multiple-source/Distance_inference-multiple_sources.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coryn Bailer-Jones, MPIA Heidelberg (https://mpia.de/homes/calj)\n",
    "\n",
    "The main reference for this tutorial is [Cluster distance inference](resources/cluster_inference.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3d0f87d2-479b-49c5-9219-35dd71c8ae54"
    }
   },
   "source": [
    "# Global settings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Relative to the root directory, ensure that the R codes (*.R) are \"Rcode/\" and the data files (*.csv) are in \"data/\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbpresent": {
     "id": "ba432e7c-ac3d-4650-a06d-4ea0d7127f20"
    }
   },
   "outputs": [],
   "source": [
    "rootDir <- \"./\" # directory containing Rcode/ and data/ directories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbpresent": {
     "id": "082aeada-6ebe-46da-bfa7-b1864f78dd20"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: spam\n",
      "Loading required package: dotCall64\n",
      "Loading required package: grid\n",
      "Spam version 2.2-0 (2018-06-19) is loaded.\n",
      "Type 'help( Spam)' or 'demo( spam)' for a short introduction \n",
      "and overview of this package.\n",
      "Help for individual functions is also obtained by adding the\n",
      "suffix '.spam' to the function name, e.g. 'help( chol.spam)'.\n",
      "\n",
      "Attaching package: ‘spam’\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    backsolve, forwardsolve\n",
      "\n",
      "Loading required package: maps\n",
      "See www.image.ucar.edu/~nychka/Fields for\n",
      " a vignette and other supplements. \n"
     ]
    }
   ],
   "source": [
    "setwd(paste(rootDir, \"Rcode\", sep=\"\"))\n",
    "conv <- pi/180 \n",
    "source(\"general_functions.R\")\n",
    "source(\"distance_functions.R\")\n",
    "setwd(\"../\")\n",
    "library(MASS) # for truehist\n",
    "library(fields) # for image.plot\n",
    "library(RColorBrewer) # for colorRampPalette\n",
    "mypalette <- colorRampPalette(brewer.pal(9, \"Greys\"), space=\"rgb\", interpolate=\"linear\", bias=2.5)\n",
    "mycols <- mypalette(64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "0ebe2af4-0afa-4b85-9f91-e21c0744e638"
    }
   },
   "source": [
    "# Read and check GDR1 data"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Gaia archive query for gdr1set03.csv (164 Pleiades members from the GDR1 release paper)\n",
    "\n",
    "select gaia.ra, gaia.dec, gaia.parallax, gaia.parallax_error, gaia.pmra, gaia.pmdec\n",
    "from gaiadr1.tgas_source as gaia\n",
    "where contains(point('ICRS',gaia.ra,gaia.dec),circle('ICRS',56.75,24.12,5)) = 1\n",
    "  and sqrt(power(gaia.pmra-20.5,2)+power(gaia.pmdec+45.5,2)) < 6.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "nbpresent": {
     "id": "929d9637-5d24-451b-a449-3866262b6a69"
    }
   },
   "outputs": [],
   "source": [
    "# parallaxes are in mas, angles in degrees\n",
    "dat <- read.csv(paste(rootDir, \"data/gdr1set03.csv\", sep=\"\"), sep=\",\")\n",
    "# To prevent hitting numerical limits in the likelihood calculations, retain parallaxes in mas. \n",
    "# Thus distances in this notebook are in kpc.\n",
    "# For testing use a smaller data set\n",
    "#dat <- dat[1:25,]\n",
    "# To investigate the impact of larger uncertainties, scale parallax SD:\n",
    "#dat$parallax_error <- dat$parallax_error*20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbpresent": {
     "id": "527bada4-531e-4b23-84b4-19fdc41c2cf3"
    }
   },
   "outputs": [
    {
     "data": {
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wdGRsafTuFwuGvXrqmpqR09erSoqIgm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\ngICA7h2Rpri4GP7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vtDgl4XGhq6YcOG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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First inspect the data\n",
    "par(mfrow=c(2,2), mar=c(5,5,0.5,1), oma=c(0.1,0.1,0.5,0.1), mgp=c(2.2,0.8,0), cex=1.0) \n",
    "# Show source positions on sky along with proper motions\n",
    "plot(dat$ra, dat$dec, xlim=rev(range(dat$ra)), xlab=\"RA [deg]\", ylab=\"Dec [deg]\")\n",
    "sf <- 0.03 # scale factor for visualizing PM arrows\n",
    "arrows(dat$ra, dat$dec, dat$ra+sf*dat$pmra, dat$dec+sf*dat$pmdec, length=0.05, lw=0.5)\n",
    "# Histogram of fractional parallax uncertainties\n",
    "truehist(dat$parallax_error/dat$parallax, nbins=25)\n",
    "# Histogram of inverse parallaxes, for orientation.\n",
    "truehist(1/dat$parallax, nbins=25, prob=FALSE, ylab=\"number\")\n",
    "segments(x0=1/dat$parallax, y0=0, x1=1/dat$parallax, y1=10, lw=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "514e96c0-3453-499e-bf9e-9b915c9dd340"
    }
   },
   "source": [
    "# Naive parallax combination\n",
    "\n",
    "The following methods for estimating the cluster distance from some combination of the parallaxes and their uncertainties are poor. \n",
    "\n",
    "First, it is quite wrong to estimate the cluster distance via the mean of the inverse parallaxes (image some parallaxes were negative), and is meaningless when the fractional uncertainties are large. I do it here for comparison (and it's a fair way of getting a feel for the order-of-magnitude that the data imply)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean and SD of inverse parallaxes:  0.1376619 0.02686311 kpc\n"
     ]
    }
   ],
   "source": [
    "cat(\"Mean and SD of inverse parallaxes: \", mean(1/dat$parallax), sd(1/dat$parallax), \"kpc\\n\")\n",
    "# Note that this is an SD in the sense of a spread, not a standard uncertainty in the mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next thing we could think about doing is taking the inverse of the mean of parallaxes, and estimating its variance by a first order Taylor expansion. This is a slight improvement, but still not what we should be doing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "nbpresent": {
     "id": "b42d15f5-b3d0-4439-81a2-a17c6b5d5b32"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inverse of mean parallaxes:  0.1347596 +/- 0.0005589137 kpc\n",
      "SD of inverse mean parallax in the sense of a spread: 0.002887234 kpc\n"
     ]
    }
   ],
   "source": [
    "Nstar <- nrow(dat)\n",
    "mpar  <- mean(dat$parallax)\n",
    "rNaive1 <- 1/mpar\n",
    "rNaive1SD <- (1/Nstar)*sqrt(sum(dat$parallax_error^2)) / mpar^2\n",
    "cat(\"Inverse of mean parallaxes: \", rNaive1, \"+/-\", rNaive1SD, \"kpc\\n\")\n",
    "# This gives an estimate of the distance to the cluster, together with the standard deviation in this mean.\n",
    "cat(\"SD of inverse mean parallax in the sense of a spread:\", sd(dat$parallax_error)/mpar^2, \"kpc\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could go one step further and take a (variance) weighted mean. Specifically, take the inverse of the variance weighted mean of the parallaxes and estimate the variance of this again by a first order Taylor expansion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "nbpresent": {
     "id": "28086c1f-2d80-4061-9299-8698d4896890"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inverse of weighted mean of parallaxes:  0.1337066 +/- 0.000428167 kpc\n"
     ]
    }
   ],
   "source": [
    "wfac <- sum(1/dat$parallax_error^2)\n",
    "wmpar <- sum(dat$parallax/dat$parallax_error^2)/wfac\n",
    "rNaive2 <- 1/wmpar\n",
    "rNaive2SD <- 1/(wmpar^2 * sqrt(wfac))\n",
    "cat(\"Inverse of weighted mean of parallaxes: \", rNaive2, \"+/-\", rNaive2SD, \"kpc\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "65f109e1-d41c-40e7-8f9b-ebaae91e5954"
    }
   },
   "source": [
    "# Estimate distance to cluster (no correlations or cluster spread)\n",
    "\n",
    "Rather than mucking about with inverting and averaging the parallaxes, we should think about what we want to achieve. We want to infer the distance, $r$, to the cluster given a set of parallaxes $\\{\\varpi\\}$ and corresponding parallax uncertainties $\\{\\sigma_{\\varpi}\\}$ of (some of) its members. Let's assume, for now, that the cluster is very small compared to its distance from us, such that we can consider the true distance to all the stars to be the same (\"no cluster spread\"), and equal to the distance of cluster, $r$. We proceed as for the single star case, but now using a multivariate likelihood. For $N$ stars this is an $N$-dimensional Gaussian. If we assume (for now) that the parallaxes are independent (\"no correlations\"), then this is just a product of $N$ 1-dimensional Gaussians. The posterior is\n",
    "\n",
    "\\begin{alignat}{2}\n",
    "P(r|\\{\\varpi\\}, \\{\\sigma_{\\varpi}\\}, L) \n",
    "&\\propto \\ P(r|L) \\ P(\\{\\varpi\\} | r, \\{\\sigma_{\\varpi}\\}) \\\\\n",
    "&\\propto \\ P(r|L) \\ \\prod_i P(\\varpi_i | r, \\sigma_{\\varpi_i})\n",
    "\\end{alignat}\n",
    "\n",
    "\n",
    "Let's compute and plot the posterior, using the exponentially decreasing space density prior with length scale rlen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbpresent": {
     "id": "f6825b3f-7e32-42dc-bbee-dd0244026596"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1.77400601608986e-248</li>\n",
       "\t<li>4.27814437873653e-238</li>\n",
       "\t<li>1.33664003283405e-237</li>\n",
       "\t<li>2.24270311696013e-245</li>\n",
       "\t<li>5.40055638509741e-251</li>\n",
       "\t<li>5.79439690115499e-276</li>\n",
       "\t<li>9.39661587519058e-270</li>\n",
       "\t<li>1.89726355645542e-242</li>\n",
       "\t<li>2.51469813007231e-237</li>\n",
       "\t<li>1.30269657470928e-254</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1.77400601608986e-248\n",
       "\\item 4.27814437873653e-238\n",
       "\\item 1.33664003283405e-237\n",
       "\\item 2.24270311696013e-245\n",
       "\\item 5.40055638509741e-251\n",
       "\\item 5.79439690115499e-276\n",
       "\\item 9.39661587519058e-270\n",
       "\\item 1.89726355645542e-242\n",
       "\\item 2.51469813007231e-237\n",
       "\\item 1.30269657470928e-254\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1.77400601608986e-248\n",
       "2. 4.27814437873653e-238\n",
       "3. 1.33664003283405e-237\n",
       "4. 2.24270311696013e-245\n",
       "5. 5.40055638509741e-251\n",
       "6. 5.79439690115499e-276\n",
       "7. 9.39661587519058e-270\n",
       "8. 1.89726355645542e-242\n",
       "9. 2.51469813007231e-237\n",
       "10. 1.30269657470928e-254\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 1.774006e-248 4.278144e-238 1.336640e-237 2.242703e-245 5.400556e-251\n",
       " [6] 5.794397e-276 9.396616e-270 1.897264e-242 2.514698e-237 1.302697e-254"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4.97529090261854e-280</li>\n",
       "\t<li>2.81809923707271e-237</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4.97529090261854e-280\n",
       "\\item 2.81809923707271e-237\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4.97529090261854e-280\n",
       "2. 2.81809923707271e-237\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4.975291e-280 2.818099e-237"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the length scale of the prior\n",
    "rlen <- 1 # in kpc\n",
    "# The unnormalized posterior is computed by the function ud.distpost3multi,\n",
    "# which by default assumes no correlations in the likelihood.\n",
    "# As it involves a product of lots of small numbers, the posterior density can \n",
    "# drop below the numerical precision, so check this here before trying to normalize.\n",
    "r <- seq(from=0.130, to=0.140, length.out=1e3)\n",
    "#r <- seq(from=0.100, to=0.200, length.out=1e3) # to use with x20 uncertainties\n",
    "dense <- ud.distpost3multi(r=r, w=dat$parallax, wsd=dat$parallax_error, rlen=rlen)\n",
    "dense[sample(length(r),10)] # print 10 random samples\n",
    "range(dense)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "nbpresent": {
     "id": "e682dff8-45c9-4e99-aa25-b3ae3ef6df0f"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior mean, SD for rc = 0.1337133 0.0004282268 kpc\n"
     ]
    },
    {
     "data": {
      "image/png": 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evvf/97h8PRpTsDylJcXCzRiXyRkZHB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\n/we6rKKQwR/ngQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Estimate the normalization constant, mean, and standard deviation of the posterior\n",
    "# directly from the tabulation (using pdfmom)\n",
    "mom <- pdfmom(dense, r)\n",
    "cat(\"Posterior mean, SD for rc =\", mom$mean, mom$sd, \"kpc\\n\")\n",
    "plot(r, dense/mom$Z, type=\"l\", xlab=\"distance r [kpc]\", ylab=\"P(r | {w},{wsd},rlen) * const\")\n",
    "abline(v=c(rNaive1, rNaive2), col=\"red\")\n",
    "# Note that in this case the mode is very close to rNaive2, because the data are highly \n",
    "# informative compared to the prior, so the maximum of the posterior is very \n",
    "# close to the maximum of the likelihood. The prior will only have a visible impact on\n",
    "# the posterior once rlen ~ 0.001 or so."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estimate distance to cluster (with correlations, no cluster spread)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "f3e500a4-3557-4a32-9d4e-ed5c10f0bb03"
    }
   },
   "source": [
    "## Invent a simple model for spatial parallax correlations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I now allow for correlations between the parallaxes. Given a set of $N$ parallax measurements, their correlations are determined by the $N \\times N$ covariance matrix $C$. The likelihood for the $N$ measurements is no longer a product of $N$ one-dimensional Gaussian functions, but is rather an $N$-dimensional Gaussian\n",
    "\n",
    "$\n",
    "P({\\boldsymbol \\varpi} | {\\mathbf r}, C) = \\frac{1}{(2\\pi)^{N/2}|C|^{1/2}}\\exp\\left[-\\frac{1}{2}\\left({\\boldsymbol \\varpi} - \\frac{1}{{\\mathbf r}}\\right)^\\mathsf{T} C^{-1} \\left({\\boldsymbol \\varpi} - \\frac{1}{{\\mathbf r}}\\right)\\right]\n",
    "$\n",
    "\n",
    "where\n",
    "\n",
    "$\n",
    "\\frac{1}{{\\mathbf r}} = \\left(\\frac{1}{r_1}, \\frac{1}{r_2}, \\ldots \\right) .\n",
    "$\n",
    "\n",
    "To illustrate this approach I invent a model (unrelated to Gaia!) which specifies that the correlation between any two parallax measurements, $\\varpi_1$ and $\\varpi_2$, is a function of the angular separation, $\\theta$, of the two sources on the sky\n",
    "\n",
    "$\n",
    "\\rho(\\varpi_1, \\varpi_2) = a\\exp(-\\theta/\\theta_{\\rm len})\n",
    "$\n",
    "\n",
    "\n",
    "where $\\theta_{\\rm len}>0$ is some fixed angular scale and $0\\leq a \\leq 1$ gives the amplitude of the correlation at zero separation. The elements of the covariance matrix $C$ are \n",
    "\n",
    "$\n",
    "C_{i,j} = \\rho(\\varpi_i, \\varpi_j)\\sigma_{\\varpi_i}\\sigma_{\\varpi_j}.\n",
    "$\n",
    "\n",
    "Provided the two sources are not widely separated and not near the poles, we can approximate their angular separation as\n",
    "\n",
    "$\n",
    "\\theta = \\left( [(\\alpha_1\\!-\\!\\alpha_2)\\cos(0.5(\\delta_1\\!+\\!\\delta_2))]^2 + (\\delta_1\\!-\\!\\delta_2)^2  \\right)^{1/2}\n",
    "$\n",
    "\n",
    "where $(\\alpha, \\delta)$ are the RA and declination of a source.\n",
    "\n",
    "In the code that follows, the function parcor computes $\\rho$, and parcovmat computes $C$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0276160478548459"
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      "text/latex": [
       "0.0276160478548459"
      ],
      "text/markdown": [
       "0.0276160478548459"
      ],
      "text/plain": [
       "[1] 0.02761605"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>0.057828708 </td><td>0.0025803245</td><td>0.0018530974</td></tr>\n",
       "\t<tr><td>0.002580325 </td><td>0.1509670341</td><td>0.0001667215</td></tr>\n",
       "\t<tr><td>0.001853097 </td><td>0.0001667215</td><td>0.3664019852</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t 0.057828708  & 0.0025803245 & 0.0018530974\\\\\n",
       "\t 0.002580325  & 0.1509670341 & 0.0001667215\\\\\n",
       "\t 0.001853097  & 0.0001667215 & 0.3664019852\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 0.057828708  | 0.0025803245 | 0.0018530974 | \n",
       "| 0.002580325  | 0.1509670341 | 0.0001667215 | \n",
       "| 0.001853097  | 0.0001667215 | 0.3664019852 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]        [,2]         [,3]        \n",
       "[1,] 0.057828708 0.0025803245 0.0018530974\n",
       "[2,] 0.002580325 0.1509670341 0.0001667215\n",
       "[3,] 0.001853097 0.0001667215 0.3664019852"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.92764345466248e-05"
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      "text/latex": [
       "1.92764345466248e-05"
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      "text/markdown": [
       "1.92764345466248e-05"
      ],
      "text/plain": [
       "[1] 1.927643e-05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The following R functions implement the above.\n",
    "# Function parcor computes correlations between parallaxes for sources according to\n",
    "# amp*exp(-sep/len), where sep is the angular separation on the sky of two sources,\n",
    "# len is the length scale (sep and len have same units), and 0<=amp<=1.\n",
    "parcor(dat$ra[1], dat$dec[1], dat$ra[2], dat$dec[2], amp=0.5, len=0.5)\n",
    "# Function parcovmat computes the covariance matrix for a given set of sources \n",
    "# and the parameters for parcor\n",
    "(mat <- parcovmat(dat=dat[1:3,], amp=0.5, len=0.5))\n",
    "# d.likemulti computes the density of an N-dimensional likelihood (i.e. for N sources) with\n",
    "# specified covariance matrix (parcovmat). For independent parallaxes, use parcovmat=NULL.\n",
    "d.likemulti(w=dat$parallax[1:3], r=0.12, wsd=dat$parallax_error[1:3], parcovmat=mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "e0b785f6-40ba-4047-96e6-c5787c08c539"
    }
   },
   "source": [
    "## Naive parallax combination (with correlations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "This would be equivalent to maximum likelihood, which is equal to maximum posterior with a uniform (non-truncated) prior. So we'll just skip this and get to the more general posterior solution. (The parallax combination method doesn't give a probability distribution. It just gives one estimator and a (symmetric) standard deviation.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "4a53e630-f3f4-4ed4-abc4-92c7813c4b64"
    }
   },
   "source": [
    "## Posterior distance estimate (with correlations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "nbpresent": {
     "id": "f04ff921-f0aa-4816-a5b1-e53f80309630"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "6.46501369030646e-08"
      ],
      "text/latex": [
       "6.46501369030646e-08"
      ],
      "text/markdown": [
       "6.46501369030646e-08"
      ],
      "text/plain": [
       "[1] 6.465014e-08"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "6.46501369030645e-08"
      ],
      "text/latex": [
       "6.46501369030645e-08"
      ],
      "text/markdown": [
       "6.46501369030645e-08"
      ],
      "text/plain": [
       "[1] 6.465014e-08"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rlen <- 1 # in kpc\n",
    "# ud.distpost3multi accommodates parallax covariances when its argument parcovmat!=NULL\n",
    "# Test the function: the following two numbers should be identical\n",
    "ud.distpost3multi(r=0.120, w=dat$parallax[1:4], wsd=dat$parallax_error[1:4], rlen=rlen)\n",
    "ud.distpost3multi(r=0.120, w=dat$parallax[1:4], wsd=dat$parallax_error[1:4], \n",
    "                  parcovmat=diag(dat$parallax_error[1:4]^2), rlen=rlen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "nbpresent": {
     "id": "c7d0b350-6e4d-4b89-9242-2b6a29aa0e39"
    }
   },
   "outputs": [],
   "source": [
    "# Compute the covariance matrix\n",
    "mat <- parcovmat(dat=dat, amp=0.5, len=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "nbpresent": {
     "id": "6ec825ef-98fd-4174-a000-cd265fb5491b"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With    correlations: Posterior mean, SD for r = 0.1341392 0.0007135305 kpc\n",
      "Without correlations: Posterior mean, SD for r = 0.1337133 0.0004282268 kpc\n"
     ]
    },
    {
     "data": {
      "image/png": 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YwUAxCqfF+KVWrshKBjB4S8UAp2jBQDoEN+7bFTqmPn1+EJIYTFYtm7d6/s5QDw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\noqOFwUDHDghFPgwBs9ls77777pYtW3bs2NHe3m4ymWbMmDF79mz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sQqmpqaWlpZ2/9ujRw2Qy9e7d+/zXnDhxol+/fsrVAADyaG7+bqHT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ns02LHreogy2FlaklLJ0bXd3d0TEhI4ujiA7njycicy\nmSw4ODg4OJiHagAAJKisjAwMyNSUfcVuiirKWbFcjrHDo1gAjXhCsKutrY2Pj6+qqvLz83Ny\ncuKnJgAASXl0rZOsrCx7e3sTExMBK+okKytOe+xyc3MbGhrEt24zgDZp6ynqt99+6+zsPGDA\ngOHDh7u4uPztb3+rqKjgrTIAAIkoL286cyIrK0tku8Q24rLHzsPDQ6VS5eXlcXR9AB3x2H8Y\nnTlzZtasWQYGBqNGjbKzs7t06dKePXtqamqioqL4rA8AQPSUSrKyanwl1kXsiMjSkiorqaGB\nOOhUc3Nzk8lkIk69ANrhsf9z/utf/5LJZGfOnGGXHa6vr58+ffqBAwcSEhL69OnDY4UAACL3\naLAT6yJ2RA8+RXk52dho/NrGxsYODg6ZmZlY6x7gaTz2UezFixdHjhzZ+D+YoaHhe++9R0Qx\nMTE8lQYAIA0tNooVd7DjcpgdVjwBeEqPDXbFxcW+vr5Nj7Avi4qKOC8KAEBKysok8igWwQ5A\n6z022KnV6maTtoyNjYlIpVJxXhQAgJQolY09diqVKjc3V6zDyCwtSSbjLth5eHhkZmZydHEA\nHYG1hQEAONakx45dnViswU5fn8zMOO2xQ7ADeEoIdgAAHGvSY5eVlSWTyVxdXYWtqPO4XMrO\nw8MDj2IBnlJbU9ZjYmLWrl3b7OCZM2eaHWx5DgAA/KnJ5AkRr07M4jjYFRYWVlZWYvNxgE5r\nK9idP3/+/PnzzQ5GR0dHR0c3PYJgBwDQlibLnYh4SiyL42BHRFlZWX5+fhw1ASB5jw123333\nHZ91AABIVpNgJ/oFeLkMdk5OTnK5PDMzE8EOoNMeG+xmzpzJZx0AANKkVlNlZeOWYpmZmQqF\nQtiKnoq1NZWWcnRtPT09V1dXzJ8AeBqYPAEAwKWyMlKrG7dqyMzMRI9dGxQKBYIdwNNAsAMA\n4BIbg/Aotn2wlB3AU0KwAwDgEvvg0sqKiGpqagoKCtgpAmJlaUllZdxdXqFQZGRkcHd9AMlD\nsAMA4JJSSTIZu9xJdnY2wzDinhXL5Rg7IvLw8ECwA3gaCHYAAFxSKsnMjAwMiCgzM1NfX9/F\nxUXomp4Cx8FOoVBkZ2dj70qATkOwAwDgUpO1TjIyMlxdXQ0M2lpAVNtxH+zq6+vz8vK4awJA\n2hDsAAC4VFraGOwyMzPFPcCOiKysqKqK6uo4uryHh4dMJsPTWIBOQ7ADAOCSUknW1uyPWVlZ\nog927GfhbGKssbGxo6Mjgh1ApyHYAQBw6dFtJyQS7Lh8Guvp6YlgB9BpCHYAAFx6dIyduBex\nIz6CnUKhSE9P5+76ANKGYAcAwKWyMjbYMQyTlZUl7v3EiMjcnAwM0GMHoLUQ7AAAuFRSwu4n\nVlBQUFVVJfpgR0RWVlz32CHYAXQagh0AAJcezoplw4rox9gRkbU119vFZmRkMAzDXRMAEoZg\nBwDApdJSdlxaZmamjY2NpaWl0AU9NY6XsvP09Kyurr5//z53TQBIGIIdAACXHga7jIwMKXTX\nEZGNDdfBjogwfwKgcxDsAAC41CTYsZFF9KytqaSEu8ubmZk5ODgg2AF0DoIdAABnqquptpYN\ndunp6VKYOUFENjacBjsi8vT0TEtL47QJAKlCsAMA4Az7yPJhj51Egh3HY+yIyMvLCxNjAToH\nwQ4AgDOSDHbosQPQYgh2AACceRjslEplaWmpRIIdx2PsiMjLywvBDqBzEOwAADijVJKRERkb\ns1MBJDJ5guNZsfTwUaxarea0FQBJQrADAODMw20n0tPTLSws7O3thS5IE3jpsaurq8vNzeW0\nFQBJQrADAODMw2CXlpYmke46IrKxobo6qqrirgWFQqGnp4ensQCdgGAHAMCZh8FOOjMniNhP\nxGmnnZGRkYuLS2pqKndNAEgVgh0AAGdKShoXsZNUjx1xG+yIyMvLC8EOoBMQ7AAAOFNa2vgo\n1svLS+hqNMTGhmQyKi7mtJGuXbti8wmATkCwAwDgTJPJE9LpsTMwIAsL9NgBaCcEOwAAzpSU\nkI1NcXGxUqmUTo8dEdnYcN1jh2AH0DkIdgAAnCkpIRsbSS1ix7K15brHztvbOy8vr7q6mtNW\nAKQHwQ4AgDMlJWRtnZaWZm1tbcPOOZAG7ncV69q1K8Mw6LQD6CgEOwAAziiVZG2dmpoqqeew\nRGRry/WjWCcnJzMzMwQ7gI5CsAMA4EZDAymVZGeXlpbWtWtXoavRKO577GQyGYbZAXQCgh0A\nADdKSohhyMZGmsGO4x47IuratWtKSgrXrQBIDIIdAAA32D4tW9vU1FRJzZwgPh7FEpGPjw96\n7AA6CsEOAIAbxcVEpLa2zsjIkFqPnZ0dP8EOPXYAHYVgBwDAjeJiMjbOLiqqra2VWrCztaWi\nIq4b6dq1a1pamkql4rohAClBsAMA4EZxMfscVk9PT6FQCF2NRtnaklJJDQ2cNuLj41NbW5uT\nk8NpKwASg2AHAMCNkhI22Lm5uRkZGQldjUbZ2RHDUGkpp40oFApDQ8Pk5GROWwGQGAQ7AABu\nFBeTjU1qaqq3t7fQpWiarS0RcT3MzsDAwMPDA8EOoEMQ7AAAuFFaSjY2KSkpUhtgR0R2dkTE\nwzC7bt26IdgBdAiCHQAANwoLyc4uJSVFgj12xsZkasrPxFgEO4AOQbADAOBGURHZ2SUnJ/v4\n+AhdCgd4mRiLYAfQUQh2AADcKC6uNjUtKSmR4KNYIrKz4+dRbEpKCsMwXDcEIBkIdgAA3Cgq\nym9oICIJPoolInt7fnrsqqqqsOIJQPsh2AEAcKOoKLu62t7e3traWuhSOMBLj52Xl5eBgUFS\nUhLXDQFIBoIdAAAH1GpSKlOVym7dugldCjfs7KiwkOtGDA0NPT09McwOoP0Q7AAAOFBSQmr1\n3aIiac6cIJ4exRKRr68veuwA2s9A6AI6jGGYtLS01NTU8vJyIrKysvLx8fHw8BC6LgCAJoqK\niCgxLy+wb1+hS+EGLz12RNStW7e7d+/y0BCANIgp2BUWFn744Yc//PDD/fv3m72lUCheeeWV\nZcuWmZmZCVIbAMAjiouJ6FpGxhSp9tjxMsaOiHx9fY8dO8ZDQwDSIJpgl5eXFxoamp6e7u3t\nPXr0aIVCYW5uTkRlZWWpqalnzpxZs2ZNVFRUdHS0lZWV0MUCgM4rKGBMTdPv35fsGDu+HsV2\n69YtNTW1vr7e0NCQh+YAxE40we7dd9/NycnZs2dPREREy3dVKtW2bdsWL168Zs2ajRs38l8e\nAMAjCgvrrayoqkrKY+xqa6migszNOW2ne/fu9fX16enpko3IABolmskTv/7668yZM1tNdUSk\nr6+/cOHCqVOnRkVF8VwYAEAriooqTUzs7e1tbGyELoUbDg5ERAUFXLfj5uZmamp6584drhsC\nkAbRBLvi4uIn/sPX39+/5fA7AAABFBWV6On5+voKXQdn7O2JiIf5E3p6et26dcPEWIB2Ek2w\nc3Z2vnbtWtvnxMbGuri48FMPAEBbCgvvq1RSfnpoZkampvxMjO3evTt67ADaSTTBLjw8/MCB\nAxs2bKitrW35bkVFxbvvvnv48OHHPasFAOBVYWFWdbWUe+yIyN6eh0exhGAH0BGimTyxZs2a\n6Ojo5cuXr1u3Ljg4mJ0VyzBMeXl5WlpabGxsdXX10KFDV69eLXTiapxmAAAgAElEQVSlAABE\nhYVS3naCZW/PW4/dF198wUNDABIgmmBnZWV1/vz5rVu37t69Ozo6Wq1WN75lYGAQEhIya9as\n2bNnGxiI5hMBgISpCgqyq6vHdu8udCFccnDgJ9j5+fndv3+/pKREsjNRADRHTDHI2Ng4MjIy\nMjKytrY2IyOjvLxcJpNZWloqFAqsbwQAWkV9716BTCbZtU5YPD6Klclkt2/fHjRoEA/NAYia\naMbYNWIYJicnJzMzMzMzMyMjIzMzMy8vT+iiAACaUKkMystljo6mpqZCl8IlR0d+gp25ubmb\nm9vt27d5aAtA7MTUY4ctxQBAHIqLZWq1pbe30HVwzMGBLl7kpyl/f38EO4D2EE2ww5ZiACAa\nhYVE5NCjh9B1cMzBgZ8eOyLy8/O7desWP20BiJpogh22FAMA0SgoUBO59ekjdB0cc3Sk/Hx+\nmurRo8eRI0f4aQtA1EQT7Nqzpdi5c+eioqI6FOyqqqq2bt3a0NDQxjmXLl3qWK0AoNtU9+6V\nEvnqQo9dWRnV1JCxMddN+fn5paenV1dXm5iYcN0WgKiJJti1c0uxgwcPduiySqXyt99+U6lU\nbZyTk5PToWsCgI4ruHmzlMjPz0/oQjjm6EhEVFBA7u5cN9WjRw+VSpWUlBQQEMB1WwCiJppg\nx9GWYs7OzseOHWv7nO3bt8+fP79DlwUAXVaclKTU1+8u+R0O2WCXn89DsHNwcHBwcLh58yaC\nHUDbRLPcCbYUAwCxqE5Pr7a0lMlkQhfCMQsLMjbmbf5Ejx49bty4wU9bAOIlmh47bCkGAGLR\nkJv7oDdL8rp0oRbrT3GkR48emBgL8ESiCXbYUgwAxMKguFgeEiJ0FbzgMdj17Nnz999/56ct\nAPESUwzClmIAoP0YhjGrrDSU9mZijfgNdikpKZgYC9A2MQW7RkZGRr6+vi2PFxUVlZSUSHxz\nRgDQbpmZmQ5qdV3PnkIXwgtHR96CXa9evVQq1e3bt4OCgvhpEUCMRDN5oj0++eSTbt26CV0F\nAOi0W9ev2xB16d1b6EJ4wWOPnb29fZcuXTB/AqBtouyxAwDQWmlXrugRkZOT0IXwgsdgR0S9\nevVKTEzkrTkAMZJUjx0AgODu/fEHEVGXLkIXwosuXXjbVYyIevXqdf36dd6aAxAj0fTYBQcH\nP/EcbBEBAIIrvXNHZWCgb20tdCG8cHKiggJqaCBeViTo3bt3VFQUDw0BiJdogh277UTbs1/b\n3vIVAIBrarW6NiOjzsbGRPKrE7OcnEitpvx84mWbjd69e2dlZZWWllrrSG4G6DjRPIpdvny5\nmZlZYmJizeO99dZbQpcJADotPT3dqqZGT/KbiTVihxLeu8dPa71799bX18fTWIA2iCbYvf/+\n+z4+PtOnT6+vrxe6FgCA1iUmJroaGMi53ztVW1hZkakpb8HOxMTEx8cnISGBn+YAxEg0wc7Q\n0HD37t03btz4+9//LnQtAACtS0xM7G5lJXN2FroQHjk5UV4eb6316dMHwQ6gDaIZY0dE/v7+\n9+7da2Mg3ZgxYzDwAgAEdP369eeNjHRlo1iWkxNvPXZE1KdPnyNHjvDWHIDoiKbHjmVpaWlr\na/u4d4cOHfrOO+/wWQ8AQFPx8fFOajXpWo8dj8EuICAgISFBpVLx1iKAuIgs2AEAaK3a2trk\n5GTLykrdCnYuLpSby1trgYGBVVVVycnJvLUIIC4IdgAAmnHr1i29+nqDigrdCnbOznwGO3d3\ndzs7uz/YVaABoAUEOwAAzYiPjw9yciKG0a1g5+LC5+QJIgoICGBXNgWAlhDsAAA0Iz4+PtTL\ni0hn9hNjsY9i1WreGgwKCkKwA3gcBDsAAM1ISEgIcnIiGxsyMRG6Fh65uFB9PRUV8dZgUFAQ\nHsUCPA6CHQCAZvzxxx/+1ta69RyW6MFmYjwOswsKCsrPz8/OzuatRQARQbADANCAzMzMoqIi\nT0NDcnUVuhZ+2dqSiQnl5PDWoJ+fn7m5eVxcHG8tAogIgh0AgAbEx8ebmZnZVlfrXLAjIldX\nPoOdnp5eQEDA1atXeWsRQEQQ7AAANODq1at9+vSR5eY+eDSpU/gNdkTUr1+/2NhYPlsEEAsE\nOwAADbh69Wq/fv0oN1cXe+zc3IjfEW/9+vW7cuUKny0CiAWCHQCABly7di0wMJByctBjx4P+\n/fsXFBRkZWXx2SiAKCDYAQA8rfz8/KysrGB/fyor09Fgx2+PXffu3S0sLNBpB9ASgh0AwNOK\njY01NjbuaWlJROTuLnQ5vHN3J347z/T09PA0FqBVCHYAAE8rNjY2ICDAIC+PDA3J0VHocnjn\n7k5KJZWV8dlmSEjI5cuX+WwRQBQQ7AAAntbVq1f79u1L2dnk4kL6+kKXwzsPDyLiudMuJCQk\nNjZWzeNWZgCigGAHAPC0Ll++HBISQllZuvgclogcHMjYmOdgN2jQoLKyslu3bvHZKID2Q7AD\nAHgq2dnZeXl5/fv3p+xscnMTuhwhyGTk6spzsHNxcXFzc7t48SKfjQJoPwQ7AICnEhsba2Fh\n4efnRzk5OhrsiMjDgzIzeW5zwIABly5d4rlRAC2HYAcA8FQuXrwYHBysr69PGRkPRpvpIA8P\nysjguc1BgwZduHCB50YBtByCHQDAU7l06dKAAQOIiDIzdTfYeXryH+xCQ0Nv3rxZUlLCc7sA\n2gzBDgCg81QqVVxcXEhICBUXU3k5KRRCVyQQhYL/YNe3b1+5XI6nsQBNIdgBAHTe9evXy8vL\nBw0a9GCEmc722CkUlJ1NDQ18tmlkZBQcHHz+/Hk+GwXQcgh2AACdd/HiRU9PTycnJ8rMJHNz\nsrUVuiKBKBSkUvG8sRgRDR48GMEOoCkEOwCAzrtw4UJoaCgRUVqa7j6HJSIPD9LXp7Q0npsd\nMmTIpUuX6urqeG4XQGsh2AEAdF5MTMzgwYOJiNLTyctL6HKEY2hIbm6CBLuampq4uDie2wXQ\nWgh2AACddO/evbS0tAc9dunp5OkpcEHC8vLiP9jZ2Nj07Nnz7NmzPLcLoLUQ7AAAOikmJsbS\n0rJ3795ECHbCBDsiGjZsWHR0NP/tAmgnBDsAgE46e/ZsaGiovr4+EYIdkbc3paby3+yzzz4b\nExPTwO+EXACthWAHANBJMTExzzzzDBFRURGVlpK3t9AVCcrbm1JS+G926NChFRUVGGYHwEKw\nAwDoDKVSmZCQMGzYMCJ6EGi6dhW0IqF5e1N+PpWV8dysg4NDr169Tp8+zXO7ANoJwQ4AoDPO\nnTvHLpBLRJSaSvb2ZGkpdFGC6taNiATptBsxYsSpU6f4bxdACyHYAQB0xunTpwcNGiSXy4mI\nUlJ0/TksEVlbk50dJSfz33JYWFhMTExNTQ3/TQNoGwQ7AIDOOH369PDhwx+8SE1FsCMi8vGh\nu3f5b3bo0KENDQ3YggKAEOwAADqhqKgoPj4+LCzsweu7d8nXV9CKtIOvryDBztLScsCAASdP\nnuS/aQBtg2AHANBhv//+u5mZ2YMBdkSUlPRghJmO69aNkpIEaXnkyJEnTpwQpGkArYJgBwDQ\nYadOnRo2bJihoSERUXk53b+PYEdE5OtLt28L0vKoUaOuXbt2//59QVoH0B4IdgAAHfbbb789\n99xzD16wfVQIdkTk50fFxVRYyH/LwcHBdnZ2x44d479pAK2CYAcA0DF3795NTU0dOXLkg9d3\n7pCjI1lbC1qUdvD1JT09QTrt9PT0Ro0adfToUf6bBtAqCHYAAB1z/PhxT0/P7t27P3h9+zb5\n+wtakdYwMSGFgm7dEqTxcePGHT9+vL6+XpDWAbQEgh0AQMccPXp09OjRf76+fZv8/IQrR8v4\n+wsV7EaPHl1RUYFFT0DHIdgBAHRAdXX16dOnx44d++eh27epsfcOevSgmzcFadnGxmbIkCH/\n/e9/BWkdQEsg2AEAdAC7ddWIESMevG5ooKQkPIr9U48elJgoVOOTJk365ZdfhGodQBsg2AEA\ndMChQ4eGDx9uamr64HVyMtXWUq9eghalTXr1opwcKi4WpPFJkyalpqbGx8cL0jqANkCwAwBo\nL4ZhDh06NHHixD8PJSaSpSW5ugpXlJbp2ZP09OjGDUEa9/LyCgoKioqKEqR1AG2AYAcA0F6X\nL1/Oy8ubMGHCn4du3qSePUkmE64oLWNqSt7edP26UO1Pnjz5p59+Eqp1AMEh2AEAtNfBgwcH\nDhzo4uLy56GEBAoIEK4irRQQQMI9DJ0yZcrNmzdvCNRlCCA4BDsAgPY6cOBAeHj4I4fi46lP\nH4HK0VaCBrvu3bsHBQXt27dPqAIAhIVgBwDQLteuXUtJSZk8efKfhyorKTUVPXbNBQbS9euk\nUgnVfkRExJ49exiGEaoAAAEh2AEAtMv+/fuDg4O9vLz+PJSQQAyDKbHN9e1LVVWCbCzGioiI\nSE1NvXTpklAFAAgIwQ4A4MkYhtm7d29ERMQjR+PiqFs3srQUqCht5eJCzs4UFydU+x4eHs88\n88x3330nVAEAAkKwAwB4sgsXLmRmZjYPdlevUt++AlWk3fr2FTDYEdHLL7+8d+/e2tpaAWsA\nEASCHQDAk3333XdhYWGPzIcloqtXKShIoIq0W0gIXb4sYPtTpkypq6vD9mKggxDsAACeoKam\nZv/+/S+99NIjR6uq6MYNCgkRqCjtNmAAXbtGwnWYWVhYTJ069auvvhKqAAChINgBADzBwYMH\nVSpV84VOYmNJrcaj2Nb17091dQIuekJEr7322smTJ1NSUgSsAYB/CHYAAE+wY8eOadOmmZmZ\nPXL08mXq0QMzJ1pna0vdu9P58wKWMGDAgICAgO3btwtYAwD/EOwAANqSlJR0+vTpV199tfkb\n589TaKgQFYnE4MHCBjsiWrhw4c6dO6uqqoQtA4BPCHYAAG3Ztm1bv379+vfv3/yNixdp8GAh\nKhKJIUPo/HkSdJXg6dOnE9H3338vYA0APEOwAwB4rIqKiq+//nrhwoXN37h7l+7dQ49dW4YO\npXv36M4dAUswNTWdN2/ep59+qlarBSwDgE8IdgAAj7Vr1y65XN58+ToiOnOGXFzIx0eIokTC\ny4sUCjpzRtgqFi9enJ6e/ssvvwhbBgBvEOwAAFqnUqk2btz4+uuvGxsbN38vOpqGDxeiKFEZ\nMYJ+/13YEpycnGbNmvXRRx8JWwYAbxDsAABa9+OPP+bl5b3++uvN32AYOnWKwsKEKEpU2GCn\nUglbxYoVK65du3b06FFhywDgB4IdAEArGIb56KOPXn31VQcHh+bvXb9OeXn0l78IUZeoPPcc\nKZV05YqwVXh5eb300ktr1qxhBJ3JAcAPBDsAgFZERUUlJSWtWLGilfeOHyd/f/Lw4L0osXFw\noP796cgRoeug1atXJyQkHDx4UOhCADiHYAcA0JxKpXrvvffmzZvXfHNY1pEjNG4c70WJ07hx\ndOiQ0EWQQqFYuHDhypUr6+vrha4FgFsIdgAAze3atSsrK+vvf/97K+8VF9OFCwh27fX88xQf\nT1qwr9eqVasKCwu3bNkidCEA3EKwAwB4REVFxerVq1esWOHo6NjK27/8QpaWNGQI73WJU+/e\n5ONDUVFC10G2trbvv//+P/7xj7y8PKFrAeAQgh0AwCPef/99uVy+bNmy1t8+cIAmTSIDA36L\nErOpU2nvXqGLICKaN2+et7f3kiVLhC4EgEMIdgAAf0pMTPz00083btxoYmLSytslJXTiBLVc\nrxjaMH06Xb1Kt24JXQfp6+t/8cUXUVFRP//8s9C1AHAFwQ4A4AGVSjV37tyxY8c+//zzrZ+x\nbx/Z2mJp4o7p1Yv69aOvvxa6DiKifv36rVixYt68efn5+ULXAsAJBDsAgAc+/vjjpKSkzz//\n/LFn7NxJM2fiOWyHvfIKffMN1dUJXQcR0Zo1a9zc3GbPno1l7UCSEOwAAIiILl26tHbt2q1b\nt7a+xAkRxcVRbCzNmcNvXZIwcyZVV9OPPwpdBxGRXC7fs2fPuXPnsM8YSBKCHQAAFRYWTp06\n9aWXXpo2bdpjT9q8mcLCyM+Px7qkwtKSZs+mTz8Vuo4HfH19d+7c+d577x0+fFjoWgA0DMEO\nAHRdXV3dlClT7OzsNm/e/NiTsrNpzx5aupTHuqRlyRKKj6djx4Su44EpU6asWrVq+vTpcXFx\nQtcCoEkIdgCg0xiGmTNnTlJS0s8//9z6TFjW+vXk709jxvBYmrR4edGLL9KaNaQ1I9vWrl0b\nHh4+duzY27dvC10LgMYg2AGA7mIYZvHixYcOHTpy5IhHG3u/pqbSl1/S2rUkk/FYneSsWUPx\n8bR/v9B1PCCTyb766qshQ4aEhYXduHFD6HIANAPBDgB0lFqtfv3117/99tvDhw8HBQW1deqy\nZTRgAD1uDRRoJ4WCli2j5cupvFzoUh4wMDDYu3dvaGjo0KFDL1y4IHQ5ABqAYAcAuqiqqmrK\nlCn79u07duzYkLb3Bzt4kA4fpjaG30H7rVpFhoa0fLnQdfzJ0NBw3759U6dOHTFixK5du4Qu\nB+BpYTUmANA5d+/efeGFF8rLy2NiYnr06NHWqbm5NG8evf02BQTwVZ2kmZrSrl00fDg99xxN\nnix0NQ/o6+t//vnn/v7+r7322tmzZzdt2mRhYSF0UQCdhB47ANAhDMN88cUXffv2dXFxuXz5\n8hNSXU0NTZlCPj60Zg1fBeqAZ56hdeto1iy6elXoUh6xePHis2fPRkdHBwQEHD9+XOhyADoJ\nwQ4AdMXVq1efffbZyMjIDz744MiRI3Z2dm2dXV9PERGUk0MHDpChIV816oaVKyk8nEaPpoQE\noUt5xMCBA+Pj4ydMmDBu3LiJEydiRgWIkfiCHcMwqampJ0+ePHjw4MGDB0+dOpWZmSl0UQCg\n1f74449p06b179/fwcEhMTHxjTfekLU9v7W0lMaPp8uX6bffyNmZrzJ1hkxGX31Fzz1HQ4fS\niRNCV/MIc3PzTZs2xcXF1dTU9OnTZ+rUqRcvXhS6KIAOEFOwKywsXLp0qbOzs7e393PPPRce\nHh4eHj5ixAiFQuHp6blu3brKykqhawQALVJZWfn9998PGzYsKCiotLT03LlzUVFRXl5eT/i1\nmBgKDqbsbIqJIV9fXirVPQYG9N13NG8ejR1Ly5aRln17BwQEnDhx4syZM1VVVaGhoUFBQRs3\nbszJyRG6LoAnk4llF+S8vLzQ0ND09HRvb+8hQ4YoFApzc3MiKisrS01NPXPmTG5ubkBAQHR0\ntJWVlWab3r59+/z588vLy9kWAUDLpaWl/f7777/++uvx48cNDQ0jIiIWLFgQ0J7ZD4mJ9OGH\ntG8fvfIKffop4X95Hhw9SvPnU0MDvf02zZ5N2jdrITk5eefOnbt3787Ozu7Xr9+YMWOGDx8e\nEhJiamoqdGkgmLq6OiMjo/Pnz4eGhgpdS3OiCXZz5sz57rvvvv3224iIiJbvqlSqbdu2LV68\n+I033ti4caNmm0awA9BmNTU1qampt2/fvnnz5rVr1y5dupSTk+Ps7Dxq1KhJkyaNHj3a2Nj4\nCZe4dYtOnKAff6Tz52nYMPrgA9K+L2spq6qizZvp00+pooImTaLx42noUHJxEbqsRzAMc+XK\nlUOHDp08eTI2NlYmk/Xq1SswMLBnz57+/v7e3t6enp5GRkZClwk8QbDTAGdn5zFjxuzcubON\ncyIiIi5cuKDxIXcIdgBcq66urqmpaXxZWlrKMIxKpSorK1Or1Uqlsrq6uqqqSqlUlpSUlJSU\nFBYW5ufn37t3Lzs7Oy8vj4gsLS179OgREBDQv3//0NBQf3//B9eqqKD6elKrSamkmhoqK6Pi\nYioqopwcysigpCS6do1KSqhrV5o4kV5+mQIDBfkTAKqro19+oR9/pN9+o5IScnWlXr3Ix4c8\nPMjJieztydqaLCzIzIxMTYmNUJaWpK/Pf6UVFRWXL1++cuVKfHz8zZs379y5w969Tk5OTk5O\nLi4u9vb2tra2NjY2VlZWFg8ZGBjY2NgQEftz0x9YVlZWenpiGh+ly7Q52IlmHbvi4mIfH5+2\nz/H39z948GCHLpuWljZgwICGhoY2zqmtrSWiJwy1brczf/lL4KlTGrkUgPbr3D8drR/+YP/w\nB5lMxv4/qKenJ3tIj2Vhoc8wsrIyuniRLl6k7dufcHVjY7K3J1dX8vCgAQPotdcoJISeOPAO\nuCaX05QpNGUKqVR04wbFxdGtW5ScTFeuUG4uFRVRdXV7LyWTkbX1k0/rLHOiMKKwxtcmJmoj\nI7VarS4vVyuVzO3barWaeRS14/8FZUdq0NRfSbrmj7CwYSdPCl0Ft0QT7Jydna9du9b2ObGx\nsS4d7L1XKBT79+9vO9jduHFjyZIlhhpa78B/w4ZULZsFBiAgPT09MzOzpkdMTEz09fXZHwwM\nDORyuVwu7+TVLSyI7RFh+3gsLMjcnExMnrZo4JS+PvXpQ336ND9eW0uVlVRaSgxDpaUPDpaV\nkUrFc4Et6bVvKmJtbW19fb1arW6c6ldVVaVWq5ueU641+61Jkv/IkUKXwDnRBLvw8PCNGzdu\n2LBh8eLFLccxVFRUrF+//vDhw++8806HLqunpzds2LC2z9HsCNkugYFd8KwHAKCjjIzIyIhs\nbYWuo/OMiNi/vSwFLgSkTDRj7JRKZVhY2NWrVy0sLIKDg9lZsQzDlJeXp6WlxcbGVldXDx06\n9Ndff9X4TKULFy4MHjy4tra2890GAAAAIBUYY6cBVlZW58+f37p16+7du6Ojo5v2XRsYGISE\nhMyaNWv27NlNB6ICAAAA6BQxxSBjY+PIyMjIyMja2tqMjIzy8nKZTGZpaalQKDQ1AA4AAABA\nvMQU7BoZGRn5Yjl4AAAAgEdhyRwAAAAAiUCwAwAAAJAIBDsAAAAAiUCwAwAAAJAIBDsAAAAA\niUCwAwAAAJAIBDsAAAAAiUCwAwAAAJAIBDsAAAAAiUCwAwAAAJAIBDsAAAAAiUCwAwAAAJAI\nBDsAAAAAiUCwAwAAAJAIBDsAAAAAiUCwAwAAAJAIA6ELEAG5XE5ERkZGQhcCAAAA2oKNB9pG\nxjCM0DWIQHx8fENDg0Yu9e6771ZVVb366qsauRpAh/zxxx9btmzZsWOH0IWAjpo7d+6iRYsC\nAwOFLgR00ZdffmlqavrPf/5TI1czMDAICAjQyKU0C8GOb7Nnzyair7/+WuhCQBcdOXJk2rRp\nFRUVQhcCOsrc3Hzfvn3jxo0TuhDQRTry9y/G2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAA\ngEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBPaK5Zt2bi0HOkIul+MO\nBAHhDgQB6ci9hy3F+FZSUkJENjY2QhcCukitVmdmZnp6egpdCOio9PR0Dw8PPT08LAIB6Mjf\nvwh2AAAAABKBfzYBAAAASASCHQAAAIBEINgBAAAASASCHQAAAIBEINgBAAAASASCHQAAAIBE\nINgBAAAASASCHQAAAIBEINgBAAAASASCHQAAAIBEINgBAAAASASCHQAAAIBEINgBAAAASASC\nHQAAAIBEINgBAAAASASCXccolcqlS5d6enoaGRm5uLjMnTv33r17T/yt+vr6lStX6uvrBwcH\nt3y3sLBw2bJl/v7+pqamnp6ekydPvn79euO7u3btkrXmn//8pyY/GIgBF7dfamrqnDlzfHx8\nTExMunbtGhERkZiY+PSNgiTxfwfiCxAacXH7NbV06VKZTDZ37tynb1RYBkIXICY1NTVhYWFX\nr16dPHlyUFBQSkrKN998c+rUqStXrtjZ2T3ut27dujVz5sy7d++2+m5RUdGAAQPS0tLGjx//\nwgsvpKen79279/Dhw6dOnRo8eDARlZaWEtH06dM9PDya/iL7LugOLm6/uLi4YcOG1dXVTZ06\n1dvbOzk5ef/+/T///PPp06cHDRrU6UZBkgS5A/EFCCwubr+mYmNjP/vsM400KjwG2u3f//43\nEX388ceNR/bs2UNES5cufdyvKJVKExOT4ODgu3fvGhkZ9evXr9kJixYtIqL//Oc/jUcOHjxI\nRGPGjGFfrlmzhoiuXLmi0Y8C4sPF7RcWFiaTyaKjoxuPREVFEdGECRM63ShIlSB3IL4AgcXF\n7deovr4+MDCwT58+RDRnzpynaVQbINh1QL9+/SwsLKqrq5se9Pb27tKli1qtbvVXioqKli1b\nVldXxzBMqzdWZGTkqFGj6uvrG4+o1WpTU1OFQsG+fPPNN4no7t27GvwgIEZc3H6rVq1auXJl\n0yMNDQ2Ghoa9evXqdKMgVYLcgfgCBBYXt1+j9evX6+npHT9+vFmwE+kXIIJde9XU1Ojp6Q0f\nPrzZ8ZdffpmIUlJSnniFtm+spg0ZGho2nslev6CggGGY+/fv5+fnd7x2ED3ebr+0tDQimjRp\nkkYaBckQ5A5k8AUIDMNwfPslJyebmJi88cYbJSUlTYOdeL8AMXmivTIyMtRqtUKhaHacPZKa\nmqqphrZv315fXz9jxgz2pVKpJKKNGzfa2dl16dLF0dHR29v7+++/11RzIAo83H5lZWWnT58O\nDw83NzdftWoVP42CWAhyBxK+AIGIOL795s2bZ29v/8EHH/DZKKcweaK9ysvLicjc3LzZcQsL\nCyIqKyvTSCvR0dHLly8fNGjQwoUL2SPs2OEffvhh8eLFXl5eSUlJW7ZsefHFFysrK+fNm6eR\nRkH7cX37WVtbs3+DTp8+ff/+/T4+Pjw0CiIiyB1I+AIEIuLy9tu1a9fvv/9+6NAhc3Nz9mbj\noVGuIdg9LYZhiEgmkz39pfbs2TN79uzevXsfOnRILpezB1evXr1o0aJRo0Y13l4zZszo16/f\nypUrZ82aZWRk9PTtgnhp6vZbsGBBQUHBnTt39u7dm5WV9c0333Tt2pXrRkECuL4D8QUIbXjK\n2y8/P3/ZsmXTpk0bP348b43yAMGuvaysrKi1kM4eYd/tNMyrv2wAAA6mSURBVIZh1q5du27d\nunHjxu3du7fpPxHCwsKandyjR4+xY8dGRUUlJCT079//adoFseD09iOijz76iP3h7Nmzo0eP\n/utf/3r16lWuGwUREeQO1NfXxxcgEGe335tvvskwzKZNm/hslAcYY9deCoXCwMCAHdjbFPug\nvfHBQScwDDN37tx169ZFRkb+8ssvLTt+W3J0dCSiioqKTjcK4sLd7dfMs88+O3bs2ISEhKSk\nJN4aBe0nyB34uHPwBahruLj9jh49unfv3pUrV9bX12dnZ2dnZ+fm5hJRVVVVdnZ2WVmZeL8A\nEezay9DQsH///nFxcZWVlY0HVSrVmTNnFApFs8UzOyQyMnLnzp2ffPLJv//9bz29R/6LVFRU\nbN26dffu3c1+5ebNm/RwCCfoAi5uv3v37gUGBrIzvJpiHzRUVlZyd8+D6AhyB+ILEFhc3H6/\n//47Ea1YscL9oZ49exLRnj173N3dP/zwQxF/AQo0G1eUtm/fTkSrV69uPPKf//yHiP7xj3+w\nL6urq69du5acnNzqr7c63frAgQP0+NUOVSqVm5ubqalpYmJi48HDhw8TUWBg4FN9GBAbLm4/\nb29vuVx+6dKlxiN37twxNzc3NzevqqpqT6OgO/i/A/EFCI00fvvdvHnz0KP27t1LRCNHjjx0\n6NCtW7fa06h2kjEMw3+aFKn6+vqwsLCYmJgJEyb069fv9u3b+/bt69Onz/nz583MzIgoMTGx\nd+/eI0aMOHnyJPsr0dHRR48eZX/esGGDg4ND4z9Ply9fbmdn5+Pjk5KS8sYbb5iYmDRr7u23\n37axsTl48OALL7xgYmIybdo0V1fXmzdvRkVFmZqanjp1CuNLdAoXt9/p06dHjhypp6c3efLk\nrl275uTk/Pjjj5WVlZs3b2b3RHlio6A7BLkD8QUILC5uv2ZNlJaW2tjYzJkzZ8eOHe1sVEsJ\nnSxFpqKiYsWKFQqFQi6Xu7m5sUsaNr57/fp1IhoxYkTjkcYRwS2xa6m38Z8mLS2Nvci5c+cm\nTpzo6upqaGjo7Ow8c+bMO3fu8Pu5QSto/PZjGObq1asRERFeXl5yudza2nrEiBG//PJL+xsF\nnSLIHYgvQGBxcfs11WyB4vY0qp3QYwcAAAAgEZg8AQAAACARCHYAAAAAEoFgBwAAACARCHYA\nAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAA\nACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAA\nEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACAR\nCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFgBwAAACARCHYAAAAAEoFg\nBwCCMTAwGDhwIPtzRESETCa7d++esCXxbNGiRbKHtm3bRg//HLKzszXelp+fX2Nb6enpGr8+\nAGgDA6ELAAAgIgoMDCwtLTUyMmrPyevXr58yZYqPjw/XVfHjq6++cnR07NOnD6etbNu2raKi\n4ssvv/zll184bQgABIRgBwBa4Z133nnnnXfac2ZeXt7KlSsDAwMlE+zCwsI8PT25bmXYsGFE\ndPLkSa4bAgAB4VEsAIjMlStXhC6hY9RqdV1dndBVAIBOQLADAJ78+uuv/fr1MzExcXR0nDt3\nbmlpqUwma3y36Ri72traTz75JCAgwMrKysLCok+fPp988olarSai8ePHT5o0iYjGjBkjk8li\nYmLYX7948WJ4eLibm5uxsbGnp+eLL77YdBjZzJkzZTJZdXX16tWrFQqFiYmJn5/fxo0bGYZp\nPCczM/Oll17q0qWLiYlJz549//Wvf9XX1ze+e+/evQULFnh4eMjlcgcHh+eff77tfDlt2jQ9\nPb2ioqIRI0aYmJh0+umnWq2ePHmynp7e999/T0Th4eEymSw/P3/evHlOTk5GRkZ+fn5bt25t\n+ittfxAAkDY8igUAPsTExEycONHKyurdd991dHQ8ceLExIkTmwa7phYsWPD111//7W9/W7Bg\nARGdPHlyxYoVGRkZW7Zseffdd21tbb/77rv33nsvKCioR48eRBQbGzt8+HBbW9vXXnvN2dk5\nOTl569atJ06cuHnzpp2dHRGxQ/dmzJhhZWW1c+dOmUz24YcfRkZGWlpavvLKK0SUl5c3cODA\n0tLSOXPmeHp6njlz5q233rp+/fquXbuIKD8/f8CAAUqlcuHChX5+ftnZ2Z9//vmQIUN+++23\nZ599ttWPIJfLGYZ56623GIZZtWpV9+7dO/fn9tZbb0VFRW3YsGHmzJlEZGhoSESTJk0KCAj4\n4YcfSktLP/roo9dff93AwODVV1994gcBAOljAAC4N3r0aCK6cOFC45H58+cT0YABA9iX06ZN\nI6K8vDyGYUxNTQcNGtT015ctWzZ58uSGhgaGYT766CMiOnr0aOO727dvHzRo0JkzZxqPbN68\nmYg2b97MvpwzZw4RTZkypfGE1NRUIho3bhz7cu7cuUR0/PjxxhPGjRtHRNevX2cYZt68efr6\n+rGxsY3vZmZmWlhYBAcHP+7zsnlx1KhRKpWqjT+WhQsXElFaWlrjEfbPISsri2GYLVu2ENHy\n5cubvdv0gxQXF5uZmXl6erbngzAM8+abbzZrEQCkBI9iAYBzarU6Ojray8tr0KBBjQfZYNcq\nuVyenp5+//79xiMbNmz46aef9PX1Wz3/tddeu3DhwtChQ9m2GhoaevfuTUTNFvVgwxbLy8vL\n2Ng4JyeHfXngwAEPD4+RI0c2nvDZZ5+dOnXKycmJiH788Uc/Pz9XV9d7DxkaGoaGhsbGxhYW\nFrZaEtsZ+fLLL+vpdfJr9tChQ2+++eZLL7308ccfN3trxowZjT/b2NgMGTIkPT09KyvriR8E\nACQPj2IBgHN5eXnV1dXe3t5ND7bxdHLVqlXLly/v3r37+PHjR4wYMWrUKBcXlzaur1art23b\n9vXXX9+8ebOqqqrxeENDQ9PTFApF05dGRkbs4LN79+6VlJT069ev6btdu3bt2rUrW3xxcXFx\ncbGzs3PLpjMzM+3t7R9XWLdu3doouw1xcXEzZswYOHDgV1991fKBta+vb9OX7OfKyMgwNDRs\n44MAgC5AsAMAzrFhy8TEpOlBY2Pjx42xe+uttwICAj7//POff/559+7dMpls1KhRmzdvftz6\nJitXrvy///u/IUOG7Ny5093dXS6XJyYmzp49u9lpcrm81V+vqKhoWV6jyspKIgoMDGQfATfT\ndmaytrZu4902vPjii5WVlYmJidnZ2S1XQjE3N2/6kh1BWFNT0/YHAQBdgGAHAJxjo0Z1dXXT\ng+Xl5UyTSanNPPfcc88991xdXd2FCxd27969c+fOsWPHJiYmtgxnNTU1n332mZub28mTJxvX\nN1Yqle0vj81JbCpqycLCgogaGhrYYYL8GDhw4MKFC8PDw2fMmHH27Nlmz6Cb9krSw+hpZmbW\n9gcBAF2AMXYAwDknJye5XJ6SktL0YGJi4hN/US6XDxs27Msvv1ywYMHdu3fj4+NbnpOXl1dT\nUxMcHNx014ro6OgOlWdjY3Pjxo2mQfPOnTtbtmy5ceNGly5d7O3t7969W1xc3PS3CgoK2t9E\nR+3cuXPSpEkrVqy4cOHCP/7xj2bv3r59u+nLu3fvEpGXl1fbH4S7agFAeyDYAQDnDAwMQkND\n09LSzp8/33iQnbja0oULF1xdXb/99ttWr0NEbPdVY/+fk5OTTCbLyMhoPO3WrVvsr9fU1LSz\nwr/+9a/5+fn79u1rPLJ27drFixezg/BeeOGF2trapgUXFBT06dPn+eefb+f1O2fdunXBwcEf\nfvjhuXPnmh7fsWMHu6ofEaWkpFy8eLFnz57s9Ii2PwgASB4exQIAH1asWBEdHT1u3Lj58+e7\nuroeO3aspqbGxsam5ZnBwcE2NjavvvpqTExMYGAgwzBxcXHffPPN4MGDAwMD6eGwtvXr16em\npj7zzDMhISHjx48/dOjQ/Pnzhw4deuPGjS+++OKHH34YO3bskSNHdu/ezS5o3LZ169YdOXJk\n1qxZMTExnp6e0dHRhw8ffumll9gW165de+TIkXXr1mVnZw8ZMiQ3N3fbtm0lJSWLFy/W9J/T\nIwwNDXfv3t23b98ZM2YkJCQ0jtirrq4eNWpUeHh4VVXVZ599Vl9fv3r16vZ8EACQPmFXWwEA\n3bF3797evXuzOze88sorJSUl7u7uffv2Zd9tuo5dfn7+kiVLunXrZmZmZmlp2bt37w8++IAd\nk8cwTF1d3eTJk01NTd3c3A4cOMCe/7e//c3BwcHc3Hzo0KFnz55lGOb99983Nzd3dnbOy8tj\n17G7e/du03qsrKx69uzZ+DItLW3mzJmOjo7GxsY9evT45JNPamtrG9/Ny8tbsGCBu7u7oaFh\nly5dJk6c+L///a+ND9tqiy21vY4da8eOHfRw7Tr23aSkpDfffNPFxUUul/v7++/atavpNdv+\nIFjHDkDaZMzjBy8DAACnFi1a9J///CctLa3l1NdWRURE7Nu3Lysry83NrXMtLlmyZNOmTe1v\nEQDEBWPsAAAAACQCY+wAAAQWHR19+/btnj17uru7c9dKTExMRUVF01kmACA9CHYAAAKbNWsW\nEW3durWNbdae3ty5c+/cucPd9QFAG2CMHQAAAIBEYIwdAAAAgEQg2AEAAABIBIIdAAAAgEQg\n2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBIId\nAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEA\nAABIBIIdAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAAgEQg2AEAAABIBIIdAAAA\ngEQg2AEAAABIxP8DXc0quxq+jRQAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the posterior (scaled to have maximum=1) on a grid and plot (in black)\n",
    "r <- seq(from=0.125, to=0.140, length.out=1e3)\n",
    "#r <- seq(from=0.050, to=0.250, length.out=1e3) # to use with x20 uncertainties\n",
    "dense <- ud.distpost3multi(r=r, w=dat$parallax, wsd=dat$parallax_error, parcovmat=mat, rlen=rlen)\n",
    "mom <- pdfmom(dense, r)\n",
    "cat(\"With    correlations: Posterior mean, SD for r =\", mom$mean, mom$sd, \"kpc\\n\")\n",
    "plot(r, dense/mom$Z, type=\"l\", xlab=\"distance r [kpc]\", ylab=\"P(r | {w},{wsd},{wCov},rlen)\")\n",
    "# Overplot (in red) the posterior (obtained earlier) without correlations\n",
    "dense <- ud.distpost3multi(r=r, w=dat$parallax, wsd=dat$parallax_error, rlen=rlen)\n",
    "mom <- pdfmom(dense, r)\n",
    "cat(\"Without correlations: Posterior mean, SD for r =\", mom$mean, mom$sd, \"kpc\\n\")\n",
    "lines(r, dense/mom$Z, col=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "8d0560aa-0fb5-4248-b7c6-99c0e8b3131b"
    }
   },
   "source": [
    "# Estimate cluster distance and size (no correlations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reference document: [Cluster distance inference](resources/cluster_inference.pdf)\n",
    "\n",
    "We now assume tht the cluster has a finite size, such that the true (unknown) distances to the members cannot be assumed to be equal. We want to compute the posterior \n",
    "\n",
    "$P^*(r_c,s_c|\\{\\varpi\\},\\{\\sigma_{\\varpi}\\})$\n",
    "\n",
    "where $r_c$ and $s_c$ are cluster distance and size respectively. The cluster center in (RA, Dec) is assumed known. For the sake of illustration I assume the true stellar distances are drawn from a 3D isotropic Gaussian of mean rc and standard deviation sc. (This is not a very good cluster model in reality. You could easily modify the code to use a different isotropic cluster distribution.) \n",
    "\n",
    "As shown in the reference document, the likelihood in the much more general case is a marginalization over the N unknown distances, i.e. an N-dimensional integral (equation 10)\n",
    "\n",
    "$\n",
    "P(\\{\\varpi\\} | C, \\{{\\boldsymbol \\alpha}\\}, r_c, {\\boldsymbol s}) = \n",
    "   \\int P(\\{\\varpi\\} | \\{r\\}, C) \\, P(\\{r\\}| \\{{\\boldsymbol \\alpha}\\}, r_c, {\\boldsymbol s})  \\, d\\{r\\} \n",
    "$\n",
    "\n",
    "where $P(\\{\\varpi\\} | \\{r\\}, C)$ is the likelihood (multivariate Gaussian). The other term reflects the geometry of the cluster stars, which is given by equation 15. Here I neglect any correlations between the parallax measurements to reduce the likelihood to a product of N one-dimensional integrals. In that case the likelihood can be written as given in equation 17. (Note that that equation does not yet assume the Gaussian or even isotropic model for the cluster.)\n",
    "\n",
    "We can now proceed in three different ways to deal with the likelihood.\n",
    "1. Nelgect the *angular* extent of the cluster, but not its finite depth. We can then assume that the true distances of the stars from the cluster center (z) are along the l.o.s, and thus drawn from a 1D Gaussian with mean 0 and stdev sc. The resulting integral has no analytic solution. This can be made tractable - solution in form of an error function - using a binomial approximation of $\\varpi-1/r$ with $r=r_c+x$ (where $x$ is the distance of the star from the centre of the cluster). This is done by the R function d.likecluster1 in distance_function.R, but the binomial approximation is poor, so this is not demonstrated below.\n",
    "2. As 1, but now using a numerical integration (Gaussian quadrature) of the likelihood (instead of the binomial approximation). This is done by the R function d.listcluster2, with argument costheta=NULL, and is demonstrated below. This is given by equation 20 in the reference document.\n",
    "3. Assume the cluster has a spherical Gaussian profile. For this we must specify the angular separations of the stars from the cluster centre, costheta. The integrals are done numerically (Gaussian quadrature). Sometimes the integrals don't converge (presumably due to limitations of the R function \"integrate\"), so for those specific cases (given star and rc,sc values) I revert to case 2 (for which there is no justification other than that's robust). This can also be done by d.likecluster2 by passing values for costheta, but it currently doesn't work too well so is not demonstrated below.\n",
    "\n",
    "Our model has two parameters, the cluster distance, rc, and cluster size, sc. I use separable priors. For rc I again use the exponential decreasing space density prior. For sc I use a gamma distribution (appropriate, because it is zero for negative sizes). I compute the posterior on a regular 2D grid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The cluster size and distance prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "nbpresent": {
     "id": "a706b705-a0d3-46ff-b068-6a8773eedca9"
    }
   },
   "outputs": [
    {
     "data": {
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EgpW9ZvPUvUTg6OII14kLCPfg8QHgzs\njDtI3zTwfj9y3buLrCWJK0it4wn7+LgEx8p/4CS8Qdrq9m80YOSAu12llI1wyzywfvXqRF9D\nBjiCVP01ra8swqXQ1YRHAxvjDVLHG7LfipLK9lTwypQx5bPP8MVMvyi3n/YgpfmTnf32erAP\n5dHAvniDVCZ3aoNnFEyif6wqq9FvyuzZk3pVZLefk9lRe5D2MtIBcu9EUK6fBvbFG6SAJTkb\nywN9v3Bg4IqcrfT5rtEyO2oP0udBpCMtzgZ+SXk4sC3eIFV8ImdjUkXfL6wwIG+7RxWZHbUH\nKYF4PrrWj9EeD2yKN0j9A1d5f2WuKqlgpgR3vjWSp7lldtQepCfaa3xhMV6pSHd9F2yMe1mX\ncqxCq44ty7OoP32/MKZb3naHqjI7ag9Sp1EaX1iMv1xbaQ8I9sR9HenPfuGMsTKKlnUZ45pz\nOXvrwkT2lMyO2oNU9yWNLyxOA7k+AXIQjGzIPKZ0WZdz9VlYy/4jR/RtGsKay13q1BykzBKf\naHthsWbeRHxAsCWeIB0/4/knj4JXps6N9fNeRgpotPiq3H6ag3ScfDmW3zBRJCjAEyTWRsNt\nFJf3Ju1MLurizMVp8dc8rDVI37nIx/TcjMmEwDeeIPWY6fknj+LXX/3lu0OFHz1+f9w1tdk/\nqrvK8k4Fba+TEd+Q/JBgP8beRvHtcM+P+Td43r7qbJTb71V2QVsBmnm/C9jiOkp+TLAdQ2cR\n+todliktYqHdhrfxc2+X2VFzkAb00vY6GRlRuOEcfDJ0FqF7KxyQpOiq3tMS20LayeyoOUgt\nJml7nZxh99MfE+zG0FmESj8pSee86/t5DC0ts6PmIMW8oe11cj4P0viFDRzE0FmESk6WpMuu\nD7O2pwfL7Kg1SFcDEjW9TtblUivpDwo2Y+gsQk1qXpKkRk96N9Pry62aojVIB9kBTa+T1723\nDgcFezF0FqG1LHbd1Z0Vlqdd2Xovk7uTVWuQEv31uH3ondK4KQl8MPb099IwFlInhvn7M9eT\ncqOqtQbpzWhtfck7E7hBj8OCnXAG6fK2jaqm9T35wv0xoUFlYkf9KLub1iBNaabpZb7cSzyk\nHOyHL0hLIxhz9dR4hk2G1iD160vcSLaXY3Q5LNgIV5A2ugLb9KrB6Cd/0xqk5lOIG8l22PWT\nLscF++AKUgc/z4uvPMh+Jm1J0h6kqjpcRvK6XZfFa8BGuIJUtq33589sAWFDWTQGKV2vswJT\n6utzXLANriD5ZX0JT2VPEzaURWOQDuu1EHmSS8GN9OBkXEFi2dMDs6lk7eTQGKRvXJepO8mW\nWYX8TRfsxVZBWhZF3Uiu4W30OjLYg62C9Kxu9+B9EUi83gbYDF+QGk/1Ys2zfhF2pTFIjz5E\n2EMBaaXe1+vQYAt8QSqAsCuNQbp/PGEPBWHgKsjiCtKyAgi70hikOvMIeyhoWYTstEfgdOZc\n+lJjkEp9RN3INafpFksHO+IP0q4Uz4/d8oNQ1dIWpDPsB9IuCmgxRr9jg/XxBulKP7bR8yuB\n9ae8Z0dbkH5mpwh7uM7c6vodG6yPN0hzWPuDnl+/92BzyXrSGqQ1JQhbuN4B8jlcwU54g1S7\nQ85Guzok/WTTFqSFtQhbKKTODD2PDhbHG6TgF3I2ZstNZqKWtiD9N46whcJHx4yrUDzeIEU+\nnrMxQsEasoppC1KfAb730e57P1X3AoOz8Aapd0jWnQuZK4Iob07VFiSdbuvLkVFBbroWcDju\nFfvKs5i4ji0jWRTlauLagnTjIsIWChvUSdfDg6VxX0c6OjCCMRahaMU+xTQFKTN4LWUPhfwv\nhHzJGLANipENx5Wu2KeYpiCdZLuI2yjo3xDq1QDBPviDlO49yvYfSBf/1hSknewcZQ+FdRyi\n7/HBwniDlD68myTtu5GxxpSTcmkK0sdhhB0UZXF5FQsGgLPwBmkmGydJbfxGjvCjvF6pKUgL\nahN2UJS//bbpXAEsizdIdT1vSH+5hkrSgFvpmtIWpAn3EnZQpLsn6l0BrIo3SKELJekNtkmS\nEsLpmtIWpL66Xo/1euY2vSuAVfEGKexVSepZMk2S5ofSNaUtSPfq/n7xMzukdwmwKO6Pdr2k\nY2FdPRtDKEeMagpSzYWEHRStmn634IK18QZpBrunAkuUpKVuyvkSNAUp9GPCDor2+H26lwBr\n4g1Sav+Q0s97fkfVpbypTkuQzrEkwg6K9qVb50tVYFVUczZ8l8bfSx4tQdrNTlC2UKQrpd/T\nvQZYkn0mP1kXaMDl0ocwKxcUyT5BWhJD30ch75TBrFxQFPsE6dl7dGjkeqcDNhpQBazHPkF6\nrLsOjRTSfKwRVcBy7BOkLoasmPzCTUZUAcuxT5DufE6HRgrZz/YYUQasxj5BqkQ5+XjxahuS\nV7Aa3iAd7/x9zg9KGoKUHpBI20MxnmxiSBmwGN4gJbMPcn5Q0hCkY+w32h6Ksdn/pCF1wFps\nE6Qd7B/aHoqRXvYtQ+qAtdgmSB9T3sYhp9+DBhUCK7FNkBbWpG2hWB+GphpUCSzENkGa0oK2\nhWJdCP7coEpgIbYJ0pCetC0Ur+1jRlUC67BNkNqPo22heAsqkc7hB7ZgmyDVf562heIdde00\nqhRYhm2CVPEd2hZk1J9mWCmwCu4hQlczc38QUh8kowY2eE2tb1gpsAq7jLU7xn7XpZOiJLn+\nNKwWWIRdgrSTndelk6JkVl5gWC2wCLsE6TM9VzS/3mNtDSwGlmCXIL1WQ5dGivZ5kDHj+sA6\n7BKkZxrr0kjRLod9aGA1sAK7BGmkoUNJu1KuPA12QBCklJ1niZq5Rn2Quo6k7kHOWzdgVi4o\ngDtIm+5kbK0kdd5A1pKkJUiN/4+yvi8p/t8YWQ7MjzdI29xhbTxBOlkhaCtdUxqCVO0NwvK+\nNaVcMgBsgDdInaKPHPe+I52I7kLXlIYglfiUsLxvc4y6+wksgjdIN8yUsoIkzYgi60lDkM4z\nYweSJhs0QwRYBW+QApblBGmJm6wnDUHay/4iLK9ALczKBfnxBqnyxJwgDYqhaknSEKSvXVcI\nyyuAWbmgAN4gPRqe5A3S6Wmu4XRNqQ/SyrKE1ZXArFxQAPcEkdH+dVi9ukEs+m+6ptQH6eVb\nCasrkVH+TYMrgqlxX0c6MawMY6zsY6TL5akO0sQ4yvJK9Kc8SwmWRzCyIfNYMuW7kZfqIA3q\nQ9yBT6tLXjK6JJgYT5COFETYleogdTBs6pNcF0PWGF0STIwnSKwgwq5UB+nOOYTVlekwxPCS\nYF48QepREGFXqoNU+W3C6sosLm/A4s9gFWS3UVw4zt1LHrVBygxaR1hdmb/9thheE0yLLEjL\nKnL3kkdtkM6wHwmrK9Twv8bXBLPiDlJKwrjRHsMqhZH1pD5Iv7FjhNUVmnGL8TXBrHiDdCgy\n51RD4LN0TakO0td+Am60282SjS8KJsUbpN5hCZvYkg2TooXe2LcykrK6UjcaNksymB5vkKLj\npatshyTtiaS8Z1RtkBLqEhZXbGwzEVXBlHiD5F4kZTDvUswTKNcnUhukya0Iiyv2tX+KiLJg\nRrxBipouSSErPRvLRZ5sGNKLsLhi6WWXiCgLZsQbpC4VN0n1m132/FkuR9eU6iB1eoKwuHIY\nuAq5eIO0JbiRNI9V7lKP9aZrSnWQGs4kLK7cRyX+FVIXzIf7OtKOxVLG+GDm6kT5fUFtkKq/\nTlhcuYshnwipC+ZDM7Ih9SDtPQVqg1RS0EjsjoPE1AXT4Q/SLu9b0W7aIToqg/Qv20ZaXrHX\ny6WLKQxmwxukK/3YRs+vBNafcvYRlUE6yA4RFlfhhP+3YgqD2fAGaQ5rf9Dz6/cebC5ZT6qD\ntI2J+tLfGDOuQhbeINXukLPRrg5JP9lUBukTymtYqsy+UVRlMBfeIAW/kLMxO5ikn2wqg/S6\nkauMFZDMfhVVGkyFN0iRj+dsjChP0k82lUGa2ZCwtjq3UA56B+viHv0dkjXsO3NFEOXaWyqD\nNLYjYW11JtwtrDSYCff9SOVZTFzHlpEs6jBdU2qD1HswYW11trkoZ08Cy+K+jnR0YARjLGIw\n6S2qKoPU5inK4qpkVnpFWG0wEYqRDceTKSc+8VIZpHovEtdXYXhrcbXBPPiD5L22n7b9h0yi\nhrKoDFKldyiLq7Mu8Iy44mAavEFKH95NkvbdyFhjtWvsyVEZJPeXhLVVuhKxXFxxMA3eIM1k\n4zzfUfxGjvCbQdeUyiCdYz8Q1larV3eBxcEseINU1/OG9JdrqCQNoFxYRV2Q9rGjhLXVWhmW\nKrA6mARvkEIXStIbbJMkJYTTNaUySN+xy4S11fon2Nh1oMGUeIMU9qok9SyZJknzQ+maUhmk\n/1FmWL324q5igWlwf7TrJR0L6+rZGFKLrCe1QXpN7MhR3JQE/EGawe6pwBIlaamb8oYCdUGa\ncQ9hafVS/Cmn9ANr4g1Sav+Q0t4JR6PqniLrSW2QBA61y9JsjNj6YAJUq1F8l8bfSx51Qeoj\neOaEuVVJr0aDFZEt60JKXZBaixtql+WQS8CiMmAudghSrOjJ7O+YIrgBEM4OQYpeqlsjyky/\nTXADIJwdghTyuW6NKLOL7RXcAYhmgyBd9C4rI1Yt4xdVB3OxQZAOiZrVLk98I9EdgGA2CFKS\nyvmNdbDVT8AatmAmNgjSWsqJwLTBDeeORxWk5MZNO7/8D38/2VQFaVllqrLajYwT3QGIRRWk\nHxlb0m06fz/ZVAVpbj2qstolBp4W3QIIRRWktORkSSJb20VVkCaY4N3gatm3RLcAQtngO9LQ\nh/VrRLGBnUR3AEIRBCll51miZq5RFaSuI6nLa/BpsPBThyASd5A23cnYWknqvIGsJUllkJpN\npSyt0eVS74tuAUTiDdI2d1gbT5BOVgjaSteUuiDdkkBYWbOePUR3ACLxBqlT9JHj3nekE9Fd\n6JpSF6TI9wgra/ZBKO0yumAtvEG6YaaUFSRpRhRZT+qClBFA+qlSq4shH4tuAQTiDVLAspwg\nLXGT9aQuSKeZOW6re6Cf6A5AIN4gVZ6YE6RBMVQtSeqCtI+ZY2GVdyIol6MGi+EN0qPhSd4g\nnZ7mGk7XlKogfcfMMdPpP8FfiG4BxOEN0vFo/zqsXt0gFv03XVOqgrSmJGFhHu2GiO4AxOG+\njnRiWBnGWNnHTpC1JKkL0psxlJU5vFH2qugWQBiCkQ2Zx5Ip34281ATp+frExbU6FfCV6BZA\nGIIgHd68/nviJfvUBCneNEvmxY0Q3QEIwx2kxVWZVx3SETJqgjSkJ2VlHgujMkS3AKLwBukV\nFtpm6OMDmwYyyjmx1ATpATOMWc3yt/9m0S2AKLxBqnln9hKq+6NvIerIS02QTDFmNVuL0aI7\nAFF4gxS4OmdjThBJP9nUBMkcY1azJFTCJOBOxRukcrlnqpZUJOknm5ogVTDPYsh/+X0vugUQ\nhDdIA3MHNHR4gqSfbGqCJHJJ8+s1GSu6AxCEN0gnGnb76NfDv61u32rfEQ+irlQE6bz4eVbz\nvByDz3YOxRskVhBRVyqCdID9QVSUwFE/ytsbwUJ4g/TAQz3yI+pKRZB2MLLZ9Ag0olwAFCyE\nbBahC8oGN2QeWL96deJhH3upCNJayvuguL1YBZ/tnIksSMuUnLVLGVM++yNgzPSLcvupCNLy\nCkr3NMKfrm2iWwAhuIOUkjButMewSmG+X3isKqvRb8rs2ZN6VWS3n5PZUUWQXq6rdE9D3IPP\nds7EG6RDkTmnGQKf9f3CgYErcrbS57vkRgGoCNK0Zkr3NAQWZnYo3iD1DkvYxJZsmBStZAaS\nCgPytntUkdlRRZBGPqB0T0McwWc7Z+INUnS8dNV7JWdP5De+X+jO9641Te4kgYog9R6kdE9j\nNBonugMQgTdI7kVSBvMOjJnQwvcLY7rlbXeoKrOjiiC1/Y/SPY3xIq7JOhJvkKKmS1LISs/G\ncgUnG8a45lzO3rowkT0ls6OKIN09S+mexjjit0V0CyAAb5C6VNwk1W/miceQcr5feK4+C2vZ\nf+SIvk1DWPN/ZXZUEaQarynd0yBNxojuAATgDdKW4EbSPFa5Sz3WW8ErU+fG+nlP8QU0Wiw7\nUYiKIJVepXRPg8zDNVkn4r6OtGOxlDE+mLk6pSh78eW9STuTi5pK8VSf7tfEKg5SumuTwj2N\n8pfft6JbAOPRjGxIPahuBvnz8b8VeuzsyKHXNFUcpBT2i6rKBmg+SnQHYDwxK/YdYWtkn1f+\n0W4vO8rdDbFXMAeKA/EGKfPN9vXqZPP9wkG5erLWg+Su/ygP0hZmutVUTgSY7dMm6I83SHMZ\nc4dnU/BCpfcuKQ/SZyEKdzTQfY+J7gAMxz2L0I0/K3/hGP/b1531+pW9d1Zu4VnlQVpaWXl5\no7wWibmLHYc3SMHPqXnljnp+o7wRofuO9NKtauob47SZppEAY/AGKUbdwIKrs0KqfEoZpCkt\nVdU3RnuTjf8D/fEG6ZlYlctr7b+X9fibLkgju6orb4i3I9JEtwAG4wlSsseBvk0+2p2cRenL\nl5SJmE0WpF6DlZY10Plg+f88sB+eIGmdQejEw4wsSGYb/J3tQSXjpcBOeII0qCAVR/h83B7Z\n55UHyWyDv7OtLCk7JQXYj5iRDb4oD9JNi3RtRKNLYStFtwDG4g1S1miYkx++dZCqoSzKg3TD\nB6SFqfQx1w3woDu+IH17l3eqhi9LMeb/MmFTyoOU4a9krgjjfRosN0kS2A9XkHaFsWWSdKFs\n8PiJlVyUU3ArDtJZ9gNhWTpXblgiugUwFFeQHvH/xPNzEUuQpAOBAwm7UhwkU838nd8w06xs\nC4bgClK1Dt6fnd3ejzEda9I1pTxI5pr5O59N/tQrvYOpcQUpaKrnR2aZrCkax5Yg60lFkNYF\nmvS+7ozK80S3AEbiCpK/9yLOHvZf7/ZEf7qmlAfpPQVTrogx/h7RHYCRuIIU6Z12OIGt9W4P\nLEPXlPIgvXIzYVVSSUzxmCmwAa4gxVW/ImXUD/Xeo5pRuTFhV4qDNKMhYVVaN/+f6A7AQFxB\nWsJaJHRh3vtB08cyVTcm+aA4SOPbEVal9fQtojsAA3EFKaMbY6zBGc9WO1b1PGFXioM0yLyj\nQ/e7fhTdAhiHc4hQ4rxVWbdVD21Nej1HcZC6jqQsS6shlkpyEKJBq+kEreSjOEgtJtMWpjSv\nEqblcg7OIKV9oMv8jIqDdAs14LEAACAASURBVPuLepSncSIgUXQLYBjOIGW4pxM2c43iIEW/\npUd5Im0pR02BufF+tGvVSo/PL4qDFPaxDtWpvBOeKroFMApvkE71b/PuDnVzNiigNEhX2GbC\nqtQuhprzZinQAW+QtMzZ4JvSIJ1kuwirkuvTWXQHYBTeID3UZ6CGORt8URokE06hn98X7lOi\nWwCDWHvOhq1Mbt0/4dKjXhHdAhiEIEgpW9ZvlZvIWwOlQVobRFuX2thGojsAg3AH6ZsG3u9H\nrntJv6woDdK7FSir0vvBhSHgDsEbpK1u/0YDRg6421Xqd7qmFAdpQW3ConqoO1V0B2AM3iB1\nvCH7rSipbE+ijryUBukZs390mlXDpHfwAjHeIJWZlrPxTHmSfrIpDdI4895Fke0oVmZ2CN4g\nBSzJ2VgeSNFODqVBMvFdFDnihonuAAzBG6SKT+RsTKpI0k82pUEy810U2d6OwDAhR+ANUv/A\nVd5fmatKipjXrtUkwqK6uBiKWcAdgTdIh8qxCq06tizPov6ka0pxkO54gbCoPvq1F90BGIH7\nOtKf/cIZY2UGHyNrSVIepGpvUFbVRWIAZop0AoKRDZnHko8TdZNLaZDCPyIuTC+z2lzRLYAB\neIJ0/IznnzyEXSkMUobfV4RFdTLxNtEdgAG4lr5sI/g2ijPMAhP17HOZc8EMIMUTpB4zPf/k\nIexKYZAOskOERfXSeLToDkB/lr6NYiezwnJeiyPTRLcAurP0LEIb/K0wku18CfOfEgFelp5F\naFWEHsXJ9e4kugPQnaVnEXqjmg616a3HpST7s/QsQi/cQVhTPxnRz4tuAfRm6VmEJrUirKmj\nyXVEdwB6s/QsQiO7EtbU0UHXdtEtgM4sffq7j1XmBG75qOgOQGecQbq8bSP1ODsvhUFqb5WF\nU94ON/W0YcCPL0hLIxhz9VQ4T7cKCoPU+Gnyyvq4FL5MdAugL64gbXQFtulVgz1A2pGXwiDV\nmUdeWSePthTdAeiLK0gd/DwvvvIg+5m0JUlxkCq/TV1YL9td+0W3ALriClLZtt6fP7MFhA1l\nURik0E+oC+vmtgmiOwBdcQXJb5T3Zyoj/6qiLEhX2TfUhXXzciXi1UHBXLiCxOKzf00layeH\nsiClMF1GzOridPAa0S2AnqwcpGRGOeGKznpirSRbs3KQkth56sL62RBAOj0MmAxfkBpP9WLN\ns34RdqUsSNa4HSlHZo0ZolsAHfEFqQDCrpQF6cMyhCV19yzm07czriAtK4CwK2VBer06YUnd\nHQvYILoF0I+VB60+X1/3Rih1eUh0B6Af/iDtSvH82E07L5ayIFnldqQcn7lPiG4BdMMbpCv9\n2EbPrwTW/wpRR17KgjSKfpCfntKjZ4tuAXTDG6Q5rP1Bz6/fezDKmXmVBalvf8KSBni6Jk43\n2BZvkGp3yNloR3k7tbIgdX7C9z5m8ldAougWQC+8QQrOXVhldjBJP9mUBan5VMKSRuhCORst\nmApvkCIfz9kYYfwasvWsts7DWpxusC3eIPUOybo6krkiqC9VS5LSIFV9k7CkETKqzRLdAuiE\ne8W+8iwmrmPLSBZ1mK4phUGKWEVY0hAzq+sxnSaYAPd1pKMDIxhjEQJW7LPE6kgFnQxaK7oF\n0AfFyIbjYlbsO8+SiMvqrwduprAp/iB57/xM2/4D6SUSRUE6zKw3D8JGf8pPwGAevEFKH95N\nkvbdyFhjykm5FAXpF5ZCWNIYmbdMEt0C6II3SDPZOElq4zdyhB/l7TaKgrSZUY5KMsi8Clh1\nzJZ4g1TX84b0l2uoJA24la4pZUH6tARhRaOcC31PdAugB94ghS6UpDfYJklKCKdrSlmQlkcR\nVjTMsGaiOwA98AYp7FVJ6lnS83FlfihdU8qCtKA2YUXD/OyyztRHoBz3R7te0rEw7+oqQ2qR\n9aQwSDMaElY0ThOsTGFHvEGawe6pwBIlaambcmUIRUF6qg1hReO8F2qFpdhBJd4gpfYPKe1d\n2DGq7imynhQG6TFr3rp9Jepl0S0APao5G74jPaurKEi9hlCWNM60Wri/z34sPPlJO6ssM3ad\nY4FfiG4ByFk4SI2f0b0PfTzcXnQHQM7CQbrVqt81vvNLFt0CULNwkKLf0r0PncRabLIJ8M3C\nQQr/SPc+dLI0/B/RLQAx6wbJgvf15bpcPkF0C0DMukE6x3bq3odeJtfELec2wxuk452/z/lB\nSUmQrHhfX65j7s9EtwC0eIOUzD7I+UFJSZCseF/fNX1ai+4AaFk3SN8yC98it8O1W3QLQMq6\nQfoshLamsZoMFd0BkLJukN6tQFvTWKtCLPzBFAqzbpAWUt4AZbj0alYd4ARFsm6QnruLtqbB\nXoy6LLoFIGTdIE2Mo61psH/CLTvCCYpg3SCN7Epb02jjbsNtSTZi3SD1HUBb02iHA74U3QLQ\n4R4idDUz9wchJUHqPJq2puF6WnPOCSiSdcfatZyiexv6SsLEXDZi3SDVf173NnTWknJtNhDL\nukG6cbHubejsM/dR0S0AFesGKfJ93dvQWWad/4huAahYN0g2WPzurXDMFWkXlg1SKiO+B0qA\ntMrPiW4BiBAEKWXnWaJmrlEQpBPMBjciPF8R44RsgjtIm+5kzPMhq/MGspYkRUFKZn9SVhTj\nn9KviW4BaPAGaZs7rI0nSCcrBG2la0pJkHYyO3y/mIDJG2yCN0idoo8c974jnYjuQteUkiBt\ndNnhj+DfIcSDq0AQ3iDdMFPKCpI0g3L9PAVB+rgUYT1xht8pugMgwRukgGU5QVriJutJUZDe\nrkxYT5yDGLpqD7xBqjwxJ0iDYqhakhQFaf4thPUE6t1SdAdAgTdIj4YneYN0epprOF1TSoJk\n0YUvC9nl2iK6BSDAPUFktH8dVq9uEIv+m64pJUF6yi4zw3XpKLoDIMB9HenEsDKMsbKPnSBr\nSVIUpOHdKAsKtN31k+gWgB/ByIbMY8mU70ZeCoLUZxBxTWFaW3MtXCiAIEiHN6///jhROzkU\nBKmTbdYY+trvN9EtADfuIC2uyrzqkN7UoCBILax+g2yeZo+I7gC48QbpFRbaZujjA5sGsqV0\nTSkJkvVvkL3mywAshWl5vEGqeeeZrN/7oymv6ygIkvVvkM3TcKDoDoAXb5ACV+dszAki6Seb\ngiCVe4+wnmCfBR4S3QJw4g1Sudz1J5dUJOknm4IgBX9OWE+0u7E2hdXxBmlg7oCGDpRn0XwH\nKY19S1hPtE/df4huAfjwBulEw24f/Xr4t9XtW+074kHUle8gnWJ2mhQu8068JVkcb5BYQURd\n+Q7SQXaIqJYprHEfEt0CcOEN0gMP9ciPqCvfQfqJnSaqZQ53DRbdAXAhm0XoAuXgBt9B+oZd\nJawn3meBB0S3ADzIgrTM2LN2n5YgLGcGDfuL7gB4cAcpJWHcaI9hlcLIelISpBWWXkG2CF8G\n7BXdAnDgDdKhyJzTDIHP0jWlIEiLbiIsZwrNeonuADjwBql3WMImtmTDpGiD57V7Ppaynhl8\n7bdLdAugHW+QouOlq2yHJO2J/IauKQVBmtKCsJw5tH5AdAegHW+Q3IukjKxZuCdQ/sn2HaQn\nOhGWM4ftru2iWwDNeIMUNV2SQlZ6NpYbe7JhUG/CcibR5T7RHYBmvEHqUnGTVL/ZZUkaUo6u\nKQVB6v4YYTmT2O2fKLoF0Io3SFuCG0nzWOUu9RjlW4TvILWNJyxnFn0bEi9qDYbhvo60Y7GU\nMT6YuTqlkPWkJEiN/o+wnFkcCvpIdAugEc3IhtSDlyiaucZ3kG6dR1rQJEbdki66BdDGqiv2\nxSzRvQkBToS9IboF0IY3SJlvtq9XJ5ui12YeWL96deJhH3v5DlKZVYrKWc20yrRv7WAU3iDN\nZcwdnk3BK1PGlM8eUBQz/aLcfr6DFGjPRRwulJ8lugXQhHsWoRt/Vv7CY1VZjX5TZs+e1Ksi\nu11uwT2fQbrEbDr1/CulT4luAbTgDVKwmnW5BwauyNlKn+8aLbOjzyCdYL+qqGshV2uNEd0C\naMEbpBg1H0UqDMjb7lFFZkefQdpvh6WYi7Q6CHf4WRFvkJ6JvaL8he58t1pMk1vhz2eQfmBn\nlZe1liaYU9+KeIKU7HGgb5OPdidn8f3CmHxLsXSoKrOjzyB97bLtBZetft+LbgHU4wmS6hmE\nxrjmXM7eujCRPSWzo88gfVpSSaPW9PA9GChkPTxBGlSQ7xeeq8/CWvYfOaJv0xDW/F+ZHX0G\n6V273Wmez6FgG83G7BjGjmxInRvr533zCmi0WHYSIJ9Bst+d5vk8VTVVdAugFn+QvF9W0rb/\noPTjyOW9STuTizpBcbRh7DXR7B/5o9jvTvN8zpefIboFUIs3SOnetVz33chYY5/T3hd05tB1\nD6S+NOuaB3y9I021353m+SwOOya6BVCJN0gz2ThJauM3coSfkr9Fv2kbE/tS9ttRvNwHRJ8f\n7cbYeinw9HqY5M5qeINU1/OG9JdrqCQNuNX3C38MZCUCWeOsyYb5gjTY3nNXbfTbIboFUIc3\nSKELJekNtkmSEhQMWn0g8KPMy3MD7/QOWOULUo9hCvq0sO6NcArcWniDFPaqJPUsmSZJ80N9\nv7BK1qrDie4OGbxBajfedzUr+yPkbdEtgCrcH+16ScfCuno2htTy/cLg7JXI32ZjeYPUdLrv\napY2LcrHeUswF94gzWD3VGCJkrTUreA9olbOZHT/ZS9wBqneXN/VLO1SVZu/59oNb5BS+4eU\nft7zO6qugvtoxrgWZF2HzezHxo/iClKN13xXs7bV7t9EtwAqUI1s+C5NwQtTqrE2WRuZo+TH\n5vkMkp3WNC9G2zjRHYAKxg4ROjVybM7WqhpcQQr5THMPVrE36H3RLYBy1pxF6CqjnLLfpCZU\nwvkG67BmkM6wH3XvQbh/q44T3QIoZs0gHWb7de9BvI8DVEwsA2JZM0i72UndezCBzndniG4B\nFLJmkLYwR8yjeLjkItEtgELWDNKXAbq3YApzIv4W3QIoY80grY7QvQVTuFrP3qPcbYQqSMmN\nm3Z+mex0ra8gLY2mqmRy2/3Xim4BFKEK0o+MLelGNpLUV5Dm30JVyeyeqCo7STqYBVWQ0rzz\n2pGdAfAVpJkNqCqZ3YWYJ0S3AEpY8zvSROeMQ/vcf5voFkAB/iDt8q55uZt2pIGvII3qQlrO\n1PrUVTIeGATjDdKVfmyj51cC669iDnCffAVpwCOExUzuVLkpolsA33iDNIe1P+j59XsPRnmr\nna8gdR9OWMzs3g/8SXQL4BNvkGp3yNlop2zpS2V8BaltPGEx0+taX3ZaWjAD7oXGXsjZmB1M\n0k82X0Fq/AxhMdP7+wZH/edaE2+QIh/P2RhRnqSfbL6CdNtLhMXM7103hoGbHW+Qeods8P7K\nXBHUl6olyXeQqr9BWMwCut5BeSoHdMAbpEPlWUxcx5aRLOowXVM+gxTpsLuwT0TizJ3JcV9H\nOjowgjEWMZh02ndfQQr5nLKaBawK2C66BZBFMbLhePJxmmau8REkR0zZUFCfmx1xB5Z1Gb4+\nkiI+gnTWCVM2FHS2yuO+dwJxhK2PJMtHkP5kClZ+tplE/3WiWwAZxq6PpJSPIO1h1J8lLWBs\nRQVz2YIohq6PpJiPIG1jDrxJ5/JtD4huAYpn6PpIivkIUqKfE1cP2hW8WHQLUCxD10dSzEeQ\nPi5FWMs6EkpiXn3TMnR9JMV8BOmdioS1rCOzQ73LonuAYhi6PpJiPoL0KmVoLSSlIs6Bm5Wh\n6yMp5iNIc2IJa1nJV/4fi24Bimbo+kiK+QjS1BaUxaxk8g2UQxqBDk+Qkgo9U/gRbXwEaVwH\nuWftLL1ZI4wDNyWeILmvvyvoRTd3P9l8BGnow0R1rOdoJNaWNSWeID3puntN3qOZ/7vL9R+a\npnwFqddgojoWtA5fk0yJ6zvSJ+VYzZGrdx2/dHzXqhE3snKfUHXlI0idxlAVsqAppQ+IbgEK\n4zvZcHFWeZar3Cy6cTs+gtRqMlkl60mPuyNVdA9QCO9Zu8wdMwd3btF58MwdlGti+QjS3c8R\n1rKck1UGim4BCiGbsvgC5YBsH0GqvYCwlvVsDcL6Y6ZDFqRllMN2fASpylLCWhb0atBW0S3A\ndbiDlJIwbrTHsEphZD35DFLEasJaVjSokgNvyDI37lmEInPONQQ+S9eUryAFfklYy4ouN2iM\nmfXNhXteu7CETWzJhknRG+h68hWkVPY9ZTErOho1VHQLUABvkKLjpatshyTtiaSc2Ec+SCns\nF8Ja1vR90HzRLUB+vEFyL5Iyst4gJlAOJJUP0iF2kLCWRb0ZmCi6BciHN0hR0yUpZKVnY7lx\nJxt2sZOEtaxqbJl9oluAPLxB6lJxk1S/2WVJGlKOrikfQdrCMFmiJKW3q3VGdA9wDW+QtgQ3\nkuaxyl3qsd50TfkI0voAwlLW9c+t9+KWCtPgvo60Y7GUMT6YuTqlkPXkK0gfUU5YZGF/VBgk\nugXIRTOyIfUg7Yct+SAtq0RazLq2l6C8eAc8yIYIkZIP0kKHzn1S2Gr/5aJbgGzcQUr79sMV\n2ch68hUkx859UtiLQV+JbgGy8AYpqdy1G5LomvIRpKnNCUtZ3JjSuDhtCrxBuif88Zdey0bX\nlI8gjW9PWMriMnpUwrxCZsAbpJJv0fWSRz5Ij/bQo6ZFXW51M1apMAHeIJX/mq6XPPJB6oOz\nvvmcv6MB5dJUoA1vkEaPpOslj3yQuozWo6Zl/X3jfbinQjjeIF3q1nnZV5uz0DXlI0hxEwlL\n2cChSg+mi+7B8XiDtKOq8WftGs4kLGUHv5bt78QFo0yFN0h3ux8YPzUbWU++glQ3gbCULSSF\nj0CSxOINUrAu95fJB6nqm3rUtLRvS2ImY7F4g3QD5Veja+SDFLlSj5rWlhiCL45C8QZp6AS6\nXvLIBynkcz1qWtzaoKmiW3A03iCdaz9s/Z7kLHRNyQcpnVFOD2EbnwVNE92Ck/EGiTHDz9qd\nYzsJS9nHp3hPEog3SH0GDspF15R8kP5iewlL2chnQfieJIwF70fay/7SvQFrWhs8HmfBBbFg\nkHayc7o3YFGJJXE9SRAL3tj3DcOAmOJsDu+H/zlCWPDGvs9DCCvZTVLZrpdF9+BIFryxb2VZ\nwkq282ulONxVIYAFb+xbUlWPkrZxqOZdmIjWeBa8sS+hrh4l7eNEbC3MjW44C97YN7OBHiVt\n5J/7on4Q3YPjWPDGvkn3ElaypbQ+YV+I7sFpLHhj3xOdCCvZU+Z/AxaL7sFhLHhj35BehJXs\nanFAfIboHhzFgjf29RyiR0m7WRf+4EXRPTiJBW/s6zRGj5K2s7ta/SOie3AQC97Y12qSHiXt\n52TTCltE9+AcFryxr8Eswkp2ljY4CLNbGMWCN/ZhEiHF5geOxKJ+xrDgjX1VlxBWsrmvyzU5\nJroHZyC7H+nCce5e8sgGCZMIqXCkQRRmuDACWZCWVeTuJY9skEI+I6xke2nDA+bgZj/9cQcp\nJWHcaI9hlcLIepIPUrpLl3Gy9rU8tNMZ0T3YH2+QDkXmnGoIpFwXWC5I51kSYSUn2FM35nvR\nPdgeb5B6hyVsYks2TIreQNeTfJCOsd8pSznBpSEBz2LAkL54gxQdL11lOzx/60VSfqeVC1Iy\nwwV71d4Lb3lUdA/2xhsk9yIpg3k/OExoQdaTfJB+YvjEr96hRmU+EN2DrfEGKWq6JIV4z0cv\nN+pkw7cM69NpcHV6QF9MY6Yf3iB1qbhJqt/ssiQNKUfXlGyQ1rkJCznJtpq0X2QhP94gbQlu\nJM1jlbvUY73pmpIN0uoIwkKO8u/jfsMxw5BOuK8j7VgsZYwPZq5OKWQ9yQfp7cqEhRwmsVq1\nRNE92BTNyIbUg5comrlGLkgLa5GWcpYLI/wGnxXdhC1Zb+7v52N1L29n39SM+lB0D3bEG6T6\nDXI16jSH7O86uSBNb0ZVxZlSJwZ2/EN0E/bDG6RKpRhj/p5/ggIZi6Easi8XpCfvJyriWLsb\nl3wOtykR4w3Svx2brz0vXfiyZb+rKS/5DybqSi5Iw7sRFXGuzNdvuAUnHWjxBmlE8+xlRNJb\nTJWkYVQn1OSC1K8fUREnOzXU76HDopuwFd4glcudiPCNGElaFEjRkiQfpG4jiIo4246GJab+\nK7oJG+EN0rWltGcGSdLU8iQ9yQfp/ieJijhc5tsVKy/DmHAqvEGKLZ095dMv5W+WdpTrQNSV\nXJCaTScq4ngXJ5eI/Up0E3bBG6RP/FjN9g91rOtir0vNgqjuH5MLUuzzREVAOtLfr93Popuw\nB+4LshvvC/aeAG+4UpLe3EbVlVyQbl5IVQUk6ef7/R45ILoJOyAY2ZB+dN9h4ssSckGq8jZt\nLafb1CjwUdwqyc16Q4TKrNK9vMOsuSPo8b9EN2F1PEFqUEB9wq7kghSENbSoZa66NXjkn6K7\nsDaeIPl7BAR6viG5PP9EVCHsSiZIV5ku6184XMaqeu4h+0V3YWW8H+3ONB3xU6r0z3c9W1He\nxywTpHMM66PqIfOThv4P43+tZrxBGtg9Z6OdQXN//8X2EhaCfBJbu+LWYVZWbXiDFPlazsa8\nSJJ+sskEaR/DvFK6+bFX4K1vpIruwpK4hwjlTrAaH0TSTzaZIP3IcIenjv78T+lyk7GAhXq8\nQbqjTPZohm/DbyfqyEsmSJsZbqXR1YX5tQJ7YHp1tXiDtMafVYvrGFeNuSgXW5EJ0heYjUtv\nmes6+dedj0nwVOG+ILu5rXeIkLsF6dUdmSCtwmxcBvhjQoUS/b8V3YWVEIxsyDi678hVonZy\nyARpGWbjMsSVD9v41Z6Nb0tKWW6I0KuYjcsoh6dXDWj/Pk7iKWK5IL1AORQJ5GV81S80fGAi\nbv/zzXJBerqJ7tUhn4vL7g+oOGYrrtP6YLkgxbfRvToUdHJ+E7+q47chS3IsF6THu+peHQo5\nMreRK3r0pnTRfZiX5YI08BHdq0NRjsxr4V+2/+qLovswKcsFqcejuleHYqQseaBkcNv5B0X3\nYUaWC1KHsbpXh+Jd+uyxaHbzmHW0q4/YgOWC1HKy7tVB3q7Zrdwhref8iLPi+VguSA1m6V4d\nfLr46ajarGz3hb+JbsQ0LBekugm6VwdFji7tF82iHl6wC+fFJQsGqdqbulcHxQ682a8aK9Nh\n5mbHf2eyXJDKvad7dVDlz+UjbvcPbDDqXUdPNGm5IJVco3t1UO2fL59udwMr227yJ06dIM9q\nQcr0w7TvZrVv+ejGJVhU+0mrHXilyWpB+pdt1b06aJe+661RTcNYeLORi7f8I7oZI1ktSCls\nl+7VgVNm8geTOlVjrmod4t9OcsiYIqsF6Q/mwI8N1nT++8Wj4qKYK6b1qFc22H5CZKsF6Vf2\nt+7VgdCZ71//T6eagazE7d2een3jYduOhrBakHbITK8PpnVl75oXHruvqj8LqnX/8DkfbD8p\nuiFyVgvSJpdt/05zgLS9axeM63pHGcZK3NJ2yPS3En+3zYVcqwXp8xDdi4Puzv/8ScKTDzeu\nEsBYRN22AyYv+N+WI2mim+JjtSB9UFb34mCY9KPfr3r5yT4ta5dijJWtc2/vJ2Yt+XTbH/+K\n7ksDqwVpabTuxUGAf5M3fzBv0uCODauW8GSqRHRs296jp89fsS7p0HnRrSljdJAyD6xfvTrx\nsI+9ig/SK7U5ioMVXPxj26dvvfDUwC5Na5cL8C70Xfamu1v3GBY/a+GKz7/bddikaygYG6SU\nMeVZlpjpstfpig/SnFjNxcGCzh/auX7lolnxw3q0blCrQnDWH55SlW++K67rI8Pjn31p8cpP\nE5P2HDojfhZLQ4N0rCqr0W/K7NmTelVkt8tN0l58kKY301ocbCAtZX/SV/9btnDWfx8f2P2+\nRndUjwzN/puZRZSvfmtsXJvujwwdE//MrAWLVqz8Yv3WpF8PHDljzFuYoUEaGLgiZyt9vmu0\nzI7FB+nJtlqLg02d//vAT1vXf7xy0fxZU+IfG9L9gbjmsbdWrxyRGzGP0Ihy1avfFntXXFz7\n7t37Dx06Nt4TtlkvL1r02sqVKz9bv359UlLSDwcOHDh4xkPbPPaGBqnCgLztHnKLNxcfpJEP\nai0OjnP1zOkDB35I2rx+3cqVSxa9OmvWtPj44UOH9uje/b64uLtiY2tVr14pIiIigBXi53nY\nG77q1W+K9bonzqtt9+7dVxdTy9AguZ/N2552/TpHByMjrinBivsKNWRAMU8AaJfheSc66XlL\nSva8NSVt8rxFeaK3cuX7i7zmzPKKz/Lo0C+LOYKhQYrplrfdoep1T2ZsXH/NS6y4y3PHsNAI\nmJGhQRrjmnM5e+vCRPaUzI7fFRskAFMyNEjn6rOwlv1HjujbNIQ1l7t8jSCBxRh7HSl1bqyf\n97tcQKPFsudGECSwGMOHCF3em7Qz2dfC5AgSWIw5x9ohSGAxCBIAAQQJgACCBEAAQQIggCAB\nEECQAAggSAAEECQAAggSAAEECYAAggRAAEECIIAgARBAkAAIIEgABBAkAALmDNKOwjONAZjb\nDtV/zPUPkvRTUjHaNlsmVDPUd3b9tsX9yfxJ/Z9yA4JUrP79BRZHfdSnrI8goT7qE0CQUB/1\nCSBIqI/6BBAk1Ed9AggS6qM+AQQJ9VGfAIKE+qhPAEFCfdQngCChPuoTEBmkoUMFFkd91Kes\nLzJIZ84ILI76qE9ZX2SQAGwDQQIggCABEECQAAggSAAEECQAAggSAAEECYAAggRAAEECIIAg\nARBAkAAIIEgABBAkAAIIEgABBAmAgJFBOjcmxh016HiRDxR6zuD60pWn/GJ1rS5fP2XszSEx\nXX8RVv/AwBrB1XrsElbfawwbJKr+kpxVKJ7RfHADg5Ranz34fwMCqp0q4oFCzxlcX9pTP0zv\nIMnVP1Xd1XHyI4HubwXVTwp195naOzDoe0H1vXb46xskufovsp7xXl9pPrqBQZrLnvP8XMHG\nFvFAoecMrn8+5M7kUldgmgAABgtJREFUIJ2DJFd/JFvg2fyI3S+ofivX157N1ayjoPoeV+vd\npm+Q5OpP1bAiUkEGBik2LNX7q0b5zMIPFHrO4Pqnx12R9A6SXP0xba56tjJLxAiqP/G/3q30\nwLqC6nvM8lunb5Dk6o9myZxHNy5Il/1aZv3uxw4UeqDQcwbXz/qtc5B81vc8EqhjCwrqH2Kd\nhdXfHzLqrK5Bkq3fj6VIJ07yHN64IO1l2dOITWHrCz1Q6DmD62f91jlIPutL0stsrsD657+6\nI3S7sPr3Vrmgb5Bk63dhE8swVn2Z9sMbF6QkNjLr9xy2qtADhZ4zuH7Wb52D5LO+tMl9j47r\nVvuqH85YT97PN9rrL2FrJH2DJFu/Bas29a0Jpdirmg9vfJBms9WFHij0nMH1s34bFKRi678b\nFKvnSUtf9Z8a1MTVRL9P1vL1T5TpIRkUpCLrJ354wbP1a3DEZa2HNy5Iyaxv1u9JLLHQA4We\nM7h+1m+dg+SjfuYU1v6CwPpeX4fcli6m/sMRf+sdJAX//VJXpvmzrXFBuhLQNOt3L3a40AOF\nnjO4ftZvnYMkXz9zIBuTIbB+tgfZHiH1P2ezjxw58ivreeS8kPq5+zzKNF9IMvD09z0lLnp+\npleMKeKBQs8ZXN9L79PfsvVHszn6Vpetf/z27L+cu3JfTtFWfxzLFS+k/oVX3sl6pJn2s8YG\nBmkRm+z5uYBNl6TUH/cXfCDfppD6XnoHSa7+Kl0vRfuuX8O9zbO5NzT0kpD6e9Z4vcdar/lN\nSP2MyiV2ezY/ZfU0H93AIF1pwjpOe9h1u+evgV3s3oIP5NsUUn9TfHy8fwXPDx2/7svVr8FG\nZQ1RiddxXnm5+l8FuHtO7F+SJehXXrZ+Fn2/I8nWX+0fOmhKNz+O0/9GDlq9+GSMu/Kos1Lu\nf0i+B/Jviqg/M/ejhZ4ngGXqX/toc0hMfemHh6u5S9/7iY7V5et76Rwk2fqbO1UKjOqzV/vB\ncRsFAAEECYAAggRAAEECIIAgARBAkAAIIEgABBAkAAIIEgABBAmAAIIEQABBAiCAIAEQQJAA\nCCBIAAQQJAACCBIAAQQJgACCBEAAQQIggCABEECQAAggSAAEECQAAggSAAEECYAAggRAAEEC\nIIAgARBAkAAIIEgABBAkAAIIEgABBMmKRjDGFko92BGZfWrpvP4fFIAgWdEI9saawz6CtHFN\nJwTJOAiSFY3Iioh8kCRpNIJkHATJihAk00GQzOvy7NtKhd46O8OzefiRcsG3PH8l95l8Qcro\n6lomPcBODC3vrvWKVGBXBMlACJJ5DWC9Fi58kI2QpGNRISOf78D65T6TL0hj2POS9BBrOCxx\n1Z1scYFdESQDIUjmVeIe789xD6ZLg9k6z1Z7tivnmbwgzWf/ydrq5vl5pmRVKf+uCJKBECTz\nKh31d85WRLT354GvUnL+/VqQPvHvm5m19ZH34Tbsz/y7IkgGQpDMaw4L7/3mX56N4yyu4DO5\nQfpfycZXpaytX72/hrLN+XdFkAyEIJnYl11KMlfbZCmZdSz4RG6Qwli4d8Ozddj763G2Pv+u\nCJKBECRTS9s42O+mtOOsZcGHc4N03//8GqVnbf3mfXgg+z7/rgiSgRAksxvBtksR5bzfhH5P\n2H3tsUNS9smGp9hk6dp3pKbseP5dESQDIUim9V3Fpd5fI9gPnreaFZ6th9mPOU/lBenKnf7f\neLfaZ0jS/sA6Uv5dESQDIUimlVbHPWTB/AF+jTOlo+WDRszpwPrmPpXvOtLeklXOerZaxb3y\nfDR7T8q/K4JkIATJvE4+cVPJUrc+e8GzeahPueBb5qTlPpN/iNDrrJtna9/oiu7ab0kFdkWQ\nDIQgWdGI6yJS9Kg7BMlACJIVIUimgyBZ0Qj21to/8/17UUHavLYLgmQcBMmKsu+QzVNUkHCH\nrKEQJAACCBIAAQQJgACCBEAAQQIggCABEECQAAggSAAEECQAAggSAAEECYAAggRAAEECIIAg\nARBAkAAIIEgABBAkAAIIEgABBAmAAIIEQABBAiCAIAEQQJAACCBIAAQQJAACCBIAAQQJgMD/\nA3UloR+ot7GLAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# I use the following gamma distribution as a prior on the cluster size, sc.\n",
    "sc <- seq(from=0, to=0.050, length.out=1e3)\n",
    "scPriorShape <- 2\n",
    "scPriorScale <- 0.005\n",
    "# Plot this prior\n",
    "plot(sc, dgamma(sc, shape=scPriorShape, scale=scPriorScale), type=\"l\", xlab=\"sc [kpc]\")\n",
    "# Set parameter for the exponential decreasing space density prior\n",
    "rlen <- 1 # in kpc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test of likelihood using simulated data (Careful! This overwrites the table \"dat\")\n",
    "\n",
    "You can use the following block of data to generate simulated data in order to test the likelihood for cases 1 and 2. But be aware that it overwrite the GDR1 data stored in dat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>parallax</th><th scope=col>parallax_error</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 8.487163</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 7.723657</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 8.596050</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 8.844268</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 7.884108</td><td>0.3      </td></tr>\n",
       "\t<tr><td>10.064773</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 8.576645</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 9.144403</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 9.025186</td><td>0.3      </td></tr>\n",
       "\t<tr><td> 9.101000</td><td>0.3      </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " parallax & parallax\\_error\\\\\n",
       "\\hline\n",
       "\t  8.487163 & 0.3      \\\\\n",
       "\t  7.723657 & 0.3      \\\\\n",
       "\t  8.596050 & 0.3      \\\\\n",
       "\t  8.844268 & 0.3      \\\\\n",
       "\t  7.884108 & 0.3      \\\\\n",
       "\t 10.064773 & 0.3      \\\\\n",
       "\t  8.576645 & 0.3      \\\\\n",
       "\t  9.144403 & 0.3      \\\\\n",
       "\t  9.025186 & 0.3      \\\\\n",
       "\t  9.101000 & 0.3      \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "parallax | parallax_error | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "|  8.487163 | 0.3       | \n",
       "|  7.723657 | 0.3       | \n",
       "|  8.596050 | 0.3       | \n",
       "|  8.844268 | 0.3       | \n",
       "|  7.884108 | 0.3       | \n",
       "| 10.064773 | 0.3       | \n",
       "|  8.576645 | 0.3       | \n",
       "|  9.144403 | 0.3       | \n",
       "|  9.025186 | 0.3       | \n",
       "|  9.101000 | 0.3       | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   parallax  parallax_error\n",
       "1   8.487163 0.3           \n",
       "2   7.723657 0.3           \n",
       "3   8.596050 0.3           \n",
       "4   8.844268 0.3           \n",
       "5   7.884108 0.3           \n",
       "6  10.064773 0.3           \n",
       "7   8.576645 0.3           \n",
       "8   9.144403 0.3           \n",
       "9   9.025186 0.3           \n",
       "10  9.101000 0.3           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# True cluster is 1D along the l.o.s, so strictly theta=0 for all of them.\n",
    "# We cannot expect results with case 3 to be good, as that assumes a spherical cluster.\n",
    "set.seed(12345)\n",
    "rcTrue <- 0.120\n",
    "scTrue <- 0.01\n",
    "Nstar <-  25\n",
    "rTrue <- rnorm(n=Nstar,mean=rcTrue,sd=scTrue)\n",
    "wsd <- rep.int(x=0.3,times=Nstar) \n",
    "w <- rnorm(n=Nstar,mean=1/rTrue,sd=wsd) # generates one random variable for each row of cbind(w,wsd)\n",
    "dat <- data.frame(parallax=w, parallax_error=wsd)\n",
    "dat[1:10,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute posterior using case 2 (1D approximation of cluster geometry, numerical integrations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Of 100 outer loop steps, no. remaining:\n",
      "1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71  72  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99  100  \n"
     ]
    }
   ],
   "source": [
    "# We evaluate the 2D posterior on the following regular grid.\n",
    "# This takes about 2.5 minutes on my laptop using gdr1set03.csv (164 stars), \n",
    "# so you might want to test it first using 10 simulated stars (see code for this above).\n",
    "rc <- seq(from=0.120, to=0.140, length.out=100)\n",
    "sc <- seq(from=0.0001, to=0.030, length.out=100)\n",
    "lndense <- matrix(0, nrow=length(rc), ncol=length(sc))\n",
    "cat(\"Of\", length(sc), \"outer loop steps, no. remaining:\\n\")\n",
    "for(j in 1:length(sc)) {\n",
    "  cat(j,\" \")\n",
    "  for(i in 1:length(rc)) {\n",
    "    lndense[i,j] <- d.likecluster2(w=dat$parallax, wsd=dat$parallax_error, rc=rc[i], sc=sc[j], retlog=TRUE) +\n",
    "      log(d.distprior3(r=rc[i], rlen=rlen)) + dgamma(x=sc[j], shape=scPriorShape, scale=scPriorScale, log=TRUE)   \n",
    "  }\n",
    "}\n",
    "cat(\"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior mean, SD for sc = 0.01316349 0.0009870501 kpc\n",
      "Posterior mean, SD for rc = 0.1356696 0.001145217 kpc\n"
     ]
    },
    {
     "data": {
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RNSqbSuro7GqMBwILEDAADQmN9//10i\nkXSasSOEoBoLuoHEDgAAQGOo7sQdN0/Y29tbWFiglR3oBtbYAYAqjIyMlCwYUnKMLIB+EwgE\nVlZWLBar4yAOnwCdwYwdAACAxjx//tzOzq7TIA6fAJ1BYgcAAKAxQqHQ1ta20yA6noDOILED\nAADQmMbGRhsbm06DmLEDnUFiBwCqoPrY9YTu6ABoIxQKuyZ2mLEDncHPXwAAAI3pthQ7aNCg\n+vp6WuIBQ4PEDgAAQGO6LcWyWKznz5/TEg8YGiR2AAAAGtPtjJ2dnV1DQwMt8YChQWIHAKpQ\nvsYOfezAYHW7xs7Ozq61tbW5uZmWkMCgILEDAADQmG5LsVRnO0zagQ4gsQMAANCYbmfsqIMo\nsMwOdACJHQAAgMY0NjZ2XWNnb29PkNiBTiCxAwAA0JhuZ+yYTCaTyURiBzpgQncAADAgUZsn\n6I4CoN8RiURdZ+wINsaCruDnMgAAgGY0Nze3tbV1nbEjhNjZ2WHGDnQAiR0AAIBmNDY2EkK6\nnbFDj2LQDSR2AAAAmiEUCgkhPc3YoRQLOoA1dgCgCqyxA+iKmrFDYgc0QmLXo7t37/7888/K\n75FIJLoJBgAA+j+hUMhgMKytrbtewho70A0kdj06cuTI8ePHld+D82EAAEBBKBRaW1t3O5nN\nYrF+++033YcEhgaJXY927dq1a9cu5fcMGTJEN8EAAED/1+15YhRsngDdQGIHAKpQvsaOwWDo\nMhiAfqLb7sQUrLED3cDaZwAAAM3o9jwxCtbYgW4gsQMAANAMJTN2KMWCbiCxAwAA0AyhUKhk\nxq65ubm1tVXHIYGhQWIHAKqg1tj1hO7oAOihZPOEnZ0dIQTL7EDb8PMXAABAM5TP2BFCUI0F\nbUNiBwAAoBnK19gRzNiB9iGxAwAA0AwlpVhra2sTExPM2IG2oY8dAKhC+Vo69LEDw6Rkxo7B\nYNja2iKxA23DjB0AAIBmKOljR9CjGHQCiR0ADAANDQ1RUVEjR45kMplOTk7r16+vqalR/paK\niop169aNHj3awsJi1KhRK1as+M9//qObaMFgKZmxI+hRDDqBUiwA9HctLS1z5swpLS1dvny5\nh4dHeXl5Zmbm5cuXb9265eDg0O1b7ty5M2PGDDMzs3fffdfNze3XX3/dt2/ftGnT8vPz58yZ\no+P4wXCIRCLM2AG9kNgBQH+Xnp5eWlqakpLy/vvvUyPz589ftWpVcnLynj17un3Ljh07hELh\n5cuXZ8+eTY0sXbr01VdfTUxM7D+JXW1t7bVr1wQCwfPnz+3s7BwdHX18fIYMGUJ3XKAisVgs\nlUqVzNjh8AnQASR2AKAKqkGxbr5XVlaWjY3N5s2bFSNBQUFxcXFZWVmpqandbtSoqKgghHh7\neytGJk6caGNjU1lZqf14Xyw/Pz8pKenGjRtyuZwQYmRk1N7eTghhMBivv/76tm3b/P396Y4R\n+qyxsZEQorwUixk70DassQOAfk0ikZSVlXl6epqbm3cc9/HxefLkCZ/P7/Zd7u7uhJCHDx8q\nRurq6oRCITVOo8bGxj/84Q+LFi2yt7dPT0+/f/9+Q0ODTCZraGi4f//+/v37HRwcFi1a9Ic/\n/IHKEnqvrq7u3//+d1JSUnR0dHR09I4dO06dOtXXh4A6hEIhIUR5KRYzdqBtmLEDgH6tsrKy\nvb2dzWZ3GqdGeDyei4tL13e9//7733zzTXBw8J49e8aOHVtVVfXhhx9aWlrGx8frIuieeXl5\nOTk5lZWVTZo0qeO4ra2tra3tK6+8smHDhh9//DEyMnL69On37t3rzTOlUunWrVs///xzqVRq\nZmZmbW3NYDAaGxulUqmlpWVsbGxcXBwa0OjAC2fsUIoFHUBiBwBa0d7e/s9//lP5PV5eXpMn\nT1Z+DzULYm1t3Wmc+vXZ04yUu7v7tWvX3nzzTT8/P2pkxIgRFy5cmD59em+C154333wzMTFR\neRX71VdfvXDhwrZt23r5zISEhIMHD+7evTsgIMDZ2ZnK4eRyOY/HO378eFJSkpmZ2datWzUQ\nPSglFAoZDEbX/1cVkNiBDiCxAwBVKF9jJ5fLZTJZSkqK8ocEBwe/MLFT8i1Iz52Q7927t3jx\nYrlc/o9//MPV1fXx48dffPGFv78/h8OZN2+eat9RI7Zv3674+ty5c5MnT37ppZfa2tr27t1b\nUlIyc+bMTZs2EUKMjIx27NjRy2cePnw4LS0tLCys4yCDwXB1dY2NjbWzs0tJSUFipwNCodDS\n0tLY2LinG7DGDnQAiR0AaB51LkV5ebn6j6JO2Ow6M0eNUFe7WrduXV1d3c8//+zs7EyNrF69\nevz48aGhoTwez8zMTP3A1PTll19u2rTpxo0bL730UmJiYnJy8vTp0yMjI1taWrZs2dKnR9XW\n1o4bN66nq5MnTxYIBGrHCy+mvDsxwRo70AlsngCAfo3NZpuYmHTdJMHj8Qghbm5uXd8iEolu\n3Ljh6empyOoIITY2Nr6+vtXV1Q8ePNBqwL20d+/eTz75xMvLSyaTffHFF9u3by8qKtq/f/+B\nAwf6+ihXV9ezZ8/2dPX06dOjR49WL1joFeXdiQkhdnZ2jY2N1A5oAC3BjB0A9GumpqbTpk0r\nKSlpamqysrKiBmUyWUFBAZvN7pi6KYjFYkJIS0tLp/Hm5mZCSGtrq5ZD7pXy8vJFixYRQm7e\nvFlfX79mzRpCiLe3N9WopU+ioqI2btxYXl4eEBDg5uZGTRo1NDQ8ePDg5MmTHA4nKytL0+FD\nN16Y2LFYLLlc3tjYaGdnp7OowNBgxg4AVEGtseuJZr9XaGhoc3NzxxV7+/fvf/z48dq1a6mX\nLS0tt2/fVlR+hwwZ4uLiUlZWdv/+fcVb6uvruVyujY3N+PHjNRueaiwsLKjU8/z58xMnTnRy\nciKEtLS0mJj0+fP2+vXrv/rqq++//37FihVTpkxxc3Nzc3ObOnXq6tWrHzx4wOFwVq1apfk/\nAHTxwlJsT+sKADQIM3YA0N+FhYUdOXIkKSnp9u3bU6dOvX//fk5OzqRJk6Kjo6kbHj165OHh\nMXfu3IsXL1Ije/bsWb58uY+Pz6ZNm9zc3Gpqag4cOPD06dP09PRO/fDoMmXKlB07dqxYsWLf\nvn3h4eHUYE5OztixY1V4WkhISEhICJ/Pf/jwIbWKy97e3t3dfcSIEZoMGpQSCoXKEztqPo/a\n6A2gJXqb2Mnlcj6fz+PxqL9CLBbLzc2t26oNAPRzpqam+fn5iYmJOTk5586dGzp0aEREREJC\ngqIy21VAQMDVq1d37979z3/+s76+3tbW1tPT89NPP6Wqn/1BcnLywoULc3JyPDw8oqKiCCHH\njx/fsWPH8ePHVXtgXV3drVu3Hjx4QCV2gwYNampqYrFYylMN0CCRSKTk/0ny397FmLEDrdLD\nxK6uri45Ofno0aNPnjzpdInNZq9duzY6Olr53z0A6G+srKxSUlJ66p8yYcIEqvtJRzNmzJgx\nY4b2Q1ORl5eXQCCoqKhwcXGhyq/Tpk27du1ax2PQegkNivsJsVhsaWmp5AYmk2lmZoYZO9Aq\nfUvsBAIBtfrY1dXV39+fzWZTvSIbGxt5PF5BQUF8fDyHw+FyuT11SQCA3jAyMlLSrwuUa2tr\nu3bt2uTJk8eMGaMYHDly5MiRI1V4GhoU9xPNzc0ODg7K77GxscGMHWiVviV2cXFx1dXV2dnZ\nQUFBXa/KZLKMjIyIiIj4+Pi0tDTdhwcAQAgxMjJasGDBlStXVJif60rNBsXff/99T3NId+/e\nVT88wyEWiy0sLJTfY2Njgxk70Cp9S+zy8vKCg4O7zeoIIcbGxuHh4YWFhRwOB4kdANDFyMgo\nKCjo66+/fv3119UvkqrToFgikSxevPjp06dKnt/U1KRWfAajubn5hYmdra0tEjvQKn1L7Orr\n67ttWNqRu7v7qVOndBMPAEC32Gz2qVOn2Gz2tGnT7O3tO17qa49iqkFxT8fgKm9QzGQy6+rq\nerp6/fr1GTNmYFFyL71wjR1BKRa0T98SO0dHx7KyMuX3FBcXUy2jAEBlys+KZTAYXXczQEeZ\nmZmmpqaWlpbqlzvRoLif6E0pFjN2oG36ltgFBgampaWlpqZGREQwmcxOV0Ui0a5du3Jzc2Nj\nY2kJDwCAUllZqalHrV+/3tTUNCkp6ejRo50uTZgwgcPhBAQEaOp7gRK9KcVijR1om74ldvHx\n8VwuNyYmJjEx0dPTk9oVK5fLhUIhn88vLi4Wi8W+vr7btm2jO1IAMHQymezy5ctlZWVCodDO\nzs7Ly8vHx0e1JXdoUNwfoBQL/YG+JXYsFquoqCg9PT0rK4vL5XY8a9nExMTLyys0NDQsLEyF\nQ3sAADRIIBAsWLDgzp07HQd9fHxyc3NVa8b0+PFjS0vLBQsWEELkcvmZM2eysrJefvnlgIAA\nqusTaFsvN0/U1tbqJh4wTHqY35ibm0dGRkZGRkokksrKSqFQyGAwbG1t2Wy2qakp3dEBABBC\nyHvvvdfc3PzNN9+89tpr9vb29fX1hYWF0dHRsbGx6enpfXrUkydPAgMDr1+/TgjZsGHD/v37\n33zzTQ6HQ111dna+fv368OHDNf9ngP/Vy3YnmLEDrdLDxE6ByWR2bP6p8OzZs4aGBtUagQIA\nRfnmCXih8+fP5+TkzJkzh3o5bNiwP/3pT9bW1uvWretrYrdt27YHDx784x//MDc3T0hIGDRo\n0LVr1y5evOjp6VlSUhIWFhYXF/fVV19p4Q8B/0cmk7W2tvamFIs1dqBVevhzubCwcOHChSNH\njvT09Ny7d69UKu10Q0pKyqhRo2iJDQCA8vz5cxcXl06DY8eOVdJ8pCf5+fkpKSlbtmzZtGlT\nenr6nj17YmJi5s6dy2Kx5syZk5iYeOXKFQ1FDT0Si8WEkN6UYjFjB1qlb4nd7du3586dm5+f\nX1tb++OPP27ZsmX27Nn19fV0xwUA8D9efvnlixcvdhq8fPmyCtsdamtrX3nlFeprb2/vtra2\nSZMmKa6OGjXq999/VydU6I3m5mZCCGbsgHb6ltglJiYSQk6dOiUSiYRC4SeffPLDDz8sWLAA\nndMBoF8JCQnZvHlzZGTkyZMnr1y5cuLEiYiIiHfffbfTyWC9MXz4cEX/ThaLFRIS0nGpyQ8/\n/IC9sTrQ+xk7JHagVfq2xq64uDgoKIhq2sRkMiMjIydNmrRw4cKgoKBvv/0WS4IANAUNitW0\nbdu2Z8+epaenK443tLCwePfddz/44IO+Puqtt9764IMPWltbo6OjmUzm4cOHqfHff/89Kyvr\no48+eu+99zQYOXSrl4mdjY1Nc3OzTCYzNjbWSVxgcPQt0amtre20fm7OnDkHDhzIzc2NiYmh\nKyoAgE6MjY337t1bW1tbVFT03XffXb9+vba2dvfu3Sp8/vzb3/4WGBi4c+fOTuPfffddVFSU\nv7//+++/r6GooUe9L8VSrVV1EhQYIn2bsWOz2bdv3+40+Oc///nevXs7d+4cPnx4VFQULYEB\nAHRlY2Pj7e2t5kPMzc0zMzNFIlGncT8/v/v37yuW34FW9b4USwihWlLrIiwwPPqW2C1atCgt\nLW3fvn0bN27s2IV4x44djx8/jo6OFggEra2tNEYIAIZsy5YtK1as8Pb23rJlS0/3KIqzfdK1\nCzEOxdal5uZmExOTF3ZLtbGxIYRgYyxoj74ldh988ME333wTHh5++vTp/Px8xTiDwfjqq69Y\nLFZqaiqN4QHoDSMjIywSUsGJEyc8PT29vb1PnDjR0z2qJXZAr950JyYdZuy0HxEYKH1L7AYP\nHnzr1q2PPvrIzMys0yUGg7F3715fX9/333+/vLyclvAAwMBVVVV1+gL0Q28OiiWEmJubm5mZ\nYcYOtEffEjtCiIODw2effdbT1cDAwMDAQF3GAwDQSVtb27Vr1yZPnoyFVnqjNwfFUqytrTFj\nB9qjh4kdRS6X8/l8Ho9H/f1hsVhubm7Ozs50xwUAQIyMjBYsWHDlyhX1d05AP9HLGTuCVnag\nZXqY2NXV1SUnJx89evTJkyedLrHZ7LVr10ZHR1tZWdESG4DeYDAYStbYMRgMXQYz4BgZGQUF\nBX399devv/46/l3ph97P2NnY2KAUC9qjb4mdQCDw9vauqKhwdXX19/dns9nUTqyZ6V0AACAA\nSURBVLHGxkYej1dQUBAfH8/hcLhcLovFUv6odevWHTp0SCdRA4DBYbPZp06dYrPZ06ZNs7e3\n73jpwIEDdEUFKuvl5gmCU8VAy/QtsYuLi6uurs7Ozg4KCup6VSaTZWRkRERExMfHv3Df2c6d\nO9955x3l98ybN0/1WAHAgGVmZpqamlpaWt69e5fuWEADUIqFfkLfEru8vLzg4OBuszpCiLGx\ncXh4eGFhIYfDeWFiN3To0KFDhyq/p2OrPACA3qusrKQ7BNCkPs3YoRQL2qNveUl9fb2bm5vy\ne9zd3U+dOqWbeAD0lfI+dlg31htNTU0XLly4d+9eU1OTjY3NxIkT586dy2Qy6Y4LVNHc3IwZ\nO+gP9C2xc3R0LCsrU35PcXExGrIDAL1KSkoWL17caY/XiBEjzp49O3HiRLqiApX1acautrZW\n2/GAwerzadP9XGBg4MmTJ1NTUyUSSderIpEoLi4uNze3p1otAIBuvPPOO2PHjr1586ZQKJTJ\nZM+fP7906RKLxdq0aRPdoYEqer8rFjN2oFX6NmMXHx/P5XJjYmISExM9PT2pXbFyuVwoFPL5\n/OLiYrFY7Ovru23bNrojBQCDdvv2bR6PN3z4cOoli8WaM2fOwYMHZ86cSW9goJreb57AGjvQ\nKn1L7FgsVlFRUXp6elZWFpfLbW9vV1wyMTHx8vIKDQ0NCwvDpgcAoJe9vX2nLieEEBsbm8GD\nB9MSD6gJ7U6gn9DD/Mbc3DwyMjIyMlIikVRWVgqFQgaDYWtry2azTU1N6Y4OQE8o3zwBLxQa\nGpqamrpt2zbFRpP29va9e/du3LiR3sBANSjFQj+hh4mdApPJHDNmDN1RAAB0w9jY+LPPPjty\n5IiXl5eNjU19ff3Nmzfb2toCAwPfffdd6p7PP/+c3iCh91CKhX5CnxM7AIB+69ChQ5aWllKp\ntKioiBoxMjIyMzPLzc1V3IPEbgDpUym2ublZJpNhzhu0weASu/Ly8rfffpsQcvHiRbpjAQDD\nJRAI6A4BNKlPpVi5XC4SiV54siWACgwusRMKhZcuXaI7CoABDw2KATrqUymWENLY2IjEDrTB\n4BK7sWPH3rlzh+4oAAC6IRAIpFLpoEGDrK2t6Y4F+qZPM3aEEOyfAC0xuMTO3Nx8woQJdEcB\nANCNpUuXlpSUjB071tXVteNiO+jn5HK5RCLp04wdEjvQEr1N7ORyOZ/P5/F41F8eFovl5ubm\n7OxMd1wAAD3asmVLTU3Ne++9d+3aNbpjgT4Qi8VyubyXM3YWFhampqbYGAtaom9HihFC6urq\noqKiHB0dXV1d/fz8AgMDAwMD586dy2azR44cmZiY2NTURHeMAAOekZGRSc80vsauoaEhKipq\n5MiRTCbTyclp/fr1NTU1L3xXfn7+zJkzbWxsBg0a5Ofnd/XqVc1GpXHBwcHvvfceIcTHx4fu\nWKAPxGIxIaSXiR1Bj2LQJn2bsRMIBN7e3hUVFa6urv7+/tSRYoSQxsZGHo9XUFAQHx/P4XC4\nXC5WrQIMFC0tLXPmzCktLV2+fLmHh0d5eXlmZubly5dv3brl4ODQ07uOHDmyZs2a0aNHb9my\nRSKRHDlyZP78+ZcvX/b29tZl8L1RWFjo6enZ+7QA+hsVEjvM2IGW6FtiFxcXV11dnZ2dHRQU\n1PWqTCbLyMiIiIiIj49PS0vTfXgAoIL09PTS0tKUlJT333+fGpk/f/6qVauSk5P37NnT7Vvq\n6urCw8M9PDyuXbtGrXzatGnT5MmT//Wvf/W3xO7x48czZ87Mz89fsGAB3bGAipqbmwkhvVxj\nRwixtbVFYgdaom+JXV5eXnBwcLdZHSHE2Ng4PDy8sLCQw+EgsQMYKLKysmxsbDZv3qwYCQoK\niouLy8rKSk1N7bbs+/XXXwuFwp07dyp+17q4uDQ0NNDeh6W1tZXD4fB4POok6+bmZg6H4+np\nGRISEhwcbGdnRwgxMjJycXFZvnw5TkEcKKgZu94ndijFgvboW2JXX1/v5uam/B53d/dTp07p\nJh4AfaWzs2IlEklZWZmvr6+5uXnHcR8fn8zMTD6f7+Li0vVdFy9etLCwmDt3LvUEiURia2tL\ne1ZHCFm1ahWHwxk+fDj1xzExMfH29v70008/+uijvLy81tZWQohEIqmurl6xYsWxY8fojhd6\nhZqx630pFsfFgvbo2+YJR0fHsrIy5fcUFxc7OTnpJh4AUFNlZWV7ezubze40To3weLxu3/Xz\nzz+7uLjcuXPHx8fHwsKCxWKNHDny0KFDWg/3RfLy8k6fPl1VVfXo0aNHjx7dv3//0KFD1tbW\nqampP//8MzX422+/ffvtt6dPn6Y7WOgtsVhsZGTEZDJ7eT9KsaA9+jZjFxgYmJaWlpqaGhER\n0fXvmEgk2rVrV25ubmxsLC3hARiI9vZ2mUxGHd+nhL+//x//+Efl91ATG10b9ira93f7rqdP\nnxJCFi5cGBwcvGXLFoFAkJqaum7dOolE8pe//KWXfwpt8PX1nTdv3gtvmzdv3syZM3UQD2hE\n77sTU1CKBe3Rt8QuPj6ey+XGxMQkJiZ6enpSu2LlcrlQKOTz+cXFxWKx2NfXd9u2bXRHCqDP\n5HK5XC5/9uyZ8tsaGhrU+Rak57PLpFJpZWXlv/71r7feeosaWb58+SuvvLJt27YNGzaYmND2\no+/AgQNU0tkTqVQ6atQoCwuL/Px8nUUFaur9eWIUW1vb8vJy7cUDhkzfEjsWi1VUVJSenp6V\nlcXlcqnlyRQTExMvL6/Q0NCwsDAaf6wD6AcGg6FkjZ2JiYlMJvv3v/+t/jeiOhN1nZmjRnrq\nW2RlZdXW1vbmm28qRpycnPz9/U+cOHHv3r2JEyeqH5hqRowY8cJ7qJwVBhCxWNzXGTuUYkFL\n9DC/MTc3j4yMjIyMlEgklZWVQqGQwWDY2tqy2WxsMQMYcNhstomJCZ/P7zROra7rabPUqFGj\nbt++bWT0P8uIhw4dSug+yik7O5v6QigUJiUlzZgx4/XXX7ezs6urq7t06dK9e/d2795NY3ig\nGpRiof/Qw8ROgclkjhkzhu4oAEAtpqam06ZNKykpaWpqsrKyogZlMllBQQGbze7pnEBvb++S\nkpLS0tLp06crBqniF717pxTNmEJCQmJiYiIiIhSXoqKi4uPj8/Lyli9fTlN0oCIVSrGYsQMt\n0bddsQCgf0JDQ5ubm1NSUhQj+/fvf/z48dq1a6mXLS0tt2/f7rhoKTQ0lMFgfPjhhxKJhBop\nLi6+cOHCuHHjRo4cqcPYe/Ttt98uWbKk02BgYCCHw6ElHlBHX2fskNiB9ujzjB0AaI/yPnaa\n7RgXFhZ25MiRpKSk27dvT5069f79+zk5OZMmTYqOjqZuePTokYeHx9y5cy9evEiNTJkyJSoq\nas+ePV5eXkuWLHn69OmRI0eMjY0/++wzDQamDqlU+vPPP48aNarj4P3796lWdjCw9HXGDqVY\n0B4kdgDQ35mamubn5ycmJubk5Jw7d27o0KEREREJCQmKymy3du/ePWbMmH379u3Zs8fc3NzX\n1zc+Pr5jZZZeCxcuDAkJCQ8PnzJlip2dXXNzc0lJSWpqqp+fH92hQZ/1dfOEra1tc3OzVCrF\nym/QOCR2ADAAWFlZpaSkdKzGdjRhwoSuO0kZDMbGjRs3btyo/ehUsX///vXr12/fvl2xeZ/B\nYMyfP3///v30BgYqUCGxI4SIRCJ7e3utBQUGCokdAAANHBwcTp069fTp03v37gmFQisrq7Fj\nx1L7dmHAaW5u7msplhDS2NiIxA40DpsnAADoce7cuba2Nh8fHz8/v1u3bm3ZsiUjI4PuoEAV\nqs3YYZkdaAMSOwBQBbV5oid0RzcAfPnll4sWLaqsrCSEJCYmbt26tbKyMjIyMi0tje7QoM/6\nOmNHJXbYGAvagMQOAIAGe/fu/eSTT7y8vGQy2RdffLF9+/aioqL9+/cfOHCA7tCgz/o6Y2dm\nZsZkMpHYgTZgjR2AFgkEAm081tHRURuPBV0qLy9ftGgRIeTmzZv19fVr1qwhhHh7e1dUVNAc\nGfRdXxM7go4noDVI7AAAaGBhYdHS0kIIOX/+/MSJE6nzMFpaWlQ+ybquru7y5csPHjx4/vw5\nIWTQoEHjxo2bO3cuVfUDreprg2KCHsWgNUjsAEAVDAZDZw2K9dKUKVN27NixYsWKffv2hYeH\nU4M5OTljx47t66OkUunWrVs///xzqVRqZmZmbW3NYDAaGxulUqmlpWVsbGxcXBz+i2hVXxsU\nEyR2oDVI7ADUoqViq2rfFCXaASQ5OXnhwoU5OTkeHh5RUVGEkOPHj+/YseP48eN9fVRCQsLB\ngwd3794dEBDg7OxM5XByuZzH4x0/fjwpKcnMzGzr1q2a/zPAf6lQikViB1pCW2L3008/DRs2\nbPDgwdTLu3fvSqXSyZMn0xUPAIAueXl5CQSCiooKFxcXqvw6bdq0a9eueXt79/VRhw8fTktL\nCwsL6zjIYDBcXV1jY2Pt7OxSUlKQ2GmVamvsRCKRluIBQ0bDrlipVBoaGjpx4sSffvpJMXjl\nyhUPD4+wsDCpVKr7kAAAdGzEiBHvvPPOjz/+qPjtPnLkSBWyOkJIbW3tuHHjero6efJkWuaV\nDQpm7KD/oGHGbu/evZmZmYsXL2az2YpBPz+/lStXHj58+NVXX42MjNR9VAC91Jvfkb38eU2t\nne/E3Ny898F0WhffbWxaqs9Sfex6uooVXS/01ltvXblyJTMzUy6XT58+fcGCBf7+/p6enkZG\nff687erqevbs2Z6OwT19+vTo0aPVjheUaWlp6dPfXEKIjY0NEjvQBhoSu0OHDi1ZsuTMmTMd\nB1955ZVjx44JhcKDBw8isQMAvbdr1y5CiEgkKiwsLCgoOHv2bFJSEovF8vPzy87O7tOjoqKi\nNm7cWF5eHhAQ4ObmRqX7DQ0NDx48OHnyJIfDycrK0sqfAQghhLS1tbW1takwY1ddXa2lkMCQ\n0ZDY8fn89evXd3tp1qxZf//733UcD4Byyqfouv3M3WkqrtuZuZ6oM43XbWMLKn7sq+ifrK2t\nFy5cuHDhwkePHp09e/bTTz89duxYXxO79evXm5qaJiUlHT16tNOlCRMmcDicgIAAzYUMnYnF\nYtLHuXaCGTvQGhoSOxsbm546cFZWVrJYLN2GAwBAj4cPHxYUFHC5XC6X++TJEw8Pj4CAgJkz\nZ6rwqJCQkJCQED6f//DhQ6qPnb29vbu7+4gRIzQdNXRGJXYqzNihQTFoAw2J3fz58w8cOPCH\nP/xh7ty5ikG5XJ6Tk3PgwIGVK1fqPiQA6Cvla+zghRwdHZubm6dOnTpjxoyQkBBvb29ra2t1\nHlhXV3fr1q2ODYqbmppYLBYaFGsbNcuuwq5YzNiBNtCQ2G3fvv3ixYvz5s1js9mjR4+2sLAQ\niUQ//fRTbW2to6NjUlKS7kMC6Fa3RdhOP4u7rboqBiUSScernV52GmQymV2vUoOdvktvij49\n7atATbafkMvlRkZGTCbT0tLSysqq2//6vYQGxfRSrRSLXbGgJTS0Oxk5cmRJScnatWsbGxsv\nXrx45syZK1eutLW1rV+/vqSkxNnZWfchAQDoWE1NzbVr1xYvXnzr1q1ly5bZ2dn5+fnt2LGj\nqKior49SNCiuqKhoaWl5+vRpXV2dRCJ59OjRtm3bdu3a9fHHH2vjjwAU1UqxOCsWtISeBsXD\nhw8/ePDgwYMHa2pqRCKRtbX1sGHDaIkEAIAu48ePHz9+/LvvviuXy2/fvn3+/PmMjIy4uDi5\nXN6n56jZoLi4uJiq3nZ19+7dPkVimFQrxdra2kokEolEos5kLUBXtJ08IZPJjI2NqXyutbX1\n1q1bJiYmkydP7j/1gi+//PLChQvK78HnLb3U0zZYqm6iqIp2W3Xt+M+eXra1tSn57p3OgKd+\n6CvqqtRLxQOp796pBkS9VFR5uq3Jql+QNTIyUnJcff/5i9zPNTU1Xb9+/erVq1evXv3hhx9M\nTEwWL17c14eo06BYIpH4+fn1lNgpguxrSAZFLBYzGAwzM7M+vYv6iykUCpHYgWbRkNjJZLLN\nmzf//vvv1JGIv/zyy6JFix49ekQImTFjRn5+vporiDXlpZdecnFxUX6PCq1EAQAIITExMVev\nXi0tLZXJZFOmTJk/f35CQsKMGTNMTU37+ih1GhQzmcxnz571dPX69eszZsywsrLqa0gGRSwW\nm5ub9/XDjI2NDSGksbFRcbQmgEbQkNjt3r1737590dHR1MuIiAgej0cVI9LT0z/77LO//e1v\nuo+qq2XLli1btkz5PQcPHtRNMACgZ7Kzs/38/LZs2eLn56fmr3Y0KKZXS0tLX+uw5L8zdtg/\nARpHQ2KXlZX15ptvpqamEkIeP358/vz5DRs2fPbZZ4SQ5ubm7OzsfpLYgQHqVLHqdgNsp1Ks\n4h7qC6pIqihdUauqFbVX6i29KcUqqpxUXVXxQGpcUV2lvuh2s62iPksFhk2y/URBQcEbb7xh\nbGxcVVWl5DaZTFZYWDhr1qzePBMNiumlwkGxpEMpVgsRgUGjIbGrqKgIDw+nvs7Pz5fL5atX\nr6ZeTpkyhcPh6D4kAADdmD17tkAgeOF2sdra2tmzZ/d+FwUaFNOIKsX29V3GxsaWlpaYsQON\noyGxYzAYirUIFy9etLKyev311xWXZDKZ7kMCgL5S3qAYmyd6MmLEiD//+c9vvvkmtWTexMTE\n29vbxcWlqqrq6tWrra2thJDW1tbjx4+z2ew+PfnJkydCoXDOnDmdVukJBIKzZ8/2dJAjqE+1\nUizB4ROgHTQkdmw2++rVq2+//bZAIMjNzV2wYIFiM9F//vOf4cOH6z4kMHC9qcAqvmhoaOh4\nm+JmqlpK/ZgWiUQd30IVZAkh1OcW6pd3T6i/Doq/FNQXih1F1MSAophLFWGHDBlCvVTE1pEK\ncwmgPfv27YuKioqIiGhvbyeEtLe3m5qaHjp0aNOmTSKRiMqVjYyM2Gx2enp6L5/59OnTVatW\nUbv4hw4dunv37jVr1iiuPnjwYMOGDUjstEe1UizB4ROgHTRs6ly9evXRo0e9vb2nTJkiFAoV\nZdmvv/46MzNz6dKlug8JAEA3lixZ8vDhw9bW1ra2tra2NrFY/PHHH4eGhoaEhIhEImqwtbX1\nl19+WbhwYS+fGRcXV1JS8sknn3A4nMWLF4eEhOAIH11qaWlR7eMTDp8AbaBhxi4yMvLhw4c5\nOTlMJjM1NXXOnDnUeGxs7JgxY2JjY3UfEgAALZhM5ubNmy9cuPDee++p3FXk7NmzKSkp1Jzc\nH//4xwULFrz11luDBw/+y1/+otFgoXvqzNihFAsaR0NiZ25u/tVXX3311Vedxk+cOOHp6dnX\nHo8A6lDSuJV02QZLFToVn7Bra2tJh01tVPmVukdRe6UGFU9obm4m/y3IdvyCQpXhqN8Qip6l\n1C97RfW2298fipupfXbdHizbU79ilTEYDPRx1AgGg5Gbm6vOE+rq6saMGaN4uXLlysbGxr/8\n5S8vv/wyaiA6oM6MHRI70DjaTp7oytvbm+4QAADoJBAIpFLpoEGD+tSn3dXV9cKFCzNnzlSM\nbNiw4ddff125ciWHw8EiS21TecYOpVjQhn6U2AEAGLilS5eWlJSMHTvW1dW199N44eHh77zz\nTnV1dUpKimInTVJSkpGR0ZIlS2bPnq21eIEQ9WbsqIl/AA1CYgfwf5R3JO60DZaqoSgO2aTG\nqVKsYncqVYpVVFuoEq2irkrti1SgulRQH/2p44YIISwWi3Sp3ir6WVD9ihUhdTxJVvGbptvz\nZKF/2rJlS01NzXvvvXft2rXev2vTpk0NDQ179uyJi4tTJHaEkISEBA8Pj6ioKC1ECv9HLBbb\n29ur8EYWi/XLL79oPB4wcEjsAEAV6GOnDcHBwdQXPj4+fXrj1q1bY2Jiuv5rDwgIWLhwIbIH\nrRKLxU5OTiq8kcViKT4ZAmgK1j4DANCssLBQseFGZUZGRt3m00wmc8KECWo+HJRQeY2dnZ1d\nt70nAdSBGTuAzjrtKlWcxNrpHFjqNsVL6gd0fX096VCKffr0KenQr1hxrkDH5yv2llJ1Veo3\nRKd7FEfHUtvGFREqP3YWBoTHjx/PnDkzPz9/wYIFdMcCqlB5jZ2dnR1m7EDjkNgBAOhOa2sr\nh8Ph8XjUCsvm5mYOh+Pp6RkSEhIcHGxnZ0cIMTIycnFxWb58eafDwaB/UnnGDqVY0AYkdgCg\nCgaDoWSNHfRk1apVHA5n+PDh1BwPdVbsp59++tFHH+Xl5VEztRKJpLq6esWKFceOHaM7Xngx\nsVis8oxda2urynkhQLeQ2AH0iKp4dirFKtZCdToHlnpJVV07bZWl+hIr7ulUP1WUYjv+blDU\nXhW/6amXnXoad0vRr7jjYzXVlxjUlJeXd/r06a59g1NTU1NTUxUvz5w5s3LlSt2GBipqaWlR\neY0dIaShoQGJHWgQNk8AAOiOr6/vvHnzXnjbvHnzOjYchv5MnVIs6fA5EEAjkNgBwADQ0NAQ\nFRU1cuRIJpPp5OS0fv36mpqa3r89KiqKwWBQp6nSKz8/n0oCRowYsX79+hMnTnT7e93CwiI/\nP1/n0YEq1Nk8QZDYgaahFAugIqlUSjrURqlqKfVSsaeVqroqaq+dXlIUVVdqNT1VmVXUZ6l1\nbIrqKvVSsbiNeq/iascirPLfNI6Ojn3703ahyz52LS0tc+bMKS0tXb58uYeHR3l5eWZm5uXL\nl2/duuXg4PDCtxcXF3/66acajEcj3nrrrStXrmRmZsrl8unTpy9YsMDf39/T0xMn8A44Ks/Y\nWVhYMJlMdDwBzcJPEADo79LT00tLS1NSUk6cOPHhhx8eOnToyJEjfD4/OTn5he9ta2vbsGHD\n+PHjdRBnn+zatev7779/9uzZmTNnfHx8zp49O2PGjKFDh65atYru0KAP5HK5RCJR+WQXbIwF\njUNiBwD9XVZWlo2NzebNmxUjQUFBrq6uWVlZcrlc+Xv37Nnz448/7t69W8sxqsja2nrhwoUp\nKSlZWVmpqaksFgs7YQcWiUTS3t6u8u4HJHagcSjFAvSI+hTe6QBZBarHmKIcSZVBuy2Vdmov\nrKi1UV8orlpaWpL/Nii2tramBqkvrKysOr5UnCRL3azY8Up9QYWtmELotB9W/SKsjkkkkrKy\nMl9f306TIj4+PpmZmXw+38XFpaf3lpeXJyQkvPvuu15eXtqPtM8ePnxYUFDA5XK5XO6TJ088\nPDwCAgKwZ2Jgoba6q5zY4fAJ0Di9Tezkcjmfz+fxeNT56ywWy83NzdnZme64AKBvKisr29vb\n2Wx2p3FqhMfjKUns3n777cGDB+/YsaMfHtHh6OjY3Nw8derUGTNmhISEeHt7K7J5GECohkcq\nl2KR2IHG6WFiV1dXl5ycfPTo0SdPnnS6xGaz165dGx0drZj/AADVKN880draKpVKPT09lT9k\n1apV0dHRyu+hPpt1TXqoacue5lMJIYcPH7506dKZM2esra37YbVLLpcbGRkxmUxLS0srK6tO\n3QdhoKASO5Riof/Qt8ROIBB4e3tXVFS4urr6+/uz2Wzq90FjYyOPxysoKIiPj+dwOFwul2og\nBAaOqksKBALqZaeqJVVkUfzGpa52OitW8QOd+vlO/X+l2CrbaU8rtXOW2v1K/luKVVylSrFU\nB4RBgwZRg9QXipeDBw8mhNjb21MvhwwZovin4r3ddiTWcQXW2NjY2Nj4T3/6k/Lb1KmQUqvr\netp++/vvv0dHR69cuXLJkiUqfwutqqmpuXv37pUrVy5fvpyamtrS0uLt7T1r1qxZs2bNmDGD\n7uigt1CKhf5G3xK7uLi46urq7OzsoKCgrldlMllGRkZERER8fHxaWpruwwMwECYmJkZGRlu3\nblX/UVSu3HVmjhrp6RPaX//6V7lcvnfvXvUD0J7x48ePHz/+3Xfflcvlt2/fPn/+fEZGRlxc\n3At3hED/oX4pVvHBEkAj9C2xy8vLCw4O7jarI4QYGxuHh4cXFhZyOBwkdgADApvNNjEx4fP5\nncZ5PB4hxM3Nretbvvvuu2PHjn388cdSqbSqqop0ONutqqrK1ta2/xyw1tTUdP369atXr169\nevWHH34wMTFZvHgx3UFBH6AUC/2NviV29fX13f6g78jd3f3UqVO6iQcGtE6fwqlCqqIq2m23\nYWrfq6K6Ss0nKc6TVTQu7niz4lcCtWyA+qdiIoqqripqr1RFVZGXULdR95D/Lb9qu/bKYDCU\nrLHTIFNT02nTppWUlDQ1NSlWx8pksoKCAjab3e2OqEuXLhFC3n///ffff7/jeHZ2dnZ29tat\nW3ft2qWDyJWLiYm5evVqaWmpTCabMmXK/PnzExISZsyYQe22hoGipaXFxMREsbe9r1gsFkqx\noFn6ltg5OjqWlZUpv6e4uNjJyUk38QCA+kJDQ99+++2UlJTExERqZP/+/Y8fP05ISKBetrS0\n3L9/38bGxtXVlRCybt26WbNmdXxCU1NTUFDQ/PnzIyIiXvjZTzeys7P9/Py2bNni5+dHLZ2E\ngUjlYycodnZ2mLEDzdK3xC4wMDAtLS01NTUiIqLrLjORSLRr167c3NzY2FhawgMAFYSFhR05\nciQpKen27dtTp069f/9+Tk7OpEmTFDtqHz165OHhMXfu3IsXLxJC3N3d3d3dOz6B+t05YsQI\n2vdSFBQUvPHGG8bGxlSNuCcymaywsLBTegr9kFgsVnmBHUEpFrRA3xK7+Ph4LpcbExOTmJjo\n6elJ7YqVy+VCoZDP5xcXF4vFYl9f323bttEdKfQjiqoltYq5pwVYQ4cOJf97HivpUK6lSqjU\nFjmqQwf5b+1VsUmWoqhgUqVYRbdh6lHUS8VGVyoYRWVWz5oP95KpqWl+fn5iYmJOTs65c+eG\nDh0aERGRkJAwEPsWzZ49WyAQDBs2TPlttbW1s2fPxi6K/q+lpUXNGbum3y5tigAAIABJREFU\npqa2tjaVi7kAnejb/0ksFquoqCg9PT0rK4vL5Sr6ShBCTExMvLy8QkNDw8LC8FcIQE3K+9j1\n1IVEZVZWVikpKSkpKd1enTBhgvIcyM7Orp8kSSNGjPjzn//85ptvUp8QTExMvL29XVxcqqqq\nrl69Sn0SaG1tPX78eNeezNAPqV+KlcvlDQ0NDg4OGowKDJke5jfm5uaRkZGRkZESiaSyslIo\nFDIYDFtbWzabjVXJAECvffv2RUVFRUREUB8729vbTU1NDx06tGnTJpFIROXKRkZGbDY7PT2d\n7mDhxVpaWtQsxRJCkNiBBulhYqfAZDLHjBnTdfzp06fPnj3rJwuooV9R3q+4UxmU+olM1V7J\n/zZao/bP9kRRzKW+ULzs+HxDK7YajiVLlnRc5yeRSDIyMhS7QwZicdnAqT9jR/67BhRAI4zo\nDoAGu3fvHj16NN1RAAAQJpO5efPmBQsWvPfee8jqBiI1Z+xsbW2NjIzQ8QQ0SJ9n7ABAe5Sv\nsYPeYzAYubm5dEcBKlJzxo5aKYQZO9AgJHYAnSkvd3aqjSoqsC/c59jTE/r03QGgX1EzsSPo\neAKapm+Jnaen5wvvqa6u1kEkAACg99QsxRJC7OzsUIoFDdK3xI46dkL57tdOZ0ABAACoRv0Z\nOxw+AZqlb4ldTEzMvn37SktLlWx6jY2N7akbFkBXymujBls51XEfO4D+SSwWKw5rVg2OiwXN\n0rddsUlJSW5ubqtWrZJKpXTHAgAAek4jpVjM2IEG6duMnampaVZW1tSpUz/44IPdu3fTHQ4A\nwP+YMGFC72/+6aeftBcJaIRGSrG//fabpuIB0LfEjhDi7u5eU1OjZCHdwoUL1Zw5BwBQTUBA\nAN0hgCaJxWI1Z+xYLNadO3c0FQ+AHiZ25EXtJHx9fX19fXUWDACAwvbt2+kOATSppaVF/XYn\nWGMHGqSfiR0hRC6X8/l8Ho8nFAoJISwWy83NzdnZme64APQEg8HA5gkA7IqF/kYPE7u6urrk\n5OSjR48+efKk0yU2m7127dro6Ggc3QMAAOrD5gnob/QtsRMIBN7e3hUVFa6urv7+/mw229ra\nmhDS2NjI4/EKCgri4+M5HA6Xy6VOcFfi559/vnv3rvJ7lJ/1DgAA+k39GTt7e/vnz5/LZDKc\n0QcaoW+JXVxcXHV1dXZ2dlBQUNerMpksIyMjIiIiPj4+LS1N+aMyMzNPnDih/J7m5mbVYwUA\ngAFO/c0TgwcPbm9vf/bs2eDBgzUVFRgyfUvs8vLygoODu83qCCHGxsbh4eGFhYUcDueFiV1K\nSsoL+xgPGTJExUABBjjlDYoBDIT6myeofO7p06dI7EAj9K1BcX19vZIzJyju7u5dl98BAOjY\nsWPHOn7C3LRp07Fjx2iMB/pKJpO1traqmdg5ODgQQurq6jQUFBg6fUvsHB0dqeNilSguLnZy\nctJNPAAA3frqq69WrVpVXV2tGJHL5atXr87MzKQxKh0RCklqKlmyhPj5kdmzyY4d5Mcf6Y5J\nFS0tLYQQNUuxTCbTxsYGiR1oir4ldoGBgSdPnkxNTe12W4NIJIqLi8vNze2pVgsAoBu7d+9O\nSUnpeEDO/v37d+7c+fHHH9MYlS7s3k2cnck//kFGjyavvUa8vEhODpk0iSxYQO7fpzu4vhGL\nxYQQNWfsCCGDBw9GYgeaom9r7OLj47lcbkxMTGJioqenJ7UrVi6XC4VCPp9fXFwsFot9fX23\nbdtGd6QAA5uxsbGpqWlPV42M9O1Do8bxeDx/f/9Og/PmzYuPj6clHh2JiSFffEH+8Q8SGkqY\nzP8/mJJC7t4lUVHk1VfJ3/5G4uPJAPn/h5qxUz+xc3BwePr0qSYiAtC7xI7FYhUVFaWnp2dl\nZXG53Pb2dsUlExMTLy+v0NDQsLAwExN9+4MDwMAydOjQ0tLSV199teNgYWHhsGHDVHtgXV3d\n5cuXHzx4QDVFGzRo0Lhx4+bOnav8JB6d2rKFHDhAcnPJnDmdL40fT86dIydPkvXrSWkp+de/\nyIs6UvUH1IydmqVYQsjgwYOR2IGm6GF+Y25uHhkZGRkZKZFIKisrhUIhg8GwtbVls9lKJhgA\nAHQpLCxs8+bNv/76q6enp6WlZV1d3ZUrV7788ssPP/ywr4+SSqVbt279/PPPpVKpmZmZtbU1\ng8FobGyUSqWWlpaxsbFxcXH0nwVy/DhJTyfnzxMlJzouX04mTiQBAcTbm1y8SBwddRifKlCK\nhX5IDxM7BSaTOWbMGLqjAADoxt///nehULhz506qnEcIsbCw+Otf/xoXF9fXRyUkJBw8eHD3\n7t0BAQHOzs5UDieXy3k83vHjx5OSkszMzLZu3arhP0CfNDSQv/6VxMQoy+ooY8aQmzfJokVk\n1ixy+TIZPlwn8alIJBIRQqg2+OoYPHgwj8fTREQAep3YAYD2GBkZYUmDOoyNjT/55JPExMQ7\nd+40NDSwWKyJEyeqliIcPnw4LS0tLCys4yCDwXB1dY2NjbWzs0tJSaE5sfvb34iVFenlZKSt\nLcnP//+53dWr/XneTiQSmZqampmZqfkcBweHW7duaSQkgIGxQFWDysvL582bN2/ePLoDAQBD\nd+7cuaamptdff33evHnXr1/fuHFjRkaGCs+pra0dN25cT1cnT54sEAjUCFNtxcVk/36Snk56\nX7K0tibffUdeeoksWkQaG7UZnFqamprUn64jhDg4OKAUC5picImdUCi8dOnSpUuX6A4EAAza\nl19+uWjRosrKSkJIYmLi1q1bKysrIyMjX3goTleurq5nz57t6erp06dHjx6tVqxqSk0lixaR\nvn6ctrIip08TiYQsX05aW7UTmbpEIpGVlZX6z8EaO9Agg6ukjB079s6dO3RHAQCGbu/evZ98\n8omXl5dMJvviiy+2b98eGxv79ddff/zxx1u2bOnTo6KiojZu3FheXh4QEODm5kZtg21oaHjw\n4MHJkyc5HE5WVpZ2/hC9UF1NOBzSc96pzKBB5LvviLc32biRHD6s4cA0QSQSaWTGbvDgwc+e\nPZPJZDimD9RncImdubn5hAkT6I4CYMBTvsaO/j2Y/V55efmiRYsIITdv3qyvr1+zZg0hxNvb\nu6Kioq+PWr9+vampaVJS0tGjRztdmjBhAofDCQgI0ETIKtm3j4we3efpOgU2m5w5Q954g0yc\nSKKjNRqZBjQ1NWlqxq69vf3Zs2c4LhbUp7eJnVwu5/P5PB5PKBQSQlgslpubm7OzM91xAQAQ\nQoiFhQW1H/b8+fMTJ06kzjlsaWlRbUtKSEhISEgIn89/+PAh1cfO3t7e3d19xIgRmg27b1pa\nyJdfkoQEok6iP2UK+fJLEhJCxo8nXVo600tTM3aK42KR2IH69DCxq6urS05OPnr06JMnTzpd\nYrPZa9eujY6O1shnLAAAlU2ZMmXHjh0rVqzYt29feHg4NZiTkzN27FjVHlhXV3fr1q2ODYqb\nmppYLBadDYqzs4lUStasUfc5q1eTH38kq1eT4mLi4qKJyDRDU5snBg8ezGAwsMwONELfEjuB\nQEDVMlxdXf39/akjxQghjY2NPB6voKAgPj6ew+FwuVzWQGhrDgD6Kjk5eeHChTk5OR4eHlFR\nUYSQ48eP79ix4/jx4319VP9tUJyZSf78Z6KRD9I7dpCSEvKnP5GiIqL2SQ+aoqlSLPVfDYdP\ngEboW2IXFxdXXV2dnZ0dFBTU9apMJsvIyIiIiIiPj1dh6xkAKBgbG2ONnTq8vLwEAkFFRYWL\niwv1b3LatGnXrl3z9vbu66P6aYPiujpy7RpJSNDM04yNydGjZMoU8u675MABzTxTbZoqxRJs\njAXN0bfELi8vLzg4uNusjhBibGwcHh5eWFjI4XCQ2AGA7v3222+KdW9mZmYdT8cZOXLkyJEj\nu71TOTUbFN+7d6+5ubnbS/fv3+9NAN3LzSV2dmTGDNWf0MmQIeT4ceLrS2bO1EB5VxOampqG\na+hsDCR2oCn6ltjV19e7ubkpv8fd3f3UqVO6iQcAoKOpU6dmZWX5+fkpv+3ChQurV6+ura3t\nzTPVaVDc2to6ffp0apNZT3pK+17gm2/IsmVEs8eTvPYa2bmTvPMO8fQkPf+RdUazM3YoxYJG\n6FuDYkdHx7KyMuX3FBcXUxvQAAB0bOfOnUuXLl22bNnNmzflcnmnq3K5/Pvvv1+2bNnSpUt3\n7drVy2eq06DYzMyssbFR3oOioiJCiKWlZS8j+T9iMblwgfzhD31+4wtFRhI/P7JiBVEt3dQo\nTa2xI4Q4ODggsQON0LcZu8DAwLS0tNTU1IiICCaT2emqSCTatWtXbm5ubGwsLeEBgIFbt26d\nh4dHZGTk66+/PnTo0BkzZjg6OtrZ2TU0NAgEgmvXrv3+++8+Pj5FRUVTp07t5TP7Y4Pi8+cJ\nIeRFE5OqYDDIoUPEw4P89a/kyy81//y+0NTJE4SQwYMH83g8jTwKDJy+JXbx8fFcLjcmJiYx\nMdHT05PaFSuXy4VCIZ/PLy4uFovFvr6+27ZtoztSgIENDYpVNmXKFC6XW1hY+O233169evXW\nrVvPnz+3s7NzdHR86623li1bNmvWrD49sD82KP7mGzJ/PlFhqq837O3Jv/9NfHzI7Nlk9Wqt\nfIve0WAp1sHB4YcfftDIo8DA6Vtix2KxioqK0tPTs7KyuFxue3u74pKJiYmXl1doaGhYWJhq\nLUABgC4NDQ0JCQkcDkcgEDg4OCxatGj79u3Dhg1T8pa6urqdO3fm5eVVVlYOHTp06tSpH330\n0cSJE3UWs3JvvPHGG2+8oamn9a8GxXI5ycsjvS4lq8LLi3z0EXnnHfLaazR2ttNUHzuCzROg\nOXqY35ibm0dGRkZGRkokksrKSqFQyGAwbG1t2Wy2qakp3dEBQJ+1tLTMmTOntLR0+fLlHh4e\n5eXlmZmZly9fvnXrFtWyv6unT59Onz6dz+cvWbLkT3/6U0VFxf9j787joqr6P4B/Z5gBhn2X\n1UEg3JfEJZE0RXNJnwxLMU0wrTSlBDU09VExLRJNzVJzy/xpmorlvoWiuORaWu4smqwz7DsD\nzO+P+8TDg4DMzL2z3Pm8X/2B994553vH0k/n3HvO7t27Dx8+nJCQ0JfF9zTVVVhYmJ6e7urq\n6uDgwGKzbdq0adOmTYOD6enpBw4cmDFjBosdPce9e5STQwMGcNvL3Ll05gy9/TadP086+rOd\n3alYPGMHrODbyxP1mZmZ+fv7BwQEdO/e3c/PD6kOwECtX7/+xo0bsbGx+/btmz9//tatW3fs\n2JGamrp8+fKmPrJ48eKUlJR169YdPHgwJibmhx9++Omnn6qqqpYtW6bNyp9VXV09depUR0fH\njh07Ojk5jR07tqSkhNMeHz58GBERwWkXDZ0/Tx4eVG/pFk4IhbRzJz1+TDp6tEapVJaVlbE4\nFZufn19TU8NKa2DM+BzsAIA7JiYm4qax+4zdzp07ra2tP/roo7ojoaGhvr6+O3fufPbFUoZY\nLB4yZMj7779fd+T111+3sLC4c+cOi4Wp4dtvv/3uu+8mTpy4cePGOXPmHDlyhIfvciUlUb9+\n2ujIxYW+/57i4ujUKW1097/Ky8tra2tZHLGrra3Ny8tjpTUwZjycigUAPqmsrLx582b//v3N\n/3cjqaCgoO3bt6empvo09ojVqlWrGhypqqpSKBQ632R9y5Yt06ZN++abb5hfdu3aNSwsbNWq\nVaampmq3OWHChGbOPrtrNueSkmjWLC31NWQIRUbSO+/QH39Qq1Za6pSIiJihVhafsSOi3Nxc\nZ2dnVhoEo4VgBwB67fHjx7W1tVKptMFx5khKSkqjwe5ZGzduVCgU48ePZ79EVSQnJy+pt8vW\nkCFDqqurk5OT27dvr3ab+/fvt7KyatVErCktLVW7ZXWkp1NqKrH3XsjzLV9OSUk0bhydPk1C\n7U1DMV8si+vYCQQCvD8BmsNULACwr7i4uKqqSvA8LXn2i9kU4dlxEWtrayIqKipqST3MKkh9\n+vSZPn266nfDptLSUjs7u7pf2traksbZ68svvzQzMztz5syfjdm2bZumRavk/HmytaWOHbXX\no1hM//d/dP06xcVpr1O2R+xMTU0dHR0zMjJYaQ2MGUbsAEAdza9jZ2lpWVJScvTo0eYbadu2\nrdoFME/XteRhvh9//HHSpEmdO3c+dOiQJjOeeisiIuLkyZMTJkw4duyYUItDVo27cIH69iUT\nE6126utL69dTeDj170+9e2unT3aDHRF5eHikp6ez1RoYLQQ7AGCfiYmJQCAYNGiQ5k0xY1rP\njswxR5izTVEqlYsXL46JiXnttdd2797N4t/B+mbbtm379u3LzMx8dk96e3v74OBg7ZWSlERj\nxmivuzpvv00JCRQaSjdvUr0xUe6UlpaKRKJntzhSm4eHB0bsQHMIdgCg16RSqUgkSk1NbXCc\n2X/Jz8+vqQ8qlcopU6Zs3bo1MjIyLi5O90NZ/wgJCWkwcDh06ND6w59ZWVmqtunk5DR16tRG\nT3Xt2vX06dOqNqimwkK6fZu+/lpL3TWwbh299BK98w4dPEjc733C4iJ2DIzYASsQ7ABAr4nF\n4p49e16/fr3+hus1NTVnz56VSqWtW7du6oORkZFbt25dsWLF7NmztVXs8+n87Q1uXbtGQiH1\n6KGb3s3NaedO6tWL1q0j7pfuY3HbCYa7u/uZM2dYbBCME4IdAKhDm3vFhoeHf/DBB7GxsTEx\nMcyRjRs3ZmRk1L1eWlFRce/ePWtra19fX+ZIfHz8mjVroqKi9CrVEdH//d//6boELv3xB7Vr\nR/+7MI1WdexIX39N06ZR797UqxenXWHEDvQTgh0A6LtJkybt2LFj6dKlv//+e0BAwL179/bs\n2dO1a9dZ/yyW9ujRoxdffDE4OLhuzvGTTz4hourq6meX/42Ojra3t9dm/Ubk99+pWzcd1/Du\nu3T+PL35Jt28SU3sOMeKkpISdkfs8IwdsALBDgD0nVgsPn78eExMzJ49e06cOOHi4hIREbFk\nyZJmxkuSk5OJaO3atc+emjp1KoIdV27fJn2Ya163jnr3pkmT6JdfuHvYrv6zAazw8PAoLy/P\ny8tjdwdhMDYIdgBgACwtLWNjY2NjYxs926lTpwZ7izW11RhwSKGgO3eoa1dd10FkaUn79lGv\nXvT55/Tppxx1wvozdswbzenp6Qh2oAkEOwBQR/MLPbD7jB0Yhrt3qapKL4IdEbVrRzt20OjR\nFBBAQ4Zw0QPrU7GOjo7m5uYZGRmdO3dmsVkwNvry/j8AABi2W7fI1ZVcXHRdxz9ef51mzqR3\n3qEnT7honvWpWIFA4ObmhvcnQEMIdgAAwIY//tCX4bo6X3xBHTvSG29QeTnrbbM+YkdE7u7u\nCHagIQQ7AABggz68EtuASET79lF+Pk2ZwnrbrI/YEVY8ATYg2AEAABtu3SI9fDjM0ZH27aMD\nB2jlSnYbZn0dO0KwAzbg5QkAUAdenoD/kZlJOTl6N2LH6N6dfviBxo0jf38aOZKtVrmYivXw\n8EhMTGS3TTA2CHYAAKCxW7fIzIz8/XVdRxPefJP++IMmTKBLl6hDB1aaxFQs6CdMxQIAgMZu\n3aIOHUgs1nUdTYuJocGDacQIys5mpT2OXp6QyWRVVVXsNgtGBcEOAAA0dv8+tW+v6yKaJRDQ\njh3UqhWNGEGlpZq3x/oCxUTk4eFRW1ublZXFbrNgVBDsAEAdzDN2TREK8WeLkXn4kF54QddF\nPI9EQj//THI5vfMO1dRo2BhHU7ECgQCzsaAJ/OELAAAaM4hgR0StWtGRI5SYSBERmjRTXl5e\nU1PD+oidubm5vb09gh1oAsGuSVOmTBE8j1wu13WZAAC6VlJCWVmGEeyIqEMHOnqUfviBYmLU\nbqO0tJSIWB+xI7w/ARrDW7FNWrp0aWhoaPPXjB49WjvFAADor4cPSak0mGBHRL17048/UkgI\nOTvTtGlqNFBSUkLcBDsvL6+///6b9WbBeCDYNcnNzc3Nza35a0xNTbVTDIC+aX4dOzxjZ1we\nPCAnJ7K313Udqhg5krZto/BwMjOjd99V9dNMsGN9KpaIXnjhhQcPHrDeLBgPBDsAANCMoTxg\n18CECVRYSB98QHZ2FBKi0keZqVgugl3btm2PHTvGerNgPBDsAABAMwYa7Iho+nQqKaHQUPrp\nJxo1quWfKykpEQqF5ubmrFfUtm3blJSUqqoqzAiBejBdAgAAmjHcYEdE0dG0ZAmNHUu//NLy\nDzGL2HGxdV7btm2rq6tTUlJYbxmMBEbsAEAd2CsW/suggx0RzZtHRPTWW7RjB40d25JPlJSU\ncPHmBBF5eHjY2Njcv3+/Xbt2XLQPvIdgBwAAGsjPJ7lcf3eJbaF588jGhiZMoNLSlrxLwcW2\nE3VeeOGF+/fvc9Q48B6CHQAAaODhQyIiPz9d16Gx6dNJKKT336fCQoqMbP5a7kbsiKhdu3b3\n7t3jqHHgPQQ7AADQwIMH5OZG1ta6roMN06ZRq1Y0fjylpdFXX1HTq/bIZDJnZ2eOqvD39z9x\n4gRHjQPv4eUJAFBH83vF4hk7I/LokWE/YNdASAgdOkTbttE771BlZVNXZWRkuLu7c1RC27Zt\nMWIHakOwAwAADTx4wKtgR0SDBtGFC5SURAMGUE5Oo5dkZmY+dwV7tbVr1y4vLy83N5ej9oHf\nEOwAAEADycl8eMCugc6d6eJFqqigPn3o9u1nz3Ma7Pz9/YVCId6fAPUg2AEAgAYeP6bWrXVd\nBAc8POj8eQoIoMBA2r+/wUlOg51EIvH09ESwA/Ug2AEAgLoqKyknh5/BjogsLWnPHpo3j8aO\npdmzSaFgDldVVeXm5nIX7Iiobdu2CHagHrwVCwDqEIvFzeynJGz6dULglb//JqWSt8GOiAQC\n+vRT6tWLxo+ny5dp1y5q3TorK0upVHIa7LDiCagNf/gCAIC6njwhkYg4ez9UXwwaRDdukIkJ\ndetGe/dmZWURkaurK3cddujQ4datW9y1DzyGETsAAFDXkyfk7k4iI/irxMODEhLo88/p7bdd\nX365tY0NdwsUE1GfPn1SU1OfPn3q6enJXS/ASxixAwAAdT15wud52AZMTGjBAkpKsrl790pZ\nGR09yl1XnTt3trOzu3DhAnddAF8h2AGAOkQikXnT8Iydsfj7byMKdozevb+eNCnRzY3+9S96\n+23KzuaiE6FQGBgYmJSUxEXjwG/4wxcAANRlVCN2/3gik/3y8st0+TLdvUvt29M331BNDeu9\nBAUFIdiBGhDsAABAXU+ekJeXrovQtszMTHd3d+rRg65epYULaf58CgigM2fY7SUoKOjWrVsF\nBQXsNgu8h2AHAADqMspgl5GR8Z+1TkQiioyk+/cpIIAGDaKRI+nOHbZ66dWrl6mp6aVLl9hq\nEIwEgh0AqINZx64pAoFA1wUC9+RyKiszwqnYhttOtGpFW7bQjRtUWUldutDEiZScrHkvZmZm\nPXr0wGwsqArBDgAA1PLkCREZW7CrqamRyWSNrE7ctSudPEmnT1NKCrVrRxMn0t27GvaFx+xA\nDbwNdkqlMiUl5fTp0wcOHDhw4EBCQsIT5s8gAABgxZMnZG1N9va6rkOrcnJyampqmlyd+JVX\nKCmJjh6lv/+mTp3o9dfp3Dm1+3r55ZevXLlSUVGhdgtghHgY7ORyeVRUlJubm6+v7+DBg0NC\nQkJCQoKDg6VSqbe3d0xMTGlpqa5rBADVFBYWRkVFeXt7m5mZubu7T5kyhVn9n92PgGqM8pXY\nzMxMInrOfmKDB9OZM3T+PIlENGAABQTQ1q1UXq5qX/379xeJRIcOHVK7WjBCfFsuPDMzMzAw\nMC0tzdfXd+jQoVKp1MrKioiKiopSUlLOnj27aNGi+Pj4xMREW1tbXRcLYMDMzc1tbGyaOiti\ndSuCioqKgQMH3rhxY/To0S+++GJycvL27dsTEhKuXr3q6OjI1kdAZUa4iB1RRkaGhYVFi/4G\nCQykwEB69IjWr6fZs2n2bBo/nqZMoa5dW9iXpaXlW2+9tXXr1rfeekujosGY8C3YLViwID09\n/ccffwwNDX32bE1NzYYNGyIiIhYtWrR69WrtlwcAali/fv2NGzdiY2M/+eQT5sirr746bty4\n5cuXr1y5kq2PgMqMMtj9Z62TlvPzo5UraelS2ruXNm+mbt2oa1d65x0aM6YlLxS/++67/fv3\nf/LkSWvj+6pBPXybij169OiECRMaTXVEZGJiMn369DFjxsTHx2u5MABQ286dO62trT/66KO6\nI6Ghob6+vjt37lQqlWx9BFRmlGudNHwltoUsLCgsjM6fp/v36V//om+/JamUgoJo9WpKS2vm\nc0FBQW3btt2+fbvaBYOx4Vuwy8vL8/Pza/6a9u3bZ3OzCQwAsK6ysvLmzZs9evQwNzevfzwo\nKCg7Ozs1NZWVj4A6jPUZO3WCXR1/f4qJoUeP6NIl6t2b1qyhNm3oxRdp/ny6cKHRHSzCw8O3\nbt1aW1urfqdgTPgW7Nzc3G7evNn8NdeuXVNtIB0AnmFjY+PWNLFYzFZHjx8/rq2tlUqlDY4z\nR1JSUlj5CKhMoaDMTCMMdllZWU2+EttyAgH17k0rV1JqKt28SSEh9Ouv1K8fOTpSSAitW0d/\n/kn/DC2HhYWlp6efPHlS007BOPDtGbuQkJDVq1fHxcVFRESYmZk1OFtSUvLFF18cPnx47ty5\nOikPwEjU1tYqlcrr1683f5mfn99zH0IvLi4mIuYtqPqsra2JqKioiJWPgMpMTOiTT6h7d13X\noVUKheLixYsjR45ks9Fu3ahbN1q4kORySkigU6do9WqKiCBHRwoMpKCgVi+99MH48R9//PHv\nv/8ukUjY7Br4iG/BbtGiRYmJiXPmzImJienRowfzVqxSqSwuLk5NTb127Vp5eXn//v0XLlyo\n60oB+Cw3N1ehUPTo0aP5y959990tW7ao1wXzqJxKW1yo8RFoklDOzikrAAAgAElEQVRIn3+u\n6yK07cSJE0VFRSEhIZy07uREY8bQmDFERE+fUmIiXbxIu3bR/PlfK5UPhMK/evTo8d571LUr\nde1KDg6c1ACGj2/BztbW9sKFC+vXr9+5c2diYmL9hxJEIlGvXr3Cw8MnTZrE7loMAEaovLw8\nPz+/qbPDhw/fs2fPgwcPmm/k2UG1ZzFDes8OszFHGh3wU+MjAC2xY8eOkSNH2tnZcd6TpyeN\nH0/jxxMRlZbSjRvVP/zwYMuWjl9/LXnyhKqryc2NOnak9u2pfXvy9yc/P/LyIiHfHq8CNfAw\n35ibm0dGRkZGRlZWVj5+/Li4uFggENjY2EilUhaf+wEwZiYmJnPnzm3+kQYPDw97NvYkkEql\nIpHo2TcemEflGn1ZSo2P8IBcLk9ISLh//35BQQEROTg4dOjQITg4uJnlBkElhYWFBw8e/Omn\nn7TdsaUlvfxyh5dfXllbG3n48C+nTr1kbU1//UV37tC9e3TiBKWmkkJBZmbk7U0+PtSmDUml\n5OX1n3/c3MjUVNs1g+7wMNgxlEplenr6kydPmKdtbG1tTU1NsQ4QACuuXLly48aN5q/p27cv\nK32JxeKePXtev369tLTU0tKSOVhTU3P27FmpVNrof9RqfMSgKRSK6OjodevWKRQKU1NTKysr\ngUBQVFSkUCgsLCzmzp27YMECTEBrbt++fdbW1kOHDtVVARs3boyIiBgwbNiGDRsmTpz439/T\n6mpKS6NHjyglhVJSKC2Nrlyhp0+pbquVVq3IxYU8PMjFhVxcyNWVnJzI0ZEcHcnJiRwcyN4e\no328wcNgJ5fLly9fvmvXrmfXNJFKpe++++6sWbPq/qwHADV06NChQ4cOWusuPDz8gw8+iI2N\njYmJYY5s3LgxIyNjyZIlzC8rKiru3btnbW3t6+vbwo/wyZIlS7Zs2bJixYpRo0a1bt2a+fue\n2S977969S5cuNTU1jY6O1nWZhk2pVG7fvj00NFSHMz8ikWj9+vXt2rV777334uLioqKiRo4c\n6eTkRCIR+fnRs0PRlZWUnk4ZGfT0KWVnU1YWZWXR3buUmEjZ2SSXU1nZfy+2syM7O7K3Jxub\n//xjbU22tmRtTRYWZGlJNjZkbk5WVmRpSaamZGdHAsF/dgpmfgb9IODZWp31txQLCgp6dku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sjPOr5o34+HiBQPDpp59evnx5w4YNlpaW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\ndgAAACpBsQMAAFAJih0AAIBK/D+vn1UAwPqxyAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the unnormalized 2D posterior on a grey scale (maximum set to 1)\n",
    "# as well as the two marginal PDFs (which is achieved simply by summing the grid, \n",
    "# as it's regular) which I normalize.\n",
    "dense <- exp(lndense - max(lndense))\n",
    "par(mfrow=c(2,2), mar=c(5,5,0.5,1), oma=c(0.1,0.1,0.5,0.1), mgp=c(2.2,0.8,0), cex=1.0) \n",
    "image.plot(z=dense, x=rc, y=sc, nlevel=1024, col=mycols)\n",
    "scDense <- apply(dense, 2, sum)\n",
    "mom <- pdfmom(scDense, sc)\n",
    "cat(\"Posterior mean, SD for sc =\", mom$mean, mom$sd, \"kpc\\n\")\n",
    "plot(sc, scDense/mom$Z, type=\"l\", ylab=\"P(sc | {w},{wsd},priors)\")\n",
    "lines(sc, dgamma(sc, shape=2, scale=0.003), col=\"red\") # overplot prior on sc in red\n",
    "rcDense <- apply(dense, 1, sum)\n",
    "mom <- pdfmom(rcDense, rc)\n",
    "cat(\"Posterior mean, SD for rc =\", mom$mean, mom$sd, \"kpc\\n\")\n",
    "plot(rc, rcDense/mom$Z, type=\"l\", ylab=\"P(rc | {w},{wsd},priors)\")\n",
    "# compare result with parallaxes (!) derived in GDR1 overview and cluster papers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute posterior using case 3 (3D Gaussian cluster)\n",
    "If you want to try this, you need to specify the cluster centre and then comupte the angular separations of the stars from this centre. This is done below. You then need to pass to d.likecluster2 the additional parameter costheta=cos(theta*pi/180). However, this does not work too well at present."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "clustCen <- data.frame(ra=56.75, dec=24.12) # RA, Dec of cluster center in degrees\n",
    "theta <- sqrt(((dat$ra-clustCen$ra)*cos(conv*clustCen$dec))^2 +\n",
    "                (dat$dec-clustCen$dec)^2) # on-sky separations from clustCen in degrees"
   ]
  }
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