{ "cells": [ { "cell_type": "markdown", "id": "0dcba429", "metadata": {}, "source": [ "![](Rydiqule_Logo_Transparent_300.png)" ] }, { "cell_type": "markdown", "id": "d28bd31e-2cb2-49a3-960c-21f8818a9051", "metadata": {}, "source": [ "# Analytic Doppler Solver\n", "\n", "This notebook demonstrates how to use rydiqule's implementation ([`solve_doppler_analytic`](https://rydiqule.readthedocs.io/page/api/_autosummary/rydiqule.doppler_exact.solve_doppler_analytic.html#rydiqule-doppler-exact-solve-doppler-analytic)) of the analytical doppler solver described in\n", "Omar Nagib and Thad G. Walker, *Exact steady state of perturbed open quantum systems*,\n", "[Phys. Rev. Research 7, 033076 (2025)](https://doi.org/10.1103/kgsg-3npp).\n", "It contains examples with 1D/2D/3D Doppler averaging along with detailed profiling performance to highlight improvements.\n", "\n", "This notebook can be downloaded [here](https://github.com/QTC-UMD/rydiqule/blob/main/docs/source/examples/Analytical%20Doppler%20Demo.ipynb).\n" ] }, { "cell_type": "markdown", "id": "d5f3cfdb", "metadata": {}, "source": [ "## 1D Doppler Averaging\n", "\n", "We will look at a simple case of Autler-Townes splitting in Rubidium-87 with two optical fields (blue and red). Applying an RF tone at different field strengths causes the central peak to split and shift as we scan the probe detuning. We show excellent agreement between numerically integrating the effect of Doppler broadening and the new exact method.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "aff1ed9e", "metadata": {}, "outputs": [], "source": [ "%load_ext line_profiler" ] }, { "cell_type": "code", "execution_count": 2, "id": "f1aae33d-428a-4ebf-bf8d-709950c8b5f3", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import rydiqule as rq" ] }, { "cell_type": "code", "execution_count": 3, "id": "4f739d94-2007-4a62-a8a7-47fe312b509b", "metadata": {}, "outputs": [], "source": [ "# parameters for Cell\n", "atom = 'Rb87'\n", "\n", "states = [\n", " rq.ground_state(atom),\n", " rq.D2_excited(atom),\n", " rq.A_QState(41,2,5/2),\n", " rq.A_QState(40,3,7/2)\n", "]\n", "\n", "\n", "cell = rq.Cell(atom, states)" ] }, { "cell_type": "code", "execution_count": 4, "id": "a14424e4-403d-4dfd-b36e-38e0b2d5baff", "metadata": {}, "outputs": [], "source": [ "# laser parameters\n", "detunings = 2*np.pi*np.linspace(-30,30,201)\n", "Omega_r = 2*np.pi*2\n", "Omega_b = 2*np.pi*5\n", "Omega_rf = 2*np.pi*np.array([0,5,40])\n", "\n", "kunit1 = np.array([1,0,0])\n", "kunit2 = np.array([-1,0,0])\n", "\n", "red = {'states': (states[0],states[1]), 'detuning': detunings, 'rabi_frequency': Omega_r, 'kunit': kunit1}\n", "blue = {'states': (states[1],states[2]), 'detuning': 0, 'rabi_frequency': Omega_b, 'kunit': kunit2}\n", "rf = {'states': (states[2],states[3]), 'detuning': 0, 'rabi_frequency': Omega_rf}\n", "\n", "cell.add_couplings(red, blue, rf)" ] }, { "cell_type": "markdown", "id": "2e574735", "metadata": {}, "source": [ "### Method comparison\n", "\n", "The analytic averaging method has significantly higher accuracy than the default discrete Riemann sums used by `solve_steady_state`;\n", "the default meshing having been chosen to target sufficient accuracy (~1%) for optimal speed.\n", "This function compares results from different solve methods to demonstrate the increase in accuracy.\n", "We will also time each method for comparison." ] }, { "cell_type": "code", "execution_count": 5, "id": "1fb5b9a7", "metadata": {}, "outputs": [], "source": [ "def compare_accuracy(sol1: np.ndarray, sol2: np.ndarray,\n", " rtol: float = 1e-5, atol: float = 1e-7):\n", " \"\"\"Helper function for summarizing relative and absolute differences between\n", " density matrix solutions.\n", " \n", " Note that sol1 is considered the 'correct' solution in the comparison.\n", " \n", " Tolerances are passed to numpy.isclose for defining how close something is.\"\"\"\n", "\n", " assert sol1.shape == sol2.shape, 'solutions must have same shape to be compared'\n", " abs_diff = np.abs(sol2 - sol1)\n", " null_elem = np.isclose(sol1, 0.0)\n", " sol_ref = sol1.copy()\n", " sol_ref[null_elem] = 1.0\n", " rel_diff = abs_diff/np.abs(sol_ref)\n", " rel_diff[null_elem] = 0.0\n", " print(f'Abs(diff) max {abs_diff.max():.3e}, mean {abs_diff.mean():.3g}, std {abs_diff.std():.3g}')\n", " print(f'Rel(diff) max {rel_diff.max():.3e}, mean {rel_diff.mean():.3g}, std {rel_diff.std():.3g}')\n", "\n", " close = np.isclose(sol2, sol1, rtol=rtol, atol=atol) # element-wise close\n", " close_sys = close.all(axis=-1) # density-matrix wise close\n", " if not close_sys.all():\n", " print(f'Not close matrix elements {(~close).sum():d} out of {close.size:d} total')\n", " print(f'Not close solutions {(~close_sys).sum():d} out of {close_sys.size:d} total')\n", " not_close_inds = (~close).nonzero()\n", " vals, counts = np.unique(not_close_inds[2], return_counts=True)\n", " for l, v, c in zip(cell.dm_basis(), vals, counts):\n", " print(f'\\tdm element {l:s}-[{v:d}] has {c:d} misses: ' +\n", " f'Abs-diff (max, mean, diff) {abs_diff[...,v].max():.3e}, {abs_diff[...,v].mean():.3e}, {abs_diff[...,v].std():.3e}')\n", " return not_close_inds" ] }, { "cell_type": "code", "execution_count": 6, "id": "d9e27838", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 2.39 s\n", "Wall time: 991 ms\n" ] } ], "source": [ "%%time\n", "sol_riemann = rq.solve_steady_state(cell, doppler=True)" ] }, { "cell_type": "code", "execution_count": 7, "id": "32794991", "metadata": {}, "outputs": [], "source": [ "dop_mesh_method = {'method': 'split',\n", " 'width_doppler': 2.0,\n", " 'n_doppler': 201,\n", " 'width_coherent': 0.28,\n", " 'n_coherent': 1001}" ] }, { "cell_type": "code", "execution_count": 8, "id": "2ffa6d32-2a89-4cb2-8f7b-01fe6440f798", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 3.17 s\n", "Wall time: 1.86 s\n" ] } ], "source": [ "%%time\n", "sol_riemann_finer = rq.solve_steady_state(cell, doppler=True, doppler_mesh_method=dop_mesh_method)" ] }, { "cell_type": "code", "execution_count": 9, "id": "ee6d63a0-eb1d-472e-8496-ffdc03946037", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 46.9 ms\n", "Wall time: 64.1 ms\n" ] } ], "source": [ "%%time\n", "sol_exact = rq.solve_doppler_analytic(cell)" ] }, { "cell_type": "code", "execution_count": 10, "id": "a8069944", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Abs(diff) max 1.797e-04, mean 1.61e-05, std 2.88e-05\n", "Rel(diff) max 1.137e+03, mean 0.784, std 22.4\n", "Not close matrix elements 593 out of 9045 total\n", "Not close solutions 399 out of 603 total\n", "\tdm element 10_real-[1] has 220 misses: Abs-diff (max, mean, diff) 1.797e-04, 5.971e-05, 4.712e-05\n", "\tdm element 20_real-[2] has 100 misses: Abs-diff (max, mean, diff) 1.615e-04, 3.366e-05, 3.979e-05\n", "\tdm element 30_real-[7] has 112 misses: Abs-diff (max, mean, diff) 1.604e-04, 4.080e-05, 3.453e-05\n", "\tdm element 10_imag-[9] has 73 misses: Abs-diff (max, mean, diff) 1.082e-04, 3.516e-05, 2.708e-05\n", "\tdm element 11_real-[11] has 49 misses: Abs-diff (max, mean, diff) 1.221e-04, 2.376e-05, 2.820e-05\n", "\tdm element 21_real-[14] has 39 misses: Abs-diff (max, mean, diff) 9.864e-05, 2.241e-05, 2.532e-05\n" ] } ], "source": [ "bad_inds = compare_accuracy(sol_exact.rho, sol_riemann.rho, rtol=1e-5, atol=7e-5)" ] }, { "cell_type": "code", "execution_count": 11, "id": "d19e2e0a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Abs(diff) max 5.529e-06, mean 2.95e-07, std 5.47e-07\n", "Rel(diff) max 3.176e+01, mean 0.0173, std 0.483\n" ] } ], "source": [ "bad_inds_finer = compare_accuracy(sol_exact.rho, sol_riemann_finer.rho, rtol=1e-5, atol=7e-5)" ] }, { "cell_type": "code", "execution_count": 12, "id": "2e20bd39", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "55.6 ms ± 2.45 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" ] } ], "source": [ "%timeit rq.solve_doppler_analytic(cell)" ] }, { "cell_type": "code", "execution_count": 13, "id": "30d55853-422d-468f-bbe0-a2e91c72481f", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAskAAAIdCAYAAADPmuDUAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQABAABJREFUeJzsnXd8W9X5/9/akm1Z3itxHNtJnO0shwQIGUCBsFto2dBBKc2XUqCDDnbbMPoFOtLS37d8W/iWQoGyZwlJIBBCEkII2dsZjveQbVn7/P44vood27Kd2JZknbdfesm+Pjr3uVfSvZ/znOc8j04IIVAoFAqFQqFQKBQh9JE2QKFQKBQKhUKhiDaUSFYoFAqFQqFQKI5DiWSFQqFQKBQKheI4lEhWKBQKhUKhUCiOQ4lkhUKhUCgUCoXiOJRIVigUCoVCoVAojkOJZIVCoVAoFAqF4jiUSFYoFAqFQqFQKI5DiWSFQqFQKBQKheI4lEhWKAaBlStXMm3aNMxmMzfccEOkzVEMIN/4xjcYNWoUOp2OAwcORNqcmKS5uZlp06aRlpbG6NGjI23OkPDMM88wbdo0dDod9957b6TNiVpefPFFdZ4UUYMSyYq4JBgMkp+fz9ixYznZyuyvvPIKjz/+eKdtCxcuZNOmTeTl5Z1U333l3nvvJScnh2nTpoUeZrOZpKSkTtuSkpJYtWrVkNgULbz22mssWrSI0tJSpk2bxuTJkznrrLO45557qKys7Hd///rXv7j//vu7bF+3bh0pKSm8+uqrnbbfe++93Z7zTZs2ce+999LY2Njlf5dffjmnnHJKv22LNN3ZvWrVqi5ix263s2nTJi666KIT3tfVV1/NmDFj0Ol0jBo1imnTpjFlyhTGjBnDpZdeyosvvkgwGDzh/geaq6++mk2bNg3pPh977LGQ4ExLS2PatGmUlpaSn5/P6NGjWbJkCbW1tUNqU29cdtllQ3aeXnnlFVJSUtiwYcOQ7E8ReyiRrIhL3n33XSorK9mzZw8ffPDBSfXVnUiOBN/73vfYtGlT6JGXl8esWbM6bZs1a1akzRxS/vrXv3LppZdy880388UXX4TOwznnnMP999/Pli1bBmxfiYmJFBQU4HA4Om2/7777ehTJ9913X7ciOS8vj1GjRg2YbUNFd3avWrWK++67b8D39cwzz/DXv/4VgPvvv59Nmzbx5Zdf8uWXX3LxxRdz0003sWjRIurr6wd837HCbbfdFhKcF110EZs2beKLL77g0KFDPProo/z5z3/mqquuiqyRESQ5OZmCggISEhIibYoiSjFG2gCFIhI8+eST/O53v+O//uu/ePLJJ1mwYEGkTTopxowZ06d2s2fPJi0tbZCtiR6eeOIJpk6dyuWXXx7aZjQa+fGPf8z//d//Dei+Jk2axBdffDEgff3ud78bkH6Gmmiw22azccMNNzBjxgzmzJnDZZddxooVKyJtVtTx1a9+lcmTJ7N8+XJaWlpISkqKtElDzqJFiwbsO6sYnihPsiLuqK2tZffu3Xz/+9/n7LPP5t///jdNTU2h///6178OTeNqHsC9e/d2G2M8b948XnvtNSoqKkIhDT/4wQ/C7t/n83H33XczZswYJkyYwLhx43jggQcIBAJA13jNVatWsWjRopBNr7zySpc+r7nmGq655ppej/3hhx9m6tSp7Nmzh69//euMGjWKsWPHMnPmTP71r3+F2v31r38lNzcXnU7H1KlTeeaZZ0K2p6am8sQTT4TaXnrppaSnp1NYWMjq1auZN28eOTk56HQ6vvjiC84991xKSkqYOHEib775Zhebdu3axaWXXkpBQQFjxoxh3rx5rFy5slOb3bt3c8kll1BaWsr06dMpKyvj3nvvxeVyhT1ev99PZWUlbre7y//ef/99Tj/9dKBzvOidd97JD37wA2bNmkV6ejoLFizgyy+/DLufl19+uUscpRaXDlKsa5+P5cuXc9ttt3H33XcDsHjxYqZNm8app54KwDnnnBM6fxq33XZb6P1/6aWXuO6665g6dSqjR4/mV7/6VRd7ysvLueiii0hLS2PGjBlcd911PProo+h0OiZOnMgjjzzS7XGczPvend3f+MY3Qq/Rjv+yyy7rst8VK1Zw5plnUlhYyMyZM/n000/Dnu++MHXqVL797W+zcuVK3n777U7/+9e//sXMmTMZO3Yso0aN4vLLL2fPnj2h/3c8308//TRf/epXKS0tJS0tjWuvvTbknT7+u/riiy8yd+5ciouLKSoq4k9/+lOfbHU6nfzgBz9g9OjRjB8/nkmTJnV67c6dO0PhUgsWLOCFF17gjDPOID8/H51Od8LhCX6/H51Oh16v73LcL730Etdffz2zZs3CZDJxySWX9Pn8gZxBuOSSS5g+fTrTpk1jxowZ/OlPf+oSAhMMBrn33nvJy8tj/PjxnHnmmWzcuHFAztO//vUv5s+fT35+PvPnz2fXrl2htsuWLWPixInodDr+/ve/A13XkvzhD3/g9NNPZ8SIEVx44YVdwrM62l5SUsIZZ5zBBx98gE6nIycnh3nz5vX7PVFEGUKhiDP++7//W/z+978XQgjx2muvCUD86U9/6tRm5cqVAhArV67stL2goEBcf/31nbZdf/31oqCgoNt9ddf+sssuEzk5OWL37t1CCCF27dolcnJyxPe+970u/drtdnHjjTcKn88ngsGgWLhwoXj55Zf7dJwFBQVi/vz5XbYfOHBApKeni6uvvlr4fD4hhBCvvvqqMBgM4o9//GOonXZuVq1aFdr2zjvvCEB85Stf6dTnrFmzxP79+0N/33PPPQIQ3/nOd4TH4xFCCPHDH/5Q2O120dDQ0MWWK664ImTL73//e2EymcTq1atD7caOHSvuuuuu0N9r1qwRFoul0z6744477hCAOP3008Vbb70lvF5v2PaASExMFK+88ooQQgi32y3OPfdckZ6eLurr60Pt/va3vwmgy/4Bcc899/S6LVwfQhw7fx3RPpNz584Vhw8fFkLI9w0Q77//fqidz+cTJSUlYubMmaFz/cknn4iMjIwe99eRgXjfezsWjeuvv14kJyeL2267TQSDQREIBMTXvvY1UVhYKPx+f1g7hTh2Tv72t791+/+3335bAGLJkiWhbX/4wx+E0WgUr732mhBCCK/XK6688kqRkZEhDhw40KXv4uJisXPnTiGEEOXl5WLUqFFi0aJFXY7DYrGIq666KvQZ+/vf/y4A8fTTT3dqe/znwev1irlz54qJEyeKqqoqIYQQa9euFTabTTz44IOdXjt//nyRlZUl7rzzTiGEEB6PR4wdO1Z8/vnnYc8T0Ok65PP5xLJlywQgfvKTn3Rqqx33zJkzxa5du4QQ8rN68cUX9+v83XTTTeJHP/qRCAQCQgghDh06JIqLi0PXXo377rtPmM1msXz5ciGEEE6nU1x++eUDcp6WLl0qhJDf4zlz5oh58+Z1ard///5uPz8FBQUiLy9P/OMf/xBCCFFfXy+KiorEtdde26vt5513Xo/feUXsoUSyIu445ZRTRFNTkxBCiEAgIAoLC8XMmTM7tRkskaz1+/DDD3dqd//99wudTtfpJnP99dcLQFRUVIS2HT16VDidzj4dZ08i+frrrxcmk0lUV1d32n7hhRcKu90e6r+trU0kJiaKH/7wh6E23/3ud8WsWbOEyWQKCbCDBw+K6dOnd+pLE0br168Pbfv0008FIP7zn/90ssVgMHQ6xmAwKIqLi0NCpKamRgChG5bGb3/7W1FXVxf2HDQ3N4urr75a6HQ6AQiHwyEuv/xy8fLLL4dEeUcAceaZZ3ba9sUXXwigk0iPpEh+5JFHQtuCwaBITEwUP//5z0PbnnzySQGIN954o9Prv/3tb/dJJA/E+97bNo3rr79e6HS6Tp/F559/XgAhgRaO3kTytm3bBCAWL14shJAiJikpSVxyySWd2lVWVgqTydTtd/WBBx7o1PZ3v/tdl4GJ9l09dOhQp7bTp08XBQUFIhgMhrYd/3nQPgfPP/98p9d+61vfEna7XbS2toa2zZ8/XyQnJ4u2trbQtvLy8k5/dwcgUlNTRWlpqZg6dapITk4OfW6OHzhqx/2b3/wmtK2trU2Ul5f36/yVl5d3sl0IIX7605+KiRMnhv5ubGwUdrtdXHbZZZ3arV69+qTPU2pqamiALoQQDz30kNDpdJ22hRPJHe0UQoibb75Z5OXlnZDtithFhVso4oq1a9cyffp0kpOTAdDr9dx888189tlnQxKb9u677wKEpvk1pkyZghCiywKvtLQ0cnNzQ3/n5ORgt9tP2oaioiIyMzM7bZ87dy7Nzc188sknAFitVs4555xQtoZgMMiKFSt4/PHH8fl8odCJV155hYsvvrjbfY0fPz70e0ZGBkCnKct3332X4uLiTseo0+mYPHkyH330ET6fj/T0dKZNm8ZNN93Ebbfdxtq1awkGg9xxxx29xlcnJSXxj3/8gz179vDAAw8wceJE/v3vf3PppZcya9YsDh8+3OU1U6dO7fK31WplzZo1Yfc1VHQ8p1rWgo7n9OOPPwagrKys0+umTJnSp/4H4n3vD+np6Z0+i+np6QAnlHmkJ7QQkDVr1tDS0tIlA0d2djaFhYX85z//6fLa4z8Ps2fPDvXVkdTUVEaOHNmlbXl5OUeOHOnRtnDXhObmZtavX99p+5gxY7BaraG/R40a1envnui4cK+pqYmPP/6YV155hZkzZ3a7uHHy5Mmh361WK6NGjerX+UtOTubXv/41p5xyClOmTGHatGn8/e9/7xSWsXnzZpqbm/v0We3veSoqKsJsNof+zsjIQAhBVVVVj+eoIxMmTOj0d0ZGRqfPZH9sV8QuauGeIq548sknWb16dShWFGS8pV6v58knn+T3v//9oO5fS7f07W9/u9MF3Ov1kp2djdPp7NS+J0G8ePFiKioqQn//9a9/7XPmitraWgoLC7ts18RJTU1NaNsll1zCSy+9xBdffEFzczMzZszgtNNOIz8/n5dffpmrr76al19+ucfsHh0XA2lxj1rstWaLFtfZkaamJlJTU2loaCArK4tVq1bxyCOP8PTTT/P4448zcuRI7rjjDm699dZOMbA9UVRUxC9/+Ut++ctfUlFRwa9//Wv+9Kc/ceedd/KPf/yjU1ttANWR1NTUsEJnKDl+gZVer+90TrXPRWpqaqd2x2fdCMfJvu/9ITExsdPf3X1OTpTy8nKAUC5m7fvX3eAqPT2dffv2ddl+/OdBe+3xn4fuPjcd2x4voDU0m84777xO29va2sjOzqahoaHT9pMdJGuUlpaydOlSLr74Yh588EEefvjhXvfT1/MnhOCiiy7i6NGjvPPOOxQXFwMyHWLHTCf9+az29zx19z2Bvn+uunt9x3jqgfieKaIfJZIVcUNrays7duxgx44dXf53/vnn88wzz/DII49gsVgwGAwAXXIot7S0nJQNmjf12WefpbS09IT7eeutt07Khu48R3V1dQCdvHoXXHABRqORV155haamptDinYsuuoi///3vHD58mCNHjnTxtvXHlpycHD7//POw7RwOB7/61a944IEHWL16NQ8//DC33XYbdrudb3/72z2+7rXXXmP69Onk5+eHtuXl5bFs2TLee++9bhcIdVzEqVFfX8/EiRP7cWSRQ8vNXV9fT3Z2dmh7d6nmemKw3/eh4vXXXwfgwgsvBI59/3r6/B8/uwJdPw/a92TEiBFh24Vr2xHNpg8++GDIBdbYsWMBel2YqtHX87dnzx5Wr17NI488EhLI3dHxs9qR7j6rkTxP3dEf2xWxiwq3UMQNzz//PIsWLer2fxdffDH19fW8/PLLACFx0fECWF1dHbrpdcRkMoXEtBCCV155pdtsCiAzFwBdRGEgEODqq69m586d/Tyq/nPOOeewb9++LkUE1q5di91uZ+7cuaFtqampnHHGGbzyyiu89dZbLF68GJCextbWVm655RYuuOCCk7Jlz549XQYfa9asYcmSJYA877feeisgp83POOMMXn31VVJSUnoNkXn00Ud54403uv2fXq/vVhQdLxi++OILPB5PKPtEfzEajaHPR3l5eWia3mQyAccGYqtXr+42/KO/nHbaaQBdpp/7KoRgYN/344/z3XffHZLcxZs2beJ///d/Oeuss0Lfu1NPPZWkpKQu2TOqq6vZv39/qF1Hjj9v69atC/XVkcbGxi7v37p16ygoKAgrknu6JjQ1NfHVr351UM/VoUOHADqFO4Wjr+fP4/EAx7y3GkePHu3099SpU7Hb7X36rEbyPHVHf2xXxC5KJCvihieffLLHGMqLLroInU7Hk08+CUBxcTEFBQW8+OKLCLnAlQcffLDbKdXCwkJqa2vxeDzs2rWLK664IuSJPp4FCxZw2WWX8cADD7B3715ApmG6++672bNnD+PGjRugo+2Ze++9l+TkZO644w78fj8Ab7zxBm+++SZLly7tMs16ySWXsGnTJkaPHh3y4CxYsICUlBReeeUVLr300pOyxWKx8MMf/hCfzwfIG+mSJUuYNGkSAC6Xiz//+c+dir589tlnNDc3c9ZZZ/W6j9/85jedbqw+n4+HH36YXbt2ccstt3Rpv2XLllA8rsfj4c477yQ9PZ3bbrvthI6xsLAwJJ6eeOKJUAEMLeTl8OHD+P1+rr766m6n+/vLtddeS0lJSadqfmvXru13ruCBet87HmdTUxOXXnrpSc/IhKOtrY2//e1vLFq0iLlz5/LCCy+E/me321m6dClvvPFGaDbG7/dz++23k5yc3G0Z5BdeeCGUOuzgwYM8+uijLFq0qMuAOykpibvuuiv0OX7qqafYtGkTDzzwQNiQoKuvvpq5c+fyk5/8hOrq6tAx3HrrrRiNxkHLa3706FHuuecezGYz3/ve9/r0mr6ev/HjxzN27Fj++te/ho5py5YtPPfcc536czgc/OhHP+L1118PfT6bm5tZunRpl31H6jz1RE+2D3bInmKIidCCQYViyKitrRWlpaUCEKWlpeK9997r9P/NmzeL0tJSYTQahU6nE6WlpWLr1q1izZo1Yvr06aKwsFAsXLhQLF++XBQUFIRWibtcLiGEEFVVVWLhwoVizJgxYsKECeLJJ58UK1asEKWlpcJkMnVp7/V6xT333COKi4vFhAkTRGlpqbj55ps7ZWqYPXu2SE1NFSaTSZSWlor77ruvz8f71FNPhfadmJgoSktLxccff9ypze7du8Vll10m8vPzRXFxsZg+fbp49tlnu+3v4MGDAhB//vOfO22/+uqrRVZWVijFk8Yll1wisrOzQ+f7ww8/FC+88IKYMGGCAER+fr645ZZbQu137dolvva1r4kRI0aIadOmibKyMvHkk0+G/u9yucS9994rZsyYIUpLS0VpaamYOXNml9Ra3bFy5UqxZMkSMW3aNDFlyhQxefJkUVBQIM4++2zx5ptvdmkPiF/+8pfizjvvFGVlZSItLU3Mnz9fbN68OdTm61//usjPzxeAmDBhgnj00UfFSy+9FPqMZWdniwULFoTav/rqq6KoqEhMnTpVzJ07N5T6TwghbrzxxtBK+u9///tCCCG+8pWvdDp/zz33nPjVr34liouLQynJHn30UbF///5On7G5c+eG+i0vLxcXXnihSE1NFTNmzBA33XST+OMf/yiAThlUwtHf9707u4WQmREuueQSUVhYKCZMmCB+9atfCSG6fsb37Nkjfve733U6Ti2FV3dcddVVobb5+fmitLRUTJ48WRQVFYlLLrlEvPDCC11s1Hj22WfFjBkzRHFxsRg5cqS47LLLOr0vQhzL8vD888+LK664QpSWlorU1FRxzTXXdMmqomW4effdd8Xpp58uCgsLxejRo8WyZctCbf7xj3/0+BlxOp3i1ltvFQUFBWLSpEmitLRU3HnnnaGsFdo1LDExMfSd/p//+Z8ez43Go48+Gtqndh0qLS0VJSUloqCgQHzta18Tn376aaj98Z+z47P+9Of87dixQ5xzzjkiOztbnHbaaeKKK64Q1113Xejz8c477wghZIahe++9V+Tm5opx48aJ0047LXTus7Ozxemnn35S58nlcomf/vSnnb6zTz31lPjjH//Y6Zp01VVXhe4F2ndKe4+uvfbaTp9t7R7S0faSkhKxaNEisWHDBgGIe++9t9f3RxH96IQ4LuhSoVAo4hSdTsc999zTrUcx1nn00Ue54447qK2tDS3SVPTMqlWrWLhwIStXruy1IucNN9zAqlWrOHDgwJDYpohe6uvrSU9P57e//S133HFHpM1RnCQq3EKhUCiGGV//+te7rOL/8ssvyc/PVwJZoRggnnjiCd57771O27SY5OnTp0fCJMUAo0SyQqFQDDM+/PBD/vjHP4b+Xr16Nf/617+48847I2iVQjG8OHDgAA888ADNzc2AXLz5y1/+klNOOYWFCxdG2DrFQKBEskKhiHueeeaZUK7mJ554ok8LAqOZH/7whzz99NNMmjSJMWPG8P3vf5/f//73fP/734+0aTHBbbfdxne+8x0AvvOd7/Q4uNByfL/22mtUVFQwbdq0qCk6oxh8Fi9ejMPhYObMmUyePJnS0lImTJjA22+/3af87YroR8UkKxQKhUKhUCgUx6E8yQqFQqFQKBQKxXEokaxQKBQKhUKhUByHKks9QASDQSoqKrDb7SoWSaFQKBQKhSIKEULQ3NxMXl5el6qQx6NE8gBRUVFBfn5+pM1QKBQKhUKhUPTCoUOHGDlyZNg2SiQPEFop30OHDnVbulijrKysS633E8HpdJKfn9/r/vrKQNkVrX2p8x6ZvtR5H/p+BrIvdd4j05c675HpK1rPezSeq4Hsa6jPu7Y/TbeFQ4nkAUILsUhOTg77JhsMhgH5EGj0tr++MpB2RWNf6rxHpi913oe+n4HuC9R5j0RfoM57JPqC6Dvv0XquYv289yU0Vi3cUygUCoVCoVAojkOJZIVCoVAoFAqF4jiUSFYoFAqFQqFQKI5DieQhZsmSJZE2oVsG0q5o7Eud98j0pc770Pcz0H0NJNF4jNFo00ATjccYjTYNNMP9XA338w6qLPWA4XQ6cTgcjBs3DoPB0Ol/S5YsGfAPk7a/pqamAQ2cV4RHnffIoM57ZFDnPTKo8x4Z1HmPDIN53pctW8ayZcs6bQsEAuzatatP+1PZLQaY9evXqy+XQqFQKBQKRYTpzkmpifK+oMItFAqFQqFQKBSK41AiWaFQKBQKhUKhOA4lkmMUi8XCPffcg8ViibQpcYU675FBnffIoM57ZFDnPTKo8x4Zovm8q4V7A4QK+FcoFAqFQqGIbvqj15QnWaFQKBQKhUKhOA4lkhUKhUKhUCgUiuNQIlmhUCgUCoVCoTiOiOdJfvnll/n1r3+NzWZDr9fzpz/9iUmTJvXY/qOPPuJHP/oRFosFj8fDI488wrx58/rV5w033MCOHTuwWq2hbSUlJfzlL38J/b1gwYIu+54/fz733XffSRytQqFQKBQKhSIWiKhIXrduHddddx0bNmygpKSEp59+mnPOOYft27djt9u7tC8vL+f888/n1VdfZcGCBXzwwQdccMEFbN68mYKCgn71+dxzzzF69Oiw9q1atWogD1ehUCgUCoVCESNENNzioYceYvHixZSUlABwzTXX4Pf7eeqpp7pt//vf/57x48eHvLzz58+npKSEP/zhDyfcp0KhUCgUCoVCcTwRFcnvv/8+ZWVlob/1ej0zZ85k+fLl3bZfvnx5p/YAZWVlndr3t0+FQqEYapqdPqoq3Ozf08LrL1RQW+2OtEkxh9cb5OB+F1s3NbH6/Rp2bW9GZTRVKBQDScTCLerq6mhqaiInJ6fT9pycHNavX9/ta/bt28fll1/epf2+ffv63efSpUvZuXMnfr+f0tJS7r77brKzszu1ufXWW9m0aRNCCE499VR+8YtfdBsG0hGn0xn2/xoWiyUqE2crFIrB48DeVrZ+3gQ6+XcwCO+8Usmqd6v59g8KmTjVEVkDY4Rmp48Naxpwtfo5dMDFlxvldTcv38pl146kZJLKVa9QxBsejwePx9Nru77qNIigJ9nlcgF0EYoWiyX0v+5eE659X/scN24cZ5xxBitWrGDFihV4PB7mzJlDS0tLqM20adM4//zz+eCDD3jzzTf58ssvOeusswgEAmGPKz8/H4fD0etj6dKlYftRKBTDB487wP97bC+/vWcnK9+tJhgER6qZ7FwLVpsed1uQJ367jw/+Ux1pU6Oe9R/X8+L/HcbV6seWYCAtw0JqugmdDioOufn9b/bwh6W7aW32R9pUhUIxhCxdurRP+is/P7/PfUbMk5yQkADQRfV7PJ7Q/7p7Tbj2fe3z5z//eeh3s9nMo48+SmpqKs8++yw33ngjAI8//niojd1u5+GHH2by5MmsWLGCs88+u8fjOnToUJ8q7ikvskIRHxw55OLPj+yloc4HQHqmmVlzU8kdaQNg/GQ7v/vNHiqPuHn+qcOYzHpOXZARSZOjli0bG3nqzwdAB+denMNpCzOwWA18/fp8yve18sJTh9i/x8WOLc088JNt3HR7EYVjkyJttkKhGAJ+9rOfcfvtt/fazul09lkoR0wkp6en43A4qKys7LS9srKSoqKibl9TVFQUtv2J9AmQnJxMZmYme/fu7bFNcXExAHv37g0rkpOTk1VZaoVCAcC6j+v551/L8XkFJrOOr10zknlnZnZqk5xi5s5fjecPS3ezd1cr779VrURyD7z7WhVCwIiRNs48PxuL1RD6X0FRIj+6bzwb1tbz7F8P0uz08/RfylnykzFkZCmnhEIx3BmMMNaILtxbtGgRGzZsCP0thGDjxo2cddZZ3bY/88wzO7UH2LBhQ6f2fenz1ltv7dSHx+Ohrq4uNLKorq7m17/+dac2R44cAeiXm16hUMQv77xaydN/PoDPK0jNMHHHPSVdBLKGyaznG9+U15bKI24O7G3ptl08U1vlZv+eVgAuvXoENpuh23az5qRx56/HU1CUwORpDtZ9VM+hA92H8CkUCkU4IiqS77zzTt566y127doFwDPPPIPBYOD6668H4Jvf/CbXXnttqP2tt97K9u3b+fDDDwFYvXo127dv55ZbbulznwBPPPFEJyH9q1/9CofDEVoU6HK5ePTRRzlw4AAAgUCABx54gLFjx3LmmWcOwplQKBTDif17WvhkVS1CQHFJIr9YOoH80d2HkWmMGJXAiAIZgvHh8tqhMDOmWP6m9CKnZZqZMCX8bF1mtpU77imhaFwiQgg2f9bIyneqCAaDQ2StQqEYDkS0mMjs2bN56qmnuOqqq0LV8d59991QBgm3243P5wu1Lygo4I033uDHP/4xZrMZj8fDm2++GSok0pc+AX77299y2223YTQacblcZGRksHLlSrKysgCZDeOOO+7gyiuvxGq10tLSQnFxMe+9916nKn0KhULRESEEO7c2s3dnCzPmpNLi9PONb+ZjNPbNH3HuxTls+byJnDwrgYDAYNANssWxQSAQZOOnjQCccnpan15jMOqYVpaCLcHAqner+XKjky83Orn5x8WYTBH1DykUihhBJ1RiyQHB6XTicDhoampSMckKRRzi8wZ59V9HsNoM6HQwbqKdMeOT0On6LnSDQcHKd6pxtwWYVpbCiFHhvc/xwtoP6/i/v5RjNOlY+scpJCT1z7/z+gtHeOeVKgBGjrZx6y/GkpAQUR+RQqGIEP3Ra2o4rVAoFCdJa4ufR+7Zwcp3ati3q5WpM1MYO8HeL4EMoNfrGFUohbEWf6uQcdqJSQbGT7b3WyADXHj5CL5+/Uj0ejh8oI2Hf7mThrre86kqFIr4RolkhUKhOAnqajw89MsdHDnoRq+HGaek9Bp/HI4Ro2xs39zMC08fZv8etYDP4w5gtug54+xMvn79iS+cnv+VLL75X6MxGnXUVHl45O5dVBxqG0BLFQrFcEOJZIVCoThBDh9w8cg9O6mtddOWXcW3by3i9B4yWPSVhEQjrlY/fp9g66a+V4YarjTU+xBCkOwwkZ55cumdZpySxjd/lktbwWEamtw89sAujh5WQlmhUHSPCspSKBSKE2DLpiYe+9dq1l/0D/bOfY9MWwozzbfzGVYcOJjLXEYw4oT6zs23UnXUw8H9KnVZxSEXgYDAkWo64T4aaWQlK2mggdfHv84rv3kFa4uDaTvPoXj7zVwkTiEv3zaAVisUiuGA8iQrFApFPxBC8OaODVwoLuRvv7qYL8/9Fy5HPcnmRGqo4RCH+JiPmcxkHuABBP1fG11QlAhA1RH3QJsfc7z7ahXvvlrF4fL+DxgEgj/yR+7nfr7gCw5yEGO7b8id1MTamc/z/bMWcZ7lbJ7fvppgUK1jVygUx1AiWaFQKPrIXv9+Lqy9kq+OOZ0D01cjDEEKAqP5ET/in/yT67meb/ANdrKTRhq5m7u5mIvx4+/XfsaOl6WU6+u9+Hzxndu3tlousOuvp1cg+Cbf5BZu4WmeJp10LudyHuRBdrCDu7iLElGC0Ak2Z33MlWMXMXPXeexuOzAIR6FQKGIRFW4xwJSVlWEwdK4EtWTJEpYsWRIhixQKxcnSSivPHX2bRw2/ZVvWpwDk+kbwkP5BrjVc06X9a7zGt/gW/8f/8Tqv89/8Nz/lp33e36iiBAxGHQG/4MDeVsaOt/f+omFITZUbd5scJIydmNSv1z7N0zzFUwCcxmncyI1YOZbn/n7u537d/bzO69zU+gOOJh5gT/pmvrXyIS6bMpfr8i8kldSBOxiFQjHkLFu2jGXLlnXaFggE+vx6lSd5gFB5khWK4cdudvNJYC3Lt21j5556Aoku9s97j1v9t/Fz+x2hqfueuIEbeIqnyCCDvewlmb5fG+69Yws1lV4uvDyXcy/JPdlDiUnWrKrlmf85iN1h5ME/Te3z67x4Gcc4yilnMYt5kzfDtg8S5Gc7HmP11n34CYBOkDfWgHvSPn6j/w0zmHGyh6JQKKIElSdZoVAoToKDHORiLqZElPDDhl+wfVc9trpM5q27jm1N+7nb/tNeBTLAYzxGIonUUssv+EW/bBiRbyM5xYjHE7/hFlqu6Kyc/mW1eIiHKKccM2b+zJ97ba9Hz0Pj7+DVef/NmTuvIrlqJOsMn/Ku/l1mMpMFLGAb207oGBQKReyiRLJCoVC000wz/8V/USyKeY3XEDpB0KunaPM8bjbdyG9/dibZOX2PjU0llTu4A4C/8TcOcrDPrz33klxOX5RBVo6198bDlCMHZXq2EaP6fs4baOBxHgfgW3yLUYzq82szs6z8+s7T+UHat5i+/ErSD4wDAR/wAVPEFK7iKuqo69cxKBSK2EWJZIVCoQBWspJxjGMZy/Dr/NircznjyZ9z+59e5ZHrL+Ub1xdgMPT/kvkLfkEOOYxmNO/ybp9fp6U8czbKPMHxSE2lXLRXNLbv8ci/4BfUU48dOw/xUL/3qdfruegbI/ifry7hJ39/mdtX/ZmRzjEEdUGe5VnGMIZ/8a9+96tQKGIPtXBPoVDENU6cLGMZd4m7COgCJHjtTP/w65S+fAOLFxVx7n25GAz9Ky/dETNmPuZjnuZpKqjAhYsEeq/Il2Q3otfr8HgCNDX4SEkzn7ANsYjHE2BUUQLORh/j+rhoz4+fDDI4gzM4n/P7FQN+PHkjbfzo7gns3ZnPghWLeW30//LPMb+jMamRewP3ETAEOIuzyCLrhPehUCiiGyWSFQrF8CUYgB3roPoQpGbB6ElgtoE1kTadm4/4iE/5lP2HG0jOSCetLZsfrfsDY/zjmfzzZHJGDEyBiSKKyCabKqrYy16mMKXX1+j1OrZsauLAXhcJiUbOOj97QGyJFZqb/BSNTSQh0YgjtW8DhHLK0aPnYi7mNm47aRv0eh1jJ9jJHWnD9uHN+P9yGh98cyn2mkLem/A5uwp3MU03jTM5E7tIAo8LWhqh5jDUHIKUTJh0GhjUrVahiEXUN1ehUAw/3K2w+t/w+QpwNcltZivMvRgPHjabdlBT9yU6SzbVPgP7j2RztefPXFg0l5KJyeQXJqDXn7j3uDuKKeZLvuRlXu6TSAZISDCCgPJ9rQNqSyzgbPQBkOzo+21qL3sBea51DNz7l2Q3cubiLBwpM8j622PUBus4tG8d9ePL+WLMXVg2/olZ1dmkOwX6tuPeq//8Ha69BzLzQW/otn+FQhGdKJGsUCiGF24XPHEHNFbJvw0mAmmZNJg9vGb9F1Xecjy+Nm7fWkyyt57zAE+wgSZ9PWmiBqO3FMQsBvryWE45f+bPZJLJXdzVJxGXX5jAts1Ojh6Kv8p7u7Y109Lsx+7oeznqx3gMM2bO4ZwBt0cngpRllVN60RYObjzA2m0j0TmPstvoZ/o+A5mtLaG2XrMRgz0Dg7MB7OmwbS0k74bSBWA88fLaw5pgAIRQXndFVKE+jQpFtNNQBSufg/1fwOmXQdAPPi9UH4SjeyFvLCy8AtJyIm1p5PH74Ol7pUA2mqmfWcbNp7zBi2n/JohMpWYI6BjZkMDMPfnMrLCTHfRg0fvJogI2VsDGdyB9BNxwPySlgm5gPJJf42t8j+9RQw3rWc9sZvf6mqJxsjx1bY2HYDCIXh8/a61X/aeG5iY/IwtsjJvYezGVcsp5h3cAeJiHB84QIWDLaljxT2iowgyM0elIXZDP5s+LqfvoMl4pWoszYw8fjq5hQ14jVXa54PAnzu/w4JGvoautAGcdbHwPpi2SsxrxTlsLlG+Tj00r5OyPCILBBLZEGDkeFl0FWfmRtlQRxyiRrFBEK3VH5VTtrvXyRg1QdQDsafL3xiqoq5CPHWthwhw4+7pj/483gkEpQqrLETodey9ZzMuTq/m3+IggQew+BzlHS8heMZ+Sj85nJQ44J4vzFjugfDPs3QQVe2UsaXI6bPgPJNjlNHnWKEhKOSnz0khjHOPYwQ6e47k+ieQxJXLBms8rqK3ykpUbH+LK6w3Q3CRLeY8Z37dFe8/xHAC55FJCyckb4WmDL1bBJ6/KgSpIAZeRBxn5pM8qY/5Fhfjfb6au5kayPT4Ot7zE4dbXadZtwZXUwAGLi2UTPmOOcxxTPynHtO4tdFvXwHX3xq/HtK0Ztn8qBw1CQMAnt2kEfDKue8da+Zh1rnQCJDoiZrIifonTb6lCEcXUHYUVz8C2T6RnBSA1R4rgoqmQngeWBBg9Gcq3wPp3obURNn8Ah3bAd38Ltv6V8B0OiEPbqW3dy9ZZFlqSs3ne8iUV77cxfcS5lLlO49SKxSQ2p/P5pkYWfC2TeWdmYjK3e2YnzpWPgB+O7oe6w9BYC65mKbwPboeSMig5BfKKpXg+ARaxiB3sYAUr+tTeajNgtelxtwWprnTHjUiuPio9sXo9ZGb3rZDI27wNwDzmnfiO21qg9jDUHoGd62GHLEGO3gBFpTDnQhg5DqwyO4keOPsC6e1vcwUYv/cmZr58OR9u2seBaR9xIK2KmrTtfJK/n8kZW/lpmxVd+VbEO/+L7vzvnridsYrPC3+7C7xtULpQzn7lnSavZdpMmLbocdsn8r1AwLq3wZEBucXSsxyvAwzFkKM+aQpFNOD3yfCJw7tg+f/JmwjIG8fci2DqArAcl2mhcLJ8zLsc1r0lX9dQBf/8FdzwazDExyKhWmr5PLCeukN/Z7/YyQtTD9BaPpfsj0vJ3D+bWa03cPaiUYwqTiC/MIFLrxzZc2cGI4wcKx9+nxRL/3pIer3WvyMHJMnpMmuBPQ1Ss2HhlX2+aX+Db/An/sRWtuLE2acUZYlJRtxtXmqqvX09JTGPJpJtiYY+hZj48fMZnwFwCZf0voOWRqivhMZq+R7XV4KzVn7H8sbINhkjwJIoB6ZnXi3/DoMtwcCEKcmkZ5oxW3Rs/TyTWmcrdfl7ODD+M569YjmGuhJ+smYcbV+8zYeL0plmO41ssgd0kWHUIgQ8/xBUl4NOD+NmwYj2c53ZIaQip1A+z/867N8ivcx1FdBUC5tWypHTlHkwrgzsqUN/HIq4QolkhSJStLXC3s9h90ZIz4VAQG63p8n4vAVXwMyz5U0hHAYDzL1Q3jD+/Sgc2glrX4fTLhn0Q4gU1VTzT/7JF3zBHrGHyZ9XcXplMlUjmtlpMzBv7ZlM3XUW48YnM/fSdCZMTe5/tgqjCXJGwzd/DR++ANvXSo+9s1Y+tDaWBEjLlY+GSsgtkuK5G07ndBw4aKKJF3mRb/GtXs3IH23DbNFjMsaBkGqntkaK5KSkvt2i3uM9WmjBjDm8SHa74PU/wdaPu/9/UgpMOhUyRkpRPP/rYOpfSeysHCtXfquAYFCwa1szn67OYcfaqaQdGsODN/yaGz/zkuoxs3X1/dx3dgJjdGO4iItYyEIyyMCLF0P7z7DiP0/Jax3Aed8+JpB7wmCEMdPk75422LkOPngeEHBgCzhegKzRss3EU5VgVgwKSiQPMGVlZRiO8+AtWbKEJUuWRMgiRVSxdxNs+QgObJWCSuOUC6TXOLdYeklSsvq/Cn7y6XKa8sge8Hmk58WRMaDmR4I97OFJnsSBg1nMYhe7OBKs4Df6XwOgE/C3j85iTGMSpopxWF76IQtOzee0b6WT7BiAAhzJaXDBTXD+d+V7tmeT9Po31cjzrM0CHNkN696Ug50Jc2QsZU4B2OyhxX969MxmNu/xHq/zep9E8qkLMziwp5X0rP6JtVimvlZ6zZP6mP7t3/wbgKlMxUaHGRchpCfSWScf9ZVSYIEc3FgTwJokBZYjE7IKZBjAACzW1Ot1jJ+czPjJybha/az9MIeF/5jPp/m/49w9tVyzKY+fLXyXtaa1NLW28aVtC5n6DA5ykL/yV67nem7kRiYx6aRtiTjbPpGx3QCzzoHZi/v3eosNJp0OeqOcNTu4TV7fmmph9wZ4+6/Ss3zBTdLJMECLbRWxz7Jly1i2bFmnbQHNIdUHdCJe650OME6nE4fDQVNTE8nJJ17lSTFMaaiE15+AfV903m5JkIvCFl4lQydO9uIuBGxbI4tnZIyQgjtG2c52buEW3ud9AJL9KZy/65s4m/y4moNsO+VNHP4Urtk8mrs+gKDQsWXeUiYvGjt0WSCCQWiul9PBR3bBZ+/JKXyQU8rZo2XoRnqe9E46Mnnd/hHbD71KWdNoFiZeLAVa3pgeQzb27W5h+2YnuSNtzDglPrxlf/7tHrZ87mTmnBS+dUtRr+0vaTyNUdsrmZ18Htckfg/8fhnPWncEKvZBwcRjHuHmekhMhsKpMtY/OX3IQpOEEDQcqSflf29GH/TxmzF+fj+7nMJNZ2Bz6Eiw6zhauIWNuStDr5nLXP7IH5nBjCGxcVD4fz+Gij0wagLc8MDJ54turJHCe+/ncHQfuJxQPF3GiyelyMGOxSZnghSK4+iPXlOeZIViMGltgsoDMpZu3xeATk7H5xbB+NlQOKXf07lh0enkIpjqQ9Kr3FQHjvSB638QaaWVAxxgN7t5hmd4NfgaPr0XBCRXjSR7zxTqNuSQWlnAiMp8vvr5rSz4SiYlW+4DDqAfM42pZw1AVoP+oNdLb70jQ8auzrkIPl8On7wm48Mr98kHwNT5kJrDWbiZdNBE0f6doKUqS8mGRVfC5HldwmusNgNCQFODb2iPLYLkj07A5w0ydkI3CySDQZnxxWSVnuCWRn56eAZzVx8GjgB3dX2NIx1mnC29xSlZYIpMiW+dTkfayHSYfCps/oBvHxhD4+r7aW0RBIxemrIP48sbyfhpduomfUltxgE+0X3CbDGbrwTP4ZuGGyihhEIKsXNii0eHnKZamaoSYP43BqagSkomnHqRfAghhXL1QbmvlkYZTlO+TS62XXildEQo77LiBFAiWaEYaFzNMlVb+VbQ5mnSsqU3a9JpUDJbeq8G66Kd6JCeze2fyJCAS28dnP2cANvYxv/wPxzhCGbMCATjGEcaaVT5atjk3cJ/bG9KcawHe9UIZrx+A6M2zyWjLReHw0J2jpWRs2xMmeGgQL8f6g7IzhddFdFjA6T4mr0Yys6TGTE+fVNODbuapbfYaMbS2oDTYaE23UuaNxG9q0Wm83vpcXj/nzB6ovRy2pLAmkjL/iC7397NRMdBqKiSn5v0EXKmYPwp0ZkfW5ug7Mtn3Fl3LJNBXQVc+QvSk/3YCr1MyGmEg7Wy3HNzg8zeUr4N6o/KGPApZ+DHj/C7qcmwkO4yy/OJAJ1BZiEZMQZmny9LkkcLi64Co5lseyoPTsqg3JnK9s3NHC7PpLpiIg1bv0LqtGYayjbx/Pjfczh5D28b3mJd/RYuaf4G2blWLGYjW9mKCRmW5cNHOul8h+9El9f54HawJcvwsaKpA9+/TiczzuQVy/CnygMyflkEZXaSPZ/LRYIzz5aLAlUqOUU/UOEWA4QKt4hThJCei9ojctV25QEZm1p3RE63z7kQsgvktHt63tBlnPjwRZlGzpoIP34qopkuAgR4iZd4lEdZy9ou/59SdRojdk+nucmPMTHABwv+hyRPClds+yEzVl7F+IkOxoxPIjvXitlyXBjFq3+Ez9+H7EK4+dEhOqIToKNoDAb4aevNVLh28G3X11nQNAm+/BD2bZY3dpv9WMxmwE/wk9fRB3rIbJFbJD1lJqsUIUYzGI0yn6/RJL1r29ZIkX7FncdeFwz0zaO3/h3Ys1GK8fGnhE8t6KyT+W8PbJGPgF/Olkw6TdoZDMhtPm97zHwNfPGBFDGiQ4xg2bnsO2LA7xcUsQOjs1qGoricx1Ii6nQwaiJMP4tae4AXEv8DSSncnPAT6Wn2eaWXOZq9h3s+l4tstVmlDvh8QeprvNRUeair9fAX75O8ctpvGf35GWTtnYQ/uw6R18iamc912/U0pvEzfsZlXIaeCBeg2bRCzqrkjYWSWUOzz2BQzt6tfBaa6+Q2vUEOrMZOh7GzZPhTUor8jETz50Qx4KhwC4VisPH7ZOzp+/+QWQ+6w2aHgknyojzUzDoXPnxeZsnYvhYmnzbgu6ikkgYaSGn/sWHDh49aaqmkkqMcZZfzIJ+7t/B05jLQAQLSq0eTUJmL0AfR+43Yt84mbeMZjKrPwqq3cGPWN5iXNJvMkgRs03sRcod3yefi0gE/vgGl401Yb+Bj+zY+tn+Mncks4L9g2kIpJD59U8apj58t37u2FnQBH0EBdb5UkosLsCRapOhtqpELPY/skf3WH5UhNmabHLg114OvQznrd/4XEpKlWPhilbSpcIqcujbbpIit3C/DEbSCNA1VMl/wzvXw2jLIHCU9szmFUoiLoHz4vPD+M7IaZEc2fyAfWaNgwly5zVkHuz+TmUK0wUNyOjiyIMFOQG+hsdGDMNvQm/zgPlbumeQMORMz+9xQ2rC/8iB/5jnmMY+bMcjji4XSzylZUiRrMewdMJn0ZOdZyc6TebHnuH/CjzbfxAefHWX/Zg8evYfa/N0UUIHQB0jJ0WHUGWlIrGR/4k426TfxwPb/4U0+Y0ruKEoco8jT5ZFDDplkYsaMGzeNNOLBQwEFg3OMba3QUC0dBqMmDM4+ukOvhxlnyjLgG96B1S+2OzMOS2FsTpAzEgE/rHlVhkuNGg9zL1ZxzIpOKJGsUPSFYBB2bZAX1JJZUiRrHiuQccVmmxQhoyfJBXMjS3pP3zZYJCTJm9K+zbDh3QEXyR48LGYxn/N5aJtd2EkNpJPoS6bB08yYtV/B3SpkJqd5pST67Mw/dCnO9/MQB1NJaEpHJ/QkO4yMHpvI+POSmTE7BbujjwLH75ViEbp44qKdsYzlYz5mBzuObUzNhnO7ZrvQ3fwYv/zlURpdZr7/tVFMmmABr7v90Sa9sl63jMus3N/5xXqDDMvIKZSlkAN+ec5qDsr/V5d33BMg5Oe2eJrcZDBKj23tEXA1yfYdXzPvsmMe6YwRUtCm5UkBKIIy7KjmENjTZeiDod3L3dIgX5OZL0NTCiZK+0wWjlYGefIf+9HrdUx/7EwZ1+9ulecnM7+L1+8zPuMgB2miqb9vQ2Sxp0ovf2ONFP6pWT02tVgNzJidxozZabha/Wz8tJEdW7IZ/9R0Gut8XPj1XOoMNdRbK/mwbhOb8t8n4fAYthka2batkcOz/kQwpZU0k4M2SzON+nqadPJ8jWY0H/IhGWR0zgwyEGxdLSvoZYyUpaaHGoMBTjlfzsxU7JGZhezpclBWXyEHlkG/XFjdUCkHj3ljZG76iXNV0RKFEskKRbcEAnKaru6oFMc71spFISDF2diZ8qI//Uw461opEKLNezXzK1IkH9wmK4n1sQpfgAAGDHjwUE89DTRQE6jjvfo11Bzy0+Ry0WZuIae4GGPqFvw6H+igWddMs7FZXlVsMGnfCPIOjiNPn8vZurvJyU4gOcUEFwuSHSaSko1YLAYMJ5r/11kn00mJoBR2McQUpgBwgAO9N84uwJDYDC4v1bVBJiXYu6/4Z02UXrDmBhnik9fu8TWapDgOBo49Ssrg8/dgxzopsAEQcmFbwUQpEDQv76RTZWx9Y7VcfLp3kxQXIGM9k1Kkp7B0oYzJNhg7P/w+uf/2KnUEA+3pDovk83Git7quAdBhSzCgzxjRaxGPPUhP+gSG0FM5EFgS5IDF55axs3Mv7NPLEhKNnL4og9MXyfSOAb9AbwCPJwtn4zhOK59FVcW1HDzSyu6aSo4EK9hxxmu0OCrp4rMWUONu5PtfPIJOp8MWSGB/wQbOMM7j/PQzyDRmkEYaqaR2EdCNNOLHTwY9pJn0++Ddv8v3/qu39e/cDDQ6HYwYKx8aAb+8vo+eIgX0wW1yQFexR+abfzdViuv88dLTnJwefdd4xaCjRLIifhFCTtcf3Sd/L5gAzno5Tb3lI7mIqLm+QxykXnrVys6RC1A65L+NSibMkZ5tl1PG7Z56cad/V1HF3dxNMslczdXUU0+9qOcH4gfohIEMXzaeVkFbm5+6hEpaM6vJq5lJ3v6ZAJRQwi26h7F706jeF+RAdR2uFPnICeby9axLWXB+ETl5VkymQfCoN9bI59yiyHnsT5CZyHN4hCMIRK8V15KSjdTVeKlvL7LRLQUT5aM79Mdlcyh0yJSDIGdD3C1yZiTcgtLcQphwivzdWQfoIMnRe2yzydw5m4TeEHZmo7a6vZCIvW+3p0McAqCUKA+56Y68Yhl6sn9zn0Xy8WiDTKvVgDXHQFbOsdLlgUAxtdUepn1pZm39ZpqSq5mSl0+SM4MEfxLrP6umxdpIvb0Br62Vxpyd7BmxnPUs589N6RQZCjDoDej0glpjNTcGvst40zjS9Wm8y7s8wiNcxVUsZSmjGNXZsO1r5SyHyQLjomghoYbBKEtcZ+XDzLNkaMiBLTI8Y/+X8rrpcR3Lq11dDq1O+f0wmmT6wMwRcj3EqPEDk7VDEXUokayILwJ+ubDuiw/kCmht2jfRIeN4NSr2yAskSI9P6QI4/VIZExmFCASf8zlrWMM61rGLXdyiv4WvjsjHtnsrdYfWsF5Y2FdXzYqKDXxh/Yz9ozcQMHvR+418sroOS8CGOd3H0enSS1hhOAzH7rfoAnoy3DlcePRqUnzpzEzLJiPLQlK2gcPBNpocPkaOTiBvpJWUtCFIsdVQJZ9Tep6mjlZmMQsdOrx42ctexhC++pgjRXqwGuoGIQ2cyQymtP69Jnnw0gpqA4G+FBJpoYU65MKs2cRWyA0gY+l3fwYVewele4NBR3aulZ/mXgJcgtcbxGzWE/ALWlv9vL3vKK6WAP7aIG3CzW73ZyxP8bFr3Gpcjjq2tJ9bjX9uW8GI6goEcGjkFzAe/sk/+Vfgeeb4TmO2mE2pYSoZhjRmHlhHDtCancmPzXfwOZ8zmtHMZjZzmcspnBJd5bhtiXIQOOEUaGmCA19KIdxUI2dRyrdJ4dwdSSlwxc/kTExCckQXSisGFiWSFcMLr1sKX5MF0IOnVS7YaG2EnRukV0ArKQxy9K8tVNKm1OxpMo4uLVfG9abnDbnH2IuXN3iDtaxlClOYz3xGMYogQVpppYUWmmmmhRZWej/gD56/UG7f2akPR2U+bSkpzMmx8WniVm7z/T/cDje+jGOLuWyN6RSvW4Rl72isrclMyMtlXvNZVKbv5YjlIEf2eshItzIubQTfTb2WoskjMc/o6rUdMSph0M9JJ9wueOdJ+V5NP3No9z0AJJJIBhnUUMM61vUqkvNH26ip8uBIHf7TvQ31ciCQktL7sa5nPQBWrBRTPKh2DQrj58gFlS0NMiY2dXDT+ZnN8rtrMOpIdpj4xg2dvb9CTMTnvYbDzdX8n/+fVBmO4vH7aWpuo3JNEpkHxqMPGHEnNVGwK5fEfaPZM3s5rRlVfGz4gI/5AGPATOrBYj7YOZkc4CNrI38R/ySoC7KWtTyHzMhRHCzmytYbKN4zl6ljs8lJSiOp/UePnqMc5UM+ZCMbKaWUr/JVrB1H7YNJkkNWMAW5UDUYlLOMfq+cWfS0yfA7V5Oc0bIkHCu5rdPJlI4ZI2UMfWq2DHUTSM96UoosdKKICZRIVsQ2Ffvgy/Y0Uo3V8iLUkelnHfN6VZe3C2SdvHiNnSG9BinZsgJXx+my7GsH1MwaajjIQUYykkwyO6Vl8uOnttVJg6cZU5qPpSzlZfEyDbqGTn3YAw5yWkcxefciTCY95uQgb+U8S721GszS02uvHkFSQxZmVxJ1hxy82mTDgQk/LTSbGkEHJo+NcdUzWVRzIeccvgqL3khwJPh9gglT7BQUJ6LXy0GBKBboojGkZNd6+V63NA6qV3MwySefGmr4gi+4ivA5nqfNTkUISE2PTBGMocTZ1C6S+zAb8RmfAZBHXuRTnZ0IKZlyAV9zgwxPOPWSiJqj0+kwW3QUWXK4h9tD292OAPuntVKf76GxzofOAEajHoIQ+DjI6oKXWTnyFTY71uIyteCzuBjZIsPU1jhtjNg8G6PXitfWij+vltqUQ+zV7+VX9rso9C0k/d2xJNkNtBUdoiJnB05rHU3Gzte/pKCdew/+jmmBGaRZ7WQnp5BlT8bYQcYIBLXU4sNHHnkDd2L0ejj3m523CSHXejRUydC8gF86Y5z1Mv1c6LUGGYevMXYmzLlAhuvZkqTYHjUh5kLG4gUlkhXRh7YC3+OSF45gUC4CaWuWMWEiIEfybS1yUd2hHZ1fr9MfiyN2ZMj0U0kpMldxzSGYtmhQq9C5vB7Kq+qpaGzCnOojKS/AC7zAUv1vALAErRT4Csl2jcLfYKbR5cKyfwQOSyKjixNZnr2ShqQGTG4bjqpRtCXX0+qopdnQhM7VSMoBN8mGREpG5eLMb0AfMDBu+xnMWnc5SVUjEA1WhNOCzZ9EgsXAqBGfMn/UVMbWfQ9LaiqzLbMw5ZsgH3qrORCVAhlgd3tWjezRMXtzWcIStrCFhSzsta3NJgdw7rbgYJsVcVqcUlCkZ/Yukuupx46dQgoH26zBI2+MTLG378uIi+SesFoNTJjacz7Z81gCLCFAgPX+z6ipqsDOUwgBxm3f5GsbLbQamtE5PIyeYYBRtbyd/wyf5L1Dbu0YTA2ZeN2tHM2q51BSe0pDAY62TNI9WVQmHsSDj2c//5jngjLlZnPGUUhrJTUhEUtKgOqkQ5Sb9uHSt3J6YB6/EUuxBRNw15poqHdTZB9BQU4qiRZLj2EefvwYMPQtDESnkwtotYI1IIXz/i1waDvUV8p7WEeBrDfI+9vB9ntWcz1sfE96lnOLYNQkueg2wS4LsCTa28M32hfAiqDMhR6t1+VhiBLJA0xZWRmG4+KRlixZwpIlSyJkURQjhFw01Noop8+DAXlR2bsJPn6559dNPl1WHAPpEXa3wshx8maTnie9M9ZEmaHieA8xc0K/NdHE27yNDh3nci4OOldi8gR87Cmv40BVA7ty1vNy9t8xm0z8zP9zWgJttPhd/LftQWz+RKyNabQ2Bmlp9dGQWEVLeiXZzsmk7B7F2AlJ7HF8iTUzEbexFY/ezS7LdnZZtkOq3NfEqq9ibM4g0ZnG6Z6L8Ot9tL0xFlNbImZ3AggdzZkVJASSKGs+g6IiO/OyM5jXOo6ZxukUTSjAMLmHC+fH++HwLhZVJELG3H6/TVHJkfb8yKMnR9aOk2AqUznIwVBMbTi00tSN9V4CgSAGQ2wODPrC2AlJNNZ7KSjqPYSnjDJu53bmM38ILBskxkyXua4jVCp7IDFgYI5xNgTfA0CXlMJd93V/zflJ4Osc8hzFOMdKS4WRLZua+PSjL/h093ISjuRhrxnBnNPTEfY2Wmhhh2cPLU1mPCYXbqOLL2euwpPU3G3f2xvK+cnH/4ffL/AmNLPlrBdIbMgiaW8OqS05FBQkYbQKGk11XOy+jGx9FknGBFaa/8P/Mz3BVM8MLq2+nilHTmfurBEkmxI7eawBGmhgJStx4eI8ziOd9kWvRVPgpv+WjTxtMpTGbJP3IXeLdPS4W6XTp6EK9EbZ7sBW+ejItEUyztlskYWBvlglQwnzJ8jMMuNmypkIJZx7ZNmyZSxbtqzTtkAg0EPrriiRPMCsX79eVdxzNcvwhyQHZORL4dvSAOvekl5hjbYWGSLRXC/zsmrpeVoa5bPBKNuL47xnAb/MQ2xNBGsibmOAN3iDNmoYTSKFpDECOzp0CARePLhxc6Cigc1HDrIuczkfpy/ny6T1+HWy+MGPG+8my5tHa8DFLtMOdtYfotbdhNvaQnPJUVxpMpOCtSmVn73/TwqKEwjY2vh83HqwAInAcZmqhNlH0aGZ5LRkUdA4nvP338CujS6qdFXU5e+hrnAnwu7GYU7g/pwfc0pJKWazHrNFPvw3BWlq8KPVtrZYDaRnmjt5d6/g0t7fj0M7ZYqpgB+mxrCY0GhrPbZob0IMLtZqJ5NMAGqp7aUlGE063n21kmAQTj8zo1MGg+FEMChIz7SQnmkmd2TvcZvaucsme7BNGzymLWqfIRNSLA2HeFWLDcbMkAKvBwwGHaMT8iABSIPxk5O5jHyEOJ+GOh9tLj+ZOVbMZj3BoMDrCeL1BvF6gpT7D/HjwE5qK5pp8rSCy8RpyTMZ7ZxASksO27bXU9noxGdpo3zmhwRNfpqzKmjOquAosK2DHbV79KSWFyOA/SVrcY9zs866hnWj1mBzpFHkKiQp6CAzkEnWofEkmxLITrXzQM5PcBlkoRu90DPNM5MLTedzgf588nR5NFfBiIwUEtJz0KNHIKhMbGV/en0o9ePFpd8h8fzvykXk2z+VWU7crceM09Iwej0yJAdkmNm+TfLxzpNSJKdkybSN1iR57iv3Qe1ReQ+1JcmF6SkZUDxdzqrGEd05KbWKe31BiWRF73g9ciFCc4MUpqlZx4oZNNXKZP8NVVLwVuyRVY2EkGVIx7bP53vbeq5MB7KPjBFgtrKh0Ev53HkcSXBSZJ3CLP0pWANGXDovew83QVIAg+0olYEq/un6J+9Y36DV3HnVsdlvY8KROZS6Z6I3Qb2hjk/sK6iZcQgMx0S31ZmC0WthxYcVjCpowmoz8Eneag6M296pP13AQO6eqYz8Yg5pR4oozcnD6jMxYk8ea7yfUksteocHkjyMDZZwujid08UZTD+nFLPJgMmsx2TSsTejFZ83SFaOhdR0cyj293iBLY0zkGQfgIVaI8ZJkVxz6OT7igYObJEDJ7MNcooibc0Jk046K1hBDTVcyZVk0XOWDpNJDpzcbUGqKz3DViS72wKAQK/XdS1Bfhxa/CnQc67eWMBkkVPqrU3SYWAJnxc6JggGpdNjTP+rjep0OtIyzMAxz7per8NqM2BtDzvKYAwreAtt8k+Izmsnqka14WoJkmg3YDLfyZaarXxkWM3HfMgO0w4S9TYsARvJ3lQsm2ZiLs/Db3Jj3z+a0Z/N48jUdRwZ9zltjnq2Ug+AxW9j+scp+P1SuJrnZBC0G9EF9bSl1LPRup6NrOc+cR/FjZPI/PQ0RFCgz21m/7hPaUyqxG1ydTrWhGAiV7R8i9H7z8SROp20kWdQkGNn3KhUEoIm/CY9nwY+Zqf7c3ImJ3Gu8zYc1Y0yRd3hndIh1dyetjR/vJyRBbmI8Oi+7s4upOfKAj4pWbKAj+a40spza8I80SEXHQ6HQdtJoERyvOH3tWd/sMoPv94gV+z6PO2VuzzyC3dwu0yufnR/57KwKdkyHZrGRy/JTBDHIRIc6BKTCVqs+CxGduorsUxIx04q5oARX5ufRj98aUjmE4yIUakUpO3GFXTzSM4vaTJ1WLQhIKktHb3bgi2Qzqy9C0h2mGg1OXltzD/lYjRXItYWB56EZrwJLXiNbTTW+an3erAnm2hNaKUmTVYKS2rKIHfvVLK3ziClogCj14rBa2GhfQSjc1KxeQNsdDpw+NIYay6kmDFcFrycEfk5kC9oafaTmX1MpPi8QYwmXZ/id8eU9K2gx4Ci5cNtqj2WtzSWqTognx0ZMRuPDDLDxRd8gRMn61jHBVwQvn2SEXebl5qqMLmSY5yaSg/VlR7SMsy9fp82sYnf8BvyyOOX/HKILBwkEpNl7un6ql6Lp0Q9Qsh7CAzZotrjPyvZuZ2F3TymM4/pwA+6vLbqbDdNDfIe5kg1kpxsBh1Uu+p4Uf88u3W7Oag7SJWo5OyDl1NR6aIl4GLkltkIQwC/2UNz5hFqp22iuuRLahMqsLYlo/Ma8et8tNVDZWq7YBVgdiWR4E3Gn9hKi7mJ7S372Oz3QDO0mCs5avsC0eBHWL00m2rBJMAE2OG7rXeid2XjszmoLxhHjivIfL+JUtFEXXoaaVk2PME6EkQyhY6ZGPwBdB43Po8Tk8uFrqUR0VANrY3o2trv65veP1Yoqzsu+YF0jpmtslqm2SrT5ZmsMgzEaJazlH7fsYJBwwglkmMZIbrGIQUDMs7X6+4gfN3w6RtSXNQd7bSQQKBDl5jcKUew+PQNdB2nfACfAZotfnxWF95gDW0GPfWGNmYFfQidjnqTkQqjji/S3Lw06QifjF/J7J1XkpXZRDAo+CjjHfZNPxZvZfBY0AcN+CxtmNsSWbjxeqqbpHhLSchFeJMw+iy0ptbgsTfRYq8Du8zgkH4wlxyLHavHSu3+Koz7c8n5vAx9qw2Dx4wIgq+gmkJRyJmTJjA5PZMacwWveaZzPospTZyCfjqIaeBs9OHzCUwmHUnJRoxGPecT3vthS+j8tTGZo1yo5RbLi1vAJxeMFMdg0YWO6HRysJY9OtKWnBQ6dIxkJNvYxkY29iqS+1RQJMbZtb2ZDWsayMqxcPE3wovFdayjhRZaae0SLxpz7NsMn/0HivdEZ+GN/tBQJR0syekxMbWfnWslO7frzEwBWdzBf3XeeIv0Wre5Ani9QXxegcGgIyXNhE4HgYBge9suTIkWMs7IY+8eJ1t21/Daf/Kx7B+BqTwXHZBXYmT0NAOfJ33CKGcJe2nCFWxjU+ZOmvLKO+3S6raT7RmBT+/laIOTo41yALJv7grqR+3hz0EdRo8VdL/Db5XpPW15SVy440acjT4I6Pl42gvoDW3M3TGW2XtGcOjwaiblpFGcZmee0U+qTocwGAnqdbj0bvz6IEleIwadCfehw9hsRgwGHWz+QKYqpN3rjJAyBAGJKbL6rMkixXP5Npkab8RY6ZE2WdpLz5u7Fl7pTstECTF+ZYljyrfB608g6ioIGnQInQ49evToQAcYzYiycwkSxCf8sGMjVr+cigkgMLSv3tUhaAg2sq11Cy5DkAY8zBMt6CxB1ua08H5xFesKj1KR7KbF7Kdo15mUmA4AcDBpFx/f/QbtHXVhn2MnDo8UnCmubOy+BlrSqhFGPwGLB02qexNbmJIxmlnMwmaw8dU9V/LZqhZoM2M329DlOmks3EPqqCDj83K5eNH5Ic/BfXwHioBeUuXmMY5S7uy0TafrW5qpmMdgkBep2sNQvjX2RXLGCDmbMWZapC05aQopZBvb2MrWXttqBUUa6wehoEiUUFfjBcCe0vutaTObAbpWeotFHO2hNg01kbVjINj9mczWYU+D82+KtDUDjk6nIyHRSEJi1/8ZjTqmGMeDDUiGjKxMTjk1k2/zUA+9XSSfpkvxvSJ4CtvdO2k5qqfuICQfGM2sgmIyCnW0+tuooZn1jVUYHT7+mbSaegHoBX5bW6hHfdBAgi8Jp7uN2uogfrMbl81JwOLhnbLPeafs804WFBdPYcKuBdRVe8EcYP3ZL5DoNZLkNZDRasHmWkOBK5cCTzq/brS1i0YRCsvQbv3Nvjr+VfsgI3R5jNWNpWj9FvTtJe+F0YxOr5evCQYJpKSzr6wEnclCoWk8hg//DYu/KyvZRhlKJMcoO/Z/QIbrIBlCh8Hf9f+ugIuXXKtwGQRuvY7g1J14rG2sH9HIjoxm3IZg6MOdfHQ8JQaZiL/V1MQ1Z7+GzyhCfekCetIOF5NdXkJq41hyR+Vj01nximYsrmR8FhfGoBkLZvK8+UxqLGNi9RxOF6czIT+HRJMVk87Ih8urSUw2kjbWSzC/noDRRy65ZJGFaULn2NvLTjn+iIbBgrNIkl0gRfKRPZG25ORxta9ot9kja8cAMI5xvMmblFPea9uUNPkd0aaGhyON9VIkO/pQSGQ/+wFiO/2bRs5o+dxSH1EzBoTD7ZlnMkZG1o4YQ6fTcaZhIWcaFkIh8tHNbe/y9onO33AZfvzUUMNRjkJAT24gjzSRjj8o2G9u4dO6KvQJPnjnFvbmbWJH1jq2pq7niPUAfr0Xv86Hwagjq3IMbUebCBi9jPnwQtBBbcEuNufvRhibWMsRAFbnLiR3+3ja6rx4UivZW7YCc1DOpArAEtCT6DOS7DZy94HZjK22kukJYPB7Ox3DEd8+nmlbBW1gFmaWuMdTuXcFJUokKwaKt40VfHz2VtoSmhFBA/iNNNtb8RoCeA2CxMZMRrVX8dKh44UxW/EbvaRUjiJjz6k4anJJqs9BFzDi0NtZfNoMEo1WXOZmDrq3kE0W48UEJogJnOE6C6PLQavNjz3HSPG4juLk/3U2zAwkAd1cHy+4rOP0af4AnxFFWEaOg60fS6EcywQCcgGpTjcsRHJ++/egLxku0jPkrIfT2c2oeJjgbJTHltqHGZ5qqgEY2d3FJtbIbV+A6nXLBXyJfVt5H5VoawbywleRVJw8Rozktv9gQD4AiwUml6YwuTSlQ+tZwHe6dpIMLWf6OXq4DXdbkGAwiN8vSGwxEqxqYXXSe2zXbWO3YRenmM8gi+nsaKqjqqqOhkAa9qPy+9eSXklzRiVNE/eyIW8v9uAImg+b8da5SczaScW4zfh1QQxCh9CBS5hI0AlMgQAB3UzMhsP8dJDP14mgRHKMkpRZRnNNPYEKE9l7J2PyJpBnCdKccwTSm8lPzOV7BZeRbEkk0Wzhes5jFjNIy0slmCPweYP4fAK9HmwJhk4LH67mvM47SwYGt1qqYrAZP1t6eOxpcoGFMUbLG9cehg+flwtJzrgs0tacNFqoQD29exBHjEogd6S1T0U2YpXmZimS+3KMWn7p/OEw4Lanymwt3jao2HssK1CsEQweS89YMDGytij6TJLdyNgJ3TkdkpnI9cf+TATOPvanEDfibgsSCAiMJh0mkx6DQYcz0IJllA1vbhBnWxvv1X/Mew3v46uxQI2dpKo8RJuRmWcncNi+G1tWHiZ9dN6TlEiOUW4suYgbSy7qc/uvdAja1et1WKwGLMMzi5SiO1JzpGfH6waXM2ZLOVOxVz4bTDIHaIxThPQgttCCkMtoe2w7qiiB6bNTMBijfKHoSeB2yZUKffEkawOL0YweTJOGjqRUqG+Dyv2xK5Jrj8jF4uhg9KRIW6MYZHQ6HbYEQ5ftyYYkMMjc/na7iRuyzuOG451vMULs32UUCkXfsCVJkexujV2RXH1QPjtiOC9uB0oo4XZuJ5FEfPgw07M41LKoBPzSc2MwROdq8JPB65E5W5NTw9+aggRJJRUdutBAI+ZJyYT6itgOiapuj623tacMUyhiHCWSFYp4oblBZrewJkBWjGYEqJMLSEjtufBGLGHDRjrpePHSQgtppPXY1mTSEQxKIel2BUi0D6/LdyAQZMLUZHy+IGkZ4XN5e/FyAzcAMJaxQ2DdEJA/Xs7y2GN0AAtQVyGfYzmmWqHowPC6yioUip6pLpfV6sw2mNv3UJ2oolEu1iJ9GCzWQi6qtWOnjjqaaQ4rknU6HSveqsbrDTJ1pqOHGMLYxe8T5I+2ATqSehkANCMznFixYiI6Yxn7zaRT5XMsz5Jk5sOUMyBzeHw/FYrhG9ymUCg6k5otn529Z1KIWpxysVbMesK7YQMbeJEXeYd3em1rtspLtrNx+KWB83plqIXJrDtWrr0HNJFsZxgNFGzt1Ti1FIexiE4HablQoOKRFcMD5UkeYMrKyjAYOgeyL1myhCVLlkTIIoWinbRc+dzaFFk7ThSPS8ZTA+QNkzhUoJxytrKVTWzqta3VoqeF4ZkGrrHOS3Wlh9S03j3Dz/AMj/M4c5nLEobJtdVml9VQG6ugpQmSYjBkQSt1bO2m0oZCEQGWLVvGsmXLOm0LBAI9tO6KEskDzPr160lOTo60GQpFVzLbva8up0zVpI+xiaTWJplP1uuW2TqGCdlID/9Rjvba1tq+kry1efiJ5P17WtmwpoG0TDOXXBl+ur6ccppows8wOg9GkyxN7XJKT+yUeZG2qP/sXC+9yZNOi7QlCgXQvZPS6XTicPRtEBpjd0mFQnHCZLXnkw34j4UtxBICGFcGp1wgb8TDhDzygGPFMcJhtUmR3DIMRXKzU3p3bLauKaWORxtQaAOMYYO2aE8ryBFL+Lywaz3s+HRYfT8V8Y0SyQpFvGCxyUV7cCyVWizR1h6rmTCM4lA5VjGuhppe2yYktnuSW4afSG5plnHW1oTeb0vagEIbYAwbtKwttUcia8eJUFcBQoBOD2nDZ6ZHEd8okaxQxBOJ7aFAsXgTrj0iveDDoBx1RwooAPpWdS8xSYpkV2vfY+piBU34J3RTnOB4tDLeWsXCYUN6u+hvrIqsHSdCzSH5bEsaFoV+FApQMckKRXxRdh7UV0J2QaQt6T+rnpMp4BIdUFwaaWsGjEIKAWiiqdeqe3kjbeTlW8nICp9HOBZxtcrsFgmJvd+WGmgAjg0whg1a1pamGAyH0nKYJ6ZE1AyFYiBRIlmhiCdyi8HTBn5vpC3pH0LIYihwLLZ6mDCGMYCsIldDDVn0XChl/JRk2toCvRbbiEXaWqUnubccyQECoRRww6bankZu+/G0NYPXA+YYep8b2r3fyT3n+lYoYg0lkhWKeEJLzaSlUosV3K0QaM8NnDW8vIfJJPMzfoax/SccWmlqX3tO4eFEW5sMIUlKDn8O6qknjzyaaR5+Ijk9D/QGmQquIcZmfJra86+nDI9qmAoFKJGsUMQXAb8sTX14J5QuiLQ1faehUj4bjJCUElFTBhodOnLIoZ76Xqvumc16AgFBs3P4FRMZN8FOarqZ/NEJvbb9Nt/GihUbtiGwbAgxGKFgokzRGGs422Pqh1F6RoUi4gv3Xn75ZWbNmsW8efOYP38+W7duDdv+o48+Ys6cOcyfP585c+awevXqfvd5ww03MGfOHBYsWBB63HTTTZ3aCCG4//77mTFjBrNnz+aaa66hqSlGizAoFBp6nSxNvf/L2LoRN7ZnfjDbhmV6Ka1ynBZG0BPNTh/vvlrFO69UIoQYCtOGjMwcC0VjE8kdaQ3bblhW2+vIxFNh9GQwmiNtSf+YMEfmdi6eGmlLFIoBI6Ke5HXr1nHdddexYcMGSkpKePrppznnnHPYvn07dnvXC2B5eTnnn38+r776KgsWLOCDDz7gggsuYPPmzRQUFPSrz+eee47Ro0f3aNtjjz3G888/z7p160hISOBb3/oW1113Ha+++uqAnweFYsjIbI/nDQbkIrhYSdWkTeVqpXuHGZvYxHKWo0PHZCb32C4lVVajCwbB7QpiS+w9E0SsoIWQmM3hfTfDXiSb2wcJXndk7egPAb8shpKWB+nhC8EoFLFERD3JDz30EIsXL6akpASAa665Br/fz1NPPdVt+9///veMHz+eBQsWADB//nxKSkr4wx/+cMJ9dkcgEODBBx9kyZIlJCTIqb8f/ehHvPbaa2zZsuVEDlWhiA5MFrC0T2fXxFCuZK34yTBL/6ZRSSXb2NZraeqEJEPIkd7YEGOLL8Pg9QQ5esRNQ70PgyH8TMETPMFjPMa7vDtE1g0xer2sLlkXQ2ka3S75bDSBKcY84ApFGCIqkt9//33KyspCf+v1embOnMny5cu7bb98+fJO7QHKyso6te9vn92xefNmampqOvUzYcIEEhMT+9WPQhGVJLaX44ylXMn2FMgpgrxhtlCrHa0oRhXh8+Pq9XrMFnnZbmocPnHJDXUeNqxpYO0HdZjM4UXyIQ7hxBk2VV5Ms2cTbHgHPn8/0pb0nYo9cq1DU82wDIdSxC8RC7eoq6ujqamJnJzO0705OTmsX7++29fs27ePyy+/vEv7ffv29bvPpUuXsnPnTvx+P6Wlpdx9991kZ2eH9qO9TkOn05GdnR36X084nc6w/9ewWCxYLDGU3kcxfLCnQv1RmS85VsgYCSVlMHpSpC0ZFLSqe1qRjHCYLXo87iDOpuFTda+xQR6LyaxHrw/vu9EGEsOu2p6GPVU+u/p2L4kKDu2Qax1c4WPqFYrBxOPx4PF4em3XV50GEfQku1xyeuZ4oWixWEL/6+414dr3tc9x48ZxxhlnsGLFClasWIHH42HOnDm0tLScsG0a+fn5OByOXh9Lly4N249CMWgkZ8rnxt7LIEcNWnymOfyirlhFqxzXl6p7Vpu8bDc3DR9PsnYsFmvvt6Q6ZOhNPsMrX3aI5HT53NYSWTv6g8qRrIgCli5d2if9lZ/f92tHxDzJWqzv8arf4/GE/tfda8K172ufP//5z0O/m81mHn30UVJTU3n22We58cYbT8g2jUOHDpGcnBy2DXQV4ArFkKEt1mvuXZBFDY3VMk+yaXiK5P5U3bPa5GK9lubh40lubm4XyZbeRbI2kBh21fY0kjPkcyyJZJUjWREF/OxnP+P222/vtZ3T6eyzUI6YSE5PT8fhcFBZ2XnKt7KykqKi7uMOi4qKwrY/kT4BkpOTyczMZO/evaH9aK8bOVJOgwohqKqqCtuP1ldfRLJCETHGnyIXBsXSDe3DF8HbJnPIDrOKe3Cs6p4ff69V9/ILEgj4Ra+V6WKJliZZSMSWED5bx7CutqehfS+9bpnGpJfwk6igpb0aZlpuZO1QxDWDEcYa0W/fokWL2LBhQ+hvIQQbN27krLPO6rb9mWee2ak9wIYNGzq170uft956a6c+PB4PdXV1oZHF1KlTyczM7NTPjh07aG1t7dE2hSJmSM2Wi/f8XlnuOdoJ+I+FW6RkR9aWQcKBAytWdOjYz/6wbWecksq0shTyRg6fQhotLdKTrHnJe+IIRwgiU8UNW5Gc2v4ZF0FobYyoKX2mtb2GQPowjRNXxC0RFcl33nknb731Frt27QLgmWeewWAwcP311wPwzW9+k2uvvTbU/tZbb2X79u18+OGHAKxevZrt27dzyy239LlPgCeeeKKTAP7Vr36Fw+EILQo0GAzceeedLFu2LBSD/N///d9ceOGFTJ7ccw5ThSImMLePtIUAXwykEXPWA+1iPpa83/1Ah467uZu7uIscwueu1kpTe4dRaerWZulJTugl73MttYxkJCMYQQK9V+aLSSy2Y4VEGsJnO4kKgoFjg1jlSVYMMyI6Xzd79myeeuoprrrqKmw2G3q9nnfffTdU9MPtduPzHVucUlBQwBtvvMGPf/xjzGYzHo+HN998M1RIpC99Avz2t7/ltttuw2g04nK5yMjIYOXKlWRlHbsB33bbbbS0tHDaaadhMpkYO3YsTz/99BCcFYVikNEb4MguaHXKKlk5oyNtUXg0oWCyDuscrDnkUE55r1X3zBZZmrqlefgs3BtVlIC7LcDYCeHzYKeQwrf5NplkDpFlEaJwshzA6mOgWExzg/R6AzgyImuLQjHA6MRwq20aIZxOJw6Hg6amJhWTrIh+HroO2prh8h/DpFMjbU14Pn8fXv0j2NPgjicjbc2g8SIvsoUtnMu5zGFOj+1WvlPFi/93hMwcM/f+9/CY2drwST1VFW4mT3dQUJTYY7vNbOYlXqKIIq7juiG0cIj5/H2ZfWbSqZA1KtLWhMdZDx8+L+OnL/p+pK1RKHqlP3pt+Kz8UCgUfceaKEVyc12kLekdrdqedXiWpNb4jM94jddooSWsSE60y9LU7rbhE27h80pfjamXktQuZPjbsA210Iil0tQBHySmQKJyDimGHzGwbFahUAw41nZvXXNDZO3oC872VHUJw7MktYZWmnorW8O2S3ZI34bXM3xEcsWhNhrqfb0uJP0Lf+ExHuNN3hwiyyKErr00dc3hSFvSO772VKnDND2jIr5RIlmhiEc0wamtSo9mHGmQWwR5YyJtyaCShizE0Ehj2HaOFOlJ9nqCBIPDQyh/vLKWT1bV0dQQPvdzFVU4cYYyXAxb9n8ZO6WpD26XJanrj0baEoViwFHhFgpFPJLQPjUaCyI5Ix/GBaF4WqQtGVS0xWhNhH9PUlLl4kUhZFYIuyO2fR3BYBBfe6YOR6opbFvt3GgDimGLVpq6LQZKUx/aKUtSG8O/dwpFLBLbV1eFQnFiJKbI57bwmRSiAm+bfB6mJak1tAIivWW3sCUaQvUlmhpjP8OFyxVAc4g7UsP7bTSRPOyzW4Sq7rVG1o6+4Gof1CWomGTF8EOJZIUiHrGnyOdYuAk31oDfdyy/8zBFE8kt9F6O2Nxevnk4iOSmenkMen3vFfecSM/qsBfJWj5wdwx8P13tgzpt4K1QDCNUuMUAU1ZWhsHQ+UK/ZMkSlixZEiGLFIpuKJ4uxacjBsTG6n/LFfTjy4Z1sQKtiEgrvQujkQUJtLn86HW6wTZr0HE2yjhks1mPvpcSzNoAIpvhWXkxhFZZ0u+VC+NMUTxAdLcP6rQQEYUiili2bBnLli3rtC0QCPT59UokDzDr169XeZIV0Y89VU6PiihfAOV2SYEMw7YktUYucgDgw4cLV9g0Z3POSKe+1tNrDG8s4GyS76/Z2vvEpjaAGPYiOTlNZrgQQaivguwozpXslmn5sA/zOHFFTNKdk1LLk9wXlEhWKOIRLV2T3yfLykZrZa/G9mp7egMk9u2iFqvkkMNP+SkWLAjCp0Izm6UHeTiUpm52Sk+y1Rr+M+jHTyaZtNFGHnlDYVrk0OtlDL7HBY3V0S2SPe1rBpLTI2uHQjEIKJGsUMQjJrNM2+RxwbRFkJrV+2siQWO1fDbboJep+FjHgIFUUmlr/0mk58pzJrMsTd3aEj5lWiyQnmFmwhQ7mTnhQwq8ePkO3wFgBCOGwrTIUjhVhjJEcyy+zyNDQiA2QrcUin6iRLJCEY/odHBkt7zJNVZFr0huqpXPtp4F43DCho022kKV5Xris7UNbFjTwNSZbiaVxraHPSnZSOHYRPJHh6+ip50TK1b08bDmfOJcqKsASxRXF/T7YNY54POqmGTFsESJZIUiXrEkSJHsjOLS1CGRPLyr7Wl8wAfsYAcllDCKnqfYtSwQra19X4ASrfh8fStJ3Yac1rdhG3SbooJQaeq2yNoRDr9XZrWw2MCg5IRi+BEHw3GFQtEt1nYPVXN9ZO0IR0t72ew4ycG6l71sYxs72Rm2XZJdChK3K/ZFclWFm4Y6H35/+Djsd3iHx3iMZ3l2iCyLMDo9tDZGd2lqr1aSOopDQhSKk0CJZIUiXtG8s80NkbUjHClZcVGSWsOBDJ2opTZsu4RE6Un2emNfJK/7uI5PPqhj367w+aGPchQnzl5DUYYN5Vthw7vRXZr6yG5VkloxrFHzIwpFvKKJ5NbGiJoRloyR0qNWUhZpS4aEFFIAqCe8dz8hUV66vZ7w3tdYQDuG3gqJ1CHDgrSBxLBHyxYRzVUxD7eXpO5H3lmFIpZQnmSFIl7RUqq5nJG1Ixxet3we5iWpNdKQuWYbCO/d1zzJvmGQAs7rkceQ0EeRrA0khj2xUJq6VStJHR9rBhTxh/IkKxTxSlKKfG7rvQxyxHDWyWIiRnOkLRkS0pHew0Yaw7ZLTGoXyb5hIJLbhb7mHe8JbeCQSpxkUXC0e5J97sjaEY5QSeo48e4r4g4lkhWKeGXcLHC3QnoUF2ZY87JMMzX+FEgZ/nlYM5DewyaawrZLTjGRlWPBbNEjhEAXw+WpNW94QlJ4T7ImkrVzNOxJah8MBPzRW5paCwXRBtwKxTBDiWSFIl5JTm8vTR2lca1+rxTIEDc5WDORA4EWwnv3U9LMzDpVnpNgILazb/nbU8AlJoU/CCcyLEjztg97kjp4Z5sbIC0ncrb0hLs9FCQpPr6fivgjhi+tCoXipNDifKN1Orelgzc1Tm7CC1jAT/gJOYQXREajDtABAp8/iMEYpWXFe8HnCxIItItke/jbUTLJpJEWH9X2AAwmMJrkQLElWkVye6YRVZJaMUxRInmAKSsrw2DofMNasmQJS5YsiZBFCkUPGIyw/0spkmcvBmuUVbXTciRrYiEOSCUVGzbchB+46HQ6jEYdHk8QnyeI1RqbItnvCzJ+ih2/L4i9F5H8Db5BAw2cxVlDZF0UUDhVhloYovDzL8SxQieOOAmBUcQcy5YtY9myZZ22BfqRjUWJ5AFm/fr1JCfHR+EDRYxjNMOhHSCC0FANuYWRtqgzLY3y2RyFsZiDhFZNzoOHAAEM9Cx+33+ritaWAMUlSTFcmlpH0dhE9HpdrxX3tPzIcVNxD2D8bHDWy4p20UbABzPOloPstNxIW6NQdEt3Tkqn04nD0bdrpkoBp1DEK3o9mNtvvs6ayNrSHVr+ZlN8pH8DsGDhLd7iBV7gMOErrekNcrGeqyV2c9T627NzGE3hb0UBAniQ1d3iSiRrWV183sja0R0+r8xqkZ4XnSJeoRgAlEhWKOIZrTS1MwpLU2v5m83xcwPWo2crW9nGNg5yMGxbS7vn1dXqHwrTBoVmp4+Geh/utvDHcIhDPMZj/IW/YCF+ZhYIBuRgsSkKB7FaDvM4GsQq4g8lkhWKeEaLQ47G0tQJyZBbDCOKI23JkJKIfE+qqArbzmzRRHLsepIP7HHxyao6Pl0dfpCmlaRuoilsCMqwY+saWZp625pIW9KVo/tkSeq6ikhbolAMGiomWaGIZ2xJ8lmL/40m0vJkLue8+BLJSSRRQw3VVIdtp4nkNlfsimTNC27uJR75KEcBSCBh0G2KKrTvpzsKq+5V7JUlqaO5IqBCcZIoT7JCEc8ktC8ydYUvXhER/DIGNSqLKAwidmSJ395EsqU9o0VbW+yK5DaXjEnWBH9PaF517dzEDdEskrWBdUJSRM1QKAYTJZIVinhGKyerlZeNJpobZEGRWK6UcQI4kO9JHXVh21ms8vLtjmGR7HK1e5J7SWFXg4zJjTuRrA1itXzE0YQ2sE5Q2ZwUw5f4uvsoFIrOTJwLOh1kFUTakq58+iZUHZA5kgsmRtqaISMVWTilN5GclWslK8dNckoU5tDtI5rAt1rD+2u0c6ENIOIGTYBq+YijCW1hbWKcvSeKuEKJZIUinknOAJtd5kqONjRhEGeeKk0kNxB+MWXpTAdms44Ro2I3+4e7TX7u+iqSU0gZbJOiC02AeqOwKmZbe+n0pJSImqFQDCZKJCsU8YxWyc4fhXlYPe3CIM48VddxHTnkMJ3pYdtpuYX9PjEUZg0KXk+7SLaFD7cwYyaddPLIGwqzogdNgEajSNZsirNBrCK+UCJZoYhnAn7YtxkQMPeiSFvTGZ8mklMiasZQk0kmVqy9lqY2GmUxEa83CmcB+kj+aBt+f5BRheGzVpzHeYxiFOdx3hBZFiWkZMGIcXLxajAoCwBFCyGRHF+DWEV8oUSyQhHP6PRwaLv8PeADQ5TEtwaDx6qM2VMja8sQo1WUayN8HOrB/a28/UolKakmTl2QMRSmDTh5+TZMZj2jxySGbaedi7iqtgfysz+mfUbB74uuEu2lC2TIRc7oSFuiUAwaUTQsVSgUQ05SBy9QNOVKdjmB9jCCOBPJDTTwOq/zNE+HbWexGhDB2PYk+/3yPe6tLHXcimS94Vh2Fy0lYjQghCxElJIVd+FQivhCeZIHmLKyMgyGzvF1S5YsYcmSJRGySKEIg8kCeiME/dDSBI7MSFsk0SoA6g1gia8CEjp0bGQjZsxh2yUkysu33xu7Mcm1VR6Z51mEP4aHeAgXLs7gDMYydoisixK00tStzuiJ//X7jr1nxvCfU4Uikixbtoxly5Z12hYI9D1tphLJA8z69etJTo6SC5lC0RdMZvD45Y04agjKktSGOCpB3E4uuQB48eLC1WOVucQkeW58vtj1JH+wvAa3K8ikaQ5yRvTsJa6gAg+eUMnuuOKz/0BzPYwYC5kjI22NpLlOlqS2JMTld1QRO3TnpHQ6nTgcfZsBUSJZoYh3TFbwuKSnKlqwJMiS1HGYXiqHnNDvRzlKMd2X5bYny8t3MAhebwCzOfbEiuYF1wR/d3jaf4D4y24BYLFBM9H1/WyokiWpzXEW/qKIO1RMskIR71is8tkVRTdhbdFeHE7lGjCEYm+PcrTHdglJx3wcLc2xV3UvEAiGYpITk3r211RQEfq94wAibtDCjaLp+9nSXm0vmhYSKhSDgBLJCkW8o3mDoqk0tcsJPg8Y43OySwsrqKSyxzYmkx6DQaaBa232D4ldA0mb65iwt9t7zqqinQMrVkxESfaVoUQTyW1R9P3UbDFZI2uHQjHIxOcdSKFQHGPmV6C6HIqmRNqSY3y5Gja+B4VTYMoZkbZmyEkkkdr2n3Bk5VoI+AXBYOwt3tOEvU4HFpuux3bVVAP0GJs97LElyWetwl00oIV+WFS4hWJ4o0SyQhHvODLkwiB6FipDjiYIrEmRtSNCaJ7keurDtjt9UQatLX6S7LF3KW9tkSLZaNShD1MkQzsHcZf+TUMTye7WyNrREc2THGeZZxTxR+xdWRUKxcBiao/7jabS1JogsMWnSL6d29nNbhayMGy7UGlqf+x5kltaZLiFyRw+6s+PnzTSyCZ7KMyKPmx2+exxRdaOjrjbB7FKJCuGOUokKxTxTmONLE3d0gAlZZG2RuJpF8kJ9sjaESEyyeQQh/DhC9tOK00di2ngbDYDY8YnhvI998QMZnALt1BCyRBZFmVkF8jS1NGS/g2ODWKtcZiSTxFXKJGsUMQ7zjpZmjqaYh497SWZo6V4whBjRS6IcuMO2+6TVbXs292K3y8YOSq2vHr2ZCPjJtpJTQ+fwUQ7B9o5iTtGjJOlqaNpwFgyGxJTYNzMSFuiUAwqKruFQhHvaELU1xZZOzriaReHcSqSv+RLXud1XuO1sO10eh3BYOdMEbGCz9e3ktRajmQLcZpuLBrDoSw2WZI6LQ7zViviCuVJVijincR2Ier1RNaOjvjaRXIcFhMBOMQhNrKx18VqFqsUmO622BPJTY0+Wpr9pGWEDxX5X/6X93iPZppZzOIhsi6KMBhlPLKrSVaOCbPIccgI5TGPw5R8irgiCr5tCoUioiS0l+f0hZ/aHzKEkPGXmfngyIy0NREhlVQAWggfAmO1xa5I3rSugQ/fq+WztQ1h2x3hCNVU00YUzXQMJULA2tdh/TvgjpLFe3s3wZHd0XPNUCgGCeVJHmDKysowHFfLvrva4QpF1GBPkc9+HwQCYIhweeOAH4qny99T4zOjQQopQF9EsnyvPO7YW7jnbpM2a97wntDOgQPHoNsUldiSZDJpIWSqxoQoyPiy6zPwe+D0SyNtiUIRlmXLlrFs2bJO2wKBvjsVlEgeYNavX09ycnzGUSpilMSUY7+7nGBPjZgpwLHYS71eTjXHIemkA+AivOcwlkWyZrPVGn5Qpolkzbsed+h0YLKA1y0z0GSPiqw9weCx72jHa4dCEYV056R0Op04HH0bdKtwC4Ui3rHYQN8uVFrCT30PCW6XLEltMEqBEIf0VSTbEuQgwuuJRZEsvTma0O+JVmS6sTTSBt2mqMXUvmixtSmydkB7Fpz2vNyRHlArFINMfLppFApFZ2YvhmAgOtJMHdoBa16BRAec/tVIWxMRMsgAek8Bl5puIjXdRHJq7C2gcrcLe1tCeJGsDRTiWiSbbVIgu6JAJGsDaZ1e2qVQDGOUSFYoFJCaI0MtglFQuc3llM/mOM2LiywmAjL9mRcvZrrPJTymJIm589NJjMGy1F6P9CT3JpK1BXvawCEu0SrbuZojawcc82YbzdGRaUOhGERi78qqUCgGnlAu1ihIAxcSyfHrpRrBCG7lVixYwopko7G9LLUvCgY3/cTnkTYnhqm4JxAkkYQOXWjgEJeERLIzsnYAtGrfzzjNW62IK5RIVigUUFUOFXvBkSFTr0USzVtmia0KcgOJCRPZZONp/0mi+4wGRpOM2fb7Y08kjypOwNHgIyO754p7PnzczM0AFFM8VKZFHyPHQcArC3hEGi3kwxS/Mz2K+EGJZIVCAZX7ZWnq7NEwI8K2tLWLZGsUpLqKIFasePCEjUv2eoIsf7MKv19w1vlZIc9yLFA0JhGvN0h2Xs9iS6u2p0OHidiLux4wxs2UhTsyRkTaEsgugNKFcZvDXBFfxM4VVaFQDB7Wdq+tOwpiHrWCCbbEyNoRYT7kQ17ndbazvcc2tkQDXo8gGABXa+wUFBFChLzf4YR9x5LUOuIz0wkg43/hWKW7SGIwSY92dkGkLVEoBp2Ii+SXX36ZWbNmMW/ePObPn8/WrVvDtv/oo4+YM2cO8+fPZ86cOaxevfqk+rzjjjvQ6XQcOHCg0/YFCxZ0edxzzz0ndIwKRdSjeW3drZG1A8DTbkOce5I3tv/sYU+PbaxWQ2jtVGuzf4gsO3n8foGzyYfbHQybCnsjG/kzf+Y5nhs646IRnU6WpnbWRtoSWXQIVElqRVwQ0XCLdevWcd1117FhwwZKSkp4+umnOeecc9i+fTt2e9dUVOXl5Zx//vm8+uqrLFiwgA8++IALLriAzZs3U1BQ0O8+N23axNNPP92jfatWrRrQ41UoohZru9fWEwWlf1NzpDc5MwqmliOIFodcT33YdkajHq83SEtL7IjkpgYfH74nBd8lV+T12O4oR6mmGgMRrgIZaSr2yNLUjkw4LcJV7g5ukyWpVY5kRRwQUU/yQw89xOLFiykpKQHgmmuuwe/389RTT3Xb/ve//z3jx49nwYIFAMyfP5+SkhL+8Ic/9LvPYDDIkiVLlHdYoYBj+ZHd4YtXDAkFE2HiqTB6cqQtiSiaSG6kMWw7k1mGIbTGkEjWbDUadRgMPd+GtAFCIvEdeoOt/fvpi4LsM3s3wZ6NcrGvQjHMiahIfv/99ykrKwv9rdfrmTlzJsuXL++2/fLlyzu1BygrK+vUvq99/vGPf2TevHlMnhzfN2KFAjh2E/aGL14xJKjpXADsyPekd5EsL+OxFJPc2iJt1bJz9EQDsnBF3IvkhGT5HA0xydpsUzQUHlIoBpmIhVvU1dXR1NRETk5Op+05OTmsX7++29fs27ePyy+/vEv7ffv29avPI0eO8OSTT/LJJ5+wbt26Hm289dZb2bRpE0IITj31VH7xi190GwbSEaezb3ksLRYLFovKM6mIErSbsDcKwi3crSCCcoFQHJOMfE+aCF9lzdwukttiSCS72uOnNYHfE9oAQRswxC2aIPV7QYjIlmvXrhG25MjZoFB0g8fjwePpfbalrzoNIiiSXS45rXu8ULRYLKH/dfeacO372uctt9zC0qVLSUjoOQ/rtGnTWLx4Mb/73e9obm7miiuu4KyzzmLNmjUYDD3Hx+Xn9y3H7D333MO9997bp7YKxaCTWwQzzo4O79CHL0DADxNOieu4RwcOAJyEv6CnZ5rx+YIYjbGT/aG1VYpkcy8iWRsgxL1ITkyRzyIoPbnWCOYQ12abEuP8PVFEHUuXLuW+++4b0D4jJpI1gXq86vd4PD2K14SEhLDt+9Lna6+9htFoZPHixWHte/zxx0O/2+12Hn74YSZPnsyKFSs4++yze3zdoUOHSE7ufYStvMiKqCIhGexpoI/wAim/VwpkiHtPlSaSmwmflu+0RRlUHGojvzB2iq+0uaTXu68iWfOqxy0d0yG2NkVWJGtx0QmOyNmgUHTDz372M26//fZe2zmdzj47NCMmktPT03E4HFRWVnbaXllZSVFRUbevKSoqCtu+L32++eabHDhwILT4r7GxEYArrrgCq9XKG2+8QVJS19RTxcWy2tPevXvDiuTk5OQ+iWSFIqrQylIHA1KkhsvLNZi0dvCaJsb39+hyZGhZCSVh28ViaeqQSLaGF8kGDCSQQDrpQ2FW9GIwykfALyvepedGxg4hjsVFJ6VExgaFogcGI4w1oingFi1axIYNG0J/CyHYuHEjv/jFL7ptf+aZZ7JmzZpO2zZs2MBZZ53V5z7/8pe/dHr9qlWrWLhwIc899xyjR48GoLq6mv/5n//pZMeRI0eAvodTKBQxhcEIR3bJqdRpCyE1OzJ2aCWp9QYwxfdsSzbZpJDSaxGNWCxNnZpupqAogYKi8B7Ry7mcKUzhAi4YIsuimPzxUqDqI3jb9rTJkA84FgKiUAxjIprd4s477+Stt95i165dADzzzDMYDAauv/56AL75zW9y7bXXhtrfeuutbN++nQ8//BCA1atXs337dm655ZY+99kXXC4Xjz76aKjASCAQ4IEHHmDs2LGceeaZJ3XMCkVUotPBwR1wcDs0VEXODlf7IrU4z2wBssocHKs61xNbPm9i+ZtVfPCf6qEwa0DIHWlj0rRkJk8LP2XfseJe3DPpNBgz/VhO80gggrIk9aTTICG+i/0o4oOIepJnz57NU089xVVXXYXNZkOv1/Puu++GMki43W58Pl+ofUFBAW+88QY//vGPMZvNeDwe3nzzzVAhkb702ZErrriCHTt2hH6fM2cOjz/+ODk5Odxxxx1ceeWVWK1WWlpaKC4u5r333sNqtQ7yWVEoIoTJLFeutzRGzgbNkxznXmSQmR3e4z3MmLmVW8O0FHg9IhTCEAv4fdIbaehlsaEbuUjMirruhgaOAV/4doNJMChLUhtNkV+/oFAMAREVyQCXXnopl17afQWhZ599tsu2efPmsXbt2hPusyPPPdd9qVOr1crPf/5zfv7zn/fah0IxbDDb5KKgtvALxQYVd4t8NiqR7MHDGtZgxYpA9Bh2YbXKy7jXExxK806KZqcft7t3e//IH3Hi5HROZyxjh8CyaKa9NHVr39NXDTj+9nhkozlyNigUQ0jERbJCoYgSzO3eOlcERbLZBpn5sjR1nJNJJiC9qV68PYYcWG0yas7rjR2R/NH7Nezf4wIhGD+55wWa+9lPK62qLDXAxvfg0A65uLYwQkWwag7LktRpEVo4qFAMMUokKxQKiaV9EVUkPcnpebIkdZZaINsxo0MddeSR1207q00KSJ83dhbuedtttdrC34K0cIsMMgbdpqjHYpPPkSwdf2SXLEmdOSpyNigUQ0hEF+4pFIooIiSSWyJng5rODZFIYijEooaaHtvZEtpFsi92PMma11vzgndHK60EkHHWmlc9rtG+n54IimRtAG21Rc4GhWIIUSJZoVBItIIF7tbI2aClmIrzktQAOnTYkGKkltoe21nbRbI/hkSyZms4kVzNsWwdypNMB5EcwdLxrvYBtCWCGTYUiiFEhVsoFApJyWy5an1k+OIVg8q6t2DvJlkie8y0yNkRJdiw4cJFHXU9tkmyG7EnG0Me5VhACw2xJfZ8C9K852bMGNWt6ljqN28ERbLmxY5kxT+FYghRVx6FQiFJyQJ7emTTr3lkDCpmld0CZMhFXftPT2TnWpl3VgY6nQ4hBDpd+LRq0YAWGpIQRthr3nPNmx73hESyO3I2aCJZeZIVcYISyQNMWVkZBkPnC/+SJUtYsmRJhCxSKPpINORh1bxkVlWoAOB2bmcf+5jClB7bGNtzDQshCAbBEAMOZa06YDjvtwsXCSSQTHyXJw+R0J7r3xe+uMygogl05UlWxAjLli1j2bJlnbYFAn3PKa9E8gCzfv16kpPVRV0Rg7hb4dB2qD0M0xZFxgafdhNWniqAAgpooCFsm44FOQJ+gcEQ3Z5kIQQjC2z4fUGSHT3fgiYykR/zY0ahMikAMi1i9mhIjmB8thrEKmKM7pyUTqcThyN8tU8NJZIVCoXE3QL7NkdWoGpesoSuFTLjEa3SnJYKrTv0eh0fvV+LxxNkWlkqI0ZFd3hCICCYVCodCXZHzws0VUnq48gugPGnRDYcasJcqD8KI+O9sIsiXlAiWaFQSGztMyA+b+Rs0PZtUyIZ4Eu+5D3eI0CAszirx3ZudxCvJ4ir1T+E1p0YWqgF6MJ6vVVJ6uPQwqH8XhACIhF7npQqy1GnZA/9vhWKCNAnkXzw4MH+dWo0kpfXfeJ7hUIRpSS2i+SADwKByAS3anmSE1TIEsBWtrKGNTgIPzVoNOrweogJkex1B/G4g1ishrCLDP/Nv3mRFzmP8/gaXxtCC6MUg0l+N/3tD1MEcolr6xWMyr+miA/69EkfPXp0n1dMCyEoLCxk7969J2WYQqEYYjoKU3frMdE8VAT8styt3wdJKUO77yhFE8fNhK+CaDLroBXa2qI/V/KRQ228/1Y1Vque87/Wc3njfeyjnPKwmT3iCr0ePnpJ/j77vKEvDS0EHNgq7Yid4o4KxUnRJ5F8yimn8Nxzz/WpQyEE11577UkZpVAoIoAlAXR6WczD5YyASA7IktQA9tSh3XeUkoo8Dy2Er4JoMsmiHG2uvq/ajhRtrdJGoyl8LSttYNCbFz1uMBjlI+AHV/PQi2SvG3atl7+ff9PQ7luhiBB9EsmJiYkUFBT0uVOLRS20UChiDr1exj36PNDaBJkjh3b/2lSuwSDjHhWkkQbIEs3hMJul4HTHgkhukyEhJnP42UlNJKeQMtgmxQ5GsxTJrc6h33dr07HfbSq7hSI+6FNZ6uXLl/er0/62VygUUYKxPc6xLfz0/qDg9UgvtjECsZZRiiaSXbjCtjNZ2kWyO/pFsrs9JMTUiydZ854rkdwBLbOFO/zMwqDgar8mGEzHFhEqFMMcFX2vUCiOMf1MeQNOzRn6fR/aAR++IKv+nXrx0O8/CslA5sTtTSQ7UkwkJRswRnmOZDgWEmIyhxfJ2jFrIScKjolkVwQGsa52T3IkFgwqFBFiwETyXXfdhcfj4eGHHx6oLhUKxVCTMQKaaiMT7tDWPoWs79MEV1ygiWQ3boIE0fcw+XfaogxGFtgYOz76U+e526RINvcSbqGFmGjedAVgbk+HFwlPclv7PtVMjyKOGDCR/PHHH+PxRLBcpkKhOHm0G6A/ArmS29rjbs0qL67GBCbwXb6LFSsePNjovlCIVpraH4j+tAMejwy3sFjDD8T07T/ppA+FWbFBSCSHn1kYFDTvdSSLmSgUQ8yAieQVK1YMVFcKhSJS1B+Fg9sh0QF5xUO7b7cSyceTSCKjGIUPH27cPYpkrShHwB/9KeBS08zk5VvJHRn+fV7CEvz4mcWsIbIsBsgplFkmIpH9RX0/FXHIgMYk79u3j6KiooHsUqFQDCUVe2D/ZimSZ583tPvWbsKW6C6rPNRYsYZEck/s3t7MB/+pYVRRIlNmpAydcSfAqKIEhBCMCRMaEiCAH5kFQ1Xc68D4U2Q+8+zRQ7/v3CKYdBpk5g/9vhWKCDGgIvk73/lO3HuUy8rKMBxXqWzJkiUsWbIkQhYpFP3AkiCfvRGYzvW079OsRHJH1rCGKqpYzGJy6T43bjAIrS0Bmpt8Q2xd/wm0l6U2GHsvSQ1gQU3vhwiVpo7A+2xNhIyR0putUMQIy5YtY9myZZ22BQJ9zwLUb5Gs1+v7XH0vHlm/fj3JyaqkriJG0USyu23o9615kq2JQ7/vKGYVq6innv3sZzazu21jtcoFfT5v9IdbtLkCBAIibNXzfezj7/ydZJK5l3uHzLaox2CU+cQjkaJRE+Zq4Z4ihujOSel0OnE4+lakqN8iubS0lMcffzz0dyAQ4PDhw/z73//mwgsv7G93CoUimrC1C1Rfz1P7g4Y9TaaeS80e+n1HMQkkUN/+0xPWRKk4fd7oX7j3/ltVVBxyYzTqKRzTfVGKoxylnHLsRH+2jiFl3xeyNHVmPsw4a2j3XbEbqg5A+hBX+lMoIki/RfLvfvc7zjjjjC7br7rqKq688kq+853vDIhhCoUiAljbRYs3AiK5cAo4MmFc2dDvO4pJQr4n4USyrT1ThM8X/Z5kb7u325bQc6q/OuoAOUBQdMDWPmiIxPdz53o4sluWw546f+j3r1BEgH4nJO1OIAMYjUb27t170gYpFIoIopWb9UYgnWNALtTCqGocdUQTyY009tjGlijPWSyIZH+7t9tq6zneQonkHtC+n74IfD81YW5V74kifuj33ej+++/vsq2lpYVPPvmErKysATFKoVBECM1T5Y/ATdjXnptZxTx2Qgs5aKKpxzaaV9bvi/5wC59f8yT3LJIbaABkCjxFBxLa17v4IpDHXBPJtu5DZBSK4Ui/RfJjjz3GtGnTQn/rdDrsdjuLFi3iBz/4wUDaplAohpqsUXIq1RaBWNCV/5Qe7FHjVVxyB5KRwiicSE5MMmK16TGZ9QSDQfRRXLVQ8yT3RSSrmOTj0ERyIALZLTTvdSSuDQpFhOi3SD733HN59tlnB8MWhUIRaRKT5eK5SIgsnweCfpXd4jgcyFXYTpw9tklNN7PoPDmTJ4K6EwikGzr87SngEhJ7vv1oAwIt1ETRTmK7SA4GpGd3KAt7aFU4lUhWxBH9FslKICsUwxhDex7WYBACAcLm6RpIAr5jMck2lUKxI1dxFVasTGZyj22MHXIO+/1BDMYhet/6id8fJBDQRHLPNnrwoEcf8qIr2knoIFBbm4ZYJLd7rxPVe6KIHwZshczbb7+Nz+fjoosuGqguFQrFUGM0QeU+6dVtbYTk9KHZb2vLsd+TUoZmnzFCIYXkkhu2qIZOp8Ng1BPoIEKjEZ83SF6+lYBfkBjGk/x1vk4xxSxgwdAZFwsYTMeq7fWjIMJJ4/NI7zVAQt/yyyoUw4EBE8k33XQTbreb6urqgepSoVAMNTod7P1CTq021gydSHa1x9vq9GBWFdY6ooljD+EXU366uo7WZj8lk+xhSz5HEp1Ox7SyFECHxdZzTIgHDzp0auFed5QuAE/b0H5PAn5ZktrvgwQVAqOIHwZMJG/cuJFgMPrTDykUil4wmqVIdvW8UGzAcbXH25pUZovjqaGG1azGjp1buKXHdq0tflpbArQ4/UNoXf/Q4pGNRl3Yyq1aWWpVkrobjGYpkoeyNLUQsiS1waCyzyjiigETyRkZGdTV1Q1UdwqFIlKYLeBuAVdL720HCq3MrroBd6GWWlawgjTSEAh0dC8uTUY9EKCtLXqdFV6vDAex2noWyAD/y/9SQQVTmEIppUNkXYxgMErPrts1dPvUBLm2ZkGhiBMGdA305ZdfPpDdKRSKSKB5c91DKJJ1epn2TZW87UImmYD0rvrp2Utsskjh2eaKXk/yvl0tvPtqFcvfrArbbjvb2cWuXkNM4pJ1b8FH/5YV8IaKhipZktpZO3T7VCiigH57kp1OJ7fddhvvvPMOlZWVg2FTTFNWVobhuIwAS5YsYcmSJRGySKHoJyabfG4bQpGclgtTF6j8yN2QQQYg43Q9eDDRvTfPZJI+jzZX9HqS3S65+MtoCO+faaMNgHSGKCY+ljC1Z7QYykHs0b2w41NIyYbzvjN0+1UoTpJly5axbNmyTtsC/Vj02m+R/MMf/hCj0cjf/vY3fvrTn/L444/j8Xh46aWXsFqHMB1NlLJ+/XqSk1WKHEUMY9Fuwq1Dt0+tOIIKt+hCCikABAjQRFOPuYPNFik8Pe4hzHrQT9xt0jaTOXy4hSaStQGCogOW9kHsUH4/tQHzUKacUygGgO6clE6nE4ejb1la+i2Sd+zYwZo1awB48MEHmT9/PgBf+cpXuPTSS/vbnUKhiDbM7TdhTwRiHo0Dtkxi2NCx6lwNNYxgRLftzBY5gxXNIlmLlzaZw2e28CE/D0okd4Mmkr1tQ7dPTZArkayIM/p9R+roLfZ4PPh8PkwmOf134MCBATNMoVBEiPGzwZYEhVOHbp/r34bta2HiaTD+lKHbbwygR48VK27c1NHz4ujERANWmx6dPryXNpJonmTN690dNdSEfs8ia9BtijksCfJ5KBfuKZGsiFNOaOHesmXL8Hg8TJw4kauuuopnnnmGb33rW+gjUcpWoVAMLBkjZWlq2xDmqHW3yhX76hrSLTak97CWnhdOnX5mBovOy2LKjOgt9qB5ucOJZO0YjRhDx63ogFa2fSg9yZ72fWkCXaGIE/rtSb7rrrt46623aGho4O677+bcc8/l3//+Nzk5Obz44ouDYaNCoRhKjO0Lw4YyD6tH5sXFqm7C3XEbt3GYw4xkZI9tjEYpPAP+6K2453HLcAtLGJHcQEPIe67oBm3w6nUP3T610CslkhVxRr9F8sKFC1m4cGHo761bt1JXV0d6ulqFrFAMC1wtcjW7qwkmnz40+9S8YlZVYa07JjGJAIEecyQDGIzyf/4oFsnJqSaycixk5vQsgAsp5C7uCi1YVBxHag6kj4C0nKHbp/p+KuKUPs1t9lYk5HiBrIqKKBQxjLMGdm2Qj6FC84pZVcnb7tC8qloluu44uN/Fxytr+ej9mh7bRJqx4+3MOjWVqWFCQrRj7CmLR9wzskQOXouGsMhK0TQomf3/2Tvz+KjK6/+/Z5LJZF8IkLCGPexGMIBsGTZRUNyqWIqC1j0KIvqtoJWqXytasUBNrX6rgL+KWEQtgoqAIlAVCBj2RVYjkASyb7M/vz9u7sBklswkE7I9b17zmuQ+51lmwsz93HPPcw507n3l5pRIGgE+iWR/i4TIoiISSRMmrEqcmK9gIQeLyXluiRMHOch2trOHPR5trBY7xYVWCvOvYJiMn9isSrhFcLBnj7haQESWpPZAQ4RDxbaBxK7QxnO4j0TSHPEp3KKoqIht27YhhG+38YzGKxgrJZFIAktYVZ5vq/nKzWmpmis8yrtdC2U729nMZq/FNcLClRRwFkvjLSZisSjnkCAvIvlrvuZDPmQEI7ibu6/U0poOwTpAXNpMdyVQvwtkHnNJC8MnkZyVleXIh+wLXbp0qe16JBJJQxOuimQLCAGaK5BSLDoOjHqIbFX/czVBYlDCE0op9WgTqopkc+ONSf7y0/PkXzATFa2jY5L7TWA/8zPHOEZnOl/h1TURLBb4bjUgYORtEHIFPO7njoPVCn5UKpNImgM+iWS7vfF6JiQSSYCJqBLJwq5s2KnvHe1CQL+RynN8u/qdq4mibmLzJpLDwhSRbG3UnmQ7QoA+1HOkXzHFAEQjK5e6JSISqLoQKi+GkCuQS3rfVrDbYPiU+p9LImlEyKSkEonEmcvjgstL6n8+1WMN8nauB+KIA6CMMo824RFVnuRGnN1C9XKrgt4dJSj/56RI9kCQDoKq/FsVV+LzaVYEMkBY483BLZHUB7IGbIBJTU0lKMj5BOCudrhE0mgJClZOxDaL4qmq71RTtqoNSFotBHkWTy2ZVihhKBV4rrKmimSbVWCz2QkKanw+EGtVTHJYhOe/s+otV0NMJG4IDlGK71wJkVx+2d2LSHnhImlaZGRkkJGR4XTM5kfYkBTJAWbXrl1ER8svEkkTZ2CaIl7DrsBGuvOnYPsaJRY67c76n68Jom7Yq0kkBwdrCArWYDLaCY9ohCK5KruFusnQHaq3XOZJ9kJwiFLgo8Jz+E3AqKwS4tog0MmMI5KmhTsnZUlJCTExvl2ES5EskUhcaddN8SJfiTLRFSWKV8xmrf+5miiqSK6kEoFwW1QkPCKY66YkAgJt0BXYbOknFosddXtLeKTnU0855cClEBOJG0L0UA4Yr4BIVkOuZCiUpAUiRbJEInFFzcVquwK5WCurTvTSS+WRa7iGe7iHcMIxY3abQ1ij0RAcrMFqFY2yNHVlxaVbnOFewi0qUVKbqSEmEjfoqioWVpbX/1zq51OKZEkLJKAiecKECWzcuDGQQ0okkoagKA9yTkGbTsqjPlFP9FIke6Q1relBD2zYMGL0WGgjKFiD1do4S1NbLXbaJIZgt0FIiGdP9xzmUEABoxl9BVfXxGjTUbnzor8CZaLVkI4rkWpOImlk+C2Sz5w5w5/+9CeysrIoKSlxKjCSk5MT0MVJJJIG4tR+yD4CcQnQf0T9zmWsytgQElq/8zRhNGgIJZRyyjFi9Lip7aedhRTlW0jqFkHM1Y1r41uIPojU4a3Q6bRovYTxmDChQ0cUsrCMRwamQeuO0K5L/c8Vl6iUpI5pU/9zSSSNDL9F8m9/+1vatWvHfffdR1RUFJqqQgNCCF599dWAL1AikTQA+jDl2eh5o1jAMFZ5kkPC6n+uJkwmmeSTz53cSQIJbm2KCy0UFVooKWp8panVTXvBOs9eZDt2zCjV3WRZai8EXcHS1GERVSWp6/mOkkTSCPFbJFutVtasWeO2LTy8nosOSCSSK4NaQMR0BUWyXopkb3zGZ5gxc45z9KWvWxudTvHQVlY2vspoavo3b6np8slnFavQo2ce867U0poeamlqs7H+51I31AbLLUySloffW9d79+5NZaX7mvGyMp9E0kxQYx2vhEjWh0NUK3k7twbCUS5c8sn3aKMLUb7SjZWN77v48L5ivvosh60b8zza5JDDUY5ygAOEIDeKeeT4HqU09fef1f9ceb9A/rlLF7MSSQvCb5E8YMAAxowZw5///GeWLVvG+++/73i8+OKLfi/g008/5ZprrmHUqFGkpaVx8OBBr/bbt29n2LBhpKWlMWzYMLZt21anMefOnYtGo+H06dNOx4UQvPjiiwwaNIghQ4Ywffp0iouL/X59EkmTJLTKk3wlPFU9roZBE6D/yPqfqwkTgXLh4k0kqxvijJWNL51eZaWSAk5oPIdbXOQiAKGEuk1zJ6kiWA8IMLl3WAWUIzvhwDY4daD+55JIGhl+3z95/vnnSUxM5P/+7/9c2nJzc/0aa+fOndxzzz1kZmaSnJzM+++/z8SJEzl8+DBRUa6bNs6cOcPkyZP5z3/+g8Fg4LvvvuPGG29k3759JCUl+T1mVlYW77//vtu1/fWvf+Xf//43O3fuJDw8nPvuu4977rmH//znP369RomkSRKmepKvgEhW4yrVtHMSt6giuYgijzb6UCW1msnY+DzJqnc7xEtMsnoBoHrNJR4IrzqXWUz1P5cqxMOuQCYNiaSR4bcnediwYZw6dcrtY+jQoX6N9eqrrzJp0iSSk5MBmD59OlarlRUrVri1X7p0Kb1798ZgMACQlpZGcnIyf/vb3/we0263k56ezoIFC1zmsdlsLFy4kPT0dEec9VNPPcXatWs5cEBeTUtaAKGRyrPlSsQ8SpHsC2q2h0IKPdqE6KvCLYyNLyZZ9W6ra3SHFMk+Elb1+TRfAZFsqRLJVyLdnETSyPBbJK9bt85j27fffuvXWJs3byY1NfXSYrRaBg8ezKZNm9zab9q0yckeIDU11cne1zHffPNNRo0aRf/+/V3m2bdvHxcuXHAap0+fPkRERHhcm0TSrGjfHfpeC338u/CtFVtXw4+fw4Xs+p+rCaOK5GI8h32FhmkJCgZE4wtVUL3b3kSyegGges0lHgiLVp6t5vqfSxXiqjCXSFoQfodbREREUFpayjvvvMOBAwfQaDQMGDCA+++/322IhCfy8/MpLi4mMTHR6XhiYiK7du1y2+fkyZPccccdLvYnT570a8yzZ8/y7rvv8sMPP7Bz506386j9VDQaDQkJCY42T5SUlHhtV9Hr9ej1MsWRpJES3RradL4yuYsrypQNgtKT7JVoFGFUgufvmBFj29C6rZ6OSY3PE2usEsl6H0RyJFKQeSWi6lx7JUSyejdJimRJI8dkMmEy1Xx3xVedBrUQyfv27WPChAnY7Xa6dOkCwOeff86rr77K119/zcCBA30ap6JC2TVfXSjq9XpHm7s+3ux9HfPxxx/nlVde8ZiyrjZrU+nUybdckgsWLOBPf/qTT7YSyRVHLUF7JfKwqif68MZV/KKxcQ/3EEssgxns0SY4WPEgN8aKe2ZTlUgO9SySVS+5FMk1EF7lSbbblLjk+qxWaan6fIbJ4i6Sxs0rr7zCCy+8ENAx/RbJc+bM4X//93/5/e9/76iaZLfb+ec//8kTTzzBN99849M4qkCtrvpNJpNH8RoeHu7V3pcx165dS3BwMJMmTQro2lSys7OJjo72agOuAlwiaVRoNHDhF0Uk1+dJ2Ga7FJMcLk/C3uhHP/az32u8blCQIpJt1sa3cS8yOpi4eB2tWntO7XY7txNPvNcLAQmKSI5po1zMmirrVyQ7LmLl51PSuJk3bx5PPvlkjXYlJSU+OzT9FsllZWU88MADTse0Wi0PPvgg7777rs/jxMfHExMT41LKOicnh27durnt061bN6/2voy5fv16Tp8+7dj8V1RUBMBdd91FaGgo69atc9jm5OTQsWNHQEkJl5ub63FtKtHR0T6JZImkUaPTwaEflJ9Li6CV+wpvdaay9NLPEdKT7I1QlNAXI543U+acNbJzewFx8SEMGRl/pZbmE/2uiqZ1mxD6eymXrZakbkWrK7iyJoguBAZPUC4yg+qxyIfdDj0GKUJZ5jGXNHLqI4zV709XRUUFlZWVhIWFuRyvKRShOmPHjiUzM9PxuxCCPXv28Oyzz7q1HzduHN9//73TsczMTMaPH+/zmG+//bZT/y1btjBmzBhWrVrlCB8ZOHAgbdq0ITMzk2uuuQaAI0eOUF5e7jSXRNJsCdIpJ1+btUrI1pNIrqgSyRqtLEtdA7nksotdtKIVj/GYWxubVXAxz9wowy1sVWtSQ0LcYUK5eydLUvtAkE4RyfUZl2yzKiWp4VKIh0TSgvA7u8XkyZMZOXIky5YtY9u2bWzbto333nuP0aNHc9NNN/k11jPPPMMXX3zBsWPHAPjggw8ICgpixowZANx7773cfffdDvvZs2dz+PBhtm7dCsC2bds4fPgwjz/+uM9j+kJQUBDPPPMMGRkZDuG/aNEibrrpJrfZMCSSZokal1zh+yYHvymvytQQrAOt319HLYqf+Zkv+ILv+M6jTWi48h5aLI0v3EIV7kHBnv/OH/ERn/EZRzl6pZbVdAkOAcSlmOH6QN2ToA2CoKD6m0ciaaT47Ul++eWX0Wq1pKenYzKZEEIQGhrKnDlz/K64N2TIEFasWMG0adMICwtDq9WyYcMGR5YMo9GIxXJp41BSUhLr1q3j6aefJiQkBJPJxPr16x2FRHwZ83Luuusujhw54vh52LBhLF68GFBir8vKyhgxYgQ6nY6ePXt6LDwikTRLdCFK1omK0ppta4vdppSkvhJZNJo4rWkNQCWV2LARhKtoCQtXjlktjc+T/NWn5ykrtdKuYyiJ7d3/vbPI4md+9poLWlJF5ldw4Vdlw+tQz3ts6kR5sVKSWsYjS1oofovkoKAg/vznP/P8889z/PhxhBD07NmT0NDaneRuvfVWbr31VrdtH374ocuxUaNG8eOPP9Z6zMtZtWqVxzaNRsPzzz/P888/X+M4EkmzRN0MZKxHkRzbRilJHRVXf3M0E1SRbMSICZPbDXzhEcpXemMUyUajHbNZoAvx7EkupxxAxiT7gkYLiPr9fOaeUkpSh0fDpAdqtpdImhm1vr8ZGhpK//79GTBggEMgS0EpkTQjVO9uZXn9zaHezg2SOZJrIh5lI56x6p87wiMUT7LNJrDZGlfIhRoCEhbm+bZ9BUp4m3pBIPHClfh8VpYpz/WZPUMiacT45EnevXs3UVFR9OrVy2tIxb/+9S+/Qy4kEkkjRVe1kc54BUSyLCRSI7HEAmDFSgklbr2tqicZoLLcRmR044nzVjfuRUR6Pu2oIrktba/Impo0qkg2+bdh3i+kSJa0cHwSybfeeiu9e/fm66+/5q9//SspKSlu7dR0ahKJpBmQfI0SBtG+e/3Nse87yPoGuqfAgFH1N08zIIZLqdMucIEudHGx0Ydq0GiUPZAVFTYioxvHxYfFbMde5dhWvd3VMWHCjLIJLaG+sqk0J/RV4TbGehTJ6gWy3DMgaaH4JJKPHz9OUNXO1iFDhrBhwwa3dhMnTgzcyiQSScPSvrvi6a3P1E/lRYonzGatvzmaCVq0hBFGJZVc4IJ7G62WG+9oh80qnLzKDU1F+aW/b5gHkZxHnuNnKZJ9QBXJ9epJrhLJepmeUdIy8elbNCTkUoWktWvXurRbrVY2btzIunXrArcyiUTSsKhxwvVZmtpYqTzLk7BPPMZj5JLrCL1wh06nxWa1OcIbGgMV5TZA8XCHhLgXyTkoRaB06GSeZF8IjVCezZX1N4e5SoDLHOaSForfAWs33HCDyzGbzca6deu4/fbbA7IoiUTSCDCWw4VsOHe8/uZQT/DqCV/ilaEMpStd0eC5IEdQVbEOayMqTW21CuLidcTFey5J3Y52zGc+z+K+mJSkGnFtlCp4kfWYCUQN5Qj1XApdImnOBOR+nF6vJyMjg9GjRwdiOIlE0hjIPQ2Hvoe2nWHstPqZQ4pkv1A9rGplOncc/KmYvBwTiR1CiW/TODyyUdHBXJsWT1i451OOWpJabtrzkW5XQUUZxNRjJpCOvUDYoVPv+ptDImnE+CSSV6xYwYoVKwDIyspi7NixLjaFhYUBr5ndFElNTXXEb6ukp6eTnp7eQCuSSGpJWKTybHafbiwgqGNLkewTxzlOJpm0pjUGDG5t8i+YuZhnpvBiPVZi8xOrDyWp1bR2Ychb+z7hCIeqx79zq0QQAjr0rL85JJJ6JCMjg4yMDKdjNpvN5/4+ieQuXbqQlpYGwKlTpxw/q2i1Wtq0aSPDLYBdu3YRHS1r3EuaAapItnj2WtYZdewwWdHLFzaykS/4glhieYzH3NqoxTqMxsYVbgGXQkHcsYUtfMZnDGUoM5l5hVbWhFHLxtfnngGZx1zSxHHnpCwpKSEmJsZDD2d8EslpaWkOYRwdHc2cOXP8XKZEImlyqMLVUo+eqrAIxRMW6dsXVktH3bBXQolHmxB9lUiu9N1bUt/s31PMpvW5dOwczogx7sMDDnKQvez1uilRchkVJfDfTxVP7/Cb62eOvF+UuGR74/m/JJFcSfyOSVYF8rlz5zh69CgajYZevXrRvn37gC9OIpE0IGrqt/q8nTvQoIjw9j3qb45mRBxK+e5iij3a6KtEssnYeIRNRbkVs0lg9VIFsJBCwDkftMQLoRGXPptW8yXPciDJ+kbZwNtnKCR2Cfz4Ekkjx+/sFgUFBdxxxx107tyZcePGMXbsWDp37szUqVMpKCiojzVKJJKGILxKrNht9RNyIYS8nesnapW9Mso82jg8yY0o3EL1aus8pH+DS8JfepJ9JOKysL4yz3cW6oR6F6k+c6VLJI0Yv0XyvffeS0lJCZ9++ikHDhxg//79fPLJJxQVFXHffffVxxolEklDEHnZibGiHk7CNqsilEGWpfaReOIB7yJZH6p8rZsbkUhWvdqql9sdagiJu3LbEjfo9KCtuuio9HxnodbY7WCruogNl3sGJC0Tv8MtDh8+zJEjR9BqL33Z9evXj0mTJtGvX7+ALk4ikTQgwSHQeyhotMoj0BTlwY+fKyVvDVMDP34zpDVKPG855R5t9KGKcLJY6l5MpJRS7NjrHAJhqhLsUiQHmOAQJY1ieT1cxFaWXvo5Ijbw40skTQC/RXLXrl2dBLJjoOBgunfv7vj9zJkzJCUl1W11EomkYencB0yVoPGclaDWlBUpJXXttvoZvxmi5hCuoAKBcFtUZMiIVkRGBdOuY91SqVmx8g7vYMHCLGYRTu0LSphNimBXvdzuUL3jqrdc4gO6KpFc6fnOQq0pr/JOazSyIqakxeK3e2jGjBnMmTOH06dPY7fbsdlsnDp1ivnz5zul2bj33nsDulCJRNIABNdjaWrVU1UfG46aKQMZyJ3cyS3cggX3f5MQvRaNBqyWuoVb/MzPlFJKAQV8wRd1GstkUsItQsM8n3JU77jqLZf4gK6qNkFFqXe72qCGWAWFyItYSYvFb0/y9OnTAVi6dKnTcSEEGvlBkkiaFyUFUHAeCnMhLiGwY6sndp0sQuQrbWlLP/phx44JEyG4XmCoBTtstrqFWyxlKTvYwU/8RF/68ht+U+uxwiKCiIoOJjrGc+z5LGZRQAFDGVrreVoccQlKXH99xPRXVHmndfIiVtJy8VskX3XVVSxevNirjRBC5lKWSJoDR3fBhV8goQt0GxjYsVVPVUhoYMdtxmjQoEdPJZUYMRKF64aqgotm9uwoJDIqmOGG2nlliyjiXd51eKsPc5iTnKQb3Wo13tWpcXTuEk7/q2PdtgsEduxEEeVIcyfxgcET4UI2JNRDaGN4JHRPkZktJC0av0Xy/PnzGTRoEFFR3ne7zps3r9aLkkgkjQR9lYA1et4oVmvUOEoZ7+gXRzlKHnnkkksb2ri0Wy2CnLMmwiOstZ7jPd7DgoVWtCKKKM5whrd5m1d5tVbj2WooS23Bgo2qkAzkRZPPBNdjaeqwKOiYDHFtAz+2RNJE8DsmeerUqdx555012vliI5FIGjkhVQLWWA8bg6RIrhUf8zHrWc8pTrltD4tQsluopaBrw7/5NwATmMCN3AjAZ3xW6/FqKkt9jnN8xmdsZCM6ZDpAn9HVY2lqVXjLPQOSFozfnuTU1FS+/PLL+lhLsyA1NZWgIOeE+e5qh0skTQJVwJoqAz92UBCERkKkTPnlDxFEUEopF7notj0sXBXJtdu4d5GL7GY3APdxH+1pTwYZHKv614tefo/59ec5mE12evaJpHVb1xj0X/iFvewlnHC3GTskHjixF3Z+AZ16Q4+rAzt2YR4UX4RomW1E0nTJyMggIyPD6ZjN5ns1Ur9FcnJyMqWlpW7DLR588EHeeecdf4dsVuzatYvoaBnDJWkm6KvSfpkqAj92z8FK/tWu/QM/djMmkkgA8sl32x4eqXyt221gsdjR6fy7YfhP/okVK21ow3jGo0VLN7pxkpO8xVv8lb/6vebyUisWiyDYw1oucEFZex3SzLVIgoIUj299pIA7sgMObFP2DgyeEPjxJZIrgDsnZUlJCTExvuV+91skDxw4EIPBwC233ELHjh2dvKbbt2/3dziJRNKYcYhkY+DHtsjbubVB3axXQIHb9vCIS9/JlRU2dDH+ieQ1rAHgOq5DWxWRN4UpLGYxn/O53yJZCOEItwgPd1+WWvWKRxDh19gtnrAqZ5W5Hi5izVV3j2Q4lKQF47dI/uMf/0hiYiLvvfeeS1tubm5AFiWRSBoJYYrX0nHCDCQy5rFWRKPcqSqk0G17SIgGjUbJDFZRZvWads0daqzz7dzuOPYIj3COc7SlrcciJp4wmeyO6uOql7s6qkhWveQSH1EzT5hNgR9bDbEKlRcukpaL3yJ52LBhfPvtt27bxowZU+cFSSSSRkSHHtDzGmjdPvBj//czqCiGtp0hsUvgx2+mqCWiiyhy267VagkK1mC1CCorfI+9A6XK3mM8RimlpJHmON6d7o78zGWUuU0954mK8ktrCPPgSVa94v6MK+GSSLbUg0g2S5EskfgtktetW+exzZN4lkgkTZTWnaB99/rJlVqar6SWC/L7a6hFE0ssAMUUe7SZdGs7zGY7ca3989Krwrs1rZ3yFQcRRAwxFFb980sklymp6LRaPMZHq15x9QJA4iMRVe9XvYjkqhCrMOndl7Rc/D47RUREUFpayjvvvMOBAwfQaDQMGDCA+++/v8bcyRKJpIkRXPUVYauHFFPqiT1SCiN/mMQkjBgZzGCPNqFhQVitdkd+Yl9RxWoccS4hFRe4wE520p3u3M3dPo+perODgz3HRqviXIpkP4mMVZ7tNuXzFMjqleqeAelJlrRg/BbJ+/btY8KECdjtdrp06QLA559/zquvvsrXX3/NwIEBrsolkUgaDgEU5uAIKg0UVivYqopdRMgKa/4wgAEc5jCt8VxNTy3a4W+u5NWs5t/8mzG4hs5lkslGNtKe9n6JZJtNEBkdhD7UfagFwG/5LV3pigGDX+tt8UREKxlignXKXZmAimTVkyydX5KWi98iec6cOfzv//4vv//979FqFc+A3W7nn//8J0888QTffPNNwBcpkUgaCJsF9n2n/HxzeuA22ZUXXfpZ9YZJfEKtSGfEc8aRIwdLOP+rkVatQ0ho53sFu13s4jCH6Utfl7audAXgNKf9Wm/rtnpGj29DlJcNhDZsRBFFO9r5NXaLJzgEhk5WLjiDAlyEJamfklquVWJgx5VImhB+V9wrKyvjgQcecAhkUDaKPPjgg5SX10PpWolE0nBExF76OZC5WMur4mmDgi9VDZP4RAUVHOAAP/KjR5sLOSbO/2rkYq5/5YqzyQaUjXrV6UlPAM5y1q8xrRalqImnktRwSfDLktS1oD5KUwsBiV2hS3+IlWWpJS0Xv0VyRUUFlZWu6aAqKiqoqKiHXI0SiaThCNGDpuprorwkcOOqnmSZ/s1vcsllDWu8lokO0St/M6PR6tfY5zgHQDLJLm2qdzkX/1J9OkpSB3kWyatZzVd85ffYEi6FWARSJNusl0KsgmWZcEnLxe9wi8mTJzNy5Egee+wxevToAcDPP//M3//+d2666aaAL1AikTQwwTplU1BFAEWy1aLsmpfxjn6TQAIAlVRix+4o+HE5IXol/tdY6Xtpajt2R77ifvRzaR+Ist+klFKKKfZ5k93ezCK++/oCXXtGMHSU+xLH3/M9RRRRgXS0+M2+LXD+FISEwohbAjNmZTmUXFQEuNZzLLlE0tzxWyS//PLLaLVa0tPTMZlMCCEIDQ1lzpw5vPjii/WxRolE0pDo9FUiuTRwY7buAEMmQ4znzWcS97RFuf1txUoZZY7iIpej1yteW5PRd5F8mtNYULKYqIL4ctrTnlBCMWJkL3sZzWifxi0tsVJeZvO6lkqUu5NtaOPzeiVV2GyKF7ncc0pAvyk4Dz9tVi6QJz0QuHElkiaG3+EWQUFB/PnPf6agoIC9e/eyd+9eCgoKePnll51KVEskkmaCripONJCeZFmSutbEc8kb6yk8QR+qfLWbzb6L5H3sA5Q8zGG4L0WsitiDHPR5XJNRSQGnhoBUx4IFE0o6wETkJjG/UUvHG+thz0Ags2VIJE2QWmfxDw0NpX///tjtdvbu3UtSUhKtWrUK5NqaJKmpqS4XC+np6aSnpzfQiiSSOqKvEkyBDrcAGe9YC4IIQo8eEybyyHNsqLscNd2aP57kX/iFIIIc4RzueIiHyCabPvTxeVx1Dapwr04eeY6fpUiuBaFVIrkygBvn1T0DIe4vliSSpkJGRgYZGRlOx2w23yuR+i2SlyxZQkZGBitWrCA1NZWxY8eyfft2QkNDWbNmDTfccIO/QzYrdu3aRXR0PVQnk0gail6DIbYNxAewNHXWZji6C/oMg77XBm7cFkI44Q6R7I7QMEUkm82+nwyu4iqe5Vm3m/ZUhjAECxZHeIQvmE1VItmDJ1n1huvQyewWtSG0qiKeKYAiWb0gliJZ0sRx56QsKSkhJsa3PRV+i+TVq1fz+eefk5yczKpVq8jKyuLAgQNYrVYeeeSRFi+SJZJmR1I/JQdrIEtTF19UbulaArgjvwURQQSFFJJPvtv2qwbHIuzCrxzJhRSiQUNHOnq0UUtVq5X5fMFUJZJV4V6dC1wA8BjiIakBtWy0MYCbHlWRrHqpJZIWit8iWa/Xk5yseBr+9a9/cffdd9O3b19Hm0QiaWaoeYwDmWLKVOWJVE/wEr+YylSyyaYb3dy2h4YHoQvRYvej4J4qfFvhOWxOIPie79nFLqYxzadxzTWIZNUbHoEsf1wr1AwxZt+9+zWi5kSXJaklLRy/RXJJSQllZWWcO3eOjRs3sn37dkeb0ei5ApREImmiWMxQmKukgkpODcyYUiTXiaEMJZJIj8JSLdxh86Ms9au8ihYtk5ns0SaYYDaykWCCsWEjiJo3a4fotYSGaYmIdH+6GchAnuRJR9YOiZ9Et1KK/gTyTo8UyRIJUAuR/Lvf/Y727dtjtVpJS0sjNTWVgwcP8uc//5lOnTrVxxolEklDcu6Ekou1TWdIuyMwY6per3CZJ7k26FHu2qlZIapTVmJl/55iQvRaRk+oOa1aGWUc5SiA1417femLBg1WrJzgBL3oVePYQ0fFU1xopu9V7kWcWpK6E/L8USuS+sE1EwN7wZnYFcxG6Og5Pl0iaQn4LZKfeOIJhg8fzrlz5xzxx8HBwVx33XUMHz484AuUSCQNTESVuAnk7Vxz1V2ncN82T0icucAFDnCAOOLc5iu2WO1kn65EF+K5yt3l7Gc/ACGEeI1J1qOnFa3IJ5/97PdJJFut3stSy5LUdcRRltoSuDHj2yt3jpL6Bm5MiaQJUqsUcEOGDMFms/HLL7+g0Wjo2bOnI05ZIpE0MyJiledAimRLlQc0Qork2vA937OGNZRSymxmu7RHRChf7b6GW6giuQ1t3Fbwu5wEEsgnn8Mc9mlsdQ1BHkTy13zNV3yFFi23cZtPY0ouI/iyPQNCgMa3CyOvqPsPdDKPuaRl43cxEZPJxP/8z/8QGxtLjx496N69OzExMfzhD3/AZHJ/608ikTRhImOVZ0uAPt92u1JCNzgEIqVIrg1qlokS3OeuDo9QYoXtdrD4UFDkGMcA6ECHGm3VsIif+dmntX7zZR7//eYi5aVWt+272MUOdnCc4z6NJ6lGUBDsXA/bP4FS37OOeCX/HFQUg8ZviSCRNCv89iQ/9NBD7Nmzhz//+c90794dIQQnTpzg3Xff5cKFC7z33nv1sU6JRNJQRCqCDKtF8TDVtUqesENqVarIWM/xrxLPqFX3inFfijg88tKGuopyKzEh3v9mJzgBQGc61zh3V7oCShnrmrDb7RQXWhACdDr3gquIIsB7Vg2JF4JDwGQEu1UpAhIdgPdx11fKZ31AGrSSBV4kLRe/RfJ3333HwYMHCQ93zp943333MXDgwIAtTCKRNBKi4i79XFYEsXXMQqDGTmo0EFTrop8tGrUynSeRHBIShFareJIrym3ExLk1c3CWswB0oUuNc3enOwDnOFejrckoEFURH6p3uzpq6jmZ3aKWaDRKWITJqnw+64p6MQyX7iJJJC0Uv89QvXv3dhHIAJGRkfTo0SMgi5JIJI2IYJ1STMRmgbLCuotkNWwjOCQw8ZMtEDUsopRSjzZBwRrsZkF5mfswh8uxYCGIIIeX2BsTmchxjvvkda4ovzR3aLh7kawK/fYEsKJjS0OnB1NFYErHl1924RVVw9WVRNLM8TvgaOrUqSxevBiz+VJhAbPZzOLFi5k82XN+TYlE0oRJToVe19Q91AIg+yhkfgWHf6j7WC0UNQNFOeXYcF96Wg1vqCivuTT1dKbzLM8yhSk12namM4kkYsOGwPvGwLKqOOSgIA3Bwe5PN2pctRTJdSCkKjNIeQBEcllVXLM2WBHfEkkLxidPcrduzlWdcnJy+MMf/kBCQgJCCPLy8rDb7XTu3JnZs113WrckUlNTCQpy9pi4qx0ukTQpul8FJQWBEcnFFxRvVYgsQ1xbVC+uHTu55LoVmOMnt6WiwkZCe++p1WzYKKMMDRrHhkBvRBKJBg02bJRTTiSe8/NWlCkCXadzf8dAHQOQeZLrgiqSKz3fWfAZNWRDCmRJMyAjI4OMjAynYzZbzY4DFZ9Esl6v55lnnvFqI4TgkUce8Xni5squXbuIjg5g5SOJpDGgimNLAEpTq9W8QmRe3NoSSSS3cRs6dNhxn70iKkaH1Sqw27x7e0spRSAIIohwXEPpqhNEEPvZTzbZjGc8Ixnp0ba8KtxCF+Lei5xLrsMbnURSjXNLPKCv+rupn626oIZbyM+npBngzklZUlJCTIxvmZV8EsmPPPIIM2bM8GojhGDu3Lk+TSqRSJoYpgoozIH8s9Cu5rhVr6gncr30JNeF0YymkEKPIQ/BVeEW1hpyJW9jG//H/9GVrvyRP/o09252c5rTZJHlVSTbrILQMC1hHjbt6dAxl7lYsPgk0CUeiG6t5BwPxJ0eNWRDL0WyROKTSJ41a5bHtj179rBy5Uo++ugjioqKArUuiUTSmDi2G47vATTQ37Mo8gn1lrBeiqK6EEEEhRQ6whWqc+ZEOSeOlhEWHkSnLp7f6yMc4RznvIZNVKctbTld9c8bHZPCGXtDW1q3dX/rvpJKIon0KcxD4oWrxyqp2jr0rPtY0a2UUtdtPFdelEhaCrXKv3TixAlWrlzJypUrOXbsGKGhoUyZMoU9e/YEen0SiaQxEBahPBsDcDvXVCXqQiPqPlYL5gIX2M9++tCH3vR2ac89byT7dCUdk7xXSjzDGUCppOcr7WgHQDbZXu1qKkldQQWgCH5JHbi86l5diY6HLv2hg8xWJZH4LJJzc3NZtWoVK1euJDMzk6CgIMaNG4dWq2XHjh1ERkbKQiISSXMlLEp5Nrr3WvqFsUq0SZFcJ77hGzaxiTjimMpUl3Z9qBJuYaz0XnHvV34F/MsuoWbXOM95r3ZWixLqEeyhkMi3fMtXfMVQhvo8t8QNwTrlWc1BXhfUfQeBCN2QSJo4PqWAmzBhAh07dmTu3LnodDqWLl3K2bNn+fLLL0lISCAyUrlNd99999XrYiUSSQMRXrUZ1VhR97G0WuUEHC43uNYFtereBS64bQ8LU+KATUbvIlkVuqrw9QV1k10uuV7tMr8v4L/fXuTQPvdFTzLJZAc7OMxhn+eWuOFCNuxYD9vW1H2swhylJLXwHssukbQEfPIkm0wmNBoNzzzzDHPnziU2NraelyWRSBoVqqA1e7917xNXGZSYx37D6z5WC0atUJdPvtt2fagqkr2nO8ojD/Ct2p5KN5S0oBe56NWuIN9McaEVkwdvttq/Na19nlvihqBgJRRK63fpA1d+2gw5pyAsWkn9KJG0YHz6RG3dupWTJ08SHR3NxIkTueWWW/joo4+orAzACVMikTR+IqrS5ZiNdR9LvSWs3iKW1Ao1hlgt61ydsKoKdyaTd09yAQXApXLTvtATZYNYMcUei5nAJS92aJj7U40qktvQxue5JW5wfD5NdR/LVHVeD4+q+1gSSRPH58vOjh078vTTT7Njxw4WLlzIgQMHGDZsGEeOHGHz5s0IIWpVSOTTTz/lmmuuYdSoUaSlpXHw4EGv9tu3b2fYsGGkpaUxbNgwtm3b5veYy5YtY8KECUycOJFhw4YxfPhwNm/e7GRjMBhcHgsWLPD79UkkzYLIWOU5ECLZUZZaFiuoC+rmuSKK3Lb7IpItWNChI4ggkkn2ee5kknmYh3mSJ6nEs7PEZLJVrcX9TUtV4CeS6PPcEjdExCrPVnPdwyTUu0XqmBJJC6ZW2S169+7NSy+9xEsvvcSPP/7IypUrmTt3LufOnWPJkiU+j7Nz507uueceMjMzSU5O5v3332fixIkcPnyYqCjXq9gzZ84wefJk/vOf/2AwGPjuu++48cYb2bdvH0lJST6P+dprr/H2228zevRoAP72t79x44038uuvvxIfH++Yb8uWLbV5eySS5kdcAnQdqFThsttrf1tXCPhhLWiDYMDowK6xhaHGEJfivspaRITy9W7xIpIrqOAxHkOL1q9wCz16utOdMsoopdRj+jizSRFsoWHu8yQXo8Qqq4JfUkvUi1iEkoe8Ll5g1RvtGFMiabnUOYBp2LBhLF26lN27d7uUr66JV199lUmTJpGcrHgwpk+fjtVqZcWKFW7tly5dSu/evTEYDACkpaWRnJzM3/72N7/GXL58uUMgg+I1NhqN/PLLL36tXyJpMUTGQec+0K5b3XbQm4xQWqCUpg6VeZLrgiqSyyl3G/LQrVcEholtGH2d51CGEpTCEdFEo/XzdBBNtNMY7jBXCfRwD8VE1L7+ZNaQuCE0AjRVfz+1rHRtsNvBKkWyRKISgCh/haCgIL7++mu/+mzevJnU1NRLi9FqGTx4MJs2bXJrv2nTJid7gNTUVCd7X8YcOvRSuqHy8nKWLFnCmDFjGDhwoF/rl0haDFrtZWmm6hD3WFZQ9YNGxjzWkSSSuJEbuYM7MOIaBhMWEUR4RBBa9ymKAWeR7C9HOcqXfMlXfOXRxmK2O9ZSHRs2RyGUznT2e37JZWi1yl0egDL3Meo+UVF6KVwjOt67rUTSAqhVuIUnoqN9/6LNz8+nuLiYxETnWLTExER27drlts/Jkye54447XOxPnjxZqzFvueUWNm7cyLhx4/j0008JCnL+Ip89ezZZWVkIIRg+fDjPPvus2zCQyykp8exVuRy9Xo9eL2MyJU2IyjLlBFxaWPv0bSVVmRhCQpWQC0mtiSCCa7kWM2ZMmFwKcgQHXypLLYRAo3FVy/+v6t8EJnAf/qXw/Jmf2clOutGN2bjfjxIUrCE4WOMI/bgcM2ae5EkqqPAr1EPigag4MOovxfzXBvUiVhsky8ZLmhwmkwmTqeb//77qNAigJ9lfKiqUfKvVhaJer3e0uevjzd7fMT/77DPy8/Np3bo1aWlpTjYpKSlMnjyZ7777jvXr17N//37Gjx+PzeY9nVKnTp2IiYmp8fHKK694HUciaXTs3wb7voOzx2s/hiqS5Qk4IKjC2F1pao1GcGR/KXt3F3ncvHeUo5zjnKPynT+o4R7nOOfRZtT4Nlw3JYHO3VxDayqoIJJIOtKRUEL9nl9SjRG3wjUTIa4umyA1SnrGLv0CtiyJ5Erxyiuv+KS/OnXq5POYAfUk+0N4uPKlWV31m0wmR5u7Pt7sazNmaGgoS5cupXXr1ixbtoz09HQAFi9e7LCJioritddeo3///nzzzTdMmDDB4+vKzs72yaMuvciSJoc+FEpRCg3UltIqT5VexiMHgjzyOMIRDnGITjh/8etCtJz8WRHP5SVWQkNdPfe1KSSiUlNBEbtdYPNSllqWpA4wariFpQ4ZaHR6pSS1jEeWNEHmzZvHk08+WaNdSUmJz0K5wURyfHw8MTEx5OTkOB3PycnxuAGwW7duXu19GVMIgdVqRae7lKM1MjKSDh06cOjQIY/r7d5dySF64sQJryI5Ojrar7ATiaTJoArbCvfZFHxC3VQUJoVRIPiKr9jDHnrTm4lMdGoLCtISFKzBZhWUlVmJb+t6Ya5W66tNuENNBUVs1kupyNyVpf6BH/iSL+mH9FoGhJAqb3xdciVbq0pS62RJaknToz7CWBss3AJg7NixZGZmOn4XQrBnzx7Gjx/v1n7cuHFO9gCZmZlO9jWNeebMGW699VanMWw2GxcuXKB9e2WHdV5eHi+//LKTzdmzZwH8ctNLJM2K0ACIZJu1qiR1TGDW1MJpRSsAcshx267TKR7c8jL3YWJqtT5/ComoqAVFiijCjms4R8FFM99/m0/mD4UEBbl6kn/iJ3ayk33s83tuiRvOHFJKU//4ee3HKL6o3Cmyy5LUEgk0sEh+5pln+OKLLzh27BgAH3zwAUFBQcyYMQOAe++9l7vvvtthP3v2bA4fPszWrVsB2LZtG4cPH+bxxx/3eUxQMmDs2bPH8fvChQux2WxMnToVUGKb33jjDU6fPg0oIvqll16iZ8+ejBs3rh7eCYmkCRBalQu3sg4iuddgJXZy2I2BWVMLRy3n7MmbqwtRvuIryqwubWbMjuwWvejl99xqHxs2fuVXl/aSEgtFhRaK8t2nDFTLYatCXxIAjGVQ6r5MuU8c/hF2fQUHtgZuTRJJE6bBwi0AhgwZwooVK5g2bRphYWFotVo2bNjgyCBhNBqxWC59wSYlJbFu3TqefvppQkJCMJlMrF+/3lFIxJcxExMT+eMf/8hDDz1EWFgYJpOJqKgoNm7cSI8ePRw2c+fO5be//S2hoaGUlZXRvXt3Nm7cSGio3GAiaaGEVYlko/+bvByot4J1MiY/EKjlnFWPcHUcIrncVSSf4AQC4XchEZVwwokkkjLKOMpRlzRu5VXCXBfiPgedGuqhCn1JHYmKU54rXTdx+kxlmfIcKsOhJBJoYJEMcOutt7qEP6h8+OGHLsdGjRrFjz/+WOsxQ0NDmT9/PvPnz/fY3xcbiaTFoaZ9M9VBJKubikLkxWYgSCABgAIK3LbrVZFc4RpucY5zxBFHMMHo0Lm0+8LTPE0ZZS6bBgEqypU5VaFeHVXYq0JfUkeiqjzyxjqIZLVvmNxXI5FAIxDJEomkidC+h1Kauo3/mRAc/PczJY9rUl9oKwtI1BW1Up1a3rk6IXpFoFa6EcmJJDKLWW4Frq/0ohdHOOK2NHZllUgO8SCSC1GKXqhCX1JHoqs88uY6ZLcwVYlkWehHIgGkSJZIJL6S2FUpTV2XE2hhjrJ5T+6eDwgd6ADgVqQCDB/Tmq49K+nd3/VvVpdqeyreSlOrwlwV6tVRhb0sSR0gVJFssygXorUJaTJVKs9SJEskgBTJEonEV1RhazHXrr/JqAhkgJi2gVlTCyeZZG7iJqKJRiDQ4Bz/G9dKR3Gh2W21vSKKAIglttbzn+c8X/IlJznJOJw3NVdWKH9rfah7kawKaymSA0RULGg0Slnpogu1u+NjrhLJEbGBXJlE0mSRIlkikfiGNkgpBmK1gN0OWj+T45RUZWDQaGWxggDRnvYMYhCgZKvQ4+w9VPMTW62uKb1e4RWOc5zWtGYCnnO/e6OEEnay0212DZsNgoJB76aIiUCQTjollHAVV9Vqbkk1goIhMg6EvfZxyerG2kiZolEiASmSJRKJr2g0sGej8vN1M/0/kRYr2QzQ6f0X2BK36NARQghmzJRT7iKSL+QYOXKglPIyG/1TnP9exznOec4TTu2rH/ahjzJPVaaKyxk4OJao6GC69Yp0aTNhIrTqn0wBF0BG3Q7lJRBRC5ErBHToqXiTY2WcuEQCUiRLJBJf0Ycr3mS7TRG8/orkErUkdVjg19aCySWXX/mVE5xwEZz5F82cPFaO1epc7MOO3ZFdoi99az13f/oDSkx0CSVO8c1WS80lqUMIqXVmDYkbdKFAiRKT7C8Ws7LnACBWZhyRSKCBi4lIJJImhEZzqTR1ofsKb14pU7IZyBysgWUd6/iET9jBDpe2sHAl1MFkcg63+JVfMaPElqtCtza0pz0hKLHq+9nv1KaGeLgrSZ1FFl/yJT/xU63nlrghpOpOQm0yXKjxyDq9cjEskUikJznQpKamEhTk/AWTnp5Oenp6A61IIgkgYZFKxb0S9xXevGIxKyfgMLlzPpCoG+/Oc96lLbxKJFtMzp5kVdBGEUUkruEQvqJFSxvacJazHOYwIxjhaPthSz55OUZi40Lo2sP5wugABzzGMkvqwIm9cOgHKM6DTsn+9S2+COVFEJdYL0uTSBqCjIwMMjIynI7ZbK4pMT0hRXKA2bVrF9HRMhG7pJkSHg0F56G4FqVvu/ZXYpE79Az8ulowaoiFWub5csIjlK94i9lZJB/lKABtqXuWkUQSOctZfuZnp+N5uUYu5pkxW1xPSDkodyLiiKvz/JLLsNuV0tQl7ovLeOVEFmRugNYdYMQtgV6ZRNIguHNSlpSUEBPjW7igDLeQSCS+o24IUkMn/MEsq+3VB6rQPcc5l7bwyCpPcjWRfJzjQGDSr3VESTV2hjNOx9U5w8NdfTG/8isgS1IHHDVrTIX7vNleKam68A2XmS0kEhXpSZZIJL4TVeX5Kyvyv6+6mUiK5IDSne7AJeF5ORGRVZ5ki3NMshUrccTRjW51nv8hHqIXvRjMYKfjFrMypyrUL0cV1Ekk1Xl+yWVExSrPplqkgFM/07XJjCGRNFOkSJZIJL7TuS/kn4d2tRBXP3yuxDy26Qjtuwd8aS2VXvQCLoUwXE5ElPIVb7MJrFY7wcHKzcPRjKY97ZnClDrP35Wu7GCHS2ls1ZOsCvXLUb3ePehR5/kllxFVld3EWOF/3/KiqjFkCIxEoiJFskQi8Z1OyZB/DiJqEXdfmKNs+pM75wNKP/oBkE8+NmwEcen9jYoOZsTYeHQ6LVarILjqG1+ttheImGB1jEIuheDY7XZHdosIN57kXHKBS3mWJQEiKl55VjNV+IMaohEdH7j1SCRNHCmSJRKJ76ihEqZanITVE7c8CQeUPvRhMpOJJZYyyojh0u1ynU5LXKsQ7HaB3aaIVoEISElqlSii+JIvKaKI3/N7WtMaU6VAVEV4qN5slXLKKUURZHVJPydxg1ru3WZVPqP+5CSvLHMeQyKRSJEskUj8QKdXNu2ZK5WNeL7GFxvLlRM3QIwsVBBIQgllLGMpoYRSSp1EMih5is0mm8Oze5zjvMIrtKIVz/FcnecPJ5wDHKCCCvaznzGMobzMQlCQkmxBTUOnYsLEH/gDpZTSmc51nl9yGZExSh7y4BAoL/ZPJKtxzLKQiETiQIpkiUTiO8EhsGcTCDuMuBUSu/rWr7gqH65GKzcG1QNxxFFCCUUUObJNqPxyspyiQgu9+kURHaNzCFo9eoIDdApoTWt+4RcOc5gxjCE0PJiJNycSFKxBW60EeRFFhBJKRzqilQmWAotWC6PvULzIwSG+9zOboFMf5eI3vu4ZTySS5oL8hpJIJL6j1V7yThW65uX1iCqSQ/TKGJKAUkEFe9nLt3zr0nbqeDknj5VzIUfJLnKEI0BgciSrtKMdgCNXsloGOyTE9W+txi7LHMn1hK6q6p4/pamtJkjqC72HQrgs9iORqMizlUQi8Y+wqgptRX6I5NKq4gZqWWtJQNnDHj7jMz7lU5c2VahWlCtFPU5wAoAOdAjY/J3oBMBpTgNgrUo5p2bTuJwP+ZD1rOcXfgnY/JLLUEOgLH6UplZzmPsTniGRtACkSJZIJP6hlpUu9aPqnrmyqiR17UsgSzyjplJzV1BEVyWSKysUkVwfOYrVfMvZZANw4mgZO7cXcDCr2MV2O9vJJNNthUBJADiaCTvWwd4tvvcpzK1KAaepp0VJJE0TGZMskUj8Q40p9qf0bYeeMPwWSJDFI+qDZJKBS6nVLkcfqopkZeOkKqQDUUhERRXpaq7mgotmLuaZ3YZbnOc8AD2R5cnrBZtF2Shb4sdF7JGdSknqjskwdFL9rU0iaWJIkRxgUlNTCQpy3s3trna4RNJkiayKJS139RJ6xCyr7dUnAxgAKJvijBgJ5dL7rA9Vvo+MlYonWRXSvekdsPnVXM0llCAQDq91iN5VJF/gAgB96Ruw+SWXoV7E+lOaWi0zLzfVSpoZGRkZZGRkOB2z2Ww+95ciOcDs2rWL6OhaFFqQSJoK0VVVvSr8EMnqJiJ1U5EkoHSnO8EEY8XKIQ4xiEGOttAqT7Kx0o4NG3HEYcfuELaB4Gqu5mmeJowwKqmkskqQqwJd5QIXqETJly1zJNcTqtCt9EckFynPstqepJnhzklZUlJCTIxvF4RSJEskEv/o2Au6DoTWfqSK2vWFUs46Mk7ZRS8JKFq0xBNPLrkc4ICzSA5TRLLJaKeUUn7H7wgiKKCe5DDCaEtbyihTvNkOkezsSd7HPgAiiKA1rQM2v+Qy1Ds9xnLf+1SUKM9qWWuJRAJIkSyRSPwlsRt07uNf6ERBDhRfUPIrS+qFRBLJJZdjHHM6PnBwLBqths5dIhzp12KJRRPgTVpxxFFGGQUUYDIq/zdUga5yiEMAtEEWrKg31IqWxgrf+6heZ1noRyJxQorkK4zNZsNisTT0MiSS2iM0oNWBzQ4VFb7lPdbqITIeIluB0Y/UVAFGp9O57BloLvyW39Kf/lzN1U7HY1uFEBOrI0Sv4RSnEIiA5khWOc1pPuIjznGO3sa5AISGOb/XpzgFXMqrLKkHVJFsNoIQoPHhYkgV1LGyJLVEcjlSJF8hhBDk5ORQVFTU0EuRSOpOVCflBHzqVM0iWQhI/Q0gwB6u9GlAYmNjSUxMROOLeGhCjGSkI973cnQ65XVarYIFLGAPe3iKpwI+vw0bP/MzIYTQ0/IkAOHhzqeYCUwghBBSSAn4/JIq4tspd3n0EcrmvYga9siYKsFqVn6OS6j/9UkkTQgpkq8QqkBu27Yt4eHhze4ELWlh5GUDduX2bE0FQixmiKzyKLbp7Jtnqx4QQlBRUUFenpKft1275uXNjCUWUDJcXE55mY0TR8sICw/mqOEoFVTQhS4Bnz+NNF7hFU5ykuHj4ukzMJqrUmOdbNSS1N3pHvD5JVWERoDhLmfx6w1TJXQdoGyulTHJEokTUiRfAWw2m0Mgx8fHN/RyJJK6o9eBzQrBQRBaQ2yy3aLYaYMgrGEreoVVzZ+Xl0fbtm2bVeiFHj172Usmmfye3zuOV1ZYOXqwDFtigSP92gQmBHz+0YwmiCAqqeRQWBbtNf3QV0sBJ0tSXyHCIhXxayyHmBo2SAo7dO4LoeGyZLxEUg35ibgCqDHI4eGyJK+kmaCpEpc2a822qjdL2zgEqfo5bG57AyKJ5DM+Yz3rHWIUICJS8YWc7PUDAPHE05GOAZ8/jDBHeepd0VsB57LUduy8yZt8wRcES/9M/RJaVdmysqxmW7UkdYgsSS2RVEeK5CuIDLGQNBuC/BDJwg4aLQQ1DmHUXD+HCSQ4iojsZ7/juCqSz/b4CbhUna8+UHMff2/5kT07Cqkou/T/4xSnOMxhMskkARn7Wq/8ehR+XAfbP6nZtuB8VZ7k5vm5kEjqghTJEkkjx2KxkJvrWm64QVG9wnYfKheFhEFE7KX8rbXAbDY7Yokl7tGgcaRWO8ABx/GoGB0AF5OU1HDVs18EklRSATgbf4ycsyaCgi8JLzVHcgwxhCG9lvVKiB5M5UraxZo4sA12b4AjP9b/uiSSJoYUyRK37Ny5E4PBgEajoXfv3hgMBoYPH05ycjKzZs2isvLSLvrbbruNxMREYmNjMRgMTo8uXbqwfPnyWq1BCMGLL77IoEGDGDJkCNOnT6e4uOYqb2+//TaDBg1ixIgRTJ48mbNnz3q03b9/PwaDgdDQUOLj4ykvd5+A/5133kGj0ZCSksIbb7yB2WzGYDA4MiXcfPPNDtu1a9cybNgwh/1bb73l/4uv4vz589xwww0UFxe7zGkwGBg9ejR9+vRhypQpnD592qnvoEGD+OQTHzxJtUH1CvtS3lMV0nUIt9BoNEyfPp3//ve/tR6jJdCTngBsZKPjWFh4EFotFLX7BVCyYNQXYxmLTugQGhAaO9Gxl+4efMEXAHSla73NL6midVU4jVpJzxuqTWRsPS1GImnCCElAKC4uFoAoLi52aausrBSHDh0SlZWVDbCyugGIZcuWOX4/e/asiIuLE/PmzXOymzFjhkhLS3Ppv2DBAqf+/rBo0SLRr18/UV5eLoQQ4t577xVTpkzx2mfNmjUiISFB5ObmCiGEeOGFF0RKSoqw2Wxe+yUlJQmdTieWLl3q0ma328WAAQMEIL799luntrS0NDFjxgyXPqdOnXJr7w92u11cd911Ys2aNV7nNBqNYvTo0eLaa691sps6dWqd5vdKWZEQZ38WIueUdzu7XYiSAiGK84WwWuo05a+//iq6d+8uCgoK6jROU/481sRisVggEPEiXtiF3XH80Ue/EwlHB4r2xs7igrhQb/NbhVX8oWiBuObjB8W9j3zt9LnrKroKBGK+mF9v80uquPCrEAtuEeJPtwphNnm3zZit2H6z8oosTSJpaLzptepIT7LEL9q3b4/BYGDDhg0+2U+bNo3x48f7PY/NZmPhwoWkp6c7Nlo99dRTrF27lgMHDnjs9/LLLzNjxgzatlWS4s+ePZsDBw7wxRdf1Djn1KlTWbx4MbZq3tH169eTkpLi92uoKxs2bODkyZPceuutXu30ej233347P/zwAyUlJY7jq1atwmAw1M/idHoljKKmzT52G5QVQmWJEpdcBzp06IDBYGDRokV1Gqc5M53pBBFEPvl8z/eO45a2RXTaP4xp2Y/VaznoIIKIKVPijU1tL6KtypZwkpOOQiL3cE+9zS+pIi5R+bwJARd+9W5bWfWdES3LhEsk1ZEiOcCkpqbSt29fp8cHH3zQ0MsKKFar1XHy84bBYCAkJISOHf3fSb9v3z4uXLhAamqq41ifPn2IiIhg06ZNbvsUFhayZ88epz4xMTH06tXLY5/LmTt3LidPnnQJUXjzzTdJT0/3+zVUp3o4SmRkJAMHDvRo//HHHzN27FifNppZrcoGKfXvcs8995CYmMjMmTOd7F599VVSUlJIS0sjLS2Nbdu2AVBWVuYIO3nttde4++67SUlJYdy4ceTn5/P3v/+dcePGkZyczMaNGyE4BELCsAoNjz/2GKmpqRgMBoYNG8batWsvvYaPPiJl/GQ0iV1Z98UXTJkyhZ49e/L44487vc6UlBQ0Gg3r1q1za6MyduxYPv744xrfj5ZKPPH0ox8An/O543iSwUjnrmH0jOxU72uILlIuUI0Jl+LoV7BCWQdJ9bpxUFJFUBCERyk/553xbGe1QFlVCFu7bvW/LonkCpORkeGiyS7XCDXROLabNyN27dpFdLRzhSOj0cgpD1XGTEbPMZ1arQZdiNYnW41WQ0gNtvrQuqfg2rt3L5s3b2bJkiV+912+fHmN8cmLFy8mJSWFkydPApCYmOho02g0JCQkONqq466P+runPpejisJFixZxxx13ALB79246dOhAQkLdd+OnpKSwZcsWALZs2cK4ceN4/fXXPdr/+OOP3H333TWOm5+fz/vvv8/06dOJjFRSP73//vsuAvmtt95i2bJl/Pjjj8TGxrJ9+3YmTJjAkSNHSEpKYsuWLXTp0oVPPvmEb775hrCwMEaPHs1vfvMbXnzxRR599FHefvttHnzwQeX/s1aD0Wjk83Xr2L9/P1FRURw7dowhQ4aQmZlJjx49+M2UybQOgTF3TOfQoUOsXbuWvLw8OnfuzG233caYMWP4zW9+Q+vWrRkzZoxHG5Xu3btz9OhRCgoKaNVKFj5wxzzmsYMd9KKX49jZLvvQVlppZ+tQ7/Oft+axf8JHHDdHAU8A8Cu/EkkkYxlb7/NLqoiMg/JiuOh5TwbnTyrZZ7TBkJB05dYmkVwh0tPTXZxcJSUlxMTE+NRfiuQG5snf7/XY1i8lmkef7uH4/ZlH92M22d3a9uwTyRPPXTopPv/EQcpKndNzZXwwqFZrXLhwIcuXLyc7O5vy8nI+++wzJkxwLUaQlZXldHs/KyvLqX3mzJkuws0TFRUVgBJKcDl6vd7RFog+1Zk7dy6TJk1i+/btjBw5kjfeeIP58+d77fPVV1+5hDUYjUYXO/WOQmlpKTNnzuSBBx7guuuu8zhubm6uRyGozllUVMTRo0d55ZVXmDVrltd1qjaxsbEAjBw5ku7du/PPf/6Tl156yWF34403OkJcrr32Wj755BNGjRrl6HP69GmKioqIDdYQHhLMli/XERWleK169epFnz592Lx5Mz169ADbpVzE06ZNA6Bt27b07duXrKwsJwHsi426dm/vTUvnBm7gCEfIJptyygkjjOUdF1MZVM4N2ePqff62+d0wXVWMxVZGBRXo0NGNbjzJk8xkZr3PL6miTUeoKPFuc1bJeEJUXKNJ0SiRNCbkp0JSI8888wwzZ86ktLQUg8FARkaGW5F8uacUqFM8rCrSTCaT03GTyeSxKIu3PhERET7Ne/3119O3b19ef/11kpKSKCkpoV+/fi6ZI6r3qe4hP336NF27Ou/i79BB8eI98cQTaLVar15kgOLiYoKD3X9E1Tntdjvp6eksWrSI+++/3+FJrk5paSnZ2dksW7aMdevWOY5brVZKS0udbC8v1xweHu70u/o+FhcXExulR2uu4LtvNnFf+iwsFgtBQUEcPnyYnJycqgksbseNiopyip/21UanU9KZFRUVuX2dEiXFWjvacZ7zHOUoC1lIZVA5GpuW2Kx+UM8RF5M6Xsv/WMMwBVcyhSksYQkWLMQSWy/lsCUeuHYKxHeA1l7uHoTHQLeB0Kr9lVuXRNKEkCK5gXnj3as8tmm1zrGoC/8+wKOtpprti4v71W1hboiKimLRokWMGTOG3bt3M3jwYK/2lwtm8C/cols3JT4uJyfHEdMshCA3N9fRVp3L+1xOTk6OW1HvDo1Gw5NPPsmDDz6IRqNxGxdbF9atW8fy5cvZvHmzR0GrEhsbW2NVOK1Wy8KFC1m5ciXvvPMOTz75pFs7IQSgbH689957vY5ZvVSzu9LNQgjQhbB69Zfc/8TTbN26lWuvvRZQLo7U+S5PEXf5OBqN5pKNh7nc2ajvR1ycLGvsDYHgX/yLN3iDUpSLoJR193DuiAZuqt+5bRYN0w8+zXsDX2KzZjM3czPTmEYyyWhkwYorh1p1z+g+rSUAwTro1Ae6ej63SCQtGblxr4HRhwZ5fFwej1yTbYgPtoHAYDAwePDgWmUYmDlzJlu2bPH6ULNIDBw4kDZt2pCZmenof+TIEcrLyz1my4iLi+Pqq6926lNSUsKxY8f8yrAxffp02rRpw4kTJ7yGQ/hLfn4+DzzwAI899pjDy149JOVyEhMTKSgoqHHcmJgY7r//fpYsWeLYwFed6OhoOnfuzNGjR52Of/TRR6xZs8bn1+CETs93P+6kc4d2XDtsmOOw2Wy+ZGP3oSKfH6jvRyBixJszXenKCU44BPLNBx7h2n8/TmWFD3mt64jFbOfW4w/xdK4SwnOCE7zES1IgX2nCqu6eVZQoWS7coYZjRPgWnymRtDSkSJb4zZw5c1i9ejXZ2dn1NkdQUBDPPPMMGRkZjnjiRYsWcdNNN9G/v1L61mKx0LdvX95++21Hv+eee44VK1Zw4YJSaWrp0qX079+fSZMm+Ty3Xq9n1apVvPvuuwF8RfDoo48SFRXFwoULHceeeOIJj/YjRozg+PHjPo09a9Yszp49y+rVqz3aPPvss6xYsYJfflGKSly4cIEXXnjB8X76TUgo/Xr1IPtcDkcPHQTgxIkT7N1bFWcvhJKGKoBloI8fP06/fv2kJ7kGJjDBkeptHvN4+MQfATBVut/TEEgyvy/gpx1F3LDvARaxCA0awgknjbR6n1tyGcF62LEevl0FpW4uti0mOLVf2dwXEe3aLpFIZDGRQNHcions2LFDpKWlCUAkJyeL3//+9442s9ksOnToIJKTk8Xzzz8vbr31VpGQkCBiYmJEWlqaWLduXUDWYLfbHcVAUlNTxbRp00RhYaGj3WQyiaSkJLFkyRKnfm+99Za4+uqrxbXXXismTZoksrOzPc5x5swZkZaWJvR6vUhLSxM7duxwsfnPf/4jhg4dKgBx1VVXib///e/CZDKJtLQ0ERMTIxISEpyKnLiz37VrlwBEp06dxNChQx2PqKgoj2vbuHGj6Nq1q6MgQ/U509LSRGlpqcP+zjvvdKzl7rvvFgkJCSIhIcHpb7do0SLRp08fMXLkSJGWliY2bNjgaFPfh+TkZPHBBx+IRYsWiaSkJBETEyPuvvtucfDgQcfrGjp0qPjpp5+EJfuYeOSeaaJTx45i4sSJ4v777xcDBw4USUlJ4rWFC8WXa/4trhrQXwAiLS1N5Ofni5kzZ4qYmBjF5rXXxJdffimuuuoqrzYq99xzj1iwYIHH98wXmuLnsTYcFUfFN+IbIYQQ2zbliUen7RbPPr6v3uf93z8cFI9O2y3WrzknhBDiv+K/Iktk1fu8Ejf871SlUMix3a5tJ/crbS/dKYTNeuXXJpE0EP4UE9EI4ek+jMQf1JQixcXFHlPAde3aldDQ0AZaoaQpcsstt3DHHXfwu9/9rqGX4p4L2YpHKiIWYqoVI7CaoaJMydkagNu5J0+e5IYbbnCbZtEfWuLnMWtXIf+3+BThEUH85R3P+yACwR+fOEDBBTNTZ3Zk9IS29TqXpAYWPwxFuXDdTBh+s3Pb9k9g0/+DVu1g1t8bZHkSSUPgTa9VR4ZbSCSNmHfffZeVK1dy8ODBhl6Ke4JDlGeL2bXNXnVrv46V9kCJc3744Yf58MMP6ySQWypR0coebbO5/sMtzEZljshoXb3PJamB6HjlOf+ca1vOaeU5LtG1TSKRADK7hUTSqImPj+fzzz9vvCnPQiOU2GOd3rWtvFjZWR8Wean6Vy3RaDSsXr3a5wTwEmeiYhTBarUIrFY7wcH15x8xmWxVc8rTS4MT1xZ+OQRFea5tapGRNvVfhVEiaarIbzGJpJGj1Wobb+GMkFDFi+xub57VolTzCkBWA51OJwVyHYiLD2HIyDh0IVqsVoGH9Nt1xmazYzErEXzRUiQ3PK2q8o4XX3RtU4WzLEctkXhEfotJJJLao63ySNqFEl6h/i6EEpMM7r3MkiuKTqcloV0oNpvAZq2/bSgVZZdSzEXHhNTbPBIfaV9VsbUwFyrLL0sLVwbGMuXnTr3c95VIJFIkB5rU1FSX4gtz585l+PDhDbQiiaQe0WhB2MBiAXOlEn4BSpiF6kUO8140RXJl0IVosVXasFjqLy65pFjJi63VQlh4YHKzS+pA96sgujVExkHOyUtFQ36typceEipjkiXNmoyMDDIyMpyO2Wy+54uXIjnAuNt5r+6ml0iaJWYTWIxg1F0SyRVVpa5DQi95lyUNSs5ZIxfzTHTrFUlsXP14eSOjgrnh1kSCgmThkEaBNghumw2nDjjnSg6NgH4jQBca0DzmEkljIz09nfT0dKdjanYLX5BnL4lEUjccGS5MyrOwK15lkF7kRsTxI2UcO1TG2V8q620Oi8WORgPhEdL/0mhQN+YV5l7KQmOzQuuO0Du14dYlkTQBpEiWSCR1Qx+mPFuMYKpUYh8doRZ1y2ohCRyhYcrXfXlpYEuFX46lKsWcLkR6JxsNETFKdpmCHDiyE4wVkFN1ZzNSVq6USLwhRbJE0sixWCzk5uY29DI8ExYJOj1ms5m8nw8pAlkXqtzSlaEWjYbQMCVGuLys/kTy0YOl7NlRyImjZfU2h6QW/HoM9n4LO9fD8mch6xsICobErg29MomkUSPPYBK37Ny5E4PBgEajoXfv3hgMBoYPH05ycjKzZs2isvLSLdvbbruNxMREYmNjMRgMTo8uXbqwfPnyWq1BCMGLL77IoEGDGDJkCNOnT6e4uLjGfm+//TaDBg1ixIgRTJ48mbNnz3q03b9/PwaDgdDQUOLj4ykvL3dr984776DRaEhJSeGNN97AbDZjMBiIjY0lMTGRm2++VM1q7dq1DBs2zGH/1ltv+f/iqzh//jw33HADxcXFLnNWf69jY2M5ffp0refylz/96U/KfBoNxLZFo9EyPX02//1uC+jDLxUykDQK1I10FeW+b1rxl5yzleScNZF/wU1xGUnDMWC08px9VCkikvcLdO4DwbLgi0Tilfqukd1S8FYLvLKyUhw6dEhUVlY2wMrqBiCWLVvm+P3s2bMiLi5OzJs3z8luxowZIi0tzaX/ggULnPr7w6JFi0S/fv1EeXm5EEKIe++9V0yZMsVrnzVr1oiEhASRm5srhBDihRdeECkpKcJms3ntl5SUJHQ6nVi6dKlLm91uFwMGDBCA+Pbbb53a0tLSxIwZM1z6nDp1yq29P9jtdnHdddeJNWvW+DRnWlqaOHXqVK3n8xeX11d0QfyauU1079JZFJw+LoTdfsXW4g9N+fNYF/7f26fEo9N2i6V/PlZvc7y79IR4dNpu8Y9Fx+ttDkktsNuFeGW6EAtuUR6fLGnoFUkkDYY3vVYd6UmW+EX79u0xGAxs2LDBJ/tp06Yxfvx4v+ex2WwsXLiQ9PR0wsPDAXjqqadYu3YtBw4c8Njv5ZdfZsaMGbRt2xaA2bNnc+DAAb744osa55w6dSqLFy92SQ+zfv16UlJS/H4NdWXDhg2cPHmSW2+91Sf7V155hYSEhHpelRei4+nQqTOGESNY9Pe35a75Roa6ma6yov48yZUVSkyyTP/WyNBolHRwABGxMPmhBl2ORNJUkCK5gRBCKQ97pR9C1L2QgNVqRetDrKnBYCAkJISOHTv6Pce+ffu4cOECqamXdl/36dOHiIgINm3a5LZPYWEhe/bsceoTExNDr169PPa5nLlz53Ly5Ek++eQTp+NvvvmmSwqZ2lA9HCUyMpKBAwd6tP/4448ZO3YsmhrE5unTpzEYDFx77bWEhYXx0Ucf0a1bN7RaLY899hiVlZUMHTqU1q1bM3fuXACysrKYNGkSo0aNYuTIkdx66638+uuvTuP+/PPP3HDDDQwePJhrr72Wm266iR9//JGCggIMBgMATzzxBAaDQQkp0WigdUfGXncdH/9nbd3eLEnAiYxSRLLRWH8iuaJCiXcOj5AiudFxw/1K2MXvnoMQWeBHIvGFBs/T8+mnn/Lyyy8TFhaGVqvl73//O/369fNov337dp566in0ej0mk4m//OUvjBo1yq8xly1bxsqVK9FqtRQXF6PVannppZcYN26cw0YIwUsvvcRnn31GcHAwvXr1IiMjI2ClcW02wYb/5ARkLH+YeHMiwcG19/Dt3buXzZs3s2TJEr/7Ll++vMb45MWLF5OSksLJkycBSEy8lOheo9GQkJDgaKuOuz7q7576XE5KSgrjxo1j0aJF3HHHHQDs3r2bDh06BMRDm5KSwpYtWwDYsmUL48aN4/XXX/do/+OPP3L33Xf7Pc/UqVMZOnQo/fv3p1+/foSFhTFs2DCef/55Jk+eDCifo969e/PGG28A8NJLL3HPPffwzTffAGAymZg4cSL3338/8+fPRwjBQw89xKpVq1i8eDFbtmxBo9GwePFih2AGQKule3Ifjh49SkFBQeMtp90C6dE7kiEjW9G6bf1VwjNVKp5kVZBLGhGRsXD7nIZehUTSpGjQb7KdO3dyzz33kJmZSXJyMu+//z4TJ07k8OHDREW5po46c+YMkydP5j//+Q8Gg4HvvvuOG2+8kX379pGUlOTzmK+99hpvv/02o0crmxn+9re/ceONN/Lrr78SH69sNvrrX//Kv//9b3bu3El4eDj33Xcf99xzD//5z3+u0LvTeFi4cCHLly8nOzub8vJyPvvsMyZMmOBil5WV5SSYsrKynNpnzpzJzJkzfZqzoqICAL3e2eOh1+sdbYHoU525c+cyadIktm/fzsiRI3njjTeYP3++1z5fffWVs1BEKSBTnQ8++ACA0tJSZs6cyQMPPMB1113ncdzc3FyPIvPyOY1GI6GhoU7tXbp04aWXXuJ//ud/CA0NJT8/3yGQAe666y5CQi6JpTvvvJMFCxZQWVlJWFgYK1eu5Ny5c8yePRtQLlDmzp3Lrl27PL8RVcTGxta4fsmVJy4+hNZtQ+o1FMJkVERyRKQUyRKJpOnToN9kr776KpMmTSI5ORmA6dOn8z//8z+sWLGCxx57zMV+6dKljkwLAGlpaSQnJ/O3v/3N4ZHzZczly5czdOhQx7gGgwGj0cgvv/xCfHy8Ix72hRdecIqH7devHwcOHKB///51fu1BQRom3nzly4HWphLWM888w8yZMyktLcVgMJCRkeFWJF/uKQVchKM/qO+7yWRyOm4ymRxt/vSJiIjwad7rr7+evn378vrrr5OUlERJSQn9+vXzmjXi+uuvd/GQnz59mq5dndMrdejQAVBCFLRarVcvMkBxcTHBwe4/opfPefr0abcXH7Nnz2bVqlWkp6dz5swZpzaNRsOCBQvYuXMnwcHBmEwmhBDk5eWRlJTEgQMHaNeundP7lpyc7PhceUOnU3bMFxUV1WgruXLoQpQQKYu57iFXnjCZlFCOqGgpkiUSSdOnQb/JNm/ezHPPPef4XavVMnjwYDZt2uRWJG/atMkltCI1NdUp3tSXMS8XyOXl5SxZsoQxY8Y44kNriocNhEjWaDR1CntoCKKioli0aBFjxoxh9+7dDB482Kv95YIZ/Au36NatGwA5OTmOmGYhBLm5uY626lze53JycnLcinp3aDQannzySR588EE0Gg2PP/64T/18Zd26dSxfvpzNmzcTGem9Gl1sbCwWi6XGMbt06eLyXoPyf3/gwIH89NNPbN26ldtvv93Rds8991BQUMDXX39NVFSUQ9SrMet1iV1X1xwXJwsVNCY0WsGZkxVYLXbGTmqLThf4LSnjJidQUW6lSw/fLkolEomkMdNgG/fy8/MpLi72K3705MmTXu39HfOWW26hbdu25OXl8emnnxIUFOSYR+2nUlM8rEpJSYnLo6ysDLvdjs1mczzsdrvXcRorBoOBwYMHs2jRIr/7zpw5ky1btnh9qFkkBg4cSJs2bcjMzHT0P3LkCOXl5R6zZcTFxXH11Vc79SkpKeHYsWN+ZdiYPn06bdq04cSJE17DIfwlPz+fBx54gMcee8zhZa8eknI5iYmJFBQU+Dz+1q1bOX/+vNPvQgjmz5/P448/7uTZ/e6775g0aZIjBMlsds5rO2DAAM6fP+8UpnL8+HFWrlzp+P3yDYWlpaWOn9U1N2imDYkLISFBHMwq4ejBMkpLAl9QRAiB1SIICdESKrNbSCSSK4zJZHKrwdw9fKXBRHJtY0692fs75meffUZ+fj6tW7cmLS2t1uNcTqdOnYiJiXF6XHPNNWRnZ3P48GF++uknfvrpJxdvZ1Nizpw5rF69muzs7HqbIygoiGeeeYaMjAzHe75o0SJuuukmhyffYrHQt29f3n77bUe/5557jhUrVnDhwgVACdHp378/kyZN8nluvV7PqlWrePfddwP4iuDRRx8lKiqKhQsXOo498cQTHu1HjBjB8ePHfR7/vffe4+jRo4DyZfH888/zl7/8hfnz5xMXF8dTTz3lsO3Xrx9btmzBalXE0po1a5zGmjZtGu3bt2fp0qUA2O12nn/+eadiK23atKGwsJC8vDzGjh3rOH78+HH69esnPcmNDJ1O67h7VVIU+GIfFosAlDsQISEycZJEIrmyvPLKKy76y92jU6dOPo/ZYN9ktY059WZfmzFDQ0NZunQpR44cYdmyZbUeRyU7O5vi4mKnR2ZmJp06daJPnz5cffXVXH311S7e7saGWnEPlI17999/v6PtzjvvJCEhgQkTJrBgwQJuu+02vvrqK8fGvfXr1wdkDXPmzOGOO+5gxIgRDBkyhMrKSt5//31HuxCCiooKp7/TbbfdxoIFC5g4cSLDhw/nhx9+4PPPP/eYsu6XX37BYDCQk5ODwWBg586dgOIxV8Nt1q5dy1133QUoovatt95yVL/Lysriq6++cqm4V90+MzOTf//73xiNRsaMGcOwYcMYNmwYe/bs8fj6b7/9dr755hvHXQez2ezos379escY6kN937dv386QIUM4fvw4W7ZsYffu3RiNRt59913S0tKorKzkvffew2w2079/f26++WaHl/muu+5i//796PV6vvrqK7Zs2cLgwYMZMWIEvXr14oEHHnCs77nnnmPevHncdNNNzJs3z3F806ZN/OY3v6nhrytpCNS45NLiwHuSCy6Y2bOjkMP7S9Fqm1YomUQiafrMmzfPRX+5e/jl4Kuviia+EBMTI/7yl784HZs0aZK4+eab3doPHDhQpKenOx179NFHxVVXXeXzmHa7XZjNZpexu3XrJh599FEhhBB79uwRgNi1a5ej3W63i4iICPHXv/7V7dqaa8U9ScNy8803i3/9618NvQyfOXHihOjVq5dPlYwaipb8eZyfvk88Om23+O+3FwI+9oGsIvHotN3iyd//FPCxJRKJJFA0mYp7Y8eOdYofFUKwZ88ej/Gj48aNc7IHyMzMdLKvacwzZ864VDCz2WxcuHCB9u3bA7WLh5VI6oN3332XlStXcvDgwYZeSo2YzWYefvhhPvzwQ6Kjoxt6ORI36MOUr/yy0sB7ktU4Z71ehlpIJJLmQYN+mz3zzDN88cUXHDt2DFDyyAYFBTFjxgwA7r33XqdiCrNnz+bw4cNs3boVgG3btnH48GGnDAQ1jQlKBozLb3MvXLgQm83G1KlTAd/iYSWSK0F8fDyff/457dq1a+il1IhGo2H16tUMGjSooZci8UBoqLKhrrws8CK5TBXJoXLTnkQiaR40aAq4IUOGsGLFCqZNm+aojrdhwwbHjnuj0eiUAispKYl169bx9NNPExISgslkYv369Y5CIr6MmZiYyB//+EceeughwsLCMJlMREVFsXHjRnr06OEYZ86cOZSVlTFixAh0Oh09e/Z0ioeVSK4UWq22SRTl0Ol0AatIKakf1EIiFfUgklXhHRomPckSiaR5oBGiDglRJQ5KSkqIiYmhuLjY5Vaz0Wjk1KlTdO3a1aUymkQiubK05M/jtk0XOPlzOX0GRDFkZHxAx/7w3TNs/yafXn0jmf1sr4COLZFIJIHCm16rjiyLJJFIJC2Edh3DKCm21EtIREW5Um2vPsteSyQSyZVE3heTSCSSFoIuREnNZrEEvphRZYUiksMjpEiWSCTNA+lJlkgkkhZCZbmNMycrKCq0cM21gY1zH5YWT4ekMPoOlHHpEomkeSBFskQikbQQigotHMwqITo28F/9aknqyCh5WpFIJM0DGW4hkTRyLBYLubm5Db2MBsVsNpOXl9fQy2jyxLbSAWCsDHy4hcmojKkPlacViUTSPJDfZhK3qGWpNRoNvXv3xmAwMHz4cJKTk5k1axaVlZUO29tuu43ExERiY2MxGAxOjy5durB8+fJaraH6WAaDgQULFtTY7+2332bQoEGMGDGCyZMnc/bsWY+2+/fvx2AwEBoaSnx8POXl5W7t3nnnHTQaDSkpKbzxxhuOstSxsbEkJia6lKUeNmyYw/6tt97y/8VXcf78eW644QaKi4td5jQYDIwePZo+ffowZcoUTp8+7dR30KBBfPLJJ7WeuzGh0WiYPn06//3vfxt6KU2aVq1DADCb7AGPS/7hu4sc+KkYiznwAlwikUgahHqu/tdiaK5lqQGxbNkyx+9nz54VcXFxYt68eU52M2bMEGlpaS79FyxY4NTfH9yNVxNr1qwRCQkJIjc3VwghxAsvvCBSUlKEzWbz2i8pKUnodDqxdOlSlza73S4GDBggAPHtt9+6rHHGjBkufU6dOuXW3h/sdru47rrrxJo1a7zOaTQaxejRo8W1117rZDd16tQ6zd/Y+PXXX0X37t1FQUFBncZpyp/HumI228Sj03aLR6ftFrnnA/f6zaZL417MMwZsXIlEIgk0TaYsdXMkNTWVvn37Oj0++OCDhl5WwGjfvj0Gg4ENGzb4ZD9t2rQrWsr75ZdfZsaMGbRt2xZQqjQeOHCAL774osa+U6dOZfHixdhsNqfj69evJyUlpT6W65UNGzZw8uRJlzLq1dHr9dx+++388MMPlJSUOI6vWrUKg8FQz6u8cnTo0AGDwcCiRYsaeilNFp1OS0hV2eiCi+aAjVtw0QSARnMppEMikUgamoyMDBdNlpqa6nN/KZIDzK5duzh06JDT43e/+51H+3Iv/4wYfbatpLJG20BhtVrRamv+r2MwGAgJCaFjx44Bm9sbhYWF7Nmzx+kDEBMTQ69evdi0aVON/efOncvJkyddQhTefPNN0tPT67y+6uEokZGRDBw40KP9xx9/zNixY9FoNDWObbUq1c7Uv8s999xDYmIiM2fOdLJ79dVXSUlJIS0tjbS0NLZt2wZAWVmZI+zktdde4+677yYlJYVx48aRn5/P3//+d8aNG0dycjIbN250mvfxxx8nNTUVg8HAsGHDWLt2rdNrSElJQaPRsG7dOqZMmULPnj2dSsn7YqMyduxYPv744xrfD4lnwqoq4hXlW2qw9J38i8pYIXotQUHytCKRSBoH6enpLpps165dPveX25AbmEgiPbZNYhLrWe/4vS1tqaDCrW0aaWxhi+P3LnThIhedbAR1L664d+9eNm/ezJIlS/zuu3z58hrjkxcvXuzktZ09ezZZWVkIIRg+fDjPPvuso8R4dU6ePAkopccvJzEx0dHmDVUULlq0iDvuuAOA3bt306FDBxISEmrs78v4W7ZsAWDLli2MGzeO119/3aP9jz/+yN13313juPn5+bz//vtMnz6dyEjl/9P777/vIpDfeustli1bxo8//khsbCzbt29nwoQJHDlyhKSkJLZs2UKXLl345JNP+OabbwgLC2P06NH85je/4cUXX+TRRx/l7bff5sEHH+TUqVOAUr3u888/Z//+/URFRXHs2DGGDBlCZmYmPXr04De/+Q2tW7dmzJgxHDp0iLVr15KXl0fnzp257bbbGDNmjE82Kt27d+fo0aMUFBQ0iVLdjZGwiGCKi6wUFgTOk1yUr4wVFiZzJEskkuaDFMmSGlm4cCHLly8nOzub8vJyPvvsMyZMmOBil5WV5XR7Pysry6l95syZLsLNGykpKUyaNIklS5ZQWlrKXXfdxfjx4/n+++8JCnI9GVdUKBcQer3e6bher3e01cTcuXOZNGkS27dvZ+TIkbzxxhvMnz/fa5+vvvrKJazBaDS62KlhN6WlpcycOZMHHniA6667zuO4ubm5HoWgOmdRURFHjx7llVdeYdasWV7XqdrExsYCMHLkSLp3784///lPXnrpJYfdjTfeSHh4OADXXnstn3zyCaNGjXL0OX36NEVFRcTGxhIeHs6WLVscFy69evWiT58+bN68mR49ejjNP23aNADatm1L3759ycrKchLAvtioa/f23ki8kzoijrxzJjp1CQvYmIUFiidZFhKRSCTNCSmSG5gyyjy2BeF8wsnDcwosbbXImdOcrtO6LueZZ55h5syZlJaWYjAYyMjIcCuSL/eUAnWOh128eLHj56ioKF577TX69+/PN99843Z+VdiZTCan4yaTiYiICJ/mvP766+nbty+vv/46SUlJlJSU0K9fP5fMEdX7VPeQnz59mq5duzod69ChAwBPPPEEWq3WqxcZoLi4mOBg9x9RdU673U56ejqLFi3i/vvvd3iSq1NaWkp2djbLli1j3bp1juNWq5XS0lIn23bt2jl+Dg8Pd/pdfR+Li4uJjY1Fq9Xy3Xffcd9992GxWAgKCuLw4cPk5OS4rOHycaKiopzip3210emUeNeioiK3r1NSM527RmCzioCGRZQUK57k8Eh5SpFIJM0H+Y3WwETgm3irT1tfiYqKYtGiRYwZM4bdu3czePBgr/aXC2aoXbjF5XTv3h2AEydOuBXJ3bp1A3ARaDk5OW7t3aHRaHjyySd58MEH0Wg0buNi68K6detYvnw5mzdv9ihoVWJjY7FYvMeNarVaFi5cyMqVK3nnnXd48skn3doJoYTaPPXUU9x7771ex6zupXfntVfHW716Nffffz9bt27l2muvBZSLI7Xd0zgajaZWNur7ERcX5/U1SDyjr9q4ZzIFLlVbWYkSEx8ZLU8pEomk+SB3WEj8wmAwMHjw4FplGJg5cyZbtmzx+lAFcl5eHi+//LJTfzXfcadOndyOHxcXx9VXX01mZqbjWElJCceOHfMrw8b06dNp06YNJ06c8BoO4S/5+fk88MADPPbYYw4ve/WQlMtJTEykoKCgxnFjYmK4//77WbJkiWMDX3Wio6Pp3LkzR48edTr+0UcfsWbNGp9fQ3W+++47Onfu7BDIoBT+qC/U9yMQMeItFWOlUpr68H5XT35tuWZ4Kybc2JYRY+IDNqZEIpE0NFIkS/xmzpw5rF69muzs7Hqbo6KigjfeeMMR5mCz2XjppZfo2bMn48aNAxSvYt++fXn77bcd/Z577jlWrFjBhQsXAFi6dCn9+/dn0qRJPs+t1+tZtWoV7777buBeEPDoo48SFRXFwoULHceeeOIJj/YjRozg+PHjPo09a9Yszp49y+rVqz3aPPvss6xYsYJffvkFgAsXLvDCCy/Qv39/316AG/r160d2drZDfJ84cYK9e/fWeryaOH78OP369ZOe5DpQXKSUpj6wpzhgY5pNdnQhWmJiZfo3iUTSjKjXjM0tiOZWTGTHjh0iLS1NACI5OVn8/ve/d7SZzWbRoUMHkZycLJ5//nlx6623ioSEBBETEyPS0tLEunXr6jx/ZWWlePnll8WwYcOEwWAQ11xzjZg6dao4ffq0w8ZkMomkpCSxZMkSp75vvfWWuPrqq8W1114rJk2aJLKzsz3Oc+bMGZGWlib0er1IS0sTO3bscLH5z3/+I4YOHSoAcdVVV4m///3vwmQyibS0NBETEyMSEhLElClTvNrv2rVLAKJTp05i6NChjkdUVJTHtW3cuFF07drVUQil+pxpaWmitLTUYX/nnXc61nL33XeLhIQEkZCQ4PS3W7RokejTp48YOXKkSEtLExs2bHC0qe9DcnKy+OCDD8SiRYtEUlKSiImJEXfffbc4ePCg43UNHTpU/PTTT8JisYhHHnlEdOrUSUycOFHcf//9YuDAgSIpKUm89tpr4ssvvxRXXXWVAERaWprIz88XM2fOFDExMX7ZqNxzzz1iwYIFHt8zX2iKn8dAcmhvsXh02m4x576fAjbmd1/niXUfnxV5ObKQiEQiadz4U0xEI4SbwECJ35SUlBATE0NxcTHR0dFObUajkVOnTtG1a1dCQ0MbaIWSpsgtt9zCHXfc4TXXdkvh5MmT3HDDDezatcvlM+YPLf3zmHu+khefOoxGA0tWpARkA9/C5w4DcM9DSbTvFF7n8SQSiaS+8KbXqiPDLSSSRsy7777LypUrOXjwYEMvpUExm808/PDDfPjhh3USyBJoFa+kSBQCigrqXlDEYrGTfaqS7FOV6ELkKUUikTQf5FZkiaQREx8fz+eff97iU55pNBpWr15NTExMQy+lyaML0aIL0WAxCwoumolvo6+5kxcK8y9t1IyLD6nr8iQSiaTRIC/7JZJGjlarbfGFM3Q6nRTIASS0qjJewcW6ZyJRx9DrtQQHy1OKRCJpPkhPcoBJTU11ySs7d+5chg8f3kArkkgkEmfCI4IoLbZSVFj3cIuifGWM0HApkCUSSeMiIyODjIwMp2M2m83n/lIkBxh3m4rUjUISiUTSGBgyohV5OSY6JtW9NHVhQVW1vXB5OpFIJI2L9PR00tPTnY6pG/d8QX6rSSQSSQujU9dwbDZBUJCmzmOVFCue5PAo18qMEolE0pSR98ckEomkhaHXK4LWZKx7aWpHSepI6XORSCTNC/mtJpFIJC0MY6WVMycrKC2xctU1sXUaa/CwOOLbhNCzb1RgFieRSCSNBOlJlkgaORaLhdzc3IZeRo2YzWby8vIaehkSHygqqCpN/VPdS1ObqkpSR8fIktQSiaR5IUWyxC07d+7EYDCg0Wjo3bs3BoOB4cOHk5yczKxZs6isrHTY3nbbbSQmJhIbG4vBYHB6dOnSheXLl9dqDdXHMhgMLFiwoMZ+b7/9NoMGDWLEiBFMnjyZs2fPerTdv38/BoOB0NBQ4uPjKS8vd2v3zjvvoNFoSElJ4Y033sBsNmMwGIiNjSUxMZGbb77ZYbt27VqGDRvmsH/rrbf8f/FVnD9/nhtuuIHi4mKXOau/N7GxsZw+fbrWc/nLn/70J6f5NBoN06dP57///e8VW4OkdsRW5TOurPB9l7cnzCYlZEMfKk8nEomkmVHvRbJbCN5qgVdWVopDhw6JysrKBlhZ3QDEsmXLHL+fPXtWxMXFiXnz5jnZzZgxQ6Slpbn0X7BggVN/f3A3Xk2sWbNGJCQkiNzcXCGEEC+88IJISUkRNpvNa7+kpCSh0+nE0qVLXdrsdrsYMGCAAMS3337rssYZM2a49Dl16pRbe3+w2+3iuuuuE2vWrPFpzrS0NHHq1Klaz+cv7l7fr7/+Krp37y4KCgqu2Dr8pSl/HgPFuewK8ei03SL9d7tr/GzUxH8EzysAADq8SURBVMLnDotX5h8Sv5wuD9DqJBKJpP7wpteqIy/9JX7Rvn17DAYDGzZs8Ml+2rRpjB8/vp5XdYmXX36ZGTNm0LZtWwBmz57NgQMH+OKLL2rsO3XqVBYvXuySQ3H9+vWkpKTUx3K9smHDBk6ePMmtt97qk/0rr7xCQkJCPa/KOx06dMBgMLBo0aIGXYfEO3GtFU+yEFBSZK31ODabnexTFWSfriQkpO6ZMiQSiaQxIUVyAyEQmBvgn0DUee1WqxWttub/OgaDgZCQEDp27FjnOX2hsLCQPXv2kJqa6jgWExNDr1692LRpU439586dy8mTJ/nkk0+cjr/55psueRZrQ/VwlMjISAYOHOjR/uOPP2bs2LFoNN7Fx+nTpzEYDFx77bWEhYXx0Ucf0a1bN7RaLY899hiVlZUMHTqU1q1bM3fuXACysrKYNGkSo0aNYuTIkdx66638+uuvTuP+/PPP3HDDDQwePJhrr72Wm266iR9//JGCggIMBgMATzzxBAaDwSmkZOzYsXz88ce1fJckV4LQ0CCCdcr/q4t5plqPU1RgQVR9pbSKr1t5a4lEImlsyOwWDYQFC3/mz1d83vnMJ4SQWvffu3cvmzdvZsmSJX73Xb58eY3xyYsXL3by2s6ePZusrCyEEAwfPpxnn32WqCj3u+hPnjwJQGJiotPxxMRER5s3UlJSGDduHIsWLeKOO+4AYPfu3XTo0CEgHtqUlBS2bNkCwJYtWxg3bhyvv/66R/sff/yRu+++2+95pk6dytChQ+nfvz/9+vUjLCyMYcOG8fzzzzN58mQAtm/fTu/evXnjjTcAeOmll7jnnnv45ptvADCZTEycOJH777+f+fPnI4TgoYceYtWqVSxevJgtW7ag0WhYvHixQzCrdO/enaNHj1JQUNDiy2k3ZsLCgii1WB0V82qDWpJaF6JBFyJ9LhKJpHkhRbKkRhYuXMjy5cvJzs6mvLyczz77jAkTJrjYZWVlOQmmrKwsp/aZM2cyc+ZMn+dNSUlh0qRJLFmyhNLSUu666y7Gjx/P999/71L6G6CiogIAvd7Zo6XX6x1tNTF37lwmTZrE9u3bGTlyJG+88Qbz58/32uerr75yEYpGo9HF7oMPPgCgtLSUmTNn8sADD3Ddddd5HDc3N9ejyLx8TqPRSGhoqFN7ly5deOmll/if//kfQkNDyc/PdwhkgLvuuouQkEsXS3feeScLFiygsrKSsLAwVq5cyblz55g9ezagbMqbO3cuu3bt8vxGVBEbG1vj+iUNT1h4EKUlVgoLzbUeQxXJoWGykIhEIml+SJHcQOjQMR/v4qu+5vWXZ555hpkzZ1JaWorBYCAjI8OtSL7cUwq4CEd/Wbx4sePnqKgoXnvtNfr3788333zjdv7w8HBA8YJejslkIiIiwqc5r7/+evr27cvrr79OUlISJSUl9OvXz2vWiOuvv97FQ3769Gm6du3qdKxDhw6AEqKg1Wq9epEBiouLCQ52/xG9fM7Tp0+7vfiYPXs2q1atIj09nTNnzji1aTQaFixYwM6dOwkODsZkMiGEIC8vj6SkJA4cOEC7du2c3rfk5GSSk5O9rhlAp1P+jxUVFdVoK2k4hoxqxYUcEx06h9d6jOLCqmp7EVIkSySS5ocUyQ2EBk2dwh4agqioKBYtWsSYMWPYvXs3gwcP9mp/uWCG2oVbXE737t0BOHHihFuR3K1bNwBycnKcjufk5Li1d4dGo+HJJ5/kwQcfRKPR8Pjjj/vUz1fWrVvH8uXL2bx5M5GRkV5tY2NjsVhqvhXepUsXl/caQKvVMnDgQH766Se2bt3K7bff7mi75557KCgo4OuvvyYqKsoh6kVVgKn6XBvUNcfFxdV6DEn906lLOHabwIftBR4pLlI8yRGy2p5EImmGyCCyAJOamkrfvn2dHupt9uaAwWBg8ODBtcpeMHPmTLZs2eL1oQrkvLw8Xn75Zaf+ar7jTp06uR0/Li6Oq6++mszMTMexkpISjh075leGjenTp9OmTRtOnDjhNRzCX/Lz83nggQd47LHHHF726iEpl5OYmEhBQYHP42/dupXz5887/S6EYP78+Tz++ONOnt3vvvuOSZMmOeK7zWbnW+4DBgzg/PnzTmEqx48fZ+XKlY7fL99QWFpa6vhZXXNDZ9qQeEevV77+61KauqxUyQQTGSVFskQiaXxkZGS4aLLLN/fXhBTJAWbXrl0cOnTI6fG73/2uoZcVUObMmcPq1avJzs6utzkqKip44403HGEONpuNl156iZ49ezJu3DhA8Vj27duXt99+29HvueeeY8WKFVy4cAGApUuX0r9/fyZNmuTz3Hq9nlWrVvHuu+8G7gUBjz76KFFRUSxcuNBx7IknnvBoP2LECI4fP+7z+O+99x5Hjx4FlBCT559/nr/85S/Mnz+fuLg4nnrqKYdtv3792LJlC1arkv5rzZo1TmNNmzaN9u3bs3TpUgDsdjvPP/+8U7GVNm3aUFhYSF5eHmPHjnUcP378OP369ZOe5EaO1WrnzMkK9u4uqvUYV10Ty4Qb2zJibHzgFiaRSCQBIj093UWT+bK3RkWKZIlb1Ip7oGzcu//++x1td955JwkJCUyYMIEFCxZw22238dVXXzk27q1fv77O8ycmJjJ37lx++9vfMmbMGIYNG4bRaGTjxo2OTWpCCCoqKpxikG+77TYWLFjAxIkTGT58OD/88AOff/65x5R1v/zyCwaDgZycHAwGAzt37gQUj7l6tbl27VruuusuQBG1b731lqP6XVZWFl999ZVLxb3q9pmZmfz73//GaDQ6Xs+wYcPYs2ePx/fg9ttv55tvvsFuVzx9ZrPZ0Wf9+vWOMdSH+r5v376dIUOGcPz4cbZs2cLu3bsxGo28++67pKWlUVlZyXvvvYfZbKZ///7cfPPNDi/zXXfdxf79+9Hr9Xz11Vds2bKFwYMHM2LECHr16sUDDzzgWN9zzz3HvHnzuOmmm5g3b57j+KZNm/jNb37jw19Z0pAYK+0czCph/+7al6auLLehC9HSum1ozcYSiUTSxNCIugQfShyUlJQQExNDcXEx0dHRTm1Go5FTp07RtWtXlywEEok3brnlFu64444mczfi5MmT3HDDDezatcvlc9BYkJ9Hhdzzlbz41GE0Gvjreym1SuG28fMczGY7o8a3ITrG/03BEolEcqXxpteqIz3JEkkj5t1332XlypUcPHiwoZdSI2azmYcffpgPP/yw0QpkySVat9Wj1SpV93LOuaYsrInSYgvbv73IgawS9KHyVCKRSJofcreFRNKIiY+P5/PPP28S6dQ0Gg2rV68mJiamoZci8YGgIC0RUcGUFls5l11Jpy7+pYL79ZdKLuaaCQmxotfLFHASiaT5IS//JZJGjlarbRJFOXQ6nRTITQw1RCLvvP+lqVXvc2SM9LVIJJLmiRTJEolE0kKJi1dE8oVc/8Mt8s4rfWLjZCyyRCJpnkiRLJFIJC2U1m2VgkZqeWl/yL+g9GnVWopkiUTSPJH3ySQSiaSFMnBwHJUVdtp1CPO7b1G+UllRpn+TSCTNFelJlkgkkhZKu46hxLcJAfzPBFpSrIjkhPZSJEskkuaJFMkSiUTSQgkLV7JSmM12LGbfy1Pb7XZMJsW+fUcpkiUSSfNEhltIJM2AsrIyrFYrsbGxDb2UBqOoqIjg4GAiIyMbeilNBp1OS+55E4X5ZvpeFU3XHr69dyajYPzktlitgsQOUiRLJJLmifQkS9yilqXWaDT07t0bg8HA8OHDSU5OZtasWVRWVjpsb7vtNhITE4mNjcVgMDg9unTpwvLly+u8nttvvx2NRuNy3Gw2M3v2bAYPHszgwYOZNWsWZrP3TUhCCF588UUGDRrEkCFDmD59OsXFnkvzbty40fFe9OnTB09FKufPn49Go2HYsGGsXLnSUfI6NDSULl268NBDDzls33nnHVJSUhz2n376qY/vhCuHDx9mypQp2Gw2lzkNBgMjR46kd+/e3H333eTn5zv6mUwmOnXq5Fcd+8aMzWZjypQpHDlypKGX0qQ4fbyck8fKOX2iwuc+FeVWQEkhFxwsTyMSiaSZIiQBobi4WACiV69eok+fPk6Pf/7zn+LQoUOisrKyoZfpN4BYtmyZ4/ezZ8+KuLg4MW/ePCe7GTNmiLS0NJf+CxYscOpfGz7//HMRGxsr3P13ffzxx8W4ceOE1WoVVqtVjB8/XsyaNcvreIsWLRL9+vUT5eXlQggh7r33XjFlypQa16HT6QQg1q5d69JWVlYmEhISBCBOnTrl1JaUlCQWLFjg0ufbb791a+8PRqNRDBgwQGRmZnqds7i4WPTq1Uv89re/dRyzWCxi3Lhx4vDhw7Wev7GRmZkpUlJShMlk8mhTWVnZZD+P9cHrfzoiHp22W6xadsbnPr+cKhfrPj4rftx6sR5XJpFIJHXjzTffdNFkvXr1EoAoLi6usb90AQSYXbt2cejQIafH7373u4ZeVsBo3749BoOBDRs2+GQ/bdo0xo8fX+v5ysvLefbZZ/nDH/7g0pafn88//vEP5s6dS1BQEEFBQcyZM4e33nqLgoICt+PZbDYWLlxIeno64eFKhbGnnnqKtWvXcuDAAa9rad++PSNHjuT11193aVu2bBnXXXddLV5h3Vi2bBlt27Zl8ODBXu2io6OZPHmy098tODiYTZs20bt37/pe5hVj8ODBxMfH8/777zf0UpoMago3NaWbL+zYms+u/xZwNruyZmOJRCJpINLT0100mT93T6VIbmjMRs8Pi9kPW1PNtgHCarWi1db8X8dgMBASEkLHjh1rPdcf//hHHnnkERITE13atm7disViITU11XEsNTUVi8XC1q1b3Y63b98+Lly44NSnT58+REREsGnTphrXM3fuXLZu3er0IbPb7Xz44Yd1vhg6ffo0iYmJTuEqwcHBTJkyxWOfjz/+mHHjxvk0fvW/23XXXUdsbCx/+tOfHMcsFgtPP/00KSkppKWlcd111zkuHo4fP+4IO3nnnXe488476dOnD3fccQeVlZW88MILjB49mgEDBvDTTz85xiwsLOTee+9lyJAhpKWlMWrUKP773/862t9880169+7tCM254YYb6NGjBwsXLvTLRmXs2LGsXr3ap/dEAm0SlJjiwnzfRXL2mUou5JoxVdrqa1kSiUTS4MiNew3Nn3/rua3nYPjdc5d+/8tMVzGsktQP7v3fS78vfggqSpxt/lT7uFeVvXv3snnzZpYsWeJ33+XLl9cYn7x48WJSUlIA+Omnn9i5cyevv/66W8/gyZMnCQ4OpnXr1o5jbdq0ISgoiJMnT7odXz1+uejWaDQkJCR47HM5U6ZMoWfPnixatIhVq1YB8Omnn3L99dej1+tr7F8T119/veM9WrFiBT/88AN//vOfPdr/+OOPPPDAAzWOe+bMGdasWcPDDz/sOPb1119jMBic7J577jl27tzJjh070Ov1fPDBB4wdO5YTJ07Qo0cPtmzZgkaj4csvv+Tjjz/GarXSp08fbrnlFjIyMliwYAHz5s3jySef5NtvvwXg7NmzHDp0iP/+97/odDq2bdvGzTffzPHjx4mNjeWxxx4jMjKSRx991DH2vn37SElJ4Y477qB79+4+2ah0797drXiWuKdtO0UklxZbfe5TVKgI6jaJctOeRCJpvkiRLKmRhQsXsnz5crKzsykvL+ezzz5jwoQJLnZZWVlOoisrK8upfebMmcycOdOnOe12O+np6fzjH//w6LWuqKggJCTE5XhISAgVFe43IanHqwtavV7vsc/laLVa5syZw+OPP87p06fp0qULf//73/noo4+8hmssX76cLVu2OB0rKipy+r1jx4689tprAGRnZzN79mxeeOEF+vfv7/G1lJeX06pVK69z5uXlcfbsWd566y2mTZvmcY0VFRUsWbKEf/3rX47353e/+x0PP/ww//73v/n973/vsL399tsdIS7XXHMNBQUF9OjRA4CRI0fy1ltvOWx79OjBp59+ik6n3NYfNWoUOp2OHTt2MHHiRIed3W53eOMHDhxIbGws+/btcxLAvtjExsZSWlpKZWUlYWH+F8loaagp3MrLrNhsdoKCar5LVFYlqBPb1/3CUCKRSBorUiQ3NPM/9NymqXayenq5F9tqmR+eeLvWS6rOM888w8yZMyktLcVgMJCRkeFWJKekpDgJwepeSn/429/+xogRIxg4cKBHm/DwcLeZLMxmsyPe2F0fUDI7XI7JZPLYpzozZszgj3/8I4sXL2bq1Kn07NnTyZvtjpkzZzqFNQBs2bKFMWPGOH4PDg6mbdu2CCG477776N27N08//bTHMVWRHRzs/mOszmk2m7n99ttZtGgRd911l8eLjuPHj2MymXjllVd48803HccTEhIoLCx0sm3Xrp3j5/DwcKeLjoiICKdsISEhIaxatYrPPvsMUC40CgsLycnJcRqzTZs2Tq8lKiqKkpISv21UMV5UVCRFsg8ktA9FowG7HfLOm2jX0ft7Vllhw2isypHc2bfPjEQikTRFpEhuaEL8uF1ZX7Y+EhUVxaJFixgzZgy7d++ucbNYdc+pP+EWX3/9NYWFhQ6hrQoqg8FAZGQk69ato1u3blitVi5evOgQqRcuXMBms9GtWze346vHc3JyHLHSQghyc3M99qlOeHg4jzzyCIsXL+bIkSO1Cj3xRkZGBtu3bycrK4ugoCCPdnFxcYASR+yNkJAQFi9eTK9evfjss8+47bbbvNq//vrrTuLdHdXX5W2dixYt4uWXXyYzM9Phbe7SpYtLKr3qY2g0mlrZqO+H+v5IvKPTaTFMbKP8HFKzF/lctnLHJThYQ2ycPIVIJJLmi/yGk/iFwWBg8ODBLFq0iJUrV/rV159wi/Xr1zv9vnz5cu69914n4T169Gh0Oh2ZmZlcf/31AGRmZqLT6Rg9erTbcQcOHEibNm3IzMzkmmuuAeDIkSOUl5f7lYXjscce4y9/+Qs6nY7k5GSf+9XEzz//zB/+8Af+/Oc/O8bNyspyxGlfTlhYGFFRUR4zeVxO9+7dueWWW3j99dc9iuSePXsSGhrK0aNHnUTym2++ycCBAz2+pzXx3XffMXjwYIdABmrMZV0XCgoKiI6OJjRUxsv6Sqcu4VzMM1FZUfNGvPO/KpuAI6ODfdrAK5FIJE2VBv+G+/TTT7nmmmsYNWoUaWlpHDx40Kv99u3bGTZsGGlpaQwbNoxt27b5NabVauWf//wnY8aMYezYsQwePJj77ruPvLw8pzGqF8UwGAwsWLAgMC+6iTNnzhxWr15NdnZ2g64jPj6ehx9+mDfeeAObzYbdbmfx4sU8/PDDjjjdCxcu0KlTJ4foDgoK4plnniEjI8MRg7xo0SJuuukmj7G/7khISGD16tX85S9/CdjrsdlszJgxg2uuuYbZs2c7jj/xxBMe+4wYMYLjx4/7NP6TTz7JDz/8wA8//OC2PSwsjDlz5vDmm286wit+/vlnlixZQr9+/Xx/IdXo16+fI6sIwPfff8/58+drPV5NHD9+nFGjRtXb+M2RiCjFX1JS7P2uBEBRoYXgYA1xrXT1vSyJRCJpWOo3jbN3duzYISIjI8WRI0eEEEKsWLFCdOjQQZSUlLi1P336tIiOjhbffvutEEKILVu2iOjoaHH69Gmfx8zOzhahoaFi7969QgilGMP48ePFqFGjnOZyVxjDG2oxEXfJqZti8YIdO3aItLQ0AYjk5GTx+9//3tFmNptFhw4dRHJysnj++efFrbfeKhISEkRMTIxIS0sT69atC+ha0tLSRHJysgBEWlqaeOWVVxxtRqNRPP7442LQoEFi0KBB4rHHHhNGo9HRnpOTI+Lj48Wnn37qOGa328ULL7wgUlJSRGpqqpg2bZooLCys8b3Q6/UiLS1NnDnjWnTh7bffFldddZUAxNChQ8Unn3wizpw54+iXlJQkHnzwQa/2q1evFoDo0aOHGDp0qOPRq1cvj2v7v//7P6f/q9XnnDx5spP9kCFDHGuZMGGCiImJEUlJSeLZZ58VQigFRp555hmRnJwsRo8eLcaPHy927dolhBDi/Pnzjv8TV111ldi8ebN4+umnRUJCgkhISBBPP/202Lx5s+N1paWlifPnz4vi4mJx1113iaSkJHHjjTeKJ554QiQmJork5GTx/vvvi2XLlonk5GSh1+vFhAkThBBCXH/99UKv1/tlozJ69GivBWya4uexvjm8v1gseuGI+OtLR2u03bk9X3y++qw4tK/oCqxMIpFIAos3vVadBhXJt912m7jzzjsdv9tsNpGQkCD+9re/ubV/8sknxZAhQ5yOpaamirlz5/o8Zm5urnj00UedxlDFydmzZx3HWrpIljQNzGazuOaaa8T27dsbeimNgm3btokhQ4YIi8Xi0UZ+Hl355XS5eHTabpH+u92iotzq0c5ut4sNa8+LdR+fFYX5nqsaSiQSSWPFH5HcoOEWmzdvdirqoNVqGTx4sMeiDps2bXKyB6V4xOX2NY3Ztm1bMjIynMZQYxfrM05SIqkPdDodH330EX/6059cQoZaGnl5ebzwwgusWrXKY8YPiXs6dAolNFSLEHB4X4lHu9ISKxaznaAgDdGxMtxCIpE0bxrsTJKfn09xcbFLJbXExESPJQNPnjzJHXfc4WKvFoGozZgAP/zwA9dccw1dunRxOj579myysrIQQjB8+HCeffZZoqKivL6u6umoQBHfdrsdm82GzaZsjNFoNHLTiyQgdOvWjXXr1rX4i7ywsDDWrVsXkKIuLQ2tVktCh1DOnKjg6KESBg1znxlk68YLbNmQR6++UWi1Grc2EolE0hCYTCaX9K7ucKfTPNFgIrk2RR0qKiq82tdmzIsXL/LPf/6TtWvXOh1PSUlh0qRJLFmyhNLSUu666y7Gjx/P999/7zXdVadOnVyOJSUl8Y9//IPKykrHsfbt29O+fXuP40gk/qDX61u8OKzpAlbinS7dwzlzooIzJzwX1Tl5rJzKCjvBOimQJRJJ4+KVV17hhRdeCOiYDSaSa1PUITw83Ku9v2NarVbuuusuXnzxRYYOHerUtnjxYsfPUVFRvPbaa/Tv359vvvnGbSENlezsbKKjo52Omc1mcnNz6dKliyO0Q1O9+IdEIpE0IL37RfPd1xfJPWfCbre7vdN17lflQr9nb3lBIpFIGhfz5s3jySefrNGupKTErUPTHQ0mkuPj44mJiXGpupWTk+O1EIQ3e3/GtNvtzJgxg7S0NB566KEa16uWvT1x4oRXkRwdHe0iko1GIxcuXHCU8ZVIJJLGRu+BUWi1YDbbOXOygq49Ip3aC/LNlFaVo+53dUxDLFEikUg8Uh93VBs0KHbs2LFkZmY6fhdCsGfPHo9FHcaNG+dkD0rxiMvtfR0zPT2dDh068Mc//hFQNgWqsc15eXm8/PLLTvZnz54F3IdTSCQSSVMnJCSI+LYhBAdr+OVUpUv7wZ+UUuNRMcG0ig+50suTSCSSK06DiuRnnnmGL774gmPHjgHwwQcfEBQUxIwZMwC49957ufvuux32s2fP5vDhw2zduhWAbdu2cfjwYR5//HGfx1RtDh8+zJ133klmZiaZmZn8+9//5pdffgGU2OY33niD06dPA0qRh5deeomePXsybty4+ntDJBKJpAGZcmd7JtyUQKt418wVPx8pBaB9x7ArvSyJRCJpEBo0T9KQIUNYsWIF06ZNIywsDK1Wy4YNGxwbcIxGIxbLpQpQSUlJrFu3jqeffpqQkBBMJhPr168nKSnJ5zEPHjzIq6++CuCSTm7atGmAkg1j7ty5/Pa3vyU0NJSysjK6d+/Oxo0bZalbiUTSbGnfKZzzvxopzHetvPfracW73K1XxJVelkQikTQIGiGEaOhFNAdKSkqIiYmhuLjYbUzyqVOn6Nq1qxTZknqhrKwMq9VKbGxsQy/FK0VFRQQHBxMZGVmzcT0hP4+eMRltbFqfC8D4GxPQ65U9FHa7YPFLx7iQa+L+2V3pniw37kkkkqaJN71WHZmoV+KWnTt3YjAY0Gg09O7dG4PBwPDhw0lOTmbWrFlO6exuu+02EhMTiY2NxWAwOD26dOnC8uXL67ye22+/3W1GELPZzOzZsxk8eDCDBw9m1qxZNeYLFkLw4osvMmjQIIYMGcL06dMpLi72aL9x40bHe9GnTx88XVfOnz8fjUbDsGHDWLlyJb/88gsGg4HQ0FC6dOnitEH0nXfeISUlxWH/6aef+vhOuHL48GGmTJmCzWZzmbP63+NKisKioiL+9Kc/UVRU5Dhms9mYMmUKR44cuWLrkPiOPjSIk8fK+farPD5+/1fH8V/PVJLcP4oxN7SlW6+Gu8CRSCSSK0p9lv5rSTTXstSAWLZsmeP3s2fPiri4ODFv3jwnuxkzZrgt5b1gwQKn/rXh888/F7GxscLdf9fHH39cjBs3TlitVmG1WsX48ePFrFmzvI63aNEi0a9fP1FeXi6EEOLee+8VU6ZMqXEdOp1OAGLt2rUubWVlZSIhIUEA4tSpU05tSUlJYsGCBS59vv32W7f2/mA0GsWAAQNEZmamT3MmJSXVei5/OXXqlNvXl5mZKVJSUoTJ1DBljZvy5/FKsH7NOUeJ6kN7i0VpiVl8+ZlSivrE0dKGXp5EIpHUiSZTllrS9Gjfvj0Gg4ENGzb4ZD9t2jSP2Up8oby8nGeffZY//OEPLm35+fn84x//YO7cuY70enPmzOGtt96ioKDA7Xg2m42FCxeSnp7uyJ391FNPsXbtWg4cOOB1Le3bt2fkyJG8/vrrLm3Lli3juuuuq8UrrBvLli2jbdu2DB482Cf79957r55XVDODBw8mPj6e999/v6GXInHD9bckkNQtHCFgxT9Os/ilY5w+Xkar1iF06SHjkSUSSctBiuSGQgiwWq78IwAh6Far1aeS2gaDgZCQEDp27Fjruf74xz/yyCOPuJQaB9i6dSsWi8VpA2ZqaioWi8WRAaU6+/b9//buPa7GbP8D+GfX7oJSjksJI5GQISWh2FvRNEP9xgzG5ZjCMJwyuRzGmRnUMZgjNblsM8ycF8brDCOEYV6HIxrDOIiDMZ1MToWTS6GUSre9fn/47efn2V1p16583q9Xr9c861lrPWt/n731nae117qC7OxsWZvevXujVatWOHbsWI3jWbhwIU6ePCnb5lyr1WLnzp2YMmXK87y0CjIyMmBvby+bHqFUKhEUFFRlmz179tRqxZXExESEhITA19cXALBu3To4ODigRYsWWLlyJdLT09G/f3907twZUVFRAIDjx49jxIgRUKvVGDJkCEJCQmRTJ4Cn03KGDRsGLy8vDBo0CBMnTsS///1vJCcnY+LEiQCAiRMnQq1Wy6aU+Pr6Ii4u7nlDRA3AxMQE74U7wcLSBPmPynAnsxj/vpKPbs5W3IqaiF4qRl3d4qVWXgb8tLfhrzvsbUBZcXmn2rp8+TISEhKwbt265267bdu2Gucnx8bGws3NDQDwr3/9C+fOncPatWsrfeqYlpYGpVKJdu3aSWXt27eHqamptOZ1ZW0AyJJuhUIBOzu7Kts8KygoCM7OzoiOjsauXbsAAPHx8QgICDDIIuYBAQFSjLZv344zZ85g1apVVdb/5z//iZkzZz73dcLDwzF48GB4e3vD3d0d3bp1Q48ePbB9+3Yp/j/88APGjh2LDz74AEIIzJo1CwsWLJCeRmdnZ8Pf3x+bNm3C5MmTUVZWhsDAQBw5cgTz5s3Drl270K1bN+zatQuOjo6y63fv3h2fffbZc4+bGsbv2pnjrSmdsPOvtwAAAW/aw96BX3IkopcLk2Sq0WeffYZt27bh1q1bKCgowP79+yvddfDSpUtQq9Wy42eFhIQgJCSkVtfUarUIDQ3Fl19+WeVT68LCQpibV9zUwNzcHIWFhVW2AVAhobWwsKiyzbNMTEwwf/58zJ07FxkZGXB0dMSmTZvw3XffVTtdY9u2bUhMTJSV6T+V7dy5M9asWQPg6fbm4eHhiIyMRN++fat8LQUFBfjd735X4zVzc3Ol5FfHy8sLoaGhmDlzJhYvXgwXFxdZnQULFkh9KxQKjBs3Tnb/Nm7ciNatW2PSpEkAAKVSiY8//hgFBQVVxkHH1tYW+fn5KCoqQosWXHe3MfLxbY9HOWUoflKO1/7HztjDISJqcEySjcVU+fSprjGu+5yWLFmCkJAQ5OfnQ61WQ6PRVJoku7m5yRLBZxPm57VhwwZ4e3ujX79+VdZp2bJlpStZlJSUSPONK2sDAMXFxbLy4uLiKtvoCw4OxtKlSxEbG4t33nkHzs7OsqfZlQkJCUFERISsLDExESNGjJCOlUolOnToACEEpk+fjl69emHRokVV9qlLspXKyu/ps9dMTEys9Cn+qlWrcODAAURFRSE1NVV2rqysDGFhYUhOToa5uTlyc3NlW75fvXoV3bt3l6064uPjU+V4n2VmZia9BibJjdfotzsaewhEREbDJNnAPD09YWpqKitbuHAhhg4dKq+oUNRp2oMxWFtbIzo6GiNGjMCFCxdq/LKY/pPT55lucfToUeTk5EiJti45U6vVsLKywqFDh+Dk5ISysjLcv39fSlKzs7NRXl4OJyenSvvXld+9e1eaKy2EwL1796pso69ly5aYM2cOYmNjkZKS8kJTT6qj0Whw6tQpXLp0qcJ76Vlt2rQBANmGO1XRzXHW16pVK/Tp0wdHjx7FL7/8Ipur/frrr6NXr144ceIELCwsKiT1og7z23Vj1r0GIiIiQ9NoNNBoNLKy8vLyWrdnkmxg58+fr3IzkeZArVbDw8MD0dHR+Pbbb5+r7fNMtzh8+LDseNu2bZg2bZos8R4+fDjMzMyQlJSEgIAAAEBSUhLMzMwwfPjwSvvt168f2rdvj6SkJAwcOBAAkJKSgoKCgudahSMsLAxRUVEwMzODi4tLrdvVJDU1FR9++CFWrVol9Xvp0qUKUyUAoEWLFrC2tq5yJY/KHD58GCqVStrMY8eOHRgyZAg6dOiAGTNm4MKFCzAzM8P9+/eRnJyMJUuWSFNT9J/av/rqq9i6dausLCkpCVlZWXjjjTdk02S0Wi2KiorQqtXT1REePnyI1q1bczMPIiKqN6GhoQgNDZWV6TYTqQ2ubkHPbf78+YiLi8OtW7eMOo62bdti9uzZiImJQXl5ObRaLWJjYzF79mxpLm12dja6dOkiJd2mpqZYsmQJNBqNNAc5OjoagYGBVc79rYydnR3i4uKklSAMoby8HMHBwRg4cCDCw8Ol8nnz5lXZxtvbG9evX6/1NaKionD//n0AwP3797F161YsWbIEMTExuHfvnrRle9u2bWFvb4+EhASp7b59+2R9hYWFIS8vT/oCY0lJCRYuXChNpWjbti1MTEyQk5ODpKQk2f8gXb9+HcOGDav1uImIiBpcPa/Z/NJobpuJnD17VqhUKgFAuLi4iBkzZkjnSkpKRKdOnYSLi4tYtmyZGDt2rLCzsxM2NjZCpVKJQ4cOGXQsKpVKuLi4CABCpVKJ1atXS+eePHki5s6dK9zd3YW7u7sICwsTT548kc7fvXtXtG3bVsTHx0tlWq1WREZGCjc3N+Hp6SkmT54scnJyaoyFhYWFUKlU4saNGxXqbN68WfTv318AEF5eXmLfvn3ixo0bUruuXbuKWbNmVVs/Li5OABA9evQQXl5e0k/Pnj2rHNtXX30l28QlIyNDeHl5CXNzc9GpUydZP15eXsLa2lqkp6eLuLg40bNnT9G9e3fx888/i3379gkHBwdhYWEhbazy008/CTc3N9GvXz8RFBQk5s6dK92DrKwsKTY+Pj5i0KBBYvDgweKLL76QjW/x4sXC1dVVeHl5iVOnTknlw4cPr/MmMy+qKX4eiYjIMJ5nMxGFEAZYOJeq3QtcN92iW7du/PMyGVRpaSmGDh2K2NhYeHt7G3s4tXLq1CksXLgQp0+frvJLh/WJn0ciopdXdfmaPk63IGrCzMzM8N133yEiIgJZWVnGHk6NsrKyEBkZiV27dhklQSYiIqot/pYiauKcnJxw6NChSpfDa2xatGiBQ4cOGWTjFSIiovrEJJmoGbCwsGgSiae1tbWxh0BERFQrnG7RRGm1Wty+fRtardbYQ3mpMO7GwbgbR3FxMSIiIipsvkP1i3E3DsbdOBpz3JkkNyBDfkdSCIHbt28btE+qGeNuHIaMO+9d7RUXFyMyMrJR/vJqzhh342DcjaMxx51JcgPQrRurW5eXiIxH9znUfS6JiIgqwznJDcDU1BS2trbS6gMtW7aEQqGoU5+6bRWfPHlS7dbFZFiMu3EYIu5CCBQWFiIrKwu2tra8f0REVC0myQ3E3t4eAAy2TJdWq8X9+/eRkZEh2/6X6hfjbhyGjLutra30eSQiIqoKk2QD8/T0rPCESrd3eMeOHbF//35Mmzatztd5/PgxRo8ejaSkJFhZWdW5v7/97W+YMmVKnftprH0Zqh/G3Tj9GCruZmZmMDU1hUajQWhoaJ3HBcBgfTXGMRlaY3yNjXFMhtYYX2NjHJOhNfdYNYW4azQaaDQa2XndXyZrpb62/XvZ1Habw969ezfo9WrLUONqrH0x7sbpi3Fv+H4M2Rfjbpy+GHfj9NVY494YY2XIvho67s9zPf69mIiIiIhID5NkIiIiIiI9TJKJiIiIiPTwi3sGIv5vg4K8vLxq65WXl9dYpzZ0fRiiL8Bw42qsfTHuxumLcW/4fgzZF+NunL4Yd+P01Vjj3hhjZci+GjruunOiFhtLKURtalGN/vvf/6JLly7GHgYRERER1eDWrVvo3LlztXWYJBuIVqvF7du3YW1tXeeNQoiIiIjI8IQQyM/Ph4ODQ43r7jNJJiIiIiLSwy/uERERERHpYZJMRERERKSHSXITU1xcjOXLl0OlUmHkyJEYMGAAxo4di7S0NFm9R48eYerUqRg0aBDc3d0RGRlZq29yUuUePnyIiIgI+Pj4QK1Ww83NDZ9++inKyspk9Rj3+pGamoqhQ4dCrVZXep5xN7z4+HgMHDgQw4YNg0qlwq+//mrsITVLJSUl+NOf/gSlUomMjIwK5zdv3gx3d3d4e3tj9OjRyMzMbPhBNjO7d++Gv78//Pz84OnpibfffrvC71DG3bAOHDiAMWPGYNSoUfDx8YGHhwd2795doV6ji3tdtv6jhnfnzh3RsWNHcffuXSGEEOXl5WL8+PFi4MCBsnqBgYEiJCRECCFEQUGBcHV1FTExMQ0+3uZix44dok+fPiI3N1cIIURmZqaws7MTS5culdVj3A3vm2++EYMHDxbe3t5CpVJVWodxN6yzZ88KKysrkZKSIoQQYvv27aJTp04iLy/PyCNrXtLT08XgwYPFu+++KwCI9PR02fm9e/cKOzs7ce/ePSGEEJGRkcLNzU2Ul5cbYbTNh5mZmThy5IgQ4unv0ODgYOHs7CyKioqEEIx7fXjttdfE9u3bpeODBw8KExMTceXKFamsMcadSXITU1xcLC5evCgrW79+vWjdurV0fOXKFQFAJCcnS2UajUZ06NCBH/IX9MMPP4i//vWvsrLQ0FDh7OwsHTPu9ePw4cOiuLhYBAcHV5okM+6G99Zbb4kJEyZIx+Xl5cLOzk5s2LDBiKNqfn755ReRmpoqTpw4UWmS7O7uLhYvXiwd5+bmCqVSKb7//vsGHmnzMm7cONnx+fPnBQBx+vRpIQTjXh+SkpJEaWmpdJyXlycAiH379klljTHunG7RxJibm2PAgAHScWZmJrZv347w8HCp7NixY7CyskLv3r2lMk9PT2RlZeHKlSsNOt7m4vXXX8f06dNlZZaWligpKZGOGff68cYbb8Dc3LzK84y74SUkJMDT01M6NjExgYeHB44dO2bEUTU/ffv2RY8ePSo9l5OTg4sXL8rug42NDXr27Mn7UEdxcXGyY0tLSwBPp74w7vXDw8MDSuXT/etKS0sRFRWFPn36YNSoUQAa7/udSXITlZmZCQ8PD3Tv3h2vvfYa/vznP0vn0tLSYGdnJ6tvb28vnSPDOHPmDMaPHy8dM+7Gwbgb1oMHD/Do0SMphjr29vaMZwPSxZr3of6dOXMGDg4O8Pb2ZtzrWWhoKNq3b4+EhAQcOXIEVlZWABrv+51JchPVqVMnXLhwAWlpaTh69ChmzpwpnSssLISFhYWsvu64sLCwQcfZXB0/fhw3b97EJ598IpUx7sbBuBuWLmaVxZTxbDi8Dw2juLgYUVFRWL9+PczMzBj3eqbRaPDgwQP4+fnB29sbd+7cAdB43+9MkhuJiIgIKBSKan+SkpIqtHNwcMDq1avx9ddfS98+b9myJYqLi2X1dMctW7as/xfThLxI3DMzMzF79mwcOHAANjY2UjnjXnsv+n6vDONuWLqYVRZTxrPh8D40jPfffx/jxo3D22+/DYBxbwimpqaIiIiAEAIxMTEAGm/clUa7Msn88Y9/xOzZs6ut065dO5SXlwN4+ibTcXFxAQAkJyfD1dUVTk5OuHfvnqzt3bt3AQBOTk6GHHaTV9u46zx8+BBBQUHYtGkT3N3dZfUY99p73rhXh3E3rLZt28LGxkaKoc7du3cZzwaki3Vl90E3j5PqZsmSJVAqlVi5cqVUxrjXj5KSEtl3S0xMTODs7Izk5GQAjTfufJLcSFhZWcHe3r7aH6VSiR07duDzzz+XtdX9ucLBwQEA4Ofnh8ePHyMlJUWqk5SUhA4dOqBfv34N96KagNrGHQDy8/MRGBiIZcuWYeTIkQCALVu2SH0x7rX3PHGvCeNueL6+vrIn+UIIXLx4UXrfU/1r06YNBgwYILsPeXl5+O2333gfDOAvf/kLMjIysGXLFigUCly4cAEXLlxg3OuJ/kMl4GnuostbGm3cjbauBr2QrVu3it69e4vs7GwhhBBFRUVizJgxom/fvqK4uFiqFxgYKKZPny6EEKKwsFC8+uqrIjo62ihjbg6KioqEWq0WCxYsEOfPn5d+3N3dZfUY9/pT1RJwQjDuhnb27FlhbW0trl27JoR4uk4410muP1UtAbd3715hb28vsrKyhBBCrFixwujrxjYHX3zxhXB1dRU///yz9G/58uXLxdatW4UQjHt9UCgU4tChQ9Lxjh07hImJifjpp5+kssYYd4UQ3JaqKbl16xbWrFmD06dPw8rKCo8fP4arqytWrVqFLl26SPVyc3MRFhaG3377DaWlpXjzzTexbNkyKBQKI46+6dJoNAgLC6v03LMfIcbd8A4ePIiYmBikpKTgyZMncHNzw9SpUzFjxgypDuNuePHx8Vi5ciVatGgBExMTbNq0Ca6ursYeVrNSUlICf39/5Obm4vLly/Dy8kKXLl1kS5R9+eWX2LJlCywtLdGmTRts3rwZnTt3NuKom7b8/HzY2tpCq9VWOLd161aEhIQAYNwNbcOGDdi5cydMTU1RXl4OhUKBjz76CKNHj5bVa2xxZ5JMRERERKSHc5KJiIiIiPQwSSYiIiIi0sMkmYiIiIhID5NkIiIiIiI9TJKJiIiIiPQwSSYiIiIi0sMkmYiIiIhID5NkIiIiIiI9TJKJiF7QuXPnoFaroVAo0KtXL6jVagwZMgQ+Pj7QaDQoLS19rv4yMjIQERFRP4MFMHbsWMTGxtZb/zoZGRlQKBQYPHgw/Pz8AAD/+Mc/pFj17t0bVe1j9dFHH0ltv/32W9y8eRNqtRqWlpZwdHTE+++/L9XdsmUL3NzcpPrx8fE1ji0qKgpqtRq2trb1Gmsiavq44x4RUR0pFArZlrZpaWl49913oVQq8fe//x2Wlpa16icxMREjRoyoMoGsq/nz52PQoEGYNGlSvfSvk5GRgW7duiE9PR2Ojo6yc+bm5igtLcXBgwcRGBgoO1dQUIDu3bvj3r17Fdo6OjoiJCSkQmKri1ll16qOWq2GWq1mokxEVeKTZCIiA3NycsLhw4dx7do1LFu2zNjDkXz++ef1niDXxMHBAT4+Pli7dm2Fc1u3boW/v78RRkVEVBGTZCKiemBjY4OQkBBs3rwZ5eXlAIDS0lIsWrQIbm5uUKlU8Pf3x9WrVwEAx48fx7x58wD8/1POM2fOYOLEibKpAT/++KM0xUDnk08+gaOjI9RqNaKiouDn54cePXrgm2++keosXrxYqgMA169fl6Y/fPXVVxg/fjz69++PgIAAPHz4UPZaVqxYga5du2L48OGYPXs2Jk2aBHt7e7z33nsvFJuFCxfi5MmTOH/+vFSm1Wqxc+dOTJky5YX61MnIyIC9vb0UQ7VaDaVSiaCgoDr1S0QvHybJRET1xNPTE3l5ebh27RqAp8nsuXPncPbsWfz4448IDg6Gr68v8vPz4evrK80XTkxMRGJiIoYMGYJdu3bBzc1N6lOlUlWYV/zpp58iJCQEFy5cgIeHBxISEhATE4M//OEPyM/PBwCsWbNGmg4CAD169EBiYiIA4Pvvv8fOnTtx8eJFPHjwAOvWrZPq7dy5E2vXrsWJEydw8uRJTJs2DXv37kVAQAC+/vrrF4pLUFAQnJ2dER0dLZXFx8cjICAAFhYWL9TnswICAqQYTps2Daampli1alWd+yWilwuTZCKietK6dWsAQG5uLgoLC7Fu3TrMnTtXSgSnTJmCoqIi7N692yDXs7Ozg6+vL4CnT6MLCgpw/fr1GttNmDABSqUSpqamGDZsGC5duiSdW79+Pd588004OTkBALy8vODl5VWncZqYmGD+/PnYs2cPMjIyAACbNm3CnDlzqm23bds22RNitVotPX3X6dy5M9asWQMAuHXrFsLDwxEZGYm+ffvWacxE9PJRGnsARETN1aNHjwAAbdq0wfXr11FcXIzVq1dj48aNUh07Ozvk5OQY5HodO3aU/tva2hoAkJeX99ztnm2TkpKCgIAAWf1XXnmlrkNFcHAwli5ditjYWLzzzjtwdnZGu3btqm1T3Rf3dJRKJTp06AAhBKZPn45evXph0aJFdR4vEb18mCQTEdWT8+fPw8bGBj179sSvv/4KAFi7dq0sqauNZ+cfA5DmOOszNTWt0KY2K2Xot9Nvo399Q2jZsiXmzJmD2NhYpKSkyKZ4GIJGo8GpU6dw6dIl2esjIqotTrcgIqoHjx49wvbt2zFnzhyYmprC2dkZlpaW0vxknY0bN+LkyZMAnk5D0CkrK0NRURGAp093Hz9+LJ3LzMxsgFfwVO/evfGf//xHVnbz5k2D9B0WFobS0lKYmZnBxcXFIH0CQGpqKj788EOsWrVK6vfZKSRERLXBJJmIyMDS0tIwZswY9OnTR5oe0KJFC8yfPx8bN26UplekpqZi3bp1cHV1BQC0b98eAJCTk4N9+/ZJy8e5ubnhzJkzEEKgrKwMe/bsabDX8sEHH2D//v1IS0sD8PTp+OXLlw3St52dHeLi4hAVFWWQ/oCnT9mDg4MxcOBAhIeHS+X6c5eJiGokiIjohZw9e1aoVCoBQLi4uAiVSiUGDx4shg4dKjQajSgtLZXVLy0tFUuWLBEuLi5i+PDhYuTIkeL8+fOyOpMnTxZubm5iyJAhIiUlRQghRHZ2thg1apTo37+/eOutt8TmzZsFAKFSqURqaqpYvXq16Nq1q7CxsRFTp04Vubm50rj69+8vjh49KhYtWiTVGT16tLhz546sTkJCgoiNjZXqTJ48WRrTihUrxCuvvCJUKpVYsGCBmDx5snjvvfeqjEt6eroAINLT0yvEysLCQqhUKnHjxo0K7TZv3iz69+8vAAgvLy+xb98+cePGDald165dxaxZs6qtHxcXJwCIHj16CC8vL+mnZ8+esmupVCqxfPnyGu8xEb28uOMeERFVqaioCFqtFq1atZLK/P39oVKp8PHHH1faprod9xoL7rhHRDXhdAsiIqpSQkICwsLCpOOrV6/izJkzmDBhQpVtlEolunbtit///vfw8/NriGHWWlRUFNRqNe7evQtbW1tjD4eIGjE+SSYioipdv34d8+fPR3Z2NszNzaHVarFs2TJuH01EzR6TZCIiIiIiPZxuQURERESkh0kyEREREZEeJslERERERHqYJBMRERER6WGSTERERESkh0kyEREREZEeJslERERERHqYJBMRERER6flf5GzEZzrVBfsAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colors=['slateblue', 'lime', 'coral']\n", "plt.figure(figsize=(8,6))\n", "for i in range(len(Omega_rf)):\n", " plt.plot(detunings/(2*np.pi), sol_riemann.rho_ij(1,0)[:,i].imag,\n", " label=f'RF={Omega_rf[i]/(2*np.pi):.1f} MHz (Riemann)', c=colors[i], linestyle='dashed')\n", " plt.plot(detunings/(2*np.pi), sol_exact.rho_ij(1,0)[:,i].imag,\n", " label=f'RF={Omega_rf[i]/(2*np.pi):.1f} MHz (Exact)', c=colors[i], alpha=0.5)\n", "plt.xlabel('Detuning [MHz]')\n", "plt.ylabel('Absorption [a.u.]')\n", "plt.legend()\n", "plt.title('Autler-Townes Splitting with Doppler Broadening')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "66e873bb", "metadata": {}, "source": [ "## 2D Doppler Averaging\n", "\n", "This example follows the experimental setup in Glick et al. (https://arxiv.org/pdf/2506.04504). It is a $Rb^{85}$ vapor with a $5S_{1/2} \\rightarrow 5P_{1/2} \\rightarrow 6S_{1/2} \\rightarrow 31P_{1/2}$ excitation pathway and corresponding optical fields of 795 nm, 1324 nm, and 745 nm. These fields are called probe, dressing, and Rydberg, respectively.\n", "\n", "We simulate the EIT spectra of the collinear and Doppler-free configurations using the solve_doppler_analytic function that solves the collinear configuration analytically and the Doppler-free configuration using a hybrid analytic/numeric method." ] }, { "cell_type": "code", "execution_count": 14, "id": "de2bbe0a", "metadata": {}, "outputs": [], "source": [ "# parameters for Cell\n", "atom = 'Rb85'\n", "\n", "states = [\n", " rq.A_QState(5,0,1/2),\n", " rq.A_QState(5,1,1/2),\n", " rq.A_QState(6,0,1/2),\n", " rq.A_QState(31,1,1/2)\n", "]\n", "\n", "sensor = rq.Cell(atom, states)" ] }, { "cell_type": "code", "execution_count": 15, "id": "860ef037", "metadata": {}, "outputs": [], "source": [ "# laser parameters\n", "detunings = 2*np.pi*np.linspace(-10,10,201)\n", "Omega_p = 2*np.pi*2\n", "Omega_d = 2*np.pi*10\n", "Omega_R = 2*np.pi*1" ] }, { "cell_type": "markdown", "id": "676c8465", "metadata": {}, "source": [ "### 2D Collinear configuration" ] }, { "cell_type": "code", "execution_count": 16, "id": "13590e41", "metadata": {}, "outputs": [], "source": [ "kunit1 = np.array([-1,0,0])\n", "kunit2 = np.array([1,0,0])\n", "\n", "probe = {'states': (states[0],states[1]), 'detuning': 0, 'rabi_frequency': Omega_p, 'kunit': kunit1}\n", "dressing = {'states': (states[1],states[2]), 'detuning': 0, 'rabi_frequency': Omega_d, 'kunit': kunit1}\n", "Rydberg = {'states': (states[2],states[3]), 'detuning': detunings, 'rabi_frequency': Omega_R, 'kunit': kunit2}\n", "\n", "sensor.add_couplings(probe, dressing, Rydberg)\n", "sols_col = rq.solve_doppler_analytic(sensor)" ] }, { "cell_type": "markdown", "id": "663ba5cf", "metadata": {}, "source": [ "### 2D Doppler-free configuration\n", "\n", "In this configuration, we show the ability of rydiqule to solve systems using a hybrid analytic/numeric approach, where one user-designated spatial dimension is averaged analytically and the other is averaged numerically. " ] }, { "cell_type": "code", "execution_count": 17, "id": "fd18b2db", "metadata": {}, "outputs": [], "source": [ "theta = 4.526\n", "phi = 2.556\n", "\n", "kunit1 = np.array([-1,0,0])\n", "kunit2 = np.array([-1*np.cos(theta),-1*np.sin(theta),0])\n", "kunit3 = np.array([-1*np.cos(phi),-1*np.sin(phi),0])\n", "\n", "probe = {'states': (states[0],states[1]), 'detuning': 0, 'rabi_frequency': Omega_p, 'kunit': kunit1}\n", "dressing = {'states': (states[1],states[2]), 'detuning': 0, 'rabi_frequency': Omega_d, 'kunit': kunit2}\n", "Rydberg = {'states': (states[2],states[3]), 'detuning': detunings, 'rabi_frequency': Omega_R, 'kunit': kunit3}\n", "\n", "sensor.add_couplings(probe, dressing, Rydberg)" ] }, { "cell_type": "code", "execution_count": 18, "id": "c20f8d94", "metadata": {}, "outputs": [], "source": [ "sols_DF = rq.solve_doppler_analytic(sensor, analytic_axis=0)\n", "sols_DF_1 = rq.solve_doppler_analytic(sensor, analytic_axis=1)" ] }, { "cell_type": "code", "execution_count": 19, "id": "c0ba308b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(detunings/(2*np.pi), sols_DF.rho_ij(1,0).imag, c='slateblue', label=\"analytic_axis=0\")\n", "ax.plot(detunings/(2*np.pi), sols_DF_1.rho_ij(1,0).imag, c='lime', linestyle='dashed', label=\"analytic_axis=1\")\n", "ax.set_xlabel(\"745 nm Detuning (MHz)\")\n", "ax.set_xlim(-10,10)\n", "ax.set_ylabel(r\"Im($\\rho_{10}$)\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "6e8930dd", "metadata": {}, "source": [ "Note that, for some systems, the default mesh is not sufficient to properly capture the tails of the velocity distribution. That is, the distribution normalizes to something slightly less than one. Because the analytic method is much higher accuracy, this can cause a noticeable shift in the solutions depending on which axis is sampled. This can be remedied by increasing the `width_doppler` in the mesh method on the numeric axis." ] }, { "cell_type": "code", "execution_count": 20, "id": "dd8dfdc3", "metadata": {}, "outputs": [], "source": [ "m = {\"method\":\"split\", \"width_doppler\":2.7}\n", "sols_DF_wider = rq.solve_doppler_analytic(sensor, analytic_axis=0, doppler_mesh_method=m)\n", "sols_DF_1_wider = rq.solve_doppler_analytic(sensor, analytic_axis=1, doppler_mesh_method=m)" ] }, { "cell_type": "code", "execution_count": 21, "id": "c6c6e524", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(detunings/(2*np.pi), sols_DF_wider.rho_ij(1,0).imag, c='slateblue', label=\"analytic_axis=0\")\n", "ax.plot(detunings/(2*np.pi), sols_DF_1_wider.rho_ij(1,0).imag, c='lime', linestyle='dashed', label=\"analytic_axis=1\")\n", "ax.set_xlabel(\"745 nm Detuning (MHz)\")\n", "ax.set_xlim(-10,10)\n", "ax.set_ylabel(r\"Im($\\rho_{10}$)\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "2f21456b", "metadata": {}, "source": [ "We can then recreate Figure 5b in the Glick et al. paper." ] }, { "cell_type": "code", "execution_count": 22, "id": "e8472338", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "# note that paper figure has y-normalized data for both traces, here we just match DF scale/offset to Colinear data\n", "ax.plot(detunings/(2*np.pi), (-1.55*(sols_DF.rho_ij(1,0).imag-5.155e-3)-5.21e-3), c='slateblue', label=\"Doppler-free\")\n", "ax.plot(detunings/(2*np.pi), -1*sols_col.rho_ij(1,0).imag, c='lime', linestyle='dashed', label=\"Collinear\")\n", "ax.set_xlabel(\"745 nm Detuning (MHz)\")\n", "ax.set_xlim(-10,10)\n", "ax.set_ylabel(r\"Signal (arb. units)\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "49a60d44", "metadata": {}, "source": [ "### 2D computation time and memory footprint improvements\n", "\n", "We now show the decrease in both computation time and required memory footprint of the hybrid method in comparison to the existing numeric method." ] }, { "cell_type": "code", "execution_count": 23, "id": "a3b438f0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 2min 45s\n", "Wall time: 2min 44s\n" ] } ], "source": [ "%%time\n", "sols_DF_riemann = rq.solve_steady_state(sensor, doppler=True, doppler_mesh_method=m)" ] }, { "cell_type": "code", "execution_count": 24, "id": "e57945b2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 6.12 s\n", "Wall time: 4.72 s\n" ] } ], "source": [ "%%time\n", "sols_DF = rq.solve_doppler_analytic(sensor, analytic_axis=0, doppler_mesh_method = m)" ] }, { "cell_type": "code", "execution_count": 25, "id": "50a7d8f4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total available memory: 228 GiB\n", "Min Req memory to solve: 0.68633 GiB\n", "Req memory per EOM: 0.68626 GiB\n", "Req memory for full solve: 137.94 GiB\n", "\tMandatory memory use: 7.0386e-05 GiB\n", "\tMemory use for all EOMs: 137.94 GiB\n", "\tFull output solution size: 2.2464e-05 GiB\n", "Available memory for sliced solves: 228 GiB\n", "Number of stack slices to be used: 1\n" ] }, { "data": { "text/plain": [ "(1, (201, 15))" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from rydiqule.slicing.slicing import get_slice_num, get_slice_num_hybrid\n", "\n", "get_slice_num(n=sensor.basis_size, stack_shape = (201,), doppler_shape=(601, 601), sum_doppler=True, weight_doppler=True, debug=True)" ] }, { "cell_type": "code", "execution_count": 26, "id": "377e870b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- Analytic Solver Memory Debug ---\n", "Total available RAM: 228 GiB\n", "Min Req memory to solve: 0.01075 GiB\n", "Req memory for full solve: 2.16 GiB\n", "\tFull output solution size: 2.3961e-05 GiB\n", "Available memory for sliced calculations: 228 GiB\n", "Calculated minimum slices needed: 1.0\n", "Final number of slices to be used: 1\n", "------------------------------------\n" ] }, { "data": { "text/plain": [ "(1, (201, 16))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "get_slice_num_hybrid(n=sensor.basis_size, param_stack_shape=(201,), numeric_doppler_shape=(601,), debug=True)" ] }, { "cell_type": "code", "execution_count": 27, "id": "24b5930d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time reduced by x36\n", "Solve memory requirement reduced by x64\n" ] } ], "source": [ "print(f'Wall time reduced by x{3*60/5:.0f}')\n", "print(f'Solve memory requirement reduced by x{0.68633/0.01075:.0f}')" ] }, { "cell_type": "markdown", "id": "0f137e61", "metadata": {}, "source": [ "## 3D Doppler Averaging\n", "\n", "This example follows the four photon excitation pathway in $Cs$ vapor given in Kondo et al. (https://arxiv.org/pdf/1510.01729). This pathway follows the ladder scheme $6S_{1/2} \\rightarrow 6P_{3/2} \\rightarrow 7S_{1/2} \\rightarrow 8P_{1/2} \\rightarrow 52D_{3/2}$ in cesium with corresponding optical fields 852 nm, 1470 nm, 1394 nm, and 1770 nm. These fields are labelled probe, dressing 1, dressing 2, and Rydberg, respectively.\n", "\n", "We demonstrate using rydiqule to solve this system with the collinear configuration and with a doppler-free configuration. We include the disclaimer that we ignore the hyperfine structure present in the paper. The purpose of this example is to show that with `solve_doppler_analytic`, doppler averaging over 3 spatial dimensions is now a tractable computation compared to averaging with `solve_steady_state`." ] }, { "cell_type": "code", "execution_count": 28, "id": "4c0e2267", "metadata": {}, "outputs": [], "source": [ "# parameters for Cell\n", "atom = 'Cs'\n", "\n", "states = [\n", " rq.A_QState(6,0,1/2),\n", " rq.A_QState(6,1,3/2),\n", " rq.A_QState(7,0,1/2),\n", " rq.A_QState(8,1,1/2),\n", " rq.A_QState(52,2,3/2)\n", "]\n", "\n", "sensor = rq.Cell(atom, states)" ] }, { "cell_type": "code", "execution_count": 29, "id": "8c6fc5cc", "metadata": {}, "outputs": [], "source": [ "# laser parameters\n", "detunings = 2*np.pi*np.linspace(-10,10,51)\n", "Omega_p = 2*np.pi*2\n", "Omega_d1 = 2*np.pi*10\n", "Omega_d2 = 2*np.pi*12\n", "Omega_R = 2*np.pi*1" ] }, { "cell_type": "markdown", "id": "756c6ac5", "metadata": {}, "source": [ "### 3D Collinear configuration" ] }, { "cell_type": "code", "execution_count": 30, "id": "a6e2f13f", "metadata": {}, "outputs": [], "source": [ "kunit1 = np.array([-1,0,0])\n", "kunit2 = np.array([1,0,0])\n", "\n", "probe = {'states': (states[0],states[1]), 'detuning': 0, 'rabi_frequency': Omega_p, 'kunit': kunit1}\n", "dressing1 = {'states': (states[1],states[2]), 'detuning': 0, 'rabi_frequency': Omega_d1, 'kunit': kunit2}\n", "dressing2 = {'states': (states[1],states[2]), 'detuning': 0, 'rabi_frequency': Omega_d2, 'kunit': kunit2}\n", "Rydberg = {'states': (states[2],states[3]), 'detuning': detunings, 'rabi_frequency': Omega_R, 'kunit': kunit2}\n", "\n", "sensor.add_couplings(probe, dressing1, dressing2, Rydberg)\n", "sols_col = rq.solve_doppler_analytic(sensor)" ] }, { "cell_type": "code", "execution_count": 31, "id": "81bac44c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Im($\\\\rho_{10}$)')" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(detunings/(2*np.pi), sols_col.rho_ij(1,0).imag, c='slateblue')\n", "ax.set_xlabel(\"1770 nm Detuning (MHz)\")\n", "ax.set_ylabel(r\"Im($\\rho_{10}$)\")" ] }, { "cell_type": "markdown", "id": "d3e253db", "metadata": {}, "source": [ "### 3D Doppler-free configuration" ] }, { "cell_type": "code", "execution_count": 32, "id": "efaf1a8e", "metadata": {}, "outputs": [], "source": [ "# 4 photon\n", "detunings = 2*np.pi*np.linspace(-10,10,51)\n", "\n", "theta_p, phi_p = np.pi/2, 0\n", "theta_d1, phi_d1 = 0.3834, np.pi\n", "theta_d2, phi_d2 = 2.1039, 2.6072\n", "theta_R, phi_R = 2.0598, 3.8249\n", "\n", "kunitp = np.array([np.sin(theta_p)*np.cos(phi_p), np.sin(theta_p)*np.sin(phi_p), np.cos(theta_p)])\n", "kunitd1 = np.array([np.sin(theta_d1)*np.cos(phi_d1), np.sin(theta_d1)*np.sin(phi_d1), np.cos(theta_d1)])\n", "kunitd2 = np.array([np.sin(theta_d2)*np.cos(phi_d2), np.sin(theta_d2)*np.sin(phi_d2), np.cos(theta_d2)])\n", "kunitR = np.array([np.sin(theta_R)*np.cos(phi_R), np.sin(theta_R)*np.sin(phi_R), np.cos(theta_R)])\n", "\n", "probe = {'states': (states[0],states[1]), 'detuning': 0, 'rabi_frequency': Omega_p, 'kunit': kunitp}\n", "dressing1 = {'states': (states[1],states[2]), 'detuning': 0, 'rabi_frequency': Omega_d1, 'kunit': kunitd1}\n", "dressing2 = {'states': (states[1],states[2]), 'detuning': 0, 'rabi_frequency': Omega_d2, 'kunit': kunitd2}\n", "Rydberg = {'states': (states[2],states[3]), 'detuning': detunings, 'rabi_frequency': Omega_R, 'kunit': kunitR}\n", "\n", "sensor.add_couplings(probe, dressing1, dressing2, Rydberg)" ] }, { "cell_type": "code", "execution_count": 33, "id": "31d50e7b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Breaking parameter stack into 4 slices...\n", "CPU times: total: 24min 40s\n", "Wall time: 24min 36s\n" ] } ], "source": [ "%%time\n", "sols_DF = rq.solve_doppler_analytic(sensor, analytic_axis=0)" ] }, { "cell_type": "code", "execution_count": 34, "id": "d0530c5c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Im($\\\\rho_{10}$)')" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(detunings/(2*np.pi), sols_DF.rho_ij(1,0).imag, c='slateblue')\n", "ax.set_xlabel(\"1770 nm Detuning (MHz)\")\n", "ax.set_ylabel(r\"Im($\\rho_{10}$)\")" ] }, { "cell_type": "markdown", "id": "18bca4a8", "metadata": {}, "source": [ "### 3D memory footprint comparison\n", "\n", "Here we only directly compare the memory footprint of the two methods, since the discrete sampling method results in too large a system to solve on even a moderately-sized workstation." ] }, { "cell_type": "code", "execution_count": 35, "id": "9275b5a3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total available memory: 231.27 GiB\n", "Min Req memory to solve: 820.85 GiB\n", "Req memory per EOM: 820.85 GiB\n", "Req memory for full solve: 41863 GiB\n", "\tMandatory memory use: 2.8118e-05 GiB\n", "\tMemory use for all EOMs: 41863 GiB\n", "\tFull output solution size: 9.1195e-06 GiB\n", "Available memory for sliced solves: 231.27 GiB\n" ] }, { "ename": "RydiquleError", "evalue": "System is too large to solve. Need at least 820.8490894585848 GiB", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mRydiquleError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[35], line 3\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mrydiqule\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mslicing\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mslicing\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m get_slice_num, get_slice_num_hybrid\n\u001b[1;32m----> 3\u001b[0m get_slice_num(n\u001b[38;5;241m=\u001b[39msensor\u001b[38;5;241m.\u001b[39mbasis_size, stack_shape \u001b[38;5;241m=\u001b[39m (\u001b[38;5;241m51\u001b[39m,), doppler_shape\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m561\u001b[39m, \u001b[38;5;241m561\u001b[39m, \u001b[38;5;241m561\u001b[39m), sum_doppler\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, weight_doppler\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, debug\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n", "\u001b[1;31mRydiquleError\u001b[0m: System is too large to solve. Need at least 820.8490894585848 GiB" ] } ], "source": [ "from rydiqule.slicing.slicing import get_slice_num, get_slice_num_hybrid\n", "\n", "get_slice_num(n=sensor.basis_size, stack_shape = (51,), doppler_shape=(561, 561, 561), sum_doppler=True, weight_doppler=True, debug=True)" ] }, { "cell_type": "code", "execution_count": 36, "id": "8119dc12", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- Analytic Solver Memory Debug ---\n", "Total available RAM: 231.2 GiB\n", "Min Req memory to solve: 13.54 GiB\n", "Req memory for full solve: 690.6 GiB\n", "\tFull output solution size: 9.4995e-06 GiB\n", "Available memory for sliced calculations: 231.2 GiB\n", "Calculated minimum slices needed: 3.0\n", "Final number of slices to be used: 3\n", "------------------------------------\n" ] }, { "data": { "text/plain": [ "(3, (51, 25))" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "get_slice_num_hybrid(n=sensor.basis_size, param_stack_shape=(51,), numeric_doppler_shape=(561,561), debug=True)" ] }, { "cell_type": "code", "execution_count": 37, "id": "cf92584c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solve memory requirement reduced by x61\n" ] } ], "source": [ "print(f'Solve memory requirement reduced by x{820.85/13.54:.0f}')" ] }, { "cell_type": "code", "execution_count": 38, "id": "c913b989", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Rydiqule\n", " ================\n", " \n", "Rydiqule Version: 2.1.1.dev18\n", "Installation Path: ~\\src\\rydiqule_public\\src\\rydiqule\n", "\n", " Dependencies\n", " ================\n", " \n", "NumPy Version: 2.2.5\n", "SciPy Version: 1.16.0\n", "Matplotlib Version: 3.10.0\n", "ARC Version: 3.6.0\n", "Python Version: 3.11.10\n", "Python Install Path: ~\\miniconda3\\envs\\rq_public\n", "Platform Info: Windows (AMD64)\n", "CPU Count and Freq: 16 @ 3.91 GHz\n", "Total System Memory: 256 GB\n" ] } ], "source": [ "rq.about()" ] }, { "cell_type": "code", "execution_count": null, "id": "01380423", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "RQ Public", "language": "python", "name": "rqp" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 5 }