{ "cells": [ { "cell_type": "markdown", "id": "intro", "metadata": {}, "source": [ "# Clausius-Clapeyron refiners on a regular solution\n", "\n", "`landau.refine` ships two coexistence-line tracers built on the\n", "predictor-corrector Clausius-Clapeyron idea:\n", "\n", "* `ClausiusClapeyronRefiner` — inter-phase boundaries between two\n", " *distinct* phases.\n", "* `MiscibilityGapRefiner` — intra-phase miscibility gaps where one\n", " phase splits into two compositions.\n", "\n", "This notebook exercises both on toy examples and walks through how to\n", "call them piece by piece for debugging.\n", "\n", "For the miscibility-gap demo we use a regular (one-parameter\n", "Redlich-Kister) solution with a repulsive interaction parameter\n", "$L_0 > 0$:\n", "\n", "$$f(T, c) = c\\,(1-c)\\,L_0 - T\\,S_\\text{mix}(c),$$\n", "\n", "$S_\\text{mix}(c) = -k_B\\,[c\\ln c + (1-c)\\ln(1-c)]$. Repulsive\n", "$L_0$ drives phase separation below $T_c = L_0 / (2 k_B)$.\n", "\n", "We implement the regular solution analytically (root-find $df/dc=\\mu$,\n", "pick the global minimum) so the binodal is a sharp jump — the smoothed\n", "convex-hull interpolation in `landau.phases.RegularSolution` does not\n", "resolve it cleanly at low $T$." ] }, { "cell_type": "code", "execution_count": 1, "id": "imports", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:03.426676Z", "iopub.status.busy": "2026-05-13T21:46:03.426501Z", "iopub.status.idle": "2026-05-13T21:46:05.736806Z", "shell.execute_reply": "2026-05-13T21:46:05.735458Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from dataclasses import dataclass\n", "from scipy.constants import Boltzmann, eV\n", "from scipy.optimize import brentq\n", "import scipy.optimize as so\n", "\n", "from landau.phases import Phase\n", "from landau.calculate import calc_phase_diagram, refine_phase_diagram\n", "from landau.refine import ClausiusClapeyronRefiner, MiscibilityGapRefiner\n", "\n", "kB = Boltzmann / eV # eV/K" ] }, { "cell_type": "markdown", "id": "model-intro", "metadata": {}, "source": [ "## Analytical regular solution\n", "\n", "Defines a `Phase` subclass that evaluates `semigrand_potential` and\n", "`concentration` directly via global minimisation of $f - \\mu c$\n", "(root-finding on $df/dc = \\mu$, then picking the deepest minimum).\n", "No stencil artefacts, sharp binodal jumps." ] }, { "cell_type": "code", "execution_count": 2, "id": "build-phase", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:05.739477Z", "iopub.status.busy": "2026-05-13T21:46:05.739179Z", "iopub.status.idle": "2026-05-13T21:46:05.753994Z", "shell.execute_reply": "2026-05-13T21:46:05.753047Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "analytical T_c = 580.2 K\n" ] } ], "source": [ "def _S_mix(c):\n", " c = np.asarray(c, dtype=float)\n", " with np.errstate(divide='ignore', invalid='ignore'):\n", " return kB * (np.where(c > 0, -c * np.log(c), 0.0)\n", " + np.where(c < 1, -(1 - c) * np.log(1 - c), 0.0))\n", "\n", "\n", "def _dS_dc(c):\n", " with np.errstate(divide='ignore'):\n", " return kB * np.log((1.0 - c) / c)\n", "\n", "\n", "@dataclass(frozen=True)\n", "class AnalyticRegularSolution(Phase):\n", " \"\"\"Symmetric regular solution: f = c(1-c) L0 - T S_mix(c).\"\"\"\n", " L0: float\n", "\n", " def _f(self, T, c):\n", " return c * (1 - c) * self.L0 - T * _S_mix(c)\n", "\n", " def _df_dc(self, T, c):\n", " return self.L0 * (1 - 2 * c) - T * _dS_dc(c)\n", "\n", " def _stable_c(self, T, mu):\n", " c_grid = np.linspace(1e-10, 1 - 1e-10, 4000)\n", " g = self._df_dc(T, c_grid) - mu\n", " sign_changes = np.where(np.diff(np.sign(g)))[0]\n", " roots = []\n", " for i in sign_changes:\n", " try:\n", " r = so.brentq(lambda c: self._df_dc(T, c) - mu,\n", " c_grid[i], c_grid[i + 1], xtol=1e-12)\n", " roots.append(r)\n", " except ValueError:\n", " pass\n", " if not roots:\n", " raise ValueError(f'No root at T={T:.2f} K, mu={mu:.5f} eV')\n", " if len(roots) == 1:\n", " return roots[0]\n", " # Pick the global minimum of g(c) = f(c) - mu c.\n", " gvals = [self._f(T, r) - mu * r for r in roots]\n", " return roots[int(np.argmin(gvals))]\n", "\n", " def semigrand_potential(self, T, mu):\n", " if np.isscalar(mu):\n", " c = self._stable_c(T, mu)\n", " return float(self._f(T, c) - mu * c)\n", " return np.array([self.semigrand_potential(T, m) for m in np.asarray(mu)])\n", "\n", " def concentration(self, T, mu):\n", " if np.isscalar(mu):\n", " return float(self._stable_c(T, mu))\n", " return np.array([self._stable_c(T, m) for m in np.asarray(mu)])\n", "\n", "\n", "L0 = 0.10 # eV — repulsive interaction parameter\n", "T_c = L0 / (2 * kB)\n", "solution = AnalyticRegularSolution(name='solution', L0=L0)\n", "print(f'analytical T_c = {T_c:.1f} K')" ] }, { "cell_type": "markdown", "id": "fe-plot-md", "metadata": {}, "source": [ "Visualize $f(T,c)$ at $\\mu = 0$ for a few temperatures — a clear double\n", "well below $T_c$, single minimum above." ] }, { "cell_type": "code", "execution_count": 3, "id": "fe-plot", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:05.755972Z", "iopub.status.busy": "2026-05-13T21:46:05.755772Z", "iopub.status.idle": "2026-05-13T21:46:05.908358Z", "shell.execute_reply": "2026-05-13T21:46:05.907204Z" } }, "outputs": [ { "data": { "image/png": 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oEGazmYSEBPLz8x0diihHLi4uBAcHYzQar/ocknwIIYQodzabjaioKHQ6HSEhIRiNRhm4sZpTFAWz2UxKSgpRUVE0aNDgkgOJXYokH0IIIcqd2WzGZrMRFhaGi4uLo8MR5cTZ2RmDwUBMTAxmsxknJ6erOo80OBVCCFFhrvbOWFRd5fE7lb8KIYQQQlQqqXYRQlQJ5mIb+eZiCixW8s1WCsynHy1WbDbFvl9qbhGbDiUDoNVqcDbo1MWow+X04mzUYdLrHPVRhBCXIcmHEKJC5RUVE59ZQGx6PnEZBSRmF5KeayYtr4i0PDNpuWbS88zkFhWX6Xy9jJm8M3/HZfdzNerwcTPi62rC19WIj6sRXzcTgR4mwrxdqOXjTC1vF9xM8jUoRGWTf3VCiGtmsdqIScvjSFIuR5JyOJqca0820vPMV3Qug04tzXAx6nE2qqUaet2ZXhIe2QZaBHgCUGxVKLScKSEpMFsxW20A5Jmt5KUXEJtecMn383IxEObtQpiPM/UD3GkY6EbDQHfq+rpi1EvN9PXkcr1xXnzxRV566aVyfU+LxcLzzz/Pzz//zIkTJ/D09KR379688cYbhISE2PdLT0/n4Ycf5ocffkCr1TJ06FDef/993Nzc7Pvs2bOHyZMns2PHDvz9/Xn44Yd56qmnLvre0dHRhIeHs3v3blq1agVATk4OgwYNIikpiV9//fWSM9NeC0k+hBBXJLeomL1xWfwXl8n+U9kcSczhRGouFqty0WM8nPTUOn2BD/Z0xvd0KYSvm9H+3MfFiItJh0F36Qv+4sWxvDeqy0W3F1tt5JmtZOSdLl3JNZOWp5aupOQUkZhVSFymmhhl5ltOL1nsjc8CEu3n0Ws1hPu50jDQnWahHrSs5UXzWp54OBmu+GcmqoeEhAT786VLlzJ9+nQOHz5sX3f2hb685Ofn8++///LCCy/QsmVLMjIymDp1KoMGDWLnzp32/caMGUNCQgLr16/HYrFw9913M3HiRL799ltAnU32lltuoXfv3sydO5e9e/dyzz334OXlxcSJE8sUS0pKCv3790er1bJ582Z8fX3L/fOWkORDCHFRVpvCwYRsdsdm8t/p5VhKLsoF8gwXo44GAW40CFRLD+r6ulLL24VQb2c8nSvvgq3XafF01uLpbKCun+sl980ptBCXUUBcRsHpkpscjiTlciw5l9yiYo4m53I0OZef9p65KNXzd6VlLS9ahnnRurYXTYM90F8mYRIqRVEosFT+SKfOBl2ZxhgJCgqyP/f09ESj0ZRaVxE8PT1Zv359qXUffvghN910EydPnqR27docPHiQtWvXsmPHDtq1awfAnDlzGDBgAG+//TYhISEsWrQIs9nMvHnzMBqNNGvWjMjISN59990yJR+xsbH06dOH0NBQVq9eXSGJ1tkk+RBC2NlsCgcTs/n7RDrbjqfxT1Qa2YXnt8UI9XKmRS1PmtfypHGQOw0C3An1ckarrV6DSLk7GWgSbKBJsEep9YqicCqrUE1GEnPYE5/FnrhMYtMLOJ6Sx/GUPFbujlfPYdJzY7gPHSJ86BjhR9MQD3TV7OdQWQosVppOX1fp73tgZl9cjBV3uZs0aRILFy685D65ubllPl9WVhYajQYvLy8Atm3bhpeXlz3xAOjduzdarZbt27dzxx13sG3bNrp161Zq1NG+ffsya9YsMjIy8Pb2vuj7HT58mCeffJJ27dqxePFiTCZTmWO9WpJ8CHGdS8gqYOOhZP44nML2qHSyCiyltruZ9LSu7UXrMC9a1PKiRZgnAe5XN7BQdaHRaAj1cibUy5kejQLs69Nyi9gTl0VkbCb/xWWyKyaDnMJiNh5KZuPpHjjuJj03hfvQvZE/PRoFEOYjA2zVdDNnzmTatGnlcq7CwkKefvppRo0ahYeHmhQnJiYSEBBQaj+9Xo+Pjw+JiYn2fcLDw0vtExgYaN92qeRj3LhxdO7cmeXLl6PTVU4vMUk+hLjOWG0Ku09m2C+YhxJzSm13NepO38n70jHCl2YhUq1QwtfNRI/GAfRorF4ISqql/j6RdrqkKJ2comJ+O5TMb4eSgf00CHCj5+lj2tbxvmyblprM2aDjwMy+DnnfihQQEHBecnA1LBYLw4cPR1EUPvnkk3KIrGwGDRrEqlWrWLlyJcOGDauU95TkQ4jrgLnYxpZjKfy4J4GNh5LJzD9TuqHRQOswL3o0CqBLAz+ah3pKslFGOq2GG0I9uSHUk/u6RmC1KRw4lc3mYyn8fiiFXScz7O1GPv3zBO5Oeno2DmBA82C6N/THqYIvilWNRqOp0OoPRymPapeSxCMmJoaNGzfaSz1AbYuSnJxcav/i4mLS09PtbVKCgoJISkoqtU/J68u1W3nuuedo0aIFo0ePRlEUhg8ffsn9y0PN+ysQQgClE471B5LIOavthqezge4N/enR2J/uDQPwcb362SnFGTqthuan28I8dHN9svIt/HE0hU2Hkvn9cDIZ+RZWR55ideQpXI06ejcNvG4TkZrkWqtdShKPo0ePsmnTpvN6mXTs2JHMzEx27dpF27ZtAdi4cSM2m4327dvb93nuueewWCwYDGoD7/Xr19OoUaNLVrmUeOGFF9BqtYwZMwZFURgxYsRVf56ykORDiBrEZlP4OyqNlf/Gs25/YqmEI8DdxIDmwfS/IYi2dbyldKMSeLoYGNQyhEEtQ7DaFCJjM/hlbyI/703gVFZhqUSkT9NAhrSpRef6ftJgtZq5lmoXi8XCnXfeyb///suPP/6I1Wq1t+Pw8fHBaDTSpEkT+vXrx/3338/cuXOxWCxMmTKFkSNH2scCGT16NDNmzODee+/l6aefZt++fbz//vu89957ZY7lueeeQ6fTMWbMGGw2G6NGjbqqz1QWknwIUQPEpOXx3a44vvs3nvjMM4NqlSQcA5oH066Od7XrjVKT6LQa2tbxoW0dH/43oAmRcZn8tCeBX04nIqsiT7Eq8hRBHk4MaRPK0La1qOdfsd0dhePFx8ezZs0aAPtAXyU2bdrEzTffDMCiRYuYMmUKvXr1sg8y9sEHH9j39fT05Ndff2Xy5Mm0bdsWPz8/pk+fXuYxPko888wzaLVaxo4di6IojB49+po+38VoFOVCPfavX9nZ2Xh6epKVlVWqzk2IqiavqJif9iSwYlcc/0Sn29e7m/Tc2jKEwa1CuLGuT41LOBYvXlyhd2SVzWZT2B2byerIeFZHnirV26h1bS+GtqnFoFYh1W5ws8LCQqKioggPD7/qaddF1XSp321Zr6FS8iFENXM0KYeFf8ew8t94ck7Ph6LVQJcG/tzZtha3NA2U9gPViFaroW0db9rW8ea5gU3YeDCZFbvi+P1ICrtPZrL7ZCav/XyQwa1Duat9HZqGyE2RqP4k+RCiGrBYbfy6P4lv/o7m7xNnSjnC/VwZ3i6MO1qHEuQpd5fVnUmvo3/zYPo3DyY5p5A1kadYuiOWo8m5fLv9JN9uP0m7Ot6M7ViHfjcEycy9otqS5EOIKiw9z8w322JYtD2G5JwiQC3l6NM0kLEd6tKpnm+Nq1YRqgB3J+7rGsG9XcLZHpXON3/HsG5fIjtjMtgZk4Gvq5FRN9VmXKc6NX7QN1HzSPIhRBUUlZrHl1tOsHxnHEXF6iytfm4mRt8UxsibahPi5ezgCEVl0Wg0dIjwpUOEL8nZhSzZEcu320+SmF3Ih5uO8dmfJ7ijdSj3dQ2nQaC7o8MVokwk+RCiCtkVk85nf57g1wNJ9snbmod6cl/XcPrfECxTvF/nAjyceKRXAx66uR7rDyTxxZYodsVksHRnLEt3xtKzcQD3d42gQ4RPmSZSE8JRJPkQwsEUReH3Iyl8uPEYu2Iy7Ot7NQ7g/m4RtA+XC4koTa/T2tuG7IpJ5/M/o1h3INE+ZH6LWp5M7lGfPk0CpVpOVEmSfAjhIIqi8NvBZD7YeJQ9cVkAGHVaKUIXV6RtHR/ajvUpVVW3Jy6LB77ZReMgdx7p1YB+zYIkCRFViiQfQlQym03h1wNJzNl4lP2nsgF14quxHetwX5dwAjyk8aC4cuF+rrwyuDmP9W7IV39FM39rNIcSc3ho0b80DHTj4Z4NGNA8WEZPFVWCJB9CVBJFUZOO99Yfsc8k62rUMa5TXe7rEo6vm8nBEYqawNfNxLS+jbivazjz/ormq7+iOJKUy8OLdzN7wxGm9m7Irc2DpSREOJQkH0JUgm3H05i19hCRsZmAOgrphM51uadzON4yqZuoAF4uRh7v05B7u4SzYGs0X26J4nhKHo8s3s2nfxznqX6N6dbAT9oTCYeQpvNCVKB98VmMm/cPoz7/m8jYTJwNOqb0qM+Wp3vyxC2NJPEQFc7T2cAjvRqw5ekePN6nIW4mPftPZTP+9N/lvyczLn+S64RGo7nk8tJLL1V4DJMmTUKj0TB79uxS69PT0xkzZgweHh54eXlx7733kpubW2qfPXv20LVrV5ycnAgLC+PNN9+85HtFR0ej0WiIjIy0r8vJyaFHjx40bdqUuLi48vpY55GSDyEqQFRqHu/8epgf9yQAYNBpGH1TbSb3rC8DQgmHcHdSk5C7OtThk9+PsWBbDH+fSGfIx1u5pWkgT/ZtdN03ck5ISLA/X7p0KdOnT+fw4cP2dW5uFTvR3/fff8/ff/9tn6n2bGPGjCEhIYH169djsVi4++67mThxIt9++y2gzqlyyy230Lt3b+bOncvevXu555578PLyKvPkcikpKfTv3x+tVsvmzZvx9fUt1893Nkk+hChHWfkWPth4lAVboym2KWg0cHvLEB7v04javi6ODk8IfFyNPDewKXd3Dmf2hiOs2BXHrweS2HAwidHta/NY74YV1/5IUcCSXzHnvhSDC5SheikoKMj+3NPTE41GU2pdRYqPj+fhhx9m3bp1DBw4sNS2gwcPsnbtWnbs2EG7du0AmDNnDgMGDODtt98mJCSERYsWYTabmTdvHkajkWbNmhEZGcm7775bpuQjNjaWPn36EBoayurVqys80apWyceff/7JW2+9xa5du0hISOD7779n8ODB9u2KovDiiy/y+eefk5mZSefOnfnkk09o0KCB44IW14Viq41v/znJe+uPkJGvzkp6cyN/nurbWCYCE1VSiJczb97ZkondInhr3WHW7U9i4d8nWR15iqm9GjCuY93yH9TOkg+vnX9XX+H+dwqMrhV2+kmTJrFw4cJL7nNuFcnZbDYbY8eO5cknn6RZs2bnbd+2bRteXl72xAOgd+/eaLVatm/fzh133MG2bdvo1q0bRuOZqty+ffsya9YsMjIy8Pb2vuj7Hz58mCeffJJ27dqxePFiTKaKb/xerZKPvLw8WrZsyT333MOQIUPO2/7mm2/ywQcfsGDBAsLDw3nhhRfo27cvBw4ckCmdRYX5/XAyr/50kKPJ6pdLw0A3nh/YlG4N/R0cmRCXVz/AnU/HtuPvE2m8/OMB9p/K5pWfDrLw7xj+N6AJfZoGSqPUy5g5cybTpk276uNnzZqFXq/nkUceueD2xMREAgICSq3T6/X4+PiQmJho3yc8PLzUPoGBgfZtl0o+xo0bR+fOnVm+fDk6XeVMVlitko/+/fvTv3//C25TFIXZs2fz/PPPc/vttwPw9ddfExgYyKpVqxg5cmRlhiquAydScpn54wF+P5wCgLeLgcdvacSoG8PQ66Qtt6heOkT4smZKF77bFcdbvx4mOi2fid/solM9X168rRmNgsqhPYjBRS2FqGyGiq3yDAgIOC85KKtdu3bx/vvv8++//zosyRs0aBCrVq1i5cqVDBs2rFLes1olH5cSFRVFYmIivXv3tq/z9PSkffv2bNu27aLJR1FREUVFRfbX2dnZFR6rqN4KzFY+Oj2hl9lqw6DTML5jXR7u1QBPZ4OjwxPiqum0GobfGMaAFsF88vsxPt8cxdbjaQz4YDP3dK7L1N5qb5mrptFUaPWHo1xLtcvmzZtJTk6mdu3a9nVWq5UnnniC2bNnEx0dTVBQEMnJyaWOKy4uJj093d4mJSgoiKSkpFL7lLy+XLuV5557jhYtWjB69GgURWH48OGX3L881Jjko6ToqaSYqURgYKB924W8/vrrzJgxo0JjEzXHhgNJvPTDfuIyCgDo3tCfF29rSoR/xTbOEqIyuZn0PNm3MSNvrM0rPx1g3f4kPt8cxQ//JfDCrU0Z0DxIqmLOci3VLmPHji110wxqW42xY8dy9913A9CxY0cyMzPZtWsXbdu2BWDjxo3YbDbat29v3+e5557DYrFgMKg3QevXr6dRo0aXrHIp8cILL6DVahkzZgyKojBixIir+jxlVWOSj6v17LPP8vjjj9tfZ2dnExYW5sCIRFUUm57PjB/2s+GgevcR4unE9Nua0reZfAmLmivMx4VPx7Zj06FkXlyzn5Pp+Uz+9l+6NvBjxqBmknSfdi3VLr6+vud1aTUYDAQFBdGoUSMAmjRpQr9+/bj//vuZO3cuFouFKVOmMHLkSHu33NGjRzNjxgzuvfdenn76afbt28f777/Pe++9V+ZYnnvuOXQ6HWPGjMFmszFq1Kir+kxlUWOSj5JipaSkJIKDg+3rk5KSaNWq1UWPM5lMldKyV1RPFquNzzef4IPfjlJosaHXarivawSP9KqPi7HG/PMR4pJ6NA6gYz1fPvn9OJ/8cZzNR1PpN3szk7pHMLlnfUz6ymmkeD1btGgRU6ZMoVevXmi1WoYOHcoHH3xg3+7p6cmvv/7K5MmTadu2LX5+fkyfPr3MY3yUeOaZZ9BqtYwdOxZFURg9enR5fxQANIqiKBVy5gqm0WhKdbVVFIWQkBCmTZvGE088AailGAEBAcyfP7/MDU6zs7Px9PQkKysLDw/pInk92xOXydPf7eVggtoOqEOEDy/ffsN1PxCToy1evLhC78jEpUWn5vHimv38cURtaF3P35VZQ1vQrq5Pqf0KCwuJiooiPDxcehvWMJf63Zb1Glqtbt1yc3M5duyY/XVUVBSRkZH4+PhQu3ZtHn30UV555RUaNGhg72obEhJSaiwQIS6nwGzlvQ1H+GLzCWwKeLkYeGFgU4a0CZUqFnHdq+vnyvy7b+TnvYm8uGYfx1PyGPbpNsZ2qMNT/RpfW4NUcd2oVn8lO3fupEePHvbXJW01xo8fz/z583nqqafIy8tj4sSJZGZm0qVLF9auXStZtyizv46l8uzKvZxMV0dhHNQyhOm3NcVPZpwVwk6j0TCwRTCd6/vy2s8HWbYzjq+3xbD+QBKv3nEDPRsHXv4k4rpWbatdKopUu1yfsgstvPLjAZbtVCdSCvF04hX5Eq2SpNql6rlQ0v6/vvXISIqXapca6LqrdhGiImw+msJTK/aQkFWIRoMUHwtxhTrX92Pdo93s1ZVr/jvF8cQMXu51dT1ARM0n367iupVXVMzrvxxk4d8nAajr68Jbw1py4zkN54QQl+ds1PG/AU0Y2DyYacv/IzO/gLRcMwmZBYQFGNFrZdRfcYYkH+K6tP1EGk+u2GMvJh7fsQ5P928s3WeFuEYtw7z44eEufLrxEBqKyC60cDQpl1rezrg7yQjAQiXftOK6Umix8ta6w8z7KwpFgVAvZ966swWd6vs5OjQhagwng44Hutfj0NHjGHVaLFYbUal5+LgaCfZ0RqeVXmPXO0k+xHXjwKlspi7ZbZ99duSNYTw3sIncjQlRQUx6LbV9XckyQ2puEel5ZvKKignzcZFSxuuc/PZFjWezKcz7K4o31x7GbLXh727izaEt6NFYGsMJUdF0Wg0hXk54OOmJzSigqNjG8eQ8Aj1M+LubZOyc65QkH6JGS84u5Inl/7H5aCoAvZsEMmtoc3xl3A4hKpWbk4EGATriMwvIKrCQmF1ITqFaCmLUS2PU6438xkWN9ev+RPrO/pPNR1NxMmh5ZfANfD6urSQeQjiIXqelto8Ltbxd0Go05JmLOZqcQ2a+2dGhAergaZdaXnrppQp53wkTJpz3Xv369Su1z5EjR7j99tvx8/PDw8ODLl26sGnTplL7nDx5koEDB+Li4kJAQABPPvkkxcXFl3xvjUbDqlWr7K8tFgujRo0iNDSUffv2ldtnPJeUfIgap9Bi5eUfD7Bou9qFtmmwBx+MakX9AJmTRQhH02g0+LgacTXpiE0vIN9czMn0fHIKiwnxcmxj1ISEBPvzpUuXMn36dA4fPmxf5+ZWcbP49uvXj6+++sr++twJT2+99VYaNGjAxo0bcXZ2Zvbs2dx6660cP36coKAgrFYrAwcOJCgoiK1bt5KQkMC4ceMwGAy89tprZYohPz+foUOHcvToUbZs2UJ4eHi5fsazSfIhapQTKblM/na3fTK4id0ieOKWhjLrphBVgKIoFBQX2F8HeWlIyVFIzS0kIaeA9Pxcavu6YCrnahhnvXOZ2paUzI4O6iyxGo2m1LqKZDKZLvpeqampHD16lC+//JIWLVoA8MYbb/Dxxx+zb98+goKC+PXXXzlw4AAbNmwgMDCQVq1a8fLLL/P000/z0ksvYTQaL/n+mZmZDBw4kNzcXLZs2VLhn1uSD1FjrPnvFM9+t4c8sxVfVyPvjWhFt4b+jg5LCHFaQXEB7b9tX+nvu330dlwMLhV2/kmTJrFw4cJL7pObm3vJ7b///jsBAQF4e3vTs2dPXnnlFXx9fQHw9fWlUaNGfP3117Rp0waTycSnn35KQEAAbdu2BWDbtm00b96cwMAzU0L07duXBx98kP3799O6deuLvndiYiLdu3fHzc2NP/74Ay8vrzJ+8qsnyYeo9gotVmb+eIBvT1ez3BTuw5xRrQn0kPkkhBAVb+bMmUybNu2qj+/Xrx9DhgwhPDyc48eP87///Y/+/fuzbds2dDodGo2GDRs2MHjwYNzd3dFqtQQEBLB27Vq8vb0BNYE4O/EA7K8TExMv+f5Tp04lIiKC9evX4+JScUna2ST5ENXa2dUsGg1M6VGfqb0aoNdJW2ohqhpnvTPbR2+/6HZFUUjNNZOcU4gCmHS6cqmGcdY7X9PxlxMQEEBAwNV33R85cqT9efPmzWnRogX16tXj999/p1evXiiKwuTJkwkICGDz5s04OzvzxRdfcNttt7Fjxw6Cg4OvKf5bb72VVatW8emnn/LYY49d07nKSpIPUW1JNYsQ1YtGo7ls9Yerjyu+rsXEpudjsdqIT7cS4mXE28VQZccEKY9ql7NFRETg5+fHsWPH6NWrFxs3buTHH38kIyPDPlPsxx9/zPr161mwYAHPPPMMQUFB/PPPP6XOk5SUBHDZ9htjx45l0KBB3HPPPSiKwuOPP17mWK+WJB+i2jm3N0v7cB8+kGoWIWoMN5OeBgFuxGYUkFNoIS4jn7wio8N7w1zMtVa7nCsuLo60tDR7iUZ+vjoHlfacyfm0Wi02mw2Ajh078uqrr5KcnGwvhVm/fj0eHh40bdr0su85fvx4tFotd999NzabrVw/z4VI8iGqlfjMAh5cuIs9cVlSzSJEDabXaanr60JKThFJ2YVk5JspsFip4+OCyVC1eq9dS7VLbm4uM2bMYOjQoQQFBXH8+HGeeuop6tevT9++fQE1sfD29mb8+PFMnz4dZ2dnPv/8c6Kiohg4cCAAt9xyC02bNmXs2LG8+eabJCYm8vzzzzN58uTzuu1ezNixY9FqtYwfPx5FUXjyySev6jOVhSQfotrYeiyVKYt3k55nxtvFwOyRreku1SxC1FgajYYADydcTHpOpudTaLFyLCWXMG8XPJxrxpxMOp2OPXv2sGDBAjIzMwkJCeGWW27h5ZdfticNfn5+rF27lueee46ePXtisVho1qwZq1evpmXLlvbz/Pjjjzz44IN07NgRV1dXxo8fz8yZM68onjFjxqDVahk7diw2m42nn3663D8zgEZRFKVCzlxNZWdn4+npSVZWlr1uTTiWoih8vvkEb/xyCJsCN4R68MmYtoT5VE6rbFG1LF68mFGjRjk6DHEZhYWFREVFER4ejpPTtVeJWqw2YtLyyTerI3YGejgRIHPDOMSlfrdlvYZKyYeo0vKKinnquz38tEcdeXBom1q8escNOFWxYlchRMUy6LRE+LuSkFlIWp5aFVNgtlLLxxm9VqpdqxtJPkSVFZWaxwPf7ORIUi56rYYXb2vKXR3qyJ2OENcprUZDqLczzkZ1grrsQgvHk23U8XWRG5JqRpIPUSVtOJDEY0sjySkqxt/dxCdj2tCuro+jwxJCVAE+rkacDFpOpuVTVGzlWHIutbyd8XK59BDiouqQ5ENUKTabwvu/HeX9344C0K6ONx+PaUOAdKMVQpzFxainfoAbJ9PzyS1SJ6crsFgJ8nCS0tFqQJIPUWXkm4t5Ytl//LJPHQp4fMc6PDewKcZynmRKCFEz6HVawv1cScwuJCWniJScIgotNmr7OKOTdiBVmiQfokqIzyzg/gU7OZCQjUGn4dU7mjO8XZijwxJCVHEajYZgT2ecDTriTg9KdizZRl3fqjceiDhDkg/hcLtiMnjgm12k5hbh62rk07FtpX2HEOKKeLkYMeq1xJS0A0nJpY6PC25ONWM8kJpGyqWEQ323K45Rn/1Nam4RTYI9WD2lsyQeQoirUtIOxMWox2pTiErNJy23yNFhiQuQkg/hEFabwpvrDvHpHycA6NsskHeHt8LVJH+SQoirZ9BpifBzJS6zgMx8M/GZBRQW2wj2dEIrDVGrDPmmF5Uup9DC1CWRbDyUDMDDPevzWO+GaKvghFFCiOpHq9UQ5u2Mk15LYnYhablFFFms1PZxkXmgqgj5LYhKFZuez9BPtrLxUDImvZb3R7biiVsaSeIhhChXJfPC1PF1RavRkFtUzPGUXAot1ksec6nlpZdeqrBYL7S89dZb9n3S09MZM2YMHh4eeHl5ce+995Kbm1vqPHv27KFr1644OTkRFhbGm2++ecn3jY6ORqPREBkZaV+Xk5NDjx49aNq0KXFxceX6Oc8mJR+i0vx7MoP7F+wkLc9MgLuJz8e1o2WYl6PDEkLUYJ7OBoz+bsSk5VFUbON4Si51fF1xu0AVb0JCgv350qVLmT59OocPH7avc3Nzq5AYz35fgF9++YV7772XoUOH2teNGTOGhIQE1q9fj8Vi4e6772bixIl8++23gDqnyi233ELv3r2ZO3cue/fu5Z577sHLy4uJEyeWKY6UlBT69++PVqtl8+bN+Pr6lt+HPIckH6JS/Lw3gceWRlJUbKNZiAdfjr+RIE8ZOEyI64miKCgFBZX+vk7OztQPcCP69MR0Ual51PJyxtu19IioQUFB9ueenp5oNJpS6yrKue+xevVqevToQUREBAAHDx5k7dq17Nixg3bt2gEwZ84cBgwYwNtvv01ISAiLFi3CbDYzb948jEYjzZo1IzIyknfffbdMyUdsbCx9+vQhNDSU1atXV1iiVUKSD1GhFEXhsz9P8PovhwDo1TiAD0a1loalQlyHlIICDrdpW+nv2+jfXehdXIjwcyU2I5+sAguxGfkUWW0ElsPMuJMmTWLhwoWX3OfcKpKLSUpK4qeffmLBggX2ddu2bcPLy8ueeAD07t0brVbL9u3bueOOO9i2bRvdunXDaDyTUPXt25dZs2aRkZGBt7f3Rd/z8OHDPPnkk7Rr147FixdjMpnKFOu1kCuAqDAWq43pq/ez+J+TAEzoVJcXbm2KTtp3CCEcQKvVUNvHhaTsQpJzikjOLsRcbKOWt/M19YSZOXMm06ZNK5cYFyxYgLu7O0OGDLGvS0xMJCAgoNR+er0eHx8fEhMT7fuEh4eX2icwMNC+7VLJx7hx4+jcuTPLly9Hp6ucgdkk+RAVIrvQwuRF/7L5aCpaDbxwa1Pu7hx++QOFEDWWxtmZRv/ucsj72p9rNAR5OmPUa4nPKCQz34ylWJ0Z92p7wgQEBJyXHFytefPmMWbMGJycKq9aetCgQaxatYqVK1cybNiwSnlPST5EuYvLyOee+Ts4kpSLs0HHnFGt6d000NFhCSEcTKPRoHFxcXQYAPi4mjDo1Jlx88zFHE/Ju+oh2cur2mXz5s0cPnyYpUuXllofFBREcnJyqXXFxcWkp6fb24sEBQWRlJRUap+S15drt/Lcc8/RokULRo8ejaIoDB8+/LKxXitJPkS52hOXyb0LdpKSU0SAu4l5E27khlBPR4clhBDncXcyUC/AjejUPIqKrfaeMFfaJq28ql2+/PJL2rZtS8uWLUut79ixI5mZmezatYu2bdU2Mxs3bsRms9G+fXv7Ps899xwWiwWDQR1Sfv369TRq1OiSVS4lXnjhBbRaLWPGjEFRFEaMGHHNn+dSalTy8dJLLzFjxoxS6xo1asShQ4ccFNH15ffDyTy48F8KLFYaB7kzb8KNhHg5X/5AIYRwECeDjnoBalfcfLOVE6l51Pa+su+t8qh2yc7OZvny5bzzzjvnbWvSpAn9+vXj/vvvZ+7cuVgsFqZMmcLIkSMJCQkBYPTo0cyYMYN7772Xp59+mn379vH+++/z3nvvlTmG5557Dp1Ox5gxY7DZbIwaNeqaPtOl1KjkA6BZs2Zs2LDB/lqvr3EfsUpa+W8cT63YQ7FNoWsDPz4e0wZ3mdBJCFENqEOyu3EyPZ/sQgsx6fnkFFoqNYYlS5agKMpFL/iLFi1iypQp9OrVC61Wy9ChQ/nggw/s2z09Pfn111+ZPHkybdu2xc/Pj+nTp5d5jI8SzzzzDFqtlrFjx6IoCqNHj76mz3UxGkVRlAo5swO89NJLrFq1qtRobVcqOzsbT09PsrKy8PDwKL/garDP/jzOaz+rpUu3twrhrTtbYtTL4LmiYixevLhC78hE+SgsLCQqKorw8PBKbTx5LRRF4VRmIWl56mR0/u4mgjycrrkrbk1zqd9tWa+hNe4KcfToUUJCQoiIiGDMmDGcPHnykvsXFRWRnZ1dahFlY7MpvPrTAXvicW+XcN4b3koSDyFEtaTRaAjxciLIQ72gpuQUEZtRgK3m3KNXGTXqKtG+fXvmz5/P2rVr+eSTT4iKiqJr167k5ORc9JjXX38dT09P+xIWFlaJEVdfFquNJ5b/x+ebowB4tn9jnh/YROZoEUJUayVzwtTydkGDhsx8M9GpeVhtNkeHVqPUqOSjf//+DBs2jBYtWtC3b19+/vlnMjMzWbZs2UWPefbZZ8nKyrIvsbGxlRhx9ZRXVMx9C3by/e54dFoN7wxryQPd60nRpBCixvBxNVLXz+WsSenysFglASkvNbo1ppeXFw0bNuTYsWMX3cdkMlXKULI1RXqembvn7+C/2EycDTo+HtOGHo3LZ3AdIYSoStydDNTzdyUqNZ9Ci5XjybnU9XPF6SrGAhGl1aiSj3Pl5uZy/PhxgoODHR1KjRCbns+dn2zlv9hMvFwMLLq/vSQeQohLqu59GpyNeuoHuGLS6zBb1Vlx84qKHR2WQ5XH77RGJR/Tpk3jjz/+IDo6mq1bt3LHHXeg0+mkZXw5OJiQzdBPtnIiNY9QL2dWTOpEm9qXH7hGCHF9KhnoKj8/38GRXDujXkc9f1dcjHqsNoUTqXlkFZgdHZbDlPxOS37HV6NGVbvExcUxatQo0tLS8Pf3p0uXLvz999/4+/s7OrRq7e8Tadz/9U5yCotpFOjOgntuIsizenSdE0I4hk6nw8vLyz4suIuLS7VvFxbipiMhy0xuUTHRSUUEuDvh7Wq8/IE1hKIo5Ofnk5ycjJeX1zVNQlejko8lS5Y4OoQaZ+2+BB5ZEom52MZNdX34fFw7PF1k8DAhxOWVzCly7rwk1ZmiKOQVWMgrspIMeDjp8XC+vr4Tvby8LjtfzOXUqORDlK+Ff8cwffU+bArc0jSQD0a1loZWQogy02g0BAcHExAQgMVSuSOGViRFUfh6WzRfb4sB4NYWITzSqwG662CoAYPBcE0lHiUk+RDnURSF9387yuwNRwEYdVNtXr692VVPNy2EuL7pdLpyuWBVJQ/0bIKLszPT1+zn079iic228N6IVpj0NetzVhS5mohSrDaF51btsycej/RqwGt33CCJhxBCnGNsx7rMGdUag07Dz3sTufurHZU+J0x1JVcUYVdosTJ50b98u/0kGg28PPgGHu/TsNo3EhNCiIpya4sQ5t99E65GHVuPpzHq879JzS1ydFhVniQfAoCsAgvj5v3D2v2JGHVaPhrdhrEd6jg6LCGEqPI61/djycSO+Loa2RefzZ2fbCU2vfp3Ma5IknwIkrILGfHpNv6JSsfdpGfBPTcxoLkMzCaEEGXVvJYnyyd1JNTLmei0fIZ8spWDCTJR6cVI8nGdO56Sy5CPt3IoMQd/dxNLH+hIx3q+jg5LCCGqnQh/N1Y+1IlGge6k5BQx/PRNnTifJB/XscjYTO78ZCvxmQWE+7my8sFONA3xcHRYQghRbQV6OLHsgY7cWNebnMJixn65nfUHkhwdVpUjycd16vfDyYz67G8y8i20qOXJikkdCfNxcXRYQghR7Xm6GPjm3vb0bhJAUbGNSQt3sWynzJh+Nkk+rkMr/43jvgU7KbBY6drAj8X3d8DXTWb2FUKI8uJk0DH3rrbc2bYWVpvCUyv28Mnvx6v9RHvlRZKP68xnfx7n8WX/UWxTGNwqhC/H34irScaaE0KI8qbXaXnrzhY80D0CgFlrD/HqTwex2SQBkeTjOmGzKbz60wFe+/kQAPd1Cefd4a0w6uVPQAghKopGo+HZ/k14bkATAL7YEsUTy//DYrU5ODLHklve64DFauOpFXv4fnc8AP8b0JiJ3eo5OCohhLh+3N8tAh9XI099p34XZ+Sb+XhMG1yM1+dlWG57a7i8omLuW7CT73fHo9NqeGdYS0k8hBDCAYa2rcUX49rhZNDy++EUxnyxncx8s6PDcghJPmqw9Dwzo7/Yzh9HUnA26PhifDuGtq3l6LCEEOK61aNxAIvu64Cns4HdJzMZNncbCVkFjg6r0knyUUPFpudz5ydb+S82Ey8XA4vub0+PRgGODksIIa57bet4s3xSR4I8nDianMvQj7dyLDnX0WFVKkk+aqCDCdkM/WQrJ1LzCPVyZsWkTrSp7e3osIQQQpzWMNCd7x7qRIS/K6eyCrlz7lZ2xWQ4OqxKI8lHDfP3iTSGf7qN5JwiGgW6892Dnagf4ObosIQQQpyj5OawZZgXmfkWxnzxN78dvD5GQ5Xkowb5cc8pxn35DzmFxdxU14dlD3QkyNPJ0WEJIYS4CB9XI4vvb0+PRv4UWmxM/GYXS3ecdHRYFU6Sjxriyy1RPLx4N2arjb7NAvn63pvwdDE4OiwhhBCX4WLU89m4dvbRUJ/+bi9zfjtao0dDleSjmisZPOzlHw+gKDCuYx0+HtMWJ4PO0aEJIYQoI8Pp0VCn9KgPwDvrj/D8qn1Ya+hoqNfn6CY1RFGxlWnL9/DDf6cAeLpfYyZ1j0Cj0Tg4MiGEEFdKo9EwrW8jAjxMvLhmP4u2nyQ1t4j3R7aucTeUUvJRTWUXWpgwbwc//HcKvVbDeyNa8uDN9STxEEKIam5cx7p8NLoNRp2WdfuTuKsGDkYmyUc1lJhVyPC529h2Ig03k56v7r6RO1rL4GFCCFFTDGgezNf33oS7k56dMRkMm7uNuIx8R4dVbiT5qGaOJOUw5OO/OJSYg7+7iaUPdKBrA39HhyWEEKKcdYjwZfmkjgR6mDianMvgj9SBI2sCST6qkb+OpXLnJ1s5lVVIPX9XVj7YiWYhno4OSwghRAVpHOTB9w91pnGQO6m5RYz4bBtr9yU6OqxrJslHNbFoewzj5v1DdmEx7ep4892DnQjzcXF0WEIIISpYiJczKx7sxM2nxwJ5cNEuPvvzeLXuiivJRxVXbLUx44f9PPe92uVqcKsQFt7XHi8Xo6NDE0IIUUncTHq+GNeOsR3qoCjw2s+HeG7VPoqtNkeHdlWkq20Vll1o4ZHFu/n9cAoA025pyOQe9aVHi6j+FAWKC08v5tOPRWAtUh9LXiu2M/ujqI+5yXD4F/W5RgM6A+iMp5cLPDe4gNEN9JKwi+pNr9My8/Zm1PVz5ZWfDvDt9pPEpufz0Zg2eDhVr0ElNUp1LrepANnZ2Xh6epKVlYWHh4fD4ohNz+ee+Ts4mpyLk0HLu8NbMaB5sMPiEeKCzHmQlwr5qZCXdvoxFfLToDALinKgKFt9LDz9WHR6vXJ1d2yLuZ1RrL7yA3VGNQkxuoHp9KPRFZw8wNkHXHzAxfec597qo5OnmugIUUX8uj+RqUsiKbBYqefvyufj2hHh7/h5vMp6DZXk4xxVIfnYfiKNBxf9S3qemUAPE5+Pa0eLWl4OiUVcpyyFkJMA2adOP8ZD9unHnATISVSTjOKCcngzDeidQG86/WhUH3Um0GrV7XD64q9hcfoNjPI9oL5WbGC1nF7MZz2WPC9Sn18rnQncg8A9+PRj0DmvQ8ArDAzO1/5eQpTR3rgsJn6zk4SsQtxNet4f1YqejQMdGpMkH1fJkcmHoih8uSWK1385hNWmcEOoB1+Mu1EmhxPlz2ZVE4mM6LOWmDPP81PLfi6dCVz91BICVz9wOf3c2QtMHmByV0sXTO6nX59+bnRVL9Za/RWVKixevJhRo0aVPT6rBcy5UJSrltSYc896nauWyBSkQ366WmJTcPoxP0N9bs4t+3u5BYJX7dNLnfOfS9WPKGcpOUU8uHAXO2My0Ghg2i2NeMiBA06W9Rp6xW0+Dh48yJIlS9i8eTMxMTHk5+fj7+9P69at6du3L0OHDsVkMl1T8Nej3KJinlrxHz/vVbtQDWoZwhtDm+NilGY54iopCuSlQOqR08tRdUk7BlmxYCu+9PF6Z/AIBo9Q9Q7fI+TM4hakJhqufmr1RVWuktAZ1OoTZ++rO95SCLlJamlPbqL6WFL6U/KYFacmKblJ6hK34/zzaHTgXQd864NvA/CtB34N1NfuwVX7ZyiqLH93E9/e34EZP6jDsb+17jB74jJ5c2jLKj25aJlLPv7991+eeuoptmzZQufOnbnpppsICQnB2dmZ9PR09u3bx+bNm8nOzuapp57i0UcfrZZJiCNKPo4m5fDAwl2cSMnDoNPwwq1NGduhjjQsFWWjKGopRtIBSN4PKWclG0VZFz9OZ1Tvxr3rll686oBnLfViXQX/Bq+45KMyKAoUZEDmSciMOf14esmIUddZLjE6pcEV/OpDQFMIaHLm0SO0Sv4ORNX07faTvLhmHxarQqiXMx+Mak3bOleZdF+lcq92CQ8PZ9q0aYwZMwYvL6+L7rdt2zbef/99WrRowf/+978rDtzRKjP5sNkU5m+NZtbaQxQV2wj2dOKjMW1oU7ty/1hENVKUA8kHIWmfmmwk7VcTjsKLJRka9W7br6G6+NZXF59w9W5bW/0mq6qSycflKIpaQpJ2DNKOQtpx9XnqUbWaS7Fe+DiTx+lkpAkENIOgGyCouVptJcQF7InL5OHFu4lJy0en1fDELQ2Z1K0eWm3lJLHlnnxYLBYMhrIX4Vzp/lVFZSUf8ZkFTFv2H9tOpAHQraE/7w1via9b9SstEhWkMAsS9sCp3ZAQqT6mn7jwvlq9WpQf2BT8m6jF+X4NwScCDDWrzVC1TD4uxWpRS0dSDkHKwdMlWAfVJOWCVWMaNYEMbll6cfaq7MhFFZVTaOF/3++zz3jepb4fs+5sQahXxTeIrpAGpx9++CF33XXXJUs+qoKPPvqIt956i8TERFq2bMmcOXO46aabynRsRScfiqKwfFccL/9wgJyiYpwNOp4b2IQx7WtLNcv1rDAbEk8nGqciTycaxy+8r3uwWiwf2AwCb1ATDr+Gam+R60CNSz4uptislo4kn05GkvarfyPZ8Rfe37vuWclIKwhtc/XtXES1pygKS3fE8tIP+ym02HAz6Xmmf2NG31S7QktBKiT58PT0xGKxMHjwYO677z569uxZLsGWp6VLlzJu3Djmzp1L+/btmT17NsuXL+fw4cMEBARc9viKTD72xWfx4pr97IrJAKBNbS/eHd6Kun6u5fo+ooqzWdW73Nh/1IaJsf+oFxku8E/RszaEtISQ1uoFJbgVuPpWcsBVy3WTfFxMbgok/gcJp5dTkWqbkgvxawi1boJa7aDWjWr1TTWsahNX73hKLk+t2GO/7jQP9eSlQU1pW8enQt6vQpKPgoICli9fzldffcWff/5J7dq1ueeee5gwYQJhYWHlEvi1at++PTfeeCMffvghADabjbCwMB5++GGeeeaZyx5fEcnHf7GZfLjpGOsPJAHgbNDxSK8G3N81HL1ORriv8QoyIX6nmmTE/gPxu9SBt87lGQYhrdQEI6QVBLe+7hONC7nuk48LKchQq+hKEpL4XZARdf5+Rjc1kQ27SU1GQtuBm8yKXdNZbQpfb4vm3V+PkFOkVuV1b+jPlJ71ubFu+SYhFT7Ox4kTJ5g/fz5ff/01cXFx9O7dm3vvvZfBgwc7rK2H2WzGxcWFFStWMHjwYPv68ePHk5mZyerV54+KWFRURFFRkf11dnY2YWFh5ZZ8fPDbUd5dfwRQG60PahnCM/0bE+wpgxHVSIqiNiCM2Qqxf6vJRsphzivVMLqpxeJh7dU709A2ardVcVmSfJRRXirE7VRL1+J2QPy/YM45fz+fCKjdCep0hDqdwDtcetjUUCk5Rby17hArdsVhO/2V9EC3CJ4d0KTc3qPCxvkoERERwcyZM5kxYwYbNmxg/vz5TJgwAVdXV5KTk6/2tNckNTUVq9VKYGDpEd4CAwM5dOjQBY95/fXXmTFjRoXF1KNRAB/8dpTbW4Xy4M0R1A+QVuo1iqKoPRZitqgJR/RfkHPq/P18ItQkI+xGNeEIaCrF36JiufpBo37qAqer+w5D3OnqvridavVf+gl1iVyo7ucWpCYhdTpB7Y6n/1alhLYm8Hc38eadLZncoz5z/zjOil1x9Gh8+eYIFeGaR7DSaDTo9Xo0Gg2KomCxWMojrkrz7LPP8vjjj9tfl5R8lJfmtTzZ9mwv/N2vj8aANZ7NpjYAjNl6JuHISym9j9aglmTU7ni6ZONGKdoWjqfVqY2TA5tC2wnquoJMtXTu5FaI2aZW1+Qmwv6V6gLg5AW1O6h/z+FdIagl6GTww+qsjq8rrw9pweN9GuHn5phRd6/6Lyg2NpavvvqK+fPnc/LkSbp168bnn3/O0KFDyzO+K+Ln54dOpyMpKanU+qSkJIKCgi54jMlkqvDB0CTxqMZsNnVMjag/1UTj5Fa1fv1seic1wajTCep0Vp8bXRwTrxBXwtkLGt6iLgCWAjUBidkGMX+piUlhJhxZqy6gjj1SpzOEd1OTkYBmUjJSTTny2nRFyYfZbGblypXMmzePjRs3EhwczPjx47nnnnuIiIioqBjLzGg00rZtW3777Td7mw+bzcZvv/3GlClTHBucqD7SoyDqDzjxu5p05KeV3m5wVRvs1e0MdbqopRzXSTdXUcMZnKFuF3XhSbAWq917Y7aeKe0rzIIjv6gLqLMAh3eFul0hvLs6xoy0GRGXcUXJR1BQEPn5+dx666388MMP9O3bF20Vy3gff/xxxo8fT7t27bjpppuYPXs2eXl53H333Y4OTVRVeamnk43TCce53RYNrmqpRsmXcnBLdb4QIWo6nV5NrkPbQKcparuRxD1qUh61WU1ICtLhwGp1AbXNSHjX0yUj3dTxR4Q4xxUlH88//zxjx47F37/q1l+PGDGClJQUpk+fTmJiIq1atWLt2rXnNUIV1zFznlqsfGKTmnQk7i29XatXq04iblaX0LaSbAgBaruRkNbq0nmqOjrrqd3qv6OoP9VqmtxE2LtcXUCdPyi8u/pvKbwbuDmmgaOoWq66q21mZiYrVqzg+PHjPPnkk/j4+PDvv/8SGBhIaGhoecdZaRwxsZyoYNZiOPWvWqpx4nf1C9J2TsPowBvOfEHW6QQmNwcEKspCutpWYZZCtSdN1J8QvVl9fu4Q8QFNS/9bc5Lv2ZqkQrva7tmzh969e+Pp6Ul0dDT3338/Pj4+rFy5kpMnT/L1119fdeA10vGNaktxg4ztUSkURe1CWFKNEr3l/PENPGtDRMndWHfpjSJEeTA4na5y6aq+LsqFk9tOt586XcqYfEBdtn8CGp1ashjRXf13GHaTtJ+qLMVmNUls0Nshb39Vycfjjz/OhAkTePPNN3F3PzNuxYABAxg9enS5BVcj/PM5/PwkNLkNhi2QVuEVJSv+TCPRE79DbukeTzh7q0W+JVUpMpCSEBXP5AYN+qgLQF4aRP+p3hhE/aGOLxL3j7r8+RbondVuvSXJSHBLGQ+nIigK/DAV/vsWer8EXR6r9BCuKvnYsWMHn3766XnrQ0NDSUxMvOagapSApmobgoNr4LeXoM9MR0dUMxRkqCUaJaUbaUdLb9c7qyM2lhTvBrWQxE8IR3P1hWZ3qAtA5kn17rukZ1luktoW68QmdbuTl9rIu+Smwbe+3DSUhz/fVhMPjQ4CmzskhKtKPkwmE9nZ589NceTIkSrdGNUh6naG2z+C7yfCX++rja9uvM/RUVU/lkKI3X6m+PbUblBsZ7ZrtGojuIge6peUFN8KUfV51YbWd6nL2dWlUX+oNxeFmXDoR3UBcA85UyoS0R08QhwafrX03xLY9Ir6fMBb1avaZdCgQcycOZNly5YB6iinJ0+e5Omnn3boIGNVVssR6nwfv78GPz2hXkg7ybgjl1TSpa+kGuXk31BcWHofv4Zn7ojqdFYHTBJCVE8ajTrrbkAT6DBJbSieEHnmhuPkdnXqgv8WqwuAb4MzyUh4V7V6VVzczq/gx9NVLJ0ehhvvdVgoV9XbJSsrizvvvJOdO3eSk5NDSEgIiYmJdOzYkZ9//hlX1+o7RXyF9XZRFFj/Amydo77uPBV6vSj1mSUUBdKOlx7cqzCz9D5uQWeSDbnruW5Jb5frlKVAvQkpGZMnIbJ06ScatY1ISTJSu6OMNFzCZoPNb8OmV9XXbe+Gge9WSFV0hc9qC7Blyxb27NlDbm4ubdq0oXdvxxTflKcK7WqrKLDlPfjt9ER24d1g6JfXZ793RVEnuYrZok7GFvPX+Y1Eje7q3UxJwuHXUOp7hSQfQlWQqVbNlCQjqYdLb9cZ1bmVSqpoQtpcn3PS5KfD9w/A0V/V112nQc/nK+y7tFKSj5qoUsb52LsC1jwCljxw9Yd+b8ANQ2v2hdVmg+T9ZxKNmK2Qn1p6H51Rnfm1JNkIaX19flmIS5LkQ1xQdsLpkVdPJyPZcaW3G93VNnglyYh/k5rdCF1R1LYyPz+lVlfpTGobj7bjK/RtKzz52LFjB5s2bSI5ORmbzVZq27vvvns1p6wSKiL5yLfkU2QtwtvprPrIlMOwfILa3x3Ui22fmWqxYU1gzoNTkeogQ7Hb1WTj3GoUvbM6xXydLuqXQmg7dZwAIS5Bkg9xWYqiduM9sUlNRKI3nz8hpJOnerMTdnoJbQsm9wufr7pJOqCWsJdMBuhTD4bNh+AW9l2yirLQaXS4Gct3QMUKHWTstdde4/nnn6dRo0YEBgaiOeuOXVOT796vwrLDy3hn5zsMaTCEp296+swG/0Yw8Xf46wO1f/uJ3+HTbup4IJ0eUYf3ri4/S5sN0o+riUbcDojbCUn7QbGW3s/gCrXbq41D63ZRi0H1jpnOWQhRg2k04FtPXW68T/2OStxzplTk5DZ1grxj69UF1B5zgc1OJyTtoVY7dTyg6lQ6cmo3bP0Q9n0HKKA1qO0Lu007b5DLrw98zTcHvmFyq8mMb1axpSEXclXJx/vvv8+8efOYMGFCOYdT8wS5BpFfnM9PJ37i8baPYzh7jhC9Cbo/Cc2HwqbX1OqYgz+oS3ArtftZ08FVa/RNazGkHVNHKkzaqz7G/3t+qQaAe7D6D7jWjWrCIROyCSEcQauFkFbq0nmq+j2WtE+daiF2uzrIWeZJ9fsscS/s/FI9zuShjhEU3FI9NrilOtZIVeookJ8OB1ZB5GL1c5Roejv0eE690T2H1WZlzfE1FBQXEOjimHnPrir50Gq1dO7cubxjqZE6hXTC39mflIIU/oj7g951LtAo1ycChn4BXR6HbR+pEzIlRKrLL0+rWXiD3lC7k1psZqyE3kTFRerU8unH1WQj9aj6jzX54PldXgH0TmrCVJJs1LoRPKvvHD9CiBpMpz+TjLSfqK7LTlAv3iUJScIeKMpWG8XHbDlzrN4Z/BqoF3W/RuqjfyP1e7wybq7M+ep38cltcHS9+lgyf47WoA7g1mnKJavwtyduJzEvEXejOz1q96j4mC/gqpKPxx57jI8++ojZs2eXczg1j16r57Z6tzFv3zy+P/b9hZOPEoFNYfBH0GcG7FmqloSc+hdOblUXUIsG/RurjTH9G4FHKHjWUhe3wMv/8SsKFOWoJRUFmZCbrDZGyk5QHzNPql1es2LP6cZ2FoMrBN2gTsYW1Fz9Iw9qLqUaQojqyyNYLS1oerv62mqB1COQ8J/afi3hP7VUxJKnVuEk7il9vFZ/+vs4TL3xOvu72T1IHa3V2UstTblclbrVon43Z8dDVpy6pB5W40g+eH6VdlBzaD4MWowE98uXZKw6tgqAAeEDMOkcMxjjVTU4tdlsDBw4kCNHjtC0aVMMhtIXnZUrV5ZbgJWtIhqcRmVFMWjVILQaLRvu3IC/yxVUo2TEqHWSxzdB/C7ISbj0/loDGFzU/u16k1rXabOombHVoiYe5/7hXozR/XS9aX31MbCZmnBUt3pQUaNIg1PhMDarWiKcelgdjTXliPo89SiYc8t2Do1WbdiqM6oJi1avVuMUF4ElXy3ZOHfW7XO5BqgNZOv1gPq91e/nMsoqyqLnsp6YbWaWDFxCM79mZT62LCq0wekjjzzCpk2b6NGjB76+vtLI9BIKDxzA5cefuKugFgvrxvHDiR+454Z7yn4C7zpqg6mSIdmzE9RGRad2Q0aUOqFadhxkn1ITDJsFirLU5VJ0RjUTd/VXM36PEHXoYs9aZxIOV//q0+hVCCEqmlYHfvXVpfHAM+sVRS2lyIw9XVoRe/q7+XTJRW6yWtpcXKiWKBde5vsZ1HlXPEJOl6CEqjd9Ia3VxSPkqr+b10atxWwzc0dMAL6fraHgVivOLVpc/sBydlXJx4IFC/juu+8YOHDg5Xe+zuXv3k36vHn0ah7Owrrw/dHvmdBsAlrNVZYceASrS+MBpdfbbOoft6VAzZ4t+eow7lq9Wr9ZkmGbPNQuZgZnSSyEEKI8aDRnqlguxVKofk8XZp9VIl2sPupNans+g7Naeu3kWe4NWxVF4buj3wHQ74gLGTu/Ru/nV32SDx8fH+rVK3sxz/XMrXNnkgDXg7H4DnQlOjuav+L/omutruX7RlotuPiU7zmFEEKUH4MTGILUNiAOsDt5NwfTD+KCEZ8Dp1AA186dHBLLVd1+v/TSS7z44ovk5+eXdzw1jqFOHQy1akFxMXebbwRg4cGFDo5KCCHE9abk2jPO1h4lPx+djw9OTZo4JJarKvn44IMPOH78OIGBgdStW/e8Bqf//vtvuQRXE2g0Gly7dCZzyVI6x7nybn0tW09t5VjGMep713d0eEIIIa4D8bnx/HbyNwB6J/phA1w7d0bjoM4DV5V8DB48uJzDqNncunQhc8lSNNsj6dmjJxtObmDRoUW82PFFR4cmhBDiOrDk0BJsio0OwR0wrjlAIeDWxXHjdV1V8vHii3LRvBIu7duDToc5Joax3lPZcHIDPxz/gYdaPnRl3W6FEEKIK5RVlMWKIysAGBt8O4UHngLAtZNj2nvAFbT5kMlvr57O3R3nVq0AqHsoi5b+LSmyFjF//3yHxiWEEKLm+/bgt+RacqnvVZ8WMQooCqbGjdH7O+7mt8zJR7NmzViyZAlms/mS+x09epQHH3yQN95445qDq0lKirfy//qLSS0nAbD8yHLSCtIcGZYQQogaLMecwzcHvwHggZYPkL9FHS3bkVUucAXJx5w5c3j77bcJCgpixIgRvPXWWyxatIjvvvuOL774gscff5ybbrqJVq1a4eHhwYMPPliRcVc7rl3UrrV5f22lo287bvC9gYLiAr4+8LWDIxNCCFFTLT60mBxzDhGeEfQO7Unun38C4Nqli0PjKnObj169erFz5062bNnC0qVLWbRoETExMRQUFODn50fr1q0ZN24cY8aMwdvbuyJjrpacmjVFHxhIcVISBdu3M6nlJKZsnMLiQ4sZ13Qcvs6+jg5RCCFEDZJtzrbf4E5sMRHznr1Y09PRenri0ratQ2O74ganXbp0oYuDM6bqSKPV4t6rJxnfLiZnw290mzmDG3xvYF/aPub+N5fnOjzn6BCFEELUIPP2ziOrKIsIzwj61e1H6rK3AXC/uTsag2MnApXZwSqRW69eAORs3Ag2G4+1fQyAFUdWEJ0V7cDIhBBC1CSJeYn2QcUea/sYWo2WnN/UcT5KrkWOJMlHJXK98Ua07u5Y09Io+G8PNwXfRLda3ShWivlg9weODk8IIUQN8VHkRxRZi2gb2JbutbpTdOQolthYNCYTblWg9kKSj0qkMRpx694dgJzfNgDwaJtH0Wq0rI9Zz87EnY4MTwghRA1wMO0gq4+tBuCJtk+g0Wjs1xzXTp3Qurg4MjxAko9K5977dNXLhg0oikID7wYMaTAEgNf+eY1iW7EjwxNCCFGN2RQbr2x/BQWF/uH9ae7fHFCvOXDmGuRoknxUMtcuXdGYTFhiTlJ44AAAU1tPxdPkydGMoyw5tMTBEQohhKiuVh9bzZ6UPbjoXZjWbhoA5uhoig4cBJ0Otx49HByhSpKPSqZzc8Xt5psByP7pZwC8nLyY2mYqAB9GfkhKfoqjwhNCCFFNZRVl8d6u9wB4qNVDBLgEqOt/+gkA144d0fv4OCy+s0ny4QAeAwcAkP3zzyg2GwBD6g/hBt8byLPk8er2V2U4eyGEEFfkzR1vklGUQT3PeoxuMhpQp0YpudH1GDjQkeGVIsmHA7h1747WzY3ixEQKdu8GQKfV8VKnl9Br9Px28jd+jfnVwVEKIYSoLjbHbWbN8TVo0PBSp5cwaNVxPIoOH8Z84gQaoxH3Pr0dHOUZZU4+9uzZg+30Xbq4NlqTCffe6h9B9uniMIBGPo24r8V9ALy2/TUyCjMcEp8QQojqI9ecy4xtMwAY02QMrQJa2beVXGPcundH5+bmiPAuqMzJR+vWrUlNTQUgIiKCtDSZEO1alBR/Za9dh2Kx2NdPbD6R+l71SS9M5+W/X5bqFyGEEJf0xj9vkJSfRC23Wjzc+mH7esVmq5JVLnAFyYeXlxdRUVEAREdHV8lSkLp166LRaEotVXV2XdeOHdD5+mJNTyd38xb7eoPOwKtdXkWv1bM+Zj2rjq1yXJBCCCGqtLXRa1l9fDVajZZXuryCi+HMGB75O3ZiOXUKrasrbjd3d2CU5ytz8jF06FC6d+9OeHg4Go2Gdu3aERERccHFkWbOnElCQoJ9efjhhy9/kANo9Ho8b7sNgKzvV5ba1tS3qT17ff2f14nJjqn0+IQQQlRtiXmJzNw2E4B7b7iXtoGlJ4vLWqleWzwGDEDr5FTp8V1KmSeW++yzzxgyZAjHjh3jkUce4f7778fd3b0iY7sq7u7uBAUFOTqMMvEccgfp8+eTs+l3itPTS3WBmtBsAn/F/8U/if/wxO9PsHDAQpz0VeuPRwghhGNYrBam/TGNHHMOzf2a82CrB0ttt+bmkv2r2nHBc8gdjgjxkq5oVtt+/foBsGvXLqZOnVolk4833niDl19+mdq1azN69Ggee+wx9PqLf8yioiKKiorsr7OzsysjTACcGjbE6YYbKNy3j6w1a/CdMMG+TavR8lqX1xj+43AOZxzm9X9eZ0anGZUWmxBCiKrr3V3v8l/Kf7gb3JnVdZa9d0uJ7F9+QSkowBgejnOrVo4J8hKuqqvtV199VSUTj0ceeYQlS5awadMmHnjgAV577TWeeuqpSx7z+uuv4+npaV/CwsIqKVpVSUaatfL78xqXBroGMqvbLLQaLSuPrmTl0ZUXOoUQQojryNrotfYZa1/t8iphHudft7JWfg+o1xiNRlOp8ZVFlR/n45lnnjmvEem5y6FDhwB4/PHHufnmm2nRogWTJk3inXfeYc6cOaVKNs717LPPkpWVZV9iY2Mr66MB4DlwIBqjkaIjRyjct++87R2COzC51WQAXvn7FSKTIys1PiGEEFXHwbSDvLDlBQDuueEeetQ+f7j0ohMn1DGkdDo8b7+9skMskyuqdnGEJ554gglnVUdcyMUaubZv357i4mKio6Np1KjRBfcxmUyYTKZrDfOq6Tw9ce/bl+wffiBjyRKcmzc/b5/7mt/HofRDrI9Zz9RNU1kycAnBbsEOiFYIIYSjpBak8simRyi0FtI5pHOpbrVny1iizhHm1r07hoCAygyxzKp88uHv74+/v/9VHRsZGYlWqyWgiv7wS3iPGkX2Dz+Q/dPPBD71FDpPz1LbtRotr3R+hZPZJzmccZjJGyfzVd+v8DR5XuSMQgghapJ8Sz6PbHyExLxE6nrU5c3ub6LXnn8Jt+Xnk/X9KkC9tlRVVb7apay2bdvG7Nmz+e+//zhx4gSLFi3iscce46677sLb29vR4V2Sc+tWmBo1QiksJGvVqgvu42JwYU7POfg7+3M04ygPb3yYguKCyg1UCCFEpTNbzTy66VH2pu7Fy+TFnJ5z8DB6XHDf7J9/xpaTg6F2bVw7d6rkSMuuxiQfJpOJJUuW0L17d5o1a8arr77KY489xmeffebo0C5Lo9HYM9SMxUsuOqppsFswc/vMxd3ozu7k3Uz7YxoWm+WC+wohhKj+rDYr/9vyP7YlbMNZ78zHvT6mrmfdC+6rKAoZ3y4GwHvECDTaqnuJr7qRXaE2bdrw999/k5mZSUFBAQcOHODZZ591aHuOK+F5261oXV0xR0eTv23bRfdr6N2Qj3p9hJPOiT/j/mT6X9OxKVVvtFkhhBDXRlEUXtv+Guui16HX6nm/x/s09z+/XWCJwj17KDxwAI3RWCXH9jhbjUk+qjutqyued6h/LOkLvr7kvq0DWvPOze+g0+j48cSPvLXjLZkDRgghapgPIz9k2ZFlaNDwRtc36BjS8ZL7l1w7PAYMQF/FmxtI8lGF+Iy9CzQacv/4g6ITJy65b7da3Xi588sALDy4kDf+eUNKQIQQogZQFIX3/32fz/aozQae7/A8fev2veQxllOnyF63DgCfCeMrPMZrJclHFWKsUwe3nj0BSP/60qUfALfVu43pHaejQcO3h77lxa0vYrVZKzpMIYQQFcSm2Hjjnzf4Yu8XAExrN43hjYZf9rj0RYvAasWlQwecGjeu6DCvmSQfVYzP+HEAZK1aTXFGxmX3H9ZwGK92eRWtRsuqY6t4ZvMz0ghVCCGqIavNyktbX+LbQ98C8EKHFxjf7PKlGLa8PDKXLQfOXEOqOkk+qhiXG2/E1LQJSmEhGYsXl+mY2+rdxjvd30Gv1bM2ei2Pb3qcwuLCCo5UCCFEebFYLTy7+Vm+P/Y9Wo2WV7u8WqYSD4DM777DlpODsW5d3Lp3r+BIy4ckH1WMRqPB9557Acj4ZiG2/PwyHde7Tm/m9JyDSWfi97jfuXvt3aTkp1RkqEIIIcpBRmEG96+/n1+if0Gv1fN297cZVG9QmY5VzGbS5n0FgM+ECVW6e+3ZqkeU1xmPfn0xhIVhzcggc8WKMh/XJbQLn/b5FE+TJ/vS9jHqp1EcTDtYgZEKIYS4FsczjzP6p9HsStqFm8GNj3p+RJ86fcp8fNYPP1CcmIje37/Kd689myQfVZBGr8f3XrX0I23eVyhmc5mPbRvYlsUDFhPuGU5SfhLj147nt5O/VVSoQgghrtJf8X9x1893EZcbR6hbKAsHLKRTaNlHJVWsVtI+Vxum+kyYgNZorKhQy50kH1WU5x2D0fv7U5yYSNYPP1zRsWEeYeofcUgnCooLeHTTo3wc+bH0hBFCiCrAptj4at9XPPTbQ+RacmkT0IZvB35LPa96V3SenPXrMUdHo/X0xGvEiAqKtmJI8lFFaU0mfO6+G4DUuZ+iWK6sB4uH0YOPen3EyEYjAfjkv0+4f/39JOcnl3usQgghyia9MJ3Jv03m3V3vYlNs3F7vdj6/5XN8nHyu6DyKzUbqRx8D4DNmDDo314oIt8JI8lGFeY8cgc7XF0tsLFmrV1/x8Xqtnuc6PMdrXV7DWe/MjsQdDPthGH/F/1UB0QohhLiUHYk7GLZmGFvit2DSmXix44u83PlljLorry7JWbeOoqNH0bq7V5vutWeT5KMK07q44HvffQCkfjL3itp+nO22erex9NalNPJuRHphOpM2TOLtHW9Ld1whhKgEFquFObvncN+v95FckEy4ZzjfDvyWOxveiUajueLzKVYrKR99BIDP+PHoPD3LO+QKJ8lHFec9cgQ6fz8s8fFkfr/qqs8T7hnOooGLGNFIrRdccGABw34Yxu7k3eUUqRBCiHPtT93P8B+H89mez+zVLEsGLqGhd8OrPmf2L2sxHzuO1sOjWpZ6gCQfVZ7W2Rm/+ycCkPrRR2Ue9+NCTDoTz3d4njk95+Dv7E90djTjfxnPrH9mkW+5+vMKIYQorchaxHu73mP0z6M5lnkMb5M3b3V/i1e6vIKLweWqz6uYzaR88AGgzuGic3cvr5ArlSQf1YDXyBEYQkMpTk4mfcGCaz7fzWE38/3t3zO4/mAUFBYeXMiQNUPYeHKjzI4rhBDXaEv8Fu5ccyfz9s3DptjoX7c/qwavol/dftd87owlS7CcPInOzw/f8VV/ArmLkeSjGtAajfg//hgAaZ9/QXFq6jWf09PkycudX+aT3p8Q5BpEfG48UzdNZdKGSZzIvPSMukIIIc4Xmx3Lwxsf5sENDxKdHY2fsx+ze8zmze5vXnFvlguxZmfbe7j4P/wwWtfq1cPlbJJ8VBMeAwbg1KIFtvx8Uj78sNzO2yW0C6tvX839ze/HoDWw9dRWhq4Zyps73iSzMLPc3kcIIWqqHHMO7//7Prevvp3fY39Hr9Ezruk41gxeQ6/avcrtfVI//RRrVhbG+vXwGjqk3M7rCJJ8VBMajYbAp54EIHP5CoqOHy+3c7sYXHikzSOsvn01N9e6mWKlmG8OfEP/lf2Z+99c8ix55fZeQghRUxQUFzBv3zz6fdePL/Z+gcVmoWNwR74b9B1P3vgk7sbya49hjosn4+tvAAh88kk0en25ndsRJPmoRlzatcOtdy+wWkl++51yP3+YRxhzes3hk96f0NC7IbmWXD6K/Ij+3/Xn6/1fS9dcIYQAzFYzSw4tYcDKAby36z2yzdmEe4Yzu8dsPu3zKRFeEeX+nimzZ6NYLLh06IBrt27lfv7KVr1Tp+tQwONPkLvpd3I3bSJv+z+4tr+p3N+jS2gXOoV0Yl30Oj7c/SEnc07y1s63+HLfl4xpMoYRjUbgaap+/cqFEOJa5JpzWX5kOd8c+IaUAnXW8BDXEB5q9RC3RtyKTqurkPct2LuP7B9/hNMl4FczNkhVI8lHNWOKCMd7xHAyvl1M8qxZ1F2+DI2u/P/gtRot/cP707tOb9YcW8Nnez7jVN4p5uyew5d7v2RYw2Hc1fQuglyDyv29hRCiKknJT+HbQ9+y9NBSciw5AAQ4B3Bfi/sY2mDoVY1QWlaKopA8axYAnoNuw6lp0wp7r8okyUc15Dd5Mlk//EjhgQNkLF2Kz+jRFfZeBq2BoQ2HMqj+INZFr2PevnkczTjKggMLWHhwITeH3czIxiNpH9S+RmTjQggB6kV/V9Iulh5eyoaYDRQrxQDU9ajLPTfcw60Rt2LQGSo8juw1a8jfuRONkxP+U6dW+PtVFkk+qiG9ry/+jz1K0syXSXn3PTz69EHv71+h72nQGrg14lYGhg9kS/wW5u+fzz+J//Dbyd/47eRv1PWoy/BGwxkYMbBcupQJIYQjZBVl8XPUzyw/spyjGUft61v5t2LCDRPoEdYDraZymktaMzNJmvUmAH6TH8IQElIp71sZNIqMKlVKdnY2np6eZGVl4eHh4ehwLkqxWokeOYrCvXvxGDiQ0HfervQYjmUcY+nhpaw5vob8YnWEVL1GT5daXbi93u10r9W9Uu4MxPVl8eLFjBo1ytFhiBrEYrOwNX4rq4+v5vfY37HY1FnEnfXODAgfwMjGI2ns07jS40qY/iKZy5ZhalCf8JUr0Riq/vdpWa+hknyco7okHwAF+/cTPWw42GyEffkFbp07OySOPEsePx7/kVXHVrEvbZ99vafJk55hPelbty83Bd+EQVv1/+GIqk+SD1EeLFYL/yT+w/qY9WyK3UR6Ybp9W2OfxgyuP5jb6t2Gh9Ex14H8f3cTc7pKvc7Cb3Bp184hcVwpST6uUnVKPgASX3uNjK+/wVCnNhFr1qA1mRwaz/HM46w+vpqfjv9EckGyfX1JItI9rDsdgjvgaqi+I/MJx5LkQ1ytwuJCtp7ayoaYDfwe9zs55hz7Nh8nHwZGDOT2erfTyKeRA6MExWIhauidFB05gufQIYS8+qpD47kSknxcpeqWfFhzczkxYCDFycn4TZ6M/8NTHB0SAFablV1Ju/g15lfWx6wvdVeh1+ppG9iWrqFd6RralXDPcGmsKspMkg9RVoqiEJMdw9ZTW9l2ahvbE7dTUFxg3+7r5Euv2r3oXac37YLaVZnS2bR5X5H85pvovLyI+OVn9N7ejg6pzCT5uErVLfkAyF67lvhHH0NjMBD+/UpM9es7OqRSShKRDSc3sDluM3G5caW2h7qF0jGkI20D29IusJ103xWXJMmHuJSMwgz+SfyHbae2sfXUVhLyEkptD3YNplftXvSp04eW/i0rbGyOq2WOi+PEoNtR8vMJfvUVvIYOdXRIV0SSj6tUHZMPRVGInTSJvD/+xKlZM+ouWVxlGyaV3Ilsjt/Mlvgt7EjcYW/cVSLULZS2gW1pG9iWNgFtqO1Ru9Jal4uqT5IPUcKm2IjOimZ38m4iUyKJTI4kOju61D4GrYE2AW3oGNKRTiGdaOzTuMqWtCo2GyfHjSd/505c2rWj9tcL0Gir13dfWa+h0tW2BtBoNATPfJkTgwZRuH8/qZ9+hv+UyY4O64I0Gg11PetS17MuY5uOJd+Szz+J/7AzcSe7knZxMP0g8bnxxOfGs+b4GgDcDe409W1KU7+mNPNtRjPfZoS6hVbZLxAhRPlTFIX43HgOpR/iYPpBDqYdZE/qHrKKss7bt75XfXuy0TawLc56ZwdEfOXSF3ytjunh4kLw669Vu8TjSkjyUUMYAgMImv4Cp56YRuonn+DWvTvOzW9wdFiX5WJw4eawm7k57GZA7TnzX/J/7ExSk5F9qfvIseSwPXE72xO324/zNHnS0Lsh9TzrUd+rPvW961Pfq74M+y5EDZBtzuZE5gmisqI4mnmUQ+mHOJR+qFQD0RJOOidu8LuB1gGtaRXQipb+Lavl90DR0aOkvPceAIHPPI0xLMzBEVUsST5qEM+BA8nZsIGcX9Zy6plnCP9uBVonJ0eHdUVcDa50Cu1Ep9BOgNr//njmcfan7md/mrocyThCVlEWOxJ3sCNxR6nj/Zz9iPCMIMw9jFrutQhzD7Mv5TnDpBDi2uRZ8ojLibOXdMZkx3Ai6wQnMk+QVph2wWP0Wj0NvBrQ2KcxjX0a08K/BY18GlWZhqJXS7FYOPX0MyhmM67duuI1bJijQ6pwknzUMEHTp5O/cyfm48dJmf0+gc887eiQrolBa7B/0QxFbXhltpo5mnmUYxnHOJ55nGOZxziWeYyEvARSC1JJLUjln8R/zjuXl8lLTUrcahHoGkiASwABLgEEuqjP/Z39ZVA0IcqBxWYhrSCN1IJUkvOTSclPIT43nrjcM8nGhapLzhboEki4Zzj1vOrRyLsRTXybUM+zXo38N5o691MKDxxA6+lJ8MuvXBdVypJ81DB6b2+CX36ZuEkPkr5gAW4334xrh/aODqtcGXVGe9uPs+WaczmedZyY7BjicuKIzYm1L+mF6WQWZZJZlMne1L0XPbePkw+BLoH4Ovvi4+SDl8kLbydvvE3e6qOTt7rO5I2b0Q29Vv4JiZrPbDWTWZRJVlGWupizzjwvyiKtMI2U/BRSClJILUglozADhcv3ZfAyeRHqFkqIWwi13WsT4RVBhGcE4Z7h181YQAV79pA6dy4AQdNfwBAY4OCIKod8c9ZA7jffjNewO8lcvoL4J6cR8f336P38HB1WhXMzutHSvyUt/Vuet62kiDcuJ4643DiS8pNIzk8utVhsFtIL00uNSXI5znpn3AxuuBnd1Mezn59+dDW44qRzwqQ34aRzwknvhElnwknvdN56J526rap1/xNVn6IomG1mzFYzRdai8x5LnhcUF5BnySO/OF99tOSTX5xPviXfvr7keWZRJtnm7FJjY5SVXqPH19kXf2d//F387UlGqFuofXEzulXAT6L6sGZlEf/oY2C14jGgP54DBzo6pEojXW3PUR272l6ILT+fqOHDMR87jkvHDtT+4gs0OrmgXYyiKGQUZdgTkbSCNDKKMsgoPL0UZZBZmGlfl2vJrdB4dBodeq3+zKI589ygNZR6PHcfnUaHRqNBq9HauyhrNVq0aEut16A+12g09udnry/ZVnLc5Wi4zD6X3XzpHUq25+3Iw/XG8++KyxKjoiiU/FdyY66g2Nef/dp+zFnbS9bb9z3r9aWOO/u9S57bsGG1WbEqVvtjsVJcal3Ja5tiK7Wt2FaMVbFisVrOJBk282U//7XQarR4Gj3xNJ1ZvExeeBg98HHywc/ZD38Xf3uy4WXyki7yl6AoCnFTHib3t98whIURvvI7dO7Vv11ajRvn49VXX+Wnn34iMjISo9FIZmbmefucPHmSBx98kE2bNuHm5sb48eN5/fXX0evLXsBTU5IPgKJjx4gaNhyloAC/KVOqbPfb6shis5BnziPHkkOuOZdcS+6ZR0sueZY8csw55FnyyLPkUWQtoqC4QL0DLS6iwFpAUXERhcWFFFoL7Xem4vI6JXVia+BWR4dR5Zl0Jow6Iyadyf7cqDXiYnDBRe9if3Q1uOJiUB+d9c7qa70LbgY3PE2eeJg88DJ54WpwlWSiHKV9NZ/kWbPQGAzUWbIY52bNLn9QNVDjxvkwm80MGzaMjh078uWXX5633Wq1MnDgQIKCgti6dSsJCQmMGzcOg8HAa6+95oCIHc9Uvz7BL73IqaefIfWjj3Bp2wbXjh0dHVaNYNAa8HLywsvJq9zOaVNsFFnVhMRis1BsK7YvJa/t65XiUtvP3qagYFNs2BSb/Q675K773PUlz0u2nbu+ZP/LuVz9/uXucS57/Fnbi/KLGNt07BWd/2wlJT0aNPbSEg0a1P/PvC7Z77zjzjqm5LizX599XKnzn/PeWo0WnVaHTqNDp9Wh1+jPe63VaO2lWSXb7K81Ogw6A0at8bxEQ6/VXxeNFqurgshIkt95B4CAZ5+pMYnHlag2JR8l5s+fz6OPPnpeyccvv/zCrbfeyqlTpwgMDARg7ty5PP3006SkpGA0Gst0/ppU8lHi1PPPk7XiO3S+voR/vxJDwPXRoEnUTDLCqajOijMyiBoylOKEBDwG9CfknXdqVKJY1mtojSlD27ZtG82bN7cnHgB9+/YlOzub/fv3X/S4oqIisrOzSy01TdDzz2Nq2BBrWhrxjz2OYq7YumEhhBDnU4qLOTXtSYoTEjDUqU3QzJk1KvG4EjUm+UhMTCyVeAD214mJiRc97vXXX8fT09O+hNXAUeW0Tk6Evj8brbs7Bbt2kTBjxhUVUwshhLh2yW+9Rd5ff6FxdqbW7Nno3K7f3j4OTT6eeeYZtQ70EsuhQ4cqNIZnn32WrKws+xIbG1uh7+copvBwQt99B7Rasr5bScbXXzs6JCGEuG5krlhB+gL1ezfk9ddxatLEwRE5lkMbnD7xxBNMmDDhkvtERESU6VxBQUH880/pUS2TkpLs2y7GZDJhMpnK9B7VnVvXrgQ+/RRJr79B0qw3MUbUw61rF0eHJYQQNVr+zp0kzJgJgN/DU/Do19fBETmeQ5MPf39//P39y+VcHTt25NVXXyU5OZmA0w0q169fj4eHB02bNi2X96gJvMeNo/DoUbJWfEf8449Td+lSTBHhjg5LCCFqJHNcPHEPPwIWC+79++H30EOODqlKqDZtPk6ePElkZCQnT57EarUSGRlJZGQkubnqYE+33HILTZs2ZezYsfz333+sW7eO559/nsmTJ183JRtlodFoCJ4+Hee2bbHl5BA7aRLFaReexEkIIcTVs2ZlEffgg1gzMnBq2pSQ1167bhuYnqvaJB/Tp0+ndevWvPjii+Tm5tK6dWtat27Nzp07AdDpdPz444/odDo6duzIXXfdxbhx45g5c6aDI696NEYjtT54H0OtWlhOniT2gUlYc/McHZYQQtQYtsJCYidPpujoUfQBAdT6+CO0zs6ODqvKqHbjfFS0mjjOx8UURUURM3oM1owMXDt1ImzuJ2jKOB6KEI4i43yIqk4pLibu0UfJ3fAbWnd36ixciFOjho4Oq1Jcd+N8iCtnCg8n7LNP0bi4kLd1K6f+9xyK7fKjWQohhLgwRVFInPkyuRt+Q2M0EvbxR9dN4nElJPm4zjk3b06t998HvZ7sH38kedabMgaIEEJcpdQPPyJz2TLQagl5+y1cbrzR0SFVSZJ8CNy6diHktVcBSF+wgNQ5Hzo4IiGEqH7SvvyS1I8+AiBo+gt43HKLgyOquiT5EAB4DhpE4P+eBSD1449JOf0PSAghxOWlzZ9P8ltvA+A/9RG8R450cERVmyQfws5n3DgCnnoKgNQ5H5I691MHRySEEFVf+jcLSX5jFgB+kyfj9+CDDo6o6pPkQ5Tie8/d+D/xOAAps2eT9sUXDo5ICCGqrvRvvyXpVbXa2veBB/CbMtnBEVUPknyI8/jdfz/+j04FIPntd0id+6k0QhVCiHOkf7OQpJkvA+B73734PzpVBhErI0k+xAX5TZqE38NTALUEJPnttyUBEUII1O60KR99ZC/x8Ln7bvyfeEISjyvg0LldRNXmP3kyWhdXkmfNIv3Lediycwh66UU0Op2jQxNCCIdQbDb1O/H0DLV+U6bgN/khSTyukJR8iEvyvXsCwa++AlotmcuXEz9tGorZ7OiwhBCi0inFxSQ8/4I98Qj837P4T5ksicdVkORDXJbX0KGEvvsuGAzk/LKW2EmTsObkODosIYSoNLb8fOIemUrWypWg1RL8+uv4jBvn6LCqLUk+RJl49OtL2Mcfnx6KfRsxo0djiY93dFhCCFHhLMnJxNw1ltyNG9EYjYS+PxuvOwY7OqxqTZIPUWZuXbtQ55uv0fv7U3T0GFEjR1Kwd5+jwxJCiApTePgI0SNGUnjgADpvb2ovmI9Hnz6ODqvak+RDXBHnZs2ou2wppkaNsKakEjN2LDkbNjg6LCGEKHe5W/4iZvRoihMSMIaHU3fpElxat3Z0WDWCJB/iihmCg6mzaBGuXbuiFBYSN+VhUuZ8KDPiCiFqBEVRSPviC2InTsSWl4fLjTdSd/G3GGvXdnRoNYYkH+Kq6NxcCfvkY7zvuguA1I8+Iu6hydIQVQhRrdny84l//HGS334HbDY8hw4h7Msv0Hl5OTq0GkWSD3HVNHo9Qc8/R/Drr6MxGsn9/Xeihw2n6NgxR4cmhBBXzBwTQ/SIkeT8shYMBoJenE7wK6+gNRodHVqNI8mHuGZedwymzrffog8OxhwdTdTwEWStWePosIQQosyy1/1K1J3DKDp6FJ2/H3UWzMd71CgZw6OCSPIhyoXzDc0I/24FLu3bo+Tnc+qppzn1zLPY8vIcHZoQQlyUraiIhBkziJ86FVtODs4tWxK+4jtc2rRxdGg1miQfotzofXyoPe9L/KZMAa2WrFWriLpzGIWHDjk6NCGEOE/RiRNEDx9B5uIlAPjefx91Fn6DITDAwZHVfJJ8iHKl0enwnzKZ2vO/Qh8QgDkqiujhI0j7ar70hhFCVAmKopCxZAlRQ++k6PBhdD4+hH3+OQFPPIHGYHB0eNcFST5EhXC96SbCV6/CrXt3FLOZ5FmzODluPOa4OEeHJoS4jlmSkoi9fyKJL81AKSjApUMHwld9j1vXLo4O7boiyYeoMHpvb2rN/YSgl15C4+JC/s6dRA26nYxly1AUxdHhCSGuI4qikLVmDSduG0Teli1oTCYCn32G2vO+xBAg1SyVTZIPUaE0Gg3eI0cQsXoVzu3aYsvPJ3H6i8Tedz/m2FhHhyeEuA5YEhKImzyFU089jS07G6fmzQn/fiU+48ej0cpl0BHkpy4qhTEsjDoLFhDw9NNojEby/vqLE7cNIu2LL1AsFkeHJ4SogRSrlfRvFnJi4K3kbtwIBgP+Ux+h7uJvMUVEODq865okH6LSaHQ6fO+eQMSa1bh06IBSWEjy2+8QNWw4BXv2ODo8IUQNUnjoENGjRpP06qvY8vNxbt2aiJXf4ffgg2j0ekeHd92T5ENUOmPdutT+ah7Br7+OztOTokOHiB4+glPPPUdxaqqjwxNCVGPFGRkkzpxJ1JChFO7Zg9bNjaCXXqTOooWYGjRwdHjiNEk+hENoNBq87hhMxC8/43n77QBkfbeS4/36k75ggVTFCCGuiGK1krF4MSf69Sfj28Vgs+Hevx8RP/2E98iR0rajipHfhnAovY8PIbPeoM7ib3Fq1gxbbi5Jr7/BidsHk7Nhg/SKEUJcVu6Wv4gaMpTEGTOxZmVhatiQ2gsWUOu992TAsCpKKr5EleDSujV1ly8ja+VKkt99D/OJE8RNeRjnVq0IeOJxXG680dEhCiGqmIL9+0l55x3ytm4DQOvhgf8jj+A9coS066ji5LcjqgyNVovXnXfi3rcvaV9+SfqCrymIjCRm7Dhcu3cj4PHHcWrUyNFhCiEczBwdTcqHH5H9448AaAwGvEePxnfSA+i9vR0cnSgLST5ElaNzdyfg0UfxHj2a1E8+IXPZcvL++JOoPzfjcdut+D/0EMa6dR0dphCikhVFRZE2dy5ZP/wIp6dr8Lj1VvwfnYqxVi0HRyeuhCQfosoyBAQQ/OKL+I4fT8oHH5D98y9kr/mB7B9/wqNfP3wfmCglIUJcB4pOnCD1k7lk//STPelw694dv0cexrlZMwdHJ66GJB+iyjPWrUvou+/ic8+9pM6ZQ+4ff5D9889k//wzbj164PfARJxbtXJ0mEKIclZ45Ahpn32uJh2nG5+79eiB30MP4dz8BgdHJ66FJB+i2nC+oRlhn86l8OBBUj/7jJy168jdtIncTZtw6dAB3/vuw7VzJzQajaNDFUJcJUVRyNvyF+nz55P311/29W69euH30INS0lFDSPIhqh2nJk2o9d57FD0SRdrnX5C1Zg35f/9N/t9/Y6xXD+8xo/G6/Xa0rq6ODlUIUUa2oiKyf/iB9AULKDp6TF2p1eLepw9+D0zEqWlTxwYoylW1Gefj1VdfpVOnTri4uODl5XXBfTQazXnLkiVLKjdQUWlM4eGEvPYq9X9dh/fYsWhdXDAfP07SzJc5enMPkl5/A/PJk44OUwhxCZaEBFI+mMOxHj1JeP4Fio4eQ+vigs/4cdT7dR213p8tiUcNVG1KPsxmM8OGDaNjx458+eWXF93vq6++ol+/fvbXF0tURM1hCAkh6Ln/4T/1EbK+X0XGwoWYY2JIX7CA9K+/xq1bN7yGD8OtWzc0BoOjwxXiuqcUF5P7559kLl1G7ubN9kak+pBgfMaOw+vOoejc3R0cpahI1Sb5mDFjBgDz58+/5H5eXl4EBQVVQkSiqtG5ueEz9i68x4wmb8sW0hcuJO/PzeT+8Qe5f/yBzs8Pz9sH4TV0qMxoKYQDWOLjyfzuOzJXfEdxcrJ9vUv79niPHIF7nz4yONh1osb9lidPnsx9991HREQEkyZN4u67775kA8SioiKKiorsr7OzsysjTFGBNFotbt264datG0VRUWSuWEHWqtVYU1NJ/3Ie6V/Ow7lVK7zuHIp7375yhyVEBbLm5JDz669k/fAj+du323ut6Ly98RxyB1533okpPNzBUYrKVqOSj5kzZ9KzZ09cXFz49ddfeeihh8jNzeWRRx656DGvv/66vVRF1Dym8HACn3ySgEcfVYt5V3xH7p9/UhAZSUFkJIkzX8atezc8BgzA7eab0To7OzpkIao9m9lM3p9/krXmB3J//x3FbLZvc+nYAe/hw3Hr1Qut0ejAKIUjaRQHztz1zDPPMGvWrEvuc/DgQRo3bmx/PX/+fB599FEyMzMve/7p06fz1VdfERsbe9F9LlTyERYWRlZWFh4eHpf/EKLasSQnk7V6NVnfr8J84oR9vcbFBfcePfAYOADXLl3ki7GKWrx4MaNGjXJ0GOIcNrOZvK1byVm/npz1G7CdVYpsrF8Pz9sG4TFwIMZaoQ6MUlS07OxsPD09L3sNdWjJxxNPPMGECRMuuU/ENdTNt2/fnpdffpmioiJMJtMF9zGZTBfdJmomQ0AAfvffj+9991F0+DDZP6kDllni48n+6Seyf/oJrasrrt264t6zF27du6GTRFSI89jy8sjdvJmcX9eT+8cf2PLy7Nv0AQF4DByI56DbMDVuLOPviFIcmnz4+/vj7+9fYeePjIzE29tbkgtxQRqNBqfGjXFq3Bj/xx+jcM8edeTUX9ZSnJxMzi9ryfllLej1uLRrh3vPnrj36okhVO7cxPXLHBdP3uY/yf3jT/K2bi1VpaIPCMC9d2/cb+mDy403otHpHBipqMqqTZuPkydPkp6ezsmTJ7FarURGRgJQv3593Nzc+OGHH0hKSqJDhw44OTmxfv16XnvtNaZNm+bYwEW1oNFocG7ZEueWLQl4+mkK9+whZ+Mmcjb+hvnYcfsgZkmvvYYxIgLXLp1x69wZlxtvROvi4ujwhagwNrOZ/B071J5jmzeXqqoEMNSpjUefPrj36YNT8+ZotNVm+CjhQA5t83ElJkyYwIIFC85bv2nTJm6++WbWrl3Ls88+y7Fjx1AUhfr16/Pggw9y//33o72Cfwxlra8S1w9zTAw5GzeR+9tv5P/7r31MAlCn8nZu2xa3Lp1xad8BpyaNpatgBZM2HxVLKS6m8OBB8rdvJ+/v7eTv2oVSUHBmB50O59atcOvaDbebb8bUsIFUqQi7sl5Dq03yUVkk+RCXYs3OJm/b3+T99Rd5W7ZgOXWq1HatqyvObdvg0u5GXG5sh/MNN8jAZuVMko/ypVgsFB4+Qv7OHeT/vZ38nTux5eaW2kfv749r1664deuGa6eO0gZKXFS1aHAqRHWj8/DAo+8tePS9BUVRMEdHk/fXVvL++kv90s7JIe/PzeT9uRkAjbOzWp3TogXOLVvg3KIF+gps5yTE5RSnpdm7mhfsjqRg3z6UwsJS+2jd3XG58UZcO7THpX17TA0bSumGKFeSfAhxlTQaDabwcEzh4fjcNQbFaqXo8GHyd+4kf8cO8nfsxJqZaW8vUkIfEoxz8xb2hMSpWTMZX0RUCFteHoVHjlC4/wAF//1HQWQklgsMPaB1d8e5dStc23fApX17tfpQGouKCiTJhxDlRKPT4dS0KU5Nm+IzbhyKzUbRsWPq3eXePRT+t4eiY8coPpVAzqkEctatUw/U6TCG18WpYSNMjRvj1LgRpkaN0AcEyN2mKLPitDQKDxyk8NBBig4epPDgIczR0fYRRc9mrF8P51atcGnVCudWrTBGREhDUVGpJPkQooJotFqcGjbEqWFDvEcMB8Cam0fhvn1qMrJnDwX/7aE4ORnzseOYjx2Hn3+2H6/z8sLUqJGajDRogDEiAmN4OHpvb0d9JFEFFGdkYD5+nKLjJzCfUB+LDh+mOCXlgvvr/P1watJELW1r1Qrnli2kzYZwOEk+hKhEOjdXXDu0x7VDe/s6S1ISRYcPU3josPp4+BDmqGi1ymb7dnU+jLPP4emJMTz8rKUupvBwDLVqoXVyquyPJCqAraAAS1wc5tg4zCdjMJ+IoujEcczHT2DNyLjwQRoNxjp1MDVpjFOTpjg1UcewkTZGoiqS5EMIBzMEBmIIDMStWzf7OltREUXHjlF06HQycuw4RdFRFJ9KwJqVZW8weC6dvx/G0FoYQkMx1KqFITQEY61a6vOgIDQyZHyVYCsqojgpCUtiIpZTp7CcjMUcF4slNg5zXCzWlNRLHm8ICcFYrx6miAiM9SIw1a+PqWEjdG6ulfQJhLg2knwIUQVpTSacmzXDuVmzUuttBQWYY2IwnzhBUVQU5qhozFFRmKOisOXnY01JpSAl9YKJCYDOxwd9YCD6AH8MAYHoAwLQBwagDwjAEBiIzscXnbeXzGtzlWyFhVjT0ylOS8eankZxWjrFyWqSUZyYhCUpieLExIuXXpxF6+6OMSwMQ1iYWrpVrx7GiAhM4eEysJ2o9iT5EKIa0To724eEP5uiKFgzM7HExWOJj8cSH4clPh5zXByW+FNY4uNRTl8YrenpFB08eOn3cXVF5+ODztsbnbcXei/vUq91Xl7o3NzQurmhdXVD6+aKzs0NjbNztW8kqygKSlERtpwcrDm52HJzsGbnqI85OdhycrFmZlKcnoY1Tf15FqenY01Lw5afX+b30Tg5YQgMRB8cfCbJCKuFoVYYxtph6Dw9K/BTCuFYknwIUQNoNBr03t7ovb1xbn7DedtLkpPipCSKk5PVO/DkZIqTktXXyUkUJ6eod+RWK7a8PGx5eRfslnlJWq2akLi5onM9nZw4O6ExmtCYTGhMRrQmk/rayXTmucmExmhQu3dqtKDVqL0vtDo0Wg1otfy/vfuPbare3wD+9LTraYHuF7it0yJ3Q8QgxjjCMsZC1CUkGNS/IMEsMwGRMP+BREAn1ojgsi9RE5wY5w/8g7CoAWNkGep0MSDGBLeEsIHBTYUL24XckZaNdWvP+/5R1u82NuCUnU9b9ryS5myHc8bT99r12enpCk2DTdMQ/s8lBJqOQCJhwDAgkQgQiYxYGoARgYQjgBGBEQpBBgZgDFxfhgYgA6H/Xw5ciy2N4FVEgkFgaCj+70VaWrSozcyGIyt6pCktLxeO3LzoMi8Pabm50DIyUr6oEcWL5YNoChhZTjDmqMlIYhgwgsHob/K9VxC50hv9zb63F5H/9iLSe/1y5QqM/j5ErvbBuHo1+hcxRQDDgBEIwAgEELbougyUleHfe/da9NVHsNmi5ckzA/YZHmjpnujS44E9IwOOmdmwZ8+8vsyGIzsb9pkzoc2YwVJBdAssH0QUY9M02DMyoof8/3X7+4kIpL8/Wkb6omXE6OtDJBiEhELRpzFCIUhoEDI44uNQaNTnMAyIGEDEiH5sRJcQ4/oRDQNaZgbcRUWw2e2wOezRoyN2O2AfsdQ0wGGHTbPDpuvQXDpsuuv60RYXbG5XdOnSoblcsOkuaG4XtBke2D0zoKWnQ5s2jX/7gsgiLB9EdMdsNhts06dDmz4dQI6l/9e0Awcw5//43i5EqYy1noiIiJRi+SAiIiKlWD6IiIhIKZYPIiIiUorlg4iIiJRi+SAiIiKlWD6IiIhIKZYPIiIiUorlg4iIiJRi+SAiIiKlWD6IiIhIKb63yxgiAgAIBAIJTkJE4+nv7+f9kyhJDd83hx9LJ2KTW20xxZw/fx4+ny/RMYiIiFLWuXPncN9990347ywfYxiGgQsXLsDj8cBms5nePxAIwOfz4dy5c0hPT7cg4dTF2VqDc7UG52oNztU6kzFbEUEwGER+fj40beIzO/i0yxiapt20rd2u9PR03jEswtlag3O1BudqDc7VOnc624yMjFtuwxNOiYiISCmWDyIiIlKK5WOS6boOv98PXdcTHeWuw9lag3O1BudqDc7VOipnyxNOiYiISCke+SAiIiKlWD6IiIhIKZYPIiIiUorlg4iIiJRi+YhDXV0d5syZA5fLheLiYvz222833f7LL7/E/Pnz4XK5sHDhQjQ2NipKmnrMzLa+vh5lZWXIyspCVlYWysvLb/m9mKrM3maHNTQ0wGaz4dlnn7U2YIoyO9crV66gqqoKXq8Xuq5j3rx5/HkwDrNzfe+99/Dggw/C7XbD5/Nh06ZNGBgYUJQ2Nfz8889YuXIl8vPzYbPZ8PXXX99yn5aWFjz22GPQdR1z587Fvn37Ji+QkCkNDQ3idDrl008/lVOnTskLL7wgmZmZ0tPTM+72x44dE7vdLrW1tdLe3i6vvfaapKWlycmTJxUnT35mZ7tmzRqpq6uT1tZW6ejokOeff14yMjLk/PnzipMnN7NzHdbV1SX33nuvlJWVyTPPPKMmbAoxO9dQKCSLFi2SFStWyNGjR6Wrq0taWlqkra1NcfLkZnau+/fvF13XZf/+/dLV1SVHjhwRr9crmzZtUpw8uTU2Nkp1dbUcPHhQAMihQ4duun1nZ6dMmzZNNm/eLO3t7bJnzx6x2+3S1NQ0KXlYPkxavHixVFVVxT6PRCKSn58vb7/99rjbr1q1Sp566qlR64qLi+XFF1+0NGcqMjvbscLhsHg8Hvn888+tipiS4plrOByWJUuWyMcffyyVlZUsH+MwO9e9e/dKQUGBDA4OqoqYkszOtaqqSp544olR6zZv3iylpaWW5kxlt1M+tmzZIgsWLBi1bvXq1bJ8+fJJycCnXUwYHBzEiRMnUF5eHlunaRrKy8tx/Pjxcfc5fvz4qO0BYPny5RNuP1XFM9ux+vv7MTQ0hOzsbKtippx45/rmm28iJycHa9euVREz5cQz12+++QYlJSWoqqpCbm4uHn74YezatQuRSERV7KQXz1yXLFmCEydOxJ6a6ezsRGNjI1asWKEk893K6scuvrGcCZcvX0YkEkFubu6o9bm5uTh9+vS4+3R3d4+7fXd3t2U5U1E8sx1r69atyM/Pv+EOM5XFM9ejR4/ik08+QVtbm4KEqSmeuXZ2duLHH3/Ec889h8bGRpw9exYbN27E0NAQ/H6/ithJL565rlmzBpcvX8bSpUshIgiHw9iwYQNeffVVFZHvWhM9dgUCAVy7dg1ut/uOvj6PfNBdoaamBg0NDTh06BBcLlei46SsYDCIiooK1NfXY9asWYmOc1cxDAM5OTn46KOPUFRUhNWrV6O6uhoffvhhoqOltJaWFuzatQsffPABfv/9dxw8eBCHDx/Gjh07Eh2NboJHPkyYNWsW7HY7enp6Rq3v6elBXl7euPvk5eWZ2n6qime2w3bv3o2amhr88MMPeOSRR6yMmXLMzvXPP//EX3/9hZUrV8bWGYYBAHA4HDhz5gwKCwutDZ0C4rm9er1epKWlwW63x9Y99NBD6O7uxuDgIJxOp6WZU0E8c92+fTsqKiqwbt06AMDChQvR19eH9evXo7q6GprG37HjMdFjV3p6+h0f9QB45MMUp9OJoqIiNDc3x9YZhoHm5maUlJSMu09JScmo7QHg+++/n3D7qSqe2QJAbW0tduzYgaamJixatEhF1JRidq7z58/HyZMn0dbWFrs8/fTTePzxx9HW1gafz6cyftKK5/ZaWlqKs2fPxsocAPzxxx/wer0sHtfFM9f+/v4bCsZwwRO+dVncLH/smpTTVqeQhoYG0XVd9u3bJ+3t7bJ+/XrJzMyU7u5uERGpqKiQbdu2xbY/duyYOBwO2b17t3R0dIjf7+dLbSdgdrY1NTXidDrlq6++kosXL8YuwWAwUVchKZmd61h8tcv4zM71n3/+EY/HIy+99JKcOXNGvv32W8nJyZG33norUVchKZmdq9/vF4/HIwcOHJDOzk757rvvpLCwUFatWpWoq5CUgsGgtLa2SmtrqwCQd955R1pbW+Xvv/8WEZFt27ZJRUVFbPvhl9q+/PLL0tHRIXV1dXypbaLt2bNHZs+eLU6nUxYvXiy//vpr7N+WLVsmlZWVo7b/4osvZN68eeJ0OmXBggVy+PBhxYlTh5nZ3n///QLghovf71cfPMmZvc2OxPIxMbNz/eWXX6S4uFh0XZeCggLZuXOnhMNhxamTn5m5Dg0NyRtvvCGFhYXicrnE5/PJxo0bpbe3V33wJPbTTz+N+/NyeJaVlZWybNmyG/Z59NFHxel0SkFBgXz22WeTlscmwuNSREREpA7P+SAiIiKlWD6IiIhIKZYPIiIiUorlg4iIiJRi+SAiIiKlWD6IiIhIKZYPIiIiUorlg4iIiJRi+SAiIiKlWD6IiIhIKZYPIiIiUorlg4hSgmEYqK2txdy5c6HrOmbPno2dO3cmOhYRxcGR6ABERLfjlVdeQX19Pd59910sXboUFy9exOnTpxMdi4jiwHe1JaKkFwwGcc899+D999/HunXrEh2HiO4Qn3YhoqTX0dGBUCiEJ598MtFRiGgSsHwQUdJzu92JjkBEk4jlg4iS3gMPPAC3243m5uZERyGiScATToko6blcLmzduhVbtmyB0+lEaWkpLl26hFOnTmHt2rWJjkdEJrF8EFFK2L59OxwOB15//XVcuHABXq8XGzZsSHQsIooDX+1CRERESvGcDyIiIlKK5YOIiIiUYvkgIiIipVg+iIiISCmWDyIiIlKK5YOIiIiUYvkgIiIipVg+iIiISCmWDyIiIlKK5YOIiIiUYvkgIiIipf4HHTlY0YoMrToAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cc = np.linspace(0.01, 0.99, 200)\n", "fig, ax = plt.subplots(figsize=(6, 4))\n", "for T in [200, 400, 580, 700]:\n", " f = cc * (1 - cc) * L0 + kB * T * (cc * np.log(cc) + (1 - cc) * np.log(1 - cc))\n", " ax.plot(cc, 1e3 * f, label=f'T = {T} K')\n", "ax.axvline(0.5, color='gray', lw=0.5)\n", "ax.set_xlabel('c'); ax.set_ylabel('f (meV)')\n", "ax.legend(); ax.set_title('Free energy curves');" ] }, { "cell_type": "markdown", "id": "refine-md", "metadata": {}, "source": [ "## Intra-phase: miscibility-gap tracer\n", "\n", "Feed the coarse sampling into `MiscibilityGapRefiner`. The\n", "Delaunay-based refiners do not see this boundary because an\n", "intra-phase miscibility gap appears as a single phase in landau's\n", "data model (both branches carry the same phase name). The sampling\n", "extends past $T_c$; the trace stops on its own when the gap closes." ] }, { "cell_type": "code", "execution_count": 4, "id": "refine-run", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:05.910393Z", "iopub.status.busy": "2026-05-13T21:46:05.910160Z", "iopub.status.idle": "2026-05-13T21:46:07.115181Z", "shell.execute_reply": "2026-05-13T21:46:07.114268Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MiscibilityGapRefiner: 62 refined rows (31 unique (T, mu))\n", "Input T range: [150, 830] K (T_c = 580 K)\n", "Traced T range: [150.0, 584.7] K -- the trace stops on its own once the gap closes\n" ] } ], "source": [ "phases = {solution.name: solution}\n", "Ts = np.linspace(150, T_c + 250, 30)\n", "mus = np.linspace(-0.05, 0.05, 21)\n", "\n", "coarse = calc_phase_diagram([solution], Ts=Ts, mu=mus, refine=False, keep_unstable=True)\n", "df = refine_phase_diagram(coarse, phases, refiners=[MiscibilityGapRefiner()])\n", "cc_pts = df[df['refined'] == 'miscibility-gap'].copy()\n", "print(f'MiscibilityGapRefiner: {len(cc_pts)} refined rows ({cc_pts.groupby([\"T\", \"mu\"]).ngroups} unique (T, mu))')\n", "print(f'Input T range: [{Ts.min():.0f}, {Ts.max():.0f}] K (T_c = {T_c:.0f} K)')\n", "print(f'Traced T range: [{cc_pts[\"T\"].min():.1f}, {cc_pts[\"T\"].max():.1f}] K -- the trace stops on its own once the gap closes')" ] }, { "cell_type": "markdown", "id": "plots-md", "metadata": {}, "source": [ "## Coexistence line and binodal\n", "\n", "* Left: coexistence chemical potential $\\mu^*(T)$. By the $c \\leftrightarrow 1-c$\n", " symmetry of the regular solution $\\mu^*(T) \\equiv 0$ — the refiner should\n", " reproduce this exactly within the bisection tolerance.\n", "* Right: binodal in $(c, T)$ — refined points overlaid on the analytical\n", " binodal $L_0(1-2c) = T k_B \\ln((1-c)/c)$." ] }, { "cell_type": "code", "execution_count": 5, "id": "plots", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:07.117529Z", "iopub.status.busy": "2026-05-13T21:46:07.117316Z", "iopub.status.idle": "2026-05-13T21:46:07.583954Z", "shell.execute_reply": "2026-05-13T21:46:07.582782Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5))\n", "\n", "# --- left: coexistence chemical potential mu*(T) ---\n", "ax = axes[0]\n", "cc_mu = cc_pts.groupby('T')['mu'].mean().reset_index().sort_values('T')\n", "ax.plot(cc_mu['T'], 1e3 * cc_mu['mu'], 'r.-', ms=4, label='CC refiner')\n", "ax.axhline(0.0, color='k', lw=0.8, label=r'analytical $\\mu^*=0$')\n", "ax.axvline(T_c, ls=':', color='gray', lw=0.8, label=f'T_c = {T_c:.0f} K')\n", "ax.set_xlabel('T (K)')\n", "ax.set_ylabel(r'$\\mu^*$ (meV)')\n", "ax.set_title('Coexistence chemical potential')\n", "ax.legend(fontsize=9)\n", "\n", "# --- right: binodal ---\n", "ax = axes[1]\n", "T_grid = np.linspace(50, T_c - 1, 400)\n", "c_bin = []\n", "for T in T_grid:\n", " def dfdc(c, T=T):\n", " return L0 * (1 - 2 * c) + kB * T * (np.log(c) - np.log(1 - c))\n", " try:\n", " c_bin.append(brentq(dfdc, 1e-9, 0.5 - 1e-6))\n", " except ValueError:\n", " c_bin.append(np.nan)\n", "c_bin = np.array(c_bin)\n", "ax.plot(c_bin, T_grid, 'k-', lw=1, label='analytical binodal')\n", "ax.plot(1 - c_bin, T_grid, 'k-', lw=1)\n", "ax.plot(cc_pts['c'], cc_pts['T'], 'r.', ms=4, label='CC refiner')\n", "ax.axhline(T_c, ls=':', color='gray', lw=0.8)\n", "ax.set_xlabel('c'); ax.set_ylabel('T (K)')\n", "ax.set_title('Binodal')\n", "ax.legend(fontsize=9)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "acc-md", "metadata": {}, "source": [ "## Accuracy summary" ] }, { "cell_type": "code", "execution_count": 6, "id": "acc", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:07.586162Z", "iopub.status.busy": "2026-05-13T21:46:07.585969Z", "iopub.status.idle": "2026-05-13T21:46:07.592562Z", "shell.execute_reply": "2026-05-13T21:46:07.591486Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CC refiner traced 31 coexistence points\n", " T range covered = 150.0 - 584.7 K\n", " max |mu*| = 5.10e-05 eV (analytical: 0)\n", " median |mu*| = 4.98e-06 eV\n" ] } ], "source": [ "print(f'CC refiner traced {cc_pts.groupby([\"T\",\"mu\"]).ngroups} coexistence points')\n", "print(f' T range covered = {cc_pts[\"T\"].min():.1f} - {cc_pts[\"T\"].max():.1f} K')\n", "print(f' max |mu*| = {np.abs(cc_pts[\"mu\"]).max():.2e} eV (analytical: 0)')\n", "print(f' median |mu*| = {np.median(np.abs(cc_pts[\"mu\"])):.2e} eV')" ] }, { "cell_type": "markdown", "id": "walkthrough-md", "metadata": {}, "source": [ "## Step-by-step walkthrough\n", "\n", "Driver code path for the refiner so you can poke at each stage\n", "individually. Useful for debugging the propose/solve/run pipeline." ] }, { "cell_type": "code", "execution_count": 7, "id": "walkthrough-setup", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:07.594514Z", "iopub.status.busy": "2026-05-13T21:46:07.594331Z", "iopub.status.idle": "2026-05-13T21:46:07.602726Z", "shell.execute_reply": "2026-05-13T21:46:07.601449Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coarse stable rows: 630\n", " T phase phi mu c stable f \\\n", "0 150.0 solution -1.179545e-07 -0.050 0.000009 True -5.742532e-07 \n", "1 150.0 solution -1.736684e-07 -0.045 0.000013 True -7.783286e-07 \n", "2 150.0 solution -2.557015e-07 -0.040 0.000020 True -1.047093e-06 \n", "3 150.0 solution -3.764916e-07 -0.035 0.000029 True -1.396141e-06 \n", "4 150.0 solution -5.543591e-07 -0.030 0.000043 True -1.841373e-06 \n", "\n", " f_excess \n", "0 0.000000e+00 \n", "1 -2.040754e-07 \n", "2 -4.728398e-07 \n", "3 -8.218877e-07 \n", "4 -1.267120e-06 \n" ] } ], "source": [ "# 1. Coarse stable points -- input to the refiner.\n", "sdf = coarse[coarse['stable']].copy()\n", "print(f'Coarse stable rows: {len(sdf)}')\n", "print(sdf.head())" ] }, { "cell_type": "code", "execution_count": 8, "id": "walkthrough-propose", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:07.604623Z", "iopub.status.busy": "2026-05-13T21:46:07.604401Z", "iopub.status.idle": "2026-05-13T21:46:08.071480Z", "shell.execute_reply": "2026-05-13T21:46:08.070079Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total candidates: 52\n", "\n", "First 5:\n", " [ 0] phase=solution T_seed= 157.8 T_bracket=( 150.0, 173.5) mu_bracket=(-0.0050, +0.0000)\n", " [ 1] phase=solution T_seed= 165.6 T_bracket=( 150.0, 173.5) mu_bracket=(-0.0050, +0.0000)\n", " [ 2] phase=solution T_seed= 181.3 T_bracket=( 173.5, 196.9) mu_bracket=(-0.0050, +0.0000)\n", " [ 3] phase=solution T_seed= 189.1 T_bracket=( 173.5, 196.9) mu_bracket=(-0.0050, +0.0000)\n", " [ 4] phase=solution T_seed= 189.1 T_bracket=( 173.5, 196.9) mu_bracket=(+0.0000, +0.0050)\n", "...\n" ] } ], "source": [ "# 2. propose() -- candidates from single-phase Delaunay simplices with\n", "# wide c-spread, sorted widest first.\n", "refiner = MiscibilityGapRefiner()\n", "cands = list(refiner.propose(sdf))\n", "print(f'Total candidates: {len(cands)}\\n')\n", "print('First 5:')\n", "for i, c in enumerate(cands[:5]):\n", " print(f' [{i:3d}] phase={c.phase:8s} T_seed={c.T_seed:6.1f} '\n", " f'T_bracket=({c.T_bracket[0]:6.1f}, {c.T_bracket[1]:6.1f}) '\n", " f'mu_bracket=({c.mu_bracket[0]:+.4f}, {c.mu_bracket[1]:+.4f})')\n", "print('...')" ] }, { "cell_type": "code", "execution_count": 9, "id": "walkthrough-solve", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:08.073406Z", "iopub.status.busy": "2026-05-13T21:46:08.073231Z", "iopub.status.idle": "2026-05-13T21:46:08.370889Z", "shell.execute_reply": "2026-05-13T21:46:08.369578Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "31 refined transitions\n", " T range: [150.0, 584.7] K\n", " mu range: [-5.102e-05, +5.102e-05] eV\n", " type: RefinedMiscibilityGap\n" ] } ], "source": [ "# 3. solve() on one candidate -- scan-seed + predictor-corrector trace.\n", "pts = list(refiner.solve(cands[0], phases))\n", "print(f'{len(pts)} refined transitions')\n", "print(f' T range: [{min(p.T for p in pts):.1f}, {max(p.T for p in pts):.1f}] K')\n", "print(f' mu range: [{min(p.mu for p in pts):+.3e}, {max(p.mu for p in pts):+.3e}] eV')\n", "print(f' type: {type(pts[0]).__name__}')" ] }, { "cell_type": "code", "execution_count": 10, "id": "walkthrough-run", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:08.372750Z", "iopub.status.busy": "2026-05-13T21:46:08.372573Z", "iopub.status.idle": "2026-05-13T21:46:09.182603Z", "shell.execute_reply": "2026-05-13T21:46:09.181187Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Run produced 62 rows (31 unique (T, mu))\n", "\n", "First few rows:\n", " T mu phi c phase stable border \\\n", "0 157.818689 -5.102041e-05 -0.000009 0.000641 solution True True \n", "1 157.818689 -5.102041e-05 -0.000009 0.999354 solution True True \n", "2 158.818689 -5.102041e-05 -0.000009 0.000672 solution True True \n", "3 158.818689 -5.102041e-05 -0.000009 0.999323 solution True True \n", "4 208.683848 -1.127570e-17 -0.000071 0.003999 solution True True \n", "\n", " refined \n", "0 miscibility-gap \n", "1 miscibility-gap \n", "2 miscibility-gap \n", "3 miscibility-gap \n", "4 miscibility-gap \n" ] } ], "source": [ "# 4. run() -- orchestrator that calls propose() then solve(), and\n", "# applies the per-pair straddle dedup so candidates whose simplex is\n", "# already crossed by an existing trace are skipped.\n", "out = refiner.run(sdf, phases)\n", "print(f'Run produced {len(out)} rows ({out.groupby([\"T\", \"mu\"]).ngroups} unique (T, mu))')\n", "print()\n", "print('First few rows:')\n", "print(out.head())" ] }, { "cell_type": "code", "execution_count": 11, "id": "walkthrough-plot", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:09.184616Z", "iopub.status.busy": "2026-05-13T21:46:09.184469Z", "iopub.status.idle": "2026-05-13T21:46:09.327588Z", "shell.execute_reply": "2026-05-13T21:46:09.326433Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 5. Refined coexistence points -- single contiguous trace.\n", "fig, ax = plt.subplots(figsize=(6, 4))\n", "pts_sorted = out.drop_duplicates(['T', 'mu']).sort_values('T')\n", "ax.plot(pts_sorted['T'], 1e3 * pts_sorted['mu'], 'r.-', ms=5,\n", " label=f'CC trace ({len(pts_sorted)} pts)')\n", "ax.axhline(0, color='k', lw=0.5)\n", "ax.axvline(T_c, ls=':', color='gray', lw=0.8, label=f'$T_c$={T_c:.0f} K')\n", "ax.set_xlabel('T (K)')\n", "ax.set_ylabel(r'$\\mu^*$ (meV)')\n", "ax.set_title('Refined coexistence points (MiscibilityGapRefiner)')\n", "ax.legend(fontsize=9)" ] }, { "cell_type": "markdown", "id": "2f4d3b67", "metadata": {}, "source": [ "## Inter-phase boundary: solid / liquid (ideal-solution binary)\n", "\n", "Now switch to `ClausiusClapeyronRefiner`, which handles two-phase\n", "coexistence between *distinct* phases. The example is the classic\n", "solidus/liquidus from `notebooks/IdealSolution.ipynb`. The refiner\n", "seeds via projection across the two phases' vertex centroids in\n", "each Delaunay simplex, guaranteeing a brentq bracket on\n", "`phi1 - phi2`, then walks T from that seed point." ] }, { "cell_type": "code", "execution_count": 12, "id": "6ad9672b", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:09.329632Z", "iopub.status.busy": "2026-05-13T21:46:09.329444Z", "iopub.status.idle": "2026-05-13T21:46:09.704273Z", "shell.execute_reply": "2026-05-13T21:46:09.703124Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Refined 87 coexistence points across T = [775, 1658] K\n" ] } ], "source": [ "from landau.phases import LinePhase, IdealSolution\n", "\n", "solid_a = LinePhase('A', fixed_concentration=0, line_energy=-2.0, line_entropy=1.0 * kB)\n", "solid_b = LinePhase('B', fixed_concentration=1, line_energy=-3.0, line_entropy=1.5 * kB)\n", "liquid_a = LinePhase('A(l)', fixed_concentration=0, line_energy=-1.9, line_entropy=2.5 * kB)\n", "liquid_b = LinePhase('B(l)', fixed_concentration=1, line_energy=-2.9, line_entropy=2.2 * kB)\n", "solid = IdealSolution('solid', solid_a, solid_b)\n", "liquid = IdealSolution('liquid', liquid_a, liquid_b)\n", "\n", "Ts_ip = np.linspace(200, 1800, 25)\n", "mus_ip = np.linspace(-0.3, 0.3, 21)\n", "phases_ip = {'solid': solid, 'liquid': liquid}\n", "coarse_ip = calc_phase_diagram(\n", " [solid, liquid], Ts=Ts_ip, mu=mus_ip, refine=False, keep_unstable=False)\n", "out_ip = refine_phase_diagram(coarse_ip, phases_ip,\n", " refiners=[ClausiusClapeyronRefiner()])\n", "cc_ip = out_ip[out_ip['refined'] == 'clausius-clapeyron']\n", "print(f'Refined {cc_ip.groupby([\"T\", \"mu\"]).ngroups} coexistence points '\n", " f'across T = [{cc_ip[\"T\"].min():.0f}, {cc_ip[\"T\"].max():.0f}] K')" ] }, { "cell_type": "code", "execution_count": 13, "id": "a7ff3f67", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:09.706547Z", "iopub.status.busy": "2026-05-13T21:46:09.706362Z", "iopub.status.idle": "2026-05-13T21:46:10.060882Z", "shell.execute_reply": "2026-05-13T21:46:10.059788Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5))\n", "\n", "# Coarse stable points coloured by phase + refined coexistence overlay.\n", "ax = axes[0]\n", "for ph, group in coarse_ip[coarse_ip['stable']].groupby('phase'):\n", " ax.scatter(group['mu'], group['T'], s=15, label=ph, alpha=0.6)\n", "refined_T = cc_ip.drop_duplicates(['T', 'mu']).sort_values('T')\n", "ax.plot(refined_T['mu'], refined_T['T'], 'r.', ms=4, label='CC refined')\n", "ax.set_xlabel(r'$\\mu$ (eV)')\n", "ax.set_ylabel('T (K)')\n", "ax.set_title(r'Coarse phases + refined coexistence in $(\\mu, T)$')\n", "ax.legend(fontsize=8)\n", "\n", "# c vs T view: liquidus and solidus branches.\n", "ax = axes[1]\n", "for ph, group in cc_ip.groupby('phase'):\n", " g = group.sort_values('T')\n", " ax.plot(g['c'], g['T'], '.-', ms=4, label=ph)\n", "ax.set_xlabel('c'); ax.set_ylabel('T (K)')\n", "ax.set_title('Refined solidus / liquidus')\n", "ax.legend(fontsize=9)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "cc633864", "metadata": {}, "source": [ "## Asymmetric miscibility gap (sub-regular solution)\n", "\n", "A sub-regular solution $f_\\text{mix} = c(1-c)(L_0 + L_1(2c-1))$ with\n", "$L_1 \\neq 0$ breaks the $c \\leftrightarrow 1-c$ symmetry, so\n", "$\\mu^*(T) \\neq 0$ and the binodal is skewed\n", "($c_\\text{left} + c_\\text{right} \\neq 1$). We build it as a\n", "`SlowInterpolatingPhase` with `RedlichKister(2)` fitted to control\n", "points sampling the analytical $f_\\text{mix}$, then re-run the same\n", "refiner." ] }, { "cell_type": "code", "execution_count": 14, "id": "1c95a49b", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:10.062984Z", "iopub.status.busy": "2026-05-13T21:46:10.062782Z", "iopub.status.idle": "2026-05-13T21:46:13.813151Z", "shell.execute_reply": "2026-05-13T21:46:13.812138Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "asymmetric trace: 33 pts, T=[150, 700] K\n", " median |mu*| = 14.56 meV (would be 0 for symmetric)\n", " median (c_left + c_right) = 1.275 (would be 1 for symmetric)\n" ] } ], "source": [ "from landau.phases import SlowInterpolatingPhase\n", "from landau.interpolate import RedlichKister\n", "\n", "L0_asym, L1_asym = 0.10, 0.04\n", "\n", "def _f_mix_asym(c):\n", " return c * (1 - c) * (L0_asym + L1_asym * (2 * c - 1))\n", "\n", "control_cs = (0.0, 0.25, 0.5, 0.75, 1.0)\n", "asym_line_phases = [\n", " LinePhase(name=f'p{i}', fixed_concentration=c,\n", " line_energy=_f_mix_asym(c), line_entropy=0.0)\n", " for i, c in enumerate(control_cs)\n", "]\n", "asym_phase = SlowInterpolatingPhase(\n", " name='sub', phases=asym_line_phases,\n", " add_entropy=True, interpolator=RedlichKister(2),\n", ")\n", "\n", "Ts_asym = np.linspace(150, 700, 18)\n", "mus_asym = np.linspace(-0.05, 0.05, 21)\n", "coarse_asym = calc_phase_diagram(\n", " [asym_phase], Ts=Ts_asym, mu=mus_asym,\n", " refine=False, keep_unstable=True)\n", "df_asym = refine_phase_diagram(\n", " coarse_asym, {'sub': asym_phase},\n", " refiners=[MiscibilityGapRefiner()])\n", "cc_asym = df_asym[df_asym['refined'] == 'miscibility-gap']\n", "\n", "print(f'asymmetric trace: {cc_asym.groupby([\"T\",\"mu\"]).ngroups} pts, '\n", " f'T=[{cc_asym[\"T\"].min():.0f}, {cc_asym[\"T\"].max():.0f}] K')\n", "print(f' median |mu*| = {np.median(np.abs(cc_asym[\"mu\"])) * 1e3:.2f} meV (would be 0 for symmetric)')\n", "\n", "pairs = cc_asym.groupby(['T', 'mu'])['c'].agg(\n", " lambda s: (float(min(s)), float(max(s))))\n", "sums = np.array([cl + cr for cl, cr in pairs])\n", "print(f' median (c_left + c_right) = {np.median(sums):.3f} (would be 1 for symmetric)')" ] }, { "cell_type": "code", "execution_count": 15, "id": "18269a0f", "metadata": { "execution": { "iopub.execute_input": "2026-05-13T21:46:13.815129Z", "iopub.status.busy": "2026-05-13T21:46:13.814942Z", "iopub.status.idle": "2026-05-13T21:46:14.137633Z", "shell.execute_reply": "2026-05-13T21:46:14.136306Z" } }, "outputs": [ { "data": { "image/png": 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3ZzY2Nqxp06bszJkzrH379iYvkTtp0iS2detWFhgYyGxsbFijRo10lqNlzPgSuT179tQ7p6H7fvz4MRswYABzdXVltra2rHnz5uzQoUN6t42OjmZ9+vRh9vb2rEKFCmzq1Knsn3/+0VsiNzw8nHXu3Jk5OjqyChUqsHHjxrFbt24xAGzz5s38caYukcsYY3369GGdOnXS2Xb//n02efJkVqtWLWZvb88AsIoVK7KBAweyR48e6Z3j3LlzrEuXLszJyYk5ODiw+vXrs7Vr15p0/xoZGRls3rx5zN/fn4nFYlaxYkU2YMAA9vjx4wKdhxBz4hijsUiEEEIIIYQQUlacPXsWwcHBuH//vsEVc6KiojBq1CicPn265IsjxMKoJwghhBBCCCGElCFt27ZF165dsWrVKkuXQojVoZ4ghBBCCCGEEFLG/P3330b3ubq6YtSoUYU6r0wmw+vXr/M8xsXFhW+0Soi1oekwhBBCCCGEEEJMcvr0aXTo0CHPYzZv3lzokIWQ4kYhCCGEWJnQ0FBUq1YNwcHBli6FEEIIIUTHmzdvcO3atTyPqVu3Lnx8fEqoIkIKhkIQQgixEtu3b4dQKERmZib8/Pxw9+5dBAUFoVOnTpYujRBCCCGEkDKBGqMSUgxCQ0PBcRyioqIsXUqxK0+PtbgNHjwYcXFxWLNmDebOnQtXV9ciByCLFi0Cx3EmH2/o+3nlyhW8/fbbcHBwAMdxuHnzZpFqMqak7ocQQgghhJRfFIIQHevXrwfHcWjRooWlS7EaFy5cwKJFi5CUlGTpUsoMek6N0wQWHMdBKBRauBpALpdj4MCBeP36Nb755hv89ttv8PPzM/v30Nj9WDupVIrZs2ejUqVKsLOzQ4sWLXDs2DFLl0UIIaQUqFatmtF9n376Kb0fJ6SYUAhCdGzbtg3VqlXD5cuX8ejRI0uXYxUuXLiAxYsXF+iPveHDh/NTGsq6wjzWwjyn5cHOnTvh5eWFadOmYfny5Xj16hVOnDhRojXk/n4+fvwY0dHRmDlzJsaPH4/33nsPbm5uZv8eGrsfazdq1CisXr0aw4YNw7fffguhUIgePXrg3Llzli6NEEJIARQl1NaMusz9z9bWttD1TJs2Dbdu3cKBAwcKfQ5CiGG0RC7hRUZG4sKFC9i7dy8++OADbNu2DQsXLrR0WaVOeno6HBwcrOJT/JIgFArLzWMtbu+++y6AnCkpU6ZMKbH71n7dan8/X758CUC9lF5xKsj9aGq1tMuXL2PHjh348ssvMXPmTADAiBEjUK9ePcyaNQsXLlywcIWEEEJMNWrUKOzevRvTpk1DYGAgQkND0aNHD5w6dQpt2rQx6RwbNmyAo6Mjfz2v90dyuRwqlQpyuRxisVhvf8WKFfHOO+/gq6++Qp8+fQr+gAghxjFCsi1dupS5ubkxqVTKJkyYwAIDA/WOSUlJYVOnTmV+fn5MIpEwT09P1rlzZ3bt2jXGGGMnT55kANjevXv1brtt2zYGgF24cIEtXLiQAWAPHjxgw4YNY87OzqxChQps/vz5TKVSsZiYGNanTx/m5OTEvL292VdffaV3PnOc49mzZ2z06NHMy8uLSSQSFhQUxH7++We9+8j9LzIyUmf/vXv32NChQ5mrqytr2LAh27x5s85x2vf3/vvvMx8fHyaRSFi1atXYhx9+yKRSaZ7fG1Nvd/36ddatWzfm5OTEHBwcWMeOHVlYWFiBH3dGRgarVasWq1WrFsvIyOC3JyYmsooVK7JWrVoxhULBGGN6jzW/10h+z6kp9WmfJyIigo0cOZK5uLgwZ2dnNmrUKJaenl7g58+U+9T477//WHR0tLFvlw5/f382bNgwve3BwcGsXbt2Jp3DVGfPnmVNmzZlNjY2rHr16mzjxo3886TN2OuWMd3v58iRI/W+T+3bt8/ze5jf998QY/eTX62MmfaaN8fPCkM++eQTJhQKWXJyss72zz//nAFgMTExJp2HEEKIZV26dIkBYF9++SW/LTMzkwUEBLBWrVrle3vN75mEhIR8jz1//jxr2rQpEwqFDADjOI75+vqypUuX6h27e/duxnEce/z4ccEeECEkTzQShPC2bduGfv36QSKRYOjQodiwYQOuXLmCZs2a8cd8+OGH2L17NyZPnoygoCAkJibi3Llz+O+//9C4cWMEBwfD19cX27Ztw//+9z+98wcEBKBVq1Y4cuQIAHUjyDp16mDlypU4fPgwli1bBnd3d2zatAkdO3bEF198gW3btmHmzJlo1qwZ2rVrp1d3Yc8RHx+Pli1bguM4TJ48GZ6envj7778xZswYpKSkYNq0aejXrx8ePnyI33//Hd988w0qVKgAAPD09NSpYeDAgQgMDMTnn38OZmTBpRcvXqB58+ZISkrC+PHjUbt2bTx//hy7d+9GRkYGJBJJkW537949tG3bFs7Ozpg1axbEYjE2bdqE4OBg/Pvvv/y8UlMet52dHbZs2YLWrVtj3rx5WL16NQBg0qRJSE5ORmhoqNFPN/J7jeT3nJpSn7ZBgwbB398fK1aswPXr1/HTTz/By8sLX3zxhcnPX0Hvs06dOmjfvj1Onz5t8DnQSEtLQ1RUFCZMmKC37/bt2/zID3O4c+cOunbtCk9PTyxatAgKhQILFy6Et7e30dvk97r94IMPULlyZXz++eeYMmUKmjVrBm9vb3h7exv9Ho4fPz7P778hxu4nv1pNfc1rmOPnjbYbN26gZs2acHZ21tnevHlzAMDNmzfh6+ub5zkIIYTk7fnz5/jss89w+PBhJCUloUaNGvj444/x/vvv6xz37NkzTJ48GceOHYODgwOGDRuGbt26oVu3bjh16lSey87v3r0bQqEQ48eP57fZ2tpizJgxmDt3Lp4+fWrSz3PGGFJSUuDk5GSwKfnr16/Ru3dvVKhQAaGhoZg5cya+/vpr3LhxAxEREXrHd+7cGQCwf/9+TJ8+Pd/7J4SYyLIZDLEWV69eZQDYsWPHGGOMqVQqVqVKFTZ16lSd41xcXNikSZPyPNecOXOYjY0NS0pK4re9fPmSiUQitnDhQsZYTmI+fvx4/hiFQsGqVKnCOI5jK1eu5Le/efOG2dnZsZEjR+rcT1HPMWbMGObj48NevXqlc94hQ4YwFxcXfgTEl19+aXBUh3YNQ4cO1dluaCTIiBEjmEAgYFeuXNE7j0ql0ttW0Nv17duXSSQSnU8LXrx4wZycnHRGHJj6uBlTfy8FAgE7c+YM27VrFwPA1qxZk+djNeU1ktdzamp9muf+/fff1znuf//7H/Pw8OCvm/L8FeQ5YYzpjFTIS1hYGAPAjhw5orP96dOnDAD74Ycf8j2Hqfr27ctsbW11RqiEh4fznzRpM/a6ZUz/+3nq1CkGgO3atUvnOGPfQ1O+/4YYu5+8ajX1NW+OnzeG1K1bl3Xs2FFv+7179xgAtnHjxnzPQQghxLi4uDhWpUoV5uvry5YsWcI2bNjA+vTpwwCwb775hj8uIyOD1axZk9na2rJZs2axNWvWsCZNmrD69eszAOzUqVN53k/nzp1ZnTp19LYfP36cAWAHDhzI8/aa3zOOjo4MAHNwcGDDhg1jcXFxOscdOnSIAWDnz59njDHm5+eX73NQo0YN1r9//3yPI4SYjhqjEgDqURre3t7o0KEDAPXKFIMHD8aOHTugVCr541xdXXHp0iW8ePHC6LlGjBgBqVSK3bt389t27twJhUKB9957T+fYsWPH8peFQiGaNm0KxhjGjBmjc5+1atXCkydPDN5fYc7BGMOePXvQu3dvMMbw6tUr/l9ISAiSk5Nx/fr1PJ8zbR9++GGe+1UqFf7880/07t0bTZs21dtvbAlTU2+nVCpx9OhR9O3bF9WrV+f3+/j44N1338W5c+eQkpJS4Me9aNEi1K1bFyNHjsTEiRPRvn37fPtUmPIaMaYw35fcz33btm2RmJiIlJQUk56/wtwnYyzfUSAAcPfuXQBAgwYNdLbfunULAFC/fv18z2EKpVKJI0eOoG/fvqhatSq/vU6dOggJCTF6u/xet4VRlO9/XnLXauprXps5ft5oy8zMhI2Njd52TSO8zMxM0x4cIYQQg+bNmwelUokbN27gs88+w4cffoj9+/djyJAhWLRoEf9z9ocffsDDhw/x66+/4osvvsDUqVNx5swZZGRkmHQ/sbGx8PHx0duu2Zbf7zQ3NzdMnjwZmzZtwu7duzF27Fjs3LkTbdu21fldpBlFa2pdAFC9enWEh4ebfDwhJH8UghAolUrs2LEDHTp0QGRkJB49eoRHjx6hRYsWiI+P11mdYtWqVbh79y58fX3RvHlzLFq0SO+Phdq1a6NZs2bYtm0bv23btm1o2bIlatSooXOs9h9sAODi4gJbW1t+eL329jdv3hisvzDnSEhIQFJSEn744Qd4enrq/Bs9ejSAnEaNpvD3989zf0JCAlJSUlCvXj2Tz1mQ2yUkJCAjIwO1atXS21enTh2oVCo8ffq0wI9bIpHgl19+QWRkJFJTU7F582ajgY2GKa+RvB5HQb8vub//mhVF3rx5Y9LzZ+7XgrY7d+7w00e03b59GwKBoMCvB2MSEhKQmZmJwMBAvX2GXhMa+b1uC6Mo3/+85K7V1Ne8NnP8vNFmZ2cHqVSqtz0rK4vfTwghpHAK8iHFX3/9BR8fHwwYMIC/vb29vc70lrwUNdSeOnUq1q5di3fffRf9+/fHmjVrsGXLFkRERGD9+vX8ce3atUNAQACGDBmCuXPnQiaT4dWrV3me283NLd9jCCEFQz1BCE6ePInY2Fjs2LEDO3bs0Nu/bds2dO3aFYC6/0Lbtm2xb98+HD16FF9++SW++OIL7N27F927d+dvM2LECEydOhXPnj2DVCrFxYsXsW7dOr1zG+orYazXBDPSa6Mw51CpVACA9957DyNHjjR4bEE+pS8tf+wU5nFr+rdkZWUhIiIi3z+cTX2NmKu+gr5ezHGfprp7967eKBBA3SuievXqFl/hpDhet0X5/ufFHLWa4+eNNh8fHzx//lxve2xsLACgUqVKBayQEEKIhvaHFD/88IPBYzQfUkRHR6NGjRp6H9Tk9UGAtuIItd999118/PHHOH78OD799FMA6mDm/PnzWLx4MbZs2YLY2Fh4eXmhRYsW+Oqrr9C6dWu98zDG8v0AihBSMBSCEGzbtg1eXl74/vvv9fbt3bsX+/btw8aNG/lfAD4+Ppg4cSImTpyIly9fonHjxli+fLnOHzhDhgzBjBkz8PvvvyMzMxNisRiDBw8usceUH09PTzg5OUGpVPJNp4wxxy8eT09PODs789MjzH07T09P2Nvb48GDB3r77t+/D4FAAF9fXzg4OJj8uAH1iIUlS5Zg9OjRuHnzJsaOHYs7d+7AxcUlz9vl9xox9pwW5PtiClOeP3Pfp7Y7d+7ove5VKhVOnjyZb9PNgvD09ISdnZ3BpmqGXhPmkNf/F6b8jCgqU1/zxalhw4Y4deoUUlJSdJqjXrp0id9PCCGkcIrzQ4rciivU9vX1xevXr3W2eXt7Y/369Vi/fj0qVaqEFStWYOnSpejatStu376NgIAAnePfvHmjN2KREFI0NB2mnMvMzMTevXvRq1cvDBgwQO/f5MmTkZqaigMHDkCpVCI5OVnn9l5eXqhUqZJeel6hQgV0794dW7duxbZt29CtWzer+gEuFArRv39/7Nmzx+AfyAkJCfxlzaf1SUlJhb4/gUCAvn374uDBg7h69arefmOfOpt6O6FQiK5du2L//v2Iiori98fHx2P79u1o06YNnJ2dC/S45XI5Ro0ahUqVKuHbb79FaGgo4uPj8+xObuprxNhzWpD6TGHK81eY+7x//z5iYmLyvO+XL18iISGBfwOl8d133+HVq1d46623CvRY8iIUChESEoI///xTp67//vuPH8ljboa+hwX5GVFUpr7mi9OAAQOgVCp1PqGUSqXYvHkzWrRoQSvDEEJIEeT+kMLQPy8vLwCAn58fHj9+rPd+ytQPAho2bIiHDx/q9ZIqSqjNGENUVJTeioLaJBIJRo4ciT/++AMZGRn4+++/9Y6JjIxEnTp1Cnz/hBDjaCRIOXfgwAGkpqaiT58+Bve3bNkSnp6e2LZtG0JCQlClShUMGDAADRo0gKOjI44fP44rV67g66+/1rvtiBEj+LmZS5cuLdbHURgrV67EqVOn0KJFC4wbNw5BQUF4/fo1rl+/juPHj/PJfZMmTQCom3MNGTIEYrEYvXv3LvBUhs8//xxHjx5F+/btMX78eNSpUwexsbHYtWsXzp07B1dX1yLdbtmyZTh27BjatGmDiRMnQiQSYdOmTZBKpVi1alWBH/eyZctw8+ZNnDhxAk5OTqhfvz4WLFiA+fPnY8CAAejRo4derampqSa9RvJ6Tk2tz5zPe0Hv05Qlcu/cuQMAOHr0KCZOnIjatWvj4sWLfChx7do1XLp0SW8Z18JavHgx/vnnH7Rt2xYTJ06EQqHA2rVrUbduXdy+fdss96HN0Pewbdu2qFWrlsk/I4rK1Nd8cWnRogUGDhyIOXPm4OXLl6hRowa2bNmCqKgo/Pzzz8V+/4QQUpZpPqTYvn077t69q9dHKyEhgQ8YevTogaNHj2L37t0YOHAgAHXzUWPTaHIbMGAAvvrqK/zwww+YOXMmAOOhdkxMDDIyMlC7dm2DtWhs2LABCQkJ6NatG78tKSnJ4Ps9uVwOQH/aTXJyMh4/fowJEyaY9DgIISYquYVoiDXq3bs3s7W1Zenp6UaPGTVqFBOLxSwuLo598sknrEGDBszJyYk5ODiwBg0asPXr1xu8nVQqZW5ubszFxYVlZmbq7NMsJZaQkKCzfeTIkczBwUHvXO3bt2d169Y1+zni4+PZpEmTmK+vLxOLxaxixYqsU6dOekuXLl26lFWuXJkJBAKdZUGN1WBoiVzGGIuOjmYjRoxgnp6ezMbGhlWvXp1NmjSJSaVSvXoLc7vr16+zkJAQ5ujoyOzt7VmHDh3YhQsX9M6X3+O+du0aE4lE7KOPPtK5nUKhYM2aNWOVKlVib9680XusUqnU5NeIsefUlPoK+tyb8vyZ+lpgzLQlcr/55hsmFArZ4cOHWUBAALO1tWVdunRhd+7cYQEBAaxKlSrs2rVreZ6joP7991/WpEkTJpFIWPXq1dnGjRv550mbseeOMdOXyGVM/3v44MGDAv2M0JbfErmGamXMtNe8OX5WGJOZmclmzpzJKlasyGxsbFizZs3YP//8Y9JtCSGE5C0uLo75+fkxe3t7NnXqVLZp0ya2YsUKNnDgQObm5sYfl56ezmrUqMFsbW3Z7NmzC7xELmOMDRw4kIlEIvbJJ5+wTZs2sbfffpuJRCL277//6hzXvn17vd+rdnZ2bNSoUezrr79m33//PRs6dCjjOI41bNhQ5z325s2bWePGjdmaNWvYyZMnmbe3N9u4cSOrVq0ac3NzY8+fP9c57+7duxkA9ujRo0I8e4QQYzjGTOweSEgBKRQKVKpUCb1796ZPRUm5M3bsWJw5cwYPHz60dCmEEEJIqfXy5UssWbIEBw4cQFxcHDw8PFC3bl0MHjwY48aN44+LiYnBRx99hOPHj8Pe3h7Dhg1D9+7d0a1bN5w6dQrBwcF53k9WVhY+++wzbN26FW/evEH9+vWxdOlSvaXmg4OD8e+//+pMvRk3bhwuXLiAp0+fIisrC35+fujfvz/mzZsHJycn/rjnz59j3bp1OHz4MKKiopCamooKFSqgadOm+Pzzz9GoUSOd+xoyZAieP3+Os2fPFuEZJITkRiEIKTaaIYmnT59G+/btLV0OISWqRYsW8PHxwZ9//mnpUgghhJBy6fTp0+jQoYNJIYglVKtWTaevlba4uDj4+/tjx44deOedd0q2MELKOOoJQszu0qVLuH37NpYuXYpGjRpRAELKHcYYwsPD0alTJ0uXQgghhJBSaM2aNXjrrbcoACGkGFAIQsxuw4YN2Lp1Kxo2bIjQ0FBLl0NIiYuMjERaWhqCgoIsXQohhBBCrNS0adOM7lu5cmXJFUJIOUPTYQghhBBCCCFljrVPhyGEWAaFIIQQQgghhBBCCCkXBJYugBBCCCGEEEIIIaQkUAhCCCGEEEIIIYSQcqHcN0ZVqVR48eIFnJycwHGcpcshhBBCygTGGFJTU1GpUiUIBPSZizZ670EIIYSYn6nvPcp9CPLixQv4+vpaugxCCCGkTHr69CmqVKli6TKsCr33IIQQQopPfu89yn0I4uTkBED9RDk7O1u4GkIIIaRsSElJga+vL/97luSg9x6ElA6PHz9GQECApcsghJjI1Pce5T4E0QxDdXZ2pjcihBBCiJnRdA999N6DkNLB0dGR/h8lpBTK770HTdIlhBBCCCGEkFwqV65s6RIIIcWAQhBCCCGEEEIIyUUmk1m6BEJIMaAQhBBCCCGEEEJySUhIsHQJhJBiUO57guRHqVRCLpdbugxCTCYWiyEUCi1dBiGEkEKi9x7EFPT7nhBCCodCkDykpaXh2bNnYIxZuhRCTMZxHKpUqQJHR0dLl0IIIaSA6L0HMRX9vi9+9NwSUjZRCGKEUqnEs2fPYG9vD09PT+puT0oFxhgSEhLw7NkzBAYG0idEhBBSitB7D2Iq+n1fMnx8fCxdAiGkGFAIYoRcLgdjDJ6enrCzs7N0OYSYzNPTE1FRUZDL5fSmiBBCShF670EKgn7fF7+IiAgEBgZaugxCiJlRY9R80KcwpLSh1ywhhJRu9HOcmIJeJ4QQUjgUghBCCCGkXKhWrRo4jtP7N2nSJABAVlYWJk2aBA8PDzg6OqJ///6Ij4/XOUdMTAx69uwJe3t7eHl54ZNPPoFCobDEwyGEEEJIIVAIQsqM169fAwAWLVqEpKQkaipHCCFEx5UrVxAbG8v/O3bsGABg4MCBAIDp06fj4MGD2LVrF/7991+8ePEC/fr142+vVCrRs2dPyGQyXLhwAVu2bEFoaCgWLFhgkcdTmhw8eBDVqlWDo6Mj/vzzT3Tv3h3r168vlvtKSkoCx3GIiooyuH/UqFGYNm1asdx3YXAch5s3b1q6DGKAv7+/pUsghBQD6glCyozw8HCcPHkS586dg729PaZMmQJbW1tLl0UIIcRKeHp66lxfuXIlAgIC0L59eyQnJ+Pnn3/G9u3b0bFjRwDA5s2bUadOHVy8eBEtW7bE0aNHER4ejuPHj8Pb2xsNGzbE0qVLMXv2bCxatAgSicQSD6tUmD59OpYuXYrhw4cDAPr27WvZgggxwevXr+Hl5WXpMgghZkYhCClz8hoBsmPHDuzduxd//PFHvufp2rUrZs2ahc6dO5uzPEIIsS4//QR88QWwcCHw3nuWrqbEyGQybN26FTNmzADHcbh27RrkcrnOz/zatWujatWqCAsLQ8uWLREWFoa33noL3t7e/DEhISGYMGEC7t27h0aNGlnioVgUYwwqlSrfxpyRkZF46623Sqgq81IoFBCJ6C1zeZScnFxsIcix8Hhs+vcxXqfLUK+yCwI8aTleS3uckIa7z5NRxd0Ow1tWQ5cg7/xvREol+oleRpw7dw7Lly/HxYsXwRiDn58fhg0bhmnTpkEikeS7P7dq1aphzZo1peqTmqCgILRp0waLFi3C+PHjYWNjo7NfpVJh7ty52L9/PwDg999/x7hx4/h9mZmZcHBw4I//5JNP8Mknn+DGjRsl9yAIIaQkffwxsHq1+vLw4YCzM9Cnj2VrKiF//vknkpKSMGrUKABAXFwcJBIJXF1ddY7z9vZGXFwcf4x2AKLZr9lnjFQqhVQq5a+npKSYVCNjDJlypUnHapy8/xKXI1+jub87OtYu2B9vdmKhSc02q1Wrhg8++AD79+/HrVu3cPnyZXh7e2P69Ok4efIkOI7DoEGD8MUXXyAtLQ1+fn5QqVR4++23IRAIkJiYiJCQEPTt2xfTpk3D6dOn0bdvX3z11VdYvHgxMjIyMGbMGKxatYq/z+PHj2Pu3Ll4+PAhKleujBUrVqBP9mtVKpVi2rRp2LlzJ1xcXDBv3rx8H0NKSgr69u2L48ePo3r16li/fj3atGkDAAgODkbz5s1x8+ZNnD9/Hjt27ICNjQ3mzp2LiIgI2Nvb43//+x++/vprfhWfatWqYeLEidi7dy/u3buHxo0bY+vWrfD19QWgfn3MnDkTJ06cQGZmJurXr48jR47wt7948SLee+89xMTEIDg4GL/99htcXFwK9P0jpcc/d2Px4dbr/PUnr9ItWA3J7cmrdJx5+Ao/jmhKQUgZRSFIGXDo0CEMHToUS5cuxW+//YYKFSrg/v37WLlyJWJjY3Hnzp089/v5+RX4Pk395Kckubu7A1D3BDHkr7/+gru7O/9J1NChQzF06FAA6hEiM2fOxLNnz/jjGWMIDQ3F+fPn0bp16+ItnhBCStqePTkBCAAIBMDp0+UmBPn555/RvXt3VKpUqdjva8WKFVi8eHGBb5cpVyJowZFC3eevYdEFvk34khDYS0x7axgaGooDBw6gRo0aUCgUaN++PVq3bo3Hjx8jMzMTAwYMwLJly7B06VKkpaWB4zhcuHABDRs2NHi+1NRUhIeHIyIiApGRkWjatCl69OiB4OBg3L59GwMHDsSePXsQHByMCxcuoGfPnrh8+TJq1aqF5cuXIywsDHfv3oW9vT3efffdfOvfvn07du3ahd27d+Onn35Cnz598OTJEz4ECw0NxaFDh9CsWTNkZWXh6tWr+PHHH1G/fn1ER0ejZ8+eWL16tU7gsnXrVuzfvx8+Pj7o168fPvvsM4SGhkKlUqF3796oW7cuwsPD4eTkhIsXL0IgyGnN98cff+DkyZOQSCTo2LEjvvnmG6PvZ0jJ0by3NIdj4fE48zABTf3ccO7RK7OdlxSfRQfu4lxEAtoEelIYUsZQY9RSjjGGKVOmYPbs2Zg2bRoqVKgAQD2ENzQ0FFWrVs1zv6EAZODAgYiJicHQoUPh6OiIDz/8EID6U44VK1agZcuWsLe3R3h4OFavXo3AwEA4OTkhICAA69at0zlXSkoKJk+eDD8/Pzg7O6NZs2Z4+vQpACAtLQ2TJ09G1apV4eXlhREjRiA5Odng41y3bh169+6ts61Bgwb8qA5THDhwgJ/nnduNGzfQuHFjnW0cx6Fjx444cOCAyfdBCCGlwv79QPZIOJ5KBQQHW6SckhYdHY3jx49j7Nix/LaKFStCJpMhKSlJ59j4+HhUrFiRPyb3ajGa65pjDJkzZw6Sk5P5f5rfg6XZhAkTUKtWLQiFQty+fRsRERH48ssvYW9vDw8PD8ydOxfbt283+XyMMSxbtgy2traoU6cO3n77bVy7dg0AsGnTJowaNQodO3aEQCBAmzZt0KtXL35q67Zt2zB37lxUqlQJrq6uWLhwYb7317FjR/Tu3RsikQgffvghvL29cejQIX7/u+++i+bNm4PjONjZ2aFt27Zo1KgRhEIhqlevjg8++ACnT5/WOefEiRPh7+8PW1tbDBs2jK//ypUr+O+//7Bhwwa4ublBJBKhTZs2OiNWZ82aBS8vL7i6uqJ///78bYllOTqaZ4rKxtOPMe7Xq/jtYjSm7ryJXdee5X8jYnHPk7KwJSwa4369imPh8fnfgJQaNBKklNN8YqIZ0VDQ/Ybs2rXL6HQY7U9+lEolHj58iJMnT6JKlSo4ffo0evTogUaNGvEjJ0aNGoWMjAyEhYWhYsWKuHXrFj/08/3334dIJMLt27chFosxduxYTJ48Gb/99pteTbdu3dIJKbKyshAeHq4XXOTl5s2bfKCT2/Xr1/H222/rbQ8KCsLRo0dNvg9CCLF6Bw4AhqY6zp1bbkaBbN68GV5eXujZsye/rUmTJhCLxThx4gT69+8PAHjw4AFiYmLQqlUrAECrVq2wfPlyvHz5ku8TcOzYMTg7OyMoKMjo/dnY2OhN0TSFnViI8CUhJh9/8v5LTN5+A0KOg5IxrHu3UYGmxNiJTR/dWbVqVf5yVFQUkpKSdD41Z4xBqTR9Ko+zszPs7e356w4ODkhNTeXPf/LkSWzevJnfr1Ao4OzsDAB48eKFzoc6poxwzX2Mn58fnj9/zl/XfnyAOsiYM2cO7ty5g8zMTCgUCtSqVUvnGO0gTLv+6OhoVK5cmX//Y4ix2xLLiomJQWBgYKFvv/Hfx9j072O8yZCbsSpS0gQcsOVCJMIev0KrgAo0KqQMoBDEVIwBGRkFu83hw8CZM0C7doDWGy2T2NsDJszLTUhIAABUrly5UPsLSvPJDwAIhUL+jSIAdOjQASEhITh9+jRat26N+Ph47Nu3D9HR0fxwY03TuISEBOzZswevXr3ih54uWbIEdevWRWhoqN40m1u3bqFXr1789du3b8PNzY2fa2uKN2/e8G+Ycrtx4wYmT56st93Z2Rlv3rwx+T4IIcTqffddzmWOAxo1UjdFLScBiEqlwubNmzFy5EidZpcuLi4YM2YMZsyYAXd3dzg7O+Ojjz5Cq1at0LJlSwDqhtlBQUEYPnw4Vq1ahbi4OMyfPx+TJk0qVMiRH47jTJ6eAgC96leCjUiIi08S0bK6R7G+UdeeyuHr6wsvLy/ExsYWy335+vpi6tSpWLlypcH9lSpVQnR0NFq0aAFA/YdrfqKjdacLxcTE6LxX0n58gHoK7ejRo7F//344ODhgzZo1CA0NNal+TcCSlZVFq9aVI1suRGHl3/ctXQYxAxUDzj1KxLlHifjlfBT1CikDKAQxVUYGUNghcd9/X/DbpKUBWk06jdFMb3n+/DkCAgIKvL+gcn8ysm3bNnz99deIioqCSqVCRkYGv6Z6dHQ0bGxs9G4DgD8+9/rrAoEAcXFxOm9ElEol7t69qzPq48aNGwXuwu/m5mawGV1MTAwSExMNjipJSUmBm5tbge6HEEKs1j//AKdOqS9znDrgL0cBCKBusBkTE4P3339fb98333wDgUCA/v37QyqVIiQkBOvXr+f3C4VCHDp0CBMmTECrVq3g4OCAkSNHYsmSJSX5EPLUJci7xN+cN2vWDL6+vpg/fz5mz54NR0dHxMTEIDw8HN27dy/y+T/44AN069YNISEhaNeuHRQKBa5fvw5XV1fUqVMHQ4cOxcqVK9GmTRvY29ub9P04efIkDh8+jJCQEGzevBmxsbE6I4NyS0lJgaurKxwcHPipLXmN7NDWrFkz1KpVCxMnTsTq1avh6OiIixcvolmzZsUSnhHzKUzvu2Ph8Qh7nIgH8brvOQUcIOA4CAQcRIL8P+gklqdQMahUDCrGoNJafHLxgXv498FLtK/lRWFIKUU9QUq5mjVrolq1atixY0eh9huT+xMQQ9tjYmIwcuRIrFq1Ci9fvkRSUhJ69OjBL1Hr5+cHqVRqcO6zr68vBAIBXrx4gaSkJP5fVlaW3qiViIgIiMVinVEfJ06cKHAI0rBhQ9y/r5/IX79+HRUqVDA4qiQ8PNxoEzdCCClV1qxRhx0qFdChAzB1qro3SDkKQAD1aA7GGGrWrKm3z9bWFt9//z1ev36N9PR07N27V6/Xh5+fH/766y9kZGQgISEBX331VblfPlUTDj1//hx16tSBi4sLevbsiUePHpnl/I0aNcLvv/+O+fPnw9PTE5UrV8Znn33Gr7gzf/58NG3aFPXq1UPDhg1NWtnu3XffxY8//ghXV1d899132L9/f54femzatAlfffUV3yttyJAhJtcvEAhw8OBBZGRkoFatWqhQoQLmz58PlUpl8jmIZVSvXr1Ax++/8Rzjfr2KX85H4vyjRJ19mgAEUP9xTf+s/x8ACAQcBLlG5z9LysTWSzHUK6QU45jmL9ZyKiUlBS4uLkhOTtaZKpGVlYXIyEi+wVWBp8McPgwMHgwIhYBSCezcWbApMSZOhwFyVof5/PPP8e6778LDwwMPHz7EF198gQULFvCrwxjbb2jubKtWrTBgwAB8/PHH/LbcfULCw8Px1ltv4caNG6hXrx7++ecfDBgwAOPHj8eaNWsAAH379oVcLsdPP/0Eb29v3Lp1C1WrVoWHhwf69+8PFxcXrFq1ChUqVEBcXBzCwsLwv//9T6eWHTt24L333sOVK1dQr1497Ny5EyNHjsSmTZswevRok1P6gwcPYsmSJbhy5YrO9gULFuDixYsGe39Ur14dW7ZsQdu2bU26D2ug99olhJAVK9Q9PzR27wa0pjMWB2O/X0kB3nsQkgd6vRS/Z8+eoUqVKnkeoxn50SrAAyf+i8eOK6W/8TExjZADOtT2RlV3e7QKKN4piMQ0pr73oJEgpuI49fQUU/8NGqT+hG3KFPXXQYMKdnsTAxAA6NWrF/7++28cPnwYAQEBcHV1xYABA1C7dm34+Pjku9+QuXPnYt26dXB1dcXEiRMNHhMUFIR58+ahY8eO8PDwwM6dO9En1yeKW7Zsga+vL5o2bQpXV1d8+OGHyMzMBKBusurq6opmzZrB2dkZbdu2NdgN/datW+jZsycGDx6MSpUq4cKFC+jatSuWLl1aoE9RevTogVevXuHu3bs62w2tDAMAZ8+e5esihJBS6cABoFcvQGsZTwiFwPnzlquJEEJKCc17VmP231SP/Nh8PhLjfr2K+3HqKTCad/H1KjujTY0KaOHvjiZ+bmhQxQVBPs6o6e2I6hUc4OtuBx8XW1RwtIGrvRiONiLYiAQQ0nSZEiPgAIlIAAeJEC52YlRwlKCisy2quNnBv4IDAr0cUcfHGfWruKBxVVcEeqnbI3AAlAw4/l88Nl+IpFEhpQyNBKFPY6xejx49MGDAAIPztwvq999/x59//omdO3fme2xISAhmzpyJLl26FPl+SxK9dgkhANQByDvv6G7TjE4sgWkwNBLEOHrvQcyBXi/FLyIiIs/VYUb8fAlnIl6VYEXEWgk4YHRrf3zWy/hKYaT4mfreo3xPYiWlwq1bt7Bw4UKznGvo0KEmLxd85MgRs9wnIYRYxIYNOZc5Tj0ipEYNIDi43PUBIYSQwtDuCaQ97UUz7WFAkyo4E/EKHAAGoG1gBXg720KhVEGuZJArVVCo1F/lShUUSs1lBoVK6xil1jGqnGNI4YgEHERCDmKhAGKhACKB5jIHUfY2sZDT2i7QOp6DSKB1TPZ2kYADl2ukflRiOo7eiwfHqVeQsRULseRgOE2NKQUoBCFW7dWrV3jx4gWCgihVJYQQkx0/Dhw7pr6sWQVm7FgKPwghpBD233yOqTtuAgB+OR8JX3c7ONuKAQC+7nbIkCphbyPE63QZXqfL8j0fxyH7j2wAMNzbjjFAxRhk2SGJQqmCLDs8USg121U6q5YQNU1j0yy5eZsPa0IT7cDE3UEChVIFoYDD96cegePUrxFaRte6UQhCrFqFChVQzmdsEUJIwaxZA8yapZ720qYN0LSpejUYCkAIIaRA4uLicC4qDXP23tHZ/vR1JgDdfiGJ6dDbRsoWdbiiBOTGj2EMEHIcLj5JpBDEilEIQgghhJQVP/8MTJ+ec33atGJfBYYQQsqaY+HxOBYej26+DBP2PeS3C7KnPUztVAONqhpfUpmUPzdi3uDbE48g5DgoGaOpMVaOQhBCCCGkLJDLgc8+y7muWQWGQhBCCDHZsfB4jPv1KgCgstiD3x7o5YgMmQIudmJcj0nC9ZgkC1VIrFWQjxOSM+UQcNlTY0BTY6wVhSCEEEJIWTB3LhAbq76sWQUmONiiJRFCSGkT9jiRb3T6TVgivz3iZRoA4HlSFoBUi9RGShfNhP5zEQkUglgZCkEIIYSQ0u7gQeCrr9SXP/0UkEppFRhCCsnR0RFhYWF46623Suw+t23bhu+//x4XLlwosfskhrUK8MAv5yMh4ICVXbzxMMMe9Sq7WLosUorcfZ6Mn85F8tcvRb1GllwJW7HhJrik5FEIQgghhJRmP/4IfPSR+vK0acCKFRYthxBrxXEcbty4gYYNG+Z5XFpaWskUpGXYsGEYNmxYid8vAfZef4Yj9+JQx8cZjau6wUYkwLTOgfgvNgVV3W1RsYqnpUskpUy7mp5wtBXh3wcJuPE0CfdjU9F/wwU09XNDm0BPGhViBSgEIYQQQkqr3buB8eNzrrdpY7laCCnl5HI5xGKxpcsgJehYeDxm/HELAHDkXrze/nf8fTBxx+WSLouUQfdepCA8NgVbwqKpR4gVEFi6AEIIIYQUgkql7gOioWmESkgxW716NapWrQonJydUq1YNP/30E+RyOby9vXH69GmdY+vUqYOdO3cCUI/EWLduHYKCguDg4IDhw4fjzZs3GDx4MJydndGoUSPcv3+fv221atWwYsUKNGvWDA4ODujevTtev36NiRMnwtXVFYGBgTrTR+RyORYsWICAgAB4eHigT58+ePHiBQCgefPmAIC3334bjo6O+PzzzxEVFQWO47B582bUqFEDVapU4eu8efMmf97ff/8dDRo0gLOzM/z8/BAaGmrweblx4wbatGkDd3d3eHp6YujQoUhMVPeUSElJQUBAAH766Sf++N69e2P06NEAgNDQUJ0RKoaeY2J+mv4fGo42Qng728DdQQInGxG+OJcIjjN6c5IHAQfYiARwshHBw0GCis628HW3Q4CnA2pXdEIdH+dy88/dQQJAd/lcYllWOxJkxYoV2Lt3L+7fvw87Ozu8/fbb+OKLL1CrVi3+mKysLHz88cfYsWMHpFIpQkJCsH79enh7U7JGCCGkjJs9G4iIUF8WCKgRKikRDx8+xPz583H9+nXUrl0b8fHxiI+Ph1gsxvDhwxEaGorg7NdhWFgY4uPj0bdvX/72+/fvx7lz55CVlYVGjRqhffv2WL9+PbZt24Zx48Zh1qxZOHDgAH/8zp07cfDgQTg7O6N169Zo2bIlVq5cibVr12LJkiX48MMPcfv2bQDAvHnzcO3aNZw7dw4eHh6YO3cuhgwZgjNnzuDy5cvgOA4XLlzgw4aoqCgAwIEDB3D16lVIJBK9x3vw4EFMnjwZu3btQnBwMF69eoXnz58bfG4EAgFWrlyJFi1a4PXr1xg4cCA+/fRT/Pjjj3B2dsb27dsREhKCNm3a4MiRI3j48CF27Nhh8nNMzE/T/0OzrOk3gxvpfEKfmJgId3d3KFUMciWDTKGCTKmCXKmCTJH9Vani92muay7LlSrIFQxSpQpyRe7bMb3z5NxO975yjsu1XbNNqbLgs2iYigFShQpShQqQ6u8XCTiIhQJIRAL1VyHHXxYLBRCLBLARCiAWcfw2iUgAiVAAsdaxEq194ux9NrnOIxEKIMk+j0RrW87tOIPn4cyUgGlWHNK8zlpW98j/RqRYWW0I8u+//2LSpElo1qwZFAoF5s6di65duyI8PBwODg4AgOnTp+Pw4cPYtWsXXFxcMHnyZPTr1w/n6ZMwQgghZdm6dTmNUKdPV3+lRqikBAiFQjDGcO/ePfj5+cHb25v/8GnMmDFo3rw51q1bB0dHR4SGhuLdd9+FjY0Nf/uZM2fC3d0dANC+fXsIhUK0yZ7GNXDgQIzXnt4FYMKECfD19QUA9OjRA2fPnkW/fv0AAIMHD8bSpUshk8kgFouxfv16nD9/Hj4+PgCAZcuWwcHBAU+fPuXPYcjChQvh6upqcN/69esxdepUdOzYEQDg5eUFLy8vg8c2aNCAv+zt7Y0ZM2bgk08+4be1aNECs2fPxjvvvIPY2FicPn2af0+rLa/nmBTNlgtR+OdeHPwrOKCOjzMA4N0WVRH1Kh3VKjggLiULv12M5o+vbZ+OvyLM0yNGLFL/8W1vk/+xBcbUIU1pClkUKgaFSolMudLs5zYXTeAi1gpc+NBEK2jR3q57PSdY6fWWD2KTM1GtggOOh8dj26VoDGnmi271fCz9MMslqw1B/vnnH53roaGh8PLywrVr19CuXTskJyfj559/xvbt2/lfTJs3b0adOnVw8eJFtGzZ0hJlEzMryQ7tCQkJGDx4MK5evYqQkBDs2rWr2O+TEEIKbN484PPP1ZeXL9edEkPKpMTERLx+/RoA4OLiAnd3d0RG5qw8EBgYiNjYWL6hp6enJyQSCT9iQSKRwM/PD9HR0ZDJZACAypUrQyaTISEhAQDg7u4OD4/8P50MCAjAli1bsG7dOowePRotW7bEqlWr0LBhQ9SpUwf16tXD7t27MWTIEOzcuRMnT57Uub32H/P29vY64YO9vb1eU9Lcx+e+zhhDRkYG5HI50tPT0a5dO51PbyUSSb4hSNWqVY3ui46OxogRI4w/IVoePXqEjz/+GFeuXEFaWhpUKpVej5ExY8Zg0aJF6Nq1Kxo3bmzwPHk9x6TwjoXHY+GBewDU02Byu2Bg2/pePvjsUKTedlI+yJQqyJSA+j/mcS0mib98+kEC9QexEKsNQXJLTk4GAP7Tg2vXrkEul6Nz5878MbVr10bVqlURFhZmNASRSqWQSnPGZKWkpBRj1cQYa+zQvmnTJgiFQiQlJUEgoHY5hBAr9OWXOQEIANSta7laSInx8PDQCygCAwN1rmtGP+R1jJ+fn8713CGEqQYNGoRBgwYhMzMTCxYswPDhw3Hnzh0A6j/yQ0NDYWNjAz8/P6N/6Jubh4cH7O3tcenSJdSuXdvgMcaGtuf1O9/Pzw+PHj0yqYYPP/wQNWvWxJYtW+Dq6oo///wTo0aN0jlmzJgx6N27N86cOYMDBw6gj5HRW3k9x6Rwwh4nQsCpp2kAQCUXW1R2s8se+cAgUyjVIyAUjB81cf5ppmWLtkICDvy0FIlIyE9j4aeniHJGQmimmFBflRz/xaYgOjEDDICQAy4+SaQQxAJKRQiiUqkwbdo0tG7dGvXq1QMAxMXFQSKR6P3y9vb2RlxcnNFzrVixAosXLy7OcokZmLtDuynni4yMRN26dQsdgFBXeUJIsXr8GFi4MOe6UAj8+y/wzjuWq4mUOw8ePEBMTAzatGkDiUQCR0dHiEQ5bycHDx6M6dOnY+XKlXj//fdLrC6BQIAPP/wQH3/8MTZu3AhfX18kJibi+PHjGDx4MAD1e8THjx8XaETFBx98gLFjx6Jdu3Zo27Yt3xOkUaNGesempKTAyckJzs7OePr0Kb788kud/d999x0ePnyI69ev49SpUxg9ejRu3bqFSpUq6RyX33NMCid3/4/F79TL949PhUKBZUOEOlNNZLm/avX60PT+0J56Isvui5Ez1UTJX5ZqHaM9bSX3dpnWebX3aQKdkqRiQJZchSy5CoDCpNtoem7kFZbobNdsM3AbG60eHhKRkJ+aYmPgvGKheruxcwsEJZ/OUH8Q61AqfqJOmjQJd+/exblz54p8rjlz5mDGjBn89ZSUlDyHSFq71atXY82aNXjz5g08PDwwf/58jBw5ElWqVMHOnTv55mSAukP7okWLMHjwYHAch7Vr12L9+vWIjo5Gv3798N133+HDDz/E33//jYCAAPz+++/8pynVqlXDBx98gL179yI8PBzt2rXDtm3bMH/+fGzfvh2enp7YsmUL3n77bQDqQGDp0qXYtm0bkpKS0Lp1a2zcuBGVKlXS6dAuEAgwd+5cvPvuu/D398cvv/yC5cuXIzU1FfHx8XojRn7//XesXLkSkZGRcHNzw+LFi/U+ZQGARYsW4erVq/D19cXOnTsxevRofPXVV/xjjouLQ8OGDbFhwwbUqVMHAwcOxJ9//gmO4/DTTz/h22+/xZgxY3D8+HHMnTsXDx8+ROXKlbFixQr+U5tRo0ZBKBQiNTUV//zzD5YvX44PP/zQ6OMG1J9CbdiwAevWrUNMTAyCg4Px22+/wcXFBQAQERGBjz/+GGFhYVAqlQgODsbevXsBAI8fP8a0adNw8eJF2NvbY9y4cZg7dy6NWiGkPHj1CujeHcjM/lRSKKRGqMQiZDIZPvvsM4SHh0MgEKBBgwY6q6U4OTlh4MCB2LZtG4YNG1aita1YsQKrVq1Cx44dERcXBw8PD3Tq1IkPQZYuXYopU6Zg7NixmD17NoYMGZLvOfv27YuUlBRMmjQJ0dHRcHd3x9KlSw2GIKtXr8YHH3yA77//HjVr1sR7772He/fU0y9u376N+fPn831AevXqhXfffRfDhw/HsWPHdM6T33NM8nf0XhxOP0xAMz83tK+l7uHSxM8N3wxqgKvRb9DUzw1N/NzwOl2W53lePouCV5VqOts0fR70u7mUPIVKK1zJDkekuYIZTX8Pve2asMZAmKPephkRozR8H0rdcynySGTUIZIS6WacVmIO2s1ZDYcymlEuWiNehLkClVyBjbHzaZqxujtI8FnPOrj3IgWN/dwQVMkZu689xd3nKWhdowKNCikhHGPMAhmi6SZPnoz9+/fjzJkz8Pf357efPHkSnTp1wps3b3RGg/j5+WHatGmYrmkUl4+UlBS4uLggOTkZzs7O/PasrCxERkbC398ftra2Zns85vTw4UM0bNhQr3t4/fr1MXPmTLx69Yr/pRkWFoaePXsiNjYWNjY24DgOnTt3xs6dO/kO7d7e3li/fj1atmyJcePGITExke/QXq1aNbi6uup0aJfJZFi5ciXeeecdLFmyBPv27eM7tM+aNQvXrl3D1q1b+Q7tly9fxpkzZwDoT4eJioqCv78/+vbti82bN0MikcDe3l7nuIMHD2LUqFF6HdoNvRFZtGgRli1bhp9++gnvvfceZDIZQkNDsWnTJuzevRv+/v5Yv349vvvuO4SHh0MikWDUqFFwdXXFmjVrAKjfsLRv3x579uxBcHAwLly4gJ49e+Ly5cuoVasWRo0ahT/++AP79u1Dly5dkJWVhUWLFuX7uDt06IAdO3ZAIpGgY8eO6NOnDxYtWoT09HQEBQVh2LBhmDdvHsRiMc6fP48OHTogIyMDQUFBmDZtGiZOnIi4uDj06NED06dPx5gxY3Qee2l47RJCCiAzE+jcGbhwAfDzAxYvBm7dsvpGqMZ+v5LS/d7DFEuWLMHt27exe/duS5dSppWV14u5aT5pN4f1vXww8VCsWc5FiCmoR0jRmPrew2o/QmaMYfLkydi3bx9OnjypE4AAQJMmTSAWi3HixAl+m2b4YKtWrUq6XIvQ7h6emZkJb29v1K9fH4B6zumePXv4nhp5dWivVKkS2rdvj7p166JNmzYQiUQYOHAgrl+/rnN/mg7tLi4u6NGjBzw8PNCvXz8IhUIMHjwYd+/ehUwmA2MM69evx+rVq+Hj4wOJRIJly5bh/PnzePr0aZ6PSdOh3d7eXm+fdod2gUAALy8vgwGIRr169TBq1CiIRCLY29vj+++/x5IlSxAYGAiRSIQpU6YgMzMTly5dMnj7TZs2YdSoUfz9tWnTBr169cIff/zBH9O1a1eEhIRAIBDAzs7OpMc9a9YseHl5wdXVFf3798e1a9cAAIcOHYJYLMby5cvh4OAAiUSCDh06AAAOHz4MNzc3TJs2DRKJBFWrVsXUqVOxffv2PJ9PQkgpp1IBw4erAxBXV+Cvv4CRI4HVq606ACHlV0JCAn788UdMmDDB0qWQcirscSKoBQUpjYQch4tP9Bv0EvOz2ukwkyZNwvbt27F//344OTnxfT5cXFxgZ2cHFxcXjBkzBjNmzIC7uzucnZ3x0UcfoVWrVsW6MsyECROMrg9vLpUrV8aGDRvyPY46tOct97mioqLw3nvvQSgU8ttkMhmePXtm8PZRUVE4efIkNm/ezG9TKBQ6qaL2fbx69cqkx12xYkV+n4ODA1JTU/nHFxAQYLBxW1RUFO7evavzPVKpVKV6KhchxAT/+x9w4AAgEgF//gkEBVm6IkKMWr58OT7//HMMHz4cnTp1snQ5pJzK3fvjm0EN8HaNCnwPjtz9PKQKJb+N3599/ZFUhckdHPjjdW+vNHAulf6x2duUlmjgUQBCgbrPho1YtxeHRKuvhs4UD5GQv2yjt0/3so3OMUK9YwzdXlhOuqke/y8e43+7Rj1CSpjVhiCaECA413znzZs38z0gvvnmGwgEAvTv3x9SqRQhISFYv359idRlLahDu3G5z+Xr64s1a9agW7duJt3e19cXU6dOxcqVK026D1Med178/Pzw+PFjMMb0nh9fX180adIEFy9eLPB5CSGl1PDh6gAEABQKIHuVNEKs1bx58zBv3jxLl0HKuS5B3vhxRFNcfJKIltU9ijS1IDY21uDKS4WhVOX01ZAqlbp9ObQCE2mu64YCm7yOMRTmGLucu75MlRKZcuvo26EJZfIKY3QDm4KFMnkHNkK97SIBZ/Tvl6LoWrei2V6vxHRWG4KY0qrE1tYW33//Pb7//vsSqMj6UId24z1BDJk0aRIWLFgAf39/1KpVCykpKTh16hQ6duwIJycng/fXrVs3hISEoF27dlAoFLh+/TpcXV1Rp06dQj3uvPTs2RMzZ87EggUL8Omnn+r0BOnVqxfmzJmD9evX4/3334dYLMajR48QGxurFxQSQsqAZcuArVtzrguFwOnTNAWGEEK0/HU7Fn/djUXdSs5oVs2d3+5mL0b3euqRt1ejXhf6/JL0ZDyX2uR/oJlo/uBGCdwlAyDXClR0gpPs5YJNCWbyCl20R9nIlQUbCWNtoQzHQTdkMdQcVSuMMRTE6IU4WtcbV3UDAPz7MAG3nyUhNjkLHWp5UShSTKw2BCH5ow7txju0GzJ58mQIhUL069cPT58+hZOTE9q0aYOOHTsaPL5Ro0b4/fffMX/+fPz3338QCARo2LAhvvrqq0I/7rw4Ojri+PHjmD59Oj/NpkOHDujQoQO/b9asWViyZAmysrIQEBCATz75xKTHTggpRZYuBRYsyLlOK8GUO1bes55YifL+OjkWHo+J29X96w7dLp7mpet7+WDib2HFcm5SujAGSLPDotQSus/tl2KoUWoxsfrVYYobdWgnZU1Zee0SUi4tWQIsXKi+vGKFugfI6dNWvxKMIbQ6jHHGnhu5XI5Hjx6hUqVK/NLphBiTnJyMFy9eoEaNGhCLxZYup8QtORiOzRcioflLxkYkgFDA5btca0G0r2aPf6MyzHIuS5GIBLDRmjoiFgmocawVe50uQ0qWAoC6Ueqo1tXwWS/qB2YqU9970EiQMkzToZ3WlieEECt34IA69ND0/fniC2DWLPXlUhZ+kMLTrGaWkJAAsVicZ58sUr6pVCokJCTA3t5eZyp0eZK7Aeq6dxvzn5hr+m/wPTT4f0qdqR/SXNM2cl+3EyjhX4mpp3zIs6d+yJW61/M4Z0GngBQHzdSUVGnONp1mpUIBbMRCnR4b/Nfs3hg2/HSO3Nd1e2jkdZzedqEAAgHFMblplnimRqnFq3z+1CwHqEM7IYSUEgcOAO+8k3N95MicAISUKxzHwcfHB5GRkYiOjrZ0OcTKCQQCVK1atViaNZYGeTVAFQo42EmEsJMI8zhD/iIiIhAYGFjo26tUjO+ZUdAARqr1L7/j8tye3aNDGx+MFOnZKbrcjUzzDlGE+scZDXAMHKt1Tp3mp9kjiKyFORv7EuMoBCmjqEM7IYSUEt9+m3NZIADc3Y0fS8o8iUSCwMBAyGQyS5dCrJxEIikXo4WOhccj7HEiWgXo/0HYJcjbqv9IFAg42AqEsBULAVhuyhJjTKeBaYkFMAZG4GiTKdWjadKkRgovISIBV7BRLNnXbUw8ztDoGYlQqDfyRiRU//+c+3Wd1/8DpHAoBCGEEEIs5cAB4NQp9WWOA1QqaoBKIBAIqKcTIciZGgAAv5yPhJ+HPVzsSi5MGF7PAR8fOVdi91dWaEZYOObazhggV+oGJDKFUv1VqYKlOlUqVAwKmRLpMiUAuWWKQM6ywNrhiFyhQlyKFByn/n+AGqWaB4UghBBCiCVcvAgMGaJ+V9i5M1CvHtChA/UAIYSQbGGPE8FBvZwrAEQnlmyT0k+eJZfo/ZHyLa9lgRlTN0q9+CSRQhAzoBAkH+V88RxSCtFrlpBS4OFDoHdvIDMT6NED+PNPoByu7kAIIXnRND8VcICKAWPb+CPQ21E9ikBuuPGpenv2Za3j+GPkSp2pHjKlyuj9Lwj2xJLTCSX4iE0jFnI60zFsxEKdXhc2Yq3LIkH29dzTN/SPk4gEEJTTHjPW6kbMG3x38hGEHKhRqhlRCGKEWCwGx3FISEiAp6dnuW06RUoXxhgSEhLAcVy5XC6PkFIhPh7o1g149Qpo2hTYuZMCEEIIMaAkmkTyzUt1whIlsuQqqJJjsX1cdb0wRVbo0MXw9oKSKxnkSkWx9NJQrwqjG5xI9IIW4wFLfoGMsQBGcx5ralJqDTrU9sJbVVypUaqZcaycf2yc11rCaWlpePbsGX2yTkoVjuNQpUoVODrmnolJCLG4nTuBKVOAly+B6tWBsDDAy8vSVRWLvH6/lnf03BBSOhR1dRhTaDct1QlQChW66O43ZZRMlkJpsV4chmialBoLU3I3Jc135ItOSKO1QoyR8EYk4OjD71LM1N+vNBIkD46OjggMDIRcbrkGOYQUlFgshlBYtCXhCCHFYM8edQ8QjU8+KbMBCCGEFIS1rn5RuXLlYr8PjtNMbRECFuiHzBiDQsV0RqfohC75BC0FDV0MjZJRqHJSGN0mpSVPwCHPYEXTsNT4aJi8QxmJsfBGE/IIBfmGMNb6/0tpQiFIPoRCIf1BSQghpGhkMnXooSEQqPuCEEJIOZd7BZi3KjujgqONhatSq+0uxP3XlvljvKwQCzmIhSLk9S1VMuRMFcpjOlFJUDEgU264OWlJMTa1SCISIEOqwMOXaRDQajFFQiEIIYQQUpxkMmDQICAyUn1dIKClcAkhJFvY40Sd63eep1ioEn0De/lgQ5j1NUYlZRsf+mQpjB6jotViioRCEEIIIaS4yOXqKTD79wM2NsCcOUBysjoAoaVwCSGEXwGG49TLgA5oXBm+7g58c1LNqIAsue5X7VEC/Da5ElkKFZQqK2pyYaKcaRbqT/9tsy9rvtqIBbDN9VV9nFDnq0SU/3QKUnrde5GMLReiIaDVYoqEQhBCCCGkOMjlwNChwL596gBk/34gJMTSVRFCiFUpjhVgFEoVsgyEJNoBit62XEGKVK5Euoqhb8NKJt02K7uXRmHJlOrlelNh/NN/U2n6TthqTafIHZZoByy24pypF/x+U24rFsJW61ixUFDk2kl+fNGmhietFlNEtDoMdWgnhBBibnI58O67wO7dgEQC/Pkn0L27pasqUfT71Th6bggpm3Ivt5uV62teAYopt5EaCWKy5EpYw+AXYfbKLobCFxtj4YveKBf9QMZocKM1IoZGvxCAVochhBBCLGPfPmD2bCAiAhCLgb17y10AQgghZUFBl8gVCDjYCoSwFQsBiIuvMAO0R7+YOgrG0OiX/KYg5d6mPfpFqWLIkCmRYYGVXXKPfjFpFEyukSx6o2EM3VbrNrYiAUQ0+qVUohCEEEIIMZc//wT69cu5PmsW0LOnxcohhBBrQEt6Fj+RUABHoQCONiX755326JcsfllcU0fB5NzG0G2ledw29+gXWXYgk5pHM9HikHv0i3aAoh+qGBsFkx2q6PSEMX7b3KNf6P+vgqMQhBBCCDEHxoAlS3KuCwRARobl6iGEECtw9F4cxv92DYB6SU93e3H2SAnrtyjYAyN3n7B0GSQbB8BOLISdWAjYiSFXMbP0YykKS49+EXJAplwFDrRkbkFQCEIIIYSYw1dfATduqC/TMriEEAKlimHVkQc6215nyAHILVNQAc34OxZpMsv8cU1IfrSDHwZaMrcgKAQhhBBCiuq339RTXwBg9GjA1ZWWwbVCz58/x+zZs/H3338jIyMDNWrUwObNm9G0aVMAAGMMCxcuxI8//oikpCS0bt0aGzZs0OkJ8Pr1a3z00Uc4ePAgBAIB+vfvj2+//RaOjo6WeliEWCWliuGT3bfw6GUaAPBL4M7rWRst/EvJsp5ZKYAtNS8m1utSZCKWH74PIcfRkrkFQCEIIYQQUhRHjgDvv6++PGMG8PXXlq2HGPTmzRu0bt0aHTp0wN9//w1PT09ERETAzc2NP2bVqlX47rvvsGXLFvj7++Ozzz5DSEgIwsPDYWtrCwAYNmwYYmNjcezYMcjlcowePRrjx4/H9u3bLfXQCLE6ShXDzF23sO/GcwgFHMa08YdSxUrdkp4REQkIrOJq6TIIMap+FVdU83CkJXMLiJbIpWXqCCGEFNbVq+oRH+npwNChwNat6qkwxOp+v3766ac4f/48zp49a3A/YwyVKlXCxx9/jJkzZwIAkpOT4e3tjdDQUAwZMgT//fcfgoKCcOXKFX70yD///IMePXrg2bNnqFSpkkm1WNtzQ4g5KZQqfLzrFvbffAGRgMN3Qxuhx1s+li6rUAq6OgwhxLJM/f1K79QIIYSQwnj0COjRQx2AdO4MhIZSAGLFDhw4gKZNm2LgwIHw8vJCo0aN8OOPP/L7IyMjERcXh86dO/PbXFxc0KJFC4SFhQEAwsLC4OrqygcgANC5c2cIBAJcunSp5B4MIVZKoVRhxh85Aci6d0tvAAIA7u7uli6BEFIM6N0aIYQQUlDx8UBICJCQADRqBOzZA0gklq6K5OHJkyd8f48jR45gwoQJmDJlCrZs2QIAiIuLAwB4e+sOJfb29ub3xcXFwcvLS2e/SCSCu7s7f4whUqkUKSkpOv8IKWsUShWm7byJA7fUAcj3wxqjW73SG4AAoF4/hJRR1BOEEEIIKYidO4EpU4CXLwF/f+CvvwCa0mD1VCoVmjZtis8//xwA0KhRI9y9excbN27EyJEji/W+V6xYgcWLFxfrfRBiSXKlCkN/uIir0W8AAEObV4WdWIgzDxMsXFnRuMheIVlSwdJlEFIg12Pe4HFCGvo0qEw9QoygEIQQQggx1Z49wJAhOddnzQIqVrRcPcRkPj4+CAoK0tlWp04d7NmzBwBQMfv7GB8fDx+fnE+v4+Pj0bBhQ/6Yly9f6pxDoVDg9evX/O0NmTNnDmbMmMFfT0lJga+vb5EeDyHWZNmhcD4AAYDfLkbjt4vRFqzIPNb38sHEQ5ctXQYhhXLwVix+HNGUghADKAQhhBBCTKFSAfPn51wXCoGHDy1XDymQ1q1b48GDBzrbHj58CD8/PwCAv78/KlasiBMnTvChR0pKCi5duoQJEyYAAFq1aoWkpCRcu3YNTZo0AQCcPHkSKpUKLVq0MHrfNjY2sLGxKYZHRYh1SMlS6Fx3d5CgorOthaoxHxUECPKhkX6k9IhLycLrdBl//fyjVxSCGEAhCCGEEGKKTz8F7t9XXxYIAKVSvTIMKRWmT5+Ot99+G59//jkGDRqEy5cv44cffsAPP/wAAOA4DtOmTcOyZcsQGBjIL5FbqVIl9O3bF4B65Ei3bt0wbtw4bNy4EXK5HJMnT8aQIUNMXhmGkLKox1s+6uVwOQ5KxvBF//pl5g+vXm0sXQEhpjsWHo9xv17lr8uVKgtWY71oiVxapo4QQkh+vvkG0ExnmDpVHYIEBwN9+li0LGtmjb9fDx06hDlz5iAiIgL+/v6YMWMGxo0bx+9njGHhwoX44YcfkJSUhDZt2mD9+vWoWbMmf8zr168xefJkHDx4EAKBAP3798d3331XoAaK1vjcEFJUx8LjcfFJIlpW9ygzAcizZ89QpUoVS5dBSIEcC4/HL+ciEfYkERWdbXH6k2DYioWWLqtEmPr7lUIQeiNCCCEkLzt2AEOHqi+vXAnMnm3ZekoJ+v1qHD03hJQOERERCAwMtHQZhBSYVKFEhy9P40VyFhb0CsL7bfwtXVKJMPX3Ky2RSwghhBhz4gQwYoT68pQp6kaohBBCCCFWzEYkxOSO6gBv/elHyJAp8rlF+UIhCCGEEGLIjRvA//4HyOXAoEHqKTEcZ+mqCCGElJC8Vn0ixNoNbFoFVd3t8SpNhl/DSv9qTeZEIQghhBCSW2Qk0L07kJqq7v3x66/qPiCEEFIOHQuPx5KD4TgWHm/pUgghJhILBZjSST0aZO2JCMz/8w79P5yNVochhBBCtP32m3rqS1ISUL8+8OefAC1vSggpp7RXm/jlfCT8POzhYie2cFUlY1ozJ6y5kmrpMggpNIVS3f4zXabEtksx2HoxBj+OaFpmmhcXFoUghBBCiMYff+T0AAGA6dMBFxfL1UMIIRYW9jhR53p0YoaFKil5WQ3tcftZsqXLIMQsGAOEHIeLTxIpBLF0AYQQQohVkMt1V34RCoHbty1XDyGEWIFWAR745XwkBBygYsDIt/0Q4OmILLkSmTIVMuXK7MtKZMqV/PWs7MuZMiWy5Cr+cqZcaemHpIPjADuxEHZiIWzFQthJhLAVC2AnFiJZzqFrkDfsJLr71ZcFurcRCSEUUN8oYn1uxLzBdycfQchxUDKGltU9LF2SxVEIQgghhDAGjBsHREWprwsEgFKp7gdCCCHlWJcgb/w4oikuPklEy+oeRf4EmTEGqUKlE5LkBClaoYqhcIU/1kj4kmu/afUAGTIlMmT6x1+JelOgxyYRCbQCFYFOaGInFsJW+7ImRNHapg5gtAIXsRB2EoHWZXXYIqCwhRRAh9peeKuKq9n+Hy4LKAQhhBBC5s0DtmxRj/6YMwdIT1cHIH36WLoyQgixuC5B3mb7w4njONhm/5HvapYzGqYJW7RDkkyZElJFTtiiHZzwo1YUOdu6+nLYcV+mO6pFoXubLLmKv0+ZQgWZQoXkTHkxPjLARpQrGBELYScW6IxY0d+fc0zu/blHudiJhbARCShsKUPM+f9wWUAhCCGEkPJt7VpgxQr15R9+AN5/37L1EEIIKTLtsMWtkOeIiIjATyPr53mMSpUdtuQavWJopIv2tCCT9/PhTU7YIlWoIC2hsEVnJEuu6UB5BSn576ewhVgOhSCEEELKr127gKlT1ZeXLaMAhBBCSIEIBJz6D3uJsFjvJ3fYkjtI0Z9CpDIYyuiGL6qc/QrjYUsSijds0UwN0p4eZKsXvAgM7tefUiTQHemSfXsbkQAcR2ELUaMQhBBCSPl0+jTw3nvqCeETJwJz51q6IkIIIVakatWqli6BV5JhiyYQ0e7Vor9Nd0qQsf4sxvbLtMIW9X4V3hRz2KI9KsVGK3jRnTKUHZrks9/YSBcKW0oHCkEIIYSUP7dvA++8A8hkQL9+wHffqZcIIIQQQrKlpaXBxsbG0mWUKIGAg71EBHtJ8f6ZqFQxndEp2o1xDY5u0evfotJdhcjg6BgVZMqcsEVzXHHSrDaUM5JFoDcFSNPgVidckeivNqS7X3vkiwASIYUtRUEhCCGEkPIlOhro1g1ISQHatQO2bVM3RCWEkHJo3/Vn2H/rBWp4OeKtyi6WLseq+AqTce5plqXLKLc4DrCXCGFfhNEv6rDF+GpC2iNcMuWqXCNY1P/kSmby/eW12pA5GVraWXt6kK1IYLTpra1EiMcvU5GcqUCPt3zKZcNUCkEIIYSUH4mJQEgIEBsL1KsH7N8P2NpauipCCLGIY+HxmP7HLQDA6QcJFq7G+qzv5YOphyItXQYheswVtuy78Rw/jmha7oIQCkEIIYSUD7t2AVOmAHFxQJUqwN9/A66ulq6KEEIsJuxxIgQcoMr+oNvVXgwnW5H6k3GZEhlyJZjpH4JbBe1PyDWffttnTysQCQs2fSAqlaF1DY9iqpQQy3iSkI7YZPUIJyHH4eKTRApBCCGEkDJn925g0KCc67Nnq4MQQggpx1oFeOCX85EQchyUjOHLAQ10/hhiLHtFEplu34VMufoTaPVlBTJlKmTIFMjSbM+eRpBzTHaoIlPqHJO7QaY56HxCnq67TyIUwFYsgL1ElDM9QGI4MLGXCMFJBOhQS2RgnyjnNhIh7GkFElKKHAuPx7hfr/L/37esXv6CPgpBCCGElG3p6cCMGTnXBQLgyRPL1UMIIVaiS5A3fhzRFBefJKJldQ+9T4M5juOXG3UrphoUShWyFNkhikyFDLmCH4mSaXKoouB7OmRqLhsYzSJTqhtlpmQpTKptfS8fTDwUa/JjyWsUir1Es03EN8G0yw5T7A0FMVqXtfeJhILCPM2E8PL7/748oBCEEEJI2ZWSAvTsCTx9qr4uEAAqFRAcbNGyCCHEWnQJ8rboH0EioQCOQgEcbYrnz5KijGZxsVPhnYaVTB7NktcoFHMp6GgW7RErNJqFaFj6/3tLoxCEEEJI2fT6tboJ6tWrgIsLMG+euiFqcDDQp4+lqyOEEFICijKaJSIiAt8OCcz3OGsezVJQ5h7Nwm+n0SzEilAIQgghpOyJjwe6dAHu3AEqVACOHgUaNbJ0VYQQQkqRwMD8AxCg5EezaIITs/VmkSkhU5aO0Sya6zSahRQFhSCEEELKlmfPgM6dgQcPgIoVgePHgbp1LV0VIYSQUiY2NhY+Pj6WLqP09WbJPfXIikez2EtEsBUb7r9Co1nKLgpBCCGElB2RkUCnTuqvVasCJ04ANWpYuipCCCGlUFpamqVLKDHWPJol08BXGs1CioJCEEIIIWXDgwfqAOT5cyAgQB2A+PlZuipCCLGIY+HxCHuciFYB5XP1B2JdrGk0S96hinWNZtEEKcU9mqW8/bygEIQQQkjpd/u2ugfIy5dAUJB6CowVDGEmhBBLOBYej3G/XgUA/HI+EpVd7eBkS2/7C6qRtwQ3Dpu+RC4pWwQcBweJCA6SnP93ZAqVwdEn5qYzmqWYaEazCDgOSZlyAOqfFz+OaFrmgxD6aUgIIaT0OnAA+P134OBBID0daNhQ3QTV09PSlRFCiMWEPU7Uuf48KdNClZRuKrkEDxNlli6DkGKhGc2iTcABF58kUghCCCGEWKUDB4B33sm5XrMmcOoU4OpqsZIIIcQatArwwC/nIyHgABUDRreuhuqejsiUKfj+C5pPmTPlipzLsuzpANlD/zNkSsgUxfNJt6kkIgHss3sl2NuI+GH99hIh34/Bnu+nIMq5zG8XQVjI3gpOsgSkSihUJ2Xbteg3+Ob4Q/7nRcvqHpYuqdhRCEIIIaR02rJF93qXLhSAEEIIgC5B3vhxRFNcfJKIltWLNsdfoVTp9E0wHJzohieaMEVnv1ypE8KkyxTIkucfsMgUKsgUKiRBXujHoB2k2OUKT+yzeyvYa4cp2eFJkD1Dapacv41OwCJWn0MiolVCSOnWJrACgio5m+XnRWlh1SHImTNn8OWXX+LatWuIjY3Fvn370LdvX37/qFGjsCXXm+CQkBD8888/JVwpIYSQEnXokHokCKDuHsYY0LWrZWsihBAr0iXI2yx/zIiEAjgJBXCyFZuhKl0qFdNZHSRDnnukioK/nCk3EKxoBTI622QK3SaWhQxSFgR7YsnpyDyPEQk4rUBFlNOcUpJrtIo4J1zRG62iF8Kor9MKIaSkmOvnRWlh1SFIeno6GjRogPfffx/9+vUzeEy3bt2wefNm/rqNjU1JlUcIIcQSdu0C3n0XUCiAli2B5s3Vq8L06WPpygghhBSAQMDBwUYEh2JYllWzJGvuMMXYSBbNKBXtkSynnivR1M/NYAijUKkTFoWKITVLgdQsBQCpWR+DIHuFEE1wojNSxcDoFf0QxvDoFQcbIWxFQggEFLCQ8smqQ5Du3buje/fueR5jY2ODihUrllBFhBBCLGrLFuD99wGVSh2EbNkCiKz6VxkhhBAL0F6S1d1BUqhzREdHw8/IUusyhSrf0Su5pwAVtA+LigHpMiXSi2mFkNyjVuwkIq0RK/ojWQwGK0ZGsggpYCFWrNS/czx9+jS8vLzg5uaGjh07YtmyZfDwKPvNXAghpNzZsAGYOFF9eexYYONGQCi0bE2EEELKLJnM+MowEpEAEpEALjD/NKHC9mFJlyp0RrLo3l69TbsPS6ZcvR3pZn8Ihe7DYm/CSBbqw0KKqlSHIN26dUO/fv3g7++Px48fY+7cuejevTvCwsIgNPLGWCqVQirNGaqWkpJSUuUSQggprK+/BmbOVF+eMgVYs0bdC4QQQggpY8pzHxZTUB8WUlSlOgQZMmQIf/mtt95C/fr1ERAQgNOnT6NTp04Gb7NixQosXry4pEokhBBSFIwBy5YBCxaor8+ZAyxfTgEIIYSQYle5cmVLl2B21t6HRWd/KevDYm+T90gW6sNiPUp1CJJb9erVUaFCBTx69MhoCDJnzhzMmDGDv56SkgJfX9+SKpEQQoipGAM+/RRYtUp9fdkyYN48y9ZECCGk3JDJZLC3t7d0GaWGOfqw5IX6sFAfFnMpUyHIs2fPkJiYCB8fH6PH2NjY0AoyhBBi7VQqYOpUYN069fVvvgGmTbNoSYQQYg3+uh2LMxEJaOznhnaBnpYup0x7ExePLM7W0mWQXDhwcJCI4CAx35+yCpUKWXKl3miVDJmCnz6UIVMiI1ffFVNGrmgrLX1YbsS8wf24VATX8iqTS+dadQiSlpaGR48e8dcjIyNx8+ZNuLu7w93dHYsXL0b//v1RsWJFPH78GLNmzUKNGjUQEhJiwaoJIYQUiVIJjBsHbN6snvaycSMwfrylqyKEEIvbc/0ZPv7jFgBgx5WnFq6m7FvfywfdQ09YugxCTFIcfVi2XYrBjyOalrkgxKpDkKtXr6JDhw78dc00lpEjR2LDhg24ffs2tmzZgqSkJFSqVAldu3bF0qVLaaQHIYSUVnv3qvt+PHwICATqJXDfe8/SVRFCiFW4EfPG0iUUiUjAlaqWTjfjsiAWlqKCCTEDpYpBM4hFwAEXnyRSCFKSgoODwZj+MCKNI0eOlGA1hBBCitWePcCAATnXP/mEAhBCCNHSvqYXtl6MgZDjoGQMXw6oj6bV3JEuVQ/ZT5eq+xykaw3Vz5Cqv+ps4/dl91eQKpGea/nU4qBkDHainCH39hIhHGxyLmtvt5eI4GCjHq7vkHubWLNPCIfsxpTF1XBy7oD8jyGkLDkWHo9xv17lf860rO5h6ZLMzqpDEEIIIeVERgag1bQaAgEgk1muHkIIsUJdgrzx44imuPgkES2re5j901klv3xqTjCiCVUyZQqkS7MbSUoVOduy+x+kS3MFLLkuA+p+19rXzclOLNQNRrK/8qGKZuUOG91Qhd+nCWW0tr2IjkTNmoFmr5UQa1bcP2esAYUghBBCLCs1FejVC4iJUV8XCNSNUYODLVoWIYRYoy5B3sX2R4lQwMHRRgRHGxHgZL7zqvhwRXc0SrpUf5smJMkZ1ZJrm1yJdGlOAKPBN5w0o/W9fNDnt791QhU7iVBnNIomSHHIbjKpvS336JacUS+0kgexbsX5c8YaUAhCCCHEct68Abp1Ay5fBpydgblzgfh4dQDSp4+lqyOEEGIGAgEHBxsRHGxEAMzXu48xhiy5Sh2UZE/tUQckmvBEa9qPVsiSc3zOdKEM7VEtMgU0M/Kz5CpkyWVmX83DRrOSh5FpP7r7co1usVGvAOJgkyuckQghEgrMWyghZRCFIIQQQizj5Uuga1fg1i3AwwM4ehRo3NjSVRFCCCklOI6DXfbSnnA033kZY5AqVEjNkOJsUG0+OMnMNRpFO1RR7zM8qkV7epGm4aRUoYJUocKbDPOt5AHkLJOqHYzoTPsRC9UhiiZk0ezX2ZYz4sVerN4npnCFlCEUghBCCCl5z58DnTsD9+8D3t7A8eNAvXqWrooQQggBx3GwFQuRIk2Dr5eX2c6rCVd0RqUYamYrM9J3RWvEi2Z0i2a6kDI7XeGXSTVzuCIWcnxoYpc9tcdObLixreFmt5p9utskIgpXSMmjEIQQQkjJiooCOnUCnjwBfH2BEyeAQGo8RwghxLokJyfDy4whiCZcsRUL4e4gMdt5GWOQKVV6U3yMTfvR7rGiu093xEuGTAlFdrgiVzIkZ8qRnGnecEUk4PjgJPfUHu1QRbONnzakM6pFK5zJHtUiEQrAlab1mEmJohCEEEJIyXn4UB2APHsGVK8OnDwJ+PlZuipSTixatAiLFy/W2VarVi3cv38fAJCVlYWPP/4YO3bsgFQqRUhICNavXw9v75zmcDExMZgwYQJOnToFR0dHjBw5EitWrIBIRG+pCCGWwXEcbERC2IiEcDPzuWUKlV6PlXSpEplyRa7pPznNbnUb2hoa3aKETKlejlmhYkjJUiAlS2HWuoXZ4Yq9RLuPiu60H+0pQXYS3ca1xka82IgoXCkL6Dc2IYSQknH3rnoKTHw8ULu2egpM5cqWroqUM3Xr1sXx48f569rhxfTp03H48GHs2rULLi4umDx5Mvr164fz588DAJRKJXr27ImKFSviwoULiI2NxYgRIyAWi/H555+X+GMhhBQvd3d3S5dgcRKRABKRAC72YrOeV67UnRakuySzQi800V6u2dCoFk1jW5lCHa4oVQypWQqkZikASM1Wt4CDVs8UEb80c+5pP5rQxeBqQTa5lm+WiGArpnClJFEIQgghpPhdu6Zugvr6NdCggboJqhmHGBNiKpFIhIoVK+ptT05Oxs8//4zt27ejY8eOAIDNmzejTp06uHjxIlq2bImjR48iPDwcx48fh7e3Nxo2bIilS5di9uzZWLRoESQS8w1vJ4RYnqOjGbutEh1ioQAudgK42Jk3XFEoVdlTfHT7ruTepjNyRa67XDPfi0WqzG6Cq4A0O1xRMSBVqkCqVAGkmi9c4bTDFa1pPzorAhlaJchQ3xWtfXZiIYUrBlAIQgghpHidPw/06AGkpADNmwP//AO4mXvALiGmiYiIQKVKlWBra4tWrVphxYoVqFq1Kq5duwa5XI7OnTvzx9auXRtVq1ZFWFgYWrZsibCwMLz11ls602NCQkIwYcIE3Lt3D40aNbLEQyJlwD93Y3Hiv5doXNUNbQIrWLocki315VM4eflaugxSSOYMWpQqlmv0iabvivGRKXwAw2/L2Z4bY0CaVIE0qQIJRa42B8cBdmKt5ZbzaGarGdWSs1xzTjNbO7EId18k4X5sGloFeKBLkHf+d27FKAQhhBBSfE6eBHr3BjIygHbtgIMHAWdnS1dFyqkWLVogNDQUtWrVQmxsLBYvXoy2bdvi7t27iIuLg0Qigaurq85tvL29ERcXBwCIi4vTCUA0+zX7jJFKpZBKcz4xTElJMdMjImXB0Xtx+HDrdQDArmvPLFwN0ba+lw8mhp6ydBmEFBpj4AOYV2lFPx/HAb+cj8SPI5qW6iCEQhBCCCHFY8EC4PPPAaVSPRVm3z7A3t7SVZFyrHv37vzl+vXro0WLFvDz88Mff/wBOzu7YrvfFStW6DVkJUTj4pPX4AAwSxdSQBKhACJh2R5mn6FgsJcILV0GIRYnU6igUDEwBgg5DhefJFIIQgghhOhYuBBYujTn+vjxFIAQq+Pq6oqaNWvi0aNH6NKlC2QyGZKSknRGg8THx/M9RCpWrIjLly/rnCM+Pp7fZ8ycOXMwY8YM/npKSgp8fWmIPVFrFeCBX85HQshxUDKGNYMboJm/B9KlCn4ofbrWkqfq7Tm9CzTNI9OlCp2h+Zpj5criiVfUq3sI+MaPub862uQMs9fuU6DenrPMqearY/Z+sVBQLPUW1oBgS1dAiOUdC4/HuF+v8j+nWlb3sHRJRUIhCCGEEPM6eRJYvjznulCo7gvSv7/laiLEgLS0NDx+/BjDhw9HkyZNIBaLceLECfTPfq0+ePAAMTExaNWqFQCgVatWWL58OV6+fAmv7Ma+x44dg7OzM4KCgozej42NDWxsbIr/AZFSqUuQN34c0RQXnySiZXXzz7WXKVSGAxOtsESzMod2kJKe3b8gTaobrGRIc5Y3lSlVkGWo8CZDbrZ6JUIBv3qGXsCiCUxyBSualTYcbUQ6wYpDdghT2GDl2bNnqFKlitkeGyGlVXH/nCppFIIQQggxnwsXgD591FNgAHUAolQCwcEWLYsQAJg5cyZ69+4NPz8/vHjxAgsXLoRQKMTQoUPh4uKCMWPGYMaMGXB3d4ezszM++ugjtGrVCi1btgQAdO3aFUFBQRg+fDhWrVqFuLg4zJ8/H5MmTaKQgxRJlyDvYvujQr3EqQSuZhyMZyhY0R2RkhOsZGiFLppghR/JIjUerCQVU7BizwcpQv0RKZoRLNnH+olTEZ31Cg42+sdJRNY1YoWQ4lacP6dKGoUghBBCzOPqVaB7dyA9Xd0DZNw4dSgSHKwORgixsGfPnmHo0KFITEyEp6cn2rRpg4sXL8LT0xMA8M0330AgEKB///6QSqUICQnB+vXr+dsLhUIcOnQIEyZMQKtWreDg4ICRI0diyZIllnpIhFhEcQUrmTLjI1LSpVoBi9YUoTSpQi9Y0XwtarCyvpcPJh66ZHCfWMhlhyM5wUpOkKJ73egUIRtRTsBCwQohJYZjjJW2PkxmlZKSAhcXFyQnJ8OZViwghJDCuXNHHXa8fq1eBebvv6kHSDlHv1+No+eGkJKhHazoBimGR6Tk7sHiYw/cis/S6cEiU6iKrV6xkONHpzhoT+3RCVL0e7Copw7p92BxsKFghZQvpv5+pZEghBBCiubBA6BzZ3UA0qIFcOgQBSCEEEIsTj1iRQAXe3Ghbp+amgonJyedbXKlSmuqj+6UnnQDI1LSDDS3zZBqjWDRClbkSobkTDmSM803FUg7WNHuk5K714p6VEruHizZIUuuHiwSoQAcV7ZXBiJlm1lCELlcjri4OGRkZMDT0xPu7u7mOC0hhBBrFxkJdOoEvHwJNGyoHgGS6w0jIYQQUhrFxcXphSBioQAu9oUPVgyRK1XI4Een5B+s6AYpSr0eLGlSRbEGKyIBZ7BPik6Qkit00Q5WtBvfUrBCLKHQIUhqaiq2bt2KHTt24PLly5DJZGCMgeM4VKlSBV27dsX48ePRrFkzc9ZLCCHEWjx7BnTsCDx/DgQFAUePAm5ulq6KEEIIKVXEQgFc7ARwsSuuYEVrVIpew1rdYEU7SMl9rDQ7WFGoiidYMdQnJWd0iv6yynzAkmuVIE3oQsEKMaZQIcjq1auxfPlyBAQEoHfv3pg7dy4qVaoEOzs7vH79Gnfv3sXZs2fRtWtXtGjRAmvXrkVgYKC5ayeEEGIp8fHqESBRUUCNGsDx40B2c0lCCCGkLLCzs7N0CYVWHMGKQqky3E/FQMNavsdKriAlp5mtfrCSkqVASpbCbPVqByv8EsqGll42OKpFK2DROoeNiIKVsqBQIciVK1dw5swZ1K1b1+D+5s2b4/3338fGjRuxefNmnD17lkIQQggpKxIT1T1AHj4EqlYFTpwAfHwsXRUhhBBiVlWqVLF0CVZFVEzBSoY816gUrUa0muWVc0/7yd3EVnuKUEkGK0YDFk2oYnBUi24zWwpWSh6tDkMd2gkhxHRJSeoRINevq4OPs2eBgABLV0WsEP1+NY6eG0JKhydPnqB69eqWLoMUkCZY0Q5MtIMVzdLL/AgWvR4s+qFLlrz4VgUSZgcreksoS9QrBDka6LOi14OFghUAJbA6zN27d1GvXr3C3pwQQkhpk5YG9OihDkA8PdUjQCgAIYQQg46FxyPscSJaBXigS5C3pcshhaBUKi1dAikEkVAAZ6EAzrbmH7FiKDDRDlaMBiwGtmmCFaWKITVLgVQzjljRBCuafimOuYIVTZDiaGN4GpB2sKIJZnIHK6X5Z1yhR4IIBAI0a9YMY8eOxZAhQ/Q6J5cW9GkMIYSYIDMT6NkTOHUKcHUFTp8GGjSwdFXEitHvV+PouSn7Dt+OxaTt1/nr1TzszTqFgJSMqc2c8O2VVEuXQcooJWM5U3qygxGVFc/R0A5WGBjiU6QQcICKAT+OaGoVQUixjwT5999/sXnzZnz88ceYPn06+vfvj7Fjx6Jt27aFPSUhhBBrJJUC/fqpAxAnJ+DIEQpACCEkDyfux+tcj0rMsFAlpCjmJaUjNs18n84TUpoZGrGiYoCQ43DxSaJVhCCmKnQI0rZtW7Rt2xZr167FH3/8gdDQULRv3x41atTAmDFjMHLkSFSsWNGctRJCCClp+/YBn3wCPH4M2NkBhw8DzZtbuipCCLFq3ev5YO/15/ynpEOa+aKKmx3StFbS0PQpUK+UkXM5XaqAooQ/DrYVC+DIN3HUWhnDRgRHreH02suXOtiIIBKU7Z4DdqpMZApK7woxhBSXmzFJWHvqEYQcByVjaFndw9IlFYhZG6M+evQImzdvxm+//Ya4uDh069YNBw4cMNfpiwUNSSWEECP27VOPANFYvBhYsMBy9ZBShX6/GkfPTflwLDweF58komX1gs2XZ4xBplTxS49qQpI07evZfQc0oYn2MqVp0pxVMjRhi1xZPKGKjUgdnthn9w7ICUpymjRq9jvyAUtOyOKotbKGg40IYqGgWOosrIiICFrhkhAjCvszrjgV+3QYQ2rUqIG5c+fCz88Pc+bMweHDh815ekIIISVFJgNmzcq5LhCoV4YhhBBiki5B3oX6w4DjONiIhLARCeHuIDFLLTKFig9Q0mVaoQkfsmgHKjmNHTXbMnIFLjKluqGjVKGCVCFDYrpZyoREJOBHmWiCEe2QRHv1DMdco1IMhSoSkXWFKoSUJYX9GWcNzBaCnDlzBr/88gv27NkDgUCAQYMGYcyYMeY6PSGEkJKSlQUMHAg8eqS+LhAAKhUQHGzRsgghhBSORCSARCSBmxlDlQyZJiTRXoZUPWIlZ1/uUSpKraAlZwqQTKHizytTqPAmQ26WOiVCQa5RKkKtKT85K2M45gpTNPvshLZ4+jqDH71iIxKapS5CiGUVKQR58eIFQkNDERoaikePHuHtt9/Gd999h0GDBsHBwcFcNRJCCCkpGRlA377AsWOArS0wezaQkqIOQPr0sXR1hBBCrIAmVHG1N0+oIleq1FN4tMIU7R4petOBcvVQ4Zckzd4v1YQqShVkGSokFTJUcZQIkCZT8dfFQi57WdHcgYr29B51gJLTP0W931DPldxLjhJCSkahQ5Du3bvj+PHjqFChAkaMGIH3338ftWrVMmdthBBCSlJqKtCrF3DmDODgABw6RKM/CCGEFDuxUAAXewFc7M2zjLBCqdIJRnJP78kdmhgKYNJlCsxt7Yqpf8chS64OQuRKhuRMOZIzzTNSRZS95Cg/9Sd7BIpm5Iq9JlzJ1UvF0NQfRwpVCDFZoUMQsViM3bt3o1evXhAKaWgYIYSUaklJQLduwKVLgLMz8PffwNtvW7oqQgghpMBEQgFc7ARwsStaqBIREYH7S7tDqWI6U360m9bq91gxMB1IlrMvXapAplwJAFCoGFKyFEjJMs8yvMJcoUpe/VK09xvrv2IrplCFlE2FDkG0V305e/YsNm3ahMePH2P37t2oXLkyfvvtN/j7+6NNmzZmKZQQQkgxefUK6NoVuHEDcHcHjh4FmjSxdFWEEEKIVRAKODjbiuFsa56RKkoV05nSo9NfRWtVH01okt90oAyZkj9vapYCqWYKVQQc9Fb0MdxPJfcoFaHW7XKmA9mJhRSqEKtQ5Maoe/bswfDhwzFs2DDcuHEDUqkUAJCcnIzPP/8cf/31V5GLJIQQUkzi4oAuXYC7dwFPT+D4caB+fUtXRQghhFhccS2PKxRwcLIVw8lMoYpKxZAhV+pO78nVgDbP6UAGpgsBgIoBqVIFUqXmCVU4PlQR6vVLsdcKV7TDFu39jtrXbUSwFwshEFCoQgquyCHIsmXLsHHjRowYMQI7duzgt7du3RrLli0r6ukJIYQUl2fPgE6dgIcPgUqVgBMngNq1LV0VIYQQYhViY2Ph4+Nj6TLyJRBwcMwelWGOBUtVKoZM7VBFa4lkY6GJ8SWX1dOBGAMYA9KyjwGkRa6T4wB7sVBnxElOP5XcI1K0pv5I1P1W9JZelogoVCknihyCPHjwAO3atdPb7uLigqSkpKKenhBCSHGIjFQHIJGRQNWqwMmTQECApasiRMd///2HHTt24OzZs4iOjkZGRgY8PT3RqFEjhISEoH///rCxsbF0mYSQMiotLc3SJViEQMDxwYKXGc7HmDpU0Znyo7VscobU+HLLOdOBdKcLqbJDlXSZUj1yJbXooQoAdRhSiH4qesdnBzBCClWsUpFDkIoVK+LRo0eoVq2azvZz586hevXqRT09IYQQc3v4UB2APHumDj5OnlQHIYRYievXr2PWrFk4d+4cWrdujRYtWuB///sf7Ozs8Pr1a9y9exfz5s3DRx99hFmzZmHatGkUhhBCiJXiOPXSwvYSEeBU9PMxxpAlVxmd8qPdQ0V7v7GRK+lSdagCABkyJTJkSiQUvUwAgB0/UiVnlIqDpp+KwVV/hFpTf3Kua4IWkVBgpsrKtyKHIOPGjcPUqVPxyy+/gOM4vHjxAmFhYZg5cyY+++wzc9RICCHEXO7dUwcg8fHqqS8nTqinwhBiRfr374+ZM2di9+7dcHV1NXpcWFgYvv32W3z99deYO3duyRVICCkXPD09LV0CMYDjONhJhLCTCOHpVPQAnDEGqUKlN4WHbzyrFaCkydTXja8OpA5ZlNmpSqZciUy5Eq/MNKjIVizQaTqrG5roN691MNJPxTG7H0t5DVWKHIJ8+umnUKlU6NSpEzIyMtCuXTvY2Nhg5syZ+Oijj8xRIyGEEHO4cUO9CsyrV+rmp8eOAV7mGOhKiHk9fPgQYnH+DQNbtWqFVq1aQS6Xl0BVpLw7Fh6P849eoYW/OzrVMUfnBWLtOKEYMoXK0mWQEiDgzLcCEAODTKEy++o/AJAlVyFLLkNiuqzIdQKAjUhQ4H4quiNX1FOFrka9xs2nyWhdowK6BFn/z0eOMcbMcSKZTIZHjx4hLS0NQUFBcHR0NMdpi11KSgpcXFyQnJwMZ2dnS5dDCCHF49IloFs3ICkJaNoUOHJEvRwuIcWkqL9fz5w5Y7DnmLaPPvoIa9euLWyJFkPvPUqfY+HxGPfrVUuXQUrY+l4+mHgo1tJlEFKq/DiiqcWCEFN/v5pt/ItEIkFQUBCaN29eagIQQggpF86cATp3Vgcgb7+tXgaXAhBi5fr06YObN28a3f/RRx9hy5YtJVcQKdfCHieCo/6GhBCSJwEHXHySaOky8lXk6TAAkJWVhdu3b+Ply5dQqXSHjPXp08ccd0EIIaSgDhwAtmwBDh0CZDKgQwf1NgqqSSkwduxYdOvWDefOnUONGjV09k2dOhWbN2/G4cOHLVQdKW9aBXjgl/OREHIclIxhUe+6eKuKi86yoWlZWpeluS8rdbZrD283JwEH9ZB225yeAU5aw9mdNEPYbXOGtvOXs4e2O9qIYCcRUugD4OWLZ7i96C1Ll0GIVTt1/yWm7rjJ/3xsWd3D0iXlq8ghyD///IMRI0bg1atXevs4joNSWTw/5AkhhOThwAHgnXdyrjduDBw+DNjZWa4mQgrgq6++wuvXr9G5c2dcuHABlbIb+E6bNg0//fQTDh06hPbt21u4SlJedAnyxo8jmuLik0S0rO5R5KHeShVTN140GJwokZYlR7pMidSsnOVCU6WGLqvDFQ0VA1Kz9xeFJkzRBCaaJou5wxIHGxGcbHMaMTrpHCvm+wwISukyoc7V/S1dAiFW752GlWEvEZnt52NJKHJPkMDAQHTt2hULFiyAt7f1P+DcaF4uIaRM6txZvfILAHAc8NFHwLffWrYmUq6Y4/erSqXCgAEDcP/+fZw9exbLly/Hxo0bcfDgQXTq1MnMFZcceu9BzEmlYsiQK5GWZWgESs7lnMBFiTSpXG90iuayeboF6nKQCPMYgaIOTPRCFlv9wMXRRgRhCQYq0dHR8PPzK7H7I4QUjam/X4s8EiQ+Ph4zZswolQEIIYSUOYwBixbpBiCMqZfFJaSUEQgE2LFjB3r27Ik6deogPT0dBw4cKNUBCCHmJhBwfFBQVIwxZOoEKkqkZgcm2iNQ8gpctMMVzTKh6TIl0mVKvEyVFrlGO7FQa9SJeqSJk970n1zhiW3OcqHa28X5LA8qk5lnBQ5CiHUp8k/LAQMG4PTp0wgICDBHPYQQQgpLLgc+/BD45Rf19UGDgEqV1L1AqD8TKWW+++47/nJwcDDOnj2LkJAQhIeHIzw8nN83ZcoUS5RHSJnEcRzsJSLYS0Qo6gLqjDFIFSp+So/hXimaQEWZ9zFSBeRKdaCSKVciU67Eq7SiByo2IkHOqBNJ7hEoQvSpJsDh4w8NBCqiXOGLEDYiYZHrIYSUjCJPh8nIyMDAgQPh6emJt956C2Kx7trK1v7mhIakEkLKhPR0dejx11+AQACsXw988IGlqyLlWFF/v/r75z8Xn+M4PHnypDDlWRS99yCk4KQKZfaUHsPTeNKlipweKjKty1KlXj8VmUKV/x0CqOkhwcNE00aDSIQC9dQeQ4GKVrNazUgVBxuhkX4qItiIBOCoMy0hBVZi02F+//13HD16FLa2tjh9+rTO/7Acx1l9CEIIIaXey5dAr17AlSvqxqc7dtDID1LqRUZGWroEQogVsREJYeMohIcZFjiTKVQ503dkCp3pP2lSeXZzWgVcRTI8eKMy3sBWKkeWXB2oyJQqyDJUeJMhL3J9IgGXa+qOEI626r4p2v1UDDWqzQlf1D1W7MRCClQIyaXIIci8efOwePFifPrppxAI8p5XRwghxMwePQK6dQMePwY8PICDB4FWrSxdFSGEEGK1JCIBJCIJ3BwkeR4XERGBkcGBeR6jUKrU4Yks12iU3D1UZIan/2iHK5qlkxUqhuRMOZIzix6oCDjkGoFiaEWfnOa0hvupqC/bi4WldqUfQrQVOQSRyWQYPHgwBSCEEFLSrlwBevYEEhKAatWAf/4BatWydFWEFNmOHTswZMgQk459+vQpYmJi0Lp162KuihBC9ImEArjYC+BiL87/4Hxolk5O15neY3z6Dz+CRW80i3obY9nLJmepz1VUXPbSyTmr+hjrp2JolIpQp4Gtg6RkV/ohRFuRQ5CRI0di586dmDt3rjnqIYQQYoq//gIGDgQyMoBGjdTXK1a0dFWEmMWGDRuwePFijB49Gr1790adOnV09icnJ+P8+fPYunUrjh07hp9//tlClRJCyjJHRzPMvSkAoYCDs60YzrZFD1Q0SyfzwUkeU3rSpUoj/VRyRrOomHqxOc3tzcFeItQLTDRNafV7qBgYzZLdb8XBRghRPiv9EKKtyCGIUqnEqlWrcOTIEdSvX1+vMerq1auLeheEEEK0/fILMH48oFQCXbsCu3cDTk6WrooQs/n3339x4MABrF27FnPmzIGDgwO8vb1ha2uLN2/eIC4uDhUqVMCoUaNw9+5deHt7W7pkQkgZ5OPjY+kSCk176eSi/oTkl07WjDTJY4lkPnCRZYcsWXK90SyK7KWTM2RKZJhp6WRbsSD/KT18PxX19B9jo1nyWzqZlH5FDkHu3LmDRo0aAQDu3r2rs4+a8BBCiBkxBixbBixYoL4+fDjw00+AJO85zYSURn369EGfPn3w6tUrnDt3DtHR0cjMzESFChXQqFEjNGrUiKbiEkKKVUREBAID8+4JUh5oL52MIn7molk62fiKPsp8+qnkTP9JlyohU6ob02bJVciSS/EqreiPVyISGBiBIjTST8X49B9HWxEtnWylihyCnDp1yhx1EEIIyYtCAUyaBPzwg/r6nDnA8uXqCbqElGEVKlRA3759LV0GIYQQM+A4DrZiIWzFQlRwtCny+aQKZU5wwo9AMTb9R6sprYF+KtLspZNlChUSFTIkppu2PHJexELO+Co+Bqb/GDvGyZaWTjanQoUgMTExqFq1qsnHP3/+HJUrVy7MXRFCCMnIAIYMUa/8wnHA2rXqQIQQQgghpByzEQlhIxLCPZ+VfkwhV6oM900xEKhoRqpohy/avVUy5crsczK8yZCbZelkodYUJ81UHuNLJGv3UBHCKdf0n/K+dHKhQpBmzZqhb9++GDt2LJo1a2bwmOTkZPzxxx/49ttvMX78eEyZMqVIhRJCSLn06hXQqxdw6RJgawts3w7873+WrooQQkq9Y+HxCHuciFYBHugSRH1liD5/f39Ll0BKkFgogKu9BK72RQ9UFEoV0mVK/VBFr59KTnNa3X4qOaNZ0rOXTlYWw9LJBqfxaPdWsc1rBIt6v6Glk63952uhQpDw8HAsX74cXbp0ga2tLZo0aYJKlSrxDcvCw8Nx7949NG7cGKtWrUKPHj3MXTchhJR9kZFASAgQEQG4ualHgtAyoIQQUmTHwuMx7terAIBfzkciyMcJHmYYmk/KlrcriXHhRdH/4CTEVCIhBxc7MVzschYbYQz80sk503iUUGY3mC0Mcy6dDAAOkpwpPSoVQ1RiBgSc+ufrjyOaWl0QUqgQxMPDA6tXr8by5ctx+PBhvYZlw4YNQ0hICOrVq2fuegkhpHy4fh3o0QOIjweqVgX++QfItUwoIYSQwgl7nKhzPTw2FUCqZYohVmtoLR98EfHK0mUQYvXSZcrsESs5K/2oGCDkOFx8klg2QhANOzs7DBgwAAMGDDBXPTrOnDmDL7/8EteuXUNsbCz27dun0xyNMYaFCxfixx9/RFJSElq3bo0NGzZQF2dCSOm2eLG66alcDjRoAPz1F1CpkqWrIoSQMqNVgAd+OR8JjlN/yvpOg0rwdrFFapZmGLocadlz/TVD2VOzFEX65LUg/t/enYc3VWf/A3/f7N2SUqALWhAQ2URBUKigooDooOioM7gMVEVnRFAUGBE3xAUYnVHccGFUnN/o4DLjqODGsClYVJD6FRBk06LShaVNt6z38/vjNntS2rTJTdL363l47F2SnFwqSU7O5xxPqXqWfzm6Sa9s++3LavqvQadhn+wYyNNZ8eSk09UOgyipbP+lBi9v/BFaSYJbCIzo1VntkEK0eTpMLNXX1+P000/HjTfeiCuuuCLk+GOPPYann34ar732Gnr27In7778f48ePx86dO2EymVSImIioDYQAbrnFNwEGAObOZQKEiKidjRuQh2VThmHz/iMY0atla9Y9oz19iRIXau1Ob3l6QNLE5r/tDNnnmUIRSUCpes3xn49nAoWSHNEHJU90EZIn+pBkSrqhYzdLDHbkyBEM7Zx4H+CIEtlvh5yIEb26tOrf13iThBDxSWm3kSRJAZUgQgh069YNs2fPxpw5cwAozVjz8vKwfPlyXH311S26X6vVCovFgpqaGpjN5liFT0TUPIcDuO22wASIVgvcfjvwxBPqxUUUpUR/fV28eDHmzZuHmTNnYsmSJQAAm82G2bNnY8WKFbDb7Rg/fjyWLl2KvDzfG7iysjJMmzYN69atQ2ZmJoqLi7Fo0SLodC3/XinRrw3FnsPlm0LhqzZxRkii+G37VakoDRTd7RpXaytQIiVVMo06aDXJn0yx2+0wGtkrhihZtPT1NaErQZpz4MABlJeXY+zYsd59FosFw4cPR0lJScQkiN1uh93uW6tktVpjHisRUbOqqoCrrgI++8y3T6sF3G5g9GjVwiJKVV9//TVefPFFnHbaaQH777zzTqxatQpvv/02LBYLZsyYgSuuuAKbNm0CALjdbkyYMAH5+fn44osvcOjQIUyZMgV6vR4LFy5U46lQkjLoNDDoDOjUxrGeblkokyTCJk3CJFX8fvbdRkmqyKL1FSjNSTdoAytRvAkSfYQkin/lii+hYtBp2hZIG5SVlXGZPVEKStokSHl5OQAEfDvj2fYcC2fRokVYsGBBTGMjImqx774DJk4EfvwRMJuBf/0LcLmA9euVBMjEiSoHSKSOhx56CHPmzEF6enq73m9dXR2uu+46LFu2DI888oh3f01NDV5++WW88cYbuOCCCwAAr776Kvr374/NmzdjxIgR+PTTT7Fz507873//Q15eHgYPHoyHH34Yc+fOxYMPPgiDoe1jFYlaQ6uRYDbpYTbpj39yM4QQaHS6m5b4hEuqOMMmUQK2mxIqTrdSZN7gcKPB4UZlrf04j948g04TlEQJrkTRh0miBC8H0sOk13CpDxEBSOIkSLTmzZuHWbNmebetVisKCwtVjIiIOqz33gP+8Aegrg7o3VsZgeuZAMPkB3VwCxYswC233NLuSZDp06djwoQJGDt2bEASZOvWrXA6nQEVpv369UP37t1RUlKCESNGoKSkBIMGDQr4Amb8+PGYNm0aduzYgSFDhrRrrETxIkkS0g06pBt0yG3jfdld7uMs52nqkxImieK/r9GpLPVxuGQccTlwpN7Rpri0GilCEsW/EkUfkEQp0Mj4puxYQFIlw6CDJgWW+hB1ZEmbBMnPzwcAVFRUoKCgwLu/oqICgwcPjng7o9HItX1EpC4hgIULgfvuU7bHjAHeegvIyVE3LqIEEouWZStWrMA333yDr7/+OuRYeXk5DAYDsrOzA/b7V5iWl5eHrUD1HIuES3GpIzHqtDBmatE5s23vt11uGfV2t9J8NlzliS0oqRIm6VJnc6HO4YIQytKhmkYnahqdrYxkb8iezEg9UkIqUfRhlgMp52cYddBr1VvqQ9SRJW0SpGfPnsjPz8eaNWu8SQ+r1Yovv/wS06ZNUzc4IqJIGhqAqVOBFSuU7RkzlMan+raVMhOlovYsXT948CBmzpyJ1atXx32CHJfiErWeTquBJV0DS3rbXh9lWaDB6fZLlrhb3DPlN70NeHlbjZJwsbngahqR7KlcQRvzmSa9poXLefySKmEqWYw6LvUhao2EToLU1dVh715f9vXAgQMoLS1FTk4OunfvjjvuuAOPPPII+vTp4x2R261bN+8EGSKihPLzz8DllwNbtwI6HfDcc8Af/6h2VEQJ65RTTjnuG/ujR4+26L62bt2KyspKnHHGGd59brcbn332GZ599ll88skncDgcqK6uDqgGqaio8Faf5ufn46uvvgq434qKCu+xSLgUl0g9Gr9lMEDrEqB79uzB9eOGAvCNSA47vSfc8p6wPVOUc21OZUSyzSnD5rTjcF3b+qZwRDJR6yR0EmTLli04//zzvdueNxDFxcVYvnw57rrrLtTX1+OPf/wjqqurMWrUKHz88cdx/4aHiOi4Nm8GfvtboLwc6NwZ+Pe/gfPOUzsqooS2YMECWCyWdrmvMWPG4LvvvgvYd8MNN6Bfv36YO3cuCgsLodfrsWbNGlx55ZUAgN27d6OsrAxFRUUAgKKiIjz66KOorKxEbq7SOWH16tUwm80YMGBAxMfmUlyi5CdJEkx6LUx6Lbq0camP062MSK6N0A8lUs+UkOU+dlfT/Qkca3DiWIMTQGMbnqOy1MeTRMkI7qESbnlP0HaWUY8MoxY6LvWhBCaJWCy6TSItnSVMRBS1//f/gJtvBux2YNAgpSFqz55qR0UUU219fdVoNCgvL/cmG2Jh9OjRGDx4MJYsWQIAmDZtGj788EMsX74cZrMZt912GwDgiy++AKBUjgwePBjdunXDY489hvLyckyePBk33XRTq0bk8r0HUXKora1FVlaW2mFEJHtGJEfZM8U/CeOW2/cjYZpeG7YfSsSeKeF6rJh0MOq07RoXpbaWvr4mdCUIEVFSc7uBefOAxx9Xti+7TEmIJPAbKqJEoUZJ9pNPPgmNRoMrr7wSdrsd48ePx9KlS73HtVotVq5ciWnTpqGoqAgZGRkoLi7GQw89FPdYiYg0GglZJj2yTHqgDUVzQgjYnLLShLYFy3nCJVE85ztcylKfRqcbjU43qto6IlmraSaJErzcJ7RniufcND2X+pBPqytBPv/8c5xzzjnYtGkTRo4cGau44obfxhBRTFitwLXXAqtWKdv33gs89BCgYXkodQzJUAmiFr73IEoOe/bsQZ8+fdQOI6nYXW7UNzWfDUiqRKxECT/9p8Hhbte4NJ6lPk2Jkmh6pmSalBHJWo5ITlgxqwT56KOPoNPpsGrVqpRIghARtbu9e4GJE4HvvwdMJmD5cmDSJLWjIkoqsiyrHQIREbWSUaeFUadFToahTffjcsuod7j9kiZhpvmEne4TlFSxKyOSZQFYbS5Yba42P8cMg9YviaJvdjlPQFIl6BhHJKunVUmQBQsWwOVy4YILLsDtt9+Ohx56CA888ECsYiMiSj5r1gC/+x1w7BhwwglK/4+hQ9WOioiIiFopLS1N7RA6LJ1WA0uaBpa0to1IFkKgoSmZEpg0Of6I5Fr/yT9+I5LrHW7UO9yoQNuW+hh1mpCEScDI5OCkirdyJbBKhSOSW6/Vy2GWLVuGmpoaZGdn46abbopVXHHDklQiahdCAEuXAjNnKr1Ahg8H3n0XKChQOzIiVfD1NTJeGyKi5BKLEcntRaeRAvqmZPlVqYRPooRf+pOu10KT5Et9YrYcxuVyYc6cOXjxxRfbFCARUcr497+BBQsAz/jNyZOBl15SlsIQEVHMrd5ZgZJ9R1DUuzPGDchTOxxKEfv370evXr3UDoMSQNxHJDf1VYk02afO5kKdQ1nq45IFqhucqG5wtvE5ApmGwH4p7TEiORH/feaIXH4bQ0Rt8eqrwI03+raLi5V9LEukDo6vr5Hx2rSv1TsrcPM/tni3T+qS0eYSeiIAmDksE09tqVM7DKKwvEt9/JIpicIzIlkDoKLWDo2k9GVZNmVYTBMhHJFLRBRLQijJjmnTfPs0GiAnhwkQIqI4Ktl3JGD7x8P1KkVCqcZ2ehq+PVitdhhEScczItlDFoBWkrB5/5GEqAZpcxLk4MGDKCwsbI9YiIiSQ1kZ8Mc/Ap984tun1Sq9QEaPVi0sIqKOqKh3Z7yy6YD3m8ZJwwrRLTsNtTZfGbnV7+dam7J+v76dR3CGk2HQKiM5TUpJeVbTJIksk28tfpbJt81pEYlFK9x4ufgEtcMgSlqlZdV4Zt1eaCUJbiEwoldntUMC0A5JkB49eiAnJwenn346Bg8e7P3jcDjw9NNP47XXXmuPOImI1CcEsGwZMGcOUFsLGI3AI48AJ58MfPaZkgCZOFHtKImIOpRxA/KwbMowbN5/BCN6tXzNuVsWTevwnU3JEd/ECKutaY2+zTdBwvNzbdNtgidGhOOZIgFry56LMi0iMDGirMlv2uf3c6Yp/P50g5aTItrJkSNH0LlzYnxoI0pGY/rn4bTC7Fb/+xxrbe4J8tNPP2Hbtm0oLS3Ftm3b8M033+DXX38FAJjNZhw7dqxdAo0Vrsslohb58UfgppuUEbgAcPbZwCuvAH37qhoWUaLi62tkvDapQwgBm1MOTKT4JU9q/ZInwQkX/wRLQztWpWgkBCZOmpIlmUa/ahRTaDVKplEHs1+ChVUpwJ49e9CnTx+1wyCiFopbT5AePXqgR48euPzyy737SkpKUFxcjIceeqitd09EpC5ZBp5/Hpg7F6ivB9LSgIULgdtuU5bAEBFRhyVJEtIMWqQZtMjNiv5+XG7Zb7mOK2ApT63N2ZRM8S3l8VWkBCZT3LKALABrUzVLW5j0mqDlO4GJlEyTDuYIy3o8iZY0PatSiCjxxKQxalFREZ566incf//9uPrqq2PxEEREsbdvHzB1KrBhg7J97rnAyy8ry1+IiIjaiU6rQXa6AdnphqjvQwiBRqc7bKVJwFIev2U/4apVPM0MbU4ZNqcdVbX2qGPSaqSAEZvmgKU8vsSKuZlqlUyjLmDcZjxZLBZVHpeIYqvNSRCHwwGDIfQf7D59+mDHjh1tvXsioviTZeCZZ4B77gEaGoCMDGDxYuDWW5UJMERERAlGkiSkG3RIN+iQ14ZVVk637B25aY24lCdMtUrQflkofVdqGp2oaXS26bml6bW+pIhJ71eB4tcjpSnJEinBYtJrWl2VkpOT06a4iSgxtTkJkpmZiQEDBmDIkCEYPHgwhgwZgm7duuGZZ57B2LFj2yNGIqL42bMHuPFGYONGZfv885Xqj5491Y2LiIgoDvRaDTplGNApo21VKQ0Ot7fqxNqKfil1TUt5am1O2F0yAN+4zco2VKXoNJI3QeJZvmMOTqQ0JUw8+7vKx6DP6RaQYNFquLyHKNm1uTHqxo0b8e233+Lbb79FaWkptm/fDpvNBgC46KKLMGzYMAwaNAiDBg1Cv3792iXo9sTmZEQEQBlvu2QJcN99gM0GZGYCjz+ujMJl9QdRq/H1NTJeG6KWcbjkMMt5wvdLCZ3m4xuNHO2nnaWXFODWlYcC9qUbtCE9Usxh+qX4kix+S3uazjXqWl+VQkTHF7fGqKNGjcKoUaO827IsY/fu3SgtLUVpaSm++uorLFu2DJWVlXC7Yz+PnYio1XbtAm64Adi8WdkeN04Zhdujh7pxERERdWAGnQY5OgNy2lCVIssCDU63t6msNUwixbc/sF+KXqdBl0wDrDYXHE1VKQ0ONxocblRYo69K0WulkKU83gqUsBN9Qs/NNLIqhShaba4EaamKigrk5SXGXGB//DaGqANzuYC//Q2YPx+w2wGzWdmeOhXgNzREbcLX18h4bYiSj93l9k7mCemX4leBEinJUmtzoc4RfVVKOBkGbchSniyTLuJEn3Ajk016Trqj1BG3SpCWSsQECBF1YNu3K70/vv5a2b74YuDFF4HCQnXjIiIiooRw6NAhFBQUAACMOi2MmVp0zjRGfX+yLFDvCJzSY/UmUgKTJ1b/ccj2wNHIDrdSlVLvcKPe4Ua5NfrnaNBq/KpPAnukZIXplxJuf6ZBBw2rUiiJxC0JQkSUEJxO4LHHgAULlJ8tFqUXSHExqz+IiIjIq66url3vT6ORmpIH+jbdj93lG4XsqUSxBo1D9vxsDVOt4vkvADjcMo7WO3C03hF1PJIEZBqOs5TH2HwiJcukg1HHqhSKDyZBiKhjeP994O23gS++APbvV/ZdcolS/dGtm7qxEREREbWQpyqlSxuqUtwBVSm+ShNrhKU81qB+KZ4ki9MtIASUBrV2Fw7VRP+8DDpNC5byBDabDe6XksGqFGoBJkGIKPX9+9/AVVf5tjMygBdeAK67jtUfREREFFbXrl3VDiFmtBoJZpMeZpMeQFpU9yGEgN0l+yb1BFWj+C/78W4Hj0a2OVHvUIZnOFwyjrgcONLWqhTj8ZbyHL9fikHHyYCpjEkQIkpt27YBt9zi25YkJfnxhz+oFxMRERElPIMh+qk0HYEkSTDptTDpteia1baqlHBLefwTKSGjkcP0S3HJTVUpTduosUUdk1GnCUiOZAYlT8xB45DD7c8waDkKOUExCUJEqcluBx55BFi0CPCM59ZoAFkGJkxQNzYiIiJKeL/88gv69OmjdhgpT6uRYEnTw5IWfa8UIQRsThm1/kt2/BMmwRUo/tUpfgmWhqaqFLtLhr3OjsN10Y9C1niqUkKSKb4KFXPQ6GPPz2a/c/RaVqW0NyZBiCj1bNkCXH89sGOHsv273yn9P0pLgdGjgYkTVQyOiIiIiNqTJElIM2iRZtAiNyv6+3G5ZdTb3b4RyPZmEikB+wOTKW5ZQBaAtamfSluY9Bpvc9lwS3mUZErz/VLS9KxK8cckCBGlDptNmfry+ONK9UfXrsDSpb5+IFOmqBsfERERJQ0uh+l4dFoNLOkaWNLbVpXS6HSjrikBEnEpz3H6pTQ6laoUm1OGzWlHVW30VSlajeRNnHgqTQJHIyvJErOnh4oxfLWKLkWqUpgEIaLUsHkzcOONwPffK9tXXw088wzQpYu6cRERUYt9sqMcn/1QhTNP6oTRfXPVDoc6OEvXAlQ3RN+kkzo2g06DLpkGdMmMLpnmdCu9UlozBtmXbPGNQQaUvis1jU7UNDrb9JzS9NqAZrPmMP1SskzBSRZlf2nZMew8ZEVR7y4YNyCvTXG0FZMgRJTcGhuBBx4AnnhC6feRl6dMfrn8crUjIyKiVvh4+yHc8s9vAACvf1mmcjREwAOju+Kh9VVqh0GUMBqdbjQ63aiMsipFAvDKph+xbMowVRMhqVHPQkQd06ZNwODBwF//qiRA/vAHYOdOJkCIiJLQlweOqh0CUYD8TH5fTNSeBACtJGHz/iOqxsH/s4ko+TQ0APfeCzz1FCAE0K0b8OKLSvNTIiJKSmf37oJXN/0IrSTBLQQWTByIU08wN62pd8Ha6AxaU+/0rrev9TunzuGCEO0Tk14redfD+094UPb5bafpvaMxs/zLxE066DT8zjFZ7du7F/sWDlE7DKKk97/vK/Cn/7fV++/7iF6dVY2HSRAiSi6ffab0/ti3T9m+4QZlKUx2tqphERFR24wbkIdlU4Zh8/4jGNGrc9Sl0rIsUOfwNSG0NoYmTqy2wPGYvgSLsl3fNCbT6RY4Uu/Akfro+0KkG7R+iZOgREma//7Q5IpnIoRGw6kOajjxxBOg5bUnarPxA/Pb5d/39sIkCBElh7o6YN484Nlnle0TTwSWLQMuukjduIiIqN2MG5DX5jfHGo1SvWE26QGkRXUfLrfsbTDoSZiEVKLYffusYapTbE4ZANDgcKPB4UaFNco19BKQaQgcd2lOC0yUhCZS/M/RI8PA8ZjRcDgcSE9PVzsMopTQHv++txcmQYgo8a1dC9x0E3DggLJ9883KGFyLRd24iIgoJem0GmSnG5CdHv2IVIdL9k1vaAxMkFiDlvXUhq1OccHhliEElNGZdhdQY4sqFo2EgAoUzyjMSNUpoefoYdJrOlwipaqqCtmsNCVKOUyCEFHiqq0F7rpLmfYCAN27A3//OzBunLpxERERHYdBp0GOzoCcjOgTKTanO0KixLMdWqESfI5LFpAF/MZjNkYVi04jBSZKjKGJE3OE6hRPUsWk10Z9LYiI2guTIESUmFavVqo/yprGJE6bBvzlL0BWlrpxERERxYlJr4VJr0XXLGNUtxdCwOaUmxIjTm+T2Ui9UkLPcaLO7oIsAJcscKzBiWMNzqifj0GnCWggGy5R4l+dYg5a1pNl0kGvjV+j2czMzLg9FhHFD5MgRJRYamqAOXOUig8A6NkTePll4Pzz1Y2LiIgoyUiShDSDFmkGLfLMpqjuQwiBeoc7JHFijVB5Eql/CqAsETpc58DhuugbzZr0mpBlPAHTeYy+iT3BE33MJj0yTboWNzstKCiIOk4iSlxMghBRYnj/feDVV4HPPweONM0Ov+02YOFCgN/EEBERqUKSJGQadcg06lAQZSsutyy8/VECEiV2v+1mqlNqbS40NE3ssTll2Jx2VNZG12gWADIM2pD+J8GVKGaTDgMzG1Ct7xxyTqaBE3uIkhmTIESkvjfeAK67zrednw+8+SZw7rnqxURERETtQquRYEnTw5Kmj/o+PBN7rI3heqOE3/ZPolgbnbC7lIk99Q436h1ulFubf8yllxTg1pVbQvZLEpBp9E+YhFnWkxapEa2ync6JPUSqYRKEiNT1wQfAH//o25Yk4KqrmAAhIiIir/aa2BNQjRLUKyV4GU+6QYdBJ1gCbuOd2NO0HS2tt9FsaJPZ0JHHQSORm84x6jrexB6i9sAkCBGp4+hRYOZM4J//9O3TaABZ5vQXIiIiancGnQadM43onNmyRrMulwujz/J9XBJCwO6Sw44zDl7GE7laxQW3LOCWBaobnKhuiH5ij14r+U3lCUqUhCRSQqtTskw6GHWc2EMdD5MgRBR///0vcMstQEWFkviYPRs480ygpAQYPRqYOFHtCImIiKiDO3r0KHJzc73bkiR5J/bkRjmsTgiBxqbRx9bGwL4n/tUpwU1mA5IqdheEAJxugaP1Dhytj77RrFGnCRhv7E2UGCMnTsxBSRZdHCf2ELUHJkGIKH4OH1aana5YoWz37680Qx0+XNn+3e/Ui42IiIjIT01NTUASpD1IkoR0gw7pBl3UE3tkWaDe4QqsRgnqgxJcnRJcjVLXNLHH7pJhr7PjcF30jWbT9NqQJrPmgP/6lvEEL/3JMumRaWz5xB6i9sAkCBHFxzvvALfeClRVAVotcNddwAMPAKbo3gAQERERdUQajdSUcIi+0axnYk9wH5TQZTxh9jXdptGpTOxpdLrR6HSjwhp9IiXTGLh0JzhR4p9cCR6RnGVSphexPwq1FJMgRBRblZXA9OlKEgQATj1Vqf4YNkzduIiIiIiakZOTo3YIMdMeE3ucbhl1/iOOm+uVYg/c9lSseCb21NmV6pRDNbaoYtFInkSKbxlPcK+U4Cazweek6Tmxp6NgEoSIYkMIZcztjBnAkSOATgfMmwfcey9gbFlDMiIiIiK1ZGZmqh1CQtNrNeiUYUCnjOgn9thd7oDESbg+KMGVKMH7nG4BWaCpaiX6iT0678Se8E1mzRGqU/wrWEx6NppNBkyCEFH7Ky8Hpk1TGqACwOmnK9UfQ4aoGhYRERFRS5WVlaFPnz5qh5HSjDotjJladGnhxJ5g/hN7AvughGkyG6Y6xZN0kQXgkgWONThxrMEZ9fMxaDVBDWUjN5k1R5jsY9Cx0WysMQlCRO1HCOD114HbbweOHVOqP+6/H7j7bsAQ/bcERETt4fnnn8fzzz+PH3/8EQAwcOBAPPDAA7j44osBADabDbNnz8aKFStgt9sxfvx4LF26FHl5ed77KCsrw7Rp07Bu3TpkZmaiuLgYixYtgk7Ht1RERPHWXhN7Ghxu3zIem2dqT2h1SrhqFKvNibqmiT0Ot4wj9Q4cacPEHpNe00wflHA9UZTqFM/+TCMn9hwPX7GJqH38+ivwpz8BK1cq22ecoVR/nHaaunERETU58cQTsXjxYvTp0wdCCLz22mu47LLLsG3bNgwcOBB33nknVq1ahbfffhsWiwUzZszAFVdcgU2bNgEA3G43JkyYgPz8fHzxxRc4dOgQpkyZAr1ej4ULF6r87IiovWm1XNrQEUiShAyjDhlGHfIt0U/sqXO4ghIlvsoTa5hlPMHn1DuURrM2pwyb046q2ugbzWYYtKHLetJCEynBCRXPOZkGHTQpPLFHEkIItYNQk9VqhcViQU1NDcxms9rhECUfIYDXXgPuvBOorlYqPubPB/78Z0AffbMtIkpuyfL6mpOTg8cffxxXXXUVunbtijfeeANXXXUVAGDXrl3o378/SkpKMGLECHz00Ue45JJL8Ouvv3qrQ1544QXMnTsXVVVVMLSw4i1Zrk1brN5ZgZJ9R1DUuzPGDcg7/g2IiDo4tyxQF7HJrGcJjy+pEq46xTOxp60kCcg06CIu4wnunRLcZNZs0iPdEL7RbCxfH1r6+spKECKK3sGDSvXHRx8p22eeqVR/DByoblxERMfhdrvx9ttvo76+HkVFRdi6dSucTifGjh3rPadfv37o3r27NwlSUlKCQYMGBSyPGT9+PKZNm4YdO3ZgCPseAVDe4N78jy2QALyy6QDO7t0Z3bLT1A6LqNVGFUjYeKhDf19MCSpNr0WaXou8oM/5Lrfc7HKdlhICSsLF7sKvUU7s0Wok7+hjz7Iem9ONb3+ugUZSXh+WTRmmSqKcSRAiaj0hgJdfBmbPBqxWZdrLQw8Bs2YpfUCIiBLUd999h6KiIthsNmRmZuLdd9/FgAEDUFpaCoPBgOzs7IDz8/LyUF5eDgAoLy8PSIB4jnuORWK322G3+8qarVZrOz2bxFSy7wgkAJ7321/sO6JmOERRu+CSAryz9ZDaYRAlJbcsUNPoRE2jE0BjwDFZAFpJwub9R5gEIaIk8NNPwM03A6tXK9sjRijVH/36qRsXEVEL9O3bF6WlpaipqcE777yD4uJibNiwIaaPuWjRIixYsCCmj5FIinp3xiubDkCSlJz5OX26wJymh7XRsy5eWQNvbXTC4ZZjHo9WIymNBdP8JzL4xlyaOY2BIuiSacPci/j+hqi97KmsxX+++QVaCXALgRG9OqsSB5MgRNQysgy89JLS66OuDjCZgEcfBWbOBNg4jIiShMFgwMknnwwAGDp0KL7++ms89dRTmDRpEhwOB6qrqwOqQSoqKpCfnw8AyM/Px1dffRVwfxUVFd5jkcybNw+zZs3yblutVhQWFrbXU0o44wbkYdmUYdi8/whG9Gp+zbfN6fYbXRmUJPFbBx/peIPj+Ovf3S0Ye2nUaQKTJH7r2z1TFzz7ghMo5jQd0vTh175TcqutrcVZWVGOHCGisC4+taBFrw+xxCQIER3fgQPA1KnAunXK9qhRynKYU05RNy4iojaSZRl2ux1Dhw6FXq/HmjVrcOWVVwIAdu/ejbKyMhQVFQEAioqK8Oijj6KyshK5ubkAgNWrV8NsNmPAgAERH8NoNMJoNMb+ySSQcQPyWvTm1jPasmtWdNfH6ZZ9jQQbPWvgA5Mo1pDjrqb9vnXydpeMqtropzHoNJJfc8CmJIkxMIESMcGSpk/5SQxERB4tfX2IJSZBiCiy//4XeOopoKQEsNuBtDRg8WJgxgxAw9JhIkou8+bNw8UXX4zu3bujtrYWb7zxBtavX49PPvkEFosFU6dOxaxZs5CTkwOz2YzbbrsNRUVFGDFiBADgwgsvxIABAzB58mQ89thjKC8vx3333Yfp06d3uCRHotBrNeiUYUCnjJZN5gnmGWtpbQwcZelJkvgnTKyNLtTaQxMsblnA1YJqk+ZIEpBpbHkVijKdwf9nHXRavi63t/LycmSxEoQo5TAJQkThvfYacP31vu2BA4H33gN691YtJCKitqisrMSUKVNw6NAhWCwWnHbaafjkk08wbtw4AMCTTz4JjUaDK6+8Ena7HePHj8fSpUu9t9dqtVi5ciWmTZuGoqIiZGRkoLi4GA899JBaT4naSKORvD1C0Kn1txdCoNHpjqoKxZN0sbtkZRJD00SHX6obj//AYaQbtEFLdXyVKSFVKmGOm/Rc2kpEHYMkRGuG5aSels4SJupQSkqAceOA+nplW6MBbr8dePJJdeMioqTB19fIeG3In39flHBJkuMlUepb0BelJQw6TcQkie9nXcjSHs/P6YbU64vy888/48QTT1Q7DCJqoZa+vrIShIh8hFCan952G+BsKunVagG3Gzj/fHVjIyIiSkFt7Yvicsvhkyjen13NNJh1orapL4rDJeNwnR2H66Lri+KZwhOwjKeFVSjmND2yjInXF4UJEKLUxCQIESlsNmD6dOCVV5TtK68Efvc74MsvgdGjgYkTVQ2PiIiIQunaqS+KN4ESlCQJSaLYQvunuGTRoik8zfHvi5LVwiqUgCSKSQd9O/dF2b9/P3r16tWu90lE6kvqJMiDDz6IBQsWBOzr27cvdu3apVJEREmqrExJemzZoix9WbRIGYUrScCkSWpHR0RERDHi3xflhOy0Vt/e0xcleKmONWKTWU9SxfdzcF+UaKXptREm8oQ2kw13PLgvitvdPkuNiCixJHUSBAAGDhyI//3vf95tnS7pnxJRfK1bB/z+98Dhw0DnzsCKFcDYsWpHRURERElAkiSkG3RIN+iQZzZFdR92lztMksS3fCf8Uh7fPk9flEanG41ONyqs0S3pMWg1voRJmh53npWFJa9/EzCFp7lmsxkp2BeFKBUlfcZAp9MhPz9f7TCIko8QwBNPAHfdBcgycMYZwL//DZx0ktqRERERUQdi1GlhzNSiS2b0fVHq7C6/CpTAJEltyJSeoOOevihuGYfrHDhc5wAAzDtWh0N1La9M0Wokb3VJa6tQzCY9Mk06aBOsLwpRKkr6JMiePXvQrVs3mEwmFBUVYdGiRejevXvE8+12O+x2X3bYarXGI0yixFJXB0ydCrz1lrJdXAw8/zyQ1voyWCIiIiI16bQaZKcbkJ0efV+UeocrsAql0QnJUYeD9ZowSZSgMch+fVGqG5yojrIvCgBkGYN7n7SsCsXTlNaga9++KESpKKmTIMOHD8fy5cvRt29fHDp0CAsWLMA555yD7du3IysrK+xtFi1aFNJHhKhD2bMHuOIKYPt2QKcDnnoKmDZN6f9BRERE1MFoNBKymqo1/Pui7NljxZjBvY97eyEEbE45MDESsQrFv3eK77jNKQMAau0u1Nrb1hclK6SZbPiJPAFNZ5sqVIw6DZf0UMqThBBC7SDaS3V1NXr06IEnnngCU6dODXtOuEqQwsLC484SJkoJK1cCf/gDUFMD5OcD77wDjBypdlRElIKsVissFgtfX8PgtSFKDnv27EGfPn3i8lievijBDWZrg5b3hD/uQl0bEif+DFpNmCSK/0SewDHIwct82BeF1NTS19ekrgQJlp2djVNOOQV79+6NeI7RaITRGN16Q6KkJcvAQw8BniqokSOBt98GCgrUjYuIiIgoQVkslrg9Vnv1Ram1uVATJkkSOqWn6bjdd57c1BflSL0DR+odUcWhkRCUJAk/0jg4wWJJY18Uip+USoLU1dVh3759mDx5stqhECWO6mpg8mSlCgQAZswA/vY3wBDdulkiIiKijiAnJ0ftEFrMvy9KYRS39/RFCVi+0+j0Jkk8DWTDVaF49jndArIAahqdqGl0AmiM6rlkGnVRVaF4zmVfFDqepE6CzJkzB5deeil69OiBX3/9FfPnz4dWq8U111yjdmhEiWH7duC3vwX27gVMJuCFF5QmqERERETUrAMHDsRtOYza/PuidEPrG+ULIWB3yd6ESE2zVSieBrSBxz19UersyvKeX2tsUT0Xk14TpoFs881mLd4Gs3qY9OyLkuqSOgny888/45prrsGRI0fQtWtXjBo1Cps3b0bXrl3VDo1IfW++Cdx4I9DQAPToAfznP8oYXCIiIiKidiRJEkx6LUx6LXLNpqjuw+GSAxIjgVN4wiVRAqf0ePqi2JwybE47Kmvtx3nE8PRaKfwUHmOkMceBy3wyDDpouKQnoSV1EmTFihVqh0CUeFwu4O67lSUvADB2LLBiBdC5s7pxERERERFFYNBp0DnTiM5R9kVxywJ1TYmRmjBJktqABrO+n/0TLLIAnG7R5r4omcZwY4zDV6F4EytNP2caddBpuaQnlpI6CUJEQaqqgEmTgHXrlO25c4FHHwW0WnXjIiIiIkoyHWUpTKrQaiRY0vWwpOuj6osihEC9wx1VFUptU+LF0xdFGZPsQrR9UTIM2jBJlHBjjsM3mzXq+N6/OUyCEKWKr78GrrwSOHgQyMwEli9XtomIiIio1Q4dOoQCTtLrMCRJQqZRqcSIRmBflMhVKJGSKNZGFxqdbgBAvcONeocbh6Lsi2LUaYKayUYeeWwO02A2TZ/ao46ZBCFKBa+8Atx6K2C3A6ecArz7LjBggNpRERERESWturo6tUOgJBLYFyW6+/D0RQmY0hO8fKcx3HHfBB8AsLtkVNXaURVlXxSdRgo7kSd85UlQgiVNj8wE74vCJAhRMrPbgZkzgRdfVLYvuwx47TUgjnPtiYgotT2zdg/W76pEYU46Ts7NVDscorg5M8eBZ9fuUTsMIi+jToOuWUZ0zQrfN8UtA/WO448yPh6XLHC03oGjUfZFkSQgyxi5CuVInR16nQYXn1qAcQPyonqMtmAShChZ/fILcNVVwObNyr80Dz8MzJsHaNhIiYiI2senO8rxt09/AABsLatWNxiiODvvpHRs+LFB7TCIko7w64vyS3Xkvij/+eYXLJsyLO6JECZBiJLRZ58Bv/sdUFkJdOoEvPEGcNFFakdFREQpZvP+o9BIgNz0xWGe2YhO6QbUNCol2fUOd9xiMeg0IWvXzSZl/X4KL10nFXU2Ad1yOV2PqD1989Mx/FBRBwFAK0nYvP8IkyBE1AwhgGeeAWbPVkbhnnaa0v+jVy+1IyMiohRU1LszXtl0AFpJglsIPHL5oIA3qy63HLA2vcZbgu2MsM9Xkl3T6ITNKbc4FodLxuE6Ow7XBa5x10gIGTVpCR49mab87NvvO57qDQApenv27OGEGKJ2tnpnBW7+xxbv68qIXvFPNDIJQpQs3n4beOABYNcuZfvaa4GXXgIyMtSNi4iIUta4AXlYNmUYNu8/ghG9Ood8W6fTatApw4BOGYao7t/ucoeMnqzxS6B4kic1QQkUa6Pys8MtQxZAdYMT1Q3OqGLQa6XASQn+iZKgqhNzWmiCxaTnKEoiopY63utKPDAJQpQMnnwSmDXLt33TTUoChN9cERFRjI0bkBezN6lGnRbGTC26ZIZv8nc8Nqfbr7LEb+RkmKRJuIoUlyzgdAscqXfgSJQNAD3LdCxpQQkUU1PlSZiqFIvf1AWDjr28EpXBEF1yj4iaF8vXlZZgEoQokf3yC3DvvcrEFw+NBsjKYgKEiIg6PN84SlOrbyuEQKPT3dTfxBV+GU9QVUpwlYoQkZfptFSaXhu4jCeoIsUSUpHiW9qTadRBp2USJVZ69OihdghEFANMghAloro64PHHlT+Nfh2VtVrA7QZGj1YtNCIiolQgSRLSDTqkG3QoiGKyvCwLZRSlzYWahsh9TwITLC5vpUqt3QUAaHS60eh0o8IaXRIl06g77jKeSBUpWUYdNBp+qRLJTz/9xEQIUQpiEoQokbjdwD/+oVR/HDqk7Bs5EnjiCaC8HFi/XkmATJyoZpREREQdnkYjIcukR5ZJjxOy01p9e7csUGfzqzAJ0wvFaotckdLQNJmnzu5Cnd2FX2tsrY5BkoAsoy58Y9lI+/ySKBmG1G4q63BEt0SKiBIbkyBEiWLtWmXqS2mpst2rF/DYY8AVV/iWvjD5QURElBK0GgmWdD0s6XoURnF7p2cyT8S+J0HLeIKqVGxOGUJA2WdzAWg87mOGew6BVShNCRKT8ryCjwVP5zHpNSmdRCGixMQkCJHadu8G/vxn4IMPlG2LBbj/fmDGDMAYXaM4IiIiSm16rQY5GQbktGEyT7ilOuGm83gqUmr9lvk43QJuWeBYgxPH2jiZx5KmR1bIdJ7gpElonxSjLraTeU444YSY3j8RqYNJECK1HD4MLFgAvPAC4HIp/T5uvVUZg9uli9rRERERUQoz6rTomqVF16zWf+EihIDdJbdupHFQRYq7HSbzGHWaFk7iCd2XZdJBf5ymsg6HA+np6VHFRkSJi0kQoniz24FnnwUefhioqVH2XXqpsvSlXz91YyMiIiI6DkmS2jyZp8HhDmweGzTCOGyfFJsTNQ1KU1khALtLRlWtHVW10TWVTTdoI/RCUapOzslz4cAea8gyHnOaMt5Yy6ayREmJSRCieBEC+Pe/gblzgf37lX2DBwN/+xtwwQWqhkZEREQUL5IkIcOoQ4ZRhwJL65vKyrJAncMzaSe4F0rk6TyeHiqeyTwNDjcaHG6UW8M/Tv9LCjB35Y8R4/A0lc1qdqSxLrQiJU2PTAMn8xCphUkQonj46itg1ixg0yZlu6AAePRRYMoUZRkMEREREbWIRiN5G7CiU+tv73LLqLO7gvqehBlp7JZxQb/ckIoUz2SeWrvLm1BpLc9kHqWBbKTpPIGjj/0TLOkpPpmHKJaYBCGKpbIyYN484I03lO20NOCuu4A5c4DMTHVjIyIiIuqAdFoNstMNyE4/flPZq88L3ed0yyFVJ62ZzmN3te9knkh9T8JN7vEkWIw6TuahjotJEKJYqK0FFi8GnngCsNmUdP+UKUr1BzuNExERESW8PXv2oE+fPiH79VoNOmca0Tkzuil+Nqcbtbbwy3giTeexNvqazrrktk/mMWg13sRIVoSkSaTpPPGYzEMUS0yCELUnlwt45RVlxG1lpbJv9Gil78cZZ6gaGhERERGpz9NUNtrJPDanHDSJJ8x0Hr9mssEVKbIAHG4Zh+scOFwX3WQek17TfN+TZqbztGQyD1EsMQlC1F4+/RSYPRvYvl3Z7tMHePxxYOJEpRKEiIiIiKgNJElCmkGLNIMWeVFO5ql3uEOX8UQcdRzUXLZpMo/NKcPmtKMyysk8GQZtMyONg5bx+DedNemRadJxMg+1CZMgRG21Y4fS4+Pjj5XtTp2ABx8EbrkFMBx/rSkRERERJZ6ePXuqHUK7kyQJmUYdMo06dEN0k3lq7a7j9j3xHgta8lPX1Ei23uFGvcONQzW2qJ6HZzJPuKU64Zbx+DebzeBkng6PSRCiaFVWAvPnAy+9BMgyoNcDM2YA990H5OSoHR0RERERtcHRo0eRm5urdhgJRaORYGlKKkTD5ZaVUcUhfU/CTOexhVapNDoDJ/P8Ut36prIaCcgKTpiEq0gJGHXsOz9Nz8k8yY5JEKLWstmAJUuAhQuVBqgAcMUVwF/+Apx8sqqhEREREVH7qKmpYRKknem0GnTKMKBTRnTV0g6XjFpPwiS46iRiRYoTNU1VKQ63DFkANU3LfQ5GMZlHp5GO2wvFW53iXcrjO2bSs6ms2pgEIWqp994DXnwR2LIFqKpS9g0dqkyAOfdcdWMjIiIiIkpxBl3bJ/OEH2kctHQnzHQez2QelyxwtN6Bo/XRNZU16DQt64ViClzG4zlm0LGpbFsxCUJ0PG63ssRl8WLfvs6dlWqQa68FNPyHiIiIiCjV5HB5c8rxTObJzWr9bYUQaHS6IzePDW42GzSdxzuZxyXjcJ0dh+uiayqbpteGrToJX5ESuLQny6SDjpN5mAQhiqihAVi+XKn02LfPt1+SgGuuAf7wB9VCIyIiIqLYyszMVDsESiCSJCHdoEO6QYd8S+sn88iyQL3D5as6idD3JDDB4kuu1NqUprKNTjcanW5UWNs2mSds0uQ4FSlZxtRoKsskCFGw8nLg2WeB558Hjh5V9mVkAPX1gFarVIaMG6dujERERFFavbMCJfuOoKh3Z4wbkKd2OEQJq6ysDH369FE7DEoRGo2ELJMeWSY9Tshu/WQetyxQZ3eFVqB4l/CE9knxX/JT71CayrZlMo8kAZlGXUiFyfGm83iSLhkGpams2q9DTIIQeezYoVR9/POfgKNpjV+vXsCddwI33ACsWQOsXw+MHg1MnKhmpERERFH5ePsh3PLPbwAAr2w6gMKcNJhN0U15IEp1s4abccfTn6sdBlHUdFoJORkG5GQY4JaFMpmn0YnaplHFrSUEUGtzodYW/WSeNL3Wm5B5ZdMBLJsyLO6JECZBqGMTAli7Fvjb34CPPvLtLyoC5swBLrtMqf4AlMQHkx9ERJTENvxQFbB98GgjEMV0BKKO4Eh9Gnb8alU7DKKUIQt4EyCAkhTZvP8IkyBEceF0Am+9Bfz1r0BpqbJPkpRRt7NnK0kQIiKiFHNBvzz866uD0EjKm9Grhp6AfHNawGjJmqBpCHaX3O5xaCQgK6h02hJcTt1UPp1l0kEjJf8adEpOy2/ornYIRCllW9kxPLVmr/d1aESvznGPgUkQ6lhqaoCXXgKefhr4+WdlX3o6cOONwB13AL17qxoeERHFzqJFi/Cf//wHu3btQlpaGs4++2z85S9/Qd++fb3n2Gw2zJ49GytWrIDdbsf48eOxdOlS5OX5vqUqKyvDtGnTsG7dOmRmZqK4uBiLFi2CTpf4b6vGDcjDsinDsHn/EYzo1bK12P4jJf2TJeGa+tU0hq5Dl0XofcoCqGlKshxsQSVKplHnTYj4Rkb61qQHJFKC9qU3rUEnaq2ff/4ZJ554otphEKWU0X1zceoJ2a16HWpvif9qTdQefvoJeOop4O9/B2prlX15ecDttwO33AJwBBoRUcrbsGEDpk+fjjPPPBMulwv33HMPLrzwQuzcuRMZGRkAgDvvvBOrVq3C22+/DYvFghkzZuCKK67Apk2bAAButxsTJkxAfn4+vvjiCxw6dAhTpkyBXq/HwoUL1Xx6LTZuQF6r3nS2daRknV2ZhlDT4AyZehCYUAlMoNQ0OtHQVDZdZ3ehLso17DqN5G3Q50uShDbx868+8Z+OYNBxnGRH1djIpWJEsdDa16H2JgkhwuTnOw6r1QqLxYKamhqYzWa1w6H2tmWL0u/j7beVqS4AMHCgsuTl2msBo1Hd+IiIUlQyvL5WVVUhNzcXGzZswLnnnouamhp07doVb7zxBq666ioAwK5du9C/f3+UlJRgxIgR+Oijj3DJJZfg119/9VaHvPDCC5g7dy6qqqpgMBiO+7jJcG0ShdMto9YvWVITIVniX5VS23ReTaMTrnBlKK2UptcGTEEImywJV5mSpkemITXGSXZUe/bs4XQYoiTS0tdXVoJQ6pFlYNUqJfmxYYNv/9ixSvJj/Hil/wcREXVoNTU1AICcpmrArVu3wul0YuzYsd5z+vXrh+7du3uTICUlJRg0aFDA8pjx48dj2rRp2LFjB4YMGRLyOHa7HXa73btttbLRYkvptRrvZIPWEkKg0ekOWcYTnDSJlFyptSmVJ41ONxqdbpRH8dcWrvdJuGRJuKU95jQ9THpt6x+U2k1+fr7aIRBRDDAJQqmjsRH4f/9PGXO7e7eyT6cDrrkGmDULGDxY1fCIiChxyLKMO+64AyNHjsSpp54KACgvL4fBYEB2dnbAuXl5eSgvL/ee458A8Rz3HAtn0aJFWLBgQTs/AzoeSZKQbtAh3aBDvsXU6tu7ZYE6W2B/k8DqkzDJlaCGsq3tfRLMoNM0JUh0ftUnEfqgBCVSskx6aFmFQkQUgkkQSn5VVcDSpcBzzyk/A4DFAvzpT8BttwFsaEVEREGmT5+O7du3Y+PGjTF/rHnz5mHWrFnebavVisLCwpg/LrWNViPBkq6HJV0f1e39G8r6J1Ja01DW4ZJxuM6Ow3X24z9gGOEayjabSGFD2QDl5eXIyoqiGQ4RJTQmQSh57d4NPPkk8NprgM2m7OvRQ5nyMnUqwBctIiIKY8aMGVi5ciU+++yzgMkP+fn5cDgcqK6uDqgGqaio8JbF5+fn46uvvgq4v4qKCu+xcIxGI4zsQdXhtHdD2XDLeNRqKHvcHilsKEtECYxJEEouQgCff670+3j/fd/+M89U+n1ceaWyBIaIiCiIEAK33XYb3n33Xaxfvx49e/YMOD506FDo9XqsWbMGV155JQBg9+7dKCsrQ1FREQCgqKgIjz76KCorK5GbmwsAWL16NcxmMwYMGBDfJ0QpS5IkZJmUJS0nZKe1+vataSjrWcYT3FDWJQscrXfgaL0jqueQCg1l09Jaf+2JKPHx0yIlB5cL+Pe/gb/+VZn44jFxopL8OOccNjslIqJmTZ8+HW+88Qbee+89ZGVleXt4WCwWpKWlwWKxYOrUqZg1axZycnJgNptx2223oaioCCNGjAAAXHjhhRgwYAAmT56Mxx57DOXl5bjvvvswffp0VntQwoh3Q9maRpe3KiWeDWXDLe1pz4ayJ3JJNVFK4ohcjqlLbL/+Ctx/vzLitrZW2WcyAcXFwJ13An37qhsfERGFlYivr5H6G7z66qu4/vrrAQA2mw2zZ8/Gv/71L9jtdowfPx5Lly4NWOry008/Ydq0aVi/fj0yMjJQXFyMxYsXQ9fCSsREvDZE7SXahrKebbtLbnMMrWkoG3zMv6Hs/v370atXrzbHQ0Tx0dLXVyZB+EYksQgBlJYCH3ygLHfZujXw+NVXA08/DXTtqkp4RETUMnx9jYzXhiiy9mgo21ZZRiV58tDoznjp24aWJVKalv2woSyRelr6+srlMKQ+ux1Yt05JeqxcCRw8GP48rRYoKGAChIiIiChFtaWhrCwL1Dva3lC21u5Crd0Fu8uNLw8cbVUMnoayzfU+YUNZInUxCULqqKoCVq1SKj4++QSor/cdS08HLrwQuPRSpclpcbGSAHG7gdGjVQuZiIiIiBKXRtO+DWVrGxrx7LX5zS7jiWVDWf8+J8nUUJYo0TEJQvEhBPD9975lLiUlyj6Pbt2UpMfEicD55wP+3bizs4H165UEyMSJcQ6ciIiIiDqC4IayR4640blz5xbd9ngNZWua9se7oWzIMp44NJQlSnRMglDsOJ3KONsPPlD+7NsXeHzIECWpcemlwBlnRJ7uMnEikx9EREREFFdHjx5tcRJEkiSkG3RIN+iQbzG1+rFa0lA29FhgQ1lZwFuVchCNrY4hUkPZyMt4wjeUJUp0TIJQ+zp2DPj4Y6Xa46OPgJoa3zGDARgzRkl6XHIJUFioXpxERERERAlCq5FgSdfDkq6P6vbt0VDW4ZJxuM6Ow3X2qGLwNJTNMoVWnURMpLChLKmASRBqu337lKTHBx8An32m9O7w6NoVmDBBqeQYNw7IzFQvTiIiIiKiFrJYLGqH0GKJ1FA2GtE2lPVs67VsKEstxyQItZ7bDWze7Ovv8f33gccHDPAtcxk+XGlqSkRERESURHJyctQOIS7ao6GsJ2ESbhkPG8pSomEShFqmrg749FMl6bFqFXD4sO+YVgucd56S9Lj0UqB3b/XiJCIiIiJqBwcOHECfPn3UDiPh6bUadM40onOmsdW39W8oG9LzhA1lKUaYBKHIDh70NTVduxZw+GVms7OBiy9WKj4uukjZJiIiIiIiaqH2bih7vN4nsWoo619xwoayiY9JEPJxuYAnngD+8x+gshI4cCDweO/evmUuo0YB+ugaNxEREREREbVVvBrK+o6FbyhbVWtHVW3bGsqaW5NIYUPZNmESpCOTZWD7dmDNGuXP2rVAY1D2c+RIJekxcSLQr1/kMbZERERERCmES2FSXzwbygb3SAluKPtLdeurUFrSUDZcj5SO3lCWSZCORAhlksvatUrSY906oKoq/LkaDXDzzcALL8Q3RiIiIiKiBHDo0CEUFBSoHQYlKDUaylr9tuPZUDZcj5RkbijLJEiq+/VXJenhSXyUlQUeT08Hzj0XuOACQKcDZs1SGp263cBvfqNOzERERBSV1TsrULLvCIp6d8a4AXlqh0OU1Orq6tQOgVKYag1lG53eUcbxbSirh6VpGY85TY/P9xxW7fWKSZBUc/QosGGDb4nLrl2Bx/V6YMQIYMwY5c9ZZwEGg+94797A+vXA6NHKEhgiIiJKCle/VILN+48CAF7ZdOA4ZxPR8Sy9pADjXl6ldhhECamtDWU9Xtl0AMumDItrIoRJkGRXXw9s3Ojr6fHNN8qyFw9JAs44Q0l4XHCB0tA0IyPy/U2cyOQHERFRknn8k93eBAgRtY83t9eoHQJRh/Ds2j1MgrTWc889h8cffxzl5eU4/fTT8cwzz+Css85SO6zYcDiAr77yVXps3gw4nYHn9O+vJDzGjAHOOw/IyVEnViIiIoqL9bsq1Q6BKOUcqnWpHQJRh3C0IbqeJtFK+iTIm2++iVmzZuGFF17A8OHDsWTJEowfPx67d+9Gbm6u2uG1nSwDpaW+So/PP1eqP/x17+6r9LjgAqBbN1VCJSIiInWM7peLHYd8i7qLeuVgzvh+KkZElIgE3DLglgVkIeCW/f4IAbnpv559PXRW7LVnwiU3HZMF3EKZCuIKug9ZiKDzAo8pPwNuWfbeR6TzvPfjF5PL7TsuC4SN3f92/jH5F4lTYtJIyrhfjSRBp5Gg0UjQaiRoJeVnXdMxrcbvj+Q5D9D6HYt4niRBq5W85yrnAVqNxnsfkc6LGJPnfA2U87R+j+8fU9D2m1sO4t1vfvE+/4mnnxDX6530SZAnnngCN998M2644QYAwAsvvIBVq1bhlVdewd13361ydBG8/74ymeX880OXnggB/PCDr9Jj/Xqlz4e/Ll18lR5jxgC9enF0LRERUQf25/F9AQDrd1didN9c7zalFiF8H4C9H6yFgNsd/kO87zzAJcuQZQR+QHYH3k+4D9LB96M8nt8H+bDnNZ9ccMuIeF6zyQVPDLLcbDIgUkxyK5MBSy8pwNyV7K/TEpIU+CHa/0Oz50O08mEYET/YB3zYDvog7/vALikf2iU0c17g/Xhj0vruJ9J5uqD7CYzdcx6ga0ocNJtwCBNX4HnK/WgkQOpgn+VG9OqMbpY01V6zkjoJ4nA4sHXrVsybN8+7T6PRYOzYsSgpKVEvsDvuUKawjBkDTJkCZPkNnn7/feCyy5SflywB3nsPGDLEN71l7Vrgl18C7y8rS1nW4qn2OPVUZYQtERERUZM/j++bFMkP0fShNuDDadOHdOVDLAI+2Df7wTro2/TAD/Zo/hty9/ESCZ4P22j2PP9v/wO+yfd7buHOC4kpbAIgNHlBseP/4VQrSTjc4EandH2Lv6FXPvw2fbDVIPRDtN95uvb6hj7om/e2fkMf8IHd7/E81yT4ufk/LlFrqPmaldRJkMOHD8PtdiMvL7CJSl5eHnYFT0VpYrfbYbfbvdtWaxTzgJrz5pvAU08pP7/7LjBjBmCxACeeCBQWAj//HHj+tdeGLm8xGoGRI33VHsOGKeNriYiIiMJ4YcM+rN5ZgROy03BSl4yAUvrghEPot+a+b9bb8g293LTMIDAB0PT4fkkDluZ3PMf7dt/7wbol36IHJRL8KwTCVRIcdylB0+0lSQoprK4DcPO5nVS5Zs3xJOMAAGxbQklqT2UdGu1uXDn0RI7IjbVFixZhwYIFIfsnTZoEvV7f9gf49tvQfTU1yp8dO0KPeRIg2dlA167KUpdOnQCtFvjyS+UPERFRknEGN+2mmFm9swKLP1K+/Nn60zGVoyEK5ZIFWr0WJQE8MLorHlpfpXYYRClLAvDxjnKOyG2NLl26QKvVoqKiImB/RUUF8vPzw95m3rx5mDVrlnfbarWisLAQb775Jsxmc9uD8ix30WoBtxtYsQI47TSlAuTgQWDZMmWii4ckAdOmAc891/bHJiIiShBWqxUWi0XtMDqEkn1HoJGUz5gSgD55mRhcmK12WERJ75SuGvx+2Ilqh0GUcraVVWNvZR0ElAqwzfuPMAnSUgaDAUOHDsWaNWtw+eWXAwBkWcaaNWswY8aMsLcxGo0wGo2xC2riRKXPx/r1wOjRvsan/fsr/+3SxdcTBFAaoY4fH7t4iIiIKKUV9e6MVzYdgFaS4BYCfx7fL+6lxUSpaM+ePXjsqj5qh0GUclbvrMDN/9jifd0a0atzXB9fEiK5V2a++eabKC4uxosvvoizzjoLS5YswVtvvYVdu3aF9AoJx/NNVU1NTftUgrTE++8DL7+s/Dx1auiEGCIioiSnyutrkojFtVm9swKb9x/BiF6dmQAhaicNDQ1IT09XOwyilBSL162Wvr4mdSUIoPTyqKqqwgMPPIDy8nIMHjwYH3/8cYsSIKqZOJGJDyIiImo34wbkMflB1M4cDgeTIEQxoubrVtInQQBgxowZEZe/EBERERERtVZVVRWys7PVDoOI2plG7QCIiIiIiIiIiOKBSRAiIiIiIqIgmZmZaodARDHAJAgREREREVGQgoICtUMgohhgEoSIiIiIiCjInj171A6BiGKASRAiIiIiIiIi6hCYBCEiIiIiIiKiDoFJECIiIiIioiA9e/ZUOwQiigEmQYiIiIiIiIIcPXpU7RCIKAaYBCEiIiIiIgpSU1OjdghEFAM6tQNQmxACAGC1WlWOhIiIKHV4Xlc9r7Pkw/ceRMmhrq6O/58SJZGWvvfo8EmQ2tpaAEBhYaHKkRAREaWe2tpaWCwWtcNIKHzvQUREFDvHe+8hiQ7+FY0sy/j111+RlZUFSZLUDifmrFYrCgsLcfDgQZjNZrXDSRq8btHhdYsOr1t0eN2iE6vrJoRAbW0tunXrBo2Gq2/9tcd7D/6+xw6vbWzwusYOr23s8NrGTiyubUvfe3T4ShCNRoMTTzxR7TDizmw283/kKPC6RYfXLTq8btHhdYtOLK4bK0DCa8/3Hvx9jx1e29jgdY0dXtvY4bWNnfa+ti1578GvZoiIiIiIiIioQ2AShIiIiIiIiIg6BCZBOhij0Yj58+fDaDSqHUpS4XWLDq9bdHjdosPrFh1et+TEv7fY4bWNDV7X2OG1jR1e29hR89p2+MaoRERERERERNQxsBKEiIiIiIiIiDoEJkGIiIiIiIiIqENgEoSIiIiIiIiIOgQmQVLAokWLcOaZZyIrKwu5ubm4/PLLsXv37oBzbDYbpk+fjs6dOyMzMxNXXnklKioqAs4pKyvDhAkTkJ6ejtzcXPz5z3+Gy+WK51OJq+effx6nnXaadzZ1UVERPvroI+9xXrOWWbx4MSRJwh133OHdx2sX6sEHH4QkSQF/+vXr5z3OaxbZL7/8gj/84Q/o3Lkz0tLSMGjQIGzZssV7XAiBBx54AAUFBUhLS8PYsWOxZ8+egPs4evQorrvuOpjNZmRnZ2Pq1Kmoq6uL91OJm5NOOink902SJEyfPh0Af9+SxXPPPYeTTjoJJpMJw4cPx1dffdXs+W+//Tb69esHk8mEQYMG4cMPP4xTpMmnNdd22bJlOOecc9CpUyd06tQJY8eOPe7fRUfV2t9ZjxUrVkCSJFx++eWxDTCJtfbaVldXY/r06SgoKIDRaMQpp5zCfxMiaO21XbJkCfr27Yu0tDQUFhbizjvvhM1mi1O0yeGzzz7DpZdeim7dukGSJPz3v/897m3Wr1+PM844A0ajESeffDKWL18euwAFJb3x48eLV199VWzfvl2UlpaK3/zmN6J79+6irq7Oe84tt9wiCgsLxZo1a8SWLVvEiBEjxNlnn+097nK5xKmnnirGjh0rtm3bJj788EPRpUsXMW/ePDWeUly8//77YtWqVeKHH34Qu3fvFvfcc4/Q6/Vi+/btQghes5b46quvxEknnSROO+00MXPmTO9+XrtQ8+fPFwMHDhSHDh3y/qmqqvIe5zUL7+jRo6JHjx7i+uuvF19++aXYv3+/+OSTT8TevXu95yxevFhYLBbx3//+V3z77bdi4sSJomfPnqKxsdF7zkUXXSROP/10sXnzZvH555+Lk08+WVxzzTVqPKW4qKysDPhdW716tQAg1q1bJ4Tg71syWLFihTAYDOKVV14RO3bsEDfffLPIzs4WFRUVYc/ftGmT0Gq14rHHHhM7d+4U9913n9Dr9eK7776Lc+SJr7XX9tprrxXPPfec2LZtm/j+++/F9ddfLywWi/j555/jHHlia+119Thw4IA44YQTxDnnnCMuu+yy+ASbZFp7be12uxg2bJj4zW9+IzZu3CgOHDgg1q9fL0pLS+MceeJr7bV9/fXXhdFoFK+//ro4cOCA+OSTT0RBQYG488474xx5Yvvwww/FvffeK/7zn/8IAOLdd99t9vz9+/eL9PR0MWvWLLFz507xzDPPCK1WKz7++OOYxMckSAqqrKwUAMSGDRuEEEJUV1cLvV4v3n77be8533//vQAgSkpKhBDKL6pGoxHl5eXec55//nlhNpuF3W6P7xNQUadOncTf//53XrMWqK2tFX369BGrV68W5513njcJwmsX3vz588Xpp58e9hivWWRz584Vo0aNinhclmWRn58vHn/8ce++6upqYTQaxb/+9S8hhBA7d+4UAMTXX3/tPeejjz4SkiSJX375JXbBJ5CZM2eK3r17C1mW+fuWJM466ywxffp077bb7RbdunUTixYtCnv+73//ezFhwoSAfcOHDxd/+tOfYhpnMmrttQ3mcrlEVlaWeO2112IVYlKK5rq6XC5x9tlni7///e+iuLiYSZAIWnttn3/+edGrVy/hcDjiFWLSau21nT59urjgggsC9s2aNUuMHDkypnEms5YkQe666y4xcODAgH2TJk0S48ePj0lMXA6TgmpqagAAOTk5AICtW7fC6XRi7Nix3nP69euH7t27o6SkBABQUlKCQYMGIS8vz3vO+PHjYbVasWPHjjhGrw63240VK1agvr4eRUVFvGYtMH36dEyYMCHgGgH8fWvOnj170K1bN/Tq1QvXXXcdysrKAPCaNef999/HsGHD8Lvf/Q65ubkYMmQIli1b5j1+4MABlJeXB1w7i8WC4cOHB1y77OxsDBs2zHvO2LFjodFo8OWXX8bvyajE4XDgn//8J2688UZIksTftyTgcDiwdevWgL8jjUaDsWPHev+OgpWUlIT8ezx+/PiI53dU0VzbYA0NDXA6nd73WRT9dX3ooYeQm5uLqVOnxiPMpBTNtX3//fdRVFSE6dOnIy8vD6eeeioWLlwIt9sdr7CTQjTX9uyzz8bWrVu9S2b279+PDz/8EL/5zW/iEnOqivdrmC4m90qqkWUZd9xxB0aOHIlTTz0VAFBeXg6DwYDs7OyAc/Py8lBeXu49x//Nrue451iq+u6771BUVASbzYbMzEy8++67GDBgAEpLS3nNmrFixQp88803+Prrr0OO8fctvOHDh2P58uXo27cvDh06hAULFuCcc87B9u3bec2asX//fjz//POYNWsW7rnnHnz99de4/fbbYTAYUFxc7H3u4a6N/7XLzc0NOK7T6ZCTk5PS187jv//9L6qrq3H99dcD4P+jyeDw4cNwu91h/w527doV9jaR/s749xUommsbbO7cuejWrVvIG/aOLJrrunHjRrz88ssoLS2NQ4TJK5pru3//fqxduxbXXXcdPvzwQ+zduxe33nornE4n5s+fH4+wk0I01/baa6/F4cOHMWrUKAgh4HK5cMstt+Cee+6JR8gpK9JrmNVqRWNjI9LS0tr18ZgESTHTp0/H9u3bsXHjRrVDSQp9+/ZFaWkpampq8M4776C4uBgbNmxQO6yEdvDgQcycOROrV6+GyWRSO5ykcfHFF3t/Pu200zB8+HD06NEDb731Vrv/w55KZFnGsGHDsHDhQgDAkCFDsH37drzwwgsoLi5WObrk8PLLL+Piiy9Gt27d1A6FKOktXrwYK1aswPr16/ka2Aa1tbWYPHkyli1bhi5duqgdTsqRZRm5ubl46aWXoNVqMXToUPzyyy94/PHHmQRpo/Xr12PhwoVYunQphg8fjr1792LmzJl4+OGHcf/996sdHrUQl8OkkBkzZmDlypVYt24dTjzxRO/+/Px8OBwOVFdXB5xfUVGB/Px87znBkwE8255zUpHBYMDJJ5+MoUOHYtGiRTj99NPx1FNP8Zo1Y+vWraisrMQZZ5wBnU4HnU6HDRs24Omnn4ZOp0NeXh6vXQtkZ2fjlFNOwd69e/n71oyCggIMGDAgYF///v29S4k8zz3ctfG/dpWVlQHHXS4Xjh49mtLXDgB++ukn/O9//8NNN93k3cfft8TXpUsXaLXaZn+vg0X6O+PfV6Borq3HX//6VyxevBiffvopTjvttFiGmXRae1337duHH3/8EZdeeqn3vcQ//vEPvP/++9DpdNi3b1+8Qk940fzOFhQU4JRTToFWq/Xu69+/P8rLy+FwOGIabzKJ5tref//9mDx5Mm666SYMGjQIv/3tb7Fw4UIsWrQIsizHI+yUFOk1zGw2x+TLQiZBUoAQAjNmzMC7776LtWvXomfPngHHhw4dCr1ejzVr1nj37d69G2VlZSgqKgIAFBUV4bvvvgv4oLB69WqYzeaQDyCpTJZl2O12XrNmjBkzBt999x1KS0u9f4YNG4brrrvO+zOv3fHV1dVh3759KCgo4O9bM0aOHBky8vuHH35Ajx49AAA9e/ZEfn5+wLWzWq348ssvA65ddXU1tm7d6j1n7dq1kGUZw4cPj8OzUM+rr76K3NxcTJgwwbuPv2+Jz2AwYOjQoQF/R7IsY82aNd6/o2BFRUUB5wPK31mk8zuqaK4tADz22GN4+OGH8fHHHwf0FyJFa69rv379Qt5LTJw4Eeeffz5KS0tRWFgYz/ATWjS/syNHjsTevXsDPpT/8MMPKCgogMFgiHnMySKaa9vQ0ACNJvAjtCfZpPQApWjE/TUsJu1WKa6mTZsmLBaLWL9+fcBIxIaGBu85t9xyi+jevbtYu3at2LJliygqKhJFRUXe455xiBdeeKEoLS0VH3/8sejatWtKj0O8++67xYYNG8SBAwfE//3f/4m7775bSJIkPv30UyEEr1lr+E+HEYLXLpzZs2eL9evXiwMHDohNmzaJsWPHii5duojKykohBK9ZJF999ZXQ6XTi0UcfFXv27BGvv/66SE9PF//85z+95yxevFhkZ2eL9957T/zf//2fuOyyy8KOyB0yZIj48ssvxcaNG0WfPn1SekSuEEqH++7du4u5c+eGHOPvW+JbsWKFMBqNYvny5WLnzp3ij3/8o8jOzvZO7Jk8ebK4++67vedv2rRJ6HQ68de//lV8//33Yv78+RyRG0Frr+3ixYuFwWAQ77zzTsD7rNraWrWeQkJq7XUNxukwkbX22paVlYmsrCwxY8YMsXv3brFy5UqRm5srHnnkEbWeQsJq7bWdP3++yMrKEv/617/E/v37xaeffip69+4tfv/736v1FBJSbW2t2LZtm9i2bZsAIJ544gmxbds28dNPPwkhlM9hkydP9p7vGZH75z//WXz//ffiueee44hcah6AsH9effVV7zmNjY3i1ltvFZ06dRLp6enit7/9rTh06FDA/fz444/i4osvFmlpaaJLly5i9uzZwul0xvnZxM+NN94oevToIQwGg+jatasYM2aMNwEiBK9ZawQnQXjtQk2aNEkUFBQIg8EgTjjhBDFp0iSxd+9e73Fes8g++OADceqppwqj0Sj69esnXnrppYDjsiyL+++/X+Tl5Qmj0SjGjBkjdu/eHXDOkSNHxDXXXCMyMzOF2WwWN9xwQ8p/gPnkk08EgJBrIQR/35LFM888I7p37y4MBoM466yzxObNm73HzjvvPFFcXBxw/ltvvSVOOeUUYTAYxMCBA8WqVaviHHHyaM217dGjR9j3WfPnz49/4Amutb+z/pgEaV5rr+0XX3whhg8fLoxGo+jVq5d49NFHhcvlinPUyaE119bpdIoHH3xQ9O7dW5hMJlFYWChuvfVWcezYsfgHnsDWrVsX9t9Nz7UsLi4W5513XshtBg8eLAwGg+jVq1fAZ9n2JgnBuh0iIiIiIiIiSn3sCUJEREREREREHQKTIERERERERETUITAJQkREREREREQdApMgRERERERERNQhMAlCRERERERERB0CkyBERERERERE1CEwCUJEREREREREHQKTIERERERERETUITAJQkREREREREQdApMgRJR0zj33XLzxxhstPt/hcOCkk07Cli1bYhgVERERERElOiZBiCjmJElq9s+DDz7Y4vt6//33UVFRgauvvtq776STTsKSJUu820IIzJkzB2azGevXr4fBYMCcOXMwd+7cdnxWRERERESUbJgEIaKYO3TokPfPkiVLYDabA/bNmTOnxff19NNP44YbboBGE/6fL7fbjalTp+If//gH1q1bh9GjRwMArrvuOmzcuBE7duxoj6dEREREKU6WZTz22GM4+eSTYTQa0b17dzz66KNqh0VEbaRTOwAiSn35+fneny0WCyRJCtjXUlVVVVi7di2eeuqpsMftdjuuueYabNmyBZ9//jn69u3rPdapUyeMHDkSK1aswMMPP9z6J0FEREQdyrx587Bs2TI8+eSTGDVqFA4dOoRdu3apHRYRtRGTIESUNDZu3Ij09HT0798/5FhdXR0mTJiAn3/+GZs2bUJhYWHIOWeddRY+//zzeIRKRERESay2thZPPfUUnn32WRQXFwMAevfujVGjRqkcGRG1FZMgRJQ0fvrpJ+Tl5YVdCvPwww8jKysL33//Pbp27Rr29t26dcNPP/0U6zCJiIgoyX3//few2+0YM2aM2qEQUTtjTxAiShqNjY0wmUxhj1144YWor6/HwoULI94+LS0NDQ0NsQqPiIiIUkRaWpraIRBRjDAJQkRJo0u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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5))\n", "\n", "# mu*(T)\n", "ax = axes[0]\n", "trace = cc_asym.drop_duplicates(['T', 'mu']).sort_values('T')\n", "ax.plot(trace['T'], 1e3 * trace['mu'], 'r.-', ms=4, label=r'CC trace $\\mu^*(T)$')\n", "ax.axhline(0, color='k', lw=0.5, label='symmetric reference')\n", "ax.set_xlabel('T (K)'); ax.set_ylabel(r'$\\mu^*$ (meV)')\n", "ax.set_title('Asymmetric coexistence: $\\mu^*$ drifts from 0')\n", "ax.legend(fontsize=9)\n", "\n", "# Binodal in (c, T)\n", "ax = axes[1]\n", "for ph, group in cc_asym.groupby('phase'):\n", " g = group.sort_values('T')\n", " ax.plot(g['c'], g['T'], '.-', ms=4, label='refined branch')\n", "ax.axvline(0.5, ls='--', color='lightgray', lw=0.6, label='symmetric axis')\n", "ax.set_xlabel('c'); ax.set_ylabel('T (K)')\n", "ax.set_title('Skewed binodal ($c_c \\neq 0.5$)')\n", "ax.legend(fontsize=9)\n", "\n", "plt.tight_layout()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.15" } }, "nbformat": 4, "nbformat_minor": 5 }