{ "cells": [ { "cell_type": "markdown", "id": "f3038a60", "metadata": { "editable": true }, "source": [ "\n", "\n", "# Demo - Working with Functions\n", "**Mikael Mortensen** (email: `mikaem@math.uio.no`), Department of Mathematics, University of Oslo.\n", "\n", "Date: **August 7, 2020**\n", "\n", "**Summary.** This is a demonstration of how the Python module [shenfun](https://github.com/spectralDNS/shenfun) can be used to work with\n", "global spectral functions in one and several dimensions." ] }, { "cell_type": "markdown", "id": "be63430d", "metadata": { "editable": true }, "source": [ "## Construction\n", "\n", "A global spectral function $u(x)$ can be represented on the real line as" ] }, { "cell_type": "markdown", "id": "75869282", "metadata": { "editable": true }, "source": [ "$$\n", "u(x) = \\sum_{k=0}^{N-1} \\hat{u}_k \\psi_k(x), \\quad x \\in \\Omega = [a, b],\n", "$$" ] }, { "cell_type": "markdown", "id": "174c39e0", "metadata": { "editable": true }, "source": [ "where the domain $\\Omega$ has to be defined such that $b > a$.\n", "The array $\\{\\hat{u}_k\\}_{k=0}^{N-1}$ contains the\n", "expansion coefficient for the series, often referred to as the\n", "degrees of freedom. There is one degree of freedom per basis function and\n", "$\\psi_k(x)$ is the $k$'th basis function.\n", "We can use any number of basis functions,\n", "and the span of the chosen basis is then a function space. Also part of the\n", "function space is the domain, which is\n", "specified when a function space is created. To create a function space\n", "$T=\\text{span}\\{T_k\\}_{k=0}^{N-1}$ for\n", "the first N Chebyshev polynomials of the first kind on the default domain $[-1, 1]$,\n", "do" ] }, { "cell_type": "code", "execution_count": 1, "id": "f17eb498", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.074095Z", "iopub.status.busy": "2024-02-19T13:47:50.073828Z", "iopub.status.idle": "2024-02-19T13:47:50.913544Z", "shell.execute_reply": "2024-02-19T13:47:50.912771Z" } }, "outputs": [], "source": [ "from shenfun import *\n", "N = 8\n", "T = FunctionSpace(N, 'Chebyshev', domain=(-1, 1))" ] }, { "cell_type": "markdown", "id": "51d18e17", "metadata": { "editable": true }, "source": [ "The function $u(x)$ can now be created with all N coefficients\n", "equal to zero as" ] }, { "cell_type": "code", "execution_count": 2, "id": "b77b3fc9", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.917037Z", "iopub.status.busy": "2024-02-19T13:47:50.916634Z", "iopub.status.idle": "2024-02-19T13:47:50.920164Z", "shell.execute_reply": "2024-02-19T13:47:50.919412Z" } }, "outputs": [], "source": [ "u = Function(T)" ] }, { "cell_type": "markdown", "id": "791e8067", "metadata": { "editable": true }, "source": [ "When using Chebyshev polynomials the computational domain is always\n", "$[-1, 1]$. However, we can still use a different physical domain,\n", "like" ] }, { "cell_type": "code", "execution_count": 3, "id": "8ec4daad", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.923125Z", "iopub.status.busy": "2024-02-19T13:47:50.922882Z", "iopub.status.idle": "2024-02-19T13:47:50.926517Z", "shell.execute_reply": "2024-02-19T13:47:50.925967Z" } }, "outputs": [], "source": [ "T = FunctionSpace(N, 'Chebyshev', domain=(0, 1))" ] }, { "cell_type": "markdown", "id": "c08835aa", "metadata": { "editable": true }, "source": [ "and under the hood shenfun will then map this domain to the reference\n", "domain through" ] }, { "cell_type": "markdown", "id": "ab3b7822", "metadata": { "editable": true }, "source": [ "$$\n", "u(x) = \\sum_{k=0}^{N-1} \\hat{u}_k \\psi_k(2(x-0.5))\n", "$$" ] }, { "cell_type": "markdown", "id": "ca3cb4d4", "metadata": { "editable": true }, "source": [ "## Approximating analytical functions\n", "\n", "The `u` function above was created with only zero\n", "valued coefficients, which is the default. Alternatively,\n", "a [Function](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.Function) may be initialized using a constant\n", "value" ] }, { "cell_type": "code", "execution_count": 4, "id": "761f5f53", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.929251Z", "iopub.status.busy": "2024-02-19T13:47:50.929055Z", "iopub.status.idle": "2024-02-19T13:47:50.932325Z", "shell.execute_reply": "2024-02-19T13:47:50.931883Z" } }, "outputs": [], "source": [ "T = FunctionSpace(N, 'Chebyshev', domain=(-1, 1))\n", "u = Function(T, val=1)" ] }, { "cell_type": "markdown", "id": "36f77fe7", "metadata": { "editable": true }, "source": [ "but that is not very useful. A third method to initialize\n", "a [Function](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.Function) is to interpolate using an analytical\n", "Sympy function." ] }, { "cell_type": "code", "execution_count": 5, "id": "b9ad36a9", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.934594Z", "iopub.status.busy": "2024-02-19T13:47:50.934409Z", "iopub.status.idle": "2024-02-19T13:47:50.947211Z", "shell.execute_reply": "2024-02-19T13:47:50.946640Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-6.93889390e-17 -5.47405982e-17 -1.82237827e-18 1.00000000e+00\n", " 1.96261557e-17 -3.33066907e-16 1.49457239e-16 -2.93881977e-16]\n" ] } ], "source": [ "import sympy as sp\n", "x = sp.Symbol('x', real=True)\n", "u = Function(T, buffer=4*x**3-3*x)\n", "print(u)" ] }, { "cell_type": "markdown", "id": "4a9048d9", "metadata": { "editable": true }, "source": [ "Here the analytical Sympy function will first be evaluated\n", "on the entire quadrature mesh of the `T` function space,\n", "and then forward transformed to get the coefficients. This\n", "corresponds to a finite-dimensional projection to `T`.\n", "The projection is\n", "\n", "Find $u_h \\in T$, such that" ] }, { "cell_type": "markdown", "id": "27a6add1", "metadata": { "editable": true }, "source": [ "\n", "
\n", "\n", "$$\n", "(u_h - u, v)^{N}_w = 0 \\quad \\forall v \\in T, \\label{eq:proj1} \\tag{1}\n", "$$" ] }, { "cell_type": "markdown", "id": "e76306fe", "metadata": { "editable": true }, "source": [ "where $v$ is a test function and\n", "$u_h=\\sum_{k=0}^{N-1} \\hat{u}_k T_k$ is a trial function. The\n", "notation $(\\cdot, \\cdot)^N_w$ represents a discrete version of\n", "the weighted inner product $(u, v)_w$ defined as" ] }, { "cell_type": "markdown", "id": "3ed95d25", "metadata": { "editable": true }, "source": [ "$$\n", "(u, v)_{\\omega} = \\int_{\\Omega} u \\overline{v} \\omega d\\Omega,\n", "$$" ] }, { "cell_type": "markdown", "id": "a26f170f", "metadata": { "editable": true }, "source": [ "where $\\omega(x)$ is a weight functions and $\\overline{v}$ is the\n", "complex conjugate of $v$. If $v$ is\n", "a real function, then $\\overline{v}=v$.\n", "With quadrature we approximate the integral such that" ] }, { "cell_type": "markdown", "id": "b801c1d1", "metadata": { "editable": true }, "source": [ "$$\n", "(u, v)_{\\omega} \\approx (u, v)^N_{\\omega} = \\sum_{j\\in\\mathcal{I}^N} u(x_j) v(x_j) w_j.\n", "$$" ] }, { "cell_type": "markdown", "id": "c2a63677", "metadata": { "editable": true }, "source": [ "where the index set $\\mathcal{I}^N = \\{0, 1, \\ldots, N-1\\}$ and $\\{x_j\\}_{j\\in \\mathcal{I}^N}$ and $\\{w_j\\}_{j\\in \\mathcal{I}^N}$\n", "are the quadrature points and weights.\n", "\n", "A linear system of equations arise when inserting for the chosen\n", "basis functions in Eq. ([1](#eq:proj1)). We get" ] }, { "cell_type": "markdown", "id": "aee62172", "metadata": { "editable": true }, "source": [ "$$\n", "\\sum_{k\\in \\mathcal{I}^N} \\left( T_k, T_i\\right)^N_{\\omega} \\hat{u}_k =\n", "\\left(u, T_i\\right)^N_{\\omega}\\, \\forall \\, i \\in \\mathcal{I}^N,\n", "$$" ] }, { "cell_type": "markdown", "id": "0b6dffc4", "metadata": { "editable": true }, "source": [ "In matrix notation the solution becomes" ] }, { "cell_type": "markdown", "id": "35773a2f", "metadata": { "editable": true }, "source": [ "$$\n", "\\boldsymbol{\\hat{u}} = A^{-1} \\boldsymbol{\\tilde{u}},\n", "$$" ] }, { "cell_type": "markdown", "id": "09d7d46b", "metadata": { "editable": true }, "source": [ "where we use two column vectors $\\boldsymbol{\\hat{u}}=(\\hat{u}_i)^T_{i\\in \\mathcal{I}^N}$,\n", "$\\boldsymbol{\\tilde{u}}=\\left(\\tilde{u}_i\\right)^T_{i \\in \\mathcal{I}^N}$,\n", "$\\tilde{u}_i = (u, T_i)^N_{\\omega}$ and the matrix\n", "$A=(a_{ik}) \\in \\mathbb{R}^{N \\times N}$, that is diagonal with\n", "$a_{ik}=\\left( T_k, T_i\\right)^N_{\\omega}$. For the default\n", "Gauss-Chebyshev quadrature this matrix is $a_{ik} = c_i \\pi/2 \\delta_{ik}$,\n", "where $c_0=2$ and $c_i=1$ for $i>0$." ] }, { "cell_type": "markdown", "id": "a93601a6", "metadata": { "editable": true }, "source": [ "## Adaptive function size\n", "\n", "The number of basis functions can also be left open during creation\n", "of the function space, through" ] }, { "cell_type": "code", "execution_count": 6, "id": "6b3431b4", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.950753Z", "iopub.status.busy": "2024-02-19T13:47:50.950522Z", "iopub.status.idle": "2024-02-19T13:47:50.954325Z", "shell.execute_reply": "2024-02-19T13:47:50.953799Z" } }, "outputs": [], "source": [ "T = FunctionSpace(0, 'Chebyshev', domain=(-1, 1))" ] }, { "cell_type": "markdown", "id": "b919c637", "metadata": { "editable": true }, "source": [ "This is useful if you want to approximate a function and\n", "are uncertain how many basis functions that are required.\n", "For example, you may want to approximate the function $\\cos(20 x)$.\n", "You can then find the required [Function](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.Function) using" ] }, { "cell_type": "code", "execution_count": 7, "id": "9a55e6d5", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.956650Z", "iopub.status.busy": "2024-02-19T13:47:50.956470Z", "iopub.status.idle": "2024-02-19T13:47:50.971292Z", "shell.execute_reply": "2024-02-19T13:47:50.970532Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "37\n" ] } ], "source": [ "u = Function(T, buffer=sp.cos(20*x))\n", "print(len(u))" ] }, { "cell_type": "markdown", "id": "07d341ea", "metadata": { "editable": true }, "source": [ "We see that $N=45$ is required to resolve this function. This agrees\n", "well with what is reported also by [Chebfun](https://www.chebfun.org/docs/guide/guide01.html).\n", "Note that in this process a new [FunctionSpace()](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.FunctionSpace) has been\n", "created under the hood. The function space of `u` can be\n", "extracted using" ] }, { "cell_type": "code", "execution_count": 8, "id": "d6cdcdb9", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.973843Z", "iopub.status.busy": "2024-02-19T13:47:50.973655Z", "iopub.status.idle": "2024-02-19T13:47:50.976913Z", "shell.execute_reply": "2024-02-19T13:47:50.976395Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "37\n" ] } ], "source": [ "Tu = u.function_space()\n", "print(Tu.N)" ] }, { "cell_type": "markdown", "id": "cd42b044", "metadata": { "editable": true }, "source": [ "To further show that shenfun is compatible with Chebfun we can also\n", "approximate the Bessel function" ] }, { "cell_type": "code", "execution_count": 9, "id": "f3f6e277", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:50.979208Z", "iopub.status.busy": "2024-02-19T13:47:50.979025Z", "iopub.status.idle": "2024-02-19T13:47:51.014287Z", "shell.execute_reply": "2024-02-19T13:47:51.013761Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "83\n" ] } ], "source": [ "T1 = FunctionSpace(0, 'Chebyshev', domain=(0, 100))\n", "u = Function(T1, buffer=sp.besselj(0, x))\n", "print(len(u))" ] }, { "cell_type": "markdown", "id": "527bcff6", "metadata": { "editable": true }, "source": [ "which gives 83 basis functions, in close agreement with Chebfun (89).\n", "The difference lies only in the cut-off criteria. We cut frequencies\n", "with a relative tolerance of 1e-12 by default, but if we make this criteria\n", "a little bit stronger, then we will also arrive at a slightly higher number:" ] }, { "cell_type": "code", "execution_count": 10, "id": "f909dbb0", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.016776Z", "iopub.status.busy": "2024-02-19T13:47:51.016584Z", "iopub.status.idle": "2024-02-19T13:47:51.030924Z", "shell.execute_reply": "2024-02-19T13:47:51.030480Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "87\n" ] } ], "source": [ "u = Function(T1, buffer=sp.besselj(0, x), reltol=1e-14)\n", "print(len(u))" ] }, { "cell_type": "markdown", "id": "631b5bda", "metadata": { "editable": true }, "source": [ "Plotting the function on its quadrature points looks\n", "a bit ragged, though:" ] }, { "cell_type": "code", "execution_count": 11, "id": "24ce622f", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.033552Z", "iopub.status.busy": "2024-02-19T13:47:51.033365Z", "iopub.status.idle": "2024-02-19T13:47:51.628468Z", "shell.execute_reply": "2024-02-19T13:47:51.627423Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "Tu = u.function_space()\n", "plt.plot(Tu.mesh(), u.backward());" ] }, { "cell_type": "markdown", "id": "0c9b4803", "metadata": { "editable": true }, "source": [ "To improve the quality of this plot we can instead evaluate the\n", "function on more points" ] }, { "cell_type": "code", "execution_count": 12, "id": "aa3f4008", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.631660Z", "iopub.status.busy": "2024-02-19T13:47:51.631293Z", "iopub.status.idle": "2024-02-19T13:47:51.764226Z", "shell.execute_reply": "2024-02-19T13:47:51.763705Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xj = np.linspace(0, 100, 1000)\n", "plt.plot(xj, u(xj));" ] }, { "cell_type": "markdown", "id": "f56c9597", "metadata": { "editable": true }, "source": [ "Alternatively, we can refine the function, which simply\n", "pads zeros to $\\hat{u}$" ] }, { "cell_type": "code", "execution_count": 13, "id": "39cb107e", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.766802Z", "iopub.status.busy": "2024-02-19T13:47:51.766604Z", "iopub.status.idle": "2024-02-19T13:47:51.951413Z", "shell.execute_reply": "2024-02-19T13:47:51.950859Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "up = u.refine(200)\n", "Tp = up.function_space()\n", "plt.plot(Tp.mesh(), up.backward());" ] }, { "cell_type": "markdown", "id": "df254f80", "metadata": { "editable": true }, "source": [ "The padded expansion coefficients are now given as" ] }, { "cell_type": "code", "execution_count": 14, "id": "760bd263", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.954388Z", "iopub.status.busy": "2024-02-19T13:47:51.954181Z", "iopub.status.idle": "2024-02-19T13:47:51.958604Z", "shell.execute_reply": "2024-02-19T13:47:51.958093Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 6.43655435e-02 -1.37262942e-01 1.26593632e-01 -1.31630372e-01\n", " 1.19810309e-01 -1.19499576e-01 1.07387826e-01 -9.95196201e-02\n", " 8.81197795e-02 -7.07299943e-02 6.13974837e-02 -3.40222966e-02\n", " 2.84578300e-02 6.05886310e-03 -6.23468323e-03 4.01956708e-02\n", " -3.44202241e-02 5.58353154e-02 -4.58848577e-02 4.33923041e-02\n", " -3.39778387e-02 6.26445963e-03 -3.37831264e-03 -3.27304442e-02\n", " 2.63630973e-02 -4.12313235e-02 3.07429560e-02 -7.73458857e-03\n", " 4.10441868e-03 3.29922472e-02 -2.47812478e-02 2.71654360e-02\n", " -1.81421444e-02 -2.02112290e-02 1.53660102e-02 -3.02943723e-02\n", " 1.97324599e-02 1.94051084e-02 -1.41460820e-02 2.47321146e-02\n", " -1.49668436e-02 -3.02763148e-02 1.98156190e-02 -2.08517347e-03\n", " -6.91643640e-05 3.13799203e-02 -1.81924272e-02 -3.77110141e-02\n", " 2.23051599e-02 2.82766986e-02 -1.67226896e-02 -1.59965877e-02\n", " 9.40673776e-03 7.34392211e-03 -4.28398348e-03 -2.84497604e-03\n", " 1.64428109e-03 9.53197714e-04 -5.45450869e-04 -2.80998822e-04\n", " 1.59136941e-04 7.38240716e-05 -4.13664358e-05 -1.74579288e-05\n", " 9.67744748e-06 3.74610168e-06 -2.05413769e-06 -7.34256601e-07\n", " 3.98257402e-07 1.32202237e-07 -7.09282453e-08 -2.19709845e-08\n", " 1.16601214e-08 3.38459230e-09 -1.77684428e-09 -4.85085285e-10\n", " 2.51925667e-10 6.48958256e-11 -3.33432158e-11 -8.12799381e-12\n", " 4.13195149e-12 9.55498771e-13 -4.80687010e-13 -1.05592419e-13\n", " 5.24752655e-14 1.10454430e-14 -6.02774535e-15 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n" ] } ], "source": [ "print(up)" ] }, { "cell_type": "markdown", "id": "2773efbb", "metadata": { "editable": true }, "source": [ "## More features\n", "\n", "Since we have used a regular Chebyshev basis above, there\n", "are many more features that could be explored simply by going through\n", "[Numpy's Chebyshev module](https://numpy.org/doc/stable/reference/routines.polynomials.chebyshev.html).\n", "For example, we can create a Chebyshev series like" ] }, { "cell_type": "code", "execution_count": 15, "id": "ef085fb4", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.961468Z", "iopub.status.busy": "2024-02-19T13:47:51.961274Z", "iopub.status.idle": "2024-02-19T13:47:51.964404Z", "shell.execute_reply": "2024-02-19T13:47:51.963829Z" } }, "outputs": [], "source": [ "import numpy.polynomial.chebyshev as cheb\n", "c = cheb.Chebyshev(u, domain=(0, 100))" ] }, { "cell_type": "markdown", "id": "a07fd640", "metadata": { "editable": true }, "source": [ "The Chebyshev series in Numpy has a wide range of possibilities,\n", "see [here](https://numpy.org/doc/stable/reference/generated/numpy.polynomial.chebyshev.Chebyshev.html#numpy.polynomial.chebyshev.Chebyshev).\n", "However, we may also work directly with the Chebyshev\n", "coefficients already in `u`. To find the roots of the\n", "polynomial that approximates the Bessel function on\n", "domain $[0, 100]$, we can do" ] }, { "cell_type": "code", "execution_count": 16, "id": "66dcc5f2", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.966744Z", "iopub.status.busy": "2024-02-19T13:47:51.966567Z", "iopub.status.idle": "2024-02-19T13:47:51.975599Z", "shell.execute_reply": "2024-02-19T13:47:51.975115Z" } }, "outputs": [], "source": [ "z = Tu.map_true_domain(cheb.chebroots(u))" ] }, { "cell_type": "markdown", "id": "a20a2384", "metadata": { "editable": true }, "source": [ "Note that the roots are found on the reference domain $[-1, 1]$\n", "and as such we need to move the result to the physical domain using\n", "`map_true_domain`. The resulting roots `z` are both real and imaginary,\n", "so to extract the real roots we need to filter a little bit" ] }, { "cell_type": "code", "execution_count": 17, "id": "33dc7c82", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.978537Z", "iopub.status.busy": "2024-02-19T13:47:51.978332Z", "iopub.status.idle": "2024-02-19T13:47:51.981859Z", "shell.execute_reply": "2024-02-19T13:47:51.981384Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2.40482556 5.52007811 8.65372791 11.79153444 14.93091771]\n" ] } ], "source": [ "z2 = z[np.where((z.imag == 0)*(z.real > 0)*(z.real < 100))].real\n", "print(z2[:5])" ] }, { "cell_type": "markdown", "id": "04171337", "metadata": { "editable": true }, "source": [ "Here `np.where` returns the indices where the condition is true. The condition\n", "is that the imaginary part is zero, whereas the real part is within the\n", "true domain $[0, 100]$.\n", "\n", "**Notice.**\n", "\n", "Using directly `cheb.chebroots(c)` does not seem to work (even though the\n", "series has been generated with the non-standard domain) because\n", "Numpy only looks for roots in the reference domain $[-1, 1]$.\n", "\n", "We could also use a function space with boundary conditions built\n", "in, like" ] }, { "cell_type": "code", "execution_count": 18, "id": "23287700", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:51.984354Z", "iopub.status.busy": "2024-02-19T13:47:51.984173Z", "iopub.status.idle": "2024-02-19T13:47:52.045944Z", "shell.execute_reply": "2024-02-19T13:47:52.045436Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "82\n" ] } ], "source": [ "Td = FunctionSpace(0, 'C', bc=(sp.besselj(0, 0), sp.besselj(0, 100)), domain=(0, 100))\n", "ud = Function(Td, buffer=sp.besselj(0, x))\n", "print(len(ud))" ] }, { "cell_type": "markdown", "id": "28a0c752", "metadata": { "editable": true }, "source": [ "As we can see this leads to a function space of dimension\n", "very similar to the orthogonal space.\n", "\n", "The major advantages of working with a space with boundary conditions\n", "built in only comes to life when solving differential equations. As\n", "long as we are only interested in approximating functions, we are better off\n", "sticking to the orthogonal spaces. This goes for Legendre as\n", "well as Chebyshev." ] }, { "cell_type": "markdown", "id": "cbfe6a4e", "metadata": { "editable": true }, "source": [ "## Multidimensional functions\n", "\n", "Multidimensional tensor product spaces are created\n", "by taking the tensor products of one-dimensional function spaces.\n", "For example" ] }, { "cell_type": "code", "execution_count": 19, "id": "00e8b329", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:52.049058Z", "iopub.status.busy": "2024-02-19T13:47:52.048820Z", "iopub.status.idle": "2024-02-19T13:47:52.065668Z", "shell.execute_reply": "2024-02-19T13:47:52.064968Z" } }, "outputs": [], "source": [ "C0 = FunctionSpace(20, 'C')\n", "C1 = FunctionSpace(20, 'C')\n", "T = TensorProductSpace(comm, (C0, C1))\n", "u = Function(T)" ] }, { "cell_type": "markdown", "id": "0ca369f5", "metadata": { "editable": true }, "source": [ "Here $\\text{T} = \\text{C0} \\otimes \\text{C1}$, the basis function is\n", "$T_i(x) T_j(y)$ and the Function `u` is" ] }, { "cell_type": "markdown", "id": "c6501f71", "metadata": { "editable": true }, "source": [ "$$\n", "u(x, y) = \\sum_{i=0}^{N-1} \\sum_{j=0}^{N-1} \\hat{u}_{ij} T_i(x) T_j(y).\n", "$$" ] }, { "cell_type": "markdown", "id": "9baa4116", "metadata": { "editable": true }, "source": [ "The multidimensional Functions work more or less exactly like for the\n", "1D case. We can here interpolate 2D Sympy functions" ] }, { "cell_type": "code", "execution_count": 20, "id": "f8c1a6c4", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:52.068527Z", "iopub.status.busy": "2024-02-19T13:47:52.068297Z", "iopub.status.idle": "2024-02-19T13:47:52.199742Z", "shell.execute_reply": "2024-02-19T13:47:52.199164Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = sp.Symbol('y', real=True)\n", "u = Function(T, buffer=sp.cos(10*x)*sp.cos(10*y))\n", "X = T.local_mesh(True)\n", "plt.contourf(X[0], X[1], u.backward());" ] }, { "cell_type": "markdown", "id": "99390331", "metadata": { "editable": true }, "source": [ "Like for 1D the coefficients are computed through projection,\n", "where the exact function is evaluated on all quadrature points\n", "in the mesh.\n", "\n", "The Cartesian mesh represents the quadrature points of the\n", "two function spaces, and can be visualized as follows" ] }, { "cell_type": "code", "execution_count": 21, "id": "6f50c502", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:52.202908Z", "iopub.status.busy": "2024-02-19T13:47:52.202557Z", "iopub.status.idle": "2024-02-19T13:47:52.577756Z", "shell.execute_reply": "2024-02-19T13:47:52.577252Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = T.mesh()\n", "for xj in X[0]:\n", " for yj in X[1]:\n", " plt.plot((xj, xj), (X[1][0, 0], X[1][0, -1]), 'k')\n", " plt.plot((X[0][0], X[0][-1]), (yj, yj), 'k')" ] }, { "cell_type": "markdown", "id": "205be2c5", "metadata": { "editable": true }, "source": [ "We may alternatively plot on a uniform mesh" ] }, { "cell_type": "code", "execution_count": 22, "id": "f40fd289", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:52.580463Z", "iopub.status.busy": "2024-02-19T13:47:52.580204Z", "iopub.status.idle": "2024-02-19T13:47:52.703681Z", "shell.execute_reply": "2024-02-19T13:47:52.703212Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = T.local_mesh(bcast=True, kind='uniform')\n", "plt.contourf(X[0], X[1], u.backward(mesh='uniform'));" ] }, { "cell_type": "markdown", "id": "88538f19", "metadata": { "editable": true }, "source": [ "## Curvilinear coordinates\n", "\n", "With shenfun it is possible to use curvilinear coordinates,\n", "and not necessarily with orthogonal basis vectors. With\n", "curvilinear coordinates the computational coordinates are\n", "always straight lines, rectangles and cubes. But the physical\n", "coordinates can be very complex.\n", "\n", "Consider the unit disc with polar coordinates. Here\n", "the position vector $\\mathbf{r}$ is given by" ] }, { "cell_type": "markdown", "id": "45580ada", "metadata": { "editable": true }, "source": [ "$$\n", "\\mathbf{r} = r\\cos \\theta \\mathbf{i} + r\\sin \\theta \\mathbf{j}.\n", "$$" ] }, { "cell_type": "markdown", "id": "42e1822a", "metadata": { "editable": true }, "source": [ "The physical domain is $\\Omega = \\{(x, y): x^2 + y^2 < 1\\}$,\n", "whereas the computational domain is the Cartesian product\n", "$D = [0, 1] \\times [0, 2 \\pi] = \\{(r, \\theta) | r \\in [0, 1] \\text{ and } \\theta \\in [0, 2 \\pi]\\}$.\n", "\n", "We create this domain in shenfun through" ] }, { "cell_type": "code", "execution_count": 23, "id": "abe72e5b", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:52.706780Z", "iopub.status.busy": "2024-02-19T13:47:52.706562Z", "iopub.status.idle": "2024-02-19T13:47:53.048201Z", "shell.execute_reply": "2024-02-19T13:47:53.047098Z" } }, "outputs": [], "source": [ "r, theta = psi = sp.symbols('x,y', real=True, positive=True)\n", "rv = (r*sp.cos(theta), r*sp.sin(theta))\n", "B0 = FunctionSpace(20, 'C', domain=(0, 1))\n", "F0 = FunctionSpace(20, 'F')\n", "T = TensorProductSpace(comm, (B0, F0), coordinates=(psi, rv))" ] }, { "cell_type": "markdown", "id": "cf97987a", "metadata": { "editable": true }, "source": [ "Note that we are using a Fourier space for the azimuthal\n", "direction, since the solution here needs to be periodic.\n", "We can now create functions on the space using an\n", "analytical function in computational coordinates" ] }, { "cell_type": "code", "execution_count": 24, "id": "0a65ffc2", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:53.051335Z", "iopub.status.busy": "2024-02-19T13:47:53.050964Z", "iopub.status.idle": "2024-02-19T13:47:53.065481Z", "shell.execute_reply": "2024-02-19T13:47:53.065018Z" } }, "outputs": [], "source": [ "u = Function(T, buffer=(1-r)*r*sp.sin(sp.cos(theta)))" ] }, { "cell_type": "markdown", "id": "02962d83", "metadata": { "editable": true }, "source": [ "However, when this is plotted it may not be what you expect" ] }, { "cell_type": "code", "execution_count": 25, "id": "c32f1808", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:53.067992Z", "iopub.status.busy": "2024-02-19T13:47:53.067810Z", "iopub.status.idle": "2024-02-19T13:47:53.173389Z", "shell.execute_reply": "2024-02-19T13:47:53.172869Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = T.local_mesh(True)\n", "plt.contourf(X[0], X[1], u.backward(), 100);" ] }, { "cell_type": "markdown", "id": "4ef74e8d", "metadata": { "editable": true }, "source": [ "We see that the function has been plotted in computational coordinates,\n", "and not on the disc, as you probably expected. To plot on\n", "the disc we need the physical mesh, and not the computational" ] }, { "cell_type": "code", "execution_count": 26, "id": "a42a0a42", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:53.176403Z", "iopub.status.busy": "2024-02-19T13:47:53.176104Z", "iopub.status.idle": "2024-02-19T13:47:53.299214Z", "shell.execute_reply": "2024-02-19T13:47:53.298486Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = T.local_cartesian_mesh()\n", "plt.contourf(X[0], X[1], u.backward(), 100);" ] }, { "cell_type": "markdown", "id": "e45366c2", "metadata": { "editable": true }, "source": [ "**Notice.**\n", "\n", "The periodic plot does not wrap all around the circle. This is\n", "not wrong, we have simply not used the same point twice, but it\n", "does not look very good. To overcome this problem we can wrap the\n", "grid all the way around and re-plot." ] }, { "cell_type": "code", "execution_count": 27, "id": "b9f6cc53", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:53.302005Z", "iopub.status.busy": "2024-02-19T13:47:53.301738Z", "iopub.status.idle": "2024-02-19T13:47:53.423480Z", "shell.execute_reply": "2024-02-19T13:47:53.423025Z" } }, "outputs": [ { "data": { "image/png": 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oEUVNeiz7edZvw/XmmAzIcZuHagjeB6eOxD44btQxasNNodhQh7SJq2BQCR1+Txra2sr5kueZbKx4jNoLRxwnjRoRIzguAkcWvalC3JTd0G/4wH+8aV9uediLIFHsyNYRj2Urrgr9c6h9cww9c6LIsYPz/I57UUVYUKM2xXOZjxkmYhGT2LEVND7Fi6kM28faItRrpV8f8bnjI2IjS1X5juKUvS+Vb3GjQuW3kWESNyHFzDDzPxhlPFUE2UaCxJJ3ajQH6IgXaTRH2OMqpqzqSV2y4ZE+wNVIzK2QEq8lCiZO+bjpRYWzls/r2tyXDtnXimM+djYR17GiqgThJBNHvsSNq/F3uNk2vkLg87o6s7H4tRPHUEzIvU8sDMixyqp0YgQnYiR0Sso1HWXy6lCpIgVFuaZtBMQUSeJEXGTHZcdcevjYRnvK9Pr4Tk35EDdUURNKoHDJvg9q7xzbSJAYrZE1MBSjNzoTsi6a42pAjpEc/0QPTvTgaCnTSMw1EbtGIWwJmYKygXofqnEs7wxxLHVN0Rvjy4dj9OAQ/Dek9FSF4qZqYROickuGTQNBVdpLTGGZ/Dm23hyxa7LJmxP3sqITPTgRL7iKm6qjNjaixjX1QsG3MKIKLtU4VSRHNjZ0JKeyyitCeorT98Y0jypuyhA2ZQkVW2xKxVUmZzFaM9SaLURzgJ6wKSuaE6uswhAFTqSA75RUyKgNR9jUoQoKCCeMXISOSpBQBQ0F6VoWfXHKMBqT1rc0FocWN/0sbIZb+XufbtN+0FRpL5nQsU1b6UrKrcrJY8oqOFHgRHLUJWpTpbBptvMPrtmWed+0MnCN1MjGiSIHsKuEokZxbMRRZVGd7D0QBA8lNRVS3IQWNqL4KAPKNUURJBMsNkInRDQnt5+VoWdOrLJyJ1ZRRbr4FDdiJY9K3MgqfrjiRlU1JK+0SowvEcoclxcXagUWZZzsPMXbRBWYtttJ1B4hesPpd5PFh7ihVBpxtj8YbrWlr7qiuj/Ze5V9rSjVVuLn2WO2lVa9BeM2D6GIEZyINiXVj1Eb1QPSRkyUgeq+TJGj7PvURThMER3b6Itt+qqwjkWaqu5QfDeu4oYSsaFGa+ooYEzvT/TXpO8hG9GRRXOya6drcKM56bFg0ZyYsvJCrKKa41VUvqM2WXRRGxGOT4dzrLOWpBrG8Pu86pSICDVNRrlv392JKZVP4jqFNQzVVMYqKZcqKkP1lE3llCk1RRE3dRM2dSkzF1FVTMn8O6qKLHENl2orm0qr2AGZDuf5PWB/N0U4cMVNNuWha9qX3elaTJOY0kumXcNVKS15eqSYAuKmd8p4UaCms6hpKXpKz3xvfZFSyuLZoGwSNxQo4saUiqKmoThpp9BN/nyguj/Ze1R9fcQ1bNJWKY1W0v0ZkO5QLhkXU1ZhiCmqOUgdojY2PhsRnxGbKqGmmoD8e9NFdShrUs3IYrrKxvRrWkNMU1HSYf2CKXpD8sUYhI1xfsBIzUhF6a39QoRGVRo+3GqTjMjpGrZpK5kJmVNpRTUgx5QVnShw5hgu4sbGa+OajlIJE1XEhjJOdt0yoPSFCSl2qB4cKx9NjQWJV3+PwVxMqZoyIc5RCQ5KpIZKv4ga2T1QhI7MnwPQKq4oQkfVCdnWm0PpmROrrMxEgTOHUImbOkZtQgmbKiPt2WtXIXZ0QsckUFy2YAhBqF44Rv+NI9zUh424oQobjqixFTQjnv/D7Zf8EGbvLSt2QggdVZNAignZWzQnGpDJRJPxHDAZh0pJ1VHYqMfK1+3N8fPfILHsmcMRD9TIiC6qQ91ygW0WNnzOMRtzjMbac6ZtGlTlu5AIHE0Eh2sspvpuRFTixiRsQgsa32JGh0zo5M5LDMYyM7KqkaDMjJydH8SEbGlAnmvm47hVQ6QLRdxUFbWx9dlQhU1Zosa0JkX0iPeq+/0tvk/1ZprJgbWK15elkGzSSiFTU6WkuTgRGkLvG5/4EDchRY2LoOHMlUZtMvOpUR1uRIfrz6F2QqZEc7Tl5DFlRSZWUQ0wupSUrbhRVUiJFTji57rqKFn1jryiR15JZLpWcXyiFTfNGfOLQ3o903Vz99A2v4/e+iavET3SxY2+Ue7NZX6VcNJTvqM3ZYibkVY79zIx0mznXlTEeVxhZJpjPC+8P1nVFbXiSldtJY4XGwJmP+dUWqV0o4utpCfMMx/HKqsiMUU1gCkqm/Lv7jFm1Mb0kOSmo1wqo0yiRgdXtMiYtYyHctNapnSWetdw+XVoO3jr70E3njOX0w/HS4pK0wNHl57imItdxY2N30YlbjhRGtsITRmpKmOKSnNeTF9RU1cuaSvxXPYYt2/OXO+ZE/vgzGGoKSmOuNFFbcRr6Tw6plSWKh1l6mWji3RQozU+sI3ycCM85giVal41kRyWELXM+pDbAGiiMlrTsqS5X/faDpVTtuJG18fGVtzYRFlcojMjrRnjy3Rdm/O+IzopYsRGF81JjwH8aE7SStTRnAPEaE6HGMEZkAiOy3YLlKhNKBNxiIiNa7TGNN/WSAzYRXlM11P9sarzr1CjObaRGJe5uiiOKoKjO5dbj2gwrkP0xmdKSiVuuKkmW3Rihcr+tv4/j01UhxLNAWgRHR8mZN/RnEGM5HCe31HgDIDACWEktjERD7qw0VGG6NFdQ/e73SVl5ZKq0s0dFIHD8d5UIW50URtTBMQGH0LGRFVCh1pxZZu28lJpNQdSVlHgGBgkgWPb2yZk1MY01raXjex3bpWihoJ12bjmd7iN0ClL5NhGcajl4l4FDtV/QywN5xiLqxQ3voSNrZgZYeRv9xvUv2+x40vo6Pa2sikpV4mc7BhpNGcARU4UOAYGQeBwU1J1jdrUUdhQf8fbNr7jiB4boeND5HD62/iI4tgInM7ncqNxKIGjS09Rozc2vhuZuCkzamMjZjhChopK8PSD0KlDNGcQRE4UOAb6XeCETEn5iNqEEjahRI3vog8b4aONypQQzeGKHB9RHGqaqgyBo23wZ5GeoqamTOKm6qgNRdiEEDIUQoidfhA61s0BBySaExv9DTC+U1IUkWKbjpprwsa0rr55X1ohURQa6fuT/T7XzmvLrylroNdsJwWRo2u0Z3uOcn86ymj+Z7M9A7VySjfORdzYRG1chA1X1Iwyxk8RTWnpPYhCJ713ldBJ37eugWB6TtzvyrZZILVJoGwDT7FBYG5PK01zwMJ+VpJNOwedWCbex4jiRtV4jxK1kc2Tjac069OVfIv3r19fXTZtKsdWlV1zGuiJ6+heFCjXprxn1TzdNYvjZWP14lNXik3/etLGuc7xhqY8XAVV7HA3uJSVMwP6qI1MxOhLqE3l2TNacTPanJG+OHDnq+7JVG6uK20Xj/soLec2Ccx+rCop70IpJ5cw6GXkUeD0EdnojUzcFM7N9sRNVkyIfW3EeeL4dI7snKm/TWduvpeND2GjQjWXKmpshItsnrH/TgCho52jEDnF6Jn+PVMFD3Wccn4N/7rUpadU6Lw3qnFAMXqjEjYycaMVMAGEja2Q4UARPOk96sSOiqqEjqx3TjpO1gk5Rdo3p5l0hU5WCBVEzhzqfBxTVH0CRdyE8NrUIR0VyjAcuoIqew2VVya9P1WqxpS64qStqCkhMV0VMuWUnVNG+ikEur43KnTRG8pu4FyvjU7YaK9jiNaYoIoealpKt252DVP6CpCnsFR7XPlKXbmmrbIfZ1NShT2tJLuT5/ayyuxjVcc/JnwRIzgDiI+ojUs6yqb7sDSd5BitkYknm+hMd/5MYnyZ7pWbSsrOl85jpq3kXxfZ/ejei36urzn9jm30RoSSyrJNR8nXUkdCABijNTYRHde0luq+fEd1bCM6WXylrVKU0RzhvCqSAwxuFCcKnD6AE73JipsUk9fGVzrKh7Cx9dbI1jaN18ERL6p5yjGWQsd32io/zu189z76UMhwy8NtTMhZdD1vqKmp3OeefDZUf43teS62okc13qdXhyt0XNNWKdlzRm8O0T82yKmqmKKqOT7FjbiOaqx4XDenM889FeW7EspG0PgmXTMZkqenTBVQKWLax7biSly/uG4+RSSrrJKN7cvUkqNI6S5DKA0np60sUlMqcSOfq47YqDCJCtfzAC89Ja5nmpuOl6WvAPcKLG7qyjZtlf48zUiqq7Ifp3RTVgfSVXM1VRUjOAOMKG5U0RjbdJTPiI2MUNEa2+hM79qJ8mW6nvS8ZfrKFNERx8rWNSGaw7m4CGvvv3A9iRoXKB2LZWMB2k7gUsFjEbFxida4RFxCVVypzrlEdcTPXSI6NmkrMZoDKKKLGeMxoDcdD1oUJwqcGuMSvZFFbsS1suPS47Ry8XKEjYjJWyNdK4CYoY7X3Y8Kn0LHRuRwUlUUweKLOqa7qI39KJhSU6pqKd3nnXn+hI2tiODiu8xcdS6L7muiFohyj05+rv77ShU6prRV9l9pGTmDQRI5MUVVU3yImyziHJt0VMhUlE0llGyOa6rJJGBs1pKlebL3KUthUdJXstSVaRsI2RgxXcVJVVVBKSkxT/4bVdfi7AOK4rsRcRE3MkzRGptzPuGmplRzs/Ns01dAPoXlmrYCiqkrXdpKVmklkm0KOJdTVVHgDDAFIWSI5nB8NlUJG12khotPMUO9jk7s2Agdk8iRlZLThJBa5Kj8N9mPVeXfdfbuuJqHQ0Hx3RTn0MSNLhqjI7TooXprOHOy82RCRzyuKjUH5F4d30In67vJjpWJnPSYLz/OkVd/qi+3cRCJKaoa4jM1JRM3POOxW5M+WSqK4q2hpKG4aSdOqklc3+aluwfT9QrnNF8v2djcGEV1lWmdMum36iuuudg2emNjKnYRN7YpKt/N/lyrpygCTZfCykIpNc9+zV0rrgAU0lbZsYDcuE7y4zAYhFRVKQLnmmuuwZFHHomxsTGsWrUK99xzj3Ls3XffjUajUXj9/Oc/z4275ZZbcMwxx2B0dBTHHHMMbr311tBvoxRC+W5STOmr3lrhhI3qvqimYYqo4XpnsuvaeHVM6+nuTze3cLxEkaOL4rlW5fkit6mghMTwG07cZFN7LcsHRj+JG9mxskSNDh+Ch+Md8uHV8VFaniLzdaVChuXHYRiOB4Hgb2PLli245JJL8NGPfhQ7duzAKaecgrPOOgs7d+7Uznvsscewe/fu7uuoo47qntu+fTvOPfdcrF+/Hg8//DDWr1+Pc845B/fdd1/ot1M6nJLw4tz8v7IHjmy+T2FTVrSGK2bENUOUicuuJUN333UWObZwxE7VfgCOUdOmNDylruJGRlmiRoetCdnGgFyl0JGJHFmFlc7Y7iJy+j2K00iSJOhv9tWrV2PlypX4/Oc/3z129NFH4+1vfzs2b95cGH/33Xfj1FNPxfPPP48Xv/jF0jXPPfdcTE5O4tvf/nb32JlnnomXvOQl+MY3vmG8J85262VSdmpK9pe36q90rscmpLfG9iEbWsRwUfXHkfl0ZGNlPhrZVgniONFSYFpH9Mlk7y9RjEs/Vq3DGts0zU/Ux7J/wmUjMOIvd0Da5E9lMBb/UgZ46SnX6I2NuPEhbCiMNadJ47jsmx0mj+Vu/aAaLzuuGivz6gDFnjriLuaFzw94dLLenNR8nDUVp+eznpv0fFv4NznwHJnN+nMObOeQdJ8xjY4XB+j+mz5n6uTH4Ty/g0Zw9u/fjwceeADr1q3LHV+3bh22bdumnXv88cdj8eLFOO2003DXXXflzm3fvr2w5hlnnKFcc2pqCpOTk7lX3QghbrJQysYp4oaaipLhGq3hRGfEdUziptGe9f6i3p+IKpIjjvUVyTH2DXJIL3G8PVX7gLoYOsByojOUvjd1FzeqKMlYc1r6CgXnOtwIDyd6w01fcSM6KbJ0lasfxxiRHLBUVdDbf/bZZ9Fut7Fw4cLc8YULF2LPnj3SOYsXL8a1116LW265Bd/85jexbNkynHbaafjhD3/YHbNnzx7Wmps3b8b4+Hj3tWTJEsd3Fh6XkvDeGuox1MoqUdxkoXhsbNJQIiE8NFwxYgNV+HDes0zkUAzDXJGjS1XZNv9z9eF48/EErpYyCSBdx+I6ihuR0EKGSijB4yt9JX4fTEKnNy6frup+LBE5KbpUlQ8/Tr+mqkopE2808iHwJEkKx1KWLVuGZcuWdT9fu3Ytdu3ahU9+8pN43eteZ7Xmpk2bcOmll3Y/n5ycrJXIkUVvuKhSUza+m96x7Nx81CZ/bbtIQve4ZRqKm3IKJWS4NNqzSFr5vy1UpeKyHjSNmaQwrlAe3uaXkFPW0L8vegm463nfmAzEpvOm5n7U6E0Wrrjx7bdRiZu6It6bLqVF6avD6Z/DKTUfac0odzLPlpRny8mnhf+IaXm4rEeOWDoug1s6DvRn6XhQgTN//ny0Wq1CZOWZZ54pRGB0rFmzBl/72te6ny9atIi15ujoKEZHRxl3Xh6hfTfFtYvHTH+Rq8QNtdSY05BPu4t1nwoaGem9yYROlSKHCqf5H1co1QVTON8YqWHm3HRbMfgQNyGFzWiFwmdKIWSy92zy75j66nBEja6BYCp0siInJ2wMIme41S40A9QJILE/TipkuKQNAPtN5ARNUY2MjGDVqlXYunVr7vjWrVtx0kknkdfZsWMHFi9e3P187dq1hTW/+93vstasG3X23XSPKcSNa4m3qoqIW+VETTs1Z5LSX7p7Lhwj+o8oFVaq7436ftSiVRVd1DWI1I2lzqkTJlHDSU9xoje5czUSN6PN6UrFTfYedPdh4xNyTVXJxma/V2K6SvqxRPTKUpxOfpwBLh0PnqK69NJLsX79epxwwglYu3Ytrr32WuzcuRMbN24E0Ekf/eY3v8FXvvIVAMBVV12FI444Asceeyz279+Pr33ta7jllltwyy23dNe8+OKL8brXvQ6f+MQn8La3vQ3f+ta3cOedd+Kf//mfQ78dr2SjNzooJeHdsYF9N+IxysOTE63hRGmoERqdwCiL9B5mpd2K7aM5stQWZTuG/L3pU1UqTFEcX2mmxmzxl2uduiDL0k+cTTUBXvQmf86PkLERNnVEvC9KdAegp7OoUR0x5TXanOkeG2nOsCI5KdlITRrJkW3XIKaqZOdst3IA+iuKE1zgnHvuuXjuuedw5ZVXYvfu3VixYgVuv/12LF26FACwe/fuXE+c/fv347LLLsNvfvMbHHTQQTj22GNx22234c1vfnN3zEknnYSbb74Zf/EXf4GPfexjeOUrX4ktW7Zg9erVod+ONzipKRFTakrnu5GZRSniRubLM4kbjreGKmwooqYOgkaFSej4SlmZRAonVZUVRyphYRIc8nRZcU6Z6Sxpkz9JBZXMf8PtcwOEid6YsI3kqMQNR9iMNcoVQfuSokjxLXiookZ1jCNyUkL7cboIIkdGv6WqgvfBqSNV98Gpa78birhRRW+yxzmlzyZ8RmnK8uSIIkWHTOio1pD1whGFjjim0ANHEA/Z87r+OKoeNaaeOPmxDuM0vXDYfXB0PXAkm2xS+9/Iet+oOhcPa9IQqnRFZ6w83QGYxQxF3MiEDTdaU7awkSETOyIqsVNYSzOO0idH93nWfJyKnKzAyX3czvTFOXB8OnMsjdY49ceR9cYBpP1xqhI4temDE+HhcysGG99N75i9uCnej9pbI8PWR+Oylm8411O9B045uW4MZ88pXfWsyotj/lnye0yHTy+PzGAsi9qY0lPdY5oUVJayxI3MM+IibsYa091XHcjej+qest4dW/+OzGdDEZYp0r45BD+OrNOxeC60H6cfSsejwCkZXfSGiy41pRojO6eaayNusg9YirAZBEGjgnsvMpEjzlUZkMUx+XXopmLqub6jgt43lNJwnfcmiy41ZSNussgf3DTzMFfUVNVDJ5Tgyc+niRxZ3xzA3XTM7Y+TQhY5EuouckrpgxPpEDI15dt3E0Lc5D735KWpSsg0Zg4Yg4dofyOojMQiMo8OxZsjMx+rtoIQfS5ZP46NF0fqCSL6a7hm4RDmYu4mmjb+Gwq66E1+nD+xYxO14UZpZNcoS+So0kvZ96BKZ2W/DjrvTvYaWZ9N9mPTuRRfpmOKH4fky8kiGI5TP06diRGcCimr300Kx1QsO+ZD3OgiGr6iNI2Z2eAv2bUoUKM61GhObo5l+Xfx2up5JnykmmqzZQP04scmPaWK3lCNxZSqKdU5k7gxRi4Y0Zoytm7g3ofqXlyjOz4iOZTy8d55vVldtimneG6upKqiwCkJbrdizkOB67sR53XG0SumXMRNYV1PaSeu0AiBrdhRQfHm6ESOr1RVfv3sHPl1Zec55wYBSmm4inxKwl7A6M7JxI0MjremLqJGB+UeqYJHXDd/Xi1yVONMIqd2fpwMdRU5MUVVAjapqRROaqp4jXSMu6lYha4SylQlpRM15uvWOzaavT9TGiv7fmUprOZMok1Z6dJRuvJxam8cal8cCrpr6tJPsl443tFssqlLS+nOuUZvstimpmzEDddXw2HUoxF5ilAtpYJaGp5+LcRU1mhzOpe6EtNV+bG01JWqfDyF2umY2x/Hij5IVcUITgWU7bsRx+TX9lcOro8e5P8HqFIw1LSTEzOzfl5EfER1KFVW3bGEfkS9sdk13aI4umODglbMeMitqaI3utQUJ5LjS9ywuwI3prsvn2TX5bxkmNJZsq+LLpLDEZ2qSE7vmL3pOPtzKZqOBz1VFQVOYEypKZetGAprWPhuusdKEjf0kmiioAkoTIww1+QINIrIya9Nr6yipqq40Ty9B0g9r1RBRDAUm/agMmFKT6miN9RIjq3vxlXc1EXU+IByb3UQOZTKqpSq/ThA/UROTFEFhJKa4kLpiSOmpnybil3ETfF6cnGjpK6pqex9ESqrKCksWfVUNl1lSlXptlKgpqpc0aadCBVRddqSIQvXY8PfeFP+F73tA1OEI244KShbMXNwc4o1/vez/jZPFu85m/aSpZ3GGtOsdBWnmkpWXWXT6Ti7KWdKek5XPUXdykFGHVNVMYJTIiFSU721xTF8U3FtxU2I6AuARrtNfrGwjOzI71EfyXExHefHZa/JS1vKKDMqY9tHyrguIdpD9d+YoKamstiain2LG5tIzcHNqdyLizjf9OIgvg9Z1KqMSI4v03Gum7ZgOpZ14abQL6mqKHAC4Ts15cN30ztmXzGVH1eSuCHCESxc0WI9lyF2OCJHd55q/PbVyM9UTSVCCWaELhXXNS8Tofzyp0ZobMzFKbaN5EKIG1dRUzZcASR7XzKRI37tOCInP09+TiVyeuf5IicllB8HqI/IiQInANzUlM1fu7a+G9Nf5zbl4GWKG29RFkdCiR2qyOGUj1P9ONwoDhff7RF8wGnyRxE61N44FHSpqSyciikRrrjhiBqXKIpo+FW9fGErcoDi15Aqclx65HBMxylB/TgZglc7MqjRrQweoUrCXXw33WOGhxan101+Xhhx41PENKbbxhdrPRuhpRE6ZYgcH1Cf26GETVXVWhT/jSk9pX5AaTYEO4DqQcgtB7cRNyZ8CRrbeS6CKKTIyZ9zEzm9YzTTcfZnURQ53rpy1zRVFQWOZ7LRmyy+fDfZX+oq343rNgw+GvlZixvJg98kGiiChStefAkeI4FFTm6sIurGjeLI74t2zGZMKWh64KjgPhyo+07p0EVyspQpbmxETahIDPW6KkKJHJ/djk2VVbZNAAcxVRUFjkeoG2mGMBXLsKmYqlzcFOap36CN+LDFVvCQxE5AkWNqtmiDKU3ly4ejvr79XBNN4Zc6hfRBYZOeopiLVaJG9SAsS9xwRI0PQSN2GKZ0HDbdjwzZ+ypb5KjGpdhs51CqHwf1SFXV4BYGD1Nqyn3d4nqy6E1vHr1iKjcvkLiRVg1ZiBsWM231ywKrqJBO6JQkclyiODK4aSqX/wNVlKDahPA56SkO1NRUfk44caPDVdDYCBgb4cOJ5pQpcnxXVqXomgCm2IqcHDVJVUWB4wkxNeW7JNy3qVgcJ46lV+KoxY18g0i6mVh6bZOgsBExHkQPR/CUJXJ8EypNpbyepz8MfCD+hcvFlJ7iRm9U6CqmOOJGZybWiRsbQeMajaGurzxviOZkqbPI6R6TiBxKE0BXP04dS8ejwPFA6JLwUKZi1143JnFTuGcHcUOKlFhGY5RrOYge0/2WIXJ8RXHk13VPUxXXzP9bZ1qav4BTOOkpE5SHoGkDycIxxYPdJiXFETY+xQwrWkOI5sjeg0zkyHrlmK6nEzn5cWaBy6msSqnEj5OhCpETBY4jtiXhZTbz41RM2Yib4nr+xY0WUpRmpveyxULw6ISOVuTIvjaWfXJc4UQBOdQpQuMKNbJjEjUu0ZssuioewG9KirMzt62goaafKCLHJm1FMR+7iByq0dimsqpsP05+sV4UpwqiwPEMtSScvp78X9kYV1OxrbjRddbtzLUrA/cStZGJmqzYcRE9jCiPTuRwojmUvayqjOLY7pk2KMj+Opalpzil4dzojSk15Uvc6KI2vsWMzXzTGO15yXurs8jhmI5TvPpxMtQpVRUFjgNlpaaovpvedWmmYtsuxblxnsRNYZ5r1IYrXHyKHgU+U1bF+W6pKvP69mbjQRY0HMqK3thgI25UUAWJj2ooyvq254Hi+6SKHNPWDlSRk5+j//mgmo6D+HFqWjoeBY4l1NRU2b4b23SCa5diX+LGW9TGBzLRQ1lbI76sU1biWN/7cjG2cKA+e0M0F+wX6Fs3VB+9kYkbk99GBUVQhDAS63BNW9mIHNk88ToUkUOJ6riYjkvx42QoO1UVBY4nfJeE99bN/2vy3XSPWZqKqxY3WnxHbWyhCh7LlJV8LfPXOEQUh5P27Fua+V/U6S9o8Re6+Ite1/8mxZSe6h2jR29cjMWFtRTiRrqeZUrKLs00Q3rR13NLW8lEjo8Kq5Aih2s69unHyS9SXaoqChwLVKmpUCXhXN9N7cQNoTsxqfRbBysdJfHOuJSJ64SORTRH6cvxHLUpXNfTRpz9kpLiNPOrAmqvm94YXrqFK26U6xqiNibchAtvrks0h+LLqULkpPg0HevSWBTqkqqKAodJ6G7FHN+Nz4opm/2lfHUnNoobHZQoio14sZlXRjRHFIolR3F669LG9a4t/5fyc+8bzk7iHHQN/uTGz+IX0TZ6Y2sszsIVNy5RGxsxQ8W0dohoTpayRI7seAjTsejH6adUVRQ4jlBSUyF8Nz4rpmy6FAcXN65RG4cuxcY1bdNkhmiO9LjFBqPUEn6ZedwUxSkrJaVrl2BNSREbnf/GlJ5K4UZvuIgPYZm4MaWkVFCETVnoruViQvYlcnJzmCLHprKKajpO8eXH6QwuP1UVBQ4D29QUF8ommr2x/Iop1y7FvrZe0IobHZYiwisUoaObK4G87YMhiiNC6XDsYgimVuO50C9pryw+NtfM4it6Q9kV3HfUpmxhw7m2bdrKh8ihRoq4IieFK3K8+nEyVJWqigKHiCk1Fcp3ozMV21RMuXYpttl6QdXjpjjPITqSzi8b3T17iub4SFWpzpmiOCnUNFXvGupzLlSxHxVgZzDWQU1PyY753n1bfDBzozaUdJSOsUZb+fKJSzQnHVM4RhA5pl45qlSVCEfkcCqrUrz7cWqwIWcUOExCdCum+A90IXuqqbgqcZP7XBalqFs6yqY83CVtRcAmVZXFNorDTVN5TSlViPjXqQmu/6Z3zl7odI67RW8ou4GbojbqeabIiVnE+BY9IaI5PhoCUvw4nXNuIsdkOk4J5cfJTw6fqooCxwFOt+JQvpt+EzfFORWnozhChmpo1s1XzRNQVVfl5/kxHMvQpTGl4wmpKEp1IP16jMEM741rZRXXf5PCETUqQqamZNeyTUe5ChUf0R7fJuS6iZwUU2VV95hFE0Cb0nHdXlUhiAKHgGqn8NwxQ2rKhMl3Y9OPRPXQqYW48RG14eKtW7GD0FHNJYqcEFDFjP2eU7QqrX702ajQ+W9Mzf106Lw3XCipKc5+T6GFjQkb0eMazcl9btErRzRyU0VObk2JyPFhOtZFJU0iR4YuihOKKHAc8VE1RfHd9K7nZiqujbjR4Rq1se1AzMXFE2QpclyjOCaoaaru+AA+nCqEjswYqYLapRgIm57KEio1RTnWOV6dsNFBETwu0RzZ193VfMwtHxcJIXJ0fhwZJMNxCUSBw0BWOaU6Lx7z0cxv4MWNrWAILWRM2AoyosgR4YqcLJS+OLpjvbn18OGU+dwU/zrlGIxDp6d02KSmqOJGLw6qEzYqTEJHPY9XPVa2yKH0yEnxZTpWRXGkyDocC4Tw4USB4wGflR261FR3jEXFlHdxY9Od2KWsmiMSqsLmPRBEjmuqykcUp3dOdx2/f5mV8mwk/OI1CRldKF9El54yCR1qesrkozGlpjjiRnkPTh6bWenLJzbRnM55XjQnS5kix7fpmAN5o84SqqmiwGEi89/IxxWPUVNTvk3FFHGjfS8+etzYlFK7zLPBZbsG6n1RRY6Aa6rKFds0lXo9h5upKcOMB4QsPZXiai7OrWVITVFMxRxx4xK1MQkZ34InVDQn93mfixxqFEeGzHNT9vYopQica665BkceeSTGxsawatUq3HPPPcqx3/zmN/GmN70JL3vZyzBv3jysXbsW3/nOd3JjbrzxRjQajcJr37593u9dNBhn0YkYn4QQNyLq1IVe3JB63NhEX0JHbShbMYQSOhSR4yFVpaKMNFXhmopmlZRnYVWl5+S/RBXo0lIpvrsU6wSLje+GKm5CChvTPFfB4zuaU1eRk0KtrOJg2w8KQFCjcXCBs2XLFlxyySX46Ec/ih07duCUU07BWWedhZ07d0rH//CHP8Sb3vQm3H777XjggQdw6qmn4i1veQt27NiRGzdv3jzs3r079xobGwv2Pkz/dyk9bDjXkflpemNox1w3z6SIm9znqh43IlVEbZw203QUOqo1KdfNwE1VZb9/ZaWpxDHUn/2yRUyZf0n2/iq2j9rYVE+ZvDecrrq9Mf4Eme/Uk4vg8R3NqaPIMZmOfSD7o4BjNPbtwxnyupqET3/607jwwgvxvve9DwBw1VVX4Tvf+Q4+//nPY/PmzYXxV111Ve7zj3/84/jWt76Ff/qnf8Lxxx/fPd5oNLBo0aKg966CW/pNGWMspdX4bqjbMPSuGUbc5MdbpGJ8RmxCdDVO1xxqMefNAEOE/2qycTPt3PUa020kw5nP220krcz9zMwCQ37/bmnMJEiGGmi0EyQtfYqWMqbuuEZuTFDTUzbVUyp8+W7k98D7v+bbT8O5zj6D2SN9L/uSlnB85sBx+f/j9Gu1LxnOHct93pzGvtne5wc3p/D72dHu56nImVLMya432pzGVHo8M2a0OYOp2SHlx9ljKkaabeyfbWGk1cb+dgvDzTamZ1sYbrUx3Wb+7svSTIBZ9e+GpOnXzwoEjuDs378fDzzwANatW5c7vm7dOmzbto20xuzsLF544QUceuihueO/+93vsHTpUhx++OE4++yzCxGeLFNTU5icnMy9fCH7hlCiOfYltJqUgSdTcenixkc6yod/hopVFIhYMeXDj6OaR/re2zX485Vp8RUJ7QdCpqd00RvfvhsKoczCLveh9/v4SVv56pUjW8+lukoGNU1FKRm3MRqHIKjAefbZZ9Fut7Fw4cLc8YULF2LPnj2kNT71qU/h97//Pc4555zuseXLl+PGG2/EP/7jP+Ib3/gGxsbGcPLJJ+Pxxx+XrrF582aMj493X0uWLLF6PyaDse7nw3cIXpfCqpW4CZGOovhnysDH9T35cVS4mI1d01T9hi5tpdqDalgwY9pUoIRIT2UxeW9sfTed4/r3688Q3Mi9fKG7P5e0lfZzi145rs0AZfhKU4nl4lmqNhqXYjJuCD+QSZIUjsn4xje+gcsvvxxbtmzBggULusfXrFmDd7/73XjNa16DU045BX/3d3+HV73qVbj66qul62zatAkTExPd165du0j3zTUYu4zLYvPwMBlEKxM3KmyiNgHETDIzg8SnaVk7xp/pWOvH8VxBlbuu51Jw9XVKuYwR6800JU3UOHDTU+QtFkx7V3kSNz6EjU7Q+BY7JqEjP05vEOirV052PVt8Rw4pGBtpBhI9QQXO/Pnz0Wq1CtGaZ555phDVEdmyZQsuvPBC/N3f/R1OP/107dhms4nXvva1ygjO6Ogo5s2bl3txsDEYc35BqytM/Ib/O2vVRNxIjzMrjyxIBY0obGTHrPApwhiRnNBpKm7qKn/NA9dT/Jz7gNq+ocwuqll6Jbn+ysOV65C9M/YPyZBwhYvP6E4V0ZwsOpHDidC4No9UlYtToKanyjAaBxU4IyMjWLVqFbZu3Zo7vnXrVpx00knKed/4xjfw3ve+F1//+tfxh3/4h8brJEmChx56CIsXL3a+ZxM+fjnb+nAofz2bzMrSdcsSNxVEbVSChjInCB4FHDWK47snjgqxu7bpdyLl/4H0jwfi26E2D5P9dRnaaGwjZkKkp7L4jN5w8RmRcRU8IaI52s8dIjmA+efCpw9H7IejQ/p/SNZYM2DDv+BVVJdeeinWr1+PE044AWvXrsW1116LnTt3YuPGjQA66aPf/OY3+MpXvgKgI27e85734DOf+QzWrFnTjf4cdNBBGB8fBwBcccUVWLNmDY466ihMTk7is5/9LB566CF87nOfC/12clANxr43E9T5b2TISoSVZcMhxY30uEWkx4AvcZJdp0GpgsoiVD/lzymqqmRzxLGadQsVVR5othPMKqqimm1gtuWvcipdL9JD9Ve7Kj1lay72Fc3hiBufXhrqdfYl9D8Axxqz0qorVaVV59yMtNKqUFFlqLBS3pNhHHWdlJHmDPbPDmGkNYP9bb4cSCusWq1ZtNtyddJoJUiECKvsWAiCC5xzzz0Xzz33HK688krs3r0bK1aswO23346lS5cCAHbv3p3rifPFL34RMzMz+LM/+zP82Z/9Wff4BRdcgBtvvBEAsHfvXrz//e/Hnj17MD4+juOPPx4//OEPceKJJ3q7b90O4iEb/IXw39jiRdzYbM/AFDbBoi2Ka5DFjk7kcNCUmYtl4yoaM7NIDpSPN9qzSFqdj5szCWaHeL9oBqEUvC6E3IdKF71x6Xnjur9UWcKGcm2T4EkFm0roqEROZ86QcFwvcrKIJeTye1PPN0EpF7dhqDWLGYXQMdJKAM+ip5EkDEk7IExOTmJ8fBwTExNKP05W4DTaPYHT+fjA8dmsv6A3Vhyn26JBtT0DpXux2LnYVD1l9N9oojdacVNy1KYMQUOBJHR0Akc1XzZHHJsZIwqcXBQn0xMnyX7c6n2cFTjp8SRzLI3gJLlxjQPnhM+HVOeFtYTjvfPyc+I6SVM2Lsl/nL7FNATeSrp5/24lRzPppqjSY63WrHIjweFm21hBJRqMZf4bWfM12TFZBZXOXJyN4GQFDtdc7Ds15VvUjDZ6P79Tib90oknwqProyIRO53jx/3hWlIgCJRt9yQqcbG+c7Jjs/LQvTvZ8KmKyYkY8tj/9t51+3nsv6cf72y1MH/g47YWTCpn0eBrBSY+3283usTRaM9tudnvhJN1naqMnbNoNNGaBJz7wYaigPL9T4l5UBkw7iJvmqM6F8N/I5+n/81v5M4zVQgrfjO2u2/BnAk6mp5FM+wnHk+6phAhWCEJFBUnXDhghNaHz3nCMllxMURuK/0YlbkQolVNcyhA3o41m96U6Lp7jYvLucE3Ivjo/25qNu/M9+HDEfamsKXFn8ShwLLFt8OeKj9+xlLb91KqcAh5NxL5FTVbYyI45XSOAlyi/hnp9G7Mxd+sGFaqIYzHa6OVyfiH8og0B9WFj8yDzsU6o1JQNNsLFp9iRH+eVwNvuTs4xiOfWLKkfTqiGfz6NxlHgEKCWoMoI9UefbGPN7jnPf2nrH6CE/xTMSIWrqMmKF4qA8S12WNhGcTyUjKc0S4rMAGFLxUMRuqLKFqq52Mu1SkxN+RIoPtbiRnMoItBneb5pLZ2Y9t0Pp44N/6LAkeBjB3HfG2yaMO9lZVizpFLi3vXU4sYGXyLFZZ3gURwN3I04Odi0HvCBywa3VUPZYFOGsasx4eFo+5e/Db7EjU9RQ7kG9zqlVXxpoi+u5eK9cfzfsTYdumWU3fAvChwNoRr8cTfYLNt/o40AaD0lCt8NEY644UZpbLBZ30rkBDBN576HjJ441NSVr47GdREpsr8mbboYczoXl9FR1oe52CY1RREEZYiaKq7P9eLYRHTK8uGIP88cH45rwz8fRIFDxOUXsesGmyll+W/I2D6YJQ96iripMpUU/NouqT5LvP4szFGoe1DpOhibMDZyI5qLfWO7FUMoUTPWaGGsYdeWgXJP8i0j7L4GtrvAk9e39G/Z+nB0kBv+ZUiafozGUeBYwG3w5/36vv03mr/qQ6Y+OFTij1FgEjreUlVMH47v7xX358tla5GQe7sB8B76dq4kySD7y9qXwdgVdedeu9SUT2GTChpR2MiOUakqmpSFbwp39+G4CHCgJ/R1URuj5yZAJKf672bNsdlB3GWDzbL8N97Lw6npKQsvClvcpOXoqlcJVOnHSeGYjUMYjalbNtSNupqKs/gQQCH2ogrpVVEJGuqccPdFMxv7SFNV6cPhQE3vhjYaR4EjQDUYu6eb9NUkof036nnEN+ZRKOjEAEvcUAWMJ8Fjuje2YTqk+GII2lCpK8r/GV9/MGjvw+GXqu3u4ikuDxauIDH5b4rrE8vXlb1g9OLGJjpShkAR0d1nFV2YVWmq0D6cFN8bb8qMxjkfjkfREwWOAptfqiEa/KVU4b+pS3qKhIs4cBA71qkz2yiOBxFkE73TRQm5P5tVVWXJMFZ1lIh824Z6pKpSXHw3tPX5URoqZYokCjrB6SNN5erD8bnxppQSGv5FgUMgF7mpqMFfbz2e/8ZbeXig9JS36I0vLKI7Qf04gX040WhMI2QX47rCqZ5y8d1UEaUxwY3i+EhTUbHpeVSmD0dGVQ3/osAJBOf3YUj/jQyr8vCSYaemQkEUO9YiR3a9GhFye4a6lIhXge6BU4bB2Ko02TI1pV+zXFHDuV7ZhmNfnqiqfTh1avgXBY4Gmx3EaT4Dmv/GFh9/lTt3Lx5EXPw6ffA14xqNffXCka8dbGklXHMxtUS8Dvjy33DRR0KqidjUKVLkWi5uEsOy8z58OK6U1fAvCpwMOoNxFtcGf1Q4VSimv7SlosdH9+IA6anaRG+YWKXUbLw4JbznmLrqwBE9nCZ/dYeaniqrJLwqVO+hjDSV73JxDiYfTr80/Ov/n8AA+KqW8tXgr7ee2n8jw1vpbw12t5ZShbgpK1WVuybPh9NvUP9/9It+GCSho8PVd1MlVV9fha9ycemcgD4c6403AxuNo8BhUHWDv+J1KvDfmB7SZUZvaoqzyKlRVKquWBbz1A6bdIFqk01q11uf/pu5ACcSZbMBZ4g0VV18OHaT/RmNo8BRELrBn2qDzRD+m2Dl4Z4jB32TmprjAiSk8diGupqVuW3vdYRoytdb20JkDUBqytVw7GauDpOmoq5Rlg+naqNxf/wklgB3B3Eu1A02e+P9+W+k+CgPr4o+EBg8sWZRLt4HXwMupQoVQ2hc19uDu02Da/mtDS4PRpvNNXnr1yc9VKd7SXFJU/WTD6cMo3EUOAK+dxCvk/+mzumpQUhNUemHiqq6UNfoTEROv0RvbKBGcWzSVFQ4m2/K0lRl+HDYZP7Y8G00HtyfRg/YiB3qXFdCdYOtKj1Fpi7iIPR9eFo/J14zAtfUzThpxV8Ng4K2Yy4hVTLo/ps6RHFcIy8u2zb49uHoNt608ea47Cwef4sRof4fJ6WUauy/yVGSiBnU6E2/vK+5UhIeogw1MhhQRY7f3dCr9eHYYFMhaOXDiX1wwhHKYFxH/00d0lNk6hK9qQqi4ORu1zDXozWhdzSuEyHNyrTr+4+WjDaGta/QhEhT1cWHkyIKG5uNN6tgbv9mO4DLDuIhN9jsrRPOf9M3EMXN7PSM8lXVPdHWqvcvisjcwMUrEtJ/4yJgqCKn6lSVa7m4DK4PJyX14VArASkbb1axs3gUOBn8GYL9rKNCFgkKvj1DFstNIqs2F5cqfg5Q2vuLAikyIISIwviM5LiYjYtj/KWpXNJQvv04dWn4FwWOApsdxMvaYJOK0/YMnAdmTQy3LkKlTNETmVvsnx2q+hZqQdUREgqh7zFEmoo611c/HA5VN/yLAodJ6A02OYJHlrLibM/gzX9jic/oRhQkkbqxvz13hI2v9FRIz0w/pKps0lQ22zbY0G3010cN/6LAETDtIM5fz26eGOFx6R5L8d9Yp6dCm4vrbiwOeX91f+8RKftn6x+pcMGlg2/V+BJQPnvihE5Thfbh1Lnh35wXOL53EPe9waZIKP9Njrr4OUpITZWxbr+Ui1dN0ie6YLqdv9H9Bz4fdGEzl6hLOq3MqjdfPhzKxpsmfLV0mPMCJ4Wzg/gg+G/KTE+FNBfH1FQkS5mdj6ejoCFTF8EAhI3i+MBG1FDLxeviwynLaBwFjgGfTTzr5L/JrRU4PWVFP6Vn+uleIyRm2vX/1ViW96IsyuhZw8FGlIVOU2XhlIvLcNpwM6APJ4ej0bj+/4tLxHeDP+4Gm+J1fER42P1v6pCeqjg1VfY1+o1kyK8Ho19SU3ORQd2moR8MxzJ8+nAohPDhmPBpNJ7TAufV1/yt8pyPBn++SKM1VP+NN08ONzJRYu+bfhceccNNmrBxFj+EX5aJ4Q+biBt1Ewkpfvrr0MzGLvSzD0dGmUbjOS1wfMMRNiH9N1Js/De5+YT0lA/ig79vSFqDLwzafZCqGgTqlp7K4kOgcbdu8FUuXrUPx6Xhnw+jcfzfC3W0xmeDP3GDze7cgP4br+XhnhjY6E0UZmRm+1AYzQVDscs2Df2Kj1SVL7NxmZtvprgIG44Px6nhX4akCRz3havJ46PAIRJ6g03xOqVHeAC6/yZU75uaioTSBFUd/E8WhHj2y1JTXq8zWxRZdY7W7EuKD+IpybG6Udf0VJYQ0SPbrRvU6/FETUgfjmpHcUpZeNk7i5fyP/qaa67BkUceibGxMaxatQr33HOPdvwPfvADrFq1CmNjY3jFK16BL3zhC4Uxt9xyC4455hiMjo7imGOOwa233up0j3Vp8FdYx4f/xrU8vIwHb42MxZEBwrO/xnd11ZRkG4d9s/UXLnOREGLNd5qKfF2N2HH14QRr+GdBcIGzZcsWXHLJJfjoRz+KHTt24JRTTsFZZ52FnTt3Ssc/8cQTePOb34xTTjkFO3bswP/8n/8TH/zgB3HLLbd0x2zfvh3nnnsu1q9fj4cffhjr16/HOeecg/vuu8/7/delwV8IQqanQpiLay9uahqBKguTJ8dntZRNyaipSjJSDXXw37jegy+zsWuaiurDkc717MPx3vDPIpITXOB8+tOfxoUXXoj3ve99OProo3HVVVdhyZIl+PznPy8d/4UvfAEvf/nLcdVVV+Hoo4/G+973Pvzpn/4pPvnJT3bHXHXVVXjTm96ETZs2Yfny5di0aRNOO+00XHXVVez7q7LBX9X+mxye01O8a89tYaBljn1tZGkokzByEU6zkohMGakqWeSmXwnV8K6OuEZxuGbj/Dh3743ttg0qVOkqGT4b/lEJ+pO5f/9+PPDAA1i3bl3u+Lp167Bt2zbpnO3btxfGn3HGGbj//vsxfSACoBqjWnNqagqTk5O5lwkf7R9MG2wWxx+4diD/TZWba/Z79Kbq6/cTVT67y+qpI27XECnSD/6bLK6G4xBCz2lHcY9m5BSVDyc1Gvv04eSwbPgXVOA8++yzaLfbWLhwYe74woULsWfPHumcPXv2SMfPzMzg2Wef1Y5Rrbl582aMj493X0uWLGG9D9sGf6749t/kxtp2LyacZ5mLCWOjuOhv5kABUiQiJWSaKotrV2MVaXRnJPB2DjJ8NPwrJbbYEL7JSZIUjpnGi8c5a27atAkTExPd165du1j3zw2bp+dcy2HTjrGydZJW8VsnO4ahZuZ876aTYeJTZ8gwTnK+McT4E54wtjk8OOH8uYD4u9AhBR+J9DX7Ev5Del/C/333+9lR9hwKaSp1fwVhWR8NOIPe9fz589FqtQqRlWeeeaYQgUlZtGiRdPzQ0BBe+tKXaseo1hwdHcXoKO8HIGn624cqaemjOkmrgUY7wWyr8zBIP6+MoSHvaarG8LBTmqo5PFRpJCeKrP6g0S4nTeWjJf2gsy9p91Waaiqh/X7al8i/91OJ/yogWXsA8twA1Xj726ngaQnHO59T+kXJKhGNYiZb5cz4MgeN4IyMjGDVqlXYunVr7vjWrVtx0kknSeesXbu2MP673/0uTjjhBAwPD2vHqNbUkf1laGNm5ITf07FptYmNKJbtAzQrOZYMMb+1pkhNd5zkpqlzOWtGOsyxr41NvymXlLCsNNVXUzIdoXdwLpMQD/a6ohI39PnF38v7iIrcReykTElEj4vhXRQ6OmTmfamhX9KjypbgKapLL70U/+f//B/ccMMNePTRR/GhD30IO3fuxMaNGwF00kfvec97uuM3btyIf/u3f8Oll16KRx99FDfccAOuv/56XHbZZd0xF198Mb773e/iE5/4BH7+85/jE5/4BO68805ccskl3u9f9rOnO9ZPGwd6S1NJkKWpGsNu/0FrH0WZY2JExBR19NlCwSa66qP1e8Q/1MhJne9BJvJCpqey0ZlsekrW/JEqjHxX9qWRGpcu4LnWDhYpq+C/kc8991w899xzuPLKK7F7926sWLECt99+O5YuXQoA2L17d64nzpFHHonbb78dH/rQh/C5z30Ohx12GD772c/ij//4j7tjTjrpJNx88834i7/4C3zsYx/DK1/5SmzZsgWrV6+2vs+klXS/mKaUEm09P7/Qk6EGGjMJZluNgtk4aTULxmLZMQw1u2bjpNWiVVPp0lQBUljUNatOVUX6DM+iRreJoA2ySE6I6peIO67RG/ma6oe/j4iNcm1N+ioVOraCh1JhKIvcyFo2uNJIEguZ2edMTk5ifHwcSzf/LzTHxjJN+hq5hn3pX4nZfaTEhn6Ndra8W/5vs50U9qLS9cIRx4jVVNleOKmYaUqO5XrhKLoZF6qpslVRum7Glts1GH04NayqIkeONBEcWfSqEOWSRcp0YzTnstG5rLk8Zzo/8HHWnJ6mO7PHRLN70h3T+4tKlX7tfp6JcHbXEaKePXN+73PZue6xZv58GqFJP06a6AmcVtI932gl3V4baYqq0Uq6qan03yHh8+Fmu9e8TCiLTctku/vzdI/nq1DELrFZgZN+nBU4ad+SbLlwel5s6patpMmukZsrzMlW7Mj6scj7thT/ktaVSFN8OFU2+6NEb0ziRozgyKI3lPRUNoKTFTii2DFFcLLn07nZ9FT2vChoxH9Tg7HMf5N+vL/d6kZqUoEjRnDa7Wb3WDvzb+q/6Qqc2Ub3WKPd6EVu0gDE7/dh55//BSYmJjBv3jzomDsdmjSofDiyentbH474y7s7V3gQUPDpwyGnqTzhmqYCapqqmuPpKQ7c/dnqgEs31n6B6gUZJHykx3x5kGzSU6748N/st4zY2NCYBX668QPk8VHgeITz+4EjaLygKBenzxfmhHqgE9etpciZY1Ra6VcSZRiOI/Xw4ajwkZrimoup6Skb/41MIIXqrK3z35gMxj62VpnTAucn/99FynOm6ipKHxxffxB56YdjA1fEEHviGKM4cyAawuoVVDNk24VYrUN4bjj72Ai/JH00FIuoCeFd8UGo6I2NuVhHSC+OiC//jW5TWiv/jaXYmdMCR8RUZWGzT05nHu+bI/oZXAhWLl4DyojixEhRePppg9q5hizyMAi49rypCkp6Sh6hsYvaiP4bFS6VUiI+GvylDOZPr0d8/v+uwodDWsu2XJzYE8cqWtFPEY5+utcICd/VUiGQpST6mbqlqWzEjQ9zMZVQ3Yt1dH03DP9NSpkN/lKiwDmAr4Z/dfHhcLZt0BLo4e3DbAzECEskT5k+2blgPPZFnSIhvoRUqAaHNimpOvtvfDb4e+IDH2bdw5wXOP96yaWkcbY+HF9wfThO1CVNVbHh2Ne6vsTcoNMvqSpxmwaxRDzS/9RFkPWT/yZF57+h4sNgDESBUyDrw/EhUmw33rT14QQvF/eYpiI9+Oue/gl5f3V/7xEpgy50fJtoyyRk9CZ0eqru/ptgDf4cxE4UOExsjcamsb58OByqTlP5JKaqInUjbfI3F/CVrgnpw+kHY7Gv8vAQlOG/8WkwBqLAURKq4Z84tkofjhZOmiq0AAqcqmoOD0lfkYgPRgZoY00X6pL20eHzHl021uyMddhJvGL/TYpTgz9HgzFQwl5U/YS3/aM8raOCui8Vl2S4Vdy6QcZQS7otg2lMY2iosHVDY3jYvH2DB6oSLKX5b+rim4pEHFFFWly2c/AZGfLZ+yZ0eoqKb/+NS4M/FVyDMRAjOAD0RuM6NPxLhD2ATNj6cLRUnaZiRHFKi8b4/JpEgRKpAS7bNYSqKuqtP618meZRqDrCZJOeMhHaf5Pi03/juoN4lihwJIRu+GcuQ89vUKgda+PDcd22QbpmwJ44umvMJYgiiLu/mGvkr9/xnfevM2VW5civH0ZE2IofH9iai/Vr0r5P1PJwV1T+G58N/kIQBQ4RasM/Fx+OazrU+7YNJUUVBrWMug7viyJgvbcZqCm+Sk8jgwdVePmMUpW5uWYV/psUK4NxLBMPg2vDP+pcV7hl50DgcvGyqEsUpybGat6amcid4Wdhrkd1BgndX/SUh+ygbteQUnVqqnMPbiKmDv6bFHaDPwONWTv/DRAFDpuqGv758OGo1/ZULh66J86A0M8bbZZNmZ2JI+6E9uFUic/eN7aU6b+hQtlgU4vnHcSzRIFzAKrRWAdF6FAjL2X6cPTjaviE6QOBwBJslK8xpcFin1OqmDFUbeh+WVMMlVm4DwwfuPxF7+thrF6/+ohJSp3uJaUu/pvUYLxf8RDi+G/KbvCXEgWOAhujMW/9/Dp18uFUlabiiYIKH/CGaw96NMq1waRv6hrloVagUAhpDrbZ6FFXFt0vURyOuHGJ3siv3X/+m35q8JcSBQ6DEA3/XPDpw6lDmgoYfHFASk8NYHTGB9n/V3W2haj+4pVh86DJPrCyf8VT0xc2YmnQfTg6XAWbKSLmWh5O3Z5BRiijcdUN/lLm7k+tBo7RmLJOGT4c2TGOD0dLHdNUQDVCwCF6Y+29MX396/r9IVLXCExEj0sUp+rUUNXXV+GSnjLO0YiZ9JxtOrVuDf5SosDJEGpncc6Y/Hi6D8e8lsO2DTpkD9cyozg1inZYiRsbcVLCe54rpeMmOH+JciI3dYfqwxmEVJUO1XtwMReHSk9V4b+xbfAnI0Qbh/hbTINpZ/FQDf9C+HDYa+h8OCU8YGuZqtK871reLxNuxC/sPmrBllbCDatPW3gSqsL08LPx4VDQiZyqoih1it6ESE+Zzpflv9FRhsEYiAInGGVtvFmJD6duhBRcQ0O9lyWs1FSNIlJAWEPxXE5N6R4yPoylJnz6cGz3YerMLVdsuBqLQ+IrAlMX/03VBmMgChwSNjuLU87Z3YtnH46PcvEAaSqgoqhIVtAQxYa178amPNxwnrtNQ0xF0aiqJT31YRUC3tYCbn6c9FUX9JGn8OkpHXXz36Sw/TfSgf4MxkAUOEpsuhiH2HgzuA9HN575sKwUawMvX9BksRZhtsZgDxEem41XdZFC7s+mTdQxFMZQeYmU1TrfBV01lQ8/Tlbs+BY8dRJQgKHDtAf/jW0k0OS/SSmjwZ+LwRiIAqdA6IZ/KXX14XgrF2fgLYpDFSke0k6A+d7YVVNBU230n4dQUR3a/wu7eaz7cAiJW/8yP4CLiOGmMMQHnC8fjm3JuE3KJ6TgUcGN3oTG1n8jw4f/ph8a/KVEgWMgdMM/cZ0QPhxZmsrmr/hQaSoT7CiJGJVxjNLY4Jya8gDHU+WtpUDu+v6ij2Xi1MOjJLw0gAvQPDC0AOCKnTLEkY/0lK/y8Kr9Nyl18N8AUeBYUXXDP64Px4hG7NQlTVWnKqXG8HBY3w11bGD/Dffny6Ubt8/oqBTPv0i52zXokD1syjAaU1D5cEKnqiioojsuoqYOpe2+y8PL9N/4avDniyhwiNSh4V8VPhwtHhvXUdI5qbAwCYwQBL9u7HDcl1BLxV0eIKa/ym26GfvAJVUVQki4RGoo9+RzY03X8nDj+o7+GxMc/41Ngz+XHcSzRIGjwbfRWBxjTi2l4+2UrfkvdItycR9pKgVcz0po0WGzvlX0JoBwyX0PM99nU2qSKoB99cCpS6m4LFRu47cJvU0DF5MPp/i5JJpk8U2ipKpSUVFV1KTM6/tIT+XmBPbfdH03ws+zq/9GRogGfylR4EjgGo1djZGqjTc52PhwcvjoasxB8bC33c7AV3THZY0qfTchU4khqp58dP6uiziS0TNm8n6eTQ8hysOwLlEcjh+nDLGRvQb3OmWZi3XCpUr/Tb81+EuJAoeAyWiso298OLpruXY1Zm5T0Bgast+3KV2DIVSqSnsBoH9txHEawcRt2BjCYKy8Vo1KxKnU1XSs2nQzyLU0atKXyEnxKXZc19qXJMr3EDo9RaEO/puUOjX4S6nn/9w+oKqGf2X5cKy7GuvSMKqqKoPQCSF2fIoa4z1yozfM8XoBKk9P+fJiiVFHMa3aO+/lcn4hbPSXxVezP+pf0L6MxnzTqvz+bFJVrnAFikuURkQnbDjixjY9VVf/TYr1BpvSgX4b/KVEgWPAZmdxnw3/qvLhaKFEF7h+E90c5MWOi+DxGakh3YvWs1Rf03AZkUHltUusSBQJGa3R/aVsEj2q9IMqiqN7OJp8ODb4juLIUAkXnxGfNGKjMhSrt6vgixsO2e9t1f4b5wrCwDuIZ4kCxxHXqI3Y8K+uPpxClMAkcmRjsmMdd9f2Fd3h4u26Lu+fmp5iite4bQON7l+uQuOz1KcgPiC4fxmbKMOUahPFMYkcXbqHi88oDeXedMKGI258di/OIhPAMlFTlv+G2uAvpMEYiAJHiWg0ttlZvCxs/tq2SVNZixzP0RwRX9EdyjVY+DIWa65LNRer0lM2/puQu4jPNXw9hGRwojjyMWFSVb7Fju21Kde3jdpQxI1resol8haqgs+p03e/9cF5/vnnsX79eoyPj2N8fBzr16/H3r17leOnp6fx53/+5zjuuONw8MEH47DDDsN73vMePPXUU7lxb3jDG9BoNHKv8847L+RbkcJt+Ofbh0N90LD+Mhf+6vcicmTjsuMdozki3tJZLmvYpKYoZfYezcUUKHtQ+RI8/dbxuAxyKajMx/sUKQud2VgXIfBlfOX2xilD6NgKKl9Rm85xQ3k+MXpjGseNAqVpU9soI6XBn9Fg3K9l4u9617vw0EMP4Y477sAdd9yBhx56COvXr1eO//d//3c8+OCD+NjHPoYHH3wQ3/zmN/GLX/wCb33rWwtjN2zYgN27d3dfX/ziF0O+lS4+RIrrxps6bKpUCj6ckCIncDRHBleoBE19uYgbARtzMQVbr43KYKy8DuH/gbTXFPHtyMyKspC4LHQeunKqrI01Xb04vlNV6jn+ojrcKE1xvr+oTeccT9yI3zPX8nAb/42KMhr8+STY/7JHH30Ud9xxB+69916sXr0aAHDddddh7dq1eOyxx7Bs2bLCnPHxcWzdujV37Oqrr8aJJ56InTt34uUvf3n3+Ite9CIsWrQo1O3nSFpAQ9MgU3beNCfLbKuBZjspzElaDTTaCWaHgOYM/76l1xpqoDmTHFi/iUa78xOVDDXRmMn8dA01gcznSauFRrt3c8lwC43pzM0OtYCZ7OdDwIzipsWx2TmAfJ5qDhNRuCQHruVN0ITsd+MheqNKT9ls20BFbGwZohjHpZVDGexvD2GkNYP9s0MYUfxnnpodwqiH/+hTyTBGG9PO61RFKkrGGrSfOZ8RIK6w6ZyjCRvZMY642aeI4MlwTX363mBTRqgdxLME+zNl+/btGB8f74obAFizZg3Gx8exbds28joTExNoNBp48YtfnDt+0003Yf78+Tj22GNx2WWX4YUXXlCuMTU1hcnJydyLQlk7i4vYhOpNPhzKg620SE46toJojogfw3CLdm8eU1PU6I1vyvLf1KWs3NZToKpEoZJ9GHHTVDq4nY07x+yiOLZbOfTWkEdhXCM08muFj9r4jtzYUoX/puwGfynBIjh79uzBggULCscXLFiAPXv2kNbYt28fPvKRj+Bd73oX5s2b1z1+/vnn48gjj8SiRYvws5/9DJs2bcLDDz9ciP6kbN68GVdccYXdG8mQtBKt63u2BTQVQQbdORvS9dIoT/5cJyIEdEROQxKxKTWSA+ijOUAxOmOK5oh4iO6w8SG2HH03Jlx631D8N4NE0m6goYgEtdtNtFqzmJ5tYbjZxky7iaHWLKbbLQy32t3j+9stjLR4P4u+Ijcqfj87ioObU8rz+5JhjGUiPuLnnWNDGGsU73Ff0sKYJlSdioYxx9xDKJ+OvvKLH7XpnHNLSQFFcaOK3uQEb8n+mxQn/01g2BL78ssvLxh8xdf9998PAGhIQoxJkkiPi0xPT+O8887D7Owsrrnmmty5DRs24PTTT8eKFStw3nnn4R/+4R9w55134sEHH5SutWnTJkxMTHRfu3bt4r5tJbYN/2z/QtX9BZ2N2GQfTpVHcgBzzxcbE7I4nxpJccXmGtQyesJ7Fb/eNuZi9fe+vB3E5evZnetHfP8l7cNs3B3DiORQSCMkrlEdV7L3YWsirru4yf5chfTf+G7wFwL2T+xFF11krFg64ogj8JOf/ARPP/104dxvf/tbLFy4UDt/enoa55xzDp544gl8//vfz0VvZKxcuRLDw8N4/PHHsXLlysL50dFRjI7625+F6q+hjEvHZKMuMmQ+HFkUJxuxyV2nikgO4Ceak85VzdOtleIjwmMrnKgpMIIIMoqbitNTVINx1VCiNb7h+nAokR1ZtEWGGMXZNzuMsaYpakNb2xTFKY73E9WhXoc3h1cd1Tvv128jm+MibtKPKYLHxX+jpaQdxLOwBc78+fMxf/5847i1a9diYmICP/rRj3DiiScCAO677z5MTEzgpJNOUs5Lxc3jjz+Ou+66Cy996UuN1/qXf/kXTE9PY/HixfQ3wsTGaEydKxsrEy+pyJGlpUypquJ1/IgcAF2hkz58tSkrgCZ0uCZkEy5pLZeIkMeGftwNNeuQniJ37K65IHJh/2wLI4b8tEnMZAXJ1OwwRptm4SGajW1ETuE+FKkqG3wLHZfokK90lOp43cSNr/SUSF0a/KUE+3Pv6KOPxplnnokNGzbg3nvvxb333osNGzbg7LPPzlVQLV++HLfeeisAYGZmBv/lv/wX3H///bjpppvQbrexZ88e7NmzB/v37wcA/OpXv8KVV16J+++/H7/+9a9x++23453vfCeOP/54nHzyyd7fh4+dxV2R/eUs+0tZtgGnKlUlYpuu6oy3SFkB/k3IXExpLZd0F7e/j4XvxjZ64zs9RbqmooKK1u2bfBmvuJaKUwzGIdNUVvMtTce6tI75mnapK0q6ibaOn3SU6ngdxE0W2ZYhtqZ43Qab9EX6tA/OTTfdhOOOOw7r1q3DunXr8OpXvxpf/epXc2Mee+wxTExMAACefPJJ/OM//iOefPJJ/Kf/9J+wePHi7iutvBoZGcH3vvc9nHHGGVi2bBk++MEPYt26dbjzzjvRCtDoTIRajkpp+Cf+q9q2oXOs6HVwFTm6v+pLFTk2G1VSvTkcfPh4bN6PD9+N6JPynKrSiRmbZ/Sg+WmA4pYNOlz2pRLRlQyLD0/x4SoTRK6VVSGEjihmfHh5bBr2dc4VK6Ky53Kf10TcyHYOT6M3MlEjpqc4/puUqg3GQMAqKgA49NBD8bWvfU07Jsm444844ojc5zKWLFmCH/zgB17uzxdJ071BkejFEVNVWXR+nNyaGd8Nt7KqcH+ydBXgVmGVxdQ3B/DjzQmFi4naMJabmhIpKz3lu4S8FBE02wCa+t85acWUirSSikLqw5EhS1Nlj1HTVGLqScSUqpKuyais6pzrfPM43pze3PBGZJ9eG9W5fhM3vrw3Ve8gniXuRcXAtLO47lhxM031HHGurCW+bJdx2ThflVWdOZIfFx8VVt1zjtGc7KtMfKbaPKSmdNGbMtJTZaaUyowEtYW/XjlheV3oP+R+VACtn4qpP476mCmNU69QXaioTZ3ETe46snSUxHej+/lURW/E9JRW2JS4g3iWKHAcsUtFmc5L2snPFZEDmP0rJINuCaLHVpClcwnjXVNTPqI3tukp+1YIdvNcMDYis0T34JClqWzFjukBa0pVUdZUHesc1zW9s09buZJe27b0Wyds0vO5z2eHc1/738+OGsWNOIcrbkSopmKZ78ZHagropaKqNBgDUeCQ0O0s3j3WTM91/qVusEn14+Tn0B5CqgdTbUSObedf6nzZej5ED0XYcL1DBHETCmr0xjYyY9ofzfdmtHVA58NxqVxRdTW2wcaPozrWO6eP5oQSOqKQoV7LxkSsOu/a40ZckypubCqmbMRNFlX0htv0L3QfnChwHCiIE81XUxXF0Y0NZTrOri2eK1XkAG7RHMp8ExzRE0LYpPMEZF8r1+gNZ+8pHRwxnR8j/9fuHhiDGb9EXU2Qur9wQ6epuFEc6RrULR+0KRtz2spF6NgIGc49mqI26Zjc5yWJm8KaDhVTuWME340pNZX+W4jeZNJT3ehNv5eJDyq9X85J7nPZGNtUVZZBEDnZB3My3KpHNMd0LW60h5uOoszL4NrQb1bjp+mOsRQu+TVYw2sL5S/SLNO6iE3ANJUYxQmVqqJWDeXPuQsdH2KGd09mYWPjt/ElbkKairNwfTcmcaOL3oRo8JcSBQ6RbJpKFDm5Y4ZUFdePI0P2+1L2+082LoTI8VJGDpiFSuhojg0uURvFPJutGDjeGxtzMfVnrncN9TkXqur0L/5CtzEaZ5GlqajCxrXXjQglVQXo+77Ypq065+XpJd/pLFsTse68q5k4Xbs7vmRxk8XVd5OiEjey6E3gZtZR4HCQiZzsxyqRQ4Xjx/FlOi7cg4XI6czzJHKAckzIrlDEmG6uBGl0Szqf1/NGFb1Rmc+56Cuq/ISi+9GfQ+mHw4GywzgQNlXFrSbqndNHTkLiOx3VPR5Q3IhwxE0WU8WUT9+NLr1bEDeZsaGiN0AUOM6IqSqXqir5+ukYmunYtbJKPFepyKlT2iq7pm2UiRG16R63aF5Jjd5Iz+e+x+4pK1so/zfYlJT35/pwTGkq392OAVqqSqzuyZ1jVBblz5UrdHyno7rnPIsb3ViuuHE1FWfxmpoSxE3I1FRKFDhMTKmq7jlPqaosFD9O7h4cRE5+HUeRY2M+7s53iOak82Uv7ZoWc9J70a0pQRe1kYobT8ZiTvTGJSXau7b8X05fKF+EKlPl+nCoaSrVeZcojgyVH8d3NKdzfiiY2DGt7RK1AfyIGxFfvW504iaLLrro23cj+/8WOjWVEgWOBbapKp9+HK7pOD+X1yOnM8dB5ADuIsclmqNb00bIyK7tOWpDETe+MUVvyOv0STqp7LbxXLhRHFPZOCVVxRU5gH00pzdmSPqiwJ3nGrXh9rhJ5+nuw0bc2FRMyUzFvnw3IkrfTUmpqZQocDyhSlXZmiJtmgDmjhErq4A+ETmAuwnZF+SycvW9slNSsnRfydGbKlNWQZnN/wWa/nIW/1K1MRrL/lI2palsozgiFHHBFTkhojkqVMLHJvpjayLunrcoA5fNS6/VneMobkKYirO4lIT3Fik/NZUSBY4lulSVj9JxGbam4yyq9eskckhCR3vek9CxKRdP789XSgogiRtXONEbqiXEl8G4H6H+BWxq+kfxXLimqlQiJ0Q0J/sqC5d0FOBP3IjvO6S4yVKV76Yh8d+UlZpKiQLHAVWqSjxWhh8nf12+6Vi1PlAUOblxnkSO92gOwBM53roc86M2gLu4qSJ6oxpbvDft1DmDrh9O53xYY7EOVWWV72iObFwo4eMatQHsG/iZDMUuWzCoxnFNxVlUvhsVZHEjSQOXFb0BosDxjilVRa0O8eXHyY/jlY9TeuQAfkROZ24J0RzbqIzq2kT/DttvA1hHbrjixtZ7I/8Z0403j+l3ZH8Rm9JUdYjiAHyRo1tLdl0qrqLH1UQMyEWKTXdi2bVctmAQP3YxFVN8N5ytGFJUvpsyU1MpUeA4QklVcX7payNBTD+OyXTcDyIHIAgdajTHJW1laUa2TkkxxI3LtgsUbNOeJgZpDypqw7+yojhcw3F3nkbk2KasfERoqNEeFxNxd4zk/dh0J5bdT5nihmMqzhKqW3EVRIHjgdCl47k1FCJH5sfJYltZlb2GeM7Ub8Vma4fOXLV/RYvP3jeOlVUmUcaJ2gB0ceMremMSLeaUFd9/008RHtFoLMPkwzGJnSzcKI6Iqgsv1ZOTYpOykt2Lr7QUZx2bqA1gXwZOFTcilOo5asVUllJ9N5JuxWVHb4AocLwh7jie4rt0XLa2jemYU1mVvYZ4TmU6lp3vzLXb2qF7nJq24kRcPJSKp/dFub8yxE0ITAEF3c+o1fVqJHjEX/xcTF2N83+Fc8vD7VJVsjnduZIIRYopZWWzlURIAzKlQkp1z2WIG2pnYpuKKZ++GxV1KQmXEQVOAGxSVTpCmI5l64tjXbd0kJ3vzbcXOQAhmiPDV98b8ARNdw7TbwPYixtf0RsXc3H+fvL/2lDmPlRiqTgHXcM/gBe5yWLT3dhF5AB2vpx0veyLCzfKo0ph2aSjAH89boDw4iaLTNxkcfHd1L0kXEYUOB4JlarKzWWMUT2odJVVhbUct3SQne/Nl4gcQxl57hxDXLhiI2iAnqjRbrlQkrjxhY/0lEsfsZARnVkbQaPph8NJU1GiODapqpAih7Ibebq2i+AB7EWM7n5k+OpxA9iJm8K1HSqmgHJ8N1V2K9YRBY5nQqeqdGtSTcf5Nczl46WKHIAlcoCi+DC9KNgKmvR+jaImpURx4xK9CZWeqkP6CYD8r1ED3OiO7803RaoQOUBP6FDFTnodV8Fjg+l6dRA3PiumdOImmO+mBqmplChwAmJKVZXtx8nCqawC6iFybDaelOFLBIn3xrpHRaUU4EfciIRousdNT7mO8THHBxQfDidN5SuKI1KmyEmxETvpNW0EjzjP9DLdu0jdxE0Wn6ZiZ2qWmkqJAicA3C7HNnD9OFTTcf4adJGTnxdG5HTmtpSvMrG6bipqNL1sfIkbuiDlRW9c0lN1jOhw9qOiPAxs0lSu6B6YIUQORegAebHjKnhsBAsHX92JAX2Jvqu48Wkqlp0blNRUShQ4gQjd5Vg3Rnad/DE703FxnNqQHFLkqNCJH1dRZC2mCKKme40A4qZ4Dbm4cYErSijP+8CagLWjOEXY0LdmUDyYCPNtHo6AviQZ4IscoCd0qGIHsI/u+EAUWybxRRU3hXniGIctGICwpuJBTk2llNsPfI6TtBI02g0kLaDRRu/fZkf1pp/PtoBm9rzwb3o+v7Y4poFmO29wzs5LWg00DpyfHQKaM8IxxdhkqIHGTJJZs3cd8VzSaqLRnj1wjQaaM/n7yZ7vHhtqojEj/AmQffCL5xwJEvlh7hOl605sauJnEjfkLTeY0Rtznxz9eZ/IjPxe1m030DCs3W430WrJfyan2y0Mt9rSczr2t4cw0prpfDw7hJHmjHTc1OwQRonn9s0OY6w5feDcMEYPfNw9nwxjrJE/Js5TkRUDo5I1ZIii4uDmFGmebK5vbBr4AXRxU5xn7nVTtqnYRJ26FeuIEZyAuHY5zhLCj0M1HYvHOQ9R20iO8qGfjYh43nDSCeY9pe+RK250HaN53xe6WHGB0sXbdn6VcPvhcNNU1L441KgAoO+RA+gjOdR0kE1kBzBHWEJGf7L3XIa4cSkH55qKs3B8N/3UrVhHjZ4Qg4kpVdU9Z0hV6bD143SOH/hBJvyl7kvkUM2xFBFQEDzUlw8CiJruWIO4Ka6t/n4U16ado3hv8j9Xdv6bUkUMITVlUyqexSR+XNJUAC8aoB/L2+qA632xFTuh0QmaLFWJmyymbRiycJv5+exWnFKn6A0QU1SVECJVpRoD9NJI+WPFNFeaquqsFy5d1blWPmWVfaCLaavOevmHRiGNxaWk6A9FzHTH6qqgHCqmbFJTOuqUniobbUpqtoVh4T8VN021f7aFkQNr6FJV2RSUmI7Spa7ElBMnXSWuk2JKYQF2aSzOmj6w8SqFEDeciqmymvmZfDd1S02lxAhOCXBSVSH648jO5Y/ZVcwAdENrZz29WTY7LvuSr91kRUTKhnNfuvcJ+KuY6sylpaa4PwdUdNekRDiDoumFowvrU30L04oHEzVyI3vwpbiYjlWRHGoTPZfIjsvLFWpFlurrEFrcUCumADvfjTM1Tk2l1O/JMKBQuxzbwPHjyOZ1xtlXVnEesIV1D6SstOkXg9jpXKd6scO9B4qw8VUx1Zlrl7bK3VPu5yB7XOavUq8zyFEewO0houqLI8JLR/FFTncso1tw2Y37uHAEje5968RNcSzt+2JbMWXruxnk1FRKTFHVANdUlW6tLKZUlW1lFZBPSYkVXNlz6QNaloYSH+Zi1VV2fgolnVUnTFVRKZSUlIvvJlT0xrajce76NRI/ukqqmXYTQ0K6ypSmyp7f325h5MDxbGpKhJqqEjGlrmTpKgCFlFV3/IGHvSl9la6dQklhhYIitijiTSsAPTfyczUVl+K7qXlqKiUKnBL510suxSuu+jSArBCplx9HFC7iMR8ipzNXLXRSsg95mdjJrpOiW69KbIWNaq5J3FB9N5319dE72Tyb6I0unUolROSHUg6eRebDkR2TCSAdOf+NTvAwSscpIgeA0ZeTJSsIbMRO1REeajRKJ2q6a5UkbmxNxbJzKnFjRCJu6k59/9QdUHx0OQ7hx7HZzkE8DpjTVTJfDiUFlU1luaazyoJ7L7KojSwlxRU3tqkpH9Gb2sBo7BcalRdHh5iyoJaOUz4H5Ckr0gOeudllVeKG4ilK37PpvavSXLaNGFMo4oZiKs7C8d3YdCuuc/QGiBGcWmKK4ugQIz2ydXPVTtJxxVRV4bgh6tO7n85/DjGak9KQNP/LoorI+EpnhYAjrnRG68IxyViuuKGmporXya6pvr4I3ehOO8a9li2z7SaallEal2oqXRQnm6oS4UZu0oesazSnO5cZ1QmNa9optxbTX8MRN7YVU5X5bmrYrVhH9X/mzkFCVlVlkZ1zNR2r+6Hk++DIogzpKzdPMja/Lj/CQ10r1IuC6l45URtXceMzepOfaz21r5E9UCh/OeuiOLoKK/HhaBO54URzyIKAGdVxRTQFU6M0yvUI1VVTs0PSry/H+O3TVFy276ZfiBGciuD4cURc/Dj5dfimY9l9pMg8OUAxSqOL6ohjRUz9cjr3ao7uVIVJgBWOEaI2snEmgVIQPxbRm/x62suR/TdlGow7/9eEn43ZBtAUoooSj46uH44KldlYhGo47ozVm44pkRuZUVkWzemM1RuRc2vUoMGfjyhNby35fxKqcPRpKs5i47uxpV9SUylBIzjPP/881q9fj/HxcYyPj2P9+vXYu3evds573/teNBqN3GvNmjW5MVNTU/jABz6A+fPn4+CDD8Zb3/pWPPnkkwHfSRhsuxxLxwTy43C2c0jPyXw5nCiEKarTu5Zf/04oTNdW3T81JUWJ3HBSU/SScX56ygZZD5w6RYlMO4iHjOLIsIncyKIPgGZXcUZEp0xsfDQmcaOL1lCjOL5Nxa6+m0FPTaUEFTjvete78NBDD+GOO+7AHXfcgYceegjr1683zjvzzDOxe/fu7uv222/Pnb/kkktw66234uabb8Y///M/43e/+x3OPvtstNv8je3qhm2qSga3P46L6VgldFRiJ3+f+vRVaMET+mW658Ixy5RUZz2z54aTmuJGb0zCw4fXpkpMfwGbzk8b/hpP0aamNIbjFNv0lErkmIROlWLHt6DprEkXMKrjsmNccUM1FZfhu6l7SbiMYCmqRx99FHfccQfuvfderF69GgBw3XXXYe3atXjsscewbNky5dzR0VEsWrRIem5iYgLXX389vvrVr+L0008HAHzta1/DkiVLcOedd+KMM87w/2YCErJ0PIvsnA/TMYCc8ThFTF1lxwFQGo1l6SvZHHGejDqXkKs7NNulpDpr8sUNNTVFuSebdeqCLA0lMxpnMaWpdGkoGdm+OIVzBsOxrHScmp6iHAPMO4vXKaLDrdbSeWVU5zkpK1GEcsUN11TsXBKe0oe+myzBIjjbt2/H+Ph4V9wAwJo1azA+Po5t27Zp5959991YsGABXvWqV2HDhg145plnuuceeOABTE9PY926dd1jhx12GFasWKFcd2pqCpOTk7lXnaCmqnRQSsd1KSqu6ViM5lDSIj6iOrJ5viM8oaFGbYByxY3rlgyukRzO+bIxPRhMaSjVeU4Up/C5JJJjMh67Hqtzp2LbCI1OqHDTULKIjS9xk4Xju5ExSN2KdQT7Lb9nzx4sWLCgcHzBggXYs2ePct5ZZ52Fm266Cd///vfxqU99Cj/+8Y/xxje+EVNTU911R0ZG8JKXvCQ3b+HChcp1N2/e3PUBjY+PY8mSJQ7vrBy4qSr5GuoxMrFD2XncVuj49urIcBE8vuFUWamEDdVvE0LcFL9f+XuTHTfhKlq8iZ7APXE4aSoRMSXBFTmdMX5FDsebUyY2PhqdoBHHquabxqaiRiZsXMSNre9mLqamUti/2S+//PKCCVh83X///QCARkPyl2aSSI+nnHvuufjDP/xDrFixAm95y1vw7W9/G7/4xS9w2223ae9Lt+6mTZswMTHRfe3atYvxjsshROl4FoofR3XMVF5METrpOj6iOlQ4gqeKUnHfUZvOXNl78yduuHDSU7VJZWk23QR4lSgUs7H4V3jVIocbzZG9QhBK0IjjZccpY2WiBpALG5OhGDCLGx++m+LE/i0Jl8H24Fx00UU477zztGOOOOII/OQnP8HTTz9dOPfb3/4WCxcuJF9v8eLFWLp0KR5//HEAwKJFi7B//348//zzuSjOM888g5NOOkm6xujoKEZHR8nXrAqdH8dEaD9O+n8tW0IO5H01Yim5qgGguFZ2vLimrHxcJgBknh0RrocnBMbNR0sWN1xU0RtOeipL3VJRXGzKxQF64z8VlCaAshJygOa3kZWOq8bKKDvCQxEx1Hku3prcuUIK0SRUFULH0XejQ9etOKVfozeAhcCZP38+5s+fbxy3du1aTExM4Ec/+hFOPPFEAMB9992HiYkJpRCR8dxzz2HXrl1YvHgxAGDVqlUYHh7G1q1bcc455wAAdu/ejZ/97Gf43//7f3PfTt9gMhxT5nD746TjALrQSf+/i0bk7JjedXof25qSs/ecxUbwqNb2gX5vKL3PqHDMo7gJGb1RwRJAFbciNRmNs2S7GnOFj2hIFg3Hst44NiIHUIsXyrH0eApF7ITARtD4NBKHFDayyA1A893ImIupqZRgvz6OPvponHnmmdiwYQPuvfde3HvvvdiwYQPOPvvsXAXV8uXLceuttwIAfve73+Gyyy7D9u3b8etf/xp333033vKWt2D+/Pn4oz/6IwDA+Pg4LrzwQnz4wx/G9773PezYsQPvfve7cdxxx3WrqvoZn6kqGSY/TrZ8XPxrXUxbcfw5sjHifbmkr4rrNQovClwfD3Ut3f3p5haOVyhuuNEbSom5K4VGfQKmEDslOtq9lqV3R5WmEv8y56aqZMco6SqAn7IyGXFDw005ceZwysFVaSiAlooSvTai38YkbrLIfDdzsVuxjqA/mTfddBM++MEPdiue3vrWt+Jv//Zvc2Mee+wxTExMAABarRZ++tOf4itf+Qr27t2LxYsX49RTT8WWLVtwyCGHdOf8zd/8DYaGhnDOOefgP/7jP3DaaafhxhtvRKvV5/HuA4QuHRfHZK8jfiyWbbtGdLJjsuNSfEZ1RHxFeVzgRmu65zTC0DS2LpEbHWWIIZ9kIzTZj1VRnGyEJjtGTFXVIZIDyCMzusiN76gOVzT5Gu+ahuqMt4/YdI8pxI2T74ZJv0dvAKCRJEl9+tiXxOTkJMbHxzExMYF58+ZVfTtSUoED9MREo6u6heOz+c+zv/8KYzVjZJ+L50RRUDwvrpUfr/rdp9qsU7ambo5riokiergYO/5aCJvOuubxNuKmM0a8lp/oDXt8U3FciG4Wz2eOp2tkoz25eb2Pu71wMts1ZFNU2V452RRU9uMhxfGscMmOEb04st45Yn8cUeTItnaQbcwpipwUnSixPReSMjw3dRQ2AN13M6ipKc7zO262WVN8pKqyyPrjZFNauoeQqkRYfp6fusqO01VfcUvNbdJMNmkt0zoyTPfHTeelc0zQxojXC1tWzaWUCE+mymRW8tCg0lY8pDipKhmmhylAT1cB+lSTTa8Yn4ipJptojWuJN9BLQck8Ni6pKKDzM5CtlOKIGxlzPTWVEgVOjQnlx9H95Szz4xTnSHq0eBI6srFZqEInd96j4DE97KnNCaXnNCKvs7Za2EiFIaGRHzc1xY3G+KKOaau2xPsA0PaeEuH6cQA3keMidEL7cVzEjGk+t8QbKHprenP8ChugGLXJpqRUP2PWJeEC/baRJoXw7rBIZcj8OEDx46KPJu/Hkc3prJ/354jj03vIr2326PTWMnt1ZD4d2fjcuo7VU9yIhrkHDy8NZZpHSUuZ1u6NkaemqPhKT3mh3cinqUqC4sWRYfLjABL/jcyjc+DhLPPlAPK0lclTY+vV0Y21gWM4FuGmoHrzKMJSL1hFQauK2ABq8SwT2LoI46BtpEkhRnBqjksUB5BHcnQPGtu0VciIjmy8uC43qlNY3zG1pVtTed4iWmOcR3xecH03urF1jK4YcehmnH2IhIziyNDtOt4do/jBUUci1NELwE9UR/XiYDPfV7SmN1cvbiiVUWLERpeOylZKmcRNlrmemkqJAqcP8ClyZCkomRjJXo+SturM8yd0TOkr107JFGwED2V8KGGj8zaJ1yiOU94u6bxs7X4RQdlS8dxfwAofjiu67sYUPw61fNxW6NikryjnudiKIdtOwyphk34tXUu+TVEbajoqm5LKRm5cfTeDFr0BYoqqL5E158udz5SOA8U0lK48XDZeN05MSQF+UleAPn2lmpNdO7t+dnyKLo0lvZ5DVMcksGxSUYBeCFKvIxMfIaM3of06VUIpGRfhpqpkpA9bWQm57DigTl115pnTV6r0k03JuC/vjohtGqozVy4c82uYBanvdJT4ubQcnOi7SRlEcQNEgdM3ZHvjpMh64wD5/jidcfIeON2xgvgQxwPFOeK4MoQO4MerI5unmu+Ki7DRzTel82yu1RtXjMLJPtat7yp8+gmb7Rp0okW2jYPMjwMUy8dlHpz0OKAWOjKR05ln79MRx/jEtK4uBaWfp4h6eRY24hxdelOVjspGG1XiZq6mplJiiqqPMKWqZOmqbMpKVSIurimOT+fIzpnSVp258tRVfgyE8+rKIJ9eHdV8todHmGeab7oXG58NJ3XXGc/z3cjm+xyXm1PD30w25eK6v8JV4wCaHwdQV1dRH9S9dUzeE5pPJ6SgMV2DUuKtQvU181EZBbino9LPU7JRm1xKKpOWmsupqZQa/hqJ6NCJnPyxoi8nex4we3Nk43UeC9Uavfk8f05njN5z4suro0IlXLhCKCuwXISNj5RUZ7xsbHENm+iNjr6L7DBD/QB9t3FKvxtxPMWT0z1OfGjn13ITOoDfvjWU+T69NeK53lr2wia7h5QuaqMzEWu9NoAyalMQNwKDLG6AmKLqe3rpqY7IyaascucP/F8weXPS47r0Ux3SVllcvToGewMbG1+Jjc/GOM+juPF1Ln9N2jibtV1I2o1cx2IKVI8Nx4uj2nFclt5SpawA+7RVZz196ipF1SE5xXdkx7e3RnXOJhUF+ElHZT/npKMAYY81icipe7diX8StGmq6VQMF0ZMjbumQP5YZN1ucA6i3b9Bt5VDcmoE2rzdfst2CYfuHzhj9j63J22icTxA9tgZZTurLp9dGJQ4o4kb3eTHqxp9XGGfYoqH3OWOrBkC5XYM4JydwFNs2iONE4ULZvgEobs0gMxzLhI7KwyMTOd1zmh9s7TmF0DFhEj5cfHtrVOdthQ1A22JBHEcxEQMMrw2Qj9oMUFoqbtUwR8imqwD7lJXKmyN6esQ1xTniOVm6y0dpeWeMweNi6dURr6l7UbBJZ5nu31RmLp+juA7hfkxix8c5G0w7iYfAtlxc9zATH56yHjqyh6kuZaVLW6nQnsuke0xprPyaQ4UXB9NcW2+N6rxtKgrwk47Kfi6mo8heGyAftRkgccMlRnD6OIKToorkdD4uL5rDmac6ZhvR6YwLG9XRYdNnJ4X6O9++47Fqjnw9agRGdl2b6E1hXlNzThGl0Z1TRnCEz5URHIC0+SZAj+LIxqo248yNUURnyozmmLCN9lDxHa3prOknYiPOLSNqA0iMxMLHg5SS4jy/o8AZAIGTwklZ5c4Lv0tNQocjclTXVH3eW6OeQsdFyAB0McO5pq+oDSctJbuubjxLGCnSU8U1qxc4srGqXcaBakQOYC90bMbJr+8uegZF2MjOc7w22XFzISUlElNUcxRdykrsfJw731Q/VGTpJ1PqyTVt1VnDLnXVGWfYtJJRgWVbNi5ex5Qy011fub4mVeYqbrhw0li+rx0CXRk4J01letDpUI1VPXBVKStAv8WDKY0jjtNVHynnSlJclDSXSyWU7jwlFQWoDcSqsm/AnI7SVUil6KI2MSVFJ0ZwBiiCk8JNWWU/VqWsAFo0RzzGieaojnXWsY/odMa6RXVMuBSJsIWT4bniQ9zUIXpjXlduMC6cE3WCjdEYqCSKo5rTHes5mpMbZxmxcYn0ULGJ1gByoWdbGSXO5aSjssdi1IZHTFEZGHSBk2KbsgLCenNMc1XHOuu4CZ3OeHexUydB01tXt0Y14sY0X1c9JZ6nVlAVzgUQOIC9FweoXuQAdKHTHe+SovIgemxFTfe8p5Jvca5tOgpw8NoAyvJvYHDFDRBTVJEDUFNWsmopXcpKVWnlK22lOtZZR17STEld9cbTKrB0LyohmwJ21ld/rXrr1VPc1B1qt2LZWN1DDTA/BGUPX58pK6CXptFVXeXGu6SoPMy1Pu+hSZ9qrks6SlohBdCMxHNU3HCJjf4GHHEPq6SVbcSXdP/TpMfTB5KuOSCA7p5WxTXzERXTvOw5ca5sTGeNYrNA1bVSTHtR+dqDytaEzHnwUz0r1A0zueuWRSn3024UjccqZhu5KM5su1lIVflE1tBPtTGnqilguk6KLqojihxKhEcUFpxIDUfkcOf6TkWJ8yuP2mQ+jsJGTUxRDXCKSoTizeGmrIDy0laq47K0lXqsfN2y4f5u9yFqTGuVHb3hpKfkn3tIUQmfi5VZnDSVbHyIVJVsXm4OMfVkSmFl4aazuvM8/4cLKWyAitJRQExJMYgeHANzVeAA/gzI4hiX/jequar5quMUf47qumUQStR01rYXNrJzlNRSlQJHVyIunucIHNnaqq7GAF/gyI6FEDnduQHEDmAveEKgSq/5FDYAb4sF8ZjvqA0wN8UNwHt+xxTVHEOWsgLS9FQxZZX9OJuyEsekvwtke1qlH2evmU856dNW4nzZGp11iqkr1fzsPdcJ36KGsqZNiTdX3Ljisl5jViJybDGkqcR9rHR7T6kQ58hSVUDvIasTOukD3SR0qGmslKyoqErsVCFsZHNKidpkPp6rwsaGKHDmIKn5WObNETft7HwsCJ5mXuSkYwC9Nyc7TuWX4QgdlXjhCp2qqULUqMbIjd38tblrmKI3/YwoWMTPVb6aLCqRk84HaEIHCCt2qqROwgagRW2y42LUxj+ximoOo6qy6nxs3s+KW2kljpOd11VbycarjnXWMjcLlJ0r+0VB9l5078FmDEXcqNYzrVMrGNVRUoQHlPiXOaf6KoWS8jBVRaVVPKZmgmnFkOrhL7um7rpV49KkL7tGFlNPG1PUhlohFcVNWKIHZ455cGSIvhzAvmeOeI7jr+GYkLnHOuv11486NVoD2EdsdOdsfDeyY6R1HAzGpPM+fTgA24sDmA3HgDwKo0pxUaIrFJ8OQPfqVIXsvapEl21lFFB+1AaIRmIu0WRsIAocOS4GZMCu0ory+SALHY6IEaFGSrgeHMCfuJGtZRI3lGvVTeAA1YgcwK/QAeovdlSUKWzEYyG8NkAUNzJio7+IFdyUVeFjIWUlpp5kcyifm9JWumO61JXuRR3n+rKBmtqipqvyX5uw4oZC7VNcQOEvchmUVJXswSl7KMvGpVBSSNT0FZBPYYmvuqG6N10qykfUhlwh5WAkjuLGnRjBiRGcArqUVefj/ovmUM7VHV8RG9U4irBRHbeOAllEbzrHyo3gAHZRHNk8Suk4wI/kpFBLvjlRnTJJI0i2gorisQECpqOAGLUJSCwTjzihq7LqfKwvJwdgVWml+lycC6irrVTHxHM6QougUBEKFwHkIm6o+HrfMvHhm04VoeE6Qsk4QOtuLCsdlx2TVUdRys7Th7lJ6GQf6HUSO1xho4tK+RA2smPevDbCx1Hc+CWmqCJKfKSsbCutKGkr8byquopTrSSbp6p8Clk1xcE1ZeUqbnylpnTXDQ4hnWRTHaWaR3mIpsgewLqUVQqn+imbwuK8QmN7D6r37iMdZVMhFVNS1RBTVDFFZcR3yko8p0tZyY7ZpK2o1DGF5frQ180vS9xI5wZKT0nHyJ6DhjSVbB2Zcdg2VQXQ01WAOspCbSTI7VYckqHWrHeBpBNzMWozOMQUVcQrvlJWAK8Lsuxass9VaasUjmgpM4UVOlphWr9OkRvdteuE2KkYADlVJZtLTVcB6oaA6YOYmrpSUaYA4oob2z48JmEjG+PDawNEcVMHosCJkOFs89A73vsYcPPm5NaRCKHs/Cy+RUsdH8TcewohblRQozeVw9lZ3BKOyAGKokXX9ZgqdFRQRYRvIeSziaAudcc1EQPhozZAFDchiQInwkIUOUBPjGS3ecgeL3zczP8Hd43mZMeIvyupv4upD+wqU1g+hJXqWeLDUMwRTbaUYTDOIjMbu0RxVKiiNirzsc4ULHtQ24oeGRRBkoqgssSLDq/pKCBGbfqIKHAibFxSVgCMG3cC/A04xfnZdURc/gAtI4UVIkKke85wxY1raorivdFd3wavG24yoKaqAL8iR7aGCp/iJ4UrbGzFiwpVCoyTjgIsozZAFDc1Ieh/+eeffx7r16/H+Pg4xsfHsX79euzdu1c7p9FoSF9//dd/3R3zhje8oXD+vPPOC/lWIhJkVVa9CqOk+5evrEqq+7GhOSBnXypqxVK6rurlim11la8qK8578iFuuGv3G4WHF4oPQgDK5n+FCIBqPtQPelVDQB/VTGmlkOzlA936Pq5Dqawy7R8FFKM21imp7HYLsUqqUoJWUZ111ll48sknce211wIA3v/+9+OII47AP/3TPynn7NmzJ/f5t7/9bVx44YX45S9/iVe84hUAOgLnVa96Fa688sruuIMOOgjj4+Ok+4pVVH7xUWUF0JsDys6rjsnwmWaqujDFdzm2TpToBCN1PDV6o5wvrXQijqNUUimOkRr/pRCrqnRrqKIqnGhLyN426X34jryI2Io33X2xojYArWkfEKM2JVGLKqpHH30Ud9xxB+69916sXr0aAHDddddh7dq1eOyxx7Bs2TLpvEWLFuU+/9a3voVTTz21K25SXvSiFxXGRqqBm7IC7AzIgNqEnJ2ThdLsz0XwcASGqxjyFV3inuOWmZvmUOiH6I8q1SRD5cfRpauAoqDhGIll4sCX6HERNr7Lw6n3wjIRA85GYiCKm6oJJr+3b9+O8fHxrrgBgDVr1mB8fBzbtm0jrfH000/jtttuw4UXXlg4d9NNN2H+/Pk49thjcdlll+GFF15QrjM1NYXJycncK+IfasoqPSf9WNMcECimrEypHUoKKESaSIYpNRYydUb5GqnO6d4LZ04tK6eIyNJUShipKgC5pnAiupSVjcgI1ayvrOaA1PSWaZz4NTdFbWyqpKK4qZ5gEZw9e/ZgwYIFheMLFiwopKFUfPnLX8YhhxyCd7zjHbnj559/Po488kgsWrQIP/vZz7Bp0yY8/PDD2Lp1q3SdzZs344orruC/iQgbXZVV52OzARngRXOy1xGxjeCYRE4dGwLKsInYmM5ZeXoUzzWep6ekCipGubgyiiOpqgJ6D1If0Zz0nKtJWCU6QjTj4+ASmZEhE5FeojbC51HY1Ae2wLn88suNYuHHP/4xgI5hWCRJEulxGTfccAPOP/98jI2N5Y5v2LCh+/GKFStw1FFH4YQTTsCDDz6IlStXFtbZtGkTLr20F12YnJzEkiVLSPcQ4UNJWQFpCS4OfCwZR6i0SlGlf2zFjEnAuEZ5Qggk6j2ZxlUtbuqanlLtT8UVOYA+ZQXIvTmmtJXsnAuhxY1NBMpFzIiEKv8GoripC2yBc9FFFxkrlo444gj85Cc/wdNPP10499vf/hYLFy40Xueee+7BY489hi1bthjHrly5EsPDw3j88celAmd0dBSjo6PGdSJ+0TUG7HxuH83Jngfo/W9sozyqcbZU9RAvM2oDhE9LOX8dVdEaxfEyRI52PZgjOjJClIKHNhj7FDOAOkXos/wbiOKmTrAFzvz58zF//nzjuLVr12JiYgI/+tGPcOKJJwIA7rvvPkxMTOCkk04yzr/++uuxatUqvOY1rzGO/Zd/+RdMT09j8eLF5jcQKRVuygqgRXOy47NzUijRHdk6qvU44+qIrbABwogbfnl6/bfMsxU5gDplBagrrTjpKVXzv9AihYpvMZOiFDWAVtgAMSU1CAQvE3/qqafwxS9+EUCnTHzp0qW5MvHly5dj8+bN+KM/+qPuscnJSSxevBif+tSnsHHjxtyav/rVr3DTTTfhzW9+M+bPn49HHnkEH/7wh3HQQQfhxz/+MVot8590sUy8GkShU9xEk1ZO3j2u+d1uEh42FU1VlKG74pKOAsoVN7pzKoHDHk8tFTec0wkubWWVQugA6lJy45oIE6EJRSgxA/AEje5aMSVVXzjP76Dy/aabbsJxxx2HdevWYd26dXj1q1+Nr371q7kxjz32GCYmJnLHbr75ZiRJgv/6X/9rYc2RkRF873vfwxlnnIFly5bhgx/8INatW4c777yTJG4i1aGrsup8rq6yUvVUyb5ka6vm2lQpUautbJr7+XqJ1ze9FxW2DQIB/+ImOBYPUl1VlfbBrHnI6h7OukorwL6qKjTUqqf0/WVfJtJmfNlXfkAj/9JcL6XRbvS+t9mmfenn6bgobvqCoBGcuhIjONXCaQwonqMcB9yiOyLcaE+dIjgyXKI2lPllRW9s5ijvrcwoDmAdySGvj3qloLJ4j8zkBtoJT6rXBogpqaqpRaO/SESFqsoKSBsAFjftTJFttCkeB4oPMpV3RzZXhLufVV29OpQISd3ETZ1RGY4BvUkYgLUvh7w+wpuAqXj1zRQGW0bSoInCxajNwFCP/wGROYmYsgKKKavCTs6K9IspdaRKZenW1MFNcVHTW76hXI/zHrTnLcWNLV7X1D0MOX/5ZzA+2DUPZ8D8oKemcsqEm2oyppmkk+RpJ/H6Imn6KZeGSknTUVHcDBQxghOpFFPPnM7nPZGT/cWkjeBoojQ+oztZfER6yoTqO6LgUg6uj+zUP4MeKpID5EWOrqS8ey8lfr044ooVlSlM9pR2EpGdlwmjmJLqW6LAidQCVc8cwF3smM6HEjwAX/SEhrrlg09hU7WQy9KYtRRjjO7GIiSRk0IQO6bUVdU4iRkgTNophShqgBi1GQSiwInUBlnPHCCs2JGNyT4ARbOyD3+NSmSEEj6+RQ3gT9jUSfy4iBhdFAfoPZiNEZb04e4Y1SkLZzHTXajEKI3muPj/PQqb/iYKnEityPpyyhA7pjG66I5svulaOnxGezibc/oWNtQ1zT16apaeMgignineo9ABaiN2yhAzQKAojea47P90FDaDQRQ4kdpStdiRjdNFd3TrmK6rwnUXcRXcyIlPYUMZZxI3wSI/pigOIcpjiuYADKEDkKI6gD+xU5aQyeIUpQHYogaI0Zq5QBQ4kb5AZkbOki0zzx+3FzumcZTojm693NySfDmhhA1n7VqlpWwgihyAINRshA7AEjvBYQiZFOcoDeBF1ABR2AwyUeBE+grbqE7nnD+xI13fQvCo1qbcj+va2jkVCpvQqSmj0ZjixSH6dSjRHIApdAByVMc7FmIG8CRogChqIiyiwIn0LdSoDuBf7IhjpdcgprM416Dcl2oe6XrMP/yrEDelRIA8ixyA+N5shQ7gV+xYCpkszmmnlChqIpZEgRPpe0xRHSC82DFewyG6o7uOL0IJG+7YWkEVOYDXaA5gIXQAO7HjQcikeIvSAFaiBojCJpInCpzIQMERO/IScv9iRzZHJihcRA+HUE35XMeXWTVl3Q9HRYBoDmApdACvwkWFV0EDRFET8U4UOJGBxSWF1TnvR+xQ54QQPT4e4tbprgDipvRoEKc3DmMsJ5oDyMVEmV2LVfcgEkVNpE5EgRMZeFxTWJ3zZrGjmqu7lmmOSqBI+/FUKGZc1qhdvxuRgCInC/frEEr0cLohswUN4FXUAFHYRNREgROZU4QUO5S5putR59VFzIRYqyy8p6lSGL6c3P1IHvAhRY/Ntg5WggaIoiZSCVHgROYsphQWoPfrdM7TxI5uDdU1OXM4a/rCdU32w7tKEWWzjUP258FhCwgRH6LH9R6M6OZQUl0xBRXxQBQ4kTmPj6hOZ4xa7Ihr6NZxnSOb5ws/Kayap6RUWEZmcnNt52fwIXq46xux3T4he90YrYl4JgqcSCQDJ6oD2Isd6jq6OWXh65ouD+FQ79sqTeUidLLzXdYQcPXzRFETGUSiwIlEJFCiOkAYsaNbqwx8iwnX6EJoUWftxXEVOtk1XNcR0AmWpJWEETTEMbrKwChsIj6JAicSMVC22KGu5Ytw6SwPFT0lRaycDMc+hE52nZRAqTwvDfe4YxCjNZHyiQInEmFASWEBZnNyZwxf7KjWrFMVky8/SNnvybmqypfQEdfLEtq/5LonlEAUNZEqiQInErHAZ1SnM44mdsQ164RPo2tV79FL6bhvoSNb2wbZ/fiO5iCmoCL1IQqcSMSRKsVOSPq22qkuBPLXWBPKd4MoaiL1JAqcSMQj3BQWUK7Y6QfRUnWEKkgDQM73rurvURQ1kQEhCpxIJADUqA5gJ3YGiaoFjYxgXY4pcIWsj58LD6IGiMImUi+iwIlEAhNC7PQ7dRQ1IuLDvDLBY6KENGaM1kT6kShwIpESoaawgMESO/0gaExkH/K1FTseiaIm0u9EgROJVAAnqgP4FQhliaVBEDUq+ia6wySmoCKDRBQ4kUjFcKI6Phhk4VEVVUV3TILEB1HURPqVKHAikZrAjepE6kkZoqMMorCJ9DtR4EQiNSSKnUgVRFETGSSiwIlEak5W7IhE8RPhEkVMZK4QBU4k0sfoxA8QBdBcI4qXSKRHFDiRyABjEkBAFEH9RBQwkQidKHAikTlOjALVgyheIhG/RIETiUS0xCiQH6KAiUTKJQqcSCTizFyPAkXxEonUjyhwIpFIcPo9ChQFTCTSf8xJgZMknd13JycnK76TSCSS8tCfvk97/tXX/C15raRJ32H7pxs/YBwTf1dEIvUg/b+YPsd1NBLKqAHjySefxJIlS6q+jUgkEolEIhbs2rULhx9+uHbMnBQ4s7OzeOqpp3DIIYeg0WhUfTulMTk5iSVLlmDXrl2YN29e1bdTGvF9x/c9F5ir7xuYu+99Lr7vJEnwwgsv4LDDDkOzqd/4bU6mqJrNplH5DTLz5s2bM/8ZssT3PbeI73vuMVff+1x73+Pj46RxJe57G4lEIpFIJFIOUeBEIpFIJBIZOKLAmUOMjo7iL//yLzE6Olr1rZRKfN/xfc8F5ur7Bubue5+r75vKnDQZRyKRSCQSGWxiBCcSiUQikcjAEQVOJBKJRCKRgSMKnEgkEolEIgNHFDiRSCQSiUQGjihwBojnn38e69evx/j4OMbHx7F+/Xrs3btXO6fRaEhff/3Xf90d84Y3vKFw/rzzzgv8bujYvO/3vve9hfe0Zs2a3JipqSl84AMfwPz583HwwQfjrW99K5588smA74QH931PT0/jz//8z3Hcccfh4IMPxmGHHYb3vOc9eOqpp3Lj6vj9vuaaa3DkkUdibGwMq1atwj333KMd/4Mf/ACrVq3C2NgYXvGKV+ALX/hCYcwtt9yCY445BqOjozjmmGNw6623hrp9azjv+5vf/Cbe9KY34WUvexnmzZuHtWvX4jvf+U5uzI033ij9/75v377Qb4UF533ffffd0vf085//PDdu0L7fst9hjUYDxx57bHdMv3y/g5FEBoYzzzwzWbFiRbJt27Zk27ZtyYoVK5Kzzz5bO2f37t251w033JA0Go3kV7/6VXfM61//+mTDhg25cXv37g39dsjYvO8LLrggOfPMM3Pv6bnnnsuN2bhxY/IHf/AHydatW5MHH3wwOfXUU5PXvOY1yczMTMi3Q4b7vvfu3ZucfvrpyZYtW5Kf//znyfbt25PVq1cnq1atyo2r2/f75ptvToaHh5PrrrsueeSRR5KLL744Ofjgg5N/+7d/k47/13/91+RFL3pRcvHFFyePPPJIct111yXDw8PJP/zDP3THbNu2LWm1WsnHP/7x5NFHH00+/vGPJ0NDQ8m9995b1tsywn3fF198cfKJT3wi+dGPfpT84he/SDZt2pQMDw8nDz74YHfMl770pWTevHmF//d1gvu+77rrrgRA8thjj+XeU/b/6SB+v/fu3Zt7v7t27UoOPfTQ5C//8i+7Y/rh+x2SKHAGhEceeSQBkPsPu3379gRA8vOf/5y8ztve9rbkjW98Y+7Y61//+uTiiy/2datesX3fF1xwQfK2t71NeX7v3r3J8PBwcvPNN3eP/eY3v0mazWZyxx13eLl3F3x9v3/0ox8lAHK/ROv2/T7xxBOTjRs35o4tX748+chHPiId/z/+x/9Ili9fnjv23/7bf0vWrFnT/fycc85JzjzzzNyYM844IznvvPM83bU73Pct45hjjkmuuOKK7udf+tKXkvHxcV+3GATu+04FzvPPP69ccy58v2+99dak0Wgkv/71r7vH+uH7HZKYohoQtm/fjvHxcaxevbp7bM2aNRgfH8e2bdtIazz99NO47bbbcOGFFxbO3XTTTZg/fz6OPfZYXHbZZXjhhRe83bsLLu/77rvvxoIFC/CqV70KGzZswDPPPNM998ADD2B6ehrr1q3rHjvssMOwYsUK8tczJD6+3wAwMTGBRqOBF7/4xbnjdfl+79+/Hw888EDu+wAA69atU77P7du3F8afccYZuP/++zE9Pa0dU4fvLWD3vkVmZ2fxwgsv4NBDD80d/93vfoelS5fi8MMPx9lnn40dO3Z4u29XXN738ccfj8WLF+O0007DXXfdlTs3F77f119/PU4//XQsXbo0d7zO3+/QzMnNNgeRPXv2YMGCBYXjCxYswJ49e0hrfPnLX8YhhxyCd7zjHbnj559/Po488kgsWrQIP/vZz7Bp0yY8/PDD2Lp1q5d7d8H2fZ911ll45zvfiaVLl+KJJ57Axz72MbzxjW/EAw88gNHRUezZswcjIyN4yUtekpu3cOFC8tczJD6+3/v27cNHPvIRvOtd78pt1Fen7/ezzz6LdruNhQsX5o7rvg979uyRjp+ZmcGzzz6LxYsXK8fU4XsL2L1vkU996lP4/e9/j3POOad7bPny5bjxxhtx3HHHYXJyEp/5zGdw8skn4+GHH8ZRRx3l9T3YYPO+Fy9ejGuvvRarVq3C1NQUvvrVr+K0007D3Xffjde97nUA1D8Tg/L93r17N7797W/j61//eu543b/foYkCp+ZcfvnluOKKK7RjfvzjHwPoGIZFkiSRHpdxww034Pzzz8fY2Fju+IYNG7ofr1ixAkcddRROOOEEPPjgg1i5ciVpbS6h3/e5557b/XjFihU44YQTsHTpUtx2220FgcdZ15Wyvt/T09M477zzMDs7i2uuuSZ3rorvtwnxPZnep2y8eJy7ZhXY3uM3vvENXH755fjWt76VE8Jr1qzJmelPPvlkrFy5EldffTU++9nP+rtxRzjve9myZVi2bFn387Vr12LXrl345Cc/2RU43DWrwvYeb7zxRrz4xS/G29/+9tzxfvl+hyIKnJpz0UUXGStYjjjiCPzkJz/B008/XTj329/+tvBXgYx77rkHjz32GLZs2WIcu3LlSgwPD+Pxxx8P9sAr632nLF68GEuXLsXjjz8OAFi0aBH279+P559/PhfFeeaZZ3DSSSeR1+VSxvuenp7GOeecgyeeeALf//73c9EbGWV8v1XMnz8frVar8FfsM888o3yfixYtko4fGhrCS1/6Uu0Yzs9MSGzed8qWLVtw4YUX4u///u9x+umna8c2m0289rWv7f7cV43L+86yZs0afO1rX+t+Psjf7yRJcMMNN2D9+vUYGRnRjq3b9zs41Vh/Ir5JTaf33Xdf99i9995LNp1ecMEFhWoaFT/96U8TAMkPfvAD6/v1hev7Tnn22WeT0dHR5Mtf/nKSJD2T8ZYtW7pjnnrqqdqZjLnve//+/cnb3/725Nhjj02eeeYZ0rWq/n6feOKJyX//7/89d+zoo4/WmoyPPvro3LGNGzcWTMZnnXVWbsyZZ55ZO9Mp530nSZJ8/etfT8bGxpJbb72VdI3Z2dnkhBNOSP7kT/7E5Va9YvO+Rf74j/84OfXUU7ufD+r3O0l6Juuf/vSnxmvU8fsdkihwBogzzzwzefWrX51s37492b59e3LccccVyoaXLVuWfPOb38wdm5iYSF70ohcln//85wtr/vKXv0yuuOKK5Mc//nHyxBNPJLfddluyfPny5Pjjj69VuTTnfb/wwgvJhz/84WTbtm3JE088kdx1113J2rVrkz/4gz9IJicnu3M2btyYHH744cmdd96ZPPjgg8kb3/jG2pWJc9739PR08ta3vjU5/PDDk4ceeihXNjo1NZUkST2/32n57PXXX5888sgjySWXXJIcfPDB3WqRj3zkI8n69eu749My8Q996EPJI488klx//fWFMvH/9//+X9JqtZK/+qu/Sh599NHkr/7qr2pbNkx931//+teToaGh5HOf+5yyxP/yyy9P7rjjjuRXv/pVsmPHjuRP/uRPkqGhoZxQrhru+/6bv/mb5NZbb01+8YtfJD/72c+Sj3zkIwmA5JZbbumOGcTvd8q73/3uZPXq1dI1++H7HZIocAaI5557Ljn//POTQw45JDnkkEOS888/v1A6CSD50pe+lDv2xS9+MTnooIOkvU527tyZvO51r0sOPfTQZGRkJHnlK1+ZfPCDHyz0jKkS7vv+93//92TdunXJy172smR4eDh5+ctfnlxwwQXJzp07c3P+4z/+I7nooouSQw89NDnooIOSs88+uzCmSrjv+4knnkgASF933XVXkiT1/X5/7nOfS5YuXZqMjIwkK1euzEWTLrjgguT1r399bvzdd9+dHH/88cnIyEhyxBFHSMX73//93yfLli1LhoeHk+XLl+ceiHWB875f//rXS7+3F1xwQXfMJZdckrz85S9PRkZGkpe97GXJunXrkm3btpX4jmhw3vcnPvGJ5JWvfGUyNjaWvOQlL0n+83/+z8ltt91WWHPQvt9J0ok0H3TQQcm1114rXa9fvt+haCTJAfddJBKJRCKRyIAQ++BEIpFIJBIZOKLAiUQikUgkMnBEgROJRCKRSGTgiAInEolEIpHIwBEFTiQSiUQikYEjCpxIJBKJRCIDRxQ4kUgkEolEBo4ocCKRSCQSiQwcUeBEIpFIJBIZOKLAiUQikUgkMnBEgROJRCKRSGTgiAInEolEIpHIwPH/A9qzxxYLuGB7AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "up = u.backward()\n", "xp, yp, up = wrap_periodic([X[0], X[1], up], axes=[1])\n", "plt.contourf(xp, yp, up, 100);" ] }, { "cell_type": "markdown", "id": "39be30cc", "metadata": { "editable": true }, "source": [ "## Adaptive functions in multiple dimensions\n", "\n", "If you want to find a good resolution for a function in multiple\n", "dimensions, the procedure is exactly like in 1D. First create function\n", "spaces with 0 quadrature points, and then call [Function](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.Function)" ] }, { "cell_type": "code", "execution_count": 28, "id": "f896255d", "metadata": { "collapsed": false, "editable": true, "execution": { "iopub.execute_input": "2024-02-19T13:47:53.426026Z", "iopub.status.busy": "2024-02-19T13:47:53.425837Z", "iopub.status.idle": "2024-02-19T13:47:53.605025Z", "shell.execute_reply": "2024-02-19T13:47:53.604491Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(5, 12)\n" ] } ], "source": [ "B0 = FunctionSpace(0, 'C', domain=(0, 1))\n", "F0 = FunctionSpace(0, 'F')\n", "T = TensorProductSpace(comm, (B0, F0), coordinates=(psi, rv))\n", "u = Function(T, buffer=((1-r)*r)**2*sp.sin(sp.cos(theta)))\n", "print(u.shape)" ] }, { "cell_type": "markdown", "id": "d0e41011", "metadata": { "editable": true }, "source": [ "The algorithm used to find the approximation in multiple dimensions\n", "simply treat the problem one direction at the time. So in this case\n", "we would first find a space in the first direction by using\n", "a function ` ~ ((1-r)*r)**2`, and then along the second using\n", "a function ` ~ sp.sin(sp.cos(theta))`.\n", "\n", "" ] } ], "metadata": { "kernelspec": { "display_name": "shenfun24", "language": "python3", "name": "shenfun24" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.0" } }, "nbformat": 4, "nbformat_minor": 5 }