{ "cells": [ { "cell_type": "code", "execution_count": 2, "id": "af7eae0b-87ed-45ef-892f-ad38f86d18e8", "metadata": {}, "outputs": [], "source": [ "from utils import empirical_means, empirical_dists" ] }, { "cell_type": "markdown", "id": "54bccc92-f1cd-4a4a-97f1-5e687fbf6aad", "metadata": {}, "source": [ "## Introduction\n", "\n", "In this series of exercises we will use the toolkit we've developed so far to study\n", "_random graphs_. As our mathematical model for \"random graphs\" we will take the probability space of labelled graphs on\n", "$n$ vertices in which every edge is selected with probability $p \\in [0,1]$. \n", "\n", "To be more precise, we fix the vertex set to be $V = \\{0,1,2,\\dots,n-1\\}$. \n", "As for the edge set $E$, we fix some $p \\in [0,1]$ and we set $P(e \\in E) = p$ for each of the ${n \\choose 2}$ possible\n", "edges between two vertices in $V$. To put it otherwise, the indicator function\n", "of $u$ and $v$ being neighbours (i.e. of the event $e = uv \\in E$) is $X_{uv} \\sim \\text{Bernoulli}(p)$. \n", "\n", "Therefore the probability of drawing a given $G=(V,E)$ is $P(G(n,p) = G) = p^{\\lvert E \\rvert}(1-p)^{{n \\choose 2} - \\lvert E \\rvert}$" ] }, { "cell_type": "markdown", "id": "d9f91503-ef7e-4a81-8f21-5e4f0636304f", "metadata": {}, "source": [ "The exercises below will guide us in an exploration of how the structure of $G(n,p)$ evolves as a function of $p$.\n", "More precisely, we'll be interested in the asymptotic structure of $G(n,p)$, meaning we'll imagine $n \\rightarrow \\infty$.\n", "\n", "To help us build some intuition, we'll carry Monte-Carlo experiments: we'll sample graphs out of $G(n,p)$ for varying values \n", "of $p$ (and $n$ big enough) and study various random variables on those graphs. This will help us to better visualise the content \n", "of the exercises, to formulate conjectures for their solution, and to help us verify our results." ] }, { "cell_type": "markdown", "id": "293b4558-f736-4287-9f8a-e1d6011f09b2", "metadata": {}, "source": [ "Let's start by visualising $G(n,p)$ for small $n$ and some fixed values of $p$. What do you observe?" ] }, { "cell_type": "code", "execution_count": 31, "id": "b076090d-c7c7-4cb7-8d1f-1b2de9c55417", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The history saving thread hit an unexpected error (OperationalError('attempt to write a readonly database')).History will not be written to the database.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 1 x 4" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 15 \n", "\n", "to_plot = []\n", "for p in [0,0.11,1/2,1]:\n", " G = graphs.RandomGNP(n,p)\n", " to_plot.append(G.plot(vertex_size=3, vertex_labels=False,graph_border=True))\n", " \n", "graphics_array(to_plot).show(figsize=[10,10])" ] }, { "cell_type": "markdown", "id": "70f0ded1-8eda-4f7b-ab78-19def4492bc4", "metadata": {}, "source": [ "Another way to think of $G(n,p)$ is as the so _Bernoulli bond percolation_ model on the complete graph: starting with $K_n$, we\n", "delete edges with probability $1-p$." ] }, { "cell_type": "code", "execution_count": 3, "id": "07e40ca9-5784-42af-9458-13304f44d0e3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 1 x 4" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 15\n", "\n", "to_plot = []\n", "for p in [0,0.11,1/2,1]:\n", " G = graphs.RandomGNP(n,p)\n", " to_plot.append(G.plot(vertex_size=3, vertex_labels=False,graph_border=True,layout='circular'))\n", " \n", "graphics_array(to_plot[::-1]).show(figsize=[10,10])" ] }, { "cell_type": "markdown", "id": "30f320f7-30f4-409d-824c-42b76f273573", "metadata": {}, "source": [ "## Exercise 0: Degree distribution\n", "\n", "It is clear that for $p=0$ all vertices have degree $0$ and for $p=1$ they all have degree $n-1$. \n", "As a warmup, answer the following questions:\n", "\n", "1. What is the average degree of a fixed vertex, say vertex $0$, as a function of $p$?\n", "2. What is the distribution of degrees for the same fixed vertex, as a function of $p$?" ] }, { "cell_type": "markdown", "id": "4eb39d5b-1dcc-41f2-8dfd-99c63dbd5e34", "metadata": {}, "source": [ "To help us in answering the above question, let's run our first Monte-Carlo experiments to calculate the empirical\n", "means and distributions as we vary $p$." ] }, { "cell_type": "code", "execution_count": 46, "id": "ce3f4a93-96da-44af-bb1b-644399c73722", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_range = [n/10 for n in range(0,10)] #breaking up the interval [0,1]\n", "K = 10 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "#our random variable of interest: the degree of vertex 0\n", "def degree_of_v(G):\n", " return G.degree(1)\n", "\n", "avg_degree = empirical_means(n,c_range,degree_of_v,K,verbose=False,scale=lambda n,c: c)\n", "line(avg_degree,title=\"Degree of vertex 0 in G(\"+str(n)+\",p)\", \\\n", " axes_labels=['p', 'deg.'],thickness=2,linestyle='--',marker='o') \\\n", " + plot((n-1)*x, (x,0,1),color=\"red\")" ] }, { "cell_type": "code", "execution_count": 51, "id": "1209dc3f-01de-4075-94b1-0fd204123e5c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 3 x 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c_range = [c/10 for c in range(0,12,2)] #breaking up the interval [0,1]\n", "K = 1000 #how many graphs to sample for each c\n", "n = 200 #size of graphs to sample\n", "\n", "degree_dists = empirical_dists(n,c_range,degree_of_v,K,verbose=False,scale=lambda n,c: c)\n", "\n", "def bernoulliPmf(n,p,k):\n", " return binomial(n-1,k) * p^k * (1-p)^(n-1-k)\n", " \n", "to_plot = []\n", "for c, data in degree_dists:\n", " m = len(data)\n", " to_plot.append(line2d(data,title=\"Degree of vertex 0 in G(\"+str(n)+\",\"+str(c)+\")\", \\\n", " axes_labels=['deg.', '$\\\\mathbb{P}$'],thickness=1,linestyle='--') \\\n", " + line2d([(k,bernoulliPmf(n,c,k)) for k in range(0,n)],color=\"red\"))\n", "\n", "graphics_array(to_plot,nrows=3).show(figsize=[8,8])" ] }, { "cell_type": "markdown", "id": "b727635e-2d66-4edd-9da7-a3099dc6c15a", "metadata": {}, "source": [ "As we can see above, the graph starts as a bunch of isolated vertices (at $p = 0$) and eventually ends up as a\n", "complete graph (at $p=1$). Of course this doesn't happen instantaneously: over the course, the graph develops a lot \n", "of interesting features, which will be our object of study. \n", "\n", "To get a good view of the emergence of those interesting structures, we'll often have to zoom in: having $p$ vary over the entire\n", "range of $[0,1]$ might lead us to miss a lot. Instead, we will have to figure out what range of values permits us to get a \n", "good glimpse. \n", " \n", "To demonstrate this point, let's say we want to study the point at which triangles emerge (we'll come back to this problem later on!). For our first experiment, we'll let $p$ take values over the entire range $[0,1]$.\n", "\n", "Note: as an empirical estimate of a probability, we'll often take the empirical mean of the \n", "corresponding indicator variable, here $\\boldsymbol{1}_{\\text{ num. triangles} > 0}$." ] }, { "cell_type": "code", "execution_count": 54, "id": "c0a1803c-02a5-4426-819c-c098dc3bf511", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_range = [n/10 for n in range(0,10)] #breaking up the interval [0,1]\n", "K = 10 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "#a function which computes our statistic of interest: the presence of triangles\n", "def has_triangle(G):\n", " if G.triangles_count() > 0:\n", " return 1\n", " else:\n", " return 0\n", "\n", "has_tri = empirical_means(n,c_range,has_triangle,K,verbose=False,scale=lambda n,c: c)\n", "line(has_tri,title=\"Proba. of having a triangle in G(\"+str(n)+\",p)\", \\\n", " axes_labels=['p', '$\\\\mathbb{P}$'],thickness=2,linestyle='--',marker='o') " ] }, { "cell_type": "markdown", "id": "d70d9dba-839b-4223-b2b1-1daa704c985c", "metadata": {}, "source": [ "As we can see from the plot above, the (empirical) probability of $G(n,p)$ to have a triangle\n", "seems to jump from $0$ directly to $1$ at some point. Does the emergence of triangles\n", "really happen in such a discontinuous way as the picture suggests? \n", "\n", "The answer is no! But to see this, we must zoom into the range of values for $p$ around which the transition from $0$ to\n", "$1$ takes place. This is around $O(n^{-2})$, as we'll later see. Indeed, our techniques not only predict the proper range\n", "into which we must zoom into but they even give us analytic results (the red curve) on the precise\n", "shape of this transition!" ] }, { "cell_type": "code", "execution_count": 55, "id": "f79f54e8-aa32-4cce-ab63-26e934693dc3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_range = [n/1000 for n in range(0,40)] #breaking up the interval [1,3]\n", "K = 100 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "has_tri = empirical_means(n,c_range,has_triangle,K,verbose=False,scale=lambda n,c: c)\n", "line(has_tri,title=\"Proba. of having a triangle in G(\"+str(n)+\",p)\", \\\n", " axes_labels=['p', '$\\\\mathbb{P}$'],thickness=2,linestyle='--',marker='o') \\\n", " + plot(1-exp(-binomial(100,3)*x^3), (x,0,0.04),color=\"red\",thickness=2)" ] }, { "cell_type": "markdown", "id": "e9577a9c-e2a0-4043-9d60-c4f8bb0c73d0", "metadata": {}, "source": [ "Our exploration begins with the study of the occurences of\n", "fixed patterns of interest.\n", "\n", "For a fixed pattern such as triangles, our plot above leads us to conjecture the existence of three regions: one in which the\n", "the probability of occurence is $0$, another in which it is $1$, and a transition between the two. \n", "\n", "Work by Bollobas and Thomassen shows that for all _monotone_ (= properties that are preserved by the addition of edges) properties, this is indeed the case.\n", "We will always chop $[0,1]$ into a three parts:\n", " - Subcritical regime: the probability that the structure occurs tends to $0$.\n", " - Critical regime: the probability has non-trivial limiting behaviour.\n", " - Supercritical regime: the probability that the structure occurs tends to $1$." ] }, { "cell_type": "markdown", "id": "c1f7a9d6-6b2f-49ab-8c5d-1f208c8d7f15", "metadata": {}, "source": [ "To aid you in approaching the questions below, the following recipe is often applicable:\n", " - Define $X_n$ counting occurences of the pattern of interest.\n", " - Compute $\\mathbb{E}(X_n)$ and use Markov's inequality to find the subcritical phase.\n", " - Compute $\\text{Var}(X_n)$ and use Chebyshev's inequality to find the supercritical phase.\n", " - Use the method of moments to figure out the distribution inside the critical window." ] }, { "cell_type": "markdown", "id": "156b8446-d242-4882-aea0-148806d548df", "metadata": {}, "source": [ "## Exercise 1: Edges in $G(n,p)$\n", "\n", "In this exercise, you study the occurence of edges, by answering the following:\n", "1. What's the threshold function for the presence of an edge in a random graph? \n", " _Hint_: In this particularly simple case, you can directly compute $\\mathbb{P}(X=k)$. \n", " Of course, the first moment/second moment recipe still applies.\n", "2. What's the limiting distribution for the number of edges? \n", " _Hint_: Again, $\\mathbb{P}(X = k)$ should look familiar!\n", " Consult the notes for the relevant limit theorem. \n", " If you prefer to follow the recipe, you can always attempt the method of moments.\n", "3. What's the limiting distribution for the indicator variable corresponding to the _existence of at least one edge_? \n", " _Hint_: You can either work this out directly using $\\mathbb{P}(X = k)$ or by working with the limit distribution\n", " for the number of edges." ] }, { "cell_type": "markdown", "id": "2e107518-0c6b-4507-a955-ade7e3bc2c4b", "metadata": {}, "source": [ "For $c = o(n^{-2})$ we have no edges, w.h.p. " ] }, { "cell_type": "code", "execution_count": 6, "id": "976cf71e-4b30-40eb-beea-ebf8d1ce6d14", "metadata": {}, "outputs": [], "source": [ "c_range = [x / 10.0 for x in range(0, 51, 2)] #breaking up the interval [1,3]\n", "K = 1000 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "def has_edge(G):\n", " if G.num_edges() > 0:\n", " return 1\n", " else:\n", " return 0\n", "\n", "proba_edge = empirical_means(n,c_range,has_edge,K,verbose=False,scale=lambda n,c: 1/n^3)" ] }, { "cell_type": "code", "execution_count": 7, "id": "93f4deb8-ba26-4fce-9bf4-11bfa576ba99", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "line(proba_edge,thickness=2,linestyle='--',ymax=1)" ] }, { "cell_type": "markdown", "id": "9d1eb230-0697-433c-afcb-b3ed7e7cb824", "metadata": {}, "source": [ "For $c = \\omega(n^{-2})$ we have at least one edge, w.h.p." ] }, { "cell_type": "code", "execution_count": 8, "id": "bd99ff9e-801b-4558-a32e-20e713f5e37b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "proba_edge = empirical_means(n,c_range,has_edge,K,verbose=False,scale=lambda n,c: 1/n)\n", "line(proba_edge,thickness=2,linestyle='--',ymax=1)" ] }, { "cell_type": "markdown", "id": "86933234-644f-4470-a8ff-594f25adced9", "metadata": {}, "source": [ "Inside the window $c = O(n^{-2})$ we observe the evolution of the probabilities for an edge to exist." ] }, { "cell_type": "code", "execution_count": 9, "id": "5c588a79-8f2f-49e9-8abf-a56c1ac53272", "metadata": {}, "outputs": [], "source": [ "c_range = [x / 10.0 for x in range(0, 51, 2)] #breaking up the interval [1,3]\n", "K = 1000 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "proba_edge = empirical_means(n,c_range,has_edge,K,verbose=False,scale=lambda n,c: c/n^2)" ] }, { "cell_type": "code", "execution_count": 10, "id": "71f1c7dc-dec3-4594-b25d-b72a6a51ab76", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "line(proba_edge,thickness=2,linestyle='--') + plot(1-exp(-x/2), (x,0,5),color=\"red\")" ] }, { "cell_type": "markdown", "id": "81bd1eee-8630-43e3-afdc-354051ddccbf", "metadata": {}, "source": [ "Let's now plot the empirical distributions for the _number of_ edges in $G(n,p = c n^{-2})$ as we\n", "vary the constant $c$." ] }, { "cell_type": "code", "execution_count": 64, "id": "a0143648-b160-418f-bc65-7f7fa759211c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Currently sampling with c = 1\n", "COUNTS IS Counter({0: 64, 1: 29, 2: 6, 3: 1})\n", "Currently sampling with c = 3\n", "COUNTS IS Counter({1: 38, 0: 24, 2: 21, 3: 8, 4: 6, 5: 2, 6: 1})\n", "Currently sampling with c = 5\n", "COUNTS IS Counter({1: 24, 2: 21, 3: 20, 5: 13, 4: 10, 0: 6, 6: 3, 8: 2, 7: 1})\n", "Currently sampling with c = 7\n", "COUNTS IS Counter({2: 21, 3: 21, 4: 17, 5: 12, 1: 10, 6: 7, 7: 5, 8: 3, 0: 3, 9: 1})\n", "Currently sampling with c = 9\n", "COUNTS IS Counter({3: 25, 4: 19, 5: 15, 6: 10, 1: 8, 7: 7, 2: 7, 8: 3, 12: 2, 10: 2, 9: 1, 0: 1})\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 2 x 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c_range = [c for c in range(1,10,2)] #breaking up the interval [0,1]\n", "K = 100 #how many graphs to sample for each c\n", "n = 1000 #size of graphs to sample\n", "\n", "res = empirical_dists(n,c_range,lambda g: g.num_edges(),K,scale=lambda n,c:c*n^(-2),verbose=True)\n", "\n", "def poisPmf(c,k):\n", " return (c/2)^k/factorial(k) * exp(-c/2).n()\n", "\n", "to_plot = []\n", "\n", "for c, data in res:\n", " m = len(data)\n", " to_plot.append(line2d(data,thickness=2,linestyle='--') + line2d([(k,poisPmf(c,k)) for k in range(0,m)],color=\"red\"))\n", "\n", "graphics_array(to_plot,nrows=2).show(figsize=[8,8])" ] }, { "cell_type": "markdown", "id": "9ca66b94-f9ae-4d11-a75f-c2cf67147323", "metadata": {}, "source": [ "## Exercise 2: 3-stars and 4-paths in $G(n,p)$\n", "### Main ideas: induced vs not-induced subgraphs, monotonicity, automorphisms\n", "\n", "As an extension let us ask the same questions as above but this time\n", "for the 3-star and the 4-path, the graphs depicted below. In more detail, we ask:\n", "\n", "1. What's the threshold function for the presence of a 3-star/4-path in a random graph?\n", "3. What's the limiting distribution for the number of 3-stars/4-path? \n", "4. What's the limiting distribution for the indicator variable corresponding to the _existence of at least one 3-star/4-path_?\n", "\n", "Before delving into the questions above, we have an important caveat to discuss here: what do we mean by \"occurence of a pattern\"? \n", "Earlier we discussed the occurence of edges, where it was clear what we meant.\n", "For more general graphs (such as the 3-star and the 4-path) however, the intuitive idea of occurence is ambiguous:\n", "are we studying fixed graphs as subgraph or specifically as an *induced* subgraphs of $G(n,p)$? \n", "Furthermore, do we count _labelled_ copies or _unlabelled_ ones? \n", "\n", "Concerning the first question, the notion of thresholds we introduced earlier helps us narrow it down: only in the \n", "not-necessarily-induced case does it makes sense to search for thresholds. \n", "\n", "To see why this is so, let's plot the empirical probability of having a 3-star as\n", "a subgraph and as an induced subgraph. What do we notice in terms of monotonicity of the resulting graphs?" ] }, { "cell_type": "code", "execution_count": 101, "id": "99822c75-73c8-42b7-b342-68608d497e40", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 1 x 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphics_array([graphs.StarGraph(3).plot(figsize=[3,3]), graphs.PathGraph(4).plot(figsize=[3,3])]).show()" ] }, { "cell_type": "code", "execution_count": 102, "id": "f78680cb-17ff-4648-9e07-d7021ed940d3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 1 x 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c_range = [n/10 for n in range(0,11)] #breaking up the interval [0,1]\n", "K = 50 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "def has_induced_star(G):\n", " \n", " T = graphs.StarGraph(3)\n", " if T.is_subgraph(G,induced=True):\n", " return 1\n", " else: \n", " return 0\n", "\n", "def has_star(G):\n", " \n", " T = graphs.StarGraph(3)\n", " if T.is_subgraph(G,induced=False):\n", " return 1\n", " else: \n", " return 0\n", "\n", "stars_noninduced = empirical_means(n,c_range,has_star,K,verbose=False,scale=lambda n,c: c)\n", "p1 = line(stars_noninduced,thickness=2,linestyle='--',marker='o') \n", "\n", "stars_induced = empirical_means(n,c_range,has_induced_star,K,verbose=False,scale=lambda n,c: c)\n", "p2 = line(stars_induced,thickness=2,linestyle='--',marker='o') \n", "\n", "graphics_array([p1,p2],nrows=1).show(figsize=[10,5])" ] }, { "cell_type": "markdown", "id": "e660a2fb-c93f-4acc-a256-98fe31613b82", "metadata": {}, "source": [ "Let's now overlay the empirical probabilities of a 3-star and a 4-path existing. What do you notice? \n", "How do you explain this?" ] }, { "cell_type": "code", "execution_count": 114, "id": "b3557212-e950-47f1-86dc-a622383af360", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_range = [n/10 for n in range(0,11)] #breaking up the interval [0,1]\n", "K = 50 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "def has_path(G):\n", " \n", " T = graphs.PathGraph(4)\n", " if T.is_subgraph(G,induced=False):\n", " return 1\n", " else: \n", " return 0\n", "\n", "paths = empirical_means(n,c_range,has_path,K,verbose=False,scale=lambda n,c: c)\n", "p3 = line(paths,thickness=2,linestyle='--',marker='o',color=\"red\") \n", "\n", "p1+p3" ] }, { "cell_type": "markdown", "id": "11c3b8a5-5b88-4482-a347-d7a963926350", "metadata": {}, "source": [ "What about the mean number of these two subgraphs? How do you explain the results for the \n", "case of labelled and unlabelled occurences, as seen below?" ] }, { "cell_type": "code", "execution_count": 134, "id": "8f9eb593-de03-46d4-ba45-cb3002953387", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Currently sampling with c = 0\n", "Currently sampling with c = 10\n", "Currently sampling with c = 20\n", "Currently sampling with c = 30\n", "Currently sampling with c = 40\n", "Currently sampling with c = 50\n", "Currently sampling with c = 60\n", "Currently sampling with c = 70\n", "Currently sampling with c = 80\n", "Currently sampling with c = 90\n", "Currently sampling with c = 0\n", "Currently sampling with c = 10\n", "Currently sampling with c = 20\n", "Currently sampling with c = 30\n", "Currently sampling with c = 40\n", "Currently sampling with c = 50\n", "Currently sampling with c = 60\n", "Currently sampling with c = 70\n", "Currently sampling with c = 80\n", "Currently sampling with c = 90\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_range = [n for n in range(0,100,10)] #breaking up the interval [0,1]\n", "K = 10 #how many graphs to sample for each c\n", "n = 100 #size of graphs to sample\n", "\n", "def num_paths(G):\n", " T = graphs.PathGraph(4)\n", " return G.subgraph_search_count(T,induced=False) #the built-in method counts *labelled* copies!\n", " \n", "def num_stars(G):\n", " T = graphs.StarGraph(3)\n", " return G.subgraph_search_count(T,induced=False)\n", "\n", "count_paths = empirical_means(n,c_range,num_paths,K,verbose=False,scale=lambda n,c: c*n^(-4/3))\n", "count_stars = empirical_means(n,c_range,num_stars,K,verbose=False,scale=lambda n,c: c*n^(-4/3))\n", "\n", "p4 = line(count_paths,thickness=2,linestyle='--',marker='o',color=\"blue\") \n", "p5 = line(count_stars,thickness=2,linestyle='--',marker='o',color=\"red\") \n", "\n", "p4+p5" ] }, { "cell_type": "code", "execution_count": 3, "id": "2c659254-9057-4477-a516-ce0de03c6421", "metadata": {}, "outputs": [ { "data": { "image/png": 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W5vi9997LypUrM72NiIiIZAMRO+DoHKg45JowB/D116lhrm5d6No1c8vLChw6yzUqKoro6GgKFCiQ5nj+/Pk5efJkprdJT3x8PPHx8SmvIyMjb/NTioiISKbaMQq8i0KJa7vdLlyAN99MfT1mDLjkwCmfmfKRXVxcuNmd3cxqM3LkSAICAlIewcHBN3w/ERERsVD0ETgwCSoOAlePa04fPAiXR0x17Qr16mVueVmFQwOdn58fPj4+hIeHpzl++vRpChYsmOlt0jNs2DAiIiJSHkeOHLmzDysiIiIZb+docPeD0r3TPV29unm79YMPzEdO5dBAZ7PZqFevHsuWLUtzfMmSJTRo0CDT26TH09MTf3//NA8RERHJguLPwt6vodwL4J7rus28vMxlSooVy8TashiH33IdOHAgc+fOZcqUKURFRTF+/HjWr19P//79LWkjIiIiTmr3Z4BhBjq5MeM2/PXXX4arq6vh6upqAIaLi4vh6upq9OnTJ027b7/91ihRooTh4uJilC9f3pg1a9Y175WZbW4kIiLCAIyIiIjbuk5EREQyUOJFw5gRaBhrXrzmVFKSYbz4omHs3GlBXVnUba1DZxgG9stLMF/BxcUFFyedUqJ16ERERLKg7R/B5tfgoT3gWzzNqQkToE8fcHODTz6BF1+0qMYs5LaWLbHZbLi5OXSlExEREZG0Ei+aS5WUeuqaMBcZCa+/bj5PSoIaNSyoLwtyzm41ERERyb72hEFiBFR69ZpT778Pp0+bzzt2hEaNMrm2LEqBTkRERLKOxCjYPspcpsQ37bTV/fvh00/N5x4eMGqUBfVlUQp0IiIiknXsHg9JF6HSsGtODR0KCQnm85degpIlM7m2LEyBTkRERLKGxEjY8TGU6QM+QWlO/e9/MHOm+bxAAXj12ruxOZoCnYiIiGQNu8ZBUgyEpO2dS042e+Que++91O2+xKRAJyIiItZLiIAdn0CZvuBTJM2pH3+E9evN59WqQc+eFtSXxSnQiYiIiPV2jYXkOKj0yjWnihWDihXN559+Cq6umVybE9CiciIiImKthAuwczSUeQa8C19zunlz2LQJfv8dmjXL/PKcgXroRERExFo7P4XkBAgZet0m7u7Qpk0m1uRkFOhERETEOgnnYdcYKPsseBeyuhqnlWMDXVhYGCEhIYSGhlpdioiISM61YzQkJ0HIkDSHV60yb7Vu3GhNWc7GZhiGYXURVoqMjCQgIICIiAj8NQdaREQk88Sfg19LQNlnoEbqtg/JyVC/Pvz3H9hs8NdfGjt3Mzm2h05EREQstvMTIBkqvpzm8JQpZpgDCAnRfq23QoFOREREMl/cGXMh4XLPg1f+lMPR0fDKFSuXfPopuGlNjptSoBMREZHMt/MT82eFwWkOf/wxHDtmPn/wQWjZMpPrclIKdCIiIpK54sJh93go/yJ45Us5fPQofPih+dzNzQx3cmsU6ERERCRz7fgIcIEKg9IcfvVViI01nz/3HFSokPmlOSsFOhEREck8cadhdxiU7w+egSmH//sPfvrJfJ4nD7z5pkX1OSkFOhEREck820eBixtUHJhyyDBgYOpL3noLAgPTuVauS4FOREREMkfsSdjzOZQfAB55Ug7bbPD++1Czpnmb9ZlnrCvRWWkisIiIiGSO7aPAxQMqvHTNqcaNYc0aOH7c3LdVbo966ERERCTjxZ6AvV+YYc4jd7pNXFwgKChzy8ouFOhEREQk4237AFy8zNutl0RHm9t8yd1ToBMREZGMFXMM9n4FFQeBR0DK4RdeMPdsXbXKwtqyCY2hExERkYy1/QNw8zUXEr5k/XqYONGc4dq6NRw5ArlyWVeis1MPnYiIiGScmKOw92uzd87dHzBD3EsvmT8B3nhDYe5uKdCJiIhIxtk2Etz9oNwLKYdmz4b//c98XqYMPP+8RbVlIzk20IWFhRESEkJoaKjVpYiIiGRP0Udg3zdQYbAZ6oD4eBg8OLXJxx+Dh4dF9WUjNsO43OGZM0VGRhIQEEBERAT+/v5WlyMiIpJ9/NcPjsyEtgfA3bynOmoUDB1qnm7WDP76y1xYWO5Oju2hExERkQwUfQj2fwsVh6SEuVOn4N13zdM2G3z6qcKcoyjQiYiIiONtfc/c3qvcsymH3nwToqLM5716QbVqFtWWDSnQiYiIiGNdPAD7vzd759x8ATh2DL77zjzt5wfvvGNhfdmQAp2IiIg41rb3wDMvlO2XcqhoUXMB4YYN4bXXoGBBC+vLhrSwsIiIiDjOxf2wfyLU+AjcfNKcql3bXK7EbremtOxMPXQiIiLiOJteB6+CUOaZdE/bbOCm7iSHU6ATERERxzi7Fg5Nhapvg5s3AFu2QFKSxXXlAAp0IiIicvcMAzYOgYBKUPJJAM6cgUaNoGZNc705yTgKdCIiInL3TiyCU0uh+gfgYt5THTECIiLMXrrJk60tL7vTThHaKUJEROTuJNthUQ3wCIR7l4LNxvbtULWqOQHC1xf27IHCha0uNPvSsEQRERG5Owd/ggtboNW/KVs/DBqUOpt12DCFuYymW64iIiJy55JiYfMbUKwT5KsDwMKFsGiRebpYMRg40ML6cggFOhEREblzu8dB7Emo9h4AiYlpA9yHH4K3t0W15SAKdCIiInJn4s/CtpHmjhB+ZQD46ivYudM8Xb8+dO5sYX05iAKdiIiI3Jmt74GRDJXfAODcORg+PPX0mDEpQ+okg+XYQBcWFkZISAihoaFWlyIiIuJ8Lh6APWEQMgS88gOwdKm5TAlA9+5Qp46F9eUwWrZEy5aIiIjcvhXd4PRSeGgPuPmmHN62DV57DT77DIKCLKwvh9GyJSIiInJ7zq2HQ1OgztdpwhxApUowZ441ZeVkOfaWq4iIiNwBw4ANQ8C/IpTqaXU1cokCnYiIiNy6E4vh1F8pW3wlJcE330BCgtWF5WwKdCIiInJrku2wcQjkbwRFHwLMMNe7t3mr9e+/rS0vJ9MYOhEREbk1ByfDhc3QahXYbFy4AG+YK5awdy+4u1taXY6mHjoRERG5OXscbH4dgjtCvnoAvPcenDljnu7cGe65x8L6cjgFOhEREbm5XeMh9gRUex8we+TGjjVPeXqaW3yJdRToRERE5Mbiz8G296FMH/AvC8CQIea+rQCDBkHx4hbWJwp0IiIichPb3gcjCSq/CZg7QsyebZ4qVAheecXC2gRQoBMREZEbuXgQdo+Hii+Dd0Hsdhg4MPX0e++Bn59l1cklDg90ycnJhIWF0bx5cypXrkyrVq344Ycfrmm3bNkyWrduTaVKlXj44YdZv359hrURERGRO7T5DfAIhApmips4ETZuNE/VqAFPPmlZZXIFhwe6d999l9dee42+ffsybdo0OnXqRJ8+fZgwYUJKmzVr1tCqVStq167NxIkTKVq0KE2bNmXfvn0ObyMiIiJ36NwGc6mSKiPAPRcAZ8+Ch4d5+tNPwdXVuvIklc0wDMORb9ioUSPKlSvHt99+m3LswQcfxNfXl+nTpwPw8MMPEx0dzR9//JHSJiQkhCZNmvDFF184tM3NREZGEhAQQEREBP7+/nf+wUVERLKbJa0g5jC03gouqUvX7t9vjqEbNMjC2iQNh/fQNW3alJUrV3L27FkADh8+zPr162nWrFlKm7///pv77rsvzXUPPPAAf1+xxLSj2oiIiMgdOLEYTv4B1T5IE+YASpVSmMtqHL5TxNtvv83FixcpUqQIBQoU4PTp04wYMYJ+/foBEBUVRUREBIUKFUpzXaFChTh69KhD26QnPj6e+Pj4lNeRkZF3/mFFRESyIyMZNg6F/PdAUDurq5Fb4PAeurCwMH788Ue+++47FixYwPjx4xk5ciQzZ84EzEkTAO5X7Q/i4eGB3W53aJv0jBw5koCAgJRHcHDwnX5UERGR7OngFDi/EaqPApuNFSvg7bchJsbqwuR6HB7oXn/9dQYPHky3bt2oWrUqffr0oWfPnrxxabM3Pz8/PD09U27JXnbmzBny5cvn0DbpGTZsGBERESmPI0eO3PVnFhERyTbscbDpNQhqD/kbkJwM/fvD8OFQvry5Q4RkPQ4NdMnJycTHx5MnT540x/PkyUN0dLT5B7q4ULNmTVatWpWmzT///EPt2rUd2iY9np6e+Pv7p3mIiIjIJbvDIPYYVB8JwKRJsG6deSowEEqWtLA2uS6HBjoXFxeaNWvGl19+yalTpwA4ePAgEydOpGXLlintnnnmGX755RdWrlwJwLx581i+fHnKODtHthEREZFblHAetr0HpXuDf3kuXoRhw1JPjx6tZUqyKodPivjmm2/o27cvxYoVI1++fJw5c4YOHTrwySefpLR54okn2LdvHy1atMDb25vExERGjx6dJvQ5qo2IiIjcom0jITkBqgwHYNQoOH7cPNW2Ldx7r4W1yQ05fB26yxISEggPD6dgwYK4uaWfG+Pi4lLaeFxepTCD2lyP1qETEREBog/DvHIQ8gpUHcHhw+aYubg4cHeHbdugbFmri5TrcXgP3WUeHh4ULVr0hm28vLxuOsvUUW1ERETkBjYMAY/cUNFcYG7YMDPMATz/vMJcVpdhgU5EREScxKm/4fDPUG8iuPuxejVMmWKeypsXLi1UIVmYw5ctERERESeSnATrXoS89aDk4xgGDBiQevqtt+CqxSskC1KgExERycn2fAEXtkLoZ2BzISkJHnwQfHwgJAT69rW6QLkVGTYpwlloUoSIiORYceEwrxzJwZ34X9xXnDgBhQtDo0Zw8iScPg01alhdpNwKjaETERHJqTa9SkKijdpPvseW3amHg4Jg7Fjo0MG60uT26JariIhITnR2Dca+bxk48R227E67ZeaxY9CxI8yaZVFtctt0y1W3XEVEJKcxkjF+r8+OrXFUHboOe/K1N+xsNrOn7sAB7Q7hDNRDJyIiktPs/wHbuf945tvx6YY5AMOAI0dg+fJMrk3uiAKdiIhITpIQAZte4SBdWb6z8U2bnziRCTXJXVOgExERyUm2jICkaI4X/OiWmhcunLHliGPk2EAXFhZGSEgIoaGhVpciIiKSOS5sg93jodLr1G1alBsNHbfZIDjYXMJEsj5NitCkCBERyQkMA5a0gJgj0HoL/6zypEkTSE6+tqnNZv6cOVNLlziLHNtDJyIikqMc+QVOLYGaYzgX4cljj6WGuav7M4KCFOacjRYWFhERye6SYmD9ICjSBqNIa3o9Ys5gBWjSBBYvhpUrSbNThJYqcS4KdCIiItnd9g8g7iTU+ovoaIiMNA/nzQuTJoGHBzRtammFcpcU6ERERLKzi/th+yioOBj8ypAL+P13GDUKKlc2b6+K89OkCE2KEBGR7Ox/D8O5ddBmJ7j5Wl2NZBD10ImIiGRXx3+Ho7/CPdOISfDFR/+vn21plquIiEh2ZE+AdS9CgaZMXdGJihVhxQqri5KMokAnIiKSHe0aCxf3caTgePo+Y+PwYXNG65YtVhcmGUGBTkREJLuJOQ5b38Ze+jkeeboyUVHm4a5doUoVa0uTjKFAJyIikt1sHAqu3oyY9RZr1piHypSBzz+3tizJOBoeKSIikp2c/gcOTmKL7ze8+2FuANzdYdo08POztjTJOAp0IiIi2UWyHda9QIJfKC169Uw5/OGHUKuWhXVJhlOgExERyS72fQ3nNzJo3mpOnzZHVT34IAwYYG1ZkvE0hk5ERCQ7iD8Lm15n88WefDatLmDuy/r992CzWVybZDgFOhERkexg0+tgJLHFZSReXmaImzwZ8ue3ujDJDDn2lmtYWBhhYWHY7XarSxEREbk75zbA3q+g5mi6VShItXqwfDk0a2Z1YZJZtJer9nIVERFnZhjwZyNIOA8PbAQXd6srEgvk2B46ERGRbOHgJAhfAc3/UpjLwTSGTkRExFnFhZP030vM+K8zL33YnPh4qwsSq6iHTkRExEkl/TeQi1EGz30/jvBIKFgQXnnF6qrECgp0IiIizuj4ItyOTqL/jxMJjyxA1apaby4nU6ATERFxNokXif67Lyu3tODH5U/g42Nu7eXlZXVhYhUFOhEREScT+c/ruCWE0/fbpYCN8eOhYkWrqxIrKdCJiIg4kaST/5Lr+DhenvERB8JL0aUL9Ox58+ske9M6dFqHTkREnIU9gZM/1OLIMS/qj1hFseJubNgAAQFWFyZWUw+diIiIk9g3/0OKu+/gvm/WYXNxY9o0hTkxKdCJiIg4g4gdlIp5lx83DGHz4WqMGgV16lhdlGQVCnQiIiJZnZEM//XGlqs4j73/BvbK0KOH1UVJVqJAJyIiktXt/crc3uvev3H38uapp6wuSLIabf0lIiKShe3dfBRjw1Ao0wcKNrG6HMmiFOhERESyqIgLBgdnPMvpc7nYyIdWlyNZmAKdiIhIFmQY8P3bM2hRcR7PfBvGS0Nzk7MXGpMbybFj6MLCwggLC8Nut1tdioiIyDUmfXeOrmVf4Jf/OrB0T3s2bgSbzeqqJKvSwsJaWFhERLKYHTtgzfinaFtjFiFDtjNuQhE6drS6KsnKdMtVREQkC4mNhdFD/uSJht8zeMrHtO2sMCc3l2NvuYqIiGRFw4bEMOzePizd3pTV4U+z5jerKxJnoEAnIiKSRcyaBUXPDqdIreO0G/M7Py+w4e1tdVXiDBToREREsoCTJ2HciHX8NWQ0r01/jxdeLUulSlZXJc5CkyI0KUJERLKA5KREzkyuw/Hj8OHG/5gyzV2zWuWWqYdOREQkC3DZ9QkFPDZztvF/fNFPYU5ujwKdiIiI1SL3wJYRUGEgFWvUsroacUIKdCIiIhYJD4dtW5Npau8NPkWhyltWlyROSoFORETEAoYBPXpAkdjvaNprGfYmf+Dq5mN1WeKktLCwiIiIBcaMgQ0rj/NR18FM/bcHZ9xaWF2SOLEM6aFLTk5m0qRJ/Pbbb9hsNh577DEeeuihNG127drF2LFjOXToEGXLlmXQoEEEBwdnSBsREZGsZN06GDoUpj77AvFJnhS8/xMKFrS6KnFmDu+hs9vttG3blhEjRtCiRQu6dOnCxIkTmTt3bkqb3bt3U6dOHaKjo+nRowcHDhygTp06nDx50uFtREREspKoKOjSBdpUm8UjdWbxx/nxNH8g0OqyxMk5fB26zz//nMGDB7N9+3ZKlCiRcvzixYvkypULgO7du7Nnzx7+/fdfABITEylbtiyPPvooH330kUPb3IzWoRMRkcxiGPD44/DHvFNs+aAKO87Up/6QOXh4ao0SuTsO76GbOHEibdu2TRPmgJQwB7B48WLatWuX8trd3Z02bdqwePFih7cRERHJKn78ESZPNvi2z9PYXKDEo18rzIlDODzQbd26lVq1ajF69Ggeeughnn76aRYuXJhyPiYmhvDwcIKCgtJcFxQUxMGDBx3aJj3x8fFERkameYiIiGS0XbvgueegT/OvaVNjATv8v6V4BQ2cE8dwaKAzDIO4uDhGjRrFzp076dWrF2XKlKFDhw6MHTsWgISEBAC8r9pt2MfHJ+Wco9qkZ+TIkQQEBKQ8NIFCREQymmFAr15QxG83o7sNZNmxPjTu+tDNLxS5RQ6d5Wqz2cidOzdlypTh66+/BqBdu3ZERkby0Ucf0b9/f3LlyoWbmxvnzp1Lc+3Zs2fJkycPgMPapGfYsGEMHDgw5XVkZKRCnYiIZCibDb6ZkEjC/Mc5E12E2n0+sbokyWYcvmxJzZo1yZcvX5pjxYoV4+zZsxiGgZubG5UrV2b9+vVp2qxfv57q1aubRTmoTXo8PT3x9PS8sw8nIiJyh8onvIdRdB0nq6zANyDXzS8QuQ0OH0P39NNP8+eff3LkyBEA4uLimDp1Ko0bN8Z2aafhHj16MGPGDPbu3QvA2rVrWbx4MT169Eh5H0e1ERERsdyZf2Hbu9gqvU7hynWtrkayIYf30HXt2pUNGzZQqVIlKleuzP79+ylRogSTJk1KafP888+zfv16qlWrRoUKFdi+fTvPPfccnTp1cngbERERK9jtMG4cPNPrIt4ru0NgLaj8mtVlSTbl8HXoLjt58iR79+6lcOHClCpVKqV37kqHDh3i8OHDlC5dmiJFiqT7Po5qcz1ah05ERDLCW2/BiBEwfXBfHqk1CZfWG8G/rNVlSTaVYYHOWSjQiYiIoy1bBs2bw4PV5zJ3UDv25vmSMg/0tbosycYU6BToRETEgc6ehWrVIDHK3A3igltdyvWaa051FckgDh9DJyIiklMZBvTsCceOGcwd1At3Dyjd5RuFOclwCnQiIiIO8tlnMG8e9G42gYdqzuds5bm4+mo3CMl4Dl+2REREJCfasAEGD4YyBffwafeXOOzem7xVtRuEZA4FOhERkbt08SJ07gz2pCR+evZxYihCsYdHW12W5CC65SoiInKXwsJgzx54s8N71C61luTm/4C7doOQzKNAJyIicpcGD4Z8/MuTRd4hMug1AovUs7okyWG0bImWLRERkbuVeBEW1iDJNRC3B/4BF3erK5IcRj10IiIid2vDIIg9jtsDvynMiSU0KUJEROQOfPghrF4NHJ0He7+GmqO1tZdYJscGurCwMEJCQggNDbW6FBERcTILFsArr0D7B04TvbQXFGkDZfpYXZbkYBpDpzF0IiJyG44fN7f2OnPG4NeB7WhRYzU+j2wBby0gLNbRGDoREZFbZLdD9+5w5gz0avYNbWvNw2j0q8KcWC7H3nIVERG5XSNHwtKl5m4QY58YQFxQb2zBba0uS0SBTkRE5Fb88w+MGAGuLuZuEDafInjV124QkjXolquIiMhNnDsHjz1m3nId3uFd6pRei4t2g5AsRD10IiIiN2AY0KsXHDkC91b6kzc7vA1V3oR82g1Csg4FOhERkRvYtg1++w2KBh5l2gtdSQhsiUvl16wuSyQN3XIVERG5gcqV4d/Vidh/74yvvxdezSaBi6vVZYmkoUAnIiJyE9WSX8Eo9h+2Fv8Dr/xWlyNyDQU6ERGRGzkyC3aOxlZzDOSvb3U1IunSGDoREZGr/PwzvPwyJJzdA6t7QnBHKP+i1WWJXJd66ERERK6wfz/07g1J8TH0CepI6RIFcan3LdhsVpcmcl0KdCIiIpckJEDXrhAVBd/2fp5igXuwNf4X3LXXt2RtCnQiIiKXvP46/Pcf9GzyHU81/Z7Y6j9gy1PF6rJEbkpj6ERERIDff4ePPoJqxTcS1uM5wgN64x3yhNVlidwSBToREcnxTp6EJ54Af+8IZr7YkUhbRfLfP87qskRuWY4NdGFhYYSEhBAaGmp1KSIiYqHkZHj8cTh92uD7vj0pFHiGAu1ngKuX1aWJ3DKbYRiG1UVYKTIykoCAACIiIvD316BXEZGc5sMP4ZVXYGDrT/ik22Aiqs0hoFI7q8sSuS05todORETEbod58+Cecv/wYZehHPZ9WWFOnJJ66NRDJyKSoyVEniJudg3OJZahxFN/gYu71SWJ3DYtWyIiIjlXsh2PNY/h4ZeM333TFObEaSnQiYhIjmMYlzZ+2DICTv8Nzf/E5lvE4qpE7pzG0ImISI6ybRvUrg37/1kI296Fqu9CwWZWlyVyVxToREQkx4iJgc6d4czhQwRs785ZzwchZKjVZYncNQU6ERHJMQYOhD274pnx4qPE2f3wafEj2PR/heL8NIZORERyhBkz4KuvYPyTg6hWbBPHK6/AOyDQ6rJEHEL/LBERkWzv4EHo3Ru61J/K863CWMcYStaqbXVZIg6jQCciItlaYiJ07QqFfXcwoVdv/jn6GPUff8bqskQcSrdcRUQkWxs+HHZsvsCqER04HlmcKk9/hc3FZnVZIg6lQCciItnWn3/Cxx8lMn9wJwrlPsmRiqsJyJvL6rJEHE63XEVEJNvau9dg3BP9aVZxKYtjf6Fqw/JWlySSIdRDJyIi2dYzzT4D/y/4adfXdBve3OpyRDKMAp2IiGRPxxfC+gFQYSCPP9bb6mpEMlSOveUaFhZGSEgIoaGhVpciIiIOFBcHXNgK/3SGwq2h+iirSxLJcDbDMAyri7BSZGQkAQEBRERE4O/vb3U5IiJyFyIi4L6mp1k0oA4B+QKwtfoH3P2sLkskw+XYHjoREcleDANeeDaOT9q1Jy46jreWzVOYkxxDY+hERCRb+P57g1YBvahVYh0PjlnGt3OKWV2SSKZRoBMREae3YwccWfgew9tPpvP4aTzzWl1KlLC6KpF02O2wfDmcOAGFC0OjRuDqetdvq0AnIiJOLTYWvh0+g4/bv8GbM98id9XOPPqo1VWJpGPWLOjfH44eTT0WFARjx0KHDnf11poUoUkRIiJO7cOha3ixYmNmr23P+39P5r//bPj4WF2VyFVmzYKOHc3BnleyXdqGbubMuwp1CnQKdCIiTmvRL0eodrIOB8+U4IGPl7JitReVKlldlchV7HYoUSJtz9yVbDazp+7AgTu+/apZriIi4pSOHLhI0X0PkWD34OHRc/jwY4U5yaKWL79+mAOz1+7IEbPdHdIYOhERcT7JdvLs6EZg/n3UG76Sxq0K0qeP1UWJXMeJE45tlw710ImIiPPZNIxcEfNxazqNdk9UYcKE1KFIIlmGYcAvv0CePLfWvnDhO/6jFOhERMS57PsWdnwENT7Bs+SDvPsu5M5tdVEiVzl50pzk0LEjLFpkjpG73r86bDYIDjaXMLlDGXrLdfv27YwbN46aNWvS56q+8LNnz/LDDz9w6NAhypYtS48ePciVK1eGtBERkezh4r6/8f3vGWxl+kL5/laXI3Itw4CpU+GFF+DcOfPYuHEwZgwMGGCGtyvno14OeWPG3NV6dBnWQxcbG0vnzp2ZM2cOixcvTnPu5MmT1KhRg7lz51KoUCEmTpxIvXr1iIqKcngbERHJHozIPST/7xH+PdCEXf7jdY9VMt1NFwa53CvXrVtqmMufH6ZPhxdfNJcmKVo07TVBQXe9ZAlk4LIlffv2xcPDgwMHDuDl5cXMmTNTzj333HMsXbqUjRs34uHhQWRkJGXKlOHFF1/k9ddfd2ibm9GyJSIiWdflRfXPHD9Po9h6nD9vo/7wVQQWysOuXeCmqX2SSQ5HHKbrL10Z3mQ4rUq3SnvSMGDaNHj++dQgB9CpE3z2mRnqLsugnSIypIdu5syZ/PPPP4waNSrd83PnzqVjx454eHgA4O/vT9u2bZk7d67D24iIiHOaNctcuqtli0TybO2IW9IZ2nw8nwsxefj8c4U5yTyL9i6i5lc1ORJxhADPgLQnL/fKPfZY2l65GTPg55/Thjkww1vTptC1q/nTAWEOMiDQHTx4kOeee47Jkyfj7e19zfm4uDiOHj1KyZIl0xwvWbIke/fudWib9MTHxxMZGZnmISIiWcvlRfWPHjX47MnnaVRhOR3GzGLfqTIAREdbXKDkCPZkO28ufZPWk1tTp2gdNvTdQN2gumkbTZ4Mc+akvu7UCbZtM7/AmcihgS4pKYmuXbsyZMgQqlevnm6b2NhYAPz8/NIc9/f3JyYmxqFt0jNy5EgCAgJSHsHBwbf46UREJDPY7eZ2l4YBb3d8k773fk3fb7/ifzubAObQuQEDzHYiGeV09Gnum3Qf7y1/j3eavcP8x+aT1yfvtQ3794c6dW7cK5cJHNphvWjRItavX0/VqlV55plnANiyZQtubm4888wzvPfee/j7++Pi4sKFCxfSXHv+/PmUMWy5cuVySJv0DBs2jIEDB6a8joyMVKgTEclCLi+q/9IDo3mj/bu8PGUUE//XM+X8lYvqN21qXZ2Sff1z+B86z+xMUnISfzz+B81LNjdPGAZs3gzVqqU2dnMzZ7X6+VkS5FLKcOSbVa5cmbFjx6Y5tnLlStzc3KhevToeHh64u7tTtmxZtm/fnqbd9u3bqXRpzxZHtUmPp6cnnp6ed/wZRUQkY504AT2bfMfo7oN4/9dhfLzg5eu2E3EkwzAYvWo0Q/8cSoPgBkzrOI0ifkXMkydPQr9+MHcurFpl9spdVqqUNQVfychgDz74oPHII4+kOTZ8+HCjSJEiRnh4uGEYhrF//34jV65cxpdffunwNjcTERFhAEZERMQdf0YREXGcLb/NNJJ+cjE+7/mMAcmG2S1y7WPpUqsrlezkfOx54+FpDxuMwBiyeIiRaE80TyQnG8aUKYYRGJj65atY0TASEqwt+CoZtmzJZW3atLlm2ZKYmBjuv/9+Dh06RL169Vi2bBl169bll19+we3StCVHtbkZLVsiIpKFnPgDY1kb5q7vQIePJ5FsXDsD0GYzl+46cMBhEwQlh9t4ciMdp3fkTMwZfmz/I23LtzVPXO6Vu3LSQ/788PnnmT7p4WYyPNAtXLgQNzc3WrZsmea43W7n77//5vDhw5QtW5aGDRtec62j2tyIAp2ISBZxZjUsaQH5GzP73BweedRckiq9RfUdsA6rCIZh8O2Gb3n+t+epVKASMx6dQak8pdLf7QHSX1cui8jwQJfVKdCJiFhv7Z9bqHKqCZ4FKkGz38HNh1mzzAmER4+mtgsONndIUpiTuxWTGMOzC57lh00/0LdWX8bcPwYvNy+n6pW7kgKdAp2IiKXmTtlH6IWGnIwoxNlqS2nROnfKuQxaVF9yuF1ndtFxRkf2n9/PV22+onvV7qknW7SAv/5KfZ2Fe+WupECnQCciYgnDgPGjjtPGsyGJSe40emc5Te8rwPTpVlcm2dn0bdN5eu7TBPkHMfPRmVQqcNXKGJs2Qe3akCdPlu+Vu1KGbP0lIiJyI4mJ8NKzZ2lOK9xdE2n5wR+071KAKVOsrkyyqwR7Ai8ufJHOMzvTplwb1vReQ6X8IXD+fNqG1aqZiwNbsNvD3VCgExGRTBUVBZ3aR9G1cGsKBpyi5cg/eHZwMb78UvuzSsY4HHGYxt835su1XxLWOowpHaaQ69xFczBm06aQkJD2gg4dsvwt1qsp0ImISKY5dgxaNIvj+aoPU7HoDtqM/p3hn1TglVdSZ7CKONLsHbOp8VUNTl48yYqnVvBs7X7Ypk2DSpXMiQ+bN8N771ld5l1ToBMRkUyxZQvc0yCJVxp1pUG5lXT9cj4ffVOTrl2trkyyo+iEaPrM60OH6R1oUrwJ6/uuJ9Q12Ox9e+yx1OVI8udPu5WXk1LntoiIZIqkxGTefag3bWrMp++UOXzyU2MqVLC6KsmO1h5fS7dZ3TgaeZQJD03g6epPYfv5Z3j+eadZV+52KdCJiEjGMwxqGIOo3uAHRiyexMgfHqRgQauLkuzGnmzn45Uf8/rS16lWsBrr+6ynfFIAPPKI060rd7sU6EREJEMYBiQnX1o3buu7sGsMttDPGd7lMVw04Ecc7EjEEZ6Y8wTLDi5j6D1DeavZW3jExEOlMnD6dGrDbNQrdyX9T0pERBwuIQF69jR3ejB2jYctb0LVd6FsP4U5cbgZ22ZQ7ctq7D23lyVPLmFki5F4uHqAnx/06mU2yp8fZswwlyTJZmEOcnAPXVhYGGFhYdjtdqtLERHJVi5cMO9wLVkC3e6ZhG3di1BhEFR61erSJJuJio+i/6L+fL/xex4NeZSvHvySPF650zZ6803zXxhDhmTLIHeZdorQThEiIg5z+DC0bm2uyfpQzbnMGtCBI+5PUrLzN1qXRBzq36P/0m1WN05Fn2L8A+N5suB92J59FkJD4dWc948HdXyLiIhDrF8PdeuaYa519QVMf7ETEX4PU7LT1wpz4jD2ZDvv/u9d7vnuHvL65GVDn/X02O6BrXJlc+LDiBGwdavVZWa6HHvLVUREHOe338yx5tHR0L72LKa90IWE/A+St9VkcHG1ujzJJg5dOET32d1ZeWQlrzV6jTfK9ca914tpZ7Dmzg0nT0LlylaVaQn10ImIyF358kt46CEzzHWpP5Xp/TthBD1Crvumg6un1eVJNjF1y1SqflmVIxFHWPbk37x9ogLuVaunDXOdOpldxC1aWFWmZRToRETkjn3xBfTrZy5P8mTjiUx+rhuU6I5n00ng4m51eZINRMRF8Pjsx3ls1mM8WPZBNrb/nYYDRkO3bml3e8jGM1hvhSZFaFKEiMgdO3UK6teHVqW+5Mun+mGU7outzudgU3+B3L0Vh1fQfXZ3zsac5YsHv6BbYgVo1Srb7vZwNzSGTkRE7ljBgrBq4hgKHn0JyvfHVvNTTYCQuxaXFMeIv0fw0cqPqBdUjyVPLKFknpIQGwv58pmBLhvu9nA3FOhEROSWHThgjjnPk+fSgW0jKXj0VQh5Baq9rzAnd23VkVU8Nfcp9p/fz7vN3uXle17GzeVSXPH2hokTYdw485HDe+WupD5xERG5Jf/9Zy5L8sgjkBBvwObhsOlVqDJCYU7uWkxiDIN+H8Q9391DgGcAGx5ZzLCwTbjt2Ze2Yf36MHWqwtxV1EMnIiI39euv0LWrecdr6VKD1V8OpXH+j6D6BxAy1OryxMktP7Scp+Y+xZGII4xq8SEvHSyMa8MO5q3Vw4dh+fJLmwLL9aiHTkREbmjcOGjf3gxzNlsyM4f1N8NczTEKc3JXohOi6b+wP00mNqGAbwE2dfyTwR+vxLX746kTH/buhX37bvxGoh46ERFJn90OgwfDmDHma5stmT/ff4bmxSZA6JdQtq+l9Ylz+/vg3zw992lORJ1gdKtPeGF/flzvaZd2BmvnzuYM1nz5rCvUSSjQiYjINWJioHt3mD3bfO3qksSa8U9TPc8kqDsRSj1paX3ivKLioxj651C+WPsFjYs35vf7JlHmlVFpFwjOn99c5PCRRyyr09ko0ImISBrh4ebOD//+a7729Ehk+4TulHL/BRpMgeKdrS1QnNaf+/+k19xenIk5w/gHxvPsiSBcGrRRr5wDaAydiIik8dFHqWEuMHc8hyY9SimP2dBwhsKc3JGIuAj6zOtDy59aUjqwNFv6beH5Os/jEpD72t0epk1TmLsD2ilCO0WIiKQRHw/33w9HDsSyflwH/GOWQqNZULS11aWJE1q0dxG95/UmIi6Cj1p+RJ9afbBducTNCy/A6dPa7eEu5dhbrmFhYYSFhWG3260uRUQkS/H0hFnTo/Fe0xavqNXQdAEUutfqssTJnI89z8DFA5m4cSKtSrdiQt33KDZpHtQ00q5Z+Omn4JZj44jDqIdOPXQikoMZBowdCw88AOXLXzqYGAl/t4bzm80wV6CRpTWK85m3ax595/clOjGaT1uNpucOL2wvvmjeXv3sM3juOatLzHY0hk5EJIdKSoJnn4WXXjID3enTQNwZWNISLmyF5n8ozMltORZ5jE4zOtF2WltqFK7Bto5Leeqd+di6d08dK/fJJ5CYaG2h2ZD6OEVEcqCLF6FLF1iwwHx94AAs/20PjwS2hqRIuHcJBNa0tkhxGknJSYz/dzxv/v0mvu6+TGr/E49tsWGr2zL9Gazu7tYVm00p0ImI5DAnTkCbNrB+vfna3R3mffcP93m1A5cC0Go15CppbZHiNFYeWUm/Bf3YcmoLz4Y+y7uVXiD3gFe0rlwm0y1XEZEcZNs2qFcvNcwFBMCGOVO5z+1eyF0VWq1UmJNbcjbmLL3n9uae7+7Bw9WDNb3X8NmFBuSuUT9tmOvcGbZvV5jLYOqhExHJIZYuNfdkjYgwXxcrZvDf9yMpePI1KPE41P0GXD2sLVKyvGQjmYkbJzLkjyEkJScR1jqMvrX64uriCn9/BefPmw3VK5epNMtVs1xFJAeYNAmeeip1LHqd2oksHdUPnxPfQpURUPnNtEtJiKRjy6kt9FvQjxVHVtC9anc+bvkxBXMVTG0QGQmVK0ODBtrtIZOph05EJAc4cSI1zD36cART+nXE7dQyqPcDlHrC2uIky4uKj+KtZW8xZvUYyuYty5InltDMuyKs2gwtW6Y29PeHdeu0QLAFFOhERHKAwYPNmayBnod4594HsUUcg2aLoWBTq0uTLMwwDGbtmEX/Rf05F3uOd5q9w6D6A/GYMQue72j+K2HrVihWLPUihTlL6JarbrmKSDZkt4Ora9pjyWfWYftfG2yuXtD0NwioaE1x4hT2ndvHCwtfYOHehbQp14Zx94+jZLw39OuXdtJDly4wdapldYpJs1xFRLKZo0chNBQWLrzy4Dxc/mqMzbeYuSyJwpxcR3xSPO8se4fKX1RmW/g25nSew7wucym5cBVUqnTtDNbx4y2rVVLplquISDayaRO0bg3Hj8Ojj8Ly5VDDZzysHwBF20GDSeDmY3WZkkX9uf9Pnl3wLAcuHGBQ/UG80fgNfM9FQYcOWlcui1OgExHJJn7/3QxxUVHm68KF7JQ4Oxh2jIEKA6H6KHBxveF7SM60L3w3Q6f35pcz/6NxQFVm915HpYJVzFupL7yQ/m4PmsGapSjQiYhkA99+C337mmPnAJo2jGbRm93wDJ8HtT+DctoMXa51Ie4C7337JONOzSV/NPz4J3TfvBnbJw/CBx/Ayy+nhjn1ymVpGkMnIuLEDANefx169UoNcz27nOSvYU3xPP8nNP5VYU6ukZScxOdrPqfsx8X5/PhcXl8Gu8fD45vBBnDsGDz+OPToYV6g3R6yPPXQiYg4qfh4ePppmDw59dgHr2xjSN0HscUnQIv/QWBN6wqULGnhnoUMWjyInWd28uRub96bB0WirmpkGOZC05MmwapV5n5xkqXl2B66sLAwQkJCCA0NtboUEZE78uijqWHOZoNfPv+LoTXvwebhD63+VZiTNLad3sb9k+6n9ZTWFPAtwNqaX/L9lJhrw9xlhgFHjkBcXKbWKXcmxwa65557ju3bt7NmzRqrSxERuSP9+plrzXl7G2z8eTwdct8P+epBy3/AN9jq8iSLOB19mn7z+1H1y6rsO7+P2Z1ns/TJpdTcc/HW3uDEiYwtUBxCt1xFRJzUAw/Aj99FcV/u3uS9+DOU7w81PgIXd6tLkywgPimesf+O5b3l7+Fic+Hjlh/zXJ3n8Niy3VwMePr0W3ujwoUztlBxCAU6EREnsWWLue+5zXbpwIVtPBbYEWKOQsPpUOxRS+uTrMEwDH7Z8QtD/hjC4YjD9Kvdj+FNh5Nvwy5o2x5+++3W3shmg6AgaNQoYwsWh8ixt1xFRJzJF19A9erwySeXDhycAr/XAZsr3L9WYU4AWHNsDY0nNubRGY8Skj+Erc9uZXzr8eTzyQdvvZU2zBUsCN27m8Et5V8Jl1x+PWbMtXvISZakQCcikoUlJ5tLgT37rPn8tWHxnJj7HKzsBsEd4L5/wb+81WWKxY5GHuWJ2U9Q55s6RMRFsPixhczvMpcK+SqkNnr1VfNn8eIQFgYHDsBPP8HMmVC0aNo3DAoyj3fokHkfQu6KzTAMw+oirBQZGUlAQAARERH4+/tbXY6ISIq4OHjiCZgxw3xdLN8h/hn5KEG5NmGrNRbK9L22Z0VylPOx5/l45cd8uvpT/Dz9eKfRcJ7e5onrh6Pg44/hoYdSGxsGzJtnDr50v2qcpd1u7hN34oQ5Zq5RI/XMORkFOgU6EcmCzpyBdu1g5UrzdevqC/llcHe8cvlBw5mQt7a1BYqlouKjGPvvWD5e+TGJyYn0r/ksr+zOj//Hn5lLjQDUrWuuIafQnyNoUoSISBazdy+0bg179oCLzc57Xd5iaJt3sRV5AOr/BJ6BVpcoFolLiuOLNV8w8p+RRMRH8EyVnry6LZCCT3wD4eFpG3t5QWQkBARYU6xkKgU6EZEsZNUqaNvW7KHL5xfOzJe60bj8X9iqvgOVhoFNQ59zokR7It9t+I53/vcOJy+epGeFLryxKTfFnvjJDG1XatMGhg2DBg2sKVYsoUAnIpJF2O3mnqxnzkC9MquYPehR8udNwNZoMRS61+ryxAL2ZDtTtkxhxLIRHDh/gK5VujKi0vOUrdkCYmJSG7q4QKdO8MorUK2adQWLZRToRESyCFdXmPWLwcRXx/FOh8GQtw6uTaaDT9GbXyzZSrKRzKwds3hz6ZvsOLODhys8zJzOc6hSsIrZoHlzmD/fnNzw5JMwZAiULWtt0WKpDJkUsW/fPpYvX05iYiKhoaFUr179mjYJCQnMnz+fQ4cOUbZsWR544AFcr5pR46g2N6JJESKSZSRGwb+94PB07GVfwrXWh9r1IYcxDINFexfx+tLXWX9iPa3y1+PdvcUJ/Why2lmnq1ebOz0MHGguMSI5nsMDXc+ePVm1ahX16tXD1dWV6dOn061bN7788suUNpGRkTRt2pTY2FgaN27M77//TqlSpVi4cCGenp4ObXMzCnQiYpXoaHNliWHDwCNmG/zzCMQch3rfQbGOVpcnmWzZwWW8tuQ1VhxZQcOAqry3ypvG0/81T86YAR31nZAbMBxs4cKFht1uT3m9evVqAzD++uuvlGOvvPKKUbx4cSMiIsIwDMM4duyYERAQYIwdO9bhbW4mIiLCAFLeQ0QkM5w8aRihoYYBhvH5kJ+M5Gk+hjG/smFE7LK6NMlk/x7912j5Y0uDERg1R5UxFrarZCSbq8alPu67z+oyJYtz+HSp+++/HxeX1LetU6cOHh4e7Nu3L+XYjBkz6NSpU0qPWJEiRWjTpg0zLq+e6cA2IiJZzc6dUL8+7N52gYl9n6RftceJyv0I3Lca/MtZXZ5kkk0nN/HwtIep+01djh3bwcz/SrJ2yF7u/3UbKSvHXd7VYfZsK0sVJ5DhkyLmzp1LQkICderUAcwxb/v376d8+bRb1ZQvX55FixY5tE164uPjiY+PT3kdefV0bxGRDPS//8HDD0No0O98O/Bp/H2iOBL0PcGNntQCsDnEyiMreX/5+yzYs4BSXkX4cWUhHvvjKK5XDoCqWNG8F9+ly7W7OoikI0MXNDpw4AB9+vShd+/eVLs0jTo6OhrDMAi4aqHD3Llzc/HiRYe2Sc/IkSMJCAhIeQQHB9/15xQRuRVTp0L7h6IY2b4vv79yP0ciQohpspXgxj0U5rI5wzBYvG8xTSc25Z7v7uHAhQP81P4ndrZZyON/nEoNc7Vrw6xZsHUrPP64wpzcsgzroTt69CgtWrSgXr16hIWFpRz38fEBru0Zi4iIwNfX16Ft0jNs2DAGDhyY8joyMlKhTkQylGHAhx/Cwh+WsfatHuT3D2f86i/o8W5f/PwV5LKzZCOZOTvn8P7y91l3Yh21A0KY3Xk2bcu3xeXyItHt28O5c/Dqq9CihcK93JEMCXTHjh2jWbNmVKpUiRkzZuB+xb8wPD09KV68OHv37k1zzd69eylXrpxD26TH09PzlmfAiojcraQkGPBCLKUvvsqyN8bwv52N+Gb/n4z4pLQ6X7KxRHsiU7dOZeQ/I9l5ZifNkovzxywf7o2OwfZ8m7Q7fkyaBN7e1hUr2YLDb7keP36cpk2bUrFiRWbOnImHh8c1bdq3b8+MGTOIjY0F4OzZs8ybN48OHTo4vI2IiJWM8NUMrVKdfvd+wUs/jWaF99+8O1ZhLruKTYwl7L8wyo4vy5NznqTs8XhW/ujBkrcP0WJrDLYDB+Hnn9NepDAnDuDwdegqV67MoUOHePnll9OEuYYNG9KwYUPADF4NGjTAz8+Pe++9l3nz5pErVy7+/vvvlFupjmpzM1qHTkQyhD0etrwFOz4kyb8WnT/9gUeeqshjj1ldmGSEyPhIvljzBaNXj+ZMzBk6RxXnlSmHqXrcntrI3R169IChQ6F0actqlezJ4YHujTfeIDEx8ZrjLVq0oEWLFimvL168yM8//8zhw4cpW7Ysjz766DW3Qh3V5kYU6ETE0ZLPbsDl3ychcidUGQEVh2A33LiNTWzESZyJOcPY1WP5bM1nRMdfpMfZYIZMOkCZc1c08vGBvn1h0CAoqm3cJGNkyNZfzkSBTkQcJjmR/fNGEhz5DgRUwr3RD5BHG6VnR0cjj/LJyk/4ev3XADxT6xkGzjlF0S8npzbKnRtefBFeeAHy5bOmUMkxMnwdOhGRHCFiO2fmPUExYyMj5w5j0dE3+KOFB7c2+EOcxeZTmxmzegyTNk/C18OXwfUH80LdF8jnkw/K7IOvp0L+/GZvXN++oI4CySQKdCIit8luh+XL4cQJKFzITqP8ozE2vkH4iZI88OUq1u4P5aGHzOVKxPnZk+3M3z2fMf+O4e+DfxPklpd3N+fjmYYD8G82JLVh6dKwcCE0bgxeXtYVLDmSbrnqlquI3IZZs6B/fzh6FEoX3MsPzzxJ/TKrGL1wIG/MeIe4RG+efx7GjEFj5pxcRFwE3234js/WfMb+8/up71GaAX9F037pSdyTgaAg2LcP0lnNQSSzqYdOROQWzZoFHTuCm0sCg1qP461HhnMyohCN3/kfK3abs/g/+QReeklrwzqzPWf3MP6/8Xy/8XvikuLo5FaNqb8WoM6GfWkbFipkdtMWL25NoSJXUA+deuhE5BbY7VCiBJQP+JPxT75AucK7+Wzx87w2/T2i43MBkDcvnDqlnjlnZBgGSw4sYcy/Y1iwewF5vQN5Jr4K/b7dRJFD59M2btbM3NXh3nuV3CXLUA+diMgt+G/pIT59ZBAd6/zC/3Y2ovP4n9lypGqaNmfPmmPrmja1pka5fbGJsUzaPIlx/41j6+mtVC1YlW8e+ILHOgzH69jfaRs/9BAMGwb161tSq8iNKNCJiNyIPQ5j+8eEnn6fYmXy8FjYZKau7Aqk3zNz4kTmlid35mjkUT5f8zlfr/uac7HnaFu+LePuH0fTEk2x2WzQYRuMHw8uLtClC7zyClSpYnXZItelQCcich1RO+eT9F9/ctkOs99jILVffp2LcX43vKZw4UwqTu7I6qOrGfvvWGZun4m3mzdPl2jPC/8kUuqlL9MuMTJ4MMTHw5Ah2tVBnIICnYjIVXau2UvCqgFUzbeAxTta8uIPC+jUqwK580H0sfSXI7HZzEmPjRplfr1yY1HxUUzbOo0J6yew5vgaygSWYXTFAfSYvhu/134y/0JL1ICXX069qFgx+Oor64oWuU0KdCIiQFISzJ8TTeTqkXSu8hEnKUT7T2cxZ+3DgI0jR2DsWHOWq82WNtRdHhevpUqyDsMwWHt8LRPWT2Dq1qnEJMZwf+n7mVdlJK2/XorL7x+nveD7781eOU1yECeVYwNdWFgYYWFh2O32mzcWkWzrzBmYMMHg0PJfePX+gRSofJoP5w3lg3mv4O7lQ//+8NxzULas2X7mzNR16C4LCjLDXIcOlnwEuUJEXASTt0xmwvoJbDy5kWD/YAbXH8RT50sS/MkEWDEs7QWFCqXu6qAwJ05My5Zo2RKRHG36hO0EHniRFpX/4td1bXnpp0/xzFuK55+HJ54Av3SGzKXZKaKweZtVPXPWMQyDlUdWMmH9BKZvm06CPYGHyj9E75q9uS+uKK6PPwmbNqW9qEQJGDoUevTQrg6SLeTYHjoRyXkSEyEy0lwvjsRI2PI2j+Yay/4CJXjwowW4Brfmq8nQosWNO2tcXbU0SVZwNuYsP23+iQnrJ7A9fDslc5fkjcZv0KN6Dwr7XZqdcu4c7N2belFIiLn0SJcu4Kb/C5TsQ99mEcn2Tp2Cr7+GL7+Eli0NJg6fDBtehsRIbFXfZue+gYyb6anJjE7AMAyWHVrGhPUT+GX7LyQbybSv2J6x94+leYG6uGzaDH5XTDUODIRnnoH//c9cDLhtW3MpEpFsRrdcdctVJNtas8ZcSuznnyEhwaBVlcW82+kNQkutgWKdoMbH4BtsdZlyC05Hn2bixol8s/4b9pzbQ7m85ehdszdPVnuS/InuEBZmDmSMj4dDhyBPntSL4+PN/VY1Rk6yMfXQiUi2kpBgTlwYNw7+/dc81rjCMt599HUaVfiHHWcacLziUorUaGplmXIL4pPiWbh7AZOWjmXumRW42Fx4tFInvmn7DY2KNcJ2+jS8O9oMc1FRqReGhcHrr6e+9vTM/OJFMpkCnYhkC3Fx8MEH5tJhJ0+ax+qVWcU7j75Bi8p/cTSmJqdCfqNitfvVU5OFJRvJrDi8gslbJjN942TO2y9S4wR8vBG6b7YTmHcZvN4ItkyHb781/+Ivu7yrw8MPW1W+iGV0y1W3XEWyBcMwx7vv3Ak1Sqzn7Y5v0qbGAs4lV8a33jt4lm6nIJeFbQ/fzqTNk5iyZQqHIg5R3D0/3ZaE020zhITf5GIPD+jZ01wYWAMhJYdSD52IOJ34ePjzT3jwwdRjNhu8+eJWPHcPp0PoLGLcymHUmUpg8U5g0yD4rOh41HGmbpnKpC2T2HhyI3m88tCpUie6VerCPY2743L0Jm/g4wP9+sHAgVCkSKbULJJVKdCJiNM4dsycqfrVVxAeDhs3QrVqQORu2PIWXQKmYm9YHGpMxKdEN3DRf+Kymsj4SGbtmMWkzZNYcmAJHq4ePFT+IYY3Gc4DZR7AM8kwpyQfPXbzN5syBdq1y/iiRZyA/msnIlmaYcCKFeZs1VmzzC26Lpsy4SDVur8NB34Er0LYQr/ArVRPcPWwrmC5RoI9gUV7FzF5y2Tm7ppLfFI8TUs05Zu239Ahb0Nyr9sG3/wDKz6EdevMBQNvRUxMxhYu4kQU6EQkS4qLg6lTzSC3YUPac8XyH2NC//doUfIbOB4INT6Bsn3BVSv+ZxXJRjIrj6xkypYp/LztZ87FnqNqwaq83fRtukYEE/TzQnjnfdi3787/kMKFb95GJIdQoBORLOfHH81hUWfPpj1eqdQpvn7pA+rn/QKbuy+EvAvlngM3X2sKlTSSkpNYdnAZs3bMYvbO2Zy4eIIgz/z0rt6TbjWepErBKmbD8ePNv+T0lCsH9evD3Llw4YLZRXs1m83cQLdRowz7LCLORoFORLKcfPnShrmHmh/ig57jqOj+JTYXN6jwKlQYAO6amW61+KR4/tj/B7N2zOLXHXM4F3+eYsl+dDnoQ/vlrtxzMByXpQ/B5TAHcM895k9PT6hd23x9zz3QoIH5lw/m/fWOHc3wdmWouzxTecwYbaArcgUtW6JlS0QsExNjjmsvUybt3qjJyVClCnRsuooXW31K3phfwM0fyj0LFQaBZ6BlNQtcTLjIor2L+GXVtyw49jdRRhzlItx5ZHMij2yHmicgzQIx774Lr72W+jopCf77D2rVuvGiv7NmQf/+cPSK6a7BwWaY69DBwZ9KxLkp0CnQiWS6gwfh88/hm2/g/Hlo0QL++OPSyeREOPwLyTvH4HLuX/ArC+UHQKkndWvVQheizzJv72/8suMXft/3O3FJcVQ/70mHDfF02GGuFXfNKn8VK5o9b507m3/Jd8Juh+XL4cQJc8xco0bqmRNJhwKdAp1IpjAMWLLEHD41b57ZC3el/TvPU9I+AXZ/BjFHoGBzqPASFGmtdeSscPQop5f9xpyN05gVs46/8kWS5AL1gurxSMVHaF+hPaVffh+++85s7+UFdeqk3j6tXx8C1ZMqklly7Bi6sLAwwsLCsNvtVpcikq1FR8NPP8Fnn8G2bWnPeXjAiz33MPihsRTcNNHsnSvxmNkjl6eaFeXmTHY7bNkCK1aw779FzD/9D7MKXeCfYoAPNAmHT9dC+xlbKFqscup13bpBpUpmgKtRw/wLFRFLqIdOPXQiGebMGShb1pyseKUiRQw+eOlvOlX9FM8z88EzH5TtZz68C1lSa04Vt3Y1/+vZnN+CYllYBnbnA3c7tNwHHXZA212QP9ZmBrepU6Fy5Zu/qYhkOgU6BTqRDHXvveatVoBmjeMZ2W8adfzHYLuwEQIqmbdVS3TTGnIZ6fBhc3XmFSugaVMOtQjltz2/sXDvQv7a/xcxSTEERUDrPeaj+Ukv/GrUS3v7NHduqz+FiNyAAp0Cnchdi4oylxVbuNBcPszliiFvCxbA4rnhDH3kS4pc/BziTkLhB8wgV6hF6jIU4hhJSbBpU2qAW7mShBNHWREMv5WF32oHsN0zAlebKw2LNaR12da0HrOASuTHdk9DM8BVrw7u7lZ/EhG5DQp0CnQid2zPHnNs3MSJEBlpHluwAFq3BoxkCP8H9n8Ph6YBNij5BJTvDwEVLaw6m/r5Z3MP1H//hehojvnBwrJmiPujFFz0hEJR0PpkLlq/OpEWpVoQ4BVgddUi4iA5dlKEiNyZ5GT4/XdzturChdee37zqAK2Df4T9P0D0AfAtCZXfgDJ9wTNv5hecnRiGuebLihXw6KNp1nBLOHqIf/cu4bd6ZpDbVAhckqH+cReGnSjJA8WaU71FB2z160OAgpxIdqNAJyK3JCLC7IkLCzN75q6UL/dFRj0/k0drTSRXzDLYkQuKPQqlJkL+hlp25E4lJpob2V5x+5QTJwBIKlGMDSW9WXJgCUsPLmV57DJinoL8sS48kFCMV3I1pdU9TxBYuxG46T/1ItmdbrnqlqvILenXD778MvW1zZZM56bLeO2xiVTy+wWbPQYKNoNSPSC4gxYBvhOGYXZ7Xg5w//0HsbEAJNtgSwFYWhKWlIRl5T2JJB5fd18aFW9Es+DGNPerQs3qrXFRgBbJcRToFOhErmG3m48rlxXbtMkcK1+qwD5GPPEDj9T8ER/jEOQqY+7iUPJx8C1uWc1OxzDMbTKuXny3dGnYvx8D2JXPDG9LSsLfJeCsD3gmu9DApTjNKzxA8wbdCC0SirurJjCI5HTqhxeRFBcumAv/h4XBoEHw7LOXTiRGUi3XDA5/9wPBnsvB3R+KdTaDXL4GOW+m6p1sR5WQAOvXp719WriweUsVMAyDAxcOsOT+Aiw9uZ8lJeGkH7gZNuq6l+TZ0i1oFvoo9Ys3xMtNS7yISFrqoVMPnQjbt5uTHH78EWJizGOVQuxs+XMptgM/wJFfwB4HhVqaIS7oYXDzsbRmy6S3YXxQEIwdm3bD+LNnzdC2cqUZ4Nasgbi4lNPJNtiV38bK2eP5J3wtSw4s4XDEYVxwoZZXSZqVa0XzKu24p9g95PLIlYkfUESckQKdAp3kUHY7zJ8P48alLvzr7ppAs5CltKv1K50a/Eo+3+PgXx5K9oCS3cEnyNKaLTdrFnTsaN4uvdLlHsqZM81Qt2wZNG2apslFD1hTBFYGm49VxWyc9zKwYaNqwao0K9GMZiWb0bh4Y3J75c6UjyMi2YcCnQKd5DCRkfDVV/D55+YKGP7eETxQbSHtav1K6xq/EeAdSYJHSTxKPgzFO0Heujnvlmp67HYoUSJtz9yVbDazp+7AAYyoKA6VzJMa3oLMZUTsLuBv86J+gVo0qNCSBsXuoU7ROvh76r89InJ3FOgU6CQbuZWhXadPQ90qx7i/ylza1fqV5pWW4OGWyOmkmviHPIxXmYchoLJCHJjhbdMm8570kiWwaFG6zeJdYUPhS71v3RqzMm4PJy6ay4uU9ShMgxKNaFDuXhoENyAkf4hmoYqIwynQKdBJNnG9oV2DBsGA/gZE7oCjc+Dor3D2PxKT3Nga3gSPUg9TsUVbXPyKWVa7pRISYO9e2L8f2rRJe65HD/jhhzSHDGB/HlhfGNYUNUPc2iIQ7wZeiVDHvwINaj5Mg+AG1AuqR37f/Jn2UUQk59IsV5FsIL2hXS42O8V8VpP43xwip/6KP3vMteEKP8Cp3C8S5deaGiF5rCs6s8XEwM6dsGOH2eO2Y4f52LvX3P8UzE1pc6VOQEiuWIF9gbCuCKwrbIa49YXhgrd5PigCGhyBR7eZP6udAo8/v7hm/JyISEZTD5166MTJJSVBsWLmbVZ/7wiaVFzGQzXn0bbmXAoGnOZURAEWbW1H91cexrVIc3DN5kteJCeDyxW3NHfvhvvug0OHrp3McAW7DfYsncm6PHGsP7GedSfWseHYWiKTogEo5lWIWjsuUOtAHDWPQ80TUDD6ije4YgzdTZcwERFxsBwb6MLCwggLC8Nut7N7924FOsnyrs4pAF07XiT60D/cU2YpzUKWUqvkOlxdktl9oiyz17bn13Xt+HdvXZINV5YuzUYdR4ZhDga8sqft8vNBg8zHZRERkDt3msvtNtiZD9YVc2N9xdysKwIbfSK5SAIAJXOXpFaRWtQsVNP8Wbgm+XzypXaFXq7hsqtnuYqIZLIcG+guUw+dZDXnzpl3Bi/fHbz8PG9eWP1PLJxZBaeWwKmlJJ3+DzeXJI6fL8zS7c1SHvtPlwLSTmqYMgW6drXmMznElCmwdGlqeDt/Pv12Tz8N33wDmIv1nrx4kq1t67K1gI2twZ5s9Y9jq+00McnxAJQJLEPNwjWpVbgWtQrXokbhGgR6B6b/3pD+YMXgYBgzRmFORCyjQKdAJxZbtw6+/jo1vIWHp55zd02gbpl/aRaylJZVltCw4ipsyQngmQ8KNmPWimaMmdqM5ZvKc3WAu1qW7qFLSoJ9+1LD2pkzMHp02jbdupmh7jrOecO2MgFsbVWNrc0qszV8K1tPb+Vc7DkAvN28CckfQuUClalcoHJKeLujNd/uZKcIEZEMpECnQCcZKDraHMJ1uZdt50544w2oXDm1zYIFqZMrXV2SqF1qLc1CzFuoDcv9g49nLOejc7PxeFPqtmuGT4lmEFAJbC4YhnkrtkQJOHYs/SFiWWpoV0JC6i3SK2+T7t4NiYmp7Vxc4OJF8PZOPfbee/D661z0gO2VCrA1JB/bgj3Z6h/PVk5zPOEMAG4ubpTPWz4luF1+lMxdElcXq38BIiIZQ7NcRRxk2bK0t0h37jTH4V+tTZsrAl3sSWoWXMuIR9ZQp/R/NCr/D7m8LhKb5MfJ5MYczfMO/uWaUaBsNZq5XRtGbDYzpI0daw7tstnSH9o1Zkwmh7moKPOXERQERYqkHl+zBho2vOnlyUYyRzcuY3dBN/ac3cPus7vZXWgTOz4swoHY48BpbIRTOrA0lQtU5qn8HahUoBKVC1SmXN5yeLh6ZNxnExHJgtRDpx46uUWJieZSZTt3grs7tG6d9nxw8PU3EQDIm+sMtUquY3DPNbSstRbOroXYY+Z7u+aHwNq4F2kMBZtBYC1wub1/b1kytOvMmfQnJlwuYuxYePHF1PbnzpmDATHXcwv3hd0FXNldqRB7ivuxOx/s9opmb+Jp4i6NcXNzcaNUnlKUy1uO8nnLU6VAFSoXqEzF/BXxcc+h+8mKiFxFPXQiV4mIgF270va07dxpLld2+a5g/frXBrqKFVNzTIDPBRpXWk+r0LXULbOGsnnXktvtIACGe25Iqg0lH4e8oWaQ8wm+650ZOnSAdu0yaWjXU0/BvHlmoLsBY/s2LsSeZ++5vew5Z/a07Rlalt0+Mey2nScyOQawY+M4xQKKUS5vORoHlqVX3nKUy1uOsnnLUiJ3CdxuM9yKiOQ06qFTD12OZBhm+CpUyOxtu2zMGHjppZtfnycPnD17KYMlXoTzG9i0dC0+cWsp6rUGH/ses6FbLrO3LbC2+cgbCrlKZdy2WnczWN9uNwfaXT3GzWaD1avTtu3cGaZPxwDOe8PB3Fc8CnpyqIiv+dwrlsjk2JTLCuUqRNnAspS7HNguPS8dWBovt2y+Pp6ISAbSP3slW4uLM3vWrl4CZNcuc8LChg1QvXpq++LF038fT0+oW/0MTWvsoFbZnZQrtAOW7oConRB9CDCo5uoFhWtA4AOQ9w0zwPmVg8waiH+9vb/Gjk3/nuu+fTB5cupt0l27ID4+TRMDOOfnysHD/3Lw4lEOXjhoPkI2cvAFNw4FGES52VPa+7h5UyJPSUrkLkHDgBJ0z12CErlLUCpPKcrmLatN6EVEMoh66NRDl+0kJkL79mZwO3DAnAV6PVOnQpcuqa/37E7m1QFHaFh1B9VK7KBUvh3k99yJV8IObPGXbi/aXMC3FARUBP+K4F/B7IULCLntcW8Ok97eX1fq0AFGjIAqVVIOJS39i1PtWnDMH475wXE/OOZ/6eel54cDIPqK+QW+7r6UyF2CErmLUyJ3yUvPUx95vfNiy6jeRxERuS4FOgW6DOeoJbvsdnPW6NW9bfXrw6hRadsWLgwnT6b/Pi4uUKl8NI1qHqBP551UK7EDIneam9dH7gJ7jNnQ1Rv8y6eGtssBzq9M5m2flZxsLt8REQGRkWbxFSumbRMWBq+8YrbD7FW74MW1Qa11I44Vz8OxyGMcjzrOqehTJBupadctGYokeVPULZAifkUoUqA0xYtXpXj+sgpsIiJZnG65Soa63buAV1q5EhYtSg1uu3dfc0cQuHY7LAyDetXDOXv4EPWqHqZamUOULXKIorkPE+h5CK/kw9gSzppto4Ddec2gFlgLSnRPDW6+xczeuDtxOYhFRqZ9XA5mjz8OHld0fU2bBhMnpp6/3DYqCoA4NzjtC6frVib8s1Gcjj6d8ghfM4HT7S6a5y894q/6X3b+aChyfhNFgxtSo1AN2pRrQ5FchSm67TBFytakaMW65MtdBJc7/bwiImKpHN1DZ0+ws2r0IhoNa8PykfOpP/B+XD208KijXL4LaDPsNGI5hTnBCQrzD41ItrkyYQKUKpUa2EaNMseqXfb22zB8+LXv6+6aQFDgUYrlO0zxfIeoU+kwz/U4BNGHzfFsMYfBHpd6gasP+Ba/9Chm/vQpBr4lzB44r/xp/4Are8SuDlhXPu/SBerUSb1u61Z44AHzfFTUdW9/xrnB+d2bOZ/LlXOx5zgfe55zv0zi/LzphPuQJpiFX/oZ5Xnt+wR4BlDAtwAFdh8jf3gMBaKhQDTkj4HCUVA0CopEmc897cBnn8Fzz93y35+IiDiPHBvoVg+ZRbHR/cllP0oAEAFcdA3i8MCx1Bul/RjTYxjmDk3x8amPhIS0r/PnN3ctsNvNn6FHZzGW/gST2kV3hCD6M5bZXP49GwT4RLB2+WnKBJ2G+HCIO83WdadZuvA0BQJOUzDgNEH5TpPf/zR+HmdxsV3xtfXMnxrYfC4Ftkh3OGNAtA9EJUNk1LWhLDLSDGRvvZX2gxYtCsePX/f3kGyDix4Q+ekHRHVsS2R8JOfjznNu31bOv/Ey573NbajOe136edXzWPf039cn4VIgi3OhQII7BexeFDB8yO+SiwJuARTwCKRAwZIUeOkN8vnkw9PtUsr75hvo3fvmf4FZeu8vERG5Gzky0K0eMos6H3UEDC5CSqDLdWkvzP9enml5qEtONgOSq2vaO3NxceakxCtDVHrBKj7eXCrsymGBS5fCzz/f/NqgIHOJsSu1bQvz519/zD2AzZbMywMu8uG7kfy3IoLZz/3Ke96vgQ+4eAO+gD8Y/ubPA/4l8QhIoID/aTzcEq96MxeSXQKJj3DH1e6NW5IHLrFuEGWDCANOJcPJRDgaCzFJ5gC9Kz37LHzxBQCJLhDjbg7uj3FPfUS7Q1T9mkQO6U9kfCRR8VHmz++/JDL2AlEeEOlp9o5FepLy+mI6vWWXudshT6IrgUnu5En2JBBv8rj4EujmRx4PfwK98pDHJ5DARveRJ38webzyEOgdSB7DEw874Od3+wMML6dnp9j7S0REMkKOC3T2BDunfEpQyH4UFyCS1EDnDyRj46RLUS78sxV7so2EuGQS4pKxJybT8OF8ad5r1W/n2b0mgsT4ZBLiDRLjk0mMTyYpwXxcfl6ySi56jSyd5tqXmqzn/NFokhLM97788/LDSE7GhWQ6v12J7m+USrluz8Zo3qgxDxeS0zxsGNccG7q+CyVq5Em5duorm1j/4WJcsOPhnmA+PBLwdI/HwyMh5eGZ15POPz8ESbFgj4WkaFZ9ugSPiEN4+sTh6Z2Ah3c8nj4JePgk4OFtPty9E6875MxIBmIhOcp8JF6EhIsQHw3xMRAbC+e79CGxWk2iXLyJMtyJ37yeuE8/Jt7VHBMW5wbxrubPK4NZjDtEt2pKTFIsMYkxxCTGEH3uJDHx0cS4Q9ItZBh3F3f8Pf3x9/TH70wk/nHg5+KFv6sPfu6++Hv44e8VgJ93bvx9A/HLFYh/UBn8ChfH39M/JZj5uPtYM2ng8v1tSH/vr5kzM3C7CBERsVq2DHSGYRB1aTD51daNXUKtN9unvF52L7T9C+a2AN/r3ArDZs4ctL3UP83hI5OWEXxmY0qblJ9XPc56B5H38fuxGclAMhgGF3+ajZ8RmdLGduU1LpcG+rvC+cIVyFsjGJuRjI0kEi9E47V1LTYXc7y+i6v502ZLfe5y6ZxRoABengauyUm4GYm4JMThYUvCzQVcbiNzJGLjYiLEJRpEJ8FFO0QnQ5QdIu1wMRkikiEyGc65uhPl483ZuEQiYmO5AJzFDM53yjPJHAPmkQReSeCRDL4J4G234YMb3rjj26Ql3j7++Lj74O3mjffRk/gcPoGPpx8+Pv7mOZ/ceOfKg49/Hnz88+EdkA+/3AXx882TevvSmc2dC0OHpr1dXLQofPCB2cUqIiJOy8/P74YdBtky0F1eikREREQkO7jZ8mrZMtDdTg/doUCoeg42B4LfFbcLD/qWx+4bgM3mCq42bK42gmeMwc099f7d0a/mYVuxAhdXGy6uNjZv2Ub1mtVxcXXFxdUVVxcXXNxcsJUpi98LT2GzuWC71J1m++ILOHMWm4vZpZb605Xvvvue3r36YHN1waVJU2y1Q3GxuZjJ/OJF+OmnS11yLqk/03k0/+gjlqxfn/qhDh2CTZuubXv1e3h5Qd26KZeFhoayZto0c0LBza719zdnRixfDm3a3Pwva/58c2G62xAaGsqaNWtu65qMfB9Hvpcj3icyMpLg4GCOHDly12srZqXPldXeJzv/nh35XvpdO8/7ZMXfsyPfKyu9z538rm/WQ5ct16Gz2WzX/QU1HvoQp94KopD9GC4YFD9nHi9+LnUM3QnXIBod23bTJUxKvFcjzeueISFsXzD31op8873rnpo0dyGvvv9B+if9/c3barcgZuzYtL+HKlXS7BRwq1xdXfGvUePmDa90//0QFIRx9Bg2rv03g4ENW3CQ2e42B+q7uro6ZBFoR72PI9/LkTX5+/vf9Xtltc+V1d4Hsufv2ZHvpd+1c70PZK3fsyPfK6u9Dzjmd31ZjltF1NXDlcMDxwJmeLvS5ddHBo65o/XonnPQGl/Z4n1cXWHsWGw2MK76F4Vhs5ljBseMuaNZl1nt9+PI93JkTY6Q1T5XVnsfR8mKnysr1uQIWe1zZbX3cZTs/F3Mar/ry7LlLddbkd46dFGuwRwZOMbyJUuylfS2iggONsOcZl1mCG1nlzn0e848+l1nDv2eM09G/K5zXA/dZfVGdaBgzEHWvT0bgHVvz6ZQzAGFOUfr0AEOHiTh99+Z2aEDCb//bq6HpjCXYTw9PRk+fDientlg5m4Wpt9z5tHvOnPo95x5MuJ3nWN76C7Tv0hERETE2eXYHjoRERGR7EKBTkRERMTJKdCJiIiIOLkcP4bu8iLEN1uwT+7MkiVLOH36dJpjwcHB3HPPPRZVlL38888/HD16lHbt2uHt7X3N+YSEBFauXElERAShoaEUKVLEgiqd39mzZ1myZAnFihWj7hWLbl8+98cff1xzzX333UeePHmuOS7Xd/LkSTZu3Iivry81atQgV65c17RJTExk5cqVXLhwgVq1ahEUFGRBpc7NbrezadMmjh8/TpkyZahQoUKa8xcuXGDRokXXXNeiRQvy5ct3zXG5vqioKNauXUtCQgKVK1emaNGi17RJSkpi1apVnDt3jho1alCsWLE7+rOy5cLCt+NGixDL3Xv77bcJDw+nyhULGterV0+B7i5NmTKFd999l8TERPbu3cuRI0eu+T+2gwcP0rJlSwCCgoL4999/GT16NM8884wVJTulM2fOMGjQIP744w8SEhJo06bNNYFuz549dO3alUceeQQ3t9T/pNapU0eB7hZFR0fTp08fli1bRpUqVTh9+jSHDh3i+++/56GHHkppd/ToUVq2bElCQgLFixdn9erVjBw5kv79+9/g3eVK8+fPZ9CgQeTKlYsiRYqwYsUKGjRowIwZM1L+UXjw4EG6du1K+/bt8fDwSLm2Ro0aCnS3YfTo0YwdO5by5ctjt9tZtWoVzzzzDKNHj05pc/LkSVq2bMnFixcpVaoUq1atYsSIEQwZMuT2/0BDJAM1adLEeO2116wuI9v54YcfjG3bthlLly41AOPIkSPXtLnvvvuMpk2bGomJiYZhGMb3339vuLm5GXv27Mnscp3WwYMHjYkTJxoxMTHGvffeazz55JPXtFm1apUBGFFRUZlfYDYRHh5uTJ482bDb7SnHXn31VcPX19eIjo5OOdauXTujfv36Rnx8vGEYhjF16lTDxcXF2LZtW6bX7KzmzJlj7N+/P+X1iRMnjIIFCxpvvPFGyrENGzYYgBEeHm5FidnGzz//bMTExKS8XrJkiQEYK1euTDnWuXNno1atWkZsbKxhGIYxe/Zsw2azGevXr7/tP09j6CTDHTt2jNmzZ7N69WpiYmKsLidbeOKJJwgJCbnu+dOnT7N48WJeeOGFlF6jxx9/nDx58vDzzz9nVplOr3jx4jz55JPp3s6+2t9//838+fPZt29fJlSWveTLl4/HHnsMF5fU/0t65JFHiI6OZu/evYB5G3D+/Pk8//zzKb1GnTt3pnDhwkydOtWSup1Ru3btKFmyZMrrQoUK0aBBAzZu3HhN2+XLlzN//nz27NmTiRVmH506dUrz347y5csDpOw1HxMTw+zZs3n22Wfx8vIC4OGHH6ZkyZJMmTLltv+8HH/LVTLen3/+SXh4ODt37iQ2NpYffviBFi1aWF1WtrZt2zYMw6By5copx1xdXQkJCWHLli0WVpY9ubm58f777+Pj48PKlStp06YNP/74Y8p/pOX2/fnnn3h5eVG6dGkAduzYgd1uT/OdttlsVK5cWd/puxAdHc3q1avp0aNHmuOurq6MGjWKXLlysXLlSlq1asWkSZPw9fW1plAndejQIVatWsX58+f57rvv6N69e8r//+3atStlbN2VqlSpckffafXQSYZ69dVXOXToEPPnz2f37t20a9eOzp07c/bsWatLy9YiIiIACAwMTHM8b968XLhwwYKKsq9ChQqxefNmVq5cyZ9//smWLVv466+/GD58uNWlOa3169fz1ltv8eabb6YECH2nM0a/fv0wDIMBAwakHMuXLx8bNmxg1apV/PHHH2zfvp2VK1fy6quvWleokzpy5Ahz5sxh+vTpHDt2jNq1a6f0RDv6O61AJxmqVatWKV9eFxcX3n77bc6dO8eKFSssrix7u7ydzMWLF9Mcv3jxonqNHKxEiRJUrFgx5XXp0qXp0aMH8+bNs7Aq57Vjxw4eeOABunbtyiuvvJJyXN9pxxs4cCDz5s1jwYIFFChQIOV4UFBQmolsxYsXp1evXvpO34GGDRsybdo0li5dyuzZsxk8eDCzZ5tbjjr6O61AJ5nK19cXm81GeHi41aVka5dvUx0+fDjN8UOHDlGqVCkrSspR/P399R2/Azt37qR58+Y8+OCDTJgwIc1SUvpOO9bLL7/Md999x+LFi6lZs+ZN2+s7fffq1q1LuXLlWL58OUDK99ZR32kFOskwUVFRREdHpzk2Z84cDMMgNDTUoqpyhnLlylGmTBlmzJiRcmzTpk3s2rWLBx980MLKsp8TJ06keW232/n111/1Hb9Nu3btolmzZjzwwAN8880316wLWqxYMSpVqpTmO71z5042bdqk7/RtGjJkCN988w1//PFHut/Tq7/TycnJzJkzR9/p2xAbG5tyS/WyM2fOcPjwYYKDgwEoWLAgtWrVSvOdPnDgAGvWrLmj77QmRUiGCQ8Pp02bNnTo0IFSpUqxdetWvvjiCwYMGEDVqlWtLs+pbdmyhW3btrF9+3YA5s6dS2BgIPXr16d48eIAfPrpp7Rv3x43NzdKlizJmDFjaNeuHffee6+VpTudadOmAXDq1CkSExOZNm0avr6+KeujjR49mj179tC8eXNcXFyYPHkyx44d44cffrCybKcSHh5O8+bN8fX1pUWLFkyfPj3lXNOmTSlUqBBgfqcffPBBPD09KV++POPGjeP++++ndevWVpXudEaNGsVHH33EoEGD2LdvX8qs7MDAQFq1agVAWFgYGzdupEWLFnh4eDB16lT27NnD4sWLrSzdqURFRdG0aVPatm1L+fLlCQ8P59tvv6V06dL06tUrpd0nn3xCq1at8PX1pXLlyoSFhdGkSRPat29/239mjt8pQjJWeHg4EydOZOfOnRQqVIjWrVtrUWEHmD59OrNmzbrm+PPPP0/Dhg1TXq9Zs4ZJkyYRGRlJ/fr1eeqpp9Isfis316VLl2uO5c+fn/Hjx6e8Xrx4MYsWLSI2NpaKFSvSo0cPLVh+Gw4dOsTQoUPTPTds2DCqVauW8nrDhg388MMPXLhwgbp169KrVy/c3d0zq1SnN2bMGFavXn3N8dKlS/Pee++lvF6yZAkLFiwgOjqaChUq0KNHD3Lnzp2JlTq/CxcuMHHiRLZs2ULu3LkJDQ3l0UcfxdXVNU27zZs3M3HiRM6dO0ft2rXp3bt3yvi626FAJyIiIuLkNIZORERExMkp0ImIiIg4OQU6ERERESenQCciIiLi5BToRERERJycAp2IiIiIk1OgExEREXFyCnQiIiIiTk6BTkRERMTJKdCJiIiIODkFOhEREREnp0AnIiIi4uT+D2/46I6Q8RqZAAAAAElFTkSuQmCC", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_range = [n for n in range(0,35,5)] #breaking up the interval [0,1]\n", "K = 10 #how many graphs to sample for each c\n", "n = 200 #size of graphs to sample\n", "\n", "def num_paths_unlabelled(G):\n", " T = graphs.PathGraph(4)\n", " return len({frozenset(emb) for emb in G.subgraph_search_iterator(T,induced=False)})\n", " \n", "def num_stars_unlabelled(G):\n", " T = graphs.StarGraph(3)\n", " return len({frozenset(emb) for emb in G.subgraph_search_iterator(T,induced=False)})\n", "\n", "count_paths = empirical_means(n,c_range,num_paths_unlabelled,K,verbose=False,scale=lambda n,c: c*n^(-4/3))\n", "count_stars = empirical_means(n,c_range,num_stars_unlabelled,K,verbose=False,scale=lambda n,c: c*n^(-4/3))\n", "\n", "p6 = line(count_paths,thickness=2,linestyle='--',marker='o',color=\"blue\") \n", "p7 = line(count_stars,thickness=2,linestyle='--',marker='o',color=\"red\") \n", "\n", "p6 + p7 + line2d([(x,x^3/6) for x in range(0,30)],color=\"green\") + line2d([(x,x^3/2) for x in range(0,30)],color=\"orange\")" ] }, { "cell_type": "markdown", "id": "23218d26-afd0-4fe0-bf67-3de3131ef41b", "metadata": {}, "source": [ "So far we've studied tree-like patterns, which lead to us mostly exploring the regime $p=o(n)$.\n", "Let us now turn up $p$, focusing on the sparse regime $p=O(n)$, i.e. let's look at $G(n,p=c/n)$. \n", "We'll begin by plotting the, say, three biggest components. \n", "What do you notice as you vary $c \\in \\mathbb{R}_{\\geq 0}$?" ] }, { "cell_type": "code", "execution_count": 27, "id": "ed9ec1cd-4e35-4e27-9677-cc026fe57df0", "metadata": { "scrolled": true }, "outputs": [], "source": [ "n = 1000\n", "c = 1.1\n", "\n", "G = graphs.RandomGNP(n,c/n)\n", "\n", "ccs_by_size = sorted(G.connected_components_subgraphs(),key=lambda x: x.size(),reverse=True)\n", "\n", "to_plot = []\n", "\n", "for cc in ccs_by_size[0:min(3,len(ccs_by_size))]:\n", " scale_by_size = (n*10)/cc.size()\n", " to_plot.append(cc.plot(vertex_size=3, vertex_labels=False,graph_border=True))" ] }, { "cell_type": "code", "execution_count": 28, "id": "10f3108e-a692-4516-ab86-785dec498967", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 109 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 1 x 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "to_plot[0].show(figsize=[5,5]) #plot the big one first\n", "if to_plot[1:] != []:\n", " graphics_array(to_plot[1:]).show(figsize=[3,3]) #then the two smaller ones, if they even exist!" ] }, { "cell_type": "markdown", "id": "b01dc7a7-a98a-4d00-8a34-d02d266c575a", "metadata": {}, "source": [ "## Exercise 3: Beyond trees\n", "\n", "So far we've studied small tree-like subgraphs: edges, stars, paths. \n", "Based on our simulations, we guess that $G(n,c/p)$ looks, at least locally, quite tree-like. \n", "\n", "This exercise focuses on the appearance of the first small cycles, focusing on triangles. In more detail we ask:\n", "1. What's the threshold function for the presence of a triangle in a random graph? \n", "2. What's the limiting distribution for the number of triangles? \n", "3. What's the limiting distribution for the indicator variable corresponding to the _existence of at least one triangle_?" ] }, { "cell_type": "code", "execution_count": 13, "id": "4739ea43-115f-458e-8882-eacb99694a06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Currently sampling with c = 0.000000000000000\n", "Currently sampling with c = 0.200000000000000\n", "Currently sampling with c = 0.400000000000000\n", "Currently sampling with c = 0.600000000000000\n", "Currently sampling with c = 0.800000000000000\n", "Currently sampling with c = 1.00000000000000\n", "Currently sampling with c = 1.20000000000000\n", "Currently sampling with c = 1.40000000000000\n", "Currently sampling with c = 1.60000000000000\n", "Currently sampling with c = 1.80000000000000\n", "Currently sampling with c = 2.00000000000000\n", "Currently sampling with c = 2.20000000000000\n", "Currently sampling with c = 2.40000000000000\n", "Currently sampling with c = 2.60000000000000\n", "Currently sampling with c = 2.80000000000000\n", "Currently sampling with c = 3.00000000000000\n" ] } ], "source": [ "c_range = [x / 10.0 for x in range(0, 31, 2)] #breaking up the interval [1,3]\n", "K = 100 #how many graphs to sample for each c\n", "n = 500 #size of graphs to sample\n", "\n", "num_tris = empirical_means(n,c_range,lambda G: G.triangles_count(),K,verbose=False)\n", "has_tris = empirical_means(n,c_range,lambda G: 1 if (G.triangles_count() > 0) else 0,K,verbose=False)" ] }, { "cell_type": "code", "execution_count": 14, "id": "e48a14f6-7b00-43ca-9f39-13dd758412b9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "line(num_tris,title=\"Mean number of triangles\",axes_labels=['c', '#triangles'],thickness=2,linestyle='--') \\\n", "+ plot(x^3/6 ,(x,0,3),color=\"red\")" ] }, { "cell_type": "code", "execution_count": 15, "id": "385c087e-e7df-4fe6-8066-25ed5491b638", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "line(has_tris,title=\"Probability of having at least one triangle\",axes_labels=['c', 'P'],thickness=2,linestyle='--') \\\n", "+ plot((1-exp(-x^3/6)),(x,0,3),color=\"red\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "0ca5949e-a2cd-4057-89c1-8c679450b483", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Currently sampling with c = 1/2\n", "Data points: Counter({0: 98, 1: 2})\n", "Currently sampling with c = 1\n", "Data points: Counter({0: 85, 1: 14, 2: 1})\n", "Currently sampling with c = 3/2\n", "Data points: Counter({0: 59, 1: 32, 2: 6, 3: 3})\n", "Currently sampling with c = 2\n", "Data points: Counter({1: 31, 0: 26, 2: 22, 3: 12, 4: 8, 5: 1})\n", "Currently sampling with c = 5/2\n", "Data points: Counter({2: 26, 3: 20, 1: 18, 4: 15, 0: 9, 5: 5, 7: 3, 6: 3, 8: 1})\n" ] }, { "data": { "image/png": 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WiQxiZPeXhISonUoIEV/yD6jFG5LjhjcrVqidRgihioED4fFjWLOGDBmgaVPl8KtXygJxQoi4k6LiI40bw67KykztXs8HMXq0yoGEEPHm5xq2bLdvTmtWsmuHltev1U4khEhwBQtCnTowcSJotfTq9e9Ls2YhQ6GF+AZSVHxEo4Fx81Mz3MqTX1jCmWl/ce2a2qmEEPHB0hKCGrQhM76UjTzCunVqJxJCqMLdHa5fhx07KFUKSpZUDl++LCtBCfEtpKj4jxw5IPXgTpymJPM0XXn1PELtSEKIeFJhQGnukIM2LMfbW+00QghVlCunPDw9QaeL0Vsxc6Z6sYQwNlJUfMYgDwuudJ1Hbq0PP1+WFkUIU1W4iIZ9aVxpwgYunXzHvXtqJxJCqMLdHU6ehL/+okkTSJ9eObx1Kzx8qGoyIYyGFBWfkSgRdJpTFM1vv8HIkeDrq3YkIcRXfO+eNVbtXElKCPXZKhO2hTBXtWpBgQIwcSI2NtC1q3L4M/vjCSFiodHpTGMaUlBQEI6OjgQGBuLg4KCfNw0MhDx5oGxZ2LhRP+8phIhX39oWPHkCj5zKEYgjvXLs5PZtZX6VEML4fVN7sGIFuLnB5cu8SFeIIkWUH7t1UzbFE0J8mfRUfImjI0yfDps2MabMTk6fVjuQEELfMmWCu6XdqKHZy47F/lJQCGGumjdXqodJk0iTRllpduJEKSiEiCspKr7inHNzDlpUo/Wp3+j963uiotROJITQt7Y7mmFpbUmu86vVjiKEUIu1NfTvD2vWwIMH0RvhCSHiRoqKryhSVMOMnF5k5Cm1Lo9nzhy1Ewkh9C5FCqhdG1kCSggz98svkDy5ssu2EOKbSFHxFVZW4L44FxMZxEAmsdTjFs+fq51KCKF3bm5w4QL4+KidRAjxg7534Qbs7aFnT1i0CF68AJT/jBkDHTvGQ1AhTIhM1I6jru3e039ZAR6QjcUt9rFqtQy8FsIQfXdbEBZGVLoMnCrUma2lPJk0Kf4yCiESxne1B2/eQObM0KcPutFjyJ0b7txRXrp9G3LmjL+8Qhgz6amIo7FT7Ric9HeqcQDtmrUcOKB2IiGEPkVZ2bI8rDmZj65g9kwtAQFqJxJCqCJFCvj1V/j9dzQhwTF6KH7/Xb1YQhg6KSriKGVKqD69JhtpxHT6MPDXQMLC1E4lhPjHdw93+JulJbyt7YYTTygTflhWkRbCnPXpA6GhMH8+HTuCnZ1yeMkSCApSN5oQhsroi4of/SLxLdq3B+9iM0hKMG3vDWPKlHj/SCFEHHXv3h0fHx/Onj373e9RYUBp7pADN7xlzrYQ5ixTJmWe1bRppEgchpubcjg4WCkshBCfkjkV3+jKFVhRZAqeukGUtznL5kfFSJcu3j5OCPGNfqQt0OlgdupRtH89hbT4c/ORPZkzx1NQIUS8+6HvBjdvQr58sGAB10t3oEAB5bCzszK3wsLob8sKoV/yT+IbFSoE2h69uGOdj51Zu5IutWxcIYSp0GjAso0rSQmhPltZuVLtREKYjufPnzN69Gg6dOjAhAkTePv27RfP37p1K66urjEev/76awKlBfLkgQYNYNIk8ueJompV5fC9e7BzZ8LFEMJYSFHxHUaNtybrzrkkv30GFi5UO44QQo9q9XDmOGWjh0CZRl+uEOry9fWlWLFinDp1iiJFirBjxw5Kliz5xcLi6tWrnDp1ChcXl+hH1X++2SeUQYOUboktW+jV69/DM2cmbAwhjIEMf/oRv/wCmzfDrVuQJk3CfKYQ4ov00RZMyTGP3vd+IyNP2XU+LcWK6TmkEGamc+fOnD59mgsXLmBpacm7d+9wdnamc+fOjBo16rPXjB07lu3bt3Pq1Knv/ly9fDeoUgVCQtCePE2u3Bru3VMOX7+ujI4SQiikp+JHTJoEFhboBg7k2jW1wwgh9CVVt2ZEYUlLVrNihdpphDB+27dvp1GjRlhaWgJgb29PvXr12L59+xeve/r0KV27dqVPnz6sXr0arVabEHFjcneHs2exOHKI335TDjk6wo0bCR9FCEMmRcWPSJWKF30noFm2jB5FjnL9utqBhDBf+lwJrn77FOzU1MENb7ZulSFQQvyI9+/f8/z5c7JkyRLjeJYsWbh//36s12k0GgoVKkS+fPlIkSIFffv2pWrVqkRGRsZ6TVhYGEFBQTEeP+x//4OiRWHCBH75BebMgSdPoHHjH39rIUyJFBU/aG54B05Smt+jutKjS4R8+RBCJfpYUvYfyZNDRAs3inOBK6uvo9HoIaAQZurDhw8AJEmSJMbxpEmT8v79+1iv69y5Mzt27KBHjx4MGzaMEydOcPr0aRZ+YS6jp6cnjo6O0Q8nJ6cf/wU0GqW3Yt8+HO6cp2tX+M+vIoRAioofNsjDgvGZ5pKHm/z013RZ214IE9FsaS1IkYLEm+QftRA/IkmSJFhYWHwyKfvNmzc4OjrGel3q1Klj/JwtWzaKFSvGmTNnYr3Gw8ODwMDA6Ievr++Phf9H48bKWrITJ+rn/YQwQVZqBzB2iRJB9wVFmFWzJyMYRfk+LahTJzMpUqidTAjDsHHjRnbv3o2VlRUNGjSgRo0asZ578uRJZsayrMrYsWPJkSNHfMX8lI0NNG8OK1fC+PGyKL0Q38na2po8efJw7T+TD69evUrBggW/6b1CQ0O/+LqtrS22trbfnPGrLC1hwADo2hXu3IGcOQF49Up55Mmj/48UwtjIX0k9cHGBi/VHEUAyhr/pxZAhaicSwjC4u7vTqVMncuTIQbp06WjQoAEzZsyI9fyMGTPSoEGDGI+3b9+yc+dO0qdPn3DB/+HmpgyePnxYhjYK8QNatWrF2rVr8fPzA+DWrVvs2rWLVq1aRZ+zadOmGPtQrFu3jo8XqNy8eTOXLl2iTp06CRf8Y23bKis9TplCSAh07AhOTpCQW2cIYdB0JiIwMFAH6AIDA1X5/CdPdDo327U6Hejq8Kfu9GlVYghhMB4+fKiztLTUbdiwIfrYjBkzdIkTJ47zv9PIyEhdpkyZdL/++mucP1efbUFUpFYXmiGH7qhzO13jxj/8dkKYrffv3+tq1KihS5Mmja5WrVq65MmT61q1aqWLioqKPmfEiBE6R0fH6J979eqlc3Z21tWrV09XtmxZnZ2dnW7UqFHf9Ll6/24wYYJOZ2Oj0z59psuTR6dTlnHQ6S5e1M/bC2HM4mWfCh8fH2bMmMGjR4/ImTMnAwYM+GTVh//aunUrGzdu5MWLF2TIkIHWrVt/0yY3quxT8R/Tpuoo0L8GObmDa5HrHD1nz9+r5wlhdubPn0+vXr0ICAiIHo7g5+dH+vTp2bp1K/Xq1fvqe+zcuZPatWtz7tw5ihcvHqfP1WdboNPBjBSj6BgwhfQaf+48tUeNDhMhTIFOp+PMmTM8fvyYnDlzUqRIkRivX7lyhZs3b9KsWbPoY8+fP+f8+fPY29tTsGDBT+ZZfI3evxsEBkLmzNClC3OyTKR7d+Vw+/awePGPv70Qxkzvw59u3rxJ6dKliYqKokuXLjx//pySJUvy/PnzWK+ZPXs2LVq0oHDhwvTu3ZvMmTNTvXp11q9fr+948apHTw2zcnmRnufUujSOuXPVTiSEeu7du0fatGljjG9Oly4dtra2X1xG8mOLFi2iaNGiXywo4mUJyb9pNKBr5UpSQqir28rq1Xp7ayHMjkajoVSpUjRt2vSTggKgUKFCMQoKgPTp01OnTh2qVKnyzQVFvHB0hG7dYO5c2tQL4J955qtWwcuX6kYTQm16LyrGjBlD/vz5WbRoEQ0bNmTt2rXY29szderUWK9Zv349zZs3p1+/fri4uDBy5EiqVavGhg0b9B0vXllbg8finEzAnQFM5vmhm2pHEkI1Hz58+GQJSYDEiRNHLzH5JS9fvuTPP/+kc+fOXzwvXpaQ/Ejtns4cpyxueMvqbkII6NULwsNJ4j2Xjh2VQ2FhMH++urGEUJvei4q9e/fGGNZgZWVFnTp12Lt3b6zXFClShGvXrhEWFgYo3ZW3b9+maNGi+o4X78qVA8vB7kSkz8y4t91k1yxhthwdHXnz5k2MY1qtloCAAJIlS/bV65cvX461tXWMiZyfE29LSP4td244mqUN1dnL80t+/GcBGyGEuUmXDtq1gxkz+K3D++iF4ebMgYgIVZMJoSq9FhXv3r3j1atXZMyYMcbxjBkz8ujRo1ivmzx5MqVLlyZz5syUKVOGbNmy0aZNGwYOHBjrNfE55OFHDRuXiMSLf4dDh5DxEsJcFSpUCH9/f15+NCbg+vXraLXaOC0juXjxYpo3b/7VcdC2trY4ODjEeOhbyq7NiMKSlqxmxQq9v70Qwtj07w+vXpH1yDL+uY/67BkY2QALIfRKr0VFeHg4AHZ2djGO29vbR7/2OVu2bGHlypX07duXYcOG0b17d2bOnMnhw4djvSa+hzz8MBcXaNIE+vaFgAC10wiR4FxcXEiePHmMfSemTZtG9uzZKVOmTPSxFi1asGvXrhjXnjx5Eh8fHzp16pRgeb+kQfvk7KAObnizciVotWonEkKoKkcOaNoUJk+m92+R0YdnzVIxkxAq02tRkTRpUqysrHj9+nWM469fvyZ58uSxXterVy969OjBoEGDqFWrFqNHj6Zp06b069cv1mvie8iDXsyYgS40lFvNh+HlpXYYIRJWkiRJ8Pb2ZtasWZQpU4ZixYqxfft2Vq5cicVHG8mtXbuWW7duxbh20aJF5M+fP0bxoaY0acCnuBvFuIjDk+scOaJ2IiHEl3h5eZEvXz5KlCgRfx8yaBDcv0/FFxsoVEg5dOoUfGHDbyFMml6LCktLSwoWLMiFCxdiHD979mys8yOioqJ48+bNJz0NmTNn5sWLF7F+VkIMefhRUekyMj/DKHLsncPKvud58EDtREIkrJo1a/Lo0SOGDBnC+PHjefDgAaVLl45xzurVq6lVq1aMYw0aNMDbwGZF5+pdi9ekwA1vGQIlhIHr3r07Pj4+nD17Nv4+pGhRqFEDzcQJ9OyhI0cOpadCdtcW5krvE7Xbt2/P+vXruX37NgBnzpxh//79tG/fPvqcpUuXRu+IaWlpSalSpfD29ubdu3cABAQEsHbtWsqVK6fveAnK0hJuu/TkGgWYEd6VXr9FybxtYXaSJ09OnTp1cHFx+exqUC1atCBXrlwxjtWpU8fgFmqo08iGzdbNac1KrlzSyr9lIYTSW3H5Mu3S7+HWLejRAwzwHqcQCULvRUW3bt1o1KgRhQsXpnDhwlSsWJHevXvTpEmT6HMePnzIX3/9Ff3zokWLCAkJIXPmzJQqVYqsWbOSIkWKGGOxjdWIMVYMTzmHkpwl4875bNumdiIhxPewt4dMHm448YQzkw6j0aidSAihup9/hpIlsZw8AQu9f6MSwrjEy47aAE+ePMHX15fs2bOTNm3aGK89fPiQJ0+eUL58+ehjOp2OR48e4e/vT8aMGcmUKdM3fZ4h7Kgdm3XrIKh5R5qwgaoZb3H0VloSJ1Y7lRCmxcvLCy8vL6Kiorh9+3b8tAU6HeTKBeXLw5Il+n1vIYTeJch3g82boVEjOHkS/jO8UwhzEm9FRUIz5KJCp4OmlV/xx5Hc7KA2PoOWM2GC2qmEME3x3haMGgVTpoC/v9J9IYQwWAny3UCrhXz5IG9e2LyZa9dg9mylE6Nly/j5SCEMkXTWJQCNBjwXpGKw5STa4M3ZyYfx8VE7lRDiu7i5QUgIbNlCaKjaYYQQqrOwUOZWbNnCnW03KFhQ2V178mTZ/1aYFykqEkjOnJB+cHuOU5bZ2m707BIujY0QRkibNTvPspfjRDdvqlRRO40QwiC0bg0ZM5Jj8yT+WcX24kU4flzdWEIkJCkqEtAgDwvGZZxLLm7z07FprFypdiIhxLeysIBF4W6UCtzLozN+/L3QnRDCnNnYQN++aFaswL31v/tmmcB6M0LEmRQVCcjODnosKMRMejHKcjTVcz9SO5IQ4jsk79yMSKxoyWrZs0IIoejUCZImpf69aaRLpxzavBkeP1Y3lhAJRYqKBFazJtQ4MRLbdClIM7an2nGEEN+hUYfk7KBO9EZ4MpRRCEHSpPDbb1guXkDftq8BiIqCOXNUziVEApGiQgUFyiSFGTNg2zZk4wohjE+GDHClsBvFuIjdg+ucOKF2IiGEQejRA7Raumq9sLFRDs2fD3/v7SuESZOiQi2NG0ONGtCzJ2+fhBIVpXYgIYybl5cX+fLlo8Q/syTjWY6etXhNiujeCiGE4Ujo9iBa6tTQsSNJFs+iTWNlebi3b5E5lMIsyD4VKtLduYs2XwF+t+6D1WRPundXO5EQxi+h2oKQEFiVvBs1I/+kSLJHPPOzwNY23j5OCPEdVPlu8OgRODvzuM80skxRhjnnzw9XrypLzAthqqSnQkWXQnIwOtKDbu+nsNzdBz8/tRMJIeIqSRJ4WtkNJ55QOOAwu3apnUgIYRCyZIGWLcm8dgoVy0QAyvCnZ89UziVEPJOiQkVFi8Jzt0E8JCsTQrrTv59JdBoJYTbK9CnNHXLQhuV4e6udRghhMAYOBF9f/vh5NVu2wJ07kDGj2qGEiF9GX1SoNm5ST8ZPS4R7Ui8qcxhWreTQIbUTCSHiqtr/NGxO7EZjNmIT+U5WgRJCKAoWhDp1yLNtEvXrarG0VDuQEPHP6IuK7t274+Pjw9mzZ9WO8l1SpQKXqdVZSzOm0g/3X98SHq52KiFEXFhZQeVFriQlhNXNt8h4aSHEv9zd4fp12LFD7SRCJAijLypMQYcOsKLYdOx4T5s7Q5k6Ve1EQoi4KtE8O5Qrh4x/EkLEUK4clC8Pnp7Rm9ncvAnBwSrnEiKeSFFhACwsYMyiDIzQjKYrc9k56iwPH6qdSgjjoupQSDc32LsXWW1BCBGDuzucPMndpX/h4gJ588LSpWqHEiJ+yJKyBqRvz0jazP6JSKwYV/c0m7fJIEwhvpUqbcHbt5AuHVHjJvCwYR+cnRPmY4UQX6b6dwOdDgoVIih5ZhyPKcOgcuZUeiws5LauMDHyf2kDMnKsFcNSzuUnzpNj/zyePFE7kRAiLrSOybnsVIfr7t7UqYNM2BZCKDQaGDQIh2M76VDiCqCsBLV7t8q5hIgHUlQYEAcHcPUqw5FcnZhoPYRMVjKUQghjYGEB62zdKBR1EYub1zl/Xu1EQgiD0bw5ZMnCCPtJ0YdmzlQxjxDxRIoKA9O8OVQ64YmFjTX07692HCFEHDn3qMVrUuCGNytWqJ1GCPNmUMvNWyt/zzP9tYYKmR4AyhSsGzdUziWEnklRYYhSpoRJk2DlSjh4UO00Qog4aNTChvUWLXBlBWtXRREZqXYiIcyXwS03/8svaJInZ1aWf5d3nD1bxTxCxAMpKgxV27ZQrhyRv3Zj8rhwGaMthIFLlgweV3IjE0/J9/Iw+/apnUgIYTDs7aFXLwqfX0RW+xcALFumrPEghKmQosJQWViwp8FcuHuXt0OnsHKl2oGEEF9TqmcpbpMTN7xl2wohREzdu6OxsmJu3lkAvHsHixernEkIPZKiwoBF5SvIdPowjDHM7P2AgAC1EwlhuAxhDHXNWho22bnSmI3s2fxONrkSQvwreXLo3Jn/3fEiCUrj8PvvEBWlci4h9ESKCgNWqxZcrDuCV6Ri+OueDBksY6CEiI0hjKG2sYF3jVxJSgg1Pmxh0ybVogghDFGfPli+D2Va7vlUqgTTpqkdSAj9kaLCwE30SsIg25nUZTtP527j3Dm1EwkhvqRm9+z8RTkZAiWE+FSmTODmRsegaRzeE0bDhmAp+9wKEyFFhYFzcoKioxuyk5rMpCe9O4VKV6kwGv7+/jRt2pSkSZOSPHly2rdvT1BQ0FevW758OYULF8bOzo4SJUpw5MiRBEirH6VLw+5UblRnL5Vy+8kiC0KImAYMQOP3HFl7WpgaKSqMQO8+Gmbl/J00vKDOpTH88YfaiYT4Op1OR8OGDfH39+fatWucOnWKs2fP0rZt2y9eN23aNLp168bQoUN58+YNy5cvZ9WqVQmU+sdpNNBpXzMsbKwYlmM1Go3aiYQQBiVPHmjYUFk6Xu4SChOi0elM4z5aUFAQjo6OBAYG4uDgoHYcvTt2DPZWHMNwRlMhySW23s1P2rRqpxIidn/99RcVKlTg8uXLFCpUCIAdO3ZQp04d7t69i7Oz8yfXvH79mkyZMuHp6Unv3r2/63MNpi1o3BgePIALF9TLIISZM5j24L/OnIFSpdCt38DepI2ZMwcWLYJUqdQOJsT3M/qeCkNY8SUhVKgAfm4DeUA2JoZ0o38/k6gFhQk7ceIEyZMnjy4oAKpWrRr92ufs2bOHDx8+0KpVqwTJGK/atIGLF+HaNbWTCCEMTcmSULkyz3tPwMVFx7ZtsGCB2qGE+DFGX1QYwoovCWX8VFsGJZlDJY7S2V5mgArD5ufnR+rUqWMcS5QoEUmTJsXPz++z19y/f5/UqVOzdetWMmXKRNKkSSlXrtwX51SEhYURFBQU42EQataElCkJnuvN0aNqhxHCvBjFDUd3dzI8PUdVDgLg5QURESpnEuIHGH1RYU5Sp4Y+O6oR1qgFFbb0hzdv1I4kxDfT6XRoYplooNVqefXqFevWreP48eP4+vpSrlw5atasyZ07dz57jaenJ46OjtEPJyen+IwfZ1orG7Ynbk7gnJW4toySodNCJCCjuOH4v/9B0aJMTj0RgKdPkWWohVGTosLIVKwItrOnwocPMGSI2nGEiFW6dOl4+fJljGMfPnwgJCSEtLFMCMqQIQM6nY6JEyeSJUsWkiVLxoQJE7CxsWH79u2fvcbDw4PAwMDoh6+vr95/l+9hYQFHMruRiafkfHaYw4fVTiSEMCgaDbi7U/TlPopxHoBZs1TOJMQPkKLCGGXIAGPHwh9/wJkzhIerHUiIT5UtW5a3b99y+fLl6GMHDx6Mfu1zypUr99njOp0OC4vPN1e2trY4ODjEeBiKkj1KcZucuOEtq0cKIT7VuDE6Z2fGOyi9FSdOIPtRCaMlRYWx6taNiPxFeODShRZNZVyFMDzlypWjTJky9OjRg0ePHnHr1i0GDhxIgwYNYqz8pNFomDFjBgB58+alfv36DBo0iMePHxMQEIC7uztarZZ69eqp9Jt8vzp1Nay3daUxG9mx/h3v3qmdSAhhUCwt0QwcSPXgDeRAGeI5c6bKmYT4TlJUGCmthRWuwXPJ8vYSGbfNYds2tRMJEZNGo2Hz5s2kSZOG/PnzU6pUKX766SeWLVv2xeu8vb3JkiULRYoUIUuWLJw5c4a9e/eSLVu2BEquP3Z2EFzPlaSEUC10i/w7FUJ8qk0bSJ2GobaTAVi7FmJZy0IIgyb7VBix1ashsFUXWrKaahlvcuR2euzt1U4lhLoMrS04fBisKpcnmKT8XmsXO3aonUgI82Fo7UGsJk4kcshwnKIe4kd6RoyAkSPVDiXEt5GeCiPWogXsqTieMGzp87QfY8eqnUgI8V8VK8KO5G5UZy+Xdvvx4oXaiYRQx6pVq8iXLx+JEyemSJEi7Ny5M87XzpkzBysrK5o3bx6PCVXUpQsW9onoq5kByPY2wjhJUWHENBqYMD8FHpaTacVqzk86wI0baqcSQh2Gui69hQUkatuMSKxorl3FmjVqJxIi4e3du5e2bdvSv39/Hj58SKtWrWjQoAEXL1786rVXrlxhwoQJFC1alChTXZvZ0RGL7t3oZTuXi4cC2LBB7UBCfDsZ/mQChg3V8b9xlUiLPz0qXmHPYVti2QZACJNniG2Bjw/45G+CM/f4tcRFzpxRO5EQCat69erY29uzZcuW6GMlSpQgb968LF++PNbrQkNDKVGiBBMnTuSPP/4gUaJEbPiGb9yG2B7Eys8PsmaFESPAw0PtNEJ8M+mpMAGDh2gYn3EO2blPyaOTWbVK7URCiI/lywcnnd0oyiUG1rqGadzKESJudDodJ06coHLlyjGOV61alRMnTnzx2h49elCpUiXq1q0bnxENQ7p00L49zJgB79+rnUaIbyZFhQmws4Oe8wswnT4MYRwze90nIEDtVEKIj409XxNSpqTJe2/pSRRmJTg4mNDQUNKkSRPjeOrUqfH7wjJHq1ev5sSJE0ydOjXOnxUWFkZQUFCMh1Hp3x9evYKlS9Hp4OpVtQMJEXdSVJiIWrXgUt3hvCQ1I173YNlSuRUqhCGxc7SB5s1h5Uow1XHhQnwDCwsLYhuB/fDhQ3r06MHKlSux/4ZlDT09PXF0dIx+ODk56StuwnB2hqZNCRkxmSIFIilaFHx91Q4lRNxIUWFCJnolYUK6mdRmJz0zb1E7jhDiv9zc4OlTZZ1ZIcxE0qRJsbe35+XLlzGOv3jxgrRp0372mkuXLvH69WtKlSqFlZUVVlZW7Ny5k02bNmFlZcWjR48+e52HhweBgYHRD19j/EY+aBBJXj4gr88GoqJg7ly1AwkRNzJR28REReqwbFAXLl+GGzcgSRK1IwmRoAy6LdDp0OXOjb9zWfa3Xoqrq9qBhEgYVatWJVmyZGzcuDH6WKlSpciZMycrVqz45HydTvfJSk/169cnUaJErF27Fisrqzh9rkG3B1/wobILtw77UYSLpEypwddXGeoshCGTngoTY2mlgdmzlTGZo0erHUcI8RGtToNXgCuJd29k4G/vCAtTO5EQCaNv375s27aNVatWERwczOzZs7lw4QK9evWKPmf06NGkSpUKAI1GE91D8c9Do9FEHzd1iUa4U5jL1GAPr18royaFMHRGX1QY6tr0qsqWDYYOhenTOf7HNfz91Q4kRPwzhrbAwgLul3UlKSH8HLhFdtcWZqN27dr88ccfDBkyhGTJkuHl5cW6deti/HvVarVERkaqmNKAVKpESIFSuDMBgFmzkFXjhMGT4U8myv9xGJEFCnM/ODUL3Y6ybLksNyPMg6G3BXv3gl2NCoSSmPkNd7Npk9qJhDAMWq0WnU6HpaVlrK+DMsE7rgy9PfiiLVugYUPKcIJTlOHgQfjPqrxCGBSj76kQn6dJZEs33Rwq8Bca72UcOaJ2IiEEQJUqsM3Bjf+xj3N/PufNG7UTCWEYLCwsYi0o/nn9WwoKo1evHoEZ8jCIiQDMnKlyHiG+woz+dZqXNGmg1pQqrKQVkxmAx69vCA9XO5UQwsoKbF2bEokVTSJXs3692omEEAbJwoLEowbSgK3k4QbbtsGDB2qHEiJ2UlSYsI4dYUWRqdgQTttbHsyYoXYiIQRA447J+ZO6uOGNt7faaYQQhsqqTWuCHDIykEnodPD772onEiJ2UlSYMEtLGLswHUM14/iV+ewcfopYlvYWQiSgIkXgiJMbRblEwPFr3L+vdiIhhEGyscGifz9cWUHPhr60aqV2ICFiJ0WFiSteHDRdu3KeYkwP60rfnrKyhhBq02jAqXNNXpESN7xluUghRKyS9OmEVfKkzMwyjeLF1U4jROykqDADY8ZbMjTFXApzmUzbvNi+Xe1EQoiWbW1YS3Nas5JV3lGyXKQQemQMS0zHWZIkaHr0gPnz4fVrtdMIESspKsyAoyO4zS7JH/zKGIYxpusz3r1TO5UQ+mVsXyKcnMC3khuZeMrarofVjiOESenevTs+Pj6cPXtW7Sj60aMHMqlCGDrZp8JM6HTQoNJb5h/Lw810lclzaQ1p06qdSgj9M6q2QKeD3LmhbFlYulTtNEKYHKNqD76mZ090q1bhPeYRF28nZvp0tQMJEZP0VJgJjQYmzk/O4x5TqOS3lrRX9qkdSQih0YCbG2zYAKGhaqcRQhiyfv2Ieh3AuW6LmDEDbt9WO5AQMcVbUREZGcnLly+jd8CMq3fv3hEqf1zjRZ48UGKmK1SqBN27w4cPakcSQri6KgXFli1qJxFCGLIsWbhVrBX9mYIVEcyerXYgIWKKl6LC09OTFClSkC1bNlKnTs2CBQu+eo2Pjw9VqlQhZcqUZM2alcaNG/Py5cv4iGfeNBqYM0fZQWfyZJkcKoTasmUjonR5fD29GTtW7TBCCEOWadZAMuNLS1azdCkEBqqdSIh/6b2oWL16NaNHj2bLli2EhIQwd+5cunTpwqFDh2K95unTp1SsWJEcOXLw6tUrXr58Sbt27bh48aK+4wmAfPmUbtQx42ha7J40SkKoSKuFoTfdyHB9H4vGPpd/j0KIWDmWK8CVLHUZxERCQ7QsWaJ2IiH+pfeiwsvLi4YNG1KlShUAmjVrRvny5ZkzZ06s14wbNw4HBwfmzJlD4sSJAahbty7Vq1fXdzzxt2mJh/EkIi0dLv3GsKHSXSGEWiwsQNu4KZFY0TBsNZs2qZ1ICGHIHMYNIj8+1GE7s2dDVJTaiYRQ6LWo0Gq1nDt3jnLlysU4XqFCBc6cORPrdTt37qR+/fpYWVnx+vVrouRfSLxr0jYxA2xmUZPdPPfaxIULaicSwnw16ZScP6mLG954e6udRghhyLK2Lse1ZOVxZwL37+vYuVPtREIo9FpUBAcHExYWRqpUqWIcT5Uq1RfnRzx58gStVkuhQoXIkSMHiRMnpnnz5rz+wiYvYWFhBAUFxXiIuMucGX4aU59t1GW6rhf9OgfL3Q5h1Ixtn4qPlSwJB9K7UZRLvDx0DV9ftRMJIQzZ+17ulOUk5fmLmTPVTiOEQq9FhYWF8naRkZExjkdERGBpaRnrdRqNhgULFjBv3jzevn3LvXv3uHr1Kl26dIn1Gk9PTxwdHaMfTk5O+vklzEjv3jA7xyxS8Iba50excKHaiYT4fsa82ZVGAxk71uQVKXHFm1Wr1E4khDBkxYfV4pZNAdyZwIEDcO2a2omE0HNRkTRpUhwcHPDz84tx3N/fn4wZM8Z6XcaMGalZsyZly5aN/rlr167s2rWL2Pbm8/DwIDAwMPrhK7f2vpmNDQxdmJUxDKM3M/AecIUXL9ROJUxNQEAAO3bsYM+ePYSEhHz1/HXr1rFmzZoYj9tmsCB7y7Y2rKU5rVnJyuVRsjKbED/AmHsu48LCUsPD5u7UZidFLa9w8qTaiYSIh4naFStWZN++mBur7d69m4oVK0b/HBQUxLNnz6J/rly5MsHBwTGuCQ4OJnHixGg0ms9+jq2tLQ4ODjEe4ttVqgT+rftxh5xMDO7KoAHftq+IEF+ya9cusmTJwtixY3F3dyd79uycOnXqi9e0atWKefPmsWXLlujHvXv3Eiixepyd4VLBNmTiKWl8DnH5stqJhDBextxzGVdlZzbnbbKs/FV3Ip06qZ1GCECnZydOnNBZWVnpxo0bp7ty5Yqub9++Ont7e93NmzejzxkxYoTO0dEx+ucbN27okiRJops6daru1q1buk2bNulSpkypGzp0aJw/NzAwUAfoAgMD9fnrmAU/P52uTuKDOh3o2rNId+SI2omEKQgODtalTJlSN2TIkOhj7dq10zk7O+uioqJivc7S0lK3a9eu7/5cY24L5nhpdbfIqVtKG12/fmqnEcL4GXN7ECezZ+t0FhY63f37aicRQqf3nooyZcqwY8cO9u3bR4MGDbh+/ToHDhwgd+7c0ec4ODjEGA6VJ08eDh48yIEDB6hVqxbTpk1j9OjRjBw5Ut/xxGekTQu1JlfGG1cmMZAxvV/L0Avxw3bv3s3bt2/p1atX9LG+ffty7949Tn6lr/7q1ats2bKFy5cvo9WaT+9Zs+YaVlm40ZiNbFsdihn96kKI7/HLL5AiBUydqnYSIdDodKbx9TEoKAhHR0cCAwNlKNR3iIqC2j/5s/FabrRNmpJ09dd3QRfiS0aMGMGCBQtiDHXUarVYW1vj5eUV60IM1tbW5MmTh8yZM3P27FkyZ87MunXryJ49+2fPDwsLIywsLPrnoKAgnJycjLYtGN/pAYMXZuft7BUk/6212nGEMGpm8d1g7FgYN44Ptx7hp01D1qxqBxLmSu89FcI4WVrCuiNpSTxzPEnXLERmfYkfFRgYSIoUKWIcs7CwIFmyZAQEBMR63bZt27h69So7duzg7t272NjY4ObmFuv5prYS3OAF2aB8eZJvlw0rhBBfF9axO2FaK+bkncUXmkoh4p0UFSKagwPw66/w00/QtSv8Z2lgIb6Fra3tZ1d7Cg0NJVGiRLFeV7NmzejnDg4ODBgwgBMnTvDmzZvPnm+SK8G5ucG+ffD8udpJhBAGziZtclYl+ZX277y4/FeQbGYrVCNFhYjJ0hLmzoUrV/gw5XdZ+1p8N2dnZ/z9/WMMTfLz8yMsLCzWoUyf88+Qhdg20DTJleCaNgUrK1i9Wu0kQggDp9GA1YA+JCaUzsyXzfCEaqSoEJ/QFf+Ju9W7Ejl4GB1rPuXdO7UTCWNUo0YNIiIi2L59e/SxtWvXYm9vz88//xx97ON9KPz9/T/Zm2bTpk2kSJECZ2fnBMltCHTJkhNQoS5PJ3jTvr3aaYQQhq5Rj4yss3GjL9PYtDoMf3+1EwlzJEWF+Kw+oeMI1dnT90kfPD3VTiOMUZYsWejXrx+dOnVi4sSJjBo1Cnd3d8aNGxejN6Fly5bs3LkTgL/++osyZcrg6enJwoULadGiBYsWLWL27NlYWVmp9askOJ0OBlxxI+PLS1xYdpX/7CcqhBAxJE4Mz10HkA4/mkd488cfaicS5kiKCvEJjQYmzU/GIMupNGM9Fzz3cOuW2qmEMZo4cSLz58/nzp07PH/+nC1bttC7d+8Y5zRv3jx6yenGjRuzaNEi3r17x6lTpyhYsCA3btygVatWKqRXj4UFZOhQk1ekpLXOmzVr1E4khDB0zYbnYQsNGcBk/pgTRXi42omEuZElZUWsBnvoqDahKk740vPnq+w8mIhYNjgXwmCYSltw8ybsz/sbDdlMg6KPOXvBUu1IQhgdU2kP4sq9yhkmHCpFYzbQaEVjWsuq1CIBSU+FiNXQYRrGZfAiC48oeXii3C0VIgHlyQPn8riRkWc4XjyEj4/aiYQwHl5eXuTLl48SJUqoHSVB1RpZkgNUwZ0JzJyhk41sRYKSokLEyt4ees/LyxT644Ens3reJTBQ7VRCfJ4pfoko+mtJbpMTN7xZsULtNEIYj+7du+Pj48PZs2fVjpKgKlSA9c7ulOAcSc8d5NQptRMJcyLDn8RXNavzjkk78nGTPOz8bRezZssYKGG4TKkt8PeHOenHMEA3kZ8y+ePzKDEWcitIiDgzpfYgrpYu0VG0U3HsM6Uk8Yl9ZMigdiJhLuTPk/iqyV729LeZjQt78PfaIBvrCJFA0qaFxxVdSUIoxZ9s4dgxtRMJIQxdq9Ya8ixxJ+ej/WR4fl7tOMKMGH1RYYpDHgxNlizw06i6bKE+0+nNw6vBakcSwmxU/zUbxygvQ6CEEHFiYwO2rRqDszNMnKh2HGFGjL6oMNdxkwmtb1+42mEm6RIF0OjyCLXjCGE26teH9bZu/I99XNv3HK1W7URCCINnaQkDB8KGDXDnjtpphJkw+qJCJAwbGxi2MAsWI4bDrFlw+bLakYQwC/b2UHhcU7Cy4q9uq2ROhRAibtq0ISp1Ws63nMz69WqHEeZA/jyJb9OnD+TODV27IrdMhUgYHfolx7JBPSxXeasdRQhhJB48T8Sw130ocH4Z80c+k+VlRbyTokJ8GxsbmDMHTp5kVbXFHD2qdiAhzISbm9JDePWq2kmEEEYgWzY4VaQL77Hjfz4z5O+1iHdSVIhvdidDJdYncqPGoUEM7vyKiAi1EwlhBos2uLhAypTg7U1UlNphhBDGoGNfB+bSlS7MY8HkALXjCBMnRYX4Ztmzw4LcU7BAS/tbg5g5U+1EQpj+og06axvuFG/B61krqfqzVBVCiK9r0gTWpOmFDeFk3enFgwdqJxKmTIoK8c0sLWH8wjQMxpMOLGb3sOP4+qqdSgjTptHAqPtupAx7htVfh7h7V+1EQhguk++5jCMbG2jaIx0L6ERf3VT+mBykdiRhwqSoEN/lp5/AsksnzlCCaR+60q+njIESIr4V7lSS2+SUPSuE+ApT77n8Fl26wHRbD+x5R+JFMwkIUDuRMFVSVIjvNtbTkiHJ55Kf62TaMpudO9VOJIRpa9lKwwrcaMxGNi4PldVchBBflSoVVG+XgXl0oUf4VJbPClA7kjBRUlSI75YsGbSdVZw5dGMUIxjX9Qnv36udSgjTlSkT3C/rShJCKfRgC6dOqZ1ICGEM+vSBCbhjQziRU2bIAisiXkhRIX5I69awp/xYQklM78d98PRUO5EQpq1ap2wcozxtWC5DoIQQcZI7N5Ssm445dKNj8HRunXyjdiRhgqSoED9Eo4HJ8x0ZYDGNpmzgoudu7t1TO5UQpqtRI1hj3YZq7OfQqueEh6udSAhhDIYMgRSeA0lqH0mBvdPUjiNMkBQV4oflzQuZBrTkiGUVViTrTta0MgZKJDxzWe3FwQE+1G1KBNbUDFjF7t1qJxIi7q5cucKff/7JzZs343R+REQE586dY/fu3dyTO1Y/pFQp+MU9DZrffoOZM+H1a7UjCRMjRYXQi6HDNOQ75IVjoC+WkyeoHUeYIXNa7aVxh2T8SV3c8MbbW+00QnxdeHg4DRo0oHLlysyYMYOSJUvSoUMHdF9YbeDPP/+kQIEC9OjRg+nTp1OkSBEaNWpEWFhYAiY3QQMGKP+dMkXdHMLkSFEh9CJxYkhdIQ8MHAgTJsDt22pHEsJk/e9/sM3BjSJcJsmDq2i1aicS4stmzJjB8ePHuXz5MgcOHODkyZOsWrWKFV+ZGHTs2DFOnjzJnj178PHxYffu3SxZsiSBUpuoVKmgRw+0s2bjd+WF2mmECTH6osJchjwYjSFDIGNG6N4d38ey3qUQ8cHaGlotdyEqWUqWVPHGwuhbcmHqvL29ad68OZkyZQIgf/781KxZE+8vdLXVrVuXNGnSRP+cMWNGHB0dCQwMjPe8pszfH3o97kfIOwuuuE1WO44wIUb/p8ichjwYBTs7gsfPhv37GZRtHZcuqR1ICNNUs74Nlq1bwMqVEBWldhwhYhUZGcmNGzcoVKhQjOOFChXiypUrX7w2KCiIDRs2sGzZMho2bEi2bNno1KlTrOeHhYURFBQU4yFiSpQIlmxLyQx6U/6KF6+u+6sdSZgIoy8qhOGZ/7Q2m2jIFG0f+nUKkqEZQsQXNzd49gwOHVI7iRCxCgkJISoqiuTJk8c4njJlSgK+sr1zYGAga9aswdvbm+PHj1OhQgWSJk0a6/menp44OjpGP5ycnPTxK5gUR0fo2BGm04dwbLjTcaLakYSJkKJC6F2PHvC78wwcCaTuueEsWqR2IiFMVMmSkDMnOm9v/OVmozBQtra2ALx79y7G8ZCQEBIlSvTFa52cnNiwYQP79+/n4sWLLFu2jPHjx8d6voeHB4GBgdEPX1/fH/8FTFCvXhBsmZzp9KHIqbm8v/9c7UjCBEhRIfTOxgaGLcjMSEbSg9l497vEy5dqpxKmzhznV+nQcNjJjXfeG6lVKZQvLKQjhGrs7OxIly4djx8/jnH88ePHZM+ePc7v4+TkRNWqVTly5Eis59ja2uLg4BDjIT6VJQs0aQIz6M0HEnGvk6zaKH6cFBUiXlSuDC9b9eYGeZkY3BX3gTIGSsQvc5xfpdHA3GBXEutCyXtrMxcvqp1IiM+rWbMmmzZtQvv3eNgPHz7w559/UrNmzehzfHx82LZtW/TPL17EXJkoMjKSq1evRk/2Fj+mXz8IwpEp9CfnoT/QPn6idiRh5KSoEPFmwlRrBiSeSxlOYbF0EX/9pXYiIUxP1Y7ZOEoF3PDmK6tzCqGa4cOH8+TJExo3bsyCBQuoXbs2VlZW9O3bN/qcdevW0aZNm+if69SpQ+/evVmyZAlz5syhatWq+Pn5MXjwYDV+BZNTogRUqACz6UGILjG+3TzVjiSMnBQVIt6kSwd1JlZgKW2ZyCAGd3pJRITaqURC0ul0rFy5Ejc3N9q3b8/WrVu/6fq+ffvSoEGDT4ZNiH81bQqrLd2oxn72ez8nMlLtREJ8KmvWrFy4cIE8efJw+PBhKlSowNmzZ0mZMmX0Ofny5aN+/frRPx87doz8+fNz/Phxrl69StOmTbl37x558uRR41cwSf36QTAOTGYA6XcuBGlrxQ/Q6L60naURCQoKil6/WsZQGo6oKKhR7CXrruRmK/V5M2UJ/fqpnUoklL59+7J8+XKGDRvGhw8fGD16NCNGjGDgwIFfvXbmzJnMnDmTBw8ecPXqVQoUKBCnzzTHtsCtbgALtqdjCOOovrsfNWqonUgIw2CO7cG30Gohd254fjeEB2RD07gxqTbMUzuWMFLSUyHilaUleC5MzWA8ac9Snqw+JpNJzcSDBw+YOXMmixYtolevXgwaNIhJkyYxcuTIr25edfHiRaZMmcKsWbMSKK1xa/RLMv6kLm5484W9xIQQIgYLC+jTB9LnSMKdBgNJuXURPHyodixhpKSoEPGuRAlI6d4J/2ylmBbWDU2kjIEyB3v27MHW1jbGRMymTZvy/v17Dh8+HOt1ISEhtGjRAi8vL9KlS5cASY1frVqwObEbRbjM7Y1XCQlRO5EQwlh06gQ3b0LZFd3QpEgB48apHUkYKSkqRIIY52lB2o1z0fj4wMyZascRCeDBgwekTZsWGxub6GNp0qTB1taWBw8exHpdt27dqFy5MvXq1YvT58gOumBrC8lbuvCKlDT54M3mzWonEkIYC2trZVQBiRODuzssWQL37qkdSxghKSpEwilaFH77DUaOBNmQyOSFhYVhb2//yfHEiRPz4cOHz17j7e3NmTNnmDZtWpw/R3bQVbRqZ8MaWtCalaxcHqV2HCGEMerSBVKnhrFj1U4ijJAUFSJhjRkDDg68cu3N/PlqhxHxydHRkbdv38Y4ptVqCQgIIHny5J+9Zvr06dja2tKqVSsaNGhA//79AejVq1es8ytkB11F2bJwIL0bGXlGVYuDaGVrGCHEN7p2z45VWTzQLveGO3fUjiOMjJXaAYR50SV1YGHeaXQ62JIdJ3ZSuXItcuZUO5WID4ULF8bf3x9/f3/Spk0LwJUrV9BqtRQqVOiz10ydOjXGJO579+5x5MgR6tevT/ny5T97ja2tLba2tvr/BYyMRgOjdpVE2zQXA9J6g8X/1I4khGq8vLzw8vIiKkp67eLq4UMoWBBs6UwVy4mkGTUGixXL1Y4ljIgsKSsSnPsgHVUnVceZe/Sscp0/99uh0aidSuhbaGgo2bJlo127dkyaNAkAV1dXzp49y40bN7CwUDpKGzRoQIcOHahbt+4n73Hu3DlKlCghS8p+i7FjYcIE8PdXxkgLYcbMvj34Ri4usGcPdMOL3zU90dzwUdacFSIOZPiTSHDDhmsYm86LjDyl1MHxrF+vdiIRHxInTsyqVatYuHAhRYsWJV++fBw4cICVK1dGFxQAW7du5Z5MCtQfV1cIDUVmawshvtU/+0gtpCMvrDPA6NHqBhJGxeh7Kj7u4rx9+7bcjTASW7bAlYbDcWcCVVNfZcfd3Mj/bKYpODiY06dPY2VlRenSpUmUKFGM17ds2ULBggVxdnb+5NqAgAAOHz5M1apVSZo0aZw+T+5MAhUrEmltx5XJeyhWTO0wQqhH2oNvo9NBkSJw5Qp05g/mabqiuXYN8uVTO5owAkZfVPxDGg7jotNBk9rvmbSrAA/Ixo5e+5g+Q8ZAiR9n7m2BTgdLyy2gzckulEz/hLNP0mMhfdLCTJl7e/A9li2Ddu3AmnCe2OciTZ1SsHat2rGEEZA/NUIVGg1M8bKjn83vVOMAL2at4dIltVMJYfw0Gtjj0JQIrPn5+SqOHFE7kRDCmLRsCenTQwQ2DHk3FNatg6tX1Y4ljIAUFUI12bJByRE12Ugjpuj60r9ToCyDKb6bl5cX+fLlo0SJEmpHUV3D9sn4k7q44c2KFWqnEUIYExsb6NFDeb6UtrxyyAajRqkbShgFGf4kVBUWBjXy+bL9fl4W8wv2C2bRsaPaqYQxk7YA3r+Hdim3sfZ9fcomvsyBl4Wws1M7lRAJT9qD7/PmDTg5wbt38KvNEuaF/wIXLyoTLoSIhfRUCFXZ2sLwBU6MYBTd8aKy4wW1Iwlh9OzswKGpC69IScNQb/78U+1EQghjkiIF/PKL8vxIZjc+ZHKGkSNVzSQMnxQVQnVVqkD9/T2xKJAP5yldQTYrEuKHtWpnw2pa0opVrFwu/6aEEN+mXz9lpcbrt6xINH4EbN0K58+rHUsYMCkqhEGoWNUazdy5cOYMLFyodhwhjF6lSrA3jRsZeUbYroO8fKl2IiGEMcmaFerXR1k9rmVLyJVLeivEF0lRIQxH+fLQvj24uxPm+4LISLUDCWG8LCwgf7sS3CIXrbTesiKkMCuycIOeWVnBiBGwfbty80+Iz5CiQhiWSZOIiLJgZ4GBzJqldhghjJurmwZv3GjEJjYsC1U7jhAJpnv37vj4+HD27Fm1o5iMq/ma8yF7XumtELGSokIYlHuBqegePIGGQcvYO/QoT56onUgI41WgAFzI60oSQumbbbMs2SyE+Gb+/lCjBhQqasn0pCNg1y44eVLtWMIASVEhDIqzM1j92oGTlGbq+64M6BWudiRhJGS4w+d5H8uKrkIF6gV6y87aQohvljIl3L6tPB9yuSkfcuRXhkIJ8R/x8icmIiKCbdu2MXv2bHbv3o32G26PPXv2jClTpvCnrIFotsZ5WjAk+VzycBOnTTPYvVvtRMIYyHCHz0uZEjRubrB/Pzx/rnYcIYSRsbKC3r2V5zosWJx5FOzbB3/9pWouYXj0vvldcHAwVapUITAwkAoVKrBv3z7y5MnD9u3bsbGx+eK1Wq2WKlWqcP78eWrUqMGGDRvi/LmywY1pWb4cXrftQ2fmUzOzD3tvZSFRIrVTCWMgbcFnBARAunQwbpyyTqQQZkLaA/0IDlY2wwsMBFtrLcE5i2KdLhUcOKB2NGFA9N5T4enpib+/P2fOnGHRokWcPHmS06dPM3/+/K9eO2bMGFKmTEmlSpX0HUsYGTc32Ft2FAEko8/j3kycqHYiIYxYsmRQty4fFixn61a1wwghjE3SpPDrr8rzsAgL1ucfBQcPwpEj6gYTBkXvRcX69etp3rw5yZIlAyBjxozUqVOHdevWffG6Y8eOsXjxYhYsWKDvSMIIaTQwZb4D/S2m05AtXBq7nbt31U4lhHHS6cDjRhsS3brCZLcrhMtUJSHEN+rRQxkKBdDzQH20hYvC8OFKAyMEei4qwsPDuXfvHrlz545xPE+ePNy4cSPW6968eYOrqyuLFi0iRYoUcfqssLAwgoKCYjyEacmfHzL3a8oeqjMtsgf9ur6TtkuI76DRwNOCLrwkFfWDvdm5U+1EQghjkykTtGihPH/9RsPuMqPg6FE4dEjdYMJg6LWoCA0NRafTRfdS/CNZsmQEBwfHel379u1p0qQJ1apVi/NneXp64ujoGP1wcnL63tjCgA0foWFcut9Jz3PKHBzHF2pTIcQXtGprzRpa0IpVrPKOUjuOEMII9e377/Pe++ug++kn6a0Q0fRaVNjb2wN80msQGBhI4sSJP3vNvn372L17NylSpGDKlClMmTKF+/fvc/v2baZMmRJrD4SHhweBgYHRD19fX33+KsJAJE4MfefmZF02dwZZTiafxU21IwkDJUvKflm1arAzhRsZeUbItoO8fat2IiGEsSlaFCpXVp7fuavhXN3RcPy4srqcMHt6LSpsbW3JkiUL9+7di3H83r175MyZ87PXZMiQgR49evD27Vv8/Pzw8/MjLCyMsLAw/Pz8iIr6/B01W1tbHBwcYjyEaapfH9yuu6PJnBm6dZM7IuKzZEnZL7OygjxuJbhFLlpEevMNi+sJYXTkJkP86dcPKlWCbdug+BAXKF1aeisEEA9Lyvbq1Ytdu3Zx5coVEiVKxJs3b8iVKxcDBgxg0KBBAJw4cYILFy7w22+/ffY96tSpQ6JEiWRJWRHT7t1QsyasXAmtWqmdRhgoaQtid/48bP5pLO5MoFFZf/Ye/3wPshCmQtoD/dPplHla0fbuVbbc3rlT+RstzJbeV38aOnQoWq2WSpUqMWTIECpVqkSWLFliFBB79+5l6NCh+v5oYepcXKBJE3R9+7JkegDfsKeiEAIoVgxOObuShFDSnNjMw4dqJxJCGJsYBQXA//4H5cpJb4XQf1GROnVqLl68yC+//AJAv379OH78eIw5FWXLlqVHjx6xvkejRo2oV6+evqMJE3Cy+QxCX4QS2ncoS5aonUYI46LRQNUOWTlKBdzwZuVKtRMJIYyeRkPUiNFw7hzs2KF2GqEivQ9/Uot0cZqHAwdgR7VpTKE/1RzOsu5ecVKlUjuVMCTSFnzZo0cwNusC5tGFys6+HLmT4dM7j0KYCGkP4o9Op4x8mjoVChXUMeXcz8rW2+fPf6Y7Q5gDvfdUCBGfqlaFF817cpWCTAzqgsdAWRpTiG+RJQu8+rkpURbW/F52lYxWEEJ8l9evoUED2LcP5i/QEDJwNFy8CFu3qh1NqESKCmF0Jk+3or/9XEpwDqsl8zlxQu1EQhiXjQeSYdO4HoUue2MhfwWEEN8hVSpo00Z5HhwMf9ysBFWqwMiRyKRH8yR/ToTRSZ8e6k0oy0I64IkHQzr6ExmpdiqhNllCMu4sLAA3N7hyRXkIIcR36NPn3+czZ0LksFFw+TJs3qxeKKEaKSqEUeraFVYWnEgkVrS/MYDZs9VOJNQm+1R8IxcX5Vajt7faSYQQRipPHqhdW3nu6wvrn5dXVoOS3gqzJEWFMEpWVjBhQUrcmUgbvNk7+DBPn6qdSsTme9aDMJE1JAyXtTVRTVvwfvEqZk2XuUlCiO/Tr9+/z6dOBd3IUXDtGrLDpvmRokIYrVKlwLpze45TlqkfujGgV7jakcR/PHv2jLp165IoUSLs7e1p2bIlb9++jfV8rVbL6tWrKVmyJHZ2dqRIkYIWLVrg6+ubgKnNg04Hzbe7YffmGXvdDxIcrHYiIYQx+vlnKFpUeX7+PByNKKP0hI4cCVFyw8KcSFEhjNo4TwsGJ5tLLm7TIXCarGRjQHQ6HfXr1+fdu3c8evSIGzducOPGDdzc3GK95unTpxw8eJD58+cTEhLChQsXeP78OY0bN07A5OZBo4E0tUtwi1w0C/dm0ya1EwkhjJFG82lvBaNGwY0bsHatarlEwpN9KoTR27cPSqzpR7LVc8HHB7JmVTuSAI4ePUqlSpW4evUqBQoUAGD37t3UrFmT27dvkzNnzji9z+LFi+ncuTPh4eFYxGGpImkL4u7kSdhRdizuTKBFJT+2H06idiQh9MLLywsvLy+ioqK4ffu2tAfxLCICsmeHJ0+Un2/dglz96sLt23D9ujJmWZg86akQRu9//4NkM0ZCihTQq5faccTfTp48SYoUKaILCoDKlStHv/YlERERvHv3jmvXrrFw4UJatGgRp4JCfJvSpeFYZleSEEqKI5tlXpIwGbJwQ8KytoaePZXnlSvDu3cow59u34bVq9WMJhKQ/JUWpiFpUpgxA7Ztg23bZBiUAfD39yd16tQxjtna2uLg4IC/v/8Xr23bti3JkiWjYMGCWFlZMfsLy3uFhYURFBQU4yHiRqOByu2zcoSKuOLNqlVqJxJCGKvOnZU5FQcPQpEiQPHiUL8+jB6NrPtuHoy+qJC16UW0xo2JrFaDt249aVY7VAoLA6D9zJKCWq0WjUbzxetWrVpFeHg4d+7cwdrammrVqhEVy4Q/T09PHB0dox9OTk56yW4uWrcGb9yoygH2LHmmdhwhhJFydIRixf5zcORIuHsXVqxQI5JIYEZfVEgXp4im0eD69nfsgvwotmssGzeqHci8pU+fnpcvX8Y49v79e0JCQkiXLl2c3iNHjhxMnz6dCxcucO7cuc+e4+HhQWBgYPRDVor6NjlzwqOfmhCBNUVurJK98IQQ+lOkCDRqpPRWRESonUbEM6MvKoT4WLPBORjPYPozBa/uPrJMporKly9PQEAAFy9ejD524MABAMqVKxd97MOHD7H2QoBSiABYWlp+9vV/hlR9/BDfpkG7ZGyjHm54yw1FIcQP0+lg1y7YvRult+LBA1i2TO1YIp7J6k/CpOh00MDlA1P2FuQJmdjR9yBTpn55qI2IPxUrViQiIoKlS5fy4cMHmjVrRuHChVm3bl30ORqNhunTp9O7d28WLlzIy5cvadCgAenSpeP69ev07NkTCwsLzpw5I6s/xZNXr6Bj2j/Zoq1HtdSX2etXCJkXL/TN19eXuXPn8ujRI3LmzMlvv/1GqlSpYj0/KiqKTZs2ceTIESIiIihRogRt27bF2to6zp8p7UHCe/sWypdXFmPMl0/ZB0/TojmcPq1M3LaxUTuiiCfyZ0OYFI0Gps9NRB9rLypzmBfTV8pwDhVt2rQJZ2dnypUrR40aNahcuTKLFy+OcY6trS1Wfy832KpVKwCaN2+Os7MzXbt2xcXFhX379snqT/EoVSrI8IsLIXapWF3LWwoKoXcPHz6kWLFi3Lhxg59//pljx47x008/8fr161ivKVeuHBs2bCBPnjwUKVKEKVOmUKlSJcLDZaNTQ5Y8ufIApbDYvRsYMQIeP4YlS1TNJuKX9FQIkzRmDOQa3pyfOUzbkjfZeTK5fFEyE9IW/IAePWDTJuWPfyzDzYT4Hh06dODChQucP38eCwsLPnz4QI4cOWjXrh1jx4797DVPnjwhU6ZM0T8/fvyYLFmysHnzZho0aBCnz5X2QB2bNytTKQCqVVP2k6JVKzh2TJm4bWuraj4RP+RrljBJAwfC7GzTseM9dc8MZelStRMJYQTc3ODZM2VNSCH0aOfOnTRq1Ci6xzFRokTUrVuXnTt3xnrNxwUFQLp06bC2tubt27fxmlX8uHr1wNlZeb5/P1y+DAwfrrQvCxeqmk3EHykqhEmytYWR8zMwnNF0ZS6r+57lC73swgTI8tJ6UKIE5MoFy5ernUSYkPfv3+Pn50fmzJljHM+cOTP379+P8/vMmzcP+HcTzc+RfWsMg6Ul9Onz78/TpgF58ii9FePHw4cPqmUT8UeKCmGyqlWDl81+4wqF8Azsysxpsa8wJIyfLC+tBxoNAfXbEL52EwO6hqidRpiIsLAwAOzt7WMcT5IkCR/i+OXyyJEjDBgwgEmTJpE1a9ZYz5N9awxHu3b/zq1YvVrppGD4cPD3h/nz1Ywm4okUFcKkTZ5uxdAUc/mJ8wxPM0/tOEIYNJ0O6qxqjU3EO178sZmvbHwuRJwkSZIES0vLT4YtvX79mmTJkn31+hMnTlC3bl0GDhxI7969v3iu7FtjOBInhi5dlOcRETB7NsrGOG5u4OkJfy8XLkyHFBXCpGXIABueloFOnbAaPhj8/NSOJITB0migYpusHKEirXXerF2rdiJhCqysrMibNy9X/rMU35UrVyhUqNAXrz158iQuLi706NGDMWPGfPWzZN8aw/Lbb/DPCsDz5kFICDB0KLx8qRwQJkWKCmHyEiVCuStiYwP9+6sdRwiD5uoK3rhRlQPsWvRM7TjCRLi6urJu3TqePHkCwPXr19m1axeurq7R56xbt462bdtG/3z69GlcXFzo2bMn48aNS/DM4sdlyKBMowAICPh7eVlnZ2Vs1IQJEBqqYjqhb1JUCPOQMiVMmgQrV3JvwUFlbKcQ4hP58sGdQk2IwJr8V1Zx86baiYQp6NOnD2XKlKFw4cJUrVqVMmXK0LJlS9zc3KLP8fHxYevWrdE/161bF61Wy82bN2nSpEn04+PNM4Xh69sXWreG8+ehSZO/Dw4dCm/ewJw5qmYT+iX7VAizERKk5UW+SoQ/fcnoxldYtUF29TRF0hb8uOnTIWPfZuTmFuuHXCaWbQSE+GaXL1/m8ePH5MiRg7x588Z4zcfHh7t371KvXj0ANm/eTFTUpwts5MuXj3z58sXp86Q9MGBdusDGjfDgASRJonYaoQdSVAiz8fo1NMxxlYMBRRnOaH7eM5jq1dVOJfRN2oIf5+cHv2b4k626etTKcIntvoVl80hhlKQ9MGCPH0OOHDB6NLi7q51G6IH8mRBmI2VKaD+tINPpwzDG4Nn5gSyVbUJknwr9SZcOIqu58JJUVHnmzfHjaicSQpgKrRYCA4HMmaFTJ5g8GWQ/EZMgRYUwK23bwr4yI3hFKvo+6smkiSbRUSeQfSr0rWUba9bQglasYuVy2eNFCPFjwsOVzbQLFICOHf8+6OGhTNaePVvVbEI/jL6okLuT4ltYWMDUP5LQx2ImddnOlbHbuHdP7VRCGJ6GDWF9ojZk4DmBmw7wmaHtQggRZzqdMj/7xg3YtEmZSkGmTNC5M0yZ8nf3hTBmRl9UyN1J8a0KFoRsfRqyk5pMjexJvy6hmMbMIiH0J3FiqD3iJwLS5WZZNW8sLdVOJIQwZra2yr4VoAyBmjHj7xfc3eHDh48OCGNl9EWFEN9jxEgN49L9ThpeUGb/aDZtUjuREIZnkLuGZL+5YbN909+7VglhHGQUg2Hq2hXs7JTnixbB27com1l07aosO/efXdeFcZGiQpilJEmgn1d2xjOYvkzDq9t1goPVTiWEAWrdGt69g82b1U4iRJzJKAbDlDKlsu8dKFMp5s//+4VBg5RJF9OnqxVN6IEUFcJsNWwIl6sP5D7ZmRTaDX8/GQMlxCeyZoWKFcHbW4YJCiF+WJ8+oNEoz2fNUmoJ0qaF7t2VIVBv3qgZT/wAKSqE2dJoYPocW6518eKn0KPkOOmtdiQhDI5OBzd+ckO7/wBuVWUreiHEj8mZE/7e35Bnz2Dt2r9fGDhQmWwxdapq2cSPkaJCmDVnZ2g8txq0aAH9+8sdEiMmY6jjzy87mxCusybdoVXcv692GiGEsevX79/nU6cqNy9InVqZyT1zJrx6pVo28f2kqBACYNo0ZfWJIUPUTiK+k4yhjh8aDTRol4xt1KMNy1mxQu1EQghjV748/HP/5/JlOHjw7xf691cancmTVcsmvp8UFUIApE8PY8ei++MPepU5w+vXagcSwnC0agUrcKMQVzm36LLMrRBC/BCNRumtsLICNzfImPHvF1Klgl694Pff4cULVTOKbydFhRB/W56kGxd1RWh7qguDB8lOX0L8w8kJ3ldy4SWpqPjYmzNn1E4khDB2jRvDw4ewfDnkyfPRC337KtXGpElqRRPfSYoKIf5WzcWK/vZzKcIlbBbN4dQptRMJYThatrFmNS1pxSpWLpeiWwjxY6ysPuqh+FiKFNC7N3h5wfPnCR1L/AApKoT4W4YMUH98KebTmbEMZVjH50RGqp1KCMPQuDGss3EjA895vuIAERFqJxJCmKw+fZQtuCdOVDuJ+AZSVAjxke7dYVX+8YRhS/vr/ZgzR+1EQhgGR0fIWP8nbpKbekHe7NmjdiIhhKl4/x4WLIA//vj7QLJkyjCoefOUdWeFUZCiQoiPWFnBxAUpGMBkWrGa/e77pT0T4m9ubTR440YjNrF+SYjacYQQJuD9e8iRAzp3hqFDlZ8BZcK2vT14eqqaT8SdFBVC/EeZMmDbsQ1HqcDk990Z1DtM7UgiDmSfivhXowbsSt6axLwjw+nNRMnUCmGgpD0wHnZ28PPPyvNXr5SJ24DSPdq/P8yfD76+asUT30Cj05nG4oBBQUE4OjoSGBiIg4OD2nGEkXv9Guo5X+dwYBFGMYKf9w2lWjW1U4m4kLYgfq1bBzU8K+GQ2hbN3r1qxxHii6Q9MA4XLkDx4srzXLngxg2wsACCgyFbNmjWDBmPbPikp0KIz0iZEjpMy880+jKEcUz89T5ardqpjNPLly/ZuHEjW7duJSAgIE7XXL58mfXr13P8+HGi5Ha4QWnWDBy7u6HZvx+ePlU7jhDCBBQr9m9vxe3bsGPH3y8kTQoDBsDChfDokVrxRBwZfVEhXZwivrRrB/tLDyPQJjXr0/fAQmMSnXoJauvWrWTLlo3ff/+dCRMmkD17do4dOxbr+RcvXqRYsWK0a9eOdevW0a5dO/Lnz8+9e/cSMLX4qiZNwMYGVq1SO4kQwkT07fvv82nTPnqhe3dl4va4cQkdSXwjGf4kxBe8fAkpjm3BsnFD2LQJGjZUO5LRCAoKImvWrPTq1YsRI0YA0LlzZ/bu3cu9e/ewtLT85JozZ85ga2tL4cKFAYiMjKRKlSrY2dmxJ47LDUlbkECaN4cbNwg9eYXEidUOI8TnSXtgPLRayJcPbt1Sfj5/XunBAGDKFPDwULoxsmVTLaP4MqPvqRAiPqVODZYN60Pt2tCzJ4TIijdxtXv3boKCgujevXv0sV69evHo0SNOnDjx2WtKliwZXVAAWFlZ4eLiwtWrV+M9r4g7nQ52pnKDq1dpU/gypnFrSgihJgsLZXuKf0yd+tGL3bop45LHjk3wXCLupKgQ4ms0Gpg9G169QjtyNHfvqh3IOFy7do20adOSKlWq6GP58uXD0tKSa9euxfl99uzZE6PQ+K+wsDCCgoJiPET80mhg4sUavCA1Ze55c/my2omEEKagTRv450/G2rUfLfpkbw/u7rBsGfJH2HBJUSFEXGTLxuO2Q4maOp0u5a9Jh0UcBAYGkixZshjHNBpN9FCEuJg0aRKnTp1i7BfuTnl6euLo6Bj9cHJy+pHYIo5atrFmDS1oxSpWLJPJ9EKIH2dnp3RKgHLz4q+/Pnrx118hTRrprTBgUlQIEUc9HvbnHs6M8O/KmFGyFNTX2NnZERoa+snxkJAQ7Ozsvnr9woULGTp0KKtXr6b4P2sNfoaHhweBgYHRD19ZzzxBNGsGqy3dyMBzniw7IHtWCCH0ont3pVPi4UNo2fKjF+zslHkV3t7K3AphcKSoECKOpnnZ0tt6DhX4i1fTlvMNI3jMkrOzM35+fnz48CH62LNnzwgPD8fZ2fmL1y5evJju3buzcuVKGjVq9MVzbW1tcXBwiPEQ8S9FCkhX5ydukpvab705cEDtREIIU5AmjbKJdsaMn3mxUydInx5Gj07wXOLrpKgQIo6cnaHs0CqspBUTtANw7/RaJqh+gYuLC1FRUWzdujX62OrVq0mSJAk//7MgObB06VJ8fHyif162bBldu3bF29ubpk2bJmRk8Y3c2mjwxo1GbGL9EhkTKISIZ4kSweDBsHq1skOeMChSVAjxDQYOhN+zTsWGcOqeGszy5WonMlxOTk54eHjQuXNnRo0ahYeHB0OGDGHixIkkSZIk+rz27duz9++dmXft2sUvv/xCzZo1effuHUuXLo1+CMNTuzb8mbQ1iXkHmzbxmdFuQqhC9rAyHe/fQ4ytijp0ULoxpLfC4Mg+FUJ8o717YVuN3/mdHrg4nmTV/dKkSKF2KsO1fft2du/ejZWVFQ0aNIjRSwHQrl07WrVqRfXq1dmxYwfr16//7PvEtbCQtiBh/fortJpfiXBseLFiH61bq51IiH9Je2C8wsNh/HiYMweyZoXTp5XJ2wDMnw9dusCVK1CggJoxxUekqBDiO7RoGsWADSWxQMuCTmeZM99K7Ujib9IWJKxjx2BpxUUsoBNulXxZefhzA6GFUIe0B8ZLp4OiRYlesvroUahQ4e8Xw8Mhd2746SeI5UaUSHgy/EmI7zB1hiV97eZRmMvYLPDi9Gm1EwmhjnLl4IxTE8KwpeqLVbIKlBBCLzQa6Nfv359jbIZnYwNDh8KGDUpvhTAI8VJUnDlzhmbNmlGqVClcXV258ZXJNAEBAXh6euLi4kLVqlVxd3fn5cuX8RFNCL3ImBEajCvBPLowmmFc3fNM7UhmT8ZQq8PCAv5Y44imXj1+sfLG0lLtREIIU9G8OWTIoDzftg3u3PnoxTZtIHt2GDlSjWjiM/ReVFy+fJlKlSqRKVMmJkyYgJWVFeXKlePRo0exXlO1alVCQkLo3bs37u7unDx5krJly8Z5gywh1NCjB9xoPQ67FHZ09Omrdhyz1717d3x8fDh79qzaUcxO2bKQqJMbXL2KbK8thNAXGxvo2VN5rtPBjBkfvWhtDcOHw+bNcPGiGvHEf+h9TkXTpk15+fIlhw8fBkCr1ZInTx5cXFyYNWvWZ695//59jM2w3rx5Q+rUqVm1ahXNmzeP0+fKuEmhGm9v5Y7J3r3wv/+pncbsSVugkogIpQuvTRuYMkXtNEIA0h6YgrdvwckJQkOV/e98fSFlyr9fjIyEfPkgb174aPlyoQ6991QcPHiQWrVq/fsBFhbUqlWLA1/YGem/u+va2Nig0WiIjIzUdzwh9M/VFSpVUrYB/WijNyHMirU1tGiBbtUq7tyUiRVCCP1InlxZRRaU5WXnzfvoRSsrpbdi2zY4d06VfOJfei0qQkNDefPmDenTp49xPEOGDPj6+sb5fcaNG4e9vT3/+8Jd37CwMIKCgmI8hFCFRgNz5qB78IC/6k3i4EG1AwmR8HQ6mPnGDc3z54yqeACtVu1EQghT0auXMn8L4PffISzsoxdbtlRWghoxQpVs4l96LSoiIiIAsLW1jXHc1tY2+rWvWbVqFZMnT2bx4sWkSZMm1vM8PT1xdHSMfjg5OX1/cCF+0PPk+ViUrB8/7RvP+A73YjZ4QpgBjQb2vvmJm+TG5eVyjh1TO5EQwlRkzw4NGyrP/fxg1aqPXrS0VAqKnTuRpRjVpdeiImnSpNjY2PD69esYx1+/fk3K6AFwsVu/fj3t27dnwYIFNGnS5Ivnenh4EBgYGP34lp4QIfQtbVpYlX0YfqSj38PfmDLZJLZ/EeKbuLpp8MaNhmxm3eIQteMIIUxIv37KUCgPD6hR4z8vNmumzK2Q3gpV6bWosLS0pHDhwpw5cybG8ZMnT1K8ePEvXrtx40ZcXV2ZM2cO7du3/+pn2dra4uDgEOMhhFosLGDGgsT0tphFTXZzbfQm7t9XO5UQCat+fdhs70pi3hG5bpNMMRKqkSWmTU+ZMvD0qbLL9j/LzEaztFSWlt2zB06cUCOeIB4manfu3JkNGzZw6dIlQJm4fejQITp16hR9zrx586gQvS0ibN68mVatWjF37lw6/DMbRwgjU6gQZO9Vj23UZXJELwZ2DcY09qs3DvIlQn329lCyaRYOU4kmH7z580+1EwlzJUtMm6b/rOsTU+PGULCg9FaoSO9FRYcOHejcuTOlSpUiS5Ys1K5dmzFjxlCnTp3oc/z8/Lh69Wr0z23atMHKyopZs2ZRpEiR6Me8GFP8hTB8o0bBuDSzSMEbSu8dxZYtaicyH/IlwjC4uYE3blTlADsXPFU7jhDCXFhYKL0V+/fD0aNqpzFLet+n4h8BAQE8f/4cJycnkiRJEuM1Pz8/Xr58ScGCBQG4cuUK2s8sFZIuXTrSpUsXp8+TtaiFoVi/Hi4082QMw6iV9gKb7hbiP/8ERDyStkBdUVGQP1MgF/3SMdJiNAP8B5AqldqphLmS9sA0+fuDl5eyd8XUqR+9oNVC8eKQLBkcOqRWPLMVb0VFQpOGQxgKnQ7qVA9nyv7CvCEF2/ofY+JkvXcKilhIW6C+gQOh+OTm5OUGf3ldoVs3tRMJcyXtgemJjFQ2w/PzU7bHefQIYuxksHUrNGgABw9C5cpqxTRL8k1HCD3TaGDmXBt6W8+hHCd4M20p166pnUqIhOPqqgyBKsRVTs67rHYcIYQJsbKCdu2U5xERyr4VMdSrB8WKKXMrTOO+udGQokKIeJAjB5QZXJmVGldm2A4km8Prr18khIkoVAieF6zBK01qfrH2Jko22BZC6FGPHkovBcDcucowqGgaDYweDceOwYEDquQzV1JUCBFP3N3hp8NTSGwTSeIx7mrHESJBbdxmTYpuLaj8bCWWTx6pHUcYgOXLl5MrVy5sbW0pUKAAf35lebDQ0FAWLFhAsWLF0Gg0rFixIoGSCkOXIYOykTbA27ewdOl/TqhVC0qWlN6KBCZFhRDxJFEiyF0xrbKo9sKFsna2MCtZs4JFj+7KzO2cOaFLFw4secz792onE2rYvXs3HTp0YOjQofj5+fHLL7/QqFEjzp8/H+s1S5Ys4fTp0yxYsCABkwpj0bfvv8+nTydmj6hGoyzHeOIE7N2b4NnMlUzUFiK+RUVB6dIQHs7b/edJntpK7UQmycvLCy8vL6Kiorh9+7a0BYYiJATmzCHScxLagCBW2XVE6z6YVgMzkSiR2uFEQqlWrRoODg5s2rQp+liJEiXIkycP3t7eX71eo9Hg7e2Nq6vrN32ufDcwbf/7n7KCLMCmTdCw4Ucv6nRQrpzyN/jUKaXQEPFKeiqEiG+WloTPnIvu6lUmZJzNfzacF3oi+1QYqCRJYOBA2ld+yHBGU/f9WlqPcGZNqt9YNv4pYWFqBxTxTafTcerUKX7++ecYx6tWrcoJ6cEVP+Dj3ooYS8vCv70VZ87Azp0JmstcSVEhRAJYdv0nvHTdGBoxnGG/PJWJq8LsDByVhLuN3cnKQ0Yxgnqhq2g+xJlVqXriPfEZ4eFqJxTxJTg4mNDQUFKnTh3jeJo0afDz89PrZ4WFhREUFBTjIUyXiwvky6c8P34cTp/+zwnVqkH58jK3IoFIUSFEAmjfHtbkH0soielwvQ9z56qdSIiEVbAgbNgAxy4mxaf+YLLykLEMpUGIN03cnVmRqjerpvkREaF2UpFQdDodGj0PSfH09MTR0TH64eTkpNf3F4ZFo/m3tyJFCmXPik9OGD0azp+HrywMIH6cFBVCJAArK5j4RzL6MZVmrOfgoD3o+QadEEahSBHYsgUOnXPgUu2hZOUhnnjQKHgpDftl42Gjvsp2ucJkJE2alMSJE/Py5csYx1++fEnatGn1+lkeHh4EBgZGP3x9ffX6/sLwtG4N8+bB48fQrNlnTqhcGSpVkt6KBCBFhRAJpFw5SNS+FQepzMR3v+He+4PakYRQTfHisH077DvtyFmX4WTlIUtTDyTH0UWQLRv07w8vXqgdU+iBRqOhdOnSHDp0KMbxgwcPUrZsWb1+lq2tLQ4ODjEewrQlSgS//gqJE3/hpFGj4NIl5Y6GiDdGX1R4eXmRL18+SpQooXYUIb5q4iQNQxy9yMIjsqydyMGDaicSQl0lS8KuXbDzeDLybxiF5uFD6NcP5s+HbNk48NNANv3xUuYhGbn+/fuzfft2li9fztu3b5k+fToXL16kd+/e0eeMHDmSZMmSqZZRmLBKlaBqVaW3QqtVO43JMvqiQlZ8EcYkVSroMCUvU+iPB55M6HhXJqjqidxgMG5ly0LFikDy5DBmDDx8yPPmvSl5fi7Vu2RjcVp3tix8Jd8HjJSLiwuLFi1izJgxpEuXjkWLFrFx40aKFy8e6zX79+9Ho9FEz7twc3NDo9HQsWPHhIotjJC/P/z112deGDUKrl6FNWsSPJO5kH0qhEhgWi1ULfOOJWfycYvcXBi3G4/Bsn62vkhbYDo8PGDBhFf0Yyo9mI0ODWtS9SD9lH7UckuJhdHfFhPxTdoD86HVKsOgli+HNGng/n2wtv7PSQ0aKBO2e/dWiowkSVRIarqkSRYigVlYwIz59vS2mE0N9vJy7gYiI9VOJYThGT8e1u5PxfaynmTjAXPoRqtXM6nYLhuLMgxl54o3Mu9SCAEof1v9/SE8HJ48gXXrPnPS+vXg6Qlz50L+/MrELqE3UlQIoYLChSHvwLrcyFWfqVG9sXpnmmupa7VaFi1aRNOmTWnZsiVr16796jWRkZFs3ryZJk2a8MsvvyRASmGoNBplGPRff8GK3anZXGoi2XjAH/xKa/9plHPLxoKMIzi+I0DtqEIIA9Cv37/Pp079zGJP1tYwcCBcuwZ580LdutC0KTx7lqA5TZUUFUKoxNMT8u6diSYwAEaOVDtOvOjRowdDhgyhWrVqlC5dmo4dOzJ27NgvXpM3b16WLVtGREQER48eTaCkwpBpNFCjBpw8CUt3pGHdT5PJxgMW0hG355Mo2TyrMpQhMFDtqEIIFVWsqKwsB3DxIhw+HMuJ2bMrK0SsXg1HjyoFxpw5yIoQP0aKCiHUlCULDB8Os2bB5ctqp9Gru3fvMnfuXBYtWsSvv/5Kr169mDJlCmPHjuXt27exXnfs2DG2bNlC0aJFEzCtMAYaDdSqBWfOwMJtaVlRZCqNijzAqmN7mDABsmaFMWMIehIkw6KEMEMazae9FV88uUULuHkTmjeH7t2Vtd+vXIn3nKZKigoh1NanD+TOzfv2XVm2xHSWttm7dy92dnZUr149+ljjxo0JCwvjcKy3jyBdunQJkE4YM41GGbVw4QIs25MOzYzpyqzMNm1g3DjIlpUF2cZxdEew2lGFEAmsSRP4ZyP1HTvgxo2vXJA8ubKE9bFjEBysdHW4u8O7d/Ge1dRIUSGE2mxs8C4zB7uLJznRcTE+PmoH0o+HDx+SNm1arD9afiNVqlQkSpSIhw8f6u1zwsLCCAoKivEQ5kGjUVZ5ASB9epg5k5Mr7rEssjVtH40mf52sLMjuyfHdUlyYG1li2nxZW0OvXv/+PH16HC8sX14ZMzViBMyYAQUKwJ498RHRZElRIYQBuJepEstow3jtIDw6vTKJoRvh4eHY2dl9ctzOzo5wPW7O4enpiaOjY/TD6Z9bVMIsvU+RkTl5ZpODu6ylOW0fjCB3zWwsyDGRk/tC1I4nEojsYWXeOnaEpEmV58uXw4sXcbzQxgaGDlWGQGXLBi4u0KqVsqyU+CopKoQwAIMGgVeWyVigpd6JQaxYoXaiH5csWTLevHkT45hWqyUwMJDkyZPr7XM8PDwIDAyMfvj6+urtvYXxqVJFWdhlwgonZuScQw7usoEmtL03jBzVs7Eg12TOHApVO6YQIh45OkKnTsrzsDBldNM3yZUL9u+HZctg717IkwcWLJDduL9CigohDICdHYyamwYPPOnAYtb2PM4X5jIbhSJFiuDv78/z58+jj126dAmtVkvhwoX19jm2trY4ODjEeAjzZmkJrVuDjw+MXZaZydnnkZM7bKYh7e4MJkuV7OysOlXGTAthwnr1+ndRp759v+MNNBplntbNm8qmeZ07Q6VKmMwY5XggRYUQBqJmTXjTqBNnKMH4gK4M94hQO9IPqVGjBmnTpmXixIkA6HQ6Jk6cSN68eSlZsmT0eS4uLmzZskWllMKUWVn9+51gxKIseGadTy5u8yd1cTk8SFlWcsYMeP9e7ahCCD3LnBmuX4euXcHe/gfeKFUqWLIEDh5UhkEVKQLDhsGHD/qKajKkqBDCgEybaUnfRHPJz3Vs/5iFMQ8HtrOzY82aNaxcuZK8efOSI0cOTp48yerVq9FoNNHn7dmzJ8bE7f79++Pi4sKKFSt4/vw5Li4uuLi48OrVKxV+C2EKrK3hl1/g1i0YPD8bR1wXYnHntrI+bf/+4OzM4wGzuHJGviQIYUo++lPz4ypXVuZaeHjAxIlQqJBSaIhoGp3OFKaEQlBQEI6OjgQGBsrwB2HUpk4Fm/49aM8SmhW8yZ8XM2FpqXaq7/fhwwfOnTuHlZUVxYsXj7EaFMDu3bvJmzcvWbJkAeD06dOf3ceicuXK2NrafvXzpC0Q3+TuXXRjx6Jd5o0f6dhdxIPSCzuSv3gitZMJPZD2QHxMqwULfdxOv3EDfv1VWYa2TRvlD3eqVHp4Y+MmRYUQBiYiAioWDmTTjTwcpxz+v2+ge3e1UxkPaQvEt9qzB35zucMwxtCalTwnPXuLD6bsog7kKfz1QlYYLmkPBCiLN0ydqoxe2rlTT2+q1SrDogYMUCqVKVOgbVs9d48YFxn+JISBsbaGyfMd6cs0mrCRckG71I4khEmrWBG6T8/JwLTLyYcPh/mZdud/w75IThaXnMfta/pbAlkIkbB0OmjcGJYuhV274NIlPb2xhQV06KBM2nJxgfbtoWpVuH1bTx9gfIy+qJANboQpKl8eWm5pgbZyVYos/E0mksaBtAXie9nZQe/eyqbcnafkpm/qFeTDh78oT7uz3bAtmJMlZedz74YUF0IYG41G+ff9j6lT9fwBadLAihVKl+ejR8pcizFjlLVszYwMfxLCkN26BQULKhPDRo1SO41RkLZA/KjQUPDygkmTIM1rH4Yzmmas46VdZtLOGqoMcfjP3CBhmKQ9EKCsHp05M7x+rSw53bixsqdNlSqQI4ceRyy9e6cUFFOmQM6c8McfUKGCnt7c8Bl9T4UQJi13bhg4ECZMQHfrNpGRagcSwvQlTqz8s3vwAFzH5aNb8jUU4gpWZUsqO2rlzg2LFysToIRBkp5L8TF7e2VpWYCoKFi3Drp0Ufa4y5xZmWsdEqKnD/L0hAsXIFkyZWxlp07wn41gTZX0VAhh6N6/JzxXfq6EOLNvwF48BpvvJLC4kLZA6FtgIGzfrmyox9WrSq/hxo2EpsvOxrzDqLLYlUxZrdSOKT5D2gPxj+BgZcGmHTsgKCjma+nSwbNnMXssrl6F1KmV176LVqv0VLi7Q6JEMH06tGxp0hO5padCCAP3ItiO5v6z+SlgPz4j1/HRlg5CiATg6Ph3QQHKcMQNG9BeuMSpd4Vpc6g9H7Llxft/y3n2WLoShTBUSZPCqlXKEKjTp5UOhf/9T5lTVbnyp9/1u3aF9Okhf37o0QM2b/7GDgcLC+VNbt5UduJu3VqZ0H3vnl5/L0MiPRVCGIFevaDSrEaU5hR9XG6ydpf8fzw20haIhODjA6VKQY6Qi4xgFA3Yym1NLs5UH0a1RS1Jl9GIN5cxIdIeiK8JC1N6I9Ok+fdYSAgkT84nQ441GmVD7X/mY1SooBQrcbJjB3TvrqxrO2IE9OtncnOzpKdCCCMwZgx4ppmBI4GU2T2cbdvUTiSEecuXT5lz4eJelNb2WyjOOW7pcuG6x41Ap/ysrL2KF8+j1I4phPgKW9uYBQUohcaAAcqNg483y9Pp4OJFZQWp2rWVwmPfvjh+UO3acP26UlgMHQrFisHJk3r7PQyBFBVCGAEHB+g3MzMjGUkPZvNHl4uEhqqdyrDIxEyR0FKlUoZQPHgAVfoXp7ndn5TgDHd1zrTe2ZrXGQuyqt4atJFataMKIb5BypQwfjycOgVv3ypzqvr2VXopPhYV9emxw4dh9Gj46y8I/+8q1IkTKytDnT2rzLMoVw66dVO6SkyADH8SwkjodFCzWgRTDhYlhCRsG3SC8RPkvsB/SVsg1OLnBxMnwrx5UOjDaUYykprsVro1RoyAJk1i3vYU8U7aA6Fvr17BkSNw6JAyuXvTppivd+mizM8GZTGoChX+HS5VtKiypC2gVCReXjBkiDKGatYsZa1bI57ILUWFEEbk9m3okv8YByMr0tXiD3pc7Uy+fGqnMizSFgi1PXsGEybAggVwbcFJnL1Hwt69UKAAUcNGEFytEclSSHGREKQ9EAktVy64c+fzrzk6ws8/KwVGzZrKVhb4+iozwbduVYZIeXlBliwJGVlvpFUTwojkygXlPSqwhHaM07ozuNNLTOO2gBCmI0MG5abjs2fg7FpG2Wn3+HFIlw7L5k15kroo61psIvCtDIsSwtTs3atsY+PqqrQFHwsMVGqHXr2UTbgBcHKCLVvQbdqM7tIlpWdz2rRPZ4kbASkqhDAyHh4wJ8skAOqfGMjx4yoHEkJ8VvLkH/1QtiyRu/bRMtMx/LWpaLa2MY9SF2e961aCg+TOgBCmImtWaN8evL3hyRO4dQvmzoWmTZV5WP+oUiXmdTdyNyCv1oc9mTui69+fsCIl4dy5BM3+o6SoEMLI2NnB6LmpmZV+Au1ZSnndMbUjCSHiIDQUEtcoTw3LA1TkCK+jktF0ZQPup/iJDW3/JCRYigshTIlGo4ww6NJF2cXb3x8uX4YZM6B06ZjnHjwIt5474HJzJiV1p/G5riOqRCn2F+jN+sXB+Pmp8it8EykqhDBCNWvC0IcdlfXuunWDiAi1IwkhvsLRERYuVO5cZm9bkWoWh/iZQwREJaHJ8nrcSVGSTR128C5UigshTJGFBRQqpAx/srWN+dqbN8pNQ4BzlKAEZxnIJMpcX0DpDvn4Nf1W8udXVqM1VFJUCGGkrGwslD5VHx+YOVPtOEKIOHJ2hqVL4cYNcHL9mSqaw1RlP6GRtjRaXIebyUvzftMuZMLU95MlpoWxGT5cWb726FEYORLKV7Lid5t+5Oc6VyjEVhow1qch/ueffHLtqVMQFJTwmf9LVn8Swtj16oVu0SJ2TrmBSyenf5erMzNeXl54eXkRFRXF7du3pS0QRuPmTWVd+zWrdVRlP3NSjyDny5NKT+SoUVC9ulEvM6km+W4gjNm7d3DiBBw8oIMNG+hxtycpE4ViM2mcMkrB0pIPH5T5WxERUKLEv8vXli37b89HQpGiQggjd+N0EKkr5OFoRGn8vDbRrZvaidQlbYEwVtevK8XF2DE6cj7Yq+xtcfo02tJl2FNmFFXGV8M2kRQX30LaA2FKgh4HkGj0YGwWz1MqiD/+4HBAESpX/vRcGxsoU+bfIqNkSeVYfDL64U/SxSnM3atwB36LmEYjNnN4wA78/dVOJIT4Hvnzw9q1kDOXBmrUgJMnYedOXvlFUnN6da44VmB7nwOEh5nEvUAhxDdyyJwMm4VzlCWq372Dn36iwLIB9OkcSt68Mc8ND1c26RsxQtmAL3lyZd5GfJKeCiFMQPt2Olotq44z9xjX4hqLVturHUk10hYIUxIZCc7ZdRTw3clIRlKCc5yxrcCrnqP437jKWFurndCwSXsgTFZ4OEydqnRvpk0Lc+bwvGgtDh9WVpI6eBDu3//39Fy5lEUi4pPR91QIIWDSZA2DHbzIyFOyrvHk8GG1Ewkh9MHKCjZt1qCpXZuSnKEu27AMC6XW5Cqcd/iZ3R5HjHGPLCHEj7KxUTauunZNqRhq1yZ97+a0/Pk5CxbAvXvw4IGyEZ+bGzRvHv+RpKgQwgSkTg2dJudiIoMYxEQmdbhFeLjaqYQQ+lC8OGzfDqdPa4h0qctPnKM+W7D9EIjLhJ8561CVPcP+IipK7aRCiATn7Ax79ihbdB86BHnzwrx5oNVGb8S3fLnSoRHfpKgQwkR07AgHSnjgixN973dn2lSTGNkohPhbyZKwaxecOKHh/f/qU4wLNGQT9u9fUWNsBcJ//p+yVIwQwrxoNNC6tbKUXJMm0LWrMpHi2rUEjSFFhRAmwsICZvxhR0/N71TjADdGrOHRI7VTCSH0rUwZ2LsXjh7VEFi5IUW5yPzqG7AL8INy5ZRJ3qdOqR1TCJHQUqRQdtg8ckSZlV20KAweDO/fJ8jHS1EhhAkpWhRy9KjJBhozIaIvHt0C1Y6UYGQlOGFuKlT4e0LmIQtqLWoMly/DunXw9CmUKcPZVDU5NPEMWq3aSYUQCapiRbh0CYYNUyZzFywI+/fH+8fK6k9CmJigIKiS05fDL/JyOv8vVLw4y6xWiJG2QJg9rZYd7daTzXsU+bjBMYda6IaPpELfEma3h560B8Ls3boFXbrA4cPg6qoUGWnSxMtHSU+FECbGwQHGLnPi1W+jqHrDC+urF9SOJIRISBYWzA9sTkGu0pJVpA66R8X+JTmWvC4h526qnS5BSM+lEH/LnVvp0lyyBHbuVCZyL14M8dCnID0VQpiqiAgoVgwSJ1Y20TKTW5TSFgihfF/YtQuGD4eL56NowRo87ceS+fR6KFBA7XgJRtoDIT7y8iX06wfe3lCzJuzYodfvBtJTIYSpsrZW7kZMm2Y2BYUQQqHRQK1acPYsbN5qyY2irXmy18esCgohxH+kTq2sL7t/PzRtqvfvBtJTIYQwKdIWCPEpnc487y1IeyBEwpGeCiGEEMLEmWNBIYRIWFZqBxBCiB/x4cMHXr16Ff1zcHAwoNyhFEJ8XdKkSdFI1SGE+EFSVAghjNqoUaOYMGHCJ8ednJxUSCOE8ZGhQUIIfZA5FUIIo/bfnornz59TsmRJfHx8yJgx4xevLVGiBP9n777Dmyy7OI5/00GhQMsG2XsUkD1UlCkbkTKlDlQciAMFB77uBQ4cCIp74QAFBVkiQ4bsIQpl773pgA7aPu8fN00pdKVNmqT9fa4rF8mTZ5wUSHNy3/c5a9euzfQa7tgvMjKSSpUqcfDgwUzf09wRX154DVndL6+/jrw8UqHPBiK5RyMVIuLVChYsSMWKFa/aXrRo0Uw/RPj6+mbpg4a79gMICgryyNeRF16DI/tB/nodIiKOyjMLtYsWLUpERARFixZ1dygi4kbJ7wFZeS8YPnx4ls7prv2yyh3x5YXX4Mh+WZVXXkdeoc8GIrknz0x/EhGBvDPdIS+8jrzwGkCvQ0QkK/LMSIWICEBAQAAvvvgiAQEB7g4lR/LC68gLrwH0OkREskIjFSIiIiIikiMaqRARERERkRxRUiEiIiIiIjmikrIiIm5iWRZxcXEULFgw030vXLhAfHx8qm1+fn4UKVLEVeFl2fnz57Esy6FY4uPj8fPzw8fHM77bSkpKIjIyksKFC+Pv75/hvrGxscTGxqba5uPj4xGLn+Pj4ylQoIBDxyQkJGBZVqavW0QkI57xbi4iko8kJiby+OOPU7RoUYoUKULDhg35+++/MzzmzjvvpGzZslStWtV+GzRoUC5FfDXLspgzZw69evUiODiYrl27Zum4rVu3cv3111O4cGECAwO58847OX/+vIujTd/p06d56623qF27NsWLF2fatGmZHjN27FhKlSqV6u+iSZMmuRBt2s6fP89bb71FrVq1CAoKokSJEjz00ENERkZmeNzJkyfp3bs3gYGBBAYG0qVLFw4dOpRLUYtIXqOkQkQkl73yyiv88MMPLF++nOjoaLp27Ur37t05fvx4hsfdfffdnDt3zn6bNWtWLkV8taioKCZMmMB9993H3XffnaVjYmJi6NatG9WrV+fMmTNs3bqVVatW8dBDD7k42vT9/PPPnDp1yuGfZevWrVP9XezevdtFEWZu2bJlnDlzhnnz5hETE8OKFStYsGABDzzwQIbHDRo0iBMnTnDo0CGOHz9OQkICffr0QfVbRCQ7lFSIiOSixMREJkyYwIgRI2jcuDEFCxbkjTfewMfHh6+++irT46+cduMuQUFBzJkzh1tuuQVfX98sHfPbb79x6NAh3n//fYoWLUq1atV4/vnn+f777zl16pSLI07bgw8+yFtvvUXNmjUdPjY+Pp6kpCQXROWYrl27MnbsWGrUqIHNZqNu3bo89thjzJw5M90E4b///mPRokW89dZblClThhIlSvDOO++wbt26TEfNRETSoqRCRCQX7dy5kzNnznDjjTfat/n7+3PdddexevXqDI/9+uuvCQoKIigoiN69e7Nnzx5Xh+tUq1evpm7dupQqVcq+rW3btiQmJrJ+/Xo3Rua4NWvWEBQUROHChbnxxhtZs2aNu0NK5cCBA5QsWRKbzZbm86tXr8bHx4frr7/evq1JkyYEBQVl+u9QRCQtSipERHLRiRMnAFJ9sAYoU6aM/bm0tG7dmqVLlxIbG8t///3HhQsXuPnmm4mOjnZpvM504sSJq1536dKl7c95i2rVqvH7778TFRXF4cOHqVOnDh07dmTv3r3uDg2AzZs3M2HCBB5++OF09zlx4gTFixe/apSpdOnSXvV3ISKew2urP1mWRVRUlLvDEPFKRYsWTfcbTMkdV06bSUhIyPDvZNSoUfb7VapU4fvvv6ds2bLMmTOHAQMGuCxOZ7vydScmJgJ41b/Hu+66y36/RIkSTJo0iblz5/LVV1/xyiuvuDEy2L9/Pz169KB79+6p/s2kJa2pW5n9O/R0+mwgkn05/WzgtUlFVFQUwcHB7g5DxCtFRER4RPnL/KhChQoAHD9+nJCQEPv2EydOUL58+Syfp0yZMhQvXtxjvh3PigoVKlw1zSn5W3FHXrun8fPzo0aNGm7/uzhw4ADt27enadOm/PDDDxmW661QoQLnzp1LVYLWsixOnTrl1X8X+mwgkn05/WzgtUlF0aJFiYiIsD+OjIykUqVKHDx4MNMfSIsWLVi7dm2m18jKflnZx12xKb6c7efJseU0vqJFi2Z6fnGN6tWrU758eRYuXEj79u0B04Pi77//ZsyYMfb9Muv9sGfPHs6ePUvlypVzJe7ssCyLiIgIe++HNm3aMG7cOA4ePEilSpUA+PPPPwkICKB58+ZujjZ9sbGxxMfHp/t//MKFC2zdujXVOpncdvDgQdq3b8+1117L1KlT0+w5ERkZSYECBShYsCBt2rTBsiwWLVpkLwe8YsUKzp8/T5s2bXI7fKdx5LNBRu+h2Xkuve2KIfMYsnM+xeD8GHL62cBrkwqbzZbmX0byIsaM+Pr6ZikTy8p+WT2XO2JTfDnbz5Njc0V8kjtsNhvPPPMMo0ePpnnz5jRo0IAXXniB4OBghgwZYt8vLCyMc+fO8ddff3H48GEefPBBnnjiCerUqcPOnTsZMWIEderUoU+fPm57LVFRUSQmJhIfH09iYiLnzp0DoFixYoAZjbnmmmv48ccfGTRoED169KBhw4bcfffdfPjhhxw/fpwXXniBhx9+2G3/PhMSEoiOjrZPw7pw4QLnzp0jICCAQoUKAfDaa68xadIke4Wqzp0788gjj9C4cWNOnjzJ888/T2JiYqYlXF3lyJEjdOjQgerVq/PZZ5+l6vsRHBxsn85QvXp1HnzwQV577TVq1KjBgAEDeOyxx5g8eTL+/v489NBDdO7cmaZNm7rldTiDI58NMnoPzc5zmb0nK4b0Y8ju+RSDa2LILq9NKnJi+PDhTtsvq+fKKmfG5sh+WZWf4vPk2BzZTzzPI488QmJiIs8++yxnzpyhefPmLF68ONWbe+HChUlISADMVJVHH32UN998k82bN1OqVCk6derE//73vyx143aVtm3bpqpAVbVqVcA0lPP19cXHx4fg4GD79Bo/Pz/mzp3LyJEj6dixI4GBgdx///28+OKL7ggfgCVLltC3b1/AfAB/4okneOKJJ7jnnnt49913AShUqFCqKTVvv/02r7/+Og8//DCFCxemVatWbNiwwW2jRgsXLuTkyZOcPHmSWrVqpXpuz549lChRAjCvLzlRAvjyyy8ZPXo0/fr1Iykpie7du/PWW2/lauzulNF7aHaey857smLI2fkUg2tiyC6blUe63ERGRhIcHOyRc8U9OTZQfDnhybGB58cnIuJKnvAeqBgUQ36JIc+UlA0ICODFF18kICDA3aFcxZNjA8WXE54cG3h+fCIiruQJ74GKQTHklxjyzEiFiIiIiIi4R54ZqRAREREREfdQUiEiIiIiIjmipEJERERERHLEa0rK7tmzh19++YXo6GhuvPFGbr75Zpcck10LFy5kyZIlFC5cmL59+1KzZs0M9z916hQzZ85k//79VK1alX79+rmsIVlMTAw//vgju3fvplq1atx2220ULlw4S8cePnyY9957j9q1a3P//fe7JL69e/fyyy+/EBUVxQ033ECXLl0yPcayLObOncvq1aspV64cgwcPdlkX1UWLFvHXX39RuHBhQkNDryrZeKX4+Hh+/fVXtm7dSsGCBbnuuuto27atS2JLSEhg5syZrFy5kltuuSVLzbdiYmL46aef2LVrF1WrVuW2225Lt8GaiIgn84TPBgcPHmTq1KmcO3eOVq1a0bNnzwz3//LLLwkPD0+1rW7dugwdOjTbMURGRvL999+ze/duRowYQcWKFTM95tixY0yZMoWTJ0/SpEkTQkND7T1NsuP8+fP89NNPbN26lQceeCDT35W//fYby5cvT7WtTJkyPPXUU9mOYeXKlSxbtgzLsmjdunWWfveeO3eOH3/8kUOHDlGvXj0GDhyYZvPIrFq3bh1LliwhLi6OFi1aZPrva/HixcyePTvVtoCAAF5//fVsx3Do0CFmzZrF0aNHqV69On379s3097wzPht4xUjFX3/9Rf369dmwYQPnz59n4MCBjBgxwunHZNeoUaPo378/58+fZ9OmTTRo0ICFCxemu/9PP/1Ey5Yt+fvvv/Hx8eHrr7+mRo0abN++3emxRUZG0qpVK8aPHw/Axx9/TIsWLTh79mymxyYmJjJ48GC+/vprpk6d6vTYAJYtW0b9+vVZu3YtMTExhIWF8fDDD2d4THR0NJ06dWL48OEkJCSwZ88ebrrpJqKiopwe3zPPPEPfvn2Jjo7m33//pWHDhvzxxx/p7h8VFUXz5s156aWXANP865ZbbmHYsGFOj23p0qXUqFGDb7/9lo8++oj169dnekx0dDTXX38977//PgCffvopzZo148yZM06PT0TElTzhs8HatWsJCQlh2bJlxMXFMXTo0FRNLNMyffp01qxZQ7ly5ey34sWLZzuGiRMnUrduXebPn8+4ceM4duxYpseEh4dTv3595s2bR0JCAiNGjCA0NJTs1u755ptvqFWrFvPmzWPcuHHs378/02MWLFjAvHnzUv0cSpcuna3rA3Ts2JFRo0Zx+vRpTp48SWhoKHfddVeGxxw5coRGjRrx/fffA6bRZfv27YmLi8tWDH379uWhhx7i6NGjREZGcvvtt9OnTx+SkpLSPWb16tVMmTIl1c+hbNmy2bo+mL+LLl26sGXLFnx8fJg0aRK1atVi9+7d6R7jtM8GlheoW7euNXToUPvjefPmWYC1ceNGpx6THf/++69ls9msefPm2bcNHTrUqlWrVrrHbN682Tp//rz9cVJSktW6dWurb9++To3NsizrxRdftMqXL29FRERYlmVZUVFRVqVKlaxnnnkm02NfeOEFq1+/flZYWJjVsWNHp8dmWZZVv359a8iQIfbHCxYssABr3bp16R4zfPhwq3Llytbp06ft2w4dOpTqZ+oMW7ZssWw2mzVr1iz7tgcffNCqVq2alZSUlOYxv/zyiwVYx44ds2/7+uuvLR8fHysyMtKp8e3YscM6dOiQZVmWVbJkSeu9997L9JhXX33VKleunHXu3DnLsiwrOjraqlq1qjVq1CinxiYi4mqe8NmgVatWVr9+/eyPV69ebQHWX3/9le4xPXr0sB577LFsXS8ta9eutaKioqytW7dagLV27dpMj+nSpYt1880323+Xbd261bLZbNZvv/2WrRg2btxonT171jp69KgFWH/++WemxwwfPtzq3bt3tq6XljVr1qR6vGLFCguwli1blu4x9957r3Xttdda8fHxlmVZ1rFjx6wiRYpYEyZMcEoM4eHhFmD9/vvv6R4zZswYq1mzZtm6Xlq2bt1qJSQk2B9fvHjRqlatmvXUU0+le4yzPht4/EjFtm3b2LZtG3feead9W+fOnSlfvjwzZsxw2jHZNWPGDMqWLUvnzp3t24YMGcLOnTvZsmVLmsfUr1+fwMBA+2ObzUajRo04dOiQU2MDM7x466232pubFClShL59+/Lbb79leNzSpUv5+uuv+eSTT5weU7Jdu3axZcuWVH9PHTt2pFKlSunGFxMTwxdffMGjjz5q7xILpuPw5T9TZ5g5cyalSpWiW7du9m1Dhgxh7969/Pvvv2keU7JkSQBiY2Pt2y5cuEBQUJDT60HXqlWLChUqOHTMb7/9xi233GKfKla4cGH69euX6b8HERFP4gmfDY4ePcrq1atTna9ly5bUrVs30/fUTZs28dxzzzF+/Hg2b97s8LUv17x5c4emqURHR7NgwQLuuOMO+3SnunXr0qpVq2z/LmjcuDHFihVz+Lh9+/bxwgsvMG7cOFatWpWtaydr0aLFVTEBGX62+u233xg0aJB9ulPZsmXp2rVrtn8OV8ZQt25dChUqlOnnu1OnTvHyyy8zduzYDGe6ZEXdunXx9fW1P05MTCQhISHDvx9nfTbw+KQieUpQjRo17NtsNhvVqlVjx44dTjsmJ/FVq1Yt1TzE5Otm9VoRERHMmDEjS/PhsxPf5T+H5Ph27tyZ7jDn6dOnuf322/nyyy9TfXB3RWzJ8VyuevXq6f7sNm/eTGxsLNdddx1ff/01L7zwAl999RXR0dEuia9q1ar4+KT8N8ns77Zdu3a89dZb9ilPYWFhfP7550yfPp0CBQo4PUZHpffvYffu3SQmJropKhERx3jCZ4PkY9J6T83ofDabjYIFC+Ln58eqVato1qwZb731lsPXz67k93tH43aF5LWkW7dupX379plOf3bEd999h6+vL61bt07z+dOnT3P69GmX/hx+/vlnYmNjueGGGzLcr2TJksTHx3Po0CFCQ0Pp27dvhlOmMhMVFcWoUaMYPnw4LVu2pGvXrjz22GPp7u+szwYev1D7woULAFe1EQ8ODub8+fNOOyYn8aV1HSBL10pISCAsLIzAwED+97//OTU2y7KIjY1NM77ExETi4uIoWLDgVcfdfffdDBgwgI4dOzo1nitl5+8pIiICgOHDh1OnTh3q1avHJ598wvPPP8/q1asd/uY+s/gc/buNi4tj06ZNXLx4kVKlShEQEMCSJUvYsmUL7du3d1ps2ZXea7Isi5iYGC3YFhGv4AmfDTI63+HDh9M9bvz48VSrVs3++JtvvuHee++lV69e1KtXz+E4HJWbn5EyMnLkyFQ/h7CwMDp06MAtt9ySavZHdqxfv57HH3+cF154gapVq6a5j6t/DskL1keMGEHDhg3T3W/QoEE8/fTT9i+nhw0bRtOmTfn666+55557snVtX19fypUrR1RUFAEBAWzYsIGTJ09SpUqVNPd31mcDjx+pSH4h586dS7X93Llz6VZLys4xOYkvresAmV4rMTGRO++8k02bNjF//vxsDR1mxGazERgYmGZ8/v7+aSYUK1asYPbs2cTHxzNq1ChGjRrFhg0b2LlzJ6NGjeLIkSNOiy8nf7etW7fmp59+4sUXX2TZsmUEBgbyxhtvOC225Gs5+nc7adIkZs+ezd9//82rr77K+++/z2effcZjjz3Gtm3bnBpfdqT3mnx9fZ0+fUxExFU84bNBds93+QdpgMGDB+Pj48OKFSscjiE7cvMzUkau/Dm0b9+eqlWrsmzZshyd97///qNLly7cddddvPDCC+nu58qfw65du+jUqRM9evTgnXfeyXDfqlWrpprtUr9+fVq2bJmjn0NgYCCjRo3i5ZdfZtWqVfj5+fHkk0+mu7+zPht4fFIREhICkKoyUlJSEjt37kw3o8/OMTmJb9euXamGh5I/PGZ0raSkJO666y6WLl3K4sWLrxp2cmZ8V1aV2rZtG3Xr1k1z/0qVKvHmm29SuXJlexWCQoUKERAQQLly5XJUZi2t2CD135NlWezYsSPdn13dunXx8fFJNW/R39+fxo0bs2fPHqfFlhzfnj17SEhIsG/L7O82PDycWrVqpark0bJlS5KSkjwiqUjv30Pt2rVTTfMSEfFknvDZoF69ethstjTfUx05X1JSEklJSdmuOOSomjVr4u/vn+O4XSEhISFHP4fNmzfTsWNH+vXrx8SJEzPct3jx4pQrV87pP4fdu3fTvn172rZtyzfffJOt3605/TlczsfHh1atWl1VxvhyTvts4PCycjdo0qSJNWDAAPvjqVOnWj4+PtbWrVvt28aPH29NnjzZoWOcYceOHZavr681ZcoU+7aBAwda1157rf3xuXPnrJEjR1r//vuvZVmWlZiYaN1xxx1WhQoVrJ07dzo1niu9+eabVqlSpazjx49blmVZJ0+etMqWLWu98sor9n2WLl1qjRw5Mt1zuLL6U4sWLazQ0FD74+nTp1s2m83avHmzfduECROsb775xv64e/fuVlhYmP3x+fPnrcqVK2dY2SA7du/ebfn5+Vnff/+9fVtYWJhVv359++PIyEhr5MiR9sohH3zwgVWkSBHr8OHD9n2mTJliAda2bducGt/l0qv+tHz5cmvkyJFWYmKiZVmWNW7cOKtEiRLW0aNHLcuyrNOnT1vXXHON9cILL7gsNhERV/CEzwbt27e3unTpYq+iNH/+fAtIVQXos88+sz777DPLssx77qZNm1Kd45133nHK55OMqj9NnjzZGj9+vP1xnz59rOuvv966ePGiZVmmahFgzZ8/P0cxZFT96ZdffrHefPNNy7LM56AlS5Zc9XxOYti8ebNVunRp68EHH0y3QuPvv/9uvfrqq/bHjzzyiFWrVi0rOjrasizL2rNnj1WwYEHryy+/zFYMu3fvtipWrGgNHjw4VQWmyy1YsMB69tln7Y8XL16c6vm///7b8vX1zXYMV1YeO3/+vFW3bl3r9ttvt29z1WcDr0gq1q1bZxUvXtxq166dFRYWZhUuXNh6/fXXU+3TqlUra+DAgQ4d4yxjx461ChcubIWFhVnt27e3ihUrZq1evdr+/MGDBy3A+vnnny3LsqzXX3/dAqxbb73VGjlypP12+T90Z4mJibFuuukmq2rVqtY999xjVa9e3bruuuvs/4Esy7Lee+89K6P80pVJxcaNG60SJUpYN910k3X77bdbRYoUsV5++eVU+9xwww2pyu3u2bPHqly5stWuXTtr2LBhVq1ataymTZvaS6E50zvvvGMFBgZagwcPtjp27GgFBwdbK1assD+f/Ab6448/WpZlft5t2rSxypYta913333WwIEDrYCAgFRvIM5y+PBh+7+dQoUKWe3bt7dGjhxpffXVV/Z9PvzwQwuw/+KIjY212rdvb1WpUsW65557rJo1a1otW7a0oqKinB6fiIgrecJng/DwcKts2bLWddddZ915551WUFCQ9eSTT6bap0uXLlaXLl0sy7KsM2fOWK1atbI6depkDRs2zOrQoYNVuHBh66OPPsp2DMkfEO+++24LsG6//XZr5MiRqT5cDhw40GrVqpX98d69e63KlStbzZo1s4YMGWKVKFHCuv/++7Mdw/r1662RI0daw4YNswCrf//+1siRI625c+fa93nggQesOnXqWJZlSul36tTJatOmjfXggw9aPXv2tAICAqznnnsuW9dPTEy0ypYtaxUrVsx64oknUn22uvznMHLkSKtChQr2x6dPn7YaNGhg1atXz7rnnnus8uXLW7169Uo3IchMrVq1rMKFC1sjRoxIFcPlP4dXX33VKly4sP3xHXfcYTVv3ty67777rL59+1oBAQHW/fffn+0Yhg0bZjVt2tQaOnSoNWTIEKt8+fJW8+bN7SXoLct1nw1slpXNTie57NSpU8yePZvo6GjatGlDo0aNUj3/ww8/EBQUlKqTZWbHONO///7L8uXLCQwMpEePHqkauERHRzNp0iRuueUWateuzcKFC9m4ceNV5yhatCgPPPCA02NLTExk3rx59o7a3bp1w88vZY3+hg0bWLRoEaNGjUrz+Dlz5nD+/Hn69+/v9NjAVGCYPXs2UVFRXH/99TRp0iTV8z/99BOFCxemV69e9m3R0dHMnj2bU6dOUatWLTp16uSy6TubN29m6dKlBAYG0r17d8qUKWN/7sKFC3z00Uf06tWLOnXqAGYK19KlS9m2bRsFCxakZcuWLhlSPnnyJN98881V22vVqkXv3r0B+Oeff1iwYAEjR460z9lMTEzkjz/+YPfu3VSpUoVu3bo5dVqbiEhu8YTPBufOnWPWrFn2jtpXlhWdNm0aYBqjgfkdsWzZMrZs2ULZsmW54YYbctTsLPl9/krt2rWjefPmAMyaNYvIyEgGDx5sfz4qKopZs2Zx+vRpmjRpkmmFooxs3br1qq7QANddd539vAsWLODgwYPcfffd9ufXrl3Lhg0bKFasGK1atUp3UXVmLMti3LhxaT53+c9hyZIlbNu2LdVnrbi4OGbPns3hw4epW7cunTp1ynZn8fHjxxMfH3/V9st/DqtWrWLNmjU8+uij9uc3b97MqlWrKFSoEM2bN7d/nsiu7du3s2LFCizLom7dulx//fWpnnfVZwOvSSpERERERMQzaWWmiIiIiIjkiJIKERERERHJESUVIiIiIiKSI0oqREREREQkR5RUiIiIiIhIjiipEBERERGRHFFSISIiIiIiOaKkQkREREREckRJhYiIiIiI5IiSChERERERyRElFSIiIiIikiNKKkREREREJEeUVIiIiIiISI4oqRARERERkRxRUiEiIiIiIjmipEJERERERHIkzyQVlmURGRmJZVnuDkVE3EjvBSIiIrkvzyQVUVFRBAcHExUV5e5QRMSN9F4gIiKS+/JMUiEiIiIiIu7hl90DL168iL+/v0PHJCYm4uvrm+a54uLiUm2z2WwULlw4u+GJiIiIiEgucXik4uOPP6Z8+fIULFiQqlWrMmXKlAz337dvH/feey9lypQhMDCQ2rVr88knn6Ta58033yQ4OJhy5crZb3Xq1HE0NBERERERcQOHkooZM2bw2GOPMWHCBC5cuMCzzz5LWFgYK1euTPeYH374gc6dO7Njxw7Onz/Pyy+/zEMPPcSsWbNS7deiRQuio6Ptt0OHDmXvFYmI5AGxsaC15iIi4i0cSiref/99evfuTWhoKAEBAdx///20aNGC8ePHp3vMs88+y8CBAylWrBh+fn7cdtttVKhQgfXr11+1b2JiYt6s2BIXB3PmuDsKEfESf/0FJUtC8+YQE+PuaERERDKX5aTCsixWr17NTTfdlGp7+/btWbVqVYbHJiUlER0dzfHjx5k4cSIRERH06dMn1T4bNmwgMDCQIkWK0LZtW9asWePAy/Bw48ZBjx6wdq27IxHJsyZOnEhISAgtWrRwdyg5dvgwFC8OGzbAjz+6OxoREZHMZTmpiIqKIiYmhtKlS6faXrp0aU6cOJHhsdu3b6dcuXKUL1+eUaNG8eGHH3Lttdfan69cuTLTpk0jIiKCffv2UatWLTp06MCePXvSPWdcXByRkZGpbh7pwgV47z1z//vv3RuLSB42fPhwwsPDWZsHkvdrrjGJBcDcue6NRUREJCscXqidlJR01WObzZbhMfXq1SM6OpqYmBi++OIL7rvvPqZOnWp//s4776RXr14ULFiQ0qVLM2nSJIoXL84XX3yR7jnHjBlDcHCw/VapUiVHX0ru+PxzOHsW+vSBn36ChAR3RyQiHu6mm6BUKXN/zhzz3YSIiIgny3JSUbRoUYoUKXLVqMSJEye45pprsnSOAgUKMHjwYHr27MmXX36Z7n5+fn7UrFkzw5GK0aNHExERYb8dPHgway8kN8XHw9tvw+DB8OyzcPw4LFzo7qhExMP5+cGtt5r7Fy7AvHluDUdERCRTWU4qbDYbN9xwAwuv+FD8559/0qZNG/vj+Ph4zp8/n+G5oqOjKVCgQLrPx8bGsnXr1gxHHwICAggKCkp18ziTJ8OhQ/DMM9CsGdSpoylQIpKhFSvgyBHo1y9l27Rp7otHREQkKxya/vTUU08xd+5cPvroIw4ePMirr77Kli1bePzxx+37vPHGG1SoUMH+uHv37sybN4+jR4+yZ88eXn31VRYsWMDQoUPt+/To0YM5c+Zw9OhR/vvvPwYNGkRMTAwPPvigE16imyQmwptvmmlPISFgs0FYGPz6K2SSdIlI/mRZ0L8/VKgAI0dCsWJm+++/myJyIiIinsqhpKJDhw5MmTKFzz77jMaNGzN79mxmz56datF1gQIFKFKkiP3xa6+9xmeffUaLFi3o2LEjq1evZsGCBdxyyy2p9vniiy9o0aIFffv2pUiRIqxfv57q1as74SW6yfTpsGMHjB6dsm3wYIiOhpkz3ReXiHis3bvNKAWYxKJ3b3M/Kgr+/NN9cYmIiGTGZuWRxhCRkZEEBwcTERHh/qlQlgVNm5qVlld+Erj+eihRAq5o/icizuFR7wUO+uILSB7Eff11aNgQkr9/GTIEvvrKbaGJiIhkyM/dAeRJ8+bBP//AokVXPxcWBiNGwMmTcEV5XhFvkpiYyKRJk5g3bx5+fn7ceuut3HnnnRlWg9u4cSPffvstO3bsoHz58tx1112p1mQBdOzYkcTExFTbHn74Yfpdvsggj1q6NOX+TTeZ5ndFi5qRihkz4OJF8Pd3X3wiIiLpUVLhCm+8Aa1bQ7t2Vz83YAA89hhMnQrDh+d6aCLO8uCDDzJnzhzeeOMNYmNjeeyxx9i9ezevvPJKmvv/9NNPvPPOO9xxxx106tSJtWvX0r59ez7//HPuuusu+35LlizhjTfeoGXLlvZtNWvWdPnr8QRLlpg/CxaEFi0gIAB69jR9M/v2NZWggoPdG6OIiEhaNP3J2ZYtM18xzpwJvXqlvU/PnnDmjCnzIuKFduzYQd26dZk7dy5dunQB4IsvvuChhx7iyJEjlCxZ8qpjIiIiCL7iE/Hw4cNZsmQJmzdvtm/z8/Nj1qxZdO3aNVuxecx7gYP274eqVc39du1g8WJz//x5CAw0tR5EREQ8lcPN7zzNxIkTCQkJoUWLFu4OxRgzxkyE7tEj/X3CwmDlSsigD4eIJ/vzzz8pVKgQHTt2tG+79dZbiY+PZ0ny1+1XuDKhAChWrBgX0ujsNnbsWLp27cqwYcNYtWqV8wL3YJdPfWrbFlPk4Y8/KFxYCYWIiHg+r08qhg8fTnh4OGvXrnV3KLBxI8yda/pS+GTwo73lFihcWD0rxGvt37+fsmXL4ueXMoOyZMmSFCxYkP3792fpHKdPn+bLL79MVQkOoG7duvTv35/hw4cTEBDATTfdxDfffJPueeLi4oiMjEx180aXJxWd6x6AsWPhnnvMggoREREP5/VJhUcZMwaqVzfrJjJSuDCEhpqkIm/MPpN8Jj4+nkKFCl21vVChQsTHx2d6fGxsLKGhoZQqVYrXXnst1XNr1qxh+PDh9OrVi/fff58nnniCESNGkJSUlOa5xowZQ3BwsP2WUdNMT5Y8wOPvD833/WIWVJw9C5f9fPbtgyv6j4qIiHgEJRXOsn07/PILPP00+GVh/XtYmDlmwwbXxybiZMWLF+f06dOptiUmJnLu3DmKFy+e4bGxsbH07t2bEydO8Oeff6bqawMQGBiY6nGXLl04d+4c+/btS/N8o0ePJiIiwn47ePCg4y/IzWJjTV+KgABo2RIK/DYVunUzo57vvUfS1u20aQPVqsEdd0A6+ZWIiIjbKKlwljffhHLl4LIqNhnq2BHKloXJk10bl4gLNGnShBMnTnD48GH7tvXr12NZFk2aNEn3uLi4OPr06cP+/ftZvHgx5cqVy/RaJ0+eBKBgwYJpPh8QEEBQUFCqm7cpWNAszI6IgClv7oPVq82I55NPQoUK+Dz+GCWKm1HNo0fNkiwRERFPoqTCGQ4cgO++g1GjzFeNWeHnB4MGwU8/QUKCa+MTcbLOnTtTvnx5Xn/9dQAsy2LMmDE0aNCA5s2b2/dr164dv/zyC2CmTIWGhrJ37950E4qFCxemWh919OhRXn31VW644QbKly/v4lflfgEBUGHlLybL6NkTChWC996DP/5gRPWZ9v2mTXNjkCIiImlQUuEM48ZBUBDcf79jx4WFwbFjaTfJE/FgBQsW5Oeff+a3336jWrVqVKxYkf/++48pU6akan63ZMkSDh06BMBHH33EnDlz8PPz47bbbqNdu3b2W7KKFSvy1FNPUaVKFZo3b06NGjWoWrUqU6ZMye2X6D5Tp0L37qbrHUDv3tClC21nPE4R3xjAJBVajiUiIp5EfSpy6sQJU1z+6afhxRcdO9ayoG5d0ygvg+o2Ip7q4sWLbNq0CT8/Pxo2bIivr2+q5//66y9q1qxJxYoVOXDgAHvSKaPc7opGkYcPH+bo0aNUq1YtzZ4XGfG2PhUJCaZYnI8PsHevKfbw008wcGDKTtu3Q8OGfFvlee7a9TwAa9aYBnkiIiKeQElFTv3vf/DBB2YKVIkSjh//yivw9ttw/LjpcCUiOeJtScWvv5pBzhtvhHFl36LaNy+ZLyuuWMDOU0+R8MEEasRv5QBVeOops5RLRETEE2j6U05ERMCECTBsWPYSCoDBgyE62nTgFpF8Z8kSOHXKJBfFF0w1jTOvTCgAnn8eW/FivMtIQFOgRETEs3h9UuHWjtoff2xqQT7xRPbPUbOmmf6kRngi+VJyf4oa7KbYrvXp97kpWhTfcW/Tl2l0YCG7d8OmTbkXp4iISEa8PqlwW0ftCxfg3XdNx9trrsnZucLCYN4883WliOQb586lJAaPlPvZTIHs3j39AwYP5kiNNnzII/hxUVWgRETEY3h9UuE2X34Jp0+bOvI5NWCAmccwdWrOzyUiXmP58pQpTKGJU6FXLyhcOP0DbDb8P/6QOmzno7of0qxZ7sQpIiKSGSUV2REfD2+9BbfdZiq15FSZMtCli6ZAieQzS5eaP2uyk0onN6Y/9ekypW9uTOJ9D3Lf4Ze4tfUxF0coIiKSNUoqsuOHH+DgQXjmGeedMywMVqyAdEpuikjek7yeoj8/YwUWhm7dsnRcgbGvQoECzn0PEhERyQElFY5KTISxY01DqgYNnHfe3r3NtIcffnDeOUXyEbcWbciGqChYv97cvytgCrbet5gO2llRogS8/rrpb7NypeuCFBERySL1qXDUtGnQrx+sWgWtWjn33HfcAevWQXg4XNaVWESyzlv6VMyfb2Y91mEb26hnasreemvWT5CYiNWiJVFRELVwDRUq+2Z+jIiIiItopMIRlgVvvAEdOjg/oQAzBWrbNti40fnnFhGPkjzA0J+fuViwCHTt6tDxc+f70nXXBIJ2beC/EV+4IEIREZGsU1LhiPnzYcMGePZZ15y/UyezaHvyZNecX0Q8xvPPw3//wYjyU0ns0RsKFnTo+Dp1YH7UdXzDnbT+/Vk4c8ZFkYqIiGTO65OKXJ1H/cYb0LKlGalwBT8/GDQIfvzRrN0QkTzLxwca+IRT8shmCt6ZedWnK1WvDk2awNO8iU9CPFEjnndBlCIiIlnj9UlFrjW/+/tvU//x2Wddu94hLAyOHYNFi1x3DRHxDD//DEFB0Llztg7v2xeOU46XeInCkyepxbaIiLiN1ycVuWbMGKhf3zSncqUWLaBWLfWsEMkPpk41ld8cnPqUrF8/8+eHPML+gnXgkUdSuumJiIjkIiUVWfHPPzB7tqkJ7+PiH5nNZkYrpk+HCxdcey0RcYuRI2HCsC0QHo7V3/GpT8nq1DHfdSTgz30x42HZMjN9UkREJJcpqciKsWOhalWz3iE3hIWZIva//5471xORXBMfDx99BKcnTSXCFoyt8805Ol/fvubPhXRiV+O+MGqUef8QERHJRUoqMrNjh5mi8PTTZiF1bqhZ05Ss1RQokTxn7VqIjbUYwFT+rXYrBATk6HzJU6AA/hcwDs6dg9dey9E5RUREHKWkIjNvvQVly8KQIbl73bAwmDsXTp3K3euKiEstXQoN2Ew9tnGhZ/anPiVr0MAswwL4eU0Voh9+Bt57D7Zvz/G5RUREskpJRUYOHYJvvzUToLO5kDLbBg40Cy5//jl3rysiLrVkCQxgKmcpRvX7O+X4fDabmQJVsaJZpx1x/5PmwWOPadG2iIjkGiUVGRk3DooUgQceyNFppkwxv/QdapRdpowpM6kpUCJZkqs9a7IpIQH+Xm6mPv1RqA81Qwo45bzPPw/798MHH0CFmoXMSMUff8DMmU45v4iISGaUVKTn5En49FPz1V/Rotk+zfTpZn339OkwYICDPe3Cwkx/jL17s319kfwi13rW5MDGjVD9/L/UYQd7WwxwWsubwMArCtPdcgt06QKPPw4xMc65iIiISAa8Pqlw2beT48ebeQWPPprtU2zcCHfckfJ41y749VcHTtC7t/m08MMP2Y5BRDxH8tSnMxSnRP+OrruQzWaGLQ4dgnfecd11RERELvH6pMIl305GRsKHH5ppTyVLZvs0RYtCpUqpt735pgPTnIsUgT59zBQozY0W8XpLl5ipT9MJ5cYO/i65xtGjl6pR16ljRireeMPMjRIREXEhr08qXGLSJDNl4IkncnSamjVh1SqzzrtRI7Nt3TpYvNiBk4SFwdatpgGfiHitxEQ499c/1GIXfwQNoF49519j0CCoUMGs4YqIAJ57DooXN29CIiIiLqSk4koxMfDuu3DXXea3cw4VK2ZmHzz9dMq2N9904AQ33wylS8PkyTmORUTcJykJJnWYSnTBklQZ0t5p6ykuV6aMGdS8eBFmzcIMl77zDkybBgsWOP+CIiIil9gsy7F5NadOneLLL79k//791KpVi3vvvZeimSxk3rRpE7///junTp2idu3ahIWFERwcnOPzXi4yMpLg4GAiIiIICgpy5CWl9tFHZnH29u1mqMFBv/4KXbtCoUKptyckQO3aKWuuN2yAJk2yeNJHH4VffoGDB8HX1+GYRPITp70XOJtlmfeUjh1NEQgXWLoU2rY192+99dIaLssyG0+dgk2bwN81065ERCR/c2ik4siRIzRu3Jg//viDqlWr8uOPP9KyZUsiIyPTPeaNN95g2LBhJCYmUqVKFX788Ufq1avHgQMHcnRel7h40TS7GzgwWwnFzz9DaCi0a2fmNV/Ozy/1DASH2k+EhZkTOjRvSkQ8yoYNsGePKQPnIjfcYEYrAObNg+hozKLtDz80X5R8+KHLri0iIvmc5YAHH3zQql+/vhUfH29ZlmVFRkZaZcuWtV5++eV0j9m7d2+qx/Hx8VapUqWssWPH5ui8V4qIiLAAKyIiwoFXdIVvvrEssKxNmxw+dO1ayypUyBwOlvXhh1fvc/68ZfXrZ1kLFlhWUpIDJ09KsqyaNS1ryBCH4xLJb5zyXuAKTz1lWaVLW9bFiy69zIMPprwPTZly2RMPPWRZRYta1tGjLr2+iIjkTw6NVPz+++/07dsX/0vD50WLFqVXr178/vvv6R5TtWrVVI8jIyOJjY2lbNmyOTqv0yUlwdix0KsXXHutQ4cePmyqvyaXgx8yBIYPv3q/wEAzQtGxI47Np7bZzGjFtGmqOS/ihQ4dtDj/9VQudO9rhi1dqG/flPvTpl32xKuvQoEC8MwzLr2+iIjkT1lOKmJjYzl8+PBVSUK1atXYtWtXhsceOXKEoUOHctttt9G8eXNGjRrFHZcaOGT3vHFxcURGRqa65ciMGabK0ujRDh124YJJKI4cMY/btDHFo5y+CDMsDKKiLtWKFBFvsnriOgqf2EePbwbw2WeuvVbbtimVsGfPvux7iBIlTHnZb76BFStcG4SIiOQ7WU4qYi79Zrpy8XTRokXtz6WnUKFCtG7dmmbNmnHNNdfw66+/cvTSooPsnnfMmDEEBwfbb5WubAjhCMsyv2zbtYPrrsvyYUlJpkjU+vXmcdWqpnN2QEDWL334cBZ3rFULWrY0PStExKsUmDGV45RhKTfZy0u7ir+/+aID4Px5+OOPy568915o2tQUo0hMdG0gIiKSr2Q5qShSpAg+Pj6cPXs21fYzZ85kWmGlePHiDB06lFGjRrF06VKSkpJ46aWXcnTe0aNHExERYb8dPHgwqy/lagsWmAYSzz7r0GEvv2yKMoGp3Pj776b6a1bMnm0WVTZseGkxZVaEhcHcuXD6tENxioj7WEkWTXZO5Rf6UaiwL02buv6al0+BSn6PAkz1uAkTzKLxL75wfSAiIpJvZDmp8Pf3p3bt2oSHh6favmXLFho0aJDlC/r5+dGwYUP71KbsnjcgIICgoKBUt2x74w1o3hw6dcryIT/+CK+8Yu77+MBPP4EDPwamTjUzEM6ehc8/z+JBAwea4RGHSkeJ5A8TJ04kJCSEFi1auDuUVA5NX0PFxANMZQA33ODyJRWAWbdVooQZfO3Y8Yonr7vODLE++yycOeP6YEREJF9waKH2bbfdxpQpUzh58iQAu3fvZs6cOdx22232fWbOnMmjjz6a6vHljh49ysKFC2ndurVD53WZlSvhr7/ML9gsLoSwLJgyJeXxO+9A9+6OXfbJJ1Puv/uuqWabqbJlTTM8TYESucrw4cMJDw9n7dq17g4llXOfTuUo5VhOG3sPCVcLCIADB0wV6rvvTmOHsWMhPh6efz53AhIRkTzPoeZ3MTExdO/enZ07d9KqVSuWLVvGjTfeyNSpU/G91JTtpZde4v333+fcuXMA3H///fz99980aNCAmJgYFi9eTMeOHfnuu+/s6yiyct7MZLvh1S23wK5dsHmzGXLIooQEeOIJswjy00+ztzC7Z08zDQrM2sk778zCQZMnwx13mC56VyxuFxEPa36XlMTpolX54UJvHuVDli0zxRw8wrvvmm83/vsPQkLcHY2IiHg5hztqJyUlsWzZMg4cOECtWrVSjTgAbNiwgS1bttirOwHs37+ftWvX4u/vT0hICLVq1XL4vJnJ1geJf/+FRo0c+ER/taQkh3KRVJYtg5tuMvfr1zfhZHqu6GgzYvG//zm8BkQkP/CopGLlSrj+em5kKesK3si5c44VcnCp+HgoVcpUvHOw6p2IiMiVHE4qPFW2PkgMHmwWNuzcaUqmZCApyUw/LlXKCcFeYllmsfbKlebx77+b0YtMhYXBP/+Y0RWn164V8W6elFRE3jOC6K+mUpFDtGvvw6JFuR9DUpJ5jylRAurVu+LJnj0hLg7+/DP3AxMRkTwlm9+x5wG7dpmFEU89lWlCAfDcc9CkCWzc6LwQbDZ4+umUx2++mcUDw8IgPBw2bXJeMCLiXElJ+P32Mz/THwsf+6hkbtq4ESpWNFOuPvggjR06dIDly01iISIikgP5N6l46y1T/zXNVYypffcdjBkDhw6ZxlLOrOjaq1fKt4fLl2exJ9XNN5vYJ092XiAi4lwrVhB49ghbGwzA359cW6R9uVq14NLyNn79NY3WFB06QGwsrFqV26GJiEgekz+TisOHzTqKJ56AQoUy3HXFChg6NOXxa6+ldKt1Bh+f1JWgsjRa4e9vysv++KMaWIl4qqlToUIFJm26jnPn3LNAu0gR6NrV3D9xwnxxkcq115p5Ue6YlyUiInmK1ycV2apN/+67EBgIDz6Y4W7798Ott5r1jGB2f+SR7MeanrAwM0WhWzeT52T5oCNHTDlcEfEsiYmm61z//uDjQ2BglmZZusTljfCmTbviSR8faN9eSYWIiORY/luoffo0VK5sPr2/+mq6u0VFmUXU//1nHnfoAPPmue6DQUQEBAc7cIBlmbkNN90EX37pmqBEvJBHLNReutTMd1qxwjSbc6OICChTxnw5Ur48HDx4RZW5iRNhxAgzT6pwYTdFKSIi3s7rRyocNn68+fOxx9LdJTHRFIZKTihq1TJNrF35TaNDCQWYVd5hYearx5gYl8QkItk0dSqJFSphtWzl7kgIDjbLsMAMbq5efcUOHTqYxjtXzY0SERHJuvyVVERFmaTi/vszrA37zDMwa5a5X6yYKfVaokTuhOiQsDCIjEwJVkTc79LUp+9i+1Ohkg+3324GFt2pX7+U+7/8csWTdetCuXKm/baIiEg25a+k4pNP4Px5GDky3V1Wr4Z33jH3fX3NCEWdOrkUH+bzyLRp5svDs2cz2bl2bWjRAr7/PldiE5EsWLYMjh/n49MDOHoUduxwfzuZW24BPz9zf9q0K5Icm8284WhdhYiI5ED+SSpiY2HcONM5u2LFdHdr1QomTTK/gD/8EDp1ysUYgZdeMt8qLl4MH3+chQPCwmDOHNOZTyQfy1bRBleYOpULpSqzhpaAe0rJXqlECbMeG0wBivXrr9ihQwezMbn+rIiIiIPyT1Lx9dempuLl3ebS8cADsGULDBvm+rCuNGRIyiLKDz7IwnKJgQPN8MbPP7s6NBGPNnz4cMLDw1m7dq37gkhIgGnTWFV5AGCGJ9zR9C4t/fqZWZ/33WdKzabSoYNpvb10qVtiExER75c/koqEBNMAon9/s+o6C2rXdnFM6ahRI2X+84kTpp1GhsqVM6swNQVKxP2WLoUTJ/giegBgZhbdeKObY7rkrrvg6FH49FOzjCKVatWgalVNgRIRkWzLH0nFTz/Bvn0wevRVTyUkmFzjqvrtbnT5YMo772Shv11YmJnHvX+/S+MSkUxMnUpi5ar8uKM5AI0amWIPniAgIGVdRZq0rkJERHLA65OKTOdRJyXB2LHQo4f5DX+FJ5801VD69YP33nNxsFnUtGnKWo7du7OQ8Nx6q+kM/sMPrg5NRNJzaerT3hYDsDxs6lOWdOhg6mifOOHuSERExAt5fVKR6Tzq3383CyTSGKX49FN4/31z388PmjRxXZyOuny04s03MylJWbSoSSy+/979tStF8qu//oJTp5gVONC+yRMWaafl9Ok0lmElr+T+66/cDkdERPIAr08qMmRZ8MYb5uvCG25I9dTixTB8eMrjjz+Gdu1yN7yMdOxoRiwANmyAhQszOSAszCRP//7r8thEJA1Tp0KNGvy4LeXbCU9ZT3G5UaOgbFkYMAC2bbvsifLlzWILTYESEZFsyNtJxaJFsGYNPPtsqs07d0Lfvma2AsDjj8PQoW6ILwM229WjFRnq3NmUdpk82aVxiVzu9OnTzJgxg9mzZxMZGZmlY7Zs2cKvv/7K6tWrSUpKctp53eriRZg+ncS+A9i9x0x9CgmB0qXdHFcaKlRIWad11dTK9u2VVIiISLbYLCtvzJeJjIwkODiYiIgIgoKCzMaOHU3d9XXr7N2nzp2D1q1h+3azS/fuMHOmaXTnaRITTeO93btN86qpU81iy3Q9/DD89ptZsO2JL0jylFmzZjF48GAaNWpEbGwse/fuZcaMGdxwxahgsk2bNjF06FBiY2OpWbMmmzZtIjAwkN9//51q1apl+7xXSvO9wNXmz4cuXWDjRhIbNubff03zyg4dcufyjti/3xR6AmjcGDZuvOzJX34xlSsOHsywn4+IiMiV8m5SsXq1yR5++cUMS2BGJrp3hz//NMeEhMDKlZBbnzuyY/FiM1UhJCQLO69cCddfb+ZKeeKnGckzoqKiqFq1Kg8//DAvv/wyAPfeey+LFy9m586d+KaR1K5atQp/f3+aNWsGwMWLF2nfvj1FihRh3rx52T7vldySVAwdasrJbt/u/vbZWdCyJSQvQ9u1y5SyBuDUKTO88u23cMcdbotPRES8T96d/jRmjPmav08f+6ZRo1ISilKlzBpuT04owMxGyFJCASaJql5dPSvE5ebNm8e5c+d45JFH7Nsef/xx9u7dy8qVK9M8pnXr1vaEAsDf35/u3bvz72XrgLJzXre7NPWJAQO8IqEA+/cswBVToEqVMlXyNAVKREQclDeTis2bYcYMeOaZlPbUmAJJJUqAv7/5DFC9uvtCdAmbzSzY/uUXiI11dzSSh/3333+UK1eOUqVK2bfVr18fX19f/vvvvyyf588//6Rhw4Y5Om9cXByRkZGpbrlq4UIz12nAgNy9bg5cnlT88ssVTyb3q8gbg9giIpJL8mZSMXYsVK5sPmBfpl07Myvqxx89sypLZhISTB+/DMvIh4VBZCTMmpVrcUn+ExERQfHixVNts9ls9mlHWTFu3DhWrFjBa6+9lqPzjhkzhuDgYPutUqVKDr6aHJo6FerUYXlEQ7p0gddfT1mz5alq1kxp27N27RVVoDp0gAMHYM8et8QmIiLeKe8lFXv3mqzhySfNkMQVatZM/S2dt/j7bzOb67bbYPz4DHasUweaN9cUKHGpQoUKER0dfdX26OhoChUqlOnxX3/9NaNHj2by5MmpGldm57yjR48mIiLCfjt48KADrySH4uPh119hwAAWLrIxfz4895z58sLT3XVXyv0vvrjsiZtuMoUeNAVKREQc4PVJxVUdtT/4wMwLvvdezpwxH8Dzwih+lSqmIAvAxIkQFZXBzmFhMGcOnDmTK7FJ/lO9enWOHz9OXFycfdvRo0eJj4+neibzCr/99lvuv/9+vv32W/r375/j8wYEBBAUFJTqlmsWLDAl5QYMYMmSlM2e2vTucnfckfK9yzffmPwIMAvNmjdXUiEiIg7x+qTiqo7akyfDiBFc9CtE//7w2GMweDDExLg3zpyqWDFlNte5c/DZZxnsPGiQmSt11WRpEefo2rUrFy9eZObMmfZtP/30E4ULF6bdZV0kJ0+ezLbL5tZMnjyZ++67j2+++YZBgwZl+7weY+pUqFeP+Fr1SV5HXqWKuXm6UqVMHYumTeHllyFVyxCtqxAREQf5uTsApytYEGvYQzzySMoXbYsWmUqJuT3V2tmefBK+/trcf/dd05aiQIE0dixXDjp1MlOg7r8/N0OUfKJy5co8/fTT3HfffezYsYPY2Fjefvtt3n77bYoWLWrf74477uC9996jbt26/PHHHwwZMoRevXqRmJjI5MsaNd5+++0OndcjxMWZvjAjRrB2nc1eG+Gmm9walUO++goCA9N4okMHU0EvPBzq18/1uERExPvknaQiearP/fcz4btgPvnEPCxQwPze9/aEAkxp2V69TCncw4fhhx9gyJB0dg4LM5OmDxwwi9ZFnOz111+nRYsWzJs3Dz8/P2bNmkWnTp1S7RMWFka9evUA05cieXQiuS9FsuSkIqvn9Qh//gkREdC/P0tmpGz2hqlPydJMKMD0u/H3N9/IKKkQEZEsyDvN70aPJnjsWGZ+sYtb76thH8r/7ju47POK1/v7b2jTxtyvV89Uz/VJaxJbVJTpmvfCC6a0rkg+kWvN7+68EzZsgM2b6doV/vjDbN6xA2rVct1lc03btlCypKm/LSIikgmvX1MBQHQ0TJoEQNiI0vaE4tln81ZCAXDDDeYGsHUrzJ6dzo5Fi0Lv3qoCJeIKsbGmF86AASQkmGQf4JprTIU5b2NZsGaNaRCamHhpY4cO8Ndfl20QERFJX95IKgoVIuoNU2c1uSpSnz7w6qtujMmFnn465f6bb2awY1iYGcq4rGOxiDjB/PmmH0z//mzYYL7XAPPlvpc01U7lkUegVSsYN87M6gJMUnH2LGza5NbYRETEO+SJpCI+0ZeB3/e2P27cGL79Np1pQXlAjx5mfQXAihVXNK66XJcuZvrCZQtiRcQJpk+HBg2gXj2WLk3Z7E2LtC93+ZKVzz+/dKdVKyhUSKVlRUQkS/LEx+5Tp+DkSXO/dGmYOROKFHFvTK7k4wP/+58p7LR9O9Stm86O/v4wcKBZ0Z2qXqSI5MjGjfbFTbfdZqqy3XMPdOzo3rCyq0cPswQLzKyuEycwVS5uvFFJhYiIZInXJxUTJ06kU6cQEhPbA/DTT3mj0lNmBg+GTz7JwoLQsDBTKuryzlwikn0JCWZ48NJwYYUKptDaF19A7dpuji2b/P1TKsklJJiRXsBMgVq6FC5edFdoIiLiJbw+qUhufrdhw2LANIKVy1x3HVSrpgXbIs6yZ49pP53HSq3ee2/K/c8/v9T3rkMHOH8ekpuLioiIpMPrkwoxLl5MWaSeis1mRit++QV7dy6RPGjixImEhITQokUL114oPNz8mbywKY+oVSulx8b27ZcqWjVpAsHBmgIlIiKZUlLh5S5cgPHjTRnLF19MZ6ewMNOkK936syLeL3nUcq2rv1UPD4fixaFsWb75xjSjPHfOtZfMLffdl3L/s88APz+TaSipEBGRTGSr+d2FCxc4fvw45cuXJyAgIEvHnD17loSEBEqXLn3Vc6dPn+Zk8krrS3x9fanlQAepXGt45WFOnIAqVcwgROHCpoF2iRJp7Ni8uemsrUZWkse5/L3g9tth3z6sZcspU8YUiihRwhSL8PaKczExUL68SZIKFYIjR6DY1++bBprnzkHBgm6OUEREPJXDvwL/97//UbJkSVq3bk3JkiV57733Mtx/ypQpNGrUiBo1alCvXj2qVq3KjBkzUu3z8ccf06RJE2699Vb7LSwszNHQ8qUyZUzVGTBTnz/6KJ0dw8LMSMXZs7kWm0ieFB4OISFs3WoSCoDrr/f+hAJMIpHcMDQm5tJ3EB06QFwcrFzp1thERMSzOfRr8Ouvv+b999/nr7/+4vjx40ydOpUnn3ySP/74I91jVq5cyeTJkzlz5gwnT55k2LBhDBgwgO3bt6far1GjRmzbts1+W7NmTfZeUT40cmTKB5rx482HgasMGmTKuvzyS67GJpKnJCaaVvb166fqT5G8FiEvGDrUVKL+889LFaEaNIBSpTQFSkREMuRQUvHJJ5/Qt29fWrVqBUD37t1p27YtkyZNSveY999/n4YNGwJgs9kYNWoUlmWxbNmyq/Y9fPgwp0+fdiQkAapXhwEDzP2TJ+Grr9LY6ZprTBF9VYESyb59+8xcw5CQVFWavbXpXVoaNTKluTt1uvRlhY8PtG+vpEJERDKU5aQiKSmJDRs20Lp161Tbr7/+etavX5/lC+7atYuLFy9SsWLFVNtXr15N06ZNqVy5MjVq1GDWrFlZPqfAU0+l3H/nHTMocZWwMNOv4sCBXItLJE+5VPnJqpeSVBQuDE2bujGm3NChA6xZk06JOREREQeSiqioKOLj4ylVqlSq7aVKleJU8sTiTFy8eJH77ruPJk2acPPNN9u3169fnw0bNnD8+HEiIiIYPHgwoaGhbNq0Kd1zxcXFERkZmeqWnzVpAsk/0r1705nl1KePWWj544+5GptInhEeDkFB7I4pz9GjZtMNN5giSXmZ1b6D+aZi+XJ3hyIiIh4qy0mFr68vAPHx8am2x8XF4ZeF36iJiYnccccd7N27l+nTp9vPB9CnTx+aNGkCgJ+fH6+88gqVK1fm+wym6owZM4bg4GD7rVJ+aKOdiaefTrn/1luXmlddLigIevfWFCiR7Lq0SHvJUpt9U15aT3G5mBiYPBnatYPv19QyrcM1BUpERNKR5aSiSJEiFCtWjKPJX89dcuzYsaumMl0pMTGRO++8k+XLl7N48WKqVq2a4f42m41KlSpxIINpOqNHjyYiIsJ+O3jwYFZfSp7VoQM0a2bub9wICxaksVNYGPz3H/z7b67GJpInbNmSpxdpX27jRrjjDjNj8rPPbeYNRkmFiIikw6GF2u3atWPevHn2x5ZlMWfOHNq1a2ffdurUKXbu3Gl/nJSUxF133cWSJUtYvHgxNWvWvOq8Fy9eTPU4IiKCf//9l9q1a6cbS0BAAEFBQalu+Z3NZkYrChaEhx6CNH98XbqYovoarRBxTFKSqfx02SLtggVNC5i86LrroF49c3/pUjhar4PJNM6ccW9gIiLikRxKKp577jmWL1/Os88+y8qVKxk2bBhHjx5l1KhR9n0mTJhAixYt7I/vvfdeZsyYwaRJk0hMTLSXjL18HUa7du349NNPWbt2LXPnzqV79+4EBATw0EMPOeEl5i+hobB/P0ycaJriXaVAAVMv8ocfzIckEcmaAwfgwgUSaofQt69JJm68EbLY/9Pr2GymvGyyr/a1N3MqLy97JSIiconDHbWXL1/Om2++yYEDB6hVqxbPP/88jRo1sj8/YcIEvv32W3ufiUaNGhEXF3fVeR5++GEefvhhAA4dOsTbb7/N6tWrCQwMpGXLljz55JOULFkyy3Hl147a2fL339CmDSxebCZMi+QhLnsvmDMHevQwWXvlyoBpW3HZ8rA85+RJs5Ti4kXTaPNY4RrYenSHDz90d2giIuJhHE4qPJWSCgdYlmlu0akTfPaZu6MRcYqJEycyceJEEhMT2bFjh/PfC955B15+GSIjzdf4+cSAAfDzz+b+nk73Ue3oSti82b1BiYiIx3Fo+pN4l6goGDcOXnjhiidsNrNg++efTSMvkTxg+PDhhIeHs3btWtdcYMsWCAnJVwkFpJ4CNfVkB/NzOH7cfQGJiIhHUlKRRyUkQIMGMGqUKS977NgVO4SFQUSEmdIhIpkLDyexbghHjrg7kNzVqVPK+qz3N7U3dxYvdl9AIiLikZRU5FF+fmbaAkBcHIwff8UO9eqZNsCqAiWSOcuC8HAOFgmhQgWzpOLjj90dVO7w8YF77zX3j1GOE6VDVFpWRESu4vVJxcSJEwkJCUlVcUqMESPA39/c/+gjMxU8lbAwmDULzp3L5chEvMyhQxAdzYbYEAAOHszbC7SvNGSISS5sNvivlPpViIjI1bw+qXD5PGovVqGCaV4FZqbTp59escOgQaasyy+/5HpsIl4lPByAhcdC7Jtat3ZXMLmvUiX46ivYswc6vt4Bdu82VbBEREQu8fqkQjL25JMp60rfe89MhbIrXx46dtQUKJHMbNkCgYHM+tcsLihcGOrXd3NMuezOO6FqVUwLcZtN6ypERCQVJRV5XN260Lu3uX/kiOl5l0pYmGlmdfBgrscm4jXCw4mvWY8Dh8xbZosW+Wv6UyolSkCTJpoCJSIiqSipyAeeeirl/ltvXdFIOzTUtAT+8cdcj0vEa4SHc6x4/pz6lJakdh1I+HORWcAuIiKCkop84brr4MYbzf1t2+D33y97MigIevVSUiGSnkuVn7ZYSiqSkuCll2DIN+3xO3YYa8dOd4ckIiIeQklFPvH00+bPwMA0Zjr17w///GNWYYpIakePQkQES0+nJBWtWrkxHjfy8YG//oJfT99IAr7s/lzrKkRExFBSkU907256VRw4AA8/fMWT3bqZKVC//uqW2EQ82pYtAPy+26zMrlIFypVzZ0DuNXQoRFOUNbTk9C9aVyEiIoaSinzCZoNHHoGSJdN4skgR6NIFpk/P9bhEnMVlPWvCw0kKKMheqyqQf6c+JevbF4KDYREdqLZvMRFnkzI/SERE8jwlFWL07QsrVpipHiJeyGU9a8LD8alXl3NRvqxbB6NHO/f03qZQIbj9dpNUlOEkf7y7xd0hiYiIB/D6pEIdtbPn3LkrFmz37Al+fpoCJXKl8HAICcHfH5o1g0aN3B2Q+w0dCiu5jlgCOPC1pkCJiEgeSCrUUdtxr78OlSubarIHDlzaWKIEtG+vKVAil7Mss6YiJCTzffORxo2hQfNCrOB6ah1axMaN7o5IRETczeuTCnFcXBxERUFCArz77mVPhIaa0i6nT7srNBHPcuIEnD2b/9pnZ8HQoWYKVDv+4qvPEtwdjoiIuJmSinzokUfMvGiAzz67LIe49VZTiD7VvCiRfOxS5aeHJoQwdixs3+7meDzIbbfBioAOBBPJf99uJCbG3RGJiIg7KanIh0qXhnvuMfcvXICPPrr0RLlycMMNmgIlkiw8nATfAny6sDqjR8O6de4OyHMEBUH1gS2IpjAjrl3E+fPujkhERNxJSUU+NXIk+Pqa++PHm+QCMFOg5s8386NE8rvwcA4G1iERP0DlZK/0xtv+FLr5RnoXXUSpUu6ORkRE3ElJRT5VrRoMGGDunzoFX3116Yk+fcyiizlz3BabiKewwsP5J84s0i5VCqpXd3NAHqZMGfC9uQMsXw7x8e4OR0RE3EhJRT721FMp9995xyzcpmpVaNpUU6BEgMT/wtkYb5KKVq1ME0m5QocOZqhzzRp3RyIiIm6kpCIfa9zYNNIG2LcPfvnl0hOhoTB7NsTGuikyEQ9w8iR+Z06yBVP5SVOf0tG4MRQrxoVZi5g4ES5edHdAIiLiDl6fVKj5Xc5cPlrx6aeX7vTtC+fPm7UVIvlVeLj5g5SRCkmDry+7K7Vj7VuLePhhmDXL3QGJiIg7eH1SoeZ3OdO+PXTvDmPHwtSplzbWrQv16mkKlORv4eEk2PzYRU1sNmjZ0t0Bea74GzvQ2lpJIS7w+efujkZERNzB65MKyRmbzcx0evppUldvCQ2FmTM1l0G8hrNHLRP+DWe7VZsE/KlbF4KDnXLaPKnOgx0IIJ7rWcG8eXDwoLsjEhGR3KakQtIWGmo6CS9Z4u5IRLLE2aOW0WvD7VOftJ4iYz4NQoguXIYOLCIp6bJqciIikm8oqZCrWBbQpImpBKUpUJJPFT2wheo963PPPdCjh7uj8XA2G7aOHejAIgC++AISE90ck4iI5ColFWK3cyc8/rj5VjbJspnRil9/haQkd4cmkrtOn8b35HGa3RHCF1+Y2gWSscI9O9CCtQQRwYEDsHChuyMSEZHcpKRC7IYNg/ffN+XmFyzAJBXHjsHKle4OTSR3bd1q/gwJcW8c3qR9e3xJ4kaWAWjBtohIPqOkQuweeijl/oQJwHXXQblymgIl+U94OPj6Qq1a7o7Ee9SogVWpEj0KLQbgt9/g5En3hiQiIrlHSYXY3XILVKxo7s+aBfsO+MCtt5qkwrLcGptIbjqzPJzz19TkXEyAu0PxHjYbtg4duKWoWVdx8SJ8+62bYxIRkVyjpELs/PzggQfMfcuCSZMwk8n37YONG90ZmkiuOr10C/MO1ad4cfWAdEiHDlQ48Q83hpxm/Hi4+253ByQiIrnF65MKddR2rvvuA39/c//zzyG2VVsoXlxToOQqp0+f5o477qB06dJcc801DBs2jOjo6AyP2bp1K4899hilSpWifv36ae5TpEgRChYsmOo2YcIEV7yEdBU7mlJOtmHDXL20d2vfHoClr/zFI49AiRJujkdERHKN1ycV6qjtXGXLQr9+5v7p0zD1V38zL0pJhVwhNDSUnTt3snz5cubNm8eiRYu49957MzwmLCyMatWqERYWRlxcXJr7xMbG8vPPP3Pu3Dn7bdiwYa54CWlKPH2O0vFHCCeEypXhmmty7dLer1Ilsw5l0SJ3RyIiIrnM65MKcb7hw1PuT5yIqQK1dWtKRRzJ91auXMnSpUv5+OOPqVOnDo0aNWLcuHFMnTqVvXv3pnvchg0bGDFiBMWLF8/w/P7+/qlGKnx9fZ39EtK1d475dx5OiJreZUeHDkoqRETyISUVcpXrr4dGjcz9NWtgfcnOULiw6VkhAixfvpxixYrRpEkT+7aOHTsC8Pfff+f4/EOGDLGff/z48STmYie1w3+Gk4gP26lDq1a5dtm8o0MH2LYNjhxh40bzJcV337k7KBERcTWHk4qdO3fy6KOP0rt3b0aNGsXhw4cz3D8+Pp6vvvqKIUOGEBYWxvvvv09MTEyOzyuuY7OljFZccw0cPl3QtBSeNs29gYnHOHr0KKVLl061rVChQhQpUoRjx47l6Nz9+/dn9uzZ7Ny5k6effpoXX3yRZ599Nt394+LiiIyMTHXLidgNW9hNDeIoqJGK7GjXDoBDkxfTtCl89JF6VoiI5AcOJRU7d+6kZcuWnD59mkGDBrFt2zZatmzJiRMn0j3m+uuvZ/ny5bRr146uXbvy1VdfccMNN6RKLLJzXnGtwYNh6lTYv98sqSA0FDZsMJWgRAAfn6vfPnx8fLByWH74xx9/pFmzZpQuXZpBgwbx0ksv8d577xEfH5/m/mPGjCE4ONh+q1SpUo6uX3ifWaTt7w+XDcRIVpUpAw0bUnH7IqpWNZvWr4dcHGwSERE3cCipePXVV6lVqxaTJ0/mtttu49dff8XPz49x48ale8y8efP44osvGDJkCHfccQfz5s3jn3/+Yc6cOTk6r7hW4cLQv39KJSi6d4cCBTQFSgAoW7YsJ6/obJY8YlC2bFmnXqtJkyZcvHgx3bUao0ePJiIiwn47ePBgtq917hxUPm+SikaNoFChbJ8qf7u0rqJZM/Pw/HnYudO9IYmIiGs5lFT88ccf9O7dG5vNBpjFlL169WLevHnpHlOqVKlUj4sXL46fn1+q0pPZOa/ksqJFoXNnVYESAK677jrOnDnD5s2b7dsWLzadlFs7ec7Qli1b8PHxoUyZMmk+HxAQQFBQUKpbdm34K5LKHNQi7Zxq3x727aN91ZREcMMGN8YjIiIul+Wk4sKFC5w4ceKqqQUVK1ZknwNTYsaPH4+Pj499UWd2z+vsedSSsf374ch1feHvvyGHc+bF+9144400b96cxx57jGPHjrF//36eeeYZevToQe3ate37Odpj4ocffmDChAkcPXqU+Ph45s2bx4svvkhYWFimFaOcIWDvNgC22UK0SDsn2rYFHx9uSlxs36SkQkQkb8tyUpE8n7nQFfMBAgMD053rfKV58+bxv//9j/Hjx1OxYsUcndfZ86glbadOQe/eUL06PLG4F/j4wG+/uTsscTObzcZvv/1GoUKFqFKlCnXr1qVu3bp8d0WZn7i4OBISEuyPO3bsSMGCBXnttdfYs2ePvWRscmGGHj16cOjQIVq2bEnRokV55JFHeOyxx/jss89y5XXdUDwcbDb+OlaX0NBcuWTeVKwYNG1KzYMppWWVVIiI5G1+Wd2xSJEi+Pn5cebMmVTbT58+naVvEBctWkRoaCivvfYa999/f47PO3r0aJ544gn748jISCUWLlC8OGzaBElJMHVhSb68rh2B06fDgw+6OzRxswoVKjBr1iwsy7JPXbxSTEwM/vaFOTB37lySkpKu2q9gwYIABAcHM3bsWMaOHZvheV1myxaoVo0iZQJz97p5UYcOFPruOyqUtzh8xMaGDWBZprqciIjkPVkeqfDz86N+/fps3Lgx1faNGzfSKLmpQToWL15Mr169eP7553n66aedcl5nzqOW9Pn6puQPlgXzCoXC4sVwRRIo+VdGH/yvbFxXoECBVE3tkm+OntdlwsMhJCT3r5sXdegAR4/Sq/Z2ACIiIIO+iCIi4uUcWqh91113peqYu2HDBv744w/uuusu+z6TJ0+mX79+9sdLliyhZ8+ePPfcc4wePTrb5xX3ufdeU/gJ4Ln1fbASE2HWLPcGJeJkiYkoqXCmNm3Az4+egZoCJSKSHziUVDzyyCN069aNhg0b0qpVK9q0acMDDzzAoEGD7Pvs2rWLBQsW2B/36dMHHx8flixZQteuXe23yZMnO3RecZ/SpWHgQHN/67lrOFHjOjXCkzznqeHnYd8+PlkWwqFD7o4mDyhcGFq3plnEIlq1gmHDoEoVdwclIiKuYrOy0alq9+7dHDhwgJo1a161jmHXrl3s37/fXt3pzz//JDGNrkc1a9akZs2aWT5vZiIjIwkODiYiIkJToVxg9WrsJTbfrTiOESf/h+3UKShSxL2BiVwhu+8Fd4Ss57utzWnOWhacbU6xYq6LMd948UWYMAFOnjRFHkREJM/KVlLhiZRUuJZlQYsWpjNuNfawhxqm5Xb//u4OTSSV7LwXxMTAQ0W+5auku2heJ4p125QsO8XSpaa87Nq10Ly5u6MREREX0ldHkiU2Gwwfbu7vpTr7izdWIzzJMzZuhDpJ4eyjCg2vU0LhNNddB0FBMHeuuyMREREXU1IhWTZoEJQoYe5/GdmXpN9nQWyse4MSuWTixImEhITQokULh49dvRpCCFcnbWfz94fOnWHOHMDMgjpxws0xiYiIS3h9UpGTDxLimEKF4J57oFUraPZaKD7no+GyRfki7jR8+HDCw8NZu3atw8euWqWkwmW6dcNavZpry5+iTBmYONHdAYmIiCtoTYU45OJF8+UjlgX16sH118OXX7o7LBG77LwX1Kkcw9aDhXmowBdMOH83flluCyqZOnIEKlRgMN/zI4Pp2RN+/93dQYmIiLN5/UiF5C57c2SbDUJDYcYMSEhwa0wiOXHsGAQe3IYPFrb6IUoonK18eawmTejtb6ZAqVeFiEjepKRCsq9vX9NZe+lSd0cikm3J6ykASt9Uz83R5E227t3pyjx8SOTIEZPIiYhI3qKkQrLFsmBpdFNOBlbm7BdqhCfeK3k9xUEq0qStpk66RLduBF88TXPWAabaloiI5C1KKiRbvvgC2razMflCKD4zfoWkJHeHJJItL74Iw24KJ7FOCDfc4O5o8qhWrYgrXJzuaAqUiEhepaRCsiU0FAoWhOmEEnz+KDF/rXZ3SCLZUrAglDgWTtVuIZQp4+5o8ig/P+LadlFSISKShympkGwpUQJuuw1WcD3HKcOOsWqEJ14qNhZ27YL69d0dSZ5WpH83WrCOMhxXUiEikgcpqZBsGz4ckvDlV/pQYsl0rKQ8UZ1Y8psdO8z0vZAQd0eSp/l07wpAF/5g3z5T40FERPIOJRWSbc2amUZ40wmlUvwe/vlmk7tDEnHIpEkw+21T+Smhlio/uVSZMuwv24LuzMHf3+RyIiKSd3h9UqGO2u41fDj8RTvOUow94zQFSrzLhx/C+snhHOEaLhYp7u5w8rwi/bvTr+gfRJ1NUOdyEZE8Rh21JUdiY6FSJRh36k6asYGSRzdTrpy7o5L8LKvvBRERULw4TLX6UbnoOVpGLsjFKPOp1auhdWtYvhyV2hIRyVu8fqRC3KtgQRg6FKbRl/psYfqY7e4OSfIpR0ct1641/Vbqs4Xz1bRIO1c0bw6lSsGcOe6OREREnExJheTYgw/CAltnzhNI4DxNgRL3GD58OOHh4axduzZL+69aBf7EU4udBDbTIu1c4esLXbsqqRARyYOUVEiOVakCr75TiJh23bkrSEmFeIdVq6AWO/EjkQo3K6nILYcadoN//uGBXkfIYv4nIiJeQEmFOMUTT0Cp+0OxrVsHBw64OxyRDFmWmd4fgqn8pKQi9yzy70ISNi7OmseKFe6ORkREnEVJhThPjx5QoAD8+qu7IxHJ0J49cOqUSSrOFiiDrVRJd4eUb9S/qSSraE135rB+vbujERERZ1FSIc4TFAQ33wzTp3PokLuDEUnfqlXmz/ps4VwFLdLOTQ0awDyf7tzMn/y7/qK7wxERESdRUiFOtbpCKElLl9G27nGiotwdjUjaVq82f4YQjm8DTX3KTQEBsKtmN4KJpPjWFVy44O6IRETEGbw+qVDzO88yJfYWLGx0PD+D775zdzQiabvpJrjztovUZgelblJSkdsCb2jCMcrS1ZrDv/+6OxoREXEGNb8Tp/r3XzjVqAPxFGBkyDw2bwabzd1RSX6S5feCbdugXj1YvBjatcu1+AQmToTAh++mOetYNvE/HnrI3RGJiEhOef1IhXiWa6+Ff6r3pSMLORx+jiVL3B2RSDrCTeUnQjRSkduaNoW5dKMhm9m79KC7wxERESdQUiFOV2PkrfiTQC9+Z+JEd0cjko7wcNPduUwZd0eS71x7LSy03UwCvgSvmOvucERExAmUVIjTdRtagXX+rQllOr/+iipBiUfZuhWio4EtWzRK4SaFC0O5esVZwfVce2gOcXHujkhERHJKSYU4XYECcPqmULoyj4DE83z6qbsjEknRrRsEB8POmeFY9ZRUuEu/fnCyeXe6+S8g8YKyChERb6ekQlyi0cuhFCKWrszj008hPt7dEUlel5VKcMeOwf79YEtKoHLMdmz1lVS4y8svQ9/Pu+Eff57ADcvdHY6IiOSQkgpxiXI31GBvcCNCmc7x4zB9ursjkrxu+PDhhIeHs3bt2nT3Se5PUY29BFhxmv7kbtdeC+XLw5w57o5ERERySEmFuE6fUHoyiwG946hRw93BiKR00g7hUuWn+uqm7VY2G3TvrqRCRCQPUFIhLlP1iVCCiWTK/QtRb0LxBMkjFfXZQlKx4lC2rHsDEs7f1A22bePijr3uDkVERHLA65MKddT2XLYG9aFWLc19Eo+QmAhr1pj7zQPD8akfos6Mbvboo3DNnZ24iB8nvlFpWRERb+b1SUVW5lGLm9hs0LcvzJgBCQnujkbyuS1b4Px5c79xgXCtp/AAFStCFEEs40aSZmsKlIiIN/P6pEI8XGgonDrFxUXL+OknDVqI+yRPffIhkUrRW5VUeICmTc2fc+hO2S2LIDbWvQGJiEi2KakQ12renKTyFfm2z3Ruuw1Gj4akJHcHJflR8iLtKuzHPyFWi7Q9QHJSMZduFEiIgSVL3BuQiIhkm192Dtq/fz8HDhygZs2aXHPNNVk65tixY2zevJkGDRpQrly5VM/t27ePXbt2pdrm7+9P27ZtsxOeeBKbDZ9+odwyaRo2PmDHDh8WLoSbb3Z3YJLfnDpl/rzWZwskoZEKD1CiBFStCuH7Qjhgq0yl2XOwdeni7rBERCQbHBqpSExM5K677iIkJIQRI0ZQvXp1Ro4cmeExW7ZsYeDAgTRv3pybb76ZBQsWXLXP5MmT6du3L2PHjrXf3nvvPcdeiXiu0FBKxx+mBWbdy8SJbo5H8qUZM+DsWfjggXAICjL9EcTtzGiFjdlWdy7O1LoKERFv5VBSMWHCBGbOnMmmTZtYv349y5YtY8KECUydOjXdY/bu3UufPn3Ys2dPhueuV68eCxYssN9+++03R0ITT9amDVbp0txZxCyo+P13OHDAzTFJvlSsGFQ5f2mRtio/eYRUU6D274KdO90bkIiIZItDScXXX3/NgAEDqFmzJgDNmzenc+fOfP311+ke07NnTwYNGkSBAgUyPHd8fDyrV69m06ZNxGqxXt7i64vt1lu5rcA0wCIpCSZNcndQkm+Fq/KTJ0lOKhbRgQTfAjBXpWVFRLxRlpOKhIQENm/eTNPk3wCXNG3alH/++SfHgWzevJmHHnqI0NBQypUrx+eff57h/nFxcURGRqa6iQcLDaXEmd008f0PgM8/h7g4N8ckeUqWetYkJcHWrVqk7UGSf6Wcpwj/BLVVd20RES+V5aQiOjqahIQESpQokWp7yZIlOXv2bI6CuO6669i3bx/r169n9+7djBkzhvvvv5/ly5ene8yYMWMIDg623ypVqpSjGMTFOnSA4GCerWumQJ08CT//7OaYJE9Jr2eNZUGbNnD33fDrBwdMswqNVHiMsmXN8hYfH/g7uDv89VdKQxEREfEaWU4qkqcvxcTEpNp+4cKFTKc2ZaZjx46Uv2zR5LBhw6hXrx7Tpk1L95jRo0cTERFhvx08eDBHMYiLFSgAvXrRLSalUYUWbEtu2LMH/v4bvv4a/vkh3GxUUuFRFi2CqCh4bF43M4S5eLG7QxIREQdlOakIDAykdOnSHDp0KNX2Q4cOUbVqVWfHRalSpTh69Gi6zwcEBBAUFJTqJh4uNJTCe/6jZx2zEHP1ariikrCI0yU3vQNoUyIcihQBjWx6lDp1IDAQqF0bqlfXugoRES/k0ELtzp07M2PGDPvjixcvMmvWLDp37mzftmfPHpY42MAoIiIi1eNjx46xceNGGjVq5NB5xMN16QKFCvFK4+mMHGmKvFxa8y/iMslN7wBCCId69VT5yVPZbNC9u1lXYVnujkZERBzgUPO7559/npYtW3LXXXfRs2dPvv/+e+Li4lL1qvj22295//33OXfuHABnzpxhw4YN9ue3bNnCggULqFChAvXq1QPg5ptvpmvXrjRp0oRTp04xbtw4KlasyLBhw5zwEsVjBAZCt2402TudJj897e5oJJ+4fKSi7JlwqK+pTx6tWzeYMAG2bTMJoIiIeAWHRirq1KnD6tWrCQwM5Ouvv6Zq1aqsXr06VYfs6tWr065dO/vj/fv32xvadezYkbVr1zJ27FjmXja8vXDhQooWLcr333/PsmXLePjhh9m4cSPFihXL8QsUDxMaCmvWgNbASC6IjYWNG839unUs/LaHq/KTh/rsM7j9duj4ajusggU1BUpExMvYLCtvjDFHRkYSHBxMRESE1ld4sogIKF0axo2DRx4BICHBVH7xcSjFFUnb5e8FW7YEcf31Zvvj/Q7y7i+VYdYs6NHDvUHKVbp0gfnzzf0L7btTyCceFixwb1AiIpJl+hgnuSs4GDp1gmnTOHECXn/drMucN8/dgUl2LFmyhNGjR/P8889fVco1Pf/++y/PPPMML7/8slPPm5bLpz51uEaVnzzZ5S2QdtbqDkuXmpJQIiLiFZRUSO4LDYVly1g35wTPPWdmQn30kbuDEke9+eab9OjRg4SEBM6dO0ebNm346quvMjymXbt2hIWF8ffff/Pdd9857bzpuXyRdmP/cChUCKpUyda5xLUuTyoWB3SDixdh4UL3BSQiIg5RUiG5r3dvALrEzbRX9pwzB/budWNM4pCjR4/ywgsv8NFHH/H222/z4Ycf8uKLL/L4449z4cKFdI8bO3Ys//33Hx07dnTqedOTPFJRqBCUP3ep8pPm2Xmky5OKhftqmPKyWlchIuI1vP6368SJEwkJCaFFixbuDkWyqnRpuOkmfGdM58EHzSbLgo8/dm9YknXJhRb69etn33bHHXcQERGRYUnp1q1bu+S8abEs+OorGDMGHn8cfLZpkbYnq17dzI4E2LABlZYVEfEyXp9UDB8+nPDw8BzNuxY3CA2FBQu4b0AEyQ3Zv/gCrmjYLh5q586dlCtXjsDAQPu2SpUq4e/vz86dO3P1vHFxcURGRqa6gWl50K4dPPMMvP6aBVu2aD2FB7PZoEkTc//wYTjbuhscOgSbN7s3MBERyRKvTyrES916K1y8SOnVs+jf32w6cwamTHFrVJJFMTExFC1a9KrtRYsWzdY0pZycd8yYMQQHB9tvldLqln30qKk8pqTCo10+BWptoZtMbxtNgRIR8QpKKsQ9KlWCli1h+nSGD0/ZPHGi+0KSrCtSpIi9wWUyy7JyXNI5O+cdPXo0ERER9tvBtHqghKvykze4PKlYt7kgdOxopkCJiIjHU1Ih7hMaCnPn0vraC/ZpD+vWmd544tnq16/PsWPHOHv2rH3bjh07SExMJCQHH9yzc96AgACCgoJS3QA+/RTWroX4eExSUbAgVKuW7djE9S5PKuzrKpYvN6NMIiLi0ZRUiPuEhkJMDLb5f2i0wst069aNwMBAPv30U/u2iRMnUqFCBW644Qb7tocffpi//vrL6efNiiefNINhd96JSSrq1gVfX4fOIbmrdm24+2547z146imgWzdITIQ//3R3aCIikgk/dwcg+VitWtCwIUybxm2f9uHJJ0137TJl3B2YZKZYsWJ8+umn3HPPPSxfvpzY2FhWrVrF9OnT8ff3t+83ceJEatasSbt27QB477332L17N2vWrOHUqVM8/PDDALz22msUK1Ysy+d1RIsWwG9apO0NfH3hyy8v31LF/L3NnQuXVQQTERHPo6RC3Cs0FN57j0C/eGbNKkDDhpDGOl3xQIMGDeL6669n0aJF+Pn58d1331GuXLlU+3z44YfceOON9sdVqlTB39+funXrptrv8oQhK+d1ROtWFry+Bbp2zfY5xI26d4fJk01pWZvN3dGIiEg6bJaVN4qAR0ZGEhwcnOOFopLL/v0XGjUy30TqQ584QfJ7AUTg5xdE5M7jFKpWDqZPhz593B2eOGrRIrNge8OGlJqzIiLicbx+TYWa33m5hg2hZk3zgU/ECS5f09uoERTaq8pP3iY6Gv7+G/74A2jTBooUUWlZEREP5/VJhZrfeTmbzUyB+u03syDzkjNn4Oef3ReWeK8NG1Lut26NWaRdoADUqOG2mCTrEhKgbFmTSzz2GObv7uabVVpWRMTDeX1SIXlAaCicPGlKRwIvvggVK8KAAZCD5syST61bl3K/VStMJ+06dcBPS8i8gZ8f1K9v7u/YAVFRmHUVK1eabxtERMQjKakQ92vRAipUsE+BKlwYYmLMUx9/7Ma4xCtdPmhpH6nQ1CevktyvwrJg0ybMequkJJg/361xiYhI+pRUiPv5+JgFtNOng2Vxzz0QEGCe+vJLOH/eveGJ97CslKSieHGzXEdJhfe5qglexYpw7bVaVyEi4sGUVIhn6NsXDh2CdesoVQoGDTKbIyLghx/cG5p4j/PnoW1bc79ZM7CdOmmm1imp8CqXJxXr11+60727SSqSktwSk4iIZExJhXiGNm2gVCmYNg2ASz3RANNhO28UPhZXmjhxIi1bhrBli6kE9/33wNat5snkSfriFRo0SFkCY194362bSRDtWYaIiHgSJRXiGfz8oHdvk1RYFs2bQ8uW5qlNm2DFCveGJ57vykpwBQtiFmn7+V2aByXeomDBlDwwPBwuXACuuw6Cg1UFSkTEQympEM8RGgq7dpkPgsDw4SlPTZzoppjEu4WHQ+3acFnHbvEOyVOgkpLgv/8wf4edO2tdhYiIh1JSIZ6jY0cICrJXgRowwMyIApg6FX75xY2xiXfSIm2vddVibTBToNasMdOgRETEo3h9UqGO2nlIQAD07GlPKgoWhEcfNU8lJqZuaiaSJUoqvFZyUlGzpikQB5jSspZ1qdW2iIh4Eptl5Y0lsJGRkQQHBxMREUFQUJC7w5HsmjYN+vUz06Bq1CAxEe67D4oUgQ8+MA24RTJify/Yu5egatVgyhQz7CVe5eJFs5YiOPiKJ5o1g7p1L63EFxERT+H1IxWSx3TtaoYoLo1W+PrC55/D++8roRAHbd9u/tRIhVfy908joQBTWnbePDN8KSIiHkNJhXiWwoVNYnEpqQAz9cHnin+py5fD2LEqNSsZ2LbNZKW1ark7EnGmbt3gzBmztkJERDyGkgrxPH37wqpVcPhwmk+vW2e+rBw9Gp59VomFpGPbNjMhP7k9u3g1+//zVq2gRAmVlhUR8TBKKsTz9Oxpegv8+muaT69eDVFR5v7YsfDYY2qyK2nYvl1Tn7zc0aNwzz3QuDGMGHFpo68vdOmi0rIiIh5GSYV4nmLFTHnZy6ZAXW74cPj445THH35oFnNrirWksm2bOml7ucBA+Oor0wBz9erLnujWzXTWPnbMbbGJiEhqSirEM4WGwpIlcOpUmk8/+CB8803KWosvv4Q77jAVY0QA8zW3Riq8WnBwSjP0TZsgIeHSE126mMoN8+a5LTYREUlNSYV4pltvNZOoZ85Md5c774SffjIzpQB+/BH694e4uNwJUTxLmj1rlFR4veR+FbGxZvAJgDJloEULTYESEfEgXp9UqPldHlWmDNx4Y7pToJL172+WXiSvxZ0xA265xdS3l/xl+PDhhIeHs3btWrPBZoPatd0blORYmp21wVRr+OOPy4YvRETEnbw+qbjqg4TkHaGh8OefEBmZ4W49e8KsWWb+NZhDli7NhfjEs1WrBoUKuTsKyaF0k4pu3SAiAlauzPWYRETkal6fVEge1qcPxMfD7NmZ7tqpk/nSMjgYPvvMtLqQfK5OHXdHIE6QblLRvDmULq3SsiIiHkJJhXiuypXNB4dMpkAla9MGdu2Ce+91cVziHerVc3cE4gQlS0KVKub+xo2XlY/28THfHmhdhYiIR1BSIZ6tb1/zTWRMTJZ2L1Xq6m0//wxHjjg5LvFcyU1M6tZ1bxziNMmjFdHR5osDu27dTFmodBpliohI7nE4qVi5ciWhoaE0a9aMQYMGsXnz5iwdc+edd9KgQQNmzZrltPNKPhAaalZdZ2EKVFp++AEGDjRrvvftc25o4qG2bzd/avpTnpHuFKjOnc2IhUYrRETczqGkYuPGjbRv356aNWvy/vvvU6RIEdq0acO+DD6tjR8/nscff5wOHTqwZcsWzp0755TzSj5Ruza0bQvPP2/WVzggPh5eftlUpt2zB266CXbscFGc4jmSkwpVfsozuneHN980RRi6dbvsiZIloXVrJRUiIh7AZlmWldWd+/bty5kzZ1i8eDEAlmVRt25dbr75ZiZMmJDmMTExMRS6VIHFZrPx3Xffcfvtt+f4vFeKjIwkODiYiIgIgoKCsvqSxBv89x80aQKvvw5PP+3QoYcPm0XcyfXty5aFBQugQQMXxCkeIfL99wl+/HG9F+QXb74JL70EBw6YhdsiIuIWDo1ULF68mO7du9sf22w2unfvbk8G0lIoCyUds3NeyUcaNoRHH4VXXoGDBx06tEIF05j72mvN4+PHoV07WL/e+WGKh7jnHndHILlp6FAzBerDD90diYhIvpblpOL8+fOcPXuWa665JtX2a665hoMOftBzxnnj4uKIjIxMdZM87KWXICgInnjC4UPLlIHFi00DXoDTp6FDB/j7b+eGKCJuULIk3H8/TJiQskhfRERyXZaTioRLXUsLFCiQantAQAAXL17MdgDZPe+YMWMIDg623ypVqpTtGMQLBAXBuHHwyy8wf77Dh5coYaY93XijeRwZadZ4Llrk5DhFxCXi4mDdOvj00ysWa4P5siEqyjSpERERt8hyUlG0aFEKFCjA6dOnU20/ffo0pdKq4+ni844ePZqIiAj7LSejJeIlbrvNLNp+5BHzCcNBQUFmPefNN5vHFy6YU54/7+Q4RcTp5s41o40PPJBG65pKleD22+Hddx0u6CAiIs6R5aTCx8eHxo0bs3r16lTbV6xYQbNmzbIfQDbPGxAQQFBQUKqb5HE2G0ycCLt3mw8P2VC4MMycCb16QWAgTJtmton3mzhxIiEhIbRInucmeUq6ZWWTPfWUqczw/fe5FpOIiKRwaKH2Aw88wC+//ML6S6tc58+fz19//cX9999v3+ejjz7i+uuvdyiIrJxXBID69WHECHj1Vdi/P1unKFjQJBN//226cEveMHz4cMLDw1m7dq27QxEXqFTJLJ8AU2jhqrqF9epB796mGpS97baIiOQWh5KKe+65h+HDh3PDDTdQoUIFbr31VsaMGZOqctOJEycIDw+3P161ahUNGjSgwaUanqNHj6ZBgwa8+OKLDp1XxO7FF6F4cXj88Wyfwt8fGjdOvc2ytHhbxFPZbCmjFSdOwJEjaez0zDOmT8mMGbkam4iIONinIllUVBTHjh2jQoUKBAYGpnruxIkTnD59mnr16gGmutPevXuvOkeJEiUoX758ls+bGfWpyGemTIFBg2DOnCu6YWWPZcHo0eZLznffzVG+Im6m94K865lnzP9RSJnGeJV27SAmBlatMpmIiIjkimwlFZ5IHyTyGcsyXe3274fNm82cphxYsCBlATfAa6/B//6XwxjFLfRekHdNnQoDB5r7L71kBi2vMm+e+aJh0SJo3z43wxMRydccmv4k4jFsNlOXfv9+eOedHJ+uY0fzISXZc8/Bs8+mMW9bRNwm08XaAF26QKNGMHZsrsQkIiKGkgrxXvXqmfr0r78O+/bl6FQ2m/nW8623UraNGWPWhGvNp4hnqF7dlIaGDJIKmw2eftr0s9m4MddiExHJ77w+qVAZyXzu+eehVCl47DGnnO7JJ03V2mTjx5u6+ImJTjm9iOSAjw80aWLuHzpkFmynqX9/qFYtZQGGiIi4nNcnFSojmc8VKQLvvWdWbc6a5ZRTPvQQfPWV+QAD8PnncOedkIPG8SLiJE2bQuXKcOutEB2dzk5+fuYbgp9/hl27cjM8EZF8Swu1xftZlplHvWsXbNkChQo55bRTppgmvQkJ5vGjj8IHHzjl1OJCei/I2xITwdc3CzvGxEDVqtCnD0ya5OqwRETyPa8fqRDBZoMPPzTzIS5fFJFDAwfC9OlQoIBpvPXEE047tYhkU5YSCjBfLowYAV9/DceOuTAiEREBJRWSV9SpA6NGmdXVe/Y47bS9eplWGAsXQpUqTjutiOSGYcPMtwIaYhQRcTklFZJ3/O9/UKaM0xZtJ+vYEWrVSr0tNhbOnXPqZUTEQRcvpkxPTFOxYvDgg/DRRxARkVthiYjkS0oqJO8oXBjef98s2J4502WXiY+Hfv1MX62TJ112GXGQKsHlH1OmQMuWULQoLFuWyc4jRphvAbSuQkTEpZRUSN7Spw907WpWVV+44JJLPPYYzJ4N//wD7drB0aMuuYw4SJXg8o8LF2DtWoiLy6BfRbLy5eGuu0yVuNjYXIlPRCQ/UlIheYvNZppLHD3qso66I0ZAhQrmfng43HgjHDjgkkuJSBqy1Fn7ck8+aZpafPONy2ISEcnvlFRI3lOrFjz1lGl85YIa9XXqmCkX1aqZx7t3Q9++apAnkltCQsz6a8hiUlGrlpmz+Pbb+o8qIuIiXp9UaB61pGn0aLjmGjMNygWtWKpVg6VLoUYN83jdOvjiC6dfRkTS4O8P115r7m/fnkETvMs9/bT5BmDaNJfGJiKSX6n5neRdM2aYtru//mr+dIElS8y6CoASJWDHDihZ0iWXkizSe0H+8OCD8Mkn5v7y5XDDDVk46Oab4fRpWL/eTJUUERGn8fqRCpF03XILdO9uVlafP++SS7RtC7fdZu6fOWOq2oqI6zm8rgLgmWdg40b480+XxCQikp9ppELytt27oX59GDkSXn/dJZc4csSss4iONl9+rlkDzZu75FIex7Is9uzZg5+fH1Wy2B0ws2M2bdrElW9LFSpUoHTp0lk6v94L8od16yB51uuQIfDVV1k4yLJSatEuWuTK8ERE8h2NVEjeVqOG+Xby7bfN3CQXKF8eXnzR3B80yDzODzZt2kSdOnVo1aoV1157LU2aNGFPJt3Ms3JMs2bN6Nu3L0OGDLHf5s+f78qXIl6oQQPw8zP3szxSYbOZ94PFi2H1apfFJiKSH2mkQvK+mBgzWlGrFsyb55K51BcvmhGKLM3rzgPi4+OpW7cuN954I1999RWJiYn07NmTM2fOpNsnIqvH+Pn5MWvWLLp27Zqt2PRekH80bgybNoGvL0RFQaFCWTgoMRHq1TNZyfTprg5RRCTf0EiF5H2FCpneFfPnu+xDhL9//kkoABYsWMDevXt5+eWX8fHxwd/fnxdeeIF169axcePGHB9z7tw5tm3bRkxMTG68HPFSr7wCs2bBwYNZTCjAZCBPPQW//QbbtrkyPBGRfEVJheQPPXtCr16mc52LFm1fKT4+Vy7jFuvXr6dMmTJUrVrVvq1169bYbDY2pDMXxZFj7r33Xnr06EFwcDCDBw/mzJkzrngZ4uVuuQV69DDVox1yxx1QrpyZFikiIk6hpELyjw8+gFOn4NVXXXqZpCTTuLdqVfjnH5deym1Onz5NyStq5/r6+hIcHMypU6dydMzbb7/NuXPn2L17N1u3bmXdunUMHTo03Vji4uKIjIxMdRPJUEAAPPEEfPcdHDrk7mhERPIEr08q1PxOsqxaNdMUb9w42LrVZZf59ltTjeboURg+3CQZeY2/vz9xcXFXbY+Li8Pf3z9Hxzz++OP2xzVq1ODFF1/kt99+IyoqKs3zjhkzhuDgYPutUqVK2XlJ4uXOnzeFErZsyeIB998PhQvDe++5NC4RkfzC65OK4cOHEx4enu7iUJFUnnoKqlSBRx5xSadtgMGDoXZtc3/FCvNlaF5TqVIlTpw4QdJlGVNERAQxMTHpfqjPzjFgyslalsXhw4fTfH706NFERETYbwcPHszmqxJvFR1tWtJMmQIdO2ZxqURQkMn6P/nENJkREZEc8fqkQsQhBQvChx/CwoXw888uuUSBAuYSyZ56CiIiXHIpt+nQoQPR0dEsXbrUvu3333/H19eXtm3b2rf98wEUE90AACF6SURBVM8/nDx5MsvHpDWSsXjxYgoVKpRuH4yAgACCgoJS3SR/SUyECxfM/ePHoUMH2LkzCwc++qg5eOJEl8YnIpIfKKmQ/KdbN7j1Vnj8cVOH0gU6d4bQUHP/xImUPhZ5RYMGDRg0aBD33HMPM2bMYMqUKTzxxBM8+uijlClTxr5fkyZN+P7777N8zPfff8/tt9/Or7/+yvLly3nppZcYO3Yszz//PIWyXN5H8pvgYFPcrXFj8/joUZNYZNI2BcqUgXvuMdXhkrMSERHJFvWpkPxp3z4ICYGHH4a33nLJJQ4cgLp1TZsMX1/YuBEaNnTJpdwiLi6Ot99+m3nz5uHn58ett97KI488gq+vr32fxo0b8+STTxIWFpblY3777Te+//57jh49SrVq1bj77rvp0KFDluPSe0H+dfo0tG8P//1nHlepAkuWmD/TtXev6WHz/vvm/UBERLJFSYXkX6+/Di+9ZLpnhYS47BLPPWfu33ij+YDjgt57chm9F+RvJ06YxCI83DyuXt38v6tYMYODwsLg77/NnKl0Cg2IiEjGNP1J8q9Ro0xFqOHDXbZoe9QoqFnT3F+2DH74wSWXEZFLypQxS6bq1DGP9+wxU6GOHMngoKefhv37zUpvERHJFiUVkn8FBJgV1X/9BT/95LJLjB+f8vj11/NmiVkRT1KuHCxalJLQ79xpum+n69przVqrsWP1H1REJJs0/UmkXz9T+3XbNlNm0gVCQ6FYMfOZ5bJ1zOICei+QZAcPQtu2ZtRi+nTIcK3/0qVm599/h549cy1GEZG8QkmFyIEDUK8ePPigaYznAgkJ4OfnklPLFfReIJc7fBhKljTVpDNkWXDDDaaqwrJluRKbiEhe4vXTn9RRW3KscmV4/nn44APYvNkll1BCIeIeFSpcnVAcOQLnzl2xo80GzzwDy5ebm4iIOEQjFSIA8fFmXnXZsmaNhYtLNJ0+Dbt2QatWLr1MvqT3AsnIwYOmOlTJkvDnn1fMeExKMnWfq1c306BERCTLvH6kQsQpChSACRPMvOpLzdpcwbJg0iSoXduss3BR7718SaOWkhnLggEDYPduWLPGrM1O9X/Qx8dUgpo1K6XZhYiIZIlGKkQuN3CgKWq/fbtp0+sCPXvC7Nnm/pNPuqz3Xr6l9wLJyH//mZGK06fN45tugjlzoHDhSztcvAg1aphF299957Y4RUS8jcNJhWVZrFy5kv3791OrVi2aN2+e42P+/fdfNmzYkGpbgQIFGDx4cJbj0gcJcYpDh0wb7KFDTYddF9i9G+rXh7g4s9bi33/NOnFxDr0XSGb++cf0rjh71jzu0MEMTtirQ33wAYwcaeYoVq3qpihFRLyLQ9OfYmNj6dy5M3379uWnn36iS5cuDBw4kMTExBwdM3PmTJ588kn++usv+225FsqJO1SsCC++aPpXbNrkkkvUqAFPPWXuJyTAo4+6rPeeiKShcWOYPz9lMHLRIrj1VoiNvbTD0KHmyXffdVOEIiLex6Gk4p133mHz5s38888/zJgxg1WrVjFr1iy+/vrrHB9To0YNvv76a/vto48+ys7rEcm5xx4zhe1d2Gn7mWegShVzf8ECmDbNJZcRkXQ0bw5//AFFi5rH8+dD375mBJHChU22//nncPKkW+MUEfEWDiUVP/zwAwMHDqRs2bIA1KpVi+7du/PDDz/k+Jjo6GimTZvG7NmzOXLkiKOvQ8R5khdt//23y+ZUBwamnl31xBNw/rxLLiUi6WjVKvV6ijlzzLKqixeBhx82VeA+/NCtMYqIeIssJxUXL15k+/bt1K9fP9X2Bg0asDmd2v6OHHP06FG+/fZb3nrrLapVq8Yrr7ySYTxxcXFERkamuok4TYcOMGiQWUl9VUF75+jdG7p2NfcPHoTXX3fJZUQkA23amMIJyespKlW61FemZEm47z7zBYPKtImIZCrLSUV0dDRJSUkUK1Ys1fYSJUoQERGRo2M6d+7M/v37mTFjBkuWLOHnn3/mxRdfZO7cuenGM2bMGIKDg+23SpUqZfWliGTNuHFw4YJpjOcCNhuMH28GRgDeeQd27HDJpUQkA23bmrYUTz9t/k/a29Q88YRJKD77zK3xiYh4gywnFYUufY1z/oo5GlFRUfbnsntMy5YtKVKkiP3xLbfcQuPGjZmdXHczDaNHjyYiIsJ+O3jwYFZfikjWlC8PL78MH30EGze65BK1asGoUeZ+UBDs2eOSy4hIJjp2hLFjr+h7WbkyhIWZBdvx8W6LTUTEG2Q5qShYsCDly5dn3759qbbv27ePGjVqOO2YZIGBgZxOLiSehoCAAIKCglLdRJzukUdMvdfhw023XRd49lkYPdqMUiRPhxIR91u7FsYmPQWHD8Pkye4OR0TEozm0ULtnz55MmzaNhIQEwIxA/P777/Ts2dO+zz///JNqEXZWjjlw4ECq6+zevZsNGzbQunVrx1+RiDP5+8PEibByJXzzjUsuUbgwvPEGlCjhktOLSDasXAmdOsHo70JYX70/1ogRpg23iIikyaHmd4cOHaJly5Y0bNiQrl278vPPP3Pq1CnWrFljXzfx0ksv8f7773Pu0uLWrBzTpk0bateuTZMmTTh16hSTJk2iXr16zJ07N92pVVdSwytxqdtvN/Und+yA4sXdHY1kQO8F4gzTpplKUImJUJho1pXsQpXz4Xxz5yKOXdPEvl9oKFx7bcpxR4/CJ59k7RpPPnlZJ28RES/ncEft48eP8/nnn3PgwAFq1arFfffdR3ByByHgt99+Y/78+an6TGR2TGJiIlOnTmX16tUEBgbSsmVLevfujS3V5NaM6YOEuNTRo6bTdliYWWPhQseOmSlRzz4LNWu69FJ5kt4LxFl++AHuuMPMfAwigj+5mersoT2L2UxDwFSdvv32lGM2bIBmzbJ2/hMnoHTplMcXLphK1jff7MQXISKSSxxOKjyVPkiIy33wATz+uJlondVPDQ5avhx69IDISPPnrFkuuUyeNHHiRCZOnEhiYiI7duzQe4E4xbffwr33QkICFOMsi+hAeY7QliVsp67Tkorz56FXL1iyxCQzAwc6/7WIiLiSkgqRrEpIgKZNTUH7lSvBx6ElSVkSHW0GRA4fNo9nzjQfNCTr9F4gznb0KPz7r7nvH3GKFk+3xz/yNGvfXkKNrrUoXz5l38hI8/aQFe3bp5SUHj8eHnvM3Pf1halTzdQqERFvoaRCxBHLlsFNN5m69UOHuuQSU6aYvnsA1arBli0pjbkkc3ovEJc7fhzatTPfAixdav6j5lBSEjz4YEpLDD8/s67jlltyfGoRkVzh/K9aRfKyG2+EO++EZ56BDEoe58SAAaahN8DevfDWWy65jIhkV9mysHAhFCxo/rM6oU+Sjw9MmgRDhpjHCQnQrx/MmZPjU4uI5AqvTyomTpxISEgILVq0cHcokl+89RZcvAj/+59LTm+zwYcfmm8qwTTk2rvXJZcSkewqXx4WLTL3O3SAI0dyfEofH/j8cxg82Dy+eNFMgZo/P8enFhFxOa9PKoYPH054eDhr1651dyiSX5QtC6+9Bp9+ahZtu0BISMr86thYGDHCJZcRkZyoVMkkFrGxpiX38eM5PqWvr2mJM2CAeRwXB717p+QvIiKeSmsqRLIjIQFatDDDCatWmU8CThYVBXXqmEWiALNnQ/fuTr9MnqP3Asl1O3dC27ZQsiQsXgylSuX4lBcvmgpQv/5qHgcGmuUbLio8JyKSY14/UiHiFn5+ptP2unVmvoILFC0K77yT8vjRR823liLiYWrVMmssTpwwTSbOns3xKf394aefoGdP8/iGG6BevRyfVkTEZZRUiGTX9dfD3XebRdsuaihx222m2FS5cvDyyynlJ0XEw9SrBwsWmEXbXbpARESOT1mgAPzyi/m/P3OmGa0QEfFUmv4kkhOnT5tVlfPnm4nPH3wAVao49RIHDkCxYqB/1lmj9wJxqw0bzPqKkBD44w8oUsQll7EsU9RBRMRTaKRCJCdKloR58+Dnn81UqHr1TLmm+HinXaJyZSUUIl6jaVOTTPz3n+lceeGC0y9x+DC0aZPSkE9ExBMoqRDJKZvNFJTfuhUeegieew4aNXJpuRYnzKwQEVdp2RLmzjXV4W691VSHcpLDh82a8BUrzIDIli1OO7WISI4oqRBxluSV1Rs3mhGMjh0hLCylfJMTHDxoSk22bKlF2yIe7YYbzFqr5cuhb1+n/YcNCoLSpc39U6fM28y2bU45tYhIjnh9UqHmd+JxGjY0tR+/+sqstahb13SzS0jI8amHDjUzrXbsgPfec0KseYjeC8TjtGsHM2aYylADB5o6sTlUtKiZcdm8uXl8/LjpvbdzZ45PLSKSI1qoLeJKZ86YztuffAKNG8NHH0Hr1tk+3T//mDr1SUmmEsy2bab/lqTQe4F4nNmzoU8fMxXqhx9MSeocOnvWJBP//GMeV6xovsuoVi3HpxYRyRavH6kQ8WglSsDHH5sGeTYbXHcd3H+/qRqVDY0bw7Bh5v6FCzBypPNCFREX6dEDpkyB6dNNGerExByfsnhx+PNPMzAKcOgQtG8P+/fn+NQiItmipEIkN7RsCWvWwIQJMHWqaZX95ZdmyMFBr76aMqf6559NaXwR8XB9+phRih9+MF8sZOP//pVKlTL//5Ob4u3fb0YvDh3K8alFRBympEIkt/j6wvDhZs5St25w771w440O14UsXtxUrU32yCNOrWArIq4yYAB8841Zb/Xww6bZRA6VKWOWbNSubR7v2WO+rxARyW1KKkRyW7ly8N13sHixmRjdtCk88QRERmb5FEOGQKtW5v62babnnoh4gdtvh88+M9MiH3/cKYnFNdeYCtY1asCjj8LzzzshThERB2mhtog7xcfD++/Dyy+bttnvvQf9+2epVe769dCihflMUrgwbN8OFSq4PGKPp/cC8QoffWRGLp96ygw9OqE99pkzZiRTnbZFxB00UiHiTgUKmA8VW7eaoYeBA6FzZ1MzNhPNmsEDD5j758/Dt9+6OFYRcZ6HHjJfIrz1Frz0klNOWaLE1QnFv/+aZENExNWUVIh4gsqVTWWYWbNg925T0uX55yEmJsPDXnsNmjSBX36BZ57JpVhFxDlGjDCjFK+8Am+84fTTr11rum937gznzjn99CIiqWj6k4iniYmBMWPgzTfNfKbx46Fnz3R3tyxNd7ic3gvE67zyCrz4ohmpfPhh0407h/+pExOhfn0zLRLMQOj8+aYjt4iIK3j9SIW66EqeU6iQ+ZCxeTPUrAm9eplylOkUoFdCIeLlnn/eNMjcsMFUhLv2WrPmwoHiDVfy9TWDn8nlp1evNkXnoqOdFLOIyBU0UiHiySzLzG0aMcJUinrhBVMpqkCBdA+ZPdsUlLrmmtwL05PovUC8VlKSqQ/78ccwc6b5guH2203Hy2uvzdYp//vPNMU7fRp8fMwMy27dnBy3iAh5YKRCJE+z2Uw1qG3bzAeL556DRo1MOdorHD4Mt9xiZko9/bQbYnUzjVqK1/PxgZtvNkMM+/fDyJEmuWjUCNq0ge+/h7g4h07ZsKFpkFe6tOm7p4RCRFxFIxUi3uTff03VmL//hrAweOcd0/cCOHXKNMA6e9bsumyZ+RyS3+i9QPKUixdNYvHxx2YUo1QpuOceU/qtevUsnyYqCooWdWGcIpLvaaRCxJtcey0sXWo68v7xB9SpAxMmQGIipUrB66+n7Dp8OCQkuC9UEXECf3/o29cMN2zbBnfcAZ9+atZbde8Ov/9uVmVnQgmFiLiakgoRb+PjY1pqb98Ot91mWui2aAGrV3P//WY9BZhBjY8/dmukIuJMderAu++auY5ffGGGJ2+5xYxYvP46HD/u7ghFJB9TUiHirUqUgEmTYOVK8/i66/B96IH/t3f3QVHVaxzAv7QqiC6KGAgEyOhgqaDDuyav6XQ1awQRzElGCbByHF9Cs3yhtLlZKjQ3J6kRTQFB7a6LqVdHBlHKwhdA1gEZBHEJXxBBFkRQhPvHDhsLmN67B8/u8v3M7B/7O/I8zwos59nzO78fkv75105XGzbwPIPI6JibA4sXA+fPqzejmD5d3VQ4OADz5wNnzqgXeSAieoHYVBAZOh8f9YnFv/4FZGTA671xSJ62ByZoR0MDN8UjMmqenuqrFtXVwNatQGEhEBgITJyonhrZ0CB2hUTUT7CpIDIGEol606zSUuAf/0DUr1E4J/GHK4rw738DNTViF0hEfcrSEli+HCgpUd/QPX48sHKlegPN2FigoEDsConIyBl8U8FlJIm6GDUKSEkBsrPhMvIeCkzccXNBHKxf5lQIon7BxAQIDgYOHQKUSvX60v/5j/pmqylTgEuXxK6QiIwUl5QlMlIdrY9g8m2i+jLF9u1il/PC8L2AqJu2NvWudzt3qh//w1K0RETPi00FERkVvhcQERG9eAY//YmIiIiIiMTFpoKIiIiIiHQyQOwCiIh00dLSgtraWs3zxsZGAOppUET0bFKpFCYmJmKXQUQGjk0FERm0L774Alu2bOkx7uDgIEI1RIaH9x8RkRA4/YmIDFp8fDyqqqo0j/PnzwMAiouL0dDQoHm4uLhoPddlrKqqCgBQVVXVb3MYw2tgDvVDKpW+oN9WIjJmRnOlQiqV8s2RqB8yMzPDK6+80mNcKpVqffoqkUh6fBqryxgAWFhY9NscxvAamIOISDhG01SYmJjwTZKINB8sdP+AYenSpT3+rS5jvelPOYzhNTAHEZFwjGafCiIi4MXsU8Ec+hGfOfQvBxH1X7yngoiMiqmpKeLj42FqasocIucwhtfAHEREz4dXKoiIiIiISCe8UkFERERERDphU0FERERERDphU0FERERERDoxmiVliYj62oMHD5Ceno60tDRIpVIcOXJE0PgdHR2QyWSQyWSorq7GmDFjsGzZMkyePFnQPHK5HAcPHkR1dTVGjx6NmJgYTJs2TdAcndLS0pCYmIiIiAisXr1asLiLFy+GQqHQGps1axY2bdokWA4AyM/Px44dO1BWVgZXV1ds2LABtra2gsROSEjA/v37e4xLJBLk5eUJkgNQf7/T0tJw+/ZtWFtbIywsDO+++65g8YmIADYVRETPbdKkSfD394e9vT1+/fVXweOvWbMGlZWVCAkJgb29PQ4fPgxvb29kZ2cLdtL/9ddfQ6FQICQkBDY2Njhx4gQCAwNx7NgxvPnmm4Lk6FRaWoq1a9fCxMQEN27cEDR2SUkJvL29ERUVpRmzsrISNMeRI0cQHh6OlStXIioqCuXl5YiJicHRo0cFiT9v3jz4+/trjc2fPx8uLi6CxAeAn376CbGxsfjmm2/g6emJoqIiREVF4c6dO1ixYoVgeYiIuPoTEdFzamxshFQqxZdffoldu3ahsrJS0PjNzc0wNzfXGgsICICdnR3S09MFydHS0gIzMzOtMR8fH0yePBk//PCDIDkAoLW1Fb6+vli7di22bt0KX19f7NixQ7D4vr6+mD17NtavXy9YzK6am5vh6OiI6OhobNmyRTPe2traZ0uyKhQKuLm5QSaTISQkRJCYoaGhaGtr07qqtnDhQlRXVyM7O1uQHEREAO+pICJ6bt136RZa94aic+zx48eC5ejeUCiVSpSXl8Pd3V2wHAAQFxcHNzc3RERECBq3q/T0dLz++uuYN28e9u7dCyE/Iztx4gTu3buHDz74QGu8L/d4SE5Oho2NDd5++23BYnp7e0OhUKC+vh6AujHOz8+Hr6+vYDmIiAADnv7U0dGBxsZGscsgMkhSqRQmJiZil0HPkJeXh1OnTmHfvn2Cxm1qakJgYCBaWlpQUVGB+Ph4LFmyRLD4mZmZOHbsGAoLCwWL2Z2dnR0CAgIwadIkFBUVYdWqVcjNzcWuXbsEiV9cXAwrKytUV1dj+fLlaGxshJubG9asWQM7OztBcnT16NEjpKamIiYmBgMGCPen+ZNPPsHDhw/h5OQEJycnKJVKREdHY/PmzYLlICICDLipaGxsxLBhw8Qug8ggNTQ0wMLCQuwy6G9UVlYiNDQUERERWLBggaCxBw8ejKSkJDQ1NeHEiRPYtGkT3N3dMWPGDJ1j//nnn4iNjYVMJuvTn7GMjAwMGjQIABAYGAgnJyfMmTMHq1atwvjx43WO39raigcPHuCjjz7C559/DqlUim3btsHb2xtFRUUYMWKEzjm6ksvlqKurw/vvvy9o3MzMTCQmJmLjxo3w9vbG5cuXsWHDBnh4eAj+c0VE/ZvBNhVSqRQNDQ2a5yqVCg4ODqiqqnrqHzIvLy9cuHDhqTF1Of53x8SujfXxe9u9vr6exkO6USqVCA4Oho+PD/bu3St4fIlEAk9PTwDqE/KqqirEx8cL0lQcPXoUTU1NWL58uWaspKQESqUSf/zxB86dO6dpBnTRPcYbb7wBQH1fghBNhZWVFVpaWrBjxw74+fkBUN/HYWVlhcOHDwt+8p+cnIygoCCMHTtW0Lhr167FokWLEBcXBwDw9/dHTU0NPv74YzYVRCQog20qTExMej2Js7CweOrJnUQi+dtPznQ5/qyvFbM21sfv7d/VR/qlqqoKQUFBcHNzw4EDBwSdCvM0NjY2uHjxoiCx5s6dq2lYOkVGRsLV1RWrV6/GwIEDBcnT3c2bNwEAQ4cOFSRe52sYNWqUZmzo0KEYMmQI7t+/L0iOTkqlEllZWUhLSxM0LgDcv39f6zUAgK2tLRoaGtDR0cFpkEQkmH51o/bSpUv77PizvvZZ+rK25zn+LP25Pn2u7XmOk+Gorq7WNBSHDh3qkxPw7du3o7a2VvNcoVAgLS0Nb731liDxX375ZXh6emo9zM3NNeNCnMRevXoV+/btQ3t7OwD1dL4VK1bA1tYWgYGBOscHgKlTp8LV1RXfffedJk9KSgpUKhWCg4MFydFpz549sLS0FGzFp64CAgKQmpqKu3fvAgDq6+uxe/du+Pn5saEgIkEZzZKyKpUKw4YN08u54vpcG8D6dKHPtQH6X5+hWbJkCS5duoRbt26htrYWrq6uAIBffvlFkA3RIiMjkZKSAjc3N62GYty4cYJ9ir1//36sW7cOEokE7e3tqKmp0Syb2n1lKKF4enoKuqSsSqXC6tWrcfDgQdja2uLGjRvw8PDA999/j4kTJwqSAwDKysoQFhaGmpoaDBkyBPX19di+fTsWLVokWI6Ojg44OzsjNDQUCQkJgsXtdOfOHURGRiI3NxfOzs6a/6uUlBQ4OjoKno+I+i+jaSpaW1vx1Vdf4dNPP+3TJf/+H/pcG8D6dKHPtQH6X5+hKS0t7XXVOTc3N0HuE6ioqEBdXV2PcXNzc0HuE+iqsrIS7e3tcHBw6LMpSZ1KSkowZMgQwU9iHz58iOvXr8Pe3r5PF+4oLy9He3s7nJ2dBZ+O9ujRIxQVFWHs2LEYPny4oLG7qq+vx82bN2FjY4ORI0f2WR4i6r+MpqkgIiIiIiJx9Kt7KoiIiIiISHhsKoiIiIiISCdsKoiIiIiISCcGu09FV+Xl5VAoFLC2toavry9eekm/eqWCggKUlpYiODgY1tbWYpej5dq1a7h69Sqsra3h4eEBiUQidklarly5goqKCtjZ2cHDw0Mvl0C8ffs2cnJy4OLiAnd3d7HLAaDeRffhw4daYxMmTNCsVkREREQkJINvKtavX4/ExERMnToVJSUlsLOzw8mTJ2FpaSl2acjKysL69etRV1eHsrIynD59Wm+airKyMsTExKC6uhqvvvoqiouLMXDgQBw+fBivvfaa2OXhypUriIqKwuPHj+Ho6Ij8/HxIpVIcP34co0ePFrs8jSdPniA8PBx5eXmIiYnRm6ZiyZIlcHZ2hpOTk2bspZdeYlNBREREfcKgV3/KyclBUFAQzp49Cz8/P6hUKnh5eSE4OBg7d+4UuzzI5XLY2NjAwcEBDg4OOH36tGAbM+kqPz8fTU1N8Pf3BwC0tbVh9uzZUKlUOHfunMjVAefPn4dUKtU0OI8ePYKPjw/Gjx/fJ7vO/r82btyI0tJSlJeXC7oOv65GjRqFbdu24b333hO7FCIiIuoH9Gue0P8oNTUVXl5e8PPzAwBYWFggOjoa+/fv1+yAKqY5c+ZgypQpYpfRK3d3d01DAQADBgzAO++8g8LCQvGK6sLb21vrismgQYPg7Ozc6x4BYsnJycG+ffuQlJQkdim9Ki0thVwuR35+Ptra2sQuh4iIiIyYQU9/UigUPXZPdXV1hUqlglKp1KtpMoYgKytL0N1ohSCTydDU1IQLFy6gsLAQMplM7JIAALW1tVi4cCFSUlL0Yqpdbw4ePIiCggIUFBRg+PDhyMjI4PQnIiIi6hMG3VQ0NDRgxIgRWmNWVlYAgPv374tQkeHau3cvMjMzcfLkSbFL0XLs2DHU1tbi4sWL8PX1hY2NjdglAQAWLVqEBQsW6M10tu727NmDmTNnAlDvOhwaGor58+dDoVDo3UIGREREZPgM+uzC1NQUTU1NWmOdz83MzMQoySBlZmYiNjYWO3fuxPTp08UuR0tycjIyMzNRUVGBuro6vbhH4Oeff0Zubi4mTJiAjIwMZGRkoL6+HmVlZcjIyNCLqXedDQUADB48GJ999hmKi4tx7do1EasiIiIiY2XQTcWYMWOgVCq1xm7cuAGJRKK16g093ZEjRxAREYFvv/0WsbGxYpfzVKampggPD0dubq7YpWD48OGYOXMmjh8/DrlcDrlcjvr6ely/fh1yuRxPnjwRu8QeLCwsAAB3794VuRIiIiIyRgY9/WnWrFlYtmwZamtrMXLkSADAgQMHEBQUhMGDB4tcnf47evQowsPDkZCQgA8//FDscrTcunULtra2WmOXLl2Cg4ODSBX9Zfr06T2u6Hh6eurN6k93796FpaUlBgz469dbJpPBzMxM7+6ZISIiIuNg0E1FZGQkfvzxR8yYMQPR0dHIy8vD2bNncfbsWbFLAwBcv34deXl5qKurAwBkZ2fj9u3bmDhxougnd7///jvCwsIQEBCAESNGICMjQ3Ns7ty5GDhwoIjVAZs3b8a9e/cwbdo0mJqaIicnBzKZDOnp6aLWZQgUCgXi4uIQEhICOzs7/Pbbb0hLS0NCQgKGDRsmdnlERERkhAx6nwoAaG5uRlJSEi5fvgxra2tER0dj3LhxYpcFADhz5kyv+2WEhYUhLCxMhIr+kpWVhV27dvV6bPfu3TA3N3/BFfV0/PhxnDp1Cs3NzXB2dsbChQthb28vdlm9WrduHcaOHYvFixeLXQoA9S7zqampUCqVcHR0RHh4uF5sakhERETGyeCbCiIiIiIiEpdB36hNRERERETiY1NBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6YVNBREREREQ6+S/vU+ow5tCCaQAAAABJRU5ErkJggg==", "text/plain": [ "Graphics Array of size 2 x 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c_range = [c/10 for c in range(5,30,5)] #breaking up the interval [1/2,3]\n", "K = 100 #how many graphs to sample for each c\n", "n = 1000 #size of graphs to sample\n", "\n", "res = empirical_dists(n,c_range,lambda g: g.triangles_count(),K,scale=lambda n,c:c/n,verbose=True)\n", "\n", "def poisPmf(c,k):\n", " return (c^3/6)^k/factorial(k) * exp(-c^3/6).n()\n", "\n", "\n", "to_plot = []\n", "\n", "for c, data in res:\n", " m = len(data)\n", " to_plot.append(line2d(data,thickness=2,linestyle='--') + line2d([(k,poisPmf(c,k)) for k in range(0,m)],color=\"red\"))\n", "\n", "graphics_array(to_plot,nrows=2).show(figsize=[8,8])" ] }, { "cell_type": "markdown", "id": "a55988a9-75fc-4bac-aa76-56c0c8c886e0", "metadata": {}, "source": [ "## Exercise 4: Diamonds and spatulas\n", "\n", "The diamond and spatula graphs are the two graphs depicted below. Let's try to find their threshold\n", "functions. \n", "\n", "We start with the diamond graph:\n", "1. What is the threshold function for the existence of at least one diamond?" ] }, { "cell_type": "code", "execution_count": 26, "id": "07a37fe0-02f2-4002-a1e7-ae965c6a7165", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics Array of size 1 x 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "diam = graphs.DiamondGraph()\n", "spat = graphs.DiamondGraph() #the spatula is the diamond plus a new edge, so I start with a diamond\n", "\n", "spat.add_vertex(4)\n", "spat.add_edge((0,4))\n", "\n", "graphics_array([diam.plot(), spat.plot()],nrows=1).show(figsize=[3,3])" ] }, { "cell_type": "markdown", "id": "ae5d05f2-26c1-4d2d-a4fb-902e8bd3f8c9", "metadata": {}, "source": [ "You might have noticed that so far that the first-moment calculations were enough for \n", "us to guess the correct threshold. This was certainly the case for the diamond graph above.\n", "\n", "Below we plot the probability of having at least one spatula, as well as the mean number of spatulas\n", "for $p = O(n^{-5/6})$, the potential threshold suggested by the first-moment method. \n", "\n", "1. What do you observe?\n", "2. How do you explain this?\n", "3. What is the true threshold? How is it related to the threshold you calculated for the diamond?\n", "\n", "__Hint__: Think back to the example of $X$ with $\\mathbb{E}(X) \\rightarrow +\\infty$ but\n", "$\\mathbb{P}(X) \\rightarrow 0$ of the notes. What was the intuitive cause of this phenomenon?" ] }, { "cell_type": "code", "execution_count": 17, "id": "cdd43c8b-a099-4cdc-adfa-dc79dcc730d9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Currently sampling with c = 0.000000000000000\n", "Currently sampling with c = 0.500000000000000\n", "Currently sampling with c = 1.00000000000000\n", "Currently sampling with c = 1.50000000000000\n", "Currently sampling with c = 2.00000000000000\n", "Currently sampling with c = 2.50000000000000\n", "Currently sampling with c = 3.00000000000000\n", "Currently sampling with c = 0.000000000000000\n", "Currently sampling with c = 0.500000000000000\n", "Currently sampling with c = 1.00000000000000\n", "Currently sampling with c = 1.50000000000000\n", "Currently sampling with c = 2.00000000000000\n", "Currently sampling with c = 2.50000000000000\n", "Currently sampling with c = 3.00000000000000\n" ] } ], "source": [ "c_range = [x / 10.0 for x in range(0, 31, 5)] #breaking up the interval [1,3]\n", "K = 100 #how many graphs to sample for each c\n", "n = 500 #size of graphs to sample\n", "\n", "def has_spatula(G):\n", " if spat.is_subgraph(G,induced=False):\n", " return 1\n", " else: \n", " return 0\n", "\n", "def count_spatula(G):\n", " return G.subgraph_search_count(spat)\n", "\n", "has_spat = empirical_means(n,c_range,has_spatula,K,verbose=True,scale=lambda n,c: c*n^(-5/6))\n", "count_spat = empirical_means(n,c_range,count_spatula,K,verbose=True,scale=lambda n,c: c*n^(-5/6))" ] }, { "cell_type": "code", "execution_count": 20, "id": "65d3e95a-87f8-4f8d-9714-b50e586972c3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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