{
"cells": [
{
"cell_type": "markdown",
"id": "2ad3fb18",
"metadata": {
"tags": [
"remove-input",
"hide-input",
"hide-cell"
]
},
"source": [
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "4f74b633",
"metadata": {},
"source": [
"# Phase-type models for tract length distributions\n",
"\n",
"In this tutorial, we illustrate how to use the functions in ``tracts`` to compute and depict tract length distributions under the different models of admixture introduced in the paper. These are, in increasing order of complexity:\n",
"\n",
"* The Monoecious (M) model (only defined for autosomal admixture),\n",
"* The Dioecious-Coarse (DC) model,\n",
"* The Dioecious-Fine (DF) model,\n",
"* The hybrid-pedidree refinements of the DC (H-DC) and the DF (H-DF) models.\n",
"\n",
"We start by importing the required python libraries:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c33f835d",
"metadata": {},
"outputs": [],
"source": [
"import tracts.phase_type_distribution as PhT # The phase type distribution module, containing the functions to implement the admixture models.\n",
"import tracts.hybrid_pedigree as HP # The hybrid pedigree module, containing the functions to implement the hybrid pedigree refinements.\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib.ticker import FormatStrFormatter\n",
"import matplotlib as mpl\n",
"mpl.rcParams.update(mpl.rcParamsDefault)"
]
},
{
"cell_type": "markdown",
"id": "0c64d13e",
"metadata": {},
"source": [
"Throughout this notebook, we consider two source populations and a **continuous pulse** from the first to the second. This can be represented with the following migration matrix. The `whichpop` parameter sets the population of interest (0 or 1)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "cb8b3bca",
"metadata": {},
"outputs": [],
"source": [
"whichpop = 1\n",
"mig_matrix = np.array([[0, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0, 1]])"
]
},
{
"cell_type": "raw",
"id": "b1e04b1d",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"In what follows, we compute Phase-Type densities and histograms under autosomal and X chromosome admixture, using all the models presented in ``tracts``. We consider different levels of sex-bias, in both migration and recombination rates.\n",
"\n",
".. note::\n",
" The previous migration matrix represents a demographic model of 6 generations. This is a toy framework where all the presented models are computationally efficient and can be quickly computed and compared. \n",
"\n",
".. important::\n",
"\n",
" For more realistic demographic models going up to 15–18 generations, the following models should be used depending on the context:\n",
"\n",
" - For autosomal admixture: Dioecious-Coarse (DC) or Monoecious (M) model.\n",
" - For X chromosome admixture: Dioecious-Coarse (DC) model or its Hybrid-Pedigree refinement (H-DC). Typically, the number of pedigree generations should be set to ``TP=2``.\n",
"\n",
" An example under both settings is presented at the end of the notebook."
]
},
{
"cell_type": "markdown",
"id": "47919257",
"metadata": {},
"source": [
"## 1. Choose autosomal or X chromosome admixture"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "7cdca656",
"metadata": {},
"outputs": [],
"source": [
"X_chr = False # Set to True for admixture on the X chromosome\n",
"X_chr_male = False # Set to True if admixture is considered on the X chromosome of a male individual (only maternally inherited alleles)."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "a88d4d00",
"metadata": {},
"outputs": [],
"source": [
"which_L = 1.7928357829 # Second chromosome\n",
"#which_L = 1.96 # For the X chromosome\n",
"# Set a point grid on the finite chromosome\n",
"bins = np.linspace(0, which_L+0.1, num = 50)"
]
},
{
"cell_type": "markdown",
"id": "c2d1c82b",
"metadata": {},
"source": [
"## 2. Set sex-bias\n",
"The following parameters set the sex-bias for migration and recombination rates. The user can modify these parameters to observe how differences appear between all the considered models."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "af95faed",
"metadata": {},
"outputs": [],
"source": [
"prop_of_female_migration = 0.5 # Set 0.5 for unbiased migration, 1 for only female migrants, 0 for only male migrants.\n",
"mig_m = 2*mig_matrix*(1-prop_of_female_migration)\n",
"mig_f = 2*mig_matrix*prop_of_female_migration\n",
"mig_m[-1,:] = mig_matrix[-1,:]\n",
"mig_f[-1,:] = mig_matrix[-1,:]\n",
"\n",
"rec_f = 1 # Female-specific recombination rate\n",
"rec_m = 1 # Male-specific recombination rate"
]
},
{
"cell_type": "markdown",
"id": "a16638fa",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"## 3. Compute model parameters and distributions\n",
"\n",
"For the Monoecious (M), Dioecious Fine (DF), and Dioecious Coarse (DC) models, we first compute a `PhTMonoecious` or a `PhTDioecious` object, and then compute the corresponding phase-type density or histogram using the `tractlength_histogram_windowed` method. For the Pedigree-Dioecious models, densities and histograms are computed directly from the model parameters using the `hybrid_pedigree_distribution` function.\n",
"\n",
"For comparison with the other settings, the Monoecious model is always computed using the mean migration matrix and the mean recombination rate."
]
},
{
"cell_type": "markdown",
"id": "8799a86c",
"metadata": {},
"source": [
"### 3.1 Monoecious model (don't run for X chromosome)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "82b132b7",
"metadata": {},
"outputs": [],
"source": [
"PTmodel_mono = PhT.PhTMonoecious(mig_matrix, rho = 0.5*(rec_f+rec_m)) # M object\n",
"# Density (set freq = True for frequency scale)\n",
"newbins, density_m, E = PTmodel_mono.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = True, freq = True)\n",
"# Histogram\n",
"bins, hist_m, E = PTmodel_mono.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = False, freq = False)"
]
},
{
"cell_type": "markdown",
"id": "f366998e",
"metadata": {},
"source": [
"### 3.2 Dioecious Fine and Coarse models"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fa5812c0",
"metadata": {},
"outputs": [],
"source": [
"# DF and DC objects\n",
"PTmodel_DF = PhT.PhTDioecious(mig_f, mig_m, rho_f = rec_f, rho_m = rec_m, sex_model = 'DF', X_chromosome = X_chr, X_chromosome_male = X_chr_male)\n",
"PTmodel_DC = PhT.PhTDioecious(mig_f , mig_m, rho_f = rec_f, rho_m = rec_m, sex_model = 'DC', X_chromosome = X_chr, X_chromosome_male = X_chr_male)\n",
"# Densities (set freq = True for frequency scale)\n",
"newbins, density_df, E = PTmodel_DF.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = True, freq = True)\n",
"newbins, density_dc, E = PTmodel_DC.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = True, freq = True)\n",
"# Histograms\n",
"bins, hist_df, E = PTmodel_DF.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = False, freq = False)\n",
"bins, hist_dc, E = PTmodel_DC.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = False, freq = False)"
]
},
{
"cell_type": "markdown",
"id": "e692c16a",
"metadata": {},
"source": [
"### 3.3 Hybrid-pedigree refinements"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "d0b28cbf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-------------------------------------------------------------------\n",
"\n",
"Computing pedigrees probabilities...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
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]
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"-------------------------------------------------------------------\n",
"\n",
"Done! Computing phase-type densities conditioned to each pedigree...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"9 densities to compute using the DF model.\n",
"\n"
]
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]
},
{
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"-------------------------------------------------------------------\n",
"\n",
"Done!\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"Computing pedigrees probabilities...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"Done! Computing phase-type densities conditioned to each pedigree...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"9 densities to compute using the DC model.\n",
"\n"
]
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]
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{
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"text": [
"-------------------------------------------------------------------\n",
"\n",
"Done!\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"Computing pedigrees probabilities...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"Done! Computing phase-type densities conditioned to each pedigree...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"9 densities to compute using the DF model.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
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"/home/jgonzale/.local/lib/python3.10/site-packages/tracts/phase_type_distribution.py:171: ComplexWarning: Casting complex values to real discards the imaginary part\n",
" CDF_values[bin_number] = prop_connected * ((self.inner_CDF(bin_val, L, S, exp_Sx, alpha, S0_inv) +\n",
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"-------------------------------------------------------------------\n",
"\n",
"Done!\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"Computing pedigrees probabilities...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"Done! Computing phase-type densities conditioned to each pedigree...\n",
"\n",
"-------------------------------------------------------------------\n",
"\n",
"9 densities to compute using the DC model.\n",
"\n"
]
},
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"\n",
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"\n"
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],
"source": [
"# Phase-Type density for the Pedigree-DF model (set freq = True for frequency scale)\n",
"newbins, density_hp_df = HP.hybrid_pedigree_distribution(mig_matrix_f = mig_f, mig_matrix_m = mig_m, TP = 2, Dioecious_model = 'DF', L = which_L, bingrid = bins, whichpop = whichpop, rr_f = rec_f, rr_m = rec_m, X_chr = X_chr, X_chr_male = X_chr_male, N_cores = 5, density = True, freq = True)\n",
"# Phase-Type density for the Pedigree-DC model (set freq = True for frequency scale)\n",
"newbins, density_hp_dc = HP.hybrid_pedigree_distribution(mig_matrix_f = mig_f, mig_matrix_m = mig_m, TP = 2, Dioecious_model = 'DC', L = which_L, bingrid = bins, whichpop = whichpop, rr_f = rec_f, rr_m = rec_m, X_chr = X_chr, X_chr_male = X_chr_male, N_cores = 5, density = True, freq = True)\n",
"# Phase-Type histogram for the Pedigree-DF model\n",
"bins, hist_hp_df = HP.hybrid_pedigree_distribution(mig_matrix_f = mig_f, mig_matrix_m = mig_m, TP = 2, Dioecious_model = 'DF', L = which_L, bingrid = bins, whichpop = whichpop, rr_f = rec_f, rr_m = rec_m, X_chr = X_chr, X_chr_male = X_chr_male, N_cores = 5, density = False, freq = False)\n",
"# Phase-Type histogram for the Pedigree-DC model\n",
"bins, hist_hp_dc = HP.hybrid_pedigree_distribution(mig_matrix_f = mig_f, mig_matrix_m = mig_m, TP = 2, Dioecious_model = 'DC', L = which_L, bingrid = bins, whichpop = whichpop, rr_f = rec_f, rr_m = rec_m, X_chr = X_chr, X_chr_male = X_chr_male, N_cores = 5, density = False, freq = False)"
]
},
{
"cell_type": "markdown",
"id": "272badd3",
"metadata": {},
"source": [
"## 4. Plot tract length distributions"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "3b527680",
"metadata": {},
"outputs": [],
"source": [
"# Color palette and line styles\n",
"colors = {\n",
" 'M' : 'gray',\n",
" 'DC': 'green',\n",
" 'DF': 'blue',\n",
" 'P': 'orange',\n",
" 'HP' : 'orange',\n",
" 'HP_DC': 'orange',\n",
"}\n",
"line_styles = {\n",
" 'M' : '-',\n",
" 'DF': '-',\n",
" 'DC': '-',\n",
" 'P': '-',\n",
" 'HP':'-',\n",
" 'HP_DC':'-'\n",
"}\n",
"\n",
"line_widths = {\n",
" 'M' : 2,\n",
" 'DF': 2,\n",
" 'DC': 2,\n",
" 'P': 2,\n",
" 'HP':2,\n",
" 'HP_DC':2\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "6317c4ba",
"metadata": {},
"source": [
"### 4.1 Plot densities"
]
},
{
"cell_type": "markdown",
"id": "1a165d7a",
"metadata": {},
"source": [
"#### 4.1.1 Plot for autosomal admixture\n",
"The following code produces a figure depicting all the computed Phase-Type densities for autosomal admixture. Run if ``X_chr = False``."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6622fbb7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, axes = plt.subplots(1, 1, figsize=(5,4)) \n",
"ax = axes \n",
"# Plot lines with improved color and line style\n",
"line1, = ax.plot(np.delete(newbins, whichbin), (density_df[~(np.asarray(newbins) == outbin)]), color=colors['DF'], linestyle=line_styles['DF'], linewidth = line_widths['DF'], label='Dioecious Fine (DF)', zorder = 1)\n",
"line2, = ax.plot(np.delete(newbins, whichbin), (density_dc[~(np.asarray(newbins) == outbin)]), color=colors['DC'], linestyle=line_styles['DC'], linewidth = line_widths['DC'], label='Dioecious Coarse (DC)', zorder = 1)\n",
"line3, = ax.plot(np.delete(newbins, whichbin), (density_m[~(np.asarray(newbins) == outbin)]), color=colors['M'], linestyle=line_styles['M'], linewidth = line_widths['M'], label='Monoecious (M)', zorder = 1)\n",
"line4, = ax.plot(np.delete(newbins, whichbin), density_hp_df[~(np.asarray(newbins) == outbin)], color=colors['HP'], linestyle=line_styles['HP'], linewidth = line_widths['HP'], label='Ped-DF (TP = 2)', zorder = 1)\n",
"line5, = ax.plot(np.delete(newbins, whichbin), density_hp_df[~(np.asarray(newbins) == outbin)], color=colors['DF'], linestyle=(2, (2, 2)), linewidth = line_widths['HP'], label='Ped-DF (TP = 2)', zorder = 1)\n",
"line6, = ax.plot(np.delete(newbins, whichbin), density_hp_dc[~(np.asarray(newbins) == outbin)], color=colors['HP_DC'], linestyle=line_styles['HP_DC'], linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)', zorder = 1)\n",
"line7, = ax.plot(np.delete(newbins, whichbin), density_hp_dc[~(np.asarray(newbins) == outbin)], color=colors['DC'], linestyle=(2, (2, 2)), linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)', zorder = 1)\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the second chromosome', fontsize=10)\n",
"ax.set_ylabel('Density', fontsize=10)\n",
" \n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, (density_df[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['DF'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"ax.scatter(outbin, (density_dc[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['DC'], s=30, label='Outlier',marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"ax.scatter(outbin, (density_m[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['M'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"ax.scatter(outbin, (density_hp_df[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['HP'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"ax.scatter(outbin, (density_hp_dc[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['HP_DC'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"\n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, density_df[np.where(newbins == outbin)], edgecolor=colors['DF'], s=30, label='Outlier', marker='o', facecolor=colors['DF'], zorder = 4)\n",
"ax.scatter(outbin, density_dc[np.where(newbins == outbin)], edgecolor=colors['DC'], s=30, label='Outlier',marker='o', facecolor=colors['DC'], zorder = 4)\n",
"ax.scatter(outbin, density_m[np.where(newbins == outbin)], edgecolor=colors['M'], s=30, label='Outlier', marker='o', facecolor=colors['M'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_df[np.where(newbins == outbin)], edgecolor=colors['HP'], s=30, label='Outlier', marker='o', facecolor=colors['HP'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_df[np.where(newbins == outbin)], edgecolor=colors['HP'], s=15, label='Outlier', marker='o', facecolor=colors['DF'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_dc[np.where(newbins == outbin)], edgecolor=colors['HP_DC'], s=30, label='Outlier', marker='o', facecolor=colors['HP_DC'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_dc[np.where(newbins == outbin)], edgecolor=colors['HP_DC'], s=15, label='Outlier', marker='o', facecolor=colors['DC'], zorder = 4)\n",
"\n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"ax.yaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([line1, line2, line3, (line4, line5), (line6, line7)])\n",
"labels.extend([line1.get_label(), line2.get_label(), line3.get_label(), line4.get_label(), line6.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ba7cde6f",
"metadata": {},
"source": [
"#### 4.1.2 Plot for X chromosome admixture\n",
"The following code produces a figure depicting all the computed Phase-Type densities for admixture on the X chromosome. Run if `X_chr = True`."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "35660016",
"metadata": {},
"outputs": [
{
"data": {
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czp7Pgvbv/dchaR3kpdmnOBsc/Q+yoiSX/jhrNsmlL3rIJQP1FerWsh71MvoDoDzPMmrB5xB8I3iGXehhhh1j7VafEEIIfZOBuhJMu/N5y/+/S5hJXr4JWk20tB09sARzgeO/axNCCOF4ZKAuRVlnAg66sR0BKTcDkO97mFe+WAmNHmNLlh8DE6FpbBYffz6mKkstE4PBQGRkpMPPcCwvyaU/zppNcumLXnI5dnU6MqbzfydA+WjXdDAY+C2rD0szwAR8cXKx/Yq7iJubm71LqBKSS3+cNZvk0hc95JKBuhSXXvi7NC/174X7+cKLg2QEbOajnzcy9tH5hBsKJ5ptUqms/uXjKqmzrMxmM9HR0eXKpQeSS3+cNZvk0he95JKBupIYDBoPNfrvU/Xrv03Hw6sGd7n8dx3sD/550x6lCSGE0DEZqCvRe48MwpBZONs70W8lv247xEsPzcf3wqVO/9BOcOrYP3asUAghhN7IQF2Jani60cvv2cIbmuK5b2YSVrcZ/Y0teCEA9teD4MPPl74QIYQQ4iJyClEbik7tlpqaip+fX7keG3f6PPVmhYN7OhS4s2tYLK19jsHarhd6aHDPWfAIrPzCL0MphdlsxmAwoGlata+/qkgu/XHWbJJLX+yZS04hakcRtf3ooF243KVLLsM/nQG1uoBXvQs9FGx/xm715eXl2W3dVUly6Y+zZpNc+qKHXDJQl6KiMwEXPDIWCgpP9r2ND9kfdwZav/Zfh7hvwVxQGSWWi9ls5uDBgw4/w7G8JJf+OGs2yaUvesklA3UVaNsolNb5Fz5Vu2UxfP570HAIuF7YvWHOI23rZLvVJ4QQQj9koK4iC4a9AAWFB9JvNr/PkYRkzI2fYk0m9DoJPX+dY+cKhRBC6IEM1FWkY2RdWuQ9UnjDLYNHPpmNucUknkhyYU0WbFXprFjxXukLqQJGo7Ha11kdJJf+OGs2yaUvesgls75tKM9svNJs3Huc65Y2BmMB5Phx/LnjzFp4N+/l/A5AL8JYPelkZZUthBBCJ2TWdyW50vcw3VrWo2n20MIbHud5ZN77jB/6KQEXDgNYRwLb/119pWWWmVKKtLS0K87laCSX/jhrNsmlL3rJJQN1KSpjJuBHgyeAuXDXyv9lz6TAtSa3aS0AKABmrnruitdRVmazmaNHjzr8DMfyklz646zZJJe+6CWXDNRV7Ka2jWiYORgA5ZHCIx/N5YU7ZlPXCNOCYG79A5AWY+cqhRBCOCoZqKvBBwNeAlW4u3tNxgxC6nfmaJuWjA8EPyOwZbh9CxRCCOGwZKCuBn06RlIvfSAAyvMsw+fNw7XzRZe8PPMnZMZVSy0eHh7Vsp7qJrn0x1mzSS590UMumfVtQ2XN+r7Yyk176bcmCjSFISuYMy8fI/CPNpB+Ybd3yC1w05pKWZcQQgjHJrO+K0llTjDo27UlddLuLVyu1ykemzcfOsz9b12Ja8lKrdpDtcxmM+fOnXP4iRPlJbn0x1mzSS590UsuGahLUdk7G2b2e8Xy/xVn3ybV93pMnvVYlg4dTsC4jwZU6voupZTixIkTDn8oQnlJLv1x1mySS1/0kksG6mrU/4Y2hKT2BcDsncCIjxfyf54TuD8JdubC8oLNpCYn2blKIYQQjkQG6mr27h2vWv7/bdI0unQfxo3UBOCU2cxr8wfbqzQhhBAOSAbqavbgzR2olXobAKYaJ3jy40WMjHrBcv83eX+QlXG+ytbv4+NTZcu2J8mlP86aTXLpix5yyaxvG6pi1vfFPv11C4/+3RkAQ0Ydzrwaw12z6rBRpQDwao3beW3sT5W+XiGEEI5BZn1XkqqaCTi8VyeCU+8sXEeNkwyd+yFPNhlFAxf4pDZMCFkDBXmVvl6z2UxSUpLDz3AsL8mlP86aTXLpi15yyUBdiqrc2TD33jctZyv7+fw0buw5lkNN/HnMDzy1fNgxttLXqZQiKSnJ4Wc4lpfk0h9nzSa59EUvuWSgtpN7r4uifvoDACjPcwyeOwOXqP8mmnFkPpgL7FSdEEIIRyEDtR19+tAUMLkAsCF/BnvdHwCXCxMbzLmw62U7VieEEMIRyEBdCu3CdaOryk1tG9Eq9/HCG26ZPDj/LWg+znJ/3oH3MReYKm19mqYRGBhY5bmqm+TSH2fNJrn0RS+5ZNa3DVU96/tiO48k0m5hI3DNhgI3/up/gPbRLVl8Ppu3kmF0zcd59omPL78gIYQQuqHLWd9vvfUWmqYxevToUvt9++23NGvWDA8PD6Kioli1apXV/UopJk6cSGhoKJ6envTs2ZOYmIpd77k6ZgK2bRRKZ+3ZwhsueQxb/DpzU+7jydMQWwCfnfqi0j5Vm81m4uLiHH6GY3lJLv1x1mySS1/0ksshBuqtW7fy8ccf07p161L7bdq0iUGDBjF8+HB27NhBv3796NevH3v27LH0eeedd5gzZw7z5s1jy5YteHt706tXL3JycspdV3XtbFjy1AtoOf4AxHh9TuM2Y2lqcANgt8pi1oInKmU9SimSk5MdfoZjeUku/XHWbJJLX/SSy+4DdUZGBoMHD2b+/PkEBASU2nf27Nn07t2b559/nubNm/P666/Tvn17PvjgA6Dwlz5r1ixeeeUV+vbtS+vWrVm8eDEJCQmsWLGiGtJUTIPQAG7xvnB2MoOZkctfZ1hAf8v9n5z5goL8yj+uWgghhONzsXcBTz/9NLfffjs9e/bkjTfeKLXv5s2bGTNmjFVbr169LIPwsWPHSEpKomfPnpb7/fz86NSpE5s3b2bgwIE2l5ubm0tubq7ldlpaGgAmkwmTqXC3s6ZpGAwGzGaz1buvovaifpdrNxgMaJpWrH3xU6MIe2sOxhrnOO3/A8EN/6BN6kp2mdI5ZM7jw/nDePqJxZb+RqMRpVSxXTZGo7FYjZe2V1cmg6HwfeClNZbUXtFMJpPJkstZMhXlKXqsrf56zFSk6LGXLkPPmYomJF38HHOGTBc/ny597dB7JluvHdWV6dLHlcauA/XXX3/N9u3b2bp1a5n6JyUlERwcbNUWHBxMUlKS5f6itpL62DJt2jSmTJlSrH3//v2W88AGBgYSERFBfHw8ycnJlj4hISGEhIQQGxtLenq6pT08PJygoCBiYmKsdrs3bNgQX19f9u3bZ7WhIiMjGRDyKv5+hbvxd8f+H883nsa7sc8xpWYNIvz9id69AzQXjEYjUVFRpKenc/ToUcsyPDw8aNasGSkpKZw4ccLS7uPjQ6NGjThz5gw5OTns3bvXMtuxqjO5ubkRHR1t9XuNiooiLy+PgwcPWtoqmun06dMkJiZacgUFBTlFpqKTMOTk5JCQkEC9evWcIlORgIAAQkJCSEhIICUlxSkyBQYGUrduXVxcXCzPMWfIFBERQUJCgtVrhzNkio+P59y5c5ZcoaGh1ZopIyODsrLbrO8TJ05wzTXXsHbtWst30zfeeCNt27Zl1qxZNh/j5ubG559/zqBBgyxtH374IVOmTOHUqVNs2rSJbt26kZCQQGhoqKVP//790TSNpUuX2lyurU/U4eHhJCcnW2bjVccntYzsPIInRVHgEwvA1GY/MZr+GAvSMOMC9QZD5wVA1bxbropMYN9PAJJJMkkmyeSImdLS0ggMDCzTrG+7faL+999/OX36NO3bt7e0mUwmNmzYwAcffEBubi5Go9HqMSEhIZw6dcqq7dSpU4SEhFjuL2q7eKA+deoUbdu2LbEWd3d33N3dbd53aQ1Fv+zL9atIu4+XO0MbTmTe6YcAmLz5VcaMeAdt2xMYyYe4/0HH98DNHyj8A7K1nJJqVEoRGxtL/fr1rR5XlZnK217eTEVPoKJcRf30ngmwylVafz1lKmIymThy5Eixv8XKrLG87VeaCay32aXL0msmKPm1Q8+ZSnrtqK5MJd1vs9Yy96xkN998M9HR0ezcudPyc8011zB48GB27txpM0SXLl1Yt26dVdvatWvp0qULAA0aNCAkJMSqT1paGlu2bLH0cXSzHx2Ex/koADL9/+HlzbXB48KufGWCzQ9f0fIv3qXjTCSX/jhrNsmlL3rIZbeB2sfHh1atWln9eHt7ExQURKtWrQAYMmQIEyZMsDzm2WefZfXq1cyYMYMDBw4wefJktm3bxsiRIwEsx2G/8cYb/PDDD0RHRzNkyBDCwsLo16+fPWKWm5urkXHt3rTcnrnrJXJaz7LcTj7+A6cTD9uhMiGEEPZg98OzShMXF0diYqLldteuXVmyZAmffPIJbdq0YdmyZaxYscIysAO88MILjBo1iscff5yOHTuSkZHB6tWr8fDwsEeECpky+A58UroCkOe3nyErznHetR5vJUOj44rxn/a/zBKEEEI4CzmFqA1Fp3ZLSUnB39/fLjV8+usWHv27MwBadiDLukyj/84nMAG+Gvw74B8aR3Ys1zLNZjMpKSkEBASU+L2NHkku/XHWbJJLX+yZqzynEJWB2obqPNd3aRqOfYhjvl8A0C5nNHU9l/OjigNggNaMryfut1ttQgghKk6X5/p2ROU5IL0qLH18GuR7ArDD9QPuiZxE0dz0lRxg5/Y15VqeyWTiwIEDds9V2SSX/jhrNsmlL3rJJQO1A+sYWZfuLhdOLWosYPzfK7hLawpAjoJvfnum3MusyDnP9UBy6Y+zZpNc+qKHXDJQO7hvnn0eQ2YYAKf8fyQqeBS3ehj4sy5MrXsQTq23b4FCCCGqlAzUDq52gDeP1X/LcvvNgx/zS7tuXOd5oeHv4fYpTAghRLWQgboUjjK78YMnBuOdWjjDO9dvD8/u7wMUnkeYzKNwfFmZlmMwGGjYsKHD5Koskkt/nDWb5NIXveRy7OrsrOik+vbmYjTwbs/3LLfnJs4kq+at/3XY+jiU4cLnmqbh6+vrMLkqi+TSH2fNJrn0RS+5ZKAuhSPNBBxxezfCzw8AQHme5fY/m4BWeKr245kpLPtq1GWXYTKZiI6OdqhclUFy6Y+zZpNc+qKXXDJQ68hXw9+GgsIDtNZrH3OwxkO8dBYij8PzRz8hIy35MktwrDcflUly6Y+zZpNc+qKHXDJQ60i3lvXoqo0tvGHMp/u6c/yaWoNcBbHmAsbP7WvfAoUQQlQ6Gah15ttnx2PIvHA5z4Af6OP5sOW+L/L/4vDBrXaqTAghRFWQgboUjjgTMCzIh6HhUy23ZyT8SW8Kj7M+r+CFpQNLfKzBYCAyMtIhc10JyaU/zppNcumLXnI5dnXCpk+eGopnajsAcvx3EWYYhJdWuDFDfY5iPvFjiY91c3Orpiqrl+TSH2fNJrn0RQ+5ZKAuhbkMhzzZg4vRwDs3zbbc/ixrAeM9r2VHBMwNBsM/tk+CYjabiY6OdthcFSW59MdZs0kufdFLLhmodWrkndfTKH1o4Q2P8yw/HU5rD2Ph7dwzsHea/YoTQghRaWSg1rEfn3kXLScAgJ01vmOH4bb/7oyeAgWOf7J5IYQQpZOBWseaR9TigeD/zgPe9Z8DKKN34Q1zLmx5xE6VCSGEqCyaUkrZuwhHU3RB79TUVPz8/OxdTqkKTGYCxnUjw/9vAGb63cVztX9gby5MPOPCzPv+pV7D1gAopTCbzRgMBoc/ZV55SC79cdZskktf7JmraJw5f/48vr6+pfaVT9Q652I0sKDfR2Au3JRjzq7hrYRw2sTB8uwCXvyiv1X/vLw8e5RZ5SSX/jhrNsmlL3rIJQN1KRx9JmCRAd3b0i7vmcIbrjn8dLIprhfeHC5XB/nj9y+BwjwHDx7UTa6yklz646zZJJe+6CWXDNRO4qdxr2HILDzxyUb/ddxeEAlAPvDKn6MwFzj++WyFEEIUJwO1kwgL8uHZyFmW2xsz8gi+cLadv1QKsz6RiWVCCKFHMlA7kenD7iMotRcASX7H6JnZBRdgfAA85vslZJ/CaDTat8gqIrn0x1mzSS590UMumfVtQ3lm4zmadTsO03N5K3DJBRPsjAiijde5wjsDr4HectEOIYSwN5n1XUn0+B7m5naN6eHyUuENI7xyPJiiFCr5X9IOfqfLXKVRSpGWlia5dMRZs0kufdFLLhmoS+HoMwFLsmLci7imNQHgJ5d97M9rBoAZF47u3YC5wPEPRygPs9nM0aNHdbu9SuKsucB5s0kufdFLLhmonZCvtzuvdZ5rud0p5iRmzQUAZc7nz+XD7FWaEEKIcpKB2kmNv/8WGqY/BECGWzpvxDVmRw6syID+h77j0P6/7VyhEEKIsqjQQH306NHKrkNUgTVjZmHIDAFgUs4BXjpRi0O5KaQoM899c7+dq6tcHh4e9i6hSjhrLnDebJJLX/SQq0Kzvg0GA927d2f48OHcd999ughaHnqe9X2plxavZNqxfgA0zQwnqcYJ0i5s8YWNJvDwg1PtV5wQQlylqnzW9/bt22ndujVjxowhJCSEJ554gn/++adCxToyR59gUBZTh/SlXtogAA57n+RB4+0YLmz2acdmkJVx3p7lVQqz2cy5c+ecYntdzFlzgfNmk1z6opdcFRqo27Zty+zZs0lISOCzzz4jMTGR6667jlatWjFz5kzOnDlT2XXahaNP2S+rX0fPQcuqjVEzQnAEUYbCS2GajXns/3mAnau7ckopTpw44TTbq4iz5gLnzSa59EUvua5oMpmLiwv33HMP3377LW+//TaHDx9m3LhxhIeHM2TIEBITEyurTnEFIsNr8lzTwlngSoPa6RFMCoToCOhg+hXObLZzhUIIIUpyRQP1tm3beOqppwgNDWXmzJmMGzeOI0eOsHbtWhISEujbt29l1Smu0Izh9xF2/m4A1tc4RH9PXzyKtv6f94CD7/oRQoirVYUG6pkzZxIVFUXXrl1JSEhg8eLFHD9+nDfeeIMGDRpw/fXXs2jRIrZv317Z9Yor8NPTs4lPT0ah6HUqDbO6cC3MnCTYPtqutV0pHx8fe5dQJZw1FzhvNsmlL3rIVaFZ302aNOGRRx7h4YcfJjQ01GafvLw8vvrqK4YOHXrFRVY3Z5r1falnPvma9xMLJ5dN9/NkbO3sC/domHvtwhAUZb/ihBDiKlHls77Xrl3Liy++WGyQVkoRFxcHgJubmy4H6Ys5+kzA8jKbzYy/ozt1LuwCH3c+m4RcTwoUvJOsuH1uT11et9psNpOUlOSU28sZc4HzZpNc+qKXXBUaqBs1asTZs2eLtScnJ9OgQYMrLspROPpMwPJSSnH69Cl+euoDtJwAAG5KzOaOeBdePAer1Wmmzh1k5yrLTylFUlKSU24vZ8wFzptNcumLXnJVaKAuKVRGRobTnfzEGUU1CObx8NkAHMwHz+QmlvtmpS1j354/7VWaEEKIS7iUp/OYMWMA0DSNiRMn4uXlZbnPZDKxZcsW2rZtW6kFiqrx4ZMP8v3Ybzjt/xMrPPdzvQriT+0c58yKkd/dy/+1Om3vEoUQQlDOT9Q7duxgx44dKKWIjo623N6xYwcHDhygTZs2LFq0qMzL++ijj2jdujW+vr74+vrSpUsXfvnll1If8+2339KsWTM8PDyIiopi1apVVvcrpZg4cSKhoaF4enrSs2dPYmJiyhPTQtO0Cj3OUWmaRmBgIJqmYTBorHtmAVpWLdAgId9M4IW86znDqq8ftXO1ZXdxLmfirLnAebNJLn3RS64KzfoeNmwYs2fPvuIZ0T/++CNGo5EmTZqglOLzzz/n3XffZceOHbRs2bJY/02bNnHDDTcwbdo07rjjDpYsWcLbb7/N9u3badWqFQBvv/0206ZN4/PPP6dBgwa8+uqrREdHs2/fvjLvlnfmWd+Xmvzlz0w5fAcAd2c3Za/vIRYGQ1dPDW6LBv/i20EIIcSVKc84U6GBuioFBgby7rvvMnz48GL3DRgwgMzMTH766SdLW+fOnWnbti3z5s1DKUVYWBhjx45l3LhxAJw/f57g4GAWLVrEwIEDy1RD0S8wJSUFf3//SsnlCMxmM/Hx8dStWxeD4b+dKa3HjyTacy4oiAl3pbFnfuEdXnWh3wk7VVt2JeXSO2fNBc6bTXLpiz1zlWegLvN31Pfccw+LFi3C19eXe+65p9S+y5cvL+tiLUwmE99++y2ZmZl06dLFZp/Nmzdbvicv0qtXL1asWAHAsWPHSEpKomfPnpb7/fz86NSpE5s3by5xoM7NzSU3N9dyOy0tDYCCggJMpsLDlQp3Fxswm81Wk+mK2ov6Xa7dYDCgaZrNdih+SFhJ7UajEaWUzfZLayxqN5lMnDt3jpCQEIxGo6XG/xv/Ng1e/5Ncv/3cdwa2hRtw0cyYspLg37HQ9h2HzWQ2mykoKLDkcnFx0f12Kmov2l6hoaFOk6mI2WwmOTmZ0NBQp8mkaRpKKavnmDNkKqrR1muHnjOV9NpRXZkufVxpyjxQ+/n5Wfbj+/n5lXkFlxMdHU2XLl3IycmhRo0afP/997Ro0cJm36SkJIKDg63agoODSUpKstxf1FZSH1umTZvGlClTirXv37/fctaawMBAIiIiiI+PJzk52dInJCSEkJAQYmNjSU9Pt7SHh4cTFBRETEwMOTk5lvaGDRvi6+vLvn37rDZUZGQkbm5uREdHW9UQFRVFXl4eBw8etLQZjUaioqJIT0+3uja4h4cHzZo1IyUlhRMn/vsk7OPjQ6NGjThz5gzJycns3bvX8t1MREQEWWnn+LznTH47+T1oZj7N2cYTnluJdelN+rFsMP0Jbv4Omen06dMkJiZacgUFBel+O50+fdpyyEhycjIJCQnUq1fPKTIVCQgoPDwwISGBlJQUp8gUGBhInTp1yMzMtDzHnCFTREQECQkJVq8dzpApPj6ec+fOWXKFhoZWa6aMjAzKyu67vvPy8oiLi+P8+fMsW7aMBQsW8Mcff9gcrN3c3Pj8888ZNOi/Y30//PBDpkyZwqlTp9i0aRPdunUjISHB6mQs/fv3R9M0li5darMGW5+ow8PDOXPmjOUFxRk+Uefn57Nnzx5atmxp9a64qH//6e/zY+4LmJSJuHoQ4mbgcJ7Gh6fqMHPcYYfMVPSueO/evbRs2dLpPlHv3buXVq1a4erq6hSZipjNZss2u3iXo54zFX2i3r17t+U55gyZDAZDia8des5U0mtHdWVKS0sjMDCwcnd9Xyw7OxullOXwrOPHj1s+Cd96663lWpabmxuNGzcGoEOHDmzdupXZs2fz8ccfF+sbEhLCqVOnrNpOnTpFSEiI5f6itosH6lOnTpV62Ji7uzvu7u7F2l1cXCxPtiIlfY9xab/qaNc0zWZ7aTWGhoZa/iAv7b903DMEj11FcsBaeiXCiBoGxqXkk6NiCZwzgEnPLXO4TAaDARcXl2K59Lydito1TSM0NNTyWGfIdPHji3aj2nqMHjNB4YuwredYZdVY3vbKyFS0bFu59JyppNeO6spU0v02ay1zz4v07duXxYsXA5Camsq1117LjBkz6Nu3Lx999FFFFmlhNputPt1erEuXLqxbt86qbe3atZbvtBs0aEBISIhVn7S0NLZs2VLi996lcaZJE1CYJyQkpMRcLkYDa59ehJYdxN48WJfQgJwLb0Rnpn/H5o3ln3tQHS6XS6+cNRc4bzbJpS96yVWh6rZv3871118PwLJlywgJCeH48eMsXryYOXPmlHk5EyZMYMOGDcTGxhIdHc2ECRNYv349gwcPBmDIkCFMmDDB0v/ZZ59l9erVzJgxgwMHDjB58mS2bdvGyJEjgcJ3WqNHj+aNN97ghx9+IDo6miFDhhAWFka/fv3KnbM8X/brgclk4siRI6Xmat8kjPEtPgXge48YephrApCmYMS6h8jJKvv3KtWlLLn0yFlzgfNmk1z6opdcFRqos7KyLJOs1qxZwz333IPBYKBz584cP368zMs5ffo0Q4YMITIykptvvpmtW7fy66+/cssttwAQFxdHYmKipX/Xrl1ZsmQJn3zyCW3atGHZsmWsWLHCcgw1wAsvvMCoUaN4/PHH6dixIxkZGaxevVpObXrBxZMkSjJ1SF+aZz4BwD5zNuGGwl00u1QWL83pXqX1VVRZcumRs+YC580mufRFD7kq9B1148aNWbFiBXfffTe//vorzz33HFA48JbnBCGffvppqfevX7++WNv999/P/fffX+JjNE3jtdde47XXXitzHaK49RNmEP7Gek75HqRnVn0SPWIZ4QdvBm2Hgx9A5Eh7lyiEEFeFCn2injhxIuPGjaN+/fp06tTJ8v3vmjVraNeuXaUWKOyjdoA3n92+BArc+M0jlrk+vsypDZ5GYPtoyDhm7xKFEOKqUOHDs5KSkkhMTKRNmzaWL+L/+ecffH19adasWaUWWd2c+cxkKSkpBAQElHnyxAMz5/FV+ghcgDMNwb9ooqJnHegbBw4wCaMiufTAWXOB82aTXPpiz1y6PoWoI7iazvV9OWazotHzDxHr+yUd3eHvcDAUnb++wVDossie5QkhhC6VZ5yp0FuIzMxMXn31Vbp27Urjxo1p2LCh1Y+zcPSZgOVlMpk4cOBAuXIZDBpbXvkY9/Mt2ZoL7144iZRZwbSt/+O33xZWUbVlV5FceuCsucB5s0kufdFLrgpNJnv00Uf5448/eOihhwgNDXX4S4SJ/1x8Cryyqh3gzfKBy7h9ZUfGn8vgWqM7b6Tn8n/ZZppvHsHfHe7AN6BWFVRbdhXJpQfOmgucN5vk0hc95KrQQP3LL7/w888/061bt8quRzio265txjO7FjAnYSD3JWj4u7kC+ew35/LY+9exdOLByy5DCCFE+VVo13dAQACBgYGVXYtwcLMfG0Dr7FEku+QQnhmK24X2b9Qh3p//lF1rE0IIZ1Whgfr1119n4sSJZGVlVXY9DsWZZjdCYZ6GDRteUa6Nk6bjndqJPzzjuD33v/kIU5PmkRq7vhKqLL/KyOWInDUXOG82yaUveslVoVnf7dq148iRIyilqF+/Pq6urlb3b9++vdIKtAeZ9V26zfvi6La4PcrjHF00P+JczrMsBDrX8Ia7E8BNfmdCCFGa8owzFfqOuiLnzdYjR58JWF4mk4l9+/bRokWLcl255VJdWkTwersveWV/H07km9lUTyPCTYEpE9Z0gTv2VmLVl1dZuRyNs+YC580mufRFL7kqNFBPmjSpsusQ1aSy3ny8PKAXaydP5A/XKTx/Fr4OBU0D0vbBlseg0/xKWU9ZOdubqiLOmgucN5vk0hc95KrwjvnU1FQWLFjAhAkTSE5OBgp3eZ88ebLSihOObc3Lr1IztTffZML88xfdcWQBHF9qt7qEEMKZVGig3r17N02bNuXtt99m+vTppKamArB8+XKry1IK5+bmamTb+K9wS4vkiTOw98JlxA/kwS1LhhJ7ZJd9CxRCCCdQoYF6zJgxPPzww8TExFhdPvK2225jw4YNlVacvTn6TMDyMhgMREZGVmquesH+/PTAj2g5AXQ+Ad8me9ExDn7Ly2Xwlz0oyM+rtHWVpCpyOQJnzQXOm01y6YteclWouq1bt/LEE08Ua69Tpw5JSUlXXJSoOm5ubpfvVE63dGjCWx2+IcNk5PWEGrhReKa6TSqFx9/uXOnrs6UqcjkCZ80FzptNcumLHnJVaKB2d3cnLS2tWPuhQ4eoVcu+p5KsTGaz2d4lVCqz2Ux0dHSV5Hrhvp7cV2MW0e6n6ZLVkKKTyi4y7WDOJyMqfX0Xq8pc9uSsucB5s0kufdFLrgoN1HfddRevvfYa+fn5AGiaRlxcHC+++CL33ntvpRYo9GPp2KdpnvkEP3se4a68+gAoYGXyfDj9l11rE0IIvarQQD1jxgwyMjKoVasW2dnZdO/encaNG+Pj48Obb75Z2TUKnTAYNLa99j7+KTey0iWWbvjzqC/8XNcEv98KOWftXaIQQuhOhY6j9vPzY+3atWzcuJFdu3aRkZFB+/bt6dmzZ2XXJ3TGy8OVv8d+S6vZ13LcJ47/qw1uGmDKhl/aQt9YMFToz04IIa5K5T6FqNlsZtGiRSxfvpzY2Fg0TaNBgwbcd999PPTQQ05xycuiU7ulpqbi5+dn73IqjVIKs9mMwWCo8u20ctNe+v3cmb4BGXxfdDIUgJpd4daNlbqu6sxVnZw1FzhvNsmlL/bMVZ5TiJZr17dSirvuuotHH32UkydPEhUVRcuWLTl+/DgPP/wwd9999xUVLqpeXl7VHy4F0LdrS15t/hUrMzQmngPL28Gzm4j+YVilr6+6clU3Z80FzptNcumLHnKVa6BetGgRGzZsYN26dezYsYOvvvqKr7/+ml27dvHbb7/xf//3fyxevLiqaq12jj4TsLzMZjMHDx6stlyvPXgHt7u/wxspsCyjcLCemgwddy5i4ReVd2Kc6s5VXZw1FzhvNsmlL3rJVa6B+quvvuKll16iR48exe676aabGD9+PF9++WWlFSf074cXxxKVPZL+STA+NoSXz0GugnFH32bD+q/sXZ4QQji8cg3Uu3fvpnfv3iXe36dPH3btktNGiv8YDBrbXp9F2Pl7mJl7imvxASBZKR75cyjHj+62c4VCCOHYyjVQJycnExwcXOL9wcHBpKSkXHFRourY41Jubq5Goid/gVdaN07mQyND4fXLj5jz6f/F9eRlp1/xOhz5EnVXwllzgfNmk1z6oodc5Zr1bTQaSUpKKvHsY6dOnSIsLEwXlw0rTXlm44myO5aYQvN3r6OlRzLHPU+RalbMrgVPR7SA26LBwc+3K4QQlaU840y5DmhVSvHwww/j7u5u8/7c3NzyLM7hlfPINYenlCI9PR0fHx+7HGLRIDSA3x/9hesWdeHWrPqManCM22pQeA3rjffD9d9VaLn2zlVVnDUXOG82yaUveslVro8wQ4cOpXbt2vj5+dn8qV27NkOGDKmqWqudo88ELC+z2czRo0ftmqtLiwi+uWs1q7VzxBX8165OLIedL1VomY6Qqyo4ay5w3mySS1/0kqtcn6gXLlxYVXWIq8i910Ux48wKRmzvTSv3PK7zpPAiHvumgWcoRI6yd4lCCOEw5EtBYRdj7u7BMxGL6R4Pxwqv7UKGGe5e+RwrV86ya21CCOFIZKC+ynh4eNi7BIvZjw3gTveZtIqFvVku3BQPK7JNPL57LH9t+KZcy3KkXJXJWXOB82aTXPqih1zlPtf31UBmfVev6ya+wn41gzquGtEqG4B6Bhd+uvM3WrXtbufqhBCi8lXZub6vNo4+waC8zGYz586dc7hcGya/Tn3TCM7nuVqOsT5uLqD/j72Ii91z2cc7aq4r5ay5wHmzSS590UsuGahL4Ww7G5RSnDhxwuFyGQwaW9+YQY38B/DI8SfMUHgCgmQtlzPrboS81FIf76i5rpSz5gLnzSa59EUvuWSgFg7BYNDYNXUuObm3EZ4dzDWuRjaFQwfPc/BTCyhw/CvcCCFEVZCBWjgMF6OBfdM+JSHnepq7mWhQdPBgTiL80hocfPeUEEJUBRmorzI+Pj72LqFUbq5GDkz9H2tP9mX8xdexTj8Ia7uUOFg7eq6KctZc4LzZJJe+6CGXzPq2QWZ9219aZi4NX76LV5qs4Vl/0DTYkQPzElvz0YvbMbg4/on0hRCiJDLru5I4+kzA8jKbzSQlJekil6+3OwemfM/kmO4sSYftOXDzSfikYDfDprW36qunXOXhrLnAebNJLn3RSy67DtTTpk2jY8eO+Pj4ULt2bfr168fBgwcv+7hvv/2WZs2a4eHhQVRUFKtWrbK6XynFxIkTCQ0NxdPTk549exITE1Pu+pxtZ4NSiqSkJN3kqunnxb5Xf+TJA11450gjUi48lxabdzPsjXaWfnrLVVbOmgucN5vk0he95LLrQP3HH3/w9NNP8/fff7N27Vry8/O59dZbyczMLPExmzZtYtCgQQwfPpwdO3bQr18/+vXrx549/x1v+8477zBnzhzmzZvHli1b8Pb2plevXuTk5FRHLFGJwoJ8OPjqr/ySGca9uQ0t7YtMOxn+Rgc7ViaEENXDrgP16tWrefjhh2nZsiVt2rRh0aJFxMXF8e+//5b4mNmzZ9O7d2+ef/55mjdvzuuvv0779u354IMPgMJ3SLNmzeKVV16hb9++tG7dmsWLF5OQkMCKFSuqKZmoTGFBPsRM+oXfsxpy90WDdYL7dnLX3mLHyoQQouo51HfU58+fByAwMLDEPps3b6Znz55Wbb169WLz5s0AHDt2jKSkJKs+fn5+dOrUydKnrBz5+qQVoWkagYGBusxVO8CbI2/8yMbs5tyT25DbvOD7UHA/8xvaH3fpNldp9Ly9LsdZs0kufdFLrnJd5rIqmc1mRo8eTbdu3WjVqlWJ/ZKSkggODrZqCw4OJikpyXJ/UVtJfS6Vm5tLbm6u5XZaWhpQ+OncZDIBhRvUYDBgNputvs8oai/qd7l2g8GApmk224t+D2VpNxqNKKVstl9aY1E7QJ06dSy59JbJx9OVQ69/S5tJQ5nlE4eHoQAzBlTSWupoI1F1vsdsNusqk63tdHF7nTp1LPc5S6aiGiMiIjCbzVb16D2TwWCgbt26Nl879JwJbL926DlTUXtRrqLXjurKdOnjSuMwA/XTTz/Nnj17+Ouvv6p93dOmTWPKlCnF2vfs2WM5xi4wMJCIiAji4+NJTk629AkJCSEkJITY2FjS09Mt7eHh4QQFBRETE2P13XjDhg3x9fVl3759VhsqMjISNzc3oqOjrWqIiooiLy/PapKd0WgkKiqK9PR0jh49amn38PCgWbNmpKSkcOLECUu7j48PjRo1IikpiaNHj+Lt7W15J6nHTN8NnsCc31vgbpxCO98OJBo7kpkSivev0wlqNUiXmS7eTqdPn7ZMcMnMzCQ8PJx69eo5RaYiAQEBaJqGUoqUlBSnyBQYGEjdunXZtWsX8N8eOb1nioiI4MSJE5w4ccLy2uEMmeLj4zl37hyZmZl4e3sTGhparZkyMjIoK4c4jnrkyJGsXLmSDRs20KBBg1L7RkREMGbMGEaPHm1pmzRpEitWrGDXrl0cPXqURo0asWPHDtq2bWvp0717d9q2bcvs2bOLLdPWJ+rw8HDOnDlDQEAA4ByfqPPz89mzZw8tW7bEaDTqOlNevok2r45gTtNF3OTtwV63YfxxaiG7U5qxYPw/YNB0l+nSdpPJxN69e2nVqhWurq663E4ltZvNZvbu3UvLli0t69F7pqI3Hrt377Y8x5whk8FgKPG1Q8+ZzGYzBQUFlr9DFxeXas2UlpZGYGBgmY6jtusnaqUUo0aN4vvvv2f9+vWXHaQBunTpwrp166wG6rVr19KlSxcAGjRoQEhICOvWrbMM1GlpaWzZsoURI0bYXKa7uzvu7u7F2o1Go+XJVuTiF5VL+1Z3u6ZpNttLqrHoD+vSXHrM5Gk0su+t+bR7yYOZjeeTjJkXzuWTr7aTPrUZX03Yi4urW7XWXlJ7RbbTxY8tuq3H7VSWdlvL0Wumot3Ctl479JqpqN1WLr1nKnrTYTQaLf2qK1NJ99ustcw9q8DTTz/NF198wZIlS/Dx8SEpKYmkpCSys7MtfYYMGcKECRMst5999llWr17NjBkzOHDgAJMnT2bbtm2MHDkSKNyIo0eP5o033uCHH34gOjqaIUOGEBYWRr9+/ao7oqhCLkYDu6Z9wCvHnyUu4793pMvUYe6a2pCcrLLvWhJCCEdl14H6o48+4vz589x4442EhoZafpYuXWrpExcXR2JiouV2165dWbJkCZ988glt2rRh2bJlrFixwmoC2gsvvMCoUaN4/PHH6dixIxkZGaxevRoPD49y1efoMwHLq+i7JWfKZTBobJz8Fkdywrkru4HlD/oXTtLn3QaYc1JKfbwjc8btVcRZs0kufdFLLof4jtrRyLm+9enJD//HqbjXWeUZQx4wpxY8VdMf4x17wSvM3uUJIYSFnOu7kpRn+rwemEwmjhw54rS55j7xANe2/4BbspryRoCBUf5gLEjF9EMTSD9i7zLLzVm3FzhvNsmlL3rJJQP1Vebiww6cSVGuCf1vZeCtSzie7Y35wr4iozkL04/N4dx2O1ZYMc66vcB5s0kufdFDLhmohdN58OYOPNB7J4OOBmMqGqzJJ+Xna/nrjyX2LU4IIcpJBmrhlG5s05DJQ6O562BT8hUUKHjwlIm+fzzI51++bO/yhBCizGSgLoWjzwQsL03TCA8Pv2pyNY+oxcLnttNnXzdeTfRiVRYkK8UTh6cyZdZ9dqq27Jx1e4HzZpNc+qKXXDLr2waZ9e1csnLyufmVYZh8fmAr/30fNczQngUT/sHgUvYTDwghRGWQWd+VxNFnApaXyWTiwIEDV10uLw9XNr7zP+q5vsot5v8u1vKztp3DS5pCQVZ1lVouzrq9wHmzSS590UsuGaivMhefVN6ZXC6XwaDx7UvP0z1yIXfnNsRLgx/DoKnLUXK+CYGM49VUafk46/YC580mufRFD7lkoBZXlZcf6MNjd69ijLEOHS+c3t2DdPJXNobT1X/lNiGEuBwZqMVVp0/HSB55JJoxsc0sx1q7agWY115PwvYP7VucEEJcQgbqUpR01RW9MhgMNGzYUHIBDUIDeHPsbh492o+8C4P1gTxo8/PTjH2rdxVVWj7Our3AebNJLn3RSy6Z9W2DzPq+ujw763VG+02mV6KZmPzCtjvN9Vgydjs1fAPtW5wQwinJrO9K4ugzAcvLZDIRHR0tuS4xe/SrfOf5PY1y/rtwx4+G41w/K5yd23+rrDLLzVm3FzhvNsmlL3rJJQP1VcbR/yAr6kpzjRt4F68/+A/3ZUVxYY4ZO1UWn/5+O+d3vn/lBVaQs24vcN5skktf9JBLBmohLrimaR0+n/Iv/TLvIsxgpJMHTA/Ow3fvM5xYeQeYzfYuUQhxFZKBWoiLeHm48vU7KxnsM5X5ga64G0DTIDzzZ059WQfyUu1dohDiKiOTyWwo+pI/NTUVPz8/e5dTaZRS5OTk4OHh4fDnti2Pqsq1busuAnd2pp33fydESCtwYXv4/7ixx8BKW09JnHV7gfNmk1z6Ys9cMplMlMjNzc3eJVSJqsh1c8c21BuQzJdnIil6O/ve+QL6/jmIsVP7Vvr6bHHW7QXOm01y6YsecslAXQqzk30naTabiY6OllzlEOjryeBnD/BR+uOsSXPjtWRIUzAz/wdumxjO6VMnKn2dRZx1e4HzZpNc+qKXXDJQC1EGTz35MWfqLucGc01L2y/GeK77pDGfffmuHSsTQjg7GaiFKKPBd9zOd8/F8kDONXhe+DrrmDmPZtkvsuOLHjIrXAhRJWSgFqIcAv29+XLaVsbWeJGmBjfeDIKuXop2hvUkLvYlOfGgvUsUQjgZmfVtgzPP+jabzRgMBqebuWmPXP/u2YPH5i609M6wtOUr2OY7ni53Trvi5Tvr9gLnzSa59MWeuWTWtyhRXl6evUuoEvbI1aFVK5oPT+OnzJ6WWeGuGniceYt+rzQiNi72itfhrNsLnDeb5NIXPeSSgboUjj4TsLzMZjMHDx6UXJXIYNC447G1/F33C9JNBnLNMPQUrHQ9yi2fN2XKe89VeNnOur3AebNJLn3RSy4ZqIWoBF26D8Z4bxqz4qI4eOEN+mFzPq+nzeKelyOJjY+3b4FCCN2SgVqISuLl5c2LL+1mWsgkWmiFl/YwAd+7HeJ/S5uzavnr9i1QCKFLMlBfZYxGo71LqBKOlGvME5P5c+RJ7suPxAVo4wYvhmTQJ3siG+fV4/SZc2VeliPlqmzOmk1y6YsecsmsbxvKMxtPiNLM+GgC3Qwz6ezz34SVDJPGj2oMg4ZMt2NlQgh7klnflcTZ3sMopUhLS5Nc1WjsiGm0fzCJgzkRlpnhNYyKuw0zeHBiA1b9saHExzpyrivlrNkkl77oJZcM1KVw9JmA5WU2mzl69KjkqmZu3gFEPnKc/aFvkGsuPFbz3RT40hjL4xtuYtiEW8nILn6IiKPnuhLOmk1y6YtecslALUQ1aXHTy7jef56/s1ozM7Ww7aTZxCKPtdz+dihvfvKeXesTQjgmGaiFqEYGdx86P7qLhW0XcK3mY2nfoCWzOnkcP39Qjz1Hqu6KXEII/ZGB+irj4eFh7xKqhN5y9btzOJtfSuEZY29qahoG4L3aZm4PjKP+pghmzelPelae7nKVh7Nmk1z6oodcMuvbBpn1LarToQPbWLbifl6KiLVqP5Ljwo/aNJ4ZOhaDwXnOryyEkFnflcbRJxiUl9ls5ty5c5LLwTRtdg0vjT9GYsOp5Jr/e0o28DCTnbuQ/q8059Of1tixwsqn921WEsmlL3rJJQN1KZxtZ4NSihMnTkguBxXaeQLuA9M54XEzZgUH84zEu3bnB4+jTNlxG4Ne6Mq2/c7x/bWzbLNLSS590UsuGaiFcCQuXoTf8xvcvp/PExpZmk+YTXztvZkR37bgkVcGcTol045FCiGqkwzUQjggg38z3nxxDz2DutL+otnhO1UGzzf6mpTv/XjxvXGkZebasUohRHWQgfoq4+Pjc/lOOuSsuVpHdeHPFxKZ7DuIcIORkf7Q3B0iPUy8VXsGB5b4MuHDt8nLN9m71HJz1m0mufRFD7nsOlBv2LCBO++8k7CwMDRNY8WKFZd9zPr162nfvj3u7u40btyYRYsWFeszd+5c6tevj4eHB506deKff/6pUH16OFl7eRiNRho1aiS5dKIol6u7G5OeW8Lup+N5MuQ6y6lINQ2u9c5jqt94XnizCc9/+DFms2N/11bE2beZ5NIHveSy60CdmZlJmzZtmDt3bpn6Hzt2jNtvv50ePXqwc+dORo8ezaOPPsqvv/5q6bN06VLGjBnDpEmT2L59O23atKFXr16cPn263PU5+kzA8jKbzSQlJUkunbg0l39gCJED/kS78xDnXJpbBux/c2G2doz/nXuK/i+14vX/LXf4Aftq2WbOQnLZl10H6j59+vDGG29w9913l6n/vHnzaNCgATNmzKB58+aMHDmS++67j/fe++/UizNnzuSxxx5j2LBhtGjRgnnz5uHl5cVnn31W7vocfSZgeSmlSEpKklw6UWIu3yYE9d+H1utvUrS6vHy2sPmU2cx3nvv4NHYAA8a3580vVzrsgH3VbTOdk1z2pavvqDdv3kzPnj2t2nr16sXmzZsByMvL499//7XqYzAY6Nmzp6WPEE6jZicCBp1gdNTHdCfI0nzcXMAan50My7+bT+cEM+l/yxx2wBZCXJ6LvQsoj6SkJIKDg63agoODSUtLIzs7m5SUFEwmk80+Bw4cKHG5ubm55Ob+N3s2LS0NAJPJhMlUOElH0zQMBgNms9nq3VdRe1G/y7UbDAY0TbPZDsV3t5fUbjQaUUrZbL+0xkvbnS2TyWSy5HKWTEV5ih5rq39R7bfeOpxbbx3OV9++yfsxs9hmPs8z/maC3Yw8UjuVPPUAn7/vz/4aM3hjyAMYL3l7Xp2ZihQ99tJl6HE7XVwjYPUcc4ZMFz+fLn3t0HsmW68d1ZXp0seVRlcDdVWZNm0aU6ZMKda+f/9+y4zAwMBAIiIiiI+PJzk52dInJCSEkJAQYmNjSU9Pt7SHh4cTFBRETEwMOTk5lvaGDRvi6+vLvn37rDZUZGQkbm5uREdHW9UQFRVFXl4eBw8etLQZjUaioqJIT0/n6NGjlnYPDw+aNWtGSkoKJ078d2IMHx8fGjVqxJkzZ8jMzGTv3r1omuYUmU6fPk1iYqIlV1BQkFNkKtodl5mZSUJCAvXq1btsplbN7mJe5J38u/t7eprfI8b1DnK0AADa1YG78l7msUlTad98Ite1bIbxwmlJqzNTkYCAAAIDA0lISCAlJUXX26lIYGAgdevWBbA8x5whU0REBAkJCVavHc6QKT4+nnPnzllyhYaGVmumjIwMysphzvWtaRrff/89/fr1K7HPDTfcQPv27Zk1a5albeHChYwePZrz58+Tl5eHl5cXy5Yts1rO0KFDSU1NZeXKlTaXa+sTdXh4OMnJyZZzsDrTJ7VLa5RMzpkpf+8scna+hpdW+IKwJrOA2xIU9YweXJvZCBffB5n5+FMEB/roJpMzbifJdHVmSktLIzAwsEzn+tbVJ+ouXbqwatUqq7a1a9fSpUsXANzc3OjQoQPr1q2zDNRms5l169YxcuTIEpfr7u6Ou7t7sXZN04pN2y/6ZV+qpOn9Vdluq77SagQ4efIkdevWteqj50xFT7j4+HirXHrPBFjlKq1/SbW4thyNa8vRmA9+SM6/E3g9ufArneOmHI577KVm/ks8MfNjNOMtTB46hbaNQqs8UxGz2UxcXBx169a1uRw9baeL2fpbrMway9teGZmK2Hrt0HOmkl47qitTeQ4Js+tksoyMDHbu3MnOnTuBwsOvdu7cSVxcHAATJkxgyJAhlv5PPvkkR48e5YUXXuDAgQN8+OGHfPPNNzz33HOWPmPGjGH+/Pl8/vnn7N+/nxEjRpCZmcmwYcPKXZ+D7GyoNEopkpOTJZdOVFYuQ+RTeD1wnpH1p9CVAEv7WaXY4RXLN03n4/JHGA9NuZVlf+6+0rLLRLaZvkgu+7LrQL1t2zbatWtHu3btgMJBtl27dkycOBGAxMREy6AN0KBBA37++WfWrl1LmzZtmDFjBgsWLKBXr16WPgMGDGD69OlMnDiRtm3bsnPnTlavXl1sgpkQV5sHBkxk46RklkW9w03UxgiM9gc3A7TygMWN19LlWBtGv9mCN5f+KjPFhXAQDvMdtSMpuk5ocnIyAQEBl3+ATphMJqKjo4mKinL4M/GUh+SqmM0bl1P3xCTqmvagXXS563wFfY7VwC+tAQb/h5jx6ONE1Par1HXLNtMXyVX55HrUlUS7+NXLCRTN1pRc+lDVubp0u4fwgdFofY+SW7MnZlW4nqXpsM6UwXLvaP4yjeeZ2W25edwAvtmwq9LWLdtMXySXfcknahvK805HCKeRl4bp39H0W7+Un/KyrO5yAb4P8ub3tNrkBL7GtIfux9e7+ARMIUTZyCfqSlKeA9L1wGQyceTIEcmlE9Wey80XY5fPWPl8Gh/WfYYbCLK8QES6we0Bmcyof4zpNR7ix4V+3DZpFGv/janQqmSb6Yvksi8ZqK8yFx/I70wkV+UxuBgZMXw2f0w6y+ZeK3lAa8lzPq6W77E9DTA4MJefm37A+l+v5/YxnRn+/mecTsks13pkm+mL5LIfXR1HLYSoXtd2vosvO98FeWmYd7xAwZHFuJENQKaCOQWnyPA7RdPUHYx4dyqn8zry8C2jGXbLtRgMjv29nxB6IZ+ohRCX5+aLodM83B7Igi5fkOPRiK/OG8m4MMPlkDmP5e5H2OLzNbE7bmfK9GDunvY2O48k2rduIZyADNSlcPSZgOWlaRrh4eGSSyccNleDwXjcc5g77z7IC169aaN5We7KB+6ufY4pdc/wbcR4steH8eDkNjz6wSLiz6RZ+jlstiskufRFL7lk1rcNMutbiPL59df5fPb3dM66H2VdREHx+8+783F8Hc5mNeO6do/z0v19qOHpZodKhXAM5RlnZKC2wZlPeBITE0OTJk2c7qQFkstBFGRB9BRyDy7AzZRsmYA2NAkWp4MGtNdq0CAnnPohDxIa3pmnbr8BDzfnmC6jy21WBpKr8snhWaJEF1+mzZlILgfh4gXt3sZ94Dm02/dgrnsfaWZPvr8wIVwB/6oMVnocxugTT//zvVk0z4ceLw3mnWW/kZNX/NO43uhum5WR5LIfGaiFEFXDvyWGG77F98EsfrzuC4Ya29LA4Gq5u54rhLrBkzVz+L+WSxiadQtffOzNDeP78+bSX8nKybdj8UI4DufY3ySEcGjdewyme4/BmAtMfLv8bZYdWExDFw0uXLJX0yDYBYYF5jH5/Lf8eOBXtu8IISkvim5RDzCm762EBNawbwgh7ES+o7ah6LuD1NRU/Pwq92IE9qSUIj09HR8fH4ef5Vgekkt/lFKkpybjc3opBYfmYUzbg0FTrM+CHif/62cA2mje9NL8OVoQgtHvUcbccSfXNK1jt9pL46zbTHJVPplMdoVk1rcQ1cxcAEc+Y87Pc3knfS8nzdandFxXB27ygjwFO3Phq6S67M1/mGHd72HADW3l5CpCd2QyWSVx9PO/llfRJd0klz44ay6wkc3gAk0e55nRu4ibkMvXzd9kgNaMRgZX/AxwvWdhNzcNrvWA9+rH82rYNBb83ov7JrSi25j+PDt/KUcSku0XCufdZpLLvuQ76quMo/9BVpTk0p+SshlcjAzo/xIDeAmAA9u+xZixmLzE9biaMyyHfP2QZeL/DGfA6wwa+zif+COxH9YmxNWdo/RnYOc7eeima3Bzrd7Dbpx1m0ku+5GBWgjh0Jpdcz9wP24AaTFwYCa5x1eyLvMURbPRFLBX5XDSPY4zDcHIm5xMepOvPnZjxalueAUO4JEbb6ZHm0aym1zojgzUQgj98G0C136E+7UfsT7lDF+tmMr6E7+wQ4vloDmXW7zA5cI4XNcVhgbmMTTwdyYkbuadFX58+HUQZwua0bxRPx6/5WbaNwmzbx4hykAmk9ngzLO+c3Jy8PDwcLqZm5JLX6oi287ta8g6upgO6nfc8hK4eLHNYuHgRYdlNzG4ck1BLdr55vBbam8iw+9kyI3XX/FscmfdZpKr8sms7yvkzAO12WzGYDA43ZNNculLlWcryIPY/2E69gUnT26nyfE08i7p8pAPLA4p/H+OGQ7nwx/nffkp4UZC6vblgW7Xc3O7xuXaVe6s20xyVT4ZqK+QM5/rOzo6mqioKKc7X6/k0pfqznb2dBzf/jiDP0/+xh6OsVdl82kwPHzJ66NSEHoMXJWRpgWB+OcGkpkXgWetW7ij/Q0MuKFdqRcTcdZtJrkqX3kGavmOWgjh9GrWjmDE8NmMuHA7LnYPnie/JC95FVr6QVxULppW+Kn6lAnARLzhDHieAc+DjPH4nbtOFfDPFxobzoWzLftWmtfrzaDru8j33KLKyUAthLjqRNRvBfWnAdMKG7Li4ejnHN7yEx20Pewlg5yL9jV29iqglgvc5KK4yTsOWEC6aQH3fxGMT64/2fnh4HsDN7fuRscQOdWpqFwyUAshhFddaPUyfVq9TB8gLeUMK395nw3HVnOg4DDXuJ/HcmLyCw7lw6+GU+B5CjwP4qH9RsIeX4LShnNo6238ndqSVI876NGyK/df146afl52iSb0T76jtkEmk+mL5NIf3WUzm+HMBoj7lpyT6zFkHuHj1DyeOVv85XNNHVd6euWjUfidd7oZtma48VFsY/IK6oBvZ7q2uJ6+ndrSPKJW9WepAN1trzKSyWQ65swDtRxioR/OmgucI1vy2ZP8+OtH/H38/ziUf4SjhmTizCZONvIn2JCKxn8vrb9mQu+Ewv8bgYYGN8IL/OjjaSRL8+dA/g0Eh9zMzVFR9GzXBA83x9rZ6QzbyxY5PEvHZNa3vkgu/XHWbHHHdpMcu5PmpqUUnP0Xd9MZXDQz7yTDi+eK998RAW3dC/9vUpBqhr9SvVgc3wBzfgiabyfaRl5Hn/ZRdGhSx25nVXPW7SWzvoUQ4ipTJ6IlyefNuEQNxr3ohT/9CFFrP+XJ8+s5kh9LnPEcR8yFR3U3d/3vsUYNgoyQ6ZrFcq+9wF5gHVsPG/n1UA1G+GqYDK4czGpCguEGIup046aoFnRtUa/az2cuqpcM1EIIUZV8GtHnnqn0uagpLeUMf2/+CteAXWQk/o0x+zjuZGLQYM8lZ2aJN5uI5zxfB0K4K8AZYBMmBWv+8uSu7/ypke+LVlALzbUJQXW60yWyJTe2bkJEbef56u5qJgP1VcaZdltdTHLpj7NmK0su34Ba3HrbMwBYHcyVupeu677k6Yw/OZZ3nHjDOY6RhRmoe8mrtVGDI1o2vxqzwZgIHAT+wv3sQoa7ueKakM/WXBeOZAdwLKcB8aaOeNe6jmuaNueGVo0ICSzfYWRX8/ayN/mO2obyfHcghBBVyVxgYt/uX2jltoucpL/JPbcX14IkPMhm1Bn48Hzxx6Q3ghoG67av02HYKaijuVLb7IV/QQ28Cnxo7e1Jtnskud43EFm/DR2b1Kd1wxBcjIbiCxaVRiaTXSFnnvWdnp6Oj4+P083clFz64qzZqjvX8SM72bBlObvj/yE26xintLPkGbPY3CCHS1f/+jmYmGxjGfUh4sJ35SYFWQrWnPNh8ZlA3At8MJqDcHGtR3j4dTSqH0WHJvVoVT/YKQZye/4dymSySmI2my/fSUfMZjNHjx51upmbkkt/nDVbdeeq16gtDzVqW/yOgjxI2QpnNpKV+DfZ5/aRnplCI0MK8eZ8ci90cwXqXDQKGDXw0eCUazo/uKYXdgBcNVcedfWmTfwompzN5cxfcCbflcRcH/akh7EztT5e3pGENbietg0b07ZRHcJr+Tn8tb/18ncoA7UQQjgbFzeo1Q1qdcOrBXgB71z4KcjPY/fu/2PX/j84eWYvyR4JGHNO4KHO467lYdQUsQW2F9vQ3Yy3AbwNEOqaT2uvZM4ZkxmXuwfMP2E4MoPaxwzU/M2NGUEGwtwLOJ3nzen8IM6pOpxVkWS7taZR/Xa0alCXqAYhpV7kxJ5OJxwhftUttPY8hhEwAbuzG1D3trXUDmtUrbXIQC2EEFcRF1c32nfoTfsOvW13yEtl4LZfCd/7J0fOHiAxJ4FUQxq1NVdqGDSUwmq3evxFg7oZSDKbSSKHxjWgoSvglQekAIdZlfkHtyeA5zmoud1IoHLH1+zBCD+NMA/F2YIAkk2hZBvrkeXWFDe/NjRrGEnz8GDqBftX2yf00wlH8F7XhHaeCjOQT+GJatp5HiNrXRNO3xxTrYO1DNRXGQ8PD3uXUCUkl/44azbd53Lzp33XAbTvOsDSZDKZiImJwdhkJprKh9RdkLKT9KSdeJ3aw52mk6QYzpNsyOKslsdZs5kwG3uST14Y1LMVnFAmTpAFWhaz/KC9B0AycAT4i7+y4fqD4HsIgjQX/JU7PmZ3Hq7hQtMaBaQW+JCmapKhhZJpqE+yakjDhu1pXr8hkeG18K9Rtu1ga3vFr7qFdp4KBezNg18y4TZvaOkGXgbFwVW3UPvRo+X9zVaYTCazQWZ9CyFExeVkZeCRvR9SdpN2ajcZZ/ajsk6w7GQmX2ankqLlcE4VkHJh+EloAKGXfGxcngH3JhZf9ro6cNMl1zfZkwtRcaAB/pqGv2bER7kxqoYbN/pnkV7gQZrJi3SzH8mmIP46HYyHZyiBfvUIq9uKphFNaVi3FnVr+mIwaBR8qaFROEh3iIMCCj/Vbo+AFm6gAJfBVzZ0ymSySuKMk8lSUlIICAjAYND/jM0ikkt/nDWb5Crk4VUDvDpCUEd8G0PRMPTshZ8iaSln2HdgE0GBp0k+vZeMc4dQWfG4mpJJzSigjZZOqpZHsiog/cK4GGzjk/oZU+G/CkhRihRVABQQWCOLxh4AeUAakER8PgxNAQrAcM5AZE4kx3Yd5E1/I08H5ZOjwNdQuLv7l8zCQZrC7qzKhEg3yxy7aiMDdSmcbWeDUooTJ07g7+9v71IqleTSH2fNJrnKxzegFp279AUgMBICL7rvkQs/RZLPnuRQzD+E1TjN6ZQYslKOYspOxJh/ljMZuXQlnXQtlzQtnxRVQJqCIBvvKc5d9PnLqBm5MeBGDmcdxtctH3cDuAMFqvA76du84ZVz/32ivs0by8Sy6hw8ZaAWQgjh8AJr1qFzzbtt3lcf6H9JW0Z6Ki7ZsZhz4kg5fYD0s4fJy4jn5Pkz9DOlkK3lkGcooJbmSlODOzUVKJWPpsGu8/6090ulpVvh7u5VF31HrQHbz/vToYrzXswh9s3MnTuX+vXr4+HhQadOnfjnn39K7f/tt9/SrFkzPDw8iIqKYtWqVVb3K6WYOHEioaGheHp60rNnT2JiYqoyghBCCAdSw8cfj9ptMUTcRdA1L1C/9yc0vW8Vt43YyvevHWb1lHjWvnKSu9sPY9eEVPo9lYc2WMF96YS6m8gyF35P3cINngso/FcDsswaoe6mas1i94F66dKljBkzhkmTJrF9+3batGlDr169OH36tM3+mzZtYtCgQQwfPpwdO3bQr18/+vXrx549eyx93nnnHebMmcO8efPYsmUL3t7e9OrVi5ycnOqK5bB8fHzsXUKVkFz646zZJJe+FMvlVoMkVZOMfB92ZEWgKPxOWgE7siLIyPchSdWs1hrtPuu7U6dOdOzYkQ8++AAonLQQHh7OqFGjGD9+fLH+AwYMIDMzk59++snS1rlzZ9q2bcu8efNQShEWFsbYsWMZN24cAOfPnyc4OJhFixYxcODAy9Yks76FEOLqdTrhCDV+b4GnEaj/IFrQNahz2yD2C7JNkNFj3xUfR12eccaun6jz8vL4999/6dmzp6XNYDDQs2dPNm/ebPMxmzdvtuoP0KtXL0v/Y8eOkZSUZNXHz8+PTp06lbjMkjjjrO+kpCTJpRPOmgucN5vk0peSctUOa0RGj33syKiD6dj/UFufxnTsf+zIqFMpg3R52XUy2dmzZzGZTAQHB1u1BwcHc+DAAZuPSUpKstk/KSnJcn9RW0l9LpWbm0tubq7ldlpaGgAFBQWYTIXfRWiahsFgwGw2W80GL2ov6ne5doPBgKZpNtuh+JuDktqNRiNKKZvtl9ZY1G4ymUhMTCQwMBCj0egUmcxmMwUFBZZcLi4uTpFJKWXZXkFBQU6TqUjRC2RQUJDTZNI0DaWU1XPMGTIV1WjrtUPPmUp67SiqMSi4PkHDYtA0Dc1gQDOZaHNhGSaT6YozXfq40sisb2DatGlMmTKlWPv+/fst318EBgYSERFBfHw8ycn/XYImJCSEkJAQYmNjSU9Pt7SHh4cTFBRETEyM1XfjDRs2xNfXl3379lltqMjISNzc3IiOjraqISoqiry8PA4ePGhpMxqNREVFkZ6eztGj/50dx8PDg2bNmpGSksKJEycs7T4+PjRq1IgzZ86QnJzM3r170TTNKTKdPn2axMRES66goCCnyJSUlIRSiuTkZBISEqhXr55TZCoSEBAAQEJCAikpKU6RKTAwkDp16pCZmWl5jjlDpoiICBISEqxeO5whU3x8POfOnbPkCg0NrdZMGRkZlJVdv6POy8vDy8uLZcuW0a9fP0v70KFDSU1NZeXKlcUeExERwZgxYxg9erSlbdKkSaxYsYJdu3Zx9OhRGjVqxI4dO2jbtq2lT/fu3Wnbti2zZ88utkxbn6jDw8M5c+aM5QXFGT595ufns2fPHlq2bOl0n6j37t1Ly5Ytne4T9d69e2nVqhWurq5OkamI2Wy2bLOLT6Ch50xFn6h3795teY45QyaDwVDia4eeM5X02lFdmdLS0ggMDHT8M5O5ubnRoUMH1q1bZxmozWYz69atY+TIkTYf06VLF9atW2c1UK9du5YuXboA0KBBA0JCQli3bp1loE5LS2PLli2MGDHC5jLd3d1xd3cv1u7i4lLs0mclnZWnpEukVWW7pmk220urMSgoyPIHWZb+1d1e3kwGgwEXF5diufSeqehxQUFBlsc6Q6aLH1+0G9XWY/SYCQpfv2w9xyqrxvK2V0amomXbyqXnTCW9dlRXpnJdVlPZ2ddff63c3d3VokWL1L59+9Tjjz+u/P39VVJSklJKqYceekiNHz/e0n/jxo3KxcVFTZ8+Xe3fv19NmjRJubq6qujoaEuft956S/n7+6uVK1eq3bt3q759+6oGDRqo7OzsMtV0/vx5Bajz589XblghhBBClW+csftx1AMGDGD69OlMnDiRtm3bsnPnTlavXm2ZDBYXF0di4n9nZu/atStLlizhk08+oU2bNixbtowVK1bQqlUrS58XXniBUaNG8fjjj9OxY0cyMjJYvXp1ua9q44wzHOPi4iSXTjhrLnDebJJLX/SSy+7HUTuiouPbkpOTLd9ROwOTyUR0dDRRUVHl2+3i4CSX/jhrNsmlL/bMpZvjqIUQQghROjk8y4ainQxpaWlO9+4xIyNDcumEs+YC580mufTFnrmKztdRlp3aMlDbcO7cOQDq169v30KEEEI4tfT0dPz8/ErtIwO1DYGBhVdFjYuLu+wvUE+Kjg8/ceKEU53DXHLpj7Nmk1z6Ys9cSinS09MJCwu7bF8ZqG0oOp7Oz8/Pqf4oi/j6+kouHXHWXOC82SSXvtgrV1k/CMpkMiGEEMKByUAthBBCODAZqG1wd3dn0qRJNk8rqmeSS1+cNRc4bzbJpS96ySUnPBFCCCEcmHyiFkIIIRyYDNRCCCGEA5OBWgghhHBgV81APXfuXOrXr4+HhwedOnXin3/+KbX/t99+S7NmzfDw8CAqKopVq1ZZ3a+UYuLEiYSGhuLp6UnPnj2JiYmpygg2lSfX/Pnzuf766wkICCAgIICePXsW6//www+jaZrVT+/evas6RjHlybVo0aJiNV96pTQ9bq8bb7yxWC5N07j99tstfRxhe23YsIE777yTsLAwNE1jxYoVl33M+vXrad++Pe7u7jRu3JhFixYV61Pe52xlK2+u5cuXc8stt1CrVi18fX3p0qULv/76q1WfyZMnF9tezZo1q8IUxZU31/r1623+HSYlJVn109v2svXc0TSNli1bWvo4wvaCq2SgXrp0KWPGjGHSpEls376dNm3a0KtXL06fPm2z/6ZNmxg0aBDDhw9nx44d9OvXj379+rFnzx5Ln3feeYc5c+Ywb948tmzZgre3N7169SInJ6e6YpU71/r16xk0aBC///47mzdvJjw8nFtvvZWTJ09a9evduzeJiYmWn6+++qo64liUNxcUnrDg4pqPHz9udb8et9fy5cutMu3Zswej0cj9999v1c/e2yszM5M2bdowd+7cMvU/duwYt99+Oz169GDnzp2MHj2aRx991GpQq8jfQGUrb64NGzZwyy23sGrVKv7991969OjBnXfeyY4dO6z6tWzZ0mp7/fXXX1VRfonKm6vIwYMHrequXbu25T49bq/Zs2db5Tlx4gSBgYHFnl/23l4AVN1lsR3Htddeq55++mnLbZPJpMLCwtS0adNs9u/fv7+6/fbbrdo6deqknnjiCaWUUmazWYWEhKh3333Xcn9qaqpyd3dXX331VRUksK28uS5VUFCgfHx81Oeff25pGzp0qOrbt29ll1ou5c21cOFC5efnV+LynGV7vffee8rHx0dlZGRY2hxhe10MUN9//32pfV544QXVsmVLq7YBAwaoXr16WW5f6e+qspUlly0tWrRQU6ZMsdyeNGmSatOmTeUVdoXKkuv3339XgEpJSSmxjzNsr++//15pmqZiY2MtbY6yvZz+E3VeXh7//vsvPXv2tLQZDAZ69uzJ5s2bbT5m8+bNVv0BevXqZel/7NgxkpKSrPr4+fnRqVOnEpdZ2SqS61JZWVnk5+dbzm1eZP369dSuXZvIyEhGjBhhuUhJdahoroyMDOrVq0d4eDh9+/Zl7969lvucZXt9+umnDBw4EG9vb6t2e26virjc86syfleOwGw2k56eXuz5FRMTQ1hYGA0bNmTw4MHExcXZqcLyadu2LaGhodxyyy1s3LjR0u4s2+vTTz+lZ8+e1KtXz6rdEbaX0w/UZ8+exWQyERwcbNUeHBxc7DuWIklJSaX2L/q3PMusbBXJdakXX3yRsLAwqydY7969Wbx4MevWrePtt9/mjz/+oE+fPphMpkqtvyQVyRUZGclnn33GypUr+eKLLzCbzXTt2pX4+HjAObbXP//8w549e3j00Uet2u29vSqipOdXWloa2dnZlfK37QimT59ORkYG/fv3t7R16tSJRYsWsXr1aj766COOHTvG9ddfT3p6uh0rLV1oaCjz5s3ju+++47vvviM8PJwbb7yR7du3A5XzWmRvCQkJ/PLLL8WeX46yveSiHFept956i6+//pr169dbTbwaOHCg5f9RUVG0bt2aRo0asX79em6++WZ7lHpZXbp0oUuXLpbbXbt2pXnz5nz88ce8/vrrdqys8nz66adERUVx7bXXWrXrcXtdDZYsWcKUKVNYuXKl1Xe5ffr0sfy/devWdOrUiXr16vHNN98wfPhwe5R6WZGRkURGRlpud+3alSNHjvDee+/xv//9z46VVZ7PP/8cf39/+vXrZ9XuKNvL6T9R16xZE6PRyKlTp6zaT506RUhIiM3HhISElNq/6N/yLLOyVSRXkenTp/PWW2+xZs0aWrduXWrfhg0bUrNmTQ4fPnzFNZfFleQq4urqSrt27Sw16317ZWZm8vXXX5fphaG6t1dFlPT88vX1xdPTs1L+Buzp66+/5tFHH+Wbb74ptov/Uv7+/jRt2tSht5ct1157raVmvW8vpRSfffYZDz30EG5ubqX2tdf2cvqB2s3NjQ4dOrBu3TpLm9lsZt26dVafwi7WpUsXq/4Aa9eutfRv0KABISEhVn3S0tLYsmVLicusbBXJBYWzn19//XVWr17NNddcc9n1xMfHc+7cOUJDQyul7supaK6LmUwmoqOjLTXreXtB4aGCubm5PPjgg5ddT3Vvr4q43POrMv4G7OWrr75i2LBhfPXVV1aH0ZUkIyODI0eOOPT2smXnzp2WmvW8vQD++OMPDh8+XKY3wnbbXvaezVYdvv76a+Xu7q4WLVqk9u3bpx5//HHl7++vkpKSlFJKPfTQQ2r8+PGW/hs3blQuLi5q+vTpav/+/WrSpEnK1dVVRUdHW/q89dZbyt/fX61cuVLt3r1b9e3bVzVo0EBlZ2c7bK633npLubm5qWXLlqnExETLT3p6ulJKqfT0dDVu3Di1efNmdezYMfXbb7+p9u3bqyZNmqicnByHzTVlyhT166+/qiNHjqh///1XDRw4UHl4eKi9e/daZdfb9ipy3XXXqQEDBhRrd5TtlZ6ernbs2KF27NihADVz5ky1Y8cOdfz4caWUUuPHj1cPPfSQpf/Ro0eVl5eXev7559X+/fvV3LlzldFoVKtXr7b0udzvyhFzffnll8rFxUXNnTvX6vmVmppq6TN27Fi1fv16dezYMbVx40bVs2dPVbNmTXX69GmHzfXee++pFStWqJiYGBUdHa2effZZZTAY1G+//Wbpo8ftVeTBBx9UnTp1srlMR9heSil1VQzUSin1/vvvq4iICOXm5qauvfZa9ffff1vu6969uxo6dKhV/2+++UY1bdpUubm5qZYtW6qff/7Z6n6z2axeffVVFRwcrNzd3dXNN9+sDh48WB1RrJQnV7169RRQ7GfSpElKKaWysrLUrbfeqmrVqqVcXV1VvXr11GOPPVatT7Yi5ck1evRoS9/g4GB12223qe3bt1stT4/bSymlDhw4oAC1Zs2aYstylO1VdPjOpT9FWYYOHaq6d+9e7DFt27ZVbm5uqmHDhmrhwoXFllva76o6lDdX9+7dS+2vVOFhaKGhocrNzU3VqVNHDRgwQB0+fNihc7399tuqUaNGysPDQwUGBqobb7xR/d///V+x5epteylVeJimp6en+uSTT2wu0xG2l1JKydWzhBBCCAfm9N9RCyGEEHomA7UQQgjhwGSgFkIIIRyYDNRCCCGEA5OBWgghhHBgMlALIYQQDkwGaiGEEMKByUAthBBCODAZqIUAFi1ahL+/v73LsKhfvz6zZs2ydxklevjhh4tdachRTZ48mbZt29q7DCEqTAZqUW00TSv1Z/LkyZW+zvXr16NpGqmpqZW+7MrgaG8QLhUbG4umaezcubPK15WQkEBAQABz5syxat+yZQuurq6sWbOmymsQwhHJ9ahFtUlMTLT8f+nSpUycOJGDBw9a2mrUqGH5v1IKk8mEi4v8iV4twsLCeP/993niiSfo06cPTZo0ITs7m6FDh/Loo49y6623VlsteXl5l73koRDVRT5Ri2oTEhJi+fHz80PTNMvtAwcO4OPjwy+//EKHDh1wd3fnr7/+4siRI/Tt25fg4GBq1KhBx44d+e2336yWm5uby4svvkh4eDju7u40btyYTz/9lNjYWHr06AFAQEAAmqbx8MMPl7nelStX0r59ezw8PGjYsCFTpkyhoKDAcr+maSxYsIC7774bLy8vmjRpwg8//GC1jB9++IEmTZrg4eFBjx49+Pzzzy2f8NevX8+wYcM4f/68zb0KWVlZPPLII/j4+BAREcEnn3xSar25ubk888wz1K5dGw8PD6677jq2bt1qub9o78K6deu45ppr8PLyomvXrlZvli7VoEEDANq1a4emadx4441W90+fPp3Q0FCCgoJ4+umnyc/Pt6pn3Lhx1KlTB29vbzp16sT69etLzfDggw/Sq1cvHn74YcxmMxMmTCA/P59333231MfFx8czaNAgAgMD8fb25pprrmHLli1Wff73v/9Rv359/Pz8GDhwIOnp6Zb7brzxRkaOHMno0aOpWbMmvXr1AgovgXjttdfi7u5OaGgo48ePt/obuPHGGxk1ahSjR48mICCA4OBg5s+fT2ZmJsOGDcPHx4fGjRvzyy+/WNVyueUuW7aMqKgoPD09CQoKomfPnmRmZgKFl5B87bXXqFu3Lu7u7rRt25bVq1dbHlu0F+Sbb77h+uuvx9PTk44dO3Lo0CG2bt3KNddcQ40aNejTpw9nzpyxqmvBggU0b94cDw8PmjVrxocffljq711Uk2q/DIgQSqmFCxcqPz8/y+2iK9+0bt1arVmzRh0+fFidO3dO7dy5U82bN09FR0erQ4cOqVdeeUV5eHhYLl2nlFL9+/dX4eHhavny5erIkSPqt99+U19//bUqKChQ3333nQLUwYMHi11ysLR6NmzYoHx9fdWiRYvUkSNH1Jo1a1T9+vXV5MmTLX0AVbduXbVkyRIVExOjnnnmGVWjRg117tw5pVTh5RxdXV3VuHHj1IEDB9RXX32l6tSpowCVkpKicnNz1axZs5Svr2+xS47Wq1dPBQYGqrlz56qYmBg1bdo0ZTAY1IEDB0r8nT7zzDMqLCxMrVq1Su3du1cNHTpUBQQEWOop+h136tRJrV+/Xu3du1ddf/31qmvXriUu859//lGA+u2331RiYqJlWUOHDlW+vr7qySefVPv371c//vij8vLysroK0aOPPqq6du2qNmzYoA4fPqzeffdd5e7urg4dOlTi+pRS6tSpU6pWrVpq4MCBymg0qj/++KPU/unp6aphw4bq+uuvV3/++aeKiYlRS5cuVZs2bVJKKTVp0iRVo0YNdc8996jo6Gi1YcMGFRISol566SXLMrp3765q1Kihnn/+eXXgwAF14MABFR8fr7y8vNRTTz2l9u/fr77//ntVs2ZNy9Xmih7n4+OjXn/9dXXo0CH1+uuvK6PRqPr06aM++eQTdejQITVixAgVFBSkMjMzlVLqsstNSEhQLi4uaubMmerYsWNq9+7dau7cuZa/jZkzZypfX1/11VdfqQMHDqgXXnhBubq6Wn6vx44dU4Bq1qyZWr16tdq3b5/q3Lmz6tChg7rxxhvVX3/9pbZv364aN26snnzySUuWL774QoWGhqrvvvtOHT16VH333XcqMDBQLVq0qNTfv6h6MlALuyhpoF6xYsVlH9uyZUv1/vvvK6WUOnjwoALU2rVrbfYtWm5KSkq56rn55pvV1KlTrfr873//U6GhoZbbgHrllVcstzMyMhSgfvnlF6WUUi+++KJq1aqV1TJefvllq3ouXW+RevXqqQcffNBy22w2q9q1a6uPPvrIZv0ZGRnK1dVVffnll5a2vLw8FRYWpt555x2l1H+/i4uvI/zzzz8roMTrche96O/YscOqfejQoapevXqqoKDA0nb//fdbrpt9/PhxZTQa1cmTJ60ed/PNN6sJEybYXNfF5s2bpwA1YsSIy/b9+OOPlY+Pj+VNxKUmTZqkvLy8VFpamqXt+eeft7oGcffu3VW7du2sHvfSSy+pyMhIZTabLW1z585VNWrUUCaTyfK46667znJ/QUGB8vb2trrucWJiogLU5s2by7Tcf//9VwEqNjbWZp6wsDD15ptvWrV17NhRPfXUU0qp/7bZggULLPd/9dVXClDr1q2ztE2bNk1FRkZabjdq1EgtWbLEarmvv/666tKli806RPWRLwCFQ7nmmmusbmdkZDB58mR+/vlnEhMTKSgoIDs7m7i4OAB27tyJ0Wike/fulVrHrl272LhxI2+++aalzWQykZOTQ1ZWFl5eXgC0bt3acr+3tze+vr6cPn0agIMHD9KxY0er5V577bVlruHiZRd9TVC07EsdOXKE/Px8unXrZmlzdXXl2muvZf/+/SUuNzQ0FIDTp08TERFR5toAWrZsidFotFpWdHQ0ANHR0ZhMJpo2bWr1mNzcXIKCgkpdrslkYtGiRXh5efH3339TUFBQ6lyFnTt30q5dOwIDA0vsU79+fXx8fKxqvfR32aFDB6vb+/fvp0uXLmiaZmnr1q0bGRkZxMfHW35fF/8+jUYjQUFBREVFWdqCg4MBLOu73HLbtGnDzTffTFRUFL169eLWW2/lvvvuIyAggLS0NBISEqy2c9Hjd+3aZdV2cV1FNVxaV1FNmZmZHDlyhOHDh/PYY49Z+hQUFODn54ewLxmohUPx9va2uj1u3DjWrl3L9OnTady4MZ6entx3333k5eUB4OnpWSV1ZGRkMGXKFO65555i93l4eFj+7+rqanWfpmmYzeZKqaGqln3xcosGi4ost7T6MjIyMBqN/Pvvv1aDOVhPGrRl+vTpHD16lG3bttG9e3emTp3KxIkTS+xflr+BsvwuL/3bKytby76S37HRaGTt2rVs2rSJNWvW8P777/Pyyy+zZcuWy77JKamuohoubbt4ewHMnz+fTp06FatH2JdMJhMObePGjTz88MPcfffdREVFERISQmxsrOX+qKgozGYzf/zxh83HF83cNZlM5Vpv+/btOXjwII0bNy72YzCU7WkTGRnJtm3brNountxVVF95a7OlUaNGuLm5sXHjRktbfn4+W7dupUWLFhVebkV/f+3atcNkMnH69Oliv7+QkJASH7d3714mTZrERx99RPPmzfnoo49444032L17d4mPad26NTt37iQ5OblcNV5O8+bN2bx5M0opS9vGjRvx8fGhbt26VbpcTdPo1q0bU6ZMYceOHbi5ufH999/j6+tLWFiY1XYuevyVbOfg4GDCwsI4evRose1VNKFQ2I8M1MKhNWnShOXLl7Nz50527drFAw88YPXJpH79+gwdOpRHHnmEFStWcOzYMdavX88333wDQL169dA0jZ9++okzZ85YPjlczsSJE1m8eDFTpkxh79697N+/n6+//ppXXnmlzLU/8cQTHDhwgBdffJFDhw7xzTffsGjRIuC/Tzj169cnIyODdevWcfbsWbKyssq8/It5e3szYsQInn/+eVavXs2+fft47LHHyMrKYvjw4RVaJkDt2rXx9PRk9erVnDp1ivPnz5fpcU2bNmXw4MEMGTKE5cuXc+zYMf755x+mTZvGzz//bPMxBQUFDB06lHvuuceyJ+Pee+/l3nvv5eGHH7aaFX2xQYMGERISQr9+/di4cSNHjx7lu+++Y/PmzRULfcFTTz3FiRMnGDVqFAcOHGDlypVMmjSJMWPGlPnNWkWWu2XLFqZOncq2bduIi4tj+fLlnDlzhubNmwPw/PPP8/bbb7N06VIOHjzI+PHj2blzJ88+++wV5Z0yZQrTpk1jzpw5HDp0iOjoaBYuXMjMmTOvaLniyslALRzazJkzCQgIoGvXrtx555306tWL9u3bW/X56KOPuO+++3jqqado1qwZjz32mOVQljp16jBlyhTGjx9PcHAwI0eOLNN6e/XqxU8//cSaNWvo2LEjnTt35r333qNevXplrr1BgwYsW7aM5cuX07p1az766CNefvllANzd3QHo2rUrTz75JAMGDKBWrVq88847ZV7+pd566y3uvfdeHnroIdq3b8/hw4f59ddfCQgIqPAyXVxcmDNnDh9//DFhYWH07du3zI9duHAhQ4YMYezYsURGRtKvXz+2bt1a4nfhU6dO5eTJk3zwwQdW7XPnziUxMZGpU6fafJybmxtr1qyhdu3a3HbbbURFRfHWW29d8S7bOnXqsGrVKv755x/atGnDk08+yfDhw8v1Zq0iy/X19WXDhg3cdtttNG3alFdeeYUZM2bQp08fAJ555hnGjBnD2LFjiYqKYvXq1ZbDAK/Eo48+yoIFC1i4cCFRUVF0796dRYsWySdqB6Cpi/e/CCGq1Jtvvsm8efM4ceKEvUsRQuiETCYTogp9+OGHdOzYkaCgIDZu3Mi7775b5k/1QggBMlALUaViYmJ44403SE5OJiIigrFjxzJhwgR7lyWE0BHZ9S2EEEI4MJlMJoQQQjgwGaiFEEIIByYDtRBCCOHAZKAWQgghHJgM1EIIIYQDk4FaCCGEcGAyUAshhBAOTAZqIYQQwoHJQC2EEEI4MBmohRBCCAcmA7UQQgjhwGSgFkIIIRyYDNRCCCGEA5OBWgghhHBgMlALIYQQDkwGaiGEEMKByUAthBBCODAZqIUQQggHJgO1EEII4cBkoBZCCCEcmAzUQgghhAOTgVoIIYRwYDJQCyGEEA5MBmohhBDCgclALYQQQjgwGaiFEEIIByYDtRBCCOHAZKAWQgghHJgM1EIIIYQDk4FaCCGEcGAyUAshhBAOTAZqIYQQwoHJQC2EEEI4MBmohRBCCAcmA7UQQgjhwGSgFkIIIRyYDNRCCCGEA5OBWgghhHBgMlALIYQQDkwGaiGEEMKBudi7AL0zmUzk5+fbuwwhhBBVzNXVFaPRWO3rlYG6gpRSJCUlkZqaau9ShBBCVBN/f39CQkLQNK3a1ikDdQUVDdK1a9fGy8urWjeaEEKI6qWUIisri9OnTwMQGhpabeuWgboCTCaTZZAOCgqydzlCCCGqgaenJwCnT5+mdu3a1bYbXCaTVUDRd9JeXl52rkQIIUR1Knrdr865STJQXwHZ3S2EEFcXe7zuy0AthBBCODAZqIVNmqaxYsWKalvf5MmTadu2bbWtr7zq16/PrFmzqmVdDz30EFOnTq305Z49e5batWsTHx9f6csW1W/RokX4+/vbuwxuuOEGlixZYu8yrkheXh7169dn27Zt9i7FJhmoryIPP/wwmqahaRqurq4EBwdzyy238Nlnn2E2m636JiYm0qdPn2qrbdy4caxbt67a1mfLjTfeaPn9XPxTUFDA1q1befzxx6u8hl27drFq1SqeeeYZm3W5u7tTp04d7rzzTpYvX17s8bbqv+666wCoWbMmQ4YMYdKkSVWeQ1i7+Lnn5uZG48aNee211ygoKKjS9U6ePNmyXhcXF2rWrMkNN9zArFmzyM3Ntepb2t9/SX744QdOnTrFwIEDWb9+vc3HX/yzfv16Fi1aZLltMBioW7cuw4YNs8ymrgrTpk2jY8eO+Pj4ULt2bfr168fBgwct97u5uTFu3DhefPHFKqvhSshAfZXp3bs3iYmJxMbG8ssvv9CjRw+effZZ7rjjDqsnZEhICO7u7tVWV40aNRxiBv1jjz1GYmKi1Y+Liwu1atWqlsmD77//Pvfffz81atSwWdeRI0f47rvvaNGiBQMHDrT55mHhwoVW9f/www+W+4YNG8aXX35JcnJylWcR1oqeezExMYwdO5bJkyfz7rvvVvl6W7ZsSWJiInFxcfz+++/cf//9TJs2ja5du5Kenm7Vt6S//5LMmTOHYcOGYTAY6Nq1q9Xj+vfvb8lc9NO1a1cAfH19SUxMJD4+nvnz5/PLL7/w0EMPVdnv4I8//uDpp5/m77//Zu3ateTn53PrrbeSmZlp6TN48GD++usv9u7dW2V1VJgS5Zadna327dunsrOz7V1KuQwdOlT17du3WPu6desUoObPn29pA9T3339vub17927Vo0cP5eHhoQIDA9Vjjz2m0tPTrZYzf/581axZM+Xu7q4iIyPV3Llzre4/ceKEGjhwoAoICFBeXl6qQ4cO6u+//1ZKKTVp0iTVpk0bS1+TyaSmTJmi6tSpo9zc3FSbNm3UL7/8Yrn/999/V4BKSUmxtO3YsUMB6tixY0oppWJjY9Udd9yh/P39lZeXl2rRooX6+eefS/z9dO/eXT377LM276tXr5567733rH4/8+fPV/369VOenp6qcePGauXKlVaPiY6OVr1791be3t6qdu3a6sEHH1Rnzpwpcf0FBQXKz89P/fTTT2Wq67PPPlOAWrt2rVVdF283Wxo0aKAWLFhQah9RuWw992655RbVuXNnpZRSOTk5auzYsSosLEx5eXmpa6+9Vv3+++9W/RcuXKjCw8OVp6en6tevn5o+fbry8/Mrdb2XPq+K7N+/X7m5uamXX37Z0lba378tp0+fVpqmqT179ti8v6TXm4ULFxar+80331QGg0FlZWWVef1X4vTp0wpQf/zxh1V7jx491CuvvFLqY+3x+i+fqAU33XQTbdq0sbkrFSAzM5NevXoREBDA1q1b+fbbb/ntt98YOXKkpc+XX37JxIkTefPNN9m/fz9Tp07l1Vdf5fPPPwcgIyOD7t27c/LkSX744Qd27drFCy+8UGyXe5HZs2czY8YMpk+fzu7du+nVqxd33XUXMTExZc719NNPk5uby4YNG4iOjubtt98u9kn1SkyZMoX+/fuze/dubrvtNgYPHmz5pJqamspNN91Eu3bt2LZtG6tXr+bUqVP079+/xOXt3r2b8+fPc80115Rp/UOHDiUgIKDE7VaSa6+9lj///LNcjxGVz9PTk7y8PABGjhzJ5s2b+frrr9m9ezf3338/vXv3tvy9b9myheHDhzNy5Eh27txJjx49eOONNyq87mbNmtGnT59y/+1c7K+//sLLy4vmzZtXeBlFPD09MZvNJe5mnzp1KjVq1Cj1Jy4urszrO3/+PACBgYFW7Y763JATnlSSa66BpKTqX29ICFTG/IdmzZqxe/dum/ctWbKEnJwcFi9ejLe3NwAffPABd955J2+//TbBwcFMmjSJGTNmcM899wDQoEED9u3bx8cff8zQoUNZsmQJZ86cYevWrZYnR+PGjUusZ/r06bz44osMHDgQgLfffpvff/+dWbNmMXfu3DJliouL49577yUqKgqAhg0bXvYxH374IQsWLLDcfuKJJ5gxY4bNvg8//DCDBg0CCl9I5syZwz///EPv3r354IMPaNeundWksM8++4zw8HAOHTpE06ZNiy3v+PHjGI1GateuXaZ8BoOBpk2bEhsba9U+aNAgqxMxfPHFF/Tr189yOywsjB07dpRpHbqw+hrItv3kazZqPRnZ3lZtg65fybtDiw9yN01cyqEE67+R7i3/5svnRhXr+++RKDq0OgO9y//kU0qxbt06fv31V0aNGkVcXBwLFy4kLi6OsLAwoHDOxurVq1m4cCFTp05l9uzZ9O7dmxdeeAGApk2bsmnTJlavXl3u9Rdp1qwZa9assWorz9//8ePHCQ4OxmC4ss97MTExzJs3j2uuuQYfHx+bfZ588slS3+QClt/d5ZjNZkaPHk23bt1o1apVsWUcP368bIVXIxmoK0lSEpw8ae8qKk4pVeLxgfv376dNmzaWQRqgW7dumM1mDh48SI0aNThy5AjDhw/nscces/QpKCjAz88PgJ07d9KuXbti72BtSUtLIyEhgW7dulm1d+vWjV27dpU50zPPPMOIESNYs2YNPXv25N5776V169alPmbw4MG8/PLLltulzaq9eFne3t74+vpaJsTs2rWL33//3eYn+CNHjtgcqLOzs3F3dy/XcZq2ttt7771Hz549LbcvPdWhp6cnWVlZZV6Hw8tOgmzbT76Ec7VJz/G1aks572Kz/6kUf04mW/+uzqZ62eyblxle4puDkvz000/UqFGD/Px8zGYzDzzwAJMnT2b9+vWYTKZifxO5ubmWeRv79+/n7rvvtrq/S5culoE6Li6OFi1aWO576aWXeOmll0qtx9bfTnn+/rOzs/Hw8Ch1HSU5f/48NWrUwGw2k5OTw3XXXWf1BuFSgYGBZXrtKIunn36aPXv28NdffxW7z1GfGzJQV5KQEH2vd//+/TRo0KBCj83IyABg/vz5dOrUyeq+ok92RafeqyxF7+KVUpa2S88U9Oijj9KrVy9+/vln1qxZw7Rp05gxYwajRhX/hFTEz8+v1E/6F3N1dbW6rWmaZVd+RkaGZY/DpUo6R3DNmjXJysoiLy8PNze3y67fZDIRExNDx44drdpDQkJKzZCcnEytWrUuu3zd8Cz5SRAWdJqM7EyrtgC/AvCsU6xvcEAq57MTrdpq+mfZ7Ovm7Q+e5TszVY8ePfjoo49wc3MjLCzMMkkrIyMDo9HIv//+W+yUlGX9qiYsLIydO3dabpdlULP1nC/P33/NmjVJSUkpU99L+fj4sH37dgwGA6GhoZd9fZg6deplD1nct28fERERpfYZOXIkP/30Exs2bKBu3brF7nfU54YM1JXEQQ+/K5P/+7//Izo6mueee87m/c2bN2fRokVkZmZaPlVv3LgRg8FAZGQkwcHBhIWFcfToUQYPHmxzGa1bt2bBggUkJydf9kXE19eXsLAwNm7cSPfu3S3tGzdu5NprrwWwPJkSExMJCAgAsHqhKhIeHs6TTz7Jk08+yYQJE5g/f36pA3Vlad++Pd999x3169cvddbsxYqOI9+3b1+Zjin//PPPSUlJ4d577y1XbXv27OHGG28s12McWim7nw/cbav1yQs/1v7PZt+7L/xY61DG0i7m7e1tcxBs164dJpOJ06dPc/3119t8bPPmzdmyZYtV299//235v4uLS5kHWIADBw6wevVqJkyYUObHXKpdu3YkJSWRkpJieQ6WlcFgKFe9V7rrWynFqFGj+P7771m/fn2JH0r27NlDu3btylxXdZHJZFeZ3NxckpKSOHnyJNu3b2fq1Kn07duXO+64gyFDhth8zODBg/Hw8GDo0KHs2bOH33//nVGjRvHQQw8RHBwMFE6smjZtGnPmzOHQoUNER0ezcOFCZs6cCRR+bxoSEkK/fv3YuHEjR48e5bvvvmPz5s021/n888/z9ttvs3TpUg4ePMj48ePZuXMnzz77LFD4/XZ4eDiTJ08mJiaGn3/+udh3aaNHj+bXX3/l2LFjbN++nd9//71SJr6UxdNPP01ycjKDBg1i69atHDlyhF9//ZVhw4ZhMplsPqZWrVq0b9/e5i65rKwskpKSiI+P5++//+bFF1/kySefZMSIEfTo0aPMdWVlZfHvv/9y6623VjibqFxNmzZl8ODBDBkyhOXLl3Ps2DH++ecfpk2bxs8//wwUfo2zevVqpk+fTkxMDB988EGZv58uKCggKSmJhIQEoqOjef/99+nevTtt27bl+eefr3Dd7dq1o2bNmmzcuLHCyyirwMBAGjduXOpPaW+In376ab744guWLFmCj48PSUlJJCUlkZ2dbdXvzz//dMznRrXNL3ciej48C1CAcnFxUbVq1VI9e/ZUn332mTKZTFZ9qcDhWV9++aVq27atcnNzUwEBAeqGG25Qy5cvt9wfGxur7r33XuXr66u8vLzUNddco7Zs2aKUsn141uTJk1WdOnWUq6trscOzlFLqr7/+UlFRUcrDw0Ndf/316ttvv7U6PGvkyJGqUaNGyt3dXdWqVUs99NBD6uzZsyX+fsp7eNalh0H5+fmphQsXWm4fOnRI3X333crf3195enqqZs2aqdGjRyuz2VxiDR9++KHlkJ2L6yrabm5ubio0NFTdcccdVr/b0uq62JIlS1RkZGSJ94uqUdKhSkXy8vLUxIkTVf369ZWrq6sKDQ1Vd999t9q9e7elz6effqrq1q2rPD091Z133lnmw7OK/naMRqMKDAxU1113nXrvvfdUTk6OVd/yHp6llFIvvPCCGjhwoM37ynN4VlUr+h1c+nPx83XTpk3K39//soeI2eP1X1Pqoi/5RJnk5ORw7NgxGjRoUOHJFELYkp2dTWRkJEuXLqVLly6VvvzOnTvzzDPP8MADD1T6ssXVJykpiZYtW7J9+3bq1atn73KuyIABA2jTps1lJ+HZ4/Vfdn0L4UA8PT1ZvHgxZ8+erfRlnz17lnvuucdySJkQVyokJIRPP/20XMcwO6K8vDyioqJKnKdjb/KJugLkE7UQQlyd5BO1EEIIIazIQC2EEEI4MBmohRBCCAcmA7UQQgjhwGSgFkIIIRyYDNRCCCGEA5OBWgghhHBgMlALmzRNY8WKFdW2vsmTJ5fpQhSi/F599VUef/zxKlv+vn37qFu3LpmZmZfvLCrNokWLSr0MZXU6d+4ctWvXLnZtdL1x1L9lGaivIg8//DCapqFpGq6urgQHB3PLLbfw2WefWS7PWCQxMZE+ffpUW23jxo1j3bp11ba+khw+fJhhw4ZRt25d3N3dadCgAYMGDWKbTi+PlpSUxOzZs62uMVyevwOAHTt2cP/99xMcHIyHhwdNmjThscce49ChQwC0aNGCzp07Wy7AIoq7+Hfu5uZG48aNee211ygoKKjS9U6ePNmyXhcXF2rWrMkNN9zArFmzyM3NLda/on//b775Jn379qV+/fpW6yzpB6r/d5KcnMyoUaOIjIzE09OTiIgInnnmGc6fP2/p46h/yzJQX2V69+5NYmIisbGx/PLLL/To0YNnn32WO+64w+oJEhISgru7e7XVVaNGDYKCgqptfbZs27aNDh06cOjQIT7++GP27dvH999/T7NmzRg7dmyVrvvSa2lXlgULFtC1a9di52Eu69/BTz/9ROfOncnNzeXLL79k//79fPHFF/j5+fHqq69a+g0bNoyPPvqoygcePSv6ncfExDB27FgmT57Mu+++W+XrbdmyJYmJicTFxfH7779z//33M23aNLp27Up6erqlX0X//rOy/r+9c4+J4vri+Fdxd911WRe6iC7ywxeKEJUtFIIWrBYFFaxKra9U0lqNRmzTUDTaorYqDS3E0vpoRcU2xWhp1Rix+MSqKJQfFhbkKShLAUUKorxE4fz+IDs/lp2FXUTAej/JJnDvmbl3zpy5Z+5rTj0OHDiAFStWAGh96S4vL+d+w4cPxxdffKGTpqUndVJWVoaysjJEREQgKysLhw4dQkJCAldvLX3Slnss/Me/iBc5ehZfNJsLFy4QAIqOjubS0IXoWdHR0eTg4EAikYjGjRtHu3fv1skvKSmhxYsXk4WFBUkkEnJxcaHk5GQi4o+e9fnnn5ONjQ0JhUK96FmJiYkEgKqrq7m0v/76Syd61p07d8jPz4/kcjlJJBJydHSk+Ph4Xt20tLSQk5MTubi46EUSIyKdcjrTxZ9//kne3t70yiuvkEwmIy8vL0pLS9M5HwDas2cP+fv7k0QioS1btlBVVRUtXbqUFAoFDRw4kMaMGUMHDx7kjtFoNLRw4UIaPHgwWVhY0Ny5c7lrNYSTkxPt2rVLJ81YO6irqyOFQkHz5s3jPXdbnTx+/JhEIhGdP3++w/q8rPDpfMaMGVyktMbGRgoODialUkkSiYTc3NwoMTFRRz4mJoZsbW1JLBbTvHnzjI6e1fa50pKTk0NCoZA+/fRTIjLN/tsTFxdHVlZWBvPbR57T0plOeoJffvmFhEIhPXnyhEvrzJZ7o/1nPWoGpk+fjkmTJuHYsWO8+XV1dfDx8YGFhQVSU1MRFxeH8+fPIygoiJOJjY3F5s2bsWPHDuTk5CAsLAyhoaH48ccfAQC1tbWYOnUqSktLcfLkSWRkZGD9+vW8Q60AEBUVhcjISERERECtVsPHxwdz585FQUGB0de1du1aPH78GJcvX0ZmZibCw8MhlUp5ZdPT03Hz5k0EBwejf3/9x0I7F2iMLh49eoTAwEBcvXoVycnJsLe3x+zZs3V6L0DrsOT8+fORmZmJ999/H6GhocjOzsbvv/+OnJwc7N27FwqFAkBrj9vHxwfm5ua4cuUKkpKSIJVK4evri6amJt5rqqqqQnZ2NlxdXY3SV3s7OHPmDCorK7F+/Xpe+bbzo0KhEM7Ozrhy5YpRZTFaA7Bo711QUBCuX7+OI0eOQK1WY+HChfD19eXsPSUlBStWrEBQUBDS09Mxbdo0bN++vctlOzg4YNasWdy9Ntb++bhy5QpcXFy6XJe2tNUJH7NmzYJUKjX4c3JyMqm8mpoayGQynVjWfdGWDUfaZpiE6z5X3K292+PlDpUOxX9XPfv8qYODA9RqNW/e4cOH0djYiJ9++gmDBg0CAOzatQv+/v4IDw+HtbU1tmzZgsjISCxYsAAAMHLkSGRnZ+OHH35AYGAgDh8+jPv37yM1NRWWlpYAgDFjxhisT0REBDZs2IDFixcDAMLDw5GYmIhvvvkGu3fvNuqaNBoNAgICMGHCBADAqFGjDMpqG0QHB4cOz2mMLqZPn65zzL59+yCXy/HHH3/Az8+PS1+6dCnee+89nfqqVCrOsY4YMYLLO3r0KFpaWrB//35uji8mJgZyuRyXLl3iDXav0WhARFAqlR1eU1va2oGxOtGiVCpRXFxsdFndRoIr0MD/7Dnk3UNtu5fBJYMl+Fo5WE92euF95DfpDndOHSRC7H8s9WTT6pvg8sp/AF/Tnz0iwoULF3DmzBmsW7cOGo0GMTEx0Gg03L365JNPkJCQgJiYGISFhSEqKgq+vr7cS9PYsWNx7do1JCQkmFy+FgcHB5w9exaA6fe6LcXFxSbZGB/tdWKI/fv3o6GhwWC+QCAwuszKykps27aNd6Flr9myAZij7ibu1t5F6aPS3q5GlyEizgG0JycnB5MmTeIcEwBMmTIFLS0tyMvLg1QqRWFhIVasWIGVK1dyMk+fPsXgwa0NYnp6OlQqFeekO+Lhw4coKyvDlClTdNKnTJmCjIwMo6/pww8/xJo1a3D27Fl4e3sjICAAEydO5JUlI4PIdaYLa2tr3Lt3D5999hkuXbqEiooKNDc3o76+Xi8UYPue7po1axAQEIAbN25g5syZmDdvHiZPngwAyMjIwK1bt2Bubq5zTGNjIwoLC3nrqm3QTInw09YOjNWJFrFYjPr6epOO6RYa7gIN/M9e2RPgUbtBm+qmWqChVk/23hOgtN1SgcqmBt5zNzUCaBCaVM1Tp05BKpXiyZMnaGlpwdKlS7F161ZcunQJzc3NGDt2rI7848ePuXUbOTk5mD9/vk6+h4cH56g1Gg0cHR25vE2bNnUaV/lZ7nVbGhoauhxFypBODGFjY9PFWury8OFDzJkzB46Ojrzl9ZotG4A56m5iqHToC11uTk4ORo4c2aVja2tbG73o6Gi4u7vr5JmZmQFoNfzuRDs817aBab8g64MPPoCPjw/i4+Nx9uxZfPnll4iMjOR9Y9c2krm5uVCpVM9Ut8DAQPzzzz+IioqCnZ0dRCIRPDw89Ib02jp7oHVYr7i4GKdPn8a5c+fw5ptvYu3atYiIiEBtbS1cXFwQGxurV56VlRVvPbTD5tXV1QZl2tPWDtrqxMPDo9Njq6qqMHr0aKPK6VbEhp8BpUC/R20hlABi/R61teA+aki3R60QigCx/sulkJo6LJePadOmYe/evRAKhVAqldxwa21tLczMzJCWlsY9L1oMTdW0R6lUIj09nfvfmBdiQ/faVPtXKBSorq426RgthnRiiFmzZnU4JG1nZ4ebN292eI5Hjx7B19cX5ubmOH78OG8vvNds2QDMUXcT3TH83FtcvHgRmZmZBoOmjx8/HocOHUJdXR3nXJKSktC/f3+MGzcO1tbWUCqVKCoqwrJly3jPMXHiROzfvx9VVVWdNiIymQxKpRJJSUmYOnUql56UlAQ3NzcA/3dO5eXlsLCwAACdhkqLra0tVq9ejdWrV2Pjxo2Ijo7mddTOzs5wdHREZGQkFi1apDdP9+DBA8jl8k51of1/z549mD17NgCgpKQElZWVHV6zFisrKwQGBiIwMBCenp4ICQlBREQEXn31VRw9ehRDhgyBTCYz6lyjR4+GTCZDdna2Xm+Nj/Z2MHPmTCgUCnz11Vc4fvy4nrxWJ1qysrLw9ttvG1W3bqWD4edcE05z0QTZrszIDho0iHe6R6VSobm5GRUVFfD09OQ9dvz48UhJSdFJS05O5v4eMGBAh1NJ7cnNzUVCQgI2btwIwHj750OlUuHnn382uuy2GNKJIZ516Pvhw4fw8fGBSCTCyZMnDY4E9JotG6LHlq39i3iRV337+vpSeXk5/f3335SWlkY7duwgqVRKfn5+9PTpU04WbVZ919XV0bBhwyggIIAyMzPp4sWLNGrUKAoMDOTko6OjSSwWU1RUFOXl5ZFaraaDBw9SZGQkEbWupBw7dix5enrS1atXqbCwkH799Ve6du0aEemvTt25cyfJZDI6cuQI5ebm0oYNG0ggEFB+fj4RETU1NZGtrS0tXLiQ8vPz6dSpUzRu3DidVd8fffQRJSQkUFFREaWlpZG7uzu98847BvWTkpJC5ubmNHnyZIqPj6fCwkLKyMig7du3k5eXl9G6UKlUNGPGDMrOzqbk5GTy9PQksViss/IV7VbVExGFhobSiRMnqKCggLKyssjPz4/c3Ny4cu3t7emNN96gy5cvU1FRESUmJtK6deuopKTE4DUtWLCAgoODddJMsYMTJ06QQCAgf39/OnfuHN2+fZtSU1MpJCSEFi1axMndvn2b+vXrR3fu3DFYl5cZQyvttSxbtoxGjBhBv/32GxUVFVFKSgqFhYXRqVOniIjo+vXr1L9/f/r6668pPz+fvvvuO5LL5Uat+nZycqLy8nIqLS0ltVpN3377LQ0ZMoRee+01nd0Kxtg/H2q1mgYMGEBVVVW8+aas+n6e1NTUkLu7O02YMIFu3bpF5eXl3K+tzXdmy73R/jNH3QVeZEcNgADQgAEDyMrKiry9vengwYN6WzLaOxJjtmfFxsaSs7MzCYVCsrCwIC8vLzp27BiXf+fOHQoICCCZTEYSiYRcXV0pJSWFiPi3Z23dupVsbGxIIBDobc8iIrp69SpNmDCBBg4cSJ6enhQXF6fjqIOCgmj06NEkEonIysqK3n33XaqsrOxQR3l5ebR8+XJSKpUkFArJzs6OlixZQjdu3DBaFzdu3CBXV1caOHAg2dvbU1xcnF5jxeeot23bRuPHjyexWEyWlpb01ltvUVFREZdfXl5Oy5cvJ4VCQSKRiEaNGkUrV66kmpoag9dz+vRpsrGx0bm/ptgBEVFqaiotWLCArKysSCQS0ZgxY2jVqlVUUFDAyYSFhZGPj0+Hun2Z6cwpNTU10ebNm2nEiBEkEAho2LBhNH/+fFKr1ZzMgQMHaPjw4SQWi8nf39/o7Vnae21mZkaWlpb0+uuv086dO6mxsVFP3hj758PNzY2+//573ry+4qi1Wzr5fm23OXZmy73R/vcjeoZVBC8pjY2NuH37NkaOHNnlRRQMRk9ARHB3d8fHH3+MJUuWPJcympqaYG9vj8OHD+stAGS8HMTHxyMkJARZWVm827teFIyx5d5o/19cjTIYjE7p168f9u3b91y/sqTRaLBp0ybmpF9i5syZg1WrVqG09MXd+QL0XVtmPeouwHrUDAaD8XLCetQMBoPBYDB0YI6awWAwGIw+DHPUzwCbNWAwGIyXi95o95mj7gLaTfV96RNzDAaDwXj+aNt9U74r/qywL5N1ATMzM8jlclRUVAAAJBKJwe9kMxgMBuPFh4hQX1+PiooKyOVyvc+9Pk/Yqu8uQkS4e/cuHjx40NtVYTAYDEYPIZfLMXTo0B7tnDFH/Yw0NzfrBYNgMBgMxr8PgUDQoz1pLcxRMxgMBoPRh2GLyRgMBoPB6MMwR81gMBgMRh+GOWoGg8FgMPowzFEzGAwGg9GHYY6awWAwGIw+DHPUDAaDwWD0YZijZjAYDAajD/M/gteF+dEwdYEAAAAASUVORK5CYII=",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, axes = plt.subplots(1, 1, figsize=(5,4)) # 3x3 grid of subplots\n",
"ax = axes \n",
"# Plot lines with improved color and line style\n",
"line1, = ax.plot(np.delete(newbins, whichbin), (density_df[~(np.asarray(newbins) == outbin)]), color=colors['DF'], linestyle=line_styles['DF'], linewidth = line_widths['DF'], label='Dioecious Fine (DF)', zorder = 1)\n",
"line2, = ax.plot(np.delete(newbins, whichbin), (density_dc[~(np.asarray(newbins) == outbin)]), color=colors['DC'], linestyle=line_styles['DC'], linewidth = line_widths['DC'], label='Dioecious Coarse (DC)', zorder = 1)\n",
"line4, = ax.plot(np.delete(newbins, whichbin), density_hp_df[~(np.asarray(newbins) == outbin)], color=colors['HP'], linestyle=line_styles['HP'], linewidth = line_widths['HP'], label='Ped-DF (TP = 2)', zorder = 1)\n",
"line5, = ax.plot(np.delete(newbins, whichbin), density_hp_df[~(np.asarray(newbins) == outbin)], color=colors['DF'], linestyle=(2, (2, 2)), linewidth = line_widths['HP'], label='Ped-DF (TP = 2)', zorder = 1)\n",
"line6, = ax.plot(np.delete(newbins, whichbin), density_hp_dc[~(np.asarray(newbins) == outbin)], color=colors['HP_DC'], linestyle=line_styles['HP_DC'], linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)', zorder = 1)\n",
"line7, = ax.plot(np.delete(newbins, whichbin), density_hp_dc[~(np.asarray(newbins) == outbin)], color=colors['DC'], linestyle=(2, (2, 2)), linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)', zorder = 1)\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the X chromosome', fontsize=10)\n",
"ax.set_ylabel('Density', fontsize=10)\n",
" \n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, (density_df[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['DF'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"ax.scatter(outbin, (density_dc[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['DC'], s=30, label='Outlier',marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"ax.scatter(outbin, (density_hp_df[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['HP'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"ax.scatter(outbin, (density_hp_dc[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['HP_DC'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"\n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, density_df[np.where(newbins == outbin)], edgecolor=colors['DF'], s=30, label='Outlier', marker='o', facecolor=colors['DF'], zorder = 4)\n",
"ax.scatter(outbin, density_dc[np.where(newbins == outbin)], edgecolor=colors['DC'], s=30, label='Outlier',marker='o', facecolor=colors['DC'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_df[np.where(newbins == outbin)], edgecolor=colors['HP'], s=30, label='Outlier', marker='o', facecolor=colors['HP'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_df[np.where(newbins == outbin)], edgecolor=colors['HP'], s=15, label='Outlier', marker='o', facecolor=colors['DF'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_dc[np.where(newbins == outbin)], edgecolor=colors['HP_DC'], s=30, label='Outlier', marker='o', facecolor=colors['HP_DC'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_dc[np.where(newbins == outbin)], edgecolor=colors['HP_DC'], s=15, label='Outlier', marker='o', facecolor=colors['DC'], zorder = 4)\n",
"\n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"ax.yaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([line1, line2, (line4, line5), (line6, line7)])\n",
"labels.extend([line1.get_label(), line2.get_label(), line4.get_label(), line6.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "4b429c31",
"metadata": {},
"source": [
"### 4.2 Plot histograms\n",
"#### 4.2.1 Plot for autosomal admixture\n",
"The following code produces a figure depicting all the computed Phase-Type histograms for autosomal admixture. Run if ``X_chr = False``."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "f6289e9b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, ax = plt.subplots(figsize=(5,4)) \n",
"\n",
"# Plot lines with improved color and line style\n",
"line1, = ax.step(bins[:-1], hist_df, color=colors['DF'], linestyle=line_styles['DF'], linewidth = line_widths['DF'], label='Dioecious Fine (DF)')\n",
"line2, = ax.step(bins[:-1], hist_dc, color=colors['DC'], linestyle=line_styles['DC'], linewidth = line_widths['DC'], label='Dioecious Coarse (DC)')\n",
"line3, = ax.step(bins[:-1], hist_m, color=colors['M'], linestyle=line_styles['M'], linewidth = line_widths['M'], label='Monoecious (M)')\n",
"line4, = ax.step(bins[:-1], hist_hp_df, color=colors['HP'], linestyle=line_styles['HP'], linewidth = line_widths['HP'], label='Ped-DF (TP = 2)')\n",
"line5, = ax.step(bins[:-1], hist_hp_df, color=colors['DF'], linestyle=(2, (2, 2)), linewidth = line_widths['HP'], label='Ped-DF (TP = 2)')\n",
"line6, = ax.step(bins[:-1], hist_hp_dc, color=colors['HP_DC'], linestyle=line_styles['HP_DC'], linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)')\n",
"line7, = ax.step(bins[:-1], hist_hp_dc, color=colors['DC'], linestyle=(2, (2, 2)), linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)')\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the second chromosome', fontsize=10)\n",
"ax.set_ylabel('Expected number of tracts per interval', fontsize=10)\n",
" \n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([line1, line2, line3, (line4, line5), (line6, line7)])\n",
"labels.extend([line1.get_label(), line2.get_label(), line3.get_label(), line4.get_label(), line6.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "53c27763",
"metadata": {},
"source": [
"#### 4.2.2 Plot for X chromosome admixture\n",
"The following code produces a figure depicting all the computed Phase-Type histograms for admixture on the X chromosome. Run if ``X_chr = True``."
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "55af0c51",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, ax = plt.subplots(figsize=(5,4)) \n",
"\n",
"# Plot lines with improved color and line style\n",
"line1, = ax.step(bins[:-1], hist_df, color=colors['DF'], linestyle=line_styles['DF'], linewidth = line_widths['DF'], label='Dioecious Fine (DF)')\n",
"line2, = ax.step(bins[:-1], hist_dc, color=colors['DC'], linestyle=line_styles['DC'], linewidth = line_widths['DC'], label='Dioecious Coarse (DC)')\n",
"line4, = ax.step(bins[:-1], hist_hp_df, color=colors['HP'], linestyle=line_styles['HP'], linewidth = line_widths['HP'], label='Ped-DF (TP = 2)')\n",
"line5, = ax.step(bins[:-1], hist_hp_df, color=colors['DF'], linestyle=(2, (2, 2)), linewidth = line_widths['HP'], label='Ped-DF (TP = 2)')\n",
"line6, = ax.step(bins[:-1], hist_hp_dc, color=colors['HP_DC'], linestyle=line_styles['HP_DC'], linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)')\n",
"line7, = ax.step(bins[:-1], hist_hp_dc, color=colors['DC'], linestyle=(2, (2, 2)), linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)')\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the X chromosome', fontsize=10)\n",
"ax.set_ylabel('Expected number of tracts per interval', fontsize=10)\n",
" \n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([line1, line2, (line4, line5), (line6, line7)])\n",
"labels.extend([line1.get_label(), line2.get_label(), line4.get_label(), line6.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "1e1bc374",
"metadata": {},
"source": [
"## 5. Tract length distribution for a continuous pulse during 15 generations\n",
"We consider the following migration matrix, and let the user specify the sex-bias parameters as in the previous example. Once again, ``whichpop`` sets the population of interest (0 or 1)."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "27b9ea46",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"15\n"
]
}
],
"source": [
"whichpop = 1\n",
"mig_matrix = np.array([[0, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0.2, 0],[0, 1]])\n",
"print(np.shape(mig_matrix)[0]-1) # Number of generations"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "0ad3818e",
"metadata": {},
"outputs": [],
"source": [
"prop_of_female_migration = 0.5 # 0.5 for unbiased migration, 1 for only female migrants, 0 for only male migrants.\n",
"mig_m = 2*mig_matrix*(1-prop_of_female_migration)\n",
"mig_f = 2*mig_matrix*prop_of_female_migration\n",
"mig_m[-1,:] = mig_matrix[-1,:]\n",
"mig_f[-1,:] = mig_matrix[-1,:]\n",
"\n",
"rec_f = 1 # Female-specific recombination rate\n",
"rec_m = 1 # Male-specific recombination rate"
]
},
{
"cell_type": "markdown",
"id": "b2af565c",
"metadata": {},
"source": [
"### 5.1 Monoecious model for autosomal admixture"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "ae3b297b",
"metadata": {},
"outputs": [],
"source": [
"PTmodel_mono = PhT.PhTMonoecious(mig_matrix, rho = 0.5*(rec_f+rec_m)) # M object\n",
"# Density (set freq = True for frequency scale)\n",
"newbins, density_m, E = PTmodel_mono.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = True, freq = True)\n",
"# Histogram\n",
"bins, hist_m, E = PTmodel_mono.tractlength_histogram_windowed(whichpop, bins, L = which_L, density = False, freq = False)"
]
},
{
"cell_type": "markdown",
"id": "b44b701d",
"metadata": {},
"source": [
"#### 5.1.1 Plot density"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8a3b8803",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, axes = plt.subplots(1, 1, figsize=(5,4)) \n",
"ax = axes \n",
"# Plot lines with improved color and line style\n",
"line3, = ax.plot(np.delete(newbins, whichbin), (density_m[~(np.asarray(newbins) == outbin)]), color=colors['M'], linestyle=line_styles['M'], linewidth = line_widths['M'], label='Monoecious (M)', zorder = 1)\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the second chromosome', fontsize=10)\n",
"ax.set_ylabel('Density', fontsize=10)\n",
" \n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, (density_m[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['M'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"\n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, density_m[np.where(newbins == outbin)], edgecolor=colors['M'], s=30, label='Outlier', marker='o', facecolor=colors['M'], zorder = 4)\n",
"\n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"ax.yaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([line3])\n",
"labels.extend([line3.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "91f704e3",
"metadata": {},
"source": [
"#### 5.1.2 Plot histogram"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "2ff050fb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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iZ8+ehdFoRHBwsMV4cHAw8vLyrN7njz/+wEcffYSsrCybHqOmpgY1NTXi7w3PU26eSCAIAlQqFUwmExoeYDCPN55w0Ny4SqWCIAhWxwE0OfrQ3LharQZjzOp44xobjxuNRuTk5KBnz55wd3fnIpOZyWRCTk4OevToYfHdRyVnMtdYX1+PQ4cOoUePHlCr1Vxkau41yUOmhuOMMRw8eFDcdjxkMtdu3nY9evSAm5sbF5nMzNkSEhLQWGtlspXkRp2VlYW9e/ciNjZW6l2vmsFgwIMPPohVq1ahQ4cONt1nwYIFmDdvXpPxuro6ZGdnAwACAwMRHh6OkydPory8XFwmJCQEISEhKCwshMFgEMd1Oh3at2+PI0eOWJwrNioqClqtFocPH7bYwDExMfDw8BAfzyw+Ph61tbXIz88Xx9RqNeLj42EwGHDs2DFx3NPTE7GxsTh//jyKi4vFcV9fX0RHR6O0tBR6vR6MMZSXl+P06dOIiIjgIpNZQEAAAOD06dM4f/48F5nMr73Tp0+jvLwcOTk5EASBi0zm1575NVlWVoawsDAuMpmFhISgY8eOMBgM4rbjIZP5tVdVVSW+LsPDw7nIZH7tMcbEnThXZKqoqICtJH9GPWDAALz11lu47rrrpNzNqtraWnh7e+Obb74RZ5UDQGpqKioqKrBp0yaL5bOystCnTx/xXSvwv3cwKpUK+fn5iI6OtriPtT1qnU6H+fPn47nnngNAe9Ryz2TG8x51XV0d7VErKFPDcdqjVlYmM1fvUVdUVCAgIMCmz6gl71G//vrrePbZZ/Haa68hPj4e7u7uFrdf6QEb8vDwQL9+/ZCeni42apPJhPT0dEybNq3J8rGxsU3eybz44oswGAx4++23odPpmtxHo9FAo9FYffyGDR/435N9peVaY1wQBKvjzdVorXG1tLzSMjUet7YepWcyr6vh+pSeqeE6zb/zksnMaDRa3XZSa5Q67sxMDR/T/Ditsf1aK1PDx5Nao9RxqZmskdyozRO/RowYYTFuPmOZ1C+Qp6WlITU1Ff3790diYiKWLl2KCxcuiKcjHT9+PDp16oQFCxbA09MTPXv2tLi/v78/ADQZb6tUKhXi4+MVcf5aqSibMvGcDeA7H2WTB8mNevv27Q4tYMyYMSgrK8OcOXOg1+vRu3dvbN68WZxgVlRUpIgnUk5qa2sd9j13uaFsysRzNoDvfJTN9ez+HrVS8f49avP5a+Pj45s9PKNUlE2ZeM4G8J2PsjmPlO9R27RHffDgQfTs2RMqlQoHDx5scVlrH8wTQgghxD42NerevXtDr9cjKCgIvXv3Fmc6NmbPZ9SEEEIIaZ5Njfr48ePo2LGj+G8ib7wdomqIsikTz9kAvvNRNtejz6gJIYSQVubUc30TeWOMoaqqyupHE0pH2ZSJ52wA3/komzxQo+aMyWTCsWPHJJ1HVikomzLxnA3gOx9lkwdq1IQQQoiMSWrURqMRv/32m6STiRNCCCHEfpIatVqtxsiRIy2uXETkRwln2rEXZVMmnrMBfOejbK4n+dB3z549LS7ZReRFrVYjNjZWMV87kIKyKRPP2QC+81E2eZDcqF999VXMnDkTP/zwA0pKSlBVVWXxQ1zLZDLh3LlzipggIRVlUyaeswF856Ns8iD5ohyjRo0CANx2223iJcIA+6+eRRyLMYbi4mLxqmI8oWzKxHM2gO98lE0eXH71LEIIIYQ0T3KjHjp0qDPqIIQQQogVdn2P+vfff8cDDzyAQYMG4dSpUwCATz/9FH/88YdDiyP28fX1dXUJTkPZlInnbADf+Sib60lu1Bs2bEBKSgq8vLywb98+1NTUAAAqKyvx2muvObxAIo1arUZ0dLQiZjJKRdmUiedsAN/5KJs82DXre+XKlVi1ahXc3d3F8cGDB2Pfvn0OLY5IZzKZoNfrFTGTUSrKpkw8ZwP4zkfZ5EFyo87Pz8f111/fZNzPz4/OWCYDjDHo9XpFnGheKsqmTDxnA/jOR9nkQXKjDgkJwdGjR5uM//HHH4iKinJIUYQQQgi5THKjnjJlCmbMmIFdu3ZBEAScPn0an3/+OWbOnInHHnvMGTUSQgghbZbkr2c9//zzMJlMGDFiBC5evIjrr78eGo0GM2fOxPTp051RI5FAEAQEBgZanIyGF5RNmXjOBvCdj7LJg8DsPEBfW1uLo0ePorq6GnFxcfDx8XF0bU5RVVUFPz8/zJ8/H//5z39cXQ4hhJA2yNyLKisrodVqW1zW7utRe3h4wNfXF6GhoYpp0m2ByWRCUVGRImYySkXZlInnbADf+SibPEhu1PX19Zg9ezb8/PwQGRmJyMhI+Pn54cUXX0RdXZ0zaiQSMMZQXl6uiJmMUlE2ZeI5G8B3PsomD5I/o54+fTo2btyIRYsWYeDAgQCAzMxMvPTSSzh37hxWrFjh8CIJIYSQtkpyo/7iiy+wbt063HzzzeJYQkICdDodxo0bR42aEEIIcSDJh741Gg0iIyObjHfu3BkeHh6OqIlcBUEQEBISooiZjFJRNmXiORvAdz7KJg+SG/W0adPwyiuviOf4BoCamhrMnz8f06ZNc2hxRDqVSoWQkBCoVHbPE5QtyqZMPGcD+M5H2eRB8qHv/fv3Iz09Hddccw169eoFADhw4ABqa2sxYsQI3HnnneKyGzdudFylxCZGoxGFhYWIjIxUxMnmpaBsysRzNoDvfJRNHiQ3an9/f9x1110WYzqdzmEFkatnMBhcXYLTUDZl4jkbwHc+yuZ6khv1mjVrnFEHIYQQQqyQ/8F5QgghpA2TvEfNi+rqaixZsqTZ2zUaDYYPH464uLhWrOrqCYIAnU6niJmMUlE2ZeI5G8B3PsomD222UTPGWvx8wmAwYPv27Ypr1CqVCu3bt3d1GU5B2ZSJ52wA3/komzy02UPfvr6+zf6Y32E1/AqaUhiNRuTl5cFoNLq6FIejbMrEczaA73yUTR4cskddUVEBf39/R6yq1Tz22GMICAiwetuSJUsUMxvQmkuXLrm6BKehbMrEczaA73yUzfUk71G//vrrWL9+vfj7vffei/bt26NTp044cOCAQ4sjhBBC2jrJjXrlypXi96a3bt2KrVu34ueff8bNN9+MZ555xuEFEkIIIW2Z5EPfer1ebNQ//PAD7r33XowcORKRkZFISkpyeIHOooTTxtlDpVIhKiqKy3yUTZl4zgbwnY+yyYPkCgMCAlBcXAwA2Lx5M5KTkwFcnkWthA/lzZQwJd8egiBAq9VymY+yKRPP2QC+81E2eZDcqO+8807cd999uPHGG3Hu3Dnxcpf79+9Hly5dHF6gsyjpTYUURqMR2dnZXOajbMrEczaA73yUTR4kH/p+6623EBkZieLiYixatAg+Pj4AgJKSEkydOtXhBRLplPDCsxdlUyaeswF856Nsrie5UWdmZuLJJ5+Em5vlXadPn44///zTYYURQgghxI5D38OHD0d5eXmT8crKSgwfPtwhRRFCCCHkMsmNmjFm9cP3c+fOoV27dg4pqjUoYaafPVQqFWJiYrjMR9mUiedsAN/5KJs82Hzo+8477wRweabchAkToNFoxNuMRiMOHjyIQYMGOb5CIpmHh4erS3AayqZMPGcD+M5H2VzP5rcSfn5+8PPzA2MMvr6+4u9+fn4ICQnBww8/jM8++8yZtTqUyWRydQlOYTKZkJ2dzWU+yqZMPGcD+M5H2eTB5j3qNWvWAAAiIyPxzDPPwNvb22FFLF++HG+88Qb0ej169eqFZcuWITEx0eqyGzduxGuvvYajR4+irq4OXbt2xdNPP40HH3zQYfUQQgghciH54Pz48eNx6tSpJuNHjhxBYWGh5ALWr1+PtLQ0zJ07F/v27UOvXr2QkpKC0tJSq8sHBgbihRdeQGZmJg4ePIiJEydi4sSJ+OWXXyQ/NiGEECJ3khv1hAkTrH4Na9euXZgwYYLkApYsWYIpU6Zg4sSJiIuLw8qVK+Ht7Y3Vq1dbXX7YsGG444470L17d0RHR2PGjBlISEjAH3/8IfmxCSGEELmT/D3q/fv3Y/DgwU3Gr732WkybNk3Sumpra7F3717MmjVLHFOpVEhOTkZmZuYV788Yw6+//or8/Hy8/vrrVpepqamxuK50VVWVeF/zl90FQYBKpYLJZAJjrMk6Gn8p3rx843GVSgVBEKyOA00/F29uXK1WgzFmddxajQ3HGWOIi4sTb2u8fHO1yzlTQ/Hx8QAst4mSM5lrBIC4uDjxdclDpuZekzxkajzecNvxksloNIrbzvxYPGQyY4yhR48eLs1kK8mNWhAEq9dqrqyslHyWl7Nnz8JoNCI4ONhiPDg4GHl5ec3er7KyEp06dUJNTQ3UajXee+893HjjjVaXXbBgAebNm9dk/PDhw+JZ1QIDAxEeHo6TJ0+ivLwcdXV1AP73pBcWFlpk1ul0aN++PY4cOWJxPdOoqChotVocPnzY4rmIiYmBh4cHsrOzLWqIj49HbW0t8vPzxTG1Wo34+HgYDAYcO3ZMHPf09ERsbCzOnz8vnmsdAHx9fREdHY3S0lLo9XoAl/9H2LFjR4tMZiEhIQgJCVFcJuDydurYsSPKysq4yhQeHo5Tp06hrKwMarWam0wNX3tGoxFhYWEIDQ3lJhNweTsFBwfj2LFjFrUrPVPD157RaIRareYqk1lQUBBCQ0NdkqmiogK2Epi1XcgW3HrrrfDy8sKXX34p/k/FaDRizJgxuHDhAn7++Web13X69Gl06tQJf/75JwYOHCiOP/vss9ixYwd27dpl9X4mkwnHjh1DdXU10tPT8corr+C7777DsGHDmixrbY9ap9OhrKwMAQEBAJq+C3v77bdhMBjg6+uLtLQ0Re0BGI1G5OTkoGfPnnB3d+dqj9pkMiEnJ0d8F8xDJnONdXV1OHToEHr06AG1Ws1FpuZekzxkajjOGMPBgwfFbcdDJnPt5m3Xo0cPuLm5cZHJzJwtISEBjbVGpoqKCgQEBKCyshJarbZJDQ1J3qN+/fXXcf311yMmJgZDhgwBAPz++++oqqrCr7/+KmldHTp0gFqtxpkzZyzGz5w5g5CQkGbvp1KpxAuA9O7dG7m5uViwYIHVRq3RaCy+822mVqvFP6qG67Wm8XKtMS4IgtXx5mq01rhaWl5pmRqPW1uP0jOZ19VwfUrP1HCd5t95yWRm/qjC2v9TlJqp4WOaH6c1tl9rZWr4eFJrlDouNZM1kieTxcXF4eDBg7j33ntRWloKg8GA8ePHIy8vDz179pS0Lg8PD/Tr1w/p6enimMlkQnp6usUe9pWYTCaLvWZCCCGEF5L3qAEgLCwMr732mkMKSEtLQ2pqKvr374/ExEQsXboUFy5cwMSJEwFc/jpYp06dsGDBAgCXP3Pu378/oqOjUVNTg59++gmffvopVqxY4ZB6eNDcuz0eUDZl4jkbwHc+yuZ6djVqALh48SKKiopQW1trMW7teH9LxowZg7KyMsyZMwd6vR69e/fG5s2bxQlmRUVFFocILly4gKlTp+LkyZPw8vJCbGwsPvvsM4wZM0bS4yplA0llnsDAI8qmTDxnA/jOR9nkQfJksrKyMkycOLHZSWNyv75nVVUV/Pz8UFFRAT8/P6vLLFmyxGIymZIwxsTarV08RckomzLxnA3gOx9lcx5zL7JlMpnkz6iffPJJVFRUYNeuXfDy8sLmzZvx8ccfo2vXrvj+++/tLrq1KeH8rvYwz4jnMR9lUyaeswF856Ns8iD50Pevv/6KTZs2oX///lCpVIiIiMCNN94IrVaLBQsW4JZbbnFGnYQQQkibJHmP+sKFCwgKCgIABAQEoKysDMDlL3zv27fPsdURQgghbZzkRh0TEyOefaVXr154//33cerUKaxcuRKhoaEOL5BI5+np6eoSnIayKRPP2QC+81E215N86HvGjBkoKSkBAMydOxc33XQTPv/8c3h4eGDt2rWOrs9peJ71HRsb6+oynIKyKRPP2QC+81E2eZDcqB944AHx3/369cOJEyeQl5eH8PBwdOjQwaHFOZMSJhDYw2Qy4fz58wgICJB05hsloGzKxHM2gO98lE0eJFVXV1eH6Oho5ObmimPe3t7o27evopo0AKtXyeIBYwzFxcVc5qNsysRzNoDvfJRNHiQ1and3d4srjBBCCCHEuSTv7z/++ON4/fXXUV9f74x6CCGEENKA5M+o9+zZg/T0dGzZsgXx8fFo166dxe0bN250WHHEPr6+vq4uwWkomzLxnA3gOx9lcz3Jjdrf3x933XWXM2ppVTzP+o6OjnZ1GU5B2ZSJ52wA3/komzxIbtRr1qxxRh2tjudZ36WlpQgKCpL9TEapKJsy8ZwN4DsfZZMHydXdcMMNqKioaDJeVVWFG264wRE1tQolzPSzB2MMer2ey3yUTZl4zgbwnY+yyYPkRp2RkdHk0pYAcOnSJfz+++8OKYoQQgghl9l86PvgwYPivw8fPgy9Xi/+bjQasXnzZnTq1Mmx1RFCCCFtnM2Nunfv3hAEAYIgWD3E7eXlhWXLljm0OGfi7dqqZoIgIDAwkMt8lE2ZeM4G8J2PssmDzY36+PHjYIwhKioKu3fvRseOHcXbPDw8EBQUpKiZ1HKfPGAvlUqF8PBwV5fhFJRNmXjOBvCdj7LJg82NOiIiAgA/s6V5ydGYyWTCyZMncc0113D3ZoSyKRPP2QC+81E2eZB3dU6khJl+9mCMoby8nMt8lE2ZeM4G8J2PsslDm23UhBBCiBJQoyaEEEJkzKZG/c4774hXzSoqKlLEoYIrUcJMP3sIgoCQkBAu81E2ZeI5G8B3PsomDzY16rS0NFRVVQEAOnfujLKyMqcW1RrkPnnAXiqVCiEhIVzmo2zKxHM2gO98lE0ebKowLCwMGzZswIkTJ8AYw8mTJ1FUVGT1RymMRqOrS3AKo9GIgoICLvNRNmXiORvAdz7KJg82fT3rxRdfxPTp0zFt2jQIgoABAwY0WYYxBkEQFBGadwaDwdUlOA1lUyaeswF856NsrmdTo3744Ycxbtw4nDhxAgkJCdi2bRvat2/v7NoIIYSQNs/mE574+vqiZ8+eWLNmDQYPHgyNRuPMugghhBACO65HnZqaCgDYu3cvcnNzAQBxcXHo27evYytzMiXM9LOHIAjQ6XRc5qNsysRzNoDvfJRNHiQ36tLSUowdOxYZGRnw9/cHAFRUVGD48OFYt26dxTnA5UwJM/3soVKpuP1YgrIpE8/ZAL7zUTZ5kNytpk+fDoPBgJycHJSXl6O8vByHDh1CVVUVnnjiCWfU6BS8TnozGo3Iy8vjMh9lUyaeswF856Ns8iB5j3rz5s3Ytm0bunfvLo7FxcVh+fLlGDlypEOLI/Yxn5yGR5RNmXjOBvCdj7K5nuQ9apPJBHd39ybj7u7u3F6RihBCCHEVyY36hhtuwIwZM3D69Glx7NSpU3jqqacwYsQIhxZHCCGEtHWSG/W7776LqqoqREZGIjo6GtHR0ejcuTOqqqqwbNkyZ9ToFDxPJouKiuIyH2VTJp6zAXzno2zyIDA7rrDBGMO2bduQl5cHAOjevTuSk5MdXpwzVFVVwc/PD5WVldBqtVaXWbJkCQwGAwRBgI+Pj9VlNBoNhg8fjri4OGeWSwghhEO29CIzu95KCIKAG2+8EdOnT8f06dMV06Qbammmn/lkLowxGAwGqz9nz57F9u3bW6tcmxmNRmRnZytiJqNUlE2ZeM4G8J2PssmD5FnfbcHw4cOxfft21NTUWL29uroajLFmb3c1Jbzw7EXZlInnbADf+Sib61GjtiIuLq7FQ9rmQ+OEEEKIs8n/U3RCCCGkDZPUqOvr6/HJJ5/gzJkzzqqn1Shhpp89VCoVYmJiuMxH2ZSJ52wA3/komzxIqtDNzQ2PPvqoYs7m0lZ5eHi4ugSnoWzKxHM2gO98lM31JL+VSExMRFZWlhNKaV28nkXNZDIhOzuby3yUTZl4zgbwnY+yyYPkyWRTp05FWloaiouL0a9fP7Rr187i9oSEBIcVRwghhLR1khv12LFjAcDiSlmCIIAxBkEQFDPdnRBCCFECyY36+PHjzqiDEEIIIVZIbtQRERHOqKPVKWGmnz1UKhXi4+O5zEfZlInnbADf+SibPNhV4aefforBgwcjLCwMJ06cAAAsXboUmzZtsquI5cuXIzIyEp6enkhKSsLu3bubXXbVqlUYMmQIAgICEBAQgOTk5BaXb4tqa2tdXYLTUDZl4jkbwHc+yuZ6khv1ihUrkJaWhlGjRqGiokL8TNrf3x9Lly6VXMD69euRlpaGuXPnYt++fejVqxdSUlJQWlpqdfmMjAyMGzcO27dvR2ZmJnQ6HUaOHIlTp05JelwlzPSzh8lkQn5+Ppf5KJsy8ZwN4DsfZZMHyY162bJlWLVqFV544QWo1WpxvH///sjOzpZcwJIlSzBlyhRMnDgRcXFxWLlyJby9vbF69Wqry3/++eeYOnUqevfujdjYWHz44YcwmUxIT0+X/NiEEEKI3Elu1MePH0efPn2ajGs0Gly4cEHSumpra7F3716Lq2+pVCokJycjMzPTpnVcvHgRdXV1CAwMlPTYhBBCiBJInkzWuXNnZGVlNZlUtnnzZnTv3l3Sus6ePQuj0Yjg4GCL8eDgYPFa11fy3HPPISwsrNlLbdbU1Fhc5aqqqgrA5aummA/bC4IAlUoFk8mEhpfnNo+39JWzhrepVCqrX1EzT1ZofIiluXG1Wg3GmNXxxjU2HjcajRAEASaTyeryzWVqblwOmcwaZrKldiVkavjaa1gTL5msvSZ5yNRw3PzYDetUeiZz7eZtZ/4vD5nMjEajWIurMtlKcqNOS0vD448/jkuXLoExht27d+PLL7/EggUL8OGHH0pd3VVZuHAh1q1bh4yMDHh6elpdZsGCBZg3b16T8by8PPj4+AAAAgMDER4ejpMnT6K8vFxcJiQkBCEhISgsLLS4Wpb5Ca6vr7c43B8VFQWtVovDhw9bbOCYmBh4eHg0+WggPj4etbW1yM/PF8fUajXi4+NhMBhw7NgxcdzT0xOxsbE4f/48iouLxXFfX19ER0ejtLQUer1eHC8pKZGUSafToX379jhy5IjFKWLllCkwMBDx8fEoKiriKlN4eDhKSkrAGMPhw4e5ydT4tXfu3DnuMpm3U7t27cRtx0umhtvp8OHD3GUCLm8ntVqNvLy8Vs9UUVEBWwms8dsUG3z++ed46aWXUFBQAAAICwvDvHnzMGnSJEnrqa2thbe3N7755huMHj1aHE9NTUVFRUWLs8gXL16MV199Fdu2bUP//v2bXc7aHrVOp8O5c+fg5+cHQPoe9dtvvw2DwQBfX1/MmDFDHJfDO0vGGAwGA7RaLXd71ABw4cKFJmfDU3KmhjVWVVXB19cXgiBwkam51yQPmRqOC4KAyspK+Pj4iHvYSs9krt287Xx9faFSqbjIZMYYQ3V1Nfz8/KzW6OxMFRUVCAgIQGVlJbRaLVpi1/Wo77//ftx///24ePEiqqurERQUZM9q4OHhgX79+iE9PV1s1OaJYdOmTWv2fosWLcL8+fPxyy+/tNikgcufnWs0mibjgiBYTIYDmv9udePlrnRbc8tLGbdWX0s1NjyEc+LECcTHx7e4vCNqlDpubyYzo9GIY8eOIT4+3mnPu9Txq83UkHm7NVyfkjM195rkIVNDRqMRhYWFVl+XSs1kfsyG2868nNIzmbW03VqqUeq41EzW2NWoAaC0tFTczRcEAR07drRrPWlpaUhNTUX//v2RmJiIpUuX4sKFC5g4cSIAYPz48ejUqRMWLFgAAHj99dcxZ84cfPHFF4iMjBQPe/j4+IiHsgkhhBBeSG7UBoMBU6dOxZdffinuzqvVaowZMwbLly8XDyfbasyYMSgrK8OcOXOg1+vRu3dvbN68WZxgVlRUZPHOY8WKFaitrcXdd99tsZ65c+fipZdekhqHEEIIkTXJjXry5MnYv38/fvzxRwwcOBAAkJmZiRkzZuCRRx7BunXrJBcxbdq0Zg91Z2RkWPxeWFgoef1tTXMT63hA2ZSJ52wA3/kom+tJnkzWrl07/PLLL7juuussxn///XfcdNNNkr9L3dqqqqrg5+dn0wf4zVmyZIk4wSItLc3BFRJCCOGdlF4k+YQn7du3t3p428/PDwEBAVJX5zJKOG2cPUwmE86dO8dlPsqmTDxnA/jOR9nkQXKjfvHFF5GWlmbx3TW9Xo9nnnkGs2fPdmhxzmTHt9IUgTGG4uJiLvNRNmXiORvAdz7KJg82fUbdp08f8fuBAHDkyBGEh4cjPDwcwOUJXxqNBmVlZXjkkUecUykhhBDSBtnUqBuejIQQQgghrcemRj137lxn10EcyNfX19UlOA1lUyaeswF856Nsrmf3CU8AoLq6uskH8fbOpG5tLZ1tTMnUajWio6NdXYZTUDZl4jkbwHc+yiYPdl3m8pZbbkG7du3Emd4BAQHw9/enWd8yYDKZoNfrucxH2ZSJ52wA3/komzxI3qN+4IEHwBjD6tWrERwcbDHJTEmUMNPPHowx6PV6u0/pKmeUTZl4zgbwnY+yyYPkRn3gwAHs3bsXMTExzqiHEEIIIQ1IPvQ9YMAAi+uCEkIIIcR5JO9Rf/jhh3j00Udx6tQp9OzZE+7u7ha3JyQkOKw4Z1LqIfsrEQQBgYGBXOajbMrEczaA73yUTR4kN+qysjIUFBSIl6EELgdmjFm90LZcSbkWqJKoVCrxRDS8oWzKxHM2gO98lE0eJHerhx56CH369EFmZiaOHTuG48ePW/xXKZQw088eJpMJRUVFXOajbMrEczaA73yUTR4k71GfOHEC33//Pbp06eKMeloNz7O+y8vL0alTJ1eX4nCUTZl4zgbwnY+yyYPkPeobbrgBBw4ccEYthBBCCGlE8h71rbfeiqeeegrZ2dmIj49vMpnstttuc1hxhBBCSFsnuVE/+uijAICXX365yW1KmkymhJl+9hAEASEhIVzmo2zKxHM2gO98lE0eBMbrh7XNqKqqgp+fHyorK+0+L/mSJUtgMBggCAJ8fHyaXU6j0WD48OGIi4uzt1xCCCEcktKL+PyOkg2uZs9fo9EAuDwZwWAwNPtz9uxZbN++3VEl28RoNKKgoEAxRzakoGzKxHM2gO98lE0eJB/6tnbIu6E5c+bYXYxSDB8+HNu3b0dNTU2zy1RXV4Mx1uIyzmIwGFr9MVsLZVMmnrMBfOejbK4nuVF/++23Fr/X1dXh+PHjcHNzQ3R0dJto1HFxcVc8nG0+PE4IIYRcDcmNev/+/U3GqqqqMGHCBNxxxx0OKYoQQgghlznkM2qtVot58+Zh9uzZjlhdq1DCTD97CIIAnU7HZT7Kpkw8ZwP4zkfZ5EHyHnVzKisrUVlZ6ajVOR3P5/pu3769q8twCsqmTDxnA/jOR9nkQXKjfueddyx+Z4yhpKQEn376KW6++WaHFeZsSpjpZw+j0YgjR46ga9euUKvVri7HoSibMvGcDeA7H2WTB8mN+q233rL4XaVSoWPHjkhNTcWsWbMcVhix36VLl1xdgtNQNmXiORvAdz7K5nqSG/Xx48edUQchhBBCrODzg1pCCCGEE5L3qC9cuICFCxciPT0dpaWlTa7lqZRrUvM8mSwqKorLfJRNmXjOBvCdj7LJg+RGPXnyZOzYsQMPPvggQkNDFTG13Rql1n0lgiDYfQ5zuaNsysRzNoDvfJRNHiQ36p9//hk//vgjBg8e7Ix6Wg3Ps74PHz6MuLg42c9klIqyKRPP2QC+81E2eZC8zx8QEIDAwEBn1EIchNc3IQBlUyqeswF856Nsrie5Ub/yyiuYM2cOLl686Ix6CCGEENKA5EPfb775JgoKChAcHIzIyEi4u7tb3L5v3z6HFUcIIYS0dZIb9ejRo51QRutTwkw/e6hUKsTExHCZj7IpE8/ZAL7zUTZ5kNyo586d64w6iAN5eHi4ugSnoWzKxHM2gO98lM315P9Wwkkaf/+bFyaTCdnZ2Vzmo2zKxHM2gO98lE0e2myjJoQQQpSAGjUhhBAiY9SoCSGEEBlrs41aCTP97KFSqRAfH89lPsqmTDxnA/jOR9nkwaZZ32lpaTavcMmSJXYXQxyjtrYWnp6eri7DKSibMvGcDeA7H2VzPZsa9f79+y1+37dvH+rr6xETEwMA+Oeff6BWq9GvXz/HV+gkSpjpZw+TyYT8/HzEx8fL/vy1UlE2ZeI5G8B3PsomDzY16u3bt4v/XrJkCXx9ffHxxx8jICAAAHD+/HlMnDgRQ4YMcU6VhBBCSBsl+eD8m2++iQULFohNGrh8oY5XX30Vb775pkOLI4QQQto6yWcmq6qqQllZWZPxsrIyGAwGhxTFk+rq6mY/t9doNBg+fDji4uIc+phyP4xzNSibMvGcDeA7H2VzPcl71HfccQcmTpyIjRs34uTJkzh58iQ2bNiASZMm4c4775RcwPLlyxEZGQlPT08kJSVh9+7dzS6bk5ODu+66C5GRkRAEAUuXLpX8eGbO3kAajQYAwBiDwWCw+nP27FmLjxUcQa1WK+IzF3tQNmXiORvAdz7KJg+SG/XKlStx880347777kNERAQiIiJw33334aabbsJ7770naV3r169HWloa5s6di3379qFXr15ISUlBaWmp1eUvXryIqKgoLFy4ECEhIVJLt8AYu6r7X8nw4cPRoUMH+Pr6Wv0RBAEAUFNT49DHZYyhqqrK6flcgbIpE8/ZAL7zUTZ5EJidVV64cAEFBQUAgOjoaLRr107yOpKSkjBgwAC8++67AC7PwtPpdJg+fTqef/75Fu8bGRmJJ598Ek8++aSkx6yqqoKfnx/Ky8stPmdvbUuWLIHBYICvr6+kr79didFoRHZ2tmLeKUpB2ZSJ52wA3/kom/OYe1FlZSW0Wm2Ly0r+jNqspKQEJSUluP766+Hl5QXGmLiXaIva2lrs3bsXs2bNEsdUKhWSk5ORmZlpb1lN1NTUWOy1VlVVAbi8kYxGIwBAEASoVCqYTCaLd1fmcfNyVxpXqVQQBMHqOND8V8IaL69Wq8EYa7K8Wq1uUmPjcaPRKN7X2vLOztTc+NVkMjPft/E6lJyp8Wuv8WuSl0wNX5M8ZGo4DsBi2/GQyVy7edsZjUZuMpmZs5n/7YpMtpLcqM+dO4d7770X27dvhyAIOHLkCKKiojBp0iQEBATYPPP77NmzMBqNCA4OthgPDg5GXl6e1LKatWDBAsybN6/JeG5uLnx9fQEAgYGBCA8Px8mTJ1FeXi4uExISgpCQEBQWFlpMlNPpdGjfvj2OHDmCS5cuieNRUVHQarU4fPiwxQaOiYmBh4cHsrOzxbG6ujoAl//AG46bPzcxGAw4duyYOO7p6YnY2FicP38excXF4rivry+io6NRWloKvV4PxhjKy8tx+vRpREREtGomAIiPj0dtbS3y8/MdlsnMfATk9OnTOH/+PBeZzK+906dPo7y8HDk5ORAEgYtM5tee+TVZVlaGsLAwLjKZhYSEoGPHjjAYDOK24yGT+bVXVVUlvi7Dw8O5yGR+7THGxJ04V2SqqKiArSQf+h4/fjxKS0vx4Ycfonv37jhw4ACioqLwyy+/IC0tDTk5OTat5/Tp0+jUqRP+/PNPDBw4UBx/9tlnsWPHDuzatavF+9t66NvaHrVOp0NZWZn4P35X7FG//fbb4qHvGTNmWCx/tXvUR48eRdeuXeHu7s7dHnVBQQGio6MtTvun5EzmGuvq6nDkyBF06dIFarWai0zNvSZ5yNRwnDGG/Px8cdvxkKnhHvXRo0fRpUsXuLm5cZHJzGg0oqCgAN26dUNjrZGpoqICAQEBzjn0vWXLFvzyyy+45pprLMa7du2KEydO2LyeDh06QK1W48yZMxbjZ86cueqJYg1pNBpxBnZDHh4eTT6XaO6cr819fuHMcUEQrI43V6N5XK1WW3zdi4dMDdcZGxtrdVlH1Sh1/Gozmbm7u1v9mp6SMzX3muQhU2PNfcVSyZnUanWTbSe1RqnjrZGp4b+7d+9udbmWapQ6LjWTNZJnfV+4cAHe3t5NxsvLy602xOZ4eHigX79+SE9PF8dMJhPS09Mt9rCdhedTiJ47d47LfJRNmXjOBvCdj7LJg+RGPWTIEHzyySfi74IgwGQyYdGiRRg+fLikdaWlpWHVqlX4+OOPkZubi8ceewwXLlzAxIkTAVw+zN5wslltbS2ysrKQlZWF2tpanDp1CllZWTh69KjUGIqYkm8PxhiKi4u5zEfZlInnbADf+SibPEg+9L1o0SKMGDECf//9N2pra/Hss88iJycH5eXl2Llzp6R1jRkzBmVlZZgzZw70ej169+6NzZs3ixPMioqKLA4PnD59Gn369BF/X7x4MRYvXoyhQ4ciIyNDahRCCCFE9iQ36p49e+Kff/7Bu+++C19fX1RXV+POO+/E448/jtDQUMkFTJs2DdOmTbN6W+PmGxkZqYh3P4QQQoijSG7URUVF0Ol0eOGFF6zeFh4e7pDCiP3MXzvjEWVTJp6zAXzno2yuJ/kz6s6dO1u9KMe5c+fQuXNnhxTVGng7y46ZWq1GdHQ0l/komzLxnA3gOx9lkwfJjbq5M5BVV1fD09PTIUW1BiXM9LOHyWSCXq/nMh9lUyaeswF856Ns8mDzoW/z+agFQcDs2bMtvqJlNBqxa9cu9O7d2+EFOguvn3UzxqDX69GxY0dXl+JwlE2ZeM4G8J2PssmDzY16//79AP53yksPDw/xNg8PD/Tq1QszZ850fIWEEEJIG2ZzozZfN3nixIl4++23r3jKM0IIIYRcPcmfUS9duhT19fVNxsvLy8UrUymBlCt9KYkgCAgMDOQyH2VTJp6zAXzno2zyIPmiHDfffDNuvfVWTJ061WJ85cqV+P777/HTTz85tEBHk3INUGcyX49aEAT4+Pg0u5xGo8Hw4cObPZcwIYQQ5ZHSiyTvUe/atcvqqUKHDRt2xSteyYmrZ/qZz4vOGIPBYGj25+zZs+LHDrYwmUwoKipyeT5noGzKxHM2gO98lE0eJDfqmpoaq4e+6+rq8O+//zqkqNbg6lnfw4cPR4cOHeDr69vsj/mQTMPLdF6J+dq/rs7nDJRNmXjOBvCdj7LJg+QzkyUmJuKDDz7AsmXLLMZXrlyJfv36Oaww3sXFxV3xcLb58DghhJC2S3KjfvXVV5GcnIwDBw5gxIgRAID09HTs2bMHW7ZscXiBhBBCSFsm+dD34MGDkZmZiWuuuQZfffUV/vvf/6JLly44ePAghgwZ4owanUIJM/3sIQgCQkJCuMxH2ZSJ52wA3/komzxI3qMGgN69e+OLL75wdC2tquHlM3miUqkQEhLi6jKcgrIpE8/ZAL7zUTZ5sKtbFRQU4MUXX8R9992H0tJSAMDPP/+MnJwchxbnTEaj0dUlOIXRaERBQQGX+SibMvGcDeA7H2WTB8mNeseOHYiPj8euXbuwYcMGVFdXAwAOHDiAuXPnOrxAIh3PE9AomzLxnA3gOx9lcz3Jjfr555/Hq6++iq1bt1qc7/uGG27AX3/95dDiCCGEkLZOcqPOzs7GHXfc0WQ8KCgIZ8+edUhRhBBCCLlMcqP29/dHSUlJk/H9+/ejU6dODimqNShhpp89BEGATqfjMh9lUyaeswF856Ns8iC5UY8dOxbPPfcc9Ho9BEGAyWTCzp07MXPmTIwfP94ZNToFz7O+27dvz2U+yqZMPGcD+M5H2eRBcoWvvfYaYmNjodPpUF1djbi4OFx//fUYNGgQXnzxRWfU6BRKmOlnD6PRiLy8PC7zUTZl4jkbwHc+yiYPkr9H7eHhgVWrVmH27Nk4dOgQqqur0adPH3Tt2tUZ9REA1dXVWLJkSbO3N77C1qVLl1qrtFZH2ZSJ52wA3/kom+vZdcITAAgPD4dOpwPA7+e9rqbRaGAwGMQrbDXHYDBg+/btdClMQgjhkF0H5z/66CP07NkTnp6e8PT0RM+ePfHhhx86urY2z1lX2CKEEKIckveo58yZgyVLlmD69OkYOHAgACAzMxNPPfUUioqK8PLLLzu8SGdQwgQCe66wpVKpEBUVpYh8UlE2ZeI5G8B3PsomD5Ib9YoVK7Bq1SqMGzdOHLvtttuQkJCA6dOnK6ZR83q4XhAEaLVaV5fhFJRNmXjOBvCdj7LJg+S3EnV1dejfv3+T8X79+qG+vt4hRbUGJcz0s4fRaER2djaX+SibMvGcDeA7H2WTB8mN+sEHH8SKFSuajH/wwQe4//77HVIUuTpKeOHZi7IpE8/ZAL7zUTbXs2vW90cffYQtW7bg2muvBQDs2rULRUVFGD9+PNLS0sTlWvpKESGEEEKuTHKjPnToEPr27Qvg8uUuAaBDhw7o0KEDDh06JC7H62fAhBBCSGsSGGPM1UW0pqqqKvj5+aGiogJ+fn6uLueqmWd9C4IAHx8fAABjzOKNUuMToigVYwyXLl2Cp6cnd28EKZty8ZyPsjmPuRdVVlZecVKb5M+oy8rKmr0tOztb6urIVdJoNAAgnhTFYDCgurpa/LfBYMDZs2exfft2F1fqGA0vrcobyqZcPOejbK4nuVHHx8fjxx9/bDK+ePFiJCYmOqSo1mAymVxdgkNYOymKp6cnlydEMZlMyM7O5mbbNUTZlIvnfJRNHiR/Rp2Wloa77roLEydOxJIlS1BeXo7x48cjOzsbX3zxhTNqJC1ofFIU81cO4uPjoVarm5wQhRBCiLJI3qN+9tlnkZmZid9//x0JCQlISEiARqPBwYMHcccddzijRkIIIaTNsuvcaV26dEHPnj1RWFiIqqoqjBkzBiEhIY6ujRBCCGnzJM/63rlzJx544AEEBgbis88+w86dO5GWloabb74ZK1euREBAgLNqdQjeZn03xhiDyWSCSqWCIAhWZ4Vbo4SZ4Y2z8YSyKRfP+Sib8zh11vcNN9yAMWPG4K+//kL37t0xefJk7N+/H0VFRYiPj7e7aOI4tbW14r+tzQq39qOUmeENs/GGsikXz/kom+tJbtRbtmzBwoUL4e7uLo5FR0dj586deOSRRxxanDMpYaafPUwmE/Lz88V8PF0qs3E2nlA25eI5H2WTB8mzvocOHWp1XKVSYfbs2VddEHEsey6VSQghRD5sbtSjRo3Cl19+KX6uu3DhQjz66KPw9/cHAJw7dw5DhgzB4cOHnVIocb7q6upmz8+uhM+wCSGERzYf+v7ll18sDo2+9tprKC8vF3+vr69Hfn6+Y6sjdlGr1ZKWt+VzbLl8hi01m5JQNuXiOR9lcz2b96gbTw5X+inClbKBpFKr1ZIn9Q0fPhzbt29v9jPq6upqMMZc/hm2PdmUgrIpF8/5KJs82HWZSx4o/Y1Gc8x7xQ0niV3JlT7HNn+G3dKhccD5h8ftyaYUlE25eM5H2eTB5kPfgiA0CSP3cC1Rwkw/e5hMJhw7dsyh+eTyFS9nZJMLyqZcPOejbPIg6dD3hAkTxP9pX7p0CY8++ijatWsHQP5f7SH2u9KhceB/h8fPnTtHE9IIIcSBbG7UqampFr8/8MADTZYZP368XUUsX74cb7zxBvR6PXr16oVly5a1eCWur7/+GrNnz0ZhYSG6du2K119/HaNGjbLrscmV2fIVr+XLl+Ps2bPiXrc1BoMB27dvp0ZNCCES2Nyo16xZ45QC1q9fj7S0NKxcuRJJSUlYunQpUlJSkJ+fj6CgoCbL//nnnxg3bhwWLFiA//u//8MXX3yB0aNHY9++fejZs6dTalQaT0/PVn9MWyektbTHDVx5r9sV2VoLZVMunvNRNteTfK5vR0tKSsKAAQPw7rvvArj8uYFOp8P06dPx/PPPN1l+zJgxuHDhAn744Qdx7Nprr0Xv3r2xcuXKKz6elPOrEscx73HbytfX1+7HokPshBC5k9KLXDrru7a2Fnv37sWsWbPEMZVKheTkZGRmZlq9T2ZmJtLS0izGUlJS8N1330l6bCVMILCHyWTC+fPnERAQAJXKroujOYUtn3M3PGR+NWdKMxgM+Prrr6+q2TuClDcMct1ujsBzNoDvfJRNHlzaqM+ePQuj0Yjg4GCL8eDgYOTl5Vm9j16vt7q8Xq+3unxNTY1Fc6iqqgJw+QQtRqMRwOXZ6yqVCiaTyeJrW+Zx83JXGjdfhcXaOND0zUFz42q1WryyS+PxxjU2HjcajSgqKoJWq5VVpri4OHTv3r3FTLm5ucjIyGjxRPl1dXUW55lvzFHN3hGkvmG4UjYl4zkbwHc+ymY/Hx8fTJkypdn/79mK++9RL1iwAPPmzWsynpubK/4PNDAwEOHh4Th58qTF2dZCQkIQEhKCwsJCi//p63Q6tG/fHkeOHMGlS5fE8aioKGi1Whw+fNiiscXExMDDwwPZ2dkWNcTHx6O2ttbijG7mL+EbDAYcO3ZMHPf09ERsbCzOnz+P4uJicdzX1xfR0dEoLS2FXq8HYwzl5eU4ffo0IiIiFJfpuuuuEzPp9XqLN2ABAQHiO+Dz5883yVRQUID8/Hzk5uaivr4earUaKpUK9fX1Fm9W3NzcIAgC6urqLGpvbtzd3R2MMdTX119xXBAEuLm52f2GoeFzzxueswF856Ns9mvu/3sVFRU2r8Oln1HX1tbC29sb33zzDUaPHi2Op6amoqKiAps2bWpyn/DwcKSlpeHJJ58Ux+bOnYvvvvsOBw4caLK8tT1qnU6HsrIy8drZvO1R5+TkoGfPnnB3d+cik5nJZEJOTg569OhhcahKjpkOHTp0xaMDjdGei3LxnI+y2a+lPeqKigoEBATI/zNqDw8P9OvXD+np6WKjNplMSE9Px7Rp06zeZ+DAgUhPT7do1Fu3bsXAgQOtLq/RaMTvfjekVqubnEa0uc8pmjvdqDPHBUGwOt5cjQ3HzYe9W1peaZnMfH19oVKprK5HTpl69uwp6VsIRqMRhYWFiIyM5O70tjxnA/jOR9kcQ8r/96xx+azv9evXIzU1Fe+//z4SExOxdOlSfPXVV8jLy0NwcDDGjx+PTp06YcGCBQAufz1r6NChWLhwIW655RasW7cOr732ms1fz6JZ34QQQlxNSi9y+VS3MWPGYPHixZgzZw569+6NrKwsbN68WZwwVlRUhJKSEnH5QYMG4YsvvsAHH3yAXr164ZtvvsF3330n+TvUPM/61uv1XOajbMrEczaA73yUTR5kMZls2rRpzR7qzsjIaDJ2zz334J577rmqx+T5ohx6vR4dO3Z0dSkOR9mUiedsAN/5KJs8uHyPmhBCCCHNo0ZNCCGEyFibbdRKvkRnSwRBQGBgIJf5KJsy8ZwN4DsfZZMHl8/6bm0065sQQoirKWrWt6soYaafPUwmE4qKirjMR9mUiedsAN/5KJs8tNlGzeuBBPMpRHnMR9mUiedsAN/5KJs8tNlGTQghhCiBLL5H3ZrM756qqqq4OyUecPm0eNXV1Vzmo2zKxHM2gO98lM15zFdytGWPvs016nPnzgEAIiMjXVsIIYSQNs9gMMDPz6/FZdpcow4MDARw+dSkV3pylMh8dbDi4mLuZrVTNmXiORvAdz7K5jyMMRgMBoSFhV1x2TbXqM1XLPHz8+PuhdeQVqvlNh9lUyaeswF856NszmHrziJNJiOEEEJkjBo1IYQQImNtrlFrNBrMnTsXGo3G1aU4Bc/5KJsy8ZwN4DsfZZOHNncKUUIIIURJ2tweNSGEEKIk1KgJIYQQGaNGTQghhMgYF416+fLliIyMhKenJ5KSkrB79+4Wl//6668RGxsLT09PxMfH46effrK4nTGGOXPmIDQ0FF5eXkhOTsaRI0ecGaFZUrKtWrUKQ4YMQUBAAAICApCcnNxk+QkTJkAQBIufm266ydkxrJKSbe3atU3q9vT0tFhGTtsNkJZv2LBhTfIJgoBbbrlFXEYu2+63337DrbfeirCwMAiCgO++++6K98nIyEDfvn2h0WjQpUsXrF27tskyUv+OnUFqto0bN+LGG29Ex44dodVqMXDgQPzyyy8Wy7z00ktNtltsbKwTU1gnNVtGRobV16Rer7dYTg7bDZCez9rfkyAI6NGjh7iMXLad4hv1+vXrkZaWhrlz52Lfvn3o1asXUlJSUFpaanX5P//8E+PGjcOkSZOwf/9+jB49GqNHj8ahQ4fEZRYtWoR33nkHK1euxK5du9CuXTukpKTg0qVLrRULgPRsGRkZGDduHLZv347MzEzodDqMHDkSp06dsljupptuQklJifjz5ZdftkYcC1KzAZdPTNCw7hMnTljcLpftBkjPt3HjRotshw4dglqtxj333GOxnBy23YULF9CrVy8sX77cpuWPHz+OW265BcOHD0dWVhaefPJJTJ482aKh2fN6cAap2X777TfceOON+Omnn7B3714MHz4ct956K/bv32+xXI8ePSy22x9//OGM8lskNZtZfn6+Re1BQUHibXLZboD0fG+//bZFruLiYgQGBjb5m5PDtgNTuMTERPb444+LvxuNRhYWFsYWLFhgdfl7772X3XLLLRZjSUlJ7JFHHmGMMWYymVhISAh74403xNsrKiqYRqNhX375pRMSNE9qtsbq6+uZr68v+/jjj8Wx1NRUdvvttzu6VMmkZluzZg3z8/Nrdn1y2m6MXf22e+utt5ivry+rrq4Wx+Sy7RoCwL799tsWl3n22WdZjx49LMbGjBnDUlJSxN+v9vlyBluyWRMXF8fmzZsn/j537lzWq1cvxxXmALZk2759OwPAzp8/3+wyctxujNm37b799lsmCAIrLCwUx+Sy7RS9R11bW4u9e/ciOTlZHFOpVEhOTkZmZqbV+2RmZlosDwApKSni8sePH4der7dYxs/PD0lJSc2u0xnsydbYxYsXUVdXJ57f3CwjIwNBQUGIiYnBY489Jl6opLXYm626uhoRERHQ6XS4/fbbkZOTI94ml+0GOGbbffTRRxg7dizatWtnMe7qbWePK/3NOeL5kguTyQSDwdDkb+7IkSMICwtDVFQU7r//fhQVFbmoQul69+6N0NBQ3Hjjjdi5c6c4ztN2Ay7/zSUnJyMiIsJiXA7bTtGN+uzZszAajQgODrYYDw4ObvI5ipler29xefN/pazTGezJ1thzzz2HsLAwiz+km266CZ988gnS09Px+uuvY8eOHbj55pthNBodWn9L7MkWExOD1atXY9OmTfjss89gMpkwaNAgnDx5EoB8thtw9dtu9+7dOHToECZPnmwxLodtZ4/m/uaqqqrw77//OuS1LheLFy9GdXU17r33XnEsKSkJa9euxebNm7FixQocP34cQ4YMgcFgcGGlVxYaGoqVK1diw4YN2LBhA3Q6HYYNG4Z9+/YBcMz/o+Ti9OnT+Pnnn5v8zcll27W5i3K0FQsXLsS6deuQkZFhMelq7Nix4r/j4+ORkJCA6OhoZGRkYMSIEa4o1SYDBw7EwIEDxd8HDRqE7t274/3338crr7ziwsoc76OPPkJ8fDwSExMtxpW67dqKL774AvPmzcOmTZssPse9+eabxX8nJCQgKSkJERER+OqrrzBp0iRXlGqTmJgYxMTEiL8PGjQIBQUFeOutt/Dpp5+6sDLH+/jjj+Hv74/Ro0dbjMtl2yl6j7pDhw5Qq9U4c+aMxfiZM2cQEhJi9T4hISEtLm/+r5R1OoM92cwWL16MhQsXYsuWLUhISGhx2aioKHTo0AFHjx696pptdTXZzNzd3dGnTx+xbrlsN+Dq8l24cAHr1q2z6X8Crth29mjub06r1cLLy8shrwdXW7duHSZPnoyvvvqqyWH+xvz9/dGtWzfZbzdrEhMTxbp52G7A5W+LrF69Gg8++CA8PDxaXNZV207RjdrDwwP9+vVDenq6OGYymZCenm6x99XQwIEDLZYHgK1bt4rLd+7cGSEhIRbLVFVVYdeuXc2u0xnsyQZcnvn8yiuvYPPmzejfv/8VH+fkyZM4d+4cQkNDHVK3LezN1pDRaER2drZYt1y2G3B1+b7++mvU1NTggQceuOLjuGLb2eNKf3OOeD240pdffomJEyfiyy+/tPg6XXOqq6tRUFAg++1mTVZWlli30reb2Y4dO3D06FGb3hy7bNu5ejbb1Vq3bh3TaDRs7dq17PDhw+zhhx9m/v7+TK/XM8YYe/DBB9nzzz8vLr9z507m5ubGFi9ezHJzc9ncuXOZu7s7y87OFpdZuHAh8/f3Z5s2bWIHDx5kt99+O+vcuTP7999/ZZ1t4cKFzMPDg33zzTespKRE/DEYDIwxxgwGA5s5cybLzMxkx48fZ9u2bWN9+/ZlXbt2ZZcuXZJ1tnnz5rFffvmFFRQUsL1797KxY8cyT09PlpOTY5FfDtvNnnxm1113HRszZkyTcTltO4PBwPbv38/279/PALAlS5aw/fv3sxMnTjDGGHv++efZgw8+KC5/7Ngx5u3tzZ555hmWm5vLli9fztRqNdu8ebO4zJWeL7lm+/zzz5mbmxtbvny5xd9cRUWFuMzTTz/NMjIy2PHjx9nOnTtZcnIy69ChAystLZV1trfeeot999137MiRIyw7O5vNmDGDqVQqtm3bNnEZuWw3e/KZPfDAAywpKcnqOuWy7RTfqBljbNmyZSw8PJx5eHiwxMRE9tdff4m3DR06lKWmplos/9VXX7Fu3boxDw8P1qNHD/bjjz9a3G4ymdjs2bNZcHAw02g0bMSIESw/P781ojQhJVtERAQD0ORn7ty5jDHGLl68yEaOHMk6duzI3N3dWUREBJsyZYpL/qgYk5btySefFJcNDg5mo0aNYvv27bNYn5y2G2PSX5d5eXkMANuyZUuTdclp25m/ttP4x5wnNTWVDR06tMl9evfuzTw8PFhUVBRbs2ZNk/W29Hy1FqnZhg4d2uLyjF3+KlpoaCjz8PBgnTp1YmPGjGFHjx5t3WBMerbXX3+dRUdHM09PTxYYGMiGDRvGfv311ybrlcN2Y8y+12VFRQXz8vJiH3zwgdV1ymXb0dWzCCGEEBlT9GfUhBBCCO+oURNCCCEyRo2aEEIIkTFq1IQQQoiMUaMmhBBCZIwaNSGEECJj1KgJIYQQGaNGTQghhMgYNWqiCGvXroW/v7+ryxBFRkZi6dKlri6jWRMmTGhyJaC26qWXXkLv3r3tvj89l8TVqFETkSAILf689NJLDn/MjIwMCIKAiooKh6/bEeT2BqGxwsJCCIKArKwsV5dCCHESuh41EZWUlIj/Xr9+PebMmYP8/HxxzMfHR/w3YwxGoxFubvQSIqSx2traK14ykRBb0R41EYWEhIg/fn5+EARB/D0vLw++vr74+eef0a9fP2g0Gvzxxx8oKCjA7bffjuDgYPj4+GDAgAHYtm2bxXpramrw3HPPQafTQaPRoEuXLvjoo49QWFiI4cOHAwACAgIgCAImTJhgc72bNm1C37594enpiaioKMybNw/19fXi7YIg4MMPP8Qdd9wBb29vdO3aFd9//73FOr7//nt07doVnp6eGD58OD7++GNxDz8jIwMTJ05EZWWl1aMKFy9exEMPPQRfX1+Eh4fjgw8+aLHempoaPPHEEwgKCoKnpyeuu+467NmzR7zdfHQhPT0d/fv3h7e3NwYNGmTxZqmxzp07AwD69OkDQRAwbNgwi9sXL16M0NBQtG/fHo8//jjq6uos6pk5cyY6deqEdu3aISkpCRkZGc0+FmMML730EsLDw6HRaBAWFoYnnnhC0vp27tyJYcOGwdvbGwEBAUhJScH58+cd+vwsXLgQwcHB8PX1xaRJk3Dp0qVmM5nl5OTg//7v/6DVauHr64shQ4agoKDA5ucyMjISr7zyCsaPHw+tVouHH34YALBhwwb06NEDGo0GkZGRePPNNy3WGRkZiVdffRXjx4+Hj48PIiIi8P3336OsrAy33347fHx8kJCQgL///tviflda73vvvSe+roODg3H33XdbbCdbnudffvkFffr0gZeXF2644QaUlpbi559/Rvfu3aHVanHffffh4sWL4v1MJhMWLFiAzp07w8vLC7169cI333xzxeee2KDVLwNCFGHNmjXMz89P/N18ZZqEhAS2ZcsWdvToUXbu3DmWlZXFVq5cybKzs9k///zDXnzxRebp6SleWo4xxu69916m0+nYxo0bWUFBAdu2bRtbt24dq6+vZxs2bGAAWH5+fpPLA7ZUz2+//ca0Wi1bu3YtKygoYFu2bGGRkZHspZdeEpcBwK655hr2xRdfsCNHjrAnnniC+fj4sHPnzjHGLl9+0d3dnc2cOZPl5eWxL7/8knXq1IkBYOfPn2c1NTVs6dKlTKvVNrlkaEREBAsMDGTLly9nR44cYQsWLGAqlYrl5eU1+5w+8cQTLCwsjP30008sJyeHpaamsoCAALEe83OclJTEMjIyWE5ODhsyZAgbNGhQs+vcvXs3A8C2bdvGSkpKxHWlpqYyrVbLHn30UZabm8v++9//Mm9vb4urBE2ePJkNGjSI/fbbb+zo0aPsjTfeYBqNhv3zzz9WH+vrr79mWq2W/fTTT+zEiRNs165dkta3f/9+ptFo2GOPPcaysrLYoUOH2LJly1hZWZnDnp/169czjUbDPvzwQ5aXl8deeOEF5uvry3r16tXsc3jy5EkWGBjI7rzzTrZnzx6Wn5/PVq9eLW5LW57LiIgIptVq2eLFi9nRo0fZ0aNH2d9//81UKhV7+eWXWX5+PluzZg3z8vKyuHKY+XW0cuVK9s8//7DHHnuMabVadtNNN7GvvvqK5efns9GjR7Pu3bszk8nEGGNXXO+ePXuYWq1mX3zxBSssLGT79u1jb7/9tviYtj7P1157Lfvjjz/Yvn37WJcuXdjQoUPZyJEj2b59+9hvv/3G2rdvzxYuXCiu99VXX2WxsbFs8+bNrKCggK1Zs4ZpNBqWkZHR7HNPbEONmljVXKP+7rvvrnjfHj16sGXLljHGGMvPz2cA2NatW60ua17v+fPnJdUzYsQI9tprr1ks8+mnn7LQ0FDxdwDsxRdfFH+vrq5mANjPP//MGGPsueeeYz179rRYxwsvvGBRT+PHNYuIiGAPPPCA+LvJZGJBQUFsxYoVVuuvrq5m7u7u7PPPPxfHamtrWVhYGFu0aBFj7H/PRcPr/f74448MQLPX1D5+/DgDwPbv328xnpqayiIiIlh9fb04ds8994jXuj5x4gRTq9Xs1KlTFvcbMWIEmzVrltXHevPNN1m3bt1YbW1tk9tsWd+4cePY4MGDra7bUc/PwIED2dSpUy3WnZSU1GKjnjVrFuvcubPVXIxd+blk7PLrYfTo0Rb3u++++9iNN95oMfbMM8+wuLg4i/s1fB2VlJQwAGz27NniWGZmJgPASkpKbFrvhg0bmFarZVVVVU2y2Ps8L1iwgAFgBQUF4tgjjzzCUlJSGGOMXbp0iXl7e7M///zT4vEmTZrExo0b16QOIg0d+iaS9O/f3+L36upqzJw5E927d4e/vz98fHyQm5uLoqIiAEBWVhbUajWGDh3q0DoOHDiAl19+GT4+PuLPlClTUFJSYnE4LiEhQfx3u3btoNVqUVpaCgDIz8/HgAEDLNabmJhocw0N123+mMC87sYKCgpQV1eHwYMHi2Pu7u5ITExEbm5us+sNDQ0FgGbX25IePXpArVZbrMu8nuzsbBiNRnTr1s3iOdyxY0eTQ75m99xzD/79919ERUVhypQp+Pbbb8WPGmxZX1ZWFkaMGGF13Y56fnJzc5GUlGSx/MCBA1t8nrKysjBkyBC4u7s3u0xLz6VZ47+N3NxcizwAMHjwYBw5cgRGo9FqnuDgYABAfHx8k7GGGVta74033oiIiAhERUXhwQcfxOeffy7+Tdj7PAcHB8Pb2xtRUVEWY+aajh49iosXL+LGG2+02P6ffPJJs68nYjuaCUQkadeuncXvM2fOxNatW7F48WJ06dIFXl5euPvuu1FbWwsA8PLyckod1dXVmDdvHu68884mt3l6eor/bvw/X0EQYDKZHFKDs9bdcL2CIACAXettqb7q6mqo1Wrs3bvXogEBlpMGG9LpdMjPz8e2bduwdetWTJ06FW+88QZ27Nhh0/oc9Vpw1PNjZktdtmzrxn8btrKW52oy+vr6Yt++fcjIyMCWLVswZ84cvPTSSxafQ9tT15VeTwDw448/olOnThbLaTQaSY9LmqI9anJVdu7ciQkTJuCOO+5AfHw8QkJCUFhYKN4eHx8Pk8mEHTt2WL2/eWZswz0MW/Tt2xf5+fno0qVLkx+VyraXdUxMTJNJOo3/Z+bh4SG5Nmuio6Ph4eGBnTt3imN1dXXYs2cP4uLi7F6vvc9fnz59YDQaUVpa2uT5CwkJafZ+Xl5euPXWW/HOO+8gIyMDmZmZyM7Otml9CQkJSE9Pt7peRz0/3bt3x65duyzG/vrrrxbvk5CQgN9//91icpgjdO/e3SIPcPnvpVu3bk3ezDh6vW5ubkhOTsaiRYtw8OBBFBYW4tdff3Xa6zAuLg4ajQZFRUVNtr9Op7N7veQy2qMmV6Vr167YuHEjbr31VgiCgNmzZ1u884+MjERqaioeeughvPPOO+jVqxdOnDiB0tJS3HvvvYiIiIAgCPjhhx8watQoeHl5NbtH19CcOXPwf//3fwgPD8fdd98NlUqFAwcO4NChQ3j11Vdtqv2RRx7BkiVL8Nxzz2HSpEnIysrC2rVrAfxvLyYyMhLV1dVIT09Hr1694O3tDW9vb8nPU7t27fDYY4/hmWeeQWBgIMLDw7Fo0SJcvHgRkyZNkrw+s6CgIHh5eWHz5s245ppr4OnpCT8/vyver1u3brj//vsxfvx4vPnmm+jTpw/KysqQnp6OhIQE3HLLLU3us3btWhiNRiQlJcHb2xufffYZvLy8EBERgfbt219xfbNmzUJ8fDymTp2KRx99FB4eHti+fTvuuecedOjQwSHPz4wZMzBhwgT0798fgwcPxueff46cnByLQ7aNTZs2DcuWLcPYsWMxa9Ys+Pn54a+//kJiYiJiYmJsfuzGnn76aQwYMACvvPIKxowZg8zMTLz77rt477337F6nLev94YcfcOzYMVx//fUICAjATz/9BJPJhJiYGKe9Dn19fTFz5kw89dRTMJlMuO6661BZWYmdO3dCq9UiNTX1qjK3ea7+kJzIU3OTyRpP+jp+/DgbPnw48/LyYjqdjr377rts6NChbMaMGeIy//77L3vqqadYaGgo8/DwYF26dGGrV68Wb3/55ZdZSEgIEwSBpaam2lQPY4xt3ryZDRo0iHl5eTGtVssSExMtZuICYN9++63Fffz8/Cxm3W7atIl16dKFaTQaNmzYMLZixYomk7ceffRR1r59ewaAzZ07lzF2eRLQW2+9ZbHuXr16ibdb8++//7Lp06ezDh06MI1GwwYPHsx2794t3m7tOd6/fz8DwI4fP97seletWsV0Oh1TqVRs6NChjLHLE6Buv/12i+VmzJgh3s7Y5UlEc+bMYZGRkczd3Z2FhoayO+64gx08eNDq43z77bcsKSmJabVa1q5dO3bttddaTDiyZX0ZGRls0KBBTKPRMH9/f5aSkiLmddTzM3/+fNahQwfm4+PDUlNT2bPPPtviZDLGGDtw4AAbOXIk8/b2Zr6+vmzIkCHixClbnktrrwfGGPvmm29YXFwcc3d3Z+Hh4eyNN96wuN3a/Rq/bq1NGGxpvb///jsbOnQoCwgIYF5eXiwhIYGtX79evN2e59na39/cuXMtnleTycSWLl3KYmJimLu7O+vYsSNLSUlhO3bsaPK8EGkExhhz0XsEQmRn/vz5WLlyJYqLi11dCiGEAKBD36SNe++99zBgwAC0b98eO3fuxBtvvIFp06a5uixCCBFRoyZt2pEjR/Dqq6+ivLwc4eHhePrppzFr1ixXl0UIISI69E0IIYTIGH09ixBCCJExatSEEEKIjFGjJoQQQmSMGjUhhBAiY9SoCSGEEBmjRk0IIYTIGDVqQgghRMaoURNCCCEyRo2aEEIIkTFq1IQQQoiMUaMmhBBCZIwaNSGEECJj1KgJIYQQGaNGTQghhMgYNWpCCCFExqhRE0IIITJGjZoQQgiRMWrUhBBCiIxRoyaEEEJkjBo1IYQQImPUqAkhhBAZo0ZNCCGEyBg1akIIIUTGqFETQgghMkaNmhBCCJExatSEEEKIjFGjJoQQQmSMGjUhhBAiY9SoCSGEEBmjRk0IIYTIGDVqQgghRMaoURNCCCEyRo2aEEIIkTFq1IQQQoiMUaMmhBBCZIwaNSGEECJj1KgJIYQQGaNGTQghhMgYNWpCCCFExqhRE0IIITJGjZoQQgiRMWrUhBBCiIxRoyaEEEJkjBo1IYQQImPUqAkhhBAZo0ZNCCGEyBg1akIIIUTGqFETQgghMkaNmhBCCJExatSEEEKIjFGjJoQQQmSMGjUhhBAiY9SoCSGEEBmjRk0IIYTIGDVqQgghRMaoURNCCCEyRo2aEEIIkTFq1IQQQoiMUaMmhBBCZIwaNSGEECJj1KgJIYQQGXNzdQGEuJLRaERdXZ2ryyBthLu7O9RqtavLIApDjZq0SYwx6PV6VFRUuLoU0sb4+/sjJCQEgiC4uhSiENSoSZtkbtJBQUHw9vam/2kSp2OM4eLFiygtLQUAhIaGurgiohTUqEmbYzQaxSbdvn17V5dD2hAvLy8AQGlpKYKCgugwOLEJTSYjbY75M2lvb28XV0LaIvPrjuZGEFtRoyZtFh3uJq5ArzsiFTVqQgghRMaoURNCXC4yMhJLly51dRmYPXs2Hn74YbvvP3bsWLz55psOrIgQatSEKMqECRMgCAIeffTRJrc9/vjjEAQBEyZMaP3CrtKePXuuqkE6gl6vx9tvv40XXnhBHJP6fL/44ouYP38+KisrW6Nk0kZQoyZEYXQ6HdatW4d///1XHLt06RK++OILhIeHu7Ay+3Xs2NHlk/s+/PBDDBo0CBERERbjUp7vnj17Ijo6Gp999lmr1EzaBmrUhChM3759odPpsHHjRnFs48aNCA8PR58+fSyWrampwRNPPIGgoCB4enriuuuuw549e8TbMzIyIAgC0tPT0b9/f3h7e2PQoEHIz8+3WM+KFSsQHR0NDw8PxMTE4NNPP7W4vaKiApMnT0bHjh2h1Wpxww034MCBAxbL/Pe//8WAAQPg6emJDh064I477hBva3zou6ioCLfffjt8fHyg1Wpx77334syZM+LtEyZMwOjRoy3W/+STT2LYsGHi79988w3i4+Ph5eWF9u3bIzk5GRcuXGj2eV23bh1uvfXWJuNSnm8AuPXWW7Fu3bpmH4cQqahRE6JADz30ENasWSP+vnr1akycOLHJcs8++yw2bNiAjz/+GPv27UOXLl2QkpKC8vJyi+VeeOEFvPnmm/j777/h5uaGhx56SLzt22+/xYwZM/D000/j0KFDeOSRRzBx4kRs375dXOaee+5BaWkpfv75Z+zduxd9+/bFiBEjxMf58ccfcccdd2DUqFHYv38/0tPTkZiYaDWbyWTC7bffjvLycuzYsQNbt27FsWPHMGbMGJufn5KSEowbNw4PPfQQcnNzkZGRgTvvvBOMMavLl5eX4/Dhw+jfv7/V2219vgEgMTERu3fvRk1Njc31EtISOuEJIf/fBx98gOrq6lZ/XB8fH8mfzz7wwAOYNWsWTpw4AQDYuXMn1q1bh4yMDHGZCxcuYMWKFVi7di1uvvlmAMCqVauwdetWfPTRR3jmmWfEZefPn4+hQ4cCAJ5//nnccsstuHTpEjw9PbF48WJMmDABU6dOBQCkpaXhr7/+wuLFizF8+HD88ccf2L17N0pLS6HRaAAAixcvxnfffYdvvvkGDz/8MObPn4+xY8di3rx54mP26tXLarb09HRkZ2fj+PHj0Ol0AIBPPvkEPXr0wJ49ezBgwIArPj8lJSWor6/HnXfeKR7Kjo+Pb3b5oqIiMMYQFhZm9XZbnm+zsLAw1NbWQq/XNzmMTog9qFET8v9VV1fDYDC4ugybdOzYEbfccgvWrl0LxhhuueUWdOjQwWKZgoIC1NXVYfDgweKYu7s7EhMTkZuba7FsQkKC+G/zqS1LS0sRHh6O3NzcJm8kBg8ejLfffhsAcODAAVRXVzc5y9u///6LgoICAEBWVhamTJliU7bc3FzodDqxSQNAXFwc/P39kZuba1Oj7tWrF0aMGIH4+HikpKRg5MiRuPvuuxEQEGB1efPnz56enlZvt+X5NjOffezixYtXrJMQW1CjJuT/8/HxUdTjPvTQQ5g2bRoAYPny5VdVg7u7u/hv8wk5TCaTTfetrq5GaGio1b1Lf39/AP9rXo6iUqmaHMZueKYvtVqNrVu34s8//8SWLVuwbNkyvPDCC9i1axc6d+7cZH3mpnv+/Hl07NjR6mPa+nybD/c3tx5CpKJGTcj/5+qvB0l10003oba2FoIgICUlpcnt5slfO3fuFA/B1tXVYc+ePXjyySdtfpzu3btj586dSE1NFcd27tyJuLg4AJcnW+n1eri5uSEyMtLqOhISEpCent7s57qNH6+4uBjFxcXiXvXhw4dRUVEhPmbHjh1x6NAhi/tlZWU1ecMxePBgDB48GHPmzEFERAS+/fZbpKWlNXnM6OhoaLVaHD58GN26dbNa15Web7NDhw7hmmuuaXaPmxCpqFETolBqtVo8hG3t4g7t2rXDY489hmeeeQaBgYEIDw/HokWLcPHiRUyaNMnmx3nmmWdw7733ok+fPkhOTsZ///tfbNy4Edu2bQMAJCcnY+DAgRg9ejQWLVqEbt264fTp0+IEsv79+2Pu3LkYMWIEoqOjMXbsWNTX1+Onn37Cc8891+TxkpOTER8fj/vvvx9Lly5FfX09pk6diqFDh4qTvW644Qa88cYb+OSTTzBw4EB89tlnOHTokDgLe9euXUhPT8fIkSMRFBSEXbt2oaysDN27d7eaUaVSITk5GX/88UeT2eS2Pt9mv//+O0aOHGnz80vIldCsb0IUTKvVQqvVNnv7woULcdddd+HBBx9E3759cfToUfzyyy/NflZrzejRo/H2229j8eLF6NGjB95//32sWbNG/CqUIAj46aefcP3112PixIno1q0bxo4dixMnTiA4OBgAMGzYMHz99df4/vvv0bt3b9xwww3YvXu31ccTBAGbNm1CQEAArr/+eiQnJyMqKgrr168Xl0lJScHs2bPx7LPPYsCAATAYDBg/frzF8/Lbb79h1KhR6NatG1588UW8+eab4qQ6ayZPnox169a1eMj/Ss/3pUuX8N1339n8eTwhthBYc99XIIRTly5dwvHjx9G5c+dmJw+RtocxhqSkJDz11FMYN26cXetYsWIFvv32W2zZsqXZZej1R6SiPWpCCMHlPfkPPvgA9fX1dq/D3d0dy5Ytc2BVhNAeNWmDaI+GuBK9/ohUtEdNCCGEyBg1akIIIUTGqFGTNos+9SGuQK87IhU1atLmmE+KQad4JK5gft01PDkLIS2hE56QNketVsPf3x+lpaUAAG9vb/G0mYQ4C2MMFy9eRGlpKfz9/Vs8aQohDdGsb9ImMcag1+tRUVHh6lJIG+Pv74+QkBB6c0hsRo2atGlGo9HiYg6EOJO7uzvtSRPJqFETQgghMkaTyQghhBAZo0ZNCCGEyBg1akIIIUTGqFETQgghMkaNmhBCCJExatSEEEKIjFGjJoQQQmTs/wG2bb449+AjdwAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, ax = plt.subplots(figsize=(5,4)) \n",
"\n",
"# Plot lines with improved color and line style\n",
"line3, = ax.step(bins[:-1], hist_m, color=colors['M'], linestyle=line_styles['M'], linewidth = line_widths['M'], label='Monoecious (M)')\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the second chromosome', fontsize=10)\n",
"ax.set_ylabel('Expected number of tracts per interval', fontsize=10)\n",
" \n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([line3])\n",
"labels.extend([line3.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "132f93ec",
"metadata": {},
"source": [
"### 5.2 Pedigree-DC model for X chromosome admixture"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4deb033a",
"metadata": {},
"outputs": [],
"source": [
"# Uncomment the following lines to run the hybrid pedigree distribution for the DF and DC models. Note that these can take a while to run, especially for the DC model, depending on the number of cores used and the size of the grid.\n",
"\n",
"# Phase-Type density for the Pedigree-DC model (set freq = True for frequency scale)\n",
"#newbins, density_hp_dc = HP.hybrid_pedigree_distribution(mig_matrix_f = mig_f, mig_matrix_m = mig_m, TP = 2, Dioecious_model = 'DC', L = which_L, bingrid = bins, whichpop = whichpop, rr_f = rec_f, rr_m = rec_m, X_chr = True, X_chr_male = False, N_cores = 5, density = True, freq = True)\n",
"# Phase-Type histogram for the Pedigree-DC model\n",
"#bins, hist_hp_dc = HP.hybrid_pedigree_distribution(mig_matrix_f = mig_f, mig_matrix_m = mig_m, TP = 2, Dioecious_model = 'DC', L = which_L, bingrid = bins, whichpop = whichpop, rr_f = rec_f, rr_m = rec_m, X_chr = True, X_chr_male = False, N_cores = 5, density = False, freq = False)"
]
},
{
"cell_type": "markdown",
"id": "a2cc6c08",
"metadata": {},
"source": [
"#### 5.2.1 Plot density"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "32c72c1a",
"metadata": {},
"outputs": [],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, axes = plt.subplots(1, 1, figsize=(5,4)) # 3x3 grid of subplots\n",
"ax = axes \n",
"# Plot lines with improved color and line style\n",
"line6, = ax.plot(np.delete(newbins, whichbin), density_hp_dc[~(np.asarray(newbins) == outbin)], color=colors['HP_DC'], linestyle=line_styles['HP_DC'], linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)', zorder = 1)\n",
"line7, = ax.plot(np.delete(newbins, whichbin), density_hp_dc[~(np.asarray(newbins) == outbin)], color=colors['DC'], linestyle=(2, (2, 2)), linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)', zorder = 1)\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the X chromosome', fontsize=10)\n",
"ax.set_ylabel('Density', fontsize=10)\n",
" \n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, (density_hp_dc[np.where(newbins == outbin)[0] - 1]), edgecolor=colors['HP_DC'], s=30, label='Outlier', marker='o', facecolor='white', alpha = 1, zorder = 3)\n",
"\n",
"# Add outlier point to the plot\n",
"ax.scatter(outbin, density_hp_dc[np.where(newbins == outbin)], edgecolor=colors['HP_DC'], s=30, label='Outlier', marker='o', facecolor=colors['HP_DC'], zorder = 4)\n",
"ax.scatter(outbin, density_hp_dc[np.where(newbins == outbin)], edgecolor=colors['HP_DC'], s=15, label='Outlier', marker='o', facecolor=colors['DC'], zorder = 4)\n",
"\n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"ax.yaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([(line6, line7)])\n",
"labels.extend([line6.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "d987b152",
"metadata": {},
"source": [
"#### 5.2.2 Plot histogram"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "594d3132",
"metadata": {},
"outputs": [],
"source": [
"outbin = np.max(np.asarray(newbins)[np.asarray(newbins) == which_L])\n",
"whichbin = int(np.where(np.asarray(newbins) == outbin)[0][0])\n",
"\n",
"fig, ax = plt.subplots(figsize=(5,4)) \n",
"\n",
"# Plot lines with improved color and line style\n",
"line6, = ax.step(bins[:-1], hist_hp_dc, color=colors['HP_DC'], linestyle=line_styles['HP_DC'], linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)')\n",
"line7, = ax.step(bins[:-1], hist_hp_dc, color=colors['DC'], linestyle=(2, (2, 2)), linewidth = line_widths['HP_DC'], label='Ped-DC (TP = 2)')\n",
" \n",
"# Customize x and y labels\n",
"ax.set_xlabel('Tract length on the X chromosome', fontsize=10)\n",
"ax.set_ylabel('Expected number of tracts per interval', fontsize=10)\n",
" \n",
"# Add gridlines\n",
"ax.grid(True, linestyle='--', alpha=0.6)\n",
"\n",
"# Set limits for x-axis and y-axis if necessary\n",
"ax.set_xlim(0, which_L+0.1)\n",
"\n",
"# Customize the ticks\n",
"ax.tick_params(axis='both', which='major', labelsize=10)\n",
"\n",
"handles = []\n",
"labels = []\n",
"handles.extend([(line6, line7)])\n",
"labels.extend([line6.get_label()])\n",
"\n",
"fig.legend(handles=handles, labels=labels, loc='lower center', bbox_to_anchor=(0.55, -0.2), ncol=2, fontsize=10)\n",
"\n",
"# Adjust spacing between subplots for better layout\n",
"plt.tight_layout(rect=[0, 0, 1, 0.95])\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "base",
"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": "3.10.14"
}
},
"nbformat": 4,
"nbformat_minor": 5
}