{ "cells": [ { "cell_type": "markdown", "id": "2ffd001e", "metadata": {}, "source": [ "# First steps\n", "\n", "Welcome! On this page we will guide to you through the first steps required to start working with `hopsy`!\n", "\n", "## Installation\n", "\n", "``hopsy`` is available on [PyPI](https://pypi.org/project/hopsy/), so you may just install using\n", "```bash\n", "pip install hopsy\n", "```\n", "\n", "#### From source\n", "\n", "If instead, you want to build ``hopsy`` from source, you need to download the code from GitHub or juGit\n", "```bash\n", "git clone https://jugit.fz-juelich.de/IBG-1/ModSim/hopsy --recursive # or\n", "git clone https://github.com/modsim/hopsy --recursive\n", "```\n", "and either compile a binary wheel using\n", "```bash\n", "pip wheel --no-deps . -w dist\n", "```\n", "or use CMake\n", "```bash\n", "mkdir hopsy/cmake-build-release && cd hopsy/cmake-build-release\n", "cmake ..\n", "make\n", "```\n", "Note however, that the former approach allows you to install the compiled binary wheel using\n", "```bash\n", "pip install dist/hopsy-x.y.z-tag.whl\n", "```\n", "\n", "## Polytope sampling in a nutshell\n", "\n", "Convex polytope sampling considers the problem of sampling probability densities $f$ supported on a linearly constrained space, i.e. a convex polytope\n", "\n", "$$\n", " \\mathcal{P} := \\{ x \\in \\mathbb{R}^d : Ax \\leq b \\}\n", "$$\n", "\n", "with $A \\in \\mathbb{R}^{n \\times d}, b \\in \\mathbb{R}^n$. Such probability densities can arise for example when performing Bayesian inference on ODE systems, most prominently in metabolic flux analysis [1]_. Often, those probability densities are not analytically tractable and, thus, we need to resort to numerical sampling tools like Markov chain Monte Carlo simulations. ``hopsy`` offers a variety of different samplers for this exact purpose. Moreover, ``hopsy`` aims to be a general purpose sampling library by leveraging the abstract formulation of the polytope sampling problem given earlier. Finally, since polytope sampling remains an open problem with new methods being developed as we speak, ``hopsy`` also allows to implement custom sampling algorithms.\n", "\n", "#### Sampling from a simplex\n", "\n", "In ``hopsy``, the target density we aim to sample from is defined by a [hopsy.Problem](generated/hopsy.Problem.html#hopsy.Problem), which takes the `A` matrix and `b` vector defining the linear inequality constraints, as well as `model` object. For starters, we will drop the `model` object, in which case we will be sampling the uniform density on $\\mathcal{P}$, which in the upcoming example is a simplex:" ] }, { "cell_type": "code", "execution_count": 4, "id": "4609a104", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import hopsy\n", "import matplotlib.pyplot as plt\n", "\n", "problem = hopsy.Problem(A=[[1, 1], [-1, 0], [0, -1]], b=[5, 0, 0])\n", "\n", "chain = hopsy.MarkovChain(problem, starting_point=[.5, .5])\n", "rng = hopsy.RandomNumberGenerator(seed=42)\n", "\n", "accrate, samples = hopsy.sample(chain, rng, n_samples=1000, thinning=10)\n", "\n", "plt.scatter(samples[:,:,0], samples[:,:,1])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1070eafa", "metadata": {}, "source": [ "#### Sampling a custom-implemented truncated standard Gaussian\n", "\n", "In ``hopsy``, a *model* is any Python-object implementing at least a `log_density` function,\n", "which has to implement a (possibly unnormalized) probability density $f$." ] }, { "cell_type": "code", "execution_count": 5, "id": "b4500758", "metadata": {}, "outputs": [ { "data": { "image/png": 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aRoZQQh0ei4bqqVBDoS2CIIwkZo2RaGxXL06qrEbEN6c7JAW2fI0Bd2sHms50IjMlAV82ncXKskMA4HfdzAihhFL4SwwP3buuEjaYf27RAKsXzt3agYraxojIuSIIInzEpDFi1Xb1StogLLComPqi5EmRMwYudvUN8pq4ItibJCKGh6Lx3MyA1QtX8u5naGq7oB0TyZ5HgiDMwyYIguWDuq2trXA6nWhpaUFaWpru/VXUNmLu2t2q222YNzlkq3MjQ0Zb9p/Agg37IBeuF8MOuxYVaTK2us558FLFURxrasfQzGTcPmUYEvpER/qRXoMwVujxCLjy8e3cFVnilYxEzyNBEPywzt8x6Rkxq3pC60RmdMhoxriBWAUb7lsf7CHRG3aQMpqe3VUXNatd6gvDhlpoS85ACafnkSAI6xIdy1lOzKieUFM9lcOsqoQZ47Kx5rYCZAdUpTiT4/FA8WhMzXVx7Q+gUk7CH7nKp8yUBMXv+Sa3EgRBADFqjIiJnnJrMht6QySs1RN6JmmeqgRepudlY9eiIiwsHoX0pN6S3VPt3VhRdojJUPKFSjkJKcRnbMO8yXhyTj42zJuMh2eOYfou6bZEBtEkf0BYl5gM07BUTxSO6IdH3/lMNSdCbzKs2YJbW2vcWFl2WHcIiEo5CTkCQ1sVtY1M3yPdFusTbfIHhHWJSc8IIO9iTnbEAQD+UXkcf684hpLNB3HJ0vewfEuN5H70ejbMFNwy0ptBKqUEK0Z7HonwQGFZIpTErDECBLuYrx/nQltnT9Dk7RGAp3fWSRokeidpMwduI0NApFJKsBLpXa8JCssSoSemjRHggov5urxsbD7gVtx27Yd16Drn8fuMd5IOjL8CMG3gNtKbQatdgodI7XpN9GJmLhtBSBGTOSNSvFRxVFaXQ8Qj9G5393eHez/jkRJXir+aIbhlpDfDLJVS0vWIXiKt6zVxAQrLEqGGjJHzHGtq17Qd6yS9tcatqiUS2Cdm4tAM7D3WjE1VxzUN5Eb3XDFapZSS46If0m2JTCgsS4QaMkbOMzQzWfN2apP01FwXrnx8O1PFjThwl1bX4+ondvjtLzMlAbPzB2JqrovJMDHDm2HUajcaewMRRLRAzSOJUBOTcvC+iGGCE6fO4v/941MoXQ27Dfh3yXWKZb5SkzSv/LzcRO0LjwfBah4IUUpcLiatV66eCA8UcosuxHEIkF7I0IKBYIHk4BmQmqSVmPfdHMUeLHIuaZ74q1IWuy/1HB4ENW9GqCcR0iyJPqxm8BL6oeaRRCiJWWOExfsgYrf1GiJLZuRq+i2e+KvaRB1IoKCanGEhZyiFYxKh5LjogkJu0QslIROhIiaNERbvQ1piH8zKH4hh/VJ0d6Xlib++u/8E834DPQi8hkW4JhFKjose9CoQE9Yn2pOQKbxoDbhn2J07d+L666/HwIEDYbPZ8NZbbylu//7778NmswX953Yra3qYCYv3obXjHGaMHYi7vztclyEC8IlAaZmAy498i5J3PsM9HGqJapOIAGDxGwdQfrjBcGEj0iyJHkiPgohktDY4JYyHe5Zta2vD+PHjsXr1aq7vff7556ivr/f+179/f96fNoxwhAlYRaDUJmopVu2oxXPlRyX/JqeWyGKQnWrvxq3PfWz4y0kKndEDhdyISIXk7q0Fd5jmuuuuw3XXXcf9Q/3790d6ejr398wgXGEClvirUjmuVqQSQnkmBzPCNlqT42LVpWrF8+7xCGg43cm0LYXcCCtB4UXrEbKckfz8fHR2diIvLw/Lli1DYWFhqH46iHDW0EvFXwMnmqm5LsmJWi++BgjP5GDWy8mbHBfOig2zjQGl/VuxUoW1Eo30KAgrQhV91sN0YyQ7Oxtr1qzBd77zHXR2duLZZ5/FNddcg48//hgFBQWS3+ns7ERn54UVV2trq6HHZJa0uRaUJhpRkbWsxo03q46jqa1b12/5GiBqBlkgZr2crMlx4azYMNsYUNo/AMtVqrBWolHIjbAqFF60HrpEz2w2G958803Mnj2b63tXX301hgwZgpdeekny78uWLcOjjz4a9LnRomfhXnHKDepSokK+K+fDJ89g1Y4jzL8jJyImJ2qkxJNz8jErfxDzbxtBOEXSeO6R0fsXAKQnx+NUu7QRGg5xOLV74Uu4vTcEIQevECWhHUuLnk2aNAm7du2S/fuSJUvw4IMPev/d2tqKwYMHG34c4ayh541Z+noQKmobmY0RpdWpXN6GEuGI/et1qWoNsfDeI97fYWnTLmeIiNuE2pXMqoOzdOYY/KwwhzwihCUhuXvrERZjpKqqCtnZ8qslh8MBh8MRkmMJVw29ngmWJ8SilhAqGmS7v2jE/Jcrceqs8io8HC+nHpeqHu8Xzz1qOdvF/Tu8AndyhNKVzPpbWakOMkQIy8ITqrdi8ng0wm2MnDlzBkeOXFiV19XVoaqqCpmZmRgyZAiWLFmC48eP4+9//zsAYOXKlcjJycGll16Kjo4OPPvss9i+fTv+7//+z7iziED0TLBqL5IA4K7CYVwN9QpHZuGxH45V7EURrti/1uonvXkmrPeorMaN58uPcv+OUUZEKL1VJFhHRAssFX3hDuXHEtzGyL/+9S9ce+213n+L4ZQ77rgDL774Iurr6/Hll196/97V1YVf/epXOH78OJKTkzFu3DiUlZX57SMW0Tuom9E3wqq9KLS4VI0o3WO9R6/u/VrT7+idsMPhrSL3NhFNKIXqqc1BaIn5rr3hQkwEVBvU1ZITzXAhWtEtydtB1IgENbV7xIPU77A8A87keLSczxuxSudU6uZKRDvUWdw4WOdvfTrnhGaMUiEVc15m5Q/ClBH9DHkxzNhnj0dARW0jNlUdR0VtI7fEPKuCrYgRpXtK94gXpXCb1P7Ffz9201iu8w4FvPeCICINanMQemKyUZ5VsGpYxGi0xF2lvDM81U9G5TZoqTji+R3WZ8BqnVOpmysRzZAOSeihMI0F0BMWsWJIxRctOh08xovc+RsVBvP9nRfL61Cy+aD6SWv4HavfR4KIJUiHxDgsrTMSK7BOMFrLi62e6a0liZQnaUzt/I1U2Y2z25CVylduriXcRhBE+KFE7dBDOSMmoac1NUt+RSR0nOSNu7KIgIndh1nO3+jcBt7qF5czEatvmQBnUoLmXBmCIEIPdRYPPeQZMQE9JWEs3o5I6TjJG3dlNV521zYyn7+RuQ0sYnOZKfFY+oNL4UpLRHNbF0o2W9dzRRCEPLGS02cVyBgxGJbV/W/ePICz3R640oK7s7IYMaHoOGlEDgNvEimr8VLxRQOz0VI4KsuwEAiLauMfbhzrFUuav540CggikqFE7dBBxojBsEh8N7V1Y+ErVQAurJSn5rqYV/tmZ3oblYvCG3dlD4OwDQTz11fisR+ONXTSZ1ktRYrniiAIdSifKzRQzojB8BoA4kp51fbDzN4OMyW5jcxF4Y27isaL3PRsQ69RxDownDrbbUr+zPS8bOxaVIQN8ybjyTn52DBvMnYtKvIaPaRRQBAEwQcZIwbDawCIq+cXyo8ybf/N6Q7mSZs305sngZQVniRSVuNl8vB+iucfSOAx6xVgE49VThiONAoIgiD4oDCNwfB01BURANluuYH0T03k6jgpwpIDYlYuCk/clTVpTDx/NQKPmTVBWE+MmJrJEQRB8EHGiMEoGQpqpCfFo+VsN1N+BU+mN2sOiJkrep64K4vxIp7/4tcPMBly35zuYEoQBqA7X4Y0CgiCIPggBVaTkDIA1FhYPBoryw4BYG9ApraK51FAjUTVwfIjDbj12Y9Vt3v555fj/732qWLjq/TkeDS3Bxs2WhrAUTO52MYoRV1S5iUiHVJgDTO+q3t3y1mUbD6I5rYuWU9JRnI8FhSNxMWuvlx17UoeB96qDqNW9KEcQMX8EbVjhgDVEJSUISL+jbcCRo9GAU1AkY1R1WhWV1g2E3oHYg/yjISI0up63KOS47Dm/GrZqBdRi6dD74o+HAMoyzF3nvPg/o1Vun+L1yvEey9jeQKKBrT0YjJzP5EIvQPRBev8TdU0MhhRceHL1FwX0pPjZf8urrx7PIJipQYPWnJA9Eioh0uinuWYjUoW5c2X4bmXkSDxT8hjVDWaGVVtkQK9A7ELhWkkULPMtXgu9tQ14ZRMGAAwRjU1EK1VHVpUB8Mt9CV1zBOHZmDvsWZsqjqOrL4OuNIcONnayZVUHIhZFTDhvn6skPtcHqOq0cyqarP6vYuUd4AwBzJGApALp4iW+S+uysHbn9ZzuxDDoT3BUmZstwHNbZ1Bn/OqDoZCol4N32Mura7H1U/s8Dumvo4+snklLAZKelI8PB7B670yEitcPzXIfa6MUe+4GWNFJNy7SHgHCPOgMI0PPR4Bi984IPk34fx/T++s0+RCDIf2hK+ImBweAZi/fp9u96eVhL7kXL1nOs9Jbp+ZksC031Nnu3Hrcx8zd1/mwUrXTwpyn6tj1Dtu9FgRKffO6u8AYS5kjPiwavsRxVCKHCxxXLNUU9WYnpeN1bcUQG0hzxODlsqnsYrQl5KrV4qFxaPw8MwxXL+hZxCXy0WyyvWTIpZzGHgw6h03cqyIpHtn5XeAMB8yRs7T4xHwQnmd5u+r9Rvh7dNiJBkpCVAaa3h6pZRW1+PKx7dj7trduH9jFeau3Y0rH9+O5rYuw40tLUnELI0KfY9p4ydfaZbw5x3E5a5daXV92IxVFrT22jE6CdzqGPWOGzlWRFKfJCu/A4T5kDFynj11TcyS7EoouRD1VKqYdUw82ym5e+evr8QN43uP3whjS2ni1nMOvogDMWzg6nXj+13WQVzNVb61xh02Y1UNLc+P1vsXbvQaUEa940btJ5JCH+FcsBHhhxJYz2PUy6i2ytZSqWL2MbFsx5Lp/van9Vh9ywSUbD7ILfTlC4tsu9y+tLhwG850Mve6CYTluWGtEti1qEizUJqZ8D4/eu5fODEqydOod9yI/URa6EOPWCAR2ZAxch69LyNPvxHeShW9GKGsyuruzUhxYNeiIs0DqN7yPi2NCo82tOP+4lFcvW5ExOdGqWySx1UeDmNVDZ7nJxLLM3s8AlZtP4wVZYeD/qbVgDLqHde7n0jsk2TFd4AwHzJGzsMyiaU44tDW2cPcKVcrXec8eKniKI41tWNoZjJunzIMCX20R9Ti7DYsnTkG963fF/Q31mPncffqGUD1lvdpaVS4suwQLnb1xfS8bKQmxjP1ugEuxK/VVtS8rvJQG6tq8HSJrqhtjKjyzNLqeix7uwbuVuljtqoBxYqWDt9WwGrvAGE+lDNyHpYy2NsuH4I1Jud8LN9Sg0uWvoeSzQfx94pjKNl8EJcsfQ/Lt9Ro3mdpdT1KNh+U/BvrsYfK3WtEjFsu3i6HgAvJqGKvG5ah+ZHrc7G1xq1aNhlKV7lZSaOsOQyRlKMghpPkDBERKyV5aiFcuWoEwQN5RnyYnpeNX1yVg6d3SlfVPLOzDk/dlqErDKHE8i01kr/tEeD9fMkMZYMpELn4vcjSmWxxWKPdvXJhDaMmbl9X798rjuK9arfi9vUtHVi1/TDuLx6t6llJT47HYzeNxdRcF658fLtqSOKDX18bEle52cJWLO7zSMlR4C0BB6xhQGmFQh+E1SFjxIcej4C3P1XO9hfdtUa7ELvOebD2Q+XS4rUf1uFX37+EOWSjNuDaAJRsrsG0PHX3s5HuXqVJc2quC9nORNXy3Oa2LsW/+xo7I/4jRfWYAGBF2WFc7EqVTaJLT47HnVfkYEHRSK6QxN5jzaa7ykOVNKrmPo+UHAWeEnCRcBtQLCjlLlHog7AyZIz4EAo5YrnB4qWKo4paIECvh+SliqO4+7vDmX7L6PMxItOdZdKUy2/xRcmIkjJ2WBGNTZaVJE9IYlb+INOqBKyUNBopOQo8Xg6rGFBqRILkO0HIQcaID2bHu5UGi2NN7Uz7YN0O4Dsf1iZaety9rJPmH388XnVfckaUWliKZ79qK0nekIRZrnKr9fQwsjzTrOZuvF4OKxhQSkRqOTVBiJAx4oOZ8W61weKHBRcx7WdoZjLzb7Ie59GGNlz5+HbmFZVWdy/rpFlR28i0v0BjS0seAMt+5dASkjDDVW7FpFEjDC8zV/qsJeCuNAeW3XCppSdyK3nGCEIrVE3jg1lyxCz9IXYd+Va1f4zdBtw+ZRjz77KcT0ZyPFaUHQ5JEy32yZDNnOifmuhXPfJieXATQy2wGnFWUYy0atKoaHjNyh/k9TSxYnZzN6V7J7KweDTKF3/P0oYIEFmS7wQhBxkjPpg1ubAMFu7WTswYqzzozftuDpfeCMv5yE37ZjTRYp0MpwzPYjIKm9s6/STH5cqXWeE1Nns8ApxJCbircBgyUuL9/hbKsslo6+kRquZuciWv2c5ErLmtAPcXj4oIT4IVPWMEwQuFaQIwQ46YdRCYmjsAg9ITsfbDOr9kVrut1xDhLesFlM9nzmVDsKLskOx3xRXVi+V1yEp16I7ZT8rJhCstUVbXQQxrTB7RTzUJ8obx2Zi/fp/ukEzgfvVUBGWmJGB2/kBMzXWFtGwyUpJGWQllDkw0lLxa1TOmBbNyhAjrQ8aIBEYPUDyDxawZg/Cr719iqAKr3Pm8u/8E0/d9PQ56YvZba9zoONcj+bfASVPJiFo6Mxclm/XnhvhiREVQc1sXXig/GpYBNJp6eoR6pR/pJa+RUk6tBlUDxTYxa4yoWeBGDlC8g0VCHztz+S4rUuejZaWkNTtfrcolPTkey28a67dPOSNKi0ZEIDb0ejIenjkGLmeS4RVB4UgWjIZVPhBdK/1QEA2eMaoGImLSGAm1BW7VwUJLUzktEy5LlYujjx1Tc11Bn0sZUUasiAUAjW1dcDmTuIxOq5XRBhLpq3yA33gn135ke8asbOAToSPmjJFwWeDKYYcxSE2Mxx//+TkAAVOGZ2EyZ/WBFrQ0lQP4J1wWT4a7tZN5f0auiHkNG0oWNB8e451c+xeIVM+Y1Q18IjTElDESbgtcarBobuvCb946gFPtF9rWr9pR6+1/YvaAOj0vG6tvmYDfvlWNZp9jYMHoidlIfY/MlAQ0qkjGA/yGDYUQQgPLSp9c+8FEomeMDHwCiDFjxAoWuO9gUVpdj/vWV0pud6q9G/esq8TdhcNQbGJ1Rml1PX7zVrWfMcSK0RMzzwQ+57LBWFF2OOhz8QqVzMpDyeYaw5P6oiVZUCm0YZWwh9JKP9wLC166znkMTUqPJsjAJ4AYM0asZIH3eAQse7tGdbvnyo/iufKjprieS6vrcc86aWNICd4J18gJXK3vjO/K2W6H4Xk6RuT/hHuyVwptALBU2ENupW+FhQUry7fUBJXr/37LQc3l+tFGtBj4hD5iyjS3kgW+p65JVm9DCqMVUVmNoUC0TORGicnJqXKKLCwejV2LiryTphiCMlqQTE4si2W/pdX1fkJtc9fuxpWPbzdU6VYJJWXTe9ZV4h4TVU+NxEoLCyWWb6nB0zvrgppgegTg6Z11WL6F/x00E19F44raRsMED5WwipIxEV5iyjMSSgtcbfXLO0ga7XrmNYZEtGbn6832V6vIsQHY+MmXWFA00vtZaXU9SjYfRFPbhRBUZkoCls7Uv8rXkiwY7hwHFmVTKawY9rDSwkKOrnMerP2wTnGbtR/W4Vffv8QSIZtwJgNHcjUQYQwxZYyEqsSW5aXWMkga6XrmMYYWXDsCowak6g4p6Mn253XLKwmTzV9fiafs0hM/TwiFJ1nQCjkOevRZrBT2ACLDtf9SxdEgj0ggHqF3O6N1hXgx01AORUdwIvKJKWMEMN8CZ32p1aTRlTDC9cxjDBWO/A/DJiC5CdwoT9I3pzs0T/xmrgytkONgxHMT7rCHiFW1e3w51tRu6HZmYaahzPtORWI1EGEMMWeMAOZZ4Lwv9bIbcjUlkBrhemY1hlxpDtNXl0Z6kvqnJmqa+M0OoVghx8GI58ZKFQ1Wd+23d55j2m5oZrLJR6KMWYZyuMOSRGQRk8YIYI4FzvtST8/LxprbCrD4jQNMpbVGup5ZjaFlN1xq6uqSx5PE6pZn7bkjTvyhCKFYIcdBi+KuSKjCHryVRlZ17ZdW1+P1yuOq29ltwO1Thpl/QAqYYShbISxJRBYxa4yYgZaXWhxMd3/RiIraRtR+exrvVZ8MSdmokjFkhuha4LFNHJrBNWCxuuV5J/5QhFDMzHFgvedq11CQ+H/x34D5YQ+tYTKrufZZ2h+IzPtuTtiTV80wlK0QliQiCzJGDETrSx1nt6FwZBYKR2YBkB6UWVzPWgbzQGPILDl6qWPLTElAk4JKqpQnicUtzzvxhyKEoia9LwCYkde7wudZ2fPec7VrCATrjIQi7BFNLn3WROHrx7ksoTNihqFshbAkEVmQMWIgRr3Ucq5nAKiobZRcAesZzAONIaOROzYlQ8QXKU+SWsdlnuTGUIVQ5AwBu623qoJX4E7rPVe7hqEOe0SbS591gi2WaAwZDsxIBrZCWJKILMgY0Yica9yolzrQ9ay0Ap6a69I0mIdCCZTHZS2HlCdJzbXLk9wYyjJRX0Nga40bz5cHl3+yGJB6J3Cla2hG2EPpWYs2l34kTsRGJwNHQuk1YS3IGNGAmmuc56VmMQjUVsAPFI/WVD0SCoEjPdoWNgAD0hzwCAI2VR3nNphYkxtDXSYaZ7dhUk4mHny1SvLvLMZEJE3gas9atLn0m9s6vd4uKaw6ERuZDBwJpdeEtSBjhBNW1zjLS81iELCsgF/4SFnlUeS983LezW2dmL9+X0ji81onEHEA6zjnwa3Pfuz9nNdgYl3lKxmRS2fmwpmUoMkgkkOvMaF1Ag91XxyW9yUSPQlylFbXS75bgVh1IjbSK2b10mvCWpAxIoHcgM3rGld6qVmNGpZJi7Xj7t8rjuHvFcdgt0nLf5sRn89KcTBtl5HcB83tF3QZnMnxONXeHXRuRhlMUvdYyohsbutEyWbjPUisxkT5kQZJw0HLBB5quW/W9+WDX18bFS59lpCk3Qasmhs5ybh6sWrpNWE9yBgJQGnAdiYlGOIa5zFqWCet9KR4tJztZsrNUJKoVjoHTatqxjHnL3MK0CfOjm9OdyArxYFfvfYpgGAjywiDSeoepyfF487CHCwoGukXyjLLg8RqTKzaccT7/76GA29MPhzVKqzen73HmqPCpc8SkvQIQEZKQoiOyBpYrfSasCbh785kIZQ6mt67rhJlNW6m/agZEDwuetZJa8qIfrqSRAMJPIct++tx2e/LuLvNNpzpZPq9pvYuTBnRD7PyB8Futykqw/peH17k7vGps91YUXYIE3+3FaXV9UxN5R59p0ZzV1PRmOCZXn275/J0Ou3t0PyZaeciB08oSU8nZKsQbbkvBBFKyBg5D8vk82aVuqIioL7q5Rm0WCet96p7DSWjFo++57B8Sw3uW18ZVIpbz9BaXks4waxBncWNfqq9G/esq8Sq7UeYDUYtKBkTSr8JXDAcWCfwVduPwN0qbxTqPRc5eO/99Lxs7FpUhA3zJuPJOfnYMG8ydi0qighDBIjMKhqCsAoUpjkPi7eiqa0bmSkJaG7r0hXb5hm01MSygo7z/AZXj/4PfHDoW6bf8SXwHLbsP4Gnd8onyApQDploKfEza1DnqexhTQrWs8qVS/BTQkoITikmX1pdjxVlh5j2bfSKXcu9j2SXPpWzEoR2yDNyHtaBeHb+QADyrvE5lw3Bu/tPoPxwA8qPNGBT1XFU1Db6ucDVvB029OYHiIOW3ApYCjGnYu+xZqbzkToHX/f+w5uqVb+ntKpW8wAIAJbOHONnyPBeH1Z4JlvWpGAjhNB8vQELrh3B9D3fcxEn8Fn5gzDFRzlX9ASxYvSKnSeUpIcej4CK2kbJdy2UhOp8CSIaiXnPiJiU+bm7lWn7710yAJNyMoMTIJPj0d0jyK5CfZMPtdTg+66Ay498i1U7amWPUQBwhqFjaKAWglhyNzXXhYraRpQf+RZNbWyTstJEr+YBKNl8EHa7zeuO16tRIJdoa+Rka+Qq19cbUFHbqHhvRVjOhccTpMW4Y8Hs8s5QVwipQeWsBKGNmDZGpAYyVWzB5WplNW68s185uTWwakHLoCVOWka4023oLTHMSEnwm7S31rhx5ePbuYXK1CbH6XnZ8HiA+9YHdwmWqujQOqirKdVmOxM1i7CJmLXK7fEI8HgEpCfF49RZaSOQxwjieU7MXLGbVd7JUiEUjrJSKmclCH5i1hiRG8jUEKtDRMNgy/4TqoYIIF2SqnXQMmKF/0DxaMwY5z+ha70m/VISVCfHHo+Aks3SIQPx2vz2zWqc7eqBy5kkq/uhdH1YJifR46LHkW/GKpfVMBYA3DA+m2liY31OFhaPMn3FriUXRMrDBfR6fNytHSh5V75CyAZg8RsHsOztGr/KrFB5TSI594UgwkFMGiN6+qX4DvA9HgG/fn0/83elNDy0DFpqiXIsDMlM8vu3nmtSMitPdXJkSRBubOvCwlc/BQBkpsTjxvxBKM51MRlorNotuxYV4anbCrD4jQPMeSGB/PFH41E4yrimgrxG4DM76zBhSIbqhMrynGSmJODea0ZyHW8okNSCSY4HwJbPc0EM0BzRPIIgjCUmE1i19EuRSprcXduIts4e7t/XG2bRUhYaSGCZrtYeMr+8KifIwyIF7zk3tXXjufKjzHomPNot0/OysffhqVhYPArpSfFcxwUADW1s2ilKiEmXb+47jt+8eYDbCGTRBWF5TpraunD1EztUr28okdWCkVDk5cVMXRWCILTDbYzs3LkT119/PQYOHAibzYa33npL9Tvvv/8+CgoK4HA4MHLkSLz44osaDtU4eCdGuRyBii8aNP2+EWEWuQob1sm1qb3LbzDWYiClJ/XBQ9PHyP7dt8qh4bT2CdxX7EsOXm2SOLsN9xePxt6lU72VLEtnyp+LL3rvX2l1Pa58fDvmrt2Nha9UMScJi/DogrBUYrFc31BhRJdnNXyvn1UqcQgi1uEO07S1tWH8+PG46667cNNNN6luX1dXh5kzZ+Kee+7Byy+/jG3btuHnP/85srOzMW3aNE0HrRfeySQzJQEls/Ik3Lp8fgmjdQakcio8HgG3Pvex6ndX76jFG5XHvfFzLRPsqbPn/EJOvjH+ow3t2LDnS0UlVVZYJOC1apP4hsl6PAKe3VVnqk6E1rwcKVgNsOl52Si6ZAAmLy+TNHzEY1n8+gGkJsZj8vB+YUu21NPlmZeyGjcefLXKMpU4BBHLcBsj1113Ha677jrm7desWYOcnBz86U9/AgCMGTMGu3btwooVK8JmjPDmXDS2daFkcw3sdvgNUlNG9PPrHaKEWRUYgTknPR6BuWIksOpASx6KOCFqqkziQK3vjxGCU2a3PTd61c9jQO491qzqgTl1thu3PvtxWCfkUEqlP1d+NOgzyikhiPBges5IRUUFiouL/T6bNm0aKioqzP5pWbTkXEhJn08e3s+bVKdGqHpsiOdmg/q5+cbPgd6Jlnei7J+aKBvjNwO5ycoowSkze6QYterXIvrGM8mHM2wTCql0G+TbJlBOiTwU0iLMxPRqGrfbjQEDBvh9NmDAALS2tuLs2bNISkoK+k5nZyc6Oy/kGLS2sgmS8aBVits3VBBnt+Gxm8binnXB2hkidxcOY64IMYqpuS48UDwaL5TXyepViGjtSyJ6GiYOzcDVT+wwNcbvi9JkZZTglFk6EUbpwwD8HhqeSd6IzshaMaJSzBcpD5eAC20TpGDtvh1LWE1cjog+LFnau3z5cjz66KOm/4446Sx7uxov7f6S6TuBg9T0vGysua0gbHoGgWgNl7hbO/C/pf9m3l5A74S491hzSDwirPkaRhkSZuhEGLHq16pxwjvJh3JCDtQTWTozF/PXs/VikkJ8VpbOzEXJ5mDD9Lo8F56XCNEEQt11e2HR7yGDhNCL6caIy+XCyZMn/T47efIk0tLSJL0iALBkyRI8+OCD3n+3trZi8ODBph3jSYWOplIEDlJWUVzUkxxZfvhbLqMiKd6O1MR4QxJU1eD1BlhVcErvqn/pzDH4WWGOpueKt+GiiNkTstyK+xdX5eDtT+v9Ps9IjvfRD5HG91mZnpeNaXnB7+WeuiYmY4S667Lr94Tag0ZEH6YbI1OmTMGWLVv8Ptu6dSumTJki+x2HwwGHw2H2oWn2IkgNUuGeAPUmR5Yd/IZr+7PdHtz67MfITOHX6eAlWvp6aDUIRDJTEpjE3+SMYi2hSTMnZKUV9zM767D6lgnISHFIKrD2Vmy1na/YurCYCHxWpN5Lo7rrKl3raIFHv8eKCwAicuA2Rs6cOYMjRy5UkNTV1aGqqgqZmZkYMmQIlixZguPHj+Pvf/87AOCee+7BqlWr8NBDD+Guu+7C9u3b8eqrr2Lz5s3GnYUGtHoRzGoophe9yZFquSVy8GpksCBO1HcVDsNUk/JtwjWRaDEIREo2H0RSQpymvjy+PX+m5rqwu7YR89dXGtIDRwssK+6SzQexa1FR0H3xnfQWFI3ivo9GVE3FSg4Fr34PQWiF2xj517/+hWuvvdb7bzGccscdd+DFF19EfX09vvzyQv5FTk4ONm/ejIULF+LJJ5/ERRddhGeffTZsZb2Adi+CDdZtAW7EYJCcEIf2Ln5FWRHe1b4NgDM5Hol94vzCPWZ7QvROJHoNGd+wXlmNW7LEVIrmti7ZGD1PXD/ObkPhqCw89sOxuPd88rXRZcxqGLXi1uqR1JPsHEs5FFr1ewiCF5sgKOWVW4PW1lY4nU60tLQgLS1N9/4qahsxd+1uru+kJ8fjsZvGGjbIGL0y13JOgfR1xOGMBnl7kcyUhCCZeRZevvty2O02TdeC9zrKTSTiN9QmEjNWxKXV9cy9ckSPha/HoMcjKHZalvqOmefDwqaq47h/Y5Xqdk/Oyces/EGmHQfv86PnWkci4vmqhbSi5XwJ42Gdvy1ZTWM2W2vUu+wG0qKzJ4YvZkwARpREnunswcLiUXjho6OaeoD8dsYY/H5LDXfopqGtU3HCkZswlK6jVEIxAF3JeGatiEVPyarth/HMh18o9jsSPQa7axu9zfr0eBnClXxt5Io78PmYODQDe481M50Pr2cl1nIozBYCJAiRmDNGSqvrmTLpAxHQ25I81RGPySO0y2XrmdCUVnFqgwargTIsKwV7H56KVduP4G87DqOzh920aWrr1JRDojThyBkcN4zPxjM76ySv4z3rKpGeHO9nUGU7EzHnssGaJxKzqwrEXjlD+qVg4StVqtvPX1+Jx37Y66nTG9cPR/K1UUmkUs+H3Qb46nEZ6emJxRwKo/R7CEKJmDJGxAlFK6fau3Hrc9rlsvVMaKzJiXKDxpzLBmNF2WHVY+yfmnh+YhyF7wzLwK3Pqve5AXrDWKt21DJtK6I24SgZbk/vrJP8jrhtoGfH3dLBdP6A9EQSqhWxK43NY3DqbLfXeI3EuL5RSaRSz0egMKiRuRy81zpaKm6sIl9ARC8xZYwYJcetdXDTOqHxeFPkBg0A2PjJV6qxbl/DYPLwfsyhH96wjtqEo2a48cLzHakJJ1QrYt5w26Pv1OCDX19riJch1OhZcfMkoRuph8Hj0Ym2iptwyxcQ0Y3pvWmshFGuU639K7RMaCyTcuBxiIPGrPxBmHI+pKTUs0bOMGDp4ZOe1Ie5P48var1eQtm9NZDdXwT33TA6x0Gux4fvNVdDNF73Hms2pC+PVvT0LJmel41di4qwYd5kPDknHxvmTcauRUWqkzXv86G17UEgrD2Qtta4Jfs1hbPvD0FYmZjyjBjpptbilmf9/cMnz6CittGrFqknz8HXQ1J0yQDJnjVKK1G51Wt6cjzuvCKHK5QDqPfqEY/5vTAO1k9uO4xXPvkSy2641HtNzMxxkAu3LX79AJP+yzenOzArf1BY4vpGrP61rLi1LiyMWJD09n4ahRfKj0q+R1NzXbjy8e2mqpZGS/iHIERiyhgxugkXwDe4sf7+qh1HsGrHEWQ7EzEmO1XTcbAk9qUnxePOwmFYUDRKcSBTihdvqjrOdHzpSfHehEs5tCrimoG7tdMvBGZmjoNcuC01MZ7J0BON3FDH9cOpt6F1YaF3QSL1jPa+RzlYUDQScXYbKmobTc0virbwD0EAMRamYQk78MIzuPH+fn1LB7b/+1vu4xAnicABMdB73nK2GyvLDjOVOkuFfgDgaEMb0/HNv3Ykpua6ZP8ud8xGw3vffUNgosfC5fS/52ohJ0BbuE3M2ZE7ZhuCFYHl7pPRaDmfwO/raUcvGvasZyd1rXiRe0Z736ND3vfIzPwiuWOg8A8R6cSUMQJcmFAGMFYtyKF1cJOb0PTgexy8iX0Af+6LSI9HwIY9bN2Of7/lIK58fLvkYKm3rw4PPL8hlWdgVo6DXE7DnMuGyIaFgPBpPGg9H6B3Qr3y8e2Yu3Y37t9Yhblrd8s+G3LwGPZGXCse48us6ia9BiBBWJmYM0aA3gnlTz8er2sfAvgHN3E12HnOgz/+eDxevvtyLLh2hK7jQMBxhDKxb09dk1+TMjXkVm+8x6wlYdbv+0nxXB6SwBWsFu8D72pZnLBXlB2S3I7FG2MmWlf/Rq7s5Qz7wNthxLXiMb7UvDZaFzJ6DECCsDoxlTPiS0Mb+yQqBe+EKBfnvS5PPnTBwtWjs+BMSkCPR0DceUl1LWj5Hu935JL3WPfz0ylDcV1eNjweAbc+x540G8idhTlYKTPJS2FE4nNWClsX6qwUh2oTx4XFo1TzfMxGy+rfDOG4wDyZrBQHPIKAj+uaAAiYMjxLVqSQJwmUx/gyS7U0FgXXiNghZo0RvRNMS3s3c5KeUqKfFjVYXz441IAPDjXAlZaIZTfkhjSxT8t3pJL3WPNOrsvLxpQR/dDjETQlIosVLwuKRuJiV18se7vGr0Gf3PZG6HN8cpRtteoRlENWNvTqxSwoGqX7mPTAkoydnhQPjyB4DWWzhONET1VpdT3+3z8+9fuN1yuPSyZ28iaB8hpfZqiWsh4D6/tEEFYiJsM0wIXBVCusMVqjxbvkcLf2yqA3t3VyJfaJ5A9O5/5N3iRCX3zDEWrKqIFubS2JyNIrUvk7YGRORo9HwIsfHWXa9uMIccWz3INTZ7tx67Mfe/NBrJLYqSVUpCX0ojW/SA7W921F2WFKZNWB3uRqQhsxa4z4ioBphWViCLV412/fqsbSmWyiWb6s//gY93f0VCf1T03kkucPNArk8gWynYn45VU5QYZmRko8Vt8yAdPzsr2TkVK+i5E5GXvqmpj0QnphG/is4IpnTcYWJ/mjDe1M+zUzsVNrEiir2Fmg4WpkdROrIJ4Y7qJJlB8jkqsJbcSsMQJcGEz1JkQqTQyhnjSa27vhTI7H6lsKghL5lDjWxDZRBDI9Lxurb5mAjBS2a+i7gmQ11B4oHi0ryCa18lwyIxdLZ+YiMyXBu21TWzf+592D2LK/XrVyJzMlHh/8+lrDkkNZn4H05HhMGZ7FtK1V+syI9+Dluy9HepL0MyBe642ffAlXmiOsiZ16kkD1lHYbxfS8bDxQPFpxG9/OzrTCZ4fKpsNLzOaMiEw/nxD569f3K7ZuV0KpKVY4Jo2K2kYUjswK0hVRYmhmsqbfKq2uR8nmg37dehP72NFxzhO0beAKknWSHpYlf2xS6p2l1fW4b31l0Lbu1g7JzwNpauvG3mPNmvtwBD4HrMmrd16Rg8kjlPsBWbHPTJzdBrvdpuj9ESfIhcWjsLLssOUTO+W2tULDOKX3wZf56yv97kmsCKNpUac1uys3oU7MGyOl1fWYv36fpvwNlqZYS2eOMVz1VR2Ba+C124Dbpwzj/hW5xFwpQwQITt4zQ4+hxyNg8RsHmLeXQ6tHS+o5cKUlIj05Hi3t3fLJnsnxXgVPMyoxzIbdsEwJW2Inz3OkFFIKd8M41vMINA5DoYwbbrSq04aqKzchT0wbI0aIbfk2xZKqlpm/fh9+cVUOntlZFzS5mMWU4Vmwc0xW876bg4Q+fBE7nmvn6GNH0SX9cdvkoZg8/MKLbFS/F192f9HI3UFYCi0eLTnj7GTrhfOTewYeu2ms18DQUokR7l4lPAbBlBH9DPUu8D5HrjSHqj7Oxk++9BqHVkNrW4toX+HraU9AZdPhJ6aNET3JpSmOOPzpx+NVm2IBwNuf1mP1LQUo2azcK8YI0pPjMfm85c4yYM37bg6WzOBPeOW5dp3nPHiv2o33qt1+qxQzvAAVtY3M20qhNQzC4uZNT46Ho4/dbyKUW7XxhAO27K/Hw5uq0dTWpbpfs+A1CIz0LvA+R3MnDVGt4BJzLgpHseXwhBKl81UjWlf4esMsZqnmEuzEdAKrHis31dHHO1moTcr1LR3ISEkISrZcNbcANhjXJwe4sMJmqXRZNWcCfquh8gbQfu0Ck8FYkgL5Su30WXdalHUBNjdvc3s3/vSTfOZST5ZKjOVbanDf+ko/QwTofeb0Jt3xXHet1SZGwZNcOiwrhWmf89dbN2lR7nzlkogDibYVvl51WrNUcwl2YtozosfKdbd2YsXWQ2Cd/LbWuDFlRL+g1chT9gL85s3qoMlEjmxnIgqGpOP9f3+Dtu4LuRmuNIdfy3tA3t1vxKpZ67WTWqVMzXUh1RGPii8aAPROwJOH906+vDHgOLs++zojOd6voR9r+IN1cG8404lZ+YNUt2P53S37T+DpnXWy+xCg3SWvJfbOE14yI6zE6k3iybmwco6F1Pl6BIGr07MZ8Nxbo54DvWGWSM3ViiZi2hjRGnsVWbXjCPO2m6pO4Lczgx/m6XnZ+PTrU3jq/S9U9zFpWAYOnTyNzQf8u+z2dfTBf//gUskB06zs/0k5mejr6IMznee4v+u7Smk52xU0eb1e+bV3lc0TAy6trsdftim739Vobu/2urClJuTMlHj8blYeZowb6Pc9I928LIZAj0fAw5uqVffF6pL3nRSONrRjZdkhTbF3ludNa5IhCyzhH9733so5FoHnq6ZObHY1Fs+9NfI5MOL9M0M1l2DHJgiC5YvPW1tb4XQ60dLSgrS0NEP3LSY9AeYnl26YN1lyoHxg4z68VXVC9/7XGLyCU1q19HgEjF32T7R3aSuHBoC7C4fh+fKjQdddXJmkJ8fLJqOKg+quRUWIs9vQ4xFw5ePbDRGYe3JOPhx97Ir9Yb53yX/g598d4b0m4u+rTQLi8cohl4QnfkM0BCpqGzF37W7m81HyxkhNCnKwnofSb7Gcn5n0eASs2n5YNW/EF7l314rIjWlmX2Oee2v0c2DU+yfuK5zJ4NEG6/wd0zkjAHvnTyMoq3FLfj4w3RiXqVGqiz0eAU+WHcbEkq2ySoR76pp0GSIA8GbVccXEX6WqGNG78mJ5HTZVHceL5XWGKd1m9XWoVgpt+/e3ftdELUdHADDnsiGKv8ujDsoT81daDcoJPcmhR45e7fzEsJKZ4lwXuiHzedAiKcciHOJsoVDBVcLInCUjVXMJdmI6TCMi5VpubuvC/PXGekyeKz+Ky3IygwaDwhH/gb8xhGnUMCJLvrS6HovfOCBpCNS39Pa/+dstBej2SGuJsGADkJmSgEbGPBklSjYf1L0PEXH1BAHMk3N9QOhCys0rsqLsEDZ+8qWsy5cnCY/VLd0vJUHWJa+ntF3L5Mya7G1WpYdaN2QlIq2KItTibLwJpCzb7v6iEXabjfn4KcwS2ZAxch6pWPNTdvmJRStS8efJI/ophiR40LOCK62uxz3r1BVKF2yoxH8WjdT0G+JZz8ofqLtjsZH4rp4a2pQ1KKQQ76s4CciFAZTyLljvXfmRb/Ff3xuNbGei6rNZMitPdgDXU9quZXJW6pCsZTsetBpeWnIsrOLmD6U4mxk6HfNf5leQtYJCLqGNmA/TKOHb++S+a4Ybsk8pF3ec3YbHbhpryP61ruB4mtZ5BODJbUeQnhyvWJbs6GNHRkDfH9FV7FuxYgV8Xdi811AqdLHxk69ktwWk3dCsv7tqRy2ufmIHbhifrXj9f3lVDmaMkx+4tRiuekocyw83MG3XdIbfGFRDi+GlpYoiVhut8SSQ6lWQVbuWFGaJTMgzooL4YHsEwZBQCiA9CUzNden2juipg9ezSpYTXnpyTr7sKqXHI6ieb3JCHM6ez0sxK4vg7sJhKM51+a2eJuVkIjMl3q/fDgvifdUqLd3MEbZyt3TgmZ11+MVVOXj703qmip9AeI0uPSWOpdX1+Efl10zb+jY4NAothheve1+PAmikwyt6RwqyRCBkjDDSYOBqTWoSWLX9sO4wjZZJQnQpv6dh5XaqvRsLi0dj4ydfKpbnaXUVO/rY8ccfjQ9SruVF7Mrse32VtUps+N2sPNy3fh/X74j3VYvLuscjoGQzm2cKuDAwv/1pPT749bXYe6yZ2y3NW+KqNfbO43Xr/Z0krv2zwGp4LZ05BlmpDsXrKBWGARDTjdZ4dTpIQZYIhIwRRoxKYLPbgP/7rHfiFwe70up65uz+5IS4oCqWjOR4LL9pLPckwVPSKcewrGTsWlTEHaPdU9ekanw1t3d7lWvF/Tec7mRKWv3tjDHon+bwmyx4jnHGuIH45denFEXFRAJXfVo0D7R4psSBWWuHYbUJRACwsHgUhmWl6Iq985ybWSqXrCv3nxXmqJZeS2ljzLlsSMw3WuNJIJXbltU7HEnVTQQbZIwwolcgTcQjAC98dAwvfHTM29WXpyJk7U+/AwiQVCvlQU9lgS/9UxM1JcrxeA9899/jEfDsrjrV+/Dcri+w7IZL/Y7Ldx8shsmSGbkYf1FGUN8XX6RWfVoaAOoZXPV8NxQVCDzHZ5bKpREKm0phmBVlh5iOQ+8kapXkWDl4EkglFWQ9Am59LrwKskR4IGOEET3NqeSob+ngCgVkOxO9hoeeBl5GdCsGelcxWlexWhUTWe/DydZO3LOuMmhlv7XGzaX6OGNcNqbl9Q6YZTVuvFl13C+XRGrSFo9RrjJJqv+NnsFV78BsdgUC6/EtLB5lak6FHsOLRRuDBT33ykzlWiV4DSCexUmoFWStbszFMjFvjPA8nEq9Xm4Ynx2USGg0vhNYj0fA7tpGTR4SPcmqvuh5hScOzVDtWmw7v10g4n1Y9naNbBmouFvf8JecC9h9Xj9FLiQhDphTRvTDb2bmmjKYafG8iXot7pazqKht1HUsZpaBspxbtjMRC4pGmfL7vmg1vPS+M3on0XAlx4baADKzR0y4jLlwEIlGV0zLwWt9OOVutG8y6N8rjhl2nACQkhCHP/1kPKbnZcsKk6Unx+MxhtyRTVXHcf/GKkOOS6tM9pNlh5jyZBYWj8b9xdKTVPnhBiaXrhb0DFJq0vRy0tR6WxNYeWANl0S5iO87m9XXAQhAQ1sn80DN887ITaJaz1Hr86SXcEr38/SFYt1fuNsQhAqrGV0kB6+CnAw2Sy27XB27+Pl1Jtzwtq4e3LOuEsu31OCedZWSK/xT7d24h6EO38h4q5YYOE/C7gsf1cnKQmsRJ2NFfA6eLDuMTVXHUVHbyCxPrbWduWxb+OR4b0UQyzFbSdOixyOgorYRnec8eKB4FAakOfz+bqZEuUig9setz36MW5/7mEsHhCfUxCLDLl4XlmdL6/OkBzMk23mYnpeNpTNz/cq8m9q6UbL5IPfzHe5zCSV65rVwE5NhGrWHM7AMj9flZVSyqxTPMFR3qJUQsiRYZjDqbKgN0oHXbuLQDK4yz1Pnu+hOyskMugdmJrFdCPNcSExkXV3oUaOUCyMAvZOSu7UDJe9+JnlvwllCKvWOSOXnuNISsbB4NIZlJYfEfcySqM0S6mBNSl5QNAoLikYZ2rXYDHVTNbRq5RhFaXU95q83JiwV7nMJFbzzmtWISWOE5+GUanGvNimpJTDqgcW4UXuxWEo6b588FP/fR8eCVBB9t1OLgUu7WhNkK1Pk2FrjxoOvVgXdg6Uzc00z+qRgHQj1tjOXy9+YMqIfKmobFY3EUA6sogGytcaNt6pO+N1Xufyck60dWFl2CE/dViB5fEbGulkTtVkGat5cBrlrryX3Q+/zpIVwGEAiRk+q4TyXUBLpRldMhmlYH7qyGrculxeLa90s1M5RLiTgPB8SeHLbEUVDBFBOJJNzF/IaIgDwfPlRyXswf30lbhif7XdMZsLq0hVX0XLHpEdSPdQDq1w4wTf08Xz50aD7KqcVoXQNt+w/gct+L98pmheepFOWUIfebrhawwVmPk9yhMMAEjE6LBXOcwklkW50xaRnhPWhU2txv+ztzyStc6M0PPSQleJARW2j4gozMCRwtKEdK8sOqR53ZkoCSmblyQ6+RpUOA5CtuBE/euVfX2NB0Uis230MzQY0GlSDZXVhZkVAKAdWuXDCDeOz8czOOs33V+oaLt9SIykwF9gVmQctgy6LEa+1DFrrytXM50kOLVo5RmH0pBrOcwklkW50xaRnhGWl0S8lQTVnwt3aib9uO+y3cuw65zFsItZKenI8fvXap0wrTDEk8INxA7Hxky+ZjruxrQslm2tkV6xGlA6L90Ytp+xUezf+uv2InyHS19HHbx+B+zTCYyU3EPonbI7GgDRtq2g5QrVKlvNs1bd04Gkdhogv4jXcsr9eUelWQK/HoPxwA1cysZZBlzcHiieMpDeXSI9XhhfRAALk3yOzBOqMnlTDeS6hJBweNCOJSc8Iy0qDtcX9ym2HgW0XKkO0NFgzml4XuXTHS7mBi9eAqPfR5lhQNMrvRTbCDehMjseN+YPwwkdHub/b1nnOuw/fcIEobiXlDQL0i1dJeRJcaQ5DJNVFQrFKNtKzpURWigPlRxqw8NUq1W3rWzr8yrhZkol5Gx6qDdR6Syb1TLI9HgHOpAQ8NO1iNLV1IbOvA640cxOAQ6HOK4UZnoxwnUsoCYcHzUhIZ0RmcHEmJWDu2t2G/ZYUcsmjeujr6IMz5ydjqd/z1SPwXeUdPnkGq3Yc0fSbGcnx+P3sC/X/FbWNhly7FEcc2jp71DeUQDzXP/5ovKqeBE+PHnG/gc3pmts6MX/9vpDpGJipJWDU/ZPDhl5DMbFPnKxoHcs+WHrnlLzzGZ5jWFQAwBqFe2SEToWoF6I2yUrpz4RTNyIcAlpm6dJEohgYL+F+XgJhnb9j2hgBpEtP9x5rViyhNIIfFQzCriONfoOxWCHym7eCBc2MZMO8yZJVQnr5wbhsPDlnAgAoDrqhRE2UTbz/7pazaGrrwtenzuIFlcnrl1flBKntKqnJmiVKZdbAaqQoXiBGtVKQQmrAZTWsFhaPwv3FoyX/ZqToGO8kG0tiXYFYbVKNJKxkdLHO3zEZpvHFt4yytLoeV/3vDs2rNR7+UXlc0oXP0s1WL2U1bjxfftTwSeHd/fXYdbgBj/1wrOF9fLSiFDKSGuzU3tcUR5xkfoNSCoNZJXVmSbgbkeAm3vfAEt8BaQ50nPOY8oxLhSKb27pU2w6oSdEbWTLJEy6IdN0IvZjdMymaMbO9g1nEvDEiUlpdb4ouiBInWzuxsuywn+aC1nwLG4DUxD5o7ZAO0fgiVyVkBKfO9qrArrmtQLaPz+mOc7KhJKORm1jlVpxqeZFaw0aAvlwaM1c6Ut5BFv0WJUNTKj+nf2oiPIKAW581R8I/cILeWuOWFM7yxQb1OLrR1R2sk2yk60YYQSROqoQ2yBhB72C8+I0Dhu9XTeBLHCR/8+YBFF0yAAl97Dja0KbptwRA1RCxnT+mRg1aH7w8+k4Ndi0qkhx0f7+5hik5WA9KSW6hStAMpOF0J3o8guzEJ2dwmOmuVivflUuE+4VEqCozpTfpuDjX5Te5+k4mm6qO6zpeNcQJendto+o9ttuAVXMnqF5DM0omWSbZSNeNIAgeyBgBsPuLRsPdxtnnkxxfqjiKks0HFbdtauvG5OXb8OOJgxRLHPXAWyW04NoRGDUglVl7JBDfFVvgoPu9MQNMNUbUMseN6lrMS8nmg3h2V52kEcGr6WFEt1YlNdBndtZJGhy+4YSHpo/h9taESuOg4osG1XvsEYCMFIfiNoAx1R1aPFuRrhthBFbKfSDMhYwR9Ca5Gc0j1+cioY8dWanqgx3Qq0xqliECXJhEnEkJTIZAfFwcZuUPQml1fVCJLCuyKzYdLgkbevMQHH3scLdKN8pTK9cL50pSyohQMgrkngk9OQM9HgG7axux+PUDivkIb39aH1Q1JCZ4b6o6rmlyaG7rVM3hMAbjtD/0lkxq9WzFiliXHJTAGluQMQLAyBTLXtfvhYnGCquWpTPH4GeFOd5yXpZ8gJVlh9De1a1LaVPu3LV22xWH+uU3jfUL/2SlOAAb0HAmuIRXamWl5Z6Iv+1MjkdLe7cu9VFfIwLn/19J6VdpX2o5A4Hn39zWiZLNB1W9BuK+9x5r9kvwvvqJHZonh97mZ8Hlzyyw6oWIE/SUEf2YStVZnwWtOhVaetGIRLpuhC+8Hg49142ITMgYATBleBZW7ag1ZF+r5k7AjHEXXhIzO/iykpmS4H3xeZr4rf1QuyGiJCDFOgEE5twEDvxqMXe5ldVvrxujOrkFrt7F3wbgLc3UijjRv1heh+b2bt0hI7nVPY9+itq+9U4OWvN0pHRd5ITqfCfoycP7mSKcxVPdYUQ1TDSIdfF6OKxWRUShotBAxgiAgqEZhpWg2gMeUt/VTbgITKKdnpeNhcWjsKLssMw3eq+FHgUapRXbpJxM2a6ugLywGM8gIDd51rd0YMHGfbLfE/e+au4EZKQ4JH/7qdsKsOztz2TDRKyo5RKxIqcGa0R/pA8PfYvr8rJ1Tw5a8nR8jYuEPnY/4/NiV1/VCdoMrwJPdYdR1TCRXOKqxYi1UhURhYpCR8wbI6XV9fjNm9Kxcy1IDcri6uY3bx4Ii1R8Zt/gvJUWmY68erHZgNVzC4L0EvxDBV2KOSgCpCcgVvRUy7CsOMXJYdX2I1hxfoUeDkSjbeLQDL+miBOHZhhWLfSPyuN47zO3Ykkzy+SgJU9H6V6wTNDh9ioYWQ0TiSWuWj0cVqkiolBRaIlpY8SM7rpyg/L0vGwUXTIAk5dvUyz3NQNXQLO20up606pZBAGw+7Rf1CIslpEc782n0ILWapl+KQn44NfXIqGPev/IOLsN9xePklyhZzsTcba7R1duiRriJbxhfHZQHodaSTkvrNoq5Ue+lTUMWENzS2eOQVaqg2n1zzJBh9OrEOvVMFo9HFa4blYLFcUCMWuMmKk14W4567dSFQe/hD52/OHGPEk5aLMIzN0Qz5sFrVUPvqJTWoTFmtu7gwYoOdl+qQlG64qpsa3LL2GTBbnJTjx3sxRoXQplv6E2dkV8864CXdmslSFiojVwoQOyXiMiXF6FWK+G0erhsMJ1s1KoKFaIWWPETK2Jks0H/SYE34FZznVsFoFxcZ7z/t6Y/tha8w33b7KKTinhO0DJeVd8jRrfa6xnxaTFkJGa7My6zwuuHYHCkf+BiUMzcPUTO8Le+0eOQFc2b2VINMTqo6kaRgtaPRxWuG5WCRXFEur+6CjFzIcocGUqDsyl1fUAeieqXYuKsGHeZNxdOMy041hYPDpo4C6rcTN9984rhqH6eKvm31738VFdk7CoViqG0gL3Fehd8b3GYoKsFox0/Yr3eaFMAzYtjBqQiikj+mHvseawCLexIt6eR9+pQc/5myUaaC6n/zV2ORMldVcCzy/wPYoEWM85GhE9HHImgw3yVXfhvm5WCBXFGjHrGWF9iNIS++BHEy/C1FwXmts68Zu3qrkFwKRijHF2GyblZOLBV6u4j50FV5oDC4pG+n1WWl3P3E79oowkXZPdh4f1CcmVbD6ItR9+gY5zHqbVv+819njAfY/MdP1u/ORLw/YlPrdGGtM84TiefBQpV7ZaDkc0xuojuRpGD3o9HOG8blYIFcUaMWuMNDMIb2WmxGP3kmK/hMZpedlYtf0IXiivwymfihQ13QqpgdnMUNGyGy71e2lZc0XElywzJUHX7xvRCI+3dFa8xg9vqub6njhQXpfXO/AZOeDtrm007B77riLZtVr8n8tsZyKWzsxFRkqCX3UTS0O5wHLrwyfPMAmLBRpOSjkc0Rqrj8RqGCPQW9EUrutmhVBRrBGTxkiPR2DSePjdrLFI6GMPSp5cUDQSC4pG+n3mbu3AwleqVPfpOzCbGSryBCT/eTwC06QoltU6k/QZI+GEN4HTZuutAnq+/CieLz9qaBO6xa8b14Dx5u8M9lOddaX1PndSqGm1BD7Tq2+ZIOv1k9P7qKhtNFTlFKBYfTQSqZ6hcJeGxxoxaYyweiQyUhIkE+nSk+JxZ2EOFhSN9L5QTzLqTfgOzGbGGxds2Ofnek9PYsuhuKtwGKbnZaPHI8CV5tAt7BUJyOWfmNGETg9rP/wCK7ddEKpTisUD8lotcsmhf5g9Foe/OY0Xyo/6ef2cSfG4s3BYULm1Ga5sitVHJ5HqGYpUQyoSickEVtZVlVieGWi4nDrbjRVlhzDu0X9iy/4T6PEI2LBHPS8gMFlLLcEL6F21BxoSfR3qNmTgBHuKUeRMnHC21rjRcc7D9B01QvXe2tAbltCLVPIlD2aVjbd1+et9yO0/PTle1pBSSg6dv74SF7tSsXfpVCwsHu197nqf98O48vHtfsmjoisbCDaMtLqy9SQ9EoQZiIbUrPxBmDKiHxkiJhGTxgjrquqtqhOKE0pbZw/uW78P92/cx+RBEN3sm6qOezsFyw3mIqvnTsDepVOxYd5kPDknHxvmTUbJrEuZjp8H30FenLDkkkDTk+Pxy6tymPftEXrFrBZcO8Kgow1GvH6/m5WnauCx4JubwIuZuUAsOPrYJUXj1JJDgV4D7J/VbqwsOxRkwEpVsxhd9aDXwBG1ScR3TIsxSRBE6InJMA1L87oURxxz7sG7+9lKDV/86Kifm92Vloi5k4bgrsJheLPqeFCioVxTONGQMQrfQR6Q7yIrkhQfh4emj0F3j8Cs5JqV6kBWarAsvVEMSHNg2Q2XYnpeNux2m2GCY1pyE7Yylk+bhbu1UzLBkzU59OFN1czVLD0eAc6kBDw07WI0tXUhs29vLoseV7aeDrmRrk1iBtTojYgEYtIYUcqUFmGVwOYhaKXZ2uHX2yQzJQGz8wdiaq5LccDQ2wk4OT4O7d0Xzs93kK9gqP4QPQZTc13Mxoj5MX71niQpCXFBoQ41eI/bTKl9HsqPNAQ9Q6yGlZIR7usxajnbFdQw0HXeKNQ72fHG6qOhj4gZRgMZaESkoClMs3r1agwbNgyJiYm4/PLLsWfPHtltX3zxRdhsNr//EhPDn3wm514OJ81tXXih/Chaznap9uRQC+8oIRoifR1xeOB7o7BrUZF3YOKpZpiUkwlXmrq3Qwz/sOTIaOVkq7ywnBje+t2NY5n3pyU3gUdq32xW7TgSlONhpEFYVuPGPesqg8KT7tZO3MMoTBYYUuk65/H7NwCmWL1a+EmA9vyfUFFaXY8rH9+OuWt34/6NVZi7dnfQ/dOyz2gRjyOiH27PyCuvvIIHH3wQa9asweWXX46VK1di2rRp+Pzzz9G/f3/J76SlpeHzzz/3/ttms4aLUFx97f6iEfNfrmRO8jQLHlEnI+TGz3T2YOW2wzjbfQ5LZvQaN6wT1uGTZ7Cnrgn//YNc3Ld+n+K2vjF+NY+UVuSE5bSGtwQAcy4bzHUM4c4VCcTXKzA11wWPR4AzKd6Qjs0b//WV4t8Xv3FA8Rkura7Hsrdr/EqTlST+lWC57lbWJmH16vB4TqJRPI4VCktFJtzGyJ///GfMmzcPd955JwBgzZo12Lx5M55//nksXrxY8js2mw0ul/YurGYSZ7fBbrOF3RAREd3gu79ohN1mU3yhfF3Z7pazQT1xWHl6Zx3GX5SOGeMGMoeAVu04glU7jiDbmYhfXpWDV/71dVDCa0ZyPJbfNNZvMpEzorLPN36T2g8r3mtX24jCUVlBf+cNb60oO4yNn3zF7NJm9Sr1sdtwLgSrdHHSWfzGgaCJXys29Ja8qz1np9q7Je9Dj0fAqu2HsaLscNB3tJZYs56XEedvNKxGg8cDlGxmD7dEq3icGhSWily4jJGuri7s3bsXS5Ys8X5mt9tRXFyMiooK2e+dOXMGQ4cOhcfjQUFBAf7whz/g0kuNrwjRihUFlO7+/z5BR/eF0lq5F0pc/VfUNurq1vrwpmpMC2hoxoK7pQPP7KzD6lsK4EyKR8UXDQB6j2nycGnXulI+wEPTx2DuM7ux5yh/FYvI/PWVeOyHYyWv1SPX5+IexnMTz48154DVqxQKQ0REgCiNz2/gySlPXp6TgfeqT6p+v+KLBj9jRMobogTrCr7pDJsWDut2oURNoVc0Gu5bH/zMKj2bsSgeFw15Q7EMV85IQ0MDenp6MGDAAL/PBwwYALdbuoLg4osvxvPPP49NmzZh3bp18Hg8uOKKK/D111/L/k5nZydaW1v9/jMTKwoo+RoiQO+AdM+6SmzZf0Jye72DSlNbN1ZsPYSK2sZedz5joznxxS/Z3JsrMWpAKgpHZskaIiJytfu9PXsydJ3LqbPdsjHx6XnZuIujOSGP5oiZOTGhZmHx6KB8qoyUeNxVOAyOPnGMe7lwJcSJgtc7wVJizdq6QG+LA6Mpra7HfAkjgxUxH+Y3bx7Am/v8S5ljTTyOtWzdynlDsY7p1TRTpkzBlClTvP++4oorMGbMGDz99NMoKSmR/M7y5cvx6KOPmn1oXiblZCI9Kd4yoRolFmzYh1WwYcY4fwv/aEOb7n2LoRdexAnj1uc+9n6mxzU6ZXgWVu2o5f5eIHIrap4qIIDdpc1SpWV1RNVU35YHW2vceKvqBJraupgbLQIXytGNEIFTMrZdziSmfbBuFwqMVOhtauv2tqIQ37upua6YavQWq2GpaILLM5KVlYW4uDicPOnvoj158iRzTkh8fDwmTJiAI0fkJ70lS5agpaXF+99XXykny+klzm7DnRyr5XDiEYD71ldii4+2CasCbCjRk7E/eUQ/pDN6ZuRQWlFr9WCweJ/kqrS0nk+2MxELi0dr+i4vgaJicXYbWs72VnjxhgAzkuMxebhxDSGVVvDi/VTCSqqtZin0Ar3v3T3rKvH7zTWYc9lgb6jLl2hs9MbqGS4LswYQIQ+XMZKQkICJEydi27Zt3s88Hg+2bdvm5/1QoqenBwcOHEB2tvyK2eFwIC0tze8/s7n3mpFIcbC6n9mxAUhPMt4BtWDDhZDNnromy/WQ0eMajbPb8NhN7GW4SkgNUr6l0TywurSlyopXzy3g/r2Fxb1l1wuKRsKVZr47PVA1Vc+k+ZPvXOSd6PSEEFlKrMX7qSQhb6WJ18yqK/FePV9+FCvKDiM9OT4o5KpVHdfKsL6bb1Ydp1CNReGeJR988EHccccd+M53voNJkyZh5cqVaGtr81bX/PSnP8WgQYOwfPlyAMD//M//YPLkyRg5ciROnTqFJ554AseOHcPPf/5zY89EB2IGthahMyV3vDj0PfbDcdj3ZTOe3lmn9RCD6PWQ7MMauw2dBvWQMRo9rtHpedlYc1sBlryxH83t5zQfQ8PpTvR4BMmJyJkcz1S5w+PSDiwr/MG4gV6l0mxnIvMktLB4FO738Ygsu0E98Tad8Xx86ZeSgIdnjoHLmRRUsaVn0nxmZx0mDMnA9LxszXkJPCt4pSotq1VShDJptOX887CweDSGZSVHbanrpJxMZDJUeTW1dVOoxqJwGyM333wzvv32W/z3f/833G438vPzUVpa6k1q/fLLL2G3X3C4NDc3Y968eXC73cjIyMDEiRPx0UcfITeXf2VqBnpitwuLR2HjJ1/JDti+yqbT87Ix/qJ0PLyp2k/2PTMl3u/fvDz6Tg3++OPxmr8fCrQOvtPzstHe2YMHX/tU82+XbD6IZ3fV+U1IPPdcaUIMNDya27oUyy9ZK3mynYm495qRqKht9O57aq4La24rwOI3DgQZHOnJ8XjsprHeCqXyI98y59z8/sY82Yla76Qp5uxozcnylfhnIZQdVgPv/cShGdh7rJnpd0OZNCqGaTZ+8iV2LSqKOiNEJM5uw+z8gUy5YNFUQRRNaIofLFiwAAsWLJD82/vvv+/37xUrVmDFihVafsZ09LihbQBGZKVg16Ii76CU1dcBCEBDW6fkgDRj3EBMy8sOGsSufmKHZmn3+pYOQIBqsprToATdQGEqFhpOd2JT1XHv+X5ytOm8AJmAKcOzMFlGXbO0uh6/26Jf0TRQ/IvnnqdLaKWIx8YiOBdYVihnUIjYANwwPhtXP7FD0qjZ+/BU7P6iUfb6TRnRz7DBVs+kGegVu7Mwx6/1ARvyE6eUsBWAkBgiUveeR7Bt4tAM1fdIy3smR6wkb7ImpkdLBVG0EZO9aUT0uKEFAAs2VuGXJ1q86qUiXec8eKniKN6rrsfQzGTcPmUYEvr0eosCVUEBcOl6SNHQ1ilbxSEOxXcWDpMUmuLBBmDV3AnISHHgm9MdyExOwH9t3IdmhdCA3dbrnfDuwwYIPge4aketd2XvO3AbWW3gq1eR6ojnuudS58ZzbIFaGeLqfdX2I3ihvM7PQBSF357ZWaeqlVA4MljUTYRnsFXS8NDbAwm4sApdUDQSL3xUxxVGEiX+A/MbpIwBMUHYd/9mhGjk7r2aYJuv8dRwulPV0PAIvV7T5rZuwxJdtRipkaRmKj6vcu93tFUQRRsxbYwYsYLsVS/N8JbaLt9Sg7Uf1vkNNr/fchDzvpsTZLSI6JV275+aiCkj+il2Op2a68LGT77SPLHYbcCquQXe8yytrsdDr+9XNESA4EFakPjxU+3duGddJdb4DNxGVxuIq8NeUTZ2pLrU8h6b+NvL3q5GwdBMuNL8S2cDvWRaJbzFicPdcpYpfg4or5iNKFUWDSMxKZlHcE7qnOWMASkjh0fsimXS5bn3/uqpAko2H+R+t2/MH4Tny49KLjAEif9XQ0vTx0jIwREJFGyUWpRZKZGZ8CemjZGjDe2G7GfppmpMy3Phf0sPSiapeoReo8UjCPjtTGnlWT9p99YONJ3pxNHGNry0W7lkNz053mvpq8XM9UwsHqFXBhxg8wxocTMven0/Uh3xgA0m9njhG4gCXdx6vGkv7f7Sez+lBnW1jslK7vYt+08E5SOxomSUKyWGnu3qkQ39Sa1CxTAVj9Hte86TcjK5DEFWBVfWSZf33l9QT1Xu3SRHca4Ll50/Z6kFBgCma6nFIxCpaqZyz6vLwkYU0UvMGiOl1fVYyR3DlqaxrQsfHWnA2g+Vq2XWfngUeYPS0T81UdJY8A3hbNl/AqvfVxcgO9XejVXbj2BB0UjJ5nC+6PXAfHO6g2l1mJbYB60d/BUwLWfP4dbnPkZ6kj6NESWmjOiHf+z9irsUWpywjcrHqJcY1LVKeC/fUqOrUkttxSxl5Da3deI3b1VLbq+0Cg3c1+GTZ5iE9r453aHJEFTLl+CZdEOV+OhrPMTZbYoLDPFvZTVuSUE6LR4BI5vshSPME8pEZsI4YtIYMSMM8Ebl10yegPs3Vvn9W2oFxju5rCg7hA17jjFVHuhprtc/NZFpQtBiiPhihhKuOMC3tHehQ0MptDhhG5n8JgD4f6/tR9ElA5DQx65JwnvL/nrNhgjPitnXyO2VMd8n+/7IJf1K7auitpHJGBENeK1IfZd30g1F4qOU8aC0wBD/NmVEP0UvCo9HwCg1UymPU2ZKAmbnD/RWWZllIChdM8KaxKQxYoboUFsXv0YJcKHnzMLiUVhQNAr/rHZrmlzcrZ3M7lPfFzUpIU415OI7ab0r0xvHyojD3Q3jsxUnUbnv+k7YRiR1+nKm8xwmlPwf/vTj8dwS3j0eAb9964Cm31VbMcutaFkMeUcfO6bmsikyq11P33NW6k+jhpQhwTvpGn3vpdATTjDKI2BEkz05j1NTWxeeLz+K58uPWjr/hAg9MWmMGO1uzXYm4rJhGfi/GvVOpnKsKDuM58uPovOcNqNGhNV9KiKGbuTKTQMnLdbVYUqCHW1d1hBjczkTsXRmLko283nD5FapRvefaevs8RqSalVRvseyavsR1QRikUCdD6VJTymHwpmUoF7O3Nrpt2pWctUrXc/Ac9ZiDCh5f3gnXZ57z/NsLJ05BlmpDkPCCUZ4BFjf8awUh58WDo/BCkiHKonYJSaNEaPdrY9cn4uiSwZg+Xv/1qUN0KIzPCGu5J7fVXd+X8o6HkDvROFMSsAjP8hF+ZEGbD14Ei1nL4RZAiet5ja2XIt2Cxgi6UnxWH1rASYP15Z4Kjdhy+Xe6NGGEAAsfuMAVs8twOpbCoLE0wKPpbS6nku3Y/UtBbDbbaorZrUcCtYeTuIEzpIcypp0yGsIqnl/tITFWO+9rwGs5vX5WWEOl3fKbFi8Vc7kePzqtU/9ujDzGKy+8C6giOjEJghSxZbWorW1FU6nEy0tLYb0qdmy/4TmDHdfAstdf7+5RjWJNRz0dcThsRvHoV+qw29g21rjDp4A0hIxd9IQSenoHo+AKx/frivExetN+MHYbLx7QLnZntyK2nfFVfLOZ1wdZ5fOHCM7SYhIKbCKLeH1vFTZzkQsnTnGq+ei9z5kpsTjk99OZUo2VNtvX0cfnOlUzwnaMG8yWs52SRo2UvdH/H2WydconRHxfNWMBSnlUlYFVtG4A9SfUbVzDGVYQ+m41dpf3FU4jOtdA3qfF8rxiE5Y5++Y84z0nK/5N4I7pgxFRkoCejwCtta48e5+/g61oeBMZw8WbPQ3vtKT+uDU2eBJxd3agRVlh3B34TAUB8T9jci1GZDmwE8mXoS/qMiVixPBk3MnYMbY7PNlqxcSbfulJGBW/kA4k+KxYc+XftUxUl4E3sExK9WhOnlLucSfsmuvVhJxt3Rg/vp9eOq2AszKHxT0d9778LtZeUyrTpb9qhki4n3TopnCGmKQy40Qz4HVk8ATIpL6buCxSh27llJTK5TVyh33gDQHOs55JEO64n19s+o49++RRDsRc8aIEROq6JJ94aNjeOGjY5oalIUbKUPEl+fKj+K5gCQzIwYMd2sn1u1R1k4RESeCGeOyMS3vQgnjm1XH0Xg+EQ7o9ebINQLr8QhY/AZ/kmf/1ERNbnLfibKsxo039h1nzusQUSuf9HWNqzHvuzmYMW4g07Z676/vBL73WLMhFRlyyBkuPPsSQ5R3FQ7Dm1XH/TRa1BJJeZ4NnsRSI8tq9SJ13B5BwK3Pfiz7HQG9zegyUxLQ3NZlmiAbwUckKOnGnDGiZ8D93iX/gW3//jYoLyCUhsh3hqbjX8dOhez3fFdjRg0YLMJcDxSPDpoI9tQ1Sno4TrZ2YGXZITx1W0HQZLS7tpHr/ogr++a2zqCQBYub3PelL851YdF1Y/DU+0e4pfjlJuvS6nqUvPsZ837e3V+PiUMzmFbSeu+v7wS+iXF1HK4VsZ6yUy0hFFavj1FltUYReNz/8w7bszc7fyBekFCPDYQk2s0n3CE/Vuzqm0QXegbc7f/+1sAj4Wfed3Pwj3sLsea2AmQ7Q7OSEAeSR9+pwcShGch2JnJqmGpjWFay9/9Lq+tR+Nh22Qnd9xh7AixFHvn3wBLgwElBNMxKq6XDcaXV9bjy8e2Yu3Y37t9Yhblrd+PqJ3bgYlcq1txW4M1r4MF3shbd9zwqq2Lp+BaGkmwxcZH3/i64dgQ2zJuMXYuKvIObluTQUCFex8D729zWhRfKj6LlbJeiISL1XbVngxUjymrNoscj4K0qttL+qbkuPHVbAVwK4xRJtJuP2c+rkcScMaJ1wAX0JSWKjfK0YkPvKrfHI2B6XjZ2LSrChnmT8eScfPyo4CJd+1ZDXI3tPdbslaHWcv1s6M31YEEsG/yfdz7DPesqVUMTvivG4F9lIyMlAf957Uhs/ORrWTc5IG30qL30ALD34alYWDyaS2FW7HhcfqQBy97+TPMzOH/DPmxRyGkSPTrX5bm84QBWRg1IxZSAii2198yG3tVZqFfEamEQAcBv3jyALglhPLXvAtLPBg9WNuL21DUxCSRmpvS2qPAdp+4uHIbMFP/n3uVMpLJeEwnF82okMRemEZPWeBp2GYHU4MZDoHtWdJ+WVtfjH5VfG3OQKnxzugOz8gdpkpQXJ6WSWXmq5Y5pSX2wYEMld66FeIy+TBnRj0nhE+gVZPqLyrZSbnLWl35qrgv3F4/CgqKR2P1FI+a/XKmoNhvY8VgPggDct74Sa+wFktLugY3cArsrKyE1MfImh4Yqps2SM9bU1o3Jy7fhDzfmcfWmMSKEwiMCF8o8gB6PgPIjbF7GG/MHBSUlTxnRD7+ZmWv5vIVowmohPzVizhiJdHwnW3ESDBXipOOb2La1xi3ZWTQQ3+7Bh785LRlyEffRopJcy3KMIpOH9zMlwVi8Dz0eAc/vqlOd4AINycKRWXjsh2MlyydFzFiwLH7jAJa9XaPqaRJ/OzkhDu0y6sJq8f6puS48UDwaL5TX+RldmSkJKJmV51ftFKqYNmt4o6mty7DeQTywGnFSZfk814zHkJG6P0oEVuH5npsVJr1YwcohPylizhgJ9QRuNL6dhs2QtZcjMyUBHx7+FuVHvvUKqYkrHrGbauDAOOcyf72SrTVuRR0Lp0y5MSvpyfHweAT0eAS/lRlv63oW+qcmorS6Xla5VoqtNW6/wdgM8TQ1eo+V7Xht6A0vnj1vjPCUvipNYI1tXSjZXAP7+chlKMtYecMbWnrT6A2hqJUDA/quGY/xx9KhW4SSUa2FlUN+UsSc6FlFbSPmrt2t6buOPjZ0nhMMkwHXgg0XhJI2VR0Parwnh9ETXF9HHP73h+O8ZaNqKy21Qe2B743C33cfY27ap4SUcNvWGjeTR4CF7PPqmvet5zNw+qUkYM9vixUFtBpOdxoWmjGKhcWjsfGTL5lX4SwTmHgFnApeKyXRMa2oCZ1JIQpy6RFJ03qsUloqSga92jHI3RspETYecT1xTLyrcJjpTfAINkL9vMpBomcy6HFJ5Q1yYt53h2PR6/t1hRL0Iq7WWC3apTPH4PYpw7wKkVtrTmLLgXpdxsmZzh7ct34ffvn1KSyZkavoglXrVWEDDDNEgAvCbSLixFm+uAh76prwXnU9/l5xTPP+l84cg/95l9+71tjWJRmf9b12rCWxoWRYVjJ2LSrSrZPhi/h3Ja+SGTFt3zAIKyy9acyoDJF6pypqGzXnAfBqmPB4XsUcI2qCZx1C/bzqJeaqafS4pPYeO4W9x5pMNUSuH6fc7dR3sJmUk6lYLipWLPysMAcJfeyYMqIfHH3s2LxfnyHiy9M76xSrNAC2RCqjDBEpRPe1GCa5TscA+aOCQXAmJ2j2sKgZw1l9HZr2ayb9UxO9E+Os/EFBlTO+mBE6dLecRUVtIzZVHUdFbaPu7H8xDBJY3SGHVG+awJLVUFWG6MkD4Elo5PktINjrasXS0Vgk3M8rDzHnGdHbBvzZD48afUgAevMdHrtpLDrPefDOfrfq9r0eDrfqyjKwYoFl1crLwler4EyOx+Th0pPU1hr18zGTwFWfnmfgH5XHUXbwG83HomoMa7g5zqR43U0WpdCSA2BGMlzJ5oN+xqoRq+7pedkoumQAJi/fpmgIZ6bEY+LQjKDvsiqqGo2ePABeQ0bPwi3UarGEPOF8XnmIOc+I6LoCtGllGD2RJyfE4UcFg/DID3q7XbKujLP6OlQTcdOT4zHVJ7PdrITXznMe3Prsxyh8bFvQSohHKMlMfFd9ep8BpXJcNXy7Hvd4hKAVfwNjV2Rf/nZrgVdzZmHxKDiTgtcY6Ul9kJ4cz3y+Wt24ZiTDBRoLRq26E/rY8Ycb82CD/HPQ1NaNq5/YEfRbrJ4io9Gj38JryOjRZAKUtH+IUBOu55WHmPOMAPLZ6uEgPs6Gf1Qexz8qe3MFXGkOpCfHo6W9WzHpCAJUj/1Ue7df7NjsEi53ayfuWVeJNT7uP1ahpFAhXoNwPQMlmw9iWl62bGnmnMuGMO9LfBYCPVILikZhd23jefXZ3kFo8vB+2FrjlowfS6HWm0WOiUMzmJOlbeg1mJvbu7mSwo1cdbM8B6FsUKeGnjwAHg0Tlt9ivV9WKR0lrE1MGiOAtFZGOAjMPznZ2ul9yZUGG9YVtO9AEKoSrsVvHPBOElYbiHyvwdRcF1IT41FR2whAwOU5/WC39R5z5ZfNeGk3W0M/HupbOrBq+xGsLDskWZq5suwQ+jr6qHbHBYLDcCJxdhsKR2WhcFSW3+dyE69YHZSRkqDbjbv3WDNXPtLPrshBy9kuvFV1gstoNTK5VS1kY7WQg5ZOwIA2Q0bpt+ZcNpip55JVSkcJaxOzxgjgrw44KSeTSzPCLMSBz5kcj8Q+cX6Jkr6DTe8Eqo7vQKA3X4aVU+3d2F3biMJRWZZJyAxc9UlpLbxeeRyPXJ+LGwsugt1uYzJGlETB5HihvE6xooG12v6uwmHcK3Wz48esxmdKQhzi+9j9qp4ykvug65yANo7r6Ss+p+ec9h5rVjSGrKZWqfU+ajFk5H4LADZ+8hWzp4UglIhpY8QX8YV7YGMlUwKpmQjondDnXzMEmSkJyExJgMuZ5DfY8LpcAeWVkdFUfNGA053dWPY2e4dZMxEALJ3Zu+rbsv8E7lu/L2gbLR2K197+HcDWW3L5dXM7U36MUs6JADBPxlNllC7V4FHC5J3kWa9bW1cPEHCeze38VWqi+JxeBddIU6sEtCuaajFk5H4rkkpHCWtDxogPcXYb/nrLRFyXdwKL3jiA0x3h0xIBgNXv1wK4MLD6vtRqPXbkXPihypWo/bYNq3fUqgpf6TWIbAAGpDkw57IhWLlN2WVcsrkG+75qxnO76iT/Lh7Lsrc/w86HipiMvck+8u49HgEfqyQJpyfF60qAFclMiYe7tQMVtY2KE4kej4GWSZ7FSLYZIMAnXv/mti7MX8+nRip1TSJNrVIvRkmzaw0ZEUQgMafAKkePR/BL+usRPHjq/S9M+S1epNQRAciu8EXERFI5JcfdtY14+eOj+OBwA9o6+UINamScT0xUItuZiLPdPbpDY/d/byRe+eRrQ9RVRRYWj8bFrr6SvWPk7gcALN9Sg6d3Shs7QK+OjNGeNyUpb60eAx6lTrnvAtqTHln42y0Tghr8BZKeHI/Vcwu8RqPcNVk6cwxKNh8Mu1plpBLKpn1EZME6f8e0MSK+QFtr3Hj1X18zJQ2Gi8DBcMv+eizYUKm4wkxPisfPrhjWG9dt9R98fzAuG69XHveLk6cnxaN4TH9vZY9WWBMwfzvjEvx+y7+Z9pmRHO8NX4WKNbcVAADzhM4in+1KcwCw4WSrcXk7UgaCHmNC7TxYJma5Sf+6PJdhyeILi0f75Zwoke1MxA3js/HMzuB8HfEMfnFVDp45b0iyGp+xCBkeBA9kjKjA24nSLHhXixvmTUbL2S7DG7/5Ho9TobSYhTsLh+EFhgnn9slD8dJuNln2v90yAdPysrFq+xHmCUgv/VISULHke15pbLXBl7Xv0cLi0Vh5/hyMNEhEAwHQ17+E9TxevvvyoIodX6QmrT11TZp7Q/kiPqdGGafiNVk6Mxclm0PTQTgSMbLDMhk1sQH1plGApxOl2SQl2NHe5WHe3t3agf8tZfMmaMFb0QFtbvVfXpXDEVdn33vJ5oMoznVh4yfGl9vK0djWhcnLy/CHG8cyDbSsyY3DspLxl7kT8Js3jctLChSY4ulfEjgpuFvOMv3m/PWVeOyH8tdGKi+BJafEeV6cTSnMZ7SXTLwmGSkJzH14Yg25cVOLDouRRg0RHcScAqtZkuha4TFEAKDpTKfp3pzm9m5clzcAfRP5bFUbgLc/rUd6ElvPD5utdwBiob6lAy9VHA25J6uprZtZ7ZPVCCurceP+jfv8DBEbgKR4u2a1S5FvTndwVYaUVtfjyse3Y+7a3bh/YxXmrt3N3DX41Fn2ayOipH4r/vuxm8biv6+/lGl/yQlxuq+ZL9+c7ogItcpQo9ZkD+gNZ7L0DRKNmsB3mfrZxDYxZ4yYJYluNqLMc2ZKQkh+773qk9yrdnF1yVot8veKL3HDePZV0LGmdq7jMQoBvUJu5YcbFAdbcdWvxjv73UG5PgKAs90er0fKF56psH9qIpdRJDUpNHMq5rJOQiIszbtcaWznYDt/cYwyF6KlWsZoeJvsyWGkUUNEFzFnjFhJJ4AV35p9lzMprMfCQmZfx/lETXVe/dfX+K9rRzJt2x7GBONT7d249bmPceXj22VXbnF2G5bOHKPrd2w2oH+q/7VzORPxt1smqPYkcaU54BEEuFvOIjMlQXWCfme/W3FSYEFr/5HpednYtajI21Nnw7zJ2LWoyOuin5STyWR4t3X24IHi0UGGjRZcaY6YEOiS6omkhlE6LEYZNaFEy/Ui+Im5nBEtKx+WMlUASIiz4dfTLkFWqgP9Ux24+8U96Din/8H1rdnv8QghUVHVgystEXMnDWGSim5u78Zz5XVwJvUJksYXEbVEdh1hU501k3qV+HhGij7FWUEAfv7d4cgb5AzKWbDbbYp9QjrONyw0khRHHFPZtxYjX0nrIs5uw+z8gUyVN8OykrFrURF2f9GI+S9XatZxmTtpSNSHZLTmahilwxJp4nKU2xI6Ys4zoqUT5eWMq6WuHgGAgBvGD0ThyCxMGmbMKsu34Elvx1kz8e0YOiwrhfl7bV09XkNELkQxd9IQQ3VERH5UMIg79CWgVxhNaoVkxCD6VXO7ZM6CXHjDmdybo2NG2fPPrhjGtJ0WI19txcmqMNs/NdErPPfYD8cqduFVgueZjUTUcjW27K+XvR96ugX7EknicpTbElpizhjRMpmXfnaSef+/3/Jvryv/W4O61Z5s7fR7+OUmpYxktsRRMwiUf9YymKQn9cGAtOAQxVO3FZg2UXx39H9g95LvITOF79q5WzuxavuRoM+NGESHZibL/i0wvPHy3ZcjsU+c7t+U44rhWYZMQoFIJc4GhsDUcnCkflvu3WDBChOgWajlaggAFmyolL0fLInHLNLvRhk1ZkO5LaEn5owRQN+AxUJ9SwfuWVeJg/WnDdlf4MPf4xHgTErAQ9MuxtKZY7Di5ny8/PPLcd81Iwz5PS34Jh8CvYMOa96IyKmz5/DDiRf1ntNPxvvlEZg1UfRPTURCHzv+cONY7tX0irJDQasjLZ43X+w24JbLhyp6DHyrPex2mykeI3FSmDyin+oktHRmLvbUNTHH1FlXnL4ToBRKLQ8CDTZXmvUnQDNhSdwPvG2B94Ml8VgNo4was4nE3JZIJ+ZyRkR8m0W5W87if96tYcoLCRfiw79q+xFs/ORLvxcl3UQ3vRo/nTIU1+VlB2kxxNlt+O8f5CrK1Uuxeod0Px6jOw5LNRJ0augbE9hWXq1nkBrfG9MfRX96nzlGbUZsPXBSUOo/csP4bC6RMLUVpw3B11QLgfkoy26I7YZuWp4TqfthRNfnSOhnE2m5LdFAzBojwIUBq6K20dKGiC9S6qPhMEJE+qUkyCYh6knmFL1Lf7ulADPGZRvacThwAiqtrtdsPGhpKz81tz+2HfzGbyVqt/UaImU130iKSt2zrhJ3FQ7D1FyX3+CfpTNhVoqMlAT8blae36QgNQk1nu7Ego3K3Y8DJxaeFeeknEw8+k6N7LY8hkskTIBmotWzGCiQBxjTZM8Io8ZMIim3JVqIaWNEhKxb7awoO4xR/VORkZIQNKgYcV0XbKjEKkzAjHEDDes4HFidtPiNA7qO0fc8xZW/Ege+bsFnj07H+o+P4VhTO4ZmJuOWy4ei6E/vK8aony8/iufLj3o9DwCw7G3l37Kh13Pm6GOHu7WT6Xya2rpQsrkGdjv8JmnfSWjL/hP4r1ekvV5KHg6eFSeP4SKlJBs4uWmdAKNBtlyvZ9GMMdKozsFmwKIUHOhZJfRBxghiy7qdPDwTu78wNs4Z2MJdnCyNuK4eAbhv/T6sOe8iDpxQDp88g1U7ghNJA0lxxGHOdwajOMCzsPuLRt2eJd/zZInNu1s78czOL3B/8SgAvZPdi+V1zAaW6ClhQQDw+9l5mJaXjRVbDzFdK/E35LwbpdX1quE3qRU1wLfi5FWSZSnB5J0Ao6W0U69nMZbGSED5esVKaC/UxGQCayC8yZY2AJkpCXByyqWHk8R4O5Li7dyGyCCGJF+5XhUff9HILA2vhm/mum8CZ+FI+UZtvjxz+3ew9PpLg+S9K2q1a5dIJT6yTqBi8qtYVcIqwQ7wTyQlmw9ia42b+Vr5/kZgxQCL58eXwOvBkuDbLyUBE4dmME+ARxvaTCnBjLbSTrkEVKX5NBaSe+UwImGXYCdyZlMTibPbsOyGS5lWm+J7+4cb8wBAc8O9xD52dJzj60ujlYQ4Gzq6tf3WcQ3hEPF6rNymLnrGilxuBqs7dfJwudWwtuyTwEoS0YWf1ZfdqF38xgFd3ZFZESfPv86ZgMyUBDQxlpxLeTd42ykEGhQsK/TGti5c/cQOLJ05hunebtjzpeEJsaFKtA01UqGq5rZOzD/v6SIPgD9Wz22JJsgY4SQw4e2p2wqw7O3PmOPx/VISUDIrD3Y7uJMmtSZu9oqxRT7iKjswhv+DcdlY+2Gd7PeUBtMpw7Ow6nwFDw9ylSSuNAfSGVvbhyrxWLz7//XKvqDyTRZ8vRs8uQNSK2qxLP2uwmF4s+o4mtqkr4G7pQPz1+/DL67KwTM762Rd5XMuGyKZ1C0iFy5SgzfRNpImK6lQ1VN2W1A4KiMlHjfmD4IzKQE9HsHS52QmVs5tiSbIGAGf63n6pQP8Xk7Rcl61/YjkoCgOolKVEGtuK8DiNw4wT0qOeLtmD4dVSE+Kh80moLmdv89M/9REyRi+Er+4KkfRnTp5RD9m4wG4UMosriYD5/aTrZ2WlenXqs/k693gyR0INAKl7p3N1iuBH4jofXj703qsvqUg2Og7vyjoZPQu8iZgsm5fVuPGg69W+ZfaJ8XjzsJhWFA0StMEHo6EWV8PwNYaN96qOoGmti48V34Uz/kkTVNogjALMkbA53p+4aNjeOGjY34vZ5zdhvuLR+FiV1+u0kFxAHh+Vx1+v0U9ZyDSDREAmvqGiO74xtMdWLCxiuu7b39aj4emjwkazH0H/DuvGMbURweAV1Plyse3K7rwkxl7ulgZqYoBlo6+dhuwaq5/TF3Mvwi8ZlKGiPdv6PU+ZKQkYNeiIskJmjXnhzcBk3X75yR655w6240VZYfxwkdH8dhNY7km8HAmzMbZbWg524UXyo/K5oFRrgRhFmSMQFvZmtTLqSW+GGe3oT+nUmksIV65H4zLxn+9UsX9fSkXfWl1PZa9XeOnXJqcEIf2LnnjwXdiZnHht3X2MDdYtCJS+QI9HgElm9U9iH+5OR8zxl2YsJTyL1j45nSHrKvcrBJMlv3abMreplPt3VwTuJzBFipDgCVPZtnbnyE1MR4NZzojIiRFRA5UTQNtZWtiP4fFrx9A+ZEGyUqPwMoNI38/VnA5E/GLq3Kw9sM6zWEGX2NTFDgLlFBXM0SACxOzu+Us0+9OHh45FQiBVU9SFQOsHsR+Ac8zb9JrIErvh1ny4mr7FcAW9hLA1sPECr1QWIxsd2snbn32Y9l+QgShFTJG0Ot61mrcnzrbjVuf/VjTSyl2LXW3nEVfBzmpfLEBuP97I/HBr6/F25/qG+zEyUyrwJnvxFxaXc9RhhueFaOWX119S4G3l4tvTyBftEpkaxXMYi0rNasEU26/A9IcuC5vAPN+WHqYWKEXih4PMRkkhF5ifgYsra4PEu3SgvhSrr5lAjJSHKphGt5EzEggPTkeV47Mwrv76yWrH3iusQDgyW1HcOjkac3XKNBFzyNw1i8lAQ/PHAOXM8l7D+Xc6FK/OyDNgd1fsOUzpCb2wekO/oReKRYWjw7qXWRXCCd4S58ZvHhaJbK1eP54vRo8IVKeBNHA/R5taMeGPV/ivWr2Tt6A+kRvhV4oWj3EVixzjgbV3Fgjpo0RcaVshONT3MeCDf7lk1LJZ6yTWiSxdOYY/KwwB3F2G2bkncDDm6r9yjZdzkTVMkwpeAd9kcDJrMcj4B//+or5+41tXXA5k7x5Crx5D3MnDWFKiu13Pjmz8PFtsmWurGQ7E7GgaCQWFI3UrCOhNIhrzc9gkSIPNJjUesbIHadaCaaWBFFxv6XV9VhZdkjTe6s20VuhF4pWyXit5dNmES2qubFGTBsjq7YfNlzrQa4N9+pbCpCRkgB3y1mUbD4YVYYIAGSlOrzeg5LNB/0m1syUBCydmYtpea6gVbtZ+E5mWr1QvqtQ1ryHzJR4/OHGscwlp7PyByIpIQ5/uHGs5mZ9InMuG+I1HFh0JAInfLVBXKtENsv3npwzAd+0dnh79dw+ZRgS+khHkbVONnKLALEp492Fw4LaBYhoTcL1NdDMMPSMRK9kvBV6fIU7CZjQjk0QlIrrrEFrayucTidaWlqQlpZmyD57PAImlmzVVGqqBSVXeTSwYd5ktJztkhwIxGH9qdsKAPCLvfHQq/GQgwVFI7lCK1JsmDfZO6lvqjqO+xnKilfcnI8bJwxCRW0j5q7drbr9yz+/HHabDVtr3HheokyUhyfn5GNW/iDZvytNhnLXyffesRotcsh974bx2Xj703qm/fEcZ+C5X/n4diaDUuq3We+n3DEBUL1m4rkB0gZbqCZSrca77/sSDtTusWjQ7VpURCGbEMI6f8esZ2RPXVPIDBEgug2RbGciJg7NwNVP7FCVz961qAi/vCoHT++UV0zVQ8vZbqwsO4SLXX0xNdeluaQ0MHGS1T3uSuvdTkyKVrrvGcnx+NWrVczqvWqoHaNcGINX+lyrRLaSFDnLSlaPRDtPRY/Ub2tZ9YueJ0C6bUTg78h1pVYLWRlN4H3KSnHgV699ipOt1u5gy9vlmbAWMWuMWMGlGC08cn0u9h5rZhoIdn/RqLs6RgnfSSk1MV5TSMgGeCeRitrG3gG5rwOuNIeiwqozsQ88goAt+09ITrCBGKlBoqeZmZZBXKtEtu/3xJWsWjmraFzomWx43ncpw4bVGF06cwyyUh1eAw2AqkCeEYae0QTe32U3WL+DrRWSgAntxKwxkpVCQmN6sdmA1eeVNjdVHWf6TkVto+k5I+KkVH6kgfu72T6r2UCXb3pyvHcCkZpcWjrO4dZnP4bdphxvtwFIS+qDlrPGVNAAvZOg1skgXIM4i7fC17jQc5y8iZ+Bhg1rToeYxC2i9rwbaeiZiVW8NkpYIQk4ErFK5VFMGiOiAiehD0EA7OdzDNlf8NDFq/5ecZRre7EiaGuNW9Kt3nLek5GkotaqFpITAEMNEQDI0GFcGzGIaxnQAoXn1LbTc5xaK0VEw0Zr8m40rdat4rWRwwpJwJGGlSqPYk70TEwSYx0Io5nkhDhdslyii7nHI3gHArn9iQJWU4Zn6fhFPs5w9obJSu2d0NXyEjq6rddzhlUVVgrWeyc3iJdW1+PKx7dj7trdXMqcTWfYcmXE7fQcp5KiqhK+ho0WcbVoW61rUZgOFWap8UYr4lwY6LkLl5BdTBkjentkRBt//sl4rL6lQLP6q6+LmXUgmDyin+KEEk76pyYy5SVYMRm5iaGBnRx6BnE9A1pmSgLT8Ynb6Z1s5IwJOaQMm+l52di1qEhVrVZEr6EnqjRvqjqOitpGU+XgowGz1HijDSu0HwgkpsI0entkRBMZyfHweASUbD6IM536Qgaii5k1rqxHy8AsxAnh3f0nwn0omsjsqy8HSktOAGt1S9ElA7D3WHOQa9/lTGI6Nt/t9OYu+IYa1n5Yi+3//lZ22xvGZ0saNjw5HVrDO4C1XOiRhNXDSayYmcthxcqjmDJGIiEuGyqa27tx33lVTr0EurLVBgK5CSUQLcZKelK8ppJtcUKIFHd5IGJJsR54JdVfLK9jGtAmL9/m57kRJ9SpuS5kOxMV9yHnndAz2cTZbZiUk4kHX61S3O7tT+vx0HTticG+x8trQJF4lz6smATMg9mGqBVzmWLKGInUicaqyCWEsQwEcj0/fHN5eCXkF1w7ElNG9MOtz37MfA4ZyfFYftNY7ws+KScT6cnxssq8LK3jQ40rzWFYUp5WSXUlAkNIvhOq6DWQSziU8xronWx4K3lYUFrJis/77tpGVHzRAKD3+CcP16/7QkQXoTBErZjLFFPGiBi/jaRQTUpCHNoUKjfCjZ6EsMAJJbCnijjBPvNhLdoYklELR2YxVU30dcThp1OGoXBkFiYP90/C21rjVmwRIAD4xXdz8MzOOlWvjZJRYyTLbrg0ZJOSEX2VAkXwVt8yIaiXkdnhCKNXhiwr2a01br9tVu04InmeWl3oVinRJLQTKkPUipVHmhJYV69ejWHDhiExMRGXX3459uzZo7j9a6+9hksuuQSJiYkYO3YstmzZoulg9eKbAGcW4uORnhxvyP5uvmywIfsxGrsN+MVVOYZOFnKZ+n0YXjrRna+W5GgD8Mcfj8dD0y9B4cgsvxdaHAiUSE+Ox0PTx+Cp2wqQLZMIme1MxJrbCvDYTWO9v2kG6cnxWBNCd72RCeDihLpq+xHZXkZmnpeRK0OWJF6eRF8thpLWiibCWvAYonqwYuURtzHyyiuv4MEHH8QjjzyCyspKjB8/HtOmTcM333wjuf1HH32EuXPn4u6778a+ffswe/ZszJ49G9XV1boPXgvT87Lxt1sKYNY1dvlMREYwNdeFNRITX2pinKb9GXXaggA8s7PO9MFuT10TkyaHb5M4rRn1LK77U+3d2FPX5FdVseLmfCydOQYrfjLer7qCt3qDhb6OPrjvmuF4+e7LsffhqSHNGzAjAXxF2aGgfTa3dWH+enNLC/VWuYiwViUse/sz5soFXkPJaiWahHZCmcthtcoj7jDNn//8Z8ybNw933nknAGDNmjXYvHkznn/+eSxevDho+yeffBLTp0/Hr3/9awBASUkJtm7dilWrVmHNmjU6D18bM8ZlYxUmGJLA6Uzsg7/dOhENbZ1BrtG7Codpbn7m6yaLs9uCEvbqT53Fg699qn58SfFo8UnodDkTsXRm7nm3uPZy0FDFrllfumFZyX7/1pLkyDsQaMmNaTjdiZLNB5l+xxfxqP/443FhS1wMVTJbKJ4tPVUuvrCuZJXQqvYqdgKm/JLoIdS5HFaqPOIyRrq6urB3714sWbLE+5ndbkdxcTEqKiokv1NRUYEHH3zQ77Np06bhrbfe4j9aA5kxbiDW2G341WufMuUjyDE114XCUdJCXlNzXZqMEanBMHDiq6htZNrX324pgN1uC3rQ/nWsSXeX2FCUf+l5OXmTHM0aCAL7sTy7q05xonEmxyOxT1xQMm+4SzpDmcwWimfLCIlzIw00LWqvWuTmCesSjlwOq1QecRkjDQ0N6OnpwYABA/w+HzBgAP79739Lfsftdktu73a7ZX+ns7MTnZ0X1BlbW1t5DpOZ6XnZOPB1C1a/X6t5H3KGCMAuQR3Y3ZVlMGRJxs12JmKyjEqiVkNJCjNXzKF8OUPxWywTzWM3jbXMasUXrZLqgfCUbJvtjdG7MjTSQJNSe1UzlKxYokloxyiPXSRiSQXW5cuXw+l0ev8bPNi8JM4rRuiTJ1fSd2CRoF5YPAr/LrmOWdExcN9SCZLiZ0oPrTixKJHiYMtLMXPFHMpEq1D9Fkus1oqy21ol1QMP3eVMxMLiUUzfDYU3Rs+1Zs09caU5uPNTWNRerViiSejDarkcoYLLM5KVlYW4uDicPHnS7/OTJ0/C5XJJfsflcnFtDwBLlizxC+20traaZpBMHtFPcwkmS4Kb3AonsKRPi5tMj5vZ1wIHpFeqT/xwHEo2Hwx7+VcoO4aG6resFKvlgVWwDrhgsKyaOwEZKY6gku2Nn3wV9mdLL6wrWQCaVrtqLnQrlmgS+onU8UEPNkEQuDyul19+OSZNmoS//vWvAACPx4MhQ4ZgwYIFkgmsN998M9rb2/HOO+94P7viiiswbtw45gTW1tZWOJ1OtLS0IC0tjedwmSitrsc95ydlFsTHgcdKNVMDQM++1fQRxEx9QHoQDaWlHkodBdJsUCbw+jS39Sbm8ihGWunZ0guLzohZqprRdB2J6IN1/uY2Rl555RXccccdePrppzFp0iSsXLkSr776Kv79739jwIAB+OlPf4pBgwZh+fLlAHpLe6+++mo89thjmDlzJjZu3Ig//OEPqKysRF5enqEno4fS6nose/szuFvVO4lGW38ItYmXemQQLGgx4KLp2WI5f7OM3Gi6jkR0YZoxAgCrVq3CE088Abfbjfz8fPzlL3/B5ZdfDgC45pprMGzYMLz44ove7V977TU8/PDDOHr0KEaNGoX//d//xYwZMww/Gb34DhRZfR2AADS0dSIrxQHYgIYzweW7sQJ5CgizoGfLGOg6ElbEVGMk1ITKGCEIgiAIwjhY529LVtMQBEEQBBE7kDFCEARBEERYIWOEIAiCIIiwQsYIQRAEQRBhhYwRgiAIgiDCChkjBEEQBEGEFTJGCIIgCIIIK2SMEARBEAQRVsgYIQiCIAgirHB17Q0Xokhsa2trmI+EIAiCIAhWxHlbTew9IoyR06dPAwAGDx4c5iMhCIIgCIKX06dPw+l0yv49InrTeDwenDhxAqmpqbDZjGv81NraisGDB+Orr76injcRAt2zyIPuWeRB9yzysOo9EwQBp0+fxsCBA2G3y2eGRIRnxG6346KLLjJt/2lpaZa6eYQ6dM8iD7pnkQfds8jDivdMySMiQgmsBEEQBEGEFTJGCIIgCIIIKzFtjDgcDjzyyCNwOBzhPhSCEbpnkQfds8iD7lnkEen3LCISWAmCIAiCiF5i2jNCEARBEET4IWOEIAiCIIiwQsYIQRAEQRBhhYwRgiAIgiDCStQbI6tXr8awYcOQmJiIyy+/HHv27FHc/rXXXsMll1yCxMREjB07Flu2bAnRkRIiPPfsxRdfhM1m8/svMTExhEdL7Ny5E9dffz0GDhwIm82Gt956S/U777//PgoKCuBwODBy5Ei8+OKLph8ncQHee/b+++8HvWc2mw1utzs0BxzjLF++HJdddhlSU1PRv39/zJ49G59//rnq9yJpPotqY+SVV17Bgw8+iEceeQSVlZUYP348pk2bhm+++UZy+48++ghz587F3XffjX379mH27NmYPXs2qqurQ3zksQvvPQN6FQfr6+u9/x07diyER0y0tbVh/PjxWL16NdP2dXV1mDlzJq699lpUVVXhgQcewM9//nP885//NPlICRHeeyby+eef+71r/fv3N+kICV8++OADzJ8/H7t378bWrVvR3d2N73//+2hra5P9TsTNZ0IUM2nSJGH+/Pnef/f09AgDBw4Uli9fLrn9T37yE2HmzJl+n11++eXCL3/5S1OPk7gA7z174YUXBKfTGaKjI9QAILz55puK2zz00EPCpZde6vfZzTffLEybNs3EIyPkYLlnO3bsEAAIzc3NITkmQplvvvlGACB88MEHsttE2nwWtZ6Rrq4u7N27F8XFxd7P7HY7iouLUVFRIfmdiooKv+0BYNq0abLbE8ai5Z4BwJkzZzB06FAMHjwYs2bNwmeffRaKwyU0Qu9Z5JKfn4/s7GxMnToV5eXl4T6cmKWlpQUAkJmZKbtNpL1nUWuMNDQ0oKenBwMGDPD7fMCAAbJxTrfbzbU9YSxa7tnFF1+M559/Hps2bcK6devg8XhwxRVX4Ouvvw7FIRMakHvPWltbcfbs2TAdFaFEdnY21qxZg9dffx2vv/46Bg8ejGuuuQaVlZXhPrSYw+Px4IEHHkBhYSHy8vJkt4u0+SwiuvYShBxTpkzBlClTvP++4oorMGbMGDz99NMoKSkJ45ERRPRw8cUX4+KLL/b++4orrkBtbS1WrFiBl156KYxHFnvMnz8f1dXV2LVrV7gPxVCi1jOSlZWFuLg4nDx50u/zkydPwuVySX7H5XJxbU8Yi5Z7Fkh8fDwmTJiAI0eOmHGIhAHIvWdpaWlISkoK01ERvEyaNInesxCzYMECvPvuu9ixYwcuuugixW0jbT6LWmMkISEBEydOxLZt27yfeTwebNu2zW8l7cuUKVP8tgeArVu3ym5PGIuWexZIT08PDhw4gOzsbLMOk9AJvWfRQVVVFb1nIUIQBCxYsABvvvkmtm/fjpycHNXvRNx7Fu4MWjPZuHGj4HA4hBdffFGoqakRfvGLXwjp6emC2+0WBEEQbr/9dmHx4sXe7cvLy4U+ffoIf/zjH4WDBw8KjzzyiBAfHy8cOHAgXKcQc/Des0cffVT45z//KdTW1gp79+4V5syZIyQmJgqfffZZuE4h5jh9+rSwb98+Yd++fQIA4c9//rOwb98+4dixY4IgCMLixYuF22+/3bv9F198ISQnJwu//vWvhYMHDwqrV68W4uLihNLS0nCdQszBe89WrFghvPXWW8Lhw4eFAwcOCPfff79gt9uFsrKycJ1CTHHvvfcKTqdTeP/994X6+nrvf+3t7d5tIn0+i2pjRBAE4a9//aswZMgQISEhQZg0aZKwe/du79+uvvpq4Y477vDb/tVXXxVGjx4tJCQkCJdeeqmwefPmEB8xwXPPHnjgAe+2AwYMEGbMmCFUVlaG4ahjF7HsM/A/8T7dcccdwtVXXx30nfz8fCEhIUEYPny48MILL4T8uGMZ3nv2+OOPCyNGjBASExOFzMxM4ZprrhG2b98enoOPQaTuFQC/9ybS5zObIAhCqL0xBEEQBEEQIlGbM0IQBEEQRGRAxghBEARBEGGFjBGCIAiCIMIKGSMEQRAEQYQVMkYIgiAIgggrZIwQBEEQBBFWyBghCIIgCCKskDFCEARBEERYIWOEIAiCIIiwQsYIQRAEQRBhhYwRgiAIgiDCChkjBEEQBEGElf8fICE3HNkgYOcAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class StandardGaussian:\n", " def log_density(self, x):\n", " return -x.dot(x)\n", " \n", "problem = hopsy.Problem(A=[[1, 1], [-1, 0], [0, -1]], b=[5, 0, 0], \n", " model=StandardGaussian())\n", "\n", "chain = hopsy.MarkovChain(problem, starting_point=[.5, .5])\n", "rng = hopsy.RandomNumberGenerator(seed=42)\n", "\n", "accrate, samples = hopsy.sample(chain, rng, n_samples=1000, thinning=10)\n", "\n", "plt.scatter(samples[:,:,0], samples[:,:,1])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6794f090", "metadata": {}, "source": [ "#### Sampling with a custom sampler\n", "\n", "For demonstration purposes, we next try to sample previous distribution by a sampler which proposes new states from a cube. In the easiest case, a proposer only needs to implement a `propose` method. For non-symmetric proposal distributions, a ``log_acceptance_probability`` method needs to be provided as well. This is covered in more in-depth in our [sampling user guide](userguide/sampling.rst)." ] }, { "cell_type": "code", "execution_count": 6, "id": "0ff9d4b9", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class CubeProposal:\n", " uniform = hopsy.Uniform(-1, 1)\n", " def propose(self, rng):\n", " return [self.state[0] + self.uniform(rng), self.state[1] + self.uniform(rng)]\n", "\n", "chain = hopsy.MarkovChain(problem, proposal=CubeProposal, starting_point=[.5, .5])\n", "rng = hopsy.RandomNumberGenerator(seed=42)\n", "\n", "accrate, samples = hopsy.sample(chain, rng, n_samples=1000, thinning=10)\n", "\n", "plt.scatter(samples[:,:,0], samples[:,:,1])\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "6feea8ea", "metadata": {}, "source": [ ".. rubric:: Footnotes\n", "\n", ".. [1] https://doi.org/10.1002/bit.26379" ] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }