{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from codes import utils, model, interface, solvers, hf" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "U0 = 1\n", "nk = 100\n", "filling = 2\n", "\n", "hopp = np.kron(np.array([[0, 1], [0, 0]]), np.eye(2))\n", "tb_model = {(0,): hopp + hopp.T.conj(), (1,): hopp, (-1,): hopp.T.conj()}\n", "\n", "\n", "def model_U(U):\n", " int_model = {\n", " (0,): U * np.kron(np.ones((2, 2)), np.eye(2)),\n", " }\n", " return model.Model(tb_model=tb_model, int_model=int_model)\n", "\n", "\n", "model0 = model_U(U0)\n", "model0.vectors = [*model0.int_model.keys()]\n", "model0.random_guess(model0.vectors)\n", "model0.kgrid_evaluation(nk=100)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "hamiltonians_0 = utils.kgrid_hamiltonian(\n", " nk=nk, hk=utils.model2hk(tb_model=tb_model), dim=1\n", ")\n", "\n", "\n", "def groundstate(U):\n", " tb_mf_k = interface.find_groundstate_ham(\n", " model_U(U),\n", " filling=filling,\n", " nk=nk,\n", " solver=solvers.rspace_solver,\n", " cost_function=solvers.real_space_cost,\n", " return_kspace=True,\n", " )\n", " vals, vecs = np.linalg.eigh(tb_mf_k)\n", " EF = utils.get_fermi_energy(vals, filling)\n", " densityMatrix = hf.density_matrix(vals, vecs, EF)\n", "\n", " return tb_mf_k - EF * np.eye(hamiltonians_0.shape[-1]), densityMatrix\n", "\n", "tb_mf0, densityMatrix0 = groundstate(U0)\n", "mf0 = tb_mf0 - hamiltonians_0\n", "\n", "\n", "@np.vectorize\n", "def mfRescaled(alpha, mf0=mf0):\n", " hamiltonian = hamiltonians_0 + mf0 * alpha\n", " vals, vecs = np.linalg.eigh(hamiltonian)\n", " EF = utils.get_fermi_energy(vals, filling)\n", " densityMatrix = hf.density_matrix(vals, vecs, EF)\n", " return hf.total_energy(tb_mf0, densityMatrix)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<matplotlib.legend.Legend at 0x123524050>" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlQAAAGwCAYAAABvpfsgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/OQEPoAAAACXBIWXMAAA9hAAAPYQGoP6dpAABvLUlEQVR4nO3deVyU1f4H8M8MywDDJiACCuIK7uCCiiu5USZqrmnglmVm3jZTu5l6q+stzRbLzH6mVrZoanLNzFxTUQERc0X2RURAlIEBhmHm+f1BzI1YZNgeZubzfr3mJQznmfnOgzAfzjnPORJBEAQQERERUb1JxS6AiIiIyNAxUBERERE1EAMVERERUQMxUBERERE1EAMVERERUQMxUBERERE1EAMVERERUQOZi12AqdBqtcjMzISdnR0kEonY5RAREVEdCIKAgoICeHh4QCqtuR+KgaqZZGZmwtPTU+wyiIiIqB7S09PRrl27Gr/OQNVM7OzsAJR/Q+zt7UWuhogai1KphIeHB4DyP5zkcrnIFRFRY1IoFPD09NS9j9eEgaqZVAzz2dvbM1ARGREzMzPdx/b29gxUREbqYdN1OCmdiIiIqIEYqIiIiIgaiEN+REQNYG5ujjlz5ug+JiLTxJ9+IqIGkMlk2LFjh97HaTQaqNXqxi+IiPRiYWFRaS5kfTFQERE1I0EQkJWVhQcPHohdChH9ydHREW5ubg1aJ5KBioioAQRBQFFREQDAxsbmob+QK8KUq6trndoTUdOp+PnNzs4GALi7u9f7sRioiIgaoKioCLa2tgCAwsLCWpdN0Gg0ujDl7OzcXCUSUS2sra0BANnZ2XB1da338B+v8iMiaiYVc6ZsbGxEroSI/qriZ7Ih8xoZqIiImhmH+Yhalsb4mWSgIiIiImogBioiIiKiBmKgIiIiqgeJRIKffvpJ7DLqbOvWrfD09IRUKsWHH34odjlGh4HKwGm0AmLS7qNErRG7FCIyUnPnzoVEIsGiRYuqfG3x4sWQSCSYO3dulfZ/vyUkJDRj1S1LfcOXt7d3o4QfhUKBJUuWYPny5bh9+zaeeeaZBj9mQ82dOxeTJk2qcn9sbCwkEglSUlLq9bjXrl3DlClT4O3tDYlE0mzhkYHKwE389Aye2ByB80n3xC6FyCSZmZlh6tSpmDp1aqOsttxSeXp64vvvv0dxcbHuvpKSEnz33Xfw8vKq0j44OBh37typdOvQoUOj1cNV5vWTlpYGtVqN8ePHw93dvdorTY3lnBYVFaFjx474z3/+Azc3t2Z7XoMJVCEhIfDy8oKVlRXc3d0RGhqKzMzMGtur1WosX74cvXr1glwuh4eHB8LCwqocs3XrVowcORL29vaQSCTVrl58//59hIaGwsHBAQ4ODggNDW0xqxz3bucIADh+M1vcQohMlJWVFfbs2YM9e/bAyspKr2MFQUBRaZkoN0EQ9Kq1b9++8PLywr59+3T37du3D56envD396/SXiaTwc3NrdKttsD5xRdfwNPTEzY2Npg8eTI2btwIR0dH3dfXrFkDPz8/fPnll+jYsSNkMhkEQUBaWhomTpwIW1tb2NvbY/r06bh7967uuOp6QV588UWMHDlS9/nIkSOxdOlSvPbaa3BycoKbmxvWrFlT6Zj4+HgMHz4cVlZW6N69O3777bdKXy8tLcWSJUvg7u4OKysreHt7Y926dQDKe5kAYPLkyZBIJLrPExMTMXHiRLRp0wa2trYYMGAAjh49Wqmu1NRUvPTSS7pevgoREREYPnw4rK2t4enpiaVLl0KpVFZ7bnfs2IFevXoBADp27Kjr/anvOf3rcV5eXrC1tcVzzz0HjUaD9957D25ubnB1dcU777xTbT1NbcCAAVi/fj1mzpwJmUzWbM9rMAt7BgUF4fXXX4e7uztu376NV199FVOnTkVERES17YuKihATE4NVq1ahT58+uH//Pl588UWEhIQgOjq6Urvg4GAEBwdj5cqV1T7WrFmzkJGRgcOHDwMAnnnmGYSGhuK///1v479QPT3i44pvL6Th+M1srA0ReDk2kQEpVmvQ/c1fRXnu6/8aBxtL/d4C5s2bh+3bt2P27NkAgC+//BLz58/HyZMnG1TL2bNnsWjRIrz77rsICQnB0aNHsWrVqirtEhISsHv3buzdu1cXziZNmgS5XI5Tp06hrKwMixcvxowZM/SuaefOnXj55Zdx4cIFnDt3DnPnzsWQIUMwZswYaLVaPPHEE3BxccH58+ehUCjw4osvVjr+448/Rnh4OHbv3g0vLy+kp6cjPT0dABAVFQVXV1ds374dwcHButoLCwvx2GOP4e2334aVlRV27tyJCRMmIC4uThde+/Tpg2eeeQYLFy7UPdeVK1cwbtw4vPXWW9i2bRtycnKwZMkSLFmyBNu3b6/y2mbMmAFPT0+MHj0akZGR8PT0ROvWrRt0ThMTE/HLL7/g8OHDSExMxNSpU5GcnIyuXbvi1KlTiIiIwPz58zFq1CgMGjRIr+/F36WlpaF79+61tnnqqaewZcuWBj1PQxlMoHrppZd0H7dv3x4rVqzApEmToFarYWFhUaW9g4NDlb8gNm3ahICAAKSlpem6qCt+KGr64btx4wYOHz6M8+fPY+DAgQDK/5IaPHgw4uLi4OPj0wivrv4COzvD0lyKjPvFSMguRJc2dqLWQ0TGKzQ0FCtXrkRKSgokEgnOnj2L77//vtrfnwcPHtStIA8Ajz76KPbs2VPt427atAmPPvooXn31VQBA165dERERgYMHD1ZqV1paiq+//loXBn777Tf88ccfSE5OhqenJwDg66+/Ro8ePRAVFYUBAwbU+bX17t0bq1evBgB06dIFn3zyCY4dO4YxY8bg6NGjuHHjBlJSUtCuXTsAwL///W88+uijuuPT0tLQpUsXDB06FBKJBO3bt9d9raLeiv3iKvTp0wd9+vTRff72229j//79CA8Px5IlS+Dk5AQzMzPY2dlVOm79+vWYNWuW7v2rS5cu+PjjjzFixAh89tlnVXpKra2tdSvzt27dutJj1fecarVafPnll7Czs0P37t0RFBSEuLg4HDp0CFKpFD4+Pnj33Xdx8uTJBgcqDw8PxMbG1trG3t6+Qc/RGAwmUP1VXl4edu3ahcDAwGrDVE3y8/MhkUgqdSM/zLlz5+Dg4KALUwAwaNAgODg4ICIiosZApVKpoFKpdJ8rFIo6P6c+bCzNEdjJGSfjcnD8ZjYDFVEzUyqVdd565u+sLcxw/V/jmqq0hz63vlxcXDB+/Hjs3LkTgiBg/PjxcHFxqbZtUFAQPvvsM93ntZ2XuLg4TJ48udJ9AQEBVQJV+/btdW/8QPkfvJ6enro3fgDo3r07HB0dcePGDb0D1V+5u7vr9ne7ceMGvLy8dGEKAAYPHlyp/dy5czFmzBj4+PggODgYjz/+OMaOHVvrcyqVSqxduxYHDx5EZmYmysrKUFxcjLS0tFqPu3jxIhISErBr1y7dfYIgQKvVIjk5Gd26davTawbqf069vb1hZ/e/95s2bdrAzMwMUqm00n0V57AhzM3N0blz5wY/TlMzqEC1fPlyfPLJJygqKsKgQYOq/LDVpqSkBCtWrMCsWbP0SrJZWVlwdXWtcr+rqyuysrJqPG7dunVYu3ZtnZ+nIR7xdcXJuBwcu5mNZ0d0apbnJKKGk0gkeg+7iW3+/PlYsmQJAODTTz+tsZ1cLq/zm6AgVJ2uUN0cr7+HsuqO+/v9Uqm0ymNVN/n673+cSyQSaLXaGmv5+/P27dsXycnJ+OWXX3D06FFMnz4do0ePxo8//ljl2ArLli3Dr7/+ig0bNqBz586wtrbG1KlTUVpaWuMxQHnv0LPPPoulS5dW+Vp1FwjUpj7nFKj+fNV2Dqtjb2+P1NTUKvdXzFF2cHAAwCG/OlmzZs1DQ0dUVBT69+8PoPw/34IFC5Camoq1a9ciLCwMBw8efOi8IbVajZkzZ0Kr1WLz5s1611mX/1x/t3LlSrz88su6zxUKRaXE35iCfFwBXMPF1PvIL1LDwabuvXZERPoIDg7WveGPG9c4vWu+vr6IjIysdN9f57rWpHv37khLS0N6erru9+v169eRn5+v66Vp3bo1rl69Wum42NhYvUY3Kp4nMzMTHh4eAMpHL/7O3t4eM2bMwIwZMzB16lQEBwcjLy8PTk5OsLCwgEZTeXmb06dPY+7cubreucLCwipLBVhaWlY5rm/fvrh27VqT9NrU5Zw2Fl9fX3z33XcoKSmpNEwZFRWF1q1bo1WrVgA45FcnS5YswcyZM2ttU3E1BFDe3ezi4oKuXbuiW7du8PT0xPnz56t0vf6VWq3G9OnTkZycjOPHj+t90t3c3Cpd3VAhJycHbdq0qfE4mUzWbFcXeDrZoIurLeKzC/F7fA4m9PFoluclItNjZmaGGzdu6D5uDC+88AKGDx+OjRs3YsKECTh+/Dh++eWXh/6xPHr0aPTu3RuzZ8/Ghx9+qJtAPWLECN0f4o888gjWr1+Pr776CoMHD8Y333yDq1evVntlYm3P4+Pjg7CwMLz//vtQKBT45z//WanNBx98AHd3d/j5+UEqlWLPnj1wc3PTTTHx9vbGsWPHMGTIEMhkMrRq1QqdO3fGvn37MGHCBEgkEqxatapKj463tzd+//133RVrLi4uWL58OQYNGoTnn38eCxcuhFwux40bN/Dbb79h06ZNdX5d9T2njWX27Nl46623EBoaiuXLl6NVq1Y4d+4c1q1bV+kiMX2H/EpLS3H9+nXdx7dv30ZsbCxsbW2bdOhQ1GUTXFxc4OvrW+utpsuQK7pg/zpP6e8qwlR8fDyOHj2qm5Snj8GDByM/P7/SX08XLlxAfn4+AgMD9X68pvKIb/mw5Akun0BETcze3r5RewSGDBmCLVu2YOPGjejTpw8OHz6Ml1566aHLUFQsltmqVSsMHz4co0ePRseOHfHDDz/o2owbNw6rVq3Ca6+9hgEDBqCgoABhYWF61SeVSrF//36oVCoEBATg6aefrrIkgK2tLd599130798fAwYMQEpKim6CNgC8//77+O233yotM/HBBx+gVatWCAwMxIQJEzBu3Dj07du30uP+61//QkpKCjp16qSb69S7d2+cOnUK8fHxGDZsGPz9/bFq1Sq4u7vr9bqqU5dz2lgcHBxw+vRpCIKASZMmoU+fPnjvvffw1ltv4ZVXXqn342ZmZsLf3x/+/v64c+cONmzYAH9/fzz99NONWH1VEkHfxUhEEBkZicjISAwdOhStWrVCUlIS3nzzTdy5cwfXrl3T9QT5+vpi3bp1mDx5MsrKyjBlyhTExMTg4MGDlXqTnJycYGlpCaB8jlRWVhaio6OxcOFC/P7777Czs4OXlxecnJwAlF+dkpmZic8//xxA+bIJ7du312vZBIVCAQcHB+Tn5zdJ1+SFpHuYsfU8WtlYIPqNMTCTcvkEouagz6T0kpISJCcno0OHDnqvWWVqFi5ciJs3b+L06dNil0ImoLafzbq+fxvEwp7W1tbYt28fRo0aBR8fH8yfPx89e/bEqVOnKg2rxcXFIT8/HwCQkZGB8PBwZGRkwM/PD+7u7rrbX9eu2rJlC/z9/XVrfAwfPhz+/v4IDw/Xtdm1axd69eqFsWPHYuzYsejduze+/vrrZnr1ddOvfSvYW5njfpEasekPxC6HiEgvGzZswOXLl5GQkIBNmzZh586dmDNnjthlEdWZQfRQGYOm7qECgCXfxuDgH3ewJKgzXh0n7vpYRKaipKQEU6ZMAQDs3bu31p4n9lDVbPr06Th58iQKCgrQsWNHvPDCC9XuHUjUFBqjh8qwrtelWj3i64qDf9zB8ZvZDFREzcTKygo///yz2GUYvN27d4tdAlGDGMSQH9XNSB9XSCTA9TsK3MkvfvgBRCQKDgwQtSyN8TPJQGVEnOSW8Pd0BACcuJkjbjFEVEXF2kdFRUUiV0JEf1XxM6nP+mR/xyE/I/OIryti0h7g+M1szBqo34q5RKQ/pVKp200hOzu71qv8zMzM4OjoqNuOw8bGhhuaE4lIEAQUFRUhOzsbjo6ODVpbjYHKyAT5umLDkVs4m5CLErUGVvXYr4uI9KNPj1PFxrSNsccZETWOv29cXR8MVEamu7s93OytkKUowfmkexjpU3UfQiISj0Qigbu7O1xdXavdU46ImpeFhUWjrPrPQGVkJBIJgnxd8V1kGk7czGagImqhzMzMGm3rFiISHyelG6GKbWiOx2XzaiIiIqJmwEBlhIZ0doaluRTpecVIzCkUuxwiIiKjx0BlhGwszTG4Y/lG0Me5WTIREVGTY6AyUhXDfsduMFARNSWpVIoRI0ZgxIgRkEr5K5XIVPGn30hVBKro1PvIL+aVRERNxdraGidPnsTJkydhbW0tdjlEJBIGKiPl6WSDzq620GgFnI7nqulERERNiYHKiI2quNqP86iIiIiaFAOVEQv6M1CdjMuBRsvlE4iaglKpROvWrdG6dWsolUqxyyEikTBQGbF+7VvBzsocecpSXM54IHY5REYrNzcXubm5YpdBRCJioDJiFmZSDO/aGgBwgsN+RERETYaByshxHhUREVHTY6AyciO6toZEAlzLVCArv0TscoiIiIwSA5WRc7aVwc/TEQBwIo69VERERE2BgcoEPOLDYT8iIqKmxEBlAiqWTzibkIsStUbkaoiMi1QqRf/+/dG/f39uPUNkwszFLoCaXg8Pe7Sxl+GuQoULyXkY8eeVf0TUcNbW1oiKihK7DCISGf+cMgESiUS3tx+XTyAiImp8DFQmIugv86gEgaumExERNSYGKhMxpLMLLM2kSMsrQmIOt8cgaixFRUXw9vaGt7c3ioqKxC6HiETCQGUi5DJzDOrkDAA4fvOuyNUQGQ9BEJCamorU1FT2/hKZMAYqE/KIT/lkdC6fQERE1LgYqEzII75tAADRKfehKFGLXA0REZHxYKAyIV7ONujUWo4yrYDTt3LFLoeIiMhoMFCZmFHdynupjnEeFRERUaNhoDIxFcsnnIrLgVbLCbRERESNgSulm5j+3q1gZ2WOe8pSXM54AH+vVmKXRGTQJBIJunfvrvuYiEyTwfRQhYSEwMvLC1ZWVnB3d0doaCgyMzNrbK9Wq7F8+XL06tULcrkcHh4eCAsLq3LM1q1bMXLkSNjb20MikeDBgweVvp6SkoIFCxagQ4cOsLa2RqdOnbB69WqUlpY2xctschZmUgzvUn61H1dNJ2o4GxsbXLt2DdeuXYONjY3Y5RCRSAwmUAUFBWH37t2Ii4vD3r17kZiYiKlTp9bYvqioCDExMVi1ahViYmKwb98+3Lp1CyEhIVXaBQcH4/XXX6/2cW7evAmtVovPP/8c165dwwcffIAtW7bU2N4QVGxDc4yBioiIqFFIBANdiS48PByTJk2CSqWChYVFnY6JiopCQEAAUlNT4eXlVelrJ0+eRFBQEO7fvw9HR8daH2f9+vX47LPPkJSUVGMblUoFlUql+1yhUMDT0xP5+fmwt7evU71N5V6hCv3fOQpBAC68Pgpt7K1ErYeIiKilUigUcHBweOj7t8H0UP1VXl4edu3ahcDAwDqHKQDIz8+HRCJ5aGCqy+M4OTnV2mbdunVwcHDQ3Tw9PRv0nI3J2VaGPu0cAXDYj6ihioqK0KNHD/To0YNbzxCZMIMKVMuXL4dcLoezszPS0tJw4MCBOh9bUlKCFStWYNasWQ3qIUpMTMSmTZuwaNGiWtutXLkS+fn5ult6enq9n7MpVAz7cdV0ooYRBAHXr1/H9evXufUMkQkTNVCtWbMGEomk1lt0dLSu/bJly3Dp0iUcOXIEZmZmCAsLq9MvMLVajZkzZ0Kr1WLz5s31rjczMxPBwcGYNm0ann766VrbymQy2NvbV7q1JBWB6kxCLlRlGpGrISIiMmyiLpuwZMkSzJw5s9Y23t7euo9dXFzg4uKCrl27olu3bvD09MT58+cxePDgGo9Xq9WYPn06kpOTcfz48XoHm8zMTAQFBWHw4MHYunVrvR6jJenhYY829jLcVahwISkPw7u2FrskIiIigyVqoKoISPVR0TP114nff1cRpuLj43HixAk4OzvX67lu376NoKAg9OvXD9u3b4dUalAjpdWSSCQI8nHF91HpOH4zm4GKiIioAQwiGURGRuKTTz5BbGwsUlNTceLECcyaNQudOnWq1Dvl6+uL/fv3AwDKysowdepUREdHY9euXdBoNMjKykJWVlalNaSysrIQGxuLhIQEAMCVK1cQGxuLvLw8AOU9UyNHjoSnpyc2bNiAnJwc3eMYuqA/h/1OxGVz7gcREVEDGMRK6dbW1ti3bx9Wr14NpVIJd3d3BAcH4/vvv4dMJtO1i4uLQ35+PgAgIyMD4eHhAAA/P79Kj3fixAmMHDkSALBlyxasXbtW97Xhw4cDALZv3465c+fiyJEjSEhIQEJCAtq1a1fpcQw9hAzt7AJLMylS7xUhKVeJTq1txS6JiIjIIBnsOlSGpq7rWDS30G0XcDo+F/98rBsWDu8odjlEBqeoqEi39cz169e5WjqRkTHqdaio8XD5BKKGsbGxQUpKClJSUhimiEwYA5WJqwhUUSl5UJSoRa6GiIjIMDFQmbj2znJ0bC1HmVbAmfhcscshIiIySAxUhFEVmyXf4LAfkb6Ki4sxYMAADBgwAMXFxWKXQ0QiYaAi3fIJp25lQ6vlNQpE+tBqtYiOjkZ0dDS0Wq3Y5RCRSBioCAO8nWAnM0duYSn+uJ0vdjlEREQGh4GKYGEmxbCu5SvW82o/IiIi/TFQEQDgEd82AIDjN++KXAkREZHhYaAiAMBIn9aQSICrtxXIVpSIXQ4REZFBYaAiAICLrQy92zkCKN/bj4iIiOqOgYp0HvHhqulE9eHi4gIXFxexyyAiETFQkc6obuWB6nR8LlRlGpGrITIMcrkcOTk5yMnJgVwuF7scIhIJAxXp9PCwh6udDEWlGkQm54ldDhERkcFgoCIdiUSCIA77ERER6Y2BiiqpWDX9+M1sCAJXTSd6mOLiYowcORIjR47k1jNEJsxc7AKoZRnaxQWWZlKk3itCUq4SnVrbil0SUYum1Wpx6tQp3cdEZJrYQ0WV2MrMMbCjEwDgBIf9iIiI6oSBiqrgPCoiIiL9MFBRFY/8OY8qMjkPBSVqkashIiJq+RioqApvFzk6tpajTCvgdHyu2OUQERG1eAxUVC2umk5ERFR3DFRUrYphvxM3s1Gm4ZVLRLWxsbGBjY2N2GUQkYgYqKhaAzo4wVluiXvKUpxNvCd2OUQtllwuh1KphFKp5NYzRCaMgYqqZWEmxfje7gCAA5dui1wNERFRy8ZARTWa6NcWAPDrtSwUl3KzZCIiopowUFGN+no5wtPJGspSDY7euCt2OUQtUklJCcaPH4/x48ejpKRE7HKISCQMVFQjiUSCiX3Ke6kOxGaKXA1Ry6TRaHDo0CEcOnQIGg17colMFQMV1WqinwcA4NStbDwoKhW5GiIiopaJgYpq1aWNHbq720OtEXDoSpbY5RAREbVIDFT0UBW9VD/F8mo/IiKi6jBQ0UOF+HlAIinf2y/zQbHY5RAREbU4DFT0UO4O1gjwdgIAhF/m5HQiIqK/M5hAFRISAi8vL1hZWcHd3R2hoaHIzKz5zV2tVmP58uXo1asX5HI5PDw8EBYWVuWYrVu3YuTIkbC3t4dEIsGDBw9qfEyVSgU/Pz9IJBLExsY20iszDJP8ebUfERFRTQwmUAUFBWH37t2Ii4vD3r17kZiYiKlTp9bYvqioCDExMVi1ahViYmKwb98+3Lp1CyEhIVXaBQcH4/XXX39oDa+99ho8PDwa/FoM0aM93WBhJsGNOwrculsgdjlELYZcLocgCBAEgVvPEJkwiSAIgthF1Ed4eDgmTZoElUoFCwuLOh0TFRWFgIAApKamwsvLq9LXTp48iaCgINy/fx+Ojo5Vjv3ll1/w8ssvY+/evejRowcuXboEPz+/OterUCjg4OCA/Px82Nvb1/m4lmThV9H47fpdPB/UCcvG+YpdDhERUZOr6/u3wfRQ/VVeXh527dqFwMDAOocpAMjPz4dEIqk2MNXm7t27WLhwIb7++us67yivUqmgUCgq3QxdxdV+B2IzYaA5nIiIqEkYVKBavnw55HI5nJ2dkZaWhgMHDtT52JKSEqxYsQKzZs3Sq4dIEATMnTsXixYtQv/+/et83Lp16+Dg4KC7eXp61vnYlmp0tzaQW5oh434xYtLui10OUYtQUlKCadOmYdq0adx6hsiEiRqo1qxZA4lEUustOjpa137ZsmW4dOkSjhw5AjMzM4SFhdWpp0StVmPmzJnQarXYvHmzXjVu2rQJCoUCK1eu1Ou4lStXIj8/X3dLT0/X6/iWyMrCDON6ugEAfrrEyelEQPnWMz/++CN+/PFHbj1DZMLMxXzyJUuWYObMmbW28fb21n3s4uICFxcXdO3aFd26dYOnpyfOnz+PwYMH13i8Wq3G9OnTkZycjOPHj+s9f+n48eM4f/48ZDJZpfv79++P2bNnY+fOndUeJ5PJqhxjDCb5tcW+mNv4+codvDmhOyzMDKqTk4iIqEmIGqgqAlJ9VPRMqVSqGttUhKn4+HicOHECzs7Oej/Pxx9/jLffflv3eWZmJsaNG4cffvgBAwcO1L9wAxfYyRkutpbILSzFmfhcBPm6il0SERGR6EQNVHUVGRmJyMhIDB06FK1atUJSUhLefPNNdOrUqVLvlK+vL9atW4fJkyejrKwMU6dORUxMDA4ePAiNRoOsrPK96JycnGBpaQkAyMrKQlZWFhISEgAAV65cgZ2dHby8vODk5FTlakBbW1sAQKdOndCuXbvmePktirmZFI/39sCOiBQciL3NQEVERAQDmZRubW2Nffv2YdSoUfDx8cH8+fPRs2dPnDp1qtKwWlxcHPLz8wEAGRkZCA8PR0ZGBvz8/ODu7q67RURE6I7ZsmUL/P39sXDhQgDA8OHD4e/vj/Dw8OZ9kQakYpHPI9fvoqi0TORqiIiIxGew61AZGmNYh6qCIAgYueEkUu8V4aOZfpjo11bskohEo1QqdT3XhYWFXNyTyMgY9TpUJC6JRKILUdyKhoiIiIGK6qlikc/fb+UgT1kqcjVE4rGxsUFhYSEKCwvrvPAvERkfBiqql06tbdGrrQPKtAJ+vnJH7HKIRCORSCCXyyGXyyGRSMQuh4hEwkBF9VbRSxUee1vkSoiIiMTFQEX1NqGPByQSICrlPjLuF4ldDpEoVCoV5s6di7lz59a6Lh4RGTcGKqq3NvZWGNyxfLHU8MucnE6mqaysDDt37sTOnTtRVsZlRIhMFQMVNcikiqv9uLcfERGZMAYqapBxPd1gaSZF3N0C3MxSiF0OERGRKBioqEEcrC3wyJ/bz/zEXioiIjJRDFTUYBVX+/33cia0Wi68T0REpoeBihosyNcVdjJz3H5QjOjU+2KXQ0RE1OwYqKjBrCzMENzTDQBwgGtSERGRCWKgokYxyb/8ar+fr9xBaZlW5GqImo+NjQ2ys7ORnZ3NrWeITBgDFTWKQR2d4Wonw4MiNX6/lSN2OUTNRiKRoHXr1mjdujW3niEyYQxU1CjMpBJM6FM+Of0AF/kkIiITw0BFjabiar/frmehUMUVo8k0qFQqPP/883j++ee59QyRCWOgokbTq60DOrrIUaLW4rfrWWKXQ9QsysrKsHnzZmzevJlbzxCZMAYqajQSiQQhf/ZScZFPIiIyJQxU1Kgm/rm335mEXOQWcviDiIhMAwMVNaoOLnL0aecAjVbAz3/cEbscIiKiZsFARY2uopeKi3wSEZGpYKCiRvd4H3dIJUBM2gOk3SsSuxwiIqImx0BFjc7VzgpDOrsAAMIvs5eKiIiMHwMVNYmQPxf5/Ck2E4IgiFwNUdOxtrZGcnIykpOTYW1tLXY5RCQSBipqEsE93WBpLkVCdiGu31GIXQ5Rk5FKpfD29oa3tzekUv5KJTJV/OmnJmFnZYHR3VwBAAdiuSYVEREZNwYqajIVV/uFx2ZCq+WwHxmn0tJSLFu2DMuWLUNpaanY5RCRSBioqMmM9GkNeytzZClKcCE5T+xyiJqEWq3Ghg0bsGHDBqjVarHLISKRMFBRk5GZm+GxXu4AeLUfEREZN70DVXJyclPUQUaqYm+/n/+4A1WZRuRqiIiImobegapz584ICgrCN998g5KSkqaoiYzIwA7OcLO3gqKkDKficsQuh4iIqEnoHaguX74Mf39/vPLKK3Bzc8Ozzz6LyMjIpqiNjICZVIIJfcqH/Xi1HxERGSu9A1XPnj2xceNG3L59G9u3b0dWVhaGDh2KHj16YOPGjcjJYS8EVVZxtd/RG3dRUMJJu0REZHzqPSnd3NwckydPxu7du/Huu+8iMTERr776Ktq1a4ewsDDcuXOnMetESEgIvLy8YGVlBXd3d4SGhiIzs+YeD7VajeXLl6NXr16Qy+Xw8PBAWFhYlWO2bt2KkSNHwt7eHhKJBA8ePKj28X7++WcMHDgQ1tbWcHFxwRNPPNGYL8+o9fCwR2dXW6jKtPj12l2xyyEiImp09Q5U0dHRWLx4Mdzd3bFx40a8+uqrSExMxPHjx3H79m1MnDixMetEUFAQdu/ejbi4OOzduxeJiYmYOnVqje2LiooQExODVatWISYmBvv27cOtW7cQEhJSpV1wcDBef/31Gh9r7969CA0Nxbx583D58mWcPXsWs2bNarTXZuwkEgkm/rkVzYFYXu1HxsXa2hpXr17F1atXufUMkQmTCHputLZx40Zs374dcXFxeOyxx/D000/jscceq7TlQkJCAnx9fVFWVtboBVcIDw/HpEmToFKpYGFhUadjoqKiEBAQgNTUVHh5eVX62smTJxEUFIT79+/D0dFRd39ZWRm8vb2xdu1aLFiwoN71KhQKODg4ID8/H/b29vV+HEOVdq8Iw9efgFQCnH99FFztrMQuiYiI6KHq+v6tdw/VZ599hlmzZiEtLQ0//fQTHn/88Sr7V3l5eWHbtm36V11HeXl52LVrFwIDA+scpgAgPz8fEomkUmB6mJiYGNy+fRtSqRT+/v5wd3fHo48+imvXrtV6nEqlgkKhqHQzZV7ONvD3coRWKF9CgYiIyJjoHaji4+OxcuVKuLm51djG0tISc+bMaVBh1Vm+fDnkcjmcnZ2RlpaGAwcO1PnYkpISrFixArNmzdKrhygpKQkAsGbNGrzxxhs4ePAgWrVqhREjRiAvr+bVv9etWwcHBwfdzdPTs87Paawm/Tk5/Sde7UdGpLS0FGvWrMGaNWu49QyRCdM7UP3xxx/V3q5cuYL4+HioVKo6P9aaNWsgkUhqvUVHR+vaL1u2DJcuXcKRI0dgZmaGsLAw1GXEUq1WY+bMmdBqtdi8ebNer1er1QIA/vnPf2LKlCno168ftm/fDolEgj179tR43MqVK5Gfn6+7paen6/W8xmh8b3eYSSW4nP4AKblKscshahRqtRpr167F2rVrufUMkQkz1/cAPz8/SCSSGr9uYWGBGTNm4PPPP4eVVe3zZJYsWYKZM2fW2sbb21v3sYuLC1xcXNC1a1d069YNnp6eOH/+PAYPHlzj8Wq1GtOnT0dycjKOHz+u9/wld/fyNZS6d++uu08mk6Fjx45IS0ur8TiZTAaZTKbXcxk7F1sZhnZ2walbOTgQm4l/jO4idklERESNQu8eqv3796NLly7YunUrYmNjcenSJWzduhU+Pj749ttvsW3bNhw/fhxvvPHGQx/LxcUFvr6+td5qCmUVPVO19YhVhKn4+HgcPXoUzs7O+r5c9OvXDzKZDHFxcZUeNyUlBe3bt9f78UzdxD+3ojlw+XadeheJiIgMgd49VO+88w4++ugjjBs3Tndf79690a5dO6xatQqRkZGQy+V45ZVXsGHDhkYpMjIyEpGRkRg6dChatWqFpKQkvPnmm+jUqVOl3ilfX1+sW7cOkydPRllZGaZOnYqYmBgcPHgQGo0GWVlZAAAnJydYWloCALKyspCVlYWEhAQAwJUrV2BnZwcvLy84OTnB3t4eixYtwurVq+Hp6Yn27dtj/fr1AIBp06Y1yuszJWN7uMHK4gqScpS4eluBXu0cxC6JiIiowfTuobpy5Uq1PTPt27fHlStXAJQPCzbmwp7W1tbYt28fRo0aBR8fH8yfPx89e/bEqVOnKg2rxcXFIT8/HwCQkZGB8PBwZGRkwM/PD+7u7rpbRESE7pgtW7bA398fCxcuBAAMHz4c/v7+CA8P17VZv349Zs6cidDQUAwYMACpqak4fvw4WrVq1Wiv0VTYyswxpnv5BQ3fR9U8ZEpERGRI9F6Hyt/fH3369MHWrVt1vTxqtRoLFy7E5cuXcenSJZw9exZPPfUUkpOTm6RoQ2Tq61D91fmke5i59TysLcxwfuUoONjUfekLopZGqVTC1tYWAFBYWAi5XC5yRUTUmOr6/q33kN+nn36KkJAQtGvXDr1794ZEIsEff/wBjUaDgwcPAihfamDx4sX1r56M2sAOTvB1s8PNrALsjk7HwuEdxS6JiIioQfTuoQLK/wr75ptvcOvWLQiCAF9fX8yaNQt2dnZNUaNRYA9VZT9EpWH53ito18oap5YFwUxa85WjRC2ZRqNBTEwMAKBv374wMzMTuSIiakx1ff/WK1Cp1Wr4+Pjg4MGDlZYRoIdjoKqsRK3BoHXH8KBIja2h/TC2R80LxRIREYmlSbaesbCwgEqlqnUdKqK6sLIww5MB5fsp7ohIEbcYIiKiBtL7Kr8XXngB7777bpNufEym4alB7WEmlSAi8R7isgrELoeoXkpLS7F+/XqsX7+eW88QmTC951BNnjwZx44dg62tLXr16lXlipZ9+/Y1aoHGgkN+1Vu86yIOXcnCkwFeWPdEL7HLIdIbr/IjMm5NdpWfo6MjpkyZ0qDiiCrMDeyAQ1eysP9SBpYH+8DRxlLskoiIiPSmd6Davn17U9RBJmqAdyv08LDHtUwFfohKx7MjOoldEhERkd70nkMFAGVlZTh69Cg+//xzFBSUz33JzMxEYWFhoxZHxk8ikWBuoDcA4KtzqSjTaMUtiIiIqB70DlSpqano1asXJk6ciOeffx45OTkAgPfeew+vvvpqoxdIxm9CHw84yS1x+0Exjt7IFrscIiIivekdqP7xj3+gf//+uH//PqytrXX3V0xWJ9KXlYUZZumWUOB2RUREZHj0DlRnzpzBG2+8odvHr0L79u1x+/btRiuMTEvFEgrnk/Jw445C7HKIiIj0oneg0mq10Gg0Ve7PyMjg1jNUb24OVni0Z/lq6TvOpohbDJEerKyscOLECZw4cQJWVlZil0NEItE7UI0ZMwYffvih7nOJRILCwkKsXr0ajz32WGPWRiZm3hBvAMBPsbeRp+QCiWQYzMzMMHLkSIwcOZL7+BGZML0D1QcffIBTp06he/fuKCkpwaxZs+Dt7Y3bt2/j3XffbYoayUT09WqFXm0doCrT4vuoNLHLISIiqjO9V0oHgOLiYnz33XeIiYmBVqtF3759MXv27EqT1KkyrpReN3svZuCVPZfh7mCF068FwdysXit7EDUbtVqNrVu3AgCeeeYZWFhYiFwRETWmur5/1ytQkf4YqOpGVabBkP8cR25hKTbP7ovHermLXRJRrbj1DJFxa7KtZwDg1q1bOHnyJLKzs6HVVl6I8c0336zPQxIBAGTm5UsofHw8ATvOpjBQERGRQdA7UH3xxRd47rnn4OLiAjc3N0gkEt3XJBIJAxU12OxB7bH5ZCIiU/Jw9XY+erZ1ELskIiKiWukdqN5++2288847WL58eVPUQ4Q29lZ4rJc7wi9nYmdECtZP6yN2SURERLXSe8bv/fv3MW3atKaohUhn7p9LKBy4nIl7hSpxiyEiInoIvQPVtGnTcOTIkaaohUinr1cr9PF0RGmZFt9HpYtdDhERUa30HvLr3LkzVq1ahfPnz6NXr15VLhFeunRpoxVHpm1eoDde/CEWX59LxTPDO8KCSygQEVELpfeyCR06dKj5wSQSJCUlNbgoY8RlE/RXWqbFkHePI6dAhU1P+mNCHw+xSyKqoqysDL/++isAYNy4cTA3r9fF00TUQjXZsgnJyckNKoyorizNpZg90AsfHo3HjogUBipqkczNzTF+/HixyyAikXEMhVq0WQO9YGEmwcXU+/gj44HY5RAREVWrzoGqe/fuyMvL033+zDPPICcnR/d5dnY2bGxsGrc6MnmudlZ4vHd5z9SOiBRxiyGqhlqtxo4dO7Bjxw6o1WqxyyEikdQ5UN28eRNlZWW6z7///nsUFBToPhcEASUlJY1bHRGAuYHeAICDl+8gp4BLKFDLUlpainnz5mHevHkoLS0VuxwiEkm9h/yqm8v+11XTiRpLH09H+Hs5olSjxXeRaWKXQ0REVAXnUJFBqOil+uZ8KkrLtLU3JiIiamZ1DlQSiaRKDxR7pKi5PNrTHa52MmQXqPDL1Ttil0NERFRJnZdNEAQBo0aN0q2xUlxcjAkTJsDS0hIAKs2vImpsluZSPDWoPTb+dgs7IlIw0a+t2CURERHp1DlQrV69utLnEydOrNJmypQpDa+IqAZPBnjhk+MJuJT2ALHpD+Dn6Sh2SURERAAaEKiaW0hICGJjY5GdnY1WrVph9OjRePfdd+HhUf1ij2q1Gm+88QYOHTqEpKQkODg4YPTo0fjPf/5T6ZitW7fi22+/RUxMDAoKCnD//n04OjpWeqxbt25h2bJlOHv2LEpLS9GrVy+8/fbbCAoKasqXTH/T2k6Gx/u4Y1/MbeyMSIHfDD+xSyIiIgJgQJPSg4KCsHv3bsTFxWHv3r1ITEzE1KlTa2xfVFSEmJgYrFq1CjExMdi3bx9u3bqFkJCQKu2Cg4Px+uuv1/hY48ePR1lZGY4fP46LFy/Cz88Pjz/+OLKyshrt9VHdzAss3/ro4B+ZyFZwmQ4Sn0wmw+7du7F7927IZDKxyyEySbfuFmBnREq1KxA0F7338mspwsPDMWnSJKhUqiobNNckKioKAQEBSE1NhZeXV6WvnTx5EkFBQVV6qHJzc9G6dWv8/vvvGDZsGACgoKAA9vb2OHr0KEaNGlXtc6lUKqhU/1szSaFQwNPTk3v5NYIpn0XgYup9/GNUF7w0pqvY5RARkYiyC0ow+dMI3H5QjDUTumPukJr3HK6Puu7lZzA9VH+Vl5eHXbt2ITAwsM5hCgDy8/MhkUiqDOnVxtnZGd26dcNXX30FpVKJsrIyfP7552jTpg369etX43Hr1q2Dg4OD7ubp6Vnn56TazRviDQDYdSENqjKNuMUQEZFoikrL8PTOaNx+UIwOLnJRL1gyqEC1fPlyyOVyODs7Iy0tDQcOHKjzsSUlJVixYgVmzZqlVw+RRCLBb7/9hkuXLsHOzg5WVlb44IMPcPjw4VqD2cqVK5Gfn6+7paen1/k5qXbjerjBzd4KuYUqHLrCJRRIXGVlZdizZw/27NnDq52JmpFGK+Af38fij4x8tLKxwPa5A9BKbilaPaIGqjVr1ujWt6rpFh0drWu/bNkyXLp0CUeOHIGZmRnCwsLqNF6qVqsxc+ZMaLVabN68Wa8aBUHA4sWL4erqitOnTyMyMhITJ07E448/jjt3an4zl8lksLe3r3SjxmFhJkXo4PYAgO1nxR0zJ1KpVJg+fTqmT59eaZifiJrWOz/fwG/X78LSXIovwvrD20Uuaj11mkP18ccf1/kBly5dWue2ubm5yM3NrbWNt7c3rKysqtyfkZEBT09PREREYPDgwTUer1arMX36dCQlJeH48eNwdnautl1Nc6iOHTuGsWPH4v79+5VCUZcuXbBgwQKsWLHiIa+yXF3HYKlu7hWqMPg/x1FapsW+xYHo69VK7JLIRCmVStja2gIACgsLIZeL+0udyBTsjEjB6vBrAIBNT/pjQp/qr/hvDHV9/67TsgkffPBBnZ5UIpHoFahcXFzg4uJS5/Z/VZEDa/uLsCJMxcfH48SJEzWGqdoUFRUBAKTSyp15UqkUWi23QBGLs60ME/t4YM/FDOw4m8JARURkIo7duIu1/y0PU8vG+TRpmNJHnQJVcnJyU9dRq8jISERGRmLo0KFo1aoVkpKS8Oabb6JTp06Veqd8fX2xbt06TJ48GWVlZZg6dSpiYmJw8OBBaDQa3TIHTk5OuhXes7KykJWVhYSEBADAlStXYGdnBy8vLzg5OWHw4MFo1aoV5syZgzfffBPW1tb44osvkJycjPHjxzf/ySCdOYHe2HMxA4eu3ME/x3dDG/uqPZlERGQ8rt7Ox5JvL0ErADP6e2LxyE5il6RjEJPSra2tsW/fPowaNQo+Pj6YP38+evbsiVOnTlVa9yUuLg75+fkAyocEw8PDkZGRAT8/P7i7u+tuERERumO2bNkCf39/LFy4EAAwfPhw+Pv7Izw8HEB5L9rhw4dRWFiIRx55BP3798eZM2dw4MAB9OnTpxnPAv1dz7YOCPB2QplWwK7zqWKXQ0RETSjzQTHm74hCsVqDYV1c8Pbkni1qT+F6rUNVEVbS0tJQWlpa6WsbN25stOKMCedQNY1DV+5g8a4YOMstEbHyEcjMzcQuiUwM51ARNb2CEjWmbTmHm1kF8Gljhz3PDYa9Vd2XTWqIRp1D9VfHjh1DSEgIOnTogLi4OPTs2RMpKeVXWvXt27dBRRPpa2z3NnB3sMKd/BIcvHwHU/q1E7skIiJqRGqNFot3xeBmVgFa28nw5bwBzRam9KH3kN/KlSvxyiuv4OrVq7CyssLevXuRnp6OESNGYNq0aU1RI1GNzP+yhMIOkbcdINNkaWmJ7du3Y/v27bq5mUTUOARBwJsHruJ0fC6sLczw5ZwBaOtoLXZZ1dI7UN24cQNz5swBAJibm6O4uBi2trb417/+hXfffbfRCyR6mJkDvCAzl+LK7XxcTL0vdjlkYiwsLDB37lzMnTtXr50biOjhtpxKwneR6ZBIgI+f9Eevdg5il1QjvQOVXC7XLVXg4eGBxMRE3dcetqYUUVNwklti0p/bDWyPSBG3GCIiahQH/8jEu4dvAgDefLw7xnRvI3JFtdM7UA0aNAhnz54FAIwfPx6vvPIK3nnnHcyfPx+DBg1q9AKJ6mJOoDcA4PDVLNzJLxa3GDIpZWVl+Pnnn/Hzzz9z6xmiRnIxNQ8v774MAJgb6I15jbzhcVPQe1L6xo0bUVhYCKB865jCwkL88MMP6Ny5c50XACVqbN097DGwgxMuJOfhm/OpWDbOV+ySyESoVCo8/vjjAMqv8jM31/vXKhH9Reo9JRZ+dRGlZVqM7tYGqx7vLnZJdaL3T37Hjh11H9vY2Oi9Nx5RU5k3xBsXkvPw7YU0PDeyM2xlfGMjIjIk95WlmLc9CnnKUvRq64CPn/SDmbTlrDVVG72H/Dp27Ih79+5Vuf/BgweVwhZRcxvdrQ06uMhxv0iNbafFXd2fiIj0oyrT4NmvLyIpV4m2jtbYNqc/bCwN5w9jvQNVSkoKNBpNlftVKhVu377dKEUR1Ye5mRSvjO0KAPjidBLuFda8zyMREbUcgiDgtR//QGRKHuxk5vhy7gC4Gth2YnWOfhVbsQDAr7/+CgeH/126qNFocOzYMXh7ezdqcUT6eqynO3q2TcTV2wpsPploMGPvRESmbONvt3AgNhPmUgk2P9UXPm52YpektzoHqkmTJgEAJBKJbh2qChYWFvD29sb777/fqMUR6UsqleC1cb4I+zISX59LxfyhHVrsInBERATsjk7HpuMJAIB3JvfEsC6tRa6ofuo85KfVaqHVauHl5YXs7Gzd51qtFiqVCnFxcborXYjENKyLCwZ3dEapRosPf7sldjlERFSDswm5eH3fFQDA4pGdMGOAl8gV1Z/ec6iSk5Ph4uLSFLUQNQqJRILXgn0AAHtjMhB/t0DkisiYWVpa4pNPPsEnn3zCrWeI9BB/twCLvrmIMq2Ax3u749WxPmKX1CB6ByoAOHXqFCZMmIDOnTujS5cuCAkJwenTpxu7NqJ68/dqhXE92kArABuOxIldDhkxCwsLPP/883j++ee59QxRHWUXlGDu9igUlJShf/tW2DCtD6QGsjxCTfQOVN988w1Gjx4NGxsbLF26FEuWLIG1tTVGjRqFb7/9tilqJKqXV8f6QCoBfr12F5fSuMcfEVFLUFyqwcKd0bj9oBjezjbYGtYfVhZmYpfVYBJBEAR9DujWrRueeeYZvPTSS5Xu37hxI7744gvcuHGjUQs0FgqFAg4ODsjPz4e9vb3Y5ZiMZXsuY8/FDAzu6IxvFw6ERGLYfwFRy6PRaHQ99MOGDYOZmeG/MRA1FY1WwHPfXMSR63fhaGOB/YuHoIOLXOyyalXX92+9e6iSkpIwYcKEKveHhIQgOZmLKVLL8uKYrrA0k+Jc0j2cSeDm3dT4SkpKEBQUhKCgIJSUlIhdDlGL9u9DN3Dk+l1YmknxRVj/Fh+m9KF3oPL09MSxY8eq3H/s2DF4eno2SlFEjaWtozVCB7cHALx3OA5arV4dskRE1Ei2nUnGtjPlHS/rp/XGAG8nkStqXHVeh2r+/Pn46KOP8Morr2Dp0qWIjY1FYGAgJBIJzpw5gx07duCjjz5qylqJ6mXxyE74ISodV27n45erWRjf213skoiITMreixl46+B1AMCycT6Y6NdW5IoaX53nUJmZmeHOnTtwdXXF/v378f777+vmS3Xr1g3Lli3DxIkTm7RYQ8Y5VOL66Gg8Pjh6Cx1c5Djy0nBYmNXrAleiKpRKJWxtbQEAhYWFkMuNZwiDqDEcvX4Xz35zERqtgAVDO+CN8d0Maj5rXd+/69xD9dfcNXnyZEyePLlhFRI1owXDOuCrcylIzlXix4sZeDLAcBePIyIyFBeS7uH5b2Og0Qp4om9b/PMxwwpT+tDrz3RjPQlk/Gxl5ng+qDMA4MOjt1CirrrBNxERNZ5rmfl4emc0VGVajO7minen9Db4taZqU+ceKgDo2rXrQ0NVXl5egwoiaiqzB3lh25lk3H5QjJ0RKXh2RCexSyIiMkrJuUrM+TISBaoyBHg74ZNZfY1+qoVegWrt2rVwcHBoqlqImpTM3AwvjemKV/dcxuaTiZgZ4AUHa65sTQ1jYWGB9957T/cxkam7qyhB6LYLyC0sRTd3e/zfXONYuPNh6jwpXSqVIisrC66urk1dk1HipPSWQaMVEPzh74jPLsTzQZ2wbJyv2CURERmNB0WlmPH5ecTdLYC3sw32LApEazuZ2GU1SKMv7Mn5U2QMzKQSLBtXvgHnl2dSkK3gQoxERI2hqLQM83dEIe5uAVztZPh6wUCDD1P6qHOg0nOHGqIWa0z3NvD3ckSxWoNNxxPELocMnEajQVRUFKKioqDR8GIHMk2lZVo8900MYtIewN7KHF8vGAhPJxuxy2pWdQ5UWq2Ww31kFCQSCZYHlw/1fReZhtR7SpErIkNWUlKCgIAABAQEcOsZMklarYBX9lzGqVs5sLYww/Z5AfBxsxO7rGZn3FPuiWowqKMzRnRtjTKtgI2/3RK7HCIigyQIAtb89xr+ezkT5lIJPnuqL/q1byV2WaJgoCKTVTGX6kBsJq5l5otcDRGR4fnwaDy+OpcKiQTYOMMPI31MdySLgYpMVs+2DpjQxwMAsOHXOJGrISIyLDvOJuOjY/EAgH9N7ImQP3+fmioGKjJpr4zpCnOpBCfichCZzEVpiYjq4qdLt7Hmv+WbHb88pitCB7UXuSLxGUygCgkJgZeXF6ysrODu7o7Q0FBkZmbW2F6tVmP58uXo1asX5HI5PDw8EBYWVumYvLw8vPDCC/Dx8YGNjQ28vLywdOlS5OdXHv65f/8+QkND4eDgAAcHB4SGhuLBgwdN9VKpGXm7yDFjgCcA4L3DN3k1KxHRQ5y4mY1X91wGAMwN9MYLj3QWuaKWwWACVVBQEHbv3o24uDjs3bsXiYmJmDp1ao3ti4qKEBMTg1WrViEmJgb79u3DrVu3EBISomuTmZmJzMxMbNiwAVeuXMGOHTtw+PBhLFiwoNJjzZo1C7GxsTh8+DAOHz6M2NhYhIaGNtlrpea1dFQXWFlIEZ16H8dvZotdDhFRixWdkofndl1EmVbAJD8PvPl4d65T+ac6r5Te0oSHh2PSpElQqVR13u4hKioKAQEBSE1NhZeXV7Vt9uzZg6eeegpKpRLm5ua4ceMGunfvjvPnz2PgwIEAgPPnz2Pw4MG4efMmfHx86vTcXCm9ZXv38E18djIRPm3scOgfw2BmxBt4UuMqLS3Fv//9bwDA66+/DktLS5ErImoaN+4oMOPzc1CUlOERX1d8HtrP6PfnA+r+/q3XXn4tRV5eHnbt2oXAwEC99s7Kz8+HRCKBo6NjrW3s7e1hbl5+as6dOwcHBwddmAKAQYMGwcHBARERETUGKpVKBZVKpftcoVDUuU5qfouGd8Ku86mIu1uA8Mu3Mdm/ndglkYGwtLTEmjVrxC6DqEml3StC2JeRUJSUoX/7VvjUBDY71pdBnY3ly5dDLpfD2dkZaWlpOHDgQJ2PLSkpwYoVKzBr1qwaE+a9e/fw1ltv4dlnn9XdV9P+ha6ursjKyqrx+datW6ebc+Xg4ABPT88610rNz8HGAs+NLJ8H8P6RWygt04pcERFRy5BdUIKntl1AToEKvm522DZ3AKwtjX+zY32JGqjWrFkDiURS6y06OlrXftmyZbh06RKOHDkCMzMzhIWF1WkSsVqtxsyZM6HVarF58+Zq2ygUCowfPx7du3fH6tWrK32tuvFhQRBqHTdeuXIl8vPzdbf09PSH1knimhvoDVc7GTLuF+O7yDSxyyEDodVqce3aNVy7dg1aLYM4GZf8YjXCtkUiLa8IXk42+Gp+ABys6z4yZEpEHfJbsmQJZs6cWWsbb29v3ccuLi5wcXFB165d0a1bN3h6eurmM9VErVZj+vTpSE5OxvHjx6vtnSooKEBwcDBsbW2xf//+SsOIbm5uuHv3bpVjcnJy0KZNmxqfVyaTQSYznU0hjYG1pRmWjuqCN366ik3H4zG1XzvIZQY5Kk7NqLi4GD179gQAFBYWQi6Xi1wRUeMoLtXg6Z1RuJlVgNZ2MnyzYCBc7a3ELqvFEvXdoiIg1UdFz9Rf5yn9XUWYio+Px4kTJ+Ds7FyljUKhwLhx4yCTyRAeHg4rq8r/WQYPHoz8/HxERkYiICAAAHDhwgXk5+cjMDCwXrVTyzVjgCe+OJ2E1HtF+PJMMl4Y1UXskoiImp1ao8Xz38YgKuU+7KzM8dX8AHg5m9Zmx/oyiDlUkZGR+OSTTxAbG4vU1FScOHECs2bNQqdOnSr1Tvn6+mL//v0AgLKyMkydOhXR0dHYtWsXNBoNsrKykJWVhdLSUgDlPVNjx46FUqnEtm3boFAodG0qdo3v1q0bgoODsXDhQpw/fx7nz5/HwoUL8fjjj9f5Cj8yHBZmUrwytvz7uvX3JOQpS0WuiIioeWm1ApbtuYzjN7NhZSHFl3MHoJs7r05/GIMIVNbW1ti3bx9GjRoFHx8fzJ8/Hz179sSpU6cqDavFxcXpFuXMyMhAeHg4MjIy4OfnB3d3d90tIiICAHDx4kVcuHABV65cQefOnSu1+eucp127dqFXr14YO3Ysxo4di969e+Prr79u3pNAzebxXu7o7m6PAlUZPjuZIHY5RETNRhAE/OvgdfwU++dmx7P7YYC3k9hlGQSDXYfK0HAdKsNyMi4bc7dHwdJcipOvjoSHo7XYJVELpVQqYWtrC4BzqMiwCYKAtw7ewJdnkwEAH87wwyT/tiJXJb66vn8bRA8VUXMb0bU1BnZwQmmZFh8djRe7HCKiJvX3MLXuiV4MU3pioCKqhkQiwWvBvgCAPRfTkZBdKHJFRERNQxAEvP1z5TD1ZED1u4lQzRioiGrQr30rjOneBloBeP9InNjlUAtlYWGBV199Fa+++qpeOzcQtQQVYWrbmfIw9e/JDFP1xTlUzYRzqAzTrbsFGPfh7xAE4MDzQ9DH01HskoiIGoUgCHjn5xv4v7+EqVkDGab+jnOoiBpB1zZ2eOLPff3e+/WmyNUQETWOv4epdyb3ZJhqIAYqood4cXQXWJpJcTbhHk7H54hdDrUwWq0WKSkpSElJ4dYzZBAEQcC/D1UOU7MHthe5KsPHQEX0EJ5ONpg9qPwvtzd+uoqi0jKRK6KWpLi4GB06dECHDh1QXFwsdjlEtaoIU1+cLg9Tb09imGosDFREdfDSmK7wcLBC6r0ivHeYE9SJyPAIgoB1v9zUham3JvXEU4MYphoLAxVRHdhbWeA/U3oDAHZEpOB80j2RKyIiqjtBEPCfX25i6+9JAMrDVCjDVKNioCKqo+FdW+suJ17242UoVRz6I6KWryJMfV4Rpib2YJhqAgxURHp4/TFftHW0RnpeMf7zC6/6I6KWTRAE/Ofw38LUYG9xizJSDFREerCzssC7fw79fX0+FREJuSJXRERUPV2YOlUepv7FMNWkGKiI9DS0iwtmD6wY+vsDhRz6I6IWRhAEvHs4rlKYCmOYalIMVET1sPKxbmjXyhq3HxRj3aEbYpdDIjI3N8fixYuxePFimJubi10OkS5MbTmVCIBhqrlw65lmwq1njE9EYi5mfXEBAPDNgoEY2sVF5IqIyNQJgoD3fo3DZyfLw9TakB6YE+gtblEGjlvPEDWxwE4uCBtcfqXM8r1/oKBELXJFRGTKGKbExUBF1ADLg33h6VQ+9PdvDv2ZJEEQkJOTg5ycHLDDn8QiCALW/yVMrZnQnWGqmTFQETWAXGaO9VP7AAC+i0zH77e415+pKSoqgqurK1xdXVFUVCR2OWSCKsLU5r+EqblDOohclelhoCJqoEEdnTH3z78El+/9AwoO/RFRMxEEARuO/C9MrWaYEg0DFVEjeC3YB+2dbXAnvwTvHOTQHxE1vYow9emJ/4WpeQxTomGgImoENpblQ38SCfBDdDpOxGWLXRIRGTFBEPD+kVu6MPXm4wxTYmOgImokAR2cMC+w/Bfayr1XkF/MoT8ianxarYB3fr6BT04kAABWPd4d84cyTImNgYqoES0b54MOLnJkKUrw1sHrYpdDREZGrdHilT2X8X9nkgGU90wtYJhqERioiBqRtaUZ1k/tDYkE+PFiBo7fvCt2SURkJIpKy7Dwq2jsv3QbZlIJ3p/Whz1TLQgDFVEj6+/thAV/zmVYsfcK8os49GfMzM3NMWfOHMyZM4dbz1CTua8sxez/u4CTcTmwspDii7B+mNKvndhl0V9w65lmwq1nTEuJWoPHPjqNpFwlnujbFhun+4ldEhEZqMwHxQj7MhIJ2YVwsLbAl3P7o197J7HLMhnceoZIRFYWZlg/rQ+kEmBfzG38dp1Df0Skv4TsAkz5LAIJ2YVws7fCnkWDGaZaKAYqoibSr30rLBzWEQDw+v4reFBUKnJF1BQEQYBSqYRSqeTWM9SoYtLuY+qWc7iTX4JOreXYuzgQXdvYiV0W1YCBiqgJvTSmKzq1liOnQIU14dfELoeaQFFREWxtbWFra8utZ6jRnIjLxqwvzuNBkRp+no7YsygQbR2txS6LasFARdSErCzMsOHPob+fYjPx67UssUsiohZu/6UMLNwZjRK1FsO7tsa3CwfCSW4pdln0EAxURE3M36sVnhneCQDwz/1XkKfk0B8RVe//TifhpR8uo0wrYKKfB/4vrD9sLHn1qCFgoCJqBi+O7oIurrbILSzFag79EdHfCIKAdb/cwNs/l+8FOn9IB3ww3Q+W5nybNhT8ThE1g4qhPzOpBP+9nIlfrtwRuyQiaiHKNFq89uMf+PxUEoDyzdZXPd4NUqlE5MpIHwYTqEJCQuDl5QUrKyu4u7sjNDQUmZmZNbZXq9VYvnw5evXqBblcDg8PD4SFhVU6Ji8vDy+88AJ8fHxgY2MDLy8vLF26FPn5+bo2KSkpWLBgATp06ABra2t06tQJq1evRmkph21IP308HbFoRPlVf2/8dBX3ClUiV0REYisu1WDRNxex52IGpBLgvSm9sXhkZ0gkDFOGxmACVVBQEHbv3o24uDjs3bsXiYmJmDp1ao3ti4qKEBMTg1WrViEmJgb79u3DrVu3EBISomuTmZmJzMxMbNiwAVeuXMGOHTtw+PBhLFiwQNfm5s2b0Gq1+Pzzz3Ht2jV88MEH2LJlC15//fUmfb1knJaO6gKfNna4pyzFmxz6IzJp+UVqhG67gKM3siEzl+Lz0P6YPsBT7LKongx2pfTw8HBMmjQJKpUKFhYWdTomKioKAQEBSE1NhZeXV7Vt9uzZg6eeegpKpbLGbSTWr1+Pzz77DElJSXWulyulU4UrGfmYtPksNFoBn87qi/G93cUuiRqgpKQEoaGhAICvv/4aVlZWIldEhiArvwRzvoxE3N0C2FmZY9ucAQjowAU7W6K6vn8b5KUDeXl52LVrFwIDA+scpgAgPz8fEokEjo6Otbaxt7evdU+u/Px8ODnV/h9fpVJBpfrfkI5CoahznWTcerVzwPMjO+Hj4wlYdeAqBnZ0goutTOyyqJ6srKywZ88escsgA5KYU4iwbZG4/aAYrnYyfLUgAL5u/EPb0BnMkB8ALF++HHK5HM7OzkhLS8OBAwfqfGxJSQlWrFiBWbNm1Zgw7927h7feegvPPvtsjY+TmJiITZs2YdGiRbU+37p16+Dg4KC7eXqyG5f+Z8kjXeDrZoc8ZSlW/XSVK2wTmYjL6Q8wbcs53H5QjA4ucux9LpBhykiIGqjWrFkDiURS6y06OlrXftmyZbh06RKOHDkCMzMzhIWF1emNSK1WY+bMmdBqtdi8eXO1bRQKBcaPH4/u3btj9erV1bbJzMxEcHAwpk2bhqeffrrW51y5ciXy8/N1t/T09IfWSabD0lyKDdP6wFwqwS9Xs3DwD171R2Tsfr+Vgye/OI88ZSl6tXXAnkWD4elkI3ZZ1EhEnUOVm5uL3NzcWtt4e3tXOychIyMDnp6eiIiIwODBg2s8Xq1WY/r06UhKSsLx48fh7OxcpU1BQQHGjRsHGxsbHDx4sNrny8zMRFBQEAYOHIgdO3ZAKtUvi3IOFVXng99u4aNj8XC0scBPi4fA20UudkmkJ6VSCVtbWwBAYWEh5HJ+D6mqA7G38eqey1BrBAzt7IItof1gKzPIWTcmxyDmULm4uMDFxaVex1bkwL/OU/q7ijAVHx+PEydOVBumFAoFxo0bB5lMhvDw8GrD1O3btxEUFIR+/fph+/bteocpopo8H9QZJ+OycTkjH/N2RGHvc4HcYoLIyGw/m4y1/70OAHi8tzven94HMnMzkauixmYQySAyMhKffPIJYmNjkZqaihMnTmDWrFno1KlTpd4pX19f7N+/HwBQVlaGqVOnIjo6Grt27YJGo0FWVhaysrJ0a0gVFBRg7NixUCqV2LZtGxQKha6NRqMBUN4zNXLkSHh6emLDhg3IycnRtSFqKEtzKb4I64+2jtZIzlXima+iUaLWiF0WETUCrVbAe4dv6sLUnMHt8fFMf4YpI2UQ/Y3W1tbYt28fVq9eDaVSCXd3dwQHB+P777+HTPa/q6Pi4uJ0i3JmZGQgPDwcAODn51fp8U6cOIGRI0fi4sWLuHDhAgCgc+fOldokJyfD29sbR44cQUJCAhISEtCuXbtKbTiRmBqDq70VdswbgCc+i0B06n28svsyNj3pz1WSiQxYQYkaL+++jN+u3wUAvDKmK5Y8wgU7jZnBrkNlaDiHih4mIjEXc76MhFoj4JnhHfH6Y93ELonqgHOo6O+Sc5VY+FU0ErILYWkuxb8n98LUfu0efiC1SHV9/zaIIT8iUxDYyQXvTe0NANj6exK+PpcibkFEpLeTcdmY+MkZJGQXoo29DLufHcwwZSIYqIhakMn+7fDq2K4AgNXh13D0z+ECImrZBEHAllOJmL8jCoqSMvT1csR/lwyFn6ej2KVRMzGIOVREpuT5oM7IuF+M76PS8cJ3l/DDs4PQu52j2GVRDczMzPDYY4/pPibTU1yqwfK9fyD8ciYAYOYAT6yd2IOTz00M51A1E86hIn2oNVos2BmN32/lwMVWhv2LA7kAIFELlHG/CM9+fRHXMhUwl0qwekJ3PDWoPSefGxHOoSIyYBZmUmye3Rfd3O2RW6jC3O2RyC9Si10WEf3F+aR7CPnkLK5lKuAst8SupwcidLA3w5SJYqAiaqFsZebYPncA3B2skJijxDNfR0NVxjWqiMQmCAK+OpeCp/7vAvKUpejhYY/wF4ZiYMeqi0eT6WCgImrB3ByssH3eANjJzHEhOQ+v/fgHtFqO0rckSqUScrkccrkcSqVS7HKoianKNFix9wrePHANZVoBIX088OOiQLR1tBa7NBIZAxVRC+frZo/PnuoHc6kEB2Iz8f5vcWKXRH9TVFSEoqIiscugJpatKMGTW8/jh+h0SCXA64/54qOZfrC25ORzYqAiMghDu7hg3RO9AACfnkjEd5FpIldEZFoupd3HhE/OICbtAeytzLF9XgCeGd6J86VIh4GKyEBM6++Jf4zqAgB446erOBGXLXJFRKZhT3Q6Znx+HncVKnRxtUX4kqEY0bW12GVRC8NARWRAXhzdBVP6toNGK2DJrhhcy8wXuyQio6XWaLEm/BqW/fgHSjVajO3eBvufHwJvF24vRFUxUBEZEIlEgnVP9EJgJ2coSzWYtz0Ktx8Ui10WkdHJU5YibFskdkSkACj/Y2bLU/1gK+N62FQ9BioiA2NpLsWW0H7waWOH7AIV5m+PgqKEa1QRNZbrmQqEfHIG55LuQW5phs9D++HF0V0hlXK+FNWMgYrIANlbWWD7vAFwtZMh7m4BnvvmIkrLtGKXZZKkUilGjBiBESNGQCrlr1RDd/CPTEz5LAIZ94vh7WyD/c8PwbgebmKXRQaAW880E249Q03h6u18zPj8HJSlGkzp2w4bpvXmVUdE9aDRCnj/SBw2n0wEAAzr4oJPnuwLBxsLkSsjsXHrGSIT0LOtAz6Z3RdmUgn2xmTgw6PxYpdEZHDyi9VY+FW0Lkw9O7wjdswLYJgivTBQERm4IB9XvD2pJwDgo2Px2BOdLnJFRIbjbEIugj/8HcdvZkNmLsVHM/2w8rFuMON8KdITL1cgMgJPBnghPa8Im08mYuW+K3B3sMbQLi5il2USlEolvL29AQApKSmQy3lJvSEoUWvw3uE4fHk2GQDQwUWOTU/6o2dbB5ErI0PFHioiI/HqWB9M9PNAmVbAc99cxM0shdglmYzc3Fzk5uaKXQbV0dXb+Ziw6YwuTD01yAs/Lx3KMEUNwkBFZCSkUgnem9obAzs4oUBVhnnbo5CVXyJ2WUQthkYr4NMTCZi8+SziswvR2k6G7fMG4O1JvWBjyQEbahgGKiIjIjM3w9bQ/ujUWo47+SWYtyMKhaoyscsiEl3avSJM//wc1v8aB7VGwKM93fDri8MR5OMqdmlkJBioiIyMg40FdswLgIutDDfuKDD7i/PIVrCnikyTIAj4PjINwR/9joup92EnM8fG6X2weXZfOMktxS6PjAgDFZER8nSywfa5A+BoY4HLGfmY+OlZXL3Nff/ItOQUqLDwq2is2HcFRaUaBHRwwi8vDsMTfdtxvTZqdAxUREaqVzsH/LR4iG74b9qWc/j1WpbYZRE1iyPXshD84e84eiMblmZSvP6YL75bOAjtWtmIXRoZKQYqIiPm7SLHvsVDMKyLC4rVGjz79UVsPpkAbpDQeKRSKfr374/+/ftz65kWoFBVhtd+vIxnvr6Ie8pS+LrZIfyFIXhmeCeuLUVNilvPNBNuPUNiKtNo8a+D1/HVuVQAwBN922LdE70gMzcTuTKixhOVkoeXd8ciPa8YEgnwzPCOeHlMV/4/pwap6/s3rxMlMgHmZlL8a2JPdHa1xdr/Xse+mNtIu1eEz0P7wdlWJnZ5RA1SWqbFB0dvYcupRAgC0NbRGhun98HAjs5il0YmhP3TRCYkbLA3ts8dADsrc0Sn3sfET88iLqtA7LKI6i0uqwATPz2Lz06Wh6mp/drh8IvDGKao2TFQEZmY4V1bY//iQLR3tkHG/WJM+SwCJ25mi12WwSoqKoK3tze8vb1RVFQkdjkmQ6sV8H+nkzDhkzO4cUcBJ7kltjzVDxum9YGdFTc1pubHQEVkgjq72uGnxUMwsIMTClVlWLAzCtvOJHOyej0IgoDU1FSkpqby/DWT2w+KMfv/LuDtn2+gtEyLR3xdcfjFYQju6SZ2aWTCGKiITFQruSW+XjAQM/p7QisAbx28jtf3X4VaoxW7NKJqCYKA/ZcyEPzB7ziXdA/WFmZ4Z3JPbJvTH652VmKXRyaOk9KJTJiluRT/mdILnV1t8e9fbuC7yDSk5Crx2VN94WjDVaSp5ci4X4S3D97A4T/XUvP3csTG6X7o4CIXuTKicgxURCZOIpFg4fCO6NhajqXfXcK5pHuYvDkC2+b0R8fWtmKXRyauUFWGz04m4P9OJ0NVpoW5VIJ/jOqC50Z2grkZB1mo5TCY/40hISHw8vKClZUV3N3dERoaiszMzBrbq9VqLF++HL169YJcLoeHhwfCwsIqHZOXl4cXXngBPj4+sLGxgZeXF5YuXYr8/Oq36FCpVPDz84NEIkFsbGxjv0QiUY3q1gY/PheIto7WSM5VYtKnZ3E2IVfssshEabUCdkenI2jDSXx6IhGqMi0GdXTCgSVD8MKoLgxT1OIYzP/IoKAg7N69G3Fxcdi7dy8SExMxderUGtsXFRUhJiYGq1atQkxMDPbt24dbt24hJCRE1yYzMxOZmZnYsGEDrly5gh07duDw4cNYsGBBtY/52muvwcPDo9FfG1FL0c3dHj89PwR9vRyhKClD2JeR2HUhVeyyyMScT7qHCZ+cwWs//oGcAhXaO9vg89B++G7hIPTwcBC7PKJqGexK6eHh4Zg0aRJUKhUsLOp2iWxUVBQCAgKQmpoKLy+vatvs2bMHTz31FJRKJczN/zci+ssvv+Dll1/G3r170aNHD1y6dAl+fn41PpdKpYJKpdJ9rlAo4OnpyZXSySCUqDVYsfcP/BRb3qM7N9Abb4zvxl6BahQVFWHAgAEAyn/H2Nhwr7j6Sr2nxLpDN3XzpOyszLH0kS4IC2zP1c5JNEa9UnpeXh527dqFwMDAOocpAMjPz4dEIoGjo2Otbezt7SuFqbt372LhwoX46aef6vzLct26dVi7dm2dayNqSawszPDBDD90drXFhiO3sCMiBcm5Smya5Q97rvFTiY2NDa5duyZ2GQZNUaLGJ8cTsONsCko1WkglwKyBXnhpdFeu5E8Gw6D+3Fy+fDnkcjmcnZ2RlpaGAwcO1PnYkpISrFixArNmzaoxYd67dw9vvfUWnn32Wd19giBg7ty5WLRoEfr371/n51u5ciXy8/N1t/T09DofS9QSSCQSLHmkCz6b3RdWFlKcupWDKZsjkHaPi1dS4yjTaPHN+VQErT+Jrb8noVSjxbAuLvjlH8Px9qReDFNkUEQNVGvWrIFEIqn1Fh0drWu/bNkyXLp0CUeOHIGZmRnCwsLqtJCeWq3GzJkzodVqsXnz5mrbKBQKjB8/Ht27d8fq1at192/atAkKhQIrV67U67XJZDLY29tXuhEZokd7uWPPs4FoYy9DfHYhJm0+i8jkPLHLIgN3Oj4H4z8+gzd+uop7ylJ0bC3H9rkD8NX8APi42YldHpHeRJ1DlZubi9zc2q8i8vb2hpVV1QXbMjIy4OnpiYiICAwePLjG49VqNaZPn46kpCQcP34czs5V93cqKCjAuHHjYGNjg4MHD1Z6vkmTJuG///0vJBKJ7j6NRgMzMzPMnj0bO3furMtLrfMYLFFLlZVfgoVfRePK7XxYmEnwzqRemNa/XaWfDVPEOVT6ScguxL8P3cDxP7c7crC2wEuju2D2oPaw4Bw9aoHq+v5tsJPS09PT4eXlhRMnTmDkyJHVtqkIU/Hx8Thx4gRat25dpY1CocC4ceMgk8lw6NChKr8M09LSoFAodJ9nZmZi3Lhx+PHHHzFw4EC0a9euTvUyUJExKC7V4OXdsfjlavmk4cEdnfHG491M+sorpVIJW9vy9boKCwshl3Ohyeo8KCrFh0fj8c35VJRpBZhLJQgd3B7/GNWFi8hSi2ZUgSoyMhKRkZEYOnQoWrVqhaSkJLz55pu4c+cOrl27BpmsfJzd19cX69atw+TJk1FWVoYpU6YgJiYGBw8eRJs2bXSP5+TkBEtLSxQUFGDMmDEoKirC/v37K/0ibN26NczMql5VkpKSgg4dOjz0Kr+/Y6AiY6HVCvj0RAI2nUhAaZkWEgkwrV87vDrWB672prf9BwNV7dR/zpP68Gg88ovVAIBRvq54fXw3dOLCsWQAjOoqP2tra+zbtw+rV6+GUqmEu7s7goOD8f333+vCFADExcXpFuXMyMhAeHg4AFQJPhW9WhcvXsSFCxcAAJ07d67UJjk5Gd7e3k33oogMlFQqwQujumCSf1u8e/gmDv5xB7ujM3Dwjzt4bkQnLBzeEVYWvMTd1AmCgBNx2Xj75xtIylECAHza2OGNx7thWJeqowVEhs4geqiMAXuoyFhdTL2Ptw5eR2z6AwCAh4MVXgv2RUgfD0ilxj+/ij1UVcVlFeDtn6/jdHz5HFlnuSVeHtsVM/p7ci0zMjhGNeRnDBioyJgJgoDwy5l495ebyMwvAQD08XTEqvHd0N/bSeTqmhYDVTlBEBCTdh87IlLx8x+Z0AqApZkU84Z44/lHOnP9MjJYDFQtDAMVmYIStQbbziRj84kEKEs1AIDxvd2xItgXnk7GefWbqQeqErUGB/+4g50RKbhy+3/7oAb3cMPKx3zR3tm0zgcZHwaqFoaBikxJdkEJNh65hR+i0yEIgKW5FPOHdMDzQZ1gZ2Q9FUVFRejevTsA4Pr16yazbMKd/GJ8cz4V30WmI09ZCqD8+zzJzwNhg73Rs63pXvlJxoWBqoVhoCJTdD1Tgbd/vo6IxHsAOJfG0AmCgKiU+9gZkYLD17Kg0Za/fXg4WOGpwe0xc4AXnORcAoGMCwNVC8NARaZKEAQcu5GNfx+6gaTc/13t9c/x3TC8K6/2MgQlag3CYzOxPSIFN+78b12+gR2cMDfQG2O6t2FAJqPFQNXCMFCRqatuPaIgn9b45/hu6OzKrUZaotsPivH1uVT8EJWG+0Xl3zMrCykm+7dF2GBvdHPn7zIyfgxULQwDFVG5B0Wl+PhYAr46l4IyrQAzqQSzB3rhxdFdDXK4qLi4GMOHDwcA/P7777C2tha5ooYRBAHnk/KwMyIFR65n4c9RPbR1tEbY4PaYMcCTK5uTSWGgamEYqIgqS8opxLpfbuK363cBAHZW5lj6SBeEBbaHzNxwFgY1lqv8iks12H/pNr46l4KbWQW6+wM7OWNOoDdGd2sDMxNYV4zo7xioWhgGKqLqRSTk4q2fb+jm5rR3tsGCoR0wrocb2hjAVjaGHqjS84rw9flU/BCVrhuKtbYwwxN922JOoDe6tuFwLJk2BqoWhoGKqGYarYC9FzOw/kgccgpUuvv7ejkiuKcbxvVwa7HrGRlioCpRa3A+6R52XUjDsRt3dcN6Xk42CBvcHtP6ecLBxriWtyCqLwaqFoaBiujhlKoyfBeZhl+uZuFi6v1KX/N1s0NwTzcE93SDTxs7SCQtY/jJEAKVVivgRpYCZ+JzcSYhF5HJeVCVaXVfH9bFBXMDvTHSx5XDekR/w0DVwjBQEennrqIER67fxa9Xs3Au6Z5uzSMA8Ha2wbiebgju4YY+7RxF3TOwpQaqO/nFOB2fizPxuTibkIt7fy6+WaGNvQzjerghbLA3OrvailQlUcvHQNXCMFAR1d99ZSmO3czG4atZ+D0+B6V/6V1xs7fCuB5tMK6nGwK8nZp9PaSWEqgKVWU4n3gPZxJycTo+B4k5ykpft7E0w6COzhja2QXDurigs6tti+nlI2rJGKhaGAYqosahVJXhZFwODl/LwvEbd3V7BgJAKxsLjOneBsE93RDYyQVWFk1/taBSqYS3tzcAICUlpdkCVZlGi8sZ+X8O4+XgUtoDlP2lF08qAXq3c8SwLi4Y2tkF/l6tYGnOxTeJ9MVA1cIwUBE1vhK1BhGJuTh8NQu/Xb+rW3wSAGxl5hjp0xrBPd0w0scVtjJzESttOEEQkHqvCKcTcnEmPgcRifdQUFJWqY2Xkw2GdnHBsM4uCOzkwonlRI2AgaqFYaAialplGi0iU/Lw69Us/HrtLrIUJbqvWZpLMbyLC0b4uKJdK2u0sbNCG3sZWtlYijr/qiZarYAHxWrkFKiQkF2IMwk5OB2fi4z7xZXa2VuZY0hnlz9DVGt4OZvGxsxEzYmBqoVhoCJqPlqtgMsZD3D4WhZ+vZqFlHtF1bazMJPA1c4KrvYyXchytbdCG/vyj9vYW6GNnRXsrc0bZb5RUWkZcgpU/7sVlv+brfjfxzkFKuQWqioN3/213r5ercqH8bq0Rq+2Drwqj6iJMVC1MAxUROIQBAFxdwtw+GoWYtMfIFuhQnZBCXILSx9+8J9k5tK/hK4/A9ifocvRQsCKZ2dBqxXw1me7oFBLK4Wj7IIS3cd/ne9VF61sLODuYI1BHZ0xrIsLAjo4QW7gQ5dEhqau79/8ySQioyaRSODrZg9ft8q/CEvLtMgtVOGuogR3/wxZFR/fVZQgW6HC3YISPChSQ1WmRXpeMdLziqs8vra0BOkRZwAAz3wVDall7au7W1lI4WpnhdZ2MrS2lZX/ayeDq93/Pm5tJ4OzXMZJ5EQGhIGKiEySpbkUHo7W8HCsfTPjErVG19NUEbbuKlTIVpTgbkEJMnMeIP3Ptt3c7eDu4lgpKFUEJ1f78hAltzTjcgVERohDfs2EQ35ExqmlrENFRE2jru/f7E8mIiIiaiAGKiIiIqIGYqAiIiIiaiBOSiciaiAbGy6oSWTqGKiIiBpALpdDqVQ+vCERGTUO+RERERE1EAMVERERUQMxUBERNUBJSQnGjx+P8ePHo6Sk5OEHEJFR4hwqIqIG0Gg0OHTokO5jIjJN7KEiIiIiaiAGKiIiIqIGYqAiIiIiaiAGKiIiIqIGYqAiIiIiaiBe5ddMBEEAACgUCpErIaLG9NdV0hUKBa/0IzIyFe/bFe/jNWGgaiYFBQUAAE9PT5ErIaKm4uHhIXYJRNRECgoK4ODgUOPXJcLDIhc1Cq1Wi8zMTNjZ2UEikYhdjqgUCgU8PT2Rnp4Oe3t7scsxajzXzYPnuXnwPDcPnufKBEFAQUEBPDw8IJXWPFOKPVTNRCqVol27dmKX0aLY29vzh7WZ8Fw3D57n5sHz3Dx4nv+ntp6pCpyUTkRERNRADFREREREDcRARc1OJpNh9erVkMlkYpdi9HiumwfPc/PgeW4ePM/1w0npRERERA3EHioiIiKiBmKgIiIiImogBioiIiKiBmKgIiIiImogBipqEps3b0aHDh1gZWWFfv364fTp07W2V6lU+Oc//4n27dtDJpOhU6dO+PLLL5upWsOl73netWsX+vTpAxsbG7i7u2PevHm4d+9eM1VrmH7//XdMmDABHh4ekEgk+Omnnx56zKlTp9CvXz9YWVmhY8eO2LJlS9MXauD0Pc/79u3DmDFj0Lp1a9jb22Pw4MH49ddfm6dYA1ef/9MVzp49C3Nzc/j5+TVZfYaKgYoa3Q8//IAXX3wR//znP3Hp0iUMGzYMjz76KNLS0mo8Zvr06Th27Bi2bduGuLg4fPfdd/D19W3Gqg2Pvuf5zJkzCAsLw4IFC3Dt2jXs2bMHUVFRePrpp5u5csOiVCrRp08ffPLJJ3Vqn5ycjMceewzDhg3DpUuX8Prrr2Pp0qXYu3dvE1dq2PQ9z7///jvGjBmDQ4cO4eLFiwgKCsKECRNw6dKlJq7U8Ol7rivk5+cjLCwMo0aNaqLKDJxA1MgCAgKERYsWVbrP19dXWLFiRbXtf/nlF8HBwUG4d+9ec5RnNPQ9z+vXrxc6duxY6b6PP/5YaNeuXZPVaGwACPv376+1zWuvvSb4+vpWuu/ZZ58VBg0a1ISVGZe6nOfqdO/eXVi7dm3jF2TE9DnXM2bMEN544w1h9erVQp8+fZq0LkPEHipqVKWlpbh48SLGjh1b6f6xY8ciIiKi2mPCw8PRv39/vPfee2jbti26du2KV199FcXFxc1RskGqz3kODAxERkYGDh06BEEQcPfuXfz4448YP358c5RsMs6dO1fl+zJu3DhER0dDrVaLVJXx02q1KCgogJOTk9ilGKXt27cjMTERq1evFruUFoubI1Ojys3NhUajQZs2bSrd36ZNG2RlZVV7TFJSEs6cOQMrKyvs378fubm5WLx4MfLy8jiPqgb1Oc+BgYHYtWsXZsyYgZKSEpSVlSEkJASbNm1qjpJNRlZWVrXfl7KyMuTm5sLd3V2kyozb+++/D6VSienTp4tditGJj4/HihUrcPr0aZibMzbUhD1U1CQkEkmlzwVBqHJfBa1WC4lEgl27diEgIACPPfYYNm7ciB07drCX6iH0Oc/Xr1/H0qVL8eabb+LixYs4fPgwkpOTsWjRouYo1aRU932p7n5qHN999x3WrFmDH374Aa6urmKXY1Q0Gg1mzZqFtWvXomvXrmKX06IxalKjcnFxgZmZWZVekuzs7Cp/tVdwd3dH27Zt4eDgoLuvW7duEAQBGRkZ6NKlS5PWbIjqc57XrVuHIUOGYNmyZQCA3r17Qy6XY9iwYXj77bfZc9JI3Nzcqv2+mJubw9nZWaSqjNcPP/yABQsWYM+ePRg9erTY5RidgoICREdH49KlS1iyZAmA8j+CBUGAubk5jhw5gkceeUTkKlsG9lBRo7K0tES/fv3w22+/Vbr/t99+Q2BgYLXHDBkyBJmZmSgsLNTdd+vWLUilUrRr165J6zVU9TnPRUVFkEor/8ibmZkB+F8PCjXc4MGDq3xfjhw5gv79+8PCwkKkqozTd999h7lz5+Lbb7/lXMAmYm9vjytXriA2NlZ3W7RoEXx8fBAbG4uBAweKXWLLIeKEeDJS33//vWBhYSFs27ZNuH79uvDiiy8KcrlcSElJEQRBEFasWCGEhobq2hcUFAjt2rUTpk6dKly7dk04deqU0KVLF+Hpp58W6yUYBH3P8/bt2wVzc3Nh8+bNQmJionDmzBmhf//+QkBAgFgvwSAUFBQIly5dEi5duiQAEDZu3ChcunRJSE1NFQSh6nlOSkoSbGxshJdeekm4fv26sG3bNsHCwkL48ccfxXoJBkHf8/ztt98K5ubmwqeffircuXNHd3vw4IFYL8Fg6Huu/45X+VWPgYqaxKeffiq0b99esLS0FPr27SucOnVK97U5c+YII0aMqNT+xo0bwujRowVra2uhXbt2wssvvywUFRU1c9WGR9/z/PHHHwvdu3cXrK2tBXd3d2H27NlCRkZGM1dtWE6cOCEAqHKbM2eOIAjVn+eTJ08K/v7+gqWlpeDt7S189tlnzV+4gdH3PI8YMaLW9lSz+vyf/isGqupJBIF9/UREREQNwTlURERERA3EQEVERETUQAxURERERA3EQEVERETUQAxURERERA3EQEVERETUQAxURERERA3EQEVERETUQAxURERERA3EQEVERETUQAxURERERA3EQEVEVE+RkZEYOXIkrK2t4evri6ioKGzduhUhISFil0ZEzYybIxMR1cP58+cRFBSE1atXY8qUKVi+fDlUKhVu3bqF3bt3w9/fX+wSiagZMVAREdVDYGAgOnbsiG+++QYAsHv3bjz55JOYOHEi9u3bJ3J1RNTcOORHRKSnjIwMnDt3Ds8995zuPktLSwiCgLVr14pYGRGJhYGKiEhPN27cAAD0799fd19cXBwCAgLQq1cvscoiIhExUBER6Sk/Px9mZma6z/Py8vDee+9BJpOJWBURiYmBiohIT35+ftBoNHjvvfdw8+ZNPPnkk2jfvj1u3LiB1NRUscsjIhEwUBER6alz587417/+hY8++gj+/v5wd3fHkSNH4OnpidGjR4tdHhGJgFf5ERERETUQe6iIiIiIGoiBioiIiKiBGKiIiIiIGoiBioiIiKiBGKiIiIiIGoiBioiIiKiBGKiIiIiIGoiBioiIiKiBGKiIiIiIGoiBioiIiKiBGKiIiIiIGuj/AYSbJIarAWdaAAAAAElFTkSuQmCC", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alphas = np.linspace(0.5, 1.5, 21)\n", "plt.plot(alphas, mfRescaled(alphas))\n", "plt.axvline(x=1, c=\"k\", ls=\"--\")\n", "plt.ylabel(\"Total Energy\")\n", "plt.xlabel(r\"$\\alpha$\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 2 }