{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Decision tree and random forest from scratch\n", "\n", "## Decision tree" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* A decision tree is hierarchical series of questions that will lead to different outcomes depending on the result of the questions\n", "\n", "![tree](Fig/tree2.svg)\n", "\n", "\n", "* In machine learning, the \"optimal\" questions are derived from a traning data set by recursively splitting the dataset into relative \"homogeneous\" subsets\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "using PyPlot\n", "using Random\n", "using Statistics\n", "using DelimitedFiles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* We use the example dataset from to classify Bank notes into genuine and forged bank notes available at http://archive.ics.uci.edu/ml/datasets/banknote+authentication\n", "* First download the datafile (if necessary) " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "fname = \"data_banknote_authentication.txt\"\n", "\n", "if !isfile(fname)\n", " download(\"http://archive.ics.uci.edu/ml/machine-learning-databases/00267/data_banknote_authentication.txt\",fname)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's have a quite look at the first 3 rows" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Array{String,1}:\n", " \"3.6216,8.6661,-2.8073,-0.44699,0\"\n", " \"4.5459,8.1674,-2.4586,-1.4621,0\" \n", " \"3.866,-2.6383,1.9242,0.10645,0\" " ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "readlines(fname)[1:3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is no header line and columns are separated by a comma" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "data = readdlm(fname,',');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The meaning of the columns:\n", "\n", "1. variance of Wavelet Transformed image (continuous)\n", "2. skewness of Wavelet Transformed image (continuous)\n", "3. curtosis of Wavelet Transformed image (continuous)\n", "4. entropy of image (continuous)\n", "5. class (integer)\n", "\n", "\n", "Apparently, some of the columns have been normalized.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* For the $i$th sample, $\\mathbf x_i$ (`x[i,:]`) are the features and $y_i$ (`y[i]`) are the labels\n", "* We split data into training and evaluation dataset\n", "* `frac` denotes the fraction of the evaluation data set" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "length(y) = 1228\n", "sum(y .== 0) = 679\n", "sum(y .== 1) = 549\n", "length(yeval) = 144\n" ] }, { "data": { "text/plain": [ "144" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Random.seed!(1234)\n", "\n", "frac = 0.1\n", "selecteval = rand(size(data,1)) .< frac\n", "x = data[.!selecteval,1:4]\n", "y = data[.!selecteval,5]\n", "@show length(y)\n", "@show sum(y .== 0)\n", "@show sum(y .== 1)\n", "\n", "xeval = data[selecteval,1:4]\n", "yeval = data[selecteval,5]\n", "@show length(yeval)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's have a look at the dataset" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter(x[:,1],x[:,2],10,y)\n", "xlabel(\"variance of wavelet transformed image (feature 1)\")\n", "ylabel(\"skewness of wavelet transformed image (feature 2)\")\n", "title(\"Genuine or forged banknotes\")\n", "colorbar();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a test split the data according to feature 1 accoring the threshold equal to first sample" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.6216" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ifeature = 1\n", "threshold = x[1,ifeature]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`splitflag` is true for the elements belong to subset 1 and false for elements belonging to subset 2" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "splitflag = x[:,ifeature] .< threshold;" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1015, 213)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(splitflag), sum(.!splitflag)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* A perfect question, whould split our dataset into two subsets where all labels in subset 1 would be 0 and all labels in subset 2 would 1. This would result in a perfectly homogenous or pure subset.\n", "* In CART (Classification and Regression Trees), we would use the Gini impurity index to quantify the degree of homegenity in classification problems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gini impurity index\n", "\n", "* We mesure the heterogenity within the two subsets (where splitflag is true or false) using the Gini index for each of these subsets\n", "\n", "* Gini impurity is a measure of how often a randomly chosen element from the set would be incorrectly labeled if it was randomly labeled according to the distribution of labels\n", "* So this mean:\n", " * choose a random element form the set\n", " * choose a random label from the set\n", " * the Gini index is the probability that we choose the __incorrect__ label for the element \n", "\n", "* What is the probablity to pick a correct label = probaility to pick an element with the label 1 *and* a label 1 *or* to pick an element with the label 2 *and* a label 2 ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\begin{eqnarray}\n", "P(\\mathrm{pick\\ a\\ correct\\ label}) &=&\n", "P(\\mathrm{pick\\ an\\ element\\ with\\ the\\ label\\ 1\\ and\\ pick\\ a\\ label\\ 1}) \\\\\n", "&& + P(\\mathrm{pick\\ an\\ element\\ with\\ the\\ label\\ 2\\ and\\ pick\\ a\\ label\\ 2}) \\\\\n", "&& + P(\\mathrm{pick\\ an\\ element\\ with\\ the\\ label\\ 3\\ and\\ pick\\ a\\ label\\ 3}) \\\\\n", "&& +... \\\\\n", "&=&\n", "P(\\mathrm{pick\\ an\\ element\\ with\\ the\\ label\\ 1})\\ \\cdot\\ {P(\\mathrm{pick\\ a\\ label\\ 1})} \\\\\n", "&&\\ +\\ P(\\mathrm{pick\\ an\\ element\\ with\\ the\\ label\\ 2})\\ \\cdot\\ {P(\\mathrm{pick\\ a\\ label\\ 2})} \\\\\n", "&& + ... \\\\\\ \n", "&=& \\sum_i p_i^2\n", "\\end{eqnarray}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where $p_i$ is the probability to pick an element with the label $i$ which is infact equal to the probability to pick a label $i$.\n", "\n", "The Gini index is the probability to pick an *incorrect* label, therefore $1 - P(\\mathrm{pick\\ a\\ correct\\ label})$:\n", "\n", "$$\n", "I_g(p_1, p_2, \\dots) = 1 - \\sum_i p_i^2\n", "$$\n", "\n", "The probability to pick an element with the label $i$, the probability to pick a label $i$ is just the fraction of all elements with the label i.\n", "\n", "$$\n", "p_i = \\frac{\\mathrm{Number\\ all\\ elements\\ with\\ label\\ }i}{\\mathrm{Number\\ all\\ elements}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "probability = [0.459113, 0.540887]\n" ] }, { "data": { "text/plain": [ "0.4966565556067848" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_subset = y[splitflag];\n", "classes = [0.,1.]\n", "probability = zeros(length(classes))\n", "for i = 1:length(classes)\n", " probability[i] = sum(y_subset .== classes[i])/length(y_subset)\n", "end\n", "@show probability\n", "gini = 1 - sum(probability.^2)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "giniimpurity (generic function with 1 method)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function giniimpurity(y_subset,classes)\n", " gini_index = 1.\n", " probability = zeros(length(classes))\n", "\n", " for i = 1:length(classes)\n", " probability[i] = sum(y_subset .== classes[i])/length(y_subset)\n", " end\n", " gini = 1 - sum(probability.^2) \n", " return gini\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a completetly homogenous dataset the impurity is zero:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "giniimpurity([1,1,1,1,1,1],classes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If there are as many zeros than ones, the probability to pick a random incorrect label is 0.5:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "giniimpurity([1,1,1,0,0,0],classes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We chose a threshold value (more or less) at random, so it is no suprising that it has a very bad Gini impurity index" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4966565556067848" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "giniimpurity(y[splitflag],classes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The average Gini impurity is the mean Gini impurity of each class weighted by the total fraction of each class " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4105101009290607" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N = length(y)\n", "N1 = sum(splitflag)\n", "N2 = length(y)-N1\n", "giniimpurity(y[splitflag],classes)*N1/N + giniimpurity(y[.!splitflag],classes)*N2/N" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Average Gini index is minimized" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "fitness (generic function with 1 method)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function fitness(x,y,classes,ifeature,threshold)\n", " splitflag = x[:,ifeature] .< threshold;\n", " \n", " N = length(y)\n", " N1 = sum(splitflag)\n", " N2 = length(y)-N1\n", " return giniimpurity(y[splitflag],classes)*N1/N + giniimpurity(y[.!splitflag],classes)*N2/N \n", "end" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4105101009290607" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fitness(x,y,classes,ifeature,threshold)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "thresholds = sort(x[:,ifeature])\n", "\n", "fitness1 = [fitness(x,y,classes,ifeature,threshold) for threshold in thresholds];" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Average Gini impurity index for different values of the threshold" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(thresholds,fitness1)\n", "xlabel(\"thresholds\")\n", "ylabel(\"Average Gini impurity\");\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As there are only two choises and since the datasets is relatively balanced (there are as many fakes as non-fakes), it is clear that the average impurity tends to 0.5 for really bad questions" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "bestthreshold (generic function with 1 method)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function bestthreshold(x,y,classes,ifeature)\n", " lowestavgGiniIndex = Inf\n", " threshold = 0.\n", " for i = 1:length(y)\n", " avgGiniIndex = fitness(x,y,classes,ifeature,x[i,ifeature])\n", " if avgGiniIndex < lowestavgGiniIndex\n", " # found a better threshold\n", " threshold = x[i,ifeature]\n", " lowestavgGiniIndex = avgGiniIndex\n", " end\n", " \n", " end\n", " return threshold,lowestavgGiniIndex\n", "end" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.32444, 0.24967320619032662)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "threshold,lowestavgGiniIndex = bestthreshold(x,y,classes,ifeature)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal threshold value for feature 1" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(thresholds,fitness1)\n", "plot([threshold],[lowestavgGiniIndex],\"ro\",label=\"optimal threshold\")\n", "xlabel(\"thresholds\")\n", "ylabel(\"Average Gini impurity\")\n", "legend();" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ifeature = 1\n", "threshold,lowestavgGiniIndex = bestthreshold(x,y,classes,ifeature)\n", "hist = PyPlot.plt[:hist];\n", "hist(x[y .== 0,ifeature],histtype = \"stepfilled\",alpha = 0.3, label = \"class y = 0\")\n", "hist(x[y .== 1,ifeature],histtype = \"stepfilled\",alpha = 0.3, label = \"class y = 1\")\n", "axvline(threshold,color=\"r\",label = \"optimal threshold\")\n", "xlabel(\"feature $(ifeature)\")\n", "ylabel(\"frequency\")\n", "legend(loc = \"upper left\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Among all features, determine which ones lead to the lowest average Gini impurity" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4-element Array{Tuple{Float64,Float64},1}:\n", " (0.32444, 0.24967320619032662)\n", " (5.1815, 0.37414357806062604) \n", " (8.7086, 0.4479619590280043) \n", " (0.98963, 0.49124709514298964)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[bestthreshold(x,y,classes,ifeature) for ifeature = 1:size(x,2)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed the best split was obtained for feature 1" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 0.32444, 0.24967320619032662)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function bestfeature(x,y,classes)\n", " ifeature = 0\n", " lowestavgGiniIndex = Inf\n", " threshold = 0.\n", " \n", " for j = 1:size(x,2)\n", " thresholdj,avgGiniIndex = bestthreshold(x,y,classes,j)\n", " if avgGiniIndex < lowestavgGiniIndex\n", " # found a better feature\n", " threshold = thresholdj\n", " lowestavgGiniIndex = avgGiniIndex\n", " ifeature = j\n", " end\n", " end\n", " return ifeature,threshold,lowestavgGiniIndex\n", "end\n", "\n", "ifeature,threshold,lowestavgGiniIndex = bestfeature(x,y,classes)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# from https://github.com/JuliaStats/StatsBase.jl\n", "# StatsBase.jl is licensed under the MIT License\n", "\n", "function mode(a::AbstractArray{T}) where T\n", " isempty(a) && error(\"mode: input array cannot be empty.\")\n", " cnts = Dict{T,Int}()\n", " # first element\n", " mc = 1\n", " mv = a[1]\n", " cnts[mv] = 1\n", " # find the mode along with table construction\n", " for i = 2 : length(a)\n", " @inbounds x = a[i]\n", " if haskey(cnts, x)\n", " c = (cnts[x] += 1)\n", " if c > mc\n", " mc = c\n", " mv = x\n", " end\n", " else\n", " cnts[x] = 1\n", " # in this case: c = 1, and thus c > mc won't happen\n", " end\n", " end\n", " return mv\n", "end\n", "\n", "mode([1,2,3,2])" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "mutable struct Decision\n", " value :: Float64\n", "end\n", "\n", "mutable struct Question\n", " ifeature :: Int\n", " threshold :: Float64\n", " next :: Vector{Union{Decision,Question}}\n", "end" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "split (generic function with 2 methods)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function split(x,y,classes,minsize,maxdepth,depth = 0) \n", " # return early if the tree receases maximim depth or the \n", " # minimum size\n", " if (depth == maxdepth) || (length(y) <= minsize)\n", " return Decision(mode(y))\n", " end\n", " \n", " # return early if all elements are the same\n", " if length(Set(y)) == 1\n", " return Decision(y[1])\n", " end\n", " \n", " \n", " ifeature,threshold,lowestavgGiniIndex = bestfeature(x,y,classes)\n", " #@show ifeature\n", " splitflag = x[:,ifeature] .< threshold;\n", " \n", " next = [\n", " split(x[splitflag,:],y[splitflag],classes,minsize,maxdepth,depth+1),\n", " split(x[.!splitflag,:],y[.!splitflag],classes,minsize,maxdepth,depth+1) \n", " ]\n", " \n", " return Question(ifeature,threshold,next)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some functions to display a decision tree" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "function Base.show(io::IO,d::Decision) \n", " indent = get(io, :indent, 0)\n", " printstyled(io,\" \" ^ indent,\"Decision: $(d.value)\\n\",color=:green)\n", "end\n", "function Base.show(io::IO,q::Question)\n", " indent = get(io, :indent, 0)\n", " blank = \" \" ^ indent\n", " println(io,blank,\"if feature $(q.ifeature) < $(q.threshold)\")\n", " \n", " io2 = IOContext(io,:indent => indent+2)\n", " show(io2,q.next[1])\n", " println(io,blank,\"else\")\n", " show(io2,q.next[2])\n", " println(io,blank,\"end\")\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Build a decision tree with a maximum depth of 30" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "if feature 1 < 0.32444\n", " if feature 2 < 7.8695\n", "\u001b[32m Decision: 1.0\u001b[39m\n", " else\n", "\u001b[32m Decision: 0.0\u001b[39m\n", " end\n", "else\n", " if feature 3 < -4.3839\n", "\u001b[32m Decision: 1.0\u001b[39m\n", " else\n", "\u001b[32m Decision: 0.0\u001b[39m\n", " end\n", "end\n" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "maxdepth = 2\n", "minsize = 1\n", "tree = split(x,y,classes,minsize,maxdepth)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "predict (generic function with 2 methods)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predict(d::Decision,xi) = d.value\n", "\n", "function predict(q::Question,xi)\n", " if xi[q.ifeature] < q.threshold\n", " return predict(q.next[1],xi)\n", " else\n", " return predict(q.next[2],xi)\n", " end\n", "end\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Validate the tree with the independent validation data set" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Percentage of correct predictions (for evaluation dataset): 88.88888888888889 %\n" ] } ], "source": [ "function ncorrect(tree,xeval,yeval)\n", " N = 0\n", " for i in 1:length(yeval)\n", " if predict(tree,xeval[i,:]) == yeval[i]\n", " N = N+1\n", " end\n", " end\n", " return N\n", "end\n", "\n", "percentcorrect = 100. * ncorrect(tree,xeval,yeval)/length(yeval)\n", "println(\"Percentage of correct predictions (for evaluation dataset): $(percentcorrect) %\")\n", "\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "maxdepths = 1:10\n", "minsize = 1\n", "percentcorrect = zeros(length(maxdepths))\n", "for i = 1:length(maxdepths)\n", " tree = split(x,y,classes,minsize,maxdepths[i])\n", " percentcorrect[i] = 100. * ncorrect(tree,xeval,yeval)/length(yeval)\n", "end" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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sGVq3bq19zMrKCsHBwYiNjcXVq1d1nhcUFFTouJORI0fC2NhY+7MQAtu3b0evXr0ghND5vXTp0gUpKSm4cOECgKLtI8UVHByscxY6evRomJiYYPfu3TrLubu7o0uXLjptO3bsgFqtRmBgoE7+atWqoW7dutrtqtmG77//vk4v1pAhQwrtzdBITEzE0aNHMWzYMNSqVUvnseK+d0O369ChQ3Vya/62NH9PmvcQFhaGzMzMYmV61oEDB5Cbm4uJEyfqjNEaOXIkbGxs9PZ5hUKBoUOH6rTt378fycnJGDRokM62MTY2RvPmzXX+5gYMGIDz589re6QBYPPmzVAoFOjdu7e27dl9OyMjA48ePULLli0hhMDFixdf+X0//xp5eXl4/Pgx6tSpAzs7O+3fg6F2796NatWq6YyLNDU1xfjx45Geno4jR47oLD9gwACdY9jz2/tFr/PGG2+gWbNm2jYnJye88847essW5Rj7IsbGxtp9Uq1WIykpCfn5+WjSpInO78nOzg4ZGRnYv39/oesy9HOsrOBXUcX0/fffw9PTEyYmJqhatSq8vLx0DjRRUVG4fPlyoV3emoGBGu7u7nrLREdHw8vLS6c4eF5UVBRSUlLg7OxcpNd5/gMAAOzt7fHkyZNCX+NZ//zzDz777DP89ddfSE1N1XksJSUFABAXFwcAeldymJiY6F2lEBUVhWvXrhX59/Qszetovvp4lre3N44fP/7iN1OAxMREpKamon79+i9cLi4uDs2bN9dr13R5x8XF6ayjoO1b2GOJiYlITk7GypUrC73EV/N7Kco+Ulx169bV+dnKygrVq1fXu4y2oPcWFRUFIYTeOjQ0BZNmGz6/nKmpKTw8PF6YT/Nh8rJtZQhDt+vzf0+aDz3N35O7uzs++ugjfPvtt/jpp5/g7++PgIAAvPvuuy8t3ArLB+jv83K5HB4eHtrHNVxcXPQGzEZFRQGA9uTheTY2Ntr/f/vtt/HRRx9h8+bN+PTTTyGEwNatW9GtWzed5W7fvo0ZM2bg999/1zuWaI4LryorKwvz58/H2rVrER8fDyHEK79GXFwc6tatqzeQ/9nt/ayXbe8XvU5B+1VBx66iHGNfZv369fjmm29w/fp15OXladuf/VsdM2YMtmzZgm7dusHFxQWdO3dGYGAgunbtql3G0M+xsoKFTTE1a9aswDN6DbVajTfffBNTpkwp8HFPT0+dn4t7FYlarYazszN++umnAh9/fod8tmfgWc8eJAqTnJyMtm3bwsbGBl9++SWUSiXMzMxw4cIFfPLJJ1Cr1cXK36BBA3z77bcFPv6yMRblxYu27/OPaX6P7777LoKCggp8jqTfXz+noPemVqshk8mwZ8+eAvc5zXiA8q4of0/ffPMNhgwZgp07d2Lfvn0YP3485s+fj9OnT+uMNysNhW0b4Ok4m2rVquk9/myRXKNGDfj7+2PLli349NNPcfr0ady+fVs7JgN4Os7rzTffRFJSEj755BN4e3vD0tIS8fHxGDJkyAuPC4X1rKlUKr22cePGYe3atZg4cSJatGgBW1tbyGQyDBw4sFjHnuJ4leNnUZTEMXbjxo0YMmQI3nrrLUyePBnOzs4wNjbG/PnzdXrenJ2d8ffffyMsLAx79uzBnj17sHbtWgwePBjr168HYPjnWFnBwqaUKJVKpKenv9KcKUqlEmfOnEFeXl6hA9OUSiUOHDiAVq1aldgltoUdbA4fPozHjx9jx44daNOmjbY9JiZGZ7natWsDeDpQuX379tr2/Px8xMbG6nwoK5VKXLp0CR07djT46wPN60RGRuqdfUZGRmofN4STkxNsbGwQERHx0teOjIzUa9d0FRfntZ/NYG1tDZVK9dL9pyj7SHG/lomKitLZfunp6bh//z66d+/+0ucqlUoIIeDu7v7Cg5/m9xQVFaWzDfPy8hATE4OGDRsW+lxNj87LtpUh77+0tmuDBg3QoEEDfPbZZzh58iRatWqFFStWYM6cOQat59l9/tkerdzcXMTExBTpeKMZOO/s7Fyk5QcMGIAxY8YgMjISmzdvhoWFBXr16qV9/MqVK7hx4wbWr1+PwYMHa9tf9BWHhqbH4/nJE5/vKQGAbdu2ISgoCN988422LTs7W++5hm7vy5cvQ61W6/TalMTf8fOvo+kpe9bz+1pRj7FA4e9z27Zt8PDwwI4dO3SW+eKLL/SWlcvl6NWrF3r16gW1Wo0xY8bgxx9/xOeff446deoU+XNMytmkC8IxNqUkMDAQp06dQlhYmN5jycnJyM/Pf+k6+vXrh0ePHuG7777Te0xzhhAYGAiVSoXZs2frLZOfn1+s2VY186g8/1zN2cqzZye5ubn44YcfdJZr0qQJHB0dsWrVKp33+dNPP+l12QYGBiI+Ph6rVq3Sy5GVlaW9SqggTZo0gbOzM1asWIGcnBxt+549e3Dt2jX06NHjZW9Vj5GREd566y388ccfOHfunN7jmvfevXt3nD17FqdOndI+lpGRgZUrV8LNzQ2+vr4Gv7aGsbEx+vXrh+3btxf4oZ2YmKj9/6LsI5p5SwzdF1auXKnTjb18+XLk5+ejW7duL31u3759YWxsjFmzZumdzQoh8PjxYwBPt6GTkxNWrFiB3Nxc7TLr1q17aV4nJye0adMGa9aswe3bt/VeQ6Ow/bkgJb1dU1NT9f7WGzRoACMjI519tqg6deoEuVyOkJAQnfe4evVqpKSkFGmf79KlC2xsbDBv3jyd7avx7P4FPN3HjI2NsWnTJmzduhU9e/bUmWupoOOCEAJLly59aRYbGxtUqVJFb6zG88cUzes8vy8tW7ZMr3fH0O394MEDbN68WduWn5+PZcuWwcrKCm3btn3pOoqie/fuOH36NM6ePattS0xM1OtpL+oxFnj6Pgv6aqqgdZw5c0Znnwag/RvUMDIy0p50avbNon6OFfcYU1rYY1NKJk+ejN9//x09e/bUXk6dkZGBK1euYNu2bYiNjdVeelqYwYMHY8OGDfjoo49w9uxZ+Pv7IyMjAwcOHMCYMWPQu3dvtG3bFqNGjcL8+fPx999/o3PnzjA1NUVUVBS2bt2KpUuXon///gZlb9SoEYyNjbFw4UKkpKRAoVCgQ4cOaNmyJezt7REUFITx48dDJpMhNDRU72Ajl8sxc+ZMjBs3Dh06dEBgYCBiY2Oxbt06KJVKner+vffew5YtW/D+++/j0KFDaNWqFVQqFa5fv44tW7YgLCys0K/8TE1NsXDhQgwdOhRt27bFoEGDtJd7u7m54cMPPzTofWvMmzcP+/btQ9u2bbWXoN+/fx9bt27F8ePHYWdnh6lTp2LTpk3o1q0bxo8fDwcHB6xfvx4xMTHYvn37K89mu2DBAhw6dAjNmzfHyJEj4evri6SkJFy4cAEHDhxAUlISgKLtI+bm5vD19cXmzZvh6ekJBwcH1K9f/6VjU3Jzc9GxY0cEBgYiMjISP/zwA1q3bo2AgICX5lcqlZgzZw6mTZumvdTf2toaMTEx+PXXXxEcHIxJkybB1NQUc+bMwahRo9ChQwcMGDAAMTExWLt27UvH2ABASEgIWrdujcaNGyM4OBju7u6IjY3Frl278PfffwMA/Pz8ADy9RHbgwIEwNTVFr169CpwIsaS3619//YWxY8fi7bffhqenJ/Lz8xEaGqotXg3l5OSEadOmYdasWejatSsCAgK026Zp06Z49913X7oOGxsbLF++HO+99x4aN26MgQMHwsnJCbdv38auXbvQqlUrnULZ2dkZ7du3x7fffou0tDQMGDBAZ33e3t5QKpWYNGkS4uPjYWNjg+3btxd53N6IESOwYMECjBgxAk2aNMHRo0dx48YNveV69uyJ0NBQ2NrawtfXF6dOncKBAwe0U2xoFHb8KmgcYnBwMH788UcMGTIE58+fh5ubG7Zt24YTJ05gyZIlsLa2LtJ7eJkpU6YgNDQUXbt2xYQJE7SXe2t6jDSKeowFnu7XmzdvxkcffYSmTZvCysoKvXr1Qs+ePbFjxw706dMHPXr0QExMDFasWAFfX1+kp6drnz9ixAgkJSWhQ4cOqFmzJuLi4rBs2TI0atRIO8aoqJ9jxT3GlJp/7fqrCsKQy4bT0tLEtGnTRJ06dYRcLhdVqlQRLVu2FF9//bX2MtpnJ34qSGZmppg+fbpwd3cXpqamolq1aqJ///4iOjpaZ7mVK1cKPz8/YW5uLqytrUWDBg3ElClTxL1797TLaCZTe15Bk1atWrVKeHh4CGNjY51LJ0+cOCHeeOMNYW5uLmrUqCGmTJkiwsLCCry8MiQkRNSuXVsoFArRrFkzceLECeHn5ye6du2qs1xubq5YuHChqFevnlAoFMLe3l74+fmJWbNmiZSUlJf+njdv3ixef/11oVAohIODg94EfUIYtt2EECIuLk4MHjxYODk5CYVCITw8PMQHH3xQ4AR9dnZ2wszMTDRr1qzQidwKutz3ZZkePnwoPvjgA+Hq6qrd9h07dhQrV67UWa4o+8jJkyeFn5+fkMvlBk/QZ29vL6ysrMQ777wjHj9+rLNsYfuUxvbt20Xr1q2FpaWlsLS0FN7e3uKDDz4QkZGROsv98MMPwt3dXSgUCtGkSRODJuiLiIgQffr00W4HLy8v8fnnn+ssM3v2bOHi4iKMjIyKPEFfcbbr8xlv3bolhg0bJpRKpXZSufbt24sDBw4U+jvTKOhyb43vvvtOeHt7C1NTU1G1alUxevToQifoK8yhQ4dEly5dhK2trTAzMxNKpVIMGTJEnDt3Tm/ZVatWCQDC2tpaZ2oFjatXr4pOnToJKysrUaVKFTFy5Ehx6dIlve31/OXeQjzdf4cPHy5sbW2FtbW1CAwMFAkJCXr76ZMnT8TQoUNFlSpVhJWVlejSpYu4fv16gduwsONXYRP0adYrl8tFgwYN9PaxFx2nX/b3pHH58mXRtm3bl07QV9RjbHp6uvjPf/4j7OzsdCboU6vVYt68edpj7+uvvy7+/PNPERQUpHN5+LZt20Tnzp21E4DWqlVLjBo1Sty/f18nd1E+x4Qw7BhT2mRClNCoJ6KXUKvVcHJyQt++fQv86onKBs2kh+Hh4S8cIE9EVBZxjA2ViuzsbL3u0w0bNiApKalM3CSNiIgqJo6xoVJx+vRpfPjhh3j77bfh6OiICxcuYPXq1ahfvz7efvttqeMREVEFxcKGSoWbmxtcXV0REhKCpKQkODg4YPDgwViwYAHvsEtERKWGY2yIiIiowuAYGyIiIqowWNgQERFRhVHhx9io1Wrcu3cP1tbWZW7aZyIiIiqYEAJpaWmoUaOGQZNjVvjC5t69exXmRopERESVzZ07dwy6YWyFL2w0U2LfuXMHNjY2EqchIiKiokhNTYWrq6vBt7ao8IWN5usnGxsbFjZERETljKHDSDh4mIiIiCoMFjZERERUYbCwISIiogqDhQ0RERFVGCxsiIiIqMJgYUNEREQVBgsbIiIiqjBY2BAREVGFwcKGiIiIKgwWNkRERFRhsLAhIiKiCoOFDREREVUYFf4mmEREBOSr1HiQmi11DKqgrBWmsLUwlToGABY2REQVWnJmLn4+exvrT8biYWqO1HGoghrTTokpXb2ljgGAhQ0RUYUU+ygDa07EYOu5u8jKUwEATIxkMDaSSZyMKiKTMrRfsbAhIqoghBA4F/cE/z12C/uuPoQQT9u9q1ljpL8HejWsAbkJh1ZSxcbChoionMtXqbEn4gH+e+wWLt1N0ba393LCCH8PtFQ6QiYrO2fURKWJhQ0RUTmVmp2HLeF3sPZELOKTswAAchMj9GvsgmGt3FG3qrXECYn+fSxsiIjKmbtPMrHuRCx+Cb+D9Jx8AICjpRzvtaiNd9+ojSpWCokTEkmHhQ0RUTnx951krDp2C3sjHkClfjqApo6zFUa0dsdbr7vAzNRY4oRE0mNhQ0RUhqnUAvuvPsTq47cQHvtE2966ThUM93dH27pOMCpDV6QQSY2FDRFRGZSRk49t5+9izYkYxD3OBACYGssQ0NAFw1u7w7eGjcQJicomFjZERGXIg5RsrD8Vi59OxyE1++n4GVtzU7z7Ri0MbuGGqjZm0gYkKuNY2BARlQH/3EvB6mMx+P3SPeT/b/yMm6MFhrdXg+7vAAAgAElEQVR2Rz+/mrCQ83BNVBT8SyEikohaLXD4RgJWHY3BqVuPte3N3B0worU7OvpU5UzBRAZiYUNE9C/LzlNhx4V4rD5+C9GJGQAAYyMZejSojhH+7nitpp3ECYnKLxY2RET/ksS0HISejsPG03FIysgFAFgrTDCoeS0EtXSDi525xAmJyj9JbxqSlpaGiRMnonbt2jA3N0fLli0RHh6us8y1a9cQEBAAW1tbWFpaomnTprh9+7ZEiYmIDHfjYRqmbLuEVgv+QsjBKCRl5MLFzhyf9/TFyWkd8Gl3HxY1RCVE0h6bESNGICIiAqGhoahRowY2btyITp064erVq3BxcUF0dDRat26N4cOHY9asWbCxscE///wDMzNeFUBEZZsQAsdvPsJ/j8XgyI1EbXsjVzuM9PdAl3pVYWLMG1ISlTSZEJr7v/67srKyYG1tjZ07d6JHjx7adj8/P3Tr1g1z5szBwIEDYWpqitDQ0GK/TmpqKmxtbZGSkgIbG877QESlKydfhd//vofVx2Nw/UEaAMBIBnSpVw0j/N3hV9tB4oRE5UNxP78l67HJz8+HSqXS630xNzfH8ePHoVarsWvXLkyZMgVdunTBxYsX4e7ujmnTpuGtt94qdL05OTnIycnR/pyamlpq74GISONJRi5+OhOH9afikJj29BhkITdGYBNXDGvljlqOFhInJKocJOuxAYCWLVtCLpfj559/RtWqVbFp0yYEBQWhTp06OHLkCKpXrw4LCwvMmTMH7du3x969e/Hpp5/i0KFDaNu2bYHrnDlzJmbNmqXXzh4bIioNtxLTseZEDLadv4vsPDUAoJqNGYa0csOgprVga2EqcUKi8qm4PTaSFjbR0dEYNmwYjh49CmNjYzRu3Bienp44f/48Dh48CBcXFwwaNAg///yz9jkBAQGwtLTEpk2bClxnQT02rq6uLGyIqMQIIXAmJgn/PXYLB68nQHMUrVfDBiP9PdDjteow5fgZoldS7r6KAgClUokjR44gIyMDqampqF69OgYMGAAPDw9UqVIFJiYm8PX11XmOj48Pjh8/Xug6FQoFFApFaUcnokooT6XG7iv38d9jMbgSn6Jt7+TjjOGtPfCGhwNkMk6oRySlMjGPjaWlJSwtLfHkyROEhYVh0aJFkMvlaNq0KSIjI3WWvXHjBmrXri1RUiKqjFKy8vDL2dtYdzIW91OyAQAKEyP096uJYa3doXSykjghEWlIWtiEhYVBCAEvLy/cvHkTkydPhre3N4YOHQoAmDx5MgYMGIA2bdpox9j88ccfOHz4sJSxieglcvPVWHrwBq7El//B+0IIXIh7goxcFQCgipUCQS1q4503asPBUi5xOiJ6nqSFTUpKCqZNm4a7d+/CwcEB/fr1w9y5c2Fq+nSwXZ8+fbBixQrMnz8f48ePh5eXF7Zv347WrVtLGZuIXiAtOw/vbzyPEzcfv3zhcsSrqjWG+7sjoGENmJkaSx2HiAoh6eDhfwPnsSH69ySkZiNobTiu3U+FpdwYk7t4wca8/F8VVMPOHM3dOX6G6N9ULgcPE1HFEZ2YjsGrzyI+OQtVrORYN7QZ6rvYSh2LiCoZFjZE9MrOxz3B8PXhSM7Mg5ujBTYMa84J6YhIEixsiOiV7L/6EOM2XUB2nhoNXe2wJqgJHK045QIRSYOFDREV26aztzH91ytQC6C9lxO+f6cxLOQ8rBCRdHgEIiKDCSGw5EAUlh6MAgAENqmJeX0a8G7VRCQ5FjZEZJB8lRqf74zAprN3AADjO9TBh2968oohIioTWNgQUZFl5aowbtMFHLiWACMZMPut+ninOWcCJ6Kyg4UNERVJUkYuhq8Px8XbyVCYGCFk0OvoUq+a1LGIiHSwsCGil7qTlImgNWdx61EGbM1NsTqoCZq4OUgdi4hIDwsbInqhf+6lYMjacCSm5cDFzhzrhzVFHWdrqWMRERWIhQ0RFerEzUcYFXoe6Tn58K5mjfXDmqGqjZnUsYiICsXChogKtPPveEzaegl5KoE3PBywcnAT2JiV//s+EVHFxsKGiPSsOnoLc3dfAwD0fK06vglsCIUJ72hNRGUfCxsi0lKrBebuvobVx2MAAMNbu2N6dx8YGXGOGiIqH1jYEBEAICdfhY+3XMKfl+8DAKZ398HINh4SpyIiMgwLGyJCanYeRm04j1O3HsPUWIav326I3o1cpI5FRGQwFjZEldzD1GwErTmL6w/SYKUwwY/v+aFVnSpSxyIiKhYWNkSV2M2ENAStCUd8chacrBVYN7Qp6tWwlToWEVGxsbAhqqTOxyVh2LpzSMnKg0cVS6wf1gyuDhZSxyIieiUsbIgqoX3/PMC4TReRk6/G67XssDqoKRws5VLHIiJ6ZSxsiCqZn87E4fPfIqAWQEdvZ3z3n8Ywl3OOGiKqGFjYEFUSQggs3n8DIX/dBAAMbOqKOW/Vh4mxkcTJiIhKDgsbokogX6XGp79ewZZzdwEAEzvVxYSOdSGTceI9IqpYWNgQVXCZufkY+/NF/HU9AUYyYG6fBhjUrJbUsYiISgULG6IK7HF6DoatP4dLd5JhZmqE7wY1RiffqlLHIiIqNSxsiCqo248zEbT2LGIeZcDewhT/DWoKv9r2UsciIipVLGyIKqCI+BQMWRuOR+k5cLEzx4bhzaB0spI6FhFRqWNhQ1TBHItKxPuh55GRq4JPdRusH9oUzjZmUsciIvpXsLAhqkB+vXgXk7deRr5aoFUdR6x41w/WZqZSxyIi+tcYXNhkZWVBCAELi6dTr8fFxeHXX3+Fr68vOnfuXOIBiejlhBD48egtLNhzHQDQu1ENfNW/IeQmnKOGiCoXg496vXv3xoYNGwAAycnJaN68Ob755hv07t0by5cvL/GARPRiarXArD+uaouakf7uWBzYiEUNEVVKBh/5Lly4AH9/fwDAtm3bULVqVcTFxWHDhg0ICQkp8YBEVLjsPBXGbbqIdSdjAQCf9fDB9B6+MDLixHtEVDkZ/FVUZmYmrK2tAQD79u1D3759YWRkhDfeeANxcXElHpCICpaSlYfgDedwJiYJcmMjfB3YEAENa0gdi4hIUgb32NSpUwe//fYb7ty5g7CwMO24moSEBNjY2JR4QCLS9yAlG4ErTuFMTBKsFSZYN6wpixoiIhSjsJkxYwYmTZoENzc3NG/eHC1atADwtPfm9ddfL/GARKQr6mEa+v5wApEP0+BsrcDmUS3QUllF6lhERGWCTAghDH3SgwcPcP/+fTRs2BBGRk9ro7Nnz8LGxgbe3t4lHvJVpKamwtbWFikpKexRonIvPDYJI9afQ0pWHpROllg/rBlq2ltIHYuIqMQV9/O7WPPYVKtWDdWqVdNpa9asWXFWRURFtDfiASb8chE5+Wr41bbHfwc3gb2lXOpYRERlisGFTUZGBhYsWICDBw8iISEBarVa5/Fbt26VWDgieir0VCxm/P4PhADe9K2KZYNeh5mpsdSxiIjKHIMLmxEjRuDIkSN47733UL16dchkvKyUqLQIIfD1vkh8fygaAPCf5rXwZUA9mBhzjhoiooIYXNjs2bMHu3btQqtWrUojDxH9T55KjU93XMHW83cBAB+/6YmxHerwZIKI6AUMLmzs7e3h4OBQGlmI6H8ycvLxwc8XcDgyEcZGMszrUx8DmtaSOhYRUZlncH/27NmzMWPGDGRmZpZGHqJK71F6DgatOo3DkYkwNzXGqsF+LGqIiIrI4B6bb775BtHR0ahatSrc3Nxgaqp75+ALFy6UWDiiyiY1Ow9vrziFmEcZcLCUY82Qpmjkaid1LCKicsPgwuatt94qjRxEBOCHQ9GIeZSBGrZm2DiiOTycrKSORERUrhhc2HzxxRelkYOo0ruTlIk1J2IAALPfqs+ihoioGIo1QR8AnD9/HteuXQMA1KtXj7dTIHpFX4VFIjdfjZZKR3TwdpY6DhFRuWRwYZOQkICBAwfi8OHDsLN7+t1/cnIy2rdvj19++QVOTk4lHpKoovv7TjJ+v3QPMhkwvYcPL+kmIiomg6+KGjduHNLS0vDPP/8gKSkJSUlJiIiIQGpqKsaPH18aGYkqNCEE5vx5FQDQr3FN1KthK3EiIqLyy+Aem7179+LAgQPw8fHRtvn6+uL7779H586dSzQcUWWwJ+IBzsU9gbmpMSZ19pI6DhFRuWZwj41arda7xBsATE1N9e4bRUQvlpOvwoI91wEAwW08UM3WTOJERETlm8GFTYcOHTBhwgTcu3dP2xYfH48PP/wQHTt2LNFwRBVd6Kk43E7KhLO1AqPaekgdh4io3DO4sPnuu++QmpoKNzc3KJVKKJVKuLu7IzU1FcuWLSuNjEQV0pOMXIQcjAIATOrsBQt5sS9SJCKi/zH4SOrq6ooLFy7gwIEDuH79aRe6j48POnXqVOLhiCqykL+ikJqdD+9q1ujnV1PqOEREFYLBPTYAIJPJ8Oabb2LcuHEYN27cKxU1aWlpmDhxImrXrg1zc3O0bNkS4eHhBS77/vvvQyaTYcmSJcV+PaKyIOZRBkJPxQEAPuvhC2MjXt5NRFQSitRjExISguDgYJiZmSEkJOSFyxp6yfeIESMQERGB0NBQ1KhRAxs3bkSnTp1w9epVuLi4aJf79ddfcfr0adSoUcOg9ROVRQv2XEO+WqC9lxNa160idRwiogpDJoQQL1vI3d0d586dg6OjI9zd3QtfmUyGW7duFfnFs7KyYG1tjZ07d6JHjx7adj8/P3Tr1g1z5swB8HRwcvPmzREWFoYePXpg4sSJmDhxYpFeIzU1Fba2tkhJSYGNjU2RsxGVltO3HmPgytMwNpJh7wR/1K1qLXUkIqIyp7if30XqsYmJiSnw/19Vfn4+VCoVzMx0L3E1NzfH8ePHATy9vPy9997D5MmTUa9evZeuMycnBzk5OdqfU1NTSywv0atSqwXm7np6K5JBzVxZ1BARlTCDx9h8+eWXyMzM1GvPysrCl19+adC6rK2t0aJFC8yePRv37t2DSqXCxo0bcerUKdy/fx8AsHDhQpiYmBT5K6758+fD1tZW+8/V1dWgTESlaeeleFyJT4GVwgQTO3lKHYeIqMIxuLCZNWsW0tPT9dozMzMxa9YsgwOEhoZCCAEXFxcoFAqEhIRg0KBBMDIywvnz57F06VKsW7euyPfOmTZtGlJSUrT/7ty5Y3AmotKQnafCV3sjAQBj2itRxUohcSIioorH4MJGCFFgkXHp0iU4ODgYHECpVOLIkSNIT0/HnTt3cPbsWeTl5cHDwwPHjh1DQkICatWqBRMTE5iYmCAuLg4ff/wx3NzcClyfQqGAjY2Nzj+ismD18RjcS8mGi505hrUqfKwaEREVX5HnsbG3t4dMJoNMJoOnp6dOcaNSqZCeno7333+/2EEsLS1haWmJJ0+eICwsDIsWLUK/fv30LiXv0qUL3nvvPQwdOrTYr0X0b0tMy8EPh24CAKZ09YKZqbHEiYiIKqYiFzZLliyBEALDhg3DrFmzYGv7/3cglsvlcHNzQ4sWLQwOEBYWBiEEvLy8cPPmTUyePBne3t4YOnQoTE1N4ejoqLO8qakpqlWrBi8v3iyQyo/FB24gI1eFhjVt0es1TllARFRailzYBAUFAXh66XerVq1gYlIy07+npKRg2rRpuHv3LhwcHNCvXz/MnTu3wBttEpVHkQ/S8MvZ2wCAz3r6woiT8RERlRqDq5OMjAwcPHgQXbp00WkPCwuDWq1Gt27dDFpfYGAgAgMDi7x8bGysQesnktq83degFkC3+tXQ1M3wcWhERFR0Bg8enjp1KlQqlV67EAJTp04tkVBEFcXRG4k4ciMRpsYyTO3mLXUcIqIKz+DCJioqCr6+vnrt3t7euHnzZomEIqoIVGqBebufTsY3uIUbajtaSpyIiKjiM7iwsbW1LfC2CTdv3oSlJQ/cRBpbz93B9QdpsDU3xbgOdaSOQ0RUKRhc2PTu3RsTJ05EdHS0tu3mzZv4+OOPERAQUKLhiMqrjJx8fLP/BgBgfMe6sLOQS5yIiKhyMLiwWbRoESwtLeHt7Q13d3e4u7vDx8cHjo6O+Prrr0sjI1G58+ORaCSm5cDN0QLvvVFb6jhERJWGwVdF2dra4uTJk9i/fz8uXboEc3NzvPbaa2jTpk1p5CMqd+6nZGHlsadf107t5gO5icHnD0REVEzFmoxGJpOhc+fO6Ny5c0nnISr3vgqLRHaeGs3cHNClXlWp4xARVSpFKmxCQkIQHBwMMzMzhISEvHDZot6Fm6giiohPwY4L8QCAz3r6FPnmrUREVDJkQgjxsoXc3d1x7tw5ODo6wt298Jv3yWSyAq+YklJqaipsbW2RkpLCG2JSqRJCYNCq0zh9KwlvNaqBJQNflzoSEVG5VdzP7yL12MTExBT4/0T0/w5cS8DpW0lQmBhhcldOxkdEJAWOaiQqAXkqNeb/bzK+4a3d4WJnLnEiIqLKqUg9Nh999FGRV/jtt98WOwxRefXzmdu49SgDVazkGN1OKXUcIqJKq0iFzcWLF3V+vnDhAvLz8+Hl5QUAuHHjBoyNjeHn51fyCYnKuJSsPCw58HQyvg/f9IS1Ge9MT0QklSIVNocOHdL+/7fffgtra2usX78e9vb2AIAnT55g6NCh8Pf3L52URGXY94du4klmHuo6W2FAE1ep4xARVWpFuirqWS4uLti3bx/q1aun0x4REYHOnTvj3r17JRrwVfGqKCpNd5Iy0fGbI8hVqbF2aFO093KWOhIRUYVQ3M9vgwcPp6amIjExUa89MTERaWlphq6OqFxbsPc6clVq+NetgnaeTlLHISKq9AwubPr06YOhQ4dix44duHv3Lu7evYvt27dj+PDh6Nu3b2lkJCqTzsc9wa7L9yGTAZ9252R8RERlgcG3VFixYgUmTZqE//znP8jLy3u6EhMTDB8+HF999VWJByQqi4QQmLPrKgAg0M8VPtX5NScRUVlg8BgbjYyMDERHRwMAlEolLC0tSzRYSeEYGyoNf1y6h3GbLsJCbozDk9rB2cZM6khERBXKvzbGRuP+/fu4f/8+6tatC0tLSxSzPiIqd7LzVFi49zoA4P22ShY1RERliMGFzePHj9GxY0d4enqie/fuuH//PgBg+PDh+Pjjj0s8IFFZs/5kLO4+yUI1GzOM9PeQOg4RET3D4MLmww8/hKmpKW7fvg0LCwtt+4ABA7B3794SDUdU1iRl5OK7QzcBAJO6eMFcbixxIiIiepbBg4f37duHsLAw1KxZU6e9bt26iIuLK7FgRGXR0gM3kJadj3o1bND3dRep4xAR0XMM7rHJyMjQ6anRSEpKgkKhKJFQRGVRdGI6fjpzGwAwvYcPjIx4eTcRUVljcGHj7++PDRs2aH+WyWRQq9VYtGgR2rdvX6LhiMqS+buvI18t0MnHGS2VVaSOQ0REBTD4q6hFixahY8eOOHfuHHJzczFlyhT8888/SEpKwokTJ0ojI5HkTkY/woFrD2FsJMPUbj5SxyEiokIY3GNTv3593LhxA61bt0bv3r2RkZGBvn374uLFi1AqlaWRkUhSarXA3F3XAADvNq+FOs5WEiciIqLCGNRjk5+fj3nz5mHYsGGYPn16aWUiKlN2XIzHP/dSYW1mggmdPKWOQ0REL2BQj42JiQkWLVqE/Pz80spDVKZk5arwdVgkAGBs+zpwsJRLnIiIiF7E4K+iOnbsiCNHjpRGFqIyZ9WxW3iQmo2a9uYIaukmdRwiInoJgwcPd+vWDVOnTsWVK1fg5+end4+ogICAEgtHJKWE1GysOPL0fmifdPWGmSkn4yMiKusMvgmmkVHhnTwymQwqleqVQ5Uk3gSTimvq9sv4JfwOXq9lhx2jW0Im47w1RET/luJ+fhvcY6NWqw19ClG5c+1+KjafuwMA+KyHD4saIqJyoth39yaqqIQQmLf7GoQAerxWHX61HaSORERERVSswubgwYPo2bMnlEollEolevbsiQMHDpR0NiJJHL6RiGNRjyA3NsLUrt5SxyEiIgMYXNj88MMP6Nq1K6ytrTFhwgRMmDABNjY26N69O77//vvSyEj0r8lXqTHvf5PxDWnlBlcH/fuiERFR2WXw4OGaNWti6tSpGDt2rE77999/j3nz5iE+Pr5EA74qDh4mQ/x0Jg7Tf42AvYUpDk9uD1tzU6kjERFVSsX9/Da4xyY5ORldu3bVa+/cuTNSUlIMXR1RmZGWnYfF+28AACZ0rMuihoioHDK4sAkICMCvv/6q175z50707NmzREIRSWHFkWg8Ss+FRxVLvPNGbanjEBFRMRh8ubevry/mzp2Lw4cPo0WLFgCA06dP48SJE/j4448REhKiXXb8+PEll5SoFMUnZ+G/x2IAAFO7ecPUmBcMEhGVRwaPsXF3dy/aimUy3Lp1q1ihShLH2FBRTPzlIn77+x7e8HDAppFvcN4aIiKJ/WsT9MXExBj6FKIy7dKdZPz29z3IZMBnPXxZ1BARlWPsb6dKTQiBuf+7vLvP6y6o72IrcSIiInoVLGyoUgv75yHOxibBzNQIk7t4SR2HiIheEQsbqrRy89VYsOdpb81Ifw9UtzWXOBEREb0qFjZUaW08HYfYx5moYqXAqLZKqeMQEVEJMLiwuX37Ngq6kEoIgdu3b5dIKKLSlpyZi6UHowAAH3f2hJXC4HH0RERUBhlc2Li7uyMxMVGvPSkpqciXghNJbdlfN5GSlQfvatYIbOIqdRwiIiohBhc2QogCL4dNT0+HmZlZiYQiKk2xjzKw4VQsAODT7j4wNuLl3UREFUWR+98/+ugjAE8n3vv8889hYfH/dz1WqVQ4c+YMGjVqVPIJiUrYwr3XkacSaOvphDaeTlLHISKiElTkwubixYsAnvbYXLlyBXK5XPuYXC5Hw4YNMWnSpJJPSFSCwmOTsCfiAYxkwPQePlLHISKiElbkwubQoUMAgKFDh2Lp0qW8PQGVO2q1wJz/TcY3oGkteFa1ljgRERGVNIPH2CxZsgT5+fl67UlJSUhNTS2RUESl4Y/L93DpTjIs5cb46E1PqeMQEVEpMLiwGThwIH755Re99i1btmDgwIElEoqopGXnqbBobyQAYHQ7JZysFRInIiKi0mBwYXPmzBm0b99er71du3Y4c+aMwQHS0tIwceJE1K5dG+bm5mjZsiXCw8MBAHl5efjkk0/QoEEDWFpaokaNGhg8eDDu3btn8OtQ5bbmRAzik7NQw9YMI/w9pI5DRESlxODCJicnp8CvovLy8pCVlWVwgBEjRmD//v0IDQ3FlStX0LlzZ3Tq1Anx8fHIzMzEhQsX8Pnnn+PChQvYsWMHIiMjERAQYPDrUOX1KD0HPxyKBgBM7uoFM1NjiRMREVFpkYmCphF+gfbt26N+/fpYtmyZTvsHH3yAy5cv49ixY0VeV1ZWFqytrbFz50706NFD2+7n54du3bphzpw5es8JDw9Hs2bNEBcXh1q1ar30NVJTU2Fra4uUlBQOeK6kPvvtCjaevo3XatritzGtYMR5a4iIyrzifn4bPI/8nDlz0KlTJ1y6dAkdO3YEABw8eBDh4eHYt2+fQevKz8+HSqXSm9jP3Nwcx48fL/A5KSkpkMlksLOzK/DxnJwc5OTkaH/mgObK7WZCGjadvQMAmN7dh0UNEVEFZ/BXUa1atcKpU6dQs2ZNbNmyBX/88Qfq1KmDy5cvw9/f36B1WVtbo0WLFpg9ezbu3bsHlUqFjRs34tSpU7h//77e8tnZ2fjkk08waNCgQqu3+fPnw9bWVvvP1ZXT5Vdm83Zfh0ot0Nm3Kpp7OEodh4iISpnBX0WVtOjoaAwbNgxHjx6FsbExGjduDE9PT5w/fx7Xrl3TLpeXl4d+/frh7t27OHz4cKGFTUE9Nq6urvwqqhI6HvUI764+AxMjGfZ92AYeTlZSRyIioiIq7ldRBvfYAE+Lkc8++wz/+c9/kJCQAADYs2cP/vnnH4PXpVQqceTIEaSnp+POnTs4e/Ys8vLy4OHx/1eu5OXlITAwEHFxcdi/f/8L36BCoYCNjY3OP6p8VGqBObuuAgDefaM2ixoiokrC4MLmyJEjaNCgAc6cOYPt27cjPT0dAHDp0iV88cUXxQ5iaWmJ6tWr48mTJwgLC0Pv3r0B/H9RExUVhQMHDsDRkV8n0MttP38X1x+kwcbMBBM61pU6DhER/UsMLmymTp2KOXPmYP/+/Tr3i+rQoQNOnz5tcICwsDDs3bsXMTEx2L9/P9q3bw9vb28MHToUeXl56N+/P86dO4effvoJKpUKDx48wIMHD5Cbm2vwa1HlkJGTj6/3PZ2Mb3zHurC3lL/kGUREVFEYfFXUlStX8PPPP+u1Ozs749GjRwYHSElJwbRp03D37l04ODigX79+mDt3LkxNTREbG4vff/8dAPTuHH7o0CG0a9fO4Nejim/l0VtISMtBLQcLvNeittRxiIjoX2RwYWNnZ4f79+/D3d1dp/3ixYtwcXExOEBgYCACAwMLfMzNzQ0Sj22mcuZhajZWHr0FAJjazRsKE07GR0RUmRTrXlGffPIJHjx4AJlMBrVajRMnTmDSpEkYPHhwaWQkKrKvwyKRladCk9r26Fa/mtRxiIjoX2ZwYTNv3jx4e3vD1dUV6enp8PX1RZs2bdCyZUt89tlnpZGRqEj+uZeCbRfuAgCm9/CBTMbJ+IiIKhuDv4qSy+VYtWoVZsyYgStXriA9PR2vv/466tbllSckHSEE5u66BiGAXg1r4PVa9lJHIiIiCRhU2OTl5cHb2xt//vknfHx8OKsvlRl/XU/AyejHkJsYYUoXL6njEBGRRAz6KsrU1BTZ2dmllYWoWPJUaszb/XSW6mGt3OHqYCFxIiIikorBY2w++OADLFy4EPn5+aWRh8hgv5y9jejEDDhYyjGmvVLqOEREJCGDx9iEh4fj4MGD2LdvHxo0aABLS0udx3fs2FFi4eizpn4AACAASURBVIheJjU7D4sPRAEAPuxUFzZmphInIiIiKRVrHpt+/fqVRhYig/1wKBpJGblQOlliULNaUschIiKJGVTYCCEwa9YsODk5wdzcvLQyERXJnaRMrDkeAwD4tLsPTIyLdU9XIiKqQAz6JBBCoE6dOrh7925p5SEqskVhkchVqdFS6YgO3s5SxyEiojLAoMLGyMgIdevWxePHj0srD1GRXLz9BH9cugeZjJPxERHR/zO4737BggWYPHkyIiIiSiMP0UsJITBn19PLu/s3rol6NWwlTkRERGWFwYOHBw8ejMzMTDRs2BByuVxvrE1SUlKJhSMqyJ6IBzgf9wTmpsaYxMn4iIjoGQYXNkuWLCmNHERFkpOvwoI91wEAwW08UNXGTOJERERUlhhc2AQFBZVGDqIiCT0Vh9tJmXC2VmBUWw+p4xARURljcGEDACqVCr/99huuXXs6zqFevXoICAiAsbFxiYYjetaTjFyEHHw6Gd+kzl6wkBdr9yUiogrM4E+Gmzdvonv37oiPj4eX19PxDfPnz4erqyt27doFpZJT2lPpWHowCqnZ+fCuZo1+fjWljkNERGWQwVdFjR8/HkqlEnfu3MGFCxdw4cIF3L59G+7u7hg/fnxpZCTCrcR0bDwdBwD4rIcvjI14eTcREekzuMfmyJEjOH36NBwcHLRtjo6OWLBgAVq1alWi4Yg0Fuy5jny1QAdvZ7SuW0XqOEREVEYZ3GOjUCiQlpam156eng65XF4ioYiedfrWY+y7+hDGRjJ82t1b6jhERFSGGVzY9OzZE8HBwThz5gyEEBBC4PTp03j//fcREBBQGhmpElOrBeb+bzK+Qc1cUcfZWuJERERUlhlc2ISEhECpVKJFixYwMzODmZkZWrVqhTp16mDp0qWlkZEqsZ2X4nElPgVWChNM7OQpdRwiIirjDB5jY2dnh507d+LmzZvay719fHxQp06dEg9HlVtWrgqL9kYCAMa0V6KKlULiREREVNYVeyKQOnXqsJihUrX6+C3cT8mGi505hrVylzoOERGVAwZ/FdWvXz8sXLhQr33RokV4++23SyQUUUJaNpYfjgYATOnqBTNTTv5IREQvZ3Bhc/ToUXTv3l2vvVu3bjh69GiJhCJavD8KGbkqNPy/9u48PKZ7cQP4O5lsk12CkD2yiyClVbGTCoJQt8W104tbSkJzLypaJYK22mqVKhexFL+WXKq2hkQtDUFCJRKJaIJEENllmzm/P9S0udE2E5Ocycz7eZ48j/meM2feyXjM6yzf42iF4Z3sxI5DRETNhMrF5o8u6zYwMEBxcbFaQpFuS8srwZ4L2QCAiGAfSCScjI+IiOpH5WLj5+eHPXv21BnfvXs32rdvr5ZQpNtWfJ8KhQAM7tAGXV2s//oJREREv1L55OGIiAi8+uqryMzMRP/+/QEAsbGx+Prrr/F///d/ag9IuiU+/T7i0+/DQCrBgsGcjI+IiFSjcrEZNmwYYmJisGLFCnzzzTeQyWTo2LEjfvjhB/Tp06cxMpKOkCsErPh1Mr6J3V3gbGMqciIiImpuGnS5d3BwMIKDg9WdhXTc3sQcpN0rgaXMAG/151QCRESkOpXPsSFqDKWVNfjoWDoAYO4AD1iZ8L5jRESkOhYb0ghfxmfiQWklXGxMMP5lZ7HjEBFRM8ViQ6LLLXqMr368CQBYMNgHhvr8a0lERA1Tr28Qzk9DjemDo2moqFbgJRdrBPnaih2HiIiasXoVmxYtWiA/Px8A0L9/fxQWFjZqKNIdV28XYd+lOwCAxUM5GR8RET2fehUbMzMzPHz4EAAQFxeH6urqRg1FukEQBCw/lAIAGNHZDh0drEROREREzV29LvcODAxEv3794OPjAwAYOXLkM2+rAAAnTpxQXzrSasdT7iEhqwBG+noIH8TJ+IiI6PnVq9js2LED27ZtQ2ZmJuLj4+Hr6wsTE5PGzkZarFquwMrD1wEAb/Ryhb2VTORERESkDepVbGQyGWbOnAkASExMxKpVq2BlxcMG1HA7f/oFNx+UoaWZIf7Zl5PxERGReqg88/DJkyeVfxYEAQB4wieppOhxNT6NvQEACHvFE2ZGDZoAm4iIqI4GTRgSHR0NPz8/yGQy5b2itm/fru5spKXWnczAo/JqeLQ2w+iujmLHISIiLaLyf5XXrFmDiIgIzJ49Gz169AAAnD59GjNnzsSDBw8QFham9pCkPbIflmPrmVsAgEXBPtCXcjI+IiJSH5WLzWeffYb169dj4sSJyrHhw4fD19cX7733HosN/alVR66jSq5AL4+W6OvZSuw4RESkZVT+73Jubi4CAgLqjAcEBCA3N1ctoUg7XfylAIeu5kIiARYN4WR8RESkfioXG3d3d+zdu7fO+J49e+Dh4aGWUKR9nkzGlwoAGN3VET5tLURORERE2kjlQ1FLly7F6NGjcerUKeU5NmfOnEFsbOwzCw8RAHx3JReXswthYijFvIGeYschIiItpfIem1GjRiEhIQEtW7ZETEwMYmJi0LJlS5w/fx4jR45sjIzUzFVUy7HqyJPJ+Gb2cUNrc2ORExERkbZq0AQiXbp0wY4dO9SdhbTU1rO3cPvRY7SxMMY/erUTOw4REWkxXmtLjephaSXWncgAALwd5AWZoVTkREREpM1YbKhRfRp7AyWVNfC1s8Cr/vZixyEiIi3HYkONJiO/FDsTsgEA7wT7QE+Pl3cTEVHjYrGhRrPycCrkCgGBPrYIcGspdhwiItIBDS42GRkZOHr0KB4/fgzgtxtiqqqkpAShoaFwdnaGTCZDQEAALly4oFwuCAKWLFmCtm3bQiaTITAwEDdu3GhobGoiZzMf4IfUfOjrSbBwiLfYcYiISEeoXGwePnyIwMBAeHp6YsiQIcrZhqdNm4b58+erHOCNN97A8ePHsX37dly9ehUDBw5EYGAg7ty5AwBYvXo11q5diw0bNiAhIQGmpqYICgpCRUWFyq9FTUOuELD8uyeT8Y3r5gS3VmYiJyIiIl2hcrEJCwuDvr4+srOzYWJiohwfPXo0jhw5otK2Hj9+jG+//RarV69G79694e7ujvfeew/u7u5Yv349BEHAJ598gsWLFyMkJAQdO3ZEdHQ07t69i5iYGFWjUxPZd+k2UnKLYW6sj7mBnIyPiIiajsrF5tixY1i1ahUcHBxqjXt4eOCXX35RaVs1NTWQy+UwNq49YZtMJsPp06eRlZWFvLw8BAYGKpdZWlqiW7duOHfu3DO3WVlZieLi4lo/1HTKq2rw4bE0AMDsfu6wNjUUOREREekSlYtNWVlZrT01TxUUFMDIyEilbZmbm6N79+5YtmwZ7t69C7lcjh07duDcuXPIzc1FXl4eAMDW1rbW82xtbZXL/ldUVBQsLS2VP46Ojiploufz1aks3CuuhEMLGSYFuIgdh4iIdIzKxaZXr16Ijo5WPpZIJFAoFFi9ejX69euncoDt27dDEATY29vDyMgIa9euxdixY6Gn17DzmhcuXIiioiLlT05OToO2Q6rLL67Al6cyAQD/HuQNYwNOxkdERE1L5VsqrF69GgMGDEBiYiKqqqrwr3/9C9euXUNBQQHOnDmjcgA3NzfEx8ejrKwMxcXFaNu2LUaPHo127dqhTZs2AIB79+6hbdu2yufcu3cPnTt3fub2jIyMVN5zROrx0bF0lFfJ4e9khaEd2/71E4iIiNRM5d0iHTp0QHp6Onr27ImQkBCUlZXh1VdfxeXLl+Hm5tbgIKampmjbti0ePXqEo0ePIiQkBK6urmjTpg1iY2OV6xUXFyMhIQHdu3dv8GuR+qXcLcbei0/2ji0Obg+JhJPxERFR02vQTTAtLS3xzjvvqCXA0aNHIQgCvLy8kJGRgfDwcHh7e2PKlCmQSCQIDQ3F8uXL4eHhAVdXV0RERMDOzg4jRoxQy+vT8xMEASu+T4UgAMEd26KLcwuxIxERkY5SudhcuXLlmeMSiQTGxsZwcnJS6VBQUVERFi5ciNu3b8Pa2hqjRo1CZGQkDAwMAAD/+te/UFZWhunTp6OwsBA9e/bEkSNH6lxJReKJS7uP0xkPYCjVw4JBnIyPiIjEIxFUnDJYT09PeZjh6VN/f9jBwMAAo0ePxpdffqkR5aO4uBiWlpYoKiqChYWF2HG0To1cgUGf/oiM/FJM790Oi4b4iB2JiIi0QEO/v1U+x2b//v3w8PDAxo0bkZycjOTkZGzcuBFeXl7YtWsXNm/ejBMnTmDx4sWqbpqaod0XcpCRX4oWJgaY1c9d7DhERKTjVD4UFRkZiU8//RRBQUHKMT8/Pzg4OCAiIgLnz5+Hqakp5s+fjw8//FCtYUmzlFRU4+Pj6QCAuQM8YCkzEDkRERHpOpX32Fy9ehXOzs51xp2dnXH16lUAQOfOnZX3kCLttT4uEw/LqtCupSnGvVz37wQREVFTU7nYeHt7Y+XKlaiqqlKOVVdXY+XKlfD2fnLi6J07d+rMFkza5fajcmw6nQUAWDjEBwbSBt8onoiISG1UPhS1bt06DB8+HA4ODujYsSOAJ3tx5HI5vvvuOwDAzZs38eabb6o3KWmUD46moapGgZfbWSPQp7XYcYiIiAA04KooACgpKcHOnTuRnv7k/AovLy/8/e9/h7m5udoDPi9eFaV+STmFGLHuDCQS4ODsnuhgbyl2JCIi0jIN/f5u0AR95ubmmDlzZkOeSs2cIAiIPJQCABjpb89SQ0REGqVBxQYAUlJSkJ2dXetcGwAYPnz4c4cizXX0Wh4u3HoEYwM9hAd5iR2HiIioFpWLzc2bNzFy5EhcvXoVEomkziR9crlcvQlJY1TVKLDy8HUAwPRe7dDWUiZyIiIiotpUvpRl7ty5cHV1RX5+PkxMTHDt2jWcOnUKXbt2RVxcXCNEJE2x/adfcOthOVqZG2FGn4bf8JSIiKixqLzH5ty5czhx4gRatmwJPT096OnpoWfPnoiKisKcOXNw+fLlxshJIissr8La2BsAgPmveMLUqMFHMYmIiBqNynts5HK58uqnli1b4u7duwCeTNCXlpam3nSkMdbGZqDocTW825jjta6OYschIiJ6JpX/292hQwckJyfD1dUV3bp1w+rVq2FoaIiNGzeiXbt2jZGRRHbrQRm2/3QLALBoiA+kepI/fwIREZFIVC42ixcvRllZGQDg/fffx9ChQ9GrVy/Y2Nhg9+7dag9I4lt5+Dqq5QL6eLZCb89WYschIiL6QyoXm9/f/NLd3R3Xr19HQUEBWrRoobwyirTH+awCHLmWBz0J8E6wj9hxiIiI/pTK59hMnToVJSUltcasra1RXl6OqVOnqi0YiU+h+G0yvjEvOcHTVvNmliYiIvo9lYvNtm3b8Pjx4zrjjx8/RnR0tFpCkWY4eOUukm8XwdRQirBAT7HjEBER/aV6H4oqLi6GIAgQBAElJSUwNjZWLpPL5fj+++/RujVvhqgtKqrlWPXrZHxv9nNHK3MjkRMRERH9tXoXGysrK0gkEkgkEnh61v3fu0QiwdKlS9UajsSz+XQW7hZVwM7SGNN6uoodh4iIqF7qXWxOnjwJQRDQv39/fPvtt7C2tlYuMzQ0hLOzM+zs7BolJDWtB6WVWB+XCQAIH+QFYwOpyImIiIjqp97Fpk+fPgCArKwsODo6Qk9P5dNzqJn4+Hg6Sitr0NHBEiGd7MWOQ0REVG8qX+7t7OyMwsJCnD9/Hvn5+VAoFLWWT5w4UW3hqOnduFeCr89nAwDeGeIDPU7GR0REzYjKxebgwYMYN24cSktLYWFhUWvuGolEwmLTzK34PhUKAQjytUW3djZixyEiIlKJyseT5s+fj6lTp6K0tBSFhYV49OiR8qegoKAxMlIT+fHGfZxMuw99PQkWDOZkfERE1PyoXGzu3LmDOXPmwMTEpDHykEjkCgGRh1IBABO6O8O1panIiYiIiFSncrEJCgpCYmJiY2QhEX1zMQfX80pgYayPuQM8xI5DRETUICqfYxMcHIzw8HCkpKTAz88PBgYGtZYPHz5cbeGoaZRV1uDDY+kAgDkDPGBlYihyIiIiooaRCIIgqPKEP7vMWyKRQC6XP3codSouLoalpSWKiopgYWEhdhyNtOZ4OtbG3oCTtQmOz+sNI33OW0NEROJq6Pe3ynts/vfybmre8ooqsPHUk8n4Fgz2ZqkhIqJm7blm2auoqFBXDhLJh8fSUFGtQFfnFhjcoY3YcYiIiJ6LysVGLpdj2bJlsLe3h5mZGW7evAkAiIiIwObNm9UekBrPz3eK8O2l2wCAxUPb15qTiIiIqDlSudhERkZi69atWL16NQwNfzvJtEOHDti0aZNaw1HjEYQnl3cLAjC8kx06O1qJHYmIiOi5qVxsoqOjsXHjRowbNw5S6W/nY3Tq1AnXr19XazhqPLGp+Th38yEM9fXwr0FeYschIiJSiwZN0Ofu7l5nXKFQoLq6Wi2hqHFVyxVYcfjJZHxTe7jCoQUnWyQiIu2gcrFp3749fvzxxzrj33zzDfz9/dUSihrX1+ezcfN+GaxNDfFmPzex4xAREamNypd7L1myBJMmTcKdO3egUCiwb98+pKWlITo6Gt99911jZCQ1Kq6oxic/3AAAhAV6wMLY4C+eQURE1HyovMcmJCQEBw8exA8//ABTU1MsWbIEqampOHjwIF555ZXGyEhqtO5kBgrKquDe2gxjX3ISOw4REZFaqbzHBgB69eqF48ePqzsLNbKcgnJsOX0LALBoiDf0pc81jREREZHGUfmb7cKFC0hISKgznpCQwJtjarhVR66jSq5AD3cb9PNqLXYcIiIitVO52MyaNQs5OTl1xu/cuYNZs2apJRSp36XsR/juSi4kEuCdIZyMj4iItJPKxSYlJQUvvPBCnXF/f3+kpKSoJRSplyAIWP7dk8/mby84oL0dbwZKRETaSeViY2RkhHv37tUZz83Nhb5+g07ZoUb2/dU8XMouhMxAireDOBkfERFpL5WLzcCBA7Fw4UIUFRUpxwoLC7Fo0SJeFaWBKmvkWHnkyWR803u3g62FsciJiIiIGo/Ku1g+/PBD9O7dG87OzsoJ+ZKSkmBra4vt27erPSA9n+izvyCn4DFamxthRp92YschIiJqVCoXG3t7e1y5cgU7d+5EcnIyZDIZpkyZgrFjx8LAgJO9aZKCsiqsPfFkMr63g7xgYshDhUREpN1U+qarrq7GjBkzEBERgenTpzdWJlKTtbE3UFJRA5+2Fhj1goPYcYiIiBqdSufYGBgY4Ntvv22sLKRGN++XYsdPvwAAFgf7QKrHy7uJiEj7qXzy8IgRIxATE9MYWUiNog5fR41CQH/v1ujh3lLsOERERE1C5ZMuPDw88P777+PMmTPo0qULTE1Nay2fM2eO2sJRw/x08yGOp9yDVE+CRUO8xY5DRETUZCSCIAiqPMHV1fWPNyaR4ObNm88dSp2Ki4thaWmJoqIiWFho/8R0CoWA4etO4+c7xZjwsjOWjeggdiQiIiKVNfT7W+U9NllZWao+hZpQTNId/HynGOZG+ggN9BA7DhERUZNq8O2dq6qqkJaWhpqaGnXmoefwuEqOD46mAQDe7OcOGzMjkRMRERE1LZWLTXl5OaZNmwYTExP4+voiOzsbAPDWW29h5cqVag9I9bfpx5vILaqAvZUMU3q4iB2HiIioyalcbBYuXIjk5GTExcXB2Pi36fkDAwOxZ88etYaj+ssvqcD6+EwAwL8GecHYQCpyIiIioqancrGJiYnB559/jp49e0Ii+W1uFF9fX2RmZqq0LblcjoiICLi6ukImk8HNzQ3Lli3D789nLi0txezZs+Hg4ACZTIb27dtjw4YNqsbWeh8fT0d5lRydHK0wvJOd2HGIiIhEofLJw/fv30fr1q3rjJeVldUqOvWxatUqrF+/Htu2bYOvry8SExMxZcoUWFpaKi8bnzdvHk6cOIEdO3bAxcUFx44dw5tvvgk7OzsMHz5c1fhaKS2vBHsu5AAAIoJ9VP4ciIiItIXKe2y6du2KQ4cOKR8//RLdtGkTunfvrtK2zp49i5CQEAQHB8PFxQV/+9vfMHDgQJw/f77WOpMmTULfvn3h4uKC6dOno1OnTrXW0XWR36dCIQBD/Nqgq4u12HGIiIhEo/IemxUrVmDw4MFISUlBTU0NPv30U6SkpODs2bOIj49XaVsBAQHYuHEj0tPT4enpieTkZJw+fRpr1qyptc6BAwcwdepU2NnZIS4uDunp6fj444+fuc3KykpUVlYqHxcXF6v6FpuV+PT7OJV+HwZSCf49iJPxERGRblN5j03Pnj2RlJSEmpoa+Pn54dixY2jdujXOnTuHLl26qLStBQsWYMyYMfD29oaBgQH8/f0RGhqKcePGKdf57LPP0L59ezg4OMDQ0BCDBg3CunXr0Lt372duMyoqCpaWlsofR0dHVd9is1EjVyDyUAoAYFJ3FzjbmP7FM4iIiLSbyntsAMDNzQ1fffXVc7/43r17sXPnTuzatQu+vr5ISkpCaGgo7OzsMGnSJABPis1PP/2EAwcOwNnZGadOncKsWbNgZ2eHwMDAOttcuHAh5s2bp3xcXFysteVmb+JtpN8rhZWJAd7qz8n4iIiI6n1LBYVCgQ8++AAHDhxAVVUVBgwYgHfffRcymazBL+7o6IgFCxZg1qxZyrHly5djx44duH79Oh4/fgxLS0vs378fwcHBynXeeOMN3L59G0eOHPnL19DWWyqUVtag7wcn8aC0CkuGtsfUnn98qwsiIqLmpqHf3/U+FBUZGYlFixbBzMwM9vb2+PTTT2sVkoYoLy+Hnl7tCFKpFAqFAgBQXV2N6urqP11HV22Iy8SD0iq42Jhg/MvOYschIiLSCPU+FBUdHY0vvvgCM2bMAAD88MMPCA4OxqZNm+oUj/oaNmwYIiMj4eTkBF9fX1y+fBlr1qzB1KlTAQAWFhbo06cPwsPDIZPJ4OzsjPj4eERHR9c6wVjX3C18jK9+fHKz0QWDfWCo3+A7YxAREWmVeh+KMjIyQkZGRq3zVYyNjZGRkQEHB4cGvXhJSQkiIiKwf/9+5Ofnw87ODmPHjsWSJUtgaGgIAMjLy8PChQtx7NgxFBQUwNnZGdOnT0dYWFi95mvRxkNR8/YkYd/lO3jJ1Rp7pr/MeWuIiEjrNPT7u97FRiqVIi8vD61atVKOmZub48qVK3B11dzzO7St2Fy9XYRhn58GAByY3QMdHaxETkRERKR+Df3+rvehKEEQMHnyZBgZ/XbH6IqKCsycOROmpr9dZrxv3756vzipRhAELP/18u6R/vYsNURERP+j3sXm6eXXvzd+/Hi1hqE/dyzlHhKyCmCkr4fwIC+x4xAREWmcehebLVu2NGYO+gtVNQqsPHwdAPBGL1fYWTX8MnsiIiJtxctpmomdCb8g60EZWpoZ4p993cWOQ0REpJFYbJqBovJqfBp7AwAQ9oonzIwaNGE0ERGR1mOxaQY+P3kDheXV8LQ1w+iu2nl7CCIiInVgsdFw2Q/Lse3sLwCARUN8oC/lR0ZERPRH+C2p4VYduY4quQK9PFqir1drseMQERFpNBYbDZZ4qwCHruZCTwK8E+wjdhwiIiKNx2KjoZ5MxpcKAHi9qyO82zT/WZOJiIgaG4uNhjp4JRdJOYUwMZRi3kBPseMQERE1Cyw2GqiiWo5Vv07GN7OPG1qbG4uciIiIqHlgsdFAW8/ewp3Cx2hjYYx/9GondhwiIqJmg8VGwzwsrcS6ExkAgPAgL8gMpSInIiIiaj5YbDTMp7E3UFJZgw72Fhjpby92HCIiomaFxUaDZOSXYGdCNgDgnSHtoacnETkRERFR88Jio0Givr8OuUJAoI8turvZiB2HiIio2WGx0RBnMx4g9no+9PUkWDjEW+w4REREzRKLjQaQK36bjG/8y85wa2UmciIiIqLmicVGA+y7dBspucUwN9bHnAEeYschIiJqtlhsRFZeVYMPj6UBAN7q7w5rU0ORExERETVfLDYi++pUFu4VV8LRWoZJAS5ixyEiImrWWGxEdK+4AhviMwEA/x7kDSN9TsZHRET0PFhsRPTRsTQ8rpbjBScrBPu1FTsOERFRs8diI5KUu8X4v4u3AQDvBLeHRMLJ+IiIiJ4Xi40IBEHAiu9TIQjA0I5t0cW5hdiRiIiItAKLjQji0u7jdMYDGEr18O9BnIyPiIhIXVhsmliNXIHI759MxjelhwscrU1ETkRERKQ9WGya2O4LOcjIL0ULEwO82c9d7DhERERahcWmCZVUVOPj4+kAgNBAT1jKDEROREREpF1YbJrQF3GZeFhWhXatTPH3bk5ixyEiItI6LDZN5Pajcmw+nQUAWDjYBwZS/uqJiIjUjd+uTeSDo2moqlGgezsbBPq0FjsOERGRVmKxaQJJOYX4b9JdSCTAO8E+nIyPiIiokbDYNDJBEBB5KAUA8Kq/AzrYW4qciIiISHux2DSyo9fycOHWIxgb6CE8yEvsOERERFqNxaYRVdUoEHX4OgBgeq92aGNpLHIiIiIi7cZi04iiz93CLw/L0crcCDP6uIkdh4iISOux2DSSwvIqfHYiAwAw/xVPmBrpi5yIiIhI+7HYNJK1sRkoelwN7zbmeK2ro9hxiIiIdAKLTSO49aAM23+6BeDJ5d1SPV7eTURE1BRYbBrBysPXUS0X0NerFXp5tBI7DhERkc5gsVGz81kFOHItD3oSYNEQH7HjEBER6RQWGzVSKAQs/3UyvjEvOcHT1lzkRERERLqFxUaNDiTfxZXbRTA1lCIs0FPsOERERDqHxUZNKqrlWH3kyWR8b/ZzRytzI5ETERER6R4WGzXZfDoLd4sqYG8lw7SermLHISIi0kksNmrwoLQS6+MyAQDhQV4wNpCKnIiIiEg3sdiowcfH01FaWYOODpYY3slO7DhEREQ6i8XmOaXfK8HX57MBAIuD20OPk/ERERGJhsXmOa34AN5okwAAE6RJREFUPhUKAQjytcVLrtZixyEiItJpLDbP4ccb9xGXdh/6ehIsGMzJ+IiIiMTGYtNAcoWAyEOpAICJ3V3g2tJU5EREREQkarGRy+WIiIiAq6srZDIZ3NzcsGzZMgiCUGu91NRUDB8+HJaWljA1NcWLL76I7OxskVI/8c3FHFzPK4GlzABzBriLmoWIiIie0BfzxVetWoX169dj27Zt8PX1RWJiIqZMmQJLS0vMmTMHAJCZmYmePXti2rRpWLp0KSwsLHDt2jUYGxuLGR0lFTUw0tfDW/3dYWViKGoWIiIiekIi/O/ukSY0dOhQ2NraYvPmzcqxUaNGQSaTYceOHQCAMWPGwMDAANu3b2/QaxQXF8PS0hJFRUWwsLBQS+6n7hY+RkszIxjq84geERGROjX0+1vUb+SAgADExsYiPT0dAJCcnIzTp09j8ODBAACFQoFDhw7B09MTQUFBaN26Nbp164aYmBgxYyvZWclYaoiIiDSIqN/KCxYswJgxY+Dt7Q0DAwP4+/sjNDQU48aNAwDk5+ejtLQUK1euxKBBg3Ds2DGMHDkSr776KuLj45+5zcrKShQXF9f6ISIiIt0g6jk2e/fuxc6dO7Fr1y74+voiKSkJoaGhsLOzw6RJk6BQKAAAISEhCAsLAwB07twZZ8+exYYNG9CnT58624yKisLSpUub9H0QERGRZhB1j014eLhyr42fnx8mTJiAsLAwREVFAQBatmwJfX19tG/fvtbzfHx8/vCqqIULF6KoqEj5k5OT0+jvg4iIiDSDqHtsysvLoadXu1tJpVLlnhpDQ0O8+OKLSEtLq7VOeno6nJ2dn7lNIyMjGBkZNU5gIiIi0miiFpthw4YhMjISTk5O8PX1xeXLl7FmzRpMnTpVuU54eDhGjx6N3r17o1+/fjhy5AgOHjyIuLg48YITERGRRhL1cu+SkhJERERg//79yM/Ph52dHcaOHYslS5bA0PC3uWH+85//ICoqCrdv34aXlxeWLl2KkJCQer1GY17uTURERI2jod/fohabpsBiQ0RE1Pw0y3lsiIiIiNSJxYaIiIi0BosNERERaQ0WGyIiItIaLDZERESkNVhsiIiISGuIOkFfU3h6NTtvhklERNR8PP3eVnVWGq0vNiUlJQAAR0dHkZMQERGRqkpKSmBpaVnv9bV+gj6FQoG7d+/C3NwcEolE7Dgaqbi4GI6OjsjJyeEkhhqAn4dm4eehWfh5aJbG/DwEQUBJSQns7Ozq3Ffyz2j9Hhs9PT04ODiIHaNZsLCw4D8UGoSfh2bh56FZ+Hlolsb6PFTZU/MUTx4mIiIircFiQ0RERFpD+t57770ndggSn1QqRd++faGvr/VHJ5sFfh6ahZ+HZuHnoVk07fPQ+pOHiYiISHfwUBQRERFpDRYbIiIi0hosNkRERKQ1WGyIiIhIa7DY6KioqCi8+OKLMDc3R+vWrTFixAikpaWJHYt+tXLlSkgkEoSGhoodRafduXMH48ePh42NDWQyGfz8/JCYmCh2LJ0kl8sREREBV1dXyGQyuLm5YdmyZSrfR4ga5tSpUxg2bBjs7OwgkUgQExNTa7kgCFiyZAnatm0LmUyGwMBA3LhxQ5SsLDY6Kj4+HrNmzcJPP/2E48ePo7q6GgMHDkRZWZnY0XTehQsX8OWXX6Jjx45iR9Fpjx49Qo8ePWBgYIDDhw8jJSUFH330EVq0aCF2NJ20atUqrF+/Hp9//jlSU1OxatUqrF69Gp999pnY0XRCWVkZOnXqhHXr1j1z+erVq7F27Vps2LABCQkJMDU1RVBQECoqKpo4KS/3pl/dv38frVu3Rnx8PHr37i12HJ1VWlqKF154AV988QWWL1+Ozp0745NPPhE7lk5asGABzpw5gx9//FHsKARg6NChsLW1xebNm5Vjo0aNgkwmw44dO0RMpnskEgn279+PESNGAHiyt8bOzg7z58/H22+/DQAoKiqCra0ttm7dijFjxjRpPu6xIQBP/hICgLW1tchJdNusWbMQHByMwMBAsaPovAMHDqBr16547bXX0Lp1a/j7++Orr74SO5bOCggIQGxsLNLT0wEAycnJOH36NAYPHixyMsrKykJeXl6tf7csLS3RrVs3nDt3rsnzaMY0gSQqhUKB0NBQ9OjRAx06dBA7js7avXs3Ll26hAsXLogdhQDcvHkT69evx7x587Bo0SJcuHABc+bMgaGhISZNmiR2PJ2zYMECFBcXw9vbG1KpFHK5HJGRkRg3bpzY0XReXl4eAMDW1rbWuK2trXJZU2KxIcyaNQs///wzTp8+LXYUnZWTk4O5c+fi+PHjMDY2FjsO4Unh79q1K1asWAEA8Pf3x88//4wNGzaw2Ihg79692LlzJ3bt2gVfX18kJSUhNDQUdnZ2/DyoFh6K0nGzZ8/Gd999h5MnT8LBwUHsODrr4sWLyM/PxwsvvAB9fX3o6+sjPj4ea9euhb6+PuRyudgRdU7btm3Rvn37WmM+Pj7Izs4WKZFuCw8Px4IFCzBmzBj4+flhwoQJCAsLQ1RUlNjRdF6bNm0AAPfu3as1fu/ePeWypsRio6MEQcDs2bOxf/9+nDhxAq6urmJH0mkDBgzA1atXkZSUpPzp2rUrxo0bh6SkJEilUrEj6pwePXrUmQIhPT0dzs7OIiXSbeXl5dDTq/2VJZVKoVAoREpET7m6uqJNmzaIjY1VjhUXFyMhIQHdu3dv8jw8FKWjZs2ahV27duG///0vzM3NlcdBLS0tIZPJRE6ne8zNzeuc32RqagobGxue9ySSsLAwBAQEYMWKFXj99ddx/vx5bNy4ERs3bhQ7mk4aNmwYIiMj4eTkBF9fX1y+fBlr1qzB1KlTxY6mE0pLS5GRkaF8nJWVhaSkJFhbW8PJyQmhoaFYvnw5PDw84OrqioiICNjZ2SmvnGpSAukkAM/82bJli9jR6Fd9+vQR5s6dK3YMnXbw4EGhQ4cOgpGRkeDt7S1s3LhR7Eg6q7i4WJg7d67g5OQkGBsbC+3atRPeeecdobKyUuxoOuHkyZPP/M6YNGmSIAiCoFAohIiICMHW1lYwMjISBgwYIKSlpYmSlfPYEBERkdbgOTZERESkNVhsiIiISGuw2BAREZHWYLEhIiIircFiQ0RERFqDxYaIiIi0BosNERERaQ0WGyJqNvr27YvQ0NAmeS2JRIKYmBi1bzcmJgbu7u6QSqVN9l6IdAmLDZEGmDx5MiQSCWbOnFln2axZsyCRSDB58uSmD6YD3nvvPXTu3LnJXm/GjBn429/+hpycHCxbtuyZ6zRWqSLSBSw2RBrC0dERu3fvxuPHj5VjFRUV2LVrF5ycnERMRupSWlqK/Px8BAUFwc7ODubm5g3eVlVVlRqTEWkPFhsiDfHCCy/A0dER+/btU47t27cPTk5O8Pf3r7XukSNH0LNnT1hZWcHGxgZDhw5FZmamcnl0dDTMzMxw48YN5dibb74Jb29vlJeXAwBcXFywfPlyTJw4EWZmZnB2dsaBAwdw//59hISEwMzMDB07dkRiYqJyG8/au/HJJ5/AxcVF+Xjy5MkYMWIEVqxYAVtbW1hZWeH9999HTU0NwsPDYW1tDQcHB2zZsuVPfx9lZWXKbG3btsVHH31UZ53Kykq8/fbbsLe3h6mpKbp164a4uDjl8q1bt8LKygoxMTHw8PCAsbExgoKCkJOTo1y+dOlSJCcnQyKRQCKRYOvWrcrnP3jwACNHjoSJiQk8PDxw4MCBP8386NEjTJw4ES1atICJiQkGDx6s/Azi4uKURaZ///6QSCS1sj719Hc5cuRISCQS5eOnv/tNmzbB1dUVxsbGAACFQoGoqCi4urpCJpOhU6dO+Oabb2pt8+eff8bgwYNhZmYGW1tbTJgwAQ8ePPjT90LUXLHYEGmQqVOn1vrC/89//oMpU6bUWa+srAzz5s1DYmIiYmNjoaenh5EjR0KhUAAAJk6ciCFDhmDcuHGoqanBoUOHsGnTJuzcuRMmJibK7Xz88cfo0aMHLl++jODgYEyYMAETJ07E+PHjcenSJbi5uWHixIlQ9ZZyJ06cwN27d3Hq1CmsWbMG7777LoYOHYoWLVogISEBM2fOxIwZM3D79u0/3EZ4eDji4+Px3//+F8eOHUNcXBwuXbpUa53Zs2fj3Llz2L17N65cuYLXXnsNgwYNqlXoysvLERkZiejoaJw5cwaFhYUYM2YMAGD06NGYP38+fH19kZubi9zcXIwePVr53KVLl+L111/HlStXlL/PgoKCP8w8efJkJCYm4sCBAzh37hwEQcCQIUNQXV2NgIAApKWlAQC+/fZb5ObmIiAgoM42Lly4AADYsmULcnNzlY8BICMjA99++y327duHpKQkAEBUVBSio6OxYcMGXLt2DWFhYRg/fjzi4+MBAIWFhejfvz/8/f2RmJiII0eO4N69e3j99df/8H0QNWui3HqTiGqZNGmSEBISIuTn5wtGRkbCrVu3hFu3bgnGxsbC/fv3hZCQEOVddJ/l/v37AgDh6tWryrGCggLBwcFB+Oc//ynY2toKkZGRtZ7j7OwsjB8/Xvk4NzdXACBEREQox86dOycAEHJzcwVBEIR3331X6NSpU63tfPzxx4Kzs3Ot9+Ls7CzI5XLlmJeXl9CrVy/l45qaGsHU1FT4+uuvn/l+SkpKBENDQ2Hv3r3KsYcPHwoymUx5x/NffvlFkEqlwp07d2o9d8CAAcLChQsFQRCELVu2CACEn376Sbk8NTVVACAkJCT84XsSBEEAICxevFj5uLS0VAAgHD58+JmZ09PTBQDCmTNnlGMPHjwQZDKZ8n08evRIACCcPHnymdv4/Wvv37+/1ti7774rGBgYCPn5+cqxiooKwcTERDh79mytdadNmyaMHTtWEARBWLZsmTBw4MBay3NycgQAot19magx6YvUp4joGVq1aoXg4GBs3boVgiAgODgYLVu2rLPejRs3sGTJEiQkJODBgwfKPTXZ2dno0KEDAKBFixbYvHkzgoKCEBAQgAULFtTZTseOHZV/trW1BQD4+fnVGcvPz0ebNm3q/T58fX2hp/fbDmFbW1tlLgCQSqWwsbFBfn7+M5+fmZmJqqoqdOvWTTlmbW0NLy8v5eOrV69CLpfD09Oz1nMrKythY2OjfKyvr48XX3xR+djb2xtWVlZITU3FSy+99Kfv4/e/H1NTU1hYWPxh5tTUVOjr69fKbGNjAy8vL6Smpv7p69SXs7MzWrVqpXyckZGB8vJyvPLKK7XWq6qqUh6+TE5OxsmTJ2FmZlZne5mZmXV+f0TNHYsNkYaZOnUqZs+eDQBYt27dM9cZNmwYnJ2d8dVXX8HOzg4KhQIdOnSoc0LpqVOnIJVKkZubi7KysjonqxoYGCj/LJFI/nDsaXHS09Orc1iqurq6Tr7fb+Ppdp419nS7DVFaWgqpVIqLFy9CKpXWWvasL/GGUHfm52VqalrrcWlpKQDg0KFDsLe3r7XMyMhIuc6wYcOwatWqOttr27ZtIyUlEg/PsSHSMIMGDUJVVRWqq6sRFBRUZ/nDhw+RlpaGxYsXY8CAAfDx8cGjR4/qrHf27FmsWrUKBw8ehJmZmbIsPY9WrVohLy+vVrl5eq6HOrm5ucHAwAAJCQnKsUePHiE9PV352N/fH3K5HPn5+XB3d6/18/u9SzU1NbVOgE5LS0NhYSF8fHwAAIaGhpDL5c+d2cfHBzU1NbUyP/2s2rdvr9K2DAwM6pWpffv2MDIyQnZ2dp3fgaOjI4AnJ6Vfu3YNLi4uddb536JEpA1YbIg0jFQqRWpqKlJSUursiQCeHGKysbHBxo0bkZGRgRMnTmDevHm11ikpKcGECRMwZ84cDB48GDt37sSePXvqXC2jqr59++L+/ftYvXo1MjMzsW7dOhw+fPi5tvksZmZmmDZtGsLDw3HixAn8/PPPmDx5cq3DW56enhg3bhwmTpyIffv2ISsrC+fPn0dUVBQOHTqkXM/AwABvvfUWEhIScPHiRUyePBkvv/yy8jCUi4sLsrKykJSUhAcPHqCysrJBmT08PBASEoJ//OMfOH36NJKTkzF+/HjY29sjJCREpW25uLggNjYWeXl5zyytT5mbm+Ptt99GWFgYtm3bhszMTFy6dAmfffYZtm3bBuDJPEgFBQUYO3YsLly4gMzMTBw9ehRTpkxRS6Ej0jQsNkQayMLCAhYWFs9cpqenh927d+PixYvo0KEDwsLC8MEHH9RaZ+7cuTA1NcWKFSsAPDlvZsWKFZgxYwbu3LnT4Fw+Pj744osvsG7dOnTq1Annz5/H22+/3eDt/ZkPPvgAvXr1wrBhwxAYGIiePXuiS5cutdbZsmULJk6ciPnz58PLywsjRozAhQsXas37Y2Jign//+9/4+9//jh49esDMzAx79uxRLh81ahQGDRqEfv36oVWrVvj6668bnHnLli3o0qULhg4diu7du0MQBHz//fd1Dmn9lY8++gjHjx+Ho6NjnUv9/9eyZcsQERGBqKgo+Pj4YNCgQTh06BBcXV0BAHZ2djhz5gzkcjkGDhwIPz8/hIaGwsrKqlZRJNIWEuF/D5gTEWmJrVu3IjQ0FIWFhWJHIaImwrpOREREWoPFhoiIiLQGD0URERGR1uAeGyIiItIaLDZERESkNVhsiIiISGuw2BAREZHWYLEhIiIircFiQ0RERFqDxYaIiIi0BosNERERaQ0WGyIiItIa/w8HTSWf2O2vQwAAAABJRU5ErkJggg==", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(maxdepths,percentcorrect)\n", "xlabel(\"Maxmum depth of tree\")\n", "ylabel(\"Percentage of correct predictions\")\n", "title(\"Percentage of correct predictions forevaluation dataset\");" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "maxdepths = 1:10\n", "minsizes = 1:20:81\n", "percentcorrect = zeros(length(maxdepths),length(minsizes))\n", "for i = 1:length(maxdepths)\n", " for j = 1:length(minsizes)\n", " tree = split(x,y,classes,minsizes[j],maxdepths[i])\n", " percentcorrect[i,j] = 100. * ncorrect(tree,xeval,yeval)/length(yeval)\n", " end\n", "end" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pcolor(maxdepths,minsizes,copy(percentcorrect'))\n", "colorbar()\n", "xlabel(\"Maxmum depth of tree\")\n", "ylabel(\"Minium size of leaves\")\n", "title(\"Percentage of correct predictions forevaluation dataset\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Performance does not degrate when maximum tree depth is increased for this case" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Final notes\n", "\n", "* Regression trees -> replace Gini impurity by variance and the mode by the mean\n", "* Tree prunning should be used\n", "* Random forest:\n", " * Split dataset into several so called _bags_\n", " * Derive a decision tree for each bag\n", " * For prediction, apply all trees to the feature vector and the final answer is the mode (for classification) or mean (for regression) for the answers of all trees" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "\n", "* Dua, Dheeru and Karra Taniskidou, E. (2017). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.\n", "\n", "* How To Implement The Decision Tree Algorithm From Scratch In Python\n", "By Jason Brownlee on November 9, 2016 https://machinelearningmastery.com/implement-decision-tree-algorithm-scratch-python/\n" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.6.0", "language": "julia", "name": "julia-1.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.3.1" } }, "nbformat": 4, "nbformat_minor": 4 }