{ "cells": [ { "cell_type": "markdown", "id": "2494a5a8", "metadata": {}, "source": [ "# Thermodynamic Bethe Ansatz for the Lieb-Liniger Model\n", "\n", "The Lieb-Liniger model describes a one-dimensional gas of bosons with \n", "repulsive delta-function interactions:\n", "\n", "$$H = -\\sum_{i=1}^N \\frac{\\partial^2}{\\partial x_i^2} + \n", "2c \\sum_{i < j} \\delta(x_i - x_j)$$\n", "\n", "where $c > 0$ is the coupling constant. The thermodynamics of this model\n", "is exactly described by the Yang-Yang equation [YangYang1969]:\n", "\n", "$$\\epsilon(\\theta) = \\theta^2 - \\mu - \n", "\\int \\frac{d\\theta'}{2\\pi} \\frac{2c}{c^2 + (\\theta-\\theta')^2}\n", "\\log(1 + e^{-\\epsilon(\\theta')})$$\n", "\n", "In this tutorial we solve this equation numerically using `rapidity` and\n", "compute thermodynamic quantities from the solution." ] }, { "cell_type": "code", "execution_count": 1, "id": "f21de52a", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from rapidity.core import Grid1D, Field\n", "from rapidity.models import LiebLiniger\n", "from rapidity.tba import TBAState\n", "from rapidity.utils import plot\n", "\n", "plt.style.use('seaborn-v0_8')\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "1c11758d", "metadata": {}, "source": [ "## Setting up the model\n", "\n", "We define the Lieb-Liniger model with coupling constant $c=1$ and set up\n", "a uniform grid." ] }, { "cell_type": "code", "execution_count": 2, "id": "089861ca", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Grid: 200 points\n", "Rapidity range: [-5.00, 5.00]\n" ] } ], "source": [ "# define model\n", "model = LiebLiniger(c=1.0)\n", "\n", "# define rapidity grid\n", "grid = Grid1D.uniform(-5, 5, 200, \"theta\")\n", "\n", "print(f\"Grid: {len(grid.points)} points\")\n", "print(f\"Rapidity range: [{grid.points.min():.2f}, {grid.points.max():.2f}]\")" ] }, { "cell_type": "markdown", "id": "ec94355b", "metadata": {}, "source": [ "## Solving the TBA equation\n", "\n", "We solve the Yang-Yang equation at temperature $T = 0.5$ and chemical\n", "potential $\\mu = 0.5$. The chemical potentials are passed as a dictionary\n", "keyed by charge order — charge 2 is the energy ($\\theta^2$) and charge 0\n", "is the particle number.\n", "\n", "The inverse temperature $\\beta = 1/T$ multiplies the energy charge, and\n", "$-\\mu/T$ multiplies the particle number charge, giving the standard\n", "grand canonical driving term:\n", "\n", "$$\\epsilon_0(\\theta) = \\frac{\\theta^2}{T} - \\frac{\\mu}{T}$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "dfef8f09", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T = 0.5\n", "mu = 0.5\n", "\n", "state = TBAState.from_betas(model, grid, betas={2: 1/T, 0: -mu/T})\n", "\n", "# plot filling function\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "#plot(state.filling, ax=axes[0])\n", "axes[0].plot(grid.points, state.filling.values)\n", "axes[0].set_xlabel(r'$\\theta$')\n", "axes[0].set_ylabel(r'$n(\\theta)$')\n", "axes[0].set_title('Filling function')\n", "axes[0].set_xlim(-6, 6)\n", "\n", "# plot pseudoenergy\n", "epsilon = np.log((1 - state.filling.values) / state.filling.values)\n", "axes[1].plot(grid.points, epsilon)\n", "axes[1].set_xlabel(r'$\\theta$')\n", "axes[1].set_ylabel(r'$\\epsilon(\\theta)$')\n", "axes[1].set_title('Pseudoenergy')\n", "axes[1].set_xlim(-5, 5)\n", "axes[1].axhline(0, color='k', linestyle='--', linewidth=0.5)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9e6beed3", "metadata": {}, "source": [ "## Thermodynamic quantities\n", "\n", "From the filling function we can compute the particle density \n", "$\\rho_p(\\theta)$, the state density $\\rho_s(\\theta)$, and the\n", "effective velocity $v^{eff}(\\theta)$." ] }, { "cell_type": "code", "execution_count": 4, "id": "73cd8037", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Total particle density N/L = 0.394173\n", "Free energy density f = -0.464790\n" ] } ], "source": [ "rho_p = state.rho_p()\n", "rho_s = state.rho_s()\n", "v_eff = state.v_eff()\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n", "\n", "axes[0].plot(grid.points, rho_p.values)\n", "axes[0].set_xlabel(r'$\\theta$')\n", "axes[0].set_ylabel(r'$\\rho_p(\\theta)$')\n", "axes[0].set_title('Particle density')\n", "axes[0].set_xlim(-6, 6)\n", "\n", "axes[1].plot(grid.points, rho_s.values)\n", "axes[1].set_xlabel(r'$\\theta$')\n", "axes[1].set_ylabel(r'$\\rho_s(\\theta)$')\n", "axes[1].set_title('State density')\n", "axes[1].set_xlim(-6, 6)\n", "\n", "axes[2].plot(grid.points, v_eff.values)\n", "axes[2].set_xlabel(r'$\\theta$')\n", "axes[2].set_ylabel(r'$v^{eff}(\\theta)$')\n", "axes[2].set_title('Effective velocity')\n", "axes[2].set_xlim(-6, 6)\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "# total density\n", "N_L = rho_p.integrate().values\n", "print(f\"Total particle density N/L = {N_L:.6f}\")\n", "print(f\"Free energy density f = {state.free_energy():.6f}\")" ] }, { "cell_type": "markdown", "id": "ccd7a79f", "metadata": {}, "source": [ "## Temperature dependence\n", "\n", "We now vary the temperature at fixed chemical potential and observe\n", "how the filling function evolves from the Fermi-Dirac distribution\n", "at high temperature to a step function at zero temperature." ] }, { "cell_type": "code", "execution_count": 5, "id": "840a30e4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "temperatures = [0.1, 0.5, 1.0, 2.0]\n", "mu = 0.5\n", "\n", "fig, ax = plt.subplots(figsize=(8, 5))\n", "\n", "for T in temperatures:\n", " state = TBAState.from_betas(model, grid, betas={2: 1/T, 0: -mu/T})\n", " ax.plot(grid.points, state.filling.values, label=f'$T={T}$')\n", "\n", "ax.set_xlabel(r'$\\theta$')\n", "ax.set_ylabel(r'$n(\\theta)$')\n", "ax.set_title('Filling function at different temperatures')\n", "ax.set_xlim(-6, 6)\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "32061bbc", "metadata": {}, "source": [ "## Zero temperature limit\n", "\n", "At zero temperature all states below the Fermi rapidity $\\theta_F$ are\n", "filled. We construct the zero temperature state directly using\n", "`TBAState.zero_temperature`, which uses a Gauss-Legendre grid on\n", "$[-\\theta_F, \\theta_F]$." ] }, { "cell_type": "code", "execution_count": 6, "id": "33cd2fca", "metadata": {}, "outputs": [ { "data": { "image/png": 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AyXisysR+VSb2qzKxXzuWl5dTB7+i8eqssZIp/c6a2vHyWJWJ/apM7FdlMjeQsRIzpQzgF8HMzEx+VToeqzKxX5WJ/apM7FcyNqb0O2tqx8tjVSb2qzKxX5XJ3EDecxiUIiIiIiIiIiIinWNQioiIiIiIiIiIdI5BKSIiIiIiIiIi0jkGpYiIiIiIiIiISOcYlCIiIiIiIiIiIp1jUIqIiIiIiIiIiHSOQSkiIiIiIiIiItI5BqWIiIiIiIiIiEjnGJQiIiIiIiIiIiKdY1CKiIiIiIiIiIh0zlL3P5KIyLCp1RrU1qtQr1LLW0NDIxrVGlhamqOsRoWKihpoNIC1pXnTzcoCNtYWMDcz03fTiYiIiIiIrkuj0aC8sg76xqAUEZkMtUaDsgt1KC6rQVFZDUor6lBWKW718mtlTQOqa1WoqVNB087XFvEoextLONhawcHOCq6O1nB1soGrow08nG3g7WoPL1dbODtYw4zBKyIiIiIi0pPc4kp8/utx5BRX4rHpsYiL8tJXUxiUIiJlKr1Qh7MFF5B7rhK5xVXIPVeFgpJqNKjUnfLzROZUVa1K3lBWc9Xn2VhZwM/DHgGeDgjwckSglwOCfZ3gbG/dKe0iIiIiIiJqzo7acjgXP2xO034uqq1vhD4xU4qIjF59QyMy8ipwOqcMZ/Iv4ExBBcor66/7fdZW5nBzbMpmcnG0hpO9NRxsm7Kd7Gws5ePWlhawsjSHhbkZLCzM4ORkh4oLNfJnij/k4lbX0IiaWhUqa1Worm1ARXWDTIVtzsK6NBAmnptZcEHeLuXhbItQPyeE+zkjKsgVob5OsLRg2T8iIiIiIrp5F6rr8dWakziSdk7et7Iwx/1TYjA4xhuNje2dJ9JxGJQiIqOjalQjLaccxzJLcDKrFJn5F2TNp9aIYJLvxcwkfw8HeLvZwcvNDt6udnC0s2rXVDpRU8rNzQGlpVVQtTHjSlyNqKiql9MFi0prUFhag/xzTZlb4r6YUiicr6iVt4OpxfK+CISJAFV0iBtiwtxlwMrCnEEqIiIiIiJqH/G56ctVx7UX7sVno0enx6JnVx/52QbtLl7ScRiUIiKjUFJRi6S0c0hKP4/UrDKZcdRaACrYxxGhfs4y0yjM11kGpPSZcSSCXi4yE8sGUYGuLR4TGVRieqHMnMqvkFleYl63iFOJx1Kzy+Rtxe9nZOZW9xA39Ir0RM9ID073IyIiIiKia2pQNWL5tgxs2J+t3TeyTwBuGxEJezsrGAIGpYjIYOWfr8L+k0U4fOoczha2nO4miGBTVKALuga7yoBPuL+zrNlkLEQ2VKivCKA5A70D5D5RZD09txyncspk8E1MSxRZYGL/wVPF8iZyuyICXdAnygvx3bzg6WKn70MhIiIiIiIDklV4AV/8elzO0BDELJH7J3bTa1Hz1jAoRUQG5VxZDfaeKMS+E0XILqq84nF/Twf0DPeQU9pEQMraiIJQbSEyonqEe8ibIIJRIjh17EwJkjPOobisVibXiumL4vbjljREBDijfzcf9I/2lhlZRERERERkmtRqDdbty8LP2zO0JU5iwz1kQErU0jU0DEoRkd7V1TfiQGoRdh7Nx8msshaPiZJPXQJdERflid5RnvB2s4cpEUEqcdzidqcmCnnnqnD49Dl5O5NfIZ+Tnlshb2IVjR7h7kiM9ZPT/EQmFhERERERmYbishpZO+p0Trm8b21pjtmjojC8t3+7aunqEoNSRKQ3ZwsuYOuRXOw5XigDU83En0uRBdUv2gfxXb2Y/dN8XszMEODlKG+TB4XiXHmNnN4ossrEuRRF05PTz8ubWEVwcKwfhscFwNfdtAJ5RERERESmRKPRYOfRAny38RRqL36uCvNzwkNTYgz+swCDUkSkU6KA974ThdhyOFfWS7qUj5udDKQM6uELd2db9sx1iFpSExJC5K2gpBq7UvLlm1HphTpU1apkQUNxEyv4iYKGYv64ublhXiEhIiIiIqL2q6iuxzfrUnHoVNMq3uZmZpgyOBSTBobodcGntmJQioh09sdy66FcbD6ci4qqpqVIBTHFTNRCGtrLH5EBLgabVmroxBWQ6UMjMDUxHMfPlmB7Uj4OnyqW88hPnC2VN08XW4yOD8KQnn5yWiARERERERmvpLRz+GrtSe3nK3GR/8Ep3RHh7wJjwU8lRNSpispqsG7PWfx+tACqRrV2v4+7PUbEBWBwrC8cbA1jOVIlEJlQPcI85K2ssg47kvKwLSkPJRV1OFdeiyWbTmPFjgw5rW9cvyBOjSQiIiIiMjI1dSos3ZKGrUfytPvEZ6vbRkTCxtq4FoJiUIqIOkVucSXW7DmLvceLZK2jZt1D3TC2X7AsyC1SS6nziNU1pgwOw8SBITiYWiyn8okpk2Ke+bq9Wdh4IAdDevlhQv9geLrasSuIiIiIiAzcicwSLFxzEucrauV9ZwdrzJ3YDT0jPGGMGJQiog5VWFqNFTvOYO/xQu0+EXxK6O6D8QnBCPJ25BnXMQtzMUXSR97Scsuxds9ZuXqfyFzbcigX24/kYUgvf0wZFAo3J8NbJpaIiIiIyNTV1quwdGu6HL8369vVC/eO6wone2sYKwaliKhDiOLaP2/PkNPFRB0j+QfGwpyZOAZG1O16fEbPFplsor+2Hs7FrqP5GBUfiIkDQjitj4iIiIjIQJw8W4qFa07IchyCo50V7h7bRV50NnYMShHRTamqacAvO4/h1x0ZqFc11YyyMDfD8N4BmDQoRE4hI8MT4OUol4i9dUg4ftlxBnuOFcj+W7snC9sO52HSoFDcNrarvptJRERERGSy6uobsWxrOjYdytHu69vFC3eP6woXB+PNjroUg1JEdEPqGhqx8UA21u7NQnWtSu4TFaIGxPhi6pAweLFGkVHwdrXDQ1O6Y0JCMH7anoEjaedQfbFwoujfWxLDMLiHr1EsJ0tEREREpBSpWU3ZUcVlTdlRDraWuHtsV7lyuZJWLGdQiojaRaPRyHpE3288rS2uJ8R18cS0xHAEsmaUURL99sTMnkjLKceybek4lV0mp2QuWnsSG/dn464xXdAtxE3fzSQiIiIiUnx21PJt6dh0MAfNy0XFRXnK2lEuCpyFwqAUEbVZYUk1Fm88hZSMEu2+rsGueOCWWPi62kB1cfoeGa/IQBc8e2ccTmSV4qdtZ5CRV47cc1V4+/vDsli9WGaWxdCJiIiIiDreqewymR1VVFqjzY66c0wXDOjuo6jsqEsxKEVEbYrWr9qdifX7sqBqbIrXuzvb4I5RUejf3Qfu7o4oLa3imVQI8YYnlpQd0icYv2w9jR83p6GypkGuqCim9906OAyj4wM5pY+IiIiIqAPU1Klk7agth/9YWa93pCfuHd9V8TV6GZQiomtO1Tt0qhhLNompenVNfzQszDCufzAmDwyFjbWFYiP2BJiLgvVxAfINUdSb2nY4VwYof9ySht+P5sspfdGc0kdEREREdMOS0s7hm/WpsnRGc3bU7aOiMKiHr0l81jLYyrV1dXWYN28e4uPjkZiYiIULF173e3JychAXF4e9e/e22L948WIMHz4cffr0wRNPPIGysrJObDmRMog/ih8sS8bHP6doA1I9wtzxygMJmDEsQgakyDSIJWfFHPZ/zIlHmJ+z3Jd3rgrvfH8YX646jqraBn03kYhuUmFhoRwj9e/fH0OGDMEbb7whx2JERETUOSqq6/HZymPyM1dzQCq+mzdefTABg2P9TCIgZdCZUm+//TZSUlKwaNEi5OXl4dlnn4W/vz/Gjx9/1e+ZP38+qqurW+xbs2aNfC1xCwsLwwsvvIBXXnkF77//vg6Ogsg4s6N2pRTgu42nZRqp4OFsg9tHdUGfLp4m88eRriQCUi/c2xe/J+fL9GIxpU/8rhzPLMGc8d3QK9KTp43ISP/ui4CUs7OzvJBXXl4uLwyam5vL8RcRERF17PvunuOFcuGoypqmi7sujta4Z2xX9OniZXKn2iCDUiKwtHTpUnzxxReIiYmRt9OnT8uB0tWCUitXrkRV1ZU1bcRrPPTQQxg3bpy8/8wzz+Dll19GY2MjLCyY6UF0Kbna2rqTSE4/L++L8NOYfkGYNiScmVEkmZuZYWgvf/mGKaZ1iqBUWWW9vMIzuIcv7hgdBXtbK54tIiOSkZGBI0eOYOfOnfD0bAouiyDVW2+9xaAUERFRBzpfXiun6h3NaPq8JYix9W0jIkx2DG2QQamTJ09CpVLJqXjN+vbti08//RRqtVpeubtUaWkp3nnnHTnFb/Lkydr9lZWVOH78ON58803tvn79+mHVqlU6OhIi48qOEtH66ovZUd5udnhgUjSiAl313Twy0Cl9D07ujviu3li0/iTKK+uxM6UAxzJLcN+EbrJQOhEZBy8vL3z55ZfagNSl4ygiIiK6eWqNBlsO5WLZtnRZo1XwdrXDnAndTL5Gq0EGpYqLi+Hm5gZra2vtPjFQErUNRD0od3f3Fs8XQadp06YhKiqqxf7s7Gz5taSkBLfffrusOTV48GA5hU+kqLen2K+4dQYLC/MWX5WMx2qYyi7U4as1J3D49Dl5X/ymj+0fhJkjImFjdf1sQvarMrW1X+OjvdEt1A2LN6Ri59GmrKn/LE3GkJ5+uHNsFzgYwRUf/g4rkyn1680SYyJRR6qZuAD4v//9DwMGDND7WMnU+tGUjpfHqkzsV2Viv94cUYt1warjOJ1TLu+LaigTBoRg2tDwNn3eUnq/GmRQqqampkVASmi+X19f32L/rl27cPDgwVazn5qn84kaUn//+9/h6uqK1157TU7hE1lXbeXu7tDpdXScne1gKnishuPAiUL8+/tDqKhq+n/l5+mAv86OQ0y4R7tfi/2qTG3pVzc34Ln7ErA3JR8fL0uS00B3JOcjNbsMT98Tj24hLS8kGCr+DiuTKfVrRxHZ5yLTfNmyZQYzVjK1fjSl4+WxKhP7VZnYr+1T39CIHzedwvLNp6Fq1Mh9oX7OeGJ2b0QFucFQOOv5Pccgg1I2NjZXBJ+a79va2mr31dbW4sUXX8RLL73UYn8zS8umw3v44YcxatQouS2CUlOnTpWrzPj4+LSpPSUlVZ2aKSV+CSoqatDYqIaS8VgNh6pRjaVb0rF2z1ntPpEdNetidlRp6ZX12a6G/apMN9KvXQKc8drDA/C/9alyOmhRaQ2e++h3zBwegQkDQ2Q9KkPE32Fl0kW/urk5QIkBKbHIzL///W906dKlzd/XWWMlU/r/aWrHy2NVJvarMrFf2+/YmRJ8vfYkCkuaFmKztDDD1CHhmDgwBJYW5u36vKX0sZJBBqVEsEjUiRJ1pZoDS2JKnwg8XTrtLjk5WU7RE8U4LyUKm4vA05/+9Cd5Pzw8XPuYWIFPKCgoaHNQSq3WyFtnEr8EKpWyBx/NeKz6VVxWg09/OYYz+RXyvpO9FR6a3B09LmZH3ejvIftVmdrbr7ZWFrLWVI8wdyxanyrnzP+wOU3WmnpwUnc4O7TMgjUk/B1WJlPq15v1r3/9C99//70MTDUvENNWnT1WMrV+NKXj5bEqE/tVmdiv1ydmoPyw+TR2HyvU7osOccM947rC190e0Nz45y2l9qtBBqWio6NlMEqsBBMfHy/3iSl6sbGxLYqc9+zZExs2bGjxvWPHjsWrr74qa0eJ2lPe3t6ycHqvXr3k4+np6TK93N/fX8dHRaR/B04W4au1J1FzsZi5+AP50JTucHW00XfTSGEGxPgizM9ZBkDPFl5ASkYJXvpqHx6eEmPyxRyJDNFHH32EJUuW4P3337/qSsdERER09ULmvyfnY+mWNFTVqrQLA90xKgoDYnw6vRyQMTPIoJSdnZ3MdJo/fz5ef/11FBUVyZX13njjDW3WlJOTk8ycCgkJueL7RQaUh0dT1sd9992HDz/8EIGBgXKfeM3Ro0fLlWaITIWYz7xkcxq2Hs6V98XfRJE+OmlASKdNTSXycbfHvHv6yjfnjQdz5Ap9735/GFMGh8qbxWUrqRKRfogLdp988oksdyBWOxbjrGYcLxEREV1b7rkqfLPupLaQuTC0lx9mDo+UgSkywqCU8Pzzz8sA0pw5c+Do6IjHH39cZkEJiYmJMkA1ffr0677O3Llz5ap9orh5dXU1Ro4cKV+XyFScK6/BRz8dRVZh09Lebk42+NMtMegS5KrvppEJsLI0x51juiA61A0LV5+QV45W7syUb9qPTO3BN2oiA7Bp0yY0Njbi//7v/+TtUqmpqXprFxERkaFf+P91VybW7c1C48Up7H4e9pgzvhs/a7WDmUaj6dxiSQpQXHyh017b0tJcFv8Shc4MbW5pR+Ox6l5qVik+/jkFlTUN8n7vSE/MnRTdoYEA9qsydUa/llTU4tOVx5B28SqSp4stHp/RE0HejtAn/g4rky761cvLqVNe1xh11ljJlP5/mtrx8liVif2qTOzXK6WcOY9v16eiuKxWeyF2yqBQjE8IloXMjYGlgYyVDDZTiohunIg1bz6UiyWbTsuovZigN31YOCYOCOF8ZtIbd2dbPHtnnCx8vvFADs6V1+K1bw/ggUnd0a+bN3uGiIiIiAxaeVW9/Iy19/gfhcxjQt1w97iu8HGz12vbjBWDUkQK06BS438bUrEjOV/et7OxkMWle0V66rtpRLKO1J2juyDY2wnfrE9FfYMa/7ciBVkDQzBtaDjMWQSSiIiIiAxMo1qNLYdy8fOODNTUNcp9zvZWuH10FBKiWcj8ZjAoRaQgZZV1+Pjno0jPrZD3xbKjj8+IhZ+Hg76bRtRCYk8/+Hs64KOfklFWWY/Vu88ip6gSD02Jgb0t35qIiIiIyDCI0hPion9WUVONXmFYb3/MHB4BB1sWMr9ZHPkTKcSZ/Ar8d3nTB3yhZ4SHzJDiB3wyVOH+znjxvn74+KejSM+rQFL6ebz6zQE8MbOnDKgSEREREelLRXU9lm1Jx+9Hm2agCME+jrhnbFdEBLiwYzoIg1JECnD4VDE+W3kM9RcL1E0eFIKpieEwNxfVpIgMl6ujDZ65s492ymlBSTVeuxiYigrkCpFEREREpFuiJu+mgzlYujkN1XUquc/OxhLTh4ZjRFwAP2N1MAaliIyc+IP53cZTEOtoilUfHpzMotFkXMTv7X0TuiHYx0n+LlfVqvDO90fw8JTuiGcBdCIiIiLSkfTcciz+er92tWhhcKwvZg2PhLODNfuhEzAoRWSk1BoNlm1Nx7q9WfK+o52VzC6JZCopGSEzMzOM6hsIDxdbfPpLirYA+uyRkRjbP1jfzSMiIiIiBausaZCfrXYk5UFzcV+glyPuHtsFXYKYvd+ZGJQiMtIV9hasPo59J4rkfW9XO/y/23rBh3V4yMj1jvTEs3f2wQdLk1BR3YAlm9NwvqIOs0dFcmU+IiIiIurwC/0iECUCUiJbXxA1ecVUPVHMXKwcTZ2LQSkiI1NV24D/Lj+KU9ll8n6YnzP+OrMn00lJMcTv9Lx74/HvH5NQWFKN3w5ko+RCLR6a3B3WVhb6bh4RERERKUBmQQW+XX9KLhjVbFAPX/xpRi+YNTZCdbFeL3UuBqWIjMi58hr5QT3/fLU2q+RPt8bAhh/USWFE9t8L9/TFh8uSkZZbjoOpxSivPCKnqIqpqkRERERENzpV7+cdGdh6KFc7VS/A00FO1YsJ94Cbsy1KS6t4cnWEQSkiIyFWJXvn+8MovVAn74/oE4C7Rnfh6g+kWCL49Pfbe+OLVcdlUEoEp9767hD+Prs3XBxt9N08IiIiIjIiarUG25Ly8PP2DBmYEmysLXDr4DCMjg+EpQWn6ukDg1JERiC7qBLv/XAEFVX18v6MYeGYOCBEFocmUjIxXe+RW3vg+02n5UqTucVVeGPxIRms8nSx03fziIiIiMgIiNIn3/12CllFldp9/aO9MXtkFNyceLFTnxiUIjJwGXkV+PePR2ThPRGCuntcV4yIC9B3s4h0xtzcDHeOjoKdjSVW7cpEUWkN3lx8CE/fHsfi/kRERER0VWKWyY9b0rD3eKF2n1hV764xUega7MYzZwAYlCIyYKlZpfjPsmTU1TdCJEU9MCkag3r46btZRDonsgLFKih21hZYujUdJRV1TRlTs3sj0NuRPUJEREREWg2qRmzYn41Vu86irqFR7nOwtcQ0rqpncBiUIjJQRzPO46OfjqJBpYaFuRn+fGsM+nb11neziPRqwoAQOff/fxtOyemsosbU32b3liv2EREREZFp02g0SEo7jyWbTqOorEbuExf3h8cFYNqQcC6YY4AYlCIyQAdOFuGzlcfQqNbAytIcj02PRWy4h76bRWQQRvYJlCtOLlxzQk5rFQsAPDmrF7oEueq7aURERESkJ/nnq2Qd0pSMEu0+MT4UZSCCfZzYLwaKQSkiA7PvRKEMSGk0gK21Bf46syfnOxNdZnCsnwxMif8rtfWNeP+HI/jrrF6IDmFtACIiIiJTUlOnwq87M/HbgWx5UV8Qxctnj4xEv27eXBzKwDEoRWRgGVKfrzwuA1JizjOnJRFdXXw3b7k638c/H0W9So0PliXhb7f1ZsYUERERkQlQazTYnVIg6402r1JuaWGO8QnBmHSx5AMZPnN9N4CImhw+VSyzPsQfV3sbS/z99jjWySG6jp4RHnhiRk85AKlvUOPfS5OQllPO80ZERESkYGfyK/D6twexYPUJbUAqLsoTrz6UIBfHYUDKeDBTisgAJKefwycrUmS6qZ2NBZ66vTdCfDnvmagtYsLcZd21j35qWqny30uP4KnZcQj3Z/FzIiIiIiUpvVCHn7anY+fRAu0+Pw973DE6Cj3CWIPXGDEoRaRnKWfEKntNASlRQ0pMP+JKYkTtz5h6dGqsnMpXU9dUY+rpO+IY3CUiIiJSgPqGRqzfn401u8+irqFR7hMX828dHIaRfQNl1jwZJwaliPToeGYJ/rv8KFSNalm0WawgFhHgwj4hugG9ozzx51t74P9WpKC6ToV3lxyWgSmutkJERERknDQaDfafLMLSLWk4X1En95kBGNLLD9OGRsDFwVrfTaSbxKAUkZ6kZpXiw2XJaFCpYW1pjidn9WSBZqKb1LerFx6+pbusz1ZVKwJTR/DMnXEI9HLkuSUiIiIysrpR32863aJeaNcgVzlVjxcdlYNBKSI9/YH9z7JkuWKYlaU5npjZE12DuZQ9UUfoH+0DtVqDL1YdR2VNA95bcgTP39MX3q52PMFERERERlA3avm2dOxK+aNulJerLW4bEYU+XTxhZiZypUgpGJQi0rGCkmr8+8ckWZDZ0sIMj0+PRfdQd/YDUQcaEOMr67SJFVnKq+rxvghM3d0HLo42PM9EREREhlo3al8WVu85K1dVFkTN3SmDQzG6b5C8mE/Kw6AUkY6j/u8tOSyzN0R8/+EpMegRzlUiiDrD4Fg/VNeqZNp3UVkN3v8xCc/e2Qf2tnzrIyIiIjKkulH7ThRh6dY0lFxSN2pob39MHRLOulEKx5E5kY6IQJRYEay5QN/d47oivps3zz9RJxrTLwgXauqxatdZZBdV4sPlyXhqdi9YWVrwvBMRERHpWUZeBZaIulG5f9SN6hbsittHsW6UqTDY/Le6ujrMmzcP8fHxSExMxMKFC6/7PTk5OYiLi8PevXtbffzLL7/EyJEjO6G1RNcmpup9sCwJueeq5P2pQ8IwIi6Ap41IB6YNCcew3v5y+1R2GT795Rga1U0p4URERESknxkkX/x6HK9+c0AbkBL1Px+bHsvVk02MwWZKvf3220hJScGiRYuQl5eHZ599Fv7+/hg/fvxVv2f+/Pmorq5u9bHs7Gx89NFHcHdn7R7SLVWjGp+sSEF6boW8P6pvIKYMCmU3EOmIKIZ5z9iuMlvxYGoxDp8+h0XrUnH/hG4slElERESkQ3UX60atuaRulJ2NBaYMCpOfk1g3yvQYZFBKBJaWLl2KL774AjExMfJ2+vRpLF68+KpBqZUrV6KqqikLpTUvvfQSoqOjUVhY2IktJ2pJrdFg4ZoTOJpxXt5P6O4jlzDlihFEumVubiZruP2nNgknzpbi9+R8ONlbYdbwSHYFERERkQ7qRu09UYhlW9P/qBtlBgzr1VQ3ytnBmn1gogxy+t7JkyehUqnkVLxmffv2RVJSEtStTLkoLS3FO++8g1deeaXV11uxYgVqamowc+bMTm030eV+3JyGPceaAqE9wtzxwKRomHMJUyK9EFfeREp4iI+TvL92TxY2HshmbxARERF1ovS8crz+v4P4fOVxbUAqOsQN8+/vj3vHd2NAysQZZKZUcXEx3NzcYG39R7TU09NT1pkqKyu7Ygrem2++iWnTpiEqKuqK1yopKcG7776Lr776CkePHr3hK+zi1hksLMxbfFUyUzvWtbszsWb3WXk/IsAZf53VCzbWyiuubGr9eulXJVPqsTpZWuPpO+Pwr0UHUFhSLVfm8/N0wPB+Doo7VlPqV1M/ViIiIkN0rrwGy7dlYO/xP2YribpRs0dGoneUJ2ePkOEGpURW06UBKaH5fn19fYv9u3btwsGDB7Fq1apWX+v111/XBqxuNCjl7u7Q6f9hnJ3tYCpM4VgPnizEpz8ly21fD3u8/PAguDjaQMlMoV+b8ViNm5ubA17500D8/YMduFBdj49+OopAPxdEBrrCVPB3mIiIiDpLda0Kq/dk4rf9ObK+rsC6UWRUQSkbG5srgk/N921tbbX7amtr8eKLL8p6UZfub7Zjxw4cOXIEr7766k21p6SkqlMzpcSHg4qKGjRe/A+rVKZyrFmFF/DmogNQqzWwt7XEk7N6Qd2gQmmpCkpkKv0q8FiVw87CDH+d1RNv/u+gXB3zXwv2YP7cBLg6KrueAX+HOz7ASURERE1EAGrbkTz88vsZucCMIEqXDI/zxy2JYXC2V/Y4ixQUlPLx8ZF1okRdKUtLS+2UPhF4cnZ21j4vOTlZrqr3xBNPtPj+hx56CFOnTkVDQwMKCgowcOBAuV+8ntgnalWJIurx8fFtao8ILohbZxIf5lUqZX+gN4VjFUubvrfkCGrrG2EpPvTO7ClTVJV6vKbSr5fjsSpDuJ8z5k6K1tY3eOe7Q3jurj6wszHIt8YOxd9hIiIi6sgi5klp5/HjljQUlFRr9/eO9MSsERHw8+BFHLo6gxx5i1XyRDBKZDk1B47EFL3Y2FiYm/9RG6Jnz57YsGFDi+8dO3aszIwaPHiwvP/nP/9Z+5h47rfffitvIvBF1JFq61X4cFmyDEwJj83qjehQd5MJ1BAZowHdfWVASqwEk11Uif/7JUUGky0uea8hIiIiotadLbiAHzafxsmsMu0+sajMbSMjZTFzIqMMStnZ2clMp/nz58uaUEVFRVi4cCHeeOMNbdaUk5OTzJwKCQm54vtFwMnDw0NuN39t3hbBrta+h+hmiEw6kW1xtvCCvD91SBhG9QtGaWkVTyyRgZsyOBRlVQ3YuD8LKRklWLzhFO4Z15XFN4mIiIiuoqSiFj9vz8CulAI0zylyc7LB9KHhGNjDlyuOk3EHpYTnn39eBqXmzJkDR0dHPP744zILSkhMTJQBqunTp+u7mUTSD5vTcCTtnNwe0N0H04aG88wQGQmxkMWjM3shr/gCjmeWYuuRPHi72WN8QrC+m0ZERERkcLND1uzJwoZ9Wai/OCPExsoCEwcEY2z/YLlNpIiglMiWeuutt+TtcqmpqVf9vms9JoJYDGRRR9uRlIffDmTL7ahAF9w/MZoZFkRGxsrSHI/P7IlXvtqP/PPVWLo1DQFeDogN/yPbloiIiMhUNao12HIoF8u3paOiqmkRMrFA/dBe/piaGKb4lcap87BoBtFNSMstx7cbmgKhni62eGx6rPxwS0TGx8HWCn+d1QsOtpbQaIBPfznWolgnERERkSlKTj+Pv763BV+tOaENSPUId8fLc/tjzvhuDEiRMjOliAydKGj+8U9HoWrUyDTVJ2b0hBOXOSUyamK1zEem9sD7PyShpk6F/y5Pxj/ujTeJFfmIiIiILpVTVClX1Es5U6LdF+jlIIuY9whjNjl1DI6yiW5Ag6oRH/2UjPKLVwoemBSNQG9HnksiBege6o7ZoyLx/cbTcirf5yuPyal95iJHnYiIiEjhyivr8POODOxIzpfZ481FzEXd3EExvjA355iIOg6DUkTtpNFosGhdKs7kN620d8vgUMR38+Z5JFKQ0X0DkVV4ATuPFiAp/TxW7MjA9KER+m4WERERUaepa2jE+n1ZWLsnS24L1pbmmDAgBHdN7I7a6jqoLhY3J+ooDEoRtdNvB3Lk0qdCXJQnbkkM4zkkUuCKfPeO6yozpTLyKrBq11kEeTuhHwPQREREpDBqjQa7Uwrw0/YMWaJEELlQg2J9MW1IOLzd7WUpAxGUIuporMhM1A7HMkvww+bTctvf0wEPTu7OKT1ECmVlaYG/TIuFi6O1vL9g9XGZPUWkZPX19Zg8eTL27t2r76YQEZEOnDhbile+3o8Fq09oA1LRIW548b5+eGBSd7g727IfqFMxU4qojYrLavDpihQ5r9rexhKPz4hl8WMihRP1E8Sqmm8tPoT6BjX+u/woXrq/HxztrPTdNKIOV1dXh6eeegqnTzddfCEiIuXKLa7E0q3pcmW9Zn4e9pg1IhK9Ijxk1jiRLjAoRdTGwuaf/JyCqloVxN/nP0+NgY+bPc8dkQmI8HfBveO6YeGaEzhfUYsvVx3HEyx8TgqTlpYmA1KibiIRESmXyIb65feWRczFxbapQ8IwtJc/LC04mYp0i0EpojYQq3CdvThtZ/rQcC6BSmRiEnv6ISO/AlsP58oriqt3n8WUQaH6bhZRh9m3bx8SEhLw//7f/0Pv3r15ZomIFKamToV1e7Owfn+WzP4WrCzNMbZfECYkhMDelqEB0g/+5hFdx66UfGw9kie3RSqrWH2CiEzPHaOikJlfgcyCC3I1vgh/Z3QPddd3s4g6xJ133nlT3y+WB++MJcItLl6xb/6qdKZ0vDxWZWK/Gh5VoxrbjuTh5+0ZqKiql/vEX+vEXn6YMSyiTTWj2K/KZGEg7zkMShFdQ05RJb5Zlyq3PV1s8eAUFjYnMlXiauKjU3vg5a/3y6m8n608hvn395d1p4hMnbu7Q6fWH3F2toMpMaXj5bEqE/tV/8R07D0p+Vi0+jhyi6u0+/t088Z9k7ojzN+l3a/JflUmZz2/5zAoRXSNFNePV6SgXqWGpYUZHp3WAw62LG5MZMo8Xe3kqpsfLEvGheoG/N8vKXjmjjjWXyCTV1JS1WmZUmKwXFFRg8bGpukmSmZKx8tjVSb2q2E4nVOGJRtP43ROuXZfsI8jbh8VhR7hHvJ+aekfgarrYb8qk4UO3nPc3Byu+xwGpYiucmXhq7UnUVhSLe/fOboLQn2dea6ICL0iPTF5UAhW7TqLtJxyLNuaLgd5RKZMrdbIW2cRg2WVStlBGlM9Xh6rMrFf9UN8dlm+LR0HUou1+zycbTB9aAQSYnxgbmZ2U39b2K/K1Kjn9xwGpYhasfFADg6cLJLbA2N8May3P88TEWlNTQxHem4FTpwtxYb92YgMcEF8N2+eISIiItK5iup6/LozUy7I0njxAoGdjaW8iDa6byCsLC3YK2SwGJQiukx6bjl+3JImtwM8HXDvuK6dWieDiIyPmKb0p1tiMP+rfSirrMfCNScQ5OMIHzd7fTeNiIiITERdQyN+25+NNXvOora+Ue6zMDfDqL6BmDwoFI52LD1Cho9BKaJLVNc2yOLF4gqDjbWFrCMlvhIRXc7ZwRqPTO2Bt787LAeCn/1yDPPu6cv6UkRERNSpxHTpnSn5WLHjDEov1Gn394/2xvRhEfB2NZ3FEsj4MShFdEkdqUXrUnGuvFbenzOuK/w8rl+YjYhMV1SgK6YNDZd1pTILLsg6DrNHsr4UGbfU1KZVZ4mIyPA+r6ScKcHSLWnIuWRFva5BrrhtZCTC/FgDl4wPg1JEF+1Izsf+i3WkBvfwxYAYX54bIrqu8QnBOJ5ZguOZpVi/LxvdQ90Re3FlGyIiIqKOcLbggiwxIupZNvPzsMesEZHoFeHBciNktBiUIgKQd64K3/12Sp4LH3d73DW2C88LEbWJWMnmwcnd8dLCfbhQ3YAFq47j5bn94eJowzNIREREN+VceQ1+3p6B3ccKtftcHKwxdUgYEnv6wcLcnGeYjBqDUmTyGlSN+PSXY6hXqWFpYYY/3xIDW2v+1yCitnN1tJGBqX//mISK6gZ8seo4/ja7twxYEREREbVXVW0DVu8+K1cFVzWq5T4bKwtMSAjGuP7BrHtLisFP3mTyftgs5mRXyvMwa3gkQnydTP6cEFH7iSl74/oHySl8Yirfur1ZmDgghKeSiIiI2qxBpcbmQzlYtSsTVbUquU9c5BrW2x+3JIbJLCkiJWFQikzaoVPF2HwoV273jPDA6PhAfTeJiIzYjGEROJlVJus+iFT7rsGuiPB30XeziIiIyMCpNRrsO1GIn7ZlaBdeEuKiPDFzeAQXYCLFYlCKTFZJRS2+WnNCbrs4WmPupGgWCCSim2JpYY4/3xqD+V/tR119Iz775Rjm398f9rZ8uyUiIqLWnTxbKouYi5V8m4X7O+O2EZHoEuTK00aKxlEymeyViAWrT8iUWFHx5eEpMXC2ZyosEd08Hzd73Du2q6wrJa50fr/xFB6Y3J2nloiIiFrILqrEsq3pOJpxXrvP29UOM4ZHIL6rFy+Yk0lgUIpM0qYDOdrlVMcPCEZ0iJu+m0RECjKwhy+OnjmPPccKsTOlAL0iPRHfzVvfzSIiIiKDWVHvDPYcK4Dm4j5HOytMGRyKEXEBMvOayFQwKEUmJ/dcFZZuTZfbQd6OmDYkXN9NIiIFuntMF6RmlaH0Qh2+WZ+KyEAXuUofERERmabKmgZZwFwUMlc1NoWjrC3NMbZ/EMb3D+F0fzJJDEqRSRHLqX7x6zH5VVyBeGhKd16JIKJOYW9rhQcnReOdJUfkIPSrNSfx5KyeTMUnIiIyMXUNjdh4IBtr9pxFTV2jdkW9ob385Ip6vGhFpsxg8wLr6uowb948xMfHIzExEQsXLrzu9+Tk5CAuLg579+7V7quvr8dbb72FoUOHol+/fvjLX/6CgoKCTm49Gapffj+DrMJKuT1zWDgCvRz13SQiUrDoUHeM7Rckt0W9iK1H8vTdJCIiItKRRrUa247k4vnPdmP5tgxtQKpvVy/868H+uHd8NwakyOQZbKbU22+/jZSUFCxatAh5eXl49tln4e/vj/Hjx1/1e+bPn4/q6uoW+z788ENs3LgR7777Ltzd3fHOO+/gsccew9KlS3m12sSczimTVyeEbsGuGH3xgyIRUWeaMSwcKWdKkHeuCj9sPi1r2Pm62/OkExERKZRGo8Hh0+ewfFs68s//8flUrKQ3a3gEIgJc9No+IkNikEEpEVgSQaMvvvgCMTEx8nb69GksXrz4qkGplStXoqqq6or9P//8M1544QX0799f3v/Xv/6FIUOG4OzZswgNDe30YyHDUFOnwperjkOjAexsLPHApO4yZZaIqLNZWVrgocnd8eo3B1DfIKYQH8e8e/rAwtxgk5WJiIjoBp3KLsPSrWlIz63Q7gvwcsDMYRHoGeHBxAiiyxjkiPjkyZNQqVRyKl6zvn37IikpCWq1+ornl5aWygyoV155pcV+8Vyxf9CgQVd8z4ULFzqp9WSIRHZCcVmt3L57bBd4uNjqu0lEZEJCfJ0wdUiY3D6TX4HVu5qyNomIiEgZcosr8eGyZLy5+JA2IOXubIMHJkXj5fv7y5V4zXhRnMg4MqWKi4vh5uYGa2tr7T5PT09ZZ6qsrExOw7vUm2++iWnTpiEqKqrFfnNz8ysCUt9884187a5du3byUZChSEo7h+1J+XK7XzdvDOjuo+8mEZEJmpAQgqT080jLKcfKnZnoGemBUF9nfTeLiIiIbsL58lo5TW/n0Xw5K0NwsLXEpIGhGNU3QGZME5GRBaVqampaBKSE5vuicPmldu3ahYMHD2LVqlXXfV1RW0oUTH/55ZeveP1rMTc3k7fOYGFh3uKrkunjWKtqGuRS7IKrozXunxQNK6vOf2NgvyoT+1WZdNmvj9zaA/M+3yNX4Vm4+gReeTBBpyuA8neYiIio4z5n/LLzGFbuyECDqmk2j5WlOcbEB2HigGC5Ci8RGWlQysbG5orgU/N9W9s/pl3V1tbixRdfxEsvvdRi/9UCUk8++STuvvtuzJo1q13tcXd36PRUS2dnO5gKXR7rovWHUHqhTm4/flscgvxdoUvsV2VivyqTLvrVzc0Bc2+Jwf8tT0ZOcRXWH8jB3eOjoWv8HSYiIrox9Q2N2HQoB6t3n0V1rUruEx8VE2P9cGtiGNydWSaEyOiDUj4+PrJOlKgrZWlpqZ3SJwJPzs5/THVITk5GdnY2nnjiiRbf/9BDD2Hq1KnaGlOrV6/GM888g9tvvx3z5s1rd3tKSqo6NVNKfDioqKhBY+OV9bKURNfHeuT0OWzany23B8f6IsrfCaWlVxbD7wzsV2VivyqTrvs1oZsXtoa44cTZUizdeBoxwa4I9dPNND7+Dnd8kJGIiEyDWq3BzpR8rNhxRnvRW+jTxQvThoYjwJPvCUSKCUpFR0fLYNSRI0cQHx8v94kperGxsbJOVLOePXtiw4YNLb537NixePXVVzF48GB5f/fu3TIgddddd91QQKr5D5C4dSbxQUh1Me1T6XRxrNW1DVi4+rjcdnG0xu2jovRyftmvysR+VSZd9ut9E7rhxQX75DS+z1cew4v39dPpND7+DhMREbWNRqORNSGXb01H7rk/LnBHBbrgwamx8HO1NZnPcUQmE5Sys7OTmU7z58/H66+/jqKiIlkL6o033tBmTTk5OcnMqZCQkFYzrTw8PGSmlQhE9evXT2ZPie9r5uLi0q66UmRclmxKQ1ll05TPOeO6wYFzuonIgHi52mHWiAj8b8MpOY1v1a5MTB0Sru9mERER0SXScsuxbEsaTuWUa/f5edhj5vAIxHfzhru7o85mYhAplUEGpYTnn39eBqXmzJkDR0dHPP744zILSkhMTJQBqunTp1/zNVJSUpCXlydv4nsuX4UvISGhU4+B9CM5/Tx+P9q02t7AGB/0jvJkVxCRwRkeF4ADJ4twMqtM1qWIi/JCiK+TvptFRERk8vLPV2H5tgwcOvVHUoObk42sGSXKgliYm3d6zWEiU2GwQSmRLfXWW2/J2+VSU5tWU2vNpY/17t37ms8l5RHT9hatOym3nR2sccfoLvpuEhFRq8zNzHDfxGi8uGAv6hvUWLD6BF68L16n0/iIiIjoD6JW1C+/n8HvyflQa5rKt9jZWGLSwBCM6hsIGx2s4k1kagw2KEV0I5ZsTtMWHpwzrisc7bgUKxEZLm8xjW94JBb/JqbxVXIaHxERkR6IVfTW7j2L3/Zno/5ifShxkWh030BMHBjCzxREnYhBKVKMY5kl8qqGMKC7D+K6eOm7SURE1zWiT9M0vtTspml8okZFoJcjzxwREVEna1CpseVQDn7dlYmqWpXcJyblDYr1xdTEcHi42LIPiDoZg1KkCGIFq28uTttzsrfCnWM4bY+IjGca3/0Tm1bjE1dnv157EvPu7gtzc9aqICIi6gxiZfU9xwvw8/YzOF9Rq93fM8IDM4dFINCbF4eIdIVBKVIEMfe7uKzpDeWO0VFMsSUio+LtZi+Lpy7dmo6MvApsPpSD0fFB+m4WERGRomg0GqScKcHSLely2nyzcH9nzBoega7BbnptH5EpYlCKjN7ZggvYsC9bbseGeyAh2kffTSIiarex/YOw93ghsooqsXx7Bvp08YK7M6cNEBERdYQz+RVYuiVNrnrbzMfdHjOHhcv3XK6mR6QfDEqRUWtUN011EatjiNUw7hnXhW8oRGSUxPLS903shn8tOoC6+kZ8uz4VT8zsyb9pREREN6GwpFpe7BH1G5u5OFjj1iFhSIz146q3RHrGoBQZtd/25+Bs4QW5PX1oODxd7PTdJCKiGxbq64yx/YKwfl82ktLPY//JIvRn9qdJUavVOHHiBJKSklBcXIza2lq4ubkhLCwMffv2hbu7u76bSERkFMor67ByZya2J+WhUa2R+2ytLTBhQAjGxgfBxtpC300kIgalyJgVl9Vgxe8ZcjvMzxmj+gbqu0lERDdNrPZzMLUY58pr8d3G04gJc4eDrRXPrMJlZWVh8eLF+PXXX1FSUgILCws4OTnB2toaFy5cQE1Njcyai4+Px6xZszB58mSYm5vru9lERAanpk6F9fuy5AUesRiSYGFuhpF9AjF5UAic7K313UQiugQzpchoixR+sz4V9Q1q+SZz34RuXKmKiBRBXLm9d3xXvP9DEiqq6vHj5jTcPzFa382iTvTPf/4TK1asQJ8+ffD4448jLi4OUVFRMjDVTASqjh49ih07duCdd97BJ598gtdff11+DxERAapGNbYezsWvuzJxobpBnhKxju2AGB9MHRIOL1fOqCBSVFCK6eWkT3uOFeLYmRK5PT4hGEFctpWIFKRHmAcGxvhg97FC7EjOx4AYX0SHcEUgJVu9ejWCg4Ov+riYtjds2DB5e/7552VGVW5uLoNSRGTyRG3ZfScK8fP2DO1q3EKPMHfMHB6BYB8nkz9HRIoKSjG9nPStsqYBSzafltvebnaYMihU300iIupws0dF4WhGifybJ4qevzy3P6wsOV1Lif71r3+16/kig2rq1Kmd1h4iImMhLlIv3ZqGrMJK7b4QXyfMGh6B7qGswUekuKAU08vJEPy0LV2bknvvuK6wtmKRQiJSHmd7a8weGYkFq0+goKQa6/ZlMQivYAcOHMCaNWuQl5cHS0tL+Pn5oXv37hg4cCB8fX313TwiIoNytuAClm1Nw7HMUu0+b1c7TB8Wjvhu3jA3ExP3iEiRmVJMLyd9Ss8rx7YjeXJ7QHcfXgEhIkUb1MNXTt87lV2GVbsykdDdRw66SVm+/fZbvPbaawgKCpIBKFHUfNOmTbJ+oihmnpCQIGtNsX4UEZm6orIaOU1v7/FC7T5neyvckhiGob38YWnBjGIiRQelmF5O+tSoVuPbdakQC7ra2VjKDAIiIiUTq63dM7YL5n+1Hw0qNb777RT+OrOn3E/K8cUXX2Du3Ll45pln5H2VSoUePXrgP//5D0pLS2X9qLvvvlsGph555BF9N5eISOfEwh+igLkoZN6o1mgXBhnfPxjj+gfB1prrdxEZK/7vJaOx+WAusoqa5otPHxoOF0cbfTeJiKjTBXg5Ymz/IKzdk4Xk9PM4dKoYfbt688wryIULFzBixAjt/eago8icGj9+PO644w5s2bIFf//73+W0PtaTIiJTUVuvwoZ92Vi7Lwt19Y1yn1h5e3jvAEweHAoXB2t9N5GIdB2UYs0D0ofSC3X4eUeG3A71dcKIuAB2BBGZjFsGhWHf8SKcr6jFdxtPIybMnVeFFURMy9u8eTP69et31eeIoNXf/vY3fPnllwxKEZHiqRrV2JGUh192ZsosqWb9o73lxWlvN3u9to+I9BSUYs0D0pclm06jtr4R4trxPeO6wtycU1eIyHSIKQp3jonCf5cflUH6X34/g9kjo/TdLOogTz/9tMyGEhlSjz32GGxsWs8EDgsLQ3Z2Ns87ESmWqKV3ILUYy7elo6i0Rrs/OsQNs0ZEINTXWa/tIyI9B6VY84D0IeXMeew/WSS3h/cJQJgf34yIyPTERXmhd6QnjqSdw2/7czCohx+CvB313SzqAN26dcPChQvl9LwffvgBI0eOlAEqsRJfQEAALCwskJaWhvfffx8RERE850SkSCfOlsoV9c7kX9DuC/Z2xMwREYgJdWc9RSKFaldQijUPSNcaVI3434ZTctvZwRozhoazE4jIZN05OgrHM0tQr1Lj2/WpeO7uPlz2WiHi4uKwdu1aLF++HCtXrpSr7onC5s31pUT2gL+/Pz766CN9N5WIqENlFV7Asm3pSMko0e7zdLGV0/T6d/fh+xyRwrUrKMWaB6Rr6/Zla1N3xWp79rZW7AQiMlmernaYMjgUy7dlIC23HLtTCjA41k/fzaIOYm1tLafxiVtVVRVSU1NRUFAgV+MTASkRuBJZU0RESnCurAY/7ziDPccK5OragqOdlXyfE4XMrSzN9dxCIjK4oBRrHpAunS+vxepdmXK7a5ArBnT3YQcQkckb1z8YO48WoKCkGku3pstpffa2XExXaRwcHOTFQCIipblQXY/Vu89i86EcqBqbwlHWVuYY1y8Y4xOCYWfD9zQiU2J+IzUP1q9fjyFDhuC5557T1jwoKyuT0/sOHz7MmgfUIX7YfFpOUTE3M8NdY7pwHjkRkbiaZGEui54LYkWilTvP8LwYue+++w719X+sLtUWIotq9+7dndYmIqKOVlffiFW7MvHcZ7uxYX+2DEiJcb5YVfvNPw3EtKHhDEgRmaB2h6FZ84B0QdRMEStvCCP7BCCQxXyJiLR6hHmgTxcvHDpVjI0HcjCkpx8CvFj03Fj9/PPP+PjjjzFp0iSMHz8esbGxsLK6crp6YWEhtm/fjtWrVyMpKQlvvvlmh7Whrq4OL7/8MjZs2ABbW1vMnTtX3oiIblajWo0dyfly5djyyj8C8PFdvTB9WAR83e15kolM2A3lRrLmAXUmVaMai39rKm7uZG+FqUPCeMKJiC5z+8hIHM04jwaVGt9tPI2/396bGaVGaunSpfjtt9/wzTff4Ntvv4WlpSVCQ0Ph7u4ux1wiEz0nJwfnz5+Hi4sLpk2bhnfeeQdeXl4d1oa3334bKSkpWLRokcyAf/bZZ2UdKxEkIyK6EWKBhkOnzmH5tnQ55byZKMshVtSL8HfhiSWiGwtKXYo1D6ijbT6Yg/zzTW9cM4dFsLg5EdFVip5PHBAirzyLZbQPphYjvps3z5URUavVcpU9YcyYMfImgk9iWt7Ro0dRXFwsp/WJ4NDgwYNljan+/fu3mkV1M6qrq2Vg7IsvvkBMTIy8nT59GosXL2ZQiohuSGpWKZZsPI30vArtvkAvB8wcHonYcHdeRCGiGwtKiZoHM2fOlFft2lPzoKSkBAMHDmzPjyITVV5ZhxW/N9VHCfNzxuCeXFWKiOhqJiSIouf5OFdeiyWbTyM23AM21lydzVjMnj1bBoMOHDiA+Ph4uS8wMBCzZs2SN105efKkXOFPlGho1rdvX3z66actAmdERNeTU1SJ//50FPuPF2r3eTjbYOqQcAyM8YW5uRlPIhHdeFDKEGoekLIt25qO2vpGiLeru8d2kcUPiYioddZWFrh9VBQ++ukoSirqsHrPWUwfGs7TZSRqa2tlJtRrr70mx1j6IjKy3NzcWlx09PT0lHWmxEI2Yhrh9YgPmp3xYdPCwrzFV6UzpePlsSpv1eyftqfj9+R8aJoW1IODnRVuGRyKUfGBsLZU3gUT/g4rE/vVwINSuqx5cCMFN8XPnjJliryyl5CQoN3/9ddfY8GCBaisrMSECRPwz3/+E3Z2du1uE3WutNxy7EwpkNtDevnJTCkiIrq2uChP9AhzR8qZEqzbexaJsb7wdmPRWGMwffp0jBo1Sgam3n33XXTv3l2udBwertvAYk1NzRVZ8M3327oqoLu7Q6dOx3F2Nq1xmykdL4/VuF2orseyTafx6+8ZssZh8wWTW4eGY/qIKDjadex0Y0PE32FlYr8acE0pXdU8uJGCm/Pnz5d1ES61fv16fPTRRzI45uHhgeeff15uv/jiizfcNup4ao0G3288LbftbSzlShxERHR9IhBwx+govLhgn1xee+mWdPxleixPnRGYM2eOnKY3depUOcYR46ovv/wSubm5CAsLw5IlS3TSDhsbmyuCT833xYXBtigpqeq0TCnxwaCiogaNjU0feJXMlI6Xx2rc6hsa8dv+bPy6KxPVtSq5T8Slh8cFYM7kGFiZAQ219SitbVtg2xjxd1iZ2K8dy83NofMKnXdmzYMbKbi5cuVKVFVVXbFfZHWJQd+IESPkfZF99cADD+Dpp59mtpQB2XusEGfymwoh3pIYBmf7ttctIyIydX4eDhjVNxAb9mfj4KlinDxbim4hbvpuFrWxptQbb7yBfv36afeL+k5paWk6O38+Pj4oLS2VP1dkwQvigqMISDk7ty1rWa3WyFtnEQEa1cUsDFNgSsfLYzUu4v+5qGUoasCWXqhrkbU7Y1gEgn2d4OZih9LSKv4OKxD/vypTo57fczp8wnp2djaSk5OvyFjqiIKboj6VKLh5OTGQEtlPr7zySov9jY2NMpOruXio0Lt3bzQ0NMifQYahrr4Ry7aly20fNzuM7BOg7yYRERkdUbejeZqEKHremQEC6tiaUq+//nqL/SIwJKbx6Up0dLT8mUeOHNHuO3jwoKwdyiLnRCRoNBocOX0OLy7ch6/WntQGpCIDXTDv7r54fEZP+HtePyOCiKjDMqVaIwZVa9askVlUIjgl0tH/9re/wcLColMLbopC6qJ+VVRUVIv9FRUV8nu8vf9YIlsMulxdXVFQ0FS7iPRv3b4s7Rvb7JFRsDSB4p5ERB3N3tYKU4eE4X8bTiGrsFJeyR7Sy58n2oAZSk0pUWdTjNlEGQQxlisqKsLChQtlBhcRUVpOOZZuTcPpnHLtyRABqJnDItAr0qNT68kRkfJ1aFBq8+bNsjC5vb29LJr5wQcfyNpQoo5TZxXc3LVrl7yat2rVqlavQF76vZe+VlsLd3bmijKCqVf3L6moxdo9Z+V2TJg7+nbzUsQbm6n3q1LxWJVJSf0qVjjacigXueeq8NP2DAzo4Qs7G0tFHuv1GMOx3n///QZRU0oQYzURlBIlDxwdHfH4449j7NixOvv5RGR48s5VYfm2dBw+fU67z83JRl4AGdzDr9M+HxGRaenQoJTIZmouiCmuuj333HOYNGlSpxXcFEEnUbD8pZdearUQp3idS7/30tdqz+p7nb2ijClX9xfpv/UqNcR72p9n9IK7uyOUxFT7Vel4rMqklH59eFpPvPTFbpRX1WPjoVzcO7G7Yo+1LQz9WEUASNTMFHWd9FVTShDjorfeekveiMi0iRkMv/yegR3J+dBcnAkuFiKaNDBE1i8Uq+sRERlkUEqsbvfUU0/hH//4h9wWtZ6aA0OdUXBT1K4S0wSfeOKJFt//0EMPadPQxc8/d+4cIiKaVnMTrymmAHp5ebW5PZ21ooypV/dPzy3HloM58rFhcQFwsbWQRRGVwJT7Vcl4rMqktH4N83GQ0ymS0s5jxdZ0DIj2hpernSKP9VoMZUWZto57RL0WcRM1nHRdU4qISKiubcDavVlyVT1x0VgQZTVGxwdi4oAQbd1CIiKDDUqJ1PPjx49j3LhxcHJyksGfGTNmyOCRGFxdPo2uLQU3m4uUt1Zws2fPnnK64KVEqvmrr76KwYMHy+eK7xHfm5CQIB8Xr9newV5nryhjCBXvdUkca0NDIxZvOCXv29lY4NbBYYo8flPrVx6r8rBfjdOs4ZE4ml6ChkY1fth0Gn++tUeLx9mvhmXFihV47733YGVlJUshFBYWyotoAQFc+IOIOl+DqhGbD+Vi1a5MVNWq5D4xSURM0RNT9dydr5yRQkRkEEEpsRLeqVOnUFVVJYubv/DCC9rHzpw5IwNUx44dw/vvv4/Tp09j586dHVJwU2RNiaCXyJwKCQlp9YqjyNQS7rzzTjnFr0uXLrLguXjN2267rV3T96jj7T9ZhLTcpmKJkweFwtmhbQFLIiK6PlGAdkSfAGw6mIN9J4owqm8ZogJdeeoM1BdffIG1a9fi7rvvlvdFcOrpp5/GN998o++mEZGCiYvuu48VYMWODJyvaFp0SOgd6Ynpw8IR6KWsshpEpLCg1NGjR/Hkk08iLy9PppuLmksi++j222/H7NmzZYFOcbuRmlLXK7iZmJgoA1Ri1ZrrET9fFAwVgSlRS0q8hhjokf7UNzRi6ZamWhlerrYY3TeI3UFE1MFuTQzDnmMF8qr39xtP4x9zmjKPyfCIC21irNNMrDJ84cIFvbaJiJRLfHY7mnEey7amI6f4j9IZEf7OmDk8Al2D3fTaPiIyLTcclBJZUSJTSixhHBQUJLOXtm/fLjObfvvtN3zyySdtnq7X3oKbqampV/2+1h57+OGH5Y0Mw7q9WdqrMbeNiISVpeGujEREZKxE7Y9bBofh+02nkVlwQQaohvbmdDBDJMZR4mJf86IqDQ0NqK6u1neziEiBMvIqsGxrGk5mlWn3+brbY8awCPTp4qmIVbCJyESCUhkZGbL+gagf1WzUqFGYO3euTD//97//jWeffbaj2kkKUVJRi193ZsrtrkGu6NOl7QXniYiofcQUvi2Hc1FQUi2viCd09+UpNEAiO1wsFJOfn4/PP/8cO3bsQN++ffXdLCJSkMKSaizflo4DqcXafS6O1piaGIbEnn6wuKRuLxGRLt3wXx+xCp6FxZXLgYoaT2I1vJUrV95s20iB/rf2BOoaGiGuwdw+KopXY4iIOpFYNem2kZFyu6yyHqt3N10UIMMipuuJ2pkiO1xMqxHlCV555RV9N4uIFKC8sg7frk/FC1/s1QakxCJDM4aF480/DcSw3gEMSBGRcQalJkyYgC+//FKuDnM5UVC8pqbmZttGCpNVeAEb92fJ7cE9/RDi66TvJhERKV6vCA/EhDbVB1mz+yzOl/P92RCJKTPDhg3Dt99+yzEUEd20mjoVft6egWc/2y0zZtUaDSwtzDC2X5AMRk0aGAobqysTDIiIjCYo9be//U0Omm699VasXr0a5eVNK6mdO3cOX331FcaMGdOR7SQF+GFTGjQawNrKHNOHhuu7OUREJhPsmD0ySmao1qvU+G791esykv6JBWPEqsXjx49n1jkRtZuqUY2NB7Lx3Ge78euuTNQ3qOXf/4ExPnj9oQFypoKTPVe9JiIFBKUcHBywePFiJCQk4LnnnsOAAQPQu3dvDBkyBJmZmTIodf78+Y5tLRmtY5klcpUPYUJCCFwdbfTdJCIikxHo7YhBsU31pDbuO4vc4kp9N4mu4rHHHsPGjRvlOEqsHDxlyhRs3ryZ54uIrklkQu09XogXvtiD7zaexoXqBrm/R7g7Xrq/Hx6aEgNPVzueRSJSTqFzQSxfLAZMojjn7t275coxJ06ckDcxqBJXZz08PNC9e3dZuJNM901y6ZY0bUHFiQND9N0kIiKTM21IOPadKEKDSo0fN6fh8Rk99d0kugpXV1e5WMz9998vVzMWtTp79Oghs9T79+/P80ZEV1z8XbYlHWcLL2j3iTIZtw2PQHSoO88WESk3KHVp1tTo0aPlrVlJSQmOHz8ubydPnuyIH0NGSly1ySpsuip/x5iusLOxhEql1neziIhMiruzLcb2D8LqXWdx+PQ5pGaVomtwU60pMkyiRuf8+fPx4IMP4r///a8MUonM9AULFui7aURkAM4WXMCybek4dqZEu8/b1Q7Th4Ujvps3zM3ExD0iIhMISl1tJZnExER5I9Mlrsj/tC1Dbvu422PcwFBcqGCRXSIifZg8KBTbj+TJaR1Lt6bjhXv6chVUA1ZcXIz09HRkZGTAyckJ/v7+2LVrl76bRUR6VlxWg593ZGDPsULtPid7K9wyOAzDevvLlVeJiGDqQSkiYfOhHJyvqJXbs0ZE8E2SiEiPHGytcNvorliwMgUZeRU4mFosr6aT4Xj++edx5swZGYyqrKyERqOBra0twsPD0adPH8yePVvfTSQiPblQXS+Ll285lItGtUbuEyvojesfhHH9g+VsBCIiY8O/XNRpqmobsGpXptwO93dGP37wISLSu0mDQ/HLtjScK6+V0z56R3nygoEBOXbsGKKiojB8+HBERkaiS5cuCAoKYkYbkQmrq2/EhgPZWLvnLGrrG+U+C3MzDO3tL7OjXBy4mh4RGS8GpajTrNl9FlW1Krl924hIDqiJiAyAlaUFZo6IxKcrUlBUWoNtR/Iwqm+gvptFF61cuZLngoikRrUaO5Lz8cvvZ1BeWa89KyLDdcbQcFkag4jI2DEoRZ3ifHktfjuQI7d7R3qiS5ArzzQRkYEYEOODtbvPypWaVu48g0E9fDntg4jIQIhpu4dOFWP5tgwUlFRr93cLdsXM4ZFyBgIRkVIwKEWdYsWODKga1RCLfswcHsGzTERkQMSKTLeNiMA7S47Ioufr9mZh2tBwfTeLiMjkncouw9ItaUjPq9Cei0AvBxmMig1358wDIlIcBqWow2UVXsCulAK5PaSnP/w9HXiWiYgMTHSoO3qEuyMlowTr92dhRJ8AuDra6LtZREQmKbe4UmZGHUk7p93n4WyDqUPCMTDGF+bmZnptHxFRZ2FQijqcKJwr1gOxtjLHrYlhPMNERAZq1vBIHMvYh/oGtaxZMmd8N303iYjIpJRU1GLFjjPYmZIPTdOCenCwtcTkQaEY2SdA1gEkIlIyBqWoQ53ILJFX3YWx/YLh5sSr7kREhirI21HWk9qZUoDtSXkY2y8Ifh7MbiUi0sUq1WJRoI0Hc9CgUst9VpbmGBMfhIkDgmFva8VOICKTwKAUdWhRxmXbMuS2o50VJiQE8+wSERk4UUtq74kiWQfw5+0ZeHRarL6bRESkWA2qRmw6mIvVuzO1q1SLGqyJsX5yhoG7s62+m0hEpFMMSlGHOXL6HM7kNxVlnDwwhCs5EREZAfEBSEwR2bA/GwdSi5FZUIFQX67sRETUkRrVGuxIysPybekoqajT7herVM8YHoEA1mAlIhPFoBR1CLVag5+2N2VJiSl7omAuEREZh4kDQ7AtKQ919Y34aVsG/ja7t76bRESkmJkE4sKtCEadLbig3R8Z4CJXqO4S5KrX9hER6RuDUtQh9h4vRO65KrktUo9ZlJGIyHg421tjXL8grNyZiZQzJUjNKkXXYDd9N4uIyKil55Vj6ZZ0nMou0+7z87DHjGERiIvyhJmYt0dEZOIYlKKbJuuQ7GjKkvJxt8fgWF+eVSIiIzOufzA2H8pFZU2DXJb8+bv78AMTEdENyD9fJWcQHEwtbjFVeuqQMAyM8YGFuTnPKxHRRQxK0U0T8+PPldfK7WlDwvhGS0RkhOxsLDFxQAh+3JKGtNxyJKWfl7VOiIiobcoq62TG6fYjeVBrNBf/tlpg8qBQ3Da2G2qq6qC6uNIeERE1YVCKbkpdQyNW7sqU28Hejojv5s0zSkRkpETB898OZKP0Qp2sLdUzwgPmnF5CRHRNNXUqrN2bhQ37s1Df0BR0srQww8g+gTIg5epkA1trSxmUIiKilhiUopuy+WAOyivr5fb0YRH88EJEZMSsrSwwZXAovlmXipziSuw7UYgB3Tklm4joaiUsthzOxa87M+XUZ0FUiRoQ44NpQ8Lh6WrHE0dEdB0MStENq65twJo9Z+V2VKALYsPdeTaJiIxcYqwf1u3NQlFpDVZsP4P4rt6wtGD9EyKiZmJqngjai4zS5hIWQo9wd8wcFoFgHyeeLCKiNmJQim7Yun3ZqKpVyW2xighXECEiMn4iACWK8X6+8jiKymrw+9F8DO8doO9mEREZhOOZJXJFvbOFF7T7QnydcNvwCESH8gItEVF7MShFN6S8qh6/7c+W26LmSJcgV55JIiKF6B/tgzW7s+QUvpW/n8GgGF85tY+IyFRlF1Vi6dY0pGSUaPd5u9ph+rBwWVOV9feIiG6Mwebj19XVYd68eYiPj0diYiIWLlx41eeuXLkS48aNQ8+ePXH77bcjOTlZ+5hGo8F///tfDB06FP369cOTTz6JkpI/3kzoxqzenSmLnAtizjwRESmH+HAlPmgJZZX12HwoV99NIiLSi5KKWixYfRzzF+7TBqSc7K1w15guePWhBBnEZ0CKiEiBQam3334bKSkpWLRoEV566SV89NFHWLdu3RXPO3DgAF544QU8+uijWL16NeLi4vDQQw+hqqpKPv7DDz9g2bJlePfdd7F48WIUFRXJ59ONO19ei62Hmz6g9I/2linLRESkLL0iPBAZ4CK3Rf1AsboUEZGpqK5VYdnWdDz/+R7sPFoAjVgMwtJcrqb35p8GYlTfQNbbIyJSalCquroaS5culcGjmJgYjBkzBg8++KAMKl2uuLhYBqRuvfVWBAUF4S9/+QvKysqQnp4uH9+2bRsmTpyI/v37o0uXLvJ19uzZo4ejUlaWlKpRA7FK+FRmSRERKZKoEzjjYraUWFVq48EcfTeJiKjTNajUskTFc5/tlgF5cV+MeYf28sMbfxqI6UPDYWfDCihERB3FIP+injx5EiqVSmY9Nevbty8+/fRTqNVqmJv/EUubMGGCdru2thZff/01PDw8EBERIfe5urpi69atuO++++Di4iKzqaKjo3V8RMpxrqwGO5Lz5fagHr7wdbfXd5OIiKiTdA12Q3SIG06cLcX6vVkY1ScQ9rYGOXQgIrrpFfUOnCyS2VGXrqgnskZnDo9AgJcjzzARUScwyJGlyH5yc3ODtbW1dp+np6esMyWyoNzdr1zZYvfu3Zg7d66sISWm6jk4OMj9InPqkUcekTWlLCws4OXlJaf00Y35dVcmGtUaOXd+yuAwnkYiIoUTK/GJoFR1nQq/HcjGrYn8209EynLybKksYn4m/48V9cL8nHDbiEgZnCciIhMLStXU1LQISAnN9+vr61v9nqioKPz000/YsmULnnvuOQQGBqJ3797Izc2Fra2tzLJydnaWtapEAfVrFU6/nLm5mbx1BgsL8xZfDVlhSbWcUy8M6eUHf8+mwJ8Sj/Vm8ViVif2qTOzXaxNLnMeGe+Boxnls2J+F8QnBcLCzgqEzpX4lohuTW1wpM6OS0s9r93m52mLGsAj06+YtpzETEZEJBqVsbGyuCD413xcBptaITCpxE1PzkpKSsGTJEvTq1QvPPvssnnnmGYwYMUI+7z//+Y/cFs8Rj7eFu7tDp78pOTvbwdB9vS5VpjZbWpjhnkkxcHOzV+yxdhQeqzKxX5WJ/Xp1cyZ3x98/3IGaukZsScrHPROMZxq8KfUrEbVN6YU6/PJ7hixJoREVzAE42llhyqBQDI8LgJUlg9lERCYdlPLx8UFpaamsK2Vpaamd0icCUiLb6VLJyclyWp4oiN5M1JMShc5LSkqQn5+Prl27ah/z8/OTUwNFBlVbg1IlJVWdmiklBswVFTVobFTDUOWfr8KWg9lye2gvf1ibaVBa2rTCodKOtSPwWJWJ/apM7Nfr83a2Qa9ITySlncPK7ekY1tMXTvYtM5pNsV/d3NqXMUxE+iVWEV279yw27MtGvarp74IIQI3tF4QJCSGsmUdEpAcGGZQS2U4iGHXkyBHEx8fLfQcPHkRsbGyLIufCsmXLZIBpwYIF2n3Hjh1D9+7dZWFzMe1PBKiaC5+LQJWoSyWm97WVWq2Rt84kBsyqi2+OhujnbRnySpLIkpo4IOSm2mrox9qReKzKxH5VJvbrtd2aGCqDUrX1jVi1KxOzhkfCGJhSvxJR61SNamw7kodffj8jVxMVxOXmwbF+sm6eu3PrMzGIiMhEg1J2dnaYOnUq5s+fj9dffx1FRUWyBtQbb7yhzZpycnKSmVOzZ8/GbbfdhkWLFmHYsGFYuXKlzJ4StaNEYGv69Ol46623ZHaUCFKJbZEhJQJc1Da556qw93ih3B7WO4Bv3EREJijU1xlxUZ44fPocNh3Mwbh+wXB2MOxsKSIybWIBpIOpxVi2LR1FpTXa/aJOnlhRL8ibK+oREembwU6Yfv755+WUvDlz5uDll1/G448/jrFjx8rHEhMTsWbNGrktnvPRRx/JjKlbbrkF27Ztk1lTYgqgIIqai+976qmncM8998jpf5988gkLF7bDyt/PQHMxvVlkSRERkWlqXnmvvkEtp8AQERmqU9lleP3bg/hkRYo2IBXi44S/394b/++2XgxIEREZCIPMlGrOlhJZTeJ2udTU1Bb3ReHy5kLmrRVNF8XOxY3aL6eoEvtPFjWd57gAuDnZ8DQSEZmoYB8nxHf1woHUYmw+lItx/YPh6sj3BSVllTzwwAOYPHmyzDQnMkaiDqpYUU9kdTbzcBYr6oWjf3cfmHNFPSIig2KwQSkyDGLuvWBtaY4JzJIiIjJ5tySGyekwDSo11uw5iztHdzH5c6IEarUar732Gnbu3CmDUkTGprxSrKh3BtuT8uVq0YKDrSUmDwrFyD6BXFGPiMhAMShFV3W24AIOniqW2yP7BsKFtUOIiExeoJcj+kV7Y9+JImw9nIfx/YNZa9DIFRYW4u9//ztycnKuWOWYyNDV1quwbm8W1u/LRl1Do9xnaWGO0fGBmDQwBA62VvpuIhERGWNNKTKcLCkbKwuMTwjWd3OIiMiAakuJGTBiRavVe1hbytiJVYv9/PywfPlyuZAMkTEQf3+2HM7Fc5/twcqdmTIgJVbUGxjji9cfTsBtIyIZkCIiMgLMlKJWncmvwJG0prn44kqTsz1XWCIioiZ+Hg4Y0N0Hu48VYvuRPExMCIGHC5dUN1YjR46UNyJjqX0mxqhLt6SjoKRauz8m1A0zh0cixJeBVSIiY8KgFLVqxY6mLClbawtZyJaIiOhStwwOw97jRWhUa7BqdybmjO/GE2Sgamtr5RS91nh5ecHe3v6mf4a5uZm8dTQLC/MWX5XOlI73Ro41I68CSzaewsmsMu2+YB9HzB4ZhdgIDxgq9qsysV+Vif2qewxK0RXScstxNOO83B7bLwiOdpyLT0RELfm422NQD1/8fjQfvyfnY+KAEHi52vE0GaCkpCTce++9rT728ccfY/To0Tf9M9zdHWDWiauaOTub1u+WKR1vW461qKQa3649ga2HcrT7PF1scfeEaAzvGwSLTgiIdgb2qzKxX5WJ/ao7DErRFVZerCVlZ2Mpg1JEREStmTw4FLuPFchsqdW7M3HfhGieKAOUkJCA1NTUTv0ZJSVVnZYpJT4YVFTUoLFRDaUzpeNty7FW16rw664z2LA3Gw0XnyOy+MWKeuMSgmXd04ryP6bwGSr2qzKxX5WJ/dqx3NwcrvscBqWohfS8cqScKZHbY+IDYc8VS4iI6Cq8Xe1kttSO5HzsPFogPyh6uphOhgf9Qa3WyFtnEUELlUrZQRpTPd7WjlUUMd92JE8uulNZ0yD3mZuZYVhvf9ySGKZdEdrYzpGp96tS8ViVif2qOwxKUQu/7syUX+1sLDCGWVJERHQdYsl1EZAS2VJr9mTh3nFdec6I6MaLmJ8+hx+3pqPwkiLmvSM9MXN4BPw9r3/FnYiIjAuDUqSVWVCB5PSmWlKj+gZxGV0iIroubzd7DIzxwc6UAuxIysPkgSFwd+ZKfETU/pWff9ichlPZlxUxHxGJ6FB3nk4iIoViUIquyJKysbZgLSkiImqzSYNCsetibam1e7Jw19guPHtGavPmzfpuApmYc2U1+HFLGvYc+2OFSDcnG8wYFo4BMb5y2h4RESkXg1IkZRVewOHT5+T2qD6BXHGPiIjazNfdHgndfeSHym1JeZg4MER+qCQiuhpRxPyXVcewcntGiyLmYkrwmPggWFtZ8OQREZkABqVI+nVXU5aUtZU5xvbnintERNQ+kweGYu+xQlmgeN3eLNwxOoqnkIiu0FzEfOXOM7hQ3bKI+a2JYXC+WMSciIhMA4NShJziShxMLZZnYmRcIJztORggIqL2EQWI+0V7Y9+JImw9kouJA4Lh4shsKSK6dhHzuChPzBjGIuZERKaKQSnCqotZUlaW5hiXEMwzQkREN2TyoFAZlGpQqbF+XzZuGxnJM0lErRYxD/F1wkNTYxHsaQ+Vqmn6HhERmR4GpUxc3rkq7D9RJLeH9w6AC1OmiYjoBgV6OaJvVy+Zfbv5cA7GDwhm9i2RCTtXXoOftme0WsQ8sZc/PNwdUVpapdc2EhGRfjEoZeJW7c6ERvwiWJhjPLOkiIjoJk0ZFCqDUvUNamzYl42ZwyN4TolMsIj56j2Z+G1/jqwh1VoRc66qR0REAoNSJqygpBp7jzdduRrWy58rJRER0U0L9nGSNWLEiq6bDuXICx6OdlY8s0QmVMT8l9/PoLKGRcyJiOj6GJQyYat3ZUKjEVlSZpgwgLWkiIioY0wZHCqDUnX1jdiwPxvTh4bz1BIpvIj50Yzzsm5U/vk/ipj3jvSU2ZJiIQQiIqLWMChloopKq7H74vz+xJ7+cHe21XeTiIhIIUJ9ndEzwgPJ6eex6WA2xvUPgoMts6WIlLqKswhGHTtTot0X7OOI2SOjEB3ipte2ERGR4WNQykSt3n0Wao0GFuZmctluIiKijs6WEkGpmrpGbDyQg1sTw3iCiRSkoroeK3acwbYjuTLzXnBxtMaMoREYFOvLmlFERNQmDEqZoHNlNdiVUiC3B8f6wtPFTt9NIiIihYnwd0GPMHeknCnBb/uzZXFje1sOO4iMXYNKjY0Hs7FqV6YMOgtWluYY3z9YloOwteb/cyIiaju+a5igNXvOolGtkVewJg4M1XdziIhIoW4ZHCaDUtV1Kln0XKzMR0TGWzfq0Kli/LglDcVltdr9A2J8MHNYBEtBEBHRDWFQysSUVNRiR3K+3B7YwwfersySIiKizhEZ6CJrypw4W4oN+7Iwum8g7Gw49CAyNmcLLmDJptNIzS7T7osIcMbto6JkViQREdGN4sjQRLOkzMyAycySIiKiTnbL4FAZlKqqVWHL4VxMHBDCc05kJMoq6/DTtgzsPJqPi2Wj4OFsg5nDI9E/2htmYkBJRER0ExiUMrGBxfakpiypAd194ONur+8mERGRwnUNdkPXIFeZYbFubxZG9QmEjbWFvptFRNdQ39CI9fuysGZPFuoamupGif+3kwaEYGy/IFhb8f8wERF1DAalTMiGfdlQNaohrmlNYpYUERHpyOTBoUhdcgSVNQ3YlpQnP9QSkWHWjdp7vBDLtqWjpKJO7hPjxsSefpg+NBwujjb6biIRESkMg1ImQnwQ2HIkV2736eIFf08HfTeJiIhMRPcQN4T5OeNMfoXMvhgRFyBX6yIiw5GeW47vN51GRl6Fdl+3YFdZNyrYx0mvbSMiIuUy2BFhXV0d5s2bh/j4eCQmJmLhwoVXfe7KlSsxbtw49OzZE7fffjuSk5NbPL5u3Tr5eO/evTF37lzk5jYFZ0zJ5oM5qKtvSr+eOJD1PIiISHdE3ZnJg5ree0ov1GFXStNUciLSv/Pltfhs5TG89u1BbUDK280Oj02PxdN3xDEgRUREphmUevvtt5GSkoJFixbhpZdewkcffSSDS5c7cOAAXnjhBTz66KNYvXo14uLi8NBDD6Gqqko+fujQITz11FO4//778dNPP8Ha2hp/+9vfYEpq61X47UC23I4JbbpaTUREpEu9Ij0R6OVwyaIbanYAkZ7Hhz9tz8C8L/bIKXuCWB1z9shIvPpggsysZyFzIiIyyaBUdXU1li5dKoNNMTExGDNmDB588EEsXrz4iucWFxfLgNStt96KoKAg/OUvf0FZWRnS09Pl4yLD6pZbbpEZVOHh4fI1xfeUlJTAVGw/kidXPRJYS4qIiPTB3MxMm6lbXFaL/SeK2BFEeqobtftYAeZ9vgerdmWiQaWW/z9H9gnAm38agHH9g2FpYZAfEYiISIEMsqbUyZMnoVKpZNZTs759++LTTz+FWq2Gufkfb5QTJkzQbtfW1uLrr7+Gh4cHIiIi5L59+/bhzTff1D5HBK42b94MUyEGGuv2ZcntiABndA121XeTiIjIRPXv5oMVO86gqLQGq3efRf/uPvLDMBHphqjr9t3GU0jP/aNuVI8wd8weFYUA1hslIiI9MMiglMhkcnNzk1Ptmnl6eso6UyILyt3d/Yrv2b17t6wXJa7+vPvuu3BwcEBFRQXKy8vR2NiIBx54QAa7RN2p+fPnw8fHp83tMTc3k7fOYHHxSlTz1462IzkfZZX1cvuWwWGw0uMSvp19rIaEx6pM7FdlYr/q1pRBoViw+gRyz1XhaMZ59O3q3Sk/x5T6leh6yqvqsXxbOnYm50NzcZ+Pm50sYt4zwoPT9IiISG8MMihVU1PTIiAlNN+vr28KsFwuKipK1ozasmULnnvuOQQGBsLX11c+9uqrr+L//b//h7/+9a/44IMP8Kc//Uk+99KMq2txd3fo9DdrZ2e7Dn/NxkY11u1typIK9XPG8H4hnRZc0/exGioeqzKxX5WJ/aobk4ZG4pffz+BceS1W78nCqITQTn2PNaV+JbqcqlGNjQdysHLnGdReXPDG1tpCXqgcHR/IaXpERKR3BhmUsrGxuSL41Hzf1ta21e8RmVTiFh0djaSkJCxZskQWOBdmzZqFqVOnym2RRTV48GAcOXIEffr0aVN7SkqqOjVTSgyYKypqZBCpI+05VoD8800F3yckBKO8vBr61JnHamh4rMrEflUm9qvujU8Ixv82nEJadhl+P5SNHuEeRtmvbm5NhduJDFFS2jks2XQahaU12n2JsX6YMSwcLo42em0bERGRQQelxNS60tJSWVfK0tJSO6VPBKScnVuuHJecnAwLCwtZEL2ZqCclCp2LKYBWVlaywHkzsc/V1RUFBQVtbo9arZG3ziQGzCpVxw2axTTGlb9nym0vV1v06eLZoa9vSMdqyHisysR+VSb2q+4MjvWT2VIXqhvwy44z6Bbs1mk/y5T6lUgQFySXbEqT02Obibqid47uwhWYiYjI4BhkoQWR7SSCUSKbqdnBgwcRGxt7xZS7ZcuW4f3332+x79ixYzIQJV5DBKtELalmYtU9EfAKCAiAkiWnn0dOcaXcnjAgBBZtnKpIRETU2WysLDC2X5DcTs0uw+mcMp50optUXauSmVEvLtinDUi5OlrjocndMe/uvgxIERGRQTLISIWdnZ2cbicKkotMqI0bN2LhwoW49957tVlTYqU9Yfbs2dizZw8WLVqEzMxMfPjhh/J77rvvPvn4/fffj2+//RZr166V2VPz5s2TQS9R8FypRJbUqt1NWVIujtYY3MNP300iIiJqYURcIOxsmrKhxUp8RHRjRDb/9qQ8zPt8Nzbsz0ajWiNrRU0aGILXHx6AgT18WciciIgMlkFO3xOef/55GZSaM2cOHB0d8fjjj2Ps2LHyscTERLzxxhuYPn26zIT66KOPZLbUe++9JwueL1iwQLu63vjx4+UqfO+88w7Onz+P/v3745NPPlH0m/Op7DLtUr/j+gXDytIgY49ERGTC7G0tMapvIFbtypTZvWcLLiDE10nfzSIyKiLL8LvfTuNs4QXtvj5dvHDbyEh4u7LIPxERGT6DDUqJbKm33npL3i6Xmpra4v6IESPk7Wpuu+02eTMVzVecHWwtMTzOX9/NISIiatWY+EBs2J+F+gY1Vu/OxKPTYnmmiNqg9EIdlm5Nw55jhdp9AZ4OuGN0FLqHuvMcEhGR0TDYoBTdmMyCCqScKZHbo+ODYGvNLiYiIsPkZG+N4b0D5JSjg6nFyDtXBX9PrmhHdDWqRjU2HsjBLzvPoK6+UXsRcuqQcHkhkjVEiYjI2DBioTBrLmZJiSKyYloEERGRIRvXPxibD+VA1ajB2j1n8cDk7vpuEpFBOnG2FIt/OyWDt4IoRDGstz+mDQ2XAV4iIiJjxKCUwpYAFleaBXG1zNHOSt9NIiIiuiY3Jxskxvph65E87D5WiFsTw+DJWjhEWiUVtfhxSxr2nSjS7gv3d8ZdY7pwRT0iIjJ6DEopyJo9Z6ERnWphhrH9gvXdHCIiojaZMCAE25PyodZosHZvFu4Z15VnjkyemKr32/5srNyZibqGpql64oLjrOERGNzTD+YKXrSHiIhMB4NSCnG+vFZb7HJwrJ+88kxERGQMvFztkNDdB7uPFWBHcj6mDA6FqyPfx8h0pWScxzfrUlFQUi3vi/jTiLgAOVXPwZaZ8EREpBwMSinEun1ZaFRr5KBlQgKzpIiIyLhMHBgig1IiO2TDvmy5pD2RqTlXXotPVx7DruR87b7IABc5VS/E10mvbSMiIuoMDEopQEVVPbYn5cnthGgfeLvZ67tJRERE7SKWs+/bxQsHTxVjy+FcGaRibUQyFQ0qNdbvy8Kq3Zmob1DLfc72Vpg1IhIDe/hyqh4RESkWg1IK8NuBbDmYESYOCNF3c4iIiG7IpEEhMigl6udsPJAtl7knUrqjGefx3W+nUFhaI++bmwGj44Nwy+BQ2HOqHhERKRyDUkauulYll9IWekd6ItDbUd9NIiIiuiGhvs7oEe6OlIwSbDyQg3H9g2Fnw6EKKXdVve82nsahU00rJwtdg1zxl9t6w9XOEqqLFxyJiIiUjCM9I7flcA5q6ppWZJk0kFlSRERk3CYPDJVBqeo6FbYdycN41kkkhRF100TQ9Zffz2hX1XNxsJZ11BJ7+sHd3RGlpVX6biYREZFOMChlxMRAZsP+bLndLdgVEQEu+m4SERHRTekS5IrIQBek5ZRj/f4sjOobCCtLc55VUoS03HK5ql5OcaW8LxaoEb/j04aEy6xAM7GDiIjIhDAoZcR+T87HheoGuT1pYKi+m0NERNQhJg0IwQfLklFeWY+dKfkY3juAZ5aMWmVNA5ZtTdcuTCOE+Tnj3nFduaoeERGZNAaljDj1e93es3I71NcJ3UPd9N0kIiKiDtEzwgOBXo4ym2TdniwM6ekHC3NmS5Hx0Wg02JVSgB+3pGkvJIqMqJnDIzCslz/MRVVzIiIiE8aglJHae7wQ5yvqtLWkmO5NRERKId7TJg4Mxucrj6OorAYHThYjobuPvptF1C5556rw7fpUpGaXafcNiPHB7JFRsoYUERERMShllNRqDVbvbsqS8vOwR1wXL303iYiIqEP16+aNn7dnoLisFmv2nEX/aG9egCGjqfm5alcm1u3NQqNaI/f5uNvjnrFd0D3UXd/NIyIiMijMlDJCYunggpJquT1xQAjMWRSTiIgURkzXm5AQgm/WpyK7qBJHM86jZ4SnvpulSBUVFXjrrbewZcsWqNVqDB8+HPPmzYOzs7O+m2Z0ktPP438bUnGuvFbet7Qwx+RBIfJ3mQX7iYiIrsQCDUZYm2D1nqYsKQ9nW05nICIixRoc66ud5tScIUwd76WXXsLJkyfx+eefY8GCBUhPT8c//vEPnup2KL1Qh09+Por/LE3SBqRiwtzxrwf745bBYQxIERERXQUzpYzMscwSnC24ILfHJwTLK3BERERKZGVpgbH9g7B0SzpO55TjVHYZugS56rtZilJdXY3169fj+++/R48ePeQ+kSV11113oa6uDjY2NvpuokFTazTYfiQPS7emoaauUe4TgdQ7RkfJKais+UlERHRtDEoZmdW7mq4UO9tbydWIiIiIlGx47wD53lddp5K1pRiU6ljm5ub49NNPER0d3WJ/Y2MjqqqqGJS6hvzzVVi09iRO5ZTL+2IdvZF9AjFtaDjsbTnEJiIiagu+YxqRtJxy7QouY/oFwdrKQt9NIiIi6lR2NpYY2TdQFo4W9XqyCi8g2MeJZ72D2NraYujQoS32ffPNN+jatSvc3VmUuzWqRrUMkIrfSVVjUyHzAE8H3DehGyICXPi7SURE1A4MShmR1bsztQP0EXGB+m4OERGRToyOD8SGfVmoVzUFA/58a9M0M2qb2tpaFBYWtvqYl5cX7O3ttff/97//Ye3atfjyyy/bdXrNzc3kraNZXCxT0PzVEC4QLlh9HLnFVfK+pYUZbk0Mw6RBoR1SUsHQjrcz8ViVif2qTOxXZbIwkPccBqWMhFh5KCn9vNwe1TeAaeFERGQynO2tMbSXPzYezMH+k0WYNrQaPm5/BFLo2pKSknDvvfe2+tjHH3+M0aNHy+3Fixfj1VdfxfPPP4/ExMR2nVZ3d4dOrZ/k7GwHfaqubcC3a09g9c4z0DQlRyEm3AOPzeqFQG8nxR2vLvFYlYn9qkzsV2Vy1vN7DoNSRkJcGRasLc0xOj5I380hIiLSqXH9g7HlcC4a1Rqs25uFOeO7sQfaKCEhAampqdd8jlh17+2338YzzzyDOXPmtPvclpRUdVqmlBgsV1TUoLFRDX04fLpY1o4qqaiT9+1tLDF7VCSGxQXA3MwMpaVNWVNKOV5d4bEqE/tVmdivymShg/ccNzeH6z6HQSkjUFhajX0nmtLuxZViccWYiIjIlHi42GJAjA92Hi3AzqP5uGVwGNycuDJcR/j5559lQEpkSN1333039BpqtUbeOosYLKtUug3SlFfV4/uNp7DvRJF2X98uXrhzTBf5u6du1EANjWKOV194rMrEflUm9qsyNer5PYdBKSOwdk+WTBW3MDfD+IRgfTeHiIhILyYkhGDX0QJZXPq3/dm4bWQke+ImlZWV4ZVXXsG0adMwadIkFBcXax8Thc4tLExvURWNRoPdxwrw/cbTqKpVyX2ujta4e2xX9Onipe/mERERKQqDUgau9EIddqXky+2BMb5wd7bVd5OIiIj0wt/TAXFdvHDoVDG2HMnFpEEhcLC1Ym/chJ07d6K6ulpmS4nbpTZt2oTAwECTG3d9s+6kto6nMCIuADOGRbCeJxERUSdgUMrArd+XJa8IiyoNEwYwS4qIiEzbpIEhMihVV9+ITQdz5DQ+uonzOWmSvJk6kR0lpoYu2XQa1XVN2VHebnaYOzEaXYJc9d08IiIixTLY9Wbr6uowb948xMfHyxVgFi5ceNXnrly5EuPGjUPPnj1x++23Izk5udXniSWOu3btCmNRWdOAbUfy5Hbfbt7w87h+kTAiIiIlC/NzRnSIm9zeeCBHBqeIbkZJRS3+szQZC9eckAEpcSFwbL8gvDy3PwNSREREppopJQpupqSkYNGiRcjLy8Ozzz4Lf39/jB8/vsXzDhw4gBdeeEEuYdynTx989913eOihh7B582Y4OPwRxKmoqMBrr70GY7LxQDbqGpoG25MGhOi7OURERAaTLXXibKm8eLM9KQ9j+nFVWrqx7Kgdyfn4YfNp1NQ1jbd83O3xwMRoRAa68JQSERGZaqaUqG2wdOlSGWyKiYnBmDFj8OCDD2Lx4sVXPFcU5Hz00Udx6623IigoCH/5y19k0c709PQrglzicWNRU6eS0xKEHuHuCPF10neTiIiIDILIlArza3pfXCenuZvGKmXUcc6X1+L9H5Pw9dqTMiBlZga5mMzL9/djQIqIiMjUg1InT56ESqVCXFycdl/fvn2RlJQEtbrlwHPChAl45JFH5HZtbS2+/vpreHh4ICIiQvucffv2yduf//xnGAsxba95xZfJA0P13RwiIiKDYWZmhokDQrWFqcVKaURtzY7aejgX/1iwF8fOlMh9fh72mHd3X9w2IhLWVqa32iAREZE+GeT0PZH95ObmBmtra+0+T09PWWdKZEGJJYovt3v3bsydO1cONt59913t1L36+nr885//xIsvvggrqxtbocfc3EzeOoOFhXmLr0K9qhEb9mfJ7ahAF3QPu/J4jVFrx6pUPFZlYr8qE/vVOPXr7g3/HQ7IO1eFdXuzMKx3QIv3alPqV2qbc2U1+GrtSTn1UxDZURMSQnBrYiisLBmMIiIi0geDDErV1NS0CEgJzfdFkKk1UVFR+Omnn7BlyxY899xzcgnj3r174+OPP5ZTAEWx9L17995Qe9zdHeRV2c7k7Gyn3V67OxNllU3Heef4aLi5KavA+aXHqnQ8VmVivyoT+9X43Da6C/6z5DDyz1fjZG4FBvf0N+l+pdaJC5a/J+fj+02nUXuxMH6ApwPmToqWhfOJiIhIfwwyKGVjY3NF8Kn5vq2tbavfIzKpxC06OlpO81uyZAns7e3x448/4tdff72p9pSUVHVqppQYMFdU1KCxUY1GtRpLN56SjwX7OCLcxwGlpVVQgsuPVcl4rMrEflUm9qvx6hnmBg9nW5yvqMWSDScRHeisvYiki35V2kUjJSqvqseitSdxJO2cvG9uZoYJA4Jxy+AwWFkyi46IiEjfDDIo5ePjg9LSUllXytLSUjulTwSknJ1bXtFKTk6GhYWFzIZqJupJiULnGzZsQHl5uSyULjQ2Nl0dE7WqXn75Zdxyyy1tao9arZG3ziQGzCqVGnuOFaC4rEbumzggBI2N4ud27s/WteZjNQU8VmVivyoT+9U4jesfhO82nkZm/gUkp51HzGVT3k2pX6mlg6nFWLTupFylsXllvQcnRyPCnyvrERERGQqDDEqJbCcRjDpy5Aji4+PlvoMHDyI2Nhbm5i2vai1btgy5ublYsGCBdt+xY8fQvXt33H333ZgyZYp2v8igevrpp7FixQpZDN3QqDUarN5zVm57u9khvqu3vptERERk0Ib08sevuzJxoboBq3dnXhGUItNTXavCdxtPYVfKHwXwR/UNxMzhEbBhIXMiIiKDYpB5y3Z2dpg6dSrmz58vM6E2btyIhQsX4t5779VmTYmV9oTZs2djz549WLRoETIzM/Hhhx/K77nvvvvg6uqKkJAQ7U1kYAli29HREYYmKe0ccourtFlSnTVlkIiISClEkGF0fJDcPplVhvS8cn03ifToeGYJXly4VxuQcnOywVO398ZdY7owIEVERGSADDIoJTz//PNySt6cOXPkVLvHH38cY8eOlY+JouVr1qyR2+I5H330kcyYEtPxtm3bJrOmmgNQxlSEc/Xus9oB1MAYX303iYiIyCiM6hMAW+um1dPWXHwvJdNS39Aos6PeXXIEJRV1ct/AGB/864H+iAll9hwREZGhMsjpe83ZUm+99Za8XS41NbXF/REjRsjb9SQkJFzxvYZCLE+ckVcht8f1D2bxTSIiojayt7XCiLgArN2bhcOnRdZxJUK4qprJyCyowBe/HperMAqOdla4d1xXxHdjGQQiIiJDZ7CZUqbm152Z2oHUsF5XLmlNREREVze2XxAsLZqGNWv2ZPFUmQCxCM2aPWfx2jcHtQGpXhEeMjuKASkiIiLjwKCUATiVVYpjZ0rk9uj4QNhcnIJAREREbePiaIPEnn5ye+/xQu1KtqRMJRW1eHfJYSzbmo5GtUbWi7pvQjc8MbOn/F0gIiIi42Cw0/dMybLNp+VXEYwSq8MQERFR+41PCMa2I7lyNdu1e86iS5gnT6MCHThZhEXrTqKqViXvh/o64U+3xMDH3V7fTSMiIqJ2YqaUnom6F7uP5sttUQ/DwdZK300iIiIySt6udkiIblroZNuRPJReaFqpl5Shtl6Fr9acwCcrUmRASqxRPGlgCObd05cBKSIiIiPFoJSerdrVtEqQlYW5rIdBREREN27igBD5tUGlxq87MngqFUIsBvPyV/uxIzlfu1Lx03fEYcawCG0tMSIiIjI+nL6nR+fKarA7pUBuD+ntD1fWQCAiIropgd6Osth1Uvp5rN55BqPiAmBtyaCFMRczX7rpFBavOylrRwnxXb1w7/hucnEYIiIiMm4cpenR1iN5su6FubkZJl28sktEREQ3Z9LAUPm1ulaFXSlNmTVknFbtysQ3a05oi5nfP7EbHpnagwEpIiIihWCmlB7ZXlxlb+LAUHi52UGlUuuzOURERIoQGeiCPl28cOhUsfa9loyTuHgnhPs746HJ3Vk7ioiISGEYlNKjiQNDMKCHL7qGeaK8vFqfTSEiIlKUx2bEQgVz2FqAF32M2K2JYRg/KBzW5hqoG5sCVERERKQcnL6nz5NvZgZfd3s5fY+IiIg6jih+7efpwFNq5MzMzGQ/ijETERERKQ+DUkREREREREREpHMMShERERERERERkc4xKEVERERERERERDrHoBQREREREREREekcg1JERERERERERKRzDEoREREREREREZHOMShFREREREREREQ6x6AUERERERERERHpHINSRERERERERESkcwxKERERERERERGRzjEoRUREREREREREOmem0Wg0uv+xRERERERERERkypgpRUREREREREREOsegFBERERERERER6RyDUkREREREREREpHMMShERERERERERkc4xKEVERERERERERDrHoBQREREREREREekcg1JERERERERERKRzDEoREREREREREZHOMSilYxUVFXjhhRcwaNAgDBgwAM8995zcdzXZ2dm477770Lt3b0ycOBG///47jI1Go8HcuXPx008/XfN5r776Krp27dri9r///Q9KPFZj7ldxjO+++678/e3fvz/efvttqNVqxfRrXV0d5s2bh/j4eCQmJmLhwoVXfe7x48cxa9Ys9OrVCzNmzEBKSgqMSXuO9ZFHHrmiH7ds2QJjU19fj8mTJ2Pv3r2K7df2HKux92thYSGeeOIJ+bdoyJAheOONN+TvtZL7VelMcZwkcKykrL7lWEk5f3s5VlJmvzbjWMlA+lVDOvXkk09qpk+frjl69KgmJSVFM3PmTM3jjz/e6nPVarVmypQpmqeeekqTlpam+fTTTzW9evXS5ObmGk2vNTY2al555RVNly5dNMuXL7/mc++77z7NZ599pikqKtLeqqurNUo7VmPv1wULFmiGDRum2b9/v2b37t2axMREzZdffqmYfhV9KPpH/P/csGGDJi4uTrN27dornldVVaUZPHiw5s0335T9+K9//UszaNAgud9YtPVYhTFjxmh++eWXFv1YV1enMSa1tbWav/zlL/L/6J49e1p9jhL6ta3Hauz9Kv6W3nbbbZoHH3xQc+rUKfk3SRyP6Dul9qspMLVxksCxkvL6lmMl5fzt5VhJo8h+FThWMpx+ZVBKh0SHRkdHa44cOaLdd+jQIblP/Ke43K5duzS9e/du8YswZ84czYcffqgxBgUFBZq7775bM3z4cE18fPx1g1JDhgzR7NixQ2OM2nOsxt6vIiB16fGtWLFCM2LECEX0q+iT2NjYFh/iP/74Y9m3l1u6dKlm5MiRcuAsiK/iA/H1fs+N8VhFkEL8ncrIyNAYq9OnT2tuueUW+SHnWoEaY+/X9hyrsferGDCJ4ysuLtbu+/XXX2WgXIn9agpMbZwkcKzUOmPvW46VlPG3l2MljpU4Vhqjk/+vnL6nQ+bm5vj0008RHR3dYn9jYyOqqqqueH5SUhK6d+8Oe3t77b6+ffviyJEjMAbHjh2Dn58fli9fDicnp2s+t7KyUk7DCA0NhTFqz7Eac7+KPsrPz0e/fv1atD03NxdFRUVG368nT56ESqVCXFxci+MTfXb5FEWxTzxmZmYm74uvffr0MYp+bO+xZmRkyOMLCgqCsdq3bx8SEhLwww8/XPN5xt6v7TlWY+9XLy8vfPnll/D09Lzi744S+9UUmNo4SeBYqXXG3LccKynnby/HSq0z9n4VOFaqNKh+tez0n0Batra2GDp0aIsz8s0338gaHu7u7lecqeLiYnh7e7fY5+HhgYKCAqM4qyNHjpS3tkhPT5e/+GIwun37dri6uuL+++/HtGnToLRjNeZ+FW0XLm1/8wdC0f7Lj8vY+lUcn5ubG6ytrVscn6gnUFZW1uL/qXhuZGTkFf14+vRpGIP2HKsIXjg6OuKZZ56Rb+K+vr54/PHHMWzYMBiLO++8s03PM/Z+bc+xGnu/Ojs7yzpSzUQwVdSrE3WIlNivpsDUxkkCx0qtM+a+5ViJYyVjfE8VOFa6EsdKHjoZKzEo1cFqa2vlFZKrXdW99IqPGDyvXbtWXultTU1NTYsPjIK4LwqyGduxXk/zFfvw8HDcfffd2L9/P/75z3/KD0xjxoyBko7VmPu1urpafr20/c3brbXf0Pu1rX3T2vEZej925LGKfhS/F6IY+sMPP4zffvtNFsgWmTixsbFQEmPv1/ZQWr++8847skDnsmXLTLpfDZ0pjZMEjpWacKzEsZKh/h+9Fo6V2ndejKVf24NjJWud9CuDUh1MpL3de++9rT728ccfY/To0XJ78eLFclWy559/Xn4gaI2NjY3MWLiU+KUQVxKN6VjbYurUqRgxYoTMpBG6deuGzMxMfP/99wYRvOjIYzXmfn366ae17RXH0bwt2NnZGV2/Xk4c0+V/eJvvX94/V3uuofRjRx7ro48+invuuQcuLi7afhRTTn788UejDF5ci7H3a3soqV9FQGrRokX497//jS5duph0vxo6UxonCRwrNeFYiWMlQ/0/ei0cK7XvvBhLv7YHx0r1OulXBqU6mKjjkZqaes3nLFiwAG+//bacMjFnzpyrPs/HxwdpaWkt9p07d+6KdGZDPta2Etk0zYGLZiK7Zs+ePVDasRpzv4qr2+LDn0hNDwwMbJGmLq6CGlu/ttY3paWlstaSpaWl9vjEH2MxVejy54p+M9R+7MhjFXVemgMXl/bj5b/HSmDs/doeSunXf/3rXzLQLf42jRs3Dqber4bOlMZJAsdKN8bQ+5ZjJY6VOFYyjfdUjpXO6aRfWehcx37++Wc50BJX/h544IFrPrdXr17yqrVI/W528OBBuV9pPvjgA9x3331XFBcUH5CUxpj7VQwS/f39ZXubiW2xr7U/WMbWr6K4rgjQXFrQTxyfyBoRb0qXEv11+PBhsYKpvC++Hjp0yCj6sb3H+txzz8m/WcbSjzfD2Pu1PZTQrx999BGWLFmC999/H5MmTbrq80ypX40dx0lXZ2zvqTeDYyXD7VeOlThWMqX3VI6VDumkXxmU0iGRYv7KK6/IIs9i8CyyEppvYmUZoaSkRLvCTP/+/eWKbuJDgygw9vnnnyM5ORkzZ86EElx6rGKKl6g3JK6OZmVl4bvvvsOKFSswd+5cKIGS+vWOO+7Au+++i71798rbe++912IqhjH3q5iCKKYczp8/X/bJxo0bsXDhQu3xif+rzcHE8ePHo6KiAq+99pq8miu+ijn2EyZMgDFoz7GKQry//vqr7LuzZ8/KQIAIYIk6YUqgpH69HiX1q1hI4ZNPPsFDDz0kV4u59D3V1PpVKThOupIxv6e2F8dKxtGvHCtxrKT091SOlV7Tfb9qSGdWrVql6dKlS6u37Oxs+ZwRI0ZoPvzwQ+33ZGZmau666y5Njx49NJMmTdLs3LnTKHtMHNfy5cuv2Hfpsf7222+aKVOmaGJjYzXjx4/XrF+/XqPUYzXmflWpVJrXX39dEx8fr0lISNC88847GrVarZh+ra6u1jzzzDOa3r17axITEzVfffWV9jHxf/XSvk1KStJMnTpVHtvMmTM1x44d0xiT9hz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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Total density N/L = 1.705870\n", "Fermi rapidity theta_F = 2.0\n" ] } ], "source": [ "theta_f = 2.0\n", "state_T0 = TBAState.zero_temperature(model, theta_f=theta_f)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "axes[0].plot(state_T0.grid.points, state_T0.rho_p().values)\n", "axes[0].set_xlabel(r'$\\theta$')\n", "axes[0].set_ylabel(r'$\\rho_p(\\theta)$')\n", "axes[0].set_title(r'Particle density at $T=0$')\n", "\n", "axes[1].plot(state_T0.grid.points, state_T0.v_eff().values)\n", "axes[1].set_xlabel(r'$\\theta$')\n", "axes[1].set_ylabel(r'$v^{eff}(\\theta)$')\n", "axes[1].set_title(r'Effective velocity at $T=0$')\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "N_L = state_T0.rho_p().integrate().values\n", "print(f\"Total density N/L = {N_L:.6f}\")\n", "print(f\"Fermi rapidity theta_F = {theta_f}\")" ] }, { "cell_type": "markdown", "id": "152bff51", "metadata": {}, "source": [ "## Working at fixed density\n", "\n", "In practice it is often more natural to specify the particle density\n", "$N/L$ rather than the chemical potential. We use `find_mu` to find\n", "the chemical potential that reproduces the target density." ] }, { "cell_type": "code", "execution_count": 7, "id": "2abf1dd0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Target density: 1.0\n", "Chemical potential: mu = 1.472007\n", "Achieved density: 1.000000\n" ] } ], "source": [ "from rapidity.thermodynamics import find_mu\n", "\n", "target_density = 1.0\n", "T = 0.5\n", "\n", "mu = find_mu(model, grid, density=target_density, T=T)\n", "state = TBAState.from_betas(model, grid, betas={2: 1/T, 0: -mu/T})\n", "\n", "print(f\"Target density: {target_density}\")\n", "print(f\"Chemical potential: mu = {mu:.6f}\")\n", "print(f\"Achieved density: {state.rho_p().integrate().values:.6f}\")" ] }, { "cell_type": "markdown", "id": "3756ab9a", "metadata": {}, "source": [ "## References\n", "\n", "- [YangYang1969] Yang, C. N., & Yang, C. P. (1969). Thermodynamics of a\n", " one-dimensional system of bosons with repulsive delta-function interaction.\n", " *Journal of Mathematical Physics*, 10(7), 1115-1122.\n", "\n", "- [Takahashi1999] Takahashi, M. (1999). *Thermodynamics of One-Dimensional\n", " Solvable Models*. Cambridge University Press." ] } ], "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": "3.13.12" } }, "nbformat": 4, "nbformat_minor": 5 }