{
"cells": [
{
"cell_type": "markdown",
"id": "a21b6f6f-ac6f-44c6-9934-22319396d9ff",
"metadata": {},
"source": [
"# The 1919 Eclipse: parameter inference and model comparison"
]
},
{
"cell_type": "markdown",
"id": "b131758f-4f9c-45a8-a535-7eeb314230b0",
"metadata": {},
"source": [
"Florent Leclercq
\n",
"Imperial Centre for Inference and Cosmology, Imperial College London
\n",
"florent.leclercq@polytechnique.org"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "2f98c657-9ba2-420e-a5f6-7634b0ecf3ac",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy\n",
"import scipy.stats as ss\n",
"import matplotlib.pyplot as plt\n",
"np.random.seed(3)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "5c199554-b35b-4a38-9769-5ee6e065aa12",
"metadata": {},
"outputs": [],
"source": [
"# Some plotting tools and routines\n",
"\n",
"nBins = 30\n",
"nContourLevels = 3\n",
"# 2d contour levels: (68%, 95%, 99%)\n",
"confLevels = [.3173, .0455, .0027]\n",
"smoothingKernel = 1\n",
"\n",
"def get_marginal(samples):\n",
" # create 1d histogram\n",
" hist1d, edges = np.histogram(samples, weights=np.ones_like(samples),\n",
" density=True, bins=nBins)\n",
"\n",
" # Bin center between histogram edges\n",
" centers = (edges[1:]+edges[:-1])/2\n",
"\n",
" # Filter data\n",
" pdf = np.array((centers, hist1d))\n",
" pdf = scipy.ndimage.gaussian_filter1d(pdf, sigma=smoothingKernel)\n",
"\n",
" # Clip the pdf to zero out of the bins\n",
" centers, hist = pdf[0], pdf[1]\n",
" centers = np.insert(centers, 0, centers[0]-(centers[1]-centers[0]))\n",
" hist = np.insert(hist, 0, 0.)\n",
" centers = np.insert(centers, len(centers), centers[len(centers)-1]-(centers[len(centers)-2]-centers[len(centers)-1]))\n",
" hist = np.insert(hist, len(hist), 0.)\n",
"\n",
" # Normalize all the pdfs to the same height\n",
" hist /= hist.max()\n",
"\n",
" pdf = np.array((centers, hist))\n",
" \n",
" return pdf\n",
"\n",
"def get_contours(samples_x, samples_y):\n",
" # Empty arrays needed below\n",
" chainLevels = np.ones(nContourLevels+1)\n",
" extents = np.empty(4)\n",
"\n",
" # These are needed to compute the contour levels\n",
" nBinsFlat = np.linspace(0., nBins**2, nBins**2)\n",
"\n",
" # Create 2d histogram\n",
" hist2d, xedges, yedges = np.histogram2d(\n",
" samples_x, samples_y, weights=np.ones_like(samples_x), bins=nBins)\n",
" # image extent, needed below for contour lines\n",
" extents = [xedges[0], xedges[-1], yedges[0], yedges[-1]]\n",
" # Normalize\n",
" hist2d = hist2d/np.sum(hist2d)\n",
" # Cumulative 1d distribution\n",
" histOrdered = np.sort(hist2d.flat)\n",
" histCumulative = np.cumsum(histOrdered)\n",
"\n",
" # Compute contour levels (from low to high for technical reasons)\n",
" for l in range(nContourLevels):\n",
" # Find location of contour level in 1d histCumulative\n",
" temp = np.interp(confLevels[l], histCumulative, nBinsFlat)\n",
" # Find \"height\" of contour level\n",
" chainLevels[nContourLevels-1-l] = np.interp(temp, nBinsFlat, histOrdered)\n",
"\n",
" # Apply Gaussian smoothing\n",
" contours = scipy.ndimage.gaussian_filter(hist2d.T, sigma=smoothingKernel)\n",
"\n",
" xbins = (xedges[1:]+xedges[:-1])/2\n",
" ybins = (yedges[1:]+yedges[:-1])/2\n",
" \n",
" return xbins, ybins, contours, chainLevels"
]
},
{
"cell_type": "markdown",
"id": "a1f4f890-cd97-453e-963e-082ccca41316",
"metadata": {},
"source": [
"## Data model"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "df3a9d78-8eac-412e-b3f7-5b798e267d33",
"metadata": {},
"outputs": [],
"source": [
"def Dx_11(alpha,a,b,c):\n",
" return c-0.160*b-1.261*a-0.587*alpha/19.8\n",
"def Dx_5(alpha,a,b,c):\n",
" return c-1.107*b-0.160*a-0.557*alpha/19.8\n",
"def Dx_4(alpha,a,b,c):\n",
" return c+0.472*b+0.334*a-0.186*alpha/19.8\n",
"def Dx_3(alpha,a,b,c):\n",
" return c+0.360*b+0.348*a-0.222*alpha/19.8\n",
"def Dx_6(alpha,a,b,c):\n",
" return c+1.099*b+0.587*a+0.080*alpha/19.8\n",
"def Dx_10(alpha,a,b,c):\n",
" return c+1.321*b+0.860*a+0.158*alpha/19.8\n",
"def Dx_2(alpha,a,b,c):\n",
" return c-0.328*b+1.079*a+1.540*alpha/19.8\n",
"\n",
"def Dy_11(alpha,d,e,f):\n",
" return f-1.261*d-0.160*e+0.036*alpha/19.8\n",
"def Dy_5(alpha,d,e,f):\n",
" return f-0.160*d-1.107*e-0.789*alpha/19.8\n",
"def Dy_4(alpha,d,e,f):\n",
" return f+0.334*d+0.472*e+1.336*alpha/19.8\n",
"def Dy_3(alpha,d,e,f):\n",
" return f+0.348*d+0.360*e+1.574*alpha/19.8\n",
"def Dy_6(alpha,d,e,f):\n",
" return f+0.587*d+1.099*e+0.726*alpha/19.8\n",
"def Dy_10(alpha,d,e,f):\n",
" return f+0.860*d+1.321*e+0.589*alpha/19.8\n",
"def Dy_2(alpha,d,e,f):\n",
" return f+1.079*d-0.328*e-0.156*alpha/19.8\n",
"\n",
"stars = np.array([11,5,4,3,6,10,2])\n",
"alpha_GR=1.75\n",
"alpha_Newton=0.9"
]
},
{
"cell_type": "markdown",
"id": "bfbfa8dd-81ba-4e17-a969-26b0413a3c4d",
"metadata": {},
"source": [
"## Simulations"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b33fb16f-2942-4b81-9923-a9bfff89ebcf",
"metadata": {},
"outputs": [],
"source": [
"nsims=10\n",
"a=ss.uniform(-1.,2.).rvs(nsims)\n",
"b=ss.uniform(-1.,2.).rvs(nsims)\n",
"c=ss.uniform(-1.,2.).rvs(nsims)\n",
"d=ss.uniform(-1.,2.).rvs(nsims)\n",
"e=ss.uniform(-1.,2.).rvs(nsims)\n",
"f=ss.uniform(-1.,2.).rvs(nsims)\n",
"alpha=ss.uniform(-0.75,2+0.75).rvs(nsims)\n",
"\n",
"sims_x = np.array([\n",
" Dx_11(alpha,a,b,c),\n",
" Dx_5(alpha,a,b,c),\n",
" Dx_4(alpha,a,b,c),\n",
" Dx_3(alpha,a,b,c),\n",
" Dx_6(alpha,a,b,c),\n",
" Dx_10(alpha,a,b,c),\n",
" Dx_2(alpha,a,b,c)\n",
"])\n",
"sims_y = np.array([\n",
" Dy_11(alpha,d,e,f),\n",
" Dy_5(alpha,d,e,f),\n",
" Dy_4(alpha,d,e,f),\n",
" Dy_3(alpha,d,e,f),\n",
" Dy_6(alpha,d,e,f),\n",
" Dy_10(alpha,d,e,f),\n",
" Dy_2(alpha,d,e,f)\n",
"])"
]
},
{
"cell_type": "markdown",
"id": "8e5f2579-4f10-4acf-b54d-bd511ca9bbf3",
"metadata": {},
"source": [
"## Data vectors"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "1c69c01a-1870-4779-9686-8df6bcd5f439",
"metadata": {},
"outputs": [],
"source": [
"# Using comparison plate 14_2a\n",
"dx_I = np.array([\n",
" -1.411+1.500 - (-0.478+0.552),\n",
" -1.048+1.500 - (-0.544+0.552),\n",
" -1.216+1.500 - (-0.368+0.552),\n",
" -1.237+1.500 - (-0.350+0.552),\n",
" -1.342+1.500 - (-0.317+0.552),\n",
" -1.289+1.500 - (-0.272+0.552),\n",
" -0.789+1.500 - (-0.396+0.552),\n",
"])\n",
"dy_I = np.array([\n",
" -0.554+0.554 - (-0.109+0.206),\n",
" -0.338+0.554 - (-0.204+0.206),\n",
" +0.114+0.554 - (-0.136+0.206),\n",
" +0.150+0.554 - (-0.073+0.206),\n",
" +0.124+0.554 - (-0.144+0.206),\n",
" +0.205+0.554 - (-0.146+0.206),\n",
" +0.109+0.554 - (-0.182+0.206),\n",
"])\n",
"dx_II = np.array([\n",
" -1.416+1.500 - (-0.478+0.552),\n",
" -1.221+1.500 - (-0.544+0.552),\n",
" -1.054+1.500 - (-0.368+0.552),\n",
" -1.079+1.500 - (-0.350+0.552),\n",
" -1.012+1.500 - (-0.317+0.552),\n",
" -0.999+1.500 - (-0.272+0.552),\n",
" -0.733+1.500 - (-0.396+0.552),\n",
"])\n",
"dy_II = np.array([\n",
" -1.324+1.324 - (-0.109+0.206),\n",
" -1.312+1.324 - (-0.204+0.206),\n",
" -0.944+1.324 - (-0.136+0.206),\n",
" -0.862+1.324 - (-0.073+0.206),\n",
" -0.932+1.324 - (-0.144+0.206),\n",
" -0.948+1.324 - (-0.146+0.206),\n",
" -1.019+1.324 - (-0.182+0.206),\n",
"])\n",
"dx_III = np.array([\n",
" +0.592-0.500 - (-0.478+0.552),\n",
" +0.756-0.500 - (-0.544+0.552),\n",
" +0.979-0.500 - (-0.368+0.552),\n",
" +0.958-0.500 - (-0.350+0.552),\n",
" +1.052-0.500 - (-0.317+0.552),\n",
" +1.157-0.500 - (-0.272+0.552),\n",
" +1.256-0.500 - (-0.396+0.552),\n",
"])\n",
"dy_III = np.array([\n",
" +0.956-0.843 - (-0.109+0.206),\n",
" +0.843-0.843 - (-0.204+0.206),\n",
" +1.172-0.843 - (-0.136+0.206),\n",
" +1.244-0.843 - (-0.073+0.206),\n",
" +1.197-0.843 - (-0.144+0.206),\n",
" +1.211-0.843 - (-0.146+0.206),\n",
" +0.924-0.843 - (-0.182+0.206),\n",
"])\n",
"dx_IV = np.array([\n",
" +0.563-0.500 - (-0.478+0.552),\n",
" +0.683-0.500 - (-0.544+0.552),\n",
" +0.849-0.500 - (-0.368+0.552),\n",
" +0.861-0.500 - (-0.350+0.552),\n",
" +0.894-0.500 - (-0.317+0.552),\n",
" +0.934-0.500 - (-0.272+0.552),\n",
" +1.177-0.500 - (-0.396+0.552),\n",
"])\n",
"dy_IV = np.array([\n",
" +1.238-1.226 - (-0.109+0.206),\n",
" +1.226-1.226 - (-0.204+0.206),\n",
" +1.524-1.226 - (-0.136+0.206),\n",
" +1.587-1.226 - (-0.073+0.206),\n",
" +1.564-1.226 - (-0.144+0.206),\n",
" +1.522-1.226 - (-0.146+0.206),\n",
" +1.373-1.226 - (-0.182+0.206),\n",
"])\n",
"dx_V = np.array([\n",
" +0.406-0.400 - (-0.478+0.552),\n",
" +0.468-0.400 - (-0.544+0.552),\n",
" +0.721-0.400 - (-0.368+0.552),\n",
" +0.733-0.400 - (-0.350+0.552),\n",
" +0.798-0.400 - (-0.317+0.552),\n",
" +0.864-0.400 - (-0.272+0.552),\n",
" +0.995-0.400 - (-0.396+0.552),\n",
"])\n",
"dy_V = np.array([\n",
" +0.970-0.861 - (-0.109+0.206),\n",
" +0.861-0.861 - (-0.204+0.206),\n",
" +1.167-0.861 - (-0.136+0.206),\n",
" +1.234-0.861 - (-0.073+0.206),\n",
" +1.130-0.861 - (-0.144+0.206),\n",
" +1.119-0.861 - (-0.146+0.206),\n",
" +0.935-0.861 - (-0.182+0.206),\n",
"])\n",
"# Plate VI was not used!\n",
"dx_VII = np.array([\n",
" -1.456+1.500 - (-0.478+0.552),\n",
" -1.267+1.500 - (-0.544+0.552),\n",
" -1.028+1.500 - (-0.368+0.552),\n",
" -1.010+1.500 - (-0.350+0.552),\n",
" -0.888+1.500 - (-0.317+0.552),\n",
" -0.820+1.500 - (-0.272+0.552),\n",
" -0.768+1.500 - (-0.396+0.552),\n",
"])\n",
"dy_VII = np.array([\n",
" +0.964-0.777 - (-0.109+0.206),\n",
" +0.777-0.777 - (-0.204+0.206),\n",
" +1.142-0.777 - (-0.136+0.206),\n",
" +1.185-0.777 - (-0.073+0.206),\n",
" +1.125-0.777 - (-0.144+0.206),\n",
" +1.072-0.777 - (-0.146+0.206),\n",
" +0.892-0.777 - (-0.182+0.206),\n",
"])\n",
"dx_VIII = np.array([\n",
" -1.285+1.300 - (-0.478+0.552),\n",
" -1.152+1.300 - (-0.544+0.552),\n",
" -0.927+1.300 - (-0.368+0.552),\n",
" -0.897+1.300 - (-0.350+0.552),\n",
" -0.838+1.300 - (-0.317+0.552),\n",
" -0.768+1.300 - (-0.272+0.552),\n",
" -0.585+1.300 - (-0.396+0.552),\n",
"])\n",
"dy_VIII = np.array([\n",
" -1.195+1.322 - (-0.109+0.206),\n",
" -1.332+1.322 - (-0.204+0.206),\n",
" -0.930+1.322 - (-0.136+0.206),\n",
" -0.894+1.322 - (-0.073+0.206),\n",
" -0.937+1.322 - (-0.144+0.206),\n",
" -0.964+1.322 - (-0.146+0.206),\n",
" -1.166+1.322 - (-0.182+0.206),\n",
"])\n",
"\n",
"# Assumed error on the measurements\n",
"sigma_d = 0.05"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "4e4e9f0e-c54b-4e4d-aa02-4050d963fe7a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Kp1wup1KppEwmIzNTJpNRqVRSLpeLujQAANAFIU0lm32BdXL/D1q2JwV9MADoDnP3wx+VMKOjoz42NtbVxyyXyyoUChofH9fIyIiKxWIiP3Sy2ayq1eoh7ZlMRpVKpf8FLUNIrwUA0Bkz2+Huo1HXgYN60f8KSbPfcuS6S3XUm39bz/2/n9GP7/1CIvstzQt8s0fDp9NpQhkAGAAL9cEYudSmXC6nSqWier2uSqWS2A9ORmEBAHotlCnLQDeFNJWM0T4AgPkIlwZMSJ2BkNbCAoBQhDRlOWRmdpGZPW5mO83sIy3uv8DM9pvZA40/fxJFnSEJaSqZFM6FVwBAdxAuDaBQOgMhjcICgFCEtnFEiMxsSNJmSe+QdIqky83slBaHbnf3Mxt//ryvRQaIfgsAIGSES0iskEZhAUAomLKcCOdI2unuT7n7v0vaIumSiGtqKaQplvRbAAAhG466AGA5crkcnTIAiJGRkZGWmy0kdepPoI6X9PSs27skndviuDea2YOSdkv6kLs/0o/imuYvGt2cYikpsZ/99FsAAKFi5BIAAOgapv4kgrVom7998LclZdz9DEmflPSllg9kljezMTMb27NnT1eLZIolAADJQbgEAAC6hqk/ibBL0qtm3T5B06OTZrj7j939J42vt0paYWar5z+Qu5fcfdTdR4855piuFskUSwAAkoNpcQAAoKuY+hN790taa2YnSvq+pMsk/frsA8zslZJ+4O5uZudo+oLkvn4WyRRLAACSg5FLAAAAA8TdJyV9QNJtkh6V9E/u/oiZXWVmVzUOu1TSw401lz4h6TJ3nz91rqeYYgkAQHIQLgEAEAMh7YqF+HP3re7+anc/yd2LjbYb3P2GxtefcvfXufsZ7r7O3e/pd41MsQQAIDmYFteh8X01jaxKH/5AAADaFOKuWEA3MMUSAIBkYORSBzZv26nzr92mzdt2Rl0KACAg7IoFAACAJCNcatPmbTv10dsflyR99PbHCZiAw2CKD9A+dsUCAABAkhEutaEZLE3Vp29P1QmYgMU0p/hUq1W5+8wUHwImoLWFdr9iVywAAAAkAeHSYcwPlpoImICFMcUH6Ay7YgEAAGC5opw9Qri0iPF9NV1726HBUtNUXbr2tsc1vq/W+gCgAyFNI2OKD9AZdsUCAADAckQ9e4RwCYiBqH8RdBtTfIDO5XI5VSoV1et1VSoVgiUA6JOQLvABGFxRzx4hXFrEyKq0Nr39ZNkC95ukTW8/WSOr0gscAbQn6l8E3cYUHwAAkAShXeADMLiinj1CuNSGoVTreGmhdqBTUf8i6Dam+AAAgCQI7QIfgMEV9ewRwqVFNNdcmqx7y/sn686aS+iKqH8R9AJTfIDOMC0DAPovtAt8AAZX1LNHCJcWMbIqrczRi095yxydZlocli3qXwS9wIky0D6mZQCDgc/G+AnxAh+AwRT17BHCpUXc++Q+VZ9dfFRS9dma7n1yX58qQqii/kXQbZwoA51hWgYQPj4b4ynEC3wABleUs0cIlxax7qRVOm/t6kWPOW/taq07aVWfKsJ8IV0BDGkaGSfKQGeYlgGEj8/GeArtAh8ARCXScMnMLjKzx81sp5l9pMX9F5jZfjN7oPHnT/pd42evPHfBqXGZo9P67JXn9rkiNHEFML44UQY6w7QMIHx8NsZXSBf4ACAqkYVLZjYkabOkd0g6RdLlZnZKi0O3u/uZjT9/3tciJW3etlM/eP5Ay/t+8PwBbd62s88VoYkrgPHFiTLQGaZlAOGb/Rk4/LJXtGwHuoUNhwD0W5Qjl86RtNPdn3L3f5e0RdIlEdZziOZucQcm6i3vPzBRT+Rucddcc42Gh4dlZhoeHtY111wTdUlLwhXA+OJEGegM0zKA8DU/G49cd6mOv+pGHbnu0iA+G5PWDx4Em7ft1PnXbuMiOIC+ijJcOl7S07Nu72q0zfdGM3vQzP6nmb2uP6VNG1mV1qa3n6yVK1r/N61ckdKmt5+cqN3irrnmGl1//fWampqSJE1NTen6669PZMDE6Jj44kQZ6BzTMoCw5XI5/fp/uVlHrb9cknTU+sv16//l5kT/rBNixM/mbTv10dsflyR99PbHeW+ANhGUL1+U4ZK1aPN5t78tKePuZ0j6pKQvLfhgZnkzGzOzsT179nStyI0b1uh337L2kIBp5YqUfvcta7Vxw5quPVc/lEqljtrjrFgs6ogjjpjTdsQRRyT+CmAoOFEGAOCgzdt2avuzL5aGXzTdMPwibX/2xYk9+f+dj31B137lIUnStV95SL/zsS9EXBGawdJUY9LFVJ2ACWgHQXl3RBku7ZL0qlm3T5C0e/YB7v5jd/9J4+utklaYWcvt29y95O6j7j56zDHHdLXQ+QFTUoMlSTMjltptjzt3X/R2EpGaAwAQls3bduqT33jikKUWDkzU9clvPJG4E5rf+dgX9LVdNico+9ouI2CK0PxgqYmACVgco/26J8pw6X5Ja83sRDM7QtJlkm6dfYCZvdLMrPH1OZqud1/fK9V0wHR29mhJ0tnZoxMZLEnS0NBQR+1xVigUNDExMadtYmIi0Qt6k5oDABCW0Nbw3Lxtp27/fkq2YuWcdluxUrd/P0UfJgLN77H5wVLTVF2J+h4D+oXRft0VWbjk7pOSPiDpNkmPSvond3/EzK4ys6sah10q6WEze1DSJyRd5hENTdm8bafurzwrSbq/8mxiv+Hy+XxH7XEW2oLezauakhJ5FRMAABwqpDU8myHGzIil+YZfRIgBIBEY7dd9UY5ckrtvdfdXu/tJ7l5stN3g7jc0vv6Uu7/O3c9w93Xufk8Udc4fypzUIcySdN111+nqq6+eGak0NDSkq6++Wtddd13ElXUupAW9Q/oeAwCg25IeVjSXWBia1/MeSilRSy2MrErrvLWrpYWu9brrvLWrExGUhaQZYA6nWi1pKw2nLDEBJtAPIY/2K5fLymazSqVSymazKpfLfXvuSMOlJAhtjrw0HTBNTk7K3TU5OZnIYEkKZ7v7EL/HACxdEjsyQC+FNGXc5u1nM/923I3vq2n7E3slW6BuM21/Yi+/xyKwccMavfGkVS3ve+NJqxITYAJYunK5rHw+r2q1KndXtVpVPp/vW8BEuLSI0ObIhyaE7e75HgMwW0gn0UA3hDJlvPk6JutzR/xM1j1Rr2tm5NIiGLkUjc3bduqeJ/e2vO+eJ/cm5nsMwNIVCgXVanPPG2u1Wt/WJCZcWkRIc+RDlfTt7vkeA9AUykk00C2hTBkP6ULSzMilRTByqf9CnuID9EKoU0mjXpOYcOkwmnPk55/8r1yRStQcecTXxg1rdN7RP5VPHJjT7hMHdN7RP0389xgdGeDwQjmJBrolpCnjIa1TxEUxAKHYuGGNfv/CVx8SMA2nTL9/4asTeQ4W9ZrEhEttmB8wESyh227/+If0o3u2qN4ImOoTB/Sje7bo9o9/KOLKlocpPsDhhXQSDXRDSCN9pPDWKWr2i1udkNE/BpAk8wOmJAdLUvRrEhMutan5QSola1cPJEO1WtWP7/2C9t+zRZK0/54t+vG9X1C1Wo24sqVjig9weKGdRAPdwOiYZHD5orfRP82fmfm7ETYNpcTPDLCAZsAkKdHBkhT9msTDfXmWQGzcsEa/cvpx/GJG1w0NDWlqako/vvcLqj26XZP7fzDTnkQLTfGRlOhf2EC3NU8IPnb7vx2y0K908AoanzsYNM3Pivmj+pI4erz5c/7Xtz2meovd4VJy/eHbX5OYn/PmZ/z89X2m6uKzPkLN//OP3j537aWhlPQHF57MewIs4t6n9s38nfSflVwuF9k6xIxc6lBSPviRLFNTUzNfN4Ol+e1JwRQfoHMLXfFP6kiAcrmsbDarVCqlbDbbty1wEZaQliXYuGGN1q89RjrkZ9q1fu0xiXlNjLaMt40b1ugPLjw4golgCTi837zxWzMbFWx/Yq9+88ZvRVxRchEuATGQyWQ6ao8rOp1AZ0Lc4adcLiufz6tarcrdVa1Wlc/nCZiwJKEsS7B5207dX3lWOmTkkun+yrOJufAS+vSrJP2uXUgzYJIIloDDmR0sNREwLR3hEhADUS++1i2skwF0JsSfmUKhoFpt7glarVZToVCIqCIk3cYNa3Tnpg2JPUkO8cLLIhvfJVZIm5Bs3LBGW35nXWJ/ZoB+aBUsNREwLQ3hEhADUS++1k3zpzE0JXk6A9BLof3MjI+Pd9QOLKY5xTJ7zEsSO8VyZFVa561dvegx561dnYgQuRmUtVgiTpJU9+SNtpTC24Rk87aduuzT9yb+dQC9cu+T+xYMlpq2P7FX9z65r08VhYFwCUFIWiemlVwup0qlonq9rkqlkshgqWnjhjU6O3v0nLazs0cn7iQZ6JeQ1pYZGRnpqB1YSChTLMf31do6iQmhL5NEC21CktRgJrSgDOiFdSetaiv0X3fSqj5VFAbCpQEWSicmpGHMoTi4tsRBSVpTAohCKGvLhDLNF9ELZYplSNNfm69FU5OtD5iaTMxrkcLbhCS0oAzopc9eee6CAdN5a1frs1ee2+eKko9waUCFEshs3rZTH739cUnTW68m/fWEILSOGtBPSV9bRgprmi+iFdIUy5Cmv27csEbP3VVWfWpiTnt9akLP3VVOzGsJbS0s+l9A59b9wqoW2yxMt6NzhEsDKJThss1gqbnL0lQ9jIApKZ2YVkLrqAFRSMoV/8WENM0X0QltimVI01+PeuY+7Z8VMNWnJrT/rrKOeua+iCtr38worMmftT5g8meJGYVF/wvoXPOceP4Scq5knyNHiXBpwIQyXHZ+sNSU9IAp6SPKQhr6DwCIVohTLEOa/jr50Fbtv2t6/av9d5U1+dDWxL03Gzes0XN3b1F94sCc9vrEAT1395bEvD/0v4DOEMj2BuHSAAlluGzzl8H8YKlpqs5OJVEKaeg/EIWk/e4CeiXUKZYhTX896pn79f2/fb+Oeub+xL43Rz1zn/bfczBgqk8c0P57tiRqFJZE/wvoBIFsbxAuDQjS2XgLZURZU7ODM5yansU8nDI6NkAbkj56Eei2UKdYhnDC0nxvJp57JtHvzcworHu2SJL237MlkaOwpLCmXgK9RiDbfYRLA6KZzjZP9ucbTlli0tnma1ngpShlSsxrkcIZUdaKN2Yx+yGzmQHMF8roRQALK5fLymazSqVSymazKpfLUZc08EIahSWFM/US6AcC2e4ajroA9NdCJ/lJPPk3k1qVbQuETnHUHFG2kOaIsl85/bjEhGXSwZPk2YutN0+a+WUNHGqh0YsSPzOANP15maTPwVbK5bLe9773aWJiehHsarWq973vfZKU2CAjFLlcLqj3YOOGNYnrOwJRafazrr3tcYKlZWLk0oAIaZ2ikF7LyKq0zlu7etFjzlu7OlGdg5BHYgG9wM8MsLhQpot+8IMfnAmWmiYmJvTBD34wooqWh1FY8ZakviMQtRDWwosDwqUBEdKiZSG9lvF9NW1/Yu+ix2x/Ym8igjKJtb2ATvEzAywupOmi+/bt66g9zsrlsvL5vKrVqtxd1WpV+XyegAlAYiXh3DHuCJcGyMYNa3R29uiW952dPTpRSW0oC7DNrB+1wLTElDwxQZkU5kgsoJdCWg8P6LbQNrsISaFQUK02N/Su1WoqFAoRVQQAiBrh0gDZvG2n7q882/K++yvPJq6z1gyYhhrfxUOp5C5cWK9PddQeV6GNxAL6JaT18IBuCHG66KpVqzpqj7Px8fGO2gEgrpji2z2ESwMi5KkXJpvzd5LMLOidWmBt/dRwot6XkKYsAv0Q0hpyQLeE2mf5+Mc/riOOOGJO2xFHHKGPf/zjEVW0dCMjIx21A0AcMcW3uwiXBkSI05WaVzUn69NX9ifrnrirmc0wRpM/a33A5M8SF8aEMmUR6AcCWeBQIfZZpOkdyW666SZlMhmZmTKZjG666aZE7lJWLBaVTs/9/0+n0yoWixFVBACdC3mKbxQXYAiXBkRo05VCGi6/ccMaXXh8XT41OafdpyZ14fH1RIYxzYCpuYxMypI7ZRHotZDWwwO6IbQ+y2y5XE6VSkX1el2VSiWRwZI0/TpKpdKcoKxUKiX29QAYTKFO8Y1ql1XCpQER0tXxEIfLn3nmmRoaGprTNjQ0pDPPPDOagrrg3qf2qTGoTHWfvg3gUKGthyexfgGWJ6Q+C5KB31nAYApxim+Uu6wSLg2QUK6Oh7a7UvMXQH3emlF1WeJGYTX95o3fOuSq8/Yn9uo3b/xWRBUB8RRiWM76BeiGUPosoQrp5zyk1yIRlAGdCG2Kb9S7rBIuDZDQro6HsLtSiCeWrYKlJgImYK7QwnIp7PUL0D+h9VlCE9LPeUivJbSgDOi1kKb4xmHZGMKlARFSiBHS7krNE8uhBX4Sh1JK1InlvU/ua2udjHufZIocMFsIYXlTqOsXoH9C6rOEKqSf85BeS0hBGdAvIayFF5fPTcKlARFSiBHSa2kytR61sFB7XK07aVVbO/ysO2lVnyoC4i2ksLwpxPUL0F+suRR/If2ch/RaQgrKALQvLp+bhEsDJpQQQwrjtTRPLCfrrUcnTNY9cSeWn73y3AUDpvPWrtZnrzy3zxUB8RWXzkA3hbZ+AaLR3HV0/pTR4ZSx+2gMhPRzHtJrCSkoA9CZ5ufm/D7lyhWpvn1uEi4NiJBCjJBeS4gnllLrgIlgCWgtDp2Bbgpp/QJEb7JeX/Q2ohHSz3lIr+Xiiy/uqB1AWOb3KfvdlzT35K3ncDijo6M+NjYWdRmxs9AiX1LyTmJCei1S69eTxNcxX3Nxb4Il4PBm/x4I4ee/18xsh7uPRl0HDupm/2vztp3669seO2QnVUlKyfWHb38NPx/APNlsVtVq9ZD2TCajSqXS/4IARKLX52AL9cEYuTRAQro6HtoWxVGnzL3y2SvP1ZbfWUewBLSh+XtAUhA//8BSNUcotwqWJKkuS8wIZaCfWHMJwOzdVvu9uyrh0oAJJcQIcYviUE8sWbwbaN/GDWt056YNwfz8A0CSJD2wZM0lYLDNnw1zYKKuT37jib6dGxMuDaDZo36SOMonLlstAkAvJG2NNaDbmusRqj7Z+oD6ZCLXI0S8bd62U+dfuy2RFyibQlqcHOiXcrmsbDarVCqlbDarcrkcdUlLstCyMf0MmAiXBlCUQ+W6IdRFsJu/ECT1NWEGACBuNm5YowuPnZBPzQ2YfGpSFx47kbgLY4i3UPpgIS1ODvRDuVxWPp9XtVqVu6tarSqfzycuYIrL4AvCpQET9VC5bglp/SgpnPcFAJAMZnaRmT1uZjvN7CMt7jcz+0Tj/ofM7Kx+1/jp379Ubztu4uAIpvqk3nbchD79+5f2uxQELLQ+WC6XU6VSUb1eV6VSIVgCFlEoFFSrzQ1carWaCoVCRBUtzciq9CE7dc933trVPR98Qbg0QOIwVK6bQlo/KqT3BQCamJ4cT2Y2JGmzpHdIOkXS5WZ2yrzD3iFpbeNPXtL1fS2y4dO/f6k2veN1kqRN73gdwRK6KsQ+WChTfIB+CGUR/PF9NW1/Yu+ix2x/Yi8jl9AdcRkq121JXwQ71PcFAEJYvyRg50ja6e5Pufu/S9oi6ZJ5x1wi6R982r2SXm5mx/a7UImF7tEbIfbBQpniA/QLi+B3F+HSgAh1nSIp2Z3OkN8XAINr87ad+uuvPS5J+uuvPU7AFD/HS3p61u1djbZOj+kbPgfRbSOr0lo5bIses3LYEvW9F8oUH6Bf1qxpff64UHtcxWUjjEjDpSTM928KYYhpaOsUzZakD/75Qn5fAAyeZrBU9+nbdSdgiqFWZ9S+hGNkZnkzGzOzsT179nSlOKAfbtz+lA5MHvItPceBSdeN25/qU0XLF8oUH6Bf7rjjjo7a42zjhjV6bnu55UYYz20v9+WcMrJwKUnz/UMaYhrKOkWh4X0BEIL5wVITAVPs7JL0qlm3T5C0ewnHyN1L7j7q7qPHHHNM1wsFeuXCU17Z1ePigCk+QGempqY6ao+7o565Tz+66x9nAiafmtSP7vpHHfXMfX15/ihHLiVmvn9oQ0yTvk5RqHhfACRZc/2S+cFSU92VuPVLAna/pLVmdqKZHSHpMkm3zjvmVkm/1RhFvk7Sfnd/pt+FAr0yM41kEUlbmqBYLCqdnltvOp1WsViMqCIg3oaGhjpqj7tisajJh7bqR3f9oyTpR3f9oyYf2tq33wHDfXmW1lrN5T+3jWOOl9TXzk2IQ0w3blijXzn9uER9YA4C3hcASbX7Ry+0fRy/46Ll7pNm9gFJt0kaknSTuz9iZlc17r9B0lZJF0vaKakm6X1R1Qv0SvNC3rW3PX7IfZvefnLiLvTlcjndfffdKpVKmpqa0tDQkK644grlcrmoSwNiKZ/P6/rrD50clc/nI6hm+Zo/64VCQd//27t0/MtepGKp1LffAVGGS12b7y9Nz/nX9NS5rg/9HBkZUbVabdmeZHTu44n3BUASrTtplTJHp1V9duGRSZmj01p30qo+VoWFuPtWTQdIs9tumPW1S9rY77qAfmsVMCUxWJKml/K4+eabZ6b0TE1N6eabb9b69esJmIAWrrvuOkmaE8jm8/mZ9iTK5XKR/bxHOS2ua/P9pd7O+WeIKdC5EBbBB9C+8X21RYMlSao+W2NaHIDY2bhhzcwUuaQGS1J4S3kA/XDddddpcnJS7q7JyclEB0tRizJcSsx8/1wup1KppEwmIzNTJpNRqY/Dy4CkCWkRfKDfkhq+jKxK67y1qxc95ry1qxmdCSCWNm5Yozs3bUhssCSFuZQHgKWJoj8ZWbjk7pOSmvP9H5X0T835/s05/5oerv2Upuf7f1rSNZEUq+mAqVKpqF6vq1KpECwBi5h95Wz4Za+QxJUzoB2bt+3U+dduS+SuauP7atr+xN5Fj9n+xN7EhmcAwpf08Jvd4gBI0fUnoxy5JHff6u6vdveT3L3YaLuhOee/sUvcxsb9p7n7WJT1AmhP8wrZkesu1fFX3agj1106px3AoTZv26lPfuMJSdInv/FE4gKm5s5LQwv0LIZSydt5CQCShKU8AETZn4xyQW8AgRoZGdFzx56tl73pMkma+fuoZ+6PsiwgtpodgQMTdUnSgYn6TMcgaVM0vOW2Gwu3AwC6Y/ZOUePj4xoZGVGxWGTGBTAgou5PEi4B6LoLP/hX+touk61YKUlKrVipl7/pMl14wq9FXBkQP/M7Ak1JC5jG99VabufdVPfp3Zh+5fTjGL0EAD0S5U5RAKITh/5kpNPiAIRn87ad2v7si2eCpSZbsVLbn31x4qb6AL3UDGTmdwSaDkzUde1tj7NOEQAAAFqKS3+ScAlA18TlFxuQFM11ijT5s9YHTP4sMesUseYSAABA/42sSitz9OL9q8zR6Z73wQiXAHRN8+Ry5YrWv1pWrkhxcgnMs3HDGj139xbVJw7Maa9PHNBzd29JxJS4po0b1ugPLjw0YBpKSX9w4cmJei0AAABJcO+T+1R9dvGL99Vna7r3yX09rYNwCYlWLpeVzWaVSqWUzWZVLpejLmngbdywRr/7lrWHBEwrV6T0u29Zy8kl0MJRz9yn/fccDJjqEwe0/54tOuqZ+yKurHPzAyaCJQAAgN5Zd9Iqnbd29aLHnLd2tdadtKqndRAuIbHK5bLy+byq1arcXdVqVfl8noApBuYHTARLwOKKxaImH9qq/fdskSTtv2eLJh/amtjto5sBk0SwBAAA0GufvfLcBQOm89au1mevPLfnNRAuIbEKhYJqtbnD/2q1mgqFQkQVYbZmwCSJYAk4jFwup1KppKOeuV/f/9v366hn7lepVEr0jj8bN6zRnZs28LMPzMKIawBAr7QKmPoVLEmSuXtfnqifRkdHfWxsLOoy0GOpVEqtvn/NTPV66wWl0X/j+2qssQSg68xsh7uPRl0HDqL/tbjmiOvZF8bS6XRig+RyuaxCoaDx8XGNjIyoWCwm8nUAQGh+88ZvafsTe3sWLC3UB2Pk0gAK5arZyMhIR+2IBsESMHhC+ZwBuimkEdcsTQAA8fXZK8/Vlt9Z17cRS02ESwMmpM5AsVhUOj03uEin04ldowQAQhDS5wzQTePj4x21x1lIQRkAhKjXi3e3Qrg0YELqDDTXKMlkMjIzZTKZxA4tB4BQhPQ5A3RTSCOuQwrKAADdQbg0YELrDORyOVUqFdXrdVUqFYIlAIhYaJ8zQLeENOI6pKAMANAdhEsDhs4AAKCX+JxBN4W0fldII64vvvjijtoBAOEjXBowIV01AwDED58z6JYQ1+8KZcT11q1bO2oHAISPcGnAhHTVLDQhXZ0FMLj4nEG3sH5XfDH9Nb7oTwKIirl71DV03ejoqI+NjUVdBtC25tXZ2Z3odDrNCRkALMDMdrj7aNR14KBu979SqZRa9VPNTPV6vWvPg85ls1lVq9VD2jOZjCqVSv8LgiT6kwD6Y6E+GCOXgBjg6iwAAHOxfld8Mf01nuhPAogS4RIQAwwvBwBgLhaNji+mv8YT/Umgc0wl7Z7hqAsAMH0VttXwcq7OAgAGFYtGx1sulyNMihn6k0Bn5k8lbW4cIYnfb0vAyCUgBhheDgDAXIzCADrDaD+gM0wl7S7CJSAGGF4OAMBcrLkEdIbRfkBnuIjRXYRLQEzkcjlVKhXV63VVKhWCJQDAQGNUL9AZTpSBznARo7sIlwAAABA7jOoFOsOJMtAZLmJ0F+ESAAAAYim0Ub3sSoReKhaLWrFixZy2FStWcKIMLICLGN1FuAQAAIBYCimMae5KVK1W5e4zuxIl+TUhfsxs0dsA5grtIkaUzN2jrqHrRkdHfWxsLOoyAABAj5jZDncfjboOHNTt/tf8LaKl6ekKSb2qnM1mW24Tn8lkVKlU+l8QgsP3GIB+WKgPxsglAAAAxE5oW0Sz2DJ6je8xAFEiXAIAAEDshHaizGLL6DW+xwBEiXAJAAAAsRPaiTK7EqHX+B4DECXCJQAAAMROaCfKuVxOV1xxhYaGhiRJQ0NDuuKKKxK5fhTiiZ2vAESJcAkAAACxE9qJcrlc1s0336ypqSlJ0tTUlG6++WZ2i0NXsfMVgKi0tVucma109wPz2la7+96eVbYM7BYHAEDYBmW3ODM71d0fjrqOdtD/Whw7eQEAQrDc3eLuN7N1sx7sPZLu6VZxAKavaGazWaVSKWWzWa5kAgAk6QYzu8/MrjGzl0ddDJYutAXKAQCYbbjN435d0k1mdoek4yStkvSWXhUFDJpyuax8Pj+z5XK1WlU+n5ckhjMDwABz9//NzNZK+o+SxszsPkl/7+63R1waOjQyMtJy5FJSFygHAGC2tkYuuft3JRUlXSVpg6QPuPuuXhYGDJJCoTATLDXVajUVCoWIKgIAxIW7PyHpjyV9WNKbJX3CzB4zs3dHWxk6EdoC5Yy4BgDM1la4ZGY3Svo9SadLep+kfzGzjT2sCxgoDJUHEBJOOrvHzE43s49JelTTo8Z/xd1f2/j6Y5EWh46EtEB5c8R1tVqVu8+MuOZnHUDSXHPNNRoeHpaZaXh4WNdcc03UJSVWuwt6/76kv/HGwWb2Mkkfdfcre1zfkrCgJJKGRT4BhGL+NF9penRGt0+iB2hB7zslfVrSF9z9hXn3/aa7fzaayg5F/2tw0G8BEIJrrrlG119//SHtV199ta677roIKkqGZS3o7e4fk7TazI5p3N4f12AJSKKLL764o3YAiCum+XaXu58v6auSXtLivtgESxgsjLgGEIJSqdRROxa3aLhk0/7MzPZKelzSv5nZHjP7k/6UBwyGrVu3dtQOAHHFSWd3zOqD7ZH0mOiDIUYWWoScxckBJMnU1FRH7Vjc4UYu/Z6k9ZLOdvej3f0oSedKWt+YKjcwWD8CvcTJGIBQcNLZNb+n6T7YOe6+apD7YIif0BYnBzCYhoaGOmrH4g4XLv2WpMvd/X81G9z9KUm/0bhvILBoIXqNkzEAoeCks2vogyG2QlqcHMDgyufzHbVjcYcLl1a4+975je6+R9KK3pQUP6wfgV7jZAxAKDjp7Br6YIi1XC6nSqWier2uSqXCzziAxFm/fr2Gh4fntA0PD2v9+vURVZRshwuX/n2J9wWFKUvoNU7GAADz0AcDAKCHCoWCJicn57RNTk4yiGSJhg9z/xlm9uMW7SZp5VKf1MyOlvR5SVlJFUn/wd2fa3FcRdLzkqYkTUa15fDIyEjL7VaZsoRuyuVyhEkAEq85lbw54rc5lVwSv+M605M+GAAAmMYgku5adOSSuw+5+5Et/rzU3ZczJPsjkv7V3ddK+tfG7YVscPczowqWJKYsAQDQLqaSd0cP+2CIEBvEAEB8sO5tdx1uWlyvXCLp5sbXN0v61YjqaAtTlgAAaA9XAYHW2CAG/UCACbSPQSTdZe7e/yc1+5G7v3zW7ecaW+zOP+5/SXpOkkv6W3cvLfKYeUl5SRoZGXlDq2lsAACgt7LZbMup5JlMRpVKpWvPY2Y7ohzVjEONjo762NhY1GXEVr9+NjC45k9LlqZPlLkoDiysXC6rUChofHxcIyMjKhaL/LwcxkJ9sJ6NXDKzr5vZwy3+XNLBw6x397MkvUPSRjM7f6ED3b3k7qPuPnrMMccsu34AANA5rgICrYU2qo8RMvHDtGSgc+x82T2HW9B7ydz9rQvdZ2Y/MLNj3f0ZMztW0g8XeIzdjb9/aGa3SDpH0p09KRgAACxbs1PGVUBgrpA2iGHh/ngKLcAEkCxRrbl0q6QrGl9fIenL8w8wsxeb2UubX0t6m6SH+1YhAABYEq4CAocKaVQfI2TiicWJAUQpqnDpLyRdaGZPSLqwcVtmdpyZbW0c8wpJd5nZg5Luk/QVd/9qJNUCAAAAyxDSBjGMkImnkAJMAMnTs2lxi3H3fZJ+sUX7bkkXN75+StIZfS4NAAAA6IlcLpfIMGm+kKb4hYRpyQCiFNXIJQAAAAAJxAiZ+GJaMoCoEC4BMcGuKwAAIAlCmuIHAOiOSKbFAZiLXVcAAECShDLFDwDQHYxcAmKAXVcAAP1gZkeb2e1m9kTj76MWOK5iZt81swfMbKzfdQIAgGQhXAJigF1XAAB98hFJ/+ruayX9a+P2Qja4+5nuPtqf0gAAQFIRLgExsNDuKuy6AgDosksk3dz4+mZJvxpdKUA8sO4lACwf4RIQA+y6AgDok1e4+zOS1Pj75xc4ziV9zcx2mFm+b9UBfdZc97JarcrdZ9a9JGACgM4QLgExwK4rAIBuMbOvm9nDLf5c0sHDrHf3syS9Q9JGMzt/gefKm9mYmY3t2bOnK/UD/cS6lwDQHYRLbWK4LHotl8upUqmoXq+rUqkQLAEAlsTd3+rup7b482VJPzCzYyWp8fcPF3iM3Y2/fyjpFknnLHBcyd1H3X30mGOO6c0LAnqIdS8BoDsIl9rAcFkAANrHBZlYu1XSFY2vr5D05fkHmNmLzeylza8lvU3Sw32rEOgj1r0EgO4gXGoDw2UBAGgPF2Ri7y8kXWhmT0i6sHFbZnacmW1tHPMKSXeZ2YOS7pP0FXf/aiTVAj1WLBZ1xBFHzGk74ogjWPcSADo0HHUBScBwWQAA2rPYBRmm+0bP3fdJ+sUW7bslXdz4+ilJZ/S5NCAy7r7obQDA4TFyqQ0Ml40vpl4AQLxwQQZAkhQKBU1MTMxpm5iYYIYCAHSIcKkNbBMfT0y9AID44YIMgCQhEAeA7iBcakNo28SHMtqHtbAAIH64IAMgSQjEAaA7CJfaFMo28SGN9uFKEwDET2gXZACEjUAcALrDQlywbnR01MfGxqIuI5ay2ayq1eoh7ZlMRpVKpf8FLUNIrwUA0Bkz2+Huo1HXgYPofyGpyuWyCoWCxsfHNTIyomKxSCAOAAtYqA/GyKUB0yqMWaw9zrjSBAAAgOUKZYYCAESJcAmJxdQLAAAAAACiNxx1AcBy5HI5wiQAAAAAACLEyKUBMzQ01FF73IWy812IeG8AAAAAYDAQLg2YfD7fUXuchbTzXWh4bwAAAABgcBAuDZjrrrtOV1999cxIpaGhIV199dW67rrrIq6sc4VCQbVabU5brVZToVCIqCI08d4AAICkYLQ1ACyfuXvUNXQdW+EOhlQqpVbfv2amer0eQUVo4r0B0GsLbYOL6ND/QhI1R1vPviiWTqfZJAYAFrBQH4yRS0iskZGRjtrRP7w3AAAgCRhtDQDdQbiExCoWi0qn03Pa0um0isViRBWhifcGAAAkwfj4eEftAIDWCJeQWLlcTqVSSZlMRmamTCbDEOaY4L0BAABJwGhrAOgO1lwCAACJw5pL8UP/C0nEmksA0BnWXMKMkHbECOm1AACAsNFviR9GWwNAdwxHXQD6a/7VmWq1qnw+L0mJ+xAN6bUAAICw0W+Jr1wux3sAAMvEtLgBk81mVa1WD2nPZDKqVCr9L2gZQnotAIDOMC0ufuh/LY5+CwAgBEyLg6SwdsQI6bUAAICw0W8BAISMcKlNocyRD2lHjJBeCwAACBv9FgBAyAiX2tCcI1+tVuXuM3PkkxgwFYtFpdPpOW3pdFrFYjGiipauWCxqxYoVc9pWrFiRyNcCAADCFlIfDACA+QiX2lAoFOZsTypJtVpNhUIhooqWLrQdMcxs0dsAkBShjJAF0FpofTAAAGZjQe82pFIptfp/MjPV6/WuPQ86w8KYAEIxfxcpaXpEAyeeC2NB7/hhQW8AAMLHgt7LwBz5eGJhTAChCGmELAAAAAYP4VIbLr744o7a0R+EfgBCQVgOIGmYygsAmI1wqQ1bt27tqB39wcKYAEJBWA4gSULa7AYA0B2ES23ginI8sTAmgFAQlgNIEqbyAgDmI1xqA1eU4yuXy6lSqaher6tSqRAsAUik0MJypssAYePCK4BQ0GfpHsKlNnBFGQDQa6GE5UyXAcLHhVcAIaDP0l2ES23gijIAAO1hugwQPi68AggBfZbuiiRcMrP3mtkjZlY3s9FFjrvIzB43s51m9pF+1jgfV5QBADg8pssA4QvtwiuAwUSfpbuiGrn0sKR3S7pzoQPMbEjSZkn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