Linear correlation coefficient in the presence of upper limits in astronomy using R

R censored data regression, upper limits, from Feigelson and Babu book.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear correlation coefficient in the presence of upper limits in astronomy\n",
    "======================================\n",
    "\n",
    "This jupyter notebook performs the linear regression for bivariate data in the presence of censored observations, more specifically left-censoring which is called \"upper limits\" in astronomy. It quantifies the null hypothesis probability. A few notes:\n",
    "\n",
    "- it does not take into account uncertainties in the observations\n",
    "- this computes the Akritas–Thiel–Sen (ATS) Kendall $\\tau$ correlation coefficient\n",
    "- also computes the associated null hypothesis probability\n",
    "\n",
    "The code was taken from section 10.8.3, \"Bivariate and multivariate problems with censoring\", p304 of the book *Modern Statistical methods for astronomy with R applications* by Feigelson & Babu. It was the only place where I could find a recipe for computing the correlation coefficient and estimate the associated probability for x-y data with left-censoring. On the other hand, there are plenty of examples around dealing with right-censorship in survival studies.\n",
    "\n",
    "# reads data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "working dir"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "setwd('/Users/nemmen/Dropbox/Downloads/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>68</li>\n",
       "\t<li>8</li>\n",
       "</ol>\n"
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      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 68\n",
       "\\item 8\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 68\n",
       "2. 8\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 68  8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'Star'</li>\n",
       "\t<li>'Type'</li>\n",
       "\t<li>'Teff'</li>\n",
       "\t<li>'Ind_Be'</li>\n",
       "\t<li>'logN_Be'</li>\n",
       "\t<li>'sig_Be'</li>\n",
       "\t<li>'Ind_Li'</li>\n",
       "\t<li>'logN_Li'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Star'\n",
       "\\item 'Type'\n",
       "\\item 'Teff'\n",
       "\\item 'Ind\\_Be'\n",
       "\\item 'logN\\_Be'\n",
       "\\item 'sig\\_Be'\n",
       "\\item 'Ind\\_Li'\n",
       "\\item 'logN\\_Li'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Star'\n",
       "2. 'Type'\n",
       "3. 'Teff'\n",
       "4. 'Ind_Be'\n",
       "5. 'logN_Be'\n",
       "6. 'sig_Be'\n",
       "7. 'Ind_Li'\n",
       "8. 'logN_Li'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Star\"    \"Type\"    \"Teff\"    \"Ind_Be\"  \"logN_Be\" \"sig_Be\"  \"Ind_Li\" \n",
       "[8] \"logN_Li\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Read dataset on beryllium and lithium abundances in stars\n",
    "#abun <- read.table(\"http://astrostatistics.psu.edu/MSMA/datasets/censor_Be.dat\", header=T)\n",
    "abun <- read.table(\"censor_Be.dat\", header=T)\n",
    "dim(abun) ; names(abun) ; attach(abun)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this dataset, Type = 1 [2] indicates stars with [without] known planets. The censoring indicators are 1 [0] for detected [undetected] abundances. `cen_Be` is `TRUE` if upper limit (censored)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "cen_Be <- seq(FALSE, FALSE, length=68)\n",
    "cen_Be[Ind_Be==0] <- TRUE\n",
    "\n",
    "cen_Li <- seq(FALSE, FALSE, length=68) \n",
    "cen_Li[Ind_Li==0] <- TRUE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# univariate comparisons\n",
    "\n",
    "The [CRAN NADA package (Lee 2010)](https://cran.r-project.org/web/packages/NADA/index.html) implements methods from the volume by Helsel (2005) for censored environmental data. We apply NADA functions to the *two-sample, bivariate, doubly censored dataset* of photospheric beryllium and lithium abundance measurements in stars with and without host planets presented by Santos et al. (2002, C.4). \n",
    "\n",
    "We start with univariate comparisons of abundances in stars with and without planets using NADA’s cenboxplot function (Figure 10.2). In NADA, the censoring indicator is a vector of logicals where FALSE represents detections. The group indicator is an R factor vector created with the as.factor command. The cenboxplot is similar to the standard R boxplot (Section B.6) above a horizontal line showing the highest censored value; the thick bar shows the median, the box hinges show the 25% and 75% quartiles, the notch shows an approximate standard deviation of the median, and the dashed whiskers show a reasonable range of the data excepting outliers. Any structure below the horizontal line takes the distribution of censored points into account using a robust version of the Kaplan–Meier estimator (the regression on order statistics method; Helsel 2005, Chapter 6).\n",
    "\n",
    "In this dataset, the median values of all subsamples lie above the highest censored points, so they can be interpreted in the usual fashion. The presence of planets has no effect on beryllium abundances but may elevate lithium abundances. The significance of this effect is quantified using the cendiff function which is NADA’s frontend to R’s survdiff. Here we find any planetary effect on stellar lithium abundances is not statistically significant (P > 0.1) using the logrank and Peto–Peto two-sample tests. Santos et al. (2002)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Boxplot of abundances for stars with and without planets\n",
    "#install.packages('NADA') \n",
    "library(NADA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "remove two points with NaN entries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "logN_Li1 <- logN_Li[-c(1,23)]\n",
    "Ind_Li1 <- Ind_Li[-c(1,23)] ;\n",
    "logN_Be1 <- logN_Be[-c(1,23)]\n",
    "Ind_Be1 <- Ind_Be[-c(1,23)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "construct censoring indicator variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "Li_cen <- seq(FALSE, FALSE, length=66) \n",
    "Li_cen[which(Ind_Be1==0)]  <- TRUE\n",
    "Be_cen=seq(FALSE, FALSE, length=66)\n",
    "Be_cen[which(Ind_Li1==0)] <- TRUE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: survival\n",
      "\n",
      "Attaching package: ‘NADA’\n",
      "\n",
      "The following object is masked from ‘package:stats’:\n",
      "\n",
      "    cor\n",
      "\n",
      "Warning message in bxp(structure(list(stats = structure(c(-0.39, 0.312420297457846, :\n",
      "“some notches went outside hinges ('box'): maybe set notch=FALSE”"
     ]
    },
    {
     "data": {
      "text/plain": [
       "                N Observed Expected (O-E)^2/E (O-E)^2/V\n",
       "Type_factor1=1 37       22     19.5     0.312     0.684\n",
       "Type_factor1=2 29       14     16.5     0.370     0.684\n",
       "\n",
       " Chisq= 0.7  on 1 degrees of freedom, p= 0.408 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "                N Observed Expected (O-E)^2/E (O-E)^2/V\n",
       "Type_factor1=1 37     16.2     14.4     0.233     0.665\n",
       "Type_factor1=2 29     10.3     12.1     0.277     0.665\n",
       "\n",
       " Chisq= 0.7  on 1 degrees of freedom, p= 0.415 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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W9/KDYO6NAt3XeUZhmpanNw1M0ntsOG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LZyO91yjsHv6J7h+WDeemmgLnqdrrK68u\nofre0PnNyeVSxR33oou/jTq36IWyPAQQWCbgbcnZynqZx3W6/Z4yR/G5rX5v2lzZXfmQ4g8w\n+ynuYPyDUlTxh9nJykXKXorr9OksunmpPK973qb6A0Wrcr5G+MgNSvcC/gLXxR2KHZSb/aCi\nJexBmq36P1vRNhRZbe95CeUX4U6Fbl3n7ZQ9lZgvaFYh0mKq+jot5hTld8rjig9beEi5QvkP\nZXtlZNlIA45W/E/uw6MorQWq/I1d61YNbow/7IRvbkJHaXBzZ069CLAHqRet4U+b1Dd2bbjc\nWfB7gDsg3pvdrkzQyKsUT+8v7yYqRRd/+XiE4vNiwntXN7eur7erByhllSpvj/xZJDi7o1zV\n4s7zk4rbcmZVGzHkevtLefvcky3nyuyxO5TDKP7sEV5b/kwy6OIvdML8vTeZPUiDFu5xfu32\nIOVn5W9hnPBtljs87iS1K49q5HfbTVDAuPFaxiaKbx3vBXhKma+4o+dv8SgIIIAAAvEK+MPI\ne7Lq/ZNuz+lQ1fs1/n3KTcrGir+om6YUWbytmZ5lom53V3ZRNlB8dIXjD0MLFG+PvCfMH+yu\nVeYplNEJ3KWnPa2srfjL2e8oVSzbqtJ+jbj8tnHD3zYCtvL/mMsvGjct/7rz+RYl+LaccMSI\n/I4Ad178P95LuVET/7HNEy7XOO8p9N7PdyjeC00pUaDbDpKr6I6GXyCvVSYqflN/VPGb+jVK\npw6TJimk+E3x48pkZXPF/wzNil/c7vRdp5yr+Fs7CgIIIIBAXALe7nhb5b0r3+yyaj7Cwe/r\nn1B27fI5w5psrmbszFAowxXw55AblMmKPwtUteyWqzgdpBxGi7v7aHj4PNupg+TPh//WYj7d\nDvYe7V6L9wj6c3SrwyWf07iZyjuU/RQ6SEIos4QXVLs6+Bu4ryqHt5noTxr3jWy6sjpK+2r5\nJyvdvim67d5wOv6HcSfvo8qtCgUBBBBAIA6BSVk1vHfAJ993W/yNrcumjRv+1kRglto5WdlR\nGadU8UiR8DnGH5pvUyjtBdypcPH7Q6cvu91RKaM8rYX6S552xZ07t2UzJbzvtZuecUMU6NRB\n2l/L9nGe63Wow6s1/svK3sq7FR8nXmTxci9W/Gbo4uV74zhHeVBZqPiNxnuTVld8AtwExbux\n/SL08D2Vq5QDlMsUCgIIIIBA+QKPZVXwdqaX4m9rXeY1bvhbE4Gwx2Ws2vt65boKtjt0kHyU\nS9GfpyrItWyPi+vtz26dOsT+TOsvxHs9xE5PWXbhMZ+m0WkZnjZfXtSDe5VF+YFN7ruDFMrb\nwx1uyxFo10GqylWDdhLdhYo7R48oxys+lKHbbxo31LQfUU5Q3HE6R9lKcaeKggACCCBQrsAd\n2eJfoVsfeuQ9BN2UfbOJbulm4simOUL1cVzCuUyNR73/XUNPmaKs1uVT39jldLFOFjpIrp9f\nL1XrII1RnXd25VXybWkM4e9IAZ9K4c6wS76D0RjS/O99zQeXPvRu1cB120LZq/Ta1LwC7TpI\n/y4bdx58rs6RijsOzYrfvL+keLxX6CeVf1XmKkUUb0TWUv6s7KP0eoicv508WblNOV/xIYVT\nldMUCgIIIIBAuQL3a/HhQ8P3dN/frnf6AsvnHk1WXKr4IXMr1Tt08K5e1orR/1lfT/3fSvgQ\n2WlO3u5Xufi18riygRL2xFSpPTuosu7UulTxtduoeXF/86/rbjtIxdWu9yW5DR9T8u3qfS48\nY2gC4zRn79Z9UTmuy6W8StM9lD3npC6fM4jJvKvU9fz0AGbmja/n9aMBzKuXWUzJlju+lyfV\naFp/o+Zd2l43/uBDKU/AXxx4PXT6gFpeDUe35I9k7XLb/F5WleK9Aq7zHlWp8Cjr+d6snW7r\n75UPKC9TRpatNeD7yhLF016u+BDqqpUTVWHX35mmFFlS2B79XGC2m10k3ICW9aGs7q7/9gOa\nZ4qz+UHOyVZ+X0ih/LUa4fbks2tFGpbU9qjZBsbrwf+U3rvkjcw3lW6KO0fnZhMWtTJdx7As\nbwj7LTOzGfjbO0o8An4dHqWcrpwdT7WoCQIIFCTgL63Oy5bl92d/OHpWuUe5VPGVy7zXwI8P\nU7xtcyf+aMUfNKpWpqvC+2Vxh4/Sm8CsbPLtdLtWb08tfeqw1+tp1eSu0mtTnQqksPfI2n4/\n63SuUnXWSoVr2qqDNClrk/85uz2Xx0/xhRFcirpqkA//Cy8knzPVb5mQzWBevzPi+QMXmKE5\nfkp5auBzZoYIIFAFgUNUSR96EvZe+tvKrZW3KrsoPpQslF/rjj9ozgkDKnZ7r+r7yyy+T+lN\nIBya5s844UvU3uZQ3tShg+RO/9LyqlG5JafSQVog+asqp59ghVt1kB7L2vrqHtu8STZ9kR2M\nu7NlHtpjXUdO7sPbDs4Ghm+fRk7DYwQQQACB8gTO0KJ3Uk5QzlFuUtxhelCZqZypHKjsq9yh\nUOopEDpIbn3ocFRBwqc37JhVlM8h3a+x5zXpZd1PHv2UqXT2ooduV0EfotashA3LKzRyN6Xb\nf1RvlFxuadwU8vcsLcXfHh6u3K9MUxYrvZS1NPGPlbDn7JJensy0CCCAAAKFCXiv0BcKWxoL\nqqLAn1Rpd5pfo/gzTFWKL0s+NqtsvpNXlfqXVc8rtWB/UZJKcQeJC4WVvDZb7UFyR+O+rG7f\n0633rnQqPnl+cjZRkf/Y39Yyb82We7xu71G+qrxb8blU7vysqoTi++so7gz5m8ZvKHOVfRQX\nvyhn+g4FAQQQQAABBCopED6HVGkPUr4zF+pfSfyCK53aHhd/pnUHn1KiQKs9SD6p9Vjlh4o7\nGTcrPqTB54EsVfJlaz04UQmHuF2h+z6htqjivUWTlYuUvZTNlU9n0c1Lxbtg3Tnyceutyvka\n8blWIxmOAAIIIDBUAX9B1Wq7NNoF/7ee6FDqJeAOxgHKlorPT3tCib2Eztzjqmj4kjr2OsdQ\nv9Q6SDb1e9YxMeBSh+YC/6XB7iyFuJPhPTSXKjco/icO43y7QPGbURnFG9UjlNuUfJ063V+i\n6a9Q/EZaVpmiBbue48uqAMtFoEsBf4D1azWlwxnc9I9k7XLbXuUBFSn+wsd13qMi9e1UTW9j\n3J5BZlqnhTJ+BYFUtkdvy72O9luhhfE+mJ3V2Zcpp7QX+I5G+33iD+0nq+zY92XtcxsnVaQV\nSW2POn1T56sGfVTxIWv+8O7Gb51FNysUXzXIh9n5+PAyiq9oNz3LRN3urvjcpA2UdbP4heZO\n3HzF9fSb0bXKPIWCAAIIIIAAAmkIzMo1w3tm/I18zMWnA/iy5C75ujeG8HekwNc0YHXl+yNH\nJPL4QrXjdMWfV/1ZlVKwQKcOkqtzhvJL5TDFh9s52yhPKt6b5PxMuUCJpcxVRRwfEkhJQ+BU\nNeNNypHKfWk0iVYggMAIgdeMeDyIh88MYiZdzONlmmYY3/Q+rPk+0sXymWRFAR9Sd6+ylbLb\niqOifLSrauXXkMtvGzf8bSNwu8b5c2mqZbEa9qlUG1eFdnXTQXI7vLflC1VoEHVMUsCv0+MU\nn0N2kOI9mhQEEEhP4LEKN2lt1f2WIdT/RM3zpCHMtw6zdEfDHSTvQYq95OtIByn2tUX9khcI\n31Yk31AaWGmBMaq9O0cu3XbqG1PzFwEEEChGIJyjW8zSWEo3AqGjsYkmdmIuYS+Xr172p5gr\nSt0QqIMAHzbrsJZpIwIIIIDAsAWe0wJep3xT+VC2MB+K/iVlafZ4NDdXj+ZJPGeZQP5cHu+h\n8XkdsZawByl06mKtJ/VCoBYC7iBxWdVarGoaiQACCCAwZIFnNf8PKwsVX7RoPcVXSuWwYCGU\nUH6nZbpz6qNlYu4gra/6bam45Dt1jSH8RQCBwgXcQfqk4qvTDbI8pZnFfsWYQbaXeSGAAAII\nIBAE/l53fMjUnsopykyFD75CKLj4qrV3KJOUcAhbwVXoanFh75EnZg9SV2RMhMBwBTgHabi+\nzB0BBBBAoH4C3mvhw+x8XtJYxYfdUcoRCB2OfCeknJq0Xmq+bnSkWzsxBoHCBLwHqcqXVS0M\nigUhgAACCCDQg8CdmtZXn/MeJP8u377KrxRKsQLuIH1QCYex+aq8sZWwd8uXJfflySkIIFCy\ngDtIj5VcBxaPAAIIIIBAigJfUaN2VDZS3qzQQRJCwSW/R8Z7amLsIIU9SGFvV8FELA4BBEYK\nuINEQQABBBBAAIHBC7ygWX5g8LNljj0I3Kxp/aObPtTRHZFzlZhK/hLkdJBiWjPUpdYCnINU\n69VP4xFAAAEEEEhawOeBhR/wDXtqYmpwvk75vV0x1ZG6IFA7ATpItVvllWywv4VdlNX8mUq2\ngEojgAACCJQlEPbM7KIKxPa5J3SQfGEPX5acggACEQjE9kYRAQlViFDAvyNylHK6cnaE9aNK\nCCCAAALxCoQO0lqq4naRVTNcoMGXI/dlySkIIBCBAB2kCFYCVehKYIam+pTi39iiIIAAAggg\n0K1A6CB5+rDHptvnDnu6UJ98HYe9TOaPAAIdBOggdQBiNAIIIIAAAghUWuB21T4cnh06JDE0\naEtVwpcfd6GD1HDgLwJRCNBBimI1UAkEEEAAAQQQGJKAD9O+MZt3TB2kfF24QMOQVj6zRWA0\nAnSQRqPGcxBAAAEEEECgSgJhD83rVGlf8juGEjpIvgy5L0dOQQCBSAToIEWyIqgGAggggAAC\nCAxNIHSQxmkJ/vHeGEroIPky5L4cOQUBBCIRoIMUyYqgGggggAACCCAwNIHQQfICQsdkaAvr\nYsb+/OXLjrvk69YYwl8EEChVgA5SqfwsHAEEEEAAAQQKEPi9lvFktpwYOki+3LgvO+5CB6nh\nwF8EohGggxTNqqAiHQRO1fgrlS06TMdoBBBAAAEERgq8qAE3ZANj6CDl68AFGkauLR4jULIA\nHaSSVwCL70rg5ZrqOOVNykFdPYOJEEAAAQQQWFEg7KmZpMFrrDiq8Eehg+TLj88ufOksEAEE\n2grQQWrLw8hIBMaoHqtmdXFniYIAAggggECvAqGD5G3Kzr0+ecDThw6SLz/uy5BTEEAgIgE6\nSBGtDKqCAAIIIIAAAkMTCB0kLyB0UIa2sDYz9mXGfblxl3ydGkP4iwACpQvQQSp9FVABBBBA\nAAEEEChA4H4t4+FsOWV2kHyZcV9u3IUOUsOBvwhEJUAHKarVQWUQQAABBBBAYIgC4YIIZXaQ\n8sumgzTElc2sERitAOdzjFaO5yGAAAIIIIBA1QTcIXmnso0yXVmsFF1CB8mXHfflxykIIBCZ\nAB2kyFYI1UEAAQQQQACBoQmEPTa+8M/hQ1tK+xm/kI32Zcd9+XEKAghEJsAhdpGtEKqDAAII\nIIAAAkMTCB2koS2gixn7KnouMdSlURP+IoDACgJ0kFbg4AECCCCAAAIIJCzwqNr2h5LbF362\ngg5SySuCxSPQSoAOUisZhiOAAAIIIIBAigILImlULPWIhINqIBCPAB2keNYFNWkt4OO1F2Wj\n/avjFAQQQAABBEYjMF5P2m40TxzCc3YbwjyZJQIIDECAizQMAJFZDF3AvzJ+lLK7cvbQl8YC\nEEAAAQRSFdhFDQvnAJXVRm/TXIdwNbuy6sFyEUCghQAdpBYwDI5OYIZq5FAQQAABBBAYrUC+\nU/KgZuLOStFlbS3wFQp7kIqWZ3kIdClAB6lLKCZDAAEEEEAAgcoLhA7Sn9SSTUtqzbFa7ley\n5b9Ktw+VVA8WiwACLQToILWAYTACCLQVWE1jv9h2imqN9GE3FAQQSF8g7LUp8wpy+WW7w3Zx\n+uy0EIFqCdBBqtb6orYIlC2wNKuA3zs+X3ZlhrT80MYhzZ7ZIoBASQI+rG3rbNn5TkrR1fmd\nFuj3GV8oiw5S0fosD4EuBOggdYHEJAgg8JLAT3TvQ8p6Lw1J686v1ZxH02oSrUEAgUwg7D3y\nw1klqjytZd+lbK+EQ/5KrA6LRgCBkQJ0kEaK8BgBBNoJXKWRG7WbgHEIIIBApAL5zkiZHSTz\neA+WO0j5TpuHUxBAIAIBfgcpgpVAFRBAAAEEEEBg6AKhg3SflvTY0JfWfgHhEL8NNdnE9pMy\nFgEEihagg1S0OMsbrcCpeuKVyhajnQHPq5zAmqrxNGX/ytWcCiOAQIwCYW9N6JyUWcd8HULH\nrcz6sGwEEMgJ0EHKYXA3WgEfCnqc8ibloGhrScUGLXC0Zniicr7Ce5UQKAggMGoBX047XNY7\n3zkZ9Qz7fOLNev7ibB50kPrE5OkIDFqAFk7ksAAAQABJREFUDx2DFmV+wxDwL46vms2Y8+aG\nIRznPP1jii5rKGOX3eMPAgggMDqBfCckhg7Sc2rGbVlT8nUbXet4FgIIDFSADtJAOZkZAggg\ngAACCEQoEDohvry2L7MdQwkdNf8OW/gSMIZ6UQcEai9AB6n2LwEAEEAAAQQQSF4gdJB8eW1f\nZjuGEjpI66gyr42hQtQBAQQaAnSQeCUggAACCCCAQOoCMV2gIViHDpIfhw5cGMctAgiUKEAH\nqUR8Fo0AAggggAACQxeYqCX4ctou+U5JY0h5f2dr0c9mi6eDVN56YMkIrCRAB2klEgYggAAC\nCCCAQEIC+c5HTB2kF2R8U+acr2NC9DQFgWoK0EGq5nqj1ggggAACCCDQnUDofPiy2r68dkwl\ndNher0pxldaY1gx1qbUAHaRar34ajwACCCCAQPICoYPky2r78toxldBBWl2V2iGmilEXBOos\nQAepzmuftiOAAAIIIJC2gC+f7ctou4TOSONRHH/zdQoduThqRi0QqLEAHaQar/wKNd3HaS/K\n6vtMhepNVfsT8O+VhJK/H4ZxiwACCHQS8OWzfRltl3xnpDGk/L93qwrzs2rQQSp/fVADBJYJ\n0EHihVAFgSWq5FHK6crZVagwdRyIwEWay2zlDMXnDlAQQACBXgXynY4YO0gvqkE3ZI3K17XX\ndjI9AggMUIATAgeIyayGKjBDc3co9RG4U03lmPz6rG9aisAwBEKnw5fT9hcuMRZ33N6q+P3O\n5yLFdp6UqkRBoF4C7EGq1/qmtQgggAACCNRJIHSQfDltH64dYwl7tvyl9c4xVpA6IVA3ATpI\ndVvjtBcBBBBAAIF6CLjD4ctnu4ROSONRXH/zddstrqpRGwTqKUAHqZ7rnVYjgAACCCCQukA4\nZM3tzHdCYmv3H1ShR7NKhT1esdWR+iBQKwHOQarV6qaxCCCAAAKRCIxTPbZT/CF+A8VXM/N5\nd3MVymAE8p2NmDtIbu0s5R1Kvs4eTkEAgRIE6CCVgM4iEUAAAQSSFHivWuXLSj+mnNmmhR/S\nuK8p6zaZZqaGfUbxB2ZKfwKhs+HLaLsDGnNxB84dJL9+1laeVigIIIBArQWmqPW+1Of4WivQ\neAQQ6FVgNT3B7x179PpEph+KwI80V6+P21vMfayG/zybxtO1in/36ziljJLS9uhGAdr40jIg\ne1zmu7K6ur6+oh0FgaoJJLU94hykqr386lvfU9X0K5Ut6ktQu5avqRZPU/avXctpcKoCn1fD\n3p41zp2g8xR3hA5TPpc99vBVlVOUdyqU0Qn4ctk7ZE/13pnYS76OXKgh9rVF/RBAoBCBlL6x\nGwaYDwX1hwZ/s3bsMBbAPKMUmKpaeZ0/o/BlTvNVlNQ3ds2bWKmh7fYgba+W+AeP/Zp+QHmj\n0qz4Ms+zFU/3pDJBKbKksj3aXWg2dN5XJGAfy/pjVt//6mMePBWBsgSS2h7xoaOslxHL7UVg\njCb2N6ounDfXcKjDXx+H77KG4kOTKAhUWWBvVT68f31Y969r0RgfFnagskDxOUr7KpTeBcL5\nR35mfu9M73Mq7hmhnvm6F7d0loQAAi8J0EF6iYI7CCCAAAIIDE0g/B7PHVrCLzosxRcUODub\nhsOtOmC1GB06GY9q/B9aTBPb4HBhjomq2IaxVY76IFAnATpIdVrbtBUBBBBAoCwBX8rb5dbG\nTce/4cMyHaSOVE0nCB2k4Nh0osgGhj1Irlaof2RVpDoI1EOADlI91jOtRAABBBAoV8C/ceTS\n7Z4BH1rqsqhxw98eBHx4ri+X7ZLvdDSGxPvXnTmfM+VCx7jhwF8EShGgg1QKOwtFAAEEEKiZ\nwGVZe/fU7bgu2r5fNk3oWHXxFCbJBNy5COetVqmD5Ity/D5rA3uQMghuEChDgA5SGeosEwEE\nEEAgZYFt1LirldOVI5VJyqXKtYovP/1JpV3xZb/fk01QpUPE2rWpyHH5vS9V6iDZKNSXDlKR\nrxiWhcAIgXBFnRGDeYgAAggggAACoxTwttV7ipxQFurO/OzBl3T7J2V69tg3vlLjmxV3qI5S\nXLw34axl9/jTi0DoXNyvJz3cyxMjmNYd4g8or1I2VR5QKAggULAAHaSCwVkcAggggECyAiep\nZT6Uzles8+8Zec+RfxvEZXwW3/fhX/4dpHwH6Z16/GMllEW683eKbym9CYQOUhX3voU9SG6x\n20EHqbd1z9QIDESADtJAGJkJAggggAACq9wsAycU7xXaXnFnyZ2mkPV0/z4lXx7NPfij7h+i\ntPqtpNyk3B0h4ItgTMyG5TsbIyaL9uHvVLMlin//zx2kfKdZDykIIFCEAB2kIpRZRr8CL2gG\n/hbV38Q+0+/MeH5lBJbmapq/nxvMXQSiFlis2t2S5excTSfq/rO5x77rTtG/K79Sfq0sUCi9\nC4S9R35mFTtI3sbdruyo5M+l0kMKAggUJUAHqShpltOPgL9N8zH5uyv5Dxn9zJPnxi9wkaro\n8zGuVPxBk4JAKgJzmzTE58tMbTKcQb0JhE7Fi3paFQ+xc2vdsaODZAkKAiUJ0EEqCZ7F9iww\nQ89wKPUR8OWNd6hPc2kpAggMQCDsQfIFLp4cwPzKmIU7dscor1C2VtwWCgIIFChQx8t8u81b\nKfsquyh+A6IggAACCCCAQPUFQgepiofXBf183UN7wjhuEUCgAIGUOkj+1fGPKhcrb29it5mG\n/Ujxcd3+NuaXyg3Ko8ovlPCjfLpLQQABBBBAAIGKCWyq+vry2C5VPbzOdfd5a+HqhXSQLEJB\noGCBVA6x21Zu5ys+ZtfF5y7ki89j8Mmv4/MDs/u+Uow7R85/Ku5k+ZwXCgIIIIAAAmUIHKGF\nOi7Tsyx7MIo/6+o5Jym+ol43xVfdq2rJdybye2Gq1h53jnw1RLcnnFNVtTZQXwQqLZBCB8l7\njn6tTMjWhK8MlL86kC+veqYSfovCbzozlTnKBsp2in+xfJzyYWWh8imFggACCCCAQBkC4TBw\nL/vqPivgjtGGStgGdprd2p0miHh86Ez4S84bI65nN1VzB88dJJ8K4C9y3SYKAggg0LXACZrS\nV6txvqKspeTLbD3wOL+5/I2yqjKybKkBlythPjuMnGDIj6dky262h2vIi2b2CCBQYQF/6PX7\n1h4VbgNVX1ngRA0K26NpK48e6pAqb4986LzdfIha1csH1YDwGij6M0nV7ah/OQJsj8pxb7lU\n/6ia30TObTLFxGycx3+xyfj8oPX14A+Kp/3X/IgC7ld5g1QAD4tAAIEWAmyQWsBUfLD3IL0t\ni+8XWaq8PXpCUN6Gf6dIsCEty50it8U5ekjLYLYIDFIgqe1R1S/S4L1B22Zr14fRjSy75gb4\nHKR2xW+sZ2cT7NRuQsaVInCqlnqlskUpS2ehZQisqYVOU/YvY+EsE4ESBe7Vsr03xPF9SmeB\nrTVJuCrtrM6TRz/FHaqhD/l38aF2FAQQKFCg6h0kH5cbzqN6rInb0mzY07qd12T8yEG+up2L\n9yZR4hHwOj5OeZNyUDzVoiZDFvC3picq5ytVf69SEygIIDBEgXwnosoXaAhEPi3AR8i4hHOr\nGo/4iwACQxeo+oeOFyR0a6bU7Ftm73Hw7mmfdOqTVDuVv8wmCPPsND3jixFwR9h7C11Ch7jx\niL8pC4STxX0hlrEpN5S21ULA55huo7xe2Ut5o+KLBG2i+CJBlP4EQgdpkWaTwjlI1ggdvdfp\nvg9foiCAQEECVe8gmSnsSj9M9/1BKl+8V2l2NuDQ/Igm930p1Hdlw8M8m0zGIAQQQAABBLoS\n8If27yr3KT6S4W7FV1e7SvmN4sOoHlQWKN7ufEsJX9TpLqUHgbCXxVeqdScphRI6SO4cceh/\nCmuUNiBQoMCeWtZixXuKfLnvjZR88Td1C7N42mZlogbOVjyP55W/UIosVT4ptggnf7vqdeP8\nYxELZBlRCHhdh/XON+zNV4k/ONmIq9g19ylr6L5a8PVKeP32enu1nht+16/oNlRxe+SjDNzJ\ntLM7mamUrdWQ8Nr5WCqNoh3JCiS1PUrhcKVr9FL7rPJ15a8Un0f0TeVnir998YbmfcqFig+5\n+0/FHam5ijtC/mDxXiV0rI7V/dsVCgIIIIAAAr0K7K0nXKyETr2/wPNeoznKg4q/sHtO8WHD\nqyvrKBOUbZVJiof7yzzvZTpAuUyhtBfYXqPHZ5OkdASIP8/8WfHFJ96g/IdCQQABBHoS8LdG\n4ZuWcPushv1RuUl5vMn4MF24/Z6mKaNU8Ru7Ip3Yg1SkdjzLYg9S53WR1Dd2nZsb/RQ+DMqH\n0nmb8rByjLKm0m3ZUBN+XvGRDJ7HQ0r44K+7hZQqbo98QZewHd+hEKXiFvLLrG23FrdIloTA\nqASS2h69bFQEcT5pqqq1t3KZEq5e52/n/M3c65R2V6a7ROPfqhypUBBAAAEEEBiNwBF60lqK\nv/XfRzlLeUbptjymCU9WDlFeUDZWvG2jtBfw3hUX753zeV0pld9mjcnvJUupfbQFgSgFUjjE\nLg/rzpGzieKNk4/h9puKO0e+IpZ7t/5W74FcfKKsjxWnIIAAAggg0I+Az3l1cSenn2/8fUj4\nOYo7XLsrlPYCu2Wjf6fbJe0nrdzY0EHyeVY7K1dVrgVUGIEKCqTWQQqrYJ7ulHW4XKgDtwgg\ngAAC9RHw9nTXrLmXD6DZMzUPd5C2GsC8Up6Fv/j0USIuoTPReJTG3/w5Vd5TRgcpjfVKKyIX\nSOkQu8ipqR4CCCCAQMICPiRuUda+Vw6gnROyefgLP0prAZ/35U6SS4odpAfULp+L5hIOJWw8\n4i8CCAxNgA7S0GiZ8QAF8h88ejmef4BVYFYlCIRzCb3o/P0SqsIiEehK4O5sqkO7mrr1ROM1\n6uBsdH4PQutn1HdMvtOQqlXo+OXbWt81TssRKECADlIByCyibwEfU36Ucrpydt9zYwZVEbhI\nFZ2tnKH4UskUBGIX8EUZXA5XTlHG+kGPZS1Nf4EyKXveJT0+v26Th06DL4zx+0QbHzpIPtxy\nvUTbSLMQiEog1XOQRoPsY70dl+lZlj0YxR//roUv1drtxnGHUSyjbk+ZoQY7lPoI3Kmm8r9R\nn/WdQku/rUZ8RPEFgo5XPqCcr/icJH94v19ZqLyouKyq+AJCE5Rtlbco7lxtoLicpsz0HUpL\ngXCBhlktp6j+iNBB8uvF7f119ZtECxCIW4AO0vL1429m9s0eXr188Kjura5nbamE46I7zWSj\nThMwHgEEEEAgegHv6ZyseO+nr2i3ufLpLLp5qfh3jvxht902wh2rz730DO40Exivgf7Bd5fQ\niWg8SutvvvPnPWZ0kNJav7QmQgE6SMNZKY9otgf3MOspmtbfPFIQQAABBKot8ISqP1nxeUjH\nKZOUkcU/ft2s+Fw7f0H3dcWH2VHaC/iy12OySVLuID2mNs5VJiruIFEQQGDIAnSQlgP7sLpr\nsof3Lh/MPQQQQAABBHoSeEFTe5viTFT8W0a7KD50bt0sPsxugTJfmaPMVq5V5imU7gTynYX8\nXpbunl2tqdwBnKjk21ytFlBbBCokQAdp+cpyp4iO0XIP7iGAAAII9C8wV7NwOIdSCAMuobPw\nkOb7wIDnHdvs3EE6WNlU2Vjxj95TEEBgSAJcxW5IsMwWAQQQQAABBIYqEDpIKR9eFwDzbQzt\nDuO4RQCBAQukvgdpvLw2UXzr+LCHpxQf0vC44hNlKQgggAACCCBQLQFf7nqrrMr5zkO1WtF9\nbW/QpD4s0xf3cAfpJwoFAQSGJJBiB8lvHB9XJiu+gpDfTJoVd5ZuVq5TzlWuUCjxCpyqqr1J\nOVK5L95qUrMBCqypeX1G8Yefnw1wvswKAQSqL+DLXYftex06SE+rvXcp2ynsQRICBQEEuhPw\nJbqvV/wNy2jiKwf5tyvKKL6KnevsvVyUlQXckffVnWx07MqjGZKowFS1y+v8GYXDgZuvZF8m\n2kZ7NB/NUAR6FqjK9uh4tcyvfWfDnltZzSd8L2uvr5RLQSA2gaS2R6nsQdpbr5KLlXHZq8W/\nRXGj4isDPagsVJ5T/G2Tf6PIP+QafphvUjZ8T91epRygXKZQ4hEYo6qEbwpTec3GoxtvTfwD\nmi5rKGMVDom1BgUBBCwQ9qLM1X1fBrsOxXvKjlA2UiYqcxUKAggMQSCFD5s7yeVCxZ0jf6vi\nb5V8tSB/69xN8TdPH1FOUNxxOkfxcc3uVFEQQAABBBBAID6B0EFyp6EuJd9WH2I4ty4Np50I\nFC2QwmEr/jZlLeXPyj7KWUq3nSNNuuybp5N1e4ji85J8+cypCgUBBBBAAAEE4hPwdnrTrFr5\nTkN8NR1sjW7S7Pw5xSV0EBuP+IsAAgMVSKGDtFcm4k7OrX3oeC+U9x65+Ef9KAgggAACCCAQ\nn0C+c1CnDpJPFbgtWx15g/jWEDVCoOICVe8g+RDBXbN1cPkA1sXMbB7h0qEDmCWzQAABBBBA\nAIEBCmyWm9eduft1uHtH1kifR01BAIEhCVS9g+RdzYsym1cOwCi84cwbwLyYBQIIIIAAAggM\nV2DJcGcf3dxDe8OFi6KrIBVCIAWBFC7ScLdWxC7KocrP+lgp4/Xcg7Pnz+pjPjwVAQQQQAAB\nBIoROF2L8aFnRZbNtTBf4Mm/pRjOCSpq+XsUtSCWg0CdBVLoIPmiDO4gHa7cr0xTfJnvXoov\n8vBjZVL2pEt6eTLTIoAAAggggEBhAmEvihfoL0fLKr6Kblml6I5ZWe1kuQiUIpBCB+nbkvNl\nuv0jr77E9weU8xWfk/R7xZ2mhYp/TM7Fu6X9+yoTlG2VtyjuXG2guJymzPQdCgIIIIAAAghE\nJ/BT1eg65dUl1SycA/Wklj+/hDq4c/TNEpbLIhFAoGIC66u+VynuBLWKd8E/32a8n3eeMkYp\nukzRAr18H+ZHWVnA6ySsu0+sPJohiQp8Vu0K/8/+oVjKygJJ/XL5ys1jSAkCbI/ao/u9KLwv\nfab9pIxFoFYCSW2Pqn6RhvDKe0J3JitHKrOVZmWcBnrljSxLNeBK5UDlYCW/614PKREIeJ0c\npfhY87MjqA9VKEbgIi3G/89nKL0eNltMDVkKAgjUTcDvRX5P8nvTxXVrPO1FoC4CKRxiF9aV\ndzlPzzJRt7srPjfJh86tm8Xf+ixQvEt8juI3uGuVeQolboEZqp5DqY/AnWrqDvVpLi1FAIGK\nCHysIvWkmgggMEqBlDpIeYK5euDwgVoIFAQQQAABBBBAAAEEEOhOIJVD7LprLVMhgAACCCCA\nAAIIIIAAAm0E6CC1wWEUAggggAACCCCAAAII1EuADlK91jetRQABBBBAAAEEEEAAgTYCdJDa\n4DAKAQQQQAABBBBAAAEE6iVAB6le65vWIoAAAggggAACCCCAQBsBOkhtcBgVlcCpqo1/r2qL\nqGpFZYYpsKZmPk3Zf5gLYd4IIIBAjwJ+T/J7k9+jKAgggAACQxLgl8vbw/py9P5BX/+O1bHt\nJ2VsQgJT1Rav82cUvsxpvmKT+uXy5k1kaMECbI/ag/u9yO9Jfm/yexQFAQQaAkltj/jQwcu6\nCgJjVMlVs4qm+ttdVVgPRddx7WyBa+h2bNELZ3kIIIBAEwG/F/k9ySW8RzUe8RcBBJIRoIOU\nzKqkIQgggAACCCCAAAIIINCvAB2kfgV5PgIIIIAAAggggAACCCQjQAcpmVVJQxBAAAEEEEAA\nAQQQQKBfATpI/QryfAQQQAABBBBAAAEEEEhGgA5SMquShiCAAAIIIIAAAggggEC/AnSQ+hXk\n+QgggAACCCCAAAIIIJCMAB2kZFYlDUEAAQQQQAABBBBAAIF+Begg9SvI8xFAAAEEEEAAAQQQ\nQCAZATpIyazKpBvyglq3KGuhf8GcUg+Bpblm5u/nBnMXAQQQKFQg/160pNAlszAEEChM4OWF\nLYkFITB6AW+EjlJ2V84e/Wx4ZsUELlJ9j1SuVBZXrO5UFwEE0hTwe9EZypuVi9NsIq1CAAEE\n4hCYomq8qIyPozrUAgEEKiKwmurp9449KlJfqhm/ANuj+NcRNUQgRoGktkccYhfjS4w6IYAA\nAggggAACCCCAQCkCdJBKYWehCCCAAAIIIIAAAgggEKMAHaQY1wp1QgABBBBAAAEEEEAAgVIE\n6CCVws5CEUAAAQQQQAABBBBAIEYBOkgxrhXqhAACCCCAAAIIIIAAAqUI0EEqhZ2FIoAAAggg\ngAACCCCAQIwCdJBiXCvUqZnAqRro38PZotlIhiUpsKZaNU3ZP8nW0SgEEKiqgN+T/N7k9ygK\nAggggMCQBPjdifaw/kFj/3q5f+/l2PaTMjYhgalqi9f5Mwpf5jRfsUn97kTzJjK0YAG2R+3B\n/V7k9yS/N/k9ioIAAg2BpLZHfOjgZV0FgTGq5KpZRd1ZotRDYO2smWvodmw9mkwrEUAgcgG/\nF/k9ySW8RzUe8RcBBJIRoIOUzKqkIQgggAACCCCAAAIIINCvAN/G9yvI8xFAAAEEEOgsMF6T\nbKL41nlBeUqZrzyuPK9QEEAAAQQiEKCDFMFKoAoIIIAAAkkKvEGt+rgyWdlcCYcK6+4KxZ2l\nm5XrlHOVKxQKAggggEBJAhxiVxI8i0UAAQQQSFZgX7Xs+iwf1O1EpVXnSKNW8ZeVuyruTF2u\nXK3sqFAQQAABBEoQYA9SCegsEgEEEEAgWYG91bKLlXFZCxfr9kZljvKgslB5TnGHaXVlHWWC\nsq0ySfHwPZWrlAOUyxQKAggggECBAnSQCsRmUQgggAACSQvspNZdqLhz9IhyvDJD8WWhuykb\naqKPKCco7jido2yluFNFQQABBBAoSIBD7AqCZjEIIIAAAskLHKEWrqX8WdlHOUvptnOkSVd5\nTDlZOUTxeUkbK1MVCgIIIIBAgQLsQSoQu+aL2l/t/5ISDjvphSN/7P4/6IlH9/Lk3LS/yZ7r\nH52lIIAAAoMW2CuboTs5t/Yxc++F8t4jd7h272M+PBUBBBBAYBQCdJBGgcZTRiXwQT1rECcd\nb6T5OKMpPsb/88oDo3kyzylcIN+Rzd8vvCIsEIEuBLw99YUWXC5v3PT1d6ae7Q6SD7GjxCOQ\nfy9aEk+1qAkCCAxSgA7SIDWZVzuBkzTSx9GPZg+S57uZ4uPz/a2sT3oeTfEeJDpHo5Er5zkX\nabFHKlcqo13n5dScpdZRwIfELVJWU145AIAJ2TzmDWBezGJwAn4vOkN5s+KLcVAQQAABBIYk\nMEXzfVHxjwdSEEAAgW4F/GHc7x17dPsEphuqwA2au9fH9D6X4m3Bbdm8vtDnvHp9OtujXsWY\nHgEELJDU9oiLNPCiRgABBBBAYDACZ2WzOVy3pyhjRzFbX+ThAsWX/Ha5pHHDXwQQQAABBOol\nwDd29VrftBaBQQkk9Y3doFBKnI87RLco3ovkzFW+qrxb2V5x5yd/0Rnf9+W83Rk6UPmG4ivZ\nhed/WfeLLmyPihZneQikIcD2KI31GFUr2CBFtTqoDAKVEWCDFN+qWl9VukoJnZxmt/6h2Oc7\nTHOexo9Rii5sj4oWZ3kIpCGQ1PaIQ+zSeFHSCgQQQACBOASeUDUmK77AyGylWfHFavxhYmRZ\nqgG+KIn3Jh2scJU0IVAQQACBogW4il3R4iwPAQQQQCB1AV/RzhdqcCYq/i2jXZQNlHWzeM/S\nAmW+MkdxZ+paZZ5CQQABBBAoUYAOUon4LBoBBBBAIHmBuWqhM0OhIIAAAghUQIBD7Cqwkqgi\nAjUVWFPtnqbsX9P202wEEIhTwO9Jfm/yexQFAQQSFGAPUoIrlSYhkIjA0WrHicqziq/+5fMz\nKAgggECZAv5i+XxlDcVXHPyWQkEAgcQE2IOU2AqlOQgkJLB21hZ/EPHlkykIIIBA2QJ+L/J7\nkkt4j2o84i8CCCQjwB6kZFYlDUEAAQQQSETgCLXDcQkXe2g86v3vxnrKt5VmV81rNrdNmw1k\nGAIIIFAnATpIdVrbtBUBBBBAoAoCW6mS+2YVvbrPCj+j5/vHa7vdC+ur6+3Q5zJ5OgIIIFBp\nATpIlV59VB4BBBBAAIG2Ak9r7D+3nWLFkVP08B0rDuIRAgggUC8BOkj1Wt+0FgEEEEAgfgEf\nVndNVs17468uNUQAAQTSEqCDlNb6pDUIIIAAAtUXcKeIjlH11yMtQACBigpwFbuKrjiqjQAC\nCCCAAAIIIIAAAoMXYA/S4E2ZIwIIIIAAAiMFxmvAJopvnReUp5T5yuPK8woFAQQQQCACATpI\nEawEqoAAAgggkKTAG9SqjyuTlc2VVZVmxZ2lm5XrlHOVKxQKAggggEBJAhxiVxI8i0UAgY4C\nS3NT5O/nBnMXgSgFfInu67N8ULcTlVadI41axV9W7qq4M3W54kt776hQ4hPIvxctia961AgB\nBAYhwB6kQSgyDwQQGIbARZrpkcqVyuJhLIB5IjAEgb01z4uVcdm8/dq9UZmjPKgsVJ5T3GFa\nXVlHmaBsq0xSPHxP5SrlAOUyhRKPgNfnGcqbFa9nCgIIIIDAkAT8uxP+cT4fl05BAAEEuhVY\nTRP6vWOPbp/AdEMV2Elz9+8OeZ08rByjrKl0WzbUhJ9XfD6S5/GQUvR2ge2R0CkIINCzQFLb\nIw6x63n98wQEEEAAAQSaChyhoWspf1b2Uc5SnlG6LY9pwpOVQxSfl7SxMlWhIIAAAggUKEAH\nqUBsFoUAAgggkLTAXlnr3Mm5tY+WXqjnnpM9f/c+5sNTEUAAAQRGIUAHaRRoPAUBBBBAAIER\nAuFCCx7sCy30W2ZmM9iq3xnxfAQQQACB3gToIPXmxdQIIIAAAgg0E/AhcYuyEa9sNkGPw3zh\nBpd5jRv+IoAAAggUJUAHqShploMAAgggkLrA3VkDD+2zob4ww8HZPGb1OS+ejgACCCDQowAd\npB7BmBwBBBBAAIEWAr4og8vhyinKWD/osfgiDxcok7LnXdLj85kcAQQQQACBJAS4rGoSq5FG\nDFjAl0eepuw/4PmmNLukLquawIpxh+gWxZfoduYqX1XerWyvuPPj3zkKxff9O0juDB2ofEN5\nTAnP/7LuF13YHnUW93uS35t6uYR757kyBQLVFmB7VO31F2Xt2SBFuVqoVMkCvryxPyj6Msns\n7W6+MtggNXcpc+j6Wrh/5DV0cprd+odiw28dNRvvYecpY5SiC9uj9uJ+L/J7kteR36MoCCDQ\nEEhqe8SHDl7WCCAQq8DaWcXW0K2/macgUAWBJ1TJycqRymylWRmngf4wMbIs1YArFe9N8jlI\nSxRKXAJ+L/J7kkt4j2o84i8CCCQj4MuSUhBAAAEEEEBgcAK+ot30LBN1698y2kXZQFk3i/dA\nLFDmK3MUd6auVeYpFAQQQACBEgXoIJWIz6IRQAABBJIXmKsWOjMUCgIIIIBABQQ4xK4CK4kq\nIoAAAggggAACCCCAQDECdJCKcWYpCCCAAAIIIIAAAgggUAEBOkgVWElUEQEEEEAAAQQQQAAB\nBIoRoINUjDNLQQABBBBAAAEEEEAAgQoI1PUiDf5tiT2y9XOXbh+twLqiiggggAACCCCAAAII\nIDBkgbruQRovV//WhPO2IRszewQQQAABBBBAAAEEEKiIQF07SBVZPVQTgVoL+EczQ8nfD8O4\nRQABBIoWyL8X8UO+ReuzPAQKEkjhELuDZNVrR2/NnO8bdX9R7rHv+gf7bh8xjIcIIFCswEVa\n3JGK9/QuLnbRLA0BBBBoKuD3ojOUNysXN52CgQgggEAEAs+rDv5F8kFmWsHtmpLV34f+URBA\nAIFuBVbThH7vC+dUdvs8pkOglQDbo1YyDEcAgXYCSW2Pet3z0g6mrHEj9/6UVQ+WiwACCCCA\nAAIIIIAAAhUXSOEQu720Dn6g7JCti5t0+0WlXcfJh9jNyKb/um5nZvfDja9sR0EAAQQQQAAB\nBBBAAAEEKimwumr9L4pPnvThJjcqocOkuyuVdTQkHJJ32Epjix/AIQ3Fm7NEBFIQSOqQhhRW\nSAJtYHuUwEqkCQiUIJDU9iiFQ+z8GnhO+XtlP2We8npllvIPyqoKBQEEEEAAAQQQQAABBBDo\nKJBKByk09Fe6s6PyQ2Wc8jXlEmUzhYIAAggggAACCCCAAAIItBVIrYPkxj6hvE85RlmgvFW5\nRTlcoSCAAAIIIIAAAggggAACLQVS7CCFxn5Xd16nXKusq0xXzlM2UCgIIBC/gC+mMk3ZP/6q\nUkMEEKiRgN+T/N7k9ygKAgggUEmBMar1Pyv+cTdfmMHnKL0/u+/HXKRBCBQEIhSYqjr5f/QZ\nJeUvc/qhT+qk2H4geO7ABLhIQ3tKvxf5PcnvTX6PoiCAQEMgqe1RHT50LNF6+4Kyl3KP8mol\nXOJbdykIIBCpwNpZvdbQ7dhI60i1EECgXgJ+L/J7kkt4j2o84i8CCCQjUIcOUlhZ1+vOzsqZ\nYQC3CCCAAAIIIIAAAggggEBeIIUfis23p9P9hZrgb5SfKu/JJr43u+UGAQQQQAABBBBAAAEE\nai5Qtw5SWN0X6o5DQQABBBBAAAEEEEAAAQReEqjTIXYvNZo7CCCAAAIIIIAAAggggEAzATpI\ny1WO0N1fZvF9CgIIIIAAAggggAACCNRMoK6H2DVbzVtp4L7ZiKubTdDDsM017WWKL3nYTQlX\nxPFlQykIIIAAAggggAACCCBQkgAdpOHAP6jZ/qPiy4F2U7bVRCcoL3QzMdMggAACCCCAAAII\nIIDAcAToIC13na6712QP+72ynTs6/7V81h3v7aEp3EGiIIAAAggggAACCCCAQIkCdJCW47tT\n1G/HaPncuIcAAv0KLM3NIH8/N5i7CCCAQKEC+feiJYUumYUhgEBhAlykoTBqFoQAAj0KXKTp\nZytnKIt7fC6TI4AAAsMQ8HuR35P83nTxMBbAPBFAoHwB9iCVvw6oAQIINBe4U4N3aD6KoQgg\ngEBpAh8rbcksGAEEChFIvYM0XoqbKL51fG7QU8p85XHleYWCAAIIIIAAAggggAACCCwTSLGD\n9Aa17OPKZMWX215VaVbcWbpZuU45V7lCoSCAAAIIIIAAAggggAACSQj4N4yuV/xbQqOJf/to\nR6WM4qvYuc7d/m5SGXVkmQggEJ+A3zP83uH3EAoCgxCYopn4NeWjLigIIIBAtwJJbY9S2YO0\nt9aeT5Ycl61Fn0R5ozJHeVBZqDyneG/S6so6ygRlW2WS4uF7KlcpByiXKRQEEEAAAQQQQAAB\nBBBAoHICO6nGTyv+xuth5RhlTaXbsqEm/Lzi85E8j4eUor85Yw+S0CkIINCzQFLf2PXcep4w\nDAH2IA1DlXkikL5AUtujlyWwvo5QG9ZS/qzso5ylPKN0Wx7ThCcrhyg+L2ljZapCQQABBBBA\nAAEEEEAAgZoJpNBB2itbZ+7k3NrH+rtQzz0ne/7ufcyHpyKAwGAEvCd4mrL/YGbHXBBAAIGB\nCPg9ye9NvRytMpAFMxMEEECgGwGfQxUOjdutmyd0mMaH5/kwO1/drsjCIXZFarOsqgh4T67/\nH71HOIUvc4bhntQhDcMAYp49C3CIXXsyvxf5PcnvTRxt0t6KsfUSSGp7VPUPHT4kblH2+nvl\nAF6HvnCDy7zGDX8RQKBEgbWzZa+h27El1oNFI4AAAkHA70V+T3IJ71GNR/xFAIFkBKreQfKK\nuDtbG4f2uVZ8YYaDs3nM6nNePB0BBBBAAAEEEEAAAQQqKJBCB8kXZXA5XDlFGc03zb7IwwXK\nJMXlksYNfxFAAAEEEEAAAQQQQKBOAil0kL6tFRYuznC87t+jfFV5t7K94s6Pf+coFN/37yC5\nM3Sg8g1lruIr4Lmcpsz0HQoCCCCAAAIIIIAAAgjUS8AXOah68Y/CTlYuUnxFu82VT2fRzUvF\nF3Nw58gnkbUq52vE51qNZDgCCCCAAAIDEvAPm2+n7KBsoPhw8TuVuQoFAQQQQKBEgRQ6SOZ7\nQpms+Dyk45RwqJzuvlS8MWpWlmrg1crXFR9mR0EAAQQQQGA0Au/Vk16rPKac2WYGH9K4rynr\nNplmpoZ9RpnVZByDEEAAAQQKEEilg2QqX9FuepaJuvVvGe2i+Js5b4QcX5ZzgTJfmaPMVq5V\nuGqdECgIIIAAAn0J+FxYH7p9h9Ksg+RzZH20w9uVVmWyRlyv+JDxLysUBBBAAIGCBVLqIOXp\n5uqBM0OhIIAAAgggEIPA51WJ0Dny0Qs/VLyn6AHFh4fvrByk+PxgX3ToNuWnCgUBBBBAoECB\nVDtIBRKyKAQQ6EJgP03zLqWXC8P4w2IovpiKP1B2W57ShF9VfPgtBYEYBHzRIHeQXB5U3BG6\nzg9GFL/uv6/8hfIDZUflfoUyOIEtNau/VcaNYpb597C/1vPD7yf2Oiuv++/1+iSmRwABBOok\nsIca68P/2l1Aok4etDU9AXdY/BovMtPSY1ypRX7PsKnfQyjlC/xIVfD6uL1JVaZm4zw+7EVq\nMtmyQdvq79OKpz1m2ZDi/kzJlju+uEUWviQfXWLbsrNJ4S1ngQgMTyCp7RF7kIb3QmHOCCCw\nXOBs3X2/kr/k/vKxze+N0eB1lMWKzx3spbhD9otensC0CAxZ4PXZ/H1+UqfXpq9o5/8Zd6p2\nU85SKIMT8KGNeymj2YPkWqyl+Hwyn8+8RBlN+Y2e9MhonshzEEBg+AJ0kIZvzBIQQGCVVT4h\nBIeCQF0FfMEgl1sbNx3/zsqmcAeJMliB8zQ7h4IAAgg0FcgfS9t0AgYigAACCCCAQN8C/o0j\nlw0bNx3/rpFNsajjlEyAAAIIIDBQATpIA+VkZggggAACCDQVuCwbuqduuzm0yxc2cQkdq8Yj\n/iKAAAIIDF2ADtLQiVkAAggggEDNBLZRe69WTleOVCYplyrXKqsrn1TalcM08j3ZBOFQu3bT\nMw4BBBBAAIHkBLiKXXKrlAYhUIhAUlcNKkRsuAsJV7FrdnU0X2hknuJxvmT9EUq++KT/vZX/\np4Tn36P7XsdFlilamJc/vsiFsiwEEKi8QFLbIy7SUPnXIw1AAAEEEIhE4CTV4zLFV6zz7xl5\nz1Ho4LjDETodvprjG5XpSijv1J0fhwe69blHf5fd5gZzFwEEEEBg2AJ0kIYtzPwRQAABBOoi\ncLMa6oTivUL+gVh3ltxpCllP9+9T8uXR3IM/6v4hSrMfks1Nxl0EEEAAgWEI0EEahirzRAAB\nBBBAoPEbXrcIwvHvGoUyUXeeDQ+yW3eK/l35lfJrxYfkURBAAAEEShCgg1QCOotEAAEEEKi1\nwNwmrb9fw6Y2Gc4gBBBAAIGCBbiKXcHgLA4BBBBAAAEEEEAAAQTiFaCDFO+6oWYIIIAAAggg\ngAACCCBQsAAdpILBWRwCCCCAAAIdBHwJ8F9mGXk58A5PZTQCCCCAQL8CnIPUryDPRwABBBBA\nYLACW2l2+2azvHqws2ZuCCCAAAKdBNiD1EmI8QgggAACCCCAAAIIIFAbAfYg1WZV01AEEEAA\ngYoI+Adkr8nqem9F6kw1EUAAgWQE6CAlsyppCAIIIIBAIgLuFNExSmRl0gwEEKieAIfYVW+d\nUWMEEEAAAQQQQAABBBAYkgB7kIYEy2wRQAABBBCIQGCC6vAzZWyXdVknm+7FLqdnMgQQQCA5\nATpIya1SGoQAAgggEKHAeNVpE8W3zgvKU8p85XHleWUY5WHN9OvKal3OfGtNd6zi+lEQQAAB\nBBAoTWAPLdnf1nW7ASutoiwYAQSiEvB7ht87/B5CiU/gDarSd5X7lKWK11WzLNbwWcq3lL9U\nyixsj8rUZ9kIVFcgqe0Re5DieiHSQWq/Pvx6XbX9JIxNTMAfJvkmu/VK5T2jtU2ZY/wbRicr\n7iB1U/zetmuWj+v2GuWjyq1KWYXXVnt5tkftfVIcy/ao/VpN6j2DDlL7lV3UWH976PJ044a/\nCCCAQE8Ci3qamomHKbC3Zn6xMi5biN/fb1TmKA8qC5XnFH/Zs7ric358ntC2yiTFw/dUrlIO\nUC5Tiixsj4rUZlkIpCeQxPaIb+PjeWHupqp0exJtPLUuribv1aIOU6YVt0iWFIHASarDD5Qf\nRVCXWKvgjdENsVauZvXaSe29WllLeUQ5XpmhPKN0UzbURB9RTlD8bazPH9pKcaeqyML2qL02\n26P2PqmOZXvUec2yPepsxBQIDFTAHxruHOgcmVkVBLzOve4pCFRB4CuqpA/DeULZsY8Kv0fP\n9Z4cz+uzfcyHpw5HgO3RcFxjnyvbo9jX0ADrx+8gDRCTWSGAAAII1Fpgr6z1J+u2n/OHLtTz\nz8nmtXt2yw0CCCCAQEECdJAKgmYxCCCAAAJJC4QLLbiRlw+gpTOzefgQOwoCCCCAQIECdJAK\nxGZRCCCAAALJCvhqi+Hk5FcOoJW+cIPLvMYNfxFAAAEEihKgg1SUNMtBAAEEEEhd4O6sgYf2\n2VD/kOzB2Tz8+0gUBBBAAIECBeggFYjNohBAAAEEkhY4K2vd4bo9RRnNlUl9BbwLFF/y2+WS\nxg1/EUAAAQSKEqCDVJQ0y0EAAQQQSF3g22pguDiDL/F9j/JV5d3K9oo7P/mf1/B9/w6SO0MH\nKt9Q5ir7KC6nKTN9h4IAAgggUJwAPxRbnDVLQgABBBBIW8CX5p6sXKT4inabK5/OopuXyvO6\n586Rf+uoVTlfIz7XaiTDEUAAAQSGJ8AepOHZMmcEEEAAgfoJ+DeQJitHKrOVZmWcBjbrHC3V\n8CsV703yOUhLFAoCCCCAQMEC7EEqGJzFIYAAAggkL+Ar2k3PMlG3/i2jXZQNlHWz+EdgFyjz\nlTmKO1PXKvMUCgIIIIBAiQJ0kErEZ9E9CfjyuT58hVIvAa9zr3sKAlUVmKuKOzMUShoCbI/S\nWI+9toLtUa9iTI8AAkMX8OEo4XdBhr4wFhCNgNd5s0ORoqkgFUGgD4HV9dy1s/QxG55asADb\no4LBI1kc26NIVgTVQAABBBBAAIF0Bc5Q03yoneOr2VEQQAABBCIQ4CINEawEqoAAAggggAAC\nCCCAAAJxCNBBimM9UAsEEEAAAQQQQAABBBCIQIAOUgQrgSoggAACCCCAAAIIIIBAHAJ0kOJY\nD9QCAQQQQAABBBBAAAEEIhCggxTBSqAKCCCAAAIIIIAAAgggEIcAHaQ41gO1QAABBBBAAAEE\nEEAAgQgE6CBFsBKoAgIIIIAAAggggAACCMQhsGoc1aAWBQkcpOVs22ZZ/i2O55UFyh+Uy7PH\nulmprKEhn8qGXq/bS1aaggEIIIAAAu0Exmnk2GwCv+/WqbA9qtPapq0IIIBAxAI/Vt3CjxJ2\nc/uEpv83ZasmbdowN6+vNxmf0qBD1JjjU2oQbUEAAQRKFmB7NLoVwPZodG48C4GeBDjErieu\n2k38CrV4qnKp8sratX6VVV6uNv9KOVfZtIbtp8kIIIBALAJsj9gexfJapB41EKCDVIOV3KKJ\nb9Dw9ZrEHaFtFHeMFioumyn+ts8dhjoVH/qyT50aTFsRQACBEgTYHnVGZ3vU2YgpEBiYQN0+\n8A4MLoEZPa02PNWiHY9q+O+VXyrXKBspeyo7K79VKAgggAACCAxKgO3RoCSZDwIIDESAPUgD\nYUx2Ju4kXZxr3R65+9xFAAEEEECgKAG2R0VJsxwEEKjdIVOs8t4FfqanHJM9zYdB9Frerid4\n79N2WXyYwD1ZfH7PL5RmZX8N9OFt3pt1qrK28n7FnbQ3Kt779TvlJ8p/K52Kr5j0JuX1yqbK\nHcpNyvnKLcrIcpoGrJ4buJfuh4tRfFP378uNc90+rLxF8QUtxiie/+3KzxXvhaMggAACCPQn\nwPao4cf2qL/XEc9GAAEEVhDIXzXotSuMaf3g/RoVrnjnjkEona5i58PyzlPCc1vd+gII7mCM\nLCdrgJ9zl+Lzom7IHjebz+ka545Xs7KxBroT1ex5Hva88lll5N7U59o8xxunUHbRHV/tr9X8\nl2jcVxRfzpeCAAIIINAQYHu08naD7RH/HQhEIsA5SJGsiIir8ZZc3W7N3W93dzWNdIdmgrJU\nuUDxnpSHFXes3KnwHhfvoTlEuVH5ktKs+EISVynbKN4T82vlacX12k9xx+gTym3KmUq+uJN2\ns+JOksuvlIuUB5QdlUOV7ZUvK57/FCWU/6M7ayj/lA3wbz39NLv/x+zWHTcPe4XiTtIZivdK\n+ffF9lG8F+w1yrGKN3xhXrpLQQABBBDoUYDtUQOM7VGPLxwmRwABBNoJ9PqN3bs0M+8B8d4R\n71HZUgnFHR0Pd8KhZ2HcEblxfx8Gjrj9Cz0Oe2nuHzHOD09Wwvx9+zEPHFHyy3HHZGT5vxoQ\n5vHxkSP1eLziQ+w8jTty/0vJF3eQwvO/lR+R3T8qN/7gJuM30rD52TTuVL2syTQMQgABBOoo\nwPZoxbXO9mhFDx4hgAAChQnkN0hHa6l/NSLe6+G9Kp9RvKcmdA58e5KSL+06SP7dJD/HHZ92\nnYKfZNN52vz5Pnq4QgfpZx7QooRleR5r5qZ5ve6Hzt3/zw0fedcbpYcUP3/kuUKdOkj/mj1v\nsW49n2bFe7e81+pfFHeYKAgggAACjZ+O8Puuw/ao8Ypge8R/BgIIIFCCQL6DFDZMnW69Z+X7\nyshzaNp1kNw0j5/oO23Kf2hcWL4PpcuX/B6kw/IjRtz3eVFhHq/KjfPhbGH4X+aGN7v7rdy0\n+fOhOnWQvFEPy7DRyDY0WxbDEEAAAQRW7CCF99FOt2yPGtscb7NGFrZHI0V4jEAfAi/v47k8\nNW2Bx9Q8n3PkjsbIPSvdtNzPd/LFe1B8cQgfXudOyzuUUHzlt1blD61GaLjPRwplbLij221z\n932O0L65xyPveqMbyta6c2N40OH2Fxq/QFlLcSfuYOUK5b8Vn3M1W6EggAACCPQnwPaosx/b\no85GTIFA1wJ0kLqmSm7CD6lFPi8mX/zt3Z8Ud0gW5keM8r4vhDBF8eFuk5T1ldGUB9s8Kd+5\nWTU33Ta5+xfk7ne66+d120Gy1VsUHyr4amU1ZZ8sX9GtfX+ofEehsyQECgIIINBEgO1RExQN\nYnvU3IWhCAxdgA7S0ImjXcDVqtldQ6qd9wZNV3w+08jypAbcpPjbLv8+0l8rncoLnSZoMn6j\nbJif+0iT8a0GeW9QL+V3mtgdwA8q71d2VkJHbTPd90Uqpip/q5ypUBBAAAEEVhRge7SiR3jE\n9ihIcItAwQJ0kAoGr8nifG5R6Bw9oPvfVa5TblHuV0LxnpVhlfs0460UHwL3mmEtJJuvO2Cn\nZdlYt29T3q7sp2ygeM/St5UHlXYXnNBoCgIIIIDAAAXYHrE9GuDLiVnVRaDdFcbqYkA7Byvg\nDsGHs1nerdtdlROUnyr5zpEeLruQg29dxjRuBvbXy3ZZT9li2b3h/cn/Hz2sxUxXfE7SJsoZ\nSijvDHe4RQABBBAYugDbI7ZHQ3+RsYA0BfIf7NJsIa0qWuDNWmA4xOwc3W91eNtYjdszV7lB\n783Mn/PjQ9/albM0cp5yrbJNbkKfkxVKaFN47P8dn3vkPWS/VUaO16BVFin/qCz0A5XXNW74\niwACCCBQgADbo+XIbI+WW3APgY4CdJA6EjFBjwL584W896hZ8d4id542zI30YWiDLN/TzHxI\nm8s/K1suu7fyH9fxCMUXWVhX+b0SynO6EzpJI48F98Uhlig+fG8X5UClWVlTA325cJdLGzf8\nRQABBBAoQIDt0YrIbI9W9OARAi0F6CC1pGHEKAVm6Xlho+RDyg5Xwm8L+fXmzsQPlIOUfPGl\nuAdZfO7RsdkMvVG4XvGepHHZsM106wsn/FwJe69O1P3QIdLdZeWJ7PY9uvWhg27Txtmw72S3\nvvmK8le5x77rPUYXKuH/7AIPpCCAAAIIFCLA9mg5M9uj5RbcQwABBFYQ+LEeuQPgvHaFMb0/\n8N6fMK+vj3j68blxnuZ55TfKk7nh1+j+3+Uef1D38+VkPQjzn5AfMeL+F3PTudMzsnxBAxYr\nYV6+Pzf3OAz/jIY1KzM0MEwTbo/KTXjaiPFP6/FdyuO54d4TdbRCQQABBBBoCLA9amyb5ooj\nbFvCLdsj/ksQQACBAgWK2iD5fJy/UR5Swht+uP2jhn1U8TQ+rM57ejzuV0q+DKqD5HnupriD\nlu8ohfpcqeEj9/xo0EvFh9b9RHlGCc/50ktjG3uHDtNjn/MUxodbP8cdwd0VCgIIIIDAcgG2\nRytvM9geLX99cA+BUgWanVheaoVYeFIC7gBtqWyleM/KbUo4ZE13Cy+uj/ecuT7uvM1RHlG6\nKWM00TbKfMXPXarki/+XfNU678XyIXj3KHcqPk+JggACCCBQrgDbI7ZH5b4CWToCCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIFwGBz8AAAAZSURBVIAAAggggAACCCCAAAIIIIBAQgL/A64JX5QDI0BZAAAAAElFTkSu\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Type_factor <- as.factor(Type)\n",
    "par(mfrow=c(1,2))\n",
    "cenboxplot(logN_Be, cen_Be, Type_factor, log=FALSE, ylab='log N(Be)',\n",
    "   names=c('Planets','No planets'), boxwex=0.5, notch=TRUE, varwidth=TRUE,\n",
    "   cex.axis=1.5, cex.lab=1.5, lwd=2)\n",
    "cenboxplot(logN_Li, cen_Li, Type_factor, log=FALSE, ylab='log N(Li)',\n",
    "names=c('Planets','No planets'), boxwex=0.5, notch=TRUE, varwidth=TRUE,\n",
    "   cex.axis=1.5, cex.lab=1.5, lwd=2)\n",
    "par(mfrow=c(1,1))\n",
    "\n",
    "# Test significance of possible lithium abundance effect\n",
    "logN_Li1 <- logN_Li[-c(1,23)] ; cen_Li1 <- cen_Li[-c(1,23)]\n",
    "Type_factor1 <- Type_factor[-c(1,23)] # remove NaN values\n",
    "cendiff(logN_Li1, cen_Li1, Type_factor1, rho=0)\n",
    "cendiff(logN_Li1, cen_Li1, Type_factor1,rho=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `cenken` function provides the Akritas–Thiel–Sen (ATS) Kendall $\\tau$ correlation coefficient and linear regression estimator which we apply to the stellar beryllium–lithium data plotted above. The R code below starts with new definitions for the data and censoring vectors required by cenken. In this function, “NaN” entries are not automatically eliminated. The output gives Kendall’s $\\tau = 0.50$ with associated probability $P \\ll 10^{-4}$ that no correlation is present. The output ATS slope estimate is $b = 0.34$ (confidence intervals are not provided) and the line is superposed on the scatterplot in Figure 10.3. The NADA package also gives R’s standard univariate Kaplan–Meier estimator using cenfit and univariate two-sample tests using cendiff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bivariate correlation and regression using Akritas-Thiel-Sen procedure\n",
    "cenken_out <- cenken(logN_Be1, Be_cen, logN_Li1, Li_cen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$slope\n",
       "[1] 0.3410087\n",
       "\n",
       "$intercept\n",
       "[1] 0.3192765\n",
       "\n",
       "$tau\n",
       "[1] 0.4974359\n",
       "\n",
       "$p\n",
       "[1] 2.41662e-09\n",
       "\n",
       "attr(,\"class\")\n",
       "[1] \"cenken\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cenken_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# bivariate scatterplot \n",
    "\n",
    "Comparing lithium and beryllium abundances modeled on plots shown by Santos et al. (2002). A long series of commands is needed due to the variety of symbols used for different subsamples defined by the which function. Here the arrows function plots symbols appropriate for upper limits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reproduce Santos et al. (2002) plot of stellar beryllium vs. lithium abundance\n",
    "ind_det1 <- which(Ind_Li==1 & Ind_Be==1 & Type==1) # filled circles\n",
    "ind_det2 <- which(Ind_Li==1 & Ind_Be==1 & Type==2) # open circles\n",
    "ind_left1 <- which(Ind_Li==0 & Ind_Be==1 & Type==1)\n",
    "ind_left2 <- which(Ind_Li==0 & Ind_Be==1 & Type==2)\n",
    "ind_down1 <- which(Ind_Li==1 & Ind_Be==0 & Type==1)\n",
    "ind_down2 <- which(Ind_Li==1 & Ind_Be==0 & Type==2)\n",
    "ind_both1 <- which(Ind_Li==0 & Ind_Be==0 & Type==1)\n",
    "ind_both2 <- which(Ind_Li==0 & Ind_Be==0 & Type==2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xtED+giXaoAKfoLuF2wKOQpA+X1k008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\nCiiggAIKKKCAAgoooMA9Bf4fOv0XFrmRFMoAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(logN_Li[ind_det1], logN_Be[ind_det1], xlim=c(-0.6,3.5), ylim=c(-0.2,1.5),\n",
    "   main=\"\", xlab=\"log N(Li)\",\n",
    "   ylab=\"log N(Be)\", pch=16, lwd=2) # plot detections\n",
    "points(logN_Li[ind_det2], logN_Be[ind_det2], pch=1)\n",
    "arrows(logN_Li[ind_left1], logN_Be[ind_left1], logN_Li[ind_left1]-0.2,\n",
    "   logN_Be[ind_left1],length=0.1) # plot left arrows\n",
    "arrows(logN_Li[ind_left2], logN_Be[ind_left2], logN_Li[ind_left2]-0.2,\n",
    "   logN_Be[ind_left2],length=0.1)\n",
    "points(logN_Li[ind_left1], logN_Be[ind_left1], pch=16)\n",
    "points(logN_Li[ind_left2], logN_Be[ind_left2], pch=1)\n",
    "arrows(logN_Li[ind_down1], logN_Be[ind_down1], logN_Li[ind_down1],\n",
    "   logN_Be[ind_down1]-0.1, length=0.1)\n",
    "arrows(logN_Li[ind_down2], logN_Be[ind_down2], logN_Li[ind_down2],\n",
    "   logN_Be[ind_down2]-0.1, length=0.1)\n",
    "points(logN_Li[ind_down1], logN_Be[ind_down1], pch=16)\n",
    "points(logN_Li[ind_down2], logN_Be[ind_down2], pch=1)\n",
    "\n",
    "arrows(logN_Li[ind_both1], logN_Be[ind_both1],\n",
    "   logN_Li[ind_both1]-0.2, logN_Be[ind_both1], length=0.1) # plot double arrows\n",
    "arrows(logN_Li[ind_both1], logN_Be[ind_both1], logN_Li[ind_both1],\n",
    "          logN_Be[ind_both1]-0.1,length=0.1)\n",
    "arrows(logN_Li[ind_both2], logN_Be[ind_both2], logN_Li[ind_both2]-0.2,\n",
    "   logN_Be[ind_both2],length=0.1)\n",
    "arrows(logN_Li[ind_both2], logN_Be[ind_both2], logN_Li[ind_both2],\n",
    "   logN_Be[ind_both2]-0.1,length=0.1)\n",
    "points(logN_Li[ind_both1], logN_Be[ind_both1], pch=16)\n",
    "points(logN_Li[ind_both2], logN_Be[ind_both2], pch=1)\n",
    "\n",
    "# line \n",
    "abline(a=cenken_out$intercept, b=cenken_out$slope, lwd=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.3.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}