{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When dealing with vectors it is often very helpful to decouple the direction of the vector from its magnitude. This is a trick I was first taught in high school physics, and which I have never stopped finding extremely useful. In high school physics problems were mostly in 2D and so a direction was uniquely specified by just one rotation angle. As an undergraduate I was properly introduced to spherical polar coordinates, which let you express directions in 3D as a function of 2 angles. But it wasn't until close to the end of my graduate education in physics that one day I stumbled over the idea that polar coordinates in 2D, spherical polar in 3D can be thought of as special cases of a more general formalism that allows you to turn any binary tree with D leaves into expressions for the D components of a unit normal direction vector as a function of a set of standard angles. \n",
    "\n",
    "I recently saw the outline of this idea scribbled down in one of my notebooks and I was again struck by the beauty of it, and I would like to share.\n",
    "\n",
    "At the cost of getting a little ahead of myself here is the tree that corresponds to the usual spherical polar coordinate expansion.\n",
    "\n",
    "![teaser_image](../images/binary-trees-hsp-teaser.png)\n",
    "\n",
    "To read off the expression for each coordinate you simply run up the tree from the appropriate labeled node and collect terms and then remember to put the overall vector magnitude $r$ out front of each term. I think even just this diagram alone might possibly be worth a blog post since it is much easier to remember for me than the pile of trigonometric terms that it represents. I certainly would have liked to have seen something like this as a mnemonic for spherical polar as an undergrad (or for that matter as a grad student). \n",
    "\n",
    "<!-- TEASER_END -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we shall see this is just one example of a very general way of writing out vectors as a direction times a magnitude in spaces with any number of dimensions.\n",
    "\n",
    "A (hyper)spherical coordinate system is one where we express vectors as the product of a scalar magnitude multiplied into a direction vector of unit norm, lets call the vector magnitude $r$ and the direction vector $\\eta$. \n",
    "\n",
    "$\n",
    "x = r~\\eta\n",
    "$\n",
    "\n",
    "So all the work involved in coming up with a spherical coordinate system goes into finding a way to express every possible point on the unit sphere as a function of $D-1$ angles. \n",
    "In 2 dimensions the essnetially unique answer is of course,\n",
    "\n",
    "$\n",
    "\\eta_x = sin(\\theta) \\\\\n",
    "\\eta_y = cos(\\theta) \\\\\n",
    "$\n",
    "\n",
    "which is practically the definition of trigonometry. \n",
    "\n",
    "In three dimensions things get somewhat more complicated, you can express each of the three coordinates of the direction vector as a function of 2 angles like so,\n",
    "\n",
    "$\n",
    "\\eta_x = sin(\\theta)cos(\\phi) \\\\\n",
    "\\eta_y = sin(\\theta)sin(\\phi) \\\\\n",
    "\\eta_z = cos(\\theta) \\\\\n",
    "$\n",
    "\n",
    "which you can quickly verify does indeed correspond to the expression you get simply by accumulating terms starting from a leaf node and traversing towards the root of the tree we showed above.\n",
    "\n",
    "\n",
    "If you are much like me you will probably at some point start to wonder if there is a natural way to extend this form into higher dimensions, and of course, the answer is yes. A quick search for \"hyper spherical polar\" will probably lead you to <a href=https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates>this wikipeida article</a>. There you find a set of equations which can be used to express the components of a D-dimensional unit vector as a function of D-1 angles like so,\n",
    "\n",
    "$$\n",
    "\\eta_1 = cos(\\theta_1) \\\\\n",
    "\\eta_2 = sin(\\theta_1)cos(\\theta_2)\\\\\n",
    "\\eta_3 = sin(\\theta_1)sin(\\theta_2)cos(\\theta_3)\\\\\n",
    "\\vdots \\\\\n",
    "\\eta_{D-2} = sin(\\theta_1)...\\sin(\\theta_{D-2})cos(\\theta_{D-1}) \\\\\n",
    "\\eta_{D-1} = sin(\\theta_1)...sin(\\theta_{D-1}) \\\\\n",
    "$$\n",
    "\n",
    "In the case of D=3 we can see that this gives us the same set of expressions as the usual spherical polar coordinates, though the ordering of the coodinates is slightly odd (z, x, y) instead of (x, y, z) by the most common convention. This could be helpful if you are simply out to perform some arbitrary 4+ dimensional integral with spherical symmetry and don't care too much about getting some intuition for the situation. \n",
    "\n",
    "Where do these formulae come from? \n",
    "\n",
    "You can think of the above formula as the result of a clever way of iteratively dividing up our total vector magnitude budget a little bit at a time. We start with a full budget of squared magnitude equal to 1. We put all of this budget into a single coordinate vector $[1,]$ and then we reapportion the squared magnitude between the last component and a new component which we concatenate to the end of the vector. After one such split we have a 2D coordinate system and after 2 splits we have the usual spherical polar coordinates (albeit in an unusual coordinate ordering) and after three splits we have a unit direction vector which yields a 4 dimensional \"hyper-spherical\" coordinate system.\n",
    "\n",
    "$$\n",
    "[1] \\rightarrow \\begin{bmatrix}cos(\\theta_1)\\\\sin(\\theta_1)\\end{bmatrix} \n",
    " \\rightarrow \\begin{bmatrix}cos(\\theta_1)\\\\sin(\\theta_1)cos(\\theta_2)\\\\ sin(\\theta_1)sin(\\theta_2)\\end{bmatrix}\n",
    " \\rightarrow \\begin{bmatrix}cos(\\theta_1)\\\\sin(\\theta_1)cos(\\theta_2)\\\\ sin(\\theta_1)sin(\\theta_2)cos(\\theta_3)\\\\ sin(\\theta_1)sin(\\theta_2)sin(\\theta_3)\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Because $sin(\\theta)^2 + cos(\\theta)^2=1$ splitting the last coordinate in two in this way preserves the total sum of the squares of our coordinates and so at every step of the way we are left with a unit vector. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binary Trees\n",
    "\n",
    "Any iterative splitting process can be naturally expressed as a <a href=https://en.wikipedia.org/wiki/Binary_tree>binary tree</a>. In this particular case there is a \"sine\" and a \"cosine\" child to each angle node and a coordinate associated to each non-leaf node. \n",
    "\n",
    "The leaves of the tree are the rectangular coordinates of the vector and the nodes higher up represent the splitting angles. We can transform from the angles to the corresponding rectangular coordinates by beginning with the value 1 at the root node and then tracing down to a leaf of the tree. Each time we traverse a sin edge we accumulate a factor of $sin(\\theta_{\\rm node})$ and each time we traverse a cosine edge we accumulate the corresponding cosine factor.\n",
    "\n",
    "We will use networkx to handle the graph structuing and do the drawing of the graph networks.\n",
    "Here is the code for drawing tree corresponding to the usual spherical polar coordinates in 3D, which we showed above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the expression for any of the coordinates in terms of the angles you simply traverse the tree starting from the leaf node to the root with a factor of the radius out front. $X=r~cos(\\phi)sin(\\theta)$, $Y=r~sin(\\phi)sin(\\theta)$, and $Z=r~cos(\\theta)$.\n",
    "\n",
    "I have to say that writing down spherical polar coordinates as a tree like this is rather beautiful to me. I think it looks much more friendly than the pile of equations which is normally presented to students when they are first introduced to spherical polar coordinates. Also it is much more parsimonious in terms of symbols. As a mnemonic for remembering spherical polar it seems a shame that you have to either alternate whether sine or cosine is the left or right leg of the tree, as we did above, or reorder the leaves of the tree to something other than the usual x,y,z ordering, but I still think it is easier to remember than the raw equations.\n",
    "\n",
    "But the higher dimensional coordinate equations above correspond to a really boring set of binary trees, they are maximally unbalanced trees where we always pick to expand the sin leg. Here is the tree for the four dimensional coordinate system shown above in equation form.\n",
    "\n",
    "![unbalanced 4D](../images/unbalanced_4d_polar_tree.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This has a kind of simplistic beauty. It is almost trivially easy to remember how to write out a unit vector in any number of dimensions as a function of D-1 standard angles. In fact it is so simple that for this particular spherical coordinate expansion you don't even really need the tree to remember how to write out all the terms. It is no doubt partially this mnemonic simplicity which has driven this peculiar choice for writing out higher dimensional spherical coordinates.\n",
    "\n",
    "In 2 and 3 dimensions there aren't a lot of different choices we can make with respect to our trees. In 2 dimensions we can only swap the x and y labels, and in 3 dimensions we can either split the sine or the cosine node which doesn't lead to a coordinate system which much different than the usual one.\n",
    "\n",
    "However once we reach 4 and more dimensions there are many other sorts of trees that we might in principle choose, and each of them gives us a completely valid coordinate system, with very different properties than the standard formulae above. In 4 dimensions instead of continuing to split the sine node we can choose to split the cosine node, which results in a perfectly balanced binary tree.\n",
    "\n",
    "![balanced binary tree](../images/balanced_4d_binary_tree.png)\n",
    "\n",
    "Does this configuration also correspond to a valid spherical coordinate system?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Inverse Transform\n",
    "\n",
    "Because of the properties of the sine and cosine functions if we always split the coordinates in pairs like this we are guaranteed to generate a vector which lies on the unit sphere in D dimensions. This is true regardless of which node we split or how we assign the children the sine or cosine factor. However, just because every set of angles maps to some point on the unit sphere does not mean that for any point on the unit sphere we can always find a corresponding set of angles that map to it. \n",
    "\n",
    "In the case of the regular spherical polar coordinate formulae it is not too difficult to work out an inverse formula which will map from any set of rectangular coordinates to a set of angles (plus a radius) as well as the forward map that we wrote above. \n",
    "\n",
    "In order to ensure that each and every possible binary tree we could draw also corresponds to a valid spherical coordinate system we need to show that this inverse function exists, regardless of the particular tree structure in question.\n",
    "\n",
    "\n",
    "Lets begin by considering how to determine the angles which are one layer above two leaf nodes. Since one leg is always a cosine and one leg a sine the angle will be equal to,\n",
    "\n",
    "$$\\theta = tan^{-1}(\\eta_{s}/\\eta_{c})$$\n",
    "\n",
    "where $\\eta_c$ is the coordinate value of the cosine leaf and $\\eta_s$ is the coordinate value of the sine leaf. \n",
    "\n",
    "But what about the angles which are a little higher up in the tree? Lets forget for a moment about getting the sign of the coordinates right and just focus on getting the magnitudes correct. We simply need to figure out the fraction of squared norm belonging to all the nodes below each leg of the angle node,\n",
    "\n",
    "$$\\theta_{node} = tan^{-1}(r_{s}/r_{c})$$\n",
    "\n",
    "Where $r_{c}$ is the sum of the squared magnitudes of all the coordinates down stream from the cosine child of that node and $r_{s}$ is the corresponding quantity for the sine node.\n",
    "\n",
    "We can find the appropriate inverse angles by first assigning the leaf nodes values equal to their coordinates $r_j=\\eta_j$. Then for parent nodes we can iteratively assign the values, $${\\large r_j^2=\\sum_{i \\in children(j)} r_i^2}$$\n",
    "\n",
    "until all non-leaf nodes have been assigned a value $r_i$. Then the angle associated to nodes at least one step above a leave node can be calculated simply as the arctangent of the ratios of $r$ values assigned to its children. But the \"radius\" value above is not well defined for leaf nodes which have no children. But if we simply let $r_i = \\eta_i$ for these nodes you can verify that this will result in a set of angles which will allow for correct replication of both the magnitude and sign of the child coordinates.\n",
    "\n",
    "So for example if you apply this strategy to the usual spherical polar coordinates, the inverse formulae that we arrive at are, $\\phi=tan^{-1}(y/x)$ and $\\theta = tan^{-1}(z/\\sqrt{x^2 + y^2})$ which may or may not be what you memorized in school but which is perfectly valid.\n",
    "\n",
    "For the balanced binary tree corresponding to a 4 dimensional coordinate system which we plotted above we can find the value of the root angle $\\theta_1$ as, $\\theta_1 = tan^{-1}\\left(\\sqrt{\\frac{\\eta_3^2 + \\eta_4^2}{\\eta_1^2 + \\eta_2^2}}\\right)$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An Implementation\n",
    "\n",
    "The mathematics above may seem less than convincing. I was not sure myself that this argument was airtight until I turned it into code. \n",
    "\n",
    "Lets make an implementation and have some fun. \n",
    "\n",
    "A set of instructions for a human for how to create a higher dimensional coordinate system they might read something like this.\n",
    "\n",
    "* Draw an arbitrary binary tree with D leaves\n",
    "* Label the non-leaf nodes as angles and the leaf nodes as coordinates\n",
    "* To transform from angles to rectangular coordinates start at each leaf and traverse the tree up to the root, collecting factors of $cos(\\theta)$ for left legs and $sin(\\theta)$ for right legs with the angle coming from the parent node of each leg.\n",
    "* To transform from a set of rectangular coordinates to a set of angles accumulate the sum of the squares of all leaves which are children of each angle node and label that node with it. The angle of each node is the arc tangent of the square root of the sum of the squares of the sin leg divided by the cosine leg for each node, with leaf nodes being allowed to retain their signs.\n",
    "\n",
    "Translating that process into code is mildly challenging since something like \"start at a leaf node and collect terms till you hit the root\" is more natural to explain to a human than it is to put into code but hopefully the below implementation is clear, (and hopefully correct too). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "import networkx as nx\n",
    "\n",
    "import asymptoticlabs as blog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class HyperPolarCoordinateSystem(object):\n",
    "    \n",
    "    def __init__(\n",
    "        self,\n",
    "        tree,\n",
    "        sort_nodes=False,\n",
    "        check_tree=True\n",
    "    ):\n",
    "        if check_tree:\n",
    "            assert nx.is_tree(tree)\n",
    "            assert len(tree) % 2 == 1\n",
    "        \n",
    "        self.tree = tree\n",
    "        angle_nodes = []\n",
    "        leaf_nodes = []\n",
    "        \n",
    "        #find the root node.\n",
    "        root = None\n",
    "        for node, in_degree in tree.in_degree():\n",
    "            if in_degree == 0:\n",
    "                root = node\n",
    "        if root is None:\n",
    "            raise ValueError(\"invalid tree\")\n",
    "        self.root = root\n",
    "        \n",
    "        to_parent = {}\n",
    "        to_children = {}\n",
    "        frontier = [root]\n",
    "        visited_nodes = set()\n",
    "        \n",
    "        while len(frontier) > 0:\n",
    "            cnode = frontier.pop()\n",
    "            visited_nodes.add(cnode)\n",
    "            children = tree[cnode]\n",
    "            if len(children) == 2:\n",
    "                angle_nodes.append(cnode)\n",
    "            elif len(children) == 0:\n",
    "                leaf_nodes.append(cnode)\n",
    "            else:\n",
    "                raise ValueError(\"invalid tree\")\n",
    "            for child in children:\n",
    "                frontier.append(child)\n",
    "                clist = to_children.get(cnode, [])\n",
    "                clist.append(child)\n",
    "                to_children[cnode] = sorted(clist)\n",
    "            predecessors = list(tree.predecessors(cnode))\n",
    "            if len(predecessors) > 0:\n",
    "                parent ,= predecessors\n",
    "                to_parent[cnode] = parent\n",
    "        \n",
    "        if sort_nodes:\n",
    "            angle_nodes = sorted(angle_nodes)\n",
    "            leaf_nodes = sorted(leaf_nodes)\n",
    "        self.angle_nodes = angle_nodes\n",
    "        self.leaf_nodes = leaf_nodes\n",
    "        self.to_parent = to_parent\n",
    "        self.to_children = to_children\n",
    "        #make note of which edges are the cosine and which the sine edges\n",
    "        self.edge_type = {}\n",
    "        for parent in to_children:\n",
    "            children = sorted(to_children[parent])\n",
    "            self.edge_type[(parent, children[0])] = \"sin\"\n",
    "            self.edge_type[(parent, children[1])] = \"cos\"\n",
    "        self.node_to_vec_index = {node:i for i,node in enumerate(leaf_nodes)}\n",
    "        self.node_to_theta_index = {node:i for i, node in enumerate(angle_nodes)}\n",
    "    \n",
    "    def r_theta_to_x(self, r, theta):\n",
    "        if len(theta.shape) >= 2:\n",
    "            theta = theta.transpose()\n",
    "        \n",
    "        n_theta = len(theta)\n",
    "        assert n_theta == len(self.angle_nodes)\n",
    "        x_out = np.zeros([theta.shape[0]+1] + list(theta.shape[1:]))\n",
    "        for coord_idx in range(n_theta+1):\n",
    "            current_coord_value = 1.0\n",
    "            cnode = self.leaf_nodes[coord_idx]\n",
    "            hit_root = False\n",
    "            while not hit_root:\n",
    "                #find the parent of the current node\n",
    "                parent = self.to_parent[cnode]\n",
    "                parent_angle = theta[self.node_to_theta_index[parent]]\n",
    "                edge_type = self.edge_type[(parent, cnode)]\n",
    "                if edge_type == \"cos\":\n",
    "                    factor = np.cos(parent_angle)\n",
    "                elif edge_type == \"sin\":\n",
    "                    factor = np.sin(parent_angle)\n",
    "                else:\n",
    "                    raise ValueError(\"this isn't supposed to happen... check the edge assignment logic\")\n",
    "                #accumulate the appropriate term for the edge\n",
    "                current_coord_value *= factor\n",
    "                #set the parent to the current node\n",
    "                cnode = parent\n",
    "                #check if we have hit the root node yet\n",
    "                hit_root = cnode == self.root\n",
    "            x_out[coord_idx] = current_coord_value\n",
    "        \n",
    "        #multiply in the radius vector\n",
    "        x_out *= r\n",
    "        \n",
    "        if len(theta.shape) >= 2:\n",
    "            x_out = x_out.transpose()\n",
    "        \n",
    "        return x_out\n",
    "\n",
    "    def x_to_r_theta(self, x):\n",
    "        x = np.asarray(x)\n",
    "        r = np.sqrt(np.sum(x**2, axis=-1))\n",
    "        n_theta = x.shape[-1]-1\n",
    "        \n",
    "        if len(x.shape) >= 2:\n",
    "            x = x.transpose()\n",
    "        \n",
    "        assert n_theta == len(self.angle_nodes)\n",
    "        theta_out = np.zeros([x.shape[0]-1] + list(x.shape[1:]))\n",
    "                \n",
    "        r_map = {}\n",
    "        for coord_idx in range(n_theta+1):\n",
    "            r_map[self.leaf_nodes[coord_idx]] = x[coord_idx]\n",
    "        \n",
    "        #starting at the leaves and working back to the root\n",
    "        #accumulate the sum of the squares of the leaf nodes into all parents\n",
    "        for coord_idx in range(n_theta+1):\n",
    "            cnode = self.leaf_nodes[coord_idx]\n",
    "            sq_add = x[coord_idx]**2\n",
    "            hit_root = False\n",
    "            while not hit_root:\n",
    "                parent = self.to_parent[cnode]\n",
    "                r_sq = r_map.get(parent, 0)**2\n",
    "                r_map[parent] = np.sqrt(r_sq + sq_add)\n",
    "                cnode = parent\n",
    "                hit_root = cnode == self.root\n",
    "        \n",
    "        #for each angle node calculate the arctangent\n",
    "        for angle_idx, angle_node in enumerate(self.angle_nodes):\n",
    "            c1, c2 = self.to_children[angle_node]\n",
    "            theta_out[angle_idx] = np.arctan2(r_map[c1], r_map[c2])\n",
    "        \n",
    "        if len(x.shape) >= 2:\n",
    "            theta_out = theta_out.transpose()\n",
    "        \n",
    "        return r, theta_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First lets make a helper function to generate trees of different sorts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_binary_tree(n_leaves, mode=\"balanced\"):\n",
    "    assert n_leaves >= 2\n",
    "    tree = nx.DiGraph()\n",
    "    tree.add_node(0)\n",
    "    split_nodes = set()\n",
    "    for i in range(n_leaves-1):\n",
    "        if mode == \"random\":\n",
    "            #pick a random leaf node to split\n",
    "            leafs = [node for node in tree if len(tree[node]) <= 1]\n",
    "            split_leaf = leafs[np.random.randint(len(leafs))]\n",
    "        elif mode == \"unbalanced\":\n",
    "            split_leaf = 2*i\n",
    "        elif mode == \"balanced\":\n",
    "            split_leaf = i\n",
    "        tree.add_edge(split_leaf, len(tree))\n",
    "        tree.add_edge(split_leaf, len(tree))\n",
    "    return tree\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before going any further lets verify that the transforms actually work by quickly verifying that the forward and inverse transforms compose together into the identity function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum round trip error 3.9968028886505635e-15\n"
     ]
    }
   ],
   "source": [
    "max_abs_diffs = []\n",
    "\n",
    "for i in range(100):\n",
    "    ndims = np.random.randint(2, 100)\n",
    "    rtree = make_binary_tree(ndims, mode=\"random\")\n",
    "    hpcs = HyperPolarCoordinateSystem(rtree)\n",
    "    random_xvecs = np.random.normal(size=(100, ndims,))\n",
    "    r, theta = hpcs.x_to_r_theta(random_xvecs)\n",
    "    x_inverses = hpcs.r_theta_to_x(r, theta)\n",
    "    max_abs_diffs.append(np.max(np.abs(random_xvecs-x_inverses)))\n",
    "\n",
    "print(\"maximum round trip error\", np.max(max_abs_diffs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed for any given tree we can transform a D dimensional vector to a D-1 dimensional vector of angles and back again. Really cool!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Angular Distribution of Points Uniformly Distributed on a Sphere.\n",
    "\n",
    "Lets start off by looking at what the distribution of angles looks like for a spherically symmetric set of points. In a perfect world you might expect that because the points are uniformly distributed over the unit sphere that the corresponding angles would also be in some sense \"uniformly distributed\", but alas this is not the case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ndims = 5\n",
    "npts = 50000\n",
    "xnorm = np.random.normal(size=(npts, ndims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hpcs_tree_plot(\n",
    "    hpcs, \n",
    "    ax=None,\n",
    "    layout_method=\"dot\",\n",
    "    rectangular_node_color=\"#333333\",\n",
    "    angle_node_color=\"r\",\n",
    "    rectangular_index_color=\"w\",\n",
    "    angle_index_color=\"k\",\n",
    "    highlight_node=None,\n",
    "    highlight_color=\"b\",\n",
    "):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    g = hpcs.tree\n",
    "    if layout_method == \"dot\":\n",
    "        lay = nx.nx_pydot.graphviz_layout(g, prog=\"dot\")\n",
    "    elif layout_method == \"kamada_kawai\":\n",
    "        lay = nx.layout.kamada_kawai_layout(g.to_undirected())\n",
    "    elif layout_method == \"top_down_binary\":\n",
    "        lay = make_top_down_tree_layout(2, 3)#nx.layout.kamada_kawai_layout(g)\n",
    "    \n",
    "    \n",
    "    nx.draw(g, pos=lay, ax=ax, node_color=rectangular_node_color, nodelist=hpcs.leaf_nodes)\n",
    "    nx.draw(g, pos=lay, ax=ax, node_color=angle_node_color, nodelist=hpcs.angle_nodes)\n",
    "    nx.draw_networkx_labels(g, pos=lay, labels=hpcs.node_to_theta_index, ax=ax, font_color=angle_index_color)\n",
    "    nx.draw_networkx_labels(g, pos=lay, labels=hpcs.node_to_vec_index, ax=ax, font_color=rectangular_index_color)\n",
    "    if not highlight_node is None:\n",
    "        nx.draw_networkx_nodes(\n",
    "            g, pos=lay, nodelist=[highlight_node], node_color=highlight_color,\n",
    "            ax=ax,\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"normal\" hyper spherical polar angles \n",
    "\n",
    "We will begin with the unbalanced tree which corresponds to the hyper-sphere coordinatization you can find on wikipedia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ignore some annoying deprecation warnings\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x1080 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hpcs = HyperPolarCoordinateSystem(make_binary_tree(n_leaves=ndims, mode=\"unbalanced\"))\n",
    "rs, thetas = hpcs.x_to_r_theta(xnorm)\n",
    "\n",
    "fig, axes = plt.subplots(ndims-1, 2, figsize=(12, 15), sharex=\"col\")\n",
    "axes[0, 0].set_xlim(-np.pi, np.pi)\n",
    "for i in range(ndims-1):\n",
    "    color = \"#0088ff\"\n",
    "    axes[i, 0].set_ylabel(\"Probability Density\".format(i), fontsize=18)\n",
    "    axes[i, 0].set_xlabel(\"Value of Angle {}\".format(i), fontsize=18)\n",
    "    axes[i, 0].hist(thetas[:, i], 51, (-np.pi, np.pi), density=True, color=color)\n",
    "    hpcs_tree_plot(hpcs, ax=axes[i, 1], highlight_node=hpcs.angle_nodes[i], highlight_color=color)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above diagram needs a little unpacking. The right hand side shows the tree which is being used to construct the coordinate system. Each non-leaf node of the tree represents an angle and the tree structure is repeated with a different angle node being highlighted each time. Because the leaf nodes represent coordinates in a rectangular coordinate system and the non-leaf nodes represent angles in a spherical coordinate system both the leaves and the non-leaf nodes are labeled on the basis of their given index within the appropriate coordinate set. So you will notice that there are two 0's in the above plot, one to indicate the node belonging to the first angle in spherical coordinates and one to indicate the node belonging to the first vector component in rectangular coordinates.\n",
    "\n",
    "This coordinate system is a direct successor to the spherical polar coordinates in 3D and so you may not be surprised to see that the angles in this system tend to look like the polar angle in 3D. The coordinates are constrained to lie between -pi/2 and pi/2 (or equivalently -90 degrees and +90 degrees) just like a latitude on the earth. It is only the final angle which explores the full possible range of angles from -pi to +pi. \n",
    "\n",
    "This behavior is fairly easy to understand from looking at the position of these nodes in the binary tree. The very last angle node is the only node which has a full complement of angles. When you look at where this angle is in the tree this makes sense, since the last node has two children which are both rectangular coordinate nodes. This is exactly the simple situation that we get by treating those two coordinates as being part of a 2D polar coordinate system. We incorporate that coordinate sub-system into the larger higher dimensional syste by simply multiplying by the radius of the vector spanned by just the 2 child coordinates. Likening this back to the system of earth latitudes and longitudes this is the longitude angle and just like the longitude angle of the earth it runs a full 2pi or 360 degrees.  \n",
    "\n",
    "All the other angle nodes however have exactly one leaf child node and one non-leaf child node. These are very much like the polar angles in 3D spherical polar coordinates and the fact that they are constrained to lie within -pi/2 to pi/2 is just a consequence of the fact that one of the two children nodes is a radius and therefore will always be non-negative, at least in the inverse formula given above. Because of this we populate only half the plane of possible angles. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Balanced Tree Spherical Coordinates\n",
    "\n",
    "What if we look at the angle distribution coming from a more balanced binary tree?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3trYWs3siIiKiCsvPz0fPnj3h4OCAr776Suo45daoUSP88ssvGDx4MAYNGgRPT0+pI5Eaaey7j8TERERHR+Px48eaOiURERFRMYMHD0Z2djaOHj0qdZQK8/DwwIQJEzB69Gg8ePBA6jikRqIX5fv370fLli3Rpk0bODs749y5cwCABw8ewMbGBjt37hQ7AhGJTPhW9Q8RUVWzadMmREREIDIyEsbGxlLHqZTAwEC88cYb6NGjh9RRSI1ELcqPHz8OT09PNGjQAF9//TVevqfU3NwcLVu2RFhYmJgRiIiIiAAU3us2ZcoUzJkzB05OTlLHqTQdHR1ER0fjxo0bmDJlitRxSE1ELcoXLlyIDh064PTp05g2bVqx4926dcOff/4pZgQiIiKqwa5du4a0tDTI5XI4OTmhXbt2+Oabb6SO9dosLCwQGhqKDRs24ODBgwCAs2fPSpyKXoeoRXlsbCzGjBlT4rI9MpkM9+7dEzMCERER1WDdunVD48aN0b17dzx+/BhRUVFSR1KbESNGYNSoURg0aBBatmyJt99+GxcvXpQ6FlWSqEV5QUEBDAwMSjyelpYGfX19MSMQERFRDfbw4UPI5XKcPn0anTt3homJidSR1Grs2LHIzc3F9evXAQARERESJ6LKErUob9u2LU6ePFni8f3796NDhw5iRiAiIqIaKj09HXK5XLl98uRJjBgxQsJE6pWcnIwBAwYU2Xfq1CmJ0tDrErUo9/Hxwc6dOxEUFKT8n0IQBGRlZeGTTz7B77//Dl9fXzEjEBERUQ21f//+Ittvv/02Vq5cKVEa9ZPJZJg3bx5q1aql3Pf7779LmIheh6B4eUkUEYwdOxY///wz6tati6dPn8LMzAwPHz5EQUEBvL29ERQUJObpy4WPqabqTqrlCRWzpTlvTcLPL6rRHjwAQkKA+Hjg8WPA1BSwtwe8vQEzM/Ts2RMnTpxAx44d8csvv6BVq1ZSJxaFXC7H3LlzERAQoNwGUOb4UNUielEOALt370ZoaCj++ecfKBQKtGrVCuPGjcPQoUMr3FdkZCQ+/fRTFBQUYOLEiZgzZ06R47du3cL48ePx6NEjFBQUYNmyZXB3dy+1T/5So+qORXn1xc8vqpHOngWWLgUOHCjczsn5/2NGRoBCAfTvj8dTp+KmuTns7e2lyalheXl5OHfuHLrp6ZVrfDB3LuDoKE1YKkYjRbm6FBQUoHXr1jh06BBkMhkcHR2xbds22NraKtv4+vrirbfewpQpU3Dp0iW4u7vjxo0bpfbLX2pUXVS1B/awKBcfP7+oxlm/Hpg5E8jOLiwuSyIIhQXoihVATVrLm+OjtUR/oqc6nTlzBjY2NmjRogX09fUxatQo7N27t0gbQRDw5MkTAMDjx49haWkpRVQiIiJStxcFZ1ZW6QUnUHg8K6uw/fr1msknNY6PVhOtKH/8+DG++eYbODk5wczMDAYGBjAzM0OPHj2wbNkyZeFcESkpKWjatKlyWyaTISUlpUib+fPnIzQ0FDKZDO7u7lizZo3KvgIDA+Hg4AAHBwekpqZWOAsRERFp0Nmz/19w/isXgA8AawB1ALwF4MCrr3tReFb3b5RUjA8ArAXgAMAAgJeq19WU8dECohTl8fHxsLOzw7x58/D7778jLy8P5ubmyMvLQ0xMDL744gu0a9cOly5dqlC/qmbaCIJQZHvbtm3w8vJCcnIyIiIi8MEHHxRZDukFX19fxMbGIjY2Fma82YGIiKhqW7q0cErGS/IBNAUQBeAxgEUARgC48eprs7MLX1+dqRgfALAE8BWACaW9tiaMjxZQe1Gek5ODoUOHIjU1FV988QWSkpLw+PFj3L59G48fP0ZSUhK++OIL3L9/H0OGDEFubm65+5bJZLh9+7ZyOzk5udj0lKCgIOUapN26dUNOTg7S0tLU8+aIiIhI8x48KLxp8ZWLc7UBzAfQDIUFzXsAmgM49+rrFQogIgKort+MlzA+ADAEwGAADUt7fXUfHy2h9qI8LCwM165dw88//4xFixbB2tq6yHFra2ssXrwYoaGhuHr1KsLCwsrdt6OjIxISEpCUlIS8vDyEhYXBw8OjSBsrKyscOXIEAHD58mXk5OTwSjgREZE2CwkpV7P7AK4CsFN1UBDK3Y/WUcf7qs7joyXUXpTv27cPb7/9dpnLHQ4fPhxvv/12sRs1S6Onp4e1a9fCzc0Nbdu2xYgRI2BnZwd/f3/s27cPALBy5Ups3LgRHTp0wOjRoxESElJsigsRERFpkfj4osv6qfAcwBgA4wG8qapBdjbw99/qz1YVlGN8ylSdx0dL6Km7w/Pnz2PMmDHlatuvXz9s3bq1Qv27u7sXW3d84cKFyj/b2toiOjq6Qn0SERFRFfb4camH5QA+AKCPwhsbS5SRob5MVUkZ41Nu1XV8tITai/LU1FRYWVmVq62VlRVXPiEiIqLSmZqWeEiBwhVY7gOIAFCrxJYA6tdXa6wqo5TxqZDqOj5aQu3TV549ewZjY+NytTUyMsKzZ8/UHYGIiIiqE3t7wNBQ5aEpAC4DCAdgVFofRkZA+/bqz1YVlDI++QByABT8+5Pz775iqvP4aAm1F+Va9IBQIiIi0gZeXirri5sANgCIA2ABwOTfH5UTYxUKwMtLvIxSKuV9LUbhP1aWAQj998+LVTWszuOjJdQ+fQUovNmyPKuqvPrgHyIiIqJXbTtyBMbPn+M9ALov7bdG4fSVMgkC4O4OVNfV2MzNgf79gT17ii2LOP/fn9IUAPjD1BSOpqbQFychlYMoRflff/2Fv/76q1xtuTIKERERqZKVlYUBAwYgKioK33h6wiMystgTK8vFyAiYO1f9AauSuXOBgwcrNz4GBvjq2TOca9QIu3btQt++fdWfj8qk9ukrcrm8Qj8FBQXqjkBERERabteuXWjUqBEuXryI2NhYzNm1C8KKFUA571tTMjYGVqwAHBzECVpVODoWvs9KjI/u99/jUEYG+vXrBzc3NwwZMgT5+SpnnpOI1F6UExEREVVWTk4O+vXrh+HDh2PUqFG4d+8eOnXqVHhwypT/LzzL+qZdEP6/IJ8yRfzgVcFrjI+enh527tyJQ4cO4fDhw2jUqBGOHz+ukdhUiEU5ERERVQn79+9Ho0aNcO7cOURHR+O///0vdHReKVWmTAGiogBPz8IVR4xeWXPFyKhwv6dnYbuaUpC/8Jrj07t3b6SlpaFnz55wdXXF6NGjedVcQ0SZU05ERERUXnl5efD09MSBAwcwevRobNmypXgx/jIHB2DXLiA1FQgJwdVdu5AYGwv3998vXNbPy6v63tRZHq+Mz+lNm/D09m30GTasXOOjr6+PvXv3IiIiAiNGjIC5uTnCw8Ph5OSkufdQA7EoJyIiIskcPHgQw4YNg56eHo4fPw5nZ+fyv9jMDJg1C8dNTfHZxYt4unmzeEG10b/j81NSEiIiInCjguPj7u6OtLQ0DB48GO+88w4++OADBAcHl/4PJqo0jioRERFpXH5+PoYMGYL+/fvj3XffRWpqasUKctIIQ0NDREZGYteuXdixYwcaN26Ms2fPSh2rWmJRTkRERBp19OhRNGzYEIcPH8ahQ4ewY8cO6Onxy/uqzNPTE2lpabC3t0eXLl3w4YcfQi6XSx2rWmFRTkRERBqRn5+PUaNGoU+fPnBxcUFaWhp69+4tdSwqJ2NjYxw5cgTbtm1DaGgoLC0tERcXJ3WsakPUorxv377Yvn078vLyxDwNERERVXGnTp2Cubk59u/fj/3792Pv3r3Q1+fzI7XRyJEjkZqaitatW6NTp06YNm0ar5qrgahF+blz5/D+++/D0tISfn5++Pvvv8U8HREREVUxcrkc48aNg7OzM7p06YK0tDS4u7tLHYtek4mJCU6cOIGQkBAEBQWhadOmuHjxotSxtJqoRfm9e/ewdetWvPXWW1izZg06duyILl26YOPGjcjMzBTz1ERERCSxs2fPwtzcHLt27cLu3btx4MABGBoaSh2L1GjcuHG4d+8emjZtCnt7e3z22WdSR9Jaohbl+vr6GDVqFA4dOoTr16/jq6++wv379zFp0iQ0adIEPj4+iI6OFjMCERERaZhcLsfEiRPRpUsXdOzYEampqRg0aJDUsUgk9erVwx9//IENGzZg7dq1sLKyQkJCgtSxtI7GbvS0trbGggULkJSUhMjISPTq1QshISFwdnaGra0t/vOf/+DZs2eaikNEREQiiIuLQ5MmTbB161aEhYXh8OHDMDY2ljoWacDEiRNx9+5dmJub480338QXX3whdSStovHVV+Li4rBv3z6cPHkSCoUCLVu2hI6ODqZPnw4bGxvExMRoOhIRERG9JrlcjmnTpqFTp05o06YNUlNTMWLECKljkYY1aNAAsbGx+M9//oOAgAC0bNkSSUlJUsfSChopyh89eoR169ahU6dOcHBwwKZNm+Dm5obDhw/j6tWruHDhgvJf0tOmTdNEJCIiIlKTixcvQiaTISgoCJs3b8aJEydgYmIidSyS0EcffYSUlBTUrl0bNjY2WLBggdSRqjxRi/KjR49izJgxsLS0xMcff4ysrCwsX74cKSkpCAsLg6urq7Ktq6sr5syZU+adu5GRkWjTpg1sbGywbNkylW1++eUX2Nraws7ODu+//75a3xMRERH9vxkzZsDe3h5WVlZ48OABxo4dK3UkqiLMzc0RHx+PgIAALF68GK1bt8atW7ekjlVlifr4rD59+sDAwABDhgyBr68vevbsWWp7GxsbODk5lXi8oKAA06ZNw6FDhyCTyeDo6AgPDw/Y2toq2yQkJGDp0qWIjo5G/fr18eDBA7W9HyIiIip05coV9O3bF/fv38eGDRswceJEqSNRFTVjxgzlQ6NatGiBxYsXY86cOVLHqnJELcpXrlyJ8ePHo0GDBuVq36tXL/Tq1avE42fOnIGNjQ1atGgBABg1ahT27t1bpCjfuHEjpk2bhvr16wMo/FcaEUlD+Fb1fsVszeYgIvWaO3culi9fjrfeegtxcXHl/j1PNZelpSUuXbqEpUuX4quvvsLmzZtx+PBhWFpaSh2tyhB1+srTp09x586dEo9fvHgRCxcuLHd/KSkpaNq0qXJbJpMhJSWlSJurV6/i6tWrcHJyQteuXREZGamyr8DAQDg4OMDBwQGpqanlzkBERFRTJSUloUWLFli5ciXWrFmD2NhYFuRUIXPnzsX169eRn58Pa2trfPfdd1JHqjJELcoXLFiA+Pj4Eo9fuHChQhP/FQpFsX2CIBTZzs/PR0JCAo4fP45t27Zh4sSJePToUbHX+fr6IjY2FrGxsTAzMyt3BqKqQPhW9Q8RkVjmz58PGxsb1K1bF8nJyZg6darUkUhLWVlZ4erVq/jqq68wa9YsdOjQgdONIXJRrqqIfllOTg709Mo/g0Ymk+H27dvK7eTk5GJfe8hkMgwaNAi1atVC8+bN0aZNGy5gT0REVEm3bt1C69atsWTJEqxcuRJxcXGcGkpq8fXXXyMxMRGZmZmQyWT44YcfpI4kKbUX5U+ePMGtW7eUd9c+fPhQuf3yT1xcHLZu3VpkOkpZHB0dkZCQgKSkJOTl5SEsLAweHh5F2gwePBjHjh0DAKSlpeHq1avKOehERERUfkuXLkWLFi1Qq1Yt3L59G35+flJHomqmefPmuHbtGmbOnImPP/4YDg4OSE9PlzqWJNRelH///fdo3rw5mjdvDkEQ4Ofnp9x++adz5844fPgwJk+eXO6+9fT0sHbtWri5uaFt27YYMWIE7Ozs4O/vj3379gEA3Nzc0LBhQ9ja2qJXr14ICAhAw4YN1f02iYiIqq07d+6gbdu2mDdvHhYvXoyLFy/CwsJC6lhUjX3zzTe4dOkSUlNT0aRJE2zatEnqSBqn9tVXXFxcABROXVm4cCE8PT1hb29fpI0gCDAxMUHXrl3RvXv3CvXv7u4Od3f3IvtevllUEAR89913vHGAiIioElauXIk5c+agRYsWuH79OqysrKSORDVEmzZtcPPmTcyYMQOTJk3Cpk2bEBkZiXr16kkdTSPUXpT37NlTuR75zZs3MXnyZHTp0kXdpyEiIiI1evDgAfr06YNLly7B398f/v7+UkeiGuq7776Dj48P+vXrB427vLwAACAASURBVAsLCwQGBmLcuHFSxxKdqDd6BgcHsyAnIiKq4tauXYs33ngDz549Q0JCAgtykpydnR1u376NDz/8EF5eXnjnnXeQmZkpdSxRqfVK+YubO1981VXeR6nyqzEiIiLNS09PR9++fREXF4fZs2fjm2++kToSkZKOjg7WrFkDHx8fuLm5wczMDCEhIRg5cqTU0USh1qK8WbNm0NHRQVZWFvT19dGsWbNi64irUlBQoM4YREREVIZNmzZh6tSpaNKkCf755x+0atVK6kgVlpmZiQULFuDcuXPIycnBJ598gi5dumDMmDFSR6sSkpOTERAQgJMnTyI9PR2ffPIJBgwYADc3N6mjVUjHjh1x9+5dTJo0CaNHj0ZgYCDCw8NhbGwsdTS1UmtR7u/vD0EQlGuPv9gmIiKiquHRo0dwc3NDbGws/Pz8sHLlSqkjVdr169exYsUK5faaNWuwZ88eFuX/Onr0KFavXq3cXrNmDeLi4rSuKAcKr5pv3LgRvr6+6N+/P8zMzBAaGgpPT0+po6mNoCjrCT81gIODA2JjY6WOQVRu2v70TsVsqRNUH/z8oorYvHkzfH190bBhQ/zvf/+DnZ2d1JFem7W1dZHpsr/++mu1KtReV+3atZGVlaXcvnTpEtq2bSthotcnl8vh7e2NLVu2oF+/ftizZw8MDQ2ljvXaRL3Rk4iIiKSXmZmJd955B15eXvD19cXt27erRUEOAD/99JPyz+bm5izIX/HyfQKdOnXS+oIcKLxq/tNPP+HkyZM4c+YMGjVqhIiICKljvTYW5URERNXY9u3bYWZmhsTERMTFxWH16tXQ0ak+v/5dXFzQoEEDAMCPP/4ocZqq59NPP1VOKw4NDZU4jXo5OTkhLS0NAwcOxHvvvYeBAwciLy9P6liVptb/K3V0dKCrq1uhnxd/UYiIiOj15OXloX79+li+fDmysrLg6uqK0aNHY/z48UhJSSn2ML/qYv369ZDJZLxKXoJZs2ahXbt21eIq+at0dHSwbds2HD16FCdPnkSjRo1w6NAhPHnyBKampggMDJQ6YrmpdU65l5dXpW7sDA4OVleESuGcTNI2nFNOL/Dzq5p78AAICQHi44HHjwFTU8DeHvD2BszMijUfP348Nm/eDAAwNDREnTp1EBERAQcHBw0H14z09HSEh4cjMTERmZmZMDExgY2NDTw8PFC/fn2p40mupo1Pfn4+Ro4cid27d8PU1BSPHj2Cvr4+nj17pvIicFUbH97oCf5SI+3Dopxe4OdXNXX2LLB0KXDgQOF2Ts7/HzMyAhQKoH9/YO5cwNERAHDnzh288cYbymbGxsZ4+vRptZqq8sLFixcRHByMmJgYCIKA3Nxc5TEDAwMoFAp0794d3t7e1WbufEXU9PGZPn06Vq1apdyeOHEiNm7cqNyuquPDohz8pUbah0U5vcDPr2po/Xpg5kwgO7uw+C6JIBQW6CtWAFOmoE2bNrh69WqRJt9//z38/PxEDqxZO3fuxKpVq5Cbm4vSShhBEGBgYAA/Pz8MGzZMgwmlxfEBatWqhfz8/CL77t69CwsLiyo9PpzQTUREVFW8KMhfWsKuRApFYbuZMwFAWZCbmJjAwsICrVq1Qo8ePcRMq3EvCqqcl785KIFCoUBOTo7yiml1KzxV4fgU8vX1xenTp3Hz5k1kZGSgoKAAvr6+GDduXJUeH7VeKW/evDl0dHTwzz//oFatWmjRokXZAQQB165dU1eESuGVJtI2vFJOL/Dzqxo5exZwcSlWkI8FcATAMwAWAD4HMPHV1xobA1FRQDWdOw4UTjmYNGlSkYKqVq1amDNnDt5++23UrVsXycnJWLduHWJiYoq81tDQEIGBgbC1tdV0bI1RNT4AMGLECLz33nuwsbHBwYMHsWDBgmKvrcnjU7duXcybNw9du3bFo0ePsHbtWhw8eLBIG02Nj1onmllbW8PKykp5s6eVlRWsra1L/bGyslJnBCIiIu20dGnhlJVXzAVwA8ATAPsAfAXg3KuNsrMLX1+NBQcHF5n7CwC6urq4f/8+fH194eLigvXr12Pp0qVo0qRJkXa5ubmSLyohNlXjAwCpqakICgrCvn37SnxtTR6f2bNn4/nz5+jXrx+++uorzJ07t9hFZU2Nj1qnrxw/frzUbSIiIlLhwYPCmzpVfHn98m1mwr8/1wB0frmRQgFERACpqSpXZdF26enpiImJKTYHOCcnp8iSd6dOncKdO3fQtm1b3L17V7lfoVAgOjoaGRkZ1XLVkZLGBwCOHTsGALC1tYW5ubnK19fU8TE0NISrqytGjhyJ7OxsnD9/HidOnIC7uzvWrl2rbKep8al+t2QTERFpm5CQUg9PBWAM4E0ATQC4q2okCGX2o63Cw8PLteRygwYNYGVlpXJarCAICA8PFyOe5Mo7PqWpieNjbW2NgoIC3Lp1S7nv6tWrKqdfa2J8NHKjZ25uLo4fP47r168DAFq0aIGePXvC0NBQE6cnIiKq2uLjiy57+IofAKwB8DuA4wAMVDXKzgb+/luMdJJLTExUOfXgZbq6uli0aBF+++033Lx5s9jx3NxcJCYmihVRUuUZn7LUxPExMjJCZmZmkX2ZmZmoXbt2sbaaGB/Ri/LNmzdjxowZyMjIUH5tIAgC6tWrh5UrV8LLy0vsCERERFXb48dlNtEF0ANAKID1AD5R1SgjQ62xqopXC6dXCYKARYsWIT8/H99+W/Kd8E+fPlV3tCqhrPEpr5o2PtnZ2TAxMSmyr3bt2nj27JnK9mKPj6hF+fbt2+Hl5QUrKyvMnDkTtra2UCgUuHTpEn788Uf4+PjAyMgII0eOFDMGERFR1WZqWu6m+SicU65SNZwPDKBY4fSqefPmoUGDBvj0009RUFBQYrs6deqoO1qVUNb4lFdNG5+bN29CV1cXTZs2xe3btwEArVu3Vs7seJXY4yPqnPJvvvkGb775JuLj4zFnzhx4eHhg0KBBmDt3LuLj49GqVSssWbKkQn1GRkaiTZs2sLGxwbJly0pst3PnTgiCwKXCiIio6rO3B1RM6XwAIAxAJoACAAcBbAPgqqoPIyOgfXsRQ0rHxsYGBgYqJ+1g7ty5aN68OaZPn17qFA4DAwPY2NiIFVFSpY2Prq4u9PX1oaOjo/yzrq5usXY1cXxycnJw7NgxTJ48GYaGhujQoQN69uyJiIiIYm01MT6iFuVXrlyBt7c36tatW+yYqakpvL29kZCQUO7+CgoKMG3aNBw4cACXLl3Ctm3bcOnSpWLtnj59itWrV6NLly6vlZ+IiEgjSpjKKaBwqooMQH0AMwGsAjBIVWOFosR+tN3AgQNVrixiYWGBoUOHonXr1jh48CBOnDiBEydO4N133y3WVqFQYODAgZqIq3EljQ8A+Pj4ICYmBt7e3nB3d0dMTAx8fHyKtaup47Ns2TIYGBjg0KFDWLJkCZYuXarySrkmxkfU6SsWFhalPsJUR0cHjRs3Lnd/Z86cgY2NjfKu2FGjRmHv3r3FFnOfN28ePv/8c6xYsaJywYmIiDTJ3Bzo3x/Ys6fIsohmAKLK83pBANzdq+VyiEDhqirdu3dHVFRUkbri3r17cCjHA5MEQYCTk1O1XO4PKHl8ACAwMLDIspGq1OTxefLkCWb++1TckmhqfES9Uu7l5YWQkBCVE+yfPHmC//73v/D29i53fykpKWjatKlyWyaTISUlpUibv/76C7dv38Z7771Xal+BgYFwcHCAg4MDUlNTy52BiIhIFHPnFk5BqQwjo8LXV2Pe3t4lTtEoi4GBQYXqDW3E8SmdNoyPWovyF18bvfhxdnaGsbEx2rdvj4CAAISHh2P//v1Yvnw5OnToABMTE7zzzjvl7l/VVfeX152Uy+WYPn06Vq5cWWZfvr6+iI2NRWxsLMyq6ZUFIiLSIo6OwIoVKKhg4SA3MgJWrADKccVYm9nZ2cHPz6/CyykbGhrCz8+vWj9CHuD4lEUbxket01dcXFyKLc7+opCePXu28tiLfTdv3kTfvn1LvVP6ZTKZTHl3LAAkJyfD0tJSuf306VNcuHABLi4uAAq/1vLw8MC+ffvK9fUWERGRlB6NHg3/Tz5BgK4uDORylU/4VBIEZANYbGSERZMm1YinAQ4bNgwAsGrVKuTm5pY6RVYQBBgYGMDPz0/5uuqO41O6qj4+ai3Kg4OD1dldMY6OjkhISEBSUhLeeOMNhIWF4eeff1YeNzU1RVpamnLbxcUFK1asYEFORERawdnZGemNG2PVr78C334LREQUzhfPzv7/RkZGhcW6uzvypk7FygEDkDJhAkKq6dM8XzVs2DDY2toiODgY0dHREAShyKorBgYGUCgUcHJygre3d7W/Avwqjk/pqvL4qLUoHz9+vDq7K0ZPTw9r166Fm5sbCgoKMGHCBNjZ2cHf3x8ODg7w8PAQ9fxERERimTVrFi5fvozExEToWFsDu3YBqalASEjhkzozMgrXIW/fvnCVFTMzmKJwCeAXSw57enpK/C40w9bWFgEBAcjIyEB4eDgSExPx9OlT1KlTBzY2Nhg4cGC1vWmxPDg+pauq4yMoSrt2X0M4ODhwPXOqkoSSH0yn1RSzpU5QffDzq3o4ceIEXFxcEBwcXKkLXB9++CE2b96M27dvw9zcXISERCQ2UZdEfOH+/fuIjY1FRkYG5HJ5sePjxo3TRAwiIqIqJzMzE+7u7vDw8Kj0N84bN27E0aNH0aNHD1y9elXNCYlIE0QtyuVyOaZNm4ZNmzapLMZfYFFOREQ1lYuLC2rXro1ff/31tfqJjo6GtbU1Jk+ejB9//FFN6YhIU0S9WXvFihXYsGEDRo8ejZ9++gkKhQLLli3DunXr0KpVKzg4OODQoUNiRiAiIqqy/P39ERcXh1OnTkFH5/V+JVtYWGDr1q0IDAzEgQMH1JSQiDRF1KL8p59+gpubGzZv3oz+/fsDADp37ozJkyfj3LlzSEtLw7lz58SMQEREVCWdPXsWS5YswerVq9GqVSu19Dls2DCMHj0aQ4YMQXp6ulr6JCLNELUov379urIYf3EF4Pnz5wCA2rVrw9vbG5s2bRIzAhERUZWTk5ODPn36oE+fPpg6dapa+96yZQvMzMzg7Oys1n6JSFyiFuVGRkaoVasWAMDExASCIODBgwfK4xYWFkUeBkRERFQT9OnTB3p6evjtt9/U3reOjg5OnTqFK1euYMaMGWrvn4jEIWpRbm1tjWvXrgEAatWqBRsbG0RGRiqPHz58GI0bNxYzAhERUZWybNky/P7774iKioKenjjrLVhZWSEoKAirVq3C8ePHRTkHEamXqEW5q6srdu/erdz+4IMPsG3bNvTq1QsuLi7YsWMHRowYIWYEIiKiKiM+Ph5ffvklli9fjnbt2ol6rnHjxmHw4MEYMGAAMjMzRT0XEb0+UR8edPfuXcTHx8PFxQUGBgYoKCjA9OnTERoaCl1dXQwbNgzff/89DA0NxYpQLnz4BlVVfHgQlYWfX9ojLy8PFhYWaN++PaKiojRyTrlcjjfeeAOWlpZcWIGoihP1SnmTJk3g5uYGAwMDAICuri5Wr16N9PR0pKamYv369ZIX5ERERJrg7u4OuVyu0aWAX8wvP3/+PL788kuNnZeIKk7UopyIiIiANWvW4NixYzh8+DD09fU1eu6WLVti3bp1WLp0KX7//XeNnpuIyk/UJ3q+8Msvv2D37t24fv06AKBFixbw9PTkfHIiIqr2Ll++jOnTp+Prr7+Gg4ODJBkmTZqEPXv2wM3NDffu3YOxsbEkOYioZKLOKc/KysKgQYNw9OhRKBQK1KtXDwqFAo8fP4YgCHBxccG+fftQu3ZtsSKUC+dkUlXFOeVUFn5+VW35+fmwtLRE8+bNcfr0acmzWFhYoHXr1oiJiZE0CxEVJ+r0lS+++AJHjhzBxx9/jDt37iA9PR0ZGRm4c+cOPv74Yxw7doxz3IhqIOFb1T9E1c3gwYORnZ2NY8eOSR0Fenp6iIqKwunTp7FkyRKp4xDRK0Qtyrdv347hw4dj1apVsLCwUO63sLDAqlWrMHToUGzfvl3MCERERJLYtGkTIiIiEBkZWWWmi9jZ2WHlypXw9/dHXFyc1HGI6CWiFuVPnjxBr169Sjzu6uqKJ0+eiBmBiIhI45KSkjB58mTMnj0bTk5OUscpws/PD87OzujVqxfy8vKkjkNE/xK1KLe3t0dCQkKJxxMSEtC+fXsxIxAREWmUXC6Hk5MT2rVrh6VLl0odR6WDBw8CAN59912JkxDRC6IW5YsXL8bGjRsRHh5e7NjevXuxadMmfPPNN2JGICIi0qiRI0fi0aNHOHHihNRRSqSvr48jR44gKioKq1atkjoOEUHNSyJOmDCh2L7mzZtj8ODBaNOmDdq2bQtBEHDp0iVcuXIF7du3x9atW+Hq6qrOGERERJLYunUrdu3ahUOHDqFu3bpSxylVp06dsHDhQnz22Wdwc3ND27ZtpY5EVKOpdUlEHZ2KX3gXBAEFBQXqilApXFKMqqqatiIJl0qsOH5+VR3Jyclo0aIFJk+ejNWrV0sdp9y6deuGxMRE3L17F3p6Gnl8CRGpoNbpK3K5vMI/FS3IIyMj0aZNG9jY2GDZsmXFjn/33XewtbWFvb09evfujZs3b6rr7REREan0Yh55y5YttaogB4AjR44gNzcXHh4eUkchqtFEnVOubgUFBZg2bRoOHDiAS5cuYdu2bbh06VKRNm+99RZiY2MRHx+PYcOG4fPPP5coLRER1RTe3t64f/8+oqOjpY5SYcbGxjh48CAiIyOxYcMGqeMQ1VgaKcoVCgX+/PNP7Ny5Ezt37sSff/6JysyaOXPmDGxsbNCiRQvo6+tj1KhR2Lt3b5E2vXr1Uq4H27VrVyQnJ6vlPRAREamye/dubNmyBTt37kSDBg2kjlMp3bp1w9y5czFt2jRcu3ZN6jhENZLoRXlkZCRatmwJR0dHjBw5EiNHjoSjoyNsbGyUSzKVV0pKCpo2barclslkSElJKbF9UFAQ+vfvr/JYYGAgHBwc4ODggNTU1ArlICIiAoAHDx5g1KhR8PHxwXvvvSd1nNeyZMkS2Nvbo0ePHpDL5VLHIapxRC3Ko6Oj4eHhgYyMDHzyyScIDAxEYGAgPv30U2RkZMDDwwMxMTHl7k/V1XVBEFS2DQ0NRWxsLGbNmqXyuK+vL2JjYxEbGwszM7NyZyAiopotLi4OW7duBQD06NEDMpkMGzdulDiVepw4cQJPnjzB8OHDAQABAQFIT0+XOBVRzSDqbdYLFy6EhYUFTp8+jSZNmhQ5NmvWLHTp0gULFy5EZGRkufqTyWS4ffu2cjs5ORmWlpbF2h0+fBhLlixBVFQUDAwMXu9NEBERveSjjz5CdHQ0Zs6cibS0tCK/l7SdiYkJwsPD0bt3bzRs2BDp6elITU3F8uXLpY5GVO2JeqX89OnT8PX1LVaQA0CTJk3w4Ycf4o8//ih3f46OjkhISEBSUhLy8vIQFhZW7G7xv/76C5MmTcK+fftgbm7+2u+BiIjoZS8WGLh37x709PTw4MEDiROpV0ZGBgRBUF4hr8jvaSKqPFGL8ry8PNSpU6fE43Xr1kVeXl65+9PT08PatWuVDzkYMWIE7Ozs4O/vj3379gEovAKfmZmJ4cOHo2PHjlziiYiI1OrRo0fKP+fk5GDAgAESplG/0aNHF5kuevHiRQnTENUcan140Ks6d+4MfX19nDx5stgDCfLz8+Hs7Izc3FycO3dOrAjlwodvkNRq2kOCSsKHB1UcP7/UKz09HeHh4UhMTERmZiZMTExgY2MDDw8P1K9fHw8ePEDjxo2V7QcNGoSQkBDUq1dPwtTqdeXKFbz//vv4888/lftelApljQ8RVZ6oc8qnTJkCX19f9O7dG59//jlsbW0BFP6rOyAgAKdPn0ZgYKCYEYiIiMp08eJFBAcHIyYmBoIgIDc3V3nMwMAAGzZsQPfu3ZUrgLm6umLHjh1auwRiadq0aYNz587h8uXLGDBgAJKSknDhwgWEhISUOT7e3t6ws7OTMD2R9hK1KJ84cSISEhKwYsUKnDp1qtjxWbNmwcfHR8wIREREpdq5cydWrVqF3Nxclat8vShAXywesGPHDgwbNkzTMTWubdu2uH79Onbu3InJkyeXa3z++OMP+Pn51YjxIVI3UYtyAPj222/h4+ODvXv3IikpCQqFAi1btoSHhwdat24t9umJiIhK9KIgz8nJKbOtQqFATk4OVq1aBQA1ovDk+BBpjmhFeW5urnIpxNatW5e4XjgREZEULl68WO6C82UvCk9bW1vltMzqiONDpFmirb6iq6uL3r1748CBA2KdgoiIqNKCg4OLzI1+VdOmTREdHY2FCxcWO5abm4vg4GAx40mupPF58XyR48ePY9euXRg0aFCxNjVhfIjUTbQr5Xp6erCwsFA5/4yIiEhK6enpiImJKfV31OzZs5Vrkr9KoVAgOjoaGRkZ1XLVkdLGJyQkBIsWLcLz589hbW2NDRs24MqVK/jnn3+Ubar7+BCJQdR1yocPH45ffvkFcrlczNMQERFVSHh4OARBKPF4v3798PTpU5w9e7bENoIgIDw8XIx4kittfK5fv47nz58X2SeTyYq1q87jQyQGUYvyiRMnIisrC3379kV4eDj++ecf3Lp1q9gPERGRJiUmJpY4daV27dqYNGmS8obFkuTm5iIxMVGMeJIrbXyAwm8RTp06hV27diEtLQ3R0dHF2lTn8SESg6irr7Rr1w6CIEChUOD48eMltisoKBAzBhERURGZmZklHps8eTL27duH+/fvl9nP06dP1RmryihtfIDCldUCAgLQvn17ODg4lPh07uo6PkRiELUo9/f3L/XrQSIiIimYmJio3N+6dWu8/fbbGDNmTLn6qVOnjjpjVRkljc/L5HI5zp8/D3d3dwwbNgzbt28v1qa6jg+RGEQtyufPny9m90RERJViY2MDAwODYlM0OnfuDEtLS+zfvx8AYGxsDB0dHbRo0QJjx44t0tbAwAA2NjYay6xJJY2PKrq6uirnlFfn8SESg2hzylNTU3H69Glcu3ZNrFMQERFVysCBA1WuLPLrr79i8ODBGDNmDMaMGYNdu3YhOjoaH330UbG2CoUCAwcO1ERcjStpfOrXr49+/frByMgIOjo66Nq1K9zc3BAbG1usbXUeHyIxqL0ol8vlmDx5Mpo0aYLu3bujdevW6NGjB1JTU9V9KiIiokpp0KABunfvXmyKZW5uLh4+fKj8yc7ORm5uLh49elSknSAIcHJyqrbL/ZU0PgqFAkOHDkVERASOHj0KPz8/rFy5ElFRUUXaVffxIRKD2qevrF27FoGBgbC0tES3bt2QkJCAmJgYTJo0Cb/++qu6T0dERFQp3t7e+OOPP0p9YmVgYKDK/QYGBvD29hYrWpWganwePXqESZMmlfnamjA+ROqm9ivlmzdvRtu2bXH58mXs2LEDcXFx8PHxQXh4eLErDURERFKxs7ODn58fDA0NK/Q6Q0ND+Pn5VftHyHN8iDRL7UX5lStX4OXlVeSO648//hgFBQW4evWquk9HRERUacOGDVMWnmWtFiYIgrLgHDZsmIYSSovjQ6Q5ap++8uzZM1haWhbZ92L72bNn6j4dERHRaxk2bBhsbW0RHByM6OhoCIJQZNURAwMDKBQKODk5wdvbu8ZdAeb4EGmGKEsivvqv6Rfbqu7kJiIikpqtrS0CAgKQkZGB8PBwJCYm4unTp6hTpw5sbGwwcODAGn3TIseHSHyiFOURERG4d++ecjsrKwuCICjnmL9MEARMnz5djBhEVY7wrdQJiKg09evXx7hx46SOUWVxfIjEIyjUfPlaR6di09QFQUBBQYE6I1SYg4ODyjVWidSNRXnpFLOlTqB9+PlFRFQ9qP1K+bFjx9TdZRGRkZH49NNPUVBQgIkTJ2LOnDlFjufm5mLcuHE4d+4cGjZsiO3bt6NZs2aiZiIiIiIieh1qL8p79uyp7i6VCgoKMG3aNBw6dAgymQyOjo7w8PAoclNJUFAQ6tevj8TERISFhWH27NnYvn27aJmIiIiIiF6XKHPKxXLmzBnY2NigRYsWAIBRo0Zh7969RYryvXv3Yv78+QAK7xj/6KOPoFAoylzKiYikV9L0Hk5rISKi6k6rivKUlBQ0bdpUuS2TyXD69OkS2+jp6cHU1BQPHz5Eo0aNNJqVajbOHSciIqKK0KqiXNU9qa9eAS9PG6Dw0ckvHp/8zz//wMHBQeU5U1NTYWZmVpm4VYK25we08z10funP2pj/ZVUhv8OO13t9VXgPr6O0/Ddu3NBsGCIiEoVWFeUymQy3b99WbicnJxd7UNGLNjKZDPn5+Xj8+DEaNGhQrC9fX1/4+vqWeU5tX9lA2/MD2v8emF962v4etD0/ERGVrWLrF0rM0dERCQkJSEpKQl5eHsLCwuDh4VGkjYeHB3766ScAwM6dO+Hq6sr55ERERERUpWnVlXI9PT2sXbsWbm5uKCgowIQJE2BnZwd/f384ODjAw8MDPj4++OCDD2BjY4MGDRogLCxM6thERERERKXSqqIcANzd3eHu7l5k38KFC5V/NjQ0xI4drzkB9SXlmeJSlWl7/h49euDWrVtSx6iQP//8E5999hn++usvPH78uNi3OVXV4cOH0bdvX2zZsgVjx45V7tf2v0OA9r8Hbc9PRERl06rpK1LQ9l+GYuYfPnw4BEFAXFxciW0UCgWaN2+OevXqITs7u1LnqVu3bmUjatzz588xdOhQJCUlYcmSJdiyZQuWLFlSrtf+/fffEAQBgiDgjz/+EDlp+anj71BBQQFWrlyJNm3awMDAAE2bNsWsWbOQlZWlhoRl4//HRERU1bEop0rz8fEBAAQHB5fY5tixY7hx4wZGjRoFIyMjTUWTTEJCAm7cuIEZM2Zg2rRpGDt2LNq1a1eu1wYFBcHUn9wcoQAAIABJREFU1BSNGjVCUFCQyEk165NPPsHMmTPRvn17rFu3DkOHDsX333+PQYMGqVwxiYiIqKbRuukrVHX069cPTZs2xdatWxEQEAB9ff1ibV4U7C8K+Oru3r17AKByxZ/S5OXlITQ0FCNHjoSBgQFCQkKwatUq1K5dW4yYGnX+/HmsX78eI0aMKPJ0XWtra8yYMQM7duzAiBEjJExIREQkPV4pp0rT0dGBl5cXHj58iH379hU7/uTJE/z6669o164dHB0dlft//vlnDBw4EFZWVjAwMICZmRmGDBmCCxculOu8MpkMffr0Kbb/8OHDEAQBoaGhRfbn5ORg8eLFsLW1haGhIerXrw8PDw+cP3++3O/1+vXrGDt2LBo3bgwDAwPY2Njgq6++KjIlp0ePHujduzcA4IMPPlBORUlOTi6z/z179uDhw4cYP348vLy88PTpU5X3RiQmJkIQBCxevBh79+5F586dYWRkBEtLS8yZMwf5+fnFXvPLL7/A3t4ehoaGsLa2xqJFi3Dw4EGVY6WKXC7H2rVr0alTJxgbG6NOnTro3bs3oqKiynwtAGzbtg0KhQJ+fn5F9k+aNAmGhoblykBERFTdsSin1+Lt7Q1BEFROYQkLC0NWVlaxq+Rr166Fnp4eJk2ahHXr1sHHxwfHjx9H9+7dce3aNbXmy8vLQ79+/bBo0SI4OTlh1apV+Pzzz3HhwgV0794df/31V5l9JCUl4e2338bOnTsxZswYfP/99+jYsSOWLFmCAQMGoKCgAADg7++POXPmAACmTJmCLVu2YMuWLeW6ah4UFAQbGxt0794dnTp1Qvv27fHf//63xPbh4eHw9fXFgAED8N1336Fdu3b49ttv8d133xVpt3XrVowcORK5ubmYP38+pk2bhrCwMHz55ZdlZnphzJgx+PTTT9GmTRsEBATg66+/xsOHD9G7d2/89ttvZb7+7Nmz0NXVLfIPMwAwNjaGvb09zp49W+4sRERE1ZaC6DW5uroqdHV1FSkpKUX2d+3aVaGvr69ITU0tsj8zM7NYH3///beiVq1aio8//rjIficnJ0XLli2L7HvjjTcUvXv3LtbHoUOHFAAUW7ZsUe5bvny5QhAExaFDh4q0zcjIKLGfV40YMUIBQBEZGVlkv5+fnwKAIiQkpNQMZbl165ZCR0dHsWjRIuW+FStWKAAorl69WqRtQkKCAoCidu3aips3byr3FxQUKN58802FTCZT7svLy1M0btxY0aRJE0VGRoZy/5MnTxRWVlbFcqrK/ssvvygAKIKCgorkyMvLU3Ts2FFhY2NT5vt78803FZaWliqPeXp6KgAo8vPzy+yHiIioOuOVcnptPv/H3t3H1Xz/fxx/nEpXLheSdpQuMCKNGsNIWGNb1hi5isaYYWO231yMfc02l9/vbPqKvkyuvvKVrzBErjIMZVqbmEyklEoRuq7z+6M5X+nCiVOni9f9dju3+Xw+78/78zwfaa/zOe/P+zN+PAUFBWzatEm97tKlS5w+fRoPDw+aNWtWrP3DcdIqlYqMjAxSU1OxsLDA3t6eM2fOaDXb5s2bcXBwwMnJidTUVPUrPz9fPQQjJyenzP3z8/P58ccfcXFxwd3dvdi2h1ebd+7c+UwZ169fj0qlYsyYMep1o0ePxsDAoMyr5UOGDMHKykq9rKenh6urK/Hx8eohNWfPnuXWrVv4+PjQpEkTdduGDRsyadIkjbJt3ryZJk2a8OabbxY7f3fv3uWNN97gypUrXL16tdw+MjMzMTIyKnWbsbExwFPPzCOEEELUFnKjp3hmb7/9Nk2aNGH9+vV89tlnAOpi8t133y3R/ty5c8ybN4/jx4/z4MGDYtvatGmj1WyXLl0iNzeX5s2bl9kmLS2Nli1blrrt1q1bZGZm4uDgUGJbs2bNaNGixROL0vKoVCrWr19Ply5dyMvL48qVK+pt3bt3Z8OGDXz11Vfo6+sX28/W1rZEX02bNlW/n+eff57Y2FgA2rVrV6JtaetKc/HiRe7cuYO5uXmZbW7dulVqnodMTU3JyMgodVt2djZAnZiZRwghhCiPFOXimRkbGzNy5EhWrVrFqVOn6NatG5s2bUKpVPLqq68Wa3vt2jV69+6NmZkZ8+fPp23bttSvXx+FQsG0adPIy8t74vEUCkWp60u7ybGwsBAnJyeWLVtWZn/ljflWVfJ0fYcPH+batWtcu3atzA8k+/fv54033ii27vEi/VEPM2sju0qlwsLCoti3II/r0KFDuX1YWlpy5coV8vPzMTAo/isnISEBCwuLct+PEEIIURdIUS60Yvz48axatYr169eTlpZGUlISc+fOLVFs7dixg8zMTEJCQnjllVfU61UqFampqTRu3PiJxzIzMyMtLa3E+tKuWLdp04aUlBT69etXZjFfHgsLC0xNTblw4UKJbbdv3yY5OZnu3btXuN+HfvjhB0xMTNiwYUOp+SZMmMC6detKFOWasLGxAeCPP/4osa20daVp06YNoaGh9OjRA1NT0wpnAHBxceHIkSOEh4fz8ssvq9dnZWURFRVV6kw6QgghRF0jY8qFVnTp0gUnJye2bduGr68vCoUCHx+fEu0eFumPX8VdvXo1qampGh2rbdu2REdHk5iYqF6XnZ3NqlWrSrT19vYmISGB7777rtS+bt26Ve6xDAwMeOONNwgPD+fQoUPFtn3zzTeoVCo8PT01yv249PR0du7cyWuvvcY777zD0KFDS7zefPNN9u7dS3JycoX779atG+bm5qxfv547d+6o19+7d481a9Zo1Ie3tzf5+fllztbypPMH4OXlBcCKFSuKrV+9ejXZ2dmMGjVKoyxCCCFEbSZXyoXWjB8/nmnTpnHgwAFcXV2xs7Mr0eb1119nzpw5jBo1iilTptC4cWNOnjxJSEiI+sruk0ydOpWgoCD69evHpEmTyMnJYePGjTRo0KBE248//phDhw4xY8YMDh06hKurKw0bNiQuLo7Dhw/TsGFDQkNDyz3e4sWLOXz4MG+++SZTpkzB1taWY8eOsX37dvr27cvo0aM1O0GP2bJlC9nZ2QwZMqTMNkOGDGHz5s1s3LiRTz75pEL916tXj2XLljF27Fi6devGu+++i56eHgEBAZibmxMXF/fEbw+8vLzYv38/K1asICIigkGDBtGsWTPi4+M5efIkcXFxXL58udw+nJyceP/991m9ejUFBQUMHDiQ33//HV9fX9zc3Bg+fHiF3pcQQghRK+lq2hdR+6SlpamMjY1VgGrjxo1ltjt69KiqR48eqgYNGqiaNGmiev3111UXLlwodfrD0tapVCrVunXrVG3atFHVq1dPZWNjo1q2bJnqwIEDpU5HmJeXp/r2229VXbt2VZmamqpMTU1V9vb2qtGjR5eYKrEsf/75p2rkyJGq5s2bq+rVq6eytbVVzZkzR5WZmVmsXUWmRHRyclIZGhqq7ty5U2abzMxMVf369VXt27dXqVT/mxLx0ekTH5o7d64KUN24caPY+q1bt6o6duyoMjQ0VLVq1Ur15ZdfqrZv364CVDt27NAoe0BAgKpnz56qhg0bqoyNjVWtW7dWDRkyRLV9+/Ynvk+VSqXKz89XLV26VNWmTRuVoaGh6vnnn1fNnDmz1OkxhRBCiLpIoVJV8p1sQohqZ8mSJcyaNYvw8HCcnZ11HUcIIYSo86QoF6IWy83NRV9fv9gNt/fu3aNjx45kZWWRkJBAvXr1dJhQCCGEECBjyoWo1S5fvoyHhwdeXl7Y2NiQkJBAQEAAcXFx+Pv7S0EuhBBCVBNSlAtRi7Vo0YKXXnqJzZs3k5ycjIGBAY6OjixfvpyhQ4fqOp4QQggh/iLDV4QQQgghhNAxmadcCCGEEEIIHZOiXAghhBBCCB2TolwIIYQQQggdk6JcCCGEEEIIHZOiXAghhBBCCB2TolwIIYQQQggdk6JcCCGEEEIIHZOiXAghhBBCCB2TolwIIYQQQggdk6JcCCGEEEIIHZOiXAghhBBCCB2TolwIIYQQQggdM9B1gOqgWbNmtG7dWtcxhBCiwq5du0ZqaqquYwghhHhGUpQDrVu3JiIiQtcxhBCiwpydnXUdQQghhBbI8BUhhBBCCCF0TKdFeUhICO3atcPe3p7FixeX2H78+HG6dOmCgYEBQUFB6vVHjx7FyclJ/TI2NiY4OBiAcePGYWNjo94WGRlZZe9HCCGEEEKIp6Gz4SsFBQVMmTKF0NBQlEolLi4ueHh40KFDB3UbKysrAgICWL58ebF9+/btqy6209LSsLe359VXX1VvX7ZsGUOHDq2aNyKEEEIIIcQz0rgoz8rKwsTERGsHPnv2LPb29tja2gLg5eXFrl27ihXlD2++1NMr+4J+UFAQAwcOxNTUVGvZhBBCCCGEqEoaD19p2bIlkydP5ty5c1o5cEJCAq1atVIvK5VKEhISKtxPYGAgI0aMKLZu7ty5ODo6MmPGDHJyckrdz9/fH2dnZ5ydnUlJSanwcYUQQgghhNAWjYvyHj16sHbtWl566SWcnJzw9fXlzp07T31glUpVYp1CoahQH4mJifz222+4u7ur1y1atIhLly4RHh5OWloaS5YsKXXfiRMnEhERQUREBM2bN69YeCGEEEIIIbRI46J83759XL9+nS+//JIHDx7w4YcfYmlpyahRozh69GiFD6xUKrlx44Z6OT4+HktLywr18Z///AdPT0/q1aunXteyZUsUCgVGRkb4+Phw9uzZCmcTQgghhKiw5GRYuhRGj4Y33yz679KlIN/ICw1UaPYVS0tL5s6dS0xMDIcPH+btt98mODiY/v37Y2dnxzfffMPNmzc16svFxYWYmBhiY2PJzc0lMDAQDw+PCoXfunVriaEriYmJQNGV+ODgYDp27FihPkXlUCwp/SWEEELUeOHh8PbbYG0NX3wBW7bAjz8W/fdvfwMrq6Lt4eG6TiqqsaeeErFv375s3ryZmzdvMmrUKGJjY5k3bx6tW7fG09PziVeoDQwM8PX1xd3dnfbt2zNs2DAcHByYP38+u3fvBiA8PBylUsn27duZNGkSDg4O6v2vXbvGjRs36NOnT7F+R40aRadOnejUqROpqal8/vnnT/sWhRBCCCHK5+cHrq4QHAzZ2UWvR2VlFa0LDi5q5+eni5SiBlCoShvcrYHU1FQ2bdrEunXriI6Opn79+gwfPhwjIyM2b97MgwcP8PPz47333tN2Zq1zdnaWJ3pWsrKuiqs+q9ocQtQ28vtLCB3y84NPPoHMTM33MTWF5cth8uTKyyVqpAoV5SqVigMHDrBu3Tr27NlDbm4uL774Iu+99x6jRo2iYcOGANy9e5chQ4Zw+fJl4uLiKi28tsj/1Cq/aJaivHaQv8fqR35/CaEj4eFFV74fK8jTgPHAQaAZsAgY+fi+pqYQFgbOzlUQVNQUGs9TPn/+fAICAkhISKB+/fqMHTuWiRMn0rVr1xJtGzduzNixYxk3bpw2s9YZUvgIIYQQ1dyiRUVDUx4zBTAEbgGRwOtAZ8Dh0UZZWUX779hRBUFFTaFxUf7VV1/RtWtX5s2bx8iRI6lfv3657bt06cL8+fOfOaAQQlRUaR9s5UOtEEJrkpNh/354bLDBA2AH8DvQAOgFeACbgMWPNlSpYN++ollZZFpm8ReNi/JffvkFJycnjTt2cHAodmOmKElmH5FhM9WV/GzqjvzMClEDBASUuvoyoA+0fWRdZyCstMYKRVE/n36q5XCiptK4KP/444+ZO3cu/fr1K3X70aNHWbhwIUeOHNFaOCEeV9MLlpqeXwghBBAVVXKWFeA+0PixdY2Be6X1kZUFv/2m/WyixtK4KD927BgTJkwoc3tycjJhYaV+FhSi0smV3dpNPswIIaqVu3dLXd0AyHhsXQbQsKx+0tO1l0nUeBoX5U9y584djIyMtNVdjSSFQ90jf+dCCFEHNX78eniRtkA+EAO0+Wvdrzx2k+ejnntO28lEDVZuUR4VFUVkZKR6+aeffiI/P79Eu7S0NFatWkWHDh20n1CHpOCSc1DbyTcM8jMuhHgKjo5FM6c8NoSlPvA2MB9YS9HsK7uAU6X1YWICnTpVclBRk5RblO/cuZMFCxYAoFAoWLNmDWvWrCm1bcOGDfn++++1n1CIakCK15pP/g6FEFozbhx88UWpm1YB7wLmQFPAjzKulKtURf0I8Zdyi/Jx48bh6uqKSqXCzc2NOXPmMGDAgGJtFAoFDRo0oEOHDhgbG1dq2JpKioG6R/7Oi9TGq9Daek/yMyJEDWZuDgMHQnBwiWkRzYDgJ+2vUMCgQTIdoiim3KLc2toaa2trANavX0/v3r2xsbGpkmBCc9Wp8JFCo3qSv5fKV53+HQohqsDs2XDgQIknemrExKRofyEeofGNnmPHjq3MHDp1LqluFS116b1WlJwbIYQQGnFxgeXLyZ42DeOCAo13U5mYoFi+HJydKzGcqInKLMo3btwIwJgxY1AoFOrlJ/H29tZOMiGEXH2tBeSDnhC11zYzM44VFOBrZIR+bm6JoSyPUikUZAF/f+455k2eXHUhRY1RZlE+btw4FAoFXl5eGBoaqpdV5fzAKRQKKcrriMouNKSQEUIIUZ3dvHmTMWPGMGnqVPTHjoVFi2DfvqLx4llZ/2toYgIqFYpBg7g7bhxfvv029/7v/1i6dKnuwotqqcyi/OjRowAYGhoWWxZSMAohhBB1WWFhIT169MDW1paVK1cWrdyxA1JSICCg6Emd6elF85B36lQ0y0rz5rQE/P39GT9+PG+88Qa9e/fW4bsQ1U2ZRXmfPn3KXdaGkJAQPvroIwoKCpgwYQKzZs0qtv348eNMnz6dqKgoAgMDGTp0qHqbvr4+nf6a39PKyordu3cDEBsbi5eXF2lpaXTp0oVNmzapP1jUNfLhoWw1/dzIsJYiNf3vUQhRM40fP56kpCTi4+OLb2jeHD79tNx9fXx8CA4OZtCgQSQlJdGgQYNKTCpqEq080TMnJ6fCT/MsKChgypQphIaGolQqcXFxwcPDo9gDiKysrAgICGD58uUl9jcxMSn2YKOHPvvsM2bMmIGXlxfvv/8+69atY3ItGbslBYh4EvkZqb3K+rvtWrUxhKjzdu3axYYNGwgODqZZs2ZP1cfOnTtp2bIlffv2JTw8XMsJRU2lp2nD/fv387e//a3YulWrVtGoUSPq16/PyJEjycvL0/jAZ8+exd7eHltbWwwNDfHy8mLXrl3F2rRu3RpHR0f09DSLqVKpOHLkiPqK+tixYwkOfuJsoUIIIYQQT5Samsrw4cMZN24cHh4eT92Pnp4eJ06c4Pz58yVqK1F3aXylfNmyZZibm6uXL168yEcffYSdnR02NjZs27aNl156ienTp2vUX0JCAq1atVIvK5VKzpw5o3Hw7OxsnJ2dMTAwYNasWbz11lvcvn2bJk2aYGBgoO4zISGh1P39/f3x9/cvWniQovFxhRAl1cYr9LXxPQkhnk3Pnj2xtLRk7dq1z9xXmzZt+P7775k2bRqvv/46Li4uWkgoajKNi/KLFy8yaNAg9fK2bdswMTHh7NmzNGrUiJEjR7JhwwaNi/LSZnFRKBSaxiEuLg5LS0uuXr2Km5sbnTp1olGjRhr3OXHiRCZOnFjURilzhQpRlWRMvBCippkyZQqxsbFcu3ZN42/wn+SDDz5g586d9O/fn1u3bsmT0es4jX+q0tPTi42dOnToEG5ubupC2NXVldjYWI0PrFQquXHjhno5Pj4eS0tLjfd/2NbW1hZXV1fOnz9Ps2bNuHPnDvn5+U/VpxBCCCHE40JDQ/Hz82PTpk1aryv27t2LgYEBr776qlb7FTWPxkV5s2bNuH79OgD37t0jPDycXr16qbfn5eVRUIEnWrm4uBATE0NsbCy5ubkEBgZqPD4rPT2dnJwcoGh818mTJ+nQoQMKhYK+ffsSFBQEwIYNGxg8eLDGmYTQFcWS0l9CCCF0686dOwwePJjhw4czfPhwrfdvaGjI0aNHOXnyJMuWLdN6/6Lm0Lgof/nll1m9ejVBQUFMnz6d/Pz8YsNZrly5QsuWLTU+sIGBAb6+vri7u9O+fXuGDRuGg4MD8+fPV09vGB4ejlKpZPv27UyaNAkHBwegaCiNs7MznTt3pm/fvsyaNUs9a8uSJUv4xz/+gb29Pbdv32b8+PEaZxJCCCGEeFTv3r0xMzNjy5YtlXYMR0dHFi1axKxZs/j9998r7TiielOoyntE5yOio6Pp27cvKSlFN0WOHTuW9evXA0Xjw21sbOjbt696XU2iUDrDtAhdxxCizitrTLl8a1C2rtudiYiQ319CVIb/+7//49tvv+XKlStYW1tX+vFeeeUVoqOjuXXrlnrSClF3aPw33qFDBy5evMjJkydp3LhxsadQ3blzhxkzZuDq6loZGYUQdYQU30KI6uLEiRMsX76c9evXV0lBDkVj11u0aMHAgQMJDQ2tkmOK6kPjK+W1mVwpF0LUVHKlXAjtu3//PhYWFvTr16/EM1QqW3h4ON27d+e7775j6tSpVXpsoVtP9d1IZmYmt2/fLnVaQysrq2cOJYQQQgihK3379qV+/frs3Lmzyo/t4uLCvHnzmD59OgMGDKBdu3ZVnkHohsZFeWFhIUuXLmXlypUkJSWV2a4iM7AIIYQQQlQnf/vb3zh//jwXL17U2nzkT5Nh79699O7dm8TERJ3lEFVL46J81qxZLF++HAcHB4YMGULTpk0rM5cQQgghRJUKDw9n4cKFrFy5kjZt2ug0y9GjR7GwsMDT07PKh9AI3dB4TLmlpSVOTk7s27evsjNVORlTLoSoqWRMuRDakZ2dTYsWLejevTsHDhzQdRyg6GbT3r17s27dOnx8fHQdR1SyCj3RUx7EI4QQQojaaMCAARgYGLB3715dR1Hr1asXn3zyCRMnTlQ/wFHUXhoX5Z06dSIxMbEyswghhBBCVLmlS5dy6tQpwsLCqt384EuXLqV9+/b07NmTwsJCXccRlUjjovyLL75g9erV3LhxozLzCCGEEEJUmaioKGbPns3SpUvp2LGjruOU6vjx46SlpTFy5EhdRxGVSOOPg+fOncPa2poOHTrg6emJjY0N+vr6xdooFArmzZun9ZBCCCGEENqWm5uLq6srPXv2ZObMmbqOU6YmTZqwa9cu3N3d8fT0ZPjw4bqOJCqBxjd6ajIdj0KhqJFTIsqNnkKImkpu9BTi6Q0YMIDw8HCSkpIwNjbWdZwnmjZtGmvWrOHatWtYWlrqOo7QMo2vlMfGxlZmDiGEEEKIKuPr68uRI0c4c+ZMjSjIAVauXEloaCg9e/bkzz//lPnLaxmNi3Jra+vKzCGEEEIIUSX++OMPpk+fzvz583F2dtZ1nAo5ceIESqWSCRMm8MMPP+g6jtCip/qIdeXKFU6ePMndu3e1nUcIIYQQotIUFhbSu3dvunTpwhdffKHrOBXWrFkz/vOf/xAQEMDu3bt1HUdoUYWK8h9//BE7OzvatWtH7969OXfuHADJycnY29sTFBRUKSGFEEIIIbTB09OTzMxMjh07pusoT83Dw4Nx48YxbNgwUlNTdR1HaInGRfmxY8fw9PTEzMyML774gkfvDzU3N8fOzo7AwMBKCSmEEEII8azWr1/Pnj172L9/P6amprqO80zWrl2LpaUlvXr10nUUoSUaF+VffvklnTt35syZM0yZMqXE9pdffplffvmlQgcPCQmhXbt22Nvbs3jx4hLbjx8/TpcuXTAwMCh2FT4yMpKXX34ZBwcHHB0d2bZtm3rbuHHjsLGxwcnJCScnJyIjIyuUSQghhBC1x+LFi1m1ahXXr19n4sSJfPrpp7WikNXT0+PEiRNcvXqVKVOmEBcXh6enJ/n5+bqOJp6SxkV5REQEo0aNKvNOX6VSSVJSksYHLigoYMqUKezfv5/o6Gi2bt1KdHR0sTZWVlYEBASUmCzf1NSUjRs3cuHCBUJCQpg+fTp37txRb1+2bBmRkZFERkbi5OSkcSYhhBBC1C4LFy5kypQptG3blhdeeIElS5boOpLWWFpasmnTJlatWkXr1q0JDg7m6NGjuo4lnpLGRXlBQQFGRkZlbk9NTcXQ0FDjA589exZ7e3tsbW0xNDTEy8uLXbt2FWvTunVrHB0dS3wQaNu2LW3atAGKfiDNzc1JSUnR+NhCCCGEqBsyMzOBogcFXb16laioKB0n0p7CwkI2bdoEoB5WfPDgQV1GEs9A46K8ffv2/PTTT2Vu//HHH+ncubPGB05ISKBVq1bqZaVSSUJCgsb7P3T27Flyc3Oxs7NTr5s7dy6Ojo7MmDGDnJycUvfz9/fH2dm5aCqkB1LQCyGEELXNhQsXii1nZmbWqivlN2/eZO/evcXWnT59WkdpxLPSeJ7y8ePH8+GHH9K/f388PDyAoid4ZmZmMmvWLH7++Wc2btyo8YFLe5CoQqHQeH+AxMRExowZw4YNG9RX0xctWoSFhQW5ublMnDiRJUuWMH/+/BL7Tpw4kYkTJxYdV1mz5igVQgghBJCcDAEBEBUFd+9C48bg6Ag+PtC8OVu3blU3NTMzw8/Pj2HDhukur5YplUoSExMZPXo0hw8fBij2hN/k6ykEBF4gKt2Au4X1aKyXh+Nz+fiM6Ehzq2a6ii3KoHFRPnnyZE6ePMl7773HzJkzUSgUjBgxgtu3b1NQUICPjw+jRo3S+MBKpZIbN26ol+Pj4yv0yNiMjAxef/11vvrqK7p3765e37JlSwCMjIzw8fFh+fLlGvcphBBCiBogPBwWLYL9+4uWs7P/t+2//4UvvoCBA1Hdv0+9evXYsGEDI0aM0E3WSmZhYcGhQ4eIj4+nf//+XL9+nfDD0Sw6mMH+hk7AS2Q/97+ZZv6bl8kXGxUMvHea2a82wqVfB92FF8VoXJQDbN68mSFDhrB582YuXbqESqWiW7dueHt7M2TIkAod2MXFhZiYGGJjY3nkXBt8AAAgAElEQVT++ecJDAzk3//+t0b75ubm4unpibe3N++8806xbYmJibRs2RKVSkVwcDAdO3asUC4hhBBCVGN+fvDJJ5CVBaV8605WVtF/g4P52sSEr7/7DmppQf4opVLJpUuX8FsRhuspa7KaGKPS0y/RLqteUYEe3MSFA6eyWf5bGJOn96nquKIUClVp40iqyL59+5g+fToFBQW8++67zJ07V/3IWw8PD8LDw/H09CQ9PR1jY2MsLCy4cOECmzdvxsfHBwcHB3VfAQEBODk54ebmRkpKCiqVCicnJ1avXk2DBg3KzaFQOsO0iHLbCCFEddR1u3Oxr6uFqNUeFuR/3bypEVNTWL4cJk+uvFzVhN+KMD6550ymYX2N9zHNfcDyhhFSmFcDOi3KqwspyoUQNZUU5aLOCA8HV9diBXkO8AFwCEgD7IFvgIGP72tqCmFh4Fx77yELPxyN6ynrkgX5KV84FwBJv0HnETAsoMS+prkPCOt5HWc3GcqiSxrNvnL37l2++eYbevbsSfPmzTEyMqJ58+b06tWLxYsXk5GRUdk5hRBCCFGXLVr0v6Epf8kHWgFhwF1gITAMuPb4vllZRfvXYosOZpBlYFxyQyNLcPscnN8tc98sA2MWHbhbiemEJp54pTwqKopBgwaRmJiISqWiYcOGNGrUiIyMDO7duwcUjWMKCQmhQ4ea+QlLrpQLIWoquVIu6oTkZLC2Ln5DZxkcgS+AEne6GRtDXBw0b14JAXUr+XoK1psakl2vlKL8oQOfw934Uq+UAxjnZRHn/UBmZdGhcq+UZ2dnM2TIEFJSUpgzZw6xsbHcvXuXGzducPfuXWJjY5kzZw63bt3i7bffLnNOcCGEEEKIpxYQoFGzW8BlwKG0jQqFxv3UNAGBF4DCZ+pDgYqArb9rJ5B4KuUW5YGBgfz555/8+9//ZuHChVhbWxfbbm1tzVdffcXmzZu5fPkygYGBlRpWCCGEEHVQVNQTr5LnAaOAscALpTXIyoLfftN+tmogKt2A7HqmT25Yjqx6pvyWXqFJ+YSWlVuU7969m5deeumJ0x2+8847vPTSS+zatUur4YQQQgghuFv+eOdCYAxgCPiW1zA9XXuZqpG7hfW00k+6lvoRT6fcovzXX3/l1Vdf1aijV199lV9//VUroYQQQggh1Bo3LnOTChhP0dCVHUC5ZeVzz2k1VnXRWC9PK/08p6V+xNMptyhPSUnByspKo46srKxISUnRSighhBBCCDVHx6IbNUsxGbgI7AFMyuvDxAQ6ddJ+tmrA8bl8jPPKmLu9IB/yskFVUPTKyy5a9xiTvEw6PVdyvag65RblDx48wNRUszFKJiYmPHjwQCuhhBBCCCHUxo0rdfV1YA0QCVgADf56bSmtsUpVZj813TgvB8os6Y58BfNM4NhiOL+56M9HvirRTIWCcSPkKei6VO6IfnmukBBCCCF0ztycOAcHnj93jkcfHG9N0fCVJ1IoYNCgWjkdIoC5dXMG3jtNcBMXVHr6xTcO+FvRqxyKwgIGZkTS3OrlSssonuyJt9n+/e9/12hWlYSEBK0EEkIIIYR46P79+7z++utknTvHTwYG6Oc/xRALExOYPVv74aqR2a824sCp7JJP9NSASX42sTs+5UC/ebi7u1dCOqGJJxbl58+f5/z58xp1plAonjmQEEIIIQRAUFAQ3t7eNGjQgJBz5zA6cwY++QQyyxg/XRpTU1i+HJydKy9oNeDSrwPLfwvjk3vOFSrMTXMfsLRBOMe6tGTgwIEMHjyY7du3Y2Ag0yNWtXLHlBcWFlboVVBQUFW5hRBCCFFLZWdnM2DAAIYNG4aXlxdJSUl06dIFJk8uKrBNTYuGpJRHofhfQT55ctUE17HJ0/uwvGEEprkPUBSWX5MpCgswzX3A8oYRTJnhyvbt2wkNDeXw4cM0a9aMY8eOVU1ooVZuUS6EEEIIUZV2795N06ZNOX/+PD///DM//PADenqPlCuTJ0NYGHh6Fs3IYvLYnCsmJkXrPT2L2tWRgvyhydP7ENbzOp53zmKcl4XJY7OymORlYpyXheeds4T1vM7k6X3U2/r160dqaip9+vTBzc0NLy8v8p9muJB4KgqV3M2JQukM0yJ0HUMIISqs63ZnIiLk95eo+XJzc/H09GT//v2MHDmSjRs3Fi/GS5OSAgEBXN6xgysREQwaObJo2sNx42rtTZ0VkRKXSsDW3zkSc4c7hfVoY96YTs/lM25ER5pbNSt333379jFs2DAMDQ3Zs2cPPXv2rKLUdZcU5UhRLoSouaQoF7XBgQMHGDp0KAYGBuzZs4devXpVaH9/f39mzpzJvXv3KilhzfbBBx+wb98+rl27VqH9srOzeeuttzh48CBjxoxh/fr1T/6gJJ6aTs9sSEgI7dq1w97ensWLF5fYfvz4cbp06YKBgQFBQUHFtm3YsIE2bdrQpk0bNmzYoF5/7tw5OnXqhL29PR9++KFM6yiEEEJUU/n5+Xh6ejJw4EBee+01UlJSKlyQi8pjbGxMSEgIO3bsYPv27ZibmxMeHq7rWLWWzorygoICpkyZwv79+4mOjmbr1q1ER0cXa2NlZUVAQAAjR44stj4tLY0FCxZw5swZzp49y4IFC0hPTwdg8uTJ+Pv7ExMTQ0xMDCEhIVX2noQQQgihmSNHjtC0aVMOHz5MaGiozPhRjXl6epKamkrnzp3p1q0b7733HoWFhbqOVevorCg/e/Ys9vb22NraYmhoiJeXF7t27SrWpnXr1jg6Opb4quTAgQMMGDAAMzMznnvuOQYMGEBISAiJiYlkZGTw8ssvo1Ao8Pb2Jjg4uCrflhBCCCHKkZ+fj5eXF/3798fV1ZXU1FT69eun61jiCUxNTTl8+DBbt25l8+bNWFpaEhkZqetYtYrOivKEhARatWqlXlYqlRo/gKisfRMSElAqlRr16e/vj7OzM87OzvAg5SnfhRBCCCE0deLECczNzfnxxx/58ccf2bVrF4aGhrqOJSpg+PDhpKSk0LZtW7p06cKUKVPkqrmWaFyUDxgwgG3btpGbm6uVA5c21lvThw+VtW9F+pw4cSIRERFFN0jVlzu0hRBCiMpSWFiIt7c3vXv3plu3bqSmpjJo0CBdxxJPqUGDBhw/fpyAgADWrVtHq1atuHDhgq5j1XgaF+Xnzp1j5MiRWFpaMn36dH777bdnOrBSqeTGjRvq5fj4eCwtLZ9pX6VSSXx8/FP1KYQQQgjtCw8Px9zcnB07drBz507279+PsbGxrmMJLfD29iYpKYlWrVrh6OjIzJkzdR2pRtO4KE9KSmLLli28+OKLrFy5EicnJ7p168a//vUv7t+/X+EDu7i4EBMTQ2xsLLm5uQQGBuLh4aHRvu7u7hw8eJD09HTS09M5ePAg7u7utGzZkoYNG3L69GlUKhUbN25k8ODBFc4mhBBCiGdTWFjIhAkT6NatG05OTqSkpMj/k2uhJk2acPr0adasWYOvry9WVlbExMToOlaNpHFR/vBmzNDQUK5evcrnn3/OrVu3mDRpEi1btmT8+PGcPHlS4wMbGBjg6+uLu7s77du3Z9iwYTg4ODB//nx2794NFH26ViqVbN++nUmTJuHg4ACAmZkZ8+bNw8XFBRcXF+bPn4+ZmRkAfn5+TJgwAXt7e+zs7Bg4cGBFzocQQgghnlFkZCSWlpZs2bKFwMBADh06hKmpqa5jiUo0YcIEEhMTMTc354UXXmDu3Lm6jlTjPNPDg1QqFaGhofj6+rJ3714A2rVrx6RJk5gwYQL169fXWtDKJA8PEkLUVPLwIFGdFBYWMm3aNPz8/OjVqxf79u2jQYMGlX5ceXhQ+Z724UFPy9fXlxkzZmBlZcWhQ4ewsbGpkuPWdM80+0pkZCS7d+/mp59+QqVSYWdnh56eHjNmzMDe3p5Tp05pK6cQQgghqrELFy7QqlUr1q1bx8aNGzl+/HiVFOSi+pk6dSoJCQnUr18fe3t7vvzyS11HqhEqXJTfuXOHf/7zn3Tp0gVnZ2fWrl2Lu7s7hw4d4vLly/z+++/qr6mmTJlSGZmFEEIIUY3MnDkTR0dHWrVqRXJyMqNHj9Z1JKFj5ubmREVFsWzZMhYuXEjbtm2Ji4vTdaxqTeOi/MiRI4waNQpLS0umTZtGZmYmS5cuJSEhgcDAQNzc3NRt3dzcmDVrlkyPI4QQQtRiMTExWFlZ4evry5o1azh9+jSNGjXSdSxRjXz88cdcv34dfX19bG1tWbp0qa4jVVsaF+X9+/fnv//9L56enhw9epRLly4xc+ZMmjZtWmp7e3t7evbsqbWgQgghhKg+5syZwwsvvIC5uTmJiYlMmDBB15FENWVpacnFixdZuHAhc+bMwcHBgaSkJF3HqnY0Lsr//ve/k5CQwJYtW+jTp88T2/ft25ejR48+UzghhBBCVC+xsbHY2dmxbNkyvvvuOyIiItQzoAlRntmzZ/Pnn3+Sl5dHq1atWLFiha4jVSsaF+X37t3j5s2bZW6/cOGCDOQXQggharEFCxZgb29P/fr1SUhIYOrUqbqOJGoYa2trLl++zOzZs5k5cyadO3cmOTlZ17GqBY2L8gULFhAVFVXm9t9//50FCxZoJZQQQgghqo+4uDjatm3LV199xbJly4iKisLc3FzXsUQN9uWXX3L58mXu3buHUqnEz89P15F0TuOi/EnTmWdnZ2NgYPDMgYQQQghRfSxduhRbW1sMDAy4fv06H3/8sa4jiVrCzs6Oq1evMmPGDKZOnYqzszNpaWm6jqUz5RblGRkZxMXFqaewuX37tnr50VdkZCRbtmyhVatWVRJaCCGEEJUrKSkJBwcH5syZw8KFC4mOjsbS0lLXsUQttGTJEqKjo0lOTqZly5asW7dO15F0otyi/Ntvv8XGxgYbGxsUCgXTp09XLz/66tq1K4cOHeL999+vqtxCCCGEqCQrVqygVatW5OXlcfXqVWbPnq3rSKKWa9euHXFxcXzwwQdMnDiRHj16kJGRoetYVarc8Saurq5A0dCVL7/8Ek9PTxwdHYu1USgUNGjQgO7du9OjR49KCyqEEEKIypWcnMyAAQP4/fffmTt3rkzgIKrct99+y/jx43n11VcxNzdn3bp1jBo1StexqkS5RXmfPn3U0x9ev36d999/n27dulVJMCGEEEJUHT8/Pz766COUSiWXL1/Gzs5O15FEHdWxY0fi4+OZOnUqY8aMwd/fn71799KgQQNdR6tUGt/ouX79einIhRBCiFomLS0NZ2dnpk6dyowZM7h69aoU5ELn9PT0WLVqFREREVy8eBFzc3OCgoJ0HatSlXml/OHNnVZWVsWWn+RheyGEEEJUb+vWreODDz6gRYsWREdH065dO11HEqKYLl26kJSUxIQJExg2bBj9+vVjz549GBsb6zqa1ilUZcx1qKenh56eHpmZmRgaGqKnp4dCoXhihwUFBVoPWdkUSmeYFqHrGEIIUWFdtzsTESG/v0TFZGRk4O7uztmzZ/nwww/59ttvdR3pqcTExODq6kpGRgb379+nWbNm9OrVi507d+o6WrUQGhrK6NGjycjIIDc3FzMzM0aMGMH333+v62hP5cyZM7z++utkZWWxdetWPDw8dB1Jq8q8Uj5//nwUCoV67vGHy0IIIYSoubZs2cL48eMxMzPj119/pWPHjrqO9NQaN25c7GnjqampJCYm6jBR9dKoUaNiT8tMTU2t0TOadOvWjeTkZLy9vXnrrbcYOHAgO3fuxNDQUNfRtKLMK+VVISQkhI8++oiCggImTJjArFmzim3PycnB29ubc+fO0bRpU7Zt20br1q3ZsmULy5YtU7eLioril19+wcnJCVdXVxITEzExMQHg4MGDT3zqmFwpF0LUVHKlXGjq/v37vP766/z000+8//77+Pr6oqen8a1l1Za7uzsHDx5UL1+5ckXGxD+iTZs2XLlyBSgaBXHv3j1MTU11nOrZnThxgjfffJP8/HyCgoJwd3fXdaRnprN/jQUFBUyZMoX9+/cTHR3N1q1biY6OLtZm3bp1PPfcc1y5coUZM2bw2WefATBq1CgiIyOJjIxk06ZNtG7dGicnJ/V+W7ZsUW+XxwALIYSo64KCgjA3N+fSpUtERESwatWqWlGQA2zatEn9527duklB/pjNmzer/zxmzJhaUZAD9OrVi5SUFF577TUGDhyIp6cn+fn5uo71THT2L/Ls2bPY29tja2uLoaEhXl5e7Nq1q1ibXbt2MXbsWACGDh3K4cOHefzC/tatWxkxYkSV5RZCCCGqs8jISHVxkp2dzYABAxg2bBheXl4kJibSpUsXHSfULnNzczp06AAUXZQTxXXr1o1GjRoBsGrVKh2n0S4DAwO2b99OaGgohw8fpmnTphw5ckS9/ZdffqlRhXqZRbmenh76+voVej0cf66JhIQEWrVqpV5WKpUkJCSU2cbAwIDGjRtz+/btYm22bdtWoij38fHBycmJhQsXlijiH/L398fZ2RlnZ2d4kKJxbiGEEKK6+vPPP3nxxRfp378/u3fvpmnTppw/f56ff/6ZH374odZcHX9cWFgYs2fPlqvkZThy5AjLly+vNVfJH9evXz9SU1NxdXWlf//+eHl5cfz4cbp27YqXl5eu42mszCra29u7Um/sLK1Yfvx4T2pz5swZTE1Ni92ksmXLFp5//nnu3bvHkCFD2LRpE97e3iX6mThxIhMnTizqU+n81O9DCCGEqDTJyRAQAFFRcPcuNG4Mjo7g4wPNm5do/nA2irCwMMLCwhg1ahQbN26stcV4Wloae/bs4cqVK2RlZTFv3jzs7e3x8PDgueee03U8nXv0/Ny/f79Wnx9DQ0N27drFvn37eOedd9i2bRsAO3bs4Pr161hbW5fY5/Hz06BBA52enzKL8oCAgEo9sFKp5MaNG+rl+Ph4LC0tS22jVCrJz8/n7t27mJmZqbcHBgaWuEr+/PPPA9CwYUNGjhzJ2bNnSy3KhRBCiGorPBwWLYL9+4uWs7P/t+2//4UvvoCBA2H2bHBxAeDAgQPF7s3S19dn9erVtbIgv3DhAuvXr+fUqVMoFApycnLU24yMjFizZg09evTAx8cHBwcHHSbVjbp8fgYNGoS7u3uxaTE9PDz49ddf1cvV9fzo7F+qi4sLMTExxMbGkpubS2BgYIn5Jj08PNiwYQNQdJOKm5ub+kp5YWEh27dvL/a1RH5+PqmpqQDk5eXx448/1uipnoQQQtRBfn7g6grBwUXF+KMFOUBWVtG64OCidn5+ALz55pvFmhUUFLBgwYKqyVyFgoKCmDRpEmFhYeTm5hYrqKBo5rbc3FzCwsKYNGlSrX8K5OPk/EBwcHCx5aioKPUNwdX5/Gg+CFzbBzYwwNfXF3d3dwoKCnj33XdxcHBg/vz5ODs74+Hhwfjx4xkzZgz29vaYmZkRGBio3v/48eMolUpsbW3V63JycnB3dycvL4+CggL69+/Pe++9p4u3J4QQQlScnx988glkZj65rUpV1O6TT4Cir+9bt26Ni4sLnTp1wsXFhT59+lRy4KoVFBTEihUryH78g0opVCoV2dnZrFixAiiaMKK2k/NTJCYmhmPHjhEZGcmFCxc4ffo00dHR1f78lDlPuY2NDXp6ely6dIl69eoVK37L7Eyh4M8//9R6yMom85QLIWoqmae8FgkPL7ry/VhBPho4DDwALID/AyY8vq+pKYSFgXPtvUfqwoULTJo0qVhBVa9ePWbNmsVLL71Eo0aNiI+P55///CenTp0qtq+xsTH+/v7qWVpqo9LOD8CwYcN44403sLe358CBA6V+e1KXz0+jRo2YN28e3bt3586dO/j6+nLgwIFibarq/JQ5fMXa2horKyv1cBErKyusra3LfVlZWVVqWCGEEKLWWrSoaGjKY2YD14AMYDfwOXDu8UZZWUX712Lr168vMdRAX1+fW7duMXHiRFxdXfHz82PRokW0bNmyWLucnBzWr19flXGrXGnnByAlJYV169axe/fuMvety+fns88+Iy8vj1dffZXPP/+c2bNnl7gQXVXnp8zhK8eOHSt3WQghhBBakpxcdFNnKV9eP3qbmeKv159A10cbqVSwbx+kpJQ6K0tNl5aWxqlTp0rMypadnY2/v796+cSJE9y8eZP27duTmJioXq9SqTh58iTp6em1btYRKPv8ABw9ehSADh06lPlAxbp6foyNjXFzc2P48OFkZWXx66+/cvz4cQYNGoSvr6+6XVWdn9p3S7YQQghR0zxhxrMPAFPgBaAlMKi0RgrFE/upqfbs2aPRNM1mZmZYWVmVOpRWoVCwZ8+eyoinc5qen/LUxfNjbW1NQUEBcXFx6nWXL18udch2VZyfCt/omZOTw7Fjx7h69SoAtra29OnTB2NjY62HE0IIIeqEqKiSs6w8YhWwEvgZOAYYldYoKwt++60y0unclStXSh168Ch9fX0WLlzI3r17uX79eontOTk5XLlypbIi6pQm5+dJ6uL5MTEx4f79+8XW3b9/n/r165doWxXnp0JF+caNG/n4449JT09XfwWgUCho0qQJf//73xk3blxlZBRCCCFqt7t3n9hEH+gFbAb8gA9La5SertVY1cXjhdPjFAoFCxcuJD8/nyVLlpTZ7t69e9qOVi086fxoqq6dn6ysLBo0aFBsXf369Xnw4EGp7Sv7/GhclG/bto1x48ZhZWXFJ598QocOHVCpVERHR7N69WrGjx+PiYkJw4cPr8y8QgghRO3TuLHGTfMpGlNeqlo4HhgoUTg9bt68eZiZmfHRRx9RUFBQZruGDRtqO1q18KTzo6m6dn6uX7+Ovr4+rVq1Uj/Qsm3bturRII+r7POj8Zjyb775hhdeeIGoqChmzZqFh4cHgwcPZvbs2URFRdGmTRu+/vrryswqhBBC1E6OjlDKMNBkIBC4DxQAB4CtgFtpfZiYQKdOlRhSd+zt7TEyKnXQDrNnz8bGxoYZM2aUO4TDyMgIe3v7yoqoU+WdH319fQwNDdHT01P/WV9fv0S7unh+srOzOXr0KO+//z7GxsZ07tyZPn36sG/fvhJtq+L8aFyU//HHH/j4+NCoUaMS2xo3boyPjw8xMTFaDSeEEELUCWUM/1RQNFRFCTwHfAKsAAaX1lilKrOfmu7NN98sdWYRCwsLhgwZQtu2bTlw4ADHjx/n+PHjvPbaayXaqlSqEk89rS3KOj8A48eP59SpU/j4+DBo0CBOnTrF+PHjS7Srq+dn8eLFGBkZERoaytdff82iRYtKvVJeFedH4+ErFhYWZb4hAD09PVq0aKGVUEIIIUSdYm4OAwdCcHCxaRGbA2Ga7K9QwKBBtXI6RCiaVaVHjx6EhYUVq0WSkpJw1uCBSQqFgp49e9bK6f6g7PMD4O/vX2zayNLU5fOTkZHBJ389FbcsVXV+NL5SPm7cOAICAkodLJ+RkcEPP/yAj4+PVsMJIYQQdcbs2UVDUJ6GiUnR/rWYj49PmUM0nsTIyKjW1yhyfspXE85PmUX5w6+AHr569+6NqakpnTp1YtmyZezZs4cff/yRpUuX0rlzZxo0aMArr7xS6YGFEEKIWsnFBZYvJ9egYrMV5xsZwfLloMEV45rMwcGB6dOnV3gKZmNjY6ZPn16rHyEPcn6epCacH4WqjDEpenp6JSZaf7Tpw22PryvvrufqSqF0hmkRuo4hhBAV1nW7MxER8vurtjh+/Dhb+/RhpaEhBnl5pT7hU02hIEdfn5kqFfNv3izzaY21TVBQECtWrCAnJ6fcYbUKhQIjIyOmT5/O0KFDqzChbsn5KV91Pj9lFuUbNmx4qg7Hjh37TIF0QYpyIURNJUV57XH//n0sLCzo378/wZ9/DosWwb59RePFs7L+19DEpKhYHzQIZs/Gbvhw9PX1uXz5su7CV7Ho6GjWr1/PyZMnUSgUxWZdMTIyQqVS0bNnT3x8fGr9FeDSyPkpX3U9P2UW5XWJFOVCiJpKivLaw9nZmRs3bpCYmIie3l+jS1NSICCg6Emd6elF85B36lQ0y8pfN3UmJSVhbW3Nu+++i5+fn87y60J6ejp79uzhypUr3Lt3j4YNG2Jvb8+bb75Za29arAg5P+WrbudHinKkKBdC1FxSlNcO8+fP55tvvuHixYu0adOmwvsHBQUxbNgw9u/fj7u7eyUkFEJUtordTQLcunWLiIgI0tPTKSwsLLHd29tb475CQkLUT9+aMGECs2bNKrY9JycHb29vzp07R9OmTdm2bRutW7fm2rVrtG/fnnbt2gHQvXt3Vq9eDcC5c+cYN24cWVlZDBo0iO+++67E2HghhBCiuggPD+frr79m5cqVT1WQAwwdOpQRI0bw1ltvkZiYSJMmTbScUghR2TS+Ul5YWMiUKVNYu3ZtqcX4Q5re6FlQUEDbtm0JDQ1FqVTi4uLC1q1bi43dWbVqFVFRUaxevZrAwEB27tzJtm3buHbtGm+88Qa///57iX5feuklvvvuO7p3786gQYP48MMPGThwYLlZ5Eq5EKKmkivlNVt2djYtWrSge/fuHDhw4Jn6KiwsxNramiZNmvDbb79pKaEQoqpoPE/58uXLWbNmDSNGjGDDhg2oVCoWL17MP//5T9q0aYOzszOhoaEaH/js2bPY29tja2uLoaEhXl5e7Nq1q1ibXbt2qW8cHTp0KIcPHy73TtnExEQyMjJ4+eWXUSgUeHt7ExwcrHEmIYQQoir1798fAwMD9u7d+8x96enpcfLkSS5dusTMmTO1kE4IUZU0Lso3bNiAu7s7GzduVF957tq1K++//z7nzp0jNTWVc+fOaXzghIQEWrVqpV5WKpUkJCSU2cbAwIDGjRtz+/ZtAGJjY3nxxRfp06cPP/30k7q9Uqkst8+H/P39cXZ2LnoS2IMUjXMLIYQQ2rB48WJ+/vlnwsLCMKjg3ORlsbKyYu3atXz77bccO3ZMK30KIaqGxkX51atX1TJC8jwAACAASURBVMX4w7vC8/LyAKhfvz4+Pj6sXbtW4wOXdsW7vHnRH23TsmVL4uLiOH/+PP/4xz8YOXIkGRkZGvX50MSJE4mIiCj62rd+7XwssRBCiOopKiqKuXPnsnTpUjp27KjVvseOHcvgwYN54403Sn0KtxCietK4KDcxMaFevXoANGjQAIVCQXJysnq7hYUFN27c0PjASqWyWPv4+HgsLS3LbJOfn8/du3cxMzPDyMiIpk2bAkVX6+3s7Lh8+TJKpZL4+Phy+xRCCCF0KTc3F1dXV3r27Flpw0x27NhBw4YNcXV1rZT+hRDap3FRbm1tzZ9//glAvXr1sLe3JyQkRL390KFDtGjRQuMDu7i4EBMTQ2xsLLm5uQQGBuLh4VGsjYeHh/ohRkFBQbi5uaFQKEhJSVHfUHr16lViYmKwtbWlZcuWNGzYkNOnT6NSqdi4cSODBw/WOJMQQghR2QYNGkRhYSEHDx6stGPo6elx4sQJIiMjmTdvXqUdRwihPRoX5W5ubuzcuVO9PGbMGLZu3Urfvn1xdXVl+/btDBs2TOMDGxgY4Ovri7u7O+3bt2fYsGE4ODgwf/58du/eDcD48eO5ffs29vb2/OMf/2Dx4sVA0WOIHR0d6dy5M0OHDmX16tWYmZkB4Ofnx4QJE7C3t8fOzu6JM68IIYQQVWXlypUcPXqUQ4cOYWxsXKnHsrOzY+XKlXz99decOXOmUo8lhHh2Gk+JmJiYSFRUFK6urhgZGVFQUMCMGTPYvHkz+vr6DB06lG+//bbSf8lUBpkSUQhRU8mUiDXHH3/8gYODA/PmzeOLL76osuO+9tprnDp1iuTk5Br5/2gh6gp5oidSlAshai4pymuG/Px8LC0tsba2Jjw8vMqPbWFhQbt27Th58mSVHlsIoTmNh68IIYQQ4um89dZbZGVlERYWVuXHNjAwICwsjNOnT7No0aIqP74QQjMVnhj1P//5Dzt37uTq1asA2Nra4unpWaHx5EIIIURdsW7dOvbt28fx48cxNTXVSQYHBweWLVvGp59+ysCBA3FyctJJDiFE2TQevpKZmcngwYM5cuQIKpWKJk2aoFKpuHv3LgqFAldXV3bv3k39+vUrO7PWyfAVIURNJcNXqrfY2Fjatm3Lxx9/zJIlS3QdB1dXV6KiokhKSsLQ0FDXcYQQj9B4+MqcOXM4fPgw06ZN4+bNm6SlpZGens7NmzeZNm0aR48eZe7cuZWZVQghhKgxCgsL6dWrFx06dKgWBTnAwYMHUalUMjOZENWQxkX5tm3beOedd1ixYgUWFhbq9RYWFqxYsYIhQ4awbdu2SgkphBBC1DReXl6kp6fz008/6TqKmqGhIYcPH+bYsWN89913uo4jhHiExkV5RkYGffv2LXO7m5sbGRkZWgklhBBC1GRbt24lKCiIPXv20KhRI13HKaZLly4sWLCAmTNncvHiRV3HEUL8ReOi3NHRkZiYmDK3x8TE0KlTJ62EEkIIIWqqmzdvMnbsWKZOnUq/fv10HadUn3/+Oc7OzvTp04f8/HxdxxFCUIGi/KuvvuJf//oXe/bsKbFt165drF27lm+++Uar4YQQQoiapLCwkB49emBnZ8f333+v6zjlOnLkCFlZWbz11lu6jiKEoJwpEd99990S62xsbHjrrbdo164d7du3R6FQEB0dzR9//EGnTp3YsmULbm5ulRpYCCGEqK7effddkpKSiI+P13WUJzI1NSUkJIRXXnmFtWvXMmHCBF1HEqJOK3NKRD29ij9XSKFQUFBQ8MyhqppMiSiEqKlkSsTqY+fOnQwZMoTg4GA8PDx0HUdjc+bMYdmyZVy+fBkbGxtdxxGiztJ4nvLaTIpyIURNJUV59ZCcnIyVlRWjR49m7dq1uo5TYS+++CK3bt0iPj7+qS7KCSGenfzLE0IIIZ5Rr169eP755/H399d1lKcSFhbG3bt3GT58uK6jCFFnlTmmvCwqlYrz589z9epVAGxtbXnxxRdRKBRaDyeEEEJUd5MnT+batWvExcXV2KvMjRo1Ys+ePfTv358tW7YwatQoXUcSos6pUFEeEhLCBx98wPXr14utb926NatWrcLd3V2r4YQQQojq7MCBA6xZs4bAwMBiD9aridzc3Jg2bRo+Pj706dMHpVKp60hC1Ckaf6Q/efIkHh4epKen8+GHH+Lv74+/vz8fffQR6enpeHh4cOrUqcrMKoQQQuicn58fbm5uJCUl4enpyfDhwxk2bJiuY2nFd999h52dHT179iQuLo7OnTsTHh6u61hC1Aka3+jp7u7OxYsXOXPmDC1btiy2LTExkW7dutGhQwdCQkI0PnhISAgfffQRBQUFTJgwgVmzZhXbnpOTg7e3N+fOnaNp06Zs27aN1q1bExoa+v/s3XlcFfX+x/HXALIpoii4oQiiJqiRgftPyTUx8Bpk5o4optyS0kpNza3QXLIiTYtARMUtF8wlF9TSXCiX1Eox3EgFd5RNYH5/cD2JHBb1HA7g5/l48LjOzHe+8+bbFT/M+c53GDduHJmZmZiamjJ79mzNUoyenp5cvnwZCwsLAH788Ufs7OwKHwR50FMIUUbJg54lr1mzZpw4cQJFUahevTpXrlwps9NWtLlx4wY1atTQvFRo2LBhfPPNNwZOJUT5V+yfIgcPHiQwMDBfQQ5Qq1Ythg8fzoEDB4p94ezsbIKCgtiyZQunTp1ixYoVnDp1Kk+bsLAwqlatSnx8PO+88w4ffPABANWrVycmJobff/+dJUuWMHDgwDznLVu2jKNHj3L06NEiC3IhhBDicTx4pkpVVZKTk5k1a5aBE+lWYGBgnrd8Hjp0yIBphHh2FLsoz8zMxMrKqsDjlStXJjMzs9gXPnToEM7Ozjg5OWFqakrfvn3ZsGFDnjYbNmxg8ODBAPj5+bFz505UVeWFF16gdu3aALi6upKenk5GRkaxry2EEEI8qdTU1Dzb2t50XZbt3bs3z3Z8fLyBkgjxbCn2g55NmjQhOjqaoKAgTEzynpaVlcXKlStp0qRJsS+cmJhI3bp1Ndv29vYcPHiwwDYmJiZYW1tz/fp1qlevrmmzdu1aXnjhBczMzDT7/P39MTY2xtfXl4kTJ2pdGebBnHgA7iUXO7cQQojy68aNG8TExBAfH8/du3epVKkSzs7O+Pj4ULVq1TxThWrWrMl3331Hjx49DJhY95KSkliwYAHvv/8+9+7dy/NLSFHjI4R4csUuykeOHElgYCCdO3fm/fffx8XFBYCTJ08ye/ZsDh48+Fjrs2qbyv5o8VxUm5MnT/LBBx/w448/avYtW7aMOnXqkJKSgq+vL0uXLmXQoEH5+gkMDCQwMDC3T3v3YucWQghR/pw8eZLw8HD279+Poih5Pn01MzNj0aJFtG3bFjc3NywsLFixYgW9evUyYGL9GjVqFKNGjWLGjBl88sknnDhxgoiIiCLHx9/fH1dXVwMmF6LsKnZRPmzYMM6cOcOcOXP4+eef8x1/7733CAgIKPaF7e3tuXjxomb70qVLmikpj7axt7cnKyuL27dvY2Njo2nfu3dvIiMjadCggeacOnXqAGBlZUW/fv04dOiQ1qJcCCGEAFizZg3z588nIyND682gBwXonj17OHDgAJGRkeW6IH/YxIkTee6553jzzTeLPT7BwcH4+fmVdFQhyrzHWqd81qxZBAQEsGHDBhISElBVlQYNGuDj40OjRo0e68IeHh6cOXOGhIQE6tSpQ3R0NMuXL8/TxsfHhyVLltCmTRvWrFlDp06dUBSFW7du0bNnT0JCQmjXrp2mfVZWFrdu3aJ69ercv3+fTZs20aVLl8fKJYQQ4tnxoCBPT08vsq2qqqSnpzN//nyAZ6LwlPERouQUa0nEjIwMzVKIDRs21NnFN2/eTHBwMNnZ2QwdOpQPP/yQyZMn4+7ujo+PD+np6QwcOJAjR45gY2NDdHQ0Tk5OzJgxg5CQkDxZfvzxRypWrEiHDh24f/8+2dnZdOnShXnz5mFsbFxoDlkSUQhRVsmSiE/u5MmTjBgxosCCs27dukRHR7Nz504mT56c55i5uTmLFy/WTOUsjwoan2nTptGyZUvMzc25fv06kZGR+RZqeBbGRwhdK1ZRnpWVhYWFBXPnzuXtt98uiVwlSopyIURZJUX5kxs7dix79uzROiUDIDQ0FDMzMy5fvpyvKFcUBU9PT2bPnl0SUQ2ioPFxcnLi4sWL3L9/HwcHBxYtWkRwcDB//vmnps2zMD5C6FqxlkQ0MTGhZs2aBf7gEkIIIcqSGzdusH///gL/XevWrRspKSkFvs1SVVX27dvHzZs39RnTYAobn7///pv79+/n2Wdvb59nu7yPjxD6UOx1yl977TVWrVpFTk6OPvMIIYQQehcTE6N1uVyAihUrMmLECM3c6IIoilLu1ih/oLDxAfjggw/4+eefWbt2LdeuXWPfvn352pTn8RFCHx5r9ZXY2Fi6du1KcHAwDRs2xNLSMl+7evXq6TSgEEIIoWvx8fEFvnTuzTffZOPGjVy9erXQPjIyMsrti3UKGx/IXfhh9uzZNGvWDHd3d60vDyzP4yOEPhS7KG/atCmKoqCqKrt37y6wXXZ2ti5yCSGEEHpz9+5drfsbNWpEy5Yt6d+/f7H6SUlJ0WWsUqOg8XlYTk4Ox44dw8vLCz8/P1auXJmvTXkdHyH0odhF+eTJkwv9KEsIIYQoKypVqqR1/4svvkjt2rXZtGkTAJaWlhgZGeHk5MSAAQPytbeystJrTkMpaHy0MTY2zjen/IHyOj5C6EOxi/IpU6boMYYQQghRcpydnTEzM8s3ReP777/P85boAQMGULt2bUJCQvL1YWZmhrOzs96zGkJB41O1alU8PDz46aefyMjIoGXLlnTv3p2JEyfm66M8j48Q+lCsBz2Tk5M5ePAgZ8+e1XceIYQQQu+8vb0LfDvl9evXNV9paWlkZGRw69atfG1VVcXb27sk4pa4gsZHVVV8fX3ZvHkzu3btIjg4mLlz57Jnzx6tbcvr+AihD4XeKc/JyWHUqFF8++23mr+cbdq0Yd26ddja2pZIQCGEEELXbGxsaNu2baHrlAMsXrxY635FUWjXrh1Vq1bVV0SDKmh8bt26xYgRI4o8v7yPjxD6UOid8tDQUBYvXkzNmjV59dVXadasGfv37y/WX0ghhBCiNPP398fMzOyJzjUzM8Pf31/HiUoXGR8hSlahRXlkZCRNmjThjz/+YPXq1Rw9epSAgABiYmK0fpQnhBBClBWurq4EBwdjbm7+WOeZm5sTHBxc7l8hL+MjRMkqtCj/66+/GDJkSJ6np9966y2ys7M5ffq03sMJIYQQ+uTn56cpPItaYUxRFE3B6efnV0IJDUvGR4iSU+ic8nv37lG7du08+x5s37t3T3+phBBCiBLi5+eHi4sL4eHh7Nu3D0VR8qw6YmZmhqqqtGvXDn9//2fuDrCMjxAlo8glER/9zfjBdmEPxgghhBBliYuLC7Nnz+bmzZvExMQQHx9PSkoKVlZWODs74+3t/Uw/tCjjI4T+FVmUb968mStXrmi2U1NTURRFM8f8YYqi8M477+g+pRBCCFECqlatyqBBgwwdo9SS8RFCfxS1kFveRkbFWsb8384Uhezs7KcOVdIUe3d4K87QMYQQ4rG9uNqduDj5+SWEEGVdoXfKY2Nj9XrxrVu3Mnr0aLKzsxk2bBjjxo3LczwjI4NBgwbx66+/Uq1aNVauXEn9+vUBCAkJISwsDGNjY7744gu6d+9erD6FEEIIIYQobQotyjt27Ki3C2dnZxMUFMT27duxt7fHw8MDHx+fPA+IhIWFUbVqVeLj44mOjuaDDz5g5cqVnDp1iujoaE6ePMk///xDly5dNKvBFNWnEEIIIYQQpc3jzU/RoUOHDuHs7IyTkxOmpqb07duXDRs25GmzYcMGBg8eDOQ+/b1z505UVWXDhg307dsXMzMzHB0dcXZ25tChQ8XqUwghhBBCiNKmyAc99SUxMZG6detqtu3t7Tl48GCBbUxMTLC2tub69eskJibSunXrPOcmJiYCFNnnA4sXL9a8PrnirT95brW71nbJycnY2to+wXdYOpT1/FD2vwfJb3hl/XsoLP+5c+dKNowQQgi9MFhRru350keXXyyoTUH7c3JyiuzzgcDAQAIDA4vM6e5eth+iKuv5oex/D5Lf8Mr691DW8wshhCiawaav2Nvbc/HiRc32pUuX8r2o6OE2WVlZ3L59GxsbmwLPLU6fQgghhBBClDYGK8o9PDw4c+YMCQkJZGZmEh0djY+PT542Pj4+LFmyBIA1a9bQqVMnFEXBx8eH6OhoMjIySEhI4MyZM7Rs2bJYfQohhBBCCFHaGGz6iomJCaGhoXTv3p3s7GyGDh2Kq6srkydPxt3dHR8fHwICAhg4cCDOzs7Y2NgQHR0NgKurK3369MHFxQUTExO++uorjI2NAbT2+TSKM8WlNCvr+aHsfw+S3/DK+vdQ1vMLIYQoWqEvDxLC0Nq3b8+VK1eIj483dJRi++233xgzZgxHjhzh9u3bTJ8+nYkTJxo6VpF27NhB165dWbp0KQMGDDB0HCGEEOKZYrDpK6Lse+2111AUhaNHjxbYRlVVHB0dqVKlCmlpaSWYzjDu37+Pr68vCQkJfPzxxyxdupT//Oc/xTr3999/R1EUFEXhwIEDek5aclRVJSQkBD8/PxwdHVEUBWdnZ0PHEkIIIUoVKcrFEwsICAAgPDy8wDaxsbGcO3eOvn37YmFhUVLRDObMmTOcO3eOd999l6CgIAYMGEDTpk2LdW5YWBjW1tZUr16dsLAwPSctOdnZ2UyYMIHY2FgaNmyItbW1oSMJIYQQpY4U5eKJdevWjbp167Js2TIyMzO1tnlQsD8o4Mu7K1euAGBjY/NY52VmZhIVFcXrr7/OG2+8wcqVK7l3754+IpY4ExMTzp49y/Xr1/nxxx+pWbOmoSMJIYQQpY4U5eKJGRkZMWTIEK5fv87GjRvzHb9z5w7ff/89TZs2xcPDQ7N/+fLleHt7U69ePczMzLC1teXVV1/lxIkTxbquvb09Xbp0ybd/x44dKIpCVFRUnv3p6enMmDEDFxcXzM3NqVq1Kj4+Phw7dqzY3+vff//NgAEDqFGjBmZmZjg7OzNx4sQ8U3Lat29P586dARg4cKBmKsqlS5eK7H/9+vVcv36dwYMHM2TIEFJSUli9enW+dvHx8SiKwowZM9iwYQMvvvgiFhYW1K5dm3HjxpGVlZXvnFWrVtG8eXPMzc1xcHBg+vTpbNu2TetYaZOTk0NoaCgtWrTA0tISKysrOnfuzJ49e4o89wEnJ6ditxVCCCGeRVKUi6fi7++Poihap7BER0eTmpqa7y55aGgoJiYmjBgxgq+++oqAgAB2795N27ZtOXv2rE7zZWZm0q1bN6ZPn067du2YP38+77//PidOnKBt27YcOXKkyD4SEhJo2bIla9asoX///nz22We4ubnx8ccf07NnT7KzswGYPHky48aNA2DkyJEsXbqUpUuXFuuueVhYGM7OzrRt25YWLVrQrFkzvvvuuwLbx8TEEBgYSM+ePZk3bx5NmzZl1qxZzJs3L0+7ZcuW8frrr5ORkcGUKVMICgoiOjqaDz/8sMhMD/Tv35/Ro0fTuHFjZs+ezUcffcT169fp3LkzP/zwQ7H7EUIIIUQhVCGeUqdOnVRjY2M1MTExz/7WrVurpqamanJycp79d+/ezdfH77//rlaoUEF966238uxv166d2qBBgzz76tSpo3bu3DlfH9u3b1cBdenSpZp9n376qaooirp9+/Y8bW/evFlgP4/q06ePCqhbt27Nsz84OFgF1IiIiEIzFOXChQuqkZGROn36dM2+OXPmqIB6+vTpPG3PnDmjAmrFihXV8+fPa/ZnZ2erzz33nGpvb6/Zl5mZqdaoUUOtVauWevPmTc3+O3fuqPXq1cuXU1v2VatWqYAaFhaWJ0dmZqbq5uamOjs7F/v7fKBx48b5/psKIYQQzzq5Uy6eWkBAANnZ2SxdulSz788//+TAgQP4+PhQvXr1PO0rVqwI5K7KcefOHa5du0bNmjVxdnbm4MGDOs0WFRWFq6srbm5uXLt2TfOVlZWlmYKRkZFR4PlZWVls2rQJDw8PunfvnufYg7vN69ate6qM4eHhqKrKwIEDNfsGDBiAiYlJgXfLfX19qVevnmbbyMgIT09PLl26pJlSc+jQIa5evYq/vz9VqlTRtLWysmLEiBHFyhYVFUWVKlXw9vbOM363b9/mlVdeIT4+nr///vtJvm0hhBBCPMRgLw8S5cerr75KlSpVCA8P54MPPgDQFJNDhw7N1/7XX39l0qRJ7N27N9/DjA0bNtRptj///JPMzExsbW0LbHPjxg1q1aql9djVq1dJTU3V+hKq6tWrU6NGjacqSlVVJTw8nBYtWnD//v0867G3bt2aJUuWMGPGDM3LsR7QNke7WrVqmu+nTp06JCQkANC4ceN8bbXt0+aPP/7g1q1b2NnZFdjm6tWrMmdcCCGEeEpSlIunZm5uTr9+/ViwYAH79++nVatWLF26FHt7e7p165an7blz5+jQoQM2NjZMnjyZRo0aUbFiRRRF4a233uL+/ftFXk9RFK37tT3kmJOTg5ubG7Nnzy6wv8LmfKt6frfWzp07OXfuHOfOnSvwF5ItW7bwyiuv5Nn3aJH+sAeZdZFdVVVq1qyZ51OQR7m4uDz1dYQQQohnnRTlQicCAgJYsGAB4eHh3LhxgytXrvDhhx/mKx7Xrl1LamoqW7du5f/+7/80+1VV5dq1a8Vaw9rGxoYbN27k26/tjnXDhg1JTk6mc+fOBRbzhalZsyaWlpacPHky37Hr16+TlJRE69atH7vfB7777jssLCxYsmSJ1nzDhg0jLCwsX1FeHI6OjgD89ddf+Y5p26dNw4YN2b59O23btsXS0vKxMwghhBCieGROudCJFi1a4ObmxsqVKwkNDUVRFPz9/fO1e1CkP3oX9+uvv+batWvFulajRo04deoUly9f1uxLT09nwYIF+doOGjSIxMREPv/8c619Xb16tdBrmZiY8Morr3D48GF27NiR59gnn3yCqqr07t27WLkfdfPmTdatW8fLL7/Ma6+9hp+fX74vb29vfvjhB5KSkh67/1atWmFnZ0d4eDi3bt3S7E9JSWHRokXF6mPQoEFkZWUVuFpLUeMnhBBCiOKRO+VCZwICAnjrrbfYtm0bnp6eNGjQIF+bnj17MmHCBPr3709QUBDW1tbs27ePrVu3au7sFuW///0va9asoXPnzowYMYKMjAwiIyOpVKlSvrbvvvsuO3bs4J133mHHjh14enpiZWXFhQsX2LlzJ1ZWVmzfvr3Q682cOZOdO3fi7e1NUFAQTk5O7N69m9WrV/PSSy8xYMCA4g3QI5YtW0Z6ejq+vr4FtvH19SUqKorIyEjGjh37WP1XqFCB2bNnM3jwYFq1asXQoUMxMjIiIiICOzs7Lly4UOSnB3379mXLli3Mnz+fuLg4vLy8qF69OpcuXWLfvn1cuHCB06dPF5klMjKSCxcuALmfMOTk5DBjxgwg945+//79H+t7E0IIIcodQy37IsqfGzduqObm5iqgRkZGFtguNjZWbdu2rVqpUiW1SpUqas+ePdWTJ09qXf5Q2z5VVdWwsDC1YcOGaoUKFVRHR0d19uzZ6rZt27QuR3j//n31s88+U1988UXV0tJStbS0VJ2dndUBAwbkWyqxIGfPnlX79eun2traqhUqVFCdnJzUCRMmqKmpqXnaPc6SiG5ubqqpqal669atAtukpqaqFStWVJs0aaKq6r9LIj68fOIDH374oQqoFy9ezLN/xYoVatOmTVVTU1O1bt266rRp09TVq1ergLp27dpiZY+IiFDbtWunWllZqebm5mr9+vVVX19fdfXq1UV+n6qa+98R0PpVnGUphRBCiPJOUVU9P8kmhCh1Zs2axbhx4zh8+DDu7u6GjiOEEEI886QoF6Icy8zMxNjYOM8DtykpKTRt2pS0tDQSExOpUKGCARMKIYQQAmROuRDl2unTp/Hx8aFv3744OjqSmJhIREQEFy5cYPHixVKQCyGEEKWEFOVClGM1atSgZcuWREVFkZSUhImJCc2bN2fOnDn4+fkZOp4QQggh/kemrwghhBBCCGFgsk65EEIIIYQQBiZFuRBCCCGEEAYmRbkQQgghhBAGJkW5EEIIIYQQBiZFuRBCCCGEEAYmRbkQQgghhBAGJkW5EEIIIYQQBiZFuRBCCCGEEAYmRbkQQgghhBAGJkW5EEIIIYQQBiZFuRBCCCGEEAYmRbkQQgghhBAGZmLoAKVB9erVqV+/vqFjCCHEYzt37hzXrl0zdAwhhBBPSYpyoH79+sTFxRk6hhBCPDZ3d3dDRxBCCKEDMn1FCCGEEEIIA5OiXAghhBBCCAPTa1Gelpamz+6FEEIIIYQoF/RalNeqVYuRI0fy66+/6vMyQgghhBBClGl6Lcrbtm3Lt99+S8uWLXFzcyM0NJRbt27p85JCCCGEEEKUOXotyjdv3sz58+eZNm0a9+7d4+2336Z27dr079+f2NhYfV5aCCGEEKJkJSXBp5/CgAHg7Z37v59+CsnJhk4mygBFVVW1pC4WGxtLWFgY69atIz09nfr16xMQEMCQIUOoXbt2sfrYunUro0ePJjs7m2HDhjFu3Lg8xyMiInjvvfeoU6cOAP/9738ZNmxYoX26u7vLkohClCBllvb96gclm6M8kJ9fQpQChw9DSAhs2ZK7nZ7+7zELC1BV6NEDxo8HDw/DZBSlXomuvvLSSy8RFRXFP//8Q//+/UlISGDSpEnUr1+f3r17c+jQoULPz87OJigoiC1btnDq1ClWrFjBqVOn8rV7/fXXOXr0KEePHi2yIBdCCCGEeGILF4KnJ6xfn1uMP1yQA6Sl5e5bpuSDfgAAIABJREFUvz633cKFhkgpyoASLcqvXbvGZ599Rrt27YiKiqJixYr4+/szfPhwdu3aRdu2bfnmm28KPP/QoUM4Ozvj5OSEqakpffv2ZcOGDSX4HQghhBBC/M/ChTB2LKSm5t4NL4yq5rYbO1YKc6GV3otyVVXZunUrr732Gvb29owZMwYzMzMWLFjAP//8w7fffstXX33FhQsX8PT0ZPr06QX2lZiYSN26dTXb9vb2JCYm5mu3du1amjdvjp+fHxcvXtTa1+LFi3F3d8fd3Z1kmeslRKmgzNL+JYQQpc7hw/8W5I/jQWEu087EI/RalE+ePBkHBwd69uzJtm3bGDx4MIcPH+bXX3/lzTffxMrKStPW2tqawYMHay2yH9A2/V1RlDzb3t7enDt3juPHj9OlSxcGDx6sta/AwEDi4uKIi4vD1tb2Cb9DIYQQQjyTQkJyp6Y84gbQG6gIOADLtZ2blpZ7vhAP0WtRPmPGDGrUqMHXX3/N5cuXWbRoES+++GKB7Vu0aMHkyZMLPG5vb5/nzvelS5fyPSBarVo1zMzMABg+fLiskS6EEEII3UpKyn2oU8vNwiDAFLgKLANGAicfbaSqsHmzrMoi8jDRZ+e//fYbbm5uxW7v6uqKq6trgcc9PDw4c+YMCQkJ1KlTh+joaJYvz/s76OXLl6lVqxYAGzdupEmTJk8WXghRashqLUKIUiUiQuvue8Ba4ARQCWgP+ABLgZmPNlaU3H7ee09fKUUZo9c75e+++y47d+4s8HhsbCydOnUqdn8mJiaEhobSvXt3mjRpQp8+fXB1dWXy5Mls3LgRgC+++AJXV1eef/55vvjiCyIK+IsjhBBCCPFEjh/Pv8oKcBowBho9tO95tNwph9wpLL//rpd4omzS653y3bt3F7okYVJSEnv27HmsPr28vPDy8sqzb9q0aZo/h4SEECLztIQQQgihL7dva919F7B+ZJ81kFJQPzdv6i6TKPP0WpQX5datW5r530KI8kdWThFClEvWj5beuSoBdx7Zdwew0tIWgKpVdZdJlHk6L8qPHz/O0aNHNds//fQTWVlZ+drduHGDBQsW4OLiousIQgghhBD607w5rF2bbwpLIyALOAM0/N++Y4DWp+UsLKBZM32mFGWMompbZ/ApTJ06lalTp+Z2rihalzF8wMrKipUrV/Lyyy/rMsJjk9dUC6EfhrpT/iw9ACo/v4QwgKQkcHDQOq+8L6AA3wJHAS9gP1oKc3NzuHABZFlm8T86v1M+ZMgQPD09UVWVTp06MWHCBLp27ZqnjaIoVKpUCRcXF8zNzXUdQQghhBBCf+zsoEcPWL8+37KIC4ChgB1QDViIloJcUcDLSwpykYfOi3IHBwccHBwACA8Pp0OHDjg6Our6MkIIIYQQhjN+PGzblu+NnjbA+qLOtbDIPV+Ih+h1ScTBgwdLQS6EEEKI8sfDA+bMIcfC4vHOs7SEOXPA3V0/uUSZpdM75ZGRkQAMHDgQRVE020UZNGiQLmMIIYQQQujfyJF8NGkSE9LTsQCtb/h8IEdRSFNVLo8cifPIkSUWUZQdOn3Q08jICEVRSEtLw9TUVLNd2CUURSE7O1tXEZ6IPCglxNMpbUsfyoOeQoiSMHz4cCIjI7kcE4PNokWweXPufPG0tH8bWVjkFuteXoy+coXvjh/n6tWrWFpaGi64KJV0eqc8NjYWAFNT0zzbQgghhBDlyaZNmwgLC2Pt2rXYdOsG3bpBcjJEROS+qfPmzdx1yJs1gyFDwNaWuVlZLK9Vi06dOnHgwAFDfwuilNH5kohlkdxpEuLplLY75dqU17vn8vNLiJJ348YNateuzeuvv86SJUse69w//viDpk2bMnXqVCZOnKinhKIs0uuDnoXJyMgw1KWFEEIIIZ5Y+/btqVmzJuHh4Y99bpMmTZg3bx4fffQRv/32mx7SibJKr0X5li1bmDJlSp59CxYsoHLlylSsWJF+/fpx//59fUYQQgghhNCZ0aNHEx8fz88//4yR0ZOVUaNHj6Zjx4507tyZzMxMHScUZZXO1yl/2OzZs7Gzs9Ns//HHH4wePZoGDRrg6OjIypUradmyJcHBwfqMIYTQkbIwTUUIIfRl165dfPnllyxduhR7e/un6mvr1q3UqFGD7t27yzN4AtDznfI//vgD94fW4Vy5ciUWFhYcOnSILVu2PNFcLCGEeBLKLO1fQghRHHfu3MHb2xtfX1/69+//1P2ZmpoSGxvL3r17mTdvng4SirJOr0X5zZs3qV69umZ7x44ddOrUicqVKwPg6elJQkKCPiMIIYQQQjy1jh07Ym1tzcqVK3XWp5ubGzNmzOC9997j5MmTOutXlE16LcqrV6/O+fPnAUhJSeHw4cO0b99ec/z+/fsGX6NcCCGEEKIw48eP58SJE+zbt++J55EX1nerVq3o2LEjWVlZOu1blC16LcrbtGnD119/zZo1awgODiYrKwsvLy/N8fj4eGrVqqXPCEIIIYQQT2zfvn3MmjWLhQsX4ujoqJdr7Nq1i8zMTLy9vfXSvygb9FqUT506lZycHPr06UN4eDiDBg3CxcUFAFVVWbduHe3atdNnBCGEEEKIJ5KamsrLL79Mjx49GDZsmN6uY25uzvbt29m2bRuLFi3S23VE6abX1VdcXFz4448/2LdvH9bW1nTo0EFz7NatW7zzzjt4enrqM4IQQgghxBPp1KkTFhYWbNiwQe/XatWqFePHjycoKIguXbrQoEEDvV9TlC7yRk/kjXhCFFd5XK2krL/pU35+CaEfM2bMYMqUKfz+++80adKkxK7bokULLl++TGJios7nr4vSTa93yh+WmprK9evX0fY7QL169UoqhhBCCCFEoX777Tc++ugj5s2bV6IFOcDevXupUaMGfn5+fP/99yV6bWFYei3Kc3Jy+PTTT/nyyy+5cuVKge1kBRYhhBBClAaZmZl06tQJT09PRo8eXeLXr1SpEjExMXTp0oXIyEgGDRpU4hmEYei1KB83bhxz5szB1dUVX19fqlWrps/LCSGEEEI8lW7dumFkZMSWLVsMlqFTp06MHj2agIAAPD09ZUbBM0KvRXlUVBQvv/wymzdv1udlhBBCCCGe2ty5c/npp5/49ddfMTU1NWiWzz77jB9//JH27dtz7tw5mV/+DND7Gz179eql0z63bt1K48aNcXZ2ZubMmQW2W7NmDYqiyANQQgghhCjSyZMnef/99/n4449xc3MzdBwAfvrpJ5KTkxk4cKCho4gSoNeivFmzZly+fFln/WVnZxMUFMSWLVs4deoUK1as4NSpU/napaSk8MUXX9CqVSudXVsIIYQQ5VNWVhYdO3akdevWjBs3ztBxNGxsbFi7di0rVqxgzZo1ho4j9EyvRflHH33E119/zcWLF3XS36FDh3B2dsbJyQlTU1P69u2rde3QSZMm8f7772Nubq6T6wohhBCi/PL29iYzM5OdO3caOko+Xl5eBAYG0r9//0IXzRBln17nlP/66684ODjg4uJC7969cXR0xNjYOE8bRVGYNGlSsfpLTEykbt26mm17e3sOHjyYp82RI0e4ePEir7zyCnPmzCmwr8WLF7N48WIAkpOTi/stCfFMKI/rkQshhDaLFi3ixx9/ZP/+/aX2Zt7XX3/Nzp07ad++PfHx8YaOI/REr0X5lClTNH+OiorS2uZxinJta5wriqL5c05ODu+88w4RERFF9hUYGEhgYCCQ+/INIYQQQjxbzp49S1BQEBMmTCj1U1737dtH3bp1GT58ON98842h4wg90GtRnpCQoNP+7O3t80yFuXTpErVr19Zsp6SkcOLECTw9PQG4cuUKPj4+bNy4UQpvIYRWBX0qUNbf9CmEKFxOTg7t27fHzc2N6dOnGzpOkezs7Fi+fDmvvfYavXv3xsvLy9CRhI7ptSh3cHDQaX8eHh6cOXOGhIQE6tSpQ3R0NMuXL9cct7a25tq1a5ptT09P5syZIwW5EAWQaSpCiGeVn58fKSkp7N6929BRis3X15cBAwbg6+tLYmIiNjY2ho4kdKjEFr2Mj49n37593L59+4n7MDExITQ0lO7du9OkSRP69OmDq6srkydPZuPGjTpMK4QQQojyKjIykvXr17N582YqVapk6DiPJSIiAjs7O9q3b2/oKELHFFXbRG0d2rRpE6NHj+bcuXMAbN++nU6dOpGUlETbtm2ZOXMmfn5++oxQJHd3d1nPXDyT5E55wcrK9BX5+SXE47lw4QINGjTg7bffZu7cuYaO80QuXbqEo6Mjo0aN4vPPPzd0HKEjer1Tvnv3bnr37o2NjQ0fffRRngc17ezsaNCgAdHR0fqMIIQQQggB/DuP/LnnniuzBTnkPmMXERHBl19+ya5duwwdR+iIXovyadOm8fzzz3Pw4EGCgoLyHW/Tpg2//fabPiMIIYQQQgAwcOBAkpOT+emnnwwd5an179+fV199FW9vb+7cuWPoOEIH9FqUx8XF0b9/f4yMtF/G3t5eFsIXQgghhN506dKFVq1asXz5clasWMH69eupUqWKoWPpxKpVq7C2tqZjx44sWrSIKlWqcOvWLUPHEk9Ir0V5dnY2ZmZmBR6/du0apqam+owghBBCiGfYTz/9xKFDh+jfvz+9e/eme/fuho6kM0ZGRuzZs4ejR4/y5ptvcvv2bX744QdDxxJPSK9FeZMmTQr9iGjTpk08//zz+owghBBCiGdUVlYWmZmZmu3vv/+e0NBQAybSrbt37+Zb9jk2NtZAacTT0mtRHhAQwJo1awgLCyMnJwfIfQNnamoqb7/9Nr/88ovmrZpCCCGEELq0d+/ePNuKopCWlmagNLqXmZlJhQoV8uw7cOCAgdKIp6XXlweNHDmSffv2MXz4cMaMGYOiKLzxxhtcv36d7Oxs/P396d+/vz4jCCGEEKKcSjqfTET0SY7fNOF2TgWsje7TvGoW/m80xbZedb799ltN2379+rFo0aIyty55YWxsbLh27RorVqxg1KhR3Lp1iz/++OPfBklJEBEBx4/D7dtgbQ3Nm4O/P9jaGiy30E7v65QDrFu3jqioKP78809UVaVhw4YMGjQIX19ffV+6WGSdX/GsknXKCybrlAtReh3eeYqQH++wxcoNyCG9gqXmmMX9VFQUeqQco4X6C9/vWMru3bupXLmy4QKXkNmzZ7N8+XKOLF4MISGwZUvugfT0fxtZWICqQo8eMH48eHgYJqzIp0SK8tJO/lETzyopyh9faSvW5eeXeNYsnL+HsSnupJmYoxoZF9hOycnGIiudOVZxjAzuWIIJDWzhQhg7FtLScovvgihKboE+Zw6MHFly+USB9DqnXAghhBBCVx4U5KmmFQstyAFUI2NSTSsyNsWdhfP3lFBCA3tQkKemFl6QQ+7x1NTc9gsXlkw+USi9FeW3b9/mk08+oV27dtja2mJmZoatrS3t27dn5syZstC9EEIIIYrt8M5TmoJcIysD1gTATAeYbAWfvwB/bclz3oPCPG7XqRJOXMIOH/63IH9IKOAOmAFDtJ33oDCXT9wMTi9F+fHjx3F1dWXSpEn88ssvZGZmYmdnR2ZmJvv372fChAk0bdqUU6fK+V8QIYQQQuhEyI93SDMxz7szJwus60LgHphyG7pNh2V94Ma5PM3STMwJ2Xa75MIaQkhI7pSVR9QGJgJDCzs3LS33fGFQOi/K09PT8fX1JTk5mQkTJpCQkMDt27e5ePEit2/fJiEhgQkTJnD16lVeffVVMjIydB1BCCGEEOVI0vlktli55Z+yYloRuk4Bm/pgZARNXgEbR0j8NU8z1ciYzVZuJF+4VmKZS1RSUu5DnVqmrLwK/AeoVtj5qgqbN0Nysp4CiuLQeVEeHR3N2bNnWb58OdOnT8fBwSHPcQcHB2bMmEFUVBSnT58mOjpa1xGEEEIIUY5ERJ8EcopumHIVrp2GGq75DimoRKw4oftwpUFExNP3oSi66Uc8MZ2vU75x40ZatmxZ5HKHr732GnPnzmXDhg0MHjxY1zGEEA+RVVaEEGXZ8ZsmpFe1LLxR9n1Y2R9aDAa75/IdTqtgye839fp6FsM5fjzvsodPIi0Nfv9dN3nEE9H5nfJjx47RrVu3YrXt1q0bx44d03UEIYQQQpQjt3MqFN4gJwdWDgRjU+gVWmCzm0X1U1bd1tF8+Zs3ddOPeCI6/5UxOTmZevXqFattvXr1SJb5S0IIIYQohLXR/YIPqiqsDYC7V8F/MxgXXHhXLayfsszaWjf9VK2qm37EE9H5nfJ79+5haVnER0z/Y2Fhwb1793QdQQghhBDlSPOqWZjfT9V+cP1ISPoDBsdABYsC+7C4n0qzqll6SmhgzZuDubnWQ1lAOpD9v6/0/+3Lx8ICmjXTV0JRDDovyuUFoUIIIYTQpSF9XdFastw8DwcXweWj8HFNmFwp9+vIsnxNVRSGvNFU/2ENYciQAg/NACyAmUDU//48Q1tDVS20H6F/enniYe7cucVaVSUxMVEflxdCCCFEOVKlljUtz23npwYv510WsaoDzCz6ZqCSk41XylFs67XRY0oDsrODHj1g/fp8yyJO+d9XYbKBmy1bUt3WVj/5RLHopSg/cuQIR44cKVZbRVH0EUEIIYQQ5cCWLVvo06cPjWu1wMLBM+8bPYvJIiud8d11NO+6tBo/HrZty/dGz+K4b2REj717aTxgAJGRkRgZ6e2F76IQOh/1nJycx/rKzs7WdQQhhBBClHGZmZn85z//oWfPnvTo0YMDp3YyxyoOy8zHexbNMvMec6zicO/koqekpYSHB8yZA8V8rk/D0hLz0FAmrl/PunXrsLOz4+DBg/rJKAolvwoJIYQQolTZuXMntra2xMbGsmPHDlatWoWJiQkjgztqCnMlp/CbekpOtqYgHxncsYSSG9jIkf8W5kXNRFCU3HZz5sDIkfTq1Yvk5GTc3Nxo06YNw4YNIyenGC9sEjqjqPJkJu7u7sTFxRk6hhB6Iy8P0j/1A8NcV35+ifIkKyuLN954g7Vr19KrVy9Wr16NiUn+mbZxu04Rsu02m63cUFBJq/Dv3WGL+6moKHilHGV8d+vyf4dcm7g4CAmBzZtzi++0tH+PWVjkzjv38sqd8uLunu/0VatWMXjwYCpXrsy2bdtwc3MrwfDPrjJ3p3zr1q00btwYZ2dnZs6cme/4119/TbNmzXBzc6N9+/acOnXKACmFEEII8Th+/vln7Ozs2Lp1Kz/88APr1q3TWpADuHdyYe2sNlwYdI+pFQ7R68JmWv4Rw8CbPzO1wiEuDLrH2lltns2CHHIL7bVr4cIFmDqVg40ascPCAgYOhKlTc/evXau1IAfo06cPycnJPPfcc7Ro0YKgoCC5a14CytSd8uzsbBo1asT27duxt7fHw8ODFStW4OLy71+6O3fuULlyZQA2btzIggUL2Lp1a6H9yp0mUd7JnXL9kzvlQjyZnJwcBg0axPLly3n55ZdZv349pqamj9XH4sWLGTNmDCkpKXpKWbaNGjWKzZs3c+7cucc+NyoqimHDhmFjY8P27dtxdXXVfUABlLE75YcOHcLZ2RknJydMTU3p27cvGzZsyNPmQUEOuS8yktVdhBBCiNLp4MGD2NnZsW7dOtavX8/mzZsfuyAX+jVgwACSkpJwcHCgefPmvPvuu4aOVG6VqaI8MTGRunXrarbt7e21rnX+1Vdf0aBBA95//32++OKLkowohBBCiCLk5OQwbNgw2rRpg5ubG8nJyfj4+Bg6lihA5cqV+eWXX1i0aBFfffUV9erV46+//jJ0rHKnTBXl2mbaaLsTHhQUxNmzZ5k1axYzZmh9bxWLFy/G3d0dd3d3kpOTdZ5VCCGEEPn99ttv1KpVi2XLlhEdHc2OHTuwfNxl/IRBDBs2jMuXL2NnZ4eLiwvjx483dKRyRa9FedeuXVm5ciWZmZk66c/e3p6LFy9qti9dukTt2rULbN+3b1/Wr1+v9VhgYCBxcXHExcVhK2+wEkIIIfQqJyeHUaNG4e7uznPPPUdycjJ9+vQxdCzxmGxsbIiLi+PLL79k7ty5ODk5kZCQYOhY5YJei/Jff/2Vfv36Ubt2bYKDg/n999+fqj8PDw/OnDlDQkICmZmZREdH5/u468yZM5o///DDDzRs2PCprilEWaLM0v4lhBCGdPLkSezt7fnuu++IjIxkz549VKpUydCxxFMYNWoUly5dwsrKCmdnZ6ZOnWroSGWeXovyK1eusGzZMl544QW+/PJL3NzcaNWqFd988w1379597P5MTEwIDQ2le/fuNGnShD59+uDq6srkyZPZuHEjAKGhobi6uuLm5sa8efNYsmSJrr8tIYQQQhTTu+++S/Pmzalfvz5JSUkMGDDA0JGEjtjZ2XHs2DHmzp3LjBkzaNSoERcuXDB0rDKrxJZEPH/+PN999x1LlizhwoULVKxYkT59+jB06FDatWtXEhEKJEuKifJC7oobjiyJKERef/31F127duXq1assWLCAgIAAvV1LlkQs3NMsiVhc//zzD126dOH06dPMmDGDcePG6e1a5VWJPejp4ODA1KlTSUhIYOvWrbz00ktERETQoUMHXFxc+Pzzz7l3715JxRFCCCGEnowfPx4XFxfs7Oy4fPmyXgtyUTrUrl2bU6dOMX36dCZOnIiLiwv//POPoWOVKSW++srRo0fZuHEjP/30E6qq0qBBA4yMjHjnnXdwdnZm//79JR1JCCGEEDqQkJCAk5MTc+fO5csvvyQuLg4bGxtDxxIlaPz48fz9999kZWXh4ODAvHnzDB2pzCiRovzWrVt89dVXtGjRAnd3d7799lu6d+/Ojh07OH36NCdOnNAsiRQUFFQSkYQQQgihQ1OmTMHZ2RkrKysuXbrEqFGjDB1JGEi9evU4ffo0H374Ie+99x7PP/88SUlJho5V6um1KN+1axf9+/endu3avPXWW6SmpvLpp5+SmJhIdHQ0nTp10rTt1KkT48aN4+TJk/qMJIQQQggdunDhAo0aNeLjjz9m9uzZHDt2DDs7O0PHEqXAlClTiI+PJyUlBXt7exYuXGjoSKWaXovyLl268P3339O7d29iY2P5888/GTNmDNWqVdPa3tnZ2eAPfQohhBCieGbOnImTkxMVKlTg/Pnz8gp2kY+joyN///03Y8aM4b///S/u7u7cuHHD0LFKJb0W5XPnziUxMZFly5bRsWPHItu/9NJLxMbG6jOSEEIIIZ7SP//8g4uLCxMnTmTGjBmcPHmy0Jf5CRESEsKpU6dISkqiVq1ahIWFGTpSqaPXojwlJaXQJ29PnjzJtGnT9BlBCCGEEDo0b948HBwcyMrK4u+//5al70SxNW7cmAsXLhAUFERgYCBt2rThzp07ho5Vaui1KJ86dSrHjx8v8PiJEyfkDVBCiHJB3qYqyrukpCSef/553nvvPT788ENOnz5NvXr1DB1LlEHz5s3j2LFjnD9/Hjs7O6KiogwdqVTQa1Fe1HuJ0tPTMTEx0WcEIYQQQjylBQsWYG9vT0pKCvHx8UyZMsXQkUQZ17RpUy5dusTQoUMZNGgQHTt2fKK3vZcnOq+I79y5w61btzTb169f1/rK1Rs3brBs2TLq1q2r6whCCCGE0IEbN27QrVs3jhw5wvvvv09ISIihI4lyxMjIiAULFjBs2DB69OiBnZ0dERER9OnTx9DRDELnd8o/++wzHB0dcXR0RFEUgoODNdsPf7344ovs2LGDN998U9cRhBBCCPGUwsLCqFWrFklJSZw6dUoKcqE3LVq04PLly/Tr14++ffvSpUsXUlNTDR2rxOn8TrmnpyeQO3Vl2rRp9O7dm+bNm+dpoygKlSpVonXr1rRt21bXEYQQQgjxhO7cuUP37t05dOgQo0ePljcyihJhZGTEt99+y/Dhw+nZsye2trYsX76cXr16GTpaidF5Ud6xY0fN8ofnz5/nzTffpFWrVrq+jBBCCCF0LCoqimHDhmFjY8OxY8do2rSpoSOJZ0yrVq1ISkpiyJAh9O7dm+7du7NhwwZMTU0NHU3v9PqgZ3h4uBTkQgghRCl39+5dOnTowKBBgwgICODSpUtSkAuDMTIyIjIykr1793LgwAGqVavGli1bDB1L73R6p/zBA50PlkjS9oCnNrKkkhBCCGEYq1atYvDgwVSuXJm4uDhatGhh6EhCANC+fXuSk5Pp168fPXv2xMfHh1WrVpXbu+Y6Lcrr16+PkZERqampmJqaUr9+fRRFKfK87OxsXcYQotyT9a+FEE8rNTUVb29vYmNjGTp0KIsXL8bISK8foAvx2ExMTFi1ahU7d+7k1VdfxdbWlu+//57OnTsbOprO6bQonzx5MoqiaNYef7AthBBCiNJjw4YN9OvXDwsLC3755ZcyO9X04MGDtG7dWrOtKAr169cnISHBgKlKjwcPTj6gKAodO3Zk9+7dhgv1hDp37kxycjJ9+vSha9eu+Pr6smLFinL1vhudfiePvkxAXi4ghBBClB7p6en07t2bbdu2MWDAACIiIsr03XEPDw9MTEzIysrS7OvatasBE5Uu//nPf/IU5QB+fn4GSvP0TE1NWb9+PVu2bKFPnz7Y2toSExND+/btDR1NJ8ru30QhhBBCFNuWLVuoXr06Bw4cYO/evURGRpbpghxyHwh8991382x/8cUXBkxUulSvXp2ePXtqtitWrMh///tfAybSjR49enD9+nXatGlDhw4dGDBgADk5OYaO9dTK9t9GIYQQQhQqMzOTXr160bNnT7y8vEhOTi43dxYBQkJCNL9cBAQEYG5ubuBEpUtERITmzzNnzjRcEB0zNTVl8+bNrFu3jnXr1mFra8vBgwcNHeup6LQoNzIywtjY+LG+ytNcICGEEMLQxowZw19//QXAzp07sbW1Zffu3ezYsYNVq1aVu393jYyM8PX1BZC75FpUr16dxo0bY2RkVC7ukj+qV69eJCcn88LFmymTAAAgAElEQVQLL9CmTRuGDh2quWs+evToMvV8gaKqqqqrzoYMGfJED3aGh4frKsITcXd3Jy4uzqAZhHgcsvpK2aF+oN/+5edXOZeUBBERcPw43L4N1tbQvDn4+4Otbb7m69at49VXX6VatWp4enry/fff06tXL1avXl3uinGAGzduEBMTQ3x8PHfu3KFy5co4Ozvj4+ND1apVDR3P4J618Xl4ec++ffvyxRdf0LhxY/7880+t7R8en7t371KpUiWDjo9Oi/KySv5RE2WNFOVlhxTl4okcPgwhIfDghSnp6f8es7AAVYUePWD8ePDwACAnJ4cqVaqQkpICgLGxMTExMfTo0aOk0+vdyZMnCQ8PZ//+/SiKQkZGhuaYmZkZqqrStm1b/P39cXV1NWBSw3iWx+fu3bt06tSJw4cPa/bFxMTwyiuvaLZL6/jInHIhhBCiNFm4EDw9Yf363GL84YIcIC0td9/69bntFi4EYNq0aZqCHHLfAVKrVq2Sy11C1qxZw4gRI9izZw+ZmZl5CiqAjIwMMjMz2bNnDyNGjGDNmjUGSmoYz/r4VKpUiWvXruXZ98Ybb2j+XJrHp8wV5Vu3bqVx48Y4OztrfWBh3rx5uLi40Lx5czp37sz58+cNkFIIIYR4AgsXwtixkJqaeze8MKqa227sWFi4kKlTp+Y5bGRkxK5du/QYtuStWbOG+fPnk56eTlEf9KuqSnp6OvPnzy93hWdBZHxyJScn59m+e/cuw4cPL/Xjo9PpK46OjhgZGfHnn39SoUIFnJycig6gKJw9e7ZY/WdnZ9OoUSO2b9+Ovb09Hh4erFixAhcXF02b2NhYWrVqhaWlJQsXLmT37t2sXLmy0H7l419R1sj0lbJDpq+IYjt8OPfOd2pqnt0DgJ3APaAm8D4w7NFzLS0Z4+5ObR8f2rdvzwsvvFDuXkV+8uRJRowYQfpDnxxUqFCBcePG0bJlSypXrsylS5f46quv2L9/f55zzc3NWbx4cZ56obzRNj4Affr04ZVXXsHZ2Zlt27bl++UNyu/4nD9/nv3797N69Wq8vb0JCwvLNz6VK1dm0qRJtG7dmlu3bhEaGsq2bdvytCmp8dHpUx8ODg4oiqJ52LNevXo6faPnoUOHcHZ21hT7ffv2ZcOGDXkG6aWXXtL8uXXr1kRFRens+kII8bgK+gVK38W6KINCQnKnpjxiPBAGmAF/Ap7AC8CLDzdKS2Nu9eowZoz+cxpIeHh4vqkGxsbGXL16lcDAQK5cuUK7du0ICQmhb9++XL58WdMuIyOD8PBwZs+eXdKxS4y28YHcu8ZhYWG0adMGMzMzreeW1/FxcHDAwcGBN954g7Fjx2odnw8++ID79+/TrVs3GjVqxOeff86ZM2f4+++/NW1Kanx0WpQ/+tpWXb/GNTExkbp162q27e3tC12TMiwsrFw+4CKEEKKcSUrKfahTy4fXDz9mpvzv6yyPFOWqCps3Q3Ky1lVZyrobN26wf//+fFMO0tPTWbx4sWb7559/5p9//qFJkyZ5inJVVdm3bx83b94sl6uOFDQ+kDuDAMDFxQU7Ozut5z+r42Nubk6nTp14/fXXSUtL49ixY+zduxcvLy9CQ0M17UpqfMrUnHJt/2cr6E58VFQUcXFxvPfee1qPL168GHd3d9zd3fPNPRJCCCFK1EMveNFmFGAJPAfUAry0NVKUIvspq2JiYor1ybuNjQ316tXTOi1WURRiYmL0Ec/gijs+hXkWx8fBwYHs7GwuXLig2Xf69Gmt069LYnxKZNHSjIwMdu/erfkowMnJiY4dOz72W7fs7e25ePGiZvvSpUvUrl07X7sdO3bw8ccfs2fPngI/qgkMDCQwMBDInZMphBBCGMzx4/lXWXnIAuBL4BdgN7lTWfJJS4Pff9dHOoOLj4/XOvXgYcbGxkyfPp0ffvhB6yIPGRkZxMfH6yuiQRVnfIryLI6PhYUFd+/ezbPv7t27VKxYMV/bkhgfvRflkZGRvPvuu9y8eVNzp1tRFKpUqcLcuXMZMmRIsfvy8PDgzJkzJCQkUKdOHaKjo1m+fHmeNkeOHGHEiBFs3bq1wI9phBBCiFLl9u0imxgD7YEoYCHwtrZGN2/qNFZp8Wjh9ChFUZg+fTpZWVnMmlXwk/APLxlZnhQ1PsX1rI1PWloalSpVyrOvYsWK3Lt3T2t7fY+PXovylStXMmTIEOrVq8fYsWNxcXFBVVVOnTrF119/TUBAABYWFrz++uvFC2tiQmhoKN27dyc7O5uhQ4fi6urK5MmTcXd3x8fHh/fee4+7d+/y2muvAbkPm27cuFGf36YQQgjxdKyti900i9w55VqVw/nAQL7C6VGTJk3CxsaG0aNHk52dXWA7KysrXUcrFYoan+J61sbn/PnzGBsbU7duXc1MjEaNGuV5yPNh+h4fvRbln3zyCc899xwHDhygcuXKmv29evVi1KhRtGrVio8//rjYRTmAl5cXXl55Z9NNmzZN8+cdO3Y8fXAhhBCiJDVvDmvX5pvCkgTsAl4BLIAdwApgeb4OyH3TZ7Nmeg5qGM7OzpiZmWmdgjB+/HgcHR0ZNWpUoVM4zMzMcHZ21mdMgylsfIyNjTE2NsbIyAhjY2NMTU3Jzs7O98vLszg+6enpxMbG8uabbzJ9+nQaN25Mx44dGTp0aL4+SmJ89Pqg519//YW/v3+egvwBa2tr/P39OXPmjD4jCFGmKbO0fwkhypkCpnIq5E5VsQeqAmOB+UAvbY1VtcB+yjpvb2+tiz3UrFkTX19fGjVqxLZt29i7dy979+7l5ZdfztdWVVW8vb1LIm6JK2h8AAICAti/fz/+/v54eXmxf/9+AgIC8rV7Vsdn5syZmJmZsX37dj7++GNCQkK03ikvifHR653ymjVrFvrGJCMjI2rUqKHPCEIIIUTpZ2cHPXrA+vV5lkW0BfYU53xFAS+vcrkcIuSuqtK2bVv27NmTp664cuVKsRZrUBSFdu3alcvl/qDg8YHc1eYeXjZSm2d5fO7cucPYsWMLPb+kxkevd8qHDBlCRESE1gn2d+7c4bvvvsPf31+fEYQQQoiyYfz43CkoT8LCIvf8cszf37/AFdWKYmZmVu7rDRmfwpWF8dFpUf7gY6MHXx06dMDS0pJmzZoxe/ZsYmJi2LRpE59++inPP/88lSpV4v/+7/90GUEIIYQomzw8YM4cVEvLxzvP0hLmzIFyvryvq6srwcHBj72csrm5OcHBweXuFfKPkvEpXFkYH0UtbH7JYzIyMsq3OPvD3T849ui+wp6ULgnu7u7ExcUZNIMQ2sj88fJL/UA3/cjPr/JnVv36vHX+PBaKglLIP9GqopCqqsR07EhfHb9BuzRbs2YN8+fPJyMjo9ApsoqiYGZmRnBwMH5+fiWY0LBkfApXmsdHp3PKw8PDddmdEEII8UyZNm0a0y5d4vXVq6m/YgVs3pw7Xzwt7d9GFhagqiheXvzcogX9Jk2i2vbtdO3a1XDBS5Cfnx8uLi6Eh4ezb98+FEXJs6qGmZkZqqrSrl07/P39y/0d4EfJ+BSuNI+PTu+Ul1Vyp0mUVnKnvPySO+XiUXFxcbRq1Yr58+fz1ltv5e5MToaIiNw3dd68mbsOebNmuaus/O+hzj59+rBp0yauXLmidbWz8uzmzZvExMQQHx9PSkoKVlZWODs74+3tXW4fWnwcMj6FK23jI0U58o+aKL2kKC+/pCgXD0tPT/9/9u48rqa8jwP45yZFdlNUrlSuPEpNk2LsWRtbmIytUJiaHmOdsYwl+2AwY4axNDxFjJItDJkigzyTMhr72IpqIm1CKtV5/mjcR9puubfTrc/79bqvcc75nd/53NMy33v6nd+Bvr4+bG1ty/28jfz8fLRs2RK6urr4888/VZSQiFRNpVMivvb48WNERUUhLS0N+fn5RbaPHz++MmIQERFVSQ4ODtDQ0MDx48fLva+GhgYuXLgAmUyGuXPnlvqYeSKqulRalOfn52PKlCnYvn17scX4ayzKiYioplq/fj3Onz+Py5cvQ0tLq0J9tGrVClu3bsWnn36KIUOGoFu3bkpOSUSqptJ5ytetW4dt27ZhzJgx2LlzJwRBwOrVq/Hjjz+iTZs2sLW1RUhIiCojEBERVVnXrl3DnDlzsHLlSlhZWb1TX5MmTcKgQYMwYMAAZGZmKikhEVUWlY4pt7CwgJGREU6cOIGUlBTo6ekhNDQUvXv3xosXL2BlZYXPPvsMs2fPVlUEhXBMJlVVHFNe85R3rDl/f6mv3Nxc6Ovro23btggPD1dany1atICxsTEiIiKU0icRVQ6VXim/f/8+BgwYUHAgjYJDvXr1CgBQr149uLm5Yfv27aqMQEREVCUNHjwYOTk5OHXqlNL61NTUxNmzZ3Hp0iUsW7ZMaf0SkeqptCivW7cuateuDQCoX78+JBIJkpKS5Nv19fURFxenyghERERVzpYtW/Drr78iJCSk3E8YLEvbtm2xYcMGLF26lH9FIVIjKi3KW7VqhXv37gEAateuDZlMhuDgYPn20NBQNG/eXJURiIiIqpQ7d+5g6tSpWLBgATp16qSSY3z++efo3bs3+vbti6ysLJUcg4iUS6VFee/evXHo0CH58rhx47B371706tUL9vb2CAwMxMiRI1UZgYiIqMrIz89H9+7dYW1tjeXLl6v0WL/88gtq1aoFBwcHlR6HiJRDpVMifvnll+jfvz+ys7Ohra2Nr776CklJSdi9ezdq1aoFd3d3LF26VJURiIiIqgwnJyc8f/4cZ86cUfmxtLS0EBYWhg8++ADr16/HF198ofJjElHFqbQoNzAwgIGBgXy5Vq1a+OGHH/DDDz+o8rBERERVzs6dOxEUFIQzZ86gfv36lXJMKysrrFq1CnPmzIGDgwPat29fKcclovJT6fAVIiIiAh4+fIjJkydj5syZ6NGjR6Uee86cOejSpQt69uyJ3NzcSj02ESmuUoryffv2YcyYMejUqRM6deqEMWPGYN++fZVxaCIiIlHl5+ejS5cu+Ne//oX169eLkiEkJAS5ubkYNGiQKMcnorKpdPhKZmYmhg4ditOnT0MQBDRu3BiCICAyMhL79u3Dtm3bcOTIEdSrV0+VMYiqPD4kiKj6cnFxQUpKCq5duyZahjp16iA0NBQffvghNm/ejH//+9+iZSGi4qn0Svn8+fNx6tQpTJ06FX///TdSU1ORlpaGv//+G1OnTkVYWBgWLFigyghERESi2bdvH/z9/XH48GE0btxY1Cx2dnZYtGgRpk2bhjt37oiahYiKkgiCIKiqcwMDA/To0QMBAQHFbv/kk09w/vx5JCYmqiqCQviYahIbr5TTa8Lc8rXn76+q69GjRzAyMsLkyZOxefNmsePI2dnZ4eHDh0hMTJQ/bZuIxKfSn8aMjAz06tWrxO29e/dGRkaGKiMQERFVutfjyI2NjatUQQ4AYWFhePHiBT7++GOxoxDRG1RalFtZWZX6J7I7d+7A0tJSlRGIiIgqnbu7OxISEnD+/HmxoxRRv359BAcH48iRI/Dx8RE7DhH9Q6VF+YoVK/DTTz/h6NGjRbYFBQVh+/bt+Prrr8vVZ3BwMNq2bQuZTIbVq1cX2X727FnY2NhAU1MT+/fvr3B2IiKiijh27Bj+85//wN/fH82aNRM7TrG6deuGL774Au7u7njw4IHYcYgISp59ZeLEiUXWmZiYYNiwYWjbti3atWsHiUSCGzdu4K+//oKlpSX27NmD3r17K9R/Xl4epkyZgpCQEEilUtjZ2cHR0RHm5ubyNkZGRvD19cW6deuU9r6IiIgUkZqaihEjRmDcuHEYPny42HFKtXbtWpw8eRJdu3bFw4cPOb6cSGRKLcp9fX1L3Hbr1i3cunWr0LorV67g6tWr2LFjh0L9X7x4ETKZDKampgCA0aNHIygoqFBRbmxsDAD85UJERJWua9eu0NfXV5thIWfPnoWhoSGcnZ2xd+9eseMQ1WhKrVzz8/PL/crLy1O4/4SEBLRs2VK+LJVKkZCQUKGs3t7esLW1ha2tLZ48eVKhPoiIiF6bNm0a7t27h/Pnz6vNhaHGjRvj0KFDCAgIKHGmNCKqHCp9eJCyFTd7o0QiqVBf7u7ucHd3B1AwpRgRUVVQ0vSY5Z0qkSrXqVOnsGnTJvj5+UEqlYodp1wcHBzg6emJcePGoXv37jA0NBQ7ElGNVClFuSAIuHz5Mu7fvw8AMDU1xQcffFDugloqlSIuLk6+HB8fz18eREQkqoyMDAwZMgROTk5wdnYWO06F/PjjjwgNDUXXrl1x7949tbnST1SdqPynLjg4GK1bt4adnR1GjRqFUaNGwc7ODjKZDCdPnixXX3Z2drhz5w5iYmKQk5MDf39/ODo6qig5ERFR2Xr06IHGjRur/fCP8PBwJCYmYvLkyWJHIaqRVFqUh4eHw9HREWlpaZg2bRq8vb3h7e2N6dOnIy0tDY6Ojrhw4YLC/WlqamLTpk1wcHBAu3btMHLkSFhYWMDLywtHjhwBAERGRkIqlSIwMBAeHh6wsLBQ1dsjIqIa7quvvsL169cRHh6u9leXdXV1ERAQAF9fX/n/U4mo8kiE4gZqK4mDgwNu3ryJiIgIGBgYFNqWmJiITp06wdzcHMHBwaqKoBA+pprEVtI4YqLXShpTzt9flW/y5Mn4+eefsXbtWkydOhXe3t7V6uqym5sb9u7di1WrVmHOnDnw8fGBi4uL2LGIqj2VfqyPiIiAu7t7kYIcAAwMDPDpp5/i999/V2UEIiIipQoJCcHLly/x+eefw9jYuFoV5ACwbds2SCQSzJo1C7m5uQgKChI7ElGNoNKiPCcnBw0aNChxe8OGDZGTk6PKCEREREqVmJgo/3dMTAy6d+8uYhrla9GiBbKysuTLly5dEjENUc2h0qK8Xbt28Pf3R25ubpFtubm5CAgIQLt27VQZgYiISGlyc3Px6tUr+XKtWrXQr18/ERMpX9++fQstvznrGRGpjkqnRPT09IS7uzv69OmDOXPmyJ+8ef36daxduxYRERHw9vZWZQQiIiKFpaam4ujRo7h79y6eP3+O+vXrQyaTwdHREU2aNMHBgwcBFDwjw8PDA99//z20tLRETq1ce/fuxcaNGzFu3DgEBwcjNzcX+fn50NDQKPP8EFHFqbQonzx5Mu7cuYN169bh/PnzRbbPnj0bkyZNUmUEIiKiMl2/fh0+Pj64cOECJBIJsrOz5du0tbWxbds2dOnSBY6OjhgwYAAOHjyIOnXqiJhYtXR1dXHixAn8/fffcHNzw82bNxU6P25ubpz1jKiCVDr7ymu3b99GUFAQYmJiIAgCWrduDUdHR5iZman60Arh7AVUWTjLClUUZ19Rnf3792PDhg3Izs4u9snRr0kkEmhra2PGjBkYMWJEJSYUF88PUeVQ2ZXy7Oxs+VSIZmZmmD17tqoORUREVCGvC843b2wsiSAIyMrKwoYNGwCgRhSePD9ElUdlN3rWqlULffr0wYkTJ1R1CCIiogq7fv16qQVny5YtER4ejmXLlhVa/7rwvHHjRmXEFE1J52fZsmUIDg7GmTNncODAAQwdOrTQ9ppyfoiUTWVFuaamJvT19Uv9UxcREZFYfHx8Co2NftvcuXNLLCyzs7Ph4+OjqmhVQknnx9fXF0OGDIG9vT1mzZoFT09P/Otf/yrUpiacHyJlU+mUiJ988gn27duH/Px8VR6GiIioXFJTU3HhwoUSLxz1798fz549Q2RkZLHbBUFAeHg40tLSVBlTNKWdn/v37xeaFhIApFJpoeXqfn6IVEGlRfnkyZORmZmJfv364ejRo7h16xYePnxY5EVERFSZjh49ColEUuy2evXqwcPDQz42uiQSiQRHjx5VRTzRlXZ+gIK/Ipw/fx4HDhxAcnIywsPDi7SpzueHSBVUOiVi+/btIZFIIAgCzpw5U2K7vLw8VcYgIiIq5O7duyUOXfnss89w5MgRPH78uNQ+srOzcffuXVXEE11p5wcA1qxZg7Vr18LS0hK2trbFPp27Op8fIlVQaVHu5eVV6idtIiIiMTx//rzY9WZmZujYsSOcnZ0V6ufZs2fKjFVllHR+3pSfn48///wTAwcOxIgRIxAQEFCkTXU9P0SqoNKifMmSJarsnoiIqELq169f7PoOHTrA0NAQx44dAwDo6OhAQ0MDpqamcHFxKdK+QYMGKs0plpLOT3Fq1apVZEz5a9X1/BCpgsqK8idPnuD+/fvQ1dVF69atVXUYIiKicpPJZNDW1i4yROPgwYP49ddf5csuLi4wNDTEqlWrivShra0NmUym8qxiKOn8NGnSBHZ2djh37hyys7PRsWNHODg4YOHChUX6qM7nh0gVlH6jZ35+Pj777DMYGBigS5cuMDMzQ7du3fDkyRNlH4qIiKhChgwZUuzMItnZ2UhJSZG/Xr58iezsbKSnpxdpKwgChgwZUhlxK11J50cQBDg5OeH48eM4ffo0ZsyYgfXr1+O3334rtm11PT9EqqD0K+WbNm2Ct7c3DA0N0blzZ9y5cwcXLlyAh4cHDh48qOzDERERlVvTpk3RpUsX/Pbbb6U+T8Pb27vY9RKJBF27dkWTJk1UFVFUJZ2f9PR0eHh4lLl/dT8/RKqg9Cvlu3btQrt27XDz5k0EBgYiOjoakyZNwtGjR4u90kBERCQGNzc3aGtrV2hfbW1tuLm5KTlR1cLzQ1S5lF6U//XXX3B1dS10c8fUqVORl5eH27dvK/twREQ1gmRN8S+qOAsLC8yYMQN16tQp13516tTBjBkzYG5urqJkVQPPD1HlUvrwlRcvXsDQ0LDQutfLL168UPbhiIiIKmzEiBEAgA0bNiA7O7vUoSwSiQTa2tqYMWOGfL/qjueHqPKoZPaVt+cmf71c2g8zERGRGEaMGAFzc3P4+PggPDwcEomk0Kwj2traEAQBXbt2hZubW427AszzQ1Q5VFKUHz9+HI8ePZIvZ2ZmQiKRyMeYv0kikWDmzJmqiEFERKQQc3NzrF27FmlpaTh69Cju3r2LZ8+eoUGDBpDJZBgyZEiNvmmR54dI9SSCki9fa2iUb5i6RCJBXl6eMiOUm62tLaKiokTNQDUDxwCTsnUI5O8vIqLqQOlXysPCwpTdJRERERFRtab0orxnz57K7rKQ4OBgTJ8+HXl5eZg8eTLmzZtXaHt2djbGjx+PS5cu4b333kNAQACMjY1VmomIiIiI6F2oZEy5quTl5WHKlCkICQmBVCqFnZ0dHB0dC91UsmPHDjRp0gR3796Fv78/5s6di4CAABFTU03EYSpERERUHkqfp1yVLl68CJlMBlNTU2hpaWH06NEICgoq1CYoKAgTJkwAUHDH+KlTpzjrCxERERFVaWp1pTwhIQEtW7aUL0ulUkRERJTYRlNTE40aNUJKSgp0dXULtfP29pY/PvnWrVuwtbUt9phPnjyBnp6eMt9GpVL3/IB6vocOb/xbHfO/Sd3zA+r/HkrLHxsbW7lhiIhIJdSqKC/uivfbc6Ir0gYA3N3d4e7uXuYx1X1mFnXPD6j/e2B+8an7e1D3/EREVDa1Gr4ilUoRFxcnX46Pjy/y9NA32+Tm5uLp06do2rRppeYkIiIiIioPtSrK7ezscOfOHcTExCAnJwf+/v5wdHQs1MbR0RE7d+4EAOzfvx+9e/cu9ko5EREREVFVUWvJkiVLxA6hKA0NDbRp0wYuLi7YuHEjXFxc4OTkBC8vLzx79gxt27aFlZUV9uzZg/nz5yM6Ohpbt25956eMdejQoexGVZi65wfU/z0wv/jU/T2oe34iIiqd0p/oSaRM3bp1w6NHj3D37l2xoyjsjz/+wBdffIHLly/j6dOnWL58ORYuXCh2rDKFhoaiX79+8PPzg4uLi9hxiIiIahS1Gr5CVcsnn3wCiUSC6OjoEtsIggATExM0btwYL1++rMR04nj16hWcnJwQExODlStXws/PD8OGDVNo36tXr0IikUAikeD3339XcdLK89dff2HRokXo1KkTdHV10bBhQ1hbW2PVqlXIzMwUOx4REVGVwKKcKmzSpEkAAB8fnxLbhIWFITY2FqNHj0bdunUrK5po7ty5g9jYWMyaNQtTpkyBi4sL2rdvr9C+O3bsQKNGjaCrq4sdO3aoOGnl+emnn/D999/DzMwMixcvxpo1a9CmTRvMnz8f3bp1Q1ZWltgRiYiIRMeinCqsf//+aNmyJfbs2YOcnJxi27wu2F8X8NXdo0ePAKDcM/7k5ORg9+7dGDVqFMaMGYOAgAC8ePFCFREr3ahRoxAfHw8/Pz9MnToVnp6eCAwMxNy5c3H58mX4+vqKHZGIiEh0LMqpwjQ0NODq6oqUlBQcOXKkyPaMjAwcPHgQ7du3h52dnXz9zz//jCFDhsDIyAja2trQ09PDxx9/jGvXril0XKlUir59+xZZHxoaColEgt27dxdan5WVhRUrVsDc3Bx16tRBkyZN4OjoiD///FPh93r//n24uLigefPm0NbWhkwmw8KFCwsNyenWrRv69OkDABg3bpx8KEp8fHyZ/R8+fBgpKSmYMGECXF1d8ezZMwQGBhZpd/fuXUgkEqxYsQJBQUHo0KED6tatC0NDQ8ybNw+5ublF9tm3bx+srKxQp04dtGrVCsuXL8fJkyeLPVfFyc/Px6ZNm2BjYwMdHR00aNAAffr0wW+//VbmvkDBrEkNGzYssn7UqFEAoPDXnYiIqDpjUU7vxM3NDRKJpNghLP7+/sjMzCxylXzTpk3Q1NSEh4cHfvzxR0yaNAlnzpxBly5dcO/ePaXmy8nJQf/+/bF8+XJ07doVGzZswJw5c3Dt2jV06dIFly9fLrOPmJgYdOzYEfv374ezszO+++47WFtbY+XKlRg0aBDy8vIAAF5eXpg3bx4AwNPTE35+fvDz81PoqvmOHTsgk8nQpUsX2NjYwNLSEv/5z39KbH/06FG4u7tj0IHFGh4AACAASURBVKBB+Pbbb9G+fXusWbMG3377baF2e/bswahRo5CdnY0lS5ZgypQp8Pf3x4IFC8rM9JqzszOmT5+Otm3bYu3atVi8eDFSUlLQp08f/PLLLwr387bXH1aaN29e4T6IiIiqDYHoHfXu3VuoVauWkJCQUGj9hx9+KGhpaQlPnjwptP758+dF+rh69apQu3ZtYerUqYXWd+3aVWjdunWhdS1atBD69OlTpI+QkBABgODn5ydf98033wgSiUQICQkp1DYtLa3Eft42cuRIAYAQHBxcaP2MGTMEAIKvr2+pGcry8OFDQUNDQ1i+fLl83bp16wQAwu3btwu1vXPnjgBAqFevnvDgwQP5+ry8POFf//qXIJVK5etycnKE5s2bCwYGBkJaWpp8fUZGhmBkZFQkZ3HZ9+3bJwAQduzYUShHTk6OYG1tLchkMoXf55tevXol2NnZCbVr1xbu3LlToT6IiIiqE14pp3c2adIk5OXlwc/PT77u1q1b+P333+Ho6AhdXd1C7evVqwegYGaWjIwMJCcnQ19fHzKZDBEREUrNtnv3blhYWMDa2hrJycnyV25urnwIRnZ2don75+bm4tixY7Czs4ODg0Ohba+vNh86dOidMvr4+EAQBIwbN06+zsXFBZqamiVeLXdycoKRkZF8WUNDA/b29oiPj5cPqbl48SIeP34MNzc3NG7cWN62QYMG8PDwUCjb7t270bhxYwwZMqTQ+Xv69CkGDx6Mu3fv4v79++V+z1OnTkVkZCRWrlwJmUxW7v2JiIiqG02xA5D6+/jjj9G4cWP4+Phg7ty5ACAvJidOnFik/aVLl7Bo0SKcPXu2yM2Mbdq0UWq2W7duIScnB3p6eiW2SU1NhYGBQbHbHj9+jMzMTFhYWBTZpquri+bNm1eoKH1NEAT4+PjAxsYGr169KjQf+4cffoidO3dixYoVqFWrVqH9TE1Ni/T13nvvyd9PixYtEBMTAwBo27ZtkbbFrSvOzZs3kZ6ejmbNmpXY5vHjx8XmKclXX32FrVu34t///jdmz56t8H5ERETVGYtyemd16tTB2LFjsXnzZly4cAGdOnWCn58fpFIp+vfvX6htbGwsevTogaZNm8LLywtmZmaoV68eJBIJpk6dilevXpV5PIlEUuz64m5yzM/Ph7W1NdauXVtif6WN+RZU/GytU6dOITY2FrGxsSV+IDlx4gQGDx5caN3bRfqbXmdWRnZBEKCvr1/oryBvMzc3V7i/hQsXYvXq1fj000+xadOmd85HRERUXbAoJ6WYNGkSNm/eDB8fH6SmpuLRo0dYsGBBkeLxwIEDyMzMRHBwMLp37y5fLwgCkpOT0ahRozKP1bRpU6SmphZZX9wV6zZt2uDJkyfo06dPicV8afT19aGjo4Pr168X2ZaSkoKkpCR8+OGH5e73tf/85z+oW7cudu7cWWy+yZMnY8eOHUWKckWYmJgAKHh4z9uKW1ecNm3aICQkBF26dIGOjk65M7xp0aJFWLlyJSZOnIht27ZV6OtBRERUXXFMOSmFjY0NrK2tERAQgE2bNkEikcDNza1Iu9dF+ttXcbdu3Yrk5GSFjmVmZoYbN24gMTFRvi4rKwubN28u0nb8+PFISEjA999/X2xfjx8/LvVYmpqaGDx4MCIjIxEaGlpo29dffw1BEDB8+HCFcr8tLS0Nhw4dwkcffYRPPvkEI0aMKPIaMmQIfvnlFyQlJZW7/06dOqFZs2bw8fFBenq6fP2zZ8+wbds2hfoYP348cnNzS5ytpazz95qXlxdWrFgBV1dX/PTTTyzIiYiI3sIr5aQ0kyZNwtSpU3Hy5EnY29ujdevWRdoMGjQI8+fPh7OzM6ZMmYJGjRohPDwcwcHB8iu7Zfn888+xf/9+9OnTBx4eHsjOzsauXbtQv379Im1nzZqF0NBQzJw5E6GhobC3t0eDBg3w8OFDnDp1Cg0aNEBISEipx1u9ejVOnTqFIUOGYMqUKTA1NcWZM2cQGBiIXr16wcXFRbET9JY9e/YgKysLTk5OJbZxcnLC7t27sWvXLnz55Zfl6r927dpYu3YtJkyYgE6dOmHixInQ0NCAr68vmjVrhocPH5ZZHI8ePRonTpzAhg0bEBUVhYEDB0JXVxfx8fEIDw/Hw4cPcfv27VL72LBhA5YvXw5jY2P06tULP//8c6HtBgYG8vndiYiIaiyxpn2h6ic1NVWoU6eOAEDYtWtXie3CwsKELl26CPXr1xcaN24sDBo0SLh+/Xqx0x8Wt04QBGHHjh1CmzZthNq1awsmJibC2rVrhZMnTxY7HeGrV6+E7777TujQoYOgo6Mj6OjoCDKZTHBxcSkyVWJJ7t27J4wdO1bQ09MTateuLZiamgrz588XMjMzC7Urz5SI1tbWgpaWlpCenl5im8zMTKFevXpCu3btBEH4/5SIb06f+NqCBQsEAEJcXFyh9Xv37hXat28vaGlpCS1bthSWLVsmBAYGCgCEAwcOKJTd19dX6Nq1q9CgQQOhTp06grGxseDk5CQEBgaW+T6dnZ0FACW+FJmWkoiIqLqTCIKK72QjoipnzZo1mDdvHiIjI2Frayt2HCIiohqPRTlRNZaTk4NatWoVuuH22bNnaN++PV6+fImEhATUrl1bxIREREQEcEw5UbV2+/ZtODo6YvTo0TAxMUFCQgJ8fX3x8OFDeHt7syAnIiKqIliUE1VjzZs3R8eOHbF7924kJSVBU1MTVlZWWLduHUaMGCF2PCIiIvoHh68QEREREYmM85QTEREREYmMRTkRERERkchYlBMRERERiYxFORERERGRyFiUExERERGJjEU5EREREZHIWJQTEREREYmMRTkRERERkchYlBMRERERiYxFORERERGRyEQtyoODg9G2bVvIZDKsXr26yPazZ8/CxsYGmpqa2L9/v3x9WFgYrK2t5a86derg8OHDAABXV1eYmJjIt0VHR1fa+yEiIiIiqgiJIAiCGAfOy8uDmZkZQkJCIJVKYWdnh71798Lc3FzeJjY2FhkZGVi3bh0cHR0xYsSIIv2kpqZCJpMhPj4eOjo6cHV1xeDBg4ttS0RERERUFWmKdeCLFy9CJpPB1NQUADB69GgEBQUVKsqNjY0BABoaJV/Q379/PwYMGAAdHZ0KZ9HV1ZUfi4hIncTGxiI5OVnsGERE9I5EK8oTEhLQsmVL+bJUKkVERES5+/H398esWbMKrVuwYAGWLVuGPn36YPXq1dDW1i61D2NjY0RFRZX72EREYrO1tRU7AhERKYFoY8qLGzUjkUjK1UdiYiKuXr0KBwcH+bpVq1bh1q1biIyMRGpqKtasWVPsvt7e3rC1tYWtrS2ePHlSvvBEREREREokWlEulUoRFxcnX46Pj4ehoWG5+ti3bx+GDx+O2rVry9cZGBhAIpFAW1sbbm5uuHjxYrH7uru7IyoqClFRUdDT06vYmyAiIiIiUgKFi/KXL18q9cB2dna4c+cOYmJikJOTA39/fzg6Oparj71792LMmDGF1iUmJgIouBJ/+PBhtG/fXmmZiYiIiIhUQeGi3MDAAJ6enrh06ZJSDqypqYlNmzbBwcEB7dq1w8iRI2FhYQEvLy8cOXIEABAZGQmpVIrAwEB4eHjAwsJCvn9sbCzi4uLQs2fPQv06OzvD0tISlpaWSE5OxsKFC5WSl4iIiIhIVRSeEnHgwIEICQlBfn4+LC0tMXnyZLi4uKBx48aqzqhytra2vNGTiNQSf38REVUPCl8pP378OB48eIBly5bhxYsXmDZtGgwNDeHs7IywsDBVZiQiIiKq+pKSgG++AVxcgCFDCv77zTcAJ5QgBVT44UFhYWHYsWMHDh06hKysLBgbG2PSpElwdXUt9w2bYuOVJqLCJMVPWgRhbuXmoLLx9xdRFRAZCaxaBZw4UbCclfX/bXXrAoIADBgAfPUVYGcnTkaq8t75iZ5Pnz7F1KlTsXv3bkgkEtSqVQuDBg3CV199hY4dOyorp0qV939qLFiouijpe7kkVe17nD+LLMqJRLdlC/Dll8DLlwXFd0kkkoICfd06wNOz8vKR2qjww4OSk5Ph5+eHHTt24MaNG6hXrx5GjRoFbW1t7N69G0ePHsWWLVvw6aefKjMvUbFYnBERUaV7XZBnZpbdVhAK2n35ZcEyC3N6S7mKckEQcPLkSezYsQNHjx5FTk4OPvjgA2zevBnOzs5o0KABAODrr7+Gk5MTli9fzqKcANS8ormmvV9VK+8VfSIilYuMLLYgTwUwCcCvAHQBrAIw9s0GrwtzOzuAT+SlNyhclHt5ecHX1xcJCQmoV68eJkyYAHd3d3To0KFI20aNGmHChAlwdXVVZlYiokrDD1ZEVKpVqwqGrLxlCgAtAI8BRAMYBOB9ABZvNnr5smD/AwcqISipC4WL8hUrVqBDhw5YtGgRxo4di3r16pXa3sbGBl5eXu8ckMRVXQuT6vq+qPx4FZ6Iyi0pqeCmzrfGkL8AcADANQD1AXQD4AjAD8DqNxsKAnD8eMGsLHyqOP1D4aL8jz/+gLW1tcIdW1hYFHrYDxXFwlB98GtFlYXfa0RqwNe32NW3AdQCYPbGuvcB/FZcY4mkoJ/Zs5UcjtSVwkX5rFmzsGDBAvTp06fY7WFhYVi+fDlOnz6ttHBiU5craOo+g4Y6U5fvESIiUqIrVwpPe/iP5wAavbWuEYBnxfXx8iVw9arys5HaUrgoP3PmDCZPnlzi9qSkJPz2W7GfBYlKxKuC6oUfAImIADx9Wuzq+gAy3lqXAaBBSf2kpSkvE6m9Ck+J+Lb09HRoa2srq7tKdekRr3gSVSfF/TzzAwIRKU2jt6+HFzADkAvgDoA2/6z7E2/d5PmmJk2UnYzUWKlF+ZUrVxAdHS1fPnfuHHJzc4u0S01NxebNm2Fubq78hNVATSr4a9J7rQj+ZUD98WtIRLCyKpg55a0hLPUAfAzAC8B2FMy+EgTgQnF91K0LWFqqOCipk1KL8kOHDmHp0qUAAIlEgm3btmHbtm3Ftm3QoAF++OEH5SesgVjY0mssAKsv/pwTqTFXV2Dx4mI3bQYwEUAzAO8B2IISrpQLQkE/RP8otSh3dXWFvb09BEFA7969MX/+fPTr169QG4lEgvr168Pc3Bx16tRRaVgiVWOhpFz8UEFE1VKzZsCAAcDhw0WmRWwK4HBZ+0skwMCBnA6RCim1KG/VqhVatWoFAPDx8UGPHj1gYmJSKcGoamPxSu9CjGJd3b9nS8pf9PFtRFQpvvoKOHmyyBM9FVK3bsH+RG9Q+EbPCRMmqDIHVaKadBOcuhdiJeEV6KqHXxOiGsbODli3DnkzZ6JWdrbi++noAOvWAba2qstGaqnEonzXrl0AgHHjxkEikciXyzJ+/HiFDx4cHIzp06cjLy8PkydPxrx58wptP3v2LGbMmIErV67A398fI0aMkG+rVasWLP+5QcLIyAhHjhwBAMTExGD06NFITU2FjY0N/Pz8oKWlpXCmd6HOBaA6Z68OlHX+WRgSEVWe9DFjsGjaNKyrVQva+flFhrK8SZBIkCkIONevHz7y9KzElKQuJIJQ/HeQhoYGJBIJXr58CS0tLflyCc0LOpNIkJeXp9CB8/LyYGZmhpCQEEilUtjZ2WHv3r2FZnCJjY1FRkYG1q1bB0dHx0JFef369fH8+fMi/Y4cORIff/wxRo8ejc8++wzvv/8+PMv45pdIbYGpUQrlpspR3iKSHyqoqirpe1lZ37MdAm0RFcXfX0RisLS0RHp6Oh4cOACNNWuA48cLxou/fPn/RnXrFhTrAwdid8uWmLBxIy5fvgwrKyvxglOVVOKV8rCwMACQX2V+vawsFy9ehEwmg6mpKQBg9OjRCAoKKlSUGxsbAyj4gKAIQRBw+vRp/PzzzwAKhtwsWbKkzKKciIiIqDy++OIL3Lp1C/fu3YOGkVHBFIlPngC+vgVP6kxLK5iH3NKyYJYVPT24APjp8mXY29vj0aNHlfaXfFIPJRblPXv2LHX5XSUkJKBly5byZalUioiICIX3z8rKgq2tLTQ1NTFv3jwMGzYMKSkpaNy4MTQ1NeV9JiQkKDU3iYtXxEnd8HuWqPo5c+YMvvvuO/j4+MDIyOj/G/T0gNmzS903JCQEzZo1w8CBAxEaGqripKROlPJEz+zs7HI/zbO4YTASiUTh/R8+fAhDQ0Pcv38fvXv3hqWlJRo2bKhwn97e3vD29i5YePFE4eNS5WAhQ0REVdHz588xePBgDB06tEKTYGhpaSE0NBSdOnXCxo0bMXXqVBWkJHWk2LgQACdOnMCSJUsKrdu8eTMaNmyIevXqYezYsXj16pXCB5ZKpYiLi5Mvx8fHw9DQUOH9X7c1NTWFvb09Ll++DF1dXaSnp8ufOlpan+7u7oiKiioYi1mP84QSERFR2ezt7dGgQQMcOHCgwn3Y2tpi8eLFmDlzJm7evKnEdKTOFC7K165di1u3bsmXb968ienTp8PQ0BD9+vVDQEAAfvzxR4UPbGdnhzt37iAmJgY5OTnw9/eHo6OjQvumpaUh+5/ph5KTkxEeHg5zc3NIJBL06tUL+/fvBwDs3LkTQ4cOVTgTERERUUkWLVqE6OhonD9/XuH73Uri5eWFDh06oGfPnvKLiVSzKfwddfPmTdi+MadmQEAA6tati4sXL+LEiRMYNWoUdu7cqfCBNTU1sWnTJjg4OKBdu3YYOXIkLCws4OXlJZ/eMDIyElKpFIGBgfDw8ICFhUWhLO+//z569eqFefPmyW8QXbNmDb799lvIZDKkpKRg0qRJCmciIiIiKk5ERARWrlyJjRs3onXr1krpMywsDC9fvsSwYcOU0h+ptxKnRHxbnTp1sHXrVri6ugIAunXrBl1dXRw+XPAwWW9vb8yZMwfp6ekqC6sqnBKRiNQVp0QkUr2srCw0a9YMXbp0QXBwsFL7Dg8PR/fu3eHt7Y3JkycrtW9SLwpfKdfV1cWDBw8AAM+ePUNkZCS6desm3/7q1SuF5ygnIiIiUhd9+/aFlpYWjh07pvS+u3btirlz58LT0xMxMTFK75/Uh8Kzr3Tu3Blbt26FhYUFTpw4gdzcXAwcOFC+/e7duzAwMFBJSCIiIiIxrF69Gv/9739x5coV+ZTLyrZq1SocP34c3bp1Q1xc3DuPVyf1pPBXfenSpcjPz8fIkSPh4+OD8ePHy8dxC4KAQ4cOoWvXrioLSkRERFSZrly5ggULFmDt2rXy+9pU5dy5c0hLS8Po0aNVehyquhT+yGdubo6bN28iPDwcjRo1Qo8ePeTb0tPTMXPmTNjb26siIxEREVGlysnJgb29Pbp3745Zs2ap/HgNGzbE0aNH0a9fP+zduxdjxoxR+TGpalH4Rs/qjDd6EpG64o2eRKrRt29fREVFISkpCVpaWpV23GnTpmHr1q2IjY0t1/NbSP1VaHBUZmYmUlJSin0qZ6HHzRIRERGpmY0bNyIsLAyRkZGVWpADwA8//ICQkBB06dIF9+/f5/jyGkThojw/Px/ffPMNNm7ciEePHpXYjjOwEBERkbq6efMmZs6ciaVLl8LGxkaUDOfOnYNUKsXEiRPh6+srSgaqfAoX5fPmzcO6detgYWEBJycnvPfee6rMRURERFSpcnNz0bNnT9ja2mLhwoWi5dDV1cW+ffswbNgwDB06FMOHDxctC1UehYvy3bt346OPPsLx48dVmYeIiIhIFMOGDcPLly9x+vRpsaPA0dEREydOxJgxY/Dw4UM0a9ZM7EikYgoPVEpLS8PQoUNVmYWIiIhIFNu3b8fx48cRHBwMHR0dseMAKHhaeosWLQo9rJGqL4WLcktLSyQmJqoyCxEREVGli4mJgaenJ+bNm1elnrmioaGB8PBwxMbGwtPTU+w4pGIKF+WLFy/G1q1bERcXp8o8RERERJUmPz8fXbt2Rfv27fH111+LHacIfX197N69G9u2bcPJkyfFjkMqpPCY8kuXLqFVq1YwNzfH8OHDYWJiglq1ahVqI5FIsGjRIqWHJCIiIlKFUaNG4enTp7h165bYUUo0cuRIHD58GMOGDUNiYiIaN24sdiRSAYUfHqTIPJkSiUQtp0Tkw4OISF3x4UFEFbdnzx6MGzcOoaGh6N27t9hxSpWfn49WrVqhcePGuHr1qthxSAUUvlIeExOjyhxERERElSY+Ph5ubm6YOnVqlS/Igf+PL2/dujW++OILrF+/XuxIpGQKXymvznilnIjUFa+UE5Vffn4+TExMoKOjg5s3b4odp1x27twJNzc3nD59Gvb29mLHISWq0LNb7969i/DwcDx9+vSdDh4cHIy2bdtCJpNh9erVRbafPXsWNjY20NTUxP79++Xro6Oj0blzZ1hYWMDKygoBAQHyba6urjAxMYG1tTWsra0RHR39ThmJiIioenFzc8Pjx48RHh4udpRymzBhAoYOHYrBgwfj+fPnYschJSpXUX7s2DG0bt0abdu2RY8ePXDp0iUAQFJSEmQyWaHCuSx5eXmYMmUKTpw4gRs3bmDv3r24ceNGoTZGRkbw9fXF2LFjC63X0dHBrl27cP36dQQHB2PGjBlIT0+Xb1+7di2io6MRHR0Na2vr8rxFIiIiqsYOHToEPz8/7N+/H02bNhU7ToUcOHAADRo04JXyakbhovzMmTMYPnw4mjZtisWLF+PNUS/NmjVD69at4e/vr/CBL168CJlMBlNTU2hpaWH06NEICgoq1MbY2BhWVlZFbjI1MzNDmzZtAACGhoZo1qwZnjx5ovCxiYiIqOZJSkrCmDFjMGnSJAwePFjsOBWmoaGB8+fPIzo6Gl5eXmLHISVRuChftmwZ3n//fURERGDKlClFtnfu3Bl//PGHwgdOSEhAy5Yt5ctSqRQJCQkK7//axYsXkZOTg9atW8vXLViwAFZWVpg5cyays7PL3ScRERFVD+np6cjJyQEAdOvWDS1atMBPP/0kcqp317p1a2zcuBErV65EZGQkgIIPHaS+FC7Ko6Ki4OzsXOLUiFKpFI8ePVL4wMXdXyqRSBTeHwASExMxbtw4+Pj4yHOtWrUKt27dQmRkJFJTU7FmzZpi9/X29oatrS1sbW2BF7zKTkREVB1ZWFigYcOGGDp0KB48eKCW48hL4unpiX79+qFPnz7o3Lkzmjdvjnv37okdiypI4aI8Ly8P2traJW5PTk6GlpaWwgeWSqWFng4aHx8PQ0NDhffPyMjAoEGDsGLFCnz44Yfy9QYGBpBIJNDW1oabmxsuXrxY7P7u7u6IiooqmLWgnp7CxyUiIiL18fjxY2RnZ+PIkSPo378/9PX1xY6kVMuXL8ezZ8/w+++/Ayi4/4/Uk8JFebt27XDu3LkStx87dgzvv/++wge2s7PDnTt3EBMTg5ycHPj7+8PR0VGhfXNycjB8+HCMHz8en3zySaFtiYmJAAquxB8+fBjt27dXOBMRERFVHxkZGYUeanjs2DGMHz9exETKFR8fj44dOxZad/bsWZHS0LtSuCifNGkS9u/fjx07diA/Px9AwXCTzMxMTJs2Df/973/h7u6u8IE1NTWxadMmODg4oF27dhg5ciQsLCzg5eWFI0eOAAAiIyMhlUoRGBgIDw8PWFhYAAD27duHs2fPwtfXt8jUh87OzrC0tISlpSWSk5OxcOFChTMRERFR9XHixIlCyyYmJpg1a5ZIaZTP0NAQ48aNKzT89/UVc1I/5Xp4kIuLC37++Wc0bNgQz549g56eHlJSUpCXlwc3Nzfs2LFDlVlVhg8PIiJ1xYcHUY2WlAT4+gJXrgBPnwKNGgFWVoCbG6Cnh969eyMsLAwtWrTAzz//jB49eoidWCWeP3+OTz/9VD4Lnry0K+P8UNVS7id6Hjp0CLt378atW7cgCALatGmD8ePHw8nJSVUZVY5FORGpKxblVCNFRgKrVgGvr4RnZf1/W926gCAAAwbgobMzwnNyMGbMGHFyVrLk5GQcPHgQ7h98oND5wVdfAXZ24oSlIspdlFdHLMqJSF2xKKcaZ8sW4MsvgZcvC4rLkkgkBQXounWAp2fl5RMbz4/a0hQ7ABEREZFCXhecmZlltxWEgnZfflmwXBMKT54ftabQjZ5Pnz7F119/ja5du0JPTw/a2trQ09NDt27dsHr1amRkZKg6JxEREdVkkZFFCs5sAJMAtALQAMAHAE68vd/rwrO6/0WpmPMDAJsA2ALQBuBa3H415fyogTKL8itXrsDCwgKLFi3Cf//7X+Tk5KBZs2bIycnBhQsXMH/+fLRv3x43btyojLxERERUE61aVTAk4w25AFoC+A3AUwDLAYwEEPv2vi9fFuxfnRVzfgDAEMBCABNL27cmnB81UGpRnpWVBScnJzx58gTz589HTEwMnj59iri4ODx9+hQxMTGYP38+Hj9+jI8//piPtCciIiLlS0oquGnxrTHS9QAsAWCMgoJmMAATAJfe3l8QgOPHgSfV9AneJZwfAPgYwDAA75W2f3U/P2qi1KLc398f9+7dw88//4zly5ejVatWhba3atUKK1aswO7du3H79m35VDxERERESuPrq1CzxwBuA7AobqNEonA/akcZ76s6nx81UWpRfuTIEXTs2LHM6Q4/+eQTdOzYEUFBQUoNR0RERIQrVwpP61eMVwCcAUwA8K/iGrx8CVy9qvxsVYEC56dM1fn8qIlSi/I///wT/fv3V6ij/v37488//1RKKCIiIiK5p09L3ZwPYBwALRTc2FiitDTlZapKyjg/Cquu50dNlDol4pMnT2BkZKRQR0ZGRnjCsUhERESkbI0albhJQMEMLI8BHAdQu7R+mjRRaqwqo5TzUy7V9fyoiVKvlL948QI6OjoKdVS3bl28ePFCKaGIiIiI5KysgDp1it3kCeAmgKMA6pbWR926gKWl8rNVBaWcn1wAWQDy/nll/bOuiOp8ftREqUU5H/ZJREREonN1RXEVyQMA2wBEA9AHkv2/EAAAIABJREFUUP+f157i+hAEwNVVVQnFVcr7WoGCDyurAez+598rimtYnc+PmijziZ7r169XaFaVhIQEpQQiIiIietPZW7eQkZeHAQBqvbG+FVBssV6ERAIMHAjo6akkn+iaNQMGDAAOHy4yLeKSf16lyQNwxcAA77/3nmJPlSSVKLMov3z5Mi5fvqxQZxKJ5J0DEREREQFAfn4+xo0bh71792Ja584YFB2t2CPk31a3LvDVV8oPWJV89RVw8mSFzo+gpYUp8fGIlUrx66+/on379ioISGUp9QNRfn5+uV55eXmVlZuIiIiqsYiICOjp6SEoKAiHDx/GhvBwSNatAxS8101ORwdYtw6wtVVN0KrCzq7gfVbg/Ghu2IDg5GQYGxvj/fffx8yZM1WTkUrFv1IQERFRlZGfnw83Nzd07twZNjY2SE5OhqOjY8FGT8//F55l/XVeIvl/Qe7pqfrgVcE7nJ+GDRviwoUL8Pb2xubNm9GyZUv89ddflZObAIhclAcHB6Nt27aQyWRYvXp1ke1nz56FjY0NNDU1sX///kLbdu7ciTZt2qBNmzbYuXOnfP2lS5dgaWkJmUyGadOm8WZVIiIiNfHHH39AX18fAQEB2LdvH0JCQlDn7VlFPD2B334Dhg8vmHGk7ltzrtStW7B++PCCdjWlIH/tHc/PpEmTkJiYiObNm8Pc3Bxz586txPA1m0QQqWrNy8uDmZkZQkJCIJVKYWdnh71798Lc3FzeJjY2FhkZGVi3bh0cHR0xYsQIAEBqaipsbW0RFRUFiUSCDh064NKlS2jSpAk6duyI77//Hh9++CEGDhyIadOmYcCAAaVmkUhtgalRKn2/RESq0CGw4HchkTrLz8/HlClTsG3bNvTo0QPHjh1D/fr1y97xyRPA1xe3DxzA3agoDBw7tmBaP1fX6ntTZ3n8c34itm/Hs7g49B0xolznZ8uWLZg+fTpatGiB0NBQtG7dWvWZazDRrpRfvHgRMpkMpqam0NLSwujRoxEUFFSojbGxMaysrKChUTjmyZMn0a9fPzRt2hRNmjRBv379EBwcjMTERGRkZKBz586QSCQYP348Dh8+XJlvi4iIiMrh2rVrkEql8PHxgZ+fH86cOaNYQQ4UFJazZ+PMxIkYVbcusGsXMHs2C/LX/jk/O/v0weRmzcp9fjw9PREfH49GjRrBzMwMS5YsUW3eGk60ojwhIQEtW7aUL0ulUoWnVSxp34SEBEil0gr1SURERJVr5syZeP/992FsbIykpCQ4OzuLHYne0qxZM0RHR2P9+vVYuXIlzMzM8PDhQ7FjVUuiFeXFjZpRdErFkvYtT5/e3t6wtbWFra0t8OKJQsclIiKid/fXX3+hZcuW2Lx5M7Zv344LFy6gYcOGYseiUsyYMQNxcXGoXbs2TE1NsWrVKrEjVTuiFeVSqRRxcXHy5fj4eBgaGr7TvlKpFPHx8Qr16e7ujqioqIKxmPX4Zy4iIqLKMHfuXJibm6N58+ZITEyEm5ub2JFIQfr6+rh+/TpWrFiBRYsWoV27dvj777/FjlVtKFyU9+vXDwEBAcjJyVHKge3s7HDnzh3ExMQgJycH/v7+/5/yqAwODg749ddfkZaWhrS0NPz6669wcHCAgYEBGjRogN9//x2CIGDXrl0YOnSoUvISERFRxd27dw8mJib47rvvsGnTJkRFRaFp06Zix6IKmDdvHu7fv4+8vDy0atUK69evFztStaBwUX7p0iWMHTsWhoaGmDFjBq5evfpOB9bU1MSmTZvg4OCAdu3aYeTIkbCwsICXlxeOHDkCAIiMjIRUKkVgYCA8PDxgYWEBAGjatCkWLVoEOzs72NnZwcvLS/6DvWXLFkyePBkymQytW7cuc+YVIiIiUi0vLy+YmZmhUaNGiI+Ph2dNm6awGjIyMsLt27excOFCzJkzB1ZWVkhKShI7llpTeErEnJwcHDx4EDt27MDp06cBALa2tpg8eTLGjBmj+J3SVRCnRCQidcUpEakqe/DgAfr27YvY2FisXbsWM2bMUMlxvL298cUXX+DZs2cq6V/d/fvf/8bx48cRGxurkv5jYmLQt29fPHz4EN999x0+//xzlRynulP4SvnraQtDQkJw//59LFy4EI8fP4aHhwcMDAwwadIkhIeHqzIrERERqYmVK1eidevW0NLSQlxcnMoKchKfiYkJ7t27h9mzZ2P69Ono0KEDUlNTxY6ldip0o2erVq2wdOlSxMTEIDg4GL169YKvry969OgBc3NzfP/993jx4oWysxIREVEV9/fff6Ndu3ZYvHgxVqxYgevXr0NfX1/sWFQJvv76a9y4cQPJycnQ19fH9u3bxY6kVt5p9pXo6GgcOXIE586dgyAIaN26NTQ0NDBz5kzIZDJcuHBBWTmJiIioilu/fj2MjIyQl5eH+/fvY968eWJHokrWtm1bPHjwAJ9//jk8PDzQqVMnpKenix1LLZS7KE9PT8ePP/4IGxsb2NraYvv27XBwcEBoaChu376Na9euITQ0FDo6OpgyZYoqMhMREVEVkpSUBCsrK8yZMweLFi3C7du3YWRkJHYsEtG3336LP//8E3FxcdDX18euXbvEjlTlKVyUnz59Gs7OzjA0NMTUqVORmZmJb775BgkJCfD390fv3r3lbXv37o158+bh+vXrKglNREREVcOmTZvQokULPH/+HHfv3sXixYvFjkRVRPv27REfH4+JEyfC1dUV3bt3x/Pnz8WOVWUpXJT37dsXBw8exPDhwxEWFoZbt27hiy++wHvvvVdse5lMhq5duyotKBEREVUdqamp6NChA6ZPn47Zs2fj/v37MDExETsWVTEaGhrYvHkz/vjjD9y+fRt6enoICAgQO1aVpHBRvn79eiQkJGDPnj3o2bNnme179eqFsLCwdwpHREREVc/27duhr6+P5ORk3LhxA19//bXYkaiKs7a2RmJiIlxcXDBmzBj06dMHmZmZYseqUhQuyp89e1bqo1SvX7+OZcuWKSUUERERVT3p6eno1KkTPDw88Pnnn+PBgwdo27at2LFITWhoaOCnn35CREQE/vzzT+jp6eHQoUNix6oyFC7Kly5diitXrpS4/dq1a1i6dKlSQhEREVHVsmvXLujr6yM+Ph5XrlzBt99+K3YkUlN2dnZISkqCk5MTnJyc8NFHHyErK0vsWKJTuCgv68GfWVlZ0NTUfOdAREREVHU8f/4c3bt3h6urKz799FPExcXBwsJC7Fik5jQ0NLBr1y6cO3cOFy9ehK6uLo4fPy52LFGVWkVnZGQUmlsyJSUFDx8+LNIuNTUVe/bsQcuWLZWfkIiIiEQREBAAV1dXNGzYEH/88Qesra3FjkTVTNeuXZGUlAQXFxcMHjwYQ4YMQWBgILS0tMSOVulKvVL+3XffwcTEBCYmJpBIJJgxY4Z8+c1Xhw4dEBoais8++6yychMREZGKZGZmok+fPhgzZgxcXFyQmJjIgpxURlNTE/7+/ggNDcWZM2egp6eHU6dOiR2r0pV6pdze3h5AwdCVZcuWYfjw4bCysirURiKRoH79+vjwww/RpUsXlQUlIiIi1Tt06BBcXFxQt25dREREwM7OTuxIVEP07t0bKSkp+OSTT9CvXz98/PHH8Pf3rzHDo0t9lz179pRPf/jgwQN89tln6NSpU6UEIyIiosqTlZWFYcOG4ddff8W4cePg4+MDDY1yP/ib6J1oamri0KFDOHnyJEaMGAE9PT0EBQWhR48eYkdTOYV/2nx8fFiQExERVUPHjx+Hrq4uLl68iHPnzmHnzp0syElUDg4OSElJQZcuXWBvbw9nZ2fk5+eLHUulSrxS/vqGTiMjo0LLZXndnoiIiKq2nJwcODk54ZdffsHIkSOxe/fuGjNUgKo+LS0t/PLLLzhy5AjGjh0LPT09HD9+vNpeJC7xY7CxsTFMTU2Rk5MjXy7uJs+3X+URHByMtm3bQiaTYfXq1UW2Z2dnY9SoUZDJZOjUqRNiY2MBAHv27IG1tbX8paGhgejoaAAF4+Dbtm0r35aUlFSuTERERDVBSEgIdHV1ce7cOZw+fVotx+7m5ubCx8cHv/32G3JycrBlyxZERESIHavKeP78ObZt24br16/j2bNn2LJlC27evCl2rHJzdHREcnIybGxs0LlzZ7i5uVXLq+YSoYQJyJcsWQKJRIJFixZBQ0NDvlyWxYsXK3TgvLw8mJmZISQkBFKpFHZ2dti7dy/Mzc3lbTZv3owrV65g69at8Pf3x6FDhxAQEFCon6tXr2Lo0KG4f/8+gIKifN26dbC1tVUoBwBIpLbA1CiF2xMRVRUdAm0RFcXfX6S43NxcjB49GgcPHsTQoUMRGBiodsX4a5GRkejYsWOhdQYGBqU+gbwm2bx5M6ZMmVJonZ2dHS5evChSone3f/9+jB8/HvXr10dwcDBsbGzEjqQ0Jf4ULlmypNTld3Xx4kXIZDKYmpoCAEaPHo2goKBCRXlQUJD8uCNGjMDnn38OQRAKfTjYu3cvxowZo9RsRERE1dHZs2cxdOhQ5Obm4sSJE3BwcBA70juxs7ODrq4ukpOT5euUXa+os88++wwzZszAq1ev5Ou+//57ERO9uxEjRuCjjz7C4MGDYWtrCw8PD/z444/V4h4I0d5BQkJCoYcNSaVSJCQklNhGU1MTjRo1QkpKSqE2AQEBRYpyNzc3WFtbY/ny5WU+iZSIiKi6y8/Ph7OzM+zt7dGlSxekpKSofUH+2pYtW+T/btCgAdzd3UVMU7VoaGhg7ty58mWZTIbOnTuLmEg56tevjzNnzsDPzw8+Pj6QSqW4du2a2LHemWhFeXHF8tvDY8pqExERAR0dHbRv316+bs+ePbh69SrOnTuHc+fOwc/Pr9jje3t7w9bWtmCYy4snFX0bREREVVpERIR8WrnD/2vvzuOiLPf/j7+GRZBFhFxQBxUcNUSNFNww96OliSVkJoYiHrTMb+ixo+XJyt2jx7CfmXEyFJdwTynDkFwSjplm7gu4hOCGgqIi23D//vA4J2SAQYFh4PN8PHg8nPu+7mvec/VIP1xz3df97bd8//331eppif7+/tja2gKwaNEiI6epej755BPdLHJkZKSR05SvgIAAbty4QfPmzXnuueeYNGmSsSM9lWKLcjMzM8zNzcv0U5Y1aWq1msuXL+tep6Sk0Lhx42Lb5Ofnc+fOHZycnHTno6KiisySN2nSBHj42/KIESOKXTcVEhLCoUOHHq7FtK1vcG4hhBCiqiooKECj0RAZGUlBQQFBQUF07dqVjh07cvPmTXx9fY0dsULMmTMHOzs7mSXXw8zMjICAAJydnavFLPnj6tSpQ0JCAl999RXLli3DxcWFs2fPkpubi6urK1u3bjV2RIMVe6Pn6NGjDbqx83EREREGtcvPz6dVq1bExcXRpEkTvL29WbduHR4eHro2n3/+OcePH9fd6LllyxY2bNgAPPyLp2nTpuzbt0+3Lj0/P5/bt29Tr1498vLyeOONN+jXrx/jx48vMYvc6CmEMFVyo2f1duOPNFZGneRYhgV3CixxMMujvWM+QW+0pX7TekXav/feeyxatAgzMzMcHR3JysoiMjISf39/I6SveOnp6URHR5OUlMS9e/ews7NDo9Hg6+uLo6OjseMZXU0bn/T0dAYMGMBvv/1G06ZNuXTpEra2tmRmZupdc17VxqfYorwy7Nixg9DQULRaLWPGjGH69OnMmDEDLy8vfH19yc7O5s033+TIkSM4OTkRFRWlK8D37NnDtGnTOHDggK6/+/fv06NHD/Ly8tBqtfTr14/Fixdjbm5eYg4pyoUQpkqK8urp17hTzPsxkx/sPYECsi1tdOdq52WhoOKlu0d5v38dvPs+3CAhMzMTR0dH3VZxtra23LhxAxsbG31vYdJOnjxJREQECQkJqFQqcnJydOesrKxQFIVu3boRFBRUaLKvpqjp4zNhwgSWLVume/3BBx8wZ84c3euqOj5GLcqrCinKhRCmSory6ueLsL1MuevFAwtrFLPiJ5VUBVpq52ezyP4Qb4X2pHv37sTHxxdqs2rVKgIDAys6cqXatGkTYWFh5OTklLiZg0qlwsrKitDQ0Gr7TYE+Mj5gbW1dqNBWqVRkZmZiZ2dXpcfHNDcmFUIIIaqhRwV5Vi3bUtsqZuZk1bJlyl0vCNurK8jNzc2xs7OjcePGNGzYsKIjV6pHBVV2dnapbRVFITs7m7CwMIBqV3jqI+PzUI8ePTh+/Djp6enk5uaiKArDhg1jzJgxVXp8ip0pd3V1xczMjDNnzmBpaalbNlJiZyoV58+fL/eQFU1myoUQpkpmyquPX+NO0SuhWdGCPGoknI+D3Ptg7ww9/g6dxhZqYpN7n+/an6DnYO9qsV+zPidPnmTcuHGFCipLS0umTZtGp06dqFOnDikpKXz++eckJCQUutba2prw8PBCz0KpbvSND8CwYcN4+eWX0Wg07Ny5k08++aTItdV9fNLT00lJSeHtt98uMj516tThww8/pEuXLty+fZulS5eyc+fOQm0qa3yKnSlv1qwZKpVKd7Nn06ZNn+jGTyGEEEKUbt6PmTyoa130RO/3wX8FWFjBjTMQ3gsaPw/qjromDyysWZpQQO8h1bMgh4cbSfx5SQI8/Fbg+vXrhISEcO3aNXx8fJg3bx7Dhw/n6tWrunY5OTlERESwcOHCyo5dafSND0BaWhorVqyga9euWFlZ6b22uo+Pk5MTc+fO1Ts+U6dOJS8vj/79+9OqVSuWLFlCYmKi7knxUHnjU2xRvmfPnhJfCyGEEKJ83PgjjR/sPfWvIW/4pxvNVKqHP+nnCxXlipk5O+w9SUu+qXdXFlOXnp5OQkJCkTXA2dnZhIeH617v37+fK1eu4O7uXqgoVxSF+Ph4MjIyqu2uI/rGB2D37t0AtGnThgYNGui9vqaOj7W1NX369OH111/nwYMHHD16lH379jFw4ECWLl2qa1dZ41N9f6UWQgghTMTKqJNAQfENvn0bPrSBfz0L9o2g9cAiTVQorPzG9J9qqE90dLRB39Y7OTnRtGlTvUtpVSoV0dHRFRHP6Awdn5LUxPFp1qwZWq2W5ORk3bFz587pXbJdGeNT5hs9c3Jy2LNnj25a383NjZ49e2JtrecrNyGEEEKU6liGBdmOJWxd+Moy8P1/kPwfOL/n4VKWxzywtOF4RvXcvyEpKUnv0oM/Mzc3Z9asWXz//ff88ccfRc7n5OSQlJRUURGNypDxKU1NHJ/atWtz7969Qsfu3bune0Lsn1XG+JTp/97IyEgmT55MRkaG7isAlUpF3bp1+de//sXo0aMrIqMQQghRrd0psCy9kZk5NO8OR9bAgS/A5/+KNMkwpB8T9Hjh9DiVSsWsWbPIz89nwYIFxba7e/dueUerEkobH0PVtPF58OABdnZ2hY7Z2tpy//59ve0renwMLsrXr1/P6NGjadq0KVOmTKFNmzYoisKpU6dYvnw5wcHB1K5dm9dff70i8wohhBDVjoNZnuGNtflwS/9OZ45l6ceEPF44Pe7DDz/EycmJd999F61WW2w7e3v78o5WJZQ2PoaqaePzxx9/YG5ujouLC5cvXwagVatWhW7y/LOKHh+D15TPnTuXZ599lmPHjjFt2jR8fX0ZMmQI77//PseOHaNly5aFnpYkhBBCCMO0d8zHOi+r6Il7N+BoFOTcgwItnNsJR7+BFn2KNK2dl0U7x/xKSFv5NBpNsTuHvP/++7i6ujJp0qQSl3BYWVmh0WgqKqJRlTQ+5ubm1KpVCzMzM92f9T3pvCaOT3Z2Nrt372b8+PFYW1vz3HPP0bNnT3bs2FGkbWWMj8FF+dmzZwkKCqJOnTpFzjk4OBAUFERiYmK5hhNCCCFqgtHDPdD/T7Lq4VKVeWr4xBG+nwKDw8BjSJGWCipGv9G2wrMaw+DBg/XuLOLs7Iyfnx+tWrVi586d7Nu3j3379vHiiy8WaasoCoMHD66MuJWuuPEBCA4OJiEhgaCgIAYOHEhCQgLBwcFF2tXU8Zk/fz5WVlbExsYyZ84c5s2bp3emvDLGx+DlK87OziU+jtTMzKzaPTlMCCGEqAwNmtXnpbsH+Laud+FtEe3qw7i9pV6vKtAy8O7v1G/atQJTGo+TkxPdunVj7969hWqRa9eu4eXlVer1KpUKHx+farndHxQ/PgDh4eGFto3UpyaPT2ZmJlOmTCnx+soaH4NnykePHs3KlSv1LpbPzMzk66+/JigoqFzDCSGEEDXF+/3rUDu/9Md/61M7P5v3BziUc6KqJSgoqNglGqWxsrKq9jWKjE/JTGF8ii3KH30F9OinR48e2NjY0K5dOxYuXEh0dDTfffcd//znP3nuueews7PjhRdeqPDAQgghRHXk3bcNi+wPYZOrf+eH4tjk3meR/SG8+lTPR6Q/4uHhQWhoaJm3YLa2tiY0NLTaPkL+ERmfkpnC+KiUYtakmJmZFdlo/c9NH517/FhJdz1XVSq1F0w8ZOwYQghRZh03enHokPz9VV3k5ubyUt8pHOg/jwcW1vqf8PlfqgIttfOz6Rc/m20x8yoxpXFt2rSJsLAwcnJySlxWq1KpsLKyIjQ0FH9//0pMaFwyPiWryuNT7JryiIiISgkghBBCiIdefPFFjpw4QtyHY1kYd58d9p6oUHhg+b8HC9XOy0JBxcC7vzPm+RyGfLKQ6dPNaswOaP7+/rRp04aIiAji4+NRqVSFdl2xsrJCURR8fHwICgqq9jPAj5PxKVlVHp9iZ8prEpkpF0KYKpkprz6WLFnC5MmT+fXXX+nQoQMAack3WfnNCY5nWJBRYImjWR7tHPMZ/UZb6jetBzy8kW/8+PHEx8fTtWv1vNGzOBkZGURHR5OUlMTdu3ext7dHo9EwePDganvTYlnI+JSsqo2PUYvymJgY3Ub/Y8eOZdq0aYXO5+TkEBgYyOHDh3nmmWdYv349zZs359KlS7i7u9O6dWsAunTpwvLlywE4fPgwo0eP5sGDBwwcOJAlS5YUWYbzOCnKhRCmSory6uH06dO0bduWTz75hH/84x9lvn7gwIHs37+fa9euYWNjU/oFQogqx+AtER+5fv06hw4dIiMjg4KCgiLnAwMDDepHq9UyYcIEYmNjUavVeHt74+vrW+hrghUrVuDo6EhSUhJRUVFMnTqV9evXA9CiRQt+//33Iv2+9dZbhIeH06VLFwYOHEhMTAwvvfRSWT+mEEIIUSny8/Pp2bMn3t7eT1SQA2zfvp1GjRrRr18/EhISyjmhEKIyGFyUFxQUMGHCBL766iu9xfgjhhblBw8eRKPR4ObmBsDw4cPZtm1boaJ827ZtfPzxx8DDNUDvvPNOiYvyr169SmZmpu7ru8DAQL799lspyoUQQlRZQ4YM4cGDB/z0009P3IeFhQX79u2jbdu2zJkzh+nTp5djQiFEZTB4n/JFixbx5Zdf8sYbb7Bq1SoURWH+/Pl8/vnntGzZEi8vL2JjYw1+49TUVFxcXHSv1Wo1qampxbaxsLDAwcGBW7duAXDx4kWef/55evbsyc8//6xrr1arS+xTCCGEqCrCw8P54YcfiImJeeplJ+7u7ixevJgZM2bo/SZZCFG1GVyUr1q1igEDBhAZGambee7YsSPjx4/n8OHD3Lx5k8OHDxv8xvpmvEvagvHPbRo1akRycjJHjhxh8eLFjBgxgszMTIP6fCQ8PBwvL6+HTwK7n2ZwbiGEEKI8XLx4kbfffptp06bh4+NTLn2+++679OjRg969e5Obm1sufQohKofBRfmFCxd0xbiZ2cPL8vLyALC1tSUoKIivvvrK4DdWq9VcvnxZ9zolJYXGjRsX2yY/P587d+7g5OSElZUVzzzzDPDwF4MWLVpw7tw51Go1KSkpJfb5SEhICIcOHXp4g5RtfYNzCyGEEE+roKAAHx8f2rVrx9y5c8u17507dwIPt1cUQpgOg4vy2rVrY2lpCYCdnR0qlYobN27ozjs7Oxcqskvj7e1NYmIiFy9eJDc3l6ioKHx9fQu18fX1ZdWqVcDDzd779OmDSqUiLS1N95CiCxcukJiYiJubG40aNcLe3p4DBw6gKAqRkZEMGTLE4ExCCCFEZRg2bBh37txh79695d53rVq1iIuLY+/evYSFhZV7/0KIimFwUd6sWTPOnz8PgKWlJRqNhpiYGN35Xbt20bBhQ4Pf2MLCgqVLlzJgwADc3d0ZNmwYHh4ezJgxg+3btwMQHBzMrVu30Gg0LF68mPnz5wOwb98+2rdvz3PPPYe/vz/Lly/HyckJgC+++IKxY8ei0Who0aKF3OQphBCiSlmzZg1btmwhOjqaOnXqVMh7dOjQgZkzZ/K3v/2N06dPV8h7CCHKl8H7lP/tb3/j22+/1RXms2fPZsaMGfTs2RNFUfj555+ZMmUKCxYsqNDAFUH2KRdCmCrZp9y0pKSk4OrqyltvvcVnn31W4e/XtWtXkpKSuHr1KhYWZd4FWQhRiQwuyq9evcqxY8fo1asXVlZWaLVaJk2axJo1azA3N8ff359PP/0Ua2vris5c7qQoF0KYKinKTUdBQQHNmzfH1ta20mavs7KycHZ2pnv37uzYsaNS3lMI8WSM+kTPqkKKciGEqZKi3HQEBgayYcMGrly5oltyWRn+85//4OPjw/LlywkJCam09xVClI3Ba8qFEEII8WQ2b97MmjVr2LRpU6UW5PBwCcv777/P22+/rVuCKoSoeso8U75hwwa2bt3KhQsXAHBzc+PVV19l2LBhFRKwMshMuRDCVMlMedV348YNXFxcCAwM5N///rfRcnTo0IGrV6+Smpqq29pYCFF1GFyUZ2VlMWTIEH766ScURaFu3booisKdO3dQqVT06tWL7du3Y2trW9GZy50U5UIIUyVFedXXsmVLCgoKjD5Lfe/ePRo2bMiLL77I5s2bjZpFCFGUwb8qf/DBB8TFxTH25vIWAAAex0lEQVRx4kSuXLlCeno6GRkZXLlyhYkTJ7J7926mT59ekVmFEEIIkzJ+/HiSk5OJj483dhTs7OyIjo5m69atREZGGjuOEOIxBs+UN2rUiB49erB+/Xq951977TX279/P1atXyzVgZZCZciGEqZKZ8qrrhx9+YNCgQWzYsAF/f39jx9GZNGkSS5cu5fz58zRt2tTYcYQQ/2XwTHlmZia9e/cu9nyfPn3IzMwsl1BCCCGEKUtPT2fo0KG88cYbVaogB/j0009p1aoV3bt3p6CgwNhxhBD/ZXBR3r59exITE4s9n5iYSLt27collBBCCGHKevToQf369Vm9erWxo+j1888/k5aWRmBgoLGjCCH+y+CifPbs2fz73/8mOjq6yLlt27bx1VdfMXfu3HINJ4QQQpiayZMnc/bsWfbv319ldzlxcnJi8+bNrFu3jk2bNhk7jhACKPaZu2PGjClyzNXVlVdeeYXWrVvj7u6OSqXi1KlTnD17lnbt2rF27Vr69OlToYGFEEKIqmrPnj2EhYWxcuXKKr9ee+DAgYSEhBAQEECPHj1o0KCBsSMJUaMVe6Pnk/x2r1Kp0Gq1Tx2qssmNnkIIUyU3elYdj7YcHDBgAFu2bDF2HIO1bNkSoMQlqkKIilds5V1QUFDmH1MsyIUQQojy0LNnT+rUqWNyy0Hi4+NJTk4mJCTE2FGEqNGq5mI3IYQQwoRMnz6do0ePVul15MVp0KAB69at46uvvmLHjh3GjiNEjVXsmvLiKIrCkSNHuHDhAgBubm48//zzqFSqcg8nhBBCVHX/+c9/mDdvHl988QUtWrQwdpwn4ufnx8iRI/Hz8yM1NRUnJydjRxKixjH44UEAMTExvP322/zxxx+Fjjdv3pxly5YxYMCAcg9YGWRNuRDCVMmacuPKysrC2dkZHx8ffvjhB2PHeSoFBQW4urpiZ2fHyZMnjR1HiBrH4O/Y4uPj8fX1JSMjg//7v/8jPDyc8PBw3n33XTIyMvD19SUhIaFMbx4TE0Pr1q3RaDTMnz+/yPmcnBxef/11NBoNnTt35tKlSwDExsbSsWNH2rVrR8eOHfnpp5901/Tq1YvWrVvj6emJp6cnN27cKFMmIYQQoiRXrlzht99+A6Bfv37UqlVL73bBpsbMzIz4+HjOnTvHpEmTAIiLiyM3N9fIyYSoGQxevjJz5kycnZ355ZdfaNSoUaFz7733Hp07d2bmzJnExMQY1J9Wq2XChAnExsaiVqvx9vbG19eXNm3a6NqsWLECR0dHkpKSiIqKYurUqaxfv5569eoRHR1N48aNOXHiBAMGDCA1NVV33dq1a/Hy8jL0owkhhBAGCwwMJC4ujs6dO/Prr79y7NgxLCzKvBq0SlKr1axcuZKRI0cSFxfH8ePH+eijj/j444+NHU2Ias/gmfJffvmFkJCQIgU5QKNGjfjrX//KgQMHDH7jgwcPotFocHNzo1atWgwfPpxt27YVarNt2zZGjRoFgL+/P3FxcSiKwvPPP0/jxo0B8PDwIDs7m5ycHIPfWwghhHhSR48eBR7+u+jg4EDDhg2NnKh8tWvXDnNzc44fPw48/KZcCFHxDC7Kc3Nzsbe3L/Z8nTp1yvQVV2pqKi4uLrrXarW60Gz3420sLCxwcHDg1q1bhdps3ryZ559/HisrK92xoKAgPD09mTVrFmVYMi+EEEKUKj09XffnjIwMOnbsaMQ05c/Ly6vQFsfHjh0zYhohag6Dv29zd3cnKiqKCRMmFPmaLj8/n/Xr1+Pu7m7wG+srlh/fwaW0NidPnmTq1Kn8+OOPumNr166lSZMm3L17Fz8/P1avXk1gYGCRfh6tiQfgfprBuYUQQlRf6enpREdHk5SUxL1797Czs0Oj0eDr64ujoyOZmZkUFBTo2j/6t7E62bJlC8HBwbp7stLS/vdvZGnjI4R4cgYX5W+99RYhISH07duXv//977q13ydPnmThwoX88ssv/ytyDaBWq7l8+bLudUpKim5JyuNt1Go1+fn53LlzR7dNU0pKCq+++iqRkZGFtqBq0qQJAPb29owYMYKDBw/qLcpDQkJ0D0pQqWX9uRBC1GQnT54kIiKChIQEVCpVoSWRVlZWfPnll3Tr1g1nZ2cAmjVrxqZNm6rl/Usvv/wy169fZ/PmzYwaNYr79+9z4sQJVq5cWer4BAUF4eHhYcT0Qpgug4vysWPHkpiYyKJFi9i/f3+R8++99x7BwcEGv7G3tzeJiYlcvHiRJk2aEBUVxbp16wq18fX1ZdWqVXTt2pVNmzbRp08fVCoVt2/fZtCgQcybNw8fHx9d+/z8fG7fvk29evXIy8vju+++o1+/fgZnEkIIUfNs2rSJsLAwcnJy9H5D+6gA3bt3r64ArQlPv/Tz88PPz4/w8HDGjx9v0PgcOHCA0NBQ/P39KzuuECavTPuUA5w7d45t27Zx8eJFFEWhRYsW+Pr60qpVqzK/+Y4dOwgNDUWr1TJmzBimT5/OjBkz8PLywtfXl+zsbN58802OHDmCk5MTUVFRuLm5MXv2bObNm0fLli11ff3444/Y2trSo0cP8vLy0Gq19OvXj8WLF2Nubl7yIMg+5UIIEyX7lD+dRwV5dna2wddYW1vXmMJTxkeIymNQUZ6Tk6PbCvHPhXB1IUW5EMJUSVH+5E6ePMm4cePKVHA+Ym1tTXh4eKFtfKsbGR8hKpdBu6+Ym5vTt29fk39amRBCCPFIREREidvpuri4EB8fz8yZM4ucy8nJISIioiLjGV1x4/PomSR79uxh8+bNDBkypEibmjA+QpQ3g9aUW1hY4OzsLNsLCiGEqBbS09NJSEgo8d+1qVOncurUKb3nFEUhPj6ejIyMarnrSEnjs3LlSmbNmkVeXh7NmjXjyy+/5OzZs5w5c0bXprqPjxAVweB9yl977TU2bNhQaCsoIYQQwhRFR0cX2Yb3z/r378/du3f59ddfi22jUqmIjo6uiHhGV9L4XLhwgby8vELH1Gp1kXbVeXyEqAgGF+Vjx44lKyuLv/zlL0RHR3PmzBmSk5OL/AghhBBVXVJSUrFLV2xtbRk3bhxhYWEl9pGTk0NSUlJFxDO6ksYHHn6LsH//fjZv3szNmzf1PvWzOo+PEBXB4C0R27Zti0qlQlEU9uzZU2y7Pz8FTAghhKiK7t27V+y58ePHs337dq5fv15qP3fv3i3PWFVGSeMDsGDBAhYuXEi7du3w8vIq9one1XV8hKgIBhflM2bMKPGrPiGEEMJU2NnZ6T3eqlUrOnXqREBAgEH92Nvbl2esKqO48fmzgoICjh49ysCBA/H392f9+vVF2lTX8RGiIhhclH/88ccVGEMIIYSoPBqNBisrqyJLNDp27Ejjxo357rvvALCxscHMzAw3NzdGjhxZqK2VlRUajabSMlem4sZHH3Nzc71ryqvz+AhREQxaU56WlsYvv/zC+fPnKzqPEEIIUeEGDx6sd2eRLVu28MorrxAQEEBAQACbN28mPj6ed955p0hbRVEYPHhwZcStdMWNj6OjI/3796d27dqYmZnRpUsXBgwYoHev/Oo8PkJUhBKL8oKCAsaPH0+jRo3o1q0brVq1onv37qSlpVVWPiGEEKLcOTk50a1btyLLMnNycrh165bu58GDB+Tk5HD79u1C7VQqFT4+PtV2u7/ixkdRFPz8/NixYwc//fQToaGh/Otf/2Lv3r2F2lX38RGiIpS4fGXp0qWEh4fTuHFjunbtSmJiIgkJCYwbN44tW7ZUVkYhhBCi3AUFBXHgwIESn1gZHh6u97iVlRVBQUEVFa1K0Dc+t2/fZty4caVeWxPGR4jyVuJMeWRkJO7u7pw+fZqNGzfy+++/ExwcTHR0dJFZAyGEEMKUeHh4EBoairW1dZmus7a2JjQ0tNo/Ql7GR4jKVWJRfvbsWUaPHl3o7umJEyei1Wo5d+5chYcTQgghKpK/v7+u8CxthzGVSqUrOP39/SspoXHJ+AhReUpcvnL//n0aN25c6Nij1/fv36+4VEIIIUQl8ff3p02bNkRERBAfH49KpSq064iVlRWKouDj40NQUFCNmwGW8RGicpS6JeLjvxk/eq3vrmwhhBDCFLVp04aFCxeSkZFBdHQ0SUlJ3L17F3t7ezQaDYMHD67RNy3K+AhR8Uotynfs2MG1a9d0r7OyslCpVLo15n+mUqmYNGlS+acUQgghKoGjoyOBgYHGjlFlyfgIUXFUSglT3mZmBm1j/r/OVCq0Wu1Th6psKrUXTCy6x6oQQlR1HTd66d0jWgghhGkpcaZ89+7dFfrmMTExvPvuu2i1WsaOHcu0adMKnc/JySEwMJDDhw/zzDPPsH79epo3bw7AvHnzWLFiBebm5nz22WcMGDDAoD6FEEIIIYSoakosynv27Flhb6zVapkwYQKxsbGo1Wq8vb3x9fUtdIPIihUrcHR0JCkpiaioKKZOncr69es5deoUUVFRnDx5kitXrtCvXz/dbjCl9SmEEEIIIURVU7b1KeXo4MGDaDQa3NzcqFWrFsOHD2fbtm2F2mzbto1Ro0YBD+/+jouLQ1EUtm3bxvDhw7GyssLV1RWNRsPBgwcN6lMIIYQQQoiqxmhFeWpqKi4uLrrXarWa1NTUYttYWFjg4ODArVu3ir3WkD6FEEIIIYSoakrdfaWi6Lu/9PHtF4trU9zxgoKCUvt8JDw8XPf4ZNvbZ3h2o5fedmlpadSvX1/vOVNg6vnB9D+D5Dc+U/8MJeW/dOlS5YYRQghRIYxWlKvVai5fvqx7nZKSUuRBRY/aqNVq8vPzuXPnDk5OTiVeW1qfj4SEhBASElJqTi8v097ZwNTzg+l/BslvfKb+GUw9vxBCiNIZbfmKt7c3iYmJXLx4kdzcXKKiovD19S3UxtfXl1WrVgGwadMm+vTpg0qlwtfXl6ioKHJycrh48SKJiYl06tTJoD6FEEIIIYSoaow2U25hYcHSpUsZMGAAWq2WMWPG4OHhwYwZM/Dy8sLX15fg4GDefPNNNBoNTk5OREVFAeDh4cGwYcNo06YNFhYWfP7555ibmwPo7VMIIYQQQoiqrMSHB4mHa88NWeZSVZl6fjD9zyD5jc/UP4Op5xdCCFE6KcqFEEIIIYQwMqOtKRdCCCGEEEI8JEV5KT788EPat2+Pp6cn/fv358qVK8aOVGbvvfcezz77LO3bt+fVV1/l9u3bxo5UJhs3bsTDwwMzMzOT24EiJiaG1q1bo9FomD9/vrHjlMmYMWNo0KABbdu2NXaUJ3L58mV69+6Nu7s7Hh4eLFmyxNiRyiw7O5tOnTrx3HPP4eHhwUcffWTsSEIIISqILF8pRWZmJnXq1AHgs88+49SpUyxfvtzIqcrmxx9/pE+fPlhYWDB16lQAFixYYORUhjt9+jRmZmaMGzeORYsW4eWlf0/5qkar1dKqVStiY2NRq9V4e3vzzTff0KZNG2NHM8i+ffuws7MjMDCQEydOGDtOmV29epWrV6/SoUMH7t69S8eOHfn2229NZvzh4bMa7t+/j52dHXl5eXTv3p0lS5bQpUsXY0cTQghRzmSmvBSPCnKA+/fvF/swoqqsf//+WFg83GinS5cupKSkGDlR2bi7u9O6dWtjxyizgwcPotFocHNzo1atWgwfPpxt27YZO5bBevTogZOTk7FjPLFGjRrRoUMHAOzt7XF3dze5J/yqVCrs7OwAyMvLIy8vzyT/DhJCCFE6KcoNMH36dFxcXFi7di0zZ840dpyn8vXXX/PSSy8ZO0aNkJqaiouLi+61Wq02uaKwurh06RJHjhyhc+fOxo5SZlqtFk9PTxo0aMBf/vIXk/wMQgghSidFOdCvXz/atm1b5OfRrOacOXO4fPkyAQEBLF261Mhp9SvtM8DDz2FhYUFAQIARk+pnSH5To29lmMxyVr579+7h5+dHWFhYoW++TIW5uTm///47KSkpHDx40CSXEgkhhCid0R4eVJXs2rXLoHYjRoxg0KBBfPLJJxWcqOxK+wyrVq3iu+++Iy4urkoWhob+NzAlarWay5cv616npKTQuHFjIyaqefLy8vDz8yMgIIChQ4caO85TqVu3Lr169SImJsZkb74VQghRPJkpL0ViYqLuz9u3b+fZZ581YponExMTw4IFC9i+fTs2NjbGjlNjeHt7k5iYyMWLF8nNzSUqKgpfX19jx6oxFEUhODgYd3d3Jk+ebOw4TyQtLU23W9KDBw/YtWuXSf4dJIQQonSy+0op/Pz8OHv2LGZmZjRr1ozly5fTpEkTY8cqE41GQ05ODs888wzw8GZPU9pBZuvWrUycOJG0tDTq1q2Lp6cnO3fuNHYsg+zYsYPQ0FC0Wi1jxoxh+vTpxo5ksDfeeIM9e/Zw8+ZNGjZsyCeffEJwcLCxYxls//79vPDCC7Rr1w4zs4fzD3PnzmXgwIFGTma4Y8eOMWrUKLRaLQUFBQwbNowZM2YYO5YQQogKIEW5EEIIIYQQRibLV4QQQgghhDAyKcqFEEIIIYQwMinKhRBCCCGEMDIpyoUQQgghhDAyKcqFEEIIIYQwMinKRZXWvXt3NBqNsWOUyW+//Ubv3r2pW7cuKpWK2bNnGzuSQXbt2oVKpWLNmjXGjiKEEELUOFKUiyf22muvoVKp+P3334ttoygKrq6u1K1blwcPHlRiOuN49ATJixcvMmfOHFavXs0rr7xi0LXHjx9HpVKhUqk4cOBABSetPKdPn2bEiBE8++yzODg4YGtri7u7O1OmTOH69evGjieEEEJUCRbGDiBMV3BwMJs2bSIiIoIlS5bobbN7924uXbrEuHHjqF27diUnrHyJiYlcunSJJUuWMGHChDJdu2LFChwcHLC0tGTFihV06dKlglJWrsuXL3P9+nWGDh2KWq3G3Nyc48eP88UXXxAVFcXvv/9OvXr1jB1TCCGEMCopysUT69+/Py4uLqxdu5aFCxdSq1atIm0iIiIATOpJkE/j2rVrADg5OZXputzcXNasWcPrr7+OlZUVK1euJCwsDFtb24qIWan69+9P//79ixz38fFhxIgRREZGMnnyZCMkE0IIIaoOWb4inpiZmRmjR4/m1q1bbN++vcj5zMxMtmzZQtu2bfH29tYdX7duHYMHD6Zp06ZYWVlRv359hg4dyokTJwx6X7VaTb9+/YocL25NdHZ2NrNnz6ZNmzZYW1vj6OiIr68vR48eNfizXrhwgZEjR9KwYUOsrKzQaDT84x//KLQkp3v37vTt2xeAN998U7cUJSUlpdT+v/32W27dusWoUaMYPXo0d+/eZePGjUXaJSUl6dapb9u2jY4dO1K7dm0aN27MtGnTyM/PL3LNhg0baN++PdbW1jRr1oxZs2axc+dOg9ePFxQUsHTpUjp06ICNjQ329vb07duXvXv3lnptSZo1awZARkbGU/UjhBBCVAdSlIunEhQUhEql0s2I/1lUVBRZWVlFZsmXLl2KhYUF48aN4/PPPyc4OJg9e/bQrVs3zp8/X675cnNz6d+/P7NmzcLHx4ewsDD+/ve/c+LECbp168aRI0dK7ePixYt06tSJTZs2ERAQwKeffoqnpydz5sxh0KBBaLVaAGbMmMG0adMAeOutt1i9ejWrV682aNZ8xYoVaDQaunXrRocOHWjXrh1ff/11se2jo6MJCQlh0KBBLF68mLZt27JgwQIWL15cqN3atWt5/fXXycnJ4eOPP2bChAlERUUxffr0UjM9EhAQwLvvvkvr1q1ZuHAhH330Ebdu3aJv3758//33BveTnZ3NzZs3SUlJYefOnbz11lsADBw40OA+hBBCiGpLEeIp9enTRzE3N1dSU1MLHe/SpYtSq1YtJS0trdDxe/fuFenj+PHjiqWlpTJx4sRCx318fJQWLVoUOtakSROlb9++RfqIjY1VAGX16tW6Y//85z8VlUqlxMbGFmqbkZFRbD+PGzZsmAIoMTExhY6HhoYqgLJy5coSM5QmOTlZMTMzU2bNmqU7tmjRIgVQzp07V6htYmKiAii2trbKH3/8oTuu1WqVZ599VlGr1bpjubm5SsOGDZVGjRopGRkZuuOZmZlK06ZNi+TUl33Dhg0KoKxYsaJQjtzcXMXT01PRaDQGf85PP/1UAXQ/rq6uyjfffGPw9UIIIUR1JjPl4qkFBwej1WpZvXq17tiZM2c4cOAAvr6+RW7ie7ROWlEUMjMzuXnzJs7Ozmg0Gn755ZdyzbZmzRo8PDzw9PTk5s2bup/8/HzdEoycnJxir8/Pz+e7777D29ubAQMGFDr3aLZ569atT5UxIiICRVF48803dcdGjhyJhYVFsbPlfn5+NG3aVPfazMyMXr16kZKSoltSc/DgQa5fv05QUBB169bVtbW3t2fcuHEGZVuzZg1169Zl8ODBhcbvzp07vPzyyyQlJXHhwgWD+vLz8yM2NpYtW7bw4Ycf4uDgQFpamkHXCiGEENWd3OgpntrQoUOpW7cuERERTJ06FUBXTI4ZM6ZI+8OHD/Phhx+yb98+7t+/X+hcy5YtyzXbmTNnyM3NpX79+sW2SU9Pp1GjRnrPXb9+naysLDw8PIqcq1evHg0bNjS4KNVHURQiIiLo0KEDeXl5JCUl6c516dKFVatWMXv2bMzNzQtd5+bmVqSvZ555Rvd5mjRpwsWLFwFo3bp1kbb6julz+vRpbt++TYMGDYptc/36db15Hufi4oKLiwsAr776KkOHDqVTp05kZ2fz3nvvGZRHCCGEqK6kKBdPzdramhEjRrBs2TISEhLo3Lkzq1evRq1WF9l149KlS/To0QMnJydmzJhBq1atsLW1RaVSMXHiRPLy8kp9P5VKpfe4vpscCwoK8PT0ZOHChcX2V9Kab0VRSs3zNOLi4rh06RKXLl0q9heSH374gZdffrnQsceL9D97lLk8siuKgrOzc6FvQR7Xpk2bJ+rb09OT9u3bs2zZMinKhRBC1HhSlItyERwczLJly4iIiCA9PZ1r164xffr0IsXj5s2bycrKIiYmhhdeeEF3XFEUbt68iYODQ6nv5eTkRHp6epHj+masW7ZsSVpaGn379i22mC+Js7MzNjY2nDx5ssi5W7ducePGjafaT/zrr7+mdu3arFq1Sm++sWPHsmLFiiJFuSFcXV0BOHv2bJFz+o7p07JlS2JjY+nWrRs2NjZlzlCaBw8e6P1vKYQQQtQ0sqZclIsOHTrg6enJ+vXrWbp0KSqViqCgoCLtHhXpj8/iLl++nJs3bxr0Xq1ateLUqVNcvXpVdyw7O5tly5YVaRsYGEhqamqxDzcq7YmSFhYWvPzyy/z666/s2rWr0Lm5c+eiKAqvvvqqQbkfl5GRwdatW3nxxRd57bXX8Pf3L/IzePBgvv/+e27cuFHm/jt37kyDBg2IiIjg9u3buuN3797lyy+/NKiPwMBA8vPzi92txZAncj7au/1xsbGxnDlzpto8JEkIIYR4GjJTLspNcHAwEydOZOfOnfTq1YsWLVoUaTNo0CA++OADAgICmDBhAg4ODsTHxxMTE6Ob2S3NO++8w6ZNm+jbty/jxo0jJyeHyMhI7OzsirSdPHkyu3btYtKkSezatYtevXphb29PcnIycXFx2NvbExsbW+L7zZ8/n7i4OAYPHsyECRNwc3Njz549bNy4kd69ezNy5EjDBugxa9euJTs7Gz8/v2Lb+Pn5sWbNGiIjI5kyZUqZ+re0tGThwoWMGjWKzp07M2bMGMzMzFi5ciUNGjQgOTm51G8Phg8fzg8//EBYWBiHDh1i4MCB1KtXj5SUFOLj40lOTubcuXMl9vHXv/6VW7du0bt3b5o1a0ZWVhaHDh1iw4YNODg4sGjRojJ9LiGEEKJaMta2L6L6SU9PV6ytrRVAiYyMLLbd7t27lW7duil2dnZK3bp1lUGDBiknT57Uu/2hvmOKoigrVqxQWrZsqVhaWiqurq7KwoULlZ07d+rdjjAvL0/59NNPlY4dOyo2NjaKjY2NotFolJEjRxbZKrE458+fV0aMGKHUr19fsbS0VNzc3JQPPvhAycrKKtSuLFsienp6KrVq1VJu375dbJusrCzF1tZWcXd3VxTlf1si/nn7xEemT5+uAMrly5cLHf/mm2+Utm3bKrVq1VJcXFyUmTNnKhs3blQAZfPmzQZlX7lypeLj46PY29sr1tbWSvPmzRU/Pz9l48aNpX7OdevWKS+99JLSpEkTxcrKSqldu7bSunVrZeLEiUpycnKp1wshhBA1gUpRKvhONiFElbNgwQKmTZvGr7/+ipeXl7HjCCGEEDWeFOVCVGO5ubmYm5sXuuH27t27tG3blgcPHpCamoqlpaUREwohhBACZE25ENXauXPn8PX1Zfjw4bi6upKamsrKlStJTk4mPDxcCnIhhBCiipCiXIhqrGHDhnTq1Ik1a9Zw48YNLCwsaN++PYsWLcLf39/Y8YQQQgjxX7J8RQghhBBCCCOTfcqFEEIIIYQwMinKhRBCCCGEMDIpyoUQQgghhDAyKcqFEEIIIYQwMinKhRBCCCGEMDIpyoUQQgghhDCy/w8LD7A6RoWM9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x1080 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hpcs = HyperPolarCoordinateSystem(make_binary_tree(n_leaves=ndims, mode=\"balanced\"))\n",
    "rs, thetas = hpcs.x_to_r_theta(xnorm)\n",
    "\n",
    "fig, axes = plt.subplots(ndims-1, 2, figsize=(12, 15), sharex=\"col\")\n",
    "axes[0, 0].set_xlim(-np.pi, np.pi)\n",
    "for i in range(ndims-1):\n",
    "    color = \"#0088ff\"\n",
    "    axes[i, 0].set_ylabel(\"Probability Density\".format(i), fontsize=18)\n",
    "    axes[i, 0].set_xlabel(\"Value of Angle {}\".format(i), fontsize=18)\n",
    "    axes[i, 0].hist(thetas[:, i], 51, (-np.pi, np.pi), density=True, color=color)\n",
    "    hpcs_tree_plot(hpcs, ax=axes[i, 1], highlight_node=hpcs.angle_nodes[i], highlight_color=color)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the tree structured in this way we get two angle nodes both of whose children are are both coordinates and as such we have two completely uniform angle distributions. But we also have two new kinds of nodes. Angle 0, the angle belonging to the root node runs from 0 to pi/2 radians. This is because in this tree the children of the root node are both non-leaf nodes and so will always both be assigned non-negative numbers for the inverse formula, putting our angles firmly in the first quadrant. You may be surprised to see that the distribution of angle 2 differs from the distribution of the angles with a seemingly similar situation where one of the children nodes is a leaf node and one an internal node of the tree. But instead of spanning -pi/2 to pi/2 this angle spans from 0 to pi. That is because instead of assigning the leaf child the cosine factor, in this tree layout the leaf child happened to be assigned the sine factor of its parents node (instead of the cosine factor as in the \"regular\" hyper spherical polar expansion).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spatial Distribution Corresponding to Uniform Angular Distribution\n",
    "\n",
    "So what does the distribution of vectors in rectangular coordinates look like when we pick our angles from a uniform distribution?\n",
    "\n",
    "If you consider the case of latitudes and longitudes on the earth again. If you pick a random latitude and random longitude then you are proportionally much more likely to pick a point in antartica than you would be to pick a point in an equivalently sized area in the united states. The various different longitude angles all start to pile up on each other close to the poles. The distance over the surface of the earth corresponding to differences in longitude depends on the latitude of those points. For a constant latitude $\\phi$ the distance over the surface of the earth  $r_{e}sin(\\phi)\\delta \\theta$. Because of this for points close to the equator where $\\phi$ is 90 degrees the sin factor is equal to 1 and both changes in latitude and longitude correspond to about 69 miles per 1 degree. If we are standing right on the pole then $sin(\\phi)$ goes to zero and changes in longitude become 0 miles per degree, while latitude is still sensitive. \n",
    "\n",
    "As the dimension increases this pile up of points in certain regions of the sphere becomes much more pronounced. This can easily be understood from a mathematical direction since if any node in the tree has an angle which is close to 0 then all the coordinates down stream from the sine branch of that angle node will all be exactly 0. This means that the deeper the hierarchy of the tree we use the more likely that we simply pick 0's for some of the vector coordinates when we pick uniformly in angle space.\n",
    "\n",
    "# Sampled Coordinate Vectors \n",
    "\n",
    "Lets look at the coordinate values of a few vectors corresponding to angles chosen uniformly in angle space. Because the effects are made much more dramatic by high dimensionality we will ratchet up the dimension of our examined space a bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "ndims = 16\n",
    "balanced = HyperPolarCoordinateSystem(make_binary_tree(n_leaves=ndims, mode=\"balanced\"))\n",
    "unbalanced = HyperPolarCoordinateSystem(make_binary_tree(n_leaves=ndims, mode=\"unbalanced\"))\n",
    "\n",
    "\n",
    "rtheta = np.random.uniform(-np.pi, np.pi, size=(50000, ndims-1))\n",
    "x_balanced = balanced.r_theta_to_x(1.0, rtheta)\n",
    "x_unbalanced = unbalanced.r_theta_to_x(1.0, rtheta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 8))\n",
    "hpcs_tree_plot(balanced, ax=axes[0])\n",
    "hpcs_tree_plot(unbalanced, ax=axes[1])\n",
    "axes[0].set_title(\"Balanced Tree\")\n",
    "axes[1].set_title(\"Un-Balanced Tree\")\n",
    "\n",
    "fig, axes = plt.subplots(2, figsize=(12, 6))\n",
    "for i in range(10):\n",
    "    axes[0].plot(x_balanced[i], alpha=0.5, lw=2, c=\"blue\")\n",
    "    axes[1].plot(x_unbalanced[i], alpha=0.5, lw=2, c=\"blue\")\n",
    "\n",
    "axes[0].set_title(\"Balanced Tree Random Vector Samples\")\n",
    "axes[1].set_title(\"Unbalanced Tree Random Vector Samples\")\n",
    "axes[0].set_ylabel(\"Coordinate Value\")\n",
    "axes[1].set_ylabel(\"Coordinate Value\")\n",
    "axes[1].set_xlabel(\"Coordinate Index\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see the coordinates which are very deep in the unbalanced tree hierarchy have ver small variance, since the chances of all of the angles above them in the tree being close to 1 are very small, and it requires only one near zero angle to zero out all the coordinate nodes deeper in the tree.\n",
    "\n",
    "On the other hand because the balanced binary tree has an average node depth which scales like the logarithm of the number of dimensions, and just as importantly because every coordinate sits at close to the same hierarchy depth, the amount of variance in each coordinate is close to flat in the case of the balanced tree, and every coordinate dimension shows variation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA\n",
    "\n",
    "The directions in space where the direction vectors all sort of pile up on top of each other defines in a way defines the \"shape\" of the coordinate space dictated by each tree structure. In the case of latitude and longitude coordinates we can tell where the north and south poles are because points chosen uniformly in angle will tend to pile up at the poles. \n",
    "\n",
    "We can generalize this to any number of dimensions and get a sense for where the points pile up and to what extent by using PCA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_balanced = PCA().fit(x_balanced)\n",
    "u_balanced = pca_balanced.transform(x_balanced)\n",
    "pca_unbalanced = PCA().fit(x_unbalanced)\n",
    "u_unbalanced = pca_balanced.transform(x_unbalanced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f83f63acfd0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OOusszj77bD760Y+yySabMGvWLE477bR1jltfzrfffpvNNtus2fd66623mDFjBhUVFevsmzBhAgCvv/46G220UZM/a0eyqO4oEw7IiuoXH4RJX8g7jSRJ6oL69u3b4At/kH1Rb0O8//77rFixokGxuWTJkvoi9pFHHmHRokXcd999bLPNNvV9li5t+ULklltu4VOf+lSDLwM+88wzG5Rx6NChvPbaa83uHzJkCJWVlfziF79YZ1+fPn0A2HTTTVm2bFmTP2tHcvhHR6lbsvzlh6B6Tb5ZJElSlzR69GieffbZBm2FM2G01m233Va//f7773PfffcxadIkIBtzDWuLU4CHH36Y+fPnt3jOFStWNDgG4Pe///0G5ZsyZQo333xzs3fGp0yZwrx589hiiy2orKxs8Nhxxx0B2H333QG4884764+r+1k7kneqO8rg0TB0Irz9Aix+rHaaPUmSpOIdeeSR/PrXv+bMM8/k0EMP5cEHH+Tee+/doHP169ePb33rW7z//vtsvvnm/OhHP2L16tV85StfAWDPPfdk4MCBfOELX+Ab3/gGixYt4sILL2TUqFEtnnfatGn87Gc/Y4899mDChAn8/ve/Z968eRuU8YILLmD33Xdnv/324+tf/zpDhw7liSeeYOjQoZx88smccMIJXHXVVUyePJmzzjqL8ePH8/bbb/Poo4+y6aabcuaZZ7L99ttz+OGH8+///u+89957bLbZZlxyySX0799/gzIVyzvVHcnVFSVJUhsceuihfP/73+fWW2/lyCOP5JVXXuGyyy7boHP179+f6667jiuvvJJPfvKTvPvuu9x11131wz9GjhzJLbfcwuuvv84RRxzBZZddxlVXXcVWW7X83bDzzz+fY489lnPPPZdjjz2W3r1787Of/WyDMm699db84x//YNiwYXz+85/nyCOP5NZbb2Xs2LFANhzmwQcfZNq0aVxwwQUceOCBfOUrX+GFF16ov+MOcO2113LggQfy1a9+lVNOOYUpU6ZwzDHHbFCmYkVKqUPfoBQqKyvT+iYmz8Vzd8MfjoHRk+DzHftPDpIkqaG5c+ey7bbb5h1DXcz6/txExGMppcrG7d6p7kjj9oWyXtnwjxX/yjuNJEmSOohFdUfqs1F2lzpVw/y/551GkiRJHcSiuqPVzQLy4oP55pAkSVKHsajuaH5ZUZIkqduzqO5om+8KfQfDuy/Du/PzTiNJkqQOYFHd0crKYcuPZtsOAZEkqaS6wyxnKp22/HmxqC6F+nHVDgGRJKlUKioq6lcJlIqxYsUKKioqNuhYi+pSGF+3ZPnfoKY63yySJPUQI0aMYPHixSxfvtw71mpRSonly5ezePFiRowYsUHncJnyUhiyJWyyZTau+tUnYPQ684VLkqR2NmjQIABeffVV1qxZk3MadXYVFRWMHDmy/s9Na1lUl8qE/WH2y9m4aotqSZJKYtCgQRtcJEmt4fCPUqmbWu8lv6woSZLU3VhUl8q4j0CUwcKZsGpZ3mkkSZLUjiyqS6XfxjBqN6ipgvn/zDuNJEmS2pFFdSm5uqIkSVK3ZFFdSnVT6zmuWpIkqVuxqC6l0ZXQeyN463lYuijvNJIkSWonFtWlVF4BW34k23bJckmSpG7DorrUHAIiSZLU7VhUl1r9fNXToaYm1yiSJElqHxbVpTZ0AgweA8vfhtefyjuNJEmS2oFFdalFZEuWg0NAJEmSugmL6jzUjat2vmpJkqRuwaI6D+MnAwELZsDq5TmHkSRJUluVvKiOiIMi4rmImBcRZ7fQ76iISBFRWcp8JdF/CGy+C1SvhlcezjuNJEmS2qikRXVElANXAAcD2wHHRsR2TfTbCPgyMLOU+UrKqfUkSZK6jVLfqZ4EzEspvZRSWg3cCBzRRL/vAD8EVpYyXEnVTa3nIjCSJEldXqmL6lHAwoLXi2rb6kXErsCYlNKfWzpRRJwaEbMjYvabb77Z/kk72phJUNEflsyBZa/nnUaSJEltUOqiOppoS/U7I8qAnwBfX9+JUkpXp5QqU0qVw4cPb8eIJdKrD4zdJ9t+aXquUSRJktQ2pS6qFwFjCl6PBl4teL0RsAMwPSLmA3sCd3bLLytCwRAQp9aTJEnqykpdVM8CJkbElhHRGzgGuLNuZ0ppaUppWEppXEppHDADODylNLvEOUujbhGYFx+ElFruK0mSpE6rpEV1SqkKOB24F5gL3JxSmhMRF0XE4aXM0ikM3wY22gw+WAJvzMk7jSRJkjZQr1K/YUrpLuCuRm3nN9N3ciky5SYim1rvf2/IptbbdIe8E0mSJGkDuKJi3gqHgEiSJKlLsqjO2/jJ2fMr/4Q13XdabkmSpO7MojpvA0fAyB2haiUsnJF3GkmSJG0Ai+rOoH4IiFPrSZIkdUUW1Z2B46olSZK6NIvqzmCLvaC8D7z+FHzwVt5pJEmS1EoW1Z1BRT8Yu3e27ZLlkiRJXY5FdWfhEBBJkqQuy6K6s5hwQPb84gMuWS5JktTFWFR3FiO2hwHDYdmr8NbzeaeRJElSK1hUdxZlZWsXgnEIiCRJUpdiUd2ZFA4BkSRJUpfRqqI6IgZHxF4R8emI2Li2raJjovVA4ydnz/P/AVWr80wiSZKkViiqqI6Isoj4PrAY+CfwB2B87e47I+KCDsrXswzaHIZvC2s+gEWP5p1GkiRJRSr2TvX3gNOAM4EPAVGw73bg8HbO1XM5tZ4kSVKXU2xR/Tng7JTSr4CXG+17EZjQrql6svG1RfVLFtWSJEldRbFF9SbAC83sqwDK2yeOGLcPlFXA4sdh+Tt5p5EkSVIRii2q5wAfb2bfx4An2ieO6D0AttgTSPDyQ3mnkSRJUhGKLaq/D5wWEVcBk4EE7FD7BcV/B/6rY+L1UPXjqp1aT5IkqSsoqqhOKf0ROAE4FLiP7IuK1wJfBE5KKd3dUQF7pMJx1S5ZLkmS1On1KrZjSumGiPgDsC0wDHgHeCalVNNR4XqszXaGfkPgXwvgnZdgqN8DlSRJ6sxatfhLyjyTUnoopfS0BXUHKSuH8R/Nth0CIkmS1OkVu/jLryLihmb2/b52rLXaU/0QkOm5xpAkSdL6FXun+iCyRV6acjtwcPvEUb26Lyu+/BBUV+WbRZIkSS0qtqgeDrzdzL53gJHtE0f1Nt4Chm4Fq96DxY/lnUaSJEktKLaoXgDs28y+fYFF7RNHDUw4IHt2dUVJkqROrdii+nfAORHxxYjoBxARfSPiVOBs4LcdFbBHG+981ZIkSV1BsVPq/RcwEfgFcGVELAUGk81X/RuyxWHU3sbtC1EOi2bDyqXQd3DeiSRJktSEYhd/qUkpnQjsCHwV+CnwFWD7lNLnU3KFkg7RdxCMmQSpGl7+e95pJEmS1IyiF38BSCnNAeZ0UBY1Zfz+sOCRbFz1toflnUaSJElNaFVRHRHjgdFA38b7Ukp/aa9QKjDhAJj+fXjRLytKkiR1VkUV1RGxDfAHYCeycdSNJaC8HXOpzua7Qp/B8M6L8O4rsMnYvBNJkiSpkWJn/7gaGAh8Gtie7EuLhY8PdUg6QXkv2PIj2bZT60mSJHVKxQ7/2BU4LqX0p44Mo2ZMOACe/XM2td5uJ+adRpIkSY0Ue6d6PtC7A3OoJXVLlr/0N6ipzjeLJEmS1lFsUf114P+LCAf05mHIeNhkHKz8F7z2ZN5pJEmS1Eixwz++DYwCno+IF4F/Ne6QUtq7PYOpkfH7w2O/zYaAjNot7zSSJEkqUGxRPa/2obxMqCuqp8N+/5l3GkmSJBUoqqhOKX22o4NoPbbcD6IMFs6EVe9Dn4F5J5IkSVKtYsdUK2/9NoHNPww1a+CVf+adRpIkSQWKXlExIsYAnyGbk7qpFRWPa8dcasqEA2Dx7Gx1xQ99LO80kiRJqlXsioq7Ag8BrwPjgTnAxmRLli8GXu6ogCowYX946IfZlxUlSZLUaRQ7/OMS4HZgG7Jlyk9MKW0BTAZqgO92SDo1NHp36D0Q3noOli7OO40kSZJqFVtU7wpcT1ZAQ+3wj5TSQ8BFwA/aP5rWUV4B41yyXJIkqbNpzRcVV6eUErAE2KKg/RVg63ZNpebVra74okW1JElSZ1FsUT2XbCw1wAzgqxGxZUSMAs4CXuqIcGrChAOy55emQ01Ni10lSZJUGsUW1deQragI8C2yLyjOAxYA+5IV1iqFoVvBoNGw/C144//yTiNJkiSKX/zl2oLtORGxHbAP0A94OKX0esfE0zoiYMJkeOL6bAjIZjvnnUiSJKnH26DFX1JK76WU7k4p/dGCOgd1Q0CcWk+SJKlTaPZOdUQcCDySUlpWu92ilNJf2jWZmrflZCBgwQxYswIq+uWdSJIkqUdrafjHPcCewKO124lsjuqmJKC8mDeMiIOAn9b2vyaldHGj/V8CTgOqgfeBU1NKzxRz7h5jwNBs2MdrT8IrD8NWU/JOJEmS1KO1VFRPBBYWbLdZRJQDVwDTgEXArIi4s1HRfENK6ara/ocDlwIHtcf7dysT9s+K6hcfsKiWJEnKWbNjqlNKL6aUVkdEH+AoYEBtW5OPIt9vEjAvpfRSSmk1cCNwRKP3fa/g5QCyu+BqbHztfNUvTc81hiRJkor4omJKaRVwAbBJO7zfKNbe/YbsbvWoxp0i4rSIeBH4IfDlpk4UEadGxOyImP3mm2+2Q7QuZos9oVc/eONpWPZG3mkkSZJ6tGJn/5hFtlR5WzU1JnudO9EppStSShOAbwLnNnWilNLVKaXKlFLl8OHD2yFaF9OrD4zbJ9v2brUkSVKuii2qvwb8R0R8KSK2iIg+EdG78FHkeRYBYwpejwZebaH/jcC/FXnunqd+dUWXLJckScpTUYu/kN2pBriS5sc4FzP7xyxgYkRsCSwGjgGOK+wQERNTSi/UvjwUeAE1rW5c9YsPQkrZwjCSJEkquWKL6lNphy8MppSqIuJ04F6yIvw3tSs0XgTMTindCZweEVOBNcC7wOfa+r7d1ohtYeCm8P7rsGQujNwu70SSJEk9UrHLlF/TXm+YUroLuKtR2/kF219pr/fq9iKyqfX+9w/Z1HoW1ZIkSbnYoGXK1YnUT63nuGpJkqS8FDv8g4j4JPAF4ENA38b7U0qbt2MuFWv85Ox5/j+halU2K4gkSZJKqqg71RFxNHAD2ewd48jGRN9PVlwvB9pteIhaaaORMHIHqFoBC2bknUaSJKlHKnb4xzeB7wJfrH19eUrpBGBL4B2yLxQqL+MnZ88OAZEkScpFsUX1RODvKaVqoBrYCCCltBS4mGZWPVSJ1M1X/eID+eaQJEnqoYotqpcBdYN1FwPbFuxLwLD2DKVWGrs3lPeB156CD97OO40kSVKPU2xRPRvYsXb7z8B5EXFSRHwG+CHwaEeEU5Eq+sHYvYAEL0/PO40kSVKPU2xRfTFrlxM/D3iS7MuJ/w28x9qx1spL/eqKDgGRJEkqtaKK6pTSwymlG2q3300pHUo2rnpYSmm3lNK8jgypIkyoK6qnZ0uWS5IkqWSaLaoj4s8RcVxEDGhqf0ppeUrpnY6LplYZuSP0HwbvLYK3Xsg7jSRJUo/S0p3qccD1wJKIuCkijoiI3qWJpVYrK3NqPUmSpJw0W1SnlHYg+3LiT4BdgduANyLi1xExNSJc4ryzqZ9az6JakiSplFosjFNKc1JK56aUPgRMAn4NTAX+ArwaEZdHxN4lyKli1I2rnv93qF6TbxZJkqQepOi7zSml2Smls1JKY4GPADcDnwT+HhEvd1RAtcKgzWHY1rD6fVg0K+80kiRJPcaGDuGYBTwA/LP29RbtE0dt5uqKkiRJJVd0UR0R5RFxcERcC7wB/D9ga+BcYELHxFOr1U+t57hqSZKkUunV0s6ICGAycAzwCWAo8BJwBfCHlNKcjg6oVhq7D5RVwKuPw4p3od8meSeSJEnq9lqap/qnwGLgfuAwsun19kwpbVX75UUL6s6oz0AYswekGnj5obzTSJIk9QgtDf84Hvgz2Wwfo1NKZ6aUHi1NLLXJhMnZs0NAJEmSSqKlonpkSunUlNKDKbnudZfilxUlSZJKqqXFX6pKGUTtaLNdoO/G8K9X4J2X8k4jSZLU7bkqYndUVr52yXKHgEiSJHU4i+ruqn5qPYeASCmmFdkAACAASURBVJIkdTSL6u5qfG1R/fLfoWp1vlkkSZK6OYvq7mqTsTBie1i1FB7/Xd5pJEmSurVmF3+JiN+05kQppZPbHkftav9z4KbjYfrFsNPR0HdQ3okkSZK6pZZWVNyx0estgOHAktrHiNrHm8ArHZJObbPNYdlCMAtnwsOXwwHfyjuRJElSt9TSlHq71z2Ai4D3gX1TSpumlHZKKW0KfARYBny3NHHVKhEw7TvZ9iM/h/deyzePJElSN1XsmOqLgXNTSg8XNqaU/gmcD/ygvYOpnWyxR3bHes1ymP5feaeRJEnqlootqscDy5vZtxwY1y5p1DGmXghRDk/8N7z5XN5pJEmSup1ii+rHgQsjYrPCxojYHLgQeKydc6k9DZsIu30OUg3cf2HeaSRJkrqdYovqU8m+lDg/Ih6OiNsj4mHg5dr2L3VUQLWTj54NFQPgubvglYfX31+SJElFK6qoTinNASYAZwLPAX1qn88EJqSUnu6whGofG42Efb6cbf/lPEgp3zySJEndSEtT6jWQUloJXNmBWdTR9jodZv0aFs+GZ+6A7f8t70SSJEndQqtWVIyIgyPivIi4OiK2qG3br3ZstTq7PgNh8tnZ9l+/DdVr8s0jSZLUTRRVVEfEyIiYCfwJ+BxwCjCsdvdJwHkdE0/t7sMnwNCJ8M5L8Ni1eaeRJEnqFoq9U305MBDYpvYRBfvuB6a0cy51lPIKmHpBtj39Ylj5Xr55JEmSuoFii+qDyBZ/mQc0/obbImBUu6ZSx6pbvnz5W/Dwz/JOI0mS1OW1Zkx1dTPtw4AV7ZBFpdJg+fIrXL5ckiSpjYotqv8OnBER5QVtdXesTwYeaNdU6nguXy5JktRuii2qvwnsDjwNfIesoP5CRDwE7AWc2zHx1KGmXrh2+fIlz+adRpIkqcsqdvGXp4FKYDZwItlQkE8AC4E9UkrPd1RAdaBhE2G3E7Ply//67bzTSJIkdVlFj6lOKc1LKX02pbR5Sql3SmnTlNJnUkovdGRAdbDJBcuXz/9n3mkkSZK6pGLnqX4gIrZpZt+HIsIx1V3VwBFrly+/73yXL5ckSdoAxd6pngwMambfIGC/dkmjfOx1OgwYsXb5ckmSJLVKa6bUW+cWZkT0Bg4AXm+3RCq9xsuXV63ON48kSVIX02xRHREXRER1RFSTFdQz6l4XtK8A/gu4vkR51VFcvlySJGmD9Wph313AW2RLkv8M+DEwv1Gf1cCzKaW/d0g6lU55RTbF3k2fgb/9AHY+Bvo2N+JHkiRJhZotqlNKs4BZABGxDPhzSuntUgVTDrY5NFu+fOHMbPnyA5x+XJIkqRjFjql+EtijqR0RcUhE7NR+kZSbwuXLH/65y5dLkiQVqdii+ic0U1STrbT4k2LfMCIOiojnImJeRJzdxP6vRcQzEfFURPw1IsYWe261gy32gG0/DlUrXL5ckiSpSMUW1R8GmlsZ5BFg12JOEhHlwBXAwcB2wLERsV2jbk8AlSmlnYBbgR8WmVHtZcoFLl8uSZLUCsUW1eXAgGb2DQB6F3meScC8lNJLKaXVwI3AEYUdUkoPppSW176cAYwu8txqL4XLl99/Yd5pJEmSOr1ii+pZwKnN7DsVmF3keUYBCwteL6pta84pwN1N7YiIUyNidkTMfvPNN4t8exWtbvny5+92+XJJkqT1KLaovhCYEhEzI+I/IuITEXFaRMwE9gfOK/I80URbk+tiR8TxQCVwSVP7U0pXp5QqU0qVw4cPL/LtVbQGy5ef5/LlkiRJLSiqqE4pPQQcCNQAl5ONdf4pUAVMa8U81YuAMQWvRwOvNu4UEVOBbwGHp5RWFXlutbf65csfg2duzzuNJElSp1X0MuUppekppb2AjcgK40EppX1aufDLLGBiRGxZu8T5McCdhR0iYlfgl2QF9ZJWnFvtrc9A2P+cbPuvF7l8uSRJUjOKLqoBIiKAocBYmh7K0aKUUhVwOnAvMBe4OaU0JyIuiojDa7tdAgwEbomIJyPizmZOp1LY1eXLJUmS1idSkWNlI+I/gHOBTcnGQe+eUno8Iv4IPJRSuqzjYrassrIyzZ5d7Hcl1Wpz/5wtX95/KHz5SZcvlyRJPVZEPJZSqmzcXtSd6oj4T+BS4FfAATS8Sz0dOLodMqqz2uZQGLMnLH87W75ckiRJDRQ7/OM04PyU0gVA4zHUzwEfatdU6lwiYNpF2bbLl0uSJK2j2KJ6U+CxZvbVAH3bJ446rQbLl38/7zSSJEmdSrFF9Tzgo83s2w94pn3iqFObcmHt8uXXu3y5JElSgWKL6suAsyPiXGBibduIiDgF+Brwk44Ip05m2FYuXy5JktSEYhd/uYZsMZZvAnNqm+8iWwDmwpTSDR0TT51Og+XL/5F3GkmSpE6hNYu/XAJsDhwMHA8cAoyqbVdPMXAE7POVbPu+812+XJIkiVYu/pJSWpZS+ktK6YaU0j0ppaUdFUyd2F6nuXy5JElSgV7N7YiIQ4B/pJTeq91uSQLeAeamlN5rz4DqhOqWL//zmXD/t2HrQ6FX77xTSZIk5abZohr4M7An8GjtdmL9S5N/EBGfTynd1E751FntegI8ciW8/QI89lvY44t5J5IkScpNS8M/tgSeLNgeX/vc3GMn4GbASYx7gvJeMPXCbPtvP4CV/gOFJEnquZq9U51SeqWp7ZZExOXALu2QS11B3fLlC2fAP38KU87LO5EkSVIuiv6iYkT0ioijI+LyiPh97fOnI6K+ME8pPZlS2q1joqrTiYADv5NtP3IFvPdqvnkkSZJyUlRRHREjgNnAH4BDyYaCHArcCMyKiOEdllCd25hJBcuX/1feaSRJknJR7J3qS4GhwB4ppfEppb1SSuOBPWrbL+2ogOoCGixfPjfvNJIkSSVXbFF9CPDNlNKswsba1+eQ3bVWTzVsK6g8yeXLJUlSj1VsUd0HWNbMvmWAkxT3dB/9JvQeCM/f4/LlkiSpxym2qJ4BfDMiBhQ21r7+Zu1+9WQDR8DeX862/3Key5dLkqQepdii+uvA9sDCiLgxIn4aEX8AFgLb1e5XT7fXaTBwJLz6OMy5Le80kiRJJVNUUZ1SehKYCFwNDAemASOAq4CJKaX/7bCE6jr6DITJZ2fbf70Iqlbnm0eSJKlEWlqmHICIqAAmAS+nlM7u+Ejq0ly+XJIk9UDF3KmuBh4Atu3gLOoOynvBtG9n2y5fLkmSeoj1FtUppRrgBWBkx8dRt7D1Idny5cvfzpYvlyRJ6uaK/aLit4DzI2LHjgyjbsLlyyVJUg9TbFF9LtnKiU9GxIKImBURjxY+OjCjuqIxk2Dbw7Plyx/8ft5pJEmSOtR6v6hYaw7wdEcGUTc05QJ49n/gyd9n0+2NcFi+JEnqnooqqlNKJ3ZwDnVHdcuXz7omW778uJvyTiRJktQhWhz+ERH9IuKTEfH1iDguIvyyolrH5cslSVIP0GxRHRHjyYZ93AJcAlwPPBcRB5Yom7oDly+XJEk9QEt3qn8I1AAfAfqTLVP+BPDLEuRSd+Ly5ZIkqZtrqajeCzg3pfTPlNLKlNJc4IvAFhGxWWniqVvoMxAmn5Nt//XbLl8uSZK6nZaK6s2Alxq1vQgEsGmHJVL3tOtnYdiH4N352fLlkiRJ3cj65ql2AKzaR3kvmHphtv23H8DKpXmmkSRJalfrK6rvjYgldQ/gtdr2vxa21+6TWrb1IbDFXi5fLkmSup2W5qn+dslSqGeIgGkXwa+nwSNXwu6fh0Gb551KkiSpzZotqlNKFtVqf3XLl8+9M1u+/Iif551IkiSpzdY3/ENqf1MugLJe2fLlS+bmnUaSJKnNLKpVesO2gt1OhFSTLV8uSZLUxVlUKx+Fy5e//FDeaSRJktrEolr5GDgC9vlKtn3z52DBjHzzSJIktYFFtfKz95dh4sdgxTvwu8NdwlySJHVZFtXKT0VfOOYGqDwZqlfBLSdm81cn1xySJEldi0W18lXeCw69FKbWzuB43/lw11lQXZVvLkmSpFawqFb+ImDfr8JRv4XyPjDrGrjpM7D6g7yTSZIkFcWiWp3HDp+AE+6Afptks4L89hBY9kbeqSRJktbLolqdy9i94JT7YZNx8NqTcM1UWPJs3qkkSZJaZFGtzmfYVvD5v8KoSli6AH59oHNZS5KkTs2iWp3TgGHwuT/BNofBqqXw35+A/70p71SSJElNsqhW59W7P3z6OtjzP6BmDdx2Kvzth065J0mSOh2LanVuZeVw0H/BQT8AAh78Htx5OlSvyTuZJElSvZIX1RFxUEQ8FxHzIuLsJvbvFxGPR0RVRBxV6nzqpPb8Ehx9PfTqB09cDzd8Gla+l3cqSZIkoMRFdUSUA1cABwPbAcdGxHaNui0ATgRuKGU2dQHbHgYn/g8MGA4vPgC/PRiWLs47lSRJUsnvVE8C5qWUXkoprQZuBI4o7JBSmp9SegqoKXE2dQWjd4NT7oOhE+GNp7Mp917/v7xTSZKkHq7URfUoYGHB60W1ba0WEadGxOyImP3mm2+2Szh1EUO2hFP+AmP3gWWvwm8Ohnn3551KkiT1YKUuqqOJtg2ayiGldHVKqTKlVDl8+PA2xlKX038IfPY22OGTsHoZ/P7T8Ph1eaeSJEk9VKmL6kXAmILXo4FXS5xB3UWvPvCJa2DfMyFVw51nwF+/45R7kiSp5EpdVM8CJkbElhHRGzgGuLPEGdSdlJXB1AvhsMsgyuHvP4I/ngpVq/JOJkmSepCSFtUppSrgdOBeYC5wc0ppTkRcFBGHA0TE7hGxCPgU8MuImFPKjOqiKk+C426CigHwfzfD9Z+EFe/mnUqSJPUQkbrBP5VXVlam2bNn5x1DncFr/5uNr37/dRi2NXzmFthkbN6pJElSNxERj6WUKhu3u6KiupfNdobP3w8jtoO3nsum3Fv8eN6pJElSN2dRre5n4zFw8j0wfjJ8sASuPRSeuzvvVJIkqRuzqFb31HcwHHcL7PIZWLMcbjwOHv1V3qkkSVI3ZVGt7qtXbzjiCpj8/0GqgbvOgnu/BTUu1ilJktqXRbW6twiY/E34t19AWS945Odw64mwZkXeySRJUjdiUa2eYZfj4Pj/B30GwTN3wHVHwAdv551KkiR1ExbV6jnGT4aT74VBo2HhTPj1VHj7xbxTSZKkbsCiWj3LyO2yKfc23QneeSmbcm/BzLxTSZKkLs6iWj3PoM3gpLth4oGw4h343cdhzu15p5IkSV2YRbV6pj4D4Zg/wG4nQfUquOVEePjn0A1WGJUkSaVnUa2eq7wXHPYTmPptIMFfvgV3fwNqqvNOJkmSuhiLavVsEbDvV+Go30B5b3j0arjpeFj9Qd7JJElSF2JRLQHs8Ek44Q7ouzE8d1e2tPmyN/JOJUmSugiL6g20uqqG5aurWLG6mhWrq1m5Zu1jVVU1q6tqWFOdPaqqa6iuSdTUPpLjdjunsXtnM4NsPBZefSKbcu/N5/JOJUmSuoBeeQfoqn4x/UV+cv/z7XKuCIj67SjYhmDtzqhty7aj6eMa9M36lNXuW/u6qbagLNa+Duraal/X9i8ra+HYukzRzLF179ugLSgrKzw2msnXzLENMtceW7YhP2/d+5bTb8ffcOD/foUR/3qaVb+cwoO7XMaSoZX17xvR8PMv/D2VFfYp6Ff4O4pG/WhwroZ9aKI9Gvcv+HNQ9z6N/3zVbzfTXrin+f7RZPu6xzR9rsZtdf3Wfj7NtK9zrub2R5P9G59vnRyNfq7GnzFNfeYF/YiGWZr6XdHEeRv0a+qDkiR1KRbVG6hXedC3IrvRnxLU33tOkEj1k0gkIKVUv7+pm9QNj2/cwbvaefguX+enFVfwMWYzddYX+FPNXlxddRhz09i8o6mba6l4r7t4rb8gZG1RXlbwTH2fpi8oG1/Y1R/f6OK28IKT+j5NX+AWnhsKz9kwV6xzjsKfZe0FeOGNgsKsa99j7UVzsPb9oWHu+vM3ushZ7++hlb+z4s5ZXMcGF4xNXCw2deHZ5EViCxeqLV10Fl6gNnXx2ritqYzNvW9T+2niPdb9uZrP2/iYuv2FfaPBMc3clKrrGw2z1f3ZLMzU+NwU5Fvn3Ot87o1zFXEhHg3PXfh3YL3naGJfXYyWbhhE2dq/q4V/X+v+Phb+d0CZ6A5DESorK9Ps2bPzjtFqKaUGBXXj4ruwOK9rg7XtjY+r71t7LEBNyvbXFJwvJahJiZq09nUi67O2LTtDTUrU1DRzbMHP0OyxqfDnzM5VeGxNwTkbnq+JY5t6j5q6n62JY1nbt+V8TZ0vQU01UxdfyZ5LbqacbEaQFwbuzkPDj+WFAZUkosHvIjV6z7VtBb/bgs+h8bE0eF2XkfrhQg3P33C7/s9Io4uwhvsa/tlrur3p/jTTf91jUtPtBReZjd+/4f7UYv/Ci9eW9jd7vkbhmzqumN9L4e+4MEvD33vB39N1ztvo76wkdWGN/zW58AZA3b+6Fv4LceGFc+N/OW7qwr/hhXvtcWVw8Sd2YodRg0v+80bEYymlysbt3qnOUeEVbG1LXlHUrKvg3XNgxi/g8euY+P4sJr4/CzbdEfb+Mmx/JJRX5B1S3UDhRXZTxTk0vABtcJFYe1xTF471xzS6gK672IRGF7e1zxSer6lz16x9D1LBhTUNLziaOkfdhUrhxW/dexZegDf8LJrIUntATWGuRheiazOtfY/2/r0V16/I8xX0b/Iis5kLwcb9Gl9YNr74W1//hhfFab39Gl/Q0nh/kccV5l3/RXPT++suYuv6Nv6MGl7Qtvwvy4Wf19q2ls9Nwc+yvnPT1IV4o/dd92K/8CZNMxfz9Z970xf6xd4wKPzvTU1a21b49wrW/v1v+JvpeCvWdK4pcL1TLRVr+Tsw+zcw85fwwZKsbfAY2PPf4cMnQJ+N8s0nSVIJNb7YLbyAb3ADoPZfZxv/q3HdhXVNyi7UYW0Bn1LjC+Z1bxJsOXwAA/uU/v5wc3eqLaql1lqzEp66CR6+HN5+IWvrOxgqT4Y9vgQbbZpvPkmS1GEsqqX2VlMDz98DD/8MFjyStZX3hp0+DXudASO2yTefJElqd80V1c5TLW2osjLY5hA4+R445X7Y9uNQvQaeuB6u3AN+/2mY/4/iB1NKkqQuy6Jaag9jdoejr4czHoPKU6BXX3jh3mxlxl8dAHNug5rO9YUKSZLUfhz+IXWED96CR38Fj14NK97J2jYZB3udDrt8Bnr3zzWeJEnaMI6plvKwejk8+Xt45Ofw7vysrd8QmPQFmHQqDBiWazxJktQ6FtVSnmqqYe6fsi81Ln4sa+vVF3Y5Lrt7PXRCvvkkSVJR/KKilKeyctj+3+Dzf4UT74IPHQRVK7N5ry/fDW46HhY+mndKSZK0gVxRUSqlCBi3T/ZY8iw8cjk8dXN2F3vun2DMnrDPl+FDB2ezi0iSpC7B4R9S3pa9DjOvglm/gVVLs7ahE2Hv02GnY6Cib775JElSPcdUS53dqmXw+H/DjCth6cKsbcAI2OPUbJq+/kPyzSdJkiyqpS6jeg3MuR0e/im8/n9ZW8UA+PBnYc//gE3G5ptPkqQezKJa6mpSgpemZzOGvPhA1ha1X3jc+wzYfNdc40mS1BM5+4fU1UTAhP3hs7fBl/4BOx2dtT39/+DqyXDtYfDCfS6DLklSJ+CdaqkrWboIZvwCHvsdrF6WtY3YLpvvesyesNnO0Kt3vhklSerGHP4hdScr/gWPXZvNGrLstbXt5X1g1IdhzB6wxZ4wehIMGJpbTEmSuhuLaqk7qloNc+/Mxl4vnAlvPb9un6ETYYs9sjvZY/aAYROzYSSSJKnVLKqlnmD5O9nKjAtnZM+LH8tWbizUb0jtnew9sufNd4WKfvnklSSpi7GolnqiqtXw+lOwYEZ2J3vhTHj/jYZ9yipg812yArtu2MjAEfnklSSpk7OolpTNFPLu/LV3sxfMhCXPAI3+O7DJlgV3s/eE4du4bLokSVhUS2rOyqWwaFZWYC+cCYtmw5oPGvbpMxjG7J4V2FvsAaN2g94D8skrSVKOLKolFae6Ct54eu1wkQUz4b1FDftEOWy6YzZUpG7YyOBR+eSVJKmELKolbbili9YW2AtnwOtPQ6pu2GfwmIJx2XvAiO2hvFc+eSVJ6iDNFdX+P56k9Rs8Onvs8Mns9ar3s5lFFs7MvgS5aBYsXZg9nr4169N7IIyuzIrs0bvDJuNg0OYOG5EkdUsW1ZJar89AGP/R7AFQUw1vPls7y0jtlyDfnZ/Nn/3S9IbH9t04K9AHbQ6DRtU+Ns+Gj9RtW3hLkroYi2pJbVdWDiO3zx67n5K1LXu9tsCeCa8+mY3Lfu9VWPmv7PHG082fz8JbktTFWFRL6hgbbQrbHZ496qQEH7wF7y2ufbyajdd+79Xah4W3JKlrsqiWVDoRMHB49th8l6b7tFh4F7RZeEuSOhGLakmdSzGFd00NLH977Z3t9ii8BwyHvoOg72DoMyhrb/B6cO2jdrv3Ri6II0mqZ1EtqespKysovHdtuk/jwnvp4oYFd+PCu9WitthuXHgXFOCN2/o0Ksx79WnTxyBJ6jwsqiV1T60tvD94G1YtzVaYXPle9rzqveZfr16W9V+1NJtKcEOU92ldId6rT3ZMr77Qq3ftdt1zHyjvnT2X9cru+EuSSqbkRXVEHAT8FCgHrkkpXdxofx/gOmA34G3g6JTS/FLnlNQDFBberVVT3XLRXf/6X833qV4FHyzJHu0pypovuMt7NyrKG+/rU1C8N7Gvrn2dttrzlZXXPnrVFveNXtdtR5mFv6RupaRFdUSUA1cA04BFwKyIuDOl9ExBt1OAd1NKW0XEMcAPgKNLmVOS1qusHPptkj02REqwZkUThXgLd8urVkL1aqhatfa5alVWnBe2pWqoWpE9OrP6oruu4C4r2K4tvAtfr7O/qYK9cUFfUMiXlWdtEWuL+igD6l6XNWyvL/xb2l93fKxnf+G+9eyvOx8BAbX/08S+2MB9RZyz/oKnpX2Nz1PY3FKfpo7pqD6su6/ZnC1o8/na2He9x2zocRv6Xp1EWUWn+m5Lqe9UTwLmpZReAoiIG4EjgMKi+gjgwtrtW4GfR0Sk7rCeuiTViYDe/bPHRpu277lrqmsL7iaK8OpVULV6bSG+3n2FbUXsq6nOivqaaqipqn00ep2qIdVk21Rlx0lSa510N4zdO+8U9UpdVI8CCgcfLgL2aK5PSqkqIpYCQ4G3CjtFxKnAqQBbbLFFR+WVpK6nrHxtwd5Z1dTUFt9VBQV39dqiu7mCvL5oryp41DR83WRRX3dsTfYgrd1ONdm/HKS0nv0F2y3urzs+rWd/YXvj904FzzTd1uy+lo4reK4/R6p92dy+Jo5r/P5NvW6yD0X0KeY8RfQp1OR9ubb0a6Jb043Fn7PZvus5ZkOP29D36lQ61930UhfVTf30jX9zxfQhpXQ1cDVAZWVlV/ntS5Kg9p9sy6C8Iu8kktQuSj0QZREwpuD1aODV5vpERC9gMPBOSdJJkiRJG6DURfUsYGJEbBkRvYFjgDsb9bkT+Fzt9lHAA46nliRJUmdW0uEftWOkTwfuJZtS7zcppTkRcREwO6V0J/Br4L8jYh7ZHepjSplRkiRJaq2Sz1OdUroLuKtR2/kF2yuBT5U6lyRJkrShOs/kfpIkSVIXZVEtSZIktZFFtSRJktRGFtWSJElSG1lUS5IkSW1kUS1JkiS1kUW1JEmS1EYW1ZIkSVIbWVRLkiRJbRQppbwztFlEvAm8ktPbDwPeyum9uws/w7bzM2w7P8O28zNsOz/DtvMzbB9+js0bm1Ia3rixWxTVeYqI2SmlyrxzdGV+hm3nZ9h2foZt52fYdn6Gbedn2D78HFvP4R+SJElSG1lUS5IkSW1kUd12V+cdoBvwM2w7P8O28zNsOz/DtvMzbDs/w/bh59hKjqmWJEmS2sg71ZIkSVIbWVRvoIg4KCKei4h5EXF23nm6mogYExEPRsTciJgTEV/JO1NXFRHlEfFERPw57yxdVURsHBG3RsSztX8m98o7U1cTEWfW/l1+OiL+EBF9887U2UXEbyJiSUQ8XdA2JCLui4gXap83yTNjZ9fMZ3hJ7d/lpyLitojYOM+MnV1Tn2HBvrMiIkXEsDyydTUW1RsgIsqBK4CDge2AYyNiu3xTdTlVwNdTStsCewKn+RlusK8Ac/MO0cX9FLgnpbQNsDN+nq0SEaOALwOVKaUdgHLgmHxTdQnXAgc1ajsb+GtKaSLw19rXat61rPsZ3gfskFLaCXgeOKfUobqYa1n3MyQixgDTgAWlDtRVWVRvmEnAvJTSSyml1cCNwBE5Z+pSUkqvpZQer91eRlbE/P/t3XmQXFUVx/HvT8KWCFoQJ0CChE0oFZWRAkIslEWgWANCWDUoJYqFFfalsBQVETSQWIqIgBgwQmQpCCBJSMIgIFsIQhRBtpBMFmYgEJQ1geMf93boefZMpqclL135faq6Xvft++473TUzffrOee8OLjeq5iNpCLAfcEXZsTQrSesDuwJXAkTEOxHxarlRNaV+wLqS+gH9gQUlx7PKi4i/AIsLzQcB4/P98cCIlRpUk6n1HkbE1IhYlh8+AAxZ6YE1kW5+DgHGAmcAPvmul5xU981gYF7V43acEPaZpKHA9sCD5UbSlMaR/ui9V3YgTWwLoBO4KpfRXCFpQNlBNZOImA+MIc1oLQSWRMTUcqNqWoMiYiGkyQegpeR4mt03gDvKDqLZSDoQmB8Rj5UdSzNxUt03qtHmb3J9IOnDwI3ASRHxWtnxNBNJ+wMdEfFI2bE0uX5AK3BpRGwPvI7/5V6XXPd7ELA5sAkwQNIx5UZlqztJ55BKDSeUHUszkdQfOAf4ftmxNBsn1X3TDmxa9XgI/ldn3SStSUqoJ0TETWXH04SGAwdKmkMqQdpd0h/KDakptQPtEVH5T8kNpCTbem9P4PmI6IyInSZLFgAAB7ZJREFUpcBNwC4lx9SsXpS0MUDedpQcT1OSNArYHzg6fO3gem1J+oL8WP58GQLMkrRRqVE1ASfVffMwsLWkzSWtRTohZ1LJMTUVSSLVsP4zIi4uO55mFBFnR8SQiBhK+hmcERGeHaxTRCwC5knaJjftATxRYkjNaC6ws6T++Xd7D3yyZ19NAkbl+6OAW0qMpSlJ2gc4EzgwIt4oO55mExGzI6IlIobmz5d2oDX/rbQeOKnug3wCxInAFNIHx58i4h/lRtV0hgNfJc2u/i3f9i07KFttfReYIOlx4HPA+SXH01TyLP8NwCxgNumzxauxrYCka4H7gW0ktUs6DrgA+LKkp0lXXrigzBhXdd28h78C1gPuzJ8tvyk1yFVcN++h9YFXVDQzMzMza5Bnqs3MzMzMGuSk2szMzMysQU6qzczMzMwa5KTazMzMzKxBTqrNzMzMzBrkpNrMLJN0rqSoui2QdKOkLWv0PUTSDEmvSnpb0r8knSdpYI2+X8/jXVNnPIMkjZP0bD7GK5LukLR3I69zdSFpR0nnlh2Hma0enFSbmXW1BBiWb6eRrls9XdKASgdJFwHXA8+Rrre+FzAWOAC4vMaYR+btCEnr9iaIvBjNo8B+wJh8jK8Bc4BJkj5b7wtbDe0I/KDsIMxs9dCv7ADMzFYxyyLigXz/AUlzgXuAfYHrJR0AnAIcFxG/q9rvbkm/JSW/y0lqAXYHppNWGtyflJCvyARgMbBLRLxW1X6rpEuBV+t/aWZm9kHxTLWZWc8eyduheXsyMKuQUAMQEe9GxB2F5pHAGqRVWOfz/qx1tyTtCnweOLuQUFeO83hEzK3qP1LS7FwiMk/STyT1q3r+2Fx+0iqpTdIbeaW5VkkDJF0laYmk5yR1iS/3v0HS8ZLmSHpT0u2SBhf6DZQ0XtLLefw2STsU+syRNEbSyXnltlckXSfpo4V+G0i6TNKLkt6S9FdJOxX6hKTRks6X1CmpQ9IlktauvGbgl1V9Q1Lbit57M7O+clJtZtazoXm7SNKawC7A5Dr2PxJ4NCKeBCYC+0r6yAr2+SLwLjBtRYNL2iuPOws4iJRInkZaqrloPHAt8BVApKXFrwQWAIcCDwJXSxpS2G8YaSn3U4DjgM8ANxf63AzsnY99OOnz5S5JWxX6jSTN2B8PnEmauV++LHxOiqeRlug+HRgBdALTJG1UGOtUYBPgGODnwLeA0fm524GLquIfBnynxntiZvZ/4fIPM7OCqlneLYBfA/8mJXobAmsDc7vZtTjOZqRk7qzcdB0pMT0Y+H0Puw4GOiPizV4c5kdAW0SMyo8nSwL4qaTzIqK9qu+YiBifYxMp8WyLiHNy20Ok5PoA4NKq/VpIZSgv5H4vAPdK2iciJkvaBxgOfCki7s59ZpDqv08nJbsVS4EREbEs9/skcATvJ7zHAJ8GPhURT+c+04CnSEn06VVjzYmIY/P9KZKGA4cAP4uITklzAKrKeczMPjCeqTYz62pDUuK3lJTIbQEcHhELq/pEL8c6Im8nAkTEw8Az9KIEpDfHkLQG0Mr/1mhPJP19H1Zon151/5m8nbH8gBFLSLPCXUo7SOUuL1T1uw/oIJ0ISN52VhLq3Od14DbgC4Wx7qok1NkTQIuktfLjPUklN89L6lf1BeduoEs5CTC18PgJoDjLbma2Unim2sysqyWkxC6ARcCCiKgkuC8DbwMf7+VYR5LKMpZU1Q1PAkZLaomIjm72mw98TNI6EfFWD+MPBNYEXiy0Vx5vUGivPrnxnRptlfZ1Cm214uwANs73N64RQyWOnmKoHE/AWvn+QGBn0peaomd7MVYxdjOzlcJJtZlZV8siYmatJyJiqaT7SLXD3+tpEEnbApXL3r1So8thwCXd7N5GKuvYg1Si0Z2XSMlnS6F9UN4u7inGOhTHr7RVZu8XdtNnUB9iWAzMBE6o8dzbdY5lZrbSuPzDzKw+44AdJI0qPiHpQ7m+GOAo0smG+wG7FW6P00MJSETcQyqBOF/SejWOs52kTSPi3dzvsEKXkcB7wP11vrbutEpaPjufa5dbgIdy04OkEo5dq/r0J732e+s81nRgK2BuRMws3GbXOdY7ORbPXpvZB84z1WZmdYiIWyVdDFyZk8tbgP8A2wLfJp2cN5lUT31nRPy5OIak8cAYSZtV1yoXHA3cBcyUNJZUL7w+aZb8m8BOwDzS4iZTJF1FOhFyO+DHwOWFkxQb0QHcllcnXAe4kFRnPRkgIqbkGfyJks4ilcmcBqxLuipHPa4mvY9tksaQFtjZkFS3vSgixtYx1pN5OzqfOPlaRDxVZzxmZr3imWozszpFxKmky8ZtDfwRuJN0ZYrpwAn5+sxbA90tS34taSb5iG6eJyd/raQE/Yx8jGuATwBHRcRjud/UPM4OwK3ASaRLyZ3Y0Ivs6n7SVVDGkS7B93fSpe6qHZxjHEc6cVLA7hHxDHXINeS75bF+SDoZ8Rek9/OhHnat5R5SUj+aNJt+WZ37m5n1mt4//8bMzKyrvGDKSxFxaNmxmJmtyjxTbWZmZmbWICfVZmZmZmYNcvmHmZmZmVmDPFNtZmZmZtYgJ9VmZmZmZg1yUm1mZmZm1iAn1WZmZmZmDXJSbWZmZmbWICfVZmZmZmYN+i+UYzCIk+VsdgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "plt.plot(pca_balanced.explained_variance_ratio_, lw=2, label=\"balanced\")\n",
    "plt.plot(pca_unbalanced.explained_variance_ratio_, lw=2, label=\"unbalanced\")\n",
    "plt.xlabel(\"PCA Component\", fontsize=15)\n",
    "plt.ylabel(\"Projected Variance\", fontsize=15)\n",
    "plt.legend(loc=\"best\", fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the unbalanced tree the variation piles up around just a hand full of directions and then drops off exponentially as we head deeper into the tree hierarchy. In stark contrast the amount of variation in every direction is nearly the same. \n",
    "\n",
    "So astonishingly, the balanced binary trees are such that uniformly distributed angles \"nearly\" uniformly cover the sphere! We get an even clearer picture of this by looking at the distribution of points in projection along the first couple principal components of each expansion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes=plt.subplots(1, 2, figsize=(12, 6))\n",
    "nbins = 51\n",
    "axes[0].hist2d(u_balanced[:, 0], u_balanced[:, 1], nbins)\n",
    "axes[1].hist2d(u_unbalanced[:, 0], u_unbalanced[:, 1], nbins);\n",
    "axes[0].set_title(\"Balanced Tree (Uniform Theta)\")\n",
    "axes[1].set_title(\"Unbalanced Tree (Uniform Theta)\")\n",
    "axes[0].set_ylabel(\"First Principal Component\")\n",
    "axes[1].set_ylabel(\"Second Principal Component\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of the balanced binary tree the points are very spread out, with no obvious pole structure. Whereas in the case of the unbalanced tree it is very clear that the points prefer just a very few directions in the higher dimensional space, namely the points which lie close to the dominant polar direction (recognizable as the two bright points in the above plot)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singularity Structure \n",
    "\n",
    "Inevitably in any angular coordinate system there will be points where particular directions of change will have no effect on particular angles. These are the directions where a uniform distribution in angles will start to pile up along.  We will call these spatial locations \"singularities\". "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pca_unbalanced.components_[0], label=\"Unbalanced Tree\")\n",
    "plt.plot(pca_balanced.components_[0], label=\"Balanced Tree\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.title(\"Primary Singular Direction Vectors\")\n",
    "plt.xlabel(\"Coordinate Index\")\n",
    "plt.ylabel(\"Coordinate Value\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The principal vector of the unbalanced tree points nearly directly towards the vector of all zeros except for the last coordinate entry. Looking at the corresponding binary tree structure it is easy to see that this vector is the unique vector which can be specified simply by setting the angle at only the root node. The angles at all other nodes are irrelevant since all the availble coordinate magnitude has already been assigned upstream. \n",
    "\n",
    "On the other hand the principal vector corresponding to the balanced tree doesn't seem to have any obvious interpretability at all. This is because as we saw from the projected variance plot we made above the balanced binary tree doesn't really have any directions where the points pile up! \n",
    "\n",
    "Because we are using a finite number of points to determine the principal component expansion the directions of singularity which we discover will be slightly off from the true locations of singularity in our coordinate map. PCA is mathematically equivalent to finding the eigenvectors of the covariance matrix of our data. In cases where the eigenvalues are all distinct, the eigenvectors are well defined. Whereas in situations where there are many eigenvectors with the same or nearly the same eigenvalue, any admixture of eigenvectors is also nearly an eigenvector. This makes eigenvectors of systems with flat eigenspectra somewhat ambiguous, there is no one \"right\" set of eigenvectors.\n",
    "\n",
    "In the case of PCA the amount of variance projected along a principal vector is equal to the eigenvalue of that principal vector with respect to the data covariance matrix. From the plot above where we compared the amount of variance projected along each principal vector for the balanced and ublanced trees it is easy to see that the eigen spectrum of the balanced tree is flat, making the principal vectors arbitrary. Whereas the eigenspectrum of the balanced tree falls sharply making the eigenvectors unique and well defined."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Effect of Small Perturbations on Angles\n",
    "\n",
    "This means that the effect of small perturbations in spatial location have completely different sorts of effects on angles depending on the sort of tree which has been used to build the angular space representation. In the case of the unbalanced tree coordinate system tiny perturbations in location which occur close to the maximally singular directions have dramatic effects on every angle except the root angle (which stays stable). But for perturbations which happen in the regions of space which are maximally separated from the singular directions the changes to all angles are small and smooth. \n",
    "\n",
    "In contrast for the balanced tree, even close to the maximally singular directions most angles are well determined and small perturbations correspond to small changes in angle space. However there are also almost no dirrections where small perturbations cannot cause large effective changes in angle. Lets take a look at this graphically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def make_angle_perturbation_plot(\n",
    "    hpcs,\n",
    "    xvec, \n",
    "    perturbations,\n",
    "    label=None,\n",
    "    ax=None\n",
    "):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    r0, central_theta = hpcs.x_to_r_theta(xvec)\n",
    "    rs, pturb_thetas = hpcs.x_to_r_theta(xvec+perturbations)\n",
    "    \n",
    "    for i in range(len(perturbations)):\n",
    "        ax.plot(pturb_thetas[i], color=\"b\", alpha=0.5)\n",
    "\n",
    "    ax.plot(central_theta, color=\"r\", lw=2)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "perturbations = 0.05*np.random.normal(size=(50, ndims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 2, figsize=(12, 10), sharey=True)\n",
    "\n",
    "ax = axes[0, 0]\n",
    "ax.set_title(\"Maximally Singular Vector\\n Unbalanced Coordinates\")\n",
    "make_angle_perturbation_plot(unbalanced, pca_unbalanced.components_[0], perturbations, ax=ax)\n",
    "ax = axes[1, 0]\n",
    "ax.set_title(\"Maximally Singular Vector\\n Balanced Coordinates\")\n",
    "make_angle_perturbation_plot(balanced, pca_balanced.components_[0], perturbations, ax=ax)\n",
    "\n",
    "ax = axes[0, 1]\n",
    "ax.set_title(\"Maximally Stable Vector\\n Unbalanced Coordinates\")\n",
    "make_angle_perturbation_plot(unbalanced, pca_unbalanced.components_[-1], perturbations, ax=ax)\n",
    "ax = axes[1, 1]\n",
    "ax.set_title(\"Maximally Stable Vector\\n Balanced Coordinates\")\n",
    "make_angle_perturbation_plot(balanced, pca_balanced.components_[-1], perturbations, ax=ax)\n",
    "\n",
    "axes[1, 0].set_xlabel(\"Angle Index\")\n",
    "axes[1, 1].set_xlabel(\"Angle Index\")\n",
    "\n",
    "axes[0, 0].set_ylabel(\"Angle Value\")\n",
    "axes[1, 0].set_ylabel(\"Angle Value\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Effectively we can think of this as a simple expression of the idea that angles which have more parent angle nodes above them in the tree have much more sensitive behavior than thoe that have fewer parent nodes. The root angle (angle 0 here in both cases) is always well defined no matter where in space the base vector is. But angles which lie deeper down in the tree become more and more ill defined. \n",
    "\n",
    "The degree to which any given angle is ill determined however is related to the point in space represented. If any of the angles upstream from a given angle is such that the factor which its children accumulates when calculating the coordinates is close to 0 then that angle will be ill determined. "
   ]
  }
 ],
 "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": "3.7.4"
  },
  "nikola": {
   "author": "Tim Anderton",
   "category": "",
   "date": "2019-4-7",
   "description": "",
   "link": "",
   "slug": "binary-trees-and-hyper-spherical-coordinates",
   "tags": "awesome, math, coordinate systems, higher dimensions",
   "title": "Binary Trees and Hyper Spherical Coordinates",
   "type": "text"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
