{ "cells": [ { "cell_type": "markdown", "id": "18b8e32b", "metadata": {}, "source": [ "# Run a multi-dimensional optimization\n", "\n", "This page contains a very simple tutorial to optimize a multi-dimensional cost function.\n", "Since problems with larger domains, such as multi-dimensional problems, will take many iterations of optimizers to search and find the minima, we will demonsrate how to execute these searches in parallel to reduce the amount of time it takes.\n", "\n", "The key concepts you should gain from this page:\n", "\n", " * How to define a multi-dimensional cost function.\n", " * How to use an optimization search to find the minimum of the multi-dimensional cost function.\n", " * How to call the optimization in parallel." ] }, { "cell_type": "markdown", "id": "41296429", "metadata": {}, "source": [ "## Define a multi-dimensional cost function\n", "\n", "We can increase the number of parameters in our cost function like using the 2-dimensional volcano function below." ] }, { "cell_type": "code", "execution_count": 2, "id": "ccf251e8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import mystic\n", "import numpy\n", "from mystic import models\n", "from scipy import stats\n", "\n", "def cost_func(p):\n", " \"\"\" Executed for each set of drawn parameters in the optimization search.\n", " \"\"\"\n", " \n", " # get the x and y values from Mystic\n", " # p is a list so we map each index of the list to our variables (x, y)\n", " x, y = p\n", "\n", " # get value at Gaussian function x and y\n", " var = stats.multivariate_normal(mean=[0, 0], cov=[[0.5, 0], [0, 0.5]])\n", " gauss = -50.0 * var.pdf([x, y])\n", "\n", " # get value at volcano function x and y\n", " r = numpy.sqrt(x**2 + y**2)\n", " mu, sigma = 5.0, 1.0\n", " stat = 25.0 * (numpy.exp(-r / 35.0) + 1.0 /\n", " (sigma * numpy.sqrt(2.0 * numpy.pi)) *\n", " numpy.exp(-0.5 * ((r - mu) / sigma) ** 2)) + gauss\n", "\n", " # whether to flip sign of function\n", " # a positive lets you search for minimum\n", " # a negative lets you search for maximum\n", " stat *= 1.0\n", "\n", " return stat\n", "\n", "mystic.model_plotter(cost_func, depth=True, fill=True, bounds='-9.5:9.5,-9.5:9.5')" ] }, { "cell_type": "markdown", "id": "a66f42ea", "metadata": {}, "source": [ "## Run an opitimizer\n", "\n", "We can run a single optimizer with the multi-dimensional cost function like we did before.\n", "Below we set the **initial points**, **strict ranges**, and **termination condition** for a **solver** to find the minimum.\n", "This should look familar from the prior page in the tutorial." ] }, { "cell_type": "code", "execution_count": 3, "id": "cb8da301", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The best solution is [-2.24303552e-02 9.64325450e-07]\n" ] } ], "source": [ "from mystic import tools\n", "from mystic.solvers import PowellDirectionalSolver\n", "from mystic.ensemble import BuckshotSolver\n", "from mystic.termination import VTR\n", "\n", "# set random seed so we can reproduce results\n", "tools.random_seed(0)\n", "\n", "# create a solver\n", "solver = PowellDirectionalSolver(dim=2)\n", "\n", "# set the initial position to (0, 0)\n", "solver.SetInitialPoints([0, 0])\n", "\n", "# set the range to search for both parameters between -9.5 and 9.5\n", "solver.SetStrictRanges((-9.5, -9.5), (9.5, 9.5))\n", "\n", "# find the minimum\n", "# pass the termination condition\n", "solver.Solve(cost_func, termination=VTR())\n", "\n", "# print the best parameters\n", "print(f\"The best solution is {solver.bestSolution}\")" ] }, { "cell_type": "markdown", "id": "3c02c758", "metadata": {}, "source": [ "## Run an ensemble of optimizers using multi-processing\n", "\n", "In the prior examples, we only ran a single optimizer and found a nearby local minimum.\n", "However, we can use an ensemble of optimizers to map the minima of the cost function.\n", "Below, we show how to execute an optimization search using the ``BuckshotSolver``.\n", "This is an ensemble solver available in the [solver module](https://mystic.readthedocs.io/en/latest/mystic.html#module-mystic.solvers).\n", "A short list of some ensemble sovlers are:\n", "\n", " * ``BuckshotSolver``: Ensemble from a uniform distribution of solvers in the parameter space.\n", " * ``LatticeSolver``: Ensemble from a grid of solvers in the parameter space.\n", " \n", "Recall, we did use ``SetInitialPoint`` in prior examples.\n", "So there are other ways to set initial positions." ] }, { "cell_type": "code", "execution_count": 4, "id": "fc121e18", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The best solution is [-3.16087505e-05 -2.24303335e-02]\n" ] } ], "source": [ "from mystic import tools\n", "from mystic.solvers import PowellDirectionalSolver\n", "from mystic.ensemble import BuckshotSolver\n", "from mystic.termination import VTR\n", "\n", "# set random seed so we can reproduce results\n", "tools.random_seed(0)\n", "\n", "# create a solver\n", "solver = BuckshotSolver(dim=2, npts=8)\n", "\n", "# since we have an search solver\n", "# we specify what optimization algorithm to use within the search\n", "solver.SetNestedSolver(PowellDirectionalSolver)\n", "\n", "# set the range to search for both parameters between -9.5 and 9.5\n", "solver.SetStrictRanges((-9.5, -9.5), (9.5, 9.5))\n", "\n", "# find the minimum\n", "# pass the termination condition\n", "solver.Solve(cost_func, termination=VTR())\n", "\n", "# print the best parameters\n", "print(f\"The best solution is {solver.bestSolution}\")" ] }, { "cell_type": "markdown", "id": "f6194adc", "metadata": {}, "source": [ "That took awhile, we can run things in parallel.\n", "Let's cut the execution time by using multi-processing.\n", "We can specify a **pool** like below.\n", "Running the command below, you should see it took a shorter time to complete." ] }, { "cell_type": "code", "execution_count": 5, "id": "73e3ff21", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The best solution is [-3.16087505e-05 -2.24303335e-02]\n" ] } ], "source": [ "from pathos.pools import ProcessPool as Pool\n", "\n", "# set random seed so we can reproduce results\n", "tools.random_seed(0)\n", "\n", "# create a solver\n", "solver = BuckshotSolver(dim=2, npts=8)\n", "\n", "# since we have an search solver\n", "# we specify what optimization algorithm to use within the search\n", "solver.SetNestedSolver(PowellDirectionalSolver)\n", "\n", "# set multi-processing\n", "solver.SetMapper(Pool().map)\n", "\n", "# set the range to search for both parameters between -9.5 and 9.5\n", "solver.SetStrictRanges((-9.5, -9.5), (9.5, 9.5))\n", "\n", "# find the minimum\n", "# pass the termination condition\n", "solver.Solve(cost_func, termination=VTR())\n", "\n", "# print the best parameters\n", "print(f\"The best solution is {solver.bestSolution}\")" ] }, { "cell_type": "markdown", "id": "b8bf5f1e", "metadata": {}, "source": [ "## Sample and store cached results\n", "\n", "We can store results to an archive of sampled points.\n", "Below is an example of creating an **archive**, using a **sampler**, and then plotting the results.\n", "\n", "A list of available samplers are in the [samplers modules](https://mystic.readthedocs.io/en/latest/mystic.html#module-mystic.samplers).\n", "These samplers are Mystic's interface to its optimizer-driven sampling interface.\n", "An example using the ``LatticeSampler`` is shown below.\n", "Its execution is similar to the ``LatticeSolver``, however, we can connect the archive to it for storing the sampled points." ] }, { "cell_type": "code", "execution_count": 6, "id": "0a4a87db", "metadata": {}, "outputs": [ { "data": { "image/png": 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inIYE9vjGN76Bzs5Oj69pO0AqldIS5MrKCsbHxyGTyTA9PQ2NRoOnn34aFosFXV1dqKio8NaDMAL4J47jdAzDhAH4G8MwvwPweQDvcxz3NMMw3wLwLQAPOzvIll3TQBJk/f39UKvVbttCiUs4Pj6OhoYGG1IDgSE2OYZKpUJ7eztKS0uRn5/v8Z2Zf2NgGAZyudzhMWazGSUlJRCLxTbJrWCguLiYfunsbyJisRhJSUkQi8X46le/iiuuuAIHDhxAW1sb2tra8MQTT3jUxDI9Pb3pbmkwwbIsZDIZMjIyUFZWhk996lN44oknAADPPPMMbrvtNq+Ox61Dd+7HsHP/cQD2AXjl3O9fAdDs6jhbktgkQUaE+t0Rcm1tDadOnYJYLEZ9fb1gXVIsFgekoWN6ehqTk5NobGxEfHy818/nx+i/+c1vHP4eFhaG1tZWLCwsoLW1NahDG8RNdnUTIbE0y7IYGxvDI488gqamJlx++eX4n//5H4/Oc/HFF0OhUAT68rcEyI5zApFIhIyMDOTk5OD//b//h1dffdXrYzIMI2YYpgOACsAfOY47CSCN47hZADj3b6qrY2wpV9y+Nk16c11NPalUKgwPD2P37t00qykEkUjk1/SU0WjEzMwMYmJiUF9f72v8RJN6n//85wXLWoGa8HIFcnPxxHW3d9fJNUdEROBrX/uaR+cbHh4OaDebK2z0TLvQtJ+/NWyO41gANQzDxAM4xjBMhbfH2DIWm69uwZ/IckZIq9WK/v5+KJVKNDY2uiQ14J8rrtVq0dbWhqSkJKSmpvottHDgwAFqBe3/npeXh6amJiQkJKCpqSkglk6hUNgcc2ZmxuPX4Mpd97RDjYRJCwsLAW2DtcdmCFUIlbt0Ol1AmlM4jlsE8AGAzwKYYxgmAwDO/aty9dwtQWyr1Ur3SdknyIRcaL1ej9bWVkRERKC2ttajRgBfBzhGR0cxMjKC+vp6Ks7nKwixhZJOYrGY7rcipCflLn/Bd6eHhobwyCOPePxcV+66PemdQSQSQS6XQ6VSoa2tDR0dHZiYmMDKykpAyeiP1LGvECI2UWz1BQzDpJyz1GAYJgLAlQAGAPwWAAnYbwNw3NVxNtUV57vezmrTYrHYZjMEqRmXl5d7pX7pLbFNJhO6u7sRHR1NS2b+zmOT55eUlGBwcJBmvktKStDa2opTp07h6quvtnF9BwYGnDareAp7d9qbMU9X7jq/pk7q6ELtq+SGQK6djFxOTk5Cp9NR2eLExES/BicCOYvtKViWdTAs/hAbQAaAVxiGEWPd8L7Jcdw7DMP8A8CbDMN8GcAkgIOuDrJpxPa0Nk1ibJZl0d/fD4vF4lHN2B4ikYjG7u5ABjiKioro/K+3xxACIXZLSwv27NmD8fFxyOVy/PrXv4ZCocAdd9whGHbwrbcvcSq/NCUSiZCTk+Pza+DDnvT2yi1yuRxPPPEE9u3bZ/M8+5FLIltMBjR8VTPdLGIHMsbmOK4LQK3A7+cBXOHpcTaF2N60hYpEIhgMBrS2tiI7OxvZ2dk+xbieDnCQhfVCWzMDYbEtFgu0Wi3eeustxMfHY3FxEVqtFrfddhsmJyedPtefqavDhw9TwpFpuPHxcRQVFfn6UgRRUFCAjo4Om9+dOnXK5XMYxla2mAxoEDVT+75tV+2bm0Vs+3Nu9gAIsMHE9qUtdH5+Hmq1Gk1NTS7bNd3BHbEtFgt6enpczmj7WwvX6/VQq9WorKxEUlISzGYz4uPjkZ+f7zCrLRKJUFBQQDvD/Jm6KigogFQqpdc/OzuLm266yS3pNgP2aqYWi4Xe/MbGxqgQhdCiwK1ksX3ZFBNIbNi7QFxvT4X6SeeOTqdDUlKSX6QGXJNyZWUFra2tSE1NRXl5uVOr4KnFHhsbQ21tLaKiolBbW4uxsTEolUooFAokJiZS0QQ+iouL6XsiEolQVFSE//3f/0Vubi5EIhHy8vLw4x//mAoieAt+nM2dWyoYbJDwwp8MP9kIWlxcjMbGRlRUVCA8PBwzMzNoa2tDV1cXlEol9Hq9oPUMNgKdPAsUNsRie7NOB1iPcXt7e5Gfn4+4uLiADP47IzZRJnU3wOHqGPY4cOAATY719/dj9+7dKCgowBtvvOH0tR8+fBh79+6FUqm0SZR1dXXRrRparRY9PT3UPSV93J5MF/HjbIZhAu6GC+HQoUNUMzxQyixSqRTp6elIT0+nkkjEmut06w1bZ8+eDZqAgj2CUccOBIJKbG/X6fBj3OrqakRFRcFgMASkacOelCQZx7Ksx8k4Ty22UDlLoVDgggsuQEFBAU6cOIH8/HybvxcUFOCll15CY2Oj4HljY2MRGxuL/Px86p6SaaOwsDCqk+ZMp5yfwc7OzsYbb7zh9nX4i+HhYfp+BVqZBbCVRMrOzsbCwgKmp6dhMBiogII3iq++QMhib7Z6ChBEYnu7TsdsNqOnpwcymQwXXHABdancdZ55Cj6xV1dX0dnZKbgUwNNjuAK/nGUPhUJBFS2PHz+Oyy67zLsXAseF9QaDgaqa6vV6xMTEUKKTrDI/g93W1uZwYwkGiouLMTg4GBRlFiFwHIfw8HCbQRZXiq+BcNvPG1ec1KaHh4eRn5/v0ZtHJGrsy0tA4Ik9NzeHkZERVFRUeL0F0hOLzXEcnn/+edx1110YHx93+jiWZbFnzx6cOHECl156qVfXYY/w8HBkZmYiMzPTpdseHx9vs9cq2BAKL4IJ++SZO8VXmUxGie7rRpZgdp75g4ASmy9ZdPbsWcHpJfvHKxQKqNVq1NXVCTYn+Fti4mNxcRFmsxmNjY0+ydZ4mllPSkpCX18fxsfHceDAAfT39zt9zrXXXouMjAy89957Xl+PEFy57SMjI5DJZDAajTRDf+ONNzqongQKrsKLYMCdLJK94iuRLJ6YmKBkJEQnMtGewP6cxGvaTAQshchxHIxGo40OmStCGo1GnD59mhLNWcdRICyLwWBAT08PGIZBXV1dUPZbky0eKSkp2L17t1du3uzsLBobGzEzM+PTdbkCcdtLSkrQ1NSEkpISMAyD8fFx7Nu3D4ODg27bV//6178iOTkZsbGxSE5Oxl//+len5xPqS98oeLt+KSIiApmZmSgvL0dTUxPy8vJgsVgwODiI1tZWDA4OQqVSed2UROSONxMBIzYhM2m9dOVCz8/Po62tDXl5edi1a1dQSxQajQanT5+GXC5HeHi4XzcKZ0v5VCoVOjo6UF5ebrNNhGTHPYHJZMJ3vvMdn6+ND3ty8ctMERERCAsLQ3l5uU3tnAxqjI6O0mGNN998E7Gxsbj22mtpmc1kMqG5udnpue370gP1mjyBJ0KGzkAaZXJzc1FdXY2GhgakpqZCp9Ohq6sLbW1tGB0dhVardRsa7rgYm++qisViWCwWm0yk1WrF6OgoFhcXUV9f75W74y3IAMfCwgIaGhogFotdxryewF7aiNSDl5aWBN17bzd1TE1NBUQvy16PTKjMxDCMQ6tpcXEx4uLioFarceTIEXzzm98UPL4rC+ZPX7q/CGSDClGM4Qsc8isREokECQkJNptnCFiW9SkDzzBMDoBfAUgHYAXwAsdx/x/DMI8DuAuA+txDH+U47l2X1+/12T2EvcU2GAxoa2sDwzBoaGgIKqlNJhNOnz4Nq9VKhRcCLY1kMplw5swZAEB9fb2ge19SUmIz/SSXy11qVovFYvz1r3+1sbb8n0k2l/9feXm5Q+OHsxlqe9hPbr355pvUbX/00Uddvhc1NTWCDSf2E1+B6kv3BMGc7uKHNI2Njdi9ezdkMhnMZjNaW1vR3d2N6elpjI6O+nMaC4AHOY4rA3AhgHsYhtl97m/PcRxXc+4/l6QGgkhsot0FAGq1GqdPn0ZRURGKiop8skieJtAWFhZw6tQp5Obm2hArEEk4cnNYXl7GqVOnkJOTY9MxZo+Wlhbs2rULYrEYu3btwltvveXSjTObzdizZw8GBgbAsiwGBgZw7bXXUteWvJ98TE1NoaGhAT/5yU8o2e3PwbIsampq6E3iqquuwgUXXAAATtVa3HW4jY2NYf/+/Q4z1vybRXFxMX74wx+6PE4gsZGdZzKZDCkpKYiOjkZTUxPkcjmsViu++c1vYnJyEnfeeSeOHDni1TE5jpvlOO7Muf9fAdAPwPWmSCdg3HzZvWKCxWKhX6r+/n6kpKTQ9bCVlZU+J60+/vhjNDY2ukyMcByHiYkJnD17FtXV1YLJuL///e+4+OKLfboGYP3L3traCrFYjKqqKq/jKIvFgoqKCr9DAl8RFhZGFwrwx0WFkJyc7JbcYrEYH3/8MZaWliCTyWhpKTIykg68dHV1oa6uLhgvxwEKhQLR0dFUTTTYMBqNGBgYsFlPzHEcLr30Urzwwgvo6+vDl770JU8O5WAZGIbJx7paaQWAbwC4HcAygDasW3WnCqVAEC02x3EYGBiATCbzKxMNuK9lWywWdHR0YHV1FU1NTUFZhkbiVZPJhMbGRp+SIwzDbKgFswdpGALcd4IdO3bM7fGKi4uxa9cumm0XiUQYGxtDa2sr+vv7oVKpNlTVZKOHQIRq2GQDyAUXXOApqR3AMEw0gBYAD3ActwzgfwAUAqgBMAvgWefPXkdQ3oWzZ89ibm4O6enpKCgo8DsZ5IrYy8vLaG1tRXp6utdlJk9hMBhw6tQpREREIDIyUjAxIjT4YQ+GYZCRkYHCwsKAX6OncCZzZI9LL70UJ06csMkJ8F+3XC63aTiJiIhAVlYWKisr0djYiMzMTKyurkKv19OMcrClkTaD2EIjm/5kxM9JDrcA+H8cx/0GADiOm+M4juU4zgrgRQBN7o4T0Ky41WpFb28vTCYT8vLyAra7yFniS6lUYmpqyuP91r6ArAgqLS1FQkICVCphqSn+4Mfg4CAOHDiA9vZ2m8eMj4/j9ttvd7t/K1gga32GhoY8kja+9NJLMT8/7/V5yOhleHg49Ho9ysvLsbCwQIUnhdz2QGCjiS1UNyeKML6AWX8jfgGgn+O4/+T9PoMolALYD6DH3bECSuzZ2VnExMQgJycHMzMzgskeX2BvsVmWRV9fHziOQ2NjY1Ca+8lAytmzZ2lpjuM4p64lv7RF3HZg3ZI7Ey/caLzzzju0Z7ypye1N32+QMpBEIrHZpMGfyFpbW7Ppbfdn0+VWcMX9nOz6FIAvAOg+Jz8MAI8CuIlhmBqs57zGAdzt7kABZUR2djYls71WmT/gE1uv16Orq8svNRV3YFkWPT09kEgkaGxs9Ki/WkjHDACuu+46f0sggpBKpV7NZovFYpr13igBf2c1eeK2Z2Vl2SimkIYZUtqLi4vziqhbhdi+WmyO4/4GgUQaALflLXsE9F2wVxcNlIUirvjZs2fR2dmJ8vJyr6ay+HCXzFldXUVrayuSkpJQXl7u8RfFvrTV0tICAAEjNd+SyeVyj5JbBBsxWWUPhUKBSy+9FJdeeilqampQU1Mj2AlH3PaCggLU19ejpqYGsbGxVNG0s7MTU1NT0Ov1bj+7rULszR4AAYI4timRSAJK7PHxcYhEIjQ2NvrsrpEbhLOymVqtxtDQkE+TX3K53CGm9hcFBQV44YUXEBMTg6SkJAdX9cSJEzZbLp0h0KuChJb/2Q+PHDp0CCMjI3QnGIE7wQV7t311dRULCws2bntSUpLggvqtQGx/YuxAImjEJi2l/mJtbQ2zs7NISEhAZWWlX24k0SgXWntKsra+Tn45Q2Fhoc9We3JyEk1NTVhZWcH8/DyUSiUAICEhAUlJSbjkkksEE4v8ZhypVBrwqS1PWladrS0mZbampiaPpsqIkIK9205aVflKMptBbPuby1ax2BvWUuoL1Go1zpw5g5SUFCQmJvodGwqRwGw248yZM2BZFg0NDQElNQC8+uqryMvLg1gs9trTIF1tsbGx1FUlFYCZmRnaLMOHRCKxcVnNZrPD1JYrl9bVAAmBJy2r/NZSPkQiEcRisU9LEezd9qqqKhu3fWVlBbOzs1hdXd2Q+vlWVU8Bghhj++OKcxyH4eFhTExMoLGx0e8NHAT264JWVlZw6tQpZGVlYdeuXQFNKpFOOLPZjK6uLuj1enR2dtJl9e5gXycmIDPF4eHhuPvuux0GMuy9JPJe8jEzM+OUvPbTWXzSEdLz30Nn8fvhw4dRWFhIe+TlcjntSSdrggH/JJPI3mrSJENmAkZGRnDq1CkMDAz4NHbpKbaqyAKwBV1x/tJ6svxOLBbDaDT6fU18iz0zM4Px8fGg1MBJPZ9hGJusulwux8svv4z09HRaAiPvU0lJCb73ve/h05/+tEedc4cOHRJsghGCfUPMY489hqmpKUFX2pU1JqTnw1n8XlBQgPfffx8qlcph8X1TU5PDVFkgIBKJaLWEuO3z8/PUbQ+0LJIzIcNgbkj1FEEltrcWm0gk2S+tD9QKXGKx+/v7YTAYfNoo4g4GgwGdnZ10lSrxAkg9e3BwkGbNs7KyMD4+ThNRDz30EA4fPoyysjK353Fm5eRyuQPh7733XrS2ttJ4lJAacCSv0Cgn/5z8z0EsFrtUHXVW7rJfDRSoxJ69LjvRJwc+kUU6e/YshoaGEB4eTmvnERERAZNF2pExNv/N8eaNIhJJQ0NDqK+vF1xaH4gMO8dx6O3thUwmQ01NTcBJvbi4iNOnT6O4uBi5ubk274FQZxpg6/pOTEzgC1/4gkfnErJypaWlOHbsmE2eQCQS4ac//SkaGhqQnJyMxcVFZGVl2WiY84/lzRI+d5bWntjEla+rq8PY2NiG9pGTEKa0tBSNjY1Uftkft30rx9ibvh/bbDaju7sbERERNm4rH4FIxC0sLECtVkMul/vtKglZIqVSCaVS6VS7zVlnmr2Qv6cZdP7aHuCTmLygoMDmvSIWWSQSUQv1wAMP4JFHHoHJZIJYLMadd96JgYEBJCYmIjs72+MlfO4srf37xM+mk2scGBjAddddh8jISAwNDdHcTDA02AjsZYvJKC4/2+6J275VFUqBIBDbm7lnsvyusLAQ6enpTh/nD7E5jsPU1BRmZmaQnp4ekI0i/C8s2YhJtNuc1ciddabZC/l7OiAitCeLwN6dFovFNhs7n3/+eZr/YFkWP//5z3Ho0CHMz89jcnLS5iYQExNDX6urzZtCsCe2sxIYf2cZ6aYbHBxEY2Nj0EkOrH+m8fHxiI+PB+C5237euOJCECI5IVtfXx9qampckhrwfWcWy7Lo7u7G8vIyrU/7GquT6a3PfOYziI+PR1RUFGpqavD2228jIiICVVVVLufFSWeaSCSy6Uzju775+fl45ZVXBJ/vSRmKgH9MiURClWNJokwoxo6Li4NcLkdDQwNdo6NUKtHa2ore3l6cPXvW6/VC9sR2VgJz9lyTyUQFJ6qrq92+7kBVNTx12y0Wi+B0ly/Gg2GYHIZh/swwTD/DML0Mw9x/7veJDMP8kWGY4XP/Jnh0vEAKLQCgWzQBYYEEi8WCvr4+iEQilJWVeaQqubq6isHBQdTWOmwXdfmczs5OZGdnU3me0dFRREVFub2RCKG2ttZhCQBZldPd3e3xcYjYA/ni8r+M/f39yM7OFvxi2GeSXYkk8JGQkGDj7YjFYmRnZ1NyOzsWv7ussLAQ//Vf/4XIyEhYrVZqvdxll1UqFVZXV+lyAnLMgYEBt9ctBJFI5NRV5zgObW1tQZc65rvtk5OTiImJoW57TEwM9uzZg3fffRexsbHeHJZhGCYDQAbHcWcYhokBcBpAM9YFFrQcxz3NMMy3ACRwHPewuwMG3GK76hfX6XQ4deoUEhMTUVFR4bFUrLeuuFqtRnt7O8rKymw0t/zRPRMSJuQ4zuOSkycgYYyQ3K+nOmb2EEp4Pfnkk04TZAT8pN7IyAiam5txxRVX4F//9V+pm9rW1obu7m7MzMwIDvzYW2ziynd2dqK0tNTpNTv7XpD1y0I19kCIQHoC4rbL5XJERUXRcunZs2fx+c9/HjMzM3jllVcwMjLiVXLQhSzSPgDEjXsF62R3f53evChvwdc9m5mZQVdXFyoqKpCdne3VcTwtd5Hk0/j4OBoaGmjMROAPsfn6afzj2ddoPYG7D3z//v02cr/79+93aGzxtNFFKMudmZnpVOuMwP5GQgg1PDyMf/3Xf6Vuqlwuh8ViwcDAAE6dOoXh4WEq0euMbHyC85dKyOVydHZ2YmFhwe2yCXJzIyFKUlISvvSlL/m00dNXcBxn47YfO3aMbhR57LHHfM76n5NFqgVwEkAamcU+96/jqlYBBJXYYrEYZrMZfX19UKlUPu+49qTcZTab0d7eDovFQpVJhY7jK7EPHz5MS1hSqdRhiisQIBbbPpb1dXUu8AmJXJFYCM7iYb63wDAMoqKikJubi5qaGtTV1SExMREajQZnzpzB5OQklpaWnLZ4kgTg8vIyOjs7IZVKUVdXh6amJvz3f/83SktLIRKJ6PstlUodynT25UJPYvFggcye33PPPXj99dd9aoIRkEXyCUF1xQGgu7sbUVFRqK6u9rlu7Eyon4C0hmZmZrpcQOArsXU6HTQaDT744AP84x//wMzMDPR6Pdrb291aFnu4qhqQ986+X10qlTqorvijwsI/v7OkHN/SCxFKCGKxGElJSVSiNzU1FQzD0KTT4OAgNBqNYEeifSvr/v37MTw8jJKSEpw6dYqqz5LRWOJ9CGXaSUbdn73c7uDMG/EnJBCSRQIwdy7+xrl/hSV87BA0i61SqaDRaJCdnY28vLygxT+zs7Po7u5GZWWl26SYLx1sKpUKXV1d9PjubjLuQIhtNBqhUCig1WodlhDwm0ykUimOHTvmVXOINxl0Z73hfEsvRChPIJFIkJiYiKqqKrpZY3FxER0dHWhvb6c7s0g/u5Dr7+yaiPch5FnwM+reDJl4A6FSl5/fC0FZJAC/BXDbuf+/DcBxT44X8Do26azS6XTIysoKimIoOc/Q0BBWV1c9ntH2xmKTxJhWq7WZ+goEsZeWltDf34/MzEy6LC88PBwsy8JoNOLSSy+FRqOxeZ43zSHuxiqd1ZadJeW8rV8T8K2X/WYNo9Fos/o3NzcXExMTDp+Pu0QheV+cZdqDsZcbECa2yWQSDAE9hDNZpKcBvMkwzJcBTAI46MnBAm6xJycnIZFIUFdXB5lMFhSdL7LQLywsDLW1tR6PQ3rammqxWNDZ2QmTyeSw5cN+zY+3MJvN6O/vR3V1NTIzM+myvKKiIqqzdurUKYyMjNioehJyke0jJBb1daySwJ0n4I31t4crt1QmkyEjIwMVFRVoamrCq6++Stcuh4WFeeT6A5+8Lx999BEKCgpo6MB/TXl5eT6/BmcItEIpx3F/4ziO4Tiuir/xg+O4eY7jruA4rvjcv1pPjhdwYufn56OwsJBOZQVK0JBgcXGRLm4n5/EUnljs1dVVujWzrKxMMBPui8Ume76MRiOVKeYjMjISsbGxKCwsRF1dHeLj4+mcMSkpGY1Gl2OVBN647a56wwHXY5yevGZPPh+GYVBVVYWOjg4sLi7i448/piOfOTk5uO+++1BXV+eSmDk5OThy5AgNHfivCQB9DYGKvwOtUBpoBKWllCBQ45bAJ6qh09PTqK2tRWRkpNfHcEfs+fl5DAwMoKKiAvPz86itraVSvS0tLZDL5T5ZbNIBJ5PJEBsb67ROS+JvsViM5ORkJCcng+M4rK6uYn5+Hn19fQ4953xrTBpAhHquncGdm+1r/RzwPZFUXFxMPROiRDs2NkbDvP379+PPf/6zjdghXz3F/jUlJCTY9OOTKoM7mSZX2MrtpECQs+KB0j0jsefCwgKampp8IjXgnNhEFGFkZAQNDQ2Ii4uj01jkLk+msbwlNlk2kJSURD0AYvEtFgvdzuHsmPySUm1trY01ZhgGOTk5mJ2dhclksomtLRYLrXXbu+3eeBzeTnTxEYimEYZhMDo6akPMiYkJ6s10dXVhenoaBoPBaTXEXenOFzfd2WTXVrHYQa9j++uKr62t4dSpUwgLC0NpaalXi80JSJ93RkYGbrjhBptuMavVip6eHqysrKCxsZEmP5xNY3njii8tLeH06dMoKSmhHXDkxkBWDJO4n+zUIv86w5tvvkndzF27duH111+H0WhET0+PwzWPjY357EYTuHPVXSFQ3WBCNxepVIp7770Xn/70p7Fnzx60trZiZmYGw8PDmJ+ftzEo9qU7/rH4Mk2kJ510+7nCVhYyBDaA2P5YbNLosGvXLkRFRXlsKe3X7Vx33XXU+ioUCtTU1NAhjuPHj2NpaQlf+MIXEBMTQ9fz2K/AJbGap8Q+e/Ysent7UVtbi8TERACfWMqVlRUA6x6NVCqFVCrF0tISFhYWEBkZCZZlYTabbSSECOxLPuXl5cjPz0ddXZ2DNQcg6EZ7QzZfG1zI6w0Ese0HZUwmE6qrq+lWUoVCge9973vIzs5GUlIStFotzpw5g46ODkxNTSE1NRUnT54UjL+F3mOTyYRrr73WZl3xgw8+aPOYrSyLBAR5HttXV5wIL2g0GjQ0NEAmk2FyctLjY9mLGgh9cMB6I8N3v/tdiMViBxGElpYWKl9EYmzAvStO2lqXlpZsFFo4joPVakV2djaUSiWGh4cRHx+PpKQkGkOTDDyx3BzHUWsOrN9UGIah5LWXAf7P//xPPPjgg/Rng8GAyclJOhKal5eHlZWVDRM4CBSx+TEzGYbhw2q1QqFQ0Lo5uZEaDAbMz89T6eLY2FgkJSXh73//O/1c+MM1rvDiiy/i2Wc/2YXnLCu+Y4ltnzzz1hW3WCzo7u5GeHg4Ghoa6JvnqfUfGxtDf38//dkTEvIfR9xuZzrhrjrHSJIsPDwcdXV19L0gpCaTUUlJSbBarVhYWMDQ0BCMRiNiY2MxNzeH5ORkRERE2CSFCMHJNbIsC4ZhHOrVDz74oE0iiE/8oqIi/OQnP8Hk5CRWV1fR399PtcqDsSKJvO5ANyYJdZqJRCJaKhPSPK+srKRTWfPz85iYmIBIJMLq6ioMBoPPI8H2Zdatop4CBNlie+uK63Q6dHV1IT8/H5mZmTZ/c5fRJppifFK7A9/F5lt2lmVRW1tLM+GeXIfBYEBHRwcV0yMgpCRfcv6Q/sTEBDIyMpCXlweDwQCNRoOBgQEYjUYkJiYiOTkZ8fHxEIvF1O3jW3N3GWuhjLdCocB9990HpVKJvLw8Gxc2KSmJDjEEAsEgNl9EgiA/Px9msxnl5eXUmJCb3f79+yGVSm2I3tDQAJPJhAsvvNDn1lyWZREeHm7zO51Oh4yMDL9eX6CwYdNd7nD27FnaumlPasD9TYK4395e3+DgIEwmk0PsyM+E8yFksflJMntSWywWcBxH3Whg/c5++vRpZGdnIz8/HwzDICIiAjk5OaitraV11rm5OZw8eRKdnZ20jk0aOKRSqUNSqaioCCaTSTBuJDh06BANa8bHx/Hkk0+ivLwcUqkU4+PjVEhArVb7nfgMBrH58XZpaSkdHlEqlWBZFiaTySGBSPIrJIGoUChwySWXeD1ayYdQHXtHW2z+B+lJoolYGp1O57I11B2xXcVJ+fn5mJ6epkJ1ZGCfEEChUNBeaHIOfiacD/vutdnZWYyPjzvU1onrzLfSwLr22sDAAMrLy50O44vFYrrmhuM46PV6aDQadHd3w2q1IikpCcnJyThy5AgOHjxIrdGbb74JiURCrbpQbD48PEw/E/Leky6wjIwMG5d1fHwcEokEycnJSEpK8lrNMxjEFvJCnEku8a8D+ETGqrGx0WdpbFI12ep17KC44p7qnplMJnR2diIhIcEmJhWCqwGOsbExp8TPz8/Hk08+ibKyMtx6661U/leonOVMl0zotZFOMiK7ZJ8kEyL1zMwMlEolamtrHdw4Z2AYBtHR0YiOjqYuJ9HKXllZwSuvvEI3pfBviuQa+DVylmVRVFSEoaEh6kXY16X5+l+FhYU0ATUyMgKDwUATfiREcAV+00gwYa8b5+67524MViqV4tSpUygoKKA3Vq1Wi76+PlgsFiQkJGB1ddXh++orsRmGeQnAHgAqjuMqzv3ucQB3AVCfe9ijHMd5vHVz01RKiZBhSUkJXcDmCq76vA8cOGBzB5ZKpejo6IDFYoFOp0NVVRUkEgna29upNBFf6oiQ2Fkm3P46SC+5qyQZn9TkJrC6uor6+nqfavEEYWFhSE9PR3p6OjiOw/LyMjQaDU0IkY61qKgoerPhE/vnP/85br31ViiVShQVFeGNN95web7w8HCblbeLi4s00yyVSmlsLjTss1GqJkSxdWJiAsXFxTCZTBgfH6efrUQi8XimvbS01EZyiX9jzc3NBcuyVPG2v78fkZGRSExMRHh4uD+94r8E8GMAv7L7/XMcx/2HLwfcFGIrlUpMTU151RoqZJGdJczImx8bG4va2lrBL5cQiT3ZmGk2mykpPE2S9fT0IDIyElVVVQH9ojMMQ0XxCwsLYTQaodFoMDo6itXVVcTHxyM5ORmJiYkQi8WYn5+HyWTCqVOn6IAOx3E2IQq/nGYPvnopsN48ND8/j6GhIZhMJhtrbq/mGkwUFBTg8OHDSE9PR1xcnGBmvLGx0SW57QntDKTdd3p6GqWlpWBZFlqtFj/4wQ/wwQcfQCQS4cYbb8RVV13l8R44juM+PKeaEjBsiCtOPmCr1Yq+vj5YrVY0NTV5ZblEIpGDmLtQwoysecnKynI5n+3L2tvFxUUoFAqqv03AJzWfFAaDAV1dXcjOzhZMCAYaMpnMwboSopNrrK6uplaFxOPE0yA3TlJOE4lELl3piIgIWgVgWZaej4yhGgwGmEwmn1uAvQG/riwUhzuLqb0RhhQ6n0wmQ2RkJJ577jkoFArs3bsXf/nLX3D55ZcHYsHjvQzDfBFAG4AHOY5b8PSJQbfYpEmFuK/p6ekOWzI8Ad9iuypt5eTk4OjRoz4pkboCSZIVFhZidXWV/p6fJOOTYHl5Gb29vSgtLaUzyBsJYl0TEhIwOjqK5eVlJCUlYXh4GGazmdbT+eW0sLAwweYYMpjiypoT9ZSkpCQA6xni7u5ujI2NgWVZuvqXP7gRSNjfVO1B8id8g0NI7cuKIaGs+NraGj772c/i4EGPRqbd4X8AfB/rSsHfB/AsgDs8fXLQiS0Wi6FWqzE2Nobdu3f7/CXnE9uZpc7NzUVXV1dAV+GS+Jj0ki8tLVHVD2dJMpVKhbGxMVRXV2+ItSJQKBS4/vrrMTw8TAdAxsfHkZ+fj+PHjyMvLw95eXnUfZybm8Pg4CCioqJobM7vpXbVHOPOmkdGRiI8PBylpaWQSCRYWFiASqXC8PAwIiIi6E3AD2ECG7hL1AkJVfizgEDofGtrawETFuE4bo78P8MwLwJ4x5vnB5XYHMfBYDBgfHwc9fX1HmeChcAntlBpKz8/H2+//bZbUpOQwBOrQbrgIiMjaaxOnu8sSTYxMQGtVov6+nqv92H7i+uvv56+N/xBl/HxcRw8eBCnT58GIFxOU6vV6OrqouW0lJQUxMTE0EEJAILWHHAem5MQzNUYKsuy1HuIjY31OSZ395n6qgLjDYhnEwgwDJNB1EkB7AfQ483zgxZjWywW9PT0gOM4lJaW+kVqYP3LMzk5iVtuucUmicacW4vT0+PZ6yadY+6ITTrJcnJykJWVZXM+g8EAs9kMiURiM2zR398PhmFQU1OzIWUeezir57qao+ZnfQsKCmg5bXJyEisrK1TbPCkpiU6jkWPaW3OLxWLjsgslz8gYKhlFtVgs0Gq1mJmZwcDAAKKjo2mrqzee10aV1pzBTxHD1wFcDiCZYRglgO8CuJxhmBqsu+LjAO725phBIbZOp0N7ezvy8/Mhk8n8HjoYGxvD/v37BTvLiouL8dZbb3l8LE9UVBYXF9Hb2+sQOnAcR13MtrY2REREICUlBXFxcRgcHERKSorN6tyNhlC7JfDJeGJsbCyKi4tx9OhRp26ofTltaWmJltNIHJ2SkoLIyEhBa048Gf4oqivSSSQSpKamIjU1FRzHQafTYX5+nhoFYs35O8SEsNHEDqRCKcdxNwn8+hc+XBZFUIi9vLyMiooKxMbGQq/X+y22cODAAUGLIxaL0dXV5dWx3BF7ZmYGExMTDlszyZeUzEETl3J6ehqDg4MIDw+ndfPo6OhNIffPf/5z3HLLLbQPnGEYjI+PU313juMwNDSE66+/nrrlrsAwjM2yOn6zyurqKhISEpCcnIyEhASIxWIba65UKqmLbrFYqBV3lYBjGAYxMTGIiYmhzTharRZKpRIrKyuIiYmh1tw+zNlIYgsZqo2amPMUQSF2VlYWLS8EYgWuMyvkyxYOVyoq/NZWd51kDMNQpc3GxkaEh4dDo9FAoVBAr9c71JCDjdnZWbo0wT4hFRMTY9NWKdQq6wnsm1UWFhZoeUsmk9E4em5uDouLi7R5h/8eEpEJknxzRcawsDCkpaUhLS0NHMdhZWUF8/PzUCqVYBiGWvPo6OgNq5kDwiObRqMxaIq8vmBDsuK+DhOQspbQjcHXLRxCxBZKkgGu20OVSiVmZ2dRW1tLicTvt15cXIRarcbo6CjCw8ORnJyMlJSUgGWBCUjCbmFhAXV1dYIjmPadV/6MafIz78Stv/DCC7G6ugq1Wo22tjawLIvMzEwsLy8jLi7OYTqN76q7S8ARMAxDRQ8KCgpgMpnoYjy9Xg+DwQCVShXUMVQCoVKXTqfb0AqIO2wIsX212EJlrbKyMsFxSk9hT+y1tTV0dHQgNzfXJknmrJOMWHaDwYC6ujpBa2zfoUWyzvwhDpJ19sfKcByHP/3pT/j617+OyclJp/Gz/fvvjwfFz7zz3frw8HDodDqkpqaisLAQWq0Ws7OzGBgYECyn+dscI5VKbXIBH3/8MXQ6HSYnJ21q6pGRkQG35FtdPQUIYlacnkAi8Ump1F4wAVgnjLfdYvbgD5MsLCygr69PMEkmRGqS6Y+JiUFlZaXHXxiSBSZxI0lG6XQ6n112Iurw4IMPUqF9Z/EzP6nmrSChPYRmwEnbbGxsLB1DtU+IaTQadHZ2AgCdTuOX04SaY/jhnDtrLpFIIJfLIZfLYTQaMT8/D4VCgdXVVcTFxSEpKYnmAvyFs8muraJ3Bmxhi33dddc5/I6/EtdXkDq0syQZ33oItYfm5OT4NUwfFhbm4LKTtk9PXXYyFZeVlUWHHci1CyUZjx496uA++wqhm0RHRwfS0tIEt6jyE2KknMa/scXGxtLpNHflNFfWnJ+8kslkyMzMRGZmJqxWK5aWlijRw8LCbKy5L3CmULrjLbbNCbzQPSMxtZBOGQD84Ac/8Pt6GIbB5OQk1av2ZNxyaWkJfX19KCsrc1jN6w+EXHb7uWt7l311dRVdXV0oLi5GUlKSR9a4oKDAoyy4J+DfJIqKivDYY48hOzsbaWlpHj2ff2Pjl9NI9p647K7KaUKxuTOIRLarhfwZQyXY6gqlwAa44p4mz0gLpv2gBx/+DlJYLBao1WpER0ejpqbGoyTZ3NwcxsfHUVNTE/SsJ3HZ8/LyaKMIsWxxcXGIjIzEzMwMKisr6TriQFpjT0BuEmtra+js7KQ3GF8gVE7TaDQ0hxEfH4+UlBQkJCTYWGl7a06+X3yL7gz+jKESbHUhQ2CLuOKedKUVFhb6dR0kSRYTE4P09HSPZqjHx8exuLiI+vr6oGda7cFvFLFarRgfH8fExATCwsIwMjKClJQUJCcnB9QaewqdTofu7m7s3r2bjkna31x86cMODw+n02L8ctrw8DANU5KTk+n3hdTnu7u7kZub65CII1Y1UGOoBCzLOnwfzjtiB2IbiFQqxdtvv425uTmfGhFIkqy8vByLi4vUzXeWJCPjpRKJBNXV1ZvaqggA09PTWFhYwMUXX4ywsDBaWurt7QXLsgHLsnsCEpZUVlbSL7KzTLk/EIlENtNiJEzp7e2FxWKxmVwrKChAamoqAFvlGH6m3V05DXA/hkquR8hinxdZcT7cueKuXG/gEzUUuVwOjUbjNbGnp6cxOTlJk2TLy8uUzOS6+MczmUzo6upCWlpaQJJ1/oBMlq2traG2tpZeZ2RkJJ3UEnLZSTLKPg7017LOz89jeHjYISzxZ7+Xp+CHKRaLBSqVCj09PRCLxZibm6M3OKHpNHuye1JO45fMOI6j1ry/v58myqKjoxEbGwuRSAS9Xk8tvze444478PLLL6tgK4uUCOAwgHys94nf4M0sNrBBMbYzi03khp2hsLAQb7/9Nq1ZE3kkT9xi0j5J9meT5zAMQ0sp9vG0TqdDT08PioqKkJyc7NFrDRasVit6e3shk8lcltbsXfalpSXaGCOTyajLHh4e7pdlnZubo1UE++GMQJbTPAHLspiamkJlZSUSExOh0+mgVqttymkpKSmIjo72KgHnqpwWGRmJyMhI5OTk0AWBc3NzGBoaQm9vL3p6ejxOIPJx++234+WXX/4sbGWRvgXgfY7jnmYY5lvnfn7Ym+MGzWKTVkJnX0iVSoWRkRFUVlYK/v1HP/oRvva1r9n8ztPSmcViQVdXF2JiYhySZGFhYZicnATDMDZlJWKNKioqNt2lMpvN6OrqQkpKCnJzcz1+nn0G2N5l99WyKpVKzM3NOe1s28gEHpm627VrF32dpJwml8thMpmowirxYEifgD/lND44jqPCERzHISoqCr/73e/wk5/8BL/4xS/wq1/9yuN258suuwwA7Hde78P6tBcAvALgA2wVYjsDx3EYGxuDVqtFQ0MDpFIpDAaDR8/1hNirq6vo7OxEXl6eTRaduGSkfknKSoTsZG91oFs+vYXBYEBnZ6dN3OgrIiMjYbVa8ZWvfAXDw8M2gpAMw0AulwuWbghIAnFpaQk1NTU2jwtUwswbkEx8aWmp07KjVCp1kFJWq9W0hk1GUElpytWsuTPlGP57xjAMysvLkZWVhW9/+9uorKz0e0QZQBqZxeY4bpZhGK+/CBtKbNK5JZPJUF9f73VSyt1kFj9Jxv/g7ZNkJF7LyclBf38/9Ho9ZDIZ2tvbkZCQgNTU1KBJ+LjCysoKenp6Alov57vfHMdBKpWCZVnI5XI899xzVNiQNMaQLyVpnTWbzaiqqnJ4L4KRMHMFvV6Prq4ul3rs9uBLKQOO5TT+dJqrchoAm8EVV5ricXFxgXvRfiDorjgBsaT2PdnewJXFViqVUCqVDkotzpJkZPAjLi4Ou3fvprE3v8c5JiYGKSkpVGQgmNBqtRgaGkJVVVVAGx3s3W+WZbG8vGzzmNXVVYeMMxlqIO+Nu+MGI2FGQMprFRUVtH7vC/jlNJL1VqvVLstpgGNsTvZ98V13vV7v17XZYY4oqDAMkwFA5e0BNsRisyyLM2fOoKKiwi9LJERs+yQZ+TBcNZ2sra3RHWH8hIe9ZBBx48bHxyGVSunfAu2uz87OUjnmQByb7yaT3nhykxWLxVAoFDZuc2RkJHJzc5Gbmwuj0YiOjg4qa9XX10dvbnwr5SxhFmgXnXgxgb7h2We97W9upJ+deG7EKJCkJH+tMzEIAczN/BbAbQCePvfvcW8PwLgZEPd5etxsNoNlWUxOTmJ4eBgXXHCB33e00dFRREdHUzIS5dPY2FgUFRV51Em2uLiI/v5+2lzhKUgiSq1Wg+M46rr6s8SO3wRTVVUVsLnt+vp6p5sxyBy7kNtM3k/S901aPtVqNbRaLcLCwujNbXZ2VpDA/HO7OpcnWFpaQn9/P6qqqjZ0JNJisWB+fh4ajQbLy8uIjo5GcnIy9Ho91tbWUFFRQWcOAODkyZO45ZZb0NXV5XVe5KabbsIbb7xxFkAygDmsyyK9BeBNALkAJgEc5DjOPsHmEkEjttFoRHd3NxiGgclkQmlpqd8fjkKhoA3+xLXPz8+3GcpwRerZ2VlMTk6iqqrKr/ZQk8kEjUYDtVqNtbU1n+Jyq9VK5XBLS0sDGs/Hxsa6TDKKxWIHd9xkMqGjowN5eXlOyzbEqmk0GpjNZlpW4osQ2p9b6FyeYHFxEQMDA6iurt5UAQMi8DA8PIyVlRU6gkoEHjo6OnDPPffg+PHjyM/P9/U0Ae8qCporPjQ0hLi4OOTk5KC7u9vv7jPgE1dcq9Wiv78fFRUVNlbX1Qz12NgYlpeXA9IeKpVK6fQQ2TriTVxORi6JaECgusWIG8x/r8nsM1lAKKR/lp6e7lHfN99lJ1aN7BAjU1qBqGmTfENNTU0gMsx+gWEYLCwsQCKR4LLLLoPFYoFGo0Frayvuv/9+mM1mfPvb3970vgd7BNUVJ65KX18fMjMz/c70KpVKaDQaGAwGhw/dWZKMZVn09vYiPDwcxcXFQW255Mfl8/PzgnE5f+Qy0NtB+G4wQWlpKZ577jl8/etfpzE30T8TidZX7/70pz/1OjThg0zljY6OIi0tDSKRCLOzsygqKkJLS4vX3W0jIyOoqanZ9NIjAExOTkKr1TpUBvr6+vDlL38Z3/zmN9Hb24ucnBzcc889vp4m4F/KoBHbYrFQyzE4OEjdF1/BcRzOnDmDtbU1XHTRRTbxKH8bB5+4RqMRXV1dyMjIEJwVDjb4cbnVakVcXBw0Gg127doVlDu8kAsuFottYmD7xxAS+pP4sY+riXKsK5ddCKTeXFNTE9ClD75iamoKGo3GYV5gcHAQt912G1577TVUVFQE4lTbh9h8BYyRkRHExMT41HIHfJLUkUgkiIiIoF09ruLplZUV9Pb2oqSkxKce3kBDo9Ggr68PUVFRMJvNSEhIQEpKisPkkD8QstiAbcLMPrFWUlKCM2fO+HVeoRtKaWkpjh49ipycHJtElL2wAsHc3BwmJydRU1Oz4YsWhKBUKqFWqx1IPTIygltvvRW/+tWvUFNTE6jTbU9i85Ne3oIkyQoKChAWFkYtHn9Ez37YnvRKV1ZWbonhd5VKBYVCQZN2JC5XqVRYWloKWL38ww8/xL59+wS3SpIk1ocffoi9e/fCbDZDKpXi+PHjpK3RZwjdUIQy4nxhhfn5eZplt1qtUKvVqKmp2fDxWCFMT09jbm4O1dXVNp7hxMQEbrzxRvziF79AQ0NDIE+5PYk9NTUFjuO86nsG4JAkI0mqsrIyp0myqakpqNVqVFZWbhl3TqVSoaqqStASeRKXe4r6+nqHxXMEOTk5iIqKwsDAAP2dv+UoApK04x8bcJ8RX1tbw8jICObn520aROLi4jZt6cLMzAxmZ2cdWmiVSiVuuOEG/O///i8uvPDCQJ92+xDbarXSkcyZmRkYjUavkihTU1OYnp62SZItLy9jYmICZWVlgjPURFKprKxs02eoycilwWBAeXm5x9dD4nKNRgOWZSnJPamXuypzhYWF2bRIEvhajhKCtzVschOurq4Gx3HQarVQq9XUZeevFtoIzM7OYmZmxoHUpGb//PPP49JLLw3GqbdPucvmJBKJzepZV+A4DgMDAzAajTadZMC6hVlYWMDMzAxSUlKoRSYqGomJiXQDxmaCjFyGh4fTZgZPYT9rTcIKUi93FZcXFxc7WE0Cobn3QIxY8jvN8vPzkZ+fj4mJCbdTXkQLnb/njK9syu/6I8MbKSkpQatpnz17lhoS/ndubm4OBw8exLPPPhssUgcFG2Kx5+fnoVarUVpa6vI5ZFwxLi4OhYWFgp1kfIsmEokQFxcHlUqFoqIiv6ehAgHyGlJTUwMq1EDicrVajcXFRcG4XKFQuMzS2g/RBCLG9qXTTKFQYGVlBRUVFR55Mmtra7QhiOz2JjvTAnETJ4m72tpaG+9Ao9Hg85//PH74wx/i6quv9vs8LrB9XHGO42gSZ3FxEdPT0ygvL3f6+NXVVaqUwl9a705ocHBwEDKZDAzDIDk5GampqX61efqDQI5cuoKruNxZBYCQLtAxtquMuH3oRRqF1tbWsHv3bp/CJbKdk7js/iYeVSoVJiYmHEit1Wpx4MAB/Pu//zuuvfZar4/rJbYnsXU6HcbGxlBVVSX42Pn5eQwMDHjcSQasx+1KpRJVVVUIDw+nbitp8yS1041KxARj5NJT8L2YK664QtDtLi0txenTpwPW8kngLCNOqhikl/zIkSNgWRZmsxllZWUB+Uzsb3Deuuykbl5bW2uT2FxcXMSBAwfw8MMPo7m52e/r9ADbk9hra2vo7+9HXV2dw+OmpqYwMzOD6upqh04yZ5lvsu2xoqJCcHCCZVnMz89DpVJhZWUF8fHxSE1NpXO3gQZRX9kK5bU///nP2LNnj8Pvu7q6UFhY6LQ7zdcpLGcZccB2F3l+fj6OHDmCXbt2Be1GazAY6M3dZDK5vLlrNBqMjY05kHp5eRnXX3897r//fhw8eDAo1ymA7UNsAHS1D2mjbGxspH8jWWyTyeRAUGedZGSVTGRkpM00lysQ7WiVSoWFhQXquiUnJwdkmmpmZgbT09Oorq7eEuW1tbU1FBUVYXFxkf4uISEBR44cQUxMDEZHR3H77bc71Lrlcjm6u7t9Pm99fb3TxB2wTvLl5eUN3YhJcjv2LvvS0hJGR0cdOtx0Oh1uuOEG3HXXXbjllls25DrPYXsS22q1orW1ldb/zGYzOjs7kZCQALlc7tG4JVmxk52d7XOPNXHdVCoVrZ2mpqbSZXHeHisYI5f+wF7vmw/y2i+55BIoFArBWrder/f53K4Sd4Gql/sKvsuuUqlgMBiQn5+P9PR0OnG4urqKG264AV/84hdx++23B+S8d9xxB9555x2kpqaip6cHwHrsfujQIYyPjyM/Px9vvvkmEhISthexTSYT/QL9/e9/x8UXXwy9Xo/Ozk6vkmTLy8vo7e1FaWmpzfI8f6HX66FSqaBWq6nIQmpqqtuJIqvVSq1ToEcufQWZXXYnxuiq1k0I6KtbXlVVhdHRUfqzRCIBx3EbponmDlqtFsPDwygrK6MdcLOzs3j77bcxNjaGW265Bf/yL/8SsPN9+OGHiI6Oxhe/+EVK7IceegiJiYn41re+haeffhoLCwt45plntjexd+3ahYGBAVRWVtroVrlKkqlUKpp4C+awPYnPVCqVTWOIPUlYlkVXVxfi4+PpZsnNBonxPZlddtZPTsAwDAoKCvCXv/zFoz52fh1bJBLZJO5yc3MdNqZuFhYWFjA4OOigUqPVanHXXXdheXkZy8vL+MpXvoL77rsvYOcdHx/Hnj17KLF37dqFDz74ABkZGZidncXll1+OwcHB7UvsDz74ABEREQ7jeK6SZBMTE5ifn3fajhkskAw7cduSkpKoJSfhgD8bNwMJovft6UQUIaIrcgPrMffjjz+OXbt2uSwnubpRBLKrzR8Q0Qb7UV+TyYTbbrsNn/70p/H1r3+d9rIH0iu0J3Z8fLxD/mNhYWF7dZ4RgcCBgQGwLIuGhgabWJTMUNvLu1qtVvT394NhGJsNGBuFsLAwGyEFsoJ1fn4eiYmJkEqlPq0aCjTc6X0Lgb/ryxUpx8fH8cMf/hD/93//Z9MBRnIShCDOnr8RiwM8wdLSkiCpLRYL7rzzTlx00UX4+te/To1KIEm9mQjqN9NsNuPMmTMIDw9HeHg4JQJ/sbm96202m9He3o7o6Ogt0fMtFoshlUqxtraGhoYG5ObmQq1W4+TJk+jp6aGu+0aC4zh6o/FnIuro0aMoKSmBSCRysPYkj5CdnY1Dhw4hNTUVZWVlsFqt+PWvf424uDgbQT8+xGIxjdU3E8vLy+jv73copVosFtx9992oqqrCww8/vKHhVFpaGmZnZwGs96AHq5EpqK74mTNnkJycjLS0NLS2tqKuro6qZgolyfR6Pbq7u1FYWIiUlBR/Th0wkJFLoTq7UIY9JSUlqGEDUWW1WCwBv/G5K1mRenddXZ3gaCiwddxvknC13zPGsizuvfdeZGdn48knnww6qe1d8X/7t39DUlISTZ5ptVr86Ec/2l4xNl8e6fTp09i9ezd1Y+1JrdVqMTg46Ld2dCAxOTkJtVrtUYxP9kd5m2H3BmQLqFQqDYrMk7tec2A99h4bGxP8G8MwyM3NxZtvvrlheuxCIF2A1dXVNglXq9WKBx54APHx8fjRj34UdG/wpptuwgcffACNRoO0tDQ88cQTaG5uxg033IDJyUnk5ubiyJEjSExM3F7E5ssjdXR0oKCgAJGRkQ6kViqVmJ2dRVVV1ZbQuSJbMIxGo1cjlwQGg4GW0UiGnfSw+woigEiy8cGCu6y5K5SWluLIkSNISkqyafMkFYaNECYktXx7HXKr1YqHHnoIEokE//Vf/7XpIZ4dtiexSYZbqVQiISEBaWlptJ+arFspLy/fEk0eVqsVPT09iIiI8Li7zRWIVLF9ht2d/hcfZGIsPT3d5y0qnsJ+2YAzl9sePT09gnXqtbU16smwLEt7uaOjowPucbgi9Xe+8x0YDAb89Kc/3WqkBrYjsU0mk41wvVarhUqlwuLiIliWRXx8PHbv3r0lSB2skUsClmXp+OHKygqdr3bVw+6J3ncwYd904gyedK2ZzWb6+sk+6UDpvpHdXpWVlTa9BxzH4YknnoBGo8GLL764Jb5nAthexP71r3+NwsJCh15wMt6YmJhI54xjY2ORmpqKpKSkTbmjkrU/wR65JLBarVT3jMxXk9dP3iuyXXIzBRldDXnw4W07qtVqpeOXzubLPQXRxRMi9VNPPYWJiQn88pe/3KqkBrYbsVtaWvDaa69hdHQUV155Jfbt24eVlRXMzc3hmmuuoe44aQyYm5ujO5DS0tIc9kUFC5s5cgk4ZtgjIiIQGxuL2dlZlJeXb4kNjmS8UWgkFPCvz5xs2yCv35u4nJDaPunKcRz+8z//E729vfj1r3+9JUQSXWB7EZtAp9Phd7/7HZ577jmMjo6iubkZhw4dcpA+AoS/5GlpaUhOTg7Kh0PaMTd6P5QzcByHs2fPYmhoCFKpFFKplJbRNnMrhk6nw+9//3t88YtfFPy7P8S2h6dxOfFodu/e7dCi/OMf/xgnT57E4cOHt4ScsRtsT2IDwEcffYQf/OAHePnll/Hxxx/j6NGj6OjowCWXXILm5mZcdNFFDsTlOA46nQ4qlQoajQYymSygteKtNnIJOPZ9ky+5SqWC1WoNSIbdW/A3XpaUlNi0RALrEksLCwtBOTc/Ll9dXaV5CdLeW1ZW5iDO8cILL+D//u//0NLSsmU+VzfYvsQm3WZ88hqNRrz//vs4evQoWltbcdFFF6G5uRmXXHKJIHH501gSiYSK3/kycqlQKLC8vIzKysotE3udPXuWiuYLvSb7DDuxZN5k2L3FZm28FAKJy8+ePYu5uTkkJCQgKyuLxuUcx+Hll1/GiRMncOzYsaB5OPn5+YiJiYFYLIZEIkFbW5u/h9y+xHYHs9mMDz74AC0tLfjb3/6GhoYG7Nu3D5dffrlgbXttbQ1zc3NQq9UQiUQeu6ukVZJhGJSWlm6J6SzgE/3x6upqj0IOshRPpVJBp9PRjZ+B3CyyVTZe8mEwGNDR0YFdu3ZBLBbTkO21116D0WiEQqHAH/7wh6Beb35+Ptra2gK5pmnnEpsPi8WCv/3tbzh69Cg++OADVFdXY9++fbjiiisEPzDSEKJSqcBxHLXk9o+1WCw2TR5bgdTEeyCqnb54D55k2L3FVtp4SWA0GtHe3o5du3Y5DGv89Kc/xeuvv47Y2FgYjUb88Y9/DFq4EiJ2AMCyLI3J33//fZSWlmLfvn24+uqrBT84o9FIY1KLxUJjUolEgs7OTuTk5GyZkUt+3/fu3bsDJvBHltWT5COZyPI0L6HRaKh00FboBATWw5D29nYUFxc7lP5+85vf4IUXXsCJEycQExODpaWloFYSCgoKkJCQAIZhcPfdd+MrX/mKv4c8/4jNh9VqxenTp3HkyBH84Q9/gFwux969e/HP//zPgv3lZK56ZmYGS0tLSEtLQ35+/qbJE/NB+r5lMllAOtyEwHEczUtoNBqIxWK3IYtKpcL4+PiW2XgJfELqoqIih42tb7/9Np5//nmcOHFiw0qVMzMzyMzMhEqlwlVXXYX//u//9nf/2flNbD6sViu6urpw9OhR/O53v0NGRgb27duHa6+91uYDXlxcRH9/P0pLS6nLvra2RjXIY2JiNpzkG9X3bQ9+hp3jOBsddmDrbbwEPum8KywsdCD1e++9hx/96Ed49913N62B5/HHH0d0dDS++c1v+nOYELGFwHEc+vr6cPToUbzzzjtITExEc3Mz1tbWwHEcvvSlL9lYKNLaOTc3B71eT/u3N0KDfCP7vl3BZDJRkhuNRoSHh8NgMKC+vn7LkJrM5svlcod49v3338f3v/99nDhxYkNHfPV6PaxWK2JiYqDX63HVVVfh3//93/HZz37Wn8OGiO0OZDLrG9/4Btrb21FaWoq9e/di7969SE1NdSAuy7LQarWYm5uj/dtkSCXQJDcajejs7ER+fv6WWEdEMDU1BaVSiaioKOj1+qBk2L0FIXVBQYEDcT/88EN85zvfwYkTJza8f35sbAz79+8HsJ6Mvfnmm/Htb3/b38NuL2mkzQDDMDCbzUhOTsbY2Bimp6fR0tKCW2+9FRKJBNdddx2am5uRkZEBhmHo7DTZ00xW9Q4MDCAuLg5paWkBWTSwFfq+hTA1NQWNRoOmpiYqgkFqxYODg3RR/Ua19wLrhOno6EB+fr4DqT/66CM8+uijeOeddzZlKEYul6Ozs3PDz+stdpzFdgaO46BUKtHS0oJjx47BYrFgz549aG5uRm5uroN1tl804M+Qiiu9780E2XhZVVUl+JpIhp3UiiMjI73OsHsLi8WC9vZ25ObmOhC3tbUVDzzwAN5+++2gTN9tIkKueCBA+rF/85vf4NixY9DpdLj22muxb98+my2f/MfbD6mQL7g7K0aaPLbC+h8+vN14Sdp7yY4wiURCS4mBKomxLIv29nZkZ2fbaM4D6zJb9957L956660NTThuEELEDgbUajXeeusttLS0YH5+Hp/73Oewd+9ewc40Mok0NzfndkhFo9FgZGRkSzV5cByH0dFRGAwGnzdeAuuhBWnv5TiOhjO+3rxYlkVHRwcyMzMd+gy6urpw9913o6WlBUVFRT4df4sjROxgQ6vV4re//S1aWlowPT2Nq6++Gvv37xeUSLIfUpFKpUhLS0NKSgrm5+cxNTW1pQZMSGKRCCEGKjlon2H3tpRISJ2RkeGwvqmvrw933HEH3nzzTbf71bcxQsTeSCwtLeGdd95BS0sLxsbGcOWVV6K5uRk1NTWClo40gyiVSrAsS9cYbQVicxyHwcFBAAjqxkuLxUIHVfgqKaRTyx4sy6KzsxNpaWkO5b/BwUHcdttteO2119yKLG5zbF1iHzlyBI8//jj6+/vR2tqKhoYG+rennnoKv/jFLyAWi/H888/jmmuu8eOSNwc6nQ7vvvsujh49ioGBAXzmM59Bc3MzGhsbbfTSSexaVFREZ4q9GVIJBjiOQ39/PyQSSVDUTZ2BZNhVKhWWlpZoAjIxMZFm4Ds7O5GSkoLs7Gyb546MjODWW2/Fq6++iurq6g253k3E1iV2f38/RCIR7r77bvzHf/wHJXZfXx9uuukmtLa2YmZmBldeeSWGhoa2zKikL1hbW8Pvf/97tLS0oL29HZdddhmuu+46vPvuuzhw4AAaGxsdNoV6MqQSDJDW1fDwcMHE4EZBKMO+traG9PR0h2TYxMQEbrzxRrz00kuor68PyvW89957uP/++8GyLO68805861vfCsp5PMTWrWOXlZUJ/v748eO48cYbIZPJUFBQgKKiIjp7vV0RERGB5uZmNDc3w2g04r333sN9992HyMhIGAwG6PV6m5ny8PBw5ObmIjc3FyaTCSqVCv39/TZDKsHImBPF1ejoaMjl8oAf3xswDIP4+HjEx8fTmFoqldJKA8muG41G3HTTTXjhhReCRmqWZXHPPffgj3/8I7Kzs9HY2Ii9e/di9+7dQTnfZiDobUXT09M2Ncfs7GxMT08H+7QbBplMhvHxcfzLv/wLTp8+jRtuuAG//e1v8alPfQr33HMP/vCHP9hI+EqlUmRnZ6Ouro5ufhwaGsLJkycxOjoKnU4nuLvaW5Be+ri4uE0nNR/kZpOcnIy6ujpccMEFKCsrg8ViwfXXX4/LLrsMF198cSBHIh3Q2tqKoqIiyOVySKVS3HjjjTh+/HjQzrcZ8MpiX3nllTh79qzD73/wgx9g3759gs8R+pJu9mRVoPG1r32NvqarrroKV111FZ0pP3LkCL7zne+guroazc3NuOKKK2iczV/+Z7FYoFarMTo66veQCln1m5ycvKUaOQip4+LikJeXR38fERGBiIgIsCyLn/zkJ1hcXMQzzzyDF154ISjXIWRsTp48GZRzbRa8Ivaf/vQnr0+QnZ2Nqakp+rNSqXQoaWx3CBFPIpHg8ssvx+WXXw6WZfGPf/wDR48exfe+9z2UlZWhubkZV111FXXBJRIJMjIykJGRQYdUJiYmoNPpvBpSIW7uZg+Z2IPjOPT29iImJsYhplar1Th48CCefvppXH311QCAL3/5y0G9FnvsNGMT9F7xvXv34uabb8Y3vvENzMzMYHh4GE1NTcE+7ZaCWCzGJZdcgksuuQRWqxVtbW04cuQInnnmGRQWFjrMlIvFYqSlpSEtLY0OqSiVSvT399MBDaHyEemxzsrK2jJiEsAnpI6MjHTYFqLVanHw4EE88cQTlNTBxnlhbAKVFT927Bjuu+8+qNVqxMfHo6amBr///e8BrLvqL730Et2b9M///M9+XvbOACn3kJnyrKws7N2712GmnP/4hYUFzM3NUZUQMqRCLLVQj/VmgozUEkEJPhYXF3HgwAE8/PDDaG5u3rBrslgsKCkpwfvvv4+srCw0NjbitddeQ3l5+YZdgx22brkrBP9ArBqZKU9OTsa+ffuwZ88eB4EB8niic6bVamEymZCdnQ25XL5ldlOR+nlYWJiDSszy8jKuv/563H///Th48OCGX9u7776LBx54ACzL4o477gjE6KU/CBFbCI8//jhefPFFOuL3wx/+EJ/73Oc2+ap8B9FCO3r0KN5++21ERUVh3759uO666xxmyonAX0ZGBgwGg9dDKsF8DQMDAxCLxQ5NMTqdDgcPHsTdd9+Nm2++eVOub4shRGwhBEieZkuC4ziMjY2hpaUFb731FqRSKa677jrs27cPBoMB7e3t+MxnPkNnvL0ZUgnmNQ8ODoJhGJSUlNiQenV1FTfccAO++MUv4vbbb9+Q69kGCDixt4bPFoJTMAyDwsJCPPTQQ/joo4/w6quvQiQS4ZZbbsEVV1yB06dP29S+GYZBbGwsiouLccEFF0Aul0Ov1+P06dNob2/HzMyM0/1bgQDxNgA4kHptbQ0333wzbrzxxhCpg4wdY7F/+ctfIjY2Fg0NDXj22WcddKd3EtRqNa6++mo8+eSTUCgUOHbsGPR6vcuZciBwm1ScgeM4jIyMwGKxOIy8Go1G3HLLLbj22mvx1a9+dceVl/zE+euKu2qOufDCC5GcnAyGYfDYY49hdnYWL7300iZc5caA4zhMTU0hNzeX/k6lUtGZcq1Wi8997nPYt2+f00ku+00qpLXV1yEVMudtMpkcRkJNJhNuu+02XH755XjggQdCpHbE+UtsTzE+Po49e/agp6dnsy9l06DVanH8+HG0tLRgZmYG11xzDfbv3+9UWCEQQyp88QY+cc1mM+644w40NTXhoYceCpFaGCFiC2F2dpY2ZDz33HM4efIk3njjjU2+qq2BpaUlvP3222hpaYFCocBVV12Fffv2OZ0pJ0Mq9ptUXA2pjI2NYXV1FeXl5TbEtVgsuPvuu1FWVobHHnssRGrnCBFbCF/4whfQ0dEBhmGQn5+Pn/3sZ1uq82qrYGVlhc6UDw4O4p/+6Z+wb98+m5lyPsgmlbm5OZhMJiQnJyMtLc1mk4pCoYBOp0NFRYUNcVmWxb333oucnBx8//vfD5HaNULEDiEwWFtbw3vvvYeWlhZ0dHTgsssuo3vKhWrfZEiFv0nFYrHAaDSisrLS5sZgtVrxwAMPICEhAc8888yGNMxs816GELFDCDzIdsqjR4+ira0NF110Efbv349PfepTgjLDLMuiv78fWq0WYWFhNkMqHMfhoYceou3DG9UFt817Gbau0MJOxxZT3AgoZDIZ9uzZgz179sBsNuPPf/4zjh49in/7t39DU1MTmpub8elPf5qWxaanp2GxWHDJJZeA4zg6pHLbbbdhbW0NiYmJaGlp2TKtrecjQhbbA7Asi5KSEhvFjddff31HKW4IwWKx4K9//SuOHDmCv/zlL6itrUVUVBSioqLwve99z4a4HMfhu9/9LgYHB5GRkYGPP/4Yf/nLXzasn2Cb9zKEXPHNwD/+8Q88/vjjdFrtqaeeAgA88sgjm3lZGwqWZfHoo4+ipaUFUVFRNnvKIyIi8NRTT2FiYgK//OUvIRaLwbJswPvUd3AvQ8gV3wycD4ob7mA2m7G4uIju7m7IZDKcOnWKzpRzHIeCggK0tLRQMgdj+MRToY+77roLe/bsCfj5txNCxPYA54PihjuEh4fjZz/7Gf35ggsuwAUXXACr1Ypjx47hmmuu2bAhEyHwexmOHTu203XI3SJEbA9wPihu+AqRSIQDBw5s9mXgoYcecuhlOJ8RirE9wBZU3AhhZyEUY28GJBIJfvzjH+Oaa66hihshUoewlRGy2CGEsPkIWezzCfn5+YiJiYFYLIZEIkFbW9tmX1II2wQhYm9x/PnPfw7qVowQdiZCPX8hhLADESL2FgbDMLj66qtRX18ftHU3IexMhFzxLYyPPvoImZmZUKlUuOqqq1BaWorLLrtssy8rhG2AkMXewiBNMKmpqdi/fz9aW1s3+YoCiyNHjqC8vBwikcghMfjUU0+hqKgIu3btoj36IXiOELG3KPR6PVZWVuj//+EPf9hxbZIVFRX4zW9+4+CF9PX14Y033kBvby/ee+89fPWrXwXLspt0ldsTIVd8i2Jubg779+8HsN75dvPNN+Ozn/3sJl9VYFFWVib4++PHj+PGG2+ETCZDQUEBioqK0NraiosuumiDr3D7IkTsLQq5XI7Ozs7NvoxNwfT0NC688EL6c3Z2NqanpzfxirYf3HWehRCCX2AY5k8A0gX+9G2O446fe8wHAL7JcVzbuZ9/AuAfHMf9+tzPvwDwLsdxLRtz1dsfIYt9noNhmJcA7AGg4jiu4tzvEgEcBpAPYBzADRzHLfhyfI7jrvThaUoAObyfswHM+HL+8xWh5FkIvwRgH7x/C8D7HMcVA3j/3M8bid8CuJFhGBnDMAUAigHsrJJAkBEi9nkOjuM+BKC1+/U+AK+c+/9XADQH49wMw+xnGEYJ4CIAJxiG+f25a+oF8CaAPgDvAbiH47hQWtwLhGLsEMAwTD6Ad3iu+CLHcfG8vy9wHLdtlAFDCFnsEELYkQgROwQhzDEMkwEA5/5VbfL1hOAlQsQOQQi/BXDbuf+/DcDxTbyWEHxAKMY+z8EwzOsALgeQDGAOwHcBvIX15FUugEkABzmOs0+whbCFESJ2CCHsQIRc8RBC2IEIETuEEHYgQsQOIYQdiBCxQwhhByJE7BBC2IEIETuEEHYgQsQOIYQdiBCxQwhhB+L/B13BF0IF5sjDAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from mystic import cache\n", "from mystic.math import interpolate\n", "from mystic.samplers import LatticeSampler\n", "\n", "# create an archive\n", "model = cache.cached(archive=\"volcano\")(cost_func)\n", "\n", "# sample initial points from a Uniform distribution then search for minima \n", "sampler = LatticeSampler([(-9.5, 9.5), (-9.5, 9.5)], model, npts=8)\n", "sampler.sample_until(terminated=all)\n", "\n", "# invert the model\n", "imodel = model.__inverse__\n", "\n", "# sample initial points from a Uniform distribution then search for maxima \n", "isampler = LatticeSampler([(-9.5, 9.5), (-9.5, 9.5)], imodel, npts=8)\n", "isampler.sample_until(terminated=all)\n", "\n", "from mpl_toolkits.mplot3d import axes3d\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import mystic.cache as mc\n", "\n", "# create a figure\n", "figure = plt.figure()\n", "ax = plt.axes(projection=\"3d\")\n", "ax.autoscale(tight=True)\n", "\n", "# read the archive and show the sampled points\n", "c = mc.archive.read('volcano')\n", "x, y = np.array(list(c.keys())), np.array(list(c.values()))\n", "ax.plot(x.T[0], x.T[1], y, 'ko', linewidth=2, markersize=4)\n", "plt.show()\n", "\n", "import pox\n", "pox.rmtree(\"volcano\")" ] }, { "cell_type": "markdown", "id": "264692e7", "metadata": {}, "source": [ "We can increase the number of samples and get a better interpolation of the cost function." ] }, { "cell_type": "code", "execution_count": 7, "id": "586b2f1d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for i, n in enumerate([4, 8, 16]):\n", "\n", " # create an archive\n", " model = cache.cached(archive=f\"volcano_{n}\")(cost_func)\n", "\n", " # sample initial points from a Uniform distribution then search for minima \n", " sampler = LatticeSampler([(-9.5, 9.5), (-9.5, 9.5)], model, npts=n)\n", " sampler.sample_until(terminated=all)\n", "\n", " # invert the model\n", " imodel = model.__inverse__\n", "\n", " # sample initial points from a Uniform distribution then search for maxima \n", " isampler = LatticeSampler([(-9.5, 9.5), (-9.5, 9.5)], imodel, npts=n)\n", " isampler.sample_until(terminated=all)\n", "\n", " # create a figure\n", " figure = plt.figure(i)\n", " ax = plt.axes(projection=\"3d\")\n", " ax.autoscale(tight=True)\n", "\n", " # read the archive and show the sampled points\n", " c = mc.archive.read(f\"volcano_{n}\")\n", " x, y = np.array(list(c.keys())), np.array(list(c.values()))\n", " ax.plot(x.T[0], x.T[1], y, 'ko', linewidth=2, markersize=4)\n", "\n", " pox.rmtree(f\"volcano_{n}\")\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1ca23aa3", "metadata": {}, "source": [ "You should now have an understanding of how to setup a optimization search and execute it in parallel using a **pool**.\n", "We have also shown how to attach an **archive** to a **sampler** and plot the results.\n", "\n", "On the next page, we will discuss how we can use a surrogate model to find the extrema of expensive cost functions using a surrogate model." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 5 }