{ "cells": [ { "cell_type": "markdown", "id": "c04e3ac9", "metadata": {}, "source": [ "# Differential equation resolution\n", "\n", "## Introduction\n", "\n", "We present here a Perceval implementation of a Quantum Machine Learning algorithm for solving differential equations. Its aims is to approximate the solution to the differential equation considered in \\[1\\]:\n", "\n", "$$\n", "\\frac{d f}{d x}+\\lambda f(x)(\\kappa+\\tan (\\lambda x))=0\n", "$$\n", "\n", "with boundary condition $f(0)=f_{0}$. The analytical solution is $f(x)=f_0\\exp (-\\kappa \\lambda x) \\cos (\\lambda x)$.\n", "\n", "### QML Loss Function Definition\n", "\n", "In order to use QML to solve this differential equation, we first need to derive from it a loss function whose minimum is associated to its analytical solution.\n", "\n", "Let $F\\left[\\left\\{d^{m} f / d x^{m}\\right\\}_{m},f, x\\right]=0$ be a general differential equation verified by $f(x)$, where $F[.]$ is an operator acting on $f(x)$, its derivatives and $x$. For the solving of a differential equation, the loss function described in \\[1\\] consists of two terms\n", "\n", "$$\n", " \\mathcal{L}_{\\boldsymbol{\\theta}}\\left[\\left\\{d^{m} g / d x^{m}\\right\\}_{m},g, x\\right]:=\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\mathrm{diff})}\\left[\\left\\{d^{m} g / d x^{m}\\right\\}_{m},g, x\\right]+\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\text {boundary})}[g, x].\n", "$$\n", "\n", "The first term $\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\mathrm{diff})}$ corresponds to the differential equation which has been discretised over a fixed regular grid of $M$ points noted $x_i$:\n", "\n", "$$\n", " \\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\mathrm{diff})}\\left[\\left\\{d^{m} g / d x^{m}\\right\\}_{m},g, x\\right]:=\\frac{1}{M} \\sum_{i=1}^{M} L\\left(F\\left[d_{x}^m g\\left(x_{i}\\right), g\\left(x_{i}\\right), x_{i}\\right], 0\\right),\n", "$$\n", "\n", "where $L(a,b) := (a - b)^2$ is the squared distance between two arguments. The second term $\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\text {boundary })}$ is associated to the initial conditions of our desired solution. It is defined as: \n", "\n", "$$\n", " \\mathcal{L}_{\\boldsymbol{\\theta}}^{\\text {(boundary) }}[g, x]:=\\eta L\\left(g(x_0), f_{0}\\right),\n", "$$\n", " \n", "where $\\eta$ is the weight granted to the boundary condition and $f_{0}$ is given by $f(x_0) = f_0$. \n", "\n", "Given a function approximator $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$, the loss function above will be minimised using a classical algorithm, updating the parameters $\\boldsymbol{\\theta}$ based on samples obtained using a quantum device.\n", "\n", "### Quantum circuit architecture\n", "\n", "The feature map used is presented in \\[2,3,4\\]. The quantum circuit architecture from \\[4\\] is expressed as $\\mathcal{U}(x, \\boldsymbol{\\theta}):=\\mathcal{W}^{(2)}\\left(\\boldsymbol{\\theta}_{2}\\right) \\mathcal{S}(x) \\mathcal{W}^{(1)}\\left(\\boldsymbol{\\theta}_{1}\\right).$ The phase-shift operator $\\mathcal{S}(x)$ incorporates the $x$ dependency of the function we wish to approximate. It is sandwiched between two universal interferometers $\\mathcal{W}^{(1)}(\\boldsymbol{\\theta_1})$ and $\\mathcal{W}^{(2)}(\\boldsymbol{\\theta_2})$, where the beam-splitter parameters $\\boldsymbol{\\theta_1}$ and $\\boldsymbol{\\theta_2}$ of this mesh architecture are tunable to enable training of the circuit.\n", "The output measurement operator, noted $\\mathcal{M}(\\boldsymbol{\\lambda})$, is the projection on the Fock states obtained using photon-number resolving detectors, multiplied by some coefficients $\\boldsymbol{\\lambda}$ which can also be tunable. Formally, we have:\n", "\n", "$$ \\mathcal{M}(\\boldsymbol{\\lambda}) = \\sum_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\lambda_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\mathbf{\\left | n^{(f)}\\right \\rangle}\\mathbf{\\left \\langle n^{(f)}\\right |},\n", "$$\n", "\n", "where the sum is taken over all $\\binom{n+m-1}{n}$ possible Fock states considering $n$ photons in $m$ modes. Let $\\mathbf{\\left | n^{(i)}\\right \\rangle} = \\left |n^{(i)}_1,n^{(i)}_2,\\dots,n^{(i)}_m\\right \\rangle$ be the input state consisting of $n$ photons where $n^{(i)}_j$ is the number of photons in input mode $j$. Given these elements, the circuit's output $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ is given by the following expectation value:\n", "\n", "$$\n", "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\left\\langle\\mathbf{n}^{(i)}\\left|\\mathcal{U}^{\\dagger}(x, \\boldsymbol{\\theta}) \\mathcal{M}(\\boldsymbol{\\lambda}) \\mathcal{U}(x, \\boldsymbol{\\theta})\\right| \\mathbf{n}^{(i)}\\right\\rangle.\n", "$$\n", "\n", "This expression can be rewritten as the following Fourier series \\[4\\]\n", "\n", "$$\n", "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\sum_{\\omega \\in \\Omega_{n}} c_{\\omega}(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda}) e^{i \\omega x},\n", "$$\n", "\n", "where $\\Omega_n = \\{-n, -n+1, \\dots, n-1, n \\}$ is the frequency spectrum one can reach with $n$ incoming photons and $\\{c_\\omega(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda})\\}$ are the Fourier coefficients. The $\\boldsymbol{\\lambda}$ parameters are sampled randomly in the interval $[-a;a]$, with $a$ a randomly chosen integer. $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ will serve as a function approximator for this chosen differential equation. Differentiation in the loss function is discretised as $\\frac{df}{dx} \\simeq \\frac{f(x+\\Delta x) - f(x-\\Delta x)}{2\\Delta x}$.\n", "\n", "$n, m,$ and $\\boldsymbol{\\lambda}$ are variable parameters defined below. $\\Delta x$ is the mesh size." ] }, { "cell_type": "markdown", "id": "e9df16c8", "metadata": {}, "source": [ "## Perceval Simulation\n", "\n", "### Initialisation" ] }, { "cell_type": "code", "execution_count": 1, "id": "7918962c", "metadata": {}, "outputs": [], "source": [ "import perceval as pcvl\n", "import numpy as np\n", "from math import comb, pi\n", "from scipy.optimize import minimize\n", "import time\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "import tqdm as tqdm" ] }, { "cell_type": "markdown", "id": "04323b71", "metadata": {}, "source": [ "We will run this notebook with 4 photons. We could use more photons, but the result with 4 photons is already satisfying." ] }, { "cell_type": "code", "execution_count": 2, "id": "f59b62f8", "metadata": {}, "outputs": [], "source": [ "nphotons = 4" ] }, { "cell_type": "markdown", "id": "bd3c3eaf", "metadata": {}, "source": [ "### Differential equation parameters\n", "\n", "We define here the value of the differential equation parameters and boundary condition $\\lambda, \\kappa, f_0$." ] }, { "cell_type": "code", "execution_count": 3, "id": "debd15cc", "metadata": {}, "outputs": [], "source": [ "# Differential equation parameters\n", "lambd = 8\n", "kappa = 0.1\n", "\n", "def F(u_prime, u, x): # DE, works with numpy arrays\n", " return u_prime + lambd * u * (kappa + np.tan(lambd * x))" ] }, { "cell_type": "code", "execution_count": 4, "id": "4c18efbf", "metadata": {}, "outputs": [], "source": [ "# Boundary condition (f(x_0)=f_0)\n", "x_0 = 0\n", "f_0 = 1" ] }, { "cell_type": "code", "execution_count": 5, "id": "ac67fd52", "metadata": {}, "outputs": [], "source": [ "# Modeling parameters\n", "n_grid = 50 # number of grid points of the discretized differential equation\n", "range_min = 0 # minimum of the interval on which we wish to approximate our function\n", "range_max = 1 # maximum of the interval on which we wish to approximate our function\n", "X = np.linspace(range_min, range_max-range_min, n_grid) # Optimisation grid" ] }, { "cell_type": "code", "execution_count": 6, "id": "45a02405", "metadata": {}, "outputs": [], "source": [ "# Differential equation's exact solution - for comparison\n", "def u(x):\n", " return np.exp(- kappa*lambd*x)*np.cos(lambd*x)" ] }, { "cell_type": "code", "execution_count": 7, "id": "9c8830ee", "metadata": {}, "outputs": [], "source": [ "# Parameters of the quantum machine learning procedure\n", "N = nphotons # Number of photons\n", "m = nphotons # Number of modes\n", "eta = 5 # weight granted to the initial condition\n", "a = 200 # Approximate boundaries of the interval that the image of the trial function can cover\n", "fock_dim = comb(N + m - 1, N)\n", "# lambda coefficients for all the possible outputs\n", "lambda_random = 2 * a * np.random.rand(fock_dim) - a\n", "# dx serves for the numerical differentiation of f\n", "dx = (range_max-range_min) / (n_grid - 1)" ] }, { "cell_type": "code", "execution_count": 8, "id": "355b87c8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "|1,1,1,1>\n" ] } ], "source": [ "# Input state with N photons and m modes\n", "input_state = pcvl.BasicState([1]*N+[0]*(m-N))\n", "print(input_state)" ] }, { "cell_type": "markdown", "id": "58385605", "metadata": {}, "source": [ "## Definition of the circuit\n", "\n", "We will generate a Haar-random initial unitary using QR decomposition built in Perceval `Matrix.random_unitary`, the circuit is defined by the combination of 3 sub-circuits - the intermediate phase is a parameter." ] }, { "cell_type": "code", "execution_count": 9, "id": "5dd4d6c3", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "W1\n", "\n", "\n", "Φ=px\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "W2\n", "\n", "\n", "\n", "\n", "0\n", "1\n", "2\n", "3\n", "0\n", "1\n", "2\n", "3\n", "" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"Haar unitary parameters\"\n", "# number of parameters used for the two universal interferometers (2*m**2 per interferometer)\n", "parameters = np.random.normal(size=4*m**2)\n", "\n", "px = pcvl.P(\"px\")\n", "c = pcvl.Unitary(pcvl.Matrix.parametrized_unitary(m, parameters[:2 * m ** 2]), name=\"W1\")\\\n", " // (0, pcvl.PS(px))\\\n", " // pcvl.Unitary(pcvl.Matrix.parametrized_unitary(m, parameters[2 * m ** 2:]), name=\"W2\")\n", "\n", "backend = pcvl.BackendFactory().get_backend(\"SLOS\")\n", "backend.set_circuit(pcvl.Unitary(pcvl.Matrix.random_unitary(m)))\n", "backend.preprocess([input_state])\n", "\n", "pcvl.pdisplay(c)" ] }, { "cell_type": "markdown", "id": "5d9333b0", "metadata": {}, "source": [ "### Expectation value and loss function computation\n", "\n", "The expectation value of the measurement operator $\\mathcal{M}(\\boldsymbol{\\lambda})$ is obtained directly from Fock state probabilities computed by Perceval. Given this expectation value, the code snippet below computes the loss function defined in the Introduction.\n", "\n", "Note the use of the `all_prob` simulator method giving directly access to the probabilities of all possible output states, including null probabilities. This calculation is optimized in SLOS backend." ] }, { "cell_type": "code", "execution_count": 10, "id": "597cce98", "metadata": {}, "outputs": [], "source": [ "def computation(params):\n", " global current_loss\n", " global computation_count\n", " \"compute the loss function of a given differential equation in order for it to be optimized\"\n", " computation_count += 1\n", " f_theta_0 = 0 # boundary condition\n", " coefs = lambda_random # coefficients of the M observable\n", " # initial condition with the two universal interferometers and the phase shift in the middle\n", " U_1 = pcvl.Matrix.parametrized_unitary(m, params[:2 * m ** 2])\n", " U_2 = pcvl.Matrix.parametrized_unitary(m, params[2 * m ** 2:])\n", "\n", " px = pcvl.P(\"x\")\n", " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n", "\n", " px.set_value(pi * x_0)\n", " backend.set_circuit(c)\n", " f_theta_0 = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", " # boundary condition given a weight eta\n", " loss = eta * (f_theta_0 - f_0) ** 2 * len(X)\n", "\n", " # Y[0] is before the domain we are interested in (used for differentiation), x_0 is at Y[1]\n", " Y = np.zeros(n_grid + 2)\n", "\n", " # x_0 is at the beginning of the domain, already calculated\n", " Y[1] = f_theta_0\n", "\n", " px.set_value(pi * (range_min - dx))\n", " backend.set_circuit(c)\n", " Y[0] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", "\n", " for i in range(1, n_grid):\n", " x = X[i]\n", " px.set_value(pi * x)\n", " backend.set_circuit(c)\n", " Y[i + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", " px.set_value(pi * (range_max + dx))\n", " backend.set_circuit(c)\n", " Y[n_grid + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", " # Differentiation\n", " Y_prime = (Y[2:] - Y[:-2])/(2*dx)\n", "\n", " loss += np.sum((F(Y_prime, Y[1:-1], X))**2)\n", "\n", " current_loss = loss / len(X)\n", " return current_loss" ] }, { "cell_type": "markdown", "id": "8acf5506", "metadata": {}, "source": [ "### Classical optimisation\n", "\n", "Finally the code below performs the optimisation procedure using the loss function defined in the previous section. To this end, we use a Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimiser \\[5\\] from the SciPy library." ] }, { "cell_type": "code", "execution_count": 11, "id": "281dbb29", "metadata": {}, "outputs": [], "source": [ "def callbackF(parameters):\n", " \"\"\"callback function called by scipy.optimize.minimize allowing to monitor progress\"\"\"\n", " global current_loss\n", " global computation_count\n", " global loss_evolution\n", " global start_time\n", " now = time.time()\n", " pbar.set_description(\"M= %d Loss: %0.5f #computations: %d elapsed: %0.5f\" % \n", " (m, current_loss, computation_count, now-start_time))\n", " pbar.update(1)\n", " loss_evolution.append((current_loss, now-start_time))\n", " computation_count = 0\n", " start_time = now" ] }, { "cell_type": "code", "execution_count": null, "id": "465db5d2", "metadata": {}, "outputs": [], "source": [ "computation_count = 0\n", "current_loss = 0\n", "start_time = time.time()\n", "loss_evolution = []\n", "\n", "pbar = tqdm.tqdm()\n", "res = minimize(computation, parameters, callback=callbackF, method='BFGS', options={'gtol': 1E-2})" ] }, { "cell_type": "markdown", "id": "1be681a8", "metadata": {}, "source": [ "After the optimisation procedure has been completed, the optimal unitary parameters (in `res.x`) can be used to determine the quantum circuit beam-splitter and phase-shifter angles for an experimental realisation." ] }, { "cell_type": "code", "execution_count": 13, "id": "21726b0c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Unitary parameters [ 1.90624035 0.15201242 -0.82869314 0.89828783 0.6380241 -1.04604715\n", " 4.40125344 -0.11807653 0.84899534 0.78434718 -0.25534406 3.60915677\n", " -0.66390566 -1.92075941 -3.3959869 4.64905094 2.68642653 -0.09049131\n", " -0.55289317 3.96738349 -2.48499145 1.94691379 0.81546265 -4.27745458\n", " -0.48299482 -2.61704687 -1.32399656 0.19826926 0.38186777 -1.24266346\n", " -0.35951725 -3.81589427 -0.54128274 1.5325363 0.3096436 -1.70350065\n", " -2.4345667 0.01430551 -0.92837642 1.77323448 0.42465747 0.48688715\n", " 1.17728595 -0.63465766 0.2021728 -0.21649088 -2.16424414 -1.06376279\n", " -0.83562031 0.86918988 1.83050536 0.34868688 -0.53611804 1.45509538\n", " 1.93232455 -0.08290686 0.14500095 0.24973801 -2.61256259 0.3786195\n", " -0.95858293 -0.27414401 -1.21134094 -1.27487461]\n" ] } ], "source": [ "print(\"Unitary parameters\", res.x)" ] }, { "cell_type": "markdown", "id": "3b6c5da8", "metadata": {}, "source": [ "### Plotting the approximation\n", "\n", "We now plot the result of our optimisation in order to compare the QML algorithm's output and the analytical solution." ] }, { "cell_type": "code", "execution_count": 14, "id": "6bede765", "metadata": {}, "outputs": [], "source": [ "def plot_solution(m, N, X, optim_params, lambda_random):\n", " Y = []\n", " U_1 = pcvl.Matrix.parametrized_unitary(m, optim_params[:2 * m ** 2])\n", " U_2 = pcvl.Matrix.parametrized_unitary(m, optim_params[2 * m ** 2:])\n", " px = pcvl.P(\"x\")\n", " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n", "\n", " for x in X:\n", " px.set_value(pi * x)\n", " backend.set_circuit(c)\n", " f_theta = np.sum(np.multiply(backend.all_prob(input_state), lambda_random))\n", " Y.append(f_theta)\n", " exact = u(X)\n", " plt.plot(X, Y, label=\"Approximation with {} photons\".format(N))" ] }, { "cell_type": "code", "execution_count": 15, "id": "b997c635", "metadata": {}, "outputs": [ { "data": { "image/png": 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3q2nTppQtW5aHH36YDh068OSTT952+9T/d6fvE7B9z7Zo0YJHHnkEX19fZs2alaHn3Ymnpyfr1q2jVatWlCtXjiFDhjB27Fhatmx5N5+Cu2KyZuVeIDlUTEwMXl5eREdH4+npaXQcEREREZFcKSEhgZMnT1KyZMm7XiwwpwsJCeGRRx7hypUreHt73/SY6dOn069fP6KiorI1m+R83bt3JyoqikWLFhkdJVvc7mdBRt9/a+SEiIiIiIiIiBhK5YSIiIiIiIiIGErTOjStQ0RERETknuTlaR0iknGa1iEiIiIiIiIiuZ7KCRERERERERExVJaWE+vWraNNmzYUKVIEk8mUoZVKQ0JCqFmzJk5OTpQpU4bp06ffcMzEiRMJCgrC2dmZevXqsWXLlswPLyIiIiIiIiLZIkvLibi4OKpXr87EiRMzdPzJkydp3bo1jzzyCLt27aJfv3689NJL/Pnnn2nHzJkzh/79+zNs2DB27NhB9erVad68OREREVl1GSIiIiIiIiKShbJtQUyTycTChQt56qmnbnnMu+++y9KlS9m3b1/afR07diQqKorly5cDUK9ePerUqcOECRMAsFgsBAYG0rdvXwYNGpShLLlxQUzr5MmYSpSAZs3ArNk4IiIiImI8LYgpIpAHF8TcuHEjzZo1S3df8+bN2bhxIwBJSUls37493TFms5lmzZqlHXMziYmJxMTEpLvlKlevkvjmW9C8OSlly8HYsXD5stGpRERERERERDJFjionwsLC8PPzS3efn58fMTExXLt2jcjISFJTU296TFhY2C3P++mnn+Ll5ZV2CwwMzJL8WeXshUvMqfgIMY6u2J84DgMGYClaFLp3hwMHjI4nIiIiIiK3EBQUxPjx4+/rHCEhIZhMJqKiojIl06lTpzCZTOzatStTzvf/MitvVueUnCVHlRNZZfDgwURHR6fdzp49a3Sku1KsXAlKzprK66N/Y1Dz19lfuBTmhASYMQNr1arw8stw4YLRMUVEREREcpWNGzdiZ2dH69atjY6SpkmTJvTr1y/dfQ0bNiQ0NBQvLy9jQmWD7t2737AEQGBgIKGhoVSpUsWYUJKtclQ54e/vT3h4eLr7wsPD8fT0xMXFhUKFCmFnZ3fTY/z9/W95XicnJzw9PdPdchOTycTD5XyZ+WZT2n07nLGjZvF05zEsL9cAk8UCkydjLVsWhg6Fq1eNjisiIiIikitMmTKFvn37sm7dOi7k4F/2OTo64u/vj8lkMjpKtrKzs8Pf3x97e3ujo0g2yFHlRIMGDQgODk5338qVK2nQoAFg+5+yVq1a6Y6xWCwEBwenHZPX1Q4qwNQedRn52UvMGTSeZ18YzfYiFTDFx8NHH9lKit9+MzqmiIiIiEiOFhsby5w5c+jduzetW7dm+vTp6R6/PjUhODiY2rVr4+rqSsOGDTl8+HDaMcePH6dt27b4+fnh7u5OnTp1WLVq1S1f88UXX+SJJ55Id19ycjKFCxdmypQpdO/enbVr1/Lll19iMpkwmUycOnXqptMk1q9fT5MmTXB1dcXHx4fmzZtz5coVAJYvX86DDz6It7c3BQsW5IknnuD48eN39fn55ptvKFu2LM7Ozvj5+dGuXbu0xxITE3njjTcoXLgwzs7OPPjgg2zduvWW5/rwww+pUaNGuvvGjx9PUFBQ2uMzZsxg8eLFadcdEhJy02kda9eupW7dujg5OREQEMCgQYNISUlJe7xJkya88cYbvPPOOxQoUAB/f38+/PDDu7p2MUaWlhOxsbHs2rUr7Zvp5MmT7Nq1izNnzgC26RZdu3ZNO/7VV1/lxIkTvPPOOxw6dIhvvvmGuXPn8tZbb6Ud079/fyZPnsyMGTM4ePAgvXv3Ji4ujh49emTlpeQ4lYt4Ma1HXfq835X+b07klafe44RPEUzh4dC2rW09ikyakyYiIiIikiFWK8TFGXO7y00I586dS4UKFShfvjydO3dm6tSp3Gwjw/fff5+xY8eybds27O3tefHFF9Mei42NpVWrVgQHB7Nz505atGhBmzZt0t7v/L+XXnqJ5cuXExoamnbfkiVLiI+Pp0OHDnz55Zc0aNCAXr16ERoaSmho6E3Xy9u1axdNmzalUqVKbNy4kb///ps2bdqQmpoKQFxcHP3792fbtm0EBwdjNpt5+umnsVgsGfrcbNu2jTfeeIMRI0Zw+PBhli9fzsMPP5z2+DvvvMP8+fOZMWMGO3bsoEyZMjRv3pzL97ho/4ABA2jfvj0tWrRIu+6GDRvecNz58+dp1aoVderUYffu3UyaNIkpU6YwcuTIdMfNmDEDNzc3Nm/ezOjRoxkxYgQrV668p2ySjaxZaM2aNVbghlu3bt2sVqvV2q1bN2vjxo1veE6NGjWsjo6O1lKlSlmnTZt2w3m//vpra/Hixa2Ojo7WunXrWjdt2nRXuaKjo62ANTo6+h6vLGe5lpRi/Tr4iLXqoEXWSXWfsaZislrBailWzGpdudLoeCIiIiKSR127ds164MAB67Vr12x3xMZarbaaIPtvsbF3lb1hw4bW8ePHW61WqzU5OdlaqFAh65o1a9Iev/5eZtWqVWn3LV261Ar8e703UblyZevXX3+d9ucSJUpYv/jii7Q/V6pUyfrZZ5+l/blNmzbW7t27p/25cePG1jfffDPdOa9nuXLlitVqtVo7depkbdSoUYav9eLFi1bAunfvXqvVarWePHnSClh37tx50+Pnz59v9fT0tMbExNzwWGxsrNXBwcH6888/p92XlJRkLVKkiHX06NE3zTts2DBr9erV053niy++sJYoUSLtz926dbO2bds23TH/n/O9996zli9f3mqxWNKOmThxotXd3d2amppqtVptn78HH3ww3Xnq1Kljfffdd296rZI5bvhZ8B8Zff+dpSMnmjRpgtVqveF2fcjU9OnTCQkJueE5O3fuJDExkePHj9O9e/cbzvv6669z+vRpEhMT2bx5M/Xq1cvKy8jxnB3seP3Rsiwd+Birur/Ncy98xinvAEznzsFjj8Hbb8N/hjqJiIiIiORnhw8fZsuWLXTq1AkAe3t7OnTowJQpU244tlq1amkfBwQEABAREQHYRk4MGDCAihUr4u3tjbu7OwcPHrzlyAmwjZ6YNm0aYFs7748//kg3GiMjro+cuJWjR4/SqVMnSpUqhaenZ9r0idvl+q/HHnuMEiVKUKpUKbp06cLPP/9MfHw8YJvKkpycTKNGjdKOd3BwoG7duhw8ePCuruNuHTx4kAYNGqRbe6NRo0bExsZy7ty5tPv++zUD29ft+tdMci6tLJKHBBZwZfbL9fmmnC9P+Jdm4JqpdNuxFMaNgz17YM4cKFDA6JgiIiIikle5ukJsrHGvnUFTpkwhJSWFIkWKpN1ntVpxcnJiwoQJ6XbFcHBwSPv4+pvi69MjBgwYwMqVKxkzZgxlypTBxcWFdu3akZSUdMvX7tq1K4MGDWLjxo1s2LCBkiVL8tBDD2U4O4CLi8ttH2/Tpg0lSpRg8uTJFClSBIvFQpUqVW6b6788PDzYsWMHISEhrFixgqFDh/Lhhx/edl2J2zGbzTdMmUlOTr6nc2XEf79mYPu6ZXRKixgnRy2IKffP3s7MG03L8uMbjzC149u8+tRg4hycYdUqqFMH9u0zOqKIiIiI5FUmE7i5GXPL4E4WKSkpzJw5k7Fjx6atj7dr1y52795NkSJFmDVrVoYvd/369XTv3p2nn36aqlWr4u/vz6lTp277nIIFC/LUU08xbdo0pk+ffsPaeY6OjmlrR9xKtWrVbthI4LpLly5x+PBhhgwZQtOmTalYsWLaQpl3w97enmbNmjF69Gj27NnDqVOnWL16NaVLl8bR0ZH169enHZucnMzWrVupVKnSTc/l6+tLWFhYuoLiv4tcQsauu2LFimzcuDHdedavX4+HhwfFihW762uUnEXlRB71QHEflr3xEHbt2vFs58856+UHJ05grV8fFi40Op6IiIiIiCGWLFnClStX6NmzJ1WqVEl3e/bZZ286teNWypYty4IFC9LKjeeffz5Dv6F/6aWX0hb479atW7rHgoKC2Lx5M6dOnSIyMvKm5xs8eDBbt26lT58+7Nmzh0OHDjFp0iQiIyPx8fGhYMGCfP/99xw7dozVq1fTv3//DF8T2D5HX331Fbt27eL06dPMnDkTi8VC+fLlcXNzo3fv3gwcOJDly5dz4MABevXqRXx8PD179rzp+Zo0acLFixcZPXo0x48fZ+LEifzxxx83XPeePXs4fPgwkZGRNx1Z0adPH86ePUvfvn05dOgQixcvZtiwYfTv3x+zWW9tczt9BfMwNyd7Jjz/AC2fb86TXcexvkQ1THFx8MwzMHGi0fFERERERLLdlClTaNasWbqpG9c9++yzbNu2jT179mToXOPGjcPHx4eGDRvSpk0bmjdvTs2aNe/4vGbNmhEQEEDz5s3TTS0B21QROzs7KlWqhK+v703XiShXrhwrVqxg9+7d1K1blwYNGrB48WLs7e0xm83Mnj2b7du3U6VKFd566y0+//zzDF3Pdd7e3ixYsIBHH32UihUr8u233zJr1iwqV64MwKhRo3j22Wfp0qULNWvW5NixY/z555/4+Pjc9HwVK1bkm2++YeLEiVSvXp0tW7YwYMCAdMf06tWL8uXLU7t2bXx9fdONzLiuaNGiLFu2jC1btlC9enVeffVVevbsyZAhQ+7q+iRnMln/f/JPPhATE4OXlxfR0dF4enoaHSdb/LE3lIGzd/DOH5PounOp7c6PP4bBgzM8BE5ERERE5L8SEhI4efIkJUuWxNnZ2eg4uUZsbCxFixZl2rRpPPPMM0bHEblvt/tZkNH331oQM59oWTWAEgUfope7M1dcPHlzwyx4/32IioLPPlNBISIiIiKSxSwWC5GRkYwdOxZvb2+efPJJoyOJ5BgqJ/KRSkU8WfBaI7o42xPj5MoHa6bA559DdDR88w3Y2RkdUUREREQkzzpz5gwlS5akWLFiTJ8+HXt7vR0TuU7/N+Qzfp7OzHm5Ad0d7HjHyY1P/5yA3fffQ3w8zJgBWkhGRERERCRLBAUF3bClpojY6J1oPuTj5sjPvepz5umO9H3yHZLNdvDTT/D666AfliIiIiIiIpLNVE7kU+5O9kzvUZekp5/h7db9sWCCSZNs61CIiIiIiNwFjQYQyd8y42eAyol8zNnBjkmda3GtXXveb/6a7c5PP7UtkCkiIiIicgcODg4AxMfHG5xERIx0/WfA9Z8J90JrTuRzDnZmJjz/AC8lp/JJYhzvhUyDQYPA2xteecXoeCIiIiKSg9nZ2eHt7U1ERAQArq6umLQLnEi+YbVaiY+PJyIiAm9vb+zuY5MFlROCk70d33WpRdekl5iQGMfrG+di7d0bU+HC8PTTRscTERERkRzM398fIK2gEJH8x9vbO+1nwb1SOSEAuDraM7VHHZ5Pfg3va1fpvOsPLJ07Y/77b3jgAaPjiYiIiEgOZTKZCAgIoHDhwiQnJxsdR0SymYODw32NmLhO5YSk8XR2YGbP+nRKfJvA6HAan9yB5Yk2mLdugSJFjI4nIiIiIjmYnZ1dprxBEZH8SQtiSjoF3ByZ2qshw14YytGCgZgvnMfati1okSMRERERERHJIion5AZFvV34+pUm9Ok4nMsunpi2bcParRtYLEZHExERERERkTxI5YTcVNViXgzs3ZJXn3mPJLM9pl9/hQ8/NDqWiIiIiIiI5EEqJ+SWHq/sz+OvPMfgFn1td3z0ESxdamwoERERERERyXNUTsht9XywJM4v9WB6zScASO3cGU6fNjiViIiIiIiI5CUqJ+S2TCYTw5+sTPCLA9kVUA67qChSn3sOEhONjiYiIiIiIiJ5hMoJuSN7OzPjutbjwxeGEeXsjt3WrVjfftvoWCIiIiIiIpJHqJyQDPH1cOKD11sy8ElbKWGaOBHmzDE4lYiIiIiIiOQFKickw2qV8OHhft2Z0KA9AKk9e8KRIwanEhERERERkdxO5YTclc71S3Dq9YFsLF4Vu7g4kjt2guRko2OJiIiIiIhILqZyQu6KyWTio3YPMLHHUKKc3XHYuQPriBFGxxIREREREZFcTOWE3DUXRzuGv9aC4a36AmD95BPYsMHgVCIiIiIiIpJbqZyQe1La1536g15lfuVHMFssJHZ6Aa5eNTqWiIiIiIiI5EIqJ+Seta8dyPo3h3HOszBOZ06R3PcNoyOJiIiIiIhILqRyQu6ZyWRi2AsN+aTDICyYcJgxHRYuNDqWiIiIiIiI5DIqJ+S+eLk60G1QV76r/ywAiT1fgshIg1OJiIiIiIhIbqJyQu5bvVIFSRgylIO+QThducy11/oaHUlERERERERyEZUTkileb1GZyV3fI9VkxmXubKxLlhgdSURERERERHIJlROSKRzszLwyoCPT6j4NwLWXXoaYGINTiYiIiIiISG6gckIyTXl/D1KHDeOkTwCu4aHEvzXA6EgiIiIiIiKSC6ickEzV8/HKfN95MACuUydjDQkxNpCIiIiIiIjkeConJFPZ25np/l53Zj3QEoC4rj3g2jWDU4mIiIiIiEhOpnJCMl15fw9ih39MqHtB3M+eIvaDD42OJCIiIiIiIjmYygnJEj1aVWdKx7cBcB4/Dg4fNjiRiIiIiIiI5FQqJyRL2NuZefrD3qwuXQf71BQu93gZrFajY4mIiIiIiEgOpHJCskzlot4cHPwRCfaOFNi4jsRZs42OJCIiIiIiIjmQygnJUt07N+XHxp0ASHqjH1y9amwgERERERERyXFUTkiWcnOyp/TnwznlHYDHpQguD3zP6EgiIiIiIiKSw6ickCz36AMl+O2lQQB4TZ6EZfcegxOJiIiIiIhITqJyQrLFc0N6sbJCI+wsqUR276XFMUVERERERCSNygnJFgFeLlwa+RnX7J0ovGsLV3/S4pgiIiIiIiJio3JCsk27pxrwa7PnAUh5ewAkJBicSERERERERHIClROSbeztzFQYM5wLHoXwuXiB8OGfGh1JREREREREcgCVE5Kt6lQOZGXnNwHw/GIM1tBQgxOJiIiIiIiI0VROSLZ7bORb7C5SDpfEeM689rbRcURERERERMRgKick2xUp4MaRd0cAELhoNte2bjM4kYiIiIiIiBhJ5YQYok3vdqyq/ghmq5WLL72mrUVFRERERETyMZUTYghnBzvsR39Ggr0jxfds4eJPc42OJCIiIiIiIgZROSGGafxYbf58vBMAqe++CykpBicSERERERERI6icEMOYTCYqfDGSyy6e+Iee5vTYiUZHEhEREREREQOonBBDlS9XjL/avwyA+6cjscbFGZxIREREREREspvKCTFcvdFDOO9VmILRkRwZ8qnRcURERERERCSbqZwQw/kX9mJ3r7cBKPrteJIvRhqcSERERERERLKTygnJER768A2O+JXCPSGOI/3eMzqOiIiIiIiIZCOVE5IjeLg5c3bgEADKzJ1O7NETBicSERERERGR7KJyQnKMh9/syq5S1XFKSebk6wONjiMiIiIiIiLZROWE5BgO9nYkjPwEgEorFxG5bbfBiURERERERCQ7qJyQHKVex5ZsqfYQdlYLF94abHQcERERERERyQYqJyRHMZlMOH/yEQBV/l5O6N9bDU4kIiIiIiIiWU3lhOQ41Vo3ZkutRzFjJWKARk+IiIiIiIjkdSonJEfyHDUSCyaqbw7mdPB6o+OIiIiIiIhIFlI5ITlShWYN2Fb/cQCiBr5ncBoRERERERHJSionJMfyHfMJqSYz1Xeu4+iS1UbHERERERERkSyickJyrJKNarLjoVYAxA8eYnAaERERERERySoqJyRHKzLmY1JMZqrv28i+eX8YHUdERERERESygMoJydGK1qnGzkfbApDy4XCD04iIiIiIiEhWUDkhOV7xMSNJMZmpcWAzexeuNDqOiIiIiIiIZDKVE5Lj+dWoxJ7GrQFIHP6RwWlEREREREQks6mckFyh6OiPsGCi9u6/2Lt0rdFxREREREREJBOpnJBcwa9OdfY1ag5A3LARBqcRERERERGRzKRyQnKNwp/ZFsSsu30Ne1ZuNDiNiIiIiIiIZBaVE5Jr+Deqy/66j2LGSsxQjZ4QERERERHJK1ROSK5S8FNbKdFg8wr2rt1ucBoRERERERHJDConJFfxf7QRhx94EDurhUtDhhsdR0RERERERDKBygnJdbz/GT3RaMMy9m3ca3AaERERERERuV8qJyTX8Wv+CMcq18bBkkroh58aHUdERERERETuk8oJyZVch7wHQMM1Czl68LTBaUREREREROR+qJyQXKlIh6c4W7wcbskJHB32mdFxRERERERE5D6onJDcyWTCOvAdAOot+ZmzZyMNDiQiIiIiIiL3SuWE5FrFX+1GRKEiFLwWw86PvjA6joiIiIiIiNwjlROSe9nbE9e3HwAPzJ1CxOVYY/OIiIiIiIjIPcmWcmLixIkEBQXh7OxMvXr12LJlyy2PbdKkCSaT6YZb69at047p3r37DY+3aNEiOy5FcpigAa8R7e5NYHQ4G0ZNMjqOiIiIiIiI3IMsLyfmzJlD//79GTZsGDt27KB69eo0b96ciIiImx6/YMECQkND02779u3Dzs6O5557Lt1xLVq0SHfcrFmzsvpSJAcyubpy6cVXAKgw81ui4hINTiQiIiIiIiJ3K8vLiXHjxtGrVy969OhBpUqV+Pbbb3F1dWXq1Kk3Pb5AgQL4+/un3VauXImrq+sN5YSTk1O643x8fLL6UiSHKjnsHeKdXKgQfoKQr34yOo6IiIiIiIjcpSwtJ5KSkti+fTvNmjX79wXNZpo1a8bGjRszdI4pU6bQsWNH3Nzc0t0fEhJC4cKFKV++PL179+bSpUu3PEdiYiIxMTHpbpJ3mAoU4MJzXQAoOvlrEpJTDU4kIiIiIiIidyNLy4nIyEhSU1Px8/NLd7+fnx9hYWF3fP6WLVvYt28fL730Urr7W7RowcyZMwkODuazzz5j7dq1tGzZktTUm78p/fTTT/Hy8kq7BQYG3vtFSY4UNGIwKWYzdU7uJnjWn0bHERERERERkbuQo3frmDJlClWrVqVu3brp7u/YsSNPPvkkVatW5amnnmLJkiVs3bqVkJCQm55n8ODBREdHp93Onj2bDeklO9mXDOL0o7ZFU+2/HE+qxWpwIhEREREREcmoLC0nChUqhJ2dHeHh4enuDw8Px9/f/7bPjYuLY/bs2fTs2fOOr1OqVCkKFSrEsWPHbvq4k5MTnp6e6W6S9xQZ/h4Aj+5azbo1u4wNIyIiIiIiIhmWpeWEo6MjtWrVIjg4OO0+i8VCcHAwDRo0uO1z582bR2JiIp07d77j65w7d45Lly4REBBw35kl93JpWJ+zVWvjYEnl8uhxRscRERERERGRDMryaR39+/dn8uTJzJgxg4MHD9K7d2/i4uLo0aMHAF27dmXw4ME3PG/KlCk89dRTFCxYMN39sbGxDBw4kE2bNnHq1CmCg4Np27YtZcqUoXnz5ll9OZLDeQx+B4BmaxeyY/8Zg9OIiIiIiIhIRthn9Qt06NCBixcvMnToUMLCwqhRowbLly9PWyTzzJkzmM3pO5LDhw/z999/s2LFihvOZ2dnx549e5gxYwZRUVEUKVKExx9/nI8++ggnJ6esvhzJ4bw7PEtk/+IUCjvDoVETqPnjaKMjiYiIiIiIyB2YrFZrvls5MCYmBi8vL6Kjo7X+RB4U8dk4Cg96m9Pe/qQcPERpfy+jI4mIiIiIiORLGX3/naN36xC5F4Vff4VYN09KRIWx4YtpRscRERERERGRO1A5IXmPmxsx3Wy7vFT6ZTKRsYkGBxIREREREZHbUTkheVLA+wNItrOn1rkDrJr+u9FxRERERERE5DZUTkieZCpShLAWbQHwnPwtiSmpBicSERERERGRW1E5IXmW/9B3AWi2by2rgncZG0ZERERERERuSeWE5FkOdesQWrkmjpYUor6YQD7cmEZERERERCRXUDkheZrnu28D8Phfi9hyKNTgNCIiIiIiInIzKickT3Pr+BzRBQrjGx/F/i8mGx1HREREREREbkLlhORtDg6kvNobgNq//8TpyFiDA4mIiIiIiMj/UzkheV7Bt14nycGJamHHCJ6y0Og4IiIiIiIi8n9UTkjeV6gQl9q2A6DIzB+4mpBscCARERERERH5L5UTki/4DxkIQLODf7NkyWaD04iIiIiIiMh/qZyQfMFUvTrhNetjb7WQOvEbLBZtKyoiIiIiIpJTqJyQfMN7kG1b0Zabl7Ju7xmD04iIiIiIiMh1Kick33B6+imiff0peC2Gw19PMzqOiIiIiIiI/EPlhOQf9vZYe70CQN1lszlxUduKioiIiIiI5AQqJyRf8X6jNyl29jwQephVPy0zOo6IiIiIiIigckLyGz8/LrV8EoBCM6cQl5hicCARERERERFROSH5ju87bwHQal8IS0L2G5xGREREREREVE5IvmN+sBGXylTEOSWJqInfYbVqW1EREREREREjqZyQ/MdkwvWtNwBo/tciNh69aHAgERERERGR/E3lhORLLt26cM3Vg6CoULZ9N8voOCIiIiIiIvmaygnJn9zcSOjcBYAqi3/m3JV4gwOJiIiIiIjkXyonJN/yGdAPgCbHt7Hstw3GhhEREREREcnHVE5I/lW2LBfrP4wZK/ZTp5CUYjE6kYiIiIiISL6kckLyNZ+3+wLQZttyVu4+Y3AaERERERGR/EnlhORr9m3bElvAF9/4KI58/7PRcURERERERPIllROSvzk4YH3xRQDq/jmXYxFXDQ4kIiIiIiKS/6ickHzPo28fLCYzjU7v4Y9f1xodR0REREREJN9ROSFSvDiXGzcFwPPHacQnpRgcSEREREREJH9ROSECFHjLtjDmk7tWsnTLCYPTiIiIiIiI5C8qJ0QAc+tWXC0cgE/CVc58/6PRcURERERERPIVlRMiAHZ22L3yMgAPr17A7rNRxuYRERERERHJR1ROiPzD9dWXSTXbUef8AVbODTY6joiIiIiISL6hckLkuiJFiHm8JQABs6cTk5BscCAREREREZH8QeWEyH9493sdgDZ717Bk03GD04iIiIiIiOQPKidE/sP02GNc9S+KZ2Ic56b8jNVqNTqSiIiIiIhInqdyQuS/zGbsX+oJwEPrFrPnXLTBgURERERERPI+lRMi/8elV08sJhMNzuxlxeK/jY4jIiIiIiKS56mcEPl/xYsT8/CjAHjN/omrWhhTREREREQkS6mcELkJr9dfBaDt7pX8vv2MwWlERERERETyNpUTIjdhevJJrnkXwC/2MsdmzDM6joiIiIiISJ6mckLkZhwdoWtXABqsWcReLYwpIiIiIiKSZVROiNyCy6svA/DI8a38/ud2g9OIiIiIiIjkXSonRG6lYkViatbF3mrB5ZefiEtMMTqRiIiIiIhInqRyQuQ2PF57BYCndi5nye7zBqcRERERERHJm1ROiNyGqX17klzcKHkllP2zlhgdR0REREREJE9SOSFyO+7upLbvAED1lfM5fjHW4EAiIiIiIiJ5j8oJkTtw6W1bGLP14fX8FnLA4DQiIiIiIiJ5j8oJkTupW5erZSrgnJJE0o8/kZJqMTqRiIiIiIhInqJyQuROTCZcetsWxmy1ZRlrj1w0OJCIiIiIiEjeonJCJAPsu3Uhxd6BquHH2fjrKqPjiIiIiIiI5CkqJ0QyomBB4lu3AaDEotlExiYaHEhERERERCTvUDkhkkGer70KQNv9a/h903GD04iIiIiIiOQdKidEMqppU2L9i+KZGEfYtF+wWq1GJxIREREREckTVE6IZJTZjP3LLwHQ5O/f2H0u2uBAIiIiIiIieYPKCZG74PxSTywmEw3O7GXV7+uNjiMiIiIiIpInqJwQuRuBgUQ//CgAXr/8yLWkVIMDiYiIiIiI5H4qJ0Tuktc/C2O22b2S5XvOGZxGREREREQk91M5IXKXzE+24ZqHN/6xlzn040Kj44iIiIiIiOR6KidE7paTE6kdOwJQaeUizlyKNziQiIiIiIhI7mZvdACR3Mj95Z4w+VuaH93ID38d5PWnahkdSURERCRHs1isnLkcz4nIWCJiErl4NZGLsbb/xielYrFaSbVYsfyzXbuHswM+rg54uzri5eKAn6czpXzdKF3IHS9XB4OvRkQym8oJkXtRqxYxpcrheeIIV2f+QuqTNbEzm4xOJSIiIpIjWK1WjkXEsvHEJfadj+Zw2FWOhMdyLTlzFhMv5O5IKV93Hgj0pnZQAWqX8MHHzTFTzi0ixjBZrf9Uk/lITEwMXl5eREdH4+npaXQcyaWSPx2Fw3uD2Vq0EglrQniorK/RkUREREQMExGTwOpDEWw4fokNxy8RGZt4wzGO9mZK+7oT4OWMr7sTvh62m5uTPXZmMJtM2JlNWK0Qk5BMVHwy0deSuRKXxIXoaxyPiCMsJuGmr1+msDv1SxXg8Ur+1C9VEEd7zWAXyQky+v5b5YTKCblXFy5gCQzEbLEwfNwihr3V1uhEIiIiItnqUmwif+wLY8meC2w+eZn/vrNwsjdTJ6gANYt7UyHAk/L+HpQo4Iq93f2VBrGJKZy8GMfh8KtsP32FracucywiNt0xHs72NK1QmOaV/XmkQmGcHezu6zVF5N6pnLgNlROSWa42aYbH2mAmPNiJzn9Ox9tVwwlFREQkb0u1WAk+GM5Pm8+w/lgkqZZ/307UCPTm4XK+NCxdkAeKe+Nknz2lwOW4JLadusyawxdZeSA83agNT2d7nqlZjE51i1Pe3yNb8ojIv1RO3IbKCcks1lmzMD3/POc8C7N62Ua6NipldCQRERGRLHElLok5287y48bTnI+6lnZ/1aJePFEtgNbVAijm42pgQptUi5WdZ67w5/4wlu0NS5e1ZnFvnq9XgierF9G0D5FsonLiNlROSKa5do3Ewn44xV5lcN8v+fSrN4xOJCIiIpKpzkdd45s1x/h1+zkSUywAeLs60KFOIB3rFKdkITeDE95aqsXKX0cvMnvLWVYdDCfln1EeAV7OvPxwKTrWKY6Lo6Z8iGQllRO3oXJCMlNij544TZ/KvCrNqPTnr1Qu4mV0JBEREZH7diHqGt+EHGPO1rMkp9reMlQp6km3BkG0qV4k163jEHE1gXnbzjF9wykuXrVN+yjo5siLD5aka4MSeDhre1KRrKBy4jZUTkimWr8eHnyQOAdnvv55HYOeq2N0IhEREZF7dik2kS+DjzJ7y1mSUm0jJRqUKki/ZmWpW7IAJlPu3j49ITmV+TvO8e3a45y9bJvyUcDNkX7NytKpbnEc7nPBThFJT+XEbaickExltRIfVBrXMycZ9sw7fDD30/tehVpEREQkuyWnWvhx42m+WHWEqwkpANQrWYC3HitH/VIFDU6X+VJSLSzZE8pXq49y4mIcAKUKuTGoZQUeq+SX60sYkZxC5cRtqJyQzJY6fAR2Hw5jfYlqJP25kkfKFzY6koiIiEiG/XX0IiN+P8DRf7bkrBTgyZDWFWlYppDBybJecqqF2VvPMn7lES7FJQG2Uuajp6pQzk+7e4jcL5UTt6FyQjLdqVNQsiQWTHz41RJG9G1ldCIRERGRO4qMTWTY4v0s3RsK2KY3DHi8PB3qBGJnzl8jB64mJPPt2uP88NdJElMsONiZ6N24NH0eKZPr1tcQyUky+v5bY89FMkNQELENH8KMFZ/5c7iakGx0IhEREZFbslqtLN51nsfGrWXp3lDszCa6NwxizdtNeL5e8XxXTAB4ODswsHkFVg9oQrOKhUlOtfLV6mO0+vIvNh6/ZHQ8kTxPIyc0ckIyiXX6dEw9enDCpwjblm+kfd3iRkcSERERuUHE1QSGLNzHigPhAFQM8OTzdtWoUjQLdhxLToawMAgN/fd28SIkJtpuSUm2m709eHj8e/PygsBACAqCYsVsj2cjq9XK8n1hDPttPxH/7OzRqW5xPniiIq6O2ZtFJLfTtI7bUDkhWSI2lmRfPxwS4vlg4Hd8NPploxOJiIiIpPPn/jDenb+HqPhk7M0m+j5alt5NSuNonwkDqiMjYdMm2LsX9u2z/ffQIVtBcT/s7GxFRblyULOm7VarFpQsCVm8aGVMQjKjlx/ip01nAChZyI3xHWpQPdA7S19XJC9ROXEbKickq8R36ozr7J/5pXoLHl4zn2I+rkZHEhERESExJZVPlx1i+oZTAFQp6snn7apTMeA+/i18+TKEhPx727v35sfZ24O/PxQpAgEB4OcHLi7g6Gi7OThASgrExMDVq7bblStw5gycPm0bWXEzPj7QuDE89hg8/jiULp1lZcWG45G8PXc3odEJ2JtN9GtWlt5NyuTL6S8id0vlxG2onJAss3o1NG1KjJMbPy/cSO+WVY1OJCIiIvncycg4+s7awb7zMQC88nApBjQvj8O9bH0eFgYLF8Kvv9oKCYsl/eMVK8IDD0CVKlC1qu2/xYuD+R5HZlgsttc8dco2GmP7dttt794bS4ugIGjZEtq3h4ceso24yETR8cm8t2gvS/fYFg+tG1SALzvVIMDLJVNfRySvUTlxGyonJMtYLMQVLY5b2HlGvPABH/w4XHtki4iIiGF+332BQfP3EJeUio+rA+Pa1+CRCne55fnVqzBrFvz0E/z9N/z37UOlSvDII7bbww+Dr2/mXsCtJCXBrl2wahWsWAEbNqSfPhIQAM89Bx06QIMGmTaiwmq1smDHeYYu3kdcUiqF3B35ulNNGpQumCnnF8mLVE7chsoJyUpJg9/HcdQnrClVC5+QVdTQnEQRERHJZqkWK2NWHGZSyHHgHn/Lv3MnfPcd/PwzxMb+e3/9+vDss7ZbyZKZnPwexcbC2rW2UR3z50NU1L+PlS8PvXtDt27g7Z0pL3f6Uhyv/rSDg6Ex2JlNvNuiPL0eKqVfSonchMqJ21A5IVnq6FEoV45Uk5lxU1YysMejRicSERGRfORqQjJvzt7F6kMRALzSuBQDHy+PfUamcVgssGgRjB4Nmzf/e3+5ctCrl20kQmBg1gTPLElJttEUs2fbriUuzna/iws8/zy89ppt6sl9upaUyvsL97Jg53kAWlbx5/PnquPupN08RP5L5cRtqJyQrBZdsy5eO7fyxWMv8dqy7zJnBWwRERGROzgZGUevmds4FhGLk72Z0e2q0bZG0Ts/MSXF9mb+00/hwAHbfQ4O8Mwz8Mor0KRJlu+MkSViYmzTUSZNsq1Zcd3jj8P779umotwHq9XKT5vPMOL3/SSnWilb2J2p3esQWECLootcl9H333rHJJIF3F9+EYBWO1cQcijc4DQiIiKSH2w8fom2E/7mWEQs/p7OzHu1wZ2LidRUmDbNNvWhSxdbMeHlZXvjfu6crbB45JHcWUwAeHpCnz6wZw/89Rd07GhbKHPFCttOHw8/DH/+mX4djbtgMpnoUr8Ec15pQGEPJ45GxPL0N+vZceZKJl+ISN6nckIkC9h17EiKgyPlI8+weXGI0XFEREQkj1u6J5RuU7cQk5DCA8W9+e31RlQr5n37J61cCTVrwosvwokTUKgQfPKJbfvOkSOh8F0unJmTmUzw4IO2hT2PHLGNBnF0tBUWLVrYHtuw4Z5PX7O4D4tfb0TFAE8iY5Po9P0mluy5kIkXIJL3qZwQyQre3sQ/3gKAgN/nExV/i/25RURERO7TtPUneX3WDpJSLbSs4s+sXvUp7Ol86yfs22fbcvPxx20jCry94fPPbaXE4MG2kRN5WalS8O23tkKmXz/bWhQbNkCjRrZFPo8evafTBni58OurDWhaoTCJKRZe/2UnE9ccIx/Oohe5JyonRLKI50s9AHhi/xqW7jxncBoRERHJaywWK58uO8jw3w9gtULXBiWY8HxNnB3sbv6E2Fh4+22oXh2WL7etKdGvHxw7BgMGgGs+WyehaFH44gvb9ffsCWYzLFhg2x61b1+4cvdTM9yc7Pm+a216NAoC4PM/D/PB4n2kWlRQiNxJtpQTEydOJCgoCGdnZ+rVq8eWLVtueez06dMxmUzpbs7O6Ztfq9XK0KFDCQgIwMXFhWbNmnH0HhtOkSzTsiWJ7p74x17m8NwlRqcRERGRPCQl1cKAX3fz3boTALzTojzDn6yMnfkWa0MsWwaVK8O4cbYdOZ55xra+xBdfQMGC2Zg8BypSBH74AXbvhlatbIuDTphgW4fjxx/vej0KO7OJYW0qM/zJyphM8NOmM7w5eydJKZYsugCRvCHLy4k5c+bQv39/hg0bxo4dO6hevTrNmzcnIiLils/x9PQkNDQ07Xb69Ol0j48ePZqvvvqKb7/9ls2bN+Pm5kbz5s1JSEjI6ssRyTgnJyztngOgyprfORUZZ3AgERERyQuSUy28MXsnC3acx95sYuxz1enTpAymmy1aGRZmWwSydWs4cwZKlLAVFfPnQ5ky2R8+J6tSBZYuhVWroGJFuHgRunaFRx+FQ4fu+nTdGgbxZccHsDebWLInlF4ztxGflJIFwUXyhiwvJ8aNG0evXr3o0aMHlSpV4ttvv8XV1ZWpU6fe8jkmkwl/f/+0m5+fX9pjVquV8ePHM2TIENq2bUu1atWYOXMmFy5cYNGiRTc9X2JiIjExMeluItnB5cVuALQ8vJ7fNh03OI2IiIjkdokpqfT+aQfL9obhaGfm2861eLZWsZsfvHCh7Q33nDm2KQtvvw3799vWm5Bba9oUdu2yLQ7q4gIhIVCtGgwbBkl3t47Yk9WL8EO32rg42LH2yEW6TNlCdHxylsQWye2ytJxISkpi+/btNGvW7N8XNJtp1qwZGzduvOXzYmNjKVGiBIGBgbRt25b9+/enPXby5EnCwsLSndPLy4t69erd8pyffvopXl5eabfAwMBMuDqRDGjUiPiAYngkXSNy1q9aEElERETuWUJyKr1mbmfVwXCc7M1837UWzSr53XhgbCy89JJt6salS1CjBmzdCmPGgJtbtufOlRwdbYuD7t9vG3WSnAwjRkD9+rB3712dqkn5wvz0Ul08ne3ZfvoKHb7fyOU4LZYu8v+ytJyIjIwkNTU13cgHAD8/P8LCwm76nPLlyzN16lQWL17MTz/9hMVioWHDhpw7Z1tQ8Prz7uacgwcPJjo6Ou129uzZ+700kYwxm3Ho8gIAD21ZwbbT2vNaRERE7l58Ugo9pm1l3ZGLuDjYMa17HZqUv8lWn1u2wAMPwJQptu0z33kHNm+2bRkqd69kSfj9d5g9GwoUgJ07oXZt+OwzSE3N8GlqlSjA3Fcb4OvhxKGwqzw/eROXYhOzMLhI7pPjduto0KABXbt2pUaNGjRu3JgFCxbg6+vLd999d8/ndHJywtPTM91NJLs4dOsKQJMT21gecndNu4iIiEhCciovzdjGxhOXcHeyZ2bPujQsUyj9QVarbbHLhg1tu08UKwbBwbY30Y6OxgTPK0wm6NDBNoriiSdsUzsGDYIHH7RtR5pBFfw9mf1yfQqnFRSbiVRBIZImS8uJQoUKYWdnR3h4eLr7w8PD8ff3z9A5HBwceOCBBzh27BhA2vPu55wi2apSJWIrVcXBkgrzfiUhOeMtu4iIiORvSSkWev+0nQ3H/y0m6gQVSH/Q1au2N89vv237bX779rBnDzzyiDGh8yp/f/jtN5g2DTw9YdMm2yiVX3/N8ClK+7oz++X6+Hk6cTj8Kp2+38TFqyooRCCLywlHR0dq1apFcHBw2n0Wi4Xg4GAaNGiQoXOkpqayd+9eAgICAChZsiT+/v7pzhkTE8PmzZszfE6R7Ob6z8KYLXavJvjgrXeqEREREbkuJdXCG7N2subwRZwdzEztXoeaxX3SH3ToENSrB/Pmgb29bQvM2bPBx+fmJ5X7YzJB9+628qdBA4iJgeeeg9degwzuHFjK153ZLzfAz9OJoxGxdJqsgkIEsmFaR//+/Zk8eTIzZszg4MGD9O7dm7i4OHr06AFA165dGTx4cNrxI0aMYMWKFZw4cYIdO3bQuXNnTp8+zUsvvQTYdvLo168fI0eO5LfffmPv3r107dqVIkWK8NRTT2X15YjcE3OnTlhNJuqcP8D6FZuNjiMiIiI5XKrFyoB5u1m+37Yrx+Sutalb8v9GTCxcCHXrwsGDUKQIrF1re5N8sy1FJXOVKGH7fA8aZPvzN9/YyoqjRzP09JKF3Jj9cgP8PZ05FhFLlymbtYuH5HtZXk506NCBMWPGMHToUGrUqMGuXbtYvnx52oKWZ86cITQ0NO34K1eu0KtXLypWrEirVq2IiYlhw4YNVKpUKe2Yd955h759+/Lyyy9Tp04dYmNjWb58Oc7Ozll9OSL3pkgR4h9qAoDv7wv0l4+IiIjcktVqZciifSzadQF7s4lvXqjJQ2V9/3uAbS2JZ56xTelo3Bh27LCtNyHZx8EBPv0U/vgDChWybT9auzYsWZKhp5cs5Masl+unLZLZffoW4hJTsjazSA5msubDvQ1jYmLw8vIiOjpai2NK9pkxA7p353iBYmxd9jcd65UwOpGIiIjkQGNXHObr1ccwm+CrTg/wRLUi/z6YnAy9e9t24wDo29e2EKa9vTFhxebCBdu6H3//bRu5MmIEvPcemO/8u+BDYTF0+G4T0deSaVi6IFO718HZwS4bQotkj4y+/85xu3WI5FlPP02KoxOlL59jz29rjE4jIiIiOdCPm07z9WrbQvAfP101fTERFQUtWtiKCbMZvv4avvpKxUROUKSIbXeUPn1sI1s++MC2FsXVq3d8agV/T2a8WBc3Rzs2HL/E67/sIDnVkg2hRXIWlRMi2cXTk6TWbQAovWIRYdEZWzRJRERE8ofl+0IZungfAP2alaVT3eL/PnjqlG3axurV4O5u2zXi9deNCSo35+gIEyfC5Mm2jxcssK1DkYHtRmsEevNDtzo42ZtZdTCCAfN2Y7HkuwHuks+pnBDJRtd37Xjy4FqWbD9jcBoRERHJKbacvMwbs3dhtUKnusV5s2nZfx88cAAaNbItfFm0qG3qQOvWxoWV23vpJQgJgYAA2L8f6teHzXdeEL1B6YJM6lwTe7OJxbsu8OkfB7M+q0gOonJCJDs1b06Clw++cVGc+fV3o9OIiIhIDnAk/CovzdhKUoqFxyr58VHbypiu77ixZQs89JBtTYNKlWxvcqtXNzaw3FmDBrBtGzzwAFy8CE2awPz5d3zaoxX8GN2uGgCT/zrJlL9PZnFQkZxD5YRIdnJwgPbtAai+binHImINDiQiIiJGioxNpMe0rcQkpFCrhA9fd3oAe7t//om+ejU0bQqXL9u2DF23zjZyQnKHIkVsX7PWrSEhwbYGxdixtjUpbuOZmsV4t0UFAEYuPcCSPReyI62I4VROiGQz5x62qR0tjmxk2aaM7YUtIiIieU9Cciovz9zG+ahrBBV05Yeutf/dpWHRImjZEmJjbQVFcDAULGhoXrkH7u62r+Vrr9lKiQEDbGuFpKbe9mmvNi5FtwYlsFqh/5zdbDpxKXvyihhI5YRIdqtfn7hiJXBLTiB69nzy4W6+IiIi+Z7VauXd+XvYcSYKT2d7pnSvg4+bo+3BX3+Fdu0gKQmeeQaWLrW9yZXcyd7etrPKuHG2bUa/+Qaef9729b0Fk8nE0DaVaVHZn6RUC71mbuNw2J13/hDJzVROiGQ3kwnHbl0AeHDzcnadjTI2j4iIiGS7r1cfY/GuC9ibTUzqXIvSvv+UD7/+Ch072n6z3qULzJkDTk7GhpX7ZzLBW2/Zvp4ODjB3LrRpYxsZcwt2ZhPjO9agTpAPVxNSeHH6ViJjE7MxtEj2UjkhYgCHrrZy4qGTO1kVstfgNCIiIpKdft99gXErjwDw0VNVaFSmkO2B/y8mpk2z/dZd8o7nnrONhHFzgxUroFkzuHTrKRvODnZM7lqboIKunI+6xsszt5GQfPspISK5lcoJESOUK0dM1RrYWy0wdy4pqRajE4mIiEg22Hc+mgHzdgPw0oMl6VS3uO2B+fNvLCbs7AxMKlnmscdsa4gUKGDbfeWhh+D8+Vse7u3qyJTudfB0tmfHmSje+XWPpgVLnqRyQsQgbi92B+CxHSvZcFyLHImIiOR1l2ITeeXH7SSmWHikvC+DW1W0PbBoEXTooGIiP6lXD/76y7b7ysGD0LgxnDlzy8NL+7rzbeda2JtN/Lb7Al8FH8vGsCLZQ+WEiEHsOnXEYjZTI/QIfy/fZHQcERERyUIpqRZe/2Un56OuUbKQG+M7PoCd2WT7Dfr1YqJzZxUT+UmlSvD331CyJBw/bisoTp685eENyxRi5FNVAPhi1RF+260tRiVvUTkhYhQ/P642fBgA94W/av6giIhIHvbpH4fYeOISbo52fN+lFl4uDrYh/W3b/rsrh4qJ/CcoCNatg7Jl4dQpW0Fx7NajIjrWLU6vh0oCMGDebvaci8qWmCLZQeWEiIE8utsWxmyxN4TgA+HGhhEREZEssWjneab8bfuN+Nj21Snr5wH79kHLlhAXZ1sU8ZdftPhlflWsGISEQIUKcPYsPPwwHDp0y8MHtazIoxUKk5Ri4ZUft3PxqnbwkLxB5YSIgcztniXFwZFyl86w7fe1RscRERGRTLb/QjSDFuwB4LVHStOiSoBt6P7jj8OVK7a1BxYu1Hah+V2RIraConJlCA2FJk3gyJGbHnp9i9FSvm6ERifw2i87SNbi6pIHqJwQMZKXF9eaNQfAf9lCouOTDQ4kIiIimSUmIZneP+0gIdlCk/K+9H+sPERE2HZrCA2FKlVg2TJwdzc6quQEfn6wZg1Uqwbh4fDoo3DixE0P9XR24PsutXF3smfLycuMXHIgm8OKZD6VEyIG8+hhm9rRev9a/tirhY1ERETyAqvVyjvz9nDmcjxFvV0Y36EGdgnXoE0b2+KHJUvCihW27SRFrvP1hZUroWJF2/aijz56y108yhR2Z3yHGgDM2HiauVvPZmNQkcynckLEaE88QZKLG8ViIjiw4E+j04iIiEgmmLb+FMv3h+FgZ+KbF2ri7WQHzz8PW7bYConlyyEgwOiYkhMVLmzbxaVsWTh92lZQnD9/00ObVfKj/2PlABiyaB87z1zJzqQimUrlhIjRXFxIbtMGgNKrficsOsHgQCIiInI/dpy5wifLDgIwpHUlqhfzgn79YPFi29oSv/0G5coZG1JytoAAWL36321Gmza1TfW4idcfKUPzyn4kpVro8/MOLsVqgUzJnVROiOQAbt27AtDq0N8s3XHzoXsiIiKS812JS6LvLztJsVhpXTWArg1KwBdfwIQJtgN+/BEaNTI2pOQOxYrZCorAQDh8GJo3h6ioGw4zm02Mea46pQrZFsjsN2cXqRZr9ucVuU8qJ0RygmbNSPDywTc+ipO/LjE6jYiIiNwDi8XK2/N2cz7qGkEFXRn1bFVMCxbA22/bDhgzBp57ztiQkrsEBdmmeBQuDLt3w5NPQnz8DYd5ODswqXMtXBzs+OtoJF8GH83+rCL3SeWESE7g4ADt2gFQ7a8/OBYRa3AgERERuVtT159k9aEIHO3NfPNCLTwO7oMutoWvee016N/f2ICSO5UtC3/+CZ6e8Ndf0KEDJN+4w1t5fw8+eaYKAF+vPkrI4YjsTipyX1ROiOQQzl07A9Di8AaWbj1pcBoRERG5G/vOR/PZ8kMAfPBEJSrZXYO2beHaNdtw/PHjwWQyNqTkXjVqwJIl4Oxs+++LL4LFcsNhTz9QjBfqFcdqhX5zdnHuyo2jLERyKpUTIjnFgw8S7xeAZ1I8l+YuwmrVXEEREZHcID4phTdm7yQ51crjlfzoXMMPnn4azp6F8uVh9mywtzc6puR2Dz0E8+aBnR389JNtJM5N/r04tE0lqhXzIio+mdd+3kFSyo0lhkhOpHJCJKcwm7Hv1BGAuptXcCA0xuBAIiIikhHDfzvAiYtx+Hs689kzVTH17g0bN4K3t21nDm9voyNKXvHEEzBjhu3jL7+EsWNvOMTJ3o6Jz9fEy8WB3ef+HdEjktOpnBDJQRy72KZ2NDu+hT83HjM4jYiIiNzJ0j2hzNl2FpMJxnWojs93E2D6dDCbYc4cbRkqme+FF2DcONvHAwfCrFk3HBJYwJUxz1UHYMrfJwk+ePNtSEVyEpUTIjnJAw8QW6IUzilJXJ37q6Z2iIiI5GDnrsQzaMEeAPo0KU3Dk7vgnXdsD44bB48/blw4ydveegv69bN93K0brFlzwyGPVfLjxUYlAXh73m5Co69lY0CRu6dyQiQnMZlw7vICAA9tW8XOs1HG5hEREZGbSrVY6T9nN1cTUqgR6E2/cs7QqZNtkcIePeCNN4yOKHnd2LG23d6Sk21rnOzbd8Mh77YsT9WitvUn3pi1k5RUrT8hOZfKCZEcxr7zP+XEqZ2s+mu/wWlERETkZqb8fYItpy7j5mjHV09VxKH9cxAZCTVrwsSJ2plDsp7ZDD/+CA8+CNHR0LIlnDuX7hAnezsmPP8A7k72bD11hS+DjxoUVuTOVE6I5DTlyxNTsSoOllQsc+eRatHUDhERkZzkUFgMY/48Ath2Rig+YjBs2wYFCsD8+eDiYnBCyTecnWHxYqhQwVZMtGkDsbHpDilR0I1Pn6kKwIQ1x1h/LNKIpCJ3pHJCJAdy7d4FgEd2rmbLycsGpxEREZHrElNSeWvObpJSLTSrWJj2e1bC99/bRkr8/DMEBRkdUfKbAgXgjz+gcGHYtcu2YGZqarpD2lQvQqe6xbFa4a05u7gcl2RMVpHbUDkhkgNd31K0ztn9rFu9w+A0IiIict34VUc5GBpDATdHPi+Vium112wPDB8OLVoYG07yr6Ag2wgKJyfb9rXXF2b9j6FPVKJMYXciriby7vw9WnhdchyVEyI5UWAg0bXrY8aKw/xfSdbiRSIiIobbduoy3609DsDoZiXw6f4CJCZC69bw/vsGp5N8r359mDHD9vG4cbYRPf/h4mjHlx1r4GhnZuWBcH7ZcsaAkCK3pnJCJIdy794ZgGa7V7Ph+CWD04iIiORvcYkp9J+7G4sVnn2gKM3GfwAnTkCJErZFCc36Z7XkAB06wIgRto/79IFVq9I9XLmIF++0KA/AR0sOcCwi9v/PIGIY/RQVyaHs2rcn1WxHtbBjbPxjo9FxRERE8rXPlh/izOV4inq7MPLiBpg7F+ztYfZs8PExOp7Iv4YMgc6dbetOtGsHhw+ne/jFRiV5qGwhEpItvDl7J4kpqbc4kUj2UjkhklP5+nL1oUcA8Fg4T39xiIiIGGTj8UvM3HgagAlV7HAZ0N/2wKef2obSi+QkJhP88AM0amTbYrRtW9t//2E2mxj7XHV8XB3YfyGGsSuOGBhW5F8qJ0RyMM8etl07WuwNYe2hCGPDiIiI5EPxSSm8O38PAN2rFeKBAa/8u85E//4GpxO5BScn27a2gYG2kROdOqXbwaOwpzOj21UH4Pt1J9hwXNuLivFUTojkYOZnnibZ0YnSl8+x4/e1RscRERHJd0YvP2ybzuHlzPtLv7a90StaFKZP1zoTkrP5+cGiReDiYttq9L330j38WCU/OtUtDsDAeXuITUwxIKTIv/QTVSQn8/AgrunjABRYspD4JP2lISIikl02n7jE9A2nAJhifxiHX34GOzuYNQsKFTI2nEhG1KwJ06bZPh49Gn76Kd3D77euSGABF85HXWPkkgMGBBT5l8oJkRzOq9sLALTYv5bVB8MNTiMiIpI/XEtK5Z1/pnP0Lm6iwsjBtgeGDoWHHjIwmchd6tDh31ETL70EW7emPeTuZM/n7apjMsHsrWdZo2nEYiCVEyI5nOmJJ0hycqF4dDh7Fq268xNERETkvn3+52FOX4qnmLsDb//0McTE2BYY/L+h8SK5wkcfQZs2tvVSnnkGIv4tIeqXKsiLjUoC8O78PUTFJxmVUvI5lRMiOZ2bG9eatwTA74/fiElINjiQiIhI3rbzzBWmbTgJwMzI1dhv3AAeHvDjj7btQ0VyG7PZNqWjfHk4d842miLl3+nCA5uXp7SvGxFXExm6eL+BQSU/Uzkhkgt4Xp/aceAvVu4LMziNiIhI3pWcamHwgr1YrfCm+2VKTRhje+Cbb6BkSWPDidwPT09YuBDc3SEkBN59N+0hZwc7xravgZ3ZxG+7L7B0T6hxOSXfUjkhkguYWrUi0dWNolcvcmDhCqPjiIiI5FnfrzvBobCrFLNP4Y1pH9q2X+zYEV54wehoIvevYkWYMcP28bhxMHt22kM1Ar3p06Q0AEMW7eXi1UQjEko+pnJCJDdwdiapVRsAiq34nStxmgsoIiKS2U5cjOXL4KMA/LR/NnYnTkDx4jBpEphMBqcTySTPPAODBtk+7tkT9uxJe6jvo2WpFODJlfjkf0YQWQ0KKfmRygmRXMLjn6kdLQ/9xfK9FwxOIyIikrdYLFYGL9hLUoqFvtcOE7Rotq2QmDkTvL2NjieSuUaOhMceg/h4W1kRFQWAo72ZcR2q42BnYtXBcObvOG9sTslXVE6I5BaPPUaimwf+sZc5Ov8Po9OIiIjkKXO2nWXzycsEJMfRb85o251vvQWNGxsbTCQr2NnBrFlQogQcPw4vvgj/jJKo4O/JW4+VA2D4b/u5EHXNyKSSj6icEMktnJxIebItACVXLyUiJsHgQCIiInlDREwCnyw7CMCPe37CLjwcKlSw/XZZJK8qWBDmzQMHB9tCmV99lfbQyw+V4oHi3lxNTOGdX/dgsWh6h2Q9lRMiuYhb13927Ti0nj92njU4jYiISN7w0dKDXE1IoffFHZRZ9bvtt8ozZoCLi9HRRLJWnTowdqzt44EDYfNmAOztzIx9rjrODmb+PhbJz5tPGxhS8guVEyK5SdOmJHj54BsfxamFmtohIiJyv/46epHfd1+gcPwV3l443nbn4MFQt66huUSyzeuvQ7t2kJwM7dvD5csAlPJ1Z1CLCgB8suwQpy/FGZlS8gGVEyK5iYMDlqeeAqBsyDLCojW1Q0RE5F4lJKfywaJ9YLUyc/NU7K9churV4YMPjI4mkn1MJvjhByhdGs6cge7d09af6NogiAalCnItOVW7d0iWUzkhksu4dvln147DG/hj5xmD04iIiORek0KOc+pSPF1OrKfCljW2ufczZ4Kjo9HRRLKXlxfMnWv73v/997SpHmaziVHPVsXZwcyG45eYu03TiiXrqJwQyW0aN+aaT0F8Eq5y/tclRqcRERHJlU5cjGVSyHEKxkXxwarvbHcOHQrVqhkbTMQoNWvCl1/aPh40CDZsAKBEQTfefqw8ACOXHiRci7JLFlE5IZLb2NtjebYdAOXX/kFotLZ3EhERuRtWq5UPFu8jKdXCN5un4xh1xTad4913jY4mYqxXXoGOHSE1FTp0gMhIAHo0CqJ6MS+uJqQwdPE+g0NKXqVyQiQXcuvyPADNj25k+XatniwiInI3ftt9gfXHLtHq+CbqbV1l251j6lTbtA6R/Mxkgu+/h3Ll4Nw56NIFLBbs7cyMerYa9mYTf+4P54+9oUYnlTxI5YRIbvTgg8QV8sMzMY7QeYuNTiMiIpJrXE1IZuTSg3gmxPL56n+mcwwcaBvSLiLg4QHz5oGzMyxfDp99BkDFAE/6NCkNwAeL9xMVn2RkSsmDVE6I5EZmMzxnm9pRcd1yLkRpaoeIiEhGjF91lItXE/ls/XTcLl+E8uVh2DCjY4nkLNWqwYQJto+HDIF16wB47dEylCnsTmRsIh8vPWhgQMmLVE6I5FJu/+za8dixzfy57aTBaURERHK+I+FXmb7hFA+f2E7LbcttQ9inTLH9hlhE0nvxxbRpHXTsCBcv4mRvx2fPVsVkgnnbz/H30UijU0oeonJCJLeqX59YvyK4J10jYu4io9OIiIjkaFarlaGL9+GYcI1xa/6ZzvH669CokbHBRHIqkwkmTYKKFSE01FZWWK3UKlGAbg2CABi0YA/xSSnG5pQ8Q+WESG5lMmFq3x6Ayn8t59yVeIMDiYiI5Fy/7wll04nLDNg4i0KRF6B4cfjkE6NjieRsbm4wezY4OcGSJfDNNwAMbF6eot4unLtyjbErjhgcUvIKlRMiuZhbV9vUjkePb2HllhMGpxEREcmZYhNT+HjpASqFn6DHlkW2OydOBHd3Q3OJ5ArVqqUtismAAbB/P25O9nzyTFUApq4/yc4zVwwMKHmFygmR3KxWLa4WKY5rciKRcxYYnUZERCRH+nr1US5GxTM2eCJmSyq0awdPPGF0LJHc4403oGVLSEiATp0gIYHG5Xx5pmZRrFZ4d/4eklIsRqeUXE7lhEhuZjJh7tQBgKrrl3P2sqZ2iIiI/Nfxi7FM/fskXXYuo+LZw+DpCV9+aXQskdzFZIJp06BwYdi7F959F4APWleioJsjR8Jj+SbkmMEhJbdTOSGSy13fteOR49tYtVlz/kRERP7r46UHKXjlIoP//tF2x6hRUKSIsaFEciM/P1tBAfDVV7BsGT5ujgxvWxmAiWuOcTT8qoEBJbdTOSGS21WrRnTxUjilJnNl9nyj04iIiOQYa49cZPWhCEYEf4dzQjzUrw+vvGJ0LJHcq1Ur2xQPgB49IDyc1lUDaFbRj+RUK+8v3IfFYjU2o+RaKidEcjuTCftOHQGotv5PTe0QEREBUlItfLTkAM2ObubxIxvB3h6+/x7M+uevyH357DOoWhUiIqB7d0xWK8PbVsbV0Y4tpy7z6/ZzRieUXEo/nUXygOu7djx8cicrNxwyOI2IiIjxftlyhnPnIxmx+nvbHW+/bXtDJSL3x9kZZs2y/Xf5cvj6a4p6u/BWs3IAfPLHQS7FJhocUnIjlRMieUGlSkSVLo+jJYWrs+cZnUZERMRQ0fHJjFt5hNc3zqVIVDgULw4ffGB0LJG8o3JlGDvW9vE778CePfRoFETFAE+i4pP5eNlBY/NJrqRyQiSPcHzeNrWjxoYVnLmkqR0iIpJ/jQ8+QoGzJ3llyz/bbI8fD25uhmYSyXN694Y2bSApCTp1wj4pkU+eroLJBAt2nGfD8UijE0ouo3JCJI9w/WfXjkandhH8936D04iIiBjjWEQsP244xfCV3+KQmmJbwO+pp4yOJZL3mEwwZQr4+8OBAzBgAA8U9+GFesUBGLJwH4kpqQaHlNxE5YRIXlG2LJfLVcbeaiF21lyj04iIiBjik2UHaXFgHQ+d3gVOTrYtD00mo2OJ5E2+vjBzpu3jb76BpUsZ2LwCvh5OnIiM49uQE8bmk1xF5YRIHuL0QicAam5awelLcQanERERyV5rj1xk8+5TDFk9xXbH4MFQurSxoUTyusceg/79bR/37IlXXDQfPFEJgIkhxzgZqX+TSsaonBDJQ9y6PA9A/TP7WL12r8FpREREsk9KqoWRSw7Qb/0v+MdespUS775rdCyR/OHjj6FSJQgPh969aVPVn4fKFiIpxcKQRXuxWq1GJ5RcQOWESF5SsiSXKtfAzmrh2qw5RqcRERHJNr9sOYP1wAF6bP/NdsfXX9u2OhSRrOfsbJveYW8Pv/6KafZsRj5VBSd7M+uPXWLxrgtGJ5RcQOWESB7j0tk2taPWppUaRiciIvlCdHwy41Yc5sNV32FvsUDbttCypdGxRPKXWrVg6FDbx6+9RomEKPo+WgaAkUsPEB2fbGA4yQ1UTojkMa7/rDtR59wB1q7eaXAaERGRrPdl8FHq7VrHg6d3Y3VygnHjjI4kkj8NHgx160JUFLz4Ii8/VIoyhd2JjE1i1PJDRqeTHE7lhEheExhIZLVamLGSqKkdIiKSxx2/GMucdYf5YPUPAJgGDoRSpQxOJZJP2dvbpnc4O8OKFTj+8D0fP1UFgFlbzrD99GWDA0pOpnJCJA9y7WxbGLP2llWcuBhrcBoREZGs8/HSg/TcNJ9iMREQGGj7za2IGKd8eRg92vbxgAHUS73Mc7WKAfDegn0kp1oMDCc5mcoJkTzI9YWOWEwmal04xLpV242OIyIikiX+OnqRw5v30WfTPNsdY8aAq6uxoUQEXnsNmjaF+Hjo1o3Bj5fFx9WBw+FXmbb+pNHpJIdSOSGSFxUpQmSNugAkzZlrcBgREZHMZ7FY+XTZId5bMwXnlCRo0gSee87oWCICYDbDtGng6QkbN1Lgmy8Z3KoiAONXHSU0+prBASUnUjkhkke5d/lnYcwtwRyL0NQOERHJWxbvPo/Xpr9pfXg9Vjs7+OorMJmMjiUi1wUG2rb0BRg2jHbmSGqV8CE+KZWRSw8am01yJJUTInmUa6cOWEwmHgg9zF8rtxodR0REJNMkpqQy7o+DDA3+HgBT795QtarBqUTkBl26wNNPQ3Iy5m5d+ahFGcwmWLonlL+PRhqdTnIYlRMieZW/P5E16wOQMneewWFEREQyz48bT9No3W9UvHgKq48PfPih0ZFE5GZMJvjuOyhcGPbto9K3Y+naIAiAoYv3kZiSamw+yVFUTojkYR5dbLt21Nm6imMRVw1OIyIicv+iryUz/Y/dDPjrRwBMH34IBQsaG0pEbs3XF763jXLi888Z6B5JIXcnTkTG8cNfWhxT/qVyQiQPc+n4HBaTmRqhR/nrT03tEBGR3O/btcfpvPpnCsVHYy1fHnr3NjqSiNxJ27bQvTtYrbi92osPmpYA4OvVRzkfpcUxxUblhEhe5udHZO0GAKTM1a4dIiKSu4VGX2Pl7xvosW0xAKZx48DBweBUIpIhX3wBRYrA0aM8OW8SdUsWICHZwojf9xudTHKIbCknJk6cSFBQEM7OztSrV48tW7bc8tjJkyfz0EMP4ePjg4+PD82aNbvh+O7du2MymdLdWrRokdWXIZIrXZ/aUW9bMEfDNbVDRERyry9WHuHtVVNwSk3B2rw5tGxpdCQRyShvb5g8GQDT+PF8XiQOO7OJP/eHs+ZwhLHZJEfI8nJizpw59O/fn2HDhrFjxw6qV69O8+bNiYi4+TdgSEgInTp1Ys2aNWzcuJHAwEAef/xxzp8/n+64Fi1aEBoamnabNWtWVl+KSK50fWpHtbBj/P3nZqPjiIiI3JMj4Vc5u2AZLY9swGpnh2nsWG0dKpLbtGqVNr2jxIDX6FXLH4APf9tPQrIWx8zvsrycGDduHL169aJHjx5UqlSJb7/9FldXV6ZOnXrT43/++Wf69OlDjRo1qFChAj/88AMWi4Xg4OB0xzk5OeHv75928/HxuWWGxMREYmJi0t1E8g1fXy7WbQRA6hxN7RARkdzp82UHGBL8AwCmV1+FypUNTiQi92TcONv0jiNH6L/+Z/w8nTh9KZ7v150wOpkYLEvLiaSkJLZv306zZs3+fUGzmWbNmrFx48YMnSM+Pp7k5GQKFCiQ7v6QkBAKFy5M+fLl6d27N5cuXbrlOT799FO8vLzSboGBgfd2QSK5lGdX29SO+ttXc0RTO0REJJfZcvIy7vPnUjniBKmeXto6VCQ38/FJ273D8cvxjCkWD8DENcc4ezneyGRisCwtJyIjI0lNTcXPzy/d/X5+foSFhWXoHO+++y5FihRJV3C0aNGCmTNnEhwczGeffcbatWtp2bIlqak3Hwo0ePBgoqOj025nz56994sSyYVc2rcj1WxHlfDjrP8jY8WgiIhITmC1Whnz2y4GrLNtHWr3/ntQqJDBqUTkvrRuDV27gsXCg5+8Q+NANxJTLAzX4pj5Wo7erWPUqFHMnj2bhQsX4uzsnHZ/x44defLJJ6latSpPPfUUS5YsYevWrYSEhNz0PE5OTnh6eqa7ieQrhQoR+c/UDuvceQaHERERybjl+8Kosegnil69SGqxYtC3r9GRRCQzjB8PAQGYDh9m/KHFONiZWHUwglUHwo1OJgbJ0nKiUKFC2NnZER6e/hssPDwcf3//2z53zJgxjBo1ihUrVlCtWrXbHluqVCkKFSrEsWPH7juzSF7l2e0FAOpv164dIiKSOySnWvh2wRZe32hbM8nu44/BxcXgVCKSKXx84LvvbB9+8xUfFLKtC/jh71ocM7/K0nLC0dGRWrVqpVvM8vrilg0aNLjl80aPHs1HH33E8uXLqV279h1f59y5c1y6dImAgIBMyS2SF7k89ywpdnZUijjJhmXrjY4jIiJyR7O3nqXNkml4JsaRWq0avPCC0ZFEJDO1aQNduoDFQufvhlPC1cy5K9f4JuS40cnEAFk+raN///5MnjyZGTNmcPDgQXr37k1cXBw9evQAoGvXrgwePDjt+M8++4wPPviAqVOnEhQURFhYGGFhYcTGxgIQGxvLwIED2bRpE6dOnSI4OJi2bdtSpkwZmjdvntWXI5J7FSxIZL2HALDO09QOERHJ2eISU5g3bx1ddywFwO7zz8HOzuBUIpLpxo8Hf3/Mhw8x9bTt//dv1x7X4pj5UJaXEx06dGDMmDEMHTqUGjVqsGvXLpYvX562SOaZM2cIDQ1NO37SpEkkJSXRrl07AgIC0m5jxowBwM7Ojj179vDkk09Srlw5evbsSa1atfjrr79wcnLK6ssRydU8u9p+41Rv22qORWhqh4iI5FxT/z5Jzz+m4GhJwfLYY/D440ZHEpGsUKBA2vSOUtMn0cUcRlKKhY+WHDA4mGQ3k9VqtRodIrvFxMTg5eVFdHS0FseU/OXKFVJ8C2OfmsLMH5bRtWdLoxOJiIjcIDo+mZf7fcucyW9gNZkw7dgBNWoYHUtEslLnzvDzzySWq0CNtp9yzezAzBfr8nA5X6OTyX3K6PvvHL1bh4hkMh8fLtZ/GNDUDhERybm+W3uMfn9Otv2hcxcVEyL5wZdfgp8fTkcO8f2pPwDb4phJKRaDg0l2UTkhks94dXsesO3aoakdIiKS01y8msiJGfNocGYvqY5OmEZ+ZHQkEckOBQvCpEkAPLhwKg2vnuXExTimrT9pcDDJLionRPIZ1+eeJcXOnvKRZ9j4219GxxEREUlnUvAh+q+aAoD5zTegeHGDE4lItnn6aWjXDlNKChNXT8TOkspXwUcJj0kwOplkA5UTIvmNtzcRDRrbPtbUDhERyUEuRF0jYfI0yl06Q7K3D6b33jM6kohkt6+/Bh8ffA7tY+jR5cQlpTLqj0NGp5JsoHJCJB/y7mbbtaP+9mCOhWtqh4iI5AzfLtvNG+t+BMB+6Afg7W1sIBHJfv7+MG4cAF3+mEbJK+dZuPM8205dNjiYZDWVEyL5kOtzz5Bs70DZS2fZ9Ps6o+OIiIhwKjIOr+++wT/2MomBJTD16WN0JBExSrdu8NhjmBMTmPL3ZExWC0MX7yfVku82msxXVE6I5EdeXkQ0bAKAad5cY7OIiIgAP8zfxMubfgXAafQocHIyOJGIGMZkgu+/Bzc3Sh3YRo/9KzkQGsMvW84YnUyykMoJkXwqbWrHttUc164dIiJioMNhVyn3/Rd4JF0jvvoD0L690ZFExGhBQfDxxwAMCpmOf0wkY1cc5kpckrG5JMuonBDJp9zaPU2SvSOlL59j8+IQo+OIiEg+NvOnYDrtWg6A6/hxYNY/UUUEeP11qF8fx7irjF/7HVFxSYxZcdjoVJJF9JNfJL/y9CSi0SMAmLRrh4iIGGTPuShqTf8KB0sqcY80gyZNjI4kIjmFnR1MmQKOjtQ/sJE2B9fxy5Yz7DsfbXQyyQIqJ0TyMZ/utqkd9bYFc0JTO0RExACzpi3nqf0hALh9PsrYMCKS81SqBO+/D8Ana3/AOy6aYb/tx2rV4ph5jcoJkXzM7dmnSHJwotSVC2xZtNroOCIiks9sOXmZxj99hRkr8U8+DbVqGR1JRHKiQYOgShU8Yq4wPGQK209fYeHO80ankkymckIkP/PwIPxB29QO5v1qbBYREclXrFYrC79fSIsjG7GYzbiO+tjoSCKSUzk62qZ3mM08uXc1TY5v5dM/DnE1IdnoZJKJVE6I5HM+3ToDUH9bMCcvxhqcRkRE8ou/jkbScvZEABI6PA8VKxqcSERytLp1oV8/AD5bNYn4yCt8vfqYsZkkU6mcEMnn3J9tS6KjE0FRoWxZEGx0HBERyQesVivLJ87m4VM7SbW3x/XjEUZHEpHcYMQIKFUKv6gIBq6bydS/T3IsQr9cyytUTojkd+7uhD/YFADTvLkGhxERkfxgxf4wnpk/CYCkHj2hZEmDE4lIruDmBt9/D0DXnUupevYgw3/X4ph5hcoJEcGnu21qR4NtwZzS1A4REclCFouV9V//SO3zB0l2csZl+DCjI4lIbtK0KXTrhtlqZdSfX7PxUBh/7g83OpVkApUTIoLHM0+S6OhMYHQ4W39dYXQcERHJw1bsC6XDou8ASO3zGgQEGJxIRHKdMWOgUCHKXzzNy1sWMHLpARKSU41OJfdJ5YSIgJsbYQ83A8D86zyDw4iISF5lsVjZMW4ylSNOkOjqjvP7g42OJCK5UaFCMH48AG9umIX98WN8u/a4sZnkvqmcEBEACvwztaPetmBOR2pqh4iIZL6Ve87T4fcfALD07w8FCxqcSERyreefh8cfxyklmU/+nMikNcc4ezne6FRyH1ROiAgAHk+3IcHJhWIxF9k6d7nRcUREJI+xWKzs+2wCpS+fI97LB5d3BhgdSURyM5MJJk3C6uJCwzN7aLNrJSOXHjA6ldwHlRMiYuPqSvjDjwFgp6kdIiKSyVbuOk2HZVMBML37Lnh4GJxIRHK9UqUwDR8OwPurp7Bty2H+OnrR4FByr1ROiEiaAj1sUzvqblvDGe3aISIimcRisXLs4/EUi7lIbMHCuPR7w+hIIpJXvPUW1KiBT8JVPlg9mQ9/209SisXoVHIPVE6ISBqPp57gmpMrRa9eZNvcP4yOIyIieUTwthO0/3MGAOZhQ8HFxeBEIpJn2NvD5MlYzWaeOrCWYpvXMWPDKaNTyT1QOSEi/3JxIbyxpnaIiEjmsVisnB0xGt+4KKICAnF99WWjI4lIXlO7NqY33wRg5Ipv+G7ZHiJiEgwOJXdL5YSIpFPgxS4A1N22WlM7RETkvgVvOsIzwb8A4PjRCHBwMDiRiORJI0ZgLVGCwOhwXl49k1F/HDI6kdwllRMiko5n29bEu7gREHuJHXOWGR1HRERyMYvFSujI0XgnxHKpeGlcu3cxOpKI5FXu7pi++QaAntsWc/iPtWw7ddngUHI3VE6ISHrOzoQ1aQ6AWVM7RETkPgRvPEzb1XMAcPloONjZGZxIRPK0Vq2gY0fsrBZGLf+a4Qt3k2qxGp1KMkjlhIjcoOA/u3bU266pHSIicm8sFithH43GKzGOyBJlcO3cyehIIpIfjB+PxdubquHHqff7T8zacsboRJJBKidE5AZeT7YizsUdv9jL7Ji9xOg4IiKSC63aeJi2IXMBcP1oOJj1z04RyQZ+fpjHjAGg/98/88uctVyJSzI4lGSE/pYQkRs5ORH2iG1qh72mdoiIyF2yWKyEj/gMz8Q4IkuUxfWFjkZHEpH85MUXsTRugmtyIu8s/ooxf2pxzNxA5YSI3FSh67t2bF/D2YtXDU4jIiK5yaqNh2m71lZuu3ysURMiks1MJszff4fF0YkmJ7cTO/1H9p2PNjqV3IH+phCRm/Jq05JYVw8Kx11h5y+/Gx1HRERyCYvFSsSIUXgmxnGxZDncOnUwOpKI5EflymH+YAgAHwRPZvTP67FoccwcTeWEiNycoyNhj7QAwH7+rwaHERGR3GLVxkM8GWIbNeH68QiNmhAR47zzDskVK1EoPponfvqChTvPG51IbkN/W4jILV2f2lFHUztERCQDLBYrF0eMwjMpnoulyuPW4TmjI4lIfuboiMOUH7CaTLTfu4qVE2cRk5BsdCq5BZUTInJL3m1aEOvqgW98FLt+Xmx0HBERyeFCNh2iTYhttJ3rSI2aEJEcoEEDLK+8CsC7i77gm6V7DQ4kt6K/MUTk1hwcCG3aEgD7+fMNDiMiIjmZ1Wrl4ojP8EyKJ6Jkedw6tDM6kogIAHajPiWxsD8lr4TiMW40R8I1IjgnUjkhIrfle31qx441nLsYY3AaERHJqdZvOUKrNXMBcNGoCRHJSby8cJo0EYCXN/3K5G9/x2rV4pg5jf7WEJHb8m7dnBg3LwrFR7P7J03tEBGRG1mtVsI+/BSPpGuElSyPR0eNmhCRHObpp7nWojUOllQ6TB7JH3suGJ1I/o/KCRG5PQcHwtKmdmjXDhERudHW7Udpsdo2asJZoyZEJCcymXD5fhJJLq7UPn+QvcPGEJ+UYnQq+Q/9zSEid+Tb8/rUjhDOR2qOnoiIpHdh6Ce4J10jtGQFvDtphw4RyaECAzGNHAlA7+WTmfHrRoMDyX+pnBCRO/Jp9Tgx7t4UuBbDnpkLjY4jIiI5yK6dR2kWbBs14ThyOJhMBicSEbk1hzffILpydTwT4yjx0XuciowzOpL8Q+WEiNyZvT2hTVvZPtTUDhER+Y+zH3yMe9I1zpesQEGNmhCRnM7ODs+ZU0k129Hq0N8s/vh7oxPJP1ROiEiGFP5nakftHSFc0K4dIiIC7N97gkdW2kZNOIzQqAkRyR1MNWty9dXXAHh26qes3X7C4EQCKidEJIN8WjYjysMHn4Sr7J65wOg4IiKSA5wcYhs1cS6oAoVf0KgJEck9vEd/QlThIhSLuUjYW4NISE41OlK+p3JCRDLG3p6wZq0BcNDUDhGRfO/woTM8vHw2AHZDh2jUhIjkLm5uOE3+DoB2f89n8dQlBgcSlRMikmF+16d27FzLhYhog9OIiIiRjnwwCs+keC4UK01At05GxxERuWsuTz7BucefxM5qofLwgVzQrnSGUjkhIhnm06IpUZ4F8E6IZa+mdoiI5FvHT4Ty4JKfALAOfg/M+ieliORORad/S6yLB1VCj7LhreFGx8nX9DeJiGScnR2hmtohIpLvHRg6Gp+Eq4T5FafoK92MjiMics9MAQHEfPgRAC3nTGTbul3GBsrHVE6IyF3xe6krYJvaEXpRUztERPKbs+cu0WDhdACS3nkX7OyMDSQicp+KDOjL6YoP4JacQHLvPiSnaHFMI6icEJG7UuDxR7jsVRDPxDj2TtPoCRGR/GbXsNEUio/iYqEAivftZXQcEZH7ZzZT4MdpJNvZ0+DARtZ+8q3RifIllRMicnfs7Ah77AkAHBeonBARyU8uhEdRZ94UAOLeGgAODgYnEhHJHB61qnOk+2sAVPt8KGFnwgxOlP+onBCRu3Z9146aO9cRpl07RETyje3Dv8D/6iUuefsS9PZrRscREclUFb/6lPOFAykce5kjL/Y1Ok6+o3JCRO5awccf4ZJXITyT4tk3bZ7RcUREJBtEXonlgV++AyDq9X7g5GRsIBGRTGZ2dSF5wjcAPBg8n51zlhmcKH9ROSEid89sJuxx29QOB03tEBHJF7aM/Jpi0eFEefhQatCbRscREckSQc89wc6mT2HGile/10m8lmB0pHxD5YSI3JPru3bU3LWOsPAoY8OIiEiWiolLoNL0iQCE93odk5ubwYlERLJOmRmTuOLqRamwk2x//X2j4+QbKidE5J4UataYSO/CeCRdY/+0uUbHERGRLLTp00kEXT5PjKsnZYcOMDqOiEiW8ijqz4nBwwGoOXMCodv2Gpwof1A5ISL35j9TO7Rrh4hI3nUtIZlSk78E4Fz3lzF7eRqcSEQk69V8ry97K9TGOSWJK916gtVqdKQ8T+WEiNwz/162qR0P7P6b8PArBqcREZGssGncFMpEnCbWyY1yIwYbHUdEJFuYzGY8p08mwd6RSge2su+ziUZHyvNUTojIPSvU9GEu+vjhnnSN/VPmGB1HREQyWVJyKkUmjgXgRKcXsS9YwOBEIiLZp0S9Gmx+oQ8ARUcO4dqFcIMT5W0qJ0Tk3plMhP4ztcNp4XyDw4iISGbbPPFHyl84RryjM+U+0aJwIpL/1JnwMcf9gvCJi+Z4995Gx8nTVE6IyH0J+GdqR43dfxMRdtngNCIikllSUy0U/GI0AEee6YJzgJ/BiUREsp+ruysXx3yNBRNVVi7k/MJlRkfKs1ROiMh98X30ISIK+OOWnKCpHSIiecj2qb9S6cxBEuwdKfPpB0bHERExTL0XWrPmkWcAML/6KtZr1wxOlDepnBCR+2MyEda8DaCpHSIieYXVasVxjG3UxMFWz+EeFGhwIhER45hMJspO+Ypw9wIERJzlaL/3jI6UJ6mcEJH7dn3Xjhp7/iYi9JLBaURE5H7tmr+CGke2k2y2o+SoYUbHERExXPGSRdj6lu3nYckpE4jbtcfgRHmPygkRuW+FmzQirGAArsmJHJw62+g4IiJyn5JHfgLA/iZP4F2xrMFpRERyhmZD+rChYn0cUlO49Hx3sFiMjpSnqJwQkftnMhHW/EkAnBZoaoeISG62f9UG6u5ehwUTRT/VqAkRkeucHe2xn/QNcQ7OFD+4k7OjvzI6Up6ickJEMkVAry4AVN+zgYuhkQanERGRexU17GMADtR9BN+6DxicRkQkZ6nb+AFWdOwDgM+ID0g5f8HgRHmHygkRyRR+jRsSWqgoLimJHPxBUztERHKjY1v2Um/jcgB8RmrUhIjIzTz01Qj2B5TF/Vosp7u+bHScPEPlhIhkjv9O7dCuHSIiudKFISOxt1o4WKUeRR972Og4IiI5UiFvN85/9gWpJjOlVy8lcu5CoyPlCSonRCTTFHn5n6kdezcQeUFTO0REcpMzB05Qd80iAFw+0DZ5IiK30+yFVix7tL3tD31ewxoba2ygPEDlhIhkGr+H6nPetxjOKUkc/OEXo+OIiMhdODHkE5xTkjheqjJBz7UxOo6ISI5mNpuoNHkc5z19KXQplJOvDzQ6Uq6nckJEMo/JRHgL29QOZ03tEBHJNS6eC6fWslkApL47CEwmgxOJiOR8pUsGsGXARwAU//F7YjdvNThR7qZyQkQyVZFeXQGotncjly5cNDiNiIhkxIEPPsMjMZ4z/kGU7dnJ6DgiIrlGy0EvEVKtMfYWC9Gde0BqqtGRci2VEyKSqfwfrMu5wsVxSk3m4GRN7RARyelir8RQZe5UAKLefBuTnZ3BiUREcg9nBzvcJk0gxsmNosf2c+6j0UZHyrVUTohI5tLUDhGRXGX38HEUjI8m1MefKv1fMTqOiEiuU6dhFf7s8iYABUZ9RPKp0wYnyp1UTohIpiv6sm1qR9V9G7l0PsLgNCIicitJ1xIpNWMSABd6vYbZ0cHgRCIiuVPTcR+wK7ASronXON+5J1itRkfKdVROiEim829Y+3/t3XmcjXXDx/HvObNbZsY+lsm+RoiMpZIlYykUIWvdIoVKJJJshSKVQvalyFaIZAnltu+yy74O2WaGYbZzPX9MzXMr2zBnfuec+bxfr3n1OHNm+pzXc92Mb9e5Lp0IyS+/xAQdGD/ddA4A4DZ2fjJaua+c18VMWVT6/bdM5wCA28qa2V/nhn2hOLu3CqxdoQvTZppOcjuMEwBSn82m8+G8tQMAXJkjIVE5x3whSfqj5Svyy5zJcBEAuLc6zWppUXgrSZLXW2/KunLFbJCbYZwA4BR/v7Wj9O6NunTqnOEaAMA/7R4zTfnPHVeUX0aVGvSu6RwAcHs2m03lvh6mY1nyKMuVP3W001umk9wK4wQAp8hdtaKO5y4oX0eCDozjrR0A4FIsSxk+Tbqi/K7GrRWYM5vhIADwDIUeyqHtvQdLkgrMnqYrK1cbLnIfjBMAnObc32/tmM9bOwDAlRz8boGKHN+v695+Kjq4j+kcAPAoz7zdRr88Fi67ZenaS+2l+HjTSW6BcQKA0+T7+60dezbq0skIwzUAgL/FD/lYkrSt9nPKWSjUcA0AeBYfL7vyThytSwGBynvykA680890kltgnADgNHmqPKqjeQrJx5Gog+O+NZ0DAJB0YtV6Pbx7gxJtduUd+J7pHADwSCXLFNLG13tLkvKP+lSRu/YZLnJ9jBMAnOp83aS3dgTw1g4AcAkX+30oSdpaqbYKPFbGcA0AeK6aQ3poW5FH5Z8Qp4hW/5Esy3SSS2OcAOBU+TokvbWj1N7NunzirOEaAEjfLuw+oDJrlkiSMvXtZbgGADybn4+3/CeMVayXj4rv2qA9w8eYTnJpaTJOjBo1SgUKFJC/v7/CwsK0adOmOz5/zpw5KlGihPz9/VWmTBktXrz4ps9blqUPPvhAuXPnVkBAgGrXrq0//vjDmS8BwH3KW7m8juQtkvTWjrHTTOcAQLp2tO9geVsO/V68oko1qGE6BwA8XqnqFbW+5WuSpNwD+ijqzDnDRa7L6ePErFmz9Pbbb6tfv37atm2bypYtq/DwcJ0/f/6Wz1+3bp1efPFFtW/fXtu3b1fjxo3VuHFj7d69O/k5n3zyiUaOHKmvv/5aGzduVMaMGRUeHq4bN244++UAuA9/v7Ujw/wfDJcAQPoVfeacHv5ptiQpvnsPwzUAkH6EjR6qo7kKKOu1KzrQppPpHJdlsyznvvElLCxMjz32mL766itJksPhUGhoqLp27apevf59OmHz5s117do1LVq0KPmxypUrq1y5cvr6669lWZby5Mmj7t27q0ePpD9YIyMjlStXLk2ZMkUtWrT41/eMjY1VbGxs8q+joqIUGhqqyMhIBQYGpvZLBvAPpzbuVL7K5ZRgsyv6yAllKZDXdBIApDubXumuShNH6FCewip04qDsXry7FwDSyp7Zi/Vw8waSpN+/na9HWjUyXJR2oqKiFBQUdNe/fzv1T6W4uDht3bpVtWvX/v9/od2u2rVra/369bf8mvXr19/0fEkKDw9Pfv7Ro0cVERFx03OCgoIUFhZ22+85ZMgQBQUFJX+EhnLLLCAt5Qsrq0P5isrbcujQ2G9M5wBAuhN79ZqKzJwkSbrQ6Q2GCQBIYw83q6/N4S9IkoK6ddW1qGuGi1yPU/9kunDhghITE5UrV66bHs+VK5ciIiJu+TURERF3fP7f/0zJ9+zdu7ciIyOTP06ePHlfrwfA/fuzbtI6HLCAu3YAQFrbNfhLZb12RWeDc6p8j46mcwAgXSo1dbQuZM6q/H+e1KaO75jOcTnpYjb38/NTYGDgTR8A0la+jkl37Si5f5uuHD1luAYA0g9HfIJCxo+SJB1t01F+Af6GiwAgfcqYK7suDPpYklRtznj9vvzWZ/6nV04dJ7Jnzy4vLy+dO3fzFUnPnTunkJCQW35NSEjIHZ//9z9T8j0BmBf6WBkdDC0uL8uhQ9y1AwDSzK7R05TvwilF+mdSmQ/eNp0DAOlaiTfaa/+jT8jXkSDr1Vd1/Ua86SSX4dRxwtfXVxUqVNCKFSuSH3M4HFqxYoWqVKlyy6+pUqXKTc+XpOXLlyc/v2DBggoJCbnpOVFRUdq4ceNtvycA13Ch3l937VjAXTsAIE1YlgI+/1SStLtRK2XOnsVwEACkczab8s6YqOs+/ip7dJd+6f6R6SKX4fS3dbz99tsaP368pk6dqn379um1117TtWvX9PLLL0uS2rZtq969eyc//80339SSJUv06aefav/+/erfv7+2bNmiLl26SJJsNpveeustffjhh/rxxx+1a9cutW3bVnny5FHjxo2d/XIAPIDQju0kScUPbFfkkROGawDA8+2fs1jFju1VrJePin3Y++5fAABwuszFi+pU96Tfk6tPGKYta3cZLnINTh8nmjdvruHDh+uDDz5QuXLltGPHDi1ZsiT5gpYnTpzQ2bNnk59ftWpVzZgxQ+PGjVPZsmU1d+5czZ8/X6VLl05+Ts+ePdW1a1d17NhRjz32mK5evaolS5bI35/3UAKuLLTCw9r/UMm/3trBXTsAwNliBw+VJG2v2Ug5iuQ3XAMA+FvRD/voZNHSCoyL0Y0OryrqepzpJONslmVZpiPS2r3eZxVA6lvTqZceH/ux9hV/VCX3bzWdAwAe6/h/Nyv/k5XkkE2nNmzTQ2HlTCcBAP5HzLYd8qn0mHwSE/TNWx+rzWc9TSc5xb3+/Ttd3K0DgOt46K+7dhQ/sF2Rh48brgEAz3W+X9L7mHdUfIphAgBcUIZHy+l81+6SpHrjBmvVmj2Gi8xinACQph56tJT25S8luywd5q4dAOAU5/cdVtnffpIkZXifa00AgKvK+/FAnc9fVNljIhXT5U1duBprOskYxgkAae5CvUaSpIzctQMAnOJI38HydSRob9FyKtHoadM5AIDb8fVV8IypSrTZ1WDnCs3o97XS4ZUXJDFOADAg9NWkt3YUPbhTUYeOmY0BAA8Tde6CSi+cKUmK6/a24RoAwN34Vq2iy690kiQ1Gf+Rvl+113CRGYwTANJcgXIltKdA6aS3doyZYjoHADzKnn7DlSkuRsdyFdAjHVqazgEA3IPsn32iqNyhyhv9p+J69tKRP6+aTkpzjBMAjLjQoLEkKfP8uWZDAMCDxF6LUeEZEyRJf3bqKru3l+EiAMA9yZhRmaZOkiS13LpI4z6aqvhEh+GotMU4AcCIgq+9rESbXUWO7NHlXftM5wCAR9j58WjljL6oPwOzqWzP103nAABSwP50bcW0aSdJ6vDNEH25eJfhorTFOAHAiIceLqRdRctLko6PmWy4BgDcnyMhUTnHfSVJOtLqFflm8DdcBABIqQwjP9eNHLlU+NJp+Q35SBuPXDSdlGYYJwAYE9nweUlSlh+5awcAPKgdY2eowLnjivbLoIf7v2M6BwBwP4KD5T/ua0nSqxu+15jP5igyJt5wVNpgnABgTJHX2ynO7q38pw/r4sZtpnMAwG1ZliW/zz6VJO199kVlypnNcBEA4L41bqyEJk3lbTn0zuxhem/2tnRxe1HGCQDG5C2YVzsfDpMknRo9yXANALivvfOW6eHDOxVn91bhj94znQMAeEDeo75SQlCwHj5/RPknj9a3G46bTnI6xgkARl17/gVJUs7F86V0sAgDgDPcGPyxJOn3p55R9mKFDNcAAB5YrlzyHvmFJOnNtTM0Y8pS7TkTaTjKuRgnABhV6tXWivHxU+4Lp3Vu5RrTOQDgdo6u26byW3+VJOUa0MdsDAAg9bRpI6t+ffklJmjwws/05rdbdC02wXSV0zBOADAqZ+5s2lH2cUnSubHctQMAUiqi32DZZWln+ScU+nhF0zkAgNRis8k2dqyswECVP3tANX6eoffn7/bY608wTgAwLr5Zc0lS3mULpcREwzUA4D7O/XFMj676UZIU8F4vwzUAgFSXL59sI0ZIkrqv+VY7VmzS3K2nDEc5B+MEAOPKtG+hSP+MyhZ5QWcXLTedAwBu44++Q+SXGK+DBR9WsSb1TOcAAJzhP/+Rnn5a/glx+mTxF+o3f5dOXY4xXZXqGCcAGJc1a2btqFhTknRxwlTDNQDgHiL/vKwyC2ZIkmK79ZBsNsNFAACnsNmk8eNlZcqkx07v1eRrG5U3OMB0VapjnADgGlokvbUjdNXPUny84RgAcH2/9x+uoBtXdSpHPpV+rbXpHACAM+XPL9snn0iSwsYNl+2U5721g3ECgEso1/Z5XcgQrKBrkTo9e4HpHABwaTdibqjI9AmSpPMdu8jm7W24CADgdK++KjVqJH32mZQvn+maVMc4AcAlBGUO0M4qdSRJkZO/NVwDAK5t2/Cxyh15XpcyBqtM766mcwAAacFul+bNkzp29Mi38jFOAHAZPq1bSpIKrFkmK8bzLvIDAKkhMdGhXF+PlCQdadlePhkzGC4CAKQZDxwl/sY4AcBlVGhRX6eDcipD7HWd/Gau6RwAcEnbJ8xS4bNHFOPjr5ID3zWdAwBAqmCcAOAyMvr7aM8TSbfCi5nGWzsA4J8sy5LPZ59KkvY+01wZQ3IYLgIAIHUwTgBwKRnatpIkFdz0q6wrV8zGAICL2f3jSpU9sFUJNrsKfdTHdA4AAKmGcQKAS6nYqIYOZwuVX0K8jk/+znQOALiUmMFDJUm7nqyvrCWLGq4BACD1ME4AcCn+vt46WLOBJCn+2xmGawDAdRze9Lsqbl4pScrZn7MmAACehXECgMsJermNJKngjnVKPHfecA0AuIYzHwyWl+XQnjJVlPepyqZzAABIVYwTAFxOxacra2/uIvJ2OHRi3FTTOQBg3NnDJ1VxxXxJkv97vczGAADgBIwTAFyOr7ddR2o/m/SLmbPMxgCACzj4wccKSIjVkYeKq3DzZ03nAACQ6hgnALikHK+0lSTl37dNCcdPGK4BAHMiL0SqzPxvJEnX33pbstkMFwEAkPoYJwC4pArVHtG2/KVltyydGD3JdA4AGLN90GfKGhOls1lzq1SXl03nAADgFIwTAFySt5ddp+o+J0nymz3TcA0AmHHjeqyKfDNOknS+Q2fZfHwMFwEA4ByMEwBcVr5X2yre7qW8xw4oducu0zkAkOY2j5igfJfP6kqGQJXq86bpHAAAnIZxAoDLKle2sDYWryRJOvnVBMM1AJC2EhMdyjlmpCTpaPOX5JM5k+EiAACch3ECgMuy22260LCpJCl4/lzJsgwXAUDa2TzlBxU/fVDXffxUfBC3DwUAeDbGCQAurUSHlrrqG6DsF87o2qrVpnMAIE1YliWfT4dLkg7UbaIMeXMbLgIAwLkYJwC4tOKFcmn9I09Kks6Onmi4BgDSxs7Fq1Vh30Yl2uzK/2Ef0zkAADgd4wQAl2az2XT9heaSpFxLf5Ti4w0XAYDzXfvoY0nS3qpPK8sjpQzXAADgfIwTAFxe+Zea6M+Mwcp8NVJX5i00nQMATvXH5j2qtHGZJCl7f86aAACkD4wTAFxeaM5Abaz0tCTp0rjJhmsAwLlO9x8iH0eiDpSqqNy1nzCdAwBAmmCcAOAeWrWSJOVdvVyKjjYcAwDOcfroaVX85QdJkm8v7tABAEg/GCcAuIWwF8J1JGte+cXH6sI3M03nAIBT7O83TJnirutE3sIq2Pp50zkAAKQZxgkAbiFHoL+2P1FfknRt0jTDNQCQ+i5fjNIjPyT9/hbz5tuSzWa4CACAtMM4AcBtZHypjSQp37Z1ss6eNVwDAKlr20cjlePaZZ0Pzqnib75iOgcAgDTFOAHAbVSrW1k78hSXl+VQxPippnMAINXciI1X4WljJUnn2r8mm6+v4SIAANIW4wQAt5HZ30cHaz8rSbKmzzBcAwCpZ8Pnk1Xg4ilF+2dSyfe7mc4BACDNMU4AcCvZ/9NOCTa78hzcJceBg6ZzAOCBJSQ6lH30F5Kkoy+0lXdwkOEiAADSHuMEALdStWpJbSj8qCTpzOgJhmsA4MFt/HahSp/YqzgvHxX5sLfpHAAAjGCcAOBW/H28dLLec5KkgNkzJcsyXAQA98+yLHkNHy5JOlDnOWV4KJ/hIgAAzGCcAOB2CrRvqRgfP2WLOKn4dRtM5wDAfdu+dL0q714jh2wK/eh90zkAABjDOAHA7VQqk1+rS1aVJEWMmWi4BgDuX/RHQyVJB8JqKLh8GcM1AACYwzgBwO142W263OgFSVLQwnlSQoLhIgBIuQPb9qvy+p8lSVkHcNYEACB9Y5wA4JZKvdRUFwMCFRh1STd+Xmo6BwBS7ET/j+WXmKDDxcspV3gN0zkAABjFOAHALT1SMLtWl0/6Yf7PsZMM1wBAypw6FqHKy2ZLkrzf7Wm4BgAA8xgnALglm82mG81elCTl+OVn6do1w0UAcO/2DPxUmWNjdDokv/K3a246BwAA4xgnALitx1rU1/HgEPnHXtfV2d+bzgGAe3Lp8lWVnTtZkhTzRjfJzo9jAADwpyEAt1UkV2atCwuXJEWOn2y4BgDuzeYhoxQSfVEXA7OpSLdXTecAAOASGCcAuDV72zaSpJANq6WzZw3XAMCdXY9NUOGpYyRJ515+VTZ/f8NFAAC4BsYJAG7tqWeqaWveEvKyHLo8forpHAC4o7VffqMi54/rml8GFevb3XQOAAAug3ECgFvLFeiv32s0lCQlTJ1quAYAbi8h0aFso7+QJB1r0kre2bIaLgIAwHUwTgBwe9n/01qxXt7KceSArB07TOcAwC2t+26xyh/dqXgvbxUa1Md0DgAALoVxAoDbq1m1pH4tGiZJOj9qvOEaAPg3y7JkHz5ckvRHzWcVUCi/4SIAAFwL4wQAt5fRz1snn2kqScowd5aUkGC4CAButmXFJlXduVqSlPfDvoZrAABwPYwTADxC8XYv6GJAoDJfuaj4JUtN5wDATSI//Fh2WTpY8UkFVSpvOgcAAJfDOAHAI1QtlUe/lK0pSboweoLhGgD4f3t2/KEn1iySJAX3e89wDQAArolxAoBH8LLbdK35i5KkbL/8LEVGGi4CgCTHB3wiv8R4HS9cWjkb1DGdAwCAS2KcAOAxKr8QroPZHpJvfKxips80nQMAOno0QlWXJP1+5N3rXclmM1wEAIBrYpwA4DFK5Q3Sf6vUkyRdHT/JcA0ASLs//EzBN67qXM5Q5X35RdM5AAC4LMYJAB7Fr21rOWRTzh2bpCNHTOcASMfOXbqq8t9PkSTdeONNycvLbBAAAC6McQKAR6ldp6LWFSgrSYocP9lwDYD0bMPQr5Uv8rwiMwUr/9uvm84BAMClMU4A8CghQf7aVbORJMmaNk2yLMNFANKjyJg4Ffvma0nShf+8KgUEGC4CAMC1MU4A8Di5X3pR13z8FXzmhKx160znAEiHfh01QyUjDuuGr78K9n3HdA4AAC6PcQKAx3m6UmEtL1FNknRxzATDNQDSmxvxiQoZ+6Uk6dTzLWXPns1wEQAAro9xAoDHyejnrdMNmyb93/O/l27cMFwEID1ZOWOJwg5vU4Ldrvwf9jGdAwCAW2CcAOCRSrd+Tqcz51DAtWjFz19gOgdAOpGQ6JD/iOGSpOO1npFP4UKGiwAAcA+MEwA8UrWiObSsfC1J0pWvJxquAZBe/PbzBlXftVqSlGdIP8M1AAC4D8YJAB7J28uuGy1aSpKy/neldP684SIAns6yLN0Y8om8LIeOPfakAio8ajoJAAC3wTgBwGM92ehJ7chdVF6ORF2f9q3pHAAebsP6vaq9cbEkKdvAvoZrAABwL4wTADxWqdyBWlu5viTp+oTJhmsAeLqID4fJLzFep4o9oszhtUznAADgVhgnAHgsm82mjO1aKd7upawHdku7d5tOAuChft97QrVWzpUkZfjgPclmM1wEAIB7YZwA4NHCnyqtVYUfkyRFjZ1guAaAp/pj0AgFxl7TuTwFlfXFF0znAADgdhgnAHi03EEB2l27sSTJa/p0KT7ebBAAj3P41EVVW/RN0i969JDs/HgFAEBK8acnAI9XoF0z/ZkhWBkvX5C1eLHpHAAeZtvgrxRy9ZIuB+dQrtfbm84BAMAtMU4A8Hh1y4dq0SM1JUlXRo01XAPAk0RcjtGjs5LeMna1c1fJz89wEQAA7olxAoDHy+DrrUvNWkqSAlcskyIiDBcB8BRrhk9Q4UundDUgs0Lffct0DgAAbotxAkC68ORzNbQ9d3F5ORIVO2Wa6RwAHiDyWpyKTh0tSbrQ9j9S5syGiwAAcF9OGycuXbqkVq1aKTAwUMHBwWrfvr2uXr16x+d37dpVxYsXV0BAgB566CG98cYbioyMvOl5NpvtXx8zZ8501ssA4CEq5s+ilVUbSJJix42XLMtwEQB3t2LcHJU9fUBx3r7K37+X6RwAANya08aJVq1aac+ePVq+fLkWLVqk1atXq2PHjrd9/pkzZ3TmzBkNHz5cu3fv1pQpU7RkyRK1b//vC0tNnjxZZ8+eTf5o3Lixs14GAA9hs9kU2K61rnv7KfDoIWnjRtNJANzYjfhE5Rr9uSTpdOPmsoWEmA0CAMDN2Swr9f/z4b59+1SqVClt3rxZFStWlCQtWbJE9evX16lTp5QnT557+j5z5sxR69atde3aNXl7eycF22yaN29eigaJ2NhYxcbGJv86KipKoaGhioyMVGBg4L2/MABu7Wzkda2v1kDP71ml6DYvKfO0yaaTALipRdMW65l2DZRos8vav1/exYqaTgIAwCVFRUUpKCjorn//dsqZE+vXr1dwcHDyMCFJtWvXlt1u18YU/NfKv+P/Hib+1rlzZ2XPnl2VKlXSpEmTdLd9ZciQIQoKCkr+CA0NTdkLAuARcgcFaF+9ppIk3+/nSNeuGS4C4I4SEh3y/WyEJOlEzfoMEwAApAKnjBMRERHKmTPnTY95e3sra9asirjHq+RfuHBBgwYN+tdbQQYOHKjZs2dr+fLlatKkiV5//XV9+eWXd/xevXv3VmRkZPLHyZMnU/aCAHiMMi0b6nhwiPxirskxZ67pHABuaOXSTaq5c5UkKffgfoZrAADwDCkaJ3r16nXLC1L+78f+/fsfOCoqKkoNGjRQqVKl1L9//5s+17dvX1WrVk3ly5fXu+++q549e2rYsGF3/H5+fn4KDAy86QNA+lSndG79WL6OJCl6zDjDNQDcjWVZujF0mLwth05UqCb/ShXv/kUAAOCuvO/+lP/XvXt3vfTSS3d8TqFChRQSEqLz58/f9HhCQoIuXbqkkLtcMCo6Olp169ZV5syZNW/ePPn4+Nzx+WFhYRo0aJBiY2Pl5+d3T68DQPrl7+OlGy1by7HqGwVtWicdOiQVKWI6C4CbWLt+n55e/5MkKevAvoZrAADwHCkaJ3LkyKEcOXLc9XlVqlTRlStXtHXrVlWoUEGStHLlSjkcDoWFhd3266KiohQeHi4/Pz/9+OOP8vf3v+u/a8eOHcqSJQvDBIB7Vif8Mf23YHlVP7pNN8ZPlP/HQ0wnAXADlmXp7IfDFJAQqzNFSytPvTqmkwAA8BhOueZEyZIlVbduXXXo0EGbNm3S2rVr1aVLF7Vo0SL5Th2nT59WiRIltGnTJklJw0SdOnV07do1TZw4UVFRUYqIiFBERIQSExMlSQsXLtSECRO0e/duHTp0SGPGjNHgwYPVtWtXZ7wMAB7qkXxB+u8Tz0qSHJOnSH/9HgMAd7J59wk9vSrpWjUZ3+8t2WyGiwAA8BwpOnMiJaZPn64uXbqoVq1astvtatKkiUaOHJn8+fj4eB04cEAxMTGSpG3btiXfyaPIP06xPnr0qAoUKCAfHx+NGjVK3bp1k2VZKlKkiEaMGKEOHTo462UA8EA2m0252zTX5dkjlOXPCGn5cqluXdNZAFzcwY8+V6UbV3Uhd35lb9XcdA4AAB7FZt3tPpwe6F7vswrAc/0ZHavFNV5Qu60LFd3wOWVe8IPpJAAubNeR88pW7mHlib6gS599paxvdTadBACAW7jXv3875W0dAODqcmT207GGSf/lM2DxIuniRcNFAFzZlqGjlSf6gqKCsytrp/amcwAA8DiMEwDSrbDna2l3rsLyTohX4rfTTecAcFF/nI1UtR8mS5LiunSV7uGC3QAAIGUYJwCkWzVL5NRPFZOuNREzdrzhGgCu6rfPpqjYxRO6HpBR2Xu8aToHAACPxDgBIN3y9bbL1rKlYr28lXnfbmn7dtNJAFzMiYsxKvfdOElS9MsdpKAgw0UAAHgmxgkA6dqzNUprWdEqkqQbnD0B4B+WjJ2jiqf2Kt7bRznf72k6BwAAj8U4ASBdK5k7UJtqNJIk2WbMkG7cMFwEwFWci7qhopNHSZIuN2kh5c5tuAgAAM/FOAEg3Sv6YmOdzpxDftGR0oIFpnMAuIiFU39SjUOblWizK8fA903nAADg0RgnAKR7zz4aqnmP1JYkXf1qjOEaAK7g8rU45f16pCTpQr2GshUrZrgIAADPxjgBIN3LktFXEU1flEM2ZVrzm3TokOkkAIbNm71K4Xv/K0nKObi/2RgAANIBxgkAkFSrXphWF3xUkpTw9VjDNQBMuhqboOCRI2SXpXPVn5atbFnTSQAAeDzGCQCQ9GTRHFpSraEkKXHSZCkuznARAFMWLFivZ39fIUnKPniA4RoAANIHxgkAkORltymkVVNFZMoqv8sXpXnzTCcBMOBGfKK8PhshH0eizlWsKq+qVUwnAQCQLjBOAMBfXqhcULMfqSNJuv7VaMM1AExYuGy7Gm9ZLEnK9lF/szEAAKQjjBMA8Je8wQE61qiFHLIpYM1q6eBB00kA0lB8okPXh4+Qf0Kc/ixVVt5P1zadBABAusE4AQD/o079Svq1UAVJUuLYcYZrAKSlRav3qvG6BZKkoEH9JZvNbBAAAOkI4wQA/I9aJXNpUeVnJUmJkydLsbGGiwCkhYREhy58/JkC42J0qWAx+TZuaDoJAIB0hXECAP6Hj5ddOV98TmczZZPv5UtcGBNIJxZvPKTnV8+VJGXo975k50ckAADSEn/yAsA/NK9cSLPKJl0YM3bUGMM1AJwt0WHp5Mcjle16lCLzPCT/Vi+aTgIAIN1hnACAfyiYPaMONmimRJtdfmtWSwcOmE4C4ERLth7T8ytnSpL8+vSWvL0NFwEAkP4wTgDALdSp+5hW/XVhTGvsWMM1AJzF4bB0YPho5b56UdHZc8m//cumkwAASJcYJwDgFuqWDtH8Ss9IkhImT5Vu3DBcBMAZlv9+Ss8vmy5J8u75juTnZ7gIAID0iXECAG7B38dLOV5orDOZs8vnyiXphx9MJwFIZZZlafuICSpw5ayuBwYr4PVOppMAAEi3GCcA4DZaVi2oWY8kXRgzbjQXxgQ8zS97ItT456lJv3jzLSljRqM9AACkZ4wTAHAbRXNl1oG/Lozpu3aNtG+f6SQAqcSyLG34cppKXDiu2ICMCnj7TdNJAACka4wTAHAHdetW1MrCj0mSHOPGGa4BkFp+PXBezy6cJElydHpNCg42GwQAQDrHOAEAd1C3dIh+DEu6MGYiF8YEPIJlWVr91XSVO3tQ8X7+Cuj1jukkAADSPcYJALgDfx8vhbzQSKcCc8gn8rI0d67pJAAPaO0fF/TMvPGSpPgOHaWcOQ0XAQAAxgkAuIsW/3NhzNhRXBgTcHcrx8xUhTP7Fe/rpwzv9TKdAwAAxDgBAHdVOEcmHX62uRJsdvltWCft3Ws6CcB92nDkosK/T7p+TNzL7aXcuQ0XAQAAiXECAO5JvfAKWlGkkiTJ8fXXhmsA3K/lY2Yp7ORuJXj7KGPf90znAACAvzBOAMA9CH84RAsrN5QkJU6ZKl27ZrgIQEptOXZJNeeMlSTdaPeylDev4SIAAPA3xgkAuAe+3nblbd5QR7Pklk90lDR9uukkACn089jvVe3470rw9lamD/qYzgEAAP+DcQIA7lGrygU1vXx9SVLcyC8lyzJcBOBebT9xWU/OSnpL1o0X20gPPWS4CAAA/C/GCQC4Rw9ly6Azz7XQdW8/+e7ZLa1dazoJwD1aMG6eqh/dpkS7lzIN6Gs6BwAA/APjBACkQJNaZbSgVHVJUuKXXxmuAXAvth6/pCdmJp01cb1FS6lgQcNFAADgnxgnACAFniqeU0urPy9Jsv3wgxQRYbgIwN3Mm7BQtQ5vlsNuV6YBH5jOAQAAt8A4AQAp4GW3qdLztbU1TwnZE+Kl8eNNJwG4g41HLiZfa+J60+ZSkSKGiwAAwK0wTgBACjWrmE8zKj4rSYob/bWUkGC4CMDt/DB5ker8sUEOm00ZB/YznQMAAG6DcQIAUihbJj/ZXmiqCxmC5BtxRlqwwHQSgFtYd/iCqs8eJ0m68VxTqXhxw0UAAOB2GCcA4D60fLKoZpYNlyTFj+TCmICrsSxLc6csUf2D6yRJGThrAgAAl8Y4AQD3oXxosLbUeUGJNrt8Vv8q7dljOgnA/1h76KJqzP3rrIlGz0kPP2y4CAAA3AnjBADcB5vNprr1K2lZ0cqSJGvkSMNFAP5mWZZmfbNUDfavkST5D+CsCQAAXB3jBADcp4bl8mh2lcaSJMe0b6TLl80GAZAk/XbwT9X8foLsshT7zLNS2bKmkwAAwF0wTgDAfcrg661CTeprX44C8rpxXZo40XQSkO5ZlqW505aq0d7fJEl+A/qbDQIAAPeEcQIAHkDbqgU0uWJDSVL8yC+5rShg2KoD51X3h/FJZ00820h69FHTSQAA4B4wTgDAA8ifLaOiGjfVpYBA+Zw8IS1caDoJSLcsy9IPU37WM/v/K0ny+3Cg4SIAAHCvGCcA4AG1qlFCM8rVlSQlfPa52RggHVu+95yemZd0h47Y55tKjzxiuAgAANwrxgkAeECPF8mu/9ZqqgSbXd7/XS3t3Gk6CUh3HA5LP05epLoH18uy2ThrAgAAN8M4AQAPyGaz6Zn6j+nn4tUkcVtRwISleyL03Pyksybim7WQSpY0XAQAAFKCcQIAUsHzj+bTrCrPSZIc02dIFy4YLgLSD4fD0s8TF6jW4c1y2L3kO2iA6SQAAJBCjBMAkAoy+nmrWOM6+j2kiLxib0jjxplOAtKNRbvOqumCpP/NJbRqLRUtargIAACkFOMEAKSStlULaMpftxVN+PIrKS7OcBHg+eITHVo2dq6ePLZdiV7e8h3Qz3QSAAC4D4wTAJBKCmTPqOhGTXQuU1Z5R5yV5swxnQR4vNlbTqrlTxMlSY6XXpIKFjQbBAAA7gvjBACkojZPFtXUR5+RJCUOHy5ZluEiwHPdiE/U2vFzVPXE70r08ZVPvw9MJwEAgPvEOAEAqeiJotm18ekmuu7tJ68dO6TffjOdBHisqWuP6uUlk5N+0aGDFBpqNggAANw3xgkASEU2m03NwstpbplakiTHp58aLgI8U+T1eG2fOEePnd6rRD8/efV5z3QSAAB4AIwTAJDKGpXLqx+eaCpJsi9aJB08aLgI8DzjfzusTiumSJJsr70m5cljNggAADwQxgkASGX+Pl568plqWl6kUtIDn39utAfwNH9Gx+rwlFkqd/agEgICZO/Vy3QSAAB4QIwTAOAErSvn19Sw5yVJjslTpIsXzQYBHmTUyj/U+ddvJEleXbpIuXIZLgIAAA+KcQIAnCBHZj/lbhiu3bkKy37jujR2rOkkwCOcvBSj89/MVOlzh5WYMaNsPXuaTgIAAKmAcQIAnKT9k4U04bHGkqTEkSOl2FizQYAH+HzZPr3x27eSJK9u3aTs2Q0XAQCA1MA4AQBOUiIkUJcbNFZEpqzyOndOmjHDdBLg1g6ei5a+na4SF44rITBIevtt00kAACCVME4AgBO9VKOYJldsKElKHDZMcjgMFwHu6/NFu9Ttv9MlSd593pOyZDFcBAAAUgvjBAA4UfWiObShdlNF+wbIa98+afFi00mAW9p+4rJCZkxRvqjzSsidR+ra1XQSAABIRYwTAOBEdrtNLeuU0fRy9SRJjo8/MVwEuB/LsvTlvG3qvH6WJMl74AApIMBwFQAASE2MEwDgZI3L59WCp15QnN1b9jX/ldavN50EuJU1hy6o7OwJynY9SvHFiksvvWQ6CQAApDLGCQBwMj9vLz1br6LmPVxDkmQNG2a4CHAflmVp/Jz1emXzfEmSz5DBkre32SgAAJDqGCcAIA20Csuvb6s1TfrF/PnSgQNGewB3sXhXhGp+P14Z428ovuJj0nPPmU4CAABOwDgBAGkgKMBHlZ95XMuLhMlmWdKnn5pOAlxebEKipk1fqZY7lkiSfD75WLLZDFcBAABnYJwAgDTycrWCGl8l6ewJx9SpUkSE4SLAtX2z/rheXDRevo4EJT5dR6pRw3QSAABwEsYJAEgjeYIDlO+Z2tqSt6TscXHSF1+YTgJc1pWYOC2bvlSN9/4mSfL6eKjhIgAA4EyMEwCQhjo+WUhjw5pIkhyjRkuRkYaLANf01cpDen3ZREmSo8WLUvnyhosAAIAzMU4AQBoqERKohPoNdCD7Q7JHR0mjRplOAlzOiYsx2jfzRz11dKsc3t6yfzjIdBIAAHAyxgkASGMdnyqq0ZVfkCQ5RnwmXbtmuAhwLR8v2aceK6dIkuwdO0qFC5sNAgAATsc4AQBprHKhrDpd51kdDw6R/eIFafx400mAy9h6/LISvv9B5c8ekCMgg9S3r+kkAACQBhgnACCN2Ww2vVa7hMaE/XXnjmHDpdhYw1WAeZZlaejCXXrnt2mSJHv3t6WQEMNVAAAgLTBOAIABNUvk1J7ajXQ2UzbZz5yWpk0znQQYt2R3hAr+9L2KXDolR9Zs0jvvmE4CAABphHECAAyw2Wzq+HQpja/0vCTJMWSolJBguAowJy7Boc9+3KFua6ZLkuzv95ECAw1XAQCAtMI4AQCG1C+TW+trPaeLAYGyHz0izZplOgkw5tsNx1Vn6QzlvnpRjofyS6+9ZjoJAACkIcYJADDEy27Ty0+X1sTHGkuSHIOHSA6H2SjAgMiYeE1fsFGvbZgrSbJ/PFTy9zdcBQAA0hLjBAAY1Lh8Xv1S/XlF+WaQfe8eacEC00lAmhv16yG1Xz5FGeNvyKoUJjVvbjoJAACkMcYJADDI19uuluGPaGqFZyVJ1sCBkmUZrgLSzslLMVo771c1/325JMk24lPJZjNcBQAA0hrjBAAY1vyxhzSv+guK9g2QbccOzp5AuvLJ0gN6Z8VEeVkOWU2aSNWqmU4CAAAGME4AgGEBvl56IbycplRoKEmyBgzg7AmkC9tPXNaV+Yv01NGtcvj4yDZ0qOkkAABgCOMEALiAtlXy6/snm+oqZ08gnXA4LA1asEvvrZokSbJ37iwVKWK4CgAAmOK0ceLSpUtq1aqVAgMDFRwcrPbt2+vq1at3/JqnnnpKNpvtpo9OnTrd9JwTJ06oQYMGypAhg3LmzKl33nlHCQkJznoZAJAmMvp5q3nd8pry97UnOHsCHm7e9tMquniuSv55TI6gYKlvX9NJAADAIKeNE61atdKePXu0fPlyLVq0SKtXr1bHjh3v+nUdOnTQ2bNnkz8++eST5M8lJiaqQYMGiouL07p16zR16lRNmTJFH3zwgbNeBgCkmbZV8mvuky/8/9kTP/5oOglwiquxCfpq/lb1WP2NJMne7wMpa1bDVQAAwCSnjBP79u3TkiVLNGHCBIWFhenxxx/Xl19+qZkzZ+rMmTN3/NoMGTIoJCQk+SMwMDD5c8uWLdPevXv17bffqly5cqpXr54GDRqkUaNGKS4uzhkvBQDSTEY/bzWrW+7/z57o35+zJ+CRRq86pObLpilHzBU5ihWTOnc2nQQAAAxzyjixfv16BQcHq2LFismP1a5dW3a7XRs3brzj106fPl3Zs2dX6dKl1bt3b8XExNz0fcuUKaNcuXIlPxYeHq6oqCjt2bPntt8zNjZWUVFRN30AgCtqW6UAZ0/Aox2/eE3LFqzVf7YkHdv2ESMkX1/DVQAAwDSnjBMRERHKmTPnTY95e3sra9asioiIuO3XtWzZUt9++61WrVql3r1765tvvlHr1q1v+r7/O0xISv71nb7vkCFDFBQUlPwRGhp6Py8LAJwuk5+3Xggvp6mPPiPpr7MnHA6zUUAq+uinfeq5YoJ8HQmy6tSR6tc3nQQAAFxAisaJXr16/euClf/82L9//33HdOzYUeHh4SpTpoxatWqladOmad68eTp8+PB9f09J6t27tyIjI5M/Tp48+UDfDwCcqV3VAppdvZmi/z574vvvTScBqWLNHxd0dfFS1fljgywvL9k++0yy2UxnAQAAF+Cdkid3795dL7300h2fU6hQIYWEhOj8+fM3PZ6QkKBLly4pJCTknv99YWFhkqRDhw6pcOHCCgkJ0aZNm256zrlz5yTpjt/Xz89Pfn5+9/zvBQCTMvl5q1l4OU1c01hvrf1O1gcfyPbcc5J3in7LBlxKfKJDg+bv1BcrxkuSbK+9JpUqZbgKAAC4ihT9pJsjRw7lyJHjrs+rUqWKrly5oq1bt6pChQqSpJUrV8rhcCQPDvdix44dkqTcuXMnf9+PPvpI58+fT37byPLlyxUYGKhS/IADwIO0q1pA9ao3U7uti5Rl/37p22+lu4zDgCubuu6YHvvlB5W4cFyOLFlk79/fdBIAAHAhTrnmRMmSJVW3bl116NBBmzZt0tq1a9WlSxe1aNFCefLkkSSdPn1aJUqUSD4T4vDhwxo0aJC2bt2qY8eO6ccff1Tbtm315JNP6pFHHpEk1alTR6VKlVKbNm20c+dOLV26VO+//746d+7MmREAPEomP2+1DX9EYyo3lfTXtSdiY81GAffpXNQNTfpxq97+77eSJPuAAVK2bIarAACAK3HKOCEl3XWjRIkSqlWrlurXr6/HH39c48aNS/58fHy8Dhw4kHw3Dl9fX/3yyy+qU6eOSpQooe7du6tJkyZauHBh8td4eXlp0aJF8vLyUpUqVdS6dWu1bdtWAwcOdNbLAABj2lTJryXVn9f5jFlkO35cmjDBdBJwXwYv3qdOK6Yq6/UoWQ8/LHXqZDoJAAC4GJtlWZbpiLQWFRWloKAgRUZGKjAw0HQOANzW9I3Hta/vx/pw+RhZISGyHT4sZchgOgu4ZxuOXNSgQdP149Ru8rIc0sqVUo0aprMAAEAaude/fzvtzAkAwINrVjFU655qrJNBuWSLiJC++sp0EnDP4hMd+mD+Lg1Y/nXSMNG8OcMEAAC4JcYJAHBhPl52da1XSp9XaylJcnz8sRQZabgKuDdT1x3TwysXquLpfbIyZpSGDzedBAAAXBTjBAC4uIZl82p3jWd0KGs+2S9dkoYNM50E3NX5qBuasGiH3vt1kiTJ1revlC+f4SoAAOCqGCcAwMV52W3qVreUhlVvK0myRoyQzpwxXAXc2aCf9umVldOU49oVWcWKSW+9ZToJAAC4MMYJAHAD4Q/n0tkadbUlb0nZrl+X+vUznQTc1uqDf2r/L+v10takO27ZRo6UuOU3AAC4A8YJAHADNptNveqV1OCn/iNJsiZNkvbsMVwF/NuN+ES9P2+XPlw2Wt6WQ2rUSAoPN50FAABcHOMEALiJqkWyK7DWk/q5WFXZHA6pVy/TScC/jFp1SJVWL1TYqT2yMmSQvvjCdBIAAHADjBMA4EZ61yup4U+1U4LNLi1aJP32m+kkINmh89Ga+fN2vbfqr4tg9u8v5c9vNgoAALgFxgkAcCPFQzKrwtNhmlGuniTJeucdybIMVwGSZVnqM2+33l45WVmvR8kqXZqLYAIAgHvGOAEAbubtp4trbPWWuuobINvmzdKcOaaTAM3dekoJ/12jF39fJkmyjRkj+fgYrgIAAO6CcQIA3ExIkL+eq1tBYys9L0myevWSYmMNVyE9u3g1Vp8s3KWPlo5KeqB9e+nxx81GAQAAt8I4AQBu6NXqhfTDU80UkSmrbEePSp9/bjoJ6diAhXv13Oq5KnHhuKxs2aSPPzadBAAA3AzjBAC4ocz+Pnq1/iP6uPpLkiTrww+liAizUUiXVu4/p22/bdNba2dIkmzDhknZshmuAgAA7oZxAgDc1IuVHtKu6g20I3cx2a5elfr0MZ2EdCb6Rrz6/LBLg5eOUob4WOnJJ6V27UxnAQAAN8Q4AQBuysfLrvcbltaAWh0lSdbkydLWrYarkJ58vGS/Kq/7WU8e2y7Lz08aP16y86MFAABIOX6CAAA39lTxnMpS60nNK/WUbJYlvfkmtxZFmth09JJ+XvG7PlgxXpJk69dPKlbMcBUAAHBXjBMA4Obeb1BSn9Z4WTE+ftLatdLs2aaT4OFuxCeq1/dJw0SWG9FS2bJSjx6mswAAgBtjnAAAN1coRybVq1dRX4c1lSRZPXtKMTGGq+DJPv/lD+Xf+Ksa7ftNlt0uTZgg+fiYzgIAAG6McQIAPEDXWkX1fY3mOhWYQ7YTJ6RPPjGdBA+17cRlTV++Sx8uHS1JsnXrJlWsaLgKAAC4O8YJAPAAgf4+euPZshpco70kyRo6VDp0yHAVPM2N+ET1mLNT7/w6VXmj/5QKFpQGDDCdBQAAPADjBAB4iKYVQnWiZj2tLlBetthYqUsXLo6JVPXpsgPKtWWd2m7/KemBceOkjBnNRgEAAI/AOAEAHsLLbtOARmXU7+lOivXylpYulX74wXQWPMSWY5f03Yo9Grb4i6QHOnWSatc2GwUAADwG4wQAeJAK+bMoLLzy/18c8623pKtXzUbB7V2PS3o7R69Vk5Uv6rxUoADXNQEAAKmKcQIAPMy7dUvou5otdSIol2ynTkkDB5pOgpv7eMl+5duyVq13/Jz0wKRJUubMZqMAAIBHYZwAAA+TJaOv3m5YTv1rvypJsj77TNqzx3AV3NXaQxc0d9VeffzzyKQHOneWatQwGwUAADwO4wQAeKCmFfIpsla4lhWtLFtCgvT661wcEyl2JSZO3Wfv1HurJv7/3TmGDjWdBQAAPBDjBAB4ILvdpg8bl9agp19VjI+ftHq1NGGC6Sy4Ecuy9N68XSq1bbVa7lya9ODkyVKmTGbDAACAR2KcAAAPVTJ3oOrWr6RPH28tSbLeeUc6c8ZwFdzF99tOa9OGfRr2819353jrLal6daNNAADAczFOAIAHe7N2MS2t1Uw7cheVLTJS6tLFdBLcwImLMeo3f5eG/jxS2WIipTJlpCFDTGcBAAAPxjgBAB4sk5+3BjUtp15131C83UuaN0/6/nvTWXBhCYkOdZu9Q402/6TahzfL8vWVpk+X/P1NpwEAAA/GOAEAHq5G8ZwqFf64xoQ1lSRZXbpIly8broKrGrXqsC5v26W+K5KuUWIbOjTpzAkAAAAnYpwAgHSg7zOl9F2dNjqUNZ9sERFSjx6mk+CCNhy5qFHL9uqzRZ8qICFWqlVLevNN01kAACAdYJwAgHQgS0Zfvf/8o3q33htyyCZNmiT98ovpLLiQi1dj9ebM7XpjzQyVjfhDypJFmjJFsvOjAgAAcD5+4gCAdKJ+mRBlD6+haY82kCRZ//mPFBlpuAquwOGw1H3OThXduUGvb5iT9ODYsVK+fGbDAABAusE4AQDphM1m06BGpTUmvL2OBeeW7eRJTtmHJGnCmiPas/WgPv/pU9ktS+rUSXrhBdNZAAAgHWGcAIB0JGegv3o2qajuDbop0WaXpk5NuoMH0q1tJy5r+OK9+nzRMGW/dkV65BFpxAjTWQAAIJ1hnACAdOb5R/MqR3hNjQ17XpJkvfqqdP684SqYcCUmTl1nbFfHdbNV7fjvsjJkkGbNkgICTKcBAIB0hnECANIZm82mwc+X0TfhL2tfjgKy/fmn1LGjZFmm05CGEh2W3pi5Q3l3bVa3NTMkSbYxY6QSJQyXAQCA9IhxAgDSoawZfTW4RUV1e6a74uze0oIF0rRpprOQhr745aD2bP9DXy4cJi/LIbVrJ7VtazoLAACkU4wTAJBO1SiRUxUbVteIJ1pLkqyuXaUjRwxXIS38svecRv1yQF/9+LFyRV9MOlviq69MZwEAgHSMcQIA0rH36pfU8vqttSlfKdmio2U1by7FxZnOghMdu3BN3Wbv0Lu/TlGVE7ukTJmkH35I+icAAIAhjBMAkI5l8PXWpy9W0NuNeuqKfybZtmyR3nvPdBacJCYuQZ2+3aont69Sx81/3aVlyhSpZEmjXQAAAIwTAJDOlQsN1otNqqlH/W5JD3z6qfTTT2ajkOosy9K73+9S4q7dGrbki6QHe/aUmjQxGwYAACDGCQCApNeqF1Zcg2c0ucKzkiSrXTvp9GnDVUhNX648pF83/aFx8z5ShrgbUs2a0kcfmc4CAACQxDgBAJBkt9v0WbOymtiwk3bnKizbxYuyWrWSEhNNpyEV/PT7WX2+dJ8+WzhcBS+fkUJDpZkzJW9v02kAAACSGCcAAH/JlslPI9pU1huNeuqqb4Bsv/0m9e9vOgsPaNepSHWfs0O9fp2i2oc3S/7+0vffSzlymE4DAABIxjgBAEhWqWBWNWlRU33qvJ70wIcfSgsWmI3CfTsXdUMdpm1Rwy1Lbr4A5mOPGe0CAAD4J8YJAMBNXqteWJefa/b/159o00bav99wFVLqelyiOk7bovy7N+uj5aOTHuzXT2re3GwYAADALTBOAABuYrfb9HnzcpryfBdtzPewbNHRsp57ToqKMp2Ge5SQ6FDX77br8q79+nrBEPkkJkjNmkkffGA6DQAA4JYYJwAA/5I1o6/GvFRZ3Zv20dlM2WTbv19q105yOEyn4S4sy1LfBXu0afthTfphoLLERCW9jWPKFMnOH/sAAMA18VMKAOCWSuUJVO+Xn1Kn595TrJe3NH++NHiw6SzcxVcrD+mHtX9owveDVOTCSSlv3qT/3wUEmE4DAAC4LcYJAMBtNXgkt55o1UB9n066QKb1wQdJd3qAS5q95aQ+W7pPXywarkqn9khBQdLPP0t58phOAwAAuCPGCQDAHb39dDFdatFaUx9tIJtlyWrdWtq40XQW/mHV/vPq/f3vGrj8a9U9uF7y9U2600qZMqbTAAAA7opxAgBwR3a7TZ81L6fpLbppZaGKst24Icezz0pHj5pOw1/WH76oTt9u1WtrZ6r1jp9l2WzS9OlS9eqm0wAAAO4J4wQA4K4y+/toYvsq6t/qA+3OVVj2P/+UVb++dPmy6bR0b+vxy2o/dbOe27JYPf77rSTJNnKk1LSp4TIAAIB7xzgBALgnoVkzaPSrT6rLiwN0JnN22fbvl/X881JcnOm0dGv36Ui9NHmTwrct1+Blo5Ie7N1b6tLFbBgAAEAKMU4AAO5Z6bxBGvhaHXVo1l/RvgGy/fqr9NJLUmKi6bR050BEtNpM3Kjq21fq08Wfy25Z0uuvSx99ZDoNAAAgxRgnAAAp8mSxHHr5tUbq3KiX4u1e0nffSa+9JlmW6bR0449z0Wo1YaMq7fhNXyz6VHbLIb3yivTll5LNZjoPAAAgxRgnAAAp1rRCPlXq9KLeeqaHEm12afx4qUcPBoo0sOdMpJqP26AyO9foqx8/kZcjUWrTRho7VrLzxzoAAHBP/BQDALgvnWsUUb5X26lX3a5JD4wYIQ0caDbKw20/cVkvjtugcjvXaOz8IfJJTJCaN5cmTWKYAAAAbo2fZAAA98Vms6lXvRLK9FoH9a/VMenB/v2TRgqkuo1HLqr1hI2qvm2Fxs37SL4JcdLzz0vffCN5e5vOAwAAeCCMEwCA+2az2fTBM6WU0KWLhj3RJunB7t2lTz81G+ZhVh/8U+0mb9Kzm37SF4uGy9uRKLVuLc2cKfn4mM4DAAB4YIwTAIAHYrPZNLBhaV18o7u+rNI86cEePaQBA7gGRSqYs+Wk/jNls1qvnauhS79KuivHa69JU6cyTAAAAI/BOAEAeGB2u02Dn39EJ7r11idPtk16sH9/qWdPBor7ZFmWPv/loN6Zs1Nv/TpV76+alPSJd9+VRo3iGhMAAMCj8JMNACBV2O02fdzkEcW9864G1OqQ9ODw4bJee01yOMzGuZn4RIfemfu7xizZo5ELh6nL+tlJnxg8WBo6lNuFAgAAj8MVtAAAqcZut6lPg5Iak6mn3vXx15AlX8k+dqwcVyJlnzJZ8vc3nejyIq/Hq8uMbdqz87Cm//ChKp7el3TBy3HjpJdfNp0HAADgFJw5AQBIVTabTa8/VUTlBvRQt4Y9FG/3kn3WTCXWqCmdP286z6XtOxulhl+t0ZkN2zX/2+5Jw0RwsLRsGcMEAADwaIwTAACneLHSQ6r7YTe90mKQIv0yymvDeiU8Vknau9d0mktasOO0nhu9VoU2/aZ5376jhy5HSIUKSevXSzVqmM4DAABwKsYJAIDT1CuTW28N6aRXOo3UseDc8j5xXAlhlaXly02nuYz4RIcGLNyjt2dsVddfJmvy3AEKvHFVqlpV2rBBKlHCdCIAAIDTMU4AAJyq/ENZ9NXAlurba7w25Ssl76vRctSrJ2vw4HR/ocwTF2PUYtwGLVq6Xd/Oel+dN8xJ+kTXrtKqVVKOHGYDAQAA0gjjBADA6XIF+mv823U1d+gUzS1dS/bERNn69FFceN10eR0Ky7I0a/MJ1ftitXz++5sWT31DVU7skjJlkmbNkkaOlHx9TWcCAACkGZtlpb8b0EdFRSkoKEiRkZEKDAw0nQMA6YZlWZqy9qj+GDJSfZd9rYCEWMXmyCW/ObOk6tVN56WJC1dj1ev7XVrz+3H1/G2a/rP1x6RPPPyw9P33UvHiZgMBAABS0b3+/ZszJwAAacZms+nlxwup1fgB6vrWGP2RLVR+f56To2ZNJbzXR4qNNZ3oNJZlacGO06r7+WpdXr5KSya/8f/DRIcO0saNDBMAACDd4swJzpwAACOuxyVq+LytKvFhH72w+xdJUkzhYsowbXLSxSA9yB/notV3wW7t3H9G3dZM1ytb5stuWVLevNLEiVJ4uOlEAAAAp+DMCQCASwvw9VLf5pWUbc63erf5+/ozQ7AyHD4ox+OP61rHTlJUlOnEB3YtNkFDft6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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.linspace(range_min, range_max, 200)\n", "\n", "# Change the plot size\n", "default_figsize = mpl.rcParamsDefault['figure.figsize']\n", "mpl.rcParams['figure.figsize'] = [2 * value for value in default_figsize]\n", "\n", "plot_solution(m, N, X, res.x, lambda_random)\n", "\n", "plt.plot(X, u(X), 'r', label='Analytical solution')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "id": "f819bb4b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Loss function value')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AAAAAAKHqlIqMzk7mJYSKSdmJigq3qLa1S59VNhsdBwAAAAAQorwuMtxut+68805lZmYqJiZGe/bskSTdeuutevjhh30eEP4h3GrWtOHJkpiTAQAAAAAwjtdFxu9//3stW7ZMd999t8LDw/uujx8/Xg899JBPw8G/nNM3J4MiAwAAAABgDK+LjMcee0wPPPCAvvvd78pisfRdz8vL07Zt23waDv6ld05G8d56dXS5DE4DAAAAAAhFXhcZBw4c0MiRI4+67na71d3d7ZNQRrPb7crNzVVBQYHRUfzKiNRoZcTb1OV0q3hvvdFxAAAAAAAhyOsiIzc3V2vWrDnq+nPPPaeJEyf6JJTRioqKVFpaqpKSEqOj+BWTydS3KmPNDo5hBQAAAACcflZvv+C2227T3LlzdeDAAbndbj3//PPavn27HnvsMb3yyisDkRF+ZMboFC3fUKG1u5iTAQAAAAA4/bxekXHJJZfo5Zdf1ttvv63o6Gjddttt+uyzz/Tyyy/rwgsvHIiM8CNnj0iRySRtq2xRdTPH7wIAAAAATi+vV2RI0owZM/TWW2/5OgsCQGJ0uCZkxuvj/U16o7RK15411OhIAAAAAIAQ4vWKDODCM9IlSb97aaueLt5ncBoAAAAAQCjxusgwm82yWCzHfCD4/fC84bokP0NOt0c3P/+J/vBqqVxuj9GxAAAAAAAhwOutJS+88MIRn3d3d+ujjz7So48+qt/97nc+Cwb/FWG1aNGV+RqeEqO/vL1DD64p0776dv3tu5NlMZuMjgcAAAAACGImj8fjk79Kf/LJJ7V8+XK9+OKLvridX2hublZ8fLyampoUFxdndBy/9NKWg7rp2S3qcrp197fO1HcKsoyOBAAAAAAIMN68//bZjIyzzjpLK1eu9NXtECAuzsvQL786RpJ09xvb1epwGpwIAAAAABDMfFJkdHR06P7771dmZqYvbocAM3d6jnKSo1Tb6tDf3t1ldBwAAAAAQBDzekZGYmKiTKbP5yB4PB61tLQoKipKjz/+uE/DITCEW8369TdyNf+xDXpobZmunpqtrKQoo2MBAAAAAIKQ10XGX/7ylyOKDLPZrNTUVBUWFioxMdGn4RA4Zp2RprNHJuv9XXX607+3yf7dSUZHAgAAAAAEIZ8N+wxGDPv0zmeHmvWN+9fI7ZGW//AsFQ5PNjoSAAAAACAAePP++4RWZHz88ccn/M3PPPPME34tgssZg+N01dRsPfnhPj24powiAwAAAADgcydUZOTn58tkMunLFm+YTCa5XC6fBENgurqgp8j4cE+dnC63rBafHYwDAAAAAMCJFRllZWUDncOv2O122e12SpmTkJsRpzibVc2dTm092Ky8rASjIwEAAAAAgggzMo6DGRknZ/5jG/RWaZV+9bWx+sn5I4yOAwAAAADwcz6fkdGf0tJS7du3T11dXUdcv/jii0/2lggS00ck663SKq3bU0eRAQAAAADwKa+LjD179uiyyy7TJ598csTcjN4jWdmOgWkjeoZ8lpTVq8vpVriVORkAAAAAAN/w+h3mjTfeqGHDhqm6ulpRUVHaunWrVq9erSlTpmjVqlUDEBGBZnRarJKjw9XR7dLH+xuNjgMAAAAACCJeFxnr1q3THXfcoZSUFJnNZpnNZp1zzjm66667dMMNNwxERgQYs9mksw4fvfrB7jqD0wAAAAAAgonXRYbL5VJsbKwkKSUlRQcPHpQkDR06VNu3b/dtOgSs3u0l6ygyAAAAAAA+5PWMjPHjx2vLli0aNmyYCgsLdffddys8PFwPPPCAhg8fPhAZEYB6i4yN+xrU2e2SLcxicCIAAAAAQDDwekXGb37zG7ndbknSHXfcobKyMs2YMUOvvfaa7r//fp8HRGAanhKt9LgIdTnd2lTeYHQcAAAAAECQ8HpFxuzZs/s+HjlypLZt26b6+nolJib2nVwCmEwmTRuerBWbD2rdnjpNH5lidCQAAAAAQBDwekXG448/rra2tiOuJSUlUWLgKNNH9JQXDPwEAAAAAPiK10XGL37xC6Wnp+uaa67Ra6+9JpfLNRC5EAR652RsqWhUm8NpcBoAAAAAQDDwusg4dOiQnn76aZlMJn3nO9/R4MGDVVRUpA8++GAg8iGAZSVFKTMhUk63R1v2NxodBwAAAAAQBLwuMqxWq775zW/qiSeeUHV1tf7yl79o7969mjlzpkaMGDEQGRHAxgzqOap3T03bl7wSAAAAAIAv5/Wwzy+KiorS7Nmz1dDQoPLycn322We+yoUgMTwlWu+IIgMAAAAA4Bter8iQpPb2dj3xxBP6+te/rszMTC1atEiXXXaZtm7d6ut8CHDDU2MkSXtqWw1OAgAAAAAIBl6vyLjqqqv0yiuvKCoqSt/5znd06623atq0aQORDUFgeGq0JFZkAAAAAAB8w+siw2Kx6JlnntHs2bNlsVgGIhOCSG+Rsb+hXQ6nSxFW/pkBAAAAAJw8r4uMJ554YiByIEilxkQoNsKqFodT5XXtGp0ea3QkAAAAAEAAO6kZGcCJMplMX9hewpwMAAAAAMCpCfoio6KiQueff75yc3N15pln6tlnnzU6UsjpHfi5mzkZAAAAAIBTdErHrwYCq9WqRYsWKT8/X5WVlZo8ebK+/vWvKzo62uhoIWN4CgM/AQAAAAC+EfRFxuDBgzV48GBJ0qBBg5SSkqL6+nqKjNOII1gBAAAAAL5yUltL3G63duzYobVr12r16tVHPHxt9erVuuiii5SRkSGTyaQVK1Yc9Rq73a6cnBzZbDYVFhaquLi433tt3LhRLpdLWVlZPs+JY/viEawej8fgNAAAAACAQOb1ioz169frmmuuUXl5+VFvSk0mk1wul8/CSVJbW5vy8vJ0/fXX6/LLLz/q+eXLl2vhwoVasmSJCgsLtWjRIs2ePVvbt29XWlpa3+vq6+t13XXX6cEHH/RpPny5YYe3ljR1dKu+rUvJMREGJwIAAAAABCqvi4wf//jHmjJlil599VUNHjxYJpNpIHL1mTNnjubMmXPM5++77z7Nnz9f8+bNkyQtWbJEr776qpYuXaqbb75ZkuRwOHTppZfq5ptv1vTp0495L4fDIYfD0fd5c3Ozj36K0GYLsygzIVIHGju0p7aNIgMAAAAAcNK83lqyc+dO/fGPf9QZZ5yhhIQExcfHH/E4nbq6urRx40bNmjWr75rZbNasWbO0bt06SZLH49H3vvc9XXDBBbr22muPe7+77rrriJ+FLSi+wxGsAAAAAABf8LrIKCws1K5duwYii9dqa2vlcrmUnp5+xPX09HRVVlZKkt5//30tX75cK1asUH5+vvLz8/XJJ5/0e79bbrlFTU1NfY+KiooB/xlCBSeXAAAAAAB8weutJT/72c/03//936qsrNSECRMUFhZ2xPNnnnmmz8L5wjnnnCO3231Cr42IiFBEBNseBkLvySW7KTIAAAAAAKfA6yLjW9/6liTp+uuv77tmMpnk8XgGZNjn8aSkpMhisaiqquqI61VVVRo0aNBpy4Ev17e1hCNYAQAAAACnwOsio6ysbCBynJTw8HBNnjxZK1eu1KWXXiqp52jYlStXasGCBSd9X7vdLrvdflpLmWDXuyJjX127ul1uhVlO6uRfAAAAAECI87rIGDp06EDkOKbW1tYjZnKUlZVp8+bNSkpKUnZ2thYuXKi5c+dqypQpmjp1qhYtWqS2tra+U0xORlFRkYqKitTc3HzaB5gGq8FxNtnCzOrsdquivr2v2AAAAAAAwBteFxmStHv3bi1atEifffaZJCk3N1c33nijRowY4dNwkrRhwwbNnDmz7/OFCxdKkubOnatly5bpyiuvVE1NjW677TZVVlYqPz9fr7/++lEDQGEss9mkYSkx+uxQs/bUtFFkAAAAAABOitdFxhtvvKGLL75Y+fn5OvvssyX1nAwybtw4vfzyy7rwwgt9GvD888+Xx+M57msWLFhwSltJcHoMT43uKTJqWyVRNAEAAAAAvOd1kXHzzTfrF7/4hf70pz8ddf1Xv/qVz4sMBI8RHMEKAAAAADhFXk9c/Oyzz/T973//qOvXX3+9SktLfRLKaHa7Xbm5uSooKDA6SlDp3U7yxtZK/XN9uRxOhqkCAAAAALzjdZGRmpqqzZs3H3V98+bNSktL80UmwxUVFam0tFQlJSVGRwkq00ckKzMhUg3t3bp1xaeaec8qPfJ+mT490KSOLkoNAAAAAMCX83pryfz58/XDH/5Qe/bs0fTp0yX1zMj485//3DeIE+hPWpxNK//7PC0vqdDfVu3SwaZO/e7lz1fxDEmMVEZCpBIiw5QQFabEqHBlJERqSGKkspKilJ0UJVuYxcCfAAAAAABgNJPnyyZp/gePx6NFixbp3nvv1cGDByVJGRkZ+uUvf6kbbrhBJpNpQIIaoff41aamJsXFxRkdJ6h0dru0vKRCr35ySLurW1XX1vWlXxNmMWlCZrym5CRpytBEnTs6lWIDAAAAAIKAN++/vS4yvqilpUWSFBsbe7K38GsUGadPXatDu6pbVdPqUGN7t5o6ulXX2qUDje2qqO9QRUO7WjqdR3xNQlSYrpySpf86a6iykqIMSg4AAAAAOFWnrcgIVna7XXa7XS6XSzt27KDI8AMej0cV9R0q2VuvDeUNWr2jRgcaOyRJJpN0/uhUXZyfoVlnpCvWFmZwWgAAAACAN3xeZEyaNEkrV65UYmKiJk6ceNztI5s2bfI+sZ9iRYb/crk9WrW9Wss+2Ks1O2v7rodbzTp/dKqumpqlmWPSgmqrEwAAAAAEK2/ef5/QsM9LLrlEERERfR/z5hBGs5hN+soZ6frKGenaU9OqFR8d0CsfH9Ke2ja9WVqlN0urNCY9Vj86b7guystQmMXrA3oAAAAAAH6IrSXHwYqMwOLxePTZoRY9v2m/ni6pUKujZ6ZGZkKkfnL+CF0xZYgirAwHBQAAAAB/M6AzMoYPH66SkhIlJycfcb2xsVGTJk3Snj17vE/spygyAldTR7ceX1+uR97fq9pWhyQpI96mn84cSaEBAAAAAH5mQIsMs9msyspKpaWlHXG9qqpKWVlZ6ur68mM0AwVFRuDrPeb1b6t2qaq5p9CIDrdo+sgUnTc6VeeNTtWQxEi2SwEAAACAgXw+I0OSXnrppb6P33jjDcXHx/d97nK5tHLlSg0bNuwk4vqfL55agsBmC7No7vQcXVmQpeUlFVry3m4daurUW6VVequ0SpI0KM6myTmJmpydqCk5iTpjcBwzNQAAAADAT53wigyzueeNnclk0n9+SVhYmHJycnTvvffqm9/8pu9TGoQVGcHH7fao9FCz3ttRo/e212jjvga53Ef+8xwZZlFeVrymDE3SpRMzNTItxqC0AAAAABAaBnRrybBhw1RSUqKUlJRTChkIKDKCX3uXU1sqmrSxvF4byxu0sbxBzZ3OI15zwdg0/eCcYZo2IpktKAAAAAAwAAa0yAglFBmhx+32aHdNqzaUN2jlZ1Vaua1avf+GjEmP1SUTM3TRmRnKSooyNigAAAAABJEBLTJuuOEGjRw5UjfccMMR1xcvXqxdu3Zp0aJFXgf2VxQZKKtt0yPvl+nZDfvV0f35zJRJ2Qn6yhnpmj4iWRMy42VlpgYAAAAAnLQBLTIyMzP10ksvafLkyUdc37Rpky6++GLt37/f+8R+iiIDvZrau/Xap4f00uaDWl9Wpy/+WxMbYdX0kcm6qiBb545OlcXM9hMAAAAA8MaAnFrSq66u7ogTS3rFxcWptrbW29sBASE+KkxXT83W1VOzVd3cqde3Vur9XbVat7tOzZ1OvbG1Sm9srVJWUqS+WzhUl0/MVFqczejYAAAAABB0vC4yRo4cqddff10LFiw44vq///1vDR8+3GfBjMTxqzietDibrpuWo+um5cjl9mjrwSa9uPmgnt1QoYr6Dv3p39v0p39v04TMeM0ck6rzxqTpzCHxHOkKAAAAAD7g9daSpUuXasGCBfrlL3+pCy64QJK0cuVK3XvvvVq0aJHmz58/IEGNwNYSeKOjy6WXtxzUk8X7tLmi8YjnbGFm5Q1J0JScRF2cl6kxg2KNCQkAAAAAfmjATy35+9//rj/84Q86ePCgJCknJ0e//e1vdd11151cYj9FkYGTVdPi0Hs7avTutmq9v7tWje3dfc/Zwsx64gdnafLQRAMTAgAAAID/OG3Hr9bU1CgyMlIxMTEnewu/RpEBX3C7PdpT26oNexv0r037VbK3QQlRYXrux9M1Mi04/90BAAAAAG948/77lDbtp6amBm2JAfiK2WzSyLRYXTU1W49eP1V5WQlqbO/W3KXFqm7uNDoeAAAAAAQUr4uMqqoqXXvttcrIyJDVapXFYjniAeDYosKtWjp3ioalROtAY4fmPlKiHVUtOoWFUQAAAAAQUrzeWjJnzhzt27dPCxYs0ODBg2UymY54/pJLLvFpQCOxtQQDZV9duy7/+/uqbe2SJKXFRuickSk6a3iyJgyJ16i0GFk55QQAAABAiBjQGRmxsbFas2aN8vPzTyVjQKDIwEDaVtmsP762TR/uqZPD6T7iuQirWWcMjtOUoYmaNiJZU4clKdYWZlBSAAAAABhY3rz/tnp786ysrKBfBm+322W32+VyuYyOgiA2dlCcHrt+qjq7XdpY3qC1u2q1qbxBWw82q9Xh1OaKRm2uaNRDa8tkNkmThyZq3tnDNHvcIFnMpi//BgAAAAAQhLxekfHmm2/q3nvv1T/+8Q/l5OQMUCz/wIoMGMHt9qi8vl1bKhr1YVmdPthdp/K69r7nh6VEa/6M4fra+EFKjAo7ansXAAAAAASaAd1akpiYqPb2djmdTkVFRSks7Mjl7vX19d4n9lMUGfAXBxo7tLx4nx5dV66mju6+67E2q3KSozUsJVpnDI7TuIyeR3JMhIFpAQAAAMA7A1pkPProo8d9fu7cud7czq9RZMDftDmceqp4nx5fX669X1il8Z/OGp6k/70iT0MSo05jOgAAAAA4OQNaZIQSigz4s85ul/bVt2tvbZt21bRq68FmlR5sVlltmyQpzmbVn791puZMGGxwUgAAAAA4vgEtMvbt23fc57Ozs725nV+jyEAg2lfXrhue/kibKxolSVcVZGnOhMHKiLcpIyFS0RFez/gFAAAAgAE1oEWG2Ww+7nDBYDrpgyIDgarb5dZ9b+3Qkvd26z//DY+zWZWREHn4YdPg+EhlJkRqcLxNYwfFKT6KY14BAAAAnF4DevzqRx99dMTn3d3d+uijj3TffffpD3/4g7e3AzAAwixm/eprY3XOyBQ98n6ZKuo7dLCpQy2dTjV3OtVc2aJtlS1HfV1MhFWPXj9Vk4cmGpAaAAAAAL6cz2ZkvPrqq7rnnnu0atUqX9zOL7AiA8GmpbNbh5o6dbCxQwcbO3WoqUMHGjt0qLFTZbVtqmzuVGJUmP71k+kanhpjdFwAAAAAIWJAV2Qcy5gxY1RSUuKr2wEYALG2MMXawjQ6Pfao59q7nLr6gfXasr9J33ukRM//dLpSOMYVAAAAgJ8xe/sFzc3NRzyampq0bds2/eY3v9GoUaMGIiOA0yAq3KqH5hYoOylK++rb9f1lJWpzOI2OBQAAAABH8MmwT4/Ho6ysLD399NOaNm2aTwMawW63y263y+VyaceOHWwtQUjZU9Oqb/39AzW0dyvCatYZg+M0PjNOBTlJuujMDJnNxx72CwAAAAAnY0BPLXnvvfeO+NxsNis1NVUjR46U1RpcxzoyIwOhamN5g37y+EZVtziOuH5hbroWXZnPEa4AAAAAfMrnRcakSZO0cuVKJSYm6o477tBNN92kqKgonwX2VxQZCGVut0fl9e365ECTtlQ06p/ry9XldGvsoFg9NHeKhiQG/38DAAAAAJwePi8yIiMjtXPnTg0ZMkQWi0WVlZVKTU31WWB/RZEBfG7Tvgb98LGNqm11KDk6XIuvmaRpI5KNjgUAAAAgCPi8yJg2bZpiYmJ0zjnn6He/+51uuukmxcT0fzTjbbfddnKp/RBFBnCkg40d+sGjG1R6qFmSNHtcuv7na2M1gqNaAQAAAJwCnxcZ27dv1+23367du3dr06ZNys3N7Xcehslk0qZNm04+uZ+hyACO1t7l1O9f/UxPF++T2yNZzCZdVZCl/5k9VvFRYUbHAwAAABCABnTYp9lsVmVlpdLS0k4pZCCgyACObWdVi/78+ja9/Vm1JCkzIVL3X52vyUOTDE4GAAAAINAMaJERSigygC+3fk+dfvWvj1Ve1y6L2aRfzBqln5w/UhaOaQUAAABwgigyfIQiAzgxLZ3dunXFp1qx+aAkKT0uQikxEYqzhSk+MkyD4m3KSLApIyFSuYPjNJyZGgAAAAC+wJv330cPugAAL8XawvSXK/N1zqhU3fbip6pqdqiq2XHM188ck6ofnTdChcOSZDKxcgMAAADAiWNFxnGwIgPwXmN7l/bUtqm5o1vNnU41tnfpUFOnDjZ2qKK+XZsrGuU+/F+dvKwE3fqNMzQlh7kaAAAAQChja4mPUGQAvre3tk0Prd2jZzfsl8PpVpjFpN9fOl5XFmQbHQ0AAACAQbx5/2329uYVFRXav39/3+fFxcX6+c9/rgceeMD7pABCTk5KtH5/6QS9f/MF+saEwep2efSrf32iO18pldPlNjoeAAAAAD/ndZFxzTXX6N1335UkVVZW6sILL1RxcbF+/etf64477vB5QADBKSUmQouvmahfzBotSXp4bZnmLSvR3to2g5MBAAAA8GdeFxmffvqppk6dKkl65plnNH78eH3wwQd64okntGzZMl/nAxDETCaTbpw1SvZrJskWZtaanbX6yn3v6ZfPbtG+unaj4wEAAADwQ14XGd3d3YqIiJAkvf3227r44oslSWPHjtWhQ4d8mw5ASPjGmYP1YtE5umBsmlxuj57duF8X3LtK9725XYzxAQAAAPBFXhcZ48aN05IlS7RmzRq99dZb+trXviZJOnjwoJKTk30e0Ah2u125ubkqKCgwOgoQMsYMitXS7xXohZ9O17mjU+V0e3T/O7t09xuUGQAAAAA+5/WpJatWrdJll12m5uZmzZ07V0uXLpUk/b//9/+0bds2Pf/88wMS1AicWgIY55/r9urWF7dKkm78yij94sLRBicCAAAAMFAG/PhVl8ul5uZmJSYm9l3bu3evoqKilJaW5n1iP0WRARjr4bVluvOVUknSL2ePUdHMkQYnAgAAADAQBvT41Y6ODjkcjr4So7y8XIsWLdL27duDqsQAYLzvnzNMt8wZK0m6543tenHzAYMTAQAAADCa10XGJZdcoscee0yS1NjYqMLCQt1777269NJL9fe//93nAQGEth+dN0JFM0dIkm57cauqWzoNTgQAAADASF4XGZs2bdKMGTMkSc8995zS09NVXl6uxx57TPfff7/PAwLAz2eN1riMODV1dOvWFZ8y/BMAAAAIYV4XGe3t7YqNjZUkvfnmm7r88stlNpt11llnqby83OcBASDMYtY9386T1WzSG1ur9MrHHPUMAAAAhCqvi4yRI0dqxYoVqqio0BtvvKGvfvWrkqTq6moGYgIYMLkZcfrp4WGft7+0VXWtDoMTAQAAADCC10XGbbfdpptuukk5OTmaOnWqpk2bJqlndcbEiRN9HhAAei2YOVJjB8Wqvq1L/++FT+R2s8UEAAAACDUndfxqZWWlDh06pLy8PJnNPV1IcXGx4uLiNHbsWJ+HNArHrwL+55P9Tbrsb+/L6fbomsJs/eHS8TKZTEbHAgAAAHAKvHn/fVJFRq/9+/dLkoYMGXKyt/BrFBmAf3px8wH9fPlmeTzSvLNzdNs3cykzAAAAgADmzftvr7eWuN1u3XHHHYqPj9fQoUM1dOhQJSQk6M4775Tb7T7p0ABwoi7Jz9Sfv3WmJOmR9/fq7je2c5IJAAAAECKs3n7Br3/9az388MP605/+pLPPPluStHbtWv32t79VZ2en/vCHP/g8JAD8p+9MyZLD6datKz7V31ftlscj/eprY1iZAQAAAAQ5r7eWZGRkaMmSJbr44ouPuP7iiy/qpz/9qQ4cOODTgEZiawng/x5eW6Y7XymVJF05JUt/uGy8rBavF5sBAAAAMNCAbi2pr6/vd6Dn2LFjVV9f7+3tAOCUfP+cYfrT5RNkNknLN1So6MlN6ux2GR0LAAAAwADxusjIy8vT4sWLj7q+ePFi5eXl+SQUAHjjqqnZ+tt3JyncYtYbW6v0g0c3yMXRrAAAAEBQ8npGxt13361vfOMbevvttzVt2jRJ0rp161RRUaHXXnvN5wEB4ER8bfxgLbs+TD94dIPW7qrVS1sO6LKJwXmiEgAAABDKvF6Rcd5552nHjh267LLL1NjYqMbGRl1++eXavn27ZsyYMRAZAeCETB+RoqKZIyVJ9721Q11OTlICAAAAgo3Xwz6PZf/+/brjjjv0wAMP+OJ2foFhn0Dgae9y6ty7V6m21aE7Lxmna6flGB0JAAAAwJcY0GGfx1JXV6eHH37YV7cDgJMSFW7VDV/pWZVx/zu71NHF4E8AAAAgmITEGYWXXXaZEhMT9e1vf9voKABOg6sKsjUkMVI1LQ4t+2Cv0XEAAAAA+FBIFBk33nijHnvsMaNjADhNwq1m/WLWaEnSkvd2q6mj2+BEAAAAAHwlJIqM888/X7GxsUbHAHAaXToxU6PSYtTU0a15jxTr3W3VcnMkKwAAABDwTvj41csvv/y4zzc2Np5qln6tXr1a99xzjzZu3KhDhw7phRde0KWXXnrEa+x2u+655x5VVlYqLy9Pf/3rXzV16tQByQMgMFjMJt1+0Thdv6xEm/Y1at6yEo1Ki9H3zs7RBWPTNDg+0uiIAAAAAE7CCRcZ8fHxX/r8ddddd8qB/lNbW5vy8vJ0/fXX91umLF++XAsXLtSSJUtUWFioRYsWafbs2dq+fbvS0tJ8ngdA4DhnVIre+5/z9cj7e/Xkh/u0s7pVv37hU0nSyLQYzRiVoq/mDlLhsCSZzSaD0wIAAAA4ET47fvV0MJlMR63IKCwsVEFBgRYvXixJcrvdysrK0s9+9jPdfPPNfa9btWqVFi9erOeee+6Y93c4HHI4HH2fNzc3Kysri+NXgSDQ3Nmt5cUVevWTQ/p4f6O+uMskI96mi/Mz9a1JmRqVzjY0AAAA4HQz5PhVI3R1dWnjxo2aNWtW3zWz2axZs2Zp3bp1Xt/vrrvuUnx8fN8jKyvLl3EBGCjOFqb55w7XiqKz9dGtX9XfvztJ35kyRLE2qw42dWrJe7t14V9Wa+Ezm1Xd0ml0XAAAAADHENBFRm1trVwul9LT04+4np6ersrKyr7PZ82apSuuuEKvvfaahgwZcsyS45ZbblFTU1Pfo6KiYkDzAzBGfFSY5kwYrLu/naeSX8/S3787SbPOSJfJJD2/6YAu+N/39NCaPep2uY2OCgAAAOA/nPCMjED29ttvn9DrIiIiFBERMcBpAPgTW5hFcyYM1pwJg7W5olG3v/iptuxv0u9f/UyPvL9XV0wZoiumZCkzgeGgAAAAgD8I6BUZKSkpslgsqqqqOuJ6VVWVBg0aZFAqAIEqPytBL/z0bP35WxOUHB2uA40dWvT2Tp3z53c0d2mxtlU2Gx0RAAAACHkBXWSEh4dr8uTJWrlyZd81t9utlStXatq0aSd9X7vdrtzcXBUUFPgiJoAAYjabdGVBtt6/+QL931X5mjY8WR6P9N6OGl381/f14Oo9crsDZkYyAAAAEHT8/tSS1tZW7dq1S5I0ceJE3XfffZo5c6aSkpKUnZ2t5cuXa+7cufrHP/6hqVOnatGiRXrmmWe0bdu2o2ZneMubqakAgtfe2jbd8Uqp3tlWLUk6a3iS7v1OPttNAAAAAB/x5v233xcZq1at0syZM4+6PnfuXC1btkyStHjxYt1zzz2qrKxUfn6+7r//fhUWFp7y96bIANDL4/HoqeIK3flKqTq6XYoKt+gHM4brh+cOV0xESIwbAgAAAAZMUBUZRqLIAPCf9ta26aZnt2hDeYMkKSUmXDd+ZZSunpotqyWgd+sBAAAAhqHI8BGKDAD98Xg8+venlbr79W3aW9cuSSrISdTiayYpPc5mcDoAAAAg8Hjz/pu/PuwHwz4BHI/JZNLXJwzWWwvP0x2XjFNshFUlexv0jfvXaN3uOqPjAQAAAEGNFRnHwYoMACeirLZNP3l8o7ZVtshskm6eM1Y/PHeE0bEAAACAgMGKDAA4jYalROuFn56tyydlyu2R/vjaNr2zrcroWAAAAEBQosgAAB+IDLfo3ivyNO/sHEnSHS+XyuF0GRsKAAAACEIUGQDgIyaTSf/91TFKjY3Q3rp2PbSmzOhIAAAAQNChyOgHwz4BnKyYCKtumTNWkrT4nV061NRhcCIAAAAguDDs8zgY9gngZHg8Hn17yTptLG/QRXkZ+uvVE42OBAAAAPg1hn0CgIFMJpN+d/E4mUzSy1sO6o2tlaIzBgAAAHyDIgMABsD4zHhdPTVbkvSjf27UrPvek/3dXTrYyFYTAAAA4FRQZADAALllzlh9e/IQ2cLM2l3Tpnve2K5z735Xf359mzq7OdEEAAAAOBnMyDgOZmQA8IWWzm79+9NKPbdhv4r31kuScpKj9MfLJmj6yBSD0wEAAADGY0bGKeLUEgC+FGsL03emZOmZH0/TP66drEFxNu2ta9c1D32oO18pZX4GAAAA4AVWZBwHKzIADISWzm7d/fp2Pf5huTwe6YavjNLCC0cbHQsAAAAwDCsyAMCPxdrCdOel43XnJeMlSfev3Kl/ri83OBUAAAAQGCgyAMAg/3XWUP181ihJ0m0vfqrXPjlkcCIAAADA/1FkAICBbvzKKF1TmC2PR/r505v1b8oMAAAA4LgoMgDAQCaTSXdeMl5zxg9Sl8utnzyxSfe8sU0uN+OLAAAAgP5QZACAwSxmk/569UR9/5xhkiT7u7v1/UdL1NTRbXAyAAAAwP9QZPSD41cBnG5Wi1m3fjNXi67MV4TVrFXba3T5395XTYvD6GgAAACAX+H41ePg+FUARvj0QJPmP7ZBh5o6NXZQrJ6af5YSo8ONjgUAAAAMGI5fBYAANj4zXk/NP0tpsRHaVtmi65YWq7mTbSYAAACARJEBAH4pJyVaT84vVHJ0uD450KR5j5So1eE0OhYAAABgOIoMAPBTI9Ni9c/vFyrOZtXG8gZd/Ne1+nh/o9GxAAAAAENRZACAH8vNiNPjPyjUoDib9tS26fK/fSD7u7s4nhUAAAAhiyIDAPzcmUMS9PrPZ+gbEwbL6fbonje266oH1ml7ZYvR0QAAAIDTjiIDAAJAQlS4Fl8zUf97RZ6iwy0q2dugr9+/Rne8XMogUAAAAIQUiox+2O125ebmqqCgwOgoANDHZDLp25OH6I1fnKs54wfJ5fZo6ftluuB/V+kf7+1WbavD6IgAAADAgDN5PB42Wh+DN+fYAsDptmZnjW5/aav21LRJkqxmky7MTdd3C4fqnFEpBqcDAAAATpw3778pMo6DIgOAv+tyuvXCR/v1VHGFNlc09l2/OC9Dd14yXvFRYcaFAwAAAE4QRYaPUGQACCSfHWrWkx/u05PF++RyezQozqZ7rjhTM0alGh0NAAAAOC5v3n8zIwMAgsQZg+N056Xj9dyPp2lYSrQqmzt17cPFuuu1z+TmuFYAAAAECYoMAAgyE7MT9eoN5+i6aUMlSf9YvUc/X75ZXU63wckAAACAU0eRAQBBKCrcqjsuGa9FV+bLajbppS0Hdf2yErU6nEZHAwAAAE4JRQYABLFLJ2bq4e8VKCrcorW7anXFknV6eG2ZPtxTR6kBAACAgMSwz+Ng2CeAYLGlolHXLytRXVtX3zWTSZqdO0iLrsqXLcxiYDoAAACEOoZ9AgCOkJeVoJd+do4WXjhaF+amKyPeJo9Hen1rpeY/tkGd3S6jIwIAAAAnhBUZx8GKDADB7MM9dZq3rETtXS6dNzpV/7h2MiszAAAAYAhWZJwiu92u3NxcFRQUGB0FAAZM4fBkPfK9AkWGWfTejhr95PGN2t/QbnQsAAAA4LhYkXEcrMgAEArW7a7TvGXF6uzuOZ41I96mgmFJmjkmTV+fMFjhVjpvAAAADCxv3n9TZBwHRQaAUPHhnjr96fVt+mR/k5zuz/9vYVCcTd8/Z5iuLsxWTITVwIQAAAAIZhQZPkKRASDUtHc59dG+Rq3fU6flJRWqbnFIkmJtVt32zVxdMSXL4IQAAAAIRhQZPkKRASCUOZwurfjogP6xeo/21LRJkm64YKR+ceFomUwmg9MBAAAgmDDsEwBwyiKsFl1ZkK23f3GeFswcKUm6/51d+u9ntqjL6TY4HQAAAEIVRQYA4LjMZpNumj1Gf7p8gixmk57/6IDmLSuWw+kyOhoAAABCEEUGAOCEXDU1Ww/PnaLocIve31WnRW/vNDoSAAAAQhBFBgDghJ0/Jk33XZkvSfrHe7u1sbzB2EAAAAAIORQZAACvzB43SJdPypTbI9307BZ1dLHFBAAAAKcPRQYAwGu3XzROg+JsKqtt059f32Z0HAAAAIQQigwAgNfiI8N097fPlCQt+2Cv1u6sNTgRAAAAQgVFBgDgpJw7OlXfLcyWJF2/rEQPrN4tt9tjcCoAAAAEO4oMAMBJ+/U3ztCFuenqcrn1x9e26ZqH1utAY4fRsQAAABDEKDIAACctKtyqB66drD9dPkGRYRat31Ovry1arTe3VhodDQAAAEGKIgMAcEpMJpOumpqt126cobysBLV0OvXDf27Un1/fJqfLbXQ8AAAABBmKjH7Y7Xbl5uaqoKDA6CgAEDCGpUTruR9P07yzcyRJf1+1W9ctLVZtq8PYYAAAAAgqJo/Hw2S2Y2hublZ8fLyampoUFxdndBwACBgvbzmoX/3rY7V3uZSVFKknf3CWspKijI4FAAAAP+XN+29WZAAAfO6ivAy9tOBsDU2OUkV9h656YL3K69qMjgUAAIAgQJEBABgQI9NitfyH0zQ8JVoHGjt05T/Wq6yWMgMAAACnhq0lx8HWEgA4ddUtnfrugx9qZ3WrUmIi9LXx6cpOilJ2UpRGp8dqWEq0TCaT0TEBAABgIG/ef1NkHAdFBgD4Rm2rQ//10IfaVtly1HOpsREqHJakwuHJmjY8SSNSYyg2AAAAQgxFho9QZACA77Q6nPr3J4dUXteuffXtKq9r02eVLepyHnlEa0pMuKYOS9J5o1N1SX6mbGEWgxIDAADgdKHI8BGKDAAYWJ3dLm2uaNSHe+q1fk+dNu1rkOMLxUZSdLiuPWuorps2VMkxEQYmBQAAwECiyPARigwAOL0cTpc+3t+kD3bV6dmNFdrf0CFJirCa9aPzRuiGC0bKamFONQAAQLChyPARigwAMI7T5dbrWyv1wOo9+nh/kyRp8tBELboyX1lJUQanAwAAgC958/6bv9YCAPglq8Wsb56ZoReLztb9V09UbIRVG8sb9PX712jFRwfkctPDAwAAhCJWZBwHKzIAwH9U1Lfrxqc/0qZ9jZJ6Tjv5xoTBujg/QxOzEjjpBAAAIICxtcRHKDIAwL84XW4tfneXHnl/r5o6uvuu5yRH6YopWfrWpCEaFG8zMCEAAABOBkWGj1BkAIB/6nK6tWZnjV7aclBvlVapvcslSTKbpBmjUjVjVIoKhyXrjMGxDAcFAAAIABQZPkKRAQD+r83h1GufHNKzG/areG/9Ec/FRFg1LiNOI9NiNDItRqPSYjUxO0HREVaD0gIAAKA/FBk+QpEBAIFlT02r3iytUklZvYr31qul03nUa8IsJk3KTtSMUSmaMSpV4zPjZTEzXwMAAMBIFBk+QpEBAIHL5fZoe2WLtlU2a1d1q3ZVt2rrwWYdaOw44nXxkWE6e2SyZoxK1YW56UqJiTAoMQAAQOiiyPARigwACC4ej0flde1as7NGa3bWat3uOrU4Pl+1YTWb9JUz0nRlQZbOHZXKfA0AAIDThCLDRygyACC4OV1ubdnfpLU7a7VyW5U+3t/U91xmQqR+f9l4zRyTZmBCAACA0ECR4SMUGQAQWrZVNuuZkv164aP9amjvOd71islD9Jtv5io+MszgdAAAAMGLIsNHKDIAIDR1dLn0v29u19L3y+TxSIPibLrvyjxNH5FidDQAAICg5M3776Df/PvKK69ozJgxGjVqlB566CGj4wAAAkBkuEW3fjNXz/xomoalRKuyuVPzHilRyX8c7woAAIDTL6hXZDidTuXm5urdd99VfHy8Jk+erA8++EDJyckn9PWsyAAAdHS5VPTkJr2zrVqxNquW/3CacjP4/wQAAABfYkXGYcXFxRo3bpwyMzMVExOjOXPm6M033zQ6FgAggESGW2S/ZpIKchLV0unUdUuLVV7XZnQsAACAkOXXRcbq1at10UUXKSMjQyaTSStWrDjqNXa7XTk5ObLZbCosLFRxcXHfcwcPHlRmZmbf55mZmTpw4MDpiA4ACCKR4RY9NLdAZwyOU22rQ//18Icqq6XMAAAAMIJfFxltbW3Ky8uT3W7v9/nly5dr4cKFuv3227Vp0ybl5eVp9uzZqq6uPqnv53A41NzcfMQDAABJio8M06PXF2hocpQq6jv0zfvX6MXNlOMAAACnm18XGXPmzNHvf/97XXbZZf0+f99992n+/PmaN2+ecnNztWTJEkVFRWnp0qWSpIyMjCNWYBw4cEAZGRnH/H533XWX4uPj+x5ZWVm+/YEAAAEtLdamZ340TVOHJamty6Ubn96sW57/WB1dLqOjAQAAhAy/LjKOp6urSxs3btSsWbP6rpnNZs2aNUvr1q2TJE2dOlWffvqpDhw4oNbWVv373//W7Nmzj3nPW265RU1NTX2PioqKAf85AACBJT3Opid/UKgbLhgpk0l6qrhCc/5vtd7cWqkgnp8NAADgN6xGBzhZtbW1crlcSk9PP+J6enq6tm3bJkmyWq269957NXPmTLndbv3P//zPcU8siYiIUERExIDmBgAEPqvFrIVfHaPC4cn6xfLN2lvXrh/+c6MKhyXp1m/manxmvNERAQAAglbArsg4URdffLF27NihXbt26Yc//KHRcQAAQeTskSl656bztWDmSEVYzfqwrF4XLV6rW1d8qlaH0+h4AAAAQSlgi4yUlBRZLBZVVVUdcb2qqkqDBg06pXvb7Xbl5uaqoKDglO4DAAh+MRFW3TR7jN656Xxdkp8hj0f65/pyffW+9/Tu9pMbPg0AAIBjC9giIzw8XJMnT9bKlSv7rrndbq1cuVLTpk07pXsXFRWptLRUJSUlpxoTABAiMhMi9X9XTdQTPyhUVlKkDjZ1at4jJZq7tFj2d3dp7c5aNXV0Gx0TAAAg4Pn1jIzW1lbt2rWr7/OysjJt3rxZSUlJys7O1sKFCzV37lxNmTJFU6dO1aJFi9TW1qZ58+YZmBoAEMrOHpmiN35+ru57c4eWvl+m93bU6L0dNZIkk0maPiJZ35mSpdnjBskWZjE4LQAAQOAxefx4xPqqVas0c+bMo67PnTtXy5YtkyQtXrxY99xzjyorK5Wfn6/7779fhYWFPvn+zc3Nio+PV1NTk+Li4nxyTwBA6Nhe2aL3dlRry/4mfbK/Sfvq2/uei48M0xWTh+jGWaMUawszMCUAAIDxvHn/7ddFhtEoMgAAvlRR367nNu7XsxsqdLCpU1LPlpR7rjhT00ekGJwOAADAOBQZp8hut8tut8vlcmnHjh0UGQAAn3K5PXp3W7V++/JW7W/okCR9b3qO/vuro1mdAQAAQhJFho+wIgMAMJBaHU798bXP9OSH+yRJ4RazzhqRrAvPSNOs3HQNjo80OCEAAMDpQZHhIxQZAIDT4b0dNbrj5a3aXdPWd81skr41qWeGxpDEKAPTAQAADDyKDB+hyAAAnE67qlv19mdVequ0ShvLGyRJYRaTrpmarQUXjFJqbITBCQEAAAYGRYaPUGQAAIzy0b4G3fvmDq3dVStJSomJ0CPfK9CEIfEGJwMAAPA9b95/m09TpoBit9uVm5urgoICo6MAAELUxOxEPf6DQj05v1Cj02NU2+rQd/6xTu9sqzI6GgAAgKFYkXEcrMgAAPiDls5u/fSJTVqzs1Zmk3TnpeP13cKhRscCAADwGVZkAAAQRGJtYVr6vQJ9e/IQuT3Sr1/4VI9+sNfoWAAAAIagyAAAIACEWcy659tnasHMkZKk3728Vat31BicCgAA4PSjyAAAIECYTCb991dH61uTelZmFD25SbuqW42OBQAAcFpRZAAAEEBMJpP+ePl4TRmaqJZOp77/aIka2rqMjgUAAHDaUGT0g1NLAAD+LMJq0T+unawhiZEqr2vXdx/6UG9urZTLzfxuAAAQ/Di15Dg4tQQA4M+2V7bo20s+UEunU5KUnRSl703P0dVTsxUZbjE4HQAAwInz5v03RcZxUGQAAPxdZVOnHl23V09+uE9NHd2SpMHxNv3qa2N1cV6GzGaTwQkBAAC+HEWGj1BkAAACRUeXS89/tF9/X7Vb+xs6JEn5WQm66atjNCUnUbYwVmgAAAD/RZHhIxQZAIBA09nt0sNry/S3d3eprcslSQqzmJSbEa9J2Qn6+oTBmjI0USYTKzUAAID/oMjwEYoMAECgqm7u1F/e3qm3SitV23rkqSZnDI7TddOG6pL8DEWFWw1KCAAA8DmKDB+hyAAABDqPx6P9DR3atK9Ba3bW6pWPD6qz2y1JSooO15+/daYuzE03OCUAAAh1FBmnyG63y263y+VyaceOHRQZAICg0dTerWc3VuixdeXaV98uSbr+7GG6ec5YhVs5lR0AABiDIsNHWJEBAAhWXU637n59mx5aWyZJOnNIvOzXTFJWUpTByQAAQCjy5v03f/UCAEAICrea9Ztv5uqh66YoPjJMH+9v0uV//0C7a1qNjgYAAHBcFBkAAISwWbnpeu3GGRo7KFY1LQ5d9cB6ygwAAODXKDIAAAhxmQmRenL+WZQZAAAgIFBkAAAAJUWHH1VmbCyvNzoWAADAUSgyAACApJ4y44kfFPaVGVcsWae7XvtMnd0uo6MBAAD0ocgAAAB9kmMitPxH03T5pEy5PdI/Vu/RN/+6ltUZAADAb1Bk9MNutys3N1cFBQVGRwEA4LSLjwzTfd/J1wPXTlZKTIR2VbfqW39fp6seWKdV26vFye0AAMBIJg9/Gjkmb86xBQAgGNW3demu1z7TCx8dkNPd80eGsYNiNXd6ji7Ky1BMhNXghAAAIBh48/6bIuM4KDIAAOhxoLFDS9eW6anifWrv6pmZER1u0SUTM3XN1GyNz4w3OCEAAAhkFBk+QpEBAMCRmtq79cyGCj1VvE97atv6rp85JF5XT81mlQYAADgpFBk+QpEBAED/PB6P1u+p15PF+/TGp5Xqcrkl9azSuDg/Q1cVZOvMIfEymUwGJwUAAIGAIsNHKDIAAPhyda0OPb/pwFGrNMYOitXF+RkanhKtIYlRykqMUnxUmIFJAQCAv6LI8BGKDAAATlzvKo3lJfv02qeV6nK6j3pNrM2qIYlRGpIYqZzkKE3MTtSUoYlKi7MZkBgAAPgLigwfocgAAODkNLV3a8XmAyrZW6/9DR3a39Cu2tauY74+OylKZ49M1qwz0nX2yBTZwiynMS0AADAaRYaPUGQAAOA7HV0uHWhsV0V9T7Gxo6pVG8obtK2yWV/800hkmEXnjk7RZRMzdcHYdIVbzcaFBgAApwVFho9QZAAAMPCaO7u1sbxB726r1tulVTrY1Nn3XFJ0uC7Nz9TVU7M0Kj3WwJQAAGAgUWT4CEUGAACnl8fjUemhZr285ZCe37Rf1S2OvucuGJumH583QgU5iZyGAgBAkKHIOEV2u112u10ul0s7duygyAAAwABOl1urd9boqeIKvf1ZVd/2k0nZCbpiSpa+mpuu5JgIY0MCAACfoMjwEVZkAADgH8pq2/TA6j3616b9faehmE1SQU6SvnnmYF0yMVNxNo52BQAgUFFk+AhFBgAA/qW6pVPPbtiv1z+t1CcHmvquR4ZZdOnEDH23cKjGZ8YbmBAAAJwMigwfocgAAMB/VdS3642tlXpmQ4V2VLX2XT9nZIpunjOWQgMAgABCkeEjFBkAAPg/j8ej4rJ6Pf7hPr3+6SF1u3r+aHNxXoZ+OXuMspKiDE4IAAC+DEWGj1BkAAAQWCrq23Xvm9u1YvNBSVK4xazfXTJOV0/NNjgZAAA4Hm/ef5tPUyYAAIABl5UUpUVXTdQrPztH00ckq8vl1i3Pf6JfPfexOrtdRscDAAA+QJEBAACCzvjMeD3+/UL9cvYYmU3S8g0V+s4/1ulAY4fR0QAAwCmiyAAAAEHJbDapaOZIPXr9VCVEhenj/U26ZPH7+vQLp50AAIDAQ5EBAACC2oxRqXp5wTkaOyhWta0OXfmPdVq9o8boWAAA4CRRZAAAgKCXlRSlZ348TdNHJKuty6Xrl5Xo+U37jY4FAABOAkUGAAAICXG2MC2bN1WX5GfI6fZo4TNbdMNTH6mivt3oaAAAwAsUGQAAIGSEW836y3fy9ePzRshkkl7aclBfufc9/eHVUjW2dxkdDwAAnACKDAAAEFLMZpNunjNWLy84R2eP7Dmi9cE1ZZrzf2u0t7bN6HgAAOBLUGQAAICQ1HtE6yPzCpSTHKVDTZ26+sH1lBkAAPg5igwAABCyTCaTZo5J07M/nq6RaTGUGQAABACKjH7Y7Xbl5uaqoKDA6CgAAOA0SI2N0FPzzzqizNhXxxBQAAD8kcnj8XiMDuGvmpubFR8fr6amJsXFxRkdBwAADLCaFoeufnC9dlW3akRqtJ7/6dmKjwwzOhYAAEHPm/ffrMgAAAA4LDU2Qk/+oFCD423aXdOmBU9uktPlNjoWAAD4AooMAACAL0iLs+mhuVMUFW7Rmp21+t3LpUZHAgAAX0CRAQAA8B/GZcRr0ZX5Mpmkf64v16Mf7DU6EgAAOIwiAwAAoB9fHTdIv/raWEnS717eqvd21BicCAAASBQZAAAAx/Sjc4frislD5PZIC57YpJ1VLUZHAgAg5FFkAAAAHIPJZNIfLpugqTlJanE49f1HN6i+rcvoWAAAhDSKDAAAgOMIt5q15NrJyk6K0r76dv34nxvlcLqMjgUAQMiiyAAAAPgSSdHhenjuFMVGWFW8t17zHilRRX270bEAAAhJFBkAAAAnYFR6rOzfnSRbmFkf7K7T1xat1j/Xl8vt9hgdDQCAkEKRAQAAcILOHZ2qf994rgpyEtXW5dKtKz7Vfz38oZrau42OBgBAyKDIAAAA8MKwlGgt/+E03X5Rbt/qjOseKVZLJ2UGAACnA0UGAACAl8xmk+adPUwv/PRsJUSFaUtFo+Y9UqI2h9PoaAAABD2KDAAAgJN0xuA4/fP6QsXarNpQ3qAfPLpBnd2caAIAwECiyAAAADgFE4bE69Hrpyo63KJ1e+p0qf19/fuTQwwBBQBggFBkAAAAnKJJ2Yl6ZN5Uxdqs2lbZop88sUlf+7/VemnLQXW73EbHAwAgqJg8Hg9/XXAMzc3Nio+PV1NTk+Li4oyOAwAA/FxDW5eWvl+mZe/vVcvheRnpcRG6siBbVxVkKSMh0uCEAAD4J2/ef1NkHAdFBgAAOBlNHd1a9v5e/XP9XtW2dkmSzCbpwtx0/ei8EZqUnWhwQgAA/AtFho9QZAAAgFPR5XTrzdJKPbF+n9btqeu7PnVYkn583nCdNzpNFrPJwIQAAPgHigwfocgAAAC+srOqRQ+s3qMVmw+o29Xzx6/U2Ah9Y8JgXZQ3WBOzEmWm1AAAhCiKjP9w2WWXadWqVfrKV76i55577oS/jiIDAAD4WmVTp5a+X6blJRVq6ujuu56VFKmrCrJ1xeQhSouzGZgQAIDTjyLjP6xatUotLS169NFHKTIAAIBf6HK6tXZXjV7eckhvbq1UW5dLkmQxm/SVsWkqmjlSeVkJxoYEAOA08eb9t/U0ZTLU+eefr1WrVhkdAwAAoE+41awLxqbrgrHp6uhy6bVPDump4n3aUN6gN0ur9NZnVbqqIEu/nD1WSdHhRscFAMBvmI0OsHr1al100UXKyMiQyWTSihUrjnqN3W5XTk6ObDabCgsLVVxcfPqDAgAADJDIcIu+NXmInvvJdL35i3N12cRMeTzSU8UVmvm/q/TP9eVyu4N+ES0AACfE8CKjra1NeXl5stvt/T6/fPlyLVy4ULfffrs2bdqkvLw8zZ49W9XV1X2vyc/P1/jx4496HDx40KssDodDzc3NRzwAAABOp9HpsfrLlfl69sfTNHZQrJo6unXrik91xT/WaVd1i9HxAAAwnF/NyDCZTHrhhRd06aWX9l0rLCxUQUGBFi9eLElyu93KysrSz372M918880nfO9Vq1Zp8eLFx52R8dvf/la/+93vjrrOjAwAAGAEp8utx9eX6543tquty6Vwi1k/u2Ckvj9jmKLCQ2KHMAAgRATNjIyuri5t3LhRt9xyS981s9msWbNmad26dT7/frfccosWLlzY93lzc7OysrJ8/n0AAABOhNVi1vfOHqYLxw3Sb174RO9ur9G9b+3QfW/v0NCkKI1Oj9WItBilxUYoOSZCKTHhSo3p+TghMozjXAEAQcmvi4za2lq5XC6lp6cfcT09PV3btm074fvMmjVLW7ZsUVtbm4YMGaJnn31W06ZNO+p1ERERioiIOOXcAAAAvpSZEKml3yvQS1sO6s//3qaDTZ3aW9euvXXtUmlVv19jMZuUFB2ulMMFR0pMhOIjwxQdYVFUuFVR4RZFh1sVFXH41/DD1w9/bgszyxZmUYTVLJOJQgQA4D/8usjwlbffftvoCAAAAKfEZDLpkvxMXZKfqdpWh7ZXtmh7ZYv21rWprrVLNa0O1bU6VNvapaaObrncHtW0OFTT4jjl7x1h7Sk1esuNhMgwpcZGKCUmQmlxNo1Jj9XYwbHKSY6WhVUgAIAB5tdFRkpKiiwWi6qqjvybhqqqKg0aNGjAvq/dbpfdbpfL5Rqw7wEAAHCyUmIilDIyQmePTOn3+S6nW/VtXaptdai21aG61p6Pmzu71eZwqaPLpbYup9q7XGpzHP61y9lz3eFUW5dLri+ckuJwuuVwutXU0fN5+TFy2cLMOnNIgs4dlaIZo1I1PjOeYgMA4HMBMexz6tSp+utf/yqpZ9hndna2FixY4NWwz5PhzbARAACAYNLtcquz2yWHs+fXzu7eX11qaO9WbWvPao8DDR3aVtms7VUt6ux2H3GPxKgwzRybptnjBuncUamKDLcY9NMAAPxdQA37bG1t1a5du/o+Lysr0+bNm5WUlKTs7GwtXLhQc+fO1ZQpUzR16lQtWrRIbW1tmjdvnoGpAQAAgluYxawwi1mxJ/h6l9ujstpWrd9TrzU7a/TBrjo1tHfr+U0H9PymA4oMs2jaiGRNzEpQXlaC8oYkKD4qbEB/BgBAcDJ8RcaqVas0c+bMo67PnTtXy5YtkyQtXrxY99xzjyorK5Wfn6/7779fhYWFA56NFRkAAAAnx+lya2N5g97YWqU3tlbqQGPHUa+JDLMoLtKqOFuY4iPDFBd5+Feb9Qsfhyku0qqocGvfoNLo/xhKyjBSAAh83rz/NrzI8GcUGQAAAKfO4/Fo68FmfVhWry0Vjdqyv1Hlde0+ubfJpL5TV6Ij+j+Npe96hFWxNqtiIqyKtYUd/rX30VOcMNMDAIwRUFtL/BHDPgEAAHzHZDJpfGa8xmfG911r6exWY3u3mjq61dzRrebO3o+dX/i4W82dTjV3dKuty6X2LqfaHD2/tnf1/DnN45FaHU61OpzSKZ7QYjJJCZFhSowOV3xkmGJtYYq19awYiftC4ZEUHa7B8TYNircpLdamcKv5lL4vAMA7rMg4DlZkAAAA+Ce326OO7sOnrzj6OYXlC6extDtcanU41Xa48Gh1ONXc6VRrZ7daHU61dH5ejHjLZJIyEyI1PDVGw1OiNWZQrCYPTdTI1BiZWd0BACeMFRkAAAAIamazSdERVkVHWHXCE0mPo8vpVmNHlxraulXf1qXmzm61HF4N0tLpVEvv553dqmvt0qHmDlU1OdTlcmt/Q4f2N3Ro9Y6avvvFR4ZpUnaCclKiNSiuZ/VGRkKkRqXFKCEq/NQDA0AIo8gAAABAyAu3mpUW27NV5ER5PB7VtnaprLZNe2patae2TZ/sb9JHFQ1q6ujWu9trpO01R31delyERqfHasrQJF0wNk3jMuJYvQEAXmBryXGwtQQAAADe6na5VXqwWZsrGnWwqUPVzQ5VNnVqX317v6e3pMVG6CtnpOm/zhqqcRnx/dwRAIIfp5acoi8O+9yxYwdFBgAAAHyipbNbO6tbVXqwWWt21mjNztoj5nNMH5Gs+ecO1/mjUzlWFkBIocjwEVZkAAAAYCA5nC59uKdez23cr1c/OSSXu+eP5uMz43TnJeM1MTvR4IQAcHpQZPgIRQYAAABOlwONHVr2fpmeKq5Qq8Mpk0m6emq2/mf2GAaEAgh6FBk+QpEBAACA06221aG7Xtumf23aL0lKig7XfxVm69uTs5SdHGVwOgAYGBQZPkKRAQAAAKN8uKdOv1nxqXZWt/ZdmzosSbPHDdKI1GjlJEdrSGKkrBazgSkBwDcoMnyEIgMAAABG6na59e9PK/Xshgqt3VWr//yTe5jFpPGZ8SoclqzC4UkqyElSTITVmLAAcAooMk4Rp5YAAADA3xxq6tALHx3Q5n2NKq9r1966Njmc7iNeE24168Iz0nX5pEydOzpVYazWABAgKDJ8hBUZAAAA8Fdut0f7GzpUvLdeH+6p0/qyOlXUd/Q9nxwdrssnZeqawqEalhJtYFIA+HIUGT5CkQEAAIBA4fF4VHqoWc9vOqAXNx9QbWtX33PnjEzR1VOzde7oFMXawgxMCQD9o8jwEYoMAAAABKJul1vvba/REx+Wa9WOmr7ZGlazSROzEzRjVKpmnZGu3Az+jAvAP1Bk+AhFBgAAAAJdRX27nirep9c+OaS9de1HPJc7OE5XTBmiS/IzlRQdblBCAKDI8BmKDAAAAASTivp2rdlZq1Xbq7Vqe426XD3DQs0maVCcTZmJkRqSGKWc5GiNGRSrMwbHKisxSmazyeDkAIIdRYaPUGQAAAAgWDW0demlLQf17MYKfXqg+Ziviwq3aPLQRE0fkaLpI5I1PjNeFooNAD5GkXGKOH4VAAAAoaSmxaH9De3a39Ch/Q0d2l3Tqm2VzdpR1aqu/zjiNSk6XJfkZ+jbk4doXEa8QYkBBBuKDB9hRQYAAABCmdPl1s7qVq3fU6cPdtdp/Z46tXQ6+57PHRynudOH6rKJQxRuNRuYFECgo8jwEYoMAAAA4HNOl1trdtbquY379VZpVd+MjcyESP34vOG6YkqWbGEWg1MCCEQUGT5CkQEAAAD0r6GtS89t3K8H1uxRTYtDkpQWG6FfXDhaV0weIquFFRoAThxFho9QZAAAAADH19nt0jMbKrRk1W4dbOqUJI1Ki9HNc8bqgrFpMpkYDArgy1Fk+AhFBgAAAHBiHE6XHl+/T399Z6ca27slSVlJkcobkqAzh8RrfEa8RqbHKDUmgnIDwFEoMnyEIgMAAADwTlNHt/62apceeX/vUSeeSFKszaoRqTE9j7Tovo+HpURzrCsQwigyfIQiAwAAADg5TR3d+mR/kz4+0KhP9jdp68Fm7W9ol/sY7z6iwy2aMCReeUMSNDE7UWcNT1JCVPjpDQ3AMBQZp8hut8tut8vlcmnHjh0UGQAAAIAPdHa7VF7Xrt01rdpd3drza02bdlW3qqPbdcRrTSZpXEacpo9IUX5WgsZlxCk7KYptKUCQosjwEVZkAAAAAAPP5fZoV3WrtlQ0avP+RhWX1WtXdetRr4uNsGrCkHidPTJF545K1biMOJnZjgIEBYoMH6HIAAAAAIxR3dypD3bXaf2eOn16sEk7KlvV5Tpy5kZiVFhfqXHOqBRlJEQalBbAqaLI8BGKDAAAAMA/dLvc2lnVqo3l9Vq9s1brdtep1eE84jUj02J0YW66vjZukM4cEs82FCCAUGT4CEUGAAAA4J+6XW5trmjUmp21WrOzRlsqGo8YJDo43qaL8jL03cJsDU2ONi4ogBNCkeEjFBkAAABAYGhq79aqHdV6c2uV3t1erfaunuGhJpN0/uhUXTc9R+eNSmWmBuCnKDJ8hCIDAAAACDyd3S69t6NGT364T+/tqOm7PiotRj88d7guyc9UuNVsYEIA/4kiw0coMgAAAIDAVlbbpsfXl+uZkgq1HJ6pMSjOpvnnDtd3C7NlC7MYnBCARJHhMxQZAAAAQHBo7uzWkx/u09K1ZapucUjqmaPx81mj9K1JQ2S1sEIDMBJFho9QZAAAAADBxeF06V8bD+iv7+zUoaZOSdLw1Gjd9NUxmjN+ECedAAahyPARigwAAAAgOHV2u/T4+nLZ392lhvZuSdKEzHj9cvYYzRiVQqEBnGYUGafIbrfLbrfL5XJpx44dFBkAAABAkGrp7NZDa8r00Jo9ajt80knhsCR9/5xh+soZ6bJwyglwWlBk+AgrMgAAAIDQUNfqkP3d3Xp8fbm6XG5JUmZCpP7rrKG6JD9DGQmRBicEghtFho9QZAAAAACh5WBjh/65vlxPF+/r23IiSTnJUZo+MkXnjEzRuaNTFRNhNTAlEHwoMnyEIgMAAAAITZ3dLr285aCeLqnQR/sa5P7Cu6Zwq1nnjkrR7HGDdMbgONnCzIqwWhRhNSsi7PCvVjNzNgAvUGT4CEUGAAAAgObObhXvqdf7u2v17rZq7a1rP6Gv6y00IsIsR5Qdti+UHZ9/fPg1YRbZDn9NZJhFkeEWDYqzaVhKtIYkRnJMLIIWRYaPUGQAAAAA+CKPx6MdVa16/dNKvf1ZlWpaHOp0uuTodqvT6dJAvruymk3KTo7S8JRoDUuJ1rCUGOWkRGlYSrTSY20yM5gUAYwiw0coMgAAAACcKI/Ho26XRw6nSw6nW53dPb/2lhyObrccTpc6D//a89zhX7/w+s5ulzq7Xerodqvd4dSBxg7trWtTZ7f7mN/bFmZWTnK0cpKjNTQlSsOSo5VzuPBIi41gmwv8njfvv5lQAwAAAAA+YDKZFG41KdxqVqyP7+12e1TZ3Kmy2jbtqW1TWU2b9tS2am9tmyoaOtTZ7da2yhZtq2w56mujwi3KSY7WmUPiNSUnSVOGJmpochTlBgIWKzKOgxUZAAAAAPxdt8utAw0dKqtr097ankdZXbv21rZpf0P7EYNKe6XFRuj8Mam6YGyazhnFKSwwHltLfIQiAwAAAEAg63K6tb+hXbuqW7VpX6M27K3Xx/ub1OX6fJtKmMWkvCEJfas18rMTlBwdzooNnFYUGT5CkQEAAAAg2HR2u1Syt17vbKs+5iks4Vaz0uMilB5rU3ZylMakx2p0eqzGDIrV4HgbJQd8jiLDRygyAAAAAAS7vbVtKt5br417G1RSXq89NW3Hff2gOJum5CSqICdJ00Yka1RaDMUGThlFho9QZAAAAAAINZ3dLtW0OFTd0qlDTZ0qq2nT9qoW7ahq0Z6aNjn/Y+hGdlKULsxN14W56SrISZKFY2BxEigyfIQiAwAAAAA+19Hl0uaKnlkbxXvr9WFZvbqcn8/bGBRn06UTM/XtyZkamebrs1sQzCgyfIQiAwAAAACOrc3h1JqdNXqztEpvl1apudPZ99yZQ+L1rUlDdFFehpKiww1MiUBAkeEjFBkAAAAAcGIcTpfe+axa/9p0QKu2V/dtQbGaTZo5Nk0FOYkakhilzIRIZSdFKZFyA19AkXGK7Ha77Ha7XC6XduzYQZEBAAAAAF6obXXo5S0H9a9N+/XpgeZ+X5MaG9F3Gkp+doLOGZnCyo0QRpHhI6zIAAAAAIBTs72yRa99ckhltW060Nih/Q3tqmp2HPU6k0kalxGnc0el6vJJzNgINRQZPkKRAQAAAAC+1+Zwamd1q3ZUtqj0ULPW76nTtsqWI14zZWiirp6ara9PGKzIcItBSXG6UGT4CEUGAAAAAJwe1S2den9XrV77pFLvbKuW6/CMjaTocM2fMVzXTRuq6AirwSkxUCgyfIQiAwAAAABOv6rmTj27oUJPFVfoQGOHJCkxKkw/mDFc887OUVQ4hUawocjwEYoMAAAAADCO0+XWis0Htfidndpb1y5JykyI1J2XjtMFY9MNTgdfosjwEYoMAAAAADCe0+XWS1sO6t43d/St0Pj6hEG6/aJxSo+zGZwOvkCR4SMUGQAAAADgP9q7nFr09k49vLZMLrdHUeEW/fDc4Zo/YzjzMwIcRYaPUGQAAAAAgP8pPdisX6/4RB/ta5QkpcRE6MZZo3T+6FTFR4UpNsIqk8lkbEh4hSLDRygyAAAAAMA/eTwevfrJId3zxnaVH56f0ctskjITI/WtSUN0VUG2BsWz/cTfUWT4CEUGAAAAAPi3LqdbT5fs07L39+pQU6c6ul1HPG8xmzTrjDTNnzFcU3KSDEqJL0OR4SMUGQAAAAAQWDq7XWrq6Nb6PXV6Yv0+Fe+t73vuq7npunnOWA1PjTEwIfpDkeEjFBkAAAAAENh2VLVo6doyPbOhQm6PZDWbdE1htn45e4xibWFGx8NhFBk+QpEBAAAAAMFhR1WL/vTvbXpnW7UkaVhKtOzXTFJuBu/1/IE377/NpykTAAAAAACGGZ0eq6XfK9ATPyhURrxNZbVtuuxv7+up4n3i7/cDC0UGAAAAACBknD0yRa/eMEMzx6TK4XTrluc/0c+Xb1ZzZ7fR0XCCKDIAAAAAACElMTpcD88t0K++NlYWs0kvbj6oOYvW6MM9dUZHwwmgyAAAAAAAhByz2aSfnD9Cz/zoLGUlRepAY4euenC9/vz6NnU53UbHw3FQZAAAAAAAQtbkoUn6943n6orJQ+TxSH9ftVvffWi9alocRkfDMVBkAAAAAABCWkyEVfdckacl/zVJsRFWlext0MWL1+rj/Y1GR0M/KDIAAAAAAJD0tfGDtWLB2RqeGq1DTZ26Ysk6PfrBXtW2sjrDn5g8QX7OTEVFha699lpVV1fLarXq1ltv1RVXXHFCX+vNObYAAAAAgODQ3Nmtnz+9We9sq+67Nj4zTjNGpercUamaPDRR4VbWBfiSN++/g77IOHTokKqqqpSfn6/KykpNnjxZO3bsUHR09Jd+LUUGAAAAAIQmt9ujh9bu0QsfHdRnh5qPeC4q3KKzhifr3FEpmjE6VcNTomUymQxKGhwoMo4jLy9Pr7zyirKysr70tRQZAAAAAIDq5k6t3VWrNTtrtWZnjWpbu454PjMhUueOTtGMUak6e0SK4qPCDEoauLx5/234WpjVq1froosuUkZGhkwmk1asWHHUa+x2u3JycmSz2VRYWKji4uKT+l4bN26Uy+U6oRIDAAAAAABJSouz6fJJQ/SXK/NV/P9m6dUbztHNc8Zq+ohkhVvMOtDYoaeKK/TTJzZp4p1v6rK/va/73tqh9Xvq5HC6jI4fdKxGB2hra1NeXp6uv/56XX755Uc9v3z5ci1cuFBLlixRYWGhFi1apNmzZ2v79u1KS0uTJOXn58vpdB71tW+++aYyMjIkSfX19bruuuv04IMPDuwPBAAAAAAIWmazSeMy4jUuI14/Pm+E2ruc+nBPvVbvrNGanbXaVd2qj/Y16qN9jbp/5U5FWM2akpOoyUOTNCEzXuMz4zQozsZWlFPgV1tLTCaTXnjhBV166aV91woLC1VQUKDFixdLktxut7KysvSzn/1MN9988wnd1+Fw6MILL9T8+fN17bXXHvd1Dsfn02ibm5uVlZXF1hIAAAAAwAk50NihtYdLjfV76o7ahiJJydHhGpcZr/EZcRqfGa+xg2KVlRSlMIvhmyYM483WEsNXZBxPV1eXNm7cqFtuuaXvmtls1qxZs7Ru3boTuofH49H3/n979x4U5XX/cfyzoCyoICLKJSjgXRTRICrReInEy6RWYxyN2gZjamrEaVSkqc0oBqcBbU1SUxI7bUdMJ6MmbU1irEyN15GgESoxGiXiD2OMIpEIgldgz++P1G02IGJqXHZ5v2Z23H3O2bPfg9/ZefhynvPMmqWHHnqowSKGJKWnp+uFF174n2IGAAAAADRf9/n7aFpcZ02L6yxjjIpKq5T7f2U6fKZCR76s0InSKpVdvqG9n32lvZ99ZX+fp4dFYe18FN6+tSLbt1JEYGtFBLZWp3at1MHXKj/vFqzi+I8mXci4cOGCamtrFRQU5HA8KChIx48fb9QYOTk52rRpk/r162fff+Ovf/2roqOj6/RdsmSJFi1aZH99c0UGAAAAAAB3ymKxqHuQr7oH+dqPXauu1fGSSh35skJHz1boky8rdLL0sq5W1+rzsiv6vOyK9tYzlpenhzr4WtU7xFeDIgM0KLK9+oT6NctVHE26kHE3DBs2TDabrVF9rVarrFbrDxwRAAAAAKC58m7pqf6d/NW/k7/9mDFGpZXXVXzhsk5duKzism/+PXXhis6WX1Xl9RrdqLXpy/Kr+rL8qj44Vmp/r8UieVos8vCwyNNikaeHRR6Wb1Z4LBnfW1Pj3O+P8026kBEYGChPT0+dP3/e4fj58+cVHBzspKgAAAAAALh7LBaLgvy8FeTnrSFd2tdpv1ZdqwtV11VScU2HTpfro1Nf6+Cpr1V+pVrGSDXGSLa621/eqG3cH/VdTZMuZHh5eSk2NlY7duywbwBqs9m0Y8cOzZ8//wf73MzMTGVmZqq2ltvkAAAAAACcy7ulp8LatVJYu1YaGBGgOcO7yGYzKr9arRqbTTabVGuMbDajWpuxP+/g655XHDi9kFFVVaWioiL76+LiYhUUFCggIECdO3fWokWLlJiYqIEDB2rQoEF65ZVXdPnyZT355JM/WExJSUlKSkqy75oKAAAAAEBT4uFhUUBrL2eH4RROL2Tk5eVp1KhR9tc3N9tMTExUVlaWpk2bpq+++krLli1TSUmJ+vfvr+zs7DobgAIAAAAAAPdnMcbUvZAGku7sPrYAAAAAAOD7uZPfv5vffVoaITMzU1FRUYqLi3N2KAAAAAAA4FtYkdEAVmQAAAAAAPDDY0UGAAAAAABwSxQyAAAAAACAy6CQAQAAAAAAXAaFjHqw2ScAAAAAAE0Tm302gM0+AQAAAAD44bHZJwAAAAAAcEsUMgAAAAAAgMugkAEAAAAAAFwGhQwAAAAAAOAyKGTUg7uWAAAAAADQNHHXkgZw1xIAAAAAAH543LUEAAAAAAC4JQoZAAAAAADAZVDIAAAAAAAALoNCBgAAAAAAcBkUMgAAAAAAgMugkFEPbr8KAAAAAEDTxO1XG8DtVwEAAAAA+OFx+1UAAAAAAOCWKGQAAAAAAACXQSEDAAAAAAC4DAoZAAAAAADAZVDIAAAAAAAALoNCBgAAAAAAcBkUMgAAAAAAgMugkFGPzMxMRUVFKS4uztmhAAAAAACAb7EYY4yzg2iqKioq5O/vry+++EJ+fn7ODgcAAAAAALd06dIlderUSeXl5Wrbtm2DfVvco5hcUmVlpSSpU6dOTo4EAAAAAAD3V1lZedtCBisyGmCz2XT27Fn5+vrKYrE4O5xGu1nJYiUJXBl5DHdAHsMdkMdwB+Qx3IU757IxRpWVlQoNDZWHR8O7YLAiowEeHh4KCwtzdhjfm5+fn9slN5of8hjugDyGOyCP4Q7IY7gLd83l263EuInNPgEAAAAAgMugkAEAAAAAAFwGhQw3ZLValZqaKqvV6uxQgO+NPIY7II/hDshjuAPyGO6CXP4Gm30CAAAAAACXwYoMAAAAAADgMihkAAAAAAAAl0EhAwAAAAAAuAwKGQAAAAAAwGVQyHAzmZmZioiIkLe3twYPHqyPPvrI2SEBt7R8+XJZLBaHR69evezt165dU1JSktq3b682bdroscce0/nz550YMSDt3btXEyZMUGhoqCwWi9555x2HdmOMli1bppCQEPn4+CghIUEnTpxw6PP1119r5syZ8vPzk7+/v5566ilVVVXdw1kAt8/lWbNm1fmOHjdunEMfchnOlJ6erri4OPn6+qpjx46aNGmSCgsLHfo05lzi9OnTeuSRR9SqVSt17NhRKSkpqqmpuZdTQTPXmFweOXJkne/kuXPnOvRpTrlMIcONbNq0SYsWLVJqaqr+/e9/KyYmRmPHjlVpaamzQwNuqU+fPjp37pz9sW/fPnvbwoULtWXLFr399tvas2ePzp49q8mTJzsxWkC6fPmyYmJilJmZWW/7qlWrtGbNGq1du1YHDhxQ69atNXbsWF27ds3eZ+bMmTp69Ki2b9+u999/X3v37tXTTz99r6YASLp9LkvSuHHjHL6jN2zY4NBOLsOZ9uzZo6SkJO3fv1/bt29XdXW1xowZo8uXL9v73O5cora2Vo888ohu3LihDz/8UOvXr1dWVpaWLVvmjCmhmWpMLkvSnDlzHL6TV61aZW9rdrls4DYGDRpkkpKS7K9ra2tNaGioSU9Pd2JUwK2lpqaamJiYetvKy8tNy5Ytzdtvv20/duzYMSPJ5Obm3qMIgYZJMps3b7a/ttlsJjg42Pz2t7+1HysvLzdWq9Vs2LDBGGPMp59+aiSZgwcP2vts27bNWCwW8+WXX96z2IFv+24uG2NMYmKimThx4i3fQy6jqSktLTWSzJ49e4wxjTuX+Oc//2k8PDxMSUmJvc/rr79u/Pz8zPXr1+/tBID/+G4uG2PMiBEjzLPPPnvL9zS3XGZFhpu4ceOG8vPzlZCQYD/m4eGhhIQE5ebmOjEyoGEnTpxQaGiounTpopkzZ+r06dOSpPz8fFVXVzvkdK9evdS5c2dyGk1WcXGxSkpKHPK2bdu2Gjx4sD1vc3Nz5e/vr4EDB9r7JCQkyMPDQwcOHLjnMQMN2b17tzp27KiePXvqmWeeUVlZmb2NXEZTU1FRIUkKCAiQ1LhzidzcXEVHRysoKMjeZ+zYsbp06ZKOHj16D6MH/uu7uXzTm2++qcDAQPXt21dLlizRlStX7G3NLZdbODsA3B0XLlxQbW2tQ+JKUlBQkI4fP+6kqICGDR48WFlZWerZs6fOnTunF154QQ8++KCOHDmikpISeXl5yd/f3+E9QUFBKikpcU7AwG3czM36votvtpWUlKhjx44O7S1atFBAQAC5jSZl3Lhxmjx5siIjI3Xy5En9+te/1vjx45WbmytPT09yGU2KzWbTggULNHToUPXt21eSGnUuUVJSUu939s024F6rL5clacaMGQoPD1doaKgOHz6s5557ToWFhfrHP/4hqfnlMoUMAE4zfvx4+/N+/fpp8ODBCg8P11tvvSUfHx8nRgYAePzxx+3Po6Oj1a9fP3Xt2lW7d+/W6NGjnRgZUFdSUpKOHDnisNcW4Ipulcvf3n8oOjpaISEhGj16tE6ePKmuXbve6zCdjktL3ERgYKA8PT3r7MJ8/vx5BQcHOykq4M74+/urR48eKioqUnBwsG7cuKHy8nKHPuQ0mrKbudnQd3FwcHCdTZhramr09ddfk9to0rp06aLAwEAVFRVJIpfRdMyfP1/vv/++du3apbCwMPvxxpxLBAcH1/udfbMNuJdulcv1GTx4sCQ5fCc3p1ymkOEmvLy8FBsbqx07dtiP2Ww27dixQ/Hx8U6MDGi8qqoqnTx5UiEhIYqNjVXLli0dcrqwsFCnT58mp9FkRUZGKjg42CFvL126pAMHDtjzNj4+XuXl5crPz7f32blzp2w2m/2kBGiKzpw5o7KyMoWEhEgil+F8xhjNnz9fmzdv1s6dOxUZGenQ3phzifj4eH3yyScORbnt27fLz89PUVFR92YiaPZul8v1KSgokCSH7+RmlcvO3m0Ud8/GjRuN1Wo1WVlZ5tNPPzVPP/208ff3d9i5FmhKkpOTze7du01xcbHJyckxCQkJJjAw0JSWlhpjjJk7d67p3Lmz2blzp8nLyzPx8fEmPj7eyVGjuausrDSHDh0yhw4dMpLMSy+9ZA4dOmQ+//xzY4wxGRkZxt/f37z77rvm8OHDZuLEiSYyMtJcvXrVPsa4cePMgAEDzIEDB8y+fftM9+7dzfTp0501JTRTDeVyZWWlWbx4scnNzTXFxcXmgw8+MPfff7/p3r27uXbtmn0MchnO9Mwzz5i2bdua3bt3m3PnztkfV65csfe53blETU2N6du3rxkzZowpKCgw2dnZpkOHDmbJkiXOmBKaqdvlclFRkUlLSzN5eXmmuLjYvPvuu6ZLly5m+PDh9jGaWy5TyHAzr776quncubPx8vIygwYNMvv373d2SMAtTZs2zYSEhBgvLy9z3333mWnTppmioiJ7+9WrV828efNMu3btTKtWrcyjjz5qzp0758SIAWN27dplJNV5JCYmGmO+uQXr0qVLTVBQkLFarWb06NGmsLDQYYyysjIzffp006ZNG+Pn52eefPJJU1lZ6YTZoDlrKJevXLlixowZYzp06GBatmxpwsPDzZw5c+r8cYRchjPVl7+SzLp16+x9GnMucerUKTN+/Hjj4+NjAgMDTXJysqmurr7Hs0FzdrtcPn36tBk+fLgJCAgwVqvVdOvWzaSkpJiKigqHcZpTLluMMeberf8AAAAAAAD4/tgjAwAAAAAAuAwKGQAAAAAAwGVQyAAAAAAAAC6DQgYAAAAAAHAZFDIAAAAAAIDLoJABAAAAAABcBoUMAAAAAADgMihkAACAH8ypU6dksVhUUFDg7FDsjh8/riFDhsjb21v9+/d3dji3tHv3blksFpWXlzs7FAAAmhQKGQAAuLFZs2bJYrEoIyPD4fg777wji8XipKicKzU1Va1bt1ZhYaF27Njh7HAAAMAdopABAICb8/b21sqVK3Xx4kVnh3LX3Lhx43u/9+TJkxo2bJjCw8PVvn37uxgVAAC4FyhkAADg5hISEhQcHKz09PRb9lm+fHmdyyxeeeUVRURE2F/PmjVLkyZN0osvvqigoCD5+/srLS1NNTU1SklJUUBAgMLCwrRu3bo64x8/flwPPPCAvL291bdvX+3Zs8eh/ciRIxo/frzatGmjoKAg/fSnP9WFCxfs7SNHjtT8+fO1YMECBQYGauzYsfXOw2azKS0tTWFhYbJarerfv7+ys7Pt7RaLRfn5+UpLS5PFYtHy5ctvOU56eroiIyPl4+OjmJgY/e1vf7O337zsY+vWrerXr5+8vb01ZMgQHTlyxGGcv//97+rTp4+sVqsiIiK0evVqh/br16/rueeeU6dOnWS1WtWtWzf95S9/ceiTn5+vgQMHqlWrVnrggQdUWFhob/v44481atQo+fr6ys/PT7GxscrLy6t3TgAAuAsKGQAAuDlPT0+9+OKLevXVV3XmzJn/aaydO3fq7Nmz2rt3r1566SWlpqbqRz/6kdq1a6cDBw5o7ty5+vnPf17nc1JSUpScnKxDhw4pPj5eEyZMUFlZmSSpvLxcDz30kAYMGKC8vDxlZ2fr/Pnzmjp1qsMY69evl5eXl3JycrR27dp64/v973+v1atX63e/+50OHz6ssWPH6sc//rFOnDghSTp37pz69Omj5ORknTt3TosXL653nPT0dL3xxhtau3atjh49qoULF+onP/lJnQJMSkqKVq9erYMHD6pDhw6aMGGCqqurJX1TgJg6daoef/xxffLJJ1q+fLmWLl2qrKws+/ufeOIJbdiwQWvWrNGxY8f0xz/+UW3atHH4jOeff16rV69WXl6eWrRoodmzZ9vbZs6cqbCwMB08eFD5+fn61a9+pZYtW97qvw8AAPdgAACA20pMTDQTJ040xhgzZMgQM3v2bGOMMZs3bzbfPg1ITU01MTExDu99+eWXTXh4uMNY4eHhpra21n6sZ8+e5sEHH7S/rqmpMa1btzYbNmwwxhhTXFxsJJmMjAx7n+rqahMWFmZWrlxpjDFmxYoVZsyYMQ6f/cUXXxhJprCw0BhjzIgRI8yAAQNuO9/Q0FDzm9/8xuFYXFycmTdvnv11TEyMSU1NveUY165dM61atTIffvihw/GnnnrKTJ8+3RhjzK5du4wks3HjRnt7WVmZ8fHxMZs2bTLGGDNjxgzz8MMPO4yRkpJioqKijDHGFBYWGklm+/bt9cZx8zM++OAD+7GtW7caSebq1avGGGN8fX1NVlbWLecCAIA7YkUGAADNxMqVK7V+/XodO3bse4/Rp08feXj89/QhKChI0dHR9teenp5q3769SktLHd4XHx9vf96iRQsNHDjQHsfHH3+sXbt2qU2bNvZHr169JH2zn8VNsbGxDcZ26dIlnT17VkOHDnU4PnTo0Duac1FRka5cuaKHH37YIaY33njDIZ7vzisgIEA9e/a0f9axY8fqjeXEiROqra1VQUGBPD09NWLEiAbj6devn/15SEiIJNl/vosWLdLPfvYzJSQkKCMjo058AAC4oxbODgAAANwbw4cP19ixY7VkyRLNmjXLoc3Dw0PGGIdjNy+R+LbvXrZgsVjqPWaz2RodV1VVlSZMmKCVK1fWabv5i7sktW7dutFj/i+qqqokSVu3btV9993n0Ga1Wu/a5/j4+DSq37d/vjfvNHPz57t8+XLNmDFDW7du1bZt25SamqqNGzfq0UcfvWtxAgDQ1LAiAwCAZiQjI0NbtmxRbm6uw/EOHTqopKTEoZhRUFBw1z53//799uc1NTXKz89X7969JUn333+/jh49qoiICHXr1s3hcSfFCz8/P4WGhionJ8fheE5OjqKioho9TlRUlKxWq06fPl0nnk6dOt1yXhcvXtRnn31mn1fv3r3rjaVHjx7y9PRUdHS0bDZbnX037lSPHj20cOFC/etf/9LkyZPr3WwVAAB3wooMAACakejoaM2cOVNr1qxxOD5y5Eh99dVXWrVqlaZMmaLs7Gxt27ZNfn5+d+VzMzMz1b17d/Xu3Vsvv/yyLl68aN+0MikpSX/60580ffp0/fKXv1RAQICKioq0ceNG/fnPf5anp2ejPyclJUWpqanq2rWr+vfvr3Xr1qmgoEBvvvlmo8fw9fXV4sWLtXDhQtlsNg0bNkwVFRXKycmRn5+fEhMT7X3T0tLUvn17BQUF6fnnn1dgYKAmTZokSUpOTlZcXJxWrFihadOmKTc3V3/4wx/02muvSZIiIiKUmJio2bNna82aNYqJidHnn3+u0tLSOhud1ufq1atKSUnRlClTFBkZqTNnzujgwYN67LHHGj1XAABcESsyAABoZtLS0upc+tG7d2+99tpryszMVExMjD766KNb3tHj+8jIyFBGRoZiYmK0b98+vffeewoMDJQk+yqK2tpajRkzRtHR0VqwYIH8/f0d9uNojF/84hdatGiRkpOTFR0drezsbL333nvq3r37HY2zYsUKLV26VOnp6erdu7fGjRunrVu3KjIyss68nn32WcXGxqqkpERbtmyRl5eXpG9Wmrz11lvauHGj+vbtq2XLliktLc3hsp7XX39dU6ZM0bx589SrVy/NmTNHly9fblSMnp6eKisr0xNPPKEePXpo6tSpGj9+vF544YU7misAAK7GYr57QSwAAAAatHv3bo0aNUoXL16Uv7+/s8MBAKBZYUUGAAAAAABwGRQyAAAAAACAy+DSEgAAAAAA4DJYkQEAAAAAAFwGhQwAAAAAAOAyKGQAAAAAAACXQSEDAAAAAAC4DAoZAAAAAADAZVDIAAAAAAAALoNCBgAAAAAAcBkUMgAAAAAAgMugkAEAAAAAAFzG/wOTgTYH9il8zgAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot([v[0] for v in loss_evolution])\n", "plt.yscale(\"log\")\n", "plt.xlabel(\"Number of epochs\")\n", "plt.ylabel(\"Loss function value\")" ] }, { "cell_type": "markdown", "id": "e53fa645", "metadata": {}, "source": [ "## References\n", "\n", "> [1] O. Kyriienko, A. E. Paine, and V. E. Elfving, “Solving nonlinear differential equations with differentiable quantum circuits”, [Physical Review A](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.052416) **103**, 052416 (2021).\n", "\n", "> [2] A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, “Data re-uploading for a universal quantum classifier”, [Quantum](https://quantum-journal.org/papers/q-2020-02-06-226/) **4**, 226 (2020).\n", "\n", "> [3] M. Schuld, R. Sweke, and J. J. Meyer, “Effect of data encoding on the expressive power of variational quantum-machine-learning models”, [Physical Review A]( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.032430) **103**, 032430 (2021).\n", "\n", "> [4] B. Y. Gan, D. Leykam, D. G. Angelakis, and D. G. Angelakis, “Fock State-enhanced Expressivity of Quantum Machine Learning Models”, in [Conference on Lasers andElectro-Optics](https://opg.optica.org/abstract.cfm?uri=CLEO_AT-2021-JW1A.73) (2021), paper JW1A.73. Optica Publishing Group, (2021).\n", "\n", "> [5] R. Fletcher, Practical methods of optimization. [John Wiley & Sons](https://onlinelibrary.wiley.com/doi/book/10.1002/9781118723203). (2013)." ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 5 }