{ "cells": [ { "cell_type": "markdown", "id": "a085fd7c", "metadata": {}, "source": [ "# The Collision-Based Hybrid Method\n", "\n", "The collision-based hybrid method splits the angular flux into an uncollided\n", "part, from particles that have not scattered yet, and a collided part:\n", "\n", "$$\n", "\\psi = \\psi^{u} + \\psi^{c} .\n", "$$\n", "\n", "The uncollided flux carries the sharp angular detail of the source, so it is\n", "solved with a fine quadrature (and fine energy groups). Scattering smooths the\n", "collided flux in angle, so it can be solved with a much coarser quadrature\n", "(and coarser groups). Each time step does one cheap uncollided sweep at high\n", "resolution, then iterates on scattering only at low resolution. See\n", "[Collision-Based Hybrid Method](../../hybrid-method/index.rst) for the\n", "derivation.\n", "\n", "The solver is `ants.hybrid1d.time_dependent`. It takes separate material data\n", "and quadratures for the uncollided and collided problems, plus a `HybridData`\n", "object that maps fine energy groups to coarse ones. This example is\n", "monoenergetic, so only the angles are split." ] }, { "cell_type": "code", "execution_count": 1, "id": "0f8bd4e1", "metadata": { "execution": { "iopub.execute_input": "2026-11-06T19:39:14.697003Z", "iopub.status.busy": "2026-11-06T19:39:14.696658Z", "iopub.status.idle": "2026-11-06T19:39:15.132873Z", "shell.execute_reply": "2026-11-06T19:39:15.132455Z" } }, "outputs": [], "source": [ "import os\n", "import tempfile\n", "import time\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from matplotlib.ticker import FuncFormatter\n", "\n", "import ants\n", "from ants import hybrid1d, timed1d\n", "from ants.datatypes import (\n", " GeometryData,\n", " MaterialData,\n", " SolverData,\n", " SourceData,\n", " TimeDependentData,\n", ")\n", "from ants.utils import hybrid as hytools\n", "\n", "# Plot colors: one per method, plus a neutral dashed reference\n", "COLORS = [\"#2a78d6\", \"#eb6834\", \"#1baf7a\", \"#eda100\"]\n", "REFERENCE = dict(color=\"#52514e\", ls=\"--\", lw=2)\n", "\n", "\n", "def tidy(ax):\n", " ax.grid(alpha=0.3)\n", " ax.spines[[\"top\", \"right\"]].set_visible(False)" ] }, { "cell_type": "markdown", "id": "283b1111", "metadata": {}, "source": [ "## Problem setup\n", "\n", "Reed's problem is a 16 cm slab with vacuum boundaries and five regions,\n", "symmetric about $x = 8$ cm:\n", "\n", "| Region | Location (cm) | $\\sigma_t$ | $\\sigma_s$ | Source |\n", "|---|---|---|---|---|\n", "| Scatterer | 0-4, 12-16 | 1 | 0.9 | 1 in 2-4 and 12-14, otherwise 0 |\n", "| Void | 4-5, 11-12 | 0 | 0 | 0 |\n", "| Absorber | 5-6, 10-11 | 5 | 0 | 0 |\n", "| Source | 6-10 | 50 | 0 | 50 |\n", "\n", "The thin void, the thick absorber and the very thick source region make it a\n", "standard stress test for transport discretizations.\n", "\n", "The source switches on at $t = 0$ with zero initial flux and $v = 1$, and the\n", "problem runs to $t = 20$ with backward Euler and $\\Delta t = 0.1$. Each run\n", "writes its flux at every step with `TimeDependentData(save_to_file=...)`." ] }, { "cell_type": "code", "execution_count": 2, "id": "2bb01cdf", "metadata": { "execution": { "iopub.execute_input": "2026-11-06T19:39:15.134335Z", "iopub.status.busy": "2026-11-06T19:39:15.134216Z", "iopub.status.idle": "2026-11-06T19:39:15.144403Z", "shell.execute_reply": "2026-11-06T19:39:15.143852Z" } }, "outputs": [], "source": [ "cells = 320\n", "edges_x = np.linspace(0.0, 16.0, cells + 1)\n", "centers_x = 0.5 * (edges_x[1:] + edges_x[:-1])\n", "layers = [\n", " [0, \"scatterer\", \"0-4, 12-16\"],\n", " [1, \"void\", \"4-5, 11-12\"],\n", " [2, \"absorber\", \"5-6, 10-11\"],\n", " [3, \"source\", \"6-10\"],\n", "]\n", "medium_map = ants.spatial1d(layers, edges_x)\n", "materials = MaterialData(\n", " total=np.array([[1.0], [0.0], [5.0], [50.0]]),\n", " scatter=np.array([[[0.9]], [[0.0]], [[0.0]], [[0.0]]]),\n", " fission=np.zeros((4, 1, 1)),\n", " velocity=np.ones(1),\n", ")\n", "geometry = GeometryData(\n", " medium_map=medium_map, delta_x=np.diff(edges_x), bc_x=[0, 0], geometry=1\n", ")\n", "external = ants.external1d.time_dependence_constant(\n", " ants.external1d.reeds(edges_x, [0, 0])\n", ")\n", "steps, dt = 200, 0.1\n", "times = dt * np.arange(1, steps + 1)\n", "workdir = tempfile.mkdtemp()\n", "\n", "# One energy group for both the uncollided and collided problems\n", "edges_g, edges_gidx_u, edges_gidx_c = ants.energy_grid(None, 1, 1)\n", "hybrid_data = hytools.indexing(edges_g, edges_gidx_u, edges_gidx_c)\n", "\n", "\n", "def sources(angles):\n", " return SourceData(\n", " initial_flux=np.zeros((cells, angles, 1)),\n", " external=external,\n", " boundary_x=np.zeros((1, 2, 1, 1)),\n", " )\n", "\n", "\n", "def timed(run, repeats=3):\n", " \"\"\"Run a solve several times; return its flux history and best wall time.\"\"\"\n", " best = np.inf\n", " for _ in range(repeats):\n", " start = time.perf_counter()\n", " path = run()\n", " best = min(best, time.perf_counter() - start)\n", " return np.load(path)[..., 0], best # flux history: (steps, cells)\n", "\n", "\n", "def full(angles):\n", " \"\"\"Standard S_N with one quadrature for all particles.\"\"\"\n", " path = os.path.join(workdir, f\"full_{angles}.npy\")\n", "\n", " def run():\n", " timed1d.time_dependent(\n", " materials, sources(angles), geometry, ants.angular_x(angles),\n", " SolverData(), TimeDependentData(steps=steps, dt=dt, save_to_file=path),\n", " )\n", " return path\n", "\n", " return timed(run)\n", "\n", "\n", "def hybrid(angles_u, angles_c):\n", " \"\"\"Hybrid method: angles_u for uncollided, angles_c for collided.\"\"\"\n", " path = os.path.join(workdir, f\"hybrid_{angles_u}_{angles_c}.npy\")\n", "\n", " def run():\n", " hybrid1d.time_dependent(\n", " materials, materials, sources(angles_u), geometry,\n", " ants.angular_x(angles_u), ants.angular_x(angles_c), SolverData(),\n", " TimeDependentData(steps=steps, dt=dt, save_to_file=path), hybrid_data,\n", " )\n", " return path\n", "\n", " return timed(run)" ] }, { "cell_type": "markdown", "id": "b09bb1f1", "metadata": {}, "source": [ "## Hybrid against standard S$_N$\n", "\n", "The reference is standard S$_N$ with 64 angles. It is compared with standard\n", "S$_N$ at 4 and 16 angles, and with the hybrid method using 64 uncollided\n", "angles and only 4 collided angles." ] }, { "cell_type": "code", "execution_count": 3, "id": "4563e2ca", "metadata": { "execution": { "iopub.execute_input": "2026-11-06T19:39:15.145649Z", "iopub.status.busy": "2026-11-06T19:39:15.145567Z", "iopub.status.idle": "2026-11-06T19:39:16.603738Z", "shell.execute_reply": "2026-11-06T19:39:16.603172Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Method Time (s) Rel. L2 error\n", "Reference: S_N, 64 0.234 0.00e+00\n", "S_N, 4 angles 0.026 2.16e-02\n", "S_N, 16 angles 0.066 8.44e-03\n", "Hybrid, 64 / 4 angles 0.088 5.87e-05\n" ] } ], "source": [ "ref_flux, ref_time = full(64)\n", "runs = {\n", " \"S_N, 4 angles\": full(4),\n", " \"S_N, 16 angles\": full(16),\n", " \"Hybrid, 64 / 4 angles\": hybrid(64, 4),\n", "}\n", "\n", "\n", "def rel_error(flux):\n", " return np.linalg.norm(flux[-1] - ref_flux[-1]) / np.linalg.norm(ref_flux[-1])\n", "\n", "\n", "fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(13, 4.4), constrained_layout=True)\n", "ax0.plot(centers_x, ref_flux[-1], label=\"Reference: S_N, 64 angles\", **REFERENCE)\n", "ax1.axhline(0.0, color=\"#52514e\", lw=0.8)\n", "for color, (name, (flux, _)) in zip(COLORS, runs.items()):\n", " ax0.plot(centers_x, flux[-1], color=color, lw=2, label=name)\n", " ax1.plot(centers_x, flux[-1] - ref_flux[-1], color=color, lw=2, label=name)\n", "ax0.set_ylabel(\"Scalar flux at t = 20\")\n", "ax0.set_title(\"Scalar flux\", fontsize=10)\n", "ax0.legend(frameon=False)\n", "ax1.set_ylabel(\"Flux minus reference\")\n", "ax1.set_title(\"Difference from the 64-angle reference\", fontsize=10)\n", "for ax in (ax0, ax1):\n", " ax.set_xlabel(\"x (cm)\")\n", " ax.set_xlim(0, 16)\n", " tidy(ax)\n", "plt.show()\n", "\n", "print(f\"{'Method':24s} {'Time (s)':>9s} {'Rel. L2 error':>14s}\")\n", "print(f\"{'Reference: S_N, 64':24s} {ref_time:9.3f} {0.0:14.2e}\")\n", "for name, (flux, wall) in runs.items():\n", " print(f\"{name:24s} {wall:9.3f} {rel_error(flux):14.2e}\")" ] }, { "cell_type": "markdown", "id": "19d504d1", "metadata": {}, "source": [ "At full scale the curves overlap, so the right panel shows each method's\n", "difference from the reference. With 16 angles, standard S$_N$ is off mainly in\n", "the void regions at 4-5 and 11-12 cm, where the flux comes from particles\n", "streaming without collisions and so depends most directly on the quadrature.\n", "With 4 angles it is also off throughout the scatterers. The hybrid method with\n", "only 4 collided angles sits on the zero line: its error is more than 100 times\n", "smaller than standard S$_N$ with 16 angles, and it runs in less than half the\n", "time of the 64-angle reference. Its accuracy is set by the uncollided\n", "quadrature: by the time particles have scattered, their angular distribution\n", "is smooth enough for 4 angles to capture it." ] }, { "cell_type": "markdown", "id": "28668101", "metadata": {}, "source": [ "## How coarse can the collided quadrature be?\n", "\n", "The sweep below keeps 64 uncollided angles and varies the collided angles,\n", "and compares the cost and error against standard S$_N$ at several angle\n", "counts. Points further down and to the left are better. Wall times are the\n", "best of three runs, so they vary a little between machines." ] }, { "cell_type": "code", "execution_count": 4, "id": "68b9259b", "metadata": { "execution": { "iopub.execute_input": "2026-11-06T19:39:16.605024Z", "iopub.status.busy": "2026-11-06T19:39:16.604939Z", "iopub.status.idle": "2026-11-06T19:39:18.708827Z", "shell.execute_reply": "2026-11-06T19:39:18.708415Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "full_angles = [4, 8, 16, 32]\n", "collided_angles = [2, 4, 8, 16]\n", "full_runs = {n: full(n) for n in full_angles}\n", "hybrid_runs = {n: hybrid(64, n) for n in collided_angles}\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4.8))\n", "ax.loglog([full_runs[n][1] for n in full_angles],\n", " [rel_error(full_runs[n][0]) for n in full_angles],\n", " color=COLORS[0], lw=2, marker=\"o\", ms=7, label=\"S_N\")\n", "ax.loglog([hybrid_runs[n][1] for n in collided_angles],\n", " [rel_error(hybrid_runs[n][0]) for n in collided_angles],\n", " color=COLORS[1], lw=2, marker=\"s\", ms=7, label=\"Hybrid, 64 uncollided\")\n", "for n in full_angles:\n", " flux, wall = full_runs[n]\n", " ax.annotate(f\"{n}\", (wall, rel_error(flux)), xytext=(6, 4),\n", " textcoords=\"offset points\", color=\"#52514e\")\n", "for n in collided_angles:\n", " flux, wall = hybrid_runs[n]\n", " ax.annotate(f\"64/{n}\", (wall, rel_error(flux)), xytext=(6, -12),\n", " textcoords=\"offset points\", color=\"#52514e\")\n", "plain = FuncFormatter(lambda value, _: f\"{value:g}\")\n", "ax.xaxis.set_major_formatter(plain)\n", "ax.xaxis.set_minor_formatter(plain)\n", "ax.set_xlabel(\"Wall time (s)\")\n", "ax.set_ylabel(\"Relative L2 error at t = 20\")\n", "ax.legend(frameon=False)\n", "tidy(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c1916030", "metadata": {}, "source": [ "Refining standard S$_N$ reduces the error slowly: going from 4 to 32 angles\n", "costs several times more and cuts the error by only a factor of about 4. The\n", "hybrid points sit far below the S$_N$ line. Even 2 collided angles beat\n", "32-angle S$_N$ by more than an order of magnitude, and each doubling of the\n", "collided angles cuts the error by roughly 3-4 while the cost grows slowly.\n", "\n", "This example only splits angles. In multigroup problems the collided problem\n", "can also use fewer energy groups (see `hybrid_1d_uranium_slab.py`), which\n", "saves more again." ] }, { "cell_type": "markdown", "id": "fe505f42", "metadata": {}, "source": [ "## Scattering reaction rate\n", "\n", "The scattering reaction rate density is $R_s(x) = \\sum_g \\sigma_{s,g}(x)\\,\n", "\\phi_g(x)$, where $\\sigma_{s,g}$ is the total scattering cross section out of\n", "group $g$. The helper below computes it from `MaterialData.scatter`, which is\n", "indexed `[material, group out, group in]`." ] }, { "cell_type": "code", "execution_count": 5, "id": "c3d230c9", "metadata": { "execution": { "iopub.execute_input": "2026-11-06T19:39:18.710034Z", "iopub.status.busy": "2026-11-06T19:39:18.709945Z", "iopub.status.idle": "2026-11-06T19:39:18.921665Z", "shell.execute_reply": "2026-11-06T19:39:18.921195Z" } }, "outputs": [ { "data": { "image/png": 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jRo2i6667jv773/+Kkuva2lqaNWuWOOuXnZ0t+j3y47kHJIBcSUUt/efpxaTlztxEdP2ckacMPEo4y3Hxc5fTlJs/FNmPm/fn0VOfLKcnbzAPSALoKhx0PHz4sDgx9OWXX9LChQsRfAQAkOESXw4A1jXqqbZRR3Vqg7iubTQGBvlaWq5r5T6+NgUMm7IRm3Yf3AqXrnLAL8CXA3tN1+KioAAO9vkqKFC6bfEY6XYrAUPpdlMQ0BgwVIiAnyl4yGW3nWy+Z8zu01NcXBSy+8DlIPgIDpFfXEV3vvqb6faCe86lsQPTbHqOa84ZTkdyS+n1b9aJprpXP/E9rXn/BkxOBbfAWYTz58+nGTNmiInSo0ePpo8++siur8HBw8WLF9OFF14oSrBZRkYG/fDDDxY7HPv27TMNvOFg5913301XXnklRUZGUkFBAc2dO5deffVVu64buD8OZt/y4i9UUFItbp8+ohu9dOtZNp0BT44Lp++evUwEILkH5Gtfr6Uzx/Sk0wZnOHDNwR1t375dtJgIDw9vdfgVvx/5s23jxo0UERFBl156qcUJE76/tUFb3bt3p6FDh9KcOXNM9x04cIAmTJjgwL8GAMDxuEKMg341jXqqaeCLjqobzMHB1oKG4rqN+zlL0ZVxwC/Qj4N4BgoJUFGAn0LcDuJgoJ+PuM2BvABfY8afuFYZf6e1+y0Dhsbn4Gsu3wUA+0PwERzi9ld+NU2vvuD0AXTJGYM79DyPXXc6rdyeLYYWHM4tFVkzz6L/I7iJt956i5588knKz88XpdCOyubZuXMnHT9+XNxOS2sZ5N+8ebOpByRP3v7qq6+ooaFBBB5TUlLI19c4LARA7tu/d9Ovaw+KZe69+/4D54n+vLbijPVHrp1Cj7xn7OV743M/0ZZP51NA05AagDFjxojPJB54VVVV1Wrw8bLLLqPVq1fTtddeS7t27aJnnnlGZHLz0Cy2fv16WrNmTYvfO+OMM0TwUfLhhx/SkSNHRMsLAABn4WEjHDDkYGFNo64peGhcrqrXUWFpPZGqiGoaDebAIgcLxe8YsxE56OhKZcdcphskAoLStTGwx9fi0hQkNC833ZYvt/EzDhZyViD69gG4LwQfwe7+2niY/lh/SCwnxoTSK3ec3eHn8vNV0SePzKWx/3mXGtRaeueHjXTl2UOpb0acHdcYwHE4u5AzeaTMQ0dpLego6du3b4v7AgICKDMz06HrBO6rqraBHnznT9Ptt/5vFiVEh3b4+W67aBz9vu4Qrd99nI4VVNBb32+g/7scmWdg9Nprr4kA5P3330+//vpri83yzz//iKxI7mk7eLDxZOZFF11Et99+O23atEncvuOOO8SlPU888YTocbto0SKUowFAh3EmNvcf5CBhdT0HC/VU1WAMGlbzMt/XYLyWshGlwKLxWi9KnE/NmMjhyEzCIH+FCBQG87W/goJlyy3vV1KQv4+45ttB0s+aHsvBRwCAtiD4CHal0ero/rfNE1GfvukMigoL6tRz9kyNEUNonvl0heg7ds8bf9CSl69E81sAAAd5fuEqKiyrEcszx/emWRNaBrBtwRmTr905k8Ze964oE3tp0WqaN2NIpwKa4Dk48Nien3/+WUyolgKP7IorrqBzzz1XZJZzRvep3HbbbSIzkrMquV1FVFQUnX766a0+trGxUVwknI3JOOOmvQFh3oi3BwdisF2wfdztvaPTG0RQ0DJ4aMwqFMFD03LLa36sVueU1RYBQw72hQQoKURcN12a7hM/awoGmgODPi0Din4KMRHYfvjf0uDx7xtXh+2DbdPR9428ZZejIPgIdvXJr1vpYE6JWB7VL4UuPN04gbez7rx0PH25bIfImFmxLZt+X3eQZo7vY5fnBgAAs+z8Mlrw/QbTsLDn5p9pl83Tv1s8XTtrOH348xaqqVfTkx/9SwvunY1ND6fEg2KaZ2pL/R65hNqa4KNKpRK/wxmUUi/ItoKPzz77LD3++OMt7i8uLia1Wo1/sWYHLJWVlSIY0BUHLu4G28fx24Z/v1ZNTZmGBqpq4KAiX+tlywbzzxs5Y5F/p2vrlTnOF+zvQyGiJJmDgU3X0oUzCsXPSFxIU0+xkcEisGi83/jzU/cj5KBcG4E5/pMbier5Qu4J/6ewffDeccz/K2v2pToLwUewG7VGSy9/Ye639PwtM+yWnRjo70vP3HwmXfbIN+L205+soLPH9Ub2IwCAnb3w+SrTdOvbLh5HmUlRdnvuh66ZQt/9vZsqaxvpi2U76d4rJlJ6YqTdnh88E/fMlYZqyYd6sbq6Oque45VXXrH69R544AG66667LDIfU1NTKTY2Vgy7AcsDFt7X422D4GNL2D62bRvORqys11F5rY7Kao3XFXU6quRLvXxZb3F/V01UDg1QUFig0nQdFqig0ADjdViAkkIDW/m5v1IEELn3obXHRbxt+GQH/l+1vm3wmdP+ewfbB9vGVl2VSYzgI9jNl8t2Ul6xsTTp7HG9aGS/FLtu3Vmn9aGhvRJp+6EC2nXkJC1Zc4DO7WQpIAAAmB05USo+y1lESADdfvE4u26e2IhguvmCMfTsZytFgPPVr9fSa3eeg38CaFdISAhVVFRY3FdeXm4RhLQnf39/cWmOAyQIsLXEB7rYNm3z5u2j1RmovI6DiFoRTCyr0ZoCi2U1Giooq6M6bWPTY4zBRUcOUOHYHwcJI4KUFB4kBQqNQcJwXm4KGIrAYdP9xvuMJc72LVM+1bp67/vmVLBtsH3w3nFPCD6CXWi1Onr5S3PW4z3zJjrki4azZi544Etx++lPltM543vjSxkAwE6eX7hSZJ6wWy8aSxGhgXbftjfNHU1vfrtelF4v/H073XfFREqMsX8ACTxH//796fvvv7e4b//+/eL7v3fv3k5bLwBv1KDRU2mNlkqrdVRSo6WS6qYL31ejEz8zBhi1oj/iqWk6tB7cs5CDiMZAovk6PJDvV7X6M85I7MoAIgAAmCH4CHbx06r9lJ1vzEKYMryb3bMeJWeO6Ukj+ibTlv15tDeriP7efJTOGN3TIa8FAOBNThRV0rd/7xbLUWGBIkjoCDyE7Po5I+nVr9aSWqMT/SWfuvEMh7wWeAaebP3CCy/QsmXL6MwzzySdTkfvvvsuTZs2rUU5tj0tWLBAXPj1ADwZn3TirMSSGp1FMJGvOaAov81DWuwt0M+HooJVFBmspKhgJUUGq0zXrQcYleSnQhARAMCdIPgIdvHej5tMyzyZ2lE4+/Huy06jS5t6P7713XoEHwEA7PQ5LmU9/ve8URQWHOCw7XrLhWNF0JGDj5z9yFnt3NsXvNOLL75IOTk5tH79eiooKKBbbrlF3P/8889TcHAwDR8+nB555BG64IIL6OyzzxZDZgoLC2n58uUOXa/58+eLC/d8DA8Pd+hrAThKbaOeiqo0VFilpaJKLRVWaaiIl6u0VFhpXObAoj37JnKJsjGQqKLIkOYBReP9EUEK0tdXUM/0OAryxyEpAICnwyc9dNqeoydp/e7jYrlPRixNHmY5kdLeeNBMZlKkyLT8d0sW7c0qFFNUAQCgY2rqGumTJVvFsp+vkq6fPdKhmzI+KoTOm9SPvvl7N5VV1dPi5Xvp8hlDHPqa4LrS09MpMDCQ+vTpY3G/Uqk0LT/xxBMi+Lhp0ya68MILacaMGaIXJIA3a9To6WSllvIrNJRfrhHXBRXGgKIIMlZqqabRPlHFYH8FxYSoKCZUSdHiuunSdB8v8/0cYPRTKawacFBUxINY0NMQAMAbIPgInfb+T5tNy3zAaq8J121RKhWiHPDeN5eK229/v4EW3Dvboa8JAODJvvxzJ1XUNIjli6YOFMFBR+PsSg4+svd/2oTgo5eXVVtj0KBB4gLgLWoadBaBRRFclC2XVHeuJQDvsnOwMD7Ml+LCVRTbFECMCTEGE6UL38c9FgEAANw6+FhcXEw1NTWUkpJCvr7WlV2VlpaK38vIyKCAAMeVhkH7qmob6Ju/donlkEA/uvSMrjkouOKsofTUx8upqraRvv1nNz1z85kUHoL3AbgO/nzikkEuFQwNDXXY69TW1tIvv/xCBw4coISEBJozZw4lJiY67PXA8xgMBvrw5y2m2/MvGNMlrzuqXwoN6pFAu46cpK0H8mnbgTwa1ie5S14bwBro+QiOptcbRDn08VI15Zap6XiphnJL+VotAo5Vneiv6K/yobgwFSWE+4prDi6KIGMYX/NtXxFs9FWidyIAAHh48PHPP/+k+++/X/TtUalUVFlZSQ8++CDde++9bf6ORqOh6667jr7++muKi4sTv/Paa6/Rtdde26XrDkY/rdxHtQ3GKXUXTx/k0B5hcqFB/nTJ9EEi67K+UUvf/bObrnNwmSCALfgEycsvv0x33HGHw4KP69ato8svv5zGjh0rJr7yZ+o999xDP/30kxjEAGANHuC1L7tILI8ZkEoDeyR0yYbjLHkePHPrS0vE7UVLdyD4CC4FPR/BHriX7okyNeWUSkFGjSnYeKJMQ2qtsdeurThwmBThS0mRvpTI1xEq03JcmK+Y+uzoaiQAAAC3CD7u37+fvvzyS1OPnyVLltC5555Lo0aNosmTJ7f6O08//bQ4wD548KDIeuTfv+KKK2jo0KHiAl3rqz+NWY9sXhf367p65jBTyTcPLEDwEVxFXV2dmMzKnnrqKTEwgTO7b7/9dru+Dmc4btmyxWLa61VXXSUCnnv27LHra4Hn+uz3bablq2YO69LXnjulP93zxh/UoNbS9//uoedvmUG+KnOfPwAAd1Gn1lNOiZqyihopu1hN2cWNlFWspmPFjaTWVdj0XEoFUWK4LyVGclCx6dK0zMHFxAiVVX0VAQAAXIVTg4/ND8TPOusskQGZnZ3dZvDxgw8+EJmPHHhkl112mTi4//DDD0V5DHSd3MIKWr3jmFjukRJFI/p2bbncoJ6JNLRXIm0/VEDbDubT7iMnuyxjB6A9nGkQGxsrlvk6LCyszUmpDzzwgMjobktqamqbQcvMzJbDnfgkzM8//4x/ILB60Mz3/+wxtc7gITBdibPlZ47vTT8s3ysGz/y16YgYKgYA4Mp9GA8XNtLhk410tMgYYORAY0GF1uay6NRoP0qN8qU0+XW0nwgwohwaAAA8idN7PlZXV9PRo0epqqpKBBB79epF5513XquPLSgooPz8fJEZKTdmzBjats2cuQFdQxoUwC45Y7BTSjuunDmMth/6TSwv/GM7vXjrWV2+DgDN8dTWa665RmQ/3nDDDZSUlERFRcay1ubi4+NJq237gEWe1XgqOp2OvvjiC5owYQL+UcDq1hk19WqxfMHpAygkyL/Lt9ylZwwWwUf21Z87EXwEAJeg0RlE1uKhk40i2CiuTzaKQS/W4uTEpAgF9UwIosxYf0qP8TMFGrlsWqFAWTQAAHgHpwcfd+/eTTfffDOVlJSIwQlvv/02RUREtNlDrbWDcb7Nv9+WxsZGcZFwoJPp9XpxATPeHjx8wJrt8rWs5PqiqQOcsi0vmNKf7n9rKTVqdKJk7+kbp5OKa1WcvG28jTO2zYJ/SqmmE43YOyIkQEHzp1oXDJS2hfQ509b2ue2226x+rlO566676PDhw7Ro0SK3eZ/i/5Vzt438JNLlMwY75X0zZXgmxUQEUUlFHf2+9iCVV9WdcoAY3jd0yu2jUKAks7MwcMZ7VNRqaV9+g7gcKjAGG7OKG0lr5TDp0AAFdYv1p8w4P8qM9TMux/qJPozlpcWiTz3+TwIAgDdzevBx3LhxtGPHDrH822+/iaxHnl7dWvajNAlbHkiUbrc3JfvZZ5+lxx9/vNVptGq1MeMDzAcsPMSHD3jb20k6kldOB3KKxfKwXvEUpNS0mdnlaJOHptGyTdlUXF5LS1bsoPEDU5y6bbyRM7ZNVa2Barr4v69ep7f6fS6dLOETI9JArda2D/exbS/zkbMmr7/++lO+3osvvkgfffSR6IPLJd7O+v9oK/y/ct624WDfym3ZYjk1LpQyYvyc9r45e0w3Wrh0jziR9N2fW+nc03q2+3i8b+iU24c/O6BzMHDGM5VUa2l/fgPtzWsQ1/vyGqzOZgz2V1DPeH/qmeBvuuZAY3SIstUKIHc5EQgAAODxwUe5mTNnipLqX375pdXgY3Jysvhi5/JrOS7F5r5obeGeapwRJM985MdzL7a2siy9Fe8kSf3q2jvYXfjXQdPyBVMHizO6znL5WcNF8JH9ve0EnTd1mFO3jTdyxrYJCy4lhbLrMx/j4qzLfCwvLxfXMTEx4v9HW9unW7du7QYfuSz7VP+/nnjiCXrvvffECRx3K7nG/yvnbZsf124ivcE4ZfWiaYPEe81ZLjlzmAg+slW78um688e3+3i8b9qHgAeAUXG1lvacqKf9eQ20N79BXBdWaa0ql86INQYYe3GgMcF4zQNfMEEaAADAjYKPvGPM/cnkGYt8mwOJI0eONN2Xm5srJsf27t2bQkJCRHDy999/F4NmWENDA/3zzz8iwNgWf39/cWmOD+YQRGqJd6pOtW2WrD5gWp49sa9Tt+NZ43pTaJAfVdep6ZdV++m1O88hfz+V07aNt+rqbXPrdONAF1cVFRVl6mvL26St7XPnnXd26nWefPJJevnll+mPP/5wu8CjBP+vnLNtpD6L7MJpg5z6uTZ+UIap9PrPTUdEBmSgf9sVDQzvGwCQU2v1dCC/kXbm1tPO4/W0K7ee8spPndEY6OdDfZMCqB9fkgOoT2KAKJnGNGkAAAAPCD5yqfTYsWPplltuoX79+lFFRQW9++67VFZWRjfddJPpcVwuvWHDBtqzZ48pw4czJPv27St+/7XXXqPQ0FAx1AG6bso1T5hmg3smUHpipFM3PR+gnnNaH/rqz11UWdsopqXybQBn4iyyIUOG0LXXXivaS6SlpbU5tbqjFi9eTI8++ihNnDhRTLiWT7l+5plnyM/Pz66vB57j+MkK2rAnVyz3zYilAd2cl/XIlEoFzRzXmz77fTvVNWjon81H8TkOAO0qqtLQtmP1tIMDjcfrRb9GHhLTnhB/BfVNNgca+ZqHwCgx+AUAAMAzg488DZYPnDl4+Nlnn1FwcDANHTpUBCDlfYr4gJ0Dk5IzzjhDZD6++eabojx74MCBtGbNGtHjDLrGL7Ksx3Mn9HWJzc5TWjn4yJas3o+DVnAJq1evpl9//VVkdDviM4pLtrnXY2tQFgbtWbLmgMXnpys4d2JfEXxk+BwHADnufZtbpqGt2XW09VgdbcmuE7fbE+DrQwNSAmlgSgD1TwkUgUaeMo0J0wAAAF7W85EPnN944412H8NZPc1Nnz5dXMA5flsrCz5OdI3g4+Rh3Uyl13+sP0RarY5UKqWzVwu8HLeKuOSSS0SbCUcM8uDMSr4A2OpXWfBx1gTX/BzX6fQiIxLAWTDt2rnBxqxiNW06Wktbj9WLgGPRKXo18tCsQamBNDjNeOkR70++ypZDYAAAAMDLB86A66uua6T1u4+L5YzECOqT7hp997jH4/TRPWnx8r1UVlVP63Yfp4lDM529WgAALqe0so7W7soRy92To0TZtat8jk8d2YN+WrlPfI5vPZBHo/q3PUwOwNEw7brrp1BvOFJL647Uiuv2BsNwUHFQagANzwiioelBYjkiGIc1AAAArgrf0mCTVduzSaM1ThjmYJ8rlXZyn0cOPkpZPQg+AgC0tHT9IdLrDabPTVf6HJ8+yhh8ZNy/F8FHAM9Vr9aL8un1R2rF5dDJxnaHwnCQcURmkAg4cim1vy8yowEAANwFgo9gkz83HjEtnzGqh0ttvTNH9yRflUIERzn4+PwtM1zqoBoAwNX6PbracC4OPkr+3nSEHrpmilPXBwDs62Slhlbsr6Hl+6tp49G6NgfEcL9GDjKO7RFMI7sFiQnUKpRQAwAAuC0EH8Gm/jt8MMj8fJU0YUiGS2298JAAke3IU1KPF1bSnqOFNLBHgrNXCwDAZTQ08iRp4+d4bGQwjeqXQq4kKTaM+neLo71ZRbTlQJ4oEY8OD3L2agFAJ/Yd9+c30PKmgOP+/NazG/lcMQ+EGdczWAQch6YHkp8KmY0AAACeAsFHsNrh3FLKOWmcPD5uYBqFBPm73NY7e1xvEXxkf248jOAjAIDMmp05VN9o7KM2Y0xPlxzowtmPHHw0GIj+3XKULpw60NmrBAA24GxGHhTzz75qkeXYVu/GhHAVndYrRAQcR3cLQs9GAAAAD4bgI1iN+2+1VhrnSuTrxet79+UTnLo+AAAu+zk+uie5ommjetBrX68Ty5xtj+AjgOvT6Q20KbuWlu6qor/2VFNFna7Vx/VPDqDJfUJoSr9Q6pPoj/Y4AAAAXgLBR7Da6u3ZpuWpI7u75JbrlhxFPVKi6MiJMtqwJ5eqahsoLDjA2asFAOBSwUelwodOH96NXNHYAWkU6K8SGZqrdhwTZZvo3wvOsGDBAnHR6VoPpHk7/r+583g9fbe+jtZkHaXSmpbbyU/lI7IaOdg4qU8IJYT7OmVdAQAAwLkQfASr6PV6WrsrRyxHhQVSv8w4l91ynDVz5MQm0ur0tGJbNp07oa+zVwkAwOlyCsrp0PESscy9HiNCA8kV+fupaHT/VPH5nVtYKdp9ZCRGOnu1wAvNnz9fXKqqqig8PNzZq+MyCis1tGRHJf28tZKyitUtfh7o6yMCjWcOCqPxPUMo2N/12jsAAABA10LwEazCw1vKqxvE8vjB6aRQuO6OJJdev7t4k6nvI4KPAADuUXIt4YFmHHxkq3ccQ/ARwMnUWoPo4fjT1gpad7iW9IaWGY4Te4fQjEFhIvAY5Oe6+4kAAADQ9RB8BKus3mnMemSuNuW6OV4/f18lNWp09NfGIyjZA6eoq6ujdevW0YQJE8jX13FlZitXriSNRmNxX48ePSgjw7X/n0LX4/6Jrt63t7XvGQ4+XnHWUKeuD4C3KqjQ0LebyumHzRWtllWPyAykKd196PyxSRQWhJJqAAAAaB2Cj2AVPviTTHTx4GNQgJ/Izvx3SxblFVfRkROl1DM1xtmrBV7m+PHjNH36dMrNzaWkpCSHvc7s2bMpLS2N4uLMrRCuueYaBB/BglarE/0TWUxEEA3umeDSW2h4n2QK8FNRg1pr8f0DAF3Ty3Hj0Tr6akM5/buvukWWY1KEL80eFk6zh4dTcoSKioqKKCRAiX8aAAAAaBOCj2BVv8d1btLvUTJ5WDcRfGQrt2Uj+AhdijMR169fL5bXrFlDUVFRpFQqLQKE9vToo4/SBRdc4JDnBs+w43ABVdU2iuVJQzNdunWGqe/jgFTx+S36PhaUUzr6PgI4vLT6t52V9PGqUsoqsuzlqFIQTe0fSheNjqRRmUGkUPiY9hEBAAAATgXBRzilfdlFVFZV7xb9HiWThmWallduz6brZo906vqAd6mvr6cPPvhALPOkVH9/fxowYABNmTKlxWOXL1/e7iTVsLAwGjVqVLuvd+LECRHkTE9Pp9TUVDv8BeBpOIjX2uejK+PSa2m9OWvzCgQfARyitlEvyqo/W1NKJyu1Fj+LDVXRRaMi6IJRERQXhrJqAAAA6BgEH+GU1u/JNS2fNijdLbbY4B4JFB7sT5W1jbRq+zFxZt4dgqbgGThg+PHHH1Pfvn3pq6++EmXXXJbWmhdffJHU6pbTQiW9e/c+ZfDx2WefFWXW+/bto2HDhtHChQtFIBJAfhJGwpmP7mC87Ptm455c9H0EsLOKWi19sb6cvlhXTpX1lifBhmUE0rxxUXR6v1DyVRqzHAEAAAA6CsFHOKXN+06Ylkf1d4+sKpVKSacNyaDf1h6k0so6kb05oLtr9zgD21z0VjaVVFtmaDhaTKiKvr3FvoGb33//vVO//9Zbb9Hll19OPj4+VFJSQjNnzqTLLruM1q5da7d1BPfWqNbS+t3HxXJKXBh1S44idzCsdxIpFT6k0xtok+x7CKCrcOY6X9rLTnfXTMeFa0rpk9VlYlluSt8Q+s+kaBqaHuS09QMAAADPg+AjWB189PNV0qAe7hPAmzg0UwQf2crtxxB89DAceCys6trgoyN0tux63rx5puWYmBj63//+R2effTbl5eVRcnKy3dcX3M+WA3lU36g1ZT1yoNodBAf60YDu8bTz8Enaf6yIqmobKCw4wNmrBV5k/vz54lJVVUXh4eHk7tRaPX27sYLeW15CZbU6i36OZw8OF0HHHvH+Tl1HAAAA8EwIPkK7OGvwcG6pWB7SM1EMAXAXFn0ft2XR/AvGOHV9wP5ZiJ7wmvYou5bjACQrKChA8BHctt+jZGS/FBF8NBiIth7IpynDuzl7lQDcDmcP/7qjkt76q4TyKzSm+5UKovNHRNB/J8dQUiT6OQIAAIDjuE8kCZxi64E8i4NAd9IvI1ZM5+ZhOVxyiL6PnsXe5c/2FhRkLFlrL7DY2bJrzsbhzMjmzxcQECCClgBs7a4ciyEu7mR0/1T68Octpix8BB8BbLM7t56e/Pkk7c1rsLj/rEFhdMu0GMqIRaYjAAAAOB6Cj9AueZ8tdws+8oCZcQPT6Ne1B6m8uoEO5JRQv8w4Z68WeAkeMsNZiK+99poog/b19aW4OPu+//79919644036OKLL6b4+HhatWqV6AH5zDPPUGhoqF1fC9yTRqsztc5IjQ+n1PgIcify7x15/2EAaF9FnY5eX1ZE322uEJnDkvE9g+mOM2OpX3IgNiEAAAB0GYz/BeuHzbhZ8JGNHZhmWpYGLgB0BZVKRUuWLBHZia+88opYtrc5c+aISde7d++mTz75RPSOXLNmDf3f//2f3V8L3NPOwwVU16Bp8XnoLronR4kMdulkmEEeRQGAFvR6Ay3eUkHnvHKUvt1kDjxyL8ePrkuj969NQ+ARAAAAuhwyH6FNXKa8pSn4GB8VIrJm3M24QekWwcf/nDvCqesD3mXMmDHiwv+XioqKHPIao0ePFheA1shPurhj8JGH43D247INh0UP4qy8MuqeEu3s1QJwSVlFjfTI4gLakVNvui/IT0Hzp8XQ5eOiyFfpHsOmAAAAwPMg8xHadDSvjCprG8XyyL7JbjMhVW5wzwQK9DfG2JH5CADeZp0s+MhtKNzRiL7mqe3bDuY7dV0AXHWgzKerS+mCN7MtAo8zBobSr3d1o6snRCPwCAAAAE6F4CO0iSeMSgb3SnTLLeXnq6IRfY3l4jknKyivqNLZqwQA0CW4RFk66RIREkB9M2LdcssP6Wn+/tl1xPy9BAAkpldf++FxevH3ImrUGmus06P96MP/pNHLl6VQfDimWAMAAIDzIfgIbdp1uMC0PFh28Oduxg1KazULCADAkx3OLaWSijqxPGZAqhjC5Y7k3z/cwxIAjP7eW0Vz38iiLdnG/+fsivFR9MNtmTS2RzA2EwAAALgM9zwSgS6xU5ZhMrhHgttudXmpIUqvAcBbbNhjPtkyxk1LrlliTCjFRASZMvIxdAa8nVproKd+Pkm3L8qjqnq9uC8pwpc+vT6N7j8nngL9sHsPAAAArgV7J9AqPriTMkyiw4MoKTbMbbcUl11L7Sq37M9z9uoAAHQJng4tGd0/1W23OvcblrIfeehMfnGVs1cJvMSCBQuoX79+NHLkSHIVRVUauubDHPpqQ7npvjMHhopsx5HdkO0IAAAArgnBR2hVQUm1qVyPh7a447AZSXhIAPVKixHLu4+epIZGjbNXCQDA4aSTLQqFDw110769rWXfy7PyARxp/vz5tG/fPtq8ebNLbOjtOXV04VvmoTJ+Kh967LwEevnSZAoLVDp79QAAAADahOAjtGrX0ZMe0e9RMrJp6IxGq8eBKwB4vJq6RtqXXSSW+2fGUUiQP7mzQRg6A17uj11VYrBMSbVO3E4IV9HnN6TTRaMi3foEMQAAAHgHBB+hVbtkk64HunG/R8mIvsmm5S2yUkQAAE+0/VAB6fXGybcj+hlPvrizQfLMRwydAS9rg/PhyhL6v6/yRK9HNrJbEH13SyYNSAl09uoBAAAAWAXBR2jVLg8ZNiMZKTv4lvdBAwDwRFv2mz/nRspOvrirHilRFBzg2+LkGIAn4xMIzywppFeXFpvuO39EOH1wbRpFhaicum4AAAAAtkDwEVq1+2ihuA4K8KUeKdFuv5W47DDQ37ijjqEzAODpNsuGa/HQLXenUChMWfg5JyuosqbB2asE4FA6vYEeWVxAX643D5a5dXosPXF+IvkqUWYNAAAA7gXBR2hBrdWJgzvGg1qUSvd/m6hUShraO0ks899WVF7j7FUCD3fw4EFSqVSUl+e4CetqtZref/99Gj16NIWHh1Pv3r3piSeeEPfLlZeX01VXXUXR0dHiwst8H3guqb1EaJAf9W4auOXu+qTHmpaP5pU5dV0AHEmjM9B93+TTT1srxW2FD9EzFybSjafHoL8jAAAAuCX3jyqB3eUWVpl6hXlC1mPzoTMM2Y/QFX26dDqduHaUn3/+mbZt20ZvvvkmHT9+XAQi33nnHbr77rstHnfppZfSnj17aN26dbR+/XratWuXuA88U35xFeWXVIvl4X2SPeIEEuuRav4+OnKi1KnrAuDIjMf7vskTA2aYSkH00qXJNHtYBDY6AAAAuC3POCIBuzp20nimvfnBnrsb1seY+ci2H8x36rqAZystLaUBAwaI5YyMDPLz86Orr77a7q9z4YUX0rvvvkujRo0SmY+TJk2iO+64g77++mvTYzjQuGzZMnr99ddFZmSvXr3otddeE/fxz8DzbD9k/nzj4KOnkJ8MO3oCmY/gefhk1eM/FtCy3caTB34qH3rjihQ6c2CYs1cNAAAAoFMQfIQWsgtkwcfkKI/ZQkN7mYOPOw4VOHVdwLNxafPOnTvF8tGjR6muro4+/vjjVh8bEhIiyrPbuowZM8bmwGdoaKjp9tq1a0Xwc9y4cab7JkyYQL6+viITEjxz0rVkSK9E8hTdU8zfR8h8BE8MPL7wWxH9sKXSlPH4+uUpNKmP+fMcAAAAwF1hVB60cKzA2O/R0zIfM5MiKTzYnyprGy0yg8A9Tfjve1RY1rW9O+OjQmj1+zdY9VilUmm65iAiD8xoTWVlZbul2T4+Pjb1mXz77bfpgQceMN1XUFBAMTExFq/PyxwgPXkSU4M90Q5ZZrfU69YTdEuKIv7vwP9djiDzETzMJ6vLaOFaY0Yvv8+fvziZJvYJcfZqAQAAANgFgo/QbuZjdw/q+chBnMG9EmnV9mN0srSGTpZWU0I0MgrcFQcepb527kwKUnYWBxlnzpxJkydPpvvvv/+Uj+cApCP7UYLz7DhszHyMDA2g9ATP6RPn76cSfw+fIDt6ohTvX/AY/+6rpleWFplu/++8BJoxCKXWAAAA4DkQfIQ2Mx9jIoIoMjTQo7YQl15z8FEqvZ4xFsFHd8VZiJ7wmlx23dDQ0ObPR4wYQRs2bGj3OTiDccqUKdSjRw/64YcfLAKa8fHxohSbA41SFqVer6eSkhLxM/AsfFKFT66wwT0TPW4yLvd95O+oqtpGKq2sJ7yFwd3tz2+ge7/JExm9bP7UGLpgZKSzVwsAAADArhB8BAs19WoqLK/zuEnXEs58lGcHzRjby6nrAx1nbfmzs3BPRSnQ157Oll0XFhbS6aefTunp6fTTTz+Rv7+/xc+512NjY6MIYI4dO9bUB1KtVlv0gQTPsMND+z3Ks/H/3nzUlKXfDx/h4MZKa7R0y8JcqlcbvwPOGhRGN02NcfZqAQAAANgdBs6Ahaw88wRRTww+DpUHHzHxGhwoMTFRBCA3btzY7uOknpBtXdoryy4uLhaBx7S0NPr5558pICCgxWOGDh0qsiLvvPNOOn78OOXk5NDdd98t7hsyZIhd/lZwHfJ+tkNkQ7Y8hbwP8bGT5hYhAO5GrzfQ/d/m08lKrbg9MCWAnrrA87KVAQAAAFwm+MgH0OXl5VY9lrN8Dhw4YHHJzs52+Dp6C/kEUU8aNiPpnhxFoUF+LSbCAthbUFAQvfDCC3TrrbeKadNXX3213V/j22+/pX379tHff//dYmp2bW2txeM4QNmnTx/q27cvZWRkiPvAszMf5SdbPEVP2UmxbNlwNABHWLBgAfXr149Gjhxp9+f+eHUprTts/JyODlHSm1ekUICvS+yWAwAAAHhW2fV7771HL730kig75BLA5ORkeuedd2jixIlt/s5jjz1GX375JSUlmTM6evXqRb/88ksXrbVnO5Jb6tGZjzxkY1DPRFq7M4fyiquoqLyG4iIxTRIc44477hAXrVZLRUXmYQL2cvPNN9MNN7Refs4BSAlPu0aw0buCj2HB/pSZFOnZmY+y4WgAjjB//nxxqaqqovDwcLs9746cOnrjz2KxzImOL1ycTLFhxlYdAAAAAJ7IaadYdTodbd++nZYuXSoOynn4wfTp0+ncc88Vy+0544wzLDIfEXi0n6MWZddR5IkG90gwLe89WujUdQHvwEFvvtgbl+e1Va4N3qe0sk6cVGEDeyQ45D3nbKlx4eTna2xFgMxHcEfVDTq65+t80jW1A75+cjSN6RHs7NUCAAAAcCinHZlwH7N3332XunfvLm7zwfJ9990nsiC3bNnS7u/ycAbuXcaPBfvKkZWxZSR6XtaMdFAu2ZOF4CMAeIa9ss+zgd09c5K5Uqmg9IQIsZxXXN3usCYAV/Tq0iLKr9CI5WEZgTR/aqyzVwkAAADA4VwqLYJ7l7GUlJR2H7d48WIaM2YMxcfH06BBg8TkVrCP44XG4GN0eBCFBFlOzfUUA7qZD8p3I/MRADyE/PNM/jnnadKago91jVoqq6p39uoAWG1rdh19s9G4nxXo50PPX5RMKiUGzAAAAIDn61BtHpdJv/7666LkOTY2lmbMmCEurU1atVZ1dbUYzHDWWWfRgAED2nzc+PHjxaTWnj17UkNDA9122200c+ZM2rNnT5tBy8bGRnGRcO8eptfrxQWM1Bod5ZdUi+W0+HCP3Ta902NIofARkyb3HC20+u/kx3GWjadul87AtsH2wXvH+f+v9hw9aVru3y3OYz+r+PtJciy/TJwsA0v8b++JZffurFGjp0cXmwdC3XFGHCVFos8jAAAAeAebg48ajYYmTJgg+jKedtppdPjwYfr8888pLi6OvvnmGxo1apTNK1FfX0+zZ88WO8r8XO254oorTMsc7Hzrrbfoq6++EtmQHIhszbPPPkuPP/54q1O2edANGB0vrBIBORYfEeCQARmuIjMxgo7mldP+Y0WUl19AvipjD7FTHcxxqT8HA3BQh21jC7x3sG264n2z/WCeuFb4+FBMsPFEoSeKCjHvuuw+dJxSo/2cuj6u+t6RD+YD53t3eQkdKzHucw5ODaRLx3pmaxsAAACADgcfKyoq6KGHHqLhw4eLAQc5OTmUnZ1NiYmJpuDh888/T9OmTRNDZKQ+jtbg7EUeMlNYWEjLly+n6GjbJiz7+flRQkKC6AHZlgceeIDuuusui8zH1NRUkbUZEWEs3wKi/SdqTZuhZ3q8CCh7qiG9kkTwUaPVU2WjkvolxVl1MMfvf37fIPiIbWMLvHewbRz9vtHq9HTkRLlY7p4SRempyeSp+nXnKodNYrmy3uDR31Ud5alZr+4qp0RNH68sFct8rvOJuYmkVKDcGgAAALyHytrhMJwl+PTTT1NWVpa4PWvWLBo2bJi4DB06VAyL4aDkG2+8IUqybQk85uXlicBjawcQJ0+eFMHNzMxMkf3BU7Llk1xzc3Pp2LFj1KtXrzZfx9/fX1y6agKtu8otMg/wSU+M9Ohtw0Nnfli+Vyzvyy6iAd3NQ2jaw4EAvG+wbToC7x1sG0e+b7JzS6lBrRXLA7rHe/Tnd0ZSpEXGvif/reAZXl1WRNqmePC1E6OpR7xn9tQGAAAA6FTwMTQ0lL799luxvGLFCtFj8ZJLLqFt27aJQOOhQ4fEAVJ4eLi4ZGRkiKAkZ0qGhIS0+pwcRDzvvPNo586d4rnLy8vFhXFGJT8Pe/jhh2nDhg2ipyOXfPOgmTvuuIP69+8vsh0fffRRkWl5+eWXW/OnQDtyTponXaclmHtqecPQmYumOXV1AAA6xVuGzTBp2rV8SBqAq9qRU0d/7TH2044OUdJ1k2KcvUoAAAAAXc7mdIGxY8eKYCSXK3/55Ze0f/9+Uca8atUqmjJlishSXLhwIU2fPp3efffddgfMcOl2ZGQk3XDDDTRnzhzT5a+//jI9jgOR3bp1M5VYc3/HNWvW0I033kjvvPMOXXTRRbR161YKDg7u6DaAJsdlwcf0eM8uRx/Y3XxwzkNnAADc2Z6sQovMbk8WFxlM/r7KFt9bAK6GK3Ze/MPce/WWabEU7I9MXQAAAPA+Ng+c4fLlzz77jObOnUt//vknXXbZZSI4WFpaKjIhL774YnrttdfEIJe6uro2n4eDlzwt+1SefPJJi9u9e/em999/39bVBhszH1NlmSWOVlGrpeUHamjtoVrKK1dTndpAUcFK6p0YQJP7htDobkEis9aekmLDKDI0gMqrG2i3bEIsAIA72tsFmY8HCxpo6a4qOlDQQPkVWgrw9aGYUBWN7R5MU/qFUHJk1wx+4TLr1PgIOnKiVAQfOcBj7+8IAHv4Z1817cipF8vdYv3o/BGefWIXAAAAwG7BR3bmmWfS5s2b6ZFHHhHBR852ZCNGjKAHH3zQlKXIF3AfUgYJB+VCAh3/b1dVr6NPVpXS5+vKqF5tnLIttymrjj5fWyZ22G8/M5am9Q+z22vzgWrfzDhat+s4nSytofLqeooMDbTb8wMAdKX9x4zZVaFBfpQab9+2GXtO1NMLvxXS1mPG7/rmVuyvoed/K6Rzh4XT/KmxlBTpS47GrUE4+FjboKHSyjqKiUD1A7gWvd5Ary8rNt2+c0YcqZQIkgMAAIB36nDtR9++fen7778XGY+7d++mw4cPi4Akpk66J7VGS/klxp5EKbGhXdID6fw3suj9FaUtAo+cTSOXVaym2xfl0Z1fnKDKep3d1qFvhnnA0YFj5gMEAAB3UluvpmMFxpNHfdJj7ZYFqNEZ6JWlRXTp28daBB79VD4kfxm9geinrZU0+7Us+m2HeXhZl/R9ROk1uKDl+2vE/gsblhFIU/q23gMdAAAAwBt0KPNRLjAwkEpKSsTU6R49eojJ01wSlZaWZp81hC6RV1wlztKzZAcHHxdvqaDHfywwTX5UKYkuGBlJMweH0cDUQPJV+lBpjZY2Hq2lrzaU07amg94/91TT0aJGeu+aNEqM6HxmTZ+MWNPygZxiGjsQ71kAcD+Hjpe0+rnWGbWNerr7yxO0+lCt6b7MWD+6bGwkTe4TSokRKjIYiI4UNYphGovWllFVg57q1Hq695t82nOige6dGeewcug0WfCRW4YM65PskNcB6KiPV5ealq+fFIPWAAAAAODV7NL1mgOO//zzD+n1epo9ezZNmjRJTKcG9+z36MjMx283ltMjP5gDj8MzAun3u7vTI7MTaFhGkAg8sugQFZ09OJwW/jedXrg4iSKCjMMFjhap6fJ3jtGJMmM2QWf0lQcfkfkIAG6KT560ltHdmcDjdR/lmAKPfILo9jNi6cfbu9FlY6NEWTUHFRUKH+qVEEDzp8XSsnt70LlDzeXeC9eW0VO/FJpOatlbmmwoGjIfwdVsz6kz9XrsEe9PE3qjLQAAAAB4N7sEH8PCwkTfRy675inX//nPf2jRokX2eGroIjlNJXssJc4xwcdfd1TS4z+Zh7tcPjaSPr4uvd0hBXyAO3NIOH11cwalRRuzHQurtHTjp7liUE1n9E03Bx+lfmkAAO5mf3aR3TIftToD/d9XJ2hXboO4HRqgoA+uTaP/TokxnRxqTVigkp69KIkeOy/BVI799YZyemWZYz5b0xPNwcdjKLsGF8P9rCVXT4hC1iMAAAB4PbsEHydOnEgbN26kRx99lKZMmUIpKSlUWGievAmuLyuvzLScGmu/wS7ygQWP/lBgun3txGh6YFa81c3X06L9aNGNGWL4DMsuVtOti06InmQdFRcVQlFhxiEzyHwEAM/IfOxc8PHZXwtp1cFaU+Dx0/+m06hu1mdtXTQqkp67MIkUTR/tn6wqo1+22b8HZIas7Fr+/QXgbMeKG+nf/TViOS5MRTMH23cAFAAAAIBXBB91Oh01NBgzIiQxMTH0xx9/0FVXXUVnn322uM/AzaDAbfDUUEl6on13lMtrtXTb5yeoUWt8T8wdGUF3zbB9KAKXYr97TSrFhBpLsLkX5IK/Oz4ohl+/d1P2Iw/bqahufZIrAIAr29/UNiIk0I9S4jr++b1sd5XIVmSc5fjGFSnUJzHA5uc5Z2g4PXRugun2Yz8W0P58y/2GzoqNDKbgQGM2PIKP4Eo+W1Mm+qGyeeOixHAmAAAAAG9nc/CxoKCAQkNDRZ/H5tOvL7vsMhHQmTdvHr344ov2XE9wsKNNmSMqpcLuPR+f+vmkKJVmQ9MD6eFzuSyvYzvjXKL95hWppGp65364spQ2HDUPRLCVPEvooGxoAwCAO6hr4EnX5aaS645+tuZXaOh/i83Z6dyH15aMx+YuHh1BF44yZieqtQa6/9t8UkvNfu2A/86MhHBTz2K1pnNtOMA7rFq1ip566ilavHix6FNub/VqPf22s0osB/kp6KLR5gxdAAAAAG/WobJrrVZL999/P40ZM4amTZtGzz33HJ04ccL0c5VKRbGx9pm4CY7HWapS5gj30eIApL0s3VVFS3dXi+XwQCW9ellyp7MABqUG0q1nGN9fnF3w8Pf5YsJqR8j7o8n7pgEAuMukaynLqo+sj62t3wGP/VAgplWzswaF0fkjwjsdHHxwVgL1SfQXt48UNtJbf9v3BI8UfOShNsdkfYsBWvPmm2/Sk08+SRqNRlzfd999dt9Q/+yrFgOb2FmDQik0wFipAQAAAODtOhxlWrt2LQ0fPpy6detGH3/8MfXr14++++47+64ddImTpdVU16ARy92To+z2vJX1OnrqF/OAmYdnx1NsmLFMrrOunRBNo7oFieWCCi2992/HDmrlk2HlfdMAANyBvF9tR/s9LttdTeuOGDPIE8JV9Oicjmeny/GJJh5Cw9OypSEc9iy/loKP7KisdQhAa8455xz666+/6PHHH6d3332X1qxZY/cNJe9veu4wZD0CAAAASFTUAQqFQgyYSUpKMt23cOFCuvLKK6lHjx40dOjQjjwtOMmRE+Zm/d2To+32vG//XUzltTqxPH1AqMimsReFwocem5NAc17PFkNnPl1dSrOGhlOPeGOWjbXkB+sYOgMA7kZ+0kTqYWuLmgYdPfereUAc92rkydX20ishgOZPjaXX/ywmvYHomSUnaeF/0+0S3MyQ9SeWWoeAe6qurqZFixbR119/TYmJieK6ubKyMnrmmWfE/mdERARde+21dN5555l+/tVXX9HOnTtb/B5X6cyZM4cyMzPp999/p3/++Yc2b95MDzzwgF3/hqIqDa1vCuInR/rSsHTjQDsAAAAA6EDmI+/wBQcHi51DOQ483nTTTfTee+9hu7oZecZI9xT7ZD5yid1XTYMLAn196P5z4u1ysCmXEetP/5lkDJZyK7EXf7d9wnp8VAiFBhknaB/OReYMALiXQ7LPrV5pMTb/PvfNLa429kuc1CeEpvQNIXu7ekI0pUf7mQaFSa04Ois9PrzVoWngfnr37k07duyguLg42rNnT6vtfqZOnUobNmwQQcPTTz+dLrroIvriiy9Mj+F9U95HbX4JDDQHAXmZ7+P2QOvWrbPr3/DbjioRYGd8MpRPkgIAAABABzMfQ0JCKDIykpYsWULnnnuuxc/69+9P3377ra1PCU4mzxixV9n1S78Xkq6pDeN1k2MoIdw+5dbNXT85WpQ58bCENYdqaUt2HY3INJZjW4MDoj1TY2jbwXw6XlhBDY0aCvB3zLoCANjb4aZBWX6+SkpPsK3Mk4OOi9aWmaZbPzDL/ieJxLqpfOi+c+Lo5s9OmL4fpvYLIT9pclgHpcsyHzHx2r0dPHhQDDPkfuL79+9v8XPet9y9ezfl5+eLAOXZZ59Nubm59NBDD9Hll18uHsP7pM33S+X27dtHU6ZMEZfbbruNUlNTRc9ye+C+qT/LS66Hdq5nKgAAAICn6VDZ9aOPPkqXXnqpuObJ1snJyVRYWCh6P/LZa3AvR1pkPhr7P3bUjpw6Wn3IWHqUGKGiqyfYr49kcwG+Crp5Wgw9/L1xSutry4ro8xtsK+nrmRotgo88tIEDsf27xTtsfQEA7EWn05uCbt2So0hp47Cw95eXUL3GYJpOnRplzE50hIm9Q+i0XsHiJNHJSi39sLmCLh3bue+GqNAACg/2p8raRjoqax8C7ocDj+3hUumRI0eKwKNk1qxZ9Oqrr9KRI0dEy59TeeONN8S+anp6Oq1YsYLmzp3b5mMbGxvFRVJVZZxgzROyW5uSfSC/gQ4XGh8/JC2AUqNUDpmm7Yr47+Tgq7f8vbbC9sG2wfsG/6fwmeMa8Hnc/rbh1oouGXz8z3/+IzIg/+///k+cpQ4ICBA7aZwR+f7779t/LcGhpIM2zpxJjQun0tLOTSRd8I/59288PUYECB2JMww+XlVKWUVq2p5TT6sP1tLEPtaXDvZINfe55NJrBB8BwB3kFlVSo8bYV7dHim39ejlb/NtNTa0x/Hzo+sm2l2zbgk8I3XZGrAg+sg9WlNLckRGdyn7k5+yWEk3bD+Ybt4VaS/5+HdqtARd3/Phxiz7jTLrNP7Mm+MhDZv744w8RrOQMSc6AbMuzzz4rBtM0V1xcTGq1usX9366vMy1P7qGgoqIi8qYDlsrKShGA7IoDF3eD7YNtg/cN/k/hM8c14PO4/W3TfD/LETq8l37xxReLfjubNm0SpTDcR2fGjBkUHW2/gSXQNW80KXMmIzHS5syZ5rbn1NG6w+aG67O7YNqjUuFDt06PpTu/yBO3P1pValPwkcuuJegbBgDuVnLNeslOolhj4Zoy0hrjlnTFuCiKCXV80K5/cqDoKbl8fw0VVtkn+5FbhXDwUa83UHZBOfXpwNAdcH0ajYb8/S0Hykm9HPln1jrrrLOsehz3lbzrrrssMh+5TDs2Nlb0jGxuS262uOZdqAvGJlF4kP2GNrnDfiSfCOBtg+Ajtg/eO/h/hc8c58JnMrZNR3RV9UKnjjZ4Z2P06NHiAu4pv6SaGtRau/V75GwWyQ1TYkQfsa4wrV8odYv1o6xitej7uOt4PQ1Ks27SpPygXX4wDwDgLsNmetowbKayXkffbzZmPQb4+tAV4x3XGqO5m6fGiOCjdKLowlGRpOrE94R8SBoPT0Pw0TPxie3SUsuhQiUlxu9rR5z05kBn82An4+Ba8wBbXrmasouN2ZCDUgMpMsT7+kbz8UBr2wawffDewf8rfOZ0PXwmY9u4KuwleLlDsmCbvPy4I44VN9LKA8aDyoRwFZ07rOsarvNUSZ6oKvl4tfWTT7vLyhUx8RoA3IU8U5t711rrmw3lVK829no8b3gERYV0Xalyv+RAmtg7WCwXVGjpn32dm3wtLzc/mIOTR55q2LBhtH37dtLpmtJ1iWjjxo2i7U+/fv2cum5rm1oJsNN62X9aPAAAAIAnQPDRy+05WmhaHtDJQSufrzNm0rDLxkZ1WdajZNbQMIoJNZY6/b23mo6XtuzL1JrgQD9Kjg0Tyyi7BgB3Ic/Utrbno1proEXrjK02FD5EVzlwIFhbrjwt2qL8uzP6Z5oHkOzNMn+fgWfh4YZc+vzmm2+K22VlZfT666+L4YdBQUEOe90FCxaI4CYPu2nLmkPGk66MhyoBAAAAQEsIPnq5PbKDtQHdOx585DK+n7dWiOVAXx+6YJTjez02x4ML5o0zHkjz5OrvNhnXxxpS1lBZVT2VVJizGAAAXJWUqR0VFkgxEdYFPTjTsLTGmD02fUCoQydct2VM9yDqlWAsad1xvF60yeioXmkxpGrqVSz/PgP3cuWVV9KIESPos88+o6NHj4plvvAgE8YTqr/66it64oknxHJKSoq4fu211xy6XvPnz6d9+/bR5s2bW/25RmegDUeNw2Yig5XULynAoesDAAAA4K5srrXiKX9+fl1/sAKOzXzkoS29begZ1txPWyuoXmMs45szPILCA53TbH3uiAh66+9iMUjhx60VdOv0GKumqXK/tBXbsk0H9NYeyAMAOENtvZryiqtsL7neaM5Qv2RMJDmrFxH3mXzkhwJx+4v1ZTQoLblDz+Xnq6Te6TG0N6tIlF2rNVry88XEa3fDA15qa1ue+AsONn8Xn3feeXT22WfT4cOHxdAXDkA6287j9VTbaGzSPq5HsGgBAwAAAAB2yHzkkpdx48bRhx9+SNXVnevVBM6l0eroQE6xqd9jgH/HmqQbDAYxtVRy2VjnHNAy7l12xgBjCXV5rY7+3GPde1ResojSawBwdTxcxdaS66NFjbQ5y5illRnrRyMzHVeueiozB4dRWKBxF+SvPdUie76jpJYhWp3eoo8xuI++ffuash3lF5XKMpDMQ2AGDBjgEoHH5iXX41FyDQAAAGC/4OP5558vdgjvv/9+SkxMpGuuuYZWr15t69OAC+AMP7VG1+l+j1w2d7TI2F9xeEYgdYtrOSGyK108OrLVLB9rJ14fkU2QBQBwRYflwUcrMx+/lX0eXjQqUmQgOou/r4LOHWocStaoNdCv243ltR0hbxki72MM4Oiej/JhM+N6YtgMAAAAgN2Cj5mZmfTGG29Qfn4+ffzxx1RQUECTJ0+mXr160XPPPSdug3f1e5RnPc4d2fW9HpszBkCNrQG2HaunnJJTD57JTDYPXcjK79wABAAAR8vONwcSu8k+v9obNPPrDmOZtr/Kh84dZgz8OZP8++L7zRUii74j5CfP0PcRuqrnY0m1lvblN4jlvkn+FBuKcn8AAAAAuw+c4b6PF110ES1dupSysrJEFiT37ElNTRV9ebZu3drRp4YustcOk65rG3W0dJfxgDbEX2EqeXYmzuY5b7j5oPbXHafOqEmLDzf1apIf1AMAuKLsPPNJkm5JUVaVh1bUGTPdT+8XShFBzunLK9crIYAGpRoHdBw62Uh784yBHFsh8xGcYd1hc9bjeGQ9AgAAADhu2jU3/eaAI/eA3LlzJ91000303XffUWBgII0fP57Wrl3bmacHN8h8/HtvtWnQzMwhYRTo5xoD1LmfmFRRuGR75SkzanhAQWpcuOmgvqMZOAAAXSFLdpIkM+nUfXb5c1AilTu7gvNHRLS6jrZIiA4VE78ZMh+hq+w4buyfysb2wJA6AAAAgPbYHCniaYSffPIJTZgwgXr37i36PT7zzDOi3Prtt98WWY9ffvkl3XzzzfTHH3/Y+vTQhaTeWOHB/pTSFHiz1e87jVmP7JwhrnNAGx/uS6O7GYcp5JZpxETKU5EO4CtrG6ms6tSPBwBwluym9hAcdIsINQbe2lJVr6MVB4yDMaJDlDSup+sESs4cGEa+SuOZoqW7q0inN3Qo2106gXaytIaKK1pOTQawt32yTN3+KcYMXgAAAABonc0Nat555x164YUX6Morr6QPPviA+vTp0+rjzjjjDKqs7HgDeXCskopayis2Bg77d4/v0OCBshotrT9iPMhLivClIWntHwB3tVlDw2nDUWNmwi/bK2lIetAp+z6u2JZtOrCPDnfeJFgAgLY0qrWmz29rsh7/3FMlej6yswaFkaop2OcKwgKVNLF3MP2zr4ZKqnViGveYDmSRceuQVduPieXdR07S6SO6O2BtwRsHzvBFp7Ocxq7RGejgyUaxnB7tR6EBzm9jAAAAAO7LwJWXBj2Rni86Muh1pmVxbdCb75MeJ+6zvM3Xhma3LR7Xyn0GnY4Chk9zveDjZZddRrfddpvo+dieGTNmdGa9wMF2HjYPBhrSM7FDz7FMZKkYl88aHGbqmegqpg8IpSd/PkkNGgP9taeaHjo3gZTtrGN3i6Ez5TSib0oXrSkAgPWOFZST1Bki04p+j0t3VVuclHE1Zw8OF8FH9vvOyg4FH4f0Mn+PbT+Yj+Aj2G3gDF+qqqooPNz8fyerqNEU0O+XjKxHAAAAq4NrfEKPg2s6rTGwptMag2pNtzkQZlqW7pceI27Lf5cfo23jdzmw1hSs0+lIr9eSorqa6gIDyYcDbiIIZ3wOi8Be0++J55IewwE9KRDY9DcYpOc2BQulx0rPJwscyoOJBvlzNj1eut+JXDL4+PXXX1NhYSE9//zzLX72yiuvtPkzcC07DpmDj0N7J3XoOX5vGjQj9Vh0NcH+SjqtV4joS1lWq6Otx+poVLe2D2rlGUTyYQ4AAK5EPhTrVJmPFbVa2pRlzFBPifSl/i4YKJnUJ4SC/BRUp9aLE0UPz9aTn8q2rjBDepm/x3bITq4BOII05Zr1TXK9/1MAAOBBATsp+KbVGK91Govb8mW9Rk0+ZSWkPhlMPiLopjEG6rRN16bb2lafS7ptDgjq2g786fnxWnMw0RQolAJtTb8rCzI6G+9ddmy8ITgl+KjX61uUn0gaGhrI19fXHusFDrZdFnwc3IHMx+IqDW3PMfZF7B7nR70S/MkVnTEgVAQfGR/Uthd8lE+MxcRrAHBVWU39Hlk3WcZ2a/7dX2PKUOds8I602HA0HlQ2tV8ILdlRRVUNetp4tI4m9A6x6Tl6pUZToL+K6hu1tFP2/QbgCPvl/R5dMKAPAAA2BPc4MMbBOa3adG3QmJdbXGuk22oRtGvxGIvflT+mrYBfU+ZeiwChxrhuNuJGIMZ6EugyvH/toyBSqogUCvLhZYVSLIvbCuP94jEKJfk03U9N94vbPtLj+efm3xW3mz+feCy/puW1uJ/XRSFdS+sivbbx2qfZbUMXHR9YHXzcvXs3bdy4kTZt2iR6OX744YetDqJ59NFHHbGe4KCyaz5Y650WY/PvL99fYyr7mz4gzCUPaKWMGh5mwP2ZOAj5wDnxbZaHZ8gyiOQH9wAA7pr5+Ncec4Y6f1a7qmkDQkXwkf27r9rm4KNKpaRBPRJo494Tom1GRXX9KQfxAHTUXlnmYx9kPgIAdDqzz6BpJNI0isCdedl427zcSPrGBvIpL6V6f1/y4SCdutEY2BPXjeK2CPjxc5gCiRpTELC1a9NBLdhGBMOUREoOlqnEtQiUiWu+rTIG0URATrpfKbvf+Dgfpfx3VbLnlP+uquXvSsvS/dJjpNcyBfM42KYUAbaKymqKiIoiRVOQ0DLQp5QF55pewyJY2HRbWjcfeXDQNWMhtiQYulTwccOGDfT000+Lvjec+Xjw4EGLn4eFhYk+jxdffLEj1hPsqLy63nTwygdrSqXNQ8/pn33mHmKcseKqQgKMk11XHqihoiot7cytp6FtDJ4JDfKn2MhgKi6vpSyUXQOAi5K3hZBnbDdX3aCjdU1DweLDVDTQhSfyjusZQv4qH2rUGujf/dX0yOwEm/sIcxY/Bx/ZziMnadLQTAetLXgznsh+sCn4yK0MIoIwbAYAPDAgyMG5xnoyqBvEhZqujZd6y/sam641fB8HCRtkQcP2g4nEt23sdcefusb6Ozen8m0KmjVdqzggxtfG26T0NQbUVE3X4jGWv0MqKXhnfIxBqaK6hkYKDosQjxXPafEa0nOrZM/dxs+kwF/zYJ90v5sF3DjAZigqIt+4OFJw0BC6nNXBx+uvv15cFi1aRKWlpXT77bc7ds2ga4bNyPpkWaumQUcbjhoPaBPCVS7f74hLrzn4yDj7sa3gI+uWFCmCjydLa6iuQU1BAe0PVgIA6Gqc2ccC/FSUEN32yR/+3NPqzCXXrjYUTI57PvKJIs6q56nXu0800OA02zIX5f2LdxzMR/ARHDLt+liJmuo1xiyZvii5BgAn4bJcQ0OtMUDYWEeGhjrjdWO9MSgoBQ45ENh0WwQGZcFDYwBRWm40/o4IIDZ4VjYgB8xEIM7PdC0Cbb5N1yr5tfkx5Ct7bGvXvn5NQbum3+HbTT+3eB6La1+HBu84wFZTVESBCLCBJ/R8nDdvnmPWBJwybEY+IdRaqw/Vmg5op/ZzzR5icpP7hpLCp4D0BqJVB2ronrPj23wsT46VMmc4O7R/t7YfCwDQ1XinMqeg3NQqor0zt9JJF3Z6v1Bydfx9wsFHKbve1uDjEFn/YgydAUdNu96Hfo8A0JFAoQgAWgYJOXhIrQQP9fW1pKgqo2ofA5G4v+kxpus6Yz9Ad8LHi77+5NN0EYE/scxBvgBxbXk/Lxt/bl72J4PKl6rrGyk8KoYU/oFtP14KDnLAj4OPAOAewceVK1fSkiVLaPLkyRQaGiqW28KPOeecc+y5juDISdcdCD7+0zTAhZ3e3/UPaLkkig9ieUBOVrGacsvUlBrVekajvH/asQIEHwHAtXBWdqPGePYnMzGy3dLQNYeMgbwQfwUNy2g749uVevRyciafKOK+j3fNiLPp9/tkxJK/r1JsH/n3HIA9yYOPrl75AQCdwxN7DfW1xgzD+hqLa720LH5uea2XHtt04TJjW/GpxS4JL/r4kI9fIJFfAPnILuK2f6DxNgcHxe2m+8Ul0PKx8t/lwJ+fvzHbj++Tsv7skLDCJ2GriorID5l9AJ4ZfCwpKaE9e/ZQnz59qLGxUSy3hR8Drm3bgTxTyV7v9FibfpcPaNceNh7QhgYoaLgbHNBKB7XSdG7Ofrx8XOt90tITIkzLxwsru2z9AACskXOywrScnmj+vGpu5/F6qqo39lDicmYevOXqokJUNCQ9kLYdq6fsYjWdKFNTShsnilrjq1LSwB4JtGV/Hh3OLcXQGXCI/bJhM/0QfARw7b6F6gbS11WRoa6aDHVVpBfXTcsicCgLEjYLJOobakRWosvgQKB/UNMlkHwCgo3XptuynzUFBi0CiM0Di/JAoYtXsQGAFwUf586dKy7y2+CeSipqTf3CuOSaD9ZssfdEg+mAdkwP9zigZRN7h9Bry4pNpYhtBR9TZcHHXNlBPgCAK8gtNH8upcW3HXxcddBccj2xj+sOBWtuQq8QEXxkaw/X0sWjbeu7O6Jvsgg+sq0H8mjqyB4OWU8gamhoEL0Qg4ODvWZz6PUG2tcUfOSe1xwwBwDHMfCACBEYNAYN9bWyQGLTfeagIv+sxny7vlpMUXYK7ucXGGIMEJqCgq0ECeUBRNn9Br9AKqupp5ikFFIGhhiDhRiQAQBuzi57TYcPH6ajR4/SaaedRiEh7nOQ4422Hcw3LQ/vk2zz70tlfOy0Xu5zwNErwV8cKJys1NLm7DqqU+vFgIPmkPkIAK5MnpGdJjtZ0l6/Rw7ouYvxvYLp9T+LTd83F49uu7S8NaP6p9K7izeJZe7fi+Cj43z88ce0b98+euutt8hbnCjXUG2j8QRsPwybAbC972FNBelrK8lQW0m66gryKcileqWeqLaK9LUVZKipNP1cX1Mhgou2TkLuLBEQDOSgIV9Cmpal62BSSEFFcd10f9N94mccLOTeg53IJuTSYioqIkV4DIKOAODdwUfu6fjwww/TmDFjaNWqVTR16lTxIdmvXz/asmUL+fv7239NwS427zMOU5EyRGy15pBxyjUb39N9Dmh5B4CzH7/dVEFqrYE2Hq2lKX1b9qtMjg0TE2E5u+E4Mh8BwIXLrtPijQMwmius1NChk8b+UgNSAigm1H2ys/omBlBUsJLKanW04Uid+Lz2U1l/ADeqX0qr33dgf4mJifT333971aY9VICSawCppFlkJFaXkb66nPRN1+I2Bw1F8FAWROSAIvc+bIbrr+xd2CwCg0Fh5BMUSgpxHSJuK4JCLe9vChSaAol84cxDZBgCADiEzUckK1asEH0fOfDIXn/9dbrvvvvokUceEcNmFi9eTJdeeqlNz8lTBFUqFQUFBdlU7lNRUUFxaDZrEy5Dk4yUHaRZo6JOR7tPGHcRusf5UWKEL7mTCU3BR7bhSOvBRy5DT4wOpbziKjouK28EAHAF8nYQbWU+rj9iPsA7zY2yHhmf/BnfM5iW7KgSGeo7jtfRqG7WZ9lz9npsZDAVl9fSlv0nxInR9iaCQ8edeeaZ9Oijj4r9vvPPP98jN+WCBQvEhcvLWWWDnoL9FSL7EZmP4GkMWg3paziAaA4m6qtKLW7Ll0mrdti6iIBgcDgpgsPJJ5gDhaFNwUNjAFG+bA4yhhoDiJhsDADgGcFHLrHp3bu3WOad+uXLl9NLL70ksh3PPvtsOnjwoNXP9dlnn4nfzc3NJY1GI4bV8E6eFNhsDb/mnXfeSe+99554zcDAQFHyc8EFF9j6p3jlWUqpF1Z0eJBFibE1OGDHU0jd8YCWjewWZJqkKj84b44P6Dn4WFJRR7X1agoOtK3nGACAozMfgwJ8xed4W5/VknE93Kc9hoS/Xzj4KGXb2xJ85Cz30f1S6Ne1B6m8ukEMnrF1sBpYh4OO+fn5og94aGioOBksd8UVV9Bjjz3m1ptz/vz54sInycPDw2nuiAi65vRwyi3TuFVGMXgvkaHIPRArS1q/cHCxqtQYWOQeifbmozAGB0MizMHEEOM1BYdTjU5B4YkppOSfh0Q0BRvDyUflXgkOAABwajbvOfHO5RdffCG+zP7991+KiIigzMxM8bOCggIaOHCgVc/DZ5E5cPn1119T//79Sa1W0+23304zZ84UPSSjolofCPLiiy+K1+fybv69d955R2Ra9u3bV9yGtmXllVFZlTFzcWTfZJt7kcgDdpyZ4m5CA5Q0MCWQdubW09EiNRVVaSgurOXODZcyrt9tXM4tqqQ+OHAFABfA37u5TT0f+SRJa5/h/Jj1R42f1YF+PjQwNZDcDU/nbi2Qaq2RTcFHqfQawUfHGDp0KD399NNt/nzAgAHkiTg7Nz0GJyXBBYKK3D9RBBBLSF9RTPrKUvMyX/PtyhL7ZijyIBUOEoZGkSI0Ulx8wqKblqOMP2u6iCBiYGibZcycUFJdVER+qGIDAPAKNgcfObvxrrvuEtmPhYWF9NBDD4n7uRT7n3/+oQceeMCq51EqlfTpp5+abvv5+YnS7XfffZc2bdpEM2bMaPX33n77bbruuutMO7U333wzvfrqq/TBBx/Qa6+9Zuuf47Ul18M70O9xc1aduOYB2cMyrC+RdyVjegSJ4CPbeLSOZg0Nb3fiNfd9RPARAFxBUXktNai17fZ75BMrJdXGEtGRmUE29Ut0FTxBmIeEcd/K/fkNVN2gEyePrCVvKbJp3wmad9ZQB62pd+MTvjjpC+CgwCL3SiwvJF15IenLi8SyuFQUme6zV1BRlDibgolRpAiLIh9pmYOLsp+JMme0sgAAgK4IPnJfRs46XLJkCcXHx4vhMyw7O5ueeOIJSk1NpY7ijEeWlJTU6s+Lioro+PHjNG7cOIv7x48fT5s3b+7w63oLPgiTjOxrW79HHmCQU2rcyRmUGkiBrUyKdgdjewTTe8tLTZmcrQUfLSZeY+gMALiIXFkf2tT4U/d7HOOGJdcSDpxy8JHbZGw7VkeT+rTs0duW4X2STYPD5N974NhgSXFxMUVHR4uTywBwit6KZSdJV5pP+tJ80pWebAoscrDRGGgkjXFoWGeIMufwGMtLWAwpImKblqON05T9AvDPBQAADtehhjVcev2f//zH4j7u18iXjqqtraVbb72Vpk2bRoMGDWr1Mbxjy3jnVi4mJobWrVvX5nNzViZfJNy7R0r354u3WL/ruLjmSr1hfZJa/dv5Pj6IaP6zTVnmA9oRGUFuu90GpvhTgK8PNWgM4iCdy/+bly6mxIZZBB+lv7WtbQPYNqeC9w62jT3eNzkFlpOuW/ssWn+4xrQ8qlug235ejcgMpC/Wl4vlTUdraUKvYKv/TwX6q2hAt3jadeQk7csuosqaegoN8idv0lWDdviE8D333EO//PKLGATo6+tLEydOpJdffpkGDx7s8NcHcEUGndaYtVhaQLriE6TIPUI1DVWkLy0gfVm+KIsmQ1MT9Q5mKioi40kRGUeK8NimizGQaFw2BhZ9fNEeAAAA3Dz4yEFALpnmbEfu1dh8+uGFF15o0/NxYJAnJfJzcT/Htkg70lqtsexMwsNq2jvT/uyzz9Ljjz/e6t/RfP09VU29mnYfLRTLvVOjSV1XRUV1xiBs8wOWyspKcVAnP3BZtdccfOwZ2SiyUN3VwCQlbc7RUlGVlrYdOkmpkZbvnRBfY8kiO5RTaPpb29o2gG1zKnjvYNvY432z76g5iy880KfF57BOb6DN2cbP6ohAHwr3qaSiopaf8+4gPcQcVFx3qIquGG7b/6kBGVEi+MjZj/9u3Edj+9veasSd8fZpq4rEXjjYOGXKFEpISKCPPvqI0tPTxXuShwlyAHLv3r2UkmJblQWAu9A31JK++ATpinJJV5wrrkUWYwkHF4uI9OZ9Sf6EsvZow8c/qCmwKF3iSCkFGvk6Io4Uge439BEAAMDm4GNpaanITAwODhZntfkst5ytwTx+PAceOZC5YsWKFtMS5aSd2JMnT1rcz7eTk9s+sOA+lNynUp75yOXhsbGxYmCON9iz5Sjpm86ynjY0s83tzAcsnAnI20Z+QLfnZJap3+OkQYluW3bNxvXm4GOJWM6pDqThvS3fA2ER5mFHRRUNpm3V1rYBbJtTwXsH28Ye75uyGvPB7IBeaS0+x/flNVCd2pgdOap7CCXEx7vtxxP/Zb0SGkTp9ZFiHQWERlNYoNLq/1MTR/SkL//eJ5aPFNTS7Clt71t4oq7IeP3zzz8pMDBQDA/kvt2S8847j84991z68ssv6d5773X4egB0SYBRFmTka54Q3RE+IZGkjEkiRXQiKaP5OomUUQmk4AsHFxFYBAAAD2Vz8PH3338XZ7e5zLmzARgp8Mi9Hjnw2NpZeg52cmYk/yw0NJSGDRtGy5Yto4svvtiU9ciDbnhSdlv8/f3FpTlef28JIm3Ya86YGTcovd2/mw/o5NvmZKWGjpdqTP0egwM6lDDrMkZkcvmeMfi49VgDXTDKclsEBfhRXGSwGO5wvLDCYls13zZghm3TPmwfbJvOvm/kPR8zEiNbfA5ty2kwLY/IDHL7z6lR3cx9H3ccb6DJfUOt/j81ur+5/zRPvHb3beGK+MQv75PJA4+S0aNHi6GE7m7BggXiwi1awIOHu1SXkfbkMdIVZJOOr08ar0UGYwf6LBqDihxcTCSfqESqVgZRVPe+pIpJJh//QIf8HQAAAK7O5igS74ANHTq00zvy/Dxcns2DYn788UcRiDx27Jiph2NIiLGk4L777qMNGzbQnj17xO1HH32ULrjgAho+fDiNHTtW9BXikuubbrqpU+vj6dbvNvZ7ZGMH2DYUiJv9y4cAuLsBKQHkr/KhRq3B4m9rPnSGg48nS2uoUa0lfz/3DrgCgPs7Xlgprv18leIESXNbZZ9nwz3gs5oDqIvWGfs+bjlW1yL42J4eKdEUFRZIZVX1YugMBxia9/eFzunVq5cYNMgtbDgDVcInjH/66acWvcHd0fz588WFK2bCw1ufMA/uQfSI5T6M+UdFYFHbFGDkgKOhlTZE7fEJiyZlbCop41LN13GppIhJbpG5yFnIVUVFpIyLw5RoAADwajZHVHjSNAf8OFjY2tlua/GO3M6dO0XJzmWXXWbxs+eff96U2ciBSHlJ9ezZs+nrr7+m119/nd544w0aOHAgrVq1SjwOWqfR6kTmB0uJC2tzSmpbdh6vNy0PTXf/A1o/lUJkcG7OrqMT5RqR2ZkQbtk+IDkunDbvzxPLBaXVIssIAMCZ8ourTEOxmp8A5ANr6WRKaICCesa7/4AV+ffNLtn3kDU40DiyXwot23CYSirq6FhBOWUmmVtqQOdNmjRJBCAHDBhAl156qWhnw4HI7777TpwUnjdvHjYzOIVB00i6/CzS5h0m7YlDpD1xmHR5R2wKMooMxoQMUsalWQYYY1NIEdDy5A8AAADYOfjIQUPu8zhy5EiaM2eOKIWW4/t5h/RUIiMjTZmO7Xnuueda3Dd37lxxAetw0/26BmPZ9NiBaTZvth2yg75BaZ5RLjIswxh8ZFuz62jmEMuMhmTZxOu84ioEHwHAqWrr1VRRYyyrTpJ9Pkmyi9VUVmssDR2aHkhKhftn+cWEqigl0lecJNqb10AanYF8ldb/XVLwkW3aewLBRzvjAO/SpUvprbfeEpmOP//8sxg+c8kll4hej1IFC4Aj6StLSJt7UAQadSeOkDbvEOkKj1sMfGkPD3ARQcbETFImZJKKlxMyySc0EtnSAAAAzgw+7tu3z9TonXc0m+Oz3dYEH8FJJdc2Bh8bNHo6kG884O0W50fhsob/7mx4BmfUlJpKFZsHH5NiQltkGwEAOEt+iflzqLXgo7zkepj4fPMMg9MCRfCxQWOggwUNNCDF+hNgo/qZJy2v33OcLp4+yEFr6Z14f5AnjvNAP/lQPwBH0ddWkfb4ftIe20fanH2kPbaX9JXFVv2uIjyWlCk9SZXcQwQXRbAxPh0DXgAAAFw1+HjllVeKC7hn8HGcjcFHzjbRNg3NHOIhWY9sSHogcWIQDzLYdqxlOZ/84B7BRwBwNs7Abi0zWyL/HDOeXPGc4ONvO6tMLUBsDT5yBqhOb6A1O3McuJbeac2aNbR9+3bRfxvA3gxaDWmPHyBt9m4RbNTk7CN9ce6pf1GpEoFFVXIvUqX0NAYcU3qRIsS2lkMAAABgXx2eosENxQ8ePEjBwcHUvXt3+64V2A33AZOCj+HB/tQ3I67D/R75INBTBPsrqW9SgAiuHilqpJoGHYUEKFsPPpZUO2ktAQBangRJlGVmS3YcN2Y++ql8xFAtTzpRJG8Bcvk46383JMifhvVOEv17DxwrpqLyGoqLRCmwvfTt25c+/vhjuz0feDd9XTVps3aR5uhO0hzdIQKOpGls93d8AoJJldaXVGl9TEFGLqH2UWJIIAAAgKvp0LczT6e+/vrrqbS0lO6++2566aWXxPCY22+/nVasWGH/tYQOy8orE1Ob2aj+qaRUKjocfByS5jnZNGxgaqAIPhoMRHtONNCYHsFt9nwEAHAm+UmQ5pmPFbVaOl5q7OvbNzFADNXyFL0SAijA10eUXcu/j6x12pAM0/CwtTtz6LzJ/R2wlt6pf//+otXOVVddJS5xcZYnN6OjoykxMdFp6weuTV9VSpqDW0hzZIcIOOryj/AZ87Z/QeVHqtTepErvR6qMfuKah8H4NBu+BQAAAB4SfDxx4gRde+219M4779Dhw4dFvx82ePBgMbn6r7/+ounTpztiXaGL+z1y1qSUTcPTU7vFdny6uSsalBpAX28wLu/KrbcIPiZGo+cjALhH2fXuE8a+vJ40FEzCA2a41HpLdh3llWuouFpLsaHW77qcNjidXv1qrVjm0msEH+3nyy+/pHXr1onLwoULW/x8/vz5YhgNADM01pPm8DZSH9hEmgObxPTp9iiik8i3xxBSdR9Mvhn9SZnUHRmNAAAA3hR85MzGGTNmiGmGL7/8sin4yEaMGEGrV69G8NFDgo8nK7VUUm2cFjgwJZAUHjA9VW5wqvkgfWeuZUaNv5+KYiKCqKSizmLQAwCAs8uuk2Isg4988kR+UsXTcMsPDj6y3bn1dHq/lmXnbeHvPf7u0ou+j8ccuJbeh09EX3DBBW3+nNvygPcy6LSkzdkvAo3qAxtJm7WbSKdt/cE+ClKm9CJfDjT2GCwCjsoI29oEAQAAgIcFHznYGBpq3PHnidfNfxYTE2O/tYNOW9cUfPRVKWh4nySbfnd/05Rr5kk9xCTpMX4UFqigqnq9OKDlTE/5e5qzizj4WFBSTTodT3h36uoCgBeTgo88QCU+KqSd4KNnZT6y/skBFt9LtgQfw4IDaHCPBNp+qID2ZhVRaWUdRYd7VgsRZ1m7di0VFBRgCCFY9G3U7F1P6t2rSL13PRnq2jh56+MjejX69hlFvr2Gk6rbQFIEIFgNAADgyWwOPo4aNYqef/55qqmpsQjUZGVl0aJFi+i7776z9zpCB3Fz/cO5pWJ5aK8kCgqwrWx6X545+NhXdvDnKfj9yxmdaw/XUmmNjvIrNJQc6WcRfNx5+KSYlFpcUUtxkdgxBgDnll0nRIda9O7lkyZS8DE6REnJkb4e90/UT/b9s092UsxaE4ZkiOAjW7crh2ZN6GvX9fNWubm5ouT6yiuvJE+1YMECcdHpjFUg0JKuJJ981v9KVcd2kPbIDiJ969tKEZtKfhxs5Evv4aQIDsfmBAAA8CI2Bx9HjhxJkyZNoqFDh4pG4rxDxo3Gv//+ezr99NNp6tSpjllTsNnqHeYSs3GDbCu5bn6Q1y/J84KPUpYQBx8ZDzOQBx8TZaWNfOCP4CMAOINaozMNDktqNuk6p0QtsrelIVrNKxI8QUqkr+g7XN2gp/2yk2K2DJ1549v1pr6PCD7ax/jx48XJ6Lq6OgoK8sxsUu5byZeqqioKD0ewTKIryaPGbf+SettforRaSUTaViZR+/YbS359R5Nv31GkjLat+gYAAAA8S4emXX/22Wf00Ucf0TfffEN5eXl09OhRevzxx8W0a3AdK7dlm5YnD+tm8+9LZddhAQqPzKZpXqK4K7eBzh4c3ubE66G9MLUTALreyVLzpOukZsNm+HPLk0uuGQdU+yYF0KasOiqs4l7EWooKtn7C7biBaaJtBg/SlZ+Ug85Rq9UUERFBw4YNo4suuqjFtOtBgwbRxIkTsZk9hK6iiBo3LTMFHFujiE0hv4ETxMW351AMiAEAAIDOBR8VCgVdf/314gKuH3zkfo+2Dpvhg7uiKuN57D5JAR6ZTdN8OMOeE5ZDZ+QZRvJhDwAAXUk+9Kp58HFvnmf3e5SXXnPwUToxNr6n9Zl2EaGBNLB7Au06cpJ2Hz1J5dX1FBnquduqq+zatcs0dPDbb79t8fN58+Yh+OjmDOoGatyxgho3/EaaAxuNEfxmlKm9Sd1zNEWNP5tUid08dn8RAAAAuiD4WFpaKpqKW4MHziQkJHRytaCzcgsr6GhemVge2S+FggP9OjxsRt5vy9NEBKsoKcJX9Hs8UNAgJqJKU73lmY8IPgKAs+SXmDMf5Z9LzdtjcHagp5L/bbYGH9lpg9NF8JFjJ+t3H6ezx/V2wFp6l8svv1xcwLNwH1lt1i5qWL+E1Fv/JkODseVD84Cj/7Cp5D9sGvnEJFNRUREp4+IQeAQAAIDOBR8/+eQTuueee6x5KN1999300ksvWfVYcJxV282lZZOGZtr8+/vzG73igFYKrnLwsV5toJxSNWXG+rfIMJIf/AMAdCX5yQ/55xKfLJFOFHFrjIgg7rzmmeR9hzsydIb7Pr79w0axvGbHMQQfAVrLcty0lOpXfku6E4dbbB9FdBL5j5lJAaNmkDLOXE2j1xt7zgIAAAB0OvjIzbavvvpqscwDZmbOnEkDBw6kG2+8kVJSUqiwsJAWLlxIv/76K91///3WPCU42Mrt5n6Pk4Z1IPhY4PnDZuTB1b/3GoOLfCDfWvBRmjQLANDV5J8/8nYQfLKET5p4w0mi9Bg/CvTzEX/vvg4MnRk/KN20zENnwH59H9944w1as2aNGEZ45513ij7g27dvpwsuuACb2Q3oik9Qw6rvqWHdEjLUWe7r+PgHkd+wqRQwZiapegwlH4X1vVYBAAAAbA4+BgYGigv7888/xcQ/zoaUJCcni4bjXHbxxx9/0BVXXGHN04IDS2ZWbM0Sy4H+KhrZN8Xm5zhYYMx8DPT1EQd9nqx5Ro00dCY0yJ9Cg/youk5tMfABAKArnSytMS0nRpuDj/IgnKcHH5UKH+qTGEDbc+opr1xDVfU6m34/OjyI+neLo71ZRbTjcAFV1jRQeIhnb7OuwCej+QQ0t9zhoCNLTU2lWbNm0ahRoygtzbZ+09B1NMf2Uv3ST0i9a1WLXo6qjP4UMPECUVrt44/+qAAAANB5Np/CPHz4MKWnmzMI5Ph+/jk415ETpaYy4XGD0snfz7a5QmqtQRzcsW5x/uKgz5P1TTJmOrL9zTJqYiKCxXVppXHQAQBAV5N//sRGGj+TvC1DnXWPM39W55Sobf79iU0tSLhcfZWsOgA6hrMdc3JyaMuWLTR37lzT/X5+fjR9+nT65ptvsGld8OS0+tBWqnx9PlU+fzWpd640Bx5VfqKsOvy+Tynivk8pYOw5CDwCAACA84KPvXr1op9++klMOZTLysqiRYsWiZ+Da0y57mi/x/xKPemb9kU9PeuRxYb5Ukyo0pT5yDvn8mwZVlZVT1od+hoBQNcrqTAGH31VCpGR3drJEvlJFE+VIfs+OlZqe/Dx9OHdTMv/NlUHQMcdPHiQJkyYIIKNzSccJyYmWj2oELoo6LhnLVW+dB1VvXojaQ5sMv1MERFHQXPmU9Qzv1LoVf8j34z++CcBAAAAu7MtJY5InM2ePXs2DR06lMaMGUNJSUlUXFxMa9euFeU3l156qf3XEmyyYlvn+j2eKDeXs2V6QfBRyhpadbCWqur1VFChpaRIX3F/TFPwkZVX1TtxDQHA2zMfORNbCvJwMEEavMInT/gkiqfLiJUFH4s1NDrJ9qEzKqVCnEhavsVYIgwdx6XWfOKZNQ8+rly5kmbMmIHN6wI02Xuo9ofXSHt0p8X9iphkCjrzKvIfPZN8fL1jXw8AAACcp0Odo7nfI+9Y8hnvgIAAGjlyJP32228iI1Kp9Nxpm+6Apw5K5WThwf40pGeizc+RW65v9WDPk8n7pe3Lr29Rds1KKmq7fL0AwLtxkLGksrbFyZD8Cu57qPeakuvmJ8N42I6tOGt09IBUsXzkRBnlFJTbdf28zbRp00T246uvvkrV1dXivcp9H3lI4erVq+nCCy909iqStw+SqfrwQap84RqLwKMyMZNCrnmCIv/3PQWcdh4CjwAAAOCamY+S0047TVzAtXAzfS4RZhOGZJBSaXt8+USFrtUyN28JPu7Pb6RpTVVHMRHmg/2SyjqKDjbfBgBwtJp6NWm0eos2EOxAvnEoGOvjJcHH5Cg/UimIeHMcK1Z3aBeGS6/XNk275tLra84Z7oA19Q7BwcH066+/0iWXXGLq9/32229TbGwsff/996IyBrqevraK6v74iBpWfEuk05ruVyZkUNC5N5Hf4MmYWg0AAADuE3wE17Rim7mP1cQOlFyzXFnZdXqM5/cRY70SzAfvRwrNB/Xyg33uu9Y7CcFHAOg6ZVUNrWZiHzppvr+37PPLk/kqfSglyo+OlajpeKma9Abbp/CePqI7PfnxcrH875ajCD520rBhw2j//v20detWys3NpaioKNGSJzAQE5K7mkGvp8Z1v1DtT2+RobbSdL9PSCQFzbqBAsbPJh8ldvsBAADAObAX4mGWy5rod2TYjLzsOj5MRcH+HarMdzspUb4U4OtDDRoDHT7Z2OrBPiZeA0BXK6uWBx+DWj1J0jPBO04SSUPQOPhYrzFQSY2BEuJt+/1hvZMoIiSAKmoaaMXWLNLp9B2qEAAzbrczatQocQHn0BZkUc0Xz5L26A7znb7+FDj1cgo84wpSBIbgnwYAAACcCnvcHqS+UUOrdxwTywnRIdQvM87m56io01FVg8Gr+j0ypcKHuscZD+CPl6mpXq1v0WNN6rsGANBVpDYazTOxDzUFHzkbMC3aez6rM2XfS/LhaNbiQKM0iK28uoF2HMZEZmjbggULqF+/fqK3uSsy6LRU98cnVPH05RaBR/+RZ4qejsGzb0LgEQAAAFwCgo8eZN2uHKpvNPb3mT6qR4vpk9bgjBJv6/fYPHvIYCDKKm5sZeCMceIsAEBX4QCZRPo8Umv1lNP0Wd0tzk8EIL2F/HtJ3iLE1tJrCZdeA7SFh+fs27ePNm/e7HIbSXvyGFW+dB3V/fK2qbejIjaVwm57i0KvfYqUUQnOXkUAAACAzgcfd+/eTe+//z4tX27snVReXk75+fkdfTqwg782HTEtTx/ds0PPIR3Qsgwv6fco6Rlv/nsPNZVeW/R8rETwEQCcl/koZWJnFatJp2/5ueV1wceKpo1go6kjzcHHfzYj+AjuhaeKN6z5iSqemUfaY3uNd/ooKPDMqyjyka/Ir+9oZ68iAAAAgH2Cj//73/9ECcrDDz9Mv/32m7ivurqapk6dSmq1OXgFzgk+KhQ+NGV4tw49hzzzUV7e5g3kB/FSPzV5j7UyBB8BwAUGzhw56Z39HllGrH+nyq7FcyRGUrekSLG8cW8u1dSZtyeAK9PX11D1xw9TzRdPE2mM71tlfDqF/9+HFDznFvLx9a7PAwAAAPDg4CNnPL711lvi+r777jPdn5aWRkOGDKHvv//e3usIVjh+soIO5pSI5VH9UigytGOTJnNKzcFHb+oj1vwgXsp8DA3yJz9fpVhG2TUAOLPsWsrElvo9emPmY0yI0jQILa+DmY9sSlPptUarp7W7cuy2ft6GTzi/9NJLNGfOHHr11VfFfUePHsW+oKPKrJ+7itRb/jTdFzBhLkU8uIh8uw10xEsCAAAAOC/4uHHjRrGT2bNny7LePn360N69TSUg4LSS62mjenT4efLKNOJa4UOUFOlrl3VzF7GhKgoPVFpkPnLfTOmAHwNnAMCpZddNmdiWmY8BXvWPwp/JyU3fTUXVetLpjQPSbIXSa/uYOXMmLVy4kKqqqkTQkaWmptKjjz5Kx48ft9OrgHr3Gqp8/mrSFRm3qU9AMIVe9yyFXHY/+fh512cAAAAAeEnwkXvNNDaaAzNyWVlZFB4ebr+1g471e+xM8LHcGHyMD1d51RAD6f0sZT8WVWnF5G95n7XSyjrx/gcA6Oqya/66jWrKaD9UaLwvxF9BieEqr/vHSIkyBh+1euNndUdMHJJBSj7LRkR/bjxs1/XzFmvWrKGcnBzasmULzZ0713S/n58fTZ8+nb755hunrp8n4H2Our8+p6p37iJDQ624T5ncU2Q7+g+f5uzVAwAAAHBc8JH7Ov7666908OBBi+Djzz//TF999RXNmDHD1qeETlJrtLRyW5ZY5iy9ob0SO/Q8NQ06qqw3lrFJmSXepvW+j8Gm8ryaevQ0BYCuU9ZUds2tNFQqJdU26qigwhhw6xHv3+IkoDdIjjS3BDnRdMLMVhGhgTRmYJpYPnKijI6cKLXb+nkL3g+cMGGCCDY2fx8mJiZSQUGB09bNExj0eqr9/lWqW/wGRyHFfX7DplLEPR+RMjbF2asHAAAAYBObUya6desmymmGDh1KMTExpFKpaMmSJXTo0CFx/6BBg2x9SuikDXtyqbrOGBSbNrI7KRSKTmU9enPwsVuc+aA2u7iRRmQGWQydKa1qIPOcVAAAxyqrNpZdS+0fsovNJ0C6yz6vvEmK7Pspv4PBRzZjTE9au9PY73HZ+kPU48Kxdlk/b8H7gFzxwpoHH1euXImT0Z1g0Kip+rP/kXrrX6b7gs75LwWefZ1XnnAAAAAA99ehKNWdd95J69evpyuvvJImTZpEs2bNotWrV9Pjjz9u/zWEU/rbziXXXh18lE1SlQ7ypYP+5v3XAAAcqVGtpdp6jUUGtjz4mCn7vPImyU1l182/t2x15phepuWlG1B6batp06aJ7EceNFNdXS1KhLnv4/z588U+4YUXXtjhfxtvDzxWvX+vOfCoUFLIFY9Q0MzrEXgEAAAA78l8PHLkiOj5OHjwYHFp7Wf9+/e35zqCDf0eTx/Z8by8E03DZppnlniTjFhzJtGxpoN86aC/+eRZAABHKqmsMy2bMx8bW/288iby76fOBB/7ZsRSWnw4HS+spDU7j1F1XSOFBnlnQLcjgoODRRueSy65hA4fNgZv3377bYqNjRXTrpOSkpy9im4aeLyPNHvWGu/w9aew658jv4GnOXvVAAAAALo28/Gnn36iTz75pM2fffrpp51bI7BJQUkV7T5aKJaH9U6iuMiQDm/BvHJzRo23Zj7Gh6ko0M9Y0pRd0tTz0SLzEcFHAOgaPORKIrV/OFYiy3yM8c7gY5Idej4yLl89c2wvU0/f5VuNJcRgvWHDhtH+/ftp48aNIuD477//iiE06P9tO4NWQ1UfcOBxjfEOvwAKv/UNBB4BAADAI3SsOWAbiouLMe26iy2TlYpN60TJdfODuCQvDT7ywWhmjL8pE1St1VtkPqLsGgC6SkmFcbpta2XXKiWXH3tn8DHYX0GRQcpOZz6ys5qCj1LfR7De77//Tq+//jqVlpbSqFGjxMTrKVOmUGCgcSo72DZcpuazx0mzWxZ4nP8a+fYchs0IAAAA3lV2/cMPP9AHH3xAx44dE6XVe/bssfh5bW2tOPP9999/O2I9oQ2/rztoWj57nPkgqiPymsqufZVEcaE2V+R7DC5l3JffQHoD0fFSTbOej8h8BICuL7vmDGyd3kA5TZmPaVF+5Kv03sETnJ1fXqejoiqtOEnkp+rYudQJQzIo0F9F9Y1aWrbxsOhbiIEe1uGBgy+88ALdfffdNH36dJo3bx6dd955FBRk/s4E69T98g41bllmLrW++VXy7TUcmw8AAAA8hsKWqYYDBgyghIQE07L8wjuef/31F02cONGxawwmdQ1q+neLsUwsPipElF13FB9wSRkkcaEKUii896BWXsrI/dUiQwNMt6vqzP3WAAAcqarG/HkTERJABRUaatQavLrfY/OhMwYDUUGFtsPPE+jvS5OHdRPLJ0traOfhAruto6c744wzKDc3l5YtW0aJiYl08803U3x8PF1xxRXiPp1O5+xVdAv1qxdT/bKmlkU+Cgr9z9Pk13uEs1cLAAAAwK6sTm/jqdZ82bRpk8hy5NIacC7uT9WgNh50nTWuFykUHa+ir6jTUZ1aL5YTw+xaje92MuPMAwe4v1pKhsIiSAsA0BV0euNnMlMpFZh0LSPvS8z9itM70f/yzDE96Y+mkmueej2kFwalWIv3O6ZOnSouPGyGB9B88cUXdO6554pgJE/ChrapD2yi2q+eN90Ovuhu8h88CZsMAAAAPI7NUSbu64PAo2v4Y525P9XZ43p36rnkk64TvDz4mGGR+agmpSyoy2WPAABdQf55o1AqMGymjeBjZ4bOSMFHCfo+dlxDQwNVVlaKi1arJT8/787OPRVdRRFVf/QwN3wUtwOnzaPAyRc5e7UAAAAAHKJDUaZdu3bR7NmzKT09nUJDQykkJMR0eeihh+y/ltCCXq839XvkflWTh2V2aivJm/YnhBsb+Xur9GZl10pZCTqCjwDQlZ/zEv4c4s8jibeXXafIMx9lJ886IjU+gvp3ixPLWw7kUVF5TafXz1twD/DFixeLYTPclufBBx8UrXjWrVtHzz9vzugDSwadlqo/fJAMNeXitm//cRR03q3YTAAAAOCxbJ4qUl5eLvo7XnTRRWKydVVVFc2YMYMWLlwoev9ccsklNq+EWq2msrIyioqKOuWZcn69ujpzE37m6+tL0dHR5E22HsinonLjJNTTR3SnoIDOHYjmlhmHGDBvL7sO8lNQYoRK9BE7Vqy26H+pR+YjAHQRnc6c+cgZ2NKk6+a9ab098/F4qXm7dNSMMb1ob1aR6CG5dP0huvJsTBk+lSVLloj+jpzlyCekf/zxR7F/yINooH21P75J2qM7xbIiKoFCr36cfDrROgcAAADA1dm8p/PPP//QwIED6c0336RBgwZR9+7d6cYbb6TVq1dTUlISZWdnW/1cOTk5dP/991NaWppoVs5nyk/l3nvvpYyMDBoyZIjpwmfcvc1vFlOuO1dyLfU2lKREYgc4M8bY97GqQU/VDebsIwQfAaCr6GU9ZvkkiBRkiwhSUkSwdwd4kiJ9Sdn0VZVjh+DjOaf1MS0vWX2g08/nDYKDg+mtt96iwsJC0efxrLPOcovA488//0y9evWiPXv2OOX11fvWU8M/XxpvKFUUev1zpAiJcMq6AAAAAHQVm6NMnN3IwUfGZdbc24cplUqx47l582arn+vbb78V2ZO///67Tetwzjnn0MmTJ02XFStWkLf5fa0x+OjjQzRjbC+7Bh+TvbzsmqVGm7NqiqrNEztRdg0Azhg4w4uFVcYBY2myzydv5av0MWXpHy9Rd/rE0PA+SZQYEyqW/91ylGrqzCXu0LrTTz+d5s2bJ4KQ7oL3Yb/++muKiIgQPSq7mr6+hmoWPWW6HTz3DvLN6N/l6wEAAADQ1Ww+Ra3T6USgkXHW42uvvSbKprlceseOHTRu3Dirn+uee+4R1ydOnLB1NUTQk3d43eEsu70dKyinfdlFYnlEn2SKjwrp9HPmNAUf48JUFOhnLjP2VilR5pLGkxXGA36mb2oMDwDgaPKTHZX1ejIYFC0+n7xZSqSSTlToqV5joKJqLSWE+3ZqavPM8b3pw5+3UKNGR39tOkLnTUZQqLlt27bRn3/+ScOHDxftbni5LfwYLsO2RVFRkSjj5kqa1hgMBvEYPvlta9CT91+5euaNN96gWbNmkTPU/vAa6cuN+2++fUZRAAbMAAAAgJewOXLHQUZ/f3/TWW++zeUrvCPIZdQcjHS0n376iZYuXUoajYZGjx4tdiS5/NpbSINm2NnjO19yXVGno/JaXYtJz94sJcp8EHsSmY8A4AQ6nflkR2ktL0vBR2Q+stRIBW3INmfvdyb4yM6d0FcEH9mvaw4g+NiKI0eO0Pfffy9OQvPQQV5uCz/G2uAjP88777wjWvi0VRK9fPlyuvbaa6m0tFRkLXLv8Q8//JACAgLEz++44w769ddfW/zeZZddRk888QQ988wzNH/+fIqNjSVnlVs3rv1ZLPv4B1HIvIfJh8tXAAAAALyAzcHH2267zWLHcs2aNfTNN9+IQTDnn3++6MfoSMOGDaP169fTiBEjxPAb3pHknVveUY2Pj29zGiNfJLyu0iRR+TRRd/HbGnM/qrPG9ur033Cs2Fx6lBatEpkF7rhd7Ck5wvxfo6Bclvmox7ZpDb9f8L5pG7YPtk1ny65LqvlzyPi5lBLh6/Wf0fx/KjnC3Dkmu6iBRmUGUmeMG5hG4cH+VFnbKIbONDRqyM9X6bbbh7M57Y0DfnxhfAJ4zpw5rQ4K5J/xd4K1uBSae4Dzvt1vv/3W4ufcYoeH2nCA8bHHHqO8vDyaMGGCKZORPfDAA3TLLbe0+F1u78PVMs899xx99tlnpoqb8847T5zM5gxNRzM01lPNoqdNt4Pm3k7K6ESHvy4AAACA2wYfuVE3B/2uvvpqcTssLIyuv/566ir//e9/Tcs8Hfujjz4SZ7H5rDkHIlvz7LPP0uOPP97i/uLiYlEy7k7Kquppzc4csZwaF0rRQcYSpM7YnWUOzEb7q6miokEcNDjiwOVUNDoDFdXwoBeieg2R0ofIX0UUHUwUFcQTX7smS8BfNmU2p9g8Xb2xUS22tzO2jasf6PLBnbPeN64O2wfbpiOqq2tMy/ll/DlkzPAKUdRQUVHX9CTk/9MV9UQltcbPZK3e+Jkc4kcUH0oU4OvjtP9TEap60+39xyupKFPT6eedNDSNfllzWAQgf125g04blEruiLdPW6XL9vLee+/RgQMHxNAZW37WGimDkocatubzzz8XJ7wfeeQRcc2DCu+88056+OGH6YUXXhDZj3wCuq2T0Lw9du40TpdmF154oQhi9u/fNaX1dX9+RvryQrHs23skBZx2Xpe8LgAAAIDbBh8LCgpo165dpuCjswUFBZ1yyjafDb/rrrssMh9TU1NF0JKbjruTpVu2m/qAnT9lQJs72rYo21nCu8ZieUBGFEVE1Ilt01VBJLXWQHtONNC2nHo6XqIhWdzPgp/Sh3on+tGQtEDqlehHCgeWK8WJibLVoiS9uM68HRRKFcXFxSHA1sqBHZePdeX7xp1g+2DbdERAQJBpuVpjLike2C2O4iIcW3qdW6ahbcfqaW9eA9U2tp3BlhihpCFpATQ0PZCC/RVd+n+qTy2vl7GSoajO+NncWRdMHSyCj2z1nkI6f5rjs+IcwdnVC1wWHRjYuUxUOR5mOHLkSPL1Nb/vTzvtNKqtraX9+/fT0KFD2/19/l7q0aOH6Ta3D0pJSTGVbDuyYkZXdpLq/1pkvKFUUdDF94qgvi2Zoa4Mmf3YPnjv4P8VPnNcBz6TsW1cqWKm08HHSZMm0euvv051dXUi8OdovMPH5Tvc2Jzxzpq8R05hYaHoNZmZmdnmc/BOptSnUo43sLsFSn5Zvd+0PGdSf7us//FSc/ZnZqw/+ejru2TbaHUG2pRVR//uq6HaxlPvzKt1Btp9olFcEsJVdMbAUOqb1PqBgz1wXzURfJT1fOSya3d833QF/n+JbYPtg/eO/ehlwYmSps8hnvIcH+FHCgdlgeeVaWjp7io6UmhdVUBBhZYKKmro7701NK5nME3qE0KBfl3z+RgTohAD0urVBsopVdvlc/mM0T3J31cphs5wf+VX7zgbn/fN8HDBv//+m9auXSsqSF566SWLn/P+4aeffkqPPvoo2Qu/TkJCgsV9MTExpp/ZijMt2+v9aM+KGcUPL5NCYwxk6keeQ6U+ATxZhzwFMvuxffDewf8rfOa4DnwmY9u4asVMh4KP1dXV4kzxgAEDRL+c5jtvPABmypQpVj1XfX29KNWUdhzLyspEXx8eXsMXxhmLGzZsED0d+Sz01KlTRY8fLpU5fvy46BHEG2revHnk6Sqq62n51iyxnBwbRsP72OcNwo36mUpBlBTpS+Wl5HB55Rr6bmMFFVaZ+ymyqBAldY/1o/hwXwoOUIhgX02DnvIrNHToZKM4yGQnK7W0cE05DUgJoHOHhlFooP37cqVG+YmMTHlygjwYAADgSPLPm+JqLfkEGU+KOKL9hEZroL/2VNOaw7UWn3nc8rBHvD8lR/pSRLCSfBU+VKvWix6Ux4rVlF9h/AzX6IhWHqilrdn1dN6IcOqX7LgTQ/ITHhnRfrS/oFF8p3AWvZ+qc9smJMifTh/Rnf5Yf4gKSqpp64F8GtkvxW7r7AkOHjxIixYtopKSErFfxsty3I7n4osvpssvv9xur8mBZZ6CLccnphmXYduKsx7bY6+KGc3RnVS9Z5VY9gmJoKi5t5AiKJQ8CTL7sX3w3sH/K3zmuA58JmPbuHLFjM3Bx0OHDokdPe63uHLlyhY/5zIba4OPv/zyC91+++1imcuHb775ZrH8f//3f+IiNQqXzm5z9iJP0+b+Ptu3b6fIyEjRcPzBBx8Uj/N03ABfww23eCrnxL52ycbgTNKcpuBjSpSfyKpxJH69dYfr6PedVdRUPS4MTA2g8T2DKS3at83pj1xufrCgkVbsrxElgYyDg7z+l4+LpHQ7T+pObZooK18fDoYCAHQFnawHhVpHxPn7KZH2L7cur9XSorXlpkAiiwpWiizGwWkB5O/b9ndNcZWWNhytpY1H64iHc9c06unzteU0unsQzRoa5vA+vRmxxuAjv3ZeuVpk73fWrAl9RPBRmnqN4KMlDizyhXuA5+bmtjrkxd44WJiVZTz5KuGT1Sw5Odnur2ePihne36lf/LrpdtCsG0kV4pn7qqh8wPbBewf/r/CZ4zrwmYxt46psDj5yhqG9sgylHdj2vPzyyxa3eRLit99+S97op1XmkuvZE/va5TmLqrRUrzEe4No7eNda8PCXbVWi1FqSGKGi80eEi8DnqfBBLGfT9E3yp525DfTr9ipRrl3doKcPVpTShaMiaHCa/XpMmdZJFnyUT58FAHAki8+bps8haz4rbZFbpqbPVpebWl9wBvzU/qE0oXewVYHD2DAVzRoaTqf1CqYl26tof76xvJSDkZytOW9cpEPLsNOjzdsju9g+wcezxvUWZe18sumnlfvof9dPbfOkmDfj6dNdZfLkyWIidkVFhSnzcOnSpZSYmEi9evVy2OsuWLBAXHQ6c/sVa2n2rSftsb1iWZnUnQLGd932AgAAAHA1aFznJmrqGunvTUfEcmxkMI0dkGaX5z1caG6onhnruOAjBx6/2VBhEXic2DuYbp4aY/PBNB8E8tCZO86MMa0zZ718s7GCth4zP39ncXlj0yua7pOG/QAAOJrl540UfLRf5iNnjX+0sswUeOS2F/Onx9DkviE2ZyxGBqvoivGR4mSSsmnPIqtITR+uKKU6K3r6dibzUXLUThPAYyOC6bTB6cbnzCuj3UeMGXbQOg7MHTt2jLZu3UpbtmwxXbg1ji3DDPk5uBUPl1PzMl+kMqBLL72UMjIy6LLLLhPDZ7jU+5VXXhHTrx3Zg3n+/Pm0b98+8Zq2qvvjE9Ny0Mz/ko/S5vP9AAAAAB4DwUc3sWzjYWpQG0vizp3Ql5TS0V0nHShoMC33SXRMjy59U+Bx9wnja/GqXzQ6nM4aHEaqTpR5hwQo6T+TomhkpjHbkfuU/bCpknYer7fLeqc2ZdTIM148ZTolALg++eeN9DmUJsv06wzukfjxqjJqbMp85xM5t0yLoYTwjgc3eR1Hdgui6ydHmyZfcyn3hytLqV7tmABk7wRzpuOBfPP3WWedP7m/aXnxCmP2GrTE2Yg8CIaH/nFlCk+kli7cIsdaN9xwg8hu/OOPP0QfSV7mCwcjGfca//fff0XPxSuuuILeeusteuONN+imm25yyX8WzeFtpD26QywrEzLJb8hkZ68SAAAAgFPhNKyb+FlWcj3HTiXX7EBTiRzrk9j5crXW/LazyhR45JK+eeMjqbedAp2cncPDDTiIuf5IHfFh9HebKigsUNnpTM74MBWplDyV23hQzYEAZD4CQFfRcUq3iTH4yINfOquiVkefrS4TA1pYj3g/umJ8VKeHtUi4hcd/p0SLrEdui8ETsRetK6drJkR16oRTazJi/Mhf5UONWgMdKLBP5qPUV/mu138XJ88WL99Lj12H0uvmuN/j9ddfTx9++CFlZ2fT0aNHRb/uhQsX0ieffEIPPfSQ1dube4CfCvd2/Oyzz8gd1P3xsWk5cMbV5OPA7EwAAAAAd4C9ITdQ36ihZU3N76PCAum0IRl2e24p85EPOjPs0CuruXWHa8WAGcZVfPYMPEo4MMiDDUY0ZUDy8frna8vEEIXOBjZjQ5vi801ZRxg4AwBdxeJkR9NnUHwnMhMZBxw/W1MmgoKMh3xdacfAoyQuTEXXyTIguQT7p62Vds8e52Bmz6bsx5xStamEvLPiIkNoQtN3bVZ+Oe1C6XUL69evp6lTp4re3aGhoaRSqah379709NNPi8GDixcvJm+kObaXNPs3imVFTDL5jzjD2asEAAAA4HQIProB7vVY22Cc7jxzfG/y5XQ8O6hT6+lY06TrnvH+dp90zf3EfttRZbrNGYr2DjzKA5BzhoebDkLr1Qb6an0FaWXTYjvCFHxsyjpC5iMAOGPgDH/GcYAwPLBzX9tLtlfSyUrjiZnoECVdeVoU+do58CgPQHIfSM54Z1uP1Vv0/bUXqWUIxzUPnXRQ6fVylF43V1xcLKZQs8jISHFbMnjw4BbTqd0RD5vp16+fKCO3Vv0yc3Zm0BlXotcjAAAAQEeCj0eOHKGffvqp1QuXzaxcudLUowfs4/t/95iW50zqZ7fNevhkozhYY32S7BsU5AEDX20oJylxh4fLjMgMIkfiTMXLxkRQVLAxOJtbpqE/d1d36jnjwiyHzujR8xEAuohlprUPxYSoOjV1eUdOPW3JNvbE5ZNNV54WacpMdBQuwb5glHE6Mft1RxUVVBhPptmLvGWIPfs+cuk1T72W+j6i568l+fbgYCP3ZOThLKWlpfTDDz9QamoquTtbB87oq8pIvWuVWPYJiyb/Mec4eA0BAAAAPLTn49KlS+mee+6hhoYGUxNwadnPz09MKfT396fnnnuObr/9dvuvsZeprVfTH7KS69NHdLfbc1sOm/G36wHJ4i2VVFmnN/XkOmNgKHWFAD8FXTo2gt79t1SUX685VEv9kgMsJqLaIgZl1wDgJM3Lrs2Z2LarqtfRz9vMJwZnDw+TnVxxrMFpgSLLfsOROtFD96v15XTrGbF2y7aXnzyzZ99Hnno9aWgmLd+aRdn55bTjUAEN7Z1kt+d3dzxkhkutWf/+/emiiy4S19Lta665hrxN4+alRHqdWA4YM5N8fO0zIAoAAADA3dmc8nDttddSjx496Pnnn6eysjKqr6+n6upqeuedd0QzcG5A/sEHH9D9999PO3fudMxae5Hf1x2kuqaS69mT+tmt5Jrtz3fMpOs9Jxpob57xuYP8fOiSMREiK7GrpET50ZlNwU4+dF+8pYI0HSy/lg72pWwjeRkkAIAj6ZuVXceGqTp8QogDjw1Nk60HpwXQ8AzHZqI3d/bgMEqKMK5/cbWO/t3buax0uV4JAVJLTIvvNXs4fwqmXrdl5syZdOONN5puv/vuu6I6ZsuWLbR9+3YKDw8nb8L/zxrWLzHd9h87y6nrAwAAAODWwcd//vmHevbsSffee6/o8cNCQkLEDuiZZ55Jf/zxB82bN48uueQSWrFihSPW2WtLri88fYBdn1sqT+ODtt52ynzkZv+/bDP3eeQ+jOFB9guYWmt8z2BKjfI1H+juq7ZLz0cMnAGArmLZY7bjmY98MmhfnjEjkMusZw3t+qAQZzleNJpPRBlvrzpYS3nl9im/5r8pPdqYYXa4sLHTvX7lZp3Wx3Ty7EeUXp9S9+7dafjw4eTr2zVZta5El3uQdHlHxLIqcyCpEuw3HBAAAADA3dl8JJOTk0PBwcGt/ozv55+ztLQ0qq2t7fwaerHy6nr6c+NhsZwQHULjB6Xb7bn54IwP0hgH6YL97RMgXLarimqapo32S/anASmOGTBzKtyna+7IcHrzrxJRfr36YC2NzAyiqBDb3vKYdg0AzmJxsqODmY8arYF+22E++XLusDCH93lsC0/qntI3hP7eWyP6Af+4pZJunhZNik70sZS3DuHSbp7mnVXcKLIh7SGGS6+HZdK/W7LoWEEFbTuYT8P7JJO32rZtG/35559WPZaDkNOnTyd3HzjDF53OWErdHnnWY8BY9HoEAAAAkLP5SIZ3JrnnI/f2mTXLXFLCWY4ffvghffrpp+L2mjVr6LHHHrP16UHm1zUHSKM1BvLmThlASillxA6OFDWaSvD6Jwfa5TnzyzWmYQb+vj40e1h4p4Yj2ONA97RewbTyQK0IQP6xq5ouH2fM1rWWdLDvg2nXAODMadcdzHzkvrcVdcbASc94PxropBNCkkl9Qmj3iQYqrNSKzMftx+ppuB2GkfVLDqSlTQPG9p5osFvwUZp6zcFH9u3fu706+Mhl1d9//71Vj1UqlW4ffOSBM3ypqqpqt4zcoFFT4+Zlxhu+/uQ34oyuW0kAAAAAN2DzkczYsWNFP8e5c+dSVFQUJSUlUVFRERUUFNDNN99Mc+bMoWPHjtEZZ5xBEydOdMxae4nv/r+98wCPoure+MmWbHrvEELvvTcRUEBUsKJgAfunYsFePrv+bZ+9d0WxoIKgoKhU6dI7oYeS3nuy7f+cOzub2TSyyc4m2X1/PPPs7GZ3ZvYye+fed95zzoo99vUrXRxyveeUJBIyfRL9XJLriKuYyj6d83oGUYi/+8OtqzO2RxBtO1FGxeUWkYvyeFYFdYg2NL7gDKpdAwBaScEZLjKz+mCx/HG6qH9Is94QYnRaH5rSP4Q+W5Mrnv+5p0g45A36pt1cU17H9pwuo8sGV1XYbiqcb/n+t3+nSqNZpEJ58Y6JLr0Z2JrgG8+8AEcq96wla4lU0MnQfyxp/IPQRAAAAAAACho1emZH46FDh+j555+nSy65hJ544gnat28fvfvuu+Lv7du3p0ceeaQxmwY2MvOKafX241J7xofR4B6udVqw80Smd9umOx85n9jxrEqxHhmkpRGdaw/Ndzd+eg1N7F1VafuvPcVCKG0oEYFaEum+7AVnXJdLDAAA6sOhwJWPT9XNkAay5mCxCENmhnUMEG7wlkCnWINIy8EUlVtE/sem0qtNVdGZPadcW3QmPNifJg7rItYzcotpzQ7p2gyATMW25fZ1FJoBAAAAAKhJo2/ds8B46623CiGSi8107969sZsCtbBozX57vi92PbrarSI7H9m80SOhac5HdgP+rahcylVN2d3SUhjU3p9ibOHTnBPsaKYkkjYELjQQGaSzBV2j4AwAoHlyPnIf5IzzkV2P/x4ttRd7Oa9Xy3Ji8XVCNg9yaDgXK2sKnLe4U4wkaB5KL6cKY9O2V52rz+9jX5//926Xbrs1U1lZSa+99pqIennzzTfFa0ePHm1waLYnYLWYyXjwX7Hu4x9M+m6Dm/uQAAAAAABaHI0qnZmXl0fz5s2j48ePi4GnkvPPP18MQkHT+GnFXtVCrksrLXTEVmymc6yBAnybFj6295SUv0suXtMjwTWVs11ZfGZ8zyD6YVO+eL5iXxF1ivFtsKArhEs57BrORwCAm1D2N1qtj3BiO+N6tKUMphGdAyjIr/nTYCjhmzqDOwTQ5qOlwp35z8FimtwvpEnb5PBtvrbx9z6YVkH92rkmnzEzeURXCgk0UGFJBf269gC9df/F5G9oGU7S5uSiiy6ijIwMioqKEqIjk5iYKHKCDx06VBQf9HRMJw+StbRQrOu7DyEfTcv6rQEAAAAAtAQ0jREe+/TpQ6+++iolJyfT6dOnHZb8fEngAY3nRFoebdxzUqx3S4qiXh1jXdqcB86Ui0qjTJ8mhlzz5Hi5wvV4fu/gZs8pVhtcZKHK/WikY7YQ8YYgQh1t38mkDIMEAAA3hV1HBunFjZSGUFTN9XhOt5aRBqM6XPlaZxuFbDxSQkXlZ68oXB/K65kyr7Er8DPo6ZIxPcR6UWkl/b4hmbwdLiyYkpJCW7duFXnAZXx9fUWhmfnz51Nrhytd9+zZk4YMGVLne4wHJNcjo+8xzE1HBgAAAADg4c7HpUuXUnx8PG3cuJF0ukYZJ8FZ+EER0jVjYj/Xh1yfLnNwijSF/anllFUkTRjbR+lFNdWWCE/ax/UMovk29+Pa5BJ7iN7Z4FBHe7VrM3I+AgDcg0nR30SHNNxlt+loqd31OLxTy3M9yoQGaGlopwDacLiUjGaiDYdLaFKfEJcVnXE1V53fl775Y6e96vUV41wbldDa4BvQ55xzjhAbq49TeJzIhQhbOw2pdm08uNm+7tt9qBuPDgAAAADAg52PRqORBg8eDOFRJbgYyg9/7RLrPJZX5plyFVz1WaZPYtOcj8pCAeN6tkzXo9L9GBYgTcKT0yoos1AKFT8bIs8aql0DANxMpawgCgd2w8RHo8lKm45I/TIbJUd1bZmuR5lzuwfZcz9KIdiNd5d3ifUjX52PKkVnmDH921NcpJQ786/Nhym3UHKXeiscan3s2DGxXv3av2bNGkpKSiJPx1pRRsaj0phNE9WGtNFtm/uQAAAAAAA8Q3wcMWIEbdiwgUymhgk3wDm27D9NR07nivVz+renxNgwlzfhjhRpwuSv96HODXT/1UZKdiWdyjGK9bhQXYt1PSqLx4zsEmB/vv5QwyqsRotwbVS7BgC4F2XRlJgGOh93pJRRaaXkmOyb6CfchS2ZEH8t9bXdBCurtNLW4413LLLw2CNecj+m5FRSXolrxylarYamnSfdEDSaLKIwnDfDOb7Z/ciFZoqKisTNU877yE7BtWvX0rRp08jTMR7eTmSWzjNfhFwDAAAAANSJ03HT5eXlwvU4cuRIuuyyyyg4ONjh7wMGDKBRo0Y5u1lg43tFyPU1E/u5vF3S8o2UbisOw67HplSlXptcbF/nnGIt2fUoM6RDAC3fVywKHGxPKaWJfYIp0KA5e9g1Cs4AANxMBcciOyE+sviz/nDVTZXRXVtWheu64OsHi6byTSEOFW9ofsvq9E/yp122fI+8zfE9HccoTYWjEd79caM9RcpNU7y3snFgYCAtWbKEpk+fTocPHxavffDBBxQdHS2qXSckJJCnU3mgKuQa+R4BAAAAAFwoPu7YsYNKSqTJzdy5c2v8/aabboL42EgqjSZasFKqcu1v0NEl5/YkV7PzZJWrZEBS40Ou80vNtD9Vqpgd4q+xO1daOn6+GhrcwV/kGDOZiXamlJ01LFFZcIYn9wAA4A7sIcg+PjYHdv2kZBvt6STaR/lSm4jWUY05PkxPnWN96UhGJeWWmOlQegV1T2hcPmK+rs1dR6qJj/26xItCcMkp2bRh90k6nppLHRIiyFsZOHAgHThwgLZt20anTp2iiIgIGj58OPn7t44xQVMxyuKjj4b03eouSgMAAAAA4O04LT7eeOONYgGu589NnENKEgennNODggMaHxJdFztOVOWoGpBUFYLsLFuOlZKsww3tGNAkB6W74eNl8ZHZcrxUhGLX59oM8NXYC87IFb41TicsAAAA56gqcOUj+qGzwf2ZDBdyaU2M7BIoxEc592PjxceAGilGXAlfK66d1J+e+mS5eP7dn7vovzeOI29Gq9XS0KFDxSKzcuVKEYJ96623Umuvds2L2VyzErs5P4vMaVLOS11ST9IEuFboBgAAAADwJCChtNCQ6xkT+qqyDzm0jbW2fu0a50wwWzgvlzSp48i4wR1a1yQ3NlRP7SIlR1BGgYlO50p5K+tCFENQiJMWuB8BAG5A7mtY8DpbFHJZpYX22MKN/fQ+1LtN48S75qJrnIFC/aUhSXJ6BeWX1BR7GgI71RNtjs99Z8qbVMCmLqZP6GsPC2fx0WJx/T5aOhwFsGzZMpHvkUOsuRghs3//fpo8eTKdd955lJeXR60dzl/J32nLli01/mY8+K99Xd8DVa4BAAAAAJrsfPzrr7/oxx9/pEmTJlFoaKhYrwt+jzckGXc1XDXzjw3JYj0mPJDGDero8n2UVFgoOV2qAMqFZjjRf2M4mFZBhWXSZKt7gqHFFzSoK/fjyZwCu1soMdK33kI1csEZxmy2ELWOaEYAQCuGXdYSPmd1l+86WUZyikgOPdbbqj63FrifHdJRysnLmiv3yxN6Bzfa/Xgqt0Dk9t1/ppz6N8HlXxsJ0SF03uBO9Pe/RyglPZ/W7UqhMQM6kDcxY8YMmj9/vhDGWYicOHEi/ec//6FrrrmGBg8eTOvXrxe5wT0Zk63KNaPvDvERAAAAAKDJzsfKykoqLi4Wj/J6XQv/HTjPglX7RPVM5uoJfUmnc72gt+d0GbFu1tR8jxxyrQxhbo30SfQjg21yvvtkORlN1gY7H9n5CQAAamN31DXA+bjtRFU+XxbxWiPsope/J7vrq8RX5xjQ3r+G29/VXHtBf/v6t8t2kjfBub+50Mzq1auF43HXrl0i7+OsWbPovffeo3Xr1nm88MgYT+yryveY5Poc3QAAAAAAXud8vPjii8XClJWV0fjx4ykgoHVObloq3/y+Q9Uq167K91hUbqbD6VKhmdAADXWJc31eSndg0Guod1s/MWGvMFmFI7R3W/86HTnKnJBmLwyxAwA0b9i15MCundziqvQRcaE6UcClNcIu+m7xBjqQKrnrj2VVUudY568xAxXXt+0ppXQjRbr4SIkuHtWNQgMNVFBSQYvW7KfX772QglTI09wS2bdvH02ZMoXOPfdc8bxv375088030/bt2+mWW24hb8BaWU7m1KNiXZvQiXwM3lFgBwAAAADAbTkfP/zwQ3rqqacavUNQk71H02l7cqpY7981nvp0jlOlmeQ8jcxAhTPEGdglKJtRBrTzJ009hVpaOn0VOS93nZTC0WtDinZ0LDgDAADuDLsWDuw6UPZfjc3l21JQuvJ3NtK12DHal0JtaUW2HS9Tpc/2M+jpivG9xXpJuVEIkN5Cfn4+RUY6Crr8PDExkbwF06lkIovZXmwGAAAAAAC4WHyMj4+n1FRJKAOu4WuF63HmhQNUaVZOur/zpDSRSwjTU9uIunMc1oe8DaZ/E0K3WwKdYnwp0CD9BA6mlVO5sXZHo3AcIewaAOBm7MWtzuJ83GUrNMP0a9e6Cs1Up3u8Hxn00nfdc5oLxjgvHHIxmMEdpOtTQZmZDmdIbn1Xc50i9Hqel4Venz59mpYvX25fkpOTa33NUzHJIdec77E9xEcAAAAAAJeLjxx+vXPnTpHvBzSdikoT/WCrcm3Qa2naeX1UaVaexJUbpUlcY6tTZxVWhfYlhOtE1ejWDE/m+7SVJuomM4nCBHVNZJVh195Y2RQA4H7kvsaH6hYf0wuMlFFgEuvtIvUUHtigbCotFi6UI/fLLDweSK3blV4fQzoG1pqn2JUM6dmWuiRKDkAuOnM8NZe8hcWLF9OECRPsC+d6rP7au+++Sx6f75Gdj+17NeuxAAAAAAB4pPjIla7T09NFvh+ufN25c2eH5eWXX1bnSD2UpRuSKbdQcq1ccm5PCg9Wx03oiiIxXE1VhkOuPQFliOKeU7VPcnXiV4KCMwAA98JVhKucj7W/R9lvtfaQ69pCr5XXHWdQ3mTjytlqwDelvNH9eOONN9KpU6fOurzwwgvk8c5HvUHkfAQAAAAAAPXjtEVi8ODB9OKLL9b59/79qwbiwLlCM9dPVifkmtlyrKTJlVD3KZyBfRI9Y5LbLkpPIf4aUdzgSGaFCE/3ldRGB+ejQntEzkcAgFuw5yr04dyztTsflY5tLqLlCbSP9qVgPw0VlVtEgbMKo0UUCXOGbnEGe98uV84WfbmLuWZSP3ru85VktljF9fyxmeeSTiflm/RUAgMDxeINvP/++2Ixm6X8joylOJ8s2WfEuq5dd/LRtm63MQAAAACAO3B6xNSvXz+xgKZzOrOAlm85ItaT4sLo3AHtVWlWDl2TczVyJdQ24c6HS3M11XRbaF9ihF5UJfUEuGAO5xj791ipCL0+nF5JvapN4FmL5LBHGVS7BgC40/kohV3X3y+3jeAbKZ7TL/ds40ebj5aSyUIiZ2Pvtv6NyPsYQCv3F1N+qVncXOoa53pxNj4qhC4Y0ZWWrk+m1Owi+vvfIzR5ZDeX7wc0D7NnzxZLYWGhiPapnu8RIdcAAAAAACqFXcsTonnz5tGdd95J3377rXjtxIkTtGHDhsZszmv5dtlOkqPqrpvcnzSaRv13nJW9p8vs+R6Hdgx0yF/YGNcjTwo9iZ5tDPb1/bXkFxMVvVFwBgDQbM5Hn1pdewdSqwqp9EzwtH656vvsO9O4gjFDOqif95GZddFA+/rcpdtV2w9oGZhOVFU21ych3yMAAAAAQENolNp15ZVX0uOPPy7Exh07pLDh8PBwuuGGGyg/P78xm/TKQgJyfijWtZR5o1zNpiNND7ner5j8eZr42CnGQL46aWJ/MLVchM8pEY4jpfhoRsEZAIB7q11XywZR42ZJD8VNFE+gY7Svvep1bf1yQ1Be7zYdrboOupqJQztTfFSwWP9j4yFKzylSbV+g+TGmKJ2PqHQNAAAAAKCK+Lhu3TohOO7fv5+uv/56++scjjJ69GiaP3++s5v0SlZtO0bHU/PE+vjBnSgxNky1fW1UTLqGd3Y+T1NxuZlScirFenSwlmJCPCu/kU7rQ13jpIl7aaWVTuZIFb1l2Ckq3I/VBQEAAHBb2LWj87Gs0kInsqR+OSJQS7Ee2C93j5f6ZXbuH7d9V2fzPnLbMP9yCLdZnb6bczzKOZtF7sc/qnI5A8/7Tcph1z6BoaSJatPchwQAAAAA4Jni4549e2jSpEkUFBRUI3w3KSmJUlJSXHl8Hstnv261r980ZZBq+ympMNNuW77H9lG+lBDmfL7HQ+kV9vBwT3M91hZ6nZxWM/Raea7bQyEBAEBFrFaLotq14/WWC7HIXVGPNn6NSqfR0lFebw4qQswbCoeqD+sk3XArrrCIFCRqMevCAXaDPIdec3QD8DwsuelkLc6353v0xN8dAAAAAIAaOG2VYNExIyNDrFcfdG3dupUmTpzouqPzUFKzCun39clinUO1LlQxOT3nueKE/Y11Pcrio0y3eM8UH7vEVomPRzJqOmyUzkeEXQMA3EHVjY6aBWeOZCj6ZZtz2xP7Ze56+eYXF51pDCM6B9IfuwvF+sYjJdQ/qXGpR85GUny4iGJYseUonUjLpzXbj9O4wZ1U2RdoPkwnD5Bc1gnFZgAAAADvwGK1kMlqEYVnTfI6P1psj4rn0rrZ4f3ye0y1vF96Lr3f/vk6tlPffu37sJpFpCav83Gbed1iIf4nrUt/5/dLi7S+dsL9LU98vOCCC+iee+6hRYsW2UPCSkpK6LXXXqO///6b3n//fTWO06P4aul2e/4qTlSv16lXoZQnWzIjGyE+8okpi3EGnQ+1i3TeOdkaCPLTUnyYjtLyTZSaZ6SSCgsFGqpm+z6KYkCNyT0GAACNDruulvqBOZIp9cucC5Jd7Z6Iv6+GEiP0IhVGZqFJVK0OC3DuejmiS6DD9fCO86JJLfh6zuKjfJ2H+Oh5WIsLiAz+RBVlpG+PYjMAAABAvddNq5WMVjMZLbxYpEcW1MRzXmfhzOzwHpN9XRLe5HXpc9W3YbF/VvzNapK2Ydu29Lr0/kqzmUorysknWWvfR23bV4qFsuhnJcz/m0V8jI6OFhWur732WiouLiaDwUBvvvmmePzqq6+oXbt2LjkwT8VkMtNXS7bZQ8JuUFTJVFN85Ii9xhSbYTGOhTimU4xvjdA/T6JzjEF8X+5ajmVWUJ9Ef/vfkPMRANBc4iM7H5X3qHKLTZRXYhbrSVG+pLcVzPJEusQZ7Hl4OdTc2esYpxpJivQVeYt3nSyrcWPJlVw8qhtFhQVQdn4p/br2AGXmFVNMeJAq+wLNg985l1HoRTPJnH6CtBHx+G8AAADQYsaMFRYTlZkqKbuyhIyl+WQkSVirtJioUjza1s2Oz/k9/Fl+brSYqMImxkmfs73XXNt7lduu+Sj9XRqvgpaFzkdDWvvCJgeNe/bbmA9deOGFIrfjX3/9RWfOnKHIyEgRbh0TE+P6I/QwuBJmarZUCXPyiK7UNiZUtX2lFxjpqM0d06etP4X4O++w5MmeTGcPDe2T6RTrS2sPSWItuz0dxEeF6Mp3QAAAwD3Co5TzUXkDRJkaorMiZYQnwsXAVuwrbrT4KLsfWXzkFCT/HiuhcT2kytSuxlevE4Vn3vx+PRlNFpH78aHrxqiyL9B8+Gi0pEtASD0AAABH2C1XYWbxzkTlZqN45OfKdelvivfY1its75H+Jr1e7vAZ5Xtrec1iwn+HM9dy8iFfvp5rNKTz0drWtaT30YhHWZwTj+I9Vc/5M/a/+WirPZf+Xv/ntTXef/bPS5/RK94r/a3asYo88Uph0fbaWYRGd+Uqd1p83LRpkwizPu+88+jKK6+s82/OYDabqaioSOST1Okafkjl5eXk59e6chB+rig0c8vUwaru659kacLGjFSEnjVWfJQrQnsqHaLZ2cniIoc0OuYX81GKjypVTAUAgKp+pmoQwGHXHF5dW75HvmniybQN15Of3kdUvOZ+mfNgKm8GNYRRXQLph015Yn1tcrFq4iNz89TB9NYP60WeSr7e3z9jNGmrJ+wErQZOJcQLj1MBAAC0XlGQhboyXky2R3Ol7VG5VArxT7zXVPvflc/LTUYqt1Rtk8N2vVXEM2h05KvVkp4fbc/1Ghb1pOe8zuJYlchne02jEev8mvibTZyT1vk9SnGwdqFQfi//vepztue2bfNzLflQXnYOJcTGkV7bKA8eaCJOt/q6desoPT29VoGR/8bFaBoqPqamptInn3xCn332mXBQrlq1isaOHXvWzz399NP09ttvi7DvDh060LvvvityUbZ0jqfm0nJbPqikuDA6b4i6d87XHKwSH8f2cD70q9JkEW4RJiJQS5FBnv0j9dVpqF2kLx3PqqTcYrMIbYywfWflHQI4HwEAauOYW9bHLrhxHt6jtpsjLMq1CfPMPLwy/L3Z3bn3dDmVVVrpdJ5R9NPOwMXWfHU+VGmyiusiu0rVqlLcPj6cJg3rQss2HabTmYUi2uHi0d1V2RdQn9mzZ4ulsLCQQkPVi1QBAABvh6/NLOCVmiupxCQtpaYKKjHzo+25uZKKjRWUVZBLlKmnMovR9r5K+/tqExI9yRXI4pqfRk8GrU4IfFWPevLT6oTYZjWZKdg/gAwavRDdDFpJBJTFQIMQ4yRRUFp09r/z33y1OiEI8rYl4bB2QVEWAVsL7O4r1eiEAxA0Dy5Vk5KTk6lz584Nfv/cuXNFR/Pzzz/TiBEjGvQZFhrfeustWrp0KQ0dOlQUurn00ktp7969Tu27OfjiNynXI3PTlEGkURQxcTXlRgtttuV7jAzSUs8E5x2inGdLNt94emifDOe1ZPGROZFdqRAffWoPhwQAABVgkdGOCKGQ+iAuvFJaKf2tY4yv0y7A1lr1msVHhvtnZ8XHAF8NDe0YQOsOlVB6gYkOpVdQt3j1oiZuu2yoEB+ZTxdvgfgIAADAI92ELAQWm6qWIvG83PZYQSUK8VAWCGWxUBYZqwRGY6sp6sFuP3+b2Oev9bWv+4lHfTVRUHoUf7M/dxQP5c/4OXxG2qbj+7Vnzc3HAltmZqZIh6em1gCAquLjxx9/TM8//7xwG3L4yQ8//ODwdw63Lisro23bqgS2s/HYY4+Jx9OnTzf4Myw83nLLLTR69Gjx/PHHHxfuyY8++kgIkS2VikoTff37DrGu12no+gsHqLq/LcdKqcwodeDndg9q1ARVFuGY9tGeHdono6wam5JtpIHta8n5iLBrAICbw67lyN2UbEW/7KFVrqvTPrrK3Xkiq5LObYSRkK+DLD4y7H5UU3w8f0gn6pAQTsdT80T168OnsqlLYpRq+wMAAAAaCucILLILhNIji4RFdQiI/F4WCYuM5Q4iI4uHLREW71gM9NdJomDNxVeIfdJ7lK/ZPmcTEx0WneIzNqFQrQgKADyZBouPLPa98MILtGzZMiooKKCrr77a4e8hISE0bNgwatOmDalFdnY2HTt2jM455xyH18eMGUObN2+mlszitQcop6BUrF8ypqfqFTBXK0Kux3Rr3L54kqfMh+gNJEbqRWVwjnhUTvJRcAYA0Jxh17LzkW+KyHCla28gOlgnKlRzpWp2pHPex8aIj//3a4ZdfLxtnHpiIDsNOKfzfz/6Wzz/bPFWeuWulp8aBgAAQOsRDwsqy6jAWE6FYikTjwWKdel51Tq/zn9vKSHILOAF6HwpQOtLgfyo86VA+7qBArR6CuRHft32N1731+jJWFxKCZExFOzr57ANFgbdVbUXAKCi+NirVy+xcHg0F3rp169fjfcYjUaqrKwkX191JkRsIWaiohwnDWwrrk98rKioEIsM5+6Rbcnuquzz2aIt9vWbpgxUdb8cFvzPQamitk5LNLxTQIP3x+/jz1cazXTSlu8xPEBDIX4+bmur5oSLOsSF6Sg1z0QZhSYqKTeRv6/GIezaZDJ7RVs4g3zeoF3QPjh3XIPRpEha7uNDPla+XlXdFBF9VYjWa35zSZF62p9aIQrPpOVXUmyI1qk+Jz5UR51jfOlIZiXtOlVGOUWVFB6oXh7jayb1o+e/WEXllSaa98cOeuLGsRTo7z6xmNsF4VYAANByQ5ZZEMyrLBVLvngskx6NZZRXUUIZRflUecxKhaYKB3GRcxg2V6hxsM5AQXqD7dGPgnS+FKTjRwMF6w3SIz+3rQfZhEQhKNrEQ1lE5NyBjcEeVhyJsGIAWhtOj7x/++03UXCmNvGRi8Dw39QOf64+2TCZTPVan1966SV69tlna7yelZUlxFK1OXQqlzbsOSnWOyWEUZc4f7uQqgbHs82Umi/d1eqboKOSgmySgs0a1rbsbE0tsJLJIrVpXJDUyXsL0f5WSpUKo9KeY1nUPsLx3MrNy/eq9nDmvGExABNetA/OnaaTW1hmX+ceKDcni8pNRLm2zjwmSHrNW4jyq3I77j2eSz7xVqf7nEGJPnQkk2/QEf2+NY0m9FA3l/FFIzrRgjXJVFBSQV8s3khXj+9B7uyTExIS3LY/AADwRixWiwhBzjOygFhmExJtj0aFoCieV/2dhUR35jdkITBE7yeWUL2/XTx0EBN1flUCohAWZQFREhZZPESoMQCgKbj0tj87Iv39/Ukt5IE0V9RWwkJQfYNszi15//33OzgfExMTKTo6msLCwkhtXvq2yvV462XDKDY2VtX9/XYwx74+oW8ExcSEOzVh4QtLWm4gZ/IUr3VLDKaYmADyFrpXlNOu1AKxXmAKpJiYINKzhdRGcEiIcNuCmucN/6YgPtYE7VM3aJs60BU7OB/jYmOE849I6ps6xwdQTEyw13RDvfVG+udYrljPrjBQTEyI033O5IGlNH/bKbG+M01L156rbj9+9/RzhPjIzF+ZTHddPcZtEzdvccQCAICrHYksEOZUlEhLpe2xooRy5fXKEsqtKKHsihLxXosbRER2Dobo/YV4GGZ7lBZpPVTxXLnOjywstqaKxAAAz6XB4uPWrVtp9erVtGbNGioqKqrhbuSCM59//jm9+uqrLj1ALmLDzsbg4GAhFPbu3ZtWrFhB06ZNsw+wV65cSbfddlud2zAYDGKpDk9Y1BZK8orK6Pu/d4v1IH9fun7yANX3+U9ylc/x3O7BTu+PJ0cpOVWW/o4xfl4lKHWIrjpXTuYabedJ1YSR0415U3s4c9644zfVWkH7oG2cwSHjIxec0WrpZE5VnqakKINX/dbahPuSQedDFSYrncg2ijZx9jc1ICmQQvw1VFhmofWHS8hs9SG9Vj0xcHCPtjS4RxvaeuAM7T6STlsPptKwXomq7Q8AAIAj7I5nl2FWRTFllheJR6WAqBQXeZ1diWo5EjlsmcXAcN8ACvP1lx71/tWeS+thOj8yFZVSx7i2FOrrD/EQAOBd4uP+/ftp3rx5IlSZczvm5+fXKDgza9YsuyjYEDjkubS01J6DkStp83b9/PzEwtx99920adMm2rt3r7269Q033CCKznD+yf/9738in+Mdd9xBLZG5S7dTabkk5F17QX8KDVKvwiaTX2qmnSll9iIxjSlIwBfq07nSMXOS/6gg77pbFhqgpbAArWjLUzlGUfhBq5jcKqvQAgCA2gVnfGzJ01NseXi9qdiMDN8Aahepp8MZlVRcbqGCMuf7YZ3Wh0Z3DaLfdxVSUbmFdqaU0pCO7PJXj1svGSLER+aTX/6F+AgAAC6gzGyk7PJiyqwooqzyYsqqKKJM2yM/z6wopiyb2KhGgRWufBzpG0iRhgBH0dA3oFZRkRcWHrUNLIYi8hoaM8XnvOlGIwDAs2mw+Dhz5kyx/PTTT5SXl1ev07Ch/Pzzz3TnnXeK9dDQULruuuvE+qOPPioWJiAgQAibMjNmzBBuyFdeeUWEX/fp00c4H+Pj46mlwYVJPv7lX/vz2y8fqvo+1x0qFs48ubpnYyit5EXaSHyYzivze3DVaxYfjWYrZRWayEfhfDSZ3ZejBQDgnSgrOvO8g8XItDzpplBkkFbcGPI24sMk8ZFJLzBRRCPui/F1kcVHueq12uLjFeN60WMf/ClyeP6yZj+9NHsSxYQ37toMAACeTrGxgtLLC6WlTHqsTVwsNJW7PKyZxcQIQ6BNVAykCNtjlGJd/hsXTAEAAKByzkdnnI1n45prrhFLfbzzzjs1XrvpppvE0tJZsj6ZTmVI+bkmDe9CXRIdq3SrweoDVXnCxnRr3AQnW1GdJi5UT95Im3A97TklDWzO5BlJqxAfjXA+AgBUxqzI2cfOx8xCE5ksVf2TNxIXVjVkyWDxMcL5bbDzkbtz1nZXHSimBybHqHqDzc+gp1kXDaQ3v19PlUYzffnbNnpk5rmq7Q8AAFpqYRbOkagUFVNL8+lEXiblHzFSRoX0epGJcxu7BhYKo/2CKMYQLB6j+dEQJImI8mITHP213nldBQCAFl9whgvLfPrpp7Rz507Kzc0VYboyl156qQiLBkQfLNhkb4Y7rximepOUGy20+mCRWOe8VgPbN65ITE5p7ZM9b0I5uWfxURnyAPERAODesGsf0Q/V1j95E8qbYSw+9miE+MgpNQa1D6Atx0vpRHYlHc6ooK5x6qZDuWXqYHp7/gbhZuVoiDnTR5HB1zuvrQAAz4PngVzJ+XRpHp0pLaDTZflCWDxTViBExrSyApFv0WRtetoirrzMAmKMnyQkRvsFU4x4lMTFGNsjC4t6FFkBAIAWhdOjX7PZLPItcp5FDonmx06dOtGff/4pCsJAeJTYdTiNNuw+Kda7JUXR+MGdyB0h12W2cOnzewU3OpF+tqLIqjc7H2VSqzkfTbL9CAAAVEKZW5bzHUJ8JIoO1tldi+mFjc/hNbFPsBAfmT/3FKkuPibFh9PUc3rQojX7KTOvhH5euVfkgAYAgNaAyWIWIqIsLJ5hkbGsgE6X5lOqeF5ApeaqnMSNzaEY5xciLf7SY7x/CMWK19i5KImNCHcGAAAvEh///vtvUSRm165d9NZbb1F6erqofH3mzBkaNmwYJSaikiPzwc9Vrsc7Lh/mlryJy3ZLrkdmYu+qPJnOkm1zPvIhxwR7pzvD31dDEYFayi0xU2q+yaHatdKRBAAAamBRRBRoqjkfE7zU+cgFY1iAzCg0UXahiRqbAWNC7xB68bcM4ib+c08h3XV+lOrX6LumDRfiI/PeTxvpmkn9vDKfMgCgZYZEc8hzSmkenSzJpZSSXDpZmieERRYY+W+WJlSAjvANsImJoXZhkZdYv2DyLTVSz4QOFG4IQJ8IAAAejtPK0pEjR2js2LGk0+nI19dXCJFMmzZtRMEYdkAOGjSIvJmM3GL6aaVUnTssyI9mTOzn9pDr4Z0bl0SfhbVcW85HrnKt13nv5Ign+Cw+ctEZq1WR8xHORwCAm8Ou0/Ml8ZFvivDNEW+FU4Gw+Mh1v/LKiBpTao4FTA693nq8lI5nuSf0elivRBrco42ofL3naAb9s/MEnTugg6r7BAAAmRJTBaWUSOLiydIqgZEfOVy60mJuVGMZNDpqGxBGbfzDqI14DKW2AeGU4B8qnrPIaNDq6q7onJkpKkLjZgwAAHg+usbke/T397cLjgsXLrT/rbi4WIRieztf/LZVJJZnbrh4IAX6+7o15Pq8no0Puc4pNotJnTeHXCtDr/eelorOKM2OqHYNAFAbi8LWx5My2yXFa/M9yvB1aReV1yiO5iwTewcL8dFdodf8fzj7yuF04/MLxPP3f9oI8bEV8P7774uFUw4B0BoqRR8vyaZjxTl0rJgfs20iY64o9tJY12KVsBgmhEYWFvmRRUb+O4RDAAAADaFJMbUTJkygm2++mWbOnEnh4eH02Wef0YoVK8ibqTSa6LPFW8U6h+redulQt+yXJ08yk/o0PuSak/jLxIZ6Z8i1jHKSb1Y6H1HtGgCgMg7pHRThud4uPiqvSzlNFB9fWiKFXv/lptDrS8/tSU989DedySqkPzYeoiOnc6hz20hV9wmaxuzZs8VSWFhIoaGhaE7Q7FRaTHSyJM8uLkpLjhAdM8qr5gINhas8twuMoKSAcPHYLiCCkvgxMFyIjcixCAAAwFU4rS5de+21ZDRK4V8hISFCbHz11Vfp0KFD9OWXX9KoUaPIm/ll9X4Rds1MGd2d2sWFuSXketWBpodcM+kK8TEuzLsnucq8aiaF6QE5HwEA7sz5SKQQHyO8u1+OU4iPTXE+Rofo7aHXx9wUeq3Xaen2y4fSkx8vF6In54Z+Y85Fqu4TANA6ya8so0NFGXSoKJMOF2bR0eIsOl6cQ6dK85zOv8ihz0JQtAmMvC49j6AoQyCciwAAAFqm+Bgf75hhifM7zp8/35XH1GqxWq30zo8b7M/vvHK4W/brqpBrJqtI4XwM8W7nY6BBI8TcwjKLPRSdMcH5CABwY7Vrpfjo7Y70sAAtGfQ+VGGsyk/cWkKvmRsuHkQvzV1DpeVGmrdsJz1583gKD5ZS2QAAvI+8ylI6VJhpExqz6FBhBh0uyqTMCsnI0FBYROwYFEUdAqPEY8egSPHIYiO7GwEAAIDmplGzmG+++YZ69epFAwcOtL92+PBhUQn7zjvvJG9l5dajtOtwulgf2C2BRvZp16pCrpnsIsnix/olFzbwdiKDdFRYVklWxeQfBWcAAM0Rdu2r86Egg/cWm2E4NDoqSCeqfxdWSDl4G1t/pzlCr1lovO6C/vTJoi1CgPxqyTa6b8ZoVfcJAGgZTsbk4kwhLgo3IwuNRRlO5WIM1PlSR5u42MEmLkqCYySF+uImBgAAAA8TH5OTk0WY9Y4dOxxe79KlC9100000YMAAGjFiBHkjr3+3zr5+/zWj3RLGIKpcH5DujrJLb1inwCaF+eUUS87HiCCtyFnp7bAAezxLmvDKwPkIAFAbs6Wm8zEySIvwOHb4BGuF+MjklpgpLkzrktDrIxkV1MUN7keOivh08RYhen608F+6a9oIEZINAGj9WKwWOlGSS/sL0mh/QTrtK0ijvXlnKKOy4U5GLuLSNTiWuoZEi8cuwTHUKSiKYv2CcQ0AAADgPeLj6tWrhbio09X86Lhx40QOSG8UH7fsP03/7Dgh1rskRop8j+5gzcFiKq202EOu2RnTWApLLWSyVDn+QFU7aHyqrDXI+QgAUBuLwvko3/xAvyzBzkeZ7GITxYX5uiT0esnOQrrvAvXFRy4yM3lEV/p9wyFRfGbRmv007bw+qu8XAOBaSkwVdKAgnfYXSiIji40HC9OpzCzdHGlIqLQkLrLIGENdQ2LFY6Sh8UYCAAAAoKXitMIUGBhIx44dq/VvR44cof79+5M38sb3Va7HOdNHkVbrntC4Rdvy7esX929aJUaexCmdJUByGjFKEyucjwAAd+Z8lMVHpMKQr0+Kite2VCGN5YK+IfTq0gxx4+23HQV0z8Ro0rrB9T972gghPjLvzN9AV47vDUcTAC2YMlOlEBh35Z+h3flnaE9+qgidtjag+Eug1pd6hsZTz9A46h4iORlZZIyAyAgAAMCLcFp8nDhxIt1222302muv0b333kt6vZ4sFgt98cUX9PPPP9OTTz5J3sbBlCz6be1BsR4fFUzTJ/R1y365OMz6wyX2CqBDOwY0aXvZimIzsujm7XD4OeOjmIxyjjEAAFATo6KfgfPRkUjFzbHs4qaJj+wmHd0tSKQvySg00eajJTSySxCpzZj+7alflziRJ3rHoTRas+M4jR3YUfX9AgDOTrnZKFyMLDLKCxeFaUiV6aSACOoRGieExp4h8dQ9OJYMxZUUGxtLGo135+wFAADg3TgtPsbExNDcuXNp1qxZ9NRTT1FCQgJlZGRQeXk5vfvuu9SjRw/yNt76fr19/e5pI8jg656Q5aU7C0g2x0wdGNrkHI1ysZnqYW3eTG1h13A+AgDUxmg21yI+4qZQ9etTjuKmWWO5ZGCoPXfyom0FbhEf+f+UoyRufH6BfRwB8REA92O1WimlNJe25pyk7XknaVvuKUouzCCTVZl3tyZ6Hy31CI2l3qEJ1Eu4GuOFqzFY75i6gQ0amSWZKn8LAAAAoOXTKIVp2rRpNGbMGFqyZAmlp6dTVFQUTZ48mdq1c09155bE6cwC+uHv3WI9PNiPbpwyyG2DJZ4kyVwyoGkh19XDrpXOEm/G31dD/r4+Ds5H5HwEAKiN0mEN52PNfjnQ4EMlFdYmOx+Zsd2DKNRfSwVlZlqxv4iKy80U5Kf+NfCyc3vSs5+toBNp+bR8y1HacySd+nSOU32/AHgznI9xd94Z2pp7krbnnhSPOZX1V5zW+miEsNg3rA31DUsQj91D4sigxY16AAAAoKE0+qrJ4QM333yzXQhzR2Xnlsi7P260O+Fuu2woBQcY3LLfA6nldDijQqz3b+dP7aObvl857FqnIQrxQ2iI0v2osVWbrZ6LDQAA1MAkV/+yiY+cRjjEH/2y0v1YUmGkonILVRgtZNA3vm18dRq6sF8Ifb8pj8qNVvpzTxFdMSSM1Ean09LdV42kB97+XTx/84f19MUTV6i+XwC8ibSyAtqSkyJExm25J0XexvpcjTze6xISQ/3D2lAfITa2EWHU/lq9W48bAAAA8Grxcd26dRQcHEz9+vUTz4uKiujGG2+kpUuXCjHyjTfeoMsvv5y8hZyCUvpyyTax7m/Q0e2XD3PbvhdvV7geBzXd9chuvrwSyUES5l/ltAFSqKNDzkdFFVoAAFCDymrORy4209TUGp7WL6fkSBVlc4rNlBCuaXLoNYuPzKLt+W4RH5nrJ/en//tyFeUWltGClXvp6ZvHU1J8uFv2DYAnklqaTxuyj9OmnOO0KfsEnSjJqff9oXp/GhiRSIMj2tGgiHbUP6wtBendYyQAAAAAvIkGi49Go5FuuukmWrlypf21Z555hv7++2967LHH6OTJk3TNNddQSkqKECK9gY9/+ZdKy6XJz6yLBlJ0WKBb9ltpstLSXYVi3VfnQxf0CWnyNll4lDW1cP8mb86jiAjUOUz64XwEALjb+RiBPLx1VrzmlCEJ4U1zJfVu60edYnzpaGYlbT9RRinZlZQU5UtqE+DnK25cvvjVanET8N2fNtJr91yo+n4B8BROl+bRRhYbs4+Lx5Ol0k2EuuAq00qxsVNQlENebwAAAAA0s/i4evVq6tSpE7Vt29b+2g8//EDPP/883XPPPeI553/87bff6JZbbiFPp7i0gj5auFmsazU+dM9VI92277XJxXaX4nk9gynEX+vSfI/sfATVnI+KgSlyPgIA1MZkUYiPGg2KzVRDWXzHFUVnWOC9ZGAYvbFMKgzx644CuntCNLmD/1w2lN76Yb24mTl36XZ6dOa5FOWmm5kAtDYKjeW0IesYrc06Qmsyj9TrbPTVaGlAeCINi2xPQyKTxHqYLwa5AAAAQIsWHw8fPizER5njx49TamoqXXhh1R36oUOH0qlTp8gb4AkCh0kxV53fh9rFuSdESw4JU4aKuYKsQoiP9eZ8VISho9o1AMDdBWfYgQ2qiFKIj5lFTS86w0wZEEJv/ZkpogAWb8+nO8+LEjcX1SYyNIBmXjiAPlr4L5VVmOjTxVvosVljVd8vAK0Bk8VMO/JO0z+ZR4TgyOvmOnI2GjQ6ITAOj2pPI6I6CocjcjUCAAAALYMGz2YiIyPpyJEj9udr1qyh6OhoB0EyPz+fEhMTydOpNJronR832p/fN2O02/adlm+k1QeKxXpMiI5GdnGNOyKjQFHpGoYLBwIMqHYNAHAvxmph14EGhAVWD7tmWZAl2owCKf1JU4kJ0dOoLoG09lAJpeWbaN2hYjq3ezC5g7unjaBPF20RznoWIe+9eqQIyQbAG8muKKYV6cm0PD2Z1mUdoSKTVGCxOjofjQidHhXdUYiNA8Lbkh8KwwAAAACtW3wcO3asyPn40ksvUZ8+fejFF1+kqVOnOhQm2b59u1cUnPlx+R46kyXlXLxoVDfq2SHGbfv+6d88e27GaUPCXObKSLeJj7y1iACXbNJj4DbWwvkIAHAjSoe1xlbtGlSh0/pQeABRbilRZqFJiHauuB5eNSxciI/MD5vy3CY+cpGZK8b3FuMLLmb3zR87RTg2AN6A1WqlA4Xp9Hf6QSE47sw7TVZxa6EmnYOi6ZyYzjQmupMQHFEcBgAAAPAw8ZGLyHz00Ud0++23U2lpKfXs2ZOee+45+9/37NkjnI+jR7vPBdgcWCwWeuP79fbn91/jvu/LhWZ+3iKFXOs0RFcOdU2ot8VipYxCyTkSEaQlvbb2cBZvhYVHZc5Hbi8AAFATk6Kf8eEbIKh0XYOoQEl8ZJ02u8hEsaFNKzrDnNs9iOLDdML5yCLkqdxKSoxwjwNxztUjhfjIvDN/A908ZRDpdE3P6QwkKioqqKxMSpfDBAQEkK8v3KXNRYXZROuyjtKKDElwTC0rqPV94b4BNCa6M50T00k8JgS4L80RAAAAAFyHU0mkrr/+epoxYwZlZGRQQkKCg+uxQ4cOIhTb01m6PpkOncwW66P6JdGwXu4LM1++r5Byim2FZnoFixAxV5BTYiaTLWVWXCifEpUu2a6nwI4jh2rXikIQAACgdrVrDcH5WBsiRUhWVeoQV4iPLPJePSyc3vozi6xWovmb8+jBybHkDvp2iafzhnSiFVuOUkp6Pi1cvY+uOr+vW/btDfzvf/8TUTuy4Pjuu++KcS1wH+VmI63NPEJLUvfS32kHqdBUXuv7uofE0oS47nR+XHfqH96WtKhGDQAAALR6nM5gr9PpqE2bNjVeDwoKIm8IC3n9u3X25w+40fUoh4DJTB8e7rLtpudX5cuKhfhY62SUnUcyqHYNAHBn2DWcj3U7H2XSCozUl1xTxfbywWH0/vJsMpqttHBLAd11fjT56d0T987RFCw+MjzemHZeH4cbvaBpvPLKK/Sf//wHjkc3C45rMg/TkjN7RVh1cS35G7kq9ciojkJsPD+uG7UNcN0YFwAAAAAtA5TPdIJ/dp6grQfOiPXenWJpwtDO5C4OpZfTthNSuFCnGF8a0sF1iRnlfI9VzkdQw/momPyZFaIAAACoHnYtcj5CgKpOZEDtRdOaSmSQjib1CaYlOwupoMxMf+4ppEsGuifUc0z/9jSkRxvacuAM7TuWSX9uOkwXjOhK3kBlZSWtWLFC3OSeMGFCre9JS0sT+cXDwsJo+PDhpNVWhaVzSiDeRnUMBgP5+/uTn58fPf/88/TQQw9R//79ad68edS5s/vGcd5EpcVEqzMO069n9tDyOgTHYJ2BJsb3oMnxvURIdaDO0CzHCgAAAAD3AKXJCd5QuB7ZneBON0J116Mr962sFBoboiNLVUokYHM+KsOulaIAAACoHnaNgjO1EuJHZND5UIXJ6nATzRXwdZbFR+b7jXluEx/52s7jixlPzre7H71BfHz00UeFGMiwsLh3794a73nvvffo4YcfpsGDB1NKSgoFBwfTX3/9JdIAMXfffTctWLCgxue4WOIbb7xBDz74oFhMJhO98MIL4v1//PGHG76dd8DRQdtzT9GCUzuE6JhXWVrjPaF6P5oY14MubtObRkd3JoMW0xAAAADAW8BVv4HsPJRqD4VqHx9Gl5/bk9xFcbmZft0hJeIO8NXQ1AGhLt2+PGnTa6WCM9kQH2s4H5UFZ6wQHwEAKqNM78D9jw7Ox1qFOr5hdjLXSHklZio3WlwWHt2/nT91izdQcloF7TldTntPl1Hvtq4J6z4bF43qRt2Soig5JZs27jlJG3an0Mi+SeTJsODIjkYWCZcsWVLj7wcOHKA5c+bQt99+S1dffTWVl5fTmDFjHATHzz//XCxng52VN998M3311VeqfBdv40xpPs09vYX+2nOYjpXk1Ph7qN6fLojvQRcm9BYOR18Nph4AAACAN4IRQANRVri+d/oot1agXLi1gMoqpYnolAEhFOTnun1XmiyUaytiwwVslOHFoGqCq9Mi5yMAwH0Yq+V81Lgn5WCrg/MUs/goh14nRfm6rN+fMTycnvklXTyftz6XXr66Zr5rNdBoNHT/jNH0n5cX2aMuPF18ZOdjfXz33XcUHx9PV111lXjOIdR33XWXEBELCgooNPTsN2WLi4uF67GwsFCEXw8ZMqTeyti8yPBnGIvFIhZvx2gx04qMZPo+ZSutzjxCVnKMCDFodEJwvKxtfxod3dFBcPS29uPvy65Qb/veDQFtg7bBeYPfFfqcltMf8/hTbSA+NoAjp3No0Zr9Yj0mPJCuv6A/uQtOeD93XdWd5GtGRLh0+2n5JvuQEfke60ar+DGaMIAEALix4IwUdo0bQ7WhvG6l5hldJj4yF/UPpTeXZYm8j3/sLqR7JsVQQljTK2o3hGnn9abnv1hJpzMLadmmw7T3aDr17hRH3sru3bupTx/H4jt9+/YVYiK7Ijn/49mYMmUK7dixg0JCQuicc84RYdx18dJLL9Gzzz5b4/WsrKxa80p6C6fLC2hx5j76NesA5RhrhlUPCmlDF0V1p/ERnSlIJ/0W87NzydsndCyQswDpjoldawJtg7bBeYPfFfqcltMfy2ls1ATiYwN4e/4GsthC4GZfOZz8DO6ZfDB/7Cq0h0WP7RFEnWNdm5D7RHbVILpdpOsmbZ6G0vkonwsAAKAWZrNjwRkd5qy10jZC73A9G9FFUQK7iXCak2tGhNOHK7OJU3B+vS6XHr04ltyBr15H91w9kh5+d5k9+uKLJ64gb4XFmzZtHJ2nkZGR4jE/P79B21i1alWD9/fYY4/R/fff7+B8TExMpOjoaBEi7k2waLY26yh9cWwjrcw8VOPvbfzD6OLIbnR915HULsi1N8g9ZULHfTifOxAf0TY4b/CbQp+D/rgl4i53PsTHs5CWXUjfLtsp1kMCDXTLJXWH6agx4PvinyrX401jpIG2KzmRVSU+to92n6ja2tAp7lZDfAQAqI3Z4hh2Dedj7cSH6chX50OVJqsQH/m66cqCbCw+8nWYi9r8vCWPbh8fRWEB7km7MuvCgfTy3DWUW1hGP6/cS0/eNI46JHinuMMVq7madfUwajkEW4398VIdFo+8RUAqNVXSz6d20BdHN9KR4iyHv+l8NDQhrgdd034wjY7qSDlZ2RQTFOE1beMs3Cd507njDGgbtA3OG/yu0Od4D7gKnoX3f95ElUYpJ+ItUwdTaJDrB7l1se5QCR3OqLAnvx+Y5Npk9xarNFljAg0aig6GFl0XjjkfkbcHAKAuJoXzUeOjgfhYByzKtouUbpwVlllE4RlXEhGko8sGS043zr08f3MeuYtAf1+688rh9pteHIXhrXTs2JFOnjzp8Jr8nP8GXEdGeSG9sHcZDfnzFXp8168OwiO7HB/tOZH+nfQwfTrsGhoX25W0ioJ8AAAAAAB1gRFDPeQVldFni7eKdYNea58EuIvPq7keXenmkJPzlxulCW77KL3Lt+9J6BQxj3A+AgDcmfOR+2YtrtZ10iG6KmXIcUUqEVdxwzkRJKfc/HZDrqiq7S5uu3QIBflL3++b33dQRq7k9vM2Jk+eLPI1Hj161P7ajz/+SD179qR27dqptt/3339f7KO+4jSeQkpJLj26cxGN+Os1+ujIWiowltv/NiyyPX08ZAatn3A/3dX1XIrxC27WYwUAAABA6wNWt3r4bPEWKi6TJjLXXtCf4iLdN9jafaqMthwrtU+sxvUIUjfk2oVJ+j0RPZyPAAA3onRYaxB2XS/K6xdf1wa1D3Dp/0VihC9N6hMiis7kFJvp1+0FdNWwcHIHESEBdNOUQfTOjxupwmimD37eRM/edj55GitXrqTc3FxKTk4W+RV//vln8frUqVPJ19dXFIs5//zz6aKLLqJ7771XvO/rr7+mJUuWqHpcs2fPFgsfU0MqardGDhZm0PuH1tDi07vJoqha7avR0qVt+9FNHUdQ7zD1k9ADAAAAwLOB+FgHZRVGEXItT/zmTB/lzv8Xh1yPN54TKY7B1SiLzbRXOEdATXQK2xGcjwAAtTErClsJ5yOM6fWKg9xFs1n0uOKmmiu5cUyEEB+ZL9fm0OWDwxzScajJXdNG0IcLN5PRZKFPF2+h+68Z7dYUMO7gzz//FK5GrVZLQ4cOpR9++EG8PmnSJCE+8m+AhcaPP/6Y1q9fL4q+bNy4kQYPHtzch95qOVSYSf87sJz+SNvn8HqQzkDXdxhKt3YaBYcjAAAAAFwGxMc6+OaPHZSdLzkPLx/bizq2cV+S9+S0cvp7b5FYjwrW0pQBIS7fByfllydpnKw/PgzFZhocdm1FtWsAgLqYFWHXWlGsAOpjXeh1PqLqdUq2UTgTC8vMFOLv2qIwvdr40/BOAbTpaCmdzDHS0l0FdMlA91Q9TogOoWsn9aevlm6nwpIK+vzXrUKA9CReeeWVs76HRci7775bLKDxnCrJozcOrqAFp3Y6OB3DfQPolk4jaVaH4RTm69oc4wAAAAAAyCJVCyaTmd7+oSqx+/0z3Ot6fH95VXLvm8dEka9C+HIVmYUmKiq32EPWUEm1fnwdnI8oOAMAcJ/zUYuEj07lfTyaKRVqczVc6VrmwxXZZFQUBVKbe6ePJDkt83s/bRTRGQA4Q1Z5MT25ewmNWf4m/XRqh114jDEE0TO9L6TNEx+ie7uNg/AIAAAAAFWA+FgLC1bto5T0fLE+YWhn6tslntzFvjNltGK/lFA+JkRHVw9Tx1lxOKMqNK1zLEKuz4ZeIQArRQEAAFC74IwWMddnpUuswb5+OF2d0OshHQOF+5E5lWukxdulcYI76JIYRZeM6SnWM/NK6NtlO922b2/GEwrOlJuN9HbyKhr19+v05bGNZLRKFeFD9X70WM9JtH7CA3RL51EUoMNYEAAAAADqAfGxlnDk179bZ3/u7tCm9/6ucj3eNjaSDHp1/osOp1c5Q7rEVU3awNkLziDnIwBAbZT9jFaDS/XZaBfpK1KIMIczKsS1XA3unhBtX/9oZTZVmtznhH9AMR5564f1IkoDqAsXm9m/fz9t2bKl1TU1/wb+TjtA5614R+R2LDVLory/Vk93dz2XNkx4kGZ3HUP+EB0BAAAA4AZazIymoaGsJpOJysvLHZbKSte5HP7cdJj2H88U60N7tqXR/ZLIXexMKaV/kkvEenyYjq4Yoo7r0WTmfI+S+Bjsp6HYEKT+dMb5CPERAODWsGvkezwrXPxFDr0uLrdQeoFJlf+X/kkBNKZboFhPyzfRgi3ucz8O6JZA4wd3FOsn0vJp4Zr9bts3aF0cK86mmZu+phs3z6OU0lzxmtZHQ7M6DBNOx0d6TqRQ5HUEAAAAgDeJjy+99BLFxsaSXq+nPn360MqVK+t9/1133UWBgYGi0qG8jBgxwmXHU931yBUW3cV7y7MdckupkeuRScmuJKO5yvXozu/oGTkfEXYNAHBfwRl3VVX2rNBrdfI+Mncp3I+frM6hcqMb3Y/XnmNff+O7dao5PEHrpMxspJf3/0Xnr3yHVmUcsr8+IqoDLRs7m/6v31RUsAYAAACA94mPH330Eb344ov07bffUkFBAV1++eV08cUX0/Hjx+v93GWXXebgfNy2bZtLjmfD7hTauOekWO/ePpouHNmV3MW/x0po4xHJ9ZgYoVe1iiaHpNU2WQNncz5KAoDFioIzAAB1QcEZ51GmEFFe51wNV74+r2eQvXjbD5vyyF2M6d+eBvdoI9b3Hs2gvzYfdtu+QctmW+5JmrTqPXrv0BqqtEh3mOP9Q+mDwVfTj6Nuph6hcc19iAAAAADwYppVfHzjjTfo5ptvpvPPP5+CgoLomWeeoaioKCFKng01Kg6zi0BZ4Vrjpjxb7KR77Xcp1Ju547wohxyDriY5rWpShmIzDUMUfLA5ROF8BACojVlxjYPzsWFEB2spNEC6bp/IqqQKFR2JSvfjx6uyKb/UPfkXOVJBmftRGa0BvLPgDBeUeWHvMrrsn09EuDXjq9GKvI5rzptDU9v2RYQLAAAAALxXfMzJyaHDhw/Tueee6zCo5ucbN26s97O///47GQwGioiIoKlTp4rtNJW9R9Np2SZpO21jQmjaeX3IXfy6o4D2nSkX693iDXRx/1DV9pVbbLLnwmoboacgP61q+/IkfBXNZEGYGwDAjc5HHQrONAgeQ3SP9xPrXAdGTfdj1zg/mjpAulYXllnowxVVxeLU5qJR3ahbUpRY37D7pD1iA3hfwZkdeado8ur36aMja8lCUp/RP7wt/TnuLpHXERWsAQAAANBSaLZKIxkZGeIxOrrKPcDExMTQv//+W+fnunfvTosXL6YxY8ZQamoq3XPPPUKw3LdvH4WHh9f6mYqKCrHIFBYW2t2TsoPyrR822P9+91UjRIJ/NdyV1SmtsNBbf1a5Hh++MIZ8yKqau27fmTL7eo94Q43vyM85h5Q7vntrgs8Hntiy7mhVnDdAAudN/aB90DZNzfmIPqdhv6nu8b60+WipWN93upx6JqiXWuSeCZH0995CKjNa6ftNeTRtaCh1jHZPKpM500fRHa8sFuuvf7uWfnxxhsPfuV3cFb0B3I/RYqY3D64UIday6Mhux/u7n0e3dx5NOg1uLAMAAPBszGYztWnThhYuXEgjR45s7sMBDaDZyxzXJn7VVwBlzpw59vUOHTqIfJFxcXE0f/58uv322+ssavPss8/WeD0rK0tUyk7LKaafV+4Vr4UFGWjy4LaUmVklCKrJlxvLKKtICtca2VFP7YOKKTOzWLX97T5RJWrG+vG+pDyTyvbn/Js8qcPEpQpzpdkeds3hkO46P1oLOG/QPjh3XEtFpdG+riEr+pwG9jlBZBVOde6yD6aWU3pGOWlUKqrGW71qkIHmbion1opfXHSGXrxEygWpNuf2iaH4yCAxfuGojbVbD1C3dpEO7ZOQkOCWYwHuJbU0n+7cOp+25lY5XvuGJdCbA6+kbiGx+O8AAAAPgGtgcG2MzZs3C72if//+dPfdd9OoUaMa9PkuXbqI2hhr1qyhzp07219/6qmnaNeuXcLM5SwzZsygVatW0ccff0yXXHIJNTc8BmRDG7cPaB00m/gYHx8vHquLOPycxcSGEhISQm3btqWjR4/W+Z7HHnuM7r//fgfnY2JionBdcrXsd3/ZRSaby+TWS4dS+3ZSMne1Scs30k/b88W6Tkv0+CVtKSbKV7X9lVZaKLVQCg2LDNJS9/aRNYReWfzltoH4WEVwUD75CE9qlUMX4LxpKPhdoW2cxUfhXDIY9OhznPhNdYvPpz2nK6jcRFTqE04dY9S7rs6eZKFlB45TRoGJNp8w0pGCQBrZJZDcwb3TR9Gj7/8p1uf+dZA+e/wy+9/glPVMVqQfpHu3/Uz5RimKReejofu7j6c7u4yB2xEAADyE3NxcOuecc2jYsGH0xRdfCL2CBcPHH39c1Mbo0aPHWbfBohxHfvJnfvzxRwcdhNPfOct7770nok55u2VlVZGUALQK8ZFDpDmJN6vnV155pX2wzM9vvPFG+/tMJpN43dfXt84f58mTJ4UAWRecH5KX6vCEpbiskr5csl0899Vr6fbLh7lNdHv7r2yqMEly1rUjIqhDjJSrSi0OpZeTHM3dM8GPtNraw3J4QsdtAPGxCr3OseAM2gbnjbPgd4W2cQaleMQ5H9HnNPw31bONvxAfmYNpldQ5Tr1ra6Cfhu6fFEOP/Jgqnv/vjyxa0DnILUWCbrx4EL36zT+UW1hGC1bupaduHk/t42tPPwMaX3CGFw7tak4sVgu9nbyaXj+4wv5aW/8w+mDIdBoYkdisxwYAAMC1sB5y5swZ+vLLL4XRimH34hVXXOHUzcVbbrmFPvnkE5HSbujQoY0+HhY+OZJ07dq11KlTp7O+v1evXkLg5PEZG76mTZtG9913n117YAG0a9eu9M4774jo1d27dwvz2XPPPUfjxo2zb+fEiRPiczt37qT27duLdU65x+2ifJ+SkpISev7552nJkiVkNBpp0KBB9H//938iYlaGBdyvvvpK6Eh9+/YV++3du3ej2wc0nGZNCPTII48INX/BggVCSWd3YnFxMd1xxx3293Ao9cCBA8U6q/cXXngh/fPPP+KE3rFjhxAuWci87rrrGnUMc5dup8ISaZJyzcR+FBvhnpCpTUdLaOkuKfdkWICWbh8vJY9Xkz2npKI2TI826gqdnoZeyz8VH7vFGwAA3FVwRq9D7j5n4MJtGpv2t/d0mepFwi7sF0J9E6Vr6pGMCpq3IZfcQaC/L91xxTD7+fL2/Krc1cBzCs4UGcvp1s3fOQiPk+J70LJxd0F4BAAAD8TPz88u+lXHmZvRLLyx8Pfwww83+lhYzJs+fbpwPjY0nQuLpywY8rWThb0PPviAXnvtNfvfWUBlByVrP7NmzaJly5bRiBEj6NJLLxWCIMM3/SZPniz0n0WLFokUevw9UlJSHGp5KOE5+sUXXyxqgbC4+Ntvv4ljHj16tEjVw/z999/CDfr000+LdTa9Pfnkk41uH9CKcj7OnDlTiI0cFs0nYJ8+fcRJoHQx6vV6u2uRHx988EF64YUXhPDIoiNbkr/++muKjKzKddRQjCYzvf/zJvvzu64aQe6g3GihZ39Jsz+/d1I0hfirmxy8pMJCh9KlH2qIv4aSovTU3IhiAVa+o8/rzn+eJ5camyGxvjyhrkCvlQrOMBAfAQDuLDjD/Y/acL/G/bDcJzsLd49VfbL6x1sf/r4a6hpnoINpFVRQZqETWZXUMUa9QjAajQ89NiWOrvnwhGjD9/7Oogm9g6lNuHrh3jL/uWwovfX9eiopN9I3v++gR2ee67abqEB9zpTm08yNcym5SEpRxOlfHu05ke7sck6z/84AAKC1ctV7xym7yOT2/UYF6+jHu6oceHUxadIksbC7j4UzFubGjh0rntcVDVoX7PrjMO2lS5fSRRdd5PQx33XXXSLP5GWXXSZySDYEZXoyLgjDwiE7J9l4poSFyalTp4p1zm/59ttvC8GSvzsLh+x8XLdunV3n4UiE888/v879soi5fft2oSvJAi6LnuyC/Pnnn4XQePDgQeHMlNuCHZEsWAIvKThz5513iqUuPvzwQ4fn48ePF4sr+G3dQTqdKbkPJ4/oSt2THCtvq8XHq7LpZI5UTGBAkj9dOThM9X3uPcXuD2m9Xzt/VRLw8+SVq34WV1iouNxMpZVWqjBZyGiyUqXZSiaLTXC02ARHF+5bOfHl76bT+JCvzkdM2g06Hwo0aCjIT0NBBo147uygXUz+IT4CANyE0q3n20jno9FsFX1xUYVF3IAqN1rFa5Um6VESGqVHV5sDlf0xG8fl/pgfA3ylvpiXAINGletRvyR/IT4yu06Wqyo+Mn0T/Wn6sHBR9Zqvgy8sTqcPZiWqLhBFhATQTVMH07s/bqTyShN9uGATPXNr3QNz0HrYk3+GZm38mjIrpCKEoXo/en/wdBob26W5Dw0AAFo1LDxmFLpffGwoOp1OCGmrV68Wj5s2baLXX39dhDzz86SkpAZviz9z2223CbMXOwmd4fvvvxfiH5u+nIHNZG+++SYdPnyYioqKREGY2oRLFgGV35mNZdnZ2eL53r17qVu3bg4Gs7NVtN64caPIR8kh6rJZiB85YvbIkSPi+YQJE0S4N7sseWExs770fcDDxMfm5OOF/9rX753unvLsHJL1xZoce5GZZy6LF64Jtdl5suoH37+dv8u2y/kPufPmJafERMZmSovE/YuZF+kZVZCVSuoofMXiY1SQjuJCdRQVpG3Q5FDK32XL+YiwawCAG8OuG5o/kAdY7PRLKzBSdpGZSiobnhfI1VQ5KKWOmQW52uDLX0SglmKCdRQfpneZy7NngkEInSy07jldRlMGhKieh3HOpGhasb+IMgtN9E9yCf25p4gu6CvlalKTu6eNoI8WbiajyUKfLNpC980YTcEB6rsugXqsyjhE//n3eyo1SwOZ9oGR9PWImdQxSP0UPQAA4OmwA7E17Jfdjrwwx44dEw5IdhFy2jpn4ArXLMhxtKgzsFsyLS3NoVq2nBaPw5pZCK0Oh4pPmTJFOBnZdcjFcv766y+Rf7I6tdWfkEVDFiw5AlYJC5T1zds5HJudjFzhuzqBgVIxwO7du9OBAweEE/KXX34RJrirrrpK5JFERIH6eLX4uPdYJvnoDDSwWwKN6tvwOwhNEeqe/iVNOACZm8dEUudYdd0YTH6JmU5kSwPYmBCe4DX9v91kttLx7Eo6mWsUDpqzwcYdnvjJThhleJ49dNqJ/fMeq0IEleGCkouHj0kRtegAF/k5k28Ui7/ehzpE+VLbCH297htf7hvhfAQAuAm+Xtj7H75TVQ88UMsqMtORzAoqLD+74Mh9Lot87Ejkfq/KOd64/lgcg11wtDkqhdNdes7XvLquE/ze7GKzWA6mV1BCmJ46x/iSn75peS7ZLcoCJN94K6u0irQjPVXOdRzkp6X/To2le+edEc9f/C2dRnQJpFCV06okRIeInNVzf98hcljPX76bbpk6WNV9AvVYcmYP3b31JzJapdupQyKS6PNh11KEwT1V1AEAwNNpSOhzS6Njx44ihyPXyXAWDoN+4IEHhOEfP0QAAFEKSURBVAjJ9TMaCoc5K3M1srjHhV9eeeUVe8Hg6rDwx45Fzucow8WBnaVLly7CociOSTmEmt2Q9aU/46Ix7Ljk98THx9f4u1ysh/NAzpkzRyyc15kdmCxCNqUoD2gYXi0+KnMmuUPpnr85j3amSKXpkyJ96T/j3HMHe9uJUvt6v3Z+Tf6u6QVG2p9aIUKpqwuM4YFaCjZoRYgzhzr76aVQOzXC6hoyeedjLFeEgheVWyiv1GwPQWc3zv60CkrJNVKfNn6i+E9dBWc41xJjbUxCNAAAcAKzstp1PUJcWaWF9pwpp9wSR9s591ah/hoK9uc+WUo74a/XCDeg1g1u++rwQJCd8ZyKg0PARZ9cYaG8ErO4IcRw13o6z0ip+UYhQPKNoaZcrzj0Wnb983VQbfGROb9XCI3vWUAr9xdTTrGZXv89g567omEJ2psCF55h8ZHh3I8QH1sn81O20UM7fiGLLTHNhQm96J1B08hP2/x5ugEAALgHdhxu3ryZbrjhBuHk47HQH3/8IYruPvPMM43aJouPnM6OQ6m5zoYM50HkYiwLFy6s8ZnQ0FCxyMih0/xaXfU2uLo1uzRZ1OvZs6cI22ZB0Fkuv/xyUeuDi8Ow2MmFbx566KF6P8OCKDtDuRDx3LlzRTh1ZmYmffzxx3TBBRcI8ZZdo+zkZHemv7+/CA3n9o2Odk/6PW/H60toBvn70qXn9lS9oU9kVdDrf0gJw5mnLosjQxOdHQ2BXSdbj0uCJ0/hBiYFNGnymJxeTjtPlduFR95mfKiOhrT3p/E9gmhQUoBI9M/uFXZ7GHTq5PNqCBzOzu4ZFhTbhuupe7wfDekQQOf1CKIB7fxEyLUMT4Y3Hy8VE9/aEK5w+/eA+AgAUBflnV3uR2sjt8REG4+WOgiPIX4a6p1gEP3x8E6B1CvBj9pF+lJEoE4UYmkO4ZHhgR0Ln8F+WooLZXejgfon+tPYboE0slMAJUXqxQ0sWYQ8lFFJO06WN8hZXxddYg2iwBpzMLWCisrckxfkv1PjRF5LZsHWAlp1oEj1ffbuFEcDukp3+XccSqM9R9NV36c3wK4PnjwNGTJE9X3NO/EvPbBjoV14vLrdQPpwyHQIjwAA4GVwkRl2+3HhleDgYCGScdgyV3tmEbExBAUFCedjYaFU70KG3YTVw6qbAudRvOaaa6h///7i2K+//nohBjoLh0n/9NNPIjSat8PHyO3Codp1Fd3hduJK2/x+znUZEhJC/fr1E5Wz5fySXDuEQ65jY2OFiHr33XeLkGsWeYH6eL3z8crxvSnQX93cSDx5euTHVHvOq6uHhYlJoTs4klFJ+aXShKtLnIHCArWNngizuyY1vyo5L+fo6hZnEA7H1gRPvmND9GLhtjmQVi7ypPFcf+8ZabLLjpvqn5G1R1S7BgC4M+djbXkQs4pMtP1kmb1QDKeQ4P44NqT+fDgtDT7WEH+tWDpFG+hoVgWl2AqyZRaZaOuJUhrSPqBR+Rq53x7UPoBWHSgWgua2E2U0tof6laBZXH34ohh65hdJAHx6YRr1vdefIoPUHXJdf+EAITwy8/7YRf26qO+49HRmz54tFp6sKd0fruank9vp0Z2L7c9v6jiCnulzIWl8Wtf4CgAAQNPh6w07/njhAio8VpJDjxsKF1ipft3iXI3sKJTFO3YFckj0f//73wZtk4+Bc0ByHse64GNlp+F7770n3Ir8Xs7f+MQTTzh8P95OVJRjFOiePXuEcCgzZswY4aJkZyZvJzk5WTgb2V0p54Dk7URERNg/w39btGgRGY1G0XYsQCrDrjls/IcffpAK5ZaVCVEWuA+vH9XwYF1tPlmVTXtPSzbl9lG+9OCFseQuth6rCrke0rFxhWb4x7n3TIVdeOQpYI94g3APtjbhsTrsihzWMYDaRVSFNCWnV9CpXMdqNcIthJyPAAA3IeelYQzVcj6y43GHQniMDNTSiE6BQvRqTcJjddgZ2SPejwYl+ZPe9pX5xtDWlFKRZ7gxDO5Qdd3bcrzUbTePrhwSZhc6OfyaBUi19z3tvD5ksDUc530ErYNfT++mB7ZXhbvd3vkcerbPRRAeAQAACDefs8KjnOeRP6tEo9FQXFycXazj6tKHDh1y6uYaf74hx8PFYmSRksVOdhrK8FiVt8PioRIOfVZum0VMDt/m7bBQes8999DAgQNFPkjl8dTmhOT9K4XH6rCDEsKj+2ndylET6dw2gob2VLe0+u6TZfTxKqlkPCf3f+mqBHs4ltoUlZtpf6okegYZNNQjoXH5rk7lScVZGJ7W9m/nJ3JWtuZJrhIOC++Z4EddYqo6rn2pFSI3pAybbuw5H1HtGgDgzoIz+qq+tsJoEcKj/Gd2Og5q7y+EO08hOlhHQzsE2B2f+aUWUYymMUQE6aiTrW/PLTbT0UzHG0tqwdfHZy+LF5W8GXZfLtiar+o+w4P96RJbGpncQindCmj5Va3v3vaTPdT6xo4j6L+9JnnM+AoAAIDrYVchi261LRMnTmzwdligU9PV31Q4dPvaa68VImJSUpIQDDkMG7RevDrs+sYpg1Qd4HGBk0d+PGOvunz7+Cjqm9g492Fj2Hy01L7vQR38G5Xrq7TSIpyAMn0T/US4sifSMdpXhFyfsIX87TtTLnKRce5IKezaJhpDfAQAqIzyJgdXbpY5kFYhCrcwnLe2X1u/ZsurqyacG5JzCXMuXr6OcT7euFAdRTUidHlopwC76LjhcAl1jjWQO4gK1tFzV8TTXV+fFs9fXpJBg9sHUPto9fZ/w0UDqdJopusu6KfaPoBr2JufSrdv+Z7MVmmgNiNpMD3b50IIjwAAAOqFi8TUVW2aBTrOcegJDBs2jHbu3EmlpaXCEcnOTdC68er/QR6kqzlxfHJBGp20CVks2t021j3VrRkOUWPxkWHNsTE5Jvk7sAAnC5hctCU+1DOFR4aFaC6WwwUbGK7Eejy70u5atRkfyYqCMwAANzof9TbxMbPQROmFUvoLdgX2ZeGxmQrIuAPOA9lNIRRyTt7GhF/3auPnUHgmp7gqd7HajOsRLEKwmbJKK8359oy4qacWYwZ0oHnPXkUTh1WFJIGWx5nSfJq16WsqMVXaq1q/3P8ShFoDAABoUDGWupyPdVWhbs0EBLAZyKtlK48B/4sq8fX6XPprr1ThMthPQ69c3aZRCfMby+5TZVRcLk1werbxa1ShmexiM+XYqqj66X2oe5x73CLNCTuIerfxk3VGOppVSeVGi835aK8405yHCADwJucjV4nW+pDFaqWD6VIaDYb7Y6Uj0lNJjNDbQ5fLjVZKyXE+bJr77xGdpRtw3KobD1flQnYHD18USx1tod+HMyrouV/Uz/8IWi7FxgqauelryiiXxoiDItrR24OmkRbFZQAAAADgwXj+zKUZ2HailN74I9P+/MVpCdQuUt2K2kp4UrP+UIn9+agujXM98iRJOdF1p3ja3G6bdpGSw5PNR+x+1CnFx2rFIAAAwNVYbKGYbLnmGiJp+SYqrZQEq/AALSWEeUfWFO53eynyFXN/zOkxnGVIR66YLa1zBe1yFd2H1eHCbG9f29ae7/m3nYX047/q5n8ELRMeWz2wYyElF2aI5+0DI+nLYdeRv9Zzo0oAAAAAABiIjy4mu8hED3x3hky2ec0t50bS+J5VJePdwaH0qsrUbcL1lBTl/KA2s8hMhTbnJIchc1EDb4LzP8rRjKdyjbacTJpaQyIBAMDVVBkffUir9aFjWVWOvy6xnlPwq6HiXRub2MrX1hO2dBjObmNAkpRzucJopY1H3Ot+7BhjoOeviLc/f+m3DNpzCkVhWjrvv/8+9ezZk4YMGeKS7X1yZD0tTd0r1kN0fvT1iJkUYXD+BjEAAAAAQGsD4qML4Sqkc749TVlFkvA3tGMA3T0hmtx9V33l/mL787E9Ahs1ST2eLeWqZDg5vzdNdBmDTiPC/RjWGdMLzBz9aMcM8REAoCJWu7vah8orrVRic+qx6zEi0LtuBjGdYvg6JK2fyKlsVB88pluQfRvrDhWLa7Y7uaBvCF0/KkKss3vz3nmnKbOw6loLWh6zZ8+m/fv305YtW5q8rQ1Zx+jF/X/an7816ErqGOS+XOAAAAAAAM0JxEcXin5PLEijHSmSkyEmREf/m+7ePI8Mu2PkIjfsVuR8j85Safaxux45X2V0kPP5Ij2BDlFV7kcWlJUCrBlh1wAAFeEcjwIfHyq2hVsznWy5A70NDlmOD5VEVy6ClmvLR+xs9el+idI1kUPY/z3mXvcj88DkGLsDM6PQRLPnnla1AA1oGeRUlNDsrfPtla3v6TqWJsb3aO7DAgAAAABwGxAfXcR7y7Pp912FYt1f70PvzWwrJjruFkCX24rcMGN7BokCKs5SaKwSG2OCdV7nepTx02so0ia8mthl4yA+IuwaAKAeckES7n/LbA49g86HIhtRPMxTUKb/yCp2XnxkxvYIshcU++dgidvdj1yl/O3r2oqUKMz+1HJ6+IczuKZ4+G/54Z2/UFaFFJUyJrozPdDjvOY+LAAAAMDj4ToNN9xwAx08eLC5DwVAfHQNi7fn00crs8U661OvTm9DvdpIzgZ3cjCtgk7YwqWjg7XUt63zrkemsFIhPnpZrsfqRAXp7P+vjgVnID4CANSjqhqyj92BHRWk9dqbQUxkkE7hRjfb82I6Q2yonnrb3I/FFRZapyjO5s7v8cGsRBFZwKw6UEz/+72qSB3wLH4+tYP+TDsg1iN8A1DZGgAAQINEswULFtDDDz9Mc+bMoa+++opKSxsesXHHHXfQzTffTEVFVcYk5rvvvqMXX3zRqf8BFu74OFjEMxprTxdTXl5On332mUhX8tJLL1FOTg61lHacO3cupaenN/ehAIiPTYfzRj21MM3+/KELY9xeYEYWw/7cU9W5TOwTTBp5luYE7OgrsomP7LLhYjPeDE8SGXaQIuwaAOB28dHHx96XyzdDvBWdxocibM7PCpOVysyNuz5N6B1sFzHXJpdQcXnjXJRNgXMpv3ltW9LZvsI363Ppq7UtY6AOXMfp0jx6cvcS+/NX+l9K0X5BaGIAAAB1YjKZaNKkSfTggw9SSEgIde7cmdavX099+vShU6dONajlvv32W/riiy/o1VdfdXj933//pd9//73Brc+C42WXXUbHjh0TIp7ZXHPMlJaWRgMHDqSPP/6YunXrJt4zfvz4OoVK4L1490ymiWw7USoSxptsv8Hpw8Nppi2ZvLvhXJMZBVKhm7YReurViFyPDOfRstqC0qK9OORaJtDXh/z0PlRisVYTH+F8BAC4IexaOB99HG6GeDOcCiTbFnKtdOk7A1/bBncIEDkfWcTkIm1TB4aSuxnROZCevDSOnl4o3Y1n92OQn4auHBLu9mMB6vyGH9i+kIpNFeL5tMQBNDmhF5oaAABAvaxcuZKWL19Ohw8fFsKjTFZWFhkMhga3HguAb7zxBt15550UHx/fqFZ/6KGHqFevXvTzzz8LJ2Zt8Pb9/Pxo3bp19uO77bbbSKute5x29913C1emRqOhxMREIXD279/f/nd2efJ2H3/8cVqzZg3t3r2b4uLi6Pbbb6fIyEj7+1jgZJF1586d1L59e7r++uvp6aefpnvuuUeItXWxevVqWrJkifj8oEGD6Nprr3U4XnZ7sks0NzeX+vbtS7NmzXKq7UHteLetrQnsO1NGd351isqNVruT4rGLY5tFrCuvtNAyhevxgr7BjT4OeVInT/K8HW5HdhsJl4xP1c/FZEKBAACAe5yP3J2H+mvIV+fdN4Nk4VCmseIjc16vIJF/kdl8tJTSC5rn7jwLjbPPr6p4/Mwv6fTHbil/NGjdLD6zm9ZnHxPrbfzD6Nm+Fzf3IQEAAGgF5OXlicegIEenfHR0tHBCNpTp06dT9+7d6Zlnnmn0sbDwWB8czrx48WK6//77HcS5mJgYISzWxahRo2js2LHisbCwkM455xxaunSp/e+VlZXCaXn++efTjh07xPdYtmwZjR49WjhDZVg0fP7554XwWFBQQMOHDxdi5JkzZ+rc91NPPSVEyrCwMOrUqRO99957wmkqj71Z6GQnJ/8/8PfftWsXXXwxruGuAOpSIziSUUG3fXFK5ItiRncNpFevTnB7ZWuZFfuLqdhWnZodj51iGq/K55dViWpyeJu3w3nWTuVKDiSZShOcjwAA9xSc4Zsf3h5yLePvq6FAg4ZKKixUZtIIF3o9Y9s6CfHX0rgegfTX3mJiI/tv2wvplrERzXID8Y7xUeL7fLU2V+SxfHT+GeG4H9fD/SlcgGsoNlbQ83v/sD9/sd8UCtE3LiIFAACAd3HeeedRbGwsjRkzhm666SYaMWIEDRs2TLgLnYHHNK+88gpdcMEFQhzkkGhXw8Icj1l79+4tcj1yWDi7NW+88UYKDw+vVxhVwq7GF154gS666CKH1zlvJTsZ5c+wqLlx40YhVnIIOTsy+Rhkl2PHjh3p1ltvrXO/+/fvF6Hohw4dEoKlvA/+HIuol156Kf3xxx80ePBgevfdd+2fS01NbWQLASWYzThJclo53fL5ScovlRyCg9r701vXtiVfOXGTm0nPN9KGw1LCfJ2W6KL+jZ+s8CROFjGDDD7NJqa2NHiSKgQARQ5NUy35LgAAwGU4OB997MVJgOQCZbGOU4QUlVsoIqhxN8pGdwuircfLRLqRY1mVtOtkOfVPcn+xOP7/fXByjLj+/rwln9hYf9+3Z+iNa9o0Sw5p0HTeTF5JGeVSRMqEuO50Xlx3NCsAALQQ8l+aSZZC9+dZ1oREUthjX5/1fVFRUSKM+K233qIffviBnnzySdLpdELQ4zBqZ0RIdg6OGzeOHnvsMVq4cCG5GrmgzTXXXCNEzp49e4rwbBb4tm/fTgkJCbV+jsOZ582bJ0LLeRvsVKytIjULsTIcbs3L6dOnxfO1a9dSly5dHMKrr7jiinrFxxUrVlBAQIAQOuUb/fzIYzFucxYfWUh97rnn6KOPPhLPWRit63sA54D46AR7T5cJx2NBmdnuMnx/VqJwYjQHLBb+vKVAuDaYc7sHUXhg4/9L+XvJfr5Qf7geZeTQPBH7aKMSYdcAALflfFT0Q4DC/LWUmi+F3BSUsfjYuEbhNr14QAh9vU4Kb/ptRwF1jvWlID/3X/940PvUpXFUVmmhpbsKyWi20n3fnqaXr25Dk/s2PMQKND+HCjPp86MbxLpBo6Nn+zi6OAAAADQvLDxa8jNb9H8DC14vv/yyWIqLi4UIyTkQWZhkYcwZ2P04ZMgQ2rBBuja5ktDQULsrkcOZ5XyPXbt2FeJp9YI3TEZGBg0YMECIhhzuzOHPe/fupVWrVtV4b3WhlUO55aI32dnZFBHhWG+Dt1VfuDeHUvMxc/i2EnaZsujIsPvyyy+/FOHbnPOSHZIs3rLACpoGxMcGsv1EKd3xVVWodd9EP/roxnYU3AyTFJl1ySV0Jk/KUxUToqOx3ZtWQZEncUpnCZCQTa1y0QcG4iMAwG05H5U3QQCFBlRdd+WbgY2lR4If9WnrR3tOl1NppZV+3VFI14xonoIvWo0PvTgtQYjNv+0sFA7Ih384QxVGC106KKxZjsnbef/998VSW3XPunh27+9kskrjqdldx1C7wOYpRAgAAKBuB2Jr2i/nfrzllluEc5FDjp2F8xdeffXV9PDDD4twYlciC3byI+Pr6yscibJDsTq//vqrcB9yDkc53Q27DJ2FC9VUr/7N+7RY6q7NwIV3WIBkIZGPsy6uuuoqscgFbThH5NChQx0KAAHngfjYANYmF9N9352mskppMshVMj+Y1ZYCDc0nPKbmGenvfZLNmX+zVwwJbXKYtBxKzsD5WAV3inqt9ChjNiPnIwBATapyPnLXA/GxCg5BZ4GOXf/Km2aNZcrAEDqaWSHExz2nymlnmzLq38794dcMX8dZgDToNSIEm7/jf39OE+Hl14+CiOVuZs+eLRZOhi+7O+pja04Krck8LNbb+ofRHV3GuOEoAQAAOENDQp+bEy6wUlZWRiNHjnQIU96zZ48IA24M//d//yeKtmRmZoq8iTLvvPOOqCz96KOPNmq7LOZxaDcLipdffrl4LS0tjbZu3Wp3QlaHx7b8/SoqKoSzkQvFKPMrNhR2KM6ZM0eEeXO4NfP222/X+xkuHMO5KTmPJD/KcP5IDunmAjQcms1iKufd1Ov1wp3JgiaPBUDTgPh4FhZsyadnF6WR2Ta/Gdk5kN65vm2zhVrLxU5+2JRnP6bRXQKpXWTdyn1DkR0kGh+ryPkIquCJv1J8hPMRAOC+gjN8AwR9sgy3R4ifRhRIKzNaRX/clLzLHMEwZWAozd+UL54v2lZA7SL0FNFMRX44v/Azl8WJojPzNkgh4S8vyRA3HR+6kKtH4lxoqbx+cIV9fU73ceSv1Tfr8QAAAGh9sCB37733ikrSXG2Zx4Rr1qyhHj160LPPPtuobXbo0IFuv/12ITYqxUcWDbmKdl1wxWkOh05JSRHPOZ+iVqulBx54wJ5r8ZNPPqEJEybQoEGDROGW1atXizDmu+66q9ZtTps2jV577TXq168f9e3bV4SDt2vXzunvlJSUJHI3souRc0OyiMnHJi91iaXz58+nG264gZYsWSIE2aNHj4o2//HHH8V7ysvLhfDL2+e24bbnffTv39/pYwSOQHysA/6Rf7AiWywy5/cKFlWt2ZHQnMfFeamyiiShMCFMRxP7ND0hfbnRQuVGabIboLM0S8XP1iQ+GmXlFwAA1MAeds1iG4fkopmVcGoQFh8ZfowJbloDsdMxOa2CdqaUUYWRb/Dl023jIput8Bpfbx69OFbkn/xopTQO+Xp9LmUUGuklmzMStCz+zTlBa7OOivWkgAi6InFAcx8SAACAVgiLjP/8848QxdjtyDz//PMOhVXOxocffkjDhw93eI3dfpxrkR19DLsPt2zZIlx/dcG5G+Ub4rNmzbK/rsy1yMLmvn37hEjHAiA7Hus7Vo4k4OIuLGry+/m7BQcHC8ehDIdlc95F3rYSdjZy/koZDiWfMmWKqHjNuRl5YYGRc2MyLELydlhkVDomT548SevWraP8/HzxNxZClX/nIj2bN2+mnJwc0W5cSAc0HYiPtcD5lZ5dlE6LtxfYX7tuZDg9fFGsyMnUnPx7tFRU55QFsenDw10yOVLmzQrQoZLzWcVHFJwBALil4IyGfHWOaR+AnBrEVnSm1EwxwU0fzlwyMIROZleK6tenco30644Cunxw8+Va5P/zuydEU1yojp5fnC6iHf7cU0SZhSfprWvbUpQLvjNwHa8fqJo03dttHOk1KNwHAACg8XAIMC+N4dprr61ReIUFQ3b8ybD4yG6/bt261bmdESNGiOVsGAwGmjhxYoOPj52GkydPdnht5syZ9nXOx6g8VhnOXamEXZPDhg0Tgi3z3//+Vzg75RyUPJaSt6PMBRkYGCjCqeuCxU8WIIFrwci1GhkFRrp33mmRfJ7h+R6HOc0a3TyJaZUcz6oUSehlLhscQtEhrvkvzC6uEhwDdXD1VYcFXmUHbpJLjAMAgCpUhV376iA8VicsoKo/zi42UZdYQ5Nb3E+voWtGhgunoclMtOVYGcWH6WlE50BqTqYNDafYED3d/72Ue3pHShld/f5xkQKmV5vmyU0JHNmUfZzWZx8T6+0DI+nyxCoHBQAAAOBKli5dSj/99FOdRVg4V3FDYDGyPgGuNbB//37hyGTn4vHjx+nEiRM0b948kasRtDwgPirYkVJKc749Tdm2kGZ/vQ/937QEmtQnhJqbzEIjfbM+157ncVTXQBqQFOAyh01Wkckutgb5wvlYHd/qOR+NaCMAgMqVrm2dclPyGXoqLBT6aS1UbtaIojMVJgsZXNBObcL1dPngUPpxsxT58NuOQgoL0Iqq2M3JmO5BNPe2JLrr69OUWWii9AITXf9RCj13eTxdPODshVCAunx0eK19fU63caSD6xEAAIBKcH7EsWPH1vq3sLDmi9hoDrgK+AUXXCDCx0NCQkTeSW9rg9YExEcbP2/JE2FN7HZgEsL09O7MttQ9vnknHHIV6i//ybNX2+4S60uT+zY9z6MMV9GU8z1GBGgJdQ1qD7tWRtwj7BoAoBZmRU5ZVLqum1BfE5WXScXWOA9y23DXiLR8Yy8930T/JJeI1Jvfb8yjm8+NpKSophd2awrscvxxdnua8+0Z2nmyjCpMVnrkx1Tan1pO918Q02z5Kb2d1NJ8WplxSKzH+4fSpW37NvchAQAA8GA4n2JdORU5tJgrWnsTbdu2FQto+Xi9nYIrRz+3KI2eXlglPA7tGEA/3tW+RQiPnMvq09U5QoCUC8xcOzLcpbknZdcjEx2MHEW1wZM6H0XYNecFBQAANTAr0jr4+GhIj265VkIULn3ldcwVTOobTH0TpTEAG92//CeXTuZUUnMTHaKnL29tR1cOqbqrP3ddLt3x1Sn7OAG4l+9StpLFliZhRtIguB4BAAAAAGrBq8XHvBIT3frFSZq/Od+hsMwnN7Wj8EBdizg+Fh5zbfkYI4O0NOucCJdXucxUio9BmOXW7XxUhF2j4AwAQCXMioTYnO6B+x9QkwCdxS7Mct5Hiwtz8XJ/P21oGHWOldyO7DL84p9cOpHV/AIkh+E/c1kcPXlJHMmR5huOlND094/TkYyK5j48r8JkMdMPKdvEuoZ8aHrS4OY+JAAAAACAFolXi483fnaKth4vFes8uXvhinh6bEpci5jopRcY6aOVOZRjEx4jArV069hIChEVPl1HudEi8mUxQQYN+ft69SlRJzzB9VG4TSE+AgDUwmRWOh99SOdCp7snwfeDooOkG4UcqZ5dYna54/36URHUKcYmQBqt9Pk/OXQgVSpI15zweTF9eDh9fkuSGB8wXKF7xgcnaMW+ouY+PK+Bw63Ty6VCgOfHdaMEf+TfBAAAAACoDa9WmjhhOxMdrKOvb0uiywa3jOSkPLH5aEUOFdpEQQ6FvnVcJIUGuN6VeEzh4oh1UeVsTwTORwCAu1De3IDzsX5iFKlC+HrmUKzHBXCl8Zmjw0WuZYbTs3yzPo/WJhe7fF+NYXCHAJp/VwfqkSBV+y6ttNA9807Thyuzm/vQvIJ5J/61r1/bfmizHgsAAAAAQEvGq8VHpk9bP5HfsW87/xaR52v53iL6Zl2eCPFi2kbo6T/jo0S1TVdTVmmhU3lGsa7VELWLREn6esVHpfMROR8BACphrCE+oqnrgm/OBRqkoQznPMy2RQu4Osx55ugI6tdOygHJmuPvu4ro+0354jra3HCBvG/+054m9w2xv/bBipxmPSZv4ExpPq3KOCzW2/iH0djYLs19SAAAAAAALRavFh8v7BtMc29LopiQ5hfdcotN9NnqXFqxv9iWtpyoT6KfCLWWJ1au5qhwiUjrSRG+ZJCTR4E6nI9V7WO0icMAAOBq4HxsOCzOdrGFRTOHMypUcSRyCPZVw8LovJ5B9tf2nCqnt/7MahF5Fjllyv+mJ9B9F0SLcPQBSc1/Q9XTWXhqJ1kVhWa0ijECAAAA0BIwGo30ww8/UF5entOf5fEUf/Zs1bN/+uknSk9Pb8JRAmfauzXj1SOlJy+JdXnxlsa4HdcfKqG3/symE9lSCDQb7Cb1CaYZw8NEyJca5JWa6bTN9ciaY/uoqskbOLvz0WhGVVEAgDqYOIGhDYRdnx1OGRLsJ13LC8stIvehGnARmvN7B9O1I8PITy9dDzg9yudrcunX7QUih3JzwufKLedG0Uc3JNIb1yQ067F4Aysyku3rlyf2b9ZjAQAA4FksWLCADh+W3PVKduzYQcuWLWvwdkpKSmjGjBl09OhRp4/BbDaLz+7fv7/e911//fW0c+dOp7d/6tQp+u2338R3qo89e/YIUe7kyZMN2i63D2/7bDi7XbUxN7C9WzNeLT7yQL05le19ZyTXxJKdhWS0FRjg8Gp2O47tEaTa8bHgued0mf15p2iDaiKnp6DVOFa7lsPiAQDA1VQYq25uQHw8O9xG3eKknIdMckaFyH2oFr3b+tOcSdH2StjMxiOl9NrvWbThcIm4xjYno7sGUZStEA9oGu+//z717NmThgwZ4vB6XmUpbc+VJjadg6KpXWAEmhoAAIDLmDVrFv355581Xp87dy49+OCDbmlpjUZDV199NcXExLh0uyaTie644w7q0aMHffjhh3T33XfT1KlTyWKpOXZjR+WFF14oRLkNGzY0SGy99NJLqbKyqq5FbTi7XeAavFp8bC7RkUO0PlmVQ/PW51F2UdUkc1inALp3UhS1j/ZVdf8H0nhiJk2OQv011D6q+cPOWwPcAcuYuOoAAACoAFdVdqh2rcXNobPBYlvbcOlaxsbR3afLVBUBuQDcjWMiaMqAENLZcnKWVFjotx2F9OayLNqZUuZQtRy0TmbPni0cCFu2bHF4fW3mEbLYQq7HxXZtpqMDAADg7fzxxx+1OuWWLl1a4/Vjx47RkiVLaPv27XWGZicnJ9PChQuF65LHoCzkRUVFObz/xIkTtHjxYtq1a1etguHZeOqpp4Szk92Sv//+O61bt06Ikez8U8Lbvu666+jee+9t8Lb/+usv6tChA3Xq1KnO9zi73V9++UW0z48//kgbN26k8vLyOtsvJSVFtP22bdtq3daxY8cc2q4hIessqC5fvlz8X585c6bG37ndWEDl/1v+v2nJ4Na4m6g0WWlHSiltOFxKmYVSlW0ZDnme3C+Y2kWqG/rMwuPB9Ap7uDVHEXPBneZ0gLYmtAoBoFIRFgkAAK6kwlh1jfDRoOBMQ+keZ6DsYhOVG62UX2qh7SllNDDJXzjX1YDd8CO7BFL3eAP9tbeIdp2UBqM5xWaavzmfft+loeGdA2hoxwAK8kPVIE9iVcYh+zrERwAAAM2FLDKuXLnS/hqHHF9yySW0fv16SkhIsAt+Bw4coO7du4vXL7/8cvrqq68cQrPZCXjo0CHq378/BQUFCRGPX1+1apXd/chOxfvuu49GjBhBBQUFQph0RoDkfb3zzjv09NNPU+fOne2vT548ucZ7X375ZdLr9XTXXXfRQw891KDtswB38cUX1/ueV155xantsuhXWFgoRL59+/YJVyWLpl27dnVoP94vi7ZdunQRguqUKVPo66+/tm/n7bffpocffphGjhxpb7vVq1fTr7/+ShdccEGt+2b3Kwul3bp1o5CQECEyPvroo2JhsrOz6dxzzxXHxu/h/2Pe7+uvv04tEYiPKsKuB05+v/tUOR1ILXdws8hVOi/oG0I9EgyqC4AmixTmnVZQNant3caPggyYEDUU5QQWBWcAAGpRqbhWsMClTPkA6oYdogPa+dOW46XEBcNzSsxivX87f/JTMb9zRJCOpg8Pp1FdK+mPXUV0PEsK9Skqt9Dfe4tp5f5i6hxroL6JftQjwU8UhwGtF4vVQqszpTxc/lo9DYts39yHBAAAwANhhyI76pSwOKjk1ltvpQEDBtDx48eFWMjwZ1hkZIEwPz9fvMauPBYp/f39hYA2cOBAuuKKK4RQJcMiIr+HhTk5PFpJamoq3X///fTZZ58JQYy5/fbb6e+//27wd2JHIIt1EydOFLkeWShlEZJTnChhh+F777131nyQ1Y1WLApWbzMlW7duFSlVnNnuJ5984rCPW265hR555BHhiFRiMBhE22q1WuFsZBGXxc0+ffrQ6dOnxWc+//xze9ux+Flf23HhmWnTptF3331nF1QPHjxIgwYNovPOO0+khPn2229FdCbnr5SjNBctWkQtlWYXH99880166623KCMjQ/zH8PPRo0e7/DPugE/GjEITHcuspGOZFXQks7KG4MhwmDO7JXq28VPNkaGEnSAH0yqouMLiIDwmhCHc2hm0irBrZTVaAABwJeXVcj6ChhPqr6VB7QNo64lSEX6dX2ahDUdKqWucgdqE6VRtz8QIX7p1bIQQHzn34/5UrrwthYEnp1WIRaspoA7RvtQx2kAdY3ypbYTeLeMA4Dr2FaRRVkWxWB8V1ZEM2mYfSgMAAHCCC1e/T5nlUj/uTmL8guj3sbMb/H4WsEpLSx1e48IxsjjI9OvXT4hRX375JT333HNCj+Dw4Hvuucfhcyx0sfDI9OrVS4hZ/D6l+Mihz8ptV4cdeuHh4XTttdfaX2NB7eOPP27wd5IrOb/44otCqGvfvr1wYp5zzjn0888/k6+vrxBM2Un40UcfUWxsbI0w5/qERX7vqFGjav07b5e/4wcffODUdmXRl12NRUVFog1qK/pz2223CeFR/n8JCwsTYeysV3FhnYiICIe2Y2GShdC6kNuDj5PDsxn+/2U3KzsmWXzk/1N2UXK4tyw+c6h8S6VZR0ys/P73v/8VJz4r86+++qqwnLLi3q5dO5d9Rg3KKi2UW2KmrEITpeUbKZWXPKM9l2J1uDJmrzZ+NKJzILWJ0LvFdZlZZBJVP7mytYxWQ9SnjR/FhUJ4dBZl3jWIjwAAtShX3NyA69F5wgO0NLRDAO04WSZCsCvNVtp7ppyOZ2soMVxP8WE6MujUcR+yuNkxhoVFA+WVmGjTkVLaebJMVMVmWIg8klEpFoaLvcWH6ig+XC9uCMaG6igySEcBvj4QnlsoqzOqqo8i5BoAAFofLDymlxdSS+fGG28UoqGSOXPmiPx/StiJx2LeM888I/7GOQRld50Mi3xKWKj6999/HV6Lj4+v93i4KnRSUpLD+ISfK+sinA0/Pz/xqNPphFuPt8Xux969e9O7775LDzzwgPgeLNyx8MouRs6pKLshWcBj12RdIdesC/G2a+PZZ5+l0NBQp7bL7s8rr7xSiH1Dhw4Vx8UCqiyiKuFtVHdCygInf8ekam2XmJhYb9vJ+RtZhFTCYrMcTj9z5kzatGmTaD8O954wYQLdeeeddiGypdGs4uP//vc/8WORbaQc18/WUc4l8NJLL7nsM2eDFWQ2mrCgxFWnuZJxaYVFVMvkBPLyUlBqEZMJFh15QnM2/H19qHu8H/VJ9KMusQZVigZYLFZxLGVGi3gsqjCL48wvMwvHhZIQP40I+0KodePQsXJrw4iCMwAAFW9uyTgzoAOODsiRnQJo75kKcSOO4es45z3mha+HIf5aCjJoKMhPQwG+GvLV+ogbdK5yR4YH6mhyvxCa1DeYTuYYac+pMpH+hK/RynzQKTlGsVS/YckiZIi/dHx83Q7201Cwv4b89Rry1fsIAZXfZ9D5kF6H8Hx3sSoT+R4BAKA1ww5ET9rvNddcI0Q7Fh7ZAckhuezsU8Jh19WfVy8kc7bxT2RkZI3tsOvOmZyPciEYzjkp749FOBb25CItLKKxgCqHD8vb5+JvnIuyPvGRw8LrgrfLDkEu+ML7bsh2ufgO52/ksHZ2PDLz5s0TrzkDC5P5thB4Gc4jWV/bcY5Hdj7WF0bOYu4XX3whHJQsQrJblEPqjxw5Iv6/WhrNJj7m5uYKGyqr9DJ8EowdO7bOcueN+Ux9vLI0i3SGMpEbyhXwBCAiSEtRwTqKCdFRaIBGHF9JpYV2nCqT3lSHZlnby9XFQ4vVKlwTXMGTHzmPY0OKeQYaNNQp2le4KxDC13iU4vEf/+yijjuONWFrngifjAgfRPvg3GkqlZUV9nU4HxuPr04jCs7kFJtEGhRlFEBhuUUs1eEIaL1NhOS253Exvybl3pTWq3dzPrX0e7WN39tG+orIBxZBMwtMovhcdpGp1ogJvpl4Js9IZxzH+PXCZk6+TrFerfXxocenOk48QNMpMJbRttxTYr1TUBS1C3R0OQAAAGj5OBP63BoIDg6mq666SqSiY4debWHQLOTJ5i1243FuxAcffNCp/XCaOw4V5ohTOUcji3PVYWGOi7KMHz++xt969Oghcjxy7kKlu5DFMhbNmNmzZ4tFRg475lDy6dOn13psaWlptHv37loL18iwI5BdjFw8h2/uN2S7LILy+2XhsTYnYkPgUPCHH35YfG/Ox8mwCFof7OJ88sknRbj71KlT7a+XlZWJY+dj4urXbdq0EeHX48aNE3kmWehkzYwL27Q0mk18lEuKR0dHO7zO/7msPrvqM0xFRYVYlCqzeJ3di42IPmanASev9/OVHoUrwU8jwqdkcc9k5WT3zZcX0F+4JrQUF6KjcJsIyg5PXuqD1Xd+jzN3MLwFg77q51JamCMWAABQE61Wg/64idcqvgYOae8n8h6n5Zsou8QsisHUul0riegHiQbc3Wskgf5a6sBLrEFEXBSXm6mkXIq4KKu0UnmlFM3gDCbbTUm1j92b2Zh9nMxW6dxByDUAAICWAheeYbEpLi6uVtGPhS4OR+biNFyBOSAgQOQ/dIZhw4YJxyJXxWaHITv5uBhL9SgdriZdl/jIcHg1i6Uc/tyxY0chALKYxiHljYVdj8OHD68R+txUWABk0fA///mPcGdy5es1a9Y4vR1OFzh16lQhjnK1cHaMfvrpp6Lt6jKHDR48WOz76quvFmIsC7ec83PBggWizVh8/P7774WwzNtmjYyFURZ3WYRsibS4LNk8mXDWnXe2z3A4Nsf4V8eg96EAg4bY0MYJ34VbQCM5Htg9oJcXDmnS+ghxkYXH5nQPashqc19Ij1ofK+k1VtJrreSrsZBBayV/nUW8xphKiLJKGr59nsjxj4HbFOF+jswc15b+/sePzJUNT04LAACNxUejowuGJYm8MuiPXXOtCvUhCg0iMgcQlZs10mLSkNHiQyarjxDwzFYfslh9hHzH9+usKju6eXzBIdrhgbWlhLGK0Gzlwjmdq6IgrNIx2yIiLPLjWW40gsZxpqyA9D5aMlrNEB8BAACoBjv0unbtWuN1dgfWVhSGxS02ZF1//fUOOQ85bJfFK66ZwZWVOc8ji4Ls9mMBUvme6sIdj6/4dd6uDFde5tBersQtF4thd56cL5LHLrwPDgWuT9D7559/hAjK0ascJs4imtJdqISLuPBxcM7E+sRH2dnZUBqyXf4/4JyQX331Fa1du1a4P1l4VRaKqav9uPCLMtfm/PnzRapAue24aA0X/2Hnal3tzUIuC5YsHrOjlF2T7G6V25vdq+yqZAGSi+JwW37zzTf2/9uWho/1bFY4leAQao5DZ+WWFXQZTo7KCTlrU5Qb85m6nI+cW+BMepZIGlofYsphn3c4TkBqm47Up0vW+FON0K16PuMjrastfPKELisrSyjnmOzWbJtjKel0OEcKxQNVcC9SXFREQcHBaJtaQPvUDdqmbnomBpPBWoL+uJmvVSJqQOxTckaK12q+q7aHurdZY8W1WKwWCvb3VWfjXgiPGzlJPee60gf50/qsYzQmpjP5aVG8j3+LfINEDmMDjqB96gZtg7ZpDDhvaocFLXbKcUg06xvN1SenpqaK8G+u0+EuWOdhjWjz5s1CzGup505ubq6DQMkuRa5+zeNZzu/YnHDbuKNNms35yA3frVs3WrVqlV1I5AE+K7ms2LvqM3KlIV6qE2DQiQU4wgInn3wYRNY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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def scattering_rate(flux, scatter, medium_map):\n", " \"\"\"Scattering reaction rate density, sigma_s * phi, in each cell.\n", "\n", " scatter is indexed [material, group out, group in], so summing over the\n", " outgoing group gives the total scattering cross section of each group.\n", " flux has the cell axes first and groups last.\n", " \"\"\"\n", " sigma_s = scatter.sum(axis=1) # (materials, groups)\n", " return np.sum(sigma_s[medium_map] * flux, axis=-1)\n", "\n", "\n", "hybrid_flux = runs[\"Hybrid, 64 / 4 angles\"][0]\n", "fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(13, 4.4), constrained_layout=True)\n", "\n", "# Left: how the scattering rate fills in over time (hybrid 64 / 4)\n", "snapshots = [0.5, 2.0, 5.0, 20.0]\n", "shades = [\"#b7d3f2\", \"#78a9e6\", \"#2a78d6\", \"#0b3f7f\"]\n", "for t, shade in zip(snapshots, shades):\n", " step = round(t / dt) - 1\n", " rate = scattering_rate(hybrid_flux[step, :, None], materials.scatter, medium_map)\n", " ax0.plot(centers_x, rate, color=shade, lw=2, label=f\"t = {t:g}\")\n", "ax0.set_xlim(0, 16)\n", "ax0.set_xlabel(\"x (cm)\")\n", "ax0.set_ylabel(\"Scattering rate density $\\\\sigma_s \\\\phi$\")\n", "ax0.set_title(\"Hybrid (64 / 4 angles) over time\", fontsize=10)\n", "ax0.legend(frameon=False)\n", "\n", "# Right: error in the slab-integrated scattering rate over time\n", "delta_x = np.diff(edges_x)\n", "\n", "\n", "def total_scattering(flux_history):\n", " rate = scattering_rate(flux_history[..., None], materials.scatter, medium_map)\n", " return rate @ delta_x\n", "\n", "\n", "ref_total = total_scattering(ref_flux)\n", "for color, (name, (flux, _)) in zip(COLORS, runs.items()):\n", " error = np.abs(total_scattering(flux) / ref_total - 1)\n", " ax1.semilogy(times, np.maximum(error, 1e-12), color=color, lw=2, label=name)\n", "ax1.set_xlim(0, 20)\n", "ax1.set_xlabel(\"Time\")\n", "ax1.set_ylabel(\"Relative error\")\n", "ax1.set_title(\"Error in the total scattering rate\", fontsize=10)\n", "ax1.legend(frameon=False)\n", "for ax in (ax0, ax1):\n", " tidy(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "03c06526", "metadata": {}, "source": [ "At early times, scattering happens where the scatterers have their own\n", "source (2-4 and 12-14 cm). The rate then spreads and grows as particles move\n", "through the scatterers and arrive from the central source. The error in the\n", "total scattering rate (right) follows the same ranking as the flux: about 1%\n", "for S$_N$ with 4 angles, below 0.1% with 16 angles, and around $10^{-5}$ for\n", "the hybrid method with 64 / 4 angles." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.18" } }, "nbformat": 4, "nbformat_minor": 5 }