1_chemometrics_intro.ipynb

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    "# Chemometrics\n",
    "<br>\n",
    "**Julien Wist / 2017 / Universidad del Valle**\n",
    "<br>\n",
    "**Andrés Bernal / 2017 / ???**\n",
    "\n",
    "An up-to-date version of this notebook can be found here: https://github.com/jwist/chemometrics/"
   ]
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   "source": [
    "options(repr.plot.width=3, repr.plot.height=3)"
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   "source": [
    "## Aims\n",
    "\n",
    " - reproducibility in science\n",
    " - available tools for chemometrics\n",
    " - a first **modern** publication \n",
    " "
   ]
  },
  {
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   "source": [
    "## reproducible science"
   ]
  },
  {
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   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/problem1.png\" width=\"600\">\n",
    "</center>"
   ]
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  {
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   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/problem2.png\" width=\"600\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/Problem3.png\" width=\"600\">\n",
    "</center>"
   ]
  },
  {
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   },
   "source": [
    "### a better publication for a better science"
   ]
  },
  {
   "cell_type": "markdown",
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    }
   },
   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/modernPublis1.png\" width=\"600\">\n",
    "</center>"
   ]
  },
  {
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   "source": [
    "Although internet contributed to accelerate the pace at which information is shared, it had very little effect on the way information is formatted. Publications illustrate well this phenomena. Today, data produced in the lab are mostly digital. Analysis of data, digital or not, is performed using computers. The writing and sharing of the results is done digitally. Despite this, the end product, the publication is an exact copy of a plain printed paper with close to no enhanced features. A paper from 1905 is exactly the same product as a paper from 2017, even if its production and distribution differ. Publications were introduced to allow researchers to claim authorship for their contribution, thus allowing to accelerate the speed at which information was shared. Today, publication may well be deserving the counter objective, to slow the flux of information. In some research area this fragmentation of the knowledge and data is so detrimental that it may invalidate years of research that cost billions of dollars. Here we present cheminfo.org, a platform to store and share data and code libraries to facilitate solving problems related to chemistry. In our opinion this represent a step toward a more efficient way to share contributions within the academic community."
   ]
  },
  {
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   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/modernPublis2.png\" width=\"600\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "A webpate is typically a more appropriate and \"modern\" way to share information in that not only the content is transfered but the code for its proper visualization. Usually, the raw data and the code used to manipulate them are not transfered since this latter is executed on the server. Although it is technically possible to transfer the tool to the end user, this would require instalation and configuration on the client side. "
   ]
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  {
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   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/modernPublis3.png\" width=\"600\">\n",
    "</center>"
   ]
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  {
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   "source": [
    "A better way to share information in the context of collaborative science require the author to share all the necessary information for someone else first to check what has been done and second to reproduce and extend the research. Example of such exists, but there is still room for improvement. An example is the very same tool used for this presentation/publication, jupyter."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/3layers.png\" width=\"800\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "The tree elements of collaborative science"
   ]
  },
  {
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   "source": [
    "## Useful tools for cheminformatics\n",
    "\n",
    "Raw data must be analyzed and therfore libraries of function must be developped. Today, two very powerfull option exists.\n",
    "\n",
    "- python + pandas (numerical simulation + statistics)\n",
    "- **R (statistics)**\n",
    " \n",
    "Both are high end languages and thus allow to write relatively easily pieces of code. Both are scripting languages meaning that they don't require compilation. This makes the coding and debugging much simpler tasks."
   ]
  },
  {
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   "source": [
    "See the following link to see the most common programming languages on Github: <a href=\"http://githut.info/\" >http://githut.info/</a>.\n"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### what is R?\n",
    "\n",
    "- R is a powerful and free to use tool to perform statistics\n",
    "- R is not a software for numerical vectorial algebra\n",
    "- R is free\n",
    "- R has a large community that supports its development and a lot of tutorials available\n",
    "\n",
    "Alternatively, common commercial software for statistics are:\n",
    " - Stata\n",
    " - SPSS\n",
    " - SAS\n"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### what is python?\n",
    "\n",
    " - python is free numeric simulation program\n",
    " - unlike R python is suitable for vectorial alegbra\n",
    " - python is open \n",
    " - python is supported by a very large community. New methods are rapidely implemented and shared.\n",
    " \n",
    " Alternatives to python are:\n",
    " \n",
    " - Octave\n",
    " - scilab\n",
    " - matlab\n",
    " - to some extend: mathematica"
   ]
  },
  {
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   "source": [
    "### How to get R and python?\n",
    "\n",
    "It can be readily installed for all platforms (https://www.continuum.io/downloads)\n",
    "\n",
    "Alternatively you can download R directly (https://www.r-project.org/)\n",
    "\n"
   ]
  },
  {
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   "source": [
    "\n",
    "### front-ends\n",
    "\n",
    "Because writing scritps is not always an easy task, program refered to as IDE exists to simplify writting. These programs offer an environment to suggest/auto-complete or provide easy access to help, etc.\n",
    "\n",
    "Front-ends for R are:\n",
    "\n",
    " - Desktop (multi platform)\n",
    "https://www.rstudio.com/\n",
    "\n",
    " - Online (no installation required)\n",
    "https://www.getdatajoy.com/\n",
    "\n",
    "Front-ends for python:\n",
    "\n",
    " - pycharm\n",
    " \n",
    "Among others!"
   ]
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   "source": [
    "### R\n",
    "\n",
    "From now on we will focuse on R. "
   ]
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  {
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   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/rstudio.png\" width=\"800\">\n",
    "</center>"
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   "source": [
    "### great documentation\n",
    "- https://cran.r-project.org/manuals.html\n",
    "\n",
    "### free online tutorials\n",
    " - https://www.edx.org/course/introduction-r-programming-microsoft-dat204x-0?gclid=CIHUq6rv4MoCFc5ZhgodCBYKnQ\n",
    " - https://www.datacamp.com/courses/free-introduction-to-r\n",
    " - http://tryr.codeschool.com"
   ]
  },
  {
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   "source": [
    "### online code execution\n",
    "<small>\n",
    "- http://www.tutorialspoint.com <br>\n",
    "<font color='green'>(most available language, has IDE, install.packages() works, free)</font>\n",
    "- https://cloud.sagemath.com/  <br><font color='green'>(allows to run R, scilab, julia, octave and maintain a labbook, install.packages() might work for paid subscription, allows for classroom management, otherwise free)</font>\n",
    "- https://datajoy.com (discontinued)  <br><font color='green'>(allows to install packages, not free)</font>\n",
    "- http://www.r-fiddle.org  <br><font color='green'>(allows to run simple code, very limited in size, install.packages() not available, no registration, free)</font></small>\n",
    "- google collaboratory (check if availabe)"
   ]
  },
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   "source": [
    "\n",
    "### a few dataset to play with\n",
    "\n",
    " - http://www.models.life.ku.dk/Wine_GCMS_FTIR\n",
    " - http://www.models.life.ku.dk/Wine_NMR\n",
    " - http://michem.disat.unimib.it/chm/download/datasets.htm\n",
    " - https://archive.ics.uci.edu/ml/datasets/Wine\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## the notebook for data analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've just seen that important software exists and are available to the community to perform data analysis or statistic. Using a well described, widely used, programming language instead of a close, private, commercial software is a **huge** step towards reproducible science. However a piece is still missing. The notebook. \n",
    "\n",
    "Data analysis is an experimental art, pretty much as is chemistry. Thus, data analyst need to document the steps they follow to obtain their results. Several solutions exists to "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## a first example of publication with jupyter\n",
    "\n",
    "In this example we will **publish** a simple linear regression. The function we use is the following:\n",
    "\n",
    "$$ f(x) = -1.874 + 0.075 x + 0.01 x^2$$\n",
    "\n",
    "Instead of sharing an image of the results, we provide here all the code that is necessary for another group to reproduce our findings."
   ]
  },
  {
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   "source": [
    "### experimental section\n",
    "\n",
    "**creation of the data. Here data are simulated, but real experimental data could be used instead.**"
   ]
  },
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    "#rm(list=ls(all=TRUE)) # we clear the variable space\n",
    "\n",
    "N <- 20 # we define the number of observations\n",
    "\n",
    "# we create a fake dataset using a quadratic\n",
    "#equation and adding some noise\n",
    "# first create a vector of x repeated rep times\n",
    "rep <- 2 # number of replicates\n",
    "X <- rep(seq(from=43, to=96, length.out=N),rep)\n",
    "# then create the Y vector according to the equation:\n",
    "Y <- (0.075 * X + -1.874 + 0.01* X^2)\n",
    "# create some noise\n",
    "noise <- runif(length(Y), -1, 1) \n",
    "# add some noise to Y\n",
    "Y <- Y + 3*noise\n",
    "y = Y"
   ]
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   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "x_sorted <- sort(X,index.return=TRUE)\n",
    "x <-x_sorted$x\n",
    "y <- Y[x_sorted$ix]\n"
   ]
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   "source": [
    "### results and discussion\n",
    "\n",
    "blah blah"
   ]
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       "<table>\n",
       "<thead><tr><th scope=col>x</th><th scope=col>x2</th><th scope=col>y</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>43.00000</td><td>1849.000</td><td>17.37903</td></tr>\n",
       "\t<tr><td>43.00000</td><td>1849.000</td><td>16.92747</td></tr>\n",
       "\t<tr><td>45.78947</td><td>2096.676</td><td>25.28350</td></tr>\n",
       "\t<tr><td>45.78947</td><td>2096.676</td><td>20.41811</td></tr>\n",
       "\t<tr><td>48.57895</td><td>2359.914</td><td>24.94950</td></tr>\n",
       "\t<tr><td>48.57895</td><td>2359.914</td><td>25.20949</td></tr>\n",
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       "\\begin{tabular}{r|lll}\n",
       " x & x2 & y\\\\\n",
       "\\hline\n",
       "\t 43.00000 & 1849.000 & 17.37903\\\\\n",
       "\t 43.00000 & 1849.000 & 16.92747\\\\\n",
       "\t 45.78947 & 2096.676 & 25.28350\\\\\n",
       "\t 45.78947 & 2096.676 & 20.41811\\\\\n",
       "\t 48.57895 & 2359.914 & 24.94950\\\\\n",
       "\t 48.57895 & 2359.914 & 25.20949\\\\\n",
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       "\n",
       "x | x2 | y | \n",
       "|---|---|---|---|---|---|\n",
       "| 43.00000 | 1849.000 | 17.37903 | \n",
       "| 43.00000 | 1849.000 | 16.92747 | \n",
       "| 45.78947 | 2096.676 | 25.28350 | \n",
       "| 45.78947 | 2096.676 | 20.41811 | \n",
       "| 48.57895 | 2359.914 | 24.94950 | \n",
       "| 48.57895 | 2359.914 | 25.20949 | \n",
       "\n",
       "\n"
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       "  x        x2       y       \n",
       "1 43.00000 1849.000 17.37903\n",
       "2 43.00000 1849.000 16.92747\n",
       "3 45.78947 2096.676 25.28350\n",
       "4 45.78947 2096.676 20.41811\n",
       "5 48.57895 2359.914 24.94950\n",
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       "<ol class=list-inline>\n",
       "\t<li>40</li>\n",
       "\t<li>3</li>\n",
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       "\\begin{enumerate*}\n",
       "\\item 40\n",
       "\\item 3\n",
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       "1. 40\n",
       "2. 3\n",
       "\n",
       "\n"
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       "[1] 40  3"
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    "data <- data.frame(x=x, x2=x^2, y=y)\n",
    "data[1:6,]\n",
    "dim(data)"
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   "source": [
    "Now the first thing to do is to have a look to the data. This can be done readily with a single command:\n"
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1To+LJ6w+wgkEJIJhzeYH/weKq/yPAkEEJIJixUHbdY1u4haoTpSSCEkIwY5/HU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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$x, data$y, xlab='x', ylab='y') # plot data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There is two options, if we have no idea about the model we may simple test with a single linear regression, since the data are looking to be linear. Therefore we can use a built-in tool in R that achieve just this. Exactly the same way you would ask **Microsoft Excel** to add a linear regression to your data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "fit.lm = lm(y ~ x, data=data)\n",
    "#plot(fit.lm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The line above means that we will use a routine called ```lm()```\n",
    " for linear model, and define the model as \"y=ax\", the equation of a line. If you are curious, you can uncomment the \"#\" in the cell above and see what results.<br> <br>\n",
    "And we may want to see the results and superimpose this resulting model to the \"experimental\" data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NGizp0732t1xUxNTefOnZuYmHjo0KEn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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$x, data$y, xlab='x', ylab='y') # plot data\n",
    "lines(data$x, fitted(fit.lm), col=2) # plot fitted curve\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The result looks nice, but we would like to know the regression coefficient for this model. Most complex routine in R own a procedure that is called ```summary()```. This allows will show you important parameters of the model object ```fit.lm```. If you only need the coefficient, you can simplify the output using the second line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x, data = data)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-5.1348 -1.8015 -0.4273  2.1378  6.6372 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -49.57573    2.07861  -23.85   <2e-16 ***\n",
       "x             1.49347    0.02914   51.26   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 2.964 on 38 degrees of freedom\n",
       "Multiple R-squared:  0.9857,\tAdjusted R-squared:  0.9854 \n",
       "F-statistic:  2627 on 1 and 38 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.986"
      ],
      "text/latex": [
       "0.986"
      ],
      "text/markdown": [
       "0.986"
      ],
      "text/plain": [
       "[1] 0.986"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(fit.lm)\n",
    "round(summary(fit.lm)$r.squared, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Althouth a correlation of 0.99 is acceptable, a more carefull look at our data indicates we may have a quadratic term. In order to test this, we can simple use another function in the  ```lm()``` routine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"R^2 = 0.995\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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IkTpl26lLCyKhocLObmCsZTL+6KBQAA\nxla2bNmtW7d26dJl27Zt7u7uFSpU+OvYsXe2bHExMyt24IBYWSkdUK3YsQMAAApo2rTp8ePH\nP/jgg7t37+7bt2/oqVPeFhZlIiKKOToqHU3F2LEDAADKsLa2/uijj0REZs+WTz+V4GCpU0fp\nUOpGsQMAAIpat04++UR+/lnc3JSOonqcigUAAMoJC5O+fdO//FL8/JSOogUUOwAAoIz9ixbd\n9fT8Tqcz/+9/bW1t33///aSkJKVDqRvFDgAAKGDJp59WHzLkWLVqr69Zs2/fvvHjxx8+fLhu\n3brHjx9XOpqKcY0dAAAwtqM7drScPl3eeqthVFT2I+uaNGnSt2/f7t279+nTJyoqSsfTiV8K\nO3YAAMC4bt2y8vXNLFWq/L59jz6I2MzMbN68ebGxsQcPHlQwnapR7AAAgBGlpUm3bnLnTtCQ\nIVKiRI7JypUr29raHjlyRJFoGkCxAwAAxpKVJb17y7FjHzk5PShVKtclpqamWVlZRs6lGRQ7\nAABgLB99JKGhEhxc+u23IyIiHp+/evVqQkJCrVq1jB9NGyh2AADAKCZNkh9/lIAAqVPn3Xff\nDQoKCg8Pz7Fk3LhxdnZ2TZo0USSgBnBXLAAAyH+LFsmUKfLLL+LiIiJNmzYdM2aMl5fXJ598\n0r59+/Lly//111/z58/fuXNnWFiYqamp0nHVimIHAADy2datMmKELFokXbo8HJs5c6aTk9PM\nmTOnTJmSlZVlaWnp7u5+8OBBzsO+CoodAADITzt3iq+vTJ4sAwbkmOnbt2/fvn3v3bt39erV\nKlWqmJhwhdirotgBAIB8c+SIdO4s/fvLp58+aUmxYsVef/11Y4bSMKoxAADIH2fOiIeHeHjI\nvHlKRyksKHYAACAfXLsm7dpJrVqyfLlwjtVY+B8aAADktdu3xdNTSpaUzZvFwkLpNIUI19gB\nAIA8lZ4u3bvLzZuyd6+ULKl0msKFYgcAAPKOwSADB0pMjOzZI+XLK52m0KHYAQCAXEREROzY\nsSM+Pr5ixYqNGjXy8vJ6rucGjx4tmzfLH3+IvX3+Z0ROXGMHAAD+JTU1tVevXk2bNt28eXNm\nZmZkZOQ777xTv379s2fPPuPIr76SBQtk40apW9cYQfEYduwAAMC/jBgxYvfu3VFRUXX/18+u\nXr3q5+fXrl272NhYiyfdDPHzzzJpkqxZI+7uxsuKf2PHDgAA/CMhIWHZsmWrV6+u+8iu22uv\nvbZx48bk5OSff/4598MCAqR/f5k9W7p1M1JQ5IZiBwAA/hEWFlalShUXF5cc43q93tvbOyws\nLJdjDhwQPz8ZP14++MAYEfFkFDsAAPCP5OTkihUr5jpVsWLFa9eu5Rw9dky8vKR3b5kwId/D\n4VkodgAA4B/ly5dPTEzMderChQvlczzBJDFR2rcXFxf5/ntjhMOzUOwAAMA/2rRpc/ny5d9+\n+y3H+NWrV7du3erp6fnPUHKytG0r1avL2rXyPE9CQf6j2AEAgH9Urlx55MiRffr0efRyuoSE\nhA4dOtjZ2fXs2fP/h+7dk44dxcxMNm2SokWVyYrH8LgTAADwLzNnzkxPT2/btq2trW3NmjUv\nXrx45MgRFxcXf39/MzMzEZH0dOnWTS5flr17xcpK6bz4B8UOAAD8i6mp6XfffTdy5MgdO3ac\nPHnS3d29QYMGzZo1+/9pg0EGDZKoKNm9WypUUDQpcqLYAQCAXNSoUaNGjRq5TIwdKxs3yo4d\n4uho9FB4BoodAAB4bjNnyrx5EhAg9eopHQW5oNgBAIDns3q1fPaZrF4tbdsqHQW5465YAADw\nHIKD5b335OuvpUcPpaPgiSh2AADgWSIjxddXxo2TUaOUjoKnodgBAICnOnlSvL2lSxeZPFnp\nKHgGih0AAHiypCRp00YaNZKlS0WnUzoNnoFiBwAAnuD6dfHwkKpVZd06MeOGSxWg2AEAgNzc\nuSPt24uZmWzdKpaWSqfBc6F9AwCAx6SlSbdukpwsu3fz0jAVodgBAIB/y8yU3r3l6FHZs4eX\nhqkLxQ4AADzCYJDBg2XHDtm1S6pVUzoNXgzFDgAAPOLjj2X9egkPl1q1lI6CF0axAwAA/zNx\novzwg4SE8CpYlaLYAQAAERGZP1+mTZNNm6RlS6Wj4CVR7AAAgMjPP8tHH8nKleLlpXQUvDye\nYwcAQKG3ZYv07y/ffCN+fkpHwSuh2AEAULiFh0vPnvLll/Lhh0pHwaui2AEAUIhFRkqnTjJ4\nsPznP0pHQR6g2AEAUFgdPSrt2km3bvLtt0pHQd6g2AEAUCidPi1t20qrVrJkieh0SqdB3qDY\nAQBQ+Fy8KG3aiJOT+PuLqanSaZBneNwJAAAqExAQsGbNmuPHj5uamjo5OfXv37/lCz15LjlZ\n2raVChVk0yaxsMi3mFAAO3YAAKhGVlbWe++91717dzMzswEDBvTq1evevXvu7u6ffvrp837E\n3bvSsaOYmkpQkBQvnp9hoQB27AAAUI25c+du3rx53759zs7ODwe3b9/u7e399ttv+/r6PuP4\ntDTp0kX+/lt275bSpZ+y0GAwbN++PTw8PD4+3sbGpkGDBj169ChatGie/BTIP+zYAQCgDgaD\nYfbs2RMmTHi01YmIu7v7iBEjZs+e/YzjMzPlnXfk+HHZtk0qVHjKwrt373p7e3t5eUVHR1eu\nXPnSpUsfffRR7dq1T5w48eo/BfIVO3YAAKhDUlJSYmJi+/btH59q3779t99+m5GRYWb2hD/Z\nDQYZNEh27ZKdO6Vatad/0aBBg+Li4o4ePerg4JA9cvv27T59+rRr1+7YsWPFihV7pR8D+Ykd\nOwAA1OH+/fsiUrJkycenSpQokZmZmZqa+sSDx4yRDRskJERq1Xr6t8TFxa1Zs2b16tUPW132\nl65evTo1NXXFihUvmR5GQbEDAEAdKlWqZG5ufuzYscenjh07Vq5cueJPuhli/HhZuFACAqRe\nvWd+yx9//GFra9uwYcMc48WLF+/QocOOHTtePDiMh2IHAIA6FCtWrEOHDtOnT8/MzHx0/P79\n+7Nnz+7Ro0fuh82bJzNmyPr10qLF83zLzZs3y5Url+tUuXLlbty48YKpYVQUOwAAVGPmzJmH\nDx/28fE5fPhwZmZmRkZGRERE27Ztb9++PWHChFwOWLlSRo+WlSvFy+s5v6JixYrnzp0zGAyP\nT505c8bGxuZV8iO/UewAAFANOzu7PXv23Lp1q06dOpaWlpaWlk2aNLGystq9e/drr72Wc/Xm\nzTJwoHz/vfTs+fxf0bZt2+Tk5M2bN+cYT0pKCggI8HrugghFUOwAAFCTlJSUq1evikjp0qX1\ner3BYPj7779v376dc11YmPTsKVOmyKBBL/T5FSpUGDdu3Hvvvffrr78+3Lc7cuRIu3bt6tSp\n061bt7z4IZBfKHYAAKjGkSNH3NzcGjVqdOnSpStXrly7du3MmTMVKlRo1arVhQsX/lkXESE+\nPjJ6tHzyyUt8yxdffPHBBx/4+fmVL1/excWlevXqderUqV69+pYtW0xMaA4Fmi7Xk+h41KJF\ni4YMGXL79u0SJUoonQUAUKh5enoWLVp006ZNOp3u4WBGRoaLi0utWrWWLVsmInLkiLRqJT16\nyA8/vMp3Xbp0ac+ePfHx8RUrVmzYsKGTk9MrhteMtLQ0CwuLvXv3Nm3aVOksOfGAYgAA1OH2\n7dvbt28PCwt7tNWJiJmZ2ciRI4cPH75s2TI5fVo8PKRVK5k//xW/rmLFit27d3/FD4GRsaEK\nAIA6XLp0KTMz097e/vEpe3v7Gzdu3I2PlzZtxMlJ/P3F1NT4CaE4ih0AAOqQ/c6JmzdvPj51\n48aNCmZmxTt3lgoVZNMmsbAwejoUCBQ7AADUoWLFinZ2dr/++uvjUyHr1u0oWlSKFJGgIHnS\n+ydQCFDsAABQjU8//XTatGnbt29/dHD9ypWdli2rUqqU/P67lC6tVDYUBNw8AQCAagwYMODk\nyZOenp5ubm7169fPzMw8sHfvh3v31tPri+/bJ+XLKx0QCmPHDgAANZk+ffrevXvfeOONyMjI\nw4cOfZOS4m1lVWL/fnn9daWjQXns2AEAoDKNGjVq1KiRiMhHH8n+/RIeLjVrKh0KBQLFDgAA\ndfrsM1m8WEJDxdlZ6SgoKCh2AACo0FdfyaxZsmWLNGumdBQUIBQ7AADU5rvvZNIk8fcXDw+l\no6BgUV+xMxgM8fHx8fHxKSkpBoPBysrKwcHBwcEhx/tVAADQpmXLZMwYWblSeN8XHqOmYnf/\n/v1Zs2YtXLgwKSkpx1TlypUHDx48ZswYS0tLRbIBAGAMK1fKoEGycKH4+SkdBQWRaord3bt3\n3dzcIiIiTExM6tata29vr9frdTrdzZs34+PjDx8+PH78+KCgoLCwsGLFiikdFgCAfLBxowwY\nIPPmycCBSkdBAaWaYjd16tSIiIhevXrNnDnTxsYmx2xSUtLYsWPXrFkzderUKVOmKJIQAIB8\ntGWL+PnJ1KkydKjSUVBwqeYBxWvXrq1Xr97KlSsfb3UiUqlSpVWrVjk7O69bt8742QAAyF/b\ntknPnjJpkowdq3QUFGiqKXaJiYkuLi4mJk8MbGJi4uLicuHCBWOmAgAg3+3ZI507y9ix8t//\nKh0FBZ1qip1erz9z5szT1yQkJFhZWRknDwAAxnDggLRvLwMHyuTJSkeBCqim2Lm7uwcEBKxc\nufJJC5YvXx4YGOjm5mbMVAAA5KPYWGnfXnr0kG+/VToK1EE1N098+eWXwcHB/fr1mzNnjqen\np6Ojo16vF5GUlJS4uLiQkJDY2FgrK6vJ/IUGAKANR46Iu7t07CiLFwvPasXzUU2xs7Oz27Nn\nz4ABAyIjI2NiYh5f0LBhw6VLl9rZ2Rk/GwAAeSw+Xtq2ldatZckSefL15UAOqil2IuLk5BQR\nEREdHR0eHh4XF5eSkiIier3e0dHR1dXVmVcgAwC04fRpad1aGjcWf38xU9Of1FCc+n5dnJ2d\n87DDJSQk1KpVKy0t7ZkrDQZDXn0pAABPdOGCtGkjTk6ydq0UKaJ0GqiM+opd3rK1td2+fXtq\naupT1gQGBs6dO5d30QIA8t2VK9K2rdjayubNYmGhdBqoj+qL3blz52JjYy0sLJo0aZJ9O8UL\n0el0Li4uT19z+vTpl00HAMBzu3pV3NykdGnZskV49Tleipqux1yxYkXVqlWLFSvWuXPna9eu\nici4cePs7Ox8fHzatWtnY2OzcOFCpTMCAPBSbt6Udu2kSBEJCpISJZROA7VSzY7d/v3733vv\nPYPBYGZmtnnz5vT0dD8/v5kzZ1apUqVx48ZXrlzZvXv30KFDHR0dW7durXRYAABexK1b4uEh\n6ekSHi6lSyudBiqmmh272bNnm5iYbN26NTU1NSAg4Pfff588ebKnp2dcXNwvv/yyc+fOX3/9\nVUTmzJmjdFIAAF7EvXvSsaPcvCm//y5lyiidBuqmmh27qKgoT09Pb29vEenQoYOHh0dQUNC6\ndess/3cVgo+Pj5ubW0REhKIxAQB4EWlp0rWrJCbKrl1SoYLSaaB6qtmxu3Tpkr29/cN/rVGj\nhog4Ojo+uuaNN95ITk42djIAAF5Odqs7dky2bRMbG6XTQAtUU+zKlCnzaGnL/ue///770TV/\n//13sWLFjJ0MAICXkJkpffrIwYOybZvY2iqdBhqhmmLn6OgYEBBw+fJlEbl8+XJgYGCpUqUW\nLVr0cEFiYmJgYGCtWrWUywgAwPPJypJ+/WTHDgkPl3+ffQJehWqusRs6dGiPHj1q167doEGD\ngwcP3rx509/fv1evXufOnWvVqtXff/89f/78u3fvvvPOO0onBQDgqQwGGTpUgoIkLEzeeEPp\nNNAU1RS7bt26DRkyZOHChcHBwWZmZtOmTfPz8/vrr7++/PJLf3//7DXu7u5Dhw5VNicAAE9j\nMMiIEbJ2rWzfLrzlHHlNNcVOp9P98MMPY8eOPXPmTM2aNStVqiQikydPbtasWXBwcFpaWosW\nLXr06GFqaqp0UgAAnuzTT2X5cgkJkQYNlI4CDVJNsctWvXr16tWrPzri4eHh4eGhVB4AAF7A\nhAny3XcSGCgtWigdBdqksmIHAEABFxsbGx0dnZycXLNmzebNm5d++CaJb7+VGfH4NtkAACAA\nSURBVDNk40ZxdVU0ILSMYgcAQN64ePFinz59duzYYWtrW7Zs2RMnTmRlZc2cOXPo0KEyb558\n8omsXi0dOigdE1pGsQMAIA/cv3+/TZs2VlZWcXFx2U/Uz8jIWLp06ciRI9+MjGyxapWsWCE9\neigdExpHsQMAIA8sWrToxo0be/fuPXLkSEhIyLVr12rVqtWxY8dqu3c3W748/fvvi/BALuQ/\nih0AAHkgICDA29vbw8MjOjr6zTffLFOmzI8//tgyOdk/K+sjM7NONWtyYR2MgGIHAEAeSEpK\nOnLkSO3atc+ePZv9TC5DSIihU6cJJiYrixdvcPGi0gFRKFDsAADIAw8ePEhLS9uyZUvx4sVF\nRLZv13XpopswoVKZMinDh1taWiodEIWCat4VCwBAQWYwGMzNzf+/wO3YIZ06yejR8vnnZcuW\nNRgMOp1O6YAoFCh2AADkAQsLizt37gwbNixj+3bx9pbBg+Wrr2JiYkaOHFmyZMl79+4pHRCF\nAsUOAIA8UK5cOT8/v4vr16e2bft7lSofZWW5u7s3aNDA1dU1MzPT2tpa6YAoFCh2AADkATc3\nt9Tw8C1paeeaNdvYvPmZs2cbNGgQHh7u4+OTlZXVrFkzpQOiUODmCQAA8sDoxo1Nv/zyDzu7\nRr/9tjj7/gmRvXv3Dh06dMyYMXq9Xtl4KCQodgAAvLL9+/W+vtd8fPpHR9+pVq1Zs2bW1tbH\njh07ePDgkCFDvvjiC6XzobCg2AEA8Gr27xdPT/H1Lbto0fHU1A0bNsTExFy7ds3Hx+eHH35w\ndnZWOh8KEYodAACv4M8/xctLuneXRYvExMTS0rJPnz59+vRROhYKKW6eAADgZUVHS5s20rmz\nLF4sJvyRCuXxWwgAwEvJbnU+PvLjj7Q6FBD8IgIA8OJiYqRNG+nYUZYsodWh4OB3EQCAFxQb\nK+7u4u0tS5fS6lCg8OsIAMCLyG51bdvS6lAA8RsJAMBzO3RI3N3F3V1+/llMTZVOA+REsQMA\n4Plktzo3N1m1Ssx4XhgKIoodAKBQSEpKGjFiRO3atYsVK+bg4NC3b9/jx4+/wPGHD4u7u7Ru\nLatX0+pQYFHsAADaFxMTU6dOnYiIiPfff3/jxo0ff/zx33//Xa9eva1btz7X8SdOiIeHtGol\n/v60OhRk/HYCADQuLS3N19fX09NzxYoVpv+7MG7QoEGTJk3q06dPfHx8+fLln3b8iRPSurU0\nby5r1tDqUMCxYwcA0LjQ0NDExMT58+eb/vt2h/Hjx5crV27VqlVPO/jECXF1lWbN2KuDKlDs\nAAAaFxMTU69ePSsrqxzjpqamLVu2jImJeeKRcXHi6ipNmsiaNVKkSP6mBPICxQ4AoHHp6enm\n5ua5TllYWKSlpeV+WFyctG4tjRvL2rW0OqgFxQ4AoHEODg5HjhzJyMh4fCo6OtrBwSGXY+Lj\nxdVV6tZlrw7qQrEDAGhchw4d0tPTZ8+enWN869atBw8e9PPzy3nAyZPSurXUqSO//ioWFkZK\nCeQFrgMFAGiclZXVggUL+vTpk5iY+O6779rb21+4cGHjxo1Tp06dMGHCm2+++a/VD1vdpk20\nOqgOxQ4AoH1+fn5lypQZN27cvHnzskdsbW0XLVrUt2/ff607dUpat5a33mKvDipFsQMAFApt\n27Zt27ZtSkrK6dOnq1Sp8tprr+Vcce6ctGkjTk6yaZMULapERuBVUewAAIWIXq93dnbOZeLc\nOWnVShwcZPNmWh3Ui5snAACF3rlz0rq1ODjIli20OqgaxQ4AULidPy+tW0uNGuzVQQModgCA\nQuz8eWnVSuzsZMsWsbRUOg3wqih2AIDC6sIFad1aqlSRzZtpddAGih0AoFDKbnWVKklQkBQv\nrnQaIG9Q7AAAhU9iorRuLRUrSnCwlCihdBogz1DsAACFzMNWFxJCq4PGUOwAAIVJ9hlYGxv5\n7TdaHbSHYgcAKDTOnpWWLaVSJQkO5ro6aBLFDgBQOJw9K66uUrWqBAbS6qBVFDsAQCEQHy8u\nLuLgwHV10DaKHQBA606ckNatpXZtnlcHzaPYAQA07a+/xNVVnJ3l1195Yxg0j2IHANCu2Fhp\n0UKaN5dffxULC6XTAPmOYgcA0KjoaHF3F3d38feXIkWUTgMYA8UOAKBFUVHSpo14eMiqVWJm\npnQawEgodgAAzdmzR1xdpWtX+flnMTVVOg1gPBQ7AIC27Nol7dpJr16ycKGY8MccChd+4wEA\nGvL77+LpKYMGyYIFtDoUQvzSAwC0IiREfHxkxAiZNUt0OqXTAAqg2AEANCEwUDp3lg8/lJkz\nlY4CKIZiBwBQv/XrpUsX+e9/Zfp0paMASuIOcACAyq1bJ717y6RJ8tlnT1949erVyMjIU6dO\nValSpUGDBlWqVDFOQMBoKHYAADXz95d+/eTrr2XUqKesysrKmjx58owZM8zMzKpXr56YmJiS\nktK/f/+5c+da8vZYaAinYgEAqrVkifTtK7NnP73Vichnn302Z86c5cuXp6SkHDp0KDk5edu2\nbaGhob169TJOUsA4KHYAAHVatEiGDJHvvpMPPnj6wnPnzn3zzTerVq3y9fU1+d8zUFq3bh0c\nHBwYGBgWFpb/WQEjodgBAFRowQIZMUKWLpVhw565NigoqGrVqh06dMgx/sYbb7i7u2/dujV/\nIgIKoNgBANTm669l5EhZtkz69Xue5UlJSXZ2drlO1ahRIzExMU/DAUri5gkAgKrMmCETJsi6\nddK163Meodfrr1+/nutUcnKyXq/Pu3CAwtixAwCox6RJL9rqRKRFixaxsbGnTp3KMX779u3Q\n0NAWLVrkaURASRQ7AIBKjB8v06fL+vXi4/NCxzVu3LhVq1Y9e/a8fPnyw8E7d+707t3bysqq\nZ8+eeR0UUAynYgEABZ7BIKNHy+LFEhAgbdq8xAesXbu2Q4cODg4O7dq1s7e3P3/+fGhoaIkS\nJQIDA4sWLZrneQGlsGMHACjYDAYZNUoWL5atW1+u1YlI2bJl9+zZ8+OPP1pbW0dGRhYpUmTy\n5MmHDx+uWbNm3oYFlMWOHQCgADMYZMQIWbFCAgOldetX+SQzMzNfX19fX9+8igYUQBQ7AEBB\nlZkpAwfKpk2ybZs0aaJ0GkAFKHYAgAIpM1Pee08CAiQ0VBo2VDoNoA4UOwBAwZOZKf36SXCw\nbNsm9esrnQZQDYodAKCASUuTnj1l717ZuVPeekvpNICaUOwAAAVJWpp07y4RERIeLm++qXQa\nQGUodgCAAuP+ffHxkb/+kt27xd5e6TSA+lDsAAAFw5070rGjJCTIH39I9epKpwFUiWIHACgA\nbtyQdu3kxg3ZtUuqVlU6DaBWFDsAgNKuXBEPD0lPlx07xMZG6TSAivFKMQCAos6flxYtpEgR\n2bWLVge8IoodAEA5Z85I69ZSsaKEhUmZMkqnAVSPYgcAUMjx49K8udSqJSEhUqqU0mkALaDY\nAQCUEBUlLVpIixayaZNYWiqdBtAIbp4AABjdzp3SsaP4+MjSpWJmJiLnzp3bsmXLsWPHLC0t\n33rrrW7duun1eqVTAurDjh0AwLiCgqRdO+nbV5Yvz251c+bMsbe3X7Bgwa1bt86fPz9+/Hg7\nO7vffvtN6aCA+rBjBwAwonXrpE8fGT1apk/PHlizZs0nn3zy008/9erVK3skPT19woQJnTt3\njoqKepO3igEvgh07AICx/Pyz9Okj06Y9bHUi8vnnn3/22WcPW52IFClSZNq0aa1bt54yZYoS\nKQEVo9gBAIzi+++lf39ZsEDGjHk4lpCQkJCQ0Lt378eX9+7dOywszIj5AC3gVCwAIP/NmCET\nJsjq1dKjx6PDycnJIlKhQoXHj6hYsWJycrLBYNDpdEYKCagfO3YAgPxkMMjHH8vEibJuXY5W\nJyLly5cXkQsXLjx+3Pnz58uVK0erA14IO3YAgHyTmSlDhsiaNRIYKO7uj89XrVr1zTffXLx4\ncdWqVdevX5/9uJPatWu///77y5Yta9eunfEjA6pGsQMA5I+MDBkwQAICZNs2adLkSasmTZrU\no0eP4sWLjxo1auzYsampqeHh4T179jQ1NV22bJkx8wIaQLEDAOSD1FTp2VP275cdO6ROnacs\n3Lt3b9myZR88eLBo0aI6dercu3fv8OHD5cqVu379emRkpJ2dndEiAxrANXYAgLx296506CDR\n0bJ799Nb3YMHD5YsWTJv3rxz587NmzevUaNGXl5e/v7+Z8+eHT58+Pfff2+0yIA2sGMHAHiG\nc+fOxcbGpqSk1KpVq06dOubm5k9bfeOGeHnJ9euyZ49UqfL0Tz516tSdO3dcXV1Lly7t6+vr\n6+v7cMrV1XXhwoV5kh8oPCh2AIAn+vvvvwcNGrR169ZSpUpZWVmdP3++UqVKCxYs8Pb2zv2A\nK1fEw0MyMiQ8XGxsnvn56enpImJhYfH4lIWFRUZGBo87AV4Ip2IBALm7f/++u7t7YmLiwYMH\nb968efbs2evXr/ft27dLly7BwcG5HHD+vLi4iLm57Nz5PK1ORGxtbc3MzKKjox+fio6Otre3\np9UBL4QdOwBA7r7//vvk5ORjx45ZWVllj1hZWX311Vfp6ekffPCBp6enickjuwMJCeLuLlWr\nSkCAlCz5nF9hZWXl7e09ceLE7du3FylS5OH4lStX5syZM3LkyLz7aYBCgR07AEDuNm3aNGDA\ngIet7qHRo0cnJCQcOnTon6Fjx8TFRd54Q0JCnr/VZfv2229Pnjzp5uYWGhqanJx84cKFtWvX\nNm3a9PXXXx81atSr/xRAoUKxAwDk7sKFCw4ODiJy8+bNPXv2BAYGnj592mAwVKhQQa/Xnz9/\n/v/XRUVJy5bSooVs2iSWli/6La+//npERES5cuU6dOhQtmzZqlWrvv/++x07dty+fXvRokXz\n9icCNI9TsQCA3JUsWfLy5csDBgxYuXKliBQtWvTOnTtvvPHGvHnz7t69WzJ7Z27nTvH2Fj8/\n+eEHMXnJzYIqVaps2LAhLS0tPj7e0tLS1tbW5GU/Cijk+C8HAJC7Jk2afPnll3v37g0KCrpz\n587t27dPnz7t4uLi4eGh0+nq168vQUHSrp28+64sXPjSre4hc3NzJycnOzs7Wh3w0viPBwCQ\nu4oVK966datr165t2rTJfiJJ9erVP/zwQwsLi5IlS5YMCpLOnWXkSPnuO+HeVaBg4FQsACB3\nu3bt8vHxmTt3bkhIiKurq16vP3z4cEBAgKura5WQEOndW77+WkaPVjomgH+wYwcAyN3Zs2e7\ndOly7NgxLy+v+Pj40NBQa2vrX375Jbh9++9FDg0bRqsDChp27AAAubO0tLxz587rr7/+5Zdf\n/jM6Y4ZMmNDX1LR/p07KRQOQO3bsAAC5a9y4cVBQ0D//bjDImDEycWL0f/6zwcSkXr16ykUD\nkDuKHQAgdx9++OFvv/22ePFiEZHMTBk0SBYvvrp8eY/Vq997773SpUsrHRBAThQ7AEDu6tat\nu3jx4hEjRrR3c4t7++0Ha9ZMb9vWfsiQqlWrzp49W+l0AHLBNXYAgCfq379/YycnXbduZa9c\n8atc2VSnmzNnTp8+fUxNTZWOBiAXFDsAwJNdufLG0KFSvLicPLmpalWl0wB4Bk7FAgCe4OxZ\nadFCTE1l1y6h1QFqQLEDAOTm2DFp3lwqV5awMHntNaXTAHguFDsAwGN27ZJmzaRlSwkJkZIl\nlU4D4Hmp7xo7g8EQHx8fHx+fkpJiMBisrKwcHBwcHBx0vKkQAPJEQID4+sqAATJ3rpjw939A\nTdRU7O7fvz9r1qyFCxcmJSXlmKpcufLgwYPHjBljaWmpSDYA0IiVK2XAABkzRqZPVzoKgBem\nmmJ39+5dNze3iIgIExOTunXr2tvb6/V6nU538+bN+Pj4w4cPjx8/PigoKCwsrFixYkqHBQB1\nmjtXPv5Y5s+XwYOVjgLgZaim2E2dOjUiIqJXr14zZ860sbHJMZuUlDR27Ng1a9ZMnTp1ypQp\niiQEABUzGGTcOPnuO/H3l+7dlU4D4CWp5uKJtWvX1qtXb+XKlY+3OhGpVKnSqlWrnJ2d161b\nZ/xsAKBuGRkycKD88IMEBNDqAFVTTbFLTEx0cXExefJlvCYmJi4uLhcuXDBmKgBQvXv3pFMn\nCQqSXbukTRul0wB4Jao5FavX68+cOfP0NQkJCVZWVsbJAwBacOOGeHvLxYuye7fY2yudBsCr\nUs2Onbu7e0BAwMqVK5+0YPny5YGBgW5ubsZMBQAqdvGitGwpKSm0OkAzVLNj9+WXXwYHB/fr\n12/OnDmenp6Ojo56vV5EUlJS4uLiQkJCYmNjraysJk+erHRSAFCDv/4ST0+xtZUtW0SvVzoN\ngLyhmmJnZ2e3Z8+eAQMGREZGxsTEPL6gYcOGS5cutbOzM342AFCZgwfFy0uaNpU1a4THfwIa\noppiJyJOTk4RERHR0dHh4eFxcXEpKSkiotfrHR0dXV1dnZ2dlQ4IAGoQFiadO0uXLrJkiZip\n6U8BAM+kvv+knZ2d87DDXb169cMPP8zIyHjKmoSEhLz6OgBQmL+/vPuujB4t06YJb2IENEd9\nxS5vWVhY2NraZmZmPmXNrVu3jJYHAPLR/PkyapTMmCFjxigdBUC+UHexi4qKioqKevDgga2t\nrbu7e/HixV/0E0qVKvXVV189fc2iRYt+//33l80IAAWAwSBffCHTpsnPP4ufn9JpAOQX1RS7\nHTt2hIWFjR492traWkSuXLni6+u7c+fOhwvKli37008/dejQQbmMAKCMW7dulSpV6onTmZky\nbJisXi2bN0u7dkbMBcDYnv0cuxs3bhghxzPNmjVr8eLF2c8fNhgMPj4+O3furFSp0rvvvvvh\nhx+6urpeu3ata9eu0dHRSicFACOJjY318fEpU6aMXq8vXbp0+/btIyMjcy5KTZWePWXDBgkN\npdUBmvfsYpddnvbv32+ENE8RHR1dp06d7FeKhYWFHThwwNPTMz4+/qeffpozZ05YWNjmzZvT\n09OfeV4VALQhODi4cePGOp1u8eLFMTExy5Yt0+v1zZo1W79+/T+L7tyRDh1k3z754w9p2lS5\nsACM5NmnYitXrrxixYoVK1bUrl178ODBvXv3ftqGf765du1a9klYEYmIiBCRb775plixYg8X\ndOrUqV27drt27TJ+NgAwspSUlH79+o0ZM+bh32bffvvtzp0716lTZ+DAgS1btixXrpxcvizt\n28uDB3LggFSpomxgAMbx7B27uLi4sLCwHj16nDhxYvjw4TY2NgMHDjx48KARwj3KysrqypUr\n2f98//59EXn99ddzrLG1teUOVgCFwaZNm0xMTCZOnJhjfOzYsdbW1uvWrZMzZ6RFCylSRHbt\notUBhcezi51Op3N1dV23bt2FCxemT59eoUKFpUuXNmzYsF69eosXL75z544RUopIkyZNDhw4\ncPHiRRF58803ReTxy+n+/PNPGxsb4+QBAAUdPXq0YcOG5ubmOcZNTU2bNGlyfdcuad5cXn9d\ntm+XsmUVSQhAEc8udg+VK1du3LhxJ0+eDA0N7dq165EjRwYPHmxjYzN06NCjR4/mX8RsI0eO\nTE1N7dat25UrV3x8fGrUqDFkyJC4uLjs2fT09PHjxx84cKBjx475nQQAFGcwGLKvOX7cm1ev\nfrJ1q7RuLcHBUrKkkYMBUNYLFLtsOp3OwcGhVq1apUuXFpHbt28vXLiwdu3afn5+2e/4yidu\nbm7jxo3bv3+/nZ3d+++/365du/j4eCcnp9q1a7u4uNjY2EyZMqVatWrjx4/PvwwAUEC88cYb\nBw8efPytOYbNmz8OC4tr1EhWrpQiRRTJBkBBL1DsMjMzt27d6uXlVb169SlTplhYWEyePDkx\nMTE4OLhly5Zr164dPnx4/gUVkenTpy9btqxkyZKrV6+eN29eZmZmRkbGkSNH9uzZk5yc3KVL\nl71795blpAOAQqBz584PHjyYMWPGv0aXLzd06zbLzKzc2rXyhP08ANr2XA8ovnDhwtKlS5cs\nWZKUlKTT6dzd3YcNG+bt7W1qaioilSpV8vT07NSpU3BwcD6nlffee69Xr17h4eEHDx68cuWK\nwWCwsrJydHR0c3OrVKlSfn87ABQQ1tbWP/74Y8+ePU+cONG7d29bW1uTr7+uvmzZMJGmS5Zw\ntTFQaD272Hl7e4eEhGRmZlpbW48ePXro0KE1atTIsUan0zVu3DggICB/Qv6Lubm5p6enp6en\nEb4LAAqsrl277tq1a/z48V07d552//5Akc/ffLPn/PmtWrVSOhoAxTy72AUGBjZo0GDYsGE9\ne/YsWrTok5Z5enoq8nw7ACi0mjRpsj0w0NCrl2H7dsOWLVOpdECh9+xiFxUVVa9evWcuc3Z2\ndnZ2zotIAIDnc/26+PjoEhJ0u3ZJnTpKpwGgvGcXu+dpdQAAYztzRtq3lyJF5MABqVxZ6TQA\nCgRumwIAFYqKkiZNpFIl2b2bVgfgIYodAKhNaKi4uoqHh4SEiF6vdBoABQjFDgBUZdky6dBB\nhg2T5ct5BDGAHCh2AKASBoNMmiSDB8t338n06aLTKR0IQIHzXA8oBgAoLCNDhg0Tf3/ZvFm8\nvJROA6CAotgBQIF354507y6xsbJzp/CkAgBPRrEDgILt0iXx8pLbt2X3bnnsxT8A8CiusQOA\n/GIwGM6dO3f9+vWX/4hjx6RxY7GwkP37aXUAnoliBwB57+LFi71799br9dWqVStTpkyVKlWm\nTZuWkZHxYp+yY4c0by7160t4uJQtmz9JAWgKxQ4A8tjZs2cbNGhw6tSpFStWnDlz5tChQ+PG\njfv222+7dOmSmZn5vJ+yYYO0by99+8r69WJpmZ95AWgH19gBQB4bMWKEg4NDaGhokf89Z652\n7dqenp716tX76aefBg4c+OyPmDtXxoyRqVPlk0+euTYzM/Py5cvly5c3M+P/0oHCjh07AMhL\nV65cCQkJmTp1apF/Pz24Ro0aQ4YMWb58+TOOz8yU4cNl3DhZvfqZrW7//v1ubm4lS5asXLly\niRIlWrZs+ccff7xSegAqR7EDgLwUHx8vIg0aNHh8qmHDhidOnHjawffuSefOsnatbNsmvr5P\n/6KNGze2aNHCxsZm06ZNcXFxgYGB9vb27u7uK1eufIX4ANSNfXsAyEumpqYGgyErK+vxqczM\nTFNT0ycemZwsnTrJxYuyd6/UrPn0b7l+/fr7778/adKkzz77LHvEwcHB3d29du3aw4YNc3d3\nt7GxeYUfAoBasWMHAHmpVq1aZmZmu3btenxq165dtWvXzv2whARp2lTS0mT//me2OhHZtGlT\n0aJFx40bl2P8gw8+qFix4rp16148OAAtoNgBQF4qXbp09+7dx44de+vWrUfHIyIili5dOnjw\n4FyOiYiQJk2kWjUJC5Py5Z/nW44fP16/fv3H75bQ6XSNGjU6fvz4y8YHoG4UOwDIY3Pnzk1L\nS6tbt+7cuXN37twZFBQ0bty41q1b9+vXr1u3bjlXb94srq7SoYMEBUnJks/5FTqdzmAw5DqV\nlZWl0+leJT8A9aLYAUAeK1u2bERERM+ePRctWuTu7u7n57dnz54ff/xx4cKFOZcuWSI9esjY\nsbJ0qbzIw0qcnJwiIyPT0tJyjGdmZu7fv/+tt956xR8BgEpR7AAg75UoUeKrr746fvz43bt3\nU1JS9u7d26tXr3+tMBhk0iQZOlQWLJBJk1708zt37pyVlfXFF1/kGP/666+vX7/u+6w7agFo\nFXfFAkA+Mjc3z2U0NVX695etWyUgQDw9X+Jj9Xr9ihUrunTpcvz48d69e9vZ2Z05c+aXX37Z\nsGGDv79/uXLlXjU3AHWi2AGAcd24IZ07S3y87Noldeu+9Me0b9/+wIEDkyZNGjRo0PXr162s\nrJo0abJ3796GDRvmYVgA6kKxAwAjSkoSLy/JyJADB6Rq1Vf8sLfffnvz5s0icuvWrVKlSuVF\nPgDqxjV2AGAsR45I48ZibS179rx6q3sUrQ5ANnbsACDvGQyGtWvXbt68+a+//ipevHidOnU+\nfvvtGuPGiYeHrFwpRYsqHRCANrFjBwB5LDU1tWPHjoMGDSpRosSgQYM6depkv2/f60OHHqpb\nV9aupdUByD/s2AFAHvv8889jYmJiYmJq1KghIjJjhvz118F3323y889/7NvXvHlzpQMC0CyK\nHQDkpXv37v3www9Lly6tUaOGpKfL4MHyyy/y668NvL27P3gwe/Zsih2A/MOpWADIS0ePHr17\n966Xl5dcvy4eHhISIuHh4u0tIl5eXhEREUoHBKBl7NgBQF66d++eqalpsUuXpGNHMTOT/ful\nWrXsqRIlSty7d0/RdAA0jh07AMhL1apVa5SZaWjcWKpWlT17HrY6ETl+/Litra1y0QBoH8UO\nAPJStQMHdpiY7LS2lqAg0esfjt+4ceOHH37o3r27gtkAaB7FDgDyiMEgkyZJnz6XRo3yvnjx\n3YEDT548KSLp6ek7d+5s1apVmTJlPvzwQ6VTAtAyih0A5IXUVOndW2bNkl9/fX3WrB07dsTG\nxjo4OJQsWbJ48eKurq5OTk5hYWHFihVTOigALePmCQB4ZdeuSefOcuaM7NoldeuKSMOGDWNi\nYs6ePXv8+PHixYu/9dZbZcqUUTolAO2j2AHAqzl6VDp0kAoVJCpKKlR4OKzT6WxtbblbAoAx\ncSoWAF5BaKg0by7160t4+KOtDgAUQbEDgJe1eLF4eUm/fvLLL8LFcwAKAE7FAsCLy8yU0aNl\n4UJZskT69VM6DQD8P4odALygO3fEz0/27ZPff5dWrZROAwD/oNgBwItIShJvb7l9W/btE0dH\npdMAwL9wjR0APLeICKlfX4oXl/37aXUACiCKHQA8nw0bxNVV2reXsDApW1bpNACQC4odgEJn\n27ZtXbp0sbOzK1++vKur69y5c9PT059xzNy50rOnjB0rS5eKublRYgLALV5DhQAAIABJREFU\nC6PYAShcJkyY0L59+1KlSv33v/+dP39+48aNv/rqq1atWt25cyf3A9LS5N135T//kVWrZNIk\no2YFgBfEzRMACpHffvtt2rRpgYGBHh4e2SPdu3cfOXKki4vLxx9/vHDhwpwHXL8uXbtKXJzs\n3i316xs7LgC8IHbsABQi8+bN69u378NWl61ChQqzZs1avnz57du3/7X61Clp2lSuX5cDB2h1\nAFSBYgegEPnzzz/btGnz+Li7u3tqauqxY8f+GdqzR5o0EVtb2b1bqlY1XkQAeAUUOwCFSFpa\nWtGiRR8ft7CwMDExSU1N/f9/X7ZMXF3lnXckMFBKlTJqRAB4BRQ7AIVIjRo1YmNjHx8/fPiw\nwWCoUaOGGAwyaZIMHizffitz54qpqfFDAsBLo9gBKER69eq1YMGCS5cuPTqYlZU1ceLEli1b\nVrKyki5dZPZs2bxZhg9XKiQAvDSKHYBCZOjQoY6Ojs2aNVu/fv3ff/999+7dffv2eXt77969\ne9GkSdKqlRw6JAcOiJeX0kkB4GVQ7ID/a+/eA3K8/z+Ov+9KB5UcopBTOeRQCiPRhnLanDKE\n0DAysRg2ZiyGOc/4suGLiaGZMZaznKWiUvFVTnOaw5wS0fH+/dHv27flrLvu+756Pv6az/W5\n7+vV5/f75uVz3fd1oRgxNjbeuXNnly5d/Pz8bGxsLCwsWrZsmZGREbN6de0BA8TISMLDpV49\nbccEgLdEsQNQvJibmy9YsODhw4dnzpyJiIhITk7e/dln1fv3l2bNJCxMbGy0HRAA3h7FDkBx\nZGRkVLdu3aZNm1quXCmdOsknn0hIiJiZaTsXABQIT54AUFxlZsqoUfLvf8tPP0m/ftpOAwAa\nQLEDUCzdvSs+PhIfL2Fh4u6u7TQAoBlcigVQ7BxYuvRatWr/OXTIOTW1+Zgxs2fP/t+tiQFA\nn1HsABQvK3v0cB027F65cgk//DDt5587duy4YMGCli1bJicnazsaABQUxQ5AsaFW/+ejj/w2\nbUru08f50qWegwd36dJl8uTJcXFxjx49GjNmjLbzAUBBUewAFA9Pn8qAAdXXrl3etm3VdevE\n4H+//aytrefOnbtmzZqHDx9qMSAAFBzFDkAxcP26eHjIwYNdrKzKDB787PE2bdpkZGScPn26\n6KMBgAZR7AAo3dGj0qSJmJrKiRMn1WpjY+Nnp5QoUUKlUmVkZBR9OgDQIIodAEVbvlzatJEu\nXSQsTCpUqF27dkxMzLOzYmNj1Wp1rVq1ij4gAGgQxQ6AQmVmyvjxMny4zJ0rS5dKiRIi0r9/\n/yVLlly9ejXvxKysrEmTJnl6elasWFFLWQFAMyh2AJTo3j3p0EFWrJDdu2XkyNzhoUOHOjs7\nt2jRYs2aNZcvX75//35YWFj79u2joqIWL16sxbwAoBE8eQKA4sTHS7duYmEhUVFSvXreIyVK\nlNi+fXtQUNDIkSNzblxnZGTUsWPHyMhIe3t77aQFAM2h2AHQIQ8ePFi6dGl4ePiff/7p4ODQ\nokWLoUOHWlhYvMFbhIaKr6+0ayerVom5+bPHTU1NZ86c+e233/75558pKSl16tQxMTHR2A8A\nAFrFpVgAuiIhIcHJyWnp0qU1atQYOHCgnZ3dd99917BhwwsXLrzW69VqmTVLunaVYcNkw4bn\ntrpcKpWqRo0azs7OtDoASsKOHQCd8PTp065du7q5ua1Zs8bU1DRncMaMGT179vT29o6OjjYy\neunvq6dPZcgQ2bJFNm4Ub++iSAwAuocdOwA6YdOmTffv31+5cmVuqxMRc3Pz4ODg8+fP79y5\n82UvvnZNPDzk2DEJD6fVASjOKHYAdEJ4eHirVq0sLS3zjVtbW7u7u4eHh7/wlTn3HzYzk/Bw\nadCgcFMCgG6j2AHQCY8fPy5VqtRzD5UqVerRo0fPf9myZdKmjXTtKvv2SYUKhZgPAPQBxQ6A\nTqhWrVpiYuJzD509e7ZatWr5R3PuPxwQIPPm5d5/GACKOYodAJ3QvXv3yMjIAwcO5Bvftm3b\nuXPnunbt+o/Ru3elfXtZsUL27JERI4osJADoOIodAJ3g7OwcEBDQvXv3tWvXPn36VERSU1OX\nL1/u6+s7fvx4BweH/02Nj5d33pG7dyUqSlq10lZgANBB3O4EgK747rvvypcv/8knn3z00Uc2\nNjY3b960sLD4+uuvP/vss/9NCg2Vvn2lfXv56ScpWVJ7YQFAF1HsAOgKQ0PDSZMmjRo1Kj4+\n/tKlSw4ODk5OTua59xlWq2X2bJk4UcaOlW+/FZVKq2EBQBdR7ADoFktLS3d3d3d393+MPn4s\nfn6yaxf3HwaAl6DYAdB5165Jt27y4AF3qgOAl+PLEwB025Ej0qSJmJvT6gDglSh2AHTYsmXi\n6Sldu8revVK+vLbTAICu41IsAJ2UmSljxsiPP8qSJTJ4sLbTAIB+oNgB0D23b0uvXnL2rISF\nSYsW2k4DAHqDS7EAdExEhDRuLI8fS1QUrQ4A3gjFDoAuCQ6W1q2ldWs5dEiqVNF2GgDQMxQ7\nALohLU2GDJGhQ+XbbyU4WMzMtB0IAPQPn7EDoAOuXpUePeT6dTlwQNzctJ0GAPQVO3YAtO3A\nAWnSRExN5cQJWh0AFATFDoD2qNUya5Z4eUm3brJ3r9jaajsQAOg3LsUC0JKUFBk4UHbtkvXr\npWdPbacBACWg2AHQhsRE6d5dMjJ4UBgAaBCXYgG8gczMzLNnz966datA7/L779KsmTg4SGQk\nrQ4ANIhiB+C1XLhwoWvXrubm5nXr1rW1ta1UqdKsWbMyMzPf7F2ysmT8eOnRQ0aNki1bpHTp\nwgkLAMUUl2IBvNrp06c9PDyaNGmydetWZ2fnBw8ehIWFff3111FRURs3blSpVK/1LnfuSJ8+\nEhMjoaHSrl0hRwaA4ogdOwCvNnTo0HfffXfnzp3t27evWLFi3bp1AwICDh8+vGPHjg0bNrzW\nW5w8KU2ayN27EhX1klZ34cKFoUOHOjk5WVpauri4BAQEXL16VWM/BgAoHcUOwCucO3fu2LFj\nM2fONDD4x2+MunXrDhw4cPXq1a9+i+Bg8fCQd9+VI0ekRo0Xzdq/f7+Li8vZs2f9/f3XrVs3\ncODAEydOODs7R0REFPynAIDigEuxAF4hMTHRwsLC0dHx2UNNmjQJDQ192YvT0mTECFmzRmbN\nksDAl0xMTk728fH5+OOP58+fn3ttd+TIkUOHDu3Vq9fZs2fNeMgYALwKO3YAXsHIyCgzM1Ot\nVj97KCMjw8joxf8+vHpV3n1XduyQAwde3upEJCQkxMjIaNasWXk/sWdgYPD9998/fPhw69at\nbxsfAIoRih2AV3B2dk5PTz9+/Pizhw4cOODi4vL8l73hg8JiYmI8PDyMjY3zjZubm7u5uUVH\nR795cAAodih2AF6hUqVKXbp0CQwMfPToUd7x3bt3h4SEDBs2LP8L3upBYenp6aamps89ZGJi\nkp6e/lbZAaB44TN2AF7thx9+aNWqlYuLy/Dhw52dne/fv79///7ly5ePHz/e09PzH1NzHxS2\nbp306vX6p6hVq9a6deueHVer1adOnWrH7VEA4DWwYwfg1WxtbaOionx8fIKDgz/44IPhw4ef\nP39+8+bN06ZN+8e8xERxc5O4OAkPf6NWJyI535B49uYpy5cvv337tre3dwF/BAAoDtixA/Ba\nLC0tp0+fPn36dLVa/fw7Ev/+u/j5iYeHrFnzFo+UsLe3nz59up+fX2Jioo+PT7Vq1S5evLhm\nzZp58+b961//qlixogZ+BgBQOoodgDfznFaXlSUTJ8q8eTJxokyeLAZveSlg3LhxlStXnjRp\nUlBQUM5InTp1fvnlF7brAOA1UewAFIxGHxTWt2/fvn373rp169KlSzVr1rS2ttZIRgAoJih2\nAAogOlq6d5eyZSUq6iWPlHhTNjY2NjY2mno3ACg++PIEgLcVHCwtW77yQWEAgCJDsQPw5tLS\nZMgQGTpUvv1WgoOlZEltBwIAiHApFsAbu3pVevSQ69flwIHXeaQEAKDI6F+xU6vVSUlJSUlJ\nycnJarW6dOnStWvXrl279vPvvwBAs0JDxc9PnJ0lOloqVNB2GgDAP+hTsXvy5Mm8efN+/PHH\n69ev5ztkZ2fn7+8/ZswYMzMzrWQDlC8zU6ZNk2nTJCBA5s6VEiW0HQgAkJ/eFLvHjx97enpG\nREQYGBi4urrWqlXLyspKpVI9ePAgKSkpLi5u0qRJoaGh+/btK8nHfQCNu35d+vSRM2dk61Z5\n/31tpwEAPJ/eFLsZM2ZERET4+vrOnj27UqVK+Y5ev3593Lhx69evnzFjRv5nHAEooLAw8fWV\nKlXkxAmpXl3baQAAL6Q334rdsGFD48aNg4ODn211IlK5cuW1a9c2atQoJCSk6LMBipWVJUFB\n0q6d9OolR4/S6gBAx+lNsbt27ZqHh4fBix9VZGBg4OHhcfXq1aJMBSjZ7dvSsaMsWCAhIfL9\n93yoDgB0n94UOysrq0uXLr18zsWLF0u/+aPHATzHgQPi4iL370tMjHz4obbTAABei94UOy8v\nr23btgUHB79owk8//fTHH394enoWZSpAgdRqmTVLvLykc2c5epRHSgCAHtGbL098880327dv\n9/PzW7BgQYcOHerUqWNlZSUiycnJiYmJO3bsiI2NLV269NSpU7WdFNBnf/8t/ftLeLisXy89\ne2o7DQDgzehNsXNwcDhy5MjgwYMjIyNjYmKendC0adMVK1Y4ODgUfTZAIQ4dkj59xNZWoqOF\n/ykBgB7Sm2InIg0aNIiIiIiOjg4LC0tMTExOThYRKyurOnXqtGnTplGjRtoOCOgttVoWLpRx\n42TgQFm4UExMXjTx9u3bZ86csbKyqlevnsmLpwEAtEKfil2ORo0aabDDZWRkhISEpKamvmTO\n4cOHNXU6QBfduSMDBsiRI7Jmjfj4vGhWVFRUQEBAVFRUiRIlMjIyTE1N/f39Z8yYwS3BAUB3\n6F+x06wbN2588803mZmZL5nz8OHDIssDFLXISPHxkTJlJDpaatZ80azw8HBPT88PP/xwxYoV\ndevWffToUVhY2JgxY+Li4nbv3m1kVNx/kwCAjlCp1WptZyiojz/+2MPDw8/Pr5Def+nSpcOG\nDUtJSbGwsCikUwBakHv5tXdv+fFHeenGW8OGDRs1arRq1aq8g1evXm3YsOGsWbOGDBlSyFkB\nQIekp6ebmJgcPXrU3d1d21ny05vbnbzEihUruFoKvJm7d6VzZ5k0SVavluDgl7e606dPx8XF\nff311/nGq1SpMmjQoPXr1xdmUADAG9CbCyhfffXVS46ePHkydwLPigVeISpKfHzE1FTCw6V+\n/VdOv3jxYqlSpao/73lizs7OGzdu1HxCAMBb0ZtiN3369JccjY2NjY2Nzflvih3wQjmXXz//\nXHx8Xnn5NZepqWlaWlp2dvazz/RLTU01MzMrhKAAgLehN8VORCwsLEaPHl22bNl846NHj3Zz\nc/N58bf5AIiIPHwogwdLaKgsXiwff/z6r3N1dc3MzNy/f/+zT3bZtWtXkyZNNJoSAPD29KbY\nbd269eOPP/73v/+9fPnyDz74IO+h0aNH169ff9SoUdrKBuiBkyelVy8xNpbISGnQ4I1eam1t\n7evrO3LkyP3799vY2OSO//zzz1u3bg0PD9d0VgDAW9KbL0907tw5ISGhWbNmnTp1GjRoELcg\nAd7AsmXi7i4tWsiJE2/a6nIsWrTIysrKyclp3LhxwcHBCxcu9Pb2/uijjxYsWNC0aVON5wUA\nvB29KXYiUr58+c2bN69cufLXX39t0KDBnj17tJ0I0HkPH4qPjwQGyuzZEhws5uZv9zalSpU6\nePDg5MmT4+LivvrqqxUrVlhaWh49enTkyJGazQsAKAi9uRSba+DAga1bt/bz82vXrt2wYcPm\nzJmj7USAroqOFh8fMTSUiAhxdi7gmxkbG48YMWLEiBEaiQYAKAz6tGOXq3r16vv37589e/aq\nVasaNmyo7TiATgoOlpYtxc1NTpwoeKsDAOgFvSx2ImJgYDBu3LioqCieBgHkl5IiffqIv798\n+62sWSP8bwQAig39uxSbl5OTU2xsbFZW1rO31wKKlStXrixevPj48eO29+4tuH69jKWl6fHj\nwn42ABQzet+HVCqVkZERxQ7F2aJFi+zt7WfPnu105MjqhISD9+9XuHLFb/58becCABQ1+hCg\n3/bs2RMYGNjQzu5+q1b/MjEx/eEHt0uXmnl5rVmzZuLEidpOBwAoUhQ7QL8NHz68o5nZiczM\n0rdvy/HjMmxY9erV9+zZ4+TkNG/ePLVare2AAICiQ7ED9FlmZv8LF7Y9eaJq00aiovJ++/Wb\nb75JS0uLjIzUYjoAQBGj2AF66/JladVquFq9beBACQ6WkiXzHmzWrJmIJCUlaSkcAEALKHaA\nfvr1V3F1FWNjV5Vqj5nZs8fj4uJEpHr16kUdDACgPRQ7QN+kpIi/v/TpI59+Knv2GFSpEhIS\nkpGRkW/WlClTjIyM3N3dtZIRAKAVFDtAr5w4IY0by65dcuCABAWJoeHs2bPv3LnTvHnz69ev\n50xJSUn56KOPjh49OmjQIENDQ+3mBQAUJf2+QTFQjKjVsnChfP65dO0qy5ZJ6dI5wz4+PjEx\nMbNnz65SpUrp0qWNjY3//vtvtVrt6em5ZMkS7UYGABQxduwAfXD7tnzwgUyaJP/+t/zyS26r\nyzFz5syTJ0/27NmzQoUKpqam7dq127x58969e9muA4Dihh07QOft3i1+fmJnJ9HRUrPmc6e4\nurqGhIQUcS4AgK5hxw7QYWlpEhgoHTtKr15y9OiLWh0AADnYsQN01dmz0qeP3LghoaHSoYO2\n0wAA9AA7doBOCg6WJk3ExkZiY2l1AIDXRLEDdExysvTpI/7+Mn267NghtrbaDgQA0BtcigV0\nyfHj0revmJrK8ePSsKG20wAA9Aw7doBuyMyUoCBp2VJatpQTJ2h1AIC3wI4dUOiys7MvXbp0\n9epVe3v7qlWrPmfGlSvi6ysJCfLzz+LjU+QBAQAKwY4dUIjUavWiRYtsbW1r1qzp5eVVrVo1\nBweH33777R+TNm0SFxcxMpL4eFodAKAgKHZAIfr888+//PLLr7766sqVK+np6efOnevdu7eP\nj8+KFStERJ48kcBA6d1bPv1U9u4VOztt5wUA6DcuxQKFJTY2dv78+bt27fLy8soZqVmz5vTp\n0ytWrDh69OgeNWpYffKJpKXJgQPSooV2owIAlIEdO6CwbNiwoUWLFrmtLtfwTz4JFLFs316c\nnSUmhlYHANAUih1QWC5cuODs7Jx/9PZtgy5dJqSmbmvXTjZulDJltBENAKBMXIpF8aVWq0ND\nQ3fs2HH27Flra2tXV9dBgwZVqFBBU+9vamr65MmTfwzt2SN+flK58qCGDZ3c3btq6kwAAIgI\nO3Yotp4+fdqtW7cePXrcvHmzZcuW5cqV++mnnxwdHffu3aupUzRp0iQsLCwzM1NEnj54kDxw\noHTsKP3739m6dcvp002aNNHUiQAAyMGOHYqpzz77LDY2Ni4urnbt2jkjWVlZX3zxhbe395kz\nZ6pUqVLwU/Tr12/q1Kk9e/Y0O3t2YmJiGbW6t5HRk4gIVd++NWvW9PT0LPgpAADIix07FEd/\n//338uXLly5dmtvqRMTQ0HDOnDl16tRZuHChRs5Srly53r16VduyZXViYrq9/c7Zsyv27x8b\nG3vw4MGAgAAjI/5ZBQDQMP5qQXEUHh5uZmbWrl27fOMqlapbt26hoaEaOcuf+/f3Xrq0qanp\nr25u8x89ujpvnoODw/Dhw9PT04OCgvr162dpaamREwEAkINih+Lo4cOHVlZWBgbP2bEuV67c\nw4cPNXCO4OBKQ4bcsrAwOX26T5UqffIcSUtLW7lyZWhoaO/evTVwIgAA/otih+LIzs7u1q1b\nKSkpz+6ZnTt3zq6AT4C4dUuGDpXdu391dDzq7t7smY/rmZiYuLi4nD17tkBnAQDgGXzGDsWR\nu7t7mTJlFi9enG/8zp07a9eu7dat29u/9aZN0qCB3LghMTF/1K+fmZ393FlZWVnP3S8EAKAg\n+KsFxZGxsfH8+fMnTZo0Z86c3FvNxcTEtG3btkqVKoMHD36bN01OFn9/6d1bBg+WI0fE0dHJ\nyenIkSNqtTrfxEePHkVHRz/n3sUAABQMxQ7FlK+v78qVK2fPnm1lZVW3bl1ra+tGjRrVqFFj\n165dxsbGb/x2+/aJk5Ps3SsHDsjMmWJsLCL9+/f/888/v//++7wT1Wr12LFjy5Yt26FDB039\nLAAA5OAzdii++vfv36NHj8jIyLNnz5YrV65Ro0b29vZv/C5Pn0pQkMydK4MHy/z5Ym6ee8TO\nzm7ZsmUfffRRRERE9+7d7ezsLly4sGrVqsjIyJ07d5qammryhwEAgGKHYs7MzOy999577733\n3vL1cXHSv7/cvi2//y4ffPDscV9f35o1a06fPn348OF37tyxs7N79913o6Oja9WqVaDcAAA8\nD8UOeCuZmTJvnkyeLF27yv79UrbsiyY2a9Zs69atIvL06VN26QAAhYpiB7y5ixfFz08SEmTF\nCunX7zVfRKsDABQ2vjwBvAm1WpYtE2dnKVlSEhJev9UBAFAE2LEDXtvNm/LxxxIWJt9+K59+\nKiqVtgMBAPAP7NgBr2fjRmnQQO7ckdhYCQyk1QEAdBDFDniV5GQZMED69pWPP5bDh6V2bW0H\nAgDg+bgUC7zUnj0yaJCUKiXHj0vjxtpOAwDAy7BjB7zAkycyfrx07Cjvvy9RUbQ6AIDuY8cO\neJ7ISBkwQJ48kT17pHVrbacBAOC1sGMH/FNmpsyaJS1birOzxMbS6gAAeoQdOyCP//xHBgyQ\ny5dlwwbp3l3baQAAeDPs2AEi8t87DzdpIuXKSWwsrQ4AoI/YsQNErlyRgQPl+HGZMYM7DwMA\n9Bc7dije1GpZvlycnSU9XeLjufMwAECvsWOHYuzPP2XIEDl2TL75RgIDxdBQ24EAACgQduxQ\nLOV8os7ZWVJTJTr6uo9PalqatjMBAFBQFDsUP5cuiZeXjB5975NPelWsaNW0qZ2dnaWlZb16\n9VasWKFWq7WdDwCAt0SxQ3GSu1GXkZH0yy81ly//++7d1atXJyUlHT16tHfv3p9++umIESO0\nnRIAgLfEZ+xQbFy4IIMHS0yMTJsmI0f6NmvWunXrjRs3GhgYiEitWrXc3Ny8vLzee++9rl27\ntmvXTttxAQB4Y+zYoRjIypLvv5eGDcXUNOerr3EJCSdPnpw7d25Oq8vl7u7es2fPVatWaSsp\nAAAFQbGD0p0+Le7u8vXXMn++7NghVauKyJkzZ2xsbGrUqPHsdDc3tzNnzhR5SgAANIBiB+XK\neepr48ZibS0JCTJ0aO496gwMDLKzs5/7ouzs7HzbeAAA6Av+AoNCxcdL8+Yyc6YsXCihoWJn\nl/egk5PT7du3ExMTn33d4cOHnZyciiolAACaxJcnoKNu3bq1cePG+Pj4rKysevXq9ejRo2rV\nqq/1yowMmT9fJk+Wdu3k99+lUqVnp9StW9fDwyMwMHDbtm0lSpTIHd+9e/eWLVsOHDigoR8C\nAIAixY4ddFFISEjNmjXnz59/48aNu3fvLl++vFatWkuWLHn1K0+dkmbNZP58Wb5ctm17bqvL\nsXLlyri4ODc3t5UrV0ZERGzfvn306NGdOnWaMGGCh4eHJn8YAACKCjt20Dnh4eH9+vVzc3OL\ni4vbtm2biJQsWbJp06aBgYGVK1fu2rXr81/29KnMnCkzZki3brJrl5Qv//Kz1KxZMyYm5uuv\nv546derly5ctLCwaNmwYEhLi7e2t8Z8IAICiQbGDzpk8eXKpUqVu3rz5ww8/NG/e3NDQ8OTJ\nk1OnTrWwsPjyyy+fX+yOH5dBg+TePdmwQbp3f80T2djY/PjjjyKSmppqZmam+u9XKwAA0FMU\nO+iW7Ozs/fv3lytXLjw83NraOmewatWq7du3d3V1PXPmzJ07d3LHRUSePJEpU2TuXOneXX74\nQcqVe4uTlixZUiPhAQDQLj5jB93y+PHjrKysjz766B/tTaRkyZJffPGFiNy4ceN/o8eOiaur\nBAfLpk3yyy9v1+oAAFAMih10i6GhoYiULVv22UPlypUTkczMTBGR1FQZP148PMTZWRIS5EUf\nvAMAoDih2EG3GBkZicjmzZvVanW+Q2vXrpWcenf4sLi4yIYNsnOn/PKLPK8FAgBQDFHsoFuM\njY1zvq8aEBCQkpKSM/j06dPJkydv3rzZrlSpKnPnSuvW0rq1xMdL27baTQsAgE6h2EHnjBo1\nytjYeMuWLRUrVmzWrFnLli1tbGyWLFnS3dw8XkT1xx+ye7csXSqWltpOCgCAbuFbsdA5w4YN\nO3To0I4dOzp27JjzfdXaNjattm/vn5aWPWiQLFggFhbazggAgC6i2EHnGBoabtiwYdWqVStX\nrkxISPBKT1+SlWVSqlT2H38YenpqOx0AALqLS7HQRSqVatCgQUc2bXrwwQe/pqdXCAy0unKF\nVgcAwMuxYwedpFbLihXy+edStaocOyZNm2o7EAAAeoAdO+iec+ekbVv59FP59FOJjKTVAQDw\nmih20CUZGTJrljg5iYmJnDkjQUFibKztTAAA6A0uxUJnHDokw4bJ/fuybJkMGKDtNAAA6B92\n7KAD7t8Xf39p3VqaNJGEBFodAABvhx07aNvGjRIQIGXKyN690rq1ttMAAKDH2LGD9ly4IO3a\niZ+fDB8ucXG0OgAACohiB23I+ZJEgwaSni7R0RIUJCYm2s4EAIDe41IsityRIzJsmNy4Id9/\nL0OGiEql7UAAACgEO3YoQg8eSGCgtGoljRpJYqIMHUqrAwBAg9ixQ1HZuFFGjJBSpWTnTvHy\n0nYaAAAUiB07FL6LF6VDB/H1lYEDJSGBVgcAQCFhx05RsrKyNmyuXRxIAAAcHUlEQVTYsGfP\nnsTERFtb20aNGg0dOtTGxkbjJ0pPT09KSvrrr79q1apVvXp11YuuqGZmyuLF8tVX4uoqsbFS\nr57GkwAAgFzs2ClHcnJy69athw8frlaru3TpUr169fXr19erV2///v0aPEtWVtb06dPLly/v\n5OTUpUsXe3v7mjVrbt269TlTo6PFzU2mTJF58+TgQVodAACFjR075RgyZMjdu3fPnDlTuXLl\nnJGsrKwxY8Z4e3snJiZqat9u6NChW7ZsGTNmTKlSpR4+fFimTJnExMQPP/xw9erVffv2/f9J\nyckyebIsXizdu8v27VKhgkZODQAAXo5ipxAXLlzYuHFjREREbqsTEUNDw3nz5u3Zs+eHH34I\nCgoq+FkOHjy4evVqd3f3oKAge3v7SpUqJSUl3bt379133x05cmTnzp0tLS1l2zYZPlyMjWX7\ndmnXruAnBQAAr4lLsQpx7NixSpUqNW3aNN+4oaFh586djx07ppGzrF+/3srKKjk5OT4+/vz5\n84cOHbpx40ZISEh0dPTjx48Pb9ggH34oH34o3btLXBytDgCAIsaOnUKkpKSULl36uYdKly6d\nkpKikbOEh4c/evRo586dFStWzBlRqVTe3t6qrKyDvXp5jhgh77wjMTFSv75GTgcAAN4IxU4h\nqlatevny5adPn5qamuY7lJSUVLVqVY2c5d69e/b29rmt7v/FxHSbPbuVWv1rw4a+hw6JAdvA\nAABoB38HK0Tr1q2NjY1//PHHfOOXL1/euHGjt7e3Rs5iYmJy586d7Ozs//9zaqqMHy/vvPOk\nVCknkfCmTWl1AABoEX8NK4S5ufm8efM+//zzOXPmPHr0SESys7P379/v5eXVrFmzXr16aeQs\n9erVS05Onjx5slqtlk2bpE4d+eWXpxs3dlKr75iaOjk5aeQsAADg7VDslGPgwIH//ve/58yZ\nY2VlVb16dUtLy7Zt27777rtbtmwx0NBGWseOHS0sLLbPn3+ibNksH58EF5cpPXs6jh6dmJiY\nlpbWunVrjZwFAAC8HT5jpygDBgzo2bPnqVOnzp49W7FiRWdn5/yfhysYv54907/8cnha2sWy\nZftVrXr01KnaT554e3v//vvvvr6+tWvX1uC5AADAm6LYKY2ZmZmbm5ubm5vm33rbtpIjRgSY\nmk40NV2emtq6WbMuFSsmJiYuXry4Q4cOS5cu1fwZAQDAm+BSLF5DYqK0by89eki3bkbnzk39\n88+FCxfa2dndvn37nXfe2bFjx9atW0uWLKntlAAAFHfs2OGlHj+WOXPk22/l3Xfl1ClxdBQR\nE5F+/fr169dP2+EAAMA/UOzwAmq1/PqrjBkjxsayaZN06qTtQAAA4BW4FIvnOXVK3n1X/Pxk\n0CBJSKDVAQCgFyh2+KcHDyQwUBo3ltKl5fRpCQqSZx5lAQAAdBOXYvFfarWsWSPjxkmpUrJ1\nq7z/vrYDAQCAN8OOHUREJCZGWraUTz6RTz6RhARaHQAA+ohiV+zdvy+BgfLOO1K2rJw5I0FB\nYmKi7UwAAOBtcCm2GMvOlrVrZexYKVNGQkOlfXttBwIAAAXCjl1xdfKktGghw4fL8OESH0+r\nAwBAASh2xc+9exIYKE2birW1/Oc/EhQkxsbazgQAADSAS7HFSc61188+k/LlZdcu8fLSdiAA\nAKBJFLti4/BhGTFCrlyRoCAJCBAj/k8PAIDScCm2GLh5UwYMkFatpGFDOXtWAgNpdQAAKBLF\nTtEyM+X776VOHUlIkEOHJDhYbGy0nQkAABQWdm6U6+BBGTFCrl+XqVNlxAgxNNR2IAAAULjY\nsVOiy5fFx0fatBF3dzl3TgIDaXUAABQHFDtlSUmRCRPE0VGuXpWICFm6VMqV03YmAABQRPTv\nUqxarU5KSkpKSkpOTlar1aVLl65du3bt2rVVKpW2o2lVzq1MvvhCjIxk6VLp31+K+YIAAFD8\n6FOxe/Lkybx583788cfr16/nO2RnZ+fv7z9mzBgzMzOtZNOyfftkzBg5f17GjpXx48XUVNuB\nAACAFuhNsXv8+LGnp2dERISBgYGrq2utWrWsrKxUKtWDBw+SkpLi4uImTZoUGhq6b9++kiVL\najtsEUpKkq++kk2bxNdXdu4UW1ttBwIAAFqjN8VuxowZERERvr6+s2fPrlSpUr6j169fHzdu\n3Pr162fMmDFt2jStJCxq9+7J7Nny3Xfi4SHR0dKwYc7wkydPYmNjExMTbWxsXFxcKlasqN2Y\nAACgyOjNlyc2bNjQuHHj4ODgZ1udiFSuXHnt2rWNGjUKCQkp+mxFLSNDli2TOnVk82ZZu1b2\n7s1tdatXr65ataqHh8eUKVN69uxZpUqVQYMGpaSkaDcvAAAoGnpT7K5du+bh4WFg8MLABgYG\nHh4eV69eLcpUWrBtm9SrJxMmyNixEh8vPXvmHlm5cuWQIUO++OKL5OTkS5cuPXz4cO/evYcP\nH+7WrVt2drYWIwMAgKKhN8XOysrq0qVLL59z8eLF0qVLF00eLYiOllat5MMPpU0bSUyUL74Q\nY+Pcg48fPx47duycOXPGjh1rbm4uIgYGBq1atdq3b19kZOQvv/yivdwAAKCI6E2x8/Ly2rZt\nW3Bw8Ism/PTTT3/88Yenp2dRpioif/0l/v7StKlYWsqZM7J0qVhb55sSFhaWnp7u7++fb7xq\n1ao9e/bcvHlzUWUFAABaozdfnvjmm2+2b9/u5+e3YMGCDh061KlTx8rKSkSSk5MTExN37NgR\nGxtbunTpqVOnajupRqWmyqJFMn261Kol+/bJe++9aOLVq1erVatm+rwbndSuXfv3338vzJQA\nAEAn6E2xc3BwOHLkyODBgyMjI2NiYp6d0LRp0xUrVjg4OBR9tkKhVsuvv8q4cZKRIXPnyuDB\nL38smKWl5YMHD5576MGDB5aWloWTEgAA6BC9KXYi0qBBg4iIiOjo6LCwsMTExOTkZBGxsrKq\nU6dOmzZtGjVq9HZv++jRo4yMjJdMSE1Nfbt3fnsREfLZZxIbKyNHysSJ8hq1rEWLFn/99Vdk\nZGTTpk3zjmdlZW3btq1Xr16FlhUAAOgKfSp2ORo1avTWHe5ZFy5cqF279ut8abSIHll25Yp8\n9ZX8/LN8+KGsWyfVqr3m6+zt7Xv16jVw4MBdu3bZ2dnlDGZlZX322Wd//fXXsGHDCi0xAADQ\nFfpX7DTLwcEhNjY2PT39JXPi4uIGDRpUokSJwo3y6JHMnSuzZknDhnLkiDRv/qZvsHz58s6d\nO9erV69bt26Ojo63b9/evXv3rVu3Nm/ebGNjUxiRAQCATinuxU5EnJycXj4hLS2tcBNkZsrK\nlTJ5spiYyNKl0r+/vNXuYKlSpcLCwkJCQvbu3fvHH3/Y2tr27dt3yJAhtDoAAIoJfSp22dnZ\nISEhBw8eNDEx6dy5s5eXV74J8+bN27Nnz86dO7US7y3t3SuffSaXLsmYMTJ+vDzva62vz9DQ\nsG/fvn379tVUOgAAoEf0pthlZWV17do1NDQ0548LFy7s3r37qlWrSpUqlTsnPj5+165dWgr4\n5s6elXHjZOdOGTRI9u6VChW0HQgAAOg3vblB8fLly0NDQ21sbGbOnLlkyZKmTZv+9ttvbdq0\nedE9PnTa3bsSGChOTvL0qURHy9KltDoAAFBwerNjFxwcbGRkdPDgwTp16oiIv7//lClTpk6d\n2r59+z179uTdt9N1v/4qgwdL1aoSGirt2mk7DQAAUA692bFLSEho0aJFTqsTEQMDgylTpixa\ntCgyMvL9999//PixduO9gVKlZP58iY2l1QEAAM3Smx279PT0Cs9crxwxYsTTp0/HjRvXuXPn\n3I/f6Tr6HAAAKBx6U+yqVKly7dq1Z8fHjh376NGjKVOmdO/evUyZMkUfDAAAQEfoTbFzcXHZ\nunVrcnKylZVVvkNBQUEPHz787rvvDF/6NFUAAABl05vP2Hl7e6enp69fv/65R+fPnz9kyJCs\nrKwiTgUAAKA79GbHrnPnzt99992zH7PL9eOPP9aqVevu3btFmQoAAEB36E2xs7S0HDVq1Esm\nGBgYjBs3rsjyvIUnT57s3bv39OnTIlK/fn0vLy8zMzNthwIAAMqhN8VO3+3du3fAgAEpKSk5\nj6adPn26paVlcHDwsw9GAwAAeDt68xk7vXby5MnOnTv37dv31q1bx44dO3bs2K1bt/r27du5\nc+fo6GhtpwMAAAqhUqvV2s6g644dO9aiRYu0tDRjY+O3e4eOHTtaWlpu2LAhJiYmISFBRBo0\naODq6urj4/Po0aMdO3ZoNC8AAChE6enpJiYmR48edXd313aW/LgUW+jS0tL27dv3/fffN2zY\nMCEhoXr16iLy559/NmjQYPjw4YGBgenp6W9dGQEAAHJxKbbQ3b17NyMj44svvnB2dr5x48al\nS5cuXbp048YNZ2fnL774IiMj486dO9rOCAAAlIBiV+hKly6tUqkcHR3Xrl1ra2ubM2hra7tm\nzRpHR0eVSsUDMwAAgEZQ7ApdiRIlVCqVtbW1SqXKO25gYFCuXDmVSmVkxAVxAACgARS7Qnfn\nzp3s7Ozdu3cvWbIk96sqarV6yZIle/bsyc7O5lIsAADQCPaKCp2lpaWITJgwYezYsQsWLHjn\nnXdEJCoq6tq1a+PHj58xY0apUqW0nREAACgBO3aFzsLColGjRmlpaefPnw8ICDA3Nzc3Nw8I\nCDh//nxaWpqrq6u5ubm2MwIAACVgx64oTJgwwdfXt3nz5oGBgbmDmzdvXrhw4bp167QYDAAA\nKAnFrij06NHj/PnzPXv2bNGiRbNmzUQkIiLi6NGj06ZN+/DDD7WdDgAAKASXYovI+PHjo6Oj\nmzdvfvr06dOnTzdv3jw6Onr8+PHazgUAAJSDHbui4+zs7OzsrO0UAABAsdixAwAAUAiKHQAA\ngEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ\n7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABAISh2AAAACmGk7QB6wNjYWERMTEy0HQQA\nAOiKnHqga1RqtVrbGfTAqVOnMjMztZ1C7925c6dDhw6zZ8+uWLGitrMo3PHjx9euXfuvf/1L\n20GUb/Xq1SkpKSNGjNB2EOUbP368p6dn27ZttR1E4VJSUoYPHx4SEuLg4KDtLDrNyMioYcOG\n2k7xHBQ7FJ0bN25UqlTp7NmzderU0XYWhduwYcPo0aNv3Lih7SDKFxAQcOfOnZCQEG0HUb4G\nDRp88sknAQEB2g6icHfu3Clfvnx8fHyDBg20nQVvg8/YAQAAKATFDgAAQCEodgAAAApBsQMA\nAFAIih0AAIBCUOwAAAAUgmIHAACgEBQ7AAAAhaDYAQAAKATFDkWnRIkSKpVKNx+upzDGxsas\nc9FgqYsMS100+EWt73ikGIrUxYsX7e3ttZ1C+TIzM//666+qVatqO4jyJScnZ2ZmlitXTttB\nlO/atWvly5c3MTHRdhDl4xe1XqPYAQAAKASXYgEAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUO\nAABAISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABA\nISh2AAAACkGxAwAAUAiKHTTM0dFR9QxbW9tnZ164cMHX19fW1tbU1LRWrVpfffVVampq0QfW\na/v27evWrZuNjY2JiUmVKlW6du164MCBfHNY54JYu3bts///nCsrKyvvZJa6gNRq9ebNmz09\nPe3s7MzMzOzt7Xv27BkeHv7sTJa64H766afmzZtbWlqWLFnSxcVlwYIFmZmZz05jqfWOSq1W\nazsDFMXR0fHcuXP9+/fPO2hlZfX999/nHUlISPDw8EhOTu7UqZO9vf3hw4ejo6Pd3NzCwsLM\nzMyKNrK+mjBhwsyZM01MTNzc3GxsbP7++++4uLhhw4ZNmzYtdw7rXEDh4eFLly7NN/if//wn\nMjKydevWYWFhuYMsdcEFBAQsWbLEysqqc+fO5cqVS0pK2rVrl1qtXrVqlZ+fX+40lrrgBg4c\n+NNPP5UtW7Zjx47m5uZhYWHnz5/v1q3bpk2bDAz+t+PDUuslNaBRderUMTExeeW0pk2bisiq\nVaty/piVldWnTx8R+eabbwo3n1KsXLlSRJo3b37t2rXcwaysrDt37uSdxjoXho4dO4rIhg0b\n8g6y1AV04cIFEbG2tr5+/Xru4JYtW0SkSpUqeWey1AW0bds2EalWrdqNGzdyRp4+ffr++++L\nyIoVK/LOZKn1EcUOGvY6xe7kyZMi4uLiknfw2rVrBgYGdnZ22dnZhRlQCdLS0mxtbc3NzW/e\nvPmSaaxzYfjzzz8NDAzKly+flpaWO8hSF9zevXtF5P333887mJWVZWRkZGZmljvCUhfcwIED\nRWTRokV5B0+dOiUirq6uuSMstZ7iM3bQvOzs7BkzZgwePHjEiBHLli27d+9evgk5F7Bytj1y\nVa5c2dnZ+dq1a0lJSUWXVT+FhYXdvHmzW7duVlZWISEhkyZNmjFjxr59+9T//GQF61wYli1b\nlp2dPXDgQGNj49xBlrrgHB0dDQ0No6Kibt68mTu4ffv2zMzM9u3b546w1AWXs8IODg55B2vW\nrCkiMTEx9+/fzxlhqfUUxQ6al5GRMXHixJUrVy5evNjf379atWrr16/POyExMVFE6tSpk++F\ntWvXFhF+X7xSVFSUiJQrV87Z2bl3797Tpk2bOHGil5dXixYtbt26lTuNdda4zMzMlStXqlSq\nIUOG5B1nqQuucuXKU6ZM+fvvv+vWrTtgwIDRo0d36tTJ29v7gw8+WL58ee40lrrgrK2tReTS\npUt5B3P/mLPCwlLrLYodNMzPz2/Pnj03btxITU1NSEgYMWJEampq//79Dx8+nDsnOTlZRKys\nrPK9tnTp0iLy4MGDogysj27fvi0iixcvNjAw2L9/f0pKSlxcXNu2bcPDw3v37p07jXXWuN9/\n//3mzZuenp452xu5WGqNmDhx4rp167Kzs9esWbNgwYLQ0FAHBwdfX9+cIpKDpS64Tp06icj8\n+fNzL6dkZmZOnjw5579zd+xYaj1FsYOGTZgwwcvLy9bW1szMrH79+osWLZowYUJWVta33377\nytfmXElUqVSFH1O/5dxlQ6VSbdmypVWrVhYWFk5OTps3b65UqdKBAwdOnDjx8pezzm8t5xuy\n/v7+rzmfpX4jU6ZM8fX1HTZs2KVLlx4/fnzy5Mlq1ar17dv3yy+/fOVrWerX16NHj86dO1+4\ncKFevXpDhw4dNWqUi4vL9u3bc/65Ymho+PKXs9Q6jmKHQjd48GARiYyMzB3J+Sdgzj8H83rR\nPxCRT5kyZUTE0dHR0dExd9Dc3Lxt27YiklvsWGfNunjx4t69e21sbLp27ZrvEEtdcLt37w4K\nCurdu/esWbOqV69esmTJRo0abdmypUqVKrNnz758+XLONJa64AwMDH777bf58+dXrFhxzZo1\nK1assLOzO3ToUNmyZUWkQoUKOdNYaj1FsUOhy9m3T0tLyx3J+dBG7ic5cp07d07++wEOvETO\nAuYsbF45I0+fPs07jXXWlGXLlqnV6kGDBpUoUSLfIZa64EJDQ0WkdevWeQfNzMzc3NyysrJi\nY2NzRlhqjTAyMho9enRMTMyTJ09SUlJ27tzp6OgYGxubc6UlZw5Lracodih0Bw8elH9+A6tN\nmzYisnPnzrzT/vrrr1OnTlWuXJnfF6/k6empUqnOnj2bkZGRdzw+Pl5EatSokfNH1lmDMjIy\nVq1a9ezXJnKw1AWXnp4u//38aF453wcyMTHJ+SNLXUiWLVuWnp7eq1ev3H+3sNT6Sou3WoHy\nREZGnjp1Ku9IVFRUpUqVRGTu3Ll5x3Pue7l69eqcP2ZlZfn6+gr3vXxt3bt3F5Gvv/46dyTn\npqPW1taPHj3KHWSdNSUkJERE2rdv/6IJLHUB/fzzzyJia2t79erV3MGtW7eqVKqSJUs+ePAg\nd5ClLrjExMS8N6LbvHmzmZmZhYXFhQsX8k5jqfURxQ6aNGfOHBFxcHDw8vLq3r27q6trzgds\nu3Tpkp6enndmfHy8lZWVgYFB165dR40a1bhxYxFp1qxZamqqtsLrl+vXr1evXl1EmjdvHhAQ\n0KlTJwMDgxIlSmzZsiXvNNZZU3J2L3777bcXTWCpCygzMzPnOqy5ubmPj8+nn36a85lREfnh\nhx/yzmSpC65x48Z2dnbt27fv0aNHzrXXkiVL7ty5M980llofUeygSdHR0UOGDHFycipbtqyR\nkZG1tXXbtm3XrFnz3HuUnz9/vk+fPuXLlzc2Nra3t//yyy/zbjXhlf7++++RI0dWq1atRIkS\n5cqV8/b2joqKenYa61xwSUlJKpWqYsWKGRkZL5nGUhdQWlra/PnzmzZtamFhYWhoWL58+c6d\nO+fceTsflrqAFi1a5ObmVqZMGWNj4+rVq/v7+1+6dOm5M1lqvaNS//NW9QAAANBTfHkCAABA\nISh2AAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABAISh2\nAAAACkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABAISh2AAAA\nCkGxAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABAISh2AAAACkGx\nAwAAUAiKHQAAgEJQ7AAAABSCYgcAAKAQFDsAAACFoNgBAAAoBMUOAABAISh2AAAACkGxAwAA\nUAiKHQAAgEJQ7ADgZbp166ZSqRYtWpR3cNKkSSqV6uOPP9ZWKgB4LpVardZ2BgDQXffu3XN1\ndb1161Z4eLirq6uI7Nu3r127do6OjlFRUSVLltR2QAD4H4odALzCsWPH3nvvvRo1akRHR6em\npjZs2DA5OTkqKqp+/frajgYA/8ClWAB4BXd392+++ebcuXP+/v79+vW7efPmwoULaXUAdBA7\ndgDwamq1umPHjrt27RKRPn36rFu3TtuJAOA52LEDgFdTqVTe3t45/z1q1CjthgGAF2HHDgBe\n7dy5c40aNSpRokRycnL9+vUjIyNNTU21HQoA8mPHDgBeIS0tzcfH5/Hjxxs2bJgwYUJ8fDyb\ndgB0E8UOAF5h7NixMTExn3/+ebt27aZMmdKiRYulS5f+8ssv2s4FAPlxKRYAXmbLli3e3t7N\nmjU7cuSIkZGRiFy9etXFxSUzMzMmJsbe3l7bAQHgfyh2APBCV65ccXFxyc7OjomJqVGjRu74\n77//3q1bt3feeefIkSPGxsZaTAgAeVHsAAAAFILP2AEAACgExQ4AAEAhKHYAAAAKQbEDAABQ\nCIodAACAQlDsAAAAFIJiBwAAoBAUOwAAAIWg2AEAACgExQ4AAEAhKHYAAAAKQbEDAABQCIod\nAACAQlDsAAAAFIJiBwAAoBAUOwAAAIWg2AEAACgExQ4AAEAhKHYAAAAKQbEDAABQCIodAACA\nQlDsAAAAFIJiBwAAoBAUOwAAAIWg2AEAACgExQ4AAEAhKHYAAAAKQbEDAABQCIodAACAQlDs\nAAAAFOL/AOS5+hL2hcP0AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit.lm = lm(y ~ x + x2, data=data)\n",
    "plot(data$x, data$y, xlab='x', ylab='y') # plot data\n",
    "lines(data$x, fitted(fit.lm), col=2) # plot fitted curve\n",
    "#round(summary(fit.lm)$r.squared, 3)\n",
    "print(paste(\"R^2 =\",round(summary(fit.lm)$r.squared, 3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This new model adjust better to our data than the previous one. And we may conclude that a quadratic effect exists in the phenomenon we are trying to observe.\n",
    "\n",
    "With this simple example we have demonstrated that it is fairly simple to use R for simple task usually done in **Microsoft Excel** or similar programs. We also illustrated the power of sharing not only a pdf of the class notes, but a file that contains the information and all the necessary code in order to be checked and validate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### some publications are already available in this format\n",
    "\n",
    "https://github.com/ipython/ipython/wiki/A-gallery-of-interesting-IPython-Notebooks#reproducible-academic-publications\n",
    "\n",
    "http://localhost:8888/notebooks/jupyterNotebooks/LOSC_Event_tutorial.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Homeworks**\n",
    "\n",
    "please to check and do at least one of the tutorial listed above!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**end of document**"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}