{ "cells": [ { "cell_type": "markdown", "id": "e8fa063b", "metadata": {}, "source": [ "# 4 · Elastostatics as a Minimization Problem\n", "\n", "Posing an elastic object is an **optimization**: pin part of the shape, drag a **handle**, and let\n", "everything else settle at the vertex positions $x$ that minimize the energy below. The pin and handle\n", "terms are quadratic *spring* penalties of stiffness $K$. We minimize with Newton (how that solve works is\n", "tutorial 5's job) and focus on how **different energies pose differently**.\n", "\n", "$$\n", "E(x) = \\underbrace{E_{\\text{elastic}}(x)}_{\\text{wants rest shape}}\n", " + \\underbrace{\\tfrac{K}{2}\\lVert x_{\\text{pin}} - p\\rVert^2}_{\\text{hold pins}}\n", " + \\underbrace{\\tfrac{K}{2}\\lVert x_{\\text{handle}} - h\\rVert^2}_{\\text{drag handle}}.\n", "$$" ] }, { "cell_type": "markdown", "id": "4985667b", "metadata": {}, "source": [ "Imports, and every tunable parameter of this notebook." ] }, { "cell_type": "code", "execution_count": 1, "id": "605279d3", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.040146Z", "iopub.status.busy": "2026-09-24T03:44:26.039943Z", "iopub.status.idle": "2026-09-24T03:44:26.611476Z", "shell.execute_reply": "2026-09-24T03:44:26.610844Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import os\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import igl\n", "import simkit\n", "import utils\n", "\n", "NOTEBOOK = \"004_elastostatics_minimization\" # this file's name\n", "RESULTS_DIR = utils.notebook_results_path(NOTEBOOK) # results/004_elastostatics_minimization/\n", "MEDIA_DIR = \"media\" # tracked copies for the website\n", "# material and springs\n", "MU, LAM = 1.0, 1.0 # Lame parameters, the same on every element\n", "K_PIN = 1e5 # stiffness of the pin and handle springs\n", "POSE_MATERIAL = \"macklin-mueller-neo-hookean\" # simkit material of both animations\n", "MATERIALS = {\"Linear\": \"linear-elasticity\", # plot label -> simkit material, for the comparison\n", " \"ARAP\": \"arap\",\n", " \"Neo-Hookean\": \"macklin-mueller-neo-hookean\"}\n", "# solver and checks\n", "NEWTON_ITERS = 100 # max Newton iterations per pose\n", "NEWTON_TOL = 1e-6 # stop when the Newton step is shorter than this\n", "FD_STEP = 1e-6 # central-difference step of the gradient check\n", "FD_NOISE = 0.1 # size of the random deformation the check runs at\n", "SEED = 0 # seed of that random deformation\n", "# triangle experiments\n", "N_FRAMES = 48 # handle positions per animation\n", "FIG8_AMP = (0.45, 0.6) # figure-8 half-width (x) and half-height (y)\n", "FAR_TARGET = np.array([1.5, 1.1]) # handle target of the material comparison\n", "# beam experiment\n", "NX, NY = 16, 5 # grid resolution (vertices)\n", "WIDTH, HEIGHT = 2.0, 0.4 # beam size\n", "SWING_DEG = 120 # largest swing angle of the right edge\n", "FPS = 20 # video frame rate" ] }, { "cell_type": "markdown", "id": "74911d3b", "metadata": {}, "source": [ "## The posing system\n", "\n", "`elastic_pose_system` builds the three terms of $E(x)$ from simkit: the elastic material (evaluated on\n", "$F = Jx$ with the deformation Jacobian $J$ and weighted by element area), and two `simkit.dirichlet_penalty`\n", "quadratics for the fixed pin and the movable handle. It returns the energy, gradient and Hessian closures\n", "Newton needs, each summing its terms one per line (the Hessian is PSD-projected so Newton always goes\n", "downhill). Re-aiming the handle just means building the system again; every later tutorial builds its\n", "simulator this way." ] }, { "cell_type": "code", "execution_count": 2, "id": "0c587355", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.613312Z", "iopub.status.busy": "2026-09-24T03:44:26.613161Z", "iopub.status.idle": "2026-09-24T03:44:26.616807Z", "shell.execute_reply": "2026-09-24T03:44:26.616071Z" } }, "outputs": [], "source": [ "def elastic_pose_system(X, T, material, pin_idx, pin_targets, handle_idx, handle_targets):\n", " \"\"\"Elastic energy + a soft pin + a soft handle, in stacked vertex positions x.\"\"\"\n", " n, dim = X.shape\n", " J = simkit.deformation_jacobian(X, T)\n", " vol = simkit.volume(X, T)\n", " mu = np.full((len(T), 1), MU)\n", " lam = np.full((len(T), 1), LAM)\n", " Q_pin, b_pin = simkit.dirichlet_penalty(pin_idx, pin_targets, n, K_PIN)\n", " Q_handle, b_handle = simkit.dirichlet_penalty(handle_idx, handle_targets, n, K_PIN)\n", "\n", " def energy_func(x):\n", " E_elastic = simkit.energies.elastic_energy_x(x.reshape(n, dim), J, mu, lam, vol, material)\n", " E_pin = simkit.energies.quadratic_energy(x, Q_pin, b_pin)\n", " E_handle = simkit.energies.quadratic_energy(x, Q_handle, b_handle)\n", " E_total = E_elastic + E_pin + E_handle\n", " return E_total\n", "\n", " def gradient_func(x):\n", " g_elastic = simkit.energies.elastic_gradient_x(x.reshape(n, dim), J, mu, lam, vol, material)\n", " g_pin = simkit.energies.quadratic_gradient(x, Q_pin, b_pin)\n", " g_handle = simkit.energies.quadratic_gradient(x, Q_handle, b_handle)\n", " g_total = g_elastic + g_pin + g_handle\n", " return g_total\n", "\n", " def hessian_func(x):\n", " H_elastic = simkit.energies.elastic_hessian_x(x.reshape(n, dim), J, mu, lam, vol, material, psd=True)\n", " H_pin = simkit.energies.quadratic_hessian(Q_pin)\n", " H_handle = simkit.energies.quadratic_hessian(Q_handle)\n", " H_total = H_elastic + H_pin + H_handle\n", " return H_total\n", "\n", " return energy_func, gradient_func, hessian_func" ] }, { "cell_type": "markdown", "id": "64d69455", "metadata": {}, "source": [ "## Two meshes\n", "\n", "A single equilateral triangle (pin vertex 0, handle vertex 1) and a 16 × 5 cantilever beam from\n", "`igl.triangulated_grid`, centered and scaled (pin the whole left edge, the whole right edge is the handle).\n", "Blue squares mark pinned vertices, orange dots mark handles." ] }, { "cell_type": "code", "execution_count": 3, "id": "dbe74e27", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.618394Z", "iopub.status.busy": "2026-09-24T03:44:26.618325Z", "iopub.status.idle": "2026-09-24T03:44:26.757563Z", "shell.execute_reply": "2026-09-24T03:44:26.757059Z" } }, "outputs": [ { "data": { "image/png": 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7WL169VOvderUSbxG56q012hTQL+9WVlZxfah/rOzsyt4++23C5+7du2a+EwrK6uClJSUwud37dr1lD01a9aswMnJSZwvBYcPHxb7lbwWStrHqFGjChwcHAqSkpKK7ffmm2+Kc6y4dvv371/g7e39zD5iGKbicCQIwzBVhlZ8aEWxtkv/0ffR6h19v6rl0KD20spneRnxGYapm7zzzjvFHtMK/w8//CAiHyi6gKIb6P5HUSAknVFAiSgpQSWF9yskAUWlJZRbg2QwtIpO91BagS8qMyEoqkQBRZM0btwYV65cEd+lgJ6j12hFvCjPI7+glXKK5ujVq5eQX5BshyJeKIKAZAiEQrJDMoGSkPRAsU9prxMk36HP27p1q5DUELRST1ESRaUwFBFDEQcUgVK0P+n9BPVn0cgDynlB8ofKQpEldP4ouqGknETxe0ZtpGTZFLVQtE1aWlrw8/MrlHDQ+aWICpKNUAQBSSWUxZEjR0SEC9mKou8qch5LSrOeF/rc0mRPJaG+o42g/qf+pX8pQoUq1pSEIjyK9qciCkVh95SwlaJc6For+ntO9kGRIQrZV2nQ9UdSL+or+rvoOabIlC1btog2BQYGimuNxlkkxVFIgxiGqTzsBGEYpkpQ6DT9MJNGlcI4a9MZQYMG0nxTSKoqOUGo3RS2Tv1GkxXFgIxhGEYB3RuKQjkJaLKscDJQRQ26l5TcT4EiVJ8gSQRNtikZKTkAipKWlvbUhLRk2VnKnUBO25L3WXq+5OdVlOPHjwunBEl9FBIJksFQvgiaRFOOBHIyKBw4JfNyEIocKUWdPCWhZKQkFSFZA30GTZbJgUS/HTTBVUD9STksyiq5S/KSohSVAFUGyptC5/NZjhRqE1HUmVAURW4NOiaSynz00UdCBkLyCupbkisVrc5S00RFRQkpEOXEIMlJUco7j886hxV1qFU0CeratWuFBIvaS3bwrHNa0kGocIgo7J6S+xKUR6Yk9FxpjhUFNA4gJwzlHKHtWXZHVXgOHjwonIb0uSSXIhkMOUgYhnl+2AnCMEyVoAEEDcRp4FjVQczzQt9LDgRVc4IQ1F80maH+YycIwzDlUfIeR6vX9BzlDyjtHqJYlSZHNVVRoTKmNJGiSAfK70G5Nihxo6IilYKy7kdlPV/ZCEDK0UET9pI5IigvB+XJOHHihHAQKBKlllamlZ6jBJxlRYEooDwR9H3UV+RooVwe1A+Ux0MB9QOt3FO1k9KgJKlFqY3fO8W5obwgpTkzilabodwRffv2FREm+/fvF7liKD8F5RdRVNmpSSgZL03MyTFG0Uoly7yXdx7r1atXpe+v6PmgRLRk92QHn3zyCWxtbYVtU1+VltC3uu2+tPNLOUwo70tpKHLKUJRSdHS0qKa0b98+EUFCkWHk3FSUZWYYpuKwE4RhmGpB1ZwQyob7i2GYZ0FRAEVXpkmOQpMmRZJLigyhiRjtQ1VSyoJC9SmxJ61+U2SAApJaKBNKCEkOmpIoVuYpiaZihZ+cxqGhoU/tW1oiy7KSsNIknCQxlFCUHAOU5LUo1J9UlpcSu1b2/vw876Pvo/N54cKFMo+B9iFook7VcCrymRQNQhvZD30uRTzQxL8moaSk5AChKI9Dhw4VOjyKQtEh5LSh81hUVkXVWiIiIoo9V5O/mTt27ICbm5uIBir6mVQVqDKQjEtxfZaktOeKQnZNziK6Dipyfsl5SdFLtFG/UYJWSiQ8ZcqUQmkYwzAVg0vkMgzDMAzDSIaiLK0CquZCUAUMgiZAtEpNq8AlV6XpMU1Mi65kF92H/v7uu+9qpN0VLZFLjhtyhFAei6Js3rxZ/Fs0eoHkLLQCXrT0L022yblDpX/Lg2QnVFXj999/F1EV5GApKoUhaBJO0TFUhaMklK+CcqmUB8lCCZI4lAdFIlC7qOpJyWgcxbmivBAkeZk7d24x2UZROQVBFWNKlk8mhwhNsEuTn1Qn1C+U04X6jiJAypJnUYQITfTJIUPVVhTQ+aC8XuWdR3IAVLRvn0Vp1wNVWDl58mSlPo8iWMjBQ1Wb6DgU/Pvvv8IBWV5byLYpquPcuXNlnl9CcT0rIOkPRUopZMEMwzwfHAnCMEytEp/8AJnZT6/+KTDS1YKL1eOBZE1AK2OUfK9kqG5NQQNv0mZT+C3DMExFuXbtmpCG9OzZU0zQaPJIOQAUEg6a5M6ePVusApO0jibVdF+j9/3222+ilCgl/iTZB+1Lf9NElSbVNOmqbC6P8qhoiVwqB7p69Woh4aCkr7SiThNHcoKQfIcSfyqgpJOUuLRLly6iPChNNhcsWCDkKxVJhkmQ04McSbTiT+8jeUFRhg4dKmQy48ePFwlHKdcCrdBT3gh6niQmpZXpLSnJoIkpRZyQk4ekOjRBpq0klNeBolFmzZolkm2SU4tkPZT4kibWJM+gc0XlcKltrVq1ErIeih6gHC9UlpXauHTpUuEMon4nRw59P0VckA2Qk0lRAphYs2aN6C/q9/J+k8hhRJExBE2yqRwr2RtBdqmQaVDJZIrIoRwulFOFtqKSLLJLBRS1QMllKWko2SflxaJIFYoiITt/FmTDlByUSjOTnZNThGzkeXOz0O8xRYFQ7pLevXuL64U+k/qtqBPjeSAnVf/+/cX5oP6la4vOC5338j7zq6++EvZGx0Ile6kdJF2jXCKUA4T+JqiPSBJF30EyMupn+g46htoazzCMWlGgAnCJXPnhErl19xxRudcLFy6If8sjLimzoOXMQ+VutF9FoDKCVOpOUU5QRl599dVSS/qV1W9cIpdh6jaKUqp0f3jttdcKTExMCiwsLAomTZpU6n32l19+KWjfvr0oY0qbp6dnwTvvvFMQHR1duA99Vrdu3QqMjY0LrK2tRWlVKrVbsuQolUGlzygJlRgtrTwnlf/s3bt3pUvkUpldOkZnZ+cCHR0d8b6PP/5YlD0vyblz5wq6d+9eYGhoKMrGDh48WJSKrSj0O0HfQ8c8e/bsUvfJzs4umD9/vjhWPT090e++vr4FM2bMKFa2nD6D+rg0Tpw4Id6jq6tbrBxqyRK5ClatWlXQsmXLwu+jvj5w4ECxff7555+CHj16iJKp+vr6Be7u7gUjRowoCA0NFa9TeVVqD517On+0n5+fX8G2bduKfc73338v2rBv375y+0tRLrm0rajN0Dkra7/S7IBKEAcEBIjjsLGxEe1OT08vqAhUntbLy0uUgC7ajrLss7QSuWQHVAKa2kZ9Tn2/Z88ecbxF26sokVta2eHSyiBT+Wjqf/rMpk2bFuzevVv8/tNz5b03MTFR9IPiOqBywV27di1YsWJF4T7/+9//Cjp27ChK9tJ3kA1QieiidskwTMXRoP9Bcqi8lCIDOXmBVR0KeyTvPHlyS5ZFU1X4mOruOaIQXFpJodWY8jSpFxMyMHhlSLmfuXF0GzRxMKl0dRj6m1bYaKWMQnVp5Y9WqxSvKe4lpK0njTxp42/fvi1KC37xxRdiv86dO4tVPwqTpRJ4tDJJq0UEhfJ++OGHYpWMjp8y8dOKDIWn0qohrYhRxQUKC6YwZVq9LbnqVla/UagvZZ+n9ysy/zMMwzBMVaFIEYrQocgNpuahyFOK3FF2/h2GYZ5GPWbgDMMwJSBnx+nTp0UWdQq1Lis0m5wOFGpOIcgUXk3h4gpI105hqqTVpVBohWaYks5R+DINJMkRQg4mhb6ewpbJmXL+/HkR5kzh3QzDMAyjTGjRgPKvKCQtTPVBizGKRL4KqK9pfEALKgzDyAfnBGEYRi0ZPXq0+JeywFNlgCNHjhRWVSgKRWkQ1tbWYl+KzqBqBAoNOWmraaMVHXKK+Pv7ixKE5BBRlFKkpHmU4Iyi1ijLvSLqg3TnVImAYRiGYZS9MHDnzh0+CTUALZ5Q0lcqdUv5XCgilCJHKYcH5ZhhGEY+2AnCMEydoKzyekWlKOTIKLqaU9ZrtKJGiQVLlqUkJ0hFv5dhGIZhGNWHJKy+vr5YuXKlqOhCSVspYSklPbWyslJ28xiGKQWWwzAMo5ZQ9nuCZDBUDYbkK9UFZbufP39+oVOEcoxcuXJF5PCgso5UKo8gScyxY8egKuU4KVKGHD+Upf5ZmnGqMEDOnaJbeflgGIZhGEYdobyFVBGIqt1QSWKq6ELVjKiiDcMwcsJOEIZh1BIqbUgOCSort2TJklKlMJXl22+/FaUQSSJDZQKpNKEi5wg5QFasWCFK41GSVZLiyA4N3ijRKyWQpbJ8VIKzR48ezwydJodPQkJC4RYXF1erbWYYhmEYhmGYysByGIZh1BJKXkqJSUtStCBWyWSpoaGhxZKaFWXHjh2FfxsbG4tqMKXh6elZmEBVVaDcJmPGjMHIkSPFY9IyU2WdVatWYfLkyaW+h6I/SO9cUWh1jDYFlEyWVssoVJglQwzDMAzDMExVoXE+VXGk/DzPqobJThCGYWoNI12tat2PqTrZ2dkICwvDlClTCp+jHw1K8vYsZ879+/dRv3594cxo1aoV5s6dC29v7zL3nzdvHmbMmMGnjGEYhmEYhqlRrl+/DicnpzJfZycIwzC1houVIXZObIfM7LxnOkBov6pQNNqDeTZJSUlCOmRnZ1fseXpMGe5Lo3HjxiJKhKRAaWlpWLhwIQICAkQOlLJ+cMjJQpIbBfQ+FxcXIaMhaU1tQU4bOmaqBvSsFQKG+4tti69FWeD7FvcV25by4etQNfqLihTQIp2Jickz92MnCMMwtUpVHRyM8qEywbQpIAdIkyZN8L///a9UCRKhp6cntpKYm5vXuhOEZDn0vewE4f5i21IefC1yX7FdKR++Drmv1M22FN9VntSal8EYhmHqMOShp/K/iYmJxZ6nxxXN+aGjoyOS0FKFHIZhGIZhGIaRGXaCMAzD1GF0dXXh6+uLQ4cOFfPe0+Oi0R7PguQ0kZGRcHBwqMGWMgzDMAzDMEzVYTkMw5RCSkYWJv5wFKeibqOdpz1+mNgBliZPh/IzjDpAuTqGDx+O1q1bo23btli8eDEyMzMLq8UMGzYMjo6OIrkpMXPmTLRr1w4eHh64d+8eFixYIHJ7jB49WslHwjAMwzAMo3rQglJOTg7Uhfz8fHE8jx49qhE5DEUhUyRzZWEnCMOUwjs/HsOekHjk5ReIfzV+PIbN/+3KfVXN5N6JRX7KbWha2kPb1pX7V0kMHDgQd+/exdSpU3H79m34+Phg3759hclS4+Pji/2ApaamipK6tK+FhYWIJDlx4gS8vLz4HDIMwzAMwzwHVHHvxo0bapXYv6CgQDhC6NjKy89RGegzKRm/sbFxpd7PThCGKYXgS3eEA4Sgf+kxU31kXw1H+prJyIk+Vficjqc/TIfPg657q2q5MdJEnZIx1RQUNUFVUTp37iy2999/HwMGDICqMmnSJLGVxuHDh4s9/vbbb8XGMAzDMAzDVC0ChBwghoaGsLGxqRGHgbKcIDk5OSJio7qPiT6bFu+o3xo2bFipiBB2gjBMKTRztcStlAfib7ps2zay5X6qRgdI8tQeQF5usedzLgWL561m7q8WRwjDMAzDMAzDyAw5CmhSTw4QAwMDqAsFBQXCOVETThCC+is2Nlb0X2WcIJwYlWFKwcJYD1Zm+jA10oW2tiZGdW/M/VRNpK+d8tgBkp9X/AV6nJeL9HWfVcv3/PDDDyK/RYMGDbB69erC5z/++GO0adNGSD46duyI6OjowtfoJj137txS30dyD3pP06ZNRa6M3NziThwFGRkZQipCn9G8eXOMHTsW2dnZ1XJMDMMwDMMwjPqhLhEgqtJf7ARhmBKEXbmL/eE38N9hbbHgvU7o19Edc7ZFIP+JPIapWg6QnKiTTztAFOTnIefiCbFfVdHT00NwcDD+/PNPvPvuu4VOi08//RQhISGIiIjAxIkT8d5775X7PnJiUN4Mkr+cO3cOgwYNwpkzZ0r93o8++ggdOnQQn0H7kB7yu+++q/LxMAzDMAzDMEx88gNcTMgoc6PXmWfDchiGKQI5Oj5dE4wubVxgaaqP/IICvNDaBV+tCcbWo1cxqJMH91cVoCSoFd6violSBw8eLP719PSEtra2SOJJCZQOHDiA77//XkRskIMiJSWl3PfRPvR3t27dxGvdu3eHm5tbqd+7c+dOnDx5EosWLRKPHz58WKXs1QzDMAzDMAxDkINjwA//n1OvLHZObAcXK8Ma6TQfHx8cPXoUJiYmtXJSXnvtNfTp0wcjRoyots9kJwjDFGHHiRjEJ93HW328C5/T1dFC347umL45DH3ausDEQJf7rJJQFZjq3O9Z6OvrF/5NTgiK6KAqJ5T8kyJB3N3dcfbsWSGJKe99zxOGRxrIX375BY0aNaryMTAMwzAMwzCMgszsMqKpK7lfZaBoalWH5TAM84TMRzmYtjEMvTu4C8dHUXwa2cDSzACLdkZyf1UBKoNLVWCgWUZkhKYWdJoE1Fi53LS0NJGgycHBQTgrli5dWqH3UVQIOUP++ecf8fjgwYO4evVqqftShZj58+cXOk+oSs2VK1eq8SgYhmEYhmEYpubQ0NDAF198gZYtW4qFvY0bNxZ77d69e+JvV1dXTJ06Ff7+/iKf3uzZswv3e/HFF0UuPpKJ0+Lj+PHjK5RDLyoqCgEBAfD29hbj6vT09Go/PnaCMMwTvt0VCVMTPbRq/HQlGLrY+3fywIp9FxGbmMF9VgWoDC60tJ92hNBjLW2YDptbY/3brFkzvPnmm+KmSslRXVxcKvQ+XV1dbN26FR988IH4jE2bNqFFixal7kulYym7N4UK0k29a9euIns1wzAMwzAMw6gKGhoaOH36NPbt24f//Oc/ZY5nySFCUnCKtF6wYAFu3rxZ+FpMTIxYRKScevv37xf7lZdDb+jQoRg1ahTOnz+PWbNm4d9//632Y2M5DMMAiLuTgR//uIBJA1uVKXNwsjNBqyb2+GJDCDZ89AL3WyWh8rdUBpeqxIgkqU/QaewnHCDVUR6XojyKkpSUVPg33WCLJiolL3dF3kce6bLC/w4fPlz4t7GxcYUjTBiGYRiGYRhGRkaPHi3+pTx4JB8/cuSIiPwoyVtvvSX+tba2Fvteu3YN9erVE8+98cYbIq8ebbRASJHUFDVSVg49ivqg8bYi/wctPrZv377aj42dIAwDYOrGULT0tIOz3bMT/PQKbIC5q07h38hb6NTs8cXNPD/k6LCeuV9UgaEkqJQDpKYkMAzDMAzDMAzDVA2NMhaKn5VPr6zXysqhV5r0pSbKB7MchqnzHDufgENnbwkHR3mYGOqiu78rJq8NRm5efp3vu6pCjg9dz3bsAGEYhmEYhmEYiVi9erX4l2QwVA2G5CvVRVk59ExNTUUeknXr1onnSRJz7NgxVDfsBGHqNOTImLwuBC/61YepkV6F3tPBxwnpj3Kx9tClGm+fKlFSSsJwfzEMwzAMwzCqSV5ennBIdO/eHUuWLClVClNZnpVDjxwgK1asQNOmTYVsvWQlx+qA5TBMnWbDP5eRcj8LnVo5V/g92lqaIknqnG2n8UpAA1gYV8x5oq5QtRUKU7t79y5sbGxqJGTtWY6XnJwccZOuze+tjnZTf1Gbqf8YhmEYhmEYpjyMdLWqdb9nQclLKTHpsxY+SyZLDQ0NLdznwIEDxca5O3bsqFAOParKqEigWlOwE4Sps9zLzMKsrafxWrdGwrHxPHi5WYlEqV/tiMD8EX6oy5C+z8nJCTdu3Kj1Kih0g6Vs0pqamirlBCGovdRv1H8MwzAMwzAMUx4uVobYObEdMrPznukAof2YanaCLFu2TJS/uX37tigT+f3334sav2WxePFi/Pjjj4iPjxdZY1977TXMmzevWKIUhqltvv7lDBxsjNDU3bpS7+/XyQOLNoRiZLfG8HQyR12GvLkNGzYUURm1CTlAqIIL3VfIEaJKkGecHSAMwzAMwzDM81AbDo4CNZe5P7cTZOvWrfjwww+xfPly+Pn5CQdHjx49EB0dDVtb26f237RpEyZPnoxVq1aJEpOXLl0SJW9oFVRREodhaptLN+9hzcFL+GBw60pHENhbGcG/eT1MWRuMXz97UeUiEaobmtDX9qSenCDkTCCHqqo5QRiGYRiGYRiGUQEnCDkuxowZg5EjR4rH5AzZu3evcHKQs6MkJ06cQGBgYGH9YEqoMmjQIAQFBZX5HVlZWWIrWSqHJjy0qTqKY1CHY1HFYyLPJlV38WvmAAdroyp9Vg9/V8xdFYQ/w+LR8znyiigDVTpHFUWdj4lhGIZhGIZhGCU7QbKzsxEWFoYpU6YUPkerr926dSszeQlFf2zYsAHBwcFCMhMTE4M//vgDQ4cOLfN7SCozY8aMp56nsPeizhFVhxIjqhuqcExHLtxF2JW7mPJ2O+RXINTrWfvo62mjR4ArJq8OgpetFvR05M/voArnqC4fU0ZGhrKbwDAMwzAMwzBqy3M5QcgJQVUY7Ozsij1Pj6Oiokp9D0WA0Pvat28vVuCpFvD48ePx2Weflfk95GQhyU3RSBBnZ2eh+zc3N1eLlV5FJQ11CeFXlWPKzsnD17+fRI8ANxgb6FbIAaJZjswlsLkjgiITsDsiFZP6eENWVOUc1fVj0tOr29WGGIZhGIZhGEalq8McPnwYc+fOxQ8//CByiFy5cgXvvfeeKLfz5ZdfljkJKG0iQJMcdZnoqOPxqMIxrTp4ETkFBQhsUa/aPlNTU0MkSV3421kM7OgBO3MDyIzs56iuH5O6HAfDMAzDMAxTs+TeiUV+ym1oWtpD29aVu7uCPNdomyIxKPFhYmJisefpsb29fanvIUcHSV9Gjx6NZs2a4eWXXxZOEZK8sPadqU3upj3E/F/OoH8nD2hV80SzkYsFGtW3xOyt4dX6uQxTW1DVL8rZRElmyWFNEsaKsGXLFpEUeMCAATXeRoZhGIZhGAbIvhqOpC+74+6k5kie+vjfpKk9xPPVgYaGBu7du1ejXd26dWsRMEF07twZO3fuRG3xXDNBXV1d+Pr64tChQ4XPkSODHvv7+5f6ngcPHjy1sqmoIKHupXcYuZiz7TTcnc3RuL5ljXx+347u+OXENUTEJNXI5zNMTaGo+jVt2jSEh4eL0udU9evOnTvPfF9sbCw+/vhjdOjQgU8OwzAMwzBMLUCOjuSpPZBzOaTY8zmXgsXz1eUIUWeeWw5DA+Xhw4cLzw0lOqUSuZmZmYXVYoYNGwZHR0cR6UH07dtXVJRp2bJloRyGokPo+doup8nUXc5eS8a2YzH477C2NfYdVmYG6NTKWVSe+XP6S3W+ZC6jOjxv1S+C8kMNHjxYJLE+evRouasFslT9UseKQjUJ9xf3FduW8uHrkPuKbUt9r0P6PAoMUGwVIX3NZCAvh95c4sPyKMwA6WunwGrGvmqJEt61a5fIv0fzd8U4kRbAjhw5gpycHJiammLFihVo3LixeI2CH2bPni3eR4tpU6dOLXwfVY195513RI7QNm3aiH+LHrfibyoSQD6Hs2fP4tGjR8KHsHTpUhGQoUCxb8lxZEXPz3M7QQYOHCg6gg7o9u3b8PHxwb59+wqTpcbHxxeL/Pjiiy/EZJD+vXnzpkhgSA6QOXPmPO9XM0yVSuJ2aOkE6xrO19GtrQvmrQ7Cbydj8UpAgxr9LoapDipT9YuYOXMmbG1tMWrUKOEEKY+yqn7RD+TDhw9R26hTRaHagPuL+4ptS/nwdch9xbalftchORJo4k7/ViRAIO9OHHKiT5W9A31W1Ek8unkFWrb1q9Q2bW1tHDt2TBRACQwMxJtvvimeIweFIuBh27ZtePfdd7Fnz55nvo+Okf4lh0nXrl1x4MABrFmzRjhC6NgVBVTo7w8++EC8j3KK0vMTJkwQC3YfffTRU/1GBVh0dHSeu8pipRKjTpo0SWylodD1FO0ECrGmjWGUwe6gOETfSsOUHp41/l16utro3cEdUzeG4iVfZxjo1XjuYYapEpWp+kU/bD///DMiIiIq/D1lVf0iRwqtItQW6lhRqCbh/uK+YttSPnwdcl+xbanvdUiRDvfv3xcT+aKT+bIoyKiY7F4zIwk6jh5VatuwYcNEmyivJ83pk5OT4eTkJOb7FJlBDgfql5SUlGJtV7zP09Oz8H20D/3ds2dPsU+vXr3g5uYmnqN9KWhC8ffvv/8uctMtWbJE7EuLZYrXFNDYlc4D5SylfHYKDAwqtuDNMzRGrXmYlYsvNoSgV6Ab9HVrx9x9m9jhxJmbWLLnHD591adWvpNhagv6waNk1z/99JP44akoslX9UqeKQrUB9xf3FduW8uHrkPuKbUv9rkP6LHIAKLby0LJyqNDn0n4V+bxnQQ4FxWdQlAo5Hq5fv47//Oc/CAkJgbu7u5CsdOzYsdh3FXVEKN6neL3ofiWPW/E3RX/88ssvaNSoUZltU+xb8nxU9NzwCJBRa5buPQ9dXW208S69elFNoEmVMjo3xJLd53AjKbPWvpdhKsPzVv26evWqSIhKskbyytO2bt067N69W/xNrzMMwzAMwzDVD5XB1fH0BzTLkM5oakGnSUCNlctNS0sTERkODg7CWUERIRWBokJI7vLPP/+IxwcPHixzzEgVB+fPny/2J1JTU0Ve0eqEnSCM2kIOiO92nxMOCXJM1Cb1HUzRvJEtpm0KrdXvZZjn5XmrftGPWGRkpJDCKLZ+/fqhS5cu4m+SuDAMwzAMwzA1g+nweYCW9tOOEHqspQ3TYXNrrOubNWsmcnt4e3uL5KYuLi4VHm9SNULK90GfsWnTJlGNsDS+/fZbEU1CuUebN28ucojQAlx1wnIYRm2ZsTkM3u7WaOBoppTv7x3ohnlrTuFkVCL8PYvnW2AYmXieql+ku2zatGmx95ubm4t/Sz7PMAzDMAzDVC+67q1gNXO/qAJDSVAV6DT2Ew4Qer2qFJSoVEM55BR89913YlNABVBKvk/xL+VRUchdAgICyswnVzSvqLGxcYUjTCoLO0EYtST40h38ERqPySP8lNYGcxM9dG1bH5PXBOPvOb2hpcWBV4ycPG/VL4ZhGIZhGEZ5kKPDeuZ+5N6JRX7KbWha2teYBEYdYScIo3bk5xfg0zXB6NLGBRam/58tWBl08XXG/MgEbDlyFYO7NFRqWximuqp+lYRKnDEMwzAMwzC1i3B8sPPjueGlPUbt2Hr0Km6mPMALrSumUatJdLS10LejO2ZsCUf6g2xlN4dhGIZhGIZhGMkoKT9hara/OBKEUSsyHmZj+uYw9O3oAV2dMrIm1zLNG9rg+JlbWPjbWcwc3FrZzWEYhmEYhmEYRgKo0grlzCBZso2NTZXL2srkpMjJySlWHrc6P1uRa4T6rzKwE4RRKxbtjISFqQF8GtlAFugC7d/ZA0s2h2FE10ZwszdVdpMYhmEYhmEYhlEyWlpacHJywo0bN6q9AooyKSgoENUGKadcTTh26DOp36j/KgM7QRi1ITYxAyv2XcR/BraSzovqaGOM1l72+HxdCDb/t6uym8MwDMMwDMMwjARQNZSGDRuKyAl1IT8/X1SUsba2rpHk+hQBUlkHCMFOEEZt+GJDCFo1sYeTnQlk5KWABpi7Ogj/nL2FLs3rKbs5DMMwDMMwDMNIAE3oqzKpl9EJoqOjA319fSkrDMrXIoapBP9G3sK/5xLQK7CBtP1nbKiL7v6umLw2CDm5+cpuDsMwDMMwDMMwTJ2DnSCMypObl4/Ja4OFg8HEUBcy076FIzKz87D6YLSym8IwDMMwDMMwDFPnYCcIo/KsPXQJ6Y9y0MHHCbKjraWJ/p08MG9HBJIzHim7OQzDMAzDMAzDMHUKdoIwKk3q/SzM2XYa/Tp5CAeDKtCkgRVcHEzx1fYIZTeFYRiGYRiGYRimTqEas0aGKYOvdkSIRKjebtYq1Uf9O3pg4+EruBCfquymMAzDMAzDMAzD1BnYCcKoLFE37mH935dFFIiqYWtpiEAfR5HLhOpoMwzDMAzDMAzDMDUPO0EYlYQcB1PWBsO/eT3YWxlBFenezhXn4lPwR+h1ZTeFYRiGYRiGYRimTsBOEEYl2R9+A6djktHD3xWqioGeNnoGNMDn60PwKDtX2c1hGIZhGIZhGIZRe9gJwqgcWTl5+Gx9iHAgGOrrQJVp17QeNLQ0sPzPi8puCsMwDMMwDMMwjNrDThBG5fhp30XkAwhoXg+qjqamBvp3bohvfjuLhJQHym4OwzAMwzAMwzCMWsNOEEalSLz3EF//ekYkQyUHgjrg4WSOJm5WmLUlXNlNYRiGYRiGYRiGUWvYCcKoFLO3hqNRfUs0crGAOtGngzt2nopF+NUkZTeFYRiGYRiGYRhGbWEnCKMynLmWjF9OXEPfju5QNyxN9dGltQs+XRPEJXMZhmEYhmEYhmFqCHaCMCpTEpccBJ1aOcPKzADqyAttXRB7575w9DAMwzAMwzAMwzDVDztBGJXgt5OxuJKQjm5tXaCu6OlooU8HN0zdGIrMRznKbg5Tx1i2bBlcXV2hr68PPz8/BAcHl7nvr7/+itatW8Pc3BxGRkbw8fHB+vXra7W9DMMwDMMwDFMZ2AnCSM/DrFzhGOjdwR16utpQZ1p52sHYSA9Ldp9TdlOYOsTWrVvx4YcfYtq0aQgPD0eLFi3Qo0cP3Llzp9T9LS0t8fnnn+PkyZM4e/YsRo4cKbb9+/fXetsZhmEYhmEY5nlQ7xkloxYs2XMOBgY68G1iB3VHQ0MDAzp7YOm20xjcpSFcbIyV3SSmDrBo0SKMGTNGODKI5cuXY+/evVi1ahUmT5781P6dO3cu9vi9997D2rVrcezYMeE8KY2srCyxKUhPTxf/5ufni622UHxXbX6nKsP9xX3FtqV8+DrkvmLbUj58HapGf1X0+9gJwkjNjaRMERUx8fWW0NRQj5K45eFibwqfxraYtjEUq98vPtlkmOomOzsbYWFhmDJlSuFzmpqa6Natm4j0qEi+nr///hvR0dGYP39+mfvNmzcPM2bMeOp5ijZ5+PAhapu7d+/W+neqMtxf3FdsW8qHr0PuK7Yt5cPXodz9lZGRUaH92AnCSM30TaFo3tAG9R1MUZfoHeiGuauDcPzibQQ2sVd2cxg1JikpCXl5ebCzKx5pRY+joqLKfF9aWhocHR1FdIeWlhZ++OEHvPjii2XuT04WktwUjQRxdnaGra0tTE1Na3WFgH6QbWxshLOH4f5i21IOfC1yX7FdKR++Drmv1M22DAwqVkCDnSCMtJyMSsSf4dcxZUQ71DVMjfXQza8+Jq8JxuG5faClxZM1Ri5MTEwQERGB+/fv49ChQ8LB4ebm9pRURoGenp7YSkI/jMpwRijre1UV7i/uK7Yt5cPXIfcV25by4etQ7v6q6HfxCJCRkry8fOEA6Nq2PsxNnp441QWoHHBSRhY2Hr6i7KYwaoy1tbWI5EhMTCz2PD22t7d/5o+Mh4eHqAzz0Ucf4bXXXhOSF4ZhGIZhGIaRGXaCMFKy5chVJKY9RBdfZ9RVdLQ10a+TO2ZuDUdaZraym8OoKbq6uvD19RXRHEVDGOmxv79/hT+H3lM08SnDMAzDMAzDyAg7QRjpSH+QjRlbwtGnozt0tLVQl2nqbg17KyMs+PWMspvCqDEkZfnpp59EhZeLFy9iwoQJyMzMLKwWM2zYsGKJUyni48CBA4iJiRH7f/PNN1i/fj2GDBmixKNgGIZhGIZhmPLhnCCMdCz87SysLQzQoqEN6jpUMrdfJw8s3hSGEV0bwaOembKbxKghAwcOFMmrpk6ditu3bwuJy759+wqTpcbHxxfTWJKDZOLEibhx44ZIQOXp6YkNGzaIz2EYhmEYhmEYmWEnCCMVMbfT8fNfUXj3zVbCAcAA9WyM0bapAz5bF4Jtk7txlzA1wqRJk8RWGocPHy72ePbs2WJjGIZhGIZhGFWD5TCMVHy+LgStvezhaGui7KZIxUsBDRB0+Q4ORtxQdlMYhmEYhmEYhmFUFnaCMNLwz9lbOB6VKCb8THGMDHTQo10DTFkXgpzcfO4ehmEYhmEYhmGYSsBOEEYKaGI/eW0Quvu7wthQV9nNkZJAn3rIys3HzweilN0UhmEYhmEYhmEYlYSdIIwUrD4YjczsPLRv4ajspkiLliaVzPXAV9sjkJT+SNnNYRiGYRiGYRiGUTnYCcIoneSMR5i3IwL9O3lAW4tN8ll4ulqigZM55m47XWvnh2EYhmEYhmEYRl2o1Ixz2bJlcHV1hb6+Pvz8/BAcHPzM/e/du4d33nkHDg4O0NPTQ6NGjfDHH39Uts2MmkGRDS4OpmjSwErZTVEJ+nV0x5ajVxEZm6LspjAMwzAMwzAMw6i3E2Tr1q348MMPMW3aNISHh6NFixbo0aMH7ty5U+r+2dnZePHFFxEbG4sdO3YgOjoaP/30ExwdWfbAABfiU7Hx8BX07+jB3VFBbCwM0d7HCVPWBaOgoID7jWEYhmEYhmEYpqacIIsWLcKYMWMwcuRIeHl5Yfny5TA0NMSqVatK3Z+eT0lJwc6dOxEYGCgiSDp16iScJ0zdhibwk9cGI6CFI2wtDZXdHJWie7v6uHD9HvaExCu7KQzDMAzDMAzDMCqD9vPsTFEdYWFhmDJlSuFzmpqa6NatG06ePFnqe3bv3g1/f38hh9m1axdsbGzw1ltv4dNPP4WWllap78nKyhKbgvT0dPFvfn6+2FQdxTGow7FU5Zj+CI1HZFwKPnu7XQ22TD3R19VGr8AG+Hx9CF5o5gADvfIvZbY71UCd7gsMwzAMwzAMo9JOkKSkJOTl5cHOzq7Y8/Q4Kqr0sp0xMTH4+++/MXjwYJEH5MqVK5g4cSJycnKEpKY05s2bhxkzZpT6/UWdI6rO3bt3oW5U9JiycvIwZW0QegY0gJ6uFvIllnXI2rbW3vY4FnEDC7YHY9yL7hV+X122O1UgIyND2U1gGIZhGIZhGLXluZwglV3VtLW1xYoVK0Tkh6+vL27evIkFCxaU6QShSBPKO1I0EsTZ2RnW1tYwNzeHqkN9QpM2ioqhSBp14HmP6bvd56CtqwP/ZvWgqaEBmR0gsraP2vXKC42w4tczGNPLBw7lSIrY7lQDSh7NMAzDMAzDMIwEThByQpAjIzExsdjz9Nje3r7U91BFGB0dnWLSlyZNmuD27dtCXqOrq1vqJKC0iQBNrtXFaaCOx1PRY0pIeYBFOyMx6uXm0NSU08GgKrg5msPbzRozt5zG/yZ1qNB76qrdqQrqchwMwzAMwzAMIyPPNdomhwVFchw6dKjY6jI9prwfpUHJUEkCU1TnfunSJeEcKc0Bwqg/s7aEw7OBJTycVD+qRwZ6d3DHnpA4hF5WH0kIwzAMwzAMwzBMTfDcS44kU6ESt2vXrsXFixcxYcIEZGZmimoxxLBhw4olTqXXqTrMe++9J5wfe/fuxdy5c0WiVKbuEX41CTtPxaIvl8StNixN9dG5tQs+XROE/Hw585cwDMMwDMMwDMOoZE6QgQMHitwPU6dOFZIWHx8f7Nu3rzBZanx8fLFwbsrlsX//fnzwwQdo3rw5HB0dhUOEqsMwda8kLk3Uu7R2ERN3pvro2sYFX60JwvbjMRjYoeJJUhmGYRiGYRiGYeoSlUqMOmnSJLGVxuHDh596jqQyp06dqsxXMWrELyeuIfbOfbzZ21vZTVE7dHW00KeDO6ZvCkPv1i4wNtBRdpMYhmEYhmEYhmGkgzPwMbVC5qMcTN0Yij4d3KCn8/9Jcpnqo2VjW5iZ6OHbXZHcrQzDMAzDMAzDMKXAThCmVliy+xyMjXTRyvOxbIqpfjQ0NNC/c0Ms//MC4u5kcBczDMMwDMMwDMNUhxyGYZ6H+Lv3sXTvebzzRksxUWdqDmc7E7T0tMOXG0Kx7sMu3NUMQ/eg5AfIzM4TfVGQn4/klIdIzc+AxpP8VUa6WnCxMuS+YhiGYRiGqQby7sQCMReQp+EFTXs3yAY7QZgaZ9rGUPg0toWLvSn3di3QK7AB5q4OwtHzCejg7cB9zlSIZcuWYcGCBSLhdYsWLfD999+jbdu2pe5LFcLWrVuHc+fOicdUOp2qfpW1v7IdIAN+KC0nVWyxRzsntmNHCMMwDMMwTBXIvhqO9DWTkRP9eOyVBEDH0x+mw+dB170VZIHlMEyNcvzibRyIuInegfJ5ANUVUyM9dG/nislrg5Gbl6/s5jAqwNatW0X582nTpiE8PFw4QXr06IE7d+6UmQB70KBB+Oeff3Dy5ElRBax79+64efMmZEMRAVJd+zEMwzAMwzClO0CSp/ZAzuWQYs/nXAoWz9PrssBOEKbGyMvLx+Q1wejmVx+mxnrc07VIx5ZOSM3Mxvq/L3O/M+WyaNEijBkzBiNHjoSXlxeWL18OQ0NDrFq1qtT9N27ciIkTJ4oS6Z6enli5ciXy8/Nx6NAh7m2GYRiGYZg6SPraKUBeLpBfYmGJHuflIn3dZ5AFlsMwNcbGw1eQlJGFt1s5cy/XMtpamujXyQOzt53GywGuMDdiJxRTOtnZ2QgLC8OUKVMKn9PU1ES3bt1ElEdFePDgAXJycmBpaVnmPllZWWJTkJ6eLv4l5wltNQXlAKkI9x9mIy3z/9unLHJy8zFi8WGM6t4ILzR3UnZzxLm5/ygX+plZwi4IyjnkbG2IMT2aSJnnacuRKzgdk4zpg3xhoKet1L4qjcjYFCz87SzmDG0NJ2tjyMaDrFy8/d2/eL9fU7SrwWTmFe2v0vh41Sk0c7HAsK6NpLTBVQeiEZuYjs/eaAl9XW2l9lVpBEXfwcq/ojBrSGvYW8iXDyn1fhbGLzuGKa+3gI+btVL7qiwmLT+OTt72eL2DO2Rk2Z7z4jft41daQPcZVRlrq79KcjjyFrYdu4qZb7WBtZk+ZON26gO8/9NJfDGwJZrWt1RqX5XFqCVH0N+vPvr51YcM5N+NQ07UM8aN+XnIuXgCObdjoGXrWnPtqOC4T6OgoKAAkkODZTMzM6SmpsLc3ByqDp2cxMRE2NnZSXER1cQxpWVmw/eDX/HKC43QvKENVJX8ggJoSjjAqgh0aa/49SzaN7bBvOF+dcLu1IF79+7BwsICaWlpMDWt+Tw6t27dgqOjI06cOAF/f//C5//73//i33//RVBQULmfQVEh+/fvx/nz56GvX/pgZvr06ZgxY8ZTz0dHR8PExAQ1xZWkh3hvZ/H8H6WREJOA7Ec5kOG6zc7NB/0ya2trQltTvvsPDRqysvOgpaUJbS0NyNbC7Nw85BdoiHu3DrVPsgaSoysvvwCamhrCYS3bKab7alZuAbQ0NQo3GX+bs3PyRf9pSWiDufn5yM0DtDToHMtog3nIE9fI40UT2U4xRRLn5D2+RmS1wdy8AiE5ltUGxTXy5Dqm3xHZbLDofZquEdlOsSrYII0V8vMLhA1SHyqblgUxWJ+/uPwd39sEuPnWWDsyMjLQuHHjcsfRHAnC1AgLfj0DeysjNPN4Pg8+U90lcz2waEMoRnRtjIb1ODEtU/189dVX2LJli8gTUpYDhKBIE8o7UtS5TblEbG1ta9TZQ1VgSiZBLY13B/rCxlT5EVNZ2bn4fPlxDOjcEL8fuSISSg/v7QVjA11pnMHfbAxFkwZWOBpxA442JqJ9JobKa19Jth+6hIdZObgUfw92VoYY1ssbZka60jjOg88n4K/gOOEMsTY3wOCXvGBhrCfNJCoxJRPz1gTD0sxAnNe3enrCxsywRiZRlV1omLsmCL5N7HA49DocbU0wvI8XTJR4jZRkw58XoKmliQsxSbCzMqoWG6zORRm6dk9FJuD+wxxYWxhgSC8vETEqiw3G307H4i3hsDDRh4nRExs0N6xw+2pjAWvaihPo2MoJB4Li4CShDa76PRImRnqIiL4DB2sjDOvtDdMy7tPKWPA7GByH8zHJSE57CBtLQwzp5Q2LWrpPV4TL11OxclckjAx0RK69t3o2gY25gViokGVxdPKyo+jp3wD7TsTAWYKxgkGaO7C6fCeItbsXtGxrLsrQwMCgQvuxE4Spdq7cShOhoO+/5StlmGpdghxR7Zo5YMq6YGz/tKuym8NIiLW1NbS0tERETVHosb29/TPfu3DhQuEEOXjwIJo3b/7MffX09MRWEorgqckoHkUZ3PLQ0dGEfi1KJ8pEQ/wnIuh8PW3x7cYwLFgfijEvN4eHk3IiIUsOkOm+7mRngpnjArFkazgWbAjFmAHN0NDZAjJAK2LmJvqYPjYA//vlDBZtDMXb/ZuhkYtFjU/yKjKZoNB0PR0tTB7uh9W7I7FkcxiG92mKxvUtpBhck3yDzvGUkX7Ysu8ivt96WkwAmnvYVPtqaGUnX/QO13pmmDHeBd9tVlwjzdDQSRYb1ISFGdlgIH7cEVEtNlidE1VdbS1xv/tgcGv8vOssFm8Kwwhhg5ZSrMiTDdIK/Oej2mHjnxee2KAXmntYV8gGa2NSTx/v7myB9j6O+G5zuHQ2qKWpCVsLQ8wYF4gftp/GNxtCMap/MzQsxQaV4QTR0daCoYEO3nmjJVbuJBsMxYi+TeFZ31IKZxzZIEU7fjHKHxv+OI/vt4RjcC8vNHW3grYkkcfUT56ulvBv7lA4VhitRBsssHXFPcdWMLsVAY2CUiQpmlrQaewHnRoul1vRMaUcZ5FRKz5bF4K2TR1Qz0Y+rXNdpGdAA4RfTRJVehimJLq6uqLEbdGkpookp0XlMSX5+uuvMWvWLOzbtw+tW7dW+Y49EByPR9m5kAmayM8YF4DGrhZikvJXUKxYhZIFY0NdfDbCD2297PHdlnDsOxkrBtOyQCt4Hw72FYmil26l9l1DXg3mn6lM+ya90RJd27iIiTL1X45EFb0onwpNml7u7IE1v5/Djr8viXwhMkGRKl+83U44DL/bFI79p+SzwY+HtEYHH8cnNhgrnQ2+O7BVERu8Jp0Nji60wUhhgw8ls0GKEvhyVDv4NLKR1gY/GdoGAS3q4fut4dgvoQ2+92YrvODrgh+3R+DPE9ekqmxINjhmQHMM6OIhnNa//H0ZD7Pls8FpY/zR1N36sQ0GKc8GL3X9FPma2ijQKOFi0NQCtLRhOmwuZIGdIEy1cjDiJk5duoOXAhpwz0qCob4Oevg3wOfrQ4V+kGFKQjKVn376CWvXrsXFixcxYcIEZGZmimoxxLBhw4olTp0/fz6+/PJLUT3G1dUVt2/fFtv9+/el61wj3bITwhUl5kYqFm4Ixa2k+yLnhSzQivzbfZthRF9v7D0Wg6XbI5DxQPm5S4q277WujfDO6z7Yf+oalm47jfTMbMjUvt7t3fD+oFb4OzgeS7dFSJEAt2j7XvRzxQdv+eLf8Ov4YXsEUjIeSWOD1L6A5o6YMsIP0bEp+HZjKG7czZCmfYo2DnzRExNebYF9J57Y4AO5bLBPB3e8N6gVDgXHSmmD3RU2GPbYBlPvPwIktMGoa8kiquamhDb4Vo8mGPdKczGJJxvMkMwG+3f0wLtvtsKBIIUNytW+Hv6u+GBQKxwOi8ey7RG4d1+uayTwiQ1ejEkWMvObd+UbKwzt5YXRA5rhz2MxWLaNxgq1f44zHJoibPB6pNXzKfY8RYBYzdwPXfdWkAV2gjDVBq0e0ESb9Gnk2WXkgVYAcgsKsOlonLKbwkjIwIEDhbRl6tSpouxtRESEiPCghLNEfHw8EhISCvf/8ccfRVWZ1157DQ4ODoUbfYZsuFgZYufEdtg4uo3Y3u3gjNzUNAwOdC7cRnaqj8+GtRH5N75eF4KTkbekWskjWjexx4yxAbib8gCzfz6JKzfuQSaauFph1rhAMeiaveqU0FPLhLuThZDH5ObmY+6qIETHp0o1gG1QzwxTR/kLKcLXa4MRFZsilQ2StHLKiLZwczTDN+tDceLsTZHcVSa83a0xc3wg0u5nYfbPp3D5hlw26OFkgRljA5GdkyevDY6m6L8CfLUmGBeFDUIqG/xspJ9o50Jhg7eks8FmHjaYOS4A9zKyMEtCGyTJIskYKffU3FWncEk2G3Q0x7TRASLicd6aIFyMS5GqfeI+OLIt6juYYsH6x2OFPInu04RPI1vMGB8ocq0o6z6YQY6QIevx98i9GKr5PvS/DoX1jH1SOUAIdoIw1caWY/HIystHoE897lXJIG0olcz94a8Y3El7qOzmMBIyadIkxMXFiTK2VBHGz8+v8DVKerpmzZrCx7Gxj2UZJTeqACMj5Ahp4mAiNkcqxZebBzsz/cKNkrGRPnlYLy+xbTsQjTV7ziNTgmoxRWF5TNVgeUzVoGtkUI8mGN7HG78cuoS1e88j46Fc1wjLY9RbHkM2SPlpyAZ3HIoWNkjJXWVCFeUxNVmmXt3kMWSDQ17yEja4/UA01u45j/uSjRXMJJHHPDRzwmkNN2jayFHCtyTsBGGqhaT0R1i6/6qYaNOEm5EPSnhGCbHmbotQdlMYRlpaedqJ1dBbdzLEaui1hDSpVqJYHlP1/mN5TNVXGilZ4J3kTHy9LhhXb92T7hpheYz6ymMUNvjlKH8kJmdi/tpgxEhog6okj1m2/Yx0Ei2Z5TFES7LB0f5ISLqP+WvIBuUbK8ggj5EZnq0y1cK87RFwczIXWYoZeenT0QM7jl/D2WvJym4Kw0iLpam+qIzRoqENFm0Mw6GQeKkSyREsj6kaLI+p+jXyybA2aO1pJ1YaDwXHSbVaS7A8Rr3lMWSD/x3WBq08bbFYUhtUFXkMJQWfsyqI5TGVsMHJw9uiZWMbkbxc2KBkYwUZ5DGywk4QpspExqZg67EY9O3owb0pOdbmBqKu/eS1wVJVmWAY2aCINkr4OfHVFvjzeAx+3CHXShnB8piqwfKYql8j/Tt5PEmKG4vlv5xBqmSrtSyPUW95DNngy50bPrbBk49tULaIAVWQx1AFo0CuHlNpG3ylSyNMfN1HXB/Ld5zBPcnGCrLIY2SDnSBMlaCJ9JR1waJOuo2FIfemCvCiX31E30rDriBOksow5dGkgZVISPogK0eslMmWqI3lMVXvP5bHVF1qOW20v0g6+9XqIFyITZbuGmF5jHrLY4QNjvFHdm4e5q0OQpSE92lVksdw9Zjnx7O+JaaPCUBWdh7mraL7oHw2yPKY4rAThKkSe0LiceH6PfEDyagGerra6NXeDV9uCMHDLLlqnTOMjBgb6uKTIW3QqZUTfth2GruPXJEu7JrlMVWD5TFVv0aoBGy3ti5iJXTXkSvIkawkO8tj1FseQzb4wSBfvEBRK9sjxH1aNhtUFXkMV4+pvA1+ONgXXXyd8eP2x2MFmSKnCJbH/D/sBGEqDU2gv1gfgl6BDaCvp809qUK08bKHnp42vt9zTtlNYRiVQEQMBLrho8GtcTziJhZtCkOSZJWWWB5TNVgeU/Vr5EU/VxFaHxSZgG83h+HOPbmuEZbHqLc8RiTUbPfYBk+evSVs8K5kNlgoj2moOtVjZMqJJXv1GLLBngEN8PHQNjhx5ha+3RSGu5KNFVge8xh2gjCV5oc/LkBLWwttmzpwL6oYmhT62Lkhvtt9DjeSMpXdHIZRGVzrmWHm+EDo6Whh7qognL50R7qQ17f7NsOIPt7YeywGS7dTRvgcqdpHuVYe55F4HBaenimxPGZ7hFS5YBSOBiFNCL+OH3ZEICXjkVQ26GJvKqQJpoY6Qh4TFp0otzxm+2mkSyZN6NPBXUTWHAqOldIGi8ljdsgnj3G2N8X0sQEwNtAR8phwCW2QSv0q5DHLtsstj6HqLGmS3aeLVY/ZIV/1mPr2ppgxLgCGetpCHhMefUduecz2ulc9hp0gTKW4lZKJb3dFYkAXDzGhZlQPCm1t1tAGMzaHKbspDKNS6Otqi5WoPh3csGpXJLb8FYWsnDzIRGsve5HL5G7KA8z++SSu3LgHmWjiaoVZ4wLFoGv2qlO4fF1SeUxOvnB2RcenyidNGOUvBnFfrw1GlJAmFEh1jYx/1QevvtAQa38/j837L+JRdp6c8piMLCmrJng4WWDG2EBkZ+cJG7wsqzymQE55DNngxNd88HJnD6wRNhglnQ0q5DGp6XLLYx5l5WLuqlPyVo/JL8C8NfLl7CIbnPRGS/Tv5I7Vv0diC9mgZGMFH0X1mHt1r3oMO0GYSjFjUzi83Kzg5mjOPajC9Gnvhj9C4xEUfUfZTWEYleOF1i74bKQfzl6+i6/WBuNW0n3IBMtjqgbLY6pOYAtHfP62Hy5eS8H8dcG4cVeua0Sl5DHbTmOfhNIEmeUxRIeWTsIGL8QkCRu8KZkNsjxGveUxRKdWzuI+c+7qXcxfG4ybko0VzOpo9Rh2gjDPTejlu/g9OE6EazKqDU2SXmjrgk/XBCFfpiUchlERHKyNxUqZnaWBWA09fvaWVCtRLI+pev+xPKZq2FkaiYiB+nYmImrl2Nmb0l0jqiCPIWkCy2Mqb4PTxgTA2dZYTEKPS2iDLI9Rb3kM2eD0sYFwtDbCfEnHCkPrmDyGnSDMc0ETZZowd2njAktTfe49NaCLrwsS7j3E1qNXld0UhlFJdLQ1Mf4VHwzq4Ymtf0Xh512R0lVeYnlM1WB5TNWvkRF9m2JkH2/sOHAJK3eeReYjua4R2eUx7k7mxeQxUkq0JJbHkA2+3a8ZhvX2wrYD0Vi56yweSGaDLI9Rb3kM2eDoAc0x5KUm2HYgCit3ReKBZGMFnzokj2EnCPNcbD8eg+vJmSL0kVEPdHW00LeDO6ZvDkPGQ/X2+jJMTeLfrJ4IKY1LSMOsn0/i2q00qTqc5TFVg+UxVaelpx2mjfVHQlIm5qyS7xpRKXnM1nCWx1SynDjl+7l15z5mrzqJGMlskOUx6i+PaevtIGzwRmKGyNklmw2a1RF5DDtBmApz/2EOpm8KE2GZNHFm1IcWjWxgaWaARTsjld0UhlFprMwMxGptIxcLfLMxFAeC46QaPLA8pur9x/KYqmFhoi8cDS0a2mDxpjD8JdkAW1XkMVw9pmo2+OUofzRzt8aijaFS2iDLY9RbHkM2OG20P7waWElrg0PVXB7DThCmwlA1GDMTPbRsbMu9pmaIcmidPbBi30Vcu52u7OYwjEqjqamBEX2aYlT/Zth7NOZJGdgs6eQxtBJ1NyWTq8dUApbHVP0a+X9HQyy+33oaaZJNUlStegzLY57fBgf1aIIJr7QQ0QIy2qAqyWPmcPWYStngkJe8MO7l5vjz+BMblGys4KPG8hh2gjAVIu5OBpb/eQH9OzcUE2ZG/XCyNYGvlx2+2BCq7KYwjFrQspEtZo6nAewjMYC9GJsM2VaiZowLRGNXi8IV+QKJVqKMDXXx2Qg/tPWyx3dbHof+y7RSxvKYquPZwAqzxgfgYVaOKJV8/ppc1wjLY9S/egw5u2aPD0Tmw8flui9IZoOqIo8JbFEP328Nx34JKxjJLo8hZ9esCU9Kxv98ChckGyuYqak8hp0gTIX4ckOo0PI625lwj6kxLwW44cj5BPwbeUvZTWEYtYAGsJQssFVjWyzdFoGd/15BrkQDRJbHVK885ocdZ6RayaP2vejnig/e8sW/4dfxw44IpGQ8kipZoJGBLj4d1hYdWjiKScpvh+W7RlgeU7X+666wwbDHNph6/xEgmQ1OGeGHgOb18APZoIT3aZbHqLc8xthAF5+P9IOftwOWSTpWGKpm8hh2gjDlcvR8Av6OvIVegQ24t9QcWvXq7u+KyWuDpfOUM4yqQoMHCrt+53UfHAm/jm82hCI57SFkguUx1SWPkViaMMpfDPqoTG2UqNxRINU10q+TBz58yxfHz9zEwvWhSLon1zXC8hj1rh5DNvhy54bCoXn89A0pbZDlMepdPYZs8LWujfDuwJY4qrBBycYKPmokj2EnCPNMaCJME+Lu7VzFiiaj/nTwcUJGVi7WHrqk7KYwjFpBCdBmT2iPvLx8IY8Jj06E7PIYmSbKqiCPef8tX3Rs6fSkcsc16cLCJ73Rsog0IVY6aYKbkzlmTwiEro6mkCaERsl1jbA8Rv3lMR7OFpg9sT20tTSEDYZJZoMsj1F/eUzj+paYM7E9KPsAORrCJBsrmKmJPIadIMwzWf/3ZaRmZotBHVM30NbSRL+OHpi97TRSMuQKF2SYyhCf/AAXEzLEdjPtERk5EtMeFW50j6stDPV18NnIdujU0gmrdp3Dxn0XkZ2bB1nlMRTyel+ikFfFShlF1ew/de1J0lm52sfVY6qGvq42PnyrNXoFNMDa389hg4TXCMtj1FseQzb48ZA26NnOFat/l/M+zfIY9ZbHkA2STJAchqslHSsMLUceY5B2Ay0LYpB/Nw4ywk4QpkzuZWaJiTCFqNLEmKk7eLlZwdneBF/tOK3spjC1xLJly+Dq6gp9fX34+fkhODi4zH3Pnz+PV199VexPP4SLFy+W2gEy4IdTGLwyRGxLjl6HtoUZNh6/Xrit/jeuVh0hxMtdGopJQHhUIuatDsKtpPuQUR5zJyUTc1YF4cqNe5CJJq5WmDXuSSK5Vadw+bpcIblcPabqUATqlOFtEXn5LuauDsLNu3JdIyyPUW95DNEzoIGYiJ65dEdKG2R5jHrLY4i+Hdzx8dDWiIi+I8YKNyUbK/iUIo8xSTgH3w1D8MLq3lifvxiP/tsaSVN7IPtqOGSCZ7ZMmczfEYF6NsbwdrPiXqqD9O/kgQ3/XMFFySYXTPWzdetWfPjhh5g2bRrCw8PRokUL9OjRA3fu3Cl1/wcPHsDNzQ1fffUV7O3tpT4lmdkVWznJzq39cFh3J3PMndgehvraYnBzNOKGVNVZSB5D5Q8b1+fqMZWBq8dUnXq2JkIeY21ugK/WBOGIZNcIy2PUXx5DBQFImmBpqidsULb7NMtj1F8e4+pghrnvtIepkS6+knCsYFZEHnNw40603DAEZrfOFNsn51IwkiVzhGgruwGMnETfuIe1hy7jwyGtuSRuHcXO0ggBLerhs3Uh+PWzF9kO1JhFixZhzJgxGDlypHi8fPly7N27F6tWrcLkyZOf2r9NmzZiI0p7nak4erra+GRoW/xxPAbbDkTj/NUkqVaiKNJnRN+maO6RiPV/XkB0XKpU2l+FPMbb3QorfjuLS/EpYkBmIEn0okIe4+lqgeW/UPtS0czNGrJVj6E8CMt/PSMianr6y5UEXUdbC5Nef5wocPvBS4i6JtdqrUIe09TNGit3RSI6PgUGOtpSta9PB3d4NrDE8l/OiGukkbMFZJPHNCQb/OWxDb7QxgWy2eC7A32FdGLbwWgRtSLRbbBQHtPMwxo/7z4nzrEmJZSQqH39O3qIvFgKG6zvYArZ5DGNXMzx45P7IOXHk80GP3irNQ4Gx4mxAiW3lsgEoZDHNL45E5opudAo2br8xwtS6es+g/WMfZABjQKZXEllkJ6eDjMzM6SmpsLc3ByqTn5+PhITE2FnZwdNTTkGakUhk3h13gFARwuvvNCowu+jgbFMN93qQN2O6XmP58GjHLFC/eOE9ujp6wzZkP1aqgz37t2DhYUF0tLSYGpa84OE7OxsGBoaYseOHRgwYEDh88OHDxdt2bVr1zPfT5KY999/X2zPIisrS2xF7+vOzs7ivl6TxxmVkIEhq8LK3c8w+xG0lPxzePfeA9y8cx95BQVwdzSHmbEuNKD8+09BQT40NDTxICsHl+PvQUtLA1bmBrC3NJSifQpy8vJwkSbIBYCpsR5c7U1q3Xmr6KvSoNVFcoIonEjeDaykci5T+67evAfK5Ur3fp9GNtCq4fvqs/qrNCg/zdWbadDU1ICtpSFsLQzkssHcPDFBpoyGdP262JlUW/uet6/KOsdRFPJf8Dj/l2d9C+lskKR3dI08ysoTNliZMVh19FVZUAns2Fvp4u96tsawNtOXygazc/KErENLk2xQD062xuW2ryb7qywbpPuMnq4WGjmbS2eDl6/fE3MhysHR3KO4DdZmX5VFasYjxN/OENeJi72piFKSwQZtcu7g+2vvlbuf9ZIIaNm61lg7aHxZkXG0PK5qRhoOnL6J8KtJ+OztdspuCqNkKIkjaWKnrAtGl+b1oKejpewmMdVMUlIS8vLyhCOpKPQ4Kiqq2r5n3rx5mDFjxlPPk+Tm4cOaKwGXnFKxz46OS0H2I+Un2MzPLwBF4tJKFA28JAloKIQGhjk5wI3EDNy6kyEG2tK1Lw9IuvcAyfceCIeNhmTtE7ntNCAqn2hraogKADK2Lzz6jji/kp3iJ5MTIP52Om4kpktpg9SHd7JzkZTyAJoS2yBVPtGS2AYV7ZPsFBe2MfZWGuIT0qS0wexs4GFWLu4kZ0ppg3SfzsrJZRusYh/G3LyH2FuQwgZbIqZC+yVdvQAUGNRYOzIyMiq0HztBmKc8yDTh7eHfQEyAGca/WT2cPHsLK/ZdxH/6NuUOYSrFlClTRN6RkpEgtra2NRoJkppPP4ax5e5H1ShsTJVfBjwrOxefLz+OF1q74J/QeLg5mmNoby8YK/F+XDKC7JuNoXBxMEXohdtiFWo4tc9AF7Kw/dAlsVp79cY9ONqYiPZR7gZZou2Czydg/6lYZOXkw87KEMN6ecPMSJ7+S0zJxLw1wTA30YO5iT4Gv9QE1mYUcSFPtOXcNUHwbGCFU2dvwdXBFMN6e8PYQJ4xy4Y/L4jcFpfiUuFoa4LhfbxgUsVrpDojUymnwPGzt3A/Mxt21kbS2SA5uBZvCRc5EMxM9DG0VxNYmVbcBmsjinfaihNo5WmL42ee2GAfb6Xep0uy6vdIIaE4H5MMp3JsUBlRzyTrOHslCclpD+FANtjbG6a1dJ+uCLQQsXJnJPT1tGFuSjboBStTfeF8kCVCfPKyowhsUQ9HTt8QiYbFfVCJNmiQ1hBYvaTc/azdvaBla1dz7TComIOFnSBMMVb+FYXcggKRC4JhCAo77t/ZAwt+PYM3OrjDzrzmvLdM7WNtbQ0tLS0hKyoKPa7OpKd6enpiKwnJmGpSyqRRwc/W0dUSgx2loyH+Q/uWTmjrbY8lW8OxcH0Ixr7cXDhElEHJATKFLjeubylyXSzeGIoF60Mx5uXm8HCSQ66qraUBWwtDDO/tLfpvwYZQjBnQTOQcqGkqMpnQ1Xlsa1NGtsb/fjmDRRtD8Xb/ZmjkYiHFai2VZqRz/MVof2zYex7fbQ7HkF5eaO5hXe2D/8pOvugdlLS9h199fLspDAueXCOUbFgGSGpiY2mIwS954bvNYU+ukWZo6FR5G6zOiaquthaM9HVEGVhKSCqjDdLYY+qYAKz5PRKLN4WLSShVQ6nIgndtTOrp41s0tkOX1i5YLM5xCMYOkMcGScpGTuo3XmwsruFn2aAynCDkoDEx0sW7b7bCD9tPY+GGUIzu3wwNJbJBLW1NTBsbgNW7yQbDxIJEUzerGpcJVhTqpzZeDmjv44glmx+PFei3mOS0yqDA1hX3HFvB7FYENApKSS6rqQWdxn7QsXer0XZUdEwpx1lkpODOvYeY/8sZURJXlguckQOaPDRytcSsLfJkdWaqB11dXfj6+uLQoUPFcq3QY39//zrTzQeD4oT+VyZoBXnOhPawtzLCoo1hOBAcJ131mBkqUD2mTRM7fLclHPtOxkqV1FX26jEGetoY90oL9O/kjlW7IkWETRbFX0uEpZkBZo4LgIezuXCGyGaDqlI9hiZRj20wVjobnPCqD/p1dMfPwgajpbNBGwtDzB4fKFbiH9ugXPdprh5TdRuc+JoP+nZwE5Ehv/x9WUTNy4S9lTFmT2gPJzsTfKvkscKlrp8iX1MbBSXzpmhqAVraMB02F7LAM12mkDnbTosM8bTCxzCl1Sr/9eQ1RMQkceeoGSRT+emnn7B27VpcvHgREyZMQGZmZmG1mGHDhgk5S9FkqhEREWKjv2/evCn+vnLlCmTDSLdieWyiYpPx9boQJKRkQiZotez9Qb4Y0Mkdu/+9gh92nMH9hzmQBYoYeLtfM4zo4429x2KwdHsEMh7I1b7XuzXGO6/7YP+pa1i67TTSM5Wf+6Vk9Zj3B7XC38HxWLotQkh5ZGofVUn4bKSfqFxEq923ku5LVZWAVv3GDGguIgX2HI3Bsu0R0l0jVD1mwqstsO/EExt8IJcN0u/7e4Na4VBwrJQ2SI5CssFzVx7bYELyfUAyGxz/Sgu81cMTe45eldIGqXrMuFeaixKwZIMZktkgVY+hqJADQQoblKt9nVo547MRbXH28l18LWxQrrGClpamqKL1erdG+P3IVSzboRwbzHBoirDB65FWz6fY8xQBYjVzP3TdW0GlnSDLli0TFQH09fXh5+eH4ODgCr1vy5YtwpCKViBg5ODstWRsPx6Dvh3dld0URlKszAzEj8Cna4KlWuVgqs7AgQOxcOFCTJ06FT4+PsKhsW/fvsJkqfHx8UhISCjc/9atW2jZsqXY6Hl6L/09evRo6U6Hi5Uhdk5sh42j24jt3Q7OyE1Nw+BA58JtZKf6mPa2H+wsDfHV6iCcjEyQapJHdPNzxafD2yLudhpm/3xSJEOTidZe9pg+NgB3UzJF+6jCg0w0cbXCrHGBYuA/e9UpofeWCXcnC9F/ubn5mLsqCNHxqVLZIEUjfTmqHZxtTYSz8GTkLakiGgi/pg6YPsYft5MzMWvlSZETRia83a0xc3wg0u5nYfbPp3D5hlw26OFkgRljA8Uqt6w2OHV0OzjaGGP+mhCcEDYIqQho4SiuE3IUzvpZPhskORFFTt3LyMIsCW2Qoo5njgsUubHmrDolqmnJdIodrI3x5eh2IofJ/DXBwgZlah8hnDUj2+JmYob4LaaKX0pxhAxZj79H7sVQzfeh/3WoKIsrkwOkUk6QrVu3ilXDadOmITw8HC1atECPHj1Ehv9nERsbi48//hgdOnSoSnuZGoAmtDSx7dDSCdac74F5Bt386iMmMQO/nSw/0SSjWkyaNAlxcXGijG1QUJBwcCs4fPgw1qxZU/iYnOB03yi50X4yQo6QJg4mYnM006caeLAz0y/cLIx0RcQFrSYP6u6JzfsvYs2ec3hIJSgkgpLbsTym8rA8pmrQNTK8j7dIUrntr2is3XMeD7LkukZYHqPe8hiywZF9m2JIrybY+lcU1u45J50NqqI8pkAyG/xkaBuR8PP7reHYL6ENjurXDG+99NgGxVhBMhuURR7z0MwJpzXcoGlTHzLy3E6QRYsWYcyYMSJM2svLC8uXL4ehoSFWrVpV5nuo/OLgwYNFeUQ3t5pNhsI8P7uC4nApIQ0v+slppIw8UIncXu3dMHVjqHQDD4apDto1q4dpY/xx7WYa5q46hdjb6VJ1LMtjqgbLY6qOr6c9po7xx/XEDMxbHYRrCWlSrYayPEa95TFE6yb2mDYmAPG3yQZPITYhDTKhavIYap9sEi2Z5TFEWy97TBvtj7hb6ZgrbFCusYIs8hiZeS4nCGm/w8LC0K1bt///AE1N8fjkyZNlvm/mzJmiDOKoUaMq9D20EknlE4tuimR96rLJcjyZD7PxxfoQMbGlTMgMUx6tm9jBwEAH3+2OVLr9ynQtVfcxMcqVfpEjpKGLJb5ZH4JDofHShf6zPKZqsDymalia6uPzt/3QzN0aizaE4lBIvFSrtQTLY9RbHkM2+MUoP3i7WeObQhuUqYUqJI9Jl1OiVVQeM1dCeQxFnpE8hn5PvtkQImxQtrGCDPIYWXmuWW9SUpKI6lDoxBXQ46ioqFLfc+zYMfz8889CY15R5s2bJ6JGSvt+cpCoC3fv3lV2E/DD/ivQ1dWCbxO7arlwZbv4qwN1O6bqOB4qmfv9ttPo4W0GBwvll8yV4VqqLjIyMpTdBOZJecFhT8qCrtlzHlHXkjGsjzdMDHSlk8fQKh5Vj6HrslsbF7GKJlP1mNV7zonqMf06uePFtvWlaZ9CHkPZ/ql6TJ/27ujern6tl4osr3rMH8evCWkCLVZ096svTfU2ageV32zqYYWVu86J5MLDenvD1FBXOnnMz7vPCWmCbDaoqB6z7WC0kCZQXjaKypXJBkkeI5IeCxt0R3c/F6ls8M3unmjmYS2qx1x8YoPGBjqQTR6zYmfkExv0wItt5blPkzzm81F+2PqXvDZI8pjdR68KeUzv9tQ+uWyQomporPDz7/9/H6RrWyp5zMT2WP7LGSGPkW2soCy0a3owP3ToUFF1wNrausLvoyoElHdEAUWCODs7i88wN5ej/nZVoJVemrTZ2NhUuJZxTXAzOROr/onD+Nd8oF0N7VBGnfGaRt2OqbqOx9XBDC0a22HpgXis/E9H1PVrqTrR09NTdhOYIvg0ssXMcWZikjxr5SmM6t8MjV0spJPHHAyKxa5/r+BSXKrI2yDLJEBUj+nbDM3db2P9nxcQHZeKEX2awsRQnva91rURvN2tsOK3s7gUnyLaZ2qkK1X1GE9XCyz/5aw4vyP6esPMSJ77hFcDa8wcGyCccbSaPLJfU3jWt4SGZPKYoHMJ2Ljv4pM+bCrVNULVY5q6WWPlrkhEx6WI9sniTKL29engDs8GlmISdUm0Ty4bpGgQihigxRlZbZDkMSfO3MSWA9FP+lAuG6SJvHAm7T4nbJByr8gykVfIY7waWAkbVFwjZpLcp4mmFFUzNkDYICWdpbwhVD5eFshZ887rLfFv+HXh+I+mPuwjjw0qg+eaNZATQktLC4mJicWep8f29vZP7X/16lWRELVv377Q1tYW27p167B7927xN71e1iTA1NS02CYaq6mpNpsMxzNjc7gIhaPkTQzzvPRp74b9p28g6NLdOn8t1cT9gZEHWimj1do2Tezw/ZZw/H70qnRh1yyPqRosj6l6VM1/h7VBBx9HLNt2GruPXEFuHstjngeuHlN1G5w8vC0Cm9cTNvi7sEG57tMqI49RgeoxMspjTIz0MGWEH/ybOoiold0SjhVYHvP/PNdoW1dXF76+vjh06FCxlVh67O/v/9T+np6eiIyMFFIYxdavXz906dJF/E3RHYxyCIq+gz/DrqNPB05Uy1QOM2M9dGtbH5PXBCNPssEuw9RUQs1JA1vin9DrWLQpFCkZj6TqaJWpHuNqIeQxfwXJVZVAIY+hhHcU+UOVMWSSQyrkMR1bOj2p3HFNqjwcioSaHw32xbGIm1i0KQzJ6XJdI1w9pnrkMR0krR4jIgY6eeD9Qa1w5PRNfLspVDobVMXqMbLdB0keEyBp9RiywZe7NBQ2+G/YdSzaGIoUyWxQIY9xVnL1GGXz3EuOJFMhecvatWtx8eJFTJgwAZmZmaJaDDFs2DAhZyH09fXRtGnTYhvJWUxMTMTf5FRhap/8fCqJG4QX2rrA3ESfTwFTaTr7OiMx/SE2Hyk9qoth1A0KsZ49MVA4/matPImIy3elrh7z4y9npMoIr5DHjOjj/TjPwPYIZDyQq30kj3nndR/sP3UNS7edRrpEVQkU8hgaYP8dHC/6T7bKHQ3qmWPW+EDoaGtizs8ncfrSHbmrx0hWNUEhj5nwagvsO3ENS7eflq5yR5+i1WMktEE3R3PMnhAITU0NkQySbFDm6jE/7JC9esxpZEhcPYakeLJVj/FwthA2SFDUT8QlucYKWk/kMYrqMbLZoJROkIEDB2LhwoWYOnUqfHx8RETHvn37CpOlxsfHIyEhoSbaylQTW49eRcK9h+ji68J9ylR5wtW3owdmbgmXapDGMDWJoZ4OJg/3Q5fWLlj521lsORCF7Fx5VqKKymOodCRNAmIkywjf2sse08cG4G5KpmjfFcnCwlVGHpOTL2XlDqo298EgX/QKdMOqXZHY8lcUsnLyIGX1mKRM4dCUVh6T8bhyh2ztK6wek50nrQ1+NLg1XvJvIJKmbhY2mC+lPObmXbnlManpcstjHmXJKY8x0HsctdLdzxUrd50V90HZxgqdnlSPuVEHq8dUSnw+adIkxMXFiUotQUFB8PPzK3zt8OHDWLNmTZnvpdd27txZudYyVSbjYTambw4TXnxdHS3uUabKUEZsawtDLPztLPcmU6foR6H/Q1oj9EIivloThNspmZAJlsdUDZbHVB2STE4Z0RZnLt3B/LXBSEiW6xpRKXnMZjmlCTLLY4ju7VxFrpCIaLLBIOlskOUx6i2PIV4KaIBPh7VBeNSTsYJkNmhfR+UxnIGvjvHNb5HiR9+nkY2ym8KoCSIssbMHVu6PwtWEdGU3h2FqFdJ1z5nYXmRYp9XQk+duSXUGWB5TNVgeU3Xq2Zhg1vj2sDbXx7zVQTh+9pZUq7WqIo8haQLLYyrvEJ49oT0sTR/b4IlIue7TLI9Rf3mMs52psEEzY13MXR2Ek5LZoNYTecwbL9YdeQw7QeoQ126n46f9F0XSqLpeG5qpXhxtjNG2qT0+Xx/CXcvUOfR0tPDh4NYi0fSmPy+KEoOPsnMhE6ogj5kh5DEPWB6jhvIYyg8y8bWWGPhiY2z9K0rIEx5myXWNqJo8RjZpguzyGLLBSW+0FDl/tuy/KKUNsjxGveUxFIH/3pu+InHqpn00VoiUbqzQsaUzPh/pVyfkMewEqUN8sSEUvl52cLIzUXZTGDXkpQA3nIhKxD9n5fJuM0xtQbpfCru+FJci9NNxt+WKjJJdHkOJumeMC+DqMWpaPYYIbOGIqaPbIfYWOeNOIU6y6EGVksdIWrlDdnkMXR9fjPIXkzuywVjJbJDlMeovj+ni6yyu4yvXUx+PFSSzQTsrozohj2EnSB3h38hbOHI+QUxUGaamfnh6+Lti8tog5EiW+IlhagtHcjRMbA8HS0MsWBeCgyHxUg0eWB5TNVgeU3WszQ3Faq2boxm+2RAqBtgyTeRVRR7D1WMqj60oU9serg6mWLg+BAclm+SxPEb95THC0TC+PZxsjbFgvXxjBa06II9hJ0gdIDcvH5+uDUZ3f1exisAwNbnKl5mdh9UHo7mTmTqLtpYmJg1shddfbCzK1D4uAyvXAIzlMVWDq8dUDSpdOqr/41LJVCL0cSliucqssjxGveUxZINjXm6OYb298fvRq/hesnLYBMtj1Fseo6WliQmv+mDwS00ejxW2yTdW6KjG8hh2gtQB1h66hIxHuejg46TspjB1YPJHOWfmbT+N5IxHym4OwyiVThR2/bYfblH5w5UnERWXItUZYXlM9VePKZAo7FoV5DGtmtgJ+UlK2kMRFn5RsmuE5THqL49p6/24XHdSKtngSelskOUx6i+P8W9WT+QjSkzJxEwJxwp2aiqPYSeImpNCCbS2nRYTU5qgMkxN06SBFerXM8O8bRHc2Uydx9bSCLMnBMLdyVwMwHYfuSrVAIzlMdUrj1m244xUq8nUvt7t3fD+oFb4OzheRCWlSRZxYWasj2ljAtCioQ2Wbj2NXf9eQa5E1wjLY6pug306uOO9Qa1wKDhWShu0eJKPqKm7tXDW7DpyRar7NMtj1F8eo3C4NnG1FGMF2WxQSw3lMTwrVnO+2nEazvYm8HKzUnZTmDpEv04e2HTkCs5L5s1mGGUNHsa90gJDXvLCoZA4kZQ0JV2uSCmWx1STPCYzG7NXncLl63JV7pC9egxNUuj6GP9KcxwOuy5yhSSnPYRMsDxGveUxZIPDe3uLfDD/hCpsUK77NMtj1FseQ86ut/s1w9t9m+GfkHhhg7KNFTqqkTyGnSBqzMXrqdjwzxURBcIwtZ10jPKDTFkXohYhcwxTXSGvU0f7I+1+lpDHnL50R6qOZXlM1eUxk0e0LSaPkSnhpyrIY5p52IjIqZzcPCGPOR0t1zXC8hj1l8f4NLLFrPGBonQpyWNks0GVkcc0spG2gpHs8hhfIRMMxINHOY/HCpLZoJ2ayGPYCaKmkDFOWRsM/+b1YGdppOzmMHWQHu1ccS4uBX+EXld2U5g6TnzyA1xMyBDbTVrZ09ZCYtqjwi21FsNirSjkdXwgmntY4+edkdj8V5SY8Mksj8mUKOSVVmtplWxEX2/sPRbzJOmsvPKYxwk/5Qm7VgV5jJEBlYH1R2CLevh5VyQ27b+IbImuEZbHqL88hooITB0dgHZNHZ7YoFz3aZWQx/RognGvNMefJ65h2fbTUiX8VAV5jKmxnpAJkkNk5a5IbJbMBrUqII8xSLuBlgUxyL8bBxlhJ4iasi/sOiKupYiSpQyjDPT1tNEz0A2frw8WKyqM3Cxbtgyurq7Q19eHn58fgoODn7n/9u3b4enpKfZv1qwZ/vjjD8jqABnwwykMXhkitiVHr0Pbwgwbj18v3Fb/G1erjhBNDQ2M7NcMI/s1RVBkAr5aG4yE5ExIKY+5lYY5q04hRrKQ19ZN7DFjbADupjwQIblXbsjVPq4eU3Ve79oY777ZEmEXEzFvTTBuJd2HTLA8Rr3lMcSb3T2FQzP0QsITG5TrPs3yGPWWx/y/TLAFgs8/tkHZxgodS5HHmCScg++GIXhhdW+sz1+MR/9tjaSpPZB9NRwywU4QNSQrJw+frQ/BS4ENYKivo+zmMHUYWkXR0NLEj39eUHZTmGewdetWfPjhh5g2bRrCw8PRokUL9OjRA3fulB6CeeLECQwaNAijRo3C6dOnMWDAALGdO3dOun6mks0VITu39sNhfT3tMH2svyhjPm91EI6fvSlVSKmQx0xsD3srI5HHRLaQV/MnyQwbu1pgsQgLj5W+eoxsYeGyy2MauVhizoRA6Otoimvk2Bm5rhGWx6i/PIaSvc+e0B7aWhqYt/qUdDbI8hj1l8c087AWEigNDWAujRUks0G7IvKYvzb8hpYbhsDs1pli++RcCkayZI4QbWU3gKl+Vuy7iAINDaE/ZxhloqmpgQGdG2LRb2fxZgcPOFga8gmRkEWLFmHMmDEYOXKkeLx8+XLs3bsXq1atwuTJk5/a/7vvvkPPnj3xySefiMezZs3CgQMHsHTpUvFe5vkm8hTyunnfRRHuev5qklQrUSSPoZDhv4PjRNWOy/GpUk3kFfKY5h63sf6PC4iOS4WZkS60JKmGppDHeLtbYcVvZ3EpPgXN3K0hmzzG09UCy3+h9qWid4AbZEJfTwefDvcTIddb/opC1LUUqa4RhTwm6FwCNu67KPpQT0cLMp3jgS96oqmbtQirj45PQWMXC8gmj/FsYInlv5wR10i3NvUhE7Sg+NnIdvjtn8uPbTA2BRLdBgvlMSfO3MSWA9G4HC9XUnqFPIbufT/vPifOcX17U8gmj/FqYFVogx1aOkEmjAxJJtgOOw5dEjJaYYOAdPIYj//Ng+a9XGiUbF3+4wWp9HWfwXrGPsiARoFMrqQySE9Ph5mZGVJTU2Fubg5VJz8/H4mJibCzsxM3ruok8d5DtPngV4zs30yEedUmNDCmMG91Qt2OSVnHs27veXhYG+OHie1V5lpSFvfu3YOFhQXS0tJgalrzg4Ts7GwYGhpix44dIppDwfDhw0Vbdu3a9dR7XFxcROTI+++/X/gcRZHs3LkTZ84U9/4ryMrKElvR+7qzs7O4r9fkcUYlZGDIqrBy93MyAPS0lHutk4Ph2s00cZ12bOUMQz1tQIbbD40SNIC7KQ9x+lIidLS00KSBpYgQkaJ9T6DcJSfP3hJ/O9mZwLO+Ze2370lflUZ2Th5OnLklzi9Nkil5tEz9R+0LPn8beXkFeJiVgx7+DcTKo7L6qzQSku7j3JVkaGlpoKm7DWwtDKTqw/sPsnEyMgFamhpwtjNFQ2fz6mvfc/ZVWef4WMRN8Vm0Ak6SHpn6j9pHzqS8/AIhk+nezrVy7auGviqL64kZwhFH10YrTztYmupL1Ydp97OFdIJssIGjORo4mJbfvhrsr5JkZefiWMTj+7S5iZ6IiJTNBk9FJiA/v0BEaXZrW794+2qxr8ri2s10XLn+eEGiXbN6wvGv7DYRlo8SMf30WJSH9ZIIaNnWXLoGGl9WZBzNkSBqxqwt4WhU37LWHSAM8yxoleer1UEY3cMTrSRaBWWApKQk5OXlCUdSUehxVFRUqV10+/btUven58ti3rx5mDFjxlPPk+Tm4cOaK4WZnFKxzz55NgHZj5SfGC0vLx8UiPtv2HUxyJbNCUvrJg9yckS2elnbl5tXIJxJ126lQUvS9pEGnRIGUrSchmTtIycINWoftU9Do+YdIZVoY3ZuAcIu3pbWBrOzC8Qk5eqNVCnbJ2wwW14bpPZRt/0psQ1SG8lhI7MNRl1LRnRsspTto/67k8M2WKU+zC8Q0T+y2GBLxFRov6SrF4ACgxprR0ZGRoX2YyeIGhERk4RfT14TyewYRiZopaRLGxf8d3UQ/prZSwy6mLrFlClTRPRIyUgQW1vbGo0ESc2nH8PYcvf78C1f2JjqQdnQKtnny4+jRSMbnL10Fx5O5hjSywtGSszvVDKC7JuNobAw08fFmGS4OZpjaG8vGEuUf2r7oUu4nZyJG3cy4GJviuHUPgNdaaLtaJX2jxPXRP4uRxsT0T6qRiELiSmZIgGfiZGuqGY0rLcXLE30pYpOnLsmCPVsjHD+ajLcnMwxtJdcNrjhzwtIf5AjEgu7OphiWG9vGBvoSBPJeTTiBv49fQOZD3LgaGuC4X28YFJL10hFiL+djsVbwsV9z8r8+W2wNqJep604AXcnM0ReSYL7k/u0TDa46vdI5OTm4+qNNLjWe2KDZbRPGVHCB4PjEBqViHsZWSL/lGw2ePl6KlbsPCui9qzNDUX7LIz1pYoQn7zsKLzcrBB5+a6wwaFKHisYpHkAq78rdz9rdy9o2drVXDsMKuZgYSeImkAewU/XBKNTK2cxaGEY2ejaxkUktvvlxDW83l4uzXldxtraGlpaWkJWVBR6bG9vX+p76Pnn2Z/Q09MTW0lIxlSTUiaNCn62rq6WqGikdDQeR7X279QQ/k3rYdXuSHyzIRRjXm6OBvXMlNKkkoM+0k9TdZZ+HdyxZGs4Fq4PwdiXmwuHiAxQAsP6DqYYPaAZvt0YhgXrH/cfOZRqmooMkHV1tIQU4fO324n+W0Dnd0DtS1jLQl9XW5zjaWMDRBlnsr/hfbzRzMOm2iMGKjuhoHf4N3fES/5uWLr9tIQ2qCkmyOTg+nYT2eDj9tFEpbJU5+RLV1sLZkZ6+O+wtvhus+IaaYaGTvLYIC2WzBgfiP/9EvHcNlgbE1X6+I6+Luja1hU/7jj9+D49gGxQOffp0nI0uLtaYFCPJlgsznEIxg4o3QaVMbGnfFM0X/ngLV98tzlcShukNs4c3x4/intMKEb08Ya3u7U0ThBqRXc/VzH3W/HLGSzcECruM8oaKxTYuuKeYyuY3YqARkEpyWU1taDT2A869jU7B6jomFI9RPQMfjsZi5jEDHTzkyuZFMMUHfj36eCGaZtCkflInnr2dR1dXV34+vri0KFDxXKt0GN/f/9S30PPF92foMSoZe2vChwMjkdOnlwZ4WmwNX1sAAz0tLFoYygOhchVnYVWkOdM4Oox6lo9huzu3YEt8VJAA/z021lsPxiNnNyKVVuqLVwcTEX1GBsLA1HBiFaXZbpGuHpM1W3w/UG+6On/xAYPXZLOBsnpQdVjLEz0xH1aNhvk6jFVt8EPB7dGd7/6+N9vZ/HL3/LZYCMXC8yeEAhTI10RqalMG7zU9VPka2qjQKOEi0FTC9DShumwuZAFdoKoAQ+ycjF1Yyh6tXeTKiM5w5SEkogZG+lhyW75SqnWZUim8tNPP2Ht2rW4ePEiJkyYgMzMzMJqMcOGDRNyFgXvvfce9u3bh2+++UbkDZk+fTpCQ0MxadIkyIaRbsXuieeu3MHXa4NxJ/UBZMLUSA+fj2qH9i0csfPwFZG5nhKAygKtlNEkZUAnd+z+9wp+2HEG9yVqn6J6zIi+3th7LAZLt0cg44Fc7aPqMe+87oP9p65h6bbTSM9Ufm6aou2jxICTR7RFRPQdzF8XgtspmZAJXR1tfDS4Dfq0dxMVjGSzQUX1GApV33M0Bsu2R0jVPkX1mAmvthB5YIQNPpDLBl/0qy+k3uEXE6W0QYoaoKianv6uwgZ/lOw+rage81YPT+w5elVKG6TqMeNeaS7ywJANZkhmg5QoevKwNgi98NgGEyUbKxjo62Dy8LYi6lqZNpjh0BRhg9cjrZ5PsecpAsRq5n7oureCLLATRA34fvc5GBjooHWTmtNXMUx1/ZAM6OyBpXvPI/7ufe5USRg4cCAWLlyIqVOnwsfHBxEREcLJoUh+Gh8fj4SEhML9AwICsGnTJqxYsQItWrQQlWWoMkzTpk0hGy5Whtg5sR02jm4jtnc7OCM3NQ2DA50Lt5Gd6mPG6HZCsz9n1SmcOv//xyoDFHo7sLsnxr3SQuiUqY2U9FMmuvm5iklK3O00zP75JGJu3oNMkHxnxtgA3E15INp35YZc7WviaoVZ4wLFwH/2qlPiPMsE5S6ZMS4ANuYGQtZ46lyCVOUZiZ4BDfDJkDaITZDTBqkSy/Qx/iJfzayVJ3FVMhukyLOZ4wORdj8Ls38+hcs35LJByhsxa3wArEz1pbVBSgL/wVuthe3RdRxzU677dEALR3w5qh1uJd3HrJ/ls0GSO80cFyDyhMyS0QbtTDFzfADMjXUxl8YKktkgjbFf7twQ/xnYClevP7ZBZYwVMsgRMmQ9/h65F0M134f+16GiLK5MDhCCnSAqzvWk+1iy5xwGdG4ojJ9hZIcSFfo0tsPUDaHKbgpTBIriiIuLE2Vsg4KC4OfnV/ja4cOHsWbNmmL99frrryM6Olrsf+7cOfTq1Uva/iRHSBMHE7E5mukDuXmwM9Mv3CyMdMVq8nuDfNGvozs2/nEBa/eeF4krZaKp5PIYmqSwPEZ95TEU9UOOuIHdGmPTvotYu+ecqDAiEyyPqRqUoPeLt9vB19MW320Kx/5T8tnghNd88HqhDZ6XzgZZHlP16Edy1Pg0spHWBie90QqvvNAQG/c9HivIZoOyyGMemjnhtIYbNG3kTNXAThAVZ/qmMDRvZCuSwDGMqtA7sAEOnrmJYxfKLqnKMMqga5v6+OxtP1y8lixWQ68nVqzUWm3B8piqwfKY6llNnjq6nVhFnrMqCHG30yETLI9Rb3kMQfJAmig/joyTzwZVTR7zo2QSMtnlMUSnls748u12uBSXImwwXrKxgizyGJlhJ4gKczIqEfvCrwsdLMOoEqbGenixXX1MWRuMPMmSUTKMg5WxWEWpZ22E+euC8U9YvFQRFyyPqTosj6kaVDKSopKoAgpVnTgUGi/Vai3B8hj1lsdQwk+STjSoZyps8G8JbVBl5DF3WR5TGWwtjTBrfCCc7Yzx9bpg6WxQFnmMrLATREWhiePkNcEiYZmZ8dNlJxlGdjq2dEby/SxsPHxF2U1hmKfQ1nocdj2ouyd+++fJKopkVY1YHlM1zE30RZ6Lxq4WWLwpDH8FxUrl7JJdHkMlOEf0aYq3+zbF7/9eFdfI/YdyrdayPEa95TFkg2/3ayZKl9Jq93IJbVAV5DGU54LKqlI557+C5Gqf7PIYssGxL7cQiY9ltUFZ5DGywU4QFWXzkatITHuIzr7Oym4Kw1QKHW1N9O3ojplbw5EmUTUEhilKYAtHTBvjL1bKZv50UrqElSyPqRosj6meql8zxvkj+d5DzFx5Cpfi5bpGWB6j/vIYEdk1LgB3Uh4IG7wsmQ0q5DE9VEQew9Vjnh8/bwcRHfc48fEpXJJsrMDymKdhJ4gKQj8+MzaHiQkkJehhGFWFVrLtrYzw9a8Rym4Kw5SJlZmBCLum1ZTFm8Ox51gM8vPlWUVheUzVYXlM1TAz1herta0a22LJlnD8fvQq8iS6RgiWx6i3PMbcWF84rFs0tMaSrafx+9EY6Wywr5DH+Movj+HqMZXCgqILxwbA280K3z0ZK8hkgyyPKQ47QVSQBb+egY2lEZo3tFF2Uximyjfk/p09sPrAJVxmnSIjMbRSNqp/M4zs642DQbH4dnMYUjOyIBMsj6kaLI+p+v38ze6emPiaj9DGf7spFKkZjyATLI9Rb3kM2eDgnl4Y/2pz/B0SJ6UNujmaSy+PmT0+kOUxVbDBYb29MfblZuLcksRINhtkecxj2AmiYlxNSMfPf0WLiSOXxGXUAQdrY/g1c8Bn64KV3RSGqXDYdfr9LMxaeRJnr9yVWh7zv1/lCrum6MX3B/liQCd37H4SFi5bVYK3+zbDiL7e2HssBku3RyDjgVzte61rI7zzug/2n3oiTZBMTujlZiX05zk5eeIaOXP5rtTyGNlskByuYwY0FzkG9hyNwbId8tlgMXnMdvnkMd5u1pg1IRCPsuS0wZLyGMojIbM85ocdEVJXj1m2Xb7qMS0a2mLW+AA8eJQj5DGyjRUMSlSPWS7ZWKE2YCeIivH5+hC0bWoPRxtjZTeFYaqNnv4NEHz5Lg5G3OBeZaSHQv9J+9uysS3+9+tZbDsYjZzcfCnlMZSfYY6EGeG7+bni0+FtEZuQhtk/nxTh4TLB8piqYaSviykj24kE2D/9dhZbD0QjW6JrpKg8hq4NGW3Qr6kDpo/xx+2kTNG+qzcllcdkyCmPMTbQxRej2om8TisktUGFPOaq5PKYm5JXj0lNz8IsCW3QxFAPU0f7w8/bXowVth6UywY1ilSPuRJf96rHsBNEhfj7zE2cuJgoJowMo04YGeigR7sGmLIuBNk5ecpuDsNUaPBAK7W0EnXy7C1RSjcx9YFUPcfymKrB8piqM6Czh4j8CT6fgPlrg5CYkgmZUCV5DMlPZKtgJLs8hnj1hUZ4f1AraW2Q5THqXT2GoEWJSW/4ICjyFuavDZbOBhvV0eox7ARREWiVcfLaYHQPcBVl8xhG3Qj0qYes3Hz8fCBK2U1hmArTnFaixgeKRKlzfj6FoHMJUvUey2OqBstjqg5N4OdMbC8kAHNWBeHkuVuQCVWRxwzp1aRQHiNT+1RBHtPQmSZ57aGrrSWlDbI8Rv3lMU1cSSbYHlqaEDZ4SrKxgkEdlMewE0RFWHUgCg9y8oTOm2HUEaq1Trlu5u84g7tpD5XdHIZ5rtVQWomi+/P6Py5gze/nkJWdK00Psjym6rA8puqTvE+GtkGvgAbY9OdFrPr9HB5JdI2ogjymrff/y2Moz4Vs0gTZ5TEGetpCgtfdrz42/nkRqyW0QZbHqLc8xlBfB5+NbIcXWjtjw58XpLNBjTomj2EniAqQnPEIX+2IQP9OHtAmFyLDqCmN61vCzckcc7edVnZTGOa5Bw9vvNgY77zhIxKgzV4VhPjEDKl6keUxVYPlMdXkaBjaBlHXksVEOf52OmRCleQxVHWC5THPT58O7vh4SGtciHlsg3GS2SDLY9RfHjOgc0MhEzx/NUk4GmSzwUZ1RB7DM2oVYN62CNSvZ4YmDayU3RSGqXH6dnLH1mMxiIxN4d5mVA5FyKuBnhYWrAsWpUJlGjywPKZqsDym6rjYmwp5jI25ARauD8WhELmuEVWsHiNT+1RBHuPqYCZs0NJEHwvWhUhngyyPUX95jIfTY5mgmZEuFqwPwSHJxgoGdUAew04QyTkfl4KN/15Bv04eym4Kw9QKNuaGaO/jhCnrgqX6QWCY5wl5nTLCDy+0ccFv/1zGDzvO4L5EA7Bi8pg4rh5TGVgeU/VSye8N8sXLXTyw89/LWCZKEctzjaha9RiWxzw/ujpa+HBIa/Tr6I6dhy8/KUUslw2yPEa95TF6QibYFr0CXLFTjBXkskENNZfHsBNEYmgCSNUyAn0cYWthqOzmMEyt0b1dfVy8cQ+/B8dxrzMqiWLw8N6brXDt5j0xAKNytdLJY8YFCK38oo20Ii9XyKuTrQnmTGgPeysjIU04IFlIrqrIY9o0scN3W8Kx76R8YeFdWrvgsxHtcONOhpjIR8fJFQHI8hj1rx7TvZ0rJo/ww/WEdHGfls0GWR6j/vKYXoHu+HhoG8QmpAuJlmw22EhN5THsBJGYvSHxOBeXgh7tXJXdFIap9VDQlwLd8MX6UDzMkidpFMM8Lx7OFpg1IRBWZvpYsiUcvx+9irz8fGk6kuUx1SuPoagf2VbyXu/WGO+87oP9p65h6bbTSM+Up32Eg7WRGGC7OphiydbT2C3ZNcLyGPWXxzjaGGP2xPZwsjEWNijbfZrlMeovj6lPMsEJgbC3MpTSBg3UUB7DThBJoWzBX2wIQc9AN7FKxzB1jbbe9tDW1cKyP84ruykMUyUM9HREMsie/q7461SsiBpISX8kTa+yPKb65DF3UjLFSt4VySp3UK6aWeMCxcCfQpovX5crKklbSwsTX2+JQd09cTAoTkT+yHSNECyPUe/qMSTRevfNVnj9hYY4IKkNsjxGveUx5HD94K3WGNDRHQeCYkXyY5lsUEPN5DHsBJGUH/+8AA0tTbRr6qDspjCM0iZmdLNdvOscbqVk8llgVBoaPFBVgg8H++J28uOJ8pnLdyETLI+pujxm+liWx1SF9j6OQj6Rmv4Is34+iYhLdyATLI9Rf3lMZ5JojfRDStpDkQtGNhtkeYz6y2NebOeK/w5ri7upctpgIzWRx7ATREISUh5g0W+R6N+5ITQ1NZTdHIZRGg0czeDtZoUZm8L5LDCVJj75AS4mZIjtZtojWnZGYtqjwi21FuUBDeqZY9aE9nCyNcZPO89i64Eo5OTmQRZYHqP+1WNkl8fYWhoKCZlXAyus3BmJLX/JdY2wPEb95TGUh4ju0w2dLaS0QZbHqL88hnJikaPBzdFM2KBsYwWDCshjDNJuoGVBDPLvypnfj50gEjJzSxiauFmJ8kkMU9eh1fM9IXEIkWzVnFEdB8iAH05h8MoQsS05eh3aFmbYePx64bb637hadYTQAPaDt3zRt70bjp+5ia/XhYjoEFnlMXNXB0kX8trNzxWfDm+L2AQ5K3dw9ZiqofWkDOywXl44GXkLX60NRoJE1wjB8hj1lsdoa2liwms+GNTDEyfP3sL8tSHS2SDLY9RbHkMSrUlvtMJrXRvi+JlbmL9OLhvUKEMeY5JwDr4bhuCF1b2xPn8xHv23NZKm9kD2VbkWNNkJIhlhV+5i16k4MfFjGAawMNVHlzYu+HRNEPLzVS/cTnZSUlIwePBgmJqawtzcHKNGjcL9+/ef+Z4VK1agc+fO4j30I3jvnlwT0KJkZlds5SQ7t3YTkFG/9fBvgI+GtEb6/SzMWxOEE2dvSRVSqpDH6OtqcfWYSsDVY6pO26YOmDrKH9k5eZi3OgjHz96U6hpheYz6y2MCWzjii1Ht8DArR0obZHmM+stjOvu6YMqItsh8kI2vJLTBRkXkMfs2/IqWG4bA7NaZYvvkXApGsmSOkEo5QZYtWwZXV1fo6+vDz88PwcHBZe77008/oUOHDrCwsBBbt27dnrl/XYYmeJ+uCRYTPktTfWU3h2Gk4YXWLriRnIltx2KU3RS1gxwg58+fx4EDB7Bnzx4cOXIEY8eOfeZ7Hjx4gJ49e+Kzzz6rtXaqK/XtzTBjfCDcHc2x5a+L2PjnRcgztCldHiPTAJFWyt4f5IsBndyx+98r+PGXM8ipZYfW88pjHlXQMacsecx9yTL+W5kbiFwrNFHevD8Kq38/J9U1Upo8JidPHhvUfBJVM7SXF/YcjcGyHRF4lJMntTwmM0suG7SxMMSMcYFo7mGDLQoblMgIS5PH5Epmg+NfaYG3enhiz9Gr+GFHBLIkknaUJo95IJkNOlgbi8gpkgmSDa7Zc16q+6DBE3nMV0Z7oZmfC42CEvaXnwfk5SJ9nTzjRo2C53Qlbd26FcOGDcPy5cuFA2Tx4sXYvn07oqOjYWtrW+oAOzAwEAEBAcJpMn/+fPz2229i0O3o6Fih70xPT4eZmRlSU1PFSqWqk5+fj8TERNjZ2Ykbg4Ltx2Lw2foQTBnpB10dLagaNDCmMGp1Qt2OSZWPJzwqEX8ei0HIopdhbKDzzGtJlaGoCnIYp6WliUiLmuTixYvw8vJCSEgIWrduLZ7bt28fevXqhRs3bqBevXrPfP/hw4fRpUuXCt2bs7KyxFb0vu7s7CzeW5PHGZWQgSGrwsrdr2U9Q5joKe++Sz/Ex07fxJXrqaCAp9e7NRKrpDJcrjRKoHZExabgVGQCtLU14d+8HtzqmUnRPgW3kx9g/8lr4u/Grpbw83ao9fYp+qo0MjJzsPvIFXEfNjLQEWHEMvUfVaXb/e9V5OYViFXvkX2b1nhesmf1V2mcvXwX4VF3oKWlgU6tnOFsZyJVH968c18kCaR+83KzRqvGttXWvuftq9K4dz8bvx+5UhipRI4bmfrvUVYudv77+BrJys7HiD7elWpfdfRVWYRFJSLycpL4fEpg6WBlJFUfxiWk45+w69DW0kAzD1s097Aut3012V8lSUnPwt5jV8V32lkaons7V6n678GjXHGfzssvEIvTQ17yKta+2uyrsgg6l4CL11LEddK3ozuszQyU3ibCLDMB4w8NQXlYL4mAlq0ragoaX1ZkHP3cThByfLRp0wZLly4tnITQQPY///kPJk+eXO778/LyRMPo/eRMeZ7BcnJysto4Qe7evQsbG5vCiVvmoxz4fbQLPQIbwLeJPVQRVZ5g15VjUuXjoVsVrVL2bumELwa2LPNaUgcniJWVVa04QVatWoWPPvpIOCIU5ObmCoc1ObdffvnlanOCTJ8+HTNmzHjqeXKgm5iYoKa4kvQQ7+2MLXe/hGu3kf1I+Ss/eXn5wgmipakhVqdku1zpOqRIC9LLy9q+rOw8sZAga/tycvKgpaUFumVRG+U7v3nQ0NB8bIO0AdK1MTc3H1oS22B2dh50JLZBkhdpq4INaj25D0JCG8wrkPs+nZMvHNZS26C2FsjPKqsNaj6xQepAuVr4pI15+dDWlOcctyyIwfq8b8vf8b1NgJtvjbUjIyMDjRs3Lnccrf08H5qdnY2wsDBMmTKl8DmaeJDE5eTJkxX6DAqjzsnJgaWlZZn7zJs3r9TBclJSUjHniKpDkzcFS/64DCMjHfg0tpUq1Ph5UeW215VjUuXj6dfJA8u2huOlZuZwsjIs9VpSdejmXVvcvn37qQg+bW1tcX+m16oT+t348MMPn3Ju0/fXpLMnNZ/6s3wnyLtvtIKNqR6UTVZ2Lj5ffhyOtsa4dTcT7k7mGNyzCYz0H0c/yeA8pZJ4NDCkVW+S8Qzp5aXU9pVk+6FLImHqnZQHohrP0N5eMK6l9lXE0Rx8PgG7j8aIQbaLvSmGU/sMdCELiSmZmLcmWOSCsbU0Eqvx5sZ6Ujnm564JgpGBNm4k3oe7kwWGvKTca6QkG/68gNspD5CYnIkGjuZCilJVG6zORYyjETdwKCRerHrXtzfFsN7ehRGWMhB/Ox3fbg4XEzw7KyMhJzM30pNqwWfaihOwNNPHjcQMKW1w1e+RSMvIxq2k+yJvyJBn2KAyFsgoYurkuQRkZGY/tsE+3rV2n64Il6+n4n+/nRVJmqla0PAnNijTYuLkZUfhYG0kbNDDyQKDlWyDBmluwOrynSDW7l7QsrWruXYYGFRov+dygpATgiI5KPS8KPQ4KiqqQp/x6aefihBrcpw872DZ2tpaLSNB4u/ex7oj8XjnjZbiYlNVZLoxVBfqdkyqfjz0Q+nrZY/v9sdh3Qed1TISRE+v6pMNisoj6WF5UpjaPq7Sjo3OW02eO40Kfraurhb09Z7rJ7FmoEUnAG/3a4bIK0lC3/3tpjCM6t8MDeqZSXHfoFWnF9rUh6GeNlbtisQ3G0Ix5uXmSmtfSSgMvHF9SyHnWLI1HAvXh2Dsy83FRECGeyxFqZgZ62LSGy3x7cYwLFj/uP9kqQhH+QXoHM8c3x5Lt4VjwfoQ0ZeUKFeW3yR6R88AN+TnFWDd3vPCMUd5L+SxQU0087DG0Je8RI6L6rDB6vz91tXWgpWZAT4Z2lTcXxY8aR85XWWxQXK0zprYHks2h2PBuhCM7NcUTd2spRnr0Mf379wQ6fcfiVxOizaGYrRENkjziVZN7PCGc2P8uCPi8X16ANmgmRRjQ8rnRM6F995shcWbn9jgALlskO7VM8YF4LsiNkg5OWQZR1MrKJ/OzTvp2HbgEhZtDMPoAcobKxTYuuKeYyuY3Yp4OicIoakFncZ+0LF3q9F2VHRMWauzhq+++gpbtmwROUEo3LosaKBMK4NFt6KDZXXYih7P9E3h8GlsJ1aEGIZ5Nr0C3HD4XAKOX0x86lpSl62qkMSFnBzP2tzc3GBvb487d+4Uey/JYahiDL1Wl6BVUZmSGdII+4U2LvhkaGsR+k8TFWqjTBnhvZ9UjzHQ05ayeoyjrQnmTGgvBto0ODwQLFf7ZK8eY6CvjU+HtUWnVk4i0eKOQ5fkukYAET07dbS/mNTLaINcPaZq0Ko2VcXo4OOI5TvOYMff8tlgGy8HYYOUB0ZGG1RUjzE30RPtowgMmdpHSWdnjw9EAwcz8Tv3V5Bc7aMovc9H+iGgWT38uOMMfv37snQ2GNDCCZ+97Seyiyl7rHCp66fI19RGgUaJsaymFqClDdNhcyELzzXapkgM0rFSIsKi0OPyBswLFy4UTpC//voLzZs3r1xr1ZBjF27j4Jmb6B3YQNlNYRiVwMRIFz3auWLy2mCpsp/LBEXGeHp6PnPT1dWFv7+/yEFCMkcFf//9t4iwofxP6oCRbsWSnUZEJYqVnrv3HkAmnO1MhaOhcX0LERWy4rezyJSoeoeiekzgk+oxNFmWqX0lq8f8sOOMVNVPCqvH9Pn/6jEZD+RqX7+OHqKUMyXj+3pdMO6kPpCujPqXo9vBr6nDkwpGcl0jJavHyGaDiuoxQxTVY7ZHSNU+ssEBnRvig0G+OBV567ENSnafpqiaaWOogpGdlDZIUQ2fFqkeQxWMZGqfqB7zagsMelI9RkYbfLVrI7z3ZkucjLyFBeuCpRsr2FkaiSpalAh357+XhZRHGec4w6EpwgavR1o9n2LPUwSI1cz90HVvBZV0gtCg2dfXF4cOHSp8jgbL9JgG02Xx9ddfY9asWaLqgKICAfM4AR5N5Lr51YdpDeltGUYd6dDSCfceZGPDP4+z3DOVo0mTJqLU7ZgxY0Tp8uPHj2PSpEl48803CyvD3Lx5UzhNipY2p3whERERuHLlcf9HRkaKxxRBIhsuVobYObEdNo5uI7Z3OzgjNzUNgwOdC7eRnepj+uh2YhVl9s+nEHyhevOhVMcAduJrPhjQyQPnY5Ixb00Qrt1KgyxQaPCb3T0x7pUWuByfijmrTknVPqKbnys+Hd4WcbfTMPvnk4i5eQ8y0drLHjPGBuBuygPRvis35GofhVfPmRgoJFB0foPOJ0AmKPSfqjiM6tcM0XEpmLNaPhvsGdAAnwxpI/LVyGiD7Zo6YPoYf9xOzsSslSdxVTIbdHc2x5yJ7aGno4U5P8tngySBGtG3KYb19sLF2GTMldAG+3Zwxwdv+Qrbm73qFGJuytU+cqZ/OaqdyGMy62f5bLCRiyVmTQgQ51qMFSSzQXL6kyRr0IuNcTGGbFA5Y4UMcoQMWY+/R+7FUM33of91KKxn7JPKAUI8d9w15er46aefsHbtWhFSPWHCBGRmZmLkyJHidar4UjRxKunSv/zyS1GFwNXVVQyeabt//z7qOhsOX0FyRpYo88YwTMWhH6C+HT0wZ/tppEm0aqqKbNy4UTg5unbtKkrjtm/fHitWrCh8nRJZUwUXSmqtgEqkt2zZUjhPiI4dO4rHu3fvhoyQI6SJg4nYHM30gdw82JnpF24WRrow1NfBZyPboVNLJ6zbcx7r/7iArJw8yIKGCshjmkouj3FieUyVIxo+eKs1ege6YcMfF7B273mprhGC5TFVw9LMADPHBcDD2fyJNEEuiZaejjY+HtIGL/k3EPdoGW2Q5THqLY/R19XBf4e1xYtt62Pd3gsiJ5FsNiiLPOahmRNOa7hB06Y+ZOS5nSADBw4U0papU6fCx8dHrP5RhIciWWp8fDwSEv7fM/bjjz+KqjKvvfYaHBwcCjf6jLpM+sMczNkWgX6d3KGjrR4JHRmmNvF2s0I9WxMs28/RIFWBKsFs2rRJVKWhcmLksDY2Ni58nZzX9OPZuXPnYuVu6bmS24gRI6DqvPJCI7w/qBUiLt3B3FWncONO7VXrqQgsj6kaLI+pOt3buYo8DRdikkVUyPVEua4RlseotzxGEVXz6dA2OH816bENSnafVjV5DMkYZTrHsstjiD4d3PHxkNYigfkcCccKsshjZKZSs28Kl46LixPlaoOCgoppxw8fPow1a9YUPo6NfexFLrnRILou8+P+q7CzNqqRbOsMUxeglfH+nTyw4+RNREsWVsyoNh7OFiLs2shAB1+tDcbh8OuSrUSxPKaqsDymatSzMRHyGFsLA8xfF4x/wuS6Rlgeo/7yGGd7U8x5pz2szPQxf20w/pHsPq1K8phrN9PERJ7lMc+HK8kE3wmEhYmelGMFWeQxssIhCErg8q00bD1xAwM6e4iJHMMwlYOqPrRrXg+frQuR6oeHUX3I0UAhrxR2/cuhS49XUR7Js4rC8piqw/KYqqGtpYVJb7TCG10b4bd/LmP5r2ekukYIlseotzxGR0sL773pi1e7NMRvf1+S0gZVQR4za8LjibzU1WPqySmP0dV+LBPs39FdjBWWU9SPZDYoizxGNtgJogQ+Xx+Ktk0d4GD9/yHnDMNUDgrnPB2TjAOnb3IXMtVO7/Zu+Hhoa7EKSquhV26kStXLqiKPac/VY9SyegzRsZWzSGZIspiZK0/i8vVUKeUxFNkgozRBVarHDJVYHtOltQs+G9EO8QnpwgZlSywsuzxG74nTX+rqMa+0wFsSy2Ne9HPF5OFtEXsrTcqxAstjnoadILXMwYgbCLl8V+gZGYapOpTQskdAA0xZF4xsyZJTMepBfXszzJnQHrYWhli8KRx/nLiG/Hx5VlFUQR4zkKvHqHX1GMVqrbujGRZvDsfe4zFSXSMkjxnM1WOqhJ/k8hh7ayPMntgervam+E5CG1QleYys1WMCJK8e40jJtycGiijDbzfJZ4MsjykOO0FqEZqgTVkbjB7+DYTWnGGY6iGwuSPI/fHT/ovcpUyNoKujhQ8HtxZ5aP48HoPvtoQhNSNLmt5meUzVYXlM1Vdrx77cAsN6NcFfp2Lx7Wa5rhGC5THqLY8hZ9eE13wwqLsn/joZi8US2qAqyGNmT2jP8pgqyQRbYmC3RthPNijZWIFgecxj2AlSi/x8IApZeQUI9KlXm1/LMGoPDSao0tLXv57FnXsPld0cRo150a8+Ph3eFreTH6/IR169C5nlMT9JLo/5H2n4Ja4eQ2HhMoVdq4I8xq9pPRExcC/jkVitPXtFrmtE1eQxstngU/KYHfJJEwJa1BMRA8lpD8V9+qxk9+mS8hjZZIyKnFhFq8fILI/5QUIbJJng5yP9kJT6UMqxgl2J6jGy2WBtwE6QWuJu2kPM33EG/Tt7CE81wzDVSyMXSzR0scCcbae5a5kajxiglTJXB1P875ez2PH3JeTk5kspjzknuTzmUlyqqEogU/uKVo+JTUgTA1gKD5cJ2eUxFqYUMRAoBtjkZNh+MFqqa0SV5DHULjrH12SVxyTJKY+xtjDErAnt0cTVUtyntx+S6z5dVB5z4Zrc8pirkstjbt6VUx5jZ2Ukks42crHAcgltUKdI9ZgLdbB6DM/Ga4m5206jgZM5Gte3rK2vZJg6R9+O7th+PAZnryUruymMmqOjrYn/DGyF17o2wpHwG1iwPhiJqQ8gCyyPqTosj6m6DY7o0xSj+zXF8TM3RSldma4RVZPHUI4B2Sp3yC6PIYcrTfJG9PHCsYgb+FpCG2R5jHpXjyGHKzn8h/RsgmOn5bTBgDpaPYadILVAZGwKth6LQb+O7rXxdQxTZ6EQ046tnPDpmqA6cQNnlE9nX2dMGdkWGZnZmLfqFILOJ0AmWB5TNVgeU3VaetqJqJDc3HzM/fkUgs7JdY2oijymV2ADlsdUwdEwfXQAsrJzMVfC+zTLY9RfHuPf/LFE6+EjOW3Qrg7KY9gJUsPQRGzy2mC093ES3kqGYWqWF9vWx6WEdOw8FctdzdQKDlbGmDm+PTxdrbDhjwtYt/e8GGzLgkrJY+JZHqOO8hhTYz1MG+MPv6b2WP/HBazZc06qa0QV5TGySbRkl8dYmOlj+rhAkYdj/V75bJDlMeovjyGJ1ozxAWjR0EbcB9fukWusoKOQx3T3fCLRkmusUN2wE6SG+T04DlE376F7u/o1/VUMwzypd9+7vRumbgzFwyx5flwY9ZfHjH+1BQa+6InQi4li8BCfmAFZUBl5zNgAGOhpSylNYHlM1W3wrZ5e4jo5c+kuZq8KwvXb6ZAJVZLHLNoYxvKYSjhch/X2xuj+TRFx6S7mSHafJlgeo/7ymLf7NcPw3t4Ij06U0gYDmjvis5HqL49hJ0gNQhOwL9aH4qVAN7ESxzBM7a2K6unp4Ps957jLmVqlvY8jPn/bD7l5+Vi4PgT/hF6XavDA8piqwfKY6nF2zRofCF0dTSzcEIq/Q+UaYKuKPIarx1Qen8Z2mDEmAFqawIJ1wfhHMhtkeYz6y2PaeNlj2mh/aEBOG7SrA/IYdoLUIMv+OA9tXS209bavya9hGKaU1Z4BnT2w5PfzuJGUyf3DKGHw8Lgyxq+HL4lJ1P0H2dKcBZbHVB2uHlM1jA118cXb7dCxpRN+++fy4zKwEl0jLI9Rf3mMmYkevhwdgIDm9fCrhDbI8hj1l8dQYuGpY/zR1ttB2OByyWxQR83lMewEqSFuJmdi8a5zYiJGEzKGYWoX13pmaOphjembQrnrGaXIY2jwMLhHE1y8lixCXinfhSywPKbqsDym6jb4atdGmPR6S1y5nipKcMp0jRAsj1H/6jGDejTBuFea43K8nDbI8hj1l8cM7eWFt/s1fZyPSEIbDFBTeQw7QWqIGZvD4O1mBTdH85r6CoZhyoHChf8Mv45T0YncV4xSaNesHj4f5QdtTQ18vzUce47FIC8/X5qzwfKYapLHdPbA7n+vPF7JkyhkmBwNb/dthhF9vLH3WAyWbo9AxgN52kc0drUU8hgzIz0s2ULXyFWprhGWx1RdmjBmQHMx0dtzNAbLJJQmNHW3wYxxATA20MGSrfLZoKrIY3r6u4oKRnQflKl9qiCPadnYTiSPpr6Ucaxgp4byGHaC1AAhl+9ib0g8+nTgkrgMo0zMTfTRtU19TF4TjPx81fdaM6qJrYURpo4JQCtPO/x1KhZLtpxGSvojyALLY6pOt7b18enwtohLSJeycofs1WOMDHQxeURbdPNzwf6TsVi8OVyqa4TlMeovjzE10sNnb7dDp1bOwga/k8wGVUEeQ/OeD95qjas374mompibcrVPdnmMhakBvhjdTki0/jp1TTob1FEzeQw7QaoZmmh9uiYIXdq4iNUDhmGUS5fWzki49xBbj17lU8EoVR4zsm9TDHnJC7EJaWIAe+byXWnOCMtjqkceM3tCIOytjETljgPBcoVdk1OYVrsbu1pgsYTSBLLBAZ0a4r03W+HW3QwRFi7TNUKwPEb95TGvd22Eia+1wI07ctqg/PIYM8ye0B4WJnqifQcluw+qgjyGJFqj+zdH/O0MzJXQBgPURB7DTpBqZtuxGNxIzsQLrV2q+6MZhqmk57pvR3dM3xyGjIfyJJxiao/45Ae4mJAhtptpj2hJDYlpjwq31MzaswtKlP3FqHYw0tfBz7sise1gNHJy8yCrPEa2kFdarf18VDu0b+H4pHKHXGHX2iXkMSLZokTtUwV5jIezBWaNbw87S0Os3HkW2w5ESXWNsDxG/eUxTRpYY8a4QNiYGTyxQbnu0yyPUX95TPOGNpg+1l84r3/edVa6sYJdBeQxBmk30LIgBvl34yAj7ASpRugCoiSMFA6mq6NVnR/NMEwVaNHQRqxAffNbJPdjHXSADPjhFAavDBHbkqPXoW1hho3Hrxduq/+Nq1VHiI25Ib4Y5S9K5B0/cxPfbAjF7eRMKeUx52OS8dUauUJeabV2YHdPjHulhUggR6u1MrWvuDwmjeUxlcBQXwefDG2DHgENcOzMTSxYFyLVNcLyGPWXx5gY6uK/I9rihTb1cezMDSxYL5cNsjxG/eUx5ACZMrItOvg44VjETSxcL9dYQacMeYxJwjn4bhiCF1b3xvr8xXj039ZImtoD2VfDIRPsBKlGFu08CzNTfbRsbFudH8swTDWsfvbv7IGf9l9EzO107s8ipKSkYPDgwTA1NYW5uTlGjRqF+/fvP3P///znP2jcuDEMDAzg4uKCd999F2lpck1CFWRmV2zlJDs3v9blMbQSOrSXNxKSMjF/bTBOnL0lTUgpy2OqSx7TnuUxVbDBPoFuIrKGdPHz1gRJdY0QLI9Rf3nMy5098M7rPki+91A4hGWzQZbHqL885vVujTH25ea4k/oAX0k2Vigpj/lr429ouWEIzG6dQVFyLgUjWTJHiLayG6AuxN3JwP/2XcSkga3EDzfDMHJBExJKDvjF+hBs+qSrspsjDeQASUhIwIEDB5CTk4ORI0di7Nix2LRpU6n737p1S2wLFy6El5cX4uLiMH78ePHcjh07ar39qk7rJnao72CCH3dEiJDrqGvJkGdo81geM21cAFbvPifkMVevpyJfosGXQh6z/UC0kMdQmUuKItDS0pSqegzp4qn/qH1eDawgmzymufttrP/zAqLjUtE70A0yQVX2Zo4PFBUntvwVhUtxKVJdIwp5zJb9UU9s8B60tOQZB+rqaOOjwW2w78Q1YYMUPeXuZC6dPCboXAI27rso2te1jVyS8sb1rTB9XCCW7ziDrQoblMgIFfKYDX9cEDZ45fo95OblS1c9hqQnivugk50JZJPHnDhzE1sORONyfAra+zhBJpq6W4vqMcIGD0ThUrxc90G7J/IY1x++hebDXGiUbF3+4wWp9HWfwXrGPsiARoFMrqQySE9Ph5mZGVJTU8VKpYwM/eYf3MvJxcAXPSu0Pw0iycOsTvAxyU9dP0cZD7Ixb3UQ1n/QGZ2a1YOM3Lt3DxYWFiKygqIzapKLFy8KR0ZISAhat24tntu3bx969eqFGzduoF69ivXR9u3bMWTIEGRmZkJbu3TfelZWltiK3tednZ3Ffb0mjzMqIQNDVoWVu193L2tYGulAWdCA9de/LyPm1j3k5BbgnTd8YGGiDw1JrjGaLB8Jvy5WoMjB0CvQTZSBl6F9Cigcl/JwQEMDLT1t0d3Ptdbb96z7UULyfWz44yIKUAAzYz2MfbmFVP2XnpmNVbsjkZdfgAePcvH52341/nvxPPdvGqweCIpF2MVEkRRyQOeGaORiIVUfRl65K0pbamlqoI23Azr7Oldb+6rj9/v6nQxs3hcl/raxNMCIPk2l6r/UjEdYs+e8KA2anZOPKSP8KtW+mhrr0JRp7/EYnLuSJOzxzR5N4OpgKlUfhkUliipkJJchuQdVGtGQaGxIEkFyNBDOdiYiCahM/UdRZ2v2nBOFLqioIMnyNCQaR1O7fj96BRdjU8W44e1+zeBgbSRFHxpn3MLL218udz/rJRHQsnWtsXbQ+LIi42h2glQDR84l4K2Ff+Pzt9vBxEi3Qu9R9kVUE/AxyQ+fI+Bw+HWci76DY/P7iUFCXXaCrFq1Ch999JFwRCjIzc2Fvr6+cGy8/HL5P2bEypUrMWXKFNy9W3YG8+nTp2PGjBlPPR8dHQ0Tk5pbEbqS9BDv7Ywtd7/U63eRm638xGj5+fnIzKIVEw2YGMgXrEmTAGofLZ/I2r6Mh7nCEWIqafseZOUhN78AZobKc7o9q32PsvOQnVcAU0MdKQbWqmiD9x/lyn0NP8pFXgGktcGH2XnIyZPzGlEVG6RzXCC5DZKTge4zUtpgVh5yJL1P//995nF0hSznuHneVazM+qb8Hd/bBLj51lg7MjIyhGS7vHG0HL2mwpAXbvLaYLzo71phBwjDMMqDqkqcOnsLaw5GY3SPJnX6VNy+fRu2tsVzGFEkx/+1dy/QMV37H8B/eRMShEhERYQISj1X0qiipUkqS+PWLVJXcTXclr4oDUU861mKKq0W6bqUciXXUpV6LiUaJOnfW71SFSKNZzwqr/1fv33XzJpJJo+ZTDLnnPl+1pqmc2ZPzN5nn5M5v7P3/nl5ecnXKiM3N5dmz54tp9CUh4Mk48ePLzUShP/96gz23CnOI6KKgyA/xEdSmybKGZ6rFByU4eCWt7e3HDIMaCv0LRyHSoZzFtoLfcs2inIyKffdioMgjVq2I6fGPtX2OXi9uspAEKSKvt33G919lE+9Oitr7hgAmMajP17p1YrmbvmVXu0eSF4ebpprqri4OFqwYEGFU2GqigMZUVFRckoNj/Qoj5ubm3yUxBfW1Xlx7VDJ383lcJFftureT1qCtkJ7oW/ZHo5DtBf6Vg0fc76B5NImTC6CqlsDxLiAE7kEh5KLb/WuO1XZ7yoIglTBnQdPaM7mDBoU3kaRw+oBwDRemNDf15Pmb82ghSOf1Vwz8RSXESNGlFsmMDCQfH19KScnx2g7T4fhDDD8WkXDDSMjI+VUlsTERHJxUeaQUQAAAACofp7D58ksMJJhIMTRicjJmTzf+EQxuwFBkCpY8J9fqamPh1wcDgDUJbpXK1r872M0sm8wtW3WgLSEpy7woyJhYWFyDZK0tDTq2vV/8zP37dsnhxOHhnK6s7JHgERERMiRHdu3b5driChVHVcnq5YDAAAAgNJcW3ahhrOS6X7CZCo4d0S/nUeAcACEX1cKBEEsdP7aXfp27wUa/49uSIkLoEKNvdxlbvPJCUcp8eNwuzyO27ZtK0dzxMbG0urVq2WK3HHjxtGQIUP0mWGysrKoT58+9O2331JISIgMgISHh9OjR4/o3//+t3zOD8aBFycnZQUT/Bu6U9Lbz9LD/P/dkRDFxXTr9i1q6NVQP1WGAyBcDgAAAAAsx4GORrOSqSD7MuVeOiPXAKnuKTCWQBDEwhV5eTHUZzs0Id+Gday/VwCgRkSEBdAna3+hXWl/0Mvd/O2y1Tds2CADHxzo4HmUAwcOpOXLl+tf58AIZ3DhoAdLT0+n1NRU+f+tWrUy+l1XrlyhgIDqS3tmKcMAB49yuen4iHx8PLDGBQAAAEA1kGlwRe1qXQS1KhAEscBPGdco43IuTfmn9tYSALAntd2cKbJ7C5ry7TF6sWNTcnNR1iiGmsCZYDZu3Fjm6xzU4MCvTu/evY2eAwAAAACoCVbzNNOTgiKa/O0xiujegtxrYSFAALUL6+BH5ORAX/54xtYfBQAAAAAAqhmCIGb6OvksFRPRc880rZ49AgA1ytHR4X+LpCaeoJt3H6P1AQAAAAA0DEEQM+TcfUwLt52gV3q1lBdOAKANrZo1oOAAL5q9Kd3WHwUAAAAAAKoRgiBmmLM5XV4stfb3qr49AgA20b9nK9qWcoUyLuViDwAAAAAAaBSCIJX0f1du0daUK9S/Z8vq3SMAYBNenrWod7dm9NH6VCz8CQAAAACgUQiCVAJnQuALo56dn6JG9WtX/14BAJvoE9KcruQ8oG1HMrEHAAAAAAA0CEGQSkj6JZMu3LhPL4U2r/49AgA2wylyo54PpPgNx+nRk0LsCQAAAAAAjUEQpAKPnxTS9A3HKapHILm5OtfMXgEAm+naxofc3V1pxfZT2AsAAAAAABqDIEgFlu84RW5uztStnW/N7BEAsCkHh/+lzOVj/4/cB9gbAAAAAAAagiBIOa7lPqTl209RdO8gcnRASlwAe9G8iSd1bN1YTosBAAAAAADtQBCkHDM2HqcOQd7Uwq9eze0RAFAEngKXnHGNUs7etPVHAQAAAAAAK7H7RS6u3npED/OLSjXMyd9v0e5T2TT6bx2s1dYAoCL16rpR39AAmpxwlPbNjSJx6yoV384mRy9fcm4cYOuPBwAAAAAANRUEWblyJS1atIiys7OpY8eOtGLFCgoJCSmz/JYtW2jatGmUmZlJQUFBtGDBAurXrx8pIQAy4Itfyny9YTNv+s/xbBrZy40a1HGt0c8GALbXu0szSko/Qr99sJDqZ/+ffrtLmzDyHD6PXFt2sennAwAAAACAap4Os3nzZho/fjzFx8dTenq6DIJERERQTk6OyfIpKSkUExNDo0aNooyMDBowYIB8nDpl+8wLpkaAmJJfWFztnwUAlMfrzzP0ed4C8sg+YbS94LejdGt6BOVfSrfZZwMAAAAAgBoIgixZsoRiY2Np5MiR1K5dO1q9ejW5u7vT2rVrTZZftmwZRUZG0sSJE6lt27Y0e/Zs6tKlC33++ecWfFwAgJrTeu8CchKF5ETC+IXiIqKiQrr/7RTsDgAAAAAArU6Hyc/Pp7S0NJo8ebJ+m6OjI/Xt25eOHDli8j28nUeOGOKRI0lJSWX+O0+ePJEPnfv378ufxcXF8mEtopK/696DJ+Rc8iKoqv+2EDIVp5agTsqHfVR5de5nUf2sckZ6FBdRwdkUKsi+TE5WXCPEmuc4AAAAAACoQhAkNzeXioqKyMfHx2g7Pz937pzJ9/C6IabK8/ayzJs3j2bOnGny3zcMjlTVrduPK1VuTdIJKvirwGr/LgAoXydxmaIqUS730hkiUdtq/25eXp7VfhcAAAAAAKggOwyPNDEcPcIjQZo1a0aNGjWi+vXrW+3fuVPMFxuZFZbbOzuK2jTxsOqd3j///JO8vb3lSBotQJ2UD/vIPEU5mZT77tIKyzVq2Y6cGhsHeqvCzc3Nar8LAAAAAACqEAThIISTkxPdvHnTaDs/9/X1Nfke3m5Oed1FgKkLAQ4YWDNo4FDJ38XlqiNYYe36KAHqpHzYR5VsJ99AmQWGF0GVa4CUKuBELsGh5OIbaPX9AwAAAAAA1cOsb9uurq7UtWtX2rt3r9HdZX4eFhZm8j283bA82717d5nlAQCUgtPgkpOzDHgY4edOzuT5xiekdrdv36ahQ4eSp6enHGnHmbwePHhQ7nvGjBlDLVu2pNq1a8sRbdHR0WVOiQQAAAAAUBKzbznyNJU1a9ZQQkICnT17lt566y16+PChzBbD3njjDaOFU9977z3atWsXffrpp/JL8owZM+j48eM0btw4srU6rk5WLQcA2uLasgs1nJVMLq1DjLbzCBDezq+rHQdATp8+LYPTO3bsoIMHD9Lo0aPLfQ8Hw9etWyf/BiQnJ8sFd8PDw+WaUQAAAAAAmloTZPDgwXI9i+nTp8vFTTt16iSDHLrFT69evWo0nLt79+60ceNGmjp1Kk2ZMoWCgoJkZpj27duTrfk3dKekt5+lh/lF5QZAuBwA2CcOdDSalUyFOZlUfDubHL18ydmK2WBsiYMYfP4+duwYdevWTW5bsWIF9evXjxYvXkx+fn4m32cYJAkICKA5c+ZQx44dKTMzU44QAQAAAADQ1MKoPIqjrJEcBw4cKLXttddekw8lQoADACpDBj40EvwwTGHOU2B0ARDGKc85kJ2amkp/+9vfKvwdPBKQR4W0aNFCLmBd2dTn9+7dkz/v3r1bo2mB+d/iDDy87hTWX0F7oW/ZDo5FtBX6le3hOERbaa1vcUIVxqOUVZcdBgAAqh+P5mvcuLHRNmdnZ/Ly8io3jTn74osvaNKkSTIIEhwcLKfT8LpR5qY+b968eRVqAAAAAABgjAMw9erVo7IgCAIAoDFxcXG0YMGCCqfCVHUtkZdeeolu3Lghp84MGjSIDh8+TLVq1apU6nO+Q8CLsjZs2JAcHByopuhSrv/xxx9yMVhAe6Fv2QaORbQV+pXt4ThEW2mtb/EIEA6AlDWlWwdBEAAAjZkwYQKNGDGi3DKBgYEyVXlOTo7R9sLCQhmcKC+NOePoOj94nadnn32WGjRoQImJiRQTE1Pp1Oc8FcdW+A8ygiBoL/Qt28OxiLZCv7I9HIdoKy31rfJGgOggCAIAoDGctpYfFeFU5bwmR1pamsz4wvbt2ydHaYSGhpoVdeeH4ZofAAAAAABKVHOrlAAAgKK0bduWIiMjKTY2lo4ePSqns/Ci10OGDNEPI8zKyqI2bdrI19nly5fl+h4cOOFsYCkpKXLh69q1a8usMgAAAAAASoYgCACAHduwYYMMcvTp00cGMXr06EFfffWV/vWCggI6f/48PXr0SD7nNT9+/vlnWbZVq1YybbqHh4cMhpRcZFWJeEpOfHx8qak5gPZC38KxqFQ4b6Gt0LdsD8ehttrLQVSUP0YhC6vw3J47d+7YdA65tfBQ85s3b5KPj49mUjSiTsqHfaQOPD2F19fgFLJYswIAAAAAwLq0cQUOAAAAAAAAAFABBEEAAAAAAAAAwC4gCAIAAAAAAAAAdgFBEAAAAAAAAACwCwiCAACApsydO5e6d+9O7u7ulV5Mm9cInz59OjVp0kSm++3bty9duHDBqMzt27dp6NChcsFa/r2jRo2iBw8ekJqZW6fMzExycHAw+diyZYu+nKnXN23aRGpnSR/o3bt3qbb417/+ZVSG001HRUXJPstZliZOnEiFhYVkT23F5d955x0KDg6Wx6C/vz+9++67cpFoQ1rpWytXrqSAgACZcSs0NFSfhrwsfHxxJi8u36FDB9q5c6fZ5zC1Mqet1qxZQ88//7xcYJwf3A4ly48YMaJUH+J08fbWVuvXry/VDvw+e+lX5raXqXM5P/jcrfW+dfDgQerfvz/5+fnJOiUlJVX4ngMHDlCXLl1kdhjOJsj9rarnQWtCEAQAADQlPz+fXnvtNXrrrbcq/Z6FCxfS8uXLafXq1ZSamkp16tShiIgI+uuvv/Rl+ILu9OnTtHv3btqxY4f8UjB69GhSM3Pr1KxZM7px44bRY+bMmVS3bl16+eWXjcquW7fOqNyAAQNI7SztA7GxsUZtwf1Np6ioSH6J5n7LqaYTEhLkl0W+8LCntrp+/bp8LF68mE6dOiXbYNeuXTJ4UpLa+9bmzZtp/PjxMn1keno6dezYUZ5vcnJyTJbnfhETEyPbIiMjQ9aXH9xO5pzD1MjctuILL26r/fv305EjR+Q5Kzw8nLKysozK8YWpYR/67rvvSO3MbSvGQUrDdvj999+NXtdqv7KkvbZt22bUVnz8OTk5ye8bWu9bDx8+lO3DQYvKuHLlivy79sILL9Cvv/5K77//Pr355puUnJxcpf5qVUIF7t27x2l8xZ07d4QWFBUVievXr8ufWoE6KR/2kTrweY7Pd3zeg6pZt26dqFevXoXliouLha+vr1i0aJF+2927d4Wbm5v47rvv5PMzZ87I/XLs2DF9mR9//FE4ODiIrKwsVe4qa9WpU6dO4p///KfRNv69iYmJQkssba9evXqJ9957r8zXd+7cKRwdHUV2drZ+26pVq4Snp6d48uSJsOe+9f333wtXV1dRUFCgqb4VEhIixo4da/T32c/PT8ybN89k+UGDBomoqCijbaGhoWLMmDGVPofZS1uVVFhYKDw8PERCQoJ+2/Dhw0V0dLTQGnPbqqK/kVruV9boW0uXLpV968GDB5rvW4Yqcw6eNGmSePrpp422DR48WERERFit/asKI0EAAMCu8R2L7OxsOcxXp169enJoJt9JZPyTh/R369ZNX4bLOzo6yrtjamSNOqWlpcm7PKbu1o8dO5YaNWpEISEhtHbtWjmsWs2q0l4bNmyQbdG+fXuaPHkyPXr0yOj38vQGHx8f/Ta+G3b//n05kkKNrHW88FQYvlPt7Oysmb7FI374uDE833C78HPd+aYk3m5YXtdHdOUrcw5TI0vaqiQ+1goKCsjLy6vUiBGeesbTr3jU4K1bt0jNLG0rnqLWvHlzOWImOjra6Jyj1X5lrb71zTff0JAhQ+ToGC33LUtUdM6yRvtXlfFfFQAAADvDX/KY4UWo7rnuNf7JX2oM8YUZf7HWlVEba9SJvwS2bdtWrsFiaNasWfTiiy/KNS5++uknevvtt+WXbV7jQa0sba/XX39dXmTwXOoTJ07QRx99ROfPn5dDq3W/11Tf071mr30rNzeXZs+eXWoKjdr7FteLp0CZ2ufnzp0z+Z6y+ojh+Um3rawyamRJW5XExxsfe4YXWzxd4dVXX6UWLVrQpUuXaMqUKXI6H1988fQGe2krvkjnIOIzzzwjA448FY3P5RwIeeqppzTbr6zRt3jtCp4Ow38DDWmxb1mirHMWB/cfP35Md+7cqfKxXVUIggAAgOLFxcXRggULyi1z9uxZuXCgvatsW1UVf5HZuHEjTZs2rdRrhts6d+4s5xMvWrRIkReq1d1ehhfxPOKDFxjs06eP/ILcsmVLUpOa6lv8RZnnk7dr145mzJih2r4FtjV//ny5aC7fmTdc8JPv3hsekxwE4GORy/GxaS/CwsLkQ4cDIBzU/vLLL2UAEsrGwQ/uOzwazRD6lnogCAIAAIo3YcIEuep6eQIDAy363b6+vvLnzZs35QWqDj/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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_tri = np.array([[-0.5, 0.0], [0.5, 0.0], [0.0, np.sqrt(3) / 2]])\n", "T_tri = np.array([[0, 1, 2]])\n", "tri_pin, tri_handle = np.array([0]), np.array([1])\n", "\n", "V, T_beam = igl.triangulated_grid(NX, NY) # unit square, NX x NY vertices\n", "X_beam = (V - 0.5) * np.array([WIDTH, HEIGHT]) # centered WIDTH x HEIGHT rectangle\n", "beam_pin = np.where(X_beam[:, 0] <= X_beam[:, 0].min() + 1e-6)[0]\n", "beam_handle = np.where(X_beam[:, 0] >= X_beam[:, 0].max() - 1e-6)[0]\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 3.4), gridspec_kw={\"width_ratios\": [1, 2.1]})\n", "utils.plot_mesh(axes[0], X_tri, T_tri, pins=tri_pin, handles=tri_handle, title=\"triangle\", show_vertices=True)\n", "utils.plot_mesh(axes[1], X_beam, T_beam, pins=beam_pin, handles=beam_handle, lims=((-1.1, 1.1), (-0.3, 0.5)),\n", " title=f\"beam: {len(X_beam)} vertices, {len(T_beam)} triangles\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"meshes.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"004_meshes.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "501c8ef1", "metadata": {}, "source": [ "## Check the gradient\n", "\n", "Before posing anything, compare `gradient_func` with central finite differences (`simkit.gradient_cfd`)\n", "of `energy_func` at a random deformation of the triangle, for each material, with the pin and handle\n", "aimed at their rest positions so all three terms are active. Relative errors around $10^{-10}$ mean the\n", "energy and gradient are consistent, which Newton and its line search rely on." ] }, { "cell_type": "code", "execution_count": 4, "id": "5b04dda5", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.759352Z", "iopub.status.busy": "2026-09-24T03:44:26.759223Z", "iopub.status.idle": "2026-09-24T03:44:26.768665Z", "shell.execute_reply": "2026-09-24T03:44:26.768001Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Linear |g_fd - g| / |g| = 2.6e-10\n", "ARAP |g_fd - g| / |g| = 4.0e-10\n", "Neo-Hookean |g_fd - g| / |g| = 4.4e-10\n" ] } ], "source": [ "rng = np.random.default_rng(SEED)\n", "x_test = (X_tri + FD_NOISE * rng.standard_normal(X_tri.shape)).reshape(-1, 1)\n", "for label, material in MATERIALS.items():\n", " energy_func, gradient_func, hessian_func = elastic_pose_system(\n", " X_tri, T_tri, material, tri_pin, X_tri[tri_pin], tri_handle, X_tri[tri_handle])\n", " g = gradient_func(x_test)\n", " g_fd = simkit.gradient_cfd(lambda y: np.array(energy_func(y.reshape(-1, 1))), x_test.ravel(), FD_STEP)\n", " rel_err = np.linalg.norm(g_fd.reshape(-1, 1) - g) / np.linalg.norm(g)\n", " print(f\"{label:12s} |g_fd - g| / |g| = {rel_err:.1e}\")" ] }, { "cell_type": "markdown", "id": "7adb1bd5", "metadata": {}, "source": [ "## A triangle: pin the left vertex, swing the right one in a figure-8\n", "\n", "The handle traces a **figure-8** (a lemniscate), so the free apex both stretches and compresses. At each\n", "handle position we build the system with the new target and re-solve, starting from the previous\n", "equilibrium. The × is the handle's target, the orange dot where the handle vertex actually settles." ] }, { "cell_type": "code", "execution_count": 5, "id": "4d4f1102", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.770080Z", "iopub.status.busy": "2026-09-24T03:44:26.769980Z", "iopub.status.idle": "2026-09-24T03:44:27.623151Z", "shell.execute_reply": "2026-09-24T03:44:27.622515Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = np.linspace(0, 2 * np.pi, N_FRAMES)\n", "handle_path = X_tri[tri_handle] + np.stack([FIG8_AMP[0] * np.sin(t), FIG8_AMP[1] * np.sin(2 * t)], axis=1)\n", "\n", "tri_states = []\n", "U = X_tri.copy()\n", "for h in handle_path:\n", " energy_func, gradient_func, hessian_func = elastic_pose_system(\n", " X_tri, T_tri, POSE_MATERIAL, tri_pin, X_tri[tri_pin], tri_handle, h[None])\n", " x = simkit.solvers.newton_solver(U.reshape(-1, 1), energy_func, gradient_func, hessian_func,\n", " tolerance=NEWTON_TOL, max_iter=NEWTON_ITERS, do_line_search=True)\n", " U = x.reshape(-1, 2)\n", " tri_states.append(U)\n", "\n", "fig, anim = utils.animate_mesh(tri_states, T_tri, lims=((-1.2, 1.6), (-1.2, 1.2)),\n", " title=\"Neo-Hookean triangle: handle traces a figure-8\",\n", " pin_pts=X_tri[tri_pin], handle_traj=[s[tri_handle] for s in tri_states],\n", " target_pts=list(handle_path), fps=FPS, figsize=(6, 5))\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"triangle.mp4\"), fps=FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"004_triangle.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "65777408", "metadata": {}, "source": [ "Per frame: the elastic energy of each equilibrium (left), highest on the stretching right lobe of the\n", "figure-8 (frames 1-23) and lower on the compressing left lobe (frames 24-46), and how far the pin and\n", "handle vertices sit from their targets (right). Soft springs never hold exactly; they stretch by about\n", "$\\lVert\\nabla E_{\\text{elastic}}\\rVert / K$, a few $10^{-6}$ here (zero at rest). The two curves coincide\n", "because the elastic forces on a triangle sum to zero, so both springs pull equally hard." ] }, { "cell_type": "code", "execution_count": 6, "id": "4f5b28d9", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:27.624924Z", "iopub.status.busy": "2026-09-24T03:44:27.624819Z", "iopub.status.idle": "2026-09-24T03:44:27.890391Z", "shell.execute_reply": "2026-09-24T03:44:27.889794Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu_tri = np.full((len(T_tri), 1), MU)\n", "lam_tri = np.full((len(T_tri), 1), LAM)\n", "tri_elastic = [simkit.energies.elastic_energy(X_tri, T_tri, mu_tri, lam_tri, POSE_MATERIAL, U) for U in tri_states]\n", "tri_residuals = {\n", " \"handle\": [np.linalg.norm(U[tri_handle] - h[None], axis=1).max() for U, h in zip(tri_states, handle_path)],\n", " \"pin\": [np.linalg.norm(U[tri_pin] - X_tri[tri_pin], axis=1).max() for U in tri_states],\n", "}\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 3.6))\n", "frames = np.arange(N_FRAMES)\n", "utils.line_plot(frames, {\"Neo-Hookean\": tri_elastic}, xlabel=\"frame\", ylabel=\"elastic energy\", ax=axes[0],\n", " title=\"elastic energy along the figure-8\")\n", "utils.residual_plot(tri_residuals, frames, ax=axes[1], colors={\"handle\": utils.HANDLE_C, \"pin\": utils.PIN_C},\n", " xlabel=\"frame\", ylabel=\"distance to target\", title=\"spring residuals\", ylim=(1e-8, 1e-4))\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"triangle_energy.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"004_triangle_energy.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c1fe274a", "metadata": {}, "source": [ "## Same handle, three energies, very different poses\n", "\n", "Pull the handle far up and to the right, and compare where the free apex lands under each model (dashed:\n", "rest shape, ×: handle target). We solve once per material from the rest shape, keeping each solve's\n", "per-iteration gradients (`return_info=True`) for the convergence plot below." ] }, { "cell_type": "code", "execution_count": 7, "id": "a69f7822", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:27.891703Z", "iopub.status.busy": "2026-09-24T03:44:27.891572Z", "iopub.status.idle": "2026-09-24T03:44:28.035565Z", "shell.execute_reply": "2026-09-24T03:44:28.035160Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Linear free apex at (-0.45, +1.13), 2 Newton iterations\n", "ARAP free apex at (+0.08, +1.31), 5 Newton iterations\n", "Neo-Hookean free apex at (+0.19, +1.11), 4 Newton iterations\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(12, 4))\n", "newton_grad_norms = {}\n", "for ax, (label, material) in zip(axes, MATERIALS.items()):\n", " energy_func, gradient_func, hessian_func = elastic_pose_system(\n", " X_tri, T_tri, material, tri_pin, X_tri[tri_pin], tri_handle, FAR_TARGET[None])\n", " x, info = simkit.solvers.newton_solver(X_tri.reshape(-1, 1), energy_func, gradient_func, hessian_func,\n", " tolerance=NEWTON_TOL, max_iter=NEWTON_ITERS, do_line_search=True,\n", " return_info=True)\n", " newton_grad_norms[label] = [np.linalg.norm(g) for g in info[\"g\"]] + [np.linalg.norm(gradient_func(x))]\n", " U = x.reshape(-1, 2)\n", " utils.setup_axes(ax, (-1.0, 2.0), (-0.8, 1.6), title=label)\n", " utils.TriangleArtist(ax, U, rest=X_tri)\n", " ax.plot(*X_tri[tri_pin[0]], \"s\", color=utils.PIN_C, ms=10)\n", " ax.plot(*FAR_TARGET, \"x\", color=\"0.3\", ms=12, mew=2.5)\n", " print(f\"{label:12s} free apex at ({U[2, 0]:+.2f}, {U[2, 1]:+.2f}), {len(info['g'])} Newton iterations\")\n", "fig.suptitle(\"Same pin + handle target, three elastic energies\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"materials.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"004_materials.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "73d728bd", "metadata": {}, "source": [ "Linear elasticity is not rotation-invariant: it counts the large rotation this pose needs as strain, so\n", "it poses a lopsided triangle, unlike the two rotation-invariant models ARAP and Neo-Hookean." ] }, { "cell_type": "markdown", "id": "3e27a6a6", "metadata": {}, "source": [ "Gradient norm $\\lVert\\nabla E\\rVert$ per Newton iteration for those three solves. It starts at\n", "$K \\lVert h - x_{\\text{handle}}\\rVert \\approx 1.5 \\times 10^5$ (the handle spring's pull) and falls by\n", "about 16 orders of magnitude in 2 to 5 iterations. Linear elasticity is quadratic, so its first step already\n", "lands on the minimum up to roundoff; the others end with Newton's fast local convergence (tutorial 5)." ] }, { "cell_type": "code", "execution_count": 8, "id": "2ccacb8a", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:28.037047Z", "iopub.status.busy": "2026-09-24T03:44:28.036916Z", "iopub.status.idle": "2026-09-24T03:44:28.140492Z", "shell.execute_reply": "2026-09-24T03:44:28.139921Z" } }, "outputs": [ { "data": { "image/png": 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oU/4RPXbO2jHU60L5NdRLQz1gNPxB+Ux0oaEnqs/TrFkzjBo1SgRlVNmdHltdtWPoy54+sCkRnIImSgCmAIp6nqiGkeIDurj2hb4IqP3oQq895y9sSoqmmlPz588XOT+dOnUSvQn0S5++hCkXR7VmVV7o/vQlREnfEydOFK+PhhApAFb91U5t8dtvv4nXSccAtQXlztAXPSWGU9Dz119/vdXro+EiOrYoIKRjgwJ06hm6cuWKqC1Er4sel94DOkGCAlyqcUYBAgXlf//9t+idU3yJ0jFIATDleRVmPjqqbbV48WIx7ETJ95Rbs2LFCrGflIOjCVQrjAJMal86kePWrVvi/XhTvlN+6Higv1F6n6mHioJy+vukXreCPCa9fhqup79XOlGB7hMeHi4ClODg4Fz1sQr690s90T///LMIkuk4oh8ftF8FRfXW6HilenY0TEvvGe0LpR9QT55qbxP1htMPBmpb+oyhHweU10htSz2CdNzQfV63v0wHaPs0Q8YKWzYhJzoNma7L61TzP/74Q9aiRQtxajJd6JT78ePHi9P/Vf3999/iMbp27Zptu6JG0bp163I99vnz50WdHap1lPOU5mPHjsneeecdUb+GyjJQPZq7d+9mu7/itGs6JTqv11qQOkZnz54VZQEcHBzE66OaNjlLGhTXvtBj0nXURvmhU+Cpjei5aR/pNHcqURESEpLttP1u3brlef8nT56I6+j+VFeJTuOn95Se9+LFi9luS7WWqLYUlT+gU/npcfv27StqVBX2da5fv17UU6LHozpZdCo/1fZSRWUCqGQDlUqg+mhUq2n48OEyf39/5W2oVAA9Pp0OX9iyCXQMUjkA2hc6jmmfFa9HFa3TMV5Q+bU/7Ydq6QIqT0Dt7+XlJd4Pev8vXLiQ63aKsgmqNcnyK31AqH4Tlbeg10W136g0Qc7HzO++VEKFyn94enrKLCwsRF2s7t27y3bv3v3G153f329wcLAol0ElMeg9pRIqdLzm/BvP71hSlDWZPn262C9qKyptce/ePXFsfvLJJ9luS+U3pk2bJmqx0b5QrSoq/UD1sFTrtb3u84Zplwn9o+2gjjHG3hYNv1DFdOqFKMxZXNpAieSUeExnD1IPBjM+NFxHZ/lRrxz1fjLDwTlUjDGdl3NOP8qhorwZOtVeX4IpQkOPn332GQdTRiKvuSgVeVg8ubHh4RwqxpjOo9wlqmdEeWJUA4jO6qQ8sfzKMegqyhtjxoNynShXjk78oLILVMeOTnqhXELKrWOGhQMqxpjOozPpKOGcAig6w40Sc6ngYs6zChnTJTQbAZ3pR8ntVH1fkahOw33M8HAOFWOMMcZYEXEOFWOMMcZYEXFAxRhjjDFWRJxDpSZURTkkJEQUjeTpARhjjDHDQNWlEhMTRTFfKiCcHw6o1ISCKW9vb3U9HGOMMcZ0yPPnz1GmTJl8r+eASk2oZ0rR4DQVhbrRHHV5zWTP1I/bWrO4vbm9DRUf24bR3nSGJnWYKL7n88MBlZoohvkomCqOgIrmdSqOx2Xc1trGxza3t6HiY9uw2vtN6TyclM4YY4wxVkQcUDHGGGOMFREHVIwxxhhjRcQ5VIwxxtjL0+MlEomY3kgdMjMzxUTeTDOK0t4WFhYwMzMr0vNzQMUYY8zoZWRkIDQ0FCkpKWprCwrMKFGaaUZR2psSzqkkAk1iXVgcUDHGGIOxF2YODAwUPRRUvNHS0lItBZopSKPHYppR2PamnsnIyEgEBwejUqVKhe6p4oCKMcYYjP2LmIIqqjVka2urtselqtocUGlOUdq7RIkSePr0qRg2LGxAxUnpjDHG2MsvZGacTNTQI8lHD2OMMcZYEXFApePmbl6AuqvboeOhd8X/tM4YY4wp1KhRAwcOHOAG0TIOqHQYBU87pJsgsY6EialE/E/rHFQxxpjxadOmDZYuXZpr+507d9C9e3et7BN7hQMqHbY7+SBkMhrbla/T/zKZCf5IOqjtXWOMMaYi4cgRPOnVG/dr1xH/07qho5pddIYck+OASodJrGKUwZSCiYkMmdax2tolxhhjOVDw9OKziUh/+BCyjAzxP60nHTumkbYqV64c9u7dK5b9/PxQt25dfP/99/Dw8EDJkiVz9Wpt374dtWvXhrOzMxo1aoTz588rr9uyZQtq1qwJBwcHlC1bFtOnT88WNFHy9q+//ipuY2dnh6SkJI28Rn3AZRN0mHm6q3y4L0dQZSqx1tYuMcaYUQh8/wNIoqIKdFtJdLR8QRF4vPw/fMrXiP7p5zfe39zdHeX/2A11oSHAIUOG4MWLFzh37hw6duyIHj16oEKFCvjnn3/w5ZdfYv/+/SLwokCMrnv48CHc3NzE5c8//xT1mG7evInOnTujatWqGDRokPLxt23bhiNHjojbUoVxJsc9VDrsA7uuymE+VTLLJCy8vJy7WhljrJhQMCUJDy/QBRJJPg8iKdhjFDBwKyh3d3d88cUXItihvCvqwbpx44a4bsWKFfjqq69Qv359USbivffeEwETBVqka9euqFy5suiJooBrwIABOHnyZLbHnzJliiiAamVlxaUmVHAPlQ77bshXwGaInCkxzJdlBRMLeVn9jff+hxRJIr5rNhWmJhwXM8aYOlGvUUGJHqq8gipzc5i7uan1uQqChvlU0dBcYmKiWKbild988w1mzpypvJ6KWVJvFjl8+DBmz54teqxoe3p6ugiyVNFQIMuNAyo9CKq+w1cIGDIUobcf4rP32yHL+4S4blfA7yKomtvie5ib8lvJGGPq8jZDcIocqpdDCsr/Sy74Ga45ghFto2rwn376KT755JM8K8ZTj9XKlSvRv39/0QM1adIkEYSp4gKoeeOuDT1h1fdDlEiNx097bwDBPZXDgH8HHsCkfz9Hela6tneRMcaMkmOnTij9yzJYVakME0tL8X/p5b/Avn37YjmzLi0tTXmhHqS3MX78eCxYsABXr14VaSM0GfSxY8fEPHb0WPSYlBtFwdSlS5dEvhQrGA6o9IR5gwawqlIFZZMi8P1fVyANHQyZVD7f0Kngkxh7bCySMvhsC8YY01ZQ5bt3L6r+d1P879ixY7E8D+U/2djYKC9VqlR5q/tTAvqPP/6IMWPGwMXFBeXLl8eyZcvEXIZ0Zh/lWH300UdwdHTEvHnz0K9fv2J5HYbIRMZFJNQiISEBTk5OiI+PFweiuoWGhsLm4iWETpsm1u916Y9pJZxhUWoTTEwzxLYabjWwqsMquFi7qP35jQm1tZeXl7Z3w2hwe3N7axv1ygQGBorgwtpafWdR0xAaT46sOUVp79cdAwX9fuceKj3i1O1dmHt4iOVqh3fgx6ZtkRo0GrIsG7HtTvQdDDs0DGHJYVreU8YYY8y4cEClR2hs3mXwYPmKTIZm5/ZhZqeuSHn2MaSZDmJzYHwghh4cimcJz7S7s4wxxpgR4YBKz7j06wsTW1uxHLdnDwZVc8anLVoi5dlYSDNcxfbQ5FARVN2Pua/lvWWMMcaMAwdUesbMyQnO770nlmWpqYjdvgOTOlTC4Ab1kPLsE2SleYrrYtJiMOLQCFwLv6blPWaMMcYMHwdUesh12FAqBCKWY7ZugSwzE7N61kC36lWQ8uwjZKXIi64lZSbh46Mf43TwaS3vMWOMMWbYOKDSQ5be3nB4eUpuVmQUEv46ADNTEyzuWxctK5RFStBoSJIqievTstIw8cREHAw8qOW9ZowxxgwXB1R6ym3EcOVyjJ+fKNBmaW6K1YMboE7pEkgNHobMhFrieolMgq9Pf42dD3ZqcY8ZY4wxw8UBVQ5UNdbHx0fMxq3LbOrWhU29emI5PSAAyWfPiWU7K3NsGNEYFdydkPZiADJiG4ntMsjw/cXvsfa/tTypMmOMMaZmHFDlQJVhmzZtCn3gqtpLtWHDq+12ltg0qgm8nGyRHvYe0qNaK6/75fovWHx1MQdVjDHGmBpxQKUiICAA9+/fzzWztq5yaN8eFi9n/U4+fx5pDx4oryvtbIPNoxrD2dYSGZFdkR7RRXmd3x0/zLowC1nSLK3sN2OMscIbOXIkTExMcO/ePeW2kydPim329vZiChkaaZk2bZqYUkYVpYdUrFgRpUuXRlZW9u+AWbNmwdzcXDwGVQSvVasWfv/9d36rjC2gOn36tJijqFSpUuKg2rt3b67b0BxF5cqVE2XlmzRpgsuXL2e7nob55s+fD31hYmYmP+PvpZj1r3qpSEUPB2wY3gg2FmbIiG6DtNA+dC9x3Z8Bf+Kr018hI0s+bQ1jjLHCO3Q7FF2WnkaV7w6K/2m9OCQmJmLnzp1wdXXFunXrsl1H06MkJSWJ2xw6dAh+fn7ioooCr6CgIDGdysGDuU9W6t69u3iMuLg4TJ8+HUOGDBEdDcyIAqrk5GTUqVNHBE152bFjByZPnoyZM2fi2rVr4radO3dGRESEuH7fvn2oXLmyuOgT5z59YOrkJJbj//kHmeHy16NQr6wLVg9pAAszE2TGNUFqcH+YQj6p8tFnRzH++HikZKZoZd8ZY8wQUPD0yZZreBCWiHSJVPxP64fvhqv9uei7zM7ODj/99BM2b96MzMzMPG9XrVo1tGjRAlevXs22nYIwCpref//9XAGZKlNTU/Tt2xfOzs64c+eO2l+HITKHgaBhutcN1S1evFjMrj1ixAixvnr1avz9999Yv349pk6diosXL2L79u3YtWuXiM7pIKUuzxkzZuT5eOnp6eKiQNG+Npja2sKlf39Er1kDZGYidssWeHwxOdttWlcugUV962Li9uuQJNZBUpA1HH22QiLLwMXQixhzZAxWdlgJJyt5YMYYY8aux/KziEx89Rn/OlFJ8tvJXq4r/v985y3M++fhG+9fwsEKf33aokDPRUHQoEGD0L9/f0yaNAl//fUX3ntZ7FnVrVu3xMjNN998o9xGvU5//PGHCMpoWLBTp04IDw9HyZIlc92fhgPp+5C+22rXrl2gfTN2BhNQvWkGaorSaTxZNfru0KEDLly4INZpqE8x3EddpLdv3843mFLcfvbs2bm2h4WFid6y4hAamncXsrRjB2D9ehFQxfz+OyR9esPERj5hskIjDxN83roMFp8MRlZyFSQEjoRL+U1Il6Xgv6j/MPjAYMxvMB9uVm7Fsu/6Jr+2ZtzehoCP7+zoBzQFEPRdQd8NJCIxDeEJBQuo8iORyhCWkPbG29FZ2PTcb0I5U/Tjf/ny5bC0tESvXr2wdu1a0eNEryE+Pl70KNGP/bS0NAwdOhSjRo1SPvamTZtEINW+fXuRK0UpMtSp8MUXX4jrqQ2oo4Eeg66nFBnqBaN8rILsny4o7H7S/ej106iVhYVFtutoCLUgjCKgioqKEg2VMwqn9cKODVNwRkOIChTFe3t7w9PTU/RsFccHoJeXV95XennBpEcPxP/5J2RJSbA+ew6uQ4fkutlnXl6QmNngl+MByEoth/jAMShRaRMSM2PxNOkpvrz6JdZ2XAtvR28Ys9e2NeP21nN8fOdGwQf9EKYghS7Ew8EaJi9zTgvSQ0XBU07mpiZwt7cqUA+V4nlfhwIiSldp2LChWKcRly5duiAyMlIEAZRDRb1Q9H1HgdLPP/8slhWPvXHjRgwcOFAMGRLKj6LHVHQ2mJmZoVu3bnnmIOuDjIyMArVjXih5n16/h4eHyLNWpWivNzGKgOptDR/+qhxBfqysrMRFV7gOHyYCKhKzaRNcBg0USes5fd6hEmKS07HlYhAyU70Q82gMvKpsQlRaGF4kvcDQQ0OxpuMaVHbRr1wyxhhTp4IOwanmUJmY0Fl0UP6/tG9tdK9bRi37Qz1Q1FtEKSn0w11xxh4FTDSq8s477yhvS4EBpbgcOHBAnLm3ZMkS3LhxQ+QPP378WKS3EOrJogDs3Llz2e7PjDwp/XXc3d3FAUZjxapoXXFg6jvrypVh10L+AZAZHIzEo8fyvB2dATm7Z010qy3vgUlLcUXUwzEoY1derEelRolJlW9G3tTg3jPGmP7qUtMLqwfXR1VPB1iZm4r/adaKTtU91PYc+/fvFyMhFBRRcESXmzdvijPxqDeKgquc6DrKF37x4oXIvapXr54YlVHcn4YQafjvdcnprOCMIqCiLsAGDRrg+PHj2br3aL1Zs2YwFG4j5Qn3JHpD3n9gRD7vXx20qOgu1hOT7RD9aBQqO1cX6wkZCSJR/XzIeQ3tOWOM6X9QdXBiKzyY21X836Wmen+sU9AzYMAAVK1aVXQEKC6fffYZQkJC8vy8p6HBVq1aicBq69atmDhxYrb70oUS26kMQ0HzhFj+TGT5fevqGeoGffTokVimKJzO6mvbtq2o1VG2bFlxVsOwYcOwZs0aNG7cGEuXLhUHEUXreZ3h8LbolwONX1NSoMZzqF6itzKwdx+kvyzw6bNtK2zr18/39knpEgxaexE3g+Plty9hBp9qO3E98opYNzc1x08tf0Kncp1gTDjHhNvbkPHxnXcOVWBgIMqXL58rf0ZbOT1Ms+39umOgoN/vBtND5e/vLwIpuhBKGKdlxZl6/fr1w8KFC8V63bp1RXcnFT5TRzClK2g4L7/paPJi/3LeP98S8oS7Z5FZiH48GK1KtxXrEqlEFP+kIqCMMcYYg+EHVG3atBE9NDkvqlViJ0yYgGfPnolEvEuXLolq6YbG6d13Ye4hH7dPPHYcGc+evfb2NO/f5lFN4Okoj8jvvEhF9JN+6O7bU6xLZVLMPD8TfrezV9tljDHGmAEGVEzOxNISLkMGy1dkMsRs3PTGpnk175+89sbFJ3GICeyNQVVfPg6ARVcXYdm1ZTypMmOMMZYHDqgMkEvfvjCxtRXLcX/+CUls7BvvU6mkA9a/nPePHL4bgbjgLphQd4LyNr/d+g3fX/yeJ1VmjDHGcuCAygCZOTnB+f33xbIsLQ1xO3YU6H71y7pg1eD6ohgd2X4lGIlhbfBNk1dTF+x6uAtTz0xFZlbe80cxxhhjxogDKgPlOmwoza8jlmO2boW0gOX421TxwKK+dURhOvLrv4+QGtUU81vOh5mJvPfq0NND+Ozfz5AqSS2+F8AYY4zpEQ6oDJRlmTJw6CQvd5AVGYWEvw4U+L696pbGzO7ymlRkzoG7kMTXw7K2y2BlJq8Of/bFWXx89GNRs4oxxhgzdhxQGTA31RIKfhveKqF8+Dvl8Vm7isr1L3fdhDSlGlZ1WAU7C3mZhesR1zHy0EhRXZ0xxhgzZhxQGTCbOnVg87KwZ3rAIySfPftW9/+8Y2UMalJWLNPEn2O3XIVpekWs77wertauYvuD2AcYdnCYmAeQMcYYe9uSR1Ro2xBwQGXg3qbQZ16FQuf0qol3a8mnUEjLlGKk3xWYS7zh18UPnnby7UGJQRh6cCgexz1W894zxhhTDT5oXtr//vtPuY0mN6bP6qdPn6q9oU6ePAlnZ+dc22nC5d69e/MbkwMHVAbOoV07WJSV9zIln7+AtPv33+r+NO/fkn51lfP+xadmYsi6SzDPKolNXTahnGM5sT0iJQLDDw3H7ajbxfAqGGOMERcXF0ybNo0bQwdxQGXgTMzM4Dp8WKF7qYiVuRlWD2mA2mWcxHp4QjqGrr8MC7iKnqpqrtXE9rj0OIw6PAqXQy+r8RUwxpjuO/bsGN7f/z4abG4g/qf14jBu3DicO3cOp0+fzvP67du3o3bt2qJnqVGjRjh//tUk9zQB8kcffSTmhaXLJ598guTk5CLvE82j27lzZzF3boUKFXIN4W3ZsgXVqlUT+9SiRQtcu3Yt3zl56XEGDRqEzMxMREREiGXa11KlSomJnGmmE8Vte/XqBQ8PDzHPHk0CrdpzR71oPXr0EDOk0PMq5vQtThxQGQHnPn1EbSoS//c/yAwPf+vHEPP+DW+knPcvMCoZIzZcgZWpE9Z1XocGJRuI7SmSFIw9NhYngk6o+VUwxphuouDp85OfIyA2ABnSDPE/rZ94rv7PQQpavv76a0ydOjXXdf/88w++/PJLMeVaTEyM6MmioCI6OlpcP3HiRBH83L59G7du3cL9+/fx+eefF2l/JBIJunfvjjp16iAkJAR79uzBzz//jG3btonrKfAbO3Ys1qxZg8jISHzwwQfo0qWLmGhYFV3Xtm1b1KhRQwRg5ubm6NmzJzw9PfH48WOxvzdv3sTcuXPF7aVSKQYOHCgmNA4PDxdz99K66slXhw8fFoEWvX663+jRo0VQWVxMZG9z6hfLV0Fno9bWDPERS5cievUasew2ZjQ8vviiUI8THJuCD1ZdQFhCmlhvXsENG0Y0ggyZ+PLUlzgVfEpsp5pVc96Zg54V5HMC6pOitjXj9tZlfHznlpaWJr6Yy5cvD2tr+bym/Q70K/AZzNGp0ciSZeXabm5iDlcb+Qk8r+Nu444d3XcUKIeKcpc+/vhjVKxYEStWrBDbaBiQ9n/8+PHo1KmTCJwU3nnnHdETRT09NjY2IsBRzGNLvVft2rVDSkoKTF/WLcyZQ0VBDn235WwvCor27t0resveffddERBZWlqK63/44Qdx3yNHjmDMmDEiOFq1apXy/lWqVMHMmTNFAET7Tz1qhw4dEgHPlClTxG2uXLkinoMeV7FvR48eFa+FAqycKJeM2iE4OBilS5cWPVT0mBcvXhTXU6hD7y295gYN5B0AbzoG3vb7nXuojITroEEwsZDP1Re7YyekhezmLeNii02jGsPJRv5Y5x9HY9L2G7AwtcKStkvQzbeb2E4fLt+e/RZb7m5R46tgjDHNoGCKckMLcskrmCISmaRA93/b0jMUGFFA8s033yAr69VzU2I6baMhLsXlxo0bePHihQhMMjIyUK6cPO+V+Pr6iiG0qKgobN26Ffb29uJCvUQKFEhQsKJ6Ue0dowCGhuMsXwZTisel7YrrVZ+TUNCiuJ7s3LlTBE3Uk6X6Wui5qEdO8Vqod4t6o0hqaqoY/qTHpiBH8Rz0WhSod0uBEvep3Yqzh4oDKiNhXqIEHHv2EMvShATE/fFnoR+rco55/w7eDsP0fbfFr7EfWvyA/lX6K2/705WfsOLGCp5UmTGmV6jXyMPWo0AXxSwSOdFnYkHuT8/1tkaNGiWGvTZu3Kjc5u3tjUWLFmULfihHigKgEiVKiKBH9WxAWraysoK7u7vowaK8JLrcuXOnwPtRpkwZMdSXmZmZ7XFpu+L6nGcgql5PqFeqWbNmIn+KeoMUr4Xyo1RfC/UQ0f4Rep1Xr17F2bNnxX0Uz6HNQTdzrT0z0zi34cMR/zKQitm4ES4DB8DEvHCHQAMf+bx/ozf6ixpV2y4Fwc3OEl90qiLm/nOycsKa/+RDjKtvrkZCegK+bvw1TE04hmeM6b6CDMHlzKEygQlkkCn/n//OfHSp0KVY9o/KJ8ybN08M/ynQkB8lblMyev369UUvDg1xVa1aVQQwNMT27bffih4hCjyoN2vIkCF5DvcVVOPGjVGyZEnMmDFDDLMFBARg+fLlIo+KDB48WORx0f801EhDf5TTRMOECvT869atEwnzNGRJuU/0Giio+u6770TOGPWcBQUF4e7du+jatasIomhojob5KMii16Jt/O1mRKwqVYJdy5ZiOfPFCyQeK9pZKIp5/xSWn3iEDecCRdfqhHoTMKWRfCycbLu/TQwBZkp5UmXGmGHp4NMBS9osQWWXyrA0tRT/L22zFO282xXr877//vsil0qBApcff/xR5C1RoEFDa8uWLRM9WYSWaWisevXqYliP7rt48eIi7YOFhQUOHDggeotoiI0SySdPniyCN9K6dWsRYFGPmpubmzgL8eDBg7nqW1FQtXbtWtStWxcdOnQQARM9Lg1X0hmCNPTYrVs3kVRP6DkoqKRgrmbNmqKHS9s4Kd1IktIVks+fR9DIUWLZuk5tlNu+XQRARUFB1Oy/7irXl/ari971SovlvY/2Yub5mZDK5H/Qbcq0wYLWC2Btnj3pT5dw0i63tyHj4xtvlZBcFJSzpJpbxIpXUdqbk9LZW7Nt1gxWVavKD6Cb/yH1+vUit+KId8rj0xzz/v37IEIs967YG4vbLIaFqTyJ/WTwSVFWISlDPg7OGGOMGQIe8jMy1BulOmly9Pr1anncyR0rY2COef+uPosV6+3LtsfKDitha24r1v3D/THy8EjEpMWo5bkZY4wxbeOAygg5du0Kcw8PsZx0/AQy1DAHFAVq3+cx79/DcPkpqk29muK3Tr+JZHVyL+aemFQ5LDmsyM/NGGOMaRsHVEbIxNISLkMGy1dkMsRs2qSWx1XM+/dORTflvH9D110WxUBJrRK1sLHLRnjYyIO5pwlPMeTgEDyNV/+knowxxpgmcUBlpFz69YOprXwILu7PPZDEyofniorm/VszpCFqlZb3RFFFdQqqopPk8y9VcK6ATe9ugreDt/z65DAMOzQMd6NfJbUzxhhj+oYDqpeeP38uSuDT6aRUBn/Xrl0wZGaOjnD64H2xLEtLQ9z27Wp7bJr3z29EI/i6y+f9e0Lz/vldQVK6RKyXti+NTV03iVOLCeVS0aTK/mH+atsHxhh7W4ryAsz4yNRQEJTLJqicSkwl7akGRlhYmJjr5+HDh7CzkwcFhlI2QVVGcDAed+pMnyIwc3dHxePHYGplpbbHp6G+91edR3iCvHeKhgKpwjr1YpGEjASMPzYeNyJviHUrMytxRmCrMq2gTXxaObe3IePjO+9AigpSUl0jRUXxopaTIVw2QbMK294UTNHUPDSnYaVKlcRxUJjvd66U/hIFK4qAhYqTUSl+mq27oAGVPrIsUwYOnToh8dAhZEVFIeHAATi/L++1Ugea92/zqCb4cPUFkU917lE0Pt9xA8sH1Bf5Vo6WjljTcQ0mn5qMcy/OIT0rHRNPTMS8FvPwru+rKrqMMVacqKgk1aCiYJOmUVEXmmcv55czKz5FaW8KoKmafFHeL4MJqGgG7QULFohqrfRHsWfPHjErtyqamZtuQz1QderUEdVbqWx+TvQY9MZQ2XtDRyUUKKAi0Rs2wOm999TyyyznvH+Df7uE1Mws/HMrDM62tzGvd03xPLYWtljedjmmnZ2Gw08Pi8lEp56ZisSMRPSr2k9t+8EYY69DPRtly5aFRCLJNuFwUURERIj56JhmFKW9qeJ7UYNfgwmoaAJICpJGjhyJ9957L9f1O3bsEKXqV69eLeYTWrp0qZiI8cGDB9neAOqVGjp0qCiBbwxs6tSBTYMGSL16FRmPHiP5zBnYt1LvkBvN+7dycH2MUZn3z93OEpM7VRHXW5hZ4KeWP8HB0gG7H+4Wc2DNvTQX8RnxGFNrjFoDPMYYyw991tAXK13UgR5HnZXXmW63t8EkpdNkiXPnzkWfPn3yvJ7mK6L5jUaMGCESzymwsrW1xXqVwpbp6emiV4tm5m7evDmMRbZCnxs2FMtztK3igYUfvpr375cTj+B3LlC5bmZqhhlNZ2BUTfm0OGT59eVY6L9Qq7OHM8YYY0YVUL0pUY2G8WjCRdUxc1q/cOGCWKcv7eHDh6Ndu3Zi9u03oeCLEtVUL/rKvm1bWPjIq5ynXLiItHv3iuV5aH6/mT2qK9dn/XUX+268yPbrcFKDSfi8wefKbZvubsKM8zMgkcrPEGSMMcZ0kcEM+b1OVFSUGBOnWalV0fr9+/fF8rlz58SwIJVM2Lt3r9i2efNm1KpVK8/HnD9/PmbPnp1rO+Vn0fBjcaDcsOJi3rsPMpctE8vBK1fB7ptpxfI8XXyt8ayRJ/yuyCukT955A1mpiWhWTl63inR16wpZdRmW3V0mhv9oguWohChMrT1VzOSuCcXZ1ozbW9v4+Oa2NlShxfDZnZgon/HDKMsmUE+HalI6nbVRunRpnD9/Hs2aNVPebsqUKTh16hQuXbr01s9BPVR0UaAeKkpi16eyCaqkqal41LYdsuLiAHNzVDx2FBae8mlk1I0OuW/33ha5VMTGwgxbxzRB/bIu2W5HSeqUoK7onWri1QTL2i6DnUXxnnnJp5VrFrc3t7eh4mPbMNq7oGUTjGLIj0ogUPY+1ZlSRetUIqEwrKysRMOqXvSZqY0NnAf0l69IJIjdsqXYnksx71/XmvK2p7P/aN6/gJfz/il0LtcZK9qtgI25jVi/FHoJY46MQVxaXLHtG2OMMVYYpsZyOiwV6jx+/Hi2Qm60rtpjZexcBw6EycuzW2J37ERWUvEMXRKqQ7W0f100ryCf9y8uJRND1l3Gi7jUbLdrXro5/tfxf+IMQHIr6hZGHB6BiJSIYts3xhhjzGgDqqSkJNy4cUNcSGBgoFgOCpIPK1HJBCqFsHHjRty7dw9jx44VuU501h+TMy9RAo49e4hlaWIi4v/8o1ibhiqm/29o9nn/hqy7pJz3T6GuR11s6LwBbtby4OtR3CMMPTgUzxOe81vHGGNMJxhMQOXv74969eqJiyKAouUZM2aI9X79+mHhwoVinaaXoWDr0KFDuRLVjZ3b8FclFGL8NkImKd6z62jevw2q8/5FZp/3T6GKaxVs7rpZzANIXiS9wNBDQ/Eg5kGx7h9jjDFmVAEVTWxMyc45L35+fsrbTJgwAc+ePRPJ5JSITgU+WXZWlSrBrlVLsZwZEoLEo0eLvYnc7a2wcWRjlHSUzyP4X3A8Ptl8FemS7NWKvR29xaTKFZ0rivWo1Cgx/HcjQt4ryRhjjGmLwQRUTH3cVIZBozf4aaSwprerLTaNbAInG3kO19lHUZi84yaypNmf28PWQwz/1XKXl7OgKWo+OvqRmAuQMcYY0xYOqFgutk2bwqpqVbGc9t9/SL12TSOtVMWT5v1rCGsL+WH5961QzNh3O1dA52ztjN86/SbKKJBUSSomnJggyiwwxhhj2sABFcuzrIHbyBHFPh1NXhr4uGLV4AYwN5XP37f1UhCWHAvIdTuaVHll+5XoUFZe/Z5qVU05PUXMBcgYY4xpGgdULE+OXbvC/GXCftLxE8h4+lRjLZVr3r/jAdh4PvfzW5pZYkHrBehdUV7AVSqTYvaF2Vh/+9X8jIwxxpgmcEDF8kT1qFyHDJavyGSI3rhRoy1F8/7N6K4679+dbPP+KZibmmNO8zkYWn2octuSq0vExQAnAWCMMaajOKBi+XLu2xemtrZiOX7PXkhiYzXaWiNblMf4thXEMsVGX+y8iVMPI/Mcovyy4Zf4tN6nym3USzXn4hxkSbOfKcgYY4wVBw6oWL7MHB3h/OEHYlmWloa47ds13lpfdqqCAY3LimWJVCbKKVwPis0zqPqo9kf4rsl3MIE8/4ryqb4+8zUyszI1vt+MMcaMCwdU7LVchgwFTOWHScyWrZCqTAitCRQoze1dE11qvJr3jwp/PorIe/bvflX74ceWP8LcxFys05l/n574FCmZKRrdb8YYY8aFAyr2WpZlSsOhcyexnBUdjYS//tJ4iynm/Wvm+/p5/xTe9X0Xy9otg5WZvFDouZBz+Pjox4hPj9fofjPGGDMeHFCxtyv06aeZQp85WVvQvH8NULO0o1gPjZfP+xeTnJHn7VuVaYU1HdfA3sJerN+IvIGRh0eK6uqMMcaYunFAxd7IpnZt2DRsIJYzHj1G8pkzWmk1B2sL+I1ojPKq8/5tuIzkHPP+KTQo2QDrO6+Hq7WrWH8Y+1BMqhycGKzR/WaMMWb4OKBib99LtV5zhT7zmvdvk8q8fzdp3r8tuef9U6jmVg0bu2yEl52XWH+e+BzDDg7Do9hHGt1vxhhjho0DKlYg9m3bwtLHRyynXLyItHv3tNZyinn/HK3liednAqJESYWc8/4plHMqJyZVLu9UXqxHpEZg+OHhuBV5S6P7zRhjzHBxQMUKxMTUFK7Dh2llOpr85v3bMKKRct6/A/+FYtb+O/nmd3naecKvix+qu8mLhVKC+ugjo3Ep9JJG95sxxphh4oCKFZhT794wc3YWywn/HERmWJhWW0/M+zeogTgLkGy++AzLjuee90+BcqnWdVqHhiUbivUUSQrGHhuL40HHNbbPjDHGDBMHVKzgB4uNDVwGDpCvSCSI2bxZ663XtirN+1dbub70WAA2X8h/3kF7S3us6rAKbcq0EeuZ0kxMPjkZex/t1cj+MsYYM0wcULG34jJwIEwsLcVy3M5dyEpK1noL9qlXBtNV5v2bsf8O9t8Myff21ubWWNx2Mbr7dldOqjz93HRsvqv9AJExxph+4oCKvRVzd3c49uwhlqWJiYj/Y7dOtOCoFuUxro3qvH83cDqPef8ULEwtMK/FPAysOlC57ecrP6P1jtbodqwb3t//Po49O6aRfWeMMab/OKBib81t+HDlcszGTZBJ8q4DpWlfdaZ5/7zFcmaWTJRTyGvePwVTE1NMbTwVY+uMVW6LSYsRw4ABsQH4/OTnHFQxxhgrEA6o2FuzqlgRdq1bieXMkBAkHjmiE60on/evlnLev5SMLIx8zbx/ivuMqzsOJWxKZNsug/xswalnpoocq8X+i7Hj/g6cfXEWgfGBSM/S7JyGjDHGdJu8kA9jhSj0mXzqtFiO3uAHh65dRXCibYp5/0ZsuIILT6IR+3Levz/GNkcpZ5t875ffPH8UOB19djTP6ygIK21fGqUdSov/y9iXEf+Xsi8lyjSYm/KfF2OMGQv+xGeFYtukCayqVUP6vXtIu3ULqVevwrahvByBtinm/ev/v4u4E5KgnPdv9yfN4WInT6jPq/gnDfMpeqYKIjI1UlxonsCczEzMRFAlAi7F5WXgRRd3G3cx5MgYY8wwcEDFCoV6o9xGDEfIlK+VvVS6ElCpzvv34erzeBqdgseRyRjudwXbRjeBnVXuw57yqChnygQmIqhS/L+w1UJRDDQ4KRgvkl5kvyS+QHRadJ7PnyXLUt4uL5amlqIni4Is1Z4txbKTlZNO9PgxxhgrGBNZfqWljdCBAwfwxRdfQCqV4uuvv8bo0aMLfN+EhAQ4OTkhPj4ejo6Oat+30NBQeHnJ56PTFbLMTDzq0BGS8HCKsOD7z9+wKi+f3kVXPI9JwfurziMiUZ7z1LKSO9YNawRL89y9Q3RW3+qbq/Ek/gl8nXxFkNXep/1rHz9VkoqQpBARONGky4plsZ4UjMSM/PO3XsfOwi5775ZKLxcFXbYWtjAUunhsGzJub25rQxVaTJ8lBf1+54DqJYlEgurVq+Pff/8VDdegQQOcP38ebm5uam1wQ/sQjF63DhELFopl5/794DVrFnTN/bAE9F19AQlp8rMRu9f2wi/968H0ZYX14mzrhIwE0ZOVV+8W/Z+WlVaox3WxclEGWKo9W4qeLkuzvIc2dZGuHtuGitub29pQhWo5oOIhv5cuX76MGjVqoHTp0mK9a9euOHLkCAYMeFkZnOXJ+cMPEbViJaQpKYjfsxclJk6EuYuLTrVWVU9HrB/eCIPXXUJaplTM++dqZ4nZPWsU+7Cao6UjHN0cUc2tWq7rqHOYhgyz9WolvhpaDE0OhUSad0mK2PRYcbkdfTvXdTRcWcK2RLahRJE07yBfL2lbEmamZsXyehljzFgZTEB1+vRpLFiwAFevXhVR6p49e9C7d+9st1mxYoW4TVhYGOrUqYPly5ejcePG4rqQkBBlMEVo+cWLvPNf2Ctmjo5w/vADeT2q9HTE/v47Sowbp3NN1LCcK1YOqo8xm64iSyrDpgvP4GZnhYkdKmltnyiYo+R0utQu8Wr6HIUsaZZIelcNslSDroiUiDyT6GkbXUeXaxHXcl1vbmL+KmFeJVFeEXS5Wbtx/hZjjBlrQJWcnCyCpJEjR+K9997Ldf2OHTswefJkrF69Gk2aNMHSpUvRuXNnPHjwAB4eHlrZZ0PhMmQoYrZsBbKyELt1G9xGjYKplRV0TbuqJbHgg9qYvPOmWF9y7CFc7S0xpKkPdBH1IlHgQ5eGyJ3wn5mVKXqxlAnzOYYWqUhpXiQyibgPXZDH/NbWZtaiV0vZs0U9XSqBFyXMM8YYM9CAiobo6JKfxYsXY8yYMRgxYoRYp8Dq77//xvr16zF16lSUKlUqW48ULSt6r/KSnp4uLqpjrMbKskxpOHbuhIR/DiIrOhrx+/fD5cMPoYveq18GMckZmPv3PbE+Y99tuNhaoHvtUtA3FmYWKOtYVlzykpKZ8iphXiXoCkkOEf8nZuadME95XZSYT5e8OFg4KIOtvGpwGVLCPGOMFZRBJqXTUIrqkF9GRgZsbW2xe/fubMOAw4YNQ1xcHPbt2yeS0qtVq4aTJ08WKCl91qxZmD17dq7t1OPl4OAAYyO5fx9JY+VDfaY+PnBYvw4mprpbZ2nVuRfY5B8uls1NTbCoZwU09lH/yQS6jAKqsNSwbJfw1HDl/+nSwlWDd7JwgqeNJzxtPeX/q1w8rD3EPIrkbPhZbH68GcEpwShjWwZDKgxBi5It1PwqGWOsaBITE1GlShVOSidRUVHIyspCyZIlszUSrd+/f18sm5ubY9GiRWjbtq0omzBlypTXnuE3bdo0MYSo2kPl7e0NT09PozrLT8nLC08bNkCq/1VInz2D46NHsG/dGrpq9vueyDC5he1XnkMilWHaP4HYNqYp6no7635bq4kXvFAZlfO8TpEwr8jXytbTlfgCYclhYugwL/GZ8eLyIOFBngnzHrYesDW3RWBCoHL706SnmHNzDpa0WYIOPh3U+CpZTsZyfOsCbmvDaG87OzvjGvJTh549e4pLQVhZWYkLe8Vt5EgE+19VFvrU5YBKPu9fTcSmZODwnXAx79+IDZex65PmKNifjmFTTZiv61E31/V09iElvedVCoKCrsiUyHwT5sNTwvPcTsEW1QHjgIoxpo+MIqByd3eHmZkZwqkApQpapx4lph72bdrAslw5ZDx9ipSLF5F29y6sq1fX2eY1NzPFsv71MHzDZVx8EiPm/euy9DTVKEWFEgGY1KESutTkX/J5tp2puTJxvREa5bo+IytD9GrRJVuV+ZdBF5V8yCuoehT3SMyfaGXGP1YYY/pFd5Nc1MjS0lLkRB0/fly5jYb1aL1Zs2Za3TdDQjlTrsOHKdepl0rX0bx/a4c2hLeLfOJkGv7LzJLhQVgiPtlyDYduh2p7F/USFRal+RGbl26OvlX64vMGn2Nh64X4vfvvON3/NCo6VxQ9UnlN2fPevvdwPuS8VvabMcZg7AFVUlISbty4IS4kMDBQLAcFBYl1yndau3YtNm7ciHv37mHs2LGi1ILirD+mHk69esHM2VksJxw8iMywPM7L1zE075+VRfZCl4rBqm/33MbVZzGidhVTn/F1xyuH+XIKSgzCx0c/xpRTU8TQIWOM6QODCaj8/f1Rr149cVEEULQ8Y8YMsd6vXz8sXLhQrNetW1cEW4cOHcqVqM6KxtTGBi4DB8pXJBLEbN6sF01Kc/7lJTo5A++vuoBG847hy103ceh2GJLT807GZgVHeVKUgF7ZpbI466+KSxVMaTQF9T3qK29z8OlB9NzbE1vvbRVFThljTJcZZNkEbTDWufzyIomOxqO27SDLyICpvT0qnvwXZvb20GWUO0XDfAX5Y6CJlZtXcEP7aiXRoZoHvJzkw4Ws6Me2VCbFvkf7sPjqYsSlxylvU92tOmY0nYEa7jW4mY3os0TfcVsb11x+BtNDxXSHuZsbnHrJz5aUJiUhbvdu6DpKQKdgSjG1n+L/Yc3LoUsNT9havhoSzJBIcfJBJKbvvY1m80+g2y9nsOToQ9x+ES/KDbDCMzUxRZ9KffBX77/wfqX3ldvvRt/FgL8HYN7FeWLCacYY0zXcQ6Um3EOVXfrjx3jSrbtYtihVChWOHIaJuW6fVEoJ6MuOB+BxRBIqeNhjYvvK6FJTfhZoWmYWLj6JxrF74Th+LwKh8Wl5PoanozXaV/NAh+ol0czXTSS9s8L/qrwecR3fX/weAbEBym001+BXjb7Cu+Xf5TkHC4F7TTSH29q4eqg4oNJwgxvTH+bzjz9B0qlTYrn04kVwfPdd6IM3tTX1Qt0JSRCBFQVYt17E53k76tVqWcldDA22q+oBd3suBVCY9s6UZmLbvW1YcWMFUiWpyu1NvJrguybfibMJmfqOb6Y+3NaaxQGVgeCAKrfki5cQNHy4WLauWRPldu3Uix6Ft/2jDItPw/H74Th2NxznHkeLIcGc6GXX83YWPVcdqpVEJQ97vWgLXWrv0KRQ/Hj5R5x4fkK5jRLaR9YcidG1RsPa3LqY99Qw8Jc8t7WhCuUeKsPAAVXePTmB77+P9LvyiYh9Nm+CbaPcRSAN6Y8yJUOCMwFROP5yaJDOEsxLWVdbEVhRUnuj8q6wMDPedMa3be9Tz0/hh0s/iEmeFbwdvPFtk2/xTul3imkvDQcHVNzWhiqUAyrDwAFV3uL/+gshX00Ry/bt2sF75QoYyx8l1a668TxOBFc0NPgwPCnP2zlYm6NtFQ+Re9WmigecbOSTBxuLwrQ3Df2tubkGG+9szDanYOdynUX5BZovkKmvvVnhcFtrFgdUBoIDqrzJMjPxqGMnSKjAp4kJfP/+G1a+5WGMf5RB0SnypPb74bj0JEZUZc/J3NQEjcq5vhwa9ICPm+HPLFiU9n4U+whzL83F1XD5HJLEzsIOE+pOQP+q/cUUOUx97c3eDre1ZnFAZSA4oMpf9Lr1iFiwQCw79+sHr9mzYOwfgvGpmTj1MFL0Xv17PwIJaXkXC6VcK0pq71jdA3W9XWBmanh5V0Vtbxpa3v94Pxb5L8o2R2A112qY3nQ6apWopaY9NQz8Jc9tbahCecjPMHBAlb+sxEQ8atMW0uRkmFhZoeK/J2Du6gpdpekvnMwsKa48jVGeNfgsOu+q7W52lmhb1UPkXtHZg3ZWhtH7oq72jk+Px5KrS/BHwB/KbTS1zYeVP8Rn9T+Dk5VTkZ/DEHBAxW1tqEI5oDIMHFC9Xvj8HxGzcaNYdv90AkqMHw9dpc0vHOpteRyZhKN3I0Tv1dWgWORVK1RRrZ2Cq/Z6Xq1d3e19I+KGqF31MPahcpurtSu+bPgluvt2N/qzKzmg0hxua83igMpAcED1epkvXuBRp85AVhbMXF1FL5WplW7WZdKlD8HopHScuE/BVQROB0QiJSPvOe1qlnZE+6o0NFgSNUo56lXQUBztLZFKxByAOWtXNfZsjG+bfgtfJ18YK106vg0dt7VmcUBlIDigerMXk79Awj//iGXPObPh0rcvdJGufgiqVms/djcCYQmGUa29ONs7LDkMP13+CceCjim3UaL6iBoj8FHtj4yydpWuHt+GiNtaszigMhAcUL1Z6q3bePrhh2LZ0tcXvgf+gomp7tVf0ocPQUW1dsVUOG+q1t7hZbV2Nx2s1q6J9j4dfFrUrnqR9EK5rYx9GXzT5Bu0LNMSxkQfjm9DwW2tWRxQGQgOqArm2eAhSPH3F8tlVq+CQ5s20DX6+CFY0Grt9cu6iN6rjtVKoqKOVGvXVHvT0N/a/9Ziw50NYkhQoaNPR1G7ytNOPm+jodPH41tfcVtrFgdUBoIDqoJJPHECwePkCem2TZrAZ6MfdI2+fwgmp0tw9lGUCK4o/+qN1dqre4jaV9qq1q7p9n4S90QkrfuHywN7Ymtui/F1x2NgtYEGX7tK349vfcJtrVkcUBkIDqgKRiaV4sm73ZDx9KlYL/fHbtjUqAFdYkgfgopq7fKhwfyrtTtam4sq7dqo1q6N9qYh0wNPDmCh/0LEpMUot1dxqYLpzaajTok6MFSGdHzrOm5rzeKAykBwQFVwsdt3IGyWvLinY/fuKL1QXvRTVxjyh6CiWjtdLgfmX629cXlXUVBUE9XatdneVLtq2bVl2P1wN2SQKWtXvV/5fUyqP8kga1cZ8vGta7itNYsDKgPBAVXBSdPS8KhtO2TFxgJmZqh47CgsdOgD3lg+BBXV2mlo8OSD11drl0+FUxJ1vZ3VXq1dF9r7ZuRNzL04F/dj7merXfVFwy/Qw7eHTuSaGVJ7Gwtua83igMpAcED1diJ/WY6olSvFsuvIkSg55SvoCmP8EHybau10tmB7NVZr15X2pkT13+//jl+v/4oUyavX38izEb5r8h18nQ2jdpWutLcx4LbWLA6oDAQHVG9HEh0teqlkGRkwtbdHxZP/wszeHrrA2D8EKb/oUUQSjr0Mrq4Vc7V2XWvv8ORw/HTlJxx9dlS5jRLVh9cYLmpX2Zjrb1V6XWxvQ8ZtrVkcUBkIDqjeXuj0GYjbtUsse3z9NdxGDIcu4A/B7KKS0sUEzhRcnQmIem21dnHWYLW3q9auq+19JviMqF0VnBSs3FbavrSoXdWqTCvoK11tb0PEba1ZHFAZCA6o3l76kyfijD9iXsoLFY8cgYm59k9Z5w/B11drv/AkWpwx+Lpq7V5O8mrtNDT4pmrtutzeaZI0rL21Futvr89Wu6pD2Q74uvHXelm7Spfb29BwWxtXQKV7Zaq15Pnz52jTpg2qV6+O2rVrY9fLnhNWfKx8fWHfurVYloSEIuHwYW5uHUeBUdsqHpjbuxYuTGuHA5+2wKQOlUTvlKrQ+DRsuRiEERuuoP73R/HxZn/s8n8u5ibUJzQ1zaf1PsUfPf8Q8wAq0FQ2Pff2xMY7G5EpzdTqPjLGdIOJjBImmIhsw8PDUbduXYSFhaFBgwZ4+PAh7OwKdso491AVTvKlywgaNkwsW9eogXK7d2n9jCr+VVnIdotPFUnt1Hv1pmrtNCxoZW6Knf7P8SQyCb4l7EVg1qWm7vac0Efl34F/Y8GVBdlqV1V2qYzpTaejrkdd6AM+vrmtDVWolnuoOKDKR506dXDgwAF4e3urtcELy1A/BOlL6un7HyDt7l2xXnbTRtg1ftUToA2G2taartZO+VYUXL2uWrsChdD0y2714Po6HVQpalctv74cOx/sVNauIu9XkteucrZ2hi7j45vb2lCF8pBfwZw+fRo9evRAqVKlRA/G3r17c91mxYoVKFeuHKytrdGkSRNcvny5UG/K1atXkZWVVeBgihUevZeuI0Yo12M26N5UNOztUTmFLjU9seDDOrj8bQf8MbY5xrapIGpa5UURliw9FqDzzU3FPr9r+h22vrsV1VyrKbf/EfCHGAbc92if+KHAGDMuepNDlZycLHqNKGjKy44dOzB58mTMnDkT165dE7ft3LkzIiIilLeh4byaNWvmuoSEhChvExMTg6FDh+J///ufRl4XAxy7dIa5pzy5N+nff5H+JJCbxYBQIdAGPi74uktVHJ3cGqe+apNvcdD7YYn451aoXgQktUrUwrZu2zC18VTYWchTA2LTY/Hdue8w4vAIPIp9pO1dZIxpkF4O+VGvxp49e9C7d2/lNuqRatSoEX799VexLpVKRQ/Tp59+iqlTpxbocdPT09GxY0eMGTMGQ4YMeeNt6aI65EfPx0N+hRO9bj0iFsinoHHu1w9es+VT02gDD4kUvy5LT+NBWKLKgFl2DX1c8G23aqhX1gX6ICIlAj9f+RmHn746scLcxBzDagzDx3U+1qnaVXx8c1sbqlDOoSp6QJWRkQFbW1vs3r07W5A1bNgwxMXFYd++fW98TIorBw4ciCpVqmDWy3nmXoduM3v27FzbHzx4AAcHh7d+TcZOlpSE+H79gZQUwNISjju2w9RZt3NRWOGdfBSLaX8HKnOnFP/n1LGyC8a+UwpejlZ60dz+Uf749d6vCEl91etd0rokxlUdh2YezbS6b4yxwklMTBSxgVEEVDRkV7p0aZw/fx7Nmr360JoyZQpOnTqFS5cuvfExz549i1atWomSCQqbN29GrVq18rw991CpX/iPPyHGT55D5T5hAkpMGA9t4F/wmnHodiiWHQ/A44gkVPCwx8T2lWBuaoofDt7Dk8jkbBXZR75THuPaVoCjtQV0HdWuWnd7HdbdWpetpEI773ZieNDLXrtJ93x8c1sbqlAt91Bpv4qijmjRooUYJiwoKysrcWHq4zp0CGI2bwayshC7bRvcRo+CqbU1N7GBorP56JLzQ7B1lRL4/XKQSFCPSc4Q5RdWn3osSix83qESBjQuC3MzU52uXTW+7nh0K98Ncy/NxaVQ+Q+6E89P4ELoBYyrMw6Dqg+ChanuB4eMsYJ7q4AqKCgIheHs7FwspQQU3N3dYWZmJupIqaJ1z5fJzkz3WZQqBcfOnZHwzz/IiolB/P79cOnbV9u7xTTMwswUQ5uVQ+96pbHi30fYcPYpMrKkIriavu8O/M4/xTfvVhOTNGu7ZtnrlHMqh7Ud1+Jg4EGRXxWdFo1USSoWXV2EfY/3YUazGajnUU/bu8kYU5O3+plHJQne9lK+fHksXboUxcnS0lIU4jx+/LhyG/U20brqECDTfTlLKMjeoteQGRYa3pvWtRqOf9EaPeqUUm5/HJmMURv9Mei3S7gTEg9dRgHfu77vYn+f/ehfpT9MRLYY8CjuEYYeHIqZ52ciLi1O27vJGNN0QEVBytteqJ7TjBkziryjSUlJuHHjhriQwMBAsazoNaOSCWvXrsXGjRtx7949jB07VpRaGKHyBc10n02tmrBt1EgsZwQGIunUKW3vEtMyb1dbLB9QD3vGNRflFxTOP45G9+Vn8eWumwiLz3tOQV3haOmIb5t+K8osVHerrtz+Z8Cf6LG3B/YE7IFUxj8eGNNnb5WUTr1NhelinzRpEj777DMUxcmTJ9G2bdtc2+lMPr+XicxUMmHBggVi6hiqOfXLL7+IcgqawJXS1SfxxL8IHjdOLNs2bgyfTRuhSZy0C51tb/q4Ong7DD8evI+gmBTldhsLM3zUyhcft/aFraVup4ZmSbOw48EOUW09KTNJub2+R31RMLSSS6VifX4+vjWH29q4ktLfKqCiM+YKg4b+fHx8YMg4oFIfGuZ70q276KEi5Xbvhk3NGtAU/hDUrMK0d7okC5vOP8PyEwFISJMot3s4WOHLTlXwfoMy+RYP1RWRKZFiXsCDTw9mq101pMYQfFL7E9ha2BbL8/LxrTnc1pqlVwEVGT58OFauXCnqPrG3b/DCMrY/zNgdOxE2c6ZYduzWDaUXLdTYcxtbW2tbUdo7NjlDlF7YcvEZJNJXH2VVPR3wXbfqaFHJHbrufMh5zLs4D0GJr0768bLzEiUW2pVtp/bn4+Nbc7itjSugeutzj6k2E+UzKVCuEhXPVCWRvPrFyFhhOPXqCTNXV7GccOgQMlWmB2JMwcXOErN61sCRz1uhU/WS2aawGbzuEkZsuIyA8ESdbrDmpZrjz15/inIKilIKocmhmPjvRHx64lOEJPGxz5g+eOuAKmeH1tatW8X8d6qlCoqzRAIzDlR/ymXAAPlKVhZiNm/R9i4xHeZbwh7/G9oQ2z9qilqlnZTb/30QiS7LzuDbPbcQlfRqqihdY2VmhbF1x2JPrz1o5vXqzOSTz0+i977euYqEMsZ0T5Gr4+U1YpiWpttn3DD94DJwAEwsLcVy3M6dyErU7Z4Gpn1Nfd2wb/w7WNKvDryc5EVhs6QybL0UhDYLToq6VmmZWdBVPo4+WNNxDRa0WgB3G/lwJdWuWnptKfr+1RdXw69qexcZY/kolnLDulxsj+kPczc3OL2cXkianIy4Xbu1vUtMD5iamqBPvTL498s2+KpzFdhZmontSekSLDj8AO0XncK+Gy8gVcm50iX0+dmlfBfs770fA6sOhKmJqbJ21fBDwzH93HTEpsVqezcZY+oIqLZt24Zr164hM5O7oFnxch0+TLlM09LI+JhjBWRtYYbxbSvi5FdtxXQ1ipP+XsSlYuL2G+iz8hyuPH2VrqBrHCwdMK3JNFG7qobbq7Nc9z7aK2pX/fHwD65dxZg+B1QtW7bEzJkz0bBhQ9jb2yMlJUWsr169GhcvXsyWsM5YUVn5+sK+TRuxLAkNRcLhI9yo7K2UcLDC/Pdq4eDEVmhduYRy+83geHy4+gI+2XwVT6NeTcasayiY2vruVnzb5FvYW9iLbfHp8Zh1YRaGHRyGh7EPtb2LjLHClE1QCAgIwNWrV0VPleJCZ/sphvuoQrox4bIJxSf50mUEDZP3VFnXqIFyu3cV67Ayn+qsWZpu79MPI/HDP/fEmYAKFmYmGNK0HD5rXxHOtvK8PV0UlRolalf9E/iPcpuZiRkGVxuMcXXHFah2FR/fmsNtbVxlEwodUOWFpoPx9/fH9evX8cMPP8CYcEBVfOgQffrBh0i7c0esl920EXaNGxfb8/GHoGZpo70pUX2X/3MsOvoQkYmvzv5zsrHAp+0qismZLc2LJcVULS6EXMAPl37A04Snym0lbUtiWuNponbV635w8PGtOdzWxhVQmb7tF5ti7rz8pqb58MMPjS6YYsWLvhyyTZq8fgM3OSsSqqLev3FZnPyyDT5rVxHWFvKPwvjUTMz9+x46LjmFg7dC8zyLWRc0K9UMf/T8A+PrjoelqbxHLTwlHJNOThK1q14kvdD2LjJmdN4qoMrIyICvry+6du2KP/74gwt4Mo1x7NwJ5i9/eSSdPIn0J0+49VmR2VmZY3KnKuKMwPfrl4GiY+dZdArGbr2Gvmsu4Obz7IWLdYWlmSU+qfOJqF31Tql3lNtPBZ9C77298dut35CZxScOMaYpb92nLZVKRSA1cOBAlC5dGlOmTMHDh5wUyYqXiYUFXIcMUa7H+Gl2wmRm2LycbLCobx38NaEFmvrKK/STK09j0WvFOUzcfh3Bsa8mY9YlZR3LYlWHVVjYeiFK2MiT7tOy0rDs2jJ88NcHuBJ2Rdu7yJhRKFSSwLp16xASEoJp06bhyJEjqFatmjj7j6al4aKerLg49/0QpvYvz3Latw+S6GhubKZWNUs74fcxTbF2aEP4utspt++7EYJ2i07hp0P3kZiWqZPD4p3LdRa1qyhBXVG76kn8E4w8PBLfnv0WewL24P3976PbsW7i/2PPjml7txkzKIXOunRzc8OkSZNw48YNXL58GbVr1xbrlBD26aefqncvGaO8F3t7OH/4oWgLWXo6Yrf9zu3CiiU46Vi9JA5/3gqze9aAi618fr0MiRSrTj4WFdc302TMWVKda317S3t83fhr/N7td9Ryr6Xcvv/xfsw4P0OUWKApbAJiA/D5yc85qGJMjdRyGkuDBg2wYsUK7Ny5U2TAr1mzRh0Py1gurkMGA2byytex27ZBytMcsWJiYWaKYc3LicKgH7fyhaWZ/OMyOjkD0/feFnMEnrgfrpOJ69XdqmNz182Y3nQ6HCwccl0vgwwmMMHqm6u1sn+MGaIiB1RhYWH46aefULVqVZGsXrduXezZs0c9e8dYDhalSsGxSxexnBUbi/h9+7mNWLGiUgrT3q2G41+0Rvfar07JfhSRhJF+/hi87hLuhiTo3LtgZmqGvlX6Yn+f/cohwJxBVWB8oFb2jTFDVKiAipLS9+7di549e6Js2bJYu3Ythg4dimfPnmHfvn3o1q2b+veUsZeylVDw84NMqntDL8zweLva4teB9fHnuOaoX9ZZuf3co2h0W34GX+26ifAE3ZsYniZZruhcMdd26qEq71ReK/vEmCEyLewQX//+/WFra4uDBw/i0aNH+OabbzRenI8ZJ5uaNWD7srBnRmAgkk6e0vYuMSNSv6wL/hjbHCsG1oe3q43YRqN+u64Gi/yqJUcfIiVDAl0yts7YPHuo8trOGNNQQEVn9M2YMQMvXrzA9u3b0b59+0I+NWOF5zpiuHI5ZgMX+mSaT1zvVtsLxya3xjfvVoWDtbnYnpqZhWXHA0RgtfPKc1GRXRd08OmAJW2WoIJThVxBFWNMPd5q6pnXVUl/HWdn59eWazcEPPWMZtEw35Nu3UUPFSm3e7fouVIHni5CswyhvWOSM/DL8QBsobP/VIKoal6O+PbdamhRyR26Ytu1bZh/a75YdrN2w77e++Bk5aTt3TJIhnBs65NQfZp6ply5cmJ6Gfq/oBe6/dKlS9XxmhhTMjE1hetw7qViusHVzhKzetbAkc9biZILCvdCE0TS+ki/K3gU8WoyZm1q49kGrcu0FsvRadFismXGWNGZvm2V9KysLPF/QS90exoiZEzdnHr1hJmrvKp1wqFDyAwJ4UZmWuVbwl4UBaXioDVLv/ole+J+BDovPYPv9t5CVNKryZi1NVz5XdPvYG8hL5K77/E+nHtxTqv7xJjRBVTU20Rz+b3t5Zdffim+V8CMlqm1NVwGDpSvZGUhZtNmbe8SY0KzCm7YP74FFvetAy8na7GN8qm2XAwS+VUrTz5CWmaW1lrL084TkxtOVq7PvjAbyZnJWtsfxowuh+rUqcKdTUVDfz4+PtAHKSkpIvH+ww8/xMKFCwt8P86h0g5JTAwetW0nKqeb2tmh4sl/YeaQu5Dh2+C8B80y9PZOzcjCurNPsPLkY6RkvAqiSjvbYEqXKuhRuxRMTV/OyqzB9qaP/tFHRuNy2GWxfUDVAfimyTca2w9jYOjHtq4J1XIOlfzUlAJq3Vo+7m7I5s2bh6ZNm2p7N1gBmbu6wqlXL8Tt3AlpcjLidu2G28hXdaoY0zYbSzNMaFcJfRt5i5IKO648B+Wtv4hLxcTtN7D+bCC+614djcq9mpRZU0N/s5rNwnv73xOTKW+/vx1dynVB/ZL1NbofjBkKtUw9YygCAgJw//59UfGd6Y9syembNkGWqXuT1zLm4WCN+e/VxsGJrdCqcgllg9wMjseHqy/gk81X8TRKs8Nu3o7emFBvgrKEwszzM5Gepd0cL8b0ld4EVKdPn0aPHj1QqlQp8cuKKrXnRPMJ0vCitbU1mjRpIiZtfhtffvkl5s+Xn07M9IeVb3nYt20rliVhYUg4dFjbu8RYvqp4OmDTyMbYOLIxqpR8NTx96E4YOi45he8P3EVcSobGWnBwtcGo7V5bLD9NeIpVN1Zp7LkZMyR6E1AlJyejTp06ImjKy44dOzB58mTMnDkT165dE7ft3LkzIiIilLeheQZr1qyZ6xISEiKmzKlcubK4MP0v9KmLE9Yypqp15RL4+7MWmP9eLbjbW4ltmVkyrDsbiNYLTor/MyRSjcz5N7v5bJibyjNA/O744W70XX6zGCvOpHRdQT1UNAFz7969lduoR6pRo0b49ddfxTqVbPD29sann36KqVOnvvExp02bhi1btsDMzAxJSUnIzMzEF198kW/Jh/T0dHFRTVqj53tT0lphcXLj69Fh/PSDD5F2545YL7txI+yayKen4bbWbXxsA0npEqw59RhrzzxBWuarIKqcmy2mdq2KzjU8xedecbb3qpursPLGSrFc1bUqtnXbBgtTC7U8p7HiY9u4ktINIqDKyMgQ8wru3r07W5A1bNgwxMXFid6nt+Hn54fbt2+/9iy/WbNmYfbs2bm2P3jwAA5FPMuMFU7GiRNI+X6uWDZv2hT283/gpmR6JSIxA6svhODgvZhs2+uWssenLUujuqddsT13pjQTEy5OQGCSfPaB4RWHY6Dvy7IkjBmxxMREVKlSRb1n+emqqKgoUUC0ZMlXFYoJrVOSeXGgHi0aYszZQ+Xp6ck9VFoi69cPj9atgyQkFJKLF+GakgKrCtnnLisI/lWpWdzer9CP61WVfXArOB5z/76LS4HywOpGSBJG7XiAXnVLYUqXqqLkQnG09w+tf8CgfwZBKpNi65Ot6FOjD3ydfQv9XMaOj23DaG87OzvDyqHSpOHDh7+xBpWVlZUInFQvTLtMzM3hOmSocj3Gb6NW94exwqpVxgnbP2qK/w1pAF/3Vx/m+26EoO3Ck/jp0H0kpqn/bNaa7jUxrPowZY/VjPMzkCXVXgFSxvSJQQRU7u7uIvcpPDw823Zapx4jZjycP/wApvbyKTXi9+2DJDpa27vEWKFTGzrV8MThz1thVo/qcLGV5zNRovqqk49FxXUxGXOWehPXx9Udh7IOZcXyzcib2P5gu1ofnzFDZRABlaWlJRo0aIDjx48rt1FSOq03a9ZMq/vGNMvM3h7OffuKZVlGBmK3buO3gOk1CzNTDH+nPE5+1RYftfKFpZn8Yzs6OQPf7b2NrsvO4N/7EWo7s9Xa3Fqc9aew7NoyBCcGq+WxGTNkehNQ0Zl3N27cEBcSGBgoloOCgsQ65TOtXbsWGzduxL179zB27FhRamHECK6abWxchwwGzOXpgbG//w5pWpq2d4mxInOyscA371bDscmt0a32qzyRgIgkjPC7giHrLuNuSIJaWrqhZ0P0q9JPLKdKUsVcf3p4/hJjGqU3AZW/vz/q1asnLooAipYVZQ369esn8p5onepNUbB16NChXInqzPBZeHnBsUsXsZwVG4v4vW93lidjuqysmy1WDKyPP8Y2Q72yzsrtZx9FodvyM5iy+ybCE4r+I2JS/UliEmVyMfQi9j7KXUyZMabnZRN0EU+OrFtS79zB0/c/EMuW5crB95+/YWJasN8PfGaOZnF7Fx59fB/4L1QkqQfHpiq321iY4ePWvmKI0NbSvNDtfSb4DMYdHyeWHSwcsLf3XnjYehRhj40LH9vGVYdKb3qoGHsbNjVqwLaxvLBnxtOnSDp5ihuQGWTieo86pcQw4LSuVeFgLQ+eUjOzsPRYgDgjcKf/c2TRbMyF0LJMS/Tw7SGWEzMTMffiXB76YywfHFAxg+U68lX+XMz69VrdF8aKk7XokaqAU1+1xbBmPjAzlVdVD09Ix5Td/6HH8rNYevQhuiw9jda/Xhf/H7odWqDHntJoClytXcXyv8//xeFnPFcmY3nhgIoZLPtWrWDpKy9KmOLvj9Rbt7W9S4wVK1c7S8zuVRNHPm+FDtVe5Y/eDU3A0uMBuB+WiIwsGR6EJeKTLdcKFFQ5WzvjmybfKNfnX5qP2LTYYnsNjOkrDqiYwaKcKdfh8iKFikmTGTMGFUrY47dhDbFtTBPUKJU754MGAGlqwGXHAwr0eJ18OqF92fZiOSYtBj9f+Vnt+8yYvuOAihk0p169YOYqH65IOHwYmS9eaHuXGNOY5hXc8deEFjB/OQSoik5HehKZXOBcrW+bfAsHS/k8pQeeHMDp4NNq31/G9BkHVMygmVpZwWXQywles7IQs2mztneJMY0yNTVBRQ975A6pgPIq09q8SQnbEviq4VfK9TkX5iApI0lNe8mY/uOAihk8lwEDYGJlJZbjdu9GVmKitneJMY2a1KGSfJgvx3ZHa/O3Omuvd8XeaOYln30iPCUcS64uUfOeMqa/OKBiBs/c1RVOvXuLZWlyMuJ27tL2LjGmUV1qemH14Pqo6uUghv8UgdXlp7FYfPRhgR+Hhv5mNp8JG3Mbsb7z4U5cCbtSTHvNmH7hgIoZBddhKsnpmzdDlpmp1f1hTBtB1cGJrXDm03pYPaSBSEony088ws4rzwv8OKXtS2Ni/YnK9ZnnZ4rpaRgzdhxQMaNg5Vse9u3aiWVJWBgSDh3S9i4xpjWda3hierfqyvVpe27h9MPIAt9/QNUBqOchnwbseeJzrLyxslj2kzF9wgEVMxpuI4Yrl6M3bOCKz8yojWxRHiPeKSeWqZL6uK3XCjy5sqmJKWY1nwVLU0uxvunuJtyO4jpvzLhxQMWMhk3DhrCuWVMsp9+9h5RLl7W9S4xp1XfdqqNzDXkB0KR0CUb6XUFofMGG73ydfDG27lixLJVJMf3cdGRm8VA6M14cUDGjQQm1riq9VFzokxk7mqJmab96qOPtLNbDEtIwYsMVJKYVLDAaVmMYqrpWFcuP4h7ht1u/Fev+MqbLOKBiRsWxc2eYl5LPRp506hTSHz/W9i4xplU2lmZYN6whvF3lZ+7R9DQ0/JeZJX3jfS1MLTCn+RyYmZiJ9f/d+h8CYgtWfZ0xQ8MBFTMqJubmcB06VLke4+en1f1hTBe421vBb0RjONlYiPUzAVH4bs/tAuUZVnOrhpE1R4pliVSCGedmIEuaVez7zJiu4YCKGR3nDz6Aqb29WI7ftx+SqCht7xJjOjH/39qhDWFpJv9a2OH/HCv+fVSg+35c52OUdyovlm9H38aWe1uKdV8Z00UcUDGjY2ZvD+e+fcWyLCMDsdt+1/YuMaYTGpd3xcK+dZTrC488xN7rb57/0srMSgz9KUqGLr++HEEJQcW6r4zpGg6omFFyHTIYMDcXy7HbtkGayoUJGSM965TClC5VlI0xZfd/uPgk+o2NU9ejLgZWk8+bmZ6VLgp+0tl/jBkLDqiYUbLw8oJj165iOSsuDvH79ml7lxjTGWNbV8CAxmXFckaWFB9t8sejiDfPgflZvc9EJXXiH+6P3Q93F/u+MqYrOKBiRku10GeM30bIpPxrmjFFiZHve9VAmyolxHpCmgTDN1xBZGL6axvI1sIWM5rNUK4vvroYYclh3KjMKHBAxYyWdfXqsG3SRCxnPH2KpJMntb1LjOkMczNT/DqwPmqUchTrwbGpGLXxClIyJK+9X/NSzdG7onwy8uTMZHx/8XuelYAZBQ6omFFzGzlCuRy9fr1W94UxXWNvZY71wxvBy8larP8XHI/Pfr8upqp5nS8bfgl3G3exfDr4NP4O/Fsj+8uYNnFApSIwMBBt27ZF9erVUatWLSQnJ2vvnWEaYdeyJSwrVBDLqf5XkXrrFrc8YypKOlpjw4hGcLCSn8Rx7F4E5vx157W9Tk5WTviu6XfK9Z8u/4To1DcntjOmzzigUjF8+HDMmTMHd+/exalTp2BlZaW9d4ZphImpKVyHD1Ou83Q0jOVW1dMRqwY3gLmpvCzCxgvPsO5s4Gubqn3Z9ujk00ksx6XH4cfLP3LTMoPGAdVLd+7cgYWFBVq2bCnWXV1dYf7ytHpm2Jx69oSZm5tYTjh8BNIwTqJlLKcWldwx/71ayvV5/9zDwVuhr22oaU2mid4qcujpIZwIOsENywyW3gRUp0+fRo8ePVCqVClxBsrevXtz3WbFihUoV64crK2t0aRJE1y+fLnAjx8QEAB7e3vxHPXr18cPP/yg5lfAdJWplRVcBg6Qr2RlIWHQYDzp1RsJR45oe9cY0ykfNvTGZ+0riWUa8Zu04wauPovN9/aUR/V1o6+V63MvzkVCRoJG9pUxTdObgIrymerUqSOCprzs2LEDkydPxsyZM3Ht2jVx286dOyMiIkJ5m7p166JmzZq5LiEhIZBIJDhz5gxWrlyJCxcu4OjRo+LCjINFqVKvVqRSpD98iBefTeSgirEcPu9QCe/Vl9eaSpdIMWaTP55G5Z9v2t23O1qUbiGWI1Mjsch/EbcpM0h6E1B17doVc+fORZ8+ffK8fvHixRgzZgxGjBghkspXr14NW1tbrFc5c+vGjRu4fft2rgv1epUuXRoNGzaEt7e3yJ169913xe3zk56ejoSEhGwXpr+oDlU29PPbxARRK1dqa5cY00k0QvDje7XRvIJ8mDwmOQMj/K6I//O7/cxmM2FrbivW/wz4ExdDL2p0nxnTBINIEsrIyMDVq1cxbdo05TZTU1N06NBB9DYVRKNGjURvVmxsLJycnMQQ48cff5zv7efPn4/Zs2fn2h4WFlZsZweGhr4+X4EVXvqTJ7k3ymRiO7d78eM21r/2ntWxND6JS8aT6DQERiVj+G/n8ct7lWBlnvfv9FGVRmH5veViefqZ6VjTbA1szG1g6PjY1v/2Tkx88ywBBhNQRUVFISsrCyVLlsy2ndbv379foMegBHTKm2rVqpU4HbhTp07o3r17vren4I2GGBWoh4p6tzw9PeHoKC+Ep+6DxMvLS+2Py+RSfX3FMJ/omVJh5ugk3lP6lc2KBx/b+tne9AibRruhz8rzooL6f6HJWHA6HMsH1IPpy7MBVY32HI3zMedxNfwqwlLDsCt0F75u/Cq/yhDxsW0Y7W1nZ2dYQ36aGla8deuWGAakIcTXoWFBCpxUL0x/uY8fpxzmU5UVFYXIRYu40jNjeSjjYosNwxvB1tJMrP99KxQ/Hcr7R6ypiSlmN58NKzN5OZqt97biRkT+aRWM6RuDCKjc3d1hZmaG8PDwbNtpnXoXGHsTx06dUPqXZbCqUhmwtIB5CfkcZiT6t3UImz2b5/pjLA81SzvJe6Ve/hZZc/oJNl98lmdb+Tj6YHzd8WJZBhlmnp+JjKy8c68Y0zcGEVBZWlqiQYMGOH78uHKbVCoV682aNdPqvjH9Cqp89+6F8+HDqHTmNDxnzVT2WMVt34GQqVMhk7x+HjPGjFH7aiUxu1dN5frMfbdx/F72H7gKQ6oPQQ23GmL5SfwTrPlvjcb2k7HipDcBVVJSkjjrTnHmHU0TQ8tBQUFinfKZ1q5di40bN+LevXsYO3asSA6ns/4YKwyX/v1R6uefADP5cEbC/r8QPGkSpBn8i5qxnIY09cHHrXzFMk31N2HbddwKjs91O3NTc8x5Zw7MTeQpvOtvrceDmAfcoEzv6U1A5e/vj3r16omLIoCi5RkzZoj1fv36YeHChWKd6k1RsHXo0KFcieqMvQ2nHj1Q5pdlMLGwEOtJx44j+JOxkKakcEMylsPXXaqiW215UnBqZhZGbryC4NjcfyuVXSpjdO3RYlkik2D6uemQSLn3l+k3vQmo2rRpIxKDc178/PyUt5kwYQKePXsmakRdunRJVEtnrKgc2reH95rVMLGRn+KdfP48gkaNRhbXHmMsGzq7b9GHddDQx0Ws09l/IzZcQXxqZq6WGlNrDCo6VxTL92LuYeOdHLXgGNMzehNQMaZNds2bo+y6dTB1cBDrqdev49mw4ZDExPAbw5gKawszrB3aEOXd5aeaB0Qk4ZPNV5EhkWZrJ0szS3HWH539R1beWInA+NdPuMyYLuOAirECsq1fDz4b/WDmIv/1nX7vHp4NHoJMnkyZsWxc7CzhN6IRXO0sxfqFJ9GY+sd/ucqP1C5RG4OrDRbLGdIMzDo/C1JZ9sCLMX3BARVjb8G6enX4bN0C85e5eRlPnuDZoMHIeHlyBGNMzsfNDr8Na6isnP7n9RdYciwgV/NMqDcBZezLiOVrEdew48EObkKmlzigYuwtWfn6wmfrVliULSvWM1+8EEFVekDuLwvGjFn9si5Y2q+usl7uL8cDsNP/ebbb0PQzNPSnsPTqUoQkhWh6VxkrMg6oGCsEyzKl4bNlM6wqyZNqJZGReDZkKFJv3+H2ZExF11pe+Pbdasr1b/68hbMBUdnaqLFXY3xQ+QOxnCJJwZwLc3h2AqZ3OKBirJAsPDxQdtMmWNeUFzTMiotD0LBhSPH35zZlTMWoFuUxrJmPWJZIZRi75SruhyVka6PJDSbDw9ZDLJ8LOYf9j/dzGzK9wgEVY0Vg7uKCsn4bYNuwoViXJicjaPQYJJ05w+3K2Es0ufiMHjXQoZo89zAxXSLKKYQnpCnbyMHSATOayusKkp+v/Iyo1Ow9WYzpMg6oGCsiM3t7eK/9H+xathTrsrQ0PB83HgmHj3DbMqb4OzE1wS8D6qJ2GSexHhqfJoKqpPRXBT1be7fGu+XfFcsJGQn44dIP3H5Mb3BAxZg6/pBsbOC94lc4dO4s35CZiReff464PXu5fRl7ydbSHOuGNUIZF3mR3LuhCRi/9RokWa9KJXzd+Gu4WMlLkxx9dlRcGNMHHFAxpiYmlpYovWghnPr0kW+QShE6bRpitmzlNmbspRIOVqJGlaO1fC6/Uw8jMX3fHWUSuqu1K6Y1maZsr3kX5yE+PfecgIzpGg6oGFMjE3NzeM2bC5chQ5TbwufORdSa/3E7M/ZSRQ8H/G9oQ1iayb+Cfr8chFWnHivbp0u5Lmjj3UYsR6dFi3wqxnQdB1SMqZmJqSlKfjMNbmM/UW6LXLIEEYsW8angjL3U1NcNCz6srWyPnw89wL4bL+R/QyYm+K7Jd7C3sBfrdMbf2Rdnue2YTuOAirFiQF8IHhMnwuPLL5Tbotf+hrA5cyCT8tQajJFedUvjq85VlI3x1a7/cOlJtFguaVcSXzb8Unkd1aZKzkzmhmM6iwMqxoqR2+jR8Jw1kyIssR73+3aETJ0KmeTVmU2MGbNxbSqgfyNvsZyRJcVHm6/iUUSSWH+v0nto4tlELIcmh4oq6ozpKg6oGCtmLv37o9TPPwFmZmI9Yf9fCJ40CdKMDG57ZvSoN/f73jXRqnIJ0RbxqZkY4XcZkYnp4rqZzWeK6WnI9gfbcTX8qtG3GdNNHFAxpgFOPXqgzC/LYGJhIdaTjh1H8CdjIU1J4fZnRs/CzBQrBtZDVU8H0RbPY1IxepM/UjOy4O3gjU/rfapso5nnZyJN8qogKGO6ggMqxjTEoX17eK9ZDRMb+a/t5PPnETRqNLISsk/BwZgxcrC2wIYRjeDpaC3Wbz6Pw8Tt15EllWFg1YGoXUKewP4s4RlW3Vyl5b1lLDcOqBjTILvmzVF23TqYOsh/iadev45nw4ZDEhPD7wMzel5ONiKosreS16g6cjccc/++CzNTM8xpPgcWpvIe3o13NuJONE9EznQLB1SMaZht/Xrw2egHMxd5Nej0e/fwbPAQZIaF8XvBjF41L0esHFRfTFVDNpx7ivVnA1HBuQI+rv2x2JYly8KMczOQKc00+vZiuoMDKsa0wLp6dfhs3QLzkvLJYjOePMGzQYORERTE7wczepSgPr9PLWU7fP/3XRy6HYaRtUaisktlse1h7EOsv7Xe6NuK6Q4OqBjTEitfX/hs3QoLb/kp45kvXoigKj0ggN8TZvT6NvLGp+0qinagWWkon+p2cBLmvDMHZibyM2bX/LcGj+NeVVhnTJs4oGJMiyzLlIbPli2wrFhBrEsiI/FsyFCk3ub8EMYmd6yMPvVKi4ZIl0gxeqM/7FEOw2oME9toyG/G+RnIkmZxYzGt44BKxZIlS1CjRg1Ur14dn332GU8TwjTCoqQHfDZvhnWNGmI9Ky4OQcOGIcXfn98BZtSoDtWP79dCU19XsR6dnIERG65gQKVR8HH0Edv+i/wP2+5v0/KeMsYBlVJkZCR+/fVXXL16Fbdu3RL/X7x4kY8RphHmLi4ou9EPNg0biHVpcjKCRo9B0pkz/A4wo2ZlboY1gxuiood8Xr8nUcn4dNttfNt4pvI2y68vx/PE51rcS8Y4oMpGIpEgLS0NmZmZ4uLh4cHHCNMYM3t7lF27FnYtW4p1WVoano8bj4TDR/hdYEbNydYCG4Y3gru9lVi/8jQW206bo1+V/mI9VZKK2Rdm86gC0yq9GfI7ffo0evTogVKlSolu4L179+a6zYoVK1CuXDlYW1ujSZMmuHz5coEfv0SJEvjyyy9RtmxZ8RwdOnRAhQryvBbGNMXUxgbeK36FQ+fO8g2ZmXjx+eeI25P7eGfMmHi72mL98IawsZAnpP91MwSIeRdedl5i/VLoJfwZ8KeW95IZM70JqJKTk1GnTh0RNOVlx44dmDx5MmbOnIlr166J23bu3BkRERHK29StWxc1a9bMdQkJCUFsbCwOHDiAp0+f4sWLFzh//rwI4hjTNBNLS5RetBBOffrIN0ilCJ02DTFbtvKbwYxa7TLOWD6gHl6WqMJvp0PQ0uUT5fUL/RciPDlcezvIjJreBFRdu3bF3Llz0UfxJZPD4sWLMWbMGIwYMUIkla9evRq2trZYv/5VnZIbN27g9u3buS7UI3Xs2DFUrFgRrq6usLGxQbdu3V6bQ5Weno6EhIRsF8bUxcTcHF7z5sJlyBDltvC5cxG15n/cyMyodaheErN6yk/gIH7HrdHYvaNYTspMwtxLc3noj2mFvL6/nsvIyBBJ5NOmTVNuMzU1FcN2Fy5cKNBjeHt7i14pyqGysLDAyZMn8dFHH+V7+/nz52P27Nm5toeFhYnetOIQGhpaLI/LdLetZSOGwwoypG/eItYjlyxBQlgorMeMEUPfhkJX2ttY6Ht7dyxnhXv1PfD7tQgx19/5y+/ApfIVJEricPL5SWy/sR1tPNtAF+h7W+ub0GJo78TEROMJqKKiopCVlYWSL6tOK9D6/fv3C/QYTZs2xbvvvot69eqJYKx9+/bo2bNnvren4I2GGBWoh4qCMk9PTzg6OqI4DhIvL3muACteOtfW336L6JIlEbFwkVhN/307aHplz+nTYWKqN53M+tPeBs5Q2nveB56Iz7yGf26FITXdGrbhvQE3P3Hd6oer0aVaF7hYy6d30hZDaWt9EVpM7W1nZ1eg2+n/p7EazZs3D/fu3cOdO3fwyy+/vLYHwMrKSgROqhfGiovb6NHwnDWTCvOI9bjft4u8KplEwo3OjJKpqQkW962L+mWdxXp0RFVYZ9QVyzFpMfjx8o9a3kNmbAwioHJ3d4eZmRnCw7MnI9I69RgxZghc+vdHqZ9/AszkZznF79svzgCUZmRoe9cY0wprCzOsHdoQPm62Yj3qaTeYyeTL/wT+g1PPT/E7wzTGIAIqS0tLNGjQAMePH1duk0qlYr1Zs2Za3TfG1MmpRw+U+WUZTCwsxHri0WMI/mQspCkp3NDMKLnZW8FvRGO42FpAluWApNBuyuvmXJyDxIyC5b8wZjQBVVJSkjhLjy4kMDBQLAcFBYl1ymdau3YtNm7cKIbtxo4dK5LD6aw/xgyJQ/v28F6zGiY2lEkFJJ8/L6qqZ/GZpsxIlXe3w2/DGsLS3BSS+PqQJFUW2yNSIrD46mJt7x4zEnoTUPn7+4uEcbooAihanjFjhljv168fFi5cKNap3hQFW4cOHcqVqM6YIbBr3hxl162DqYODWE+9dg3Phg+HJCZG27vGmFY08HHFkr6UQ2WCtNA+kEktxfbdD3fjcmjBizwzZvABVZs2bURtkZwXPz/5WR1kwoQJePbsmagRdenSJVEtnTFDZVu/Hnw2+sHMRX4mU/rde3g2eAgyc+QSMmYsutX2wjfvVoVM4oL0iC7K7bMuzBLT0zBWnPQmoGKM5WZdvTp8tm6B+cue2IwnT/Bs4CBkvBwKZ8zYjGnpiyFNfZAZ2xSSlHJiG02cvOJ63rNsMKYuHFAxpuesfH3hs3UrLLy9xXrmixd4Nmgw0gMCtL1rjGkclbuZ2aM62lf1RFro+5BJ5eUWN9/djFuRt/gdYcWGAyrGDIBlmdLw2bIFlhXlE3pLIiPxbMhQpN6+o+1dY0zjzM1MsXxgPdQsUREZUR3ENimk+O7cdGRkcZkRVjw4oGLMQFiU9IDP5s2wriGf5ywrLg5Bw4Yhxd9f27vGmMbZWppj3fCGcM/qhKzU0mLbk/jH+N/NtfxusGLBARVjBsTcxQVlN/rBpmEDsS5NThYlFZLOnNH2rjGmcR4O1tg4oinMYvpBJpN/3f3v1lo8iHnA7wZTOw6oGDMwZvb2KLt2LexathTrsrQ0PB83HgmHj2h71xjTuEolHbCmXw9kxcgnS5YhC+MOT4VEytM2MfXigIoxA2RqYwPvFb/CoVMn+YbMTDFNTdyevdreNcY0rnkFd8xuNRFZ6SXEekTGI3xznM/6Y+rFARVjBsrE0hKlFy+CU58+8g1SqZhQOWbLVm3vGmMa17ehL/qUmQyZTD7B+D/Bfjhw9z9+J5jacEDFmAEzMTeH17y5cBk8WLktfO5cRK35n1b3izFtmNu1G8pZyHttTUwlmHZmBh5FJPCbwdSCAyrGDJyJqSlKfvsN3D75WLktcskSRCxaJGYbYMyYalRt+2AWLGXu8g3WjzFoxzJEJ6Vre9eYAeCAijEj+SLxmDQJHl9+odwWvfY3hM2ZA5lUqtV9Y0yTHK3ssaDN98r1ZLt9GLb5CNIys/iNYEXCARVjRsRt9Gh4zppJEZZYj/t9u8irkkn4jCdmPNqVa4EuPj3FsolZOh5LN2Li79eRJeUeW1Z4HFAxZmRc+vdHqZ9/AszMxHr8vv3iDEBpBleQZsZjevOv4WLpJpbN7R/gePAh/PDPPW3vFtNjHFAxZoScevRAmV+WwcTCQqwnHj2G4E/GQpqSou1dY0wjHC0dMeudGcp165J/Yf2F/+B3LpDfAVYoHFAxZqQc2reH95rVMLGxEevJ58+LqupZCXzWEzMO7cq2Q5dyXcSyiXkKrDz/wuwDd3HkTpi2d43pIQ6oGDNids2bo+y6dTB1cBDrqdeu4dnw4ZDExGh71xjTiKmNp8LZylksWzj+BzO7O/hs+3XcfB7H7wB7KxxQMWbkbOvXg89GP5i5uIj19Lv38GzwEGSGh2t71xgrdm42bvi68dfKdSuvvUjLSsKojVfwPIaHwFnBcUDFGIN19erw2boF5iVLitbIePIEzwYNRsbz59w6zOB1K98Nrcq0Esum5omwKvkPopIyMHzDZcSnZGp795ie4ICKMSZY+frCZ+tWWHh7i/XM4GA8GzgI6Y8ecQsxg6/TNr3pdNhZ2Il1S2d/mNkF4HFkMj7a7I90CdeoYm/GARVjTMmyTGn4bNkCy4oVxLokMlIM/6XevsOtxAyap50nJjeYrFy3LbUHMEnHpcAYTNn9H6Rco4q9AQdUjLFsLEp6wGfzZljXqCHWs+LiEDR8OFL8/bmlmEH7oPIHaOTZSL5iHgNbzyNicd+NECw6+kC7O8d0HgdUjLFczF1cUHajH2waNhDr0qQkUVIh6cxZbi1msExNTDGr2SxYm1mLdXPn8zCzfSqWV/z7GL9fDtLyHjJdxgEVYyxPZvb2KLt2LexathTrsrQ0PB83DgmH5b/aGTNEZR3LYkK9CWJZBhnKVDwAmMgT07/bexsnH0RoeQ+ZrjLKgKpPnz5wcXHBBx98kOu6AwcOoEqVKqhUqRJ+++03rewfY7rC1MYG3it+hUOnTvINmZlimpq4PXu1vWuMFZtB1QahpltNsRyTGYxGda+JZZrrb/zWa7gbwsVvWW5GGVBNnDgRmzZtyrVdIpFg8uTJOHHiBK5fv44FCxYgOjpaK/vImK4wsbRE6cWL4NSnj3yDVComVI7ZslXbu8ZYsTA3Ncecd+aI/0lA+n60qJ4ulpMzsjDS7wpC41O59Vk2RhlQtWnTBg4vK0Orunz5MmrUqIHSpUvD3t4eXbt2xZEjPLzBmIm5ObzmzYXL4MHKxgifOxdRa/7HjcMMUiWXSvio1kdiOUuWhTTn31HHW/69EZaQhhEbriAxjWtUMR0OqE6fPo0ePXqgVKlSojbI3r25hxZWrFiBcuXKwdraGk2aNBGBkDqEhISIYEqBll+8eKGWx2ZM35mYmqLkt9/A7ZOPldsilyxBxKJFkMlkWt03xorD6FqjUdG5olh+EHsf7ZrcRVlXW7F+PywR47ZeQ2aWlBuf6WZAlZycjDp16oigKS87duwQw3IzZ87EtWvXxG07d+6MiIhXiYJ169ZFzZo1c10oYGKMFR79yPGYNAkeX36h3Ba99jeEzZkDmZS/WJhhsTCzwPfvfC/O/iOb7q3F3A9LwNnWQqyfCYjCt3tu8Q8KJsgHiHUIDbPRJT+LFy/GmDFjMGLECLG+evVq/P3331i/fj2mTp0qtt24caNQz029Yqo9UrTcuHHjPG+bnp4uLgoJCZykyIyH2+jRMLWzQ9ic7wGZDHG/b4csJQVe8+aJ4UHGDEVN95oYWn0o/O74IUOagd/u/4w1QxZjyLoryJBIsdM/GN4utvi0fSVt7yrTMr365MvIyMDVq1cxbdo05TZTU1N06NABFy5cKPLjU/B0+/ZtEUg5OTnh4MGDmD59ep63nT9/PmbPnp1re1hYmOhlKw6hoaHF8riM27pQ2rSBbWYmUn78SSSqx+/bj5SYGNh+951IZH8bfGxrFrf323nP8z0cCTyCkJQQXI+4jmuuuzC9YytMPyivUbXo6EPYm6ajS1U3bmsDPLYTExMNL6CKiopCVlYWSr6cwFWB1u/fv1/gx6EA7ObNmyLwKVOmDHbt2oVmzZrB3NwcixYtQtu2bSGVSjFlyhS4ueX+AyEU1NHQo2oPlbe3Nzw9PeHo6IjiOEi8vLzU/riM27pIhg5FIvXsfj4ZssxMZJ45C8nsOSjz63KY2spzTd6Ej23N4vYunLkt52Lk4ZFiecOjDdjTqyeSURU/HpR/9/xwLAhVynqieQV3bmsDO7bt7ORzPOpdDpUmHDt2DJGRkUhJSUFwcLAIphR69uyJhw8f4tGjR/joI/kZHnmxsrISgZPqhTFj5NChA8qsXgUTGxuxnnz+vKiqnsXD4MyA0JQ0fSv3FcupklTMPj8bH7Usj0FNyoptmVkyfLz5KgLCC9abwQyPXgVU7u7uMDMzQ3h4eLbttE49Q4wx7bB/5x2UXbcOpi/LkaReu4Znw4dDEhPDbwkzGJ83+BwlbeUjJBdCL2D/k/2Y3bMG2lYpIbYlpkkwfMMVRCSmaXlPmTboVUBlaWmJBg0a4Pjx48ptNDRH66q9TIwxzbOtXw8+G/1g5uIi1tPv3sOzwUOQmeMHEGP6yt7SHjOazVCu/3zlZ8SmR+PXgfVRo5R8lOJFXCpG+fkjJUOixT1l2qBzAVVSUpI4S09xpl5gYKBYDgqST0pJeUtr167Fxo0bce/ePYwdO1bkQinO+mOMaY919erw2boF5i/zHDOePMGzQYOR8fw5vy3MILQq0wrdfLuJ5cSMRMy7NA+2lmZYP7wRSjnJJ1W+9SIejecdQ+tfr6PL0tM4dJtPKDIGOhdQ+fv7o169euKiCKBoecYM+a+Cfv36YeHChWKd6k1RsHXo0KFcieqMMe2w8vWFz9atsPD2FuuZwcF4NnAQ0h894reEGYSvG30NV2tXsXw86DiOPjuKko7W2DCiMazN5V+rSelZyMiS4UFYIj7Zco2DKiNgIuMSx2pBZ/lRqYX4+Hg+y0/P8VlQ6pEZHoGgUSOR8eixWDdzdob3b7/BpmYNbm8t4uNbPQ49PYSvTn0llim42tdrH5ytndHy5xN4HpN7nj8zUxNU83KAp6M1PJ2sX/5vAy8naxGM0f92Vnp14r3RHNsJBfx+53ePMVYsLEp6wGfzZjwfPQZpd+4gKy4OQcOHw3v1Ktg2bMitzvRaZ5/O+Mf7H/z7/F/EpMWIfKofWv6AiIRXBZ9VZUlluP0iQVzy42Btrgy4vPIJuqhKO81YwHQPB1SMseL7gHFxQdmNfnj+ySdI9b8KaVKSKKlQZvly2LdswS3P9BYFNd81/Q7+Yf5IzEzEX0/+QtfyXVHe3U4M8+Wc3dLc1ERso8AqP3SWYGJaEgIikvK9jZW5qbKHSwRaFHy9DLwUgZi7vZXoEWOaxQEVY6xYmdnbo+zatQj+bCKSz5yBLC0Nz8eNQ+lFC+HYqRO3PtNbHrYe+KrRV5hxXp7jO+fiHIxvuwqTfn8A6kSiOcMV/9OZgB2rl0RUUjrC4tMQGp+GsPhUhCXQeqpYD0+Qb0+X5D8vJl33LDpFXPJDwZSHg5XK0OLL4EsEYfIeLw9HK1iZmxVLuxgrzqFSE86hMhycY1I8ZBkZePHlV0g8ckS+wcREnA0oiY4Wiezu48dxgKUBfHyrF6Uhf3T0I1wMvSjW+1Xph4b2o7DseAAeRyShgoc9JravjC41PQv8eHEpmQhLSHsVeCXkDr6oN6uo3Ows8w26xHYna9jrUV5XqJZzqDig0nCDFxZ/CGoOt3XxkUkkCJ0+A/F79mS/4uXP+NK/LOOgqpjx8a1+wYnBeG//e6KCOtnQeQMaejYs1rZOTpcogy5xEb1bqQiLT0dYAv2fhqikjCI/j4OVuTK4UibU5wi+XHQkryuUk9IZY8bCxNwcXvPmIvHffyGNi3t1xcuxkaiVKzmgYnqnjEMZfFbvM/x05SexPuvCLOzusbtYn5POCKxQwl5c8pMuyRJJ8qqB16uhRXnQFZ6Y/vq8rnQJEiNen9dlSXldjjmT6bMHXSUcDD+vS3/68hhjBsHE1BSylDzyP2QyZDwJ1MYuMVZkA6oOEKUUbkbexLOEZ1h5cyUGlBqg1ZalHClvV1txyQ8FU9FJ6SpDi7mDLtqelpl/XleGRIqgmBRxyQ8FUyXs5XldqmctvkqwtxF5XdYW+pvXxQEVY0zjLMuXR/rDh/KeKQUTE1j6+vK7wfSSmakZ5jSfgw/++gCZ0kxsuL0Bm+9shq+zL8bWGYsOPh2gi0QCuyMlqVujzmvyuuJT5Xld8mR6lR6vhDSEiyAsFQmvyeuiwE0EbAlpuPGaiRNcKa9LdWjR8eWZjCqBmIO1Rbb7UCX6pccC8CQyCb4lAjCpQyV0qVk8Q62vwzlUasI5VIaDc0yKX8KRI3jx2cRXp0ApcqiW/wLHjh01sAfGi4/v4jXl9BQcDDyoXDcBlUuQYUmbJTobVKlLSoYk29Bi7h4vyuvKu07X26BEeUXPFgVqF55EK6+jQUX6mbZ6cH21BVVc2JMxprNEuYRflomcqfQnT16e5Teegymm9x7FZp9iiYIpCqpW31xt8AGVraU5fEvYi8vrhgcjEnMHWoqhRZHXlZAGyWvyupLSJXgUkSQuOdG96PcZnWWp6V4qHvJjjGktqKIL95gwQ0L5UzlRUBUYz/mBigT2Mi624pIfqVSGqOT0HGcwKoYWX53RmF9eF3V6P4lMhqZxQMUYY4ypSTmncgiIDRBBlAL1UJV3Ks9tXECmojCptbjULpN/XldCqgS9V57F06iUbJXpqYfKt4QdNE0+LTZjjDHGiowS0BXDfKo5VLSdqQ/VvXKytcDXXaoqh/nk2+U9VFRMVdM4oGKMMcbUhPKkKAG9sktlWJhaiP+XtlmK9j7tuY2LAeVJUQJ6VU8HWJqZiP9XD25Q4Mr06sRDfowxxpiagyq6cH6g5oIqumi7vbmHijHGGGOsiDigYowxxhgrIg6oGGOMMcaKiAMqxhhjjLEi4oCKMcYYY6yIOKBijDHGGCsiDqgYY4wxxoqIAyrGGGOMsSLigIoxxhhjrIi4Urqa0ESNJCEhAcUhMTERdnaan+zRGHFbc3sbMj6+ua0NVWIxfU8qvtcV3/P54YBKjW8k8fb2VtdDMsYYY0yHvuednJzyvd5E9qaQixWIVCpFSEgIHBwcxCzY6o6OKVB7/vw5HB0d+R0pRtzWmsXtze1tqPjYNpz2pjCJgqlSpUrB1DT/TCnuoVITauQyZcqgONFBwgGVZnBbaxa3N7e3oeJj2zDa+3U9UwqclM4YY4wxVkQcUDHGGGOMFREHVHrAysoKM2fOFP8zbmtDwsc2t7eh4mPb+Nqbk9IZY4wxxoqIe6gYY4wxxoqIAyrGGGOMsSLigIoxxhhjrIg4oNJxK1asQLly5WBtbY0mTZrg8uXL2t4lg3X69Gn06NFDFG+j4qx79+7V9i4ZrPnz56NRo0aiEK6Hhwd69+6NBw8eaHu3DNKqVatQu3ZtZX2eZs2a4eDBg9reLaPw448/is+SSZMmaXtXDNKsWbNE+6peqlatqrX94YBKh+3YsQOTJ08WZy5cu3YNderUQefOnREREaHtXTNIycnJoo0piGXF69SpUxg/fjwuXryIo0ePIjMzE506dRLvAVMvKjhMX+xXr16Fv78/2rVrh169euHOnTvc1MXoypUrWLNmjQhmWfGpUaMGQkNDlZezZ89CW/gsPx1GPVL0K/7XX39VTm9DpfU//fRTTJ06Vdu7Z9Dol86ePXtEzwkrfpGRkaKnigKtVq1acZMXM1dXVyxYsACjRo3iti4GSUlJqF+/PlauXIm5c+eibt26WLp0Kbd1MfRQ0UjCjRs3oAu4h0pHZWRkiF+UHTp0yDa9Da1fuHBBq/vGmLrFx8crv+hZ8cnKysL27dtFTyAN/bHiQb2v3bp1y/b5zYpHQECASNPw9fXFoEGDEBQUBG3hufx0VFRUlPjwK1myZLbttH7//n2t7Rdj6kY9r5Rj8s4776BmzZrcwMXg1q1bIoBKS0uDvb296H2tXr06t3UxoICVUjRoyI8V/yiOn58fqlSpIob7Zs+ejZYtW+L27dsiP1PTOKBijGn91zx9AGoz98HQ0RcODYtQT+Du3bsxbNgwMbzKQZV6PX/+HBMnThR5gXQiESteXbt2VS5TrhoFWD4+Pti5c6dWhrM5oNJR7u7uMDMzQ3h4eLbttO7p6am1/WJMnSZMmIADBw6IMywpeZoVD0tLS1SsWFEsN2jQQPSeLFu2TCRNM/WhNA06aYjypxRopIGOb8qFTU9PF5/rrHg4OzujcuXKePToEbSBc6h0+AOQPviOHz+ebWiE1jn3gek7mUwmgikaejpx4gTKly+v7V0yKvRZQl/uTL3at28vhlepN1BxadiwocjtoWUOpor/ZIDHjx/Dy8sL2sA9VDqMSiZQ1zz9QTZu3FicJULJpCNGjND2rhnsH6PqL5vAwEDxIUiJ0mXLltXqvhniMN+2bduwb98+kesQFhYmtjs5OcHGxkbbu2dQpk2bJoZG6BhOTEwU7X7y5EkcPnxY27tmcOhYzpkHaGdnBzc3N84PLAZffvmlqB1Iw3whISGixBAFrQMGDIA2cEClw/r16ydOJ58xY4b4wqFTbw8dOpQrUZ2pB9Xoadu2bbaAllBQS4mPTL3FJkmbNm2ybd+wYQOGDx/OTa1GNAQ1dOhQkbRLASvlmlAw1bFjR25npteCg4NF8BQdHY0SJUqgRYsWorYdLWsD16FijDHGGCsizqFijDHGGCsiDqgYY4wxxoqIAyrGGGOMsSLigIoxxhhjrIg4oGKMMcYYKyIOqBhjjDHGiogDKsYYY4yxIuKAijHGGGOsiDigYoyxQqDq+TQZq66hSvO9e/fW9m4wZnQ4oGKMFcuXuomJCX788cds2/fu3Su2F5dZs2aJKZo0NTXUw4cPtfLc5OnTp6Itab5JVcuWLeOpkhjTAg6oGGPFwtraGj/99BNiY2MNsoVpEmcPDw+1P25GRkaR7k/z9elizxljho4DKsZYsejQoQM8PT0xf/78197u7NmzaNmypQhQvL298dlnnyE5OVlc9+uvv6JmzZq5erhWr16d7Xm+++470Ssze/Zs3Lx5U9yGLopJrYOCgtCrVy/Y29vD0dERffv2RXh4eK7epc2bN6NcuXIiKOnfvz8SExMLNOT3uueOi4vD6NGjxYSt9Nzt2rUTt8v53L/99hvKly8vAlFCE6HTZK/0HG5ubujevTseP36svB/dltSrV088n2Ki6ZxDfunp6aJNKfijx6bHvHLlivL6kydPivsfP34cDRs2hK2tLZo3b44HDx689n1jjGXHARVjrFiYmZnhhx9+wPLly8Ws8HmhAKFLly54//338d9//2HHjh0iwJowYYK4vnXr1rh79y4iIyPF+qlTp+Du7i6CAJKZmYkLFy6IYIKG4L744gvUqFEDoaGh4kLbpFKpCKZiYmLE/Y8ePYonT56I63LuCwVsBw4cEBe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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = utils.residual_plot(newton_grad_norms, colors=utils.MAT_COLORS, markers=True, stagger=False,\n", " xlabel=\"Newton iteration\", ylabel=r\"$\\|\\nabla E\\|$\",\n", " title=\"Newton convergence, far handle target\")\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"newton_convergence.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"004_newton_convergence.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1be55df5", "metadata": {}, "source": [ "## A cantilever beam: pin the left edge, swing the whole right edge\n", "\n", "The handle is now **every vertex on the right edge**. We **rotate those target points about the origin**,\n", "so the orange handles swing up and down in a wide arc: starting from rest, the angle sweeps to about\n", "$\\pm 120^\\circ$ and back, whipping the beam through large bends. Targets are marked with ×. Near the\n", "deepest folds Newton needs up to 40 iterations, so we count them per pose; the printed line confirms that\n", "none of the 48 solves stopped at the `NEWTON_ITERS` cap before its step fell below `NEWTON_TOL`." ] }, { "cell_type": "code", "execution_count": 9, "id": "1e0c60e8", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:28.141654Z", "iopub.status.busy": "2026-09-24T03:44:28.141563Z", "iopub.status.idle": "2026-09-24T03:44:29.765945Z", "shell.execute_reply": "2026-09-24T03:44:29.765441Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Newton iterations per pose: 1 to 40 (cap 100); 0 of 48 poses stopped at the cap\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "angles = np.deg2rad(SWING_DEG) * np.sin(np.linspace(0, 2 * np.pi, N_FRAMES))\n", "\n", "beam_states, beam_targets, beam_iters = [], [], []\n", "n_capped = 0\n", "U = X_beam.copy()\n", "for th in angles:\n", " R = np.array([[np.cos(th), -np.sin(th)], [np.sin(th), np.cos(th)]])\n", " targets = X_beam[beam_handle] @ R.T # right edge rotated by th about the origin\n", " energy_func, gradient_func, hessian_func = elastic_pose_system(\n", " X_beam, T_beam, POSE_MATERIAL, beam_pin, X_beam[beam_pin], beam_handle, targets)\n", " x, info = simkit.solvers.newton_solver(U.reshape(-1, 1), energy_func, gradient_func, hessian_func,\n", " tolerance=NEWTON_TOL, max_iter=NEWTON_ITERS, do_line_search=True,\n", " return_info=True)\n", " last_step = np.linalg.norm(info[\"alphas\"][-1] * info[\"dx\"][-1])\n", " n_capped += int(last_step >= NEWTON_TOL) # stopped by the cap, not the tolerance\n", " beam_iters.append(info[\"iters\"] + 1)\n", " U = x.reshape(-1, 2)\n", " beam_states.append(U)\n", " beam_targets.append(targets)\n", "print(f\"Newton iterations per pose: {min(beam_iters)} to {max(beam_iters)} (cap {NEWTON_ITERS}); \"\n", " f\"{n_capped} of {N_FRAMES} poses stopped at the cap\")\n", "\n", "fig, anim = utils.animate_mesh(beam_states, T_beam, lims=((-1.8, 1.8), (-1.8, 1.8)),\n", " title=\"Cantilever: right edge swung in an arc about the origin\",\n", " pin_pts=X_beam[beam_pin], handle_traj=[s[beam_handle] for s in beam_states],\n", " target_pts=beam_targets, fps=FPS, figsize=(6, 6))\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"beam.mp4\"), fps=FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"004_beam.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "c29dde53", "metadata": {}, "source": [ "The beam's elastic energy against the swing angle (left): zero at rest, nearly symmetric in $\\pm\\theta$, and\n", "the same on the way out and back, so each pose is a well-defined minimum rather than a record of the path.\n", "Right: the worst pin and handle residuals per frame, below $10^{-6}$ and nearly equal (they vanish at the\n", "rest frames, hence the drops at both ends), since the total forces of the two spring sets again balance." ] }, { "cell_type": "code", "execution_count": 10, "id": "f8c63f70", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:29.767805Z", "iopub.status.busy": "2026-09-24T03:44:29.767678Z", "iopub.status.idle": "2026-09-24T03:44:29.966410Z", "shell.execute_reply": "2026-09-24T03:44:29.966044Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu_beam = np.full((len(T_beam), 1), MU)\n", "lam_beam = np.full((len(T_beam), 1), LAM)\n", "beam_elastic = [simkit.energies.elastic_energy(X_beam, T_beam, mu_beam, lam_beam, POSE_MATERIAL, U) for U in beam_states]\n", "beam_residuals = {\n", " \"handle\": [np.linalg.norm(U[beam_handle] - tg, axis=1).max() for U, tg in zip(beam_states, beam_targets)],\n", " \"pin\": [np.linalg.norm(U[beam_pin] - X_beam[beam_pin], axis=1).max() for U in beam_states],\n", "}\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 3.6))\n", "utils.line_plot(np.rad2deg(angles), {\"Neo-Hookean\": beam_elastic}, xlabel=r\"swing angle $\\theta$ (deg)\",\n", " ylabel=\"elastic energy\", markers=True, ax=axes[0], title=\"elastic energy vs swing angle\")\n", "utils.residual_plot(beam_residuals, frames, ax=axes[1], colors={\"handle\": utils.HANDLE_C, \"pin\": utils.PIN_C},\n", " xlabel=\"frame\", ylabel=\"distance to target\", title=\"worst spring residual\", ylim=(1e-9, 1e-5))\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"beam_energy.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"004_beam_energy.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "934049b2", "metadata": {}, "source": [ "The two per-element fields behind the beam's elastic energy $\\sum_e \\text{vol}_e\\,\\psi(F_e)$: the element\n", "areas `vol` (uniform on this grid), and the energy density $\\psi(F)$ at the largest bend, drawn on the\n", "deformed beam. The energy concentrates at the inner corner of the fold, where the elements are crushed." ] }, { "cell_type": "code", "execution_count": 11, "id": "79dd8cab", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:29.967858Z", "iopub.status.busy": "2026-09-24T03:44:29.967745Z", "iopub.status.idle": "2026-09-24T03:44:30.157181Z", "shell.execute_reply": "2026-09-24T03:44:30.156658Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = int(np.argmax(angles))\n", "vol_beam = simkit.volume(X_beam, T_beam)\n", "F = simkit.deformation_gradient(X_beam, T_beam, beam_states[k])\n", "psi = simkit.energies.elastic_energy_element_F(F, mu_beam, lam_beam, POSE_MATERIAL)\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4.2), gridspec_kw={\"width_ratios\": [1.5, 1]})\n", "utils.plot_scalar_field(axes[0], X_beam, T_beam, vol_beam, vmin=0.0, vmax=2 * vol_beam.max(),\n", " title=f\"element area (rest), all {vol_beam.mean():.2e}\", label=\"area\")\n", "utils.plot_scalar_field(axes[1], beam_states[k], T_beam, psi, cmap=\"YlOrRd\",\n", " title=rf\"energy density $\\psi(F)$ at $\\theta = {np.rad2deg(angles[k]):.0f}^\\circ$\",\n", " label=r\"$\\psi$\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"beam_fields.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"004_beam_fields.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c17c4534", "metadata": {}, "source": [ "### Takeaways\n", "* Posing = **minimizing** elastic energy + soft pin/handle springs, packaged as an `XXX_system`.\n", "* The *same* setup with a *different* energy gives a *different* equilibrium.\n", "* Soft springs leave small residuals of order $\\lVert\\nabla E_{\\text{elastic}}\\rVert/K$.\n", "* We solved it with Newton without looking inside. **How** that solve works is next." ] } ], "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": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }