{ "cells": [ { "cell_type": "markdown", "id": "269c4188", "metadata": {}, "source": [ "# Exercise sheet\n", "\n", "Some general remarks about the exercises:\n", "* For your convenience functions from the lecture are included below. Feel free to reuse them without copying to the exercise solution box.\n", "* For each part of the exercise a solution box has been added, but you may insert additional boxes. Do not hesitate to add Markdown boxes for textual or LaTeX answers (via `Cell > Cell Type > Markdown`). But make sure to replace any part that says `YOUR CODE HERE` or `YOUR ANSWER HERE` and remove the `raise NotImplementedError()`.\n", "* Please make your code readable by humans (and not just by the Python interpreter): choose informative function and variable names and use consistent formatting. Feel free to check the [PEP 8 Style Guide for Python](https://www.python.org/dev/peps/pep-0008/) for the widely adopted coding conventions or [this guide for explanation](https://realpython.com/python-pep8/).\n", "* Make sure that the full notebook runs without errors before submitting your work. This you can do by selecting `Kernel > Restart & Run All` in the jupyter menu.\n", "* For some exercises test cases have been provided in a separate cell in the form of `assert` statements. When run, a successful test will give no output, whereas a failed test will display an error message.\n", "* Each sheet has 100 points worth of exercises. Note that only the grades of sheets number 2, 4, 6, 8 count towards the course examination. Submitting sheets 1, 3, 5, 7 & 9 is voluntary and their grades are just for feedback.\n", "\n", "Please fill in your name here:" ] }, { "cell_type": "code", "execution_count": 1, "id": "220d541e", "metadata": {}, "outputs": [], "source": [ "NAME = \"Kees van Kempen\"\n", "NAMES_OF_COLLABORATORS = \"\"" ] }, { "cell_type": "markdown", "id": "b6944e4c", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "id": "c53fbab6", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "da0f2845f08ee29eb0450f8eff343e98", "grade": false, "grade_id": "cell-3cb26b1434512d8d", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "**Exercise sheet 8**\n", "\n", "Code from the lectures:" ] }, { "cell_type": "code", "execution_count": 2, "id": "5e4391a6", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "code", "checksum": "1814f5ba5f2d71b14a4c534cfe3ad7ff", "grade": false, "grade_id": "cell-40c62687f6a2c579", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "outputs": [], "source": [ "import numpy as np\n", "rng = np.random.default_rng() \n", "import matplotlib.pylab as plt\n", "%matplotlib inline\n", "\n", "def fan_triangulation(n):\n", " '''Generates a fan-shaped triangulation of even size n.'''\n", " return np.array([[(i-3)%(3*n),i+5,i+4,(i+6)%(3*n),i+2,i+1] \n", " for i in range(0,3*n,6)],dtype=np.int32).flatten()\n", "\n", "def is_fpf_involution(adj):\n", " '''Test whether adj defines a fixed-point free involution.'''\n", " for x, a in enumerate(adj):\n", " if a < 0 or a >= len(adj) or x == a or adj[a] != x:\n", " return False\n", " return True\n", "\n", "from collections import deque \n", "\n", "def triangle_neighbours(adj,i):\n", " '''Return the indices of the three neighboring triangles.'''\n", " return [j//3 for j in adj[3*i:3*i+3]]\n", "\n", "def connected_components(adj):\n", " '''Calculate the number of connected components of the triangulation.'''\n", " n = len(adj)//3 # the number of triangles\n", " # array storing the component index of each triangle\n", " component = np.full(n,-1,dtype=np.int32) \n", " index = 0\n", " for i in range(n):\n", " if component[i] == -1: # new component found, let us explore it\n", " component[i] = index\n", " queue = deque([i]) # use an exploration queue for breadth-first search\n", " while queue:\n", " for nbr in triangle_neighbours(adj,queue.pop()):\n", " # the neighboring triangle has not been explored yet\n", " if component[nbr] == -1: \n", " component[nbr] = index\n", " queue.appendleft(nbr) # add it to the exploration queue\n", " index += 1\n", " return index\n", "\n", "def next_around_triangle(i):\n", " '''Return the label of the side following side i in counter-clockwise direction.'''\n", " return i - i%3 + (i+1)%3\n", "\n", "def prev_around_triangle(i):\n", " '''Return the label of the side preceding side i in counter-clockwise direction.'''\n", " return i - i%3 + (i-1)%3\n", "\n", "def vertex_list(adj):\n", " '''\n", " Return the number of vertices and an array `vertex` of the same size \n", " as `adj`, such that `vertex[i]` is the index of the vertex at the \n", " start (in ccw order) of the side labeled `i`.\n", " '''\n", " # a side i that have not been visited yet has vertex[i]==-1\n", " vertex = np.full(len(adj),-1,dtype=np.int32) \n", " vert_index = 0 \n", " for i in range(len(adj)):\n", " if vertex[i] == -1:\n", " side = i\n", " while vertex[side] == -1: # find all sides that share the same vertex\n", " vertex[side] = vert_index\n", " side = next_around_triangle(adj[side])\n", " vert_index += 1\n", " return vert_index, vertex\n", "\n", "def number_of_vertices(adj):\n", " '''Calculate the number of vertices in the triangulation.'''\n", " return vertex_list(adj)[0]\n", "\n", "def is_sphere_triangulation(adj):\n", " '''Test whether adj defines a triangulation of the 2-sphere.'''\n", " if not is_fpf_involution(adj) or connected_components(adj) != 1:\n", " return False\n", " num_vert = number_of_vertices(adj)\n", " num_face = len(adj)//3\n", " num_edge = len(adj)//2\n", " # verify Euler's formula for the sphere\n", " return num_vert - num_edge + num_face == 2\n", "\n", "def flip_edge(adj,i):\n", " if adj[i] == next_around_triangle(i) or adj[i] == prev_around_triangle(i):\n", " # flipping an edge that is adjacent to the same triangle on both sides makes no sense\n", " return False\n", " j = prev_around_triangle(i)\n", " k = adj[i]\n", " l = prev_around_triangle(k)\n", " n = adj[l]\n", " adj[i] = n # it is important that we first update\n", " adj[n] = i # these adjacencies, before determining m,\n", " m = adj[j] # to treat the case j == n appropriately\n", " adj[k] = m\n", " adj[m] = k\n", " adj[j] = l\n", " adj[l] = j\n", " return True\n", "\n", "def random_flip(adj):\n", " random_side = rng.integers(0,len(adj))\n", " return flip_edge(adj,random_side)\n", "\n", "import networkx as nx\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n", "\n", "def triangulation_edges(triangulation,vertex):\n", " '''Return a list of vertex-id pairs corresponding to the edges in the triangulation.'''\n", " return [(vertex[i],vertex[j]) for i,j in enumerate(triangulation) if i < j]\n", "\n", "def triangulation_triangles(triangulation,vertex):\n", " '''Return a list of vertex-id triples corresponding to the triangles in the triangulation.'''\n", " return [vertex[i:i+3] for i in range(0,len(triangulation),3)]\n", "\n", "def plot_triangulation_3d(adj):\n", " '''Display an attempt at embedding the triangulation in 3d.'''\n", " num_vert, vertex = vertex_list(adj)\n", " edges = triangulation_edges(adj,vertex)\n", " triangles = triangulation_triangles(adj,vertex)\n", " # use the networkX 3d graph layout algorithm to find positions for the vertices\n", " pos = np.array(list(nx.spring_layout(nx.Graph(edges),dim=3).values()))\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111, projection='3d')\n", " tris = Poly3DCollection(pos[triangles])\n", " tris.set_edgecolor('k')\n", " ax.add_collection3d(tris)\n", " ax.set_xlim3d(np.amin(pos[:,0]),np.amax(pos[:,0]))\n", " ax.set_ylim3d(np.amin(pos[:,1]),np.amax(pos[:,1]))\n", " ax.set_zlim3d(np.amin(pos[:,2]),np.amax(pos[:,2]))\n", " plt.show()\n", " \n", "def vertex_neighbors_list(adj):\n", " '''Return a list `neighbors` such that `neighbors[v]` is a list of neighbors of the vertex v.'''\n", " num_vertices, vertex = vertex_list(adj)\n", " neighbors = [[] for _ in range(num_vertices)]\n", " for i,j in enumerate(adj):\n", " neighbors[vertex[i]].append(vertex[j])\n", " return neighbors\n", "\n", "def vertex_distance_profile(adj,max_distance=30):\n", " '''Return array `profile` of size `max_distance` such that `profile[r]` is the number\n", " of vertices that have distance r to a randomly chosen initial vertex.'''\n", " profile = np.zeros((max_distance),dtype=np.int32)\n", " neighbors = vertex_neighbors_list(adj)\n", " num_vertices = len(neighbors)\n", " start = rng.integers(num_vertices) # random starting vertex\n", " distance = np.full(num_vertices,-1,dtype=np.int32) # array tracking the known distances (-1 is unknown)\n", " queue = deque([start]) # use an exploration queue for the breadth-first search\n", " distance[start] = 0\n", " profile[0] = 1 # of course there is exactly 1 vertex at distance 0\n", " while queue:\n", " current = queue.pop()\n", " d = distance[current] + 1 # every unexplored neighbour will have this distance\n", " if d >= max_distance:\n", " break\n", " for nbr in neighbors[current]:\n", " if distance[nbr] == -1: # this neighboring vertex has not been explored yet\n", " distance[nbr] = d\n", " profile[d] += 1\n", " queue.appendleft(nbr) # add it to the exploration queue\n", " return profile\n", " \n", "def perform_sweeps(adj,t):\n", " '''Perform t sweeps of flip moves, where 1 sweep is N moves.'''\n", " for _ in range(len(adj)*t//3):\n", " random_flip(adj)\n", "\n", "def batch_estimate(data,observable,k):\n", " '''Devide data into k batches and apply the function observable to each.\n", " Returns the mean and standard error.'''\n", " batches = np.reshape(data,(k,-1))\n", " values = np.apply_along_axis(observable, 1, batches)\n", " return np.mean(values), np.std(values)/np.sqrt(k-1)" ] }, { "cell_type": "markdown", "id": "bed55184", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "8c9a6c198119d4649dd87308e8933611", "grade": false, "grade_id": "cell-5f5adc7840fea9ad", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "## Estimating Hausdorff dimensions in various 2D quantum gravity models \n", "\n", "**(100 Points)**\n", "\n", "In the lecture we considered the model of two-dimensional Dynamical Triangulations of the 2-sphere. The corresponding partition function is\n", "$$ Z^{U}_{S^2,N} = \\sum_T 1, \\tag{1}$$\n", "where the sum is over all triangulations of size $N$ with the topology of $S^2$, each of which is represented as an adjacency list $\\operatorname{adj}: \\{0,\\ldots,3N-1\\} \\to \\{0,\\ldots,3N-1\\}$. To emphasize that we are dealing with the **uniform** probability distribution on such triangulations, we have added the label $^U$. It is a lattice model of two-dimensional Euclidean quantum gravity with no coupled matter.\n", "\n", "One can also consider two-dimensional quantum gravity coupled to matter fields (e.g. a scalar field) supported on the geometry. Formally the corresponding path integral in the continuum reads\n", "$$ Z = \\int [\\mathcal{D}g_{ab}]\\int [\\mathcal{D}\\phi] e^{-\\frac{1}{\\hbar}(S_E[g_{ab}] + S_m[\\phi,g_{ab}])} = \\int [\\mathcal{D}g_{ab}]e^{-\\frac{1}{\\hbar}S_E[g_{ab}]} Z^*_m[g_{ab}],$$\n", "where $S_m[\\phi,g_{ab}]$ and $Z_m[g_{ab}]$ are the matter action and path integral of the field $\\phi$ on the geometry described by $g_{ab}$. The natural analogue in Dynamical Triangulations is\n", "$$Z^*_{S^2,N} = \\sum_T Z^*_m[T],$$\n", "where the sum is over the same triangulations as in (1) but now the summand $Z^*_m[T]$ is the lattice partition function of a matter system supported on the triangulation $T$, which generically depends in a non-trivial way on $T$. For instance, the matter system could be an Ising model in which the spin are supported on the triangles of $T$ and $Z^{\\text{Ising}}_m[T]$ would be the corresponding Ising partition function.\n", "In other words, when Dynamical Triangulations are coupled to matter the uniform distribution $\\pi^U(T) = 1/Z^U_{S^2,N}$ is changed into a non-uniform distribution $\\pi^*(T) = Z^*_m[T] / Z^*_{S^2,N}$. This can have significant effect on the critical exponents of the random triangulation as $N\\to\\infty$, like the Hausdorff dimension. \n", "\n", "The goal of this exercise is to estimate the **Hausdorff dimension** of random triangulations in four different models and to conclude based on this that they belong to four different universality classes (i.e. that if they possess well-defined continuum limits that they are described by four different EQFTs): \n", "* $Z^{U}_{S^2,N}$: the standard Dynamical Triangulations with **U**niform distribution (U)\n", "* $Z^{W}_{S^2,N}$: triangulations coupled to a matter system called a Schnyder **W**ood (W)\n", "* $Z^{S}_{S^2,N}$: triangulations coupled to a matter system called a **S**panning tree (S)\n", "* $Z^{B}_{S^2,N}$: triangulations coupled to a matter system called a **B**ipolar orientation (B)\n", "\n", "What these matter systems precisely represent will not be important. We have provided for you a **black box generator** that samples from the corresponding four distributions $\\pi^U(T)$, $\\pi^W(T)$, $\\pi^S(T)$, $\\pi^B(T)$. It does so in an efficient manner (linear time in $N$) using direct Monte Carlo sampling algorithms and therefore returns independent samples with exactly the desired distribution $\\pi^*(T)$ (within numerical precision).\n", "\n", "The black box generator is provided by the executable program `generator` provided to you on the science server. It can be called directly from this notebook with the following function `generate_random_triangulation`, that takes the desired size $N$ and model (`'U'`,`'W'`, `'S'`, `'B'`) and returns a single random triangulation in the usual form of an adjacency list." ] }, { "cell_type": "code", "execution_count": 3, "id": "bcc7acba", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "code", "checksum": "7d6abad00aa217998ca44ecc5e89f423", "grade": false, "grade_id": "cell-266ff66f880583d7", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import subprocess\n", "\n", "def generate_random_triangulation(n,model):\n", " '''\n", " Returns a random triangulation generated by the program `generator` in the form \n", " of an array of length 3n storing the adjacency information of the triangle sides.\n", " Parameters:\n", " n - number of triangles in the triangulation, must be positive and even\n", " model - a one-letter string specifying the model from which the triangulation is sampled:\n", " 'U': Uniform triangulations\n", " 'W': Schnyder-Wood-decorated triangulations\n", " 'S': Spanning-tree decorated triangulations\n", " 'B': Bipolar-oriented triangulations\n", " '''\n", " program = \"/vol/cursus/NM042B/bin/generator\"\n", " output = subprocess.check_output([program,\"-s{}\".format(n),\"-t{}\".format(model)]).decode('ascii').split('\\n')[:-1]\n", " return np.array([int(num) for num in output],dtype=np.int32)\n", "\n", "adj = generate_random_triangulation(100,'B')\n", "is_sphere_triangulation(adj)" ] }, { "cell_type": "markdown", "id": "4518f51f", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "37e92f3a59f2d5c6d117868d04d8f0d4", "grade": false, "grade_id": "cell-6aacf5fa6d8c4eb9", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "Recall that the **distance profile** $\\rho_T(r)$ of a triangulation is defined as \n", "$$ \\rho_T(r) = \\frac{1}{V} \\sum_{x=0}^{V-1} \\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}},$$\n", "where $V = (N+4)/2$ is the number of vertices and $d_T(x,y)$ is the graph distance between the vertices with label $x$ and $y$." ] }, { "cell_type": "markdown", "id": "d59143f0", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "afcdbf86f64bd17b8ac9b4f9ec422206", "grade": false, "grade_id": "cell-8e6d6fcefb5ab644", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "**(a)** Let $T$ be a random triangulation of size $N$ and $X$, $Y$ two independent numbers chosen uniformly from $0,\\ldots,V-1$, corresponding to two random vertices in $T$. Explain with a calculation that $\\frac{1}{V}\\mathbb{E}[ \\rho_T(r) ] = \\mathbb{P}(d_T(X,Y) = r)$ and that the expected distance between $X$ and $Y$ is related to the distance profile via\n", "\n", "$$\n", "\\mathbb{E}[d_T(X,Y)] = \\frac{1}{V}\\sum_{r=0}^\\infty r\\, \\mathbb{E}[ \\rho_T(r) ]. \\tag{2}\n", "$$\n", "\n", "**(20 pts)**" ] }, { "cell_type": "markdown", "id": "dd1b43bf", "metadata": { "deletable": false, "nbgrader": { "cell_type": "markdown", "checksum": "74963ed3d7cbd9eaa06be2e66a8f939e", "grade": true, "grade_id": "cell-f86454063d193cd6", "locked": false, "points": 20, "schema_version": 3, "solution": true, "task": false } }, "source": [ "**To proof**\n", "\n", "$\\frac{1}{V}\\mathbb{E}[ \\rho_T(r) ] = \\mathbb{P}(d_T(X,Y) = r)$\n", "\n", "**Proof**\n", "\n", "$$\n", "\\frac{1}{V} \\mathbb{E}\\left[ \\rho_T(r)\\right]\n", " = \\frac{1}{V} \\mathbb{E} \\left[\\frac{1}{V} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n", " = \\frac{1}{V^2} \\mathbb{E} \\left[ \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n", " = \\frac{1}{V^2} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{E} \\left[ \\mathbf{1}_{\\{d_T(x,y)=r\\}} \\right]\n", "$$\n", "\n", "The order of summation is changed, as the sum of expectation values is equal to the expectation value of the sum.\n", "The latter expectation value of the indicator function is exactly equal to the chance $\\mathbb{P}(d_T(x,y)=r)$ for given $x, y$.\n", "For the uniformly distributed $X, Y$, we find $\\mathbb{P}(X = x) = \\frac{1}{V} = \\mathbb{P}(Y = y)$.\n", "This allows us to write the right hand side as follows.\n", "\n", "$$\n", "\\frac{1}{V} \\mathbb{E}\\left[ \\rho_T(r)\\right]\n", " = \\frac{1}{V^2} \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{P}(d_T(x,y)=r)\n", " = \\sum_{x=0}^{V-1}\\sum_{y=0}^{V-1} \\mathbb{P}(X = x) \\mathbb{P}(Y = y) \\mathbb{P}(d_T(x,y)=r)\n", " = \\mathbb{P}(d_T(X,Y)=r),\n", "$$\n", "\n", "which is what we sought.\n", "\n", "Using this result, it is just a matter of writing out the definition of an expectation value to get to the result.\n", "\n", "$$\n", "\\mathbb{E}[d_T(X,Y)] = \\sum_{r=0}^\\infty r\\, \\mathbb{P}(d_T(X,Y) = r) = \\frac{1}{V}\\sum_{r=0}^\\infty r\\, \\mathbb{E}[ \\rho_T(r) ].\n", "$$" ] }, { "cell_type": "markdown", "id": "29704f5d", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "e2cc0493d54bcf087ce14bcb2e8a8d2f", "grade": false, "grade_id": "cell-aafca9797e5cfee4", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "**(b)** We will work under the assumption that \n", "\n", "$$\n", "\\mathbb{E}[\\rho_T(r)] \\approx V^{1-1/d_H} f(r V^{-1/d_H})\n", "$$ \n", "\n", "for a positive real number $d_H$ called the **Hausdorff dimension** and a continuous function $f$ that are both independent of $N$ but do depend on the model. Show that \n", "\n", "$$\n", "\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}, \\qquad c = \\int_0^\\infty \\mathrm{d}x\\,x\\,f(x). \\tag{3}\n", "$$\n", "\n", "_Hint:_ Approximate the summation by an integral. **(15 pts)**" ] }, { "cell_type": "markdown", "id": "0c062ba6", "metadata": { "deletable": false, "nbgrader": { "cell_type": "markdown", "checksum": "2db525e8acbc2412c1c5948052526a15", "grade": true, "grade_id": "cell-bcf3b38d64a4408d", "locked": false, "points": 15, "schema_version": 3, "solution": true, "task": false } }, "source": [ "**To proof**\n", "\n", "$$\n", "\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}, \\qquad c = \\int_0^\\infty \\mathrm{d}x\\,x\\,f(x)\n", "$$\n", "\n", "**Proof**\n", "\n", "$$\n", "\\mathbb{E} \\left[ d_T(X,Y) \\right]\n", " = \\frac{1}{V} \\sum_{r=0}^\\infty r\\, \\mathbb{E} \\left[ \\rho_T(r) \\right]\n", " = \\frac{1}{V} \\sum_{r=0}^\\infty rV^{1-1/d_H}f(rV^{-1/d_H})\n", " = \\frac{1}{V} \\sum_{r=0}^\\infty xV^{1/d_H} \\cdot V^{1-1/d_H}f(x)\n", " = \\sum_{r=0}^\\infty xf(x),\n", "$$\n", "where the first equality sign is due to (2), the second due to the given assumption, the third using $x = rV^{-1/d_H}$.\n", "\n", "Now we approximate the summation by an integral.\n", "\n", "$$\n", "\\sum_{r=0}^\\infty xf(x)\n", " \\approx \\int_{r=0}^\\infty xf(x)dr\n", " = V^{1/d_H} \\int_{x=0}^\\infty xf(x)dx\n", " = cV^{1/d_H},\n", "$$\n", "using $\\frac{dr}{dx} = V^{1/d_H}$ for substitution.\n", "This yields the desired approximation\n", "$$\n", " \\mathbb{E} \\left[ d_T(X,Y) \\right] \\approx cV^{1/d_H}.\n", "$$" ] }, { "cell_type": "markdown", "id": "eba53e6d", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "ba14acd8cc24c2dfea35f3b8106cdfc8", "grade": false, "grade_id": "cell-fcab32195688a5c5", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "**(c)** For each of the four models estimate $\\mathbb{E}[d_T(X,Y)]$ with errors for $N = 2^7, 2^8, \\ldots, 2^{12}$ using (2) and based on $100$ samples each. Store your data in the file `qgdimension.hdf5`. Make an estimate of $d_H$ (with errors) for each of the models by fitting the parameters $c$ and $d_H$ of the ansatz (3). For each model, plot the data together with the fit in a log-log plot. **(40 pts)**" ] }, { "cell_type": "code", "execution_count": 4, "id": "ee683060", "metadata": { "deletable": false, "nbgrader": { "cell_type": "code", "checksum": "c3664034dec3a350f7fe0533fe2454cb", "grade": true, "grade_id": "cell-01f5fde55f35f2dc", "locked": false, "points": 15, "schema_version": 3, "solution": true, "task": false } }, "outputs": [], "source": [ "models = ['U','W','S','B']\n", "sizes = [2**k for k in range(7,13)]\n", "num_vertices = (np.array(sizes)+4)/2\n", "measurements = 100\n", "\n", "# data gathering and storing in qgdimension.hdf5\n", "import h5py\n", "\n", "max_distance = 30\n", "\n", "with h5py.File(\"qgdimension.hdf5\", \"a\") as f:\n", " if not \"num-vertices\" in f:\n", " f.create_dataset(\"num-vertices\",data=num_vertices)\n", " \n", " for model in models:\n", " models_key = f\"expectation-graph-distance-{model}\"\n", " if not models_key in f:\n", " graph_distance_expectations = np.zeros((len(num_vertices), measurements))\n", " for idx_N, N in enumerate(num_vertices):\n", " V = (N + 4)/2\n", " for idx_measurement in range(measurements):\n", " adj = generate_random_triangulation(N, model)\n", " expectation = 1/V * vertex_distance_profile(adj,max_distance)@np.arange(max_distance)\n", " graph_distance_expectations[idx_N][idx_measurement] = expectation\n", "\n", " f.create_dataset(models_key,data=graph_distance_expectations)" ] }, { "cell_type": "code", "execution_count": 5, "id": "351f7a01", "metadata": { "deletable": false, "nbgrader": { "cell_type": "code", "checksum": "000725107fe51acebc0bc68eef8c1c9c", "grade": true, "grade_id": "cell-9e8f666073e1e2df", "locked": false, "points": 25, "schema_version": 3, "solution": true, "task": false } }, "outputs": [ { "data": { "image/png": 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Z1gopO2FseyTfR8jHpRAFi2URfvZ7gO0NFmNF/j4JIf9IhHOcLSWM8hGt/bMcOFZEOotIA+A5nBOB4jtyXYFm4nT3y8Tp8rM4zDyKlfpNhXkcWISPMhbFY8n37nLXu+VhKP7Lw/E433GoXXqD7eNiDdV5u6SnL/hrW0/CeePw6eqMj/Y+zl2xkgvd4owh9XqAWNJx9mUp7v7rjfPCk1Bco6rPq+rXqvqoqvZV1Tqq2ltVJ3mlXYiz/YeJo5OIdPVeodtoW4bbPVNVvw4xlmiL9LcV7WNLuMeTch9/XIHqvnDSeCpvfRbK73IR0an343W+GEygvIOVtZDLQnmPpaHckUNVHwb+D+fNOFtwdvYLOG9X+c7PMktxuh9876Y/FOdBV09v43RlWOP+C2kAPa988nEevrwUpwvEefjusgBO39MHcd7u+AfQHKeBA/AAcIc4tz5vDTF+fzEV4nzJHXHekJXlxuU5Lx3nrtGfwMs4D1/7W0+ZtO6PaRB/jTHzf8DhIuLZzcPn/g203kCxl3M/lUrvtX35wBnAYDeGZ3GeYfjV134Nh6quVtUffUyPNE/v7Q/5+3Tzfxznu7oD52C2Aefq1MeRlLlybFug30IkbsTZHztxuhx97CfWULa1ospOSNse4TEgnONSKOsLFkug/e5ze4PFWJG/T4/1R20fea07rN+ll1DLR1T2j6pOxTkh+BHn2YqtOJX4SjdJD+A5dbr7ZeDccVkSTh4evH9T4RwH/JWxqBxLPMrDFW4eF+E8h+L9yAA4Qx+9BgyX0kMPnOhn3cH2MSLSGt+9gt4AhrgNn4nAxapa3CWzEOeZt9s80rcl8HHiMHw05HDKUqaqhtQzyc07JKr6HU79/xnOc3gf4X9YnsU4Ze7foa4/2iL9bVXA8Tfcej6S4w8EqPvCTOMZU7nqsxB/l9Gq9+NyvhhMoLxDqEfDKQvlOpZKhHfNy01E1uK8FWhaXAKo5Gz/GmNM8hORB4AF6j7/JSLvAber8zxFpSYic4DnVfW1ciy7F+dkc5yq3hlC+lOAQap6s4959wNb1HlhR6B1pOF0jeypqvvDjHcOcIWqLvaYNhXnZQpzVXVAOOszpqJE8rs00WeDBhpjjDGJqzvO67yLdcTpYVHpiMgJON0g/8S5st8T51X9YVPVmmEu4uv5uOJ1hXSH0b06X6bLYojL9vMxbWB51mVMNEXzd2mizxpyxhhjTIJS1TO8Poc91EcS6YLTdbQuzqDB56jq77HI2O32bowpK26/SxNc3LpWGmOMMcYYY4wpn5BedmKMMcYYY4wxJnFYQ84YY4wxxhhjkow15IwxxhhjjDEmyVhDzhhjjDHGGGOSjDXkjDHGGGOMMSbJWEPOGGOMMcYYY5KMNeSMMcYYY4wxJslYQ84YY4wxxhhjkow15IwxxhhjjDEmyVhDzhhjjDHGGGOSjDXkjDHGGGOMMSbJWEPOGGOMMcYYY5KMNeSM8SIiz4vInR6frxORzSKSIyJN4hmbP94xxzGOtSJyUjmXPU5Elkc7phDyvUZEngwj/T9F5MEKDMkYUw6RHH/CzCdDRLIqOp+KJCJ3i8ibFZU+GYhIOxFREakWwToOdM8NUqMZWzniuFREvolg+S9F5G/RjCmEPGuIyFIROaCcy38oIoOiHVeysYacqXTcA3NHr2khV0Kqeq2q3usuVx14HDhZVeuq6rboR+xfqAdnz5iThff3pKqzVbVLjGNIA+4AHnE/+zxBE5FMEbnS/fgicJGINI9dpMZUHSJyrIh8JyK7RGS7iHwrIkfEO65oE5FqbiOgr8e0Ee6x0Xvar/GJMnFVdOMylAsDqrrePTcorKg4os3XflPVwar6vxiHcjUwS1X/EJGjRGS3Z4NYRF7yM+159+ODwH9jHHPCsYacMYG1AGoCS8JdUBwV/huL95XAJDcU+FVVN4a6gKruBb4ELqmwqIypokSkPvAZ8BTQGGgNjAH2xTOuaPG8+6OqBcD3wAkeSY4HfvUxbVZMAkwQkdwli5VkiDHBXQOMd//+EUgFDveYfxywyWtayW9BVecC9UWkT8WHmrisIWeqnOK7LiJyi4hsEZHfReQyj/mvi8h9ItIZKO7qt1NEZrjzjxaRee7V4nkicrTHspki8l8R+RbIBQ52r67+XURWiki2iNwrIh1E5Hv3atO77p0h7zi7As8DR7lXbXd6xPeciHwhInuA/sUxu/MbichnIrJVRHa4f7fxivFe9yp3toh8JSJNPeZfIiLrRGSbiNzpeVXSMx/PfelnP/d1t3Gnu4+fLt5OESk+KfnJ3bbzvNclIl3dWHeKyBIROcPrO3pGRD53t2GOiHRw54mIPOF+t7tE5GcR6eGnOAwGvvYzL5BM4NRyLGeMCawzgKpOUNVCVc1T1a9U9efiBCJylYgsc3/7S0XE80Qv3f3N7xKRd0SkpruM3+O+iBwhTvf5ah55DBORRe7ftdxjzg4RWQqUujsoIq1E5AP3mPubiPzTY97dIvK+iLwpIruBS722dxbOyWmx44CHfEyb5bHtq8S5U/mpiLTyyCtQ3dReRL5299lUoCkBBEsvIkeKc9d0p4j8JCIZHvMai8hrIrLJ3Wcfe8wLFL+KyD9EZCWw0p02VkQ2iFNXzheR49zpg4BRwHluHfKTO72BiLzifr8bxanLU915qSLyqIj8KSJrCHAMF5HxwIHAJHf9/5a/umJeISLrgRni1T1TRC7zKJtrROQaj3UGO/doIiKT3G2d58b+jTuvTDdQKd1TxDv+cPdbybpEJEVE7hDnPGCLiLwhIg284vibiKx39+V/PPLtKyI/uvluFpHH/cR3INABmAOgqvuBH3DLvTg9XtKAd7ymdab0RY3MQN9jVWANOVNVHQA0wLnaewXwjIg08kygqiuA7u7Hhqp6oog0Bj4HxgFNcLpdfi6ln527GKfLQD1gnTttENAbOBL4N073vBFAW6AHcIF3gKq6DLgW+N7tutHQY/aFOF0K6gHeXS9TgNeAg3Aqojzgaa80FwKXAcUHy1sBRKQb8KwbW0uPfVQehcDNOCcARwEDgL+721Z8knKYu23veC4oTpfWScBXbow3AG+JiGfXywtwrtQ3AlbxVxeLk3EO/J2BhsB5gL8usYfyV2M9HMuAw8qxnDEmsBVAoYj8T0QGex+XRWQ4cDfOHfH6wBmU/n2fi3O8bQ/0pHTDyedxX1XnuesY6JH2Iv66WzAa56SzA3AKUPIskTi9LiYBP7nrHQDcJCKneKxrKPA+zvHoLa/tnQUc4548NwXqAO8CfT2mHQLMEpETgQfcbWyJU79MdOMIVje9DczHOR7f67kNfvhNLyKt3bzuw7lreivwgYg0c5OMB2rj1J/NgSfc5fzG7+FMoB/Qzf08D0h383kbeE9EaqrqZOB+4B23Dik+Hv8PKAA6Ar1w6oPixs5VwGnu9D7AOf42XlUvBtYDp7vrf9hj9glAV5yy4G2Lm0d9nDr2CSl9oSHQucczwB43zd8I/h0FEu5+83Sp+68/cDBQl7LnEMcCXXDK+13iXHgGGAuMVdX6OL+Xd/3Edyiwxr0rXczzosbxOOc233hN+01VPS8eV/m62BpypqraD9yjqvtV9QsgB+egFMypwEpVHa+qBao6AacbzOkeaV5X1SXu/P3utIdUdbeqLgEWA1+p6hpV3YXTTa9XmPF/oqrfqmqR29WvhKpuU9UPVDVXVbNxGjgneC3/mqquUNU8nANtujv9HGCSqn6jqvnAXYCGGVtxHPNV9Qd3P6wFXvARhz9H4lQeD6pqvqrOwOlu5dng/VBV57oVwVse27Afp4F7CCCqukxVf/eTT0MgO4zNKpaNUxkbY6JIVXfjnCQq8BKw1b1z08JNciXwsKrOU8cqVV3nsYpxqrpJVbfjNLDSPeYFOu7/D6fxVtwoOgXnBBichsd/VXW7qm7AaSwVOwJopqr3uMeqNW7c53uk+V5VP3aP13lemzwHp9FzKM6dt29UNRf4zWPaOlVdj3OB7VVVXaCq+4DbcXpstCNA3eTe/TgCuFNV96nqLHff+BRC+ouAL1T1C3ebpuJ0jRsiIi1xejpcq6o73H1d3OshUPzFHnD3cx6Aqr7p1mkFqvoYUAM/dbVbRgYDN6nqHlXdgtOILP4uzgWeVNUNbvl4wN8+COJud/3e3yWq+rmqrnbL5tc4FyOP80jiswy6dw2HAaPdunspTpksl3D2mw8jgMfdc5QcnO/pfCndlXSMOnfLf8K5iFHcmNoPdBSRpqqao6o/+MmjIWXr3q+BY0VEcPbZbJyux0d6TPPuQZPtrqvKsoacqYwKgepe06rjHGCKbfO6EpSL03AIphV/3WUrto7Sd602+Fhus8ffeT4+h5K3J195ACAitUXkBbdbxG6cq1wNpfSzdH94/O257a081+2eUJTrBS8i0lmcbp1/uHHcT5DuPB5aARtUtchjmvd+9rkNbqPvaZyrm5tF5EVxnrvxZQdOo69YAWXLDpQtP/WAXSFshzEmTO7Fl0tVtQ1Oj4VWwJPu7LbA6gCL+zu2QeDj/ps4jZ66OCf8sz0uAJU6LlK6DjgIaCVOF8Od4nSBH4XzfHWxkmXFeTtgjvtvhHshbi7O3YbjcU5e4a87EZ7Px5Wqf9yT7G04x8VAdVMrYIeq7vG1DeK89bg4plHB0rvbPNxrm4/FucvWFtiuqjsoK1D8ZfaVG9stblfFXW4+DfBfjxyEc6z+3SOuF3DuChbn7+97DEeg+newiPwgTtfRncAQr3j9lcFmQDWvdfvNJ5gw95s377K0zo3Ns0z7+51dgdMb5le3e+hpfvLwrnvB6VpZF+c3fzzObzAHZz8UT/N+VrQesDP4JlVe1pAzldF6oJ3XtPaU/6DtaRNOZeHpQMDzZRnluoPlh791BcrjFpwrb/3U6d5Q3C1BQsjvd8DzebpaON10iu3BuXpcLNBrg5/DuSLcyY1jVIgxgLOf20rpl8V472e/VHWcqvbG6drTGfiXn6Q/u/OLrQeauidzgPPMHc537ll+uuJchTTGVCBV/RV4HedEDpyTug4VkM9GnKv/Z+F0jx/vMft3nAZKsQM9/t6A092roce/eqo6xHP1HvkMVqdLW11VLe5mWdylrPguBO7/xdOKT15L1T8iUgfn+LzRe55HnBvd+Bu56ctsgzpvPS6O6f5g6d1tHu+1zXVU9UF3XmMRaUhZgeIvs6/Eea7rNpyGdSN1Hi/YxV/1iHc9uAHnpThNPeKqr6rFj0gE+h59Cav+FZEawAfAo0ALN94vCK3e24pzIbGNxzTPWIsb1UHr33LsN2/eZelAN7bNvpP/RVVXquoFOI3nh4D3vcpRsZ9x3iHg+fKfvThdQk8DWrq/fXB+C6fhdJX2bshV+brYGnKmMnoHuENE2rjPGJyE0/Xx/Sis+wugs4hcKM6ro8/D6cv/WRTW7ctmoI34eBlKAPVw7vLtdLsIjQ5j2fdxrkof7eY5htKV0CKc7jONxRn75aYgcewGckTkEOA6r/mbcfrf+zIHp+L6t4hUF+dB+tMp+zxFGeK8uKCf+5zdHmAvzl1aX77Ao7un231pDvCQiNR1K+Z/4VRinl1ETsDpEmuMiSIROcS9m9DG/dwWp0t18e/vZeBWEektjo4i4t2AKa83cJ5hPhT4yGP6u8Dt4rxIqg3OM7vF5gK7ReQ2cV6KkioiPSS84RJm4TyP1BZY6k77BsjA6RpafPL6NnCZiKS7x6b7gTnqdF33Wze5XU9/BMaISJqIHEvpxwFKCSF98d3LU9ztrSnOizzauHcxvwSedfdXdREpvpgYKH5f6uEce7cC1UTkLpxnz4ptBtoVX/Bz8/4KeExE6rv1fwcRKT7Gvwv80z03aASM9LcPPNbvr47yJQ2nC+NWoEBEBuM8oxeUOsMXfAjcLU6vmkPweDOyqm7FafBe5O7zy/F/QSOs/ebDBOBmcV54U5e/nqkr8JO+hIhcJCLN3N40O93JZepfdZ5zWwn09Zo1C+e84juPad+40/5QVe+78VW+LraGnKmM7sE5CHyDc/v+YWCEqi6OdMXqjCN3Gs5dr204lf5pqvpnpOv2YwbO0Ad/iEioeTwJ1AL+xDn5mRxqZuo8w3cDToPpd5z+51v469Xf43Gufq3FqTDfKbuWErfivFQlG+eZEe+0dwP/c7vAnOsVRz7OSwwGu9vxLHCJxxW6QOq7+e3AuYu2DecKqS+TgEPE481pOC9HaY7zApWNOA9zD3GvFiLOW/CGEMHzC8YYv7JxXnYxR5y38v6A81zxLQCq+h7Oc79vu2k/xnmhQzR8hHMn4iOvboVjcI4lv+Ec90ru1rkn4KfjNLh+wzlevUx4z9B+56afo6rqrncbzon4FlVd6U6bDtyJc9fnd5wT+fM90geqmy7E2a/bcS7uvREkJr/p1XlOcChOL4utOHfC/sVf55QX43RF/xWn/rgpWPx+TME5SV+Bs//3Urq74Xvu/9tEZIH79yU4DaqlOHXA+zhdPsGpF6bg1GELcBpOgTyAc1F4p4jcGiQt6jyT/k+cBuMOnH34abDlPFyPUw7+wCljEyg97MZVOPt5G05vk++8V+Aqz37z9Kqb/yycMr2X0hcvAhkELBGRHJwXn5yvXs/xe3gBp6x4+hqn/vV8ids37rRSd+PciyV71BmGoMoS95hhjDFluFfjduJ0j/wtzuFUCBG5GuimqjeFmP4GoK2q/rtCAzPGxJyIrAauUdVp8Y7FVG0i8hBwgKpG8vbKhOXelV0IDFD/LyQLtPwHwCvuS2OqLGvIGWNKEZHTgek4XSofw7kqe7jawcIYU4mJyDCc53o6e71oyZgK53anTAN+wXlr6BfAlar6cTzjMonNRqU3xngbitOtQnCekzjfGnHGmMpMRDJxnim72BpxJk7q4XSnbIXTJfUx4JO4RmQSnt2RM8YYY4wxxpgkYy878SIiB4vIKyISjTccGmOMMcYYY0zUVYmGnIi8KiJbRGSx1/RBIrJcRFaJyEgAdyT7K+ITqTHGGGOMMcYEV1WekXsdeBqP1+eKSCrwDDAQyALmicinqrrU5xoCaNq0qbZr1y5gmj179lCnjq8xEcsnkvWFu2yo6UNJFyxNoPnR3oexEsu4rZyFlsbKWWLlF61yNn/+/D9VtVlUgqpkQqmnIDG/12inj/QYEsnxJZEla11VWctZsPlWzmKbV8LWU6paJf4B7YDFHp+PAqZ4fL4duN3j8/uhrrt3794azMyZM4OmCUck6wt32VDTh5IuWJpA86O9D2MllnFbOQstjZWzxMovWuUM+FEToL5JxH+h1FPe+zNSiXj8CDVtJMcIO4bENq/KWs6CzbdyFtu8ErWeqip35HxpTekBErOAfiLSBGew0V4icruqPuBrYXfsqasBWrRoQWZmZsDMcnJygqYJRyTrC3fZUNOHki5YmkDzo70PYyWWcVs5Cy2NlbPEyi+W5cwYY4ypLKpyQ058TFNV3QZcG2xhVX0ReBGgT58+mpGRETB9ZmYmwdKEI5L1hbtsqOlDSRcsTaD50d6HsRLLuK2chZbGylli5RfLcmaMMcZUFlXiZSd+ZAFtPT63ATbFKRZjjDHGGGOMCVlVviM3D+gkIu2BjcD5wIXRWvn+/fvJyspi7969ADRo0IBly5ZFa/URrS/cZUNNH0q6YGkCzY/2PoyV8sZds2ZN2rRpQ/Xq1SsgKmNMVeddT0F0j7OJWE+FmjaSusjqKmNMrFSJhpyITAAygKYikgWMVtVXROR6YAqQCryqqkuilWdWVhb16tWjXbt2iAjZ2dnUq1cvWquPaH3hLhtq+lDSBUsTaH6092GslCduVWXbtm1kZWXRvn37CorMGFOVeddTEN3jbCLWU6GmjaQusrrKGBMrVaIhp6oX+Jn+BfBFReS5d+/eUpWjMeEQEZo0acLWrVvjHYoxppKyespEyuoqY+KrKj8jV+GscjSRsPJjqoqUwnyY8yLk58Y7lCrHjjMmUlaGTJWxbTX88n68oyilStyRM8YYk4CKCuHnd+k7907YtxVqNYKew+MdlTHGGPOXvbs5ePXrMOszqNkAugyBtNrxjgqwhpwxxphYU4WVU2Ha3bBlCfvrdqDmeS/DwRnxjswYY4xxFBXCwjdhxr203fMnpI+AAXcmTCMOrGtlpTdu3Di6du3KiBEjOProowHYuXMnzz77bEzjmDx5Ml26dOGwww7jwQcf9JnmiSeeoG/fvvTo0YMLLrig1JvUAAoLC+nVqxennXZa2PlfccUVfP755+WK3Ze9e/fSt29fDjvsMLp3787o0aP9pvUXd7t27Tj00ENJT0+nT58+UYvNmISW9SO8fhq8PRz258I5rzK/96PWiKvCEq2e6tixI48//njAtL6O62PHjqVHjx707duXJ598slwxRLOu2rBhA/3796dr1650796dsWPH+ky3c+dOzjnnHHr37k3Xrl35/vvvy8w75JBDyswzplJb+y28mAGT/gmNO7Dg8EfgzGeg3gHxjqwUuyNXyT377LN8+eWXpd4mtWvXLp599ln+/ve/xySGwsJC/vGPfzB16lQaNGjAiSeeyBlnnEG3bt1K0mzcuJFx48YxZ84cmjdvzrnnnsvEiRO59NJLS9I899xzdO3ald27d4cdw6JFixgzZkw0NgeAGjVqMGPGDOrWrcv+/fs59thjGTx4MEceeWSZtIHinjlzJk2bNo1aXKbqeWLqCsZOX+l8mFz2BPDGAZ24eWDnGEflw5+rYMY9sPQTqN0UhjwKh/8NqqVBZma8ozNxlGj1VJs2bejduzfDhw8vVU95Gjt2bKnj+uLFi3nppZeYO3cu+/btY/jw4Zx66ql06tQprDiiWVdVq1aNxx57jMMPP5zs7Gx69+7NwIEDy2zTjTfeyKBBg3jttdeoUaMGubm5Zea9//775Ofnl5pnTKW0Yx1MvQuWfgz128CwV6DHMLK//jrekflkd+QqsWuvvZY1a9Zwxhln8MQTT1C3bl0ARo8ezerVq0lPT+df//pXwHVs2rSJiy66iF69enHIIYcwd+7csOOYO3cuHTt25OCDDyYtLY3zzz+fTz75pEy6goIC8vLyKCgoIDc3l1atWpXMy8rKYsqUKVx55ZUh5blixQqOPfZYDj30UJ544gn++OMP2rRpE3bs/ohIyf7cv38/+/fv9/nAd7hxGxOumwd2Zu2Dp/L6oDr0a9+Yfu0bs/bBU0v+xb0Rl/0HfHYzPNMXVk6DjNvhxkXQ9yqnEWeqtEStp4YNG+azngLnwuPnn39e6ri+bNkyjjzySGrXrk21atU44YQT+Oijj4LmW5F1VcuWLTn88MMBqFevHl27dmXjxo2l0uzevZtZs2ZxxRVXAJCWlkbDhg2DzjOm0tmXA9PvhaePgBVTIGMUXD8PDj0HEviFPtaQq8Sef/55WrVqxcyZM7n55ptLpo8ZM4YOHTqwaNEiHnnkEQCGDBnCpk2bSi1fUFDA4MGDGTFiBAsXLmTBggV07dq1VJrjjjuO9PR00tPTOeaYY0r+njZtWkmajRs30rZt25LPbdq0KVOZtG7dmltvvZXu3bvTsmVLGjRowMknn1wy/6abbuKee+4hJSV4kS0oKOCiiy7i8ccf55dffmHlypUccsghIeyx0tvj+c9ze4oVFhaSnp5O8+bNGThwIP369SuTJlDcIsLJJ59M7969efHFF0OKz5iksXc3zLgPxvWCBW9An8udBlzGSKiRfGNsmYoR63rKs64KVE+1atWqTD1VbOTIkTz88MOljus9evRg1qxZbNu2jdzcXL744gs2bNgQcNtjVVcBrF27loULF5app9asWUOzZs247LLLOPbYY7nyyivZs2dPmXm9evUqNc+YSqOoCH6aCE/3gdmPQrehcMN8yLgtoZ6F88e6VkZARE4HTm/dujWZXl2DGjRoQHZ2NgA1Zo6m1uYlFESxQZ/WtBvZA+4Jmk5VycnJoUaNGoAz4GdRURFFRUUl8QG88847JfOLffzxx3Ts2JGTTz651HTPv7/44q9h+AoLC0lNTS2TLjc3l/3795OdnU1hYSF5eXkln4vt2LGDDz/8kEWLFtG4cWMuueQSXnrpJc4//3y+/PJLGjZsSM+ePfnuu+8oKCgotay3Dz/8kI4dO9K1a1eys7Pp0KEDqampJcucf/75TJw4EYBLLrmE1157rSRuz+3x5ivP2bNns3PnTkaMGMGcOXNKdVkJFveUKVNo2bIlW7duZejQoRx44IEcc8wxpda/d+/eMmUrkJycnLDSV+T6wl021PShpAuWJtD8aO/DWMnJyWHnzjyAmMTvbz9J0X5abZrMQeveJW3/brY0O5bf2l9EXu2W8ONSYGnI64okDhOmL0fCH79Qq7AAUqNzalCjSRc4I/CzZuHwdXz++OOP6dq1K4MHDwagdu2yJ16zZ88u9dnXwNeqWmY5X70sPvvsM5o2bUrv3r1LlbuuXbty2223MXDgQGrVqsVhhx1GtWqB9+OHH35I165d6du3LwDdu3enVq1aAAwdOrTkjuDw4cOZOHFiqfrVe5sCycnJYdiwYTz55JPUr1+/1LyCggIWLFjAU089Rbdu3bjjjjt48MEHuffee0vN69evHzfeeGPJPGMqhQ3zYPJtsHE+tDoczn0D2vaNd1RhsYZcBFR1EjCpT58+V2VkZJSat2zZsr8qiuppFAhUi1LlCFCUImUqIl+KuwAWp61Xrx4pKSmkpKQEXX758uUcd9xxpKam+k173HHHlTROioqKSq5QPvroo5x00kkAdOrUibfeeot69eqRnZ3Ntm3baNeuXal1Tp48mY4dO9KiRQvq1avHueeeyw8//MBVV13FwoULmTx5MlOnTmXfvn3s3r2b6667jjfffNNnTCtXruTII48sWf+SJUvIyMigXr16bNiwgbZt25bMS0lJKdVVxHN7PHluj7d69eoxYMAAZs+eXepqZ7C4Pb+TYcOGsXjxYgYNGlRq3TVr1qRXr14+8/UlMzMT77IYiUjWF+6yoaYPJV2wNIHmR3sfxkpmZiYNGzoXbDIyjopJfqX2U1ERLP4AZtwLO9dB++PhpDE0b304zcNdVyRxmCpl0aJFPp9N9uR9XC+uqzyP623atCl1B23Tpk2luvcX+/bbb/nyyy9p164de/fuZffu3Vx00UW8+eabXHHFFVxxxRVkZ2fzwAMPBO0i+fPPP9O7d++Sz/PnzycjI4MNGzbQsmXLUvF6NuJ8bVMx77pq//79DBs2jBEjRnD22WeXSd+mTRvatGlDv379yM7O5pxzzil5IZnnPKDUPGOS2q6NzluTf3kX6h4AZz4PPc+DEHp9JRpryMXC4AfJ83EFMBL7srMp79MldevWDXhHq9gBBxzATz/9VPJ569atNGvWrFQaz6uCvq5yAhxxxBGsXLmS3377jfr16zNx4kTefvvtUmkOPPBAfvjhB3Jzc6lbty7Tp08veZPjAw88wAMPPEB2djbz58/n0UcfLWkMDRgwgDfeeIPWrVuXrKtJkyYsXrwYcCrGCRMmcNNNN5V8Xrp0Kddeey15eXllKupQr3Ju3bqV6tWr07BhQ/Ly8pg2bRq33XZbqTSB4t6zZw9FRUXUq1ePPXv28NVXX3HXXXeFlLcxCWfVdJg2Gv74BQ44FC76EDqcmNDPFSQ7ETkY+A/QQFXPiXiFg50T9GjWVYlYT4HvusqznmrdujUffPBBSc8NTw888ACjRo2iXr16ZGZmljqub9myhebNm7NhwwY+/PDDkjc8+qqnwH9dFaye8rVNvqgqV1xxBV27duX//u//fKY54IADaNu2LcuXL6dVq1ZMnz69pGeJ57wuXbqUmmdMUsrPhe+egm+fdIYWOO5WOPZmqFE33pGVW/I1PU3EmjRpwjHHHEOPHj1KHiL39ezBpZdeyubNm+nbty/p6enlfu1wtWrVePrppznllFPo06cP5557Lt27dy+Vb79+/TjnnHM47rjjOPTQQykqKuLqq68OuN6ioiJWrVpF48aNS02/+OKLWbRoEenp6Tz88MM0bNiw5JmJ+fPn89hjj/H8889z7rnnlroaGo7ff/+d/v3707NnT4444ggGDhxY8hpqX/vS2+bNmzn22GM57LDD6Nu3L6eeemqZu3HGJLxNC+GNofDm2bB3F5z9Elw9CzoOsEZcOYjIqyKyRUQWe00fJCLLRWSViIwEUNU1qnpFfCKtePGsp7p27cpZZ51Vpp4KZtiwYXTr1o3zzjuPZ555hkaNGvmtp8B/XRWteurbb79l/PjxzJgxo+QZuuLuqZ7b9NRTTzFixAiOOuooFi1axKhRo0rWUTyvZ8+eZeYZkzRU4Zf3nReZZN4PnQbC9XOdMeGSuBEHdkeu0lu7dm3J3zk5OSV/e98R8/XsQd26dfn000/93mkLx5AhQxgyZEiZdXnmO2bMGG699daAeWVkZJR0o1q6dCnDhg0reaagWNOmTf2+tWzx4sXceeedgPOWsnPOKd+F7J49e7Jw4UKf83ztS8+4AQ4++OBSV5GNSSrb19B16aOQORtqNYZBDzovM6lWI96RJbvXgaeBN4oniEgq8AwwEMgC5onIp6pa9mHDJJVo9RT4fxbck/dxvfgumWcs/uop8F9XRaueOvbYY30++weltyk9PZ0ff/zR5z4snmdM0tq00HkGeMMPTo+Rs1+AdsfGO6qosYacSVo9evQIOmirN8/XQUdzXDljqoScrTDrYfjxVZqS4nRLOeafULNBvCOrFFR1loi085rcF1ilqmsARGQiMBRfb40xCcfqKWPiJHszXX4dB5kzoE5TOH0c9LoIUlKDL5tErCFnjDEmsH058P0z8N042J8Hh1/CnLTjOXpA2ZcnmKhrDXi+xz4L6CciTYD/Ar1E5HZVfcB7QRG5GrgaoEWLFgHfrlyssLAwpGfTQhHJusJdNpz0oaQNlCbY8tHch7EUSdzxfMNyIr5dOdS0VfUNyxUZd0phPm2yPuXA9e/Romg/69sOZd1B51KYXQdmhf62V2+J+nZla8gZY4zxrXA/zH8dvn4I9myFrmfAgLugaSfyk/AEIkn5ethQVXUbcG2gBVX1ReBFgD59+mjAtyu7otFFMRrrCnfZcNKHkjZQmmDLR3MfxlIkccfzDcuJ+HblUNNW1TcsV0jcqvDrZzDlP86bk7sMYU6D0+k35EIOjMLqE/XtytaQM8YYU5oqLPnIGUpg+xo46Bg4fwK0PSLekVVFWUBbj89tgOBv3jDGmKrij8UweSSsnQ3NusLFH0OH/uRVgQuO1pAzxhjzl99mwdS7nAfEm3eDC9+FTifbWyjjZx7QSUTaAxuB84EL4xuSMcYkgD1/woz7YMH/nGe1hzwKvS+DKI7bnOiqzpYaY4zx749fnAFSV02D+m3gzOfcAVIr14PhiUxEJgAZQFMRyQJGq+orInI9MAVIBV5V1SVxDNMYY+KrIB/mvQSZD0F+DvS9Gk64DWqXHeajsrOGnDHGVGU71sHM/8LP7zpXNAfe61SK1WvGO7IqR1Uv8DP9C8D3O/CNMSYJPDF1BWOnr3Q+TP68zPwbB3Ti5oGdA69EFVZ+BVNGwbZV0PEkOOV+aNalAiJODtaQi7NSBduHkAq2McaEa882mP0ozHsZJAWOuRGOvQlqNYp3ZCbBWD1ljInUzQM7c/PAzmRmZvLccmfM0XeuOSr0FWxdDpNvh9XToUknuPA96HxyBUWbPFLiHUBVd/PAzqx98FTWPngq/do3pl/7xiWf1z54akSVo4hw8cUXl3wuKCigWbNmDB8+vFzr27lzJ88++2zYy+Xk5HDNNdfQoUMH+vbty/HHH8+cOXPCWkdGRgYLFiwIO29jjJf8PTDrURiXDnOed7pP3rAABo6xRpzxqarVU927d2fQoEHlqqds8Gxjoix3O3zxb3j2KMj60bkDd9131ohz2R25BFFYpOzIzSd3XyHTl20mo0tzUlMie7lAnTp1WLx4MXl5edSqVYupU6fSunXrcq+vuIL8+9//HtZyV155Je3bt2flypXs2bOHrVu3smzZspCXLywsDDdUY4y3wgJYOB4yH4ScP6DLEGcogeZd4x2ZSRJVpZ5KSUnh559/ZsOGDcEXdFk9ZUyUFRbA/Necrv97d0HvS6H/f5zBvU0Ja8hFQEROB05v3bp10IFWAw4uWqRcM+EXVm3JoUjhhrcXcGjr+rxwwaF+K8lQB+4cMGAA77//PmeeeSZvvPEGZ599Nt9++y3Z2dls376df/zjH6xdu5ZatWoxbtw4evTowf33309WVhZr164lKyuLa6+9lr///e/ccsstrF69mp49e9K/f3/uu+8+xo4dy4cffkh+fj6nnnoqd9xxR6n816xZww8//MDzzz/Pnj17KCwspFmzZjRr1ozs7GwuuOACNm7cyN69e7nuuuu45JJLyM7OpmXLlvzjH/9g+vTp3H///RQWFlJUVER2djbvvfcejz32GKrKKaecwj333BN0P8RTsg6yGun6KmqgVRtk1becnBx27swDKB2/Kk3//IGD14yndt5GdtU/hDXpN7KrYTdYutn5V878knFAX1M+hUXKxa/M+auemrCQ9LYNGX9Fv4gbc4MHD+bzzz/nnHPOYcKECVxwwQXMnDkTgO3bt3P55ZezZs0aateuzYsvvkjPnj25++67Wb9+PWvWrGH9+vVce+21/Pvf/2bkyJGsXr2a9PR0Bg4cyCOPPMIjjzzCu+++y759+zjrrLO49dZbS+W/evVq5syZw1tvvUVKitNRqX379vTs2ROAM888kw0bNrB3715uvPFGLrjAeZSxbt26/N///R9TpkzhscceK7XOCRMmcP/996OqnHrqqTz00EMR7SNjqpTVM2DyKNi6DNofD6c8AAf0iHdUCckachFQ1UnApD59+lwVbKDVQANtTl+2mV82ZVOkzufc/UX8simb+ZvyGNC1hc9lQh2485JLLuGee+5h+PDhLFu2jGuuuYbvvvuOevXqMWrUKI444gg+++wzZsyYwXXXXceiRYuoUaMGq1evZubMmWRnZ9O5c2f+7//+j8cee4zly5fz888/A/DVV1+xfv165s+fj6oyZMgQFi5cyPHHH1+S/7p16+jVqxcNGzb0Gfcbb7xB48aNycvL44gjjuCMM86gXbt27Nmzh969e5dUfvfffz8pKSlkZ2dz9913M3/+fBo1asTJJ5/M9OnTOfPMM4Pui3hJ1kFWI11fRQ20aoOs+jZj5kw0LYXcfYUUtujq3C3Z8L0zlEDWPGjaGYa+TYMuQ+gVhaEEknVAX1M+mcu3sGjDzr/qqfxCFm3YSebyLX7rqVCdf/753HPPPZx22mn8/PPPXH755SUNudGjR9OrVy8+/vhjZsyYwSWXXMKiRYsA+PXXX0vVUzfffDMPPvggixcvLknz1VdfsXLlSubOnYuqcsYZZ/Dtt98yaNCgkvyXLFlCeno6qam+39D66quvlqqnTj75ZOrVq8eePXvo0aNHmYuJv//+O7fddlupeurjjz9O6HrKmISwbbUzoPeKL6FROzjvLTjkVBv+JgBryCWAJZt2k5dfultGXn4hSzftjriC7NmzJ2vXrmXChAkMGTKk1LxvvvmGDz74AIATTzyRbdu2sWvXLgBOPfVUatSoQY0aNWjWrBmbN5e9av/VV1/x1VdflTQ0du/ezcqVK0s15IIZN24cH330EQAbNmxg9erVtGvXjtTUVIYNG1Ym/bx588jIyKBZs2YAjBgxglmzZlkFaaq0wiLlkXl7WbWjyL2rP5/0tE2ML7iV1PoHwOnjIH1ElRpbxzjC6TkC/nsQLPhtq896auHarfRtU9tn3qH2Rmjfvj1r1qzhtdde46STTiI3NxdVJTs7m1mzZjF+/Hiys7M54ogj+PPPP8nKymLfvn2cdNJJ5Ofnl9RTq1evpqCgoKT3BsBnn33GlClTOOywwwDnDu7KlSs55phj/tqOvDwKCgr89qJ55JFH+OyzzwCnnlq5ciVNmjQhNTWVk08+uSRdYWEhe/bsYcWKFRxzzDHUrFmTvLw8hg0bxrRp0xgwYEDQfRFPydp7JBF7joSa1nqPZAKQWrCHdmvfpfXGzyhKqca6gy8hq80Z6ObqsPnriPJKxnIWDqvVE0D3VvWplZZKrkclWSstlW6t6kdl/WeccQa33normZmZbNu2rWS6qpZJK+5Vjxo1apRMS01NpaCgoExaVeX222/nmmuuAXzfeerevTs//fQTRUVFJV1WimVmZjJt2jS+//57ateuTUZGBvv27QOcO1G+ro76itmYqi5z+RbW7CryuKuvLNrfiMw+DzHgjIshzfeJtqn8wuk5Av57EBzevhm1fsgqU0/1atfMb4+DUHsj1KtXjzPPPJM77rijpJ4SEerVq4eIULdu3ZL1iAj169enRo0apaanpqZSs6YzZEZKSkrJ9OrVqzNq1KiSespXXH369OH222+nTp06JfVUcZrMzExmz57NnDlzSuqp/fv3U69ePWrWrFnS26Q4hjp16iAiVK9evSSPmjVrkpaWVu6eGbGSrL1HErHnSKhpq2LvkczMTBo2dM4xM47v6zy7Pf1eyN0GvUaQcuJddKjXgg5RyisZy1k47K2VCSCjS3PS2zak+DGD2mmppLdtSEaX5lFZ/+WXX85dd93FoYceWmr68ccfz1tvvQU4haxp06bUr++/8VivXr1SV+tOOeUUXn31VXJycgDYtGkTW7ZsKbVMhw4d6NOnD6NHjy5phK1cuZJPPvmEXbt20ahRI2rXrs2vv/7KDz/8EHRb+vXrx9dff82ff/5JYWEhEyZM4IQTTghtRxhTSS1Zt5n8wtIXOfKoydJGJ1ojzkRFZamnNm7cyNatW0st46ueWrVqVbnrqT59+lg9ZUwQXff9DC+eAJNuhKad4OqZMPQZqBdZT7Sqxu7IJYDUFGH8Ff0YPHYWufsKGTO0e1TeBlasTZs23HjjjWWm33333Vx22WX07NmT2rVr87///S/gepo0acIxxxxDjx49GDx4MI888gjLli3jqKOccUBq1arFhAkTaN68dMX+8ssvc8stt9CxY0dq1qxJs2bNeOSRR+jZsyfPP/88PXv2pEuXLhx55JFBt6Vly5Y88MAD9O/fv+S5vKFDh4axN4ypRPbnwZwX6D7vK2pxObnUKpkVzbv6xlSWeqpu3bo8//zzZZbzrKdq165Nw4YNefzxx8tVTx1wwAFWTxnjR1ruZo7f8jWF+3KZXvcAMs6+mdRDz7bn4MrJGnIJIjVFaFQ7jUa1ifi5uGLFVyA9ZWRk0Lt3bwAaN27MJ598UibN3XffXerznDlzSrpbvP3226Xm3XjjjSWVr79uGfXr1+ell17ymebLL78slbb4Sqp37JmZmSXzLrzwQi688MIy+RhTZRQVwqK3IfMB2L2RjI6ncPCGVJbuhiKN/t0SY6By1FOAz+fAPOup4jTF6wunniqeb/WUMV725VA4+3Ge/qYmi4oGkEsNaudWI31OQ8b3gFRrx5WLNeTi7ImpKxg7fWWpae1Gfl7y940DOkU02KoxphJRhRWTYdrdsPVXaN0bznqB1PbH8X8zZ/LgopQKuVtiqjarp4wx5VZUBD9PhGljyNzVkoV6I3mkAdF9+21VZQ25OLt5YGerAI0xwa2fA9NGw/rvoXEHOPcN6HpGSXeUFIn+3RJjwOopY0w5rZ8Dk0fCpgXQujdLDr6LvXP3lEoSrbe0V1XWkDPGmES2dQVMHwO/fgZ1msOpj8Phl0Bq9XhHZowxxpS1K8vpOfLLe1CvJZz1Ihw6nO7Lt5I2/0f2eYxkYs9zR8YachVIVUte529MuGyohdgq1X1s8udl5se8+9juTZD5oPNq5up1oP8dcOR1UKNu7GIwlZ7VUyZSVleZEvm58N04+OZJQOH4f8ExN5XUWxldmnNwgxSWu2Oe2vPckbOGXAWpWbMm27Zto0mTJlZJmrCpKtu2bSsZF8lUvOLuY5mZmTy33Bnj5p1rjop9IHk74dux8MNzUFQAfa+B42+FOk1jH4up1KyeMpGyusoAzvPbiz+AqaNhdxZ0OxMG3gONDiqVLDVF+NcRNe157iiyhlwFadOmDVlZWSXj1ezduzeqB7pI1hfusqGmDyVdsDSB5kd7H8ZKeeOuWbMmbdq0qYCITEIq2AdzX4LZj0LeDjh0OPT/DzRuH+/ITCXlXU9BdI+ziVhPhZo2krrI6ipTpWxc4DwHt2EOHNATzn4R2h3jN7k9zx1d1pCrINWrV6d9+79OwDIzM+nVq1fU1h/J+sJdNtT0oaQLlibQ/Gjvw1hJ1rhNjBQVOs8RzPgv7FoPHU6Ek+6GlofFOzJTyXnXUxDd41Ui1lOhpo2kLkrWY36yxm3iJPsPmH4PLHoL6jSDM56C9BGQkhrvyKoUa8gZY0w8qMKqac4D4ZsXOw23M8ZBh/7xjsxUIiJyOnB669atS8Y5CyQnJyekdKGIZF3hLhtO+lDSBkoTbPlo7sNYimXcVs5CSxNJOawoKYX5tMn6lAPXv0dKUQFZbc9m3UHDKdxdG2bNDrp8Tk4OO3fmAVR4/MlazsJhDTljjIm1jfOdZwnWzoZG7WDYK9D9bEhJiXdkppJR1UnApD59+lyVkZERNH1mZiahpAtFJOsKd9lw0oeSNlCaYMtHcx/GUizjtnIWWppIymHUqcKyT+GrO2HnOuhyKpx8Lwc26cCBYawmMzOThg2d59AzMir2OfRkLWfhsIZcBMK50hnt1ngiXoGqrFefIpWsVzkjXV8yl7OKulpYK3cT7X97k+ZbvyW/egPWdbyaTa1ORrdVh1mzIlp3LK9yFudX2a90GmOMAf74BSbf7lx8bN4NLvkEDs6Id1QGa8hFJJwrndFujSfiFahKd/UpSpL1Kmek60vmchb1q4XZm+Hrh2DB/yC1BpwwkrSjr6dTjXp0ik4OMb3KWZxfZb/SaYwxVVrOVph5Hyx4A2o2hFMfg8MvhVRrPiQK+yaMMaai7N0N3z0F3z8NhfnQ+1I44Taoa2PmGGOMSVAF+TD3Bfj6YdifC/2uhRP+DbUaxTsy48UacsYYE20F+TD/NacSzP0Tup8FJ94JTTrEOzJjjDHGN1VYMQWmjILtq6HjQDjlfmjWOd6RGT+sIWeMMdFSVARLPoQZ98KOtdDuOBg4Blr3jndkxhhjktwTU1cwdvrKvyZM/rzU/BsHdOLmgeVsdG35FabcDqtnQJNOMOJ96DQwgmhLKx37HgDajfwr/ohir8KsIWeMMdGweobzJso/foYWPWDEB9BxAIjEOzJjjDGVwM0DO5c0dk556EsaNmzIO9dE+Ex07nbIfADmvQI16sKgB+GIKyG1ehQi/ktx7PZcc3RZQ84YYyKxaZEzFtyamdDgQDjrRTh0uA0lYIwxJnEVFsCPr8LM/8K+3dDncsgYBXWaxDsyEwZryBljTHls/w1m3AeL33ceAD/lfucqZrUa8Y7MGGOM8W/VdOc5uK2/QvsTYNAD0KJ7vKMy5WANOWOMCUfOVpj1iHMlM6UaHHcLHHMj1GwQ78iMMcYY//5cBV/9B1ZMhkbt4fy3ocsQewQgiVlDzhhjQrEvB354Fr4dC/vz4PCL4YSRUL9lvCMzxhhj/Mvb6VyAnPMCVKsJA+9xhhSwHiRJzxpyxhgTSOF+ZyDvzIdgzxY45DQYMNpex2yMMSaxFRU6g3nPuA9yt0Gvi2DAXTaWaSViDTljjPFFFZZ8BNPvdcbTOfAoOP8taNs33pEZEzIROR04vXXr1mRmZgZNn5OTE1K6UESyrnCXDSd9KGkDpQm2fDT3YSzFMm4rZ6GlCTS/sLCQnTt3+p3fcMcvdFz1CnX3/MbOBt1Y1XsUOfU6wI9LgaUhbUNFsHIWXdaQM8YYD0Wq1Nu1nDY5vzB94nwyWtQg9YJ3oPMp9hyBSTqqOgmY1KdPn6tCeeV3NF8NHsm6wl02nPShpA2UJtjyyfp69VjGbeUstDT+5hcWKXmzv0RSalDYoisZXZqTmuLWT9t/g6l3wrJJzpuUh79Ow25n0idB6i8rZ9FlDTljjHEVbvqF52YuY0l+c/LI4N1q/Umv0YTxnY4kNUEqQWOMMVVXYZFy8Stz2LRHUfK4YcJC0ts2ZPxF3Uj99gn4/mnnRVz974Cjr4fqteIdsqlA1pAzxpgd62Dm/WQuXMGS/deTS00Acgtg0YZdZC7fwoCuLeIcpDHGmKouc/kWFm3Yibqfc/MLWbTuTzKfuIQB+TOh5/lw0mio3yqucZrYsIacHyJSB3gWyAcyVfWtOIdkTFJ4YuoKxk5f6XyY/HmZ+TcO6MTNAxPkRSG522HWozDvJUBY0vYe8taUfotXXn4hSzftTtiGXKn9zR4A2o38a78n1P42xhgTkSWbdpOXX1hqWl6BsrRaNwZccge06ROnyEw8JHxDTkQaAi8DPQAFLlfV78uxnleB04AtqtrDa94gYCyQCrysqg8CZwPvq+okEXkHsIacMSG4eWBnbh7YmczMTJ5b7jSK3rnmqDhHVVpK4T6Y/Rh88yTk50D6hZBxO903VSdt3Y/s86gja6Wl0q1V/bjFGozn/k7G53KMMcaErnur+tSqnkLu/qKSabWqCd1O+ye0OSCOkZl4SPiGHE4Da7KqniMiaUBtz5ki0hzIU9Vsj2kdVXWV13peB54G3vBaPhV4BhgIZAHzRORToA3wi5us9KUPY0xyKiyARW/Sb84YyN8OnQc7r2Ju0Q2AjHrKwQ1SWL6jiCKF2mmppLdtSEYXe1WzMcaYOMvPJeP3V0kvqsYiDiaXGm491YiMQxKz14ipWAndkBOR+sDxwKUAqpqP09XR0wnAdSIyRFX3ishVwFnAEM9EqjpLRNr5yKYvsEpV17h5TgSG4jTq2gCLgJQobZIxJh5U4dfPYfoY+HMFe+t3ocaIt+Cgo0slS00R/nVETR5clELuvkLGDO1e+m1gxhhjTKypwi/vw7TRpO7eyPjDzub0X9uwO62R1VNVXEI35ICDga3AayJyGDAfuFFV9xQnUNX3RKQ9MFFE3gMux7m7FqrWwAaPz1lAP2Ac8LSInApM8rVgOOPzRHsMiUQcN6Wix0yxsXlin1ek5WznzjyAqI5fFW45a7BzKQeveZ0Gu5ezp3Ybfut+O2trdqfub/nwW9n15O7Zg+SnUkcgdfMyZm9eFjSmRBDr30dVGJ/HGGPibuN8+HIkZM2FlofBsFdIPegoCh/6ktYNayXs89smNhK9IVcNOBy4QVXniMhYYCRwp2ciVX3YvZP2HNBBVXPCyMPXJQx1G4uXBVownPF5ov38SiKOm1KRY6aEE0eiSdYxUyJdX2ZmJg0bOs/IZWQEf0Yu6uWsWwuYNgZWfAl1D4DTx1In/SJ6pFbjzyDlLJy4E0Wsfx9VYXweY4yJm92/c8iysZA5A+o0hzOehvQRkGKdxMxfEr0hlwVkqeoc9/P7OA25UkTkOJyXoXwEjAauDzOPth6f2wCbyhWtMSb+dmXR5den4OsZkFbXeQau33WQVjv4ssYYY0w87d/rjAU3+3GaF+yDY26C426Bmon70i0TPwndkFPVP0Rkg4h0UdXlwABgqWcaEekFvAScCvwGvCki96nqHSFmMw/o5HbP3AicD1wYtY0wxsRG3g745gmY8wItCgvgyL87lV/txvGOzBhjjAlMFZZ+AlPvhJ3r4ZDTmNvgNI4ceEG8IzMJLKEbcq4bgLfcN1auoWx3x9rAcFVdDSAif8N9OYonEZkAZABNRSQLGK2qr6hqgYhcD0zBGX7gVVVdUlEbY4yJsv17Ye4LznACe3dDz/OYU3sAR51ybrwjM6ZC2XinxlQSv/8Mk2+Hdd9A8+5wyadw8Ansted/TRAJ35BT1UWA39ENVfVbr8/7ce7Qeafze0lDVb8Avih/lMaYmCsqhJ8mwsz7YXcWdBwIJ42GAw5ln1V+JoZsvFNjTHlUz98Jn/4TFrwBtRrBqY/D4X+D1IQ/PTcJwkqKMSa5qMLyyTDtbti6DFodDmc9B+2Pj3dkpuqy8U6NMaEryIc5z9NvzgOg+c6jACf8G2o1jHdkJslYQ84Ykzw2zCV90Sj4eik07gDD/wfdhoLY+DkmPmy8U2NMyFRhxWSYMgq2r2FX4940ufAFaNop3pGZJGUNOWNM4vtzpTOY97JJ1K7eEE59zO1+Uj3ekRlTacY7heQdHzCc9JGOeRrJeKiJLFnHPE2WclZ7z3o6rnqFxjsWsad2G1YfOpr1NTpTd/FGnHftBV/HRyvz+WT1/r8S7NhOu5Gfl3wc2qE6Z3VKC3l74sHKWXRZQ84Yk7h2/w5fPwgLxkP1WtD/P8zZfyjHHTE43pEZU6zSjHcKyTs+YDjpIx3zNJLxUBNZso55mvDlLHe78yz3j69Cjbow6CHqHHEFPVOrsz3MspSR4fTjLk/sicLKWXRZQ84Yk3j27oJvx8L3z0JRARxxJRz/L6jbjMIkvNJtKjUb79QYU4YUFcAPz0PmA7BvN/S5AvqPsiFxTFRZQ84YkzgK9sG8V2DWI5C3HXqcAyf+BxofHO/IjPHJxjs1xpSxchp9frwRcrPg4Aw45QFo0S3eUZlKqEIaciISyuWGIlXdWRH5G2OSTFERLf7IhKdugF3rnYrvpDHQKj3OgZnKKsr1lI13aoxxnuee8h9YOQWp1RLOnwBdBtsLuUyFqag7cpvcf4FKbipwYAXlb4xJBqqwajpMu5uum3+BA3rCGWOhw4nxjsxUflGrp2y8U2OSyxNTVzB2+krnw+TPy8y/cUAnbh7YOfQV5u2Erx+GuS9A9dow8F7m7evKCYeE804jY8JXUQ25ZaraK1ACEVlYQXkbY5LBxvkwdTSsnQ0ND2Jp11voNvwOSLG3qJuYsHrKmCrq5oGduXlgZzIzM3lueQ0A3rnmqPBXVFQI81+Hmf91Xmpy+MVw4p1Qtzlqz3ObGKiohlwov4Zy/GKMqRpKXS30IeyrhYlk22qYcS8s+QhqN4HBD0Pvy9jyzXd0s0aciR2rp4wx5bfma5h8O2xZAgcdA4MegJaHxTsqU8VUSENOVfd6fhaROsBeVS30l8YY85fiq4UA573wPVDOq4WJJGcLfP2Qc/UyNQ2O/zccfQPUrB/vyEwVZPWUMaZctv8GX90Bv34GDQ+E4f+DbkPtOTgTFxX1spMUnLdqjQCOAPYBNURkK04f/xdV1f/tBmNM0itSZUduPvl79zL9nafIWPkgqYV50PtSOOE2qNci3iGaKszqKWNMWPZl037NGzB7EqRUd7pQHnU9VK8Z78hMFVZRXStnAtOA24HFqloEJW8J6w88KCIfqeqbFZS/MSaOCouUR+fl8dv2AgoQbljYkvR69zL+uuNIbd4p3uEZA1ZPGWNCUVQEP70N0+/hoJzNcNgFMGA01G8Z78iMqbCG3MuqOt57oqpuBz4APhCR6hWUtzEmnoqKyJzyMWu3w36ch8hzqcWifXXJ3FafAc3jHJ8xDqunjDGBrfseJo+E3xdBm77M73wrvc+4Ot5RGVOiohpyF4lIb+AWz+cNPLmvXzbGVCZrMmHqaJZsaE8ew0rNyssvZOmm3QzomphdKku/YGYPAO1G/vVa6qR+wYzxxeopY4xvOzfA1LtgyYdQvzWc/TIceg7ZX38d78iMKaWiGnKDgAeAGSIyXFW3VFA+xphE8PtPMO1uWD0DGrSl+9HXk/ZtCvs8To9rpaXSrVXivtjE83XUGRkZ8Q7HVDyrp4yp4oqf5c7dV8j0ZZvJaF+H1O/GwnfjnAQn3AbH3AhpdeIbqDF+VNRbKxUYKSJnA7NE5HFgEc5zCLkVkacxJg52rIUZ98Ev70GtRnDyf+GIK8lIrcHBiyezfEcRRQq101JJb9uQjC7Wr9IkBqunjKnaCouUR+btZZVbT93w1jzSZSXjUx4h9dCz4aQx0LBtvMM0JqCKuiOHiJwGXAnkA4cDFwHdRWSHqnasqHxjSUROB05v3bo1mUEGfszJyQmaJhyRrC/cZUNNH0q6YGkCzY/2PoyVSOPeuTMPIGrfQTj8ra96/i4OWvcerTZ9iUoKWQeew4a2Z1GQXxe+/QGA67oW8tAi567cRd2q0bNZHrNn+e+WYuUsMrGOO5r5xfJ45qkq1FPGGN8yl29hzS6nEQeQWyAsknZkDv6UAccfH9/gjAlRRQ0/sAZYBjyhqlO95rWpiDzjQVUnAZP69OlzVbCuWNHurhXJ+sJdNtT0oaQLlibQ/GTt8hZp3M8td8aRy8gIPo5chZez/D3w/bPw41jYvwd6XQwZIzmofisO8rFsm+bOy05uOjd6sVs58y3WcUczv1gez4pVlXrKGOPbkt82kl+owF/jv+VpGkv3t2RA/MIyJiwVdUduiKr+6muGqmZVUJ7GmIpSuB8WvOEM6J2zGQ45DQbcBc26xDsyY8rL6iljqqL9efD903SfN41aXE0uf40Dl+jPchvjraKekfNZORpjkowqLPkYZtwL21ZB2yPh3PFwYL94R2ZMRKyeMqaKUYWlH8NXd8Gu9WQccgYHr63G0l3Ys9wmaVXYM3LGmCS39hsOX/AvyF4JzQ6BCyZC50EgEnxZY0xCCOdZbkjeZx/DSR/pc7aRPIObyGIZd6zLWd3sNXRc9TINdy0hp047Vh12Lzsb9eTqOjk8tEii/ix3qGntee7kyStez3IHYw05Y0xpfyyG6WNg5Vek1WgCQ5+Bwy6AlNR4R2aMCVM4z3JD8j77GE76SJ+zjeQZ3EQWy7hjVs5ytsD0e2Dhm1C7MZz2BHUP/xvpbn1WUc9yh5rWnudOnrzi8Sx3KGLakBORlsB2Vd0Xy3yNMSHYuQFm3g8/TYCa9eGkMczd15Xje50S78iMiRmrp4ypBAr2wZzn4etHoCAPjvoHHP8vqNUw3pEZE1WxviM3HuggIh+o6q0xztsY40vudpj9GMx9yfl89A1w7M1QuzFFSdhtw5gIWT1lTLJSheVfwJT/wI7fnMcBTv4vNLXRREzlVFHDD/wPuEpV8z2nq+pJIiJAt4rI1xgThvxc54rlN0/Cvt2QfiFk3G4DoJoqweopYyqZzUthyu2wJhOadoGLPoCOJ8U7KmMqVEXdkdsAfC8iw1R1bfFEEekJ3KSql1dQvsaYYAoL4Ke3YeYDkL3JuWI5YDS0sPNWU6VYPWVMJVA9fzd8fgv8+CrUqA+DH4Y+l0Nq9XiHZkyFq6jhB+4QkR+AaSJyI1AduAmoB4yriDyNMUEUdzmZNgb+XA5tjoBhL0O7Y+IdmTExZ/WUMUmucD/Me5m+c++Fwr1wxJVOr5LajeMdmTExU5HPyM0CJgOTgC3Auao6qwLzM8b4s/4HmHoXbJgDTTrBeW86g3rbUAKmarN6yphktHIqTBkFf64gu1E6jS94Hpp3jXdUxsRcSkWsVESeAX4BcoCuwAzgnyJSuyLyM8b4seVXmHABvHoK7FgHpz0Jf/8Bup5ujThTpVk9ZUwS2roC3jwH3joHigrhgon83PNua8SZKqui7sj9Atyqqnnu5wtF5BbgBxE5R1VXVFC+xhiAXRsh8wFY9Bak1YUT74Qjr4O0OvGOzJhEYfWUMckibwd8/TDMfRGq14aT74O+10C1NPg9M97RGRM3FfWM3PM+pj0mIguBLwB7D6wxISgsUnbk5pO7r5DpyzaT0aU5qSn+76RV258DU0c7b6MsKoR+18Jxt0KdJjGM2pjEZ/WUMUmgsAAWvA4z/us05nr/DfrfAXWbRbTaJ6auYOz0le6nPQC0G/l5yfwbB3Ti5oGdI8rDmFioqOEHRFXVe7qqzhCR/oHSGGMchUXKxa/MYdWWHIoUbpiwkPS2DRl/Rb+yjbn9e2Hui/Sb8xAU7IGe50L/UdCoXVxiNybRWT1lTIJbkwmTb4ctS+GgY2HQA9CyZ1RWffPAztw8sDOZmZlkZGREZZ3GxENFda2cKSIfAJ+o6vriiSKSBnQSkfuAmcDrFZS/MUkvc/kWFm3YSZF7GpmbX8iiDTvJXL6FAV1bOBOLCuHnd5yrlbuz2N34cJoMHxu1ys6YSszqKWMiVPrOVlnlurO1fQ18dSf8+hk0PBDOfQO6nmHPdRvjQ0U15AYBlwMTRKQ9sBOoCaQCXwFPqOqiCsrbmEphyabd5OUXlpqWl1/I0k27GXBIc1j5FUy727la2TIdznyWX9YrGdaIMyYUVk8ZE6HiO1sA573wPQDvXHNU+Va2dzfMfhR+eA5SqsOAu+DIf0D1mtEK15hKp6KekdsLPAs8KyLVgaZAnqrurIj8jKmMureqT620VHI9GnO10lLplrYZXr8R1n0LjdrDOa9BtzMhJQXWZ8YtXmOSidVTxiSIokLnxVzT74U9W+CwC51GXP2W8Y7MmIRXkePIAaCq+0XkNFV9qaLzMqYyyejSnPS2DflhzTaKFGpXF9LTNpIx7Rao2xSGPAq9L4XU6vEO1ZikZvWUMXGy7juYPBJ+/wna9oMLJ0Lr3vGOypikUeENOVevGOVjTKWRmiKMv6If5zzxOQfm/MQZhdPJkBWk9h8JR10PNerGO0RjKhOrp4yJkRp7t8B7l8KSj6B+axj2CvQYZs/BGROmWDXkBonIi8ACYD7ws6rui1HexiSnvbtJ/W4cE3LGUU0LqHbkFXD8RKjbPN6RGVMZWT1lTEXL3wPfPEHfuWMhJRUyboej/wlpteMdmTFJKVYNuSnAKKA3cCJwEzAiRnkbk1wK9sGPrzqDn+ZtZ37NE3in3t8YN2RYvCMzpjKzesqYilJUBL+8B9NGQ/bv/Nn8eFqMeA4atIl3ZMYktYoaR24w8JOqbnIn/aCqO4Bp7j9jjLeiIlj8Psy4F3auh/YnwMAxjJu0N96RGVPpVIZ6SkTq4LywJR/IVNW34hySMWVl/Qhf3gYbf4RWvWD4/1i2Jo8W1ogzJmIpFbTeYcCnIrJBRKYCPUTkIhHpISKpFZRnVIlIHRH5n4i8JCJ2VdZUHFVYNQ1ePB4+vApqNoCLPoRLPnEqPWNMRYhqPSUiqSKyUEQ+K29AIvKqiGwRkcU+5g0SkeUiskpERrqTzwbeV9WrgDPKm68xFWL3Jvjwanh5AOzKgjOfgytnwIH94h2ZMZVGRQ0/cCWAiNwEdAJ+A/oDLwLbgbAuw7iV6o/ARlU9rTwxicirwGnAFlXt4TVvEDAWZ/ygl1X1Qf6qICeJyDuAXelMUhUyYGm0bFzgdDX5bZYz8OnZLzsPfKdU1DUWYwxEv54CbgSWAfW9Z4hIc5yhDbI9pnVU1VVeSV8Hngbe8Fo+FXgGGAhkAfNE5FM3xl/cZKUHnTQmhgqLlB25+eTuK2T64g1k/DmB1G+fcIYWOO4WOPb/7AVdxlSAin5G7jJVPaz4g4g8C/yrHOuxCtKUW1QHLI2Wbathxn2w5EOo3QQGPQR9LoNqNeIbVxSUbjjvAaDdyM9L5se14WxMWRHXUyLSBjgV+C/wfz6SnABcJyJDVHWviFwFnAUM8UykqrNEpJ2P5fsCq1R1jZvfRGAoTp3VBlhExfWwMSagwiLl4lfmsGpLDkWq3PDmPNJFGX/YQFJPuQcatYt3iMZUWhXdkNstIr1VdT6Aqs4XkbDO4KyCNJVKzlb4+iGY/xqkpsHx/3Le2FWzzDWKpFXccM7MzCQjIyPe4RgTTMT1FPAk8G+gnq+ZqvqeiLQHJorIe8DlOBcPQ9Ua2ODxOQvoB4wDnhaRU4FJvhYUkdOB01u3bk1mZmbQjHJyckJKF4pI1hXusuGkDyVtoDTBlo/mPoyl8sa9aEsBC37Lo0hTACGXGiyQbjyV0pv0n9YCa6OWly+VtZwFm1/Vylm884plOQuHqGqFrBhARDoBbwJLcV7nfCiQrqohd5AWkfeBB3AqyFt9da0UkX8DRwPvAdcDA1U1x0e6dsBnnl0rReQcYJBHN5uLcSrI23Du4O0FvvH1ELlHBXnVm2++GXA7cnJyqFs3et0KIllfuMuGmj6UdMHSBJofjX34wJw8AG7vVyui9YQjJyeHBjVTaJP1KW03fERqYT6bWp3MuoPOI79G46DLhxOzlbPQ0lR0OYuHWMcdzfyiVc769+8/X1X7hLN8pPWUiJwGDFHVv4tIBn7qKTftRJyLjB1UdaufNO0oW08NB07xqqf6quoNIW0k0KdPH/3xxx+DpovmBZhI1hXusuGkDyVtoDTBlk/Wi1jlijt7M+PeeJsnNnREPa55C/B/Aztzw4BO0cvLj8pazoLNr1LlLAHyilY5E5Gw66lAKvSOnKquFJGjcZ4364nTPXJUqMu7FeQW9wppRoB8HnYryOdwKsgyjbhA2fhepe4BLgu0oKpOAib16dPnqkh/rOFKxANXMhy0nlvudK3MyIhR18qCfFa88x86L/sI9myFbkPhxLto3bQjrUNcRTgxWzkLLY1VjomVXyzLmbdI6yngGOAMERkC1ATqi8ibqnqRZyIROQ7oAXwEjMa56BiqLKCtx+c2wCY/aY2peAX74IfnYNajdN/XhVopN5Jb9NfsWmmpdGtVeXqaGJOoKnwcOVUtxLlT9l45FrcK0iSnoiJY+hFMv5fOO36Dg46BCyZCm6hdhDHGREkk9ZSq3g7cDuBxR867juoFvITzmMBvwJsicp+q3hFiNvOATm73zI3A+cCF4cZqTMRU4dfP4as7YMdv0HkwGQPvI/3jP/lhzTaKFGqnpZLetiEZXZrHO1pjKr0KefZLRBZEI42q3q6qbVS1HU7FNSNABTkU5w5aYxG5L4xwSypIEUlz8/k0jOWNKW3N1/DyifD+5VC9Fj8feidc+rk14oxJINGqp0JUGxiuqqtVtQj4G7DOR34TgO+BLiKSJSJXAKhqAc4Fyik4dwzfVdUlUYrNmNBsXgJvnAHvjHBezHXRh3DhRFKbdWT8Ff3o2LwubRrW4qkLejH+in6kpvjq8GSMiaaKuiPXVUR+DjBfgAZRyqukggQQkb8Bl5bJ0KkgM4CmIpIFjFbVV1S1QESKK8hU4FWrIE25/P4zTLsbVk+HBm3hzOeh57lsnzUbxCo0YxJM1OspVc0EMn1M/9br836cC5De6S4IsO4vgC/CiceYqNizDWb+13lJV80GMORR6H0ZpP51CpmaIjSqnUaj2jCga4s4BmtM1VJRDblDgItwHiD3J6xX+lsFaRLWjnXOUAK/vAs1G8LJ98ERV0H1mvGOzBjjX9TrKWMqlcL9MPcl+PpB2Jfj1GsZI6F28Jd0GWNio6IGBF8nIgep6joAEemvqjPdvw9X1Wh1VzEmfvZsg9mPwryXQVLg2JvhmJugVsN4R2aMCcLqKWMCWPEVTBkF21ZChwFwyv3Q/JB4R2WM8VKRLzvx7Et2ATDT/fta4OoKzNeYipW/B354Fr4dB/k50OsiOGEkNAj1PZTGmARh9ZQxnrYudxpwq6ZBk45w4bvQ6WR7PMCYBFWRDblqItJLVRdSurK0o4FJToUFsPANyHwQcjZDl1PhpNHQrEu8IzPGlI/VU8YA5O2g48qXYdaXUL0OnPxf6Hs1VEuLd2TGmAAqsiFXBNQRkQsAEZFLgKlAxY1AbkxFUIVlk2D6GNi2Ctr2g3PfgAOPjHdkxpjIWD1lqrbCAuclJjPvp3XeTuj9NzjxDqjTNN6RGWNCUJENuTuBk4C6wHfAGuBwoFMF5mlMdK39FqbeBRt/hKZd4PwJ0GWwdTMxpnKwespUXatnOt0otyyFdsfxY9NzOOK0S+MdlTEmDBXWkFPVTcAbxZ9FpDvQCrBX+5vEt3kJTBsDK6dAvVZwxlNw2IWlXrdsjEluVk+ZKmnbavjqTlj+OTQ8CM4dD11PZ8/XX8c7MmNMmGJ2VuqOzbYEeDdWeRoTtp0bIPMBWPQ21KgPJ90Nfa+BtNrxjswYU8GsnjKV2t7dMOsR+OE5Z0DvAaPhyL/bUDnGJDG7vWAMQO52+OZxmPMioHDUP+C4W2y8HGOMMRXuiakrGDt9pd/5Nw7oxM0DO5dv5UWFsPBNmHEv7PkT0kfAgDuh3gHljNYYkyisIWeqjMIiZUduPrn7Cpm+bDMZXZqTWrgX5jwPs5+AfbvhsAug/+3Q8MB4h2uMMaaKuHlg55KG2nkvfA/AO9ccFfmK134Lk0fCHz9D2yOd4QRaHx75el2+GqDtRn5e8ndEDVBjTFDWkDNVQmGRcvErc1i1JYcihRsmLCS94V7GF40iNWcjdDrFGUqgRfd4h2qMMcZEZsc650VdSz+G+m1g2CvQY1jUX9Tl2QA1xsSeNeRMlZC5fAuLNuykyH2peG5+IYu2FJJ5wNEMuPRSaHdsXOMzxhhjIrYvB755Ar57CiQFMkbB0TfYc97GVFLWkDNVwpJNu8nLLyw1LY8aLD30Nga0szeNG2OMSWJFRfDLuzDtbsj+HQ4913lZV4PW8Y7MGFOBrCFnKr+ty+m+6mVq0Y9capVMrpVWjW6t6scxMGOMMSZCG+bB5Ntg43xodTic+wa07RvvqIwxMWANOROyYG/VGtqhOhkZsYsnqN2bnKEEFr5JRrW6pDfpww/boUihdloq6W0bktGlebyjNMYYY8K3a6NzB+6Xd6HuAXDm89DzPEhJiXdkxpgYsYacCVmwt2plZmbGI6yy8nbCt086Y+UUFULfa0g9/lbG12rC4LGzyN1XyJih3Z23VqZE98FvY4wxpkLl5zrPwH37pFPHHXcrHHsz1Kgb78iMMTFmDTlTeezfC/NeglmPwt6dzjMCJ/4HGrUDIBVoVDuNRrVhQNcW8YzUGGOMCY8qLP4Apo6G3VnQbSgMvKekjjPGVD3WkDPJr6gQfn4XZv4Xdm2ADgOcoQRaHhbvyMrNxuYxxhhTYtNC+HIkbPgBDjgUzn7B3rZsjLGGnEliqrByqvOMwJYl0DIdhj4NB2fEObDI2dg8xhhT9RQWKTty88ndV8j0ZZvJaKWkzrwXFr0FdZrC6eOg10WQkhrvUI0xCcAaciY5Zc2HaaNh7Wxo1B7OeRW6nWUPeRtjqgwRqQM8C+QDmar6VpxDMhEoLFIufmUOq7bkUKRww5tzSWc549PeJfXo6+H4f0HNBvEO0xiTQOys1ySXP1fBu5fAyyfClmUw5FH4x1zoMcwaccaYmBORmiIyV0R+EpElIjImgnW9KiJbRGSxj3mDRGS5iKwSkZHu5LOB91X1KuCM8uZrEkPm8i0s2rCTInU+5xamsEg7kjl4Gpx8nzXijDFl2B05kxyy/6DTiufg66lQrSacMBKOvh5q1It3ZMaYqm0fcKKq5ohIdeAbEflSVX8oTiAizYE8Vc32mNZRVVd5ret14GngDc+JIpIKPAMMBLKAeSLyKdAG+MVNVhjdzTKxtmTFSvLy9+N5jT2vqDpLs2szIH5hGWMSmDXkTGLbu9t5zfL3T9OyYB/0uRxO+DfUtfHfjDHxp6oK5Lgfq7v/1CvZCcB1IjJEVfeKyFXAWcAQr3XNEpF2PrLpC6xS1TUAIjIRGIrTqGsDLMJ62CSvPX/CjPvoPv8nanE9udQsmVUrLZVurerHMThjTCKzhpxJTAX74MfXYNbDkLsNup/NvDon02/IBfGOzBhjSnHvmM0HOgLPqOocz/mq+p6ItAcmish7wOU4d9dC1RrY4PE5C+gHjAOeFpFTgUl+YjsdOL1169YhjfWZk5MTtTFBI1lXuMuGkz6UtIHSBFs+1FikaD+tN35Bu7XvkFqYR8c2p9J+Rw2W7nCuBNRIhYPqKvLHUjI3Lwu6vkhF87uPZV6VtZwFmx/L7yuarJxFlzXkTGLRIvj5PZhxL+xcB+2Ph5PGQOvDyUvCA5YxpvJT1UIgXUQaAh+JSA9VXeyV5mH3TtpzQAdVzfGxKn/Ed7a6B7gsSGyTgEl9+vS5KiMjI2hGmZmZhJIuFJGsK9xlw0kfStpAaYItH3T9qrDyK5gyCratgo4nwSn3c1CzLnxapAweO4vcfYWMGdqdjC7NSU3x9fVHXzS/+1jmVVnLWbD5sfy+osnKWXRZQ84kjtUz6D3/FshZAy0OhYs+cMaEk9hUYsYYEwlV3SkimcAgoFRDTkSOA3oAHwGjgevDWHUW0NbjcxtgU0TBmvjYuhwm3w6rp0OTTnDhe9D55JLZqSlCo9ppNKoNA7q2iGOgxphkYA05E3+bFjpjwa3JpFrN5nD2S9DjHHsLpTEm4YlIM2C/24irBZwEPOSVphfwEnAq8Bvwpojcp6p3hJjNPKCT2z1zI3A+cGG0tsHEQO52yHwQ5r0MaXXhlPvhiKugWlq8IzPGJDFryPlh4/PEwPY1MOM+WPwB1GoMgx5kbm5HTugZzqMjxhgTVy2B/7nPyaUA76rqZ15pagPDVXU1gIj8DbjUe0UiMgHIAJqKSBYwWlVfUdUCEbkemAKkAq+q6pKK2iATRYUFMP81mPlf2LsLel8K/f/jDO5tjDERSuiGnIjUBGYBNXBifV9VR5dzXa8CpwFbVLWH17xBwFicCvJlVX2Qv8bnmSQi7wDWkIuWnK0w6xH48VVIqQbH3QrH/BNqNkDtOThjTBJR1Z+BXkHSfOv1eT/OHTrvdH7f5qSqXwBflDNMEw+rZ8DkUbB1mfO89ykPwAE9gi9njDEhSuiGHDY+T+WyL4eD1k6E7ybB/jw4/BI44Tao3zLekRljjDFRUSt3E7x9Pqz4Ehq1g/PegkNOtee9jTFRl9ANORufp5Io3A/zX4evH6L9nq3Q9XQ48S5o1jnekRljjDHRsXcXfP0wR8x7HqrXhJPuhiP/DtVqxDsyY0wlldANOag84/NEewyJeI+bsnNnHkCp6WXSqdJs63e0/208tfN+Z2eDbiw+5B8UtOgFSzbh66VrFT1miq+4K1qyjpkS6foqanweG5vHt1jHXRXG5zEmJEWFsHA8TL8Xcrex+YABtBzxLNSzt04aYypWwjfkKsv4PNEeQyLe46Y8t/x7ADIyjvKd7rdZMHU0bFoAzbvBWWNp2OlkCr7+Oq5jpviKu6Il65gpka6vosbnsbF5fIt13FVhfB5jglr7DUweCX/8AgceBYPeZ/mKXbS0RpwxJgYSviFXzMbnSRJ//OIMJbBqGtRvA2c+Bz3Pg5TUeEdmjDHGRMeOtTD1Llj6CTRoC+e8Ct3Pdp6DW5EZ7+iMMVVEQjfkbHyeJLJjHYcsewIyv4aaDWDgvdD3auc5AWOMMaYy2JdD+zXjYfYk5wJl///A0TdA9VrxjswYUwUldEMOG58n8e3ZBrMfg3kv0UyBY26EY2+CWo3iHZkxxhgTHUVF8PNEmDaGg3L+cHqaDBgNDVrHOzJjTBWW0A05G58ncdUo2svg3I9h3IeQnwPpFzK3RgZHDRwe79CMMcZUYU9MXcHY6Sv9zh/aoTphPVa5fo7zHNymBdC6Nws6/R+HD70m4jiNMSZSCd2QMwmosIDCBeM5+48PWV/YhOltzyNj6OWkHtCNfQn65jhflXq7kZ+X/H3jgE7cPNCGQjDGmMrg5oGdS47p573gvODqnWtKv5grJLuynGe+f3kP6rWEs16AQ89l96xZUY7Y6iljTPlYQ86ERhV+/YzCqfdw8e/nsEAvYy9p1N5YjfRJuxl/hffwfonDs1I3xhhjAsrP5aC1E+GbjwGF4/8Fx9wENepWWJZWTxljysMaciaoBjuXwCv3QdY8MuucxqLU7uwtcEZtyM0vZNGGnWQu34K9l9IYY0zSUoXFH8DU0bTfnQXdzoSB90Cjg+IdmTHG+GQNOePf5qUwfQy9Vkx2upWcPo4l248kb/qqUsny8gtZumk3h1pLzhhjTDLauMB5Dm7DHDigJwsP/ju9zvxHvKMyxpiArCFnytqVBTMfgJ/ehrR6rGl/MQdf8DCk1ab7ss3USkslN7+wJHmttFS6taoPmzfGMWhjjDEmTNl/wPR7YNFbUKcZnPEUpI9g16zZ8Y7MGGOCsoac+UveDpj9OMx5AVA48u9w3C2sn/szB6fVBiCjS3PS2zbkhzXbKFKonZZKetuGZHRpzuzNy+IbvzHGGBOK/Xvhh2ecOq9gnzN0znG3Qs368Y7MGGNCZg05A/vzYO6Lznhwe3fDYedD/1HQ8MAySVNThPFX9GPw2Fnk7itkzNDuZHRpTmqKxCFwY4wxJgyqNN36HTzzT9i5DrqcCiffC006xDsyY4wJmzXkqrKiQvhpAsy8H3ZvhE4nOwOcHtAj4GKpKUKj2mk0qg0DuraIUbDGGGNMBP74BSbfTo+1s6F5N7jkEzg4I95RGWNMuVlDripSheVfwrQxsHUZtO7tjI/T/rh4R2aMMcZERWGRsiM3n4K9e5j+v3vJ+O0JUms1YEWna+l8/n8h1U6BjDHJzY5iVc36OaQvGgVfL4XGHWD4/6DbUBDrGmmMMaZyKCxSLn75e9Zu3sl+UrhhVzfSG45j/PVD2DTvZzpbI84YUwnYkayq2LoCpo+BXz+jdvWGcOrjcPglkFo93pEZY4wx0aNK5ozJLPotj3xqAJBLTRbl1iFz/X4b89QYU2lYQ66y2/07ZD4AC8dD9TrQ/w7m7O/BcUcMjndkxhhjTHRt+RWm3M6S5Q3I02GlZtmYp8aYysYacpXV3l3w7Vj4/lkoKoC+V8Px/4I6TSnMzIx3dMYYY0zUVNufDV/8C+a9AjXq0r3PGGotqG5jnhpjKjVryFU2Bftg3ssw6xFnXLhDh0P//0Dj9vGOzBhjjImuwgL48VX6zRkDhbnQ+zLo/x8yajUmfescG/PUGFOpWUOusigqhF/egxn/hV3rocOJzlACrdLjHZkxxhgTfaumw5RRsPVXchr2pNEFz0OL7gCkgo15aoyp9Kwhl+xUncps2mjYvBhaHgZnjIMO/eMdmTHGGBN9f66Cr/4DKyZDo/Zw/tv89HttMtxGXDEb89QYU9lZQy6ZbZwPU0fD2tnQqB0MewW6nw0pKfGOzBhjjImuvJ3OYwNzXoBqNeGkMXDkdVCtBvyRGe/ojDEm5qwhl4y2rabbkoch81uo3RQGPwK9L4VqafGOzBhjjImuokJY8AbMuA9yt0Gvi2DAXVC3ebwjM8aYuLKGXDLJ3gxfPwQL/kcTqsEJt8HRN0CNevGOzBhjjIm+32bD5Nth8y9w4NEw6AF79tsYY1zWkEsG+7Lhu6fgu6ehcB/0vpQ51Y7l6P5nxTsyY4wxJupq5v0B71wEyyZBgwNh+OvQ7UwQe1mJMcYUs4ZcIivIh/mvwdcPQ+6f0P0sOPFOaNKBfBsLzhhjTGWzLxtmP07fueOcxwX63wFHXw/Va8U7MmOMSTjWkEtERUWw5EOYcS/sWAvtjoOBY6B173hHZowxxkRfURH8NAGmj4GczWxpkcEBI56D+q3iHZkxxiQsa8glmtUznaEEfv8JWvSAER9AxwHWncQYY0zltP4HmDwSNi2ENkfA+W/z66ocDrBGnDHGBGQNuUSxaRFMuxvWzIQGbeGsF+DQc20oAWOMMZXTzg3OhcvFH0C9VnD2S9DjHKfeW5UZ7+iMMSbhWUMu3rb/5rxSefH7UKsRnHI/9LkCqteMd2TGGGMSmIjUAZ4F8oFMVX0rziGFJj8Xvh3r/EPh+H/DsTdBWp2orP6JqSsYO31lqWntRn5e8vfQDtXJyIhKVsYYE1fWkIunXRvhmb4gqXDcLXDMjVCzQbyjMsYYEyIRaQu8ARwAFAEvqurYcq7rVeA0YIuq9vCaNwgYC6QCL6vqg8DZwPuqOklE3gESuyGnCr+879yF270Rup/tPP/d8MCoZnPzwM7cPLCz3/mZ9rIwY0wlYQ25eGrQGgY/BJ0HQ/2W8Y7GGGNM+AqAW1R1gYjUA+aLyFRVXVqcQESaA3mqmu0xraOqrvJa1+vA0zgNQzzSpgLPAAOBLGCeiHwKtAF+cZMVRnezomzjfPhyJGTNhZaHwbBX4KCj4h2VMcYkNXsAK976XG6NOGOMSVKq+ruqLnD/zgaWAa29kp0AfCIiNQFE5CpgnI91zQK2+8imL7BKVdeoaj4wERiK06hr46ZJzPp89+/w0XXw0onOW5jPeBquyrRGnDHGRIHdkTPGGGOiQETaAb2AOZ7TVfU9EWkPTBSR94DLce6uhao1sMHjcxbQD6cx+LSInApM8hPT6cDprVu3DqlLYU5OTlS6HqYU5nPAmvconPUpogVktT2bdQcNp3B3bZg1K+pxhJM+lLSB0gRbPlr7MNZiGXc084pkXYlczoLNt3IW27xiWc7CYQ05Y4wxJkIiUhf4ALhJVXd7z1fVh0VkIvAc0EFVc8JZvY9pqqp7gMsCLaiqk4BJffr0uSojhDd8ZGZmEkq6ABnC0k9g6p2wcz0cchqcfC8HNj6YcJ6ECzeOcNKHkjZQmmDLR7wP4ySWcUczr0jWlcjlLNh8K2exzSuW5SwcidkVwxhjjEkSIlIdpxH3lqp+6CfNcUAP4CNgdJhZZAFtPT63ATaVI9SK9fvP8Ppp8N7fIK0eiw67F85/CxofHO/IjDGmUrKGnDHGGFNOIiLAK8AyVX3cT5pewEs4z7VdBjQWkfvCyGYe0ElE2otIGnA+8GlkkUdRzlb49J/wwvGwZSmc+jhcM4udjXrGOzJjjKnUrGulMcYYU37HABcDv4jIInfaKFX9wiNNbWC4qq4GEJG/AZd6r0hEJgAZQFMRyQJGq+orqlogItcDU3CGH3hVVZdU0PaEriAf5jwPsx6B/blw5N/hhH9DrYbxjswYY6oEa8gZY4wx5aSq3+D7GTbPNN96fd6Pc4fOO90FAdbxBfCFv/kxpQorJsOUUbB9DXQ6GU65H5p2indkxhhTpVhDzhhjjDGh2bIMJt8Oa2ZC084w4gPodFK8ozLGmCrJGnLGGGOMCSx3O8y8H358FWrUhUEPwRFXQGr1eEdmjDFVljXkjDHGGOPf4g/hs5th327ocwX0HwW1G8c7KmOMqfKsIWdC9sTUFYydvrLUtHYjPy/5e2iH6iThkCbGGGMCqdMMWqXDKQ9Ai27xjsYYY4zLGnImZDcP7MzNAzv7nV9Ro9YbY4yJo/bHOf+MMcYkFBtHzhhjjDHGGGOSjN2R80NE6gDPAvlApqq+FeeQjDHGGGOMMQZI8DtyItJWRGaKyDIRWSIiN0awrldFZIuILPYxb5CILBeRVSIy0p18NvC+ql4FnFHefI0xxhhjjDEm2hK6IQcUALeoalfgSOAfIlLqSWsRaS4i9bymdfSxrteBQd4TRSQVeAYYDHQDLnDzaANscJMVRrgdxhhjjDHGGBM1Cd2QU9XfVXWB+3c2sAxo7ZXsBOATEakJICJXAeN8rGsWsN1HNn2BVaq6RlXzgYnAUCALpzEHCb6fjDHGGGOMMVVL0jwjJyLtgF7AHM/pqvqeiLQHJorIe8DlwMAwVt2av+68gdOA64fTGHxaRE4FJvmJ6XTg9NatWwd9Y2NOTk5U3+oYyfrCXTbU9KGkC5Ym0Pxo78NYiWXcVs5CS2PlLLHyi2U5M8YYYyqLpGjIiUhd4APgJlXd7T1fVR8WkYnAc0AHVc0JZ/U+pqmq7gEuC7Sgqk4CJvXp0+eqjCADqGVmZhIsTTgiWV+4y4aaPpR0wdIEmh/tfRgrsYzbylloaaycJVZ+sSxnxhhjTGWR8A05EamO04h7S1U/9JPmOKAH8BEwGrg+jCyygLYen9sAm8KJcf78+X+KyLogyRoAu8JZbwWuL9xlQ00fSrpgaQLNbwr8GUIciSba330s87JyljxiWc6inV+0ytlB0Qmn8gmxnoLE/F6jnT7SY0iw5e0YEtu8Kms5Czbfylls80rMekpVE/Yfzt2yN4AnA6TpBfwKdMB5lu1t4D4/adsBi72mVQPWAO2BNOAnoHsFbMuLibK+cJcNNX0o6YKlCTQf+DHa30ss/kX7u49lXlbOkudfLMtZtPOLZTmzf5Xzew0nfaTHkBCOL3YMiWFelbWcBZtv5Sy2eSVqPZXoL/E4BrgYOFFEFrn/hnilqQ0MV9XVqloE/A0oc9VRRCYA3wNdRCRLRK4AUNUCnDt4U3BepvKuqi6pgG3x+ZxdnNYX7rKhpg8lXbA00d5PiSCW22TlLLQ0Vs4SK79YljMTWLJ+r+Gkj/QYUlnLXLLWVZW1nIWbX7KwchZF4rYUjUl4IvKjqvaJdxymcrNyZoyJhB1DTCxYOTNgr9U3yeXFeAdgqgQrZ8aYSNgxxMSClTNjd+SMMcYYY4wxJtnYHTljjDHGGGOMSTLWkDPGGGOMMcaYJGMNOWOMMcYYY4xJMtaQM0lLRM4UkZdE5BMROTne8ZjKSUS6isjzIvK+iFwX73iMMcnD6ikTC1ZPVV3WkDMJRUReFZEtIrLYa/ogEVkuIqtEZCSAqn6sqlcBlwLnxSFck6TCLGfLVPVa4FzAXvVsTBVn9ZSJBaunTCisIWcSzevAIM8JIpIKPAMMBroBF4hIN48kd7jzjQnV64RRzkTkDOAbYHpswzTGJKDXsXrKVLzXsXrKBGENOZNQVHUWsN1rcl9glaquUdV8YCIwVBwPAV+q6oJYx2qSVzjlzE3/qaoeDYyIbaTGmERj9ZSJBaunTCiqxTsAY0LQGtjg8TkL6AfcAJwENBCRjqr6fDyCM5WGz3ImIhnA2UAN4IvYh2WMSQJWT5lYsHrKlGINOZMMxMc0VdVxwLhYB2MqLX/lLBPIjG0oxpgkY/WUiQWrp0wp1rXSJIMsoK3H5zbApjjFYiovK2fGmPKy44eJBStnphRryJlkMA/oJCLtRSQNOB/4NM4xmcrHypkxprzs+GFiwcqZKcUaciahiMgE4Hugi4hkicgVqloAXA9MAZYB76rqknjGaZKblTNjTHnZ8cPEgpUzEwpR1XjHYIwxxhhjjDEmDHZHzhhjjDHGGGOSjDXkjDHGGGOMMSbJWEPOGGOMMcYYY5KMNeSMMcYYY4wxJslYQ84YY4wxxhhjkow15IwxxhhjjDEmyVhDzhhjjDHGGGOSjDXkjDHGGGOMMSbJWEPOmCpIRDqKyC9e02qIyG8i0i1ecRljjDHFrK4yJjBryBlTNa0B2oqI5zHgauBrVV0ap5iMMcYYT1ZXGRNAtXgHYIyJPVUtEpH1QDtgjYjUAm4BMuIZlzHGGFPM6ipjArM7csZUXcuAQ9y//wF8qqpr4xeOMcYYU4bVVcb4YXfkjKm6lgFdRGQWTuV4ZJzjMcYYY7xZXWWMH3ZHzpiqq/gq543AW6q6Oc7xGGOMMd6srjLGD1HVeMdgjIkDEekJ/A+oDxyuqrviHJIxxhhTitVVxvhnd+SMqbqWA4cCL1rFaIwxJkFZXWWMH3ZHzhhjjDHGGGOSjN2RM8YYY4wxxpgkYw05Y4wxxhhjjEky1pAzxhhjjDHGmCRjDTljjDHGGGOMSTLWkDPGGGOMMcaYJGMNOWOMMcYYY4xJMtaQM8YYY4wxxpgkYw05Y4wxxhhjjEky1pAzxhhjjDHGmCRjDTljjDHGGGOMSTLWkDPGGGOMMcaYJGMNOWOMMcYYY4xJMtaQMwlNRHJE5OB4x1ERROR1Ebkv3nFEk4hkiEhWhOs4TkSWRyumCOK4W0TejGD5JSKSEb2IQsqzmYgsF5GaIaTtKSLfxSIuYyobEXleRO6MwnouFZFvohFTOfMfISJfxSt/T9GoE6P1vURKRNaKyEnlXDYudaCIXCMiT4aRfq6IdK/AkEwIrCFnABCRY0XkOxHZJSLbReRbETki3nGpal1VXVMR6xYRFZGOFbHuZFXRjctQ9rmqzlbVLhUVQ0Xwtd9UtbuqZsY4lJHAa6q6142ru4h8JSI7RGSniMwXkSFufD8DO0Xk9BjHaEzCc0/E89yLiTtE5HMRaVs8X1WvVdV74xljNKjqW6p6cjTWVZF1aqgN3mT8Xrz3WzzqQBFJA+4AHnE/t3PjynH/bRaRZ0WkusdijwL3xDJOU5Y15AwiUh/4DHgKaAy0BsYA++IZV7yJSLV4xxBNybA9yRBjohKRGsDfAM+7iJOAqUALoDnwT2C3x/y3gGtiFaMxSeZ0Va0LtAQ249SRCSPS42VlO96KSGq8Y0hiQ4FfVXWj1/SG7m/gUOAo4B8e8z4F+otIyxjFaHywhpwB6AygqhNUtVBV81T1K/eKffGVsG9F5Cn3jt2vIjKgeGERuUxElolItoisEZFrPOZliEiWiNwiIltE5HcRucxj/usi8ox7tTNbROaISAeP+SVXqkJIe7LbrWyXe+XoaxG50tcGi8gs98+f3KtN53nEepuI/AG8JiIpIjJSRFaLyDYReVdEGnus50j3TuZOEflJAnSlE5FeIrLAjf0doKbX/NNEZJG7ru9EpKfHvLYi8qGIbHXjeNqdniIid4jIOnf/viEiDdx5xVfUrhCR9cAMd/p7IvKHu59mids1QkSuBkYA/3b3ySR3eisR+cDN+zcR+adHXLXc72WHiCwF/N7FDWOfl+qe6bH/s0VkqYic5THv0v9v777jo6j2/4+/TgKhQ5AiJUgTkSodK0QRBSyg2ACxt+vVn3rv9QtWsOK19y4WULBfG1IloIJUkSodJPQWICSQZPf8/phNTMIm2c325P18PPJ4ZHfOzPnsZHY+OTPnnDHG/GKMedYTw0ZjTP98y5t7PuMhY8x0z/Ez3rPsmG6gppjuMKXYb3nbMsZUMsa8aIzZ5vl50TgNL1++IwM8n/uQMWarMeY/RezinkCatTbVs15doDnwjrU2y/Pzq7U2/1XtFKBPbiwicizPHe4vgLa575l8d+HzfYfvN8bs8Xz3h+UrW8tzbt7tOVc/aIzx+v+XMeYlY8wWY8xB49xBPyvfstHGmC+MMeONMQeB67ysX2Rd5u9c/oIxZh8w2hS602WMOdkYM804PXNWG2OuKPSZveZgb+d3z/vF5bXOppicmK9cG+BN4DTPttPyxfOGMWaSMeYwTqMi/9+ltjHme8++2O/5PSnfdlOMMY959skh4/ReqJtv+TWefbjXGPNQoXN6gV4YpphhBcaYHsaYuZ59sN0Y86px7oAVmxfzf35PrGnG6bJ/sY9/E+P5W+8yTt5aaoxp7y1GoD8wq4hlWGt34VwUbJvvvSPAIiAod3SldNSQE4A1gMsY86Expr8xpraXMj2BDUBdYBTwlfm7QbMLuBCoCVwPvGCM6ZJv3QZALZw7fTcCrxWqYwjOHcDawDrgiWJi9VrWc/L9ArgPqAOsBk4vaiPW2l6eX0/xdN/8NF+sxwFNgVtw7mAMAnoDjYD9wGueOhsDPwCPe9b5D/ClMaZe4fo8J+3/AeM8ZT8HBudb3gUYi3N3pA7wFvCtcRoA8Th3TDcDzXD240TPqtd5fs4GWgDVgVcLVd8baAOc73n9I9AK5w7NYpy7Mlhr3/b8/rRnn1zk+QfgO+APT719gLuNMbnbGgW09Pycj3NHyCs/9nlh64GzcI6hR4DxpuAVwJ44f++6wNPAe8YY41n2CTAfZ5+OBoYXFZ8PfN5vXtZ9ADgV6AScAvTA6caSq7jvyHvArdbaGkB7PA1yLzrg7Idce3G+I+ONMYOMMccXXsFz9TUbiKmurCLhZIypClwJ/FZMsQY456DGOOfBt40xud+rV3C+3y1wzsfX4ORKbxbgnCeOwzl/fW4KjnkdiJPrEvGcgwopqa7cXF6fQrnWGFMN55/1TzzLhwCvm4LjoLzmYG/n9xLyWrE5MT9r7SrgNmCuZ9uJ+RYP9cRQAyjc9TIOeB8nt5wAZHJsfhzq2T/1gQScPI4xpi3wOs5Fuob8fX4uDRdwD87xcRpOHr3d89mKyot44qiIk4OnemK8E/g437EFRf8PdR7QC+difSLOMby3iBgL548CjDGNcHJ84e/AKpycJhGihpxgrT0InAlY4B1gtzHm20L/+O0CXrTWZntONKuBCzzr/2CtXW8ds3BOOGflWzcbeNSz7iQgnYL/OH5lrZ1vrc3BSUydigm3qLIDgBXW2q88y14Gdvi/N3ADo6y1R621mTgJ6AFrbaq19ihOY+Ay43RJuRqYZK2dZK11W2unAQs9sRR2KlCRv/fhFzgJO9fNwFvW2nmeu6If4nRtPRXnn/5GwL3W2sPW2iP57qoMA5631m6w1qbjNGSvMgW7zIz2rJcJYK0da609lO/znGI8d/G86A7Us9Y+6rmjswHnGLnKs/wK4Alr7T5r7Rac/e6vwvu8AGvt59babZ59/Cmw1rNPcm221r5jrXUBH+Ik3eONMSd44n/YE/svOF1BSsXP/VbYMJzvwC5r7W6cpJu/UVncdyQbaGuMqWmt3W+tXVxEHYnAoXzxWpwG/ibgOWC7ce4ktiq03iHPuiJS0P88d38OAn3xjB8qxkOe89gsnIt8V3guxF0J3Oc5f2zC+T56vahkrR1vrd1rrc2x1j4HVKJgvpxrrf2f53xY4HzpY13brLWveLZf+Hx7IbDJWvu+Z/li4Evgsnxl/MnXxeW1knKir77x9DRwe+4Q5fHsxy+ttRnW2kM4DZzehdZ/31q7xrMvPsv3eS4DvrPW/mKtzQIexvkfyW/W2kXW2t88+3QTToO2cBxFORXnAu1Tnjz2E86F3SH5yhT1N8nGaeCeDBhr7Spr7fYi6kkkX/7IZ4/nO7AVOIxzESE/5Y8IU0NOAOeKl7X2OmttEs5V/0bAi/mKbPX8Y5hrs6cMnrt4vxmnK0YaTkOmbr6yez0nmFwZOCemXDuKWVZYUWUbAVvyfR4L5O+asML8PWg3fyOzsN2FkkFT4GtPl4Y0nKtPLpwxR02By3OXeZafidOQKKwR3vdh/nr+XWhbTTzrNcFprOTfh/m3m387m4EKnvhy5e0XY0y8MeYp43RVPIjzTz4U/Hvl1xRoVCiu+/Ntv8B+LxSLrwrv8wI83VuW5Ku/faF4844Ja22G59fqntj25XuPQrH6rBT7rTBvf6dG+V4X9x0ZjPOd2myc7sKnFVHHfpykncdzAeIOa21LnL/lYeCjQuvVANJ8/Bwi5ckg69z9qQTcAcwyxjQooux+a+3hfK9zv+N1ce70FP7+e727Y5wu1qs8XeHScO4E5T/P5D+f/5gvrw3zsa7izoFNgZ6FzvfDcO425vInXxeX10rKib4q8vMYY6oaY94yTvfIg8BsINEUHEvn6/8UGRR9N6tYxpiTjNOtc4cnjifxL3dssda6871X+G/q9TN4Gn2v4vQi2mmMeds4cyJ4c0z+8Kjr+Q5UBX4FJhdarvwRYWrIyTGstX8CH+D8w5yrcb7uauB0U9hmnLE1X+LMXnS85ws/CchfNhy2A/n7vpv8r60zg2B1z8/PxWyn8BW3LUB/a21ivp/K1umStgUYV2hZNWvtU0XE520f5q/niULbqmqtneBZdoLxPjB9G06yzL/NHJyB+d4+01Ccrjnn4vyD0MzzvvFSNjeujYXiqmGtzb3ruB0nMXv7TL4q8iqnMaYpzh3AO4A6nuNrOb4dX9uB4zzdonLlj/UwTnLKrSseOKZbrIe/+60wb3+nbSWs42zY2gXW2oE43Wr+h3PV2JuleMa7FrGdLTgJPe977ekuk0AxXWpEyjvP3aSvcC7inVlEsdqerom5cr/je3DujBT+/heeVALPRcYROD0danvOdwcoeL7LO9dYa/vny2sf+1hXceeqLcCsQuf76tbafxSzTnGKy2sl5cTCioq7uM/zb5y7mT2ttTVxuhmC7/kj//8UVXC6h+YqkD8o2Ngt7A3gT6CVJ477fYwBnGOoiSk4ptLr8eONtfZla21XoB1Ofri3iKIl5Y9MnP8LTzP5xhHiDNv4w5dYJDTUkJPcwc3/Np5BwMaZYnkIBftC1wf+nzGmojHmcpwv7yScfwIrAbuBHONMNBGJga8/AB08Y4Eq4MysVNyJFZzGTknPqHsTeMLToMA4z+ka6Fk2HrjIGHO+545NZeMMUk7ysp25OA2s/2eMqWCMuZSC3QPfAW4zxvQ0jmrGmAuMMTVwxnhtB57yvF/ZGHOGZ70JwD3GmdSjOs6Vvk+LuHsHztWzozhXFqt6yhe3T+YDB40zGUkVz+dsb/5+NMVnwH3GGVSehNN/vzi+7PP8quEk6t3gTKxDwQsMRbLWbsbp6jraGJPguZOVf/zaGqCyZz9XxBmzVtSkH/7ut8ImAA96jp+6ON10SnxGnSfuYcaYWtbabJwuXq4iis/Hudrc2LNubWPMI8aYE40zKU5d4AYKfq+TgZ+s011URLzwnJMH4oxBWlVM0Uc839mzcLopfm6dLt+f4eSRGp5c8i+8f/9r4OSJ3UAFY8zDOGPPfeJnXd58D5xkjBnuyfUVjTHdjTPZiC8KnweLy2sl5URv204ynklCfFQDZ1xcmnHG9I/yY90vcPL76Z46H6Fg42sJMMAYc5xx7tLeXUIcB4F0Y8zJQOGGcXH5Yx5Oo/H/PH+PZJw8NrGI8nk8f7uenvx2GDhC0fljEsV09/RctB+Oc/dvb773uuKMq5QIUUNOwOnj3BOYZ5yZn37Duevx73xl5uFM9LAHp5/5ZZ7+54dwJgT5DOfW/FACGIdUWtbaPcDlOJNd7MWZWWkhxT9CYTTwoXG6fFxRRJmXcD7PVGPMIZx909NT5xacuzT34yTeLThXu475Xnn62F+KMzHJfpxxDF/lW74QZzzBq57l6zxlc5PzRcCJwF84XUav9Kw6Fmew+GxgI86JurjG1Ec43TK2Ais5duDyezjjsdKMMf/LV3cnz/b3AO/i3JUCJ7lt9iyb6omlOKMpeZ/nsdauxBnjMRcn2XXA6d7hq2E4g8v34kxK8ymeY8JaewBnwPm7/N3/v6iHmfu137ys/zjO8bgUWIYzWYqvz+sbDmwyTpec23DGZh7Dc4x9kG95Fs6dw+k4/0Qsx/ns1+VbbRjOxQoROdZ3xph0nO/PE8C11toVRZTdgXPu3oYzTuk2T+8WcM7Jh3EmGfkFZzKRsV62MQVnUqU1OOebI/jfHdzXuo7hyefn4YyB3ub5TP+l6AtchY0m3/m9hLxWbE704idgBbDDGLPHx3heBKrg5K3fOLZbYJE8f+c7cRpM23H+T9rF3/9TjMO5E7UJJ/d9euxW8vwH53+jQziN28JlR1NEXvTsp4txZpXcgzMByzX5jq3i1PTUtx/neNqL03vKm++Ak43TSyO/NM93YCdOLr04X3fYi4EUa61PvUskNEzB7skixzLGXAfcZK0tqktJ1PF0Q0gFhllrZ0Y6HokOxpni+k9rrT9XZmOGcWZM/RnobL1MHFOobAfgbWttUWPuRMQHnrsk4z1jzKUM8vR4ScPpHrkxwuGEhHEepdPWWnu3j+XnATdaa5eHNDApVpl6GKSUb8aZEn8eTleKe3G6QRQ3XbSUcZ4uoPtw7hieh3MH1dsYxjLBOjNinuxj2WU4V1hFRKQQY8xFwAyc/yWexelNsSmSMYWSdR6l40/5nqGKRXynrpVSlpyG88yxPTjdAQeVdFdCyrwGOA+9Tsd5NMI/rLW/RzQiERGJBQNxuphuwxlacpVVNzaJMupaKSIiIiIiEmN0R05ERERERCTGqCEnIiIiIiISYzTZSRDUrVvXNmvWrNgyhw8fplq1asWW8Ucg2/N3XV/L+1KupDLFLQ/2PgyXcMat48y3MjrOoqu+YB1nixYt2mOtLeqh7uWaL3kKovPvGuzygZ5DAjm/RLNYzVVl9TgrabmOs/DWFbV5ylqrnwB/unbtaksyc+bMEsv4I5Dt+buur+V9KVdSmeKWB3sfhks449Zx5lsZHWfRVV+wjjNgoY2CnBCNP77kqcL7M1DReP7wtWwg5widQ8JbV1k9zkparuMsvHVFa55S10oREZEYY4xpYYx5zxjzRaRjERGRyFBDTkREJAoYY8YaY3YZY5YXer+fMWa1MWadMWYkgLV2g7X2xshEKiIi0UANORERkejwAdAv/xvGmHjgNaA/0BYYYoxpG/7QREQk2miykxDJzs4mNTWVI0eOAFCrVi1WrVoVtO0Hsj1/1/W1vC/lSipT3PJg78NwCSTuypUrk5SURMWKFYMclYhEG2vtbGNMs0Jv9wDWWWs3ABhjJuI8qHhloPUVzlMQ3PNsNOYpX8sGkovKW65SnhKJHDXkQiQ1NZUaNWrQrFkzjDEcOnSIGjVqBG37gWzP33V9Le9LuZLKFLc82PswXEobt7WWvXv3kpqaSvPmzUMQmYjEgMbAlnyvU4Gexpg6wBNAZ2PMfdbaMYVXNMbcAtwCcPzxx5OSklJgefXq1Tn++ONp3LgxxhgAXC4X8fHxQQk8kG35u64/5X0pW1yZktYP5j4Mp9LEba3lwIED/PHHH6Snp/u8Xnp6+jHHY2kFsi1/1/WnvC9lSypT3PJg7sNwCmfcsXqc+UMNuRA5cuRIXiNOpDSMMdSpU4fdu3dHOhQRiRxvScRaa/cCtxW3orX2beBtgG7dutnk5OQCy1etWkVSUlKBPBXMC2bReMHR17KBXFQsbxcda9SoQXp6Ot26dfN5nZSUFAofj6UVyLb8Xdef8r6ULalMccuDuQ/DKZxxx+px5g+NkQshNeIkUDqGpDyoejgVPr0aDm6LdCjRKBVoku91EhC0HaVzjARKx5CUC9YNf0yEH0dGOpICdEdOREQiI3M/pPyXbgvfhoRqsHMF1GwU6aiizQKglTGmObAVuAoYGtmQRETKkS0L6LL4/+DQWmjcFbIyIKFqpKMC1JATEZFwc+XA4g/gpycgcz87Gp5Ho2GvQfV6kY4soowxE4BkoK4xJhUYZa19zxhzBzAFiAfGWmtXRDBMEZHy4cBWmD4aln1GpYTaMOhN6HglxEVPh0Y15AJgjLkIuKhx48bHDGKsVasWhw4dynvtcrkKvA6Ur9t74403eO+99zjllFPYvHkz06dPZ9++fbzzzjvcfPPNQa2ruHLTpk1jxIgRuFwurr32Wv71r395Lbdv3z6GDx/OypUrMcbw2muv0bNnT9q3b0+1atWoUKECFSpUYNasWT7Fnt8///lPLrroIvr161dy4RIcOXKEfv36kZWVRU5ODgMHDuSBBx44ptztt9/O5MmTqVevHvPmzTtmucvlonfv3jRs2JDPP/+8yLqCObjaH9E4iFwDyL0Ld9ylrS9x/x+cuO49qh/eTFqt9qxr+xA7TH3WLCxd2yRW/17eWGuHFPH+JGBSmMMJm5dffpk33niDLl26sHHjRubMmUNaWhrjxo3j9ttvD1sckydP5q677sLlcjF8+HBGjRrltVxaWhrXX389y5cvxxjD2LFjOe200/LWz87O5pZbbmHkSP+7YN14441ceumlXHDBBYF+HLZs2cI111zDjh07iIuL45ZbbuGuu+46ptxLL73EO++8g8vl4tZbb+Xuu+/OW/bCCy/w7rvvYoyhQ4cOvP/++1SuXDng2ESiWlYGzHkFfn0R3C4469/Mt905q1P/SEd2LGutfgL86dq1qy1s5cqVBV4fPHjwmDKB8HV7rVu3ths2bCjw3rJly2y7du2CXldR5XJycmyLFi3s+vXr7Z49e2zHjh3tihUrvJYdMmSIfeedd6y11h49etTu37/fWmtt06ZN7caNG32O2ZsuXbrYLVu2BLSNXG632x46dMhaa21WVpbt0aOHnTt37jHlZs2aZWfPnl3k/n7uuefskCFD7AUXXFBkXYWPpeLMnDnT57Kh3p6/6/pa3pdyJZUpbnmw92G4hDtuv+vbs87aT4ZYO6qmtS+0t3bF/6x1u0u3rSLiABbaKMgJ0fjjS56yNri5KhrzVFFl8+epo0eP2vbt2/uVp/zJc8UJZp7atm2bXbRokbXW+cytWrU6Jqbc/Xz48GG7b98+26dPH7tmzRprrbWpqam2WbNmNiMjw1pr7eWXX27ff/99r3X5k6esDe75KhrzlK9llauirC6329plX1j7fDsnV3063Np9G0u3rSLiCHaeip57gxJ0t912Gxs2bODiiy/mhRdeoHr16gCMGjWK9evX06lTJ+69995it7Ft2zauvvpqOnfuzMknn8z8+fP9jmP+/PmceOKJtGjRgoSEBK666iq++eabY8odPHiQOXPmcOONNwKQkJBAYmKi3/XlWrNmDWeeeSYdOnTghRdeYMeOHSQlJZV6e/kZY/L2Z3Z2NtnZ2V4HfPfq1YvatWt73UZqaio//PADN910U1BiEolKRw7CtIfh9VNhQwr0eRj+uQDaDgRNklDuRWueGjx4sF95ytc8V1go81TDhg3p0qUL4Mws2aZNG7Zu3VqgzKpVqzj11FOpWrUqFSpUoHfv3nz99dd5y3NycsjMzCQnJ4eMjAwaNdIYVimjtv0O7/eHL26AKolw3Q9wxUdQu1mkIyuWulaGw48jqbL1d4gP3u6uVKc1XPx8sWXefPNNJk+ezMyZM6lbty4PPfQQAI888girV69myZIleWUHDBjAu+++W+AknZOTQ//+/XnggQe44ooryMjIwOVyFajjrLPOyutO6Xa7ifP0G3722Wc599xzAdi6dStNmvw96VpSUpLXboYbNmygTp06XH/99fzxxx907dqVl156iWrVqmGMYdCgQcTHx3Prrbdyyy23FPvZc3JyuPrqq3n11Vfp0aMHt99+OyeffHKx63j7TPnl/0zgdIvs2rUr69at45///Cc9e/b0afu57r77bp5++umgdrkViRpuFyz5GGY8Bod3wSlDnUZczYaRjky8+XEk7FhGFVdO0HJVNOYp+DtXFZenGjVqxNKlS4+Jt6g85Wueyy8ceSrXpk2b+P3334/JU+3bt+eBBx5g79695OTkMGnSpLzHCDRu3Jj//Oc/nHDCCVSpUoXzzjuP8847z6f4RGLGoZ0w41EnX1WtAxe9BJ2HQ1xsPAtSDTkBYNKkY4df/O9//6NNmzb07+/0Ca5a9dgZen7++ee834t6Bo1zJ7kgb3evcnJy+OOPP3j99dfp2bMnd911F0899RSPPfYYv/76KzVq1CAzM5O+ffty8skn06tXryI/z1dffUWbNm3o0aMHAO3ataNKlSoADBw4MO9K6eWXX87EiRMLPAQ1/2cqTnx8PEuWLCEtLY1LLrmE5cuX0759e5/W/f7776lfvz5du3YtM+N7RPJsngM/joAdS6FJTxg60ZnpSyQAwchT4D1XBZqnOnbs6NP6+YUjT4EzjnTw4MG8+OKL1KxZs8CyNm3aMGLECPr27UuVKlU45ZRTqFDB+ddw//79fPPNN2zcuJHExEQuv/xyxo8fz9VXX+1z3SJRK+co/PY6zH7W+f30O6DXvVC5VqQj84sacuHQ/ykyg/yA0KOHDpEQtK15t2TJEk499dRiy/hyRy4pKYktW7bkrZOamuq1e0ZSUhKNGzfOu2J42WWX8dRTTwHO1dFDhw5Rv359LrnkEubPn19sQ27p0qV07fr3P46LFi0iOTmZLVu20LDh33cE3G53geRY+DPlV9SVzsTERJKTk5k8ebLPDblff/2Vb7/9lkmTJnHkyBEOHjzI1Vdfzfjx431aXyQqpf3ldKNc8TXUbAyD34P2g9WFMhb0d861wcxV0ZinwPsducJ5atu2bX7lqQEDBviU5/ILR57Kzs5m8ODBDBs2jEsvvdRrHDfeeCM33ngjhw4dYsyYMXldO6dPn07z5s2pV8+ZTfbSSy9lzpw5ashJbLMW/vwepj4I+zdB6wFw3uNQp2WkIysVNeTKoerVq/vUna9Bgwb88ccfea93796dd0LP5csdue7du7N27Vo2btxIzZo1mThxIp988onX+ho3bszq1atp3bo1M2bMoG3bthw+fBi32w3A4cOHmTp1Kg8//DAAffr04aOPPqJx48YFtlWnTh2WL18OOMlxwoQJ3H333SxatIiVK1dy2223kZmZ6TXR+nKlc/fu3VSsWJHExEQyMzOZPn06I0aMKHG9XGPGjGHMmDEApKSk8Oyzz6oRJ7HraLozu9ecVwADvUfCGXdFzXN2JPaEKk+B91yVP081btyYL7/8kokTJ3qtz1ueKi7PRSpPWWu58cYbadOmTZEzRQPs2rWL+vXrs2XLFr766ivmzp0LwAknnMBvv/1GRkYGVapUYcaMGXndLkVi0o7lMHkkbPoZ6rWB4V9Dy3MiHVVA1JArh+rUqcMZZ5xB+/bt6d+/P88884zXsQfXXXcdQ4cOpUePHlSqVIlHH32Uiy++2O/6KlSowKuvvsr5559PdnY2N910E+3atQOOHfPwzDPPMGzYMLKysmjRogXvv/8+O3fu5JJLLsHtduN2uxk6dCj9+vXD7Xazbt06jjvuuGPqHD58OAMGDKBTp060bt2axMRE2rRpw+eff85zzz1H9+7d+eGHH9i9e3ep9uH27du59tprcblcuN1urrjiCi688MJjPtOQIUOYOXMme/fuJSkpiUceeSRvkLxIzHO7YdlnznN2Dm2H9pdB30egVnAma5DA+fOYHAjuo3J83Za1lvT0dCpVqgQ4Da3ExER69OhB27Zt6du3L48//jiDBw/m1VdfLXC3avDgwUyaNIkePXpQsWJFHnjgAQYMGFCquJ5++mn69u2Ly+Vi2LBhnHDCCRw6dOiYev/73/8yZMgQsrKyaNasGa+//jqZmZkF1h8+fDgnnHACBw4cYO3atVSsWPGYOi+55BLGjx9Px44dadWqFbVq1SIpKYnx48fz6KOP0rVrVyZPnszevXtL9TeZO3cu48aNo127dnldPx9++GHOP//8Ap9p0KBB7Nu3jwoVKvDMM89QoUIFDh06RNu2bbnooovo1KkTFSpUoGPHjgwZMsRrLP48JgeC+9iQaHxMjq9l9aic8NRVMesAzTd+TMPt08ipUI2NrW5he8N+2C1xsMW3WMJ5nPklmFNgltefaH78QDDWDfTxA/6UKW554WXLli2z99xzj0+x5Ro0aJA9evSotdbahx9+2C5dutSv9Usj0L+9Hj/gfzlN6Rx6i/73prVvn+NM0fxWb2s3/1bqbUXrtM5l6SeaHz8QjHUDffyAP2X8yWOxkqesDezvpccPlK6sclVopcyYau2cV619som1o2tbO+n/rD28t1TbitY8pTtyErPat2/P888XPyNaYfmnVX7kkUeCHZJI2XdwG0wfTZeln0L142HQG9DxKojT02xEClOeEokAa2HtVLovuBsyt0HLPtBvDNRrHenIgk4NORERKVl2pjMG7pcXwO1i8wmX0XTYi1ApeJM4iYiIBGT3aph8H6yfAVUawdDPoNV5ZXbSLTXkRERi2AvT1vDSjLXOi8k/HLP8rj6tuKfvSaWvwFpY8RVMGwUHtkCbi+G8x9j4xyaaqhEnIiLRIGMfzPovzH8HEqrD+U+yIPMkep/UN9KRhZQaciIiMeyevidxT9+TSElJ4Y3VzmQRn956WnA2vm2JM8PXX3Ph+A5ON8rmZ3kWbgpOHSIiIqXlyoFF78PMJ+DIAeh6HZz9AFSri43ByWD8pYaciIgUdGgn/PQo/P4xVK0DF74IXa6BuPgSVxURESksJL1H1v8Ek++H3augeS84fww08O15vmWFGnIB8Gda52BO6Rzo9vxd19fyvpQrqUxxy4O9D8Ml0Lj9mdY52FPcRuO0zprS2bv09HTS0jIBSh2/cWeTlPotTTd/Tpw7m61JA9nU7Apc6dVgdsHnVsXq9OEiIhJ+Qe09sne980Dv1ZOgdjO48mM4+YIyOw6uOGrIBcBa+x3wXbdu3W5OTk4usGzVqlUFHjha1MOySyuQ7fm7rq/lfSlXUpnilgd7H4ZLoHFXrlyZzp07+1Q2JSWFwsdiIALZnr/r+lrel3IllSluebD3YbikpKSQmOgkx+RkP5OjtfDnDzD1Adi/CU7qD+c/QZM6LWlSTH3B2k/hPM5ERCRGHTkAs5+B396ECpXg3NFw6u3O7+WUGnIRVuBWsxcBT1QgIlKcnSuccXAbZ0O9k+Hqr+DEPpGOSqKI8pSIRJTbBb+Pg58eh8N7oPMwOOdhqHF8pCOLOD34J8Lu6XsSm566gE1PXUDP5sfRs/lxea83PXVBQMnRGMPw4cPzXufk5FCvXj0uv/zyUm0vLS2N119/3e/10tPTufXWW2nZsiU9evSgV69ezJs3z69tJCcns3jxYr/rFpEiHN4D398Db54JO5ZB/2fgtl/ViJNjlLc81a5dO/r161eqPLVw4UK/6xaRYmz6Bd7uDd/dBce1hFtmwsDX1IjzUEMuSrjclv0ZWWzdn8mMVTtxuW3A26xWrRrLly8nM9MZNzNt2jQaN25c6u2VNkHedNNNHHfccaxdu5b58+fzwQcfsGfPHp/Xd7lcftcpIkVwZcPc1+HlLrDoQ+h+M9y5GHreAvHqpCFFKy95asWKFbzxxhvKUyKRtH8zfHYNfHABZKbBZWPhhsnQyLehJuWFGnJRwOW2DH9vHut2pZOalsmdE35n+HvzgpIk+/fvzw8/OLMDTZgwgSFDhuQt27dvH4MGDaJjx46ceuqpLF26FIDRo0dzww03kJycTIsWLXjjjTcAGDlyJOvXr6dTp07ce++9ADzzzDN0796djh078sQTTxxT//r165k3bx6PP/44cXHO4daiRQsuuOACAAYNGkTXrl1p164db7/9dt561atX5+GHH6Znz57MnTu3wDYnTJhAhw4daN++PSNGjAh4H4mUG2umwuunwZT7IKkr/GMODHgaqh4X6cgkypWVPDVq1Khj6veWp5o3b648JRIJR9NhxqPwandYO815lMAdC6D94HI5mUlJ1JCLAimrd7FkSxq5+TAjy8WSLWmkrN4V8LavuuoqJk6cyJEjR1i6dCk9e/bMWzZq1Cg6d+7M0qVLefLJJ7nmmmvylv35559MmTKF+fPn89RTT5Gdnc1TTz1Fy5YtWbJkCc888wxTp07Nu8u2ZMkSlixZwuzZswvUv2LFCjp16kR8vPdpy8eOHcuiRYtYuHAhL7/8Mnv37gXg8OHDtG/fnnnz5nHmmWfmld+2bRsjRozgp59+YsmSJSxYsID//e9/Ae8nkTJt92oYPxg+uRysG4Z86oyFq39ypCOTGFFW8tSiRYv49ddfC9Qf7Dy1fft25SkRf7ndsOQTeKUr/PwctB0IdyyE3v8HFatEOrqopX40UWDFtoNkZhXslpGZ5WLltoP0aRNYH+COHTuyadMmJkyYwIABAwos++WXX/jyyy8BOOecc9i7dy8HDhwA4IILLqBSpUpUqlSJevXqsXPnzmO2PXXqVKZOnZo3o+LBgwdZu3YtvXr18jm+l19+ma+//hqALVu2sH79epo1a0Z8fDyDBw8+pvyCBQtITk6mXr16AAwbNozZs2czaNAgn+sUKTcy90PKUzD/HUioDuc9AT1ugQoJkY5MwsSfx+RA0Y9LWbxxt9c89fum3fRIquq1bl8fvdK8eXM2bNjA+++/z7nnnktGRgbWWg4dOsTs2bMZN24chw4donv37uzZs4fU1FSOHj3KueeeS1ZWVl6eWr9+PTk5Objd7rx6v//+e6ZMmcIpp5wCOGPh1q5dyxlnnPH358jMJCcnp8hHBj3zzDN8//33gJOn1q5dS506dYiPj+e8887LK+dyuTh8+DBr1qzhjDPOoHLlymRmZjJ48GCmT59Onz7RPf40kEfl+POYHIjdx5f4U16PyvHO26Nyah74kxPXvUvNQ2s5WKMV6zr/i4O1WsPva4GiJ1rypa5YPM78oYZcFGjXqCZVEuLJyJckqyTE07ZRzaBs/+KLL+Y///kPKSkpeVcSAaw9tkuM8dy2rlTp76lc4+PjycnJOaastZb77ruPW2+9FfA+zX67du34448/cLvdeV1WcqWkpDB9+nTmzp1L1apVSU5O5ujRo4Az5b63q6PeYhaRQlw5sOh9mPmEM11zl2vhnAehWt1IRyZh5s9jcqDox6V0aV6PKr+lHpOnOjerF/AjY2rUqMGgQYN48MEH8/KUMYYaNWpgjKF69ep52zHGULNmTSpVqlTg/fj4eCpXrgxAXFxc3vsVK1bk/vvvz8tT3uLq1q0b9913H9WqVcvLU7llUlJS+Pnnn5k3b15ensrOzqZGjRpUrlyZxMTEvO3Ex8dTrVo1jDFUrFgxr47KlSuTkJAQ9Y/PCeRROf48Jgdi9/El/pTXo3K8K/ConM5NYPpoWPY51GgIl7xFzQ5X0CUuOB0GY/U484e6VkaB5Nb16dQkkThP19+qCfF0apJIcuv6Qdn+DTfcwMMPP0yHDh0KvN+rVy8+/vhjwDnI6tatS82aRTcea9SoUeBq3fnnn8/YsWNJT08HnG6Pu3YV7GbTsmVLunXrxqhRo/IaYWvXruWbb77hwIED1K5dm6pVq/Lnn3/y22+/lfhZevbsyaxZs9izZw8ul4sJEybQu3dv33aESDnQ4ehiZybKSf+B49vDrbPhohfViJOAlJU8tXXrVnbv3l1gHW95at26daXOU926dVOeEimC21oOHT5MrZ2/MeOFG3Ct/B563et0ozzlKghSI6680B25KBAfZxh3Y0/6vzSbjKMuHhnYjuTW9YmPC86gzqSkJO66665j3h89ejTXX389HTt2pGrVqnz44YfFbqdOnTqcccYZtG/fnv79+/PMM8+watUqTjvNefhwlSpVmDBhAvXrF0zs7777Lv/+97858cQTqVy5MvXq1eOZZ56hY8eOvPnmm3Ts2JHWrVtz6qmnlvhZGjZsyJgxYzj77LOx1jJgwAAGDhzox94QKZuqZGznP/s+oPvR3yCxKVwxDtpcpMHhEhRlJU9Vr16dN99885j18uepqlWrkpiYyPPPP1+qPNWgQQPlKREvXC43L/26g43pCaziRH6Ju51OTRIZl9w7aOeS8kYNuSgRH2eoXTWB2lUJeFxcrtwrkPklJyfTtWtXAI477ji++eabY8qMHj26wOt58+bldbf45JNPCiy766678pJvUd0yatasyTvvvOO1zI8//ligbO6V1MKxp6Sk5C0bOnQoQ4cOPaYekXLpyAGY/Qxd5r/JNHcXbqrwKEPOHUzyyY2JVyNOgqgs5CnA6ziw/Hkqt0zu9vzJU7nLladECtm6mJQv3mJtel8ycbpBZ7jjWLL9CCmrdwXtnFLeqCEXYS9MW8NLMwoO5Gw28oe83+/q0yqgh62KSBnldsHv4+Gnx3Cl72WI+S+/ZzfClWWY89lyOjVJZdyNPXWVUwKmPCUipXZoh/M4gSUfs8IMy2vE5QrW5H7llRpyEXZP35OUAEXEP5t+hckjYMcyaHIqKad9xLIf9+PyMjW8kqMESnlKRPyWfQR+ew1+fh5yjsIZd9Gu/vUkfLaSo/kmwA3m5H7lkUYUiojEiv2b4bNr4IMBkLEfBr8HN0xmxdF6FJoZPu8qp4iISNhYCyu/hdd6OHfimveGf86Dvo+S3KEZLWrFhWzSpPJId+RCyFqbN52/SGnocQsCwNF0+OUFmPMKmDhIvh9OvxMSnOd3tWtUk4R4dJVT/KY8JYFSnpI8O5bB5Ptg089Qvy1c8w20SM5bHB9nuLd7ZZ5aEheSSZPKIzXkAlDcg1arV69OamoqtWrVwhgT0IM2vQlke/6u62t5X8qVVKa45cHeh+FS2rittRw4cIDDhw8H9QGk/ojGB62Wq4esWjfH70yhxYaPqJS1n531e7OhxTUcpS7MmZ9XzFhL0+qWtQcMFqgUD02rW8yOlaTsXBWS0MrDg1bLusqVK7N3717q1KmjxpyUirWWvXv35j3DT8qpw3vgp8dg8UdQOREueA66XAfxxzYz4kzwJ00qz9SQC0BxD1rNzs4mNTWVrVu3AnDkyJGgnugC2Z6/6/pa3pdyJZUpbnmw92G4BBJ35cqVOeWUU6hYsaJP5YP90MlofNBqqB6y+veEDgY4fMw6YZ/QYct8mDwSti6CRl2g/2cc36QHRae9mWG9ylkeHrRa1iUlJZGamlrguWrBPM9GY57ytWwguai85arKlSuTlJQUgogk6uVkwfy3YdbTkH0YetwKySOgSu1IR1ZuqCEXIhUrVqR58+Z5r1NSUujcuXPQth/I9vxd19fyvpQrqUxxy4O9D8MlVuMub3IndEhJSeGN1ZUA+PTW08IfyIGtMH0ULPscqjeAQW9CxytLfEiqrnKKvwrnKQju+Soa85SvZQPJRbF6zo/VuCUCrIU1U2DqA7B3HZzYF85/EuppUqRwU0NORCQaZGU4Y+B+eQGsG876N5z5L6hUPdKRiYiIOHb9CVPug/U/QZ1WMOwLaNU30lGVW2rIiYhEkrWw/EuYNgoOpkLbgdD3UajdLNKRiYiIODL2QcpTsOBd5wJjv6eg+00Q79vQDwkNNeRERCJl62Jnhq8tv0GDDnDpW9DszEhHJSIi4nDlwMKxkPIkHDkAXa+Hsx+AanUiHZmghpyISPgd2uk8X2fJx1CtLlz0MnS+GuLiIx2ZlDHFza7sTazORupP+UBnvg1kVtxoFs64dZz5VibSMyzX3vc7J657j2oZW9if2JF17UZzuHozWLCs1NtMT08nLS0TIOTxx+px5g815EREwiX7CPz2Ovz8HOQchdPvgF73QuVakY5MyqjiZlf2JlZnI/WnfKAz35ZmVtxYEM64dZz5ViaQ4zAge9Y5E5msmQy1m8PFn1C79QC6B+ExJSkpKSQmOhOKJSeHdkKxWD3O/KGGnIhIqFkLq76DqQ9C2mZoPQDOexzqtIx0ZCIiEiP+fkyOx+QfCiwP+DE5mWkw+xmY9xZUqAznPgKn/gMqVCr9NiWk1JATEQmlHcuccXCbfoZ6bWD419DynEhHJSIiMSb3MTkA5//3RxITE4PzmBy3y3mY90+PQ8Zep6v/OQ9BDT3KJtqpISciEgqH9zhJcfGHTtfJAc86g8TjddoVEZEosfFn52LjzmVwwunQbww06hT0agreTTwMQLORf99RDPhuYjml/yhERIIpJwvmvw2znoasdOhxC/QeAVWPi3RkIiIijv2bYOpDsOpbqNUELnsf2l0CQRgH503u3cRYHUMardSQExEJBmthzRRngPjedXDiuXD+k1CvdaQjExERcRw9BD8/D3Nfc2ZKPvtBZ+KtilUiHZmUghpyIiKB2vUnTLkf1s+AOq1g6Odw0nmRjkpERMThdsMfE2DGI5C+EzpeBeeOgpqNIh2ZBEANORGR0srYBylPwYJ3IaG6cweu+81QISHSkYmIiDj+mgeTR8C236FxN7jqE0jqFumoJAjUkCuCMaYa8DqQBaRYaz+OcEgiEi1cObBwLKQ8CUcOQNfr4OwHnId7i4iIRIMDqTBtFCz/Amo0hEvehg6XQ1xcpCOTIIn6hpwxJhF4F2gPWOAGa+3cUmxnLHAhsMta277Qsn7AS0A88K619ingUuALa+13xphPATXkRATW/+TM8LX7T2jeC84fAw3al7yeiIhIOGRlwK8vOT9Y6PV/cObdkFAt0pFJkEV9Qw6ngTXZWnuZMSYBqJp/oTGmPpBprT2U770TrbXrCm3nA+BV4KNC68cDrwF9gVRggTHmWyAJWOYp5grexxGRaOa2lv0ZWWQcdTFj1U6SW9cnPs7A3vUw5QFY8yPUbgZXfgwnXxCyGb58pSmdRUQEcCbdWv4lTHsYDm6FdpdC30cg8YRIRyYhEtUNOWNMTaAXcB2AtTYLp6tjfr2BfxhjBlhrjxhjbgYuAQbkL2StnW2Maealmh7AOmvtBk+dE4GBOI26JGAJoHvQIuWAy215ZsER1u1347Zw54Tf6dS4OuOa/kj8/LegQiU4dzScervzexTQlM4iIuWLy21Jz7Ic3p/59wXH7Yud3iJb5kHDU2Dwu9D09EiHKiEW1Q05oAWwG3jfGHMKsAi4y1p7OLeAtfZzY0xzYKIx5nPgBpy7a75qDGzJ9zoV6Am8DLxqjLkA+M7bisaYi4CLGjduTEpKSrGVpKenl1jGH4Fsz991fS3vS7mSyhS3PNj7MFzCGbeOM9/KFLV8ya4cNqS5cFvnLltGloslG3cyM3UO7Rr3ZmPzq8nKqQ2/+N27O+TC/f0IZn3hPM5ERGKZy20Z/t48th22WDK585PFdKqyk3FH7ya+ej24+FXoNNR5tICUedHekKsAdAHutNbOM8a8BIwEHspfyFr7tOdO2htAS2ttuh91eOsXZT2NxeuLW9Fa+x3wXbdu3W4u6Up4sK+WB7I9f9f1tbwv5UoqU9zyWL3jEM64dZz5Vqao5UtnrCXLvabAe5kksKrrI5w7qBcNS4wucsL9/QhmfeE8zsoSTcolUv6krN7Fki1pWM/rjGw3S7JrkHLKKPpcciNUrhnR+CS8or3LYCqQaq2d53n9BU7DrgBjzFk4k6F8DYwqRR1N8r1OArb5H6qIxLp2NY9Q2RTsvV0loSJtW+uh3lI0Y0yiMeYLY8yfxphVxpjTSrmdscaYXcaY5V6W9TPGrDbGrDPGjPS8nTsp183AxQF8BBGJESu2HiAzK6fAe5lUZmX9C9WIK4eiuiFnrd0BbDHG5P4X1QdYmb+MMaYz8A7OuLbrgeOMMY/7Uc0CoJUxprlnMpWrgG8DDl5EYsfRQzD9EZJ/PJfOZh0JOEmyakI8nZokkty6foQDlCiXOynXycApwKr8C40x9Y0xNQq9d6KX7XwA9Cv8Zr5JufoDbYEhxpi2OBcec4cGaFIukbJu+1LarXqRKhwp8HaVhHjaNlIjrjyK6oacx53Ax8aYpUAn4MlCy6sCl1tr11tr3cC1wObCGzHGTADmAq2NManGmBsBrLU5wB3AFJzk+5m1dkWoPoyIRBG3G5Z8Aq90g1+eJ779QP55VnOaHZ9IUmIVXhnSmXE39nRmrRTxIt+kXO+BMymXtTatULHewDfGmMqedW7GGYddgLV2NrDPSzV5k3J5Jv0qPCkXxEY+F5HSSN8N3/4/eKsXyYcn06leHMbTuVIXHMu3aB8jh7V2CVDk4+ettb8Wep2Nc4eucLkhxWxjEjCp9FGKSMz5ax5MHgnbFkPjrnDleGjSneyUFGpXTaB2VejT5vhIRynRr8xMygWxO4mNP+UDnTApkEm7olmsTsxVVo8zgMMH01j/0V003fwZce6jbE26kM1Nr+KmCtXYOPsw2dZwddsKdKyXyc+zZ/n8OSJJx1lwRX1DTkQkqA6k0mblc5AyG2o0hEvegg5XQJxuaEiplJlJuSB2J7Hxp3ygEyYFMmlXNIvVibnK5HFmLayZTMa8kVTN3A6tzoPznqBJvZPyJnWoOf9HEhMTufuKUg3JjRgdZ8GlhpyIlA9ZGTDnZfjlReq6XdDrXjjjbqhUPdKRSWzzNinXyMKFvEzKdYefdWhSLpHyYNcq53lwG2ZiqybBsC+h1bmRjkqilBpyIlK2WQvLv4Rpo+BgKrQdxIIaAzj1nCsjHZmUAdbaHcaYLcaY1tba1RQ/KdcFwEZgvDHmcWvtgz5WkzcpF7AVZ1KuoUH7ECISeRn7YOaTsHCsc4Gx339ZmHEivdWIk2KoISciZdfWRc6VzS3zoEFHuPRtaHYGR2Jw/IpEtdxJuRKADRzb3TFvUi4AY8y1wHWFN+KZlCsZqGuMSQVGWWvfs9bmGGNyJ+WKB8ZqUi6RMsKV7TTeZj4JRw9Ctxsg+X6oVgerXCUlUENORILqhWlreGnGWufF5B+OWX5Xn1bc0/ekkMaQcHQffP0P+OMTqFYPLn4FOg2DuPiQ1ivlkyblEpHSqL1vMbzxf7BnNbRIhvPHwPFtIx2WxBA15EQkqO7pexL39D2JlJQU3lhdCYBPbw3TYOzsI/Dba/SY/zRYF5xxF5z1Hz0kVUREoseedTDlfk5ZOwWOawFXTYDW/cHoUTfiHzXkRCT2WQurvoWpD0HaZtLq9KTu0DegTstIRyYiIuLITINZT8P8t6BCFda3uJaWQ5+BCpUiHZnEKDXkRCS2bV/qjIPb/AvUbwvXfMPyvyBZjTgREYkGbhcs/hB+etyZ1KTLcDjnIbYsXElLNeIkAGrIiUhsSt8NMx+HRR9CldpwwXPQ5TqIrwB/pUQ6OhERiVJhHcu9cbZzsXHncmh6BvQbAw1P8SxcWeyqIiVRQ05EYopxZ8OcV5zuKdkZ0PM2SB7hNOZERERKEI6x3JUzd8DEYfDn91DrBLj8Q2g7UOPgJKjUkBOR2GAtrJlM9wX/gsxtcGJfOP9JqBfaGTBFRER8dvQQ/PwcPea/4ox9O+dBOO0OqFgl0pFJGRSShpwx5jgfirmttWmhqF9Eyphdq5yuKRtmQpXGMOwLaNU30lFJDFOeEpGgcrudR97MeBTSd7Lr+LNpMOwNqNkwaFUU6BIKsH8fzUb+3TU0HI/3kegSqjty2zw/xd0/jgdOCFH9IlIWZOyDlDGw4D2oVB36PcWCjFb0bnVupCOT2Kc8JSLBsXkuTB4J25dAUne4agJ/rjtEgyA24uDvLqEAKSkpJCcnB3X7EntC1ZBbZa3tXFwBY8zvIapbRGKdKxsWjoWZT8LRg9D1ejj7AahWB5uSEunopGxQnhKRwKRtgWkPw4qvoEYjuPQd6HC5Mw5uXUqko5NyIFQNOV9GjIbpCcEiElPWTYfJ98Oe1dC8tzPD1/HtIh2VlD3KUyJSOlmH4deXnB+A3iPgjLsgoVpk45JyJyQNOWvtkfyvjTHVgCPWWldRZUSkfKuSsRU+uRLWTIbazeGqT6D1AM3wJSGhPCUifrMWln4G00bBoW3QfjCc+wgkNol0ZFJOhWqykzjgKmAY0B04ClQyxuwGJgFvW2vXFrOJmGCMuQi4qHHjxqSU0N0rPT29xDL+CGR7/q7ra3lfypVUprjlwd6H4RLOuKPtOEtLywQodhsVstNpuvkzum/9npy4BDa3uJbUpIuwOyrCjlmliqk0x9nXa7P4Zn2259VhgAKDyAe2rMglrRKKrTeSwv39CGZ94Tyf5SoveUpEgiR1EZ1/HwEHV0PDTnDZWGiqm/YSWaHqWjkTmA7cByy31rohb5aws4GnjDFfW2vHh6j+sLDWfgd8161bt5tLGnAa7EGpgWzP33V9Le9LuZLKFLc8Vgf2hjPuaDvOEhOd5/MkJ3tJdm4XLP4QfnocMvaxvUEfGl79Bi2r16dlgDGV5jhLToaXfNx+NAp33MGsL5zns3zKRZ4SkQAd3A4zHoE/JlA5oTYMfA1OGQpxcZGOTCRkDbl3rbXjCr9prd0HfAl8aYypGKK6RSTabfzZeZzAzmVwwunQbwyr16TRsHr9SEcm5YfylIgULTsT5r4KP78A7mw48x7m04OzOg+IdGQieULVkLvaGNMV+Hf+8Qb5WWuzvb0vImWD21r2Z2SRcdTFjFU7SW5dn/i0TTDtIVj1HdRqApe9D+0uccbBrUmJdMhSvpSLPOXPEACI3S6z/pQPtHt2IEMEolmsDgMI+hAAa6m3ew4t139A5aO72F33VNa3vJ4jFRqE9TgrabmOs/DWFYkhAL4IVUOuHzAG+MkYc7m1dleI6hGRKORyW55ZcIR1+924Ldw5YTGdqqUx7uhdxMfHw9kPwul3QMUqkQ5Vyq9ykaf8GQIAsdtl1p/ygXbPDmSIQDSL1WEAgWzrp5kzsQlxZBx14Tq+Dck1txM/9X7Y/Csc3x76vUe95r2oV4q6NNzEu/J4nIXyM4dq1koLjDTGXArMNsY8DyzBGYeQEYo6RSR6pKzexYYDTiMOICPLzZKsBFJa3Uafy2+Dmo0iG6CUe8pTIuXbMRccx/1GJ/sn4xJXE3/hC9DlWoiLj3SYIsUK2UhNY8yFwE1AFtAFeBbYYoxZF6o6RSQ6rNh2kCyXLfBeJpVZ2Wy4GnESNZSnRMqvYy44uiuwxLQhpd806HaDGnESE0L1+IENwCrgBWvttELLkkJRp4hEibQttNv4PlXoQgZ/d52skhBP20Y1IxiYyN+Up0TKMWtZsXQhWS43+e9pZLrjWbnHRZ/IRSbil1CNkRtgrf3T2wJrbWqI6hSRSMo6DL++BL++TLKFk6u2YklmFdwWqibE06lJIsmtNSulRA3lKZHyaOdKmHIf7dYeoAr/jwwq5S3SBUeJNaEaI+c1OYpIGWQtLPscpo+Gg1uh3aXE932EO35fz1NLnEHkjwxs58xaGWciHa0IoDwlUu4c3gspT8LCsVCpJskX3E+z2ZX5c7/VBUeJWaG6IyciAXhh2hpemrG2yOV39WnFPX1PCmNERdi6CH4cCanzoeEpMPhdaHo6AHFmA7WrJlC7KvRpc3yEAxURkXLJlQ0L3oWUMXA0HbrfBMn3EV/1OP6TOVMXHCWmqSEnEoXu6XtSXkPtyrfmAvDpradFMqSCDm6HGY/AHxOgWn24+FXoNAziQjZ/koiIiH/WTocp98GeNdDibOg3Buq3yVscZ4wuOEpMC2tDzhjTENhnrT0aznpFJEiyM2Huq/DzC+DOhjPuhrP+DZU1pkDKBuUpkTJgz1qYcj+snQrHtYAhE+GkfmB0t03KlnDfkRsHtDTGfGmt/U+Y6xaR0rIWVn4DUx+CA3/ByRfCeY85CVKkbFGeEolVmfth1tMw/22oWBXOexx63AoVEiIdmUhIhOrxAx8CN1trs/K/b6091xhjgLahqFdEQmD7Upg8Ejb/CvXbwTXfQovekY5KJCDKUyJliCsHFn8IPz3uNOa6XgtnPwjV60U6MpGQCtUduS3AXGPMYGvtptw3jTEdgbuttTeEqF4RCZb03Zy0+jVImQZVasMFz0OXayFeQ2ulTFCeEglQNEzMlbh/Kbx1P+xaAU3PdMbBNewY0jpFokWoHj/woDHmN2C6MeYuoCJwN1ADeDkUdYpIkORkwbw3YfYzNMg6DKf+A3r/n9OYEykjlKdEAhfRibn2bYCpD9Hpz+8h8QS44iNoc7HGwUm5EspL67OBycB3wC7gCmvt7BDWJyKBsBZW/whTH3ASZKvzWJg4kB79ro50ZCKhojwlEmuOHISfn4Xf3oC4imxofjUthj4HFStHOjKRsAvJXOHGmNeAZUA60Ab4Cfh/xpiqoahPRAK0cyWMGwQTh0BcBRj2JQz7nIxqSZGOTCQklKdEYozbDYvHwStd4deXoP1lcOci/mp6uRpxUm6F6o7cMuA/1tpMz+uhxph/A78ZYy6z1q4JUb0i4o+MfTDzSVg4FipVh37/he43QnzFSEcmEmrKUyKxYvMcZ9Kt7X9AUg8YOhEad/UsXB3R0EQiKVRj5N708t5zxpjfgUnAiaGoV0R85MqGBe9Byhg4ehC63QDJ90O1OpGOTCQslKdEYkDaXzDtYVjxNdRsDJe+Cx0u0zg4EY9QPX7AWGtt4fettT8ZY84uroyIhNja6c6DUveshhbJcP4YOF4zrUv5ojwlEsWyDsMvL8KclwEDvUfCGXdBgno+i+QXqq6VM40xXwLfWGv/yn3TGJMAtDLGPA7MBD4IUf0iUtietU4Dbu1U50HeV02A1v11ZVPKK+UpkWjjdsOyz2H6aDi0zRkH1/cRqKXx2iLehKoh1w+4AZhgjGkOpAGVgXhgKvCCtXZJiOoOCmNMNeB1IAtIsdZ+HOGQREonMw1mPQ3z34KKVaHvY9DzVqhQKdKRiURSzOcpkTIldSH8OAK2LoRGneHyD+CEnpGOSiSqhWqM3BGcRtDrxpiKQF0g01qbVprtGWPigYXAVmvthaXcxljgQmCXtbZ9oWX9gJdwEvi71tqngEuBL6y13xljPgXUkJPY4nbBog9g5hPOpCZdhsM5D0H1+pGOTCTigp2nRKSUDm5z7sAt/RSqHw+D3oCOV0FcSCZWBwo/yPwwAM1G/pC3PBwPMhcJhlA+Rw4Aa222MeZCa+07AWzmLmAVULPwAmNMfZzkeyjfeydaa9cVKvoB8CrwUaH144HXgL5AKrDAGPMtkIQzqxmAK4DYRcJvwyyYfB/sWgFNz4B+Y6DhKZGOSiQqBSlPhZ16jkhMy86EOa/CL887Fx7P/Bec9S+oVCPkVec+yDwlJYXk5OSQ1ycSKqG73FFQ59KuaIxJAi4A3i2iSG/gG2NMZU/5m4GXCxfyPOR1n5f1ewDrrLUbrLVZwERgIE6jLrdTdrj2k0hAKmduh4nD4KOLIesQXP4hXPeDGnEiJSt1ngLnoqAx5ndjzPcBbGOsMWaXMWa5l2X9jDGrjTHrjDEjPW/n9hy5Gbi4tPWKhJW11Nv1C7zaA2Y+DieeC3fMh3NHhaURJ1KWhPyOnEc/Y8zbwGJgEbDUWnvUx3VfBP4P8PrtttZ+7hnfMNEY8znOmIe+fsTWGNiS73Uq0BOnMfiqMeYC4DtvKxpjLgIuaty4MSkpKcVWkp6eXmIZfwSyPX/X9bW8L+VKKlPc8mDvw3AJJG63taTuyuSIC178bDod68UT52VykvicDJpu/pzuqd/iMhXY3PxqUpMG4t6dALNmRST29PR00tKcR3QF6/jxtZyOs9iqL5zns2IEkqdAPUdESrZtCUy+j3Z/zYHjO8Cg76H5WZGOSiRmhashNwW4H+gKnAPcDQwraSVjTO6YtkXGmOSiyllrnzbGTATeAFpaa9P9iM3blH3WWnsYuL64Fa213wHfdevW7eaSbs0H+/Z9INvzd11fy/tSrqQyxS2P1S4QpY3b5bYMf28e2zMycFt4e3kOnZpUZ9yNPYmP8xy2bjcs+RhmPAqHd7Hj+LNpMOwNWtRsSIsIxp67bmKiM6FKcvJpQatLx5l34Y47mPWF83xWjFLlKSjQc+QJ4F9eivQG/mGMGWCtPeLpOXIJMCB/IWvtbGNMMy/r5/Uc8dRXuOfIEtRzRCLI5bbsz8gi46iLGat2kty6/t95CiB9l5Onfh8PVeuw+qTbaX3V4xAXH7mgRcqAUD1Hrj/wh7V2m+et36y1+4Hpnh9fnQFcbIwZgDObWE1jzHhr7dWF6jsLaA98DYwC7vCjjlSgSb7XScC2IsqKhE3K6l0s2ZKG2/MUq4wsF0u2pJGyehd92hwPm+fC5BGw/Q9I6gFDJvLnukM0qNkwonFrELnEgiDmKSgjPUcgdu+0+lM+0Lv6gdzxj2aljdttLc8sOMLafW4scPv4hbSoFce93SsTb3NISv2Opps/I86dzdakgWxqdgUHjli2z/45onGXZt1wHmclLS9vx1mk64qSniPHCNUducHAY8aY44E/gSXGmKtxrhqustb61AXEWnsfcB+A547cf7w04joD7+BcDd0IjDfGPG6tfdDHWBfgPDOoObAVuAoY6uO6IiGzYttBMrMKflUys1ys3LCFPstHwoqvoGZjuPRd6HCZ8zy4dSmRCTYfDSKXGBGUPFWWeo5A7N5p9ad8oHf1A7njH81KG/eMVTvZnP47nmuOHHXB5nSDzT5M71UPwv6NcFJ/OP8JmtRpSZMA6gpm3KVZN5zHWUnLy9txFum6oqTnyDFC0hXDWnuTtbYb8BywBqeBdTYwH9gc5OqqApdba9dba93Atd7qMMZMAOYCrY0xqcaYGz2x5uDcwZuCM77hM2vtiiDHKOK3do1qUiWhYLeTKvEu2i64H1ZPgt4j4I4F0PFyPdRbxE9BzFO5PUc24UyWdY4xZnzhQl56jvhDPUckanm/6JjNytmfO88rvforGDoR6rSMUIQiZVeox8hdb63Nmy7PGPM6cG9pNmStTQFSvLz/a6HX2Th36AqXG1LMticBk0oTl0ioJLeuT6cmify2YS9ua6lKFp3ca0lulwR934PEJiVvRERKElCeUs8RKe9yLzpm5GvMVSGLtt36wEXvQXy4pmMQKX9C/e06aIzpaq1dBODpeqLBMSI+iI8zjDu/Ah+/P4ED2fG0rRNP8qCbiG8+ItKhiZQl4chTeT1HAIwx1wLXFS7k6TmSDNQ1xqQCo6y171lrc4wxuT1H4oGx6jki0SL5xNp0qpnOkj2GTBKoEuemU9P6JF98JsSpt4hIKIW6IXcDzpXHlTjTOXcAskNcp0jsO7gNpj9C/NKJXBRXm4l1rqfPXQ9BnCamEwmyoOUp9RyRcmftNOIn38e4Q+t4v8pgvqp4Af++5IxjZ60UkZAIaUPOWrvWGHM6zkNLO+KMQbs/lHWKxLTsTJjzKvzyPLhz4Mx7uHvtWRyJq8o/1IgTCTrlKZFS2L0GptwP66bBcS2JHzqRaTNrUsMYZ1ZlEQmLkHdc9sz89bnnR0S8sRZW/g+mPgwH/oI2F0Hfx+C45hxZPzfS0YmUacpTIj7K3A8p/4UF70DFanDeE9DjFqiQACnKVSLhFqrnyC221nYJtIxIubD9D/hxJPw1B45vD4O+g+a9Ih2VSJmmPCXiB1cOLHofZj4JR9Kgy7VwzoNQrW6kIxMp10J1R66NMWZpMcsNUCtEdYsUUPAB1ceK2AOq03fBjEfh9/FQ9Ti48AUnOcbFl7yuiARKeUrEF+tnOt0od62EZmdBvzHQoEOkoxIRQteQOxm4GjjmWTr5+PSwVZFA5T6gGuDKt5yuH5/eelrkAso5Cr+9AbOfhZxMOO2f0OteqJIYuZhEyh/lKZHi7F0PUx+C1T9AYlO4YpzT7V/PLRWJGiFpyFlrNxtjmlprNwMYY8621s70/N7FWrs4FPWKRDVrnQd5T3kA9m+Ek/o54wvqnhjpyETKHeUpkSIcOQizn3EuOFaoBH1Gwam3Q8XKkY5MRAoJ5WQn+S/ZDAFmen6/DbglhPWKRJ+dK2HySNg4C+q2hqu/hBPPjXRUIuWd8pRILuuCxR85Xf4P74ZOw6DPw1CjQaQjE5EihLIhV8EY09la+zsFk6XuyUv5cXgvrda8CbOmQKWa0P9p6HYDxFeMdGQiojwl4tg8h66L/gPpG6DJqTD0M2iseX5Eol0oG3JuoJoxZghgjDHXANMAG8I6RaKDKxsWvAspY2h05BD0uAmS73MmNRGRaKE8JeXb/s0w7WFY+T8qVqoLg9+D9oM1Dk4kRoSyIfcQcC5QHZgDbAC6AK1CWKdI5K2d5szwtWcNtDibBXUupceAayIdlYgcS3lKokLYZ1c+mg6/vgi/vgwmDpLvZ76rE706nB+8OkQk5ELWkLPWbgM+yn1tjGkHNAJWhKpOkYjavcZpwK2bBse1gCET4aR+ZMyaFenIRMQL5SmJFmGbXdnthmWfwfTRcGg7dLgczh0NtZJwp6QEvz4RCalQ3pErwFq7Aic5fhauOkXCInM/pPwXFrwDFavCeY9Dj1uhQkKkIxMRPyhPSZm2ZQFMHgFbF0GjLnDFR9CkR6SjEpEAhK0hJ1LmuHJg8Qfw0xNOY67rtXD2g1C9XqQjExERcRzY6tyBW/YZVG8Ag96EjldCXFykIxORAKkhJ1IaG1Jg8n2wayU0PRP6jYGGHSMdlYiIiCMrA+a84oyFc7vgrH/Dmf+CStUjHZmIBIkaciL+2Lsepj4Eq3+AxBOcriltLtYMXyIiEh2shRVfwbRRcGALtB0IfR+F2s0iHZmIBJkaciK+OHIQfn4WfnsD4io6D0k99Z9QsXKkIxMREXFs+93pLfLXXGjQAS55E5qdGemoRCRE1JATKY7bBUs+hhmPweFdcMpQpxFXs2GkIxMREXEc2gkzHnXyVdU6cNFL0Hk4xMWHtFpvj01oNvKHvN+D/tgEESlADTmRomyeAz+OgB1LoUlPGDoRGneNdFQiIiKOnKPw2+sw+1nn99PvgF73QuVaYak+/2MTRCT81JCTcsPltuzPyCLjqIsZq3aS3Lo+8XFexral/QXTHoYVX0PNxjD4PWg/OKzj4HSVU0REimQt/Pk9TH0Q9m+C1gOcR9/UaRnpyEQkjNSQk3LB5bYMf28e63al47Zw54Tf6dQkkXE39vy7MXc03Znda84rgIHeI+GMuyChatjj1VVOERHxasdymDwSNv0M9drA8K+h5TmRjkpEIkANOSkXUlbvYsmWNNzWeZ2R5WLJljRSVu+iT+t6zvN1po+GQ9uh/WXQ9xGolRTRmEVERPIc3gM/PQ6LP3S6Tg54FrpeD/H6V06kvNK3X8qFFdsOkpnlKvBeZpaLlX+uos8vQ2HrQmjUGS7/EE7oGaEoRURECsnJggXvQMp/ISsdetwCvUdA1eMiHZmIRJgaclIutGtUkyoJ8WTka8xVicuh7eLRUGsbDHoDOl4FcXGRC1JERCS/NVNhyn2wdx207AP9xkC91pGOSkSihBpyRTDGVANeB7KAFGvtxxEOSQKQ3Lo+nZok8tuGvbitpSpH6cQGknudDb3+BZVqRDpEERG/KE+VPbmTcsVn7mXG63eTvPMD4uu2hKGfQavzwjrplohEv6huyBljKgOzgUo4sX5hrR1Vym2NBS4Edllr2xda1g94CYgH3rXWPgVc6qnvO2PMp4ASZAyLNzCu51a+Sf2Ira5E2p7QgOTBtxFfp3mkQxORGKY8JcHicluGv/MLm3fuJ4uK3HnwLDrVPZNxt15EfEKlSIcnIlEo2vuRHQXOsdaeAnQC+hljTs1fwBhT3xhTo9B7J3rZ1gdAv8JvGmPigdeA/kBbYIgxpi2QBGzxFHMVXk9iyLYl8H5/4r+6gS4V/2Jf/dPoc8t/1YgTkWBQnpLAuXJI+W4cSzbu4igVscSRQWWWHKxOyvq0SEcnIlEqqhty1pHueVnR82MLFesNfOO5Koox5mbgZS/bmg3s81JND2CdtXaDtTYLmAgMBFJxkiRE+X6SIhzaCd/8E95Ohj1r4cIXGVn3FVZWOiXSkYlIGaE8JQFb/xO8eSYrFvxEJgkFFmVmuVi57WCEAhORaGesLZxvoovnSuQi4ETgNWvtCC9l/g84HfgcuAPomy+x5i/XDPg+f5cVY8xlQD9r7U2e18OBnsAI4FXgCPCLt7EHxpiLgIsaN2588/jx44v9HOnp6VSvXt2nz+yLQLbn77q+lvelXEllilvuaxzGnU1S6rc03fw5ce5stja+kE3NrsBVoRpj5mUCcF/PKiVuJ1iC/bcPZ106zmJHuOMOZn3BOs7OPvvsRdbabkEJyg9lJU9BdP5dg10+0HNIIOeX/KpkbKPl+vepu3c+mZUbMKHOnfx3U3OO5ru3Wike/nFKJTrVD/1ImFjNVWX1OCtpuXJVeOuK2jxlrY2JHyARmAm0L2L5ROAgUK+YbTQDlhd673Kc8Qa5r4cDr/gTW9euXW1JZs6cWWIZfwSyPX/X9bW8L+VKKlPc8hK373Zbu/I7a1/saO2omtZ+fKW1e9YVKHLFm3PsFW/OKTHOYAr23z6cdek4ix3hjjuY9QXrOAMWWuWpUuepwvszUNF4/vC1bCDniBK3n5lm7ZQHrH2kjrVPNLL25+etzT5ic1xuO+Ttubb5yO9t0xHf2zYP/WiHvD3X5rjcJcYbDLGaq8rqcVbScuWq8NYVrXkqqic7yc9am2aMScEZP7A8/zJjzFlAe+BrYBTO1U5fpQJN8r1OArYFFKyE384VMHkkbJwN9U6Gq7+CE/tEOioRKUeUp6RYbhf8Ps55qPfhPdB5GJzzMNQ4HnBmsRl3Y0/6vzSbjKMuHhnYjuTW9YmP00yVIuJdVPepN8bUM8Yken6vApwL/FmoTGfgHZzxAtcDxxljHvejmgVAK2NMc2NMAnAV8G0QwpdwOLwHvr8H3jwTdiyD/s/Abb+qESciYaE8JT7Z9Au83Ru+uwuOawm3zISBr+U14nLFxxlqV02gce0q9GlzvBpxIlKsaL8j1xD40DP+IA74zFr7faEyVYHLrbXrAYwx1wLXFd6QMWYCkAzUNcakAqOste9Za3OMMXcAU3AuiI211q4I1QeSIHFlw/x3IOUpyEqH7jdD8kioelykIxOR8kV5Soq2fzNMewhWfgO1msBlY6HdpXoenIgERVQ35Ky1S4HOJZT5tdDrbJwrn4XLDSlmG5OASaUMU8JtzVSYcj/sXQstz4Hzx0D9kyMdlYiUQ8pT4tXRdPjleZjzKsTFw9kPwOl3QsXwTbQlImVfVDfkRPKrengLjB8M66Y7XVOGfAonna8rmyIiEh3cbo7f8RO8ciuk74AOV8C5o6FW40hHJiJlkBpyEv0y90PKU3Rf8DZUqgHnPQE9boEKCSWvKyIiEg5b5sOPI2izbTE07gpXjocm3SMdlYiUYWrISfRy5cCi92Hmk3Akje0N+9Lo6tehWt1IRyYiIuI4sBWmj4Jln0ONhqw6+W7aXDEK4qJ6PjkRKQPUkJPotH6mMw5u10podhb0G8OaP/fSSI04EREpxgvT1vDSjLVFLh/YsiLJyUGoKCsD5rwMv7wIWOh1L5xxNzvnLqSNGnEiEgZqyElUqZKxHSYMgdWTILEpXDEO2lzkjIP7MyXS4YmISJS7p+9J3NP3JACufGsuAJ/eelre8pSUlMAqsBaWfQHTRsHBVGg7CPo+CrWbBrZdERE/qSEnPgvpVc4jB2H2M3Rf8DpUrAx9RsGptzu/i4iIRIOti+n8+31wcBU06AiXvg3Nzoh0VCJSTqkhJz4LyVVOtwt+Hw8/PQaHd7OzwTk0HPYG1GgQjJBFREQCd2gHzHgUlnxClYo14eJXoNMw59ECIiIRooacRM6mX2HyCNixDJqcCkM/Y/XagzRUI05ERKJB9hH47TX4+XnIOQqn38m8uNM4q8uASEcmIqKGnETA/s0w7SFY+Q3UTILB70H7wc44uLUpkY5ORETKO2th5bcw9UFI2wytL4DzHoM6LXEFOsZORCRI1JCT8DmaTvMN4+Hnb8HEQfL9cPqdkFA1pNV6G9vXbOQPeb/f1adVXpdREREp53Ys45Q/HoS05VC/LVzzDbRIjnRUIiLHUENOQs/thqWfwvTRNE3fAR0uh3NHQ62ksFSff2yfiIiIV4f3OOO1F39E9fhqMOBZ6Ho9xOtfJRGJTjo7SWhtmQ+TR8LWRdCoC4tb3UOXgbdFOioRERFHThbMfxtmPQ3Zh6HHrcyrcCZn9rgw0pGJiBRLDTkJjQNbYfooWPY5VG8Ag96EjldycPbsSEcmIiLijINbMwWmPgB718GJfeH8J6HeSeSEeRychgCISGmoISfBlZUBc16BX14A64az/g1n/gsqVY90ZCIiIo5df8KU+2D9T1CnFQz7Alr1jVg4GgIgIqWhhpwEh7XU3zkbXv0nHEyFtgOh76NQu1mkIxMREXFk7OPEtW/DrMnOBcZ+T0H3myC+YqQjExHxmxpyEriti2HyfbTd8hs06ACXvgXNzox0VCIiIg5XDiwcCylP0jjzAHS7Hs5+AKrViXRkIiKlpoaclFot1z743z9hycdQrS6rT/onra96DOLiIx2aiIiUcy63ZX9GFjUytjDjhddIPvQ98S16sbDOpXS/8LpIhyciEjA15MR/2UcYmP4pl6RPhD05cPod0Otetv/2O63ViBMRkQhzuS3D30zhr51pHKUWd6ZfSqcGQxh3dX8O/6xJt0SkbFBDTnxnLfz5PUx5gKGHNrOg0ql0v+V1qNMy0pGJiIg4jhwg5ct3WPJXc45QGYAMW4kle+NJWbMbXW4UkbIiLtIBSIzYsRw+vAg+vRoqVuXx457k2eNGqxEnIiLRwe2Che/Dy11YsWo5mVQqsDgzy8XKbQcjFJyISPCpISfFO7yHk1a/Dm+dBTuXw4Bncd3yM7Nd7dm6P5MZq3bicttIRykiIuVY4v5l8FZv+P5uqHsS7frfSpWEgp2OqiTE07ZRzcgEKCISAupaKd7lZMH8t2HW0zQ8egh63gK9R+CqXJvh781j3a503BbunPA7nZokMu7GnpGOWEREypv9m2DqQ3Ra9S3UagKXvQ/tLiHZQqeV8/htw17cFqomxNOpSSLJrevz885VkY5aRCQo1JCTgqyFNVNg6gOwdx207MOC4y6hR//hAKSs2smSLWnk3oTLyHKxZEsaKat3adyBiIiEx9FD8PPzMPc1iItnY7NhNB/2HFSsAkC8gXE39qT/S7PJOOrikYHtSG5dn/g4E+HARUSCRw05+duuP2HK/bB+BtQ5EYZ+Bq3OI2PWrLwiK7YdJDPLVWC13HEHHdSSExGRUHK74Y8JMOMRSN8JHa+Cc0exefEamnsacbni4wy1qyZQuyr0aXN8hAIWEQkdNeQEMvZBylOw4F1IqA7nPwndb4YKCccUbdeoJlUS4snI15jLG3ewc2s4oxYRkfLkr3kweQRs+x0ad4OrPoGkbp6FayIamohIJKghV565cmDhWEh5Eo4cgK7XwdkPQLW6Ra6S3Lo+nZokatyBiIiEx4FUmDYKln8BNRrCJW9Dh8shTvO1iUj5poZcebX+J5h8H+z+E5r3gvPHQIP2Ja4WH2c07kBEREIvKwN+fcn5wUKv/4Mz74aEapGOTEQkKqghV97sXU/7ZY9DygKo3Qyu/BhOvgCM7w0xjTsQEZGQsZb6O2fDq7fDwa3Q7lLo+wgknhDpyEREoooacuXFkQMw62mY9xaJJh7OHQ2n3g4VKpW4qoiISFhsXQST76PtlnnQ8BQY/C40PT3SUYmIRCU15Mo6twsWfwQ/PQ4Ze6HzMOZXPpfTz7wk0pGJiIg4Dm6HGY/CH59Atfr82fpOTr7yEYjTdMgiIkVRQ64s2/QL/DgSdi6DE06Dfl9Ao85kpaREOjIRERHIPgJzX3WeCefOhjPuhrP+zY7fFnOyGnEiIsVSQ64s2r8Jpj4Eq76FWk3gsrHOGAM/xsGJiIiEjLVOjpr6IKT9BSdfCOc9Bse1iHRkIiIxQw25suToIeeq5tzXnO4oZz8Ap98JhR6SKiIiEjHblzqzJm/+Beq3g2u+hRa9Ix2ViEjMUUOuLHC7YelEmP4IpO+AjldCn1FQq3GkIxMREXGk74afHnPGbVepDRc8D12uhXj9KyIiUho6e8a6v+bB5JGwbTE07gpXjocm3SMdlYiIiCMnC+a/5cycnJ0Bp/4Dev+f05gTEZFSU0MuRlU6shu+uBGWfwE1GsIlb0GHKyAuLtKhiYiIOOPgVv8IUx6Afeuh1Xlw3hNQ76RIRyYiUiaoIRdrsjJgzsv0mP+c02jrda8zy1el6pGOTERExLFrFR2XjoZZS6DuSTDsS2h1boSDEhEpW9SQixXWwvIvYdooOJjK3npnUH/oG1C7aaQjExGRCDDGVANeB7KAFGvtxxEOCTL2wcwnYeFYasRXhn7/he43QnzFSEcmIlLmqCEXC7Yucmb42jIPGnSES99m5aZs6qsRJyISUcaYJsBHQAPADbxtrX2plNsaC1wI7LLWti+0rB/wEhAPvGutfQq4FPjCWvudMeZTIHINOVc2LBzrNOKOHoRuNzC/Ym/OOPXisIfywrQ1vDRjbYH3mo38Ie/3gS0rkpwc5qBEREJADbkiRMWVzkM7nJko//gEqtWDi1+BTsOcRwtsSgl7OCIicowc4N/W2sXGmBrAImPMNGvtytwCxpj6QKa19lC+90601q4rtK0PgFdxGobkKxsPvAb0BVKBBcaYb4EkYJmnmCu4H8sP66bD5Pthz2pokQznj4Hj25KdkhKRcO7pexL39C16HF5KhOISEQm2qJ4ZwxjTxBgz0xizyhizwhhzVwDbGmuM2WWMWe5lWT9jzGpjzDpjzEjP27lXOm8GwntJMfsI/PwcvNIVln0OZ9wFdy6GLtc4jTgREYkK1trt1trFnt8PAauAws9+6Q18Y4ypDGCMuRl42cu2ZgP7vFTTA1hnrd1grc0CJgIDcRp1SZ4y4c/ne9bBx1fA+MHgzoarJsDw/8HxbcMeiohIeRTtd+TK15VOa2HVtzD1IUjbDK0vgPMegzotw1K9iIiUnjGmGdAZmJf/fWvt58aY5sBEY8znwA04OcdXjYEt+V6nAj1xGoOvGmMuAL4rIqaLgIsaN27s052o9PT0EstVyE6n6eZPabz1B9xxCWxucS2pSRdhd1SEHbP82lYgcZS2vC9liytT0vqBfO5ICmfcwayrrB5nJS3XcRbeusJ5nPkjqhty1trtwHbP74eMMblXOlfmK9Yb+IcxZoC19ojnSuclwIBC25rtSbKF5V3pBDDGFL7SuYRwXOncvtQZB7f5F6jfFq75xumiIiIiUc8YUx34ErjbWnuw8HJr7dOe/PIG0NJam+7P5r28Z621h4Hri1vRWvsd8F23bt1uTvZhYFhKSgpFlnO7YPGH8NPjzqQmXYYTd85DtKxeH2+XG4vdViBxBFjel7LFlSlp/UA+dySFM+5g1lVWj7OSlus4C29d4TzO/BHVDbn8Yv1KZ1Gt8YpZaTTf+AkNt08lp0J1Nra6je0Nz8P+BfxV9DYjfQUqLS0TKDjWQFefvIvVq0+Bbi9UVzp1nHkX7rjLw5VOXxljKuI04j621n5VRJmzgPbA18Ao4A4/qkgFmuR7nQRsK120pbRxtnOxcedyaHoG9BsDDU8JawgiIlJQTDTkysKVTq+t8QOp8PppkJ0BPW+jYvIITqpSG18elRqJK1DeZgK7bvLhvN8HtkzgpZuL366uPsVWXdF4pVNXOb0Ld9zl4UqnL4wxBngPWGWtfb6IMp2Bd4ALgI3AeGPM49baB32sZgHQynPRcitwFTA04OB99evLMO0hqHUCXP4htB0IxlvqFBGRcIr6hlyZvtJZKwlOvxPaDoJ6vjTfIkszgYmIHOMMYDiwzBizxPPe/dbaSfnKVAUut9auBzDGXAtcV3hDxpgJQDJQ1xiTCoyy1r5nrc0xxtwBTMF5/MBYa+2KEH2eY7W5CFxH4bQ7oGKVsFUrIiLFi+qGXLm40tn7/8JWlYiIBJe19he89+zIX+bXQq+zcfJW4XJDitnGJGBSUctD6rjm0OveiFQtIiJFi+rHD/D3lc5zjDFLPD8DCpXJu9JprXUD1wKbC2/Ic6VzLtDaGJNqjLkRwFqbg3MHbwrOtNGfhfVKp4iIiIiIiJ+i+o5cubjSKSIiIiIi4qdovyMnIiIiIiIihaghJyIiIiIiEmPUkBMREREREYkxasiJiIiIiIjEGDXkREREREREYoyx1kY6hphnjNmNl0ceFFILOBDEagPZnr/r+lrel3IllSlueV1gjw9xRJtg/+3DWZeOs9gRzuMs2PUF6zhraq2tF5yQyhYf8xRE59812OUDPYeUtL7OIeGtq6weZyUt13EW3rqiM09Za/UThh/g7WjZnr/r+lrel3IllSluObAw0n/HaPjbh7MuHWex8xPO4yzY9YXzONNP2fy7+lM+0HOID+cXnUPCWFdZPc5KWq7jLLx1RWueUtfK8Pkuirbn77q+lvelXEllgr2fokE4P5OOM9/K6DiLrvrCeZxJ8WL17+pP+UDPIWX1mIvVXFVWjzN/64sVOs6CSF0rJWYYYxZaa7tFOg4p23SciUggdA6RcNBxJqDJTiS2vB3pAKRc0HEmIoHQOUTCQceZ6I6ciIiIiIhIrNEdORERERERkRijhpyIiIiIiEiMUUNOREREREQkxqghJzHLGDPIGPOOMeYbY8x5kY5HyiZjTBtjzJvGmC+MMf+IdDwiEjuUpyQclKfKLzXkJKoYY8YaY3YZY5YXer+fMWa1MWadMWYkgLX2f9bam4HrgCsjEK7EKD+Ps1XW2tuAKwBN9SxSzilPSTgoT4kv1JCTaPMB0C//G8aYeOA1oD/QFhhijGmbr8iDnuUivvoAP44zY8zFwC/AjPCGKSJR6AOUpyT0PkB5SkqghpxEFWvtbGBfobd7AOustRustVnARGCgcfwX+NFauzjcsUrs8uc485T/1lp7OjAsvJGKSLRRnpJwUJ4SX1SIdAAiPmgMbMn3OhXoCdwJnAvUMsacaK19MxLBSZnh9TgzxiQDlwKVgEnhD0tEYoDylISD8pQUoIacxALj5T1rrX0ZeDncwUiZVdRxlgKkhDcUEYkxylMSDspTUoC6VkosSAWa5HudBGyLUCxSduk4E5HS0vlDwkHHmRSghpzEggVAK2NMc2NMAnAV8G2EY5KyR8eZiJSWzh8SDjrOpAA15CSqGGMmAHOB1saYVGPMjdbaHOAOYAqwCvjMWrsiknFKbNNxJiKlpfOHhIOOM/GFsdZGOgYRERERERHxg+7IiYiIiIiIxBg15ERERERERGKMGnIiIiIiIiIxRg05ERERERGRGKOGnIiIiIiISIxRQ05ERERERCTGqCEnIiIiIiISY9SQExERERERiTFqyImUQ8aYE40xywq9V8kYs9EY0zZScYmIiORSrhIpnhpyIuXTBqCJMSb/OeAWYJa1dmWEYhIREclPuUqkGBUiHYCIhJ+11m2M+QtoBmwwxlQB/g0kRzIuERGRXMpVIsXTHTmR8msVcLLn938C31prN0UuHBERkWMoV4kUQXfkRMqvVUBrY8xsnOR4aoTjERERKUy5SqQIuiMnUn7lXuW8C/jYWrszwvGIiIgUplwlUgRjrY10DCISAcaYjsCHQE2gi7X2QIRDEhERKUC5SqRouiMnUn6tBjoAbysxiohIlFKuEimC7siJiIiIiIjEGN2RExERERERiTFqyImIiIiIiMQYNeRERERERERijBpyIiIiIiIiMUYNORERERERkRijhpyIiIiIiEiMUUNOREREREQkxqghJyIiIiIiEmP+P2w/hSemYx85AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Fitting and plotting\n", "from matplotlib import pyplot as plt\n", "from scipy.optimize import curve_fit\n", "\n", "# Define a dictionary of model names for the plot titles.\n", "model_names = {\"U\": \"Uniform triangulations\",\n", " \"W\": \"Schnyder-Wood-decorated triangulations\",\n", " \"S\": \"Spanning-tree decorated triangulations\",\n", " \"B\": \"Bipolar-oriented triangulations\"}\n", "\n", "d_H_list = {}\n", "\n", "with h5py.File(\"qgdimension.hdf5\", \"r\") as f:\n", " num_vertices = np.array(f[\"num-vertices\"])\n", " expectations = {model: np.array(f[f\"expectation-graph-distance-{model}\"]) for model in models}\n", " \n", " fig, axs = plt.subplots(2, 2, figsize=(12, 8))\n", " axs = axs.ravel()\n", " fig.suptitle(r\"Graph distance expectation Monte Carlo simulations and Hausdorff dimension $d_H$ fits using $\\mathbb{E}[d_T(X,Y)] \\approx c\\,V^{1/d_H}$ for different triangulation models\")\n", " \n", " for idx_model, model in enumerate(models):\n", " # Calculate mean and standard deviation of the expectations.\n", " # TODO: Look at whether I store the right data and do the right calculations.\n", " mu = np.mean(expectations[model], 1)\n", " sigma = np.std(expectations[model], 1)\n", "\n", " fitfunc = lambda V, c, d_H: c*V**(1/d_H)\n", " popt, pcov = curve_fit(fitfunc, num_vertices, mu, sigma=sigma)\n", " d_H_list[model] = popt[1]\n", " num_vertices_fit = np.linspace(np.min(num_vertices)/2, np.max(num_vertices)*2, 1000)\n", "\n", " ax = axs[idx_model]\n", " ax.set_title(f\"{model_names[model]} ({model})\")\n", " ax.errorbar(num_vertices, mu, sigma, label=\"Monte Carlo\",\n", " fmt='.', markersize=10, capsize=4)\n", " ax.plot(num_vertices_fit, fitfunc(num_vertices_fit, *popt),\n", " label=r\"fit: $c = {:.2f}$, $d_H = {:.2f}$\".format(*popt))\n", " ax.set_xlabel(r\"$V$\")\n", " ax.set_ylabel(r\"$\\mathbb{E}[d_T(X,Y)]$\")\n", " ax.set_yscale(\"log\")\n", " ax.set_xscale(\"log\")\n", " ax.grid(True, which=\"both\", ls=\"-\")\n", " ax.legend()\n", " \n", " fig.tight_layout()\n", " fig.show()" ] }, { "cell_type": "markdown", "id": "b505b3cf", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "be7888d11d6b9ca0f2666739857578cb", "grade": false, "grade_id": "cell-032c7f8d6147d9f9", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "**(d)** Produce a *collapse* plot for each of the four models as follows: plot \n", "$$V^{1/d_H}\\,\\mathbb{E}[\\frac{1}{V}\\rho_T(r)] \\quad\\text{ as function of } x = r / V^{1/d_H},$$ \n", "where for $d_H$ you take the estimate obtained in the previous exercise. Show errors in the mean distance profiles via shaded regions (just like in the lecture). Verify that the curves collapse reasonably well. **(25 pts)**" ] }, { "cell_type": "code", "execution_count": 22, "id": "988bfe95", "metadata": { "deletable": false, "nbgrader": { "cell_type": "code", "checksum": "7b7eceb7923231bc3710d4e3036265b6", "grade": true, "grade_id": "cell-faf328e7505cf6a2", "locked": false, "points": 25, "schema_version": 3, "solution": true, "task": false } }, "outputs": [ { "data": { "image/png": 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RiUn4fUHcB5VCTFY7HoeejW824HaEyCmzkFcskJ6ZROkl1bs34HMNUD7tfNpaoqivNbDsrT4mzpJkTR+F3xOkp9VNTJIFk0W9RRXldKc+pcoRyXAYn9sFQNDvY+0Lz1K/Yys55ROYedUN6I0mnH1e/J6PSyEmawyNFX4qVjdgsRuZPN+E1dBPuE8bjDhm3FSsNis7N6xg65rXmTDrQuJijFRWRrFuWT/5bfuYcFERBhP0tbuxxZqxxprUmBNFOY2pugPliLxuFzIcxtnTzdt/+yP1O7cxcfES5t5wC1LqcXR6PpFEJNFseK2T3atayMyPYv5CG5kpUVgsNoQQ2Ox6omw6Ro8rZ9r8C3D0drD5jX8T9Y+fMHn7b8nKDlK7x8l7j+ymp8UJgKvfR1+7m1BQjTlRzl633347KSkpjB079sB93/nOdxgzZgzjxo3jiiuuoK+vD9CWBr7lllsoLy+npKSEX/3qVxGK+mMqkShH9FFvrdXP/ht3Xy/n3nonZeecRzgscfZ6CQ8OSpQSuhp0rHymgYFON5Nn2Jg0JQqjSXt7RcfGkJ2fitliQPr9BNdvIOWV15la1YQnGGBtQQa+zhYKa19m0nRByB/kg3/vZfeqFsKhMAFfiJ5WFz63mq9LOTvdeuutByZy/MiiRYvYtWsXO3bsoLi4+EDCeP755/H5fOzcuZPNmzfz97//nbq6ughE/TGVSJTDCgUD+D0e+tpa6Wqsp3zhBWQUlwAcKIVICb5eNxXLHOxY0UV8gp75F8SSmWM+cJwoq47YOD26rk54/U28P/wJ/iefRro9pC+6gHMuuhxpjWJtSS7ejauxte9g1nwTWQVWKla3sOyJfQx0e5FhSX+nh4BPzdelnH3mzZtHQkLCJ+47//zzMRi01ocZM2bQ1NQEaCsculwugsEgHo8Hk8lETEzMKY/5YKqNRDksr1OrWqrevB6dXk/+hCkHHhtwuvH6vThqvNTs0BEMQNl4KwXFH8+fJXRgt4QJbF1H27vv4tuzBwwGbNOnY5gzm0BmBghIAOZfchVLX/4PO/IzmP7SswQyshg3IZf0ogy2LW/nvUcrGHduFoWTknH1+YhLtUbiKVFGgJ++tpuKlsOPmzpWpRkx/PiSsuM6xqOPPsp1110HaGuavPLKK6Snp+N2u/n973//qSR0qqlEohyWZ8BBKBikZusmskrGYrHbAQj4gnT199K6Q9JbayAqOsyoqT6ssV46PXoMOiOm3i7Mm9fQtupD5IATQ1oq8TffjH3BAvSxsQD4fT4cfT2EwyGiY+OZOGs+G1e8R41FUPj6C7iuv420eAOLbh3Dpnca2fpuA61VfUy5OA9rrEn15lJGjF/84hcYDAZuuukmADZs2IBer6elpYXe3l7mzp3LeeedR0FBQcRiVJ9G5VMCXi+hQIDmfRX4XE4KJ08/8JjT5aF5u47+OkFKfoDM4gA6PYQDAfS7d6PfuA4qq/DqdDCxFHnOdAIlRTgMJtzChdHjx6AzYtAZsMbH4B1wIo0mcseU0tpQy36qSK7cTdzODXgnz8VqNjPn2iJqtnay44Mm1jxfxYV3lWNKU29d5cQ73pLDifb444/z+uuvs3Tp0gOl/aeffprFixdjNBpJSUlh9uzZbNq0aeQmEiHEo8ASoENKOfYwjwvgj8BFgBu4VUq55dRGOfJ4nFrRvnrTeqJiYkkv0iZclGFJr8uHo1GQnBMguySA6O7GtGE9po0b0TmdyMR4wldcAHOmQJxWbyuBQDhAgACekEc7iUEPsTGQkYDf7SPU4SR/8ni62lvZXpjF7Jf/i3FUPmGrBdHfx6jJKeiNOja9UUfdzi5scWZVKlHOam+//TYPPPAAK1aswGr9uDo3JyeHDz74gJtvvhm32826deu4++67IxcokW9sfwxYfJTHLwSKBv/uBP52CmIa0aSUeJ1O3I5+WvZVUDBpKjr94PxXxii6WwQyBImZAaKefJLoXz+AeflyKMwh/I3bkPffC0vOPZBEPiXKAhkpUJgLyQlgNGKKtaNPTyAYb2XMzGk49YK9yTEEn34KGerD7O8Fv4/csYnY483sXtmCs0etBa+cPW644QZmzpzJvn37yMrK4pFHHuFrX/saAwMDLFq0iAkTJnDXXXcB8NWvfhWn08nYsWOZOnUqt912G+PGjYto/BH9SSelXCmEyDvKJpcB/5bafMvrhBBxQoh0KWXrqYlw5PG5tLEjtVs3IqU8UK1lT0ikw+Gmq8IDNjc9e14gY8d2es6ZhG7xbGzJ6ejFIRMuSkAAOgEx0VpysZg/dU4Ak91GMDMNvD7ySsqo27OblOoWMt59F9MllxATsuKPzqBsbgbrX62ldnsX9ngLpihVKlHOfM8888yn7vvCF75w2G3tdjvPP//8yQ5pWE73T2Em0HjQ7abB+z6VSIQQd6KVWsjJyTklwZ2NPE4HUkqqNq0nJa+AmKRkjBYLZlsMTTvrcXWG2ZD1Ll98ZR2VGfCDmdvBsQMcYNNFEau3Ea23EaO3YRY27NYEUhNTiA3FE+2MJsYfQ6wplmhTNHrdJxOPJTGeoNNJevloultb2FEoiH37HXRjRmM0mYmJsZM/IZk9H7aye3ULeeOTSIyyR+iZUhTlI6d7IjncvBiHXbhCSvkw8DDAlClT1OIWxyAUDOJ3u+msr2Wgq5Ox55wHQFR0DN39fXTs6EcSprBpK4kD0P+FS7k7PRZHyIUj5Bz8140DDy3hPvp8jbidTmTH4V8Om9FGjCmGGHOM9q8phhmJU8lJiqV09iw2vPUWu3LTmPT4Ezjv/Q5GsxlrlpWyuZmsfamami2d2OMtmFWpRFEi6nT/BDYB2QfdzgJaIhTLWe+j6eKrN6/HYDKRUz4BodNhsdmpbKqkc7+f1uh9XPtuL3J8CXnls8n7aGe9HuKitQZ0k5GWPi9uX5CwDOMJugjrPJhNPhz+fhx+BwP+ARx+B/2+fga8fbS52tjVtYu1LWv5Wfn/YPfEMGbCFPZs2UBzdz+5L7+M48YbSbBYyCvLYM+HUexe3UL+hCTMWdGResoUReH0TySvAl8TQjwLTAf6VfvIyeN1DhDw+ajfsZXccRMxms1Y7HZcHi/tu9oJefUk9a3H6A8jr75Q2ynKorV9RNtAp/XdcPmCuH3a6Hed0GEzRgPRWHQ6RqdGodcfVNB0tIGvH+yptIY83LvyXp5ufoE7k68naUyYxOZGdgtBwvoN6EpLGTCasBujKJubyZr/VlG1uYPoBAtmq1quV1EiJaK9toQQzwBrgdFCiCYhxBeEEHcJIe4a3ORNoAaoAv4BfCVCoZ71Aj4vQb+fhl3bCPr9BxrZo6JjaOtsp3Ovl4DOw8KN25FzpkBGKiTEQW4mxEYfSCJI6Hb6AVi+x8O+Fv+Bc3gDYZp6PQQ+moDR3aclEQBnO+k6C9eOvpbNHVvYLqsJJkVTNnMWGAxsL8rG9/SzeDra8fd0kJVjICHDxp41rTi6VQ8uRYmkiCYSKeUNUsp0KaVRSpklpXxESvmQlPKhwcellPKrUspCKWW5lHJTJOM9m3kGBqu1Nq0nOimZ5Nx8DCYzQm+gs6aR3lYdZtdmdLowXHa+VpWVGPep4/R5AviDYfY0+3lpo4uHljr4sPLjL/pAKExznwe/ewBcHZ/c2dXBRcnTKIwt5MmqZ/BEGwkl2xk3Yw49Rh01dhO+p57B0deLYaCD0lmpuB1+9m9sx+tSEzoqSqREehyJchrQxo4M4OjsoKOuhlFTpiOEIComhvaudrr2uhBhPRP3rIOF84hJzSI7bxw5cflkR2eTZc8iw5ZBsiUFEYwl2pjIK5u8pMYYKc208p91Tt7bEcSit2LRWzGEBP0tTYRDAmM4jMXZgRjsV6H39fGlomtxBVw83/4aMjGG6IJMMvMKqUxNoK+misCq1bgHekmP85KUZWfPh604ulSpRDlzNTY2smDBAkpKSigrK+OPf/wjAD/5yU/IzMxkwoQJTJgwgTfffPPAPjt27GDmzJmUlZVRXl6O1xu5z8Dp3kainAK+wXVHqrdsQOh05E+cCkJgsdvp3LWT5oYgen8f5mAzuotvJT46BVtq1qcWm2rp8xBtNPHB7mZa+/38aEkpE7Pj+Ovyal7f1o7Ha+Jr5+Rjc9YgzKkIf4i8Tb/A0LwR5n4LOWYJ9e42coDLcxbxQv3bTE+czOjEdEpmzKC7vZXtRdnMeuUV9MWjMI2yUTIphlWvtlC5oZWYJAsWm2orUc48BoOB3/72t0yaNImBgQEmT57MokWLAPjmN7/Jt7/97U9sHwwGufnmm3niiScYP3483d3dGI2Re++rEomCd2CAcChEzZaNZBSXYI2JxWKz4+jvob/RQajPRm7TeuSFi7DGJhKVnvmpJOINhOhx+en3BHhmQwOTcuKZkhuPQa/j6+eO4sZpOSzd28HPX9uGZ/CXU+LuxzA0byAUmwOrfovY+RyZUcnoEFyRMpUsaxqP7X+SgM2AJ8HCxLkLGNDBvvREfI8/iWegl9RYHynZNvaubaOv0402dlVRzizp6elMmjQJgOjoaEpKSmhubj7i9u+++y7jxo1j/PjxACQmJqLX64+4/cmmSiQjXDgUwud20bp/Hx5HP4WXXAlAVEwMtTu30VTvB2nC7t2O8byvEx+bdmAG34O19XuREp5YV483GOaOufkfTykvBDdMyyHF6OVPH3ZwzwcB/l74IfFVL9FXcAmdY28nZ9vvMa/7G0a/m9TyK2n19XBX/iX8cPc/eanjLa5LWII1J43CknKq9+wkpboF/auvYb7xZsaUmln5jovKdW3EJVmx2FWpRDlGb90HbTtP7DHTyuHC+4e8eV1dHVu3bmX69OmsWbOGBx98kH//+99MmTKF3/72t8THx1NZWYkQggsuuIDOzk6uv/567r333hMb9zCoEskId/DYEbPNRuaYMvRGIzLgp7+9m746SXzvPsLnTycqykZ0Vt6njjHgDTDgDVLd6eTd3W0sKU8nO95KlEmHYbCrr97bx8XZXn42N4rkgT3k7PoL3fHj6Rx7B+iMNEy8B0/BBbDlcRI2P4FNZ2aUPYuL0mawtPEDamUL7jgzxdOmYo+NY8eoLDzLl+PavpWUFEFqdhR717XR2+5SpRLljOV0Ornqqqv4wx/+QExMDF/+8peprq5m27ZtpKenc8899wBa1dbq1at56qmnWL16NS+99BJLly6NWNyqRDLCeQYG8DqdNO3ZRfGMOegNBqKiY2iv2kd3qx/CcVh8bxA7cwnxSVnobLZP7C+lHCyNSP6xqoaYKCPXT8tBCMiKt6ITgoa2LqRTW91tVlwvV0f9gRZ/Mjd2f5Vvd0vGJgNCT1P5V0k3WLHv+i85fhf7JlzDtVnnsrF3L49W/osfl36fgXgT0+YvYtmr/2V/bjpl//43lp+OYvToeFY2eti7to24VCtRdlMEnk3ljDeMksOJFggEuOqqq7jpppu48kqtZiA1NfXA41/84hdZsmQJAFlZWZxzzjkkJSUBcNFFF7FlyxYWLlx46gNHlUhGtIDfR9Dvo3bbJsKhEKOmzADAICXdnV20bm1HH/QQnpWEOcpEXFbhp47R4/LjDYRZXdXF7hYHn5uRi91sIN5mwmLUYxIh8vXtWE06RNBDxrr/xSCDdMz6EZhjuHeZm5XNg+0tQkdrye04Sm9CV/kWBRsexYKOL+VfRru3mzdaXyFsMWLMTCavuISG6ChcbjfOxx8jOU1HepaJyg1t9LapthLlzCKl5Atf+AIlJSV861vfOnB/a+vH469feuklxo7VVtu44IIL2LFjB263m2AwyIoVKygtLT3lcX9EJZIRzDswgJSS6s3rSczKIS4tHYvdTn9zHe7OAXyBXIzeHeRNmEV8ag56i+UT+4fCknaHD28gxKNr6ihItnFeSSp6nSAtxqIt6t5Ti14GyYgxkbX195gcDbRNvZe41Bz+eJ6VUUkWfr6qnxeqB9+KQtBefAO94+7AXLeavDV/Yawtk4Upk3mzdRUt3kocVknR5GmgE1RPKiO4eQv+tcsYU2Yh6A+zZ00LXqcaV6KcOdasWcMTTzzBBx988Imuvvfeey/l5eWMGzeOZcuW8fvf/x6A+Ph4vvWtbzF16lQmTJjApEmTuPjiiyMWv6raGqE+GjvS09JEX1sr0y6/BgBjKExzdycdy3cR1i/AO9aPJcpAYvaoTx2jY8BLKCx5cUsTXU4f3z6/WEsisRb0OgG99RBwASA2P4ql+UNcU76MO3UyAPaYRH52ZQa/eXcfD23sodMdw51jJToh6Cq4nJDeQuLWv5C74nd8bvaX2Nq7n0caX+YH2bfiS0uisHQc+3dto2BUPjz1JHE/HUtmrp39mzoYMzOdDLvxU73LFOV0NGfOnMOWoi+66KIj7nPzzTdz8803n8ywhkyVSEYov8dNOBSietN69AYjeeMmotPr8fd04m5qw+1Ih1AX5WXlxOVkYzR9sjTiC4bodvrpGPDywpZm5hUlUZYRS5RJR4LNBM4O8PRoG1ctha1PwpiLsU28lrQYC9JoI2DPwmzQc9/iEi4uT+eF3Q5+uUHiD2kfqN7cxXRM+TbWripKVv6ZL2YtpNHTwbvO9QS87eROn4TBYKRyVA4gcf7zQUaXmAgFw1SsbsEzoEolinIqqEQyQnkGBggG/NRt20z22HGYoqyYgiF6Hd1431hOX1wxA5nN2O1mEjM+3TbyUXfff62pAwG3zsoHICMuCrwOcAxO0tyxF1Y8AGnjYPbdIATRNiuZBaXo9drbT68TfGleAbfOymNFrZP7VgVx+rVk4sg6h9Zp38fS18TVm//LnLjRvNy6mi5DPx5jH0UTJtLa2oTzovMJ7a/CsuF1sgusVG3poLvZiQyrthJFOdlUIhmBwmFt7Ejj7p34vR4KJ09HhsMIt5v+vftxdMeC0DG6KIXY3EyiTNZP7O/0BXF4guxq7md1VRdXT8oiOdpMnNWIVQShtw6Q4OqEd/8HrAmw6H9BbwShh4QCbFEWClNsmI3aW1AIwVWTsrhnUTF7Orzc/YGPDpc2uaMrfTqN03+I0dnFj6u2Y9MZeaT1LcIiSNK4DMyWKPa4+9FNGI/3lRcoyvQgw1Irlai2EkU56VQiGYF8bjcMNrLb4uJJKxiF3uvD5XMgXnqdlrQZDEQ3k5WWSHJWwaf2b+3zEApLHl5VQ3K0mSsmZqLTQVq0EXprQYYg6IN3fwABN1zwS4iK03aOzwVjFABmg56CJBtW88cjcuePTuEnl5bR6Q7x/5Z6qenTkok/dRKVM/6HJK+T73X3Uu1qZrlvN0FDiFETS+hsbaZ32kQIhYjatYzc4mhqtnXS2ehQpRJFOclUIhmB/G43zt5u2qr3a9PFh8MYfT56N23E0xbCF5VCYrbEmp1CjCnmE/t+1N33vYp2artc3D47H4tRT0q0BaOjAYJerbfWigegsxIW/AASBpNRTCZYPjkq3qDXUZBkI+6g9UTGZ8Vx/5XjQOj45lI3W9tD2rbJk9g27V4WubzM8/p5oW05XTiJHZuJ1WalomoPYlQh3hUfUDRa60eye1UL7gE/iqKcPCqRjEB+j5uazRsBKJg8DdnvwCf9hJ9/nbqcmQR1fkoK00jNzPnEfqGwNvjQ6Q3yxLo6yjJimF2YiNmoIyncCT6HtuHWJ6H6A5h2B+TN1u6zJoI95bDxCCHITrCSEmM+cF9+ko3/u3o8SdEWvr/CzdL64OBhJrBh6j18t9+PKRTgmY43CAnImz6W3u4uOkoKkd3dWOo2k18WR92ObjrrHYRVqURRThqVSEaYgN9HKBCgevN60gqLsNrsGEMh+lcsh9ZOOpImIlN6sOYnER8V/4l9Owd8hMKSZzY24PQFuXNuAUIIMkwehKtT26h2FWx6BEadB+Nv1O4z2SE2m8+SGmMhKz6Kj3rsJkebeeCqcZSkx3D/WjfP7glgEHqi4kdTM/lbfN0ZYpevg609K4gpTCU6PpY9PW2EbTZ8y9+nuMSE0MGulS14VKlEOc3l5eVRXl7OhAkTmDJlCgDPP/88ZWVl6HQ6Nm36eDmm9957j8mTJ1NeXs7kyZP54IMPIhU2oBLJiON3u2mrqcLV10vh5OmEenoQhAi+8DpVo6agx0pRUQLJqanodR+3XfiCIbqcPhp73Lyxs5XzS9MoSLYTZwhg9w6Ovu2ugmW/gOQSmPcdEAL0ZojPhyGO54i3mchLsh1YcNFuNvDTS8uYV5TEI9s9/HmLH7vOjrCnk1r2dSb7JU85tyO7N5M9bQxOp4vWsgKCO3di6m+gcEIS9bu7aavpV20lymlv2bJlbNu27UDSGDt2LC+++CLz5s37xHZJSUm89tpr7Ny5k8cff5zPfe5zkQj3AJVIRhif20315vWYLFFkFhShD4Toe+dtRE8vu/InETS7SSxLJDUu+RP7tff7CIe1+bQsBh03z8hFyABpoRaQYfD0wjv/A2Y7XPBzMJgP9NBCP7xxr3azgcJkO0aDlnyMeh33nD+aKydm8tp+Hz/90Ee0iCdoiefC/FsICh3P9HxAvrmR2JQE9hEkJCW+5W8yemwUeoOO3Stb8LpVDy7lzFJSUsLo0aM/df/EiRPJyMgAoKysDK/Xi8/nO9XhHaBGto8gMhzGM9BP4+4dFEyaCgMDGMMhfK+8SUNxHrG+McSN8ZOYmIRJ//Gkhy5fkH5PgI11PWxt7OOLc/OJtehJDzVh1Icg5Id3fwiePrj0T1p7CALi88BoOVI4R2Ux6ilMtlPf7cbjD6ETgttm55NkN/OPVTX8j9fAd2bGEmuVLE6cxys9K7mw5XXGFi5gzVo/DaNzKfhwHVEXXsyoKTnsW9tGa1U/BROSP/vkyoj1wIYH2Nuz94Qec0zCGL477bufuZ0QgvPPPx8hBF/60pe48847h3T8F154gYkTJ2I2mz9745NElUhGEL/XQ3tNFaFAgIyCUeDz0//Gq+Dx8t7YMnToyJ6QTGpi0if2a+33EAiF+efqWrLjo7hobDo2TwsJxqDWQ2vV76F9F8y/D5IHfz3FZIIl5jBRDJ1xsEdXTNTHv3cuGZ/BfReOobo3xA+X6xnwWpiVMIMccxq/Skqk2PEmaYl6qqKM+J1uvBuWMboohMGsZ9eKJvze4HHFpCgny5o1a9iyZQtvvfUWf/nLX1i5cuVn7rN7926++93v8ve///0URHhkqkQygvjcblr27UFvNJJoj8Xo8eB8eylNE3KJ80xEl+AlPjODGGv0gX16XX48/jCvbm+htd/LTy8pw+LrJsXkRggD7HgeKt+CSbdA4QJtJ2sS2E/ML3+dTpCbaKO130PXYIP5rMIk4i438fPXK/jFyii+PC3INakX84eGf/Gj9Hx+6NrIk92TqM1MYszGnVgm7yG/tICq7X30trpIzf/0wlyKAgyp5HCyfFRVlZKSwhVXXMGGDRs+1TZysKamJq644gr+/e9/U1j46dknTiVVIhlBfC4nzfsqSM3JRyfB9eorSOC/kxJJ8KSTNTaelPjEA9uHw5I2h5del5//bGxkWl4CU9L1xAY7sZsM0LAO1j8E+fNg8i3aTqZoiM064bGnx0aREWc50GZfmh7DA1ePw2Q08bs1djr70lmYMIsVpgDLc/Mpju6kLsGOp7YBf3MDhfnaaPe969oIhcInPD5FOR4ul4uBgYED/3/33XcPTBl/OH19fVx88cX86le/Yvbs2acqzCNSiWSECAYC9LW14uzpJi0rB31HJ/7Va+mcXY7eOQqpC5M02kpyfMKBfToGfARDksfX1hEIhbljZgZmZyNJ0SZtZt+lP9Ma0+d/D4RusIdW3pB7aA1Xot1MTqL1wOGz46385urxZCXY+NsGO5aBc0gzJfFHe5DE4lhCQFVyHIFNO7DqOknJ0FO9uQ23Q3UFVk4v7e3tzJkzh/HjxzNt2jQuvvhiFi9ezEsvvURWVhZr167l4osv5oILLgDgwQcfpKqqip/97GcHpp3v6OiIWPyqamuE8HvcNO+rACA1LQPvM88joyw8OzVM0bbJxOUbSUtJxKDXuvz6g2G6nD4q2wdYureDqyZmkKdrJ86sxxQYgHe+BwYTXPALbcqTY+yhNVwxFiOFyXbqul0EQ5J4m4lfXlHOr97aw1M7YF7xFWzT/5OHs7K5qMFDo4yhcMs2zAumU1iSwtqlfmo2tzFuYa6aYl45bRQUFLB9+/ZP3X/FFVdwxRVXfOr+H/zgB/zgBz84FaENiSqRjBB+t5uWyj3EJCYT1dpJYOcuBs6fRYvDgDloI6XESkrCx9Vabf3aWiMPr6wh3mrk5tESo/STYNHB+z8FZyec/3Owp3K8PbSGK8qk9eiyDE74aDUZ+PGSMuYVx7GyspBE/yw2B/bROKEQhGBfXDzWVf8kPb4Ti1Wwf0MLPrdqdFeUE0UlkhFASonL0Ud7TRVpOXkEXn0VEuN4ZVyY4s5p6K2SjMJ4rFYtEXzU3XdFZSf72ge4bVIcdlwk2c3o1j0ILVtg3rchtUw7QWzWcffQGi6TQUdBsh27RSsBGfQ6vr2ojCUTYqitWYwhmMDLpk3Ys1JojrfTstdL/LafUVgkaW/w0lnbe0rjVZSzWUQTiRBisRBinxCiSghx32EejxVCvCaE2C6E2C2EuC0ScZ7pAl4Pbfv3EQ6FSA6ECdU34L9kIWvdleT2lZI0OorUxMQDVT2t/V48/hCPfVhHcXIUF2R6iTLqia5+HSpehnHXQ7FWV4s1CWxJRz75SaTXCfISrcTbtAkfhRDcPmsMN8xIYKD5avrkAOuLXeiFYIcxDdHawISBnyEE7F3TQDAQikjcinK2iVgiEULogb8AFwKlwA1CiENXr/8qUCGlHA/MB34rhDChDIvPo3X7NRhNxNU2gtnEqmJBRmcJQurIKI0mPk4rUWjdfUM8v7mRHpefr47XoReClIHd8OGfIGcGTPuidmBzzEnpoTUcQgiy4q2kxmqDsYw6ExeX53D7jAmE+qaz3ryXYHoc7bE2drZPJc69hZzEFuoqBnB2OiMau6KcLSJZIpkGVEkpa6SUfuBZ4LJDtpFAtNB+KtuBHkBVbg+Tz+Ue7Pabh9y1Gzl2NG95NlDWPRtrip6snGQMJv2B7r5t/V5e3tbMeXkmSpP0xAc7MC37KcTlwLk/BJ0eDJaT2kNruFKiLeQkaD26Yk3xTMmL4/bx1yGDMTwzugVjWFLRF8BlK2Ucj+H3Sfavq1OzAivKCRDJRJIJNB50u2nwvoM9CJQALcBO4BtSysMOAhBC3CmE2CSE2NTZ2Xky4j0jhUMhupsacPX1kmK2gsNBc1kKrn5BrDOF5DFRJMZps/x2OrXuvo+uqUUv4AvjTRiCbhJW/QQQ2gJVJhvoDFoPrYMmdTwdxFqNFCTb0OsESZY0RqfGMdV+DX5rJ44EQafVTF1bMdn6jcREOaja1ofP4Y502IpyxotkIjncT9lDfx5eAGwDMoAJwINCiMO26kopH5ZSTpFSTklOVvMpfcTn0XprASS2dSJ1Ol7O7qS0eyZCB3llyUTZjfiDYToHfGxv7GNtTTc3lppIskiytvwG4WiGRT+FmAwO9NAyRG5en6OxmgwUptiwmy3Em5NZUjYNnXMCb4zX1pCvqmrDEz+RsaaX6ekI0byzIcIRKwrcfvvtpKSkfGIQYk9PD4sWLaKoqIhFixbR26t1EBnKFPKXXnrpUQc0nmiRTCRNwMGLVGShlTwOdhvwotRUAbXAmFMU31nB73bRsq+C2KQUTLv3EBidw+rQXop7JxOTZSQjLRmdXke7w0swpC2fm27Xc9VoE6kVj2Ns2QBz7oaMidoBY7PBHH3Uc0aa2aB1D06PTiLabGdh2sUMWINgkDTqBR3hyYwxv49eF6RyUxd+lyfSISsj3K233srbb7/9ifvuv/9+Fi5cyP79+1m4cCH3338/8NlTyL/44ovY7fZTFjtENpFsBIqEEPmDDejXA68esk0DsBBACJEKjAZqTmmUZzhnbw8ddTWkJiRBRyfbR5uI86RidFtJK4rBajfj9gfpcwd4a1crDT1uvjTBRFLT+8TsfxHKroSSS7SD2ZLBlnj0E54m9DpBQZKNUfHZzBuTj8FdztrRffiMBmq31BNOKaPIsoqGKj/99U2RDlcZ4ebNm0dCQsIn7nvllVe45RZt6qFbbrmFl19+GTj6FPJOp5Pf/e53p3ywYsRGtkspg0KIrwHvAHrgUSnlbiHEXYOPPwT8DHhMCLETrSrsu1LKrkjFfKYJ+Ly0Vu4lHAoR39sPwLPZLcx0Xw9AQWkaZquB6k4XDk+Ap9Y3MCE9inMtlaR8+BfInAwzv6IdzByjzeh7BhFCUJAcR7cnjXPSzmOZ9XfM2RVHfV8fxfZzGGt9mb3uBezf2ElCQTZ6y6kZUKmcvtp++Ut8e07sNPLmkjGkff/7w96vvb2d9PR0ANLT0w87BcqhU8j/8Ic/5J577sFqtR5f0MMU0XEkUso3pZTFUspCKeUvBu97aDCJIKVskVKeL6Usl1KOlVI+Gcl4zzR+j4fmfXswmMzEVFbjyI6n0e4lt2cs0WkmktNj6fcE8PhDPLWhAbc/yFfGG0jd9bBW+jjvJ1rD+mnWQ2u4RqdksLh0EjrfKOpT3HTbLLTtaMaelUmKsYrq3W487c2RDlNRhuXQKeS3bdtGVVXVYadUOdnUXFtnMa9Lax9JTkvHuLGCpefGUijGEO42kjE3DlOUgdp+N7VdLt7e1crFJQmUhHdi7quGOd/U2kJO0x5awxFjMZIZk8qcxHNZU/5PrvvARt3+GtJmLGas7R0+6PsqDTs7KcnIQhhPz04EyqlxLCWHkyU1NZXW1lbS09NpbW0lJSXlwGOHm0J+7dq1bN68mby8PILBIB0dHcyfP5/ly5ef9FjVFClnqXA4RGd9DW5HPwlerf703QIn87xLACgoS6U/EMQfCPPPVTXYTAZuKTOQUPsG0miDokVoPbTyT9seWsNRkJjE4uLp+PWp+Ew+Wkx6HE0DZBRYMIsBqnb04+s8tK+HokTOpZdeyuOPPw7A448/zmWXacPsjjSF/Je//GVaWlqoq6tj9erVFBcXn5IkAsNIJEKIhCH8xZ3EWJVh8Hs8tAzO9ptQ30xvooneVCuJHblY443EZVrpGPDxYXU3O5r7uXlqOgmBVqzNqxGjF4PRqg1ANJ/a3h8ni91sIDspi2nR89hQ0offoKduww5cyXMZY11BU6OOnoYuCEZu3Wtl5LrhhhuYOXMm+/btIysri0ceeYT77ruP9957j6KiIt577z3uu0+bRep0m0Iehle11TL4d7SKcj2Qc1wRKSeENm38HqITErGv3MTrU+CcuItwrQ1TNCWZ/mAYbyDEo2tqyUu0siRfkLznPUQ4CKWXgy0FrAmfeZ4zSVFiCouL5vJT5zvMk0FaXV4KHQHyRwXYvl1P1eYOkvNbMKbmRzpUZYR55plnDnv/0qVLP3XfUKaQz8vLY9euXScktqEYTtXWHillgZQy/0h/QPfJClQZHmd3F531tSTo9YhQmI3FgknuhcgwpBTFMRAM8fLWZjoGfHxxTi5mfw/2mjchayokFg4OPjy7WM0GCtLymWSZSV26g16bhbZNuxB5U8gy76RmbxBXZ7cqlSjKMA0nkcw8QdsoJ1kwEKBpbwUyHCaxo4t+myC6ZDzhJgsmqwFdiplul5/nNzcxqzCRSYlhUns2INxdUHaFNqPvGdpD67MUJ6dz4agFrB0TREhJa20tLmeQUfn9uALRNGxrJNyv2koUZTiGnEiklN6DbwshbIMz+B5xGyUy/B43LfsqMJhMxO+rZdMoWJB6Af31AVLyYwjqdTz2YR1hKbltdj6WYC/2qtchOg1yZoL1zBh0eCysJiOjMooZY52M2+Kizaynu7qJuLJSbPoearf34O3ugYB6KyvKUA2nsV0nhLhRCPGGEKID2Au0Dq4T8n9CiKKTF6YyHF7nAM2Ve4iz2zH7gtSWJpDqKCHkl1izbOzrcbKispMrJ2aRYQmQ6qtFtG6Dksu0tUVO8nK5kTYmLZtF2QtYV+ImaNDTtnU7breXoqx2mgby6d5XBc62SIepKGeM4VRtLQMKge8BaVLKbCllCjAXWAfcL4S4+STEqAyDlJL2mmq8AwPY+3vwGiF3+iIGakLoDAJbjp1/rqol0Wbi6slZxIb7sFa+BnoTjLlIq9Y6y1lNJkpyyrClj0ZIP13uAXq7XaRPzEcQonZ9Nb7eHgioObgUZSiGk0jOA34BLDl4KncpZY+U8gUp5VXAf050gMrwBLwemvftBiC1upGdhQamZi6gt85PTKaNNW19VHU6uXVWHlZ9iBTRDfvfhcKF2hQoplM7tUKklGYXsDBpHlWZTvqtZjo2bCUkPeQkdVDZXYa7ZhcMqFKJogzFcNpIAoMJ5LyjbXNColKOmc/jpnlvBVHRVhL7/fgmFBPojcY3EMSSaePJTY2UpEVzTnEyKXonpur3IOiFsssjtmRuJNjMUYwrnEjH6FSEDNPTUEPfgJ/cCen4ZDTNazcRcvaqUolySjQ2NrJgwQJKSkooKyvjj3/8I3DkqeQ/0tDQgN1u5ze/+c2B+5555hnKy8sZN24cixcvpqvr5E9PeCwj27cKIX4shFCj4k9DA12ddDXWY/INEBIwasHlOKokCFjl1yZnvHNeISaDIJF+2P0ypJRC6liwxEU6/FOqJKeIeSmzcVpd9FgNtO6pxhznJcbqYm9HCf7azTDQGukwlRHAYDDw29/+lj179rBu3Tr+8pe/UFFRccSp5D/yzW9+kwsvvPDA7WAwyDe+8Q2WLVvGjh07GDduHA8++OBJj/9YkkE22pTvLUKIV4QQPxNCXHOC41KOQSgYpHH3TpCStKYO6vKiSEgbQ2eVB2OimddrujivJJVRKXYyTF50zRugv1Hr8ms7e7v8HkmsLZZJedPYXxJFSK+jc+sW+gb85JVF0x4YTd+6t5HuXvCrVRSVkys9PZ1JkyYBEB0dTUlJCc3NzUecSh7g5ZdfpqCggLKysgP3SSmRUuJyuZBS4nA4Dkw5fzINu3uOlPJaACGEGSgDyoHpwPMnNjRluLTR7BXojQYKWt3suqIcV78dd08rlck6jHodn5uZi82sJybcD7tegqh4KJg/IhrZD6c4p4hxudNhy4eEwj4a2noYWxyHfnOIvW1FJNZswGSN1yauVM56q56rpKvReUKPmZRtZ+61xUPevq6ujq1btzJ9+vQjTiXvcrl44IEHeO+99z5RrWU0Gvnb3/5GeXk5NpuNoqIi/vKXv5zQ6zmc4XT//cTPVSmlT0q5RUr5uJTy24fbRjm1fC4nLZV7MOkCCCBt/gV07NGarVZ43Vw/NZsEm4kMm4SeKmhYC2MuBnvKWd/l90iSE9OYljWDxqwQA1FmGtdsZMDnI7vQRKX3HAIbnwZPnyqVKKeE0+nkqquu4g9/+AMxMYddVRyAH//4x3zzm9/81EqIgUCAv/3tb2zdupWWlhbGjRvHr371q5Md9rBKJMuEEC8Ar0gpDyx0Pbi64RzgFrQuwo+d0AiVIWvZvw+fy0XmQDdN6SbiMifSt9ZFn0ESFW/mkvEZJNhMWPydUPGqVpVVcqm29sgIJYRgVEExCeXjEY37iO3ZT3X3AMVFdur2m6luy6K0ajUGS6w2dYxyVhtOyeFECwQCXHXVVdx0001ceeWVwJGnkl+/fj3//e9/uffee+nr60On02GxWJg+fTrAganlr7322k+1q5wMw2kjWQyEgGeEEC1CiAohRA2wH7gB+L2U8rGTEKMyBAGfl+Y9Wrff0fUDOMbn43TbcbZ52KMPcsecPKJMelLtRq1b6943IG+ONk28yRbh6CMrJTGLOdlzcNm89NtMbNtYScgaJj5Jx07vEtj8KHj7wO+KdKjKWUpKyRe+8AVKSkr41re+deD+I00lv2rVKurq6qirq+Puu+/m+9//Pl/72tfIzMykoqKCzs5OAN577z1KSkpOevxDLpEMTn/yV+CvQggjkAzcLKX89ckKThk6n9tN477dGEwCSyiMfca5dO7zIwBduoVpBUmkxVjQe3ug6n3wOT5uZB/hjGYzeXnFrBiXQ3hdF5m1a9nfMY7s0QnsWJNOe6eV9Kpl6CxxqlSinBRr1qzhiSeeoLy8nAkTJgDwy1/+kvvuu49rr72WRx55hJycHJ5//uhN0RkZGfz4xz9m3rx5GI1GcnNzeeyxx056/MdUMT44XqRFCJF3YsNRjpWjs53epkbifP10xRswF85g33+7MQnJlefkE2XSE28zQVsn7H5JWzo3c6rW2K6QmpzN7DEL2bnu3xh1gnf2dnPXnGSMJtgRuIr0Tf+CwnPAl3rWrNGinD7mzJmDlPKwjx1uKvmD/eQnP/nE7bvuuou77rrrRIU2JMc7FmSxEOJhIcRdQoipgz25lFMsHA5Rv3M7AMWNA3SPzabBYcPeH8SfZCQ/PZrMuCjwOqB1K3RVjtguv0ditceQkzkKT340LouJjL3Lqe7oJrPITK1rAp6+AeT+99Vod0U5jONNJO8A3wWqgHOBR487ImXY/B4PjXt3IfSQ6PJhmDqX91Z3YkIwbkIqibFmokx6cHdppRGjDYrOV9VaBxE6HanpeYybei4iHKbIVceL9W5s2QakFOwKX4/c/Dh4e8F3YruHKsqZ7pgSyeBMwAZgnZSyV0r5vpTyASnlTSc4PmUIvE4nbfv3YQm4cVl1NGbMJqrbT1gvyBwTR1qMBYJ+6KmFmhUwejFEp4PeGOnQTyv22AQKskqQsdBvtWKp3kato4/kLCO7nOciBzph39uqVKIohxh2IhFCfA1oB+qBbwkh7jjhUSnD0rKvgoDHQ36rg7aSdD6ok4wK6onLspGdHo1Br9NKI3vfgHAASi8b0V1+j8RoMpOUnk/GtGmEdYLzW1fzYr2LuAILXp+RPeI6rVTi7gLfQKTDVZTTxrGUSO4ByqWUmWhdgmcLIX5yQqNShizg91G/W2sfyez14CqfQXO9C1tYkFIUS0p8FEgJznbY8wpkToHkMarB+Ahi45MoHT0FjCE8ZjP6ukrqfH1EJxjY7r4EXJ1aQlalEkU54FgSiRPoAJBStgJfAK48kUEpQ+d3a9OiGPAT1klWx89hVEAPAsompyKEAE+vVqXlGlxKV5VGjshis5OQmkPs+GLcZiNXNL3NS00uEoqi6HOYqbNcgdz6pFYq8ToiHa6inBaOJZH8DXheCDFq8HYOoOaPiJDethb6W1tJ7x6gZVQSy5olY6WJuEwbKemDpQ5XF1S8DPZUbRDiCJvldziETkdsUhqTxs1F6kP4TQYMdTU0yH5MUTq2eq9GeHq0WZOd7ZEOVzmLhEIhJk6cyJIlS4AjTyHv9/u57bbbKC8vZ/z48SxfvvzAMfx+P3feeSfFxcWMGTOGF1544ZTEPuxEIqX8K/AU8E8hRA9aj619QohrhrvcrhBisRBinxCiSghx3xG2mS+E2Da4pO+K4cZ7NguHQ9Ru3wxAbpebmsJpmDwSm0+SPSYek8WgzRHVvgtatmptI/YU0KkVAI4mKjqG+NQcokpzcFgtXN34Oi81uUgqttLabqUtejFy29Pg7FClEuWE+eMf//iJUehHmkL+H//4BwA7d+7kvffe45577iEc1tYa/MUvfkFKSgqVlZVUVFRwzjnnnJLYj+kbRUr5opRyPpACTAI+AGYBfx/qMYQQeuAvwIVAKXCDEKL0kG3i0EbTXyqlLAPUdPUH8bs9NFTsQIgQVp+fV2wzmWawADBqgjYnD+7B0ojeqE3QOEJn+R0Oo9lCTFI6U8bPQ4oQGEDf1EiTzonOINgWvBnhc8CuF1RbiXJCNDU18cYbb3DHHR/3XTrSFPIVFRUsXLgQgJSUFOLi4ti0aRMAjz76KN/73vcA0Ol0JCWdms/78U756pNS6oEdwOPD3HcaUCWlrAEQQjwLXAZUHLTNjcCLH00SKaXsOM54zyru/j46qquIH3DSlBPPfp+FJdJATIqRxEw7hEPQ1wiV72hL6cblgMEU6bDPCFExMSRmFaArTqFrXzc31L3CYxk53JWfSm2NpHfMQuJ2PIsouxyiU8ESG+mQlRNg2WMP01Ffc0KPmZJbwIJb7zzqNnfffTe//vWvGRj4uDfgkaaQHz9+PK+88grXX389jY2NbN68mcbGRoqLtQknf/jDH7J8+XIKCwt58MEHSU1NPaHXczjHW8ch4MAMwMOVCTQedLtp8L6DFQPxQojlQojNQojPHzEQIe4UQmwSQmz6aMKys13trq2EA0EKOtxsyZpEqtGAoT9I9uh4TBY9uHug8u2DltJVjexDFWWPJiY+lamT5iMJY8SPobWFFouLcAh2yNsQfhfseE6VSpTj8vrrr5OSksLkyZOHtP3tt99OVlYWU6ZM4e6772bWrFkYDAaCwSBNTU3Mnj2bLVu2MHPmTL797W+f5Og1x1si+WhymBeFEA9LKV8dxr6Hm5vj0MlmDMBkYCEQBawVQqyTUlZ+akcpHwYeBpgyZcrhJ605iwS8Xup3bQMkiU4Pr9hmcFFsDHR6yBuXpPXWcnVoI9lTSiB9IpijIx32GUPodERFx5CSXUQoP4ZWKbip9hUeSfsKX8pOZn+NYMqYhVh3/RdRfpXWkSEqLtJhK8fps0oOJ8OaNWt49dVXefPNN/F6vTgcDm6++eYjTiFvMBj4/e9/f2D/WbNmUVRURGJiIlarlSuuuAKAa665hkceeeSUXMOxDEj87mHuvgzIEUI8JYQY6oT+TWjL9n4kC2g5zDZvSyldUsouYCUwfrgxn428LifNeyuw+ty0JNvptsWT6xFYY0yk5sdojcD1Hx60lK4qjQyXNTaO2PhUJk2ehxRgCzkxdLTRbvPi80p2G26DoA+2Pat6cCnH7Fe/+hVNTU3U1dXx7LPPcu655/Lkk08ecQp5t9uNy6UtafDee+9hMBgoLS1FCMEll1xyoBfX0qVLKS0tPew5T7TPLJEIIZ47+CYwAXjg4G2klCHgQSHEU8D3hRB+KeX/fMahNwJFQoh8oBltHfgbD9nmlcHjGgAT2pK+v0ehrbYKv2OAog4XqzLHMScnAe8uDwUTk7FYjdDXpJVGLHFa+4ia5XfY9AYD1uhYsvLL2Ji5lKaw5PM1r/GPpC/yxcR49lbpGDdqIZbdL8G4a1SpRDmhjjSFfEdHBxdccAE6nY7MzEyeeOKJA/s88MADfO5zn+Puu+8mOTmZf/3rX6ck1qFUbTmklAe6Eggh/nboBkKIJcBYoAQwA97POqiUMjg43co7gB54VEq5Wwhx1+DjD0kp9wgh3kZrzA8D/5RS7hpCzGe1cChE1db1AKQ63KwaP4Nb7XZcIQ955YmIcAA692lL6Y6/UZtXS3X5PSbW2Dhi49IYO2kmlc3LiPd2YejuoCsvGmtNmP22WxkbXorY9jTEZKlEohyX+fPnM3/+fAASExMPO4V8Xl4e+/btO+z+ubm5rFy58mSGeFhDSSS/OOT2wSWNj9o54oG3gN9IKYNDPbmU8k3gzUPue+iQ2/8H/N9QjzkS+NwuGvbsxBDy0W81YSzMx94dxG/Rkz0mYbDL7yvaxqWXqll+j4PBZMJqj6GweDI7kldRH4rlluo3+Efi7dxujWFvVQyj8xZjqngVxl2n9eBSpT9lhPnMn6lSyloAIcSWwds9Bz2mG/z3CSnldmDDSYpTOUhfexsDLW3kdLtYk1bKkrJMeuodpBfGYrEZwNGizQeVOwcSR4FBLRNzPGxx8cQlpDNqwiSCej1p7hb0vV30J0o6moPUx9+s9RLZ+oTqwaWMSMOp7ygRQuw4yt9OQP30PcmklFRuWYuQkNbnZkfWDMYbLQQ8IXLKEtH5+6HqPW0p3bGqkf1EMFosRFmjKR07G08s1CbFclv1W7zkHkBnEOyriiNQcDHsfRN6arRu14oyggyn+++YIWwTOtZAlKEJ+LzU7N6KkEGQYQrmTsVd60SnF+SXJ4KrCXa9qC2lmz0DLDGRDvmsYIuLJ96VQcb4MnpX7qa4rZawowdnYjQNVT46ym8gs/ZNxJbHIaFAq95Sq0+eMaSUWpf5EeBIS/oejyGXSKSU9cBsKWX9Uf6aTniEyie4Hf10V9eQ2u9mY3oxF0/Mo6O6n5TcaGzREpo3akvpll6uSiMnkNlqxRoVzaSJC/DawtSmxHJb9Tu85nchw7CvJpZg0WWw/z3t+ff0RjpkZYgsFgvd3d0n5Qv2dCOlpLu7G4vFckKPO9wBifOBpwGEEAuklMsG/z9JSrnlhEamHFb1zs2IQJjMXhdVc2cR5wFXn4/SOenovd2w6yUwWqH4QrAmRDrcs4otLp44VyZxZQU4N9QxqW0vHlcPnvgsqit8jL36OlKqXkNsfgwSi1Sp5AyRlZVFU1MTI2VGDIvFQlZW1gk95nATycGfihuAZYP/vws49UNCR5hQMMieLWuBMDavj/JLF9Kzrx9Aq9bq2Qo1y6HkEojLAp0+ovGebcw2G/aoaKZOPZ/3tz9ETXIcd9S+z39Lr+Nyn5nq+lgSx1yFYddT0LkHotNUMj8DGI1G8vPzIx3GGW24gwsMQoiJg/8/OKmon12ngM/tonXfHmLdXvan5zG1bBRN+3pISLeREOuFPa9pS+mWXaZm+T0JhBBY4+JJTMnBPCadPlsUpa076Pb04rMJ9u304ci5Gkw22PQvrfdcWDUbKme/4SaSMGATQtwACCHE54UQ6Xx6jizlJKjfX4FuwEdWjwvd5DkIR4DeVjdZY+LRezu0sSOZkyG1HIwntg5U0UTZo4mJimXG9AsJGMLUJcVwZ/37rBA+3P0BGlriCJZeA3WrtHVg+hs/+6CKcoYbbiL5IVCANgDxQ6AGbT2SYS1opQyflJJt67V1vRIHPEy47lKadnYDUFBqhepl2nriZVeoAYgnkdDpsMbGkZJRgByVQEeMjQmNW2kI9BEwCSp2+HDmXAnmGNj0qNborhrelbPcsBKJlLJFSvlvKeVfpZSPAr2ADdh9UqJTDgh4PdRUbMcS8NGTkkJqXgH1O7uJTrSQnOTR5tWyp0L+fLU2xkkWFRNDjCWWaTMuIKyDusRovtjwHusMPnpbPLT1xBEqvx4a10PrDuhvgtCQJ3xQlDPOcU3AJKXcLaV8Tkr5tRMVkHJ49Y31mDsHyOxxEzt7Lp4OL11NTvLL4zH17IaWLdp0KNEnfxGbkU6n02ONjSUrtwRTQTLN8dFMqdvI/vAAIR1U7AjgyrlUS+wrHgDfAPQ3RDpsRTlp1Ex+Z4i1q5cigBSHi5zLL6NyozYVR/FYk1Ya0RthzCVgTYxsoCOENSaOGEssE2aeixTQHBfNrc1vsN0UoHW/g15nAqF592kN7usfAm+/GvGunLWGlUiEEN8UQlwghDh0JUPlJPJ4fFTs3IguHIKYaOKLSqjb0U1KbjQJlk7Y/w4UnquNqFZdfk8JvcGALTqWlIIxxOSkU5scy/T9m9mNEylh964A3tgJ2vTyFa9Aw3qtiivoj3ToinLCDbdE8k9gCXCJEOKHJyEe5TBqmlqIbe8mrc9N3Oy5NO/tw9XnI7/MhrHmDQh4oFQ1sp9q1rh44ixxjJoxEyl0dMTYuabjP1Qag9Tv7MPhsSInfwHi87UqLk+P6sWlnJWGm0iKgLrBtUJ+djICUj5JSsnLy5ZjCkGqw0X6kkvZv6kDvVHHqGKpVWsll0DWVDBGRTrcEcVgNBJljyF/7FRi0lLYnxbHnIrd7DT0Ew6EqdgTxhuMggXf1ybRXPU7rYrL1RXp0BXlhBpSIhFC3DS4hG4s4B6s4jrckrvKCdbn8lG/90OQErvJiL64nMY9PWQVxxDdd/BSuqo0Egm2uDisRiujZs8iLPR026M5v/dRmgwhqjZ1MSCTkYmjYMptULtCm5nZ0awt0asoZ4mhlkg6gb8C/wucD6RKKR84+i7KibByTxMZXa0kOj3En3c+tdt7CPhCjCo1od/7sraUbtEi1eU3QoxmC6aoKIonziY2NYXK9HjO2VHPTksbQVeQ/Xu9+EiAcddD6lhY80cYaIU+1YtLOXsMKZFIKd8F1ksp5wKfB+wnNSoFAI8/xAurNxHtg+QBN2nX3kj1lg6ioo3kJDZC/Ycw5mKIyVSTA0aQLS4eg95I6bxzCen09FpjmOx4iF5dmIp1rThlAtJo1aq4ZBiW369VdTk7Ih26opwQw2kjiRFCTAZ8aIMQlZNsf8cA7gZt/WVrShz+6HTaqvvJG2MjqvZVbaPSy1WX3wgzRVkxmMwUTJhGfFoaVekJLNrSy66Y/fi7fNRV9uMzZWkJf+ZXoWUr7HpB6xoc8EQ6fEU5bkNtI5kM3APMBh4C3jmZQSkQDIV5dl0NY7vrsHn95F9yJZUbO5ASisYEEXtfh9zZkDIG9MOdxFk50Wxx8QidjvELzieo09EXFUue4194RJitqxpwuXXabMCjL4acWbDhYW01xb4GGAHrYChnt6GWSMqA/wNygVeAV09aRAoAHQNe3tlZRbRXEO/1krLkKmq2dRGfaiHdu1SrGim7Qs3ye5qw2O3ojUYyx04gKTOT6rQELtzkZEfiVvytPvbt6cKrSwRzNMz7NhhtsOyXWi8utc67coYbahvJv6WU3wC+CwwAPxRC/OmkRjbCvbq9hZz+FSAEtpw0eroEfe1uCkpMGPa+DHG5kDcXTNZIh6oMssUnIHQ6Ji5YTFAncFhiSXY8jVsXZPuKBtrbXdrrZkuGefdA937Y8jg428HvjnT4inLMhjtpY1BK+YGU8ntSyv93soIa6RzeAC9taWZqZxWGYIiya29h3/o2hA5Gp+6Hzr1QdjnY1VK6p5MoezQGk5mUMaWkZudSk5rAJesDbE9dRrgzyJ5dbfS7whCbpf0IKL4Qtj0NbTuhrx7C4UhfgqIck2Oaa0uNITm51uzvYl9bJzafwB7ykzRlLnU7u0nPjSKu5UVtKd3RF2tdf5XTij0hEaHXM37+Iq1UYo4hpectnHovO1e1UF3fT9gSr712s74G9hRY/ktt1PtAa6TDV5RjMtTG9ucO+nseuOMkxzVi+YIh/rOpkbkD7xPUG4guzKal0oXXGWBUoQ9RvQyKL4D4XNXl9zRktloxRUWRPLqE9Jx8atPiuXZViL0pb2IdgPVbGqlrG4C4HG1N9/nfA0crrPsbuDrA54z0JSjKsA21ROKQUl47+HcN8P6JOLkQYrEQYp8QokoIcd9RtpsqhAgJIa4+Eec9nVW2DbB6fxfTO/cjpGTSjXdQuaEDo1lHse4NbSnd0stVI/tp7KNSybj5iwgKQXtMDNN2rcZpHKBlcy+VtT30ekJaMkkfD+Ou05ZJblir9eJSVVzKGWaoieQXQogxB93+n+M9sRBCD/wFuBAoBW4QQpQeYbsHGAFdjsNhyTMbGjD5+zH6dJhEiITMcpr39ZBTqMdU/TJkToKMiarL72nMaLZgttlJKh5NZv4oalMTmFURoMX2BmkBPc8sraGmxYFXZwVbCky9XZu5ecWvwdWuTaGiKGeQofbaqgXeFEI8KoTIkVKeiIUVpgFVUsoaKaUfeBa47DDbfR14ATjrhwF3DPh4c1cbVznexhllJrool7rtfYSCkpLUPQhXh5pX6wzxUamkfN55hJDUZKdw6ap1DJh6yGkP8sy6Wuq73YTs6WCOHZzYcQBW/k5bMtnriPQlKMqQDaexfQywFVghhPiDEOJ4uwxlAgfPqd00eN8Bg+ueXIE2CPKs9+KWJvrcAUqaqgGYfMmNVG1uxx6jI7vnSW3FvcLzwKQmFjjdGYxGomJiSCwqIquwiPr4aJL6QoR9b5IWMrB9axfrKztp7vNq7V1JxTDlC1C3Eva/q03GGQ5F+jIUZUiGnEiklH4p5Z+BErQv/fVCiP8VQkQf47kP11J86BDfPwDflVJ+5idKCHGnEGKTEGJTZ2fnMYYUOU5vgBe3NDNZthGURoReEhc/ms4GJ6MyW9G1b4dx12qjo5Uzgi0uAWEwMG7hhYTCYapKC7h4zQYGTO3MC8Bvl1ZS1+Wiy6eD6Azt9U0bB2v+pLWV9DdF+hIUZUiG3f1XSumVUv4GKAe8wBYhxLeP4dxNQPZBt7OAlkO2mQI8K4SoA64G/iqEuPwIcT0spZwipZySnHzmja9YUdlFVaeTS5vfpNsehb0oh7otWg1imftBiM+Dsqu1nj7KGUFvMGCLjSMhv4Cc0aU0GnWEjAbSW94mIWAm0xnm12/vobnXg9sU/3EvLgYndnR3gacv0pehKJ9p2IlECJEnhFiM1gU4B22k+y+P4dwbgSIhRL4QwgRczyFTr0gp86WUeVLKPOC/wFeklC8fw7lOa4FQmGc3NhCrl6TWNxDW6Zgw5yJqtnWSGttNnG8XzPwaRKeqLr9nGGtcnDYH1wUXEwqHqZkylqm7NuLRtbIgFGJ3ywBPb2igocdNMDoL4rJh5tehdRvs/K9WxRUKRvoyFOWohpxIhBA7hBA9wMvArUAc8AFwC8cwrbyUMgh8Da031h7gOSnlbiHEXUKIu4Z7vDPZ3lYHa6q6+FxwL91WG1IPsZZ8BvpClOr+q03OmDVVNbKfgXQ6Pfb4BGLTM8krG0eTy4k7I4Wy/W9h9dpYHBXkuY2NrK/podERhNhsGH2h9ppv+Ad0VUK/WrtEOb0Npw/pFUCNlCduqlIp5ZvAm4fcd9iGdSnlrSfqvKcTKSVPrte+KCbseYcdsTbspfnU7ehHL4IUmj+EmX/T5mfSGyMcrXIsomJicfX3Me6Ci6nfvYP6iWWMeWMZVXnnU9gXTXqSnt++u4/cBCs2UwwptiRtYsfnb4Nlv4DLH9JGwlsTIn0pinJYw2lsrz6RSUTRdDh8vLmzlYUJkkC3AykEU6YuoGGvmwLzh5gnXALx+RCdHulQlWMkhMCekEhMUgr54yfR0NqEa9pExu15nShvLBeb2/EFw/z6nX209HkZMKeCPQ3mfQe6q2HzY1rDeygQ6UtRlMM6prm2lBPn+c2NDHiDXNuympb4aIJ2HfqBBPwBPcWxm2HiTRCTATr1Up3JtAkdTZQvuhApJU05GSR4azF76jE2RnPVKEFFq4Mn1tXT2OsjEJMNeXNg9EWw/RmtzUQtz6ucptS3UwR5/EFe2NJMfoKFqC0r6LNZiC8voHFHJ1ZdD1nz5mi/TFVPrbOCPSGR6IQkCidNo766kuClFzGm8jVs/jiMnXs5Z5SdF7Y0sba6mwanQNpTtU4W9lRY9itt3RJXV6QvQ1E+RSWSCFq6t4PaLhe3WTrpEjokkpmFk2juiGVU/G4MJRdoU44rZwWz1YbREsXYc88HoEkXJi41TLSjGnt9DrNiG8lLiuL371dS1+miLRyrtY3N/542M/C6v2rTpwR9Eb4SRfkklUgiJBSWPL2+gWiLgUlb36UpwY4n1YB/TwthDIyaW6oNPjSYIx2qcgJFJyRij09g1NQZVO3eQdQN11NY/ybWYBx7aqq4dbKFUFjy63f20drvo9+SARkTYPz1sPd1qFutqriU045KJBGyu6WfdTXdXFYQTc+eHfiMRrKLUqlpjCfB2kXahDKtSkM5qxgtFsxWG2ULFhGXlo4+PpbEWUXE9e4jt34Cbe0r+eI5GexrH+CxD+toGgjhs6XDlNsgoRBW/p/W8O4866eeU84gKpFEyBNr6wG4tmMzLdE2gvowC3xddASKKBifgIjPVoMPz1L2hERssXFc/YOfkzV5GmnXXEte3xpM4Rhqq3rIMzexpDyNV7e3sHp/F43eKMJRyXDu/2jrlaz6DThaIOCN9KUoCqASSUS0Ozy8uauVWYVJ6D94k5Y4G54sSUtrGkKEGTM7B8zHOoWZcrozmExERccghMCQmEhUUgLpVy8koaeCsY1zWNHwBpdOsFCUYudPS/dT0+miRSRB0miY+gWtemvfm1oVl+qRr5wGVCKJgP9sbMLlC3FLkpvm3m6kTseE6Fb2+RaSnm0kNj8/0iEqJ5ktPgEx2KXbmJFByvSp5Fpq0Qk74Qoz7e3r+fp5WSDggbf30j4QoteUDuXXaIthffhn6KkCZ3uEr0RRVCI55XyBEM9vbqIw2UbBmjdoSozGGRVgnMuOKxhP0dRUNYJ9BNAbDERFxwCgs1gwpySRd+MlJPbupqTjXF5qeAWzbOGrC/Ko7nTxz9U1NHsMeKOSYf7gYqLL74f+ZvC7I3gliqISySn3zu52GnvcXDsule6Vy+m1RWFN6aVKdw1Gk6BoTmGkQ1ROEZ1ef+D/hpQU4nLTKRgVQuqtjNtczObGN8lLc3LZhHTe2tXGin2dNATiCMXlw6yvQ+t22PmcquJSIk4lklMoHJY8tb6euCgj57Vvos1iQiK52tRBrWMsuWXxmKNUaWQkEjod5qwMCi6eT5KrkjTvAt6rXUZb1ybOH69jTFo0Dy6rorrTTQspUHyhNvJ94yPQvksbZ6IoEaISySm0q7mfDbU9XDI+nZ6XnqIhMRpDjBNn0h0Eg4Ixs9Xgw5FMHx2NPTOB0XPSCOlMXL/5PB6qeQRnsJ7b58dh0AseeHsvbW5BtyEJ5n4bzHZY9kttunnVJViJEJVITqHH1tah1wmuSPfhq2vHZzQyN66XyoE52OJMZJeo2V1HOnNGOrmTR5GiayZsnE15rZ2Hd/4Bg6mHL81Po67bzcOramgNxuCxpmsTO/ZUw6Z/aaPe+5sjfQnKCKQSySnSOeDl7V1tzC1KovflB2mJj0aIEGmTr6GtOcyoySno9OrlGOmE0Yg9L52xC0cR1hlYuO8q+j19PLPvz2SmOLl8YgrvVbTzfkU79eFkgjlzYMzFsP1ZaNkKrg7orVdtJsoppb65TpGn1jfg9oe4cmIchmWbaE6wUZTopcqzCICSWRkRjlA5XRiTEskYk8qY1F56Y0r5xubr2euo5N2mpzmnLExZRjR/XVFNVZePZpkEM74KsZnw9vegaRN4eqCnBsLhSF+KMkKoRHIK+AMhnt/UxOjUaJybHyJAFGGhJ2/q+ezb5iVrTDyJmcNeZFI5i9kLMxmzsJg0XzWO0GRuar+C1a0r2dr7PjfNtmA16rXxJf4ouvTJcMkfISYT3r4Pqj8An0Or8gqHIn0pygigEskp8OauVpr7PCyZEIP/zfdpSIzGbpb0iIUEfGEmL86NdIjKaUYfFUVsbgoTLyzA7m4lvmoGswIzebnmP7QFd3DrvDiaej38dXkVLeFE3JZUuOQPkFIKS38Gu18CvxO69qsFsZSTTiWSk0xKyZPrGkiwmvB6nmdMVZheWxS55RPZt8VD5uh4MovVeiPKp9ly0ogtzGBSVgeEgkzbdgn55PJM5UNYYxu4bFI8yys7eXdvF/WhZALGGLjo/yB3Fqz5o9YAH3BryURNPa+cRCqRnGTbm/rZVN/LorEW+t5+jc6YaG0yRts5BHwhplyYi9CpyRmVTxM6HXGjs0m+cAHlnW/hDURx1Z7bsUgzT+37M5OLnIzNtPH3ldVU9oRo1GUgjVZY9FNtnMmWx2HNHz5OJmoEvHKSqERykj22phaDThCyvsjM7QGakqNJSs+godJEZnEcmaNVaUQ5Mr3dTnx+Mjm3Xsmo5ncY6IvljuYv4wwM8FztX7h6hg67Wc/9b++l06unzZQNRiuccy+MvwEqXoEPfgYBF3RXgW8g0peknIVUIjmJOhxe3t7dxvSiMLXb3yfRYcZlNBGVNJWAN8SUi/MRaqp45TOY0tOJL85i9JXTSenairMujTuct1E3UMMHHU/wubk22h1e/vRBFZ1uQb8tD4xRMP1LMOPLULNca4T3DUB3NXj6InxFytlGJZKT6Ml19XgDYSwx/2Xu9hDNidHo9Hp623PJHB1PliqNKEMgDAbMmWkkTBjNhOnR2Fyt6LYVclX4UrZ2raMx/A6XTIpmTVUXb+5spckRxBdXAEYbjLtOW6q3ZRu8fjd4eqG3DlzdEb4q5WyiEslJEgiG+c+mRgozHOzo28Q5FWFaEmOJSSkhGDAw9eK8SIeonEEM8fFYUuJJnD+TSRltEAqTt34ys/RTeL/pZZLSdlCeZeGfq2vZ2zpAY5+fcEIhmGOg+AK44BfaQMVXvw4DLdDfAANqCnrlxFCJ5CR5bUcL7Q4fiQnPMmNvmD6znQDg844mc3Sc6qmlDJsxMxN7cjRpl59PuW4rLhnDgg3nMcqQy0u1jzJ/QgexUdr4kk6HnxaHDxIKICoecmbCxb/RSiSvfF0bsDjQoi3bqyjHSSWSk+SJtfUkxDWxJ1TDdVtDNKcmYDDbCctspl2sFq5Shk8IgTEnh5gUG/k3XkShaxPd/nQ+V3ElsTo7Lzb8hatm+el2+vjD0kp6nH563QGIzwNbMqSVw6V/0g726v+Dtp3g6tSqutSUKspxiGgiEUIsFkLsE0JUCSHuO8zjNwkhdgz+fSiEGB+JOIdra0MvWxt7yUx5hqKeIPY2Ix1RJoShhKwxiWSo0ohyjIROhzkvj9h0O2Nvmkeys5K2rmy+2nYd/qCHFT1/4+JJBtbX9vDKthaa+zx4AyGIzYLodK2EctmfISoO3rgH6j/USilqShXlOEQskQgh9MBfgAuBUuAGIUTpIZvVAudIKccBPwMePrVRDp/TF+TvK2uIjd5Nnb6br2zV0RJvRwJCX8LUJXmRDlE5wwmDAUtBPnE5CUy+ZBRRvh569mRzl/daWt1NtJueojzHyGNr69jT4qChx004LCE6DWJzIDoDLv2zVlJ59wdQ+Y42pUp3FYSCkb485QwUyRLJNKBKSlkjpfQDzwKXHbyBlPJDKWXv4M11wGm9YEevy887u9r4YG8baan/paw7SNZ2Pc0ZqegMqWSXFpFZpEojyvHTmUxYC3JJLk5j6jQTYWHA+GEmN+gvoKJvKxn57xNn1XH/23vpcPho6vVoO9oStQQSlQBL/gAZE2D5r2DHfwbHmqgpVZThi2QiyQQaD7rdNHjfkXwBeOtIDwoh7hRCbBJCbOrs7DxBIQ5du8PLo2tq+e4LO8iNX0mLwcM9bxtxWMw4CKEzljLtEtU2opw4uqgobEV5pE8pZHxOHwOWDIrez+Mc0xQ+7HiL2ZN20+/x8/v3Kul1+2nodhMMhbVqrcRCMEfD4vuhYD6s+xus/zsEPNBVCQFvpC9POYNEMpEcbiTeYVv8hBAL0BLJd490MCnlw1LKKVLKKcnJyScoxM8mpaSm08lPXt3Nnz+ooiwjCpHwNjdtCmJvCNA0ZSKgI7NkOhmj4k5ZXMrIoLfbiSvOofC8sRRGNdFuKeGi5aWMMRWwsutJ5k9sZ3NDLy9sbqLfE2B/h5N+T0BLIomjtLEm5/4QSi+D7c/Ail9rU6p07we/K9KXp5whIplImoDsg25nAS2HbiSEGAf8E7hMSnlajaIKhsJsrOvhq09t4a1dbVw1KYtzs/9D0BHikpU6vGNLqe1uRW8uZ/bVYyMdrnKW0sfFET8qnfLLykmSbdTJ8dy5ZRqJulh2+f/B2HwnT6yvZ2dzP8GQpKHbTWOPm5AhCpKKtClVZt8Nk26ByrfgvR9rSaS7CryOSF+ecgaIZCLZCBQJIfKFECbgeuDVgzcQQuQALwKfk1JWRiDGI/IFQ7y6vYW7nthCbbeL7y4ew1dm23mpexXfeT2ETmdmZ3YqYCar9ALSC+MiHbJyFjOmJJNUlMa0y4uxhF3UdZXyrbpFhENB3LGPkhQT4Kev7eaVbc2EwpI+d4DK9gEcQd3HyWTKbTD7G1pPrje/A95+rTeXp/ezA1BGtIglEillEPga8A6wB3hOSrlbCHGXEOKuwc1+BCQCfxVCbBNCbIpQuJ/g9Ab489Iq7v3vDsxGHb+/dgKfm5nL62u/w+RtkNcI/ZddTGdLA4ao2cy+ZlykQ1ZGAHNmOimjU5i+KIWQwUJzzVi+3nod3b420ov+Q0Gqjn+uruWe57dR1eEkGJLUd7lpcgQIJYwCUzSUXQELfwgdFfDa3eDuGpxSpSvSl6ecxoQ8CwciTZkyRW7adHJyTofDyw9e3sW7Fe1Mzo3nJ5eUUpIeQ0/rJm5//lZ++Ygkqmwc78ea8LoM5E36KlfcM+WkxKIoh5JSMrC3hoYNdWxY1o3XFIc/v4JHMh5hRuJCcg3X8sIGrZ1kybgMbpqeg9VkwGgQZMaaifY0ayWRpk1a1+CoeG2Nk9gssKdBTHqkL1E5SYQQm6WUx/RlpUa2D8POpj4+98gG3q1o57qp2fzlxkmUZ8Vh0Ake/uAebntTYjCYaJgzDXd/LwbLAmZcMSrSYSsjiBCC6OI8MiZkMXeukfj+Koz147i+5its6FyGW7ea+y6L49ySBF7b3sJXn97CuppuAkFJXbeXZpFG2JIAWVO07sF+lzY/V1clONugr/EzY1BGHpVIhkBKyevbW/jcIxto6HHzoyWl/PiSUtJiLQDU7X4O54ZuShsh6otfZOe6VRgsY8geW056QVxkg1dGHKHXE19aQPKUMUyfaSGn8T3i2kdz7Z57WNrwMg1du1gyWXDvklRsJj2/eHMPv3izgi6njx5XgP3+BFymREgZA5c9CHqTVs3VslWr6uqpVaPglU9QieQzBENhfvdeJd/4zzZsZgMPf34yt8zKw2oyaBuEQjz51i+4frlEN6GELf0dSCnQm+cy/bKCyAavjFjCaCSmpJDkc2dQNiWO0orHiO9P4+qd3+bNff/lneoXSLS7+ObFdq6bmsyWhj6+8tQWXt3egscfosYbSxuJhGNytGRiT4E374XaleDtg849al0T5QCVSI6i3+Pny09t4c8fVDE5N56nvziduUXJ6A9aGrdixS8oeyeAMOjg9juo274FY9R0skpySC+IjWD0ykinM5mwFeWTevUScsqTmLzlt8T6zVy56xu0VLXy590/YnfXJmaOCfODy5IZnWbjH6tq+PZ/t1PV4aQzHEt1MBGPKREu+RMkF8P7P4E9r0HID7212kJZavDiiKcSyRHsbx/gqr+t5b2Kdj4/M5fHbp1KbqLtkxu5e1n1n2cY0wTx3/g6q994CZM1HgyTmHGpGsWuRJ4uKgpLfi5pd95CYmEyU9f8LzFGH+dX3s6kuvN4tvYhnqr8EyF9G7fNN/HlBel0Dfi45/ltPLK6ht6wnZpQKp2hKMIX/haypsGq38K6h7Q14H0O6NwL/c2qumsEU4nkMN7b3cZVf/uQlj4PD1w1jp9cUobVbPjkRl4HGx+/gxlroLM0kda4RPraWjGYzyFrTDJpatyIcprQ2+1YcnNJv+du7OmJTF76I1KopbhxNrdXfZ+m3nr+vOtHLG97jVGZbn5weSLnliTy8rYWvvL0FtY1+2k3ZNPg0uE596cw5mLY8Sw8eyPselErnbg6tC7D7p5IX64SAar770GklPxx6X7+tHQ/mXFRPHjTJMZnxX1yo3AYuqsIr/wdSx9cTlyvIPfZ53j2V/+LNSYLr38JV987WSUS5bQT7OrCW7mfrsf+jXvlcpoKF7M/ewlGW5AtY19mjW41KVGpXJRzI6NiymjtMfH0h7009HiYWZDIl2ZlkilbiDdDoqsKseFhaN2mzSY89QtQuACEDkx2rbuwMSrSl6wMw/F0/1WJZJDbF+Qbz27jvT3tzC1K4o/XTyTBZvrkRn4X7HgOVvyaddvcxG60UvflRUhdDns/XIkt6TZSC/K4/JsTT+DVKMqJE2hrI9jVjatiL93/fIQuh5Fd5XciTSZ042t5zvYs7cFOJiRN4/zMa4g2JLK2UsdLmzvQ6wSfn57F5dkubPogKXYzlvZNsP5h6KmGxCKY/iWt6zACrIkQkwE6faQvWxkClUgOMdxEUtfl4o7HN1Hd6eRL5xRy7wXF6HQH1fpJCW274P0fQ/VSXOEsql8Is6fYwqz7n+S5H99HevFcejumcOV3JqnpUJTTWqC9g1B3F0F/gO433qf79XfYUfg5XLZ0Mka52Fawgtfcy9ELPYuyL2NK4gLcXivPr3OyvclBUYqNu6fHMNruJt5qJCHKgKh+HzY9CgNtkDkJpt0JyWNAZ9BKLLbESF+28hlUIjnEcBLJB3vb+caz25AS/u+acVw49pCRu343fPhn+PBPEPQhx93I5oe2EmrvovefP6Hz+Q9xdHZgir6d5NwkVRpRzgjS7yfQ0UGwtw9nez/dzz7Hzt5cOpMnkGJtI/5CH/8eeIutA3vItGezJOcmcmxF7G008dS6Dga8AS4bl8YtY80k6AZIjTZhFkGtR9eWf2uj4wsWaFVesVnaLMOxmWCyfXZwSkSoke3HQErJn5fu547HN5FkN/PyV2d9OonUrYFHL4Dlv9TWb7jxP7TV52Gr6+LtK7PJdCTQUVtNdMpC/F49M9S4EeUMIUwmTFlZWAoLiC3IIO1LdzBtSR4FvR/S4U7D+PAO7vXO5570m/H6nfy94n5ea3yM7PQufnRFMueOSeal7W188dU23u9OotZjo8enQ5ZdBdc/DZM+Dw1r4blbYPXvob9BGx3f16BWYTwLjcgSidsf5O5nt/FuRTvnlaTyx+snYDu4V5anH5b+FLY8/vEU29PuxNvQSvWVV7B+lKT4939jxy8eJhi0oTNfx5xriphwXs7JvzhFOQlC/f24G1vp73DT9+EmjK8+QnhgADF/Fq7L5vFicCNv9KzCYrBwUe41jIubTWevlX+v6aKx18PswkS+OCeXXIuLDIMTs16Cuxu2PKGVUvRGGHctjLsOzDHa+vG2JBCHW5ZIiQRVtXWIoyWSui4XX3h8I7VdLr65qJivLRiFOPjNXPEqvP09cDRB8WI4/+eQVIQMBKi66kp6mqp56n+mcUnPTHa8/xrmmBtZdMe5jJ6edoquTlFODikl/vZOvK2d6P0u+p57joG33kJYrcgrF9MwPZtH+96iwllFfkwhl+TeTKq5gA/3wgtb2jDqdXx+Zh4XliaTaXaRRD+Eg9DfBBsfgZplYImFiZ+D0kvBHKtVe5ntkb50BZVIPuVIiWTZ3na+/sw2dAL+fMNEzhmd8vGDjjZ441uw7w3tzX3+z6HkMhhsdO988EG6HvwLv71Cz62XPMj6P/4Og6WUy7/zbXLHJp2qS1OUk04GgwQ7Ogj29uKvraP70UfxVVSgy88lcMPFrEnt44nut3EEBpifdR5zUy8h6EvimbX97GjqZ3RqNF9dMIqyDDtZJhdmbzeEA9C5Dzb8HZq3QHQaTLkdRp032LsrUyu1KBGjEskhDk0kUkoeXFbF796tpCjVziO3TCU7wfrRg7DhYfjg59oSo1O+oK3HYI4+sL93715qr76atcVQdfO1pL7cRdDfxJXf/wP541R1lnJ2Cnu9BNvaCA44ca1ZQ++//02opwfd3Ok4LpvLf+RG3u35kBhTDJcVXE+xfSo76gXPbejB5QtxxcRMbpiWQ16ilSSdE5zt2uDFpk3a+vDd+7W2x6l3Qs4MrbrLnqKquyJEJZJDHJxInL4g3/qP1h6yZFw6/3f1eKJMg/3a2yvg1a9B82bImKhNm50x4RPHkn4/1VddRX9bA7+8rogF+y/E1/cSU5bcyDmfu/HUXpiiREDI6dQSSm8fff/9L47XX0eYTXDZ+VRNSeefzrep9jZRHFvEhOQ5pBnL+GCngbX7vSRHG/nyOaOYPzqFzDgL5oBDSygBN1Qv06q8BlogfYI2BiVjolY6scRE+rJHHJVIDvFRIqnudPLFf2+ivsvNfReO4Y65+Vp7SMALy38Fax/URt8u+IHW7133yU5szQPNbPj5txjzyg4eXjKR/L7zCLreIjoxltv/8Df0BlUUV0YGKSWh3l6CHR346hvoeeQRvDt2gNmEnFDGlnFW/pWyl45wPwJBjr2QZEM5u/YV0dmTwNR8G7fPyWF8ZhqxUSasoQGEs12bq2vv61qXYU8v5M+DqXdAWjnEZIHB9NnBKSeESiSHmDJlirz/329w93+2YdQL/nLTJGYVDrZjVK+A1/+ftnxoyaVw8W+14vQgKSXrWtfxRMUTNG9Zxc8fC7J16gX0ihSCng+JTU3nyvt+QkJGZmQuTlEiSIZCBLu6CHR24tuzF+fKlbg+/BDpciFj7DimjGL9WAvvxTVRH2gDIEqk4ugqQbhLWVQ8min5CRQnJ5BmTyBW58Ue6MLo6Yadz8GO/0DQp83nNfk2SCkFe+qnfuQpJ55KJIfILh4r9Vc+QFlGDA9/fgqZcVHg6oa379PerLHZsOT3ULTowD7ugJuXq17mmb3PUOeoI05n59ePSbqj57Hf7iEcqKVwykwu/vo9GC2WCF6dokSeNqCxk/CAg7DXh3vLFgZWLMe7ZSsEg8j0FJzTxrChzMxycwOV3lokYcLBaIIDJRh9pRTGljI2PZ4J2YmMT7KQIB3Y3C1E7Xoa9rwKQg/l18CEG7Rlfs12re3SaFXtKCeBSiSHMKcXya/+4Xl+eWU5FoMOtj0F7/wP+J0w46uw4HsHJpSrd9TzZMWTvFbzGq6Ai1Fxo7h+1DXMfqWOD9d102RrQ8oB5t10K1OWXPHJrsKKMsJJKQk7nYT6HYQHHAT7HbjXrsW5cgW+PXu1jYrzGZhSyupRBtaIBqr9lYTwQdhEwFlMcKCUqGAJo1OTGJ9mZXoyTDA2El/xJMbaD7TeXMklWnVXWjmkjdPWjjdFa8lFTQ55QqhEcoj8MeWyZs8ORHcVvPb/oP5DyJyirfSWUkJYhlndvJonKp5gXes69ELPgqz53GI+h7Tle+h7823WpU2m21CD0WLjqvt+QGZJaaQvS1FOa1JKwi4XYYeD0MAA/uYWXKtW4Vq5kkBzMxgMyHGlOCaVsq3YwqZwNbucFbhC/SB14MvH21dC0FmKXZ/E2GQ9i6PrWBhcQ6prL4ae/QgZAgQk5EPqWC2xZEzSen9ZYrWZh1W7yjFRieQQUyZPlpt+ey2s+g0YLLDof2HSLfQHBg5UXzU7m0m0JHJT4mLO32sm+OZ7+Gtq8ZutrC2fjStQQ2zqKG742U+wxcZF+pIU5YwTdrkIObRSiq+yEteKFTjXrCHc14ewWdFPm4R3+jh251nY5N3Htv6dtHtbADCHM/A7SnD2lhL2ZhBjFkxKCrDYXsdM434y3HsxdFYgAm7tZLbkj0ssGZMhfTxExWqlFr3hKFEqH1GJ5BBTcmxy0+0GKLsSFt/PvkAfz+x9hjdq3sAb8jI1eiy3dY4ha3UV3k2bQUos5eUEz13EW+vWE/C2kT95MZd/+8vo1BTYinLcwm43oYEBgj09eDZvwblyJe7165E+H/rkZPQlRYQyU+nIiGJtkoO1of1UuWqQSCwiDkMwG5czGbczmbAvBatIZmyikQtim5lnriLXU4mhYxe4u7QTGm2QVqaVWrKmais72lO0EotquD8slUgOMSXbKte+/xLLzIKn9jzFlo4tWISR29yTWLBLIFZtRPp8GLOyiL7kUvTnXMiu3dVsef0fSCmZfuWXmHPt+ZG+DEU5K4W9XkL9DoLtbThXr8G1Zg2+6mrCfX0HthGJ8QQyk2lMNbAzycOOJBe7bb2ExOD3lRQQiifo1RKLIZRCri2VhbF6LrI0UeivwthRgeitHTygXltzPm2cllhyZ0NcjjYbsWr3BFQi+ZTc0hw56qdFdLjamepI4ub6bDLXVhPu6UXExKBbdCWu0nPo9Npp2teDo30FIe969MYUFn/1XsbMHBPpS1CUESHs8xF2OAh7vQTa2/FVVmpVzHV1+OvrtbaVj9aCN5vwZSbRm2GnOd3MvpQQm2MGaKaTMB/PKBwORCMCqcQZUii2xXFelJ85wU4yuqrRd+5HhAPahrHZ/P/27jVGqvqM4/j3N7MzO7M7u1IuCyuCK0pssaYVK1DbqphalcTyok3EF9qaJkajpq02jRpTrbXaF40JxhfUVBNNjKYX2xCjNb3Qal94C1FQKLgiAQqCXBd2Z+fM5emLc9BhXNhhh53Zs30+yQnnzP8/Z/4PT3afPZf5H3qPFpavw8zzIN3Rgv+FicELSY2uuVl75NrLWPzOMG3bPmKo63TyFy1j4PQvsftgmqGB/VRKe0i27UO2nfzANs5ZdClX33Y76Xa/tde5VrJikUohwIoB5YHDBO+/z/DmTRT6PwgLzNat2FB0bURCM2dQmNPDx2fkWDe3gzVTA3bnd5K3jyARfLLfhHUwtW0G81NZzisHLBjcx5wD2+gMBslYhXS6m/YZ59LWORM6pqKOaSjXgzp7UK4nvAW5a+Yx0ydNJrEtJJKuAlYCSeC3ZvarmnZF7cuAIeD7ZrZ2tP0u6Oy2lYtXMHDmV9iX6WJ4eB+V8h7EXqz8MeVS/ugHMGVWLxdd8x3Ov/xbfmuvcxOcBQHlQoHitu0Mb9hAYfNmCv39BFu2UNq9m9zSpcx6bCVBJaBQKvDG9i38o38D6/dsYefgfwkSH5FIf0yibfC4n9FmRrZiZKxC1oxMxciYkTUjW6mQJkEm0UZ7Ik2mLUN7KksmlaO9vZv29m4y2WlkO2bQkZtFR9cscp0z6Up3k0vnyKVyJCfodddYFhJJSWAzcAWwA3gTuM7MNlT1WQbcTlhIFgMrzWzxaPueM63XfnzlMqyyF6wMQLItxfQz+5jZdzYz+ubR0zePGXP7/MuFzk0CZkbpwAEoFEj19h6339a9A6zdvp8dA7vZdvhD9g8fYDDIM1QcJl8Kl6BcoFgpIBskaUOkEnmSiQKJRAAKIFGirDLlRIVARvEkr91nTGSVJJtIkVGKbCJNR7KdbLKdjmSGjrYsnakOOto66Ux3kkt30dV+Grn2LnKZ0zh7yny6slMh2Q5t7XCKClMjhaSV98UtAvrNbAuApOeA5cCGqj7LgactrHavSZoiqdfMdp1ox1KB3nN66J1/MTPPOpuevnl8rnc2ieTE/EvAOdcYSaSmTh21X9/0bvqmdwN9hH+bnli5YhwplBjIFzmULzIwXOTgYMCBfIFD+SKHhooczBc4OHSEfP4AVtiDgj0kSwdJVg7SZgNkkkdIa4hkMk8yMQyJAEvkKSXKDEkMJRIMJsRehf/mo38rxzlD8sSu3SwaLnyyXbQkRdoIlCIgXIrREihaVwojCQLQsTcYSEQNY9bKQjIb2F61vYPPZnakPrOBzxQSSTcBNwHMnTuX6x54+JQO1jn3/yeZEKdlU5yWTTFnDO8vlStRISoxMBwVo3yRw4USVEpYsYDKAaoUUClaLxegXKBSHiQoDVIqHyEoDxFU8pQqg+zs7ebvFaFyQLISLonKp+vhUiRpAalKQKYSkLQisgJggCEzwnNRRngjXGNnplpZSEYqgbXR1NMnfNHsceBxCCdtbGxozjnXuLZkgikdaaZ0xODb9veO/aikld/M2QHHFPkzgJ1j6OOcc66FWllI3gTmSzpLUhpYAayu6bMauEGhJcCh0a6POOeca66Wndoys5Kk24CXCW//fdLM3pN0c9S+CniR8I6tfsLbf29s1Xidc86NrKWzmZnZi4TFovq1VVXrBtza7HE555yrn89e5pxzriFeSJxzzjXEC4lzzrmGeCFxzjnXkEk5+6+kw8CmVo9jnEwH9rZ6EOPI44s3jy++zjWzMU1tPFmfQblprJOPTXSS3pqssYHHF3ceX3xJemus7/VTW8455xrihcQ551xDJmshebzVAxhHkzk28PjizuOLrzHHNikvtjvnnGueyXpE4pxzrkm8kDjnnGtIbAuJpKskbZLUL+muEdol6dGofZ2kha0Y51jVEd9lkg5JejtaftaKcY6FpCcl7ZH07nHa45670eKLc+7mSFojaaOk9yT9cIQ+sc1fnfHFOX8ZSW9IeieK7+cj9Dn5/JlZ7BbCaec/AOYBaeAdYEFNn2XAS4RPWVwCvN7qcZ/i+C4DXmj1WMcY3yXAQuDd47THNnd1xhfn3PUCC6P1LmDzJPvZqye+OOdPQC5aTwGvA0sazV9cj0gWAf1mtsXMAuA5YHlNn+XA0xZ6DZgiqbfZAx2jeuKLLTN7Bdh/gi5xzl098cWWme0ys7XR+mFgIzC7plts81dnfLEV5eRItJmKlto7rk46f3EtJLOB7VXbO/hssuvpM1HVO/avRoeoL0k6rzlDa4o4565esc+dpD7gAsK/aqtNivydID6Icf4kJSW9DewB/mpmDecvrlOkjPSU+tqqWk+fiaqesa8FzjSzI5KWAX8G5o/3wJokzrmrR+xzJykH/BH4kZkN1DaP8JZY5W+U+GKdPzMrA1+WNAX4k6Qvmln19byTzl9cj0h2AHOqts8Ado6hz0Q16tjNbODoIaqFT5pMSZrevCGOqzjnblRxz52kFOEv2WfM7PkRusQ6f6PFF/f8HWVmB4F/AlfVNJ10/uJaSN4E5ks6S1IaWAGsrumzGrghugNhCXDIzHY1e6BjNGp8kmZJUrS+iDCX+5o+0vER59yNKs65i8b9BLDRzB45TrfY5q+e+GKevxnRkQiSssA3gf/UdDvp/MXy1JaZlSTdBrxMeIfTk2b2nqSbo/ZVhM+CXwb0A0PAja0a78mqM77vArdIKgF5YIVFt1xMdJKeJbzzZbqkHcB9hBf9Yp87qCu+2OYO+BpwPbA+Os8OcA8wFyZF/uqJL8756wWekpQkLIC/M7MXGv3d6VOkOOeca0hcT20555ybILyQOOeca4gXEueccw3xQuKcc64hXkicc841xAuJc865hnghcW6CkTRP0hOS/lDz+vckXVS1faWk65s/QueO5YXEuSaS9BtJl0paX/N6u6QPJS2IZn3+wQhvvxBYJ+kxSQ8BPyWcBcG5lvJC4lwTRN8kBlgM/BuYI6n65+8m4F9mtuE4708BJeBm4CkzuwdoB2ZLulBSt6Q7xi8C547PC4lzNRQ+Ie+KaP1BSY+OcT+/l/SIpDXA3ZK+AGyOZl/dBvRF/bLAncD9J9jdJcCrhNOar5fUBewFPg8sBR4ifHaGc00Xy7m2nBtn9wEPSOoh/MX97epGSa8SPj2v1k/M7G9V2+cTTv63NHrfHcBforaNhEVgC3ArsNrMtkb9pgG/BC6QdLeZPQxcATwIZIBVhHMgbQYyZvZrSbcAIz7a17nx5oXEuRpm9ko0u+sdwGXREUR1+zdG24ekDDAVeKDq5Sv5dAK8jcC5kl4hLCRLqva/j/AUVrVcNHX5s9Fy9HPujlZ7zGw7zrWAT9roXA1J5xM+j2KvmV08QvuoRySSLgTuN7Nrou0OYI2ZLY62rwUuJzzFlTWze8clGOeawI9InKui8NnUzxA+t/pRSVea2cvVfeo5IiE8rbWuanspsKZqeyNwF+HzIBY2NGjnWswvtjsXiY4angfuNLONwC848QXwE6ktJFfz6fURgE1Rn8fN7NAYP8O5CcFPbTnXBJLWAovNrNjqsTh3qnkhcc451xA/teWcc64hXkicc841xAuJc865hnghcc451xAvJM455xrihcQ551xDvJA455xriBcS55xzDfFC4pxzriH/AxjaGL1BdOlAAAAAAElFTkSuQmCC\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "models = ['U','W','S','B']\n", "sizes = [2**k for k in range(7,13)]\n", "num_vertices = (np.array(sizes)+4)/2\n", "equilibration_sweeps = 500\n", "measurement_sweeps = 2\n", "measurements = 200\n", "\n", "max_distance = 15\n", "\n", "for model in models:\n", " d_H = d_H_list[model]\n", " \n", " # Code mostly copied from lecture 8.\n", " mean_profiles = []\n", " for size in sizes:\n", " #adj = generate_random_triangulation(size, model)\n", " #perform_sweeps(adj,equilibration_sweeps)\n", " profiles = []\n", " for _ in range(measurements):\n", " #perform_sweeps(adj,measurement_sweeps)\n", " adj = generate_random_triangulation(size, model)\n", " profiles.append(vertex_distance_profile(adj,max_distance))\n", " mean_profiles.append([batch_estimate(data,np.mean,20) for data in np.transpose(profiles)])\n", "\n", " #for profile in mean_profiles:\n", " # plt.plot([y[0] for y in profile])\n", " #for profile in mean_profiles:\n", " # plt.fill_between(range(len(profile)),\n", " # [y[0]-y[1] for y in profile],[y[0]+y[1] for y in profile],alpha=0.2)\n", " #plt.legend(num_vertices, title=\"V\")\n", " #plt.xlabel(\"x\")\n", " #plt.ylabel(r\"$\\mathbb{E}[\\rho_T(r)]$\")\n", " #plt.title(\"Mean distance profile (errors shown as shaded regions)\")\n", " #plt.show()\n", "\n", " for i, profile in enumerate(mean_profiles):\n", " rvals = np.arange(len(profile))\n", " plt.plot(rvals/num_vertices[i]**(1/d_H),\n", " [y[0]*num_vertices[i]**(1/d_H - 1) for y in profile])\n", " for i, profile in enumerate(mean_profiles):\n", " plt.fill_between(np.arange(len(profile))/num_vertices[i]**(1/d_H),\n", " [(y[0]-y[1])*num_vertices[i]**(1/d_H - 1) for y in profile],\n", " [(y[0]+y[1])*num_vertices[i]**(1/d_H - 1) for y in profile],\n", " alpha=0.2)\n", " plt.legend(sizes, title=\"V\")\n", " plt.xlabel(r\"$x = r/V^{1/d_H}$\")\n", " plt.ylabel(r\"$V^{1/d_H}\\,\\mathbb{E}[\\frac{1}{V}\\rho_T(r)]$\")\n", " plt.xlim(0,3)\n", " plt.title(f\"Finite-size scaling with Hausdorff dimension $d_H = {d_H:.2f}$\")\n", " plt.show()\n", "\n" ] }, { "cell_type": "markdown", "id": "d8f25787", "metadata": { "deletable": false, "editable": false, "nbgrader": { "cell_type": "markdown", "checksum": "7f19410ed936f838773ee891b059d1a3", "grade": false, "grade_id": "cell-65ae9c46ece5b657", "locked": true, "schema_version": 3, "solution": false, "task": false } }, "source": [ "**(e) Bonus exercise:** Make more robust estimates of $d_H$ by optimizing the quality of the collapse. You could do this (for each model separately) by taking $\\hat{f}(r) = \\mathbb{E}[\\rho_T(r)] / V_0$, where the right-hand side is the mean distance profile for the largest system size with $V_0 = (2^{12} + 4)/2$ vertices. Then according to our assumption, for another size $V \\leq V_0$ we expect $\\mathbb{E}[\\rho_T(r)] / V \\approx k \\hat{f}(kr)$, where $k \\geq 1$ is a scale factor that should be $k\\approx (V_0/V)^{1/d_H}$. Making sure to interpolate the function $\\hat{f}(r)$ (using [`scipy.interpolate.interp1d`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html#scipy.interpolate.interp1d)), this scale factor can be determined by fitting the curve $k \\hat{f}(kr)$ to the data $\\mathbb{E}[\\rho_T(r)] / V$. Then $d_H$ can be estimated by fitting $k$ versus $V$. **(20 bonus points, but note that maximum grade is 10)**" ] }, { "cell_type": "code", "execution_count": null, "id": "ed4424ce", "metadata": { "deletable": false, "nbgrader": { "cell_type": "code", "checksum": "199ffddc14c77d4174b92a61368cd5c9", "grade": true, "grade_id": "cell-e24b0602e4e8257d", "locked": false, "points": 20, "schema_version": 3, "solution": true, "task": false } }, "outputs": [], "source": [ "# YOUR CODE HERE\n", "raise NotImplementedError()" ] }, { "cell_type": "code", "execution_count": null, "id": "c9e50c10", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }