{ "cells": [ { "cell_type": "markdown", "id": "15e3e695", "metadata": {}, "source": [ "# Rejection-free Monte Carlo: the Lennard-Jones fluid\n", "\n", "This notebook reproduces the Lennard-Jones example of E.A.J.F. Peters and G. de With, *Rejection-free Monte Carlo sampling for general potentials*, Phys. Rev. E **85**, 026703 (2012), with `spheropack.rejection_free`.\n", "\n", "In the rejection-free method all particles move along straight lines. For every pair, the increase of the pair potential along the path is accumulated (decreases are free), and the pair reflects like an elastic collision when the accumulated increase reaches $-kT\\ln u$ with $u$ uniform in $(0, 1]$. No move is ever rejected, and positions sampled at equidistant times follow the canonical distribution $\\exp(-U/kT)$." ] }, { "cell_type": "markdown", "id": "4e157bb4", "metadata": { "spheropack-header": true }, "source": [ "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/computational-chemical-engineering/spheropack/blob/main/docs/notebooks/05_rejection_free_lennard_jones.ipynb) [![Download notebook](https://img.shields.io/badge/download-notebook-orange?logo=jupyter)](https://computational-chemical-engineering.github.io/spheropack/notebooks/05_rejection_free_lennard_jones.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "id": "5b16876a", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:50:59.335424Z", "iopub.status.busy": "2026-10-01T23:50:59.335203Z", "iopub.status.idle": "2026-10-01T23:50:59.339869Z", "shell.execute_reply": "2026-10-01T23:50:59.339140Z" }, "spheropack-header": true }, "outputs": [], "source": [ "# Install spheropack when it is not available (for example on Google Colab).\n", "import importlib.util\n", "\n", "if importlib.util.find_spec(\"spheropack\") is None:\n", " %pip install -q spheropack" ] }, { "cell_type": "code", "execution_count": 2, "id": "79a43525", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:50:59.342235Z", "iopub.status.busy": "2026-10-01T23:50:59.342007Z", "iopub.status.idle": "2026-10-01T23:50:59.668134Z", "shell.execute_reply": "2026-10-01T23:50:59.667359Z" } }, "outputs": [], "source": [ "import time\n", "from pathlib import Path\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import spheropack as sp\n", "from spheropack import rejection_free as rf" ] }, { "cell_type": "markdown", "id": "572a8de2", "metadata": {}, "source": [ "## The potential\n", "\n", "The truncated and shifted Lennard-Jones potential, $U(r) = 4\\epsilon[(\\sigma/r)^{12} - (\\sigma/r)^6] - U_\\mathrm{LJ}(r_c)$ for $r < r_c = 2.5\\sigma$. Approaching particles accumulate potential increase only inside the minimum at $r = 2^{1/6}\\sigma$; separating particles accumulate it between the minimum and the cutoff." ] }, { "cell_type": "code", "execution_count": 3, "id": "2f84c756", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:50:59.670781Z", "iopub.status.busy": "2026-10-01T23:50:59.670614Z", "iopub.status.idle": "2026-10-01T23:50:59.779503Z", "shell.execute_reply": "2026-10-01T23:50:59.778780Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkMAAAG2CAYAAAB8joKsAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjExLjIsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvgI3uAAAAAAlwSFlzAAAPYQAAD2EBqD+naQAATZtJREFUeJzt3Xl4U1X+BvA3adI03RdaWqC0pZTNsggCsu/MsCkgiDIgigiyOywOKIgKAz9FHUFARhQRlEVZZFFwRJFNFtmpZSlLaYG2tHTfkqa5vz/aBiq0tMlNbm7yfp4nD+Tm3nu+UEtfzzn3HIUgCAKIiIiInJRS6gKIiIiIpMQwRERERE6NYYiIiIicGsMQEREROTWGISIiInJqDENERETk1BiGiIiIyKkxDBEREZFTYxgiIiIipyarMCQIAvbu3YshQ4YgOjoaf/zxxyOvmT9/PqKjo8u9Bg0aZINqiYiISA5UUhdQHbNmzcKJEycwaNAgbNmyBXl5eY+85tatW6hVqxY++ugj0zE3NzdrlklEREQyIqsw9Pbbb0Or1eLmzZuYPHlyla/z9vZGdHS0FSsjIiIiuZJVGNJqtWZdd+TIEbRp0wY+Pj7o1KkTZsyYAXd3d5GrIyIiIjmSVRgyh7e3NyZNmoQuXbrg1q1bmDdvHrZv346jR49CrVY/9BqdTgedTmd6bzQakZ6ejoCAACgUCluVTkRERBYQBAE5OTmoVasWlMpKpkkLMpSYmCgAEPbt2/fIc4uKisq9j4+PF1QqlbBu3boKr5k3b54AgC+++OKLL774coBXYmJipVnB4XuGVKryf8SwsDCEhYUhJiamwmtmz56NadOmmd5nZWWhbt26SExMhLe3t9VqfZTzNzPx/KpjCPFxw8/TukhWx/127dqF/v37S10GERHRA7KzsxEaGgovL69Kz3P4MPRXRUVFuHPnTqWhRqPRQKPRPHDc29tb0jAU4A8oNe4oVrlKWsf9fH197aYWIiKih3nUFBdZrTNUFfPmzTOtI6TX6zF37lzk5OQAKJkLNGXKFOj1egwdOlTKMs2iUbkAAHRFRokruadmzZpSl0BERGQRWYWh7du3Izo6Gj179gQAvPTSS4iOjsaKFStM59y6dQtxcXEAALVaDU9PT0RGRiIiIgL+/v74/fff8dNPPyEqKkqSP4MlNKqSL5fOYD9h6OTJk1KXQEREZBGFIAiC1EVUVWZmJm7evPnA8aCgIAQFBQEAbt++jfz8fNSvX9/0uSAISEhIgJ+fn1lDOtnZ2fDx8UFWVpakQ0J3c3VotWAvAODawr5QKqV/si0lJYW9Q0REZJeq+vNbVnOGfH194evrW+k5tWrVeuCYQqFAWFiYlaqyHY3axfR7fbERbkqXSs62jVWrVmHOnDlSl0FERGQ2WQ2TObuyYTLAfuYNMQgREZHcMQzJiEqpQNnImM5QLG0xpRYsWCB1CURERBZhGJIRhUJx74kyO5lEPX36dKlLICIisgjDkMxo1GVPlNlHz9D9T/IRERHJEcOQzJTNGyq0kzlDTz31lNQlEBERWYRhSGbsbZjs1KlTUpdARERkEYYhmbm38KJ9DJMFBgZKXQIREZFFGIZk5t6cIfvoGXrYHm5ERERywjAkM/a2P9nVq1elLoGIiMgiDEMyY2/DZF27dpW6BCIiIoswDMmMvW3Wum7dOqlLICIisgjDkMzY29Nks2fPlroEIiIiizAMyYxpAnWRfQyTLVy4UOoSiIiILMIwJDP2Nkz2xhtvSF0CERGRRRiGZMbehskWLVokdQlEREQWYRiSGXt7mmzkyJFSl0BERGQRhiGZuTdnyD56hn777TepSyAiIrIIw5DM2NswWWRkpNQlEBERWYRhSGbsbZhMp9NJXQIREZFFGIZkxt6eJktNTZW6BCIiIoswDMmMRm1fe5O1bNlS6hKIiIgswjAkM/Y2TLZjxw6pSyAiIrIIw5DM2Nuu9RMmTJC6BCIiIoswDMmMm9q+eoY+/PBDqUsgIiKyCMOQzLiVzhkqsJO9yebMmSN1CURERBZhGJKZsjBUaCfDZAsWLJC6BCIiIoswDMlM2TBZoZ30DL3yyitSl0BERGQRhiGZsbdhsu3bt0tdAhERkUUYhmRGa2frDLVq1UrqEoiIiCzCMCQzZT1D+mIjio2CxNUAKSkpUpdARERkEYYhmSnrGQLsY96QXq+XugQiIiKLMAzJTNkK1IB9hCHuWk9ERHLHMCQzSqUCrqWByB4mUe/fv1/qEoiIiCzCMCRDWjtaa2jEiBFSl0BERGQRhiEZsqe1hpYtWyZ1CURERBZhGJKhe6tQSx+GuB0HERHJHcOQDNnTMBm34yAiIrljGJIhjR2tQj158mSpSyAiIrIIw5AMae1oztDatWulLoGIiMgiDEMyZE9zhrp16yZ1CURERBZhGJIhN5X9hKG4uDipSyAiIrIIw5AMaV3tZwK1VquVugQiIiKLMAzJkD2tMxQQECB1CURERBZhGJIhjcp+niY7c+aM1CUQERFZhGFIhuxpmGzAgAFSl0BERGQRhiEZcrOjnqHPP/9c6hKIiIgswjAkQ1rXki+bzg7CELfjICIiuWMYkiHTOkMG6cMQt+MgIiK5YxiSIdMwmV76MDRjxgypSyAiIrIIw5AMudnRBOpPPvlE6hKIiIgswjAkQ26q0nWG7GCYbODAgVKXQEREZBGGIRkqmzNkD8NkJ0+elLoEIiIiizAMyVDZOkM6g/TDZMHBwVKXQEREZBGGIRmypwnUKpVK6hKIiIgswjAkQ2XrDNnDnKHr169LXQIREZFFGIZkqGxvMnvYqLVz585Sl0BERGQRWYaho0ePYs2aNUhOTq7S+QaDAfv27cPGjRvx559/Wrk66zMtulhkhCAIktayfv16SdsnIiKylKwmfOzZswezZs1CcXExYmJisG/fvkdO4E1PT0evXr2Qnp6O6Oho7N+/H6NHj8bHH39sm6KtoGwCNVAyibosHEnh9ddfl6xtIiIiMciqZ6i4uBhr1qzB7t27q3zNG2+8gYKCApw/fx47d+7Ezz//jKVLl+Knn36yYqXWVbbOECD9UNmiRYskbZ+IiMhSsgpD/fr1Q4sWLap8viAI2LhxI0aPHg1PT08AQNu2bdG2bVtZD++oXJRQKRUApN+5nhu1EhGR3MkqDFVXYmIisrKy8Nhjj5U7Hh0djZiYmAqv0+l0yM7OLveyN1q1fWzJwY1aiYhI7hw6DGVlZQEAfH19yx339/c3ffYwixYtgo+Pj+kVGhpqzTLNorGTVahHjRolaftERESWcugwpNVqAQB5eXnljufk5Jg+e5jZs2cjKyvL9EpMTLRqneawl7WGfvnlF0nbJyIispSsniarrrp160KtViM+Pr7c8fj4eERGRlZ4nUajgUajsXJ1lnGzk7WGGjRoIGn7RERElnK4nqHff/8d27dvBwC4urqiV69e2LRpk+nzlJQU/Prrr+jfv79UJYri3lpD0oahgoICSdsnIiKylKx6hq5cuYJDhw4hIyMDQMm6Q/Hx8WjRooXpKbPVq1fj6NGjePrppwEA7733Hjp06IBnn30WTz75JL788ku0aNFC9nNd7GUC9d27dyVtn4iIyFKyCkPJycn47bffAJRM3E1OTkZycjJ8fX1NYahDhw7lFmKMjo7G2bNnsXr1aly6dAnjxo3DmDFjoFarJfgTiEejLp0zJHHPUPPmzSVtn4iIyFKyCkMdO3ZEx44dKz3npZdeeuBYeHg43n33XWuVJYmyYTKp1xnatWsXGjZsKGkNRERElnC4OUPOwl6GycaPHy9p+0RERJZiGJIpNzsZJvvoo48kbZ+IiMhSDEMypbWTp8m4HQcREckdw5BM2cuj9dyOg4iI5I5hSKY0djKBety4cZK2T0REZCmGIZmylwnUW7dulbR9IiIiSzEMyZS9TKBu3bq1pO0TERFZimFIpuxlzlBSUpKk7RMREVmKYUim7GWYrLhY2jBGRERkKYYhmSobJpN6AnV4eLik7RMREVmKYUim7GWY7ODBg5K2T0REZCmGIZmylzD0/PPPS9o+ERGRpRiGZMrNTuYMrVixQtL2iYiILMUwJFPcjoOIiEgcDEMyZS/rDHE7DiIikjuGIZlyu287DkEQJKtjypQpkrVNREQkBoYhmSoLQ0YB0BdLN29ozZo1krVNREQkBoYhmXJ3dTH9vkAv3VBZz549JWubiIhIDAxDMqV2UULtogAA5EsYhi5evChZ20RERGJgGJIxd1cVAGnDkIeHh2RtExERiYFhSMbKhsry9QbJavD395esbSIiIjEwDMmY1hSGpOsZOnfunGRtExERiYFhSMY8SofJpJxA3adPH8naJiIiEgPDkIyV9QzlSThMtnr1asnaJiIiEgPDkIy528EwGbfjICIiuWMYkrGyMCTlMBm34yAiIrljGJIxe3i0fubMmZK1TUREJAaGIRmzh0frlyxZIlnbREREYmAYkjF7eLT+mWeekaxtIiIiMTAMyZiHHQyTHT9+XLK2iYiIxMAwJGP2MEwWEhIiWdtERERiYBiSMXsYJnNxcZGsbSIiIjEwDMmYPaxAfePGDcnaJiIiEgPDkIzZwwrUHTt2lKxtIiIiMTAMyZg9LLq4ceNGydomIiISA8OQjNnDdhwzZsyQrG0iIiIxMAzJmD2sQP1///d/krVNREQkBoYhGbOHR+u5USsREckdw5CMlU2gLigqhiAIktTAjVqJiEjuGIZkrOzRekEACouMktTw4osvStIuERGRWBiGZEyrvrfgoVSP1//888+StEtERCQWhiEZUyoVcFOXfAmlery+cePGkrRLREQkFoYhmZN6s9acnBxJ2iUiIhILw5DMSb0KdWZmpiTtEhERiYVhSOakXoW6adOmkrRLREQkFoYhmdNKPEy2e/duSdolIiISC8OQzHlIvPDiK6+8Ikm7REREYmEYkjmp9yf7+OOPJWmXiIhILAxDMif1MBm34yAiIrljGJI5D9MEammGybgdBxERyR3DkMzde7Remp6hV199VZJ2iYiIxMIwJHNSP1q/efNmSdolIiISC8OQzLmb5gxJM0z25JNPStIuERGRWBiGZM5d4mGymzdvStIuERGRWBiGZE7qYTJBECRpl4iISCwMQzKnlXiYLDQ0VJJ2iYiIxMIwJHMeEi+6eOTIEUnaJSIiEovswtDq1avRvHlzBAcHo1evXjh9+nSl50+bNg2+vr7lXu3bt7dRtdanlTgMPfvss5K0S0REJBZZhaENGzZg/PjxmDlzJg4fPozIyEh0794dSUlJFV6Tn5+PLl26ID4+3vT66aefbFi1dZU9TSbVnKFPP/1UknaJiIjEIqswtGjRIrz00ksYMWIEIiMjsXz5cmg0mkf+QFar1eV6hry8vGxUsfVJvVErt+MgIiK5k00YyszMxPnz59GjRw/TMRcXF3Tv3h2HDh2q9NpffvkFtWrVQuPGjTF27FikpKRYu1ybkXoFam7HQUREciebMHT79m0AQM2aNcsdDwoKMn32MLVr18bSpUtx9OhRrF69GrGxsejQoQPy8vIqvEan0yE7O7vcy16VDZPpDUYUG23/mPvUqVNt3iYREZGYZBOGyiiV5UtWqVSVrnUzd+5cjBw5EnXr1kW7du2wbds2JCYmYuPGjRVes2jRIvj4+Jhe9vz4eNk6Q4A0Q2VffPGFzdskIiISk2zCUFBQEAAgLS2t3PE7d+6YPquKwMBAhIWF4dKlSxWeM3v2bGRlZZleiYmJ5hVtAxqVEkpFye+leKKsd+/eNm+TiIhITLIJQzVq1EC9evVw8ODBcscPHDiAtm3bVvk+eXl5uHnzZqUBSqPRwNvbu9zLXikUivv2J7N9GLpw4YLN2yQiIhKTbMIQUDI/5fPPP8fhw4eh1+uxaNEiJCcnY9y4caZzpkyZYlpHSKfT4aWXXsLly5chCAKSkpLwwgsvwNXVFc8//7xUfwzRaSV8osyRnswjIiLnpJK6gOqYPHky0tLS0LdvX+Tl5SE8PBzff/89oqKiTOfk5+ebJjxrNBr07NkTQ4YMQVxcHNRqNTp16oTDhw+jdu3aUv0xROfh6oJUSNMz5OPjY/M2iYiIxKQQZLjTpiAIKCwshFarfeCzgoICGAyGB3os9Ho9XF1dzWovOzsbPj4+yMrKssshsz5LDuJCUjbWvNQaXRtWff6UGFavXo3Ro0fbtE0iIqKqqOrPb1n1DJVRKBQPDUIAKjxubhCSAy+NdHOG/v73v9u8TSIiIjHJas4QPZyHpmTOUG6h7ecMrV692uZtEhERiYlhyAF4uqkBADk624chbsdBRERyxzDkADxLh8nyJAhD3I6DiIjkjmHIAXiWDZNJEIb+9a9/2bxNIiIiMTEMOQBPTekwmQRzhj766CObt0lERCQms8JQQkICBg0ahKCgIKhUqgdeZFuebiV/51L0DA0dOtTmbRIREYnJrOQyevRo6PV6LFmyBH5+fmLXRNXkJeGcoSNHjqBevXo2b5eIiEgsZoWho0eP4sqVKwgODha7HjKDR2kYkuLR+tDQUJu3SUREJCazhslCQkKgVHK6kb0oGyaT4tF6IiIiuTMr0YwePRpvvvkm9Hq92PWQGcoerc/VFdm87cTERJu3SUREJCazhsnWrVuHCxcuYNOmTQgNDYVCoSj3eUxMjCjFUdV4uZXNGbL9dhzt2rWzeZtERERiMisMjR07Vuw6yAJSzhn67rvvuNYQERHJmllh6LXXXhO5DLJE2TCZvtgInaEYGpWLzdqeNm2azdoiIiKyBotnQet0OhQWFopRC5mpLAwBth8qe++992zaHhERkdjMDkOrVq1C/fr1odVq4e7ujvr162PVqlVi1kZV5KJUQKuWZud6btRKRERyZ1YYWrx4MaZPn47nnnsOO3bswM6dO/Hcc89h+vTpWLx4sdg1UhXce7zetk+UcaNWIiKSO7PmDC1btgwbNmxAv379TMf69euHdu3aYeLEiZg5c6ZoBVLVeGlUSM3R2bxnaPTo0TZtj4iISGxm9QwlJSWhU6dODxzv2LEjbt++bXFRVH1lPUN5etuGoT179ti0PSIiIrGZFYYiIyOxdevWB45v3rwZkZGRFhdF1efhWjpMZuOeoccee8ym7REREYnNrGGyuXPnYtSoUdizZw/atGkDADh27Bi2bt2KtWvXilogVY1UO9dnZWXZtD0iIiKxmRWGhg8fjtq1a2Px4sX45JNPoFAo0KRJE/zyyy/o3Lmz2DVSFXhJtPBiTk6OTdsjIiISm1lhCAC6dOmCLl26iFkLWaBsFeo8G/cMNW7c2KbtERERiY1bzzsIqXau/9///mfT9oiIiMRW5Z6h8PDwKt80Pj7ejFLIEp4SDZO9/PLLNm2PiIhIbFUOQ1xp2L55SfRo/ZIlS/jfBhERyVqVw9CYMWOsWQdZSKpH6xmEiIhI7jhnyEFI9Wg9t+MgIiK5q/acofj4+EfOH+KcIduT6tH68ePH27Q9IiIisZk1Z4hDI/ZHqkfrv/32WwYiIiKSNbPmDHH+kP2R6tH6du3a2bQ9IiIisZk1Zyg1NRUrVqwwvV+9ejUaNWqEfv36ITk5WbTiqOpMw2Q6AwRBsFm7iYmJNmuLiIjIGswKQzNnzoSPjw8AIDk5GZMmTcLzzz8PQRAwffp0UQukqinrGRIEIF9fbLN2FQqFzdoiIiKyBrO24/jxxx/xn//8BwCwZ88edOvWDfPmzcPt27fx+OOPi1ogVY1W7QKlAjAKJfOGyuYQWVudOnVs0g4REZG1mNUzpNfrUVRUBADYu3cvevbsCQDw9PSETqcTrzqqMoVCYQpAtpw3dPToUZu1RUREZA1mhaEOHTpg4sSJWLFiBbZt24YBAwYAAI4dO4Ynn3xS1AKp6qR4vH7IkCE2a4uIiMgazApDy5cvR25uLpYtW4b3338f9evXBwAsXbqUj91LSIqFF1euXGmztoiIiKzBrIkl4eHh2L179wPHd+7caXFBZD4Pje3DEMMvERHJnUXbcZw+fRrr16/H+vXrcebMGZFKInNJsXM9t+MgIiK5M6tn6Pbt2xg+fDj2798PT09PKBQK5OTkoFu3bvjmm28QEhIidp1UBV4SDJO99tprNmuLiIjIGszqGRozZgwEQcCFCxeQk5OD7OxsXLhwAQaDAa+88orYNVIVle1cb8swtGrVKpu1RUREZA1m9Qzt27cPFy9eRFhYmOlYo0aNsHbtWjRp0kS04qh6TFty2HCYrE+fPjZri4iIyBrM6hkKCQmBSvVgjlKr1Rwik5C3mxoAkFNYZLM2z58/b7O2iIiIrMGsMDRq1CiMGzcOSUlJpmNJSUkYN24cRo0aJVpxVD3e2pIwlFVguzDk6+trs7aIiIiswaxhsk2bNuHChQsIDQ1F7dq1IQgCbt++jeLiYly7dg3ffvut6dyYmBjRiqXK+UgQhry8vGzWFhERkTWYFYbGjh0rdh0kgrIwlG3DOUMXLlzgquNERCRrZoUhPk5tn7xLJ1Bn27BnqFevXjZri4iIyBosWnSxoKAAFy5cEKsWspCPu+2HydasWWOztoiIiKzBrDCUm5uLESNGwNPTs9yj9M8++yxOnjwpWnFUPaZhsoIiCIJgkza5HQcREcmdWWFo9uzZuHXrFv74449yx1988UW88847ohRG1VcWhgxGAfn6Ypu0ye04iIhI7syaM7Rt2zYcOHAA9erVK3f8ySefxLBhw0QpjKpPq3aBSqmAwSggq6DItHGrNc2aNcvqbRAREVmTWT1DaWlpCAoKAgAoFArT8YKCApsNz9CDFAqFzR+v/+CDD2zSDhERkbWYFYZatGiBH3/8EUD5MLRkyRK0bdtWnMrILPfPG7KF5557zibtEBERWYtZ4ygLFizA4MGD8fvvvwMA3nvvPezZsweHDx/Gr7/+KmqBVD1eNu4ZOnToEMLDw23SFhERkTWY1TPUs2dP/PTTT7h+/TqCg4Px8ccfw93dHfv370fHjh3FrpGqwdbDZPdv1ktERCRHZs+wbdeuHbZv3y5mLSQCW69CXVxsm6fWiIiIrMWiRRfJ/vhoS/KtrXqG7t+sl4iISI6s/+y1yLKysrB161akpKSgadOm6Nu3b7lJ3GJdI1febradQN2mTRubtENERGQtsuoZSkhIQNOmTfHZZ5/h1q1bGDt2LAYPHlzp4/zmXCNntn6abMuWLTZph4iIyFpk1TP0r3/9CyEhITh48CBUKhUmT56MJk2aYPPmzRg6dKho18iZrSdQT5061SbtEBERWUu1eoYiIyMxdepU/Pzzz9Dr9daq6aGKi4uxfft2jBw5EipVSYZr0KABOnfujM2bN4t2jdx52zgMLV682CbtEBERWUu1eoY++eQT7Ny5Ey+//DIyMzPRq1cv9O/fH3379kXNmjWtVSOAkuGugoICREVFlTseFRWFY8eOiXYNAOh0Ouh0OtP77OxsCyq3LVv3DHGjViKqjmKjgMKi4pKXwXjv90UP/l5fbITeYERRsRG60l/1hnvHSj4XSn8tRlGxUPL5fdcZHXNGhENaO7oNAr00krRdrTDUt29f9O3bFwBw9uxZ7Nq1C5999hnGjh2Lli1bon///ujfvz8ef/xx0QvNzc0FAPj4+JQ77uvra/pMjGsAYNGiRQ/dcHbYsGFQq9XVqtvWcgqLcOd6OrJUSjz1W6DV27t8+TIaNGhg9XaIyDYEQUCxIKC4GDAIRhQXl7433nsZjA++NwoCjMaSc41GAUahJPjce1/yewedrkki+MeeGnBTu4h6z6KiqnUMmD1nqHnz5mjevDnefPNNpKam4scff8SuXbvwwQcfwMvLC/369cN///tfc2//AE9PTwAlT4bdLzMz0/SZGNcAwOzZszFt2jTT++zsbISGhmLTpk3w9vY2q35bSbibj86L98FNrcSO+X2s3t7t27dRq1Ytq7dDRJUzFBuRqzMgu8CA7MIi5BQakPOXX+8dL/l9rs6AfF0x8vQG5OuLkaczQGcwml2DAtX7oeKqUsJNpYSb2qX0Vfp7lQs0aiU0KhdoVEqoXRRwVSmhdlHCVaWEa+mv979Xq5TQuCihVing6uICtYsCapUSLg765LAjahPhL3oYys7OfqBD5GFEmUAdGBiIUaNGYdSoUSgqKsKBAwewa9cuMW5tEhoaCq1Wi7i4OPztb38zHY+Li0PDhg1FuwYANBoNNBppuuosVTZMVlhkhM5QDI1K3P+w/mr37t14+eWXrdoGkTPRG4zIzNcjI78IGfl6ZObrkZlfhIz8otLjetPvM/OLTAEnXy/uAqgqpQLuri7w0KjK/+qqgrtGBQ9XF7i7quChcYHWtSTAaF1LA42qJNxo7gs3pqCjvneOUsmgQvZB9KfJ1Go1evTogR49eoh6X5VKhaeffhrr1q3Dq6++CpVKhcuXL+PAgQNYv3696bwdO3bg5s2bmDBhQpWvcSRebiooFIAgANkFBgR6WTcMNWvWzKr3J5I7o1FAZkER0nJ1SMvRITVXh7Rcvel9Wq4Od/P0uJtbEnzyLAw1bmolvNzU8HZTwctNDS83Fbzd1PDWlr7XqEqOadXw1Kjgqbkv3NwXclxVslp5hcgisnq0/r333kOHDh3QuXNnPPHEE9i6dSsGDBhQ7hH5HTt24OjRo5gwYUKVr3EkSqUCXhoVsgsNyCoosvpktPT0dKven8heCYKArIIiJGUVIjm7EMlZhUjKKkRK6fvU0qCTnqeHoZqzeJWKkl5eP3dX+LqX/OpT+qufuxq+7q6mz7zLAk9puGGIIao+WYWhunXrIiYmBlu2bEFKSgpWrlyJfv36lVtN+qmnnkLLli2rdY2j8daqTWHI2vLy8qzeBpEUCouKcTOjAIkZ+biZUYBbGQVIyS5EUlYBkksDT2FR1efX+GjVqOHpihqeGtTw0iDQU4NAL43pmL9H+YDDISQi25FVGAJKngwbPXp0hZ8/9dRT1b7G0fho1biZUYDsQuuHoUaNGlm9DSJrMBoF3M4qQMLdfCRm5CMx/V7wSUzPx50c3aNvAsDfwxU1vd0Q4uOGYB83BHuXvEqCjgY1vFwR4KFhjw2RHatWGKpooUJvb280bNgQYWFhohRFlrHllhx79+5FkyZNrN4Okbky8vS4lpaHa6m5uJ6Wh+tpebiWmof4u3mPfHLKw9UFof7uqOPnjjp+WgT7lIYe75LgU9PbTfSnX4jI9qoVhh41z2bIkCFYs2YNPDw8LCqKLFO2WasthslefPFFq7dBVBUZeXpcSsnBpeQcXErJweXkHFxJzUVmfsXfB2oXBUL93RHq545Qfy3q+JX/vZ+72qGH1ImoRLXCUEZGxkOP5+Tk4Ny5c5g5cyYWLFiARYsWiVIcmce0CnUlPwTEsnTpUq5CTTalNxhxOSUHsUnZuFwafC4l51Q6rFXLxw0RgR6IqOGBejU8ERHogcganqjl6waVC4eviJxdtcKQr69vhcdDQ0NRo0YNjBo1imFIYj7upcNkNpgzxCBE1qQzFONyci7O38oqfWXiUnIOioof/nRWHT8tGgV7oUFNLzQM9kL9IE9E1PCAu6vspkcSkQ2J+i9E06ZNkZCQIOYtyQy23J9swYIFDEQkCkEQkJhegJMJ6TgRn4GzNysOPj5aNR6r5Y2GwV5oWBp8omp6wVPD0ENE1Sfqvxw3btxAcHCwmLckM3i7lXxZbRGGytZzIqouvcGImNtZOHUjAyfiM3AyIQOpDxnq8tGq0bS2D5rW8Sn5tbYP6vhpOZeHiEQjWhi6evUqJk6cKPrK01R93qanyQxWb2vDhg2YOHGi1dsh+SsqNuLczUwcvnIXv19Nw+mEzAee5lK7KBBd2wet6vrh8bp+aFaHwYeIrK9aYaiiXp+cnBzk5+ejRYsWWLBggSiFkfnKhskybdAz1KlTJ6u3QfJkNAqITcrGkat3cfhqGo5fT39g/yw/dzVahfmjVZgfngj3Q9PaPnxUnYhsrlphaNKkSQ897uXlhYYNG6JXr15wceE/ZFLz93AFUPKosbXFx8dzfzIyyS4swsHLadh36Q5+u5SKtNzyw15+7mq0j6yBdpEBeLJeACIDPdjrQ0SSq1YY4kRZeSgLQ+n5egiCYNUfNgy/zk0QBFxNzcWvF+/g14t3cCI+o9w+XB6uLmhbLwDtIwPQPrIGGgV7cZsJIrI7fPTCAZWFIb3BiDx9sVWfsAkJCbHavck+CYKAC0k52B2ThB/PJ+Fqavn96eoFeqB7wyB0bxSEJ8L9uQ0FEdk9hiEH5O6qgptaicIiIzLy9FYNQ3/88Ue5jXHJMQmCgD9vZ+OH80nYfT4J8XfzTZ+5uijRtp4/ujcqCUBhAVyBnojkhWHIQfm7u+J2ViHu5ukR6u9utXYGDx5stXuT9G7czcPWU7ew7fQtJKTfF4BUSnRtEIi+TUPQvXGQaQsYIiI5YhhyUP6eJWHI2pOo//vf/3IumYPJyi/CrvO3se3ULZy4cW8LHje1Et0aBqFv0xB0axTEBQ6JyGHwXzMH5edeMm/orpXDEIOQYxAEAUevpeObYzfwv9gU6EvX/1EqgI5RgXimZW30alKT21oQkUPiv2wOKsBGj9dzOw55y8zXY/PJm1h/PAHX7psI3SjYC4Nb1sbTLWqjprebhBUSEVkfw5CD8vOwTc/QtGnTrHp/so7zN7Pw5e/X8cO5JNMq0B6uLnj68doY3qYuomv7SFwhEZHtMAw5KFv1DH366aeYPn26VdsgcRiNAn69eAerDl7DsevppuONQ7zxj7Z1MfDx2pwHREROif/yOSi/+xZetKb+/ftb9f5kucKiYmw5dRNfHLpuGgpTKRXo1ywEo9qH4/FQX64CTUROjWHIQfmXTqBOt3LP0NmzZ9GwYUOrtkHmydMZsO7oDaw6cM00XOqlUWF427oY1T4ctXy1EldIRGQfGIYclK32JwsICLDq/an68nQGrD1yA6sOXjOF4dq+WozuGIFhrUM5FEZE9Bf8V9FB+dtoArVWy94Fe5GrM2DtkXisOnANGflFAICwAHdM6lYfAx+vDbULt8UgInoYhiEHVRaGsgqKYCg2QmWlH4SXL19G+/btrXJvqpqiYiM2Hk/Ax3vjTOE3PMAdk7pHYWCLWlb72hMROQqGIQfl6+4KhQIQBCAjvwiBXhqrtNOjRw+r3JceTRAE/Bybgv/bc9E0MTo8wB1TekThqeYMQUREVcUw5KBclAr4atXIyC9CRr7eamHoq6++4qKLEjiTmImFP1zA8fiSR+T9PVwxtUcUhrety+EwIqJqYhhyYH4ersjIL8LdXD1Q0zptMAjZVmqODot2X8DWU7cAABqVEi93jMCrXSO5WSoRkZn4v5AOzLTwohXXGlqwYIHV7k33GIqN+Or3eHT/8DdsPXULCgXwTMs62DejK17/eyMGISIiC7BnyIHZYrPW2bNnW+3eVOJUQgbmbItBbFI2AKBpbR+8+/RjeLyun8SVERE5BvYMObAAT+uvNfT+++9b7d7OLl9vwDs7/8Qzn/6O2KRseLupMH9gNL6f2IFBiIhIROwZcmB+NliFevjw4Va7tzP7/Uoa/rX1HBLTCwCUDIm90bcRAjytMxGeiMiZMQw5sLK1hqwZhg4cOICRI0da7f7OJqewCAt/vIgNxxMAlKwcvXBwU3RpEChxZUREjothyIH522ACdUREhNXu7WxO3kjHa5vOmHqDRj4Zhn/1acTtM4iIrIz/yjow05YcudYLQwaDwWr3dhaGYiOW/noFy36Ng1EA6vhp8cHQ5niyHvd9IyKyBYYhB2aLnqHk5GSr3dsZxKfl4bVNZ3AmMRMAMLhlbbzz1GPw4qPyREQ2wzDkwO7frFUQBCgUCtHbaNWqlej3dBY/nk/C65vPIVdngJebCgsHNcWA5rWkLouIyOnw0XoHVhaG9AYj8vTFVmnj+++/t8p9HVlRsRHv7ozFhG9OIVdnQJtwf+x5rTODEBGRRNgz5MDcXVVwd3VBvr4YaTk6q0zEnTx5suj3dGTJWYWYuP4UTt7IAACM61IPM3s35KaqREQS4r/ADq5sg9bUXJ1V7v/BBx9Y5b6O6MjVu+i39CBO3siAl5sKn41shdl9GjMIERFJjD1DDi7QU4Mbd/ORmmOdMMSNWqtm/bEEvLU9BgajgMYh3lg5oiXCAjykLouIiMCeIYdn6hmyUhjiRq2VMxQb8faOP/HGtvMwGAUMaF4L2ya0ZxAiIrIj7BlycGVhKM1Kw2Rjxoyxyn0dQVZBESZvOI0Dl1MBANN7NcCk7vWt8lQfERGZjz1DDi7Q07o9Qzt37rTKfeXuZkY+nvn0dxy4nAqt2gWf/qMlJveIYhAiIrJD7BlycNYeJmvRooVV7itnF5KyMWr1cdzJ0SHExw2rXngC0bV9pC6LiIgqwDDk4Kz9NNndu3etcl+5OnrtLl5ZewI5hQY0rOmFNaNbI8RHK3VZRERUCYYhB2ftnqGCggKr3FeOfjyfhNc2noG+2Ig24f5Y9cIT8HHnthpERPaOYcjB3T+B2mgUoFSKO2clKipK1PvJ1TfHbmDO9zEQBOBvj9XEkuceh5vaReqyiIioCjiB2sEFeJSEoaJiAVkFRaLff9++faLfU25WH7qON7eVBKHhbetixT9aMQgREckIw5CDc1Up4Vc6VHPHCkNlL7zwguj3lJOV+6/i3V2xAEq21vj3wGi4iNz7RkRE1sUw5ARqersBAFKyC0W/9yeffCL6PeVi6S9x+L/dFwEAU3pEYdbfG/HReSIiGWIYcgJBpWEo2QphyBm34xAEAR/8dAkf/XwZADCjdwNM69WAQYiISKYYhpxAsHfJvKE7VghDzrgdx5Jf4rBs3xUAwJt9G2NSd04iJyKSMz5N5gSCrdgzNGnSJNHvac8+O3AVH++NAwDM6dcYYzrVk7giIiKyFHuGnIBpmCxL/AnUX3/9tej3tFfrjt7Awh9L5gjN6N2AQYiIyEEwDDmBsp6hOzni9wx16dJF9Hvao80nb2Lu9zEAgAldIzk0RkTkQBiGnECwT1nPkPhh6OrVq6Lf097sPp+E1zefBQC82D4cM//WUOKKiIhITAxDTiDI+94q1IZio6j3dnV1FfV+9ubYtbuYuukMjAIw7IlQvNW/CZ8aIyJyMLKdQF1UVAS1+tH7Pul0OhQVlV952cXFBVqt82yeWcNDA5VSAYNRQFqu3tRTJIaaNWuKdi97czklB6+sPQG9wYjeTWpi4eCmom9nQkRE0pNdz9D8+fMREBAANzc3NG7cGHv37q30/KlTp8LX1xfBwcGml7PMcymjVCoQVLpHmdhPlJ08eVLU+9mL5KxCjFp9HNmFBrQK88PS5x/nytJERA5KVmFo+fLlWLx4MbZs2YLc3FwMHz4cAwYMeOS8lYEDByI3N9f0On78uI0qth/3nigTNww9/fTTot7PHmQXFuHFL48jKasQ9QI98PkLT3CvMSIiByarMPTxxx/j5ZdfRteuXaHVajF37lwEBQVh5cqVj7zWYDDYoEL7Vcu3JAwlZRWIet9Vq1aJej+p6Q1GjFt7EheTcxDopcFXL7WBn4djz4siInJ2sglDd+/exZUrV9C5c+dyx7t06YKjR49Weu2uXbug1Wrh7e2Nvn374uLFi9Ys1S7V8imZI3U7U9ww5EjbcQiCgLnfx+DItbvwcHXBly+2Rqi/u9RlERGRlUkahnQ6Xbnhq4e9BEEAAKSkpAAAAgMDy90jMDAQd+7cqbCNxx57DLt370Z+fj7+/PNPuLq6olu3bkhPT6+0ruzs7HIvuavlWxaGxB0mc6TtOFYfjsemE4lQKoBlw1siuraP1CUREZENSBqGpk6dWm5i88Ne169fL3eN0Wh84H1ljzpPnjwZ3bp1g1qtRmhoKNatW4esrCxs2rSpwmsWLVoEHx8f0ys0NNSyP6gdKAtDt0TuGZo+fbqo95PKvkt38O8fYgEAb/RtjG6NgiSuiIiIbEXSMLRy5cpH9gzVq1ey5UGtWrUA4IFeoDt37iAkJKTKbXp5eaF27dq4du1ahefMnj0bWVlZpldiYqIZfzr7UtvXOsNkK1asEPV+UrhyJwdT1p+GUQCefaIOXu4YIXVJRERkQ7KZM+Tr64vHHnsMv/zyi+mY0WjEr7/+io4dO5qO6XQ6FBRU/AP/7t27SEhIqLS3R6PRwNvbu9xL7somUKfm6qA3iLfw4lNPPSXavaSQkafHy1+dQI7OgDbh/lgwsCkXVSQicjKyCUMAMGvWLHz55ZfYtGkTEhISMGXKFBQUFGD8+PGmcyZOnIjWrVsDKAlGvXv3xq+//oqUlBT88ccfGDx4MAICAjBixAip/hiS8PdwhUalhCAAKSKuNXTq1CnR7mVrxUYBkzecxo27+ajjp8WnI1rCVSWrbwkiIhKBrFagHjFiBPLz8/HOO+8gJSUFTZs2xd69e01DaADg5uYGd/eSJ4A0Gg3efPNNvPfeezh9+jT8/PzQqVMnbNiwAf7+/lL9MSShUChQy1eL62l5uJVZINpTUn+d0C4nH/18CYeupEGrdsHno55AgKdG6pKIiEgCsgpDADB27FiMHTu2ws+XLVtW7n2XLl2cbsXpitTydcP1tDxR5w1pNPIMEP/7MxnL95Us1vnekGZoFCz/oVAiIjIPxwScSNlaQ7cyxAtDcty1/npaHqZ/e28X+qea13rEFURE5MgYhpxI2dBYYka+aPfs2rWraPeyhXy9AeO/PokcnQFPhPnhjb6NpS6JiIgkxjDkROqWhqGEdPHC0Lp160S7l7UJgoA3t8XgYnIOanhqsPwfnDBNREQMQ04l1L9kmCwxXbxhstmzZ4t2L2vb+Ecitp2+BRelAsuGP46apZvXEhGRc2MYciKhfiU9Q0lZBSgqFmetoYULF4pyH2u7nJKDt3f8CQCY0bshnqwXIHFFRERkLxiGnEiglwYalRJGQbyVqN944w1R7mNNBfpiTPzmFHQGIzo3CMS4zvWkLomIiOwIw5ATUSgU9yZRizRUtmjRIlHuY03v7voTcXdyEeilwUfPNodSyRWmiYjoHoYhJyP2JOqRI0eKch9r2Xn2NjYcT4RCAXw8rAVqcGFFIiL6C4YhJxPqVzKJWqww9Ntvv4lyH2tIuJuPN7aeBwBM7FofHerXkLgiIiKyRwxDTqZugAcAICE9T5T7RUZGinIfsRmKjZiy8bRpPaHXekZJXRIREdkphiEnE1GjZJjsWqo4YUin04lyH7Et33cVZxIz4eWmwsfPtYDKhf+pExHRw/EnhJOJqOEJALhxNx9Go2Dx/VJTUy2+h9jOJmZi6a9xAID5T0ejjp84m9ISEZFjYhhyMnX8tHBRKlBQVIyUnEKL79eyZUsRqhJPgb4Y/9x0BsVGAf2bheDpFtx3jIiIKscw5GTULkrTE2XX0ywfKtuxY4fF9xDTwh8v4FpaHoK93bBgYDQUCj5GT0RElWMYckLhAeKFoQkTJlh8D7Hsu3QH647eAAAsHtoMvu6uEldERERywDDkhMrmDcWLEIY+/PBDi+8hhow8PV7ffA4A8GL7cHSKCpS4IiIikguGISck5hNlc+bMsfgelhIEAW9sO4/UHB3qB3liVp9GUpdEREQywjDkhCKDSnqGrqbmWnyvBQsWWHwPS20/cxu7Y5KhUirw8bAWcFO7SF0SERHJCMOQE4oK8gIA3EjPR2FRsUX3euWVV8QoyWx3cgoxr3Q3+qk9ohBd20fSeoiISH4YhpxQDU9X+LqrIQiW9w5t375dpKqqTxAEzNkWg6yCIkTX9sarXe1zNWwiIrJvDENOSKFQIKp0qOzKHcvCUKtWrcQoySw7zyXhf7EpULsosHhIc6i5yjQREZmBPz2cVFTNkqGyuBTLwlBKSooY5VRbao4O87bHAAAmdYtC4xBvSeogIiL5YxhyUmU9Q3F3ciy6j16vF6Ocapu3IwYZ+UVoHOKNCd04PEZEROZjGHJSZZOoL1vYMyTFrvU/nEvCj+dLnh77YGgzDo8REZFF+FPESTUMLglD8XfzkKczmH2f/fv3i1VSldzN1eGt0uGxCV0j8VgtPj1GRESWYRhyUoFeGgR5aSAIwMVk84fKRowYIWJVjzZvx5+4m6dHo2AvTOoeZdO2iYjIMTEMObEmtUomHV9Iyjb7HsuWLROrnEfaE5OEXeeS4KIseXrMVcX/fImIyHL8aeLEyp7AirUgDNlqO46MPD3mfF8yPDaucz00rcPhMSIiEgfDkBNrUhaGbpsfhmy1Hcc7O/9EWq4eUUGemNqTw2NERCQehiEnVjZMdjE5G4Zio1n3mDx5spglPdTPsSn4/sxtKBXA4qHNoVFx7zEiIhIPw5ATiwjwgKdGhcIio9mP2K9du1bkqsrLzNfjjW3nAQCvdK6HFqG+Vm2PiIicD8OQE1MqFWhWOvfm7M1Ms+7RrVs3ESt60Lu7YpGao0O9QA/8s2cDq7ZFRETOiWHIyZX1tJxNzDTr+ri4OPGK+YtfL6Zg66lbUCiAxUOaw03N4TEiIhIfw5CTa14ahs6YGYa0Wq14xdwnq6AIs7eWDI+93CECrcL8rNIOERERw5CTe7w0DF1OyTFrJeqAgACRKyoxf1csUrJ1iKjhgem9G1qlDSIiIoBhyOkFebuhtq8WRgE4nZBZ7evPnDkjek37Lt7B5pM3S4fHmkHryuExIiKyHoYhQtsIfwDAset3q33tgAEDRK3l/uGx0R0i8ES4v6j3JyIi+iuGIUIbUxhKr/a1n3/+uai1LNgVi+TsQkTU8MAMDo8REZENMAyRKQydScxEYVFxta4VczuOfZfu4LvS4bH3OTxGREQ2wjBEiKjhgRqeGugNxmrPGxJrO46sgiLM3lIyPPZS+wi05vAYERHZCMMQQaFQoGP9kqfCDsalVuvaGTNmiFLDv38oGR4LD3DHzL9xeIyIiGyHYYgAAF0aBgIA9l+uXhj65JNPLG77lwsp+PZE6dNjQ5tzeIyIiGyKYYgAAJ2iSsLQn7ezcSensMrXDRw40KJ2U3N0eH3zOQAliytyeIyIiGyNYYgAADU8NYiuXbKL/W+Xqt47dPLkSbPbFAQBs7acw908PRoFe2EGh8eIiEgCDENk0rNxTQDATzHJVb4mODjY7PY2HE/ELxfvwNVFiY+fa8G9x4iISBIMQ2TSJzoEAHAwLg05hUVVukalUpnV1rXUXMzfFQsAeP3vDdEo2Nus+xAREVmKYYhMGtT0RL0aHtAXG/HLhTtVuub69evVbqewqBgT159GQVExOtQPwOgOEdW+BxERkVgYhshEoVCgX7OS3qFtp29V6ZrOnTtXu523d/yJC0nZCPBwxYdDW0CpVFT7HkRERGJhGKJynmlZBwBwIC4VtzMLHnn++vXrq3X/zSdvYuMfiVAogCXPPY5gHzez6iQiIhILwxCVE17DA20i/CEIJcHlUV5//fUq3/ticjbmfF+yyvRrPRqgY1QNs+skIiISC8MQPeC51qEAgK+P3oDeYKz03EWLFlXpnpn5eoz/+hQKi4zo3CAQk7vXt7hOIiIiMTAM0QP6N6uFmt4a3MnRYcfZ25WeW5WNWvUGI179+iSup+Whlo8bPh7GeUJERGQ/GIboAa4qJV4qfcJr+b4rKCquuHfoURu1CoKAN7adx9Fr6fDUqLD6pdbw93AVtV4iIiJLMAzRQ414MgwBHq64npaHjccTKjxv1KhRFX4mCAL+/cMFbD55Ey5KBZYNf5zrCRERkd1hGKKH8tSoMLVnFADgw58vV7hf2S+//PLQ44Ig4L09l/D5oZJ1iBYOikbXhkHWKZaIiMgCDENUoefb1EWTEG9k5hdh9pbzMBqFB85p0KDBA8cMxUa8veNPrNx/FQAwf2A0hrWua/V6iYiIzMEwRBVSuyjx0bDmcHVR4peLd/DB/y49cE5BQfm1iLLyi/Dil3/gqyM3AABvD2iCkU+G2aReIiIic8guDKWlpeGDDz7AmDFjcOnSgz+cHyYhIQHz58/HpEmT8N///hc6nc7KVTqORsHeWDi4KQBgxW9X8e7O2HKP29+9exdAybDYz7Ep+PuSAzh0JQ3uri7478hWeJFbbRARkZ2TVRhavnw5mjdvjtjYWHzxxRdISkp65DWxsbFo3rw5Tp06hdDQUCxduhTdu3dHUVHVNiIlYEirOnijbyMAwOrD19F36UGsOxKPs4mZUAWGY+2ReAxcfhivrD2BpKxChAW4Y/Or7fG3x8zf0Z6IiMhWFIIgPDgRxE5dvHgRERERSE1NRWhoKPbt24euXbtWes2AAQOQn5+PvXv3QqFQICkpCREREVixYgVGjx5dpXazs7Ph4+ODrKwseHs779NQu88nYc73Mbibpzcdyz6+Fd5tBgMANKWP5E/pUR/urubtZk9ERCSWqv78ltVPrEaNGlXrfL1ej59++gnLly+HQlGyyF9ISAi6deuGnTt3VjkMUYk+TUPQPrIGvjuZiP/FpuDG3TzU7DIYDerUQMf6NTC4ZR0EemmkLpOIiKhaZBWGqishIQFFRUUIDw8vdzwiIgIHDx6s8DqdTlduXlF2dra1SpQdH3c1xnSqhzGd6gEoWXRxzsuPXoWaiIjIXkkahr788kscPny40nMWLVqEwMBAs+5f9qSTl5dXueNeXl4PPAX11zbfeecds9p0NlXZjoOIiMieSRqGIiMjUVxcXOk5Go35wy5l44MZGRnljqenp1c6djh79mxMmzbN9D47OxuhoaFm1+HIFixYwEBERESyJmkY6ty5Mzp37my1+4eGhsLb2xuxsbHo06eP6fiff/6J6OjoCq/TaDQWhTBnMm7cOKlLICIisoisHq2viq+++grz5s0DACiVSgwbNgyrV69GXl4eAOCPP/7A0aNH8fzzz0tZpsPYunWr1CUQERFZRFZh6Pfff8eYMWPw+uuvAwAWL16MMWPGYMeOHaZzDh48iC1btpjeL1y4ECqVCs2bN8fgwYPRs2dPjB8/vlxPEZmvdevWUpdARERkEVk9TRYYGIgnn3wSANC9e3fT8Tp16ph+/+KLL6Jv376m9zVq1MCJEyewb98+pKSk4K233kKLFi1sVrOjq8rCl0RERPZMVmEoKioKUVFRlZ7TsWPHB46p1Wr07t3bWmU5tUdNgCciIrJ3shomI/vz1zWciIiI5IZhiCxS2eKVREREcsAwRBbhU3lERCR3DENkkRUrVkhdAhERkUVktWu9VLhrPRERkfxU9ec3e4bIIgsWLJC6BCIiIoswDJFFpkyZInUJREREFmEYIousWbNG6hKIiIgswjBEFunZs6fUJRAREVmEYYgscvHiRalLICIisgjDEFnEw8ND6hKIiIgswjBEFvH395e6BCIiIoswDJFFzp07J3UJREREFmEYIov06dNH6hKIiIgswjBEFlm9erXUJRAREVmE23FUAbfjICIikh9ux0E2we04iIhI7hiGyCIzZ86UugQiIiKLMAyRRZYsWSJ1CURERBZRSV2AHJRNq8rOzpa4EvvTu3dv/r0QEZFdKvv59Kjp0QxDVZCTkwMACA0NlbgSIiIiqq6cnBz4+PhU+DmfJqsCo9GI27dvw8vLCwqFQupyHik7OxuhoaFITEzk0292jl8r+eDXSl749ZIPa36tBEFATk4OatWqBaWy4plB7BmqAqVSiTp16khdRrV5e3vzHwGZ4NdKPvi1khd+veTDWl+rynqEynACNRERETk1hiEiIiJyagxDDkij0WDevHnQaDRSl0KPwK+VfPBrJS/8esmHPXytOIGaiIiInBp7hoiIiMipMQwRERGRU2MYIiIiIqfGdYZk6sKFC0hPT0eHDh2qdL4gCLhw4QL0ej2io6OhUvFLbytpaWm4ePEiGjVqhBo1alR6bkJCAhISEsodU6vVaNu2rTVLpFJpaWlITExEeHg4/Pz8qnRNQUEBYmNj4ePjg/r161u5Qiqj0+lw6dIl+Pr6IjQ09JEL4p47d+6BrYOCgoLQoEEDa5ZJpZKTk5GUlFSt763U1FTEx8cjLCwMQUFB1i1QIFnZuHGj0LZtW8HPz09wcXGp0jVxcXFCkyZNhMDAQKFu3bpCSEiIcOjQIStXSrGxscLIkSOFkJAQAYCwYcOGR14zb948wdvbW+jQoYPp1a9fPxtU69yOHz8udO3aVahRo4bQokULQavVCqNGjRJ0Ol2l123dulXw8fER6tevL/j4+Ajt27cXUlNTbVS1c8rKyhImTZok+Pr6Cs2aNROCgoKEZs2aCWfOnKn0urZt2wp169Yt97317rvv2qhq53Xs2DGhXbt2Qp06dYTmzZsLbm5uwgsvvPDI760ZM2YIGo1GaNKkiaDRaITJkycLRqPRanUyDMnMvHnzhN9//1348ssvqxyGWrduLfTt21cwGAyCIAjCxIkTheDgYCEvL8+apTq9LVu2CF999ZWQk5NTrTDUoUMHG1RH9/vmm2+E3377zfT+6tWrQmBgoDB37twKr0lMTBS0Wq3w0UcfCYIgCDk5OULz5s2FoUOHWr1eZ3b58mXhk08+EQoKCgRBEASdTicMHTpUiIiIqPS6tm3bCvPnz7dFiXSfTZs2CWfPnjW9v3LliuDl5SX85z//qfCar7/+WtBqtcLJkycFQRCEs2fPCu7u7sIXX3xhtToZhmSqqmHo3LlzAoByPUG3b98WlEql8N1331mzRCpVVFRUrTDUpk0b4fTp08KlS5eEoqIiG1RIDzNixAihW7duFX7+/vvvC35+fuW+RmvWrBFUKpWQkZFhgwqpzJ49ewQAwq1btyo8p23btsKMGTOE48ePCzdv3rRhdfRXTZo0EWbMmFHh5927dxeGDBlS7thzzz1n1f9R5ARqB3f69GkAQKtWrUzHQkJCUKdOHdNnZF9OnDiBf/zjH+jWrRtCQkKwfv16qUtyOkajEadOnap0DtDp06fRrFmzcvPv2rRpA4PBgPPnz9uiTCr1xx9/wNPTEzVr1qz0vBUrVuCVV15BkyZN0LJlS5w7d85GFTo3vV6PQ4cO4eeff8Zrr72G3NxcvPrqqxWef/r06XI/s4CS7y1r/sziLFoHl56eDnd3d7i5uZU7HhAQgPT0dImqooq0bdsW169fR926dSEIAj788EO88MILiIqKQuvWraUuz2m8++67iI+Px9atWys8Jz09HQEBAeWOlb3n95btnD17FosWLcKcOXPg4uJS4XkTJ07EkCFDoNVqkZubi3/84x8YOHAgYmJi4O7ubsOKnU9WVhZmzZqF7OxsXL16Fa+//jrCw8Mfeq4gCMjMzHzo91Z+fj50Op1VVqpmz5CDU6vV0Ol0EP6y0HhBQQFcXV0lqooq0qdPH9StWxcAoFAoMGPGDERERGDz5s0SV+Y8Vq5ciUWLFmHDhg1o2LBhheep1WoUFhaWO1ZQUAAA/N6ykbi4OPTp0wfPPPMMZs2aVem5I0eOhFarBQB4enriww8/xPXr13Hs2DFblOrUAgMDcejQIZw7dw5nz57Fp59+irfffvuh5yoUCqhUqgq/t9RqtVVqZBhycGFhYSguLkZKSorpmNFoRHJysumHLtm3oKAg3Lp1S+oynMKqVaswdepUbNy4EU899VSl54aFhT3wdSl7z+8t67ty5Qq6deuGbt264csvv3zko/V/VTakxu8t26pfvz4GDRqE3bt3V3hO3bp1H/q9VadOHSiV1oktDEMO6MSJE7h+/ToAoFOnTtBoNNixY4fp8/379yMzMxO9evWSqkQqlZCQUO7/TPPy8sp9npKSgnPnziE6OtrWpTmdzz//HJMmTcKGDRswaNCgBz4vKCjAoUOHkJmZCQDo1asXzp07hxs3bpjO2b59O2rXro3GjRvbqmyndO3aNXTr1g2dO3fG2rVrHzo8dvbsWVy+fBlAydfOaDSW+/x///sfAPB7y8r++m8aUBJk7x8Gu337Ng4dOmR636tXL+zatcs0oiEIAnbs2GHVn1mcMyQzly9fxp07dxAXFwcApv+AmjVrBm9vbwDAkCFDMHDgQHz88cfw8fHBG2+8gZkzZ0KhUMDT0xOzZs3C8OHD0axZM8n+HM4gMzMTMTExKC4uBgBcunQJhw4dQkhICCIjIwEAn332GVauXIm0tDQAQJcuXfDMM8+gRYsWSE1Nxfvvv49atWpVOtmQLLdx40aMHTsW//znPxEUFGT6vnJ3d0fLli0BADdu3ECnTp2we/du/P3vf8eAAQPQvn17DBo0CHPmzMG1a9fw0Ucf4YsvvrDa/70SkJSUhG7duiEgIADjxo3DkSNHTJ+1aNECnp6eAICXX34ZjRo1wtdff424uDi88sorGD16NCIiInD27FksXLgQI0eORIsWLST6kziHfv36oUePHmjZsiUMBgM2b96MAwcOmMIoAHz77bf45z//aQo///rXv7Bp0yaMHDkSw4YNw5YtW3D9+nWrThfgrvUyM3/+fPz0008PHP/000/RtGlTAMDQoUPRqVMnTJkyxfT5mjVrsGXLFuj1evTu3RuTJ0/mvAYrO3bsGKZPn/7A8YEDB2LGjBkASoZltm/fjl27dgEomXi7bNkyHDt2DB4eHmjbti0mTJhgmutA1rFw4UL8+OOPDxwPCwvDN998A6CkF2/48OH48MMPTSuC5+TkYPHixThy5Ai8vb0xatSoRw6vkWVOnDiB11577aGfffHFF6Z5XmPGjEFYWBjmzp0LAIiJicHKlStx+fJl1KpVC0899RQGDx5sq7KdVk5ODlasWIHDhw9DoVCgUaNGGD9+fLkJ1N999x2WLFlSrnfo8uXLWLx4Ma5evYqIiAjMmDHDqj2uDENERETk1NiXS0RERE6NYYiIiIicGsMQEREROTWGISIiInJqDENERETk1BiGiIiIyKkxDBEREZFTYxgiIqei1+uxceNG07YaREQMQ0QkWzt37kRycnK1rsnOzsbzzz+P+Ph46xRFRLLDMEREsnTnzh0MHjz4oZt0Vkaj0WDYsGHw8/OzUmVEJDfcqJWI7EJeXh527tyJ/v37Iz4+HpcvX0arVq0QFhb20PN/+OEHPPHEEwgMDHzo50VFRTh69Ciys7PRvHlz1KlTB0BJGBo4cCB8fHzKnX/p0iVcvHgRkZGRaNy4Mb777jv06tULAQEB5WpLTk7GhQsXULduXTRv3hwAcO7cOVy/fh2PPfYY6tevX+6+3377LYxGI1xcXBAWFobHH38carXa0r8uIhIRwxAR2YXU1FQ8//zz6N+/P+Li4tCsWTMEBQVVGIZ27dqF/v37P/SzmzdvokuXLnB3d0e9evUQExODUaNG4a233jINk50+fdq0Y/n8+fPx73//Gx07dkRKSgpCQ0Oxe/duHDlyBAEBAabaunTpgvT0dNSpUwd79+7F5MmTkZSUhNjYWISEhGDfvn347LPP8MILL5hq2b59O4qLi2EwGHDu3Dmo1Wrs2bMHoaGhov8dEpF5GIaIyK64u7sjNjYWSmXFo/h6vR4///wz3nrrrYd+/sUXXyA4OBiHDx8GABiNRuzcufOh5168eBFvv/02tm/fjv79+0MQhHJh5n5RUVH47LPPoFAosHLlSowfPx6TJk3CmTNnAAAffPAB5syZU+76sl3vy+p49tln8dZbb+HLL7+s9O+BiGyHc4aIyK5MnDix0iAEAPv374evr69pmOqvtFot7t69i1u3bgEAlEolnn766Yeeu23bNjRo0MDUy6RQKDBjxoyHnjt27FgoFAoAQLt27UzHyrRr1w6JiYkoKCgod11sbCx27dqFb7/9FoGBgTh+/Hilfz4isi32DBGRXQkJCXnkObt27UK/fv0q/Hz8+PE4c+YMoqKi0KRJE/Tq1QuTJk1C7dq1Hzg3MTER4eHh5Y799X2Z+yddazSaCo/pdDpotVoUFBRgwIABOH36NFq3bg0fHx8kJibizp07j/wzEpHtsGeIiOxKWc9LZX744YcK5wsBgJeXF9avX4/U1FQsXLgQMTExeOKJJ5CXl/fAuf7+/g+sOZSRkVHtuh9m3bp1iIuLw40bN7Bnzx5s2rQJw4cPhyAIotyfiMTBMEREsnLhwgXcvn0b3bt3r/CcsuExDw8P9O7dG0uXLkVycjJu3LjxwLkdOnTAyZMncfPmTdOx7du3i1JrcnIyateuDU9PT9OxLVu2iHJvIhIPh8mISFZ27dqFHj16QKvVVnjOp59+iiNHjqBv377w9fXFN998g2bNmqFBgwYP9AL16dMH7du3Nw2lpaSkYPXq1QCq1ktVmf79+2P+/Pl47bXXEB0djW3btuHMmTPVXhuJiKyLPUNEZBc8PDwwbNgweHl5VXpeZY/Ul1mwYAHmzp2LpKQkHD16FIMGDcLBgwehUqkeuujijz/+iJdeegknTpyAq6srvv/+ewAw1fKw2ry9vTFs2DC4u7ubjvn7+2PYsGFwdXUFALRs2RIHDx6EwWDA4cOH0a9fP2zduhWDBw+u1t8NEVmXQuDgNRHJRGZmJoKCgnDt2jXTIopiSE9Ph7+/v+n9559/jmnTpiEtLc0UbIjIcXGYjIhk4/r165gwYYKoQQgA5syZA4VCgZYtW+LixYtYvnw55s+fzyBE5CTYM0RETk+v12PNmjU4ceIE/Pz80K9fP3Tu3FnqsojIRhiGiIiIyKlxAjURERE5NYYhIiIicmoMQ0REROTUGIaIiIjIqTEMERERkVNjGCIiIiKnxjBERERETo1hiIiIiJwawxARERE5tf8HrUPZUXC1pC8AAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lj = rf.LennardJones(epsilon=1.0, sigma=1.0, cutoff=2.5)\n", "r = np.linspace(0.9, 3.0, 400)\n", "plt.plot(r, lj(r))\n", "plt.axhline(0, color=\"k\", lw=0.5)\n", "plt.axvline(2 ** (1 / 6), color=\"k\", lw=0.5, ls=\":\")\n", "plt.ylim(-1.2, 1.5)\n", "plt.xlabel(\"r / sigma\"); plt.ylabel(\"U / epsilon\");" ] }, { "cell_type": "markdown", "id": "55ad53e8", "metadata": {}, "source": [ "## The state point of the paper\n", "\n", "1000 particles at number density $\\rho = 0.317$ and temperature $T = 1.085$ (Lennard-Jones units), close to the critical point. To avoid huge initial energies the particles start from a random packing of spheres of diameter $0.9\\sigma$, generated with `spheropack.pack`." ] }, { "cell_type": "code", "execution_count": 4, "id": "33b042d0", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:50:59.781577Z", "iopub.status.busy": "2026-10-01T23:50:59.781424Z", "iopub.status.idle": "2026-10-01T23:50:59.839304Z", "shell.execute_reply": "2026-10-01T23:50:59.838437Z" } }, "outputs": [ { "data": { "text/plain": [ "System(n=1000, dim=3, density=0.317, potential=LennardJones(rc=2.5), kT=1.085, method='collisions', time=0, n_reflections=0)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n, rho, T = 1000, 0.317, 1.085\n", "L = (n / rho) ** (1 / 3)\n", "start = sp.pack(n=n, radii=0.45, container=sp.PeriodicBox(L), seed=1)\n", "system = rf.System(start.positions, box=start.container, potential=lj, kT=T, seed=1)\n", "system" ] }, { "cell_type": "markdown", "id": "0b1de7c6", "metadata": {}, "source": [ "Equilibration: the potential energy per particle settles within a few tens of time units (time is the contour length of the moves; the move velocities are Gaussian with unit variance per component)." ] }, { "cell_type": "code", "execution_count": 5, "id": "ecf63c7b", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:50:59.841583Z", "iopub.status.busy": "2026-10-01T23:50:59.841397Z", "iopub.status.idle": "2026-10-01T23:51:07.797629Z", "shell.execute_reply": "2026-10-01T23:51:07.796794Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "583643 reflections in 7.9 s\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "times, energies = [0.0], [system.potential_energy() / n]\n", "t0 = time.perf_counter()\n", "for _ in range(50):\n", " system.run(2.0)\n", " times.append(system.time)\n", " energies.append(system.potential_energy() / n)\n", "print(f\"{system.n_reflections} reflections in {time.perf_counter() - t0:.1f} s\")\n", "plt.plot(times, energies)\n", "plt.xlabel(\"simulation time\"); plt.ylabel(\"U / N\");" ] }, { "cell_type": "markdown", "id": "5ebedb9e", "metadata": {}, "source": [ "## Radial distribution function\n", "\n", "Sampling every 2 time units; `rf.radial_distribution` advances the system and averages $g(r)$ over the samples. The reference data of the paper are three long Metropolis runs and the paper's own rejection-free run." ] }, { "cell_type": "code", "execution_count": 6, "id": "6a368266", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:51:07.800396Z", "iopub.status.busy": "2026-10-01T23:51:07.800101Z", "iopub.status.idle": "2026-10-01T23:51:57.901535Z", "shell.execute_reply": "2026-10-01T23:51:57.900709Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sampling took 50 s, 4065407 reflections in total\n", "mean |difference| on bins of 0.05: 0.0021\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t0 = time.perf_counter()\n", "g = rf.radial_distribution(system, n_samples=300, interval=2.0, r_max=5.0, bins=1000)\n", "print(f\"sampling took {time.perf_counter() - t0:.0f} s, {system.n_reflections} reflections in total\")\n", "\n", "def load_reference(name):\n", " local = Path(\"../data\") / name\n", " if local.exists():\n", " return np.loadtxt(local)\n", " url = f\"https://raw.githubusercontent.com/computational-chemical-engineering/spheropack/main/docs/data/{name}\"\n", " return np.loadtxt(url)\n", "\n", "ref = load_reference(\"GofR_LJ_all.dat\")\n", "metropolis = ref[:, [1, 3, 5]].mean(axis=1)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "axes[0].plot(ref[:, 0], metropolis, \"k-\", lw=2, label=\"Metropolis (paper)\")\n", "axes[0].plot(ref[:, 6], ref[:, 7], lw=1, label=\"rejection-free (paper)\")\n", "axes[0].plot(g.r, g.g, lw=1, label=\"spheropack\")\n", "axes[0].set_xlim(0.8, 5); axes[0].set_xlabel(\"r / sigma\"); axes[0].set_ylabel(\"g(r)\"); axes[0].legend()\n", "\n", "coarse = lambda a: a.reshape(100, 10).mean(axis=1)\n", "axes[1].plot(coarse(g.r), coarse(g.g) - coarse(metropolis), \"o-\", ms=3)\n", "axes[1].axhline(0, color=\"k\", lw=0.5)\n", "axes[1].set_xlim(0.8, 5); axes[1].set_xlabel(\"r / sigma\"); axes[1].set_ylabel(\"g - g(Metropolis), bins of 0.05\")\n", "print(f\"mean |difference| on bins of 0.05: {np.abs(coarse(g.g) - coarse(metropolis)).mean():.4f}\")" ] }, { "cell_type": "markdown", "id": "49eaea97", "metadata": {}, "source": [ "The rejection-free sampling reproduces the Metropolis result within the statistical noise. The paper's rejection-free run (time 339240) is far longer than this example; the noise of the difference shrinks with the square root of the sampling time.\n", "\n", "## The DPD liquid of the paper\n", "\n", "The second example of the paper: DPD particles (soft repulsion $\\frac{a}{2}(1 - r/r_c)^2$) at the conventional density $\\rho = 3$ with $a = 25\\,kT$, where the particles overlap strongly." ] }, { "cell_type": "markdown", "id": "83e76b82", "metadata": {}, "source": [ "## Event chains\n", "\n", "The paper's second implementation moves one particle at a time: at a reflection the moving particle stops and its partner continues in the same direction. With irreversible chains (directions $+x, +y, +z$ in turn, the default) this is considerably faster. Time is again the mean displacement per particle." ] }, { "cell_type": "code", "execution_count": 7, "id": "6a765c9e", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:51:57.903955Z", "iopub.status.busy": "2026-10-01T23:51:57.903822Z", "iopub.status.idle": "2026-10-01T23:52:50.733433Z", "shell.execute_reply": "2026-10-01T23:52:50.732587Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "event chains: 1500 samples in 51 s\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAGxCAYAAADF4QrHAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjExLjIsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvgI3uAAAAAAlwSFlzAAAPYQAAD2EBqD+naQAA+ZFJREFUeJzsnXeYVOXZh+/p23uHXXrv0gQRVLB3EEvQaEyiJhhrYrAlxsTyxVhj7xolahQrYgcEUXrvZVl22WV7nz5zvj/eOdNndmZ2dhfk3Ne1186cOXPOO+2c33me5/09KkmSJBQUFBQUFBQUFLoNdU8PQEFBQUFBQUHheEMRYAoKCgoKCgoK3YwiwBQUFBQUFBQUuhlFgCkoKCgoKCgodDOKAFNQUFBQUFBQ6GYUAaagoKCgoKCg0M0oAkxBQUFBQUFBoZtRBJiCgoKCgoKCQjej7ekBHE84nU4qKytJTU1FpVL19HAUFBQUFBQUIkCSJFpbWykqKkKtjk/sShFg3UhlZSXFxcU9PQwFBQUFBQWFGCgvL6d3795x2ZYiwLqR1NRUQHyAaWlpPTwaBQUFBQUFhUhoaWmhuLjYfR6PB4oA60bktGNaWpoiwBQUFBQUFI4x4lk+pBThKygoKCgoKCh0M4oAU1BQUFBQUFDoZhQBpqCgoKCgoKDQzSg1YAoKCgrHOU6nE6vV2tPDUFDoMXQ6HRqNplv3qQgwBQUFheMYq9VKaWkpTqezp4eioNCjZGRkUFBQ0G0+nYoAU1BQUDhOkSSJqqoqNBoNxcXFcTOYVFA4lpAkCaPRSE1NDQCFhYXdsl9FgCkoKCgcp9jtdoxGI0VFRSQlJfX0cBQUeozExEQAampqyMvL65Z0pHK5o6CgoHCc4nA4ANDr9T08EgWFnke+CLHZbN2yP0WAKSgoKBznKL1pFRS6/3egCDAFBQUFhZ8dCxcu5Jlnngl5/2gg2jEdja8hXvycX1soFAGmoKCgoPCzY9WqVXz99dch73c3b731Fs8//7zPsmjH1NOvoSv5Ob+2UChF+Mc7TeVgrPfcT8qGjOKeG4+CgoLCz5CVK1dSV1fHDTfc4F42b9482tvbe3BURw/H43uhCLDjmaZyeHo82C2eZVoD3LheEWEKCgpHLYsXL+bDDz8EID09nRNOOIHLL7+8UzPXXnvtNZxOJ8OHD+eLL76gtbWVuXPnMmXKlKj2K29nxIgRLFq0CJ1Ox8SJE1m+fDlms5nf/OY3ANx+++2UlpbS2NjIrFmz3M9vaGjgP//5D3v37mXw4MFce+21pKSkhBx3fX09b775Jvv376e4uJjLL7+cPn36uB+3WCz897//ZfPmzWRnZzNnzhyGDRsW9j0YNGgQ3333Hc3NzcyZM4dp06axfPlyPv30U/R6PVdeeSXDhw/3ee6BAwd46623qK6uZtCgQfzqV78iPT0dgJ9++om33nqLp556ysfqZMmSJSxfvpyHH3444L2QxzJmzBgWL15MW1sb5513HjNmzPDZ76ZNm1i4cCFarZZTTz2V1tZWDh06xC233BLyPTtaUFKQxzPGel/xBeK+d0RMQUFBIQKqmk2s2l9HVbOpy/fVq1cvTjzxRE488UTy8/N58MEHufDCCzu1zeXLl3P33Xfzq1/9iqSkJMxmM9OnT+fjjz+Oar/Lly/nnnvu4YYbbiAvL4+xY8dSXFxMfn4+2dnZ7uenp6cHpN127tzJ8OHD+fDDD+nXrx+lpaWcfvrpIce8e/duRo0axbp16xg8eDAHDx5k7NixrFmzxr3OnDlzeOKJJyguLsbpdHLllVfy008/hXwPFixYwO23305aWhqtra3MmDGDX/7ylyxYsICioiIqKiqYNGkShw8fdj9v/fr1jB49mm3bttG/f3/ee+89xo0bR1NTEwD9+/fnhRde4Pvvv/fZ38MPP0xraysQmIKU38ff/e53JCcn43A4OP300/n888/d66xYsYJJkyZx5MgRsrOzWbBgAX/4wx/44osvQr5nRxNKBExBQUFBARCGlCabI+rnfbC+gr9+sh2nBGoV/O2CEcwZ3zuqbSTqNBHPQhs7dixjx4513//Nb35D7969WbNmDZMmTYpqv940NTWxYcMGioqKAOGM/sc//pELLrgAlUoV8X4tFgvLly93R4AAhg4dSl1dnTsCFozf/e53jBs3js8//9z9XlRUVIRc/8Ybb+SKK67g0UcfdS/LyMjgz3/+M0uXLsVsNvP555+zdu1axo8fD8CCBQvcwigYOp2O5cuXuy0ZNmzYwPfff8/u3bsxGAyAiGi999573HrrrYCI5p133nm88847APzhD39g2LBhPPzwwzz88MPk5eUxa9Ys3n77bU455RQAysvLWbFiBQ8//HDIsahUKpYtW0ZycjIAdXV1vPLKK5xzzjkA3HnnnVx55ZW8+uqrAFx//fX069cv5PaONhQBpqCgoKAAgMnmYPhfvuzUNpwS3Pvxdu79eHtUz9tx/5kk6SM/JX377bcsW7aMmpoaHA4HOp2OnTt3dkqATZ061S2+AC677DIeeughDh8+TO/evSPe79SpU33EVyS0t7ezYsUK3nvvPR8hKu/XH6PRyNKlS9Hr9dxwww1IkoQkSZSWlrJp0yYAEhIS6NevH//85z9ZsGABY8aMQa/Xk5eXF3IcU6ZM8THlHThwIDqdzi2+5GWyMLTb7fzwww+8//777sf1ej1z585l+fLl7mXz5s3jD3/4A08//TQGg4GFCxfSv39/nxRvsLHI4gtgyJAhfPLJJ4Dw6vrpp5+466673I+npKRw9tlnux3tj3aUFOTxTFI2qP0OeFqDWK6goKBwlHLHHXcwb948rFYro0eP5sQTTyQhIcGdzoqV7GzfY19OTg6A+4Qe6X4zMjKi3ndTUxNOp5P8/PyI1m9sbMThcDBy5EgmTJjAxIkTmTRpEpdddplPROybb74hPT2diy66iNzcXG644YawETDZEV5GrVYHXSab+DY0NGC3293vlUxOTg7V1dXu+xdffDE2m82dQnz77beZN29e2Nfov1+NRuOzX4fDEfCZ+d8/mlEiYMczGcUw8bew+jlx/+xHYMjZSgG+gsJxSqJOw477z4zqOUeazcx6bDlOybNMrYJvbptBQXpCVPuOBEmSeO6553jrrbfc9VcOh4Obb745qnEHo7y83Od+WVkZAMXFxZ3eb0fp1dzcXAwGA/v372fatGkdbi8nJwe9Xk+/fv3CpjX79evHiy++CMCOHTuYM2cO9913H0888URE4+6I3NxcEhISKCsr46STTnIvLysro6SkxH0/OTmZCy+8kLfffpuBAweydetWPvjgg07t12AwUF5ezuTJk93L/T/DoxklAna8Y2nx3E7JVcSXgsJxjEqlIkmvjeqvf24KD80ehcYlMDQqFQ/NHkX/3JSothOtC7l31Ompp57CaDR2+vWvWbPGXaAuSRJPPvkk06ZNIzc3t9P7zcrKoqGhIeTjer2eOXPm8Nhjj/lEqL755pug6xsMBubOncsjjzziE2lqa2tjyZIlgIgSeT9/+PDhDB06lPr6+E20UqlUzJ49m2eeeQaLRUzqqqysZOHChcyZM8dn3SuvvJLPPvuMZ555hkmTJjFo0KCY96tWqzn//PN5/vnnsdvtgJiJuXjx4thfTDejRMCOd5oOeW6bm3tuHAoKCscsl00sYfrgXA7WGembk0RhemLHT4oRlUrFn//8Z6677jo++eQTamtrKSsr8xFJsTJ8+HAuu+wyxo8fz6FDhygtLXULmM7u97zzzuPRRx9l9uzZZGVlcfvttwes89RTT3H++eczbNgwTj75ZMrLyykuLvaxqfDm6aefZs6cOQwfPpwZM2ZgNpvZuXOnuy5Kp9Pxz3/+k9tuu41Ro0ZRUVHBjh074m54+s9//pOZM2cyevRoxowZw/Lly5k8ebKP5xnA6aefTnp6Oi+++CJPPvlkp/f78MMPM336dMaOHcuwYcNYvXo1w4cP75ZG2vFAEWDHO81eM2wUAaagoBAjhemJXSq8vLnnnns477zz2LZtG9nZ2ZxyyiksXrzYx5vK39gzEqPPsWPH8uSTT7J69WpaW1uZNWuWT01RJPu99tprcTqdAdueMmUKO3fuZO3atbS0tJCenh4wpuzsbH744Qd+/PFHDhw4wNChQ5kwYULI15CRkcG3337Lhg0b2LFjBzk5OUyePJnMzEwAUlNT+eqrr9i2bRtbt24lMzOT6dOn+xTZexNs7Ndffz06nc5n2U033URaWpr7fq9evdiyZQvLli3jyJEj3HbbbZx44okB29dqtSxcuJDS0tKA6Jj/aws2lnPOOcfHw2zAgAHs2rWLr776Cp1Ox1NPPcWf/vQnH6+xoxmVJElSx6spxAP5R9fc3Ozz5e0xnE54IB8cVnH/5D/CzHt7dkwKCgrdhtlsprS0lH79+pGQEHm91s+Ra665BrvdzltvvdXTQ1GIkKqqKsxms9t64uDBg4wePZqnnnqKa665Jurthfs9dMX5W4mAHc+013rEFygRMAUFBQWFYwaNRsMFF1xAcXExBoOB7777jnPPPZcrr7yyp4cWEYoAO55p9pstoggwBQWF45RQqUOFo5e8vDzWrl3LDz/8QH19Pffffz+jRo3q6WFFjCLAjmcUAaagoKAAwPTp03t6CAoxkJCQwMyZM3t6GDFxbFSqKXQNcgG+1pXr9rakUFBQUFBQUOgyFAF2PCMLsNyh4r8SAVNQUFBQUOgWFAF2PCMLsPyR4r8iwBQUFBQUFLoFRYAdz8gmrAWKAFNQUFBQUOhOFAF2POOOgI0Q/61t4LD33HgUFBQUFBSOExQBdrxibQeTqy9Z3gjPcqUQX0FBQaFbWbduHWvXru30djZt2sSPP/4YhxEpdAeKDcXxSvNh8d+QBsnZoEsCm1GkIZOyenZsCgoKCscIGzduxGKxBG29EylPP/10XFz4X375ZSoqKvjoo486tR2F7kERYMcrsgdYem/xPyHdI8AUFBQUFCLihRdeoK6ujvfff7+nh8K4ceMoKSnp6WEoRIgiwI5X3AKsWPxPSIfWKiUFqaCgcMywc+dO9u/fT3FxMaNGjXI3YT5w4AA7duzgvPPO81l///797Nixg/PPP7/DbYBIDUqSxMiRI9myZQttbW1MnDjR3Qtw+/btHDhwgNbWVrcAmz59Onl5eUHHu3v3bvbu3cvgwYMZPHhwwOMmkynofgB27drFtm3bAEhPT2fkyJEUFhb6PH/8+PGYTKaIxy9TUVHB9u3byc7OZsyYMQHNtxW6BkWAHa/IBfhyBMzg+kEqETAFBYVoaSoHY73nflI2ZBR32e7a2tq44oorWL9+PWPHjmXv3r1kZ2fz8ccfk5+fj9Fo5Pzzz2fXrl0MGTLE/bx77rkHs9nM+eef3+E2QKQGt27dislkoqioiCNHjlBfX8+yZcsYMmQIW7duZf/+/VgsFt555x0AhgwZEiDAWltbmTdvHt9//z0TJ06koqKCk046iZdfftm9zs6dOxk/fnzQ/YAQe/I+GhoaWL16Nffffz+33367exv+KciOxg/w8MMP88ADDzBlyhTa2towmUx88MEH9O/fP86fmoI/igA7XvEXYAnp4r8iwBQUjl8kSZQiRENzBTx/MjgsnmUaA9ywwnN8iQRdEqhUEa36pz/9CZvNRmlpKQaDAYfDwSWXXMKf/vQn3nzzTUaOHMno0aN5++23uf/++wEh2j755BPefPPNiLYhs2PHDtatW8eIESNwOp3MnDmTRx55hJdffpnLL7+cZcuWdZiCvPXWW9m1axc7d+50R60++OADn3XC7Qdgzpw5zJkzx73+unXrmDZtGrNnz6Zfv34h9x1uuzabjfvuu4+PP/6YM888ExCRtvb29og+B4XOoQiw4xW3APNKQYIiwBQUjmdsRniwqPPbcVjgmUnRPeeuStAnd7ia3W7nP//5D/Pnz2fJkiVIkoQkSfTt25f33nvPvd6VV17JCy+84BZgixYtQq/Xc95550W8DYBTTz2VESPETHG1Ws0pp5zC119/HfHLstlsLFy4kKeeesonZegtpiLdT1tbG5s3b6ampgaHw0FaWhrr1q0LK8DCbVetVqPT6di9ezdnnHEGKpWKoUOHRvzaFDqHIsCOV2QT1oAImFIDpqCgcPRSU1NDe3s7a9euZf/+/T6PTZs2zX37iiuuYMGCBfz000+ceOKJvP3221xyySUYDAYqKysj2gZAVpbvrHCDwYDZbI5qvCaTyScVGoyO9vPRRx9x7bXXUlxcTElJifvxmpqamLer0Wh44403uPXWW3nooYeYMWMGl19+ORdddFHEr08hdhQBdjzidEBLpbgt12kkKDVgCgrHPbokEYmKhiNb4NWzApdf+wUUjI5u3xGQkpKCSqXihhtu4NJLLw25Xu/evZkxYwZvv/02/fr149tvv+Xbb7+NahvxIC0tDZVKRX19fccrh2H+/Pn85S9/4ZZbbnEvy83NRZKkTm139uzZzJ49m507d7JkyRKuvvpq/va3v/nsR6FrUIxYj0faasBpA5UGUgrEMiUFqaCgoFKJNGA0f2m9QWvw3Y7WIJZHs50I67/S0tI48cQTeemllwIeq6qq8rk/b9483n33Xd566y169erF9OnTo95GR6SkpGCxWEI+npqayuTJkwM8vqIRZA6Hg5qaGncqEWDFihXU1dVFNVZ/TCYTzc3imD9s2DBuu+02LrroIlatWtWp7SpEhhIBOx6R67/SikDj+gooAkxBQSEWMorhxvXdOgvy2WefZebMmcyaNYtLL70Us9nMt99+S+/evXnmmWfc611yySXMnz+fv/3tb8yfPx+Vl8iLdBsdMX78eF555RVefPFFsrKygtpQ/Pvf/2bmzJlcfPHFnH/++ZSXl7NkyRJ++umniPah0Wg455xzuOWWW7j99tupra3lscceIykpsqhhKFpbW5k6dSqzZ89m1KhRVFRUsGjRoqDCVCH+KALseMTfhBU8AkzxAVNQUIiWjOIuFVz+jB07lu3bt/Pqq6/y/fffk5OTw3XXXce5557rs156ejp33303mzdv5pprrol6GxMnTsThcPg8b+jQocycOdN9/7LLLqOtrY0ff/yRlpaWoDYUEyZMYOvWrbz88st89913DB06lM8//zyq/SxcuJCnn36a7777juzsbD777DPeeustBg4c6F7H34i1o+3m5eWxZs0aXn31Vb755hsyMzP5/PPPOfnkkwPfdIW4o5I6m0BWiJiWlhbS09Npbm4OMMLrVn54Er7+C4y6FOa4rnT2fgNvz4GCUXDDyp4bm4KCQrdhNpspLS2lX79+JCQk9PRwFBR6lHC/h644fys1YMcj/h5goKQgFRQUFBQUuhFFgB2PKAJMQUFBQUGhR1EE2PGIfx9I8NhQWFrB6ez+McVIVbOJVfvrqGo2dbyygoKCgoLCUYJShH880hSmCF9ygrXNI8iOYt5de4g7F23FKYFaBQ/NHsVlE0s6fqKCgoKCgkIPo0TAjjcsrWBuEre9BZg2ATR6cTvGNGR3RqOqmk1u8QXglOCuRduUSJiCgoKCwjGBEgE73mg+LP4npPtGuVQqsay91iXAoptS3t3RqNK6drf4knFIEgfrjBSmJ3bZfhUUFBQUFOKBEgE73vBvwu2NQa4Di84LrCeiUf1yklH7GWdrVCr65nTOmFBBQUFBQaE7UATY8UYwE1aZGGdChotGdRWF6Yk8NHuU+75KBQ/OHqlEvxQUFBQUjgkUAXa80QUCrF9OMv5d3LojGnXZxBJSE0QW/abTBikF+AoKCsckFoslbD/JSLFarZjN5jiMKDwWiwWbzdbl+4knJpMJu93e08PwQRFgxxvhUpAxCrDC9ESmD85139eoVN0WjbI5hGWG1j8fqaCgoNANWCyWToue66+/nl//+tedHsttt93G5Zdf3unthKOlpYX+/fuzZ8+eLt1PvHnssce4+uqre3oYPihF+McbwUxYZeSifHP0/SBzUw3u28vvOIXemR1Ev5rKO928V5IkzDYhwNqtjg7WVlBQUIg/N998M3V1dbz//vs9PRQMBgOJiV174fvQQw8xY8YMRowY0aX7iTe33HILxcXFrFmzhkmTJvX0cABFgB1/BDNhlXFHwJqi3mxdmyd8nqTv4GvVVA7/Hg8Or5C71gA3ro9KhFkdHsNYo/XoCi0rKCh0DzabDZ1OF7DMZrORlOR7IWi327FYLCQnJ3e4DcCdFjQYxAWm0+lErfYkjqxWK3a7HYfDQVtbGwCJiYloNJqQ47Xb7Wi14Y+R/vuRxyiPJ9Q+HnroIZxeRtodjd8bh8MRdtwARqORF154gUWLFoXcR7DtRDL2SLbjv82OPjNJkjCbzSQmJpKcnMxll13GE088wcKFC8O+zu7imEtBHj58mIceeohbbrmFV155BavVGpfndLTOwoULueGGG3z+/v73v8ftdXULTge0VIrbcawBA18B1tDewWdirPcVXwB2i29ELALk6BdAu0WJgCkoHE8888wz9OnTh8TERAoLC/nLX/7irvFZunQpGRkZ1Nf7HlPuuOMOTjvttIi2ASI1eMkll3DNNdeQk5NDUlISs2fPpqVFZAn+7//+jzfeeINPP/2UgoICCgoKWLFiRdDxPvvss+4mz/379+e///2vz+PNzc0h9wPw+OOPu/eRkpLCxIkT+eGHH3y24Z+C7Gj8AMuXL2fs2LEkJSWRl5fHTTfdRHt7e9DX8OWXX2K325k+fbrPPubMmcMvfvELsrKySEhI4IorrvDZRiRjj2Q7kX5mc+bMYd68eaSkpHDiiSe6Hzv33HP56KOPItIN3cExJcB27drFqFGj+PHHH8nNzeWRRx5h1qxZYQvrInlOJOt8//33rFmzhrFjx7r/hgwZ0qWvN+60HgGnHdRaSC0IfDwhQ/yPRYC1er7QHQqwOGGxe0SXEgFTUDh+eOaZZ3j00Ud5//33sdlsLFu2jP/973/83//9HwAzZ84kOzub//3vf+7nOJ1O3nnnHa688sqItiHz2WefMWnSJCorK9mzZw+bNm3ikUceAeDee+/l17/+NRdddBFtbW20tbVxyimnBIz3ySefZMGCBTz66KMYjUaWLl0aINTC7QeEeJT30dTUxCWXXMJFF11EU1NT2Peqo+3OnTuXuXPn0t7ezp49exg2bBg//fRT0G2tWrWKsWPHBkTRFi9ezIABAzh8+DDbt29n48aN3HHHHVGPvaPtRPqZLV68mPHjx1NfX8/mzZvdyydOnIjJZGL9+vVh37NuQzqGuOCCC6RTTjlFcjqdkiRJ0uHDhyW9Xi+99tprnXpOJOtcf/310pw5czo1/ubmZgmQmpubO7WdmCn7SZL+miZJj48M/vimd8Tjb1wQ1WadTqc08K7FUp8/fyb1+fNn0pKtVeGfcHij2I//3+GNUe33UH27e59XvbI6qucqKChIkslkknbs2CGZTCb3MqPNKG2v297tf0abMeJx9+rVS3rllVckk8kkGY1Gqb29XXr++eelwYMHu9e55ZZbpGnTprnvf/3115JWq5Vqamoi3sbVV18tTZkyxWffCxYskGbOnOm+39G5wel0SgUFBdL9998fcp1I9uON0WiUWltbpfz8fOmzzz5zL58/f7504YUXRrxds9ksqdVqafny5SHH5s0VV1wR8FqvvvpqqU+fPpLD4XAv+9///ifp9Xqpvb094rFHsp1IP7PRo0cHHb/D4ZDUarX03nvvBX082O9BpivO38dMDZjNZuOLL77g3//+NyqVmPFWVFTEqaeeyieffMI111wT03Oi2e6ePXu47bbbSE9P5+STT/YJZR8ThKv/gphTkM0mGzaHxwis0dhBBCwpG1ABXuZhWoNreeT4RMAsSgTsWKSq2URpXTv9cpIVD7ejhNLmUi777LJu3++7573L8OzhHa5XU1PD4cOHufHGG7npppt8HpPrhwDmzZvHk08+SVlZGX369OHtt9/mjDPOIDc3N+JtAPTr18/nfnp6eodRJ//xHjlyhKlTp4Zdr6P97Nu3j1tvvZVly5ZhsVjQ6/UYjUbKy8tj3q7BYOAPf/gD5557LrNnz+bUU0/lvPPOIycnJ+i21Gq1T42ZjH9UbPz48VitVg4cOMDIkSMjHnu47eTl5UX8mQ0dOjTo+J1OJ5IkhayD626OGQFWVlaG1WoN+DL169cvIJcczXMi3a5KpaK4uJiCggIOHz7M+eefzy9+8QteeumlkGP293bxzrv3COFmQELMAsy7/gsiSEFmFENaoace7ex/wpBzop4F6VMDpsyCPOZQmqkfnfRL78e7573bI/uNhg8++ICzzz475OMTJkxg8ODBLFy4kFtvvZVFixbx/PPPR7UNwH1hHivyyd7hCH+M6mg/l19+OcOGDWPPnj0UFhYCUFJS0qG3VUfbfeKJJ7juuuv48ssvWbhwIX/4wx/48MMPmTVrVsC6xcXFLF++PGC5/2uT78uTDSIde0fbgcg+s2DF+QDV1dVIkkRxcXTnmq7imBFgJpNoa5OamuqzPC0tDaMxuON6JM+JdLv33HMPvXr1ct+fO3cuJ598Mpdccglnnnlm0P0/9NBD/O1vf+vwtXUb4UxYIWYBVtvqK7giqgEzee3DZoxafIFSA3YsE6p91fTBuUokrIdJ1CZGFInqKfLy8igpKWHx4sUdnojnzZvH22+/zcCBA3E6nVx44YVRb6Mj9Hp9WHGVm5tLSUkJS5cu5YwzzohpHw6Hg40bN/Kvf/3LLWDKy8s5fPhwTNvzZ/jw4QwfPpxbb72VuXPn8tJLLwUVYNOmTePJJ58MmIG4YcMGn2U//vgjSUlJ9OvXL6qxh9uOwWDo9Ge2du1aUlJSOOGEE2J6frw5OuJwEZCWJjyq/EO/jY2N7sdieU6k2/UWXyC+iCUlJaxatSrkmO+8806am5vdfx2FiruUpnKo3u573x9vHzBJCnw8BP4RsMaOBJi1HWxeM1u8xxUFyizIY5eeaF+l8PPhgQce4IUXXuCRRx7h0KFD7Nmzh+eee4758+f7rDdv3jy2b9/OX//6V2bPnu1jSxHpNjqiX79+bN26lUOHDtHW1hZUjN133308+eSTvPDCC1RWVrJ69WouueSSiPeh0WgYPnw4L774IpWVlWzevJnLL788aDowGsrKyjjvvPP47rvvqK2tZePGjWzatIlhw4YFXX/WrFmkpqby1Vdf+SyvrKzkD3/4A4cOHeL777/nrrvu4sYbb8RgMEQ19nDbgc5/Zh9//DGXXnpphzYg3cUxI8CKi4tJTU1lx44dPst37NgR0hAukufEsl0Zs9kc9srHYDCQlpbm89cjNJXD0+Ph0I/i/opHxX1/ESZHwJw2sEXeSNtfgNV3JMDa63zvV+8Ivl4HKBGwYxelmbpCZ7jyyiv54IMP+PTTTznhhBO44IIL2LFjB/fee6/Pev379+fUU0/l0KFDXHXVVVFvIyEhgYSEBJ/n6fV6HyH3q1/9ijFjxnDiiSeGtKH41a9+xWuvvcYrr7zC6NGjuf322/n9738f1X4WLlxIVVUVo0eP5tJLL+X8889n7Nix6PV69zr+RqwdbbdPnz787ne/48EHH2TkyJFcccUVXHrppdx9990Br0He/k033cQLL7zgs3zOnDkkJiYya9YsLrvsMmbPnu1j0xTJ2CPZTqyfGYggy4cffsgtt9wS9LX1BCpJiiLU0cP85je/YfXq1axevZqkpCTWr1/PxIkT+fTTTzn33HMBeOuttygtLXV/IJE8p6N17HY73377rU+q8bXXXuPaa69lxYoVTJs2LaLxt7S0kJ6eTnNzc/eKscpN8OKMwOXXLYeisZ77kgT3Z4HkhNt2iTqtCHjky108s3Q/vTISOdxkYnTvdD65Mcx7UrEeXj4NNAbhB6bWwl1VoNWHfk4QPt9axe/f3uC+f+DBc1ArLYmOGd5de4g/f7AVEFMyHp6j1IB1N2azmdLSUrc/lYJCR5jNZsaNG8fChQsZN24c11xzDXa7nbfeeqtT243XdkLx97//nerqap5++umQ64T7PXTF+fuYiYCBqKmSJIlx48Zx6aWXMmvWLH7729+6hRTAsmXLePfdd6N6TkfrqFQqnnnmGU444QSuuuoqZsyYwY033sgjjzwSsfg6JlCpYqoDkz3ABuenABHUgLXXiv95Q8X+nHaoi76vmHcEDMBsV9KQxxKXTSwhz9XCauawfEV8KSgcAyQkJLBz507GjRvX00OJinvvvTes+OoJjo5EaITk5uayYcMGvvnmG6qrq/nzn//M+PHjfda56qqrfAodI3lOR+toNBo++eQTduzYwcaNG8nMzGT8+PHk5+d37QvuCQxpYGoES+QzNuUU5OCCVJburo3ACd+VgkzOBV0yHFol6sAKRkY1VO8aMBB1YB22QVI4apAkiSaTDQB7J2tZFBQUeoaEhIQOZ2J253aOJY65s5Ver+ecc84J+fiMGYGpto6eE+k68kyRY46kbFBpQPKKEIXy3YolAiYLsDwxk9RodWC2OUjQhejjJUfAknMhM0UIsJroC/EtNt+Il6gDMwRfWeGoo93qwGoXwqvVfHwdeBUUfi74W3v09HaOJY45AaYQAxnFkDsEanbAzL/CgNOE+Apm/RCTABMRr745yWjVKuxOiUajNbSdgFyEn5wDWQPE7RhmQprtgREwhWOHeq/JGy2uSJiCgoLC8cIxVQOmECM2k6fGatQlovA+lO9WlAJMkiRqXSfSvFQDmcmikL6+LUwa0jsClu+aaRqDALP4pSCVmZDHFt6zZZUImIKCwvGGEgE7HqjaLArdk/NCtyGSiVKAtVrs7jRSToqB7GQ9ta2W8O2IvAVYnstvprUKjA2QlBXRfgF07YcZoSp137c39oa+kT9foWdpaPMWYEoErCc5hibDKyh0Gd39O1AE2PFAxTrxv/dEMdMxHFEKsLpWEf1K1mtI1GvITBIRsLCF+HIKMikHDKmQ2RcaD4ooWL+TI9ovTeX8dtNcfm/w7MfxqR76bYjJVV+h+6lv96Qg260OHE4JjWIj0q1oNKJO02q1+vhHKSgcj8jdb0K1Moo3igA7HqhYK/73Hh9+PYhagMlppByXnUBWchQCLNnV8DVvRPQCzFiPTvLdh8ZpBWN9zwmwpnKxf5lQdXYKQKBhb5vZTnpS9xz4FARarZakpCRqa2vR6XRHTZNiBYXuRJIkjEYjNTU1ZGRkuC9MuhpFgB0PHF4v/vee2PG6BpfBXIQ2FHIELCfFV4CFbEckSb4pSBB1YLsXQ/W2iPZ5VCJ3G7B7dQXQGuDG9dGJsONIxDX41Qm2mG2KAOtmVCoVhYWFlJaWUlZW1tPDUVDoUTIyMigoKOi2/SkC7OdO6xFXE24VFEVgnBdtCrJNFmBCeMlF+A2hasDMzaLVEXgiYHIhfk1sLYmOCoz1vuILxP1oInLxEnHHCP4RMKUQv2fQ6/UMGjQIq7UD/z4FhZ8xOp2u2yJfMooA+7kj13/lDRf1Vh0RpQCrdUUx3BEwVwQjZApSTj/qU0HnqjlxC7Cd4HSAOoIfQVI2djRo8VhP2FV6tMG8zY4V4iHijiECBZhSiN9TqNVqpRWRgkI3oyT8f+4clgvwI6j/gk5EwFwCzPU/tACT0485nmVZ/UGbADajqAWLhIxi1iR66sV2O3vx9Mh3f5ZC5edKQ7uv2GxRImAKCgrHEYoA+7njPQMyEhJcNWDmKGvA5CL8JLkGLEQ0w+hXgA8i4iXbUUThB1ZoK3ffzlM1c4ScMGt3NUFm74XqNqAAeLziUhNEIF6JgCkoKBxPKALs54zTAYc3iNu9JkT2nBgjYLnuGjCRgvRPL7nxL8CXyYvSkNVmosTu8QDLVLXhNDVF9tyuoPGA7/15H0Rfu5WUDWq/qgDNz1PESZLk/o70y0kGlBowBQWF4wtFgP2cqdkJtnbQp4hWRJEgCzC7KbAeKQh1fjVg2cnif6PRGtzUzt+CQsbtiB/hTMgjW9HgpFZKp0WTKTbZXhHZc7uCgyt97ydmRp8OzSiGvtN9l1349M8yrerdB7JPtizAlAiYgoLC8YMiwH7OyPVfvU6IrLAdPDYUEFEa0r8GLMNVhO9wSsFrekJFwKJtSeSK7G129qc5oRcAaebycM/oWtwCzJWKbK2MfhtWIxz6UdwuGCX+1+7q9NCORuQ+kIk6DXmu9LUSAVNQUDie6LQA2717N4sXL2bjxo3xGI9CPJENWCNNP4IQanrXbMkOvMCMVjtGq5iFKNeAJeg0JOuF2AtaiN+RAGs8CJa2jsdZKQTYFucA2pNFhCjLcrjj53UFbTUuoaSCvtPEspaq6LdTulxEHtOLYfINrmXfx22YRxP17VaKqOPExHIG2PczQlWKqqUHI5gKCgoK3UxUNhQ33ngjTz/9NACtra1cccUVLF682P34KaecwqeffkpKSkp8R6kQGxVRGLB6k5AO1lYwN4Vdra5VCKwEndotugCyUvS0N5hoaLe663vceLch8iY5B1Lyoa1aiJneHYhGVwRsi9SfmaktUAM5thiiTvFAjn7ljxRC8uAKaIlBDO5y/ZaGnA39XKnIwxvA0hqZhUgkHCVGr+3VB/nOcDsJVhtsgl8YwLZbD01KKykFBYXjg6giYM8884z79n333cfOnTtZsmQJFRUVLFmyhEOHDvHggw/GfZAKMWBu8aSvOhIz/kRYiF/rlX5UefWY9MyEDBYBC1EDBpHXgZmboX4vIFKQZPYVT7fHEHWKB7IA6zsNUgvF7dYox+J0wp4vxO0h50BGCWT0AckBZT/GZ5yy0euLMzx/T48Xy7sZU3M1CSrfmi+dZPUVhwoKCgo/Y2JOQX744Ye88sornHXWWfTq1YuzzjqLV155hUWLFsVzfAqxUrkBkMSJPCUvuudGKMD8679kMsP1gwyVggQvAdaBI37lJgDKpVwaSUOT3R+AIulI+Od1Fd4CLE3Uo9ESZTTu8Hrx3hjSoM9JYpkcBTsYpzRkOKPXbqbJpBTcKygoHN/ELMAqKiqYONE3tTVx4kTKy3uwEFrBg+z/FU39l0yEXmChBFhWqHZETofnZB9MgEVqReHqbbnZKYRXYsFAAAqkerB3czuVthqo2w2ooM9USHNFwKIVYLtd6cdBp4NWvH9uAfYzrANrMSoF9woKCsc3UbcikmvAkpKS2LVrF+PHexzWDx06RP/+/eM3OoXYcRuwxiLAIoyAuWrAclP1PsvlFGRABMzYALisKYJ5W3mnICUJVEHMTcFdgL/ZOQCAtOxetEsGklUWrPUH0ecPDjvuuHJwhfifPxKSsnxTkOFegz+7l4j/Q87xLOvrcvqv2gKmRmFt8TPhsC0Jh6RCo/JYlVjQYYin59lRUu+moKCgEIyoBNiQIUPcAqygoIA33njDR4C9/vrrXH/99fEdoUL0SJJXC6IoC/Ch61KQsgt+YhZognz19MmAWhT/7/sGcocGP2EeFjNut7gEWGaynr1SHsNU5Vhr93WzAHOlH/u5xFJakfhvM4rXEYloqt8v6vXUWhg4y7M8rRByBkPdHjj4Aww7r3NjTcoGjQ4cXum/HnLrb203oXKJcac2GbW9nQXO3/N4vATScdbYXEFB4dgjKgG2a1d4T6IzzzyTk08+Oew6Ct1AU5moJ1LroGB09M/vpADLTg5RhB+sD6R7zOXw3BRAmHPy9iXBT5htNdBSgYSKbVJfDFo1Wo2aCgoYRjn2ugOB2+5KvOu/QDQYT8wUEauWqsgEmBz96nMSJGb4Ptb3ZJcAW9F5AZZRDGc8AEvuEPdHXQoz/9IjgmRq40eoVVBfOJ2UtEwMuz+m0FGF3eFEq4mDPeFx1thcQUHh2COuRqynnXYaOp0unptUiJamctj6gbidNcAjeqJBNmPtwAesowhYQDuicAX4kRaIu+wnrJmDaCeRBJ2wvziiKQBAaiglaprKRWG//BfprMDWaiGOUEHJFM9yuRA/UjPWYOlHmXjXgUlOz21LS8+IEauRWeavAGgeeQ2aPicCMF69lzaLUhumoKBwfBB1DZjD4eCbb75h1apVVFdXI0kSBQUFTJ06lVmzZqHRROi4rhB//NMudbvE/WjTLhFHwOQ2RH41YHIEzL8IP5wFRaS46r+MOaOhCgxacQ1Roy0EG6ibDka3vc6kqspc0a8CV/2XTGqhqGOLpBDf2OBxvx9yduDjch1YzQ5oq4WUIOI1GtpqPLfr9nRuWzEibf0fabRzyJmLbsgZaC1iHCeo99JqspKRpO9gCxGg2FkoKCgc5UQVAauoqGD8+PFuy4nVq1ezdu1atx3F+PHjOXy4h9zIFeJnMxBxEb4rApYaYhZkNBGwSHFFwFqzRWpVjoDV6UTtla65LLrtdeY9K3UV4Pf1S7u7Z0JG4AW29yvh9ZU/EjL7BD6enC0eA0/Bf2do9xJgjQcj6vcZVyQJ55qXAPiP43Sy0xKhYDRm9GSq2jBX747PfrZ9EGShChIy4rN9BQUFhU4SlQCbP38+OTk57Nmzh4qKCjZu3MiGDRuoqKhg9+7d5ObmMn/+/K4aq0J34bahCCLAXOk6y6ENlFj3UkRdoA2FK4LRara7Gy4D4QVYUraIPPnjnTKTJHcErClDiBI5AtaY0FvcbysX63UH/vVfMm4vsAguRnZ/Lv4Hi37JxDMN2eaVkpac0NDNNXPlq9FUb8Us6fhUPZMkvRY0OnZrBgGgLl/T+X00H4at74vb5z4GV3/mSqtLsO/rzm9fQUFBIQ5ElYL85ptv2L17N7179w54bPDgwbz22msMHTo0boNT6CHcETC/GjCvdJ0BWGwAs6TDYDkVEkvcq6Un6lCrwClBk9FKXlqCeMDdhijIrLuMYpH2M9YDEnx8o0jjbXlXNBMHaDokHlfraEgdDGxxR8CMiYXYJTVahxlaj3iiUB1Rvjqy9fxpPeJy43f5f3kTiRt+U7nYxh5RC+V+jcHoezL89Gz8I2AAdXshb1jntxspa14E4CPHSWhSPGnbvfrhjDFtx3BkXef3sfIxcFjEpIYJ1workJl/gc//CEsfhFGX/KwsPRQUFI5NooqAGQwGmptDp6Wam5sxGIJEMRS6h6Rs0Pi9/7HYDMhpGv8IWJB0XYLKhsrY4LNMrVaRmRTEjNVdAxYiBZlRDEVjoWgcnPmAWLbuNU8tlcuAlfwRmJzi2kGOgBkMCVRKrtfZGGEhfnsdLPu/wOWRvGdy9KtgVODJ3B0BCyHAZCH7yizRfBvgf9eELv7vMxVUaqjfF73Bqz9yBCxbRJxirgOLZeJC6xHY8TEA/3GcQbZX7eChZBHRTKvdENt4vMe1/g1x+9S7PD5s438lbE1MDfD9vzq3D4WeJdZJMwoKRxlRCbC5c+cye/ZsPvjgAxoaGpAkCUmSaGhoYNGiRVx88cXMnTu3q8aq0BEZxfCL98RtQypctzw23yM5AmZtBUdss9LcXmBt3gIsihqwfjOgZKqIZKx4TCxzpR/pdQIWV2pTjoAl6zUcklwtlyKZCSlJ8MlNYKqHrIHQe7JYPvXmjt+zpnLY8ZG4nTs08ATgrgELkYKMtu4sMQMKx4jbpZ2IgkmSJwLW19XuqG5v9NuJpadkUzksexicdhpTh9AopbjtSgCq0kRNX1rbAWHhESsr/gVOm0jbeqeGNVqPqF/9gvBeUzj2OIr6mSoodJaoBNhjjz3GxIkTmTt3LtnZ2ej1enQ6HdnZ2VxyySVMnjyZRx99tKvGqhAJatcs1NRCEU2KxWZAtqEAXyuKKAq2s2KJgHmjUsGpd4rbG96A5gq3AStFJ2C2OcRQXRGwJIOWQ1K+eDySCNiGN0X7H40eLn0dil2GtZKjY/H19HjY+am4v/W9wBOAnII0NYDN3PFYIqForPi//cPYr/rNzeBwfR5yv8n6GARYtAKyqRz+PR7WvwZAZutuvjPcTn99k3sVdVIO+52u960ixjRkQylsfEvcPuWuwMcHzoKBpwuB9slNSgTlWOQo6meqoNBZoqoBS05O5q233uKf//wnP/30E0eOiObHBQUFTJkyhcLCCOtuFLoOOcLRmZmGWj1oE0V6zNLisVio2hSwqk2lRxckXZflb8Zqt4DFldKM1Iai33RR/3RwBXz/iGf/vcZj2R8YASuTBVhHEbD6/fDFAnH7tHtFGrHMZQXReDD8cyMx+EzM9Lx/rZWQ1cn2XE3lsMElLPYsEX+xuLrLEUhDmnjNICJg0bRMigVjvYhkepGgslGkb3ffT0vUslEaxACqRF3eoNMj377ccsgVYaNkKvSZEnzdqX8QhfhlK0X0BBSHfAUFhR4hah8wgKKiImbPnh3vsSjEg3h4bYFIQ7aZfOvA9roKxgefDXuW4JTg7ZEvck2QE1eAGat8harWRmcFcMqd8PoKWP+6uK9NAH0yZptIjbojYHotu90RsIPBt9VUDm3VosDfZhRtmqbcKB7LcE0iaDoU+dhCoVKJNGTDAVEH5i/A5Fo9b1ESru7MWC+iNt7E4ure5iXOs/qLujJLi3hPUgsi304H9iSRkpHoMW1OTdCx3jmISzTfRzcxIpiP2+G1Ynmw90ZOr3ujOOQrKCj0AHF1wr/xxhu58cYb47lJhWiJh9cWBHqBtR6B/d+J22c+QJlhMGoVDHAEjzZlJYuTqzsCJo8rKRvUUXztMkp8ozN2MzwzEV2bKEY3yBEwg1cNWLAUpHyifnkm1O4Uy6o2e+q0ZA+upih9xELhdsMPUoifUQwXPStupxbFXqsXLXJ0NCVPCL4M12uOtg6sbFXgsnAC0mELujjNR4BpWe909fCsWB957WGwiKTDdvylpI6XwvRg3yW1pkf6mSr8TOjB305MEbBQfPHFF/HcnEIsxE2A+XmBbf2f8I0qngzZA/hJN5k+lj0MavweuC3g6VnJYjZmg9HWuXEZ6wN9vewWNOZ6QOcTAXMLMGO9sNBISPPdTsCJ2uqJfKQXe16vqSmwJ6NMUraIHHn7kwUTH3IdWLhCfBAzPuX6rq6mze8zyBksxGrdHk8z8UjYtVj8zx8F1VtFy6tffhxaQAaJSJolHUkZee77qQk69kq9MKqSSLK1Q812z8QDhfAcT43H5ckvBWNFb9Sl/wBdsu9vXeGYparZRGldO/1ykilMT4xtI3JJgkxSdujfQQ//duIqwPbt2xfPzSnEQjxTkODxAtv8jvg/5nIAvnFO4DL+Q27tKrC2gz7Z5+lyBKyh3RLfcbmw2oUoS/CKgLWRRIs6nTRnsxAW0ZzADSmQlAPGOpGGDCXAMoqhcBxUrodT74VBs4L/wDtyw6/ZIf5H4sElm9T6HySiver3joAB5AyCvV9GFwGr2ixEl0YPc1+DpydCw37QhOkBK89eHXI2zFjA1a+tYW+rgefy+rlXSU3QIqFml24YJ1jXQ/marhFg8XovjyaOxsbj0Z4EI1nX2CBsaQBm3gsDToVt70PtLvjxWc+kHYVjknfXHuLORVtxSqBWwUOzR3HZxJKOn+hNtIKqo0kd3t9LexxapPkRVwGmcBTgjjTlhV+vI7xTkEe2ClNUjR5GXAzAGmMh5c5ciqmF/UvF1agXbh+w9k5GwEJgtfvNgtSLr/IRdYEQYA3+AiwCd/zMPi4BVgaFo0Ov11Ih/g88LXT0qqOG3DWuNGgkAkw2qd3yHnx3vyigv/y/0Z9c3TVgXgIMopsJufFt8X/IOeL5hWPE5Ij938HYXwR/zh5XZHzML5AKx/CjqQorTvdEDRACDGALgzmB9aIObNJvOx5PpBFJGfm9XP08/Pg09JkGFz//84sU9STRnASjWXfty2BrF5HXgTNFacIpC4SH3k/PwuTrfXuyKhwzVDWb3OILhIn3XYu2MX1wbnSRsKgvRkKcF/57uaiN9T6u2MNcZMaI0oz750ZX1IDJ0a8hZ0NiJla7k2azna+147lW/YVop+MnwLJdKUhPDVgUFhTehIhYNJIG2LxmQYqvcoWqgMHsDqwD827B47UdnxN1Rokwew1XiG92Fa0DZA8IvZ47BRlEgEmSlwAbHnob3mQUw4BThABrq41NMMjfjRSvFCREbsZqtwjbDYBxV4r/A2cGCDCfNILtsJiMoNbBgFNptzrc7am8jVjTEsTBba1jENeAiIBFgjbBcwy97G1I7x0+2gLisSHnCAHWWKqIL2+iiVyFItRJsHKz77Y1Otj2YWQnTGs7/PScuD3tFk9d6LALRa/U6m2w6t8w66/RjVXhqKC0rt0tvmQcksTBOmPkAkySPBHSSNn03+DLg9XuOqyByzpJVAKsoqKC8847j82bN9OrVy9yc3NRqVTU1NRw//33M2bMGBYvXkyvXr3iPlCFCIlV6Pgje4EZ693u5Yy5AoB6V1rxO2kC1/KFiHA4HR4PMiDTnYK0IkkSqnBtiMLh06II9zaOfF4LVHn5gIl9HwplRbHvG/G//6kw6z7PWLwP8nJRemOYQvwGl4Fncm7wGXUy4dzwWw6L2YdqLWQPDL0NfzJdKbu2I0HTvh0SEAFzCbCmcrCZQNfBgW73EmGSmloIA04TywacBiseFQLM6eSddRXc+eFWJFca4YOxGxgHwhTVkEp9vbCeSNRp3FFL8ETAVlv7gVYtopCtRzqenbnzY8AJhWMDLgLCUjgaUInPoq3WI0qDEQ9R0pUEiwKq1NFHg7q6Hua9eVGs7Hc23viW8NXL7AvDL/IsV6tFx4N3fiEMdqfMj1uZg0L30S8n2d2+TkajUtE3JymyDUgSfHs/bHg9+OPWtsBle76CNS8ELtcYYNqtsPzhyPbdCaISYN7NuAcNGuTz2J49e5g/fz7z58/no48+iucYFSLFZvYYp8arBmzXZ6J2KClbGFkCda3iSuBA0mjQZIiTU/lqn56IcnrJ6nDSbnWQ0pnIXEZxwAnAYhdRKP8IWKlTngl50LOyd+RmyvzQacNIrChkB/WOhJNcA9ZaFSBO3dGv7EHCcy1SkrKEhYe5Sby+/BGRPxcCa8CSsoVnmalRvK6CkeGfv8mVfhxzhef19J4E+hQw1lO7bw13Lqp3nzqdEpi3fy7mWg8+E/DYkninH8ETAauzGZCKhqOq3iaiYMMvCD+mbR+K/yPnhF/PH0Oq+Azr94q6tkGzgq8XTpTA0SHMUvKF75ytHU69B5b/n7AtObTa852OhHjVkllaI183pRDaglykrH0FLnxa3HbYRHQLYOpNoquBN0POEZNZKjfCysc9HQ9+Dhxt4r+LxlOYnsgtswbx2NeiHEIFPDh7ZPjol3sskqgBlI/xaq3wA/Rm6UNw9See41bdPvjgN+L2qEtcdkQqz2sy1h99Akxpxn2UI4sctS58dCYS5OfLodhRc92F1nVt4iCdmZoEvc8UDbN3LfYRYEl6LQk6NWabk8Z2a+cEWBACnPD14oe1z5YLGnxTkHu+CIzcBCMSKwpZgGWFST+CiDKp1MJZv73WN5ITTQG+P1n9xImmoTQ6ASZJgbMgVSohAivWiDRkOAHWUuWJIo71imRo9cIwd/fnGHd8hcR490OpGJmg2i3uuASY3JrKO/0IkJLgORRZCieSUL1NiPpwAqylCsp+ELddtYlRUTjGJcA2hhZgoUTJpoUi8ufv5dYTMw/LfhDiKzkPTr5dLFv6D/jyTpEi7u66qGApbY0uuIXEBU/Ae78MfI83/kf8Hqf/CbZ9AM3l4vWNDRJFU6ng1Lvh7UtEs/cBp4mTqCwOQomGo03c+HO0zW6VO1p00Xd+ZC/POWtM7wxPAX6wzwkC3xsQ34MxV3jWr9sjfB/LVsJX98JZD4qymneuEMbgxSfChc8FvxD2L33R9HARvtyMO5gAA6UZd4/jLXI662zuL+Bc6UeAWpcAy0kxiKvPLe+KOrAz/uGz36wkPZXNZurbrRTHKzXqIqAXpEF8lffYcoQAa64Au1X8sDYtdL2Gy30jUf5k9BX/G8tCu8PXu2b6hqv/AnGVnlIgivBbKv0EWJT1X95kugRYpA3HZaxtnsbfcgQMRBqyYk3HMyG3vOOyITkRcvyifwNOg92fU1D7AyrGuyNgJ6u3oFM5sGcNQusyo5XT1/4RMJ1GTaJOg8nmwJjSlwQQkzsqN4U+Me74CJCENUosJ4CisWIWXdXm6J+77MHAZT0183DPl+L/4DNESu6km4VtTN1u+OavcMG/I9uOuSk+45Hfz1FzPUbHbdWw8NLAdVMKAksMdnwCKx+F7/4B7fUi9Q2ixlCXEHyfuUMAlajTectlEq4xwNWfwpvnB4qYX34Gb54XH3HTVUKuueLomt1atTmgo0U8x1PeYHLfPtLiauEWTISqdTDh2uCt8Qad4ZsxKRorxP//roGfnhFlFgd/EMIsJR8u+09w8RWs9MWuhweizDp0QFQCTG7G/eCDD3LqqaeSmZkJQGNjI8uWLWPBggVKM+6eJJ5WD94Fhxl9fa6i67wF2MCZ4kDXcABqd0OeJwKamSwEWGO7VcwujNfYAEuICFgtGUjaRFR2k7hq1qfA3q/Fk4JdPXuT7rqwsLWLKe/JQerV5BqwSGq30go9AqzXCZ7lnY2AQWQNx72R6790yb61Y/JMyHCF+JLkmf04Lsh7OHAmAIaqdczoY2BZmfh+zNSI3p3aIWe6V5VTkPIkDW9SE7Rk2qrJWOVKIdVsF+2CQp0Yt30g/kebfpQpHCv+V8YgwBKzRSP3nkaSRGsqEB0qQJxQzn8SXjtL9Dwdc4VPdDokOz8LXBatRYckeQybR1/mSfc3lYe2//AvMSgaK070Pz4Nq5/zLP/pOZj4m9AWFf51Yw4LvH5OYDrKbhGz3OIhbuIVpfIWcXaLiDaveTHy53clkiT6uH7RtTYf5Q1G9+3qVjNmm4OEYBFopy147VYoRlwsyhl+ehZW/Muz3NQYvr+x//eypSX0ujGiNOP+ORGvNF9TOXx6k9f9g/D0BLdDsFwDlpOqF7U0/V099XYv9tmMHOVobm4SrX/iMTYXcgTMoBNfYYNWjVoFoMKR7gpdN5SK6JzkELVKstgIhS7BM3ux6WDg45IUeQQMIK1I/PeeUeN0CKEKMQowV1ujhgPRPc9/BqRMR1YUTeUigli/V8w47D0p+Jgy+4HTzkkaEd1T4+Qswzbx+OCz3KuGSkGCS4CpWlE7/WYbBWu23FgGFWtFmte7KDsaZKuR5kOuE3gQtEFqULQGuPi5wOU9Qd0eUQ+oMUD/UzzL+0yBE64Wtz+8HsrXhnf5NjeL3wp4IsHDLoxeSNTvExc+Gr2n4Tt4IgrXLff8hdv2qEsClzmCfA86wl98yYQUzxHY1XgTj+bgsoh7cYb4e/UM+P6f8YtIxoLsDr/vW3j1LPjsVtGFpAspb/QIMEmCw02m0CvnRRmJGhUk+iobcfcgSjPunxPuk2wnPcCM9YH1Gl5Xh3IELDfFFcUYco7oE7nrc08NCh4BZm5y2Ta4+jjGA7kGTE5BqlQqkvVaWi12LGl90Na7rCjkwvFQHlX+ZJQIwdR0CHqN933MWO/pDBBJg+1UlwDzdsNvPCgOZNpEMaMrWuSZkNGmIP1nQMq4rSj2gtPp2ybK/+reboYXpwc/cQ6cCWtfZkDLaqA/Y1T7SbY3giEdSk50rxaqCB+EG37wpkVB2O4qvu87DVLzI32WLwnp4nNsOCCsNILVB8pCPKUAfuESKHJEyD+iE8vMw84ip+f6nSzMhL2ZfB1seEN8l19x1biFis6seUlM4MkdBtP/CB/8WgjTaFNLcvSrZAro/WawBZlME5o4NYc/8yFRC+fPjDth+UOByz+/A8580NdYOJaUYp2fKXm4bQQTcQCTbhCRJ++0n0bXYUSy027ywaJ6AJN+Bxte7TITY+8UJMChBiMDUkOsPOuv8N5VkY+lsyU5XYTSjPvnhDsC1rXTsH1SkCD8wT67BQ6vg73fiP0nZbvNWK0tLgEWj9o0F+4ImNYjGJIMGlotdkzJJSSDSFHV7hLCb2SE39eMPqL4O5gVhVyAn17csWUDBHfDl9OPuUPC16OFQk5BNpULkRzOgd4b/xmQMpl9xawhm1GkS9O96jujmRU3QAiw4aZ1wBWc5ko/SgNnovIaoycFGTwCFiIOFdiOSk4/jujkcahwrBBglZuCC7ADy8T/wWcGzp6Va0SqtsCnN4saub1fw8Rfd25M0SCb3HpFGd0E66cZ0mPL1Zv05Nug9wRx+8g2sb42irrefd+K/+Emu3QFoToc9JoQfPmA0+CHxwK/3xVrPGLVe/1Q0bpQUapFft+BWNKSY6+AqTeKz+v7R8SM9CHnhd1GXNzkQwnCsZfD1Pmi3nfJHSINf93SuNR/SZLkTkH2y0mmtK6digYjpAVJ0mkNon42iD3RUTWJIgIUJ/yfE3EudA9FgABz2BBXrBK87arH0RroM06cJKW2+AtD/wgYyFYUFtqSi8kBOPSjeGDY+ZHPCg03E1JOP0YS/YLgbvjROOAHI6VACEq7WaR6Ih2L/wxIGY1ORNXq94ooWHrwCTYd0ncaqLUUOKooUVVzmloIsIaiU/C+JpVbUwVLQaYl6NgvpWJX69H6pyG3vAu9xonbdfvgyBYhHId1YFPREYVjYPui0IX4+5eK/wNODXxMjugUjRUn4q/vhS8WCEsE75o/6JpCbWODuFgA9yzTmNjwphhbZl8haOXm1sZ6IcJ6j+9wE4A4aR9cIW676gJjJtqWUSH8AqNabm4RwqJ2Z+DrClUbdnhDZK8n3DYqw2xD/o5NmS8E2L5vQnr2xc1N3h7GcDSjGMZfA9/+XaRx22o8x8xO0Gyy0WoRFwxTBmRTWtfOoQYj2F31uzmDYPZLgMr3txPpb+gobUGmCLCfE/GqAevgy1rX5lUDBh4vFm/sFvK1bfEdlxehImAARvwONoPOiHzD4bzA3PVfEZqnBnPD70wBPogUYWY/cZJoOBC5AAsVAQORhpQFmLfQCGZeGIqENDEbsewHLtUsY4S6DKekYq1uAt6xmfo2OQUZGFVJS9RSSQ5vjl/EteNcuYc9X8Cyh0Qxdt+ThJjevkg81v/U4BMlokGOalVtCnyspcp1MlZBvxnhtzP1D0IM7foM3p0HF78o6iNBnNDiNePOm71fi6hb/sjo/L5cv8eqZhMHqxuYtPJJNAAn3eLx2Co6AfZ9LTpDRCrAyteISGpyXvQ1Ov6EE07hnhPs8WiWX/gMvBxF9E6OkE66zjPJp6UK3rk8sue31cB3QXzL/MVB8YmQXiLSwrs/DzrxpLSunQKpjkyVx4etUUqNzk0eYOs74R/XGsSM220fwK5PoXhi5NsGHE4Hexr3UN5aTp+0PvRL7+dOP+akGBicJ1Lph+tbYdfLADSf+HsakjNwOB04nEbs9dvFbcmBzWHD4rBgdVqxOsSfxWEhTZ9GSVoJfdL6kNzB98kpOWm1ttJqbaXF2uLzf0L+BErSoowiRogiwH5OyCfZzgqdMF9Wu8NJgyuN5PDvHeFHWqIOsKAxN8RnXC4kSQoaAUvSaymijiFr7/Z9wic3ipqUSE524dzwo5kBCZ4i/JYqj61FZywoZLJkARZFHVhbmO9GziDYTeBMyO0fBa4b7qpxwGlQ9gO/1XwOwAZpEGuqVW4BJklSBylIkaqsIhuKXO9P0VgwNQkBtuh6+M0A2Pq+eCzStHI45H6hjQfFrKjETM9jpcs963RU26VSiZN31SZhH/CGtyu/Kzrsjd0i6tiGnutrXBpNZMw9+zFI+lHelv+FFMCXd/NBbS/+9Gkpl6q/Y4quCqMhjyTvOsle44UACxed8We/nH481beWMFaiqhmLE9GUBbTVeCJ+J/7eUx4QitIVvmlspwMW/VbMEM8aCBc9I6LbEPg9UKth9KViFt/md4MKsAH6Rr4y3I5V46BVraZNraJRpaeqWcun+9Nos7VhdVhxSA6ckhOHU/x34qR3Sm/G5Y2jWNKgkmc8e6M1cBg7a/d9xLa6bRRlZDAqwcDwnZ+SPOtvYUtLbE4bO+p3sL56PeuOrGNjzUbabJ6LO61KS5ahFwm90klO6MMhexn63E2UmfZzaaqTiqxiWrc/DtsfD//+hiE7IZuStBJKUktQq9Q0WhpptjTTaG6kydJEs6UZKcQEjIdOfqjnBdjQoUPZtWsXAPfddx/33XdflwxIoRPE04YixMHvtR8Oum+f/++VosYgROcpWYAZLPXxGxdgd0ruMLt3BCxZryFT1YrGGXoCQYfIkYTm8kAvMLcLfgQzIMEjwGztonhfl+iJosUaAQOvQvyDkT8n3ASNYDMhW4+I9i8AZzwgUowQViBIA2ai+u7vGFTi/d/u6EPFwd2AEFOh+kDKpLq83FrNfrVLZ/xDWFKUfg+vnQPmRpF+lG0kOkNiphDdTWWilqu/V6QrXPox6LYyYOZfxUnVhxAXKl/fK/68iTQy5rB56q1CCTD/C6nWKvhoPtTtpviLaxjDFdykEdHEl9unMbfdSaGcqZdTqJGm2MBTgD+gk+nHniSaVNXOT0QEsmicr/gKIXydX99LpQb2FI2gzlTHiLINDD2wDI0uCS5/28fCB8BoM/Jj1Y8sK1/G/qb9aBxW1IV5aFs3oVnyKzS6BOxOO82WZlqsLTSa6jH2DzIRbqtwdNeqtRg0BtQqNVqVFrVKjUalwSlBvbkWCYkslY5xWSmM1fdh5JRbqTDVsrZhJ+ua9lD59a9QoaJPWh9qjNUYC/NRSTb6LzqHkfnjGZw5GKPdSL2pnnpzPfWtldSZ6qi2NGBx2kjUJDAu/wR+NWA241NK6JdcSJnxCHutjXx04ACVmp206L/jg4OL0aWlkeJoZpjNyhn5k+g9Zh65iblo1VrP2NUatCotWrUWvUaPQWNAr9Gj1+jRqrS0WFs41HKIstYy8b+ljAPNB1ChIiMhg+LUYkbljCIzIZN0Qzrp+nRS9amkGdJI06WRZkgjWZeMVt11caqIt1xaWorVakWv1/O3v/1NEWBHG5LUJak+b6qaTTy4xFMfIdcYnPL7QeQHcQ1OycwH2kiyNYplSfERYHL0C/wiYIY4/FDSe4vZbHazMI+UDVSdzsjbEMnoEj2tg1qrxMHaaRd9NtNCqNZIiMULLNQsSPCdCSmz7GFh3Fo8WdSfRDB5wqhNJ8lLs16t+5rL6pZhrT8BfXYf6l21gwk6tU8fSBm5H2SAANNoxcy056cJ8QXifXzplPi4cBeNdQmwTR4BJkme9JK3vUNHyO9lJMjfDW8ivVgoWyVmLSblBM7W9cbnQmosXPUBjpfPZBK7+dBwn3u16zWfsq3sVgpHu6w5ilwCrG6PqI1KSAs/nvY6Tx1dNO9XHNlUs4lH1j1CRWsFo3JGMTp3NGNyxzAyZyTJuo5nX9eZ6lhVv5GVJ17K6poNqMzN5Nnt5OUMI2/na+Ql5ZGbmIuEhNluxrztdcwZ6Vjye2Fd/ZBb4Og0OgxnLsDgsCEBB9oq2FO1lr32Voy7X4TdnphoSp/ejEsfxISaVUxQWclNzGXF4RUsK1/G6qrVWJ1W+qX3Y0yuiNQ66kqxmxpxmJpwJPQhSZtESWoJ6YZ09u2p4NQjb5HhdJLidJLqdJLslEi6chGpxVPQB3Fydxftq4wMTf6Rc1LeZ5PBwDMGB+Z1D6JCxZCsIZzW9wwmFkxkfP540g3pOJwOShdezNYj69ieNoStTXv54uAXpOhSyE7MJlubTK/ydYy22chzOBhrtjDUoUI39k5YdJ3w8gKygHFaA2WD32bVoelce8oAbjilH1f+7XneNfwFSaNHdc2jMc3sTzekMyp3FKNyR0X93O4i4jPWmDFjuOaaa5g4UeR7n3jiiZDr3nLLLZ0dl0K0mJs8njdxEjr+lNa1B0xGc0gSB6xZ5MtX2ksfhL1fQp+TSM3vB+wnzdkkHOfi7AEGoNf4RsA6jUYHab1FrUVjmUeAtVYKQaLWRldvk9ZLfDYtlSLFBSL61ZnZoG4BFoUXWLgImCwoWw6DpU1Evza8KZbNui/isRqba0n2WzVBZWNv+SEGZfcJa8IKnhRkizmIGYXTEbgsXi7chWNFw/nKTZ5ltbtE03Ntgqi/6Swava+5sdYAFz8vDEH9CVcELeN2vz8zunRf0TjaTr6H9OW+kTeDykZJgpcNQEqup+aoapNoNxUOOVqYPyp2W5AYOdJ+hCc2PMHiA4sZljWMOYPmsK1uG69te402WxtqlZqBGQPpk9aHNL2IbKTpxV+KLoW9TXv54fAP7GwQF5cjskcwZ+jl6Eq/p6ZyHbVtR9hWt41qYzUN5gZUqDCo9SRIRhJSk0mw1aOrXovD6RC1SK4aJKvDilNy0je9L4P6nMJp1bsZfGAVg602MhwOthkMrEtMYF1+Gs9vfh6Tq1OFRqXhhPwTuOmEmzil+BT6pHkVuWt6wRd/Bl0TzP7QvViSJB5Y8hcutrUHvD+7d+8hu29gDWNVs4kFH2xFAlRSAg9bljLW1oxxxOXo5jzNgaYDFCQXkG4InMCkUWsYOGwOA/ct5+LaOrh+ue8KlZtgzceBH9b7vwpcZrfQ2lADZFCSnURqgoHfJXwNEjT2P5+sztoqHcVELMBef/11/vKXv/DGG28A8PLLL4dcVxFgPYCcfjSkh27X0Un65SQHVLO4O9anu1JTZz4gPMEOLCWzRaSss5EbhMe3D6Req0at9pzxk/RaGqVU7Co9WsnvZBfNbJcM14mn6RCUTBbL5OhXRp/IrR9AWFHUbBcCTPbu6kz6EXxTkKFaJnljNXoK6oN9BklZQrQb60SKdOVjwrx28FmROai7MFqDiCRgd3UbgwhvwgphImBdjVwH5j0TUhYUfaZG93sKlcL65We+LU/kWYbBWHybaBwcqu7Mx/0+RPoxDOlDpsPywOVuXz+ZXieI38Hh9QECrNHcyLrqdaypWsO2um0UNFcxPD2NYb1HMNzcQFaCZ+ySJFFvrudQyyEOtR6iwdxA37S+DMsaRkFyAaog31+rw8repr3srN9Jg7mBkrQS+qf3p09aHwwaMU6z3czr21/n1W2vkqhN5P6p93PBgAvQuOq4nJKT0uZSNtduZkvtFqraq6hqq6LF2kKztZlWaytOyUmmIZOpvaZy1fCrmFo0lexE17Giz7nw7xOgvglufod396m5c9FmnJKKqzVf8TfdG9B7IlzyRWRvfOUm2O4RQidYLJxgsXDd2NuwFYxgR/0Oao21TCyYGFT0AKL268u7RG1e3V53+cCmPaX82vqfoPZp/X9cAGk2399yUjYbDmncx/I5mhWMVR+gVUpk97BbmaDWMSRrSPjXM+QcYT9UtUnM8o3kQkitc0e/vHE2VQAZFGcmQUsls6RVAGzv/QtO7nirxywRC7Dhw4fz/vui+FWlUrFt27YuG5RCDHSDB1hheiIXji3io01iVp9GpQrsWJ8zSBwktr2PduW/SE+8iiynLMDi1IYoyAxIgGSDhkpy+PeId7h1qpfginbKf2Yf0bzV2w0/2hmQMt5u+PEowAchEFUaEZFrPeLxGwuFPDlDm+CZmedPzmA4VAeb3xHRIFQw8y9RDavdEkKAVbVyHqH7QMqEjYB1JUUue4uG/aJWLyEdDrgEWLTptGhn7wUrkq/eCi+eAmc97Pn+eDWQlg5vwN5wAJ1aG13KMwQS0KJWUd9eSf0RGw3mBqwOK6q0NEhOQnXoW1QHhuCQHGyv386aI2vY2yjS1SWpJYzJHU111RZeS0+jtWEVvDuDguQC+qf3p95Uz6HWQ+7oDkCSNgmjXXg+ZRgyGJI1hGFZw8hLymNv4152NuxkX+M+7JIdtUpNqj6VZoswQFaholdKL/pn9Gdf4z5qTDVcNewqrht9HSl6XyNatUrNgIwBDMgYwOxBgRM2nJITo81Iki4JtSpIFDF7gJhpe2Apbate5s6VU3BKYr1zNT8B0DLgPDpIzkaETq1zpxnDkpIrLD72fiWsWU67BySJhMU3UqhqpEGbT9aVr4I+haq6evb97y+crNkWYEYraQ18mvkCRbTQS1XL3VpReP8fxxlcXByhrURKrogOH1olZmZOvt79UG2riWCX241nPE7mFzcGLP+T6Ql2qO6gOOtUWPscWhysdg5lm9RPEWD+mExhWgQo9AxdXP8lMyhfnMBnDM7h4Tmjg09vnv5HMUV55yeMT5xJtrFrImDe9V+Au66oihwoiuBgFgp5JqS3FUW09V8ybjf8ys5bUMhodKJWralMRNU6EmBuD7C80NEyeRty771hF0B+dFYCzapUzJKOBJVHQJklHWtrxD47TkGGiYB1pY9PUpYn3XZkq2i3dPAH8Vj/CAvwvQkygUWSJFZVrmJp+VImFkxkRu8ZJAQTa6ZG+Oh34rN95wr34iZdAj/OWsDKdc/wY4KOpr7FjDVbmPzO2Uw+73lG9D0NndoTma1ur2Zj7UY21WxiU80mak21aFQaUbwsSah7F6GRnLSr1dRrNNhUKlj158DXkpcDtjJYIR7rldKLiQUT+dWIXzGxYCIFyQVQvR2+fRanNpGK369gR8t+dtTv4GDzQcbkjuH8AedTnFpMSWoJvVN7Y9AYqDZWs7N+J7sadrGzYSdfHvySWlMtgzIGMTx7OHMGzWF49nAGZQ4iUZtIk7mJ0pZSSptLOdB0gNKWUsbkjmH+uPm+KbooUKvUAaItgIm/hgNLMWx5G600ASs68mlgklq0E9ubPYsITTrix+jLPALslLuw//AUw1p+wCLpOHTGS2S5JswUFsFfN6ZSvvdBfqFd6rMJld3CiZVv85ThO/Qqz4XT9folaKQ6IMIL1qHnCgG281MfAWbZ8mHAqmZJRzkFZPr9jiVUpKuMLNT/A90WG6x9CYCP7FNRebUniged7hIQZ2ISYAkJIiS/bt06du7ciSRJDB8+nAkTJsR1cApR0E0u+M0mcXIdnJ8a+gucNwyGXwg7PuImxxvo5B94BGOL5AcSMgLmqgFrD5EKixi5xsvbisJtQRHhDEgZWdjU7/PMWuxsBAyE/1dTmagD6yhN6PYACyGAm8pdUS8v9iyJPK3gok6Tx2mWR5neW8XDs0fTbLZx9os7qLQk0Wy0dZiCTE8UAqI1WAQsTGTJ4RSRGYvDwvj88cGjGR1ROFoIsMpNgErMXE3KER5bIbA5bexu2E1BcgE5icG/23anna/LvubVba+yq2EXeYl5vLv7XVJ0KZze53TO7X8uEwomuNNmANbznqDi/Xkc1OnYodezKjGBbQY90q5XGajXcG6bkVyHg7UJBl5PTeLpFX8k6cckxuePJ1WfyqaaTVS2iyi1bC8wrdc0YTng+tuw7yAHqmrpk5mBrRbarZncefFZnNCrhOzEbAwaA5KlBemRQUhISDdvhuRcknRJgS/SNftR3XcaJVmDKMkaxFl9w6dGC5ILKEgu4NQSj8CVJCloOhIgIyGDcQnjGJc3Lux2487gsyG1CF1rJWep1/KJcyrnaoT57TrnEHr1ieJ4EK+LiCHngC5JXCB+sQD1GiFYntBeyx8n+KaKf33yAO7fNStAgAFco/s6YJnGaY2urnLYefDV3WJSiLFBXMyUr6XXDlGi9IRtNl87hURtJo3/DZsGQ31/x1trrDR/cKuI1C3zeKL9VfcfFtScBsSniD4uXQLiTEwCrLa2lssvv5zvvvuOlBRxBdHW1sZpp53GO++8Q25u10ZhFIIQyum8EywrX0ZeUh7Dsz2CockoTqIZScFPojLOk29n397F7DTs4ZPUTM41ORnfQUuTSH8gISNgrlmQps4KsGBu+NE04fZGnu0oO5Yn58ZHJGf1E2mySGZChpsBCeJg6N+02BHlgRhos9ipJIe61HwoGks6oMtug3ojPx08zLaW79CmNdGkauanqmaStckk6ZJI1aeSk5jjjoCZbU5sDic6jZ+Q8oosHWk/wqrKVfyw6Ql+qvqJFquIshYlF3HxoIu5aOBFIjrjhSRJ7GncwzeHvmHpoaUk65K5eNDFnNHnDJKKxgoT1apNnpmJ/WcEFLg3W5pZeXgly8uXs7JyJa1W4eFVnFrMuLxxjM0by7jccRSlFPHJ/k94ffvrHG47zNSiqbx8xstMKphEWUsZi0sXs/jAYj7c9yF5SXlMKZxCnamOgy0HqWqrxNlbRE7THQ5ONJmZ29rGVJOZfIfnu/3LllbswM7LXmW1vZGfqn6ioq2CmX1mMi5PiJVQwvCu8q2srD7EpaMGsVvbypJtR9iyL5vZw/t6VkrKESnO2l1QvROGBIk0eYv33CFRi3ZvQomvHkWjhfFXw7KHmKf9hk+sU93pR/XIi6OLosRiLhsMY72nMfaaF1ADDklF6siz0ah938NJ/bIYlJcCzYGbOaQfQIl1f3T79iezr5h4Ub1VmCYPPRc++DUqyUFZ4Vk8UToHuTDtgYvkchXfCPG+IxW8Zr9MCDAvElQ22hqrOzc+F3HrEhBnYhJgN998MyaTia1btzJypLhC3LZtG7/97W+5+eabWbhwYVwHqRABcUxB2p12Hl//OG/ueJNEbSLPzXqO8fniKqbJKKITcrTCmz2Ne1h1eBXrq9ezoWYDLb0L0UoS2Q4Hi1I1zPv2Lm4Z91t0QQwLo/mBhI6Aia9zu6WTRdxuL7AKMftOkjzRq6hTkK4ImDwDrrPpR5lomnK7Z0DGT5wbbUYeX/84vVJ6cW7/c8lNynVHrmQhBTCit44q1Tfcte7vWKV2EnvBkhpY8pXv9gwaA71TepPQ24BkzeHtHS30SS+g1dbqNkuU/5c2l3Kg+QBqlZqROSOZN2weU4tEFHDR3kW8uu1Vntv8HNN6TWPOoDlkJWTx7aFv+absGyraKkjVpTKjeAYN5gb+8sNf+L81/8c5WaOZrdcxvGoTKpeotfQ9mfLGfZS1lLG/eT8/Vv7IxpqNOCQHw7KGufdbbaxmU80mNtZsZPGBxTgkhzsKd0afM3j8lMcZlu353Pum92X+2Pn8fszv2VK3hc/2f8bGmo0UphRyRp8z6ONU0+e7B+lrs5HtcHrqqs9/Cj69yed90wKj0gcwqmgsvxn1m4g/v2bX7zgjUcflk0pYsu0IizZUsODsob4XNr3GCwF2eD0M8YtqNZXDv8d7mkX/+LRIH8XDGuRo4oRf4lj2f0xW7+IU9UbGq/cioeKEs66JflvxMJc11gtLGy80KolzBwVe4KpUKs6eNALzV76lARZ0ZJ73d1j0i4DnRM2w84QA2/i2MEluKoO0IjQXPAFPenzkRvfOCPr08gYTToJHrWtbLTicUoCwlIk0pVha146/b7hDkqLvEhBnYhJgixcvZsOGDQwY4IkGjBw5krfeeovx47s9I64AcRNgLdYW7lh+Bz9V/cQfJ/yRFRUr+N03v+PZmc8yoWCCOwXpLcCckpMXt7zIs5uexaAxMCZvDFcOv5IJVicjP78bnSTxUkYaL/AJ6/d/wENnv06/4ik++43mB2IJGQFztSKyOlhdtZo6Ux3n9j83+jchtdAzW6elUognpx20iZ6arkhJ81s/HulHiM4LrKMIWJQYbUbmfzufbXXbcEgOHt/wOFOLpqJpnwiqLFITtDSaG/nPjv+w2v42+mwrmc5T0badyq7DDp76xTDG9U3CaDNitBtptjRT0VpBWUsZ+6o2IKVu4/ENK3EiTjLJumQyDBlkGjLJSMhgfP545o+dz+TCyQGzxcbmjeWOiXew5OASPtjzATcvvVm8XQlZzCyZyaySWUwsmIjONZO1orWCj/Z9xId7P+C9XoUMtbSS5WimrHcRldsfR9r+GAApuhTG54/nrsl3MaP3DPKTfa0W5JSb0WZka91W9jXtY3qv6RSnhT7ZqlQqxuSOCSy+biqHrx4Eh9dJVmuA3GFxq4NrMnki2dMG5tArI5HDTSa+2HaEi8Z5edQVjYNNbwd3xDfWe8SXTLysQY4iGjU5rHFO4Ez1Gp7UPQ2AOWcEif5R4x6mT1aQ9DBw6uTxnPf1k+gsje5lZ04Yzk0lgwK+T5LGgCra75PsQ1e20rOsvZaKIzU+q22uaGJU78DZneVh6rzsTomqZhO9MwNfWzQpxYwgAQP3DP4eJCYBZrPZ3KlHb5KTk7FaI/CwUYg/cXDBL20u5abvbqLB3MBzs55jStEULh1yKX/47g/8/tvf88zMZ9wCLCPJNWPN2sJdK+7i+4rv+d2Y3/GbUb9xn9xq96wm0WUc9rumFqYZzdyZl83cZTfyp4l3cOmQS1GpVDicDjSGGvTpG1AlHEatr0GltqBS27hv4zPY11swOUwkahP55fBfkmwV82KCRcBU2haqDO/xm6/ECeNgy0F+P+b30aU31BpxAmk4IOosrC5vnaz+7pRUxMWciZme5tngEwHrVEGo3AMyEi+wcH0gIaralHZbO7//5vfsbtzNi2e8SP/0/nx58Es+2f8Jm5seJ2VQAutNoznzg60AzOp1Ee9925+GhGzxeUlmSjLyKU7NCDqUT777huoWCx/Nn0zvHEjTpwU1kAxHij6FuYPnMnfwXHY37MZkNzEqZ5RPnZVM79Te3DjuRm4YcwOrnhnNx2obDpWKM516+k69jz5pfeiT1oeshKyIvkNJuiQmF05mcuHkqMbsQyyNpaPE+0JKo1Zx6YRiHv9mD/9dc8hXgMkn18PrAy1Pgnmz/Qz5eNNh1tsncqZ+DekqMQEtsW4bPD3+mIj21bdb2GvOQCLDvWzXOjNzZ+VQ6Po+zXtlNU1GG//85amMiPb1BDvnOGzUHDnss2hLRRMQmMYubzDSKKXiUOtFDZoLCzoapVTKGwIFWLQpxQ83+o5FrSJwBn8PEJMAmz59OrfddhvPP/88qaliVlxLSwu33HIL06d3YNin0DWEM9qMgB8O/8Cflv+J3KRc/nvuf929rxK1ifz7tH9z03c3Mf/b+Uj2a4FiMhL17G7Yza3LbqXJ0sTTM59mem/fz76yyXcq8iirlfcOH+Husb/gH6v/weelomfgzoadmOwmDEXgtGbjMBcg2dOY0q+QUUW5JGoTSdAmcLDlII+vf5wkzWvoMk5GrzvHvW2H08GK6o9I7v8sFnQ8OO1Baow1PLHhCUw2E7dPuD06EZZR4hJgZaIXIbjrv95Zc4g7P9yKFEkxp0olImpuDzARAet0QWhmX/Hf3BTYw9CfjuoDIzyxt1pb+d03v2N/035eOP0Fd+Tm0iGXcumQS7nhnS/57vDnmBLLuHLYlVw1/CqStGl8+O1X7v6hELwPpExqgo7qFgtGKyHrl6KhQy8jF1q1lunpQ5h+wNVOZ/jJkDuh506u0TaWjhJ3KYHrQmruhN48+e0eVpc2cKC2jf65rgvs/JHCRNbUKNLw3uUDW97t9DiOBf63vgKkIDONeyraF+SCKVzkqrSuPaAZlju7MMD1fSo0s31fPdvb0oi+jXqo9KAZMNA/N5kDte1sLg9SiIYQYJXksH3OUkZneqKKf/60nMpSNeUNRqYM8H1t0WRMalrMvPmjqOfVaVTYHBKPXTrW90Kjh4hJgD355JOcffbZFBUVMWyYuKLfuXMnubm5LFmyJK4DVIiQTqQg39/zPn//6e+cVHQS/zf9/0jV+3pFeYuwVdYX0RivYX29mWeWPUzf9L68cPoLFKcGHoSKMgKvLpIkibuGXc3spCt4ccuL5CfnM6N4BsOzh5Ol7ccZj64DhM3FaxcERhF+PfLX/PGbR2gp+Jhtqh/4eN/N9E/vzz9W/4Od9TuxtUxC33Iu5w843z32h9Y8hNlh5q7Jd0U+Q867KbfRFV3MHui+8pJ/+xEVcyZlewSYw0Z1+V7uXLSncwWh+mRIycfZVs3esuUcTkojOzGbnMQcchJz3GaVQNgImMPpoNZUyxFrPUcsR8hMyGRM7hgStL7moy3WFm74+gYOthzkpTNeYmRO4OxApzUba+0ZXHvSSK48wXOlO6wojc3lTe77oWZBgqd+rMXUzemdpnI46OVOuuND2PP5MRHhiAXvGjAQv9UZg3NZuruWd9eWc+c5rkitVg8Fo0QE7PB6jwCr3w/rXw/ccLysQY4Stlc2s72yhbGaOHTZiBcZxXw6/VNeWLLWfRy64eyJnB/ie9ovJxm1Ch/B4p9+G5yfyg/76tl1pDXIFmKjoskEGLhobC8e+3oPe2taMVrtPm3IrHYnVS0iO1BQMhBSPced5DwNlB7iUENgijKYKbhaRdCU4rPL9mOxOzmhJIPUBB3L99S6e9L2NDEJsCFDhrBz507+97//sX37dlQqFTfddBNz587FYAg/062zrF69mmeffZbq6mpGjRrFHXfc0eGsy0ieE691egS71TNzK0oBtqthFw+sfoA5g+Zw9+S7g6ZpABK0Cfzz5MeZ8upVJJa8wqObnFww4ALuOfEeErXBRUNuXhF2tR6tV1jZodaTm1dEbkYxJ/f2tdhbU9rgvm1zBG9gXJJWwuk5t7Ju0zjyBq3gnh/uAWBI5hCenPEKv3q+Brta5Z7S/othvyBRm8hfV/0Vk93E36b+LbLmqnIhftMh0YYIIHsAG8saQ19NBhNPTeW+9TOvn0Ou2kCB9AiV5ES2DT/KW8v5qeonVmensyZLS+PqewPWkWcWpunT0BiMaAryUG97Fu3et9CoNbRZ26hqr6LGWIND8k0lyaaQEwsmMrFgIv3S+zH/2/lUtFbw8hkv+8yK9Ub27/IuwgcYV5zhFmCh+kDKpCWEsaLoSoz1gSm1n2E9E4Dd4aTVNVHFu5bz8kklLN1dy3vryjlpYA6D8lPE97HoBCG+KjfCqEtEX9RPbhL1XyVT4KyHcEdBYkyJHq38b10FACf2z4LyHh6Mi6pmEzcvqcMpeaKRtyypZ8IYU9DjR2F6Ig/NHsVdi7bhkKSgBtpDC8RF957qGARYiBKGnU3iuzW5Xxb5aQaqWyxsO9zCpH6eLgmVTSYkSRwX/DsxlLhq2oLViBWmJzI4P4Xd1W3uZQk6TUCxfmWTiYWrhZ/j7WcM4bMt4lguonM9T8zdiw0GA1deeWU8x9IhK1eu5LTTTuOmm27iggsu4JlnnuGkk05i48aNJCcHb7YayXPitU6PIaeOVBrR4DdCLA4Ld664kwHpA1gwaUFI8SVjtWkwVfyShPxPuf+ss5g75JLwab2MYjQ3reeSxz/DZHXywEUjGTtkQMgDdLnXlU5bmJmMZpsDpzWfSUm3ctUpGspbypnVZxYmqwR8hcMpYbE73UX6Fw+6GIPGwF0r78LisPDQyQ+hU+uQJAmzw4zZbsZkN+HwPgEnpYNWg6ppP/lNlegAsgfy/neHA8bjfTVZ2izMIuW2J1X1OzlSkEuDRs14s4Vz2o1MMpnJVrdS6cwJug2H00F5azlV7VVUG6upbq/miPEI1e3VHGg+wOG2w2IGoC6ZS+rbOHHoXPpPv5MGcwN1xjrqzHXUGmupM9XRamnCaV2FQwWOpBycai02p43ClELG5493+zEVJheSn5xPVVuVu8XM2zvf5rnNwpg1w5DBK2e+wtCsoSE/F/kzk0WUzNjiDPftUCasMj3Wjug4osXrvfUWYKcNzSPFoKXRaOOXr67xpMZ7nQBrgcOuC4kNb4iCa12S6Gcpp8N/ZljtTj7eJH7v08cNhaouMgKOklhm9F02sYTpg3M5WGekb05SwHqDXQbbMUXAgpQwWA2ZbPiXsJXol5vMmN4ZfLWjmi0VTT4CTBZXvTOTAs4lxS4BFiwCZrE7ONQg6vEevGgkr/94kD3Vbdz5wVZevnqCe1tPL92H1eFkcr8spg7IZt1BMRHhSMvRYSYfswDrCe6++24uvPBC/vWvfwFw5plnUlhYyEsvvRSy/2Qkz4nXOj2GnGJKzomqMe9TG56irKWMd897N6JC5yaTDSQdCS2XcenQMyLahyqjBHPOKLYfbqE2dRhkhG7UW9Ho+VGEOwHLNhQJOg0jskcwIltULSTpPUclo9XhM0vynP7nYNAa+NPyPzHjnRnYJTtmuxkpIJ7lRXEvoIr8NAdXSakUVOv5blcVKhXupuRqFTxw8QgOtm/i3tWvsLpK+H3p1XoKUwop0KbQ32ZjtMXJ90mJfJyaQpbDwbC0rezYrsJhKkGtaefqmSre3fcCW+q2sL1uu7tVC4gZfPlJ+eQn53Nq8alMKpjEhIIJpP74HOx7AExmcKUeB2f6taZpKodvnxV1PKc+2WHfyLSsNIZkDWHesHk4nA72NO5hS+0WJhdOpm9637DPlaNWKX4RMG8BZtCqqWoOfqUOnnZEigDrOmQvv1SDFq2X11pdm8XHwkVOjZ/22xGillPu+fe1q0XVaff8bMUXwLc7q2k02shPMzB57Bjov54d+0v50/tbyEs18Nrvz+qRaF+/nGSfYxBENqOvMD0x5O9OFmB1bRbq2yxk+/cF7Qi/2sRDNW04JWGOnZtiYEyxEGCbvEoRQFhQABRnBo7LHQFrCBRLG8qaMNkc5KQYuGJyCeP7ZnH+v1fy7a4a/reugksnFnOo3sh7a0XY8vYzhqBSqShMFynOyqZjPALW3RiNRlauXMnrr7/uXpaSksKsWbP46quvgoqgSJ4Tr3V6lBjqv9ZUreHNHW/yxwl/ZFDmoIie454BGWRKbzhKspLYdrgl6JWMN96h5nApKNmI1X8WpEatIkGnxmxz0m6xB/QcnFkyk1fPfJXVVatJ1CaSqEsU/7WJJGoSfVOTpkZ47ypsKhWfJyfxRFYG9m3Xo8+dzGVDruDT9e00mSzccqGVj2r+zPad2xmWNYxHZjzCxPyJnllzlZtgvWjAe0dDEzv0epakJLEkaSdJfVchOQyoNBb+Vw65dbmMyR3D9WOuZ0T2CIpSishLyvOt5/ImEi8wtzjP7bhptx8atYZh2cN8PKzCESoF2Sc7iSS9BqPVwYG6dk56+LuQkw7S3BGwbk5BdmWro6MM+Xec5vc7DlWsvc9ZRK4uWXQHePNCsLQI883JN8RtTEdbixiA99aJk/ecE3qL1FZGMZkDc9gutbK7TYUjrTc9URlWmJ7IlZP78J+fRGF50J68UZJs0FKclUh5g4k91W1MiVaA+VFaJ2aO98tNRqVSMdplP7GlwrcQXz7mlwSx0Ch2zXysa7ME1I6t2CvOedMGZqNSqRhSkMptZwzm4SW7uP+zHUwZkM1T3+3F7pQ4eVCOO+pWmCEE2JFjPQXZ3VRUVOB0OunVy3fmQq9evVi6NLDNQqTPidc6wbBYLFgsngN6S0tLB68yRqK0oGi1tnL3D3czsWAiVw2/KuLdeGZORWcLUOy+kulAgDV4C7COI2AGXeDhL1mvxWyzYgzhhj82byxj88Z2NGRxeWlXgd3MSSYzc825XKaeiCHrJz5r/AF94ViSKOOl3bVMKpjEC7NeYErRlMCUrNeJXQWMsFoZ0aLitqv+wxn//ZZDxm0MzhzAy5fPIT8pP7qZmpF4gXVBh4RQeASY74n9SIvZ5/MIN+mgx1KQcbR4ONpp8rOSkQlVrN3f0AQ2129TbslVt1t45MXh/TkaW8RUt5hZvkf8di4Z39u9PC81AY1ahd0pUdtqoSA9IdQmuhRZsJzYP4vHLxsbF9E6JD+N8gYTu4+0BMw6jJaDLgHWN1uU54zulQGIdGJju5VM18WxfMwvDiLA0pN0pCVoaTHbKW8wMaTAMzls5T5xzps2yHNc++3J/flmRzXryhr59Rtr2euqD7v9DM9MaDkCVtX8M0pBOp1OtmzZQq9evbqsKF32F0tM9P2iJSUlhfQei+Q58VonGA899BB/+9vfApZfdtll6HTRRZHC0lAKtUZI2wTvX9Dh6jvrd1JvrkeVr+KiZy6KeDeVTSZqqlrYkGzggi8zIn7e4UYTNUdaePVLAxteDv28lfvq3NEtgPM2P4s6iCDZUdlCTbOJ175PYdm/fevvDu6rw2RzcN36rKBu/VFRagGrOEAckcool1SMKc7ALNWzp+kz7HY9fdNLqM2q5WEeDr0d2xiPEz6IdOCaP7Bpfz1Gq53WxDVc9/GX0Y/PYYN9RmAfLD1X+Jf501wOR4yQvBcWd/zdiBWnJFGxS0TbfrvtObReqfCGdis1hxoDnnPpmqfcB2KZ8gYjNdWtvPuVgZ1vZnTZeI9njjSbqalsxp6s54JvfO1LsppM7KjyXCgOL0zjt+utUNbutxUjrLgSEgKNNaOh3WLnxwP1PsuufR9eGZgTYLTcneyraeNIfTtpCTpu2fGCz2ONe+sw2x1ctv7pzh9jYmTXkVZqGo1syU7m+s86aCgeIftq2qipb+eBbxNZVJjWqW3trGqhpsnE0uXJXPCOq12h63h33pp/u2dCryltoMVs4+XVGXySGhh1qy6tp9Vs55rVGeS6Hrc5nG5x/NKWXN70yoSYrA7qDtRR43UR8ZtVae4Z+XanRM3uGmqAc9c9HdJhPxg2W/yj8jEJsJUrV/Lmm2/y4osvAnDxxRfzySefkJCQwGeffcbMmTPjOkiAzExxoKiv9/2x1tfXux+L5TnxWicYd955J7fddpv7fktLC8XFxbz77rukpXXuC+7D13+BH56EE+fBWQ+GXfWrg19x+/LbeWPaG26rhkh5ecUB/rF4JxeMKeKpKyJvirtybx1XvrKaAbnJfHL7KUHXsTmcDLlnic/V9xv3zApai3DTfzfyyeZKbjlvOL+e5tvW6KwnvmfXkVYe+PVkpg3qpI/UW5fAPtGw9nHbuZSPvonHLhsLwG3vbmLRxsPcePZQbpgRZX9IF5Me+IaaVgtDC1L55JYY/PMkCR7uA5Zm+P2/grc5+v5f8N3fYezFcNEzMY0zkvRQXZuFCf/4BoBPHzzH58BW1WzipIe/C4isvLfg1IDtLdpQwW3vbebkQTn859edMDNVCMkbqw7y10+2c86oAp6dF9i55Mlv9vD4N3uZ1DeT926YKtLoL84I3NB1T0LR2Kj2LX+XSrKSWLG3joc+30neuMBo599+e2KnozCx8s6aQyxYtJU8xNzOeXN8I3KXPLeKdWWN3PGLEzh3dBB/sG7gl6+u4fs9tfx1TvyihZ9sruSm/25kVEkGi35/Uqe2dfmLP2I70MDfLx3D7BNEBPHmdzby8aZKLjt9MDfNFGUvJ/z9axLarbxy0zRGFAWK+d+9tZ4l247w2/OGc63rWL94SxU7F25gcH4KX97q+72sajYx9aHvfFLpjSoVn3oda0b99UtaLXaevG0GA/PCi1fvY1+yykZ6eucuOPyJvGLbiz//+c/8+te/BmDDhg2sXLmSXbt28fDDD3PvvYFT4uNBr169yMvLY8MG35YYa9euZdy44GIgkufEa51gGAwG0tLSfP66hAhTkLXGWu7/6X5O73M65/U/L+rd+LvgR0qfbHk6sQmn//QdF5VNJpySqOtK0osr31AzIUPVgAHu57ZbO5/C2mvzzNYplQoZ2cvz48tNE8KwttUS8LxIkdNyMY9VpYKsvuJ2qDRkJ/tAvrv2ECc9/B2/eGk1Jz38He+uPRR0PTllmGLQBlxVytPgNa5oZriaFTl92aIU4XcZnn6uwUsJzhghmphvq2zB7oifX5L3d2na/y3lzkVbg37OPdkipqrZxJ0fbnXflxDpcu+UVaErmtKTaaxwqbtYGZIvW1G0IUnBj9ORcrBOjK9fjidDIfeCFI74IvopGzSHeh3BrChW7pPrvwKPaeFMZ2UirQPzP/Z9sD7+PiQxCbBNmzYxZoxwwf7mm2+YPXs2Q4YM4be//S1bt27t4Nmxc8011/Dyyy9TXS06pH/66ads3bqVa665xr3OI488wq9+9auonhOvdXqMCIvw//7T39Gpddx74r3R1Rq5aDLGVoRfmC7qJqx2J9Wtwb/08kyX3pmJHdYBec+C9CfZIJ5r7KQAq2o28dV+zwFWhZNXF69wH3Rlz5qaGAWYJElu4WW0dKKlS5hC/KpmE3VHXAeNGPpAhmr3EezEE6wRtzeXTSxh5YJT+e9vT2TlglNDXrW7i/BN3VyEfxzh6QMZ/Hc8JD+V9EQdRquDbZUtnjpGb6KcoOD/XZK5eeYgHrhoJN6a/e5zh/VYIX5pXTv+2sP/BF7kqiM63NQzAszhlKhwCZI+2fGzQOqXk4xWraLNYu/UazNa7Rxxmat6C7AxrkL8zRXNSJLkFlXpiboA6xqZ3n71w5IksWKvCDicHCTDIdcxeuMv6AvSOxbQVc0mFvgd++7/dGfI9WMlphRkZmYmu3fvZsyYMXz88cfceOONANTV1YVNyXWW++67j507dzJw4ED69evH3r17eeyxx5gyxdPYeffu3axduzaq58RrnR4jAgG2rHwZS8uX8uiMR8lMiO0zagoxe6ojtBo1vTISOdRg5FB9cK8a+cdYnJVERaOJ6hYLLSFmwkUUAeuMqAEOl+3lOs1i9/0n9c9ilnRsLxtL4ejR5KWJg3BtCEHZESabw32g71S0LkRPyHfXijTKQm0pORr4sVpNtN/UaPyG2rwiYKEINw1eRomAdT3efSCDoVarmNg3i292VrOmtJ6x0wd0eoLChxsOB3yXAE7sn82UAdmcNiyPOc+torLJHHRGXHfhLRhk/E/gcj1RVQ9ZGVQ1m7A5JHQaFQVp8ZsEoNeqGZCbwu7qVvZUtwZtgB0JsljNTNKR4TVha0RROhq1itpWC0dazB4LiqzQxwR/K4qyeiMVjSZ0GhWT+2cFrB+J6WxhWscRsFBCPN7EJMDmzZvHWWedxaBBg9i3bx/nnnsuAIsXL+aCC7qu0DcxMZFPPvmEAwcOUF1dzZAhQ8jK8v0Q/vSnP/nMNozkOfFap8foYKabyW7i4TUPc1LRSZze5/SYd+NJQUY3CxJEGvJQg5FDDUYm9w+8cnaH1DOT3PtpiyUCpo9PBKxPggmdylfEJahslCTEJwLmnV4125w4nFJUBaFugsyEdLdLkiBHJaZ9P7Omhb6nhvbfCkawdh+h0kMtISwooiW1p2woepDutmDwb0MUjMn9ZAHWwHXTB8TUg7Kq2cTOqhY+3nSYjzdVBTzu/V0qTBetkP67ppy1ZQ3MGh7aL7ArKUhLcFumyGMMOIH38Ey6Q/WeY2VMx4wwDC5IZXd1K7uPtHHa0Ng+A7cFhZ+YTdRrGJyfys6qFjaXN7m9uIrDCL0SLzNWEf0S57oTSjJDdtToyHRWnrlaGUaAhTr2xZuYjpYPPfQQw4cPp6ysjJdeesld21RTU8M999wT1wEGo3///vTv3z/oY0OGBG++G+458V6nW5EkrwhY8Bqwl7a8RK2xlhdPfzGm1KNMs8vAMdoUJIR3NQaPCWvvzEQO1osfcKgUZNgImCE+ETD/thj+y/M6WQPmn3Y0Wu0B9g0RoXMd5Gp3iWLppGxK6xPd0QZZgFVL6RG3OpIpTE9k7oTevOdqx6JWEbJ2y5OC7NysMDkVYbE7sdqd6IN8xj8nesKCIZQNhTeyb9Ka0oaYLg7kCKx30GDawBxW7a/DKQUXNhP6ZPHfNeVut/KeYH9tO0arA71GxStXT2Sg3I7JCzkCdriHImCHuqD+S2ZoQSqfbobdR2K3TJKP332DRBPH9E4XAqyi2X0cDxfxLMpIQKUSGYO6NmvY9KM34aLtRe4asNAC2r/VkUal4p7zh3Ht42F3GzUxCTC1Ws3VV18dsPyvf/1rpwekECWWVtGTDYIKsNLmUl7b/hq/GfUbStI6d2CXD9zpURbhA/TpQIB5pyA76gdo7YYImM0pEe5VylOiW812zDZH1FPm/ScYGK2O6MVLUzl85DLDbDksZqppDQy4+gdUKtBIdjJV4gDSSHpMhc1iZpIQYO/fMIUT+gSP+sqvp7MRMG8X/VazLXpH7mOIYDV2dy7aGl1T9hgIZcTqzYiiNJL1GlrMdnYfaWV4UeQTiOT6GW/xpVbBI3NHA4SMTEzsK75bWyqaYvpNyfvuTDRxfZnoRzu2OJOTBwfPKMgRsLo2Cxa7A4O2e+0yyhrk+q/4CzDZEd+7x6I/Hb3HB2qFAOsfRICN7p3BO2vL2VLRRKJO/NZ7hxFgBq2GwrQEKpvNHKxv58f9Ig3u7f8VLZ4asPAC2uw6z9xz7jDOHV1IssrGtTHvNTgxHy3r6+vZvHkzDQ0NAY9dcsklnRqUQhTI0S9dMuh9v/CSJPHA6gcoSCrg1yN/3eldxeqED76h5GB4WlIkuU/isc2ClAVY5yJgB9oN9JF0JKi8RKBX4XGqQet23a9psVAS5cHQf3ztYXpfht5Iva+/GIDdQr6mnV9MKuGb1ZvEIknNny4+MaYTkvdn4N22xp9QLvjRolGrSNZraLc6aDXbf9YCLFiNnVOCxZur+M30rouyeybThC4l0GrUjO+bxfd7allTWh+VAAtWP+OUhPCaMiA75PewOCuRvFQDNa0WtlQ0+/QMjIR4RBPl6Nv4vqHrZLOS9Ri0aix2J9XN0f/2O4t8DO2KWjm5Kff+mjZsDic6v998JO9x2AhYsccRXxaywdoQedM7K4nKZjOLt1TRarGTnqhjlNeM9GjxpJBDCzCL3eEuizl/TBH5aQm0tBwlPmAfffQRV155JWazmZSUQB8NRYDFkaby8MWvsgVFEJuBLw5+weqq1Tw781kStJ0r1nQ6JU/xbgwRMHcKsj5QgJmsDuraLK71Et2F3LHNghTLOivA1jQm8yvLo5zWR8M/LhwpFnq99yqVitxUA+UNJmrbzFEfhP0FV2fH60+f7CR3+rFRlc5lk/rGtB3viRD17aFNh+OVgpS3IQuwnzPBnOcBHvh8J3ZJ4oIxhRysN8a1NkySJJo7mAUpM7mfEGCrSxu45qR+Ydf1JpJC9mCoVKL4f/HWKtYebIhKgIWasRttNHF9mRBgE/qEFmAqlYqijERK69o53GTqfgFW33UCrFdGorsGrqy+nYF5Hvf5SN/jUDVgICJsBq2aVrOdVrOIsnWUSi3JSmJNaQMfbBCR+KkDsjtV+ybXgDWbbAEtjmTKG4zuXpZ5QQxi40VMBRZ33HEHd911F2azmaampoA/hTjRVA5PjxepJfnv6fFiuUyIGZBt1jYeWfsIs0pmcXLvkzs9lFaz3X1VG4v7s3yQqm+3BkS25CnVqQYt6Ym6DmfCRRIBiymi5MWmQ01UkkPmgInCbLJobEARcl6q+CHXtERfB+Y/87Gz4/WnotFErkuA1TjT3A2Yo8V7IkRDWzgB5oqAhZkFGSnxLMSvajaxan/dUdN6xJvC9ET+6NUmRa2C8X0ykYCHl+xi6sNLO/RfixaTzYHNIX7IHf2OJ3vVgUXjC+W/3Wh6FU5wRZ7WHQzMrIQj3IzdSKlvs3DAJR7GhxFg0LOF+O4IWBcIP7Va5U5D7jrS6vNYaW3H73Gz0eb29uobxCJDp1Ezwi+a2isj/PdCFpryMebkTqQfQdSZyhf5oWZC7q/17WXZVcQkwCorK7n55pvRao+ZVpLHJsZ63+bAIO57R8RCCLBnNj1Dm62NP0/6c1yGIke/EnWamGoe0hJ0ZLquuP2jYHL9V++sJFQqVYcpyO6IgG0qF1fCY4szQq4jF+TXtkUvwAKL8GMYbzB/JgCNlopGkzsCViels7OqNXC9CPD+DOrbQ7/OVtd6KZ1MQYKnNimUDUmkRGoi25PI/e2KMxP5YcFpvH/DFO44y3ciUTj/tWiR0486jcpt2RKKUb3TMWjV1Ldb2V8buibIn52uVkbZyfoOfd/8kevA1pU14ghh2hwMedaaN9Eaum441ATAwLyUDmd6u60ourmpc7PR5j4Wd5Vdh9uQ1U+ArSsLnBzh/x6XutKP+WkGtyejP2O8jqn5aYYOa/38bSo6KsCPBDkKFkqAyVG8/jnxafMUipgE2MiRI9mzZ0+8x3Lc4HTEMd0UxAV/V8MuFu5ayO/G/I6C5IK47KYj88ZICFUH5qn/Ej+0lDARELvDid11YA4WAUvUdd4Jv8Vsc18BhRNg8kzIWCJg/uIypvHKDaSvWw7XfgXprgjdD09R0WgkB5cAI92nv19U4zR7C7AIImBxSUGKz78zXmDRmMj6P687I2b7aoSwGVOcQWF6IiqVKuh3LtpoTii8XfA7urI3aDWcUCIiQatLI49IbTssvmtjijPC1nwFY2hBKsl6Da1mO3uqI79oKExPDIi4RBp1k1nnKsAPl36U6SkzVvnYmZNiCGnD0FnkiwLvCNie6laeXrrPZz1VkFnRpXXi+xws+iUzxuWID5Cf2nFpjLfQ7JWREJfZn4UdWFEccF1wBEujxpOYBNgvf/lL5s2bx4cffsjWrVvZtm2bz59CeD55/iKqtq9g85pl1O5Z7ZtSjBa/CFiDuYFbl97KwIyBXDn8yjiMVuA5cHdCgLl+lOUBAsx3WrXshh7MB0yOfkEHTvidsKHYUt7sGk9i2CJwdwQsBisK/1maMY83o1ikR0smw9zXQaWGLe8ytHG5OwJWK6W7oxLR0hpxCjK8E340pLpnwcYuwGJJSfVExEwWYANyPVfakbh5x4rHhDWyz8nbjiJSth4W37uRURTuy2g1ak7oE30ass1i92lXY9CquHhc76j2vV4uwI9AgLnbEXWzACtrEBeGXTEDUkYWYLIANtsc3PTfjVjtTmYMzuXWWaKP49CCtIDIZqnr99U/N7RwqfD6nLYcbu7wd7ahrMl9+3CTOS6/y4K08FYU7ghYmNcRD2ISYPPnz2fnzp3Mnj2b0aNHM2rUKJ8/hfA8kV7Nns8uYcznF5K78AwcT50QXITJBqveqDS+LUDaa8T/5FwsDgs3fXcTRruRp057Cp2689EImaYO3LMjocQVSpYPIjJuCwpXBCzcCViu/4Ku6wXpST+GPxC7I2AxuOG3+QmuePSupPcEOOlmAP6ieonBKlG0WtcZAeYVqWuIKALWtTVgkUaook1JxRox6yxyas+7KbDs5u0doIokmhPJe+MpwI/MTFl2G199IPI6sG2yAItxptoEl9XJ2ij8wFYfqMfulCjOSiQzSYfFLrGtsjni51vsDra4xj2hb8fF/5HMpOsKunIGpIwswMoajJisDh75cje7jrSSnaznkbmj+cXkPmjUKnZWtXCwzvdYLguXUBGwqmYTj33tmz0L9zurajbx0JKdEa8fKYUdpJA9VhpHYQqyqqoq7J9CeE40Wbg5P5fvE8WPWOO0UltTGbji+lfF/wGnway/idtJ2ZBW5FnHlYJ0JuVw98q72dWwi6dPe5peKb3iOuZYG3F70ydL/CgPNfj+eDwtKcRBxTMLMvAELEfA9Bo16iAzYTy9IGOPgG0qbwI8vctCIXuBxVQD5h8Bi9csyFPuxJw5hBxVC9M1oi9rAlbaqg9ii6GxcpvF8xnUhRFgbe4i/PilIP0FeDQRqsL0RKZ71YqoCC9i4lHEHS2SJLkjYN4CDISb93PzTgAgP9XQYQ1VpO9NtP1cxxVnotOofFrHhMNsc7DX9ZpiFWATYyjE9xh05roF1Nqo0qbNWO1OspP19I0gutTLbcbazSnILpwBKZOTYiA7WY8kwas/lPLKStFl45+XjCYvNYHcVANTB4ggwKebfc9bB8PMgITof2dd9bssDFMD1my0ucst+h2NEbCCgoKwfwrheaCunpONJhbk5nDINZEhoK/Y4fWw+3ORUjr7n3Di7yAxS0S89n/nWc+Vgvx33Y98dfArHjr5IUblxj8K6XHBj74NkUyxX2NVmYpG3xSk+wQcpAg/3AxI8O4FGVtESZIktwAbV5IRdt3OzIIMqAGL1yxIrYGtw2718WH6o+5/fKm9lbIDu6PenE8KMlwRfhxTkMGMeGOJUJm90tVnjSwIK2LiUcQdLbVtFlrMdlSq4CesKf2FgKxutYSdERrNe9NRH0h/EvUaRrtqdlaX1odfGdh9pBWHUyIrWe8+yUXL2JIMNGoVlc3miAXOyn0uATYwxy3goomgrfNKP0Yy602OoLSa7SEnC0VLJBHM7oiAgceQ9ZEvxTHjqhP7MHOYpzXRBWNEEODjzZXuyKgkSR2m7qJNr3dVOj5cO6IDrjq2vFRD2N628SBiAfbTTz/x008/+dwO9acQHg3wYG09WU4HN+fnYFSpKMzwO1gtfVD8H30Z5AwSs91GXyqWbXzLs157LYtSknm5/GtuG39bp3o9hsNdA9aZInzXlWVFo9E9w6nZZHMXW/f2K8Jvs9hx+l3+yBEwQ4iZM7ITvsXuxB5DxKei0URdmxWtWuVygQ+NHAGrb7dGNWMLPDVfckQxnj5gFbY0/M8hCSobhyqiqzWUJCkiGwqHU6LdNf74piA9+472StjhlNy1SABHWsKnigrTE90mkTLRFnFHixz9Ks5MClrPmJ6kc3sQyVGlYETz3sTSzUK2o4ikEF9O+40oSot5+n6SXuuuH4skClbVbGJfTRtqFUwdkOM1k7Ih4PgRCnmG34QwBqzepBi07u9pPOrAIo1gltV3nQu+N/4fnSzIZM4cWYBeq2ZfTZt7hnVdm7AYUqtCe3vJ6XW5r2JHFiXRrh8pnghY4GfXXfVfEIUR65QpUwBxUJZvhyIaz5jjEYdKR6Zk54nqOn5RlM9fcrJ4xLvW+9Bq2PeNqPeacYdn+dh5sPp5ERkzNoAhjR+d7fw9L5e5/c7n6hGB7aHiRbRXzsEoSEtAr1FjdTipajbROzPJHQ3LTta7Z/XIERBJErVR3jPrOoyAGTwnMqPNQVoY9/ZgyNGvYYVpHU6Pzk7Wo1KJk31Du9UtyCJBrvnKTTHQZLTF1QcsVIPwUr96jY6w2D0zTgHarY6gLWK8IwDxsKEIJsCCpYXCXQnvr23zEbX7a9qQJCmsKPB+rakJWi4ZH13z6WiRZ9r6px+9GZyfSk2rhX3Vbe4Zif5E0zQ9Ehd8fyb1y+LZZfsjKsSXZ0DGmn6UmdA3i80Vzaw92MCFY8OXU6x0pR9H9c4gPUnHyF7pJOo0NBlt7KttCxAP/kiSxIYyOQIWuflrr4xEdh1p5XCTiUEd7MMb/1Y++2raWPDBVvfnF8rg1Gp3uqNjXRkBq2o2uVv+yNz3yXZmDc9zjyctQcdpQ/L4YvsRPt58mOFFae7jS6/MxLBWRR01y+7s+pEgb6PRaAs4prnrv3K7tv4LooiAtba20tra6nM71J9CeDQ3rKD2F1/xw6BnmV8j8WVKMq9+dZPH82vpP8T/cfMgy6slSeFoKBgt2s9s/R97j6zn9rwcJpvM3DX1r11qGBdJA9+O0KhV7iiXHEqv8PIAkzFo1eg04rX4h/c9HmDBv7p6jRqtK2Ydy8zCzS4BFs5+QkarUZOdLE5k0c6ElAWXXMgfzwhYdYhoT7QCTBZAKhXuzyNYIb6cHtNr1XHpixcsBRms/uhvF44IeTB21/EVZ6BSCUuLcDYaTqfE/hrx/qhV4rVv84qgdQX7Q9R/eTMoXzwWzpKhMD2RU4fkue+Hq3driXIWJAgxpFaJ3+xnWyrDpsi2V8ozIDsnwDx1YB2nEeX0o1zzp9Oo3eUDkYjG0rp26tut6LVqRvaKfOZmLIX43pGuqQ99x1lPfM9ZT3yPf8giWATzcJMJpySOfdFc7EVLaV17ROO5cKxIQ362uQqnU3LXf4WzoJApTE+MyqIk2vU7Ii1B6y5X8a8D83iAdX0ELGIBlpKS4m47JN8O9afQARm9yR08mV/Oncvq5AeY12TiKV07q/93Bax7DUq/B5UWpv8p8LnjhLXEoU1vcN2KP1Jkt/OvNgltMEPOONIcBxsKCGxJ5O8BBqLVR6h2RJ4IWPATvUql6tRMyE1RCDCAXLkOLMqZkO0ucShbWcRlFqSLvW16zJLv52SWdGysVUcVnZYFUIpBS5ZLaNYHSUPKn1FaHKJfQNBOCM8v3w+Ig768n2GFoaMOspCe3C+LItdBW76yDUZlswmTzYFOo3KLmRV7g8xCjiPuAvwwV9py9GZPmBQkgOR1ypxzQq+Q9W5NUc6CBPH5y8ajNy7cGDJFZnM42eVKR3WmVx94IlG7q1vdx55gOJ0SP7gE2LSBnkkXciF+JClMOf04pnd6VBcQ0VpR+NfqSQivLXuQNGmwCKZ3/VdXXmxHWnd16tA8UgxaDjeZWH+o0d1FoDuES2dRqVRedWC+n588M7k7UpAxFeEDlJWV8ec//5kLLriACy64gAULFnDo0NHnNH00o1Kp+MOcmdTWzGGSycyfTLuoWnK761EJAsqCgVFzOaJP4LeaRlKcEs8fqSElqXOtGSLB04g79iJ88NQuyAeTcr8CfJnUIFEQ6DgCBrF7gdkcTnfd0NgOCvBl3DMho42AWeUImDgIdMa3zBtJktjYnMpplkcpn/sFXLccy7VLmWV9lO3G9KjGKUcfUw1aspLlerfA58fThFVsx3cW7M6qFpburkWtgltnDWbqAHGiDVeTtLmiCRCmj/KB9EAYN3dZDPXNTuaUIeL3JM+s6yrcHmB5oQ/0g10RsL0dmJJur/TYjDSH8U+LpZazqtnE4UbPSSpUkf+e6lasDiepCdoA9/JoyU010C8nGUmCDYdCR8F2Hmmhrs1Kkl7DOK8U7aS+kVtZePy/omv+Lc+EDGXm6U+wWj2Af10ymodnj/IRPX85f1hAtOeQy2W+JKtrhUGkdVcJOg1njBCF+Z9sqvSYsB4DAgyCz4R0OiV3M/F+XWxBATEKsM8//5zBgwfz5Zdfkp+fT35+Pl988QWDBw/miy++iPcYf9YMK0xjyOgTeaS2nkSnxM35uRzRaEBy+LYcclGncvLb3qI25aXqOnKcTh8X/K4iHk74EOiG7zZhzfQXYLFFwCB2L7DdR1qx2J2kJWjpF0EYHXAXSYequwqFnHKMdwSsxSRmZVWSQ+7gSVA0FkPJCRhy+gBE5YgvF+CnJGjdqdZgKUjZqiJeM4b8nfBfcEW/zh5VSN+c5A7NQc02hzsSM6Y43W1yeiBMCtbbDkLuNbfhUGPce3TKtFns7okBA3NDR/LkZshVzeaQrZlqWy0+37/wPmDRR7IjTUltl+u/itLjEqGRHenXholiyfVfJ/bPRu9VFzrONZPycJOpw5mU0Tjge+N2U48wAhZqpu1Jg3K4fFIJPyw4zW0Qmp8WKGC7awYkiLqrlQtO7bCVlFyft3hrlfs31NXu8fGiIC3QC6yqxYzZ5kSrVvlkZbqKmATYrbfeyr333sumTZt46aWXeOmll9i0aRP33HMPt956a7zH+LNn3uRiMpxOnqip5YhWw3m9C3k8M51mm+8Jo9nSzPVfX0+71sDLR2ooaHZ5riV3fQQsHk74EESANcoeYL5f9lApyKgiYFGKmo1edUPBPMaCkRdjBKyti2rA5IhiTopvj7XhrpqcaASYLIC8U5DBa8DiZ8IqtiO+Y1a7k/21bXy6RXzPfzdjAOBxZ19/MHi/wB1VLdidEjkpenplJDIgggiYtyFqn+wkemcmYnNIEVkvxIJc/5WTYggbjUpP1LlPynurg49frruS6/QCLG28aI7SBwwiT0nJMyCjqaMKhzyb8budNSFF5cog6UcQxwB5JmU4P7DGdqt7MkQkDvjeyBGhSGvACtIS3L93CIwsFaYncvYoYeO0bHdNwPO7awakTCR1VycNyCY7WU+D1/t4rAiwoozACJh8jCjJTkIb5QSuWIhpDxUVFdx4440By2+88UYlDRkDsnXCMKuNz8srubq5lf+mpXLOytt5fdvrWBwW2m3t/P6b31NjrOGls16j2OAXLu9MO6MOMNscbuHTGRsK8FhRHGowIkmSxwMsIAIW3A3fEk0ELMq03iZXM95I678gthSkzeHE6no/3RGwOEVaKlyCtpff1ZtcLxVNU253CjJBR3aKEGB1QWrAWuIswLwjaY9/vQeHU+LkQTnumXXDCtNINWhptdiDOvxvdhvpZqBSqdyzmcLVgHlHwFQqlbvhb1elIT376/hkNaiDNKScfpziSs3Wt1t9OkbI2B1Ot7deNDVgbmd+1/1QRf6ddcD3R66r3FXdGrTuzGxzuKOgwRo0ywJuTZgI2npX/deA3GQyk6Mrr5BP4JVNpohqK3/YV091i4VEnZpXrp4QNLJ0iqv+cNnu2oBtuiNg3STAIkGrUXPu6EL3fY2aALF+tFLgnkThEffd1YRbJiYBNmzYsKA9H7du3crw4cM7PajjjWpHsrtoOkWS+ENTM4vKa5meP40nNjzBeR+ex2++/A0Hmg/w/OnPM0Cd6Jue3L4Inh7fZSJMTlto1CpSO5lmkoVWk9HGgbp2zDYnKhXuIl8Zdz9ISww1YPrYImCeFkQZET8nL4YifO96L1nAxSsC5p5VGiDARDQgmpZEbXIRvk8KMlgNmJyCjE8NmEbtmYTxmSv6dYMr+iU/Pt41Sy5YGnKzVyQTPMW0ZQ1Gt/D1x78no5yGXNlVAqw2sAdkKAblyb35wkfApg7IdjejD+bw7T2pIdoJE5dNLOGVayYAItJ29qhCn8cdTskdXe3IPy8S/FvWBKs7W3ewEYvdSX6aIehM0kgK8ZftERMthhdGH7WTT+AWuzNsmy6ZV1YeAMR7OXNYftDI0uR+WSTo1BxpMfs0w5YkqVtTkNEgm7ICOJww45Fl3dJHtbMEm8XqsaDonihexALMu9n2L3/5S+bOnctTTz3Fjz/+yKpVq3jqqae49NJL+eUvf9mV4/1Zst+ayWmWRznX8oD771LjI1zQ704+uvAjRuWM4mDLQZ6Z+QwjskcI8SX5nbDtlqA1Y/HAO/3Y2dqOZIOWHFfUZ5XLa6YwLcGnfgM8flIx1YDF0I6oxWxzh9C7OgIm13vpNWp3RLHdao+Lf55c7+IvwOQTzIHatqDRkWAEK8IPWgMW5wgYeKKYIGbUya1PZMLVgW2uEIJktKuVVEFaAkl6DQ6n5yTmTX2bhUajDZXKI4imDshGpRIGqMHETGcJ1YIoGO5C/JrwEbARRWluQ+dgdUlNrm4Wqf/f3p3HN1Vn/QP/3KxN970UWlp2ZBFBULCKu8/4IDLigiiPjoj6qAwgjoKMuA/LOD/ncXcGUUeUEQWVURZxm7GgyFakQNmhULsvdE2zfn9/JN+bmzTLTXqTtPS8Xy9fkvSmuWna5OSc8z1fvSak8sqVQzIxOCseZhvDhn3uW845fq/siNOpFVkFJ2e4bOExR/B06cAMr69LfJTFkaoWNHj5vV2z8zQ+2F4KwBHoBxs06DVq8bUsUBnyeE0Lvj9cA0EA7r4k3+dxMVo1CpyZzO8lZci6VjPazDYIQse/7Wjz3PEgUvuodhbvAXMrQUZ4Jafsv0LpZttz585FZWUl5s6di0suuQQFBQXidXPmzAnn+Z6T+qXHoVJIxwHWT/yvUkhHfnos8pPy8dIVL2Hb9G0YkzUmKufHX7g72//F8U25tzmzCzlePtH5asKXlwFzvHkHE4DtO+N4085NNSAtXv5Ij1Ca8Hm5MVavFofPMga0W4Kf3O+JlyBzPEq6mQmO/d3szLHYQA5pb5c4hsJPD5hSYyjW7Dzt9vM8P6djU7drlZv7JtFn28xiGWGUcwsdQRDEvhRvfWA8GOqTbIDB+buTHKvD+c5SWjjGUXjbhNsXPuTT2yywpnaL2Bs0vHeSOHLD28q8UKbgSwmCgJvH5AAA1u0uc/sa7/8a1jtRdv+kP976zgBXdhNwZSe9lR8BIC1eL/b/8VETHB8JwTGEFjT09hPwSr237RQA4OqhmQF7pPgq3H8fdv3e8ec4OzFGkVl7Sir18qEm3PuoKoE/d9KSPX99iFQfm+wALNAG3LQZd+hcy35d190/sb9bilolhL8h0BclpuBL5TlXGP50wpEB8+z/Anz3gIkZMD9T6nlQE0xfVeFRx6fNIVnBlSKkJUS598e37YnTacSSkeP6zveBiQGYR0lXEISgy5C8Xyher0V6vL8mfL4PZOd/PzzfGAHgnztOd3hjHJmTBL1GhTpJ8y8A7HNmv/LSYt16evr7WQl5zEcwdKnzjZ03eivFbLWLb6jyAjDHMVVNJvFvkStxZr96J8W47b/obTaVEn/HN43uA5XgCGikg32Ly5QrPwIdRyHwl8Zlmw/hnztOo67FJGb+CgZ6D8AAV6bUcyXlyRplNnkWA14/AVhjmwVrnQHrzEv7BfyevA9sd2mD+Jyd6YL9X1y49msMtySDVvwgX9XUjnaLTawgRGIKPhBEABZoA27ajLtzHMt+r8LF/Rxp80R/L5KxaY69IaU0esf1YaDEFHwpPvOLv7h4mxnkWgXpowfMx1ZEABCnDy4Dtmbnafzth5MAgG9LqoIqRcTpNWLGTW4WjAdqcXo11CpBDMKUmAXmqwcMkDbiywvApGMo/A1i5aVKJbYh8lZ6sjN0eGPUa9Rep53vk8z/kvK3EtLXQFTeB7btWK3sPQXlKK1rhc3OEKdTiysc/UmM0YqBlWcjPg9C+CrX3n5mU4krIDvxd5yZGCP+XD7d48qCuVZAKhOAAe6jELYtvBL3FOQDAJ74tBjz1uwF4Hhe/U2FH5ffMQBjjOHL4o6JglCCBl7y9VeC/OfO0zBabBjaKwET+gd+jc5NjcXAzHjY7EzM8vGAvav1fwHh268x3ARBcFvJWlrXBsYcGX/+gTPcopdWIR1kJxlw3XBHc6vfLTiSc4HZu4H7/+P6b/Zux/VhoNQUfM7zRcSzXAa4SpCeWxHJyYAZxFWQgTNKSpQigu0DcwVgGuf/Q5/cL9VotIgZQ89VkIC0EV9uCdKZ2dJrkObsAWsxWWGyugeKSq6CDObT9EX9HG9m0jfXvc5S8iiPPj5/KyF99WON6ZuCWJ0atS1mlFTKX7wQiGsAa7zsnkpXGdI9gJT2fwGusoq331/eStDZYco3X+goQ36651fY7Qx2O8PBcr4HpDIjKDg+CqF3ciyeumEYZhY4Mkh8deqJmla/H5h4AFZc1gij8wPZK98ew+qfHbfhP/5QgwZ/JV/AseL5Hz+eAuDIfsl9vq8YzMuQjsw8713MkzmfMNLkzg3ravgHoMrGdnGQbP/0uLDuNCBFAVgXwxtHd5c2+P/UnZwL9L7A9V+Ygi9AOgVfqRKk+5upt4F3ib7GUDgzYL424wakqyADZ5TkNPsGEuxKSB5o8fOMDXHVpic+rVy6sbnUsN6uEqSchn/XGAoNEg0acY9NzzKkkpPwg/k0zfvAeAaMMSbZSso9E8Obar2VIH3tyajTqHCxs4Sl5GpIsf8riDLH4Ezve0LyFZA8ABM/0XuZBdZodPbqdfLv+LphWUiIcWxBs/1kHUrr29BiskKvUQX1mIIlCAJmXZbvNsw00AemnBQDeiXGwGpnKDrTgLcLT+Cv3zhWVy6+YRh+XHhVp4IGMePoowT51YFKVDS2Iz1e57ZaMJArhzrHURypgd3OcLre8XvruWNIV6L0fo2RIM1gHo/gJtyccsuWiCKGZSciVqdGo9GCYzUt4l5w0cSn4CcFMTvIH88MmLcXlfgY7yVIeT1g8jNK/dLjIAiOJngu2FJE8BkwZw+YM/MV6twyT7z86C37BThW+OnUKjSbrChrMAZ8MW+WlCAFQUBKnA41zSbUtZjdXmSle0YqYdq4vpg4OAOnatuQnx7r8wV9TF4yNM5p52UNbVAJAmpbTFCrBAzL9gjAnCXI+lYzGlrNYn9Yq8kqZi+89WNdNigD3x+uwdZjtXhAMgqjM6QZMLn468AxyZ6QJqtNvDy8Dy9Bet/fDlBuN4sYrRo3nJ+Nf+44g3W7fxWbxs/LTgz78MpTdW0+p/J7+z0RBAHj+qXii1/K8eRn+8UA/NFrB+NeZz9WZwIG8Q3cSwBW0WjEy85g786L89wGIwcyNt+Rfa1pNuFgRZMrA9aFA7DuKFsyC4x/YI/kIFnKgHUxGrVKHIPgbwuOSFJqCj6XEa8XM1hatYAsL30wvkqQ8nrA5O8FmZ1kwLSxruxhKKWIjCBXQrZ5ZMBCndzvybUC0vu5a9UqMciQMxFf7O1ynl+aj5WQ/DilVkEC8j5Nx+o0Ys/RjpP14gq5IVkJYhlaeix/sT1R6wpieDYqPV7ndTgpX2H388l62eM7AvHV9O8Pb8SXZsCOVLbAamdIjtWit/Ox8Z9Xc7u1w4eXUKbg+8JXQ27aXyFmIJUuP3oTSsM3X9zEg6/LB6dj9lUDFTkfXoKsajbBanOtYl6z8zQuWfYdjlY77jPY/ki9Ri0uLti8vxJVTY7Xlq7YA9ad9ZL0gJ2I4CbcnKIB2G9+8xu8+OKLMJsDD6UjvvEBgrtlbCQbCUqXIFUqQXwhSY3TeS3d8Tf9ppBWQQbXU8UzQZcNSg+pFBFsBqxFzIDxEqRSGTDvIyikglkJ6VlaTIvvOIyVMab4ZtzBuFiyyo3P//Ls/+L4C6t01aTnAFZPAzPjkZWoh9nq6OXp7Gwju53huPNNWc4QVo73gFU3m8RASmx8l+y9GKfXiIGwZ2O4kquZL8xLQX5aLNrMNqzZeUY8j3ALtuG7otGI9b+Uu1239WituA9nZ2Uk6KFRCbDZmfgBrKLRiIWfFrtl1ZdtPBT0786VztWQHzl73BJiNIothCIO2W49YJHfSknxDNjbb7+N8847T+lv26OIm9CWdo0MWKPCqyABiP1EVU0mr9uMSPcDlDZ9B5UBk7kKkgcuo3OTQypHBDsLrE0yBwyQ9Kx1MsPy61nfKyA5vhJy69Fav28IjDG3HjAA4jBW6UpIo8Um7seo5CBWuXiT9c+SDJhn/xfHtxc54SUA85WNEgRBDGiXbjrU4Xe1otGIH4/7/1lKVTS1w2ixQaMSgtrTL16vQR9nv9ER50BWz/4vzldfkpKrmQVBwFRnFszszPz0Sgq8olMJwTR8n6xthWe7o83LqtpQqVWuDH5FoxEmqw3P/uuAl/sMfsQFL+3y7b/6psZGrDm8p+Al5GPVLWhwfrDptgHY5s2bcfjwYWzZskXJb9vjjO6bDJUAnKk3okqhT2qdcVaB5etSFY1Gt202vE1OlvYTtUiyYHxYqawMmMy5XK7p8aGl94PuAXNm5uJ5Ez4fm9HJ/SDFfSCTfQdg/PdpV2mD18CXa7fYxcDKswQpbcLnz41KcJ9eHynj8lMhCI6gas9pR8bYVwbM2yiKQAFYRaMReyRDPO0MWLCuGK9/fwxv/ec4CpZ9hztW/Oz3ZynF7y8/PQ7aIPulPMuQrhEU7gGYty1WAOlAZWV6OW8a3cft8sz3dkZsCxq5Dd+RmFHF++4+3lmGKa9tw+YDVR2OCeU+eycbMETSAxypTbh7Ev77Y3R++M1OivG6gClcwtIDNmCAMs2qPVVCjBZDezleVP2Oo4gQpSfhn6xt9dlIy6lVgjhfS7oSkmfD/GbAglgFCQC/BmheD4SvgqyRuwrSWWrkWybx823t5H6QgUqQFY1GrNx6Urzsb8sQ3j8kDay8BWC8RByv10Tl03lSrFZ8kzJZ7TBo1T5X4nkbxhqoH8vb7yoAvPjVYSzbdEhcQSt3+xVfM8fk4I34R6taYLMzHHKOE/EcfsozYJ6N4XwVpFJ/xxq1+/PdFbegicSMKr6/6JpdZ3CoshkGnRq/uyRPkfu8YmiG+O9gNwsngaXEat22wYtk/xcQwirIAwcOYM2aNfjhhx9QVuYYxJebm4uJEyfi9ttvp/KjQsblp+BgRRN2nqp3220+0mx2Jk5EV+qTM/9Uag+w8jAhRotWs809AJOTAZPM1WKM+Q0MGGNiBsxf5sgfngGrazXDarMHXAnWKja3q93OtzMZsOZ2i1gq9hVI+hu54fnm0GzqGFilOnvAaiUlSCWn4Ifq4n6pYkZ1SFaCz5+/uCl3XSusNjvsDAEn0nv7XRWc13uOtPC3Go9zrYAM/oV+kGQUxcnaFhgtNhi06g4lE2/DWBljaFRoFSR30stIDzk/g0iTu6o2FBWNRnH3Bc5kseGBywfggcsHdPo+mWR3stXbT+P8PkndZsZWd+AYxhojvg5EsvwIBJEBO3DgAH7zm99g9OjR+OabbzBq1CjMnDkTM2fOxPnnn48tW7bg/PPPx/XXX4+DBw+G85x7BLERvzS6GbDmdovYz6DUJ2e5n0rF/SBNrtVcYgbM716Q8vdXdOwDZocguPoBgpUap4NaJYAx73sleuIlSJ7qViIDxoPIlFitz3EQwZRjWrw01rsyYK5Sa3MYNuIOlkUSHf1SdtZnGax3kgExWhUsNoYzDUZxIn28XuNzIr2339VlN4/Eh/ddDM+4Xk6ZKZg9ID0Nlgxj5eXH87IToPZ4UnkJUtoD1ma2wWJz/JyUCsC60xY04ZpR5S1Dyndu6Ox9VjQa8fbWE+LlUPerJP5JNxPnfaKRIvtV85prrsG8efPwj3/8A1lZWV6PqaqqwnvvvYerr76a9oTspLHOgawHK5rQarKKjeWRxvu/YnVqt1RtZ8n5VBrvZUNusQfMz4a00v0VT9S2+N2fjg8vzUzQh7zJrVolIC1Oh+pmE6qbTF7Hakj5mgPWmTEUZfWB+9h4MLFgnWPyv0qAz9JIs6S0yPEmfLceMFN0A7CKRiM+2uEKuPib1MTBGR0el0olID8tDocqm3GipkUsHQ3I8D/52tfv6tOTh+GZfzk+bPr7WUqJQ18zgp/vx4O22haTOBjW2++2dHsVjmdHtWrB7e+jM/jv06JP98PGWLfZgkZJcrP5oQgmY01CJ/1ZRroEKfsd9ciRI1iwYIHP4AsAsrKysGDBAhw5ckSRk+vJspMM6JNsgM3umu4dDUqPoJAK9AnR24bccjJgn+w+I/578qtb/TYGd7b8yGUmOhvxWwL3gXlOwufBdaAxFP5W3IlDWAM8jmnj+oq7Lfzxv8/zWc5oMfHSoiuw4mMopFm+aJcgg93JYIBkS6JgBqJ6+1393SX9xD0yV9w1NmBpqKHVLP7sQilBxuk14grXzfsrAXifvSUOYz1rFHc8cM3y0ynaq9ddt6BRSjh7zLpThrE7k67eVWqYtFyyA7CEBN+f2Ox2O/bu3YuampqAxxL5eBYsmgNZ+dJ1pabgB0Mcxup8k7fZmVhG8ZWt8tzbMVBjsGvz6s69qGXEO0dRNAVeCem5F6ScDNianaf9rrgLNIRVir85+NvpSjoFn+MlyOZ2136Q0S5BBvsmxT/hnqhtCWkgqqfBzpWJ/IOKPz+frAPg2H8u1JVWvAzJe/S8ZcD4G4rJaheX1is1Bd+b7rgFjZLCFYR2102uuxtpqf62v/0UsZW8QIirILdu3Yr7779fvHzTTTdh9OjR6Nu3L7799lvFTq6n431g0VwJ6VoBGfk32AS9ewlSOg/MVwYs2IwIL0GGugKSc62EDByAtXkMYg3UA8aDSn8r7oIJwHjWpr7Nd7+a5xR8wLE/J+83amh1vLE3eSlVRlKwb1LSYaydWZHo+n6+N/mWWrPzNB78YA8AoLKpPeQXeT6KAnDM0pNe5vQaNdKd2Ur+5tKk4BBW0lG4gtCenmEMt4pGI/4lGdQb6ZW8Ib1qLliwAC+99BIAYM+ePdi6dSsOHTqEzZs3Y/Hixbj66qsVPcmeipeKik43yFpdFw5NYgkyihkwZzAgbajX+fhZBNuToVQJUu52RIwxSQlS3ipIOb0gwcwyE5vpW3wHYN4yWyqVgJRYHWpbTKhrNaFXUozXZv1IC2aVGy9BHq9uEceUdCYDJn4/yWwxTzyAlj6FvvrUAhmU6aou5KfH+cwE9042oLbFjIrGdozok+Sa5UcBWLeTnWSgrFeYeB/UG7k+u5De0ffu3YtRo0YBAL755htMnToVQ4YMwX333Yfi4uIAtyZyDc5MQEKMBq1mm9vg0khSeghrMPibepNHBkyjEnwGozwjwttcBPhvji5TKgPGe8ACBGDtFrsYTHlmwHzNLfNWZhMEuAWVgTbilkr10svlydVc7/68p8e7zwJz9YBFbxUkENxgTsDx2I0WG3RqVaf21xsgZtR8B2DBZmX9OVXnPsXfVyZNuskwIG0loACMEC7afXYhBWApKSk4fPgwAGD9+vW46qqrAAC1tbVISUlR7ux6OJVKwIXObYl2RakPLJov3PFiCdJxDjwDFhNgFde0cX3xl1scHxD6pcf5TdvzEmRuJwMwsQcswDBW6f6UfDVanGRumTc8qJTSq1VQOaPMFpNV7PWRE4B5GyfhydsqSEBSvhQDsOiPoQhGQoxW3DoKcASxncks8wzYqdo2cecAT0q9yFc0GvHG98fcrvNVLvHMjCq5DyQh54po99mF9Mpz55134je/+Q0mTpyIY8eOYdKkSQCADRs24MYbb1T0BHs6176Q0ekDc62eikYGzL0EyTNgehnjMC5ybtJc1mD0+cbYaLSIzcy9FVsF6T8DJjbg69RQOd+VeUN2m59VkHzfPQDISzWg3WrHok+LHYNknUFkkkGLRBmlwJTYjhPtPfGg11cAxoexRnsMRSikS807U34EHL83eo0KZptdzEJ6yk4yYMH1Q8XLckdWeAomk8ZXQlacdXwgcJUgaZo6IVLR7LMLKQBbunQpli1bhmuuuQY//PADEhMdS6Grq6vx5JNPKnqCPR1vxP/xWC3KzyqzgWwwGqPaA+Y+hkJuBgxw9HTxN8Yz9f4b8FPjdJ3e/ysj3vGGV91kEpf+e+O5DRHgKkGabXZxNpWnBmfDvCAAb/3PWOjUKnx7qBqfFf0qaxNuKW/jJDz5Cqw8s2diCVLffTIr/SVN951pwAccM+B4WdNfIz6fYp+TEoNtC68K6UU+mEyaaxYYz4CFbxUkId1dtFbyhhSAqVQq3H333XjqqacwZMgQ8fqnn34avXr1UuzkiGPfNwBoaLPg0uXfR3SJLBDdF25xEr7zTd5kkZ8BU6kE8Y2Wr3bz5BpB0fk/Ot6Eb7LaxayaN+JG3JIAzCDZxNroow+MrzpMNmhxXnYi5l4zCADwzL8OYE/pWQDyFxLwgarN7VZYbN4DvhYfpUXPYazdrQQJAP0l243wYLQz5DTiH3ROrr8wLzXkF/lgyiWuWWCODBiVIAnpemS/am7fvh0AMH78ePHfvowfP75zZ0UAOD69Pv2v/eJlvkQ2lNVToeoSJUieAbMG3gdSamBmPEoqmnC8pgXXoOMAYaVWQAKOICpBr0GzyYrqJpPPUiAvQcZKgi6dRgWd2pGtazVbvfbb8QwYLx8+MLE/Nu+vRPGvjXjj38fcvhZIskErrhRtaDUj08vkftcYCvdzEbNnzhJkk5d5YV0dz3wCwDNfHESMVt2psoN0tIUvJc6Ns4dldxycGgy5Kz759VVN7bDZmevvmDJghHQZsl81J0yYAMCxjJ7/2xd/JRgiX1fYiiKan5zjPeeABZEBA1wr1HxlwMQZYAoEYACQkahHc40VNc0mn71F4jZEHiXPWL0a5ja7z2GsDc6MU4qzBKhRq/CXW0fhv18uhM359/bxrjMYk5ccMJjg4yTqnJPZvQVg3gaxAtISJO8Bc/x+yOk96woqGo34x0+nxMtMgQ81sjJgFXzvxs4FYIC8sQSZCXqoVQKsdobaFhONoSCkC5JdgmxubkZzc7Pbv339R5QR7SWyjDFxFWQ0x1C0mK2w25mYAfO3DZEUD4J8vTEqNYKCk7MSUpwBpnfP4onDWH004td7ZMAAINGggV3yYSeYzXo9VzN68jVegt+urtUMi80u9uV1lxKkkiMhuAEBhrG2mqzi+AglAjA5NGoVspxl8fKzRhrESkgXJDsAi4+PR3x8vNu/ff1HlMF7PqRB2B/+a3DEsl/tFldTeDRLkIw5AhdXBkxeCXKApAfMW1Y2mOGlcvBM0s6T9T6DILEE6bG6kJckfY2i4BmMFEkgfLK2FZ6PSm4wIQ2kPDHGXE34HufpKkGa3PbojNZm8cEKx4eafs5Ma22LCY1tHbckOlTZDMYcWakMyQiMcMt2ZnZP17eJfYnJUdhSjBDiXdA9YHJQD5hyeM/H3e/swJGqFqTFRe4FnJcf1SohKlvN6DUqaNUCLDaG5nZr0BmwfulxEARHn1Jti7nDm5+SPWCAq0z4wc+nsXrHaSydOrJDOZAPW43vUIL0P4qCZ6p44AQEP/VfSsyAeRmb0Wa2id+zYwnS8TNsareK52TQqqGNwi4NoeAfahZ9uh82xhSZ+xOv16BXYgwqm9pxvLYFY/q6z0IsUbD8GAw+jPWwZIhzYjfJVBLSEwTdAyYH9YApKzvJgP8a3gtHqo7hx+O1uG1cbkTuV9zA16CFIAgBjlaeIAhIiNGivtXs2AA6yAxYjFaN3JRYnK5vw7HqFrcArM3sCiCUKEFWNBqx7ViteNnXgglXBsyzBOk/AyY24UsCsM4EE/5KkDz7pVYJ4rBYLsng2A/SZmfieI/uUn7kgtm6SK7+GXGobGrHiZrWDgEY7/8a1juyARifbccDwAS9JirbmRFCvJP9ykm9XdE1YUAaXv3uGH48XgfGWEQCoq6wciohRoP6VjNaTBaYgsyAAY4+sNP1bThe04IJA9LE63kDfkKMRpHyqr9yoLcAzDOjGBtgOyKxCd/juQg1mEjzsyG3dAq+5++Zo4Ffi9oWs9jX1N0CMED5/fUGZMTjx+N1XvsNo50B49uY0QpIQroW2a+c1NsVXWP6pkCnUaG62YTjNa2dnuAtR1eYHcQDlaYQMmCAIwD77lB1h5WQZQqXH3m5kwUoB7Y6AyzPwa/idkQ+ZojViz1gHXt4Qgkm5GTAfJWdU+N0qG0xo7TOkQGL7yYrIMOJj6I44RGA2ewMhxQaQREs1zBWx6IQGsJKSNfSqXz0rl27sGrVKrz//vvYtWuXUudEvIjRqsVtiX46UReR+2zsAkvXpbPAgu0BA3xvlswzYEoMYQUcb3bznMNRAd9DMl0ZMPcgMlAG7Gxbxx6wzkh1rtjk87ykAm2wzfvAeAaM+oqkoyjcV0KW1rXCaLEhRqsSJ+ZHiueHC1oBSUjXElIAVlNTg6uvvhrjxo3DQw89hIcffhjjxo3D1VdfjZqaGqXPkThN6O8oof10vDbAkcoQe8CiuHJKuh1RqBkwADjumQFrUHYFJADcPSFf/Pe3j17udR6XzwxYgB4wnqlS6rnwnOcl5WsKPpfqXAl5uq579oCFwwDn71lpXSuskt0FeP/XkF6JUHsuvwyz7GT3+W60DyQhXUtIAdjcuXNhNBpRXFwszv4qLi5GW1sb5s6dq/Q5EqdLBvIArA52HxtMKymaU/C5BHEYq0WyF2QwGTDHG2N5Y7tbeU/pFZCA4+ekcw6J9fVmK27G7dkD5mcVpMVmF/uyFMuA+QnAmgOUIHnwdtrZhB+NFbJdTXZiDGK0KlhsDGckk/b5FkTDshMifk5pcTrx9xGgHjBCupqQArANGzZg1apVGDFihHjdiBEj8MEHH2Djxo2KnRxxd35OMmJ1ajS0WcTG2nDqCj1gYgnSZIXJGnwGLDlWh3RnxkY6KPNX5z6QSg1hBRyrNjMT+DDWjuMdAGkAJn8VJA+EBUG554IHYA1t5g7BvGsKvvf74re1Om+XQD1gjr1H0/lAVle2lTfgR7r/C3D8PvJGfIBKkIR0NSEFYBaLxWtTflxcHMxm75O1Sedp1Spc1C8VQGh9YBWNRvx4vFbWpHQAUZ2Cz0lLkKFkwAC4NuWucQWtZQpvQ8SJAViT92n4rkn48jNgfAQFHwGhBN7Mb2euQJsLVIJMi3efp0YlSIf+XvoNldyCKBTSAIy2ISKkawkpAJs4cSLmz5/vNpqiqakJ8+bNw8SJExU7OdJRqH1ga3aeRsGy73DHip9RsOw7rNl5OuBtGrtACZIPAm1qt4SUAQOkfWCODJjJahMzVEo14XOZCY43PF8ZsDYfe0H6y4CJQ1gV7MXTaVRi4OQ5DZ/v7+g5BZ9L8yiDUgbMQWzEd/6e1bWYUNXk+D0YGqUArLdkEQitgiSkawnpo+vLL7+M66+/Hr1798Z5550HACgpKUFGRgY2bdqk6AkSd5cMSAcA/HyiHlabXdZgxYpGI574tFicbu5rSKinxi6RAZOsgnRmwPRBZsAGSrYkAoCKs47sVIxWpVhPFZeZ6H8/SD7igW89xPlbBXnWyxBWJaTF6dAsmWjveY7+xlBI+QrUehpxFEWt4/esxDl+Ij8tNmp9ctJGfCpBEtK1hPSqMGTIEJSUlOCTTz7BgQMHIAgC5syZg1tvvRV6feS2yumJhvVORGKMBk3tVuwvb8IFuckBb+NvA2J/ARhfBZkUxdVTbqsgQ8yA8RVqx5ylIWkDvtIDbV0lyI4ZMKvNLg6T9XxD9jcHrL614z6QSkiN0+FUXRvqW93PtUnsAZObAaMADOg4iiJaA1ilektK7NH8OyaEdBTyK6der8eMGTOUPBcig1olYHz/NGw5WIWfjtfJCsBC3TOwS62CNFlgd67uD7YHbKBkRIDFZkeZswFfyREUHN+Qu8pLCbLN4spueW5F5C8DJm5DpPA4kFTnPK8OJUixB8z7896xB4wyK4ArA1bfakZDq9m1BVE0AzDJByyLZDwGIST6Qh7EWlpaigULFuDGG2/EjTfeiIULF+L06cB9RZ21evVqXHzxxcjPz8fkyZOxf/9+RW4T6JgFCxagV69ebv9dccUVSj2soFzi3FLnR5l9YNlJBvzhuiHiZZWAgHsG2uxMXA3HM0/RIC1BhpoBy06MgUGrhsXGcLq+TRzCquQKSM5fEz7PbmnVQofHwEuSbV56wBq8bMStBHEWWEtwJchkgxbStQC+MmU9TaxOg97OpvcTtS1dIgP2S9lZ8d+/e3eHrN5PQkhkhBSAbdy4EYMHD8ZXX32FrKwsZGVlYfPmzRg8eDA2b96s9DmK1q5di9/97ne47777sGHDBqSnp+OKK65AdXV1p24j55jGxkaMGzcOe/fuFf9bt25d2B6rPxOcfWA7T9XDbJX3qfayQRniv1+67QKvQ0Kl/vHjKfHfk1/dGrUXbv7m3plVkCqVgAGZzhVq1S2Kb0MkxZvwa7xkwFpN3oewAq6m/FYvqyD5fo1KD8TlPWWeGbBAk/Ad+0G6zoVKkC683F1S0Sz2HEZ6E26uotGIV749Kl7mvZ9yV0ETQsIrpADskUceweLFi7F3716sWLECK1aswN69e/Hkk0/ikUceUfocRS+88ALuvvtuzJo1C8OHD8eKFSugUqnw5ptvduo2cr+vXq93y4ClpaV53l1EDM6KR1qcDu0WO/aeOSvrNtJRA54N4J4qGo14YcNB8XI0X7jde8CcTfhBZsAAV3/OsZoWyRT8MARgia6ynmfJx9dG3ICrJGm02DrM5XJlwJQt9aVJZoFJBRpD4TgXCsC86e/cbuirA5Ww2hmSDFq3URCR5K/3kxASfSEFYGVlZZg9e3aH62fPnh22MmRTUxN++eUXXHvtteJ1Go0GV199NX744YeQbxPM9/33v/+N/v37Y/To0ZgzZw7q6iKzJ6MnQRAwYYBrKr4c0gDMaPFfUuxKL9z8zd1ss6PJmZkJNgMGuFZCHq9uVXwfSKnUWB00zvpcbYt7FoyPmPAWAEvHUng+Pw1+NuLu1Ln6mIYfaBK+9LYAkEg9YCKeAfvR+Xc5LDtR8YUecvHeTyk5vZ+EkMgIKQA777zzvPZRFRcXY9iwYZ0+KW9+/fVXAEBWVpbb9VlZWSgvLw/5NnK/b1ZWFpYuXYrNmzfjpZdews8//4yCggIYjb6zQiaTCU1NTW7/KYWPo9i0v0JWZoqvaASA9gABWL/0OHi+Z0TrhVsamPByq14bfAaMN+IfrmpCpbM/q0+y8o9HpRKQ4ewDq/JYCcnLi55DWAFHUMl/5p6zwBrCNIaC7+ko3ZDbbmeuHjA/ma10ZyO+RiVArwm5lfScw6fh25yfYKLZ/5WdZMDSqSOhdv5i+dognhASHSHVDu666y7ceuuteOKJJzBu3DgwxrBr1y4sXboUixYtcgvOpNsVeZo7dy7WrFnj9762b9+O/Px8MOZ4QdNo3E9Zo9HAZvMeUMi5jdzv+8wzz4ifZAcPHox//etfyM3NxUcffYR77rnH6/0vXboUzz77rN/HFyreF3SoshkFy77D0qkj/fZ1uWXAvKy0k8pOMmDWpf2wovAkgOi+cKtVAuL1GjEoAICYEN7weWbiQHkTGHM0wvOGeaVlJuhR0djeoRG/TZyC3zGAFAQBcTrH42wz2QDJ1oE8Q6V0BszbhtxtFhucfxJI0PvObPEMWIxWhcqmdnpTd+K9hly0+r+4aeP6YuLgDJyqbUN+eiw9T4R0ISEFYHzDbW8bb8+ZM8ftMg9wvHnuuefwxBNP+L2vjIwMt//X1rqv/KupqUFmZqbf2/q7jdzv61lGyMrKQl5eHkpKSnye+xNPPIH58+eLl5uampCbm+vzeLkqGo14acth8bKcwaruJcjAjfsX9UvDisKTGJARhw9mXRzVF+6EGPcALJQMWF5aLNQqQcxM9E42QKXQtj6eMhJiADR2mIbPH4PnFHwuVqdGi8nqlgELx0bcnLQEyRiDIAhi/5dGJfgt9ZY7s64tJpusDwA9Ra/EGMTq1OI4kWiOoOCykwwUeBHSBYUUgFVUVChy50lJSUhKSpJ1bEZGBvLz87F161ZMmTJFvL6wsBC//e1vQ75NKN8XAIxGI8rLy5Genu7zGL1eH5bBtKEMVm0KogdMekxGgj7qL96evUihZMD0GjX6psbiZK1jSGY4VkByrmn47gFYm58SpHh9s8ltFlg4NuLmeABmttnRYrIiIUYrbkMUH6Px2btU0WjEdyWuFcJyd1boCQRBQP+MOOz/tQlqFRDvJdtJCCFAiD1gnvOw/P2npNmzZ+Ptt9/G7t27YbPZ8NJLL6GsrAz333+/eMyjjz7qNp9Lzm0CHWMymfDggw+KCwzq6+sxc+ZMqFQq3H777Yo+RjlCaa6VZsAC9YABQLvZ98iESJOuslOrBFnbL3nDV0IC4Q3AssRRFO4lSF/bEHH8euk0/HBsxO26P42Y5WpwTtsXp+D7acA/WdsKz7w2ra5z4YswbHbgir/8m2ZvEUK86tS7665du1BSUgLGGIYNG4axY8cqdV5ezZ8/H1VVVZg4cSLsdjsyMjKwdu1aDB06VDymsbHRrZwo5zaBjtHr9Rg7diyuueYaVFZWwmKx4JJLLsEPP/yAvn0jX3bhzbUL1xWDARAQeLBqMD1ggCsDZgih3Kc06aT1ULJf3IDMOHzjrBiHYwo+xzNgnk34vAfMV3AT52UafkMYNuKWSovT49ezRtS1mtA3LTbgFHwg9J0VeoKKRiN+OdMoXqbsICHEl5ACsJqaGtx+++347rvvEB/vyCq0tLTgqquuwkcffST2VSlNEAT8+c9/xpIlS9Dc3Izk5OQOZZKXXnoJFoslqNvIOebee+/Fvffei5aWFsTFxUVtaTk3bVxfHK1qwdtbT+LGC3oH7L/hpSwguBJkTBcIwKSr8ULp/+IGSjJg3hrhlSJOw/fIgLUGyCrGetkPskEcwhqeUQ+pcTr8etYoNuLzLJ2/Dbb5B4BFn+6HjTFaXSfhLztIPx9CiFTITfhGoxHFxcXiKsf9+/fjvvvuw9y5c7F69WpFT9KTRqNBSkqK168lJnpvevV3m2CO4QFnV9A3zZFxkDMNP5g5YIArC2PQRX/EQKIkAOtMBuyUs/8LAP60sQQJMZqwNI7zafieG3LzwMpX8OctA8Y34la6AZ9L9ZiGz6fgB9peiFbXeUfZQUKIXCG9m23YsAGrVq1yGzExYsQIfPDBB9i4caNiJ0f841vTeE4y90YagJnk9IB10RJkqBmwikYj3vzPcfEyC+N0/yxnCbK2xSSuugT8zwEDJD1g5o4ZMKVHUHCeoyiaZfSAcdlJBkwYkEbBlwTN3iKEyBVSBsxisXjNBMXFxcFsDhwMEGWkOMtS0vKiN9KNtQGZJUgxAxb9JnxpMBDq0M9QVo6GKi1eL2ZB6lpNYkbMlQHzswoSrtWSgKsHTOkhrJznNHyxBEnbC4WMsoOEEDlCejebOHEi5s+fj+bmZvG6pqYmzJs3DxMnTlTs5Ih/PCviuZWMJ15W4rpfE37ne8AiuS2LWiUgzTkpXlqGFAexBloFKcmA1Yc5A5biGYDxDBgFYJ1C2UFCSCAhvcq+/PLLuP7669G7d2+cd955AICSkhJkZGRg06ZNip4g8S1ZkgHjgzS9kZYfAXmDWF0BWPR7wJRYBRnpxvHMBD1qmk3ORnzHrLuWEDJgPLup9EbcnK8SpL8mfEIIIZ0X0qvskCFDUFJSgk8++QQHDhyAIAiYM2cObr311rAMHiXe8ayI2WZHm9nm843ds0QpZw6YqwQZ/QyYWwmyExm5SJaGMhP0OADPDJizB8zPJHzAIwPWyldBRqYJ31WCpA22CSEknEIKwCZPnowvvvgCM2bMUPp8SBBidWro1CqYbXY0tJl9BmAdMmBySpDmrjOGQqlVkEDktmXJSnSuhJRMw28JYRXkWWcJMlyrINPieQbMcZ7NJvlN+IQQQkIX0rvZ999/j7Y2mnodbYIgICUucCM+D8DSnW+2wcwB6xqT8Du/CjLS+CywKueG3IwxVwbM1ypIL3PAwrURN5ca5zjP+pbgxlAQQgjpnJACsGuvvRbr1q1T+lxICFJkjKLgARjPysgJwLrSGIp4BTNgkZLhkQEzWe3iSAqfPWAeGTCrzS5uDZQSxkGsgGNIbLvF5pqETxkwQggJq5BeZXv37o177rkH69evx7Bhw6DTuX86f/LJJxU5ORIYb8RvkJEB65UYgwPlTTA7gwF/ewuKTfhdYBCr+yrI6J+PHK5p+I4ATJrV8hXUevaAnTWGbyNuLjFGA41KgNXOUN9qph4wQgiJkJACsN27d2Ps2LEoKytDWVlZh69TABY5PAN21k8GrIlnwJJixOtMVpvf8mJbF+oBk/YjxWiifz5y8GxjjbMEKe4soFX7DHw9V0HyGWBJBm3IG5AH4ihj61DTbHIEYDSGghBCIiKkV9m1a9ciJyfH69e8BWQkfMRp+K2+M2C8PywrwRWAGc3+A7B2c9cpQcZoXYsNulsGrKbFBLudBRxBAXTMgIW7/4tLcwZgtS0mtATYMJwQQogyQno3y83NDelrRHkpYgkycA9YSpxWnCQfqA+sKzXhA64yZHfJgKU7B7FabAwNbWbXEFY/m4CLGTCzDYwxsawcrv4vjveBnWkwgjl3C6BJ+IQQEl6KphPa2tpgMNDk50gKpgk/yaAV53r5mwVmsdlhdTaMd4UMGADEODNfJmvgBQRdgU6jEgOb6mYTWkz+Z4ABrgyYzc5gstrF5zRcIyg4/v1P1zk2K9eqhZC3fCKEECJPUB9zpb1dnn1edrsde/bswQUXXKDIiRF5gmnCTzRoYdCqcRYWGM2+p+FLs2MxXaAJf83O0/j1rKOX6vXvjyM3NRbTxvWN8lkFlpmgR32rGdXNJrQFmAEGuGcb28y2sA9h5fg0/NI6x2iZeL3G564KhBBClBFUALZ161av/wYArVaL/Px8PPbYY8qcGZFFThO+WwbMmdHyV4LkQ1hVAqALU/O3XBWNRjzxabF4mQFY9Ol+TByc0eX32ctMjMGhymZUOxvxAf89YGqVgBitCu0WO1pN1rAPYeX4LDAxAKPyIyGEhF1Qr7T//ve/AQC33HIL1q5dG47zIUHimynLKUEmG7TiqkY5AVisLvqZkJO1rXBWQ0U2xnCqtq3rB2CSURS8qd1fCZJ/vd1idmbAeA9YmAMw54De0/WOACxBTyMoCCEk3EJKb1Dw1XXwBu2zPlZBWm12cQWetAfM33ZEPDjrCiMo+qXHwXNqg1oQkJ8eG50TCoIYgDW1B9yGiBOn4ZutYlAd9ib8WPcdEigDRggh4RdyfenLL7/ETTfdhFGjRonX/eUvf0F9fb0iJ0bk4dmRZpMVFlvHvi4+SR1w9YAB/pvwu9IQ1uwkA5ZOHQm1MxOnFgQsmTqiy2e/APcMGF8FGWhVqTgN32RzBWARasLnaAo+IYSEX0jvsKtWrcKMGTMwaNAg7Nu3T7xeq9Vi2bJlip0cCSzRoAWvEnrbD5KXH+N0amjVKjGr5S8A60ozwABg2ri+2LrwSvzzvvHYuvDKbtGAD7hvyN3qXAUZaL6WdBYYH8Qa7h4wviE3RyMoCCEk/EIKwJYvX461a9fiz3/+s9v1kydPxurVqxU5MSKPWiWI29R4a8SXNuADcJUg/QRgbV0sAAMcmbAJA9K6ReaLy0zkGbB2cSui2AAlSNcsMKtkEGtk5oBxVIIkhJDwCykAO3bsGAoKCgDArUk7PT0dNTU1ypwZkY2XIfkbtpR0BAXg2szabxO+WILsOgFYd5Tp3HmgqskkTrcP1ITPM2BNRqtkI+7wZsBSYnWQrrWIpyZ8QggJu5ACsF69euHw4cMA3AOwr7/+Gv369VPmzIhs/maB8awYP0YcxCqjCb8rZcC6owxnD5jZakdFo2MUhb8xFIArQCs/awQQ3o24ObVKQLLkPqgESQgh4RdSADZr1izMmjUL27dvhyAIKC0txd/+9jfcf//9eOCBB5Q+RxKAv1lgTZ4lSBljKNopA6aIGK0aic5g5mStY8p8XICfKS9RljU4ArDEmPBtxC0lLUNSAEYIIeEX0ivtokWL0NDQgMsvvxw2mw35+fnQaDSYO3cu5s2bp/ApkkBc2xH5bsLnAVgwc8C6whiK7i4rMQZN7S3iAgm5GbAyZwYs3A34XGqcDsdrHEEibcRNCCHhF9IrrUqlwv/7f/8PixcvRnFxMex2O0aOHInU1FSlz4/IIM4CC6YJ389WRF2xCb+7ykzU42h1i3g54BwwZwD2a4NjKGq4G/A5aaBHARghhIRfp15pk5OTcdlllyl1LiRE/qbhdwjA5IyhsPBJ+BSAdRZvxOcCZsCcAVptC18BGakMmF78d0IMNeETQki4BRWA3XLLLbKOo0n5keWvCd9XACZrFSRlwDqND2PlAq+CdP96uIewcmnUA0YIIREV1CvtunXrkJeXhwsuuCBMp0NC4a8Jn/ceJTmPidHJmITPe8AoA9ZpmYmhZcC4SPaAcVSCJISQ8AvqlfbBBx/E6tWrUVpainvvvRd33nknUlJSwnVuRCbKgHVdnhmwQGVdz595coR6wKTT8PnMMkIIIeET1Pr2N954AxUVFXjkkUfw8ccfo3fv3rjjjjvw7bffgjEWrnMkAYirIL0MYvUcQxGjdQ5i9TcHjJrwFSMNwDQqAXqN/z85zwxZaoR6wPaVNYr/nvzqVqzZeToi90sIIT1V0AOGDAYD7rrrLvzwww/45ZdfkJubizvvvBP9+/cPx/kRGcQSpNHSIRAOpQmfJuErR1qCjNWp3QYXe+OZIYtED1hFoxHvbDspXrYzYNGn+1HRaAz7fRNCSE/VqQmPOp0OMTEx0Ol0sFqpbBEtvExlszNx+xoAsNjsaHVms4KaA0YlSMVIM2CB+r+8HROJVZAna1vhmcC2MYZTtW1hv29CCOmpgg7A2tvbsXr1alxzzTUYOnQoDh48iL///e8oLS0Nx/kRGWK0ajFzIm3E5+VHAOJEdtccMBklSMqAdVqcXiM2tcsJwDwzYKlx4e8B65ceB5VHYk4tCMhPjw37fRNCSE8VVAD28MMPIzs7G0uXLsWkSZNQVlaGTz75BL/5zW+gUoV/uxTim7dp+GedAViCXiNuZ+MqQfoexNpOGTBF8SxYoG2IHMdEPgOWnWTA0qkjoXaWR9WCgCVTRyA7yRD2+yaEkJ4qqFWQb7zxBvLy8jBkyBBs27YN27Zt83oczQGLvORYLX49a3Qbxsr7vxIlGy3zoMpss8Nqs3vdZ7CNtiJSVEaCHidqW2G1M1Q0Gv0GNrEeYyjCvRE3N21cX0wcnIFTtW3IT4+l4IsQQsIsqLTVzTffjLFjx4brXEgneJsF5tmAD7iXFdut3rNgRpqEryieUTxQ3oSCZd/5XWGoU6ugcdYDkwyR2Yiby04yYMKANAq+CCEkAoLKgFFmq+sSZ4G1ukqQniMoALiNQWi32LwO3WynVZCKqWg0uo144CsMJw7O8BroCIKAWJ0aTe3WiA1hJYQQEnmyP17X1NTI/qbBHEuUITcDJgiCaxirl0Z8i80Oi82xJI56wDrvZG0rPCfkBVphyJv1IzWElRBCSOTJDsBGjBiBxYsX4/Rp3+WTkydP4o9//COGDx+uyMkR+VK8TMMXtyHy6CPiw1i9zQKTXkc9YJ0XygpDXvqN1BBWQgghkSe7BPnzzz9jwYIFGDhwIEaMGIELL7wQWVlZYIyhsrISO3fuRElJCaZOnYodO3aE85yJF8nON+t6Lxkwz0yKQatGAyxeZ4HxrJggIODUdhIYX2G46NP9sDEma4Wh1tn3pdfSz58QQs5VsgOw/Px8rFmzBqdOncLHH3+Mbdu2Yffu3RAEATk5Ofif//kf3HbbbcjLywvn+RIfUpzzoryVIBM9M2B+ZoGJDfjawFPbiTzBrDBcs/M0DlU2AwA2FVdizc7TmDaub6ROlRBCSIQE1YQPOAKxxx9/PBznQjrBtR+kqwTprQcM8L8hN21DFB7ZSYaAqwsrGo144tNi8TKD/4Z9Qggh3RfVOM4RcpvwAf/7QRppBljUnKxthZ22BCKEkB4h6AwYAMybN8/n1/R6Pfr374+bbroJmZmZoZ4XCZK3SfjexlAAku2I/GXAKACLON6wLw3CaEsgQgg5N4UUgJWUlGDLli3IyMjA8OHDIQgCiouLUVtbi4kTJ2L16tVYsGABCgsLMXLkSKXPmXiR7OwBM1psaLfYEKNVi6sgPZvwxQ25zR0HsfIMGA1hjbxQGvYJIYR0TyEFYAMHDsTAgQPx17/+FTqdI/NiMpkwb948qNVqfPfdd5g9ezYeffRRbNmyRdETJt4l6DXQqARY7Qxn2yzolaQOrQRpoRJkNNGWQIQQ0jOEFICtX78ev/zyixh8AY7S4/PPP4/Ro0fjtddew+LFiyn7FUGCICA5VovaFjMa2sxIjdOJwZSvOWD+xlBQE370yGnYJ4QQ0r2F1ITf0NCAqqqqDtdXVlaioaEBAKDVamEw0JtIJCWLfWBmMfsFAAkx8jNg7dQDRgghhIRdSAHYlClTcNttt2HTpk2oqalBdXU1Nm3ahGnTpuHGG28EAHz22WeYMmWKoidL/EuR7AfJA7CEGA3UHqPY5cwBowCMEEIICZ+QSpBvvfUW5syZg8mTJ8Nmc7xhq9VqzJgxA6+88goAoE+fPrjjjjuUO1MSUIqXDJhn+RHwPwesjUqQhBBCSNiFFIAlJibivffew0svvYQjR45AEAQMGjQIqamp4jGTJk1S7CSJPNJZYI1Gxzwwbxs6yxrEShkwQgghJGxCCsC41NRUjB8/XqlzIZ3ER1E0tFn8Z8B0fnrAKANGCCGEhB1Nwj+HuJUg23wHYK45YDSGghBCCIkGCsDOIbwJ/2ybBY1GK4Dge8CMFrvbMYQQQghRHgVg5xBvYygS/QRg7RZvk/AdgRtNwieEEELCR5EAbO3atUp8G9JJriZ8/z1gMTIm4VMPGCGEEBI+igRgt956qxLfhnSSOAdMugrSoOtwnEEXeBI+9YARQggh4UMlyHMIL0E2Gi2ob3UEYME34VMPGCGEEBJuFICdQ/jML8aAMw1GAME34bdTCZIQQggJO0UCsFWrVinxbYLS3t6u+G1sNhvOnj0Lq9Wq+H1HglatQkKMY7RbTbMJQPBzwNqcTfiUASOEEELCR5EAbMaMGUp8G1mefvppJCcnIz4+HoMGDcLmzZs7fZvy8nI888wzyMvLQ0pKCrZu3arYfUcab8Tn/GXALDYGi819JaSRBrESQgghYdetSpCvvvoq/u///g9ffvkl2tracM899+C3v/0tjh071qnb/OMf/wBjzO9qzlDuOxpSPLYe8tcDBnTMgrVTDxghhBASdt0qAPu///s/zJo1C5deeil0Oh0WLVqEXr164a233urUbZ544gk8++yzyMnJUfS+oyFZkgETBIglSSm9RgVBcPxb2gdmtdlhtlEARgghhIRbtwnAamtrceLECVx22WVu10+cOBE///yzYrcJ5/eJBGkGLDFGC5VK6HCMIAiuYaxmVwmy3er6N5UgCSGEkPDp1GbcndXW1gaz2ez3mMTERKhUKlRXVwMA0tPT3b6emZnpMwgK5TZKfh+TyQSTySRebmpqkn2foZJmwLyVH7kYrRptZhvara4MGG/AFwRHlowQQggh4RFSADZv3jyfX9Pr9ejfvz9uuukmZGZm+v0+f/jDH7B69Wq/xxQVFaFfv37iZbvdvWncarVCEDpmeaRCuY0S32fp0qV49tlng76fzkiRGYAZvMwC49kwg1Yd0s+HEEIIIfKEFICVlJRgy5YtyMjIwPDhwyEIAoqLi1FbW4uJEydi9erVWLBgAQoLCzFy5Eif3+eNN97AG2+8Ies+e/fuDQCoqqpyu766ulr8mhK3UfL7PPHEE5g/f754uampCbm5ubLvNxSpca6gy38GrOM0fHEbIur/IoQQQsIqpDrTwIED8dBDD6GsrAzff/89vvvuO5SVleF///d/MXLkSJw6dQrTp0/Ho48+qtiJJicnY8SIEfj222/F6+x2O7777jtceuml4nVGoxHNzc1B3Uap+/ak1+uRmJjo9l+4yS1B8h4vbwEYbUNECCGEhFdIAdj69evx3HPPQadzvdnr9Xo8//zzWL9+PdRqNRYvXozdu3crdqIAsGjRIrz77rv48MMPceLECTz88MMwmUx48MEHxWN+//vfY8KECUHdxmw24+zZs2KPVktLC86ePes2cFXO9+kK3EqQsYFLkO2SEiTNACOEEEIiI6QSZENDA6qqqpCWluZ2fWVlJRoaGgAAWq0WBoOh82coMX36dBiNRixfvhxVVVUYOXIkvvvuO2RnZ4vHxMbGumWa5Nxm7dq1eOihhwAASUlJ4mDZhQsXYuHChbK/T1eQHCu3BOktA+Zowo+lAIwQQggJq5ACsClTpuC2227Diy++iLFjx4Ixht27d+MPf/gDbrzxRgDAZ599hilTpih6sgAwc+ZMzJw50+fXX3nllaBvc8cdd+COO+7o9H13BSlxQTbhSwMwZxM+lSAJIYSQ8AopAHvrrbcwZ84cTJ48GTab4w1crVZjxowZYgDUp08fWUENUZbbJHzm+zixB8xMTfiEEEJIpIUUgCUmJuK9997DSy+9hCNHjkAQBAwaNAipqaniMZMmTVLsJIl8/9pbLv57+eZDSInTYtq4vh2OE3vAaBUkIYQQEnGdGsSampqK8ePHK3UupJMqGo1Y9FmxeJkBWPTpfkwcnIHsJPd+vBgxAJNMwndmw6gHjBBCCAkvGnd+DjlZ2wq7R9nRxhhO1bZ1ONZbE36bMwCLoQCMEEIICSsKwM4h/dLj4Ln1o1oQkJ8e2+FYr034VIIkhBBCIoICsHNIdpIBS6eOhNq5jZBaELBk6ogO5UcAMOgcT710Dlg7BWCEEEJIRER1M26ivGnj+mLi4Aycqm1Dfnqs1+AL8DWGggaxEkIIIZFAAdg5KDvJ4DPw4rwPYqUMGCGEEBIJVILsobzNAWujDBghhBASERSA9VDe5oBRDxghhBASGRSA9VD+VkHSVkSEEEJIeFEA1kPpvQxipSZ8QgghJDIoAOuhvGXAeAmSJuETQggh4UUBWA/Fs1zt3prwqQRJCCGEhBUFYD0U9YARQggh0UMBWA/FAzCrncFic/SBiXPAqARJCCGEhBUNYu2hYnSu2NtosUElCDBbHYEYlSAJIYSQ8KIArIfSqVVQCYCdOfrA+P6RADXhE0IIIeFGJcgeShAEtz6wNkkzvl5DvxaEEEJIONE7bQ8mbkdksblNwRck2TBCCCGEKI9KkD2YXuMaxqoSqAGfEEIIiRQKwHow6YbcPOdFDfiEEEJI+FEA1oNJN+TmVUfKgBFCCCHhRwFYD+ZtGCtlwAghhJDwowCsB4uRlCA5CsAIIYSQ8KMArAczaB2LYKUZsBgqQRJCCCFhRwFYDybtAXNdR5NJCCGEkHCjAKwHM3gpQcbq6FeCEEIICTd6t+3B+Bwwo8UG5rwuhnrACCGEkLCjAKwH4xmwdotdDMCoCZ8QQggJPwrAejDpGAo7c4RgBh31gBFCCCHhRgFYDyZtwmfOAIx6wAghhJDwo3fbHkw6B4xnwKgHjBBCCAk/CsB6MGkJ0sZLkBSAEUIIIWFHAVgPRj1ghBBCSHRQANaD8WCr3WKD3U4ZMEIIISRSKADrwXi/l9Fsg03DM2D0K0EIIYSEG73b9mAx0h4wyoARQgghEUMBWA/mGkNhpwCMEEIIiSAKwHow6Rwwq11wXEdN+IQQQkjYUQDWg4mbcVtsUNscARjNASOEEELCjwKwHowHWzY7E0uQNAmfEEIICT+qN/Vg3vq9qAeMEEIICT8KwHowrVqAWiW4XafX0K8EIYQQEm70btuDCYLglvGK0aqg8gjICCGEEKI8CsB6OGnTPZUfCSGEkMigAKyHi9G6fgWoAZ8QQgiJDArAejjPEiQhhBBCwo/ecXs4PgvM89+EEEIICR8KwHo46gEjhBBCIo8CsB7OvQRJARghhBASCRSA9XDSACyWSpCEEEJIRFAA1sO59YBRBowQQgiJCArAeji3HjDKgBFCCCERQQFYD0c9YIQQQkjkUQDWw0lnf1EJkhBCCIkMCsB6OGrCJ4QQQiKPArAeTtr3RSVIQgghJDIoAOvhqAmfEEIIiTwKwHo4A03CJ4QQQiJOE+0TCEV5eTmqq6sxcOBAxMfHK3ab6upqnDhxAsOGDUNiYqLb106ePImqqiq362JjY3H++eeH9iC6CGnWi3rACCGEkMjoVhkwk8mEadOmYcCAAbj11luRlZWFN998s9O3KSoqwu23347hw4djwoQJ2LNnT4fvs3z5ckyaNAnz5s0T/1u+fLmijy8aaAwFIYQQEnndKgP2/PPPY+vWrTh27Bj69OmDdevW4dZbb8XYsWMxbty4kG9TVFSEKVOmYMmSJRgwYIDP+7/yyiuxdu3asDy2aKHNuAkhhJDI61YZsJUrV2LWrFno06cPAODmm2/GsGHD8M4773TqNjNnzsT06dOh0+n83r/ZbMa+fftQWloKxpgCjyj63LYiohIkIYQQEhHdJgArLy9HZWVlh0zXxRdfjKKiIsVu48/GjRtx++23Y8yYMejXrx+++uqroL9HV0ODWAkhhJDIi2oJ8vjx46ipqfF7zOjRo6HX61FfXw8ASE1Ndft6Wloa6urqvN42lNv4cu211+KZZ55Br169YLVasWDBAtx8883Yt28f+vfv7/U2JpMJJpNJvNzU1BTUfUaCNOhqbrdE8UwIIYSQniOqAdjq1auxYcMGv8esXbsWOTk50Gq1AOAW0ACA0WgUv+YplNv4cvPNN4v/1mg0WL58OVauXIn169fjkUce8XqbpUuX4tlnnw3qfiJtywHXys5b3voJS6eOxLRxfaN4RoQQQsi5L6oB2OLFi7F48WJZx+bm5kKlUqG8vNzt+vLycuTl5Sl2G7k0Gg3S09Px66+/+jzmiSeewPz588XLTU1NyM3N7dT9Kqmi0Yilm0rEy3YGLPp0PyYOzkB2kiGKZ0YIIYSc27pND1hsbCzGjx+PL774Qryura0N33zzDa6++mrxuhMnTmDfvn1B3SYQxhja29vdrjt27BhOnTqF4cOH+7ydXq9HYmKi239dycnaVtg91hLYGMOp2rbonBAhhBDSQ3SrMRQvvPACrrvuOixevBgTJkzAK6+8gtTUVNx///3iMUuWLMH27duxf/9+2bepqalx60c7ePAgYmJikJOTg5ycHFgsFlx44YV44IEHMHz4cJw+fRovvPACRo0ahenTp0f2h6CgfulxUAlwC8LUgoD89NjonRQhhBDSA3SbDBjgmMP17bff4vDhw1i+fDkGDhyIbdu2uWWWBgwYgFGjRgV1mx07dmDevHn405/+hIsvvhjvv/8+5s2bh82bNwMAdDodvvrqK5SVlWHZsmXYtGkT5s2bh59++gkxMTGR+wEoLDvJgKVTR0ItCAAcwdeSqSOo/EgIIYSEmcDOlYFW3UBTUxOSkpLQ2NjYpcqRFY1GnKptQ356LAVfhBBCiIdwvH93qxIkCY/sJAMFXoQQQkgEdasSJCGEEELIuYACMEIIIYSQCKMAjBBCCCEkwigAI4QQQgiJMArACCGEEEIijAIwQgghhJAIowCMEEIIISTCKAAjhBBCCIkwCsAIIYQQQiKMAjBCCCGEkAijrYgiiG+72dTUFOUzIYQQQohc/H1bye2zKQCLoObmZgBAbm5ulM+EEEIIIcGqq6tDUlKSIt9LYEqGc8Qvu92O8vJyJCQkQBAERb93U1MTcnNzcebMGcV2au+q6LGem+ixnpt60mMFetbj7UmPtbGxEX379kVDQwOSk5MV+Z6UAYsglUqFnJycsN5HYmLiOf+HwNFjPTfRYz039aTHCvSsx9uTHqtKpVzrPDXhE0IIIYREGAVghBBCCCERRgHYOUKv1+Ppp5+GXq+P9qmEHT3WcxM91nNTT3qsQM96vPRYO4ea8AkhhBBCIowyYIQQQgghEUYBGCGEEEJIhFEARgghhBASYTQHrBsxmUzYs2cPMjMzMWDAAFm3aW5uxuHDh5GRkYG8vLwwn6FyLBYLdu/ejdTUVAwePNjvsS0tLdi7d2+H60eNGoWEhIQwnaFyampqUFZWhn79+ske8Gc0GnHw4EEkJSVh4MCB4T1BBdXX16O0tBR5eXlITU31e6zZbMaOHTs6XD9s2LCAt+0K2tracPjwYaSmpsr+2zObzThw4AAMBgOGDh0a5jNUTnt7Ow4dOoSkpCTk5+cHHDS9devWDtcNHDgQvXr1CtcpKu7o0aOoqqrC6NGjERcX5/dYm82G/fv3Q61WY9iwYYrOkoqE48ePo6KiAueff77feV8///wzLBaL23V9+/ZF3759w32KnbJr1y60t7e7XZeTk4P8/Hy/t2OM4eDBg7BarRg+fDg0miBDKka6vIaGBrZgwQLWp08fFhcXxx544AFZt3vrrbdYbGwsGzp0KIuNjWU33HADa21tDfPZdk5TUxN78sknWU5ODouPj2d33nlnwNvs3LmTAWDjx49nBQUF4n8HDhyIwBmHbvv27WzixIksIyODXXDBBcxgMLCZM2cys9ns93affPIJS0pKYoMGDWKJiYns0ksvZXV1dRE669Ds2bOHXXPNNSwtLY1dcMEFLDY2lt1xxx3MaDT6vM2ZM2cYADZmzBi35/WHH36I4JkHr7Gxkf3v//4vS01NZWPGjGFpaWls5MiR7JdffvF7u2+++YZlZGSwfv36sbS0NDZq1Ch2+vTpCJ11aFpbW9mcOXNYWloaGzNmDMvIyGBDhw5lO3bs8Hkbi8XCALARI0a4Pa+ff/55BM+8c44dO8aSk5MZAFZUVOT32J07d7K+ffuynJwclpWVxQYOHNjlX5ukzpw5wzIyMhgAVlhY6PfYtLQ0NmTIELfndeXKlRE609Dl5eWxgQMHup33a6+95vc2hw8fZkOHDmWZmZksNzeX9enTh/34449B3S8FYN3A/v372dKlS1lVVRUrKCiQFYAVFRUxQRDYxx9/zBhjrKqqivXt25c98sgj4T7dTjl+/Dh77rnnWHl5Ofuv//qvoAKwhoaG8J+gglatWuUWTBw9epSlpaWxZ5991udtSktLmV6vZ6+88gpjzBGwjhgxgk2fPj3s59sZa9asYd988414ubS0lGVnZ7PHHnvM5214AFZSUhKJU1TM0aNH2apVq5jVamWMMWYymdikSZPYhRde6PM2DQ0NLCUlhS1atEi8zWWXXcauvPLKiJxzqM6cOcPefvtt8UODxWJht912GxsyZIjP2/AA7Pvvv4/QWSrLZDKxsWPHsgULFgQMwEwmE8vLy2P33nsvY4wxm83GbrrpJjZ8+HBmt9sjdMahs1qt7LLLLhMfq5wA7J///GeEzk45eXl5bMWKFUHdZvTo0Wzy5Mni3/kDDzzAevfu7fdDpScKwLoZuQHYnDlz2NChQ92ue+GFF1hKSgqz2WzhOj1FBRuA7dy5kxUVFbGWlpYInF143H777ezaa6/1+fUlS5awtLQ08Y+eMcbefvttptVqWWNjYyROUTGzZs1iEyZM8Pl1HoBt3ryZ7d69u9s9PqklS5awXr16+fz6O++8w3Q6ndtj/PLLLxkAdvLkyQicoXJeeeUVFh8f7/PrPAD78MMP2a5du7p89tbTI488wmbMmMGKiooCBmAbN27s8Bzu2rWLAWA//fRT+E+2kxYvXsx++9vfsqNHj8oOwF5++WW2c+dOVl1dHaGz7Ly8vDy2bNkytnPnTlZZWRnw+D179jAAbPv27eJ1Z86cYYIgsM8++0z2/XavQjSRraioCBdeeKHbdRdddBEaGhpQWloapbMKr6lTp2L69OlISUnBvHnzYLVao31KQbHZbCgqKvLb01VUVIQLLrgAarVavO6iiy6CxWLBgQMHInGaimCMYffu3bL61373u9/hrrvuQnp6Ou655x60trZG4Aw7r7i4GP/5z3+wYsUKvPrqq3juued8HltUVIRBgwa59ddcdNFF4te6uoMHD+KHH37AO++8gxdffBEvvPBCwNvMmTMH99xzD7Kzs3HzzTejrq4uAmfaORs3bsTnn3+O119/XdbxRUVFSEtLc+slGjNmDNRqdZd/Xv/zn//g3XffxYoVK4K63VNPPYVZs2YhLy8P1157Lc6cOROmM1TWn/70J8yaNQsDBgzAxIkTceLECZ/H8uduzJgx4nU5OTnIzs4O6nmlAOwcVV9fj7S0NLfr+OX6+vponFLYpKSk4JtvvsHp06dRUlKCrVu3YuXKlVi6dGm0Ty0oTz/9NMrKyvDII4/4POZceV6XL1+OkpISPPbYYz6PiYmJwdq1a1FRUYH9+/fjl19+waZNm/D4449H8ExD9/e//x2PP/44FixYgBEjRuC6667zeay355UvNOgOz+s//vEPPP7443j88cfRv39/TJo0yeexgiBg5cqVqKmpwb59+3DkyBEUFxfj/vvvj+AZB6+iogL33nsv3n//fdkbT3t7XgVBQGpqapd+Xuvq6jBjxgysXLkS6enpsm+3fPly1NXVYe/evTh16hQaGxsxffr0MJ6pMp5++mnxvHmC4tZbb4XNZvN6fH19PRITE6HVat2uT0tLC+p5pQDsHKXVajus6jAajQAAnU4XjVMKmwEDBuDqq68WL1900UW499578dFHH0XxrILz2muv4cUXX8SaNWswaNAgn8edC8/ru+++i6eeegqrVq3CyJEjfR6Xnp6Om2++Wbx83nnnYd68ed3meX311Vfx888/o7y8HKmpqbjmmmt8ZmW9Pa/8cnd4XpcvX47t27ejvLwc/fv3x5VXXtnh8XBqtRozZ84UV0rm5eVh0aJFWL9+vc/bdAUPP/ywmJXcunWruPJ67969OHLkiNfbeHteAcffbFd+Xh955BGcd955iI2NxdatW7F7924AjqxuSUmJz9vde++9YnY+MzMTzz33HLZt29bls2D33HOPGEylpaVhyZIl2LNnT9ifVwrAzlF5eXn49ddf3a7jl3Nzc6NxShGVlZXV4fF3VW+++SYeffRRfPLJJ34zB4D/57WrL/UGgPfffx8PPPAA3n//fdxyyy1B3z4rKwv19fVd+o3aU0xMDH7/+9/j2LFjOHbsmNdjuvvzyul0OsydOxdlZWXYv3+/7NtlZWXBZrOhsrIyjGfXOampqairq8PChQuxcOFCvPzyywCAl19+GWvWrPF6m7y8PFRXV7uNZmhqakJLS0uXfl6TkpLQ1tYmPtYXX3wRgOO1atWqVbK/T1ZWFgB0m9diLtB55+XlwWw2o7a2VrzOZrOhqqoquOc1hH41EkW+mvDPnj3LCgsLxTETr732GouLi2NNTU3iMXfccQcbN25cxM61s3w14Tc1NbHCwkLxsXlrur/yyitZQUFB2M+xs9566y2m0+l8LsFvbW1lhYWF7OzZs4wxxtauXctUKhU7c+aMeMz8+fNZ3759u/yqqvfff5/pdDq2evVqr19vb29nhYWFYlO2t+f19ttvZwMGDAjreXaWt/N+7733mCAIrKqqijHmaEQvLCwUG5W3bt3KALDdu3eLt/nzn//MEhMTg1pVFWneHuvatWsZAHbixAnGGGN2u50VFhayiooKn7eZN28eS05OZhaLJbwnrCBfTfhbt25lZWVljDHHilhBENiGDRvEr7///vtMo9GIvwvdga8m/J9++omVlpYyxrw/r8uWLWNarZbV19dH5DxD4e28X3vtNaZSqcTnkTHGduzYIS6mqKurYzqdzm3ExpYtWxiAoEaMUADWDfAXsMLCQjZy5Eg2ZcoUVlhY6PZi/fXXXzMArLi4mDHmeOMeMmQIu/LKK9nnn3/OnnzySaZWq9mWLVui9TBk27p1KyssLGQXX3wxu+6661hhYaHbXKGffvrJbRXR73//e/bggw+ytWvXss8//5zdcsstLCYmhv373/+O1kOQZdWqVUwQBPbYY4+Jz29hYSHbs2ePeExxcTEDwL7++mvGmGNZ+Pjx49mFF17I1q1bx5YvX840Gg378MMPo/UwZPn000+ZWq1ms2fPdnusO3fuFI85efIkAyCuInruuefYXXfdxf75z3+yL774gt17771Mo9GwdevWRelRyPPnP/+ZzZgxg61evZp99dVXbNmyZSw5OZk9/PDD4jE1NTUMAFu1apV43eTJk9ngwYPZmjVr2Ouvv84MBgN76aWXovEQZHv99dfZbbfdxj744AO2ZcsW9pe//IWlp6ezu+++WzzGaDQyAOzNN99kjDH2t7/9jU2dOpWtWrWKbdy4kc2dO5dpNBr21ltvRelRhMZXAKZWq9mLL74oXr7vvvtY79692apVq9g777zDUlNT2eOPPx7hs+0cXwFYUlISe/rppxljjH3++efsuuuuY++++y7bvHkz++Mf/8j0er3fsTpdwddff82uuOIKtnLlSrZ582b2zDPPMIPB0GFETp8+fdijjz4qXl68eDFLTk5mK1asYB9++CHLyclhd911V1D3TZPwuwGLxYKFCxcCABITE1FbW4uFCxciLy8PH374IQAgOTkZBQUF4kTm2NhYFBYWYtmyZXjllVeQkZGBb7/9FpdffnnUHodcf/zjH2G1WqHRaNDa2oqFCxciMzMTn376KQDHz6CgoEBshP3rX/+KVatW4eOPP0ZrayuGDh2KQ4cOdfnJ/ydPnsQll1yCH3/8ET/++KN4ff/+/fH+++8DAOLi4lBQUCBOyFer1fjqq6/w4osv4o033kBSUhI+++wz3HDDDdF4CLIdP34c48ePR1FRkdsqoezsbHzyyScAHKW6goICsWn5ySefxNq1a/H555+joaEBgwYNQnFxcZefEP/YY49h/fr1WLduHaqqqpCTk4PVq1fj+uuvF4/RarUoKChAZmameN3HH3+Mv/71r3j77bdhMBiwcuXKLt/A/NBDD6Ffv35Ys2YNysvLkZOTg5UrV2Ly5MniMSqVCgUFBcjOzgYA3H///cjNzcWaNWtQWVmJ/v37Y/v27R1WbXd18fHxKCgoQHx8vNv1l156KXJycsTLb7zxBt588018+OGHUKlUWLp0KWbNmhXp0+0Ug8GAgoICJCUluV0/YcIEseQ2ZcoUpKWl4b333sOZM2eQl5eHr776qsu/51xzzTVITEzEypUrcerUKeTm5mL9+vW49tpr3Y676KKL0K9fP/Hys88+i379+mHdunWwWq2YP38+Zs+eHdR9C4wxpsijIIQQQgghslATPiGEEEJIhFEARgghhBASYRSAEUIIIYREGAVghBBCCCERRgEYIYQQQkiEUQBGCCGEEBJhFIARQgghhEQYBWCEEBICs9mMjz76CGfPno32qRBCuiEKwAghPd4XX3wR9EbQTU1NmD59Ok6dOhWekyKEnNMoACOE9GjV1dWYOnUq1Gp1ULfT6/WYNm0aUlJSwnRmhJBzGe0FSQg5p7S2tuKLL77ADTfcgFOnTuHIkSO48MILfe4NumHDBowdOxYZGRlev26xWLB9+3Y0NTVh1KhR4j5/er0ev/3tbzvsj3f48GEcOnQIAwYMwHnnnYdPPvkE1157LdLS0tzOrbKyEiUlJejbty9GjRoFANi3bx9OnjyJ4cOHY+DAgW7f9+OPP4bdbodarUZeXh5Gjx4NrVbb2R8XISRKKAAjhJxTampqMH36dNxwww04evQozj//fGRmZvoMwL788kufm5mXlZXh8ssvR2xsLPr374/9+/fj7rvvxlNPPSWWIIuKinDBBRcAAJ5//nn86U9/wqWXXoqqqirk5uZi06ZN+Omnn5CWliae2+WXX476+nrk5OTgm2++we9//3tUVFTg4MGDyM7Oxvfff4+///3vuOuuu8RzWb9+PWw2G6xWK/bt2wetVovNmzcjNzdX8Z8hIST8KAAjhJyTYmNjcfDgQahUvjstzGYzvv76azz11FNev75y5Ur06tUL27ZtAwDY7XZ88cUXXo89dOgQnnnmGaxfvx433HADGGNuAZTUoEGD8Pe//x2CIOCtt97Cgw8+iNmzZ2Pv3r0AgL/85S948skn3W7/4Ycfiv+22+247bbb8NRTT+Hdd9/1+3MghHRN1ANGCDknPfzww36DLwD4z3/+g+TkZLEE6MlgMKCurg6//vorAEClUmHKlClej/3ss88wePBgMZsmCAL+8Ic/eD32/vvvhyAIAIAJEyaI13ETJkzAmTNnYDQa3W538OBBfPnll/j444+RkZGBHTt2+H18hJCuizJghJBzUnZ2dsBjvvzyS0yaNMnn1x988EHs3bsXgwYNwrBhw3Dttddi9uzZ6NOnT4djz5w5g/z8fLfrPC9z0sZ9vV7v8zqTyQSDwQCj0YjJkyejqKgI48aNQ1JSEs6cOYPq6uqAj5EQ0jVRBowQck7iGSZ/NmzY4LP/CwASEhKwevVq1NTUYMmSJdi/fz/Gjh2L1tbWDsempqZ2mAnW0NAQ9Hl7s2rVKhw9ehSlpaXYvHkz1qxZgzvuuAOMMUW+PyEk8igAI4T0SCUlJSgvL8dVV13l8xheeoyLi8N1112HV155BZWVlSgtLe1wbEFBAXbv3o2ysjLxuvXr1ytyrpWVlejTpw/i4+PF69atW6fI9yaERAeVIAkhPdKXX36Jq6++GgaDwecxb775Jn766Sf893//N5KTk/Hhhx/i/PPPx+DBgztku66//npccsklYpmyqqoK77zzDgB52Th/brjhBjz//POYN28eRowYgc8++wx79+4NenYZIaTroAwYIeScEhcXh2nTpiEhIcHvcf7GT3AvvPACFi9ejIqKCmzfvh033XQTCgsLodFovA5i3bhxI+655x7s2rULOp0On3/+OQCI5+Lt3BITEzFt2jTExsaK16WmpmLatGnQ6XQAgDFjxqCwsBBWqxXbtm3DpEmT8Omnn2Lq1KlB/WwIIV2HwKiJgBDSw5w9exaZmZk4ceKEOFhVCfX19UhNTRUvv/3225g/fz5qa2vFYIoQQgAqQRJCeqCTJ0/ioYceUjT4AoAnn3wSgiBgzJgxOHToEF5//XU8//zzFHwRQjqgDBghhCjEbDbjvffew65du5CSkoJJkyZh4sSJ0T4tQkgXRAEYIYQQQkiEURM+IYQQQkiEUQBGCCGEEBJhFIARQgghhEQYBWCEEEIIIRFGARghhBBCSIRRAEYIIYQQEmEUgBFCCCGERBgFYIQQQgghEUYBGCGEEEJIhP1/JKcL1PrcBmsAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "chain = rf.System(start.positions, box=start.container, potential=lj, kT=T, seed=2, method=\"event_chain\")\n", "chain.run(100.0)\n", "t0 = time.perf_counter()\n", "g_chain = rf.radial_distribution(chain, n_samples=1500, interval=1.0, r_max=5.0, bins=1000)\n", "print(f\"event chains: 1500 samples in {time.perf_counter() - t0:.0f} s\")\n", "\n", "plt.plot(coarse(g.r), coarse(g.g) - coarse(metropolis), \"o-\", ms=3, label=\"all particles moving\")\n", "plt.plot(coarse(g_chain.r), coarse(g_chain.g) - coarse(metropolis), \"s-\", ms=3, label=\"event chains\")\n", "plt.plot(coarse(ref[:, 8]), coarse(ref[:, 9]) - coarse(metropolis), lw=1, label=\"event chains (paper)\")\n", "plt.axhline(0, color=\"k\", lw=0.5)\n", "plt.xlim(0.8, 5); plt.xlabel(\"r / sigma\"); plt.ylabel(\"g - g(Metropolis), bins of 0.05\"); plt.legend();" ] }, { "cell_type": "code", "execution_count": 8, "id": "681f118b", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T23:52:50.735640Z", "iopub.status.busy": "2026-10-01T23:52:50.735486Z", "iopub.status.idle": "2026-10-01T23:53:02.092391Z", "shell.execute_reply": "2026-10-01T23:53:02.091510Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dpd = rf.System(n=375, box=sp.PeriodicBox(5.0), potential=rf.DPD(a=25.0), kT=1.0, seed=2)\n", "dpd.run(20.0)\n", "g_dpd = rf.radial_distribution(dpd, n_samples=400, interval=0.5, r_max=2.5, bins=200)\n", "ref_dpd = load_reference(\"GofR_DPD_110925.dat\")\n", "plt.plot(ref_dpd[:, 0], ref_dpd[:, 1], \"k-\", lw=2, label=\"paper\")\n", "plt.plot(g_dpd.r, g_dpd.g, lw=1, label=\"spheropack\")\n", "plt.xlabel(\"r / r_c\"); plt.ylabel(\"g(r)\"); plt.legend();" ] }, { "cell_type": "markdown", "id": "a6aabdd2", "metadata": {}, "source": [ "## Notes\n", "\n", "- The move velocities are not physical momenta: their magnitude only sets the time scale of the moves, and they are conserved by the reflections. `system.redraw_velocities()` draws new ones; the paper found that this is not needed for ergodicity.\n", "- Any pair potential with at most one minimum fits the method: `rf.LennardJones`, `rf.WCA`, `rf.DPD`, `rf.SoftSpheres` (harmonic, Hertzian) and `rf.HardSpheres`, where every approach to contact reflects." ] } ], "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }