{ "cells": [ { "cell_type": "markdown", "id": "8d0e3a56", "metadata": {}, "source": [ "# 10 · Resolution and Cost: the Accuracy/Speed Trade-off\n", "\n", "Refining the mesh improves accuracy but makes every solve more expensive. We\n", "measure both on a cantilever sagging under gravity:\n", "\n", "* **cost**: Newton-solve time vs. vertex count (10 resolutions),\n", "* **accuracy**: tip deflection converging to a very fine reference,\n", "* the punchline: a super-fine mesh is accurate but **too slow to iterate on.**" ] }, { "cell_type": "code", "execution_count": 1, "id": "2b976de0", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:37.236899Z", "iopub.status.busy": "2026-06-09T05:30:37.236686Z", "iopub.status.idle": "2026-06-09T05:30:37.746233Z", "shell.execute_reply": "2026-06-09T05:30:37.745954Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import time\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import simkit\n", "from simkit.solvers import newton_solver\n", "import utils" ] }, { "cell_type": "markdown", "id": "641361fb", "metadata": {}, "source": [ "## A timed static solve at any resolution\n", "\n", "`GravityBeam` is our standard static simulator: it builds the mesh, precomputes\n", "the per-mesh constants once, and composes three energy terms — the elastic\n", "material, a fixed **pin** on the left edge, and **gravity** — summing them\n", "one per line. The beam is soft enough ($E = 800$) that the sag is large and\n", "obvious. `gravity_scale` lets us ramp gravity for the animation, and `.solve()`\n", "returns the settled equilibrium." ] }, { "cell_type": "code", "execution_count": 2, "id": "450acb83", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:37.747407Z", "iopub.status.busy": "2026-06-09T05:30:37.747326Z", "iopub.status.idle": "2026-06-09T05:30:37.749723Z", "shell.execute_reply": "2026-06-09T05:30:37.749513Z" } }, "outputs": [], "source": [ "class GravityBeam:\n", " \"\"\"Cantilever sagging under gravity: elastic + pin + gravity, solved with Newton.\"\"\"\n", "\n", " def __init__(self, nx, ny):\n", " X, T = utils.triangulated_grid(nx, ny, width=2.0, height=0.3)\n", " self.X, self.T = X, T\n", " self.p = utils.precompute(X, T, ym=800.0, pr=0.4, rho=1.0, gravity=-9.8)\n", " self.psi = utils.make_material(\"Neo-Hookean\")\n", " pin_idx = np.where(X[:, 0] <= X[:, 0].min() + 1e-6)[0]\n", " self.pin = utils.PenaltySpring(self.p.n, self.p.dim, 1e7).set(pin_idx, X[pin_idx])\n", " self.gravity = utils.Gravity(self.p.f_g)\n", "\n", " def energy(self, x):\n", " E_elastic = self.psi.energy(x, self.p)\n", " E_pin = self.pin.energy(x)\n", " E_gravity = self.gravity.energy(x)\n", " return E_elastic + E_pin + E_gravity\n", "\n", " def gradient(self, x):\n", " g_elastic = self.psi.gradient(x, self.p)\n", " g_pin = self.pin.gradient(x)\n", " g_gravity = self.gravity.gradient(x)\n", " return g_elastic + g_pin + g_gravity\n", "\n", " def hessian(self, x):\n", " H_elastic = self.psi.hessian(x, self.p)\n", " H_pin = self.pin.hessian(x)\n", " return H_elastic + H_pin\n", "\n", " def solve(self, iters=30):\n", " x = newton_solver(self.X.reshape(-1, 1), self.energy, self.gradient, self.hessian,\n", " max_iter=iters, do_line_search=True)\n", " return x.reshape(self.p.n, self.p.dim)" ] }, { "cell_type": "markdown", "id": "fbb7c3f6", "metadata": {}, "source": [ "## Cost and accuracy across 10 resolutions\n", "\n", "We loop **explicitly** over ten resolutions: build a `GravityBeam`, time its\n", "`.solve()` with `time.perf_counter`, and record the vertex count, solve time,\n", "and tip deflection (the $y$ of the right-most vertex). A very fine mesh serves\n", "as the \"ground truth\" tip deflection, and the **error** of each run is its tip\n", "deflection's distance from that reference." ] }, { "cell_type": "code", "execution_count": 3, "id": "19f2a9b2", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:37.750613Z", "iopub.status.busy": "2026-06-09T05:30:37.750567Z", "iopub.status.idle": "2026-06-09T05:30:39.221400Z", "shell.execute_reply": "2026-06-09T05:30:39.221205Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fine reference: 2700 verts, 639 ms, tip_y = -1.5929\n", " 10 verts 3.0 ms tip_y -0.6471 error 9.46e-01\n", " 21 verts 6.0 ms tip_y -1.0354 error 5.57e-01\n", " 40 verts 11.4 ms tip_y -1.2861 error 3.07e-01\n", " 70 verts 14.5 ms tip_y -1.4194 error 1.73e-01\n", " 114 verts 22.5 ms tip_y -1.4883 error 1.05e-01\n", " 234 verts 38.0 ms tip_y -1.5424 error 5.05e-02\n", " 374 verts 63.8 ms tip_y -1.5629 error 3.00e-02\n", " 660 verts 127.8 ms tip_y -1.5772 error 1.56e-02\n", " 1064 verts 207.3 ms tip_y -1.5849 error 8.00e-03\n", " 1610 verts 300.5 ms tip_y -1.5894 error 3.52e-03\n" ] } ], "source": [ "resolutions = [(5, 2), (7, 3), (10, 4), (14, 5), (19, 6), (26, 9), (34, 11), (44, 15), (56, 19), (70, 23)]\n", "\n", "verts, times, tips = [], [], []\n", "for nx, ny in resolutions:\n", " beam = GravityBeam(nx, ny)\n", " t0 = time.perf_counter()\n", " U = beam.solve()\n", " dt = time.perf_counter() - t0\n", " verts.append(beam.p.n)\n", " times.append(dt)\n", " tips.append(U[int(np.argmax(beam.X[:, 0])), 1])\n", "\n", "ref_beam = GravityBeam(90, 30) # fine \"ground truth\"\n", "t0 = time.perf_counter()\n", "ref_U = ref_beam.solve()\n", "ref_time = time.perf_counter() - t0\n", "ref_tip = ref_U[int(np.argmax(ref_beam.X[:, 0])), 1]\n", "print(f\"fine reference: {ref_beam.p.n} verts, {ref_time*1000:.0f} ms, tip_y = {ref_tip:.4f}\")\n", "\n", "verts = np.array(verts)\n", "times = np.array(times)\n", "errors = np.array([abs(t - ref_tip) for t in tips])\n", "for n, dt, ty, e in zip(verts, times, tips, errors):\n", " print(f\" {n:5d} verts {dt*1000:7.1f} ms tip_y {ty:.4f} error {e:.2e}\")" ] }, { "cell_type": "markdown", "id": "0789c9b8", "metadata": {}, "source": [ "## Compute time vs resolution, and accuracy vs resolution" ] }, { "cell_type": "code", "execution_count": 4, "id": "85699636", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:39.222384Z", "iopub.status.busy": "2026-06-09T05:30:39.222322Z", "iopub.status.idle": "2026-06-09T05:30:39.381334Z", "shell.execute_reply": "2026-06-09T05:30:39.381107Z" } }, "outputs": [ { "data": { "image/png": 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oyvWmbW96x0eOr3xute8rIqKcJK2BpEuZdE3SyibS+lm6V0nLJ/0u69LlLGVrIm0ZbR65J0qLh7TmyQxpHZOS/r1cch/JfUZat8i9UUuhIC0z5D4qLZj0y2kpt0furdJSQ1rAaJYvX65aaUnL+PQYclzk3iD3QGkdpJHWJtKSXVpa7dmzJ9lycvz1yzGp3ZdlnmPHjum6RWrbLC2ypduakPuVdI2SVv5y39Hux3K8pJWSHJuUZZOU9yxp9SbHQesNoEntHEuZTrZVtl3//t+mTRv1WdLKNFI2km2QFlM5dW82hpTH9D8HUmaSVkamKs9mR9ktM+c+NXJt6PeukGccucbkmtIn06VbnnxWTF0W1MjnSL+1pZxf6U1gaHmVLBuDUmQ15ItJCxgYQvriS/PTlCPMyBem3DBT9tVPWaDRvkil2Xdq01Pmb5L3kmbF+iTngkiZ9yYr5CYkTXmli5A0d9Z/SeFHS6ZoSqkdGwnySOE05XT94yLbKl3cUm6ndlzS21bt/KQ8fxKgSquZtjQtTm0dEixLSQoW+p8BueFLwUeaL0tzdClsSpBSP1glP6WpuNZtUwqN8rsE7aTQL90ZpGl9RgUBCezJuvXXK+8j3RekYCdNpSW/QXBwcJaDUinPnVYQzij/WFrHVM6pFFik0JHyvErzfO2cynISbJLubPI5kebbkh9MP4eAsddodkvv8yKFUa3AZ8rjS0SUXeR+IsEnCUhJN3+5v8lLHjClK7sEJDQS/NAqXNIi88j3oylH6ZV1pdYdX7rsaEEICRrIPUa6jgntPqI9rGa03XK/l66K+rm05P+SbiGjUQgNOS5y75B7YsqBVeS+of3d2PuGdLOT9UkgSsh9VwIj0l1LKw/L/VirkEt5P5Z7rwTiUubtSauclPI4yHFPWQEo7yepKVK+lwQThHb/lwCXlPNkW+XcSoAjK7mBMnNvNoZsY8qgquy7qcqzmZHRZyQz596Q90nv2UfKtto6TVkWTGtbtP1meco6MKcUWQ25CUsSRslbYAxDa+8kUGDMdP0E5lndFv3ayozITUECUmklKtUSRZpSasfAkOMi2yp98qdOnZrqvClvelmlX7NqLC3hp9QuSUFX8kZIMk0JCkm/dgn4Se2s9KHXfz+ZX2qEpFWPFLqkACk1ZzLMb1rHSHs/WZfkbJCglOQ+0lphye8S5BJZDUpl9fOb8pjKOdWSr6e2bv18TZL4Xh4qpCWZHA+pNZb8BRJ0038IyUwNuymuJVMw5fcDEZEpSc4ZqWyRwJS8UpJyhOQnMiVjv5ul5U/KYI7MKy1gpGJGcvtIUEnux5KLRu4pxrRM1m8RIvmMJA+UPLDLfUhyceYEQ+4bUt6V+79UdEleU9leCdTp5yvUjsPXX3+NGjVqpLrOlDkUs1JOkveT8yL5rlKjBWikjCoteaR1jJQV5CW5juQcpEz+bgkssTyb0TZl5twb8z6GvL+py4IsT1k3BqXIqkiCTRmxREZKSS8xpfD391dfmhLN12qrhNQOSnI9+bspyXtJMEO7KQtJfii0lj1aTYe8v77UWoSkVbCTpq3SHVBa6GSmcJGVJvbGkm2VbnDSlNjY99XOj9Tqat0OhDQdlpZnGSWJ1F+HJKXXmlhrZJr+Z0BqaOQlASE5j1owSBI2Si2P1FBKQVlL4q6RwrTsn7yksCLJQyXAJIEqrfYwNbJ+6dr522+/qYK2/vtpQSn5LGnBKUs4n9o5lUKJ1H7pf9bTIoU4ecmoiNICTT63MniAJMvPyjVqimspvc9LSpLgXmr5OFQ5EeUWEnSSAIE26q4+6X4jiZfl+1jKEvLdnlGln8wjiZZjY2PTHFDFmO/mtEgCaSk/SQBDAhmalN3BtNbphlRWSktmuZfLPVeSZMv264+kmxZDjovcOyThutzP9ANsct/Q/p4Zsn3S6kjuSVLhJUngJRm5/rZplbbplTcy2natrKXfikq6hKVsoSLvJxV0hryXdD2TbZWXHBfZDxkcRxJjp9U6La17dVbvzaYoJ2WlPJsdTHHuLaUsSHkDu++RVZHaGbnxSHcpeXBNrZm1NuSsDC8stNFANFoth+QVMjX9Wjf5spbfpeAjNzHtxio1AVq/e82PP/74zLq0G2zKgp3035bgiIw0l5IEbFLOb+h6s4NsqwRc5s2b98zfpFCYXnNryVslo23Islofdq2QbWhTXlmHFMjlxqc/lK3U7Ejz4pSfAQkMSc2yjPKjBYmkBkrymMlIKFJwl9xdGqnFTUmrscpoiGDpPiGfDan1lGbyMvSttg1SeyQ5KAxpJSXn05Am2qYio9PIZ1iGEE7ZGkh+l4KskJxK+udNSIFECuzascnKNaoVyPSvJbkuJGid2WMkQ5vL+ZMHIf3rQx5IpHZP214iIksn91gJPEllnoxumvIlOS8lHYKMIidklCt56E5t1FPtu17mka5SqbUw0uYxppyTFq3FhP49Rv6vle/0W4ZLRc6CBQtUK6LUtkcjgQvpTiZD2Es5QkZbS5mCIDWGHBe5NwQGBuq62gm5/8lIZNJiROt2aCx5bzkWEkiTijE5l/rBFymPyL1QRi2UYFFKknMrI1I+lS6UMiqcvtTOsZTppFJYWkClJPdM7Z6vlQM0ct/XKhLTKxtpIy+mLJ9m9d5sinJvVsqz2cEU595SyoKUN7ClFFkV+QKWoXSl9khaVkgNmnR3khYnEnnXhuAVkphS+lrLQ6rciKRQIMEGual17do1WesbU5AcS9J9S95TAg4S+JAuXdLsWutSJ32yJU+AFFSkpkX2R4ZFTa0vuhb8kGau0gdbvvylpk/2Q4bilaav0jxamt5LcENam8j+S6FNCpxpSWu92eGVV15RTc8lsaa0HJKaEQkcSM2WTJeCjQSO0qplk6FoJdmmtHKSAoG0kJJhaeW4GVJTpQV9JGGkHDdJQirBTDlG0nrtf//7X7L5JQgkhVVZt9adT46PJFeVbZUhn/UTT8oww1LwluCJFMTlPErBW5oja8unV/iScyEBKKlJ1PZHCthSuJGXIUEpWYcUhKUGWHJmSAFYvybV1OTYS82WDAEt50OuJQnaSb4SKbRLcngZwliCe/LQI593qUWTQsmvv/6qjqcUtLN6jUoQT/KByHZIcFACe9I9JWXhx9hjJE3h5cFFWmJKIn9t2Gm5duXzSESUG0iwSYJOMox9auT7U8omcs+TMtV7772nEoHLd7bkAJLvTflulfVIxY58X0uZS4a2l+9SrfJG7lXSeltawkgCbmPKOWmR7nqynNxLJBAgrUEk4XhqFVLSvV7ut9LlXu4/0nJD7k1S/pIykj7Zfq18lFrFXmoMOS7yvtIKSMqfkpxcyheyzIEDB1Sli6ED9KQklWpyH5SKGjmXKVt2yYO95OqRe5bcE6WsU6xYMXXMpMwlx23Dhg3pvoe0xpZujdLFSj4rEqyTIJyUYSVop1/WkmMh+y3BMdlXORZy/qVlm+yvHHdZRiqO5RhJ2U3KQ9JKTj4PEljSbxWdklT8yaBDcr+WcoPc16WML6+s3JvlsyTpEeR8ybmQIJWU01Pm18qu8mx2MMW5t5SyIOUROT38H1F2kOFoBw8enFiyZEk1hKgMB9y4cWM1bGhUVJRuvtjY2MSJEyeq4VEdHBwS/fz81NDA+vMIGeZUho1PSS6hESNGJJumDen79ddf66bJkLkyTO7Vq1cTX3jhhURXV9fEIkWKqCFg4+Pjky0vw8HKMLMyT4ECBRKHDh2aePbs2WeGq5WhdEeOHJlYuHBhNTxryst57ty5arhgFxcXtf9Vq1ZNHDt2bOLdu3fTPXbprTflULxpDWGr7W9KMqxt5cqVk02ToWYnT56spsuQzLLPst1yXp4+fZqYke+//16dH1m2Xr16athdWb5du3bPDG2b1pCzy5cvT6xZs6ZaR8GCBRP79++fGBAQ8Mx8586d0w3Fq2/SpElq+oQJE5JN37lzZ2KXLl0SfX191edQfspwuimHS07Le++9p9Yrx0df2bJl1XT5POlLbajtsLCwxH79+iV6enqqv2lD9qZ1TFIbljs1aZ17zerVqxObNGmiPgfyqlixorpWLl68qP5+7dq1xNdeey2xTJkyic7Ozuq4t2zZMnHHjh3J1mPoNZpy2GQhx6dNmzbqvMr19n//939q2HNDj1Fax0K2Ub5P5NqSYa07deqUeP78eYOOj6xLpsu6iYhyinxvyXdveHh4mvO8+uqr6ns3KChI/f7o0aPEt956K7FYsWLqnla8eHF1v9f+rg05/8EHH+i+s4sWLZr40ksvJbtfGVrOSassIeQ7V77f8+XLl+jl5aXKfNoQ8Sm/s2Xd3bp1U9/xss8VKlR45n4toqOj1fZ4eHgkRkZGGnwsDTku9+/fTxw0aJDaVplHymQptzO18mNa5S/NvHnz1N+knJfWNp84cSKxe/fuiYUKFVL3Q7nH9erVS5VRDLmnS7lQjpecS7nvtWrVKvGff/5R6xs2bFiyeUNDQ9U9Wsopsp+yv40aNUr85ptvVHlPrFq1SpWFvb291TwlSpRQn4F79+5leKz/+usvVcaT5VIeE0PuzWlZt25dYqVKlRLt7e2TfYZSK7cKOb9aWcEU5dm0jn/Kso2xZTdDzn1q0nofrQxz5MgRg7bfVGXB1J63hOyPnAvK/Wzkn5wOjBFZO6kxklqi1JrQkmlJbgKp3ZWmw6k1oyYiIiJKSVppSAJxaSk7f/58HqB0SOtlyQ8mrWEkTyYRUVYwpxQR5VoyMl3KuLp0HZBm4dKVjoiIiMgQv//+u8q1o588nZJyIqWk5XpkWYuITIE5pYgo15J8S5L3SfqiS9Lz48ePq9pNyS8g04iIiIjSIyMGyuh4kkeqZs2amU48bq0kh5Pk65SE4ZJzcf/+/Sq5uuQsldxJRERZxaAUEeVakizUz89PJTLVkllLDaeMhKefcJyIiIgoNTKynIy6J4m2JfhCycnIeDIC35QpU9RoaVryc+m6R0RkCswpRUREREREREREZsecUkREREREREREZHbsvpfBKF53795F/vz5YWNjY76zQkRERBZDBlQIDQ1VI3PZ2rI+zxAsQxEREeVtiQaWnxiUSocEpCRfDREREdHt27dRvHhxHggDsAxFREREhpSfGJRKh7SQ0g6iu7s7AgMDUbRoURjC0HmNWac1ssT9N+c2mfq9TLG+zK7D2OV4PZker6e8ez0ZswzvT8YfT0nuK5VUWrmAcr4MZYnfd+Zkqftvru3KjvfJ6jqzsjzLUDmL15PlXU9ZWQevp5ynnQNDy08MSqVD67InhSl5hYeHq5+GMHReY9ZpjSxx/825TaZ+L1OsL7PrMHY5Xk+mx+sp715PxizD+1Pmjye78ltOGcoSv+/MyVL331zblR3vk9V1ZmV5lqFyFq8ny7uesrIOXk85L+U5yKj8xMQIRERERERERERkdgxKERERERERERGR2TEoRUREREREREREZsecUlkUHx+P2NjYZ6bLtKioqAyXN3Q+a2WJ+5+ZbbKzs4O9vT3zjRAREREREeWAxMRE9XxuzLOcMc9+fMbPnudgBqWyICwsDAEBAerDn5JcDJLgKyOGzmetLHH/M7tNrq6u8PHxgaOjY7ZsFxERERERET0rJiYG9+7dUyO+hYaGZsuzH5/xs+c5mEGpVMycOVO95EOnDWmofVDlgy4SEhIQHByshjcsWLBgpg4+WQ+Jmj969AiXLl1SnwdjIsXaZ8pUTLG+zK7D2OWMmd/QeU19PHMbS9x/c25TXr6ejFmG15Nxx9OYwi0RERGZlzybX79+XbXa8fX1VUESQ5/HJJhlaDDF0HmNWWduJo1zZF8fPnyojn+5cuVga2t8higGpVIxYsQI9ZIoq4eHB4oWLaqGNJTCqUQAhTTxk78XKVIELi4uz6yDH1jDWOIFm9ltks/BzZs3VVDK2dnZoGX0P1OmYIr1ZXYdxi5nzPyGzmvq45nbWOL+m3Ob8vL1ZMwyvJ6MP55ubm5GnQsiIiIy7/ObBKb8/PxUVzJjnuUkiGLo/IbOa8w6czt5BnZwcFDPwXIeDH0O1sdE51mUlb6TZF0yExUmIiIiIiKirOPzWO487nyKJiIiIiIiIiIis2NQioiIiIiIiIiIzI5BqRwSc+MGHnw7FffHjlM/5XdL0qJFC0ybNs0s77Vv3z4UL17cLO9FREREREREpO96UDgmb72Akb+dUD/ld3PIly8fzpw5k6dPBhOd54Anq9fg3oQJkpBKUtYjzMYGj+bPh8+kSfDs3g3W7MaNGyhVqhQeP34MT09PNa1p06YICAjI6U0jIiIiIiKiPGbF0dsYv/q0yhctI8rJzzl7rmJyj2roWcfPZO9TsmRJ1fCja9euumlhYWHI69hSysykRZQKSCUkAPHxyX7e+/BDxNy8ae5NIiIiInrGxo0bUaFCBTXE808//cQjREREVufGo3AVkEpIBOITEpP9HLf6NG6YqcVUdpNgW7zEHfTExcWp6caIjY018ZaxpZRJXe/xEuKCgtT/tQhrSvGhoUmBqNQkJOBat+6wy58/w/ey9/JCqdWrMpxv6tSpKhorLZMKFSqEDz/8EG+88Yb62+LFi/H555+rYa+rVKmC77//HrVq1XpmHdWrV8c777yDAQMG6Ka1b98ezZo1w/vvv6+iu+PHj8f69esRFRWFdu3aYcaMGfDw8HhmXfXq1VM/te56M2fOhL+/v4oWP3nyRNd1UOY7duwY/v77b1StWhWrV6/GvHnz1PxOTk5q/d26ddMda/n9xx9/RGBgIGrUqIFZs2bhueeey/D4EBER0bOkoDpmzBjs3r1b3c9r166t7rtSliAiIrJ0nWbsx8PQ6AznC4mKVQGo1Mj0jt/vQ35nB/V7IhJhg2ef8Qvnd8KGkU3SfZ+ePXvi1q1b6Nu3L+zs7PDyyy9j9uzZKmZw4sQJ9Qz7ySef4OjRoyhSpAhWrlypfk6ZMkX33JtSRs/B0jJr6NChWLduHU6dOoXDhw+jWrVqahl578uXLyMoKAgXL17EqFGjcO7cOfj6+mLChAlqO4W2TX5+fli+fDkGDRqEb7/9FqbEllImJAGpuPv31Sv+wQPd//VfiRER6a5D/p7acs+8/g1+pefSpUsqCLV9+3aEhobi0KFDuqDQ3r17MXz4cMyZMwcPHz7ESy+9pIJJT58+fWY9r7zyCn799Vfd7/KB37lzp7qQxGuvvYbg4GCcPn0a169fV9HTt956K9VtkgtBSHc9CWZpH/aUfvvtNxUkk/Xmz58fzZs3R8GCBVUAbeLEiRg8eLAuSisX3vz587FhwwZ1UXXv3h2dOnVCTExMhseIiIiIUr9fV65cGcWKFVP5LqQySsoTlkLKAClrfImIiDQSkAoMicrwFRGT/r0kPCZeN+/9kNTXaUjwS4JMJUqUUM+58hwsQaHUbN26VT2zy3OwNDCR5+WrV6+mOq8hz8GLFi3Czz//rN5TWj+LpUuXqnt6SEiIup9KHKBPnz4qLiDrlGftAwcOJNum+vXr48GDB/jss89M/iFjUMqEpPWSfZEi6mXn7a37v/7LxtU13XXI31Nb7pmXl1eG2yMRWImeSsQzMjJSRVolMiokyCRBJWnt5ODggNGjR6NAgQLYtGnTM+vp378/9uzZgzt37qjf5UKSPFASLZUPrrRikhZMkiPKzc0Nn376qYqiZqWwKNsmhWFpFSWR4fDwcLz99tuwt7dXF+ajR49w89+ujvLe8p7SvUD+LvPJ/koQjoiIKC+SyicpmEqNp9TC/v7778/MI/dPqUV1dnZWhU2t4kjcvXtXBaQ08n+tHGAJ9u/fjwULFqhCOBERUWqtl4q6O2f4cnW0S/fguTna6eYt4p76OuW9TKV8+fKqdZM818p9vGXLlur5OzWGPAdLQxQJRklswNHRUU0bO3asKh/Is/aWLVtQuHBhjBw5UsUFpDFIv379VCBLI72qXn31VfUerhnEMzKDic5NSL87nUQntZOeMqfU1Q4dU+/CZ2uL0mvXwNHf3yTbU6ZMGfVh+uGHH1QzuwYNGqjmf9KsT1oqSTe5ZNtfqlSqCcd9fHzQqlUrLFmyRH2Af/nlFxXE0hKXJyQkqGWT74qtalGlX6A1hgTQNPLBT/m7flI42QYJYsmFpn/8mTydiMh6Sc2edC2TShIXF5ec3hyLI5U50v1eWjNLzWlKUnkk3fOkplYCUtLVv23btqoJv7e3t9HvFx0drV4aqX3NLlLpJe8lgTNp8f3888+jbt26qaZNICKivCmj7nSaS/ceo933f6Xahc/WBtj0dlOU9HJL9xnflPxTxALk97QqhQx5DpbWWSnpT5N5pYJKX+nSpVXlVnrrMCUGpczMsWRJNcqeJDXXRt/Tfsp0UwWkNL169VIviZh+9NFHqiueDDkpOZ3kQ6xPftdyPaUky3311Vfo0KGD6hbYo0cPNV1aS0kASgqGhkRNZV5Tk22QwrQ0OyQiIusnTdpXrFiB+9KdPS5O3ZsoOeluJ6+0SJcAaZ4vlVZCglPSWlpaH0meSKlB1S8Ey/+1FACp+fLLL1X3+pSkgkoCZEK64BsqrXlvP47ChvOPEJhQHj6+HrC7/4+q5ZWyjdTuSovtvMKY42mN25Ud75PVdWZleWOXNcX1lNVtsCaWuu95+XoyZh1al24JyEjrX2PSuJQs5IYvulbG//1+TuWLSsobJfmjoKb7ujskW5+h605tPqk8kW1N+bfYf6fJPsgzuf7f5feGDRumuj55dv/mm29UpVJa768dF33604oWLapS8OjPI90FpWGKtk0Z7bc2n3Tvk9ZW2rmTFEKGYFAqB3h27wbX2rXwZNVqRN++DSc/P3i+1MPkASmp7ZRkak2aNFERXckJIU3uhERUpTmg/JQaUuk7Kl3i0irYSxc6afr37rvvqv/LurQPsSQplxxS0grLy8tLFUAPHjyYakI2aRoogSn5oEvSVFMYMWKECrhJay1pmii1s1J7Lq27JB8VERFZjwsXLqiuaNJSRrp5t2nTJqc3KdeRwqMMJiKDlWjk3izHUu7fQgJQZ8+eVcEoSXQugR9JfJoWWZe0vNLIvVgqjaSc4O7urgqnUsA1RFrzJg3Zff6/hwYbZ+RDRfQv+kDV9Eo6ARnMJS8kYzfmeFrjdmXH+2R1nVlZ3thlTXE9ZXUbrIml7ntevp6MXYcMtiUVIForJmNaM8k9sU/9kmhQpjCWH72NgMeRKF7ABb3r+OlaSOnPa8i605pP7onyfJ7ybw4ODmqatHiS5OPS20kqjbZt24Y///xTJSZPbX3yDC45nqTLX1rPwdq6U3s/0blzZ3X/llF2hwwZosoBy5YtU/d9bZukjJDefkvPKZlPWlpLUFA7d4ZWFDEolUMkAOX9zphsbQIo65YC5Pnz59UHSZrxS6IzIbWJ8uF+/fXXdaPvyQdP8kKlRlpBSesoWV4uDn0y7eOPP1ZN5yWwJV3tevfunWpQSrpYyLxSeyvbJ8nMs9ocUC5GuQike8Lt27fVBSiBOLkYiYjIOkiBZ9euXSrxptzTpFZQKlXYZct4kodJajT1u8YL+V2CfkIqsWR0HcllIcdeuu+nF+yRvBTyyi7Xg/4bsjup/loNO4SncMace36Y1qICQh8FqkFRiIiIjCUBqHHtKmbrgfu///s/lfdJAkmSt0lGzUtJev/ICPTvvPOOCvIsXrxY5YzKrudgySstcQBJzyMVTNJSWhqsyHrMhUEpK1a1alX1gU7LwIED1Ss1EpFNaeHCheqVknz4pRuAvAwhrZrkJbSg3JMnT9J8b0mqJi99ksBdIw8kb775pnoREZF1kta/EpCSe46MGJvd+Q0oqfZUXpZAWkmpAKTe/V8jHS3OJ/pibN+WuiClDK8tFW0pc14SERHlFOmpJK+0nmu1SiEZUU9eGcnoOThlup7U3k9rHf3XX3+luo5PPvkE2Y1BKSIiIrJ4FStWVN3LpNWv1oVcG0Dkyeo1iL1zBw7FisGzR3eVv5HSJl3tpWZVcnLpk9+la4Elku4UqRWkhbSeWn7kNpqU9UKjMoVUF47NmzerfGMyyEvr1q116QuIiIjIspg+6zQRERFRFkkA4vDhw9i/f7+uNrBx48bJAlISjJIRbR8tWICQrVvVT/n9yZq1PP7pkBbKktdx586dumnSRU9+l2Sqlkjye6TXVTM4PAb9fzqEnrMP4sS9SPTp00flspIW43PnzrXYJMZERER5HauNiIiIyKJI1+6NGzeqEdUkYaYEUCQnYbJ5btzAPUm8nZDwzPIywq0MKGLqAURyk7CwMFy5ckX3u4ysc/LkSZVzSbo+SlJT6cJfp04d1WxfRrGVFkbaaHyWplcdP8zZczXD+Y7efIxX5h9GrRKeGN7mJYRcOqwStksCV8mP1ahRo2wZCZiIiCirPjFDVzlLxKAUERERWQwZMGPFihVqWGFJ8NmrV69nAlJaKymk1XLGxkaNcCsDiuRVR48eVUEYjTYyngSiZIASGZDk4cOHKsejjJpbo0YNbN269Znk58aaOXOmemlDSMu6JdiV1SHsnSVBbBt/fLHjpm6obs341iXgZG+LhYcDcSM4Sk07fusJBi95gspFC6J71YZ4cPGYanknATltuOrczlJbf+XlIeyzsryxy2blejLVNlgTS933vHw9GbOO2NhYdd+RSi2pzJKfxjBmfkPnNXYbcjPZVzn+UnbT7rFy7kJDQw1a3iYxrQ76eZh+gerSpUsquao2pKL+B1+GXJTCjXzwiWQoUhniU7oLWEuBl4jInKQ1jwx2IffYsmXLomnTpml+n4Z98CHi0kjKCVtbOLRoDjdpSWUCUqiSoZafPn2qvuMpY1JG8vDw0B0zUw1hfyMoXA3ZfeVuMMr6Fkw2ZHdCQiI2n72H73dexqX7YcmWq+3jhFfq+qBLw0qqG6Bsn5TtcuvojRzC3vKGsM/K8sYua6rrKSvbYE0sdd/NtV3Z8T6mWKcx65DnMClDyOAW0hrWmNHttYG3TDmvMeu0BvrHX2Ij2rlLWRZIC1tKpWLEiBHqpR1ESfqZskAlB15q/uTDltoHjh9Yw1jiBZvZbZJ8HJI4Vmr2DQ1UmvomYO4bQFaWY4EqbxSqzLlNefl6MmYZS31Ake/Q33//XVUItW/fHnXr1k0zYBCyeTOeHD2a9spsbOBepiy8TfSA6eaWFPQgyxmyO7XPp62tDV6s5osOVXyw9VygCk5dCEyqpT12LxrH1t/AT8eCMbyxHy7sXo1ixYqpUZB4fomIiHIOg1JERESUY6TBtgSfpGZTuupFRETAz88v1Xnjnz5F4GeTELJxY0YrhedLPbJng8niSXCqQ1UftKtcFNvP31fBqfP3QtTfzt4JwbiVx9HezQZhFy8iICBABaakJRwRERHlwH2bB52IiIhygnR5njNnjmrWLQoVKpRmQCr84EFc69I1WUDKuVo11VUPdnbJfvpMmpSnk5zTf8GpdlWKYtPbTTD3ldqoUiyp60BYohNWh5XDyVgfhIWHY9myZVi/fkOeyv9BRERkKRiUsnIlS5ZU3SHEkiVL1KgzlkK2p3nz5jm9GURElAOto/7++2/8/PPPuH//frJR4lJKiI7G/S+/wq1BryEuMFBNs3V3h+8336DUiuUos2UzCr32GtzbtVM/5XfP7t3MuDdk6aQl3guVi2LDW00wf2AdVCvugQTY4kRcMWyKroiQBCecOHEc02bOQWxcUoJ2IiKinPTVV19h7Nix2bJuyZVZpkwZBAUFwRIwKJWH9O/fH3+llRQ2h7Znz549WQq4yYhMkqjU09MTtWrVwsSJE9Uw2Ckvuv/973+q9l3mlwvw008/RVxcnG4eGYlI8kHly5dPDZctPy0pgEdEZC2kNcrq1auxbds2lcRcRoGrXbt2qvNGnT+P6z16IPjnn3XTXBs2QOl1v8PjxY7qd2kRJaPsFZv6rfrJFlKUXnCq9XNFsG5EYyx8tS6q+3niYUI+rIuuhAtxhbEjKD/af78f607eQXwCxwEiIqLssWPHDjWYizxzenh4qFyax48f1/1dWpBPnTo1WVBqyJAhqqu5pDuYNm1amo0+unTpkuH7y/PzgAED8Pnnn8MSMKcUmYWMpJQdI9L99ttv6Nq1q0qMe+LECYwbNw5r167FwYMHVQBK3rdt27Yqcfkff/yBcuXK4eTJkxg0aBDOnDmDlStX6tZVtWpV9TdLTL5ORGQNpEZu+fLl6meRIkVUDimpCEgpMT4ej+YvwMMZM+QGoqbZODrC+913UODll2EjXfXI4kcwFoGBgWpgmOwYwj4rw41X9ABmdSuFQ7dCMf/QPRy89293zwdhGL3sBDZt3IA6NaqjfU1/2Nta5gh9HMLe8oawz8ryxi5r6uspM9tgTSx13821XdnxPqZYp6HrkGc+ue/Ic5wMOGVsd2xj5jd03rTm27BhAwYOHIivv/5a9WiKi4vDvHnz0KxZM/W8KhV1CxcuRJMmTdRga9p6KleujO7du+Pjjz9Wy6S2/nXr1qFDhw4GbWPfvn1Rr149tT5XV1eD9im9fZXj/+DBA90zv5w7aRxiCAalTOzbb79NlrhVI0Nba1FLiYLu3r071fmkgK7l05g/fz6ePHnyzHu88847mdo2aQ0kUVUJvGgtjd58802sWbMG586dUy2NFi9erHt/+VBJC6Ndu3apbZRtmzx5MpycnFRrJGnpJMGf6OhoVK9eHTNmzFA/xSeffIKjR4+qdckDiASBtGOjvz3fffcdTp06ZdD2pEdaOdWpU0fVvlesWFFdyLIuiRZfvHgR165dU1FoIRe6BK6ee+45NfR4ixYt0l23DG85ePBgHDlyRL2PLCdfGFm9eImI8hq5r0hASu4VHTt2TLWyIiYgAHfHjUfksWO6aU7PPYdiUybDqVw5M28xZccIxhkxZF5TjQ7ZzRfoWr889l8JwvQdl3H05mP42z1Gsfj7uH30D7x/pjS6Pt8cXWsWg72d5QRDLXG01bw+hH1WlucIxjmL15PlXU/GriMqKkpVgGgNC7SfKZ8/U3s2P3z4MPbt25fqfCmfzR8/fvzMyMCpPZun1chBnv3fffddjB8/HsOHD9dN//DDD9Uz5/vvv6+eTzdv3qwaXuivY9SoUbpuffb29s+sXwJz0gJLnsnlb7Kds2bNwg8//KByeMoz76+//qp7Ji5fvrzK5SnP89JSKytSjkKvnTtDR7e1nLsr5QgJ+khro4cPH6oPzYQJE3QXTOfOnVVh8urVq6pVkQSPJk2apPvg9evXT108kg+kZs2a6qKV5TRbt25F/fr11UPIZ599lqXtMZR042vTpo2uW6B0D5EHH+3i00gXPtm27du3Z7jODz74QH1xyYOU7KtEteWLgIiIMiY1Z1qrmUqVKuG1115TBcGUASm5fzxZvQbXO3f5LyBla4tCQ4ag1PJlDEhRtpGCe9NyhbFyWEMsfaM+vP3KYF9MSSTABuVirmL7+pXo+M12rDx6G7HxCTwTRESUKZcuXcKNGzfUc3RK/fr1w/79+xEZGakakUhDC2Ps3btXde+TluiaFStWqAYmEpSS0WalQYg+KZdpDVZyEp+sTUyLlKbXBUxaAMkro/lef/11ZDdpTVSqVCn1f2n5JJFXIa2cLl++rHJQSb9VaRX0f//3fxg2bJgKMEmtp+QB0Ugup++//x53795FsWLF1LQqVarg1VdfVf83NIiT1vYYQ95f65MrgaS0cpX4+vqq4JdGAm8S1NJI8ElaSMmDk0R75QtEuv8x1xQRkWGk2faqVatUAUmak4vUWr/GBQfj3kcfIWzHTt00h+LF4Tv5K7im8R1OlB3BqUZlvdTr4NUK+HHbSeQLPIlidqHwijyKH9c+xIxdxTGiZRl0r1UcDhbUcoqIiJCpHkY1atRQ3dgyIs/mWU3zoiUWl+fQlHx9fVUlXnBwsGqRJc/bxpBugZ06dUo2TXJSSesl0aNHDzXIjD55D3mvnMa7aR4nLaE00jJJ6/cpARjpOii5PiRQI6+XXnpJtRQSEsGVAJJ0uZMPs/wU+hn8S5QoYbLtMcadO3d0OUq8vLxUoCw1Mr1w4cLJckrJPkvLLvkpASktOCWBLmmBJfspXROlpRgREaXt5s2bmDNnjqqdkwKW1loqpdA//8S1Tp2TBaQ8enRHqd9/Z0CKckzDMoXw65utMXDAADx0Lw97JMDbNgy3giMwbvUZtPzmT/x2+BZi4lgeICIiw8izqUjt+fTu3buqC5w8xxYoUEB1gzc2KCU9nYx5tpb3kPfKaQxKUaqkJluiqhKc0V4yCoA2sp30zz127JhqYigfZgliCf3ue9LCytxkG6UvrZYn6vnnn1d9clNe1NLt8NChQ+rvGZHj8OOPP6oHLLnYZ8+erXJSERHRs+Q+IK1sf/75Z5XfQRJ3SpN0KWjpSwgPx72PP0HAsOGIf/RITbMrUADFf5gB388/h10+w/IQEGWnBmUL44f/9UWLLn3gVCIpb6YIfRKM99ckBacW/30T0XGpB12JiIg0ksfJ399fpatJ6bfffkPjxo3VYF3SeuvChQsGHzjJxyzlL+mpZIzz58+r98ppDEpRqurWrasCU5J0TSKq8iGXoMyWLVvU3yXII0nMJLIqgSrp2peTpOWSdNnr2bOnighr3QZffvlllT9KEsVJwnOpqZf5unXrhhdffBEtW7bMcN3SF1dq+uUYSIsxebBiTikiomdJs3YZ1VQGg5BBMWRkF/meTVlJEXnyJK51744ny5frpuVr0QKlN6xH/jZteGjJ4rSqWR6/DG6E1cMbob1fAro7n0N9h1sIfBKOD38/ixZf/4lfD95AVCyDU0RElHY3ccnr9OWXX6rE6fIc/eTJEzWY2LJlyzBlyhQ1n3TD0wZG0y9jSUJ3ee6V0ffk//Izra57GZFne+nlJJWHOY1BKUqVBF42btyousLJaHOSKFwShl+5ckX9fcyYMWoeyRMiEdmGDRvmyJGUB578+fOr4Jj085V8T9J6SyLMQvr8ysORdM1r1aqVarYo3RAlya6MCmgIaREm682XL5/aT3mflE0jiYgo6d4hBSypHBgyZIiqEdSXGBuLh99/jxv9+iP25i01zcbVFUU/nYjis36E/b/N2oksVW3/Ahj/YjW4uOVDJfsH6Ox0HoVswnHvaRQmrDunglOLDlxncIqIiFIljSNkxHgZLV7KSyVKlFDJyCUIJQNxiVdeeUUN3PXo35bk4oUXXlDPuDJS4Hvvvaf+rw1CllrXvYz88ssvqiGHoSPkZSebRP3+VpSMNpyxdAlLOZyxRCalC5gk5ZYWQykZmgQtq8nScjtL3P/MblNGnwlzDEFr7uFXs7KcqYcHz8w2WBtL3H9zblNevp6MWSY7rie5X2oJObUhmVOOrhd97Trujh2LqLNnddNcqleH75TJcPT3h6XR3/+U5QHKWhnKmGOflXmyk9zzpfX46dOnkQgbHI/1wZk4H/V/4Z3fCcOal0G/+iXg7JC866op5PT+5/R2Zcf7ZHWdWVmeZaicxevJ8q4nY9eh/xwmrbONeZYz5tnPnM/4X375pa4VVXpk4C4ZqS8wMPCZsldapCdUzZo1cfDgwWQ5ljMr5XOwdu4MLT9x9D0iIiLKFOkSvX37dpw4cUINDiEFm5Q1blL39XjpUjz4+hskRkX9W/qwR+ERb6LQ4MGwMXB0VsodZs6cqV5aYnspJEugUkgh1VCGzGvM+rJDgwYNVN5JqbWujbso42mHtUFJQ3E/CI3GpxvP44ddl/By7SLoVrUwnB1M20Ehp/c/p7crO94nq+vMyvLGLmvq6ykz22BNLHXf8/L1ZMw6YmNj1X1HgkESFJGfxjBmfkPnNXYb0ho5MKP1yEBk33zzjSpvGfqekmJB8kkZsn5DyDrk+MuAYVpgTM6doYOWsSRIRERERpPaL8kfFRAQoGrBtLwG+mLvP8C9Dz5A+P79ummOpUrBd8oUuFQ1Lhkn5Q4jRoxQL612VLomWGNLKY1sQ7Vq1bB161bVteKNcOD7nZex7VzSaMXBEXH4ft8dLD3xEEOalcbLDfzh6pj14rel7H9KbCnFllK5Ea8n62gppbXUFtbQUspQkkrH2ATnpiZ5riSFg1TU6LeUMrRrIINSREREZBRpor1q1SpERESgbNmy6N69uy6XnyZk6zYEfvwx4p8+1U0r8PLL8H5nDGxTzEuUm0luSxloRXh4AJPa+aNe4iWcSCyJjf88VtODwmLwxeYLmL3nGgY3LY0BDf3h5sRiOBEREe+GWcSUXMTPAhHlJUeOHFG5dOT+17x5c/WS0WQ08aGhuD9pEp6uW6+bZl+4MHy++AL5mjbJoa0mMh/J0RFw/TL8Xe9gfpc2WHM9EZvP3INkcQ0Oj8HkrRcwd+9VvNG0NAY2Kol8DE4REZkEn81z53Hn6HuZJM3TTNUHk6yDtBgQhiaYIyLKjby8vFSrqP79+6NFixbJAlLhhw7jWpcuyQJS+du1Q6n16xiQojxDRiuWYG1kZCT2b1+PF9xuY9Ob9dG5ui+0y+VxRCy+3nYRTSbvwoydlxESFZvTm01ElGtpz1/a8xjlrudgtpTKJHt7e7i6uqps93LwJcu/PglWSd/KjBg6n7WyxP03dpskMiwXoiR28/T01AUsiYishXy/SX4gSYwpI6uMGjUqWa6EhJgYPPxuGoIXLZIvRTXNNn9+FP1oAtxffDFZ4IrI2kk5QAK20rV17dq1OHnyJG7cuIH3unfH263L4Yddl7H+1F0kJAJPImLx7R+XMG/fNbzepDRebVwSHi6s3CIiMvZ7V57DpLwiOS4ll6GhZQ9jnv34jJ89z8EMSmWSfMgleZfk1bh58+Yzf5fs84acFEPns1aWuP+Z3Sa5ECWhKxGRNZEh7zds2IAKFSqgR48e6v6nH5CKungRd98bi+hLl3TTXOvXh++XX8DB1zeHtpoo5xUvXhxDhw7FH3/8gWPHjqmHnrLe+TCtT82k4NTuK/j9xB0VnAqJisN3Oy7hp/3XMKhxKbzeuBQ8XBmcIiIylPYcJgGS4ODgbHn24zN+9jwHMyiVBVIoL1euXKpd+ORikOzzGTF0PmtlifufmW2S1nKWFlwjIsoKKXht2rQJR48eVa2DpdWHfq1jYny8ahn1cNp0JMYmdT2ycXBA4TFjUHDgANikaEFMlFfLitKdr0GDBihUqJBulKh8iRGY2qsG3m6VFJxae+IO4hMSERoVp0bvW7j/umo19XqTUvB0Nc8ITkRE1tBoRCoAtO9bUz/78Rk/e56DGZTKIum2J8MepnZyUpue2fmslSXuvyVuExGROT19+hTr169XXdQLFCiAXr16oWBUFB58OxWxd+7A1sMdUWfOIursWd0yThUqwHfKFDhXKM+TRZSC/gPS5s2bcf78ebRu3VoFq77pWR0jW5XFj7uvYvXxAMRJcCo6DjN2XcGC/ddVMnRJil7QjcEpIqLMPp+b4tmPz/jZg0EpIiIi0nn8+DF++uknlSOgfPny6Nq1K6I3b8HVCROkGhKQvAv6o6zY2KDQ66/B6+23YavXrY+IUlemTBlcunQJ27dvVz/lGvMv5IHJL1XDWxKc+vMKVh5NCk6Fx8Tjxz+vYtFfNzCgYUkMbloKhfI58dASEZHVYFCKiIiIkuUFKFGiBPLnz4/27dsj9uZN3JOAVBpJQH2/ngKPF1/kESRl5syZ6iXdP0VgYCDCw8PV/+/du2fwUTJkXmPWZ0mkm0j37t3x559/qgToP/74Ixo3bqy6yNrb2ODthoXRs7I7fj16HxvOPVLBqYiYeMzecxWLDlxH92pe6F+7iBwAWCJznZfseJ+srjMryxu7rKmvp8xsgzWx1H3Py9dTVtbB6ynnyTkIDQ01aF4GpYiIiPI4yXFz69Yt1TJKcjJIdz0JJsj/n6xek/aCdnaIvngJYEyK/jVixAj1CgkJUSM2SuJTGQVJCqeS68MQhsxrzPoskWy7BKH+/vtv7Nq1C7t374avr6+alvR3oFaFknjvSSRm/XkVy4/cRkx8AqLiErD0+AOsPv0QrzQoiSHNSyM8Oh4rjt5GwONIFC/ggl51/FDKyy1H9stc5yU73ier68zK8sYua+rrKTPbYE0sdd/z8vWUlXXwesp52jlwczPsXsSgFBERUR4mwacVK1aoPFKvv/66ejDWT2geceRImq2kpBuf5JgioszlPWnUqJHqznfixAn1MyVfTxd81rUK3mxZBnP2XMPSw7cQE5eA6LhE/LT/uurWJwnSbW1skIhEde3O2XMVk3tUQ886fjwtRERk8Tg0DhERUR518uRJzJ8/X+WRqlWrVrLRZxLj4hD4xReIPHky7RXY2MChWDHzbCyRlSpSpAjatWunCwYfOHBAJUOP/XdUS+Hj4YJPOlfGvrEtMahxSTjaJc0rXfskw1t8YiISEqECVPJz3OrTuBGU1G2SiIjIkrGlVA7nQzB2ndbIEvffnNtk6vdi/23L+zyZE6+nvHs9GbPM7du38ddff+HChQtqGN8WLVqornsy2p5ICA5G+MSJiD99Jv0VJSYipnkzi/zcmYK2X4bmRCDKKil7SqupR48e4dq1a+jWrRuK6QV+i7g74+NOldH9ufz4YOstnA54mup6JMC1/OhtjGtXkSeFiIgsGoNSOZgPwZj5rJUl7r85t8nU78X+25b3eTInXk9593oyZhmZ79ChQyogVbBgQZU/SlpqaCKOn8Cd0aMR/+CB+t3GwQH5O3ZEyPr1SaPvych7//70mTQJnnXqwBrpH09DcyIQZZUEiQcPHoytW7fqWjI2b94cTZs2Vd39NF5uDvAv5Iazd56qllEpSYup6w/DeEKIiMjiMShFRESUxzRp0kT9fPHFF+Hs7Kz+n5iYiMe//Yb7X34F/NttyL5IERT/fjpcqldH4eHD8GTVapVDSrrseb7UA47+/jm6H0TWyMnJCV26dFGtFzds2KBG6bt8+bIKIEslqUaSmttogeJU7Ln0EBtP30XHqj7J8sQRERFZEgaliIiIrJwEnA4ePIjq1aur36UF8EsvvaT7e0JUFAI//gRP163TTbOvUQOlZv4A+0KF1O8SgPJ+Z0wObD1R3vTcc8/Bz88P69evV935tACyRkbZk6TmaYmMTcBbS0/g9+fuYlLXKijqkXx5IiIiS8CgFBERkRWLjIzEmjVrcOXKFdy9exeNGzdO9veYgAAEjHwb0f/8o5tW8LXXEN+vry4gRUQ5I1++fOjbt6/Kbero6KimBQQEIDo6GmXK+KhR9iSpubSEkuCz9vM5H3ecuxui5t/xz30cuvYI4ztURN+6JWBry1ZTRERkORiUIiIislKSF2nFihV48uQJihcvjhdeeEE3cIcI27cfd959FwlPk5Il27i6wvfzSXBv395qk5cT5TYSaJLglIiIiMDy5cvVyHzSxa9nnedQt2RBldQ84HGk6tLXu44f/Au5YsvZQHy07iyCwmIQGh2HD9aexfqTd/Fl96ooXThpfURERDmNQSkiIiIrdPz4cTWsvIzmVbduXbRt21YlUZagVGJCAh7NmYOH38/Q5aOR7nnFf5gBp3LlcnrTiSgN0oWvTp062LNnjwo4S5fcdu3apTrKXoeqPmhUphA+3/QPVh4LUNMOXQ9Gu+n7MLpNOQxuWhoOdv8lTyciIsoJvBMRERFZmZs3b6oEyTJalwwp36FDBxWQEolhYQh4ayQeTv9eF5DK17o1Sq5ayYAUkYWTa1pG45NWUoUKFcKpU6cwe/Zs3LhxI9X5PV0d8XXP6lj8en34FXRR02LiEjBl60V0nXlAjd5HRESUk9hSioiIyMr4+/urB9dKlSrB29tbNz3q0iWEvjkCCQFJrSZgY4PCo0ah0JDBsNEbbp4os2bOnKle0kJPBAYG6rqMGtMl1JB583IXU7muJTB16NAhnDt3Dr/99hv69eunyzuVUpl8wM99ymPewXtYfvIBEhKhck51+WE/+tYqgtcb+MDZ3jTfAeY6L9nxPlldZ1aWN3ZZU19PmdkGa2Kp+56Xr6esrIPXU86TcxAaGmrQvAxKERERWYFbt27h6tWraNKkifq9RYsWyf4esmUL7n7wIRIjItTvdh4e8P3mG+RrmjQ/kSmMGDFCvUJCQuDh4aFGenR3d1eFUx8fH4PWYci8xqzPGsn+y8h88qpZs6Ya0ECC0UJLeJ6aL0sUR+9GTzB+9WlcCAxFfCKw+Nh97L8Rii+7V0PDMlkb3MBc5yU73ier68zK8sYua+rrKTPbYE0sdd/z8vWUlXXwesp52jlwc3MzaH5WixIREeViCQkJ2L17N7Zu3ap+SlJzfYlxcbj/1WTc+d8YXUDKqdJzKLl6FQNSRFagTJkyqFKliu77YNGiRThw4ID6f2pq+Hli/VtN8M7z5eH4b06pG48i0Hfe33h/zWk8jYw16/YTEVHexqAUERFRLiUjcS1duhR79+6Fi4sLXnnlFXh6eur+HvfoEW699jqCFy3STXNo2xYlly6FY/HiObTVRJRdHj58iPv372PHjh345ZdfnglSaxztbTGydTlsHtUEdfwL6Kb/dvg2np+6B9vOBfIkERGRWTAoRURElAvduXMHc+fOVV32pAtP9+7dUbJkSd3fI0+exPXuPRBx+HDSBAcHFP34I7iOGwtbZ+ec23AiyjZFihTB8OHD1XeBDHgwa9YslQxduvSlpqx3fqwY2hCfdqkMN8ekwRAehEZj6K/H8OaSY3gQGsWzRURE2YpBKSIiolxGHjClu97Tp09Rv359DBw4UNdvX/72eNly3HhlAOLu31fT7L294f/LzyjQt2+auWaIyDpILq8BAwbghRdeUAnnf//9d6xatSrN7ny2tjYY0LAkto9pjpYVCuumbz4TiOen7sWKo7fTDGoRERFlFROdExER5TISWJKWUXfv3kXlypV10xOiohD46Wd4umaNbpprnToo9t1U2Bf+72GTiKz/O6Jhw4Yq39TatWuRP39+2GYwwmYxTxcseLUu1p+6i4kbziM4PEbllxq76jTWn7yLL7pVRYlCrmbbByIiyhvYUoqIiCgXCA4Oxs8//4zHjx+r3wsUKJA8IBUYiJv9+icLSBUcOAAlFi5gQIooj/L29sYbb7yBNm3a6KZJd76YmJg0g1ldahTDjjHN0bWGr276/itBaDttL37adw3xCWw1RUREpsOgFBERkYW7ePGiyh9148YNnDhx4pm/hx04gNChwxB1/rz63cbFBb7ffIMi778PGweHHNhiIrIUdnZ2sLe3132XSHe+OXPmICAgIM1lCro5Ylqfmlg4qC58PZJy0EXGxmPSpn/Q/ccD+OdeiNm2n4iIrBuDUkRERBZKcsDs3LkTy5YtUy0bJEdMy5YtdX+XPC9Bc+fh9uAhSAxJekh0KFECJZctg8eLHXNwy4nIEkkC9Jo1a6qWlwsWLMDu3btV3qm0tKzgrXJNDWzoDy0d3amAp+g0Yz++3X4R0XFpL0tERGQIBqWIiIgsUHh4OJYsWYL9+/cjX758Kpm55IjREpXHh4Xhzttv4+HUqRK9UtPytWiBUqtWwrlC+RzeeiKyRE5OTujcuTN69+4NFxcX7N27VwWngoKC0lwmn5M9JnapglXDGqKsdz41LS4hETN2XUGH6ftw9EawGfeAiIisDYNSREREFujOnTu4du0a/P39MXToUPVTE33lCm707IXQP3YkTbCxgfOrr6L4jzNh5+6ecxtNRLlCxYoVMXz4cJQvX14NmPDHH39kuExt/4LY9HYTvN2qLOxtk4LjVx+Go+ecg/ho3VmERceZYcuJiMjacPQ9IiIiCyHd8bSh1+VhsV+/fihdurTKCaMJ2bYd995/HwkREep3W3d3FPt6CkLLl4dNBqNrERFppAVmnz59cPLkSTVKnyYuLk6XgyolJ3s7jHmhAjpU88G41Wdw6vYTyFfWLwdvYsf5+3ineTH08PHhQSYiIoOx9EpERGQBJGeUJCDetGmTblq5cuV0AanEuDjc//pr3Bk1SheQcqpQQXXXy9e8eY5tNxHlXtIdWHJMuf/bwvLBgwf4/vvvce7cuXSXq1jUHWuGN8KHHZ+Di0PSd9Tdp1F4Z/1VjFp2Ao/Cos2y/URElPuxpRQREVEOe/ToEVasWKEeCAsXLoxq1aol+3tccDDujHkHEX//rZvm3rkTfCZOhK2LSw5sMVHqZs6cqV5a8uzAwECVH03cu3fP4MNmyLzGrM8aZcf+y+h8YWFhWLVqlWpB1bhxY5WHKi0dy7qgZuGKmLzrFg7fClXT1p28iz8v3Mf/mvvhhQoFdHnwcsP+Z3WdWVne2GVNfT1lZhusiaXuu7m2yxKvp6ysg9dTzpNzEBqadF/ICINSREREOeiff/7BunXrEB0djSpVqqBTp04qSKWJPHMGAW+PQpxWMLO3R5Hx41Ggf79se9gjyqwRI0aoV0hICDw8PFC0aFHVCkcKpz4GdusyZF5j1meNsmv/ZZ3SdXjt2rW4cuWKCpR37doVpUqVSmcZYHkFf6w+fgcT159FaHQ8nkbF45NtN/DnjXB83q0qinm6WPz+Z3WdWVne2GVNfT1lZhusiaXuu7m2yxKvp6ysg9dTztPOgZubm0Hzs/seERFRDkhISMCOHTtUC6nY2Fi0b98e3bt3h6Ojo26exytX4ma//rqAlF1hL/j/vAgFX+7PgBQRZQtfX18MGTIE9evXV8HFX375BQcOHEh3GQmQv1S7OJa9Ugkdq/73EPnnxYd4Yeoe/PzXDSQkJOXLIyIi0segFBERUQ6OsJc/f368+uqrqFevni7QlBgTg3sTJiBwwkdIjI1V01xq1UKp1avhWrs2zxcRZSsHBwe0a9cOr7zyimrx5ufnZ9ByBd0cMLN/Lcx9pTaKuCd1+wuPicfH68+pUfquPDCsKwcREeUd7L5HRERkRpGRkXBxcYGtrS1eeuklNdqejIKlib13D2GjRiH+wkXdtAIvv4wiY9+DjV4rKiKi7Cajf44cOVI34IJ8f506dUoF0eU7LC0vVC6KBmUK4astF7D00C017djNx+gwfT/ealUWw5qXgaM968aJiIgtpYiIiMxCgk+HDh3C9OnTVfJnIX3t9QNS4X//jevde+gCUjbOzvCdMhlFP/yAASkiyhFaQEr88ccf2LZtG37++Wc8fvw43eXcnR3wRbeqWDakAUp5JeUViYlPwNQ/LqHTjP04eftJtm87ERFZPraUIiIiymYxMTHYsGEDzp49q0ayktGtYm7cwJPVaxB75w7si/lK1ArBCxZKsim1jEPx4ij+www4V6zI80NEFqFFixZ48uQJrl+/jtmzZ6sufjVq1Eg3x12D0oWwZVRTTN95GXP3XkN8QiIu3g9F9x8PYFDjUnjnhfJwdeQjCRFRXsU7ABERUTYKCgpSycwfPnwIb29v9OrVC3Z/7sHVCRMkO7AKRule2s25fj2Umj4ddp6ePDdEZDFkJEXJM3X48GE1UMP69etx8eJFNWpoeqMsOTvYYVy7iioJ+rjVp3Hubggk7/n8/dex/XwgvuxWDU3KeZl1X4iIyDKwMzcREVE2uXnzJubNm6cCUtWqVcPrr7+O/KGhKom5ahEVH5/0Uy8gVaB/f7h98QUDUkRkkaRVlIzMJyP0yZDfEpS6dOmSQctWKeaBdSMaY3z7inD6N6fU7eBIvDz/EN5deQpPImKyeeuJiMjSMChFRESUTaSrnuSS6tChA7p27QpHR0fVZU+1kEr1rmwLW1dX2KSTQJiIyBIULlxYBdq7dOmiuvCJhIQE1V05PfZ2tirR+dbRzdCgdEHd9FXHAtBm6h5sOn1PfW8SEVHewFIvERGRCUm+qKioKPX/okWLYvTo0ahbt64u54rkkNLyRqVG/Z2IKJckQdfPKSUj80muqdu3b2e4rCQ/X/pGA3zZvSryOyVlFAkKi8GIpccx5NdjCHya9D1KRETWjUEpIiIiE3bXmzNnDtatW6er6Xd1dU02T4IErNJqBWBjA4dixXg+iChXCg8PV6PyLVy4ELt27UK8dFFOh62tDfrWK4Ed7zTHC5WK6Kb/cf4+np+6B0sP3UKCJJ8iIiKrxaAUERFRFkkA6uDBg2qYdGkpJd1aUut+8njlSoTt2pXeiuD5Ug+eDyLKlZo0aYK+ffuqYPy+ffswf/58lVMvI0XcnTHnldr4sX8teOVzUtNCo+Pwf2vPoO+8v3E9KNwMW09ERDmBQSkiIqIsiI6OxqpVq7B9+3aVM6pPnz5o1aoVbFPkhQr++WcETvgo+cJ2diqPlPbTZ9IkOPr783wQUa5Vvnx5DB8+HBUrVsS9e/cwd+5c3LhxI8PlpAtgh6o+2DGmGXrWLq6bfuh6MNpO24sf/7yCy/dDMXnrBXy05br6yWAVEVHul9SBm4iIiIwWERGhuqkEBQWhSJEi6NWrFwoW/C9xr5AWU0GzZiHo+xm6aQUHDYJn7154unqNyiElXfakhRQDUkRkDdzc3NT34cmTJ3H06FEUM6JbsqerI77uWR1dahTD+2tPq9H5YuISMGXrRfWy/XeciF1XnmDOnquY3KMaetbxy76dISKibMWgFBERUSa5uLjA29sbxYsXVyPsOTg4PBOQevDNNwiev0A3zeutt+A14k3VKsD7nTE89kRkleQ7rmbNmskSoV++fFm1Lq1SpUqGyzcp54Vto5th6vZLmL//OrQO0boUU/92kR63+jTqliyIkl5u2bYvRESUfRiUIiIiMoIk7r116xZKlSqlHrS6d++uuuppD12axIQERE6bhpj1G3TTvMeORaHXBvF4E1GeoX03ynfnxo0bERISgosXL6pAvgT20+PqaI8PX6yExxExWH38TprrX370Nsa1q5gt209ERNmLOaWIiIgMFBoaqpKZ//rrr2qkPW1I9GcCUnFxuDt+/H8BKRsbFJ04kQEpIsqz5LtSkqDLQBBnz57FrFmzcO3aNYOWjYlP1HXbS0lG57sdHGHajSUiIrNhSykiIiIDSKJeSWguQ56XKVNGPVilJiEmBnffeQehf+xImmBnB9+vvoRHp048zmT1Zs6cqV7SKkYEBgaqa0ZI0mtDGTKvMeuzRpa6/xltV6dOnXDkyBGcOXNGBfilK1+9evVgb5/2Y4mnQzzSiEmpbn3HbjzCmSu34OXmkK3bnp3LG7usqa+nzGyDNbHUfTfXdmXH+5hinZldB6+nnCfnQCpzDcGgFBERUTokL9TBgwexY8cO9f9mzZqhefPmz4yuJxIiIxHw1kiEHziQNMHBAcW/m4r8bdrwGFOeMGLECPWSLloeHh4oWrQo3N3dVeHUx8fHoHUYMq8x67NGlrr/hm6Xn5+fyjf1+++/qzxTbdq0UZ+XtLzWwh1Ljt1P+31DYjBg6QV81aMa2lYumq3bnh3LG7usqa+nzGyDNbHUfTfXdmXH+5hinZldB6+nnKedAxn0whDsvkdERJSOP/74Q72cnJzQr18/tGzZMtWAVHxoKG69MVgXkLJxcYHbF58zIEVElArJyzd8+HDVpU8LSIWFhSEhIeHZeb3c1Ch70oXPztZG91N6Tud3TqpjfxwRi6G/HsP7a04jIiaOx5yIKJdgSykiIqJ0yMhRd+/eRZcuXVCgQIFU54l7/Bi33xiMqHPn1O+2+fLBb85sPPX15bElIkqDs7Mz/P391f+ly+fSpUtV7qlu3bqhYMGCyebtWcdPjbInSc2v3A1GWd+C6F3HD+4uDioQte1cUkuq3w7fxt/XgjGtdw1U9/PksScisnBsKUVERJTCuXPnEBGRlDjX29sbAwcOTDMgFfvgAW4NGKALSNl5eqLEokVwrV2bx5WIyEAxMTFwdXVFQEAAZs+ejWPHjqku0/pKermpUfY+bV9K/ZTfC7o5YvbLtTG5R1W4ONip+a4HhaPHrL8wc/cVxCckXwcREVmWPBGUktoWeZh46aWXcnpTiIjIgklN/ebNm1VC8927d+umpxxdTxN75w5uvvwKoi9fUb/bFy4M/19/gUuVymbbZiIia+Di4oL+/fujffv2Khi1ceNGLFu2THXpy4h8R/euWwKbRzVF9eJJXQHjEhLx9baL6Dv3bwQ85uh8RESWKk8EpUaNGoVffvklpzeDiIgsmCRmXrRokRoVytPTE/Xr1093/ujr13Hj5VcQe+uW+t3B1xf+SxbDqVw5M20xEZF1keCSjMQ3dOhQ+Pr64tKlS6rVVFRUlEHLS+6pVcMbYWSrsirvlDh8Ixjtp+3D7yfuZO/GExFRpuSJoFSLFi2QP3/+nN4MIiKyUNeuXcOcOXNUt5Fy5cphyJAh8PLySnP+qIsXcfOVAYj7d6hix1Kl4L90CRxLlDDjVhMRWSf5/n3ttdfUaKeS109yTxnKwc4W77xQAcuHNkTxAi5qWmh0HEYvP4lRy07gaWRsNm45ERHluqDU3r170alTJ1UbIrUjMjRsSjNnzkTJkiXVDUlqrg8fPpwj20pERNbn4cOHWLx4scohJZUYMhKUdCNJS+Tp07g5YCDig4LU704VK8J/8a9wKJq5YciJiOhZkvBcRjtt06aNbtqOHTtw69/WqRmRpOjSna9bzWK6aetO3kWH6ftw6NojHnIiIguR40Gp8PBwVK9eXQWeUrN8+XKMGTMGH3/8MY4fP67mbdu2LR48eKCbR2pQqlSp8sxLRksyRnR0tOq+of8iIiLrVrhwYTRu3FjlMmnevHma+aNE+OHDuPXqICQ8fap+d65eDf4/L4J9oUJm3GIiorzn3r17OHDgABYuXKgqqCUHYEbcnR3wXe8a+L5vTeR3Thp0/M6TSPSZ9ze+3nYBsfEJZthyIiJKT9K3cw6SZIbySsvUqVMxePBgDBo0SP0u/co3bdqEBQsWYPz48WrayZMnTbItX375JSZOnPjM9MDAQBU8026IhjJ0XmPWaY0scf/NuU2mfi9TrC+z6zB2OV5PpsfrybDP4KNHj3Dnzh1Uq1ZN/V6pUqVUj5/+77GHDiH8o49liCj1u32NGnD6fBIeyCh9/47UZ8pzkpnlTH3fscTPkzlp+x8aGprTm0KU5/n4+KBfv35Yv369KvtL+VwGM5IRUjPSubovavsXwJjlJ3HoejBkUL+Zu69i3+UgTOtdA6UL58vzx5eIKM8GpTIaGlaGg33//fd102xtbVUz3oMHD5r8/eR9pFWWRlpK+fn5oWjRonB3d1eFU7khGsLQeY1ZpzWyxP035zaZ+r1Msb7MrsPY5Xg9mR6vJ8M+g6dOnVKjOsXFxamgVFrL6B/PkK3bcGfCR0BsUi4St+bNUHz6dNhmkOfEXNeTMcvw/mT88XRzczPqXBBR9pCcf8OHD1cjpF6/fh1z585F69at0aBBg3RbuYpini5YOrgB5u69hm+3X1Sj850OeIqO3+/HR50qoXlxi34sIiKyWjnefS89QUFBqmlukSJFkk2X36V2xFASxOrZs6ca5rt48eJpBrScnJxU8En/RURE1kGCUBKM0nIXdunSxaAgzpO1v+OOVFj8G5DK364d/GbMyDAgRUREpufq6qrK9l27doW9vT2uXr1q8LJ2tjYY3qIM1r7ZGKULJwWbI2Pj8f6aMxi/8RqCw5NawhIRkfnkiSoBSYpIRER519OnT7Fy5UrVZa9AgQLo1auXagWbkeAlS3D/s0m63z26d4fPZ5/Cxs4um7eYiIjSIq2iJM+sv7+/SoiutZKSCu1ChQpl2GqqanEPbBzZBJ9v+gdLDiUlTt977SnaTtuLb3pWR/PyhXnwiYjMxNbSh4OVG839+/eTTZffDXmYICIiEtJCSgJS5cuXx5AhQwy6h0QtXZosIFXg5ZfhM+kzBqSIiCyEp6cn8ufPr3s+kNyzq1evRmRkZIbLujra4/NuVfHTgDoo5Oaopj0MjcbABYfxyfpziIrNOJE6ERFZeVDK0dERtWvXxs6dO3XTEhIS1O8NGzbM0W0jIqLc48UXX8Tzzz+PPn36wDmDbneJiYl4MPU7RM37STet0NChKPLB/8HG1qJvm0REeZa0jpJWUufOncOsWbNw5coVg5ZrU6kItoxuigb+/6XtWPTXDXT54QD+uceRuImIsluOl67DwsLUCBraCHqStFD+f+tWUlNaSTw+b948/Pzzz/jnn39UckMZCU8bjY+IiCglqSWX2nIZZU94eHigUaNGGXbpSExIwP3Pv8CjuXN10wqPGQPv/43OcFkiIso5MgqfjNgt3/UyYuaSJUtUPtnYf/MBprtsfmdM7VIGEztXhpN90uPRxfuhKjD1075rSEhINMMeEBHlTTmeU+ro0aNo2bKl7ndt9LuBAwdi0aJF6N27Nx4+fIiPPvpIJTevUaMGtm7d+kzyc1OaOXOmekmSdSHvK4EwwSHsTc8Shxw35zaZ+r1MsT5zDWHP68n0eD3dUzlF/vjjD/VQIqO4tmjRwqBjlxgfj8hvvkXM1q26aS5vv43YTi9m6bia63oyZhlTz2ettP2XzxIRWT5JfC6tYmWUPhnU4siRI3jy5An69euX4bJS8TCwUUk0LFMIb/92AhcCQxETn4BJm/7BnksPVa6pIu4c4IKIyOqCUvKwIF0l0vPWW2+pl7mMGDFCvUJCQlTtuuQekZH4OIS96XEI+8wNF5+dx9NcQ9jzejI9Xk/3VCWC1IzLSHt169ZF27ZtVW7CjCTGxODO2HH/BaRsbeH63nvwH/RqjpyTzCxn6DKmns9a6e+/m1vSKF1ElDuULFkSw4YNw7Zt21CrVi2jli1fJD/WvdUY32y7iHn7rqtp+y4HqSToX3WvinZV8u73IhGRVXbfIyIiyioJQu3duxfr169Xv3fr1g0dOnQwKCCVEBWFgJFvI1QLSDk4oNjUqXBs15Ynhogol5L8gV26dIGfn5/6PSIiAsuWLdN1606Pk70dPuhYCUveqI+i/7aOehIRi2GLj2PcqtMIj47L9u0nIsorGJQiIqJcLyAgABcuXEDBggXxxhtvoFq1agYtFx8WjttDhyFszx71u42TE/x+mAF3BqSIiKzK8ePHcfHiRcyZM0elD8mop4ZoXNYLW0c3Rfsq/43YuvzobXT8fh9O3n6SzVtMRJQ3MChFRES5lvZQIV012rRpo5LcGppzMP7pU9x6/TVEHDqkfrd1dYXf3LnI17x5tm4zERGZX+PGjdGxY0f1/02bNuG3334zKF+cp6sjfuxfC1NeqgY3x6TWtzceRaDHrL8wY+dlxDMJOhFRljAoRUREuTIY9eeff6ruelpgqnTp0qq7hiHigoJwc8BARJ06rX639fBAiYUL4Fa/XrZuNxER5QxJZF6nTh0MHToUxYoVw+XLlzFr1izVytaQZXvV8cPmUU1Rw89TTZNg1Ld/XELvOQdxOzjCDHtARGSdGJQiIqJcRfKCLF26FHv27FEPFWFhYUYtH3vvHm6+/AqiL15Uv9sVKgT/X36GS/Xq2bTFRERkKQoVKoTXXntNDbYUFRWl7imG8i/khpXDGuLt1uVga5M07ejNx2g/fR+2/PPIoC6BRERkYaPvERERGeru3btYsWIFnj59qpLXvvTSS8ifP7/By8fcuoVbrw5C7N276nd7Hx+UWDAfTqVK8SQQEeURtra2aN68OSpXrqyCVCIhIQF37txRrajS42BnizHPl0fz8l4YvfwkbgdHIiw6Dp9uv4kT92MxqWsVeLg4mGlPiIhyP7aUIiKiXJOkdsGCBSogVa9ePQwcOBDu7u4GLx99+TJu9n9ZF5ByKFECJRf/yoAUEVEe5eXlpbrmiZMnT+Knn37CH3/8oUZ0zUht/4LY/HZT9KhVXDdtw6m7aD9tL/6+lvEIf0RElMQmke1MnzFz5kz1io+Px6VLl9RIHcbUxBMRkWnJrWrLli0IDAxEs2bNULZsWaOWj7t4CeFjxyIxJET9bluyJPJ98zVs/60hJ0qPJEOuUKGCCogaEwjNi1iGotzq9u3bqlu4dOeTkVxbtWqlfhpix6XHmLLrFkKj49XvEuZ6uU4RDG7go1pWERHlRaEGlp8YlEpHSEgIPDw8dAfx3r178PHxMegEGDqvMeu0Rpa4/+bcJlO/lynWl9l1GLscryfTs8brKTY2Fg4OSd0g5EFB8kd5e3sb9V4Rx47h9tBhSPg395RzlSrwmzcX9gUKZOu2Z2UdmVnO1PcdS/w8mZP+/qcsD1DOl6H4+bTM69Nc5yU73kfWKZ9ZGZnv/PnzsLOzU4Gphg0b6lpTpefkpZv46s+7+PtasG5alWLumNa7Jsp658vwvVmGyjmW+n2S26+n3FKG4jOJ6WnH1NDyE0P3RERkkaSl6vfff6/ySAlXV9c0A1JpCTtwALfeGKwLSLnUqY0SixZmGJAiIqK8R+4zkquwW7dusLe3V135Dh8+bNCyRfI7YukbDfB++4pwsEsKYp29E4IXZ+zD4r9vMgk6EVEaGJQiIiKLIslmd+3ahd9++w3h4eGqy15mhO7ciYBhw5EYGal+d2vcGCXmzYNdvvRrrImIKO+SVlHVqlXD8OHDUbNmTdSqVcvgZW1tbTC0eRmsfbOxrnVUVGwCPvz9LAb/chRBYdHZuOVERHlo9L3r169j3759uHnzpupOUbhwYfWlLc1bnZ2dTb+VRESUJ8g9ZfXq1bh27Rry5cunaqz9/f2NXs/TDRtxd/x4ID4pv0f+59vA99tvYevomA1bTURE1ka6nHTu3Fn3+4ULF3D69Gm8+OKLqkVVeqoU88CGt5rgi83/4Ne/b6ppO/55gHbT9uHrntXQsoJxrX6JiKyZUUGpJUuWYPr06Th69CiKFCkCX19fuLi4IDg4GFevXlUBqf79+2PcuHGZeoggIqK8S7rpLV++XPU/L1GihApIZWaQicfLVyDwk08kO7r63b1zJ/h+8QVs7DNVD0NERIQjR46oChNJiC7BqnLlyqV7VFwc7fBZ1ypoWbEwxq46jaCwGNVSatDCIxjY0B/vd3gO955GYcXR27hyNxhlfZ+iVx0/lPJy49EmojzF4BK6tIRydHTEq6++qmqx/fz8kv09OjoaBw8exLJly1CnTh38+OOP6NmzZ3ZsMxERWekIe9Jdr0GDBmjTpo1KMmusRwsW4sGUKbrfPfv0RtGPPoKNLXurExFR5vXt2xd//vknDhw4gKVLl6rnneeff149H6WnVcUi2DKqGcauOoXdFx+qaT8fvIktZwPxMCwatjY26v6368oTzNlzFZN7VEPPOsmfs4iIrJnBQamvvvoKbdu2TfPvTk5OaNGihXp9/vnnuHHjhqm2kYiIrJSMrhcfH69a2hYrVgxvvfUWPD09jV6PFOgjFy3Ck59/0U0r+Npr8H7vXYNGTSIiIkqPJD6XCpPy5ctj7dq1queItJzq1auX6kGSnsL5nbDg1boq4fmkTf8gOi4BD0KT8kvF/9uqV2vdO271adQtWRAl2WKKiPIIg6uO0wtIpVSoUCHUrl07s9tERER5gHT9nj9/PtasWaMblSizAakHk6cgWi8g5fX2SAakiIjI5KR7+bBhw1QvEsmDaGg+XakgeaVhSWx6uwm88jmmO9/yo7dNuMVERJYtUwk2jh8/DgcHB1StWlX9vm7dOixcuBCVKlXCJ598kmEzVks3c+ZM9ZLaeyEjP0mXEnHv3j2D12PovMas0xpZ4v6bc5tM/V6mWF9m12Hscrye8u71JK1pd+/erVpKubm5ISAgQNVCGysxPh6R301DzKZNumnOI95EXLdumR61L6NtN9c6MrOcqe87lvh5Midt/0NDQ3N6U4jIgkgPEckr1bJlS13uwydPnqjnIy8vr3SXLeudH/VLFcLmM/fwbxupZypaAh4njRpLRJQXZCooNXToUIwfP14FpaTZap8+fdCtWzesXLlS1RhMmzYNudmIESPUS5LtysgbRYsWhbu7uyqc+vj4GLQOQ+c1Zp3WyBL335zbZOr3MsX6MrsOY5fj9ZQ3r6eEhATs2rVL5eSwtbVVrXDr16+fqS52ibGxuPv+//0XkLKxQdFPJ6KAifIZ5qbryZhleH8y/nhK4JSIKCUtICUV2Tt37sTTp0/xwgsvqHxT6d3XShRyha2tDeITng1LScPhou5OPNhElGdkKvPrpUuXUKNGDfV/CUQ1a9ZMJfxbtGiRSoJORESUkrSKWrx4sQpISUF+4MCBKql5ZgJSCdHRCBj9P4Rs3Jg0wd4erh9+YLKAFBERkaGkkkV6jMj9bPPmzWrE8vRaWMooe1q39ZRk6o7zD3AxkC00iShvyFRQSr5EpbZb7NixAx06dFD/lxH5goKCTLuFRERkFaR7Xr58+VCyZEkMGTJE5eUwRsyNG3jw7VQEjBqNax06ImznTjXdxtERxb//Ho6tWmXTlhMREaVNglHPPfecyjVVvHhxXL16FbNmzcK5c+dSnb+Ul5saZc/WBrCztVE/9etnrj8KR+cf9uPXgzfSDF4REeXp7nvSJHXSpElqBIo9e/aoL11x/fr1DEefICKivEMK03fv3oWvr68qtHfq1Al2dnaqVtkYT1avwb0JE5JK7f/m+1McHOA3ZzbcGjZEWB7Pf0RERDmrYMGCGDRoEPbv36+ekVatWqWejVLLM9Wzjp8aZU+Sml+5G4yyvgVRv1RBfLXlAi4EhqoR+iasO4c9l4Iw5aVqKOiWu3P2EhGZtKWU5IySZOcydPcHH3yAsmXLqunyxduoUaPMrJKIiKxMTEyMSmY+b948VWssJAmssQEpaSGlAlLSQlc/ICXi4uDg62vKzSbKlq6rrVu3xuXLl3l0iayc3OMktcnrr7+Odu3a6QJSqbV4KunlhnHtKuLT9qXUzxYVvPH7iMZ4tVFJ3Tw7/rmP9tP34q8r7I1CRNYpUy2lqlWrhjNnzjwz/euvv1Y14ERElLc9evQIy5cvx8OHD1G4cGE1aERmSSupNNna4smq1fB+Z0ym10+U3SQYe/r0aR5oojxEWgjLS7N27Vo1aIIEqNMbbdbZwQ6fdK6MZuW98O7K0wgOj8H9kGj0n38IQ5uVwTsvlDfTHhARmYfB1dWG9Gd2dnZWBS8iIsq7/vnnH8ydO1cFpKQl7RtvvJHhENnpiZRKkH/zGD4jMRGxd+5kfmOJzOTll1/G/PnzebyJ8qDw8HDcuHEDf//9t7o/BgYGZrhMq4pFsHVUUzQtp7W0AmbvuYqXZv2F20+izLDVREQW1lKqcuXK+Oijj9C9e3c4Oqbdp1mapk+dOhX+/v4YP368qbaTiIhyASlwb9u2TXVfaN++vUr4mt49IyNPN2xExOHDac9gYwOHYsUyvX4ic4mLi8OCBQvUADG1a9dWLSb0SdmJiKyTXO/Dhw9XI/OdPXtWdWtv2bKlSnuSXpd2b3dn/DyoHn7afw1fb7uI2PhEnAp4ileXhuKzrg7oXqtYpkawJSLKlUGpGTNmYNy4cXjzzTfx/PPPq2Tn0iRVWkc9fvwY58+fV0n9ZJQJyTUlX7xERJS3SMuoY8eOoXPnzmpE1nuZTD4urXODZs1C0PczMpoRni/1yNzGEpmRPIjWqlVL/f/SpUvJ/saHSiLr5+Ligh49eqB8+fIqOLVz505Vmd+3b990l7O1tcGQZmXQsLQX3l52AteDwhERm4B3Vp7C3ssP8VnXKnB3Zk8VIsoDQSnp/3z06FEVeJI8IUuWLMHNmzcRGRmpumXUrFkTAwYMQP/+/VGgQIHs3WoiIrIYt27dgqenJ9zd3dX9QCovsvKQnRgTg3sTPsLTdet001zq1kXksWNJo+9JH4Z/f/pMmgRHf38T7QlR9pGk/0REVatWVT1Kfv/9d5WL18nJyaCDUrW4BzaObIJP1p/DymMBatq6k3dx/NZjTO9TE7VK8PmLiPJIovMmTZqolzWbOXOmesX/O8qT9PuWvuDCmFp/Q+fNbEsCa2GJ+2/ObTL1e5lifZldh7HL8XrK3Z9dac0krT+ky563t7dqHZVaMMqYbUoICUH4Rx8j/tQp3TTnoUPg2Ls37O/eRczmzUgIDIRt0aJw7NABkcWKIVJv/Xn5ejJmGd6fjDueoaGhMKWAgKQHSuneSkR5j1TivPLKK2qUWu2+eeHCBdXCOGXXXn1uTvb4umd1VPO2x5TdAQiNisPt4Ej0nH0Q/2tTDsNblIWdLbvzEVEeGH3P2o0YMUK9QkJC1IhRRYsWVTcPKZz6+PgYtA5D5zVmndbIEvffnNtk6vcyxfoyuw5jl+P1lLs/u1KQXr9+veqyLbW8LVq0SDbKUGa2KebWLdweNRrxN26o322cnOA7ZQrc276QNIOsv06dNJfPy9eTMcvw/mT88UzvIdFQCQkJmDRpEr799luEhYWpafnz58c777yDDz74IN28MkRkfSQYpbWSCg4Oxpo1a1QXP6ngkS5+6WlTviBaVC2F0ctP4tjNx4hPSMQ32y9h3+UgTOtTAz4eLmbaCyKirGMJiIiIjBIUFKSStEpAqkiRIhgyZAgqVqyYpaMYcfw4bvTug5h/A1J2hQrB/5ef/wtIEeVyEnj64Ycf8NVXX+HEiRPq9cUXX6icnRMmTMjpzSOiHCSV4I0bN0ZERAR+++03bNiwQVX+pMevoCuWD2mAUa3LQWscdeh6MNpN24etZzMe3Y+IyFKwpRQRERlMujFJQEoKy9WrV0fHjh3h4JC1BKtPN23Cvff/T+WSEo5ly8Bv9hw4FueoemQ9fv75Z/z000+qFYSmWrVqKFasmMrD9vnnn+fo9hFRzpHcUq1atUK5cuWwdu1aHD9+HNevX0e3bt1Ul7602NvZ4n/Pl0fjsl4YvewE7j6NwtPIWAxbfAz96pfAhI6VzLofRESZwZZSRERkMOluVLduXRWM6tKlS5YCUmqEvdmzcfedd3UBKdeGDVBy6VIGpMjqSPec1FoUyjT5GxGRBKCGDRumRuqU0c2lm7x0/c1IvVIFsWVUM3Ss+l8X7qWHbqHTD/tx+WEEDywRWTQGpYiIKMPWUYcPH9b93qZNG9SpUyfrI+z93wd4OG26bprHSz1QYu5c2Lm784yQ1ZGWhdJ9LyWZJn8jIhKOjo7o1KkT+vTpg65du+ryzWkDMKXFw9UBP/Srick9qsLFwU5Nu/IgDK8vv4iFB66riiAiIqvqvnf16lUsXLhQ/Zw+fboaeWnLli0oUaIEKleubNqtJCKiHHHz5k2sWrVKJWb28vJC6dKls7zO+KdPEfD2KEQcOqSbVnjMGBQa/EaWAl1ElmzKlCmqheGOHTvQsGFDNe3gwYO4ffs2Nm/enNObR0QWpkKFCrr/yyjg0v23QYMGqFevXprLyD20d90SqFOyIN7+7QTO3Q1BbHwiJm44j72XHqqR+7zyJSVXJyLK1S2l9uzZg6pVq+LQoUNqpAhtFJlTp07h448/NvU2EhGRmUmN6l9//aXy4Mh3fLNmzVCyZMksrzfm9m3c6NtPF5CycXREsWnfwWvIYAakyKo1b94cly5dUjlinjx5ol7du3fHxYsX0bRp05zePCKyYPfv31dJ0Ldu3YrFixerIFV6yhTOhzVvNsLgpqV003ZffKiSoEtwiogo17eUGj9+vBrWeMyYMSq/iEYS9KXWNJ2IiHKP6Oholcfi/PnzcHZ2Vg/RGQ1PbYiIEycQMOItxP+bP8euYEEUn/kDXGvWNMFWE1mu2NhYtGvXDrNnz2ZCcyIymrRSllxTkgT92rVrCAgIUF38qlSpkuYyTvZ2+KBjJVQqZIfPd9xGUFi0eg1YcFgFq95rWxGO9szkQkQ5L1PfRGfOnFEPKSlJFz4ZKpyIiHIv6YotAamiRYtiyJAhJglIhWzZglsDX9UFpBxLl0bJ5csYkKI8QQYEOH36dE5vBhHlYgUKFMCrr76K1q1bIy4uDqtXr8bGjRszXK6Bvzu2jGqKFhUK66bN23cd3WcdwNWHSb1diIhyXVDK09MT9+7de2b6iRMn1NDGRESUe0mr1/r16+O1115TheCsUCPszZ2HO/8b898Ie/Xro+RvS+GYzjDXRNbm5Zdfxvz583N6M4goF5Ok502aNFEJ0AsXLozixYsbtFzh/E5YMLAuJrxYCY52SY9/Z++E4MXv92PFkdtMgk5Eua/7nowGMW7cOKxcuVLlAJGhSg8cOIB3330XAwYMMP1WEhFRtpERfXbu3ImaNWuqQq67u7vqapRVibGxiPzmWzzVS+Ls0a0bfCZ+onJJEeUl0rJhwYIFKtF57dq14ebmluzvU6dOzbFtI6LcRQYekZbMdnZ2uvu45PqtW7euapmZGltbG7zepBQalE5Kgn71YTgiY+MxdvVp7Ln8EKMaFYaPmfeDiCjTQakvvvgCI0aMgJ+fn/oSrFSpkvrZr18/fPjhhzyyRES5REhIiBpdT0YAe/jwIfr372+S9caHhCBg1CjEHPxbN63w6NEoNHQIE5pTnnT27FnUqlVL/V8SnuvjqJNEZCx7+/8e4/7++28V8JZeKzKAgo9P2uGlyr4e2DCyCT7b+A9+O3xLTdt0+h6OXX+EGf3dULdkQZ4MIrL8oJSjoyPmzZuHCRMmqEKWjMwkNezlypWDNZg5c6Z6SaBNBAYG6ka5SK3bYloMndeYdVojS9x/c26Tqd/LFOvL7DqMXY7Xk+kZc0zv3r2rWkhFRkaqSoZGjRqZ5PMTL9+Z499Hws2bSRMcHOA6fjxiW7VU36fZKS9fT8Ysw/uTccczNDQUWSHliYkTJ6qRi7PaJZaIKCVpfSkj9Ene359++gktWrRA48aNVXe/1Lg62uPL7lXRrJwXxq85g6eRsQgMjUHvOQcxslU5jGxVFvb/dvMjIrLIoJSmRIkS6mVtpBWYvKQFgYeHh0r2K91ZpHCaXs2DPkPnNWad1sgS99+c22Tq9zLF+jK7DmOX4/VkeoYeU8nz9Ndff6mAlPxfhqqXlylaa0SeOoXbb41EwqNH6ncbDw+UmDULrrWyf4S9vHw9GbMM70/GH8+UXe2MJV1sXnjhBfzzzz8MShGRyclIudJCSgYm2bRpE3bt2oXLly+r3FPpaV/VB9X9PDF6+Ukcvh6MhERg+s7LOHAlCNP61EDxAq48W0RkmUEpeYiR7h67d+/GgwcPVE4pfWvWrDHV9hERkYlJbaoEpLRCbNmyZU2y3pBt23F37FgkRker3x1LlYLTZ5+aJSBFZOlk6HYZyr1UqVI5vSlEZMXfM9JgYP369bh69SqOHTumpqXH19MFvw1ugMkbTmD+oUDEJyTi6M3HaD99n2pN9WI1X7NtPxHlTZlqlzl69Gi88soruH79OvLly6daE+m/iIjIcknrzy5duqgkqaYISElFxaP583Fn1ChdQMq1bl01wp4dR2QlUiZNmqQGhJEh3KUVlrTG1n8REZmC9O6Q/JDSSqply5a66dH/3p9TY2drg0H1fLBiaEMUL+CipoVGxeGtpScwdtUphEfH8eQQkWW1lPr1119Va6gOHTqYfouIiMjkTp8+rSoSOnfurLrpVa9e3STrlRH2Aj+bhCcrVuimeXTpAp/PPk0aYS8y0iTvQ5TbaWUm7RrUD+rK71oeSyKirEp5nz9//rzq1iffPxUqVEhzudr+BbB5VFN8uPYs1p+6q6atOBqAozce4/u+NVGlGBsfEJGFBKWkNVTp0qVNvzVERGTyYei3bduGo0ePqpF6JJl54cKFTbLu+NBQ3Bk1GuF//aWb5vX2SHgNH87RxIhSkJQHREQ54cmTJ2pQk2XLlqnBqdq2bQsnJ6dU53V3dsD0PjXQvHxhfLTuLMJj4nEtKBzdfjyAsW0rolVFb6w6HoCAx5GqVVWvOn4o5ZW1vHtElLdlKij1ySefqFFkFixYABeXpCaeRERkWZ4+fYqVK1fizp078PT0RO/evU0WkIq9cwe3hw1D9OUr6ncbBwf4fPEFPDq9aJL1E1kbGUwgt+nWrRv+/PNPtG7dWuUSJaLcSSqkJNfU2rVrceLECdVyWq7vtAaskpZWPWoXVy2n3l52AqcDniI2PhGfb/5HvexsbJCIpFaec/ZcxeQe1dCzjp/Z94uI8nBOqV69euHx48fw9vZWwxvXqlUr2YuIiHKWJFSeO3euCkiVK1dO5Y+SXFKmEHnmDK737qMLSNl5eqLEooUMSBFlYN++fXj55ZfVA6Jcm1pKhP3791vksRs1ahR++eWXnN4MIjKB4sWLY+jQoahdu7ZqObVo0SKcPHky3WVKerlh1bBGGNa8TLLp8YmJaqQ+SYouP8etPo0bQeE8T0RkvpZSAwcOVKM5SMGqSJEi7KZBRGRhjhw5goiICJXktGnTpib7ng754w/cfW8sEqOi1O+O/v7wmzMbjiVLmmT9RNZq9erVapAYSUB8/PhxXdJhadH4xRdfYPPmzbA0LVq0UC2liMg6ODo64sUXX1R5pbZv325QOhZHe1uMb18Rd55EYMOpe6nOI2WM5UdvY1y7itmw1URk7TIVlJJEeZKjpEmTJqbfIiIiypSEhATd/2V0vXr16pls+HlJxhy8cBEefP21/KKmudSpjeIzZsC+QAGeMSIDRt+bPXs2BgwYoPK6aBo3bqz+Zqy9e/fi66+/VpWEMpqfdMuR0bb0zZw5U80TGBiokh7PmDFDfS8QUd4mLahl9F2twur+/fs4c+aMalGddiWWDWxtoFpGpVZGkBxTRERm677n5+enhhslIiLLIA+dkvPl9u3b6ndnZ2fTBaTi4hA4cSIeTJmiC0i5d+qEEgsWMCBFZKCLFy+iWbNmqQ4eI11pjBUeHq4CTRJ4Ss3y5csxZswYfPzxx6pllswryY0fPHigm6dGjRqoUqXKM6+7d5NG3SIi66UffJKWmgcPHlTdiaX1ZmokqXlaASsJVD0IiVLd+YiIzBKU+vbbbzF27FjcuHEjM4sTEZEJSU6I+fPnqwfbK1eS8jyZSnxYGG4PfxNPli3XTfMaMQK+UybD1tHRpO9FZM2kBUJq16fkk8rMiMbt27dXLawkWXFqpk6disGDB2PQoEGoVKmSaqXl6uqqBqnR/+44e/bsMy9fX1+jt0e6I4aEhCR7EVHuIN8j8h0lCdBnzZqlWk1J6yd9Mspeymn6Dl0PRt+5fyPgcYQZtpiIkNe770kuKclVUqZMGVXAcXBwSPb34OBgU20fERGlIS4uDlu2bFGtIOzt7VX+F1OO8BV77x5uDx2G6EuXkiY4OMB30mfw6NKF54TISBIgksThEhSS1gbSGklaJrz77ruYMGGCSY9nTEyM6tb3/vvv66bZ2tqiTZs26j2zw5dffqlGZk6tFae06hLSzdBQhsxrzPqskaXuv7m2KzveJ6vrzMryxi5r6utJck1JMEpyUq5Zs0YFrSVVi7S8FvLv/7Xxxxc7bkLaS2nhKS1OJT8O3whG2+/24L2WJfBChQK5Ku8wryfLu56yso6cvp4ysw3WRvY/NDQ0+4JS06ZNy8xiRERkItIqauXKlerBtkCBAmpU1PRqMI0VefYcAoYPR9zDh+p3Ow8PFP9hBlzr1jXZexDlJePHj1d531q3bq0q9qQrn5OTkwpKjRw50qTvFRQUhPj4eDUYjT75/cKFCwavR4JYp06dUkElGblLvnMaNmyY6rwSAJPughppKSXpHqT1haR8kMKpj4+PQe9ryLzGrM8aWer+m2u7suN9srrOrCxv7LKmvp60+dq1a6e69UqOOmk1JZVd+su+4eODNtVLqaTmkkNKuvT1ruOHB6HR+N/yk7jzJBLhMQn4ZNsNHAuMwaQuVeDhmrzxgiXi9WR511NW1mEp15Mlfkebi7b/bm5u2Tv6HhER5ZzIyEiVmFRG0JHkxlKTaaoamdCdO3Hn3feQGJmUtNTBvwT8Zs+Gk4lyVBHlRdJi4IMPPsB7772nuvGFhYWpbnX58uWDpdqxY4fB80qATV5ElLtJIFladkqaFgksi6ioKNjZ2aneMSW93J4ZZU+mbRndFJ+sO4c1J+6oaRtO3cWxG8H4pld1NCrjlSP7QkS5g8FBKanx0pKbZ5QngEnQiYhMT1pCSbccefCT2gcpNHp7e5usebys//Evv+D+V5P/G2GvVi0Un/kDE5oTmXBIdglGZScvLy/1ACmBa33yuzxwEhGlR1ICyOh8Wtlgw4YNapAEyT2VVs45d2cHTO1dAy0reuODtWcQEhWHu0+j0P+nQxjStDTGvFAeTvZ2PPBElPmglHQPkVp4eQDy9PRM9SFIvrRkujQZz81kJBt5afuRnfkQjF2nNbLE/TfnNpn6vdh/2/I+T6YgtZS7d+9W3X8kwbHkh9G+nzJ7/uMDAhCzZQsSAgNh610ECUEPEbtjp+7vDq1awXHcWDyMipIVZ3rbeT2ZJx+CMcvw/mTc8TQ0J4IlBb5q166NnTt3qpaUQr475Pe33norpzePiHIR+e6QFlLSLVgGVZGux02bNtWVQ1LqVN0XdUoWwDsrTuGvq49UHdecvdew93IQpvepgfJF8pt9H4jISoJSu3btQsGCBdX/5cHImo0YMUK9pEWYDNWcXfkQjJnPWlni/ptzm0z9Xuy/bXmfJ1Od1/Xr16s8UpLXRb6LXVxcsrT/T1avwT1JriwVDFJiTEhI9nevN4fDa+TILLfC4vVknnwIxizD+5Pxx9PQnAjmJN3/9Efzk/wvkphYvh9KlCih8jtJuoU6deqgXr16Kh+oVLDJaHxERIaSVpcS3C5fvjw2btyIP//8E5cvX1atpgoVKpTqMj4eLlj8en3M338dX2+7iJj4BPxzLwSdZuzH++0rYmCjkrkqCToRWUhQSn9Ep1KlSqk+xim/TKSl1O3bt027hUREeZiMrLd582bVcrNu3bpo27atKiBmRcyNG0kBqRSBKE3hd96B1+A3svQeRJS9jh49ipYtW+p+15KMSyBq0aJF6N27Nx4+fIiPPvpItaiU5MVbt259Jvl5bm5tboktrc3JUvefo++Z57iZu/eG9Jrp0aMH9uzZo573Zs+eje7du6seNGl5sZwLKniWV4nPrz2KQnRcAj7ZcB5bTgfgw+f94eVmOUnQeT1x9D1Tf1Ys9TNlNaPvSVBK68qnLzg4WP0tt3ffIyKyhObyksNBWj5Is/nOnTujWrVqJlm3tJJSLaRSY2uLhAzyBhJRzpNRsTIacVO66pm7u565WptbYktrc7LU/efoe7l79D1D5itdurQKit+6dQsVK1bMsMWTrHLzcyUxeesFLDxwQ007dDMEA5ZewJfdq6FdlZzPc8friaPvsTdULhx9T8sdlVpTchkBioiIskbL1SBN43v16vVMJUBmyfd3xNGjQDqVB7F3kkbOISLTki4vkgJBEgZL4FmftGgiIrJ08gwoLbflpTl06JAKPj/33HOpLuPsYIePO1VGywreeHflKTwIjcbjiFgMW3wMvev44aNOleDmlKnHUiKyAkZd/VrTcPkymjBhAlxdXXV/k9ZR8oUkzcOJiChzpMWplr+vQ4cO6rvVVMH+yDNncf+rrxB54kTaM9nYwKFYMZO8HxH9Z968eRg+fLgaGU9aD+lX7sn/GZQiotxIuufu2LEDcXFx6jmwXbt2apTg1DQrXxjbRjfD+2vOYOu5pIFalh+9jb+vP8J3vWugVokCZt56Isp1QakT/z7ISE37mTNn1OguGvl/9erV8e6775p+K4mIrJy0mpA8Dfv27UOfPn1UQlHptievrIoNDMTD777D03XrM545MRGeL/XI8nsSUXKTJk3C559/jnHjxvHQEJHVkO45r776KtauXatSDsigC5IE3d/fP9X5C7g5YtbLtbDyWAAmrj+H8Jh43HwUgZ6zD2Jkq7J4q2VZ2NulPrIfEVkno4JS2qh7MnLL9OnTVTNNIiLKmoiICKxZswZXr15VhTv9gH9WJERE4NH8BXg0fz4So6J00x1LlYJb0yZ4vHjJf6Pv/fvTZ9IkOKZRkCSizHv8+DF69uzJQ0hEVqdYsWIYOnQo/vjjDxw5ckQNttCoUSM1GIO9/bOPm9I6tFcdP9QvVRCjl5/EiVtPEJ+QiGk7LmPPpYeY1rsG/AtZ3qinRJQ9MtV5d+HChabfEiKiPOjOnTtYuXIlnj59qkY1lYfW/PnzZ2mdiQkJqlWUtI6Ke/BAN93OwwNeb72FAn16w8bBAQX798eTVatVDinpsictpBiQIsoecm1v374dw4YN4yEmIqsjLbsl7YC09F63bh0uXbqkBmRIjwSeVg5tiJm7r+L7XZdVYEoCVO2n78MnnSqjZ53iGSZSJ6LcjxnliIhyyPnz51ULKckbVb9+fTz//POws7PL0jolifn9L79C1Llz/020t0fB/v3gNXw47PSGbpYAlPc7SbkCiSh7lS1bVuXj/Pvvv1G1atVnuua+/fbbPAVEZBXfdZI/T1qBa99zjx49UvkyUwswSVe9UW3KoWl5L/xv+UnVlS8iJh5jV5/GrgsP8EX3qijoZpoW5ERkmRiUIiLKIZLsWLrrSTCqSpUqWVpXzO3bCP9sEp7s3Ztser5WreD93rtwKlUqi1tLRFkxd+5c5MuXT+WOk5c+eVCzlqDUzJkz1UuC7SIwMFAlQtaGiDaUIfMasz5rZKn7b67tyo73yeo6s7K8scua+nrKzDYYsj4JTq1atQoFChRQLafSag3u4wAs6FUO0/cGYP25R2qaJEM/euMRPnzeH/X9szdtDK8ny7uesrIOa7yechvZ/9DQUIPmZVCKiMjMo+vZ2trC09NT1RqOHDky1XwLhooPDUXQrNl4/OuvSIyN1U13qlgRRcaPg1uDBibaciLKCkn+mxeMGDFCvUJCQuDh4aGC75KDVAqnPj4+Bq3DkHmNWZ81stT9N9d2Zcf7ZHWdWVne2GVNfT1lZhsMJd8F8j1w48YN1Tq8ffv2qFatWprd8r5/pTg6ngvE+NWn8TgiFkHhsRj9+xW82qgkxrevCGeHrLUoTw2vJ8u7nrKyDmu+nnILbf+l8t0QHNqAiMhMLl68qFpLrFixQg2dLDIbkEqMi8Pj337D1RfaInjBAl1Ays7LCz6TPkOp1asYkCKyUDKKsbyIiKydBKUHDBiAF154QZV9fv/9d9VySlpQpaVt5aLYNroZmpUvrJu26K8b6PzDfpy/G2KmLScic8l0UOrXX39F48aN4evri5s3b6pp06ZNU4ntiIjoPwkJCdi1axeWLVuGmJgYlU8mK7mjwvbtx/Vu3RA48VPEP36sptk4OsKpf3+U2boVni+9BJss5qYiItP75Zdf1PXv4uKiXtJaQMpTRETWTFpFNWzYEEOGDEGRIkVUTk0ZOEvKR2nxdnfGz4PqYmLnynCyT3pkvXQ/DF1nHsDcvVeRkMDAPlGeDkrNmjULY8aMUSMsPHnyRJc3QLqjSGCKiIiSSC6VJUuWYN++fSqfzMCBA1XBLDOjyURfuYJbg4fg9uDBiL58RTfdvWNHlNmyGS5vvA67fBxCmcgSTZ06VSX/lbKTtJaUV7t27dRofN99911Obx4RUbbz9vbGG2+8oRo2NG3aVKUzSI+UlQY2KokNI5vgOZ+knFIx8Qn4YvMF9P/pEO4+ieRZI8qrQakZM2Zg3rx5+OCDD5LV9tepUwdnzpwx5fYREeVa0dHR6rvy2rVr8Pf3x9ChQ9VPY8U9fozATz/FtS5dEb5vn266S/XqKLnsNxT79hs4FCtm4q0nIlOSspNU6k2ePBmdO3dWrylTpuDHH3/E999/z4NNRHmCpC1o06aNaikqpHGDdOcLCAhIc5nyRfLj9xGNMLR5aWh1egevPUK7aXux4dRdc206EWUT+8wm66xZs+Yz052cnHQjrBAR5XXynSij6knz9NatWxvdZS8hJgaPf12MoNmzkaA3eoW9rw+8x7wD944dMtXiiohyJulno0aNnpku0/L6CD1ElHddunQJ586dU136mjVrplpQpVZecrK3w/vtn0Pz8oXxzopTuPc0CiFRcRj52wnsuvAAE7tUhruzQ47sAxHlQEupUqVK4eTJk89M37p1K5577rksbhIRUe4VGxub7PtRglGS3NOYgJQkQA7Zvh3XXuyEB19/rQtI2bq6ovDo0SizeTM8XuzIgBRRLlK2bFnVZS+l5cuXo1y5cjmyTUREOU2eHXv16qXy7O3ZswcLFixAUFBQmvM3KuOFraOaoVN1X920tSfuoP20fTh8PdhMW01EOd5SSvJJyXC/UVFR6uHp8OHD+O233/Dll1/ip59+MukGEhHlFo8ePVIPnQ8ePICDgwMqV65sdOAo8tw5PPhqMiKOHPlvoo0NPHp0h/eoUbAv/N9INESUe0ycOBG9e/fG3r17VT4VceDAAezcuTPVYBURUV4KTPn5+WH9+vW4fPky5syZg7Zt26rUMKnxcHXAjL410bqiNyb8fhah0XG48yQSvecexPDmZTC6TXk4/pscnYisNCglCeokmv3hhx+q4Tz79eunRuGbPn06+vTpY/qtJCKycBcuXFDDHEseKemyZ2zLh9j7D/Dwu+/wVEYw1Rsq3rVBAxQZPw7OFStmw1YTkbn06NEDhw4dUknN5btCexCTir3UUiLkVjNnzlQvbRCcwMBAXWoHY7opGjJvXu/2aKn7b67tyo73yeo6s7K8scua+nrKzDaYWosWLVC0aFEcPHhQ5ZgqlkG+zPpFbfFzvwr4dPtNnLwTpopPP/55FbvO38PHbUuiZEFng987p/c9LXn5esrKOng95Tw5B6F66UdMHpQS/fv3Vy8JSoWFhanRFIiI8hrJF7Vr1y7V4kFGkZHRtOrVq2dwC6mEyEg8WrAAj36aj8TI/0aRcfT3h/e4scjXsiW76RFZidq1a2Px4sWwZtKSXl4hISHw8PBQD5ju7u6qcOrj42PQOgyZ15j1WSNL3X9zbVd2vE9W15mV5Y1d1tTXU2a2IbtIQ4caNWqo7w1Jii4kQFW8ePFU55dNXl3OH3P2XsXU7ZcQl5CICw8iMGjZBXzQsRJerl8iw3KUpex7Snn5esrKOng95TztHLi5uWVfUGrSpEkqICW5pVxdXdXLmpizls/YdVojS9x/c26Tqd+LtRLm/TxJy4dTp06p70EZTUYewOQ7IyOJCQmI3bkTkfN+QuLDh7rpNvnywWngADh16YIwBweEGbAufbye8u71ZMwyvD8ZdzwNrelLSQIz8mCl/T892nxERHldwYIFdf+XJOgyOp+M1te+fXs4Oz/b+snO1gZvtiiLZuUKY9SyE7j6MBxRsQmqa9/uCw8wuUc1FM7vZOa9ICJDZSootXLlSnz88ceoX78+Xn75ZZWczsvLC9bCXLV8xsxnrSxx/825TaZ+L9ZKmP/zJIEoCWBL7oN8+fIZtEzE8eO4/+VXiDpz5r+J9vYo0LcvvN4cDvsCBTK1Lbye8u71ZMwyvD8ZfzwNrelLqUCBAmo90prc09Mz1dp6yc0p07WKMCIiSv49Ks+Zp0+fxs2bN9G1a1eULFky1UNUpZgHNo5sii82/4Nf/76ppsnIfO2m7VWBqTaVivDQEllLUEpaBUjUesmSJfjmm28wevRoPP/886r1lHxRWFvLKSIijTa4gxSIihQpogJRkivGEDEBAXjwzbcI3bo12fR8LVrAe+xYOJUuxQNNZEWka69W47979+6c3hwiolxHuvMNGTIEO3bsUOWvn3/+GQ0bNkSrVq103fv0uTja4bOuVdCqojfeW3UKQWExeBQegzd+OYp+9Uvgw47PwdUx0xlsiCgbZPqKlFGlvvjiC/WSXCpLly5Vwalhw4Zl2ESdiCg3iomJwYYNG3D27FnVgmLw4MEG5XuKDwvDozlzELzoZyTGxuqmO5Uvr5KYuzVqlM1bTkQ5oXnz5rr/S8oDGV0q5XeGBLpv376dA1tHRJQ7yIjG0nWvfPnyWLdunUqEHhcXhw4dOqS5TMuK3tg6uhnGrz6NHf88UNOWHrqFv68+wrQ+NVCtuKcZ94CI0mOSsTKlWbuMxufo6IhYvQcuIiJrERQUhJ9++kkFpKQrjrSOyigglRgXh8fLluPqC23xSHJH/fv9aFeoEIp+OhGl1q5hQIooj5Cg1EO9/HGa4OBg9TciIkpfmTJlMHz4cNSqVQtNmzbN8HB55XPCvAF18EW3qnBxsFPTrgWFo/uPf+GHXZcRn/DfaMdElAtbSl2/fl21jpLXxYsXVW3gxIkT8dJLL5l2C4mIctj58+dVzZy0lJJEmx07dlRB+PSEHTiAB19NRvTly7ppNo6OKDhwIAoNHQI7A/NPEZF10HJHpSQjGKeWuJeIiJ4lDSE6deqk+10Gl/njjz/UNMndl5J870q3vQalC+J/y0/iVMBTNULfN9sv4c+LD/Fd7xqZfyAmIpPI1DXYoEEDHDlyRD2cDRo0CH379kWxYsVMs0VERBbkyZMnWL16tfq/NBOvU6dOui2koq9exf0pUxC+Z2+y6e4d2qPwmHfgWJzflUR5yZgxY9RP+d6YMGFCsrybktxcRvCU4c+JiMh4x44dw7Vr1zBr1izVxa969eqpltNKF86HVcMb4fudlzFz9xVII6mjNx+j/fR9+F/zYnitaFGDUjIQkYUEpVq3bo0FCxagUqVKpt8iIiILIrVu0jJKuuwVL148zfniHj9G0A8z8XjZMnnS1E13rlYNRcaPh2utmmbaYiKyJCdOnNC1lDpz5kyyVpbyf3mAevfdd2EtZs6cqV7aaILSiiE8PFz9X0YiNJQh8xqzPmtkqftvru3KjvfJ6jqzsryxy5r6esrMNliCmjVrqpxTkgRdWrXLgFzStU9aVKWmX1V3VC5UHp9uu4G7ITEIi47DZ9tv4q/rT/FeqxLwcLasdlN5+XrKyjp4PeU8OQehoaEGzZupq+7zzz/PzGJERLmCDDksD48SjJJaM8ldkJbEmBgEL12KoB9nIUFvkAf7okXh/c4YuMs6bE2Svo+IciFt1D1pWT59+nS4u7vDmo0YMUK9ZNAbDw8PFC1aVO2zFE5lgAhDGDKvMeuzRpa6/+barux4n6yuMyvLG7usqa+nzGyDpY3QJ8GpNWvW4MaNGyp/X/fu3VG6dOlU55fdbFy5JD5Zfx6rjweoaTsvP8G5+1H4tld1NC7rBUuQl6+nrKyD11PO086B5B43aVBKa35uiKlTpxo8LxGRpZCWDH///bfKTSD/r1q1Kvz9/dOcN2znTtz/+mvE3rylm27j6gqvwW+g4KuvwjaNWjoiynumTZumRotKLdG5DGtu7cEqIqLsVLhwYbzxxhvYs2cP/vrrrwxzf+Z3dlABqFYVvTF+9SmERscjMCQK/X86hMFNS+HdthXgZJ+UHJ2Ispe9sc3PM8K+uESUG0VHR2P9+vUqqbmTkxO6deuWZkAq6p9/cP+ryYg4dOi/iTY28OjWDYVHjYJDEW/zbTgR5Qp9+vRRiXjffPPNZNNXrFihvns2b96cY9tGRGQN7Ozs0KpVK5X/Uwv0R0REqOB/WikYOlbzQXHnGEzZew8HrjxS0+btu459l4MwvU9NVCia36z7QJQX2Rvb/JyIyNpIM295MAwKCkKRIkXQq1cvFCxY8Jn5Yh88wMPp0/F0zVppKqWb7lqvHoqMHwdn5tkjojRIQvPUWpK3aNECH3zwAY8bEZGJ6Lc83bhxIy5cuKDyTDVr1kwFrlLyzu+IX1+rjwUHrmPK1ouIiU/AhcBQdPphP8a1q4hBjUrC1pZJ0ImyS5YzuQUEJPXDTS8BMBGRJdu/f78KSEnCYckjJQkz9SVERSF44UIEzfsJiRERuukO/iVQ5L33kK91a7YSJaIMW2Om1n0vNjYWkZGRPHpERNlAynaSK3Tv3r24fPmyyjXl5fVszigJOr3RtLTKJzV62UlcvB+KmLgEfLbxPP68+ADf9KyOIu7OPEdE2SBT2XcTEhLw6aefqgSW0r1FXjJC1Weffab+RkRk6SQnlKZDhw6qu16XLl2SBaRknqcbNuJq+w54OP17XUDKNn9+eI8bhzIbNiB/mzYMSBFRhurVq4e5c+c+M3327NmoXbs2jyARUTaoUKGC6jYtPyX58pw5c1TLVf1yoL7nfNyx7q3GeL1JKd006crXdtpebDmT+0YnJLLallLSzHz+/Pn46quv0LhxY11Lg08++QRRUVEcnY+ILJoMTyojtEi3GQmqSw6patWqJZsn4vgJ3J/8FaJOnf5vop0dCvTpA6+3RsC+QAHzbzgR5VqTJk1CmzZt1HDlrVu3VtN27tyJI0eOYPv27Tm9eUREVktGAOvdu7fKkbxt2zZs3boVBQoUQPny5VOd39nBDhNerISWFbzxzsqTuB8SjScRsRi+5Dheql0cn3SujIeh0Vhx9DYCHkeieAEX9Krjh1Jeho00RkQmCEr9/PPP+Omnn9C5c2fdNHmgK1asmIpEf/7555lZLRFRtpOhgletWoXw8HBVOEmZzDz2zh08+PZbhGzekmy6W/NmKDJ2LJzKlOFZIiKjSSXewYMHMWXKFJXDzsXFRZWdpJKvXLlyPKJERNlIBuOqVasWSpUqhZMnT+q+d9NqMSWalPPC1lHN8H9rz2DL2UA1bdWxAOy68ACPI2Jga2Ojlpd1z9lzFZN7VEPPOn48j0TmCErJCAYVK1Z8ZrpMk78REVkaKTTIA+GOHTvU/yXZZfPmzXV/jw8Lw6O58xC8aBESY2J0053KlYX3uPHI1ySpVSgRUWbVqFEDS5cu5QEkIsoh0kKqZcuWut/37NmDO3fuqFxTUlnwzPxujvixfy2sPn4HH687i/CYeASHJ5UT47WA1r8/x60+jbolC6IkW0wRZX9OKUkY98MPPzwzXabJ34iILC3B8MqVK/HHH3+orno9W7dG5eMncO/d93D/m2/wcNYsXG3bDo/mztUFpOwKFkTRTz5BqbVrGZAiIpO4evUqPvzwQ/Tr1w8PHjxQ07Zs2YJz587xCBMRmVl8fLwame/KlSsqv9+1a9dSnU9aQkm3vS2jmqFoOsnOZb7lR29n4xYTWadMtZSSpucyQpW0OGjYsKGaJi0Qbt++jc2bN5t6G4mIsuTp06eqwOHj44O2+d0RMWQoHtnYyKgNutotjY2DAwoOHIBCQ4fCLn9+HnkiMgmpjW/fvr3qxiejQEmOKW9vb5VjSrrwSbdiIiIyHzs7O7z++utYv349zp49i19//RX169dXef9SjsQsShRyRZ2SBbDp9D2k1ulPWuJLjikiMkNQSrq8XLp0CTNnzlTRZSFNHiWflK+vb2ZWSURkcjL8ur29vXrwe+WVV1AoJgY3O3VOCkalwq1pUxT9+CM4Fi/Os0FEJjV+/HgViBozZgzy6wW8W7VqlWrr89xKyobykhYIIjAwUOXwEzLylaEMmdeY9VkjS91/c21XdrxPVteZleWNXdbU11NmtsFaNGrUSOUY/fPPP9XIfPKc265du2Tf1ZoCjgmwtZGue8+uR+o5PezjTXoc8/L1lJV18HrKeXIOZHCpbAtKCQk+MaE5EVkieRiS0VWke8yAAQNga2sLPz8/PPh2atoL2drCuWJFBqSIKFucOXMm1XxSEjQPCgqymqM+YsQI9QoJCYGHhweKFi0Kd3d3VTiV1qqGMGReY9ZnjSx1/821XdnxPlldZ1aWN3ZZU19PmdkGayL7XqdOHVSpUkX1+pFgeunSpVXFZkqvtXDHkmP3U12PxKkuPYqFs3shlYvKFNuVV6+nrKyD11PO086BjHyZbTmlZBjN/fv3636XGjFJ3ik5Eh4/fpyZVRIRmYQ8CC1atEgNsy7d9uR3ER8aihDpXpxGKylt5D0iouzg6emZas2tjAIqoxcTEVHOcnZ2Vr1/XnvtNV1A6vr168meb0t5ualR9qS1lJ2tjfopGSE0h28E48UZ+3Hq9pOc2AWiXClTQan33ntP96AnNX/SFL1Dhw7qopX/ExHlBBk9Zc6cOQgICFBD/Q4ZMkQ9CEYcOYLrXbqmH3SysYEDHwyJKJv06dMH48aNUzXwkgw3ISEBBw4cwLvvvqtadBIRkeUEp0RERIQaKEeSoB8/flzljBI96/hh1zstMKRZaXSs5othzctgas/qKPRv66g7TyLRc/ZBLDl0U7cMEZm4+54EnypVqqT+v3r1anTq1AlffPGFulglOEVEZE5yw5eHu127dqn/t2jRAs2aNUNibCzuf/01ghcsfCaheSorgedLPcy1yUSUx0g5Sbq1SVdi6WIs5Sj5Ka3MZUQ+IiKyLC4uLqpMKaM3b9iwQeWakude6ZJU0ssN49pVTDZ/o7JeeHPJMRy/9QQx8Qn4YO1ZHLvxGJ93qwoXR7sc2w8iq2wp5ejoqCLHQkbge+GFF9T/CxYsqGtBRURkLtLqQLrqyXdT//791WAM0Zcu40bPXgiev0AXkHKtUwfe772n8kfBzi7ZT59Jk+Do78+TRkTZQr6f5s2bh6tXr2Ljxo1YvHixGixGRnuSEaCIiMjyypf16tXD0KFDVT7lixcv4scff1Q/U1PUwxnLhjTEoMYlddPWnLiDbj8ewPWgpAEfiMhELaWaNGmiuunJsMaHDx/G8uXL1XSJHhfnqFVEZCZhYWHIly+f+n/btm1Rvnx5lCldGo8WLMTD775TLaWEjYMDCo8ejYKvDoSNnR3yt2mNJ6tWq+580mVPWkgxIEVE5lCiRAn1IiKi3MHLy0vlmdq7dy/27duH33//HaNGjdJ189PnaG+LjztVRm3/Ahi76jQiYuJxITAUnWfsx9c9q6NdlaI5sg9EVheUkqGL33zzTaxatQqzZs3SJejcsmWLGj6TiCi7nTp1Cps2bUK3bt3w3HPPqYSUruHhuPXqIEQcPqybz6l8efh+PQXOFSropkkAyvsd5r8jouxlTJ7NqVPTGR2UiIhylLRobdmypcpZGh4ergtISTfs1Fq7vljNFxWL5sewxcdx5UEYQqPjMGzxMZWHamzbCrC3y1SHJSKrlKmglNTwSdPzlL777jtTbBMRUZri4uKwbds2HD16VAWiYmNjVR6pkA0bEDLxUyD83+bRNjYoOGgQCo96G7ZOTjyiRGR2MrKeoV1EiIjI8un3CpIy6YIFC1CmTBmVeyplcKqsd36sG9EY41afxsbTSaOvzt17DSdvP8EPfWvC2/3ZllZEeVGmglJERDlB8kbJKCgyyl6BAgXQq1cvFHZ2xp3/jUHo1q26+ex9feD75Vdwq1+PJ4qIcsz06dNRuXJl5owiIrJCjx8/VvmU9+/fjytXrqB79+4oXLhwsnncnOwxo29N1PEvgEmb/kFcQiIOXw9Gxxn7VWCqfulCObb9RJaCQalUzJw5U72kOaaQ4Zulmaa4dy8pym0IQ+c1Zp3WyBL335zbZOr3MsX6MrsOY5czZn5pcSAtpKKjo1VrTWlCHXP4MC5PnoLER4908zk8/zxc3x6JkHz5EGKBn63sxusp715PxizD+5NxxzM0NBSZUbNmTVWGkIeU0qVL48iRIyhUiA8gRETWQL7bhw8frnoQycAVc+bMQZs2bVC/fv1kLWDl/682LoWqxT0xYslxBIZE4WFoNPr9dAjj21XEG01LscUs5WkMSqVChmyWl0S+PTw8ULRoUbi7u6vCqY+Pj0EH1tB5jVmnNbLE/TfnNpn6vUyxvsyuw9jljL2eSpUqpVobtGrVCo1q18bDb6fi8ZIlunnsPDzgNHoU/Pv2RV7F6ynvXk/GLMP7k/HHU4b/zgxPT09cu3ZNPbjcuHEDCQkJmVoPERFZJrk/SMt9yXUq+ZWlAvXy5ctqNGhbGeVZjyQ/3/h2E7z92wn8dfUR4hMS8fnmf3Ds5mNM6VkN7s4OObYfRDmJQSkisliRkZGqZZT2cDdy5EgkXr6CGy/1RMy1a7r53Bo3hs8XXyAoIal1IxGRJejRoweaN2+ugltSU16nTp00u/JJ8IqIiHIf+X6vUaMG/P391ch8vr6+zwSkNF75nPDr6/Ux9Y+LmLn7qpq29VwgLt4PxayXa6FiUXczbz1RzmNQiogstpXCihUr4OTkhI4dOyIxLg5hCxfi4cwfJbOkmsfG2Rne772LAv36JTV7zoPd9YjIcs2dO1flGJFcI2+//TYGDx6M/Pnz5/RmERFRNpB8pwMHDlQD8GgOHz6MqlWrwsXFRTfNztYG77WtiJp+BTBmxUmERMXhelA4us48gC+7V0W3mv8lUyfKCzIVlJL8Sl999RV27tyJBw8ePNMcnbV9RJQVkj9q8+bNalQTaVmQcPcubr43FpEnT+rmca5SBb5TJsOpdGkebCKyWO3atVM/jx07hlGjRll9UMqceTktMYeeOVnq/ptru7LjfbK6zqwsn515OZlH0PTH3xDSbXv79u3Ys2ePGp1Pf+Q+UbkAsKBPBfzfpmu49DASUbEJ+N/yU9h3/g5GNSsOR3vbPH09ZWUdvJ5ynpwDQ3NyZioo9cYbb6iL65VXXtE1SSciyioJQkl//OPHj8Pe3h5du3ZFiYsXEfjBh0BUVNJMtrbwGjYUXsOHw8aBfe+JKHdYuHCh+imtpq5evYpmzZqpmnOpUbemcpS58nJaYg49c7LU/TfXdmXH+2R1nVlZPrvzcjLPrWmPv6Ekn6A8lB88eFBVttarV08lQnfQK7/K264v44eP153D8qO31bQ1Z4Jw9XEsPn6+OGpVKIm8eD1lZR28nnKedg4MzcmZqaCUPDRu2rQJjRs3zsziRETPkFp1eWi7e/cuChYsiB4vvID476Yh8M8/dfM4lCiBYlMmw6VGDR5BIspVgoOD0bNnT+zevVsFoSQRrozI9/rrr6suH99++21ObyIREZmQVLC+8MILKF++vMo1JV35pEdRt27dVN4pjbODHSa/VA21/D0xYd05xMQl4FTAU7z6Wxhm9HND8/KFeV7IqqWegS0DUniSh0YiIlOR5L9ly5ZFxYoV0bd8eYQNeg1hegEpz169UHrtGgakiChXGj16tKodv3XrFlxdXXXTe/fuja1bt+bothERUfYpWbIkhg0bhurVqyMoKAh79+5Ndb7edUtgzfBGKFEw6R4REhWPVxcexrQdl5CQ8F+eKiJrk6mg1GeffYaPPvoIERERpt8iIsozpNvKhQsXdAkhm9apiyZnzuDhqNGIDw5W0+wKFYLbF5/D59OJsM3ksOxERDlN8opMnjz5mZwi5cqVw82bN3Nsu4iIKPs5OzurtBS9evXCiy++qJuujTKtqVLMAxveaoI2z3mr36WIPG3HZQxadASPw2N4qsgqZar7njQxl3wIRYoUUZFf/X6xQvLBEBGlJyoqCkuXLlX5VTp37owKiYm4O3YcYgMCdPPka90aPp99iocpbthERLmNJPvWbyGl361PRhklIiLr99xzzyXLu/PLL7+oPFO1atXS5Rf0cHXA3FfqYMrGk5h78C6kkdSeSw/x4oz9+LF/LVT388zBPSCykKCURHmJiDJL8katWbMGYWFhKF6sGDx27cbN+fOBf0fytHV1RZEP/g8e3bsn3aAtdIQhIiJDNW3aVD18SGtzId9tMnrxlClT0LJlSx5IIqI8RiolZJCfjRs34tKlS+jUqRPy5cun/mZra4OBdYuiaSU/vP3bCTwKj8GdJ5HoOfsgPu5cCf3qlbCqQTIob8tUUOrjjz82/ZYQUZ4gLSllBBJJbF67QgVUWLkS0efO6/7uUqsWfCd/BUc/vxzdTiIiU5LgU+vWrXH06FHExMRg7NixOHfunHooOXDgAA82EVEeU7lyZTVCqVTUSlBq1qxZKjAl+VU1jct6YePbTTBiyXEcv/UEMfEJ+GDtWRy7+Rifd60KF0e7HN0HohzLKaU5duwYFi9erF4nTpwwyQYRkfU6dOgQNmzYAFtbWzR1y4eyX3yJOC0g5eCAwmPGwP/XXxiQIiKrU6VKFfXQ0aRJE3Tp0kV15+vevbsqP5UpUyanN4+IiHJAoUKF8Nprr6F58+aIjIzE8uXL8afeQD/Cx8MFy4Y0xKDGJXXT1hy/g24/HsD1oPAc2GoiC2gp9eDBA/Tp00ddMJ6eSX1anzx5opqfL1u2DIULc9hKInpW1apVcfHsWVQ/fBiOe/ZCG0fEsWwZFJsyBc6VKvGwEZHV8vDwwAcffJDTm0FERBY2AnWLFi3UwBfr1q1D+fLln5nH0d4WH3eqjFolCmDc6tOIiInHhcBQdJ6xH1/3rI7/b+8+wKOo2reB37vpvRBSCSShBJGe0EEQlaZ0iIJSlWZUFPUTX/XF7osVwfxpFopKbypSpXcpAaRKIEB6AqT37H7XOTErJUA22zf3z2slOztz5sxsTnb2mXOe06upv0nqTmSyoNSLL76InJwc2e28Ilnb6dOnMWrUKLz00ktYsmSJXipHRJZP9AwQ4+MDAwNRsn072s2dB1V2tuZ171EjUfuVV6B0dDRpPYmI9O3EiRNVXrd58+Z8A4iIarCgoCBMmjRJkytK9JwSnUBED1tb2/Kv7X1bBOKBADdMWHwEcel5yCkqxcQfj2DCQ2F4vWc4bG10GghFZDlBqY0bN2Lr1q23zB7QpEkTxMTEoEePHvqsHxFZKJHAV3yQ7t69G16enhh45Spy16/XvK7w8UHwZ5/CpUMHk9aTiMhQWrZsKb9cqNXqWxLSiufCzctEnj0iIqrZbv5cOHToEM6dO4ezZ8/K4d6+vr5yeQNfN6x7oTOmrjqB306UTwY0d9dFHLuaiW+Gt4KvG2/0kmVRVvfLpp2d3R3LxTLxGhHVbPn5+fjpp59kQMrF3h4R27bfEpByf/xxuH3/HQNSRGTVLl26hIsXL8p/V61ahdDQUPzf//0fYmNj5UP8LPJJideIiIhu1q5dO9nxIzU1FfPmzcP+/fs1NzVcHWwxa1grvNu3CWyV5YGsQ5eu4/GZe+S/RFbfU6p79+6YPHmyHKYnhuQIiYmJeOWVV+TMMkRUc4m/BcuXL0d2djb8FQq0WbYcToWF8jWluzv8//tfeDzxOJKTy+/sEBFZq3r16ml+Hjp0KGbOnIk+ffrcMmQvODgY77zzDgYMGGCiWhIRkTlydHTEkCFD5FDwDRs2YPPmzTIthvi8EDkKRa+q0Z1C0ayOB6J/OoaU7EKk5xRh2PwDmNqrMZ7rEnpLzysiq+op9c0338gvnCEhIfIOn3iIu39i2axZs/RfSyKyCGLs+6JFi+TfggdSUtB5yVJNQMq5Q3uErVsrA1JERDXNyZMn5bXS7cQykZeTiIjodiKo1KJFC0ycOFHe6IiPj5ePm0XU88ZvL3VGx/q15PMylRof/X4Gk348ipzCEp5Uss6eUuKu3tGjR2VeKTHGVRD5pR599FF914+IzFxxfDwyV61GXtwFKMPC0F6lRsn+Awj+5wNTYW8P39dehdczz0ChZPJFIqqZxHXSJ598gm+//Rb29vZyWXFxsVx2c45OIiKi24kZ78WkYiLHVHh4uCYXYVFREZydneHj6oDFz7bDl1vOIWZ7nHx946kUnEvNwTuPN8Gfl68j4UYB6ng5ISoyGKE+LjzJZNlBKdET4sknn8Rjjz0mHxXExdXSpUsxcuRIfdaRiMyUCEadnz4dcQ0aoMWxY7i+bTtunpDW4YEHEPTZp3Bo0MCEtSQiMr05c+agb9++qFOnjmamPTEkQ9wF//XXX01dPSIiMnPi86Jx48aa57t27ZIdRfr3748GDRrARqnA6z0bo1WwF15ZHoucwlJcysjD2IV/4p+0U7KMuTvjMH1wcwyNDDbdwRDdpFrdFsaMGYOsrKw7lufk5MjXiKhm9JA6PHs2tj72KM6HN0JiUNAtr3s++SRCly1lQIqICEDbtm1l0vMPP/xQBqXE46OPPpLLxGtERETaEBOM5ebmysmF1q9fj5KS8qF6jzbxw/oXu6B+7X97Q6nU5Q8xtE/8+8aqE4jPyOMJJ8vtKXX71MYVEhISZNI1IrJuxenp+G3WLJzs0hkKlQotjx5FUELCvysolbBxd5dD94iIqJyLiwvGjx/P00FERDoTE4yJHlJr1qzB4cOH5UyvAwcORFBQEOrWckb3xr64mH4J5fP13Up8l192+Cre6PVvzysiiwhKtWrVSv4Ci4doBLa2/24uxrSKhtCrVy9D1JOITKw0PR3ZW7YgbcsWbHdyQpqfHxzzC9Bh717Uzsi4Y/2SxEST1JOIiEwnJiZGPsR1oZCSkoK8vPK78drMulqVdWv6LK7mevzGqpch9qNrmbpsr+22+m5P1amDNTHXY79fvUSOQhGI2rdvn5yZ77vvvkPv3r3lUPH41EyIfiTqSqJSKpUaF5Kua8o3x/akSxlsT6Yn3gMxkk7vQamK6YpjY2PRs2dPuLq63tIgxGx8gwcP1ra+RGSmStLSkLN5C3I2bkT+kSPyU+1Y61ZICwlB7dQ0tN+3TzO73i0UCtjdNpyPiIisX3R0tHyIWVhF73l/f3+4u7vLi9OAgIAqlVGVdbUpzxqZ6/Ebq16G2I+uZeqyvbbb6rs9VacO1sRcj12beomZ+c6cOYM///xTdiQRnUcaBGZh24XMSqNSYkmh2kb+jRY3D8ytPelSBtuT6VW8B6KHuN6DUtOmTZP/iuDTU089BQcHh+rVkojMlio9Hde3bEX25k0oOHL0jg+yZsdPwNXBARF16yG7qKjyQtRqeA5hgJqIiIiIyBjETK4iEXpFmp12XgXYoUzFGVVtccf4jvV3/50hc0s9386HbxBZXk6puLg42UWwQ4cOcHR01H+tiMioSlJSkLNpE7I3bUbB0aPIvum1UhsbHGkTiQYFBWjUoQPce/VC0/Bw+YHn0qIFkt9+W/aMksGrf/4N+PBD2Nerx3eRiIiIiMhIKgJSYgh17P6daG+XhTrKTOwvDUW+2g4KKKBSqzV5ppYfTsDJq9fx3RhvBHo68X0iywlK7d+/H19++SVKS0vRpk0bdO3aFd26dUOnTp3g5MRfZiJLUJKUJINQIhhVEBtb6TqFTZpgT6uWuK5SQRESgk4jR94yyYHnoIFwjmiNzJWrkB13Ae71G8geUgxIERFVTiSjFUMsKu5qR0ZG8lQREZFe2djYYOTIkTIJOhISMNThDLJrN4dv3TA8GRmM4wmZspdUYYkKZ1Lz0XfWHsQ83Rrtw2rxnSDLCEpt2bJFBqQOHjyIXbt2YefOnZg5cyaKiopkkGrPnj36rykR6aw4IbG8R9TmTSg8fqLSdZT16sH7iSeQ/GATbDx4EMXFxWjWrBmeeOKJSmfdFAEo31enoCw5Gb5mOB6fiMgciBmKhw0bhr1798LT01Muy8zMRMeOHbF06VKZlJaIiEhfvL29MWbMGPndXHxfd08+jHDfEvi7hiCkZRAa+rph/OLDSLhRgGt5xXj624N4+/EHMLpjSKXX/ERmFZSSG9rayp5RtWvXlr/wbm5uWLt2Lc6ePavfGhKRTooTEsoDURs3ofDkyUrXcWjYEG69esK9Z09kODkh9vRp7Nu9G0qlUs7gIYLN/HAiIqq+5557DiUlJbKXVHh4uFx27tw5+YVBvLZx40aeXiIi0itxLf/QQw+hQYMGsteU+Nx55JFHZAqeJoHu+PWFzpiw8AAOXclBmUqN9349jZMJWfh4UDM42tnw3SDzDUrNmzcPO3bskBFX0TuqS5cucvje22+/jebNm+u/lkSkleIrV5C9aRNyRCDq1KlK13EID4d7r55w69kTDmFhmuW5587J4SUi0Dx06FAEBwfz7BMR6UhcM4l8nBUBKUH8PGvWLHkdRUREZCiBgYEYP3480tPT5TW+kJWVBTcXF3zZvwF+PJGNOTvj5PLVxxJxLjUHc56JQLC3M98UMs+g1MSJE2UPqVdffRXPP/88XF1d9V8zItJKcXw8CleuwsV9e1F0ujxfye0cHnhA9oZy69kDDqGht7ymVqtlbygxdbeYXdPX17fK03gSEdG9iQC/6Cl1O5GMVnxZICIiMiQ7OzvN541IxfPzzz/Ln8WNkam9m6JpkDv+38oTyC8uw6mkbPT7Zg++Gd4anRpwdj4yw6DU6tWrZS4pkQNh2rRpaNWqlewpJR6dO3eGszMjqkTGUHTxEnI2lw/NK7rL0FnHJk3g1qsX3Hv2qDQBuQhGifxwYujtiBEj5LLQ2wJWRESkm88++wwvvvgiYmJiNMnNRa/UyZMn4/PPP+fpJSIioxE3REQnk1OnTslhfaLXVJ8OHTR5pi5fy8eN/BKM+O4g3uz9AJ7rEspUHmReQakBAwbIhyB+gXfv3o0VK1bIRMhi3GphYaG+60lE/yiKi9MMzSs6f77S8+LYtKlmaJ79PYbfieG3v/76q/xAcnBwkF16iYhI/0aPHo38/Hy0a9dO5uWsuFMtfh47dqx8VLh+/TrfAiIiMhhx3T9kyBA5jPy3337D1q1b8ffff8vv+L9Ed8bkZcew41w6VGrgo9/P4ERiFqYPbgZn+2qnpCa6q2r/Vl27dk3mRxC5pcRDfKn18vJiXgQiAyj6+29kb9qMnE0bUfT3hUrXcRT53Dp2QNCQobCvE3TfMkUAavny5cjIyICfnx+ioqLkpAXJyckGOAIiopptxowZpq4CERHRLcQM2yLp+f79+3Hp0iXMnTtX9uD9blQbzNh6HrO2lX/v+PV4Ev5OzcG8EZGoW4ujosgMglLil1fMHiOCUCKb/7hx49C1a1cmOSfSEzGkTgSiRG8o0SuqOK488eDtnFq0KB+a1+Mx2AUFyYCSfUDAfcsXQeRffvkFxcXFst2KXo5inDkRERnGqFGjeGqJiMjsiPzQIoWHSOchvhuIIJXwao9wPBjogVeXxyKvuAxnU3LQ95s9mDmsFbo2qm3qapMVqXaicxGEatq0qf5rRFRDkpJnrlqNvLgLSKvfAJ6DB8GuXj05HC9740bkbNqM4osXK93WqVWr8qF5PXrArgoBqMpcvXpVDhvp06ePzG0iEpwTEZF+ZWdny8kjKn6+l4r1iIiIjE18F2jfvv0tN8h///13NGzYEOte6ITxi4/gYnoesgpKMPqHQ3i9Zzgmda3P7xBkuqBUdHS0/FdEUkU3v/r162vyIxDRvYlgVPI774i//uIvPq7t2Ilr334LG29vlF27ducGCgWcWrfWzJpn5+dXrVMs8keJ8ePCY489hpYtW8Lf359vFxGRgYge5aIHq5jN1NPTs9KL94qZT0XSWSIiInOQmpqKI0eOyAk5IiIisHzcw5i65gy2nkkVX1/w6cZz+CsxC58OaQFXB8YBSDfV+g0qKCjACy+8gIULF8rn58+fR1hYmJxVJigoCFOnTtWxWkTW20NKBqRUqjteuyUgpVDAOSJCDs1ze+wx2Pn56rTfy5cvY+XKlejVqxcefPBB2NjYMCBFRGRg27Ztk7n6hO3bt/N8ExGRRRA3rsUEHWvXrpXBKdER5b/9B6BZkAe+2lo+0dLvJ1Pwd2ou5o2MRKiPi6mrTDUtKCWCTsePH5cJzsWX3AqPPvoo3n33XQaliO7RS+qeDTIgALXGPQf3xx6DbW3dx2qLO/AicaGYUUP8zBmdiIiMR6Q6qBAaGorg4OA7ekuJv81iSDUREZE5qVu3LiZMmIBNmzbh2LFjWLDgB3Tu3BnfjmiNV5afQE5RKf5Oy0W/b/bg66daonvj6o3mIFJW5xSIiOk333wjfylvvrgSPTDi7pKQmaimE188cvfsqbSXlKRUwrlVK3gPH66XgJQYrid6R23ZskUO2xs2bBhnxyQiMhERlBKznt5O3CwQrxEREZkb8R2iX79+eOqpp+Dk5IS0tDQ80sRf5plq6Osq18kpLMWzCw/j661/Q6VSm7rKVFN6SomLKpEf4XZ5eXlMdkZUCVVenhy2V3TmzN3Pj0IhZ9DTh4yMDCxduhTXrl2T3W+joqJkbhMiIjKNitxRt8vNzdXMdERERGSOwsPD8fzzz8ufxWdZWG1XzB4Uis93pWHj6fI8U2JY319JWfgyqoWpq0s1ISglZutav369zCElVFxkffvtt+jQoYN+a0hk4YouXkTCSy+h+MJ9ehGq1fAcMlgv+7S3t5e530QyczHDnp2dnV7KJSIi7UyZMkVzrfTOO+/A2dlZ85pIbi6m4BZ/q4mIiMyZi8u/eaMSExPx86IF6BQaiibdWuCrnVdlYGrL6VT0j9mLj3rVQzUnCacaqFpBqY8//hi9e/fG6dOn5bTyX3/9tfx537592Llzp/5rSWShsjdtRvKbb0KVny+fK11d4TFgAG78/LNm9r2KfwM+/BD29epVe1/iy43orVgxtfjEiRPh6urK3otERCYk8nBU9JQ6efKkvGlQQfzcokULvPbaayasIRERkXbEDZY6derg4sWLcExKwvTuXfDh3hxkF5biYnoenl12Fl896YSeD3KmbzJQUErkkoqNjcX//vc/NGvWDJs3b0br1q1lQmXx3JyI5KEjRoyQ419tbW3lXcqhQ4eaulpk5dSlpUj76itc/+57zTKHhg1RZ9ZM2IeEwHvEM8hcuQrZcRfgXr+B7CGlS0AqOztb5o/KycnBpEmT5BcdNzc3PR0NERFVV8Wse2PGjJE38cRNAyIiIksm0oKI2fn27t0rJz87s28LXg9/AEtTauFUaiHyi1WYsPgIXureAC8/2ghK5Z3D14l0CkoJ9evXx/z582HuRCBqxowZsmt8SkoKIiIi5HCmm7sfEulTaUYGEqe8ivxDhzTL3J94AgHvvwflP8M2RADK99UpKEtOhq+OfVvFFK2rVq2SvaTEzE6ixxQREZmXH374wdRVICIi0hulUiknUWrQoAFWr16Ni+fPICo0DIf9m+LX40lynZnbLuBkYhZmPNUKHk5MJ0J6DkpZioCAAPkQRMJnHx8fOdMNg1JkCPnHjiFx8ssoTUsrX2BrC7833oDXM0/rfRidGAoihsz+8ccf8mcx9XijRo3kzBhERERERESGJr5rjx8/Htu2bUPz5s0x0t8fIe4KxOxJhJiMb/u5dPT/Zg/mjohEuD9HctCdlNAyGmpjY3PPh+iZpI1du3ahb9++CAwMlF/a165de8c6MTExCAkJkbPTtGvXDodu6oGijSNHjsheJKI3CZE+iaDQ9R9/wuWRozQBKVtfX9RbtEgO1TNEQEoM19u6daucqvXpp59Gt27dmD+KiIiIiIiMSkyq1LNnTxmgEt97BjR2w+S6yQhxKpavx1/Lx8D/24vfTybznaE7aBVBWrNmzV1fE/mkZs6cCZVKpU2RcsiRSPI5duxYDBo06I7Xly1bJmeumTNnjgxIiaF44hf+3Llz8PX1leuIoXki4frtRK4rEewSRO+okSNHWsSQQ7IsIol58rR3kf3rr5plzm3aIOjLL2Bbu7ZB9in+2Iuefzdu3EBUVBQ8PT0Nsh8iIiIiIiJtxMXFITMtEY8okxHvFYJtN7yQX1yG5386iknd6uO1HuGwYZ4pqk5Qqn///ncsE8GhqVOn4tdff5W9Nd5//31tipSz+InH3Xz55ZcYN26cTBAqiODU+vXr8f3338v9CiLp+r0UFRVhwIABcv2OHTvecz3xuDl5NNG9FMfHI+GlySg6f16zzHvsWPhOeQUKLXsNVsXly5dRt25dGZQSEw506NBB696JREREhiJ6t4tHRX5Dkc+zYmbY5OSq3yGvyrralGeNzPX4jVUvQ+xH1zJ12V7bbfXdnqpTB2tirsduqe1JTH4mZujbvXs36hZexHBPT6zLCkau2gGzd8Th6MU0vNc7FB6OtgapF9uT6Yn3QEzCVRUKtRgHVA1JSUmYNm0aFi5cKHsuffLJJ2jatGl1ivq3MgqF7I0lAkhCcXGx/GUWw5QqlgmjRo1CZmYm1q1bd98yxeENHz4c4eHhePfdd++5rnj9vffeqzTwxpnM6HYle/Yi73//E939yhc4OcH5jf8H+65d9X6yxMW96I14+vRpGVjVta0REVHViYsqcR2RlZXF2fOqSNzY8/Dw0JwzcXFakePzfqqyrjblWSNzPX5j1csQ+9G1TF2213Zbfben6tTBmpjrsVtDexKfBeI7+8WLF6GwscWuwmBcKK0l1wn2dsLcZyLRJNBdr/ViezK9m9//m68F7kbrLhaiwI8//hizZs2Sw+ZEkmWRdd8QMjIy5JdxPz+/W5aL52fPnq1SGWKaSjEEUCRdq8hXtXjxYhm9vd2bb74phwpWECdR5J8Sw6QMcUGlzXrWyhyP/351UpeVIX3mLGTOnatZZl+/PurMmgmHsDC97quiza1YsQKJiYlymJ743RW/k9UtTx910sd2bE/6Z4ntyZz3ZUntSZtt+Pmk/fnk5ChERETaE9+hn3nmGfz555/YsmULnn+4AT7al4drecW4er0Ag2bvxfTBzdG/ZRBPbw2mVVDq008/xfTp0+UX4iVLllQ6nM/ciCFOVc1zJRJGiwfR3ZRev46k115D3r79mmVuvXoh4MMPYePqovcTJ+4qrFq1Cvn5+WjYsCEGDhzI2fWIiIiIiMgiiNFQbdu2RePGjeXoo/YRhZi0+E+kJSciucQdk5fG4mRCFqb2bgxbG63mYaOaGJQSOZnEdPMNGjSQw/bEozKrV6/WS+V8fHzkjH6pqam3LBfP79ZThMhQCk6cQMLkl1FaMbbZxga+r70G79GjDDLrnRiqJ4auiiGoDz/8sOyRaIj9EBERERERGVLF8K1ATydENy7G/uvnca7UB4dKgvHtnks4nZyNWcNaoZYrO4nUNFoFpcTsdcb8Umxvb4+IiAg5RLAip5To9SSev/DCC0arB9VsIiiUuWw5Uj/6COqSErnMxscHdb76Us6yZyihoaFy9kgRkKpfv77B9kNERERERGQsDzQOx9kzpxF+IwOBNjnYVRyKfXFAv2/2Yu6ICDQN8uCbUYNoFZRasGCB3iuQm5uLCxcuaJ5funRJzqbn7e0tZxkTOZ5EYvPIyEjZ7W/GjBlyFpeK2fiIDElVWIiU995H1po1mmVOrVsj6KuvYOfnq/f9iVmKRB61oKAg2Svx2WefZe8oIiIiIiKyGiJv88SJE7Fp0yYcPXoUfRzO4kSJP2IzAzF49j58MqgZOgTYmLqaZCQmn0v+8OHDsidIhYpE4yIQJYJgTz75JNLT0/Hf//5XfmEXydU3btx4R/JzIn0rvnoVCS9NRtGZM5plXiNHwO/116Gws9P7/kQwdv369XLGyejoaNlTkMP1iIiIiIjI2ojvOn379pWz265dtw4t8lNQqLbD6VI/TFl+HFEta+OjoX6wY54pq2fyoFS3bt3k8Kh7EUP1jDlcLyYmRj5EjxVBBMNE76yK2XiqqqrralOmNTLH47+yZg3yP/oY6tzc8gWOjnB+7VWoH3kEKRkZet1XQkIC9u3bhzNnzsgcaq1bt8a1a9dMej6rW4a227E91Yz2ZMw66XtfltSetNmGn0/anc+cnByt3wsiIiK6v0aNGiH6+eexa/ceFOX54/SfCXL58tg0xGcdRMzw1qjtxjxT1szkQSlzJHqpiEd2djY8PDxkUnWRmI1T2Fv/FPbqsjJcmv4pihYt0iyzDwlBnVkz4dCwod73d/78eezcuRNJSUnw8vJCVFSUTkn8LWkKe7Yn629Pxq6TvvdlSe1Jm230vZ61uvn4XVz0P7sqERERQfM527tXT/QG0CzYC9//ugthijTsvhSKvrP2YM6ICLQM9uTpslKcc5HoH6U3buDqxEm3BKTcHnsUIStXGCQgVVpail9++UUGpES31fHjx3NWSSIiIiIiqrGGta2LwWFqmQB9gOMpOOUlImrOfiz784qpq0YGwp5SRAAK/jqFxJdeQklSUvn5UCrhO+UVeBsw0bitra2cXdLOzg6dOnVi/igiIiIiIqrxxo96Gmt+3YATsUfQzf4SLpZm4Z1VxTiRkIVpfR+EvS371lgTBqWoxstctUrOsKcuLpbnQuHpieAZX8GlfXu9n5uCggIcPHgQDz30EJRKJRo3blyjh8cQERERERHdTHxP6ti2NdpGtsJ3Py5DWOF1+NnkYNOhIsRezURkPS9czy9BHS8nREUGI9SHw+wtGYNSVGOpioqQ+uGHyFyxUrPMsUVz2L/1FlyaNzdIfpLly5cjMzMTrq6uiIyM1Ps+iIiIiIiIrEFwUCDefvVFzP55HQovnkWe2h6nkrLlQwxmUSoUmLszDtMHN8fQyGBTV5eqif3eqEYqSUzE5eFP3xKQ8ho+DPUWL4aydm297+/YsWP47rvvZECqTZs2aNWqld73QUREREREZE1EypMXRw5Gp35PowB2cpmXIh/eyEOZSg2VGnhj1QnEZ+SZuqpUTewpRTVO7u49SHrtNZRlZcnnCkdHBLz3Ljz69zdIMvPff/9dBqVE7qh+/fqhuQF6YREREREREVmrU2mFsFEooFKXoav9RXgoinCsNAAnSwOgUCix7PBVvNGrsamrSdXAoBTVGGqVChlz5iBj1jeAWi2X2dWtizqzZsIxPNwg+9y7d68MSNWqVQtRUVHw9fU1yH6IiIiIiIisVcKNAqjlf0ocKwlER/vLiLBLQrAyC7tLQuXrZJkYlKpETEyMfJSVlcnnKSkpyMvL0+QFqqqqrqtNmdbIGMevyslB/sefoPTAAc0y244d4PTmm7jh6ioqYZA6hYWF4caNG3K4nvh9qqxcfR+/Psqrbhnabsf2pH/m+PfEmHWqye1Jm234+aTd+czJydH6vSAiIiL9EUnN5azoajUuq7yRVuiKzvbxqGOTjX7K07iWqoJa3ZKn3AIxKFWJ6Oho+cjOzoaHhwf8/f3h7u4uL06rOlNaVdfVpkxrZIzjLzx7FgkvvoTSq1fLFygUqD35JdQaPx4KpVKvdVKpVNi1axeCgoLQsGFDuSw4ONhox6+P8qpbhrbbsT3pnzn+PTFmnWpye9JmG34+aX8+XVw4qw8REZEpiVn2RFLzCgWwx5bihmhsk442dgnwzTyNmb8fRVTrQJPWk7THoBRZtcy1a5Ey7V2oi4rkcxtPTwR+/jlcO3fS+77y8/OxevVqxMXFwcfHB/Xr15fTmRIREREREVH1hfq4yFn2RFJz0WNKrVbLXFLnynyRpHKHrzIXF3anIKdYgal9a8sE6WQZ+E6RVVIVFyP1k0+QuWSpZplj06ao8/UM2AUF6X1/iYmJWLFiBbKysmTPqKFDhzIgRUREREREpCdDI4PRJsRbJjUXOaTEkL4nI4Ox4a8UTN94Vq7z7cEk4OoxNKvng169esHBwYHn38wxKEVWpyQ5GQmTX0bhiROaZZ5RUfB76z9Q6vmPkojQHz16FBs2bJA5o9q1a4fHHnsMNjY2et0PERERERFRTRfi43LHLHuTutWHnY0CH64/AweU4vq1dMTeSEB8fDwGDBiAevXqmay+dH8cW0RWJW//flwaNFgTkFLY2yPgo48Q8P57eg9Iyf3l5WHLli2yV9TgwYNlNJ4BKSIiIiIiIuN5rksY3u//IIpgh1+KmuBMaW1kZmZiwYIF2Lp1K0pLS/l2mCn2lCKrIHosXZv/LdJnzBDZxuUyMUwvaObXcHrwQYPsT4xldnV1lUP1RCL82rVr630/REREREREdH8jO4QgPzcH07ddwYGSerha5onHXK5g7969uHDhAkaNGgUnJyeeSjPDnlJk8cpycpDw4otI//JLTUDKpUsXhK5aaZCA1Llz5/Djjz9qou0ioTkDUkRERERERKbVv6kPPh3cXEy4jkSVB5bkNEapeyC8vLzg6OjIt8cMMShFFq3w/HnEDxmK3K1/lC9QKOATHY3guXPkTHv6pFKpsG3bNixduhSXLl3C5cuX9Vo+ERERERER6Z4Q/auollAqIIfzLU4NwEF1A6jU5a8fP35cTlBF5oHD9yoRExMjHyJxtZCSkiJzBwnJyclVPrlVXVebMq1RdY+/eOsfyP/iC6CwUD5XuLnB+T9vorR9e6Skpuq1TgUFBTIgJWbZE10+H330UTg7O+vlvdP3+2/KOmm7HduT/pnj3xNj1qkmtydttuHnk3bnMycnR+v3goiIiExnQKsg2Nko8dLSYyhTAatjU1CqjsXUbv5Yt24d7O3t0adPH/j4+PBtMjEGpSoRHR0tH9nZ2fDw8IC/v7/MGSQuTgMCAqp0Yqu6rjZlWqPqHL+6uBipn36G/B9/1CxzaPIA6sycCfs6dfRep4SEBPmHS/w+1K1bF0OGDIGbm5vO+6lsX+ZQXnXL0HY7tif9M8e/J8asU01uT9psw88n7c+ni4uLVu8FERERmd7jzQNgo1TgxSVHUVKmxi/Hk1BSWobh3R/Bzh3bsWbNGoSFhckJq0SHAzINDt8ji1KSmobLo0bjxk0BKY+BAxHy8896CUhV5uzZszIg1b59e4wcOVJvASkiIiIiIiIynF5N/THnmQjY25SHPjacSsWiiw4YNWYs/Pz8cPHiRcyePVsmQifTYE8pshh5hw4hccqrKMvIkM8Vdnbwe/tteEYNlTPh6ZMYumljYyN/7t69u4ygiwcRERERERFZjkce8MP8UZEYv+gwikpV2HI6FaVlKswaNQZbN22QOaa2bNkiv+8pley3Y2w842T21Go1rn3/A66MGasJSNkGBKDezz/B68kovQekRNK7efPmyT9OgvjDxIAUERERERGRZeraqDZ+GN0GTnblHQ+2n0vHpJ9j0aJ1G4wePRqDBg3SBKSKi4tNXNuahUEpMmtluXlIfPkVpH36qei+JJe5dOyI0NWr4NSsmUGG6q1evRppaWmIj4/Xe/lERERERERkfB0b+GDBmDZwti8PTO3+OwOv/nIBPv5BcihfxeQmM2fOxM6dO+Xs62R4DEqR2SqKi0N8VBRyNm3SLKs1cQKC58+DrZeXXvcl/uBs3boVy5YtQ2lpKXr16oV+/frpdR9ERERERERkOu3CamHxs23h6lCeyehoQi5G/3AIuUWl8vmNGzfkSJ0dO3bg+++/x7Vr1/h2GRhzSpFZKI6PR+aq1ShJTIRdUBBsfWsj/asZUOXny9eVbm4InP4/uHXvrvd95+XlYeXKlbJnlEhi/vDDD6NVq1Z63w8RERERERGZVkQ9b/z4XDuM/O4gsgtL8Wf8DYz47iAWjm0rZ1ufNGkSfvnlF/z999+YO3cuevTogYiICL5tBsKgFJmcCEYlv/MOIHJDqdX/Pv7h0KgR6syaCft69QyyfxEJz8jIQEhIiJwOVHTZJCIiIiIiIuvUMtgTP49rj+Hz9yO7sAzHrmTimW8PYtHYtvB0dcWwYcNw5MgRbN68GevXr8eVK1fQoUMHU1fbKnH4HplUWUJCeUBKjNcVOaPEvzcFpFy7d0fIsqV6D0iJQFT+P72wXF1dMWbMGIwYMUL+TERERERERNataZAHYgY1hLeLvXx+IiELw+cfxPW8YjmZVmRkJCZMmICgoCA0atTI1NW1WgxKkUkVb9hQ3kOqMgoF7OuHQenkpN99FhfLZObfffcdCgsL5TJvb29O/0lERERERFSDNKjtjKXj28PH1UE+P52cjWHzDiAjt0g+r1WrFsaOHYumTZvK5yL/8LZt2zTfI0l3HL5XiZiYGPko+2e2t5SUFJl3SEhOTq7yya3qutqUaW1USUmaWfXuoFAgJy4OKj2en8zMTGzZskUmsPPy8pLdMEUeKVO+J/relz7Kq24Z2m7H9qR/5vj3hO3JOO1Jm234+aTd+eSwbiIiIuvVyM8NyyaIoXwHkJpdhHOpOXhq3gH8/Fw7+Lo73tJ54cCBA9i9ezdOnDiBAQMGyBQwpBsGpSoRHR0tH9nZ2fDw8IC/vz/c3d3lxWlAQECVTmxV19WmTGtTeO48Mo/F3n0FhQLu9RvAV0/n5/Tp01i3bp3sKdW8eXM8/vjjsLcv76ppqvdE3/vSR3nVLUPb7die9M8c/56wPRmnPWmzDT+ftD+fLi4uWr0XREREZFnq13bFsvEdZGAqKasQF9Jy8aQITI1rhwCPf0futGvXTt6sOnToEBYuXIiOHTvKibJsbRlaqS4O3yOjE/mcri9ajPihQ4GsrHutCM8hg/Wyz61bt2LFihWyu2WfPn1kVLuygBQREREBV69eRbdu3dCkSRN5I0d8hhIREVmzEB8XLJvQAXW8yoNQlzLy8OTcA0i4UZ6LWLCzs0Pv3r3xzDPPyBE3+/btw/z585GammrCmls2BqXIqErT03F1/ASkfvwx1MXFcpmtn195XikbG0B0jfzn34APP9RbgnNnZ2fZ200kNG/Tpo1MXEdERESVE3d8Z8yYIXsZi5mHXn75ZU0qAyIiImsV7O0sA1P1ajnL51eu58vA1JVr/wamhPr162PSpEny5k1aWhpOnTplohpbPvYxI6PJ2bYNyW+9jbIbNzTLHIYMRsg776A0JQWZK1ehJDERdkFBsoeUrgEp8cehdu3aMgAlpu9s3bo1HB0d9XAkRERE1k0MXawYvijSGPj4+OD69escykhERFYvyNOpfCjftwdwMT0PiZkFeHLefnzdPww3Z0pwcnLCkCFDcO7cOTRs2FAzKqigoMB0lbdA7ClFBqcqKEDyu+8i4floTUDKprYPgufPh1N0NJQODjIA5fvqFAR9+YX8V5eAlPhDsH//fsyZM0f+K4jAFANSRERkLXbt2oW+ffsiMDBQfsatXbv2jnXEpC0iAav4/BM5MET+i+o4cuSInPwlODhYDzUnIiIyf/4ejnJWvoa+rvJ5clYhnl/1Ny6k5dyynvgMbty4MWzEaB8AJ0+exNKlSxEbGyu/l9L9MShFBlV4+jQuDR6CzKXLNMtcu3dH2Lp1cO3SWe/7KyoqwqpVq+RQA5EzSkzhSUREZG3EULoWLVrIwFNlli1bhilTpmDatGk4evSoXLdnz56yF3GFli1byimub38kiZlx/yF6R40cORLz5s277+evmCDm5gcREZEl83UrD0w19i+frT0jr0TOyncu5dbA1M3EpFoqlUpOsCXyMebn3zrsj+7E4XtkEGqVCtd/+AFpM74GSkrkMoWjI/ymToXnk1EGyemUnp6O5cuXIyMjA35+foiKioK3t7fe90NERGRqIsmqeNzNl19+iXHjxslcioLoPbx+/Xp8//33mDp1qlwm7uLeL9AkJgYR64vZhe7lk08+wXvvvXfH8pSUFE0uKjGjYVVVZV1tyrNG5nr8xqqXIfaja5m6bK/ttvpuT9WpgzUx12Ovye1JlzL03Z5m9AvF5LV/41xaATJyixE1Zy9mDmqIRrXL807dLCgoCAMHDsT27dtx5swZxMfHo2vXrqhbty5qkuTkZDlLYVUwKEV6V5KSgqSpbyL/wAHNMocmDyDo88/hEBZmkDN++fJl/PTTTygpKZF3gx9//HE5MwIREVFNI+7SiiF3b775pmaZUqnEo48+qhnWfj9iyMHo0aPRvXt3jBgx4r7ri32JnlkVRE8pMdxP5KMSE42Ii9OKHFX3U5V1tSnPGpnr8RurXobYj65l6rK9ttvquz1Vpw7WxFyPvSa3J13KMER7Eq8un+SPYXP24HRqPrIKy/DSmjgsfrYtmtfxrHQbkQRdBKb27t2LjRs3yu+nkZGRqAmS/zmnLi4uVVqfw/dIr7I3bcbF/gP+DUgpFKj13LMIXbrUYAEpQVz0enl54YknnkD//v0ZkCIiohpL9BgWOaBEr+Gbieei51JViItoMQRQ5KoSw/zEQ+TJuBsHBwcZfLr5QUREZC08nOzw9cCGiKjnJZ9nFZTg6fkHcfTKv5N43UzkmBI3g0SPZdF7SuSdosqxpxTphSovDykff4ysVav//eXy80Pg9Olwad/OIGdZdAcUD5HkVVwMT5gwQd4JJiIiIt107txZ5sQgIiKicq4ONlg4ti3GLvgThy5dR05RKUZ+dwg/jGmDNiGVp40Rw/aeffZZTfoakbdRzNb30EMPaZKj13T8Bk86KzhxAhcHDbolIOXWsyfC1q01WEBKjM2dO3culixZoslVwYAUERER4OPjIy90U1NTbzkd4rnoWUxERETV4+pgiwVj2qBj/fIJtXKLSjHq+0PYH3ftrtvcnE9ZTMglZtAVOR5Fz2ZiUIp0oC4rQ8bs2YgfNhwll6/IZQpnZwR8/DGCZnwFG09P/e9TrZZDChYtWiSDUa1bt4aTk5Pe90NERGSpxOyzERER+OOPPzTLRK8n8bxDhw4mrRsREZGlc7a3xfej2+ChRrXl8/ziMoxZcAh7/r5/kGnIkCFo1KiR7DElOlkcOnRIfsetyTh8rxJiemXxEPkYDD1zjLZlmguVOCcff4Kym/JL2DzwAJzf+g8KgoJQUMWcFdocv0jcumPHDtlLSgzXe/jhh2V3yNvvBOuDMd8Tfe/Lmma6qCntSZ/M8fjZnozTnrTZhu1Ju/NZ1dljjCk3NxcXLlzQPL906ZKcTU/MOis+G0XS8VGjRsmkqm3btsWMGTPktUzFbHxERERUfY52Npg3IgLRPx3FH2fTUFiiwtiFf2LuiAg0vkdaRVdXVzz11FM4duyYTIC+YcMGnD9/XuZFdnNzq5FviUJd08Ny9yBmjvHw8EBWVpZBZo7RZj1zkvXbeqS8+y5UubnlC5RK+EycAJ9Jk6DQcsa7qh6/uMM7f/58GSAUQw+ioqJkYnNDMOZ7ou99WdtMFzWhPemTOR4/25Nx2pM227A9aX8+b78eMAfiJo24OXM7EYhasGCB/Pmbb77BZ599Jj87RaLymTNnol07wwyrr+zGnrjIFnkzaupFNhERWb+SMhXe2XAJO+Oy5HM7GwU+6hOKLmH3HzUkri+2b9+OtLQ0DBgwALVrl/e8shbipl54ePh9r5/YU4qqrCwnBykffIDsX37VLLMLDETgZ5/COSLCoGdS5IsSQw5EL6k+ffrA1pa/ukREVHN169btvt39X3jhBfkwpujoaPmoCOSJG0mGuLFnjkF4YzLX46/JU9jrsj1v7JkW25P5tSddyjBFe/p2bABeXhaL9SeSUVKmxpvrL+KbYa3Ru9m9yxVlNWzYEAkJCbKXs5Cfny+/+zo6OsJSVZwnFxeXKq3PROdUJflHjuBS/wG3BKTc+/ZF6Lq1BgtIibusBw8e1Mz+07x5c/Tr148BKSIiIiIiIjILdjZKfP1kSwxoGSifl6mAF5Ycwy/Hk+67rVKp1ASkxM2mdevWYfbs2XJYfk3B7iZ0T+qSEpnMPGPOXDGGTi5TurrCf9o0ePR9wmBnT9xhXbFihYwaFxUVySkziYiIiIiIiMyNrY0SX0S1lP+uPJKAMpUaLy89huTMAmQWlCDhRgHqeDkhKjIYoT6V9yBSq9UyRY0Y/i4m9mrfvj0eeeQRq++UYd1HRzopvnIFia+/jsLjJzTLnCIiEDh9OuzrBBns7Iqo8MqVK2XXxQYNGqBNmzYG2xcRERERERGRrmyUCnw6uDlKigqw7q9rUKmBTzachVJR/rpCocDcnXGYPrg5hkYGV9prqlevXnJ2PtFj6sCBA4iLi8OgQYPkcHhrxeF7VGmENnP1GlwaMPDfgJSNDWq/PBn1Fi00WEBK7HfPnj1YvHixDEiJfBnDhw+Hk5MT3yUiIiIiIiIya0qlAv+ve13NUD5BBKfEQ/SeEv++seoE4jPy7lpGWFgYJk6ciGbNmiE9PV1O+CX+tVbsKUW3KMvMRPK77yFn40bNMru6dRH02adwatHCoGfryJEj+OOPP2QQSkSDRS8pIiIiIiIiIkuhVCgQ4OEI0UGqsilJRI+pZYev4o1eje9aRsV3YtFrSowk8vHxgbViUIo08g4cRNLUqShNSdEs8xg8CH5v/gc2rlXLnK8LMV11UlKSzB/l6Xn/KTSJiIjIvMTExMiHmKxESElJQV5enmY2nqqqyrralGeNzPX4jVUvQ+xH1zJ12V7bbfXdnqpTB2tirsdek9uTLmWYQ3u6kHwDCoUYDVT5CKELSderVFatWrXkQ3yeCseOHZMBq/DwcBncMlfi2HJycqq0LoNSBHVxMdJnzcK1b7/TtBqlhwcC3nsP7r16GvQMiSRuIqm5aFQigZuYXY+IiIgsU3R0tHyIz3YPDw+ZA8Pd3V0vU25ru441M9fjN1a9DLEfXcvUZXtTTGGvax2sibkee01uT7qUYS7tqUGgN7ZdyKw0KqWAQr6u7fHl5+cjNjYWJSUlSE1NRd++feHiYvjOI9qqOE9VrRtzStVwRRcvIf6pYbg2/1tNg3Fu1w5h69YaNCBVWlqK3377DTt27JD/ioZFREREREREZOnELHuiR1RlytRqPFlJovP7cXZ2xrhx42TA59y5c5g9e7b819IxKFVDiQZyY+kyXBo0CIWnT5cvtLOD7+uvoe4P38POgNn9s7KysGDBAplDys3NDU8//TTs7OwMtj8iIiIiIiIiYwn1cZGz7ImZ98SsfBUz8FU4npBZrXJr166NZ599Fl26dJE9p5YuXYpff/3Vojt5cPheDVR6/TqS334Hudu2aZbZh4Yi8PPP4PTggwbdt5jSctWqVSgoKJBJ2zp06GDV01sSERERERFRzTM0MhhtQrxlUvOEGwXIKyrFtrNp8rW31vyFVsFeqFvLWetybWxs0L17dzRs2BBr1qxBYmKiWeeXuh8GpWqY3D17kfTmVJSlZ2iWeT71JPzeeANKJyeD7ru4uBirV69GYWGhbESdO3fWJGwjIiIiIiIisiYhPi63zLI3ZVksVh9LRG5RKV5cegwrJ3aAnU31BrAFBwdj4sSJckIRkZ9ZEN+vRW8qEbiyFAxK1RCqoiKkf/klri9cpFlm4+WFgI8+glv3h41SB3t7ezmtpYjihoWFGWWfRERERERERObg/QFNcfTKDcRfy8fxq5n4csv5W4JW1fmOLR6CmGRk4cKF8PLywsCBA2VwyhIwp1QNUHj+POKHRt0SkHLp3Blhv6wzeEBKRGqXLVumGeNav359BqSIiIiIiIioxnF1sMXMYa1g+0+SqTk747Dn739HMelC9I4KCQmRs9/NmzcPBw8evGuydXPCnlKViImJkY+ysjJNYEV0iRPEG1xVVV1XmzK1IX4Bi9esQcGcuUBF4jM7OzhNmADbgQOQXloqdg5DETMB7NmzR57H/fv3yzGvxjx+XRizTvrelz7Kq24Z2m5nSe3JUpjj8bM9Gac9abMN25N25zMnJ0fr94KIiIioMs3reOL/9QrHx7+fhYgZvbI8Fhsnd0EtVwedTpiLiwuioqIQGxuLjRs3ysf58+fRv39/uLu7m+2boVBbQujMRET3Nw8PDzlbnHgTxcWpmH6xKqq6rjZlaqM0PR1J/3kLebt3a5Y5NGyIwM8/h2N4I73v75Z9l5Ziw4YNOHr0qBzb2rdvXzRv3tyox68LY9ZJ3/vSR3nVLUPb7SypPVkKczx+tifjtCdttmF70v583n49QFW7sScuhMUNKjHTLhEREf1LpVZjytoLOHil/MZXxxB3fN6vvt4Slotrlx07dsgONuLaRQSrlErjDpQTN/XCw8Pve/3EnlJWKGf7diS/9TbKrl/XLPMaOQK+r74KpYNu0df7yczMxPLly+XFvLe3t/zl9/PzM+g+iYiIyDxER0fLR0UgT8ywa4gbe+YYhDcmcz1+Y9XLEPvRtUxdtueNPdNiezK/9qRLGZbUnmaN8Eafr3cjI7cY++KzseFiEZ7tHAp9EPsXI5XEiCXxvTwoKAjGUnH8oudWVTCnlBVRFRQg5f33kTDpeU1AysbHB8Hz58H/P/8xeEBKOHHihPwlbNy4McaNG8eAFBEREREREdFtfN0c8UVUS83z/204g78Ss/R2nkTPqE6dOuGBBx7QjGj66aefcPHiRbN6LxiUshKFZ87g0pChuPHzEs0y14cflsnMXbt0Mei+xQjQilGgnTt3ljPsiR5Sjo6OBt0vERERERERkaXq2qg2xj9UPjN9SZkaLy05hryiUoPsKy4uDhcuXMDixYtlup2KychMjUEpC6dWqXDtu+9xKepJFMfFyWUKR0f4vzsNdf4vBrbe3gbdf0FBAX7++WccO3ZME41t1qyZ3sbCEhEREREREVmr13qEo1mQh/z5YkYe3v3llEH2I/I7jRw5Ug6rP3TokJyhLykpCabGoJQFK0lNxZVnn0XaZ59pZtdzaPIAQlevgtdTTxk8MCR+gefOnSujrSdPnrSI6SaJiIiIiIiIzIW9rRIzh7WCi72NfL7iSALWxSYaZF+hoaGYNGmSnIgsIyMDq1atgkqlgikx0bmFyt68GSnv/BdlWf+MOVUoUOvZsaj90ktQ2NsbfP9iZr3ff/9dzq7Ttm1b9OjRg72jiIiIiIiIiLQU6uOCDwY0xZTlx+Xzt9f8hVbBXqhby1nv51Kk2Rk4cCAaNWoEV1dXo8/KdzsGpSyMKi8PKZ98gqyVqzTLbP38EDj9f3Bp397g+xfjTkUwKjY2FnZ2dujfv78crkdERERERERE1TOodR3s/jsDa44lIqeoFC8tPYYVEzvAzsYwQaMHH3wQ5oDD9yxIwcmTuDho0C0BKbcePRC2bq1RAlIVQSmRrb9WrVp47rnnGJAiIiIiIiIi0oP3+z+Iev/0joq9mokvt5y3+vPKnlIWQF1Whmvzv0X6N9+IeRzlMoWzM/zfegsegwYaZdhccXEx7O3t4ezsjGeeeUYmR3NwcDD4fomIiIiIiIhqAjdHO8x8qhUGz96HUpUac3bGoVN9H3Ru6ANrxaCUmStJTETiG2+g4PARzTLH5s0R9NmnsK9Xz+D7F0nPduzYgb/++gvjxo2Dk5MTateubfD9EhERkeWJiYmRD5FzUkhJSUFeXp78OTk5ucrlVGVdbcqzRuZ6/MaqlyH2o2uZumyv7bb6bk/VqYM1Mddjr8ntSZcyLL09+doCEzsG4ps9iRBziU1ecgSLn34AXs52sBTi+HNycqq0LoNSZixr/XqkvPseVBVvplKJWhPGo/bzz0NhZ/hfyPz8fJmNXwzXc3FxQWZmpgxKEREREVUmOjpaPrKzs+Hh4QF/f3/Zu1pcnAYEBFTppFVlXW3Ks0bmevzGqpch9qNrmbpsr+22+m5P1amDNTHXY6/J7UmXMqylPU3p44/jqUUyx9S1/FJ8tisF349uYxGTi1Ucv4ghVAVzSpmhstxcJL3xBpJefU0TkLILDES9RQvhO3myUQJSiYmJmDt3rgxI1a1bFxMmTDDLP9ZERERERERE1kSpVOCLqBbwcbWXz7efS8cPe+NhjRiUMjP5R4/iUv8ByFr3i2aZ+xNPIHTdWjhHRhqlDkeOHMEPP/wg73K2b98eI0eOhJubm1H2TURERERERFTT+bo54vOhLTTP/7fhLP5KzIK1YVDKTKhLS5E+cxYuPzNC5pESlK6uCPzsUwR9/hlsjBgUEnkgbGxsMGTIEPTs2VP+TERERERERETG0y3cF+O6hMqfi8tUeGnJMeQVlU9+Zi2YU8pEiuPjkblqNfLiLiDZ1xcFscdRdPas5nWn1q0R+Ol02NepY5T6iF5RojeUGKPapk0bNG7cWOaAICIiIiIiIiLTeL1nYxy4eB0nE7NwMSMP7/5yCp/d1IPK0jEoZQIiGJX8zjuASFKmUiFTpNSvYGMDn+jn4TN+PBS2xnl7zp49i7Vr16Jjx4546KGHZGCKASkiIiIiIiIi07K3VWLmsFZ4YuZu5BWXYcWRBHRu6IP+LYOs4q3h8D0T9JCSASmVSoyTg5zj8SZBX3xePrueEQJSKpUKW7duxbJly1BSUgIHBweD75OIiIiIiIiIqi7UxwUfDGiqef72mr9w5Vq+VZxCBqVM0EtK9pCqjI0NCk+dNko98vLy8OOPP2Lv3r1wdXXFqFGj0K5dO6Psm4iIiIiIiIiqblDrOhjYqrx3VE5RKV5aegwlZSpYOgaljEwmMb+td5SGWq1Jcm5I6enpmDt3Li5duoR69ephwoQJqFu3rsH3S0RERERERETV837/B1GvlrP8OfZqJr7act7iTyVzSlUiJiZGPsQsdEJKSorsWSQkJydX+eRWtm6Rp8c9txGva7OP6hBD9WxtbdG8eXO0bdsWOTk58mEqhj5ec6+Tvvelj/KqW4a22+nanvRRB2tjjsfP9mSc9qTNNmxP2p1PU35GEhEREVVwc7TDzKdaYfDsfShVqTF7Zxw6NfCRD0vFoFQloqOj5UPMSOfh4QF/f3+Z+FtcnAYEBFTpxN5t3eKRIxG3dNldt6szahTsq7gPbRQXF+PGjRvw8/OTzydNmgQ7OzuYmjbn1BrrpO996aO86pah7Xb6aE+61sHamOPxsz0Zpz1psw3bk/bn08XFRav3goiIiMhQWgR74vWe4fhkw1k5COuVZbHYMLkLarlaZo5oBqWMzD4kBAEffojkt98uzy0lfov++Vcst69XT+/7vHbtGpYvX47c3Fw5VE8E2MwhIEVERETWxZC9zauzjjUz1+M3Vr0MsR9dy9Rle/Y2Ny22J/NrT7qUURPa0xMNnfDHKTccupKDtJwivPjjIXzerz4Ud8tfbWTi+Kva05xBKRPwHDQQzhGtkblyFbLjLsC9fgN4DhlskIDUmTNnsHbtWtlTqlmzZnB0dNT7PoiIiIgM3dtc23Wsmbkev7HqZYj96FqmLtuzt7lpsT2ZX3vSpYya1J6+GeGNPl/vRkZuMfbFZ2PjxSKM7RwKU6s4/qr2NGdQykREAMr31SkoS06GrwF+YVUqFf744w/s27cPSqUSvXv3Rps2bcwmckpERERERERE1ePr5ojPh7bA6B/+lM//t+Es2oZ6o2nQvfNYmxvOvmeF1Go1li1bJgNSbm5uGD16tExozoAUERERERERkXXoFu6LcV3Ke0cVl6nw0pJjyCsqhSVhUMoKieCTmFkvNDRU5pAKDg42dZWIiIiIiIiISM9e79kYzf7pHXUxIw/v/XrKos4xg1JW1Dvq5MmTmsSiDz74IEaMGMEZg4iIiIiIiIislL2tEjOHtYKzvY18vvxwAn45ngRLwaCUFRBJzFevXi0f27Zt0yzncD0iIiIiIiIi6xbq44IP+jfVPH9r9UlcvZ4PS8CglIXLyMjAt99+i7/++gt+fn6IiIgwdZWIiIiIiIiIyIgGtQ7CgJaB8uecolK8uOQYSspUZv8eMChlwU6fPo358+cjPT1d5pB69tln4e3tbepqEREREREREZERKRQKfDCgKerVcpbPY69m4qst583+PWBQykKdPXsWK1askDmkHn/8cQwYMAB2dnamrhYRERERERERmYCbox1mPtUKtkqFfD57Zxz2Xsgw6/eCQSkL1bBhQ5nMfMyYMYiMjGT+KCIiIiIiIqIarkWwJ17vGS5/VquBV5bF4lpuEcwVg1IW5PLly7KHlGBjY4MhQ4YgKCjI1NUiIiIiIiIiIjMxrksYujT0kT+n5RTh9ZUnoBYRKjPEoJQFEL88+/fvx8KFC7FmzRrk51tGFn0iIiIiIiIiMi6lUoEvolqglou9fL7tbBoW7Is3y7eBQSkzV1RUhJUrV2Lz5s1wcHDA4MGD4excnriMiIiIiIiIiOh2vm6O+Dyqheb5J7+fxamkLJgbW1NXgO5OzKq3bNkyXLt2Df7+/oiKioKXlxdPGREREZmlmJgY+RATsQgpKSnIy8uTPycnJ1e5nKqsq0151shcj99Y9TLEfnQtU5fttd1W3+2pOnWwJuZ67DW5PelSBtvTvxq7A8Na+WLJsTQUl6kwafGfWDCsMZzsbGBI4j3Iycmp0roMSpkplUqFn3/+GZmZmWjZsiX69OnD2fWIiIjIrEVHR8tHdnY2PDw85E01d3d3eXEaEBBQpTKqsq425Vkjcz1+Y9XLEPvRtUxdttd2W323p+rUwZqY67HX5PakSxlsT3d6b7Af/krbh5OJWbhyowhzDl3Dp0P+7UGlbxXvgYuLS5XW5/A9M6VUKtG3b1888cQT6NevHwNSRERERERERKQVe1slZg5rBWf78t5Ryw8n4JfjSTAXDEqZEXFXcd26dSguLpbPw8LCEBERAYVCYeqqEREREREREZEFCvVxwQf9m2qev7X6JK5eN48J1Dh8z0xcunQJq1atknkXfHx80KlTJ1NXiYiIiIiIiIiswKDWQdj9dzrWxiYhp6gU4xcfxkMNayMpqxB1vJwQFRksg1fGxqCUianVauzduxd//PGH/Llr167o0KGDqatFRERERERERFZCoVDggwFNcfRKJq5cz8eZ5BycTc6BGJglXpu7Mw7TBzfH0Mhgo9aLw/dMqLCwEFu2bMHWrVvh4OCA4cOHo1u3bjKfFBERERERERGRvrg52mFq78aa52oxyZoaKFOp5b9vrDqB+IzyWXONhdEPEzpx4gTi4+NlZvoJEyagYcOGpqwOEREREREREVmxk4lZsndUZUSPqWWHrxq1Phy+Z0Jt2rSRyc1F7yhbW74VRERERERERGQ4CTcKoPinl9TtREoh8boxsaeUCYko5IMPPsiAFBEREREREREZnEhqLmIRlRHLxevGxKAUEREREREREVENEBUZLHtEVUYsf5KJzomIiIiIiIiISN9CfVzkLHtKBWCjVNzyr1ge4uMCY2IiIyIiIiIiIiKiGmJoZDDahHjLpOYih5QYsid6SBk7ICUwKFWJmJgY+SgrK5PPU1JSkJdXPi1icnJylU9uVdfVpkxrZI7Hb8w66Xtf+iivumVoux3bk/6xPdXc9qTNNvx80u585uTkaP1eEBEREZmzEB8XvNGrsamrwaBUZaKjo+VDzIzn4eEBf39/uLu7y4vTgICAKp3Yqq6rTZnWyByP35h10ve+9FFedcvQdju2J/1je6q57Umbbfj5pP35dHEx/l1DIiIiopqAic6JiIiIiIiIiMjoGJQiIiIiIiIiIiKjY1CKiIiIiIiIiIiMjonOiYiIiMjiJosxx4kdjMlcj99Y9TLEfnQtU5ftOVmMabE9mV970qUMtifTE+9BVSeKYVCKiIiIiCxqshhznNjBmMz1+I1VL0PsR9cyddmek8WYFtuT+bUnXcpgezK9ivegqhPFcPgeEREREREREREZHYNSRERERERERERkdAxKERERERERERGR0TEoRURERERERERERsegFBERERERERERGR1n37sHtVot/xUzyAhiSsOqZpCv6rralGmNzPH4jVknfe9LH+VVtwxtt2N70j+2p5rbnrTZhp9P2p/PiuuAiusCMv01lDn+vTMmcz1+Y9XLEPvRtUxdtuc1lGmxPZlfe9KlDLYn06t4D6p6/cSg1H1OphAcHKzP94iIiIgs9LrAw8PD1NWwCLyGIiIioqpcPynUvO13VyqVCklJSXBzc4NCoUCbNm3w559/oiqqsq6IHIqA19WrV+Hu7o6aSJtzao110ve+9FFedcvQdju2J/1je6q57Umbbfj5pP35FJdK4oIqMDAQSiUzH5j6GorXT+b5996Y9TLEfnQtU5fteQ1lWmxP5teedCmD7cn0Kt6Dql4/safUPYgTV6dOHc1zGxubKgePtFlXrFdTg1LanCdrrJO+96WP8qpbhrbbsT3pH9tTzW1P2mzDz6fqnU/2kDK/ayheP5nX9ZMxP4cMsR9dy9Rle15DmZY5Xj/V9PakSxlsT6Z383tQlesn3u7TQnR0tEHWrcnM8TwZs0763pc+yqtuGdpux/akf2xPNbc9abONOf6emCOeJ9OdT557yz1HxqqXIfaja5m6bM9rKNNiezK/9qRLGWxPpqfte8DheyYkup+LyGFWVpZZRueJLAnbExHbE9UM/HtPxDZFZK74GaU99pQyIQcHB0ybNk3+S0RsT0Tmgp9PZM74+0nENkVkrvgZpT32lCIiIiIiIiIiIqNjTykiIiIiIiIiIjI6BqWIiIiIiIiIiMjoGJQiIiIiIiIiIiKjY1CKiIiIiIiIiIiMjkEpIiIiIiIiIiIyOgalzNTAgQPh5eWFIUOGmLoqRBbv6tWr6NatG5o0aYLmzZtjxYoVpq4SkcXKzMxEZGQkWrZsiaZNm2L+/PmmrhLRLXgNRaQfvH4i0h9eP92dQq1Wq+/xOpnIjh07kJOTg4ULF2LlypV8H4h0kJycjNTUVPklOiUlBRERETh//jxcXFx4Xom0VFZWhqKiIjg7OyMvL08Gpg4fPoxatWrxXJJZ4DUUkX7w+olIf3j9dHfsKWWmRK8ONzc3U1eDyCoEBATIgJTg7+8PHx8fXL9+3dTVIrJINjY2MiAliOCUuLfF+1tkTngNRaQfvH4i0h9eP90dg1IGsGvXLvTt2xeBgYFQKBRYu3btHevExMQgJCQEjo6OaNeuHQ4dOmSIqhBZBX22qSNHjsg7FcHBwUaoOZF1tifRBb1FixaoU6cOXn/9dRnoJTKX308i0n974vUT1XS8fjIcBqUMQAxnEBfr4o98ZZYtW4YpU6Zg2rRpOHr0qFy3Z8+eSEtLM0R1iCyevtqU6B01cuRIzJs3z0g1J7LO9uTp6Ynjx4/j0qVL+Pnnn+XwWCJz+f0kIv22J14/EfH6yaBETikyHHGK16xZc8uytm3bqqOjozXPy8rK1IGBgepPPvnklvW2b9+uHjx4MN8eIj20qcLCQnWXLl3UixYt4vkk0sNnVIVJkyapV6xYwXNKesdrKCLTtydePxHp9/OpAq+f/sWeUkZWXFwsu78++uijmmVKpVI+379/v7GrQ1Qj2pT47Bg9ejS6d++OESNGmLC2RJbfnkSvKDERh5CVlSW7s4eHh5uszlRz8BqKyLjtiddPRPprT7x+ujsGpYwsIyND5rPx8/O7Zbl4LmYFqyB+gYcOHYrff/9d5uxgwIqo+m1q7969sou6yKUgEp6Lx8mTJ3lKiarRni5fvowuXbrIYR7i3xdffBHNmjXjuSSD4zUUkXHbE6+fiPTXnnj9dHe293iNTGjr1q08/0R60rlzZ6hUKp5PIj1o27YtYmNjeS7JbPEaikg/eP1EpD+8fro79pQyMjFDkZgO8vaksOK5mKqeiNimiEyFn1Fkzvj7ScT2RGSO+PmkGwaljMze3h4RERH4448/NMtEDw7xvEOHDsauDpHFY5siYnuimoF/74nYnojMET+fdMPhewaQm5uLCxcuaJ6LKbPFUAdvb2/UrVtXTr06atQoREZGym58M2bMkFO2jhkzxhDVIbJ4bFNEbE9UM/DvPRHbE5E54ueTAd00Ex/pyfbt2+U0kbc/Ro0apVln1qxZ6rp166rt7e3l9JEHDhzg+SdimyIyOH5GkTnj7ycR2xOROeLnk+EoxP8MGfQiIiIiIiIiIiK6HXNKERERERERERGR0TEoRURERERERERERsegFBERERERERERGR2DUkREREREREREZHQMShERERERERERkdExKEVEREREREREREbHoBQRERERERERERkdg1JERERERERERGR0DEoREREREREREZHRMShFRFQF3bp1w8svv8xzRURERFRFvH4iovtRqNVq9X3XIiKqIXbs2IGHH34YN27cgKenp2b59evXYWdnBzc3N5PWj4iIiMjc8PqJiKrLttpbEhFZmZKSkru+5u3tbdS6EBEREVkCXj8RkS44fI+ILNK8efMQGBgIlUp1y/L+/ftj7Nix8ud169ahdevWcHR0RFhYGN577z2UlpZq1lUoFJg9ezb69esHFxcXjBs3TvaSEry8vOTro0ePrrT7eVFREd544w0EBwfDwcEBDRo0wHfffad5/a+//kLv3r3h6uoKPz8/jBgxAhkZGZrXV65ciWbNmsHJyQm1atXCo48+iry8PAOeMSIiIqrpeP1EROaGQSkiskhDhw7FtWvXsH379luG2G3cuBFPP/00du/ejZEjR2Ly5Mk4ffo05s6diwULFuCjjz66pZx3330XAwcOxMmTJ2XQatWqVXL5uXPnkJycjK+//rrS/YuylyxZgpkzZ+LMmTOyfBGAEjIzM9G9e3e0atUKhw8flnVKTU1FVFSUfF2UO2zYMBk8E9uKLu+DBg0CR1MTERGRIfH6iYjMjsgpRURkifr3768eO3as5vncuXPVgYGB6rKyMvUjjzyi/vjjj29Zf/HixeqAgADNc/En8OWXX75lne3bt8vlN27cuGV5165d1ZMnT5Y/nzt3Tq6zZcuWSuv1wQcfqHv06HHLsqtXr8ptxLZHjhyRP8fHx+tw9ERERETa4/UTEZkT9pQiIoslekSJnk1iKJ3w008/4amnnoJSqcTx48fx/vvvy95LFQ8xPE/0UsrPz9eUERkZqfV+Y2NjYWNjg65du1b6uti36MF1874bN24sX4uLi0OLFi3wyCOPyOF74o7l/PnzZWJ1IiIiIkPj9RMRmRMmOicii9W3b1855G39+vVo06aNHLL31Vdfyddyc3PlcDwxLO52IsdUBZFLSlsiD9S9iH2Luk2fPv2O1wICAmRAa8uWLdi3bx82b96MWbNm4a233sLBgwcRGhqqdX2IiIiIqorXT0RkThiUIiKLJYJLIugkekhduHAB4eHhMrG5IP4VeaFEAnJt2Nvby3/Lysruuo7o4SQSrO/cuVMmKL+d2LfowRUSEgJb28r/zIok6p06dZKP//73v6hXrx7WrFmDKVOmaFVfIiIiIm3w+omIzAmH7xGRRRNd0EVPqe+//17+XEEEehYtWiR7S506dUomFF+6dCnefvvte5YngkMiYPTbb78hPT1d9nq6nQg2jRo1SiYqX7t2LS5duiSTlS9fvly+Hh0dLZOui2Tmf/75pxyyt2nTJowZM0YGu0SPqI8//lgmQb9y5QpWr14t9/XAAw8Y4AwRERER3YrXT0RkLhiUIiKLJma58/b2lr2ihg8frlnes2dPGVgSw+PE0L727dvLoX0i6HQvQUFBMpA1depU+Pn54YUXXqh0vdmzZ2PIkCF4/vnnZb4oka8qLy9PvhYYGIi9e/fKAFSPHj1kz6qXX34Znp6eMt+Vu7s7du3ahT59+qBRo0YyUPbFF1+gd+/eej47RERERHfi9RMRmQuFyHZu6koQEREREREREVHNwp5SRERERERERERkdAxKERERERERERGR0TEoRQupMv0AAABySURBVERERERERERERsegFBERERERERERGR2DUkREREREREREZHQMShERERERERERkdExKEVEREREREREREbHoBQRERERERERERkdg1JERERERERERGR0DEoREREREREREZHRMShFREREREREREQwtv8P7p4gcFALF9gAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(12, 5))\n", "utils.loglog_plot(verts, {\"solve time\": times}, xlabel=\"vertices\", ylabel=\"Newton solve time (s)\",\n", " colors={\"solve time\": \"#d62728\"}, ref_slopes={\"linear in DOFs\": 1},\n", " title=\"Compute time grows with resolution\", markers=True, ax=axes[0])\n", "utils.loglog_plot(verts, {\"tip error\": errors}, xlabel=\"vertices\", ylabel=\"tip deflection error\",\n", " colors={\"tip error\": \"#1f77b4\"}, ref_slopes={\"O(1/n)\": -1},\n", " title=\"Accuracy converges to the fine mesh\", markers=True, ax=axes[1])\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "b750ffdd", "metadata": {}, "source": [ "## Watching three resolutions sag (clearly!) under gravity\n", "\n", "Ramp gravity $0 \\rightarrow 1$ and solve each frame for three resolutions, then **hold\n", "at full gravity** so every beam settles to its final equilibrium and visibly\n", "comes to rest. They converge to nearly the same big droop — but the finest\n", "one took far longer per frame." ] }, { "cell_type": "code", "execution_count": 5, "id": "523e7dcd", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:39.382345Z", "iopub.status.busy": "2026-06-09T05:30:39.382292Z", "iopub.status.idle": "2026-06-09T05:30:43.189131Z", "shell.execute_reply": "2026-06-09T05:30:43.188837Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ramp = np.concatenate([np.linspace(0.0, 1.0, 22), np.ones(12)]) # ramp up, then hold at rest\n", "panels = []\n", "for nx, ny, label in [(7, 3, \"coarse\"), (16, 6, \"medium\"), (32, 11, \"fine\")]:\n", " beam = GravityBeam(nx, ny)\n", " f_g_full = beam.p.f_g.copy() # scale gravity for the ramp\n", " states = []\n", " for g in ramp:\n", " beam.gravity.f_g = g * f_g_full\n", " states.append(beam.solve())\n", " panels.append({\"states\": states, \"T\": beam.T,\n", " \"title\": f\"{label} ({beam.p.n} verts)\"})\n", "\n", "fig, anim = utils.animate_meshes_grid(panels, lims=((-1.2, 1.2), (-1.8, 0.3)), fps=20,\n", " suptitle=\"Same beam, three resolutions, sagging under gravity\")\n", "utils.show_video(fig, anim, \"media/10_resolution.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "d1989451", "metadata": {}, "source": [ "## Why \"just refine it\" is a trap" ] }, { "cell_type": "code", "execution_count": 6, "id": "e94376bc", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:30:43.190306Z", "iopub.status.busy": "2026-06-09T05:30:43.190233Z", "iopub.status.idle": "2026-06-09T05:30:43.192079Z", "shell.execute_reply": "2026-06-09T05:30:43.191891Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "good-enough ( 114 verts): 22.5 ms/solve (7% tip error)\n", "fine ( 2700 verts): 638.8 ms/solve\n", "\n", "The fine mesh is ~28x slower per solve for a tip deflection\n", "within 7% of it. Interactive editing (many solves/second) is impossible\n", "long before that accuracy is worth it -- pick the coarsest mesh that captures the behavior.\n" ] } ], "source": [ "i_good = 4 # a mid-resolution mesh\n", "rel = errors[i_good] / abs(ref_tip)\n", "print(f\"good-enough ({verts[i_good]:5d} verts): {times[i_good]*1000:8.1f} ms/solve ({rel*100:.0f}% tip error)\")\n", "print(f\"fine ({ref_beam.p.n:5d} verts): {ref_time*1000:8.1f} ms/solve\")\n", "print(f\"\\nThe fine mesh is ~{ref_time/times[i_good]:.0f}x slower per solve for a tip deflection\")\n", "print(f\"within {rel*100:.0f}% of it. Interactive editing (many solves/second) is impossible\")\n", "print(\"long before that accuracy is worth it -- pick the coarsest mesh that captures the behavior.\")" ] }, { "cell_type": "markdown", "id": "ce2365da", "metadata": {}, "source": [ "### Takeaways\n", "* **Cost** rises steeply with vertex count; each Newton step solves a bigger\n", " sparse system.\n", "* **Accuracy** improves with resolution but with diminishing returns.\n", "* A super-fine mesh is accurate yet **too slow to iterate on**.\n", "\n", "---\n", "That completes the offline SimKit tutorial series (1–10): building and\n", "understanding the deformation gradient, elastic energies, the elastostatic\n", "minimization, the solvers and line search that drive it, time integration,\n", "contact, and the resolution/cost trade-off." ] } ], "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }