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308 lines
121 KiB
Text
308 lines
121 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "12d4c736-839c-41c2-974e-e472550b1ec4",
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"metadata": {},
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"source": [
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"# Solutions\n",
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"\n",
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"All code required to solve the exercises is provided on this page, with the output included by default. To use the code interactively, click {fa}`rocket` --> {guilabel}`Live Code` on the top right corner of this screen and then wait until all cells are executed. You can also download this page as a notebook to work with on your personal computer.\n",
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"\n",
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"```{note}\n",
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"On this page we adopt the notation of lower-case $q$ used in other sections of this chapter, and do not use the upper-case convention to denote a random variable.\n",
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"```\n",
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"\n",
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"First we import a few packages and define the distributions of $q_1$ and $q_2$ as described on the previous pages."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "baaf5a2b-e837-46f1-bf9d-56bf9cec708c",
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"metadata": {
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"tags": []
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import scipy.stats as stats\n",
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"\n",
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"s = 0.198\n",
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"loc = 0.000\n",
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"scale = 98.058\n",
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"q_1 = stats.lognorm(s=s, loc=loc, scale=scale)\n",
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"q_2 = stats.lognorm(s=s, loc=loc, scale=scale)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a2724e09-9815-4f02-af62-2d595019c1b3",
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"metadata": {
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"tags": []
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},
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"source": [
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"## Part 1\n",
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"\n",
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"We can use Monte Carlo simulation to evaluate the problem easily. Remember, there are four essential steps to Monte Carlo Simulation:\n",
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"\n",
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"1. Define distributions for random variables (probability density over a domain) \n",
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"2. Generate random samples \n",
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"3. Do something with the samples (deterministic calculation) \n",
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"4. Evaluate the results: e.g., “empirical” PDF, CDF of samples, etc.\n",
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"\n",
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"The solution below also uses the method of moments on the MCS sample to compare the Normal and Lognormal parametric distributions, as well as includes the \"exact\" analytic solution for Parts 2 and 3.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "0b46ebdf-1a24-4de9-a426-286f3f2720a7",
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"metadata": {
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"tags": []
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The 99th percentile is index: 9900\n",
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"The 99th percentile from the sample is: 275.9 m^3/s.\n",
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"The inverse CDF of the Normal dist gives: 266.3 m^3/s.\n",
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"The inverse CDF of the LogNormal dist gives: 276.4 m^3/s.\n"
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]
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},
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{
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"data": {
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"image/png": 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",
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
|
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},
|
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"metadata": {},
|
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"output_type": "display_data"
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}
|
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],
|
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"source": [
|
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"N = 10000\n",
|
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"sample_1 = q_1.rvs(size=N)\n",
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"sample_2 = q_2.rvs(size=N)\n",
|
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"q = sample_1 + sample_2\n",
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"\n",
|
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"q_as_N = stats.norm(*stats.norm.fit(q))\n",
|
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"q_as_LN = stats.lognorm(*stats.lognorm.fit(q))\n",
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"\n",
|
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"plot_values = np.linspace(100,400,50)\n",
|
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"plt.hist(q, bins=plot_values,\n",
|
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" density=True,\n",
|
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" edgecolor='black')\n",
|
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"plt.plot(plot_values, q_as_N.pdf(plot_values),\n",
|
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" linewidth=2.5, label='Fit with N')\n",
|
|
"plt.plot(plot_values, q_as_LN.pdf(plot_values),\n",
|
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" linewidth=2.5, label='Fit with LN')\n",
|
|
"plt.plot(plot_values,\n",
|
|
" stats.norm.pdf(plot_values, loc=200, scale=np.sqrt(800)),\n",
|
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" ':', linewidth=2.5, label='Part 2 and 3')\n",
|
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"plt.xlabel('Discharge, $q$ [m$^3$/s]')\n",
|
|
"plt.ylabel('Density [--]')\n",
|
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"plt.legend()\n",
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"\n",
|
|
"get_index = int(np.floor(0.99*(N + 1)))\n",
|
|
"print(f'The 99th percentile is index: {get_index}')\n",
|
|
"q_percentile = np.sort(q)[get_index - 1]\n",
|
|
"print(f'The 99th percentile from the sample is: {q_percentile:.1f} m^3/s.')\n",
|
|
"print(f'The inverse CDF of the Normal dist gives: {q_as_N.ppf(0.99):.1f} m^3/s.')\n",
|
|
"print(f'The inverse CDF of the LogNormal dist gives: {q_as_LN.ppf(0.99):.1f} m^3/s.')\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "1fae3f87-afc0-4c3d-a6f3-f634a5422304",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "13773486-ddd6-4bc7-a012-b44fc1f67ed8",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Part 2 and 3\n",
|
|
"\n",
|
|
"Error propagation, as introduced in previous chapters, is a method that relies on a linearized approximation of the function of random variables and assumes that the random variables themselves are normally distributed. This results in the relatively simple equations for computing the moments of the function based on the moments of the random variables, applied below. In this case, since we are only using the moments of the lognormal variables in Part 2, the distribution is identical to that described by Part 3, so the solution is the same.\n",
|
|
"\n",
|
|
"The expectation is simply:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}(q(q_1,q_2))= q(\\mu_{q_1},\\mu_{q_2}) = \\mu_{q_1} + \\mu_{q_2}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"And, given independent random variables, the variance is:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sigma_q^2 = \\sigma_{q_1}^2 + \\sigma_{q_2}^2\n",
|
|
"$$\n",
|
|
"\n",
|
|
"The partial derivatives have been left out, as they are all +1, and the covariance term is zero. Plugging in values from the exercise:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\mathbb{E}(q)= 100 + 100 = 200\n",
|
|
"$$\n",
|
|
"\n",
|
|
"And the variance:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sigma_q^2 = 400 + 400 = 800\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Finally, we can compare the distibution to those found above (see figure). The two normal distributions are very similar to each other, which tells us that the asymettry of the lognormal distribution does not have a big influence on the distribution of $q$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "6da9930f-5409-4bee-a8ea-e4c505355425",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Part 4\n",
|
|
"\n",
|
|
"Here we will use the analytically computed value of the distribution of $q$ and compare the design value $q_{design}$ to the value found with a Monte Carlo Simulation using `scipy.stats.multivariate_norm` and a covariance matrix to generate a plot and compute values. The solution is more complicated that you were expected to provide, in order to illustrate various approaches and insights.\n",
|
|
"\n",
|
|
"First we find the variance of $q$, which adds an additional term now that the random variables are dependent:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sigma_q^2 = \\sigma_{q_1}^2 + \\sigma_{q_2}^2 + 2\\sigma_{q_1}\\sigma_{q_2}\\rho_{q_1,q_2}\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Resulting in:\n",
|
|
"\n",
|
|
"$$\n",
|
|
"\\sigma_q^2 = 400 + 400 + 2 \\cdot 20 \\cdot 20 \\rho_{q_1,q_2} = 800(1+\\rho_{q_1,q_2})\n",
|
|
"$$\n",
|
|
"\n",
|
|
"Design values are computed below, and as the plot illustrates, increasing correlation coefficient results in a higher likelihood of observing high values of $q$, and therefore the design value increases. The opposite is true with no dependence, as well as negative dependence.\n",
|
|
"\n",
|
|
"The code cell below does the following:\n",
|
|
"- define the analytically derived moments of $q$\n",
|
|
"- set up the expectation and covariance matrix for $q_1$ and $q_2$\n",
|
|
"- sample from the joint distribution of $q_1$ and $q_2$ and compute the corresponding sample of $q$\n",
|
|
"- evalue the empirical design value, $q_{design}$\n",
|
|
"- print and plot relevant results\n",
|
|
"\n",
|
|
"_Change the values in the cell below to explore the problem, especially $\\rho$ and $N$, which can have profound influences on the result: $q_{design}$ and the accuracy of the MCS, respectively._"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "5122d9c9-f239-4914-aa54-3e0cfef79f2f",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"The correlation coefficient is: 0.50\n",
|
|
"The mean value of q is: 200\n",
|
|
"The variance of q is: 1200.0\n",
|
|
"The design value for q~N(mu,sigma) is: 280.6 m^3/s\n",
|
|
"\n",
|
|
"For N = 10000 samples, the 99th percentile is index: 9900\n",
|
|
"The 99th percentile from the sample is: 279.3 m^3/s\n",
|
|
" ^ this is the 1% design value, q_design, from MCS\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
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+/fRT6ty5M3l5eVFQUBAlJCTQb7/9pnGOJavJzp8/b/AxfYYNG0YAqHfv3gbrNvW7IDL83hjz6aefUuvWrcnLy4vatGlDn3/+ud73A1qrySZPnkw9evSgpk2bkre3N9122200btw49So40Y4dO+iRRx6hoKAg8vb2platWtG4cePUjxv6nYm/96KiIvWxb7/9lrp06UI+Pj4UFRVFaWlp9MMPPxAAUiqVkn4PJ0+epMTERGrcuDEFBATQ4MGD6fvvvycAtHbtWo1zf/nlF3ryySepWbNm5OnpSeHh4fTAAw/QwoULJfxmGZNGIKrTN8sYcytiDpvdu3ejR48ezm4OYwbNmDEDU6dOxcmTJ52SJZw1bDxMxhhjzKHmzZsHAGjXrh1u3ryJTZs24YMPPsDw4cM5EGJOwcEQY4wxh/Lz80NWVhZOnDiBqqoqNG/eHJMmTVJnGmfM0XiYjDHGGGMNGi+tZ4wxxliDxsEQY4wxxho0DoYYY4wx1qDxBGoJamtrcfr0aQQEBEhOs88YY4wx5yIiXLlyBZGRkRoJPbVxMCTB6dOnER0d7exmMMYYY8wCxcXFRtM2cDAkgbj/TXFxMQIDA53cGsYYY4xJUVFRgejoaJP72HEwJIE4NBYYGMjBEGOMMVbPmJriwhOoGWOMMdagcTDEGGOMsQaNh8lsRKVS4ebNm85uBmtAPD09IZPJnN0Mxhir91w6GNqyZQtmz56NvXv3orS0FKtXr8Zjjz2mfvzq1auYPHky1qxZg7KyMsTExODVV1/F//3f/6nPqaqqwoQJE7Bs2TLcuHEDDz74IBYsWGCzzQCJCGfOnMHly5dtUh9j5mjSpAnCw8M55QNjjFnBpYOha9euoUuXLnj22WcxePBgncfHjRsHpVKJJUuWICYmBj/99BNGjx6NyMhIJCQkAABSUlLw7bffYvny5ZDL5Rg/fjwGDBiAvXv32uRbtRgINWvWDH5+fnxTYg5BRLh+/TrOnTsHAIiIiHByixhjrP5y6WDokUcewSOPPGLw8R07dmDEiBGIi4sDALz00kv4+OOPsWfPHiQkJKC8vByfffYZvv76azz00EMAgCVLliA6OhobNmxA//79rWqfSqVSB0Jyudyquhgzl6+vLwDg3LlzaNasGQ+ZMcaYher1BOr77rsP33zzDUpKSkBEUCqVOHbsmDrI2bt3L27evIl+/fqpnxMZGYmOHTti+/btBuutqqpCRUWFRtFHnCPk5+dnw1fFmHTivz2er8YYY5ar18HQBx98gA4dOkChUMDLywsPP/wwFixYgPvuuw/ArSEsLy8vNG3aVON5YWFhOHPmjMF63333XQQFBamLqezTPDTGnIX/7THGmPVcepjMlA8++AA7d+7EN998gxYtWmDLli0YPXo0IiIi1MNi+hCR0ZvIlClTkJqaqv5ZzGDJGGP2pqquxsEFC3D9+HH4tWqFTqNHQ+bl5exmMebW6m0wdOPGDbz22mtYvXo1/vOf/wAAOnfujAMHDuD999/HQw89hPDwcFRXV+PSpUsavUPnzp1Dr169DNbt7e0Nb29vu78Gxhira+fEiWiemYmuKpX62OkJE3AyNRX3zprlxJYx5t7q7TDZzZs3cfPmTZ1daGUyGWprawEA3bt3h6enJ9avX69+vLS0FIcOHTIaDLFbCgoKIAiCOm3AF198gSZNmji1TZYSBAFr1qxxahumTZuGsLAwl2gLcz07J07E3bNnI7xOIAQA4SoV7p49GzsnTnRSyxhzfy7dM3T16lX8+eef6p+Liopw4MABBAcHo3nz5ujTpw/S0tLg6+uLFi1aYPPmzfjqq6+QmZkJAAgKCsLzzz+P8ePHQy6XIzg4GBMmTECnTp2MDqM5g0qlQmFhIUpLSxEREYHY2FiHrA7avn07YmNj0bdvX6xbt87u12uojhw5goyMDKxevRr33nuvzjw21rCpqqvR/J+/W9rfUD0A1AKIzsyEavp0HjJjzA5cumdoz5496NatG7p16wYASE1NRbdu3fDmm28CAJYvX4677roLTz/9NDp06ICZM2finXfewahRo9R1ZGVl4bHHHsOTTz6J3r17w8/PD99++61LLUPOz89HTEwM4uPjMWzYMMTHxyMmJgb5+fl2v/bnn3+OsWPHYuvWrTh58qTdr9dQHT9+HACQkJCA8PBwHoZlGg4uWIBIlcrgH2QPAFEqFQ4uWODIZjHWYLh0MBQXFwci0ilffPEFACA8PByLFy9GSUkJbty4gd9//x2pqakak6N9fHzw4YcfoqysDNevX8e3337rUpOh8/PzkZSUhFOnTmkcLykpQVJSkl0DomvXrmHlypX4v//7PwwYMED9e7VUdXU1xowZg4iICPj4+CAmJgbvvvuu+vHMzEx06tQJ/v7+iI6OxujRo3H16lX14+Iw3HfffYe2bdvCz88PSUlJuHbtGr788kvExMSgadOmGDt2LFR1hhJiYmLw9ttvY9iwYWjcuDEiIyPx4YcfGm1rSUkJhgwZgqZNm0IulyMhIQEnTpxQP15QUIC7774b/v7+aNKkCXr37o2///7bYH0HDx7EAw88AF9fX8jlcrz00kvq1zZt2jQMHDgQAODh4WF08v7333+PNm3awNfXF/Hx8fjiiy80hiqZe7r+T7Bsq/MYY+Zx6WDI3alUKiQnJ4OIdB4Tj6WkpGjc+G1pxYoVaNu2Ldq2bYvhw4dj8eLFetsi1QcffIBvvvkGK1euxNGjR9WZwUUeHh744IMPcOjQIXz55ZfYtGkTJmrNg7h+/To++OADLF++HOvWrUNBQQESExPx/fff4/vvv8fXX3+NRYsWITc3V+N5s2fPRufOnbFv3z5MmTIF48aN05grpn2N+Ph4NG7cGFu2bMHWrVvRuHFjPPzww6iurkZNTQ0ee+wx9OnTB7/++it27NiBl156yWAQc/36dTz88MNo2rQpdu/ejVWrVmHDhg0YM2YMAGDChAlYvHgxgFtz1kpLS/XWU1xcjMTERDz66KM4cOAAXnjhBUyePFnS757Vb36tWtn0PMaYmYiZVF5eTgCovLxc4/iNGzfo8OHDdOPGDYvqVSqVBMBkUSqVNngVunr16kXZ2dlERHTz5k0KCQmh9evX67Tv0qVLRES0ePFiCgoKMljf2LFj6YEHHqDa2lpJ11+5ciXJ5XL1z4sXLyYA9Oeff6qPvfzyy+Tn50dXrlxRH+vfvz+9/PLL6p9btGhBDz/8sEbdQ4YMoUceeUT9MwBavXo1ERF99tln1LZtW412VlVVka+vL/34449UVlZGAKigoEDS61i0aBE1bdqUrl69qj72v//9jzw8POjMmTNERLR69Woy9XGbMmUKtW/fXqNdkyZN0ngPtFn7b5C5hpqqKiqRyUgFEOkpKoBOyWRUU1Xl7KYyVq8Yun9r454hJzLUQ2DpeeY4evQodu3ahaeeegoA0KhRIwwZMgSff/65xXWOHDkSBw4cQNu2bfHqq6/ip59+0nhcqVSib9++iIqKQkBAAJ555hmUlZXh2rVr6nP8/PzQqs6337CwMMTExKBx48Yax8Q9uUQ9e/bU+fnIkSN627l37178+eefCAgIQOPGjdG4cWMEBwejsrISx48fR3BwMEaOHIn+/ftj4MCBmDt3rtH34MiRI+jSpQv8/f3Vx3r37o3a2locPXrUyG9Mt557771XowdK+3Ux9yTz8sLJf3Kb1Wo9Jv5cnJrKk6cZsxMOhpxI6uaa9tiE87PPPkNNTQ2ioqLQqFEjNGrUCB999BHy8/Nx6dIli+q88847UVRUhLfffhs3btzAk08+iaSkJADA33//jUcffRQdO3ZEXl4e9u7di/nz5wPQ3ErC09NTo05BEPQeE9MnGGNoWKu2thbdu3fHgQMHNMqxY8cwbNgwAMDixYuxY8cO9OrVCytWrECbNm2wc+dOvfWRkSSe5mSIJiuGKFn9d++sWdiVloYzWos7SmUy7EpL4zxDjNmRSy+td3exsbFQKBTqvdW0CYIAhUKB2NhYm163pqYGX331FebMmaOxbxsADB48GEuXLlXPdzFXYGAghgwZgiFDhiApKQkPP/wwLl68iD179qCmpgZz5sxR54ZauXKl1a9FpB2o7Ny5E+3atdN77p133okVK1agWbNmCAwMNFinuJJxypQp6NmzJ3JycnDvvffqnNehQwd8+eWXuHbtmrp3aNu2bfDw8ECbNm0kv4YOHTro5B8yFIAx93TvrFlQTZ+OA1oZqKO4R4gxu+KeISeSyWSYO3cuAN0eBPHn7Oxsm6cB+O6773Dp0iU8//zz6Nixo0ZJSkrCZ599ZlG9WVlZWL58OX7//XccO3YMq1atQnh4OJo0aYJWrVqhpqYGH374If766y98/fXXWLhwoc1e07Zt2zBr1iwcO3YM8+fPx6pVq5CcnKz33KeffhohISFISEhAYWEhioqKsHnzZiQnJ+PUqVMoKirClClTsGPHDvz999/46aefcOzYMbRv395gfT4+PhgxYgQOHToEpVKJsWPH4r///S/CwsIkv4ZRo0bh+PHjSE1NxdGjR5GTk2P1Cj9W/8i8vNA1JQW9PvwQXVNSeGiMMQfgYMjJEhMTkZubi6ioKI3jCoUCubm5SExMtPk1P/vsMzz00EMICgrSeWzw4ME4cOAA9u3bZ3a9jRs3xnvvvYcePXrgrrvuwokTJ/D999/Dw8MDXbt2RWZmJt577z107NgRS5cu1Vh2b63x48dj79696NatG95++23MmTMH/fv313uun58ftmzZgubNmyMxMRHt27fHc889hxs3biAwMBB+fn74/fffMXjwYLRp0wYvvfQSxowZg5dfftlgfT/++CMuXryIu+66C0lJSXjwwQcxb948s15D8+bNkZeXh2+//RZdunTBwoULMWPGDLN/F4wxxswjEE9UMKmiogJBQUEoLy/XGFaprKxEUVERWrZsCR8fH6uu4awM1O4gJiYGKSkpSElJcXZTbK6goADx8fG4dOmS3q1QbPlvkDHG3I2h+7c2njPkImQyGeLi4pzdDMYYY6zB4WEyxhhjjDVo3DPE6r2622i4G3FLGsYYY/bDPUOMMcYYa9A4GGKMMcZYg8bBEGOMMcYaNA6GGGOMMdag8QRqxhhrAFTV1Tiotc0HZ7dm7BYOhhhjzM3tnDgRzTMz0VWlUh87PWECTqam8gawjIGHyVgDdP36dQwePBiBgYEQBAGXL192dpMYs5udEyfi7tmzEV4nEAKAcJUKd8+ejZ0TJzqpZYy5Dg6GXIVKBRQUAMuW3fqv1h8uWxIEwWgZOXKkza+5ZcsWDBw4EJGRkRAEQWd3dgB4//33ERYWhrCwMGRlZWk89vPPP6N79+5Q2eD38uWXX6KwsBDbt29HaWmp3j3aGHMHqupqNM/MBKD7x178OTozE6rqaoe2izFXw8NkriA/H0hOBk6d+veYQgHMnQvYYaPW0tJS9f+vWLECb775Jo4ePao+5uvra/NrXrt2DV26dMGzzz6LwYMH6zx+8OBBvPnmm/juu+9ARBgwYAD69u2Ljh074ubNmxg1ahQWLVpkk/3ajh8/jvbt26Njx45W18WYKzu4YIHG0Jg2DwBRKhUOLFiArm64tx9jUnHPkLPl5wNJSZqBEACUlNw6np9v80uGh4erS1BQEARB0DiWk5ODVq1awcvLC23btsXXX3+t8XxBEPDRRx/hkUcega+vL1q2bIlVq1YZveYjjzyC6dOnI9FAcHfkyBF07twZDzzwAB588EF07twZR44cAQDMnj0b999/P+666y5Jry8vLw933HEHvL29ERMTgzlz5qgfi4uLw5w5c7BlyxYIgmB0P7iZM2ciLCwMAQEBeP755zF58mR07dpVUhuY61CpVCgoKMCyZctQUFBgk97F+uL68eM2PY8xt0XMpPLycgJA5eXlGsdv3LhBhw8fphs3blhWcU0NkUJBBOgvgkAUHX3rPDtZvHgxBQUFqX/Oz88nT09Pmj9/Ph09epTmzJlDMpmMNm3apD4HAMnlcvrkk0/o6NGjNHXqVJLJZHT48GFJ1wRAq1ev1jh2+PBhatq0Kf3999904sQJatKkCR0+fJj++OMPat26NVVUVEiqe8+ePeTh4UFvvfUWHT16lBYvXky+vr60ePFiIiIqKyujF198kXr27EmlpaVUVlamt54VK1aQl5cXffLJJ/T777/T66+/TgEBAdSlSxdJ7XAUq/8Nurm8vDxSKBQEQF0UCgXl5eU5u2kOsWfWLMN/X+qUPbNmObupjNmFofu3Ng6GJLBbMKRUSvpDRUql1a/BEO1gqFevXvTiiy9qnPPEE0/Qo48+qv4ZAI0aNUrjnHvuuYf+7//+T9I19QVDREQfffQRtWnThtq0aUMfffQRERE9+OCDtHr1alq1ahXdcccd1LVrV9q8ebPBuocNG0Z9+/bVOJaWlkYdOnRQ/5ycnEx9+vQx2saePXvqfY0cDNUfeXl5JAiCRiAEgARBIEEQGkRA1BCCoZqqKtqflUXbxoyh/VlZVFNV5ewmMRciNRjiYTJnqjN3xybn2cCRI0fQu3dvjWO9e/dWD1mJevbsqfOz9jnmGjVqFI4ePYqjR49i1KhR+OKLLxAQEICePXvihRdewOrVq5GZmYmnnnoKVVVVZrX/jz/+MGt45MiRI3pfI6sfVCoVkpOT9W5yKx5LSUlx+yGzqpMnbXqeq9k5cSLO+vmh67hx6DVvHrqOG4ezfn68Qo6ZjYMhZ4qIsO15NiIIgsbPRKRzTMrzrHHhwgW89dZb+PDDD/Hzzz+jTZs2aN26NeLj43Hz5k0cO3ZM7/P0tVXfDZG5t8LCQpzSnodXBxGhuLgYhYWFDmyV4/m1amXT81wJpwxgtsTBkDPFxt5aNWYoiBAEIDr61nkO0r59e2zdulXj2Pbt29G+fXuNYzt37tT5uV27djZrR0pKCsaNGweFQgGVSoWbN2+qH6upqTH4jb5Dhw5629+mTRuzVqK1b99e72tk9UOpxN5UqefVV51Gj8ZpmQy1Bh6vBVAik6HT6NGS6lNVV+NAdja2jx2LA9nZTluSzykDmK3x0npnksluLZ9PSroV+NTtwRADpOzsW+c5SFpaGp588knceeedePDBB/Htt98iPz8fGzZs0Dhv1apV6NGjB+677z4sXboUu3btwmeffWaw3qtXr+LPP/9U/1xUVIQDBw4gODgYzZs31zh3/fr1+OOPP/DVV18BAO6++278/vvv+OGHH1BcXAyZTIa2bdvqvc748eNx11134e2338aQIUOwY8cOzJs3DwsWLDDr95CcnIwRI0ZovMbffvsNt912m1n1MOeIkNibKp6nUqlQWFiI0tJSREREIDY21iZpHJxN5uWFk6mpCJ89G7XQDBzEAKk4NRVRErblcKUs1pwygNmc3WcvuQG7TaAW5eXpriqLjr513M60J1ATES1YsIBuu+028vT0pDZt2tBXX32l8TgAmj9/PvXt25e8vb2pRYsWtGzZMqPXUSqVOhNZAdCIESM0zrt+/Tq1adOG9u/fr3H8k08+obCwMGrevDl99913Rq+Vm5tLHTp0IE9PT2revDnNnj1b43EpE6iJiN555x0KCQmhxo0b04gRI2jixIk8gbqeqKmpIYVCoXcCNf6ZRB0dHU01NTUus+KspqaGlEol5eTkkFKppBobriLdNm4cnRMEjb8xp2Qy2pGWJun5O9LSSAWQSmvitXhMaj22sm3MGEkTw7eNGePQdjHXw6vJbMjuwRDRreXzSiVRTs6t/9pxOb21YGA1mLtLT0/nYKgeEVeTaQdEdVeTucqKM3sFZDVVVbQpPp7KtAKh84JA21JTjT5PXKG1Z9YsKhEEnUCobkB0SiYzuYrLlqu+9mdlSQqG9mdlWXwN5h44GLIhhwRD9QgHQ66jof4blEpfkBEdHU15eXnq3iN9PUfavUf2bqM9ArIdaWl0QSsIktKjsyMtjUpkMmlpPyQuz9dXZ4kZPVPaaqqqqEQmszpAY+6Pl9Yzxhq8xMREnDhxAkqlEjk5OVAqlSgqKkJiYqJLrDizdQoAcYJzQbduuGf2bAQbWElpaJKxoRVaUrScNEnvCi57rPoS50IB0JkcXnculEzCXCjGAPCcISm4Z4i5Kv43aLmcnByDvUJ1S05Ojt3aYGgunXZRSki8ammPjjiUZKq3xVTR19tk7x4cfa/ZnLlQzP1xzxBjjBlh7ooze7BVCgBrenTEfckOLliASJXK4nwr+nqbTNUprvo6aOZqT9G9s2Yh7Pp1HMjKwvYxY3AgKwvh1687fHUbq/9cOhjasmULBg4ciMjISAiCgDVr1uicc+TIEQwaNAhBQUEICAjAvffei5N1sqlWVVVh7NixCAkJgb+/PwYNGmS0a9wSxEn9mJPwvz3LxcbGQqFQGEwWKggCoqOjEWvHPF+2CMiM5dyRQky4aIvNWrWDG0dsFCvz8kLXlBT0+vBDdE1J4aExZhGXDoauXbuGLl26YN68eXofP378OO677z60a9cOBQUF+OWXX/DGG2/Ax8dHfU5KSgpWr16N5cuXY+vWrbh69SoGDBhgkzT8np6eAIDr169bXRdjlhD/7Yn/Fpl0MpkMc+fOBaCbPV38OTs72675hmwRkFnao6OdcNGWWajF4MadM2Az9yJQPflqKQgCVq9ejccee0x97KmnnoKnpye+/vprvc8pLy9HaGgovv76awwZMgQAcPr0aURHR+P7779H//79JV27oqICQUFBKC8vR2BgoMZjpaWluHz5Mpo1awY/Pz+bbknBmCFEhOvXr+PcuXNo0qSJXYdy3F1+fj6Sk5M1eoyjo6ORnZ2NxMREh1w/KSkJgGZPn/i3JDc312g7to8di14GvjAaIl5lR2oqes2ZA+BWD9NZPz+EGwisagEI/xRT9s6ahe5paai+ehXlgYGQExmss1QmQ/j169yjw+zC2P27rnqbgbq2thb/+9//MHHiRPTv3x/79+9Hy5YtMWXKFHXAtHfvXty8eRP9+vVTPy8yMhIdO3bE9u3bDQZDVVVVGhuBVlRUGGxHeHg4AODcuXM2eFWMmadJkybqf4PMMomJiUhISHBaBurExETk5ubqBGQKhUJSQGZJr4oY0MTMnYudMhnunTXLZLZqqYEQAERMmoSCVavQZt8+RBr4vm1uBmzG7Kne9gydOXMGERER8PPzw/Tp0xEfH49169bhtddeg1KpRJ8+fZCTk4Nnn31WZ4fzfv36oWXLlvj444/1XmvatGnIyMjQOW4sstTeP4sxe/P09HSLLSPYLZZuCWKqR6cugmZAIwYku9LS1JOOxW03IutMJdB+nili8AQjzyuRyVDshK08WMMitWeo3gZDp0+fRlRUFIYOHYqcnBz1eYMGDYK/vz+WLVtmMBjq27cvWrVqhYULF+q9lr6eoejoaJO/TMYYcwZxNRmgf/+xawAaQ39gom+oSlVdjYMLFuDq0aNo9/HHkBOZFQwBhgOoWgBlgoCgigp4NW5ssh6xLdePH4dfq1boNHo0D6kxyaQGQy49gdqYkJAQNGrUCB06dNA43r59e/VqsvDwcFRXV+PSpUsa55w7dw5hYWEG6/b29kZgYKBGYYwxV3XvrFnYlZaGM1o9SaUyGTbHxyMAhntoxBVgWx54QL0TvbhC6+bRowixIBCCieuFEuHwp5+arGPnxIk46+eHruPGode8eeg6bhzO+vlZlKiRMWPqbTDk5eWFu+66C0ePHtU4fuzYMbRo0QIA0L17d3h6emL9+vXqx0tLS3Ho0CH06tXLoe1ljDF7MpRzx/uOOyQ9P37bNo1gY/v48YhTKu3WXlPL6e2RuZoxQ1x6AvXVq1fx559/qn8uKirCgQMHEBwcjObNmyMtLQ1DhgzB/fffr54z9O2336KgoAAAEBQUhOeffx7jx4+HXC5HcHAwJkyYgE6dOuGhhx5y0qtijDH7EHt06jJ3gnW4SoXwf4bc7Lk21li7jOVO8sCtobbozEyopk/nITNmG3bNg20lQ6nqR4wYoT7ns88+o9tvv518fHyoS5cutGbNGo06bty4QWPGjKHg4GDy9fWlAQMG0MmTJ81qh9R03owxZkhNTQ0plUrKyckhpVJp9w1g1de1cpsNS0utFVtw8K70zFak3r9dumcoLi7OZIbd5557Ds8995zBx318fPDhhx/iww8/tHXzGGMuxNLVWI6gL5eRQqHA3Llz7Z7LyNiSeXsRV5PpW6IPmF5O74jM1YzVVW/nDDHGmCg/Px8xMTGIj4/HsGHDEB8fj5iYGOTn5zu7aeqkitrbAJWUlCApKckhbTQ0wdpeygBsi47GZa3jpTKZxjJ+QzhzNXO0erO03pmkLs1jjDmeGGxo/ymTmsFZpK9nCYBVvU0qlQoxMTEG90MUBAEKhQJFRUUO6cUSl6lfys1F/LZtdrvORUFAcJ3346Ig4Je4ONy/bp2kOT5SsmFz5momheT7twOG7Oo9njPEmGuqqakhhUKhd24hABIEgaKjo03Oz8nLy9OpRy6Xk1wu1zimUCgoLy9PcvsMzXvULhs2bLD2V2GWmqoqKhEEg/N6bD1fSPXPsW2pqZLbuCMtjVT/PFe7LhVAO9LS7PJ72Z+VRdvGjKH9WVlG5zWx+kHq/ZuDIQk4GGLMNZkTbBiavJyXl0eCIEiqRxAEEgRBckCUk5Mjqd7g4GCNOh0x2XpTfLxdgiBjAdZNgLaNGye5jTvS0qhEJtOo45RMZpdASN+1Sux0LeY4HAzZEAdDjLkmc4KNuj9HRUVRRkYGLVmyhEJCQiTVYaq3SV8AIzVYE+vNy8vT20tlbo+UFNvGjHHI6jHtYm6vjiN6a5zRC8UcQ+r9m+cMScBzhhhzTQUFBYiPj3fKtZVKJeLi4gAYXi02ZMgQZGVloba21kAt/xIEAcHBwSgrK9P7GCB9/pMUB7Kz0XXcOJvUBUDy/mWuNt+H5ye5N7ffjoMxxmJjY6FQKNTBgiOVlpYCMLxa7NSpU5gzZ46kQAgAiEhvICQ+BgApKSlQaWVkNkSlUqGgoADLli1DQUGBzvM6jR6N0zIZpLRO7KIyRuo7IG7/cXDBAonPsK+DCxYg0sgmt67WXmYfHAwxxuotmUyGuXPnAoDDA6KIiAioVCokJyebzIdmC0SE4uJiFBYWmjxXSqoBMf8QAJ2ASPvVmPPqpJ7rKjmCOKcRAzgYYozVc4mJicjNzUVUVJTGcblcbpfrCYKA6OhoxMbGorCw0OCyeXsRe6QMMSev0b2zZmHLXXfpBEPaYaUHzAuIpHCVHEGc04gBnGdIEp4zxJguV8v4rN0elUpl8z0ItefuLFu2DMOGDbPpNUypO1dJm7l5jcTNUAHp34wNZbGuBVDq4QGf2loEw/CwGQE47eGB8Bs3LJqDI+ZKun78OPxatUKn0aOtmssjZc5QmSDg2KhR8G/TxurrMcfiPEM2xKvJGNPkqBVP5qq7ouvHH380e6VY3aIvz1B0dLTGazRntZi1RUrOJKntUSqVFu9ZZmzVldTl+pvi4y16f+21/N3YajLtVXK83L5+cYu9yRhjrsdQxmdxGMaWK57MbZf2ii5zeXh44IsvvlAPgwHGM1CLE7hLSkrsOm9I7JHKzs422vtmagit7nkHFyxAV4mTsevS13tSKpOhODUV3jduAEqlyTq877jD7OvW7cWqK1ylQvjs2dgJmNzmw5B7Z83CTgDNMzMRWed3oq93yxbXYy7IIaFZPcc9Q4zdYquMz7ZmTuJEU0WpVJp9bUuu4+3tLflc7R4pQ6T2DL3//vu0uF8/m2SV3hQfr879Y81u88byCZnqxVLhVjJGa3MQiW0oHDWKzguC3a/H7I+TLtoQB0OM3WLOMIyjmArQzC1Tp041O/NzRkaGWdcwJ3CbOnUq1dTUSMpKLf4upNTfx4pAyFBQUFNVRReMbPNRC9AFQdAJIkwNf1kaZBkKsEwlcrQmqGOuhYMhG+JgiLFbpGZ8zsnJcVib7DlvR+o8KKm/F0uKUqk0a46W2EtmKiDyAOgkdOfJWFLEoEBKMHReKxiSkv1ZarbsbWPGaNSrL8BS3nWXyXlHllyPuSap929eWs8YkywiIsKm59mC1HkyltC3HF0fe77eb7/9FoMHD5a0VB74N9VAcHCw0XprASTX+X/txwjA9xLbWP755ziQnY0Dc+dCTmRwJZkAIIRIncBQVV2N5pmZAHTnIok/R2dmwrt5c0ntEJe/i/OLwrXmRIWrVOizezci9By/e/Zs7Jw4UaMeqddjbsBBwVm9xj1DjN1iahjGGXOGHLGiKzQ0lKqMzA+pqamh0NBQu7dDyu+7pqbGrGG7x//pIarb4/H3P8enmtlDVCYIks4rHDWKiKQPR+2ZNUvynCFT84ukDPk5ao4Ssz/uGWKM2ZyxjM9SVzzZmjlbcgiCALlcDoVCYdY1zp8/j6ioKIM9RDKZDE8//bRZddoCkWZW6vz8fLRo0QLp6emS61gNIAZAHICh//y35T+PZeBWxGTw+lo/NyFjZ/+r88KF2DlxouSszlUnTxrMli3+XJyaCpmXl8ntNQz9K6m77Yax7Nza12PugYMhxphZDGV8VigUTllWXzdAM4WIsGjRIpw4cQJKpRI5OTmYOnWqpOdeuHDB6JDZgAEDJLfZ1kpLS9UpD0pKSsx+fi2AzQCW//NfABB/o8aSJxrKVG0qJAoAcPfs2aj67TdJ7avavx8+kZHYmZqKM1qB9mVBwOb4eNw1fToA67fNEJ9/76xZ2JWWpnO9UpkMu9LSeFm9m+EM1BJwBmrGdLlaBurc3Fw89dRTRjcyDQwMxPnz5+FV5xt9QUEB4uPjJV1DO4NzXRs3brR5xmupNmzYgJEjR9psa5A+AApsUpNhYsZqAUB4ba3eb+baAddpQcCJlBRUHTiALkol6s6KOi2T4WRqKnwiI9F13DiL23UgKwtdU1LUP9s64zVzLKn3b066yBiziEwmM7gthDOEhISY3NG9oqICCoUCCxcuVPdgmZM4se6wlLg3mRgMfvPNNzZ7Lebw9vbGgQMHrA6EhgwZgtDQUMybNw+OmP7uASCqthbK+HiEK5U623zoeyciiBCRlaX3MXUyxHHjcFomM7i9hr4eLeCf4EwmQ6fRozWOy7y8NIIj5p4sCoYs+dD37dsXvr6+llyOMcYMEnuo8vLyJJ1//vx5jUzZMpkMWVlZeOKJJyRfc/78+Rg8eDAuXrxoUZtlMpnJwE2qqqoqTJgwwep6tm/fjueeew4AYL/1ebq877gDW65exX27d+sEL9pBi4B/gxl9Q3S1AFp88AFOJCcjPDNTJ8Cq/ed5+o4Dt+YBRXGvT4Nk0TCZh4d5U40EQcAff/yB2267zdxLuQQeJmPMNVm6BUfd4a61a9davY2HVHK5HCtWrEBsbCy2b9+O1atX44MPPrD7daUKCQnBhQsX4AHgBIAo2H9iaWGrVuj9zzwdW13rQFYWKk+f1tleo0Qmwx933ok2+/ZpHD8tk+Ho/ffD+447eCjMzUi9f1scDJ05cwbNmjWTdH5AQAB++eUXDoYYYzZjaI80c2RkZGDatGlW1WGOVatWISkpCcCtHq3w8HBcuHDBIdc21+MAcv/5f3sHRIaGriy1fcwY9PrwQ4Pzfeoer/rtN7QtKEBknX8D4vwjniRd/9l1ztCIESPMGvIaPnw4BxGMMYtUV1djwYIFOH78OFq1aoXRo0dDJpMhOTnZ6iBm7ty5DguEgFs9L6LCwkKXDYSAW0vuk3BrVVm0jevWDn5sGQgB/yZDNDTfRzy+c+JE9NGzsSxvxtrw8GoyCbhniDHH0F6h9t133yE7O1tjfo1MJkNSUhJWrFjhxJZaZvDgwRg8eDAiIiJcbojMEA8AsQAeBPCGk9tiijgJOvz6dZPDXKrqapz18zM40boWQJkg4NioUfBv04aHzuopuw6T1XXjxg0QEfz8/AAAf//9N1avXo0OHTqgX79+1lTtMjgYYsy29C3Ld+TcHUEQEBwcjLKyMrtfy114ADgLQA79PTnGhrrE3EP2HG4TJ0HrywGkb7js4IIFZi3B56Gz+kny/dvaVNd9+/aljz76iIiILl26RGFhYaRQKMjHx4cWLFhgbfUugbfjYMx29G06KpfLHbqFhSAIZu80z+XWFh0qGN7SwljZFxBg9nPMKae0NlsVGdywtWtXs+qvu3GsqKaqivZnZdG2MWNof1YWb8/hghy2a71cLqdDhw4REdEnn3xCnTt3JpVKRStXrqR27dpZW71L4GCIMdsQd1R35g09NDSUli9fTm+++abTg4v6WPTtZeboosKtgGbPrFlGA5EdaWnqIEb7+ZYEdHX3JDMUZOkLyJjzSL1/Wz1M5ufnh99//x3NmzfHk08+iTvuuAPp6ekoLi5G27Ztcf36dWuqdwk8TMaY9VQqFWJiYhwyDCby9/dHYmIivv/+e40hMQ8PD9TWau86ZZxcLsfFixcdOuHaVYnziCIAhAHIduC1xXdtc3y80aXwUuYEifmGzB2+U8bHqyde68tXxNt1uA6HzRnq3LkzXnjhBTz++OPo2LEj1q1bh549e2Lv3r34z3/+gzNnzlhTvUvgYIi5M0dtq2HOtheuaOXKlepVbI4M6FydPXMSbWnVCh2PH9fYduOCIEAAIK+7FN7DA0f79NEIjqTOCRIDGHPafhFAEwPPMWcSN7M/h80ZWrVqFXl6epKHhwf17dtXfXzGjBn08MMPW1u9S+BhMuau9M3fUSgUlJeXZ/Nr5eTkOH2Ix5qiVCqJiGjlypUOneNUH4o4l0h7OMrSUnc4qu68nE3x8Xqvoz3kVSKTkbJbN0nXUnbrpjPcZYuyPyvL5p8hZj6p92+r9yZLSkrCfffdh9LSUnTp0kV9/MEHH8Tjjz9ubfWMMTsxlLSwpKREY7sKW4mIsO2OV76+vrhx44ZN6zRG3Bl+yJAhPFSmZTVsl5NI7Kn5+9VX1VtjdE1JUQ97Abo9Mtqr2MJVKoTv3y/pek2eeQYniovhlZWFEBPvay2Ay4KAYAnv//V/smqz+sHiXs3XXnsNu3btAgCEh4ejW7duGtt03H333WjXrp1VjduyZQsGDhyIyMhICIKANWvWGDz35ZdfhiAIyM7O1jheVVWFsWPHIiQkBP7+/hg0aBB3cbMGT6VSGUxaKB5LSUmxyf5ZKpUKBQUFKCkp0Ug6aK2JEyciKioKgmDrlH36NWvWzCaJHt3VagAxAN6ysh5xDk+b7GwUdOuGA9nZ6qXxkQbm/+irAwBq8G9wpa0Wt7bnuH7yJO7NzNQJcLTfZbGeXyRuTiwmfmT1g8XBUGlpKQYMGICIiAi89NJL+N///oeqqipbtg3Xrl1Dly5dMG/ePKPnrVmzBj///DMiIyN1HktJScHq1auxfPlybN26FVevXsWAAQNstkkiY/VRYWGh0S8FRP/uzl6XGNgsW7YMBQUFJj9H+fn5iImJQXx8PIYPH24y43Ljxo01fpbL5WjatKneczMyMlBZWQkickhAtGjRIv4iZUItgE0WPlc7+AghQtyBA+g6bhzO+vnh8pdfmlWfB25tsSBuzKrdTgD4OzkZMf8kvjTV21Qqk2FXWhruX7cOp2Uyk0FWp9GjzWovczJrxuJqa2tpy5YtlJaWRm3btqXGjRvT448/TosXL6bz589bU7UOALR69Wqd46dOnaKoqCg6dOgQtWjRgrLqjNNevnyZPD09afny5epjJSUl5OHhQevWrZN8bZ4zxNyN1Pk7OTk56udInV9UU1NDSqWSUlJSJM858fDw0Pg5ODiYMjIyqKamhmpqaig9PV3v88Rl+jyHx3WKB24tvbfV/CGC5UvhDRUxJ9H+rCxJ5xc89pjG0n1jS/a1cxEx53JYnqG6Dh8+TO+99x716tWLvLy8KDY2lmbPnk2nTp2yum5ANxhSqVQUHx9P2dnZREQ6wdDGjRsJAF28eFHjeZ07d6Y333zT4LUqKyupvLxcXYqLiyX9MhmrL5RKpaQbmzhp2FB+IDGBoRgQ6QuYLCl16121ahXJZDKj5wcGBtLEiRMpICDA6cEAF9tPqKZ/6qqB5UGR2J5N8fHqwGbbmDGSnrttzBidz5C+PEOGEj8y53FKMFTXuXPn6NNPP6VBgwbR7Nmzra4P0A2GZsyYQX379qXa2loi0g2Gli5dSl5eXjp19e3bl1566SWD1zL0LZSDIeYuampqSKFQGEyAKAgCRUdHq3tmjAU44rmrVq2yaUJFQRC4x6ceF3slZ7Smh6juKjUiMqtnSF9yR85A7frsFgxdvHiRysrKiOhWwJObm0sHDx60rJVmADSDoT179lBYWBiVlJSoj0kNhh566CF6+eWXDV6Le4ZYQyD29mgHMNq9PVJ7kUJDQ51+A+biWsUDoD4APQVQPECXYfvgyJIiLnuvqaqiEpnMYA+WCqCbWsc4y3T9IjUYMmsC9aeffooePXqge/fu+Oijj/D4449j48aNeOqpp7Bo0SJzqrJaYWEhzp07h+bNm6NRo0Zo1KgR/v77b4wfPx4xMTEAbq1yq66uxqVLlzSee+7cOYSFhRms29vbG4GBgRqFMXeTmJiI3NxcREVFaRxXKBQay+pLS0sl1Xf+/Hmbt5HVb7UANgNY/s9/7blRqznEZe8yLy+cTE0FoH+StQDdNoerVLh79mxsT03FgexsbB87Vr3ijdVj5kRYnTt3phs3blBZWRn5+/vTuXPn1JFXly5dLI7cpAA0e4YuXLhABw8e1CiRkZE0adIk+v3334no3wnUK1asUD/v9OnTPIGasTrECc85OTmkVCqppqZG43GpPUNcuBgrfeD8HiGxaCdE1Df/5yYMz3niHqP6wy5JF2UyGXx8fODj44Pbb78doaGhAIDAwEC7LG29evUq/vzzT/XPRUVFOHDgAIKDg9G8eXPI5XKN8z09PREeHo62bdsCAIKCgvD8889j/PjxkMvlCA4OxoQJE9CpUyc89NBDNm8vY/WRTCZDnJHcKbGxsVAoFCgpKQER6TwuCAJCQkK4Z4gZZduUm4aJ/0L13ZHErTK0l73fO2sWVNOn48CCBbh+/DhunjqFPkby2unbzyxcpUL47NnY+U99rH4xq9eyUaNGqKysBABs3rxZffzKlSu2bdU/9uzZg27duqFbt24AgNTUVHTr1g1vvvmm5DqysrLw2GOP4cknn0Tv3r3h5+eHb7/91i57LzHmjmQyGebOnQsAOl96xJ/nz58PhUJh9pciHx8f2zSSuTxpg622Yyi3UHFqqt49w2ReXuiakoJeH34IT4XC7OuJN9PozEweMquPzOluunLlinrlVl1nz56lvXv3mtV1VZ/wMBlj+pfNR0dHayyr1zchWywpKSmUnp7OK8QaaLFH/iHtck4QaNu4cbQtNZXOC4LGY1KWvYurwzb17m3TYTjmPFLv31bvWt8Q8K71jN1iaof7/Px8nV3do6Oj1dvk6NsLjTUcjwPI/ef/6w5LiP8iLJlscRnAga5d0WTECHQaPRq7p05F88xMRNbJjn5eEPBHSgp6ZWYarGfnxIk6zyML27R9zBj0+vBDC57JbE3q/dvqjVoBoLKyEr/++ivOnTuH2lrNzslBgwbZ4hKMMRdgan5RYmIiEhISdAImAIiJieFAqIFbDf0bul4AEALzgg/653lBV64g7p9tXHZOnIi7Z8/WOVdOBHlWFnY2aqR3Ps/28ePR00CgZElAxPuS1T9W9wytW7cOzzzzjN49hwRBcIs9wLhniDHrFBQUID4+3tnNYC7CA0Asbk2qLv3nZ0v2NFPGxyN+061nirvahxvYzFWcPB1+/brGnKHtqam4OyvLYM+AOcGQoWsw55F6/7Y67cOYMWPwxBNPoLS0FLW1tRrFHQIhxpjlxI1d8/LynN0U5kK08w8ZzvpmnGfr1upcP1uHDDG6q70HgCiVCgcXLFAf2zlxIu41EggB5gVCgOEJ2sy1WT1Mdu7cOaSmphpNYsgYa3j0zR9iTB9LV5r1XLQI5q4LFhMuqqqr0dzIHCJtpnqIzshkOJmaysvq6ymre4aSkpJQUFBgg6YwxtxFfn4+kpKSJAdCgiAgKCjIzq1irqoQQDF0l8ObYskNTJzPc3DBAqM9SdoE/DvRW1T7T1HGxyPs+nUOhOoxq+cMXb9+HU888QRCQ0PRqVMneHp6ajz+6quvWtVAV8BzhhiTrrq6GlFRUXrnETJmiLGVZuZMYDZ0vvZ8nu1jx6LXvHmWNfYfJTIZirk3yKU5bDVZTk4OfvzxR/j6+qKgoEAj6ZogCG4RDDHGDKu73P6PP/7Ahx9+yIEQM5uhlWa1gFlDYfoCIfEbf3FqKqL+mc9jzYqvzZ06Iei559Bp9Gh1fax+szoYmjp1Kt566y1MnjwZHh6usg0fY8wReF4Qs6XVANZCc6XZwx06YPLhw1bXrR0kdRo9GqcnTDC4+syYoOeeQ9eUFKiqq3EgOxvXjx+HX6tW6DR6NE+erqesHiYLDg7G7t270cqN8yrwMBljt2j3Ak2bNo1zBzG76gOgwAb16Fv2XjcvkZShubp16EvueJonUbscqfdvq4OhcePGITQ0FK+99po11bg0DoZYQ2EswzT3AjFn8ABwAkAUbLDiB8CBrCx0TUlR/2wo8zRpXU+c3L0rLQ0A9AZRdc/hgMg1OGzOkEqlwqxZs/Djjz+ic+fOOhOoM81YusgYcx59wY5CoVBv0spbaTBnqAWQjFuTq2th3eRq4N+l9SLtHev9WrXC9eJitM3MhLzOeR4AygQBtSoVYv75TGgHZx7/tDE6MxOq6dN5yKwesbpnyFhWWUEQsGmTJXlFXQv3DDF3Jy6F1/5zIAgCiAhyuRxlZWVOah1jt1abaU+uroH53+g3P/YY7luxwmigUnD33eize7dOoFWLW8GXlABMuweKOYfDeoaUSqW1VTDG7MjU5qoqlQrJycl6e33EYxwIMWfTN7l6G4DeAG7z8sKsmzchJzIZqPRZswan/fwMzu3ZnpqKPrt3632uB3RzDRmi3QPFXJtNNmpljLkmY0NfiYmJAIDCwkKeB8TqBXEbj7o2A0B1NULMqCdcpUL47NnYCWgERKrqarTOzjYaUEkdluPNWusXi+aj/frrrzq70xvz22+/oaamxpJLMcYsZCgLdElJCZKSkpCfnw8AKC21dDMExlxDhJnnize+6MxMqKqr1ccPLliAUIkzRwzdAQm35hZ1Gj3azFYxZ7IoGOrWrZtZ3eY9e/bEyZMnLbkUY8wCUoa+UlJSoFKpEBFh7q3EOD8/P5vWx5gploTz+jZuNWdoS9/2HKKmRNg9daoFrWLOYtEwGRHhjTfekPxHr7pO5M0Ysz9TQ19EhOLiYhQWFiI2NhYKhQIlJSV6gydBEBAcHIyLFy+qn1v3MSJCYGAgKioqANzaoocxRxL3NlPAutVlUoe2zgsCPIgQrOcxMUjiFWX1i0XB0P3334+jR49KPr9nz57w9fW15FKMMQtIHfoqLS2FTCbD3LlzkZSUpA5u6iIiLFq0CAB05h/5+/vj6tWr6kCIMWcQl9/nwfzl9nUDIFNZqcVPxsH778cDm7VnL/1L7HU6sGABryirJywKhniXesZcm9ShL/G8xMRE5Obm4qWXXtIZApfL5epzEhIS8M4772Du3Lm4ePEirl69atuGM2ah1QAGA1gESJpMXQvgjEymMbdH5uWFk6mpCJ89WyenkWjzXXfBp1MnwEgwJOIVZfUHbybGmBsSh77qbpysLSQkBOvXr8cbb7yBjRs3oqamRu9cwIsXL6onXK9duxbTpk1TD5kx5kpWAwgD8ACAtwCsxK3eHH2TnT0AeNfW6sztuXfWLOxKS8MZmeb2sOcFATvGjUPcrl2Sh9N4RVn9YXXSxYaAky6y+khcTQbAJpmjg4OD4eHhwTvSs3rlcRjuLTK2fYaquhoH62SlrrsJq6q6Gmf9/AwOp+nbB405h8P2JmsIOBhi9RXvJ8YaOlN7m4lL4ZtWVpoVuBja5JX3J3MtUu/fPEzGmBtLTEzEiRMnoFQqsWTJEoSEmJOajrH6Lxa3tvAwdLMTAIQQYcvDD5tVr6HhtFKZjAOheoh7hiTgniHmDgoKCozuJciYO3oKwDIJ510UBASZ2TsEGB9OY87nsL3JtN24cQMXL15EVFSUxvHffvsNd9xxh60vxxiTiDNNM3fg4+ODyspKyedL/VcfTGTRUniZlxcvn3cDNh0my83NRZs2bfDoo4+ic+fO+Pnnn9WP/fe//7XlpRhjZrJ1pum6xFVrycnJCA0Ntdt1GDMnEAJuJWSUul/Cpdxcje05WMNh02Bo+vTp2LdvH3755Rd8/vnneO6555CTkwPANqtZGGOGqVQqFBQUYNmyZSgoKIBKpdJ4XFxubw9RUVHIy8tDdnY2FtTZ3oAxZ6sFkC3x3Pht23DWzw87J060Y4uYK7JpMHTz5k31t8IePXpgy5Yt+Pjjj/HWW28ZzXfCGLNOfn4+YmJiEB8fj2HDhiE+Ph4xMTHqzVgBqDNN20PdLzs8SZu5mhkALsDwXmJ1hatUuHv2bA6IGhibBkPNmjXDr7/+qv5ZLpdj/fr1OHLkiMZxxpjtSN2dXiRmlLalutfiuUnM1dQCeAmGEzDWZWhHe+berA6G9u/fr96I9euvv0ZYWJjG415eXli2bBk2S0hdzhgzjzm704tBk74s03UNGDAAAMzuzSUipKSkoFmzZmY9jzFHWA0gCUCJhHP17WjP3JvVwVCPHj3QuHFjdOrUCZMnT8bXX3+N9evX49y5cxrn9e7d29pLMca0SN2dvqCgwGDQpO2XX37BqlWrdFaESlFcXIzCwkKzn8eYI6wGEINbW3VIwXuLNRxWB0Pff/89mjZtijvuuAMeHh5YunQp+vfvj4iICEREROCRRx7B5MmTsXz5clu0lzG3YmrSsylSh6QKCgokZ6EuLi5GSEiIRrLGoKAgyW2aM2eO5HMZc7RaAJsknst7izUcVgdDycnJ+PTTT7F8+XJ89dVX2L9/P3744Qe0bNkS48ePR+fOnfHLL78gLS3N7Lq3bNmCgQMHIjIyEoIgYM2aNerHbt68iUmTJqFTp07w9/dHZGQknnnmGZw+fVqjjqqqKowdOxYhISHw9/fHoEGDeGsC5hKkTHo2xV7L5deuXQuZTIa4uDhERUWhvLxc8nN5J3vm6goBFMPw/KFaACVaO9qboqquxoHsbGwfOxYHsrN5vlF9Q1by8fGhv/76S+d4Xl4ePfnkk1bV/f3339Prr79OeXl5BIBWr16tfuzy5cv00EMP0YoVK+j333+nHTt20D333EPdu3fXqGPUqFEUFRVF69evp3379lF8fDx16dKFampqJLejvLycAFB5eblVr4cxUV5eHgmCQLg1p1NdBEEgQRAoLy9PUj01NTWkUCj01iXWFx0dTRs2bND7uLEitiEnJ0fyc7y9vc2+Dhcutii+vr5mnf84QKp/CtUp4rEdaWmSP8870tKoRCbTqKdEJjOrDmYfUu/fVgdD8fHxNGnSJJ3jf/31FwUEBFhbvRqgGQzps2vXLgJAf//9NxHdCpg8PT1p+fLl6nNKSkrIw8OD1q1bZ7CeyspKKi8vV5fi4mJJv0zGpBADGEN/pMUARmrALgZW2gFR3cDKVNCkrwQFBdHo0aPplVdecfqNjgsXUyUtLY3kcrlZz3kcoJPQDIZOmRnE7EhLs1lQxWzPYcHQkSNHKDAwkJ5//nk6dOgQqVQqqqqqonHjxlHz5s2trV4NMB0MrV+/ngRBUL/ojRs3EgC6ePGixnmdO3emN99802A96enpej84HAwxW1AqlZL+UCuVSsl15uXl6QRY0dHRtHLlSlIqlZSTk0MZGRlOv2Fx4eIqRfyysGr5ctqflUXbxoyh/VlZVFNVJflzV1NVRSUymU4gJBYVbgVX5tTJbEtqMGT13mTt2rXDrl27kJycjE6dOsHLywsqlQqenp749NNPra1essrKSkyePBnDhg1Tb8Z25swZeHl5oWnTphrnhoWF4cyZMwbrmjJlClJTU9U/V1RUIDo62j4NZw2O1EnP+s5TqVQoLCxEaWkpIiIiEBsbCwAIDg7GzJkzcf78eYSGhiIqKgoXLlzAuHHjNObIiTmGTC2vZ8zdKRQKZGdnIzEx0eI6Di5YgK5GFj2IS/Qt2fOMOZZNNmpt27Yt1q1bh1OnTmHfvn3w8PBA9+7d7boXUl03b97EU089hdraWklbARCR0Rwq3t7e8Pb2tmUTGVOT+rnQPi8/Px/JyckmgxuFQoGhQ4di9uzZOnWK540YMQJffvml2W1nzF3MmTPHokCo7i71Vfv3S3oOL9F3fTbdtV6hUNht7yNDbt68iSeffBJFRUXYtGmTulcIAMLDw1FdXY1Lly5p9A6dO3cOvXr1cmg7GROJe4SVlJTozfsjCAIUCoW61wf4N8u09vn6enhKSkr0BkJ1rV692sLWM+Yexo8fj8TERMhkMsnP2TlxIppnZhrtDdKHl+i7Pptux+FoYiD0xx9/YMOGDTrbDHTv3h2enp5Yv369+lhpaSkOHTrEwRBzmrp7hGn3UIo/Z2dnq/9IG8syrY+U8yoqKsxpMmNux9wEoTsnTsTds2cjXCsQEich6WPJEn3mHC4dDF29ehUHDhzAgQMHAABFRUU4cOAATp48iZqaGiQlJWHPnj1YunQpVCoVzpw5gzNnzqi3BwkKCsLzzz+P8ePHY+PGjdi/fz+GDx+OTp064aGHHnLiK2MNXWJiInJzc3WyPCsUCuTm5mp035vKMs0Ys4zU+Xuq6mo0z8wEoHvTFL/OaAdEYg6j4tRUyLy8LG0icxT7z+W2nKFVNyNGjKCioiKDqwTqrsK5ceMGjRkzhoKDg8nX15cGDBhAJ0+eNKsdnGeI2UtNTY16tZdSqdS7nN6cPD9cuHCRXqSu2NyflaV3tZixYu4SfWYfUu/fApHEvvcGrKKiAkFBQSgvL9eYk8SYIxQUFCA+Pt7ZzWDMrSgUCpw4cULSnKGtr7yC+yQszlH27g3vbt3g16oVOo0ezT1CLkDq/dumE6gZY7YXGxsLuVzOy+EZs6Hnn39eUiC0atUqfPnll/hOQp1Nk5J4CX09Zdc5Qx4eHnjggQewd+9ee16GMVaHsbQRjLFbpGyKPHHiRDz55JP44do1m+9lxlyLXYOhzz//HH369MGrr75qz8sw5tYKCwvN6hXy8PDAhAkTMGTIEA6MGLNQbm6uOkVFLYDkf45rB0Q8Udo98JwhCXjOEDNFX2Zoc/KXGLNs2TIMGzbMJnUxxm7ZsGEDHnzwQb2PqVQqRERE4Pz58xrHHwcwF0Dd/QhOeXjg1PjxuHfWLLu1lVmO5wwxZmdiALR27VosXbpU4w+nQqHA3LlzrUr1L/rjjz+sroMx9i+5XI64uDiDjxcWFuoEQgCwGsBaALEAIgCUAnjpiy8w7L//tU9DmcNYNUx248YNbN26FYcPH9Z5rLKyEl999ZU11TPmsvLz8xETE4P4+HhkZ2fr/OEsKSlBUlIS8vPzrb5Oenq6VXUwxjQtWrTIaM+tsfxDtQA2A1j+z38jed9Kt2BxMHTs2DG0b98e999/Pzp16oS4uDiNf0Dl5eV49tlnbdJIxlyJuDWGsUSI4ujzqFGjsHTpUhQUFEiasFmXmHmaMaZJLpcjPT0d/v7+Zj8vLy/PZI+t1P0DQ0NDNbbNYfWXxcHQpEmT0KlTJ5w7dw5Hjx5FYGAgevfujZMnT9qyfYy5FHO2xiAinD9/HsOHD0d8fDxiYmLM6inizNOM6VdWVoaMjAx4eJh3C/P19UVCQoLJ88T9A02ZP3++zeYGMueyOBjavn07ZsyYgZCQENx+++345ptv8MgjjyA2NhZ//fWXLdvImMuwJkAxd+hM6lYBjDVUV65cMev8U6dOSdqPTNw/0NhqzLS0NDzxxBNmXZ+5LouDoRs3bqBRI8351/Pnz8egQYPQp08fHDt2zOrGMeZqrAlQxN6klJQUSUNmUrvqGWPSSf0Mi/sHavcQhYaGYtWqVZjFq8fcisWrydq1a4c9e/agffv2Gsc//PBDEBEGDRpkdeMYczXWBihEpN4t29hqFuDfrvqSkhLJO9Yzxowz5zOcmJiIhIQEu6XNYK7D4p6hxx9/HMuWLdP72Lx58zB06FD+A87cjhigWJvMUMq3U7Gr3hzx8fGQy+WWNosxtxYdHW32hGeZTIa4uDgMHToUcXFxHAi5KU66KAEnXWR1iavJAFgc8CuVSpM9Q3Wv9+KLL+LixYsWXYsxdouUlWTMvUi9f9t1Ow7G3JE4lyAqKkrjeGhoKJKTkxESEmLwuYIgmP3tNDExEStXrrS4vYwxIDAwUNJKMtYwcc+QBNwzxPQxtAWHoZ4jcWgtNzfX7G+nKpUKMTExvNSeMSuY0yPL3AP3DDFmZ4bmEhjqOVIoFBYFQuK1MjMzbdJuxhoqTlfBDOG9yRizA3usQgkNDbVhCxlreDhdBTPEqmDo5s2b6NevHz7++GO0adPGVm1irN4wtlu92HNkq3r5Wy1j+gmCAA8PD6P5u2Qymd7NVxkDrAyGPD09cejQIauXGTNWH+Xn5yM5OVljHo9CoUBWVhZCQkIs7hEyVG/v3r1t2n7G3IF4/0lNTcX7779vcIWnSqXCkCFDIJPJeEUZ00VWSk1NpUmTJllbjUsrLy8nAFReXu7spjAXkZeXR4IgEACTRaFQUF5ens3r5cKFCyg6Olr9+Vq1ahXJZDKD5wqCQNHR0VRTU2PPPw/MhUi9f1s9Z6i6uhqffvop1q9fjx49eujsIsyTPpm7MWezVuDfPcmMTZ5WqVQoKCjAiy++yMlKGZMgJSUFCQkJGj2vISEhRofKyIwM8KxhsToYOnToEO68804A0NmPjIfPmDsyd7NWIoIgCOo/3tpDZvqGxRhjhsnlcrz//vs6nyWp8+p4/h3TZnUwpFQqbdEOxuoNS/6Qit9IP/zwQ4SFhannEq1duxZJSUncG8SYGcrKyvT27khdLWbtqjJjCydY/cRL6xkzkzV/SMeNG6f+f4VCgRs3bnAgxJgF9H0pMbW5sSAIUCgUZu9PVpehBQ5z587lidn1mE2SLhYWFmL48OHo2bMnSkpKAABff/01tm7daovqGXMpttqs9dSpUygrK7NRqxhrWPR9Kam7ubH251P8OTs72+JeHDG7vPaQtjgvMD8/36J6mfNZHQzl5eWhf//+8PX1xf79+1FVVQUAuHLlCmbMmGF1AxlzNcb+4DLG7M9Y7449MsADxhdOiMdSUlKMTuBmrsvqYGj69OlYuHAhPvnkE3h6eqqP9+rVC/v27bO2esZckqE/uIwx+8vMzDTau5OYmIgTJ05AqVQiJycHSqUSRUVFVg1jmVo4UXelGqt/rJ4zdPToUdx///06xwMDA3H58mVrq2fMZenbcuP8+fNITU3llWGM2ZGUrWmsyQCvD69Uc29WB0MRERH4888/ERMTo3F869atuO2226ytnjGXpu8PbmJiojpAOnv2rMakacaY9ZwRcDhqpRpzDquHyV5++WUkJyfj559/hiAIOH36NJYuXYoJEyZg9OjRtmgjY/VWp06dbDLZmjH2L2cEHKYWTgiCgOjoaKtWqjHnsbpnaOLEiSgvL0d8fDwqKytx//33w9vbGxMmTMCYMWNs0UbG6g19y27lcrk68WLdyZfaPzPGjLPF0nhLiQsnkpKS9H6WAetWqjHnEshGf42vX7+Ow4cPo7a2Fh06dEDjxo1tUa1LqKioQFBQEMrLyxEYGOjs5jAXJS671f5IiX845XK5xlL66OhovPDCC0hPT3d0Uxmrd8SAY9q0aWjdurXTkh3q+8ITHR2N7OxszjPkgqTev60Ohp599lkMHz4cDzzwgNsOBXAwxExRqVSIiYkxOHFaEARERUXhiy++wLlz59R/yAEgJibGYJI4xtgtjRs3hre3t8YXitDQUDz99NM6e5TZG2egrj8k37+t3RF24MCB5O3tTZGRkZSamkr79++3tkq1zZs304ABAygiIoIA0OrVqzUer62tpfT0dIqIiCAfHx/q06cPHTp0SOOcyspKGjNmDMnlcvLz86OBAwdScXGxWe3gXeuZKUqlUtIO20qlUue54k71vFs9Fy6WF4VCod69njGR1Pu31ROov/nmG5w5cwbp6enYu3cvunfvjg4dOmDGjBk4ceKEVXVfu3YNXbp0wbx58/Q+PmvWLGRmZmLevHnYvXs3wsPD0bdvX1y5ckV9TkpKClavXo3ly5dj69atuHr1KgYMGMCJsZhNWbPslnMWMWa9U6dOGcwCrVKpUFBQgGXLlqGgoID//jNdto7CiouLadasWdSuXTuSyWQ2qxfQ7Bmqra2l8PBwmjlzpvpYZWUlBQUF0cKFC4mI6PLly+Tp6UnLly9Xn1NSUkIeHh60bt06g9eqrKyk8vJydSkuLpYUWTL3VFNTQ0qlknJyckipVFJNTY3OY1OnTpX07VVfz5Bo/PjxTv92zYVLfS6CIFB0dLTGZzQvL48UCoXGecHBwZSRkaFxHnNPUnuGbBoMVVdX0+rVq2nw4MHk4+NDkZGRNqsb0AyGjh8/TgBo3759GucNGjSInnnmGSIi2rhxIwGgixcvapzTuXNnevPNNw1eKz09Xe8HjYOhhkffH1KxO17fY+b8ka5r5cqVTr+RcOHiLkX80iEOQRs6Ty6X89Cam3PYMBkAKJVKvPjiiwgLC8OIESMQEBCAb7/9FsXFxbaoXq8zZ84AAMLCwjSOh4WFqR87c+YMvLy80LRpU4Pn6DNlyhSUl5eriz1fB3NdxjZlHDx4MAYPHiwp07SpZbcqlYpzcjFmQ6WlpUb3EhOVlZVh8ODBvMEqsz7PkEKhQFlZGfr374+PP/4YAwcOhI+Pjy3aJon2Cjb6J5+LMabO8fb2hre3t03ax+onKZsySqVQKIwuuy0sLMSFCxcsaidjTFdERITJvcTqSklJQUJCAq8Ia8Cs7hl68803cfr0aaxZswZPPPGEwwKh8PBwANDp4Tl37py6tyg8PBzV1dW4dOmSwXMY08ecP6SGTJ06VdIGkbyXEWO2UTcLtDmfK95glVkdDL300ks6w1CO0LJlS4SHh2P9+vXqY9XV1di8eTN69eoFAOjevTs8PT01ziktLcWhQ4fU5zCmjy0ClA4dOiAuLs7kt03ey4i5M0cn4BWHo839XOXl5fFKswbMomGy1NRUvP322/D390dqaqrRczMzMy1qGABcvXoVf/75p/rnoqIiHDhwAMHBwWjevDlSUlIwY8YMtG7dGq1bt8aMGTPg5+eHYcOGAQCCgoLw/PPPY/z48ZDL5QgODsaECRPQqVMnPPTQQxa3i7kXfQnUbBGgSK1D3POId7pn7mT48OEYOXIkCgsLkZGR4ZBrTpgwQd0La+7nat68eZg3bx4UCgXmzp3L2aQbGktmZ8fFxdGlS5fU/2+oxMfHW1K9mqFEdiNGjCCif5MuhoeHk7e3N91///108OBBjTpu3LhBY8aMoeDgYPL19aUBAwbQyZMnzWoHJ110X4ZWi61cuZLkcrlFK1lMrRzTJy0tzekrcLhwsXUJCQmh4OBgk+cFBwdTQECA1dfTt6ze3GSmYgJUXmXmHhyytL66upri4uLo6NGj1lTj8jgYck+G/lCa88dT+1xL/pDW1NRIXqLPhYs7Fi8vL5vVpZ3LKy8vz+wvNpZ8oWGuySFL6z09PXHo0CG33ZOMuS9rV4vJ5XKsWrVKJ2u0QqFAbm6uWV3stpiszVh9Vl1dbbO6tOf7JSYm4uzZs8jIyEBwcLCkOoiIJ1U3MFZPoH7mmWfw2Wef2aItjDmMtQFIWVkZQkJCcOLECSiVSuTk5KhXjiUkJJiV+n/t2rUWt4MxpknfXD2ZTIY333wT586dg1KpxJgxYyTVxSs9Gw6r8wxVV1fj008/xfr169GjRw/4+/trPG7NBGrG7MUWf+TWrl2LuLg4xMXFqY/l5+cjOTlZI9AyNiEzPz8f2dnZVreFsYZOEAQoFArExsbqPKa9SOKxxx4zuOdlXbzSs+EQSMqYgBHx8fGGKxcEbNq0yZrqXUJFRQWCgoJQXl6OwMBAZzeH2UBBQYHRf7tS5eXlqYMcMWO19kdKHEbWHj5TqVSIiYmR1EPl4eGB2tpaq9vLmDur+3kU6fuCEhUVhcrKSly8eFHvsLgYWBUVFXEixnpO6v3b6mCoIeBgyP2IgUhJSYnZGaXrUigUOHHiBAAYDWz0/XE1JyCbNm0aBEFAenq6xW1lzJ3J5XKcPXtWI3gx9gVFPFb3/8WfAd0vL6x+knr/tsneZIzVNzKZDHPnzgWgu6WLOQsCTp06hXfeecfkHCR9EzLNGaq7ePEiFi1aJPl8xhqasrIyjc+XqUUSgiBALpfbZBEEq/+snjPEWH2VmJiI3NxcvXN8srOzUVhYKGk+T3p6OlJSUiRds24AZM58hIULF9p0xQ1j7qju50vKF5SysjJs2LABMplMI+kqD401PBwMsQYtMTERCQkJOhmoZTIZgoODJU9uXrp0qaTz6gZA5mTI5UCIMdPqfr6k9ryeO3cOQ4cOtVeTWD3BwRBr8GQymcaKMJE5wcr58+cREBCAK1euGDxHLpdDpVJBpVJBJpOph+oGDx5sTfMZa/D0rSST2vPKK8YYYOGcoV9//ZVXtjC3V3dekRTGAiHg1pyGhx56CDExMcjPzwcAJCQkICAgwKp2MtaQiXP8xA1aReKXGUNzAOvucM+YRcFQt27dcOHCBQDAbbfdhrKyMps2ijFXkZiYaPNNJktKSpCUlIT8/HwUFhaaDKIYY4YZmvAsZZGEdgDFGi6LgqEmTZqgqKgIAHDixAnuJWL1lkqlMpkt+vXXX4dCoTC7bkPfSMXVLSkpKSgpKTG7XsbcWXR0NNLS0iAIgt4gRhAEZGRkaGR9N7TyS1wkwSvGmCkWzRkaPHgw+vTpg4iICAiCgB49ehiMrv/66y+rGsiYvUjNFi1+w0xKSgIgbe8yU+eJS+3Pnz9vYesZcz+hoaH4888/4eXlhXvvvdfgSk9zghhjiyQYE1mcdHHdunX4888/8eqrr+Ktt94yOO8hOTnZqga6Ak666H7MzRYtPkf7j7O1lixZgsmTJ1ud/JExd5GRkYE333wTwL89twUFBQCg3v7GFoGM9hYdHCC5J8n3b6N72kswcuRIqqiosLYal1ZeXk4AqLy83NlNYTZQU1NDCoWCAOgtgiBQdHQ01dTU6H2uUqmkqVOnGny+OSUrK4teffVVm9TFhYu7lLy8PCIiysvL0/msKhQK9eOWsle9zPVIvX/bZDuOy5cv47PPPsORI0cgCAI6dOiA5557DkFBQdZW7RK4Z8i9SN0GQ6lU6l1yD5jezkOc22BsPp32NgCMsVuio6ORmZmJJ5980qzeWyks6RVm9ZfDtuPYs2cPWrVqhaysLFy8eBEXLlxAZmYmWrVqhX379llbPWMWMTYxWmoyNmPnyWQyDB061GAwQ0Tw8/MzWj8HQozpV1xcjOeff97gVhrArQUI+hY8GGNqiw5L62VuwNouqPvuu49GjhxJN2/eVB+7efMmjRgxgmJjY62t3iXwMFn9YqoLXKlUSuqqVyqVRq8hCILB5w4ZMsTpQw1cuLh7MfYZ1ccWn31Wv0i9f9ukZ2jSpElo1OjfhWmNGjXCxIkTsWfPHmurZ8wsYhe49iTnurl9rE3GZuzbpWjt2rWWvwjG3ExwcLDk/fvMod17aypVhi16hZl7sjoYCgwMxMmTJ3WOFxcXc2Zd5hDiH8ClS5di1KhRJrvAAViVjM3UBpAAUFlZadZrYMydvfbaa0hISLB5vXW30sjPz0dMTAzi4+MxbNgwxMfHa2R71z5far2sgbC2C2rs2LGkUCho+fLldPLkSSouLqZly5aRQqGg5ORka6t3CTxM5rr0DYmZKmIXuL7nRkdHm1xRkpOT4/ThAS5c6lP56quv1Ks4jQ0vm1Pkcrl6xaehYWtBEEgQBPVn2lQbjK0kZfWT1Pu31cFQVVUVvfrqq+Tl5UUeHh7k4eFB3t7elJKSQpWVldZW7xI4GHJNpubtGCo5OTnqOsSl8jk5OaRUKiX9EZQ674ALFy63SlZWlsZn1tDnVi6XU0ZGhqQ6MzIy1J9hc1JlGGqDduDE3IPDgiHRtWvX6Ndff6VffvmFrl27ZqtqXQIHQ67H1B9AY8XayZE1NTUUHBzs9BsMFy71pSxZskT9+dHXIysGQTU1NZJ6kOr2ClkyKdrSXmFW/0i9f1u0HYc+fn5+6NSpk62qY8woKfN2tAmCAIVCYfUu1TKZDMnJyUhPT7eqHsYairp7g0nZHkPc/sZQLq5Fixapz7dkUjRv0cG0WT2BmjFnMHe1h613qX799dchl8utroexhqDuHnxStsEwtMFqdHQ08vLyNJIiWjopWiaTIS4uDkOHDrXZFh+s/rJJBmp3xxmoXY/ULNKi0NBQPP3000hISLDZN8D8/HwMHjxY8vnivyHGGpro6GgUFRVh7dq1kjZHFkkJnFQqFcLCwlBWVmbw+nK5HGfPnuWApwFy2N5kDQHPGXI9UuYVhIaGUnJyMoWGhmoc196DyJJJ1KIVK1ZInsSdmJjo9LkbXLg4q2RkZEha8WXJ3wK5XG702nXnGLGGxeETqN0ZB0OuydSqkLS0NJN/fK3ZsNHcZf2vvfaa029IXLg4qxhbdGDNknbOKs2McVgGauDWZNbhw4ejZ8+eKCkpAQB8/fXX2Lp1qy2qZ0wvQ/MKFAoFVqxYgWXLlhlNwPjSSy9h8ODBRrNVG2Io07UxixYtgq+vr+TzGXMnFy9eNPgYEaG4uBiFhYUATGeSrouzSjNbsDoYysvLQ//+/eHr64v9+/ejqqoKAHDlyhXMmDHD6gYyZkxiYiJOnDgBpVKJnJwcKJVKFBUV4ciRI0YDFSIyOMeATGzYKGU7Dn0uXLiAGzdumPUcxlyRoa1sDJ0rdbFBaWmppEzSdXFWaWYT1nZBde3alb788ksiImrcuDEdP36ciIj2799PYWFh1lbvEniYrH7Jy8uzWde+vq51TrrIpaEWuVxOK1eu1JsnCIDeIWsAlJSUJKl+S+YVcVZpZozDhsmOHj2K+++/X+d4YGAgLl++bG31jJlF7LWxFX1d69zdzhqqsrIyhIaG4vjx43j//feRkJCAhx56CC+++CKmTZuGyMhIjfM9PG7dYnJzc43WK+YA++STT0zuLajdWyuTyazaa5AxwAbDZBEREfjzzz91jm/duhW33XabtdUbVVNTg6lTp6Jly5bw9fXFbbfdhrfeegu1tbXqc4hI/SH19fVFXFwcfvvtN7u2izmPJckYjTl79qzOH1/ubmcN2XvvvYeQkBBMmDABa9euxYYNGzBz5kxMmzYNlZWVyMjIUG+IbGyuj0gMWF588UWTQ9t15xXVZWz+YG5urt5l+4xpsLYL6r333qMOHTrQzp07KSAggAoLC2nJkiUUGhpKH374obXVGzV9+nSSy+X03XffUVFREa1atYoaN25M2dnZ6nNmzpxJAQEBlJeXRwcPHqQhQ4ZQREQEVVRUSL4OD5PVH+ZsoiqXyyUti9e3FD8kJMTpQxZcuLhqMbXUvW4Rt8GQ+tmtu7egNmvSZDD35NCl9a+99hr5+vqqx3V9fHxo6tSptqjaqP/85z/03HPPaRxLTEyk4cOHExFRbW0thYeH08yZM9WPV1ZWUlBQEC1cuFDydTgYqj+kzufJyMgwuWmkWPTNV1i5cqXTbzhcuNTnMnXqVI2AhZfIM3twykatu3fvpp9//pmuXLliq2qNevfdd6lFixZ09OhRIiI6cOAANWvWTP3N4fjx4wSA9u3bp/G8QYMG0TPPPGOw3srKSiovL1eX4uJiSb9M5nxSkjEqFAqNHayl5ArSNwkzLS3N6TcULlzqa9Hu4eGJ0MweGkTSxdraWpo8eTIJgkCNGjUiQRBoxowZ6se3bdtGAKikpETjeS+++CL169fPYL3p6el6P4wcDNUPppIxaq9IqampoaysLEl/wLW/za5YsYI8PDycfmPhwsWWJSAgwO7X0NfDY+5nlzFTHLZrfWpqqt7jgiDAx8cHt99+OxISEhAcHGztpXSsWLECS5YsQU5ODu644w4cOHAAKSkpiIyMxIgRIzTaUhcRGc2TMWXKFI3XVVFRgejoaJu3n9mHOJlS3x5I2dnZOpMpZTIZwsLCJNU9ffp0TJ8+Xb2fUrNmzTQm7DPmDvr27YuxY8di7ty5WLNmjU3rFleOxcbG6jxm7meXMZuxNuqKi4ujwMBA8vf3pzvvvJO6detGjRs3pqCgILrnnnuoSZMm1LRpU/rtt9+svZQOhUJB8+bN0zj29ttvU9u2bYnI8mEybTxnqH4yZzKlubmDxG+qKSkpTv8Wz4WLPUpeXh5NnTrVpnVK7eHhidDMVhzWMyT2+ixevFi9I2xFRQWef/553HfffXjxxRcxbNgwjBs3Dj/++KO1l9Nw/fp1dR4LkUwmU39Tb9myJcLDw7F+/Xp069YNAFBdXY3Nmzfjvffes2lbmOuRyWSIi4uTdG5sbCwUCgVKSkokZZamf3oXly5damUrGXNNL730EnJycqyqIzg4WGMbDqk9POZ8dhmzCWujrsjISL29PocOHaLIyEgiItq7dy/J5XJrL6VjxIgRFBUVpV5an5+fTyEhITRx4kT1OTNnzqSgoCDKz8+ngwcP0tChQ3lpPdNL6uoyLlwaSvnpp5/MWiavXTZs2MA9PMypHDaB2t/f3+CWBY0bNyaiW8NVAQEB1l5KR0VFBSUnJ1Pz5s3Jx8eHbrvtNnr99depqqpKfU5tbS2lp6dTeHg4eXt70/33308HDx406zocDDUc5u5Ez4WLO5epU6davL1N3VWbjDmLw4KhYcOGUcuWLSk/P5+Ki4vp1KlTlJ+fT7fddps638+yZcuoe/fu1l7KaTgYch9S5iKI59h6vgQXLvWtiPni8vLyKCoqSuMxUyvO5HI5r/5iTuewYOjKlSv0wgsvkJeXF3l4eJCHhwd5eXnRiy++SFevXiWiW5u27t+/39pLOQ0HQ+5BX6+PdnbpuqTkLOLCxZ3Lhg0b1J+HqqoqysrKojFjxlBWVhZVVVVRXl6ewWE0Xg7PXIHD8wxduXKFfvnlFzpw4IDDki46CgdD9Z84H8jcP9jG8p44+0bFhYs9i1wuN5qcVKFQ6N3Bvm7hRInM2RwSDFVXV1NcXJw6A7S74mCofhN7eCz9g63vRhAdHU1vvvmm029YXLjYq2RkZFBNTQ2tWrVK7+PmfCHQnlfKS+eZozisZygkJISOHTtmbTUujYOh+s0Wex7V/eO9YcMGSk9Pp8aNGzv9hsWFi6UlOjqaxo8fbzSDenBwsE0yrNfdesPc4WrGrCH1/q2ZpMcCzzzzDD777DNrq2HMbkpKSiSdV1paavAxMe+Jt7c3hgwZgoyMDFy9etVWTWTM4Z566ilkZmYazaB+8eJFm2RYP3z4MAoKCpCbm4ukpCSN7NLArc9oUlIS8vPzrb4WY5YQiCRkmDNi7Nix+Oqrr3D77bejR48e8Pf313g8MzPTqga6goqKCgQFBaG8vFydWJLVD/n5+Rg1ahTOnz9v8lylUmk00Vt+fj4GDx5sw9Yx5hw5OTmYOHGiTlBibzKZDCqVSu9j4jYdRUVFkMlkDm0Xc19S799WZ6A+dOgQ7rzzTgDAsWPHNB4ztv8XY/aWn5+PpKQkkxmlje2VJFKpVEhOTrZ1ExlzuPHjxyMiIsLhgRAAg4EQABARiouLUVhYyNmnmcNZHQwplUpbtIMxmxKDF6kdn9nZ2Ua/jRYWFjrl5sGYMYIgSP43DtzaPun999936W1kjA1XM2YvVgdDosOHD+PkyZOorq5WHxMEAQMHDrTVJRiTTGrwEhoaioULF5rcK4n/QDNXZO4sh3379iE3NxcpKSn2aZANREREOLsJrAGyOhj666+/8Pjjj+PgwYMa31LEITJj3aKM2YvU4CUrK0tvIKRSqVBYWIjS0lJERESgWbNmtm4iYw5XXFyMJ554wtnN0EvKcDVj9mJ1MJScnIyWLVtiw4YNuO2227Br1y6UlZVh/PjxeP/9923RRsb00g5YYmNj1UNdUr9dRkVF6RzLz89HcnKyRs+SQqGAXC5HWVmZbRrPGFMTvzybGq5mzG6sXcMvl8vpl19+ISKiwMBA+v3334mIaOPGjdS1a1drq3cJnGfI9ZjKVSJlKw2ZTEYrV67UqddQpmpD9dQtcrmcoqKiOEM1F7cocrlcZ7uN6OhoysjIsKpemUymUyfnGWL24LCki02aNKHjx48TEdFtt91GmzZtIiKiP//8k3x9fa2t3iVwMORapG6tYeg87edoB1DW3kCsvVFw4eLM8tprr2lkhtaXLVrqvn36trERBIFWrlzJGaiZQzgsGLrvvvto9erVREQ0dOhQevjhh2nr1q30zDPP0B133GFt9S6BgyHXYe7WGqtWrdL5Fqp9fmhoKC1ZsoRGjhxpk5vJkiVLDG5eyYWLqxdjmdjrMrZvnyAIlJaWpncbG+4BYo7ksGBo3bp16n/cx48fp/bt25MgCBQSEkIbN260tnqXwMGQ6zB3aw2p59uyvPLKK06/oXHhoq8EBwcb7M2xZFNVQ/v21e1t5R4g5kxS799WT6Du37+/+v9vu+02HD58GBcvXkTTpk056SKzOamrxMTzHL0kXiaTYf78+Q69JmNSJScnY9q0aTr5iSydwJyYmIiEhASDCxnEbWwYc3U2yzNUV3BwsD2qZUzyKjHxPEfnLOFUEsxVyWQydOjQAbm5uXpXS2ZnZ5vMt2WoXg54WH1n9d5kALBx40Zs3LgR586d09nU7/PPP7e2eqfjvclch0qlQkxMDEpKSvQmnNPe38jU+YzVV8b2+TJEEATk5uYa7c1hzJ1IvX9bvWt9RkYG+vXrh40bN+LChQu4dOmSRmHMlmQyGebOnQtAd+87fV39xs5nrD5LTU01+980Ean32IuLi8PQoUMRFxfHgRBj1k5OCg8Pp6+++sraalwaT6B2PaYmbko5nwuX+lpSUlKs+nedkZFh988oT55mrkDq/dvqYTK5XI5du3ahVatW1lTj0niYzDUZy0Bt6PwXXngBX3zxheMayZgdKJVK9Tyd6upqLFiwAMePH8fly5exZMkSSXXk5eVZNEdICkNZ3OfOnWu3azKmj9T7t9XB0KRJk9C4cWO88cYb1lTj0jgYcg8qlQrNmjXDxYsXnd0UVs+Zu1u8La9bd06cvqBDqujoaHU9tpSfn4+kpCSd3484pJebm8sBEXMYuwZDqamp6v+vra3Fl19+ic6dO6Nz587w9PTUODczM9Pc6l0OB0PuoaCgAPHx8c5uBnMDvr6+uHHjhlOuLfboGAo6zFG3h8kWxAULhoIz7WCOMXuTev+2aGn9/v37NX7u2rUrAODQoUMax3nCKnMljs45xNyXswIhkUqlQnJystW9U2vXrrVpMFRYWGi0l4qIUFxcjMLCQl6Oz1yKRcGQUqm0dTsYszupOYec+a2fMWMEQUBKSgqCgoIsGhrTtnTpUrz//vs266UxNykqY67C6qX1jNUXsbGxUCgURnssPTw88MorrziwVYzdEhgYaHIYXuxZKSgosMk1z58/j8LCQpvUBZifFJUxV2F1MPTuu+/qTaz4+eef47333rO2esZspm7OIUNqa2sxZ84cDBkyxEGtYgzw9/fHmTNnsGDBAodf25a9NKa+cAiCgOjoaMTGxmocV6lUKCgowLJly1BQUMCZ3JnDWR0Mffzxx2jXrp3O8TvuuAMLFy60tnrGbCoxMRErVqwwOSywYcMGs+oVBAFyuRxNmza1pnmsgbp27RratGmD48ePSzo/Li7OZNARGhoqqS5b9tKYmxQVuLX6LCYmBvHx8Rg2bBji4+MRExOD/Px8m7WLMVOsDobOnDmj98MUGhrK48LMJYWGhhr95klEKCsrM6tO8TmrVq3S++XAFEEQ1AEVa5hKSkowbdo0Sf8GLl68aDLomD9/vkW9NNZKTExEbm4uoqKiNI4rFAqdZfXiijjt+U8lJSVISkrigIg5jNXBUHR0NLZt26ZzfNu2bYiMjLS2esZsTmqQHhwcbPaKyO+++w5Hjx41+LiPj4/e41FRUcjNzcVzzz1n1vWY+zBnZdj48eORkJBgNOh44oknzO6lsZXExEScOHECSqUSOTk5UCqVKCoq0giEjK2IE4+lpKTwkBlzDGtTXc+cOZPkcjl9/vnndOLECTpx4gR99tlnJJfLacaMGdZW7xJ4Ow73olQqJW1ZMGTIELO3OQgJCbFoe4WmTZtadD0uDbcolUoiMr3thblb1ziK1M+h+DoZs4TU+7dFS+vrmjhxIi5evIjRo0ejuroawK1vv5MmTcKUKVOsrZ4xmxMneRpLDBccHIwVK1ZIrlMQBISEhOD8+fMWtenSpUtmXY8xsYdTJpMZzdmTmJjokrvU8zJ85kqsDoYEQcB7772HN954A0eOHIGvry9at24Nb29vW7SPMZtbu3atwTxCliQKFZ/z9NNPIzs725qmMSaZOROfTQVMzsDL8JkrsXrO0I0bN3D9+nU0btwYd911FwICAvDRRx/hp59+skX7TCopKcHw4cMhl8vh5+eHrl27Yu/everHiQjTpk1DZGQkfH19ERcXh99++80hbWOuR5ywaWiCdHBwMKZNm2bWBGpxjkZCQoKtmskaKHG7iqioKIdPfHY0S5fhM2YPVgdDCQkJ+OqrrwAAly9fxj333IM5c+YgISEBH330kdUNNObSpUvo3bs3PD098cMPP+Dw4cOYM2cOmjRpoj5n1qxZyMzMxLx587B7926Eh4ejb9++uHLlil3bxlyPlC0MfH190apVK0n1jRkzRmNiqJSkjoyZMnfuXHzwwQcArJ/47Mr5eyxZhs+Y3Vg7OUkul9OhQ4eIiOiTTz6hzp07k0qlopUrV1K7du2srd6oSZMm0X333Wfw8draWgoPD6eZM2eqj1VWVlJQUBAtXLhQ8nV4ArV7kDphMysry+KJnXl5eSQIAgmC4PQJtlzqV5HL5RqTmq2d+Kzv+QqFwukTp7W56gRv5h6k3r+tDoZ8fX3p77//JiKiJ554gqZNm0ZERCdPniRfX19rqzeqffv2lJKSQklJSRQaGkpdu3alRYsWqR8/fvw4AaB9+/ZpPG/QoEH0zDPPGKy3srKSysvL1aW4uFjSL5O5tpycHEk3pSVLlpBCoTAY0AiCQNHR0TqrdkT6/rjL5XKn3mh9fHycfrPnYrxs2LBB59+SqZVihohBufY1xEDd1QINS18nY6Y4LBjq1KkTzZ07l06ePEmBgYG0fft2IiLas2cPhYWFWVu9Ud7e3uTt7U1Tpkyhffv20cKFC8nHx4e+/PJLIiLatm0bAaCSkhKN57344ovUr18/g/Wmp6fr/WPFwVD9Zs5SXkM9PFJvJlVVVZSVlUVjxoyhrKwsWrFihdNusgEBAfTjjz/S3Xff7fQbPhf9RS6X2ywAqKmp0QnG6xZTwTxj7sRhwdCqVavI09OTPDw8qG/fvurjM2bMoIcfftja6o3y9PSknj17ahwbO3Ys3XvvvUT0bzB0+vRpjXNeeOEF6t+/v8F6uWfIPYk3Cak9PpZ23+t7nkwmc/oNl4trF1v11nD+Hsb+5bA8Q0lJSbjvvvtQWlqKLl26qI8/+OCDePzxx62t3qiIiAh06NBB41j79u2Rl5cHAAgPDwegu2XIuXPnEBYWZrBeb29vTg3ghsQJm0lJSRAEQWMitb4Jm5bkZxFXq5HWJG1XmrjKXI8gCEhJSUFCQoLVE4Y5fw9j5rN6NRlwK+jo1q0bPDz+re7uu++2aI8mc/Tu3Vtn64Njx46hRYsWAICWLVsiPDwc69evVz9eXV2NzZs3o1evXnZtG3NN5uybBPybn2Xo0KGIi4szeqOSslqNMX2ICMXFxSgsLLTo+XVXjZ09e1bSczh/D2P/sqhnKDU1FW+//Tb8/f2Rmppq9NzMzEyLGibFuHHj0KtXL8yYMQNPPvkkdu3ahUWLFmHRokUA/v22NWPGDLRu3RqtW7fGjBkz4Ofnh2HDhtmtXcy12Ssjb2FhocGs1qxh8fDwQG1trfrngIAASek8LOmtyc/PR3Jyssa/PZlMZrA3UsxlxPl7GPuXRcHQ/v37cfPmTfX/G2LvfCt33XUXVq9ejSlTpuCtt95Cy5YtkZ2djaefflp9zsSJE3Hjxg2MHj0aly5dwj333IOffvoJAQEBdm0bc232yMjLww71W0pKCnJzc20S0Iq9g0lJSWjXrh2aNGmCCRMmmHyeub015g7Lcv4exvQTiPv0TaqoqEBQUBDKy8sRGBjo7OYwF1VQUID4+HhnN4NZSKlUIjY2FtOmTcP06dNtXr+U3pqioiLJQYpKpUJMTIzR4E37mtHR0cjOztYZDmbMXUm9f1s1gbq2thZffPEF8vPzceLECQiCgJYtWyIpKQn//e9/ORMvq3dUKpXFw2diBuqSkhKeN1SPiIFIr169LJ6zI4Wte2ukDMuqVCpkZWUhLCzMZTZoZcwVWRwMEREGDRqE77//Hl26dEGnTp1ARDhy5AhGjhyJ/Px8rFmzxoZNZcy+9M29UCgUmDt3rslv0mIQlZSUhOzsbL2r1ThAcj1iIPLUU0+hVatWDpnzpd1bo1AoLOqtkTosGxYWhqFDh5pVN2MNjqVr9z///HMKCAigTZs26Ty2ceNGCggIUCc/rO94Ow73Z03GXil5hcT8RHl5eU7PRs3l3xIaGkoDBgxw+HWzsrLU2Zarqqosyr7M+YQYM83uSRf79u1L7777rsHH33nnHaNZnusTDobcmzUZew0FUWJJSUnRucHV1NRQRkYGBQcHOz0YaMglKCjIadfOyclR//uxdP8wc5OIMtYQ2T0YCgsLo/379xt8fN++fXbfjsNROBhyb5Z+w66pqaGoqCiD55u6GYn7MT388MNODwy4OLbU3fJF378bqfuHWbttDGPuTur92+KkixcvXjSaxTksLAyXLl2ytHrGHMbSjL3vvPMOSkpKDJ5PJhLpyWQyxMbGYs+ePZKu//7770OhUPDCBBcik8mQkJAAhUIh+TlyuRy9evUymKBTPJaSkmIyc7m5SUQZY/pZPIFapVKhUSPDT5fJZKipqbG0esYcRmpul7rn5efnIz09XdLz9AVb4oTrjRs34sKFCybrCA0NRUpKinq1Jk/I1k872aG91dbW4ptvvsGKFSsQGhqK0tJS/PHHH0b/bZSVlWHmzJlGJ2vXDaRN5cOyVxJRxhoSq1aTjRw50uAeXlVVVRY3ijFLWbI03tSSeO2MveK2G1IdPnwYBQUF6rboW7VmytNPPw2ZTKbuCTD3+Q1BaGgo/vrrL3z66af48ccfsW7dOqvrFAQBUVFRqKys1Bu0EhEEQcD48ePVOYJUKhU++OADlJWVGazzgw8+kHR9qb2W9kgiylhDYvEw2YgRI9CsWTMEBQXpLc2aNcMzzzxjy7YyplZ3L6aCggKoVCrk5+cjJiYG8fHxGDZsGOLj4xETE4P8/HyjdYkbuAK6WdP15YAxd9uN6dOnq9syceJEJCUlmR3IDBgwQP3/iYmJOHHiBLKyssyqQ6rHHnvMLvXa2/nz59G+fXs0b94cP/zwA/Ly8nSGr0JDQ82u98UXXzTae6c9HFpYWGgwEBLPN/Z4Xc2aNdP5d84YswO7zlxyEzyB2nUYWollarn6ypUrTdatb2WPuCS+rpycHIsmzRpbdWaq6FthVFVVpbOE3xZl6tSpTp9gbKx4eHiYPEd8v8VJ6nWXsYeGhkq6TmhoKOXl5Ul+v8UVYlLPDw4ONroSTC6XW7zSjDF2i91XkzUkHAy5Bmty9MhkMlq1apXJa2jfPPWtBJO6+syWRd/qIHu144033rAqcLN3WbFiBYWEhFj8fqekpEi6zpIlS8z6PYurDaWen5GRYXAlmDn/DhhjhnEwZEMcDDmfqXw+UostbiKm8rvYq2gv1be0h8pUCQwMdOjrMqfI5XLasGGDVe+3OcFNVVUVvf/+++Tt7S35fTEn/4+hPEPGgn7OH8SYdBwM2RAHQ85lKimiOcVWNxFD+V0cUaZOnUpKpdKsoKA+FB8fH8mv35r3W2qSzfHjx0sehtQOuszJ/6PdGyn1feXM0oyZxsGQDXEw5Fy2Hg6y1U1E37d6RxaxB8GVh7TqBgHGApa0tDRq2rSppLrMndNUd+sLMTBKS0sz+pyEhATJ9cvlcoPZyaXMQdNm7hwlxphhHAzZEAdDzmXr4SBb3kTqfqt39MTj+hAEyeVyWrlypU5QEBgYSElJSbRhwwZauXKlWa9lw4YNFgehCoXCZCAESJukXbcYCrClzEHTxnuOMWY7Uu/fAhFnbjOloqICQUFBKC8vR2BgoLOb0+AUFBQgPj7eZvUplUq75GSxdTulEAQBwcHB8Pb2xunTpx16bakyMjLQqlUrbNiwAWvXrtXITC/m8JGy1FzM91RUVIS1a9di8ODB9my2WXJycmy2M7xKpUJMTIzJvFdiXiPGmGGS79+OiMzqO+4Zci5zJiwb+0Zv74mnzppYjX96S9LT0x1+XUcW7bk2K1eutEtqAUuKrXtpeM8xxmzD7nuTMeYoxpIiiuRyOfLy8rBixQq9j+tLnuiMdpp6zFJr1qxBkyZNbF6vq5DL5Tp7bT3xxBNYvny5E1t1672Mjo5WZye3Fd5zjDEHc1BwVq9xz5Br0DchVS6XU0ZGhkZvj6UTV+3ZzuDgYMrIyNA7f0ZfEXsEkpKSnN7r4Qplw4YNZv2+HVEc0UtjyZwjxti/eM6QDfGcIdchde8xS/Yos3U733nnHcydOxcXL15UH1coFMjKykJISIi6bRcuXMC4ceM0tuiIjo5GdnY2EhISjM4fcXdS58dUV1djwYIFOH78OIgI8+fPt+q6/v7+uHbtmtFzxPeIe2kYc11S798cDEnAwRAzV35+PpKSknQCGHGITHuow1jwJtYFoEEFRIZ+V9r0bXxr7e71eXl52LlzJzIzMzX2A/Pw8MCjjz6K8ePH887wjNUDHAzZEAdDzBziaiBDm7FashrIkp3u65PGjRvDx8dHY0NUKT0vhoJOU9LS0vD555/rrGKTy+VYtGiR+pp1e5xatWqF0aNHw8vLy6xrMcach4MhG+JgiJlD6hJ7c5f4i71HeXl5mDdvnhUtdF0hISEYPnw4EhISTPa8mAo6DZHL5Th79iyAW+9VQUEBACAuLg5xcXHc28OYG5F6/27kwDYx1iCUlpba9DyRTCZTB0/uGgxduHAB2dnZkoagCgsLLeopKysrQ2FhIeLi4vDggw/iwQcftLS5jDE3wUvrGbOxiIgIm56nLTY2FgqFwi5L9B3hySefROPGjY2e89JLL2nM1dGnpKTE4jaYG4gyxtwbB0OM2ZipYMXa3DTG8hmZEyCNGDECgiA4NKhKT0/HSy+9hKtXrxo9r6ysDG+//bbBx/Pz8zFu3DiL22FpIMoYc08cDDFmY1KCFWuTPxpLyrdixQp4eBj/aHt4eOCjjz7SW0dgYCB8fHwsbpshCoUCb7zxhnqOjikZGRnIz8/XOS5Omj5//rzZbbBXkkTGWP3GwRBjEqlUKhQUFGDZsmUoKCgwOoxj7wzCKpUKwcHBmDlzJrKysrBkyRIolUoUFRXhySefxPjx440+v7a2Fm3atAEAnDhxAkqlEjk5OcjIyEBFRQUqKystbpu+AFAQBMydO9fsADAlJUXj96xSqZCcnGxRigFHZCFnjNVTdkv76EY4AzXTl+VYoVCYzD5sjwzCUtuSlpZmdO8u7QzK4t5qhs6XWkJDQzV+1s7+vWHDBrPqq7vvl9Qd3QMDA0kulxttB2PM/XEGahvipfUNmzkJFO2d+drcZI43btxAREQEysvL9dZXN+dRYWGhpJQApixZsgRRUVEGfwcqlQphYWGSdqoHNHeEX7ZsGYYNGyapDU899ZRTs5AzxpyPl9YzZoQ523oYGpYhIgiCgJSUFCQkJGDt2rU6iREVCgXmzp1rky0bzGmL+Fp+/vlng4GQ+Lzi4mL178IWoqKijOZPkslkWLRoEQYPHiypvrqTnaVOfI6KitJIRcAYY8bwnCHW4OTn5yMmJgbx8fEYNmwY4uPjERMTo3eyrqlcNmIw8c477yApKUnn3JKSEiQlJemt21xS21JYWKg+Zk7OI2tXWJkzOTkxMRGrVq0y2lOjrz57r9RjjDVMHAyxBkUcZpIatEgNJubOnWuwxwbQnQhsibVr10o6r26bzcl5JCV/kdjNbItVcklJSVi2bJnexwzV54iVeoyxBsh+05Ycb8aMGQSAkpOT1cdqa2spPT2dIiIiyMfHh/r06UOHDh0yq16eQO0eTE0QFgSBoqOjNSY5S52wK6XUnQhsrry8PMnXmTZtms5rFgRB0mvOy8tTT6w2VL9cLteZnBwaGkorV660+LVpvy+mJjtb8hzGWMMj9f7tNsHQrl27KCYmhjp37qwRDM2cOZMCAgIoLy+PDh48SEOGDKGIiAiqqKiQXDcHQ67LnNVaUgObukGLlGBCOzAwVHJycix+jeas8pLL5Rq/B0MBjvZqsrrnmwoa8c+KrbrHpayuM/YazV11Z4+Veowx99KggqErV65Q69ataf369dSnTx91MFRbW0vh4eE0c+ZM9bmVlZUUFBRECxculFw/B0Ouydzl7jk5ORYFLaaCiYyMDLv2DFnSO6V9LXN7UqqqqnSWyJsqhoIrxhhzFqn3b7eYM/TKK6/gP//5Dx566CGN40VFRThz5gz69eunPubt7Y0+ffpg+/btBuurqqpCRUWFRmGuxdy5P4Dle4aZSqD4+uuv23VSryWrvLSfk5iYqJFcUUzQaGiV2/bt283O8Ew2nB/FGGOOVO+X1i9fvhz79u3D7t27dR47c+YMACAsLEzjeFhYGP7++2+Ddb777rvIyMiwbUOZzViyxBz4dyVSSUmJ3ueKOXdiY2N1lt4nJCQgISHB4HL8uXPnIikpCYIgaNRtzqRe7Wv26tUL27dvx+HDh83+HTVr1sxgvU8++aTJtli6zJ7qrGjjZe2MsXrD7n1UdnTy5Elq1qwZHThwQH2s7jDZtm3bCACdPn1a43kvvPAC9e/f32C9lZWVVF5eri7FxcU8TOZCLJn7I5Iyf8bSbNPWTOrV91xj2aNNlQ0bNhisV8prMTdLtHaxdH4UY4zZUoMYJtu7dy/OnTuH7t27o1GjRmjUqBE2b96MDz74AI0aNVL3CIk9RKJz587p9BbV5e3tjcDAQI3CXIclS8xFpoa8AFicL8jcoSiRoSE/a4aazp07Z9FQoq3oG5I0Z283xhhzKAcFZ3ZRUVFBBw8e1Cg9evSg4cOH08GDB9UTqN977z31c6qqqngCdT1WU1NDISEhVk9Y1rcSyZKl97Z4PbbYD0y7bNiwwarXInWyudR6Le2hYowxa0i9f9frOUMBAQHo2LGjxjF/f3/I5XL18ZSUFMyYMQOtW7dG69atMWPGDPj5+Una34i5nsLCQly4cMHkeaGhoUYnLOvbqqGgoEByhmdbzYcxlVXaXOK8JwBWvRZLslEbmh9laD81sYdKez81xhhztHo9TCbFxIkTkZKSgtGjR6NHjx4oKSnBTz/9hICAAGc3jVlA6sTep59+2uwsxOZsXWEr1tRlLAPzuXPnrLq+lGzU2r9fcaixbmBjarI7wKvPGGPOV697hvQpKCjQ+FkQBEybNg3Tpk1zSnuYbUntsUhISLBb3dbu4WWLujIyMvDJJ5/obAqbnZ2NxMREnc+BudcXt70wtkJu+fLlCAkJMbrZrTn7qfHqM8aYswik7ysb01BRUYGgoCCUl5fzZGonU6lUiImJMbg8HgCio6NRVFRkds+QqbrFIShL6rb0msbaAMDgUn9bvZb8/HwkJydrBDTR0dHqoMuUZcuWSRqSzsnJwdChQ02exxhj5pB6/3b7YTLmXkxt1CkIgsUbdTpjE1Bj19Sm3QZx3tPQoUMRFxdnlw1NLV0hJ3JGbxtjjJnNfnO43QevJnM99tyo0xmbgErJM2RJG5y9oam5G8UyxpgtSb1/8zCZBDxM5pq0Myvrm7PiinVLvaaYgdraNjjjtdQlriYDoHfuEa8mY4zZi9T7NwdDEnAwxJh1rJ17xBhjluBgyIY4GGLMes7uoWKMNTxS799ut7SeMVvjm7ht6Et0yRhjroCDIcaM0De8o1AoMHfuXB7eYYwxN8FL6xkzwJkbnboj3qiVMeaqeM6QBDxnqOERkxYayp5sjwSM9uTsoT7uYWOMOQMnXWTMCuZsI+Hq8vPzERMTg/j4eAwbNgzx8fGIiYlxWM+WrXvYuIeJMWZrHAwxpoczNm21B2cP9dl6o1ZnB3aMMffEwRBjerjDNhKusGO8LXvYnB3YMcbcFwdDjOkRGxsLhUJhcL8wQRAQHR2N2NhYB7dMOlcY6rNVD5srBHaMMffFwRBjejhj01Zbc4WhPlv1sLlCYMcYc18cDDFmQGJiInJzcxEVFaVxXKFQ1Iv9tFxhqM9WPWyuENgxxtwXJ11kzIjExEQkJCTUywzUYiBSUlKid3hJTA9gz6E+sYctKSkJgiDo3ahVSg+bKwR2jDH3xT1DjJkgbiMxdOhQxMXF1YtACHCdoT5b9LC5wxwuxpjr4mCIMTfmKkN9iYmJOHHiBJRKJXJycqBUKlFUVCT5+q4S2DHG3BNnoJaAM1Cz+s7ZGahtRV8m6+joaGRnZ7v8HC7GmONJvX9zMCQBB0PMXbhDUOQOr4Ex5hhS7988gZqxBsJd9gcT53Axxpit8JwhxhoAzt7MGGOGcTDEmJvj7M2MMWYcB0OMuTnO3swYY8ZxMMSYm1u7dq2k8zh7M2OsoeJgiDE3plKpsGTJEknncvZmxlhDxcEQY26ssLAQFy5cMHleaGgoZ29mjDVYHAwx5sakDn09/fTTnKuHMdZgcTDEmBuTOvSVkJBg55Ywxpjr4mCIMTdmaoNTALzBKWOsweNgiDE3ZmqDU0EQeINTxliDx8EQY27OVXauZ4wxV1Wvg6F3330Xd911FwICAtCsWTM89thjOHr0qMY5RIRp06YhMjISvr6+iIuLw2+//eakFjPmHImJiThx4gSUSiVycnKgVCpRVFTEgRBjjKGeB0ObN2/GK6+8gp07d2L9+vWoqalBv379cO3aNfU5s2bNQmZmJubNm4fdu3cjPDwcffv2xZUrV5zYcsYcT9zgdOjQoYiLi+OhMcYY+4dA+jYsqqfOnz+PZs2aYfPmzbj//vtBRIiMjERKSgomTZoEAKiqqkJYWBjee+89vPzyy5LqraioQFBQEMrLyxEYGGjPl8AYY4wxG5F6/67XPUPaysvLAQDBwcEAgKKiIpw5cwb9+vVTn+Pt7Y0+ffpg+/btBuupqqpCRUWFRmGMMcaYe3KbYIiIkJqaivvuuw8dO3YEAJw5cwYAEBYWpnFuWFiY+jF93n33XQQFBalLdHS0/RrOGGOMMadym2BozJgx+PXXX7Fs2TKdx7SXFBOR0bwrU6ZMQXl5uboUFxfbvL2MMcYYcw2NnN0AWxg7diy++eYbbNmyBQqFQn08PDwcwK0eorqZeM+dO6fTW1SXt7c3vL297ddgxhhjjLmMet0zREQYM2YM8vPzsWnTJrRs2VLj8ZYtWyI8PBzr169XH6uursbmzZvRq1cvRzeXMcYYYy6oXvcMvfLKK8jJycHatWsREBCgngcUFBQEX19fCIKAlJQUzJgxA61bt0br1q0xY8YM+Pn5YdiwYU5uPWOMMcZcQb0Ohj766CMAQFxcnMbxxYsXY+TIkQCAiRMn4saNGxg9ejQuXbqEe+65Bz/99BMCAgIc3FrGGGOMuSK3yjNkL5xniDHGGKt/pN6/63XPkKOI8SLnG2KMMcbqD/G+barfh4MhCcStOzjfEGOMMVb/XLlyBUFBQQYf52EyCWpra3H69GkEBAQYzU9kLxUVFYiOjkZxcTEP09UT/J7VT/y+1U/8vtU/jnrPiAhXrlxBZGQkPDwML6DnniEJPDw8NPIXOUtgYCB/0OsZfs/qJ37f6id+3+ofR7xnxnqERPU6zxBjjDHGmLU4GGKMMcZYg8bBUD3g7e2N9PR03iKkHuH3rH7i961+4vet/nG194wnUDPGGGOsQeOeIcYYY4w1aBwMMcYYY6xB42CIMcYYYw0aB0OMMcYYa9A4GGKMMcZYg8bBkItbsGABWrZsCR8fH3Tv3h2FhYXObhKrY9q0aRAEQaOEh4erHyciTJs2DZGRkfD19UVcXBx+++03J7a44dmyZQsGDhyIyMhICIKANWvWaDwu5T2qqqrC2LFjERISAn9/fwwaNAinTp1y4KtoeEy9byNHjtT57N17770a5/D75ljvvvsu7rrrLgQEBKBZs2Z47LHHcPToUY1zXPXzxsGQC1uxYgVSUlLw+uuvY//+/YiNjcUjjzyCkydPOrtprI477rgDpaWl6nLw4EH1Y7NmzUJmZibmzZuH3bt3Izw8HH379lVv/svs79q1a+jSpQvmzZun93Ep71FKSgpWr16N5cuXY+vWrbh69SoGDBgAlUrlqJfR4Jh63wDg4Ycf1vjsff/99xqP8/vmWJs3b8Yrr7yCnTt3Yv369aipqUG/fv1w7do19Tku+3kj5rLuvvtuGjVqlMaxdu3a0eTJk53UIqYtPT2dunTpovex2tpaCg8Pp5kzZ6qPVVZWUlBQEC1cuNBBLWR1AaDVq1erf5byHl2+fJk8PT1p+fLl6nNKSkrIw8OD1q1b57C2N2Ta7xsR0YgRIyghIcHgc/h9c75z584RANq8eTMRufbnjXuGXFR1dTX27t2Lfv36aRzv168ftm/f7qRWMX3++OMPREZGomXLlnjqqafw119/AQCKiopw5swZjffQ29sbffr04ffQRUh5j/bu3YubN29qnBMZGYmOHTvy++hkBQUFaNasGdq0aYMXX3wR586dUz/G75vzlZeXAwCCg4MBuPbnjYMhF3XhwgWoVCqEhYVpHA8LC8OZM2ec1Cqm7Z577sFXX32FH3/8EZ988gnOnDmDXr16oaysTP0+8XvouqS8R2fOnIGXlxeaNm1q8BzmeI888giWLl2KTZs2Yc6cOdi9ezceeOABVFVVAeD3zdmICKmpqbjvvvvQsWNHAK79eWtkt5qZTQiCoPEzEekcY87zyCOPqP+/U6dO6NmzJ1q1aoUvv/xSPZmT30PXZ8l7xO+jcw0ZMkT9/x07dkSPHj3QokUL/O9//0NiYqLB5/H75hhjxozBr7/+iq1bt+o85oqfN+4ZclEhISGQyWQ6kfC5c+d0omrmOvz9/dGpUyf88ccf6lVl/B66LinvUXh4OKqrq3Hp0iWD5zDni4iIQIsWLfDHH38A4PfNmcaOHYtvvvkGSqUSCoVCfdyVP28cDLkoLy8vdO/eHevXr9c4vn79evTq1ctJrWKmVFVV4ciRI4iIiEDLli0RHh6u8R5WV1dj8+bN/B66CCnvUffu3eHp6alxTmlpKQ4dOsTvowspKytDcXExIiIiAPD75gxEhDFjxiA/Px+bNm1Cy5YtNR536c+b3aZmM6stX76cPD096bPPPqPDhw9TSkoK+fv704kTJ5zdNPaP8ePHU0FBAf3111+0c+dOGjBgAAUEBKjfo5kzZ1JQUBDl5+fTwYMHaejQoRQREUEVFRVObnnDceXKFdq/fz/t37+fAFBmZibt37+f/v77byKS9h6NGjWKFAoFbdiwgfbt20cPPPAAdenShWpqapz1styesfftypUrNH78eNq+fTsVFRWRUqmknj17UlRUFL9vTvR///d/FBQURAUFBVRaWqou169fV5/jqp83DoZc3Pz586lFixbk5eVFd955p3qJInMNQ4YMoYiICPL09KTIyEhKTEyk3377Tf14bW0tpaenU3h4OHl7e9P9999PBw8edGKLGx6lUkkAdMqIESOISNp7dOPGDRozZgwFBweTr68vDRgwgE6ePOmEV9NwGHvfrl+/Tv369aPQ0FDy9PSk5s2b04gRI3TeE37fHEvf+wWAFi9erD7HVT9vwj8vgDHGGGOsQeI5Q4wxxhhr0DgYYowxxliDxsEQY4wxxho0DoYYY4wx1qBxMMQYY4yxBo2DIcYYY4w1aBwMMcYYY6xB42CIMcYYYw0aB0OMMcYYa9A4GGKMMWa1K1f+v727D4qqeuMA/t2FfeFNYWFgFxQrCQcCluLFGdkZQQRiBjApK0IEsRycCVSm1igp0xpzS3zJoUGagj/QZjJJygFkKMKgEFwkBjemUAerDbR0Vpbkbc/vj37eYWF32QUFJp7PjH/cc/ec89zDAR7PPfdyBxEREQgNDUVwcDBKS0vnOiRCrEZ/joMQQsiMjY2NYWhoCI6OjhgcHERQUBBaW1vh7u4+16ERMiVaGSJknomOjsaOHTvmXVvzBWMMW7duhUQiAY/Hw6VLl6yu+18cj5mIjo4Gj8ezeRxNsbOzg6OjIwDg7t27GBsbw3T/r52VlcXF9eWXX84oLkKsQckQIbNk/A94gUAALy8vxMXF4ZNPPoHBYOA+d/r0aezbt28OI53fampqUFZWhq+//hparRZBQUFW153LsW1sbERycjK8vb3n1S/5l156yeZxNOf27duQy+VYsmQJlEolPDw8jM5nZWXhtddem7KdI0eOQKvVzjgeQqxFyRAhs+jJJ5+EVqvFtWvXUF1djZiYGGzfvh1JSUkYHR0FAEgkEri4uMxxpOYNDw/Paf89PT2QyWRYtWoVpFIp7O3trao3PDw8K2Nrbnz0ej3kcjmOHTv2QPu3laOjo03jaImrqys6Ojpw9epVnDhxAn19fdw5g8GAs2fPYt26dVO2s3jxYkil0hnHQ4i1KBkiZBaJRCJIpVL4+PjgiSeewOuvv44zZ86guroaZWVlACbfyjl16hSCg4Ph4OAAd3d3rF27Fnq9HsC/v2AOHDgAPz8/iEQi+Pr64t133zXq02AwQKlUQiKRQCqVYs+ePUbna2pqoFAo4OrqCnd3dyQlJaGnp4c7Hx0djZdffhn5+fnw8PBAXFwcgH83zKanp8PJyQkymQyHDh2aFDtjDCqVCo888ggcHBwgl8tx6tQpi2M0NDSEvLw8eHp6QiwWQ6FQoLW1FcC/Kwu5ubno7e0Fj8fDQw89ZLYdU3GPj6+kpAQ+Pj5Gq3IAkJKSgszMTKvjNzc+EyUmJuKdd95Bamqqxeu3xs8//4yYmBiIxWL4+/ujpqYGfD4fFy9enHHbwL/XlJubix07dsDNzQ1eXl44fvw49Ho9Nm/eDBcXFyxfvhzV1dUm63t5eSEkJASNjY1cWVNTE/h8PlauXAnA8rwmZLZRMkTIHFuzZg3kcjlOnz496ZxWq0VaWhqys7Oh0WjQ0NCA1NRUbi9GQUEBDhw4gMLCQly+fBknTpyAl5eXURvl5eVwcnJCS0sLVCoV9u7di7q6Ou68Xq9Hfn4+WltbUV9fDz6fj/Xr1xslCeXl5bC3t0dTUxNKSkoAAPn5+WhqakJVVRXq6upw/vx5qNVqo753796NTz/9FB999BG6urqwc+dObNy4Ed99953Z8VAqlfjiiy9QXl4OtVoNPz8/JCQk4O+//8aRI0ewd+9eLFmyBFqtlkuSzDEV9z0bNmzAzZs38e2333Jlt27dQm1tLdLT022K31I/91t3dzciIyMRHh6Orq4uvP/++9i0aRP4fD4ee+yx+9ZPeXk5PDw8cOHCBeTm5mLbtm3YsGEDVq1aBbVajYSEBGRkZGBwcBAA0NfXB51OBwDQ6XRobGzEihUruPaqqqqQnJwMPp8/5bwmZNYxQsisyMzMZOvWrTN57rnnnmMBAQGMMcZWr17Ntm/fzhhj7OLFiwwAu3bt2qQ6Op2OiUQiVlpaarbP1atXM4VCYVQWERHBdu3aZbZOf38/A8A6Ozu5NkJDQyf1LRAI2Oeff86V3b59mzk6OnKxDwwMMLFYzJqbm43qbtmyhaWlpZnse2BggAkEAlZRUcGVDQ8PM29vb6ZSqRhjjB06dIgtW7bMbPz3mIp7/NgyxlhKSgrLzs7mjktKSphUKmWjo6NWx2+qn6kAYJWVlTbVuSc+Pp5lZWUZlT377LMsMDDQ5rYmjsf48vHzZnR0lDk5ObGMjAyuTKvVMgDshx9+YIwx1tbWxuRyOQsJCWHBwcGsuLjYqE1/f39WVVXFGLM8r8ebyTgRYouZ3yQmhMwYYww8Hm9SuVwuR2xsLIKDg5GQkID4+Hg888wzcHNzg0ajwdDQEGJjYy22HRISYnQsk8nQ39/PHff09KCwsBA//vgjbt68ya0I9fb2cptqw8PDjdq4cuUKRkZGEBkZyZUtXrzYaCXg8uXLuHv37qTbRsPDw3j88cdNxtrT04ORkRFERUVxZQKBAJGRkdBoNBav05SJcU+Unp6OrVu3ori4GCKRCBUVFXj++edhZ2dnU/xT9XO/XL9+HefOnUNHR4dRuVAohFwuBwCsX78eDQ0NiI2NnfKWpCXj542dnR3c3d0RHBzMld1bgbw3l8LCwsw+kabRaPDbb79h7dq1ACzPa0LmAiVDhMwDGo0GDz/88KRyOzs71NXVobm5GefOncOHH36IN954Ay0tLXBwcLCqbYFAYHTM4/GMboElJydj6dKlKC0thbe3NwwGA4KCgow2Ajs5ORm1wf5/O2NiAsfG3ea418fZs2fh4+Nj9DmRSGQyVkvtmkoWpzIx7omSk5O5jb0RERE4f/48ioqKbI5/qn7uF7VaDYFAgMDAQKPyzs5OvPDCCwCAvLw8ZGdno7y8fEZ9mZo348vufT0m7rkypaqqCnFxcdyctTSvTX0fEPKg0Z4hQubYN998g87OTjz99NMmz/N4PERFReHtt99Ge3s7hEIhKisr8eijj8LBwQH19fXT7vuvv/6CRqPB7t27ERsbi4CAANy6dWvKesuXL4dAIMCFCxe4Mp1Oh19++YU7DgwMhEgkQm9vL/z8/Iz+LV261GS7fn5+EAqF+P7777mykZERtLW1ISAgYNrXaY6DgwNSU1NRUVGBkydPwt/fH2FhYdOO/0Hj8/kYGxvjnjwEgNraWnR0dHArQzExMfPuacQzZ84gJSXFqMzcvCZkLtDKECGzaGhoCH/++SfGxsbQ19eHmpoa7N+/H0lJSdi0adOkz7e0tKC+vh7x8fHw9PRES0sLbty4gYCAAIjFYuzatQtKpRJCoRBRUVG4ceMGurq6sGXLFqvicXNzg7u7O44fPw6ZTIbe3l6r3gPj4uKCzMxMvPrqq5BIJPD09MRbb70FPp/PrRi4uLjglVdewc6dO2EwGKBQKKDT6dDc3AxnZ2fuia3xnJycsG3bNq5dX19fqFQqDA4OWn1NtkpPT0dycjK6urqwceNGo2u0NX5LBgYG8Ouvv3LHV69exaVLl7jrtEZYWBgEAgEKCgqQm5uL9vZ2KJVKAOCSofmmv78fra2tRu9VsjSvCZkLlAwRMotqamogk8lgb28PNzc3yOVyHD16FJmZmeDzJy/ULlq0CI2NjTh8+DB0Oh2WLVuGgwcPIjExEQBQWFgIe3t7vPnmm/jjjz8gk8mQk5NjdTx8Ph+fffYZ8vLyEBQUhBUrVuDo0aOIjo6esm5RURFycnKQlJSERYsWQalU4vr16xCLxdxn9u3bB09PT+zfvx9XrlyBq6sr90oBc9577z0YDAZkZGTgzp07CA8PR21t7QPbT7JmzRpIJBJ0d3dzt5pmEr85bW1tiImJ4Y7z8/MBAJmZmdxrFcrKyrB582azT1V5e3vj448/RkFBAUpLS5GYmIicnBx88MEH8/a9PF999RVWrlwJT09PrmyqeU3IbKO/TUYIuS/0ej18fHxw8ODBB7aK81+3Z88eNDQ0oKGhweo6SqUSHR0dqK2t5coaGhpw7NixKTdQR0dHIzQ0FIcPH55mxFNLSUmBQqHgVrBswePxUFlZiaeeeur+B0bIOLRniBAyLe3t7Th58iR6enqgVqu5d/NY84ZhYlptbS1UKpVNdX766acZ3SIrLi6Gs7MzOjs7p92GJQqFAmlpaTbVycnJgbOz8wOJhxBTaGWIEDIt7e3tePHFF9Hd3Q2hUIiwsDAUFRUZPX5NHjwfHx+oVCouGU1ISIBarYZer4dEIkFlZSUiIiJM1v3999/xzz//AAB8fX0hFApnLW5L+vv7uRc4ymSyWXtajyxclAwRQgghZEGj22SEEEIIWdAoGSKEEELIgkbJECGEEEIWNEqGCCGEELKgUTJECCGEkAWNkiFCCCGELGiUDBFCCCFkQaNkiBBCCCELGiVDhBBCCFnQKBkihBBCyIJGyRAhhBBCFjRKhgghhBCyoP0POFIWDeaFHy8AAAAASUVORK5CYII=",
|
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"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"rho = +.50\n",
|
|
"N = 10000\n",
|
|
"\n",
|
|
"mu_q = 200\n",
|
|
"var_q = 800*(1 + rho)\n",
|
|
"\n",
|
|
"mu_q1q2 = np.array([100, 100])\n",
|
|
"cov_q1q2 = 400*np.array([[1, rho],\n",
|
|
" [rho, 1]])\n",
|
|
"\n",
|
|
"q1q2 = stats.multivariate_normal(mu_q1q2, cov_q1q2)\n",
|
|
"sample = q1q2.rvs(size=N)\n",
|
|
"\n",
|
|
"q_1_dependent = sample[:,0]\n",
|
|
"q_2_dependent = sample[:,1]\n",
|
|
"q_dependent = q_1_dependent + q_2_dependent\n",
|
|
"\n",
|
|
"get_index = int(np.floor(0.99*(N + 1)))\n",
|
|
"q_percentile = np.sort(q_dependent)[get_index - 1]\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.scatter(q_1_dependent, q_2_dependent,\n",
|
|
" color='black', label='All samples of q')\n",
|
|
"ax.scatter(q_1_dependent[q_dependent>q_percentile],\n",
|
|
" q_2_dependent[q_dependent>q_percentile],\n",
|
|
" color='red', label='Top 1% of q')\n",
|
|
"\n",
|
|
"print(f'The correlation coefficient is: {rho:.2f}')\n",
|
|
"print(f'The mean value of q is: {mu_q}')\n",
|
|
"print(f'The variance of q is: {var_q:.1f}')\n",
|
|
"print(f'The design value for q~N(mu,sigma) is: ',\n",
|
|
" f'{stats.norm.ppf(0.99, loc=mu_q, scale=np.sqrt(var_q)):.1f} m^3/s\\n')\n",
|
|
"print(f'For N = {N} samples, the 99th percentile is index: {get_index}')\n",
|
|
"print(f'The 99th percentile from the sample is: {q_percentile:.1f} m^3/s')\n",
|
|
"print(' ^ this is the 1% design value, q_design, from MCS\\n')\n",
|
|
"\n",
|
|
"plt.xlabel('Discharge of river 1, $q_1$ [m$^3$/s]')\n",
|
|
"plt.ylabel('Discharge of river 2, $q_2$ [m$^3$/s]')\n",
|
|
"plt.title('Samples of river discharge')\n",
|
|
"ax.axis('equal');\n",
|
|
"ax.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.4"
|
|
},
|
|
"widgets": {
|
|
"application/vnd.jupyter.widget-state+json": {
|
|
"state": {},
|
|
"version_major": 2,
|
|
"version_minor": 0
|
|
}
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|