piercing_number_probabilities-Google_Colab.ipynb

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        "<a href=\"https://colab.research.google.com/github/tiasondjaja/circular_societies/blob/master/piercing_number_probabilities-Google_Colab.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "# Approval Voting in Circular Societies:  Piercing Numbers and Agreement\n",
        "*Kristen Mazur, Mutiara Sondjaja, Matthew Wright, and Carolyn Yarnall*\n",
        "\n",
        "This Jupyter Notebook is a companion to the paper [title + link goes here].  [Some more blurb]\n",
        "\n",
        "## 1. How to use this document\n",
        "+ First, run the code cell in the \"Setup\" section below.  Do not modify anything.  This code cell must be run at the start of each session.\n",
        "+ Run the code cells in the remaining sections\n",
        "\n",
        "For the interested readers, [the code documentation is linked here](https://github.com/tiasondjaja/circular_societies/blob/master/DOCUMENTATION.md)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iY6TPjpSBP-Y",
        "colab_type": "text"
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      "source": [
        "## 2. Setup\n",
        "\n",
        "Run the code cell in the \"Setup\" section below once each time the notebook is started. Do not modify anything."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F9I5hP_gf2xD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import scipy as sp\n",
        "import cvxpy as cp\n",
        "import matplotlib.pyplot as plt\n",
        "import itertools\n",
        "\n",
        "# Part 0 ----------------------------------\n",
        "# Define the Set class (approval set)\n",
        "class Set:\n",
        "    # Initialize Class\n",
        "    def __init__( self, name, left_endpt, right_endpt, modulo ):\n",
        "        self.name = name\n",
        "        self.left_endpt = left_endpt\n",
        "        self.right_endpt = right_endpt\n",
        "        self.modulo = modulo\n",
        "    \n",
        "    # Method to print set name and left- and right-endpoints\n",
        "    def printSetInfo( self ):\n",
        "        if self.left_endpt <= self.right_endpt:\n",
        "            print( \" \" + self.name + \": [\" + str(self.left_endpt) + \", \" + str(self.right_endpt) + \"]\")\n",
        "        elif self.right_endpt == 0:\n",
        "            print( \" \" + self.name + \": [\" + str(self.left_endpt) + \", \" + str(self.modulo) + \"]\")\n",
        "        else:\n",
        "            print( \" \" + self.name + \": [0,\" + str(self.right_endpt) + \"] U [\" + str(self.left_endpt) + \", \" + str(self.modulo) + \"]\")\n",
        "    \n",
        "    def editSet( self, newname, newleft_endpt, newright_endpt, newmodulo ):\n",
        "        self.name = newname\n",
        "        self.left_endpt = newleft_endpt\n",
        "        self.right_endpt = newright_endpt\n",
        "        self.modulo = newmodulo\n",
        "        \n",
        "    def isPointInSet( self, point):\n",
        "        check = False\n",
        "        \n",
        "        if (self.left_endpt <= point and point <= self.right_endpt):\n",
        "             check = True\n",
        "        elif (self.left_endpt <= point and self.right_endpt <= self.left_endpt):\n",
        "             check = True\n",
        "        elif (point <= self.right_endpt and self.right_endpt <= self.left_endpt):\n",
        "             check = True\n",
        "            \n",
        "        return check\n",
        "  \n",
        "# Part 1 - MAIN ----------------------------------  \n",
        "\n",
        "# Define the CircularSociety class\n",
        "\n",
        "class CircularSociety:\n",
        "    \n",
        "    # Initialize Class\n",
        "    def __init__( self, name, modulo, isUniform = 0, tick = 0.5 ):\n",
        "        self.name = name\n",
        "        self.modulo = modulo # modulo > 0; the circular society is represented as [0, modulo) with 0 = modulo\n",
        "        self.approvalSets = [] # initialize with empty approval sets\n",
        "        self.numVoters = 0\n",
        "        self.tick = tick\n",
        "        \n",
        "        # List of all endpoints and setnames (useful when checking for left-right alternation)\n",
        "        self.list_setnames = []\n",
        "        self.list_left_endpts = []\n",
        "        self.list_right_endpts = []\n",
        "    \n",
        "    # method that returns a set given its name\n",
        "    def getSet( self, setname ):\n",
        "      for A in self.approvalSets:\n",
        "        if A.name == setname:\n",
        "          return A\n",
        "      return None\n",
        "    \n",
        "    ### DISPLAYING / OBTAINING BASIC INFORMATION ABOUT THE CIRCULAR SOCIETY----\n",
        "    \n",
        "    # Method to print list of approval sets\n",
        "    def listApprovalSets( self ):\n",
        "        for A in self.approvalSets:\n",
        "            A.printSetInfo()\n",
        "            \n",
        "    # Method to print society information\n",
        "    def printSocietyInfo( self ):\n",
        "        print(\"Circular Society Name: \" + self.name)\n",
        "        print(\"Spectrum: [0, \" + str(self.modulo) + \"].  (Note: we identify 0 = \" + str(self.modulo) + \")\"  )\n",
        "        print(\"Number of Voters: \" + str(self.numVoters) )\n",
        "        print(\"Approval Sets:\")\n",
        "        self.listApprovalSets()\n",
        "    \n",
        "    # Method to list the endpoints of the sets, from 0 to N\n",
        "    def listSetEndpoints( self ):\n",
        "        N = self.numVoters\n",
        "        orderedendpts = []\n",
        "        orderednames = []\n",
        "        setindices_ordered_left = np.argsort(self.list_left_endpts)\n",
        "        setindices_ordered_right = np.argsort(self.list_right_endpts)\n",
        "        left_i = 0\n",
        "        right_i = 0\n",
        "        \n",
        "        for step in range( 0, 2*N ):\n",
        "            if left_i < N and right_i < N:\n",
        "                if self.list_left_endpts[ setindices_ordered_left[left_i] ] < self.list_right_endpts[ setindices_ordered_right[right_i] ]:\n",
        "                    orderedendpts.append( self.list_left_endpts[ setindices_ordered_left[left_i] ] )\n",
        "                    orderednames.append( 'L' + self.list_setnames[ setindices_ordered_left[left_i] ] )\n",
        "                    left_i += 1\n",
        "                else:\n",
        "                    orderedendpts.append( self.list_right_endpts[ setindices_ordered_right[right_i] ] )\n",
        "                    orderednames.append( 'R' + self.list_setnames[ setindices_ordered_right[right_i] ] )\n",
        "                    right_i += 1\n",
        "            elif left_i == N and right_i < N:\n",
        "                orderedendpts.append( self.list_right_endpts[ setindices_ordered_right[right_i] ] )\n",
        "                orderednames.append( 'R' + self.list_setnames[ setindices_ordered_right[right_i] ] )\n",
        "                right_i += 1\n",
        "            else:\n",
        "                orderedendpts.append( self.list_left_endpts[ setindices_ordered_left[left_i] ] )\n",
        "                orderednames.append( 'L' + self.list_setnames[ setindices_ordered_left[left_i] ] )\n",
        "                left_i += 1\n",
        "        return orderednames, orderedendpts\n",
        "      \n",
        "    \n",
        "    ### FINDING, EDITING, ADDING, REMOVING APPROVAL SETS-----------------------\n",
        "    \n",
        "    # Method to find an approval set by name\n",
        "    def findApprovalSetName( self, setName ):\n",
        "        for ind, A in enumerate( self.approvalSets ):\n",
        "            if setName == A.name:\n",
        "                return ind # if set name found, return index\n",
        "        return -1 # if set name not found, return -1 \n",
        "    \n",
        "    # Method to add a new approval set into the society\n",
        "    def addApprovalSet( self, setName, left_endpt, right_endpt ):\n",
        "        # Check that setName is different from names of sets already on the list\n",
        "        ind = self.findApprovalSetName( setName ) # if not found, ind = -1\n",
        "        if ind == -1:\n",
        "            newSet = Set( setName, left_endpt, right_endpt, self.modulo )\n",
        "            \n",
        "            # Update attributes\n",
        "            self.approvalSets.append( newSet )\n",
        "            self.numVoters += 1\n",
        "            \n",
        "            # Update list of all endpoints\n",
        "            self.list_setnames.append( setName )\n",
        "            self.list_left_endpts.append( left_endpt )\n",
        "            self.list_right_endpts.append( right_endpt )\n",
        "            \n",
        "        else:\n",
        "            print(\"Set is not added because this set name has already been chosen.  Please pick a different set name.\")\n",
        "\n",
        "    # Method to remove an approval set from the society\n",
        "    def removeApprovalSet( self, setName ):\n",
        "        for ind, A in enumerate( self.approvalSets ):\n",
        "            if setName == A.name:\n",
        "                self.approvalSets.pop(ind)\n",
        "                self.list_setnames.pop(ind)\n",
        "                self.list_left_endpts.pop(ind)\n",
        "                self.list_right_endpts.pop(ind)\n",
        "                self.numVoters -= 1\n",
        "    \n",
        "    # Method to edit the endpoints of an approval set\n",
        "    def editApprovalSet( self, setName, newleft_endpt, newright_endpt ):\n",
        "        ind = self.findApprovalSetName( setName ) # if not found, ind = -1\n",
        "        \n",
        "        if ind == -1:\n",
        "            print(\"Set name is not found\")\n",
        "        else:\n",
        "            A = self.approvalSets[ind]\n",
        "            A.editSet( setName, newleft_endpt, newright_endpt, self.modulo )\n",
        "            self.list_left_endpts[ind] = newleft_endpt\n",
        "            self.list_right_endpts[ind] = newright_endpt\n",
        "    \n",
        "    \n",
        "    ### AGREEABILITY, AGREEMENT NUMBER, PIERCING NUMBER -----------------------\n",
        "    \n",
        "    # Method to check (k, m) agreeability (brute force)\n",
        "    def checkAgreeability( self, k, m):\n",
        "      setNames = [ A.name for A in self.approvalSets ]\n",
        "      subcollections_m = [list(i) for i in itertools.combinations(setNames, m)]\n",
        "      good = [] # is the society k,m agreeable? will store 1 or 0 for each collection of m sets\n",
        "      bad_m_sets = []\n",
        "      for collection in subcollections_m:\n",
        "        good_m_sets = [] # will store 1 or 0 for each collection of k sets\n",
        "        subcollections_k = [list(i) for i in itertools.combinations(collection, k)]\n",
        "        for collection1 in subcollections_k:\n",
        "          setname = collection1[0]\n",
        "          A = self.getSet(setname)\n",
        "          left = A.left_endpt\n",
        "          left_list = np.array([self.getSet(setname1).isPointInSet(left) for setname1 in collection1 ])\n",
        "          left_good = np.prod(left_list)\n",
        "          right = A.right_endpt\n",
        "          right_list = np.array([self.getSet(setname1).isPointInSet(right) for setname1 in collection1 ])\n",
        "          right_good = np.prod(right_list)\n",
        "          set_good = 1 - ( (1-left_good) * (1-right_good) ) # good if at least one is good\n",
        "          good_m_sets.append(set_good)\n",
        "        good_m_sets = np.array(good_m_sets)\n",
        "        good_m = 1 - np.prod(1-good_m_sets) # good if at least one is good\n",
        "        if good_m == 0:\n",
        "          bad_m_sets.append(collection)\n",
        "        good.append(good_m)\n",
        "      good = np.array(good)\n",
        "      is_kmagreeable = np.prod(good) # good if all is good\n",
        "      return is_kmagreeable, bad_m_sets\n",
        "    \n",
        "    # Method to the find agreement number (and the location)\n",
        "    def findAgreementNumber( self ):\n",
        "        Names, Endpts = self.listSetEndpoints()\n",
        "        agreement = 0\n",
        "        agrement_location = Endpts[0]\n",
        "        \n",
        "        # At each point, the number of intersecting sets changes only when an endpoint is encountered,\n",
        "        #  therefore, we will check the number of intersecting sets only at endpoints\n",
        "        for i in Endpts:\n",
        "          numSets_contain_i = 0\n",
        "          \n",
        "          for A in self.approvalSets:\n",
        "            if A.isPointInSet( i ):\n",
        "              numSets_contain_i = numSets_contain_i + 1\n",
        "          \n",
        "          if numSets_contain_i > agreement:\n",
        "            agreement = numSets_contain_i\n",
        "            agreement_location = i\n",
        "          \n",
        "        return agreement, agreement_location\n",
        "      \n",
        "    def findPiercingNumber( self ):\n",
        "      # Finding piercing number using an integer linear program (ILP) formulation\n",
        "      # (a linear program (LP) that is constrained to have integer solutions)\n",
        "      \n",
        "      # First, find constraint matrix/data for LP used to find piercing number\n",
        "      # Candidate piercing points are the endpoints of the intervals\n",
        "      _, orderedendpts = self.listSetEndpoints()\n",
        "      N = self.numVoters\n",
        "      M = 2*N\n",
        "      Mat = np.empty( [ N, M] )\n",
        "      for i in np.arange(0, N):\n",
        "        for j, p in enumerate(orderedendpts):\n",
        "          A = self.approvalSets[i]\n",
        "          Mat[i, j] = A.isPointInSet( p )\n",
        "      \n",
        "      # Next, vector of coefficients of objective function\n",
        "      c = np.ones(M)\n",
        "      \n",
        "      ## Solve ILP using cvxpy\n",
        "      x = cp.Variable(M, integer = True)\n",
        "      objective = cp.Minimize( cp.matmul(c, x) )\n",
        "      constraints = [ cp.matmul(Mat,x) >= np.ones(N), 0 <= x, x <= 1]\n",
        "      prob = cp.Problem( objective, constraints )\n",
        "      val = prob.solve(solver='GLPK_MI')\n",
        "      piercingNumber = int(np.round(val))\n",
        "      piercingSet = np.transpose(orderedendpts)[ np.round(x.value) > 0]\n",
        "      \n",
        "      return piercingNumber, piercingSet, x.value, Mat\n",
        "    \n",
        "    # implementing the linear society piercing number algorithm\n",
        "    def piercingAlgorithm( self, startingPoint = 0 ):\n",
        "\n",
        "      orderedendptnames, orderedendpts = self.listSetEndpoints()\n",
        "\n",
        "      if startingPoint > 0 :\n",
        "        temp1 = [ x for x in orderedendpts if x >= startingPoint ]\n",
        "        temp1names = [x for i, x in enumerate(orderedendptnames) if orderedendpts[i] >= startingPoint]\n",
        "        temp2 = [x for x in orderedendpts if x < startingPoint]\n",
        "        temp2names = [x for i, x in enumerate(orderedendptnames) if orderedendpts[i] < startingPoint]\n",
        "        orderedendpts = temp1 + temp2\n",
        "        orderedendptnames = temp1names + temp2names\n",
        "\n",
        "      uncovered_setnames = []\n",
        "      N = self.numVoters\n",
        "      for i in range(0, 2*N):\n",
        "        if( orderedendptnames[i][0] == \"R\" ):\n",
        "          uncovered_setnames.append( orderedendptnames[i][1:] )\n",
        "\n",
        "      # currently, uncovered_setnames contains all sets' names\n",
        "      piercingSet = []\n",
        "      while( len(uncovered_setnames) > 0): #while there are uncovered sets\n",
        "        current_point = self.getSet(uncovered_setnames[0]).right_endpt\n",
        "        covered_setnames = [setname for setname in uncovered_setnames if self.getSet(setname).isPointInSet(current_point) ]\n",
        "        uncovered_setnames = [setname for setname in uncovered_setnames if not self.getSet(setname).isPointInSet(current_point) ]\n",
        "        piercingSet.append( [current_point, covered_setnames] )\n",
        "      return piercingSet\n",
        "\n",
        "\n",
        "    ### HARDIN'S TRANSFORMATIONS (ELIMINATE CONTAINMENT, LR-ALTERNATION)-------\n",
        "    \n",
        "    # Method to check if Left-Right-alternating\n",
        "    def is_LR_alt( self, findRRL = False ):\n",
        "        L = self.listSetEndpoints()\n",
        "        numEndpts = len(L[0])\n",
        "        \n",
        "        # determine if LR alternating; if findRRL is True, also find names of sets where of RRL endpoints occur\n",
        "        isLR = True\n",
        "        RRLsets = list()\n",
        "        for i in range(0, numEndpts):\n",
        "            # determine if LR alternating\n",
        "            if L[0][i][0] == L[0][(i+1)%numEndpts][0]:\n",
        "                isLR = False\n",
        "            # find names of sets where of RRL endpoints occur\n",
        "            if ( findRRL ):\n",
        "                if(L[0][i%numEndpts][0] == \"R\" and L[0][(i+1)%numEndpts][0] == \"R\" and L[0][(i+2)%numEndpts][0] == \"L\"):\n",
        "                    RRLsets.append( [ L[0][i%numEndpts][1:], L[0][(i+1)%numEndpts][1:], L[0][(i+2)%numEndpts][1:] ])\n",
        "        \n",
        "        if findRRL:\n",
        "          return isLR, RRLsets\n",
        "        else:\n",
        "          return isLR\n",
        "        \n",
        "    # Method to check if a pair of sets has containment \n",
        "    def checkContainmentPair( self, setPair ):\n",
        "      Set1Name = setPair[0]\n",
        "      Set2Name = setPair[1]\n",
        "      indSet1 = self.findApprovalSetName( Set1Name )\n",
        "      indSet2 = self.findApprovalSetName( Set2Name )\n",
        "      containmentIsFound = False\n",
        "      \n",
        "      if (indSet1 == -1 or indSet2 == -1):\n",
        "        print(\"At least one of the set names is not found\")\n",
        "      else:\n",
        "        A1 = self.approvalSets[indSet1]\n",
        "        A2 = self.approvalSets[indSet2]\n",
        "        \n",
        "        if( A1.left_endpt <= A1.right_endpt and A2.left_endpt <= A2.right_endpt): \n",
        "          # Case 1: A1, A2 both don't wrap around\n",
        "          if( A1.left_endpt <= A2.left_endpt and A2.right_endpt <= A1.right_endpt ):\n",
        "            containmentIsFound = True # A2 is contained in A1\n",
        "            \n",
        "          elif( A2.left_endpt <= A1.left_endpt and A1.right_endpt <= A2.right_endpt ):\n",
        "            containmentIsFound = True # A1 is contained in A2\n",
        "          \n",
        "        elif ( A1.left_endpt <= A1.right_endpt and A2.left_endpt > A2.right_endpt ): \n",
        "          # Case 2: A1 doesn't wrap, A2 wraps around\n",
        "          if( A1.right_endpt <= A2.right_endpt or A2.left_endpt <= A1.left_endpt ):\n",
        "            containmentIsFound = True #A1 is contained in A2\n",
        "            \n",
        "        elif ( A1.left_endpt > A1.right_endpt and A2.left_endpt <= A2.right_endpt ): \n",
        "          # Case 3: A1 wraps, A2 doesn't wrap around\n",
        "          if( A1.left_endpt <= A2.left_endpt or A2.right_endpt <= A1.right_endpt ):\n",
        "            containmentIsFound = True #A2 is contained in A1\n",
        "          \n",
        "        else: \n",
        "          # Case 4: A1, A2 both wrap around\n",
        "          if( A2.right_endpt <= A1.right_endpt and A1.left_endpt <= A2.left_endpt):\n",
        "            containmentIsFound = True # A2 is contained in A1\n",
        "            \n",
        "          elif( A1.right_endpt <= A2.right_endpt and A2.left_endpt <= A1.left_endpt ):\n",
        "            containmentIsFound = True # A1 is contained in A2\n",
        "            \n",
        "      return containmentIsFound\n",
        "    \n",
        "    # Method to detect any containent and identifying pairs\n",
        "    def checkContainmentAll( self, findContainmentPairs = False ):\n",
        "      N = self.numVoters\n",
        "      approvalSetNames = self.list_setnames\n",
        "      containmentPairs = []\n",
        "      containmentIsFound = False\n",
        "      \n",
        "      for i in np.arange(0, N):\n",
        "        setName1 = self.list_setnames[i]\n",
        "        for j in np.arange(i+1, N):\n",
        "          setName2 = self.list_setnames[j]\n",
        "          \n",
        "          if ( self.checkContainmentPair( [setName1, setName2]) ):\n",
        "            \n",
        "            containmentPairs.append( [setName1, setName2] )\n",
        "            containmentIsFound = True\n",
        "            \n",
        "      if findContainmentPairs:\n",
        "        return containmentIsFound, containmentPairs\n",
        "      else:\n",
        "        return containmentIsFound\n",
        "    \n",
        "    # Method to eliminate a pair of containment\n",
        "    def eliminateContainmentPair( self, containmentPair ):\n",
        "        smallSetName = containmentPair[0]\n",
        "        largeSetName = containmentPair[1]\n",
        "        indSmallSet = self.findApprovalSetName( smallSetName )\n",
        "        indLargeSet = self.findApprovalSetName( largeSetName )\n",
        "        \n",
        "        if (indSmallSet == -1 or indLargeSet == -1):\n",
        "            print(\"At least one of the set names is not found\")\n",
        "        else:\n",
        "            # Swap the right endpoints of the two sets\n",
        "            ASmall = self.approvalSets[indSmallSet]\n",
        "            ALarge = self.approvalSets[indLargeSet]\n",
        "            \n",
        "            small_right_endpt = ASmall.right_endpt\n",
        "            small_newright_endpt = ALarge.right_endpt\n",
        "            large_newright_endpt = small_right_endpt\n",
        "            \n",
        "            self.editApprovalSet( smallSetName, ASmall.left_endpt, small_newright_endpt )\n",
        "            self.editApprovalSet( largeSetName, ALarge.left_endpt, large_newright_endpt )\n",
        "\n",
        "    # Method to eliminate all containments\n",
        "    def eliminateContainmentAll( self ):\n",
        "      \n",
        "      containmentIsFound, containmentPairs = self.checkContainmentAll( findContainmentPairs = True)\n",
        "      maxIt = 100\n",
        "      it = 0\n",
        "      \n",
        "      while(containmentIsFound and it < maxIt):\n",
        "        for setPair in containmentPairs:\n",
        "          self.eliminateContainmentPair( setPair )\n",
        "        containmentIsFound, containmentPairs = self.checkContainmentAll( findContainmentPairs = True )\n",
        "        it = it + 1\n",
        "      \n",
        "            \n",
        "    # Method to eliminate a set of RRL endpoints\n",
        "    def eliminateRRLTriple( self, RRLsets ):\n",
        "        Set2Name = RRLsets[1] # first set is unchanged\n",
        "        Set3Name = RRLsets[2]\n",
        "        indSet2 = self.findApprovalSetName( Set2Name )\n",
        "        indSet3 = self.findApprovalSetName( Set3Name )\n",
        "        \n",
        "        if (indSet2 == -1 or indSet3 == -1):\n",
        "            print(\"At least one of the set names is not found\")\n",
        "        else:\n",
        "            # Swap the right endpt of Set2 and the left endpoint of Set3\n",
        "            A2 = self.approvalSets[indSet2]\n",
        "            A3 = self.approvalSets[indSet3]\n",
        "            \n",
        "            set2_right_endpt = A2.right_endpt\n",
        "            set2_newright_endpt = A3.left_endpt\n",
        "            set3_newleft_endpt = set2_right_endpt\n",
        "            \n",
        "            self.editApprovalSet( Set2Name, A2.left_endpt, set2_newright_endpt)\n",
        "            self.editApprovalSet( Set3Name, set3_newleft_endpt, A3.right_endpt )\n",
        "    \n",
        "    # Method to eliminate all RRL (to achieve LR-alternation)\n",
        "    def eliminateRRLAll( self, maxIt = 10000 ):\n",
        "        isLR, RRLsets = self.is_LR_alt( findRRL = True )\n",
        "        \n",
        "        numIt = 0\n",
        "        while( not isLR and numIt < maxIt):\n",
        "          for triple in RRLsets:\n",
        "            self.eliminateRRLTriple( triple )\n",
        "          isLR, RRLsets = self.is_LR_alt( findRRL = True )\n",
        "          numIt = numIt + 1\n",
        "        \n",
        "        if ( not isLR ):\n",
        "          print(\"Max iteration reached but the society is still not LR-Alternating\")\n",
        "\n",
        "    # Method to transform into a uniform society\n",
        "    def uniformize( self ):\n",
        "        self.eliminateContainmentAll()\n",
        "        self.eliminateRRLAll()\n",
        "        \n",
        "\n",
        "        \n",
        "    ### VISUALIZATION --------------------------------------------------------\n",
        "    \n",
        "    # Method to visualize the sets\n",
        "    def visualize( self, drawAgreement = False, drawPiercing = False ):\n",
        "        \n",
        "        ## Set up grid\n",
        "        fig = plt.figure()\n",
        "        ax = fig.add_subplot(1, 1, 1)\n",
        "        # Major ticks every 1, minor ticks every self.tick (default = 0.5)\n",
        "        major_ticks = np.arange(0, self.modulo+1, self.modulo * 0.1)\n",
        "        minor_ticks = np.arange(0, self.modulo+1, self.tick)        \n",
        "        ax.set_xticks(major_ticks)\n",
        "        ax.set_xticks(minor_ticks, minor=True)\n",
        "        #ax.set_yticks(major_ticks)\n",
        "        #ax.set_yticks(minor_ticks, minor=True)\n",
        "        # Different thickness settings for the major and minor grids:\n",
        "        ax.grid(which='minor', alpha=0.2)\n",
        "        ax.grid(which='major', alpha=0.5)\n",
        "        plt.yticks(np.arange(0, self.numVoters+1, step = 1) )\n",
        "        \n",
        "        # Draw the intervals\n",
        "        for ind, A in enumerate( self.approvalSets ):\n",
        "            if A.left_endpt <= A.right_endpt:\n",
        "                x = [A.left_endpt, A.right_endpt]\n",
        "                y = [ind+1, ind+1]\n",
        "                plt.plot( x, y, 'ro-')\n",
        "            else:\n",
        "                x = [A.left_endpt, self.modulo]\n",
        "                y = [ind+1, ind+1]\n",
        "                plt.plot( A.left_endpt, ind+1, 'ro-', self.modulo, ind+1, 'r>-')\n",
        "                plt.plot( x, y, 'r')\n",
        "                x = [0, A.right_endpt]\n",
        "                plt.plot( 0, ind+1, 'r<-', A.right_endpt, ind+1, 'ro-')\n",
        "                plt.plot( x, y, 'r')\n",
        "                \n",
        "        # Draw one of the points that attains agreement number\n",
        "        if drawAgreement:\n",
        "            a, pos = self.findAgreementNumber()\n",
        "            plt.plot( [pos, pos], [0.8, self.numVoters], 'blue' )\n",
        "        \n",
        "        # Draw the piercing points\n",
        "        if drawPiercing:\n",
        "          piercingNum, piercingSet, _, _ = self.findPiercingNumber()\n",
        "          for pos in piercingSet:\n",
        "            plt.plot( [pos, pos], [0, 0.2 + self.numVoters], 'green', linestyle = 'dashed' )\n",
        "\n",
        "# Part 3 - generating random circular societies ----------------------------------    \n",
        "\n",
        "# Define function to generate a random fixed-length circular society\n",
        "def generateRandomFixedLengthSociety( societyname, N, modulo, p, tick = 0.5 ):\n",
        "    # N is number of voters\n",
        "    # modulo is the circumference of the circular society\n",
        "    # p is a fraction between 0 and 1 that controls the length of approval sets\n",
        "    #    The length of each set is p times modulo\n",
        "    # tick = 0.5 : controls tick marks in the visualization\n",
        "    \n",
        "    CS = CircularSociety( societyname, modulo, tick = tick )\n",
        "    \n",
        "    for i in list(range(N)):\n",
        "      left = np.random.uniform(low=0, high=modulo)\n",
        "      right = (left + p * modulo) % modulo\n",
        "      CS.addApprovalSet( \"Set \" + str(i+1), left , right )\n",
        "    \n",
        "    return CS\n",
        "\n",
        "# extras:\n",
        "# Define function to generate a circular society with a random approval sets\n",
        "def generateRandomSociety( societyname, N, modulo, epsilon = 0.5, mode = 1, a = 1, b = 1 ):\n",
        "    # epsilon = 0.5 is the perturbation of the right-endpoints\n",
        "    # N is number of voters\n",
        "    # mode lets us choose how the approval sets are generated\n",
        "    #   mode = 1: endpoints are chosen uniformly at random from [0, modulo]\n",
        "    #   mode = 2: left endpoint is chosen uniformly at random from [0, modulo]; \n",
        "    #             set length is from the beta distribution with parameters a, b\n",
        "    \n",
        "    CS = CircularSociety( societyname, modulo, tick = epsilon )\n",
        "    \n",
        "    for i in list(range(N)):\n",
        "      if mode == 1:\n",
        "        left = np.random.uniform(low=0, high=modulo)\n",
        "        right = np.random.uniform(low=0, high=modulo)\n",
        "      elif mode == 2:\n",
        "        left = np.random.uniform(low=0, high=modulo) \n",
        "        right = (left + np.random.beta(a, b)* modulo) % modulo\n",
        "        \n",
        "      CS.addApprovalSet( \"Set \" + str(i+1), left , right )\n",
        "    \n",
        "    \n",
        "    return CS\n",
        "  \n",
        "# Define function to generate U(N, h) (Hardin's uniform circular society)\n",
        "def generateUniformCircularSociety( societyname, N, h, epsilon = 0.5 ):\n",
        "    # epsilon = 0.5 is the perturbation of the right-endpoints\n",
        "    \n",
        "    CS = CircularSociety( societyname, N, tick = epsilon )\n",
        "    \n",
        "    for i in list(range(N)):\n",
        "        CS.addApprovalSet( \"Set \" + str(i+1), i, round( (i + h - epsilon) % N, 1) )\n",
        "    return CS"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kUQENXpu_Gp_",
        "colab_type": "text"
      },
      "source": [
        "## 3. Piercing Number Probabilities \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g5wuVcMTbmBE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# -----\n",
        "# function to approximate the probability of various piercing numbers\n",
        "# arguments:\n",
        "#   N: number of approval sets\n",
        "#   p: length of the approval sets\n",
        "#   nSoc: number of randomly-generated societies\n",
        "#   maxTau: max piercing number to approximate the probability of\n",
        "# returns array of probabilites for tau in 1, 2, ..., maxTau\n",
        "def computePiercingProbabilities(N, p, nSoc, maxTau):\n",
        "\n",
        "  modulo = 1 # circumference of the circular society platform\n",
        "  piercingNumList = np.zeros( nSoc )\n",
        "\n",
        "  # generate random societies\n",
        "  for i in range(0, nSoc):\n",
        "    S = generateRandomFixedLengthSociety( \"Fixed length society 1\", N, modulo, p, tick=0.05 )\n",
        "    piercingNum, _, _, _ = S.findPiercingNumber()\n",
        "    piercingNumList[i] = piercingNum\n",
        "  \n",
        "  # compute probabilities of piercing numbers\n",
        "  probs = np.zeros(maxTau)\n",
        "  for i in range(maxTau):\n",
        "    probs[i] = np.sum( piercingNumList == i+1 )/nSoc\n",
        "\n",
        "  return probs, piercingNumList\n",
        "\n",
        "# -----\n",
        "# function to compute conjectured probability of piercing number equal to k\n",
        "def probConjecture(n, k, p):\n",
        "  return sp.special.comb(n, k)*( (1 - k*p)**(k-1) )*( (k*p)**(n-k) )\n"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DPF2-SJ1cfd_",
        "colab_type": "text"
      },
      "source": [
        "### 3.1. Simulations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mOyFYnMdSDwz",
        "colab_type": "text"
      },
      "source": [
        "#### 3.1.1. Simulations for a given $p$ and $n$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yJPhp3rECfg9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "outputId": "85a7b4f4-15e3-4c47-875a-92a7d558c308"
      },
      "source": [
        "# ---\n",
        "nSoc = 1000 # number of randomly-generated societies\n",
        "maxTau = 6\n",
        "modulo = 1 # circumference of the circular society platform\n",
        "\n",
        "n = 6 # number of approval sets\n",
        "p = 0.19\n",
        "\n",
        "simulated_probs, piercingNumList = computePiercingProbabilities(n, p, nSoc, maxTau)\n",
        "\n",
        "conjectured_probs = np.zeros(maxTau)\n",
        "for i in range(maxTau):\n",
        "  conjectured_probs[i] = probConjecture(n, i+1, p)\n",
        "\n",
        "# print results & stats\n",
        "print('-----------------------------')\n",
        "print('Number of approval sets: ', n)\n",
        "print('Length of each approval sets: ', p)\n",
        "print('Number of randomly-generated circular societies: ', nSoc)\n",
        "print('-----------------------------')\n",
        "\n",
        "# piercing number stats\n",
        "print('Piercing Numbers - Summary Statistics')\n",
        "print('Min: ', np.min(piercingNumList))\n",
        "print('Max: ', np.max(piercingNumList))\n",
        "print('Mean: ', np.mean(piercingNumList))\n",
        "print('Median: ', np.median(piercingNumList))\n",
        "print('Standard deviation: ', np.std(piercingNumList))\n",
        "print('-----------------------------')\n",
        "\n",
        "for i in range(0, maxTau):\n",
        "  print('Fraction with tau = {0} : {1}'.format( i+1, simulated_probs[i]) )\n",
        "  print('Conjecture says: {0}'.format(conjectured_probs[i] ) )\n",
        "\n",
        "print('-----------------------------')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-----------------------------\n",
            "Number of approval sets:  6\n",
            "Length of each approval sets:  0.19\n",
            "Number of randomly-generated circular societies:  1000\n",
            "-----------------------------\n",
            "Piercing Numbers - Summary Statistics\n",
            "Min:  1.0\n",
            "Max:  4.0\n",
            "Mean:  2.901\n",
            "Median:  3.0\n",
            "Standard deviation:  0.5283928462801138\n",
            "-----------------------------\n",
            "Fraction with tau = 1 : 0.001\n",
            "Conjecture says: 0.0014856594\n",
            "Fraction with tau = 2 : 0.191\n",
            "Conjecture says: 0.193917648\n",
            "Fraction with tau = 3 : 0.714\n",
            "Conjecture says: 0.684843714\n",
            "Fraction with tau = 4 : 0.094\n",
            "Conjecture says: 0.11977113599999997\n",
            "Fraction with tau = 5 : 0.0\n",
            "Conjecture says: 3.562500000000013e-05\n",
            "Fraction with tau = 6 : 0.0\n",
            "Conjecture says: -5.378240000000024e-05\n",
            "-----------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t-bF7fLrKf_f",
        "colab_type": "text"
      },
      "source": [
        "#### 3.1.2. Results for a range of values of $p$ and $n$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1MxCqpA5HnCM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "d952aaf9-e825-4657-8f53-0cd51ae292ab"
      },
      "source": [
        "# loop over n and p\n",
        "\n",
        "# ---\n",
        "modulo = 1 # circumference of the circular society platform\n",
        "nSoc = 100 # number of randomly-generated societies\n",
        "maxTau = 5\n",
        "\n",
        "# specify range of values of n and p\n",
        "minn = 5 # number of approval sets\n",
        "maxn = 45 # number of approval sets\n",
        "stepn = 20\n",
        "nvals = np.arange(minn, maxn+1, stepn)\n",
        "numNs = len(nvals)\n",
        "minp = 0.01\n",
        "maxp = 0.19\n",
        "numLengths = 3\n",
        "pvals = np.linspace(minp, maxp, numLengths)\n",
        "\n",
        "\n",
        "simulated_probs = np.zeros( (numNs, numLengths, maxTau) )\n",
        "conjectured_probs = np.zeros( (numNs, numLengths, maxTau) )\n",
        "simulation_aves = np.zeros( (numNs, numLengths ))\n",
        "conjectured_aves = np.zeros( (numNs, numLengths ))\n",
        "\n",
        "for i, n in enumerate(nvals):\n",
        "  for j, p in enumerate(pvals):\n",
        "    simulated_probs[i, j, :], piercingNumList = computePiercingProbabilities(n, p, nSoc, maxTau)\n",
        "    simulation_aves[i, j] = np.mean( piercingNumList )\n",
        "\n",
        "    for k in range(maxTau):\n",
        "      conjectured_probs[i, j, k] = probConjecture(n, k+1, p)\n",
        "    \n",
        "    conjectured_aves[i, j] = np.dot( conjectured_probs[i, j, :], np.arange(1, maxTau+1).reshape((maxTau, 1)) )\n",
        "\n",
        "\n",
        "# summarize results in a table\n",
        "import pandas as pd \n",
        "\n",
        "summary = pd.DataFrame({\n",
        "    'n': [ item for sublist in [[x] * numLengths*maxTau for x in nvals] for item in sublist],\n",
        "    'p': [ item for sublist in [[x]* maxTau for x in pvals] * numNs for item in sublist],\n",
        "    'tau': np.arange(1, maxTau+1).tolist() * (numNs * numLengths),\n",
        "    'estimated probability': simulated_probs.reshape( numNs*numLengths*maxTau ),\n",
        "    'conjectured probability': conjectured_probs.reshape( numNs*numLengths*maxTau )\n",
        "    })\n",
        "\n",
        "expvalue_summary = pd.DataFrame({ \n",
        "    'n': [ item for sublist in [[x]* numLengths for x in nvals] for item in sublist],\n",
        "    'p': pvals.tolist() * numNs,\n",
        "    'simulation average': simulation_aves.reshape( numNs*numLengths ),\n",
        "    'conjectured expected value': conjectured_aves.reshape( numNs*numLengths )\n",
        "    })\n",
        "\n",
        "summary"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[5.0000000e-08 7.8400000e-05 8.4681000e-03 1.7694720e-01 8.1450625e-01]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "4.805881199999999\n",
            "[0.0005 0.064  0.441  0.432  0.0625]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "3.492000000000001\n",
            "[6.516050e-03 3.402064e-01 6.007401e-01 5.253120e-02 6.250000e-06]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "2.6993052000000004\n",
            "[2.50000000e-47 2.46625075e-37 6.79108097e-31 4.92225425e-26\n",
            " 4.12699862e-22]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "2.0636962028199546e-21\n",
            "[2.50000000e-23 2.01326592e-14 3.53664542e-09 1.20172223e-05\n",
            " 3.16679478e-03]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "0.015882053383706768\n",
            "[1.22469073e-16 4.02286692e-08 1.81097132e-03 5.49300113e-01\n",
            " 1.19039732e-01]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "2.797832105372163\n",
            "[4.50000000e-87 8.53396945e-71 1.46089352e-60 6.37448404e-53\n",
            " 9.05065773e-47]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "4.525331415603921e-46\n",
            "[4.50000000e-43 6.96650567e-28 7.60801173e-19 1.55627052e-12\n",
            " 6.94489586e-08]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "3.4725101800416076e-07\n",
            "[8.28649658e-31 5.23264822e-16 1.46441188e-07 2.67400801e-02\n",
            " 9.81318024e-01]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "5.013550881205913\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>p</th>\n",
              "      <th>tau</th>\n",
              "      <th>estimated probability</th>\n",
              "      <th>conjectured probability</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>0.01</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>5.000000e-08</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5</td>\n",
              "      <td>0.01</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>7.840000e-05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5</td>\n",
              "      <td>0.01</td>\n",
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              "      <td>0.00</td>\n",
              "      <td>8.468100e-03</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>5</td>\n",
              "      <td>0.01</td>\n",
              "      <td>4</td>\n",
              "      <td>0.17</td>\n",
              "      <td>1.769472e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>0.01</td>\n",
              "      <td>5</td>\n",
              "      <td>0.83</td>\n",
              "      <td>8.145062e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5</td>\n",
              "      <td>0.10</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>5.000000e-04</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>5</td>\n",
              "      <td>0.10</td>\n",
              "      <td>2</td>\n",
              "      <td>0.05</td>\n",
              "      <td>6.400000e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>5</td>\n",
              "      <td>0.10</td>\n",
              "      <td>3</td>\n",
              "      <td>0.51</td>\n",
              "      <td>4.410000e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>5</td>\n",
              "      <td>0.10</td>\n",
              "      <td>4</td>\n",
              "      <td>0.37</td>\n",
              "      <td>4.320000e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>5</td>\n",
              "      <td>0.10</td>\n",
              "      <td>5</td>\n",
              "      <td>0.07</td>\n",
              "      <td>6.250000e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.516050e-03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.38</td>\n",
              "      <td>3.402064e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.58</td>\n",
              "      <td>6.007401e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.04</td>\n",
              "      <td>5.253120e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.250000e-06</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>25</td>\n",
              "      <td>0.01</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>2.500000e-47</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>25</td>\n",
              "      <td>0.01</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>2.466251e-37</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>25</td>\n",
              "      <td>0.01</td>\n",
              "      <td>3</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.791081e-31</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>25</td>\n",
              "      <td>0.01</td>\n",
              "      <td>4</td>\n",
              "      <td>0.00</td>\n",
              "      <td>4.922254e-26</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>25</td>\n",
              "      <td>0.01</td>\n",
              "      <td>5</td>\n",
              "      <td>0.00</td>\n",
              "      <td>4.126999e-22</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>25</td>\n",
              "      <td>0.10</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>2.500000e-23</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>25</td>\n",
              "      <td>0.10</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>2.013266e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>25</td>\n",
              "      <td>0.10</td>\n",
              "      <td>3</td>\n",
              "      <td>0.00</td>\n",
              "      <td>3.536645e-09</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>25</td>\n",
              "      <td>0.10</td>\n",
              "      <td>4</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.201722e-05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>25</td>\n",
              "      <td>0.10</td>\n",
              "      <td>5</td>\n",
              "      <td>0.00</td>\n",
              "      <td>3.166795e-03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.224691e-16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>4.022867e-08</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.810971e-03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.48</td>\n",
              "      <td>5.493001e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.52</td>\n",
              "      <td>1.190397e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>45</td>\n",
              "      <td>0.01</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>4.500000e-87</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>31</th>\n",
              "      <td>45</td>\n",
              "      <td>0.01</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>8.533969e-71</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>45</td>\n",
              "      <td>0.01</td>\n",
              "      <td>3</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.460894e-60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33</th>\n",
              "      <td>45</td>\n",
              "      <td>0.01</td>\n",
              "      <td>4</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.374484e-53</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>34</th>\n",
              "      <td>45</td>\n",
              "      <td>0.01</td>\n",
              "      <td>5</td>\n",
              "      <td>0.00</td>\n",
              "      <td>9.050658e-47</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>45</td>\n",
              "      <td>0.10</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>4.500000e-43</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36</th>\n",
              "      <td>45</td>\n",
              "      <td>0.10</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.966506e-28</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37</th>\n",
              "      <td>45</td>\n",
              "      <td>0.10</td>\n",
              "      <td>3</td>\n",
              "      <td>0.00</td>\n",
              "      <td>7.608012e-19</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>38</th>\n",
              "      <td>45</td>\n",
              "      <td>0.10</td>\n",
              "      <td>4</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.556271e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>45</td>\n",
              "      <td>0.10</td>\n",
              "      <td>5</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.944896e-08</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>40</th>\n",
              "      <td>45</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>8.286497e-31</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41</th>\n",
              "      <td>45</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>5.232648e-16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>42</th>\n",
              "      <td>45</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.464412e-07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>45</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.07</td>\n",
              "      <td>2.674008e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>45</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.93</td>\n",
              "      <td>9.813180e-01</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     n     p  tau  estimated probability  conjectured probability\n",
              "0    5  0.01    1                   0.00             5.000000e-08\n",
              "1    5  0.01    2                   0.00             7.840000e-05\n",
              "2    5  0.01    3                   0.00             8.468100e-03\n",
              "3    5  0.01    4                   0.17             1.769472e-01\n",
              "4    5  0.01    5                   0.83             8.145062e-01\n",
              "5    5  0.10    1                   0.00             5.000000e-04\n",
              "6    5  0.10    2                   0.05             6.400000e-02\n",
              "7    5  0.10    3                   0.51             4.410000e-01\n",
              "8    5  0.10    4                   0.37             4.320000e-01\n",
              "9    5  0.10    5                   0.07             6.250000e-02\n",
              "10   5  0.19    1                   0.00             6.516050e-03\n",
              "11   5  0.19    2                   0.38             3.402064e-01\n",
              "12   5  0.19    3                   0.58             6.007401e-01\n",
              "13   5  0.19    4                   0.04             5.253120e-02\n",
              "14   5  0.19    5                   0.00             6.250000e-06\n",
              "15  25  0.01    1                   0.00             2.500000e-47\n",
              "16  25  0.01    2                   0.00             2.466251e-37\n",
              "17  25  0.01    3                   0.00             6.791081e-31\n",
              "18  25  0.01    4                   0.00             4.922254e-26\n",
              "19  25  0.01    5                   0.00             4.126999e-22\n",
              "20  25  0.10    1                   0.00             2.500000e-23\n",
              "21  25  0.10    2                   0.00             2.013266e-14\n",
              "22  25  0.10    3                   0.00             3.536645e-09\n",
              "23  25  0.10    4                   0.00             1.201722e-05\n",
              "24  25  0.10    5                   0.00             3.166795e-03\n",
              "25  25  0.19    1                   0.00             1.224691e-16\n",
              "26  25  0.19    2                   0.00             4.022867e-08\n",
              "27  25  0.19    3                   0.00             1.810971e-03\n",
              "28  25  0.19    4                   0.48             5.493001e-01\n",
              "29  25  0.19    5                   0.52             1.190397e-01\n",
              "30  45  0.01    1                   0.00             4.500000e-87\n",
              "31  45  0.01    2                   0.00             8.533969e-71\n",
              "32  45  0.01    3                   0.00             1.460894e-60\n",
              "33  45  0.01    4                   0.00             6.374484e-53\n",
              "34  45  0.01    5                   0.00             9.050658e-47\n",
              "35  45  0.10    1                   0.00             4.500000e-43\n",
              "36  45  0.10    2                   0.00             6.966506e-28\n",
              "37  45  0.10    3                   0.00             7.608012e-19\n",
              "38  45  0.10    4                   0.00             1.556271e-12\n",
              "39  45  0.10    5                   0.00             6.944896e-08\n",
              "40  45  0.19    1                   0.00             8.286497e-31\n",
              "41  45  0.19    2                   0.00             5.232648e-16\n",
              "42  45  0.19    3                   0.00             1.464412e-07\n",
              "43  45  0.19    4                   0.07             2.674008e-02\n",
              "44  45  0.19    5                   0.93             9.813180e-01"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E3OTJDQTUl0E",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 901
        },
        "outputId": "b0c45376-4d96-4a5e-ab8b-d55769db70e9"
      },
      "source": [
        "print(summary.to_latex(index=False)) "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\\begin{tabular}{rrrrr}\n",
            "\\toprule\n",
            "  n &     p &  tau &  simulated probability &  conjectured probability \\\\\n",
            "\\midrule\n",
            "  5 &  0.01 &    1 &                   0.00 &             5.000000e-08 \\\\\n",
            "  5 &  0.01 &    2 &                   0.00 &             7.840000e-05 \\\\\n",
            "  5 &  0.01 &    3 &                   0.02 &             8.468100e-03 \\\\\n",
            "  5 &  0.01 &    4 &                   0.16 &             1.769472e-01 \\\\\n",
            "  5 &  0.01 &    5 &                   0.82 &             8.145062e-01 \\\\\n",
            "  5 &  0.10 &    1 &                   0.00 &             5.000000e-04 \\\\\n",
            "  5 &  0.10 &    2 &                   0.09 &             6.400000e-02 \\\\\n",
            "  5 &  0.10 &    3 &                   0.39 &             4.410000e-01 \\\\\n",
            "  5 &  0.10 &    4 &                   0.43 &             4.320000e-01 \\\\\n",
            "  5 &  0.10 &    5 &                   0.09 &             6.250000e-02 \\\\\n",
            "  5 &  0.19 &    1 &                   0.02 &             6.516050e-03 \\\\\n",
            "  5 &  0.19 &    2 &                   0.32 &             3.402064e-01 \\\\\n",
            "  5 &  0.19 &    3 &                   0.60 &             6.007401e-01 \\\\\n",
            "  5 &  0.19 &    4 &                   0.06 &             5.253120e-02 \\\\\n",
            "  5 &  0.19 &    5 &                   0.00 &             6.250000e-06 \\\\\n",
            " 25 &  0.01 &    1 &                   0.00 &             2.500000e-47 \\\\\n",
            " 25 &  0.01 &    2 &                   0.00 &             2.466251e-37 \\\\\n",
            " 25 &  0.01 &    3 &                   0.00 &             6.791081e-31 \\\\\n",
            " 25 &  0.01 &    4 &                   0.00 &             4.922254e-26 \\\\\n",
            " 25 &  0.01 &    5 &                   0.00 &             4.126999e-22 \\\\\n",
            " 25 &  0.10 &    1 &                   0.00 &             2.500000e-23 \\\\\n",
            " 25 &  0.10 &    2 &                   0.00 &             2.013266e-14 \\\\\n",
            " 25 &  0.10 &    3 &                   0.00 &             3.536645e-09 \\\\\n",
            " 25 &  0.10 &    4 &                   0.00 &             1.201722e-05 \\\\\n",
            " 25 &  0.10 &    5 &                   0.00 &             3.166795e-03 \\\\\n",
            " 25 &  0.19 &    1 &                   0.00 &             1.224691e-16 \\\\\n",
            " 25 &  0.19 &    2 &                   0.00 &             4.022867e-08 \\\\\n",
            " 25 &  0.19 &    3 &                   0.00 &             1.810971e-03 \\\\\n",
            " 25 &  0.19 &    4 &                   0.65 &             5.493001e-01 \\\\\n",
            " 25 &  0.19 &    5 &                   0.35 &             1.190397e-01 \\\\\n",
            " 45 &  0.01 &    1 &                   0.00 &             4.500000e-87 \\\\\n",
            " 45 &  0.01 &    2 &                   0.00 &             8.533969e-71 \\\\\n",
            " 45 &  0.01 &    3 &                   0.00 &             1.460894e-60 \\\\\n",
            " 45 &  0.01 &    4 &                   0.00 &             6.374484e-53 \\\\\n",
            " 45 &  0.01 &    5 &                   0.00 &             9.050658e-47 \\\\\n",
            " 45 &  0.10 &    1 &                   0.00 &             4.500000e-43 \\\\\n",
            " 45 &  0.10 &    2 &                   0.00 &             6.966506e-28 \\\\\n",
            " 45 &  0.10 &    3 &                   0.00 &             7.608012e-19 \\\\\n",
            " 45 &  0.10 &    4 &                   0.00 &             1.556271e-12 \\\\\n",
            " 45 &  0.10 &    5 &                   0.00 &             6.944896e-08 \\\\\n",
            " 45 &  0.19 &    1 &                   0.00 &             8.286497e-31 \\\\\n",
            " 45 &  0.19 &    2 &                   0.00 &             5.232648e-16 \\\\\n",
            " 45 &  0.19 &    3 &                   0.00 &             1.464412e-07 \\\\\n",
            " 45 &  0.19 &    4 &                   0.04 &             2.674008e-02 \\\\\n",
            " 45 &  0.19 &    5 &                   0.96 &             9.813180e-01 \\\\\n",
            "\\bottomrule\n",
            "\\end{tabular}\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0-sVRD8k1s_H",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 328
        },
        "outputId": "d90eb9be-20b2-4ce0-cd4b-bf85e93e86ad"
      },
      "source": [
        "expvalue_summary"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>p</th>\n",
              "      <th>simulation average</th>\n",
              "      <th>conjectured expected value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>0.01</td>\n",
              "      <td>4.83</td>\n",
              "      <td>4.805881e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5</td>\n",
              "      <td>0.10</td>\n",
              "      <td>3.46</td>\n",
              "      <td>3.492000e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2.66</td>\n",
              "      <td>2.699305e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>25</td>\n",
              "      <td>0.01</td>\n",
              "      <td>20.08</td>\n",
              "      <td>2.063696e-21</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>25</td>\n",
              "      <td>0.10</td>\n",
              "      <td>7.13</td>\n",
              "      <td>1.588205e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4.52</td>\n",
              "      <td>2.797832e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>45</td>\n",
              "      <td>0.01</td>\n",
              "      <td>31.28</td>\n",
              "      <td>4.525331e-46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>45</td>\n",
              "      <td>0.10</td>\n",
              "      <td>8.23</td>\n",
              "      <td>3.472510e-07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>45</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4.93</td>\n",
              "      <td>5.013551e+00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    n     p  simulation average  conjectured expected value\n",
              "0   5  0.01                4.83                4.805881e+00\n",
              "1   5  0.10                3.46                3.492000e+00\n",
              "2   5  0.19                2.66                2.699305e+00\n",
              "3  25  0.01               20.08                2.063696e-21\n",
              "4  25  0.10                7.13                1.588205e-02\n",
              "5  25  0.19                4.52                2.797832e+00\n",
              "6  45  0.01               31.28                4.525331e-46\n",
              "7  45  0.10                8.23                3.472510e-07\n",
              "8  45  0.19                4.93                5.013551e+00"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1AcGQG0fxTjI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "384c8039-2dee-454a-a83f-db7c240ba358"
      },
      "source": [
        "n# loop over n and p\n",
        "\n",
        "# ---\n",
        "modulo = 1 # circumference of the circular society platform\n",
        "nSoc = 100 # number of randomly-generated societies\n",
        "maxTau = 5\n",
        "\n",
        "# specify range of values of n and p\n",
        "minn = 5 # number of approval sets\n",
        "maxn = 25 # number of approval sets\n",
        "stepn = 5\n",
        "nvals = np.arange(minn, maxn+1, stepn)\n",
        "numNs = len(nvals)\n",
        "minp = 0.19\n",
        "maxp = 0.19\n",
        "numLengths = 1\n",
        "pvals = np.linspace(minp, maxp, numLengths)\n",
        "\n",
        "simulated_probs = np.zeros( (numNs, numLengths, maxTau) )\n",
        "conjectured_probs = np.zeros( (numNs, numLengths, maxTau) )\n",
        "simulation_aves = np.zeros( (numNs, numLengths ))\n",
        "conjectured_aves = np.zeros( (numNs, numLengths ))\n",
        "\n",
        "for i, n in enumerate(nvals):\n",
        "  for j, p in enumerate(pvals):\n",
        "    simulated_probs[i, j, :], piercingNumList = computePiercingProbabilities(n, p, nSoc, maxTau)\n",
        "    simulation_aves[i, j] = np.mean( piercingNumList )\n",
        "\n",
        "    for k in range(maxTau):\n",
        "      conjectured_probs[i, j, k] = probConjecture(n, k+1, p)\n",
        "    \n",
        "    conjectured_aves[i, j] = np.dot( conjectured_probs[i, j, :], np.arange(1, maxTau+1).reshape((maxTau, 1)) )\n",
        "    print(conjectured_probs[i, j, :])\n",
        "    print( np.arange(1, maxTau+1).reshape((maxTau, 1)) )\n",
        "    print( conjectured_aves[i, j])\n",
        "\n",
        "\n",
        "# summarize results in a table\n",
        "import pandas as pd \n",
        "\n",
        "summary = pd.DataFrame({\n",
        "    'n': [ item for sublist in [[x] * numLengths*maxTau for x in nvals] for item in sublist],\n",
        "    'p': [ item for sublist in [[x]* maxTau for x in pvals] * numNs for item in sublist],\n",
        "    'tau': np.arange(1, maxTau+1).tolist() * (numNs * numLengths),\n",
        "    'estimated probability': simulated_probs.reshape( numNs*numLengths*maxTau ),\n",
        "    'conjectured probability': conjectured_probs.reshape( numNs*numLengths*maxTau )\n",
        "    })\n",
        "\n",
        "expvalue_summary = pd.DataFrame({ \n",
        "    'n': [ item for sublist in [[x]* numLengths for x in nvals] for item in sublist],\n",
        "    'p': pvals.tolist() * numNs,\n",
        "    'simulation average': simulation_aves.reshape( numNs*numLengths ),\n",
        "    'conjectured expected value': conjectured_aves.reshape( numNs*numLengths )\n",
        "    })\n",
        "\n",
        "summary"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[6.516050e-03 3.402064e-01 6.007401e-01 5.253120e-02 6.250000e-06]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "2.6993052000000004\n",
            "[3.22687698e-06 1.21303401e-02 4.33752656e-01 5.59415601e-01\n",
            " 1.21870498e-03]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "3.569277801874671\n",
            "[1.19851003e-09 2.24268224e-04 9.89570126e-02 9.21968093e-01\n",
            " 1.12375439e-02]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "4.041379668123063\n",
            "[3.95683931e-13 3.21551122e-06 1.49181273e-02 8.29745648e-01\n",
            " 4.48929202e-02]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "3.5882080043760425\n",
            "[1.22469073e-16 4.02286692e-08 1.81097132e-03 5.49300113e-01\n",
            " 1.19039732e-01]\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]]\n",
            "2.797832105372163\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>p</th>\n",
              "      <th>tau</th>\n",
              "      <th>estimated probability</th>\n",
              "      <th>conjectured probability</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.516050e-03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.30</td>\n",
              "      <td>3.402064e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.60</td>\n",
              "      <td>6.007401e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.10</td>\n",
              "      <td>5.253120e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.00</td>\n",
              "      <td>6.250000e-06</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>10</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>3.226877e-06</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>10</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.01</td>\n",
              "      <td>1.213034e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>10</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.47</td>\n",
              "      <td>4.337527e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>10</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.52</td>\n",
              "      <td>5.594156e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>10</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.218705e-03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>15</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.198510e-09</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>15</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>2.242682e-04</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>15</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.09</td>\n",
              "      <td>9.895701e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>15</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.85</td>\n",
              "      <td>9.219681e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>15</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.06</td>\n",
              "      <td>1.123754e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>20</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>3.956839e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>20</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>3.215511e-06</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>20</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.03</td>\n",
              "      <td>1.491813e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>20</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.77</td>\n",
              "      <td>8.297456e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>20</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.20</td>\n",
              "      <td>4.489292e-02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.224691e-16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2</td>\n",
              "      <td>0.00</td>\n",
              "      <td>4.022867e-08</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.810971e-03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4</td>\n",
              "      <td>0.52</td>\n",
              "      <td>5.493001e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>5</td>\n",
              "      <td>0.48</td>\n",
              "      <td>1.190397e-01</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     n     p  tau  estimated probability  conjectured probability\n",
              "0    5  0.19    1                   0.00             6.516050e-03\n",
              "1    5  0.19    2                   0.30             3.402064e-01\n",
              "2    5  0.19    3                   0.60             6.007401e-01\n",
              "3    5  0.19    4                   0.10             5.253120e-02\n",
              "4    5  0.19    5                   0.00             6.250000e-06\n",
              "5   10  0.19    1                   0.00             3.226877e-06\n",
              "6   10  0.19    2                   0.01             1.213034e-02\n",
              "7   10  0.19    3                   0.47             4.337527e-01\n",
              "8   10  0.19    4                   0.52             5.594156e-01\n",
              "9   10  0.19    5                   0.00             1.218705e-03\n",
              "10  15  0.19    1                   0.00             1.198510e-09\n",
              "11  15  0.19    2                   0.00             2.242682e-04\n",
              "12  15  0.19    3                   0.09             9.895701e-02\n",
              "13  15  0.19    4                   0.85             9.219681e-01\n",
              "14  15  0.19    5                   0.06             1.123754e-02\n",
              "15  20  0.19    1                   0.00             3.956839e-13\n",
              "16  20  0.19    2                   0.00             3.215511e-06\n",
              "17  20  0.19    3                   0.03             1.491813e-02\n",
              "18  20  0.19    4                   0.77             8.297456e-01\n",
              "19  20  0.19    5                   0.20             4.489292e-02\n",
              "20  25  0.19    1                   0.00             1.224691e-16\n",
              "21  25  0.19    2                   0.00             4.022867e-08\n",
              "22  25  0.19    3                   0.00             1.810971e-03\n",
              "23  25  0.19    4                   0.52             5.493001e-01\n",
              "24  25  0.19    5                   0.48             1.190397e-01"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2hFGYZhyyhAI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "outputId": "caeabd1f-6f34-4909-ec70-e84d4e7a447a"
      },
      "source": [
        "expvalue_summary"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>p</th>\n",
              "      <th>simulation average</th>\n",
              "      <th>conjectured expected value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>0.19</td>\n",
              "      <td>2.80</td>\n",
              "      <td>2.699305</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>10</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3.51</td>\n",
              "      <td>3.569278</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>15</td>\n",
              "      <td>0.19</td>\n",
              "      <td>3.97</td>\n",
              "      <td>4.041380</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>20</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4.17</td>\n",
              "      <td>3.588208</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>25</td>\n",
              "      <td>0.19</td>\n",
              "      <td>4.48</td>\n",
              "      <td>2.797832</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    n     p  simulation average  conjectured expected value\n",
              "0   5  0.19                2.80                    2.699305\n",
              "1  10  0.19                3.51                    3.569278\n",
              "2  15  0.19                3.97                    4.041380\n",
              "3  20  0.19                4.17                    3.588208\n",
              "4  25  0.19                4.48                    2.797832"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vbuizB20SIUV",
        "colab_type": "text"
      },
      "source": [
        "#### 3.1.3. Variability of simulation results"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fNWdJ6e_R9-0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# ---\n",
        "nSamples = 500 # number of times we sample\n",
        "nSoc = 100 # number of randomly-generated societies, per sample\n",
        "maxTau = 6 # compute piercing num probability for each k = 1, ..., maxTau\n",
        "\n",
        "n = 10 # number of approval sets\n",
        "modulo = 1 # circumference of the circular society platform\n",
        "p = 0.1\n",
        "\n",
        "simulated_probs_all = np.zeros( (nSamples, maxTau) )\n",
        "\n",
        "for s in range(nSamples):\n",
        "  simulated_probs_all[s, : ], _ = computePiercingProbabilities(n, p, nSoc, maxTau)\n",
        "\n",
        "conjectured_probs = np.zeros(maxTau)\n",
        "for i in range(maxTau):\n",
        "  conjectured_probs[i] = probConjecture(n, i+1, p)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H5RFHBFuXrX0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 221
        },
        "outputId": "45427886-d96c-40b5-9cc6-261b0aa26cab"
      },
      "source": [
        "pmax = 97.5\n",
        "pmin = 2.5\n",
        "for i in range( maxTau ):\n",
        "  print(\"{2}% Interval for the probability that tau = {0} is approximately: {1}\".format(i+1, np.percentile(simulated_probs_all[:,i].T, [pmin, pmax]), pmax - pmin))\n",
        "  print('Conjecture says: {0}'.format(conjectured_probs[i] ) )"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95.0% CI for the probability that tau = 1 is approximately: [0. 0.]\n",
            "Conjecture says: 1.0000000000000005e-08\n",
            "95.0% CI for the probability that tau = 2 is approximately: [0. 0.]\n",
            "Conjecture says: 9.216000000000005e-05\n",
            "95.0% CI for the probability that tau = 3 is approximately: [0.      0.03525]\n",
            "Conjecture says: 0.012859560000000011\n",
            "95.0% CI for the probability that tau = 4 is approximately: [0.11475 0.27   ]\n",
            "Conjecture says: 0.18579456000000003\n",
            "95.0% CI for the probability that tau = 5 is approximately: [0.4     0.59525]\n",
            "Conjecture says: 0.4921875\n",
            "95.0% CI for the probability that tau = 6 is approximately: [0.2  0.38]\n",
            "Conjecture says: 0.27869183999999986\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cqnjtDyMbGBv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 221
        },
        "outputId": "0d07f0fa-365c-4144-edc2-5d1a4e2fd685"
      },
      "source": [
        "pmax = 80\n",
        "pmin = 20\n",
        "for i in range( maxTau ):\n",
        "  print(\"{2}% Interval for the probability that tau = {0} is approximately: {1}\".format(i+1, np.percentile(simulated_probs_all[:,i].T, [pmin, pmax]), pmax - pmin))\n",
        "  print('Conjecture says: {0}'.format(conjectured_probs[i] ) )"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "60% CI for the probability that tau = 1 is approximately: [0. 0.]\n",
            "Conjecture says: 1.0000000000000005e-08\n",
            "60% CI for the probability that tau = 2 is approximately: [0. 0.]\n",
            "Conjecture says: 9.216000000000005e-05\n",
            "60% CI for the probability that tau = 3 is approximately: [0.   0.02]\n",
            "Conjecture says: 0.012859560000000011\n",
            "60% CI for the probability that tau = 4 is approximately: [0.15 0.21]\n",
            "Conjecture says: 0.18579456000000003\n",
            "60% CI for the probability that tau = 5 is approximately: [0.45 0.54]\n",
            "Conjecture says: 0.4921875\n",
            "60% CI for the probability that tau = 6 is approximately: [0.24 0.32]\n",
            "Conjecture says: 0.27869183999999986\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1NS-YQF2Qddr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "774079e6-a8fa-49df-d1cb-6038bb4c477c"
      },
      "source": [
        "mean_simulated = np.zeros(maxTau)\n",
        "std_simulated = np.zeros(maxTau)\n",
        "percentile_of_conjectured_among_simulated = np.zeros(maxTau)\n",
        "\n",
        "for i in range(maxTau):\n",
        "  mean_simulated[i] = np.mean(simulated_probs_all[:,i])\n",
        "  std_simulated[i] = np.std(simulated_probs_all[:,i])\n",
        "  percentile_of_conjectured_among_simulated[i] = np.sum( simulated_probs_all[:,i] <= conjectured_probs[i])/500\n",
        "\n",
        "print(percentile_of_conjectured_among_simulated)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.    0.994 0.67  0.526 0.522 0.454]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EB3Nl2Cbch5-",
        "colab_type": "text"
      },
      "source": [
        "### 3.2. Visualizations of conjectured probabilities vs. simulation results for a range of approval set lengths"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Jr2RvQXakufV"
      },
      "source": [
        "#### RESULTS FOR 4 APPROVAL SETS"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NMG00EmakwQj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "6459fc82-a9ba-4a31-8e65-1da5b23feb66"
      },
      "source": [
        "numTau = 4\n",
        "numProbs = 80\n",
        "pvals4 = np.linspace(0.01, 0.8, numProbs)\n",
        "prob4 = np.zeros( (numProbs, numTau) )\n",
        "\n",
        "for r in range(numProbs):\n",
        "  prob4[r],_ = computePiercingProbabilities(4, pvals4[r], 10000, numTau)\n",
        "  print(\"finished p = \"+str(pvals4[r]))\n",
        "\n",
        "prob4"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "finished p = 0.01\n",
            "finished p = 0.02\n",
            "finished p = 0.03\n",
            "finished p = 0.04\n",
            "finished p = 0.05\n",
            "finished p = 0.060000000000000005\n",
            "finished p = 0.06999999999999999\n",
            "finished p = 0.08\n",
            "finished p = 0.09\n",
            "finished p = 0.09999999999999999\n",
            "finished p = 0.11\n",
            "finished p = 0.12\n",
            "finished p = 0.13\n",
            "finished p = 0.14\n",
            "finished p = 0.15000000000000002\n",
            "finished p = 0.16\n",
            "finished p = 0.17\n",
            "finished p = 0.18000000000000002\n",
            "finished p = 0.19\n",
            "finished p = 0.2\n",
            "finished p = 0.21000000000000002\n",
            "finished p = 0.22\n",
            "finished p = 0.23\n",
            "finished p = 0.24000000000000002\n",
            "finished p = 0.25\n",
            "finished p = 0.26\n",
            "finished p = 0.27\n",
            "finished p = 0.28\n",
            "finished p = 0.29000000000000004\n",
            "finished p = 0.3\n",
            "finished p = 0.31\n",
            "finished p = 0.32\n",
            "finished p = 0.33\n",
            "finished p = 0.34\n",
            "finished p = 0.35000000000000003\n",
            "finished p = 0.36000000000000004\n",
            "finished p = 0.37\n",
            "finished p = 0.38\n",
            "finished p = 0.39\n",
            "finished p = 0.4\n",
            "finished p = 0.41000000000000003\n",
            "finished p = 0.42000000000000004\n",
            "finished p = 0.43\n",
            "finished p = 0.44\n",
            "finished p = 0.45\n",
            "finished p = 0.46\n",
            "finished p = 0.47000000000000003\n",
            "finished p = 0.48000000000000004\n",
            "finished p = 0.49\n",
            "finished p = 0.5\n",
            "finished p = 0.51\n",
            "finished p = 0.52\n",
            "finished p = 0.53\n",
            "finished p = 0.54\n",
            "finished p = 0.55\n",
            "finished p = 0.56\n",
            "finished p = 0.5700000000000001\n",
            "finished p = 0.5800000000000001\n",
            "finished p = 0.59\n",
            "finished p = 0.6\n",
            "finished p = 0.61\n",
            "finished p = 0.62\n",
            "finished p = 0.63\n",
            "finished p = 0.64\n",
            "finished p = 0.65\n",
            "finished p = 0.66\n",
            "finished p = 0.67\n",
            "finished p = 0.68\n",
            "finished p = 0.6900000000000001\n",
            "finished p = 0.7000000000000001\n",
            "finished p = 0.7100000000000001\n",
            "finished p = 0.72\n",
            "finished p = 0.73\n",
            "finished p = 0.74\n",
            "finished p = 0.75\n",
            "finished p = 0.76\n",
            "finished p = 0.77\n",
            "finished p = 0.78\n",
            "finished p = 0.79\n",
            "finished p = 0.8\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.000e+00, 3.100e-03, 1.144e-01, 8.825e-01],\n",
              "       [1.000e-04, 8.100e-03, 2.114e-01, 7.804e-01],\n",
              "       [1.000e-04, 2.050e-02, 2.943e-01, 6.851e-01],\n",
              "       [6.000e-04, 3.480e-02, 3.744e-01, 5.902e-01],\n",
              "       [3.000e-04, 5.180e-02, 4.290e-01, 5.189e-01],\n",
              "       [6.000e-04, 7.720e-02, 4.825e-01, 4.397e-01],\n",
              "       [1.500e-03, 1.030e-01, 5.203e-01, 3.752e-01],\n",
              "       [2.000e-03, 1.263e-01, 5.583e-01, 3.134e-01],\n",
              "       [2.600e-03, 1.534e-01, 5.777e-01, 2.663e-01],\n",
              "       [3.900e-03, 1.895e-01, 5.925e-01, 2.141e-01],\n",
              "       [5.500e-03, 2.306e-01, 5.894e-01, 1.745e-01],\n",
              "       [6.600e-03, 2.654e-01, 5.859e-01, 1.421e-01],\n",
              "       [8.600e-03, 2.999e-01, 5.777e-01, 1.138e-01],\n",
              "       [9.800e-03, 3.428e-01, 5.652e-01, 8.220e-02],\n",
              "       [1.460e-02, 3.834e-01, 5.413e-01, 6.070e-02],\n",
              "       [1.790e-02, 4.147e-01, 5.244e-01, 4.300e-02],\n",
              "       [2.050e-02, 4.580e-01, 4.863e-01, 3.520e-02],\n",
              "       [2.430e-02, 5.010e-01, 4.522e-01, 2.250e-02],\n",
              "       [2.700e-02, 5.355e-01, 4.229e-01, 1.460e-02],\n",
              "       [3.330e-02, 5.762e-01, 3.836e-01, 6.900e-03],\n",
              "       [3.730e-02, 6.128e-01, 3.461e-01, 3.800e-03],\n",
              "       [3.700e-02, 6.555e-01, 3.062e-01, 1.300e-03],\n",
              "       [5.110e-02, 6.850e-01, 2.638e-01, 1.000e-04],\n",
              "       [5.600e-02, 7.192e-01, 2.247e-01, 1.000e-04],\n",
              "       [6.720e-02, 7.432e-01, 1.896e-01, 0.000e+00],\n",
              "       [7.080e-02, 7.845e-01, 1.447e-01, 0.000e+00],\n",
              "       [7.850e-02, 8.049e-01, 1.166e-01, 0.000e+00],\n",
              "       [8.830e-02, 8.288e-01, 8.290e-02, 0.000e+00],\n",
              "       [9.490e-02, 8.432e-01, 6.190e-02, 0.000e+00],\n",
              "       [1.098e-01, 8.526e-01, 3.760e-02, 0.000e+00],\n",
              "       [1.228e-01, 8.576e-01, 1.960e-02, 0.000e+00],\n",
              "       [1.332e-01, 8.614e-01, 5.400e-03, 0.000e+00],\n",
              "       [1.485e-01, 8.513e-01, 2.000e-04, 0.000e+00],\n",
              "       [1.586e-01, 8.414e-01, 0.000e+00, 0.000e+00],\n",
              "       [1.648e-01, 8.352e-01, 0.000e+00, 0.000e+00],\n",
              "       [1.899e-01, 8.101e-01, 0.000e+00, 0.000e+00],\n",
              "       [2.032e-01, 7.968e-01, 0.000e+00, 0.000e+00],\n",
              "       [2.210e-01, 7.790e-01, 0.000e+00, 0.000e+00],\n",
              "       [2.359e-01, 7.641e-01, 0.000e+00, 0.000e+00],\n",
              "       [2.610e-01, 7.390e-01, 0.000e+00, 0.000e+00],\n",
              "       [2.780e-01, 7.220e-01, 0.000e+00, 0.000e+00],\n",
              "       [3.007e-01, 6.993e-01, 0.000e+00, 0.000e+00],\n",
              "       [3.145e-01, 6.855e-01, 0.000e+00, 0.000e+00],\n",
              "       [3.403e-01, 6.597e-01, 0.000e+00, 0.000e+00],\n",
              "       [3.648e-01, 6.352e-01, 0.000e+00, 0.000e+00],\n",
              "       [3.835e-01, 6.165e-01, 0.000e+00, 0.000e+00],\n",
              "       [4.193e-01, 5.807e-01, 0.000e+00, 0.000e+00],\n",
              "       [4.504e-01, 5.496e-01, 0.000e+00, 0.000e+00],\n",
              "       [4.751e-01, 5.249e-01, 0.000e+00, 0.000e+00],\n",
              "       [5.008e-01, 4.992e-01, 0.000e+00, 0.000e+00],\n",
              "       [5.386e-01, 4.614e-01, 0.000e+00, 0.000e+00],\n",
              "       [5.558e-01, 4.442e-01, 0.000e+00, 0.000e+00],\n",
              "       [5.941e-01, 4.059e-01, 0.000e+00, 0.000e+00],\n",
              "       [6.287e-01, 3.713e-01, 0.000e+00, 0.000e+00],\n",
              "       [6.672e-01, 3.328e-01, 0.000e+00, 0.000e+00],\n",
              "       [6.953e-01, 3.047e-01, 0.000e+00, 0.000e+00],\n",
              "       [7.262e-01, 2.738e-01, 0.000e+00, 0.000e+00],\n",
              "       [7.581e-01, 2.419e-01, 0.000e+00, 0.000e+00],\n",
              "       [7.948e-01, 2.052e-01, 0.000e+00, 0.000e+00],\n",
              "       [8.125e-01, 1.875e-01, 0.000e+00, 0.000e+00],\n",
              "       [8.453e-01, 1.547e-01, 0.000e+00, 0.000e+00],\n",
              "       [8.737e-01, 1.263e-01, 0.000e+00, 0.000e+00],\n",
              "       [8.923e-01, 1.077e-01, 0.000e+00, 0.000e+00],\n",
              "       [9.188e-01, 8.120e-02, 0.000e+00, 0.000e+00],\n",
              "       [9.386e-01, 6.140e-02, 0.000e+00, 0.000e+00],\n",
              "       [9.497e-01, 5.030e-02, 0.000e+00, 0.000e+00],\n",
              "       [9.676e-01, 3.240e-02, 0.000e+00, 0.000e+00],\n",
              "       [9.782e-01, 2.180e-02, 0.000e+00, 0.000e+00],\n",
              "       [9.840e-01, 1.600e-02, 0.000e+00, 0.000e+00],\n",
              "       [9.919e-01, 8.100e-03, 0.000e+00, 0.000e+00],\n",
              "       [9.963e-01, 3.700e-03, 0.000e+00, 0.000e+00],\n",
              "       [9.988e-01, 1.200e-03, 0.000e+00, 0.000e+00],\n",
              "       [9.993e-01, 7.000e-04, 0.000e+00, 0.000e+00],\n",
              "       [9.999e-01, 1.000e-04, 0.000e+00, 0.000e+00],\n",
              "       [1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00],\n",
              "       [1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00],\n",
              "       [1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00],\n",
              "       [1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00],\n",
              "       [1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00],\n",
              "       [1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t4IsLT3wUJLA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "897b07a7-fb1a-4b5d-c70a-91298c9c2c6d"
      },
      "source": [
        "# mounting a google drive\n",
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/gdrive; to attempt to forcibly remount, call drive.mount(\"/content/gdrive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2tSbkfnyxdJB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.savetxt('/content/gdrive/My Drive/ApprovalVoting/preliminary_files/prob4.csv', prob4, delimiter=',')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MehAS-VUk3-L",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "outputId": "ee17d0ac-07d0-46e4-d6cc-6bb1b598fa62"
      },
      "source": [
        "conjectureVals = np.array([ [probConjecture(4, k, p) for k in range(1, numTau+1)] for p in pvals4 ])\n",
        "\n",
        "plt.figure(figsize=(10,6))\n",
        "plt.plot(pvals4, prob4, zorder=5)\n",
        "plt.plot(pvals4, conjectureVals, color=\"gray\", linewidth=1, zorder=1)\n",
        "for v in [1/4, 1/3, 1/2]:\n",
        "  plt.axvline(x=v, color='k', linestyle='--', linewidth=1)\n",
        "plt.ylim((-0.1,1.1))\n",
        "plt.title(\"Approx. Probability of Piercing Numbers (n = 4 sets)\")\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"τ=\"+str(i) for i in range(1,numTau+1)], loc=1);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "207byt9vVXLt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3b8cba7a-bc23-4954-b287-0e1ed877c367"
      },
      "source": [
        "plt.savefig(\"/content/gdrive/My Drive/ApprovalVoting/2020_paper_supplements/approx_conj_probs_tau4.png\", bbox_inches='tight')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XG1m6UgIWkqo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mj2ZOaZplJ4K",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "06162688-f5e9-4b37-f936-b10f76df133c"
      },
      "source": [
        "plt.plot(pvals4, conjectureVals)\n",
        "plt.ylim((0,1))\n",
        "plt.title(\"Conjectured Probability of Piercing Numbers\")\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"τ=\"+str(i) for i in range(1,numTau+1)]);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3N8Gxe9EdM2A",
        "colab_type": "text"
      },
      "source": [
        "RESULTS FOR 6 APPROVAL SETS"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "md4mcZSUBXr1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "187fdb4c-265d-4a6b-e6c0-ed7b75451945"
      },
      "source": [
        "numSets = 6\n",
        "numTau = 6\n",
        "numProbs = 40\n",
        "pvals6 = np.linspace(0.01, 0.30, numProbs)\n",
        "prob6 = np.zeros( (numProbs, numTau) )\n",
        "\n",
        "for r in range(numProbs):\n",
        "  prob6[r] = computePiercingProbabilities(numTau, pvals6[r], 1000, numTau)\n",
        "  print(\"finished p = \"+str(pvals6[r]))\n",
        "\n",
        "prob6"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "finished p = 0.01\n",
            "finished p = 0.017435897435897435\n",
            "finished p = 0.02487179487179487\n",
            "finished p = 0.03230769230769231\n",
            "finished p = 0.03974358974358974\n",
            "finished p = 0.04717948717948718\n",
            "finished p = 0.054615384615384614\n",
            "finished p = 0.062051282051282054\n",
            "finished p = 0.06948717948717949\n",
            "finished p = 0.07692307692307691\n",
            "finished p = 0.08435897435897435\n",
            "finished p = 0.0917948717948718\n",
            "finished p = 0.09923076923076922\n",
            "finished p = 0.10666666666666666\n",
            "finished p = 0.1141025641025641\n",
            "finished p = 0.12153846153846153\n",
            "finished p = 0.12897435897435897\n",
            "finished p = 0.13641025641025642\n",
            "finished p = 0.14384615384615385\n",
            "finished p = 0.1512820512820513\n",
            "finished p = 0.15871794871794873\n",
            "finished p = 0.16615384615384615\n",
            "finished p = 0.1735897435897436\n",
            "finished p = 0.18102564102564103\n",
            "finished p = 0.18846153846153846\n",
            "finished p = 0.1958974358974359\n",
            "finished p = 0.20333333333333334\n",
            "finished p = 0.21076923076923076\n",
            "finished p = 0.21820512820512822\n",
            "finished p = 0.22564102564102564\n",
            "finished p = 0.23307692307692307\n",
            "finished p = 0.24051282051282052\n",
            "finished p = 0.24794871794871795\n",
            "finished p = 0.2553846153846154\n",
            "finished p = 0.26282051282051283\n",
            "finished p = 0.2702564102564103\n",
            "finished p = 0.2776923076923077\n",
            "finished p = 0.28512820512820514\n",
            "finished p = 0.2925641025641026\n",
            "finished p = 0.3\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.   , 0.   , 0.   , 0.029, 0.259, 0.712],\n",
              "       [0.   , 0.   , 0.001, 0.063, 0.372, 0.564],\n",
              "       [0.   , 0.   , 0.008, 0.121, 0.409, 0.462],\n",
              "       [0.   , 0.   , 0.015, 0.154, 0.478, 0.353],\n",
              "       [0.   , 0.002, 0.023, 0.225, 0.485, 0.265],\n",
              "       [0.   , 0.   , 0.04 , 0.279, 0.5  , 0.181],\n",
              "       [0.   , 0.002, 0.061, 0.361, 0.44 , 0.136],\n",
              "       [0.   , 0.002, 0.081, 0.396, 0.437, 0.084],\n",
              "       [0.   , 0.003, 0.116, 0.462, 0.356, 0.063],\n",
              "       [0.   , 0.006, 0.156, 0.465, 0.321, 0.052],\n",
              "       [0.   , 0.012, 0.18 , 0.505, 0.277, 0.026],\n",
              "       [0.   , 0.013, 0.184, 0.537, 0.249, 0.017],\n",
              "       [0.   , 0.024, 0.249, 0.512, 0.207, 0.008],\n",
              "       [0.   , 0.022, 0.323, 0.498, 0.148, 0.009],\n",
              "       [0.001, 0.025, 0.351, 0.509, 0.11 , 0.004],\n",
              "       [0.   , 0.042, 0.384, 0.476, 0.094, 0.004],\n",
              "       [0.   , 0.055, 0.414, 0.48 , 0.051, 0.   ],\n",
              "       [0.   , 0.063, 0.478, 0.42 , 0.039, 0.   ],\n",
              "       [0.001, 0.065, 0.492, 0.417, 0.025, 0.   ],\n",
              "       [0.001, 0.091, 0.558, 0.334, 0.016, 0.   ],\n",
              "       [0.001, 0.116, 0.592, 0.279, 0.012, 0.   ],\n",
              "       [0.001, 0.118, 0.658, 0.219, 0.004, 0.   ],\n",
              "       [0.001, 0.134, 0.646, 0.218, 0.001, 0.   ],\n",
              "       [0.001, 0.168, 0.67 , 0.161, 0.   , 0.   ],\n",
              "       [0.002, 0.198, 0.684, 0.116, 0.   , 0.   ],\n",
              "       [0.003, 0.241, 0.656, 0.1  , 0.   , 0.   ],\n",
              "       [0.001, 0.246, 0.682, 0.071, 0.   , 0.   ],\n",
              "       [0.002, 0.25 , 0.709, 0.039, 0.   , 0.   ],\n",
              "       [0.004, 0.294, 0.663, 0.039, 0.   , 0.   ],\n",
              "       [0.002, 0.343, 0.645, 0.01 , 0.   , 0.   ],\n",
              "       [0.002, 0.392, 0.602, 0.004, 0.   , 0.   ],\n",
              "       [0.009, 0.442, 0.548, 0.001, 0.   , 0.   ],\n",
              "       [0.003, 0.463, 0.534, 0.   , 0.   , 0.   ],\n",
              "       [0.005, 0.486, 0.509, 0.   , 0.   , 0.   ],\n",
              "       [0.008, 0.546, 0.446, 0.   , 0.   , 0.   ],\n",
              "       [0.01 , 0.572, 0.418, 0.   , 0.   , 0.   ],\n",
              "       [0.012, 0.653, 0.335, 0.   , 0.   , 0.   ],\n",
              "       [0.006, 0.673, 0.321, 0.   , 0.   , 0.   ],\n",
              "       [0.015, 0.719, 0.266, 0.   , 0.   , 0.   ],\n",
              "       [0.008, 0.772, 0.22 , 0.   , 0.   , 0.   ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WR2cX4cNBlzc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 231
        },
        "outputId": "789806de-73da-4593-f87a-eb3ec65688be"
      },
      "source": [
        "conjectureVals = np.array([ [probConjecture(numSets, k, p) for k in range(1, numTau+1)] for p in pvals6 ])\n",
        "\n",
        "plt.figure(figsize=(10,6))\n",
        "plt.plot(pvals6, prob6, zorder=5)\n",
        "plt.plot(pvals6, conjectureVals, color=\"gray\", linewidth=1, zorder=1)\n",
        "plt.axvline(x=1/6, color='k', linestyle='--', linewidth=1)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Approx. Probability of Piercing Numbers (n = {0})\".format(numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"τ=\"+str(i) for i in range(1,numTau+1)], loc=1);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-95-89be6c05c009>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mconjectureVals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mprobConjecture\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumSets\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumTau\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpvals6\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpvals6\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprob6\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mzorder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpvals6\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconjectureVals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"gray\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mzorder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'pvals6' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "45qlgDE9PMBh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "2d7ebb93-00b9-44d9-a011-0a74adb9a1b5"
      },
      "source": [
        "plt.plot(pvals6, conjectureVals)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Conjectured Probability of Piercing Numbers (n = {0})\".format(numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"τ=\"+str(i) for i in range(1,numTau+1)], loc=1);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mKZSBx5gidH7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "c4eb6a1d-9249-410f-84bc-218cddb27fa7"
      },
      "source": [
        "k=3\n",
        "plt.plot(pvals6, prob6[:,k])\n",
        "plt.plot(pvals6, conjectureVals[:,k])\n",
        "plt.axvline(x=1/(k+2), color='k', linestyle='--', linewidth=1)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Computed vs. Conjectured Probabilities for $\\\\tau = {0}$ (n = {1} sets)\".format(k, numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"computed\",\"conjectured\"]);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2M_YgCR2PUAX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "6b720bf9-c24f-490b-bd13-e9fb440df6f6"
      },
      "source": [
        "k=4\n",
        "plt.plot(pvals6, prob6[:,k])\n",
        "plt.plot(pvals6, conjectureVals[:,k])\n",
        "plt.axvline(x=1/(k+2), color='k', linestyle='--', linewidth=1)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Computed vs. Conjectured Probabilities for $\\\\tau = {0}$ (n = {1} sets)\".format(k, numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"computed\",\"conjectured\"]);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oj-x4D5cg_JA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "235cf294-9f29-4024-fff1-84ebd7ca769f"
      },
      "source": [
        "k=5\n",
        "plt.plot(pvals6, prob6[:,k])\n",
        "plt.plot(pvals6, conjectureVals[:,k])\n",
        "plt.axvline(x=1/(k+2), color='k', linestyle='--', linewidth=1)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Computed vs. Conjectured Probabilities for $\\\\tau = {0}$  (n = {1} sets)\".format(k, numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"computed\",\"conjectured\"]);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "10kwQGvtiyBI"
      },
      "source": [
        "RESULTS FOR 10 APPROVAL SETS"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "JEFiFsupiyBW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "28ce57c7-c311-4ce7-8b2f-4f008399ee22"
      },
      "source": [
        "numSets = 10\n",
        "numTau = 6\n",
        "numProbs = 40\n",
        "pvals6 = np.linspace(0.01, 0.30, numProbs)\n",
        "prob6_100 = np.zeros( (numProbs, numTau) )\n",
        "\n",
        "for r in range(numProbs):\n",
        "  prob6_100[r] = computePiercingProbabilities(numSets, pvals6[r], 1000, numTau)\n",
        "  print(\"finished p = \"+str(pvals6[r]))\n",
        "\n",
        "prob6_100"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "finished p = 0.01\n",
            "finished p = 0.017435897435897435\n",
            "finished p = 0.02487179487179487\n",
            "finished p = 0.03230769230769231\n",
            "finished p = 0.03974358974358974\n",
            "finished p = 0.04717948717948718\n",
            "finished p = 0.054615384615384614\n",
            "finished p = 0.062051282051282054\n",
            "finished p = 0.06948717948717949\n",
            "finished p = 0.07692307692307691\n",
            "finished p = 0.08435897435897435\n",
            "finished p = 0.0917948717948718\n",
            "finished p = 0.09923076923076922\n",
            "finished p = 0.10666666666666666\n",
            "finished p = 0.1141025641025641\n",
            "finished p = 0.12153846153846153\n",
            "finished p = 0.12897435897435897\n",
            "finished p = 0.13641025641025642\n",
            "finished p = 0.14384615384615385\n",
            "finished p = 0.1512820512820513\n",
            "finished p = 0.15871794871794873\n",
            "finished p = 0.16615384615384615\n",
            "finished p = 0.1735897435897436\n",
            "finished p = 0.18102564102564103\n",
            "finished p = 0.18846153846153846\n",
            "finished p = 0.1958974358974359\n",
            "finished p = 0.20333333333333334\n",
            "finished p = 0.21076923076923076\n",
            "finished p = 0.21820512820512822\n",
            "finished p = 0.22564102564102564\n",
            "finished p = 0.23307692307692307\n",
            "finished p = 0.24051282051282052\n",
            "finished p = 0.24794871794871795\n",
            "finished p = 0.2553846153846154\n",
            "finished p = 0.26282051282051283\n",
            "finished p = 0.2702564102564103\n",
            "finished p = 0.2776923076923077\n",
            "finished p = 0.28512820512820514\n",
            "finished p = 0.2925641025641026\n",
            "finished p = 0.3\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.   , 0.   , 0.   , 0.   , 0.   , 0.   ],\n",
              "       [0.   , 0.   , 0.   , 0.   , 0.001, 0.005],\n",
              "       [0.   , 0.   , 0.   , 0.   , 0.006, 0.043],\n",
              "       [0.   , 0.   , 0.   , 0.   , 0.019, 0.111],\n",
              "       [0.   , 0.   , 0.   , 0.004, 0.027, 0.158],\n",
              "       [0.   , 0.   , 0.   , 0.001, 0.058, 0.266],\n",
              "       [0.   , 0.   , 0.   , 0.01 , 0.104, 0.336],\n",
              "       [0.   , 0.   , 0.   , 0.024, 0.14 , 0.415],\n",
              "       [0.   , 0.   , 0.004, 0.033, 0.251, 0.404],\n",
              "       [0.   , 0.   , 0.   , 0.056, 0.314, 0.431],\n",
              "       [0.   , 0.   , 0.007, 0.095, 0.371, 0.412],\n",
              "       [0.   , 0.   , 0.004, 0.143, 0.435, 0.339],\n",
              "       [0.   , 0.   , 0.013, 0.161, 0.51 , 0.296],\n",
              "       [0.   , 0.   , 0.025, 0.254, 0.506, 0.196],\n",
              "       [0.   , 0.   , 0.017, 0.311, 0.523, 0.148],\n",
              "       [0.   , 0.   , 0.036, 0.375, 0.5  , 0.089],\n",
              "       [0.   , 0.   , 0.052, 0.431, 0.482, 0.035],\n",
              "       [0.   , 0.   , 0.092, 0.518, 0.37 , 0.02 ],\n",
              "       [0.   , 0.   , 0.106, 0.585, 0.304, 0.005],\n",
              "       [0.   , 0.001, 0.15 , 0.635, 0.213, 0.001],\n",
              "       [0.   , 0.002, 0.192, 0.678, 0.128, 0.   ],\n",
              "       [0.   , 0.002, 0.24 , 0.686, 0.072, 0.   ],\n",
              "       [0.   , 0.003, 0.295, 0.673, 0.029, 0.   ],\n",
              "       [0.   , 0.008, 0.363, 0.615, 0.014, 0.   ],\n",
              "       [0.   , 0.01 , 0.43 , 0.56 , 0.   , 0.   ],\n",
              "       [0.   , 0.021, 0.498, 0.481, 0.   , 0.   ],\n",
              "       [0.   , 0.017, 0.555, 0.428, 0.   , 0.   ],\n",
              "       [0.   , 0.024, 0.657, 0.319, 0.   , 0.   ],\n",
              "       [0.   , 0.039, 0.733, 0.228, 0.   , 0.   ],\n",
              "       [0.001, 0.045, 0.8  , 0.154, 0.   , 0.   ],\n",
              "       [0.   , 0.061, 0.838, 0.101, 0.   , 0.   ],\n",
              "       [0.001, 0.067, 0.884, 0.048, 0.   , 0.   ],\n",
              "       [0.   , 0.085, 0.905, 0.01 , 0.   , 0.   ],\n",
              "       [0.   , 0.101, 0.889, 0.01 , 0.   , 0.   ],\n",
              "       [0.   , 0.1  , 0.897, 0.003, 0.   , 0.   ],\n",
              "       [0.   , 0.169, 0.83 , 0.001, 0.   , 0.   ],\n",
              "       [0.   , 0.191, 0.809, 0.   , 0.   , 0.   ],\n",
              "       [0.   , 0.208, 0.792, 0.   , 0.   , 0.   ],\n",
              "       [0.001, 0.247, 0.752, 0.   , 0.   , 0.   ],\n",
              "       [0.   , 0.308, 0.692, 0.   , 0.   , 0.   ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "IpBmKNiciyBi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "outputId": "5d1c9747-a7d1-43fa-ba3e-d1244a24e439"
      },
      "source": [
        "conjectureVals = np.array([ [probConjecture(numSets, k, p) for k in range(1, numTau+1)] for p in pvals6 ])\n",
        "\n",
        "plt.figure(figsize=(10,6))\n",
        "plt.plot(pvals6, prob6_100, zorder=5)\n",
        "plt.plot(pvals6, conjectureVals, color=\"gray\", linewidth=1, zorder=1)\n",
        "plt.axvline(x=1/6, color='k', linestyle='--', linewidth=1)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Approx. Probability of Piercing Numbers (n = {0} sets)\".format(numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"τ=\"+str(i) for i in range(1,numTau+1)], loc=1);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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79+9nxIgRXj3cFx8fz6FDh/jhhx8YPHgw/7slpyqvKjExXymlqpquXbuit4WrmTIzMwkLC3Oq7c8//8zu3bsZOXKkRybgl1X//v2ZNm0amzZt4vLLLy/Tvjk5OSQlJZGZmemm6DwrMDCQ2NhY/Pz8nN5HkzCllFLKhTIzM4mMLPJiuIssX76c7du3M3LkSEJCQiohsorz8/PjjjvuYObMmTRs2JCoqCin901KSiIsLIymTZtWuyqaMYYzZ86QlJREs2bNnN5P7x2plFJKuZAzE/NXrlzJli1bGDFiBKGhoZUUmWtERkbSu3dvvv322zLND8vMzKRevXrVLgED29XQ9erVK3OVT5MwpZRygwkTJng6BOUhpU3MX7VqFevXr2fEiBFOD1t6m06dOhEbG8sPP/xQpmH36piAFSjPa9MkTCml3GDixImeDkF5SEmVsDVr1rB27VpGjhxJrVq1Kjky1+rfvz/Hjh1j48aNng7F7b755hvat2+PxWJx6ZXPmoQppZQb6Gr5NVdxlbB169axatUqRo4c6XXLUJRHwfywxYsXc+LECU+H41YdOnTgu+++o0ePHi49riZhSinlBseO6drTNVVRlbANGzawYsUKRowYQe3atT0UmesVzA+rKuuHTZ48mfj4eKKjo4mJiSE+Pp4pU6aUul/btm1p3bq1y+PRqyOVUkopF8nLyyM3N/eiey1u2rSJZcuWMXLkSOrWrevB6NyjU6dOHDx4sEzrh02as50dyakujaNdw1pMGNi+xDYJCQkkJCQwceJEQkNDGTduHADdu3cnLS3tkvavvfYavXr1cmmcjjQJU0opN+jcubOnQ1AeUDAUWZCIbNmyhSVLljBixAjq1avn4ejcp3///kyfPp2NGzdWyZ/9FStWeKRfTcKUUsoN1q9f7+kQlAc4DkVu27aNn376iXvvvZeIiAgPR+ZeBfPD/v3vfxMTE1Pq+mGlVazcrXC1TithSilVjYwZM4apU6d6OgxVyQoqYcePH2f+/PmMGDGC+vXrezqsShEREUGfPn345ptvGD16tFfcgLw4kZGRHD169ML3nqqE6cR8pZRyg2nTpnk6BOUBVquVgIAAvv32W/r06VOmFeWrg44dO9K4ceMyrx9W2YYOHcqCBQt44IEHnGr/n//8h9jYWFatWsUtt9xCnz59XBKHVsKUUkopF8nMzOTcuXM0adKEjh07ejocj+jXr5/Xzw+Ljo4u03pfQ4YMYciQIS6PQythSimllIskJiZitVrp16+fp0PxmJq0flhFaRKmlFJu4DjfRNUM586dY/v27bRt29ar50NVBsf5YVVh/TBP0SRMKaXcQK+OrFny8vKYNWsWDRs2rPZXQjqrY8eOREVF8dtvv3k6FK+lSZhSSrnBoEGDPB2CqkTLli0jKCiIOnXqFHvfyJqoR48erF69mpycHE+H4pU0CVNKKaUqIDExkc2bNzN48OBi7xtZU0VFRREbG8uGDRs8HYpX0iRMKaWUKqeMjAy+//57Bg8eTEhISJH3jazpunfvzsqVK716yQpP0SRMKaXc4IMPPvB0CMrNjDHMnj2bjh070rx5cwCthBWhYcOGREVFVekJ+k888QRt2rShY8eODBkyhJSUFJccV5MwpZRygzFjxng6BOVma9as4fz589xwww0XntNKWNF69OhBVlZWla2G3XzzzWzbto0tW7YQFxfH3//+d5ccV5MwpZRyg8L3plPVy7Fjx1ixYgW33XYbPj4+F57XSljRGjVqhMViwWq1ejSOyZMnEx8fT3R0NDExMcTHxzNlypRS9+vduze+vrb17bt160ZSUpJL4tEV85VSSqkyyM7OZtasWfTt25c6depceD4vL4+cnJxyrRGWnp3Ol7u/5Pt939MivAUDWwykR2wP/H38XRm6RwUGBpKWlkZQUBDy49NwfKtrO4i+DPr9o8QmCQkJJCQkMHHiREJDQxk3bhxQtht4z5gxg7vuusslIWsSppRSSpXB/PnzadSoEZdddtlFzxdUwcpSBT2XeY5Pd37KFzu/IC0njc71O7Pl9BaWHFlCLf9a9G3al4EtBtIpslOVr676+vri4+OD1Wol2NPBFOLsDbxfeuklfH19GTZsmEv61SRMKaXcYMCAAZ4OQbnB1q1bOXLkSJFz/soyFHki4wQf7fiIb/d8S2ZuJr2a9OKByx6gfb325ObnsubYGuYkzuG/+//L13u+plFYIwY2H8iA5gNoVKtRuWLPzstmf8p+9pzbw6HUQwxtNZTYsNhyHau8QkNDSU1NJajv3z2aVBbu25lK2MyZM5k7dy6LFy92WeyahCmllBvMmTPH0yEoFzt79iw//vgjw4cPx9//0mHCzMzMUiflH0k7woxtM5i9bzb5Jp9bmt/C/R3up0XtFhfa+Fp8uTbmWq6NuZaMbhksOrSIOYlzeG/ze7y7+V3iI+MZ2GIgfZr2ITwg/JI+jDGcyTzD7rO72X1uN7vP7mbPuT0c/P0guSb3Qru1x9fyUd+P8LH4XHIMdwkICEBEnDpX7hQZGXnRrcVKq4T9+OOPvPrqq/z8888EB7uujqdJmFJKucHAgQM1EatGCm5L1L17dxo0aFBkG6vVWmwlbN+5fUzfNp35B+bjK74MbTWUUe1HlVqJCvEL4daWt3Jry1s5nnGcHxJ/YM7+Ofx19V/5x9p/cH3s9fRt1pesvCz2nN3D7nO2hOts5tkLx4gKjqJ13dbc0OgG4urEEVc3jq2ntvLcyuf4fNfn3Nvu3vKfmDISEUJDQ0lPTy/z0K0rDR06lAEDBnD8+HE+/PDDUtuPHTuWrKwsbr75ZsA2Of/999+vcByahCmllBvMnTvX0yEoF1q6dCkhISFcddVVxbYpqrqz/fR2pm2dxuLDiwnyDWJEuxGMaDeCyODIMscQHRLNA5c9wP0d7mfn2Z3M2T+HeQfmsejwIgD8Lf60rNOS62OvJ65OHK3rtiauTlyR1bJmtZqx4OACpmyYQs/YnuUe4iyPggn6WVlZHruSNDo6mnXr1jndft++fW6JQ5MwpZRSqgTJycls2rSJhx9+uMTKjWMl7Pes33l6xdOsOLqCWv61eLjTw9zT5h5qB9aucDwiQrt67WhXrx2Pd32czac2UyegDo1rNcbX4tzbuojwwtUvMGT2ECaumsj03tMrrSolIoSFhZGWlnZheLKm0nXClFJKqWLk5+fzww8/0KtXL0JCQkpsWzAxPyMng0cWPcLqY6t5tPOjLLx9IY/EP+KSBKwwX4svXaK60Lx2c6cTsALRIdE83vVx1h5fy7d7v3V5bCUJDAzEGFOlV9F3BU3ClFLKDarqyuDqYuvXr8fX15dOnTqV2tZqtWLxtzB28Vi2n9nOP6//Jw9c9gAhfiUnb550W6vbuCr6Kl5f9zrHM45XWr8Fc8OKuiKxJtEkTCml3GDq1KmeDkFVUHp6OsuWLeOWW25xasgs3ZrO9FPTWX9iPS9f9zI3Nb6pEqKsGBFhwjUTyDf5TFo1qVI/PAQFBZGXl0dWVlal9eltNAlTSik3eOihhzwdgqqghQsXcvnll1O/fv1S2+bm5/JF6hdsTd/KxGsm0r95/0qI0DUahTXi/zr/H78c/YW5iZV3QYnjlZI1lSZhSimlVCGJiYkcPnyYHj16lNo23+Tz/Mrn2ZW/iwebP8jQVkMrIULX+kObPxAfGc8/1v6D09bTldZvcHAwubm5NXZumCZhSimllIPc3FzmzZtHv379ilyU1ZExhr+t/htzE+fSLacbd7S4o5KidC2LWJh07SQyczN5ec3LldZvVZkb9vzzz9OxY0fi4+Pp3bs3ycnJLjmuJmFKKeUG//3vfz0dgiqnlStXEhERQevWrUtsZ4zhtXWv8c2eb3jwsgdpn97eo6vAV1Tz8OY8HP8wPx36iYUHF1Zav8HBweTk5JCTk1NpfZbVE088wZYtW9i0aRMDBgzgxRdfdMlxNQlTSik36NKli6dDUOVw9uxZ1qxZQ79+/Upt++7md/l4x8fc0+Ye/nL5X8p070hvNar9KNrVa8dLa14iJTOlUvqszGrY5MmTiY+PJzo6mpiYGOLj45kyZUqp+9WqVevC1xkZGXrvSKWU8mYxMTG6TEUVY4xh/vz5XHvttYSHX7rKvKMZ22bw/ub3GdJyCE9e+eSFNa+qehLma/HlxWte5O65d/PKb6/w9+5/d0s/r6x9hV1nd130XHZ2Nn5+fuVOcNrUbcOTVz5ZYpuEhAQSEhKYOHEioaGhjBs3DnDuBt7PPvssH3/8MeHh4SxdurRcMRamlTCllFIK2LFjB7///jvdunUrsd2Xu75k8vrJ9G3alwlXT8AiFjIzM6vN6u+t67bmwY4PMjdxLsuTlldavz4+PuTl5VVaf45WrFjBpk2bLnkUJGAAL730EkeOHGHYsGG8/fbbLulXK2FKKaVqvKysLBYsWMDtt9+Oj49Pse1m75vNS2teomdsT17u/jI+Flvb6jAU6WjMZWNYdGgRk1ZN4vtbvyfMP8ylxy+qYpWfn8/JkyeJiIjA19e96UnhZNmZSliBYcOG0b9/fyZNmlThODQJU0opNxg9erSnQ1BlsHTpUlq0aEHjxo2LbbPg4AJe+PUFrm5wNa/1fA0/i9+FbVartUpPyi/Mz8ePv177V4bNG8br615n4jUT3d6nxWIhJCSE9PR0atd2/S2eHEVGRnL06NEL369YsaLE9nv37qVVq1YAzJ49mzZt2rgkDh2OVEopN9AV86uOY8eOsW3bNm6++eZi2yxPWs5Ty58iPjKef93wLwJ8Ai7aXt0qYQAdIjowst1IZu2dxepjqyulz5CQEDIzM8nNzXVrP0OHDmXBggU88MADTrV/6qmn6NChAx07dmThwoW8+eabLolDK2FKKeUGXbp0Yf369Z4OQ5Wi4AbdN954I8HBwUW2WXBwAc+seIbWdVvz9k1vE+x3abvqVgkr8Ej8Iyw5soSJv07ku0HfFfnaXclisRAYGIjVaiUszLVDoI6io6NZt26d0+1nzZrllji0EqaUUm6wYcMGT4egnLBhwwYsFguXX375JduMMczYNoNxP4+jXb12vN/r/WLnRlXHShhAoG8gk66ZxNH0o0zZWPpSDq4QHByM1WqtEVcXaxKmlFKqRkpPT2fp0qVF3qA7Nz+Xv67+64WrIKf3mU7twOLnKVmt1mqZhAF0ierCH9r8gc93fs6Xu74kO8+9txjy8/PDGOPVi7e6iiZhSinlBg0aNPB0CKoUP/30E506dSIqKuqi5zNyMhi7ZCzf7PmGBzo8wCs9XrlkDlhhmZmZ1XI4ssCjnR8lvn48L615iX7f9eOTHZ9wPue8W/oSkQvVsOpOkzCllHIDV91bTrnHgQMHOHjwID179rzo+eMZxxk5fySrk1cz4eoJPNrlUSxS+ltlda6EAQT7BfNR34/44OYPaFKrCa/+9ip9Z/Vl6pappGanury/oKCgGjEkqUmYUkq5wcSJEz0dgipGXl4e8+bNo2/fvhfdoHv32d0MmzeMpPQk3rnpHW6Pu93pY1b3ShjYKlTXNLyGGX1m8Em/T+gQ0YG3Nr5Fn2/78OaGNzljPeOyvnx9ffH19SUrK8tlx/RGmoQppZQbuGIhR+Uev/76K3Xr1r1oradfjv7CiPkjAPio70dcG3NtmY5ZXSfmFye+fjzv9nqXbwZ+wzUNr+HDrR/Sd1Zf/rH2HxzPOO6SPoKCgjh/3j1Dnt5CkzCllFI1RmpqKqtWraJv374XJuN/s+cbxi4eS+Najfm8/+e0rtu6zMetrktUlKZN3Ta83vN1Zg+eTZ+mffhq11f0+64fE36dwOHUwxU6dlBQEFlZWeTn57so2op7/fXXERFOnz7tkuNpEqaUUqrGWLJkCV26dKFOnTrkm3wmr5/Mi6te5OqGVzOz70yiQqJKP0gRalolrLBm4c3423V/44ehP3B7q9uZu38uA78fyPjl49l8anO55nZZLBYCAgK8ZoL+kSNHWLhwYYl3VSgrtyZhItJXRHaLyD4ReaqI7Y1FZKmIbBSRLSLS353xKKVUZSnLQpCqchw7doz9+/dz3XXXkZWXxfjl45mxbQZ3xt3JWze+RYhfSLmPXVMrYYU1DG3Is92eZcHtC7ISMAgAACAASURBVBjZfiQ/H/mZ4fOGM2T2ENJz0snNL9tK+AUT9F1l8uTJxMfHEx0dTUxMDPHx8UyZ4tz6ZwkJCbz66qsuvUm721bMFxEf4B3gZiAJ+E1E/muM2eHQ7Dnga2PMeyLSDpgHNHVXTEoppWomYwwLFy7k+uuv57w5z18W/IVNpzbxWJfHGNV+VIXeWPPz88nOziYgoORlLGqSiKAIHuvyGA91fIgfD/zId/u+IzUrlT3n9tgWvP3XDPL27Ke0s26AnOxs0v38Sv0/CmjbhuhnnimxTUJCAgkJCUycOJHQ0FDGjRsHlH4D79mzZxMTE0OnTp1Kibhs3HnboiuBfcaYRAAR+RK4FXBMwgxQy/51OKDXdCulqoWuXbtW+8vrq5I9e/aQkZFBy/YtGT5/OMfSj/Ha9a/Rp2mfCh87KysLf39/LBad4VNYiF8It8Xdxm1xt7Fl+xbqBtYlJSuF/Ow0JNeKr8UXX4svlmLSMcE2LJmXn4+vj4/b4izpBt7nz5/n5ZdfZuHChS7v151JWAxwxOH7JOCqQm0mAgtF5M9ACNCrqAOJyBhgDODSsVillFLVX15eHj/99BN9+vThtfWvkZSWxPTe0+ka3dUlx68Jy1O4gp/Fj+iQaOoH1yftuedJyUohPTudbGzJWp3AOoT5h12yLlt2djYpKSlERka6bCiw8HFKqoRFRUVx4MCBC1WwpKQkOnfuzNq1a4mOjq5QHJ6+gfcfgJnGmNdF5GrgExHpYIy56FIIY8xUYCpA165d9aOlUkopp61fv57w8HCOBx1n9v7ZjL5stMsSMKj+C7W6mkUshAeEEx4QTk5eDueyzpGSlUJSWhI+4kN4QDgRQRH4+fgBF9/GyHFdt4qIjIzk6NGjF74vqRIGcPLkyQtfN23alHXr1hEREVHhONxZOz0KNHL4Ptb+nKMHgK8BjDGrgECg4q9KKaU8bMKECZ4OQWGrUi1fvpxrb7yWF1e/SPPw5vyx0x9d3odWwsrHz8eP+sH1aVW7FU1qNSHUP5RzWec4kHqArFzbQq3uuI3R0KFDWbBgAQ888IDLjlke7qyE/Qa0EpFm2JKvu4F7CrU5DNwEzBSRttiSsFNujEkppSqFrpjvHZYvX05cXByfH/mcExkn+KT/J/j7uKaaUkArYRUnIoT6hxLqH4o1x8qhtEMcSD1Ak1pNCPINIigoiNOnT1OrVi2XDElGR0eX+wrmgwcPVrj/Am6rhBljcoGxwAJgJ7arILeLyIsiMsje7HFgtIhsBr4ARhmdyaqUqgYaNmzo6RBqvHPnzrFp0ybCO4Tz1e6vuLfdvXSKdO3VbaBrhLlakF8QzWo1w4KFg78fJD07vdrexsitc8KMMfOwLTvh+NwLDl/vAMp2bwillKoCjh075ukQarzFixdz+RWX88qmV2gU1oixl491Sz+6RpjrBfgG0Cy8GYfSDnE47TAxoTEXbmNUnRJevZ5WKaVUtXPkyBGOHDnChuANHEk7wqRrJhHk655ESSth7uHn40ezWs0I8g0iKS2JTMn0utsYVZQmYUop5QadO3f2dAg1VsHCrI2ubMRnuz7jrtZ3cUX0FW7rTyth7uNj8aFJrSaE+Ydx/Pxxsv2zveY2Rq6gSZhSSrnB+vXrPR1CjbV9+3ay87L55NQnRIVE8WjnR93an1bC3MsiFhqFNaJ2YG3STTonrCeqzULImoQppZQbjBkzxtMh1Ei5ubksXryY061Ok/h7IhOunkCof6hb+9QkzP1EhIYhDakXVA8rVo6kHSHfVP1hSU3ClFLKDaZNm+bpEGqkNWvWYCINs47MYlCLQVwXc53b+9ThyMohIkSHRBNuCSctO43DqYfJy8+rlL4nTpx44Ybf8fHxzJs3r/SdnODpFfOVUkopl8jIyGDFyhWsabWGOjl1GH/F+ErpVythlat+aH3yU/JJz0nnYOpBmtRqgq/F/elMQkLChRt+u4pWwpRSSlULP//8M6ebn2Zf6j6e6/Yc4QHhldKvVsIql5+fHwEmgAbBDcjKy+LA7wfIzst2at/JkycTHx9PdHT0hcrWlClT3Bxx8bQSppRSbuB4XzrlfqdOnWLlrpUsiVxCn6Z9uKnxTZXSrzGGrKwsrYSV0Yqv93D6SHq598/Ly8NgsFiEzLws1nKCmCb16Hl32xL3S0hIICEhgYkTJxIaGnqhslXSDbx79eoFwNtvv83HH39M165def3116lTp0654y+gSZhSSrnB+vXrddX8SrTwp4VsjdlKiAnh6SufrrR+s7Ky8PPzw2LRgaXKZLFYyMnJwdfHn0CfQDLzMknLTiff5GORsv9flHYD74cffpjnn38eEeH555/n8ccfZ8aMGeUN/wJNwpRSyg0GDRpUbS6j93YHDhxgaepSDgQd4JXur1AvqF6l9a1DkeXT/c64Ch/j9OnThIaGEhgYSHp2OodSD3E84zgNQ0v/8FP4/pOlVcKioqIuPDd69GgGDBhQ4fhBkzCllFJVWH5+Pl//9DUbQzbSs2FP+jXrV6n966R8z3G8jVGofygRQRGctp4mxC+k1PmAkZGRF00ZKK0SduzYMRo0aADAf/7zHzp06FDxF4AmYUoppaqwjZs2ssx/GQE+ATzX7blLKhzuppUwzwkKCiI1NZX8/HwsFguRwZFk5GaQnJ5MkG8Q/j7+xe47dOhQBgwYwPHjx/nwww9L7Wv8+PFs2rQJEaFp06Z88MEHLnkNmoQppZQbuOqPtCpeTk4OH6z6gKTQJCZdMYmokKjSd3IxrYR5jsViISAgAKvVSkhICBaxEBsay/6U/SSlJ9G0VtNi54dFR0ezbt06p/v65JNPXBX2RXQmoVJKuYGumO9+C1YuYH3oero16MaQlkM8EoPVatUkzIOCgoIuupekv48/DUMbYs2xcur8KQ9G5hxNwpRSyg0qe1isprFarUzbNQ1jMbxw9QseO9+ZmZk6HOlBgYGB5Obmkpube+G58IBw6gTW4bT1NOnZ5V8GozJoEqaUUqrK+XTxpyQGJTKq/SgahTXyWBxaCfMsESEwMPCiahhAdEg0AT4BHE0/Sm5+bjF7e54mYUoppaqUcynn+Oz4Z0QERvDgZQ96NBathHlecHAwVqv1oiVhLGIhNiyWPJPH0fSjXrtcjCZhSinlBq5aR0hd6s2f3uSM3xkSuiYQ7Bfs0Vh0Yr7n+fn5YYwhJyfnoucDfQOJDo4mPTudM5lnPBRdyTQJU0opN5gzZ46nQ6iWDh87zLy0ebSv254BzT2f6OoSFZ5XMCSZlZV1ybY6gXUI8w/j5PmTWHOsReztWZqEKaWUGwwcONDTIVRLLy1+CauPlae7PV2u29O4mlbCvENgYCCZmZmXPC8iNAxtiK/4kpSeRF5+Xrn7eOutt2jTpg3t27dn/PjxFQn3Al0nTCml3GDu3LmeDqHaWbtnLWty13BLs1voFNnJ0+EAWgnzFv7+/uTm5pKXl4ePj89F23wtvsSGxXLg9wMcyzhGTGhMma+mXbp0KbNnz2bz5s0EBARw8uRJl8Tt+Y8RSimlVCmMMfz917/jY/EhoWuCp8O5QCth3qFgSLKoahhAsF8w9YPr89abb9ExviPR0dHExMQQHx/PlClTSj3+e++9x1NPPUVAQAAA9evXd0ncWglTSinl9b5b9x37ZB9jO431yMr4RTHGaBJWTktnTuXkoUSXHrNOTGO6DLmLkJCQIrdHBEXw8J8fZtTDo/jszc+oXas248aNA0q/gfeePXtYsWIFzz77LIGBgbz22mtcccUVFY65xCRMRCxAN2PMrxXuSSmlahBvvSS+KsrOzeatbW8RGRjJyPYjPR3OBVlZWfj5+V0y/KU8w9fHh+zs7Av3kixMRIgJjWH/7/tJzU4l3PzvJt+l3cA7NzeXs2fPsnr1an777TfuvPNOEhMTK7xIcIlJmDEmX0TeAS6vUC9KKVXDTJ06VW9d5CJvLXuLM5YzvHb1awT6ek/VSatg5XfDKPf8bpw+fZrs7Oxi/1/8fPyICY0hz+SRlvO/yldplbDY2FiGDh2KiHDllVdisVg4ffo0kZGRFYrXmeHIxSJyG/Cd0Y92SinllIceekiTMBc4m3GWL458wWV1L6N3k96eDuciulCr9ymYF1ZSchzmH0ZsdCwHDh8gLTuNMP+wUithgwcPZunSpdxwww3s2bOH7OxsIiIiKhyvMxPzHwK+AbJFJFVE0kQktcI9K6WUUqV4cdGLZFuyeaG75+4PWRy9ZZH3KUjCSqsZjbx7JKuXreZPD/3JqePef//9JCYm0qFDB+6++24++ugjl/w8lloJM8aEVbgXpZSqpnJPnSJz126y9uy2/btrF9mHD/Np48ac/mAqoT17EhDXyusSiKpg58mdLDm3hP6N+9OmbhtPh3MJrYR5H19fXywWCzk5Ofj7+xfbrmGDhmzesNnp30t/f38+/fRTV4V5QalJmNgiHAY0M8b8VUQaAQ2MMWtdHo1SSnkpk51NVmIiWbvtydbuXWTu3kPemf/dDkUiI8mMjialQweaJCZyavJkTk2ejG/DBoRefz1hPXsSfNVVWLR6UipjDC8sfYEACWD8Na5ZGNPVtBLmnQICAsjKyioxCQO84oORM3PC3gXygRuBvwLpwDtAxa/NVEopL5aXksLJNyZj3byZrMREsN+bTvz9CWjVipAe3cmIjCTJ15ed58+TFxxM69atadasGbt27eL48RPkrFlNw+RjRHw7i5QvvkQCAgi55hpCe/YktOf1+EV5x3IL3mbB3gXsytzFnzv8mbqBdT0dTpF0Yr53CgwMJDU1lbAw7x/IcyYJu8oY01lENgIYY86JSMnppVJKVXG5585x+L77yd6/n+CruxHaowcBbVpDk6Ycyslm2/797N+/n4jwcOLi4rijdWsiIyMvfLpu3bo1xhjM6Ac5efIkB/fs4czyFbB+HdHr1pG+dCkAvnFxhN90E2E33kDQZZd58iV7jZy8HF5Z8wqRPpHcF3+fp8Mplq6W751KWj3f2ziThOWIiA9gAEQkEltlTCmlqqXcM2dsCdihQ8S+9x457duxe/dudu/eTfKWLTRr1oy4uDj69u1LaGhoiccSEaKiooiKioLu3THGcOrUKY6sXEnqsmX4b95Czvvvc+a99wj/y19o+MjDlfQqvdf0DdM5nX+aN657Az8fP0+HU6zMzMwqUW3xJsYYtw8DOq6eX9zCre5QngUknEnCpgD/AaJE5CXgduC5MveklFJVQO6pUxy67z5yjiYT9so/+HzHdlJXryIuLo5u3brRvHlz/PzKnxiICPXr16f+kCEwZAjGGE4fPMiRp58h/623yGnejCZ9+7rwFVUtZ6xn+HDHh7QPas/NLW72dDgl0on5ZRMYGMiZM2eoV6+e2xOxgIAArFZrpSVhxhjOnDlT5uFpZ66O/ExE1gM32Z8abIzZWY4YlVLKq+WcOMnhUaPIOXGCvKef5vOtW+nVqxfx8fFlftMYPXq0U+1EhMhmzag7bSp7Bt3K2WeeJTU0jMuuu7Y8L6HKe2XlK2SbbF688UVPh1IqnZhfNrGxsSQlJXHq1Cm392WMITU1lRMnTlTaBPzAwEBiY2PLtI+z944MBgqGJDXtV0pVOznHjnFo1CjyTp/h+JjRbD6WzPDhw2nQoEG5jjd16tQytfcJC6PZu+9w4K67OD1pIkuefJIbbrrJK67gqiw7z+xk/tH59K7Xm7iIOE+HUyqthJWNn58fzZo1q7T+Zs6cyTXXXENcnPf+LJW6WKuIvAB8BNQFIoB/i4gORyqlqo3spKMcuncEuafPsPW2oSSFhjJ69OhyJ2AAXbp0KfM+gW3bEv3sc0QcSSL3q6/4+uuvyc7OLncMVYkxhknLJxGYH8hzN1WNtxithHm3uLg4du/e7ekwSuTMivnDgCuMMRONMROAbsC97g1LKaUqR/aRIxwacS85KSms7NObut26cc899xAcHFyh427YsKFc+9W+8w5qDRxIo5W/UvdoMjNmzCAlJaVCsVQFa46tYXvqdu5pdg91gut4Ohyn6BIV3i0uLo69e/eWa8J8ZXEmCUsGHH/KAoCj7glHKaUqT/bBgxy6dwQ5qWksv+kmrh0xghtvvBGLxZk/je4hIjSYOAH/pk1p8t0sLm/ajA8//JDDhw97LKbK8P7a9wk0gTx8XdW4OtQYo8ORXi4iIgI/Pz+OHz/u6VCKVexfGhF5S0SmAL8D20Vkpoj8G9gGVP+PZUqpai0r8QAH7x1BZloavw0cwG1PjKNNG9fdGqciQ5mWkBBi/jWZ/PQMor/4gkEDBvDVV1+Vu7rm7Q6lHGJ9ynoGNR5EoG/VqCxlZ2fj4+Pj9etQ1XTePiRZ0se9dcB6bMtTPAMsBZYBzwKz3R6ZUkq5Sda+fRwcPhxrRgYH7hvFH55+moiICJf2kZycXKH9A+PiiH7hBc6vWUPtBQu47777WLlyJT/++CP5+dVrqcYpK6YgIoy5aoynQ3GaDkVWDa1bt2bPnj2eDqNYxSZhxpiPSnpUZpBKKeUqmbv3kDhsOOetVqzPPM3AP/2p1HvMlcfEiRMrfIzaQ4cQPnQop997n8Bdu3nwwQc5deoUn3/+OZmZmRUP0gukZKSw9PRSekT3ICqk6tzCSVfLrxoaNWrEuXPnSEtL83QoRXLm6sgBIrJRRM6KSKqIpIlIamUEp5RSrmTdsYP9w4Zhzc2h1pQ36Xb77W5bAmLSpEkuOU70888R0LIlyU88gW9qKsOGDaNevXpMnz6dMw43D6+q3l76NjmWHB68/EFPh1ImWgmrGnx8fGjZsqXXVsOcmX36L2AkUM8YU8sYE2aMqeXmuJRSyqXO79rFvmHDyRahyccf06J7d0+H5BRLUBAxb/6L/Kwsjj72OJKXR79+/bj66qv597//XaUTsYyMDOafmE/r8NZ0iuzk6XDKRCthVUdcXFyVTsKOANuMN1/jqZRSJcg+cYJ9o+4j38eHNt98Tb327T0dUpkENG9Og0mTsK5fz6k33wRs65Bdf/31zJo1i7y8PA9HWD4zFs8g1TeVEZeNqHKL0molrOpo2bIlBw8eJCcnx9OhXMKZJGw8ME9EnhaRxwoe7g5MKaVcIS89nT3D70UyMmj24XSCmjatlH7XrVvn0uOFDxxA7bvu4sz0D0lbuhSArl27UqtWLRYvXuzSvipDSkoKPxz/gToBdejbtOrdK1MXaq06goKCaNCgAQcOHPB0KJdwJgl7CTiPba2wMIeHUkp5NZOTw54HRyNJSdR/7Z/U6lS1hrwKi3rmaQLatiX5qafJOXoUEWHQoEFs27aN/fv3ezq8Mpm1eBbJAcnc1eYu/H1cf2GEu+kaYVWLtw5JOpOENTTGDDXGTDDGTCp4uD0ypZSqAGMMiU+Mh02bCH78MaL69KnU/rt27eryY1oCAoj912TIzSXpsccw2dkEBwczePBgZs+eTUZGhsv7dIeTJ0+y4OQCLGLhzrg7PR1OuWglrGopSMK8bWaVM0nYPBHp7fZIlFLKhY6+MZnsH3+EO++k2YNV68q7kvg3aUKDl14ic/MWTr7+OgDNmzenY8eOzJ492+veZIoyf/F8DoQeoE/TPkQGR3o6nHLRSljV4q2r5zuThD0M/CgiVl2iQilVFZz+5hvSpk0j65praDNpoqfDcblafftQ5957OfvRx6T+uACAG264gYyMDNauXevh6Ep2+PBhVqasJDM/k2Fth3k6nHLTiflVjzcOSZaahNmXpLAYY4J0iQqllLdLW7GCkxMmcr5VSzq+967HrrqbMGGCW48f9cQ4gjp1IvmZZ8jauxcfHx9uu+02li9fzokTJ9zad3kZY1i0eBEH6hzgsojL6BjZ0dMhlZsuUVH1VMkkTER6FPVw5uAi0ldEdovIPhF5qpg2d4rIDhHZLiKfl/UFKKVUgcxduzg89s9YIyK47NNPsQQEeCwWV6yYXxLx9ydmyhQsIcEcGTuWvNRU6tatS+/evZk1a5ZXXo6/d+9e9mTv4XjWce5pe4+nw6kQrYRVPY0bN+bs2bNetXq+M8ORTzg8ngfmABNL20lEfIB3gH5AO+APItKuUJtWwNPAtcaY9sCjZQleKaUK5Bw7xv777ifbz4+4Tz7GPzzco/E0bNjQ7X34RdUn9s03yTmazNEnnsDk5dGxY0eioqJYuHCh2/svi/z8fBYvXkxydDIRQRH0aVK5F0q4mlbCqh5vXD3fmeHIgQ6Pm4EOwDknjn0lsM8Yk2iMyQa+BG4t1GY08I4x5py9r5NlC18ppSAvNZV9o+4jLz2dhu+9S1iTJp4OiWPHjlVKP8GdOxP97DNk/LycU2+/jYhwyy23sG/fPnbt2lUpMThj69atnA84z8aUjdzZ+k78fPw8HVK5GWO0ElZFtWrVir1793o6jAucqYQVlgS0daJdDLbV9h33iynUJg6IE5GVIrJaRIpcsU9ExojIOhFZd+rUqXKErJSqrkx2NokP/ZH8w4cJ+9tfibriCk+HVOlq33034bffxpn33if1p58IDAxk6NChzJ07l9RUz19HlZuby9KlSznT+Ay+Fl/uiLvD0yFVSE5ODhaLBV9fX0+HosqoVatWHDhwwGuG652ZE/aWiEyxP94GVgAbXNS/L9AK6An8AZgmIrULNzLGTDXGdDXGdI2MrJqXMyulXM8Yw+EnnyJ340bMnx6h2a2Fi+2e07lz50rrS0SIfv55Ajt25NiTT5G1fz+NGjXiiiuu4D//+Q/5+fmVFktR1q1bR+36tVl8YjH9mvYjIijCo/FUlC5PUXV52+r5zlTC1gHr7Y9VwJPGmOFO7HcUaOTwfaz9OUdJwH+NMTnGmAPAHmxJmVJKlerEG5M5P38+6YMG0mHsWE+Hc5H169dXan+WgABip7yJBAWR9Kex5KWl0b17d/Lz8/n1118rNRZHWVlZ/PLLL2S2yOR87vkqPyEfdKHWqs6brpJ0Zk7YRw6Pz4wxK5089m9AKxFpJiL+wN3Afwu1+R5bFQwRicA2PJnodPRKqRrr3FdfcW7aNM517UqXf/zD0+FcYsyYMZXep190NLH/mkx2UhLJ459EgKFDh7J69WqOHi38Gbhy/PrrrzRv0Zw5R+fQKbITHSI6eCQOV9JKWNXmTavnOzMcea2I/CQie0QkUUQOiEipiZIxJhcYCywAdgJfG2O2i8iLIjLI3mwBcEZEdgBLgSeMMWfK/3KUUjWBddMmjk16kXPNmnHFtKlYLOWZ3upe06ZN80i/wVdcQdRTT5G+dCmn33mX8PBw+vfvz6xZs8jKyqrUWNLT0/ntt98IahfE4bTDVXpxVkdaCava6tWr5zWr5zszq/BDIAHbcGReWQ5ujJkHzCv03AsOXxvgMftDKaVKlZ+VxcEnxpMZHEzHj2bipxWJS9QZdg+Z27Zx+p13CGzfjnY33si+ffuYP38+gwcPrrQ4li9fTseOHfn+8PfUD6pPrya9Kq1vd9JKWNUmIheqYQ0aNPBoLM58fPzdGDPfGHPSGHOm4OH2yJRSqgjHp0yBI0eo9eR4QuvX93Q4XklEiJ40kcAOHUh+YjxZiYn07duXpKQktm7dWikxnD17lm3bttE4vjErk1falqWwVN1lKRxpJazq85Z5Yc4kYUtF5J8icrWIdC54uD0ypZQqJHPHDlL+PZP0K6+k5R3evcyBp+ZgFbAEBBD71hQkIICksX/GJzub2267jR9//LFSVgxfunQpV111Fd8d/A5/iz93tPbu/6+y0DXCqj5vWT3fmSTsKqAr8DLwuv3xmjuDUkqpwkxODomPPU52YCCXvfGGp8MpVWVfHVkUvwYNiJk8mexDh0h+6imio6Lo1KkTP//8s1v7TU5O5uDBg3To0oH/7v8v/Zr1o25gXbf2WZl0tfyqz8fHh759+3p8cr4zV0feUMTjxsoITimlCiS/8y5y8CB1nnqSwIh6ng6nVIMGDSq9USUIuepKop4cT/qixZz54AO6d+/Ozp07OXPGPbNKjDH89NNP9OzZkx8O/YA111otlqVwpJWw6qFTp07UqlXLozF43yVFSilVSOaePaRMm0Zm1640ufNOT4dT5dS5915qDRrIqSlvkbtmDd26dWPJkiVu6Wvv3r2kp6fTsVNHvtj1BZ3rd6ZdvXal71iF6MR85SqahCmlvJrJy2NfwmPk+fvTbrL3D0N6IxGhwaRJBLRtQ/K4J+gSE8ORI0dITk52aT/5+fksWrSIXr16sfLYSpLSk6pdFQx0Yr5yHU3ClFJeLen99/HZv5+648cTUIVuW/bBBx94OoSLWIKCaPTWW5Cfz5k33qBHjx4sXrzYpX1s3LiR4OBg4uLi+GznZ0QFR3Fj4+o3e0UrYcpVnFmsdWgRj5tERK8NV0q5VeaBA/z+3vvkXH45MXff5elwysQTK+aXxi8mhnpjRpO+aDGt8/JISUkhMdE1NynJzs7m559/pnfv3qxKXsXqY6u5u83d1WZZCkdaCVOu4kwl7AFgOjDM/pgGPAmsFJF73RibUqoGM/n57P6/RzE+PrT512RExNMhlYm3xlt35Eh8o6I4/drr3NizJ4sWLXLJFWK//vorTZo0QWoJT654kpa1W3JPm+o3FGmM0UqYchlnkjBfoK0x5jZjzG1AO8BgW7riSXcGp5SquQ5+MBX/PXuIeGIc/lFRng6n2rAEBRGZ8CiZW7cSe+gQADt27KjQMdPT01m7di09bujBuJ/HkZOfw+Sekwn2C3ZFyF4lNzcXAF9fZ244o1TJnEnCGhljTjh8f9L+3Fkgxz1hKaVqsvOHDpH+7rvkd+xI9LDqcb9BbxI+aBABbdty6o3J3Ni9O0uWLCEvr0x3pbvI0qVLiY+PZ9reaWw5vYUXr3mRpuFNXRewF9E1wpQrOZOELRORuSIyUkRGArPtz4UAKe4NTylV0xhj2PV/jyIitHzjda8d1ivNgAEDPB1CscRiIerJ8eQkJ1NnG5qh2AAAIABJREFU5UrCw8PZuHFjuY516tQpdu3ahbWJlS92fcG97e6ld9PeLo7Ye+gaYcqVnEnC/gTMBOLtj4+BPxljMowxN7gxNqVUDbRv2jSCdu0iMiGBgNhYT4dTbnPmzPF0CCUK6daN0Ouv5/T7H3DjFVewfPlycnLKPrixaNEiml/RnJfWvcTl9S8noUuCG6L1HloJU67kzIr5xhjzrTEmwf741nh6nX+lVLWUfuQI1rffgfbtqD9yhKfDqZCBAwd6OoRS1X9iHPnnz+M76zsaNWrE6tWry7T/wYMHOXryKB+d+4gg3yD+2eOf1fJqSEdaCVOu5OwSFXtF5HcRSRWRNBFJrYzglFI1hzGGHf/3KD75+bR4/XXEUrWXMZw7d66nQyhVQMuW1L7jDs59+SU9WrZk1apVWK1Wp/Y1xrBg4QL2NNvDobRDvNrjVaJCqv8FFFoJU67kzF+5V4FBxphwY0wtY0yYMcazN1tSSlU7u6ZPJ2zHDiL/8hf8mzb1dDg1RuSfx2Lx9ydnxgzatm3LL7/84tR+27ZtY6vPVladW8XY+LFc1eAqN0fqHbQSplzJmSTshDFmp9sjUUq5RV5OPvvWn2TZZ7s4suOsS9aEcrXfjxwh6513sbRuTeT993k6nBrFNyKCemNGk/bTIq62T9BPTS15sCM3N5cvf/6SlX4ruT72eh647IFKitbzdKFW5UrOLHSyTkS+Ar4HsgqeNMZ857aolFIVduZoOjtXHmP3muNkZuRgsQjbVyQTE1ebboNbEN083NMhArZhre0Jj1E7J4cm/3wVqSbrL3ljslucuiNHcu6LL0l76206j36QZcuWMWjQoGLbL1m1hGVhy4gKieKl617CIlV76LgsMjMzqVOnjqfDUNWEM3/tagHnAcdrjg2gSZhSHmCMISkpibS0NDIzM8nKyiIrK4vMzEys6VmkHgHr0QDy0v0xYsgPSSEz8jjZfr/Tsl4XzhxIZ9ar62naMYKrBjUnIjbUo69nx1dfU2fbNur96U8ExsV5NBZXmjp1qlfeuqgolqAgIh99lGNPP02n9Axm7t/HqVOniCziXp3pGem8tvM1rEFWpvacSniAdyTzlUWHI5UrSVX6tAbQtWtXs27dOk+HoZRHnDt3jnnz5nH27FmioqIICAjA3z+A/DR/Ug/5kHIoj/xcCKnnR9PLa9OiawThdUMIDAwkOzub5cuXs23LDprV6kLKXgvZmXm06hrFlQObUbt+5a9ubrVa2dCvH/Vy84hbvAhLQEClx+AuIlKlqmEmL48Dt99B/u+/c+KF5zl68iR33nnnJe0e+/b/2bvvuKqv+4/jr3Pv5bL3BgEVUUQEFHDviTijMZrExOzZpG3apml/bRKTpm3apE3bjKqNJo0ZxhjjHkjcIgguFMXBEEX2kn3H+f3haIYi6l3g9/l4fB/Ey73f86ZV7rlnfM4LpDSk8PLgl5ndc7YVklrXZ599Rnx8PL169bJ2FEUHIYTIklImXOt71x0JE0K8KKX8ixDiX1wa+foeKeXzJsyoUNyR6iqa2Lo0B5VGhZOb9nuXo5sWJ9dL/611UpOesY+9e/cyZMgQ5s6dS0uDgRP7LnB8zwVqShuxs4fIgYH0HhqEfze3HxU51Wq1JCcnM2jQILZt20ZdfRHdXOLJP1zO6awyeg8NJDG5Ky6elvuUn7ZwIYElpfj9/nedqgPWEQm1Gv8Xf8XZhx8h4uRJMhoaOHfuHF2+U6ttU+4mUupTmBQ2ibsj7rZiWutRRsIUptTWdOSVxfjKsJNCYSa7V5yivOgiPl1cKc2vpfGiDn3LtY6PkQiNkSDvYVRmOrL+QDbnT1RjNEoCursz+oFIesT7oXW48QoDLy8vZs2axYULF0hNTaWlax0h9v04sfcCuWklRI8KJj4pDEcXrel/4O84d+4c9qtWofb3x2P2nTeiYoucBw/GZeRIqhf/h5F//Supqak8+OCDCCG4UH+Bl/e9TJA2iAXDF3TYkwxul1KiQmFK1/2NLaVce/nrx5aLo1DcOYpyqsg/XMGgGd2JT+p69fHWZj1NF1upqagnfXcWxWfL6NG1F84OHjTVtdJ0sZWWJgMxY0PoPSQQr0DnW2o/MDCQefPmkZ+fz9atW1FFqvEXfTiSWkTOrmLixoUQNy4UraPpF8objUb2vvcefUvL8H3lZVRa83b4rGHNmjXWjnBL/H71S/KmTSdw9272erhz5swZQruF8lzKc+iNet6d8C6Omju3E6KMhClM6Ya/XYUQKcBsKWXN5T97Al9IKSeaO5xC0VkZDEZ2fXkSN19HYseGfO97dvZqTp3JZ/PmzfTs2ZOnHphj1l/63bp147HHHiMnJ4dvv/0Wl1hvPFoi2L++gCPbz9FneDB9hgXh5mO6N96M9HS6pWegCQzEfdYsk93XlsTHx1s7wi25UsC15osvGPPO30lNTaU8tpzculye6/ocET4R1o5oVcpImMKU2vMR1/dKBwxASlkthPAzYyaFotM7uv081SWNJD8Tg8ZOffXxKwvv6+rqmD17NiEhIW3cxXSEEPTp04fIyEgOHjzIjh07CBrQHceLIRzcXMiBzYWERXsTPSKY0D7eqFS3PhVVV1fHic8+Z2BxMT4LFnTKUTCA4ODgDrUw/7t8f/IsdWvX4rR6DWfjXFmTu4ZYXSyPjXzM2tGs6srZmppOUkZFYX3t+ZtkEEKESinPAgghwrjGQn2FQtE+jXWtZKzNI7SPF137egNgMBjYt28fe/bsYciQIQwePBi1Wn2DO5meWq0mISGBmJgY0tPTSUv7luQnptNQZEfO7mLWv3cEVy8H+owIoveQIJzcbr4DtXHDBvqfPIldUBAed80ww0+huF0aX1+8H3+M8n/8k9JgT9y83fj10F+j6uBHSd2uK1ORd+p6OIXptacT9ltgtxBiByCA4UDHKH6jUNig9NVn0LcaGTY7AiEE586dY+3atbi6uvL444/bRCFIrVbL8OHDCQsLY/ny5dx7770kTB5C/qEKju48x75v8shYm094P1+iRwYT2MOjXW9Mubm5GPbvx66wEO/XX0N00lGwzsDroYco/O9ipm+uwWPKJIw6o7UjWV1zc7MyFakwqTY7YUIIFeAO9AcGXX74Z1LKCnMHUyg6o7LCOnL2XiBubAieAc6cPHmSNWvWkJSURJ8+fWzuE3ZoaCgzZszgiy++YP78+fSI96NHvB/VJQ0c3XmeE2klnMoswyvImT7Dg+k1KAD76yzkb21tZeOGDSSdPIWmSxc8ZnTuUbDHH3/c2hFuy6G64ywd0sKz6yVdtF1JS0sjJibG5v6OWpJyZJHC1NocW5ZSGoEXpZQVUsp1ly+lA6ZQ3AJplOxafhJHVy2Jk7tRVFTE6tWrmTt3LtHR0Tb75hYREcGECRNYtmwZNTWXlod6Bjgz/J6ePPTmUEY/EInGTsWu5Sf56KU9bP/0BLprlNnYvn07fZqakKdO4fP0Uwg7O0v/KBa1aNEia0e4ZS2GFl7Z+wpHYjxpDg7CZdU30NpKfn6+taNZlTISpjC19kzwbxVC/FIIESKE8LpymT2ZQtHJnMwooSSvjsEzwqmtr2b58uXMmDHje8UwbVVMTAxDhgxh2bJlNDQ0XH3cTqsmamgQs3+TyOzfJBAR78exXcVkbz/3vdeXlJRw+NAhumXsxy4kBPc2ziXsLDrq7kiAhYcXUlBXQELtALq+/DL64mKGnskjLS3N2tGsShkJU5haezphc4BngZ1A1uVLKeCqUNyE1mY9e1edwa+rG0FRTnz66aeMHz+eiIiOs91/4MCBREVF8emnn9LS0vKj7/uFuTHmwd4E9nAnZ0/x1Z2BUkrWr1/PeHcPdCdO4PP0051+FAzgwIED1o5wS3Krcll6dCm9jb2ZN2weniNH4jX/QTSbN2O3fTtlZWXWjmg1So0whandsBMmpex2jau7JcIpFJ1F1sYCGmtbGTAjlE8/+5TExERiY2OtHeumjR49mqCgIL744gv0ev01nxM1NIjasiaKT12auszKykIAbps2YhcWivu0qRZMrLgZeqOel/e+jJPaiaG6ocTFxQHg96tf4TxsGNF79nLo00+tnNJ6lBphClO7YSdMCOEkhPidEGLR5T9HCCGmmD+aQtE51JQ2cmhrET0H+vNt2nq6d+/OkCFDrB3rlgghSE5OxtnZmZUrV2I0/njHXHi8H1oHNTl7iqmvr2fbtm2Md3en5fjlUbA7pMZSYGCgtSPctGU5y8ipzKF/TX/uSrrrakkKodEQ/Le3sQsNwe+jj6nJzbVyUutQRsIUptae6cilQCtw5V3jPPAHsyVSKDqZPV+dQm2nolx1DDc3NyZOnGizi/DbQ6VSMWPGDFpbW1m3bt2PCpLaadX0HBDAmQPlbFqfQr/YWHSfLEMbFob7lDvn81txcbG1I9yUoroi3jv0HtEO0YwKGEVoaOj3vq92cyPs3/9Go1Jx9ulnMNQ3XOdOnZeyMF9hau3phIVLKf8C6ACklI1cqhemUChuoCC7goLsSpy7NmJQtTBjxowO3QG7QqPRMGfOHMrKykhNTf3R96OGBWHQGSnOqSder6clNxefZ5+5Y0bBAF599VVrR2g3KSUL0hagFmp6FfVi/Pjx13yetmtXvP/0R9QXLnDuF79AGq512HznpSzMV5haezphrUIIRy5XyRdChAM/XpWrUCi+x6A3snvFKbSuUO9QxD333GOVKvjmotVque+++8jNzWXv3r3f+55nkCPSoQl3Y1eqPvg32m7dcJs82UpJrWPBggXWjtBuq06vIr0knRGMYMyAMbi5uV33uYFJSVyYlETjjh2Uv/MPC6a0PmUkTGFq7emEvQJsAkKEEJ8CqcCLZk2lUHQCh78torasiWbPQuY9cD/29vbWjmRyTk5OzJs3j4yMDA4dOnT18V27duEaZqC+XEdFSQs+zz6L6EQd0M6kvLGct/a/RR+3PgRVBLVrvWLET3/KuagoKhcvpnbNGguktA3KSJjC1NqzOzIFmAk8BHwOJEgpt5s3lkLRsTXUtpCxNg+Dcy3znp6Bs7OztSOZjbu7O/PmzSM1NZXc3FwqKirIzMxk8twhqIw6Snsl4TYpydoxFdfxx/Q/0mpsJaYkhokTJrbrcOrQ0FCKkiZCdDQXfvd7mr7TAe/MlJEwhaldtxMmhIi8/LU/EAZcAIqB0MuPKRSK69j6yWH0OgOTHulvE2dBmpuPjw/33nsva9asYeXKlYwYMQK7A+n4lWVR4hHDdapZdGqZmbZfTjGlMIWtZ7cyxWsKXZy7EBkZ2a7XCSEYNGwY+0ePQuPvT9FPnkN34YKZ01qfMhKmMLW2RsJeuPz17Wtcb5k5l0LRYeVk5nHuaD3hgzyJ6BNm7TgWExQURL9+/SgrK6NH9+5UvPc+YepCdHrB6axSa8dT/EBtSy1/TP8jvTx64XjMkaSkpJvaNBIZGUm1Xo/m5d8jm5ooevZZjI2NZkxsXXq9HqPRiN0dUGhYYTnX7YRJKZ+4/HX0Na4xlouoUHQcVZVVpH5yDK2zirFzO14x1tvR0tLCkSNH6N+/P/veepvWvDwiHrsLD38ncnZ3/lGSH0pISLB2hDa9nfk21c3VTJATiImOwc/P76Zer1KpGDRoEBkXLhD09lu0HD9B8W9+i7xG7bjO4MpUZGfY3aywHe0p1uoghHhBCPG1EGKlEOJnQghlPFah+IGWlhY+e389qhZnRtwTidbhzinHAJcO6O7RowdJEyYQsHMnxpAQ3CZOIGpoECV5tVQV33l1pWzVvgv7WHV6FXd3vZu603WMGjXqlu7Tr18/CgoK0MXE4PfLX3Jx82Yq3v/AtGFthDIVqTCH9uyO/C/QB/gX8O7l//7EnKEUio5o47rNqMsDCejuRs8B/taOY1GlpaUcOXKEsWPHUr9xI07V1RyIiOBifT29BgWgUgty9nas4qWdVZO+iQV7FxDmGoZ/nj+jRo265cXmWq2W+Ph49u3bh9cjD+M+YwYV775L3aZNJk5tfUq1fIU5tKcTFi2lfFRKue3y9TiXOmIKhU0zGo00NDRQfK6I/SmbaKyrNVtbJ0+epChDh9SrGDG31x01ZSGlZMOGDYwaNQone3sq3nsf+169CLl7FuvXr8fR1Y5usT7kppVg0HXOqapreeWVV6wd4ZreO/ge5+rPMT9oPoZmA/37394+qwEDBpCdnU1zczMBry3AMS6O4pd+Q3NOjokS2wbl3EiFObRnvuSAEGKQlHIfgBBiIGD7234UnVZNTQ21tbU0NDTQ0NBAY2Pj975euZqbm3FobkBVdAZamti55AMiBg9jyIzZ+IR2NVmexsZG1n++E21td+KTu+Ib6mqye3cE2dnZ6HQ64uPjKf/HP2ktLKTLe+8SNnIkixYt4ujRo0QNDeLMgXLyDpcTkXBnjBLaYsX87PJsPjn+CbN6zOJc2jlmzpx59XzIW+Xq6kpkZCSZmZkMHz6cLu/+i/zZ91D0zLN0+2oFGh8fE6W3LmUkTGEO7fnXFw/sFUIUCCEKgDQgUQiRLYQ4YtZ0CsV3GI1Gtm3bxqJFi0hNTSU7O5uSkhIMBgPe3t5ERkYyYsQI7r77bubdM5u+DgLV6aN4+/qS/PyL+EfFcHLvLj7+1U9YvuA3nM5Mx2i8vWNXpJSs+Xo9jlXd8AlxISG5q2l+2A6iubmZlJQUkpOTadi2jcqFC/GYfTeuY8eiVquZPn06mzdvxiNEi4uXPcf33DlTkkFBQdaO8D2thlZe3vsyPo4+DGgeQEhICGFhptm9O2jQIDIyMtDr9Wh8fAh571305eVUffyxSe5vC5Q1YQpzaM9ImFJlUWF1TU1NfP311+h0Op555hlcXFyu+TyDXs+BjWtIW/EZUkqG3/cQ8ZOno9bY0XvoCMovFLN2yULOnTjKub++jrtfAP2SphI9ejz2Tk43nevIkSNUHtGiMqgY91AUas3tjSp0NNu3byciIgJfnY6CX7+EQ3Q0/r/73dXvBwUFERcXx+bNm+g9JIH96/Kpq2jCzafzT+tcsLG6WYuzF3O65jRvDnyTo2uO8uSTT5rs3v7+/vj7+3P06FHi4uJwiIrCZdQoar5ehe9zzyG0WpO1ZS1KoVaFObSnYn5hW5clQirubCUlJSxevBgfHx8eeOCB63bAzuceZ9lvfsbOZUsIiY7hobffZ8D0u1Fr/lfXxzcwiEf+bwF3vfoX7Hr3o1GnZ/t/F7Pw6fl8u3Qh1RfOtztXbW0tqSszoc6VQdPC8Q6+dq7OqrS0lOzsbMYMGcL5559HaDR0+cc7qH5wPNPIkSMpLS1F41sPAo7vta3OyZ0gtyqX/xz5D1O7T6Uhu4EBAwbg7u5u0jYGDx5MWloaUkoAPOfcg6GykovXOOC9I1JGwhTmcGftoVfYlMa6WvZ++SneXUIIieqLd5dQxA/Wpxw+fJgtW7YwadIkoqOjr3mfpot17PrsI7K/3YKrty/Tf/k7eiQOarPt7uHhPPv7V9m3bx97tmzCy9jC4ZSNHNy8ju79Eug3aRphfeOuu8BeSsmqL9fhWN0N/x7uxI4LubX/ETqoK4vxR48aRe0f/0jLmTxC/7MYu+DgHz3Xzs6OadOmsWLFCsJ7jeb43gskTu6KSt25Rw1vd8G7qeiNen6/5/e42btxt/fd7DqwixkzZpi8ne7duyOE4MyZM/To0QPnoUOxCwqievmXuE2aZPL2LK25uRl//ztjPaPCcq7bCRNC2EspWywZRnFn2bP8E45s/d9WdkdXN7pERRMS1Zfg3tHsP5pDXl4e8+fPv2YhSSklx3aksnPZEpob6kmYOpPBd9+L1qF9UwZqtZqhQ4fSt29fNm/eTK2bDz1dHTh3IIOVb/wen5Aw7vr1K7j5/rjtjIwMmk55oFKpGDs/CpXqztkNCZemYXU6HV2PHaN8w0Z8f/5znNs4+Dk0NJQ+ffpQVXCehhpnzuZU0bVv51iwfT1ZWVnWjgDAR8c+4njVcf4y7C/sWreLKVOmmKXquxDi6mhYjx49EGo1HvfMpvydf9BaUIC2a1eTt2lJysJ8hTm09VE0DUAIccs1wYQQSUKIXCHEaSHES208b5YQQgohbLvEtMJkKooKyU7dQr9JU3nsXx8y8emf0b1/IiVnTvHt0oV88uJznPxiCSEttZw/mEFFUeHVaY4rr1/+6kts/uAdPAODeeDP/2DkvEfa3QH7Ljc3N2bPns3UmbMo1KtwH5HE8IeepLaslG8/Wvjj7BUV7F17HGOdI8PujsDd985aJ9Lc3MzWrVuZGBJK+V/fwmXcWLyfePyGrxszZgwVLflonVTk7O78C/SfeOIJa0cgrzaPDw59wPiw8ajPqAkJCSE8PNxs7UVHR1NeXk5JSQkA7jNngkZD9ZcrzNampSglKhTm0NZ0pFYIcR8wRAgx84fflFJ+3daNhRBq4D1gPHAO2C+EWCOlzPnB81yBnwLpNxte0XHt/HQpWkdHBs+6F0dXN9z9/IkeNY7CwkK++mwZ3bw8cNS3UHQsmzP79wHg6OZOSFRfHF3dyP52M1pHJyY8+TzRo8b9aBrzVoSHh/PUU0+RlpbG9rQ0wvoP5EzaDvIO7Kd7/0Tg0g7Nrz9fh0N1KF36eBM1zLZ2wFnC9u3bifTzp+WNN9CGhBD0pz+1qy6aVqtl6rSprF2cTkG2kYbaFpzd7W/4uo5q8eLFLFq0yGrtG4wGXt7zMo52jjza9VE2frWRp59+2qxtqtVqBgwYwL59+5gxYwZ2fn64jh5N7apV+P7sp6g68AJ9ZSRMYQ5tdcKeAu4HPICpP/ieBNrshAEDgNNSyjwAIcQXwHTghxX8XgfeBH7VzsyKDq7wyCHyD2YyYt4jOLq6AZemFjMyMti1axczZs+hR48eVx+vKy+l6Fg2RTnZFB3L5mJlOX1GjmPEvIdxcjPt4mKNRsPw4cPp27cvXy5fjr2HF99+tJDQ6Fg0Wi07d+zEWBiAnb2GMQ9E3lFFWeHSJomjhw4x8+AhWhsbCVu6BLVr++uidevWjZCYHIq3w4m0C8QndTVX1Dve5yc+53D5Yd4Y+gZ7tuxh7NixODs7m73d+Ph4/vnPf1JXV4ebmxsec+dwMSWFi1tScJ8y2eztm4OUktraWtzc3KwdRdHJXLcTJqXcDewWQmRKKT+8hXsHA0Xf+fM5YOB3nyCE6A+ESCnXCyGUTtgdwGg0sGPZh7j5+tNv4hQAWltbWbduHeXl5Tz66KN4enpefb4QAne/ANz9AogePR4pJfqWFuzM/InUw8OD++6/n8Ul52nJOcD+NSsJGzKSgylFaOuDGftoL5w9Ou8ozrVcWYw/obiYlsOHCf7b29hHRNz0fZLvGsei9M0c2X6W/hPD7riOrCUUXSzinwf/yfDg4fiW+1JtX01cXJxF2nZ0dCQmJoaMjAzGjRuH8+DB2IWEULN8eYfthDU0NKBWq3G6hTI2CkVb2jOH84kQ4nkhxFeXr+eEELe9qlMIoQL+BvyiHc99QgiRKYTILC8vv92mFVZ0fNd2ygvzGX7vg2i0Wqqqqvjwww9RqVQ88sgj3+uAXYsQwuwdsCtcXFyY98xzSE9f9q36kpVLVmBfE0yPBD8iEu+8XVJHjhzB6+hR7Lak4DV/Pm7Jybd0H3t7e2JGhdJYo6cwp/P+ez5/vv3lTkxJSsmre19FLdT8PPrn7Np1aTG+JTu7gwYN4sCBA7S2tiJUKjzumU3j/v205OVZLIMpVVRU4NNJKv8rbEt7OmHvc6lq/vuXr/7AB+143Xngu/v2u1x+7ApXIBrYfrkS/yBgzbUW50spF0kpE6SUCb6+vu1oWmGLdC3N7P7ivwT06EmvISOoqqpiyZIlJCQkMH36dLPs2Lpdvr6+JD3xEwxGA4ZTp3F00TJybi9rx7K45uZm0pcvp1fqtzglJOD3yxt+dmrT0El9ERrJjlWHTZTQ9lhrd+RXp74ioySDF+JfIHNbJoMGDcLb29uiGTw9PenatSuHD1/6/9dj5kyws6Nm+ZcWzWEqSidMYS7t6YQlSinnSym/vXw9DCS243X7gQghRDchhBaYC6y58k0pZa2U0kdK2VVK2RXYB0yTUirnUnZSWetXU19VycgHHr20wP3rrxk2bBiJiYk2PSXl7OmFcOuLoTmf8P51OLjYXmfR3HZs2MDAHTvRuLsT/Pe/IW6zw6zRqokcFMDF84LTufkmSmlbpk2bZvE2SxpKeDvzbQYGDCRKH0V1dTVDhw61eA64dLD3/v37kVKi8fbGddxYar/5BmNLx6t8pHTCFObSnk6YQQhxdU+zEKI7cMMD96SUeuAnwGbgOPCllPKYEOI1IYTlfzsprKqhppqM1V8RMWAIXSL7sG3bNpycnBg4cOCNX2xFLS0trPk8BXtGoXbwImvTxzQ3Nlg7lkVdKC7G/oN/o62tIfidd9CYaDS678hQhFSx6Yu96HQ6k9zzTial5LW01zBKIy/Fv8TmzZuZMmUKarXaKnmunEtZUFAAgOecORhqa7m4ebNV8twOpROmMJf2dMJ+BWwTQmwXQuwAvqUd67gApJQbpJQ9pZThUso3Lj/2spRyzTWeO0oZBeu89q74FIOuleH3zScvL48jR44wffp0mx4BA9iwbhMOFd1x93Vm6vM/xdjUwGdv//l7Ncs6MyklR15+Gf+iIvxf+g1O/fuZ7N6+Ia74hblid9GXbdu2m+y+d6p1eevYdX4Xz/d7nhP7TtCzZ09CQ0OtlkcIcXU0DMBp4EC0YWFUd8ApSaUTpjCX9pwdmQpEAM8DzwG9pJTbzB1M0XlUnjtLduoWYicko3Xz4JtvvmH69OkW2S5/O06cOMG5zFb0TSrGzu9NeHw8PQcNozrnMClrf/Q5olM68vHHhOzeg9vUqXjef5/J7997aBD6eg3ZGacoLS01+f2taeHCHxf6NZeKpgr+nPFn4nzjGOo8lJMnTzJu3Dh0cBKyAAAgAElEQVSLtX89MTExFBQUUFtbixACj3vuoSkri5ZTp6wdrd10Oh0NDQ0mP2tToYD2jYQhpWyRUh65fHW8CX2FVV0pzDrorjmsXr2avn37mrVqtyk0NTWx8cudqKq9iRsbQlDEpV2bo+Y/hp2dluwNq8jOzrZySvO6mJ8Pf38HdffuBL62wCyjlj0T/dFoVXRxiiYlJcXk97cmS1bM/2P6H2nWN/PKoFfYuH4jEydOtInColqtlr59+5KZeWmSw33mXQg7uw41GlZZWYmXlxcqExSEVih+SPlbpTCrwuxD5B3Yz8C77iH7RC4NDQ2MGTPG2rFuaPOGrThWheMZ6MzA6d2vPu7q5cPg2fdBdQWbvljG2bNnrZjSfKTRyMnnn0cjJd0+eB+VmY5r0Tpq6JHgT22hpLqiltOnT5ulHWuw1FT7loItpBSm8HTc0xQfLcbT05OoqCiLtN0eiYmJHDx4EL1ej8bTE9cJE6hdvRpjU5O1o7WLMhWpMCelE6YwG2k0smPZEtx8/QnqN4CdO3cya9Ysqy0Ubq+ioiLO7tEjdSrGPxyFxu77eftPmoZ3l1BcKi+wYvkXVFVVWSmp+eS/9z5Op07j++sX0V5eYG0ufYYFoWsxEO6eSEpKCkaj0aztdSY1zTW8kf4GUd5RTA2Yyr59+0hOTraptZY+Pj4EBARw7NgxADzm3IPx4kXqNm6ycrL2UTphCnO6YSdMCPG1EGLy5eKqCkW75ezaRnlBHoNn3883a9YwYcIEvLy8rB2rTUajkXVL0lA3ujNsdgS+oT8+kket0TDm4adorK4i1A4+++wzmjrIp/r2aD5zhsaFCzH2i8P3PtOvA/uhgO7u9BzgT+H+BrQGVw4dOmT2NjuLN/e/SV1LHQsGL2DThk2MGDHCJtcuJSYm/m+BfmIi2u7dqVm+3Mqp2kfphCnMqb3FWu8DTgkh/iyEuPMqVSpu2ncLs+bV1hMYGEhsbKy1Y91Q6up9GC94E5HoT/TI4Os+LzQ6hsihIzmfmUaony9ffvklBsMNK7fYPKnXc+q555F2Gnq+8w+LjagMv6cn9i522Fd0Y9u322htbbVIu+Y0ZcoUs95/57mdrMtbx6N9H6W5qJmWlhYGDBhg1jZvVUREBA0NDZw/f/7yAv3ZNB0+THNurrWj3ZDSCVOYU3t2R26VUt7PpUr5BcBWIcReIcTDpji+SNE5XSnMGjZsLAUFBUyebPtnxpUUVZKbchE3XwdGz7vx4dwj5z2CSq1Bf+Y4Wq2WdevWdfjSFcXvvocmLw/Pl17Czt/PYu06uNgx6r5e1Ja04CMj2bNnj8XaNpe1a9ea7d4NugZe3/c64e7h3B9+P1u3bmXq1Kk2u3hcpVKRkJBwdTTMY8YMhFZr86NhUkqqqqosfuKA4s7Rrn+xQghv4CHgMeAg8A8udco613YmhUlcKcwa1i+BtKM5zJo1C3t72z7s2qA3subdLNQqDVOejcPO/sbr1ly8vBly973kH8qkX7cQSkpK2L17twXSmkdzTg61ixbRlJBAlzlzLN5+9zhfIhL9aSxwInP3Uerq6iyewZSmTp1qtnu/k/UOpQ2lvDrkVbanbicmJobAwECztWcK/fr1Izf30uYctYcHrkkTqV2zFmNjo7WjXVdtbS2Ojo5otVprR1F0Uu1ZE7YK2AU4AVOllNOklMullM8BLuYOqOh40r76DIOulRoXLwYPHkxw8PWn9WzFxqVZ6Go1jH6gN54B7a9f1u/yIv1dy5Ywe+ZMMjIyKCwsNGNS8zC2tJD/8xdodXAg6p2/Wy3HiDk9sXfS4NkQxbepHbsc4bp168xy34NlB1meu5z7et+H60VXzp49y6hRo8zSlik5OTkRGRnJwYMHgUsV9I319dRt2GDlZNenTEUqzK09I2GLpZRRUso/SSkvAAgh7AGklD86bFtxZ6s8d5YjqZvxiYpF6+ZhtXPrbkZuxgUKsy4S0s+ZyIFBN/VatUbD2Eeeoq68jOPbNpOcnMzatWs73DE8pe+8A4WFOL34Kxys+KZzaVoykpYaQcH+i5SUlFgtiy1qMbTwyt5XCHQO5Kk+T7F+/XqSk5M7zEjNgAEDyMzMxGg04ti/P9oe4TZdM0zphCnMrT2dsD9c47E0UwdRdA47P12KRmtPqdqBu+66y6a2yl9LdUkD3/73OBo3HZMfbc+59D8W0ufSIv39q78iwNMdf39/duzYYeKk5tOYlUX1Rx9TlZBAz7lzrR2H7v18iUjwQ1sTxMZV33b4dXamtOjIIvJr83l58MvsTN1JWFgYERER1o7VboGBgbi5uXHy5EmEEHjeM4fm7Gyac3KsHe2alE6Ywtyu2wkTQgQIIeIBRyFEPyFE/8vXKC5NTSoU33P26GHyDuxH7xfMtFl34+r64/IOtqS1Wc/69w9jMOqY+mw/1JpbX9Q8ct4jqO3s2LZ0IUlJSRw6dIji4mITpjUPY0MDRb96kUYXF6Lffsvaca4aPrcn9k52NOa6k3vipLXj3BJTdx5zq3JZkr2EaeHT8Kn3oaCggKSkJJO2YQmJiYlkZGQA4D59GsLe3mZHw5ROmMLc2nrXmQi8BXQB/ga8ffl6Afit+aMpOhJpNLLjkw9ROznTa8RYevbsae1IbZJSsv3TXGrLmug+yoGgsNvbCeji5c3gu+8j/1AWJ7ZtYfz48axZs8bmy1aU/uUvGIqL4bmf4O7vb+04Vzm6aBl1Xy9odiT1i4MdsoDrokWLTHYvg9HAq3tfxc3ejWd6P8O6deuYMWOGzW94uZaoqCjKy8spLy9H7e6O26RJ1K1di6G+wdrRfqSiokLZGakwq+t2wqSUH0spRwMPSSlHf+eaJqX82oIZFR1A9rYUygry0HTtycRJk6wd54aO7jjPqf2l4F/OxFnDTHLP/pOm0WvICHZ+upSmMydwdXW16VIL9Tt3UrP8S87Hx9N/3jxrx/mR8P5+hMf7QZkvu7fut3acm/bkk0+a7F7Lji/jaOVRXkp8iR2bdxAXF0doaKjJ7m9JarWa/v37/69cxZx7MDY2Urd+vZWTfV9TUxM6nc7mR/QVHVtb05FXfit3FUK88MPLQvkUHUBDTTU7ln2IdHHnnqefQ6PRWDtSm0rz69i94hRG5zomzR9gsmOUVGo1yT/5Bb2HjWLP8k8IopX09HTKy8tNcn9TMtTUUPzb/+Oipwe9//C6zdaXGjm3J1pHDYfXl9HU2GztOFZRdLGIdw++y6guo/Cp9KG+vr5D7IZsS0JCAtnZ2bS0tOAYF4d9z542VzOssrISHx8fm1/XqujY2vrNe2Wfvgvgeo1LoQBg+3//Q2tzM32mzMTPz3IFPm9Fc72OTYuzUdkbCRwg6d69+41fdBNUajVJz/6cPiPHcWDNSrpqjKxevdrmptNKXnsdfVUVtQ89TJdu3awd57ocXbWMvr83qhZn1i6x3VFFc5FSsiBtAWqVmmd6PcP27du56667bP781RtxdXUlPDycw4cPX6qgP+cemnNyaMo+au1oVynrwRSW0NZ05MLLXxdc67JcRIUtKziUxYk9OyAwjLGTzVec0hSkUZKy9BiNta3Ue54gafJ4s7SjUqmZ+NTz9B0zgbP7dtFy5jjp6elmaetW1G3YQN2GDZzs14/h8x+0dpwb6hHvR1iMJ2VHJYW5HadkxZo1a277Ht+c/ob0C+n8rN/P2LNpDyNHjsTX19cE6azvygJ9KSXu06YhHB2p+dJ2RsOU9WAKS2hrOvKfbV2WDKmwTbqWZrZ++D4qJxfG3P+QzdcqytxYwNljVWhCKxk+MREXF/PVGhYqFeMf/wmx45Npzstl92cfUVVVZbb22ktXVsaFBa9R5+9P+K9+iYODg7UjtcuYeX3Q2KvY/OERjAbbGlW8nvj4+Nt6fXljOX/N/Cvx/vH4lfjh4OBAYuKtlVGxRaGhoWg0GvLz81G7uuKWPIna9Rsw1NdbOxqgjIQpLKOt6cisG1yKO9y+lV9QW1aKQ+9Y4vr3t3acNp3NqSRjXT6+PbUYPapISDB/nWGhUjH20afplzQVVdl5vnjzNatOS0opufD732NobKRwxnSiO8CB6lc4uWkZeW8vdHUadn59zNpx2uV2T4r4U8afaNG38FT3pziQdYDp06d3qvVJQojvlavwnDsX2dhI7de2se9L6YQpLOFGuyOve1kypML2lJ8tIHPdKvANZPLc+236zaG+uoWUD3Pw8HekyLCfKVMmW2whuhCC0Q89Qf/k6TQVnGb5m68jrdQRq1mxgoYdOznWvz9jH3zQpv8/u5bIgUF4ddNw7NsyKottY7TEXFILU0kpTOGJvk+wf/N+kpOTO+Uuvb59+3L27Flqampw7NsXx4R4KpcsxdjaatVcBoOBmpoavLy8rJpD0fm1NR35zuWva4UQa354WS6iwtZIo5GUxe+istMSPGiETW+Vl0ZJ6sc56HUGnHtXExnV0+JnWQohGPXgY/QZl0zxof2sf//vFu+ItRYWUvbnN6nv1g2fBx/okGtdhBBMfXIAqAxsWHiww0xL3qy61jreSH+DSK9IAooCCAkJISoqytqxzEKr1RIbG0tmZiYAPk89jb6khNpvvrFqrurqatzd3W1+p7fiNjXXWTtBm9ORn1z++hb/K9T63UtxhzqSuokLJ0/QGhDKxMlTrB2nTUe2n+PciWqix/ty5txxxowZY5UcQggmPvY0AfGDyN21jU0fvIPRaJlCrsamJs49/1OMajUHhw1l+MiRFmnXHFw8HOib5E9dqY6DKWetHadNjz/++C297m+Zf6OquYpHgx+lIK+ASR2g7t7tSExM5ODBg+h0OpyHDsEhOprKxf9B6vVWy6RMRd4BGirgvQGw799WjdHWdGTW5a87uHRWZDVQBaRdfkxxB6qvrmLXZx/j6B9E3LgkPD09rR3puqqKG0hbdYawaC+OFu9h3LhxODo6Wi2PEII5L7yEJiyCnJ3fsum9v2M0c0V9KSUlr71Oy8mTHBg+nLFz53b4T/fDJvdF49VE+to8akobrR3num6lYn7GhQxWnlrJvRH3cmzbsQ5bFf9meHl5ERwczLFjxxBC4PP0U+iKiqjbuNFqmZSdkZ2clPDNM8jGKuhqmmLdt+qGC2OEEJOBM8A/gXeB00KIzv3RTHFd2z5ejK61hSb/EEaMGGHtONdl0BvZ+lEOdvZqPPu2oNXaERMTY+1YaDQaZj3/C2RwN47v3s6Gf72FwYyf+Gu++oraVauoGT8Op+HDCA8PN1tblqJSqUh6JBaj0UD62jPWjnNdN7s7sknfxKtprxLqGkpQQRCxsbGEhYWZKZ1t+W65CpfRo7GPiKBi4UKrrZ9URsI6uYzFcGozO+zHUSqsW/KlPauT3wZGSylHSSlHAqOBv5s3lsIW5R3cz8m0Xdh368noSZNt+hP6/nX5lJ+9yOC7u7I3YyfJyck2sxC9S5cu9J04Ba/YRHLTdrH+n38xS0es6dgxSl//A6r+/UgLDe2Qhz1fT1iPLriGGTidVU5teZO141zTgQMHbur5Hxz6gKKLRdzncx+NdY2MHj3aTMlsT48ePWhubub8+fMIlQrvJ5+k9fQZLm7dapU8SiesEys9htzyOwrseqId+iz+Vj4ztz2dsItSytPf+XMecNFMeRQ2StfcTOqHH+Ds44cI6kpcXJy1I13XhdM1HNhcSO8hgZwqPUBMTIzV/6H90JgxY7jo4knUpOmcSt/LsR2mfbMx1NZy/qc/Q+3pybexsUyeOtWqU7HmMOH+eKQ0krH+9I2fbOMySzL5OOdjpoROoTi9uFNUxb8ZPyxX4TYpCW1YGBX//jdSSotmkVIqnbDOSteEccXDNEk7igf8jiFDh1o7UZu7I2cKIWYCmUKIDUKIh4QQ84G1QMc7TVdxW/Z+9Rl15WU0B4SSNGmSzZ412NqsZ+tHObh6O9BtiBNnzpyxyXP27OzsmDp1KserLuIT2pUDG9aY7M1GGo0Uv/QbdCUlFM2di39EBL169TLJvW1JYIgvHt3gZEYZ9dUt1o7zI4GBge16XklDCb/Y8QtCXUMJyQth+PDhNn/8lznExcVx6tQp6uvrEWo13k88TkvOcRp27bJojoaGBtRqNU5OThZtV2F++o2/RVWRy4nInzF43DRrxwHaHgmbevlyAEqBkcAooBzoXB+pFW0qK8gja/03+EbFEhARSTcbPmtwz4pT1FU2M+bBSLakbmL8+PE2O23arVs3IiIiUAd3pfLcWQqzD5nkvpX/+ZD6bdvQPv44BxsbOtU05A+Nv68/0ghpa3OtHeVHiouLb/icFkMLP9/2c1oMLcxzmYer1pWBAwdaIJ3tcXR0pE+fPlfLVbhPnYomKJCKDyw7GqaMgnVOumNr0RxYQl5AMv1m/9Jmlqe0tTvy4bYuS4ZUWI/RaCBl8bs4uLhSYufE+PHmOW/RFPIPl5Oz5wL9J4RxvuY0Dg4OREdHWztWm8aPH0+pHuxd3Diw/vZrIzXsS6f8nXdwmTiRDQKSk5M79Sd6/xAvvLqrOLmvnMY66xb4/KFXX321ze9LKXk97XWOVh7lpxE/pehwUaerin+zBg4cSGZmJnq9HqHV4v3oozQdPEhjhuUmX5SdkZ2PruoshpVPUuMYSrdHl9rUv7H27I50EEI8K4R4Xwix5MpliXAK6zucspGS0ydx7xtPbHyCzf5yaqxrZduyE/iEuBA12pcdO3YwadIkm/rHdi0ODg5MTErC6BNA/qEsKs8X3fK9dKVlnP/FL9B27crxMaMJCg6md+/eJkxrm66Mhu1ZnWPtKN+zYMGCNr+/PHc5q8+s5uFeD1O8s5iZM2fi5uZmoXS2ydfXl4CAAI4ePQqAx6xZqH18qFxouVpOykhY52LQ66j4z2w0UofbwysQdrZ1Xm57FvZ8AgQAE4EdQBeUhfl3hItVFez+/GMCI/twocXASBst8imlZNuyE7Q2GRj3cBTbtn9LbGxsh1lX06dPH1zDeyHUag5uXHtL95A6HedfeAFjYyPq37xE9unTnb7I5xW+Xdzx7qbl5L4KmuptazTseg6UHuDNjDcZETwCl2wXBg0aRPfu3a0dyyYMGjSI9PR0pJSoHBzwfvhhGvam0XT4sEXaVzphnYfRaOTooqcIbDyBKvlNVH6R1o70I+3phPWQUv4eaLh8ZuRk4M5ctHCH2fbRIgx6A83+oYwcNQoHB9v6BHHF8T0XKDhSweC7wqnXVZKfn2+zHcZrEUIw5a6ZGD19ObYjlab6m/+MU/a3v9OUlYXfKy+z7vBhJk2a1KmnIX9o7L2xYFCxc1W2taPcUElDCS9sf4Fg12BG1I/A08OTIUOGWDuWzQgPD0ev11NYWAiA59w5qN3dqfj3Qou0r3TCOgcpJTs+/wfRZaswRk5BlWCbq6ja0wnTXf5aI4SIBtyBjjHEoLhlZ7LSOZW+lx4jxtKMuOnCk5ZSW97IrhWnCO7lSfTIIDZs2MCECRNsdjH+9fj6+hIxfAz61hayUzff1GvrtmyhaulSPO+7lyxnZwICAjrtWYPX4xfqhndXe07vq6K1SXfjF1jAlQXm39VqaOWF7S/QpG/iCb8nqCyuZNq0aTY/bW5JQggGDhxIeno6ACpnZzznP0j9tm00nzhh1rZ1Oh0NDQ14eHiYtR2FeUkp2bRmJf3z30Pl6o9q2r/ARv+NtacTtkgI4Qn8HlgD5ABvmjWVwqpam5tIXfJvvLuEktekZ8KECTZZksJoMLJ1aQ5qtWDs/N7sz9yPs7Nzh+2AJN01C9w8yVz/TbuLt7YWFHDht/+HQ0wMunnzOHx5FOxONHJ2HzCo2bri5oqkWoqUkjfS3yC7IpsXer9A7t5c5syZ0+E+MFhCTEwMZ8+epbq6GgCv++9H5exMxULzjoZVVlbi5eVlk7/vFO0jpWTLli10z12Im74CMWsxOHlZO9Z13fBvmpTyP1LKainlDilldymln5TSMuPCCqs4ui2FixXlBA4eibePDz169LB2pGs6sPksJXl1jLi3J9jp2LVrl01Vxr9Z9vb29Js0jabaGk6m77nh868czC3UagLe+itrNm5k0qRJODs7WyCt7QkM98A7zJG8jBpamqy/NiwhIeF7f15xcgVfn/qahyIfonhHMdOmTbPZjS7WptVq6dev39XRMLW7O5733cfFTZtpycs3W7vKVGTHt23bNlTH19CrMQMx/BdWPxvyRtqzO9JbCPEvIcQBIUSWEOIdIYTym6OTklJyOGUjft17cCT/LBMmTLB2pGsqK6xj/7p8IhL86JkYQEpKCv369evwv0BHTZ+JysmFXV9+1ubzpJSULHiNllOnCHrrr+w5eRJfX98OOwpoKsNmRiL0dmxZnmHtKN9zqOwQf8r4E0ODhuJ53JO4uLhOWUDXlBITEzl8+DAtLZcK8Xo9NB9hb0/lLRyM3l5KeYqObffu3RQdTWNc01oIToBRL1k70g21Z8z1C6AMmAXcDVQAy80ZSmE9548fo+p8EeqAEPr06YOvr3UPN70WfauBrUtzcHTTMuLeXhQUFFBYWGjTB4q3l0qtJmHydC6WnOfM4YPXfV7NihXUfvMNPk8/TW337hw6dKhDjwKaSnBPD7xDHCnIvEhTo22cKVnWWMbPt/+cIOcgJuom4qB1sMlTHGyNu7s74eHhHDp0qYixxtsbj3tmU7t2La3nzpulTWUkrOPat28fB7Myud9xO0IaYdZ/QG1n7Vg31J5OWKCU8nUpZf7l6w+AbR3EpzCZw1s3YufoyPkmnc2+UexddYbqkkbGzu+NnYOKDRs2MHHiRLRarbWjmcTAKTNQabVsXbb0mt9vyc+n9A9v4Dx0KB5PPsHq1atJSkrCxcXFwkltjxCCQdMiUOnt2fTFPqtmeeWVV64uxG/QNfBsl2cpOl3EXXfddcd3ltvrygJ9o9EIgPcjjyBUKir/s9gs7SmdsI5HSsmOHTvIyMjgschaNOczYPLb4GW7J7t8V3s6YVuEEHOFEKrL1z3AzW3fUnQIjbU1nNy3B/ugMIYMH26TJQ5K8+vI3naOmDFdCOntRUZGBm5ubp2qKKnWwZHYsUnUn83nxOEfH2VUufg/IARBf/4Tu/bswdvbmz59+lghqW0Ki/bGM8iRcwebuHix3mo5Xn31Vf6c8WcOlx/ml31+ybEdx5gzZ06nO0jdnLp06YKTkxOnTp0CwC4gAPe77qJ25dfoSstM2paUksrKSqUT1oFIKdm4cSPHjx/nsYl9cdz3D+h7D8TOsXa0dmvrAO+LQog64HHgM6D18vUF8IRl4iks6ej2rRgNehqc3RkwYIC141zT0Z3nsLNXM3Bad+rq6ti1a1eHqIx/sxImzwABW5YtvToKAKC7cIHatWvxuPtuynQ6Dhw4wOTJkzvdz387hBAMnBKOSufApi9uvMHBXLpN78aKkyuYHzmfkp0lJCUl4e+vTCLcjCvlKvbt+9+opvfjjyGNRqqWXnuk+FbV1tbi5OTUaUbUOzuDwcDXX39NaWkpD88Yg9OG58G9C0x+y9rRbkpbZ0e6SindLn9VSSk1ly+VlPLOPlujE5JGI0e2bkLj6cPo5CnY2dneXHpLk57TmWVEDPBH66AhJSWFhATbPUrpdrj5+hExYAj64rOkp+29+njVRx+BlHg8NJ/Vq1czYcIEZRryGrrH+eLu70DJER1VlVUWb/9w+WGcpjoxJGgI/qf86dWrF3379rV4js4gKiqKyspKSkpKANCGhOA+ZTLVy5ejv1zCwhSUqciOo7W1lc8//xydTse8cbHYL5sCLbUw+yNwcLd2vJvSrmIoQohpQoi3Ll9TzB1KYXmF2YeoLStBBHQhNjbW2nGu6WR6CXqdkT7DgsjPz6eoqIjhw4dbO5bZxE+egdTr2P3NV9TX16Ovrqb6yxW4T55M2unTeHp6Km/s1yFUgsTk7qh0TmxasduibZc0lPDCthfQV+uZwhQMegPjxo2zaIbORK1Wk5iYeLVcBYD3E08gm5up+vhjk7Wj7IzsGJqamvjkk09wdXXlnnhf7D6ZBio7eGQzBPe3dryb1p4SFX8GfsqlIq05wE+FEH8ydzCFZR1O2QB2WsbePdcmCxVKKcnZU4xPiAtewU5s2LCBpKQkmxyxM5WgnpEEhEfgUFvB1q1bqf5kGbKpCd3UKWRlZSnTkDcQkeCHq7cDlccFxcXFFmmztqWWp1KeolHfiGadhtNHTzN79mzUarVF2u+s4uPjOXHiBA0NDQDYh4fjOmEC1cs+xVBXZ5I2lJEw21dXV8fSpUsJCQlhWlgjqs/vAY9QeCwF/DrmuuD2vNsmA+OllEuklEuAJC6dH6noJC5WVXAmMwP74K5E2egC7/KzF6koqidqaBDp6el4eHh0+jpLQgj6J0+ntbaG/Iw0Kj75BMdRI1mVmcnUqVNxdXW1dkSbplKriE8KQ9XizOaV5l8b1qhr5NnUZym6WMTr8a/z0JSHmD179h1bPNeUnJyciIqK+t5RUD5PPoGxvp7qz9quqddeSifMtlVUVLBkyRJiY2KY4HgU8c1TEDoYHtkIbkHWjnfL2jvk8d2DtDrWhKviho5s3YyURsbMud9mR1aO7S5GY6fCP9KRPXv2dMrF+NfSc9BQXDy98Cw7Dxcvcqh7OFFRUZ2+A2oqkYMCcfbQ0pDvQH6++Sqt64w6frHjF2RXZPP6oNfJ3ZpLWloaXbp0MVubd5qBAweSmZmJ/vKRXg5RUbiMHEnVRx9jbGy87fsrnTDbVVxczMcff8zIEcMYWvsNpC6A6Lth3soOtwbsh9rTCfsjcFAI8ZEQ4mMgC3jDvLEUlmI0GDiweR32foFE9bfNQ7pbm/WcyiglPN6PLVs3MnjwYLy8bPcsMFNSa+yIHTeJyos1nAsNptBey9ixY60dq8NQ26noNz4M0ejMllW7kVKavA2jNPLynpfZfX43/5f4f1zYeYGIiAhWrVpl8rbuZH5+fjC67DUAACAASURBVPj5+XHs2LGrj3k/9SSGmprbXhvW1NSETqdTRpdtUF5eHp9++ilTJo6l38m/w/7FMOR5mLkYNB3/3NU2O2FCCBVgBAYBXwMrgcFSSqVifieRm76X1vqLDJo209pRrut0Vhm6FgPagAYaGhoYMmSItSNZVFizHpXRyIkgX1paWmhqso1K8B1F1PAgHF3sMJR4cPz4cZPeW0rJX/f/lXV563gu7jn0B/V4e3szfvx4k7ajuGTQoEHs27fvamfaqV8/XCdMoGLhInS3se7vSn2wO2F0vSPJyclh5cqVzJk6nl7pL8KJ9ZD0Z5jwOtjg2uVb0eZPIaU0Ai9KKS9IKddcvkoslE1hAbu//hK1oxP9Rtvum0bO7mLc/R1IP7KdadOm3VGLnKXBQP1/l+HbpEOvayK6V09SU1OtHatDsdOqiR0XgqxzJnXdHgwGg8nu/eHRD1l2fBn3974fnzOXprKmTp2qvJmbSY8ePdDpdJw9e/bqY/6/fhGA0r/89Zbvq0xF2p6srCw2btzI/OmjCE15DIoPXSpBMehpa0czqfZ0JbcKIX4phAgRQnhducyeTGF2xfl51BblEzN2ImqNxtpxrqniXD2l+XXo3SroH9+fwMBAa0eyqLotW9CfPYtvwmCMej1uLQ2cOXOGoqIia0frUPqO7IK9kwZtTRD79+83yT1XnlzJPw78g+RuycRWxVJTU/O9nZDnz5vnfMM72ZXird8tV2EXHIz3E49zcdMmGtLSbum+SnkK2yGlZOfOnezevZtHJw/Ab8390FAGD6yCPjOsHc/k2tMJmwM8C+zk0nqwLCCzzVcoOoTNy5YihCBh0jRrR7munN3FCBU0aIoZOXKkteNYlJSSs39/hyZPT8b+9nd0je3P0dRNjBs7hvXr13+vkr6ibVpHDX1Hd0Ff5cjurfuvljq4ValnU3lt32sMDR5KsiqZ/Lx87r333u+VTMnKyrrd2IpriI2NpaCggJqamquPeT/6KHYhIZS88QZSp7vpeyojYbahtbWVlStXkpuby+NjeuDx9b3/qwHWdai145nFDTthUspu17i6t+fmQogkIUSuEOK0EOKla3z/BSFEjhDiiBAiVQgRdis/hOLmlZaUUHniKF3j4nHz8bV2nGvStxrITb+A3qmKaTMno7HR0TpzKfzmGzRnzxLwzNNotFr6J0+noaYadW0VTk5O3zvKRXFjsWNCsHNQ42PozbZt2275PvtL9vPijheJ9o7mIc+HOJh5kHnz5v3oTMhp02z3w01HptVqiYuLIyMj4+pjKnt7/H/zG1pPn6Hq009v+p5KJ8z6qqur+fDDD9GoVTzcT4vTqgc7fA2w9mhPsVaHy52lr4UQK4UQPxNCOLTjdWrgPWASEAXcK4SI+sHTDgIJUsoY4CvgLzf/IyhuxcbP/ovQ6+g/0XYPQDhzoIzWJgNdYl0ICQmxdhyLampq4vy/3gVvbwLnXDqMtmtsf7yCQziwYTWTJ09m9+7dVJvw2JbOzsHZjrixITRcUJF7qPDqMTg340TVCZ7/9nm6uHbh52E/Z8/2PcybNw83N+UkN0saMGAAhw4doqWl5epjLqNH4TxiOBX/ehd9eXm772UwGKipqbljdlzbojNnzrB88d+Z4naC6WcXoFn3fKeoAdYe7ZmO/C/Qh/9n77zDo6rSP/65M5PMpPfeQwoJhNA7oXcICEpTQFSKLqBrwV1d9+daVnfXLZZ1EdB1FUHpTVoQSAgtdAIkJCG915nUmcnM3N8fwQjSAiSZJMzneebJ5M45534nmfK957znfeFT4LPr979tQr++QJooiumiKP5c+HvKjQ1EUTwkiuLPCV5OAKakOq1Abm4uZUmJ2Lq44hfZw9hy7sjpmHREcw0TZww3tpRWRRRFYj77N475+bgufA7hekFhQRDoOT6a4oxr1BUXMHDgQH788ccWSbvQUYkc5YvcUoa7EMHevXvv62+XU5nDkpglWJtb81bYWxzac4hZs2aZZlCMgL29PQEBAVy4cKHxmCAIuL/xBqJWS/FHf2/yWBUVFdjZ2T1yM+1tAVGnIWnLXxHWzWBx3af4pH6NYOcDj61qiAFr5znAmkJTTFhXURSfvW6YDomiuJAGI3YvvIAbo4dzrx+7E88Ce5owromHQBRF9m7dApUVdBs5Domkbe40LMquQJmnIbS/G3J5+88Fcz+cPHkSx8OHkdjZ4fDEEzc9Fh41HIWVNWd372DAgAFUV1dz6dIlIyltf8gtZPQc64cyR0ddWcMW+KZQWlfKophF6EU9f+7xZw7tOMS0adPw8rrzR9oXX3zRXLJN3IafA/RvNNLm/v44LliAavt2as+ea9I4pqVII1ByFf2e36P5oBNhF9/HX1GFMPi3sPwcPL0LImeCtOOWpLuRppiws4Ig9P/5F0EQ+tHMgfmCIDwF9AZuu8dYEIRFgiCcFgThdMl9TDObuJXU1FSqM1KQSKV0bcNpKfZ/nwCCyKBJXY0tpVXJy8vj/PYdOF27huPcuUh+VfLGTK6g26hxpJ06gbIgj8mTJ7N//35qmyFj+KNCxDBvLGzMcNCGEBMTQ/09ArmrtFUsiVlCmbqMD/t+yJHtRxg/fjydOnW6a79FixY1p2wTv8LHxweFQkFqaupNx52XLEbm7k7he+8iNiEdiWlnZCuhqYaz38KXY+DffeHkSsqtQ9DNWIfk5Ssw8o/g2KRw8w5FU0xYL+CYIAiZgiBkAseBPoIgJAqCcPEu/fKAGwN5vK8fuwlBEEYBbwLRoihqfv04gCiKq0RR7C2KYm8Xl7YZRN4eMBgMHNi/H0l5MUF9B2Jl72BsSbcl/VomqkwB/25OWNqaG1tOq6FWq9m0aRNDK8oRLC1xeHLObdv1GB+NwsaGLR++jZ2Fgi5durB///5WVtt+MZNL6TXOn7IsNS4Wfhw7duyObet0dSw/uJxrqmt82P9Dzv54lsGDB9O1670vDky5wlqWn9NV/HqDisTSErcVr6G5koRy48Z7jmOaCWthcs/AjmXw91DYsRStqohY85GcH7Eej5d+QhY+EaSP7lJwU0zYOCAAGHr9FnD92CRg8l36nQKCBUEIEATBHJgF7LixgSAIPYAvaDBgxfcv38T9kJiYiKAspb6ulshR440t57bU19fz4/pYBIOMiKhHJxhfFEW2b99OuLMzHInH4YknkDnc3iRbOzgy7XdvU1dVxeY//5GB/fqSmZlJenp6K6tuv3SJ8sTKXo6szJOTJ06iUqluaVNTX8PzB57nTNEZ3u73Nmk/pdG1a1f69u1rBMUmbkeXLl0oLS2loKDgpuM248dj2bcvJf/8F7p7bF4xmbAWIvsEfDMF1oyAxE2I4VNI7PMRnxrm4jfnH/SKGme6UKFpKSqy7na7Sz8dsBTYByQBG0RRvCwIwjuCIPy8d/tvgDWwURCE84Ig7LjDcCYeEp1Ox6FDh7CoLMfBwwufLhHGlnRbDh8+jKLWHRtHBT5hj85upYSEBFQqFV3S0kAiwXHB03dt794pmCmvvklFQR4//vNDxowaxa5du+65tGaiAZmZlN4T/CnNrqGzd28OHDhw0+MqjYpF+xdxvvg8fx70Z1QnVHh6ejJs2DDjCDZxW6RSKYMGDeLw4cM3HRcEAbc/vIm+upqSf318x/6iKJpMWHOTfRK+mQpfjYXCSzD6XepfvMwW/UiO54k8+9xz+Pv7G1tlm6FFiy+JorhbFMUQURQ7iaL4/vVjfxRFccf1+6NEUXQTRbH79ZspsU4LcerUKZws5JRlpRM5enybvALJz8/n4ukktOVmhA/2QJC0PY0tQX5+PnFxcUwbOZLKLVuxmxKNmbv7Pfv5RXRn/NJXyU9J4uqPm/Fwdyc2NrYVFHcMwgZ6YOusoDbDiuys7MZSOOXqcp7b/xxJ5Ul8FPURtWdrUSgUTJgw4b7eN5Mmtd30Lx2JXr16UVhYeEuFAkVICA5PzkG5YQN1NxT9vpGamhqkUimWlpatIbVjk5MA3z4GX42BwkQY/S68dBFll3l89d1GJBIJCxYswN7e3thK2xQdowKmibuiVquJj4/Hvr4WqZkZ4UNHGlvSLej1erZv306wUx8EAToP6Ni5YX6mpqaGjRs3MnHiRAzbdyBqtTg9+2yT+4cOGMzIZ54n/ewpFAWZnDt79oHyXz2KSGUS+kwMoCy3hu6BQ9i7dy+F1YUs2LuATFUm/4z6J8XHitHpdEybNg3JfRYM3rlzZwspN3EjMpmMIUOG3DIbBuCydClSR0eK3n0P8TYVJkyzYM3Az+bry9FQcLHRfDFoOZdSMlizZg2RkZFMnTr1pooSJhowmbBHgKNHjxIUEEDm6ROEDhiChbWNsSXdQnx8PLY2dpSm6fGLcMbaoeOnpaivr2f9+vV07dqVUB8fKtatw2bMGOQBAfc1TvcxExj4xJOkHIvDT6pn586dppJGTSSkrxv2bpYUXtBTK63lyZ1PUlhTyMdRH5NxKAOFQsHMmTMfKIfU5Ml3C5k10Zz06NGDkpKSW2qqSm1tcX3lFerOn0e1/dZoF9POyIcg5xR8O+26+boAo99pNF91eglbtmzh8OHDzJ49m/79+7fJ1Ze2gMmEdXBUKhVnzpzBUyFFW1dH5Oi2F5BfXFxMQkIC3QIGUlepJXxwx58FMxgMbN68GWdnZ0aMGEHF999jqK7GadHCBxqv//RZdB87kZyEo+hy0m8q6WLizkikEvpODqC8oIZzNddQqpX8vf/fSdyTiKurK4899lhjQe77ZdeuXc2s1sSdkEqlREVF3bYcld3UKVhERlL80Ufoq6puesw0E/YA5J6GtdPhy1FQcB5G/QlevAiDXgRzK9LT01m5ciUKhYLFixffNZeeCZMJ6/Ds27ePPn36kHLkMC6+/ngEdza2pJswGAzs2LGD4cOHk3lWhZW9HL8uHTsgXxRF9uzZQ319PZMnT0bUaCj/3zdYDRqERZem5EG+FUEQGPH0YkIHDKH2aiJHtmy47Y4/E7choBKldRFhGVEsUCzg6KajhISEMH5824ydNHF7IiMjUSqVZGZm3nRckEhwe+st9OXllH7275seM5mw+0CngfVzYM1IyDsLo95uMF+DXwK5NfX19ezdu5dt27YRHR3NhAkTTMuPTcBkwjowaWlpFBYWEuzhRnHmNbqNvr/A4tbg5MmTyGQyQgK6kH2ljLCBHkikHftlefToUXJycpgxYwZSqRTV1q3oS0txesjknoJEwvilL+PXrQeS7FQ2f/mFqaTRPbhSdoVnYp7hSsBhbOqc0CVbo9friYiIaHPvFRN3RyqVMnToUA4dOnTL696iaxfsn3iC8rVr0dyQ3NVkwu6DI/+Aqz/CsDfgpUQY/FuQWwNQUFDA6tWrqa6u5vnnn79nImMTv9Cxv+0eYXQ6HXv27GHcuHFcPhyDmVxB2OBhxpZ1E8XFxcTHxxMdHU3ysYY8P2GDPIysqmW5ePEip0+fZs6cOcjlcgy1tZR9+RUWkZFY9u3z0ONLZWZEv/x73AKCqDgVT/yeH5tBdcfkfPF5ntv3HJYyS14a8xwGeQ3WNf5EDRnaLMlvTQa49YmIiKCmpoaMjIxbHnP57UtIrK0pfO99RFGkvr6empoa0269plCcDEf+DhEzYNjrjebLYDBw5MgR1q5dy5AhQ5g+fToWFhZGFtu+MJmwDsrx48dxcXHB19OT5KNxhA0ehrwNbcPWaDRs2LCB0aNHY2/vQNKxAnzDHLF16rhv4IyMDPbv399gwIqLKXz3PVKjhlKfm4vT80uabebF3MKSab9/GxsnFxLWriEnJblZxu1IJBQksChmEQ4KB97t+i6Htx2m5wQfNNUGbHQ+lJWV3VIO535ZtWpVM6k10VQkEskdZ8NkDg64vvQitSdPUrV3L2VlZTg6Ot73rtdHDoMBdi5vMF7jPmg8XF5eztdff01GRgaLFi0yzR4/IKZXXwdEqVRy/PhxRo0Ywa6P/4K+vp7IMROMLasRURTZuXMnvr6+dO/enezLZVRXaDp0QH5RURGbf/iBqc7O1L38CumTJqPcsAHr4cPxW7cOm2ZOAmppa8es//sAmVzO5j//EVWxKW3FzxzJPcILP72Ap5UnbwW/RezOWB5//HEGjonEI8iOs3uzGTViNPv27UPfhNqDd2Lx4sXNqNpEU+natSsajYa0tLRbHrOfMQN5WBhFf/krpbm5pqXIpnDmK8g5CWP/DFbOiKLI2bNn+fLLLwkPD2fu3LnY2dkZW2W7xWTCOiD79u2jb58+HFu7hqyL5xizeBmu/m2nMGpCQgJlZWVMmNBgDK/E52NhY4Z/t475gVienMypF19iwtZt1H/4F+oLC3F99RWCYg/j9be/YtmzR4uc19bFlSf+8B56rZbv//R7alXKFjlPe+JA1gGWH1pOoF0gr/m+Rvy+eObMmUNAQACCINB/SiC1Ki3qfAscHBxMu0zbIYIgMGzYMA4fPnzLbJggleL+1h/QFRai/ewznBw79iagh6YyHw78CQKHQeRsqqur+f777zl16hTz5883pZ5oBkwmrIORmppKYWEhdUnnST15jGHznqPr8NHGltVIbm4ucXFxzJgxA5lMRo1KQ2ZiQ0C+VNZxXo6iXk91bCyZCxdROPUxAi9cwKZnT3xWfUGn/ftweu45ZK3wBeDZKZiBC5ZQXV7G5j//EW1dbYufs62yN3Mvr8a+ShenLjzv9DwJsQnMnz//pi30nsEO+IQ5cHZfNsOHjiQ+Pp6amhojqjbxIISFhaHX67l69eotj1n27Inz0qVYnDiJ6/ETt+ltopHdr4Feizjxn5w5e5aVK1fi6urKc889h6urq7HVdQg6zreeicZgfD+hniuxP9F/+ix6TZxqbFmN1NbWsnHjRqKjo3G4Xpw66VgBokEkbFDHWIrUlZVRumo118aMJWfxElRnz6IaNYqgAzH4/OdzrKOiEFo5BmXA6HE49x9GcVYGMav//UgGjO/L3Mfv4n5HN5duzLWYy6Uzl1iwYAEuLi63tO0X3Ql1dT35F9VERERw8ODBBzrnjh2mUrjGQhAEhg8fftvZMADnF56nODgY6XffUXWbTPsmgKSdkLwLVY8XWLPlJy5cuMBTTz3FyJEjHzh3nolbMZmwDsSxY8ewqCji2tHD9Bg3mYFPPGlsSY0YDAa2bNlCREQEoaGhAIgGkaSj+XiF2mPv2nY2DTwoVYcOkTZ8BCX/+AdmXl7kzprF1Zd/S79PPsbcyAkLpz2zEIOHH8lHY7l0KMaoWlqbfZn7eD3udbq5dGOaYRoZVzPuWsPOLcAW/27OnIvJZkDfwaSkpDTWlbwfevXq9bDSTTwEISEhSKVSkpKSbn1QEDjeuxfmnTuT/8qrN6WtMAGoVRh2vYLKwpevkizo27cvCxYswL0JNW1N3B8mE9ZBUCqVnNyxhcorFwgfMpzh8xe2qbX6uLg4dDodI0aMABoM2PFt16gsVXeIgPzaM2fIe+m3yIODCfxxF6nz5pLt481jM2a0id1XNjY2TFr4Atg5cvC/KynNzjS2pFZhf+Z+Xo97nS6OXYgqjqKyrJKnn34aa2vru/brFx2Atk5HcnwxkyZNYuvWrajV6vs6tylTuHG5MTbs12W8VCoV5jY2+P7ncwRLC3Je+A26igojKW1bGAwGitf/BmqKuRS4mOeXLicyMrJNfZ90JIz/7WCiWdiy+j9IctLo1LsfY5a82OpLXncjLS2Ns2fP8vjjjyORSNDW6di9MpFz+7MJH+xJUC83Y0t8KNRXU8h5/gXMPDzwWb2Ki+XlJCUlMXv27DaVMTosPJzOE6dhECTs/NdfqL9PU9He2J+5nxVxKwi1DSUyNZJAn0CeeuopFArFPfs6e9sQ1MuVCz/l4OsZQGBgIHv37m0F1Saak6CgIORyOZcvX77p+M9JWs3c3fH59FN0RUXkvfgSYn29kZS2DXJzc9n57zdxzdpJXbf5DHpiaZPeLyYenLbzTW3igYnbsZWK08fwDo9g0ouvI32AYsMthUqlYtu2bUyfPh1ra2tUJbVs+usZsi6VETUrhGFPhiKRtN8rLG1uHjnPPYdEocBnzRqulZQQFxfHU089hWUbysv2M+MmTcYyojfleTn89N+VxpbTYsRkxbAibgUBigC6X+vO1IlTGTFixH3NSvaZFIBOq+fs/mzGjh1LTk7OLV/mJto2P8eGxcbG3jQbdmOmfIvu3fF49x1qExIaE7k+atTU1LB9+3Y2ff8dY7U/Itr5YDXxfWPLeiQwmbB2TubFc5xa91/svXx4bMVbyMzNjS2pEb1ez8aNGxkwYAB+fn7kJJez8YPT1FZqiF4eScQw73Y9xa0rKyPn2WcxaDT4rFlNZm0NO3bsYNasWY0bD9oaUqmU2YtfAE8/Lh8+wJW4Bws6b8scyDrAa7Gv4Sl4MqJiBEueWUJISMh9j+PoYUVIP3cSD+eirRGZNm0au3fvprKyskn9Fy58sGLsJpqXgIAArK2tSUxMbDz263JFdlOm4LTwOZQ//EDFunXGkGkUDAYDCQkJfP755ygUCpZ2r0dRlYUw6Z+NWfFNtCwmE9aOKbyWyta/voPM2oY5f/oQc4u2NfOyf/9+rK2tGTBgABcP5bDzkwtY2sl54ne98e7cvvPz6KuryVm4iPqiInxW/ocUtZodO3Ywe/bsNh8LZGtry5QXXgIbO2LW/JuyvBxjS2o2fsr6iVdjX8VZ58zTtk/z/LPPP5Qh7jMxAAGI+eoy7u4e9OvXj23btjVptsSUMb9t8HNsWGxsbGPy3dvVjHR56SWshw+n6M8fUHPsmDGktio5OTmsXr2aK1euMH/+fMb29Ed2/GPo+jgEt520Rh0dkwlrp5TlZrPp/bfQCxIef/NdLGxsjS3pJi5dukRqaiqTJ0UT+91VjvyQil9XJx5f0Qs7l7ZlFu8Xg1ZL7tJlqK9exetf/+SiVstPP/3E/Pnz8fb2Nra8JhEUHEzE1FnoDSK7/vUX6rUaY0t6aH7K+olXDr+Co9aRd7q9w4wpDbnoHgY7FwuGPdWZ/FQlx7deY/Dgweh0Oo4fP37PvqbdkW0Hf39/7O3tuXDhAnV1dRQVFeHmdnMsqiCV4vm3vyEPDCT3pd+izcw0jtgWpqCggHXr1rFp0yYGDhzI/PnzcXV2hp0vgpkljPvQ2BIfKUwmrB2iKi5i0/tvUa/TETlzPl4BbScbPjRcZe7Zs4fJEx5j38okrhwtoNc4PyYsicDcou3Eqz0Iol5P/msrqD1xAo/33iNBr+f06dN3zDnVlhk1YSK2PfpTmp3J4f+tNrachyImI4aXD7+Mk86J1eNWM7D3wGYbO7SfOxHDvLlwIIdrZ0t47LHHOHr0KIWFdy8Fdfbs2WbTYOLhGT58OHFxcZw6dYrQ0FCsrKxuaSO1tsL7P58jSCTkPP8C+iYuPbcHioqK+OGHH1i/fj1BQUEsW7bsl3qPZ7+G7OMw9n2wbl+fY+0dkwlrZ9QoK9j03h/Q1NYiCe/J8HFtpyYkgFarZcOGDfSPHErcV9kUZ1Ux+tlw+k/thNCOA/ChoeZl4TvvUrVvHy4rXuOITEp6evpdc061ZSQSCbOX/AY8/bh4YC/Jx+KMLemB2JW8i1djX8VD8OCHGT/QybtTs59j0ONBuAfacfDbZAx1ZowZM4YtW7ZQ/4jvpmtP+Pj44OzszLFjx+jfv/8d25l7e+P96Sdoc3LIe/kVRJ2uFVU2PyUlJWzatIlvv/0WX19fli1bRt++fX+ZJa4sgJj/g4Ao6N52cks+KphMWDtCU1vD5vffolpZjiE4gomPP/xyS3MiiiK7du3CQeLHlV21iAaY9mpPQvp0jAR/pZ9+hvKHH3B4ZgEHra2pqKhg3rx5t72ibi9YWVnx+IuvIVrZsv+LT1AWFhhb0n2x/tR63jjxBr4KXzbM3ICzTcvUH5XKJIxb1BUzuZS9X1yic3A4rq6uHDhw4I59PDw8WkSLiQfHy8sLnU53z8Ldln364P5/f6QmPp7iv/2tldQ1L+Xl5WzdupWvv/4ad3d3li9fzoABA25Nm7OnoTQRk/4F7XijVHvFZMLaEYe/+ZLSnGwCRk/GM6QzQUFBxpZ0E6dOnaLwgp7y8xY4eVnzxO974+rXtmLVHpTy776j9PPPsZ4yhf1ubgiCwJw5c5DL5caW9tD4+fvTe+Y86nV6dv7zA3TtYHbHYDDw6Z5P+fDyhwTbBrNu2jps5S37WrOylzNuYRdUJXUc/CaZCRMmkJycTFpa2m3b5+fnt6geE/eHKIokJyfj7u7OmTNn7tne4YkncJg3l/L/fYNy06ZWUNg8KJVKtm/fzpo1a3B0dGT58uUMHjwY89vtnE/a1VCeaOgKcGr+GWQT98ZkwtoJ2ZcucOnQfrqOGkdyQTFjx441tqSbSL5yleM/5CAWOdG5vztTX+6BlV37NygAlbt3U/Te+1gMjWJPgD+OTk5Mnz69Tc1CPixDx4zFqfcgijPTifvuK2PLuSPFtcV8cfILJn09idXFq+ns2JmvJ32NjblNq5zfM9iBQdODSD9fQvKREqZOncqOHTuorb21MPrbb7/dKppMNI309HREUWTChAnEx8ej1Wrv2cdtxQqsBg2i4E/vUHv6dCuofHBUKhW7du1i1apV2NjYsGzZMoYOHXrnC0V1Jex+Fdy6wsDlrSvWRCNCe0tM17t3b/F0G38zNDf1GjX/e20pgiCg6B2FX0AAgwcPNrasRq4mpbBv1WWkdXYMejyIyJE+7Tr/141UHz1KzpLnMQsPZ/+A/nTu1o3hw4d3mOd3I2q1mv/87mUMBdlEv/omwX0GGFsSADmVORzIPsCBzANcLLsIgLvcnUkhk3im6zOtZsB+RhRF9n95mWtnipn8YneSsk9TUVHBjBkzbnpdCILwSCb+bKusXbuWLl260KNHD7Zv345UKmXSpEn37KevrCRzxkz0KhX+Gzdgr/0xhwAAIABJREFU3sZ2QKtSjlEU+yXlRXm4unvh7R+IucIKpGYgNb/hpzlIZL/cT9wIF3+A534Cb9NO3pZEEIQzoij2vu1j7e1D4lE0YbFrv+L0zi1EzJjHteIyFi5c2GZmYVJSUtnzxUVkNQ4Mn9uZ8EHtvw7kz9QlJpI1/2kk7u7sixpC3+HD6devn7FltSh5ubmsf+s15KKeeX/9FDvX1i8pJYoiKRUpHMw+yIHsA6RUpADgpHOih3UPnh36LF3cuhjVCGvVOjb/9Qy1lVqmrejBD1vW0rdvX3r27NnYxmTC2g7FxcV8++23vPjii8hkMjQaDStXrmTcuHGEhobes78mI4PMmbMwc3fHb906pNbGjQMVqwopj/0CSeJGHDQ5iEhAaoag1wL38Zrr/wKM+6DFdJpowGTC2jGF11JZ9+Yr+PcZQLpoxjPPPIOjY9tIdJqamsruL84jq3Zi8BPBRI70MbakZkOdlET2gmcwKOTEjBjB0KlT6datm7FltQrxP8Vw8st/4+YfwOx3/tYqZbAMooGLJRcbjVdOVQ4CAt2cuuGqcsW5wpnZE2cTEBDQ4lqairKolo0fnMLezZLB83xYu+5bnnnmGZycnACTCWtLbN++HQcHB6KiohqPZWdns3HjRhYvXnzPgu5wfVZ80WKshw7F+7NPW78+r7YW3eXt1Bz7CpuSU0gQqbEPRdF3AdLIJ8Dq+mYDg74h0F6vBX39Dfd1Nx8XJODV0xSM3wrczYS1jekUE7dFr9Oxf+XHWNjakqETeOzxx9qMAUtLS+PH1Wcxq3ah35TADmXAao4dI3fZcgwWFhwaPJhxs2cTHBxsbFmtxqARo8i4lEjRsYPEf/8NQ596pkXPd774PK/FvUZhTSEyiYx+7v14OvxpHModOH/0PL1792bIzCFtZvb3Z+zdLBn5dDh7ViaSfEhJVFQUW7duZcGCBUilUh6li8W2THV1NcnJySxbtuym476+vvTo0aOx0sW9ZlatBw3C7Xe/o+j99yn518e4vvzblpTdgMEAmUfQnv4WydWdyPRqZDJHVBHPYB+1GCuX28ziSaQgsQAzi5bXZ+KhMQXmt2FO7dhMSXYmBr9g+g8eQqdObWP3SlpaGrtWn8Ks0oWe4/zoPd7f2JKaDdWOHWQvWozWzo6fRo9i8uLFj5QBg4YZnJnPL0Xq6cvpnVtIO3Wixc4VlxvHwv0LMZeY88GQD4idGcvbEW9TGV9J7tVcnn76aYYPH97mDNjPBHZ3odc4P67E52Nd742FhQVxce0z31pHJSEhgS5dumBpeWuljqFDh1JTU9Nkw+zw1JPYz5hB2apVqHbubG6pv1CcjBjzNrq/h8E30YhXtlPoOIDKaeuxeuMaDtP/gXA7A2ai3WEyYW2UsrwcTmxej5WPP+6duzJwYPNlAH8Y0tPT2fXlCcxUbnQb7k3/KW0rW/+DIooipatXk7/idVQeHiTOnsW83/4WH5+OM8N3P5ibmzN7xR8QLW3Y9cnfKM3JavZz7Li2g+UHlxNoH8g3479hrM9YTsae5Ntvv6Vnz548/fTT7aIKQd/oQHzCHDjyfSoDe4zkzJkz5OTk0Lv3bVcfTLQi9fX1nDlzhgEDbr/JRCqVMm3aNA4fPkxJSck9xxMEAfc/vIllnz4UvPkH6i5caD6x2ho48zXiF0Ph836IRz8mR2tLavc34NVUvH+zDdtuE6C1l0FNtCim/2YbRDQYiFn1KYJUhugbTHR0dJvYjZeens72NfGYVXgSNsiDwU8EtwldD4uo11P43nuU/P0f5AUEIL71B2Y/9xy2th0jx9mD4ubhyeRX3kAnimx8/4/UVVc129j/u/w/3ox/k97uvflq7FdU5FXw+eefU1lZyfPPP0/Pnj3bzWtLIhEY/WwXLGzNiFt7jTEjx7NlyxZjyzIBnD9/Hh8fn8Y4vdvh5OTEiBEj2Lp1a2OB77shmJvj9cnHyFxdyVm6lPp7lK+6J8XJiLtfw/BRCOx8kdKiPE45TSfjsd34v5FA8NTXkVu3v4ocJpqGyYS1QS7E7CEv+Qr1nn7Mnjf/1gzHRiAjI4PtX8VhXu5NcG9Xhj3Zud2XIQIwqNVkL1uG8rt1ZPfoQZcv1zAgKqrdGICWJrRrBGNeeJlaZTnfv/cWhiZ8Sd0NURT5x+l/8NHpjxjjN4bXg15n43cb2bNnDxMnTmT69OlNCpJua1hYmzN+cQR1lfVkxmnp2iUC4Lb5w0y0DqIocuLEiTvOgt1Iz549sbGx4dChQ00aW+bggM9/PkesqSX3hd9gqKu7P3E6LVzajG7NWPi8H4aEL0khkLPdP0Dywgn6LPuKTpEDTJ9DjwAmE9bGqCwtIfa7/yLaOjBt0W/aRE3CjIwMtn51CPNSX/y7OTNyQTiSDmDA9EolKXOepObgIcqnTmHEN//Dw7PjpNhoLroNHMyAOU9TnpHGxn/+5YHH0Rl0vHX0Lf57+b9M8JxAl8wu7P1xLz169OA3v/lNm6sAcb+4+tkSNTuEnKQKrKr9mDt3Lt98843JiBmJq1evolAo8PX1vWdbQRCIjo7mwoULZGZmNml8eXAwnn//CHVSEvlvvNG0nbDKbHT7/4/6v4XCpmeozkvmitdMCmYfJPT3cfSc+gJO9yipZKJj0TajXR9RRFEkZvVn6Orr6f3kswQGGj/eKjMzk61f/4S8tCHuZezCLkil7d+7q3NySHlqLtKSEsxeX8GgBQuMLalNMzB6Osq8HJIOH2D7V6uY8syi++pfp6vjtdjXiM2NZYA4AK9kL3pF9SIiIgJJB4pxCR/kSVG6ijN7s3jjhb+QW32Zb775hnnz5t02MNxEy3H8+HEGDGj6bJKVlRXR0dFs27aNJUuWoFAo7tnHZvhwXF99heK/fURpcDAuL7xwayODHkNqDHVxn2GZF48EyLeKQN/nTbyGziPc7DblhEw8MphMWBsiKf4wmefP4NSjH0PHjDO2HDIzM9n89X4sSoJw72TH+CXdkJlJjS3roSk4doyiZcuR6XS4r/wPTjfkDjJxZ8YuXIoyP4+0/bvYbWPH+MdnNOkLTqVRsXD3QpJUSQxWD2bJgCUdznzdyJBZIahK1Rz472VGzAtH7CTy7bffMnfuXJMRayXy8vJQqVSEh4ffV7/g4GCCg4PZvXs306ZNa1Ifx2eeQZOSQuknnyLvFITtsIFQkYlYnk51egLSxB+w1BQjSGzI7zQLh1G/xdvDtLPRRAOmZK1thNpKFauXPYfBXM4Ln61BLr/3VVhLkpWVxaav92BZHIqztzVTXuqBuUX79uyiKHLu66+R/eOfSG1s6PTf/6IIDTG2rHZFbaWKb3/3IjVV1YQ9MZdxk+++aeTM1TO8evxVyilnacBSnh3ybIc1Xzei0+p56bGPCPPpw9A5oeSrL5ORkcG8efOwsDDlb2ppNm3ahJeXV5PiwX5NfX09q1atIioqioiIiFsbiCLUlEJFBpRnQEUGhqJrZK9MQF2iwX9kCQoHXWPzCruuSPsvwrbPbJCZZr0eRUzJWtsBOz/7BzqNmmmv/59RDZgoipw7d45Du05gVRqGvbslk5d3b/cGrLq6miPvvYfvjp2Y+fsT8NWXmLm7G1tWu8PS1o7HVvyR9W+9RvKuTRgkUiZMnHiLEcvMzGTL4S1sFDeik+lYOWIlA7zaRi3K1kBmLuWLfW+x9V+niF13lSEzwyCAxqVJkxFrOZRKJenp6UyePPmB+puZmTFt2jTWrl2Lr68vdlYKSNkHV7ZDydUG86WtbmwvIqCzcEExzJ7a7TquxXshWToFtz7DcejUAwcLh+Z6aiY6IO37m7WDcDHuELkXzhA2ajwB4V2NpqOmpoadO3dSkV2PTVk4Vo4Kol/sgcLK+LszHxSdTseZ06fJ+/e/CTt1Gos+ffD592dIH/H0Ew+Dq38g4174Lbv+9SHpB/ewXacjOjoag8FAUlISp0+fJqM2gwN2BzCTmbFm9Bq6OHUxtuxWp1tkBOMXR7B39SWO/JDKoCc6I/r/sjRpMmItw8mTJ+nevTtyufyBx/Bwd2dMmB0Fa2ZjW38ZQa0EK9eGMj/+g6hVuJFdJSW5WENKsQYf3yBCQkLwnyhSsnARir2p2M/5A8JDaDDxaGBajjQy1SoVq5Y9i4WVNQs/WY3MSOkorl69yq4dP+IuRKJME3DysmLibyKxcTTusuiDotfrOX/+PJfWr6fLufNY5eVhO2E8Hh9+iMTctCTQHBz94VtObPkBReduGJw9qK2txdPTE1knGf/K+BcOCge+GP0FfrZ+xpZqVPQ6A/u/vEz6uRIGTOtEiZhMVlaWyYi1AGq1mo8//pglS5ZgZ2d3/wOUp8PFDXDhe6jIQCeYUe42GOcRvyFfEczV1GukpKRQU1NDcHAwoaGhBAYGYn7DZ0rl3n3kvfQSdlOm4PHhB6Y0EyZMy5FtFVEU+e4v7yBq1ES/+a5RDJhWq2Xfvn2kX8nHubIPyrJ6Ikf60H9qYLsMwjcYDCQmJnJuwwbCzpylb2YmMnd3nN99B/vp01u/6G4HRaPRYB4YiszZHXVyIpKuMqp8DSR4JhCfFk+gfSArR63ExbLtZ7xvKRYtWsSqVauQyiSMea4LB766wvEt1+g3JRTRV2Tt2rXMnTu3SbvwTDSNs2fPEhQUdH8GrK4CLm+FCz9AzglAQAyIQhm5iPNqH46evoBk0ykcHNIIDg5m0qRJeHl53TG20XbcWDTLllL66WfIQ4JxevbZ5nlyJjokppkwI/LjD+tJ3vIdkWMmMurZ51v9/Dk5OWzdshVHQxBVaRZYWJsxcn44PuFto0j4/SCKIklJSSRs2kTwqdM4pqYidXDAecli7GfNQmJaFnhoRFEkOzubc+fOkZycTEBAAHIfGanfrqe+upadA/MRLRVM6zyNJT2WYGv+aC/5CoJwU+4og97Aga+TSD1VRJ9J/pTLUsjJyTEZsWZCr9fzySefMHPmTDzvle9Pp4W0mIYZr5S9oNdS7xBEvnMU5/TBJOdXYmtri7+/PxKJhNTUVJYsWdLkxNmiKJL38stU7d2H518+xC46uhmeoYn2imkmrI2h1+uJ2beP5D1bsXZ0JurJp1v9/LGxsZw7mYi7vhfKXC2BPZwZ/mRnFNbtK/5LFEVSU1M5vnUb/idO0C85GYmVFY7Ll+E4bz5SaytjS2z3VFdXc+HCBc6dO4cgCHh38UYxQsH/cv9HTmoOLt2tGX/UhXlXe+A6eDyqy9UYQg1gWvW9CYlUwqgF4UilAqd2ZdJrfDCiN40xYiYj9nBcuXIFBweHXwyYwQBV+Y07GG/8KZZdQ9BWoTW3J8N2MMdr/amWBOJvF0BwQACjpvndVLmhpqaGmJgYJkyY0CQtgiDg+ec/k1NaRv6K16nPz8dp8WLT0qSJWzDNhLUy5eXlbPp+PZpLZ9CWFTP993/Cv3uvVjt/SUkJW7duxbzWmfosJwwGGDIjmLCBHu3uAyI9PZ34nTvxjD+K15UrCDIZjnOfwvHZZ5E5mHYkPQzV1dWkpaWRnNwQv+Qb4ovKQ8XR8qOcLzmPgEBfj75Ed4pmpO9ISi4ns+XDPxHUdwB2vQZy8uRJ+vXrx6BBg5DJHs1rvV/PhP2MaBA59F0ySUcL6DHGF6Uilfz8PJ566imTEXsQyjMQS65y7Md1hLsrcBCVDWarIgv0msZmoiClTu6KUmJPgcaSPMtwJMEj8QsIwt/fHxsbmzueQq1W88UXXxAREcGwYcOanGbFoNVS8OYfqNy5E7vp0/B4+22ENlCGzkTrcreZMJMJa0UuXrzIvh3bsMpLR1upZOySFwkbMrxVzi2KIgkJCcQeOoKfrB+lafW4BdgyakE49q7tJ4GkKIrk5ORw5MfdOMbF4nfpMoIo4jDjCZwWL8HMzdXYEtsloihSUFBAamoqqamplJaWEhAYQLVbNRd0F4jPj6feUE+QfRCTAicxMXAi7lY3p/g4tXMLcWu/YtDMuXQeMZb9+/dTWFjI2LFjCQkJaXcm/2HJz8+/47KYaBCJ/T6Fy3F5RI70odIqjfz8PKZPn46D6QLi3pRdg8tb4NIWKL7SeFg0s0K096NW4UaFYE+hxoKsKgllBlusvTrj4eWDl5cXnp6edzVdt6O6uprNmzcjkUiYNm0aVlZNm2UXRZHSTz+l9PP/YDVwAF4ff4z0Ps9ton1jMmFGRqPRsHv3bnKTryBJuwSiSPSrb+ITfptEgC1AZWUl27dvp64UzIsDqFVq6T3Bn14T/NtNCaKKigoSz50jMzYWx/R0Ai9dRlCrsYuejPPSpZj7+BhbYrtDo9GQnp7eaLzkcjnBwcF4BHiQoE5gQ8oGCmoKcFQ4MiFgAtGdouns2PmOZkoURfZ89neS4g8T2LMPnQdGITi58tOhw9jb2zNu3DicnJxa+Vkaj507d941V5UoihzZkErioVwihnkheBVz/PhxevXqxZAhQ27acWcCUGY3BNBf2gIF5wHQe/VF5T2cQ1eV1CncqdDKqK6pwcPDA09PTzw9PfHy8sLe3r5ZLgIMBgOHDh3i4sWLPP744/jcx+eOcvMWCv7v/5AHBODzxUrMTHVqHxlMJsyI5Ofns3nzZpwkBoqPx2Lt4MC03/8JR0/vFj+3Uqnk1KlTnD93Hj+L3pReEbFxUjD6mS64Bz7A9u1WRNTpUF66TMaBGFSnT6PIzcOuogJBrwfAZvQoXJYvRx4cbGSl7Yvy8nJSU1NJSUkhNzcXb2/vxlItFZIKvkv+jl3XdqHWq+nr3pc5YXMY6j0UmaRpS4r1Wg3HN60nOT6WqrISZGbm+PfohcTZnaSCYnr27kNUVNQjYTDutBx5I6IocnRzGhcO5NAlyovu4904dPgQGRkZjBw5km7duj1yM4g3UVUIl7dhSNyIJK/hc19p1Yk0RTfOavwoq1dgb29PeXk5Y8eOxdfXF2dn5xavypCSksKOHTsYNGgQ/fv3b/L/qOb4cXKXLUdiYYH3yv9g0eXRy5/3KGIyYUZAFEWOHz/O0fh4whxtuHpgNx6dQpi64i0s7exb9Lzp6emcPHqa/PRyvJ2DECusKc+ro/MAd4bMDMFc0bZidESDAW1WFupLl6i5cBHlqVMY0tOR1tc3NLC0xKJrVyy7RaDo2hWLiAjMvLyMK7odYDAYKC4uJi8vj9zcXHJyctBoNAQFNSSWDAwMxMzcjCO5R1ibtJYTBSeQS+VMDJzInM5zCHV88Pp2osFAfkoyV48f4erxI9SqlMjkcuRuXtQqrBk1fQYRkZEd2mA0xYRBw3v2xLZrnN2XjcLajE49XLDzEzh1JQ6JRGDcuHF4e7f8RVtbQKvVUp6TQv3FzVhl7MOh8goCIkWCC1nWvVF6D8fKuyuurq64uLhga2vLrl27sLGxYfjw1gnt+BmlUsmGDRuwt7dnypQpTU4Oq05JIWfJEvRKFV5//wibVtZtovUxmbBWprq6umH5r64Oz/oakg7HENx3IOOXvYKZefOmStDrDSgLaynMVJJ8LoOCzAoEtQJ0vxgtawc5gx4PJqhX24mX0ubmUXUghurYWNSXLmOoqgJAJ5Wi9vTAIiICjyFDsI7sjrm/3yOf30tv0HO57DLH8o9xPP84iaWJeFp7EuIQQohDCKEOoXjJvdCV6cjPzyc3N5eCggJsbW3x8vLC29sbb29v3NzcEASBam0129K2sS55HTlVObhaujIrdBaPhzyOg6J5Y5IMBj25Vy5z9VgcKSePoq6uApkMuZsXgyY/Rrchw5B2wOD9ppowaDBiWYllpCQUknGxFJ3WgKWtOXa+AlmqRPzC3Bg9etR9xzG1NURRpLa2loqKCsrLy6kqzkJfmISkPA1FVRZOunz8xFwkGKi19KY2cByy7jOxDex9y+xWQUEBMTExVFZWsmDBgibHaDUnOp2OvXv3kpGRwYwZM3Bzc2tSv/riYnKXPI86ORm3P7yJ45w5LazUhDExmbBW5Nq1a2zfvp2u4WFUn08g49wpek16jKFPLnhoI6Gr11OYXklpThVludWU5lVTnl+DQX/9fyiI2LrI8QhwxNnHGievhpulrfGXfkRRRHvtGlUxMVTGxKC5kgSAxsODAjs7dP5+eAwZQudRo7B+kEzXHZD86nyO5R/jWP4xThScoEpbhYBAuFM43Zy6kVWRRaoylZL6ksY+cuR4y70JdQylu2d3urp1JcghCAtZQ2b27Mps1iWvY1vaNmrqa4h0ieSpsKcY6TcSM0nL79rS63RkX7pA8tFYrp44il6rQSpXEDpgCF2GDMc7vAsSSftLEnw7Vq1axaJFi+67X71GT2ZiKWmni8m6VIZeZ0BmKVJrVkT4AG9GTBzQ5HxVD0VNGWTFQ2Y85J4GMwuwdm0o32PtAtZuv9y3cm14TCZHq9VSWVmJSqWioqKCivJyNCXXEMpSMVdl4kw57lIVDvoSFPqqxtOJUjm4hCAEjYKu08GtK9xmplSpVHLw4EEyMjIYOnQoPXr0QCo17mvm4sWL7Nu3j9GjR9O9e/cm9THU1JD36mtUHzqE44IFuL726iN/sdlRMZmwVkCv13Pw4EESExMZN2I4Z77/mpLMDEYsWEz3sRMfeNwapYasS2VkJpaSk1SOTmsAwNxSgt68Fo2gwi/UnZ4Dw/Hq5NKmAu1FUUR96RKV+/aj3LcXQ04uABVubuT7+iIM6I9bt26Eh4fj6Nj+EsQ2NzX1NZwqPNU425VZmQmAs9yZcMtwfEVfnGucqS2rpbKyEhcXF7y9vXH2cEZto6ZAV0CqMpWr5VdJqUihVlcLgICAn60fjgpHzhWfQyqRMtZ/LE+FPUVXZ+PVKtVptVxNOM7RnVupzE5HMBiQW9sQOmAI4YOH4RnS+ZH/UtLW6ci4UELq6WKyr5QhGkA00+Df3Yn+Y8Nw9m7GmbGaMsg62mC6MuOh+HLDcTNL8OqFKOoRq4qguhiJtuq2Q6hRUI0lGpkdOnMb7KjCRlOAVK/+pZHCHlxCwTnk+s9QcA4Ge1+4iwGvq6vjyJEjnD9/nr59+zJw4MA2FVtYXFzMhg0b8PPzY/z48U1KzSLq9RR98CEVa9diM3o0nn/9CxJTKasOh8mEtSAqlYq0tDTOnDmDtbU1Q3r1YM8nf0VdVcXEF1fQqVff+xpPNIgUZ1eRmVhKVmIZJdkNH3bWDnKcAxWI1lWk5iZi52RF3759CQsLM/pV4I2IOh3K4yco2r4dXXw8UqUSgyCg9PZG17sXtqNG4xPZDScnpw4dD9QUKrWVXCm7wvmi88TnxHO54jI6UYcZZniL3jhVOeGucSfQPhAXZxecnZ1xcnLC2dkZR0fHu/7fDaKBvKo8UipSuFpxlavlV8mvyWeo91Bmhs5sc+WEigoKSNi/m8yzCWiK8hFEEbmNLcH9BxM5fDRugUHt7vVyP8uRTUFdU0/6uRIuHsmkLKsOELB1kRPS14PA7i44e1vf39+othwxMx5d2mGErHhkZVcB0EsVqGw7U2QZQp4sgByDC9W1aiorK5FKpdja2mJvbYGzhQFHcx32Mi02kjqsxBoUOhVSdTlCdQnUloGt562Gy8r5tjNcd0Kn05GQkMDRo0cJCwtj6NChbXZZVqPRsHPnTsrKypgxY0aT042U/+9/FH34FxTdIvD5/HNkj9Au4kcBkwlrRnQ6HdnZ2aSlpZGWlkZNTQ2dOnUiNDQUK72Wnf/4ADOFgsdW/BG3wKAmjalV68hNqiAzsZTMS2XUVWoRBLB2kyG1r6NaKKCsOh9nF2e8vb3p0aMHHh4eLfxM741araa8tBTlxYvUXExEf+kSFpcuYa5WY5DJ0IaHYzlyBF5TpmDt7n7vATsgOp2OyspKiiuKSSxO5Er5FdKq08jWZFMulje2c9Y7EyQLort9d3p59MLdxR1nZ2esrKzanfl4WCoryjm5bzdpJ49SU5CLIIqY29oR2HsAfcZOwMUvoF38TZrbhN1ItVLN4e1nSD9XilRtDQjIrUV8Ogn4BOiws1Giq1Oiq63EUFeJXl2JqKlB1FYj1ahwqruGs64QAC1mFJr5UWIVisohArVjOJY2dlhZWd10s7GxaXLweXMgiiKJiYkcPHgQd3d3Ro4ciYtL27p4uB0/52SMi4sjOjqa0NCmbXCpjIkh/7UVyJydsb7fYH0BzDw8kXcKxDywE2aeHo/8LHJbwmgmTBCEccDHgBRYI4rih796XA58A/QCyoCZoihm3m1MY5gwpVJJamoqaWlpZGVl4ezsTFBQUENOJQ8PBOBS7AEOrP43jp7ePPa7/8PW+fZB8Fq1jupyDVUVapSFtWRdKiUvRYlBLyIxE5HY1lElFGDuqMXb36Mxz42Hh0erZx43GAy/xHVUVFBRVkbttWsYUlIwy8rGrqQE+4oKpDodAKKlJeYDBuAyeRI2UVFILNtPEliAam01GaoM0lXppKvSya/Ox0Jmga25LXZyO2zNbbGWWSNHjlyUY6Y3Q6aTgQY0ag11dXXU1tairFKSXp1OjjaHYmkxKoUKpUSJKDS81xxkDgRZBxHuGE6kWyS9vXvjYGlK0Hk7aqsqOb1/D8nH4qjKzQLAzNYen+696Dt2Ih6BndpsDNndTJgoiuj1eurr62+6aTQaNBoNWq0WjUaDvqYCoTIPSXUBZrWFmNUVI9eUYqEpx1JXjpVehVZvRaamD9fU/cnVdsOAGZaScgLkCXRSnMDT/BJSoSG1iyhIMZhZonOJAP/ByIKHIfXuA7K2s6wHDdUwYmJikEqljB49Gj8/P2NLum9yc3PZvHkzBoOhMWeZp6cnHh4eWN7hs7Hu4kXyV7yOrrz8to/fEZ0OQ21t46+CQoF5QADywEDMOwUiD+yEvFMgZn5+SNrQEu6jglFMmCAIUiAFGA3kAqeA2aIoXrmhzQtAN1EUlwiCMAt4TBTFmXcbtzVMmE6nIysri7S0NFJTU6mrqsTHzRUXO1ts5GZoKlVUlZVSVVZKZWkJ1eVlGPTWodZvAAAU+UlEQVQ6fLt2Z9j8l9DUSamuUFNZWoeypIaq8jqqKzTUVerQa2/+exvM1egtlDj4meEX5oK3jzeenp53fJP+GlEUMVRWoistRVdahr6stPG+rrQUXVkpBlUlgqUlWFtjsLREb2GBzkKB1twcjZk5GpmUWqmUOomUagFqdTpqa2rQFxbiUVODW2UVdqUlKPLykagbYjsEuRxFly5YRHRF0bXhZu738LsYRVGkUltJmbqMsrrrN3UZpXWljfcrNZXYym1xtnDGSeGEk8X12/X7zhbO2JjZNP4v9Xo9Op2u8UuuqLqIDFUGWVVZZNdmk1ubS74mH6VO2ahDggQ7wY56sR61qEYn6O6oWUBAISiwklphLjWnSFuEXmz40nNQONDVqStdnRtu4U7hOFs4P9Tf6FGlVqXkYuxPXIo9iOq6IRMBwcwcmcICcytrFDa2WNk7YOPohL2LK45u7ji4umFl74CFrS2CIEGv16PX6zEYDA3367Xo69UYtGoMOg2GevX1mwaxXtNwTK9Hd73f7W869HrDL2Pr9az95r/MemJawzg6LaJOg6jXgk6LqNciE0TMpWAmAXOpiLkgYiPUYGNQYaVXYllfjplBfdPfQBSk6Cyc0Vt7INp4gq0nUitHZJb2SORWqA3WpKTLSEmRUlygQDRIQVKPwqkOtxBrwvsH4uPv0zqB/U1EFEV0Oh1qtZqKigri4uKoqKhg5MiRhIWFtYtZzzshiiJKpZK8vDzy8/PJz8+noKAAKyurW4zZw84y6ioq0Kano7l2De21dDTp6WivXaM+P/+XRlIp5t7emHfqhDwwAKmDAxJLSwQLCySWlkgsrZBY/nzfEsn144KFhWlm7SEwlgkbALwtiuLY67//HkAUxQ9uaLPvepvjgiDIgELARbyLqJY2Yes//BMlFzMRxXoMogaDqAEMv2olIAiWCBJLBMEaQWKNIHVEIu9Og/e8oaWhColeicSgRKqvQGJQIrn+U6ovR2pQ3Zc+iQEs6kSs6kSsag1Y1IrIfi0P0Eug1kKg1kJArRAw14rINaDQiCg0IpK7/Nt10ob+8utpunQSKHWWUugqpchVSpGrjDJHCf/f3r0Hx1Wedxz/Pru6IjvGQeBgBSG5Fra5u5BmbEiAhjghoRHT2NimtCkBkrZM05lOOiWTtAN0muukQztNS01CEgLFBmYKxiUNcQLJBJSAY1wbDK5tYRtMjK8xFpa02t2nf5xX1lqWpdXl7NFKv8/M63333PY5zx5Lj949e46nRv/DMYfTkc5zJJ2jI53jSDpHboDNphym5NJMzaWozafoTOV5O53jnXSe/ADLV+Sj5afkUkzNpanJpzhQmWVfZQ+d6b6dr84bp/dUMiO0M3oqmdFTRX2ugjSGYWBG1vJ0ppzOVJ530jk6U3mOpnIctTxHe/upPBnLM6OnisZMNWf1VDM9VxFtIybD+99b7OUShrmuD/r0hCmD/sgpmNlvreMW6emBjg4nl+1r2ayRyRk92RR5HyjnTnU6R6XlSJmTtjwVlidtTio8pi0f5vVNS+GYlea0jQxVdFsN3VZNl9WEfg3dqRoyFjXMijqnytyp7IHKLqjKOCk38uZ0pXLk8LCJvu30f36yacPn/d7zvuf9f9SbGalUatgXW/Xwj0dbD9vm+Md+y0Wv17d3vbtqx/XtuOmjeZ3e1+jLph9byd3D22qkwsInvj8jex/MnVQ+SzqbJZ3Pks7lSOeypHMn/8NyIG6GW7QHHhLixwK1Y33v3VOjYLmRHkPH/78/cWr/JwXsuIe+fr9QZpxzHkvvuG2E8RVnsCIszs+3GoDXC56/Abz/ZMu4e9bMDgOnAfsLFzKzzwCfAWhsbIwrXgCO7jtENt+BWR0pexeVqVpSVJOmhjTVpPOVpL2ClOexbBbzHJbPkvKjVGaepCpziKrMISozh6jK/JaU94xpfPkUdNTCgTpoPwOOnAJv11l4DO0UOFpL+A8Dxx+lhjlUZ+CULqjrKnjshFO6oa7TqczCb+qNne+BN+shW+FANrTuE+IaKQNOzTln5pzpmTzTc867c870bEE/50zNOwP9WM4DR1LGwbRxKLSDFalj/UPpFIcqjIMp4z3ZPBe9k6cxk6exJ0djJs/puZH/eJAEVQCnQg8Vx1qWND1UkPE0XfkKurJVdOYq6Mqm6c6myeRS9GQryXkVPW7kC5oD7hZ9+9BDcdD723SEf6i6+/G/oOj7ZdT3SMH84349B3ngaGgw0PjVUMdvT2hpIO1GVXmdBjw6NnR+Cvmxf0bwUsN4odG8zkjlQ+sBSIVW4PjwhxfcgLvu/R5L7WSv22/64T17Yg9lMGVxhUR3XwGsgGgkLM7Xuvmbd8e5eYnB5DzlX8a7OE/Md3fy+TxdXV3s2rWL9vZ22tvb6e7uprm5mVmzZjFr1iym6Zp7E0o+nyeTydDV1XXs/MGuri7279/Ps88+O6wvAsj4EGcRthsovLvpe8O0gZZ5I3wcOY3oBH0RETkJMyOdTlNXV8e8efOYN28eEH2JqL29ne3bt7N27Vpqa2uPFWRNTU3U1NQkHLmMRiqVoqam5oT38ZxzzqGxsZGHH36YvXv3cvnll5f1uXSTSZznhFUQnZj/IaJi6wXgBnd/uWCZ24ALCk7M/0N3v36w7SZ9iQoRkWLEORJWDHdnz549x0bJ3njjDc444wxmz57NZZddVvJvW0v8jhw5wsqVK5k+fTqtra3j6gsYk1mSl6j4GHA30ekI97n7P5rZXcA6d19tZjXAD4D5wEFgmbu3D7ZNFWEiIsPX09PD66+/TltbG3V1dbS2tmq0ZALKZrM88cQT7N27l2XLlukj6XFAF2sVESmxkd47Mm6ZTIbvfve7XHDBBSxcuDDpcCQG7k5bWxttbW0sWbIk9i+0yeAGK8J04Q8RkRh89rOfTTqEAVVVVbFs2TLa2trYunVr0uFIDMyMhQsX0trayqpVq1i/fn3SIclJqAgTEZlkpk2bxpIlS3jsscfYv3//0CtIWZo9ezY33XQTzz33HE8++SS5XC7pkKQfFWEiIpNQY2MjV199NQ899BCdnZ1JhyMxqa+v55ZbbuHQoUM88MADHC24vZEkT0WYiEgMVq9enXQIQ5o/fz4tLS08+uij5PMD3HpDJoSamhqWL1/OzJkz+fa3v81bb72VdEgSqAgTEYnBJZdcknQIRVm0aBEATz31VMKRSJxSqRQf/vCHufLKK7n//vt59dVXkw5JUBEmIhKLhoaGpEMoSiqVYvHixWzdupUXX3wx6XAkZhdeeCE33HADa9asYU/Ct+wRFWEiIpNebW0ty5cvZ+3atezatSvpcCRmDQ0NXHTRRWzevDnpUCY9FWEiIkJ9fT3XXXcdjzzyCIcPH046HInZvHnz9JHkOKAiTEQkBrfeemvSIQxbS0sLCxYsYOXKlWQymaTDkRg1NDTQ2dnJgQO6XXOSVISJiMRgxYoVSYcwIgsWLGDGjBk8/vjjid77UuJlZsyZM0ejYQlTESYiEoNy+XZkf2bGtddey9tvv83Pf/7zpMORGM2dO5ctW7YkHcakpiJMRCQG5XyrmIqKCq6//nrWr1/PK6+8knQ4EpPm5mb27dtHR0dH0qFMWirCRETkBFOnTmXp0qWsWbNGF/ecoNLpNLNnz9ZoWIJUhImIxODMM89MOoRRmzlzJtdcc41O1J/A5syZoyIsQSrCRERi8OabbyYdwpg4//zzmTZtGjt37kw6FIlBS0sLO3fupLu7O+lQJiUVYSIiMbjjjjuSDmHMNDc389prryUdhsSgurqaxsZGtm3blnQok5KKMBGRGNx5551JhzBmmpqa2LFjR9JhSEzmzp2rS1UkREWYiIgMqqGhgQMHDtDV1ZV0KBKDOXPmsG3bNnK5XNKhTDoqwkREZFAVFRU0NDTovLAJasqUKdTX12u0MwEqwkREYrBu3bqkQxhT+khyYps7d66uCZcAFWEiIjKk5uZmFWETWO/V83WrqtJSESYiEoNLL7006RDG1MyZMzl48CCdnZ1JhyIxOO2006itrWX37t1JhzKpqAgTEZEhpdNpzjrrLI2GTWC6oXfpqQgTEZGi6LywiU2Xqig9K7fPf81sHzDYV3Tqgf0lCmeyUW7jpfzGR7mNl/IbH+U2XqXI79nufvpAM8quCBuKma1z94l1MsY4odzGS/mNj3IbL+U3PsptvJLOrz6OFBEREUmAijARERGRBEzEImxF0gFMYMptvJTf+Ci38VJ+46PcxivR/E64c8JEREREysFEHAkTERERGffKqggzs4+a2RYz22Zmtw8wv9rMVoX5vzKzpoJ5XwjTt5jZR0oZdzkYaW7NrMnMOs1sQ2j3lDr28a6I3H7QzNabWdbMFveb9ykz2xrap0oXdfkYZX5zBcfu6tJFXR6KyO1fm9lmM9toZj8xs7ML5unYHcIo86tjdxBF5PbPzGxTyN8vzOzcgnmlqxfcvSwakAa2A7OAKuB/gXP7LfMXwD2hvwxYFfrnhuWrgeawnXTS+zRe2ihz2wS8lPQ+jNdWZG6bgAuB+4HFBdPfDbSHx+mhPz3pfRpPbTT5DfM6kt6H8dqKzO1VwCmh/+cFPxd07MaY3/Bcx+7ocvuugv4ngP8J/ZLWC+U0EvZ7wDZ3b3f3DLASaO23TCvw/dB/FPiQmVmYvtLdu939NWBb2J5ERpNbGdyQuXX3He6+Ecj3W/cjwI/d/aC7HwJ+DHy0FEGXkdHkVwZXTG6fdvej4ekvgfeGvo7doY0mvzK4YnL7dsHTOqD3BPmS1gvlVIQ1AK8XPH8jTBtwGXfPAoeB04pcdzIbTW4Bms3sRTP7mZl9IO5gy8xojj0dt0MbbY5qzGydmf3SzK4b29DK3nBzezPwwxGuOxmNJr+gY3cwReXWzG4zs+3A14HPDWfdsVIR14Zl0vgN0OjuB8zsEuAxMzuv318ZIuPV2e6+28xmAT81s03uvj3poMqNmd0IXApckXQsE9FJ8qtjd5Tc/VvAt8zsBuBLQMnPXSynkbDdwFkFz98bpg24jJlVANOAA0WuO5mNOLdhyPYAgLv/mujz83Nij7h8jObY03E7tFHlyN13h8d24Blg/lgGV+aKyq2ZXQ18EfiEu3cPZ91JbjT51bE7uOEefyuB3tHEkh675VSEvQC0mFmzmVURnRze/xshq+mrZBcDP/XoTLvVwLLwDb9moAV4vkRxl4MR59bMTjezNED4i6yF6CRciRST25P5EbDIzKab2XRgUZgmfUac35DX6tCvBy4DNscWafkZMrdmNh/4D6ICYW/BLB27QxtxfnXsDqmY3LYUPP04sDX0S1svJP0thuE04GPA/xGNtnwxTLuL6AAFqAEeITqR7nlgVsG6XwzrbQGuSXpfxlsbaW6BTwIvAxuA9cAfJL0v460Vkdv3EZ138A7RyO3LBet+OuR8G3BT0vsyHttI8wssBDYRfRNqE3Bz0vsy3loRuV0LvBX+/28AVhesq2M3pvzq2B2T3P5zwe+up4HzCtYtWb2gK+aLiIiIJKCcPo4UERERmTBUhImIiIgkQEWYiIiISAJUhImIiIgkQEWYiIiISAJUhIlIUcysI4ZtXmxmHyt4foeZfX4U21tiZq+Y2dNjE2HpmNn3zGzxKLdxXD5FZHxTESYiSbqY6Ho+Y+Vm4FZ3v2oMt3lS4e4R48lY51NEYqQiTESGzcz+xsxeMLONZnZnmNYURqHuNbOXzewpM6sN894Xlt1gZt8ws5fClazvApaG6UvD5s81s2fMrN3MPneS119uZpvCdr4Wpv09cDnwHTP7Rr/lp5jZT8xsfVivtSDmV83swRD7o2Z2Spi3w8y+HpZ/3sxmh+nfM7N7zOxXwNfD6NMvw/79V7ia+Vwze77g9ZvMbFNvnCF3L5nZCjOzIXL9OTPbHLa/MkyrM7P7QlwvmlnrQPk0sytCf0NYbmrx77KIxC7pq9qqqamVRwM6wuMiYAVgRH/IrQE+CDQBWeDisNzDwI2h/xKwIPS/CrwU+n8K/GvBa9wBPAdUA/VEV7iv7BfHTGAXcDpQAfwUuC7Mewa4dIDYK4B3hX490VXcLcTswGVh3n3A50N/B31X2v4TYE3ofy/sczo83whcEfp3AXeH/gagOfT/FvhS6L+7IK4fEO4yEba7eIDY3wSqQ//U8PjlgtyeSnRl8LoB8vlEwb5NASqSPo7U1NT6mkbCRGS4FoX2ItGtquYS3V8N4DV33xD6vwaazOxUYKq7t4Xp/znE9v/boxvD7wf2AjP6zX8f8Iy773P3LPAgURE4GAO+bGYbiW4F01Cw3dfd/dnQf4BoNK3XQwWPCwqmP+LuOTObRlQY/SxM/35BLA8DvaN7S4FVoX+Vmf0qjIz9PnDeELFvBB40sxuJilyI8n+7mW0gKjxrgMYB1n0W+KcwonhqyJeIjBMqwkRkuAz4irtfHNpsd/9OmNddsFyOaARquMZiG/39EdHI2SXufjHR/fhqwrz+927zIvrvFPGaq4DrzewcwN19q5nVAP9GNOJ1AXBvQRwn83HgW8DvAi+E89AM+GTBe9Do7q/0X9HdvwrcAtQCz5rZ3CLiFpESUREmIsP1I+DTZjYFwMwazOyMky3s7r8FjpjZ+8OkZQWzjwDDPU/peeAKM6s3szSwHPjZEOtMA/a6e4+ZXQWcXTCv0cx6R7luAH5RMK9wJKuNftz9MHDIzD4QJv1xbyzuvp2oiPw7+kbBeguu/SF/g34b0sxSwFnu/jTRR5rTiD5W/BHwl73nk5nZ/LDKcfk0s99x903u/jXgBaJRSxEZJ8bbN3tEZJxz96fMbB7QFmqADuBGooLjZG4G7jWzPFGRcjhMf5q+j9W+UuTr/8bMbg/rGtHHl48PsdqDwBPhI8B1wKsF87YAt5nZfcBm4N8L5k0PH2F2ExV7A/kUcE84ob8duKlg3irgG0BziP23ZnYv0Tlye4gKo8GkgQfCx54G/EvYxj8AdwMbQ6H2GnAtJ+bz8lB05oGXgR8O8XoiUkLm3n8kXkRkbJnZFHfvCP3bgTPd/a8SDgszayI64f78AebtIDrJf3+JwxKRSUIjYSJSCh83sy8Q/czZSfQtPhGRSU0jYSIiIiIJ0In5IiIiIglQESYiIiKSABVhIiIiIglQESYiIiKSABVhIiIiIglQESYiIiKSgP8HLsnQXZF4GycAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "32Ra6g8wiyBs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "c7afd4fa-52da-4acd-98cd-ed9e9d351f3a"
      },
      "source": [
        "plt.plot(pvals6, conjectureVals)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Conjectured Probability of Piercing Numbers (n = {0} sets)\".format(numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"τ=\"+str(i) for i in range(1,numTau+1)], loc=1);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GcNipvYftadu5f+X9NI9tzsvnv0xQQFApuf+hqKiI5ORkCgoKKiXH6+1fJ6Mwg9+2/EZEUESlyjCT0NBQkpKSCAoqvy3Ko0YMUms0Go0130aIy/jD4ZzD3Pn9nUSHRPPGwDeIDPbMg3dycjJRUVE0adKkUr0NpRQHsg+QW5RLs9hmXjdnVQWlFGlpaSQnJ9O0adMql+fXzvo0Go2mGKMHYSiIzMJM7lh+B4X2Qt7895vUDq/tcTkFBQUkJCRU2hQlItSPqI8gHMo5hD+5KxIREhISKt07KolWEBqNpkZQ6OxBFNoLufeHezmYfZBXB7xKi7gWFS6rquMUQQFB1IuoR35RPmkFFXVSbC7eHIPRCkKj0dQIrPk2gsICeHTVo/yW8hvP9XuOHnV7+EyemJAYooKjSMlLocDmnS92f0MrCI1GUyMozLexO3cn3+7/lge6P8DFTS8uP5OJiAj1IuthEQuHcw5Xi6lpwYIFtGvXDovFQnUsGNYKQqPR+D1KKaz5NjZlbGRIsyGMbVuRAHrmEWRxmpps+RzPP15+hirSvn17Fi5cyHnnnWd6XaAVhEajqQEU5FtRDrCEwH97/tevXF3EhMQQHRJNan6qx6aml19+mc6dO1O3bl0aNGhA586dmTZtWrn52rRpwznnnFNVkT1GT3PVaDR+z4d/fAw05sJWFxATEuO1cp/8civbDlc9KKFCkW/Lx8JRujaswxPD2pWZfvz48YwfP55JkyYRGRnJAw88AED//v3Jzs4+Lf2UKVMYOHBgleWsKFpBaDQav2Zvxl7mbf6EkTxIp6QOvhbHLYIQbAnGai+kyFFU6XJWrVrlRamqjlYQGo3Gb7E77Dz+y+NEEQuU7qivsjwxtOwv/YrgUA52p++u0MK5kqYy3YPQaDQaD/l4x8f8kfoHjzd/kZTfOWUltb9hEQvxofEnp716EjsiMTGRQ4f+cfznbz0IPUit0Wj8koNZB5n22zTOSzqPTtFGyHpv9yC8TVxoHCLCiYKygmn+w8iRI/nmm2+4+eabPUq/aNEikpKSWLNmDUOGDOGiiy6qirjl4t+trdFozkocysGkNZMItAQysfdEjm+0A/7dgwAItAQSGxJLRmEGtcNrE2gpW966detWaD3DiBEjGDFiRFXF9Bjdg9BoNH7Hp7s+Zd3RdTzQ/QHqRtQ1YkHg/z0IgPjQeJRSpBek+1qUKqMVhEaj8SuO5Bxh6sap9KrXi5EtRwLGKmqxCIHB/v/KCg0MJTI4khMFJ2p8zAj/b22NRnPWoJTiybVPGiYml+A/xa6+/WmBXFnEh8Zjc9jIslZ9jYUv0QpCo9H4Dcv2LWP1odX8p+t/SIpKOnm8MO/0YEH+TGRQJMEBwaTlp/mVO/CKohWERqPxCwrthbyy8RVax7dm9DmjTzlnLbDViPGHYkSEhLAECmwF5NvyfS1OpdEKQqPR+AVzt8/lcO5h7u92PwGWU3sLJaPJ1QRigmMIkAC/ixdREbSC0Gg0PiejIIO3N79Nvwb9OLf+uaedd40mV1MIsAQQFxpHVmEWVrvVK2U++OCDtG7dmo4dOzJixAgyMjK8Um5paAWh0Wh8zozNM8i15XJ/t/vdni/Mq3k9CDAGqwGPF86Vx4UXXsiff/7J5s2badWqFc8//7xXyi0NrSA0Go1POZh1kHk75zGixQhaxrV0m6Ym9iDACE0aHRJNekE6dof95PHKuvseNGgQgYFGO/Tu3Zvk5GTTZAe9klqj0fiYV357hSBLEHd1vsvteeVQWAvtBIeb8Lpa+ggc3eLdMut2gMEvnNxNCE0gqzCLzMJM4sOMHoU33H2/9957XHXVVd6VvQRaQWg0Gp+xKWUT3+7/ljs73UlieKLbNNZCOyj/d7NRGuFB4YQFhpFWkHbSV1NpeOqs79lnnyUwMJBrr73WW2K6pWa2uEajqfEopZiyYQq1wmpxfbvrS01XmGfEVzDFxOTypW8mCWEJJGcnk1OUQ1Rw1MnjlXH3PWvWLL766iu+//570xcOagWh0Wh8wvIDy/kj9Q8mnTuJ8KDwUtNZ8w3bfXBozX1dRQVHEWgJ5ETBiVMUREXdfS9btozJkyfz448/Eh5eept5Cz1IrdFoqp0iexEvb3yZFrEtGN5ieJlpix31hZgxBlFNWMRCbEgsOdYcbA7byeMVdfd99913k52dzYUXXkjnzp0ZN26cWSIDugeh0Wh8wCe7PuFg9kHe+Pcbpy2KK0lhDfLkWhbRIdEczz9OtjWbuNA4oOLuvvfs2WOWeG7RPQiNRlOtZFmzePOPN+ldrzf9GvQrN/3JHkQNVxChAaEEBQTVKAd+ZSoIEbGISJ/qEkaj0Zz5vLP5HbIKs5jQfYJHg6w1KRZEWYgI0cHR5FpzTzEz+TNlKgillAN4vZpk0Wg0ZzhHc4/y0faPGNp8KK3jW3uUp/AM6UGA4Z9Jocix5vhaFI/wxMT0vYhcLpWYTyUiF4vIThHZIyKPuDnfSERWiMjvIrJZRC6paB0ajabm8Pbmt3Hg4O7Od3ucx5pnIyDQQkBQzbeIhwaGEmSpOWYmT1r8dmABYBWRLBHJFpFyr05EAjB6H4OBtsDVItK2RLL/Az5RSnUBRgNvVEh6jUZTYzicc5hFexZxecvLqRdZz+N8hQU1KxZEWYgI0SHR5BTlnOJ6w18pV0EopaKUUhalVJBSKtq5H+1B2T2BPUqpvUopKzAPuKxk8UBxWTHA4YoIr9Foag4zt8xEEG7pcEuF8lnzbYSEB5kkVfUTHRyNUorsotMXxPkb5SoIMRgjIhOd+w1FpKcHZTcADrrsJzuPuTIJGCMiycAS4J5SZLhNRDaIyIbU1FQPqtZoNP7EoZxDLN69mMtbXk7diLoVymvNtxEcemb0IADCAsMItASSVVhxM9PEiRPp2LEjnTt3ZtCgQRw+bO43tScmpjeAc4FrnPs5eG/g+mpgllIqCbgEmCMip8mklHpbKdVdKdU9MdG9vxaNRuO/zNw8E5GK9x6gONxozR+gLqZ4NlNlzEwPPvggmzdvZtOmTVx66aU89dRTJklp4ImC6KWUugsoAFBKpQPBHuQ7BDR02U9yHnPlZuATZ7lrgFCglgdlazSaGkJydjKf7/mcK1pdQZ2IOhXOb5iYzhwFATD7rdmM/NdI6tevXyF339HR/1j3c3Nz/cIXU5FzwFkBiEgi4PAg33qgpYg0xVAMo/mnF1LMAeDfwCwRaYOhILQNSaM5g3h789tYxFKp3gOYGwvixXUvsuPEDq+W2Tq+NQ/3fLjMNA9NeIjLbrqMGf+bQYOEBhVy9/3YY48xe/ZsYmJiWLFihVdlL4knrT4NWATUEZFngSswZh+ViVLKJiJ3A98AAcB7SqmtIvIUsEEp9QUwAZgpIuMxFNANSilVyWvRaDR+xsGsg3zx1xeMbj2a2uG1K1VGYQ0NFlQWxWYmq92K6yvPE3ffzz77LM8++yzPP/88r732Gk8++aRpcpbb6kqpj0RkI8aXPsBwpdR2TwpXSi3BGHx2Pfa4y//bgL6ei6vRaGoSMzbPINASyM3tPXNGVxK73YHN6jBtkVx5X/pmEh0cDQKF9sKTxyoSMOjaa6/lkksu8a2CcBKO0QtQQJhp0mg0mjOGA1kH+GrvV1zd+upSgwGVR1Gxq+8zrAcBEBEUQUKtBI6lHDt5rLwexO7du2nZ0gjL+vnnn9O6tWer0SuLJ9NcHwc+AOIxBpDfF5FyTUwajebsZsbmGQRZgri5Q+V6D3BmudkoiYgwYuQIVny3gptuusmjPI888gjt27enY8eOfPvtt7z66qumyuhJq18LdFJKFQCIyAvAJuAZMwXTaDQ1l32Z+/hq71eMaTOGWmGVn5h4pjjqK40WDVswf/l8GkU38ij9Z599ZrJEp+LJNNfDGLOLignh9OmqGo1Gc5IZm2cQbAnmxvY3VqmcMyUWRGlEBEVgEUulFs1VB6W2uohMxxhzyAS2ish3zv0LgXXVI55Go6lp/J35N0v+XsLYtmOr1HuAMycWRGlYxEJ0cDRZ1izqqXpYTl8n7FPKavXiMEcbMaa5FrPSNGk0Gk2N560/3iIkIIQb2t1Q5bLOdBMTGJHmMgozyCvKIzI40tfinEKpra6U+qA6BdFoNDWffZn7WPr3Um5odwMJYQlVLq8w78zuQYCLmcma5XcKwpNZTJc64zWcqIi7b41Gc/bx7p/vEhwQzNh2Y71SnrWguAdx5jjrK4lFLEQFR5FlzcLf1gl7YvB6BbgeSKigu2+NRnMWcTjnMF/99RWXt7y8ymMPxRTm2wgMCcAS4F+2eW8THRyN3WEntyjX16KcgietfhD4U7vA0Gg0ZfHen++BUOWZS65Y82yEnEGuvksjMjjypJnJE1566SVEhOPHj5sqlyeGvYeAJSLyI3ByTbhSaqppUmk0mhpFSl4Ki3Yv4rLml1U43kNZmOmoz5+wiIWIoAiPehAHDx7k22+/pVEjz9ZOVEkuD9I8C+RhrIWIctk0Go0GgA+2foBN2Srtc6k0Cs9AV98AL7/8Mp07d6Zu3bon3X1/NPMjrHYrVru1zLzjx49n8uTJprv6Bs96EPWVUu1Nl0Sj0dRI0gvSWbBrAZc0vYSG0Q3Lz1ABrPk2QiPNCzd69LnnKNzuXXffIW1aU/fRR8tMM378eMaPH8+kSZOIjIzkgQceoNBWSJ9+fbDmWwmQU81qxc76Pv/8cxo0aECnTp28KnNpeKIglojIIKXUt6ZLo9Foahxzts2hwFZQ6XgPZVGYbyM68ezwDxocEMzHSz4mPCichlGnK9q8vDyee+45vv22+l7FniiIO4AHRKQQKAIEUHomk0ajybJmMXfHXAY2Hkjz2OZeL9+abzN1DUR5X/pm42omEhHGXjqWrOwsQgJCTkk3ZcoU6tSpw99//32y95CcnEzXrl1Zt24ddet6b9zHFU/iQejxBo1G45Z5O+aRU5TDrR1uNaV8a779jB6kTkxM5NChf1zbfbPiGw5lH6JZTDPCgk7vOaWkpJz8v0mTJmzYsIFatcyL0lxuy4vIee6OK6V+8r44Gs2ZT+HevWQtXYrt6FHCe/Yios+5BCZUfdVxdZNXlMecbXPo36A/bRLaeL18W5Edu81xRiuIkSNHcumll3L06FHeffddIoOMldQ5RTluFUR140nLP+jyfyjQE8M/0wWmSKTRnIFY9+8na+lSspYuo3DnThDBEhlJxoJPAQhp24bIvn2J6NuXsK5dsQQH+1ji8lmwawEZhRnc1vE2U8q3OoMFncluNurWrcuGDRtO7gdaAgkNDCW3KJdEyg6ytG/fPpOl88zENNR1X0QaYqyu1mg0ZWBNTiZ72TKyliylYNs2AMK6dKHOo48SddFFBNZKoGDbdnJXryZ39WrS3p9F2sx3kNBQwnv2IG70aKIu8M/vsEJ7IbO2zqJX3V50rt3ZlDrOBkd97ogIiuBEwQnsDjsBFt8uEqxMyycD3u9PajRnCEopUl95lbQZMwAI7diR2g8/TPTFFxFUr94pacM6tCesQ3tqjbsde04ueevXkbv6F3JWriT5zruo89hjxF83xheXUSaLdy/meP5xXuj/gml1nMnR5MoiMiiStPw08mx5RAX7dgjYkzGI4rgQYCys6wz8ZqZQGk1NxWG1cuTRx8j66itiRoyg1l13EpyU5FHegMgIogYMIGrAABwPPsDhBx7g2LPPYk8/Qa177qmWhVGeUOQo4r0/36NTYid61u1pWj3WvLOzBxEeFI6IkFuU6/8Kgn/iQgDYgLlKqdUmyaPR1FjsmZkk33MveevWkXjffSTcflulX+qWkBAavPwyRyZN4vgbb2I7cYK6EyciAb73S/T13q85nHuYx3o/ZqrSOtmDOANXUpeFRSyEB4aTU5Tja1E8GoPQcSE0mnIoOnSIA7fdjvXAAer/bzIxQ4eWn6kcJDCQek8/TWBcPGkzZ2LPyKT+5Bd9OoBtd9h5d8u7tI5vTf8G/U2t6x9X32eXggDDed+x3GMU2YsICjBvJXl5eGJi6gtMAho70xcvlGtmrmgaTc0gf+tWDo4bhyoopNHMmUT07uW1skWE2hPuJyAujpTJk0nOyiRp+nQsERFeq6MifLf/O/Zl7eOlf71kusnrbGrVdBYAACAASURBVB2kBmOgGiC3KJfYgFifyeGJs753galAP6AH0N35V6M568n58Uf2XzcWCQqiyccfeVU5uJJw043Ue/55cn9dx/4bbsSWnm5KPWXhUA7e3vI2zWKaMbDxQNPrK8yzgUBwiO/NatVNaEAoAZaA08xMkyZNOuncr3PnzixZssRUOTxREJlKqaVKqRSlVFrxZqpUGk0NIH3+Jxy88y5CmjShybx5hLRsaWp9sSOGkzR9OoW7drH/2jEUHT1qan0l+fHgj+xO380tHW7BIuYH8LHm2wgODUQs/jE4X52ICJFBkeQW5Z4WZW78+PFs2rSJTZs2cckll5gqhyd3eYWI/E9EzhWRrsWbqVJpNH5O5ldfc/SJJ4jo15fGc2YTVLt2tdQbdcEAGr0zE9uxYxya8ADK4aiWepVSzNwykwaRDRjcdHC11GnEgjgzew/u3H1PmzbtlDQRQRHYHDYK7YWllGI+nhj3ivvM3V2OKfRKas1ZSuGePRx5/HHCunWj4WuvIUHVO4gY3qMHdR57jCOPPkr6vHnEX3ON6XWuPbKWLce3MLH3RAIt1TMmUGiyoz6AVZ/s4vhB784WqtUwkv6jWpWZxp27b4D+/fuTnZ0NgEJRaCsk0BLIK1NfYeBAw6z32muvMXv2bLp3785LL71EXFycV+V3xZNZTANMq12jqWE4cnNJ/s99WMLCaDB1arUrh2JiRgwn66uvSJ3yElHnn09Q/fqm1vf25repHVab4S2Gm1qPK2dLNDlXVq1adcr+7vTdBAcE0zi6MQB33HEHEydORESYOHEiEyZM4L333jNNnrOr9TWaKqCU4sjjT2D9+28avfcuQXWqx6zkDhGh7lNPsXfYMI5MmkTDGTNMm1X0e8rvbDi2gYd6PERwQPVNsS3MtxEZG1J+wipQ3pe+2ZS8Z649CDAWJdqVnWlTpzHowkHUqVPn5Llbb72VSy+91FT5TFUQInIx8CoQALyjlDptXb6IjMKYRquAP5RS5veXNZpKkD53Lllff03iffcR0bu3r8UhOKkBte+7j2PPPUfWl18SM2yYKfW8vflt4kLiuLzl5aaUXxrWfBvB9Xwznbe6KOnuu2QPIqswi4PZB2kS3QSAI0eOUM/prmXRokW0b29usE/TpiKISADwOjAYaAtcLSJtS6RpCfwX6KuUagfcZ5Y8Gk1VyN+8mWPPv0DEv84j4TZzYh9UhrhrryGsc2eOPfsctjTvTy7cmraVnw/9zNh2YwkPCvd6+WVReBaYmEaOHMk333zDzTe7j+UdERSBICenuz700EN06NCBjh07smLFCl5++WVT5fNkodxIN4czgS1KqRQ354rpCexRSu11ljMPuAzY5pLmVuB1pVQ6QDnlaTQ+wZaeTvJ99xGUmEiDF19ELOZP8fQUCQig3jNP8/eIkRx79lkaTJ3q1fLf2fwOUUFRXHXOVV4ttzyUUljz7We8o76S7r5LEmAJICwojJyiHOpQhzlz5lSjdJ71IG4G3gGudW4zgYeB1SJyXRn5GgAHXfaTncdcaQW0EpHVIrLWaZI6DRG5TUQ2iMiG1NRUD0TWaLyDcjg4/PDD2FOP0+DVVwmI9d2q1tIIadGCWnfeQdaSpWR//73Xyv0r4y+WH1jO1W2urnancTarA+VQZ3wPwhMigiIosBVgc9iqvW5PFEQg0EYpdblS6nIMc5HCmP76cBXrDwRaAucDVwMzReS0J1Ap9bZSqrtSqntiYtlBNDQab5I2Ywa5P62izqP/JayDufbeqpBw882EnHMOR598CntWllfKfGfLO4QFhjGmTfW7Gz+b3WyUpDjKXG5RbrXX7YmCaKiUOuayn+I8dgIoKiPfIaChy36S85grycAXSqkipdTfwC4MhaHR+JzcX34hddp0oi+9lNjRo30tTplIcDD1nnkG2/HjpPxvSpXLO5h1kCV/L2FUq1HEhZo3z740CvPOzlgQ7ggLDMMiFr9VECtF5CsRuV5Ergc+dx6LADLKyLceaCkiTUUkGBgNfFEizWKM3gMiUgvD5LS3gteg0Xgde0YGhx58iODmzaj35CS/icVQFmEd2hN/4w1kLFhA7tq1VSrr3T/fJVACub7d9V6SrmKc9OR6lrn6doeIEBEUQY415zS3G2bjiYK4C5iFESioMzAbuEsplVvWIjqllA24G/gG2A58opTaKiJPiUjxfLxvgDQR2QasAB7Ufp40/kDKSy9hz8igwZQpPvOcWhkS776boMaNODLxcRx5eZUq42juUT7/63NGtBxBYrhvTLpnazS50ogMiqTIUYTVYa3Wej1ZSa2AT51bhVBKLQGWlDj2eImy73duGo1fkLdxIxkLPiX+ppsIbd3a1+JUCEtYGPWeepoD11/PiTkfUuv22ypcxqyts0DBTe1v8r6AHnJyDCJUKwiAiOAIyIVcay4hYeYuHnSl3B6EiIwUkd0ikikiWSKSLSLeGQXTaPwMZbVydNIkAuvXI/Huu3wtTqWI6NWTiH79OPHBBzjy8yuUNzUvlU93fcrQ5kOpH2mu+46yODkGoU1MAARbgmkQ2YCo4CimT59O69atadeuHQ899JCp9XrS+pOBoUqp7aZKotH4AWnvz6Jw9x6S3ngDS3j1LgzzJrXuGMf+a8eQsWAB8WPHepzvvT/fw+awcWtH3y4G1LOYTkVEiA2NZcWKFXz++ef88ccfhISEkJJi7tIxT8YgjmnloDkbsB48yPE33iDqwguJuqBm+6gM79aN8O7dSXv3PRxWz+zWx/OPs2DXAi5tdikNoxqWn8FErPk2xCIEBvvPokRv4om7b3e8+eabPPLII4SEGGam2ia7mfdEPW8QkfkYM45OOiZXSi00TSqNpppRSnH0qaeRgADqPPaor8XxCgnjxnHwllvIXLyYuFGjyk0/689ZFDmKfN57gGI3GwGmzx5bMettUvZ7d+Jk7cbNGHBD2WM/nrj7dmXKlCkMHDiQXbt2sWrVKh577DFCQ0OZMmUKPXqYF+DTEwURDeQBg1yOKUArCM0ZQ/ayZeSuMhbEBdWt62txvEJE3z6Etm9P2sx3iB05Egks/XFPy09j/s75DGk65KRraV9irYZYEP5ISWd9JbHZbJw4cYK1a9eyfv16Ro0axd69e01TpJ7MYrrRlJo1Gj/Bnp3N0eeeI7RtW+KuvdbX4ngNEaHWuNtJvvsespYuJWbo0FLTfrD1A6wOK7d1rPisJzOorlgQ5X3pm0157r6LKe5BJCUlMXLkSESEnj17YrFYOH78OGZ5mCj1DojIQ0qpySIyHaPHcApKqXtNkUijqWZSX34Fe9oJGr7xJhJwZoW4jLzgAkJatuD4jBlEDxni1tHgiYITzNs5j8FNB9Mkpkn1C+mG6ogm5w+U5+67JMOHD2fFihUMGDCAXbt2YbVaqVWrlmnylTUCVDwwvQHY6GbTaGo8+Zs3kz53LnHXXOPXvpYqi1gsJNx2O9Y9f5XqyO+DrR9QYCvwm94DnD3R5Mpz912Sm266ib1799K+fXtGjx7NBx98YOo4Tal3QCn1pfPvB6bVrtH4EGWzceSJSQQmJpJ43398LY5pRA++mNTp00l7awZRAwee8kJJL0hn7o65XNz0YprFNPOhlKdytvQgynP3XZLg4GA+/PBDEyU6FU8Wyn3n6mFVROJE5BtzxdKc7diK7ORmFpKVlm+a/5kTH35I4fbt1Hn0UQIiI02pwx+QwEASbr2Fgq1byf159Snn5mybQ4GtgNs73u4j6dxjzbefFT0If8eTO5ColDrplE8plS4ivgvGqzljKMgtYv3Xf5NxLI/CPBvWfBsFeTaseTbsNsfJdI3axdN/VCti63hv4ZotLY3j018j4rz+RF00qPwMNZzYyy7j+OtvcPytt4js3w+AzMJMPt7xMYOaDKJ5bHMfS/gPyqGwFpwdJiZ/x5M7YBeRRkqpAwAi0hg3g9YaTUU4uO0E33+wjfzsImo1jCQkPJDIuFBCwgP/2cICKci18fu3+5n71K90HtiI7pc0ISik6gPJqa+9hqOggDqPPFIjPLVWFQkOJuGmmzj23HPkrV9PeI8ezN42m9yiXP/rPRTaQZnrZkMpdcbed2/2uD25A48CP4vIj4AA/QH/Gc3S1CiKrHbWLPqLLSuSiasbzpC7OpHYqOxoZW361mPNor/47Zv97Fp3lL5XtKR518RKP+CFf/1FxicLiLvqKkKa+Y/d3Wxir7yC42+9xfG3ZhDTsRUfb/+YCxtfSMs4/wrBYrabjdDQUNLS0khISDjjlIRSirS0NEJDQ71SXpl3QEQsQAzQFejtPHyfUuq4V2rXnFWk7M9i+fvbSD+aR8cLkjh3eHMCg8vvDUTEhDDwhra061efn+bv4puZf5LUOo7+V7Uivl7FXXGn/G8KlrAwatVQZ3yVxRIWRvyNN5D60lRWfvUSOUU5jOs0ztdinYbZnlyTkpJITk7mTA1fHBoaSlJSklfKKvMOKKUczvUQnwBfeaVGzVmHw+5g47L9bPh6H+ExwQz7T2catomvcDn1WsRy5X97sPWnQ/z6xV7mP72OTgMb0nt4cywWz74Ec9euJWflSmo/MIHA+IrLUNOJu/pqjr89k4DZixl430BaxbXytUinYXY0uaCgIJo2bWpK2WcantyB5SLyADAfOBnzzhlyVKMpk4yUPJa/v41jf2fRskcdzhvditCIoEqXZ7EIHc5PokW32vyy6C9+//YAAH1Gtig3r7LbOfbiZILq1yfuuusqLUNNJiAykr2DWtP1s/V0jRnia3HccrIHoV19+xxP7sBVzr+u/XEFnD3GW02lyD5RwMIpv+GwORh0czta9qjjtbLDooL599g2BAZZ+P3bA8TXj6B173pl5sn8/AsKt2+n/ktTsIRUX9AVf+JEwQlebrSdVyxCrW82QNeBvhbpNHQ0Of+h3HUQSqmmbjatHDRlYrPaWfrWFmxWOyMf6OZV5eBKv1EtaXBOHCs+3MHRvZmlpnPk5ZH6yiuEdupI9CWXmCJLTeCdLe+QEmYl8IJ+ZCxejKOgwNcinYaOBeE/eLJQLlxE/k9E3nbutxSRS80XTVNTUUqx4sMdpB7M5sKb2hFf37yYzgEBFi6+rT2RcaEseXMz2Sfcv/DS3n8fW0oKdR4+O6a1uuNo7lHm75jPsObDSBpzM47MTLKWLfO1WKdReFJBnFl+sWoinkTjeB+wAn2c+4eAZ0yTSFPj2fTdQXatO0avYc1o2tE8R2LFhEYEMeTOjtiLHCx5czNFhfZTzhelpJD27ntEXXQR4V27mC6Pv/LWH2+hUNzR6Q7Ce/UkuEkTMubN97VYp2HNtxEQaCEwSCsIX+OJgmiulJoMFAEopfIw1kNoNKexf2saaxbtoUX32nS7uPriCsTXi2DQLe1JS87h+1nbUI5/FgulTpuGKiqi9oT7q00ef2N/1n4W71nMqHNGUT+yvhHCcvRV5G/aRMGOHb4W7xSszmBBGt/jiYKwikgYztXTItIcl8hyGk0xGcfy+PadrSQkRXLBdW2q3ZTTuH0CfS5vwV+/p7Lu678BKNi5k8zPFhJ/7bUEN2pUrfL4E6///jrBAcHc0uGWk8dihw9HgoNJn+9fvYizxZNrTcATBfEEsAxoKCIfAd8DD5kqlabGUZhvY8mbm7EECIPHdfCKO4zK0OnfDWndpx4bvt7HrvVHSXlxMgHR0dS6w/8WhFUXO0/sZOm+pYxpM4ZaYf+Y/AJiY4kePJisz7/AnpNbRgnVy9niybUm4Mkspu+AkcANwFygu1JqpbliaWoSDofiu/e2kpmSz+Db2xOdEOYzWUSE868+h3rNY/hh1jaObEmm1l13EhAT4zOZfM3036cTFRzF9e2uP+1c7OircOTlkfX11z6QzD26B+E/lKogRKS1829XoDFwBDgMNHIe02gA+PWLvezfkkb/0a2o3zLO1+IQEGTholvbElSYxZ+dxhE54kpfi+QzNqVs4sfkH7mp/U3EhJyuJMM6dyakVSvS588zza16RSnMt+sehJ9QVg+ieETvJTfbFJPl0tQQ9mxM4bdl+2nXvz7tz2vga3FOUvTDMtpunklBYAy//XDY1+L4BKUUr/72KvGh8VzT+hq3aYoHqwu3bafgzz+rWUL3WPOK9CpqP6FUBaGUus35d4Cb7YLqE1HjrxTkFPHj3J3UaRpN/6v8x6ePo6CA1GnTqNs4glY96/D7dwfISMnztVjVzprDa9hwbAO3dbyN8KDSY2nEDBuGhIeTPm9eNUpXOoUFOliQv1DuXRCRUOBOoB/GTKZVwFtKKf9bgqlxS1ryQdKS95ObkU5uRga5GenkZaY799MpKiyg25Dh9LzsSgICPX8wf1m4B2uejQFjWhMQ6Ml8h+oh/aOPsR09Sv0XX6R26xb8/cdxVi/YzZC7OvlatGpDKcWrv79K/Yj6XNmqbBNbQGQkMUOGkPnll9R5+GECoqOrScrTcdgd2Aq1iclf8OQuzAaygenO/WuAOcDZa9itQfy29EtWfPA2OO3LIhbCY2OJiIkjIjaWWo2akJ+dxS+ffMSe9WsZfOd4ajVqUm65h3dnsP2XI3QZ1IiEBv4TrtOemcnxt98m4rz+RPTqCUD3IU1Ys/Av9m05TpMO5i/c8we+P/A929K28XTfpwkOCC43fexVV5GxYAGZn39B/HVjqkFC91gLjEWOZrn61lQMT+5Ce6VUW5f9FSKyzSyBNN5BORz8+OF7bPx6Mc2796bPldcQGRdPaFQUFsvpU1B3/bqa5e+8wZxH7qPPldfQY9jlWALcT1W12xys/HgnUfGh9BjiX26T02bOxJGVRe0JE04e63RBQ7avPsLPn+ymYet4AoL8p7djBnaHnem/T6dpTFMubeaZV5yw9u0I7dCB9PnziBtzrc/ckZx09a3HIPwCT56U30SkOFgQItIL2GCeSJqqUmQt5MtXXmDj14vpMngowyb8l9pNmhEeE+tWOQC06tWXG156gxY9evPzvNnMnfgAackH3KbdtPwA6UdyOW90K5+td3BH0ZEjnJg9h5hhwwg955yTxwMCLfQf1ZLM1Hw2fe/+ms4kFu1ZxN7Mvdzd+W4CLZ6/aONGX4V1z1/kb9xoonRlox31+ReeKIhuwC8isk9E9gFrgB4iskVENpeVUUQuFpGdIrJHRB4pI93lIqJEpHuFpNecRl5WJguefozd69Zw/thbueCG20tVCiUJj45h6PhHuPS+h8lIOcach+9l3eef4rD/49so63g+G77eR7MuiTSpBj9LFSF1+mugFIn33nPauUbtEmjaqRYblu4nJ/3MHT7LseYw/ffpdKndhQsbX1ihvNGDB2OJjCR9/icmSVc+WkH4F54oiIuBpsC/nFtT57FLgaGlZRKRAOB1YDDQFrhaRNq6SRcF/Af4taLCa04l/ehh5k58gNS/9zJ0/CN0G3JZpco559z+3DDldZp26cGqj2cxb9LDWPPzUErx49xdiEXoP8q/4hgX7NpF5uLFxI0ZQ1AD99Nt+13ZEmVX/PLZnmqWrvqYuWUmJwpO8FCPhypsJrKEhxNz2WVkL1uGLT3dJAnLRseC8C88WUm9v6ytjKw9gT1Kqb1KKSswD3D3xnoaeBE4cz/rqoHDu7Yz9/8eoDA3lysff5ZWvfpWqbyI2DiGTXiUwXdP4OjuXXzz1jT2bEzhwNY0eg1rRmScd4Kie4vUqS9jiYgg4bZbS00TXSuMLhc1YveGFA7t8s0L0EySs5OZs20OQ5sNpX2t9pUqI/aqUaiiIjIXLvKydJ6Rk264eQuPKX9gXWM+Zo7WNQAOuuwnO4+dxLkiu6FSqsx1/iJym4hsEJENZ2qg8aqwe/0aFjz1GCEREVz9zBTqt2rjlXJFhLb9B9Dv6rHsWvszy9/9mFoNI+lwvv8siAPIW7+enJUrSbj1VgLjyl7J3fWixkTGh7Bq/i4cdkc1SVg9TN04lUBLIPd2vbfSZYS2akVYt26kfzLfJyurM1PzCAwJIDxaKwh/oCxXG6bGZBQRCzAVmFBeWqXU20qp7kqp7omJiWaKVeNIP3qYJdOmkNi4KVc/PYW4uvW9XkePYZcTW68deSdW0K6vBUuA/8wCUkqRMuUlAuvUIX5s+XGmg4ID6HdFS9IO5fLnT2fOCuuNxzby3f7vuLHdjdSNqFulsmKvvIKi/QfI31D9c1EyU/OJSQw7a4M6+RtlPelrAERkTiXLPgQ0dNlPch4rJgpoD6x0Dn73Br7QA9WeoxwOvpsxHUtAAEMn/JfwaHMc0qUeyKYg/1+EhMexev508jIzTKmnMmR/9x35f/xB4j13Ywn1zOzVrEsiSa3jWPflXvKzrSZLaD4O5WDy+snUDq/t1iFfRYkeNAhLRAQZPjAzZabkE5voO2ePmlMpS0EEi8g1QB8RGVly86Ds9UBLEWkqIsHAaOCL4pNKqUylVC2lVBOlVBNgLTBMKaWn0HrI5u+/4eC2LfzrupuJijdnRpHDoVj50U7CY6IZ/vBj5Gdn8fW0/+Fw2MvPbDKqqIjUqS8T3Lw5McOHe5xPROg/qhVFBXbWfrHXRAmrh6/2fsW2tG3c1/W+Ml1qeIolPJzoSwaTtWxZtboBdzgUWcfziamtFYS/UJaCGAf0B2IxZiu5buWuvlFK2YC7gW+A7cAnSqmtIvKUiAyrquBnO1nHU/npo/do1L4jHS4YZFo921YdIvVANv1GtSSpdSv+fdMdHPjzD9Ys+Ni0Oj0l47PPsO7bR+0J9yMVcBECEF8/gnb967Nj9RGyjuebJKH55BXl8erGV2mf0J4hzYZ4rdyYESNR+flkf1N9MatzThTgsCtiEquu5DTeodSnSin1M/CziGxQSr1bmcKVUkuAJSWOPV5K2vMrU8fZiFKK5e+8jsPh4MLb7jXNXmvNt7Huq7+p3zKWFt1qA9DhgkEc2rmNtQvnU69Va5p16WFK3eVhz8kldfprhHXvRuSAAZUqo+vFTdi2+ggblu7jguu8M7Bf3by/9X1S8lOYcv4ULOK9saGwLp0JbtqUjIWLiL38cq+VWxaZqYaijtEmJr/Bk1/UHBG5V0Q+dW73iEiQ6ZJpSmX7zyv5+/cN9LtqLLF1qjYgWRa/f3eA/Owi+lze4hQl9O+b7yCxcVOWTn+JzJRjptVfFmnvvoM9LY06D1V8vn8xkXEhtO1fn51rjp58OdUkjuYeZdafs7i4ycV0qd3Fq2WLCDEjRpC/cSPWffu8WnZpnFQQ2sTkN3iiIN7AWE39hnPrCrxpplCa0snNSGfFrLep16o1XQZ75menMuSkF7LpuwO07F6bOk1O9e4ZFBzC0Pv/i8Ph4MuXX8BWVGSaHO4oOnqUE+/PInrIEMI6dqxSWd0uaoxYhI1L93lHuGrkld9ewaEcjO823pTyYy67DCwWMhYtNqX8kmSm5BEQZCEixtQJlJoK4ImC6KGUul4p9YNzuxHwjV1Bww/vz6CoIJ+Lbr/XYxcalWHdl3txOBS9hzd3ez6ubn0uvms8x/buZuXsd0yTwx2pr04Du53E8VV/MUbEhhhjEWtrVi9iS+oWvt77NWPbjaV+pPenNgME1alNRP9+ZC5ejLKbPynh5BRXi57i6i94oiDsInLyLSEizQDfT2E5C9m97hd2rf2Z3iNHk5DUyLR60g7lsGPNETqcn0R0rdK7+y17nEu3IZfxx7dfc3jXdtPkcaVg+3bDpcZ11xGc5J0Fe10vaowloOb0IhzKwYvrXyQhNIFbOtxial2xI0ZiO3aM3F9+MbUe+EdBaPwHTxTEgxguvleKyI/AD3iwuE3jXQpycvj+3TdJbNyUHpddYWpdvyz8i+CwQLpf0qTctH1GjSEyLp4f3p+Bcpi7MlkpxbHJkwmIjqbW7bd5rdxTexH+H3lu4e6F/JH6B//p+h8igiJMrSvyggEExMSQsXChqfUoh9IKwg/xxBfT90BL4F7gHuAcpdQKswXTnMrKOe+Ql5XJReP+U6GobxXl4I4THNiaRreLmxAaUf5chODQMM4bcxPH9u7hz5XLTZMLIHfVKvLWrKXWXXcSEOPdRYHFvYgNS8tyL+Z7jucfZ+rGqXSv053hLTxf+1FZLMHBRA8dSs7y77FnmLdAMjezEHuRg5jaeoqrP+HRvDilVKFSarNzKzRbKM2p7Nv8O1tXLqfH0JHUadbCtHqUw/B0GhUfSocBnptvWvf9F/XPacuquR9QkJtjjmw2Gyn/+x9BjRoRN3q018uPiDF6ETv9vBcxed1kCmwFPH7u49XmjiL28pGGA7+vy3SZViUyU/QUV3/Ef5zqaNzicNhZ+cFMYuvW49wrrjG1rl3rj3H8YA69LmtGYJDnA+AiwgU33k5+dhZrPp1rimwZixZRuHsPtSdMQILNceR2shexZJ8p5VeVnw/9zNJ9S7m1w600jam+SH6hbdoQ0qaNqR5e9RoI/0QrCD9n55qfSUs+QN9RYwg06cUIYCuys/bzv0hsFEWrHnUqnL9O0+Z0/PdF/L7sy1Ij0VUWR24uqdOmEdalC1GDKhYEpyJExITQvn8Ddv56jIwU/+pF5BXl8czaZ2ga05SbO9xc7fXHjhhBwdatFOzcaUr5mal5WAKEyHj/ciN/tlOughCRhSIyxOl9VVONOOx21iz4mFoNG3POuf1NrWvzimRyThTSZ2TzSk8z7HvVdQSHhRkD1l50FZ323vvYU49T5+HKL4rzlC4XNfLLGU1v/fEWh3IO8XjvxwkOqH5X2NFDL4WgIDJNGqzOTMknulYYFj3F1a/wdKHcNcBuEXlBRM4pL4PGO2z/eSXpRw7R58prEYt5+rkgp4iNS/fTuH0CSa3jK11OeHQMfUeN4cCff7Bn/RqvyFZ0LIW0994j6uKLCevc2StllkVETAjtz/OvXsSOEzuYvW02I1uOpHtd3zg7DoyLI2rAADK/+BJl9b4H3IxU7aTPH/FkFtNypdS1GCuo9wHLReQXGIIjWwAAIABJREFUEblRu9wwD7vNxprP5lK7SXNa9DzX1Lo2LNlHUYGNc0e4XxRXETpdeAm1GjZm5ex3KbJWfT5D6vRpKJuN2vebs1rYHV0GNSIgQNjoB2MRdoedp9Y8RUxIDPd3u9+nssRePhJ7ejrZP/7o1XKV0lNc/RWPPktFJAG4AbgF+B14FUNhfGeaZGc5W39cTuaxo/QZda2pZpXM1Hy2/JhM6z71SGgQWeXyLAEBDLjhdrJSj7Hhy6qZIwp27CBz4SLir7mG4EbmLQwsSURMCO3+1YCd63zfi5i/cz5bjm/hoR4PERNiTrwPT4no25fAxESvD1bnZVmxFdq1F9eycDhg+ZOQVb1BrjwZg1gErALCgaFKqWFKqflKqXuAqr9RNKdhKypi7WfzqdfiHJp1Nderya9f7MViEXoNbea1Mhu170ir3v1Yt/hTso6nVKoMpRRHn37GWBR3xzivyeYpXQc19nkv4ljuMab9Po0+9ftwSdNLfCZHMRIYSMzwy8j56SdsXgz9q530ecD3k+DnqbDDvKnG7vCkBzFTKdVWKfW8UuoI/BOOVCmlo7+ZwJ8/fEt2WqrpvYeU/VnsXn+MTv9uSESsdx2k/WvMTQD8+OH7lcqf9cUX5G/cSOKE+wmIjfWmaB4RHh1Mu/5GL8JX8SKeX/c8doed/+v9f34TgjNmxEiw28n84ovyE3tIlp7iWjYb3ofVr0L3m6GHua5VSuKJgnjGzTHvjEBqTqPIWsivi+bToHVbGnf0rgtnV5RSrFn0F6ERQXS5qLHXy49OrE3Py65g15pVHNy6uUJ57dnZHPvfFEI7dqy2WATu6HxhI8QCv3/r3Wm7nvDDgR/4/sD3jOs0joZRDcvPUE2ENGtKWJcuZHy20Gsz1TJT8xGLEJWgp7iexp7l8PUEaHEhDJ4M1fyhUKqCEJG6ItINCBORLiLS1bmdj2Fu0pjA5u+WkZN+gr6jxpj61Xhw+wmSd6TT/ZImhISZ47qj+7CRRCfWZsXsdyrkp+n4a69hT0uj7sSJps7eKo/IuBDanFuPbb8cJjej+hwIpBek88zaZ2gV14qx7cZWW72eEnvF5Vj37iX/t9+8Ul5mSh5RCaEEBOiZ9Kdw9E/45Aao3RaufB8CzHOxUxpl3ZGLgClAEjAVeMm53Q88ar5oZx9FBQWs+3wBjdp3pGG7qsU5KAvlMHoP0bVCaX+edzyiuiMoOIR+o8eSum8vO375yaM8Bbt2ceLDj4i98krCOrQ3TTZP6XpRY5TDCJ5UHSileOKXJ8gozOC5fs8RZPG/iYLRgwdjiYggY8GnXikvMzWfWG1eOpWsI/DxKAiJhGvmQ0iUT8QoVUEopT5QSg0AblBKDXDZhimlzHXteJby+zdfkZeZQZ9R15laj6tLjYAgc7/aWvc5j8Qmzfh53pxyAwsppTj29DMEREaSOP4+U+XylOhaYbTqWYetPx0iP9v78/9L8unuT1lxcAX3db2Pc+L9c8mRJTyc6EsvJWvZMuxZWVUqS/1/e+cdHlWVNvDfOzPpvUFCIAkQehGkdxQBe0GKq1gQe9217Lfr6rqubcW6tlUUxIaigIIoIEjvTXpNQgglhfQ6yZTz/XEHCBhCSGYyk+T+nuc899x7zz33PffOnPee9r5KkZ+lT3E9i/JiTTmU5WvKIcR1H3EXoroupomOaIKIPHFuqCf5mgwVZaVs/mkuCT16EdvBdf6RrRYbG+elEBUXRLteF29S42IRg4Ght95F4clMdi75pdq0hT//QunmzUT95c+YwsJcLltN6XVlPFarnR2/HXXpfVIKUpiyaQoDWwxkYueJF77AjYSOHYsymylYsKBO+ZSXWKkos+pWXE9ht8GceyBzN4ybATGXuFWc6j4fTxmaDwSCqgg6TmTbL/MxFxUyaNxtLr3P7pXHKco1M+Cm2pvUuFjiu/ckruslrJ87i/LSkirT2IpLyJoyBd/OnQkdN65e5KopYdEBJF7ajJ0rjmEucY17VYvNwt9W/Q1fky8vDXoJg4dbtvHt2gWfTp3In123bqZ8h+VcvQXhYPEzcHChNiDdfpS7pam2i+ljx/aFqkL9idj4MZcUs+XnH2jbux/Rie1ddp/yUgtbFqbSqnM4rTrV3qTGxSIiDL1tEuaiwvMunsv+8EOsWVlE//M5xOg6V6q1pddV8VjMNnatOOaS/N/b/h77cvfxwsAXiPKPcsk9nImIEDpuLOV791G2e0+t8zlt5ltfAwEbPoKNH0H/h6Hvve6WBoDzDouLyLvVXaiUesz54jRNtv0yn/KSEga6uPWwbXEa5aXOMalxsTRvk0iHgUPZ8vOPXDLqGgLDziio8qQkcr/4gpCbx9SLvaXaENkyiITukexYdpRLRrTC29d5M0o2pm9kxu4ZjGs/jsvjLndavq4m5NpryZryOvmzv8eva5da5VFwsgwEgiOauILY9iUs+j/oeC2MetHd0pymunbs1gsEHSdQXlrK7wvnk9inP80SnLea+VyK88rZsewo7fs2J6qVe3oIB0+4HbvVyoY5Z3xGKKXIePllDP7+NHvSsz3Z9roqnvISK3tWOc/cQUF5Ac+seYb44Hie6v2U0/KtD4zBwQSPHk3hTwuwl9bOJEnByVKCwnxdPlnCo9n+Dcx/FNpeDjdPA4PntKAvNIvpvKE+hWzM7FjyC+aSYvrdNMGl99m0IAWllFNNalwsodExdL/iKnb+tpjcE8cBKFq8mNL1G4h67DFM4fXX7VUboluH0LJjGL8vTcNaYatzfkopXlj/ArnmXF4b+hr+Xg1voDZ0/DjsJSUULlxUq+sLspq4Fded38O8h6D1ULhlJnh51mLB6mYxvePY/iQi888N9Sdi48VSbmbLgh9I6NGL6LbtXHaf3BMl7F+XTrdhLQmOdO+fccDNt2Dy9mHNt59jKy4m8z+v4dOxI2G3uFZBOoveVydQVljBvnXpdc7rx6QfWXJkCY/2fJTOEZ2dIF3943fppXi3aVPrweombcV1zw/ww30QNxD+9C14ed5zqK4j9UvH9o36EKQpsuu3xZQVFtDfxa2H9T8m4+VrovdVCS69T03wDwmlz3VjWPf91+w5fhKvrCxavvM2Yqr/VaK1oUW7UGISQ9i2+AidB7fAaKpd10haYRqvbnqVvtF9uavLXc4Vsh4REULHjiVryhTKDx3Cp13NP3TKSy2Yiy1N04rrvp9g9mRo1U9b6+Dtmc+gui6mrY7tSjTbS3lALrDecUynDlgtFjbPn0Orzt2I7ei6r8ej+3NJ3ZnNpaPj8A30jFW5va69ET8/f7bu30n43ZM8dmC6KkSEXlclUJxXzoGNGbXKo9RSyp9X/BkvgxcvD37Z46e0XoiQG28AL6+LbkU0WSuuBxbC95Mg9lK47XtttbSHUhNz39cAycC7wPtAkohc5WrBGjt7ViylOC+XfmNc13qw2eys+e4QwZG+XDLCcwy+GcsrSMzIJTfQj+KhA90tzkUT1zmcqLggti06gt1WcxtTAHZl55k1z5Ccn8zrQ18nOiDaRVLWH6bwcIJGjKDgx3nYL8LbXEFTtOJ6aAl8dwdEd4OJc9xmQqOm1OTT5U3gMqXUcKXUMOAy4G3XitW4sVmtbJo3m5h2HYjr6rqVkrtXHCf3RAmDx7XD5OU5MyMyX3mV2KMZhIRFsOb7mdjtdR/wrU9EhN5XJ1BwsoxDmzMv6toPt3/Ib2m/8XTvpxkY2/CU4/kIHTcWW0EBRUtq7kPs1BqI4KaiIJKWwre3QbNOcPtc8HWvA6iaUBMFUaSUSqq0nwIU1SRzEblSRA6ISJKI/K2K80+IyF4R2Skiv4mI8+1OeyD7166k8GQm/cfc4jKLraWFFWxacJi4zuEkdI90yT1qQ9GyZRTMm0fUffcy5M57yU5LZe+q5e4W66Jp3T2SyFaBbFpwGJu1Zq2IRamL+Hjnx9yUeBO3dXLtmpf6JmDAALxiYy/KgF/ByVICQn3w8vacjxeXsfM7mHkLRLaH238EP88xJVMd1c1iGiMiY4AtIvKLiNwlIncCPwGbL5SxiBiBD4CrgM7An0Tk3M7234HeSqnuwGxgSi3L0WCw221s/OE7miW0pXVP1/lb2jgvGWu5jcHj23mMsxlrXh7pzz+PT4cORD34IO37DyImsQNrv/2CCrN7nPLUFjEI/a5vQ2G2uUYzmvbm7OW5Nc/RI6qHRzkAchZiMBA69mZKN2ygIq1mlm+bxAwmpTRnP3Pv1Qak71oA/p49nbsy1bUgrnMEXyATGAYMB04CNXmrfYEkpVSKUqoC+Ba4oXICpdRypdSpFTYb0EyLN2oOblhLXvpx+o+Z4LJKIutIIXvXpdP98paERQdc+IJ6IvOll7Hl5dPiP68i3t6ICMPvvJfivFw2z3OO6ej6JL5rBDFtQ9jy8+Fq10Vkl2Xz2LLHCPUN5e3L3sbb6F2PUtYfIWPGgMFA/uw5NUpf0NituNptsOhvsOSf0OUmrVvJr/69I9aF6mYxTaou1CDvWKCy+ctjjmPnYzKwsKoTInKfiGwRkS0nnegLt75Rdjsb584iomUciX36u+geitWzDuIX5E2fa1q75B61oXDxrxT+/DORDz6Ab6cz1mpbtO9Ix0HD2PLTDxSerJ3/anchIvS7oQ0lBRXsWnm8yjQVtgr+svwvFJQX8O5l7xLp5zndfc7Gq3lzAocOJf+HuSirtdq0FWYrpYUVjXcGk8UMsyedsa1083QwOdetb31Qk1lMviLysIh8KCLTTwVnCuEwLd4beL2q80qpqUqp3kqp3lFRnm/I7Hwkbd1I9tEj9LtpvMs8pR3clEFGSiEDbmyLt4s8xV0s1txcMl54Ad/OnYm8774/nB9y610gwqqZM+pdtroS2z6MVp3D2bboCBVlZ1eKSile3PAi209u56XBL9EpwnVm3D2F0PHjsJ3Mpnhl9TPhT/n5bpRrIMry4MubYO88GPUyXPkKuNEzYl2oidRfAtFoHuZWonUD1WSQ+jhQeW5lS8exsxCRK4B/ANcrperPr2M9o5Ri49xZhEbH0GHAEJfco8JsZd3cZJolBNOxv2dMn1RKkfHCv7EVFRHzn1cRrz+uxQiOjKLP9WM4sG4Vx/fvdYOUdaPf9W0wl1jYsexsfxFf7fuKH5N+5IFLHmB0wmg3SVe/BA4diql5c3K/+qradKetuDa2LqaCYzD9Sji+RbOrNPARd0tUJ2qiIBKVUs8BJQ4bTNcA/Wpw3WagnYi0FhFv4BbgLBMdItIT+BhNOTSs/oWLJHXHNjJTkuh74zgMLjJnveWXVEoLKxg6oX29+Xq4EEULF1K0eDFRjzyCb/vzmzLvc93NBIZHsPzzTy7Kf7Un0DwhmDY9oti+JA1zseYvYsXRFbyx5Q1GxI3gwUsedLOE9YeYTITfcTul6zdQtuf8ZsAb5RqI9J3w6UgoPKGtceg21t0S1ZmaKIhTHlLyRaQrEAI0u9BFSikr8AiwGNgHfKeU2iMi/xaR6x3JXkdzSPS9iGxvrDaelFJsmPMtQZFRdB5ymUvukZ9Zyo7fjtJxYAzNWwe75B4XS0VqKunP/wvfbt2ImHx3tWm9fH0ZeutdZKYcYu/qhjftte/1rakot7Ht1yOsO76OJ1Y8QafwTrwy+JUGv1L6YgkdPx5DYCC5087fE12QVYpfkJfHdIPWmd+/hmkjtfjdizTje42Amvxyp4pIGPAcWgtgL/BaTTJXSv2ilGqvlGqrlHrZceyfSqn5jvgVSqnmSqkejnB99Tk2TNJ27eDEwX30uf5mjCbXmLtY8/0hTF4GBtxY/74eqsJeUsKxRx9FDAZi366ZraWOg4YRk9iB1d983uCmvUa0CKR93+bsWJbG3xY/S5uQNnw88uMGaaG1rhiDggidMJ7CRYuoOFa1gyVtimsjeDYWM8x/TLPI2rIP3L8KmtfON4YnckEFoZT6VCmVp5RaqZRqo5RqdsrbnM6FUXY7q7+ZQXBUM7pd7pp+6NRd2RzZnUOfa1vjH+z+KZRKKU7841nKk1No8dabeLesmdN1MRgYfue9lDTQaa+BA8xYbTYGZFzH1FFTCfHx/JWyriL8jjvAaCT3sxlVni842QjMfOelwvRRsO1zGPyEtgAusOFOoqmKmsxiihCR90Rkm4hsFZF3RCSiPoRrDBxYv5rMlCQGjZ+IqYoB2rpSYbayetZBwqL96TbcM5aR5E6bRtGiRTR74i8EDhp0Udc21Gmvu7N388S2RzgWu5uE4z0wFTfwyq+OeDVvTsi115I/Zw7WvLyzzlkrbBTnlTfs8YeDi+HjoZCbqpnqvuJ5MDaS7rJK1KSL6VsgC7gZGAtkA7NcKVRjwWa1sGbWl0TFt6bT4OEuucfa2UkU5pgZflvHWpuedibFa9eS9dbbBF15JeGTJ9cqj9PTXr/+zLnCuYgDuQe4f8n9hPiEcP+ksYgIm38+7G6x3E7E3ZNQZjN5M2eedbwguwFbcbXb4LcXYeZ4CI2D+1dAh8Zru7QmNUqMUupFpdRhR3gJaO5qwRoDO5YsoiAzgyG33uWSdQ+pO7PZu+YEPUfG0aKd+1doVhw7zoknnsSnbRtavPxSrVeKn572un61x097Tc5P5t5f78Xfy59po6fRJrYVXYfHcmBDBnkZJe4Wz634tGtH4PDh5H31NXaz+fTxM1NcG9gYRFEGfDUGVr8BPSfC5CUQ7j4PjfVBTWqtX0XkFhExOMJ4tJlJOtVQXlrKhjnfENe1OwmXXOr0/MuKKlj21X4iYgPd6kb0FPayMo49+ijKbqfl++9jCKibiY+GMO01tSCVe369B5PBxKejPiU2UBtr6TU6HpO3kY3z9VZExOS7seXlUfDDD6ePNbgprkrBjlnwQT9I2wDXvwc3fOCRHuCcTXXG+opEpBC4F5gJVDjCt8Afl8PqnMWWBXMpKypkyK2TnG5zSSnFipkHKC+1cMWkzm53+K6UIv355ynfv58Wr0/BO77uRnkrT3vdsbR2/o5dSXJ+Mvf8eg92ZefTUZ8SH3ymzH5B3lwyohXJ27JIT8p3o5Tux693b3wv6U7OZzNQNs1eVcHJMnwCTPgGeIYDq2opTIdv/qS5Bo1sDw+sgUvvcLdU9UZ1tpiClFLBjq1BKWVyBINSyjMm2nsoxXm5bFnwAx0GDHGJr+kDGzNI+f0k/a5rQ2RL93ujyvvyKwrn/0Tko48QNHy40/LtOHg48d17svKraeRlnHBavnVlQ/oGbv/ldmzKxtSRU2kT+scWXM9RcQSG+7D86wPYLJ7ZAqoPRISIuydjSUujaMlSQFsD4fHdS0rB9m/gw36QslwzmXH3Ioh0ne94T6RGn54icr2IvOEI17paqIbOhjnfYLdaGXTL7U7PuyjXzOpvDxKTGEKPkXFOz/9iKdm4iczXXiPw8suJfOABp+YtIox+4HGMJhOLPnjbIxwLzT00lweXPEjzgOZ8ffXXdAjvUGU6b18Tw/7Ugbz0Erb9eqSepfQsgq4YgVd8HDnTpqGU8nwz34UnYOYE+PEBiOoED6zVTGYYmoDfinOoyTTX/wCPoy2Q2ws8LiKvulqwhkruiWPs/G0x3a+4irDoFk7NW9kVv32+F6Xgirs6Y3CzOY2yHTs49tBDeMfH0+K1/7hkID4oIpIRdz/IiYP72PLTDxe+wEXYlZ13tr7D8+uep29MX7646gtaBFb/fhO6RZLYuxlbFqY26QFrMRqJmDQJ865dFG3YRHGu2TNnMCkFv38FH/SHw6tg9Ksw6ReITHS3ZG6jJv/oq4GRSqnpSqnpwJVo9ph0qmDNt19g8vZhwM23OD3vHcuOcvxAPoPHtyM40r1/sLJdu0mbfA/GiAjiPpuOMch1vnU7DhpG+36DWDvrK04eqf+BX7PVzNMrn2ba7mmMaz+O90e8T5B3zco7ZHx7vLyNLP9qP8quXCyp5xJy440Yw8NJmTEfpSDcg/yUAHB0s2YqY97D0LwzPLgWBjzUJFsNlanpJ1/lOZRNd3noBThxcD+HNq6jz3Vj8A9x7rTTnBPFbPgxhYTukXQaGOPUvC8W8969pE2ejDEkhPgZn+HV3LWznkWEEfc8hG9gIAvffxOrxXLhi5xETlkOk3+dzJIjS3iy15M81/85vAw1H1z1D/Zm4M2JpCcVsHet54yj1DcGX1/CJt5GcmYAXt5CfDcPWWubfxTm3APTroD8NG120l2/QIRnmKxxNzVREK8Av4vIDBH5HNgKvOxasRoeSilWff0Z/iGh9Lr2RqfmbbPaWfrZXrz9jFw2saNb3VWaDxwgbdLdGAIDiPv8c7xaOLcb7Xz4B4cw6v7HOJmWyvrZMy98gRNIyU/htl9u42DuQd4a/hZ3db2rVs++08AYYtuHsm5uMiUFjdai/QXxv3EcWc160ZI0vH3dvOq4vBiWvQzv94Z9P8GQp+DRrdr6hgbqu8EVVPskRMQA2IH+wFxgDjBAKaWvpD6HlG2bOb5/DwPG3oq3r3O7fzb8mEz20WKG39bRrbaWyg8dIu2uSYivL/EzZtTYxpKzaNurL90uH8XmeXM4fmCfy+6jlOKn5J+47ZfbKLOWMX30dK6Iv6LW+YkIw2/riM1iZ/WsQ06UtGGRtM+M3eBF5MZvsGRkuEcIu12zvPpeL1g1BTpeA49shhHPgY/rukkbKtUqCKWUHfirUipdKTXfEdz0Zj0Xm9XK6pkzCI2Oodvlo5ya987lx9i+9Chdh8XSpof7DIGVp6RwZNLdiMlE/Ocz8I5zzwyq4XfcQ1BkFIs+eAtLpdW5ziLfnM+TK5/kmTXP0D6sPd9c8w3dorrVOd/Q5v70vjqB5G1ZHN6Z7QRJGxZKKfasPk6zWF+CSk+Q9cab9SuA3a55eJs6VLO8GtJSWwk9drpmMkOnSmrSlloqIk+JSCsRCT8VXC5ZA2Ltd1+RcyyNYRMnY6yBWeuakrQ1i9XfHaT1JZEMmXB+ZzuupvzwYdLuvAuAuM9n4J2Q4DZZvP38ufKhP5OflcFKJ9tqWnd8HWPmj2H50eU8funjTB89/YIzlS6GnqPiCG8RwKpvDlBhrt5nc2MjPSmfvIxSuo5oTeR991G4YAHFq1e7/sY2q7YK+n8D4Ls7oKIExnyiKYdWfV1//wZOTRTEBOBhYBXa+MNWYIsrhWpIHNm1nc3z59B9xJUk9unvtHxPHMpj6Wd7iW4dwqjJXdw2pbU8JYW0uyahbDbiP5uOTxv3m/Vo1bkbva65kR2//kzq9q11zs9sNfPqxle5f+n9BHkHMfPqmdzT7R6MTp7BYjQZuGxiR4rzy9k4L8WpeXs6u1edwNvPRGLvZkTcfx/ebdqQ8a8XsJeWuuaG1nLYOgPe76WtghaD5gL04c3Qfbw+zlBDauIPonUVwf21hAdQWljAwg/eIrxFS4bfeY/T8s05XszPH+4iONKXax7ujsnbPVPtipYuJXXceJTFQtxn0/Fp5zmrSAdPuJ2IlnEs/ui/FOfm1DqfvTl7mbBgAjP3z2Rip4nMunYWnSI6OVHSs4luE0K3obHsXHGMjMMFLruPJ1FWVEHy71l07B+Nl7cRg7c3Mf9+Acvx45x8733n3qyiFDZ8BO/2hJ8eB78wuGWmttit29hGaZLbldRkoZyviDwhInNFZI6I/FlEfOtDOE9GKcXi/72DuaiQax57Gi8f5zySolwzP723Ay9vA9c+eolb7NUom42st97m2COP4t2mDa3nzMa3Q9Urht2Fydubqx99ivKyMma//BylhRdX2ZZZy/jf9v9x28+3UVxRzMcjP+b/+v4fvibX/7T739iWgBAfln2xn4qyxt/VtG99OnarosuQM5Ma/Hv3JnT8eHI//5yy3ef3XV1jTh6ERX+HtzrBov+D0HiYOBfuXa4NROsthlpRk6f2BdAFeA943xH/0pVCNQR+X7SAlG2bGTpxMs0SnNOgMpdY+Om9HVjMVq59tAfBEfW/GM6al8fRe+8jZ+pUQseNI/6rL/GKce+6i/PRLKENN/31OQoyM5j76vOU16C7wq7szEuax7U/XMuHOz5kZPxI5t4wl4EtBtaDxBrefiZG3NmJgsxSFn68C5u18dpqUnbF3tUniEkMIbzF2Yvjmj31JMaIcNL/+RzKWgtFaa2A3XNgxrXwQR/Y9Am0vRwmLYS7F0LiCHDjlPDGQE0URFel1GSl1HJHuBdNSTRZslJTWPX1dNpc2oeeVzrHNJXVYuOX/+2k4GQpVz3Y3S1G+Mr27CH15rGUbt5M9Iv/JubFf2Pw8al3OS6GVl26c90Tf+fkkcP8OOXfWMrPP7NpY/pGJiyYwLNrn6WZXzNmXDmDKcOmuMU1aKtO4Vx2R0eO7c/jt8/3NdpV1scO5FFwsuys1sMpjMHBRP/jWcr37iP38y9qnmnuYVjyvNZamH035B+BEc/DE3th3GcQX3/KvrFTkw65bSLSXym1AUBE+tGEB6kt5WZ+/u8UfAODGP3gn52yaM1uVyyZvpf05AJGTe5Cyw5hTpD04sif+wMZ//oXxogI4md+jV+3uk/trC/aXNqHqx55kp/ffZ35b73KjU8/i9F0pmsuOT+Zt7a+xapjq2gR0IIpQ6cwOmE0BnFvt0PH/jGU5Jez4ccU/EO8GTzWc8Z4nMWe1cfxDfCi7aVVT9EOGj2KwMsu4+R77xE0ehTeLc/jNrf4JOybB7t/gCNrQIyaJ7fek6DN5XoXkouoiYLoBawTkTTHfhxwQER2AUop1d1l0nkgKz7/lNz044z9x4v4B9f9y7O81MLSGftI3ZnN4HHtaNe7fp312UtLyZwyhfxvZ+Hfvz+xb72JKbzhzWLuOHAoFWVlLJn6Hr+89ybXPP402eYcPtrxEXMOzSHAFMATvZ7g1k634mP0nFbRpaPjKSmoYMfSowSE+NDTAyz0OouSgnIOb8+m++UtMXlVPdFCRIj+53OkXHMtGf96gVafTD3z0VWSA/t/gt1zIXU1KDsbTNq5AAAa5ElEQVREdoDhz2grnkPqd6FmU6QmCuJKl0vRQDi4YQ07f1tEnxvGEt+tR53zyz5WxMKPd1OcY2bw+HZccnkrJ0hZM5TdTuGCBWS9+RbWzEwi7plM1J//jDhxHUd9033EaCrKSln55TR25O9mTps9IHBLh1t44JIHCPOt/5bZhRARBo9rR2lBOevmJBEQ4k37vtHuFssp7FuXjt2uquxeqoxXTAxRf/kLmS+/TOHsmYQkKk0ppKwAZYPwtjDkSehyEzTrrI8r1CMXrA2UUk3bmL2Dwuwsfp36HtFt2zFo/MQ657d/fTorZh7A19/EjU9eSkzb+usHL9uxg4xXXsG8Yye+XboQ+9ab+PfqVW/3dwUWm4Vfj/zKTJmNITGfHvvhVv++THjwH8QFe/ZXucEgXDGpM2VFO/jt8334BXnTqlPDa8VVxu4YnI7tEEZo82qcA9kscGwzYdFJFESbyHzpBQKuzsLUPA4GPgpdx0B0d10puImG+7lYj5Tk5zH/zVex2+xc89hf67Ra2mqxsfq7Q44/TyijJnetN/tKlsxMst58k8L5P2GMiiTmlVcIufEGl/hxqC9yynL4/uD3fHfgO06WnSQhOIFbbnuQqA357Fq8kNQFy2h5y+0YPNxss8nLyNUPdmPuG9tY+NEubnryUqLiGq5toKN7cynKNTNgTBVWUfOPQvJvkLQUUlZCeSEiRmKu7MnhL9LJKp1Ai8c/0pWCB6AriAuQkXyIeW+8hLm4mGse/yuh0bWf8lmYXcbiT3aTdaSIS0fH0+/61hiMrq+c7WYzOdOnk/PJp2CzEXHffUTcdx/GQA+zyV9DiiqKWHF0BUuPLGX18dVY7BYGxQ7ihY4vMCh2EAYxoDrawWpn87zZHNuzi9EPPk5ES89uSfj4e3Hdoz2YM2ULP72/g7F/7eV2vx+1Zfeq4/gFedGmezik74SjGyFtg7YtOKolCm6pdRslXgFthuHrG0KE99vkTJ2K14cfEvnQQ261XKwDolTDml7Xu3dvtWVL/Uyi2rtqGb9OfQ//kFBueOpZmreuvY34I3tyWDJ9D8oOI+7sVC+G9ywnTpA/Zy75s2djzcwkaNQomv316fPPFPFgCsoLWH50OUuOLGH9ifVY7Baa+TVjZMJIxncYT5uQP65FUUqxf90qln32MZayUgaMvZXe141xqr0sV5B7ooS5b2zFYBQGj9cmLjSYirIkm+KDO/hiKvRssZUBxnehokg7FxQDrfpBXH9ocxlEdfhDK0FVVJD+3HMUzJtPyA3XE/3iixi83WfBuDEhIluVUr0v6hpdQfwRu83Gqq8/Y+vPP9Kyc1eu+8vfaz1jKSOlgG2Lj3B4RzYRsYFceX9XQpu5zmG7slgoWrGC/O+/p2T1GgACBg4k4r77COjXcIyTKaU4WnSUjRkb+e3Ib2xM34hVWYkJiGFk/EhGxo+ke1T3Gk1VLS3I57fpH3FwwxqatW7L6Aced9riRleRc6KYZV/sJyu1kPiuEQy7tQNB4R5kwMBuh7zDkLETMnadCUXpbCqawOaSW5jY8S1CEttrCqFVP81qag0UnVKKnI8+4uR/38Wvdy9avvcepjDPm2DQ0NAVhBMoKy5iwTuvkbZrOz1GX8vwO+656C9OpRRpe3PZtugIJw7l4xNgovvwlvQcHY+Xi+wqVaSlkf/9bPJ//AHbyWxMzZoRcvMYQm8eW+9+G2qDXdlJyk9iW+Y2tmZuZWvmVk6WnQSgZWBLRiWMYmT8SLpEdKn11/TBjWv5bdr/MBcX0e+m8fS7afxZ6yU8DbtdsWv5MTbMS0ZE6H9jW7oNi0Xq03CjpQxyUyD7EOQcgpxkLX5yP1QUa2nECFEdUc27kWQexMrNLWmeEMx1f76ouugPFCz4mfRnnsEUE02rjz7Cp3VrJxSo6aIriDqSnZbKj2+8RHFONiPueYhul12cbwe7zU7Stiy2LU4j51gxgWE+9Lgijk6DYpzuQctuNlO2fTslGzdSumEjZb//DgYDgcOGETpuHIFDh3jslFWlFJmlmRzKO8TBvINsP7mdbZnbKKwoBKCZfzN6Ne9F7+a96dW8F21C2jiti6WsqJDlM6ayb80KIuMSGHb7ZOK6dMdg9NxB7MLsMlbOPEDa3lyi2wRz2cROfzBbUWvsNijK0MYFCo5pbjcLjkJeKmQnOcYLKtURwbEQkah1D0V3h+huENWRvBwbq749yLH9eUTFBTHy7s6EOcHvdOm23zn2yCMom42W771LQN+G0wr2NHQFUUsKs7M4uGEt6777Gm9/f65/4u+0aF8zi57KrsjLKOXovlx2Lj9KYbaZsGh/eo6Kp33f5hhNzhmEtpeXU7Z9B6WbNlG6cSNlO3agLBYwGPDt0oWgyy8jZMwYl/uHvhjsyk5OWQ6phakcyjtEUn7S6W2xpfh0urigOHo173U6xAbGurzPPXnrRpZ+8gHFebn4BYfQrs8A2vUfRKvO3TxyjEIpxcFNmaz57hAVZiu9rkqg56i487dIlYKyPCjOguIMbVuUAcWZWijK0JRB4Qmwn+Pj2y9MM3YX2U5TBhGJWjy8LficbQLGUmFj68JUfv81DZO3kf43tKHL0FinmqevOHqUow88SEVaGjEvvEDomJuclndTwuMUhIhcCfwXMAKfKqX+c855HzRjgL2AHGCCUiq1ujydoSCUUuQcSyNp03qStmwgMyUJgNiOXbj28b8SGH5+h+o2q52TaUWcOJRPenIB6cn5lJdohsaatw7m0tHxtO4eWetuAFtxMRWpR6hITT0rlB88iKqo0BRCp0749+2Lf7+++PfujTGw/u02We1W8svzyTfnc7LsJBklGZwoOUF6cfrpeEZJBpZKlU+wdzDtwtqRGJpIu9B2JIYlkhia6BZbSKCZTTm8fSsHN6wlZesmLOVmfAODSOzTn/b9BhHX7RL3dkEpBVYzmAuhvAjKCyjLLWD1UguHDnhhMNiJDi+kZVg6LYOSaWY8hLE8G0pzoSwXbBV/zNPkC4HNISgaQlpBaCvNu1pInCPe6g9K4Hwc3pnN6lkHKcox06FfNANvTnTZlG1bYSHHHn+c0vUbCLv1VoKuHI1ft24Y/BrmLC934FEKQkSMwEFgJHAM2Az8SSm1t1Kah4DuSqkHROQW4Cal1ITq8q2tglB2O+lJB0navJ6kzevJSz8BQEy7DiT2GUBinwGEt4jFZrFTWlRBWVEFpYVaOBXPPlpMZmohNotmfTO0uT8xbUOISQwhpm0oIc38zvryVVYrqrwce3k5qqwMa34+trx8bHl5WsjPx5afhzUvD2vWSSqOHMGWXckdpQheMTF4JyTg0769phR698IYHHzx5VcKi91Cua2ccls5FbYKKmwVp+Ml1hJKLCWUWkoptZSetV9sKSbfnE9eeR555jzyyvMoOjUzpRKCEOUfRUxAjBYCtW1cUBztwtoR5RflsbNxLBXlpO7YxqENa0neupGKsjJ8/ANoFp9AUHg4weHhBIWFERwWQlBYMMGhwXiZjFolbKvQFnzZKsBWfiZurdAq+FPBYj5nv0zzcGYp1fwYWEq0/VPx8uI/ft07OFHRicPmvhyzdCfbkgAY8DKU0yI0k5bN8omNrSAgIhjvsEiMIc2Q4BgIbAY+wbVaX2Cz2DGXWigvtVJWVMH2pUdJ3ZlNWEwAw/7Untj2rh9EVhYLGS+/TP63s7QDJhO+HTvid2lP/Hv2xK9nT7yiG8cqdFfgaQpiAPAvpdRox/7fAZRSr1ZKs9iRZr2ImIAMIEpVI1RtFcRH999DSX4GIBgNUXgZYzGaWiGGQBAjSowo8cVurHqGkdjL8a7IwK80Gb/SFAJKk/G2FCEKDHYQBSYbmKwKLyuYrGC8gBVnBZT5QqmfUOIv5IQKOWFCdpiB7DAhN0ywmAQFKJRjC3YBe6Vjp/ZtKGyOuFWU4xjYRGGtRb0sCnyV4KeEILsQaDcQZBeC7AaCK8VD7EKkzUiEzYAJQc56fWfi50xodBz74/ZUHKWQ0+eU43p1Jo06k14Ldi29sv/huEGdOn9m34AdAzZE2TFgx4gNg7JjtyuOloSQVBRBXoUfhRYfiq0+pyU4ha/Bgslgxyh2jKIwiMIo9rO2VT12OwYUBuwi2DFiF8c+BuxidGwN2MWE3WDCbvTGZvTCavTBYvDFYvTFYvKjMLgVeeHtMdqNBBfZCC60Elxgw6/87L+PXcBuAJtRtGAAu7H6H4QohdEKJpvCZFV/+C3bDHAs1pvM5l6oi2wt17XO8SsrpsWJJFqeSKLl8SRapKfgZdVaSwVB4WRHxmL28cfsG4DZx59yH3/Mvtq2zMefYy3aYfGu2h6XonrZLiT6Bc9Xyv/ctFVees7Be4a0ZlSX2inB2igIV3a2xgJHK+0fA/qdL41SyioiBUAEcJZXdxG5D7gPIC6udoudvH1DUKYWeBkiMWBElA2xlCCqELBqlYS9HIOtCJOtCIO1EKOtCKOtCIOtCIOqQDn+aEqgzAdKfDl9zC5gM4HFZMBiAqsJLI6gxYVSX6HUD8r8tK3Zh7P+XKLOVKKnKjdvO45KEgxKs8/+x33BqMDg2JoAg5LTWyPgpSoFBC8F3gq8lBb3UYKfXfBT4GsXfBX4OPI8JVHVaDWHwnbW0bOrxkqtKqkqzdlVP6e3ldVIJdUhjrho57QKt1IacYQz6uDMVgwONaFtT1fGGB3qwlFJBxqwNzdgEyNemAhWBiwWO9YKG7YKG/YKK+YKC3al2ZCzK0Eppf3pldIqQQVnVJXhLDVXNep0hSAKxG7HYLc6ghmDPQ+j3YqX0p55CBuJMXqTH9aanPBEjoe3xdI8AJ8KRWipHS+bo4K3g9GuMNm0jxaTXWG0Vl+T2QGzl2DxFaxGAxYjWIyCxQhWo1DkK1R4CZTXzuFRXRqSxQZfTrbsyo6WXQEw2KzEZB8jLj2J+PQkwgqzCcnLwre8FL/yUoz2s3+bWeExfH7jExQEVW3O5EKiXUh2uVAOUmVU++Wfe6mcnV99t8A9bzSuCpRSU4GpoLUgapPH3f9906ky6ei4C7vNRkVZGccP7CFl62ZStm0i8uABECEmsT1tLu1L2159iYrXp4UqpVBlZdiKirAXFlKenIzh2ef4+y9vEjftU3za1n7xa1OgyXQx6eg0VpRSZB1OJmWbpiwykg8BcPmk++l55XVuls7zMO/fT9q990KFhZYf/Q//nj3dLVK9UJsuJlcaAtoMtBOR1iLiDdwCzD8nzXzgTkd8LLCsOuWgo6PzR0SE5m0SGTD2T9z2yts88PGXtO7Zm5VfTjs9Q0/nDL4dO5IwcyaG0BDSJt1N0YoV7hbJY3GZglBKWYFHgMXAPuA7pdQeEfm3iFzvSDYNiBCRJOAJ4G+ukkdHp6kQEBrGVQ8/gV9IKAv++1qNfHU3NbxbtSJh5kx82rbl2MOPkP/jj+4WySPRF8rp6DRSju3fw3cv/J0OA4Zw9aNPeewUY3diKy7h2KOPULp+A82efoqIyZPdLZLL8LQuJh0dHTfSsmMXBo2fyP61K9m9fIm7xfFIjIEBtPr4Y4Kvvoqs198g87UpKPsF5qc3IXQFoaPTiOl7w1jiuvVg2Wcfk31Udw5ZFQZvb1q88QZhEyeS+9lnFMw/d6i06aIrCB2dRowYDFz9yJN4+/mx4J3XsJSb3S2SRyIGA83/8Qym6GiKly13tzgeg64gdHQaOQGhYVz9yFPkHD/K8hlT3S2OxyIiBA4ZTMm6dZohTB1dQejoNAXiu/eg343j2LXsV/atXelucTyWgMFDsBcXU7Zzp7tF8Qh0BaGj00QYOO42WnTozJKp75OXccLd4ngkAQP6g9FI8erV7hbFI9AVhI5OE8FgNHLNY09jNJlY8M5r2Ky1s6PUmDEGB+PXo8dpd71NHV1B6Og0IYIjo7jsznvJOpxM+sH97hbHIwkcMhjznj1Ys7MvnLiRoysIHZ0mRkKPXgAcP7jPzZJ4JgFDhgBQsnatmyVxP7qC0NFpYvgHhxDWoiUndAVRJb6dOmGMiKBY72bSFYSOTlOkRfuOnDi4v87OexojYjAQOHgQJWvWoGy2C1/QiNEVhI5OEyS2Q2fMRYXkpR93tygeScDgIdjy8zHv3XvhxI0YXUHo6DRBWrTvBMCJA3o3U1UEDBoIIk1+uquuIHR0miDhLWLxDQjkuK4gqsQUHo5v166UrGraCqLBmfsWkZPAuVbHIjnHj3UDp7GVBxpfmRpbeaDxlamxlQfqVqZ4pVTUxVzQ4BREVYjIlou1c+7JNLbyQOMrU2MrDzS+MjW28kD9l0nvYtLR0dHRqRJdQejo6OjoVEljURCNzYZxYysPNL4yNbbyQOMrU2MrD9RzmRrFGISOjo6OjvNpLC0IHR0dHR0noysIHR0dHZ0q8WgFISJXisgBEUkSkb9Vcd5HRGY5zm8UkYRK5/7uOH5AREbXp9zVUdsyiUiCiJSJyHZH+Ki+Za+KGpRnqIhsExGriIw959ydInLIEe6sP6mrp45lslV6R/PrT+rzU4PyPCEie0Vkp4j8JiLxlc411HdUXZka4jt6QER2OWReIyKdK51zXV2nlPLIABiBZKAN4A3sADqfk+Yh4CNH/BZgliPe2ZHeB2jtyMfYwMuUAOx2dxlqUZ4EoDvwBTC20vFwIMWxDXPEwxpymRznit1dhlqU5zLA3xF/sNJvriG/oyrL1IDfUXCl+PXAIkfcpXWdJ7cg+gJJSqkUpVQF8C1wwzlpbgA+d8RnAyNERBzHv1VKlSulDgNJjvzcTV3K5IlcsDxKqVSl1E7Afs61o4ElSqlcpVQesAS4sj6EvgB1KZMnUpPyLFdKlTp2NwAtHfGG/I7OVyZPpCblKay0GwCcml3k0rrOkxVELHC00v4xx7Eq0yilrEABEFHDa91BXcoE0FpEfheRlSIyxNXC1oC6POeG/I6qw1dEtojIBhG50bmi1YqLLc9kYGEtr60v6lImaKDvSEQeFpFkYArw2MVcW1tMzspIx+WkA3FKqRwR6QX8KCJdzvmy0HE/8Uqp4yLSBlgmIruUUsnuFqomiMhEoDcwzN2yOIvzlKlBviOl1AfAByJyK/As4PIxIU9uQRwHWlXab+k4VmUaETEBIUBODa91B7Uuk6MJmQOglNqK1tfY3uUSV09dnnNDfkfnRSl13LFNAVYAPZ0pXC2oUXlE5ArgH8D1Sqnyi7nWDdSlTA32HVXiW+BUy8e178jdAzTVDNyY0AbFWnNm4KbLOWke5uwB3e8c8S6cPXCTgmcMUtelTFGnyoA2mHUcCPf08lRKO4M/DlIfRhv8DHPE3VoeJ5QpDPBxxCOBQ5wz2OiJ5UGrIJOBduccb7DvqJoyNdR31K5S/DpgiyPu0rrOrS+6Bg/uauCg40X/w3Hs32hfBAC+wPdoAzObgDaVrv2H47oDwFXuLktdywTcDOwBtgPbgOvcXZYalqcPWr9oCVrrbk+la+92lDMJmOTustS1TMBAYJfjD7sLmOzustSwPEuBTMdvazswvxG8oyrL1IDf0X8r/f+XU0mBuLKu001t6Ojo6OhUiSePQejo6OjouBFdQejo6OjoVImuIHR0dHR0qkRXEDo6Ojo6VaIrCB0dHR2dKtEVhE69ISLFLsizh4hcXWn/XyLyVB3yGyci+0RkuXMkrD9EZMa51mVrkcdZz1OnaaMrCJ2GTg+0OeTOYjJwr1LqMifmeV4cq+U9CWc/T50GjK4gdNyCiDwtIpsd9vpfcBxLcHy9fyIie0TkVxHxc5zr40i7XUReF5HdIuKNtphoguP4BEf2nUVkhYikiMhj57n/nxz29XeLyGuOY/8EBgPTROT1c9IHOvwKbHNcd0MlmfeLyNcO2WeLiL/jXKqITHGk3yQiiY7jM0TkIxHZCExxfLVvcJTvBxEJE5GOIrKp0v0TRGTXKTkdz263iEy9kLVfEXmskm+Ebx3HAkRkukOu30Xkhqqep4gMkzO+E34XkaCav2WdBo+7VxDqoekEHHb4gVFoztcF7SNlATAUzc+CFejhSPcdMNER3w0McMT/g8M3BnAX8H6le/wLWIdmeiASbaWz1zlytADS0MyXmIBlwI2OcyuA3lXIbsJhk9+Rb5JD/gQ008uDHOemA0854qmcWRV7B7DAEZ/hKPMp0yk7gWGO+L+Bdxzx7UBrR/z/gGcd8fBKcn2JY1U955j+qJTmBGfMS4Q6tq9UerahaKt4A6p4nj9VKlsgYHL370gP9Rf0FoSOOxjlCL+jmQ3pCLRznDuslNruiG8FEkQkFAhSSq13HJ95gfx/Vppxw2wgC2h+zvk+wAql1EmlmVT/Gk1BVYcAr4jITjQzDrGV8j2qlFrriH+F1go5xTeVtgMqHf9eKWUTkRC0Snul4/jnlWT5DjjVKpoAzHLELxPN2+Au4HI0ezzVsRP42mHZ1Oo4Ngr4m4hsR1OKvkBcFdeuBd5ytMRCHc9Lp4mgKwgddyDAq0qpHo6QqJSa5jhXXimdjdqZpHdGHudyG1qLo5dSqgeanR9fx7lz7dWoGsRLanDPWcB4EWkPKKXUIRHxBT5Eayl0Az6pJMf5uAb4ALgU2OwY9xDg5krvIE4pte/cC5VS/wHuAfyAtSLSsQZy6zQSdAWh4w4WA3eLSCCAiMSKSLPzJVZK5QNFItLPceiWSqeLgIvtF98EDBORSBExAn8CVl7gmhAgSyllEZHLgPhK5+JE5FTr4FZgTaVzlVsA6zkHpVQBkCdnHEDdfkoWpfkosAHPcab1cEoZZDueX7WzlkTEALRSSi1H66YKQesqWgw8emr8QkROmbw+63mKSFul1C6l1GvAZrTWnk4TwdNmUOg0AZRSv4pIJ2C9o34qBiaiVYbnYzLwiYjY0SrQAsfx5ZzpKnm1hvdPF80x/HK0L+mflVLzLnDZ18BPjm6dLcD+SucOAA+LyHRgL/C/SufCHN1S5WiKqCruBD5yDG6nAJMqnZsFvI5myhmlVL6IfII2JpOBVmlXhxH4ytGVJcC7jjxeBN4BdjqUyGHgWv74PAc7FKIdzZrowqpuotM40a256jQIRCRQKVXsiP8NiFFKPe5msRCRBLTB565VnEtFG/DOrmexdHScgt6C0GkoXCMif0f7zR5Bm22jo6PjQvQWhI6Ojo5OleiD1Do6Ojo6VaIrCB0dHR2dKtEVhI6Ojo5OlegKQkdHR0enSnQFoaOjo6NTJf8PpdVg8BOnB3AAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6wwwlkK3rzSk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "f38a10f7-f6a9-4d15-bbbb-0c9d46341b95"
      },
      "source": [
        "k=5\n",
        "plt.plot(pvals6, prob6_100[:,k])\n",
        "plt.plot(pvals6, conjectureVals[:,k])\n",
        "plt.axvline(x=1/(k+2), color='k', linestyle='--', linewidth=1)\n",
        "plt.ylim((-0.1,1))\n",
        "plt.title(\"Computed vs. Conjectured Probabilities for $\\\\tau = {0}$  (n = {1} sets)\".format(k, numSets))\n",
        "plt.xlabel(\"length of approval sets\")\n",
        "plt.ylabel(\"probability of piercing number\")\n",
        "plt.legend([\"computed\",\"conjectured\"]);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HMU-8KTZr4fD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}