{ "cells": [ { "cell_type": "markdown", "id": "4edf4131", "metadata": {}, "source": [ "# 11 · Mass Springs: from Hooke's Law to a Sagging Cable\n", "\n", "The spring is the simplest elastic element there is: two point masses joined by\n", "one edge. We start from its energy, watch Hooke's law fall out of a derivative,\n", "add inertia and compare time integrators in *phase space*, then glue many springs\n", "into a cable and let it sag under gravity.\n", "\n", "| step | what we do |\n", "|---|---|\n", "| **1** | build the spring energy and collapse the spring — Hooke's law appears |\n", "| **2** | add mass; march Forward / Backward Euler & BDF2; read the phase portrait |\n", "| **3** | chain springs into a cable; sag it with and without inertia |" ] }, { "cell_type": "code", "execution_count": 1, "id": "94601c94", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:44.607632Z", "iopub.status.busy": "2026-06-09T05:30:44.607387Z", "iopub.status.idle": "2026-06-09T05:30:45.123070Z", "shell.execute_reply": "2026-06-09T05:30:45.122790Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import simkit\n", "import simkit.energies as energies\n", "from simkit.solvers import newton_solver\n", "import utils" ] }, { "cell_type": "markdown", "id": "a5b4ea12", "metadata": {}, "source": [ "## 1 · The elastic energy of a single spring (Hooke's law)\n", "\n", "A spring has endpoints $x_i$ and $x_j$. We build its energy in four small\n", "steps, each throwing away information we do **not** want the energy to care about:\n", "\n", "1. **edge vector** $d = x_j - x_i$ — kills *translation* (sliding both\n", " nodes together leaves $d$ unchanged);\n", "2. **current length** $l = \\lVert d\\rVert$ — kills *rotation* (only the\n", " distance matters);\n", "3. **strain** $l - l_0$ — how far we are from the rest length $l_0$;\n", "4. **energy** $\\psi = \\tfrac{1}{2}\\,k\\,(l-l_0)^2$.\n", "\n", "The stiffness is $k = ym/l_0^2$; dividing by $l_0^2$ makes the energy\n", "mesh-independent. This $\\psi$ is exactly `mass_springs_energy_element_d`.\n", "Differentiate once and the **force** drops out,\n", "\n", "$$\n", "f = -\\frac{d\\psi}{dl} = -k\\,(l-l_0),\n", "$$\n", "\n", "linear in the stretch and pointing back toward rest — that *is* Hooke's law,\n", "derived from a quadratic energy rather than assumed." ] }, { "cell_type": "code", "execution_count": 2, "id": "10b6fca0", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:45.124258Z", "iopub.status.busy": "2026-06-09T05:30:45.124178Z", "iopub.status.idle": "2026-06-09T05:30:45.216572Z", "shell.execute_reply": "2026-06-09T05:30:45.216360Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rest length l0 = 1.000, stiffness k = ym/l0^2 = 1.000\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "l0_val = 1.0\n", "X = np.array([[0.0, 0.0], [l0_val, 0.0]]) # node 0 pinned at origin, node 1 at rest\n", "E = np.array([[0, 1]])\n", "\n", "ym = np.array([[1.0]]) # per-edge stiffness\n", "vol = np.ones((1, 1)) # one element, unit quadrature weight\n", "l0 = simkit.edge_lengths(X, E).reshape(-1, 1)\n", "k = float((ym / l0 ** 2).flatten()[0]) # effective Hooke stiffness\n", "print(f\"rest length l0 = {l0[0,0]:.3f}, stiffness k = ym/l0^2 = {k:.3f}\")\n", "\n", "# energy + force as the spring is collapsed (l -> 0) and stretched (l -> 2 l0)\n", "lengths = np.linspace(0.02, 2.0 * l0_val, 200)\n", "d = np.column_stack([lengths, np.zeros_like(lengths)])\n", "psi = energies.mass_springs_energy_element_d(d, ym, l0).flatten()\n", "dpsi_dl = energies.mass_springs_gradient_element_d(d, ym, l0)[:, 0] # = k (l - l0)\n", "force = -dpsi_dl # Hooke restoring force\n", "\n", "fig, (ax_e, ax_f) = plt.subplots(1, 2, figsize=(11, 4.5))\n", "ax_e.plot(lengths, psi, color=utils.SPRING_EDGE, lw=2.5)\n", "ax_e.axvline(l0_val, color=\"0.6\", ls=\"--\", lw=1.5)\n", "ax_e.set_xlabel(\"spring length $l$\"); ax_e.set_ylabel(r\"energy $\\psi=\\frac{1}{2}k(l-l_0)^2$\")\n", "ax_e.set_title(\"Energy is a parabola about the rest length\"); ax_e.grid(True, color=\"0.92\")\n", "ax_f.plot(lengths, force, color=utils.SPRING_NODE, lw=2.5)\n", "ax_f.axhline(0, color=\"0.6\", lw=1.0); ax_f.axvline(l0_val, color=\"0.6\", ls=\"--\", lw=1.5)\n", "ax_f.set_xlabel(\"spring length $l$\"); ax_f.set_ylabel(r\"restoring force $f=-k(l-l_0)$\")\n", "ax_f.set_title(\"Force is linear in stretch (Hooke's law)\"); ax_f.grid(True, color=\"0.92\")\n", "fig.suptitle(\"Collapsing / stretching a single spring\", y=1.02); fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "a06360a0", "metadata": {}, "source": [ "Now collapse and re-stretch the spring, revealing the energy curve in lock-step\n", "so the quadratic well around $l_0$ is unmistakable." ] }, { "cell_type": "code", "execution_count": 3, "id": "c8c85b27", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:45.217603Z", "iopub.status.busy": "2026-06-09T05:30:45.217536Z", "iopub.status.idle": "2026-06-09T05:30:47.114583Z", "shell.execute_reply": "2026-06-09T05:30:47.114327Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sweep = np.concatenate([np.linspace(0.1, 1.9, 45), np.linspace(1.9, 0.1, 45)])\n", "\n", "# build each frame's spring state with an explicit loop\n", "states = []\n", "for s in sweep:\n", " states.append(np.array([[0.0, 0.0], [s, 0.0]]))\n", "\n", "psi_sweep = energies.mass_springs_energy_element_d(\n", " np.column_stack([sweep, np.zeros_like(sweep)]), ym, l0).flatten()\n", "\n", "fig, anim = utils.animate_springs_energy(\n", " states, E, sweep, {\"elastic\": psi_sweep}, rest=X, lims=((-0.4, 2.2), (-1.0, 1.0)),\n", " xlabel=\"spring length $l$\", ylabel=\"elastic energy\", scene_title=\"spring (gray = rest)\",\n", " title=\"energy vs length\", colors={\"elastic\": utils.SPRING_EDGE}, pin_pts=X[:1])\n", "utils.show_video(fig, anim, \"media/11_spring_collapse.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "f8dd9e39", "metadata": {}, "source": [ "## 2 · Adding inertia: integrators and the phase portrait\n", "\n", "Now give the free node mass $m$ and let it move. With displacement-from-rest\n", "$u = q - l_0$, Newton's second law is a harmonic oscillator,\n", "\n", "$$\n", "m\\,\\ddot u = -k\\,u, \\qquad \\omega = \\sqrt{k/m}.\n", "$$\n", "\n", "Writing the state $y = [u, v]$ (velocity $v=\\dot u$) gives $y' = A y$\n", "with $A = \\begin{pmatrix}0 & 1\\\\ -k/m & 0\\end{pmatrix}$. The exact motion\n", "conserves $H = \\tfrac12 k u^2 + \\tfrac12 m v^2$, so in the\n", "position–momentum plane $(q,\\,p=mv)$ it traces a **closed ellipse**\n", "forever. A good integrator keeps that loop closed:\n", "\n", "| scheme | one step | phase-space behaviour |\n", "|---|---|---|\n", "| **Forward Euler** | $y_{n+1} = (I + hA)\\,y_n$ | spirals **outward** (gains energy) |\n", "| **Backward Euler** | $(I - hA)\\,y_{n+1} = y_n$ | spirals **inward** (numerical damping) |\n", "| **BDF2** | $(3I - 2hA)\\,y_{n+1} = 4y_n - y_{n-1}$ | **nearly closed** (2nd order) |" ] }, { "cell_type": "code", "execution_count": 4, "id": "888f15f2", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:47.115736Z", "iopub.status.busy": "2026-06-09T05:30:47.115666Z", "iopub.status.idle": "2026-06-09T05:30:47.119836Z", "shell.execute_reply": "2026-06-09T05:30:47.119592Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "omega = 1.000, period = 6.283\n" ] } ], "source": [ "k, m = 1.0, 1.0 # stiffness (= ym/l0^2 from section 1) and mass\n", "A = np.array([[0.0, 1.0], [-k / m, 0.0]])\n", "omega = np.sqrt(k / m); period = 2 * np.pi / omega; I2 = np.eye(2)\n", "print(f\"omega = {omega:.3f}, period = {period:.3f}\")\n", "\n", "# the three integrators as analytic 2x2 maps on the state y = [u, v]\n", "fe_step = lambda y, h: (I2 + h * A) @ y # Forward Euler\n", "be_step = lambda y, h: np.linalg.solve(I2 - h * A, y) # Backward Euler\n", "bdf2_step = lambda y, yp, h: np.linalg.solve(3 * I2 - 2 * h * A, 4 * y - yp) # BDF2\n", "\n", "def integrate(kind, h, n_steps, y0):\n", " \"\"\"Roll the chosen scheme forward and return (position, momentum) and energy.\"\"\"\n", " ys = [y0.copy()]\n", " if kind == \"Forward Euler\":\n", " for _ in range(n_steps):\n", " ys.append(fe_step(ys[-1], h))\n", " elif kind == \"Backward Euler\":\n", " for _ in range(n_steps):\n", " ys.append(be_step(ys[-1], h))\n", " else: # BDF2, bootstrapped with one BE step\n", " ys.append(be_step(ys[0], h))\n", " for _ in range(2, n_steps + 1):\n", " ys.append(bdf2_step(ys[-1], ys[-2], h))\n", " Y = np.array(ys); u, v = Y[:, 0], Y[:, 1]\n", " qp = np.column_stack([u, m * v]) # (position, momentum)\n", " H = 0.5 * k * u ** 2 + 0.5 * m * v ** 2 # total energy\n", " return qp, H\n", "\n", "y0 = np.array([1.0, 0.0]) # displaced and at rest\n", "h = 0.1 # coarse step so the schemes visibly differ\n", "n_steps = int(round(3 * period / h)) # ~3 oscillations\n", "schemes = [\"Forward Euler\", \"Backward Euler\", \"BDF2\"]\n", "\n", "# run each scheme explicitly\n", "traj = {}\n", "for s in schemes:\n", " traj[s] = integrate(s, h, n_steps, y0)" ] }, { "cell_type": "markdown", "id": "78b2ae5c", "metadata": {}, "source": [ "### The phase portrait\n", "\n", "Position vs momentum. Forward Euler spirals **out**, Backward Euler spirals\n", "**in**, and BDF2 sits right on the exact energy-conserving ellipse." ] }, { "cell_type": "code", "execution_count": 5, "id": "e44de165", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:47.120696Z", "iopub.status.busy": "2026-06-09T05:30:47.120647Z", "iopub.status.idle": "2026-06-09T05:30:47.149237Z", "shell.execute_reply": "2026-06-09T05:30:47.149026Z" } }, "outputs": [ { "data": { "image/png": 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UeY5DhfAsedyp6hwqK1Q4lSgpHGg96Hih4qpFjzXFOV+W36LumB6CMtz++eefYutPwozcxJTlWVIgl9zn5YVi3xTbTPB0hKVHUG6olgrFRVCsBrmraECllNCSF1Q6uSlVmU5wsuLQhYreRxdgqt1DkKWHLD5z5szhQYMCQukOiO5ayCVCQdWUmvw86P0UL0Sm+rNnz3LdHwokVRT1okdaX0rRVbhsLly4wHd19J1Ux6Us0ABM1hS60NPgTdYlRUpyadCARwMZxbZQnRYKmCXXRlktJfR9dHGnbUQDJIkGRX2lkvTu3Zt/B6W307ak30zfRQMy1copmV6vyn1dGmRxIhcmXfxpXWiQp21HA0HJQYO2Jbm9aL3pWKHyCFevXuX9Vda4ropCAdMkFCm9mu70yTJFMWiKgNPnWQto39BASAKHrFkUM0eCjcRM0ZpAFCtCaey0T8niQ4OhIp1fAZVaoOWQNYyOfTq+aJtQkDBtj4pSnuNQITLpOKKEB9r+dGyp6hwqK2QNofgmOmaKpn7TupC1ePbs2bxtaLuSJbK0uCTFb6Fjl8QtXXvoN6k7poegY4GEM4lBuobRdqTrBsVTKoK/FZDlrKT1iOLOFEKcrI70++hYI2hf0HZQQBZUen/JhA5BKWg6fUygfhQprv/880+F3ldaOvDff/8ta9WqFae8e3p6ymbNmiU7fPhwsfcFBQXJXnvtNVlgYKDM3Nxc5ujoKOvQoQOnzpdk586dsrZt23JKOE2ULkzppnfu3HnmOitSxW/fvs2p2ZTu6+DgIJsyZQqnHRclNzdXtnDhQpm/v7/MxMRE5uPjI5szZ84TadeUGvq01GJKM6W0Yvrd9L2K9HXFelCqakmoJED//v1l9vb2nMI9ePBgTmmm99PnSm7/oqnCUVFRvC70u8qSKkvpvVRigPYJ/cYaNWpwCnLRlOfypqyXZV+XBqWHz5w5k1O1af1pv9L86tWrS12Xixcvyl588UU+VmgffPPNN6Ueh6WVQHhaynppv5H2Wcn0XzpWaTvTb3RxcZHNmDGDj0la5rlz5567jS5fvizr2rWrzNramlP56Tg/c+ZMsfdQKYGWLVvycUDfQ8c4lWRQpOQruHnzpvJ4oW1Rq1Yt2UcffVTplPWyHofEokWLZF5eXjKJRFLsu1RxDpWHlStX8jYtmW4fHx8vGzVqlMzW1pZ/C80rSmQU/c2Uyj516lTep1S2oaqHPCoPQtclWk/6Hb169ZLdu3fvifeVdm4r9nNpU8myGWvWrOHjLiUlRe2/Sdcxoj+liSGBQBegeAhyjVEWjQjg003I+kFptuqIZakM5Mahyszh4eFPlHUQVA1k3SCLD1moqOCmoHSaNGnC5xG5sgXPRsT0CAQCg6dkxg7F9JCLikohCMGjOai0BcXZUNaftmc6agqqM0XB5RQiIHg+IqZHIBAYPBRQT/WpKJWbrAsUE0bBpRTbI9AsVBqBJkHpUBwjZbIJyoYQPQKBwOChIFeqm0MihzKBKJiVivgNHTrU4LeNQKBPiJgegUAgEAgEBoGI6REIBAKBQGAQCNEjEAgEAoHAIDComB6K/qdy91T8TjRlEwgEAoFAP6DqO1QQlQqdltZI2yBFDwmeon1wBAKBQCAQ6A9hYWFcCf5pGJToUTR4o42i6IejjdYoag5Ipf+fpVYFYh/oM9SyhFLHqU4LtXUQVD3iWqR5xD4oO9TrkYwaz2vkalBXE4VLiwSPNoseuuDT+gnRI/aBoULnAJ0LdB4I0aMZxLVI84h9UH6eF7oiTAkCgUAgEAgMAiF6BAKBQCAQGAQG5d4SCAQCgWozZsgVSVWsBepxb+Xm5nIvOBHuAJiYmMDY2LhS21SIHoFAIBCUm5ycHERGRiIjI0NsPTWKSkUwsyizAt4GlJllbW1d4W0qRI9AIBAIygUNxMHBwXzXTXVRTE1NxaCsRksaBfMbuuiRyWSIjY1FeHg4atSoUWGLjxA9AoFAICi3lYeED6UIW1paiq2nJoToKY6LiwtCQkLY5VdR0SMCmQUCgUBQsQFE1BITVCGqsHYJ0SMQCAQCgcAgEKJHIBAIBAKBQSBEj0AgEAgEWkRSUhK7cih+RR1Uq1YNu3fvhiEiRI9AIBAI9JKXX34ZZmZmnOKsmFavXg1dZ8GCBZzRVfR30fTPP/9oetW0HpG9JRAIBAK9ZenSpXjnnXcqtQzKFqLCeOqgosvu1auXRqw1uWrcFlWBsPQIBAKBoFLI8vKQGxVVZRN9X2U5cuQImjRpAjs7OzRt2hTHjh1T/m/s2LEYP348hgwZwk1vv/32W+7e/d9///H/9+3bx+6nQ4cO8fMbN27A3t6eK1OnpaWhb9++cHV15WW3b98e165dK2alIcEyefJkODo6Yvbs2cjOzlY+9/f3x6+//qpS9xXN02tPg357y5Yt+TfUq1cPe/fufea20GWEpUcgEAgElSIvLg73X+5QZVux+p8nYOLuXuHP379/n4XJli1b0KdPHxYF9Hjr1i0WHcS2bduwa9cubN++ndtA/P777zhx4gRq166NP/74A4GBgfy8W7du/Pyll17i2jFUv+jVV1/F1q1b+fn777/PgoEEkyLlmsTS999/j6+//pprHn366ac4e/Ysbt68yXWP6PNVxfXr1zF48GDs3LmT3YFnzpxBz549ceHCBdSqVavUbaHLCEuPQCAQCPSWOXPmsAVDMaWnp2PHjh08wA8YMIBjYwYNGoS2bdvy4K6gS5cu6Nq1K9ciIiHSoUMHFjkEiZz58+cXe/7KK6/wPFlDhg4dCisrK5ibm2PhwoW4e/cuIiIilMuuX78+W1Dou2nZJL4++OADrm5N60jLfh4HDhwo9rtoIotReVm7di2vC60//VbaDmSJ+vnnn5+6LXQZYekRCAQCQeUGEmdntr5U5feVlSVLljwR00OtDEq6ewICAvh1Bb6+vsX+T6Jn+fLl3AqBJrLGzJgxg/tinTx5Ep988gm/LzMzk18/ePAgEhISlAUc4+Li4OXlVeqySRD5+fkpnxedfxpkjVFFTE9ISAiLtg0bNihfo9YXJN4UlFxfXUaIHoFAoBPl+JGbi4LsbMiyslCQlVX4mA1ZdtFHej0bRqamMLa1gcTGttijkbm5wfcwUgdGUmml3E1VDTWtPH369BODP8XfPK3aNMX/kCvqm2++UbqyyCry5ZdfcmAvWW+IFStW4NKlS7x8+h5KP3dwcJAfw09ZNll4Hj58iBdeeIGfh4aGVur3USZX0Uaw1Bj2afj4+ODtt9/GZ599ZhCVt4XoEQgEakeWn4+8qCjkhIUjJywUuWHhyE9KUgqWgqxMFissZLLpeRbyMzKQUETooKCg8itiYgJjGxueJLa2JR7pdVsY29kWEUs2MLa1VT4amZkJ0aQHkPuJLDN79uxhiwkF7pK15lnp7CRySBSRyCGLD0EuoQ8//JBdP4p4nZSUFHZrkdChoGZyWz2P4cOHs+ggEUXuo48//rhSv48Cs8lVR+47siKtWrXqqe+dOHEixyXRb6DfR1aey5cvs7usTp060DeE6BEIBCqhID0dOeHhyA0LQ05oGHLDCx/pOcUz5OaqZ0tLJGzBkZAgoUdTU8hyc5GfmoqC1NTi76XXExJ4qghGJiaQenjALDAQZoEBMA2sLn8MCISxtZVqfo9A7VSvXh2//fYbx/uMGjWKXVsUqEuPz4JcXJS5pYjf6dixI6ZOnap8TkyfPp1dX25ubnB2dsaiRYuwZs2aZy537ty5iImJYWsRuZXoOcXsPIv9+/ezRacomzdvRr9+/VjQjRgxght0UjbW6NGjnyromjRpwgKJvvPff/9lq07jxo3x+eefQx8xkhW1uek5pMAphTA5ObmYv1KboMh/8gNT6qI+mRR1CbEPSkdWUIC82Fi5iAkjcRMqfwwNZbGTHx///I1rYgJTT0+Y+PhA6uQkFynmZjAyM4eRuRkk5hb8KDMxQWZ+PqwdHSG1tFK+hx/JRWVG76Xn5rzMpzUiJAsTibH8FBJAKaU+5qekoCAlRS6SCh/zU+m1VBSkpZX5uJG6u8vFUPVAFkHyxwBIHRygb+cBZfAEBwdzphNZNQTqQXRZR5mPu7KO78LSIxAInrjQ5j56hMxLl5B581ahyCHLTThkZcgOkdjZwdTHByY+3jD18VU+mvp4szAwMjZ+7jLIxC5LSoK1vT1nuFQU+i5yS9EEyINIywOLprS0x4IoOZm3Rc6DB8h+EITsBw+QVxgvQe47mtL//rvYMoydnGAWEADT6oEwU4qhQEhdXYSrTCCoYoToEQgMHBrYs+/dQwaJnEuXkHHpMvKio5/+AYkEJh4eMPH1gak3iRsfmPr6wMTbh4WNsZ0d9AUWTXZ2xX6T1YsvFntPflo6coKDkH3/AXKCHvBjdtADjluiOCSygGXQVKJFAMUJkWXINDAAZoVuMvOGDXXWMiQQ6AJC9AgEBgYFBmfduIGMi5eQcfkSMq9cfTL2hSwUDg6waNwYpv7+LGZMCq01Jp6eHNsiKNxO1lawaNCAp5LbOSckBNn37xexDN1HzsNQeSZaaioyr17lSYmREczr1IFV6xdh+eKLsGzWTO7CEwgEKkGIHoFAz6GYlYzLl5F56TJbc0jwUKBvSUy8vXmQtWjWFJbNm7PYeVqsjOD5UGC1ea1aPBWFtj25yFgMBQUpLUM5D4LYfZh1+zZP8d//wKn3Fk2bsnWJhJB53bplcg8KBILSEaJHINAzqDcRWXEyL1/iR3JdoWS+gpERzGrVYpFj2awpLJo1g4mbm6ZW2aAgKxnF+NBUFFlODjKvX0f6mbNIP3cOmdeu8WsZ587xFPvFF5xeb/XCC7B8sRULIdNq1YQwFQjKgRA9AoGOkxsRgbSTp+SuqouX+HlJyGJg3rABLJs1l4ucJk24No1Ae6B9RBY2mlymTUV+WhrHAaWfPYuMs2eRfe8+B1OnHj3KE0Hp82wF4qlVuSoVCwSGiBA9AoEOQqnjKYcOI+XgQWReufLE/8kiYNmkCSyakyWnGczr1+f6NQLdwdjaGjYdOvBE5MbEsMUn/ew5pJ85w8HmlDmW/NtvPBFmNWuyACJLkGXzFqJ2kEBQAiF6BAIdIS8xEalHjrLQybhwoZjLSuriAsuWLeXxOM2aw6xGdRiJOk96hYmrK+z69OGJygrkBIcg/ewZuSXo/AUOjM6+e5enhB9/BKRSWDRqxCLIul1bzgwTMVoCQ0eIHoFAi6H6MKnHj7PQoVgP5OUVq/9i27ULbHv04GBXIXIMBxIvZgH+PDmOGAFZXh4HP3M80NmzyLx8mQOmudbSpUuI++YbmPr5wa5/PxZNlIEnqBwLFizA1atXVdL0s7JQBWVqqkrd0lXN2LFjuSUFtd/QB4ToEQi0jIKMDKT9+SeSSeicPMXBrEXdVjZdOsOuRw+27FCjR4GAjgOLhg15cp40EQWZmVxvSWEJyr79L3IePkTsl18h9qv/wbLVC7Dv3x82nTtDYmGhtxvw5ZdfxtmzZ7khKAlF6hZOYmXw4MEwFP78809un2FlVbxNCvX3opYZhoa4YgoEWkBBTg7ST51CyoGDSD1xArLMTOX/JJaWsO7UEbbdu8O6TRsOeBUIngUJGeu2bXgisoODkbxnD5J37+Gq0Rlnz/EksfoYNt26sgCiDD59dH8tXbqUrSDkEjx48CD69++Pli1bws/PD7pGbm4uC7jyQu0ZqNu7rqyvOhHNnQQCDUHuh7RTpxAxew7utW6D8LemsBuLBA/1lrLp2hVeX32FGmf+hteyZRzQKgSPoCKY+fvD9Z13UP34Mfiu/wG2fXpzDzPqS5a88zc8HDkKD7p2Q+zq1dyCpLzk5RcgMjmzyib6vvJCgo46qpOr5s6dO/wadUHv27cvXCleys6Ou4xfu3at2OeoGWejRo24nxMJpY0bN5a6fOq2Tu+LjIxE9+7d8e233/Lr1AuKWqnMnj2bn5P4okagly5d4uezZs3i5drY2KBu3br45Zdfillp6L3UsJSsVK1bt+bXv/nmG/j4+MDJyYm/t7Luq3feeUf5nMQRbauQkJBS3//gwQP07t2b14vWm5qbUp82grYNudrmz58Pd3d3DBs2DNqGsPQIBFXc8oFq55C4ST18GPlF775MTGDdti3H6Fh36CAybwQqhwobWrVuzVP+vDSkHjqEpN275aUOQkMR97+vebJ84QXY9u0DWfPmgKPjc5cbm5aNF5f8UWV77OycV+BhVz63HA3M1CE9MzOTB2bFa9QRfevWrTA2Nsb777+PIUOG4L///uOBn94/ZcoUFiLkKouLi8OjEqKQ+sRNnDiRxcDJkydZPJE76cSJE5g0aRILl2rVqvFz4vr168jPz+fu5gQJpffee48FDH0PdX1v3rw5N9UkUlNTWYjROhF//PEHC51Dhw6hWbNmWLhwIW7evImqICMjgzvLk0jauXMnoqKi0KNHD3h4eGD8+PH8HlqXgQMHIjQ0lLeNtiEsPQJBFUD9meI3bMT9Tp0ROmYMknbskAuewkHI49NPUPP0KfisWQ273r2E4BFUSUq8/aBBqLZ5MwIPH4Lzm5OVAc4Z588j6oMPEde3HyI/+BDp5y9AVng3r2vMmTOHrTsU0zJgwADMnTuXLTsEWW+GDh3K/6Ou3SQg7t69i4jCWlerV6/G22+/jVdeeYU7zdPnFGJFIQLIXUbWnMOHD7PgIUj0kNhRiBRaBoki6gROz1966SVl5/oRI0bwckl0kWWkdu3aOHPmjPI7SJh99tlnsLS05GnLli38mRepOKWpKccolYzXKQmtH20D+yLT8ePHy70tDxw4AAcHBxY99N1kfaLfRqJRAW0DEmX0f1pfbUNYegQCNZIbHYPEzT8hcfuOx/2tjIy4do5tzx6w6dIFUicnsQ8EGoUyu1ymTYPzlCnIuPAPknftQsqRI+xqTdm9mycTLy/Y9esHu359AReXYp93sTZj60tVQd9XVpYsWaJ039y/fx99+vThQZ+sM2T1mTFjBsf6JCQkKIUIWXS8vLzw8OFDjB49+qnLpuwtEjIXL16EmdnjdWratCmysrJw69YtFjlk8SGRcerUKX7epUsX5Xu/+OILfP/99wgPD2frErnc6PsVkNuL1lcBCTKyOimgmBmytFRFTE9ISAhbcoquD4kycrUpoO2m2I7aiBA9AoEaoL5K8es3IHnfPm4uSUisrGA/dCgcR44QKcMCrYTKHli1eoEn17kfImrXLuQdPYbMf/7hWJ+4Vat4Mu3cGQVjx7C7lpAaS8rtbtIE1atXZ3fM/v37WfSsWLGCY2tOnz4Nb29vFgZkyaC4G4JiVkgoPQ2KsaH4ls6dO+PYsWOoV68ev05WG4oP2rFjB4upOnXqsLXo6NGj7AIjIUbQ95KlhoQQWZBILJDrTfH9REkB4enpyWKsaLAwxRFVFGtra7ZYKXjWskjckEvt3LlzT32PNgseQrvXTiDQIehClX7hAsImTkJQr97yKrm5uZC6usJ15nuo/ucJuM2aKQSPQCcgkW7eowd8f9yIwKNH2ApETWmJrJs32T2bExyM3OhorhOkC5Clgqw6DRo04OdkpSG3FgkdsrB88MEHxd5Pwuirr77CX3/9xRaNmJgYXClRAZ1iWUjEUKwLxesoIBcXfZZcWQSJng0bNvD31a9fX/n9JJAoKJiWv379+ufG5wwfPpxdXOfPn0dOTg6nnqenp1d4mzRt2pRdcyR2KH6IXHxPo1evXoiOjma3H1myKDaJgsIVrjxdQIgegaCS0N0utYQIGToMoaPHIO2vv/h1qorssXgxqh87Cqfx40WvK4HOYurjA5cpbyHwyGH4bvqRa0WRm5bifKglClWBpka32ih+KDiZrBk0tW3bFp06dcK8efP4f1SnhkSHm5sbCxGKkylKv379sHLlSrz11lvsImrRogVu3LhRagbU8uXL2eJDLi+F6CFRQ2KHoOVbWFjw6wq6deuGQYMGsQgjCw65w9q0kZcZeBq0/osWLeJgYXJrkVhSiKhnxfQotoF14URuPWLkyJEszCiWiKxMlOH2NOhzZNEiVx0FZ1PwNQWCU0CzrmAkK2pH03PoAKQDlw4ACmDTRugAJnOoo6Oj1psJ9ZWy7gMqAJe0axcSNv7ImS8KqGig0/jXYNW+vV7WPakKKOuDXA0UO0DpvgLtOg/oLj/owQP42DvAJCVZ6eaCRAKpgyOkzk7cTV5QOWh4pnOBzgFxLQEfd8HBwZzZRhaziozv4moiEJSTvIQEJG7ZisStW5GfmCh/USKBTdcucHptPCwaPPuuSyDQl/gfEydHmLm7IT8hAXlx8ZDl5yEvPg55CfGQOjrC2NkZEiF+BFqEED0CQRmhMv7xGzciedduyLKy+DUq8GY/YAAcx41lF4BAYIi1f6jhLfWCk4ufOHZz5cXH8w2C1MFBLn5EJXGBFiBEj0DwHDKvX0f8D+uRevQo2fz5NWMHBziMHAGHV1/li7pAYOiQ5Ufq7AxjR0e2gObFkvjJZeGTl5gIY3JVurgI8SPQKEL0CARPIfPKFcR98SUyLl5Uvmbi6wun18ZxvRJJCZ+yQCAoFD9OTnxjQBleFOhMLVdICOUnJsHY3k4uforUtREIqgohegSCElAKbsqSJYg9clT5mnmjhhyvY9OpI5vzBQJBGcQPxfXY28vFD7m9cnJ4nial5UeIH0EVIkSPQFBIQXY2EjZsRNzatcou5xZNmsB1+ruwaN5cZE8IBJURP0UtP0XFj12h5UdYTgVVgBA9AoOH0kLT/vgD0Z8tRW5YGG8PibMz3GbOhB11oxZp5wJBpaHziIOayfKTnCwXP9nZPE+Tsa2tXPxYaH9lZ4HuIkSPwKDJfvAA0Z8uRnphgz+qLeIwbhwkgwbC1ttbCB6BQB3ix96eLTwFKSnIi4lFQXYW8lNSeGLx4+4uAp4FakGIHoFBQhdX6iGUsGUrVcLj16w7dYTb++9D6uXFRdkEAoF6xQ8JH4mtLTfjzYuJQUFWofhJS4NJYRo8uccEAlUhjiaBQUGVYxN//hkPunVHwo+bWPCYBgbC54fv4fPNN6LWjkCgCfFja8vnoamvr7ySc0EBJxTkPAhCfvrjZpjlhbqRU/dzap9A3cqpIegvv/yi7MNF303/owq+zs7O3CJi48aNxRp+UkNQqohctIUD9b8ifvzxR7Rs2ZIrAVNLCOrDpYpu5gL1oTOihxq6Ud8TOnBdXV25Jwo1OhMIykrG5csIGTwEUfPmcxE1iY0N3D6Yg4Ddu2D9nH43AoGgasSPWfXqXO8HMGK3V05wEHIePapwX6+lS5dyM1FqU7Bs2TKMGDGiWJfy8PBw/l9YWBjee+89brhJjUZLNtqkZSimbdu28evUnZyWSU04qW8WNe188803K7klBOpEZ9xb1OWWmr6R8KFeJNQNt0uXLrh9+zasrKw0vXoCLYbuGGOWf46U/fvlLxgZwX7QILi8+w5nlQgEgsqRV5CHuMw41W1GG0Bmao3cqGgUZGUC0fEwiguB1NWFb1ZcLF0glUjLLaqomSb1c6Mb5po1axb7PzUDpf9Tx3VqTPrOO++gbt26z1zm5MmTlfPUC2rSpEmYMmVKOX+soCrRGdFz6NChYs/JBEkWn0uXLqF9+/YaWy+BDqSgf/cdZBlyE7lF06Zw+/ADWNSrp+nVEwj0BhI8nX/tXGXfd6TPAXg4+Ja7geq+ffuQmZnJ3cTJSlMarVu35o7ndKP9PNFTEvpMw4YNy/UZQdWiM6KnJNRJlaAOwE8jOzubJwVkwlQc/DRpIwpfMj1q6zrqRAr68T8Qu3y5MgVd6uYGlxnTYdOzJ9/xPWvbin2gecQ+0O59QM/p9aJTVZIdEoLcHHNIXZzZcvss5syZw3E5NBbk5OTg008/hYuLC8f0EKWtv5eXF+Lj45X/O3DgAFuIFGzfvh1du3Yt9pnff/8d33//PU6dOqWW7VHV21gbUeyP0sbwso6XOil66MeR6bFNmzaoX7/+M+OAyD9bkkTqC1NB/3BVQesoKD95oaFI++JL5P7zj/wFU1NYDhsGy1EjkWdhUa7tKvaB9tzcCDRHaedBbm4uX4fpOkqTvYk9fu/3u9rXhYqGFsTEwdHIEnmxMchPToLEzQ1Glpalv18mwyeffIJp06bx8/v372PAgAEcuNy5s9wypfgNRXn06BGLHHqdfmf37t2xc+fOYu8p+pkTJ05g1KhR+Pnnn1GnTh2Vjy/aPl5VFYr9QdeFkpa61NRU/RU9FNtz8+ZNnD59+rkKf/r06cUsPT4+PuyzpYNeG6GTlC4ytI6iKF75tlvKb7sQt3ixspqydadOcJn5XrkzssQ+0Dz5+fl8YaOsGGPR9kMjPOs8yMrK4v9RVhNPkMLL1Ev9K0WXbddALmyobGsRFgZjO3tI3d1gJC0+pNF6S6gidOHrtWvXRo8ePdgqQ0KGUPwGBWfPnkVERARnctHr9PmiyyjJH3/8gWHDhmHr1q0cZ6qOgf5p321oSAv3B10XKIaq5P/KtAzoGBQktn//fpw8eRLe3t7PfC+lKtJUEsVBrI0oTHSKk1XwfKiuR9SCBUg5KL/TNPHxgcfCBbBq3VrsAx1FnAfavQ/oOb2umKoUIyOYuLlxZefciAgUpKezxacgLZXd2NTuoug6FV1HcmmR4KHsX8Vriv+TkCOLDY0xEyZM4PR2xf+LPhblzz//xKBBg7B582Z069ZNrS4tcRMM5b4qbQwv63ipM6KHdv7UqVOxa9cuPtD8/f01vUoCLSDj8hVEvPceX/wI2z694T5vHoytrTW9agKBQI1Qo1LTatXkLS0ioyDLz+PrAPXzMvH0VPbyev/99zF37lyeJ5cVubfmzZuHqKgofo1unmnANDU15XAJeu/YsWPLtA4UPkEehKFDhxZ7ndLaBdqJVJdcWmQ+3LNnD9fqURywZOaiVEOB4RUZjP/uO8R+s4p8IZBYWsJ9/jzY9e2r6VUTCARV3dLC2ppLU+QnJqIgI4Pby0idnHDi+HEYPcU9Wq1atTIFB1MQ9NMgy5BAt9AZ0bNmzRplhc2ibNiwocyqXKAf5EZFIWLmLGQUBiubN2gAr8+Xw9TPT9OrJhAINADF8ph6eSGfgo/J5ZWdzTE/ZAUiq4+xjY3YLwLdEj0iXU9ApB47hsgP5/LFjHCaMB4u06bByNRUbCCBwMAxtrKCJDAQefHx3MhUlpuLnIcPIXVyhtTNVfTxEuiO6BEYNtSIMHrpUiRt287PjV2c4fnZZ6J9hEAgKAY1KOVmpXZ28kDntDTkxcehIDODkxwk1NtLYLCI9CCB1pN19y5CBg9WCh6rl9ojYM8eIXgEAsFTkZiasstb6urKzynWJ+fBA+7gLjBchKVHoN11QrZtQ8zSZZBlZ3P3ZdeZ78Fh1CiRvikQCMoU6Gzi6sqJDlSdnZqW5oRQDy83ruYs0sANDyF6BFpJXmIiIud+hLTjx/m5qb8/vFaugHmdOppeNYFAoGNQdpdR9erIDQ1jN1deTDQ/UvBzyYKGAv1GuLcEWkf6+QsI7tdfKXjsBw+C/85fheARCAQVhmJ5TP2rcSo7UZCayqntBRnyCu4Cw0BIXIHWQJkWsatWIX7td+TbgsTGBh6LPoatGiqdCgQCAw1y9vCQu7sePeJrTnZwEEzc3WHs6CjcXQaAsPQItAK6AD0cNRrx365lwWPRpAkCdu8SgkcgEKgcyuwyDQyExMycrze5kZHIDX/ERU+rsr9cw4YNuY+kIWNvb89dFogtW7ZgxIgRav0+IXoEGifz1i0EDx2GzKtXqYEKnN98E34/bYKJVxU0MBQIBIbbxiIwgHt4EdS/KzsoiMtjVAYawGkgfx6bNm1CjRo1uPWFQM7w4cNx4cIFXLlyBepCiB6BRkk7/TdCR41GflwcNwr03bgBLtOmiuBCgUBQNe4uLy+u2kyNTClLlIRPXlKS2r971apVGDduHHSJvLw8tS6feqCRpWf16tXq+w61LVkgeA5Ju3cjbNIkrp9h4uuLatu2wqplS7HdBAKBSqDGn9Q13dfXF66urhg9ejSSC6u5z5w5Ey+99BKXxpA6OmLftWvw79ABMbGxyA0PxwyyOPv5ca/HunXr4pdffim27EuXLuGVV16Bo6MjXFxcuCF2fHw8unfvzt9hbW3N06lTp55Yr4iICLZm0PcXZdu2bWjUqBFsbW35uzdu3Miv0zquWLECgYGB/H3U0T0oKKhYH7Fly5ahVatWvL603LCwMOVnqemqu7s7L7dmzZrYv3+/8rPbt29nNxtZp1q0aIEzZ84o/0dtn2bNmoUuXbrAysoKS5Ys4eVnZGQo3xMZGcnNWh89esTPL1++jA4dOvB6Vq9eHevWrVO+t6CgAB999BHc3Nzg6enJwq8kHTt2xL59+6A2ZAZEcnIydZfjR20lPz9fFhsby4/6SkFBgSx2zbey27Vq8xQ0cJAsNy5Opi0Ywj7QdnJzc3kf0KNA+86DzMxM2e3bt/mxKHXr1i11unfvHv+fHp/2HgWHDh0q9f+9e/cu928YPHiwbPjw4bLExERZWlqabNiwYbKRI0fy/7Kzs2XNmjWTLVy4UBYSEiJzcHCQHTp4UJYdEiLLuHFDtn7JElno+fOynIwM2bZt22RmZmayoKAg/mx4eLjM1tZWtmrVKt4G6enpspMnT/L/Tpw4IbOzs3vmeh04cEDm4+NT7LW9e/fKHB0dZcePH+dtHh0dLbt06ZIsJydHtnHjRpmnp6fs+vXr/H3Tp0/nbaI4P/z8/GQNGjTg9aP/d+/eXTZmzBj+3+HDh2Xe3t6yR48e8fOHDx/K7ty5o1wPLy8v/h76zp07d/I6xBVej1966SWZi4uL7Pz583zdzsjIkNWrV0+2efNm5XovX75c1qlTJ56PjIzkz+/YsUOWl5cnu3HjhszDw0N27Ngx/v8PP/zA6/Lvv//yNhs7dqxMIpHwNlNA303jdERERJmPu/KM78LSI6hSKFAwauFCxH75pbK6st+PG5VppAKBQKAKYmNjsXPnTrYmkBWDLBUff/wxduzYwUHEZJ0gy8oXX3yBHj16YPz48ejavTtbnU3c3DCsV284W1oiPyQEg3v2RO3atZVWkM2bN6NZs2Z48803YW5uDktLS7Rr167M65aYmMhWl6KQS+ftt99m6xG5ecgy1aRJE+X3TZs2DQ0aNODvW7x4MVtyKP5FAa2Lv78//59cRGSJIkxMTJCVlYVbt24hNzeXrV5k7SFo25DFq2nTpvydAwYM4N958OBB5XJfffVVtGzZkjPbLCws2Fr2008/Kf9P8/SaYr59+/YYMmQIjI2NOV6JXHhbt25VBiqTRYy+g7bZZ599xtafoii2C20jdSBS1gVVRkFmJh69N1NZf8du0EB4LFgg4ncEAj2BBtZnQe6O572na9euz31PWQgJCeEBlYRAUWhwj4qKgpeXFwcSkwuH3D1//PEH/58Gd6mLC75avx4/rFuHR9HR/FpaRgYLKeLhw4f82Yri4OCAlJSUYq/RMhXioSTh4eHswlJgZmbG7iF6XQG5rxSQwEtNTeV5cjUtXLiQ3Ur//vsvOnXqhM8//5y3C22jDz74APPnz1d+loSRwlVFkEgqCgmquXPnslsrJiYGDx48YLFE0PJIMBUN5CaBqRCE5NYjt50CcnPRbymKYrvQNlIHwtIjqLIKy6FjxykFj/Nbb8Fj0SIheAQCgVrwoeaiEgkPtElJScqJrB4keIhff/0V586dQ8+ePfHWW28pP3v69Gl8vHgxftyyBVFXriLyzBnUrV4deQkJkBUU8MB9//79Ur+XvvN5NG7cmIUFxRwpeNYyvb29WVAoyMnJ4d9Fr5cFsgLR7wwNDWWRQVYjxTaiWKGi2yc9PR2zZ89+6u+hbUcxQ2S9IcsOCR4SWYrl9e/fv9jySHwpLEck1EjcKSDRlJ2dXWz5t2/fZjHk4eEBdSBEj0Dt5ISH4+HwV5F57RpgbAz3RR/DZeoUUQhMIBCoDbJ89OvXjwOZ4+Li+DWy8OzatYvnSQBMnDgRP/74I6ePU2Dxd999p7Q2kHvGzcMDUj9fbD56FLfv3+fsLurd9eqwYexa+vbbb3nQpsBeRcAyDdg00NOA/jRo8Cfh89dffylfo3X56quv+DWyUNHnFanbZF355ptvWBDQ95GlhcQHuZ2exz///MNuORJKFhYWLFCkha03SOgtX76cXWEU8Ey/49ixY8UsSKVBFinabiR8ilqnRo0axRYzciuSxYimq1ev8jooUtLJpXbnzh1kZmZizpw5T4gq+jyJUHUhRI9A7TV4QoYN5wuFkYUFvFd9A4fBg8VWFwgEaoeynxRZSRQrQm4WGuDJ5UJCguJNKDOJ/kfxPZSpRC4gyo4aNGgQx9CQuPgvPBytX3iBl0nZpq65uTh2+DAP+iRyyPVEViOiVq1aHB9EGV/03WQ1Kg0SHBs2bFA+J4G2cuVKft3Ozo7X+caNG/w/EhYUC9OrVy8Wc9euXeMMJ4V4eRYk4MjS4+TkxJ8lCxGJK6J3794cV/P666+zO4lcXvS/knE2JSHrTnBwMAsWikFSQNvq8OHDWLt2LVtqaNvQ71G4rF577TWMHDmS90NAQADHLFE2mAL6Xor7KWp1UzVGFM0MA4E2PB1MlE5YMohMW6CdnpCQwOl+ZTGTajNpp07j0dtv80WCSrz7fLsGFg0bQtvRp32gq1A9EDKN06BRlgu7oGrPA3IR0aCnCJw1FPKTk9lyTVWcjai4YbVq3NOrQsvKz+dBn8RWvXr1Sn0PDc90LtA5YAgd4bdu3YoDBw6w8CmNZx13ZR3fxdVEoBaSftuFyHnzaPTibAjfdd/BtEgAm0DwNOhCX5CTg4K0NL7gU8ZfQXYOZDnZ7F4oyJY/Pp7P4R5K1E/J2M4Wxra2kNjaKeeNKjgoCQSltq+QSJATGiZ3dQUFyYVPiWDcskDus+vXr4uNXATKFKNJnQjRI1D5gBW/di1iv5SbT80bNGALj0hJF+SnpiI3LIzvlKnPUW7443nqeE1CRyFm6E6aiFfBZiMxJLGzYwHEgojFUOFzOxJIhc8dHGBGXbg9PQ3irlpQMYxtbGBazQ+5Dx+y2M4JDpYLHwOyeOkyQvQIVIYsLw9Riz5B0o4dyho83l98wYOOQP+R5eQgNyICOWHhyH0UjpywsEJxE87ipqCwEm6lMTGBxNSU3QtG5maQmJrByESK/PR0FCSnoCA9vdjbyb1KU15kZJkWT8erafXqMAsMhBk9Vpc/CjEkUGBsZQUjf3+OVaTrHgsfPz9xrdMBhOgRqK4Gz4z3kFZY68J+8CC4z58vUtL1lNyYGGRevoLMK5eRdes2i5q86GilheZZUINHE29vmPh4w5QevbzZymJkZspuAhIzBcbGSMvJgZ2zM6SWVpCYFYocEjvGxs9cPg1CZFUikZWfkoL8ZJpoPhkFiudF5xXvi49n4UYCKev6dZ6eEENKIVREDHl4cA8ngWEhsbCAaUAAcoJJ+OQiOyQEpr6+MLa21vSqCZ6BED2CSpOflo6wCRPkXdKpBs+UKXB+603hItATqC5JzoMHyCCRc/kSP5Kb6mmQOCFRw4KmcDL1eTxflkGBYnmykpJgUoFAZiOpFFIqbFbO4mYUO5T76BGy799H9v0HyL5/j+dzHgTJ44dIDN24wVOx77O0VFqFzOvUgdWLrdhSZAguMgPKg3l6p/aAQotPTg5yHj6EqY8Pu04F2nm8CdEjqBQUhxE+ZYpc8Bgbw2PhAtgPGiS2qg5TkJWFrJs3kXHpMjIvX0bG1auluqYkVlawaNwYFo0awdS/GltsTLy9uJqtLg74ZEGiO3WabIqk4T4WQw8KBdE95NB8UBBkWVmQFRFDyYU1YKSurrB68UVYtWnNj7RN9AlqbUBQXReq/WLIkKvV1N8fuVQBmoKbQ8Pk50GRqsQC1UC1hhRB4BVFiB5BhaHBIGLGe8g4d45qt8Pzs89g17uX2KI6BlWZZXFDlpxLl5B5+zbVon/ifeTGsWzSBBbNmsKyaVOY1az5XFeTPlBcDHUoLoYiIpB97z6yH9xH9r177PKjGKa8mBgk79nDE0Hbyqp1axZBls2bs2tEl6FBh8oJKArwUR8lXRS6qkTm4cHHA900ZIeGQpqZKbc4VmaZBpay/rwSCtQGhI61ypSxEKJHUOGTMWrBAqQePcrP3T78UAgeHYKCjFMOHULK778j+/a/T77ByAhmtWqxuLFoSiKnCUw8PTWxqtothnx8eCoqhnJCQ5F+5gzS/z6D9PPnOXYo++5dnhI2buQUetqmLIJat4Z53To6KR4VvZ6eVXnYEF3BFCNGri7ExkJiY8PZXpUq31BQwHWSDF30ELQdqBdYZbaFKE6oZehKYbyYFSsRv26dMobHZYr6KmhWNbqyD8oL3YWm/H6Ixc4TcSkWFuymInFj0aQpLBo3qtTFurLoS3FCsgaRq1AhgjKoFUsJKxrVfrFs1arQEtQGpt7yvlC6ch5QkT1qNyAo3G45OYhe8pncAk5JHUMGw3Hs2AoN1LQPqNgeFd3Tp2tRRTE1NX3qdihrcUIherQMXRhw439Yj5jly3neYcQIuM39UK/uQnRhH5SV3OhopLJF55Ay0FyB1NMDtt26w7ZLZ5jXq6dVRfz0RfSUhNLp0//5Ry6CqB/S/QdPvMe8YUPYD+gP2x49NBoQq0/nQVVD9XsiPvgQKfv28XP7YUPhPm9eubP8xD4oO6Iis0AtJO38TSl4bHv2hNuHH+iV4NEH8mJjkXL4CFIO/Y7MS5eLpZFL3dxg260rbLt3h3mjRmLfVTEU/G3z8ss8KURp+pmzchF09izy4+I4VT7q+nW2Fth06gS7Af1h1aqVTrrADBW6gfBc+hkk1lZI2rYdSdt3oCAtHZ5LFmvVzYUhoj+3UAK1k3rsGCI/+ojnrdq3k5/A4g5Qa4KRU48c5RidDOpoXKRhoLGLM2y7dIVtj+6waNJE7DMtwsTNDfb9+/FE8RtZ165xC5eUgwe5DUfKgQM8URC5Xb++sO/XT7Rz0RHo2kjWHWMbW8R/9x1S9u9nS5/Xl19UqG2FQDUI95aWoa3mzPTzFxD2+uscoEcDp+/6H3Q+A0XX9kFp8SJpJ04gcdt2pFP8QH6+8n/U4NWmS2fYdu8By+bNdM5KoK/urbJCGUCpR48heddvSD97rpi1zqJ5M9j3H8AWO7IcGfp5oAvErVuH2BUreZ7it3zWflsm4SP2QdkRMT2V2CiaRBsP8sxbtxA6egzfpVDqrd9Pmzj4Ul/Rxn1QckBM3r0bCRs2cjE0BbRP5EKnOyxbttTpatiGLnpKBqAn7d6N5F27ixWFpKKItl27wq5/P1i2aKFyV6W2nwe6RuL27Yha+DELWJvu3eC1YsVzra5iH5QdEdMjUAnZwcEIe/0NFjxUTdfn+3V6LXi03YWVuGUrErduRX5iovxFIyPYdOoI+yFD5HEfIl5A76BSAS5vvgnnSZOQcfEii5+Uw4e5KCIVQ6TJxMeHxQ+5v0RpAe3EYdgwTmmP/ngRUn8/hBhPT7jNnKnp1TI4hHtLy9AmZZ8bFYWQV19FXkQkjJ2dUW3rFi7Qpu9o0z4gsoOCkfDjj2zd4Q7kdOKam3OGj+OYMXoZ4yEsPc9v/ZJ6+DCSdv2GzIuXHv/DyAi23bvBefJkmNWooVfngb4QvWw5Etav53n3+fPgMHz4U98r9kHZEZYeQaXIS0xE6IQJLHiowJbv9+sMQvBoCxTUSlWS49dvkDdxLYzpMHZyguPIEbAfNqzS1V4FuouxtRXsBw7giVyc7P7avYc7yacc/J1LFNh07crix7xWTU2vrqAIru/NYJcllZKIWvQJpO7usOnwuLilQL0IS4+WoQ3KnlxZD197DVnXrnPzSApatmzWDIaCJvcBBSdTAGv8hvW8/RVQN2fHcWNh16ePQWR+CEtPxY+duFWruCWGApvOnbkBsHnt2jp3LdJXqEdX6LjX+MaGCoP6bdoEiwb1n3yf2AdlRgQyV2KjaBJNH+TcQHTSZK4bQg1EvVd9o6wpYihoYh+Q0KRUZXJjUe8mBRSg6vjaOFi/9JJBpZoL0VNxKG6Exc/q1ci+c0f5unWnjhwbZF63rk5ciwzBmv5w2HC21HH4wPbtT1TjFvtA9eO7OJIFxRuIznpfLngArsNjaIKnqqESAPEbN+L+Kx0R/emncsEjkXBNnWq//MyZcmT6NiTBI6gcdKzYdu0C/12/wfubr2FWpw6/nnbsOIIHDETYm29xRqZAs5B72mfddzB2cOCilGETJ3LfLoF6EVdSgZLoTxezn5lw++ADdqUI1EfayZMI6tsPMZ8t5YsdpSA7jhmNwCNH4LVyJSwaNBCbX1Ap8UMVnf1/2wnv1auUFh6KEQsZOAhhkyYj88ZNsYU1CMVJ+qxZzWEEOQ8eIHzqNLa2C9SHED0CJnnvXk6FJpzfnAzH0aPEllFjNlboxIkIe2MicoKDAamUGxLWOPEH3ObM0ZqGkwL9gOr32LzyCqrt/BXea1bDvL48diTtzz8RMngwH4uZ1x/HjwmqFovGjeH5+XLOvMu4cAGRH87lRAaBehCiR4DsBw8QOX8BbwnO+Jg6VWwVNZCfksL9lIL69EH6Xyf5NYrVCdi7F26z3xf1jwTqFz8dOrDblCoCU2NTgo7FkCFDEfr6G8i8KdxemsC2c2e+BhDUpDT2q680sh6GgBA9Bk5BZiYevfMOZJmZMPH1hccni0QTSjXESiXu+BkPunbjQGXk5cHU3x8+363lwccswF/VXykQPFP8kNiutmM7x5RYNGrEr6efOoWQIUMQ9elirgMkqFqo5pZDoYU9/tu1SPzlF7EL1IAQPQYO1YnIvnefK/l6fbESxjY2ml4lvSL9wgUEDxyEqPnzuYoy1TxymzMbAXv3wLp9e02vnsDQxU+7dvDbvg0+338P83r1uFFt4k8/IahnT6QeO67pVTQ43N5/HzadO/F81IKFSD99WtOrpHcI0WPAJO3ajeTffuN51zmzYUEXPYFKyH30COHvvMs9y7L/+4/99fZDhyLw8CG+oxPtIgRaJX7atkG1n3dwAoPE0hJ50dGImDYNyXPmIDcyUtOraDBQY2DPZctg3qghNxB+9M67yCtSc0lQeYToMVCy799H1Mcf8zw1v3tWKXRB2SnIyEDs//6HBz16KjPhqNYOZdB4LFwAqaOj2JwCrR1wKYEh4OABpbUh59RpBPfqzW5ZWV6eplfRIJBYWMBn9Wrup8b91WbOEsJThQjRY6ADc7gijsfPFx6LRByPKkj76y886N4DcavXcI8savzo9eWX8N30I8wLa6UIBNqOibs7vL/+Gp5ffw2JqytfJygAn4KdRaBz1SB1cuKYP4mdHQri4hA++U3kp6ZW0bfrN0L0GCBRHy9Czv0HMDI1hfcXX8DY2lrTq6TzJeWjPvkUYRMnsVuAysq7vD2N75htu3UVgeECncSm4ytw2PyTPLhWIkHW7dsc6By9ZIkIdK4CzPz94fXN14CpKXLu3sWjt9+GLDe3Kr5arxGix8CgVgfUrZtw+2BOmUvSC0qHehyFDB6CxM2b+blV6xcR+PtBbvQoMTcXm02g01B8j+vs2aj288/yawW1pvhxE4J69ULqcRHorG6o56HNhx/wfPqZs4icN1/U8KkkQvQYEFl37yrjeGx79ODAWkHFoOJhCVu3InjQYGTfvQuYmMB11izOgiH3gECgT1jUrycPdJ4zmyuH50VFIfytKQibMgW5UVGaXj29xrxjR7jMmMHzybt2IX7td5peJZ1GiB4DgRpaUiaALCsLpn5+cP94oXC7VKJRYPibbyH640Ucu2NarRqqbd8Gp9fGiR5ZAr3FiCqHjxmDwAP7Yf3KK8p+XkE9eiJh009cj0qgHhxeGwf74cN4nhIlMi5fEZu6ggjRYyBWCbLw5AQFcRyP11dfijieCkLNWIP79EXaiRP83H7wIM7MEun+AkPBxMMDPqtXcTNTqZsbJ0ZEL17MbVXohkCgnrIC7h98IG8hUlCAiFmzkJ+WJjZ1BRCixwCgWjzJe/byvNuHH8K8dm1Nr5JOdkOPXr4coa+NR15sLCS2tpyZRZlvFPcgEBga1Mw04MB+OIwYwc/T//4bwQMHIvPGDU2vml5Ctb08ly/jRInc8HBEf/KppldJJxGiR8/JukNxPIt43rZXL9gPGazpVdI5soODETJsOBJ+WM/PLZs3R8Ce3ZyZJRAYMpT56f7RXHh9/T9IrK2RFxGJh6+OQOL27SLgVk0ZXZSAQlBCSsrvv6vja/QaIXr0Po7nHWXcifuCBSKOp5xuwaSdOxE8YCCn68LYGC7vvA3fHzeyiV8gEDxumOn/6y8wq1mT06qphULk7Nnc20+gWuwHDYJ1p448T42iRcXs8iFEjx4P2JELFiInOBhGZmaFcTxWml4tnaEgNRWR02cg8sO58iKO3t6otmUznCdN4sq1AoGgOBzQv2M77Pr24efkUg8ZOgw5ISFiU6k4vofc6lIXFxSkpCBi1vsiiLwcCNGjpyT9+itS9u3jebe5H8K8Vi1Nr5JO9c1KmjQZqYcP83PbPr3hv3sXLBo31vSqCQRa30LB47PP4L5gPsegUDkHKuuQcvSopldNr5A6OMDjsyU8n/HPP4hfL3e9C56PED16SG5EBKIXL1EO2GQOFZSNzFu38HD4q8h/+BBG5ubwXLYUXsuWiWw3gaAclgiHYcPgt2UzpJ4eKEhLw6Op0zgRQPTvUh3WbdpwCQEi9n9fixYhZUSIHj2EysSTS4YuOB7z54s4njKSdvIkHo4ajfy4OBjZ28FnwwbY9ZGb6gUCQfmwaNgQ/jt3wqpNG35OiQCh417j7EeBanCZ/i7MyIqfm4uImTO5fIDg2QjRo4dNL1OPHuN5qusgsRJxPGV1B4ZNfpO7GlN3Y4dvv4VFo4Zq3lsCgf67YahxpvNbb5EJiF0xlBiQcemSpldNL5BQvObnyzluk+I3o5cu0/QqaT1C9OgRBVlZ3PiSsHqpPaw7yiP8Bc8O+CbTcOTcj4D8fJg3agjfbVth7O0tNptAoAIo8N9l6hT4rP0WxnZ2bOl5OHoM4jduFGntKsCsRg24vvcezyft2IHUP/5QxWL1FiF69Ij4dd8jNyyMqy67f/ihcGs9B0qtjfzgQ8StXs3PSST6bdwIqaNjVewugcCgsG7fHtV27oR5vXp8gxHz2VI8mj4dBdnZml41ncdh5AhYtWvH85RxKlyIT0eIHj0hJzQU8evW8bzTG2/A1NdX06uk1VAJ97BJk7mBH+Hw6nB4/+8rzj4RCATqwdTbC35bt8B+yBB+nvr7IYRPnixiUVQQPO65+FMYOzoiPzEREXM+gKygQBW7TO8Qokdfemt98gm3SjDx9YXT6xM0vUpaTW50DAcsU9l8wvW9GXD76CNRf0cgqKI4FI+PF8Lto7n8PP3MWYSOn4D8lBSx/SsB1e3x+PQT+TY9fRqJm7eI7VkK0tJeFOgWqceOIf3kKZ53n/shX1QEpZN97x5CJ07kcvmgXjZLlsCuV0+xuTQA3YnmxcUhN/wR10aiUguU3kziPT87C9lpaciCEZCXx689MeXmAMZSjhMxtreXP/K8/FGieG5n//g1c3Oxr7UExxEjONGCXMyZV67g4Zix8P3he+FergQ2HTpwN/akbdsR8/nnsHzhBZjXqqm6naYHCNGj48g7HMtr8th07sR+c0HppF+4gPApU7mKqcTGBt7ffAOrF1qKzaVGC2R+QoJc0ISHI4cfCwVOeDiLHBIvzyJLxetEzWFNAwM5+NOsenX5Y80akLq6ihg4DWDfrx/vk0cz3kP2v//i4chR8N2wHiZubppYHb3AbdYsZJy/gJygIE5jr/bLz+JGuAhC9Og4cWu+RV5kJHfedZsjb0QneJKUw0cQ8d57HLws9fCA73drecATqI781FRkXrvOd+08Xb/OlpvnYmTEosPE0xPGtracfgsTKXJlgJm1NSTmZpCYmnKAPk8mj+dlebksYvOTkpCflIz85CcnshQVvUnIunGDp6KQCGYBVFIMiaB2tWPbpQskq1cjfOpUHqgfjhjJwsfUx0f9X66HUFwipbEHDx3GFbFjV64UY0MRhOjRYbKDgjjtk3CePJkHDUHptYsezZjBg59Z7drwWbsWJm6uYlNV0opD1prMy5eRwSLnKl9gIZOV+n5jF2eYennDxMvr8eTtBVMvL0g9PVnUFCUvLw9JSUmwt7eHVCqt1HoWpGegIDmJBVBudDSy799nN2f2vfvIefCArU3Ua41+C03F1tvJCZYtWsCqTWuugCvOMfVg3a4tfL9fx8kFdFyx8Fn/AwtQQfkxr1sXru+8jZjlnyPhx02watce1m3lRSINHSMZXRUMhJSUFNjZ2SE5ORm2trbQRgoKCpCQkABHR0dIJE+PM6fdRtVNM86dg2lAAAJ27+I7X0FxqAgaBUnKsrJgXr8+30Ea29ioZB8YEnS8Zd28xcXlyIpDQocqVz+BiQks6taFRZMmPJHFxMTTo9yxNKoSPc+D2iLkhIUViqB7SkGUExzCadUloXONKgyTCLJq0UKvi39q4jzIvHkLYRMmsOXOmAobfr8OFpTibqBUZh9QzFzoa+N5jKCbjoC9e7lYpKGP70L06OhBnnzgACJmyAtS+W7cAKtWrapwLXWDLIoRGD2G7+JpsOJeQGU46YXoKSJ0btxAyu+HuPkqxeCUhAYmi6ZNYdmkMYscEpaqCKSvKtHzNApyclj4ZN26hfQzZ3ii+KRimJjAskkTuQhq2wbmderASI9EsqbOA042eG0815qRWFtzRWfLpk1hiFR2H+RGRSGobz8UJCfDrm9feC79DPqKED2V2CjafpBTjZmg7j34omDbowe8Vq6o8vXUdnJCQhAyYiTy4+O5B1m1rVth4u5eps8asuhRCp1Dh5F66NATQse0eiAsmzRVCh0TPz+1BABrWvSUdtec/d9/SPv7b6T/fQaZly5xfFhJAWjVujVse/aAdbt23GVcl9HkeUB1x0LHjuPjj+IVvb/5mt2LhoYq9kHS7t2InC2P96z2yy+waFAf+ogQPZXYKNp+kEcv+QwJP/7IpvWAgwdFfEopdzcPXx3BF0yKyfDb/BPM/P1Vug/0z3V187FF59GjJ+IDbLp3g223blUWXKptoqckFBCdcfEi0k6fZhFEsUFFIXeCfd++sBswAGYBAdBFNH0e0HlMLnzqKUUC0uuLlbDp1AmGhCr2AQn2kKHD+GbGomlTtnir40ZF0wjRU4mNos0HedadO9ywj+INXGe/D6exYzWyntpKXmIip73SIESmcb9NP/KgrUsX+6q0hlGjVRI7pQqdbiR0umqkure2i56S5EZGsguMmv2mnTpVLB6I3H72AwfAplt3GFvrTgyQNpwHefHxHJNHVjYYG8PzsyWw690bhoKq9kHG5ct8I0h4ffkF38DoG0L0VGKjaOtBToqdBnTKMDGrWRP+v+2EkQ4MCFVFflo6QseOZasFpT1ToTPL5s118mKvTqtO5sWLiN+wEWknThTLtjKrWwe23brDtmsXmPr5aXQ9dU30lKz4nbx3D5J3/sbCUgG5aWiwIQFk0ayZ1t9ta8t5QFl3YRMnIfPqVS5v4PHJJ7wNDQFV7gPqc5Zy8HfOnAw4eEDvavcI0VOJjaKtB3nSb7sQ+cEHPE8mSstmzTS0ltoHNS0Me2MiMs6fB6RSjgGwefllnb7YqxKKP6FaRQkbN7IoVGBarRrs+veXW3Q0LHT0RfQUE5hXriLpt51IPfh7sf5StK3J9WXXr5/Wuqe16TwoSE9H2FtTOBOJLD4+337Lae76jir3AVlzH3TvwSUaXKZPh/Mbr0OfEKKnEhtFGw9yCl5+0KUrZ5DQhZLMvILHacfhb7+DtOPH+U7Qc/nySrWW0KaLvSoKBib9/AsSNm/mIpYKLFu2hOPYsbB++SWtzDjSB9FTctAm0UkCKPPipcf/MDGB/YABPADRHbg2oW3nQUFmJh6SJffadY5npMal5rVqQZ9R9T6I+eJLxK9dy1WwAw8f4n5dhja+a/5IFpSJpO3bWfDQye46U56qLpC7/CLnfiQXPNR7bN5HopcWxeuEP0L0kiW4/9LLiFm+XC54pFLY9u6Nar/+yrFONq900ErBo4/QeWs/oD+qbd6MgN8PwumNN+QDTm4uknbswP1u3RE5f8ETsVWCItvQwgI+q1bBxNtbbvmZOIldiYKy4/T66xxkT1bH2P/9zyA3nbji6QAFWVmI3/gjzzuMGAGpk5OmV0lr3AcxS5ciefdufu7yzttwGD4chgwV1wt/91086NKFK7HSxY1aLDiOfw3Vjx6B1/JlsKhvuMXetAHKJHSd/i6qHz8G90Ufyy08JcVPKTWRBIDU2Rk+a7+FxNYWeVFRCJs8iQWQoGwYW1vB9Z13eD7p151cy8zQEKJHB0j67TeufkvBuY5jRmt6dbSGhA0beWAnyFXjNHEiDBXKWota9AkXIkv9/RDZxXkwdftgDqqfOAG3mTNh4uGh6dUUFIEqqDsMHozA3w/KxQ+1kVGIn67dELlAiJ/SMAsMhPfXX7NrMPv2v3g0fQa7uAVlw65fP5jVqcNJDFT+xICaMjBC9OhAAGrC9z/wvP3gwcLKUwjVSIlZIS/KSIG4ru/P0vpsGLUdH5t+woNu3ZG4ZQunSlMBQa8vv2SfvePo0TqVJm3Q4ufQ78XFz3Yhfp6G1Qst4fnJImVvvejFiw1u8K4oRsbGcJs9m+czLlxQhgYYCkL0aDkpBw/KTd1SKZxeG6fp1dEKqHYH3d3RAG/eoAHcFy4wSMFD9WCC+vXnCz6VmTe2s4PbR3MRsHs3Z2OJcgY6LH4+Xvik+Fm4EHklW2EYMNRWwXnKFJ5P3LoNCYUhAIKyiUabzvJCj9HLlnPbFUNBiB4tD9KN+24dz1NBLtHhGZDl5yNi5kzkxcRAYmcHry++eKJDt76THRSE0DfeQNjrb8grAUulcBg9CoFHDsNxxAghdvRB/AwZohQ/1EaFxc+27Qjq0RNJu3YLq0Yhzm+9yeKHiFm2DClHjmhy1+kUrjNnsoswNzQUiZu3wFAQokeLST1+XD6oGRnB6fUJml4drSBuzbdIP3OW5ylt39Rbu9J81Ql1no76dDGC+vRF+slT/JrVS+0RsHcP3D/4gC09Av0TP9UPHYL7ggUwtrfnYyByzhx5e4aHD2HokIXXY9HHsHzhBY5RiZg5C5nXrml6tXQCU19fOI4axfNxa9YYjBVRiB4thfzT8Wu/43mbLl10tn+PKqEy/3GrVvG804TxsOnQAYZyLCT+8gsedO2GxJ9+oiI2MA0MhM+67+C7dq04NgxB/AwbyqnuCqsGFekj8Ru39rsnGp8a4vbx/t9XMA0IgIyKlE5+Eznh4ZpeLZ3AefIkGDs6oiA1FbEUHG4ACNGjpWScPausnOukZ5UzKwLV43j03ky+m6MS/i5vvw1DgO6+wt+agqiP5nE5fo7bmUtxO7u4k7fAcJA6OMBz6WfwXf8DTHx9eYCP/eIL7sWXceUKDBk6L3y+W8sNhqmeGVVnp/NF8JztZmMDl2lTeT5px8/IuntX7zeZED1aSsI6eSyPVdu2sKhn2HVVKB310YzpfDEzdnCA18oV3HVZ30k7/TeC+vZF2h9/8HNqW8AZWSNHGMTvF5SOVevW7NKkAocUz5V97x43k4z6+GOuwG2omHp7w2fNahiZmyMnKAjhU6dxywXBs7EfNAhmNWpwmYuYpcv0Pl5MiB4tJPfmTWScv8DzzhPfgKET+9VX8tL91GLi8+UwcXODPkOZFFQ/I2zCBOTHxskDtr/8Ep6LP+W4DoFAYm7OBQ79d/4K80YN2QJKGUxBPXsh5ehRg91AFg0bwnP5Mr5WUDp25Efz9H4QryxGUilcZ7/P8+l//430kyehz+iU6Dl58iR69+4NT09PDmDbXViJV9/I+GkzP1o0bQqLCnQJ1ydST5xA/Lrved75zTdh3aYN9Bm6aw8ZPAQJP8rTbylAM2CPPAVdICgJ9Z6qtnUruzyp1QVlNT6aOg3h095GfkqKQW4w286duW4XkbxnD5J379H0Kmk91m3awLqwQXP0Z0v1Ok5Mp0RPeno6GjVqhFWFwaz6SNadO8j5+2+llccQ688ooD5EEbPn8Lzli63g/OZk6Ct0N5qwZQuCBw1G9p077LZwfW+GPH7D3V3TqyfQ8mJz5PIMOLAf1p068mupR44gePBgZN3R/xiN0nAcMwa2PeVNh6MXLUJOWJimV0nrcZ01i687OcHBSNy+A/qKTome7t2745NPPkH//v2hryR8L7dqmNWqBav27WGokC8+/N3pXHSPGjN6LV/OF3d9LbYYPmkyohd9wsGpptWqodr27XCaMEFvf/PTOkrTjU1cXBzCw8MRExPD3dYVolC4KZ4NiWOfb75h946RhQVyH4YiZOhQJO/bB0ODbhap+bDUw4P7z0W8P1u0qngOZgH+cHhV3rsw9ptvuDyCPiKFHpOdnc1T0dbziosrTdpGTmiovG8S3am8PsGgL/TUGTzr+nVAIoHHis8hobTKKtpnim1Oj+r+TmqnEfHudOTHx/Nzu8GD2TQvsbTUymO0Ity/fx93795FREQEIiMjEf4oHKGPQjFu2jjYVLfB1YirmN9pPvJz8p/4bP1l9eHi54K88DycmnEKxibGMLczh6OTI7zcveDj4YOtP22FRCJBbGwsHj16hBo1asDKynBbb9j07AnTmjXxaNrbyH34kGvXZFy5CtdZMzm9WxvPA3VgZGMDjyWLETbuNWRevsyFXp0m6VZ/vqreB06TJiF5z16+2Yz/aTMXf9QVyrp99Fr0LFmyBAsXLnzi9cTEROUdpDaRunoNR9Abe3sjt0ULJBhIsaiS5PxzEcmFcU1Wr7+OrIAAZGlgW9Bxok6yjh5D6uLFXG3XyM4ONu/Pgmn79kjKygJo0iHoohwWFoZr166xwKlZtyYcmzpiy/0t2DNpD3KiimfRGBkb4V//f2HXwo4/a1HbAhJTCSRmEn40khpBViBDnnkeYjNjkZOfA9vmtpDlypCXloeohCg8evgIF4wuoMmWJrzMhL8SELFB3p3c2tkaAQEBaFCrAdq1aYeBAwfCoHBygu3ab5H66WLknDqFpK1bkXb9OmwXfQxjFxetOg/USvXqsBg+HJlbt3KNr7wG9WFCzTZ1jKrcB+YDByJj/XokbN0KowH9udG1LpBaxsxFI5mOmhLIfLlr1y7069evXJYeHx8fPoBsbW2hTeRGRyO4S1cOILOe/T48R40yyHgeylwK6duP71ApiNf7h+9hJJFUfTHAxEQ4ODioZR9w/M4PPyBu5RdKV6bXmtU6Gbuzb98+rFm/BmfPnkVK7OPAWft29vAe783ziacSIcuXwcTRBFJ7KUzsTWBsbQwjSeW3bUFOAYskIvNhJlKvpCI7KpsnEloFWQWwaWQDv3f90CugF6SnpUiLSUPLli3x8ssvw03PMwGVx9qXX8lvqJyc4Lnic1i2bKnx86Aqrymhw4Yj+7//YEKu419/YUuqLqCJfZAXH4+gjp04xMB90SLYDRwAXYDGd9pOycnJzxzf9drSY2ZmxlNJyBROkzaR9OMmFjxSd3eYd+3KB7i2rWNVEL9+PQseqkPjvmA+jKVSjZlJ1bEPqOYQxe4k7dihrMNE6ei60An94cOHOHDgAG7duQXnoc747d5viD0Yi+h90TDzMoNjB0dYBFrA3NscZh6PzzuHdg5PLMvHxgdNXZuikWsjVLevDi9rLziYOcDE2AQFsgJk52QjISkB1rbWHHmYL8tHfkE+P2bkZeDf+H9x+tFpHAw+yO8nLPwseCo6YOQl5aEgW/7//UH7EbwpGOn/pSvf41/XHwN7DcSE1yagVq1a0Edc3ngDlg0acJNecqOGjZ8A1+nT4fjauGcOpOo8D6o6vd/r8+UIHjgIuSEhiP38c3gsWABdQBP7wNTFBbZ9eiP5151cAd5+0ECdEL1l3T56bekpTQna2dk9VwlWNXmJibhPyjojA65zZkPWsyccHR11+kJT0ZimoF69+Q6DMrVcpk3T2IWGXIuq3gcF6ekInz4d6X/J62DYDRoIj/nztbbQIG2Hc+fOYe++vfhl9y8I+i+IXyfXU+2va8PYwhj56fI4HGOrJwOux9Ybi/7V+6OaXTVIjMq3Hcn9nJSUBHt7e0jLKXzTc9MRnByMnfd24te7vxb7H7nMyAKU8SADabfSkHYzDflp+fB92xevD3sdbzd5Gwd3H0SPHj1gY2MDfSKX4qneeQdZ164r29t4LF78VMGtrvNAUyT8tBnRn37K895rVutEGxtN7YOsu3cR3Efe8oQySKkgprZT1vFdp0RPWloaB0USTZo0wcqVK9GhQwc+IHx9fXVW9MSv38AdgqnwXMCxoxzToS8XmnLFhEycyI00TXx8ELBvL9+h6cuFJjcmhjO0sm7f5ucub0/joEFtvIOi308WlfmH52NJryWAjMrVG7ObiCbr+tYseBQE2gViapOpaOnREjamqhEKlRE9pZGdn43zkeex9MJShKaGFhNBmSGZMPcy53iijHsZCPo0CFJTKXr26onRI0azADLX0LGoDldPzGefcSFDwqxGdfj88ANMXF31XvTICgq4PUX66dPcb4qqWkudnaHNaHIfhL42nvsdUlNj6vGn7eil6Pnzzz9Z5JRkzJgx2Lhxo86KnqABA5B9+184jhkNl/ff16sLTVlJOXKEs00I6qFjrcF0fVVfaLLv30foG28gLyISMDGB5yeLlI0jtQXKfNq+fTvWrl+L+DrxcO7qrAwOJneVhb9FsRicBS8uQJ/APuyOUgeqFj2lEZ8Zj9VXV+Pnuz8rXyPLVfL5ZCSdT0LGnQx+zcTSBGNHj8V3a+QNgPUBKtoXOW8+l0igPl5+G9bDxMtLr0WPoodfcN++nI5NxfjI4qONNx7asA/STp5kkUgEHDyg9Y2N9VL0VBZtFD00IJJLh6j2668wq1tH7y40ZXH7POjZC3lRUbDp3BneX/9Pby406ecvIHzKFO5iLLGx4d9m1aoVtIVLly5hxRcrsGPHDhTkFUBiLoFzD2e49il+59/CvQULHV/b51tUdUX0FCUrLwvrb67HmmtrlK/lJuQqBZBFNQt4jfXCT91/guyRDLVr14aFxeP4IV0k/cIFtj5SHRuqZ0PCh2pE6bPoKXmD5b5gAXew11Y0uQ9kBQU8NlEfM/thQ7U+Dqqs47v+HMk6SvK+/fxo6u8P83p1YYjErlrNgsfI0hJuH8grMOsDqX/+idAJE1jw8KCyZbPWCB6611mwegGaN2+ObVu2wTzQHN6TvFH7q9pKwdM7oDcujryIG2NuYH3X9VUmeDSBudQcbzZ+k3/r5VGXMbvlbM42c+7ujOoLqsNzpCe/b8TeEWjxcgu4erpi1qxZHNytq1i1bAnfDeshsbVFXmQkQkaOMogu27ZduigzkqI/+wzZQcGaXiWtxEgi4crWBLXyoNhTfUCIHg1CSjqlsFqqXZ/eWm1mVRd0kVX0mXJ56y2YeHhAHyALz6O33+EaPGa1a3OFZfOaNTW6TllZWfj666/xv+P/Q8NNDfGz5Gc4vOSAwIWBCJgTAPtW9hzX8nOvn3nwX9xuMcyMdaNGhyoxkZhgRJ0RvA2ujrqK6c2mc/A2IwNcerkgxywHy5cvh3+gP8aNH4egIHmQt65h0agR/Db9yDEu+XFxCB01Gpk3b0Hfcf/gA3brybKyEDFrll73mqoMdn37cKwpbaekHY/dwLqMED0aJPPKFeRGyIup2fbqBUMUfVELPwby82FWowYcR4+CPpB54wbCJ0/meAkKFKW7aRO3JwNFq4rc3Fx899138Pb3xrRp0/DJV5/w6xSM7DXOi9O8R9YZicsjL/NAX8dJ94q3qQtjiTHG1R/H24VcW1QTyLmLM2osqQG/GX6cor9x/UbUal4L4cnh0EXMa9eG30+bIHV1RX5yMkLHjkXG5cvQZ6g5q9eypYCxMbJu3kSsHvdzrAwSc3N2bRGJW7ZwZq2uI0SPBkneK7fyWDRpAlMfHxgaZDLNvHSJ56kmj7ambpe3S3rYhNc5ToKy0Hy+/wFShyfr1FQF+fn52LRpE3yr+2LixIlISk+C+1B3tlQo2NVnFw/o77d8X21ByfpCY9fGvK1ODj0JBwsH2DSwgf8cf1R7vxo8XvVA993d0WZbG2zYtAGhoY8zxHQBs8BAdr9SMHNBWhpCx09A+tlz0GcsGjeG86RJPB//3TqDcO1VBIdXX+UEjLzYWKQckrdJ0mWE6NEQpJgVBxC5tgwN8g9Tfy3Crn9/WDZrBl2HOjlTmifdLdNds6YtPEs2LuHMxpi4GLgOcEXNZTU5RoVcWMcHH+cBvLpDdY2tn67iYO6AU8NO4cqoKxhWexis61hzOw0iIS4B48ePR2CNQMybN48bqOoKdOPlt/knDmaWZWbi0eTJyD79N/QZ58mT2MpM1apjlsmvR4LiUDkDux49eD5h44863w9SiB4NkXbqFDd1g1QKm27dYGjEfvEl8hMTIbGzg+vM96APqbAkeOhuiHzgVNDL1FvehqEqocDaE1dPoMGPDbBdsh3ur7qj1vJaHJxM7qyDAw6y2HG11JwY0xekEinmtpqL66OvY1IjucVAaiuF3zt+MHY2xqJFi+BX3Q9byC2gIwMFxdSR8DGrWVN+Y/bhh0gpbIKsjxhJpXB9/32ep/o9dF0WPInjWHlAM9UZy7x4EbqMED0adm1Zt2unMfeHpsi8fh1JP8uD4qgcvtTREbputQqbMB65YWHc08dn3Xcwq169yoOUF368EAE1A9BnVB9+jerqUPwJVUve3Xc3ix1q/yBQLZSA8Fbjtzjrq6FzQy7eWH1RdXiM9EBSahJGjhyJAa/qRv8iggr2UXCzeYP6HG8XOWuWXosB67ZtuAAfEb10KbeKERTHvE4dZb+2+I3yxBNdRYgeDZCfmoq0Eyd43q634QUwx379DT+aN2wI+8GDoMvkp6UjbOIkZN+7DyNTU3ivWQOLBg2qdB3++OMPVK9THQvmL4CJkzzNWsH2XttZ7ATaB1bpOhkilPW1pecWnB52mrvIO3VyQo2lNeDY0RFXPK+w9Y0qQyv6KWkzZK30/uEHSOvWZeHz6J13kXVHf2Ne3GbO5KDmnPsPkPRr8dYlguLWnrQ//kCODpdqEKJHA6QeOcKmY8ogsNaB/i+qhNJh0wvvGl2mTq3yDuqqpCA7G+FvvYWs69fZTen11ZeweuH53atVWcBvyrQp6NixIyIjI+E2xA2BiwJhXc+a68yQ2KnnVK/K1kcgx87Mjrc9Wdek1lJ4jvKETUN5e466C+qidoPauKgDLgJja2vYLf0MJt7eXEA0bNIkbqeij5Bl1mHoEJ6P/d/XfGMqKA5VsDbx86UiX9zHTFfR3RFHDwoSUvVhiY5XdS0v8YU9XMzr1YNV2zbQZaIXL0HG+fPk34DnZ59VeQPD/cH78dPZn2BZ05LdKS49XCCRSnBhxAWuMyPQLGRdI/Gz/KXHAbJZ4Vm4f+c+Wr7QEh988AGys7OhzUgcHOC1ZjVXE6cChuGT3+TMRH3EecoUSKytkZ+QgPjv9KfliEqLFY4ezfNJv/2G/JQU6CJC9FQxudHR8oHSALO2qOVG6tGjPO80aaJOF2NM3rsXSTt28LzrzJmw69Wzymru/G/V/1B/Q318dOYjeI33gv9sf5i6muKLl7/gQdZCalhCWtvpVq0bV7YmHF92ROCCQJj5mGHJkiVo1qKZsomyNqezc2sYqRRZt27h0cxZkOXnQ9+g2ELK5lJkKeWE62bdJXVi368fV/CWZWQg6RfddAOqv6mNoBgp+w+weVDq4gLLF14wqK0TV3j3RAX7bDp2hC7X4omcv0BprXMcN7ZKvjciIgK9B/TG5fOX4TnWkwdQysgikfP3sL+1vs5OTl4BIpIyEZ2Shay8An7OU36+cj47rwDGEiPYmBlDWpADLxfAydoc9pamsDWXQmqsm/dpVNmaBOnPd37GIixC4EeBiNkXg1t7b6F+k/p4FPIITk5O0FaofYrHwoWI/PBDpB0/jpjln8NttjzrSZ9wGDkSidu2Izc8HLErV8Jr5UpNr5JWIbGygsOQwYj//gckbN7MTbIpA06X0K211QOSC9tO2PbsCSNjYxgKVMMm5cBBnnd64w2djeWhwOXwaW9zHRPyb3ss/rRKLFYnT55kwZMSnwKnrk6wb2vPr//Y7Uc0dWsKbSEjJw83wpPxMD4D4YkZCEvM5MfwxExEpWSR3q8UJHz8nKxQw80atdxsUNPdhh897Mx1wnI4pNYQdK3WFW23t4VbfzdY1bJCVmgWXt7/Mv4e/jdsTbWjEXJp2A8cgJzQUHZRJ2zcCFM/XzgMHw59QmJmBtf3ZnDgdsrB3+EwchQsmzbR9GppFQ4jRiB+w0Z2d1J8qm1hDR9dQYieKoQqfmb/9x/P2xpY1lb8uu85C4SqFNt27w5dhGqtRM2bh5zgYBiZmcH7q69gbGOj9u/84osvMGPmDEhMJPB50wd2LeWF8Kg4HtWK0SSRyZm4GJKISw8TcTk0EbciUpBf8GxlQ5Ycc6kEpkUnY3o05vm8/AIkZ+QiMSMH6TnF3SgpWXm48SiZp6LYmElZCNX1tEXb6s54MdAZdhYmWh3o/Mm5T7ADO2Bd15pfb/VDK/gd8cO3X34LPz8/aCMub09DblgoC4KoRZ9wBWfr9vJ0b33BpmtXWDRtiszLl7khabXt23T2Jk1dtZxsu3ZFysGDiP/xR50TPUYyXamaVYWt59VFzIqViF+3DqaBgQjYv6/UO1NKZ01ISICjoyMkenKiURzTg06duamf+8cL4TBEniWhrTxtHyRs2YLoRfK+VR6ffsp3vuomLCYMAXUCuOeT71RfmHuZo4d/DyxtvxSaICkjB0duRePkvVhcfpiIiOSsJ94jMQJ8HC3h7WABH4fCx8Ln3g6WcLE2g4Te9JzMtKSkJFjZ2CIjV4akzFwkZeQiPi0bQXHpuBuVirsxqbgXncYusdLWobGPPdrVcEH7ms5o5G2vla6xR2mP0G2nvDhp0rkkhH8bDntnexw5eAQtWrTQyvOAshZDx4xF5tWrXJfKb+sW7t+lb7XEQobIe055fv55lcXs6cp4kFlk+/jv3aPxZsrlGd+FpacKm2smH9ivrM2jC6Z4VZGwfj0LHqm7O+z69YMuQid59GdyoWE3YIDaBQ/1zbqZcBMjfx+JajOqwcTRhON3VnVchfbeVXtnTVaXw7ejcOB6JP6+H4e8EpYcG3Mpmvo6oJmfA5r7OaCRjz2szFRzaTExlsDJTAon69K7vZNVKSwhA3eiU1kIXQpNxLmgeGTlFuByaBJPXx2/x+vYJtAZfRp7omMdV5hJtcO17GXtxZ3cG//UmLvcU32f8O/C0bpda/yy/Rf008LzhVxA3qtXIWToMC7IGTZpMvx/+ZnjFPUFi4YNYdu7N1L27UPMyhWw6dSRm28K5Jg3aABTf3+2eqceOaoVoqesCEtPFZHxzz94OEqe7hd47OhTWxRoq7KvKHkJCbj/SkfIsrLg9sEHOtFJveQ+oIrLwQMHIi8iEma1arG5W52lBoKCgtCuWzuYDTSDVW0r5esnhpyAs8XjwoPqFjpHSOjciMTpe8WFDgmIjrVd0dLfiYVODVfr51puyovC0mNvbw9pOQMls3Lz2Qp18l4cTt2LZZdbURwsTdCviReGNPdBHQ/tiaEZ/ftoXIm5goz7GXj41UPkp+Vjxecr8O6772rkJul516LsoCCEDBuOgpQUWLVrB5/v1urVzVxuRAQedO8BWXY2XN59F84T36jyddDm8SDmyy8R/+1a7l0WsG+vzlh6hOipIqIWL0bipp/YV1xt6xadPMgrQswXX3Lgo7GjI6ofP6YTdYmK7gO6hIdNnoz0v05y5oL/zl+5IaO6uHTpEl7q/BLSk9LhOUaeoVWV8Tv3Y1Lxw+lg7Lz8iLOpisbMdK7nhp4NPNC2hrPaLSWVET0liUvLZgvVoZtROPZvNHLzHwu4Bl52GNLcG30ae2lFDNDaa2vxzdVvkBObg4crH0JiKUHszVhYmT8Wv1VFWa5FqX+cQPibb/K827yP4EgdufUIxcBObrzAI4e5RUdVos3jQda//yK4v9ziHXDwIMwC/HVC9GjXVtRjMi78w4/W7dvBUKDiVYlb5ALPcexYnRA8JUncuo0FD+GxeLFaBc/hw4fxYtsXkZGWAd8pvix4+lXvx0Gv6hQ8FNZ35n4cxm24gE4rT2LbhTAWPCR0BjTxwg9jmuPiR52wckhjdKzjpjWuobLibG2Gvo29sGZkM5z/oBPm9aqL2u7yAHQKiP5ozy20/PQY5u+5iahSYpSqkomNJuK7zt/B1MUUAXMD4Pe2H1rtaIXk7GStbFpq80oH2A8ezPPUpTw7KBj6hNOE12Hs7MwFGeNWr9H06mgVZrVrc2IKQVlcuoIQPVVAflISsu/c4XlF0zZDIHHrVhSkpXExK4dXdS+1NS8mBrFffMHz9sOHwbZrF7V918GDB9Gjdw8UGBeg2qxqsG1mixnNZmBRm0Vq+04SNr9dDkfP/53Gq9+fx4k7sfw6uauWDmyAf+Z2wsqhuil0noajlSlea+uP399uh71T2mBkK19211Ew9I9nH6L9shMaFz8ver6IwwMPc6NY6tpO1J1UF4OGDWILmLZB9XpMfH3ZhR0xaxbH7+kLxtZWcH5zMs8n7drF13KBHHJlKq6JQvQIipFx6RIXJDQyN4dF/foGsXXozijhx0087zhyBPfx0TVili7jnkMUoEnd4NXJ7G2zYWRmhGrvV4NVDSvMfWEuxtZXT9HDggIZfr4YxgP89J+v4XakPOalXQ1nbBzXAkfebY+hLXxhbqIfQudpF+yG3vb4pF8D/PNhJyzqV59r/eTkF4qf5SewYO8tjYkfT2tPbidCkIUn7WYafvv5NwwcPJCrcmsT5Pb1XPoZIJEg6+ZNxK1Zo39ViO3suDaXaEZaHJsuctGTdfs212LTBYSlpwpdWxaNG3MnbkMg5cgR5CcmwsjCAg6jtD94uSQ5588j9fffed7tgzlqrcfTa1cvyDrJUP2T6rDwtWDrztDa8nRQVXMhOAF9Vp3GrF+vc7FAE2MjDGzqzZaPn8a/gJdruepVMGpZIHE3qpUf/pz58mPxk1eAjWdClOInObPqhQZV2qZYLtofPpN8YNvSFnt378WAgQO0rmeXZZMmcJ40kefjvl3L6ez6AsXzUBViImHzFr2yZKkii0vq4cHzlMWlCwjRUwWk/yO/Y7Nsqdm6G1VJyl55NL9N506QOjhAlyjIykLqSrlby6ptW9h0k9dRUTVHjx6FcytnBMfL4yBM7E2wvP1yjuNRNZTW/daWyxiy9ixuPkqhHqkY2twHp99/BSuGNNKqLCZNQS48pfjpWw/uto/FT6eVf3HKflXH1VAs1+WRl2EkNYLPRB/YvWiH/fv249URr3JZA23CefJkmJMlu6AAj2a9z1ZSfcGBArSNjZEXFYXUY8c0vTra5eLqIrf2pBw5DF1AiJ4qCObN/ldehdlKw8XGqgoqRph+9hzP2/XpC10jYd06FDx6xFY593kfqcXycf78eXTr1Q2JNxI5U4f4X4f/oZu/agVWenYelh/+Dx1p0L4Rya+1rOaIfVPaYumghnCzFbVHShU/L1bDX7NexoLedTmgOzY1G29tvYwJP17Eo6RMVCXUU+2fEf9wDR/v171h28IWv/32G06fOQ1twsjEBJ7LlrEbPzc0FNFLl0G/qhDLB3eF214gx6Zwu2Rdu47cSPk1Ri9FT0xMDE6dOsUTzQueE89jagrzhg0NqqmqsYszrF5sBV2Cao9wy4zCTvCmvr4q/44HDx6gY7eOkEHGhQfNPc2xttNadPDtoNLvofo6HVf8hVUnHrDFgioirx7RFDsmtkJ9L3krC8Gzxc/YNv44NuMl9Gjgzq8d/y8GnVf+xWn9z2u3oUrMpeY4/+p5GEmM4P2GN/zf98eUoCnIL9Auaw+lLbvOfI/nk37+mVPa9QXH0fI6a+S6o2KlAijDNhSFKVOPHtU/0ZOamopRo0bBy8sLL730Ek80P3LkSM6PFzw9nocqmRoCyYWuLbuevXSqqSr31lr4MRWJgbGvLxxee03l3xEfHy+vw5OcDp/JPrAMtGTB09qrtcq+IzsvH5/sv42RP5znuB1LU2PM7FoLx6bT4O1hcDE7lYWsYatHNMP3o5vD084cGTn5WLT/Nvqt+hv3Y9KqbD0sTSxxethp7sGmKFpZf3V97N69G9rmCiK3MBH50UfIi4+HPkDXcPNG8hvXhE0/aXp1tAYjiQQ2nTvzfMrhI/oneiZMmMCm+f3793PxMJpo/uLFi5g4UR7IJiheiZmwNBDXVtadO8r0fLu+faBLUMn5jPPned76vRmQqCHofPSE0XgU/AgeIzxg28QWkxtNVqngoeKC/Vedwfen5XFCLf0dcXT6S3irQ3W9zsaqCjrVdcOR6S9hXJtqHBNFNX76fnMavxe6DauqWemfQ/5UPqeWFf0H9ueSB9oCiWrqTWdsZ4f8+HhEf7oY+mbtSTl0iN34gsdNWglq0pqr5Z6fcoseEjjr169H165dueohTTS/bt067Nu3Tz1rqaPkp6VxKp8hiR6FlYdKk1PxKl0hPzlZ2VuLeu6YNm2q8u9Iz03H/Xb34T7cHU6dnBBgF4A3G8ur2arCSvXTuYdcc4dS0KUSI8zqVgvbXm8FL3vdKwqprVibSTG/dz3serMNfBwtuAv85C2Xsfjgv9wdvipwsnDC0UFyNwKJZ+rJNnDoQNy7dw/agombK9w++ojnqRu3vmRzUdCu1M2NrcFUuFQgx7J5M666T2EN2h7oXW7R4+TkxKWeS0KvOehYlo66yaR4noICDvCzaNwI+o4sPx8p++RNVW379NYpN0r8unXIT0jgQoouhTEJqiQ2LhattraCqZMpnLvKS9nv7qsat0RCeg5e33QRH+2+yUX2/J2tsHNya7z5cnUYq7gnlkAOdXCnYPCXa8ljGb47GYQR35/ngOeqwN3KHeu7roeZuxm8J3sjKz0LPfv2RFpa1bnbnodtzx7sEiLohkIbK0qXF7qWO4wYwfNJO3agILNqg9q1FSNjY9h06sTzqVru4iq36Jk7dy6mT5+OqKgo5Ws0P3PmTHxUqOwFxV1b5Ac2hA695BqiKsZk+7fr3Ru6AjUUVdy1OU+cqPL+OidPnoS7jzuS/3kc83Z51GWViMKQuHQMWP03jv0rNykPa+GD/VPbcqdzgXqxtzTF+jEt8E6nGuzuOh+cgF5fn8KlhwlVsulbuLfAgBoDYFPfBm4D3XDv33sYO26s1ogLOr5d35/F82Tp0fbBsKzYDx7EGWpUnTlZeDeeyOKicY8aTeuN6FmzZg3OnTsHX19fVK9enSeaP3PmDNauXYumTZsqJ0Mn3cDieZL3yF1bli+8ABN3ebaLLpD4009cQdrY3h4Ow1RbFJBuCLr37w7IADMveSD7X0P/gomk8s0tLz1MRP/VfyMkPoODlSkz67OBDWFlpv7GpAI51F3+nU41sX5sC25YGp2SjaFrz2HftYgq2UQLWy/kR+eezrBtbotDNw9plbWHihbadJeXYYhZsQIFOfLyDLoM1R2z6ysvxZGwaZPWiExNY9WyJVeuJu+GNru4yn117NdP9YXT9BEqzJV185bB1Och0aBIV7TrozsBzPmpqUj4aTPPO44dwyX1qbOxKqA+SX0G9UFGQga8J3lzavrWHlvhaC7vnF4ZKHj2nR1X2Z3lYmOGDWNb6GwaOg0a9DvkUz6ngpsbG+nUYNKhlitb2CZtvoRbESl4e/sVZObmY0hzeUNGdUJWw6Y/NeUaPlTEcNKpSdjSQ97oVxtwnTEDaceOIzcsDIlbtsJpnHraq1QljqNGsnsr5/4DpJ85A+s2bWDoGJmYwKZjRyT/9htXZ3YYMgR6IXrmz5+vnjXRMzIuXwGoYirH88j92vpM6vE/WPgYmZnBpos8fVEXoItwQWoqJDY2Sl+9qpg3fx7++fsfOHZ0hH0re0xvNh0NXBpUerlUI+aTA7cpZpCbg24Y1wLeDpbQVuLTsvFfVCpCEzK4MnRYYibPP0rMQGpWHoud0jA2AmwtTNiCQhOljtd0s0ENN2vUcLVBgIuVVmWk+ThaYvsbrTD+x4vc7oNafWTl5mP0i9XU+r1kNaQGpV13yjNorsVcw3sr3sO81+dxoommMfX2hsPIkUjYsIH7ctn166tzVdpLYla9Oqflp58+zdYeIXrk0LWfRE/6uXPs/iPrubYh7OBqjuehBqPUu8VQsrZI6etKc1GyxiVs3Ki8c1Nlf6379+9jyZIlMK9mDvdhclffuPrjKrVMsoBQfRhqi0C0CnDE2lHNWRBoC2SdCY5Lx8WHibgYkoCLIYkIiqtYO4J8GZCYkcuTnGQcuf04TZhitKs5WeGFAEe0re6CNtWdOM5Gk9iYm+DHcS3xxk8XcepeHObtucV1fSa9FKj2BqUft/4Y887MQ+rVVKz4agUirkVg66at0AaoLxcNhpQlGf/tt3CbMwe6juPoUSx60v86ieygYC7MaOhYtW4NibU1CtLSuDCl/YD+0DaE6FEThlSfJy82Ful//61ztXkSd/zMdyPcUFDFTVGjLaLhO80Xpq6mXExO0TG7Mp3RZ++8jl8uhfPzfo09uY0EVQ3WNCTG/glJwP7rETh8K7rUDCZqbErWKKoK7etoyVYRHwdLOFiawMxEwr/DvPCR4mSS0rLwKDYR+VJzpGXnc8NPshLdi0nD3eg0xKVlgwoik6CiaduFMA4mbuBlh7bVndG5rhtnWGkig9DC1Bjfj2mOKVuv4OjtaHz2+3/IyM7Du51rqnV9+tfoj023N+Fe43uwbmCNbT9tw+D+g9G/v+YHHqrZ4/zWW4hevBgJW7dxAUNTPz/oMmTpMfX3R05wMBK3boX73A9h6EhMTWH9Sgek7N2H1CNHhOgxFMjNk3njBs9btmwJfSfl90McvEZ1Gkjp60pT0fj163ne4dXhKjW3Z+dlY9KxSVx8kFjWfhl3zK6M9WTRgdtKwTP55UDM6lpLoyUBSIRdDk3E/uuROHgjEjElhA7FGTX3c0AzPwe0qOaIup62MDEue96Em7UJ3MzzYW9vD6n0yXuzxPQcFkBUIPDM/TicC4rnmjnXw5N5Wv3nA1R3tcagZt4Y0MQLrlXcY4zEGwWWv/fLNey5GoH//XGfsxqnd66p1u/9rc9vaLipIbxe88L9ufcxZvwYvPjii3DXgsQCShJI2LIZuQ9DEfP5Cnh//T/oeiVih+HDEL14CRcrdJszW6cq0KuzlhGJHroRplp12mb5F5YeNcCFuPLyuCuvZRP9j+dRWHmoTgMFs+kCSb/uRH5cHKeeOo5VXWDl33//jU4jOnF/JHMv+UDb3b97pZb51fF72PC33KX1ejt/jQoeilHZfeUR1p0KwoPY4m6rFtUc0KuhJ9euIWuOOtfRwcqUq03TNL6tP/cWuxqWhNP3YnHiTiyLIWoRQVaW5Yfv4KWaLhjxgi9eqe1aZduORN7KIY1hLjXGjoth+N/xe7xdSIipC/ptJHwG7B0AzzGeCFsdhjcmvYG9u+XuZ01C/Qdd33sPj6ZO46SHjIsXYdm8OXQZmy5dWPTQtYSu+5bNmsHQsWrbFkaWlpBlZCDtxJ+w690L2oQQPWpMVTevX4+zgfQZWV6evKkqHeytXoAuIMvJQfz38qai9kMGq6wuT1ZWFoaMHILsR9nKgfXSSPm2qUzQ8pfH5JV2hzb3wQc96mhE8JBlZfO5h/jxbAji0h6nHTfxtWehQw05Pew0V/nZVCpRiqDpXWrhXnQqW8Z+u/yIXWF//BfDU10PW0zrWANd6rqxG03dUHHIxQMaID49B8f+jcac365zhewXA53U9p01HGrAy9oLaAkkX0zGgaMHEBYWBh8f9WeSPQ+6MbJo3gyZFy8hZvnn8Nu+TaeKmJaESnNQHTbqME4ZS0L0gGvSWbdvj9RDh5B26qTWiZ4Kd1kXPJ3sO3f50dIAsray/v2Xg9Z0yZWXvP8A8qKi2CrlNH68ypb72bLPEBESAdcBrjDzNONGoqbGFQ+s/fliGAcuEz0bePDgWdUDRHJGLq/Di58dx4qjd1nwkMB49QVfHJ/xErdjIEuLJgVPadRws2GBeHbOK9wotFMdV36dWnRQWnmP/53itH9y01WF8PlqWGPU97JFbr4ME3+6qPZGpfv7yyuje47wRM3PaiJSWnX9wZ4FHb9uM2fyfOa1a8i8ovvtKWwLm22S9UqXyiyoE4UFj8SgtiFEjxrIefiQH02rqTdVVRvIuCAP0DUNDFR5JWN1QVkkhG2vXjChPjoqIDw8HIsWL4KpuymcujhxY8jKNBKlAZkClwlyzXwxtHGVtpSgPlLUy+vlz0+wtSkrt4CDjt/uWANnZr+Cxf0bINBFu3z1T3MxUaPQ78e0wMFp7dC9vjy2hVLoqWdWv9V/4+ajx5Wy1QUVjPxhTAt42JkjJSsPr238h1P51YVUIsVXHb6C1E4Kqa0U44+MR2paKrQBi0aNYNGkCc8nbtb9buWKDuO5ERHIuiW/STF0LBo1Uo6FVPFemxCiRw39p3JDQ3nexNcX+k56YVdyqxd0w8qTEx7OsQSEXX/VFdp8e8bbKMgugMerHpBIJTgx5ESFl3U7IoULD5IRgoKBvx3ZjK0rVcWZB3Ho9fVp7uVF6eK25lJ81KsuzszuyBlIztbyytK6BgVTrxnZDIfeaceWMzKaUdBzn29O45P9t5GenafW76c6QyR8rEyNuU4R9UujGCl18YrvK8r5xFOJcPZ0xoMHD6At6d5EyuEjyC3S0kgXoSw0s1q1eF5RoNXQMa9Vk2O4iKzr2mXtEaJHxZDbRJYrryti6ldN7+N5yDevU66twnpCJp6eKguizM/Px59xf8KmiQ1sGtrgjYZvVLjNREpWLt7ccokL9lHxvR/GtuAU6KpyZU3ddgWvrjvPlhAyLI1q5Yc/Z3ZgF1ZVrYe6qe1ui1UjmmLPW21Qz9OWxeX3p4PReeVfOFakDpC6hNc3rzblbXs5NAnLDt1R6/ede/UcP5q6mCInNQeT3poEbYBie6SUUZafrxfdyhUFWSlNW7i4wILHvF49pRtT50UPBWxeuHAB+/fvx969e4tNhk5OoZWH4kVMPDSfJqpOsm7d4vR8XalHRBej5D17eN62bx9OOVUFD1IewHO0J3ynyi17UxpPqfD6zfrlOvfSsjAxZgtPVRUepArC3b86qewZ9WKAEw6+3Q6L+tWHo5VmC/6pi4be9ix85vasw73LIpKzMGHTRbxfWElZXXSo7YqZXWvz/Pq/g/H3/Ti1fZeViRUmNpwIq9pWsHvBDscOH8OpU6egFd3KX32V55N+/plLSOiDi4tq9uRoiTVNW1xcmVd1XPQcOnSIG4y2atUKffr04V5cikkbimBpSzyPiY+P3tdsSC+M5zGrUR1SJ/Vlo6gKSimlGiGq7A92584d9P9VftwbSYyw/KXlFQ42ptiZQ7fkpv5P+9fnlgvqJje/ACuO3MGw787yoG9tJsXKIY2w9fUX2CKi70iNJZjQLgBHp7+EjrXlwc6UXj5wzRmExssFvTp4o30AZ5oRM36+xlY2dTGliVyEU4A9XfHfm/2eVlgjuFu5mRkXCE3ZLw+81lXMatRQFlsULi45Fo0LRc+NG5CpqJ+hRkTP1KlTMXjwYERGUuZDQbGJzPyGTk7hoGpqAPE8GRcUVad1xLVVaOWhOxAz/8qXjKfjvUvPLrg/7z5khVlA3arJO0qXl0sPE7imDDG8pS8GNFVfLRcFj5IyMWTtWXz9x3128VAFYwr2pe/W5TTiikBp5FRFeUHvupBKjLhpaK+vT+H4v+pxd1FQOolLEplRKVn4aM9NqJNFbRbBzM0MDm0dcOHMBRw5cgRa0a28T2+eT9j0k1YIsYpC5wvV7CFSjoi4HsKiYUN+pN6GZAHTWdETHR2N6dOnw01FWS96m7nlp9+ih+KWFPV5LF/Q/vo8BTk5SDn4O89Tw0NVsGPHDoQ+CIVdCzu28mzvub1Cy6Esnre2XEFegYxjTOb3rgt1QxlL/Vb9jSuhSRzQO/WV6vhl0ovwddL/PnHPGrjGtvHHjomt4GZrxllW1Dz06+P31DIgU1uOhX3kcQ97r0Vgz9VHUBf9qsuD9l36usDMywwx6THQBhxGygOas+/eRcb5yrVq0Za4nux//0VOWBgMHamHB6QuLlrn4iq36Bk0aBD+/PNP9ayNHpATWuje0vG+MmWJ56GKm4RlS+2P56HKoAUpKdz13rZ75SokK6w8M+bOgMRcAqeuctdePWf5AFbuOJ5fr/Pdvo25FGtGNFN75/C/7sZi6Nqz3COL0tC3TmiFGV1qlatNhKqgOjkxqVkIik3jrDVqbXH2QTxXVw5JyOTCgtl5VWtBbubniAPT2nFcE0H1iRYf/FctwmdAUy8u7EjM3X0TEUmZUKe1x9TJFNU/qY5lqcugLVk+ipumBB1PXzevX58HeoIKFRo6RkZGj11cWhTMXO6KzN988w27tygYrkGDBjAp0XZg2rRpMFTIb5kbKlf4pr76LXrSC+/KzGrWVGnfKnW7tmxefhnG9vaVXt7PP/+MqOAouPR2gdRaiqODKnaRO3QzCsf/k991Lx/USO2WFip4OOe3G9wklFoibBzXAgFVVG8nMjmTA6ZJ0DyMz+C0bWoiSplqz8PZ2pR7adFUw9UGjXzsubmoumoXUVr+T+NbYvZvN/DrpXCsOxXMjU8/6Vdfpd9JA8On/RpwN3rqX0biirK71GXt+ejvj5Suy/O3zqNl3ZYad2VS+nrG+fNIO/4Hl5Qw9Va/a1dtLq7OnZC46SeO63Ea/xoMHYtGjZB69BgytShtvdyiZ9u2bewPNjc3Z4tP0ROG5g1Z9HC6eo68RL9pNT+DKEqoC6nqeQkJSDt5UmVd4OmO/4MFHxSz8rhblT9TLy07Dwv23eJ5KprXrbBwnrr45o97+PyIvFp4I287TodXZ80dyoD6804MjtyKxvngBI4hKgvUkZ0qFxeFKkHHpSXgXFCC8jWyjLUOdOKu6h3ruMHT3kLlQc7LBjbkuJuNZ0Kw7UIo1/JZMaSRSq1i1EdsXu+63JWdGri+1jYRTX3VcyPxceuPMe/MPMT/EY9W41rh5F8n0a5dO2gS65dfhom3N3LDw5G4eQvcZr8PXa7OTKKHkyaio1VW/FTXM7iy795FQXq6VrRlKrfo+fDDD7Fw4ULMnj0bEhWl/OpbPA+5UKgni75Cwi7j8mWet9SBooSpx49zA1hjOzvuCVNZcimeqUEGXBrJrTwH+x+s0HJWHrmL6JRsLlZHg546+f5UkFLwUEuG/w1vAktT1bfeIwvSybuxnPp+5HY0C7uiUKFD6rxObSLI0qSYbC1MYG4i4e7kZEnJys5BeEw8jEytkJZTgIcJGbgfncqd1e9EpyIoNh2pWXk4fCuap3l7b6FNoDM38+xaz11lNYWoPxfFWJHw+ebEfY69Ib4c2lilvbuoWOJ632Cu3UOFEndObq0WC0z/Gv1Z9FjXsQZkwOJli/F7O3msm6agLFeHESMQs3QpknbuhMv0dyEpLGyna1g0bQpjJyfkx8cj9dgxOI4YAUPGnGr1UBZzfj4yb97SiiK25b7q5eTkYOjQoULwPCtzy9sbRlL97eWaSfE8mZlk2tOJLskZ5wqrRrdrp6wSWhlS8lPg2lue3kz42PpUKJB44xl5RgM1yFRn7ypyaX1y4F+e79nQA18NbcxWDFWSmZOPXy+FcZE/cl0pMDWW4KVaLmhf04W7sNd0tSmTWKD1s7cwgb29JaRSKbuzihKTkoUzD+K5xg3FKJFr6PT9OJ5szKTcG4xS0V1sKm/JIvHxXtdasDQz5mKCJHx8HC2UtXZUAX3Hhz3rcqo8CZ/fb0ahRwN5fIi6rD02jWxw6MAhrtIcGBgITWLfvx9iVqzgTJ+Ms2dh/dJL0EVIwNl07Mi1h8itY+iiR2JpySEQFNxNcT3aIHrKfeUbM2YMZ60InpG5pefp6oqGqvQ7tT2eh1xRylYZKugCHxcXh+4bHwdCf9TqowpZQz7cdYPTxKnr95gX1ecKPXwrqngPryGqFTzk7vnq2D20WfoHPtpziwUPaRoSOZ8PboSLH3XCutHNubIz1f1RlXXE1dYc/Zp4YfngRjg7pyM2vdYSfRt7wkwqQWp2HtaeDEK7ZX/g4323EZ2imsJ3b75cHa+1kZc6WHXiAXb8I7/JURVkASNRSlD5AnUFcJO1h2DXrAz48qsvoWkozs6qMCGCLCS6jCJ1nUIA8pPV39dN27Fo1FCrgpmlFclaWbZsGQ4fPoyGDRs+Eci8cuVKGHo1Zn2P51GKOxXUulE3OUFByI+LU1lq/fLPl+PSiksInB8Icx9zDK45uNzL2HohFNfCkzlVnIoQqtrqouDM/ThM3XqFxRUNqGtGNlVZDy8Sk3uuRmDJ7/+yi44g99TQ5j4Y3zagSlPfyR1GIosmauOx40IYix7K/KKKxxSL806nGnitrX+lY3E+7FkH4YkZ7Lr7YNdNjiNqV0OelqsKZnerjaO3ojnI+6ezD9lapQ5ae7bG37K/+Rhe98M6fPrJp7C11WwxSutOnZB+5ixSj/8B9wULdLa4K2ez0riYm4vMGzdh3bYNDBmLRo2RtH0HMq9f4+uGpgPny30FuHHjBpo0acLurZs3b+LKlSvK6erVqzBkch6GGESj0ZwQ+e9UVCDVZtLPnVP22qJgycpA7VdWfbsKJk4mXOukvlP9cp/AqVm5+PywvN/SiBd80URNAauUFTVp8yXk5BegtrsN1o9pobIYnlsRyRj07VluikqCh1o4yLuvd8TCvvU1WuvH1twEr7cPwOn3O3AsDtXbyczNx5Lf/0Pvr0/j0sPESgusr4Y14UBwsti9ufkyb2tV4eNoibFt5D37qGhkRo56mqAua7+Mj13HTo4wCTBhC6amIbcQkZ+QgMwrV6CrUDySeW2565MGekPHojCYOT82DnkR8pg4TVLuq+CJExXvHq3PGFK6+mNLTzWdiechK09l7zCot1x6cjrce7hzMcLvunxX7mVsOvsQyZm5HHcys4vqYkKKQm6RKVsvc3E9GvTJ9WNnaaKSmjrfnw7C8sN3lNlV/Zt44f1uteFuZw5tgmodjWvjj6EtfPDlsXvc4oOaqA769gwmvRSIGZ1rVtjCRkHS349pgb7fnObWHe/uuIodE19UWSr7Wy9XZysPHSe/XX6Eka1Ufz2xM7PjR8eXHHmy9dB8yxHKdKIBktwglPKtC/GCz6pGnHXjBrKuaU+qtqYwreYHia0t10mjfWvi5aXR9RHpVyrCUNLVqbO6otqotlt6SIgqUutVEc+zZsMawAjcuJGwMS1fbyy6a6fBlxjTuppKhEhpLDn4H7vPaBD+enhTjn+pLFRAcMyGC1h88D8WPGQ9ogyjL4Y21jrBUxSybn3Qow72T22LJr72oPqCa/58gJE/nOffVFEoQHrFkMbsorz4MBFr/ryvsnWm42JgM/nAQKny6mrPMP/F+cr514+8rhVthKjODUFBwLrclsKiYYPHfad0+HeoAmrsrGhJoQ1xPeUWPR06dMArr7zy1MnQ43kglcKksCqnPpIbGcm+asK0mnZberLv3FEGElY2nicxMRF/HfsLVnWtYGJvgp+6l7967NbzoUhIz2F3EMWXqIMD1yN5oCRmdq2lbGpZGa6EJqLHV6dw6p7cBTK2dTXsfqsNxwnpCnU8bPHrpNaY9kp1fk71fnr+r3LurhcDnbhxKEHWpGthSSpbX9rGxP2YNM5IUwcDagzgx5zYHByadgifffYZNI1NJ7noyY2I4IwfXcW8cJAnV13uI/W1F9G5juvXruue6GncuDEaNWqknOrWrctp7JcvX+YKzYZKTshDg0hXV8TzUHdkqZYX3lJkbZFFqrJ1k6jBrrmvOexbyVOnG7s2LnehPgquJchd4Wil+jok1BX8/cJMLeoY/oYKgmCP3Y7G8HXnuDggtaz4fnRzLOhTT+2tMtQBWb6oPMCGcS1gb2nCbThGfn+e6wpVlOmda3IGHvVNIzcX7WdVUN3VBu1qOPP8hr/l55yqkRjJL/8mDibITczFdxu+07hVgm6kzGpU1/ksLvodEjs7rbFuaBqLwnYUWbdvcx9EnRI9X3zxRbGJ2lKcPn0a77zzzhOZXIZo6THR80ajSnHn58dmS12J56ksll6WCJwXCPu2FWth8cvFMB5kKaV6QjvVW3losJq75yYXA6SO4VQ1uLLp4VvOP8QbP11EVm4BAl2ssHdKW3Sqq91Ctyx0qOWKfVPaIsDFioOcJ/x4EYduRlZoWVRM8athjTkrLiguXem+VAWK9Pg//otBcFw61MGefntgJDViMU/Nc+nmVdPYdO6sdHHpdN+pQiNA1vUbMHQsCrcFhYBk//efRtdFZaPWyJEjsX79ehgq+Uly07bUWX53pq/oSuYWxR5l/POPyuJ5pv4xVXkxW9dlXbk+m5NXwHEkxPCWvnC1UX0MDBWzU1gsFg9oAHtL00pXcP5w101Od2/u58DxO5RZpC/Qb/l54otspaEMtze3XGbXYEWg6tIKq9rqE/crFStUFKqr5O8sL9v/Y6HLUtUE2MnX27aZPJB577690BYXV/a9e8rrjU7H9WhR3ylN1mFShENouuO6ykTP2bNnuR+XoSLLkvcVkljoz8DwzMwtLQ/Wpgsm9XpRRX+wzZs348SHJ5AVIR/MXnAvn4iiCr6U5UM9pRQxIKqErDtUhE/RzoAGy8pADTYVFZy71HXD5gkvVFpEaSPUd2zbG61Y1JG4e/fnq/gn5HFvr/Iw6eVAXl56Tj6+OCov3llZyFI3urBwJR1DefnPb8xaEeo41oFlDUtILCX4Zfcv0DRmdepwiQldd3Ep4nrIpSMrjIM0ZCyUcT06JnoGDBhQbOrfvz9atWqFcePGYeLEiTBUCjLlA6LEQn3tBLTK0qPtQcxB8vgZY2fnSlvfdu7eifT/0rnPFlHe1HdybRF9GnmpvCkmQYNsVEoW9/D6qFflengdvR2tjAsi8UQdv3Uxfqes2FmYYP24FpyNRha51zddxIPYtHIvh3pzvdelJs/v+CcM/0amqGT9qEIzHW4UAP9PSOVqDD2N+a3nw8jYCDYNbfDfrf84aF8bupXruotLkbEky85G1l3VCGG9iOv591/dEj1UtdPOzk45OTo64uWXX8bBgwcxf/7jFEhDo4B6UdEJa6G/1i7yx1JWhS64t3KCFeKscutJabyHjhyCRTULSG2lmN1ydrk+T4XrqMM4Mbh55YojlsZ/USnKbK13O9esVPo4ZR9RfR8qutfU116lFZy1GSpouH5sC65plJSRi9c2/sNFJMvL4OY+LJ7IakS1jFQBuUIVHdeppYg6qOsoF8pug91Q++vacNCC1jLUeZ3IvHkTBVmqcRdWNVJHR5j4yPvyZQkXF8htWW3Hdvjv3qXZ/VLeD2zcuFE9a6LjcANOUpHm+mvpyQkPpwp1OmHpUVikzCrZKuOff/5BVmoWXF6Wu4wG1RxUrs/vviJPV6Xg4pbVKp8+XpL/Hb/HIoUGW0Wac0VIzsjluJbsvALUdLNmEaCOLuzaClng6DcP/vYs9w+bv/cWVg5pXO7ssFndauG1jRc5+JgsRoEu1pVet2713Dm1/sitKK4yreoy/orlmTrJXZg5+TkwNdasO9OcAl9pvfLzkXX7X1g2bQJdDeDNDQvjVG2H4cNhyEhdXHjSNOW+jQsICEB8fPwTryclJfH/DBXF3YjEUo9FT6GQkFhZwdjJCdpMTrA8i8a0WuVEz4HfD/CjdQP54GVmbFaujKrfCkUPVS5WVbNNBfdjUjmAmXinU8UrDNN6vvfrNTxKymQX2bcjm+llDM/zqOdpx6KCoErI+66Vv2T+yzVdOSuM2KiiVPOu9eTlFigu7MYj9TSw7BvYlx8zQzMx8cOJGi9UaGxtDdPC8STrxnXdb7YpLD1aQ7mvkiEhIaWeENnZ2XhkwEWYlO4tPQ7mVqarV6um8aZxzxvElbFHlWyVsevALkgsJLAMsER3/8fd1cvClbAkZapx/6aqL72++sQDrjBMlhkKOK4olGZNsTzEkoENEaAC64SuMqS5D7rWk2/LD3bdQFRy+VwrJGyp/YUiIJwsaJWFepmRJU+dLq63m77Nj8nnk7Fx6Ubuq6gtac7UtFPXg5m58XFqqqZXR1Ae0UN9h2giqMO64jlNu3btwqJFi1BNy10e6sQQ3Ft50fKBUZFZoa3kxcYqM7cqa+lxHe8K32m+XMtkSuMp5frsb5fD+bGxj71K3BwlCxHuKbREvPly9QpbkWg5y4s0QO3TSLv3rbohMf/ZgIZwtTFDalYelh0qf02RgU29OECaagBt/6ewUnsl6VZfbu05fEt+DqoaF0u528Gyujz79MyZM9A05g3q82OmDlt6zOvW5Sr9BPXiEuiQ6OnXrx9PdFEYM2aM8jlNw4YNw9GjR7FixQoYKobg3irIyFC6t7QZZW0PY2OY+lQueDjWMhbWdeSCxcdGHpRY1qaf+65FKgdBVfPtyQccy+PraIleDT0qbBFbsO8Wx/H4OFpUOvNLX3CwMsWcHvJmsOSeLG97CYqFonpMxNYLoSqpcvxKbVdlWwrK5FIXCtFz8vRJaEv2U+7DUGUdNF1DYmYG81q1eF64uHRM9BQUFPDk6+uLmJgY5XOayLV1584d9OrVC4aKIbi3lKJHy4WdMnOLWoJUokr4vXv3kB2drRy0yuPSO/sgnrtkSyVG6NVQtdaTlKxc7LwktyJNfjmwwrE85NKigFtioY62llAXfRt5oZG3vI3Ax/tvl1u4KDL1KCj638hUlfQOU2TSXQtXjwCY0WwGpDZSmLqb4thfmk8VNyOxUHj+Zt68BZ2P69GCvlOCCsT0BAcHw1nPqw6XFy48lZen93V6FMJOYmmpG0HMlczcWrhoIe69fw/5qeUP6iTRQ1C6MVkOVMnvNyLZOkO1YShAuiKQJWphYUHDznXd8Ept3W8voUrIXTivMKiZMqdOFjZbLSvkzqzhKrcQHlJBHI6JsQT1POVVk1XZ2LQovQLlN61UqDDuURz3m9MkElNTmNeurfPBzGaFv0FR2FWgWSqUk3r8+HGeFBafohhiK4qidST0W/TILT1GWv4bHwcxV070nD53GiYuJlyfZ3jt8qWbng2KV3biVjWUWUR0r+9eYesMLYOytch6ME+4tUqlmZ8jF2j8624sB3uXt9I17Z97f9znvl7UmLSyNPK2x5XQJFwPV08Gl5O5/Fi1bWwLWZ4MGRkZMDMre7aiuoKZKRZGl4OZTTzk7ufcqCi2GGpzEoghUG5Lz8KFC9GlSxcWPXFxcVy9s+hkiBRkyC0ghJEeBzIr3Vta3mpD0fy1MgUUU1NTEfYgDBb+8v05tNbQMn+W3Fo3C1OLVS16SKgoih1W1MpD7Qy+/UveC2xwM2+96qmlasa3lQtn6mt2N7p8bqquhcHHd6PTKlTluSSNfOyUlh51dENXDMbUh8tnog8CAwOhabheT2Ews6Y7wFcUqZvciirLyEBBWuWPA0EVW3q+/fZbLlA4atSoSn61/vXdIiT6XJE5QzfcW/kp8hYAxo4Vryz74IFcFJh7yfenv13ZrUYXghO4Ki91VG/iW7Gu7M8rduhhZ45WARUTVAduRHKsCRXTm9he8wObNtOuhjOXBCDhsuHvECwZIB+EywI1M6VA89CEDJz4L6bSGXxk6SHi03NY/Ho7qPc8LJCpp9dXRZp25sfGcfaoibtcSOoSRdc5LyoKxjby8gMCHbH05OTkoHXr1upZG31wb+lzILMypsdC77PMggp7d5m5y837EqOynypnHsjjP5pXc4CZVLXBwXuuykVP38YVK3ZId8vf/iX/bZSeTjVgBM+2fox+UV6K4/ebkcgtR9NP+uwL/o7Kmk2VpZqTFWzM5fep18LU4+KqZiv/rY82PsKQV4dA05CLWnEe62r2k8TGBkaFN4rk4hLomOiZMGECtm7dqp610fEaPboQ76IKMaHNv1FWUMBm5MpapNLS0mBsZQxTN9MKBzG3DlRtwH9kciZbHIiKpqnfjkxRNsOc0K5yMU+GAsXmkL6kvlznCmO1ykrjQkufKoKPSeTWdJNbCR4myOtQqZox9cbwY3ZkNg7/fljjLiUjiQTm9eX1erJ0NIOLxK9JoYtLiB4ddG9lZWXhu+++w7Fjx9CwYUOYlEgJXrlyJQw2Xd3MjE9SfUUXsreKxldJLCtu6ek+uDs2OG3gi349p3pl/lx8Wjb+i5LHflTU/fQ0FAMuFb4j10ll3GNU4ZfaLgiej5O1GV7wd+LgdGr70a6GS7ldUuGJmYhLy4azdeUCg91t5Zbk6HJWii4rbb3a8qO5pzkS7iQgOjoaThpuOUMV4DPOn0euDlf8l7q7cVZpXpR6iksKyk65R+jr16+jcePGkEgkXKr8ypUryunq1aswRAoys/TetcUWFIXo0eJA5oKMx3fAlXFvPUx7qLxLa+fdrsyfU2TWmJtI0LCwzouqOPdAHsBMLpOKuLaomOHewirO/SoYBG2odG8gj8s4dju6XNYPEpd0LBBXQytv7XErFD1RKeoRPW6WcouEwsJJJUo0jdTNtVhFeF3ExE1+/ORGC/eWzll6Tpw4oZ410YNAZoXfVt9deBIr7f2divYTlV3PL7/4Eqk2qbBpaINGLo3K/Lmgwl5b/s7WXFtFlSjS4CtqQTofHI/olGxuXm3o7SbKi8JVGZOaXa4gYiocWd/TDhcfJuJmRDI6VaJHGuFuJ7cURaVkQx0oMrik9vKhgcqSaBqlayhW8+tSGUsPISw9mqfCV+X79+9zD67MwsFQ075frXD76LGlR/Ebtb0WkSLuqDJuuNzcXBxedxiJp+QlGALs5N2ey0JQYWqyotO2qqCBlrKAKpMGf6qwwF4TH3t42mvvPtRGApytYFsYREy1csqDn5P8WIhIenwOVdbSoy73lgKpnfaIHqlroWCIjtHZcUaRwZUnLD26J3ri4+PRsWNH1KxZEz169FBW7Rw/fjxmzJgBQ3ZvGUILCq0XPQpLj1QKI9OKVUJOSJC7kagkP+FkUXaRERSbrhwkVcnFEPk62VuaoFZhMGt5Oa/Ggon6DrkTG/vKSyBcLWdQMpUXICJVIFQUMT2xadnsrlQHLd1bcqkGz9GeaN++PbTFvSXLykJBYTkKXa3Vkxsp3Fs6J3reffddDl4ODQ2FZZE76aFDh+LQoUMwRIwKu+gqWlHovaVHi914j/uDWVa48mlsbCw/GtvI083NjMsefBpc6N5StaWHGk0S1IqgIvE8GTl5yngjVQdYGwoNveQxWorst7LiXih6olQhegqXRYKHAqPVgbuVO1chd3zFkW9utcW9ReTqaFyPwtJDxQnzRYFC3RI9R44cwdKlS+HtXbx7dY0aNfDQQHuLSGzkRcfyUyvfWFBbkWU/vsBSlpq2W3oqE8SsED0KS09ZSc/OUwaYUkyPKlHEClGtlopA/aPyCmTcALWZX8WLNhoy3g4WFbLYeKhQ9NiYmxQ73tQZzMzfkaOe1PjyILG1VVrRycWli0iLFijUUeFmsKInPT29mIWnqEtA031aNIWxrTx9WFdNr2WhqEurqNVHe1tlVNwFR+1VKiJ6FFYewl/F7q0QZYB0xZZ781GKslu3pWmFWu4ZPB6FcVAUm1Oe2BJFHE5qdl6lhUpRG5+6olvI0kM8mPcAgwYM4Bg3TUIWW2UGV4xuCgZje3ulu13U6tEx0dOuXTts2rSp2AFJTUeXLVuGDh06wBBRlBWnAVempy4uifVjy0WBFlu0jIwLB/T88ndGV2Bvbw+bpjYwdTetkDXG2dqUa+moChpggyspeh7Gq8ftZkh4FlpsqMN9YkbZhYCF6eOq3OWp6FwaRT226orpfXQ7AlaxvghYUBPZb+ai2dYX0PGrodhzYi80hUlhMLOuurdYuCmCmUWtHt0SPSRuqDhh9+7duSXFrFmzUL9+fZw8eZLdXupm1apVqFatGszNzfHCCy/gwoUL0IYy4wr0taFc0d+ozT5pibV8UM8vkrpeXjp37gy/aX6w8CuftUiRnaPqBp6xqdnIyMmvlOgJia+ce0wApaWnvJlYkiJKpbLBx0ZqtvV8tOFT/JC8HmnO4TCSyI85eoy2+w8fPpzL/9dkILCuureIx1WZ5ck/Ah0RPSRw7t69i7Zt26Jv377s7howYAAXJ1R3V94dO3Zg+vTpmD9/Pi5fvoxGjRqha9euGk+r1BVBUBk4eLnw4q3Nwk4Ry1O0Xk9VoXBd2BaJu1AFDwtT1Sl+uaKCKiQuQy1uN0PC2kyK/VPb4uLcThxQXlaKxp1XOuFKjZYesuTsMtrBYsrIqLhFSv5cxv/XhMXHRFHnRkctPYSw9GgHFXLu29nZ4cMPP0RVQy0uXn/9dYwbN07Z8f3AgQNYv349Zs+eDU1RtGuuvsb1UHsNEhQkeLTZvWVc6IajYorkalRm1pWD3bt3I+zbMLgNdIOpS9ldXGmFosfKTLVNRlOz5K4UKzNphQoe5uUXKAOsfRy1t9yALlC/MIOrPBS19FS2zkwx9xZUy/+ubwHsjGBkJHvqd8tkRvj6+hb07dAHmqjVk6ujMT1FhZsu/waDFT3Uf4vaUZCFheJ5itKnj3pOBnKlXbp0CXPmzFG+Rq0wOnXqhLNnz5b6mezsbJ4UpBQKkry8PJ5UhYwGVpry8pCTlARpJZatuCjm5+c/sW01jUL05CanqHT7qZKCIrWSclJSlEHm5eHGjRtIPpcM5x7yKrxl/a1pheLE0sRYpdsnNbNwuaYVW65CNMnXTaK1+64oinXUhXV9HgVF4styKnntyc97vCxVXscoWDna9s4TFp6S0P+jbO/wddXYWLXi/pnf6+ykdG/p6jEhK0z0KcjOLvNv0ObxQNso6zYtt+ihWjyjR49WZriUDNainaMO6Pto2W5FajYQ9Py///4r9TNLlizBwoULn3g9OTlZ5QeQkbU1ZElJSI2KYuFTWWgdtQ1ZYdZeWkwM8lXwG9VB0eMvKSISxhXYz+SyJYyM5bfVSWX8rUlp8jgPY1lemT9TFuKT5JY1M2OjCi03Li1HOZ+bmY6kJN0ZNKjbva4TXliwkijISkdSQcVT14u2n8jPykBSkmqutwmJ8coYnudB7wsNewgHe0dUFdmFGWQFOTkqPbeqkqxs+XmYl5Nb7t+gjeOBtpFaRg9EuUXP1KlTMXjwYMybN+8JAaJtkFWIYoCKWnp8fHzYPWdbAQvAs0iytUVuUhIsCgpgay/vrFwRSNnTAU7rWNHieuoi1dYWdFk0LyjgDCdtJN/YGPLaxYC11BhmFVhPxR2sYvuX9bfmyuSuJ0dbK9VuH6n8gmdjYVqh5SbnP66m7eZkD/tKdvquqrs2EjzW1taQVsBFqU1kxTy21Hm6Vq4wZEjq48EywMsFZlLV9HezsrKCrMC4TMKH3ufr41ellp50axuQnZ5OSW299jyPAktL0JkolUjK/Bu0eTzQNsjzUxbKfTWJjo5mIVHVgsfZ2ZlPMvr+kuvjXqTwU1GoblBptYPoIqrqCym5UfjSlpFRqWUrLFD0W8u6E6sKhatIlpGutQNRUXeWUWZmhdZTUYeqIE++L8q6jIxc+futzU1Uun2y8uUmbivTih23uUVCNKwszLR235WGOs7VqiYxUy4kXGwqv+3jM/KU7UiszCvWZqU0aL3cUmpxltazXFwymQTuKbWqvCabsbRQYMnKfj5qGxLlb5CV+Tdo83igbZR1m5Z7Kw4aNAh//vknqhpTU1M0a9YMx48fL3ZA0PMXX3wRmsbYVh7MnJ+ivUG+qkoHL0jTfJXWp2FkbKzsdl+Q/tjCUR7IusCfzyqoUPaWVZG6LKogq1BMmZlU7KJXNPg5t1DICaoOKjlAuKjAwkZd3glXG9WLjmkNR7CqeFqstfx1Gaby+6oYhZVDRxuOKpJBGBGbo1HKLZm/+eYbdm+dOnUKDRo04D5cRZk2bRrUBVmYxowZg+bNm6Nly5b48ssvOf5Ckc2lSSTWhQUKU/Uze4swVv5G7RZ2EitL5GdkVDhtneo/ufR2gYl9+VLPqWgdYWaiWtFDbhEis7BWT3mxKewOTqRk5cLBSnUWAsHziUmVx/A4q0D0xBZm4bnaqL65MWVkXdxwg9PSKUurqMWHLDwkePrLhlZ55pa+iB5ICq8LQvTolujZtm0b99+i4oBk8SnqZ6R5dYoeampKfZEonigqKgqNGzfmwGptiC2SKCw9qbofePm8qszaXovI2Moa+bFxKEirmDhr1aoVp6tXtTh5Vn0YIjWrYgHIResGVXQZgopzJ0p+HFZTQY0kdVp6iEXjPoTNryb4LfgvpDk/4hgfiuEhlxZZeDQieBjdFz1GhQWbKlu2QFDFoofq81BGFNXF0YSPccqUKTxprxUkRe8bq2pzcUJC6uyMnJAQ5EZGVen3WhX2tFLU61EVCktNRZdrbmIMU2MJcvILkFKY/i6oGmiAu/lIHojeoAI1fkoSXWjpcbFVX0yNR10PpKeHIuFQPNwtvXDitS9h16aN2r6vTBTeXOu0XDAS7i1tQFKRejlkcRFBVYZn6dEV95ZpQAA/5gQFVejzV69exb2595B4OrFcn7MuFCfpahI95JqqKE7WphXqEC6oHOGJmUgptK7V97JVmdUoQI2VteMz4zmIP3J7JGLOR1RpltZTUTgUdNlKImJ6dFP0UEwNtYMQFMfYxgA6rRdWns7X8t9oGuDPj9khwRX6vIWFBbLDs5EdmV0uc7TSDaVy0WOitPQUVLCPQXVXuZXufqz+inJt5EahlYeEq28le7LFpWUjolC0VqQydFmJz4pHQYY8nsfGSKpdQcA6LXqEe0sbkFak+Bs1HT18+DAaNmz4RCAztYowRBSun3wtt4JUBhMvT37MjYyELCcHRqbaGRBr5i8XPTnBIZAVFDy+YJYRquVE5CbILStJ2UlwMHd47ucU7SdUbelRxOTQ9Z6sPfaWphUSPafuxeF+jBA9Vcm1cHldHerVVdk6KwoBZSqVoKbb49Y3qubf+H+RlyI/hh0l2iF69CGQWWRvaQfSipTob9KkCc/fvHmz2P8MuXiSoj6Mtrt+KoNZodsI+fnICQ2FWfXq0Gb3FvXfyouKgomnXKyVp06Pua25UvSEpISUSfRYmxVaZFQcLEwWAnnfIyAoLh1Nfcsvemq4ygdJIXqqlj//i+XHlv6VK0pI3AyXi546HrYV6sFWVu4k3kFOrLx6cL1cwFgrigEa6X7mkzKmRz1dCwRqEj0nTpwo70cMAmVmU2oqu0P0UQAaOzlBYmeHguRkZD8I0lrRQyKHrFBkjcoODi636CHc3N0QkRDB81djrqKJq1zoPwvrQkuPqgOZLUyN4WVvwfEhJFqa+j5fgJWkhpv8+HwYn87WIlV3ghc8SVhCBu5Ey2+COtepfIapwtLTQAWxQc9DIXpeSM+F1NUVGkcPApmNCoWqrIIuaoFqqNTtQnh4OE+CIpWAqTFcBevDaDsk5BTWnpygB9DmAoWmfn48nxNUsbgeH28f5CXm8QXqz7A/yxV7k6yGDKlAF7loeVBB9xRlDlHLArrennsQr+K1E5TGsX/l1ePdbM1UEsSsED0NvdRveTGxM4FVXSsEWFjxjY5ABYjsLd0UPVQF+eOPP+ZeIH5+fjxRH5FFixYZdBdYEy8v5XxOyEPoK8og4QqKiSrP4AquWAbXu2+/C9+3fXn+cszlMn3G28GCHx/GZ1Q44Ph5gcgPKhiITGnrLf3lDSJP33+yWfD/2zsLMKkKLgx/u7PdXezSpXSXgCihtLTSvyAooICdgEopSIMKklLSiEFLSXfXArtsd9fM7P+cMzsrKLExu1Pn5bnP3JndWe7Mnbn33BPfJ5Rc0NP2Gd9iZ34jkjLyJ+9Ksok5MVPTg+TaxBUVPqiAAH9/g8haaw2OH7SZMTpkess4gx7S6SFV5mnTpuHs2bO8TJkyBfPmzcPnn38Oc0Xh7AyrPJHE7Nu3YKrYVqzEt9m3DTfTo4vgrFXzVnCu5ZwvKFaYbExGjgqReXoquiJ/+qoYjcjPVfbi28M3JegpDRXm48Hx+UFPcdlzRRNAeTnZoJpfyTUxn4+5kL9eIcQJll7F70XSBcoYTW+Ulbc3jBURJzTSnp4VK1ZgyZIl6Nr1H2VOmuIqU6YM3nrrLUyePBnmim2lSlBGRSHrlmEHBMXBppImg0K9MkWZjCr9Ca6iZ6TUWWperFysCpzp0YoABsekIcBNk/nRBVXygp6Q+HQun7naF74n57kqXsAfmmbokLh0lPUs3gi18HjWnQiFUp3L1hMt8oLN4rArL+h5sbovFIUIxAvLjlt7kavKxb3Z9/CsnScs69eFIWAKQY9kegyDQp+x4uPjUb169f88To/Rz8wZm8qaLEhWEUXxjCWwe3AyylCxqaAJzigILYqMQGJiIq6MvILIDZrXmKl8eubGSmGJ8l4OxSpDPY6aD/TkHA8uWk/OM34u+SW4TWekF6+kUKrUWHM8hNdfaxzEI+bFISUzB8fy9nm7Z0vWcmdnyBZkRWYh9WIqLMNSoPAqfsCmC0wi6NFixm0ghkChv4116tTh8ta/ocfoZ+ZMfunnlumWt7STUQRNcBkqthSA5mlIZZw9W+jnU5+as6czMkM1wc7hsMMFel5Fr+L13hSkJ+fvIjYiW1paoFeDQF7fePq+zvuOBA27r0RxeZMyMq810TTUF4cDN2KQo8qFvbVCk60rQXKRi4y7GbzeEHawlKBHZ6gSNArvhiEBYL4UOughYcKlS5fi2Wefxeuvv84LrS9fvhzffvstzBk+0VLQExoKdZZGzdfU4MkobenIgCe4LO3t4ZAXhKcdPVakv1G3dl1khWXxBNf0k9ML9JxKPhp7ACpv6RptmaQ4jcg962uCnrDEjCIHT8KTWXlUM8jQ/llf+Lna6SSIIlpW8eLgt6TJDNEE+jVsKeiRnh5doYzVfN8U3oaRPTNXCh30tG7dGjdu3MArr7zCJQBaevTogevXr6Nly5YwZ2zySj+UviTDS1PFVtvXY8CZHsKhaVO+TTtWtKCnUd1GyM3JZTuKyLTIwo2Wl4Ddg7YRmZqZI4vooRXk4YAWlTUnsrUnNCUYQXccvR2Ho3mlqEHNyhf772Ur1dh/LbpUSltXozWfB8r0WNpZIsjaGpaGoNFjIuUtZWxsviGyoD+KpDEeEBBg1g3Lj8PK3Z0F/FRxcci6dQt21arBFNH2yxTV0LO0cGzWFLHz5yPr6lUoExJ4/xSGZs2a8W36zXTYlbErVNBD48W6FgF81t8Fbg7WSEzP4WyPtlRVWF5rXA5HbsXh90sRHEBpJ8OE4kGipNP+uMrrzSt5omlFTTmyOOy8HMmGpVaWFnhRB1NgT+K7E0s4q0mZnrKudrC0sIBVlSrQN7lKJVR5/aJWRpwlUcbmBW6exvsaTIEiddhlZmbixIkT2LFjB7Zv3/7QYu5oG30NfaRbJ5keAw967GvVgoWDprE4/fiJQj+fM5cWQHakRp02NuPpZSUaJ9Y2rp7IG1nWFdSToy1x/Xmp6E3kL9X042kwsrWYt++mDrfQvPn9YiTO51lFfPRydZ3o26w8qskYd6zlDw/HkvW6Oxa3hSWPAwYH4A17N1iXK5dvMqxPlHFx+Z5bkukRSj3o+fPPP1G2bFk0bdqUx9a7d++ev1DJy9zR9vUYeulHF2U8uvqiDIqhQg3XDg0a8HrasaOFfr63tzfmHZoHv35+fH/H7R1PfQ71XDQsp8kolUTPTLc6GkuN/dejEZNStL4xarB9+0XNFfz28+Hix6UDclRqfLvzGq93ru2P2oHFb1a9HJ6Ek3c136/BzYvfEP0k0rM11ikWCgu4NXVDd1sX2NWsAUNAGa3JkBh70KOKiTX6bJVZBj1jxoxB7969ERERwQrMDy7kwG7u2ORNcGWZsEChTfny+ZoTWTcMO1PgmNfXk37seJGe37de3/z1madnFug52mzM37d1LwLYproPPB1toFLnYtu5sCL/HcocaLM9M3dd1+k2miM/HgzG3bh0LkO91143Ze1VeQ3R5NBeFL+1wrDt0hW+zY7L5jIdYVezJgypn4eyTpZ2xW8M1we5KhWU2hKd9PQYV9ATFRWF8ePHwzdPfVh4zATX3XvIzdG9B5MhYGlrC7s8rab0E4UvG5V2Xw9BjeU5RdAVUmQqELc7DqlXC96Y3KySplH4WmQKYlN1O8VH7trd65XJHzvXnqCKku15t31VXv/jUiT25lkmCIXnakQyZu+5wevDWlZEeS/NBF9xSEzPxta8oHZws/IlbgWx4spi5CpzcevTW7D8VBNs2dWoaVi9MMac5SEbjbykgKFoH5krhQ56evXqhb/+KpgBozn39ECpRHaI6U7HODbXNPmmHS182ag0sa1eHYo8w8SijK5nZWUhYnUEEg5qygz3U54u6le7jCucba1KrMSlbWCmoOpyeHKR/06HGn54obpmOufzrZd07g5vDtB01fhfzrOOTlVfJ4xrp5vG319OhSIzR82N613rakqaJVmaC1P9hYw7GVBnqtEsx5YzuXbP/FeEVh8oo6JNZlzd2F+HWQY9JEK4efNmDBkyBDNnzsTcuXMfWswdiuK1rsSmbEfh0FQT9GRcuABVquG6ypNNhkOTJryeXoTRdX9/f1SrXQ0p51P4Snj03tEFUmZukje5c7QESlzP+Lvku3avO1n0wJqyB192qwEHGwXCkzKlzFUEqBGcMj1U1prZuy5srRQ66a/56bDGPqVvw6AS1+Y5eUdTdkm9oslmPmfnyMMKlo7Fz1jpgqwb1/8pqxsp2myVhZ2dwbyv5kqhg561a9di165d2LRpE5uMzpo1K3+ZPXs2zB06keRPcBmweF9xcWhQHxakeKxUIv3USRhDiSv1yBEefy0s/Xv1hzpdjbQbabidVLB92rySJoVNo+ElQd9GGgf4DafuI7oY5qaB7g54N68HZfnfd3Ho5j9No8KTOXgjBgv2a3r3Rr9QGbUCdeN+vvTwHUQlZ7EC8+vPaYRAS5K15zXZ2uQzybB0sERte3vY1awFQyHj8mW+NZTG6qKgekCjxxBc682ZIrmsT5o0CUlJSbh79y7u3LmTvwQb+AhzaaENekw500OKx/b16/N6uoGXuJxeeJHT9XTgSfv770I/XzuVmHw6ucCj683zBADJIPROrO4zYb0bBMLXxRZZSjW+P1C8792Q5uV54ozag95eexb3E9J1tp2myq3oFIxac4a90OqXdcOoNpV18nepB0y7P4e3qggfl5Jt3KWS5l+pnyArOguZ9zLR0s8LNhYWBhNgUPOvMjyC1+1rGMY2FUuY0NMwFK7NmUIHPdnZ2ejbty8sDdRd26CcyE1Yq4dwzBPvS/vbsIMea18fOLZowetJW7cW+vk1atSAX1k/vhKmxuEvjnzx1OdU83VGkIfG3HPL2aJPWT0OKnmMbK0Jrlcfv4folKJne6ipeUH/+vB2tkVCeg7e/PkMMnNkEvNxJKRl4/UVp5CSqUQZN3v8MLAhN5jrgnl7b3Ig4uVkgzdaaY4jJcnGU5ryaHZ4NiztLdE3S6MF5Ni4MQyBzLwsD8lP2FbWTWCpD5R54+piQaF/Cv1NHTx4MNavX18yW2Mi2FaqnK9YTKOKpt7MnHXzZv5YqaHi2r0b36bs2QtVcuGafykdPemzSfDu4o1cVS4OhR0q0HN61NM0HG8+UzLmnq82LsuBCmV7fixmtsfXxQ4LXqvPvSkXw5Lw2dZLRZ4MM2WylCqM/Pk07sWlcy/UksENeR/oAsoIrs5zZ3+nbVU45TXDlxT0mfzxjOYiwLmuM5rNrYfnHB1hU64cbAwkwMi8dIlvbatVyzc6NkbEgsKIgx7S4iHTUfLgIs0eGl9/cBH+GVvPzc5Gzv2nT/sYK3Y1auQrthbV36q0cH7xRd5W2ifJf/xZ6Oe/MfwNeL7gCcs8teWkLI3ybkHMPe8nZODEXd2qM/872/Pz8XtFFivUQi7un3R8Jn8c/uvfrkrg8wCU/Rq56jSO34kHtWXM6VePm8p1xTd/XoNSnYuKXo7o1ygIJc2hW7FIcVn2z/9/sAysLCzg3K6twfSdmEI/D6GM0/b0yOSW0QU9Fy9eRL169bi8denSJZw9ezZ/OXfuXMlspZFh5ecHyzz7A1MucZHjukOTxsVyMi8tSNTM5aWXilziIkbVHcW9D2qlGtNPPN11vaynAxqX10xxbTpdMsFv/yaabA+NN9NJs7gMbVGee3wImiD6brdGf8bcychWYfjKU9h/XZPRnNS1hk4NQPdciWK9JOKDl6rrrFz2JJYe0ezb+P3xLMtgcVTjG+b04oswFDIvXzH6fp5/NzIL+qXQ36z9+/c/dtm3b1/JbKUxTnDlmY1mnDsPs+jrOXrU4LMCrq9059uMs2dZrLCw2J63xc0PbiLlbAp+Df61QM/p2UAjJPj7xYh8qX9dZ3ve76D5rG04fZ9dvov72f2i87P5mYZ5+25hvpn7c9F++9/ykzh0U3PimvxKTZ04qGuJT8vGR5sv8vrz1bzRoUbJC79SKe1Ywho2GI35PQYZx1PhYGnJkhv2derAECDPLWVEhEGpQxe3p0csKPSPdCOXEA5NNdowRZkWMiYcmzXnWzo4FSWQKE3s69WDdTnNqHdiEbI9L7d/mb8xCYc0QoWHww4XyO7BztoSadkqdswuCWiSq0kFTUbp0y0Xue+kuMamk1+phW55ongzdt3AhG2XoFSpYW5EJWfitcXHcTQ4jkta3/Ssjf5NdOeDRRcKtM9oasvV3hrTe9YuldISGZnaeB5kbZ6cmBwMqFCFp7acX3iBta0MrolZK/pqhKjT0zWKzJLpMQgM49Ntgjg1b57/xTVkU87iYlOhPKzyLEkMXZ2ZTiau3TQNzUnbtyNXXbiTuJ+fH9p2aIvUi6nIic/Bm3vefOpznO2s8VINjWHpptO6n+LSvq4pPWrBRmGJ4Ng0LNxf/JIqTXTN7F0Hr+RZXqw4eo/LO+ak2nzqbjw6zzuMc6GJ+e9HHx332mw7F55f1vq6e01uKC9paB9uPKMphSbsTwAsgF5pmn4w57aGU9rK0DYxP1NdowlmpGRey/O2owqAgTSImzMS9JQQlCK2oL6e3FykHy+a2aUxQCdcbYnL0PV6CNeumqCHtD+K4hs2esRoIPefbE9k2tOzNz3zbCOO3I5lfZeSoJK3E95qo7kaXvTXbZ04p5Oy9Hd96mBsW421AvWz9Fr0N0LjTVvHh7IvPx+7h1cXH+PmcHcHa6z6X2P0yGtM1xWRSZn4YtulfGf2LnVK1m5Cy4q/70Id+A1yEnKQfDYZtWpXQqBCwX2IDnkGvYaAqfTzaDNWNhUqiBqzASBBTwlBKVnHRo14Pe2IiZe4tD5cx44b/Ii+TWAZOORpkCRu3FTo53fs2BFe/l6I3xsPdbYa7Ta2e+pzWlTyync0X6CDLMzjePP5Sqjo7YhslRrj1p/TidYOBbVj21bF7L51OZNEfl8vzzlULLNTQyYuNQtvrzvHI/vkp0UO57+OeQ7NK+u2AZVKhe9uOIfkTCV8nG3xVbeapfb6Fh24AkurdCQdTwLUwJgyGuNZx9atYGlAY+HacXWaEjVmMq9ogje7Z5/V96YIEvSULI4tmuf39ZjiCUILXx1aWECdkmIUWS233r35NvmPPwptCmttbY1P3v8EduXtoErTBBVZqqyn9siQTQGx7VxYiSg0E+T79G2v2vlaO5N+1Vxh6gJydl8zvAn8Xe24PPLehvMsYkhNuKYAfT9p37T97gB+PR/Oj3WvG4CNI5uzVYeu+WrHlXyLEurjcXcsnWBj7t6bUAfM4XXP9p7oMbkrmt7RuKq7dNBMNxoCOVFRUEZF8boEPYIukUxPCeKY19eTExaGHBN2XLf28clv3E7cvAWGjsvLL2kamlUqxP74Y6GfP3bsWAybPQzW7po+g48PffzU53SuHcD6K6RRuDDPr6kkaFDOAx/nae2sPRHKbt26omF5D/w5thUHA8SflyPRftZBbDgVClUJiC+WFmS7QQrL76w7x4rUVM6izNasvnVhb6MokfIS9UgR49tVRZs8p/uSJjgmFatPBENhq3Ett7C0wFzH1rBSq7kvz/nFF2AopO7/i28V7u6wraIb53p9oM7KQtYtzfddMj2GgQQ9JYhNpUqw8vExiykutzx/qpTdu6FKKZm+FV1hYWUFrxEjeT1p6zZk3w8rdMlnasupnB1Qpiix+97up2byqBFW68+0+WxYifbF/K9Fee4RIahMcyns6UKKBYUmjGb3q4f5r9XjdZo6en/jBXSZdxhHbuneUb4kIaPWidsv44UZB7DvmiYQoL6aPeNbc2arJKao/roenZ+Bo+m4MXkZwNJg+p/XYF3mJ+QqcxG2NAyVEisibb2mxOv+aj+DahZO2beXb52ef571wIyVrOvX+eKKsHtWczEi6BcJekq6yTcv22PqQY9zu3bcpJeblcVlI0PHtUtnWJcpwy7xcUsWF/r51hbWCP4qGPdm3eOAZ8nFJU99Dp3kyno4cFZk4V+3SvRzRyWTyj5OyFaq2TYhMV23ZSjKXO0e1wp9GgbyKPeViGT0X3IcQ5adwMm78QZdzqWS3NTfr6LVt/vZWZ56oMhDa/Gghpj3aj14OunGVuLf3IhKwZg1Zznb16Cce6mNpxMn7sRj5+VwWDkGI/FYIhIOJuDZE45QxcdzsKMt+RoCqtQ0pOeJnRpS9qk4/TzWZctC4aI79W6h6EjQU1p9PdTkq1SatOu6S8eXeT1pS9EUj0sTOtB7jniD15M2bUZOZOE0dBQKBXq36Y2M4AykXkrF3LNzoVKrnjoNNTov20ONwGGJGSgpHG2t8P2ABnC0UbANxtDlJ3U+bk4O4N/0qoPf326JllU0jb5/XY9B7++Posv8w6xCXVzNIF1BQRiNoI//5RyaT9uLHw4Gs4q1pom4Bva911qnCsuPmtQigcOULCUC3cmktAELS5bWa5/y+1XYlVmnESPcEQMrByv0TdZM+Ll06mRQ7t9pR44gNycHFra2+ReNxop2Ak1KW4aDBD0ljHacm5p8taOLpoprXomLFI+zgu/A0HHr3h1W/v58gI1b8lOhn//1hK9hYW2BqF+i+GQyfPfwpz7nlfplOKtAk0ElrXRMmR7yh6LS2tmQRAxbcbJE3NPJf2rV602wfGijfNuNS2HJeHfDebSYto+bdingKAnT1YIEG2SnQb1Hvb4/is1nwjjY8XC0wacdn8HBD9pgYLPy3AReUlBw2/fHoxx8kono0iGN4FVC2aRH8dvFCJwLjYe1y0UknUhCdmQ2xvTtD5ubms+f+4ABMCRS80pbFPBo7XyMFe0xX4Iew0GCnhKGvFa0lhSmXuIixWNyaC6Ov1Vpywp4Dh/G64m//IKcaE1fR0EJCgrC2LfHIjM0E0nHknAy8iRSsp/cz0SeStpJrnUnQ1n4riRp+6wva+1QFeVYcDze/Pk0l7xKguer+eCXkc2wY8xz6FG/DI+4x6Zmc9BBAUeTqXtZfXj/tWidl9u05KjUOB4ch2l/XMNLsw+i6dS9HHTdzNMtaljOHTN618GRD1/A8FYVSzzbci8uDX2+P8qu7JR1o4Cnqq/GpLc0SM7MwZTfrsLOfwNLLERtiOIsz1A7h/zvrL0BmXlSNjz1rwMmUdoic+PMvMDSroaMqxsKEvSUAvl9PSau18OKx3nZnqRt2wxes4dw69mTm83pABX/09JCP//zTz+HrZMtojZF8Uml+dqnp+P7NAxCnUBX1u35ZPPFErd36Fa3DKa+UitfYHDs+rMl+n/WLOOK7/rUxZGPXsBHL1dHnSA3fpyE/lYfD+FSW90vd+OFGX9h/PpzbIlATdA0XVTQTBT1RVET9el78Vh17B4+2XIRryw8gjqTdqHvj8fw/YHbrClEeDra4H8tKmDXuFbY+GZz9GoQWCJTWf/mdkwq+v5wjDM9znZWWDWsCTvZlyYTt11GeEo8rN3OIvVyKnLicjDx3Q9hdfAQ/9xjoGFledJPn4EqKYklMKiJ2Zjhqa2cHF6XTI/hYKXvDTCXoCd+2TKknz8PdVqaSatyunbripg5c1hjg5zXnZ5rAUPG0tYWnsOGIWrKFCSsXw/PN4bD0t29wM93d3fH1C+n4usdX/NUDGyA4KRgVHSt+NjnULmJbCO6zj/CDcDUTDus5eN/Xxf0a1yW/b8o6/H7xUhYWJxjW4WSzHSQ+/vI1pV4CU/MwK7LkTzmfuZeIjcPk2UGLTTN9iBUevJxtoECubC1seZeKNIeUqpzuQmZloT0bA4aHwVlteoEurF5Z5tqPqhVxpW1kkoTalomzy6tp9bPrzdBrUDXUt2GPy5G8Hvr/MyXfN+lngu6z+2OQZluSFUqOdinAQRDLG3Z161r9I7kGXmlLasAf1gV4pgilCwS9JQCDg0bcOMs9Y6knTwJZyO/gnkS1v7+3MdEpbykLVsMPugh3Pr0Zr0eVWwsYhcshM9nnxbq+ePGjUPZTmUx8ehEvt9tazdcHKxxzX4cNQJcMbR5eSw5fAczd93Ay7X8udenJHn9uQrIyFaygehvFyIQlZSJHwc15CCjpAlws8eQFhV4oebmqxEpOBuSwOW9i/eTuN+FAiFCG9gUBApwyns64hl/Zzzj54Lq/i6oX9atxCawCgJlrUavOcOaP5Rlon6nZwNKd3InOiWTs18Kp6v5zcyUiV3beyHuvtyJH3Pv39+gxtRpG1P27jOJ0taDk1vGbqNhakjQU0qTTfYNGiD92DEOBkw56CFce/Tg15myZw9UyckGP6ppaWcHr7feRNSXXyFh7Vo4d+sK0Dh7IehZtSe++OsLpFxIgWsjV9buaVfuyVfR49pVxe8XIxCelIkJ2y5jyeCGKGlGv1CFTVBJK+bUvQQuCS0b0ggVvZ1QWlDTcN0gN160UJNzXFo2Z4QikjIQkZiBlLQ02NjaQQ0LqFS5nK2hAI0Wz7xbP1c7ONhYGcxJe/GhYO4nop5tmgxbPawJqpRiD492Oz7adBEJ6VlwfmYFMu9nInRhKGbNn4X4+QuQm5HBWR5DK21l3biJnPv3ed3pBdMJeqS0ZVgYxtHCTEpc2qDH1CGnZksnJ6hTU5H8+x9w79cXho57375I2ryF/X6iJk6C86KFhf4b1Q5Ww5bVW6D4UIHxGI9zA89BYal44lj5pG412b18z9Uo7LwciQ55juwlyeDm5Xlseszas9xg22PR3/hhQAM0qai/sWUKaKgcRgv1ACmVSiQmJsLNzQ1WVoZ/mErPVuKDjRew40IE369X1g2L+jfgoKy0oQZ5Elt0KPcDTxWSEGFWRBZqq32QtHk+/473O28b3GSUtrRlU748bCuWbLm3NBqys/Lc1SXoMSykkbmUR9ezb91mXxlThjInLh078jqVuIwBUn31mzSRzr7IunoVGZsKb0Y686uZsLCxQPiKcKhz1GiyRmPN8SRIG6Z9nj4MZXuSMjSNjyXNi8/44pcRzeDrYovE9BwM+Ok4NxQbsqigoXI3Ng2vLPg7P+B5rUlZrHujqV4CHpoWo74tC6skKBzuIW5PHGtJjXlnDIJ27qSUGmyrVoVr9+4wNLSlLScTKG1l3Q5moVZCgh7DQoKeUoIkyBWumkbGtL+PwtRx65Gn2XP+PLJul5yzuC6h2rvHwIG8nrbkJ+REaE5iBaVChQr4cuKXrINCAnBkRLrn3p6nPm9i1xo8zhyZnIl3fzlfano2NGW1dVQL1tkh3aAvtl3mySrqBxGeDgWIm8/cR9f5h3E9KoVH9Kf3rIUpr9QqUd2fJ43r0+cnPVsFpypTkR2TjaiNUfAs44nPOndDWt7Els/77xuctUNWcHC+q7rziy/CVEpbVEa08vbW9+YIDyBBTylBBxmHvGwPKY6aOnZ16sAmL0Udv2IljAXvt8fAys8PyMhA9OQphX7+h+99iArVKiD2t1jupRj31zik56Q/tcl3as/avE5lLlILLi38Xe2xcWQzvNq4bL6icodZB/HnpcIpVJsbZFI6eNlJjP/lPJIzlfBzsWONor6NNO+jPgKwCds1fVo2nvv5ftjyMORm52L9srVInTc/v8zu1PI5GBoJq9fwLR0zSDvI2Ek/fpxv7WpppCIEw0GCnlLEqWVLvk3dvx/q9JIznDQEaFLEY+gQXk/csgU54eEwBkhOwOeTT3g9dd8+bsYuDNbW1li3Mk/u/9cYfqwgZa6udQIwpHl5Xv925zX8fbv0zDupt2hqj1rsPUUNwjR1RH5d7284j5TM0im3GQukD7Q0T+H54A3N/n2lXhn8/k7LhxqzSxsSgFxzPAQWNjGw9aEyFuBQyQH9X++PBqlpyLp2jUfdfD54H4aGKjU1vwzu3v+1UvMjKylInyz1L41LvFPrVvreHOFfSNBTijh3aA8LOzvW6knetQumjlu3brAOCGCBLhoJN6ZGbJu8q+HIryezAWJhaNy4MX7/7XeUef2fCbCF557eGP1Jx2e4AZaqW2+vPYuo5NItM1F/0Z9jW+HF6j58f8Pp+2gz4wDWngjhk725cy0yGT0X/Y0vd1zhEhJJDCwb2giz+tYtlbH/x0H6R5N/p9F0JZwqzeTHLBQW6DmmJ1bMW8y6WQT18dhVrw5Dg4RM6SKQLjhcuxler1FhyTh3DqpEjdK6sQssmiIS9JQiCicnuHTowOs0KWTqsM3DiBG8nkimnoXskdEnTmPHwsLeHsrISMTOm1fo57/80svY1FPTDK1MVmLR+UWITHtyycjGyhILXqvPJ1CybyCtF+rTKE1oeopG5ye/UpP7jEhc7+PNF9Fp7iEcuqnJbJgbd2LTMG79OXScc4h1hSgRQVm5neNasfihPrkUloR31p1joUbnZz5jVfDIXyKhSldh4YsLETtvPn+G6WKLJrYMDSrDaUtbFJQpnIxfuJUy+drSlrWPfj8fwn+RoEcPGjZE+okTyA4Nhanj9kp3ViSlbE/c4sUwFhS+vvAaM5rX41etQvrZs4X+G9U9qkPxuwI3P72JnMQctNvY7qnTUdTfM6dfXT6xnrybgOl/XENpQ+WF/k3K4a/32/AkEokZk6XDwJ9OYOiyE7gZ9WR/MVMhND6dS3xtvzuALWfDOANXzdcZG0c25+ZzMg/VJ2Sm+vqKk8jIUcG73E5+LGJNBGJ/j8XQjKFIP3mSleAJr7fegjX1qhkYJOORHRycX9oyBVL2aYIe5xfa6HtThEcgQU8p49CoIayDgoxqnLu42R6vN97g9cQNG5ETaTwNsuQ+zeOmajXCxo2HMj6+0H/j016fQpWiwv0f7iNXlYsW656uUN2yijfGt63K66TY/Msp/QTHlPWhSaQ/3mmFllW88r272s8+yNpCR2/HmeSIO3llkZpxmxl/cYmPSnsVvBw5GKXenQbl9G8pkJal5IAnKjkLrq4xyHTYj6TjSUj4KwFNWzXFO6+/gYiPPqZUCjcGe77+Pxgi8T+v5lvH5s2MXpuHyLpzJz+IMwWBRVNEgp5SxsLSEq6vaOrWiVu2GoUppy6yWzQRRTYccYuXwFiwsLJCmVnfwdLZmUsE4e+9X+j91bt3bwwZPgRpV9MQuS6SXdg/P/L5U583qk1ltH1Gkxr/aNMFto3QF9X8nNlKYfnQRqji48SllN1XovDq4mPoOPcwNpwKLbBRqKFCZUQSh6RMVsvp+7gpmLy+gjzs2ZV997hWbNxKvmmGsK1U0rocngxrKxXUATNZfDBsWRicPJywZf0WxE7/hocHLBwcEDB9msGNqBPZ98PyS0FkiWEKpO7XNDBTdpv0kATDQ4IePeBGwmAWFlBGRCDt2DGYOpbU2/PGcF5P3LABOVHRMBZsypVDwLSpvE5q2rELFhT6b/ww/wfUa1YPcbvjEH8gHltvbcW2W9ueqlA879X6aFzeg8sq5Iy+/7p+37fnq/lwo/OSQQ3RvJJGvflqRDLe33gBz03fx1NnV8KTjSr7Q8KC0/+8hubT9mHEqtOcyaL3m5qUaaJt37vPsys7mZ4aAuRbRr1eJG0A5MKuyqdQpipxb9Y97ufZ+stWOF6+jKTNm/n3fT/8EDZl9TNG/zQS16/jLCoNO5hKwy9NfBLObV4w+ik0U8UwvslmBn3JtQrNSZs0BydTx61XL1j5+iI3OxtxS4wn26MVS/McPozXYxcuQuqBA4V6vo2NDXZu2wnPAE9E/RIFVYYKnx35DFfiNAJmj8PeRoElQxqySziJB45cdRrHguOgTyjT0fZZX6wZ3hR/vNMSfRoGcgM2NV4v2H8bHecewvMz/sLUP65y06+hBUC0PRSYLfrrNvp8f5S3ldZjUrL4tZE69tIhDXHwgzasXWRtIMEOQdk0Csx2XtYouvvV/FbzAzUNSSgwb+48tK5bFxGff8EPO7VuzWa6hog6M5PL3YT7a68aZCaqsCgTEpB+5gyvO0k/j8FikWtoR6USJDk5Ga6urkhKSoKLnk0wk377DeHvvsc9L1UOHcxXa1ar1YiPj4eHhwcsLQ3ngKur+n3U11/za660ezesfQ1zsuFR+4C8dEL+9zo3oFu6uqLCpk2wCSycKenFixfx2eHPEOzwj/jg/j774WWv6Zd5HOQ43veHo7gZncrNs2RiSf5UhgJNeK09HoLt58N5Gx+EMiZUpmtQ3gP1gtzY86sgV8C69N5KTM/GoZuxOHAjhrV1olM09gBaynk6oG+jIM7o+DiXvnVEQXt4hq04haN5Qe8z9X7G/UyNgjGxudNmVPasjPujRnO2QeHmhoq/bi+WGnBJHosSN29BxCefwMLWFpX/2g8rd/33SRWXpO3bEf7Bhzx6X/Xo33ycKy6mfD7Q1/ldgh49oc7Kws2WraBOTobvF5/D47XXTP5DTq/5drv2UEZHw33QQPjliQAaGo/bB8qYGNzp0ZNv7WrUQLk1q2Fpa1vov19rRS1khmfCytmKl1MDTsFW8eS/Q5o9vb8/ipD4dLg5WGP9G82418bQuBWdgj8uRuKPS5G4EpH8n597OdmyFhEtdQPdUM7LEb7Otv8pHxUl6CH7jtCEdFyNSGFNnWsRKWwPcTcujfuQHqSityNaV/VG+2f90KQC7WfDLUUkZ+Zg6LKTOH0vgaf6WjTZi/NJuxH7RywsHSyx9su1aBXYCombNiHi08/4OWXmzIFLh/bF+n9L6lhE19l3e/Ziqwbq9wuYMhmmwP2x45Dy559wfvklBM6apZO/acrnA10jQU8x3pTSImLSJCSuXccn0AqbNprFhzx+5SpETZnCV3iVdu8ySB2LJ+2D9FOncG/wEEClglvfvvAnk9JCEh4RjrJVysLGxwblPygPhb0C5wedh6WF5VNHqCnwIY8uCh5W/K8RagRoMoSGCJlfUvBDJbmzIYmPNVOlshLZOAS42XFmiMb2XewUyM7KhLOjI2ytrWClsIC1wgL0j/4OZb94Sc9GQt46BYQkGvgoHGwUaF7JC62reeP5qt4I8jAsh/HHQa9t0NITuBiWxNIBnVtfwv6on5FwOAFhS8JQtmpZ3LhwA+pbt3BvwEDkZmTAtVtXBEyfXuz/u6SORdTHGDJkKK+X37SRPe+MHXV2Nm42a87CswHfTIdr1666+bsmfj7QJRL0FONNKS0yLl7C3d6amnuFbVthV62ayX/IqZZ/q107qGJi4TF4MHw//giGxtP2Qdyy5YjOO6n4T5uqaUwvJB9+/CG+mfYNHJ9xRLlx5WBpY1mgwIcyKX1+OMYneRIPnN+/vt4F8gqahbkTl8bBz9mQBL6lbExJCD1TCbC6nzOq+zujup8LnvF3ZnNVfZiAFrdsOGDJcdZIsrK0wIB2kdgUMotH00O/D4WnvyfOHjsLPxsb3O3dhzOo1HhffsMvUOjg+FYSx6JctRp3+/Rlc1GHZk1RLk9HyNhJPXwEocOGAQoFqh45zOVFXWDq5wN9nN/1q65l5tjVrAHbKlWQdfMmT1vYffwxTB1LOzt4DRuGqKnTkLBuHdwHDix0b4y+8RgyGBlnzyJl1y5Efv4FZ6vIyLEwTJsyDVFxUVixeAWfwMqOKos6K+vg3MBzUFg+/uRc2ccZG0Y243IHZTaoz+OrbjVZRNCQofJRJW8nXqh3Rjt6TQJ74YkZCE/KQHhiJu4n0G0Ge35lZucg18KSdXKUqlzkqNU07MPlPVKtdneweeDWms1TKdChbJGxT85cDk9i/7PQ+AxuFB/dKRuLb8xC8tlkhP4YCmdPZxw/eBxlPDxwd+BADnioLzDoh+91EvCUFMl//JHvpu7z3nswFbRTWw716+ss4BFKBunp0TNxy5cjetp0KNzdUeXAX8i1sjL5yJ6yPbc7doQyPAKOrVsh6PvvDeokVZCrKzJJvNd/ALKuX2e7irI//QSH+vUK/f/06NcD2zZsg2tTVwQOD2TPpDMDzsBaYf3E58alZmHYylOcMSFGtq6EDzpUM+jelMKgy0ZmY2PT6fssjpilVHM2771u1vju0li2M7n+3nXYOdjhzNEzqFalCu6PeVtzwrW2RtmflsCxcWOdbYeuswxUAgru2Ak59+/DpUsXlPn2G5gC1KN068UX+Xjm8+GH8MwzWtYFkunRfabHNM+qRgTXfq2soEpIQEqeM685ZHv8PtcI9KUdOMjNf8boo0YnGZvy5bmPInTECG7MLAx0ItmwegM6dO7A5S3tt7H+z/WRocx44nM9nWyxdnhTvFxTYy3w/YHbGLPurNGLBJoz2Uo1vth2Ce9uOM8BTyVvR4zplsABD2HlYoUGYxvg2IFjqF69OqK/nZGfYfD/8kudBjwlQeLatRzwWFhbw/udd2Aq0IUPBTyEcxvT0BsyZSTo0TNWHh75XxRzMCHV4tymDZzzzFcjp0yBKvm/kz6GjpWXF8ouW8rqq+qUFIS8PgxZt28X6m9YW1vj182/4vrv1znblavOhTpLjcarG7N685Ows1awQekbrTTy/aTaTD0g1O8jGBc0nUcK1yuP3uP7L9XwQ4smB7Dg0hQuaZF3m53CDienn0Tt2rWRsG494pcv598lU1/yuDNk6PtNGldaexdjK2k/iZS8wNOmYkW+CBIMGwl6DADXVzQmpKkHD/I4tLng+8knsHRy4qbm6JnfwRix9vfnZkyFtxdn60jLJ/v+/cL9DbrydfTG4X6HEb48HHdn3mWX7OZrmyMu48lihFTO+qTjM/iqWw2e7jl1LwEvzzmIwzdji/nKhNLixJ14dJp7mEfSaR9SmfK+4wRsub0RcfviEDI3BKmrU3FywEn+/dQjRxD51Ve87vzSSwbpnv5v4n78EaqkJFi6uMBrhMaLz1RKWyl/aDLVTpLlMQok6DEAnFq15JMmdWmSwJW5QOKEPu+O5/XE9evz1UyNDZqYoZ4eaiRVRkUhZOj/imS14WLjggH1ByD9RjruTL/DV/fP//I87iVrrv6fxMBm5bFkcEM421mxCeWAn47j6x1XpNxl4BNtSw4F47XFx3hSy93BGsuHNsSikFdwN/kuordFI2JlBLwDvXH4l8P8nMxr1xD2zliWTLCrU5stUsjPz5AhDzCSqiC8RowwqUbfjFOneBCFcO3aTd+bIxQAw/62mAlkbKnVdUjevMXgpPtLEtK6sa9bl9cjJ0xgmwpjxK5qVQQtWQxLBwfkhIYi5PX/sSx9YaDy1pzv5uCzLz5D5r1M3P7yNjLuZaDzls5YdUVz0ngSL1T3ZW8sEtvTOrR3X3AE1yOfXCYTSp8bUSno9f3f+Pq3q2xsSlYjG99qiFFH2yJXmYuIVRGI3hKNyjUq49KpSyhfvjwyLl5kjSh1aiqXVIMWLOD+OEMnZs5c/l7TNrsPMA1jUS3xa9bwrUPDhrCrJgajxoAEPQaCWw9NiSv7zh1kHz0Kc4GuUv0mTeJm7qybtxC31Hh1O+xr1ULg94tYeDH71m2EDhvOKf3CBj5fTfoKS5cvhSpZheDJwUg5n4JvTn6DlutaQp2rfuLzaVybfLE+fKk6i/mRxkuX+Yex9PAdziwI+jcM/W73DXSaewhn8ibvBjUrh4WDKqH7b635fsxvMYjfF4+mLZvi9N+n4ePjg/TTp1nQT52UxB52ZZf8xD1lhk7m1av52WufsWOLpGBuqORERyNl9x5ed++vUdQXDB8JegwE20qV4PTCC7yevnSZWWV76ArJc6hGoTV24UJk33t6OcdQoQmawLlzOIjLvHwZd1/rj+z7YYX+O0MHD8XhA4fh6uMKG2+Nh09iViJr+SRmak6Wj4MUjt98vhK2vNWC7RZoKujLHVcweNkJ1sUR9MPJu/HoOOcQ5u69yQaylX2csHFkM1Sreh4dt/5jGeHZ3hOfTvwUB/ce5NFbVjAeNpzVfq3LlEG51T/DtmIFo9iN0TNmUuMLbJ95Bi6dO8OUSPxlA2krsL+Zc9u2+t4coYBI0GNAeI16i2+V164h7eBBmNtrtw4K4jR4xMSJRh30kbt14JzZmozP7du427cvlyYKS/PmzRF7NxZLBmpc6dNuprFDe8v1LXEk7MhTn08qxL+NaYmBTcvxfTLdfGHmX5i396b0+pSydxbp7pCFyO2YNM7AjW1bBVtHNcHQA60x7cQ0VlmO/lXTB3Z++Hl8PeFrbnBPPXAAoW+MYFkEmgyigMcmUCPuaOhQw3XaEc3n1Pf99wy+96gw5ObkcB8i4danD4/hC8aB6XwKTQDyoHFq04bX4xYsMOoTf5G0eyZO4PX0o8eQbOQN3c4vvohyK1dA4eEBVVwc7g0chJS9ewv9dxQKBZtJrmu5Dve+u4fbE24j404GRu4ZifF/aZrAn4S9jQJfda+JpUMawtfFlr2pZu6+gRdm/IVt58LM6jNW2pCSNL3HbWcewJrjIfxYw3Lu+OOdlmhbNxvN1jWCOluNiDURCF0UipT9KTjU7VC+MGXy7t0IHT2GLwRsq1RGuVUrYe2n0WUydNTp6Yj6UjNh5vjcc4VWLDd06LvMk7ZWVhz0CMaDBD0Ghmdetifz0mWkmolYoRanFi1YqZWImja90I3AhoZ9nToov34dbCpUQG5mJu6PHoP4lSuL9LeerfAs5nwzBznxOQj+Opgdtnfd2cWO7QmZCQVqct7/3vN4+8UqsLO2RHhSJt5Zdw6vLPwbZ0KM+302NKh3aseFcHSYfZDf4+iULDjbWuHr7jWx/o2mmHHhfbz626vIDMtE8FfBiNsVh9oNa+PWxVusQE0k7fgNYWPHATk5sHv2WZRduZLLKMYClbWoTE3ZTt9PTM9eJ2G1poGZylo0hSoYDxL0GBh0gLNp+Ryvx843r2wP4fvRhzz6TZo30dONX6beJigI5deugUOjRtzbEDVlKiInT0GuSlXoBufRo0fjzMkz8AnyQeT6SNybdY+tCVqtb4WPD3381M+Kg40Vxrerin3vPo9X6mnE4c6FJqLHwr/x9tqzCEt8sgq08PRg54+LEXh5ziGMXnMWt6JTWXeH3uvd41ujU10X1P25DpcmE/9O5KwdBT5fTPwCp4+eRkBAAO/D+J9XI/z993ksnQLnssuXwcrd3WjefiprJeRNNZEkhW1FjXimqUAj6uknNZpJ7q+9qu/NEQqJBD0GiENeUy81wqbuN69sj5WnJ3w+eJ/Xk7Zu5SteY4d0SYJ+WpKfxUpYtQr3336HSwCFpW7dupwR6PlaT6ReTEXqlVR+fEfwDtReWRvX468/9W8EuNljVt+62DqqBRqU05xMt58PR5sZf+HDjRdkxL2QUKCy83IkOs07jDdXn8H1qBSQlVzXOgHYNa41vutTB6tvLuDgVIuNnw18g3xx9MhRTJowif3FyJMu4qOPEfX11xwgU6AcRPpPBmwg+ijl5YhPPuV1hyZNWH3Z1EhYu5ZvqeTIFzOCUSGGowaG1mAu44sJ7KtDmZ/ymzYalCFnaZxEqBSUuncvm3lSiYh0cEqLkjL5o9cVM3cu4hZ9z/ftatZE4IL5sPb1LdLf27dvH3ZZ7cJvd35DdnQ2YAGe9PKw88CeXnuealqq3abfLkZg6u/XHsr0tKzihdefq4DWVb318tkzBsNRmorbczUKC/+6hUth/9iodKrtj7EvVkEVX2cciziG4buGs70IjaHb+NjAubYz9vbeC09bT+7Z4r91/z6bh2Zdvcr3Xbt35x43ferwFOV7EP7hh0jath2Wjo6ouH0bT5uZEmQ0fKtVa75g8ZvwBdxfLdlMjxiO6t5wVIIeA0P7IXeIjMK9Xr34scCFC+H8gqbB2VxQpaTgTq9eyLkXwlMr5TduYJPP0qCkDzSJmzYhYsJEHnelUp7fV1/Cpf0/I8uFJTY9FuXqlWNBQ5+ePvBs6wkLSwtMbzkdHSt2LLB+zPZz4fjp8B3W9tFCY9UU/FCJhry+SgtDDnpuRadg/clQbD4ThrgHfM7I/PWdtlVQ3c8FMekxeGGDRoIi424GwpaHIfNuJnxr+SLifMRDgWTqoUMIe+991uAht3S/Tz6GW79+er/QKez3IHnXLoS9rTES9Z88GW49NdpjpkT86tWI+uprDuoqHzgAhZNjif5/EvQUHAl6ivGm6JMHP+RhY97mbIc5ZnuIzOvXcbdvP24Cdm7XDmXmzimV96A0DjRpR48i7P0PoIrVeGS59uwBP/IicyzaQXTPnj3oP7Q/ou9Hw66cHfxf9Ydjdc3f2tptKyq5VSrQ36HMz5FbcfjpcDD2X//HB87D0QavNS6LbnUDOINhbkFPWpaSm5Mp2NGKChJWlhZoX8MXo9pURo0AV+Soc9BjWw+2kSD/tKjNUYjfG8+NBKPeHoXpX02HY94+zlWrEffDD4iZO4/LWVY+PigzZzYc6tWDIVCY74EyNhbBXbpyLx7pjVEG09SOV/TdCO7chWUo3Pv3h9/nn5X4/ylBT8GRoKcYb4o+efBDnn3tGu706MmPBy5cAOc88UJzgtRcwz/4kNd93n8Pnq+/bjIHGmVcHCI++xyp+/fzfeuyZVHm22+4ebUopKWl4fMJn2P27NnIVeXCuZ4zyo4uCwuF5uSzuetmVHGvUqiMxtIjd7Hp9H1kKdUPZX861vJHx1p+qObrXCInN0MIeqgxmSbbfjkVih0XInjc/8H3oG/DILxSvwy8nGz5hPjjhR8x/9x8/jlZSdz48AZy4nJQq2EtrF66GrVq1Xook0mfa+2+JxuDMrO+M6gJrYJ+D7gcPWo0l+MV7u6o+Ot2o1CLLixpx44jZMgQXq/42w4WlC1pJOgpOBL0FONN0Sf//pCHjh6N1D17YfvsM6iwaZPJXT0VhMgvv0TCmrVkKY6yy5bBsUljkznQ0Akjcf0viJo2jTNaUCjg9dabbMxInmxFITg4GCPHjcSJmBMIGhGU//9oPzubum5CVfeC90jFp2VjzfF72HQmDHdi0x76GSk+d6zpj5dr+eFZfxedfT71FfREp2Ti0I1YHLwZw2KO9Nq1ONgo0Lm2P/o2CkL9su78WlVqFeadnYefLv3EfTtZEVmwK6Ppw6l0vhK61OiCoUOHPvQ5yrh0GeHvvpuvPO4xeBB83nvP4ATuCvo9SNy8BRGffMLrZebMgUuHopdqDRkaPkjZtQsOTZui3PLSscuRoKfgSNBTjDdFn/z7Q5555YrZZ3vU2dm4N3AgMs9fgMLTExU2bypy829R9kFpkBV8h8eUaWKPIBPWgG+/4ZH34gQOf0f+jbd2vsUeXo7POMKrgxesXDVBxMYuG1HNo1qB/x4FTjSZ9PuFCG5+JnXhBynv6YAWlb04IKhfzp3vFzUIKq2gh3qZTt9NwIGbMTh4IxZXI/5pSNZSr6wb+jUKQqfaAXCy1WxLhjKDG5TPx5zn9yXlXAqiNkWxjtJz85/DnkH/bSSn5teYefMRv2IFfci4Sd//q6/g2rkTDJGCfA9ywsIQ3LUbW2S4dO2CMt8Yv8zEo8iJjMStF9uyjACV2YvTg1cYJOgpOBL0FONN0SeP+pBLtgfIiYjg4I96BiggILVjCxubUtsHpQEp78YsWIi4H3/kHg9ybPf97DO4vtK9WBmUW7duoV3Hdrh78y4srC3g3tIdXi975Xt6zX9hPqs+F/b/uBmVwsHPHxcjORj6N9QHVC/IjQMgCoTqBLmyVpC+gp7MHBVr55DDOTnPX41Mwam78Q+VrQgXOyu0rOKNVlW9+JZG/LVEpUWh7UaNz5JaqUbSsSTE/hmLrPtZ/N6OeXsMvvriq/8cX1IPH0HkxInIuX+f71PmNmDqNIN25n7a94B6kkKG/g/px4+zCSqVtYxpvL4w0NRl7MJFsPLzQ+U9u4uchS0sEvQUHAl6ivGm6JNHfcjJqfjOK5pJCGoQJIsDc4Saf0NeH8ZXyaT/4feZRg/E1A406adOcb9HTng437dv2AC+H34E+1o1i/Watm/fjo8mfoTr569zY61HGw8EDAzI/x0fBx+s7bSWbwsLBRM0vn36XgLO3Et4aKrpQSPUKj5OCPJwYDf4QHfNUsbNgW/dHKzzA6+iBj2UuUlMz0FCejbuxqbnBzjXIpNxNy6drSH+DQkI1glyQysOdLxRJ9AVVoqH9/vZ6LMY9Meghx4LnhqM9OvpUNgpMHLESHz8/sco868RbVIVj542jce4CQs7O3iPGQ2PwYNL7cRZUt8DbSBAkA4VKaqbIqQ9dLtde6iSkuD9ztvwevPNUvu/9X0sMiYk6CnGm6JPHvchvz9mDFJ272G3YirvmGNvDxH742LEfPcdrwfMmFEipQFDONBQo2vU15ORtG1b/mOu3brBe/y4YpX2qBSzd+9efDDhA4R6hMKvl8bLKf1WOuyC7GBpq3m9I2qP4KUgWj+P+j9C4tO5CVgTBCVy0PGIeOMhqGeGgiFqDCZTTqiVcLCzha21AtYKS15sFBZ8m61Sc7+NNsDR3v47a/MoyIOsmp8Lqvs5o06gG1pU9oSbw3+zhrcTb2Pwn4ORlJXE9zPuZSAjOIODRaLy7cpo5NAIb418K98+4sH3IPnXXxE1dRpnJwnH5s3gN2lSsUqWpcmTvgdJv/6K8Pc/4HWPoUPh+6Fm3RSJnvkd4hYvhqWLCyrv2slio6WFIRyLjAUJeorxpuiTx33IH8r2zJ/Hni/mSGkIFxrSgSb9zFlucs68cIHv02umCTbP1/8HS/t/yi5FQaVSITojGp3Xdca5MedY3NCtuRs8nvfgAEjL8peWo75P/WIF2jTyff5+ImddwhIycD8hg8UQaXmwWViXkN9VNT/nfxZfze2jAhwt95LvYfAfgxGXGcf3VWkqJB5NRMKhBNZBogzZir9XYGDjgY99P0hoMHLiJKQdPsz3SYvJ5+OPOGg1pouVx30P0s+cQcjgIew07tS6NU+WWuSJLJpiL8/tDi8hNyur1KZHDfVYZOhI0FOMN0WfPOlDLtmeRwgXliuHcuvW6tSbyNAONNQ7kbxjB19xKqOi+DHqofAZP46tLSyKuY3p6en46aefMHP+TNy7oZkosg20hWsjV3h38oaF1T8n6p5VemJ0vdHwstfdSDIFROGJmkDofmIGEtOyuUyVmpYOS2sbqNRAtioXOSp1/mJpYcE9QxTAuDtYw92B1q35Me06NR0XJMgISQ7B/3b+D1HpmveWoEms+z/eR/KpZB4/t7SzRM8+PTH+zfFo0qTJI/9uTnQ04hYvQeL69dyfRdD+8f34I1h5aLJDxsSjvgcU0N3t0xeq+HjYVq2KcmvWlLhAnz4J//RTJG3azL08lf78o9QVsg3tWGTISNBTjDdFnzzpQ55Juj3dX+H1gOnT+MrRXHlQuJBdqFcsh8LZ2aQPNOqMDMQtXYq4JT8hN0NjGWFXqxafVB3q19dJFu3YsWP4YckPWL9xPdQOalSZWoVP8JmhmfnB0IMn/AnNJqBzxc6ws9LtyaCkprfUuWpcjL2I7059hzPRZ/75/5KVSDmfAoWTAi71NMcGmnir5lUN74x4B7169coXFfzPtsbGcrCTsG4dZwQIsl8gGwmnli1hrPz7e0AXG3dffRXZt25D4eWFCuvXmZzNxL+NRYO7deceQv8pU+DWQ3PsLU0M9VhkiEjQU4w3RZ887UMe9sEHSN7+q0YE7PffjMp9WdekHjyI0FGjgZwc2Nerh7I/LeGJJ1M/0ORERSFm1mw2ZNXi+Nxz8BgyBI4tmuukhEJBR2hoKLJdszF2/1j8PfVvJJ9OhpWbFY++Oz3rBMdnHWHj+XCpqF25dni1+quo6VUT9lb2eg96MpWZ2Hl3Jz478rB6rjpbzX1MadfTkHY1Dek304FcsIr1nn170MSvCTIzM2H/hBIiiUvG/bSUHcVZY4kycD4+8Bw5Am69esGyhKYLS4sHvwcWajVC33wLaYcO8dRkuVUriyyiaSzQ6yXxSNsqVVBh6xa9lPAM/VhkSJhc0DN58mT89ttvOHfuHGxsbPiAaI5BDx1ogzt24kkCMiUMmDYV5gz7/Ywbz/oZDs2aIuj772Fpa2sWB5qMi5e43yfj9On8x8j52X3QILh27Vrs9+FBDhw4gI2bN2L7n9sRciMk//GAIQHcA8TbE5IBW39bWFr/9z3rWqkrulfuzqKIzjbOsLSw1EnQQ4cv6r+5EncF+0L2YcutLZzN+ffvKJOUyArL4kCNgkLq0Qn7KYx/Ts3bLV9oiaF9h6JLly6835+4bQkJiF+6FPE/r87PuCm8veA1/A249e2j0/ddnzz4PYieMhUJP//Mj5f5biZcOhbM081YoQnKewMG8nrg94vg/PzzetkOYzkWGQImF/RMmDCBD4D379/n/gNzDXr+rYBadtlSODZrBnOGrSo+/Ii1bZyefx6B8+YWS93WmA409PVNO/I3C97RVbgWhYcHO0C7v9pP55YAkZGR7PD+287f4NreFYeUh6BMVeLa6GuAAqxIbF/enpuhyVXcqYbTQ31BJY1WP4dKctpFlaKZ6qr6bVU0frYxBpQZgLN/nkWb59ugfv36sC7A54X6WahfJ2H1GhYaJEgs03P4MLj366dXR/SSQPs9sPjzT0R/PZkf8xozGt6jRsGUoe/UvX6vIuP8eTg0aoSypAmmpwZ0YzoW6RuTC3q0LF++HGPHjjXroIdHgkkU7Ngx9muquH2byR1wC0vCuvUs/kY4v/wSysyYUeR0tLEeaLJu3UL8ipU85q5tpKXgj5ppSRemJIXwYmNjMWfuHBw6cQhnTp9BSmyeWKEFUGNxDQ56Uq+kInprNGy8bLh3RuGoWei+c11NP1Z2XLYmQLEAO8XTLZWdLO0t+feI5LPJyI7OZkNPZYKSn0MeV749fOHa2JWbkK+MvILc7FxY2FggqGoQWjdqjcb1G6Nv377wLoS/lTorCym7diNx0yb+vj0YVHoOG8ZBZXGn6AwV+h5E/vEHksj7TqWCS6dOCJjxrVFNoBWFB93iaTpUn2U8Yz0W6YOCnt8NWx2rmGRlZfHy4Jui/SDRYohoY1C6fdI2+k74Ane7v4KckBDEzF/A+i3mjGuf3lClpSHm22+R8sefCLe1g9/XXxVpsqmg+8DQsK5YEb6TJsLznbc5I5G4Zi1UcXFI2ryZF/IMcunSGU5t2uhca4QOypMmTnooG3T58mW+faXPK9w8PD14On4L/w3pNzRZEi32lezzg564P+MQt1szLv4g7s+7o8wQTdMs/Tztyj8WGApbBbwCvDCy5ki81fctuNi4YF/QPpSlC4KKFf9zsijIPiWJCJraoak5dd5xg7AODIRb375wo2Anr3/MmD4jhSHz5k0kfzGBAx67unXh+/VX/J0wsuvkQkFj+NHfzeJ1p/btYVurll73r7Eei/RBQd8fk870TJw4EZMm/XMgftCQ0VlHkz76JH3VKqT98CObVLr/tARWlSvD3ElbugzpS5fyul3PHnAaO9bkr0wfB2V7svbsQfr6X6C6ffufHygUsG7YELZtnodty5awdHUt1e0iN3j6/iYkJPAtlZZoDJzYt38fzp0/B4tci/yDGB2iateujfZ5fkfnz5/nJmO6mvP39+erO13sY3VKCrJ270Hmjh1Q3rjxzw9sbGDbqhXsOneCdf36xZYIMAZUkZFIHPM21BERsPTzg/uPP8DSCMfuC0vG1m1InTFDc0xdtRJWZcvqe5OEApKSksIXOQZd3vroo48wffr0J/7O1atXUb169SIFPY/K9AQFBfHB1lDLW7Q7aPvc3TUuzk/83Zwc3O3VG9k3b/Loctk1q01WJKww71/MjJlIWKZxQfYYPhze48aW2D4wBuj1pB87juStW3kaRZ2a+s8PFQo4NGkC5/bt4NS2rcHoyZBwIh28KKBRlOBnOjs0FGlHjiD98BG+1Y6cE7bVqsG1V08u65SmCq++yQ4JQejQ/0EZEQELBweUXf0z7KoV3JjWWKE+reCXXoYqNhZu/frC94sv9L1JJncsKkno/E7vk0GXt959910MGTLkib9DkVtRsbW15eXfULrbUOuj2qtb+oA/dRttbRHw9Ve42+9VZF68iKS16+AxSDNxYM74fvA+cjPSkbhuPeIXL4bC0RFeI0eUzD4wEpxbNOeFHOvp5J6ycxdS9u3j0k3633/zEvXlV3Bo3JgDIMfGjWFTsaLesholtQ/IDTzt+AlWS049cpgFLh/E0tkZLp07wa1nL9jVeNbsTjRZwXcQOmQIlNHRmvfi22854DGV78GTiFu5kgMeCvSoWdsQXrMpHotKioK+P3oNeqihsDBNhcJ/oSY79/79eZw0evZsOLd9EdYB/5hImiN0gPD74gseJyajx5jZs2HpYA+PQQ8bRpojpB3j3KYNL1T+Sjt2DMk7dyJlz16ok5K4WVfbsEteQ/T5sq9bBw716sGudm0onJxgTOSqVMi6cQOphw8j7fARtlAgXacHsfL2hmOLFnBq1ZL7nUy1MflpZN64gZD/vc4nfrLOCFyyGOn+/jAHlPHxiF/yE697DhnCnwnBNDGaRuaQkBDuYqdbSn2TXg9RuXJlOBnZgVjXeI8di5Q9e6CMjETkl18hcNFCs7tC/TeUofCfPBnq9Ayk7N6NqClToc7M4vFic39vtJDInFOrVrzkTpzIGZCUnX8i9cBBvtKnLBCNweePwltYsFCbfd26LAZJwRDZgBhCjwtr8cTEIOvGTVbSpUCHl9u384UDtdBEGznXOz33HIs6kp2CuX8mMq9c0QQ8iYk8mUZSGDZVqiA9Ph7mALnFU3mLXrvH//6n780RShCjaWSmMtiKFSv+8/j+/fvxfAGFo0xlZP1RUKni/lsa/Ywys2fB5aWXSnArjQfKZtwf8zZSDxzg+9Sj4T9hwhN1fMx9TJQDiIgIZJw7h/Rz55Bx9hxPM0Gp/M/v0vto5e/P2UVeytBtmbz1MrD29SmSZtK/xQl5aig9nU/KyoREvs0JC9MENnlBDj32OGwqVOAAx+m5Fqy9ogvlblMh4+JFhLw+jINcynCUXb4MtpUqmc33gHqYbnfqzBlA388+g8eA/jAUzGUf6AKT1ekpDqYc9BD33xmLlJ072Ren0m87OEUtaBq+KQOWuGEDvx2k3Bw4Zw4Uj/kMyIHmEe9JZiYyL1/WBEJnzyLj3HkugzwVS0s2R6WTKZXWLGysAWtrDoT+u9jAwsqKG61zEhKQTf0VaalQJyZxQEP78WnQ37GpVAm2VavArmpVzkzZVq8Oa19f+So8gvQzZxH6xhv8npOpZrnly2BTvrzZfA/o9Bf6xgjOZpLmWaUdv3IG1FAwh32gK0Snxwzx/fQTpP39N5+MyJHb/8v/juubI3Qi9PtyEmzKlUX0jJlIP3oMd197DUHf/wCbQNM1TNQlJH7p0KABL57abFB4OE8/UcYlJywcOeHhmnW6jYxkfRcya6SsES26xMLengMpDmoeCHC43FYMNW5zIu3ECYSOfJMzaJSVI9Nem8BAmBN0IaQt35JxryEFPIKZ9/QIT8faxwc+777LysSJv/wC165d4NCwobx1ec3NpKBrHRiE8A8/ZKfou/36IWjhAtjXri3vURHeTy5fPcZlO1ep5L4gDoDCw6GMjePHcnOyOWPz7wUPrFs6OMLC1QXZtnZw9PODjacHj4w/uJi7AnlxST1yBPdHjeZ+J+tyZVFu+XJYm0nTspbs+2GInqaRTHHt0YOb+wXTR4IeE8OtT28k/form1BGfDGB3YGN3e1Zl7i81AHWfr4IfWsUZ8TuDRqMgG+mwyVP+E7QDVSm0vb56NNlXfgvKfv3I+ydsdzvRqVAalqmCyZzIletZv9Cal6mnjTK8gjmgRQJTXFqicpa1tbIDg5GHCk2Cw9B00fkqUM6NHSlSyeAuKXLTFpeXxDo8x27eLEmw5OdzVNr5VauMLuAh0j4eTXST5zg9YDJX0NhAgr9QsGQoMcEockLrzfe4PXYH39ExuXL+t4kg8MmKAjl165hNWJyZ4/+5htETprEJRhBMDVUqWkIGzsOMTO/4z4rkhygHh4rT+rQgtkJMEbPnMnr7q+9BsfmzfW9SUIpIkGPieI54g3YVqnMvRJhY96GMiFB35tkcNB0W9nFP8L1lVf4Pik4h775FlQP2jQIgpGTdecO7vbry5OdhPtrr6IcBTzu7rmj+DkAACjqSURBVDA36KIm4uOP2W6EprV83ntX35sklDIS9Jgo1MdTZs5cWDo6ciNp+Hvvszqt8DA0reE/ZTK8x77D92mSI2TAQKjCw+WtEkyif+du7z7cuK/5rE9htXJznVKiMnbG+fMstBkwbaroNZkhEvSYMLYVK8B/2lReJ7+lmHnz9L1JBjuJ5DVyJAJmzOBx5+wbN5AwZCiStm2TPh/BaBt1Y+bNx/0339Jo8Pj7o9zq1XDroclqmiOZ12/kHwM9/jcUDvXr63uTBD0gQY+J49KuHTyHD+f1uO9/YOVm4dG4du6k6XPw82PtksiPP+E+CCkNCsaEKjmZ1dljFyzg+9S3VmHTRtjXqglzhRq3wz/6iMv9NpUrwfvtt/W9SYKekKDHDKDSjWPzZrwe/sGHyL57V9+bZLDQ1V/5LZth27Yt36c+iDtduyH18BF9b5ogPBWy5KByVupff/F9j6FDUfanJbDy8DDrdy/2+++RRVYqCgUCpk2Hpa2tvjdJ0BMS9JgBFvRFnzkTVgH+nOomLyrSpxAe3+DsMnEC/L+ZDktnZzayDB02DJGTp7AdgyAYIsl/7sSdvv2Qfe8eK1YHzJwB3w8/YM0kcybj4iXE5kl3UBnbvmYNfW+SoEck6DETaFKD/KaoZ4WuBiM++1z6VZ6CS+fOqLhtKxwaN+b7CatW4U6vXuxILQiGgjotDZFfT0bY2LEaSwmSY1i3Fq6dOsHcUWdlacpaKhVsn30GXiNH6HuTBD0jQY8ZYV+rFny/+JzXk3//HQkrV+p7kwweUhQm12mfDz7QNDnfus1X0yTyJtNwgr5JPXQIt7t0QcLPP/N9x1YtUWHjBthVq6bvTTMIYubMRfbt2/zdDZg2TXzZBAl6zA333r3h1rsXr0d98y3ST57U9yYZhcq15/+GovzGDWxqSc2QJPJ2b/Bg9u8RhNKGmuvD3v8AocPfgDI8gstZZKUQtGgRl2cFIP30acQvW8ZvhdfbY9iUVhAk02OG+H72Gexq1uSU7/1x45ETFa3vTTIK6OqZAh+PIUP4fsap07jTvbuMtgulaiWR9OsOBHfshORff+XHHFu0QMVff4XH4MHcvydogkIa2iC1dfs6deD5v//J2yIwEvSYITS5EDh3DrtVk+km9wJkZ+t7s4zmvfP96EMuedFoOzWGh3/4EV9xU6+UIJQUJDIaOnIkwt9/H6qEBM7oBEyfhqAli2ET+Gi3e3OEjmWkQp8TFsbig6RVJsGgoEWCHjPuVSnz3UzA0hIZZ88iavo3+t4ko8KxaVNucnbp2JHvpx0+jOBu3RExYSKUsbH63jzBxIQG439ejeDOXZB24CA/5tKpEyr+/htcu3VjcU0h773KzUXEpElIP3VKo7o8cwZsK1SQt0fIR4IeM4aM9rzHjuX1hNWrkbR9u743yaigK20KHIMWL9b0+qjVSFy/Hrc7vITYHxfz5IggFIesW7dw77X+iPr6a5aZoOxi4KKFKDNzhlmahT6N+GXLkbRpM6/7vP8+nNu00fcmCQaGBD1mjufwYXBupxHii/hiAjKvXdP3JhkdTi2fQ4Utm+H35SQoPD15hDjmu+8Q/HJHJP32m0gDCIVGnZGBmAULcOeVHsg4dy7fEbzijl/lRP4En7Hob7/ldddePeExVNN7JwgPIkGPmUOpcf+pU2FToQJyMzNZuFCVlKTvzTI6SADOvU8fVNq5E54jRsDC1lZj9Prue7jX71Wknz2r700UjADKDsav+hm32rdH7Lz5yCXbhIoVUW7Navh98TkUTk763kSDJPP6df6uUeOyQ8OG8CdTVSn7CY9Agh6BD6SB8+bCwsEBOaGhuD92rJRmiojCyRE+48ai0h+/w6VLF36MXJ3vvfoa7o8bh+z79+UTJzyy+TZh3ToujUZNngxVTCws7Ozg9dZbqLB1i5hjPgHqoQt9800u/5EwYxk6lpmpi7zwdCToERjbypURMGUKr6cfPYawd2Siq9iN4t9+g/K/rId9nptzyh9/cskr6ttvoUpJkU+egFylEombNuH2yx0ROXESlJGRfMJ2HzQQlXfvgvfbY2ApJ/AnZsYoO01aRZZOTghatJDV5wXhcUjQI+Tj8lIH+E2cwOtkWBj2wYd8UBaKjn3t2ii3+meUmT0b1oGBXK6I/2kpbrdrj5h582XSy0whNW8aHLjdqRMiPv2Mx6thbQ23V/uh0q6d8PvkE1h5e+t7Mw1+Uivyiy94+pSmUMvMmsUXb4LwJMzbiU74D+79+kGdkYno6dOR8uefiLC1hf/UKaxKLBQN6i2ggNLphTZI+Hk1YhctgioxEbELFiDuxx/Z48tj0EDYPfOMvMVmMH5O36uY+QuQHRyseVChgFuPV9gM07qM6O0UlLgfFyNpm2bi1Pfjj3mgQBCehgQ9wn/wHDoEuZkZ7FuTtG0b9xZQBkgaA4sHlSnIzsL1le5IWLsWCWvWsjhk0pYtvJCxqcfgQXB6/nkRUzPBrETKnj3cnJx144bmQUtLuHbtCq+33oRN2bL63kSjInnXLsTMmsXrbv36wn1Af31vkmAkSNAjPBLPkSM540OZCNKesbSzhc9HH0ngo4svnbs7vN96C57DhiHljz8Qt2IFsq5cRfqJE7xQM6bHwAFw7dGTG6MF40UZH4+krduQuHHjP5kdyvx17AivUaNgW1GE8wpL5pUrrIJOODRrCr9PP5XjklBgJOgRHglldbzHjYU6MwMJK1chfsVKNjX0yRMzFHST+SFFXZeuXZFx6hTiV65Eyp69PEEXNWUqYubOg1vPnnAfOAA2gYHylhtRCSvt76Mc6KTs3csGtVqc27eH1+hRYn5ZRHKioxH61ijkZmTApnx5BM6eLc7pQqGQoEd4YuBDtfLcjEwkbtiAuO9/gKWdPbxGjpB3Tcfvs0OjRrxkh4Yi4eefkbhxE/t6xa9YgfhVq+D84gvwGDQI9g0bylWtgZITGYnEzZuRtHETazRpUbi7w7V7d7j16gnbSpX0uo3GjJp0xEaN5gk3SxcXVqYWR3mhsEjQIzz1hEz9POqsTCRv/xUxs2fD0t6OHZ0F3WMTFMSBpteYMUjavJmF6ijzk7J7Dy825crBuUMHzhjY1XhWAiA9Q9N4qQcOIGHDBqQdOsxWJIyFBdu8uPXuBecXXhDdmOK+z0oll7QyL17kxu/AObPFU0soEhL0CE+FHIpJwyc3Mwspu3Yhauo0WNjawb1fX3n3SlAwkjI77v37s3xA/PIVSD95Etn37nGfFS006UPBj3P7drCvU0cm7EoR2g+UjUvcuoWFBLVY+frCrWcP7scS53PdBZZh777Hxx7C7/PP4NismY7+umBuSNAjFNhmocyMb3F/TBZf2UZOmsQZH+pJEUo24HR+8UVesm7fRvLOnUjZuQtZ16+ztkv8smW80MnWuW1bOHdoD4cGDWT6qwR0dTIvXULqwUNIPXwImecv/PNDhQJObZ6HW69ecHruOf6uCLpBnZ2NsHHjkUq9UQC8x41jWQ1BKCoWuTRLaSYkJyfD1dUVSUlJcHFxgSGiVqsRHx8PDw8PWBqgNg4poIaOHMmqzSwI9t1MuLz0EkwJQ98H2kwDje1SAEQn4wch01MOlDq0h2PjxkbZ6KkkpeLERLi5ucFKT0GEMiYGqYePIO3QIaQdOfIfTzrrsmU50HHt3g3WPj4wNfT9PaBjTdjb7/BFFuHzwQcs+WBO6HsfmOL5XYIeA8MYPuTkcRMy/A1knD4NWFmxb5dzmzb63iyz2gcPQhmf5N27kbJrNzLOnHnoZ5aurtxT4tCkMZfAaOLFGPSW9BH0UBmFHM1TDx3mbA7JCPwb2+rVWQTPqVUr2FNGzQg+H8b4PdA2LVOwSfh++inLOJgbxnYs0icS9BTjTdEnxvIhV6WmImTo/7ixkDIJgd8vglOLFjAFjGUfPIqcqGik7NEEQNQDlN9YmwdNu9jVrcMBEC+1a0Ph7AxzDHooya2MiEDq4cPchJx29ChPzD0ITQk5tmgOp+dawvG552Dta3oZHUP7HtBFFY2lpx87xvdpkMJcS1rGfCwqbSToKcabok+M6UNOVgr3Bg/h/hJSbQ768Qcupxg7xrQPniaMRzoxqX8d4AyGKi7uv79kYQHbypVgpw2C6tThsWrqJTKloIcyB1m3bvNnNevGdWRev8HrqoSEh3/RwgJ2NWtyNsexZUvY16pltj06+vgeqFLTEDpyBDJOneZ94f/Vl1xCNFdM5VhUGkjQU4w3RZ8Y24dcGReHewMHsdosuUMHTJvKarPGjLHtg4JmNagMlnHuPDLOa5bMq1cfEs7TYunoCLvatTQBUMWK7Bhv7e8PKx+fUusPKmrQo3md4RzYUFCjDW6oB+rfWS8tCg8POD7XAk4tW8KxRQtYeXjo8JUYL6X9PaDscSiVzfMMRP2nTIZb9+4wZ0zxWKTv87t5XsIIOsPK0xNlly1F6LBhyLp5C2Hj30V2SAg8R4wwit4Rc4H2Bak60+LauVN+9iPzytX8IIgWKveo09K4UZ2b1R/E0pKnxCgA4iWAlgBY8f0AWJcJ4FH7koK2lzIztCjpNl6zrkpMgDImFlm3brGvFW3/47AK8Idd1WqwrVoVttWqsjKyDWW25ISiV1TJyQgZNhyZFy7wNFzAtGlw7dJZvxslmCQS9AjFxtrXF+XWrEHY2HHceBgzew6y79yF31dfstWCYJhY2tnBoX49XrTkREXlZ4OoXys77D6UUdGASsWZEgqKaMl43N90duaAiFSIqSzEpSFrurXOv29hbcUN8I96TFs2VcbFIzMmBsmpKXxflZDI1gMFfm0ODnmBTbX84IbuKww0w2vO0P4N+d/r7KmFPGkMU5sIFQwHCXoEnUDNsEE/fI/IyZORuHYdu7NTOaXMvLlssCkYTwBr3aE9XDq0f0gNVxkdjZyICOSE0xKOnAhaIqCk9bBwbj4l1CkpyEpJKfHtJB84hbsbrNzcOcCixaZiBdhxkFONM1CSvTGOvjMKeLKuXQNoIGLWd6w3JQglhQQ9gs6gK3a/L76AbfnyiJo2HemnTuFev1c5GKJRacF49yv39QQEAA0e3UdDwQ4HRWHhHBSpU5KRm6PkgEmz5FCjzlMfQ24uFG5usHRzQ469HRz9/GHt6ZkX2LhxAE3rlvb2+ngrBB2ijI1FyNChXBanXrEyc+eYlPSFYJhI0CPovHeEfLmsg4JYOp4aSO/27ccZH1OY7BIevc+pbEQLZVpMRZxQKFlpBQp4eADC1haB8+fzxJwglDTSDi6UCCSIV+7nVTzxQ0q2Ia8PQ+LWrfJuC4KZQxdCIYPyJj5J6oI0viTgEUoJCXqEEsO+Rg2U/2U9bJ95hkejIz76GNFz5iD3MaPDgiCYNqmHDuFO7z4c+Fg4OGi0vcQ8VChFJOgRShRrPz+U/3kVnPJq9XGLvkf4e++xr44gCOYB9X3F/vAjQt8YAXVyMksflFuxXEreQqkjQY9Q8h8yR0cEzp8Hj8GD+H7y738gZPAQFjYUBMG0Id0kkrOImTWLG9XtGzZAhU0bWe1aEEobCXqEUoFsDXw//hh+E75g8TGyRbjbpy8LygmCYJrwIEO/V5Gycyffd3/tNZRbuhRWXl763jTBTJGgRyhV3F99lRsXKftDOj50QEzNc1IWBMH0+neybt5kixr/yZPh98XnvC4I+kKCHqHUIY8jUnAmSwBytaY6f8K69Vz3FwTBBPt3Vv8Mt5499L1pgiBBj6Af7KpVRYX162FHdX2VCpETJyL83XdZkl4QBONE+ncEQ0cyPYLesPL2RrmVK+DSqVN+g3Nw125IPSzlLkEw+v6d/v1Rbtky6d8RDAoJegT9fgDt7REw41sEfPsNm1WSxxM5tkd+9TXUhTCYFATBgPp3pkyB3+efsb2EIBgSEvQIBmFj4NqlCypu3waHpk35sYTVq3GnR09kXLyo780TBKGw/Ts9XpH3TDBIJOgRDAZrf3+UXfoTfD/+iK8Ws+/c4XR5zIIFGjNKQRAMBunfEYwRCXoEg8LC0pINS0m8zPbZZ7jJOXbefNx9rT+y7tzR9+YJggCwzhaVs6R/RzA2JOgRDBLbKlVQYd06eI4YAVhaIvPCBS53JaxdK6PtgqDH7E7klCm4++prGsNQ6d8RjAwJegSDhQ6oPuPGotzPP8M6KAi5GRmInPQlQkeMQE50tL43TxDMChIRpenKhJWr2E7Crk5tzshK/45gTEjQIxg8DvXroeLWLXDr3Zvvpx08hDtduiL5T81orCAIJYcqKQnhn36K0NeHsYq6hb09992VX7OGM7KCYExI0CMYBWRb4f/VlwhcuBAKT08+EIeNHYvwDz+EKiVF35snCCZJ1oEDfIGRtGkz33do1pSnLKnvjvz0BMHYkKBHMCqcX2iDir9uh1PbF/l+0rbtCO7WDWnHT+h70wTBZFDGxPBFRfKnn0EVG8saWv5ff4WyS5fCJihI35snCEVGgh7B6LDy8EDgvHlsYEgZIGV4BEIGD0bExIlQxsXpe/MEwah1dxK3bMXtzl2Qums3P+b04ououGMH3Hr1Yk0tQTBmJOgRjBI6+JKBYYVtW2HfoAE/lrhuPW6378BiaerMTH1voiAYFdn3wxA6bDgiPv4Y6qQkLiO7fPklAubOgbWvj743TxB0ggQ9glFjExjI/l1+EyfyQZpGamNmzcLtlzsiads25KrV+t5EQTBo6DsSv+pnBHftirQjGt87127dUOHX7bB9oY1kdwSTQoIeweihhkr3fn1RaedOeI4cAQtbWygjIhD+4Ue426u39PsIwmPIun0b9/oPQNTkychNT4dVgD+CFv+IgOnToHBzk/dNMDkk6BFMBoWTI3zGjkWlnX/ylSosLJB55Qr3+4S+NQpZwcH63kRBMAhUqamImTsPd7q/goyzZ/Nd0Stu/xVOLVvqe/MEocSQoEcwOaz9/PhKtfzGDXBo0oQfS923D8FduiLyy6+gjI/X9yYKgl5QZ2Qg7qefcLttO8QuXIjcnBzYVKjAJqHkik4XDoJgykjQI5gs9jVqoOzyZQhctBA2FSuyj1fCmjWaZufFi6HOytL3JgpCqaDOzua+nVvt2iP62xlQJSby5KPXmNGosHULHPKGAQTB1LHS9wYIQklPeTm3acMp+8QNGxAzbz5U8fGImfkd+3j5jBsPl04d2ehUEEwNyuQkbtmC2EXfc58bQYrKHgMGwON/Q2Hl7q7vTRSEUkWO9IJZYGFlBfdXX0WlXTvh+cYbmmbn8AiEv/8+7vbth/STJ/W9iYKgM3JVKiRt347bnToj8osJHPCQl53H4EGovHsXfN4dLwGPYJZIpkcwKxROTvAZP46nvaJnz0by9l+RefEi7g0cxCrPPu++C+ty5fS9mYJQ5PHzlF27ETNvHrJv39Y8aGUFt1494TVyJPe7CYI5I0GPYJZYBwSgzDffwGPQYERPn86ZntQ9e5G6bz8HP4pu3ZD7/PP63kxBKLCScupff/FEVtbVq5oHLS3h2rUrvEa9JdYRgpCHBD2CWWNfswbKrlyB1P37ucEz+84djfz+rt3IfOYZeAwaxD0/ljY2+t5UQXhksJN+9Cii58xB5vkL+Y+7dOwIr9GjYEsN/IIg5GORS98aMyE5ORmurq5ISkqCi4sLDBE1qaPGx8PDwwOW0lxb6n0QKfv2IX7lKmQ80ONDSs/uffvArV8/WPuIHH9poFQqkZiYCDc3N1hZybXZo0g/cwYxs2Y/1I9GPlneb4+BXbVqxd4HcizSP7IPdH9+l6OJIDyg7OzSrh2fOKKPH4dq+69I+e03qOLiELtwEWIXL4HLSy/BY9BA2NeqJe+boJfR85Tdu5H4ywakHz+e/7jjc8/B+5235XMpCE9Bgh5BeNQXo0oV+Ez+Gr7vvYvEX35Bwpq1UMbEIPnXX3mxr1uXgx/ndu1gYW0t76FQopCaOAU6SVu3ssaOFoeGDeE99h2+FQTh6UjQIwhP+oJ4esLrzTfh+frrSN65C/GrViHzwgVknDuHsHPnYOXnx6Pwbn16ywiwoFPUmZlI2bULCb/8goxTp/MfpyCbgm23fn3h0KiRGIIKQiGQoEcQCgBpnLh26cwLBTzU95O8axeUkZHs6k6S/q5du8B94EDYVa0q76lQZDJv3EDiho2ss6NOSsp/nOwi3Pr0gWv3bhJgC0IRkaBHEAoJlbbK1K0Ln6goLnslrl/PJQc6UdHi0LQpl76cWrViUURBKIgnVvIff3IplYLqB4Nt55c6wL1PH9g3aCBZHUEoJnJEFoQiYu3rC59xY+H15kgk79jB2Z+sGzeQfuwYLwo3Nzi9+AKXIhybN5exd+E/ZF69yvYoSb/ugDolJf9x2yqV4da7D2cP6XMkCIJukKBHEIqJpZ0d3Hr1gmvPnkg/foL7fsjVnbI/SZs280Lmjk6tW8O5fTv2AaP7gnmiTktD0u+/c2MyqYFrsbCzg8vLL3N/GGUTyTdOEATdIkGPIOgIOkk5Nm3CizI2Fil79vJ4cdrx43yiS/79d16oZEEjxhQAkRmqwtVV9oGJo4yPR9rhw0g9eIgDYnV6ev7PbKtX50DHtXNnKAxUP0wQTAUJegShJL5YXl7s70WLKimJLQKSKQA6dBi5WVl84qMlwsoKjo0bawKgF1+Elbe37A8TEbrMvHRJE+QcOqTJ6DygA2vh4ADXTh25MdmuZk3J6ghCKSFBjyCUMJTJce3WjRe6wk89dJgzQGR9QRmgtL//5iVy0pewr1dPEwC1bQebwDKyb4wIZUJCfjaHblUJCQ/93NLJCY4tWnCDu3OHDlA4SYlTEEobCXoEoRSxdHCAS4f2vJC6LvkmUQYode8+PklmnDnDS/S06bB79tm8AKgtbCpVkmyAATqaZ16+jNSDB3nJvPBwNoewrVaNgxynVi01fToiZCkIekWCHkHQE2RiSs3NtOROVCL99BnOANGijIpC5pUrvMTMngOFhwdbDNjVqQ372nVgX7uW9H/oK5tz5G+kHTrIGTtVfPzD+9TRkSf1HFu15IZ1az8/fWymIAjGHPTcvXsXX331Ffbt24fIyEgEBARgwIAB+PTTT2Ej7teCCUB6Po5NGvPi+8nH3A9CwQ8JIObcC+GTa+qBA7xosalYEfa1a8O+Tm3Y1a7NooiSSdAd5MWsjIhA5rXrHHxSySrjwgVygXzo92yrVIFT61ZwbNkKDvXqcqO6IAiGiVEEPdeuXWO32R9++AGVK1fGpUuXMHz4cKSlpWHGjBn63jxB0CkWlpaaYKZ2bXiPH4+ckBBknD+PjPMX+KSbee0akJOD7OBgXsiPiZ9nZ8clMW0gRLdWAQFSFiug5UPWzVvIun6Ng5ys69dZGflBReQHS5QOzZtpylaUzfH3l2+AIBgJFrl0OWOEfPvtt1i0aBGCg4N1bj2vTyi4i4+Ph4eHBywtLfW9OWaJoe8DdVYWsq5e5QBIGwjlhIY+8ncVXl55QVAdTUaoZk0onJxg6CiVSiQmJsLNzQ1WOlS15uxNdDSyrj0Q3Fy/juw7d/6TwdFiYW8P26pV4NCgIffmONSvbxbZHEP/HpgDsg+g8/O7UWR6HgW9MPoyPoksOjlkZT30pmg/SLQYItoYlG4NdRtNHYPfB9bWsK1dmxe3Af/owJARKpuhXrjII9Kk8KuKjc0fj2csLGDl78/ZCTJLtfb3y7vV3veHpaur3rNDutgH1Ciefes2Z28ouMm6foNvH3Qp/zf03thWrwa7atW4Cdm2WnVYlw3i7Fv+tuU1MZs6Bv89MANkHxScgn5GjTLTc+vWLTRo0IBLW1TmehwTJ07EpEmT/vM4ZYecnZ1LeCsFQX/QSVkVGgrllSvIuXyFb5W3bwMq1dOfbGcHhY8PLH18NLe+vrD0/Wedbin7UdrkKpXITUqCOjExf8ml24SEh+/zY4nIpYucxx3ebGxgVbEirCpXglXlylBUrgyripVg6SLHBUEwRlJSUlCxYsWnZnr0GvR89NFHmD59+hN/5+rVq6hevXr+/bCwMLRu3RrPP/88lixZUuhMT1BQEBISEgy2vEW7g7bP3d1d71fb5oqp7gMytaSyTnZICJQRkciJjORGXb6NjHzI++lpWLq4aLJEPr6wsLWFhUIBWClgobACFApY8LoCUFjxOj/24LrlP7//4M9zs7OhSohHTlw8MqOjYZmSzAEMZbIe1V9TEKx8ffOyNrRU5VubcuXEDNZMvwfGhOyDgkPnd/qsGnTQExMTg7i4uCf+DkVu2gmt8PBwDnaaNm2K5cuXF7rOLD09QkEw1zq6KjU1PwjKiYjgQCgnPC8oynuc1KQNAmtrWLm7Q+Hpqbn18IDCwx1WfOuRf2tToQL/XCg85vo9MCRkH5hYT4+3tzcvBYEyPG3atOGy1rJly+RLKAg6hhqcFVWq8Aj2o6DrI+qHyQkP1wREEZFQxsQgNycHUCmRq1QhV6XkElquSv3AY6qHf5732KPWKftj5e4BS3d3KB0d4ODnD2svz/8EM6RuLNkHQRAKi1E0MlPAQxmecuXKcR8PZYi0+In4lyCUChRkUNaEMyc1ahjl9JYgCOaNURxNdu/ezc3LtAQGBj70MyPswxYEQRAEQQ8YRaF2yJAhHNw8ahEEQRAEQTCZoEcQBEEQBKG4SNAjCIIgCIJZIEGPIAiCIAhmgQQ9giAIgiCYBRL0CIIgCIJgFkjQIwiCIAiCWSBBjyAIgiAIZoEEPYIgCIIgmAUS9AiCIAiCYBZI0CMIgiAIglkgQY8gCIIgCGaBBD2CIAiCIJgFEvQIgiAIgmAWSNAjCIIgCIJZIEGPIAiCIAhmgQQ9giAIgiCYBVYwI3Jzc/k2OTkZhoparUZKSgqsrKxgaSkxqewD80SpVPL3gL4D9F0QSh85Fukf2QcFR3te157nH4dZHU3oIEoEBQXpe1MEQRAEQSiB87yrq+tjf26R+7SwyMSi5vDwcDg7O8PCwgKGGq1SUBYaGgoXFxd9b45ZIvtA/8g+0D+yD/SP7IOCQ6EMBTwBAQFPrJKYVaaH3ojAwEAYAxTwSNAj+8Dcke+B/pF9oH9kHxSMJ2V4tEjTiCAIgiAIZoEEPYIgCIIgmAUS9BgYtra2mDBhAt8Ksg/MFfke6B/ZB/pH9oHuMatGZkEQBEEQzBfJ9AiCIAiCYBZI0CMIgiAIglkgQY8gCIIgCGaBBD2CIAiCIJgFEvQYMHfv3sXrr7+OChUqwN7eHpUqVeLJruzsbH1vmlkxefJkNG/eHA4ODnBzc9P35pgFCxYsQPny5WFnZ4cmTZrgxIkT+t4ks+HgwYPo0qULK9uScv3WrVv1vUlmx9SpU9GoUSN2D/Dx8UH37t1x/fp1fW+WSSBBjwFz7do1ts744YcfcPnyZcyaNQvff/89PvnkE31vmllBQWbv3r3x5ptv6ntTzIL169dj/PjxHOCfOXMGderUQYcOHRAdHa3vTTML0tLS+D2nwFPQDwcOHMCoUaNw7Ngx7N69Gzk5OWjfvj3vG6F4yMi6kfHtt99i0aJFCA4O1vemmB3Lly/H2LFjkZiYqO9NMWkos0NXufPnz+f7FPiTH92YMWPw0Ucf6XvzzArK9GzZsoUzDYL+iImJ4YwPBUOtWrWSXVEMJNNjZCQlJcHDw0PfmyEIJZZVO336NNq2bfuQZx7dP3r0qLzrgtke9wk59hcfCXqMiFu3bmHevHkYMWKEvjdFEEqE2NhYqFQq+Pr6PvQ43Y+MjJR3XTA7KNNJGeYWLVqgZs2a+t4co0eCHj1AKXpKGz9poX6eBwkLC8NLL73EvSXDhw/Xx2bD3PeBIAhCaUO9PZcuXcK6devkzdcBVrr4I0LhePfddzFkyJAn/k7FihXz18PDw9GmTRueIPrxxx/l7dbDPhBKBy8vLygUCkRFRT30ON338/OT3SCYFaNHj8aOHTt4oi4wMFDfm2MSSNCjB7y9vXkpCJThoYCnQYMGWLZsGfc3CKW7D4TSw8bGhj/re/fuzW+epfQ+3acTgCCYA2SJSY371ET+119/sWyJoBsk6DFgKOB5/vnnUa5cOcyYMYM7+LXIVW/pERISgvj4eL6lfpNz587x45UrV4aTk1Mpbol5QOPqgwcPRsOGDdG4cWPMnj2bR3WHDh2q700zC1JTU7l/UMudO3f4M09NtGXLltXrtplTSWvNmjXYtm0ba/Vo+9lcXV1Zs00oOjKybuAj0o870NOVgFA6UBlsxYoV/3l8//79HJQKuofG1UmegQ72devWxdy5c3mUXSh5KLNA2eV/Q4EoHZOEkod6Ch8FZfufVpYXnowEPYIgCIIgmAXSICIIgiAIglkgQY8gCIIgCGaBBD2CIAiCIJgFEvQIgiAIgmAWSNAjCIIgCIJZIEGPIAiCIAhmgQQ9giAIgiCYBRL0CIIgCIJgFkjQIwiCUakFk1ptYmLiE3+vfPnybF8hCILwIKLILAiC0ZCdnc0+aL6+vhz8kC3C2LFj/xMEkU+do6MjHBwc9LatgiAYHmI4KgiCUbmwF8Rs19vbu1S2RxAE40LKW4Ig6AwyYB09ejQv5Ajt5eWFzz///CGD3ISEBAwaNAju7u6ciXn55Zdx8+bN/J/fu3cPXbp04Z9TtqZGjRr4/fff/1PeonUy5E1KSuLHaJk4ceIjy1shISHo1q0bnJyc4OLigj59+iAqKir/5/Q8MjZdtWoVP5e2vV+/fkhJSSnU66fX0apVK9jZ2eHZZ5/F7t27ebu2bt1arPdVEATdIEGPIAg6hRzprayscOLECcyZMwffffcdlixZkv9zcok+deoUtm/fjqNHj3JA1LFjR+Tk5PDPR40ahaysLBw8eBAXL17E9OnTOVj5N82bN+fAhoKYiIgIXt57773//J5areaAh8piBw4c4EAkODgYffv2fej3bt++zcHJjh07eKHfnTZtWoFfN/0/PXr04GzU8ePH8f333+PDDz8s5LsnCEJJIuUtQRB0SlBQEGbNmsUZjmrVqnHgQveHDx/OmRAKdo4cOcJBC7F69Wp+DgUcvXv35qxMz549UatWLf55xYoVH/n/UHBBGRn6f55U8tq7dy9vw507d/j/IVauXMkZpJMnT6JRo0b5QQv1CDk7O/P9gQMH8nMnT55coNe9Z88eXLt2DTt37kRAQAA/NmXKFM5kCYJgGEimRxAEndK0aVMORLQ0a9aMgx2VSoWrV69yFqhJkyb5P/f09OTgiH5GvP322/j666/RokULTJgwARcuXCjW9tDfpWBHG/AQVHpyc3PL/z8JKmtpAx7C398f0dHRhf5/tAGP9rULgmA4SNAjCIJBMWzYMC4/UaaFMjQNGzbEvHnzSvz/tba2fug+BW6U/REEwXSQoEcQBJ1C/SwPcuzYMVSpUgUKhQLPPPMMlErlQ78TFxeH69evc/ZFC2VMRo4cic2bN+Pdd9/F4sWLH1viogzSk6D/MzQ0lBctV65c4WboB//P4qL9f6i36MHXLgiC4SBBjyAIOoV6csaPH8+BzNq1azlL88477/DPKPihpmLq7zl8+DDOnz+PAQMGoEyZMvw4Qbo71BdDPThnzpzB/v37OaB4FFSSSk1N5d6b2NhYpKen/+d32rZty/1B/fv3579HDdY0Pda6dWvOIukK+n+qVq2KwYMH8+s6dOgQPv30U539fUEQio8EPYIg6BQKKDIyMtC4cWOexKKA54033sj/+bJly9CgQQN07tyZe15oeotG0rXlJcrc0PMo0HnppZc4kFi4cOEj/y9qhqaMEE1ikTbPN99885/foTLVtm3beASexskpOKHm6PXr1+v0dVtaWmLLli35r53KdAVtghYEoXQQRWZBEHSq00N6N2IB8cBB1sKCg6Hu3bvLJ00Q9IxkegRBEARBMAsk6BEEQRAEwSyQ8pYgCIIgCGaBZHoEQRAEQTALJOgRBEEQBMEskKBHEARBEASzQIIeQRAEQRDMAgl6BEEQBEEwCyToEQRBEATBLJCgRxAEQRAEs0CCHkEQBEEQYA78H7pSxzUoSKMnAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = utils.phase_plot({s: traj[s][0] for s in schemes},\n", " title=f\"Phase portrait of a spring oscillator (dt = {h})\")\n", "theta = np.linspace(0, 2 * np.pi, 200)\n", "ax.plot(np.cos(theta), m * omega * np.sin(theta), \"k--\", lw=1.2, label=\"exact (conserved)\")\n", "ax.legend(loc=\"upper right\", fontsize=9); plt.show()" ] }, { "cell_type": "markdown", "id": "6ea4ac7a", "metadata": {}, "source": [ "Same story as a time series: the total energy each scheme *should* hold flat." ] }, { "cell_type": "code", "execution_count": 6, "id": "863d271c", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:47.150248Z", "iopub.status.busy": "2026-06-09T05:30:47.150195Z", "iopub.status.idle": "2026-06-09T05:30:47.179257Z", "shell.execute_reply": "2026-06-09T05:30:47.179073Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.arange(n_steps + 1) * h\n", "fig, ax = utils.line_plot(t, {s: traj[s][1] for s in schemes},\n", " xlabel=\"time (s)\", ylabel=\"total energy $H$\", colors=utils.INTEGRATOR_COLORS,\n", " title=\"Energy drift: explicit gains, implicit loses, BDF2 holds\")\n", "ax.axhline(0.5 * k * y0[0] ** 2, color=\"0.5\", ls=\"--\", lw=1.2); plt.show()" ] }, { "cell_type": "markdown", "id": "4d55ea16", "metadata": {}, "source": [ "And the same three integrators as actual oscillating springs, side by side." ] }, { "cell_type": "code", "execution_count": 7, "id": "c7054b11", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:47.180188Z", "iopub.status.busy": "2026-06-09T05:30:47.180140Z", "iopub.status.idle": "2026-06-09T05:30:49.512221Z", "shell.execute_reply": "2026-06-09T05:30:49.511993Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E = np.array([[0, 1]])\n", "stride = max(1, (n_steps + 1) // 90)\n", "\n", "# build one panel of spring states per scheme with an explicit loop\n", "panels = []\n", "for s in schemes:\n", " u = traj[s][0][::stride, 0]\n", " states = []\n", " for ui in u:\n", " states.append(np.array([[0.0, 0.0], [1.0 + ui, 0.0]]))\n", " panels.append({\"states\": states, \"E\": E, \"title\": s})\n", "\n", "fig, anim = utils.animate_springs_grid(panels, lims=((-0.6, 3.2), (-1.0, 1.0)), fps=20,\n", " pin_pts=np.array([[0.0, 0.0]]),\n", " suptitle=\"Same spring, same dt: explicit grows, implicit shrinks, BDF2 steady\")\n", "utils.show_video(fig, anim, \"media/11_oscillators.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "c054f7a1", "metadata": {}, "source": [ "## 3 · A cable: many spring elements glued together\n", "\n", "One spring resists only *stretch*. Chain many end to end and pin both ends, and\n", "the assembly behaves like an elastic **cable**: under gravity the interior nodes\n", "drop until tension balances weight (a catenary sag). Pure springs carry no\n", "*bending* stiffness, so this is a cable, not a stiff beam — bending would be\n", "the next ingredient.\n", "\n", "With flattened vertex positions $x$ the total potential is\n", "\n", "$$\n", "\\Phi(x) = \\underbrace{\\textstyle\\sum_e \\mathrm{vol}_e\\,\\psi_e(x)}_{\\text{elastic}}\n", " \\;-\\; \\underbrace{f_g^\\top x}_{\\text{gravity}}\n", " \\;+\\; \\underbrace{\\tfrac12 x^\\top Q x + b^\\top x}_{\\text{pin penalty}}.\n", "$$\n", "\n", "simkit assembles the elastic term with the edge-displacement operator $J$\n", "(so $d = Jx$ stacks every edge vector) via `mass_springs_*_z`.\n", "\n", "* **Without inertia** (quasi-static): the cable sits where $\\Phi$ is\n", " *minimised*; hand $\\Phi, \\nabla\\Phi, \\nabla^2\\Phi$ to Newton.\n", "* **With inertia** (dynamic): each Backward-Euler step minimises\n", " $\\Phi(x) + \\tfrac{1}{2h^2}\\lVert x - \\tilde x\\rVert_M^2$ with momentum\n", " target $\\tilde x = x_n + h v_n$; the cable overshoots and rings down to the\n", " *same* equilibrium." ] }, { "cell_type": "markdown", "id": "822b40ea", "metadata": {}, "source": [ "### The cable simulator\n", "\n", "`CableSim` composes the cable's terms from `utils` — the spring elastic\n", "energy, both endpoint pins, and gravity. Its `energy / gradient / hessian` are\n", "the **static** potential $\\Phi$, summed **one term per line** exactly as Newton\n", "wants. A separate `step()` adds the Backward-Euler inertia term (its own line)\n", "and does one implicit solve, so the same potential drives both the quasi-static\n", "and the dynamic runs." ] }, { "cell_type": "code", "execution_count": 8, "id": "270d3ce2", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:49.513319Z", "iopub.status.busy": "2026-06-09T05:30:49.513243Z", "iopub.status.idle": "2026-06-09T05:30:49.518166Z", "shell.execute_reply": "2026-06-09T05:30:49.517931Z" } }, "outputs": [], "source": [ "class CableSim:\n", " \"\"\"Horizontal chain of springs pinned at both ends, sagging under gravity.\"\"\"\n", "\n", " def __init__(self, n_nodes=21, length=4.0, ym_val=40.0, rho=1.0, h=0.04):\n", " X = np.zeros((n_nodes, 2)); X[:, 0] = np.linspace(0.0, length, n_nodes)\n", " E = np.array([[i, i + 1] for i in range(n_nodes - 1)])\n", " n, dim = X.shape\n", "\n", " Be = simkit.edge_displacement_jacobian(X, E)\n", " J = sp.sparse.kron(Be, sp.sparse.eye(dim)).tocsc() # d = J x stacks edge vectors\n", " l0 = simkit.edge_lengths(X, E).reshape(-1, 1)\n", " ym = np.full((E.shape[0], 1), ym_val); vol = np.ones((E.shape[0], 1))\n", "\n", " self.spring = utils.SpringEnergy(J, ym, vol, l0)\n", " self.M = sp.sparse.kron(simkit.massmatrix(X, E, rho=rho), sp.sparse.eye(dim)).tocsc()\n", " self.gravity = utils.Gravity(simkit.gravity_force(X, E, a=-9.8, rho=rho).reshape(-1, 1))\n", " self.pin = utils.PenaltySpring(X.shape[0], dim, 1e8).set([0, n_nodes - 1], X[[0, n_nodes - 1]])\n", " self.inertia = utils.Inertia(self.M, h)\n", "\n", " self.X, self.E, self.n, self.dim = X, E, n, dim\n", " self.pin_idx = np.array([0, n_nodes - 1])\n", "\n", " # ---- static potential Phi(x) = spring + pin + gravity (one term per line) ----\n", " def energy(self, x):\n", " E_spring = self.spring.energy(x)\n", " E_pin = self.pin.energy(x)\n", " E_gravity = self.gravity.energy(x)\n", " return E_spring + E_pin + E_gravity\n", "\n", " def gradient(self, x):\n", " g_spring = self.spring.gradient(x)\n", " g_pin = self.pin.gradient(x)\n", " g_gravity = self.gravity.gradient(x)\n", " return g_spring + g_pin + g_gravity\n", "\n", " def hessian(self, x):\n", " H_spring = self.spring.hessian(x)\n", " H_pin = self.pin.hessian(x)\n", " return H_spring + H_pin # gravity is linear: no Hessian term\n", "\n", " # ---- one Backward-Euler step: static potential + inertia term ----\n", " def step(self, x_n, v_n):\n", " self.inertia.update(x_n, v_n)\n", "\n", " def energy(x):\n", " E_static = self.energy(x)\n", " E_inertia = self.inertia.energy(x)\n", " return E_static + E_inertia\n", "\n", " def gradient(x):\n", " g_static = self.gradient(x)\n", " g_inertia = self.inertia.gradient(x)\n", " return g_static + g_inertia\n", "\n", " def hessian(x):\n", " H_static = self.hessian(x)\n", " H_inertia = self.inertia.hessian(x)\n", " return H_static + H_inertia\n", "\n", " x0 = x_n + self.inertia.h * v_n # inertial guess = momentum target\n", " x_next = newton_solver(x0, energy, gradient, hessian, max_iter=20, do_line_search=True)\n", " v_next = (x_next - x_n) / self.inertia.h\n", " return x_next, v_next\n", "\n", "cable = CableSim()\n", "X, E = cable.X, cable.E\n", "n, dim = cable.n, cable.dim" ] }, { "cell_type": "markdown", "id": "2cd0e178", "metadata": {}, "source": [ "### Without inertia: static equilibrium via Newton\n", "\n", "No time, no velocity — just minimise $\\Phi$. We record every Newton\n", "iterate and watch the flat chain relax into its catenary sag." ] }, { "cell_type": "code", "execution_count": 9, "id": "4b47feb4", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:49.519139Z", "iopub.status.busy": "2026-06-09T05:30:49.519082Z", "iopub.status.idle": "2026-06-09T05:30:50.467967Z", "shell.execute_reply": "2026-06-09T05:30:50.467705Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "static: |grad| = 3.60e-08, max sag = 0.883\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# explicit Newton loop, recording every iterate\n", "static_states = [X.copy()]\n", "x = X.flatten().astype(float).reshape(-1, 1)\n", "for _ in range(40):\n", " x = newton_solver(x, cable.energy, cable.gradient, cable.hessian, max_iter=1, do_line_search=True)\n", " static_states.append(x.reshape(n, dim).copy())\n", "x_static = x.reshape(n, dim)\n", "print(f\"static: |grad| = {np.linalg.norm(cable.gradient(x_static.flatten().reshape(-1, 1))):.2e}, \"\n", " f\"max sag = {-(x_static[:,1].min()):.3f}\")\n", "\n", "fig, anim = utils.animate_springs_energy(\n", " static_states, E, np.arange(len(static_states)),\n", " {\"potential\": [cable.energy(s.flatten().reshape(-1, 1)) for s in static_states]}, rest=X,\n", " lims=((-0.5, 4.5), (-2.6, 0.6)), xlabel=\"Newton iteration\", ylabel=\"potential energy\",\n", " scene_title=\"static sag (gray = rest)\", title=\"energy minimised\",\n", " colors={\"potential\": utils.ENERGY_COLORS[\"potential\"]}, pin_pts=X[cable.pin_idx])\n", "utils.show_video(fig, anim, \"media/11_cable_static.mp4\", fps=12)" ] }, { "cell_type": "markdown", "id": "3e23416d", "metadata": {}, "source": [ "### With inertia: Backward-Euler dynamics from rest\n", "\n", "Release the flat chain and march it in time. It falls, overshoots, and oscillates\n", "— the kinetic energy rings down as it settles to the static shape above." ] }, { "cell_type": "code", "execution_count": 10, "id": "64de10c4", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:50.469002Z", "iopub.status.busy": "2026-06-09T05:30:50.468943Z", "iopub.status.idle": "2026-06-09T05:30:53.704550Z", "shell.execute_reply": "2026-06-09T05:30:53.704254Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dynamic: settled max sag = 0.893 (matches static), final KE = 2.97e-04\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n_steps = 150\n", "\n", "# explicit dynamic loop from rest, recording kinetic energy each step\n", "U = X.flatten().astype(float).reshape(-1, 1)\n", "V = np.zeros_like(U)\n", "dyn_states, ke_hist, t_hist = [X.copy()], [0.0], [0.0]\n", "for step in range(n_steps):\n", " U, V = cable.step(U, V)\n", " dyn_states.append(U.reshape(n, dim).copy())\n", " ke_hist.append(0.5 * (V.T @ (cable.M @ V))[0, 0])\n", " t_hist.append((step + 1) * cable.inertia.h)\n", "print(f\"dynamic: settled max sag = {-(U.reshape(n, dim)[:,1].min()):.3f} (matches static), \"\n", " f\"final KE = {ke_hist[-1]:.2e}\")\n", "\n", "fig, anim = utils.animate_springs_energy(\n", " dyn_states, E, t_hist, {\"kinetic\": ke_hist}, rest=X, lims=((-0.5, 4.5), (-2.6, 0.6)),\n", " xlabel=\"time (s)\", ylabel=\"kinetic energy\", scene_title=\"dynamic sag (Backward Euler)\",\n", " title=\"kinetic energy rings down\", colors={\"kinetic\": utils.ENERGY_COLORS[\"kinetic\"]},\n", " pin_pts=X[cable.pin_idx])\n", "utils.show_video(fig, anim, \"media/11_cable_dynamic.mp4\", fps=25)" ] }, { "cell_type": "markdown", "id": "686991bf", "metadata": {}, "source": [ "### Same equilibrium, two roads\n", "\n", "Quasi-static minimisation and full dynamics settle to the **same** sagged shape." ] }, { "cell_type": "code", "execution_count": 11, "id": "812e9268", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:53.705643Z", "iopub.status.busy": "2026-06-09T05:30:53.705571Z", "iopub.status.idle": "2026-06-09T05:30:55.293841Z", "shell.execute_reply": "2026-06-09T05:30:55.293522Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nf = 80\n", "\n", "# resample both runs to nf frames with explicit loops\n", "qs = []\n", "for i in range(nf):\n", " j = min(int(i / nf * (len(static_states) - 1)), len(static_states) - 1)\n", " qs.append(static_states[j])\n", "\n", "dyn = []\n", "for i in np.linspace(0, len(dyn_states) - 1, nf).astype(int):\n", " dyn.append(dyn_states[i])\n", "\n", "fig, anim = utils.animate_springs_grid(\n", " [{\"states\": qs, \"E\": E, \"title\": \"without inertia (quasi-static)\"},\n", " {\"states\": dyn, \"E\": E, \"title\": \"with inertia (dynamic)\"}],\n", " lims=((-0.5, 4.5), (-2.6, 0.6)), fps=25, pin_pts=X[cable.pin_idx],\n", " suptitle=\"Cable sag: minimisation vs dynamics settle to the same shape\")\n", "utils.show_video(fig, anim, \"media/11_cable_compare.mp4\", fps=25)" ] }, { "cell_type": "markdown", "id": "5a4380ea", "metadata": {}, "source": [ "Finally, a quick parameter study: softer springs (smaller `ym`) sag more." ] }, { "cell_type": "code", "execution_count": 12, "id": "3258752b", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:55.294942Z", "iopub.status.busy": "2026-06-09T05:30:55.294870Z", "iopub.status.idle": "2026-06-09T05:30:55.332060Z", "shell.execute_reply": "2026-06-09T05:30:55.331863Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# explicit stiffness sweep: fresh CableSim + static solve per material\n", "sags = {}\n", "for ym_val in [10.0, 40.0, 160.0]:\n", " cc = CableSim(ym_val=ym_val)\n", " x0 = cc.X.flatten().astype(float).reshape(-1, 1)\n", " xs = newton_solver(x0, cc.energy, cc.gradient, cc.hessian, max_iter=60, do_line_search=True)\n", " sags[ym_val] = xs.reshape(cc.n, cc.dim)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 4.5))\n", "utils.setup_axes(ax, (-0.5, 4.5), (-3.2, 0.6), title=\"Softer springs sag more\")\n", "cmap = plt.get_cmap(\"viridis\")\n", "for j, (ym_val, xs) in enumerate(sags.items()):\n", " ax.plot(xs[:, 0], xs[:, 1], \"-o\", ms=4, lw=2,\n", " color=cmap(j / max(1, len(sags) - 1)), label=f\"ym = {ym_val:g}\")\n", "ax.scatter(X[cable.pin_idx, 0], X[cable.pin_idx, 1], s=70, marker=\"s\",\n", " color=utils.PIN_C, zorder=5, label=\"pinned\")\n", "ax.legend(fontsize=9); plt.show()" ] }, { "cell_type": "markdown", "id": "8f023020", "metadata": {}, "source": [ "### Takeaways\n", "* A spring stores $\\tfrac12 k (l-l_0)^2$; differentiating gives the linear\n", " **Hooke force** $-k(l-l_0)$.\n", "* With inertia the integrator decides the energy behaviour: **Forward Euler**\n", " gains it (unstable), **Backward Euler** bleeds it (damped), **BDF2** nearly\n", " conserves it — vivid in the phase portrait.\n", "* Many springs make an elastic **cable**; gravity sags it into a catenary, and the\n", " quasi-static minimisation and the dynamic Backward-Euler run settle to the\n", " **same** equilibrium shape." ] } ], "metadata": { "kernelspec": { "display_name": "simkit", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }