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@canyon289
Created July 28, 2023 11:52
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{
"cells": [
{
"cell_type": "markdown",
"id": "2692d84f-6092-470e-b9ae-1ca96fe3374a",
"metadata": {},
"source": [
"# Space Rockets"
]
},
{
"cell_type": "code",
"execution_count": 96,
"id": "c4057af4-1645-4ff7-8f79-4485837df883",
"metadata": {},
"outputs": [],
"source": [
"import arviz as az\n",
"import pymc as pm\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import preliz as pz\n",
"from scipy import stats"
]
},
{
"cell_type": "code",
"execution_count": 187,
"id": "061bf270-0261-4ce2-8d74-aebb6ac25322",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'3.11.1+1919.ge3961fc10'"
]
},
"execution_count": 187,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.__version__"
]
},
{
"cell_type": "code",
"execution_count": 188,
"id": "fe68f35f-3980-42d6-9f38-8c2648e2b1b1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'0.16.1'"
]
},
"execution_count": 188,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.__version__"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "32a268ed-d68c-41fa-a1f7-11b72eb40133",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Collecting git+git://github.com/arviz-devs/preliz.git@main\n",
" Cloning git://github.com/arviz-devs/preliz.git (to revision main) to /private/var/folders/nf/ch8x562s5q30j7qbf07161qr0000gp/T/pip-req-build-11e2hc2m\n",
" Running command git clone --filter=blob:none --quiet git://github.com/arviz-devs/preliz.git /private/var/folders/nf/ch8x562s5q30j7qbf07161qr0000gp/T/pip-req-build-11e2hc2m\n"
]
}
],
"source": [
"!pip install git+git://github.com/arviz-devs/preliz.git@main"
]
},
{
"cell_type": "markdown",
"id": "45118844-8ded-4d0b-acb3-c0fb15203a51",
"metadata": {},
"source": [
"## Figure out priors"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "06460a95-8841-4c11-8e50-a2b4985da06a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<Axes: >"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pz.Normal(mu=5, sigma=2).plot_pdf(pointinterval=True)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3b2bca70-7ade-492f-b8ac-eb8a3af19567",
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "Undefined distribution, you need to first define its parameters or use one of the fit methods",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[0;32mIn[10], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mpz\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mTruncatedNormal\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmu\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msigma\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlower\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot_pdf\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpointinterval\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n",
"File \u001b[0;32m~/miniconda3/envs/pymc/lib/python3.10/site-packages/preliz/distributions/distributions.py:269\u001b[0m, in \u001b[0;36mDistribution.plot_pdf\u001b[0;34m(self, moments, pointinterval, interval, levels, support, legend, color, alpha, figsize, ax)\u001b[0m\n\u001b[1;32m 221\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mplot_pdf\u001b[39m(\n\u001b[1;32m 222\u001b[0m \u001b[38;5;28mself\u001b[39m,\n\u001b[1;32m 223\u001b[0m moments\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 232\u001b[0m ax\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[1;32m 233\u001b[0m ):\n\u001b[1;32m 234\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 235\u001b[0m \u001b[38;5;124;03m Plot the pdf (continuous) or pmf (discrete).\u001b[39;00m\n\u001b[1;32m 236\u001b[0m \n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 266\u001b[0m \u001b[38;5;124;03m ax : matplotlib axes\u001b[39;00m\n\u001b[1;32m 267\u001b[0m \u001b[38;5;124;03m \"\"\"\u001b[39;00m\n\u001b[0;32m--> 269\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[43mvalid_scalar_params\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m)\u001b[49m:\n\u001b[1;32m 270\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m plot_pdfpmf(\n\u001b[1;32m 271\u001b[0m \u001b[38;5;28mself\u001b[39m,\n\u001b[1;32m 272\u001b[0m moments,\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 281\u001b[0m ax,\n\u001b[1;32m 282\u001b[0m )\n\u001b[1;32m 283\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
"File \u001b[0;32m~/miniconda3/envs/pymc/lib/python3.10/site-packages/preliz/internal/distribution_helper.py:70\u001b[0m, in \u001b[0;36mvalid_scalar_params\u001b[0;34m(self, check_frozen)\u001b[0m\n\u001b[1;32m 68\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mis_frozen:\n\u001b[1;32m 69\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m check_frozen:\n\u001b[0;32m---> 70\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[1;32m 71\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUndefined distribution, \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 72\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124myou need to first define its parameters or use one of the fit methods\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 73\u001b[0m )\n\u001b[1;32m 74\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[1;32m 76\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mkind \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;129;01min\u001b[39;00m [\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdiscrete\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mcontinuous\u001b[39m\u001b[38;5;124m\"\u001b[39m]:\n",
"\u001b[0;31mValueError\u001b[0m: Undefined distribution, you need to first define its parameters or use one of the fit methods"
]
}
],
"source": [
"pz.TruncatedNormal(mu=5, sigma=2, lower=0, upper=None).plot_pdf(pointinterval=True)"
]
},
{
"cell_type": "markdown",
"id": "371f57f2-2923-4a67-8657-233e664a2d2a",
"metadata": {},
"source": [
"## The data"
]
},
{
"cell_type": "code",
"execution_count": 177,
"id": "f7522ddb-0f53-439d-9e25-87f2ec97980f",
"metadata": {},
"outputs": [],
"source": [
"first_stage_lt = np.array([4,4, 3, 4, 3, 1])\n",
"x_label = \"First Stage Lead Time (Days)\""
]
},
{
"cell_type": "code",
"execution_count": 178,
"id": "520cfbd5-de5f-4b57-a65a-d7de45fc0d2e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x200 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize= (10, 2))\n",
"\n",
"from numpy.random import default_rng\n",
"rng = default_rng(1)\n",
"\n",
"y_loc = stats.norm(0, .2).rvs(len(first_stage_lt), random_state=rng)\n",
"ax.scatter(first_stage_lt, y_loc, alpha=.7, label=\"Observed\")\n",
"\n",
"# ax.scatter(first_stage_lt, np.zeros(len(first_stage_lt)) + np.norm)\n",
"ax.set_ylim(-1,1)\n",
"ax.set_yticks([])\n",
"ax.set_xlabel(x_label)\n",
"ax.legend();"
]
},
{
"cell_type": "code",
"execution_count": 174,
"id": "d6802db9-300a-4f57-ac85-ccb3e8e3e79a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x200 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize= (10, 2))\n",
"\n",
"# ax.scatter(first_stage_lt, np.zeros(len(first_stage_lt)) + np.norm)\n",
"ax.scatter(first_stage_lt, y_loc, alpha=.7, label=\"Observed\")\n",
"\n",
"ax.scatter(np.array(first_stage_lt).mean(), 0, label=\"Mean\")\n",
"\n",
"\n",
"ax.set_ylim(-1,1)\n",
"ax.set_yticks([])\n",
"ax.set_xlabel(x_label)\n",
"ax.legend();"
]
},
{
"cell_type": "code",
"execution_count": 175,
"id": "4bd7bbb0-0e6c-45dc-9861-e34d43aa5e2a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pz.Normal(mu=first_stage_lt.mean(), sigma=first_stage_lt.std()).plot_pdf(pointinterval=True);"
]
},
{
"cell_type": "markdown",
"id": "49d410d7-6149-471c-96d5-aad6d8210697",
"metadata": {},
"source": [
"## Estimate Lead Time\n",
"Note: This code doesn't need to be repeated but I do so to make the slides better"
]
},
{
"cell_type": "code",
"execution_count": 183,
"id": "a6c7b6f8-c6fb-4478-a563-7644fddc6cf7",
"metadata": {},
"outputs": [],
"source": [
"with pm.Model() as first_stage:\n",
" # Prior\n",
" mu = pm.Normal(\"mu\", 5, 2)\n",
" sd = pm.HalfNormal(\"sd\", 1)\n",
"\n",
" # Likelihood\n",
" lead_time = pm.TruncatedNormal(\"first_stage_lt\",\n",
" mu=mu, sigma=sd, lower=0,\n",
" observed=first_stage_lt)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "188f0c4b-a5da-48d8-9b9d-7ad69b42c9a1",
"metadata": {},
"outputs": [],
"source": [
"with pm.Model() as first_stage:\n",
" # Prior\n",
" mu = pm.Normal(\"mu\", 5, 2)\n",
" sd = pm.HalfNormal(\"sd\", 1)\n",
"\n",
" # Likelihood\n",
" lead_time = pm.TruncatedNormal(\"first_stage_lt\",\n",
" mu=mu, sigma=sd, lower=0,\n",
" observed=first_stage_lt)\n",
"\n",
" # Prior predictive\n",
" fs_prior_c = pm.sample_prior_predictive(samples=5000)"
]
},
{
"cell_type": "code",
"execution_count": 184,
"id": "1c90e7b5-5399-4547-b4df-fab1ff43d098",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling: [first_stage_lt, mu, sd]\n",
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [mu, sd]\n"
]
},
{
"data": {
"text/html": [
"\n",
"<style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
" background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
"</style>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [8000/8000 00:02&lt;00:00 Sampling 4 chains, 1 divergences]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 26 seconds.\n",
"There were 1 divergences after tuning. Increase `target_accept` or reparameterize.\n"
]
}
],
"source": [
"with pm.Model() as first_stage:\n",
" # Prior\n",
" mu = pm.Normal(\"mu\", 5, 2)\n",
" sd = pm.HalfNormal(\"sd\", 1)\n",
"\n",
" # Likelihood\n",
" lead_time = pm.TruncatedNormal(\"first_stage_lt\",\n",
" mu=mu, sigma=sd, lower=0,\n",
" observed=first_stage_lt)\n",
"\n",
" # Prior predictive\n",
" fs_prior_c = pm.sample_prior_predictive(samples=5000)\n",
"\n",
" # MCMC Sampling for posterior estimation\n",
" fs_lt = pm.sample()"
]
},
{
"cell_type": "code",
"execution_count": 166,
"id": "0ebbcc1d-0249-4af2-85cb-63d5f22544e0",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling: [first_stage_lt, mu, sd]\n",
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [mu, sd]\n"
]
},
{
"data": {
"text/html": [
"\n",
"<style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
" background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
"</style>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [8000/8000 00:02&lt;00:00 Sampling 4 chains, 1 divergences]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 21 seconds.\n",
"There were 1 divergences after tuning. Increase `target_accept` or reparameterize.\n",
"Sampling: [first_stage_lt]\n"
]
},
{
"data": {
"text/html": [
"\n",
"<style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
" background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
"</style>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [4000/4000 00:01&lt;00:00]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with pm.Model() as first_stage:\n",
" # Prior\n",
" mu = pm.Normal(\"mu\", 5, 2)\n",
" sd = pm.HalfNormal(\"sd\", 1)\n",
"\n",
" # Likelihood\n",
" lead_time = pm.TruncatedNormal(\"first_stage_lt\",\n",
" mu=mu, sigma=sd, lower=0,\n",
" observed=first_stage_lt)\n",
"\n",
" # Prior predictive\n",
" fs_prior_c = pm.sample_prior_predictive(samples=5000)\n",
"\n",
" # MCMC Sampling for posterior estimation\n",
" fs_lt = pm.sample()\n",
" \n",
" fs_ppc = pm.sample_posterior_predictive(fs_lt)"
]
},
{
"cell_type": "code",
"execution_count": 167,
"id": "45d616d1-db32-492c-b240-f932c9ef68b3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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KXEJasI+2nAEABKml+OlQDib1iYXeYoe/Qoo+8cHo82AwGGN4+YcjKDfZ8PtLQyHhuRoL3CrThiaK/88uMSI+VF1jXIifAv+c1B1Tv0zHi98fQXJ0IILVcipwCSFNiM6aEHJz81AfQOt/q0dFLiEt1LlCPVYfzMHdvWOwbM9FTB3UFiO7RGLioj9wT59YvDCyI4DKGyksnNwDEp4D7+Y62+utP5aLmT8cxernUtEjNqjGmGFJ4YgNVuH3EwV4JDUBQzqGAwBMVgdU8hufq0kIIR5BZ00IaXq+etYUaJ1nqYlH8d5OgBDSMB9sPg2VTILsUhM0KhlevLUjZq06iivlJgzuGIa9F0rw3qZTYIwhMdwfCaF+tTdazZAO4QgPUOCF7w6jwuz67ndLH00BALzw3WEwxpB5RYshC7fjz/PFjZo+QgghhHhT5VlTe2Eh7Pn5Df8pKoJgpksDSPOiIpeQFigjR4tfM/Jxa+dI7L9YilfGdMJ3+y9j84kC/N/tyegTH4xtpwqx5UQhDFbXt553R6OW4T9TeiOnzIT/W5vp8vb8naMCcUePKJQbbZj/20m0C/PDwMQQxATRjSoIIYSQFq/qrGlDf+isKfECKnIJaYEWbjqFELUMhy+XoXObALQN9cN7m05hYq9oPJqaAACYM64z1swYBH8319/Wpm9CMF4Zk4R1R3Kx+mCOy7h/3dsTCimPL/64CLvAsOjBPuKZ4wY8pYwQQgghhJAGoyKXkBYm7XwJdp8txoxbO2LhPT3wxvgueGXVEbQP98fcCcl44bvDuFxqrHyoubzxl90/O7Q9BncIxTu/nMDl0pofzq6QSfDq2E5wCAwfbz0LAHAIDHN+OoYPN59pdA6EEEIIIYTUFRW5hLQgjDEs3HQK0RolHhoQj0EdwrDm8BWU6K348P5eyNdasPdCCbKKDR77mzzP4b3JPcFxwKxVRyEINZ+ZfXJIIqb0j8PyPy/iXKEeEp4DQHdaJoQQQgghzYuKXEJakC0nC3E4uxzJ0YGY/+tJ/JaRhzWHr+DFkR3RLUaD5OhA7Hp1BIYmhXv070YHqfD2hK7Yl1WKZX9edBn3yugkSHkO0789CMYY/nl3N8wc08mjuRBCCCGEEOIOFbmEtBAOgeH9TaeREKLC7rPF0Fsc+GbfJfSM1WBM10j8b+8lMMY8MkS5JpP6xGBs10isOZwDh4uzuWEBSsQEq3CmQI+fj+aKz8w9lF2G/6VdbJK8CCGEEEIIqY6KXEJaiJ+PXsHpggpEB6vBAMwck4QvH+uHzx5NwYp92fhoy1noTPYm+/scx2HhPT2x+tlBV4ci1+xf9/YEALy1NhNmW+WdnVcdyMHnu7PE14SQpvfJJ5+gR48eCAwMRGBgIFJTU/Hbb795Oy1CCCGkyVGRS0gLYLUL+GDzGXSM8Me+CyUY360N/OVSKKQSRAYq8fadXfHLC4OhUcuaNA+NWgalTAKd2YbNJwpqjOkVH4x+bYOhM9vx0ZbKm1DNGd8ZG18aAqVM0qT5EUKuiY2NxYIFC3Dw4EEcOHAAt956KyZOnIjjx497OzVCCCGkSVGRS0gL8MP+bFwuNUGjksFfIcWe8yWYvfoosooNKDVYwXEcojTN91zaj7eexfMrDqGoouaHu//9rm4AgM92ncflUiMClTKo5VI4BIbzRfpmy5OQm9mECRMwfvx4dOzYEUlJSfjHP/4Bf39/7N2719upEUIIIU2qaS7eI4R4jNFqx3+2ncPAxBD8+/5eOFuoR5i/AjKewysrj8BkE/DrX24Rr39tDi+M7IgJPaMRHqCo8fed2wTimaGJWP7nRfxjw0l8+khfAMBb6zLx+/F87Jw9An6NeH4vIaR+HA4HVq1aBYPBgNTU1BpjLBYLLJZrB650Op3nE+F5QBAa93lPtOPJtnytHV/Miaat+drxxZxo2lpmTp5up5nRXiYhPm75nxdRVGHBpw/3gUomxZCO1+6cvHByDxTrrc1a4AJAoFKGHrFBAICzBRXoGBlwQ8yc8V0QpJbj3Y2nsOtMEYYmheORgQkY2jEMajkNWyakOWRkZCA1NRVmsxn+/v5Ys2YNkpOTa4ydP38+3nnnnSbLhVepII2I8EBDHCAENr4dT7bla+14si1fa8eTbbXWdjzZlq+148m2fK0dT7blY+3wquYbbViFY4zVfJtUN3Q6HTQaDbRaLQIDPfSlEkJuoDXaMGThNiSE+oHngFKDFeN7RGHm6CQopN4vFNcduYKXfjiCb58agEHtw274fU6ZEeM/2o0gPzm2vDwMcildIUGaBm2Xama1WpGdnQ2tVovVq1dj6dKl2LlzZ42Fbk1ncuPi4mieEkII8Rl13d7THichPmzJrvPQme0o1luQU2bC5TIThnUMx5TP9uK9Tae8nR7GJLdBuzA/zF51DBVm2w2/dwgMeosd2SVGLNuTJb7/7b5L+MeGE82ZKiE3Jblcjg4dOqBv376YP38+evbsiY8++qjGWIVCId6JueqHEEIIaYmoyCXERxVWmLFsz0X0iNUgT2tGudGGB/rFIaVtCPq1C0GXKO/vgKrkEnxwXy/k68z42y83Fq0JoX64v18ceA7495YzyNeaAQCXS004U6CH3dHI61cIIfUiCILT2VpCCCGkNaJrcgnxUYu2nYPV7sClEgP8FVIoZTzmjOsCubTyX1/RKy4IM4a3x3+2ncPQpHBM6Bnt9Pvnb+2I1QdzYLEL+OevJ/GfKb0xa0wSpBI6xkZIU5ozZw7GjRuH+Ph4VFRUYMWKFdixYwc2bdrk7dQIIYSQJkV7mYT4oMulRnyXno1eccHQmuzQW+yYe0dXvLvpFI7llHs7vRu8MLIj+rcLwaurj+FknvMdWWOCVHiwfzwA4OejufjzXLFY4JboLbhcamz2fAm5GRQWFuLRRx9Fp06dMHLkSOzfvx+bNm3C6NGjvZ0aIYQQ0qSoyCXEB/17y1lIeA5v3d4ZShmPkZ0j0Cteg+2nCnGmwPeeMyuT8Fj8YB8EqWV4+n8HUG60Ov1+xogOeHBAPOJD1Pi/tZmw2B1wCAx3LtqDd2oY5kwIabwvvvgCFy9ehMViQWFhIbZs2UIFLiGEkJsCFbmE+JiLxQasPXIFDw9IwOd/XAQAvDOxK+JC/LBl5jDc0yfGuwm6EB6gwKcP90WBzoIXvjvsdL1tRKAS8+7qjn/e3R0Xig1YsvMCJDyHv03sijfGd/Zi1oQQQgghpLWhIpcQH7No+zlIeQ4rD17Ghow8/OXWjsjI0cIhMPgppM3+TNz66BkXhH/e3R1lRiv0FvsNv+d5oEtUABZtP4eLxQaM7BKJxHB/L2RKCCGEEEJaKypyCfEhl0oMWHP4CtpolBAEhrdu74Ku0YF47ttD+DUjz9vp1cnkvrH46bnBCFLL4RCcH8P9x9linMqrgJTn8Na6TDDGUKK3YNaqozh6udw7CRNCCCGEkFaFilxCfMh/t58HzwGXSoyYMaIjnhySiKFJ4fjqif64vXuUt9OrM7mUh8nqwGPL0p2ej/vM0PbQqGWI0iix+2wxfjmWB6VMgrTzJThTUOHFjAkhhBBCSGtBjxAixEdcLjVi9cHLCFLLUWa0Ijk6AFqjDRq1DMOSwr2dXr3JpTxC/OQIUsvE9zRqGV4ZnYS31h1HuzA//H39CQzvFI6ds4fTI4XITW3Hjh3YtWsX8vLyXD7HluM4fPHFF82cGSGEENLyUJFLiI/4745z4HgOJQYrOrcJQIHWgiErtuGHZ1LRJSrQ2+nVm4Tn8O/7e4nXEJcbrQhSyzGlfzy+2ZuNCrMNxRUWfPD7Gbx9Z1cAQG65CdFBKm+mTUiz0mq1mDhxInbv3g3GmNtYKnIJIYSQuqEilxAfkFNmxKoDOXh4YAIm941Fl6hA5JQZcVfvGHSMaLk3ZqoqcHecLsTzKw5j6dQUDEwMxTsTuyK7xIjMXC2+TruIe1NiceBiGf6x4SR2vToCbTRKL2dOSPN47bXXsGvXLnTo0AHPPvsskpKSEBAQ4O20CCGEkBaNilxCfMAnO84DjMFsc0CjkkHCc0gI9cPfJnbzdmoe0TM2CDFBKjz11QGsmDYAAxNDMTAxFLeZ22DDsTz839pM/Of+3rA5BAQoqVsiN49169YhMjISe/fuRUhIiLfTuemYbCaY7KZGt6OSqqCS0SiUloa+/5aJvjdSF7Q3SYiX5Zab8MP+bHAch+/3X0ZciBrni/R4586uCFDKam+gBQj2k+N/T/bH5E/T8OiX6Vj5TCqSIgPwW0YeIgMVOJxdjj8vFOOpIYneTpWQZqXVajF+/HifLnANBgMkEskN70skEiiVSqc4V3ieh0qlalCs0Wh0OZSb4zio1eoGxZpMJhQbilFkKoLAhBvi1X7XYs0mMwThxhgA4DkebcPaijvLZrMZDofD5fT5+flda7eWWLVaLY6IsVgssNtvfDRbQ2JVKhV4vvI+CFarFTabzSOxSqVSXFbqE2uz2WC1Wl3GKhQKSKXSesfa7XaX17gDgN6hR5m9DAITYLfbYbW4blcml0Emq9wmOxwOWMyV7fIcj3BVOEJU19ZhmUwGuVwuxprNZtftVosVBAEmk+virT6xUqkUCoUCAMAYg9Fo9Ehsfdb7puojyi3lqECFuN6ajCa3671Kfa3dqtiavrea+ghX6z3gvC7XJ5b6iMb1Ee6WDSesAbRaLQPAtFptQz5OCKnm7Z8zWdvX1rOE19azOz/ezb7ac4GN/XAnM1nt3k7N47JLDGzAP7awfvM2s0vFBrbqwGWW8Np6NnzhNtbrnU2sVG9hGzPz2NrDOd5OlbQwLXW71KNHD3bbbbd5O40aVc1TVz/jx493iler1S5jhw0b5hQbFhbmMjYlJcUpNiEhwWVscnKyU2xycrLL2ISEBKfYlJQUl7HBocEsszhT/EkZ5DpWpVaxEmOJ2O748ePdzrfqJk+e7DY2uyiblRhLWImxhD3w8ANuY09fOi3GPvH0E25js7KyxBxmzZrlNjYzM1OMnTt3rtvY9PR0MXbhwoVuY7dv3y7GLlq0yG3s+vXrxdhly5a5jV25cqUYu3LlSrexHy/5mB0vPs4yizPZ4hWL3ca++e6b4vLw5dov3cYuXLhQzCE9Pd1t7Ny5c8XYA4cPuI19/qXnxe/48MnDbmOffPpJMfb0pdNuYx94+AExNrso223s5MmTnZZhd7FN1Uf06tNL/N4yizNZdFy0y9j2ndo7rcvtO7V3GVufPiIsLMwpdtiwYS5j1Wq1U2xtfUTVd1FiLGF33n2n29j69BGFhYViDtOnT3cb2xL6iNq293QmlxAvKjda8d2+bPH1Pyd1R9doDaYMSICsFd5tOC5EjW+e6o/7luzFQ1/sxcqnUzGkYxgOXiqDxebAwk2ncaXcBLPNgYm9YrydLiFN7oUXXsALL7yAc+fOoUOHDt5Oh/iYAmMB1FzlmaXahmcWmgphN9rrFFsfZpsZpabSynZt7tvVmrVirNHm+mxgU9Jb9WIOeqvebaxdcH0myxssDtdnnQHAYDMg35gPACgyFbmNtQpWFJoKITBBnB+umOwmsV13Z3FJzUw2U63LUvXvwOZwffYSgPi9AYDZ4XoUAFC/PuJmw109ClMvOp0OGo0GWq0WgYEt766vhPiKRdvO4v3fzwAAUhNDMXNMEvq19d1hi56SeUWLKZ/tRaRGiQ/v64kHPtsLjVqG3HIzvnqiP27pEAYJz3k7TdKCtOTt0muvvYZvvvkG8+bNw+jRoxEbG+vtlABcm6e5ubk1zlNvDVeufj1eY4crm61mlFnLwHDjZ+o6XJkDh8TwRHHYY2OGIpaaSlFgLBDzUalV4vBCq8XqfnhhtVibxYZASSBkkpoveanP8EJexqPCUTk01Gq1wm5znYNCqXAailgVy3M8guRBTvk0Zriy3qiH1qatcZi5XCF3Gq7sagiyhJMgQBUAK2cFA2vwcGUOHCLVkR4ZrlxsKMbFkos1Lo9VsTJ5ZQ6CIMBsqrldHjwClAGwS+xgYGCMwWR0P7RZrqjMoXosBw4hihCn762hw5U5cNAbXB90qE8fYRNsMEvM4nxqyHDlmr63hg5XLjWVIrs0G3aHm6HC1foTi9lSYx8h4SRQSpRgCiZOm6vYKjX1ETV9b0DDhiurpCpImMSnhivrdDpER0fXur2nIpcQLzHbHBi8YCtKjTbwHIfUxBBcLDFi+6zhrfIs7vXSs0rx6Jf70DM2CPf0icHrP2UgWC1HdJAK62YMhsAYJDwndsiEuNNSt0tVG3DGWK3LOsdxbndKPM3T89RTN4ux2C0uC5z6qNqhNNgNLouKuuDAoY26jdPOckOVmkqRb8xvVD5AZZGjlqphcpgaNZ88NY88lU9T5OSJ7z9UEerygEJ9WOwWlwdd6sNT0+bp5ciXvn9fXm995XvjOR4RqgiPzCNPquu2iYYrE+IlPx26ghJD5RGsJ29pi5dHd8LlMuNNUeACQP92IVjySAoClVL0igtCn4QQnMzT4YXvDuPjbWex8kAO/jOlF/om+FbnSognxcXF3TQHckx2k9MwvIao2sEVmNDoHcrG7mxXZ3PYah0SWhcWu/vhqvXV2PnkyXlU1Z4vfW+ewIGD2VE5IsATy7Yv8tRy1Bq/f1/ma+t/c6MilxAvcAgMn+w4Bz+5BAqZBM+N6ACVXIKkyJvr+ZjDksLF/1eYbbijRxQ+3noWX6ddRK+4YEj5m6PgJzevixcvejuFZtUad7puhiKH1K41Ltutna8enPIlnppH3nhcExW5hHjB78fzcLnMBJ4DApRSzF51FEun9vN2Wl6zMTMPz35zCAsn98DZQj0YgC5RgegZF+Tt1AghpE6oyCGk5aCDU7Xz1DyqGvZMRS4hrRxjDO9tqrzZ1OvjOiM+xA/+ipt7VRzVJRILJnXHPX1icb5IjyU7L+DTnecxvnsblJtsGNQ+zNspEkIIIaSVoYNTtWup8+jm3rMmxAvSzpfgQrEBYf5yPDG4HaQ3yTW47kglPB7oHw8AeHhAAnacLsTpfD2e/OoA9BY79r85CkqZxMtZEtJ4u3btAgD0798fSqVSfF1XQ4cObYq0CCGEkFaFilxCmtlbazMBABabAxsy8uh5sNVoTTbctXgPhnQMw4UiA/K0Zvzrvp5U4JJWY/jw4eA4DidPnkRSUpL4uq7cPUqCEEIIIZWoyCWkGZ3O1+H81bO4iWH+CPdXeDsln6JRyTA5JRZLdl7A00MT8cP+y/hm7yVM6h1z09yBlrRujz76KDiOg0ajcXpNCCGEEM+hIpeQZvTZriyoZDx+em4w4kPVtX/gJjRzdBK2nSzEhmN5mD22E/5vbSYeXLoXTw9pjxGdI7ydHiGNsnz5crevCSGEENJ4dDEgIc3kUHYpfjyUA3+lFGoFDb91RSGV4L17eyJPa8KJXB2iNEqknS9FZm65t1MjhBBCCCEtABW5hDQDxhie/d8hAECp3oqLxQYvZ+TbesUFYdqQRKxIz8bYrpEAgN8yCsBY4x4iTwghhBBCWj8arkxIM1hz+AoKKyyQ8hx2zh6OmGAaqlybl0cnYfOJAmw7VYTEMD+cyNNh8fZzeP7Wjt5OjRCPMxqN2L59O86ePYuKiooaD+hwHIe33nrLC9kRQgghLQsVuYQ0MZPVgTfWZAAAnhvengrcOlLKJPjnpO544LO9eGRgPC4UG/D+72cwMDEUKW1DvJ0eIR6zfPlyvPzyy9DpdOJ7jDGnG1JVva5rkTt//nz89NNPOHXqFFQqFQYNGoR3330XnTp18nj+hBBCiK+h4cqENLEPNp+G2Vb5IOx7+tLjgupjYGIoJvWOwbojuRjTpfKmU3vOFXs5K0I8Z8uWLXjyySfBcRzeeOMNpKamAgCWLFmC2bNno0OHDmCM4fnnn8eXX35Z53Z37tyJGTNmYO/evdi8eTNsNhvGjBkDg4EulSCEENL60ZlcQprY7ycKAAD3pcSibai/l7Nped64vQteHp0EP4UUfy7chsxcXe0fIqSF+Ne//gWO47B9+3b07NkTjz/+ONLS0jBt2jQAwLx58/Dqq6/is88+w9NPP13ndjdu3Oj0evny5YiIiMDBgwcxdOhQj04DIYQQ4muoyCWkCZ0vrEB2qRGBSinevaeHt9NpkcKuPkuYMYapqQlYvOMCXvz+MGaOTkJCqJ+XsyOkcfbv34+BAweiZ8+eNf5eKpXi/fffx9q1azF37lz8+OOPDfo7Wq0WABAS4nqov8VigcViEV9XHz7tKTzHQ2BCoz7viXY82ZavteOLOdG0NV87vpgTTVvLzMnT7TQ3KnIJaSK7zxZh+jeHwBjw2rjOTtfXkfp755cT+C0zDxIOWHckF4U6C1ZMG0DzlbRoer0e8fHx4muFovKgTkVFBQICAgAAPM9jwIAB2Lp1a4P+hiAIeOmllzB48GB069bNZdz8+fPxzjvvNOhv1IVKqkKEqvHPuubAIQABHsjIc235WjuebMvX2vFkW621HU+25WvteLItX2vHk235WjsqqarRbdQXFbmENAGDxY5Zq45Cb7HDXyHBg/3ja/8Qceuu3jHoGOkPm0PA2z+fQNqFEqw6mIP7UuK8nRohDdamTRuUlpaKr6OiogAAZ86cQd++fcX3S0tLYTKZGvQ3ZsyYgczMTPzxxx9u4+bMmYOZM2eKr3U6HeLiPLd+qWQqqGTNv6NDCCHk5kM3niKkCXyw+QwKdRYwAP99qC+dbfSAXnFBeGhAAqamtkWvOA1kEg7zfz2JcqPV26kR0mCdO3fG2bNnxdeDBg0CYwwLFy4UHyP0559/Ytu2bQ26M/Lzzz+P9evXY/v27YiNjXUbq1AoEBgY6PRDCCGEtERU5BLiYQcvleKLP7LAc0D/diEY0jHM2ym1KqsP5sAuMNgcDOVGG/71+xlvp0RIg91+++3IyspCeno6AGDkyJHo0aMHVq9ejZiYGPTt2xcjRowQhxzXVdUdmdesWYNt27ahXbt2TTQFhBBCiO+h4cqEeJDNIeD1nzLAAXAwYPbYTnQW18MExpB5RYcApRRGqwO944O8nRIhDfboo48iKSkJkZGRACqvv92wYQOefPJJbNmyBfn5+dBoNHj11Vfx8MMP17ndGTNmYMWKFVi3bh0CAgKQn58PANBoNFCpaMgwIYSQ1o1jVeOh6kGn00Gj0UCr1dJwJkKqEQSGpX9k4b2NJzEwMQz/e2qAt1NqdQSB4Z5P/8SlEiMqTDZMTonF/El05+qbXWvcLhmNRmi1WkREREAikdTrs64Ori1btgyPPfZYndpojfOUEEJIy1bXbROdySXEQ7JLDPjb+hPwk0sBjsO8u13fxZQ0HM9z+PvEbrhz0R/o3CYA36Vfht3BcEvHMEzsFePt9AjxGLVaDbVa3aDPNuD4NSGEENJqUJFLiAcIAsOMFYdxOl8Hq4NhSv94eoZrE+oWo8HDAxPwv7RLAID1x/Kw62wRRidHQi2nbo0QQggh5GZGe4OEeMC3+y4h44oWPAfIJRzeGN/Z2ym1eq+M7oRfjubCTyFFTpkJJpsDn+68gJmjk7ydGiH1UlhYiP/+97/YtWsX8vLyYLFYaozjOA7nz59v5uwIIYSQloeKXEIaacW+bMzbcBJBKhnKTTbMHNMJAUqZt9Nq9TRqGd4Y3wWzVx9DclQAThfosWTneUzpH4coDd1Yh7QMJ0+exLBhw1BSUkJDjAkhhBAPoUcIEdIIgsCwcOMpWO0Cyk02tAlU4Jmhid5O66ZxT59Y9E0IxvkiA5jAYHMIeH/TaW+nRUidzZ49G8XFxZg0aRIOHDgAnU4HQRBc/hBCCCGkdlTkEtIIB7PLoDPboJJV3vn0s0dT6JFBzajqJlSRgQr0TgiGwID4kIbdqIcQb9i9ezc6deqElStXok+fPvD39/d2SoQQQkiLR0UuIQ0gCAyf7TqPLlGBGNetDYw2B+7oEYUesUHeTu2mkxwdiJ2zR2D1s6kY2TkCn+w8j3OFFTT0k7QIjDH06tWLDo4RQgghHkRFLiENcCi7DAt+O4Uvdl/Arxn58JNL8MF9Pb2d1k2L4zhkFRtgFxhkPIe7Fv+JtUeueDstQmqVkpKCS5cueTsNQgghpFWhG08R0gBp50sgMGDpH1lgAD64vxfkUom307qpnSvUY+eZIvSK1eBIjhZvrT2O27pGQSWn74X4rrfffhsjR47EL7/8ggkTJng7nZbBagCsRs+0JVcDcnrcGyEueWp98+S65os5EZ9DRS4h9ZCRo0XGlXJ8tPUs4oJVyCkz4d6UWIzt2sbbqd30xnRtgyWP9MXAdqF49cej2HS8AK/+eBQfT+nj7dQIEe3ateuG91588UVMmjQJDz74IEaPHo3Y2FjwfM0DrYYOHdrUKfo+qxGoyAPQ2Btx8UBAFO3kEuKOR9Y3D69rvpgT8TlU5BJSDws2nkJ6VgnUcgkul5kwe2wnzBjRwdtpkavGdm0Dh8AwuH0Y9l0owS9H8/BQ/2IMbB/m7dQIAQAMHz68xutvGWP43//+h2+++cbt5x0OR1Ol5pLBYIBEcuOICIlEAqVS6RTnCs/zUEkE8exLrbGqa48BMxqNztfY2y2A2QAwBo4D1NVjTSa4uhz/+liT2QiBNwBczTer8/O7tvNrMpnc3t26eqzZbHb7PdUnVq1Wi8uLxWKB3W73SKxKpRIPpFitVthsNo/EKpVKcVmpT6zNZoPVanUZq1AoIJVK6x1rt9tdPncaAORyOWQyWb1jHQ4HzGazy1iZTAa5XF7vWEEQYDKZPBIrlUqhUCgAVPYvRqPrM59uYw0GwFi5vgGAhOehVCqu/droOgcxlhOuNlX39d5trMkEFQQxp/qs92IsxwOsvHL6xFgOavW1/qDO671cDZODpz6iDrGe6CPcLRtOWANotVoGgGm12oZ8nJAWa9bKI6zta+tZ4uvrWb95m5nBbPN2SuQ6GzPzWMJr69mUz9JYwmvrWc+3NzE9fU+tXkvZLk2dOpU99thjDf5pTlXz1NXP+PHjneLVarXL2GHDhjFWUchY7lHGcg+zsJAgl7EpPZMZyz0s/iTERrmMTU5KZOzKIfEnOSnRZWxCbJRTbErPZJexYWFhTtM2bNgwl7FqtZoxi75y+ioK2fgxo9zOt6o4VlHIJt81wW2sXq8Xc5g6darb2MLCQjF2+vTpbmOzsrLE2FmzZrmNzczMFGPnzp3rNjY9PV2MXbhwodvY7du3i7GLFi1yG7t+/XoxdtmyZW5jV369VJy/K79e6jZ22eefiu2uX7/ebeyiRYvE2O3bt7uNXbhwoRibnp7uNnbu3LlibGZmptvYWbNmibFZWVluY6c/M02cD4UXTriNnfrg/WKsPt99u5NvH+W0HrmLHX/rLZVxuYcZqyisvY+oJiwszGVsSp9elW1ezcGjfUS1vsdtHxESdDXuKGMVhbX3EdWMHz/e7XyrbvLkyW5jb+Y+orbtPZ3JJaQWNoeAr9Mu4dHUBPRrF4ItJwtgdzB0ahNA13v6oBGdIhARqMCf50vwyMB4fLsvG6/9eAwfT+lNd7AlXrd8+XJvp+Bl186+uNXS7o5effikw/VZOwBARbWb4tldnwVrUoYSQH/1bFFt1zbaPHT9c3MxlV6bx6ZS97F212eEG8WiB/RFlf83lrmPtRquxXpyXgv2a8ukobb5YLw2z9ycmW04DnDUMq8dtmvzAXDfB7AmfGZ4ffoexgCOVU6bw/UZSQDO09ZUy11t9MVA1UltWy3fc1UfIW+5j2XkGKv/lkSn00Gj0UCr1SIwMLAp8iLEZ2w/VYjHl+/H8sf64afDV7AhIw/fPz0QKQnBVDT5KLPNgYmL9qDMaMWDA+Lw7y3n8MqYJLxwa0dvp0aaSEvaLm3btg05OTlISUlBcnKy29gTJ07gwIEDiIuLw4gRI5opw0pV8zQ3N7fGeVrv4coOfeWONGNuhzjyHAeV6lq7TkMROR6QqgG7J4YrWyEoQwCJrMb4eg1XVkgAUwnAGMxmCxzuYtXXcnCK5TjAPwrwDxd/36ihiOV5gD4flSc9nKmUimrDC22wuWyXhyokGrxMeTW2EUMROd6pOGnUcGVjBWAurbEgUchlzsOVrS7y5TjIQxIgC46+FtvQ4cr6Iqd5LZNKIZdXi7W4nrZrsTwEv0iYJK6flV2v4crmMiisxQBjlUOQTa4PvkglEigUle06xV63vgENHa7MAzI/GLTFqGl5BG5c7123y4OX+0EltaPRw5Wvm7Yb+giTGYKbMslPrRKnzaQrhcDcDEF2td5fN21QhcAvMKhabAOHK9stgLkM1ee3WqWsFmuF3U27lX2EFAiIglWu8anhyjqdDtHR0bVu76nIJaQWNoeASf/9E4nhflh3JBd3947Bh/f38nZapBYncrW4c9Ee9IkPwtGccljsDJ8+3Ae3dYvydmqkCbSU7dLly5eRlJSEuLg4HDx4EAEBAW7jKyoqkJKSgpycHJw9exbR0dHNlGkTzFN9kVjkNtjVHUrY9I0/2yu2ZUTjbmAjAWSqxufE8YA6DJDIG5FLNXazWHg3KiePzqPGtlO9rcbObw4IiHE6qNBgHlm2PZiPx3Ly0PrWJOutj+REfVLdePBO1nXdNtFwZUJc+GzXedzSIRzfpWcj44oWJ3K14Dmg1GAFY4zO4vo4uZSHQ2BIv1iGKI0SRRUWvPT9Eax+To1uMRpvp0duUkuXLoXVasXChQtrLXABICAgAO+99x7uuusufPHFF3jrrbeaIcubTR2HULvCeXDopM0EGEvgsULQYzw1jxrZjlNbjXV1CG31YaQNZa9liHqdeDAfwEM5Ee9obX2Sd+5kTUUuITXQmW346s9L2HWmGH+cK4ZGKYXB6oBGJcP79/akArcF6BARgNXPpeKH/Zex8kAOAEApk+DJr/bj5+dvQWSgspYWCPG8zZs3Izw8HHfddVedP3PnnXciMjISv/32GxW5NwVfKgRbOY/swHvwgILPHuQgNzcfKrrroeYH8RFykwtUyvD3u7piX1YJIgIU0JrtsAsM/7q3J8IDFLU3QHxC34QQ/G1iN3SNDoRMwsFktUNnsuHJr/bDYHF9bRshTeXUqVPo169fvT+XkpKC06dPN0FGhNzsru7AN/Sn0QWph/NpkpwIaXmoyCWkmo2Z+Xhv0ykwxlCstyJYLUdhReWNKP5yaweM6Bzh5QxJfVWY7bhSZkL7cH/4K6UY1y0KJ/Mq8PyKQ7A7aEeANC+DwQCNpv7D5TUaDfR6fRNkRAghhLQ+NFyZkGr2XyzF4ewyWOwCusdoUGqwgOOAYUnheGlUkrfTIw0QHqDA44Pb4bZubaBRyaBWSNArLgh//fk4/vrzcfzjrm40/Jw0m+DgYBQUFNT7cwUFBQgODm6CjAghhJDWh87kEoLKW+YDwOwxSfCTS/H78XxM+/oAHAIQH6LGR/f3Bs9TIdRSvTiqIzq1CUCYvxxTPtuLTScK8MTgtlixLxuf7rzg7fTITSQ5ORl79+51++iP6xmNRqSlpdX6uCFCCCGEVKIil9z0TudX4J5P/kR2qREzVx3FH+eL8XXaReSUmRCkluHbpwZAo675OYqk5XAIDO/8cgJRGiUOXSpFntaMu3vH4N2Np7DuyBVvp0duEnfccQcMBgPmzZtX58/MmzcPJpMJEyZMaMLMCCGEkNaDilxy0zNY7TBY7Jj/60n8mpGPCT2icOBSeeWZvmkDERus9naKxAMkPAeD1Y5ObQLw4qgk/JaZjzaBCgxsF4LZq45h74USb6dIbgLPPvssIiMjsWDBAsybNw+C4Pq6cEEQ8Pe//x0LFixAZGQknnnmmWbMlBBCCGm56JpcctOy2gXIpTx6xwWhZ1wQVh7IwaTeMfj5aC5u6RCK/7s9mYYotzL/uvr4J4fA8PORK/hk5wVM7BWN+BAVnv76AH6aPggdImp/dikhDaVWq/Hjjz9i1KhRmDt3Lj7//HPce++96NOnD8LDwwEARUVFOHToEFatWoWcnBwolUr8+OOPUKvpgBshhBBSF1TkkpuS1mjD/Z+l4bFBbXF/vzi00ajw/Ij2WJF+GQ7GqMBtpapuMHU6vwJdozU4V6jHuiO5mNQnBrvPFGHql/uxZsYgRATQM3RJ0xk0aBD+/PNPPPLIIzh+/Dg+/PDDG2Kq7hPQtWtXfPPNN+jZs2dzp0kIIYS0WFTkkpuSQsajXbif+PrhAfF4d+NplBmsWPxQH3SOCvRidqSp7csqwZ5zxZg7IRnrjuThp0NXMKJTOPZeKMGTyw/gh2cGQi2n7pE0nV69eiEjIwMbN27Ehg0bcOTIEZSUVA6ZDw0NRa9evXD77bfjtttu83KmhBBCSMtDe3HkpmKxO+AQGKx2AYU6CxZsPIXtp4uw+2wRjFYHZo5OwvjuUd5OkzSxxwa1xaQ+sdCoZHhwQAI+3XkB7248he4xGhzP1eKFFYex5JG+kErotgWkad12221NVsju2rUL7733Hg4ePIi8vDysWbMGd911V5P8LUIIIcSX0B4cuanMXHkUD3y2F5M/+RNHLpcDALaeLIDVLmBQ+xDMGNHBuwmSZsFxHDQqGRhjWLTtHCIDFfCTS3AiV4dQPwW2nirE278cF4eMEtISGQwG9OzZE4sXL/Z2KoQQQkizojO55KaSHBWIrScLYHMwOASGKI0SpVIrAODfD/SGhK7DvaloTTZ8v/8yxnVrg+ggFfK0JtgFATIJh2/2ZiM2WI1nh7X3dpqENMi4ceMwbty4OsdbLBZYLBbxtU6na4KseIBzfUfpOn3eI+14si1fa8cXc6Jpa752fDEnmraWmZOn22leVOSSVk8QGE4XVKBAZ8ZXf16E2SZAo5LhlTFJ2HAsFxeKDFj5TCrdbOgmFKSW4+fnByPET46pg9rigc/2wmCxo098MILUMiz47RSiNEpM7BXj7VQJaXLz58/HO++803R/QK4GAjxwOQjHA0pN49vxZFu+1o4n2/K1djzZVmttx5Nt+Vo7nmzL19rxZFu+1o68+Z8OQEUuabUYY2AMWLz9HD7ccgYCA6I0Srw+rjMeHZiAv284gX1ZZfjogV7oGRfk7XSJl4T6KwAAMgmP2GAVsooNOFeox5rpg1ButOKl748g84oOb97excuZEtK05syZg5kzZ4qvdTod4uLiPPcH5H6VP4QQQkgToyKXtErnCvV4eOk+zBzTERsy8uCnkOJvd3bF7T2iIZfyeG/TKXyXfhl/GdmRztIRAECBzoycMhPm3dUNB7PLEBeixof39cbof+/EN3sv4f5+cYgIVMBiExAeoPB2uoR4nEKhgEJByzYhhJCWj4pc0qIxxnC+yIAdpwux/XQhesUFYfbYzogOUkIp4zF33QkoZTz+80BvjOgcAQD4fNcFLN5+Ho8MTMDLozp6eQqIr+gZF4Tts4ZDLuUxpmsb5GvNMNrseKBfHNYevoLHlqVjct9YLNp2DgMSQzC4Qxj6xAejfbg/wvzl4jN4CSGEEEKId1GRS1och8BwKLsMmzLz8fuJAmSXGgEAndsEINxfAbPNgceW7cfFEiMSw/zwzVMDEB2kAmMMi7efw/u/n8GEntF4586uVJgQJ3Jp5c0RfsvIw4s/HMHkvrFYsS8bXaMDcb5Ij98y8/D44LbYc64ECzeeFj+nkPLQqGTQqGQID1BgxbSBAIC1h6/ALjBM7hvrlekhhBBCCLkZUZFLWozcchN+2H8ZKw9cRp7WDLmUx9COYXh2WHuM6ByOKI0KQOXZ3TB/OR4eEI+37+wKqYSHIDD8bf0JLP/zIu7pE4sF93QHT3dSJi6ktg/F44PbYvaYThjQLgRvrsmEhONwpkCPGI0KPz8/GFqTDafyK3C+SI/ccjN0Zht0JpvTgZP1x/KgNVnFIvflH44gIVSNe1PiEBOk8tbkkZuEXq/HuXPnxNdZWVk4cuQIQkJCEB8f78XMCCGEkKbFsQY8CFKn00Gj0UCr1SIwMLAp8iLkBh/8fhqLtp/D8E4RuKdPLIZ3CoefovI4TbHegjfXZKBAa8H79/VA+3B/sdgoNVgxc+UR7DhdhGeGJeL12zrTGVxSZ0arHZP+uwcOAThbqAcAPDIwAX+bWPtIAMYYTDYH1HIp7A4Bj36ZjrQLJQCAkZ0jMXN0EpKjqQ/1BNou3WjHjh0YMWLEDe9PnToVy5cvr/XzNE8JIYT4mrpum+hMLvFZxXoL/m9NJu7uE4OxXdtg6qC2uL9/vNMZMEFgWHvkCuZtOAm92Y4gtQyFOgs6RAQAALadKsAbP2Wi1GjF/EndMaU/nb0g9VNutMFfIcNr4zrjcqkRp/J0+Gx3FtRyCV4f5/6ACcdxUMsru1mphMeKaQNxpdyElfsv46u0ixj/n924s2c0/u/2LogIpEdYEc8aPnw4GnAcmxBCCGnxqMglPocxBo7joFHJUGq0QmuyAbj2qJcqmVe0eGtdJg5nl6NvQjDevac72oX5Q8JzOF+kx3sbT2Pj8Xx0igzAl4/1ozNmRGS327Fq1SoAwL333gup1HVXGB2kwqpnU8FxHPq1DcH8X08ixE+GJbsuYPOJAnz1RH/EhdT9+W8xQSq8PDoJTw5ph6W7LmDJrgvYfroQr4/rjCn94mkYPSGEEEJII/HeToCQKowx/H48H3cu2oMygxUyCY8fnh6I+1Jqfk7j1pOFOH91+Oj0Ee2RGOaPtPMl+Mt3hzHmw13YfbYIr97WCev/cgsVuKRRqp+tbR/hj0m9Y9A9RoMLxQYMf38HFvx2EoJQvzNmgUoZZo7phN9fHopecUF4c00mpn97yNOpE0IIIYTcdOhMLvEJl0uNePvn49h6qhBdogJRarQi2M/5sSx2h4AV6dnQqGRoH+6PZ4Yl4vHBCfj9eAEOXyrDW2sykas1I0gtw1O3tMPTQxNvOPtLSGNVHXSxOQQ8viwdf5wrwac7L+DAxTIsf7wftp8uwpCOYQhSy+vUXkKoH75+oj/WHrkCf4UMQOUdxDmAzuoSQgghhDQAFbnEqyx2Bz7beQGLtp+DTMLjr3ck49HUBEglzoMM9l4owds/H8ep/ArEBqtgtDrw8qiO+PloLvZfLIOE5zA8KRxv3ZGMW7tEQCGVeGmKyM1CJuGx7PH+ePn7w1ifkQ+TzYETeTq88N1hLHm4D8Z2i0KBzowTuTqktg+FUuZ6meQ4Dnf3vvaYoU92nEPahRJ8MbWf288RQgghhJAbUZFLvGbnmSK88/NxXCg2YMLVm+9EXnfznTytCW/8lIHtp4sQpVHilTFJOHypDHvOl+CtdcfRMcIfb4zvjLt6xdCNe0izk0l4/GdKH8QEn8KSXRfw1Z8XsWBSd/x3x3kkhPkhPasUf113HLtfHYG4EDVO5eugNdqQ0jYEEjdnadtoVGgb6kcFLiGEEEJIA1CRS5pdTlnl0OQtJwuRGOaHb54cgFs6hom/N1rtWLo7C4M7hEFntmHPuRLIJBzAGP71+xkEKqW4LyUOk/vGokeshh4HRLyK5znMGd8F4QEK/OPXk8i4ooPeYseEj//As8Pa47tpA8QbU3315yX8mpGHQ2+NBgDsv1gKP7n0hmvGJ/eNFZ+tezxXi4+2nMW8u7rRgRxCCCGEkDqgIpc0m6q7JtscDIeyyzF7TCdMG5oIuZTHnJ+OISkyAA8PTMCqAzlYtO0cyo1WmG0OAAw2B0NsiBqvjuuMcd2i6AwX8TlPDUlEhwh/vPj9EQiMoU98MD7edg6bTxTgvck90T1WgzfGd8aU/nHiWdx5G05CIeWx8plUAMC5wgrxDuFVsooN2H22GKM/3IW/TeyKO3tG04EdQgghhBA3qMglzWLehhM4kl2O1c8NQrswP3QI98P+S6WYIe0AACiqsKDcaMPXaZeQVWxAmL8cX+65CLmUx+SUODw2qC2SIgO8PBWEuDe8UwTWv3ALnl9xCPuyStE3IRiXS404cKkU3WM1CFDK0CM2SIz//NG+KDNUPiLLZHXgzkV78NCAeLx5ezKAygNDd/SIRtdoDWatOooXvz+CVQdyMGtsJ/SKC6ohA0IIIYQQQkUu8RiHwMQzUL9l5GL1wRx8/GAfqOVSpGeV4mxBBax2AXIpjwf6x4uxRy6X41KJEWcL9VBdPUNrtQv4y60d8OigtgijOySTFiQuRI0fnxuEL/7Iwgebz0Ah5eEQGMw2B9Yfy4PWZMNDA+KhlEkQEaBEREDlEGQJz+GD+3qibZgfgMqzuk9/fRAf3N8LveKCsPKZVHyz9xI+3nYWdy3egyEdw/Boalvc2jnC7fW9hDSWwWCARHLj6BmJRAKlUukU5wrP81CpVA2KNRqNYKzmR3RxHAe1Wt2gWJPJBEEQXObh5+fXoFiz2QyHw+GRWLVaLY7csFgssNvtHolVqVTg+cobPFqtVthsNo/EKpVKcVm5PtZotcNkddQYa7PZYLVaXbarUCjE55nbbDZI4IBaXvMubPVYu90Oi8Xisl25XA6ZTFbvWIfDAbPZ7HLaZDIZ5HJ5jbHXqx4LJsBgNNUpVhAEmEyuYwPUCgQHVC5rjDEYjUaXsVKpFAqFosbY66etPut99ViVXAJmcz1/qY9oWGxr6iPcxVbvI9wtG05YA2i1WgaAabXahnyctAK55Ub2ffolVmG2McYY+yE9m3V4YwPbc66ILdx4kvX9+2aW8Np69k3aRcYYY9klBpZTZhQ/X1RhZmcLKpjN7mBf7r7AOr35K0t4bT1L/ecW9sXuC0x/tV1CmoLNZmMrVqxgK1asYDZb0y1r5wsr2MNL97KE19azfvM2szs/3s0SXlvPUuZtZou3n2Vak9XlZzNyytnDS/eyogozY4yxtPPF7H9pF1mZwcI+2XGOpf5zi9jWqTwdY4wxh0Nokumw2R2s3GBll0sN7FSejh24WMp2ni5k+7NKmuTvNQRtlzyvap66+hk/frxTvFqtdhk7bNgwp9iwsDCXsSkpKU6xCQkJLmM7de7CiivM4k+nzl1cxsbFxzvF9urT12VsWFiYUw7Dhg1zGatWq5nBYhPbHTXmNrfzrXoOd941yW3spfwSMfaBBx92G3vqwmUx9olpz7iNPZR5Soyd8ZeX3cbuST8kxs6e86bb2N93/CHGzv37P93GfrnyF5aRU84ycsrZG/Pecxu7+KsfxNh5H/zXbewXX38r5vDF19+6jf3086Xid7x+/Xq3sYsWLRJjt2/f7jZ25pt/E/P9bv02t7HPvfway8gpZyeuaNnGXeluYx975gWx3Y1pR93GPjHtGTHfwsJCt7FTp04VY/V6vdvY0bdPFHPIyCl3Gzvk1jEsI6ecHc/Rstwyo9s+YtAtQ5zWjdBQ131En75969xHJCcnO8UmJye7jE1ISHCKTUlJcRlbvY8wWGxs0C1DXMaq1Wqnaautj6hu8uTJbmP1er0YO3XqVLexDekjDBYbmzVrltvYzMxMMYe5c+e6jU1PTxdjFy5c6DZ2+/btYuyiRYtu+H1t23s6k+sDGGM4X2SASi6BWiZBgFJ6wyN0mpvVLuBUvg5RGhXCAxQ4la/D7FXH8LeJXdE7Phgnc3V47ccM6C12WO0M208VgOc4PPj5Pkh5DgMTQ3FHjyRM6BkNoPLsltnmwIZjefj56BVsO1WIKI0KDoHhSrkJnSID8OzwRNzRIxoyL087IZ6SGO6P/z05AOlZpfhw8xmkXSiBSiaBTMJh4cbTWLztHN66IxkP9I+/4bPdYjT435MDxNcbM/OxMTMfU/rH49lh7TGwXSguFOux+2wxEkIrjzzP/+0k9mWV4ufnbwEA/JaRh8IKC9RyCeRSHla7AKtDqPzXLsBgdaBNoBIPDqj8+y//cATJUYGYNjQRNoeAgf/cCr3FDou95qPT/doGY9Wzgzw92wipM7vAkKc1O712xXFdrM3h+qxLfZmsDhRoLRDAXK4vVarnYLK5PkMDAPk6M9T2yjMZxlpiCyossMnNYj7uFFZYILuah8Hi+mwOAFSY7eK06c3uY0v0VnH6KmqJrdybr/bCXSyrFltLcJnRJuZQZnR9lggAbLV8Vw1VfdpcnDS8IVbgagmsZ7tNqT5/mzGA8ZWjmdx9zmoXnNYNwU2wm9W8UQTGUKK/drbZXX/CGMRYi80Bm919bPVpq62PqJ6DtQ6x5qvlnKUefYShDn2EQmtBpKbljqbkGKv/aqLT6aDRaKDVahEYGFj7B4hbBosdXeduEl9LeA5tApWICVYhMcwPydGBSI4KxIFLZVi+5yKUMh5KmQQalQwRgUosvKcHVHIJzhfp4RAYEkLVdXpObLnRCrvAEOavgNnmwNx1xzEqORKp7UNxLKccD36+D48Naou37+yK3HITpny+F/3bhuC9e3vCaLVj4D+3Qnd1I9Yxwh8pbYMxMDEUwztFQKOSQRAY+KvDKP+95Qw+23UBRqsDiqs72wzAkI5heHxwW4zoFEE30yHNxm63Y9WqVQCAe++9Vxza1tQOXirDd+nZWH8sF2abAH+FBEOTwnFvShykHIe1R3IxuEMoBrUPQxvNjXdSLtZbxOH7t76/A/Ghaix/vD8A4GSeDifzdDhToMfr4zoDACZ8/Acyrmhd5sNzwOAOYWIxPf3bg+garcGMEZXXyr/983Go5BL4K6Twk0vgp5BW/v/qT6ifXBxe7W20XfK8qnmam5tb4zz11nDlEr0F+TozGKscXqhSVR9e6H4oYvVYi9mEiAA5Ql1cElOfoYhmJkWetjIni9kMh+BueOG1dqvH8jyglkpgqFYMqFTXhhdaLRbYHe6GF16LtdsskHPMqa3qlMprwwttVits9pqLQZ4HQgL8YbIzMOY+FgAUimrDC6vF1jRtTrE2G2w218OV5fJrQ5AdDhtkzOFy2qrH2u12WK01D5HlOSAyyB9+KoUY29DhylabA6Umm5iPTCqDrNpwZYvFzXDlq7E8DyglHEp0epfFYPV2BUGA2VzzcGWeA8ID1Qjwq1yPWCOGK18/bRJeAkW19d5odDNc+WoszwNqmQRF5TqX08ZzPJRO633N7XIcEB2kRmx4ULXYhg1XLtFbUKirPIBTFVu9jzCbTBCY6/VerfaDhOOglPEo0erhcNNHuFrvq6taTziZSsyptv6kpj5CwnFQSvkb1pH69CdKpQoSCY8ojRIBcs6nhivrdDpER0fXur33epFrd1QeuVFIeSikEiiuFnA3E6tdwOYTBZXXPdgcKNFbkVNmwuUyI84X6lFiuNbx+yskCFTKoJZLwXGA1SFgy8vDIJPyePH7w1h3JBc8V3nmNCJAgcRwf7x7Tw8AwN9/OY6wAAWeG165A5v81m/oGBmATm0CkKc1Y++FEvAc53SEKcRPhkNvjQEAvP7jMQiMYeHkngCALScKEKSWoWNEAGRSDqfzK5BVbMC5Qj2O5pTj2GUtlj3eD1nFBny77xIyr+hgFxhC/WS4r188pvSLR3zotc6EkObirSK3is5sw28Zedh8ogC7zxaL6xzPXTtCHaCQom2YH14b1wltApUo1lthcwgI85dDLZPgXJEBFruA9uH+qDDbcN+SNNzTJxb3psTBZLVj/8UytA1VQcLz0Fvs0JntV/tZHjIJBwnPo0O4H3onhMDmEPDf7edhtFVu8OaM69Kk03+l3ASeA6I0qtqD64iKXM/z1XlaoreIBWVjcBwQpVG6LHKbO6eqQsBgdX/Gqznb8rV2miInk1UQC4qGqCpyfHEetcZpo/W2+drx5Lz2pLpum7w+XLlIb8GQhdud3lPJJAjxkyPET45gPzlC/eS4LyUOqe1DUWaw4s/zJRiQGIIwfwUsdgcsdgEKKQ+5hPe5s4EOgcHmEMTCPfOKFkFqGWKD1TBZHVh35AoMVgeMFjsMVgcMFjsMVjscAoPBUln0fvRALwSqZPjPlrPIuKJFkBrIKjHAcXVvuNNbvyFAKYXJJkDGcwgLUKDCbMflUiMOXipD7zgN2ob546u0S7ALDN+lZyM+xA8atRzHcrTI05oREahAn/hghAcoEO4vR1iAAsFqOdoEKpGvNcNks6N/uxCU6K1Y8NtJFOutKNFbMKlPDCIDldh6sgBv/3ICQOWOup9CCrsgYPKnaQCAMH8FHugfh3HdojCgXYjXh2MT4k2BShnu7xeP+/vFw2R14FhOOQ5ll+PQpVKcyKtAntaECosdGVe0eHhpep3bXXUwB6sO5tQrF4WUR4BSimK9FTwH8ByHnFIT1HIJJDwHnucg5TnwHAcJz1UOPQMTN5x39Y5B9xgNjFY7ApSVZzm2nyqEQ2AYlRwJoHIYdEyQCrPGdgIA3PnxHxjXvQ3m3dW9XrkS4kkcKg8yVx8a2FC1DRMkvkuo1p816PN1GGbsLa1x2mi9JXXl9SI3UCnDB/f1hMUuwGJzwGhzQGu0odRgrfwxWnGpxIBbO0cAAE4XVGDGikP4btpAhPkrsP5oHl5ZdVRsr+pMhVTCo3KkLAeeA1Y/OwjxoWr8L+0iluy6gB2zhkMq4fHB76fxa2Y+OFTu3HFXd/J4vuo1B41Khq+fqBwSuOC3U9CZbfjn3ZU7Z6//eAyXSoww2x0w2wSYbQ6YbQ6Yrv5rtgm4rWsbfPpIXwDAlM/24v5+cfi/O5JhtQt4/acMMXeVTAI/hQRquRRSCQe92Q6e42C2OTCxVwwuFOlxKr8Cf7+rO1ITQ/F/azKw5nAuGBh0Jrt4rK76uH8AeP2nTKfX2aUmZJdeG+JSWGFBYUXDOovtp4tueE8u4ZEQqkZSRABS2oagf7tgtA/397kDEIT4ApVcggGJoRiQGAqgPYDKES655WaUGCyoMNtRYbbjQrEehToLdGYbDBY7rHYBfgopJvaKhpTnsebIFRTqzJX9Fwc4GNC5TQCm9I/HqTwd5v92Crd1awONSoaTeTpsOVmIKf3joFHJcfBSKbRGG/onhsBkdeDAxVKUm2wI8ZOLB9ysVw/Wcai8nsghMAQopeiTEIxF286hQGfGLy9UXgv8+e4LsDuuFblquQRK2bUDW/MndUdsMI3iIF7GAWabA2UGm0fOdhFCmgGtt83GkwcUVHKJyzuiNxWvF7l+Cikm9Ymtc3yvuCBsfnkoYoIrh7l1i9Fg7oTkq0WyAMvVYlNgTPxhDFArKs+kRgepMDAxFPzVgisqSIUuUYGVF7gzVPtc5XUJAqvMsYqEr1wxqljsAhyMIVApQ0QAD5VMAmW1Hz+5BB2rPd/1k4f7Iiqo8lqGAKUU+94YCfXVL762x4A8eUsinrwlUXz9/n298P59vZxiBIGB4yrz0lsqd471Zjv0lsqzwzZBgN3BYL968xmTzQ6e52FzCDiRWzmcWBAq5wHHATFBKsQEqWEXBORqzQhQSBF49cZYVUUrB8BPIUF4gBJtNEpEBSrFa3EJIfUnlfCID1XXazh/VUFZky5Rgbi7Wj9barDiTEEF+sQHQy7lsfdCCTZm5uON8V0gl/JYdeAyVh3IwcpnUwEAX/yRhc0n8vH905Wvv/rzIk7k6vDu5MpLIZTSyiHRVT56oDdU8muXnfzjbucztmO6tqnzdBHS1Frj2S5CWjtab5uBhw4o8OAQqVE0e5Hr9WtyCSGkuXn7mlziebRd8jxfnaeeuibX165/a83X9tG0NV87vpgTTVvLzMlXr+1tMdfkEkIIIaT1M1rttT7api7oOjpCCCG1oSKXEEIIIU2u+rNkG4quoyOEEFIXVOQSQgghpFnQdXSEEEKaAx0OJYQQQgghhBDSalCRSwghhBBCCCGk1aAilxBCCCGEEEJIq0FFLiGEEEIIIYSQVoOKXEIIIaSVWrx4Mdq2bQulUokBAwYgPT3d2ykRQgghTY6KXEIIIaQV+uGHHzBz5kzMnTsXhw4dQs+ePTF27FgUFhZ6OzVCCCGkSVGRSwghhLRCH3zwAaZNm4bHH38cycnJ+PTTT6FWq/Hll196OzVCCCGkSTXoObns6kPudDqdR5MhhJDmYLfbYTQaAVT2Y1IpPTK8pavaHrHGPIS1FbFarTh48CDmzJkjvsfzPEaNGoW0tLQaP2OxWGCxWMTXWq0WgOe29RV6C4wVFgho+Hck4Tg4ZDzMVqFR7XiyLV9rxxdzomlrvnZ8MSeatpaZk6fa4cGhgrNCJiga3EZ1dd3eN2jPrqSkBAAQFxfXkI8TQojPeOqpp7ydAvGgiooKaDQab6fhdcXFxXA4HIiMjHR6PzIyEqdOnarxM/Pnz8c777xzw/u0rSeEEOJratveN6jIDQkJAQBkZ2fTzkQd6HQ6xMXF4fLlywgMDPR2Oj6N5lXd0byqH5pfddcS5xVjDBUVFYiOjvZ2Ki3WnDlzMHPmTPG1IAgoLS1FaGgoOI5rVNstcZmqjvL3Lsrfuyh/76L8ndV1e9+gIpfnKy/l1Wg0LXJme0tgYCDNrzqieVV3NK/qh+ZX3bW0eUUHXa8JCwuDRCJBQUGB0/sFBQVo06ZNjZ9RKBRQKJyHkwUFBXk0r5a2TF2P8vcuyt+7KH/vovyvqcv2nm48RQghhLQycrkcffv2xdatW8X3BEHA1q1bkZqa6sXMCCGEkKZHd1shhBBCWqGZM2di6tSpSElJQf/+/fHvf/8bBoMBjz/+uLdTI4QQQppUg4pchUKBuXPn3jCsidSM5lfd0byqO5pX9UPzq+5oXrUO999/P4qKivDXv/4V+fn56NWrFzZu3HjDzaiaQ0tfpih/76L8vYvy9y7Kv2E4Rs9bIIQQQgghhBDSStA1uYQQQgghhBBCWg0qcgnxUW+//Tbatm3r7TQIIYQQ0kRoW09I06AilxBCCCGEEEJIq0FFLiGEEEIIIYSQVqNBRe7ixYvRtm1bKJVKDBgwAOnp6Z7Oq1XYtWsXJkyYgOjoaHAch7Vr13o7JZ81f/589OvXDwEBAYiIiMBdd92F06dPezstjzlz5gzuvvtuREREQKlUIj4+Hvfeey/sdjsA4OjRoxg6dCiUSiViYmLw97//Ha7uCffJJ5+gR48e4kO1U1NT8dtvvzXn5LRYCxYsAMdxeOmll7ydik96++23wXGc00/nzp29nRZpBXxxv6G25d1sNmPGjBkIDQ2Fv78/7rnnHhQUFDi1kZ2djdtvvx1qtRoRERGYPXu22K97Wm37FIwx/PWvf0VUVBRUKhVGjRqFs2fPOsWUlpbioYceQmBgIIKCgvDkk09Cr9c7xRw7dgxDhgyBUqlEXFwcFi5c2Cz5P/bYYzd8H7fddpvP5F+X/ZSMjAwkJiaC53lwHAe1Wo0JEyY4besHDBgAiUQCjuPg5+eH33///Ya/tWPHDvTp0wcKhQIdOnTA8uXLmyX/4cOH3/AdPPvss04xdVnmmyL/2vZ9PLW+NkXudcnfl+d9TWran/K574DV0/fff8/kcjn78ssv2fHjx9m0adNYUFAQKygoqG9Trd6vv/7K3nzzTfbTTz8xAGzNmjXeTslnjR07li1btoxlZmayI0eOsPHjx7P4+Him1+u9nZpHdOjQgfXr14+tXr2a7dixg3377bfsoYceYhaLhZWUlLCQkBDWpUsX9v3337M1a9aw1NRUFhsbyxISEm5o6+eff2YbNmxgZ86cYadPn2ZvvPEGk8lkLDMzs/knrAVJT09nbdu2ZT169GAvvviit9PxSXPnzmVdu3ZleXl54k9RUZG30yItnK/uN9S2vD/77LMsLi6Obd26lR04cIANHDiQDRo0SPy93W5n3bp1Y6NGjWKHDx9mv/76KwsLC2Nz5sxpknxr26dYsGAB02g0bO3atezo0aPszjvvZO3atWMmk0mMue2221jPnj3Z3r172e7du1mHDh3YlClTxN9rtVoWGRnJHnroIZaZmcm+++47plKp2JIlS5o8/6lTp7LbbrvN6fsoLS11ivFm/nXZTwkMDGRyuZzNnTuXLVmyhHXo0IGFhYU5besVCgXr1q0b++CDD1iXLl0Yz/NMo9GIbVy4cIGp1Wo2c+ZMduLECfbxxx8ziUTCNm7c2OT5Dxs2jE2bNs3pO9BqteLv67LMN1X+te37eGJ9barc65K/L8/767nan/K176DeRW7//v3ZjBkzxNcOh4NFR0ez+fPn1/uP30yoyK2fwsJCBoDt3LnT26k0WlFREQPA1q1bV+Pv33zzTSaXy1lOTo74nl6vZ6GhoTUWuTUJDg5mS5cu9US6rVJFRQXr2LEj27x5Mxs2bBgVuS7MnTuX9ezZ09tpkFbGV/cb3C3v5eXlTCaTsVWrVonvnTx5kgFgaWlpjLHKoo3neZafny/GfPLJJywwMJBZLJYmzf36fQpBEFibNm3Ye++95zQNCoWCfffdd4wxxk6cOMEAsP3794sxv/32G+M4jl25coUxxth///tfFhwc7JT/a6+9xjp16tSk+TNWWeROnDjR5Wd8KX/GbtxPOX/+PAPAXn31VTGm+jLz5ptvMqlUyjiOE5cZvV7P/Pz8GMdxYs6vvvoq69q1q9Pfuv/++9nYsWObNH/GWK3bx7os882VP2PX9n08tb42Z+7V82es5cx7V/tTvvgd1Gu4stVqxcGDBzFq1CjxPZ7nMWrUKKSlpTXsVDIhNdBqtQCAkJAQL2fSeKGhoUhMTMTrr7+OpUuX4ty5c06/T0tLw+DBgxETEyO+5+fnhwkTJtTatsPhwPfffw+DwYDU1FSP595azJgxA7fffrtT30VqdvbsWURHRyMxMREPPfQQsrOzvZ0SacF8fb/B1fJ+8OBB2Gw2p7w7d+6M+Ph4Me+0tDR0794dkZGRYszYsWOh0+lw/PjxZp2OrKws5OfnO+Wr0WgwYMAAp3yDgoKQkpIixowaNQo8z2Pfvn1izNChQyGXy8WYsWPH4vTp0ygrK2vy6dixYwciIiLQqVMnPPfccygpKRF/52v5X7+fkpWVBQBYt26duK2vvsykpaUhNjYWPXr0EJcZPz8/3HbbbWCMictMWlraDduqsWPHenx9cbWf9e233yIsLAzdunXDnDlzYDQaxd/VZZlvjvyv3/fx1PraXPPe1b5bS5j3rvanfPE7kNYnuLi4GA6Hwyk5AIiMjMSpU6fq/ccJqYkgCHjppZcwePBgdOvWzdvpNBrHcdi8eTPefvttvP766ygpKUFiYiJee+01PP3008jNzUWvXr1u+Nz161l1GRkZSE1Nhdlshr+/P9asWYPk5OQmnIqW6/vvv8ehQ4ewf/9+b6fi8wYMGIDly5ejU6dOyMvLwzvvvIMhQ4YgMzMTAQEB3k6PtEC+vN/gbnnPz8+HXC5HUFCQ02ciIyORn58PAMjPz69xuqp+15yq/l5N+VTPNyIiwun3UqkUISEhTjHt2rW7oY2q3wUHBzdJ/gBw2223YdKkSWjXrh3Onz+PN954A+PGjUNaWhokEolP5V/TfkpBQQFkMhn69+/vtK3nOA75+fnIzc2FRCK54TtKSEgQ86v6t6bvUafTwWQyQaVSNUn+APDggw8iISEB0dHROHbsGF577TWcPn0aP/30k9vcmit/V/s+R44c8cj62tTz3t2+m6/Pe8D9/pSn+kxPTkO9ilxCmsOMGTOQmZmJP/74w9upeExiYiK+/vprMMZw9OhRLFq0CM888wzatWuH6OjoGy7MB1Dje1U6deqEI0eOQKvVYvXq1Zg6dSp27txJhe51Ll++jBdffBGbN2+GUqn0djo+b9y4ceL/e/TogQEDBiAhIQErV67Ek08+6cXMCPE8d8u7JwoJUj8PPPCA+P/u3bujR48eaN++PXbs2IGRI0d6MbMbudpP4Tjuhm39F198gYsXLyI6OhonT568oa3CwsLmSlvkKv+nn35a/H/37t0RFRWFkSNH4vz582jfvn1zp3kDV/s+LYW7fTdfn/ctcX+qXsOVw8LCIJFIbtj5LigoQJs2bTyaGLk5Pf/881i/fj22b9+O2NhYb6fjcRzHoVevXvjggw8AAJmZmRg0aBD27NmDK1euiHEGgwG//PKLy3bkcjk6dOiAvn37Yv78+ejZsyc++uijJs+/pTl48CAKCwvRp08fSKVSSKVS7Ny5E//5z38glUrhcDi8naJPCwoKQlJS0g1D7Ampq5a031B9eW/Tpg2sVivKy8udYqrn3aZNmxqnq+p3zanq77mbz23atLmhoLLb7SgtLfXJaUpMTERYWJjY//hK/q72U6ovM9dv6y0WCwYNGoTCwkLk5OSInzEYDNiwYYNTfq6mITAw0CMHX+qznzVgwAAAcPoOapu/TZm/q30fT62vTT3v67Pv5mvzvrb9qcjISJ/7DupV5MrlcvTt2xdbt24V3xMEAVu3bqXrAUmjMMbw/PPPY82aNdi2bdsNw41asmPHjmHEiBH49NNPsWXLFmzatAnPPPMMZDIZRowYgZdffhn+/v4YM2YMVq5cibVr12L06NH1WpkFQYDFYmnCqWiZRo4ciYyMDBw5ckT8SUlJwUMPPYQjR45AIpF4O0Wfptfrcf78eURFRXk7FdJCtaT9hurLe9++fSGTyZzyPn36NLKzs8W8U1NTkZGR4VR4bd68GYGBgc0+qqZdu3Zo06aNU746nQ779u1zyre8vBwHDx4UY7Zt2wZBEMQd6tTUVOzatQs2m02M2bx5Mzp16tSkQ5VrkpOTg5KSErH/8Xb+te2nKBQKcByHV199VdzWT5kyBQAwadIkvPzyy1Cr1Thx4gQ+//xzcVsPVB4Ar1pmUlNTnb7Hqmlo7PrSkP2sI0eOAIDTd1DbMt9U+dekat/HU+trc+ZePf+a+Nq8r21/KiUlxfe+g/reqer7779nCoWCLV++nJ04cYI9/fTTLCgoyOlOWaRSRUUFO3z4MDt8+DADwD744AN2+PBhdunSJW+n5nOee+45ptFo2I4dO5xun240Gr2dWqMVFBSwRx99lHXs2JGpVCoWHBzMhg4dyn7//Xcx5vDhw2zIkCFMoVCw6Oho9re//Y399a9/rfHuyq+//jrbuXMny8rKYseOHWOvv/464zjOqT3iGt1d2bVXXnmF7dixg2VlZbE9e/awUaNGsbCwMFZYWOjt1EgL5qv7DbUt788++yyLj49n27ZtYwcOHGCpqaksNTVV/HzV4zDGjBnDjhw5wjZu3MjCw8Ob7BFCte1TLFiwgAUFBbF169axY8eOsYkTJ9b4CKHevXuzffv2sT/++IN17NjR6RE85eXlLDIykj3yyCMsMzOTff/990ytVnvkETzu8q+oqGCzZs1iaWlpLCsri23ZsoX16dOHdezYkZnNZp/Iv7b9lIKCApaUlMSkUilTKBQsMDCQBQQEsC5duohtHDhwgKnVasbzPAsPD2ePPPIIU6vVNT5CaPbs2ezkyZNs8eLFHnkMTG35nzt3jv3tb39jBw4cYFlZWWzdunUsMTGRDR06VGyjLst8U+Vf276PJ9bXpsq9tvx9fd67cv3+lK99B/Uuchlj7OOPP2bx8fFMLpez/v37s7179zakmVZv+/btDMANP1OnTvV2aj6npvkEgC1btszbqfmcJ554giUkJDC5XM7Cw8PZyJEjqcCtBypyXbv//vtZVFQUk8vlLCYmht1///3s3Llz3k6LtAK+uN9Q2/JuMpnY9OnTWXBwMFOr1ezuu+9meXl5Tm1cvHiRjRs3jqlUKhYWFsZeeeUVZrPZmiTf2vYpBEFgb731FouMjGQKhYKNHDmSnT592qmNkpISNmXKFObv788CAwPZ448/zioqKpxijh49ym655RamUChYTEwMW7BgQZPnbzQa2ZgxY1h4eDiTyWQsISGBTZs27YYDId7Mvy77KZ5aZrZv38569erF5HI5S0xM9Mi+UG35Z2dns6FDh4rP8u3QoQObPXu207NavZl/bfs+vjzva8vf1+e9K9fvT/nad8Axxlj9z/8SQgghhBBCCCG+p17X5BJCCCGEEEIIIb6MilxCCCGEEEIIIa0GFbmEEEIIIYQQQloNKnIJIYQQQgghhLQaVOQSQgghhBBCCGk1pA35kCAIyM3NRUBAADiO83ROhBBCSL0wxlBRUYHo6GjwPB2/9QTa1hNCCPE1dd3eN6jIzc3NRVxcXIOTI4QQQprC5cuXERsb6+00WgXa1hNCCPFVtW3vG1TkBgQEiI0HBgY2LDNCCCHEQ3Q6HeLi4sTtE2k82tYTQgjxNXXd3jeoyK0athQYGEgbPkIIIT6DhtV6Dm3rCSGE+Kratvd04RIhhBBCCCGEkFaDilxCCCGEEEIIIa0GFbk+7lKJQfz/mYIKXCjSezEbQgghhBBCCPFtDbomlzSPzScK8Nw3B7Fl5jC0DfPDin3Z+PFgDtLfHAWVXOLyc3+eL8aGY3ko0JmhNdnAgUMbjRL/uLsbApSyZpwCQgghhBBCSHNyGE0QTKZGt8OrVJCoVR7IqPlRkevDBiSG4LFBbRHiLwcA/GVkR4zoHCEWuCV6C0L9FXAIDOuP5eKWDmEI9VfgRK4OGzLyEBusQpBKDofAkFVsgL+i8uv+cPMZcBzw4IB4RAQovTZ9hBBCCCGEEM8STCbYCwsBQWh4IzwPaUQEFbnEczJytOjUJgCBShn+745k8f0QPzmGJYUDAH7NyMOrq4/hjfGd8eWeizhXqMf79/bE5L6xmDqoLZ68pZ3Lu46dL9JjQ0Yeluy8gGlDEzF9eHsoZa7PDBNCCCGEEEJaEEEAGGvc51swKnJ9TLHeggc+S8O9KXF4+86uLuN6xGoQF6LCG2sy0TZUjU8f7osxyZEAAJnE/aXWix7sg9klBnyw+Qz+s/UsNmbmYdGDfZAUSc+XJIQQQghp6Wi4KrnZUZHrY0L95Fj0UO0F52e7LuBkXgWmDWmHZ4YmYuXBHAgsAjzq9ozIhFA/fPRAb9zTJxbzNpyA2s01voQQQgghpOWg4arkZkdFro/hOA4jOkXUGjdjRAcM7RiOUcmRWH0wBx9uPoOhHcPRLUZTr783NCkcGzsMBc9zEASGX47lYkKPaPB83YplQgghhBDig27y4ark5kZFrg95dfVRdGoTiCdvaVfj7zNytPh89wW8d28PRAYqEZlcedOoyX1j0TchGO3C/AAA+Voz2mjqfkOpqoJ288kCvPj9Eew5V4wFk3pQoUsIIQQGgwESyY2jfSQSCZRKpVOcKzzPQ84gDp+sLValunbmyGg0glXbUa8+fJLjOKjVapex1V0fazKZYNMbXA7p9PPzc4oV3Ozw+wX4A0Ll3zWbzXA4HK5jq7V7fez1Q0PVarV4fw2LxQK73e6y3frEqlQq8HzlpU1WqxU2m80jsUqlUlxW6hNrs9lgtVpdxioUCkil0nrH2u12WCwWl7FyuRwymazesQ6HA2az2WWsTCaDXC6vd6wgCDC5GWJcn1hmsaBqrWWMwegmViqVQnG1XadYjoPUYIBMqRBj67PeV491GE2oKC52GXv9eu+uXamfH/xDQ8TX9Vnv69tHuF3v69NHuFnvq3MYTVDxfJ1iAdfrPbNZ4TAanQ5yqFWqa7FWq/s+QqkEL5WAWa0w5OU3uo+o6ts80Ue4WzacsAbQarUMANNqtQ35OKmBze5gz3x9gH289UyNvz+Tr2M93t7Ebnl3K8stN7K8chP7YvcF9vyKQ+zRL/ax51ccYl/svsA2n8hn7edsYLvOFLr8Ww6HIP6/QGdieeUmxhhjgiCw/2w5wxJeW89eXXXUKY4QQnwZbZc8r2qeuvoZP368U7xarXYZO2zYMGYtLmHGEyeZMfM4CwsOdhnbp2tXZsw8Lv7ER0e7jE1OTnbKITk52WVsQkKCU2xKSorL2LDgYKcchqT0cxmrVqmY6UKWOG1jhwx1O9+qt3v3mDFuY8suZTNrcQmzFpewRx54wG3slVOnxdhnn3jCbWxWVpY4H2bNmuU2NjMzU4ydO3eu29j09HQxduHChW5jt2/fLsYuWrTIbez69evF2GXLlrmNXblypRi7cuVKt7HLli0TY9evX+82dtGiRWLs9u3b3cbOn/u2+F38+ftmt7H/N/tVMfbo/gNuY2fNmiXmkJWV5Tb22SeeqFzOMjLZpZ273MY+fOdEZszIZMaMTFa0L91t7OTJk53WI3ex1fsIa3EJU6tULmOHpPRzWjfc9RF9e/VyyiEhIcFlbJP1EWFhYpzdYGRDBw12GatWq8Xv2FpcwsaNGu12vlX1JXXpI4rS94uxD0+c6Db20s5d4vf89P3u+5OTGzcx4/ETzHQhi730uPv+5MDadWIObzw33W2sJ/uI2rb3dCbXR0glPD59pG+NR5fytCZM/TIdShmP/z7YB//6/Qx+OpQDgQFxISqE+ytwoViPX47mQsJVXm8b4ld5RO6H/dlYtuciNr40FACw4LdTWHM4B/veGAUAePe30/jzfDHS5owEx3F4dFBbCAz4cMsZKGU83pnYrflmAiGEkNatrsMnGzPE0lOccqhDPuK01RJbvd1aQu0FBbBfPbPEarmJkL2wUDwz44kbDrVU9go9bCWl4v/dESyuzwg3hlBRAXt+fmUOJSXuY/X6ylieh6CvJV+TWZw2W1m521jm5uyfb2J1X+8ZE+cDALfDqpnD4RTbFPNFMJnAbG6WJcbE5QEABDcjBioDqvWTtc0Sxuoe21C1fS/Vc2iyJOqPYzVVVbXQ6XTQaDTQarUIDAxsirxuKgaLHQarvcZn1hosdtzzyZ+4Um7C3yZ2xT82nILOZMPjg9vioQEJiA+9NqziUokB3++/jG/2XoLFJuCZYYloF+qHracK8fGU3uB5DptPFOBUng4vjOwIADiUXYZyoxW3do6EzSFg7L93YWBiKAKUUnyTdgkbXxqKuBD1DXkRQogvoe2S51XN09zc3BrnaX2HK0uNpsodPcZgMBrdxqqqtWs0ma4dAOY4SCMjIbs6VLGxQxEtRcWwFxTUuBPnVz3WbHY9FJHn4R8aCnZ1aKDZYnE/XLlau06xPA9OpRLbAeo3vNAp1mYDQkPF+XS9lj5c2ZCXD3tRUY3FjUIudx6u7Kpdnoc6JgbqNpHXYhs4XNlWUuq0HMlkMsirx7ppV4zleTCFAsbycpdFm0wmhVxWbbiyq2HQEglkajXkDgfAWMOHK/McJMEh4K5OS2XTDRuuzKwW6HKuuCyYrl/vXfYRPA+Jnx+UgDifnPqI63AcB3X1yx+qYnke0vBwp3WkocOVbSWlqLh4EUJD1vvrpo1TqaAGxPlUW39SYx9RQ1/iMtaFyuHKUnAqFSzactisbvoIpfJaH2Gz3bjeV+u3PdFH6HQ6REdH17q9pyLXB3y77xL+uu44tr8y3KloBSqfafvE8v24o0cUPt+VhZhgFT57pC86urn7crHeggW/ncLqgznoFReERQ/2Rmxw7YWqzSHgyz+y0CchGH3jg5FTZrohH0II8UW0XfI8T89TW0mpWOQ2GMdB2qaNy+LNKzm52KH0WjuAx+eTr/HM93a1gLta3DUGs1rgKC3zne/f08uk2dy4m1BJJOAUCt+aNg+uIx5ZHgHf60t8cF4Ddd820XBlHzCkQzjmjOtcY0HZPtwfM0cn4eUfjmBgYig+eagvNGpZDa1cE+avwPv39sSoLpGYvfoo7vj4D3zyUF+ktg91+zmZhMczw9qLr9MvlsLmcGDHmWIM6RhGz9ElhBBCWgIOYFar85DOBmq9z0nlIJjNYG7OnNbJ1QKuVWuNd2n24DrCrLUMPyZeQUWuD4gPVeOpIYlO72XkaLH64GUMbh+GV1YeRb+2IfjysX5Qyur+PNvburVBclQgnvp6Px75Yh/+eXd33Ncvrk6f1ZlteHfjKQxKDEXahRKs2HcJv7xwC9RyWmQIIYR4iQd3TIHWvHPqoQKO5yEJCvLMNb48J96BurE8+r21xgKO1AEd5GjtqGLxsnVHriA2WI2+CcHie0arHTNWHILF7sCqA5eRHB2IL+pZ4FaJD1Xjx+cG4fkVh/Hqj8dwvliP18Z2rvXxQIFKGdZMH4QojQr7L5biwc/34q/rjuP9e3vWOwdCCCHEMzy0YwrcHDunjS3gGPNoIdDoYa/V2iLEI+ggR6vF1x5CmgpjDO9tOo2v/rzo9P7CjadxucwICc9BrZDh80dT4K9o+PGIAKUMX0xNwdTUBCzZeQHPfnMQRqvri82rxAarIeE5dIkKxKQ+sVh9MAdrDuc0OA9CCCHEI6p2TBvzQzunddfY+V01r+l7I4Q0EypyvYjjOGx+eRj+744u4nvpWaX4Ku0iEkLUKNBZsPjB3ogMvPGuy/UllVQ+DuidO7tiy8kC3PtpGvK1rh9OXt3cdZnYfCIf/dsG4+2fT8Bgqb1AJoQQQgghhBBvoOHKXqaSS6CSVw5DZoxh3oYT0KhkuFhixFt3JGNAovubRdXX1EFtkRCqxgsrDmPi4j+w9NF+6B6rcfuZWWM7YdrQRASp5SiqsMCvEWeVCSGEEEIIIaQp0ZlcL7HaBUz9Mh17zhWL73Ech2lD2kFrtGFCz2g8Mbhtk/zt4Z0i8OP0QZBJeNy3JA0bM/PcxscGq9E1WoOYIBW6x1QWxDllrp9xSAghhBBCCCHeQkWul+RrzSissMB+9U6DOrMNV8qMePvnE+gY6Y8Fk7qLD2xuCkmRAVg7YzCSowPx7DeH8PbPx2G2OcAYQ4W58sHMDoHhr+sysf1UIQDgg99P4+Gle7Fi3yXc+q+dOJ1f0WT5EUIIIYQQQkhD0LhTL4kPVeO3F4eAMQbGGKZ/ewhHL5cDDFjySEqzDAkO81fgu2kD8d6mU/h8dxZ+PpoLngMGJIZi8YN9IOE5bDlRgCiNCiM6R8BfKUVmrg4D2oUiUCnFK6uOYO30wZBK6FgJIYQQQgghxDdQdeIFdocAm6Py7oAcx2HbqUL8cbYYFWY7Pri/F9qF+TVbLifydMgqrhx6XGqwokRvhdXuEO++/OeckXhueHsAwK2dI9AtWoN/bz0LgQGZV3T4fHdWs+VKCCGEEEIIIbWhItcLtp4qRP9/bMH5Ij2sdgGv/XgMAPD8iA4YnRzZLDmkZ5XikS/24a7Fe3DwUilmj+2EnbOH44H+8dh8ohCj/rUTG47lgVV7dliHiAB89/RALJjUHRqVDADw3qZTOJWva5acCSGEEEIIIaQ2VOR6QZRGiXHdo5AQosY/NpxAsd6KXrEazByd1OR/+3KpEfctScN9S9JwKr8C/3d7F/zx2q2YMaIDEkL9MH9Sd/w0fRCC1HLMWHEIdy7agx2nC8Vi1yEwfLztHNqGqvHggHgIDHj+28MoM1ibPHdCCCF198knn6BHjx4IDAxEYGAgUlNT8dtvv3k7LUIIIaTJ0TW5XtAjNgg9YoOQeaUc3+y9BJVcgq+fGgCeb5obTVntAnLKjEgM90eInxwGix1/m9gV96XEQSmT3BDfJz4Yv7xwC34+egUfbj6Lx5btR7+2wZg5uhNS24diySN90TbMD/4KKYZ0CMNLPxzBA5/txf+e7I8IDzzTlxBCSOPFxsZiwYIF6NixIxhj+OqrrzBx4kQcPnwYXbt29XZ6hBBCSJOhM7nN7HyRHlfKTThXWIFHv9yPyEAlfnw2FYFKmUf/TvVhxn/57jAeX74fgsDgp5Bi/Qu34NHUtjUWuFUkPIe7e8di6yvD8M+7u+NKmQlTPt+LBz/fC4vdAf+rN8Ya1z0KXz6WgqxiAx5aug+CwFy2SQghpPlMmDAB48ePR8eOHZGUlIR//OMf8Pf3x969e72dGiGEENKk6ExuM3t/02kcuFgKgTFIeA7fPT0QCaGVN5pyCAz7skqw83QRMnO1uK1bFB4ZmIAygxWPL9+Pv4zsgFs7RyJPa8IvR3MRrJYj1F8OtVwKq12A3mLH5VIjjuVocSi7DKueTUVssBpPDmkHk9Uh5lCfRxPJJDweHBCPe/rG4Pv0y1i8/Rzu+SQN/doGQ2e24+MpvdE+PAASnoNaLkETPvWIEEJIAzkcDqxatQoGgwGpqak1xlgsFlgsFvG1TtcE91vgeUAQGvd5T7TjybZ8rR1fzImmrfna8cWcaNpaZk6ebqeZUZHbzJ68pR3Ss0phsDigkksQHqCAIDD8eCgHi7efw8USIxRSHl2iAuGvqDzTanUI0KhkkEsqX58t0OOfv55y+TfiQ9To1zYEZlvlAtmvbUij81ZIJZg6qC3u7xeHb/ZewuLt51BmtOH1HzMw765umDshGa//lIHv91+GWi7B2K5t3J4pJoQQ0vQyMjKQmpoKs9kMf39/rFmzBsnJyTXGzp8/H++8806T5cKrVJBGRHigIQ4QAhvfjifb8rV2PNmWr7XjybZaazuebMvX2vFkW77Wjifb8rF2eJWq8bnUE8eqj2utI51OB41GA61Wi8BAD32pN4HCCjPuX7IXRRVmmG0C7k2Jw/O3dsDL3x9B+sVS9IwLwjNDEzGiUwRUcvcFosnqQInBglKDFUarA3IpD3+FFFEaJQI8PPS5JgaLHV+lXcSSnRegNdkwrlskCnQWnMyrgNnmwBvju2Da0MQmz4MQQgDaLrlitVqRnZ0NrVaL1atXY+nSpdi5c2eNhW5NZ3Lj4uJonhJCCPEZdd3eU5HbTEoNVoz9cCcqzHYMTQrHjjNFWDSlN+b8lAGrQ8DbE7piUp+Yeg0l9gWlBgve33QGvxzNhd5ih1TCoXuMBqufHdRkN9IihJDr0XapbkaNGoX27dtjyZIltcbSPCWEEOJr6rptohtPNQOtyYaHv9iLIr0VQ5PCsf10Ie7uFY1XVh6FRi3DuhmDcU/f2BZX4ALAf7aew7ojV/Dri0PwSGoCbA6GK+UmpF0oQXaJEdtPF3o7RUIIIVcJguB0tpYQQghpjeia3CZmsNjx+LJ0nCsw4MupKcguM2LH6SL8ZVQSBncMR2piKMIDFN5Os8EeTU3A8E7hiA1W4W8Tu2Fir2i89mMGHv5iHxJD/XBFa8LqZwehW4zG26kSQshNZc6cORg3bhzi4+NRUVGBFStWYMeOHdi0aZO3UyOEEEKaFBW5Tchid2Da1wdwNEeLTx7qg1u7RKLcaEW0RoWYoMqfli4x3B+J4f7i674JIfjl+Vsw7qNdOF9sgFLK48mv9mPDX4YgzL/lFvOEENLSFBYW4tFHH0VeXh40Gg169OiBTZs2YfTo0d5OjRBCCGlSVOQ2EcYYXl19DH+eL8Hf7+qKRdvPQSHlsf10EVYeuIw/X78VQWq5t9P0CLtDwJJdFxAbrMLEXjFQySV4fHBbzP35BKx2AYU6C575+iBWPpsKCV2nSwghzeKLL77wdgqEEEKIV9A1uU3kg81nsO5ILuaM64yUhBDwHIfnVxxGuL8c/32oT6spcAFAwnPYcrIAh7PLxfceGdgWt3QIg1zKQymT4GB2Gd5am+m9JAkhhBBCCCE3BSpym8DmEwX4eNs5PDggHk8PTUSXqEAM7xSOCosdwztHYHgnDzwn0IdwHIfvpg3E23d2Fd/jeQ7/uq8nVHIJ4kLUUMl4rEjPxtLdF7yYKSGEEEIIIaS1oyLXw66UmzBr1VH0jAvC2xO6QmeyQ2ey4dMd56GWS9ApMsDbKTYJpazyub6lBiuqnkoVGajEwsk9oTVZ8cnDfSGX8Ji34SR20B2XCSGEEEIIIU2EilwPcggML353GAJjWDSlN+RSHot3nEP/f26B2S7gtm5tIJW03lmenlWKgfO3Yl9Wqfje6ORI7Jg1AsM7RWDFtAHgADz11QGcL6rwXqKEEEIIIYSQVotuPOVB36Vn48ClMnz0QC/EhagBVBZ5y/ZkQSbh8M+7u3k5w6bVI1aDxwa1RWyw812jVXIJbA4BO04XYdbYTvjvjnN4bNl+/PjcIEQEKL2ULSGEEEKai8lmgslu8khbKqkKKlnLf0IFIaTpUJHrIcV6CxZuPIUhHcNwZ89o8f2sYgNsDoa5E5KhlLXu2a2USfDG+C41/i5fa8ZXaReRGO6P/z0xAA9/sQ9PLN+P1c8OEoc6E0IIIaR1MtlNKDQVQmBCo9rhOR4RqggqcgkhbrXuqqsZzf/1FMw2Ae/c2RUcV/mYnBX7LuGjrWfROz4Ijw1q690Em9HJPB0OZZfhoQEJ4ntxIWr8696eePp/B7H2yBVMTW2LT3aex/RvDuKLx/qJ84wQQm5GO3bswK5du5CXlweLxVJjDMdx9Fgg0qIJTAADa3QbhBBSGypyPeBkng4/HsrB9OHtkRjuDwAoN1rxf2szITDgL7d2vKmKuJ8O5eCnQ1dwV68Y+CmuLWJjurbBc8Pb45Md5/HW7V3QM1aDbaeL8N8d5zFjRAcvZkwIId6h1WoxceJE7N69W7xpnytU5BLiWZ4aQk3DpwnxPVTkesCHm88gUCnFM8Pai+9JJTxkEh5Wu4DRXSO9mF3ze35ER0wf3sGpwK3yyugknMzTYfGO89g5ezj+uu443t90Gn3ig5DaPswL2RJCiPe89tpr2LVrFzp06IBnn30WSUlJCAhonXfhJ8TXeGIINQ2fJsQ3UZHbSBk5Wvx+ogCvjE6CRiUT3/9s13lY7AJGdom46W6upFFXzgfGGPJ1ZkRprnX8UgmP/0zpjUKdBQFKGWaPTcKGjDxM+/oAdr16K0L85N5KmxBCmt26desQGRmJvXv3IiQkxNvp1MhgMEAiufHeCRKJBEql0inOFZ7noVKpGhRrNBpdnuXmOA5qtbpBsSaTCYLgurjx8/NrUKzZbIbD4fBIrFqtFkeCWSwW2O12j8SqVCrwfOXTHqxWK2w2m8tYSAGLYKlTrFKpFJeV62OtdiuMVqM4XFmhVIixNpsNNqvrduUKOaRSqRhrMBigEBQ1xioUCjHWbre7HP4PADaHTRxCbbfbYbVYXcbK5DLIZJX7Nw6HAxZzZbscOPgJfk75yGQyyOVyMdZsNrtut1qsIAgwmVyfWa5PrFQqhUJRmRNjDEaj0SOx9Vnvm6qPsDgswLVd7gb3Edefgac+4pr69BH1iXXXR7iLtdlssFor1093y4YT1gBarZYBYFqttiEfb1UeX5bOer2ziVWYbeJ7K/dnsyHvbmUJr61nGTnlXszOu975+Tgb8I8tTGey1vh7QRDY139msfuX/MkSXlvP7l78BxMEoZmzJIS0Bi11u6RSqdg999zj7TRqVDVPXf2MHz/eKV6tVruMHTZsmFNsWFiYy9iUlBSn2ISEBJexycnJTrHJyckuYxMSEpxiU1JSXMaGhoWyEmOJ+DN4yGCXsWq1mhmtRrHd8ePHu51v1U2ePNltrF6vF2OnTp3qNrawsFCMnT59utvYrKwsMXbWrFluY/cc2MNOlpxkx4uPs+mz3bf7/e/fs+PFx9nx4uPslbmvuI39cu2XLLM4k2UWZ7I3333TbeziFYvF2Hkfz3Pf7jdfit/bl9986Tb2w08+ZMeLj7PM4ky2eMVit7FvvvummMOXa923u3DhQnH+pqenu42dO3euGJuZmek2dtasWWJsVlaW29jp06eLsYWFhW5jp06dKsbq9Xq3sXfefafTuuEudvTY0WKc0Wr0WB/Rq08vcZk8XnycRcdFu4xt36m9GHe8+Dhr36m9y9j69BFhYWFinNFqrLWPqD7PRo8d7Xa+tbQ+IjMzU4ydO3eu29j09HQxduHChW5jt2/fLsYuWrToht/Xtr2nM7mNcLagAttOFWL22E7wrzY01+4QUKK3ontMILrFaLyYoXdN6hODduF+8JPXvJidLzLg7+tPoneCBqF+chzKLsd/tp7Fi6OSmjlTQgjxjo4dO9b9qDRpNgITkG/MF19bHa7P8DEw6Cw68dpOm8PNWVEApaZrz5J3164vqTrbWdtNo6rHNPYGU65wcH+Pk3JLufjdlVvK3cbaBddnsrzBbHN9xhcAzHazuPyUm8vdxlrsFjG2zFTmPtZxLdZgct8fmR1mp3WjtnbzjfnikG5Pqs9NzOoaJzDBaf10t3wwMDHWYrfAKrjvI6rPM4vD9egCoH59RKmpFBbeUqd2bzYcY7Xc6aIGOp0OGo0GWq0WgYGBTZFXi/DGmgz8dCgHaa+PRLBf1fARho+3nUW4vwIxIWoMSwr3cpa+wWJ3QCG9cbjb2sNX8NIPRzC4QyjSzpeAMeDH5wahT0KwF7IkhLRULXW7tHTpUrzwwgvIyMhAhw6+dQO+qnmam5tb4zz11nDl6jcLauxwZbPVjDJrWY07wWq/a7Fmk9nlUEQePMI0YTA5TBCYAIvZ4n54YbV2q8fyHI8geRBkkmvjMBszFNFhd7jcua/P8EJexkNr14KBwWa1uY11GoJcLZYHD7VUDYPdgMYOV3bYHJAJMqe2XMW6G4LMg4dGrYGVs6Kxw5VDFCFO31tDhyubrCYU6ApcXiMslUmdhiubTTW3K+Ek8FP4QZAKlcUgYzAZ3Q9tlisq260eK+EkUEqUTvNaIpFAobw2NNtocD+0WaFUgAOHUEUorGbX87c+fYRNsMEsMYs5mYwmt+u9Sn2t3arYqmWyar2tKdbdeg9UrstV86ikogQOof7rfXVVOXFKTsyptv5EpVaJ673VYoXdbgfP8QhXhSNE5XwJTEOGK5tsJmiN2kYPV64aGu6J4co6nQ7R0dG1bu/pTG4DlRms+OlQDu7uHSsWuIwxrD2Sg8Xbz+O9e3tQgXtVRo4W074+gPfu7YEhHZ3nyV29Y6A12TD35+PoEx+EQ9nleGxZOva8fisClDIXLRJCSOvw1FNP4ezZsxg2bBjmzZuH0aNHIzY21ttpOfHz83O6RsxdXH3arKvqhSkAWEwWGASDuBOoM+qcP+DmRF/1WAkngVKlhFqmrvVMj1Ll+t4aPCp37qrOLMmV7u8tUf1vVY/lwUMilcDguDZtFaYK5w+7mbbqsRJOAqVM6bQD7xRrrlu7Ek4CJa5Nu0wug0xet21z9diqnXdmr/lssEx2rYCstV2ZzG1b1UmlUrHgvR4PHjKpDFa7tdbY60kkErFoqel7g/3qTxV3J5+vxlYVS0q10u10Vf2O4zmo/Gq+2RUPHgqp4lpxysFl7PXtVo+t7XsDnIs3VzhwMDvMMPE1L49XE4DWqK3+oRpVLdvV52/1wrQ2VbGupq36/xWqmq/7rh5bNT1KlfvvrbrqBwmqq+lgUG39SfWcZQoZZApZ5XXiaj/4qVz3swqFQrwO2x2T3YRyRzkEznWxX1t/wnM8/BQ35iOXy8WDNrWp3ke4K/qroyK3gb7bnw2zTcATg9uK76VdKMHMlccwPCkMveOCvJabr0kIU6Nv22C0C6t5ZZs6qC10Jhs+3nYOqYmhSLtQgqe+OoDvnx54Uz16iRBy86k6Ss0Yw1NPPeU2luM4t0fefZ2nHtdisVta9fNWPTltjW3LV+eRL6J5XbvWvN76GpvD5jTsuaE80d966zujIrcBHALDN2mXMKRjGDpGXnvUQ7doDe7tG4NVB6+gSG9FfGjdj1S3ZoFKGRY/2AdA5Y7cz0dzcVu3Nk7Dl5+/tQPu6BmNKI0Sw97bjn1Zpfh8dxaeHprorbQJIaTJxcXF3TQH8zzxuJaqs12EEEJqVnXmvMxadlP3t1TkNsAf54qRqzXjrTuSnd5/a10mtp8qRMcIP/SJD/JOcj5u55kivPj9EXw8pTcm9IwW3+c4TjzTOzW1Ld77/TTe23gKo7pEIDHc31vpEkJIk7p48aK3U2hWLfWMACGEtDQ3e3/LezuBlmjlgcsI9ZNjZJdIAJVndh9eug+/HM2FzmzHlP4JN82R+foa3ikCPz43CHf0iAIAfLvvEv7560mnGwbkac1gDJBIODy/4hAs9rqNvSeEEEIIIYQQKnLrqcxgxebjBbi7dwzk0srZV6K34FS+DowBMp7D3b1jvJylb+ubECweBMguMeJ4rlZ8/XXaRYxKjsDDA+Nhtgk4kVeB6d8c9Ga6hBBCCCGEkBaEhivX09ojV2B1CLivX5z4nkImgcnqQMcIf/RtGyLebZnUbs74LhCEyrO4gsCwZOcFjOwSgb9P7AYw4Jt92dh6qghbTxaIZ84JIaSl2rVrFwCgf//+UCqV4uu6Gjp0aFOkRQghhLQqVOTW0+qDOegVF4SkqzecOpRdhj1ni2GwOvDRlN7oEtVyns/oK3ieE//dOXs4jDYHOI7DwwMT8M2+bPgrJHh19TFs+MstiAxU0lBwQkiLNXz4cHAch5MnTyIpKUl8XVd1fXQCIYQQcjOjIrcezhXqcTxXh3f+v737jmvqev8A/rnZCSPsJcOBgBMVHOCu1j1brdrWVWvr6LC2rvbbqr/6raN72mHVb5fWam2d1L2pGwUnKE6W7EDIPr8/kEggCUMgAZ7368VLc/Pck+ee3HVyzz13RBsAgEqrxwvrTkGlM6BToAvCfJwqKIFURMDnwZlf3A081McJf86KBp/HYfx3sRj0+RG4yUTY+FIUvJzr72hvhJDGa9KkSeA4DnK53OQ1IYQQQmoONXKrYNuFFPA4YEi74kGTJEI+Jndvhs/3JeLcnVz8cvIOJnYLsnGWDQfHcegU6AoA6BfmhR3xaVAU6aDWFY/2diwxE0HuMgS4VfwgckIIsQfr16+3+poQQgghj48Gnqokxhh2XEhB92APeDqJjdP+SUiDu4MIfA4Y1MbHxlk2XJ+P7wh3BxH0DBj8+VEk3MvDoq0X8Z+/EmydGiGEEEIIIcSOUCO3ki6l5ONmZqHx2a5Ltl3C0u2XUKTVQ60z4MnWPsbGL6l5fD4Pu17vCSGfQ4FahzHfnsArfYKxeHjxs4pzlRqsP54Mrb5+P9OLEEIIIYQQ8niou3IlbbuQAhGfh4FtfMAYg0ZvgJNYgAUDwzDrt3MY1yWg4kLIY/F2luC7iZF4Yf1pqHUGXLyfi3FdAgEA2y+mYtnOK+jR0hPBXo42zpQQQqpGqVTi4MGDSExMhEKhMHl2eAmO4/Duu+9Wqrzly5fjzz//xNWrVyGVShEdHY2VK1ciNDS0plMnhBBC7A41civBYGDYfiEFvUM9IZcKAQBv9A+BVMjDe39fQhMXKXq19LRxlo3DE2FeePWJYHx5IAnbLqTitX4hSMktwpC2Pohq7mZs4N7NVtK9uoSQemH9+vV44403kJ+fb5zGGDMZkKrkdWUbuYcPH8bs2bPRuXNn6HQ6vP322xgwYAAuX74MBweHGl8GQgghxJ5QI7cSztzOQWqeCm8PaYXkzELoDQzfHErCyZvZOPBmb6Tlq8Dn0eiYdWXukyG4lqbAnsvpGP7lMXAcwBjw2fgOCPZywr83s/D8mpP45rlOGED3SRNC7Ni+ffswbdo0yOVyvP322zh48CBiY2Px3Xff4caNG9i6dSsSExPxyiuvICIiotLlxsTEmLxev349vLy8cPbsWXrWLiGEkAaPGrmVsP1CCmQiPvq38sa8zRcQeyML306MQPcWHhAL+Qhyp1/F6xLHcfj6uU546psTiL+fB7lUALlUhOfWnMTsPsF4qVdzvPJEMHrS1XVCiJ37+OOPwXEcDh48iPDwcEydOhWxsbGYPn06AGDZsmWYP38+vv/+e7z00kvV/py8vDwAgJubm8UYtVoNtVptfF36ynJN4XE8GFj1x07gcbwaKacmy7K3cuwxJ1q2uivHHnOiZaufOdV0OXWNY+Zu/KlAfn4+5HI58vLy4OzsXBt52Q2d3oCuH+xHj5Ye+Hx8R+QUanA1TYEuzdww6uvjmNgtCM90pvtxbSGvSIsv9idi58UUFKh1iAxyw6HrDxDq7YQts6LhKBZApdVj/5UMDG3va+t0CSG1qL4elzw8PBAWFoZjx44BAKZOnYqffvoJer3eGGMwGBAcHIyOHTtiy5YtVf4Mg8GAESNGIDc31/g55ixZsgRLly4tN72m6rRIW4QiXdFjl8OBA0OVT11qtSx7K6cmy7K3cmqyrIZaTk2WZW/l1GRZ9lZOTZZlb+VIBVJIhdLHLgeo/PGeruRW4PiNLGQVajC8ffGoykIBD3/H3cft7ELE38+D88N7dEndk0uFeHdYa7zYsxme++EkDl1/gBHhvvCRS+EoLl61/3ciGStirqGldy+EeDvZOGNCCDFVUFCAwMBA42uxuHiUfoVCASen4n0Wj8dD165dsX///mp9xuzZs5GQkGC1gQsAixYtwty5c42v8/PzERBQcz/iSoU1d5JDCCGEWEON3Apsi0uBXCqEm4MIz635Fx0DXLHx9F3cziqEh6MY/Vp52TrFRs/HWQKxgAc3BxG2XUhFe385Eu4Xd83763wK3h/Zlhq4hBC75OPjg+zsbONrX9/iXifXr183uQc3OzsbRUVVvwr6yiuvYMeOHThy5Aj8/f2txorFYmMjmxBCCKnPqJFrhUqrx55LaRja3hdZhRpkFWiw+dw9RAS54vStHLzYszmEfHrUsK1xHIfPxncEA0Pyg0Is3nYJI78+jr6hnshRavHu3wlIyijAgNbeCHCT0ajLhBC7ERYWhsTEROPr6OhoMMawatUqbNy4ERzH4cSJEzhw4ADCw8MrXS5jDK+++iq2bt2KQ4cOoVmzZrWRPiGEEGKXqIVmxaFrGVCodRgR7ocnW3vjxZ7NkJanQnMPB+gMDOPoXly7EerjhDAfZwxu54sBbbzRI9gDR65nIqtQjVY+zvjfiVt4/seTmLspztapEkKI0dChQ5GcnIxTp04BAPr164f27dtj8+bNaNKkCSIiItC3b18YDAbMmTOn0uXOnj0bv/zyC3777Tc4OTkhLS0NaWlp1boaTAghhNQ3dCXXiu0XUuHpJIabgwg6nQHfH7mJ1r7OmNajGUJ9nNDMg0ZVtjcqrR6J6QU4mZyNMZ38wfEY/jyXAiGfg1jIR2SQ5ZFFCSGkrk2aNAkhISHw9vYGUHz/7c6dOzFt2jTs27cPaWlpkMvlmD9/Pp5//vlKl7t69WoAQJ8+fUymr1u3DlOmTKmp9AkhhBC7RKMrW1Cg1iHi/b14qlMTbItLQc+WHoi5lI7Px3fAyA5NbJ0esUKnN+DDf67huyM30dzDAW8OCMGhaw+w5dw9CPkcnusaBGepEIFuMozu2AQcR884JqS+a4jHJaVSiby8PHh5eYHP59f55zfEOiWEEFK/VfbYRN2VLdh7OQ1qnQFPdfLHh2PDcS+3CP6uUuQUanD6VnbFBRCbEfB5WDSkFTZM7watwYDZv52HSmfAL9O6YmSHJlh3/BY+25eIuZsuYPwP/+JuttLWKRNCSDkymQy+vr42aeASQggh9Rk1ci3YFpcCf1cpIoNc4e0sRsL9fDzfNRAf7L6KXfGptk6PVEJUC3fEvN4Lr/Vrif1X0jFp7SnweRxWPNUOXZq6ggNw8mY2+n50CGuPJaManRoIIYQQQgghdobuyTUjs0CNI4mZGNbOF+uO38LpW9lwcxCB4zhodAaM7xxYcSHELjiIBZj7ZAgmdgvC1weTsPH0HYT5OGPTjGjcyCjAqn+u4p9L6fi/HZchE/Exvgt9t4SQupWRkYFvvvkGR44cQWpqKtRqtdk4juNw48aNOs6OEEIIqX+okWvGzoup0BsYBHwOa48nY/srPZCYocC7f11Cx0AXhPrQM1frG08nMZaMaIM3+odAKCi+B/en2FvYezkdH4xui8/3J2LR1njcyVZiUlQQfORSG2dMCGkMrly5gt69eyMrK4t6kxBCCCE1hLorm7H1/H20beKMj5/pgB2v9ICrgwgCPg/X0hWYQFdx6zW5TAiZqPi3nc7N3NDERYqeLT1x8K0+iAxyxTeHbiBq+QGsOXrTxpkSQhqDefPmITMzE0899RTOnDmD/Px8GAwGi3+EEEIIqRg1csu4lVmIuLu5GBnuh6tp+Xjm+1hcTctHrlKDMB8nDG3va+sUSQ0Z1t4PRxc8gQA3GXgch+TMQgAAA7Bs5xXM2XgeOj2dVBJCas/Ro0cRGhqKTZs2oVOnTnB0dLR1SoQQQki9R92Vy/gr7j4A4LdTd/GgQAMXqQi+cinCfJzRN9SLHjfTAOWrtPhg5xWsm9oZl+7n4+tDSbibXYS/4lJw9k4O/prdHe4OYlunSQhpgBhj6NChAx1bCCGEkBpEjdxSGGP4Oy4F3Zq5IcBNhqgW7nh7SCskZSggFvAgEdJjHBoijc6Ag9cyEBHkivFdAvFMZAB+PXkHS7Zfwt3sIjzx0WF8MLodhrTzoRNRQkiNioyMxO3bt22dBrEXmkJAU0OPteN4AKuB3kgiGSByePxyCLE3NbW90TZil6iRW8rFe3lIzizErD4tIBLw0MHfBQYDw4v/O4NgL0esmdzZ1imSWuDhKMaBN/vAQVy8OfB4HCZGBWFwW28M+/I40vNVmP3bOXQPdscv07pSQ5cQUmOWLFmCfv36Yfv27Rg+fLit0yG2plECilQAj9s45QNCKaBVPmZZPMDJl07gScNUI9sbbSP2ihq5pWw9fx8iPgepkIdXNsRh7pMh6BDggltZSrw5INTW6ZFaVNLAPXMrG3oDQ9fm7vBwkiBmTk88v+YkLqfmI+5OLhIzCtDSyxGZBRp4OlEXZkJI1Rw5cqTctNdffx1PPfUUnn32WTz55JPw9/cHj2d+yIxevXrVdorlFBYWgs8v35OJz+dDIpGYxFnC4/Eg5RuMV00qjJU+GuFeqVSajjxd6qoJx3GQyWSWY0spG1tUVGR1MC8HB4fKxwphXDaVSgW9Xl+pcsvF6tSAqhB4uAwyqcT4w6parYHOSrkmsRoVdBoG6B6VVZpUIjauYxqNFlqdznyhHAepg8E4gItGo4FWq7WYg0QiMa4rVYnVarXQaDQWY8ViMQQCwaPYghyLV+BKx+p0OouP5AIAkVgCoYBfuViRCEKhEACg1+uhUqkevVnmqrlQKIRIJDIfW0bpWAMDipSWtw2TWIMBRUVFFmMFMmeIndwAFPdUVCotX7EUCAQQi8WViq3Kdl/lfUSp7f6x9hGlWN1HFBYCykfbCMcBslLlFhWpYLAy6r2DTApwhoexld+fPNY+ogyZTFZqH6GGrmRbNnOV2mKsGVKptHgfIZJBA6HVbdkYi7rZR1hbN0ywasjLy2MAWF5eXnVmt0tqrZ5FvL+HDfjkMAtasIO1eS+G5So1bPr/TrOI9/cytVZv6xRJLdPrDWzgp4fZM9+eMJmeq9SwQZ8Vrxdt34tha4/eZKH/2cUu3s21UaaEkLLqy3GJ4zjG4/HK/XEcZ/G90n91qaROLf0NGTLEJF4mk1mM7d27N2OKDMZSLjCWcp55uLlYjI0Mb81YynnjX5C/r8XY1q1bm+TQunVri7FBQUEmsZGRkRZjPTw8TGJ79+5tMVYmk5ks25B+PazWW+llGzOsv9XYgsTjjN0/x9j9c2zy2OFWYzMu7jfGzpr8jNXY5H93GGPfmjHRamxC7P7i5VNksMWL3rIae+rQP8bYVe+/ZzX24MGDxvr96quvrMbu2LHDGLtu3TqrsZu+W2Ws303frbIau+6LFcbvbcdPX1iN/eq/C43lHtz8g9XYVf+ZY4w9tesXq7GL5778MPYiSzi6y2rsWzMmGctNPrnTauys6VONdZaRkWE1dvLkycbYgoICq7Fjxowx2TasxVZ5H1GKh4eHxdjIiE7G9YwpMlhQYIDF2NZhoSaxrcNCLcYG+fsatwt2/xyLDLe8P/FwcymOSznPmCKj4n1EKUOGDLFab6XzHTPK+nZfkJZsjJ387DirsRnx+43rT4X7iJM7i7cNRQZ76y3r231CQoJx2RYvXmw19tSpU8bYVausb58V7SMqOt7TldyHDlxNR2aBBlOim+LaHgVe7NkMhWod9l1Jx+y+wRAJaCDqho7H4/D9xEi4O4pMpsulQmx6OQrjv/8Xl1Ly8dGeaxje3g+t/ZwBAFfT8hHs6QgBn9YRQoh1kyZNauS3PBhg7spiOfXymcEPl62i1EsvW31YTJ36UZdOtcJ6rPIBoCgewBPq/FpPzSzGHtVxpdYjg+k8lguuQrnViOUq02W2qsvWQDGDaTdjg+UrkjBoH62TJa/tXell01m+Wg8AKEgFDA+vPusquL+4uAld6oW1WIbHv23CtriHv8JUSX5+PuRyOfLy8uDs7FwbedW5yWtPISmjAM08HHAlNR+H5vXB9gup+M9f8Ti64Ak0cZFWXAhpMLR6A45cf4B+rbyN0xQqLcZ9F4vLqQo4igX4541ecJYI0GPlQbg7iPDmgFAMbusDHq8xn8ASYhsN8bhkayV1mpKSYrZOq9wVUV9QfLLJGAqVlk/ceBwHqfRRucqiokfnZRwPkLoD/OJuo4/dXVkgsXgvXZW6KzOlcdlUKjX01mJlj84nTGI5HiCQmXQxrn53ZR10nLgGuivzIHVyA0+vBBizHgtAIhaV6opYKpbjAEdfwNHzUezjdFfOvl98cm9m2cQioWl3ZY2FRg3Hg0gmhxBqgDHrsQBEQoFpd2W1xlhO2e9NKBBAJDITa4YxluPBwJeiSJFlsQFbulyDwYAilYXu1RwHgUsAxO7+AGAf3ZU1hSjMeWAxtkrdlQ1aSPGovk32EWWU7YJsjDXzvVWvuzIHODVBEd+xZrorFzyAgyHXmFNF+xOz+wgzy2Yx1gKpRAweXwDIPKDR4/G7Kz+8zaQmuivn5+fDz8+vwuM9NXIB3MtRoueqg2jjK0dCSh7+b2QbTIpqCgC4m61EgJvMegGkwfnxWDLe33EZMXN6Iszn0TquUGkx/rtYXElT4NvnI/Bka28cvJaBVTHXcDVNgbZNnPHmk6HoE+rZyK/WEFK36tNx6cCBA7h37x4iIyPRunVrq7GXL1/GmTNnEBAQgL59+9ZRhsVqvE4LHhgbgtXG8QChQw0MqAQYB4wp1fCqthpdtoLHv0pXU2XVWDnFDYEaqWvAvurb3soBara+a2oEYp0KKMpBzQ2qZif13SjW7RoawK6G6qiyxybqrgxg05l7YKy426mzRIAJXQKh0RkgEvCogdtITewWhBaeDiYNXABwkgix8eUoTFp7CrN/O4elI9ogqoUHdr3WE9svpuDjPdcxdf1phPk4YVqPZhjRwQ9iAT16ihBS7O7duxg6dCgCAgJw9uzZCuMDAgIwevRo3Lt3D4mJifDz86uDLOuDSnZ7tqZS3UMJqY84QK8pbjA9rhppnD5smNJ2W0895vdmo++s0TdytXoDNp2+i1a+TriSqsCSEW3A5zgM/PwIhof74bV+LW2dIrEBkYCHPqFeAICE+3mQCHkI9nICUNzQ/d8LXTBxzUm8vTUBrjIhtr3SAyM7NMGQdr7YcTEF3x9JxrzNF/HhP9cwrUczvNy7hS0XhxBiJ9asWQONRoNVq1bBycmpwngnJyd8+OGHGDVqFH788Ue8++67dZBlY1HDDQFiRQ3WNUD1XRnaIkCZBbtonFLDlNhAo2/k7opPRVq+CnrG0DHQBaM7NsH+KxlIzChAsJejrdMjNqY3MMz5PQ5uMhF+f7mbsQuys0SIn1/sirGrY3EtXYFRXx/Htld7oImLFKM7+mNUhyY4cSMLPxy9iYv38ozlHbyagagW7pAI6eouIY3R3r174enpiVGjRlV6nhEjRsDb2xu7d++mRm5Nq9GGALGqRuoaoPquCmqc1j76AcdeNepGLmMMa48lo4mrFDwAMx9ebVt9+Ab8XaUY0NrbegGkwePzOKx+rhOcJMJy99g6S4T4Y2YUxqw+gevpBRj19XFsf6UHfOTFN/Z3D/ZA92APaPXFB4mkDAWmrj+NpSPaYHJ0U6i0evB5HIQ0KjMhjcbVq1fRvXv3Ks8XGRmJEydO1EJGhBoCdYm6q5IGiH7AsUuN+uz63J0cXLiXh6HtfNDc0xE9WnrgWFImzt7Owey+wfRIGAIAaOntBB+5BIwxfPjPVcTdzTW+5ywR4o8Z0Wjp5YAHCjUWbLlYbv6SRmxzD0f8/lI3jOxQfE/d5rP30OW/+/D21njE3siC3tCIHwdASCNRWFgIuVxe5fnkcjkKCgpqISNCCCGPr9SjqKr7V88f2WNvGnUr7sdjyRDyOdzJKsL6qZ0hEwnw3eGbaOIixdOd/G2dHrEzeUVa7LiYiqPXTbukyKVCbJ7ZHSHejjiRlImD1zLMzs/jceja3B0usuLn8LbydUafUC/8ff4+JvzwL6KW78fS7Zdw7k6OxUdgEELqN1dXV6Snp1d5vvT0dLi6utZCRoQQQkjD02i7KyemK7ArPg0RgS4ID3AxdkX9fHwH3MlWQiRo1O1/YoaLTIRts3vAUVK82Zy9nQ0HsQBhPs6QS4uv6E768SSm/+80OgS44odJkXB1EFksLyLIFRFBrlBp9Th4NQPbL6bgt5N3sO74Lfi7SjE83A8jO/iVG+GZEFJ/tW7dGv/++y+KiopMnglpjVKpRGxsLLp06VLL2RFCCCENQ6NtyX1xIAkOIj5yi7Q4mvgAjDHoDQzujmJ0DKRfy4l5cpkQfF7xDyLLd13FvD8edU92EPHx84td0dpPjjO3czDg0yPIKbT8APgSEiEfg9v54pvnInD23Sfx2bgOCPV2wpqjN/H9kZvGOLXO8kO7CSH1w7Bhw1BYWIhly5ZVep5ly5ahqKgIw4cPr8XMCCGEkIajUTZyE9MV2H4hBV2aueHjseF448kQbL+YiuFfHkOGgkY1I5Xz45TOWP5UOwCARmdAlw/24++4FGyZGY3uwe54UKBGj5UHcC9biVuZhZj440mcu5MDALiVWYiFWy7iUkqeSZmOYgFGdWyCH6d0xul3+uPNAaEAgPh7eej2wX6cvZ1dtwtJCKlRM2bMgLe3N1asWIFly5bBYLB8D5bBYMD777+PFStWwNvbGy+//HIdZkoIIYTUX42yu/IHu68AKL7Hu0NgcXfR1zech4eTGB4OYhtnR+oLuVQIeZPiAWSKtHqMjfBHC08HCPk8fDimPfp9fBiFGj2e+PgwPn6mPQrVOmh1xSe0mQVqHLyWgSndmwIATiVn46+4+3hrQCjcHnZxdpGJ4CIr/iyJkIfeIZ4I8S5+rubZ2znwlUvg50Kj8BFSn8hkMmzZsgX9+/fH4sWL8cMPP2Ds2LHo1KkTPD09AQAPHjzAuXPn8Mcff+DevXuQSCTYsmULZDKZjbMnhBBC6odG18g9nZyFg1cfQMjn4OciRWpeETafuYeUPBU+n9ARPB5XcSGElCGXCrFoSCvjaz8XGa68Pxg/HruJD3ZdxcI/4/HpMx3Qtbk7ACCyqRtOvt3fGH/jQQEOXs3A4uGtAQBKjQ4y0aPNs6W3Ez4b3xFA8aOvFm65iNtZSozrHICZfVpQY5eQeiQ6OhonTpzAxIkTcenSJXz66aflYkoGn2vTpg1++eUXhIeH13WahBBCSL3VqLorGwwMc36/AAAY08kfm8/eQ2K6At8cuoGh7XzRuambjTMkDc20Hs1xeF4fBHs54aWfz2L6T2dQpCl/b+2ELoE4tuAJiAV86A0MY7+NxX93XjZbJsdx+N8LXTCucwB+P30XfT48hP/bfhm5yorv/yWE2IcOHTogPj4eu3btwqxZsxAdHY3Q0FCEhoYiOjoas2fPxq5duxAfH1/tBu6RI0cwfPhw+Pn5geM4/PXXXzW7EIQQQoidalRXcn88loz7uUVo6eWI/45uh4WDW+HLA4kQ8Dj8Z1irigsgpBr8XWX44+UojPsuFnsvp6PnqgNYN6UL2vmbPiuzZEArvYFhYBsfhPk4GV/rDcxkxG8/FyneH9UWM/u0wFcHk7D+RDK2nLuH1/u1xPPdgmh0cELqiUGDBmHQoEG1UnZhYSHCw8Pxwgsv4KmnnqqVzyCEEELsUaM5E07LK8LKmKvgccA3z3UCj8dBLivuYrplVjR85dTdk9QekYCHX17sioggV2QWaDDiq2P4eM9VaPXlB50RCXh4rV9LDGjjAwD49eRtDP3iqNmRmv1cpPhgdDvEzOmFjoEu+L8dlzHg08P451IaPWuXkEZu8ODBWLZsGUaPHm3rVAghhJA61Siu5DLGMGXdaegMDK/0DcaiP+MR4CbD/EGh8JVLjYP5EFKbHMQCbHo5Cp/uvY6vDybhywM3sCs+DV9M6Ig2fnKL8zXzcECXZm5wkQkBFF/Z5Ze5dzzE2wnrp3bB4esP8N+dl/Ht4RsY0Nq7VpeHENKwqNVqqNVq4+v8/Pxa+BQewFkeUbpS89dIOTVZlr2VY4850bLVXTn2mBMtW/3MqabLqVscq8blnvz8fMjlcuTl5cHZ2bk28qpRn+27js/2JaKZhwP+mdMLn++/js1n70EuFSLm9V402BSpc+fu5ODNTReQX6RFbpEWM3o3x6tPtIREyLc63wOFGmO/PYFlo9qhR0sPszE6vQHZhRp4OUuQnq/CJ3uu480BIfByltTGohBiF+rbcamucRyHrVu3YtSoURZjlixZgqVLl5abXmN1qikENMrHL4fjAexxTyZruCx7K6cmy7K3cmqyrIZaTk2WZW/l1GRZ9lZOTZZlb+WIZIDI4fHLQeWP9w3+Su6ZW9n46kAiPJ3E+PXFLuBxwKWUfGQVaPDZOBpNmdhGp0BXHHizN/JVOizbcRlfH7yBTWfu4ovxnRDVwt3ifCqtHv6uMvi5FDdYC9U6SIV8k/VYwOcZG7Tn7+Rid0IqXu0XXLsLRAip9xYtWoS5c+caX+fn5yMgIKDmPkDkUGMnOYQQQog1DbqRm5RRgJd+OoNAdwdsndUdtzILMX9zPI4lZWLl0+2sNiYIqW0cx0EuFWLewFCcu5ODGw8KMeGHf9GlqRu+fLYjvM1ceQ1wk+GXF7saX7/39yXczCzAnzOjwXHlf7AZ1NYHPVt6wEEsAGMMr2+MQ3QLd4yNDCjX5ZkQ0riJxWKIxfSseEIIIfVfgx14KjmzEE+vPg6FWoePx4RDLhXivb8TcCwpE3OfDMG4zoG2TpEQAICXswT75vbGN891goejCKduZaPb8v1YfSgJBoP1uwmeCPPCiHA/YwN3zdGbSMooMIlxEBf/lqVQ65CWp8LCP+Mx9IujOHL9Qe0sECGEEEIIITbUIK/kXribi5d+PgMDA9r6ydHKt3hgqV+mdcUvJ29jZh/quknsC8dxGNLOF4Pa+OC3U7fxxf4krIy5hn1XMtApyAX+LjL0DfVCoLvMZL6h7X2N/0/LU2FlzFUI+TwEezlCpdUjV6mFj7z4irCzRIjfX+6Gfy6lYcXuq5i09hR6h3hi/qBQqwNfEULqp4KCAiQlJRlfJycnIy4uDm5ubggMpB96CSGENFwNauApxhj+OHMP7/wVD1+5FGsmReBKmgLfH7mJ/03tAg8n6oZF6gfGGLaev4//7ryCrFKPDvJ3laJ7Cw8MauuDvmFe5ebLVWog4PPgKBZgV3wqZv92Dttf6YG2TUwbsRqdAT//extf7E9EXpEWT4R5YXbfYEQEudb6shFSG+z1uGRLhw4dQt++fctNnzx5MtavX1/h/FSnhBBC7E1lj00NppF7KSUPK2Ou4cj1B3CVCTGknS+upObj3J1c+LtKwQH4c1Z3eFJDl9QjeUotVv1zFb+evAMHER8BbjKk5aswvnMgFg4OQ4Fah/Hfx6KNrxxtmzijla8zwnyd4SgWICW3CDsupuDFHs3B43FYc/QmbjwoxH9HtTUOVKVQafHzv7fx49FkZBVqMDbCHx+ODbfxUhNSdfZ4XKrvqE4JIYTYmwY9urJOb0C2UoP0PDXO3s7GroQ0nErOhpOYj7ZNnJFwPx+/nrwDH2cJPhobDj+5BNsvpsLDUWTr1AmpErlMiP+ObofxnQPx0Z5rOHz9ATwdRfBwFEGl1SOvSAt3BzH2XUnH72fuGuf7+tlOGNreF8Pa+2HvlXS09nVGXpEWeUUaYwP3VHI22vvLMatPMKZGN8PG03fg4Vj8I1C+SovNZ+7h6Qh/yKVCmyw7IYQQQggh1VEvr+S+szUev568Y3wtE/Hh7yJBpyA3bDx9F12bueHpCH8Mb+8Hqcj6c0cJqU/O3MrGx3uuI/ZmFlxkQoyN8MeELoFo5uGA9Hw1rqTm40paPoa180OguwwbTt3Boj/jAQBiHoOvVI/ubZvhxR7NMfDzo5gcFYR3hrYu9zk7LxZ3dd7xanFX59S8IjiKBXCSUIOX2CdbH5caIqpTQggh9qZBd1d+6acz2HM5HUBxA7e5hwMKNXokZxZiZp8WWDAoDADw6d7rEAl4mNWnhdnHqxBSX51KzsZPsbfwz6U0aPUMYT5OeCLMCx0DXRHuLzc+J1el1eN6ugIJ93Kx/dg5pBXxkcukOL6gL87eycXmM/dw7k4O3B3FyFSo8WLPZujbygtOYiGyC9UI9ioetO31jeexOyENUc3d0TvEE71DPdHcw4G2K2I3bH1caoioTgkhhNibBt3IzS7UwMAYnCQC8DkOb/5xAX/HpWBO/5Z4vV9LcBwHxhjmb74IAZ/D8qfa13mOhNSFBwo1tl9Iwd7L6Th9Kxu6h48cchIL4OUshoNYAI7jwIHhQWY2VHpAzxejUKOHVm990xfyOfi7ShHi5QQfuQQ5Sg0upyqMjyjylUsQEeSKyCBXRDZ1Q5iPEwT8BvtUMmLnbH1caojstU6VGh2KNPoaKUsq4kMmqpd3bhFCSKPUoBu5JbILNXh943kcTczE20PC8FKvFgCAArUOjmIBDAYGnYFBJKATb9LwqbR6XE7Nx8W7ubiTXYQMhQoqrR4GBugNBmSkpULMZ2gXGgxnqRBOEuHDLsgCOIgEKFRrEX8/H4UaHWJvZCG/SAuFWgfGYGw8C/kcwv1d4O0sgUqnx9VUBe7nFgEAhof74csJHcEYw5Zz99G1mRsC3GTWUiakxtjLcakhsdc6zSpQIz1PDQOqfPpiggcO3nIx3B1pQEpCCKkvGvTAUyVm/nIWcXdz8fHYcDwd4Q8A+HJ/IrZfTMHWWd3hIBZAxKPulKRxkAj56BToik6B5R8DpNPp8McffwAAxg5rBYHA/KY/smPxv1fT8pGWp0KGQo19l9ONtwcAwL0cJc7czgEANPNwwPjOAfByEqNzUzcAQFq+Cm/9cQHLRrXF892CkJxZiC/3JyLY2xEhXk5o6e2IAFeZcQAsQgipKgMYqv4TfZkyuMcsgBBCiN2qd41cjc4Ard4AB7EA7w1vjTylFlfTFMhQqODlJEE7fzmKtHpIhDTgFCHVFebjjDCf4l/HRoT74fsjNyDg8ZCap0LfME+8sP4MujV3w6WUfGw6cxcGBkgEPDzRygtdmrnh/0a0QZ9QTwBAam4RTiZn48/z943lS4Q8tPB0REsvR7T0dkJLL0dEB3vAUVzvdkmEEEIIIcTO1KszSr2B4anVx9He3wUfjG6HNn5y3M4qxLNrTkIo4GFityD0CfVCn1AvW6dKSIMhEfLxWr8Q42ulRoc1kyKRp9KCnb6Ls7dzYGAMGr0Bey+nY1d8GgDg832JiGjqCncHIXgcsGF6V0iFfJy5nYPLqfnILtDgzO0c/BWXAgA49FYfOIoF+Ov8fRy6loGPxoZDwOdBodLC8eG9xYQQQgghhFTE7hu5Or0Bx29koVdLD/B5HIa080Vr30f9r/1dZbiweACcJXa/KIQ0CDKRAP1bewMAnu7kD6VGh9O3cnAiKRM3MwvxYo9m2BWfin8upZl0c57ww0kI+Rw8ncRIyVWhfRM55FIhHIR86BjD+zsuIaKpGyQCPm5nK7Hoz3gotXqcuZWD7EI13BxEaOMnf7gPcEJSRgF85FJ4OYnh5SymwWMIIVXCobh3WFaB+rHLogGsSENVUwO9NeRthAbDs092WYuFah3+vZmFo4mZ+OdSGlLzVNg8IwqRTd0wq0+wSSyfx0EupWd3EmIrMpGg+LFCIZ7GaV2bu2NAGx9cT1fgZmYhbmYUIKtQAwBwlPBRpNHj4v08k3JuPCjEiRvZ8HORwEcuxcFrGWAM0OoN4PM4ZCrUOHL9AQ5czTCbh5NEgHeGtML4LoHIVWqw70oGwnycEOzlSLcvEPIYCgsLweeX34b4fD4kEolJnCU8Hg9SqbRasUqlEqXHyCwsVEOpVIExgOM4SKWPBrgrKjKNLa1srEpVhGytCkVag9lBrGQyh0exRUUwMIP5fMGhma+b8cRUpVJBr7d8wuvgUKrcCmJlMpmxF4tarYZOp6t0bL5SZfHEWyqVgscrHpRTo9FAq9VazlcmBbjKxUokEuO6UjaWxwEGZj5Wq9VCo9FYLFcsFhvHktBqteBDb7EhUDpWp9NBrbb8I4ZIJIJQKKxyrF6vh0qlshgrFAohEomqHGswGFBUVFQjsQKBAGJx8aBqjDEolcpqxWYVqJGR/2igNz6PD3Gp7V6ptLwtl8TywMHVQYjMnHyLsVXZRzhIhHCXO5XKwfp2L5PJqhVbVFQEg8H8dg882paLNHrcTsuFjlnblh9t92qVCnpD+VgeOHg5ixHo7WacVpv7CGuxVdlHVCXW2j7CWmzpfYS1dcMEq4a8vDwGgOXl5VVndhM5hWq2YvcV9s7Wi2zK2pOs58oDrOnCHSxowQ7W6t3dbNr602zf5TSm0xse+7MIaay0Wi377bff2G+//ca0Wq2t02GMMabR6dmdrEJ24Eo6++rAdfbFvutsweY4FvafXazt4hgW8f5e476g9F+LRTtYu8UxrN3iGBb6zi4WtGAH67D0Hzb0i6Ns0ZYL7LkfYtn8zReM8c0X7WQDPjnM5mw8z25kKBhjjOlpf9Lg1ORxiRQrqVNLf0OGDDGJl8lkFmN79+5tEuvh4WExNjIy0iQ2KCjIYmyLkDB28W6u8a9FSJjFWD//AJPYNuEdLca6urmbxEZ2624xViqVsUyFypjvkCFDrNZbaWPGjLEaW1BQYIydPHmy1diMjAxj7KxZs6zGxsReYPH3cln8vVw25eVXrcceOcUu3ctj8fdy2cw3FliN3bDjgLHcue/8n9XYtZu2G2PfXvah1div//e7MXbZJ99Yjd20aZOxHjZt2mQ1dt26dcbYHTt2WI396quvjLEHDx60Grtq1Spj7KlTp6zGLl682BibkJBgNfatt94yxiYnJ1uNnTVrljE2IyPDauzkyZONsQUFBVZjnxw60mTbsBbb84kB7OLdXJZwP5fdzFAwqdTyPiKyW3fjdxx/L5e5urlbjO3QKaLS+4jWrVubxLZu3dpibFBQkElsZGSkxVgPDw9jXKZCZXUfIZHKTOqs5xMDrNabPewjkpOTGWOMFaq1bPZrb1iNPXbqHMtUqFimQsXmLXrHauypU6eMOaxatcpq7MGDB42xX331Vbn3Kzre2/xKrlpnwI/HkuEsEcDbWYKOgS4YE+GPyKauiAhyhVhAV2AIaYiEfB4C3GQIcJOhb9ij++hf7h0MtU6PMB9nZBao0fW/+/FMZ3/0DvFCal4RkjMLodEZkKvUIkepQU6hBtlKDa6nK5BgvDqcZSxPb2BIyihA0gMFktIVcHUQQcDjcO5OLjycxPB0FGF8l0BEBLnCTSaCVMSn+38JqQWlu/RZGxlZZ2AmXYgNjzuMMimHsUffQWVqt2Q064piq1IuQ6n1oIJg03Ib7vpQpLV8ZQ0ovmJYsm3kFFrvZq/TW74Caa9svakbmOm+R2ewnBBjMMaqtTXTVdkeFWn0UKqtr5cPFGrI84p7KxSorMfWJZs/J5cxRieUhNQyk0cIjR1r8RFC9kat0+N4UiZaeDoiyN0Bp29lY+y3sdgwvRuiWrgj7m4ufvn3NuYPDIWXswR7L6fhfydu4bV+LaHWGfDF/kScvpVT6c8T8gCOx4OfXAKpkA8ej4OXkxihPs5wlgrgJBHCWSKAs0QIJ8nD11IBXGUi6hJtY/b6TNf6rKROU1JSzNZpVbsrK/U84/NtrXVx5HE8SEp1WyzdBZnPcZAIeCjU6h+7u7JGXQQJnzOWVVZluytzHNDC1934vF176a6cnluItHyV2WWTSB51L9RqNNDqzHcZ5PEANydHFOmKG7nWYgFALC7VvbBULI8HyAR8k7o2idVqodVa7q4sEj3qgqzXaeEkBIQCnoUcKt9dWe4ohdxBWqlYa92Vy96TWd3uykVqLdKyFRafAS0UCCEs1V1ZpTLfXZkHDh7OUjg9XDb2GN2VNVo9sou0xu+tWt2VeYBMyMeD3HyLDdmy272lcjkO8HORwd/TpVRs9borl+2KXe6WBivbPVC8j+BzHCRCHrLyCqC30rW5Ut2VOcBNJoJLqa7Y1d1HmLu3tzrdlbMK1LjzIB8aq92Kre9POA7wcZbA3VFcI92V8/Pz4efnZ//PyaUGLiHEErGAjyfCvI2vA91keG9YawR7OQIAMhVq/HszC2pd8YFFp2fIUWrR1MMBXk7FDdWTydkY2cEPCffzcSzpAa6lKXArsxAPCh6dUI3vHIBcpRbJmQXILNAgR6nBraLinf8lAAevPahErhz4HAdXBxGC3B0gE/ERdycXIT5OaObhAI3OgO0XUjAs3Bdtm7ggPa8Ia4/fwvxBoZgc1RQJ9/Pwzl8JeKN/CPq39kb8vVysOZqMJq5S8DgOGr0BBsaMVzTYwysrYyL80baJHNfTFfgp9hZm9G4Bf1cZjidmYmvcfRgYg95Q/NcrxBPPRAaYzV+nN8DAANHDE8ecQg14HAe5jMY8aOwcHBxMGmbW4qxRFqiNVwSlUuuxpc9XJZJHJ50lJ8tMY75hWvoEtSISqdRqWWVjLSl7GlO64V9hDmViyzaWVIVlG36WT9vKxgpEEshk/AqXTSgSGRtOZfF4eHjyqq8w1lq5FX1vQqHQ2ICsuFwheEI+CjTm76WGTgeg9Mm7+R8geeAg1AI6k4HHrNSv2gCozcdqwaFAxz3KR2cAiko3bK38CPowtqSxJJHJrH5nJe9xHM/idsTjAYzHN/6oVHEODFCVz5fPcZCIRZBxIos5lW68VUQmc6j01VpL5fI4gC8UlRkwzsqyMaDIQqxAxEFSZhsp/X+xxPJ2XxJb8rxtiVRa6WUTW9hH8HgAT1j2ezPNuaz8/LI/zPDBAwcHBzEcHMSWcxCLjT9sVEQoEkEgrPp2X4LjAAcHSbl8RCKR8QeeCssttY+w1ug3+VxbX8klhNS++noltzZlFahxLU2BO9lKjOscAI7j8Mmea4i9mYUN07vhZmYhZv16DkkZBRWW5SgWIMzHEWdu58JRzIezRAi1zmAcbKsqRHwOThIhirR6KM0MGlNyPl2y45aJeODzeFBqdNAbAD4H6C3s1d0dRDj77pMAgOk/nYFSo8OvL3YDAIz8+jjcHURYO6UzAKDfx4fQxk+OLyZ0rPIyaPUGKDX64m5OGh3kUiHcHcUoUOtwLDETRVodijQG6AwGDGvvBzeHyh3krKHjUs2r6TrNKlAjNc/8lcXKKmksFVaiYVpXZfE4wM1BZPyB6HGotXrkKnUWr+RVVkmD6bGXrabqyB6/t4flFFlqLFeSvdV1TZZlb+WULou+N8s4DvCVS4y9Sx5HTey3azIfoPLHJjrTJYQ0Su6OYkQHixFdatrcAaHG/4d4O+H3l7ohs0ADhUoLjd4Ajc4Atc6AezlKZOSrkKHQQKc3QCYSIKqFG+b0D4FWzzDtf6dR9laeCZ0D0LmZG66nK/Dt4ZsQ8AABnwceAI7H4clW3nBzEOFOlhL/JmcDYJAKixuwHAeE+8uRo9TCSSLA5ZR8aPUMWr0BQj4fHAd0beqGdIUaPs4SXE1TQK3TQ2dgcJYIIRLwEO4vh5uDCJ/vS8SZ29nIyFeB4zjM/OUs/FykmNQtCBIhH98evoGU3CI0cZGhUK3Doj8vooWnI17s2RwA8M7WeGQXah41YrU69G/ljTn9Q6DW6dFu8R5oytwL9taAELzyREtkFagx45ezJu9FBLnWSCOXEJvhAJVWj5xCbY2cdJdc7X4cJVeXSMUet76prm2DvjdSEWrkEkKIBe6O4mr98pj03yHIK9Iiq1CDrAI1CtQ6hHg7IcBNhtS8IshEAhQ+7JZY0gV5UlRThPo44cLdXMhjbwN4OMDKw+PwWwND4edS/GilrefuP3wfxnuLVo1pD5lIgM1n7+HA1eLnE5d0bRYJeMYrsp/suQaVVg+pSACdwYDkzEJo9Qa8O6w1AGDKulOIv1c8gBePx4Gfwpl0n0zKKECuUvvwfh8+fKQSuD9spIr4PLzUqzmkIj6kwuL3pSI+2vgV/9LqK5ciZk5PyIQCSEQ8CHk8ONEzzkkDQSfdhBB7UJPPAK/Pg2pRd2VCGgHqrkwaOjou1Tzqrlw/y7HHnGjZ6q4ce8yJls02OdlLl27qrkwIIYQQQggh5LE19t4ljz9KAiGEEEIIIYQQYieokUsIIYQQQgghpMGgRi4hhBBCCCGEkAaDGrmEEEIIIYQQQhoMauQSQgghhBBCCGkwqJFLCCGEEEIIIaTBoEYuIYQQ0kB9/fXXaNq0KSQSCbp27YpTp07ZOiVCCCGk1lEjlxBCCGmAfv/9d8ydOxeLFy/GuXPnEB4ejoEDByIjI8PWqRFCCCG1ihq5hBBCSAP0ySefYPr06Zg6dSpat26Nb7/9FjKZDGvXrrV1aoQQQkitElRnJsYYACA/P79GkyGE1A6dTgelUgmgeLsVCKq16RNit0qORyXHp8ZOo9Hg7NmzWLRokXEaj8dD//79ERsba3YetVoNtVptfJ2Xlweg5o71igI1lAo1DKj+d8TnOOiFPKg0hscqpybLsrdy7DEnWra6K8cec6Jlq5851VQ5PHBQcBoIDeJql1FaZY/31TrTVSgUAICAgIDqzE4IsaEXX3zR1ikQUmsUCgXkcrmt07C5zMxM6PV6eHt7m0z39vbG1atXzc6zfPlyLF26tNx0OtYTQgixNxUd76vVyPXz88Pdu3fh5OQEjuOqnVyJ/Px8BAQE4O7du3B2dn7s8hoiqqOKUR1ZR/VTMaqjitlrHTHGoFAo4OfnZ+tU6q1FixZh7ty5xtcGgwHZ2dlwd3d/7GO9va43lUX52xblb1uUv21R/qYqe7yvViOXx+PB39+/WolZ4+zsXC+/vLpEdVQxqiPrqH4qRnVUMXusI7qC+4iHhwf4fD7S09NNpqenp8PHx8fsPGKxGGKxaXcyFxeXGs3LHtebqqD8bYvyty3K37Yo/0cqc7yngacIIYSQBkYkEiEiIgL79+83TjMYDNi/fz+ioqJsmBkhhBBS+2j0GUIIIaQBmjt3LiZPnozIyEh06dIFn332GQoLCzF16lRbp0YIIYTUKrto5IrFYixevLhcNynyCNVRxaiOrKP6qRjVUcWojuqPcePG4cGDB3jvvfeQlpaGDh06ICYmptxgVHWhvq83lL9tUf62RfnbFuVfPRyj5y0QQgghhBBCCGkg6J5cQgghhBBCCCENBjVyCSGEEEIIIYQ0GNTIJYQQQgghhBDSYFAjlxBCCCGEEEJIg1Fnjdyvv/4aTZs2hUQiQdeuXXHq1CmLsevXrwfHcSZ/EomkrlKtc0eOHMHw4cPh5+cHjuPw119/VTjPoUOH0KlTJ4jFYgQHB2P9+vW1nqctVbWODh06VG4d4jgOaWlpdZOwDSxfvhydO3eGk5MTvLy8MGrUKFy7dq3C+f744w+EhYVBIpGgXbt22LVrVx1kW/eqUz+NbV+0evVqtG/f3vjA9qioKOzevdvqPI1l/SGPpyrnAHVlyZIl5bbvsLAw4/sqlQqzZ8+Gu7s7HB0d8fTTTyM9Pd2kjDt37mDo0KGQyWTw8vLCvHnzoNPpaiXfio6DjDG899578PX1hVQqRf/+/ZGYmGgSk52djeeeew7Ozs5wcXHBtGnTUFBQYBJz8eJF9OzZExKJBAEBAVi1alWd5D9lypRy38egQYPsJv/KHENqap2pjXO8yuTfp0+fct/BjBkz7CL/io5P9lz3lcnfnuvenBUrVoDjOMyZM8c4ze6+A1YHNm7cyEQiEVu7di27dOkSmz59OnNxcWHp6elm49etW8ecnZ1Zamqq8S8tLa0uUrWJXbt2sXfeeYf9+eefDADbunWr1fibN28ymUzG5s6dyy5fvsy+/PJLxufzWUxMTN0kbANVraODBw8yAOzatWsm65Fer6+bhG1g4MCBbN26dSwhIYHFxcWxIUOGsMDAQFZQUGBxnuPHjzM+n89WrVrFLl++zP7zn/8woVDI4uPj6zDzulGd+mls+6Jt27axnTt3suvXr7Nr166xt99+mwmFQpaQkGA2vjGtP6T6qnoOUFcWL17M2rRpY7J9P3jwwPj+jBkzWEBAANu/fz87c+YM69atG4uOjja+r9PpWNu2bVn//v3Z+fPn2a5du5iHhwdbtGhRreRb0XFwxYoVTC6Xs7/++otduHCBjRgxgjVr1owVFRUZYwYNGsTCw8PZv//+y44ePcqCg4PZhAkTjO/n5eUxb29v9txzz7GEhAS2YcMGJpVK2XfffVfr+U+ePJkNGjTI5PvIzs42ibFl/pU5htTEOlNb53iVyb93795s+vTpJt9BXl6eXeRf0fHJnuu+Mvnbc92XderUKda0aVPWvn179vrrrxun29t3UCeN3C5durDZs2cbX+v1eubn58eWL19uNn7dunVMLpfXRWp2pzINuPnz57M2bdqYTBs3bhwbOHBgLWZmP6rSyM3JyamTnOxRRkYGA8AOHz5sMeaZZ55hQ4cONZnWtWtX9vLLL9d2ejZXmfppzPuiEq6urmzNmjVm32vM6w+pvKqeA9SVxYsXs/DwcLPv5ebmMqFQyP744w/jtCtXrjAALDY2ljFW3Gjj8XgmP3ytXr2aOTs7M7VaXau5lz0OGgwG5uPjwz788EOTZRCLxWzDhg2MMcYuX77MALDTp08bY3bv3s04jmP3799njDH2zTffMFdXV5P8FyxYwEJDQ2s1f8aKG7kjR460OI895c9Y+WNITa0zdXWOZ+4Y2Lt3b5NGS1n2lD9jj45P9a3uy+bPWP2pe4VCwVq2bMn27t1rkrM9fge13l1Zo9Hg7Nmz6N+/v3Eaj8dD//79ERsba3G+goICBAUFISAgACNHjsSlS5dqO9V6IzY21qQ+AWDgwIFW67Ox6tChA3x9ffHkk0/i+PHjtk6nTuXl5QEA3NzcLMY05nWpMvUDNN59kV6vx8aNG1FYWIioqCizMY15/SGVU91zgLqSmJgIPz8/NG/eHM899xzu3LkDADh79iy0Wq1J3mFhYQgMDDTmHRsbi3bt2sHb29sYM3DgQOTn59f5fiI5ORlpaWkm+crlcnTt2tUkXxcXF0RGRhpj+vfvDx6Ph5MnTxpjevXqBZFIZIwZOHAgrl27hpycnFpfjkOHDsHLywuhoaGYOXMmsrKyjO/ZW/5ljyE1tc7U1X7V0jHw119/hYeHB9q2bYtFixZBqVQa37OX/Msen+pb3Vs6vtaHup89ezaGDh1a7nPs8TsQVHmOKsrMzIRerzdZIADw9vbG1atXzc4TGhqKtWvXon379sjLy8NHH32E6OhoXLp0Cf7+/rWdst1LS0szW5/5+fkoKiqCVCq1UWb2w9fXF99++y0iIyOhVquxZs0a9OnTBydPnkSnTp1snV6tMxgMmDNnDrp37462bdtajLO0LjXke5eBytdPY9wXxcfHIyoqCiqVCo6Ojti6dStat25tNraxrj+k8qpzDlBXunbtivXr1yM0NBSpqalYunQpevbsiYSEBKSlpUEkEsHFxcVkntLrt6X1v+S9ulTyeda2x7S0NHh5eZm8LxAI4ObmZhLTrFmzcmWUvOfq6lor+QPAoEGD8NRTT6FZs2a4ceMG3n77bQwePBixsbHg8/l2lb+5Y0hNrTN1cY5n6Rj47LPPIigoCH5+frh48SIWLFiAa9eu4c8//7SL/C0dn+Li4upF3Vs7vtp73QPAxo0bce7cOZw+fbrce/a4/td6I7c6oqKiTH7ZiI6ORqtWrfDdd9/h/ffft2FmpL4IDQ1FaGio8XV0dDRu3LiBTz/9FD///LMNM6sbs2fPRkJCAo4dO2brVOxSZeunMe6LQkNDERcXh7y8PGzevBmTJ0/G4cOHLTZ0CamvBg8ebPx/+/bt0bVrVwQFBWHTpk30Y7ENjB8/3vj/du3aoX379mjRogUOHTqEfv362TCz8ur7MdZS/i+99JLx/+3atYOvry/69euHGzduoEWLFnWdZjmWjk/1hbXjq73X/d27d/H6669j79699WYAzlrvruzh4QE+n19udK309HT4+PhUqgyhUIiOHTsiKSmpNlKsd3x8fMzWp7OzMx2YrejSpUujWIdeeeUV7NixAwcPHqzwaqOldamy22Z9VJX6Kasx7ItEIhGCg4MRERGB5cuXIzw8HJ9//rnZ2Ma4/pCqqYlzgLri4uKCkJAQJCUlwcfHBxqNBrm5uSYxpfO2tP6XvFeXSj7PWj37+PggIyPD5H2dTofs7Gy7XKbmzZvDw8PDuL+1l/wtHUNqap2p7XO8qhwDu3btCgAm34Et87d0fKovdV+V46u91f3Zs2eRkZGBTp06QSAQQCAQ4PDhw/jiiy8gEAjg7e1td99BrTdyRSIRIiIisH//fuM0g8GA/fv3W7zPqyy9Xo/4+Hj4+vrWVpr1SlRUlEl9AsDevXsrXZ+NVVxcXINehxhjeOWVV7B161YcOHCgXJctcxrTulSd+imrMe6LDAYD1Gq12fca0/pDqqcmzgHqSkFBAW7cuAFfX19ERERAKBSa5H3t2jXcuXPHmHdUVBTi4+NNGl579+6Fs7Nznfd8aNasGXx8fEzyzc/Px8mTJ03yzc3NxdmzZ40xBw4cgMFgMJ5QR0VF4ciRI9BqtcaYvXv3IjQ0tFa7Kptz7949ZGVlGfe3ts6/omNITa0ztbVfrc4xMC4uDgBMvgNb5W9OyfHJ3uu+ovzNsbe679evH+Lj4xEXF2f8i4yMxHPPPWf8v919B1UeqqoaNm7cyMRiMVu/fj27fPkye+mll5iLi4txdK2JEyeyhQsXGuOXLl3K/vnnH3bjxg129uxZNn78eCaRSNilS5fqIt06p1Ao2Pnz59n58+cZAPbJJ5+w8+fPs9u3bzPGGFu4cCGbOHGiMb5keO158+axK1eusK+//rrBP0KoqnX06aefsr/++oslJiay+Ph49vrrrzMej8f27dtnq0WodTNnzmRyuZwdOnTIZAh6pVJpjCm7rR0/fpwJBAL20UcfsStXrrDFixc32EfAVKd+Gtu+aOHChezw4cMsOTmZXbx4kS1cuJBxHMf27NnDGGvc6w+pvorOAWzlzTffZIcOHWLJycns+PHjrH///szDw4NlZGQwxoofhxEYGMgOHDjAzpw5w6KiolhUVJRx/pLHYQwYMIDFxcWxmJgY5unpWWuPEKroOLhixQrm4uLC/v77b3bx4kU2cuRIs48Q6tixIzt58iQ7duwYa9mypckjeHJzc5m3tzebOHEiS0hIYBs3bmQymaxGHsFjLX+FQsHeeustFhsby5KTk9m+fftYp06dWMuWLZlKpbKL/CtzDKmJdaa2zvEqyj8pKYn93//9Hztz5gxLTk5mf//9N2vevDnr1auXXeRf0fHJnuu+ovztve4tKTsitL19B3XSyGWMsS+//JIFBgYykUjEunTpwv7991/je71792aTJ082vp4zZ44x1tvbmw0ZMoSdO3eurlKtcyWPuyn7V1InkydPZr179y43T4cOHZhIJGLNmzdn69atq/O861JV62jlypWsRYsWTCKRMDc3N9anTx924MAB2yRfR8zVDwCTdaPstsYYY5s2bWIhISFMJBKxNm3asJ07d9Zt4nWkOvXT2PZFL7zwAgsKCmIikYh5enqyfv36GU8gGGvc6w95PNbOAWxl3LhxzNfXl4lEItakSRM2btw4lpSUZHy/qKiIzZo1i7m6ujKZTMZGjx7NUlNTTcq4desWGzx4MJNKpczDw4O9+eabTKvV1kq+FR0HDQYDe/fdd5m3tzcTi8WsX79+7Nq1ayZlZGVlsQkTJjBHR0fm7OzMpk6dyhQKhUnMhQsXWI8ePZhYLGZNmjRhK1asqPX8lUolGzBgAPP09GRCoZAFBQWx6dOnl/shxJb5V+YYUlPrTG2c41WU/507d1ivXr2Ym5sbE4vFLDg4mM2bN8/kWa22zL+i45M9131F+dt73VtStpFrb98BxxhjVb/+SwghhBBCCCGE2J9avyeXEEIIIYQQQgipK9TIJYQQQgghhBDSYFAjlxBCCCGEEEJIg0GNXEIIIYQQQgghDQY1cgkhhBBCCCGENBjUyCWEEEIIIYQQ0mBQI5cQQgghhBBCSINBjVxCCCGEEEIIIQ0GNXIJIYQQQogJjuNM/ng8HuRyObp164bPPvsMWq3WZrmtX78eHMdhyZIlNVZmUlISRCIR5s2b99hl9enTBxzH4datWybTmzZtCo7jHrt8SziOQ9OmTWut/Lr+nNLOnz8PjuOwatWqOv1cUn8JbJ0AIYQQQgixT5MnTwYA6PV63Lp1CydOnMDJkyexY8cOxMTEQCBoGKeSixYtgkgkwvz5822dCjGjY8eOGDFiBJYvX44XX3wRbm5utk6J2Dm6kksIIYQQQsxav3491q9fj59//hlHjx7FiRMnIJFIsH//fmzcuNHW6dWIc+fOYfPmzZg2bRo8PT1tnY7du3LlCvbv31/nn7to0SLk5uZi5cqVdf7ZpP6hRi4hhBBCCKmUrl27YsqUKQCAf/75x7bJ1JDVq1cDACZNmmTjTOqHsLAwtGjRos4/t1u3bggODsbatWuh0Wjq/PNJ/UKNXEIIIYQQUmlt2rQBAGRkZJhMZ4xhw4YNGD9+PEJCQuDg4AAnJyd06dIF33zzDQwGQ7mylixZAo7jsH79esTHx2PEiBFwdXWFg4MDevfujRMnTlQpt48//hg8Hg9hYWG4e/duhfEFBQXYuHEjWrZsiYiIiHLvp6amYtWqVejduzeaNGkCkUgEHx8fPPXUUzh9+nSVcquumJgYjBgxAt7e3hCLxQgICMCwYcOwZcsWs/F6vR4rV65ESEiIMX7BggVQq9XlYuPi4jB//nxERETA09MTYrEYzZs3x6xZs5CSkmK2fHP35B46dAgcx2HKlCnIzs7GzJkz4evrC7FYjLZt22Lt2rVmy0pISMDzzz+P5s2bQyKRwNPTEx06dMCcOXOQmppaLn7ChAnIzMzE1q1bK6g10thRI5cQQgghhFSaQqEAAHh5eZlMV6vVePbZZ7Fv3z74+Phg+PDh6NatGy5duoTZs2fjhRdesFjmmTNn0K1bN9y6dQsDBw5Ey5YtceTIEfTr1w8JCQmVyuvtt9/GW2+9hYiICBw7dgwBAQEVznP48GEUFBSgT58+Zt//+++/sWDBAqSnp6N9+/YYPXo0/Pz8sHXrVnTv3h179uypVG7V9eabb2Lw4MHYuXMnWrZsiaeffhotWrTA8ePH8f7775ud59lnn8WyZcsQGhqKAQMGQKFQYNWqVZg2bVq52BUrVuDTTz8FAPTo0QNDhgwBYwyrV69GZGSkxYauJbm5uYiKisK2bdvQs2dPdO/eHVevXsW0adOwZs0ak9izZ8+ic+fO+PXXX+Hk5ISRI0eiW7du0Gq1+Pzzz3Ht2rVy5Zd8Tzt37qxSXqQRYoQQQgghhJQCgFk6TezVqxcDwH755ReT6Vqtlm3dupVpNBqT6RkZGSwyMpIBYIcPHzZ5b/HixcbP+vzzz03emzNnDgPAJk6caDJ93bp1DABbvHgxY4wxvV7PXnrpJQaA9e3bl+Xn51d6ORcsWMAAsO+//97s+xcvXmQJCQnlpsfExDCRSMRatGjBDAaDyXu9e/dmAFhycrLJ9KCgIIt1as7PP//MADA/Pz92/vx5k/eUSiXbs2ePybSSemzVqhVLTU01Tr958yZzcXFhAFhSUpLJPAcOHGBpaWkm0/R6PVu6dCkDwKZOnVouLwAsKCjIZNrBgweNnz9+/HimUqmM723dupUBYIGBgSbzTJo0iQFgH330UbnPuHLlCktJSSk3PS8vj/F4vHJlEVIWXcklhBBCCCFWGQwG3LhxAzNnzsSRI0cwcuRIjBs3ziRGIBBg1KhREAqFJtM9PT2xfPlyAMVXRs3p3r07XnvtNZNp//nPfwAAR44csZiXRqPB+PHj8f3332PUqFHYvXs3nJycKr1cFy9eBACEhoaafb9du3bG7tmlDRw4EGPHjsWNGzcqfaW5qj744AMAwCeffIIOHTqYvCeVSvHkk0+ane+LL76Aj4+P8XWzZs3w/PPPAwCOHj1qEtu3b194e3ubTOPxeHjvvffQpEkTbNu2rUo5Ozs746uvvoJYLDZOGzVqFNq2bYs7d+6YPFbpwYMHAID+/fuXKycsLAy+vr5my/f19cWdO3eQk5NTpdxI49Iwxn0nhBBCCCE1ztxzXadPn47vvvvO4jNf4+LisGfPHty+fRtKpRKMMWMX58TERLPzDBgwoNw0d3d3uLm5mb03EwAKCwsxbNgw7N27F1OmTMGaNWvA5/Mru2gAHt1X7OrqajFGrVYjJiYGp06dwoMHD4yDHsXHxxuXqV27dlX63IqkpKTgypUrcHFxwTPPPFPp+YRCIfr27VtuekhICACYrcusrCxs27YNCQkJyM3NhV6vBwBotVpkZWUhOzu70o/siYiIgLu7u9nPT0hIQGpqqvF+3oiICOzevRuzZ8/GsmXL0KNHj0o9ksrNzQ3379/HgwcPrH5vpHGjRi4hhBBCCDGr5Dm5KpUKFy5cwNWrV/HDDz8gOjraOMpyCY1GgylTpmDDhg0Wyytp7Jbl7+9vdrqTkxOys7PNvvfZZ59Bp9NhyJAhWLt2rcVGtzV5eXnGzzGnZDCs0lcgy7K0TI+jZNCs5s2bV2m5fHx8zDb0S5av7OBTGzZswEsvvYSCggKLZSoUiko3cq19j2U/f968eTh27BgOHTqEvn37wtHREVFRURg6dCimTJkCuVxutixnZ2cAxff/EmIJdVcmhBBCCCFmlTwnd+PGjbhy5QpWrVoFAJg9ezZu375tEvvJJ59gw4YNaNeuHXbv3o309HRoNBowxoyDCDHGzH4Oj1f1U9LBgwdDLpdjz549FkcarkhJQ8pcQ5UxhmeeeQa3bt3CjBkzEBcXh/z8fBgMBjDGsGjRImOcvahKPd6+fRtTpkyBRqPBZ599hsTEROOVd8YYoqKiAFRt+ary+c7Ozjhw4ACOHj2K+fPno3Xr1jhw4ADmzJmD0NBQi1f9S36YcHFxqfRnkcaHGrmEEEIIIaRS5s2bhwEDBkCpVGLp0qUm75U81mXDhg0YNGgQvLy8jPfn3rx5s8Zz6dSpE/755x/IZDJMmDABf/75Z5XLKBkh2tzV4qtXr+Lq1auIjIzE6tWrER4eDicnJ+OV1dpYphIlI0PfvHmz1hrRu3btgkajwWuvvYbXX38dwcHBkEqlxvdrc/lKcByHHj16YOXKlTh58iRSUlIwYcIEpKen45133jE7T8m9uJ6enrWeH6m/qJFLCCGEEEIqbcWKFQCAn3/+2eRqbknjw1yX1U2bNtVKLl27dkVMTAykUinGjx9vcWArS8LDwwHA7ONqrC1PTk4O9u7dW42MK8fPzw+tWrVCbm4u/vjjj1r5DGvLd+TIEaSnp9fK51rj5eWFJUuWAIDZAb3y8/ORkpKCwMBAuh+XWEWNXEIIIYQQUmkdO3bEqFGjoNPpjN2XgUeDG3377bcm8Zs3b8ZPP/1Ua/lERUUhJiYGYrEYzzzzDLZv317peXv27AkAOH36dLn3goODwePxcODAAZOusyqVCjNmzLB4r3BNWbhwIQBg7ty5xlGgS+fwuI3sku/rl19+QWFhoXH6/fv3MWPGjMcquzK+/fZbJCcnl5u+a9cuADD7nOPTp0+DMYbevXvXen6kfqNGLiGEEEIIqZIlS5aA4zisXbsWaWlpAID58+eDz+dj4cKFiIyMxLPPPovOnTtj7NixeOONN2o1n+joaOzevRtCoRBjxozBzp07KzVfr1694OjoiEOHDpV7z8vLC9OmTUN+fj7Cw8MxbNgwjB07Fk2bNsWBAwfKDbxV0yZNmoRXX30V9+/fR6dOndCzZ088++yz6Nu3L3x9fTFv3rzHKn/EiBFo06YNzpw5g+DgYIwZMwbDhg1DSEgIXF1dER0dXUNLYt63336L5s2bo02bNhgzZgzGjx+PDh064I033oBEIsF7771Xbp6S72no0KG1mhup/6iRSwghhBBCqiQ8PByjR4+GSqXCJ598AqC4wXjs2DE88cQTuHnzJnbs2AGRSIQtW7Zg9uzZtZ5Tjx49sGvXLgiFQjz99NOIiYmpcB5HR0dMmDABSUlJZq/mrl69Gh9//DGaNWuG/fv34+jRo+jfvz/OnDmDoKCg2lgME1988QX+/vtv9O/fH5cvX8aWLVuQlJSEHj16YPHixY9VtkgkwtGjRzFz5kxIJBLs2LEDV65cwauvvoq9e/eWe95xTXv//ffxwgsvgOM47N+/H9u3b0dRURFefPFFxMXFoXv37uXm2bBhAzw8PDB69OhazY3UfxyzpyHhCCGEEEIIqUNxcXHo2LEjXnnlFXz55Ze2TodYEBsbi+joaMyfPx8rV660dTrEzlEjlxBCCCGENGrPPPMMdu7cieTkZOOIy8S+jBw5EkeOHMGNGzcq/dxe0nhRd2VCCCGEENKoLV++HFqt1mQgLWI/zp8/j23btmHRokXUwCWVQldyCSGEEEIIIYQ0GHQllxBCCCGEEEJIg0GNXEIIIYQQQgghDQY1cgkhhBBCCCGENBjUyCWEEEIIIYQQ0mBQI5cQQgghhBBCSINBjVxCCCGEEEIIIQ0GNXIJIYQQQgghhDQY1MglhBBCCCGEENJgUCOXEEIIIYQQQkiD8f+BIQql8wUMNgAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 1200x400 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace(fs_lt, kind=\"rank_bars\");"
]
},
{
"cell_type": "code",
"execution_count": 168,
"id": "f95dbe2c-5ea6-4e46-b087-b40ace7c6f00",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1472x552 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_posterior(fs_lt);"
]
},
{
"cell_type": "markdown",
"id": "4b7b8d34-b232-41b1-9902-2f340597e845",
"metadata": {},
"source": [
"### Prior and Posterior Predictive"
]
},
{
"cell_type": "markdown",
"id": "c7eebb89-d254-496a-bb57-fc0876859f93",
"metadata": {},
"source": [
"#### Prior Predictive"
]
},
{
"cell_type": "code",
"execution_count": 181,
"id": "cdf3f9f3-0d01-41f6-bc0b-763f25a47588",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 181,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"prior_samples = fs_prior_c.prior_predictive.first_stage_lt.to_numpy().flatten()\n",
"az.plot_kde(prior_samples, ax=ax)\n",
"ax.set_xlabel(x_label)\n",
"ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"id": "37196ce4-8e6f-4e88-afc6-56cbe3e60e0d",
"metadata": {},
"source": [
"#### Posterior Predictive"
]
},
{
"cell_type": "code",
"execution_count": 180,
"id": "8a16aa74-9a82-4d01-8c64-258349b66e30",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"posterior_samples = fs_ppc.posterior_predictive.first_stage_lt.to_numpy().flatten()\n",
"az.plot_kde(posterior_samples, plot_kwargs={\"c\":\"C1\"})\n",
"ax.set_xlabel(x_label)\n",
"ax.set_yticks([]);"
]
},
{
"cell_type": "markdown",
"id": "a78064ba-527f-41dc-8b38-6d429f6cab8d",
"metadata": {},
"source": [
"#### Both together"
]
},
{
"cell_type": "code",
"execution_count": 182,
"id": "03d73012-c2f8-4601-8ed4-979edad57ea4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 182,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"az.plot_kde(prior_samples, ax=ax, label=\"Prior Lead Time Belief\")\n",
"az.plot_kde(posterior_samples, ax=ax, label=\"Posterior Lead Time Belief\", plot_kwargs={\"c\":\"C1\"})\n",
"ax.set_xlabel(\"Days\")\n",
"ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"id": "e0c44b80-1666-49d2-9832-56c9fcf668e5",
"metadata": {},
"source": [
"## Rocket Lead Time\n",
"Leaving it as exercise for everyone here.\n",
"\n",
"Repeat the. steps above and add the posterior predictive samples together"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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