQBI0QURUEQRAEjRBRFQRBEASNEFEVBEEQBI0QURUEQRAEjRBRFQRBEASNEFEVBEEQBNKG/wcsUgpD2uiGVgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "梯度下降终点 [-6.72989676e-02  8.04354857e-05] 牛顿终点 [0. 0.]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 目标函数 f(x, y) = x^2 + 10y^2\n",
    "# 梯度 g = [2x, 20y]\n",
    "\n",
    "def path_gd(xy, eta=0.08, steps=20):\n",
    "    xy = np.array(xy, dtype=float)\n",
    "    hist = [xy.copy()]\n",
    "    for _ in range(steps):\n",
    "        x, y = xy\n",
    "        g = np.array([2.0 * x, 20.0 * y])\n",
    "        xy = xy - eta * g\n",
    "        hist.append(xy.copy())\n",
    "    return np.array(hist)\n",
    "\n",
    "def path_nt(xy):\n",
    "    xy = np.array(xy, dtype=float)\n",
    "    # 牛顿法：H = diag(2, 20)，H^{-1} g = [x, y]\n",
    "    # 所以一步更新：xy_new = xy - H^{-1} g = [0, 0]\n",
    "    return np.vstack([xy, np.zeros(2)])\n",
    "\n",
    "start = np.array([-2.2, 2.2])\n",
    "pg = path_gd(start)\n",
    "pn = path_nt(start)\n",
    "\n",
    "xs = np.linspace(-2.4, 2.4, 200)\n",
    "ys = np.linspace(-2.4, 2.4, 200)\n",
    "X, Y = np.meshgrid(xs, ys)\n",
    "Z = X**2 + 10 * Y**2\n",
    "\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.contour(X, Y, Z, levels=[0.3, 1, 3, 6, 12, 20], colors=\"#64748b\")\n",
    "plt.plot(pg[:, 0], pg[:, 1], 'o-', color='#d97706', label='梯度下降 20 步')\n",
    "plt.plot(pn[:, 0], pn[:, 1], 's-', color='#16a34a', label='牛顿法 1 步')\n",
    "plt.legend()\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.title('病态山谷：牛顿法一步到位，GD 之字形')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print('梯度下降终点', pg[-1], '牛顿终点', pn[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "70129e61",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GD 终点     [4.89447037e-02 4.38739013e-05]\n",
      "牛顿终点    [0. 0.]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def path_gd(xy, eta=0.08, steps=20):\n",
    "    xy = np.array(xy, dtype=float)\n",
    "    hist = [xy.copy()]\n",
    "    for _ in range(steps):\n",
    "        x, y = xy\n",
    "        g = np.array([2.0 * x, 20.0 * y])\n",
    "        xy = xy - eta * g\n",
    "        hist.append(xy.copy())\n",
    "    return np.array(hist)\n",
    "\n",
    "def path_nt(xy):\n",
    "    xy = np.array(xy, dtype=float)\n",
    "    return np.vstack([xy, np.zeros(2)])\n",
    "\n",
    "start = np.array([1.6, 1.2])\n",
    "pg = path_gd(start)\n",
    "pn = path_nt(start)\n",
    "\n",
    "print(\"GD 终点    \", pg[-1])\n",
    "print(\"牛顿终点   \", pn[-1])\n",
    "\n",
    "xs = np.linspace(-2.2, 2.2, 200)\n",
    "ys = np.linspace(-1.6, 1.6, 200)\n",
    "X, Y = np.meshgrid(xs, ys)\n",
    "Z = X**2 + 10 * Y**2\n",
    "\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.contour(X, Y, Z, levels=[0.3, 1, 3, 6, 12, 20], colors=\"#64748b\")\n",
    "plt.plot(pg[:, 0], pg[:, 1], 'o-', color='#d97706', label='梯度下降20步')\n",
    "plt.plot(pn[:, 0], pn[:, 1], 's-', color='#16a34a', label='牛顿法 1 步')\n",
    "plt.legend()\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.title('病态山谷：牛顿一步到位，GD 之字形')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0125ff72",
   "metadata": {},
   "source": [
    "修改参数，把10改成5/25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d9a9b700",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c=   5  GD 第15步 |y|=3.932e-11  (牛顿仍一步到 0)\n",
      "c=  10  GD 第15步 |y|=5.642e-04  (牛顿仍一步到 0)\n",
      "c=  25  GD 第15步 |y|=1.722e+07  (牛顿仍一步到 0)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def path_gd_c(xy, c, eta=0.08, steps=15):\n",
    "    xy = np.array(xy, dtype=float)\n",
    "    hist = [xy.copy()]\n",
    "    for _ in range(steps):\n",
    "        x, y = xy\n",
    "        g = np.array([2.0 * x, 2.0 * c * y])\n",
    "        xy = xy - eta * g\n",
    "        hist.append(xy.copy())\n",
    "    return np.array(hist)\n",
    "\n",
    "start = np.array([1.6, 1.2])\n",
    "\n",
    "for c in [5.0, 10.0, 25.0]:\n",
    "    p = path_gd_c(start, c)\n",
    "    print(f'c={c:4.0f}  GD 第15步 |y|={abs(p[-1, 1]):.3e}  (牛顿仍一步到 0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65ef2887",
   "metadata": {},
   "source": [
    "拟牛顿直觉"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b85f5e98",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "驻点应该接近 ±1 或者 0\n",
      "牛顿 x0=0.8: [0.8, 1.113043, 1.015175, 1.000334, 1.0, 1.0, 1.0]\n",
      "割线 0.5,0.8: [0.5, 0.8, 1.793103, 0.867138, 0.914708, 1.022814, 0.996857, 0.999895]\n",
      "牛顿 x0=0.1: [0.1, -0.002062, 0.0, -0.0, 0.0, 0.0, 0.0] <-- 靠近 0（极大）\n"
     ]
    }
   ],
   "source": [
    "def fp(x):\n",
    "    return x**3 - x\n",
    "\n",
    "def newton(x, steps=6):\n",
    "    hist = [x]\n",
    "    for _ in range(steps):\n",
    "        h = 3 * x * x - 1\n",
    "        if abs(h) < 1e-12:\n",
    "            break\n",
    "        x = x - fp(x) / h\n",
    "        hist.append(x)\n",
    "    return hist\n",
    "\n",
    "def secant(x0, x1, steps=6):\n",
    "    hist = [x0, x1]\n",
    "    for _ in range(steps):\n",
    "        g0, g1 = fp(x0), fp(x1)\n",
    "        if abs(g1 - g0) < 1e-12:\n",
    "            break\n",
    "        x2 = x1 - g1 * (x1 - x0) / (g1 - g0)\n",
    "        x0, x1 = x1, x2\n",
    "        hist.append(x1)\n",
    "    return hist\n",
    "\n",
    "print('驻点应该接近 ±1 或者 0')\n",
    "print('牛顿 x0=0.8:', [round(v, 6) for v in newton(0.8)])\n",
    "print('割线 0.5,0.8:', [round(v, 6) for v in secant(0.5, 0.8)])\n",
    "print('牛顿 x0=0.1:', [round(v, 6) for v in newton(0.1)], '<-- 靠近 0（极大）')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "054db08e",
   "metadata": {},
   "source": [
    "牛顿法和割线法解的是$f'(x)=0$，得到的是驻点；  \n",
    "驻点不一定是极小值，二阶方法不保证找最小值；  \n",
    "割线法不需要二阶导数；  \n",
    "牛顿法解方程对，但做优化可能错（可能停在鞍点或极大值）。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fa1209c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "牛顿一步： [1.2 0.8] --> [0. 0.]\n"
     ]
    }
   ],
   "source": [
    "xy_nt = np.array([1.2, 0.8])\n",
    "g = np.array([2.0 * xy_nt[0], -2.0 * xy_nt[1]])\n",
    "H = np.array([[2.0,0.0],[0.0, -2.0]])\n",
    "xy_nt_next = xy_nt - np.linalg.solve(H,g)\n",
    "print('牛顿一步：',xy_nt,'-->', xy_nt_next)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3e949770",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GD eta=0.08\n",
      "第1步 [1.008 0.928]\n",
      "第2步 [0.84672 1.07648]\n",
      "第3步 [0.7112448 1.2487168]\n",
      "第4步 [0.59744563 1.44851149]\n",
      "第5步 [0.50185433 1.68027333]\n",
      "第6步 [0.42155764 1.94911706]\n"
     ]
    },
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m在当前单元格或上一个单元格中执行代码时 Kernel 崩溃。\n",
      "\u001b[1;31m请查看单元格中的代码，以确定故障的可能原因。\n",
      "\u001b[1;31m单击<a href='https://aka.ms/vscodeJupyterKernelCrash'>此处</a>了解详细信息。\n",
      "\u001b[1;31m有关更多详细信息，请查看 Jupyter <a href='command:jupyter.viewOutput'>log</a>。"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "xy = np.array([1.2, 0.8], dtype=float)\n",
    "print('GD eta=0.08')\n",
    "for i in range(6):\n",
    "    g = np.array([2.0 * xy[0], -2.0 * xy[1]])\n",
    "    xy = xy - 0.08 * g\n",
    "    print(f'第{i+1}步 {xy}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "649ab198",
   "metadata": {},
   "source": [
    "GD 在鞍点上，y 方向越走越大，并不是走向最小值。鞍点上：x 收敛、y 发散；\n",
    "牛顿法一步到鞍点，解方程对，但做优化错。\n",
    "二阶方法找的是驻点，而不是最小值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0de2385b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 作业1：改参数：c 改成 50，看 GD的y是否爆炸？\n",
    "#作业2：coding出牛顿法、泰勒展开、麦克劳林、拟牛顿、XGBoost、LightGBM的动态运行图，每个理论方法需附上不少200字的观察与理解，格式采用htmL+css"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce80d8cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c=   5  GD 第15步 |y|=3.932e-11  (牛顿仍一步到 0)\n",
      "c=  10  GD 第15步 |y|=5.642e-04  (牛顿仍一步到 0)\n",
      "c=  25  GD 第15步 |y|=1.722e+07  (牛顿仍一步到 0)\n",
      "c=  50  GD 第15步 |y|=5.697e+12  (牛顿仍一步到 0)\n"
     ]
    },
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m在当前单元格或上一个单元格中执行代码时 Kernel 崩溃。\n",
      "\u001b[1;31m请查看单元格中的代码，以确定故障的可能原因。\n",
      "\u001b[1;31m单击<a href='https://aka.ms/vscodeJupyterKernelCrash'>此处</a>了解详细信息。\n",
      "\u001b[1;31m有关更多详细信息，请查看 Jupyter <a href='command:jupyter.viewOutput'>log</a>。"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def path_gd_c(xy, c, eta=0.08, steps=15):\n",
    "    xy = np.array(xy, dtype=float)\n",
    "    hist = [xy.copy()]\n",
    "    for _ in range(steps):\n",
    "        x, y = xy\n",
    "        g = np.array([2.0 * x, 2.0 * c * y])\n",
    "        xy = xy - eta * g\n",
    "        hist.append(xy.copy())\n",
    "    return np.array(hist)\n",
    "\n",
    "start = np.array([1.6, 1.2])\n",
    "\n",
    "for c in [5.0, 10.0, 25.0,50.0]:\n",
    "    p = path_gd_c(start, c)\n",
    "    print(f'c={c:4.0f}  GD 第15步 |y|={abs(p[-1, 1]):.3e}  (牛顿仍一步到 0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d57b2142",
   "metadata": {},
   "source": [
    "1. 从梯度下降的更新公式出发\n",
    "你要求解的是 $f(x, y) = x^2 + cy^2$。\n",
    "对 $y$ 求偏导：\n",
    "$$\\frac{\\partial f}{\\partial y} = 2cy$$\n",
    "梯度下降更新：\n",
    "$$\n",
    "y_{k+1} = y_k - \\eta \\cdot (2cy_k)$$\n",
    "把 $y_k$ 提出来：\n",
    "$$y_{k+1} = (1 - 2\\eta c) y_k$$\n",
    "这就是一个等比数列，公比是：\n",
    "$$\n",
    "q = 1 - 2\\eta c$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab58f063",
   "metadata": {},
   "source": [
    "梯度下降稳定的条件是：\n",
    "$$|1-2\\eta c|<1$$\n",
    "\n",
    "即：\n",
    "$$\n",
    "0<\\eta<\\frac{1}{c}\n",
    "$$\n",
    "你现在 $\\eta=0.08$：\n",
    "\n",
    "$\\cdot c=5$: $1/c=0.2$, 稳定\n",
    "\n",
    "$\\cdot c=10$: $1/c=0.1$, 稳定\n",
    "\n",
    "$\\cdot c=25$: $1/c=0.04$, $\\eta=0.08>0.04$, 其实已经开始发散了，只是可能还没到特别大\n",
    "\n",
    "$\\cdot c=50$: $1/c=0.02$, $\\eta=0.08$ 远大于它，强烈发散"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
