{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "826a74cf-5fa1-4b53-9e1c-dcbae385e605",
   "metadata": {},
   "outputs": [],
   "source": [
    "####################################\n",
    "# This Sage worksheet is written by Leslie Hogben \n",
    "# based on code written by numerous other people, some of whom are listed.\n",
    "# It documents examples in Nordhaus-Gaddum bounds for sum and product throttling\n",
    "# by Ryan Blair, Gabriel Elvin, Veronika Furst, Leslie Hogben, and Tony W.H, Wong \n",
    "#################################### "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a6b103d1-7869-486b-8c9c-c3258aea7dbe",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Compiling ./mr_JG-master/Zq_c.pyx...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xrange test failed: define xrange = range\n",
      "Loading Zq_c.pyx...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: -ld_classic is deprecated and will be removed in a future release\n",
      "ld: warning: passed two min versions (11.0, 11.0) for platform macOS. Using 11.0.\n",
      "ld: warning: passed two min versions (11.0, 11.0) for platform macOS. Using 11.0.\n",
      "Compiling ./mr_JG-master/zero_forcing_64.pyx...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Zq.py...\n",
      "Loading zero_forcing_64.pyx...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: -ld_classic is deprecated and will be removed in a future release\n",
      "ld: warning: passed two min versions (11.0, 11.0) for platform macOS. Using 11.0.\n",
      "ld: warning: passed two min versions (11.0, 11.0) for platform macOS. Using 11.0.\n",
      "Compiling ./mr_JG-master/zero_forcing_wavefront.pyx...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading zero_forcing_wavefront.pyx...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored\n",
      "ld: warning: -ld_classic is deprecated and will be removed in a future release\n",
      "ld: warning: passed two min versions (11.0, 11.0) for platform macOS. Using 11.0.\n",
      "ld: warning: passed two min versions (11.0, 11.0) for platform macOS. Using 11.0.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading minrank.py...\n",
      "Loading inertia.py...\n",
      "Loading general_Lib.sage...\n",
      "---sshow, multi_sshow, tuple_generator, minimal_graphs, empty_array, all_one_matrix, elementary_matrix, eigens_multi, sort_dictionary, has_minor, etc.\n",
      "Loading oc_diag_analysis.sage...\n",
      "---gZ_leq, find_gZ, find_EZ, diagonal_analysis, etc.\n",
      "Loading xi_dict.py...\n",
      "---SAPreduced_matrix, has_SAP, find_ZFloor, Zsap, etc.\n",
      "Loading mu_dict.py...\n",
      "---get_mu_from_dict, find_mu, etc.\n",
      "Loading SXP.sage...\n",
      "This code contains extra copy of Z_game, Zell_game, Zplus_game, for the completeness of Zsap_game program.\n",
      "Loading matrix_forcing.py...\n"
     ]
    }
   ],
   "source": [
    "# Run this cell first\n",
    "# F-1 load main minimum rank/maximum nullity and zero forcing functions\n",
    "# zero forcing, PSD forcing, and minimum rank code\n",
    "# developed by S. Butler, L. DeLoss, J. Grout, H.T. Hall, J. LaGrange, J.C.-H. Lin,T. McKay, J. Smith, G. Tims\n",
    "# updated and maintained by Jephian C.-H. Lin \n",
    "load(\"minrank_aux-master/load_all.py\")\n",
    "load_all(local=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8d83d39c-0693-42ec-a5fe-ab66c8e92ec1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scroll through to the type of product throttling you want and enter all its functions cells"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1a96e47-91d0-4c50-b294-5ae2b14f993a",
   "metadata": {},
   "outputs": [],
   "source": [
    "####################################\n",
    "# Standard zero forcing\n",
    "#################################### "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bd7b51f1-1ed9-464c-91c1-005162c904aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-Z-1 additional function for zero forcing number using brute_force\n",
    "def Z(g):\n",
    "    z=zero_forcing_set_wavefront(g)[0]\n",
    "    #len(zero_forcing_set_bruteforce(g))\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9ab95b94-4fe3-4ccb-999e-f2336588ac5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-Z-2 Function for propagation time of set S, pt(G,S)\n",
    "# adapted by Leslie Hogben from Steve Butler's skew propagation time code (F-10)\n",
    "# input: a graph G and a set S of vertices\n",
    "# output: pt(G,S) = prop time of S in G (if -1 is returned then S is not a zero forcing set)\n",
    "def ptz(G,S):\n",
    "    V=set(G.vertices())\n",
    "    count = 0\n",
    "    done = False\n",
    "    active = set(S)\n",
    "    filled = set(S)\n",
    "    for v in V:\n",
    "        N=set(G.neighbors(v))\n",
    "        if v in active and N.issubset(filled):\n",
    "            active.remove(v)\n",
    "        if (v in filled) and (v not in active) and (len(N.intersection(filled)) == G.degree(v)-1):\n",
    "            active.add(v)   \n",
    "    while not done:\n",
    "        done = True\n",
    "        new_active = copy(active)\n",
    "        new_filled = copy(filled)\n",
    "        for v in active:\n",
    "            N=set(G.neighbors(v))\n",
    "            if len(N.intersection(filled)) == G.degree(v)-1:\n",
    "                if done:\n",
    "                    done = False\n",
    "                    count += 1\n",
    "                N.symmetric_difference_update(N.intersection(filled))\n",
    "                u=N.pop()\n",
    "                new_active.remove(v)\n",
    "                new_active.add(u)\n",
    "                new_filled.add(u)\n",
    "        active = copy(new_active)\n",
    "        filled = copy(new_filled)\n",
    "        # print filled\n",
    "        for v in V:\n",
    "            N=set(G.neighbors(v))\n",
    "            if v in active and N.issubset(filled):\n",
    "                active.remove(v)\n",
    "            if (v in filled) and (v not in active) and (len(N.intersection(filled)) == G.degree(v)-1):\n",
    "                active.add(v)\n",
    "    if len(filled)==len(V):\n",
    "        return count\n",
    "    return -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1bdc057a-5e00-449a-9dfb-3eef5fd73213",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-Z-3 Functions for standard propagation time \n",
    "# ptk(G,k) = min prop time over zero forcing sets of G of size k\n",
    "# adapted by Leslie Hogben from Steve Butler's skew propagation time code (F-10)\n",
    "# this is the function used to compute propation time of G and also throttling\n",
    "# input: a graph G and a positive integer k >= Z(G)\n",
    "# output: pt(G,k) = min prop time over zero forcing sets G of size k (if order+1 is returned then k<Z(G))\n",
    "def ptk(G,k):\n",
    "    V=set(G.vertices())\n",
    "    sets = subsets(V,k)\n",
    "    pt=len(V)+1\n",
    "    for S in sets:\n",
    "        count = 0\n",
    "        done = False\n",
    "        active = set(S)\n",
    "        filled = set(S)\n",
    "        for v in V:\n",
    "            N=set(G.neighbors(v))\n",
    "            if v in active and N.issubset(filled):\n",
    "                active.remove(v)\n",
    "            if (v in filled) and (v not in active) and (len(N.intersection(filled)) == G.degree(v)-1):\n",
    "                active.add(v)   \n",
    "        while not done:\n",
    "            done = True\n",
    "            new_active = copy(active)\n",
    "            new_filled = copy(filled)\n",
    "            for v in active:\n",
    "                N=set(G.neighbors(v))\n",
    "                if len(N.intersection(filled)) == G.degree(v)-1:\n",
    "                    if done:\n",
    "                        done = False\n",
    "                        count += 1\n",
    "                    N.symmetric_difference_update(N.intersection(filled))\n",
    "                    u=N.pop()\n",
    "                    new_active.remove(v)\n",
    "                    new_active.add(u)\n",
    "                    new_filled.add(u)\n",
    "            active = copy(new_active)\n",
    "            filled = copy(new_filled)\n",
    "            # print filled\n",
    "            for v in V:\n",
    "                N=set(G.neighbors(v))\n",
    "                if v in active and N.issubset(filled):\n",
    "                    active.remove(v)\n",
    "                if (v in filled) and (v not in active) and (len(N.intersection(filled)) == G.degree(v)-1):\n",
    "                    active.add(v)\n",
    "        if len(filled)==len(V):\n",
    "            if count < pt:\n",
    "                pt=count\n",
    "    return pt\n",
    "# propagation time pt(G)\n",
    "# input: a graph G\n",
    "# output: propagation time pt(G)=pt(G,Z(G))\n",
    "def pt(g):\n",
    "    ptg=ptk(g,Z(g))\n",
    "    return ptg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bf8473de-8c35-47ab-9471-fa8175558868",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-Z-4 Function for product-x (initial cost) Z throttling number\n",
    "#\n",
    "# This function computes th^x(G) by minimizing th^x(G,k)\n",
    "# It is known theoretically that this is always at most the order of the graph.\n",
    "# To run on all graphs first comment out the print statements\n",
    "#\n",
    "# input: a graph g\n",
    "# output: product throttling number th^x(g) and least k such that th^x(g) = th^x(g,k)\n",
    "def thZx(g):\n",
    "    nn=g.order()\n",
    "    saveko=Z(g)\n",
    "    ptko=ptk(g,saveko)\n",
    "    savept=ptko\n",
    "    saveth=saveko*(1+savept)\n",
    "    print(saveko, savept, saveth)\n",
    "    for ko in [saveko+1..nn/2]:\n",
    "        ptko=ptk(g,ko)\n",
    "        print(ko, ptko, ko*(1+ptko))\n",
    "        if ko*(1+ptko)<saveth:\n",
    "            saveko=ko\n",
    "            savept=ptko\n",
    "            saveth=saveko*(1+savept)\n",
    "    if saveth>nn:\n",
    "        saveko=nn\n",
    "        savept=0\n",
    "    return saveko*(1+savept), saveko "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7e7f651e-d394-4bc6-8d89-f744138108a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-Z-5 Functions for product-* (no initial cost) Z throttling number\n",
    "#\n",
    "# This function computes th^*(G) \n",
    "# It is known theoretically that this is the least ko such that pt(G,k0)=1.\n",
    "# To run on all graphs first comment out the print statements\n",
    "#\n",
    "# input: a graph g\n",
    "# output: product throttling number th^*(g)=\n",
    "def thZa(g):\n",
    "    ko=Z(g)\n",
    "    nn=g.order()\n",
    "    ptko=ptk(g,ko)\n",
    "    savept=ptko\n",
    "    saveko=ko\n",
    "    while ptko >1:\n",
    "        print(ko, ptko, ko*ptko)\n",
    "        ko=ko+1\n",
    "        ptko=ptk(g,ko)          \n",
    "    print(ko, ptko, ko*ptko)\n",
    "    return ko*ptko, ko"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5102652c-4c46-45d9-b3e7-1fb75a544dc4",
   "metadata": {},
   "outputs": [],
   "source": [
    "####################################\n",
    "# PSD zero forcing, propagation, and throttling\n",
    "#################################### "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3c3c7c23-6dee-41a2-9eac-8df3b76fcd7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load PSD propagation time funtions, including pt_plus(G,S) = PSD propagation time of a set S\n",
    "# code by Nathan Warnberg\n",
    "# updated and maintained by Jephian C.-H. Lin \n",
    "load(\"psd_prop_time_interval.py\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4c4aeab2-9a08-4929-9307-6b38312a4105",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Functions for PSD propagation time\n",
    "\n",
    "# function to compute pt_+(G,k) = minimum PSD propagation time over sets of size k\n",
    "# input: a graph G and a positive integer k \n",
    "# output: pt_+(G,k) \n",
    "def ptpk(G,k):\n",
    "    ord=G.order()\n",
    "    V = G.vertices()\n",
    "    S = subsets(V,k)\n",
    "    ptp = -1\n",
    "    for s in S:\n",
    "        ptps=pt_plus(G,s)\n",
    "        if (ptp < 0):\n",
    "            ptp=ptps\n",
    "        if (ptps >= 0) and (ptps < ptp):\n",
    "            ptp=ptps\n",
    "    return ptp\n",
    "\n",
    "# function to compute pt_+(G) = pt_+(G,Z_+(G))\n",
    "# input: a graph G  \n",
    "# output: pt_+(G) \n",
    "def ptp(G):\n",
    "    ptpg=ptpk(G,Zplus(G))\n",
    "    return ptpg "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6e7f913a-a050-419a-bdb0-b7918d910232",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-8 Functions for PSD throttling number\n",
    "# This function computes th_+(G)=thp(G) by minimizing thp(G,k)\n",
    "# input: a graph g\n",
    "# output: PSD throttling number thp(g) \n",
    "def thp(g):\n",
    "    z=Zplus(g)\n",
    "    t=ptpk(g,z)\n",
    "    thz=z+t\n",
    "    kmax=min(z+t-1,g.order())\n",
    "    for k in [z..kmax]:\n",
    "        ptkg=ptpk(g,k)\n",
    "        if k+ptkg<thz:\n",
    "            thz=k+ptkg\n",
    "    return thz\n",
    "# This function computes th_+(G)=thp(g) by minimizing thp(g,k) and \n",
    "# returns both th_+(G) and the least k such that th_+(G) = th_+(G,k)\n",
    "# input: a graph g\n",
    "# output: the set [thp(g),ko] such that thp(g)= thp(g,ko)\n",
    "def thpk(g):\n",
    "    z=Zplus(g)\n",
    "    ko=z\n",
    "    t=ptpk(g,z)\n",
    "    thz=z+t\n",
    "    kmax=min(z+t-1,g.order())\n",
    "    for k in [z..kmax]:\n",
    "        ptkg=ptpk(g,k)\n",
    "        if k+ptkg<thz:\n",
    "            thz=k+ptkg\n",
    "            ko=k\n",
    "    return [thz,ko]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "67a7ee6c-0b31-4f56-8b34-b3e1b17f96ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function for product-x (initial cost) PSD throttling number\n",
    "#\n",
    "# This function computes th_+^x(G) by minimizing th_+^x(G,k)\n",
    "# To run on all graphs first comment out the print statements\n",
    "#\n",
    "# input: a graph g\n",
    "# output: product throttling number th^x(g) and least k such that th^x(g) = th^x(g,k)\n",
    "def thpx(g):\n",
    "    nn=g.order()\n",
    "    saveko=Zplus(g)\n",
    "    savept=ptpk(g,saveko)\n",
    "    saveth=saveko*(1+savept)\n",
    "    # print(saveko,savept,saveth)\n",
    "    for ko in [saveko+1..nn/2]:        \n",
    "        ptko=ptpk(g,ko)\n",
    "        # print(ko,ptko,ko*(1+ptko))\n",
    "        if ko*(1+ptko)<saveko*(1+savept):\n",
    "            saveko=ko\n",
    "            savept=ptko\n",
    "    if nn<saveko*(1+savept):\n",
    "        saveko=nn\n",
    "        savept=0\n",
    "    return saveko*(1+savept), saveko \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4d8ac7be-6543-4347-83ff-9bde5fc240df",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function for product-* PSD throttling number\n",
    "#\n",
    "# This function computes th_+^*(G) by minimizing th_+^*(G,k)\n",
    "# To run on all graphs first comment out the print statements\n",
    "#\n",
    "# input: a graph G\n",
    "# output: product throttling number th_+^*(G) and least k such that th_+^*(G) = th_+^*(G,k)\n",
    "def thpa(g):\n",
    "    ko=Zplus(g)\n",
    "    nn=g.order()\n",
    "    ptko=ptpk(g,ko)\n",
    "    savept=ptko\n",
    "    saveko=ko\n",
    "    saveth=saveko*savept\n",
    "    # print(saveko,savept,saveth)\n",
    "    while ptko >1:\n",
    "        ko=ko+1\n",
    "        ptko=ptpk(g,ko)\n",
    "        # print(ko,ptko,ko*(ptko))\n",
    "        if ko*ptko<saveth:\n",
    "            saveko=ko\n",
    "            savept=ptko\n",
    "    return saveko*savept, saveko"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09549aab-eab9-483e-bfe2-26c52c0a6997",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Lemma 3.2 proof computations\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ffc50c66-d143-4582-85ab-2e793dda7a3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# thpx NG product lower bound 2n no exceptions for n= 6\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e35386cf-f0e6-4009-821d-1a6b20a82a9e",
   "metadata": {},
   "outputs": [
    {
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     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=6\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpxg=thpx(g)[0]\n",
    "    thpxgc=thpx(gc)[0]\n",
    "    k=k+1\n",
    "    print(k)\n",
    "    if thpxg*thpxgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpxg, thpxgc)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4c6c1ccf-cf77-4d36-a386-79cbfb7050f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# thpa NG product lower bound n-1 no exceptions for n= 6\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9f21b8d8-82e9-4177-9b3a-3374780c26e7",
   "metadata": {},
   "outputs": [
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     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=6\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    if max([g.degree(v) for v in g]) >=1 and max([gc.degree(v) for v in g]) >=1:\n",
    "        thpag=thpa(g)[0]\n",
    "        thpagc=thpa(gc)[0]\n",
    "        k=k+1\n",
    "        print(k)\n",
    "        if thpag*thpagc<nn-1:\n",
    "            show(g)\n",
    "            print(thpag, thpagc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0dcc9879-3ac1-46f8-9bce-ee835b5976fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# thp NG product lower bound 2n no exceptions for n= 6, 7, 8\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e79a2bc4-2f2a-4149-af87-b8673084d197",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=6\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpg=thp(g)\n",
    "    thpgc=thp(gc)\n",
    "    k=k+1\n",
    "    print(k)\n",
    "    if thpg*thpgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpg, thpgc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cbd10358-38aa-436c-8201-7b6ac8532a02",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of vertices:\n",
    "nn=7\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpg=thp(g)\n",
    "    thpgc=thp(gc)\n",
    "    k=k+1\n",
    "#    print(k)\n",
    "    if thpg*thpgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpg, thpgc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b86c9edf-6281-4133-a7c4-cfa93cede2e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of vertices:\n",
    "nn=8\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpg=thp(g)\n",
    "    thpgc=thp(gc)\n",
    "    k=k+1\n",
    "#    print(k)\n",
    "    if thpg*thpgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpg, thpgc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45a5be5e-2880-4046-bc0c-d92b0c81ff3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# NG product lower bound Remark 3.3\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3ed84585-3075-4e92-b868-220402a2cafb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# usual bound 2n=8 for thp n=4 \n",
    "# exception for thp n=5 so bounds are 8 and 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "44bf0170-030d-4843-b49c-2c2a78e81619",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=4\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpg=thp(g)\n",
    "    thpgc=thp(gc)\n",
    "    k=k+1\n",
    "    print(k)\n",
    "    if thpg*thpgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpg, thpgc) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a6be7792-4419-4a0a-aff1-aff800306730",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 11 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "17\n",
      "18\n",
      "19\n",
      "20\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 10 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "21\n",
      "22\n",
      "23\n",
      "24\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 11 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "25\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 12 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "26\n",
      "27\n",
      "28\n",
      "29\n",
      "30\n",
      "31\n",
      "32\n",
      "33\n",
      "34\n"
     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=5\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpg=thp(g)\n",
    "    thpgc=thp(gc)\n",
    "    k=k+1\n",
    "    print(k)\n",
    "    if thpg*thpgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpg, thpgc) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "20010f98-4376-4eab-9c29-40f563834b39",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# thpa NG lower bound n-1 for n =4, 5 no exceptions so 3 nd 4 \n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "368e6484-20aa-4948-8fcb-a0d045df82e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=4\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    if max([g.degree(v) for v in g]) >=1 and max([gc.degree(v) for v in g]) >=1:\n",
    "        thpag=thpa(g)[0]\n",
    "        thpagc=thpa(gc)[0]\n",
    "        k=k+1\n",
    "        print(k)\n",
    "        if thpag*thpagc<nn-1:\n",
    "            show(g)\n",
    "            print(thpag, thpagc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f823fa95-0d16-462e-8ce7-0f71a135d3ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "13\n",
      "14\n",
      "15\n",
      "16\n",
      "17\n",
      "18\n",
      "19\n",
      "20\n",
      "21\n",
      "22\n",
      "23\n",
      "24\n",
      "25\n",
      "26\n",
      "27\n",
      "28\n",
      "29\n",
      "30\n",
      "31\n",
      "32\n"
     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=5\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    if max([g.degree(v) for v in g]) >=1 and max([gc.degree(v) for v in g]) >=1:\n",
    "        thpag=thpa(g)[0]\n",
    "        thpagc=thpa(gc)[0]\n",
    "        k=k+1\n",
    "        print(k)\n",
    "        if thpag*thpagc<nn-1:\n",
    "            show(g)\n",
    "            print(thpag, thpagc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73c35675-f278-4679-a281-e181f6205a6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# no exceptions for thp n=4,5 so bounds are 8 and 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e99bcf4e-fe25-4153-834e-c6b69662374f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n"
     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=4\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpxg=thpx(g)[0]\n",
    "    thpxgc=thpx(gc)[0]\n",
    "    k=k+1\n",
    "    print(k)\n",
    "    if thpxg*thpxgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpxg, thpxgc)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5174b123-2610-44ad-b1be-0de8176854da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "13\n",
      "14\n",
      "15\n",
      "16\n",
      "17\n",
      "18\n",
      "19\n",
      "20\n",
      "21\n",
      "22\n",
      "23\n",
      "24\n",
      "25\n",
      "26\n",
      "27\n",
      "28\n",
      "29\n",
      "30\n",
      "31\n",
      "32\n",
      "33\n",
      "34\n"
     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=5\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    thpxg=thpx(g)[0]\n",
    "    thpxgc=thpx(gc)[0]\n",
    "    k=k+1\n",
    "    print(k)\n",
    "    if thpxg*thpxgc<2*nn:\n",
    "        show(g)\n",
    "        print(thpxg, thpxgc)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c6ea0264-7e5d-4f24-8253-d38d4b2b6ea2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a25071b2-05b2-46ed-9695-1889aff9c5dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Theorem 3.7\n",
    "# Comuptation of Z_+(complement of F_c) for c=3,4,5\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0bf13e5f-f1c1-45ea-bf98-6495d0e6bf72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 22 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OBQoUIACWL1+ec+bM4cePHzW6blbxxx9/UCQS8fDhwyrL8vT0ZLt27UiSgwcPpqWlZYY+G4lEwq5du1IoFHLTpk0qry8vX758YVhYGKtWrUoANDU1ZefOnXns2DFd6KsOHemgUcNAknXq1GG1atWUni+VSvnXX38RADt16qSQM1tZkpKSuG/fPjZv3pxisZgGBgYMDAzksWPHcuwuYsWKFQTAOXPmqEVe//79WbRoUZI/fRYAGB4enuGcpKQkBgQEUCwWc+fOnWrRQxEePnzIv/76S5Y1X6hQIY4aNYr37t3Lcl106MjOaNwwrF69mgD45MkTleSsWbOG+vr6rFmzplJHU8ry5s0bTpkyhU5OTgRAJycnTp48mW/evMkyHVTlzJkz1NfXZ7du3dRm2NatW0cAfP/+PUmyevXqrFGjRqbzEhMT2aJFC+rr6/PgwYNq0UVRpFIpT58+ze7du9PMzIwA6OnpyQULFuSa3aEOHaqgccPw7ds3Ghsbc+LEiSrLOnHiBC0tLVm6dGk+evRIDdrJj1Qq5fHjx9m+fXtZCY5mzZpx79692boEx7Nnz2hra8uqVauqdbf18OFDAuCePXtIkmvXriUAuZ6+4+PjWb9+fRoZGfHEiRNq00kZfvz4wY0bN7JBgway0NcWLVpwx44dutBXHb8tGjcMJBkYGMhSpUqp5Wn13r17LFasGK2treXK1tUEnz594pw5c1i+fHkCYIECBTh27Fg+ffpUK/qkx/fv31mpUiUWKlSI7969U6tsqVTKfPnyyRLYYmNjaWFhwSFDhsg1PznU1dTUlBEREWrVTVnevHnDmTNnsmLFigTAfPnysV+/frx06VKOPULUoUMZssQw7Nu3jwAYGRmpFnnv37+nt7c3DQ0NuXnzZrXIVAapVMrz58+zW7duNDU1pUAgoL+/Pzdv3pwlvpDMdGvVqhVNTExS1TNSF/Xr12fdunVl/+/fvz+tra3lfu/fv3+nj48PzczM1Pa3oS6uXbvGwYMH087OjgBYpkwZTp48OVU9KR06ciNZYhgSExNpa2vLgQMHqk1mbGws27ZtS4FAwKlTp2r9ie7bt29cunQpPTw8CIA2NjYcMmSI1hyb48ePJwBu3bpVY2v89ddftLCwkH32N2/eJACFoo6+fv3KypUr08rKijdv3tSUqkqTmJjIffv2sV27djQ0NKRAIGDt2rW5Zs0aXeirjlxLlhgGkhwwYABtbW2ZmJioNpkSiYQjRowgAPbo0UOtslXh+vXr7N+/Py0sfpamrlatGtesWcMfP35kyfpbt24lAI4fP16j6+zfv58AUmSoV6lShX5+fgrJ+fjxI52dnWlra5utI4S+fPnCpUuXyirLmpqaslOnTjx69Kgu9FVHriLLDMOlS5cIgPv371e77GXLllEsFrNu3bpKZ/NqgtjYWK5bt46+vr4EQHNzc4aEhPDq1asaW/PatWs0MTFhq1atNL6L+vjxY6oifCtXriQAPnz4UCFZ7969Y+nSpeno6JjlgQXK8OjRI44fP57FixcnABYsWJAjRozIsEGVDh05hSwzDFKplKVKlWL79u01Iv/w4cM0MzNj+fLl+ezZM42soQpRUVEcPny4rFxD5cqVuXjxYkZHR6ttjXfv3rFQoUKsVKlSlh1zODk5pSi9HRMTQzMzM44YMUJhWa9evWLx4sVZpEiRHNNLQyqV8syZM+zRo4esSKOHhwfnz5+v1kKQOnRkJVlmGEhy4sSJNDY21lg9olu3brFw4cLMnz8/L126pJE1VCUhIYHbtm1jgwYNKBQKaWJiwi5dujAiIkKlJ/z4+HhWrVqVNjY2WRod1b59e1auXDnFa3369KGdnZ1S4Z5Pnz5lwYIFWaJEiRyVK0L+3CFu2rSJDRs2pEgkop6eHps3b87t27drPRhBhw5FyFLD8PjxY6Xq/yvCmzdv6O7uTmNjY61k1yrCs2fPOH78eBYqVEjW73jWrFkKP2lKpVJ269aNenp6PHPmjIa0TZu5c+dST08vRQ+Nq1evKlVZN5kHDx7Q3t6e5cqVkyXQ5TTevn3LWbNmsVKlSgRAKysrhoSE8OLFi1oPlNChIzOy1DCQZNWqVVOEOGqCmJgYNm/enAKBQGPlntVJUlISDxw4wJYtW1JPT48GBgZs164djxw5IpdTc+7cubKualnNhQsXCCBVTknlypVZr149peXeuXOH1tbWdHFxydJMd01w/fp1DhkyhPnz5ycAli5dmqGhoTnmuEzH70eWG4YlS5ZQKBTy1atXGl1HIpFw8ODBBMC+fftm6+zkX3n79i2nTZvGkiVLEgCLFSvGSZMmpft5HT58mCKRSK2hwIoQHx9PfX39VAY4LCyMAoFApWOta9eu0cLCgp6enmr1xWiLpKQk7t+/nwEBATQyMqJAIKCfnx9Xr16d68u968hZZLlh+PTpE/X19Tlz5swsWW/hwoUUiURs1KhRjvrySaVSnjx5kkFBQTQ0NKRIJGKTJk24e/duWVhuVFQULSwsWLduXa2G6np4eDAgICDFa9++faOpqanKrT0vXrzIvHnzsnr16mm2EM2pfP36lcuWLZM1jTIxMWGHDh3k3iXq0KFJstwwkGTz5s3p4uKSZevt27ePpqamrFSpUo5s2vL582fOnz9fVqrBwcGBQ4YMYbFixViiRAmtH7X069ePxYoVS/V69+7d6ejoqLLROnPmDE1MTFinTh219APPbjx+/Jh///23rFBjgQIF+Oeff/LOnTvaVk3Hb4pWDENyAlZ6Xb80wdWrV+no6EhHR0eNlYjQNFKplJcuXWL37t0pFosJgN7e3ty0aZNWo17Cw8MJIJXTPLnT265du1Re48iRIzQ0NGTjxo1zbXE7qVTKs2fPsmfPnrLQV3d3d86bN08X+qojS9GKYYiLi6OFhQX//PPPLF335cuXrFSpEvPkycN9+/Zl6drqZOjQoRQIBPzjjz9YpUoVWcG3QYMGaeUp88GDBwTAvXv3pnhdKpWyUqVKbNy4sVrW2bt3L/X09Ni6detsk+WuKWJjY/nvv/+yUaNGFIvF1NPTY9OmTblt2zZd6KsOjaMVw0CSPXr0YMGCBbP8PPXbt2+yOPNFixZl6drqYM2aNQSQwkdz8+ZNDhw4kFZWVgRAHx8frlq1KsvO5KVSKa2srDh27NhU1xYsWEChUKi24nNbt26lSCRihw4dfpuz+OTQVxcXF1noa58+fXJl+1kd2QOtGYZTp04RgFbq8SclJbFv374EwMGDB+eYG8y5c+doYGDATp06pXlDiIuL44YNG1irVi0CoJmZGXv37s3Lly9rXLd69erR398/1etfvnyhsbEx//77b7WttX79egoEAvbo0eO3uzHeuHGDQ4cOpb29PQGwVKlSnDRpUrbM9teRc9GaYZBKpSxcuDCDg4O1pQJnz55NgUDAFi1aZPuIlxcvXjB//vz08vKSywH78OFDjhgxQhY77+rqyoULF2qsltS4ceNoaWmZ5o26c+fOLFSokFoN8PLlywmAAwYM+O2MA/m/3JfAwEBZ6GvNmjW5atWqHBV9pyN7ojXDQJKjRo2imZlZhk3kNc2OHTtobGxMd3f3bFuC4cePH3Rzc6OjoyNfv36t0NzExETu2LGDjRo1olAopLGxMTt16sQzZ86o9Yaa3HMjKioq1bWIiAiNFFCcP38+AShVlyk3ER0dzeXLl7NGjRoEQGNjYwYFBfHQoUM5Jn9HR/ZCq4bhzp07BKDVZjvkz8qvdnZ2LFy4cJZGSsmDVCplu3btaGRkpHIzmxcvXnDChAksXLiwrPnMzJkz1VJ2IrnS6tq1a1Ndk0qlLFeuHJs3b67yOv9lxowZBMAJEyaoXXZO5MmTJ5wwYYIs9NXR0ZHDhw/n7du3ta2ajhyEVg0DSbq5ubFJkybaVoNPnz5l+fLlaWZmxsOHD2tbHRmhoaEEwI0bN6pNpkQi4aFDh9i6dWvq6elRX1+fbdq04aFDh1Q67nFycmLfvn3TvDZnzhyKxWKFdzzy8PfffxMAZ8yYoXbZORWpVMqIiAj26tVL1hfEzc2Nc+fOzbH1p3RkHVo3DLNnz6aenl62iNP++vUr69SpQ7FYrJW6Q/9l586dFAgEHD16tMbWePfuHWfMmMHSpUsTAIsUKcIJEyYolQgYGBhId3f3NK99+vSJhoaGDA0NVVXlVEilUv75558EwAULFqhdfk4nLi6OmzdvZuPGjSkWiykWi9mkSRNu3bo1VyYM6lAdrRuGN2/eUCQSceHChdpWheTPstjdu3cnAI4cOVJrjs2bN2/S1NSUzZo1y5KoKalUytOnT7NTp040MjKiUChko0aNuHPnTrlzBubMmUN9ff10bzZBQUEsVqyYRt6PVCpl//79CYArVqxQu/zcwrt37zhnzhy6uroSAC0tLdm7d2+eO3cuS/7Wc0oE4O+O1g0D+TPU0dvbW9tqyJBKpZw6dSoBsF27dlnuHP/w4QOLFi3KChUqaCXC5MuXL1y4cKEsbt7e3p4jR47MtCvb+fPnCYDnz59P8/rJkycJQGNHdVKplD169KBQKOT69es1skZu4ubNmxw2bBgdHBwIgCVLluTEiRPV2s8jMjKSISEhdHVxoYGBAQHQwMCAri4uDAkJUdlvpkMzZAvDsG7dOqXaQWqaf//9l4aGhvT29s6yc9mEhAT6+voyX758fPz4cZasmRGRkZHs1asX8+bNSwD08/Pjhg0b0twVxMXFUV9fn3PmzElTVnIXvzZt2mhMX4lEwqCgIIpEIqX7QfxuJCUl8eDBg2zfvj2NjY0pEAjo6+vLlStXKl3VNioqir7/HyXlYGPNjvX9OLN/Dy4dMZAz+/dgx/p+dLCxJgD61qiRZjSbDu2RLQxDTEwMTU1NNd68XhkiIiJobW3N4sWLp2h6ryl69+5NsVislcS/jIiJieHKlSvp4+Mjy74dOHBgqiguDw8PBgYGpitnxowZ1NPT47t37zSma2JiIlu1akU9Pb0cXfpEG0RHR3PlypWyPuXGxsZs3749Dx48KHfoa3h4OI2MjFjUwZ5bQkcz4dQeSiP2p/pJOLWHW0JHs6iDPY2MjLhu3ToNvzsd8pItDANJdujQgSVKlMiWyUqPHj1iqVKlaGlpyZMnT2psnYULFxIAlyxZorE11MHt27c5aNAg5suXjwBYpUoVrlixgt+/f2ffvn1ZvHjxdOe+f/+e+vr6nD59ukZ1TEhIYOPGjWloaMijR49qdK3cypMnTzhx4kSWKFFCVtV32LBhGYZ0h4eHUyAQMMi/Fr8d3Z6mQfjvz7ej2xnkX4sCgYDh4eFZ+A51pEe2MQyHDh3K8Hxa23z69Im+vr7U19dPM1ZfVY4dO0axWMyQkBC1y9YUcXFx3LRpE2vXrk0AzJs3r6wcR0ZRZm3btmXJkiU1/hAQGxvLOnXq0MTEhKdPn9boWrkZqVTKc+fOsXfv3rLQV1dXV86ZMyfFzu/+/fs0MjJikH8tJp3ZS2nEfhaysyGAVD+9mjdMYRySzuxlkH8tGhkZ6Y6VsgHZxjAkJSUxf/786cbBZwfi4+PZqVMnAuD48ePVdmN7+PAhraysWKtWrRxbNfTRo0ccNWoUbW1tZZ3n5s+fn2aviKNHj2ZZnayYmBhWr16defPm5cWLFzW+Xm4nLi6OW7duZZMmTWShr40bN+bmzZtZvVo1FnO0T7FTeLt3A1/tXif7OTh7EgHw6Pwpae4cijrY07dGDW2/zd8eAUkimzB48GCsXr0aL1++hJ6enrbVSROSmDhxIkaPHo2OHTtiyZIl0NfXV1ret2/fUKVKFcTGxuLChQuwtLRUo7ZZT2JiIiwtLeHg4IAHDx5AX18frVq1Qrdu3eDt7Q2BQACSKFGiBDw9PbFmzRqN6/Tt2zfUqVMH9+7dw/Hjx1GhQgWNr/k78OHDB2zYsAGrVq3CpUuXAABbQkejWQ3vdOcM+GcR9pw5j/v/LodAIEh1fevx02j55wRERkbCxcVFY7rryBihthX4lfbt2+P9+/c4ePCgtlVJF4FAgFGjRiE8PBzr169H3bp18fnzZ6VkSaVSBAUF4enTp9i5c2eONwoAoKenBx8fHxQtWhTPnj3D6NGjcfr0aVStWhVlypTBjBkz8OHDB3Tr1g3//vsvPn36pHGd8uTJg3379qFw4cKoXbs27t69q/E1fwfy5cuHkJAQXLx4EQEBAbDPZ4VGPp7pjk9ITET4gaPo3LBumkYBABr7eMHBxhorVqzQlNo65CBbGQZnZ2eUK1cOa9eu1bYqmRIQEIDDhw/j+vXrqFKlCh49eqSwjDFjxmDnzp1Yv349ypQpowEttYOHhwcuXLiA/Pnz488//0RUVBSOHDmCihUrYsSIEXBwcMDp06eRmJiI1atXZ4lO5ubmOHjwIKytrVGrVi08fPgwS9b9Xbh39y5qu1eCWCxKd8z2ExH48v07OjWone4YsViEWq7OOBcRoQk1dchJtjIMAoEA7du3x/bt2xEdHa1tdTKlatWqOHfuHJKSkuDp6Ylz587JPXfDhg2YOHEiJk+ejAYNGmhQy6zHw8MDHz9+lN18hUIhatasifXr1+PVq1eYOnUqHj58CKlUiqFDh2L8+PF48eKFxvXKly8fDh8+DFNTU9SqVQvPnj3T+Jq/Czdv3YKzU7EMxyzfvR/1PCvD3toqw3HOTkVx4+ZNdaqnQ0GylWEAfj6Jx8fHY9u2bdpWRS6cnJwQERGBEiVKwNfXF//++2+mcyIjI9G5c2e0b98eQ4YMyQItsxZ3d3cAwIULF1Jds7KywoABA3Dz5k38888/SExMRGhoKAoVKoSGDRtix44dSExM1JhudnZ2OHLkCIRCIWrVqoXXr19rbK3fBalUivj4eOQ1MU53zNPXb3H44lV0beyfqTwzUxPEx8dDKpWqU00dCpDtDEOBAgVQo0aNLHFKqovkJ9FmzZqhdevWmDp1KtLz6b9+/RpNmjRBhQoVEBYWlu5Za07GysoKxYsXx/nz59MdIxAI0K9fPxQuXBjNmzfHwoUL8fbtWzRt2hQFCxbEiBEjNHbc4+joiCNHjiA2NhZ+fn54//69RtbJ7ZDEnTt3MGvWLIiEQkTH/Eh37Io9B2FjYYYGVdwzlfv1ewwMDAwgFGa729NvQ7b85Nu3b4+jR4/i5cuX2lZFbgwNDREeHo5Ro0Zh2LBh6NGjR6on37i4ODRr1gwksW3bNhgaGmpJW83j7u6eoWEAfh4xBQcHY9u2bWjTpg0uXryIK1euoEWLFliwYAGKFy+OWrVqYf369YiLi1OrfkWKFMHRo0fx8eNH1K5dW+kAgt8Jkrh37x4WL16MBg0awMzMDGXKlMGgQYMgEAhwLSptQy6VSrFyzyF0qF87Qx9EMteiHqF8uXLqVl+HAmRLw9CiRQsYGBhg/fr12lZFIQQCAf7++28sX74cK1asQMOGDfH161cAP79UPXr0wLVr17B9+3bY29trWVvN4uHhgStXriA+Pj7DcZ07d0ZCQgLCw8MBABUrVsS8efPw+vVrrF69GklJSQgICICDgwMGDBiAW7duqU3HEiVK4PDhw3jx4gX8/f1zhF8rKyGJBw8eICwsDG3btkW+fPlQqlQp9OzZE3v37sWPHz/g6uqKadOmoV1AAA5fuoakJEkqOYcvXsGzN+/QpWGdTNdMSpLgSOQ1eHp5aeIt6ZCTbJXH8Ctt2rTB3bt3ce3aNW2rohRHjx5F8+bNUaBAAezZswebNm3CkCFDEB4ejoCAAG2rp3HOnz8PT09PXLhwAZUrV85wbNOmTfHkyRNcuXIlzaO1e/fuYdmyZVi5ciXev38PT09PdOvWDa1bt4apqanKul6+fBk1a9ZE+fLlsX//fpiYmKgsMydCEk+ePMGxY8dw7NgxHDlyROaDEQqFkEqlyJcvHxo3bowmTZqgVq1ass/q8uXLcHV1zTSPITN0eQzZBK2k1cnBzp07CYDXrl3TtipKc/v2bRYuXFhWRmD48OHaVinLSK60Onfu3EzH7t69mwB44cKFDMfFx8dz8+bNrFu3LgUCAU1NTdm9e3deuHBB5Sz0iIgImpqaslatWlrtQZ7VPHnyhCtXrmTHjh1ZsGBBAqBAIKCRkZHs3x4eHpw0aRKvXbuW5uccHx/PIUOGUCQUspCdrdw1knSZz9mXbGsY4uPjaWVlxaFDh2pbFZU4efIkhUIhRSIRt27dqm11shR3d3e2b98+03FJSUl0dHRkt27d5Jb95MkTjhkzho6OjgRAZ2dnzp07l58+fVJa3+PHj9PIyIgNGjRgfHy80nKyM8+fP+fq1avZuXNnFilSRHbzt7CwoKGhIQHQ3NycgYGBDA8Pz7SzYlRUFN3c3Kinp8dhw4bRyMiQgf41ZbWS5P3R1UrKXmRbw0D+LEHt4OAgd7nf7ManT59YvHhxli5dmo0bN6ZAIOCsWbOyZQVZTRASEkInJye5xo4dO5YmJiYK1/9PSkrinj172KxZM4rFYhoaGrJ9+/Y8ceKEUp/zgQMHqK+vzxYtWuTYulW/8vLlS4aHhzM4OJjFihWTFbGzs7Ojvb09BQKBzLCOGDGCZ86ckev7JpVKuWrVKpqamrJ48eK8ePEipVIpvby8CIDtlayuqiu9nT3I1oYhIiKCAHjkyBFtq6IwiYmJ9PPzo6WlJR88eECJRMIhQ4YQAENCQnLFTScz1qxZQwD8+PFjpmOfPn1KoVCoUsnx169fc/LkySxevDgBsESJEpw6dSrfvHmjkJydO3dSLBYzICBArptkdmpX+fr1a65fv549evSQlcsGwIIFC7JcuXK0srIiAJqYmLBJkyZcsmQJnz9/rtAaX79+ZUBAAAGwY8eOMmM+efJkAmC/fv1k/Rg2h47KsB/D5tBRLJzfVtePIZuRrQ2DVCplsWLF2LlzZ22rojD9+/enSCRKZdQWLVpEkUjEBg0aaKVtZ1Zy//59AuD+/fvlGl+/fn26ubmpvK5UKuWxY8cYEBBAAwMDisVitmjRgvv27ZN797lp0yYKhUIGBwenuvFnp3aVb9++5aZNm9irVy+WLl1aZgiKFy9OHx8fVqxYkfr6+rKKt/369eOBAwfS7cudGRERESxSpAjz5s2b4ka+e/duCgQCjho1imTqDm4d6vlxRr/uXDpiIGf0684O9f7XwU0kEnLXrl1q+Tx0qIdsbRjIn0cMefLkYUxMjLZVkZulS5cSAOfPn5/m9f379zNPnjysVKkSX7x4kcXaZR1SqZSWlpb866+/5Bq/fft2AuDly5fVpsPHjx85e/ZslitXTvbkPG7cOD579izTuatXr6ZAIGDfvn0plUqzRbvK9+/fc8uWLQwJCWHZsmVlhsDJyYmNGjVigwYNZDsmPT091qpVizNnzuS9e/dUOsJMSkrixIkTKRKJ6OnpyUePHsmu3b59m3nz5mWTJk3SNaJurq4pjKibqytDQkJ4/vx5li5dmlWrVv1tjlhzAtneMERFRREAN2zYoG1V5OLUqVPU09Njjx49MvxDv3btGh0dHeng4MCrV69moYZZi7+/P+vXry/X2MTERObPn5+9evVSux7JzWaCg4NpYmJCgUDAevXqcevWrUxISEh33uLFiwmADRs21Eq7yk+fPnHbtm3s378/K1SokGJHEBgYyO7du7NBgwayntx2dnbs0qULt2zZwq9fv6q0djIvXrygr68vBQIBR44cmeLz+vTpE52cnFi2bFm5/ENpHbslN+nSdW/LPmR7w0CSnp6ebNiwobbVyJQnT57Q2tqa1atXz/Bmk8zLly/p4uJCU1NT7t27Nws0zHrGjBlDKysruZ8GR44cybx58/L79+8a0yk6OpphYWF0d3cnANra2nLYsGHp9vQOCgpSyaGqyA3v8+fP3LlzJwcOHMiKFSvKnMNFihRhp06dOG7cOA4YMIBubm4pwknHjx/PyMhItfs7duzYQUtLS9rb26dqkZqYmMg6derI/Giq0LJlS+bPn1/h4AMdmiFHGIZ58+ZRLBZrtIG8qnz79o3Ozs4sXLgw379/L/e879+/s1GjRhQKhVywYIEGNdQOe/bsIQC5bxyPHj0iAC5fvlzDmv3k2rVr7Nu3L83NzQmANWrU4Nq1a2W5DMntKtv/0q5yTNfAVK0qbS0tlArB/Pr1K3fv3s3BgwfT1dWVQqFQduTVsWNHzp8/nwsWLGCnTp1k3fHMzc3Zpk0brl69WmPfiR8/frBPnz4EwCZNmqQZtvrHH39QJBLx8OHDKq/39OlTGhkZcciQISrL0qE6OcIwvH//nmKxWK5kKW0gkUjYokULmpqa8vr16wrPT0pKYr9+/QiAgwYNylZRLqry/v17AlDoSKVOnTr08vLSoFap+fHjB9euXcsa/+9DsLCwYN++feleuXKqdpVjugaybNFCKVpWvt27Qa6krW/fvnHfvn0cOnQo3d3dKRKJfvosHBzYvn17Ll26lAcPHuTUqVNZo0YNisViAmDZsmU5dOhQnjhxQuMRbTdv3mS5cuVoaGjI+fPnp7nbW7VqFQFw9uzZalt3woQJFIvFvHPnjtpk6lCOHGEYSLJRo0b08PDQthppMnbsWALg9u3bVZIze/ZsCoVCNmvWLEc52zOjWLFi7N+/v9zj//33XwLgjRs3NKdUBty/f5/Dhg2jpaUlAXBL6OgUN/sxXQPp7FRU7uStzaGjCIDly5eXGYL8+fMzICCAS5Ys4Y0bN7hnzx726dNHlnRmaGjIBg0acMGCBXzy5EmWvG+pVMoFCxbQ0NCQZcuWTffzP3fuHA0MDNilSxe1OoxjY2NZrFgx+vn56RzRWibHGIaNGzcSQLrnwNoi+SY2YcIEtcjbuXMnjY2NWblyZb5+/VotMrVNQEAAPT095R4fHx9PGxsb9uvXT4NaZU7v3r3pYJ0vlaN5TNdAGhsaMH8+SxbOb8s2ftX5YPOKdA1Dwqk9tLW0YPHixblo0SLevXuXT5484cKFC2VObQAsVKgQe/fuzT179vDHjx9Z+l4/fPjApk2bEgB79+6d7vovX75k/vz5WaVKFaVDXjMiuTzKli1b1C5bh/xk2yJ6/yU2NhZ2dnYYMGAA/vrrL22rAwC4evUqvL290ahRI6xfv15tvRUuX76Mhg0bQl9fH3v27EHZsmXVIldbzJ49G8OGDUN0dDT09fXlmjNs2DAsWbIEr169gpGRkYY1TBs3V1eUs7PEitGDU7y+L+IifsTFo0QBB7z99BkTV67H3acvcHPdYliZ5U1TVqfx03Hh8XM0adIUe/fuxY0bNyASieDj44MGDRqgQYMGKF26tFb6cxw/fhzt27dHbGwsli9fjiZNmqQ5Li4uDtWrV8erV69w8eJF2NnZaUSfRo0a4fr167hz5w6MjdNv/qNDc2TLsttpYWRkhJYtW2Lt2rXpNsHJSt6+fYvGjRujdOnSWL58uVq/0C4uLjh//jzy5s0Lb29vHD58WG2ytYGHhwfi4+MVqpQbHByML1++YMuWLRrULGPSa1dZz6syWvj6oHzxIvBzd8HuGX8DAFbtPZSuLGenorh/7z6WL1+OSpUqYePGjfjw4QOOHz+OIUOGoEyZMlluFBITEzFy5EjUrFkTJUqUwPXr19M1CiTRvXt3XL9+Hdu3b9eYUQCAWbNm4c2bNwgNDdXYGjoyJscYBuBnA59Hjx4p1FtZE8THx6NFixZISEjA9u3bNfJUU6BAAZw+fRpeXl6oV68eli9frvY1soqKFStCT08vzVaf6eHk5ARfX1+EhYVpULP0kaddZTImRoYoX6wwop6/SneMmakJpCRevXqFVatWoXXr1jA3N1ejxorx+PFjVKtWDVOmTMGECRNw6NAhODg4pDt+5syZWLNmDZYvXw5XV1eN6lasWDEMHToUU6dOxYMHDzS6lo60yVGGoXr16nB0dNRq20+S6N27Ny5evIjt27fD0dFRY2vlzZsXu3btQteuXdG1a1eMGDEiR/bBNTQ0RMWKFTPt6PZfunfvjpMnT+Lu3bsa0ix9hEIhDAwMMmxXmUx8QgLuPHmO/FaW6Y5JblcpFovVqaZSrF+/HhUrVsTbt29x+vRpjBgxAiJR+p3V9u/fj6FDh2L48OFo165dluj4559/ws7ODgMHDsyS9XSkJEcZBqFQiMDAQGzcuBEJCQla0WHOnDlYvnw5lixZAk9PT42vJxaLsXDhQkybNg2TJ09GQECA2ttcZgUeHh4KG4ZmzZrBysoKS5cu1ZBWGVOubNk021UOnhOGE5ev4/GrNzh/6y5ajZiI6Jgf6FjfL11Z2aFd5ffv39G5c2cEBASgQYMGuHLlSqZ/w/fu3UPbtm1Rr149TJgwIYs0BYyNjTFz5kzs3r0bu3fvzrJ1dfw/WnV9K8GNGzcIgDt27MjytQ8cOEChUMhBgwZl+dokuXnzZhoaGrJKlSrZOtkvLVavXk0ACvdLGDhwIK2srDQSAZMZISEhdLCxThWV1MavOvPns6SeWEz7fFZsXsObN9ctzjAqycHGmiEhIVn+HpK5dOkSnZycaGJiwpUrV8oVDvrlyxeWLFmSpUqV4pcvX7JAy5RIpVL6+fmxWLFiv1XzpOxAjtoxAEC5cuXg7OyMtWvXZum69+/fR5s2bVC3bl1MmTIlS9dOpkWLFjh+/DgePHgALy8v3Lt3Tyt6KIOHhwcAKORnAIBu3brh48eP2L59uwa0Sp9Xr17B3NwcL9+9x67TKX1a6//+Ey93rUP8qd14sSscm0NHo0yRQunK2nk6Ai/fvUfnzp01rXYqpFIppk+fDi8vL+TNmxdXrlxBx44dM3V0SyQStGvXDm/fvsXOnTthZmaWRRr/D4FAgDlz5uDp06eYMWNGlq//O5PjDAMABAUFYefOnfjy5UuWrPflyxc0btwYtra2WL9+fYbnsZrGw8MD586dg76+Pry8vHDy5Emt6aIITk5OsLCwUNgwlC5dGj4+PliyZImGNPuJRCJBREQERo0ahUqVKsHBwQGTJk2Chbk5Bs1ZgphY5Y7vYmLjMHTeMvjWqJHlPYzfvHmDevXqYciQIRgwYADOnj0LJycnueaOGDECBw4cwMaNG+WeowlKly6NAQMGYOLEiXj27JnW9PjdyJGGoV27dkhISMiSUMZfn5x27dqllSen/1KkSBGcPXsWlSpVgp+fX5bvnpRBIBDA3d1dYT8D8NMJffToUbVHqHz69Anr169HUFAQ7OzsUKVKFSxcuBBly5ZFeHg43r17h+UrVuD52/foOXWOwo5/qVSKnlPm4Onrt+jVu7dadc+MvXv3okKFCrh+/ToOHjyIqVOnyp1DEh4ejqlTp2LatGmoU6eOhjXNnNGjR8Pc3ByDBg3Stiq/D9o+y1IWPz8/1siCpuGDBg2iUCjkwYMHNb6WosTHx7NTp04EwHHjxmX7MgJjxoxhvnz5FNbzx48fNDc357Bhw1RaXyqV8vr16wwNDaWPj4+sYF16bS2vXLlCCwsLFitWjAKBgEFKVld1cnKivr4+w8LCVNJfHuLi4jhgwAACYP369fn27VuF5l+8eJGGhobs0KFDtvp7Wrt2LQHw0KFD2lbltyDHGoaVK1cSAJ8+farxNWbNmqWxNVRFKpVy4sSJBMCgoCCtOGnlJbncwcOHDxWe27dvX9rY2DA+Pl6heTExMdy5cyd79uzJAgUKyN3W8vr167SysqKbmxs/f/7M8PBwhdpV/tqPIT4+nr169SIA9uzZU+H3IC937tyRdWxTprf4q1ev6ODgQA8Pj2zn7JVKpfTx8WGpUqU09vnp+B851jBER0fTyMiIoaGhGpF/9uxZ6uvrs2vXrtnqySk91q1bR319fVavXl2uHsva4N27dwpXWk3m+vXrBMDNmzdnOvbRo0ecO3cu/f39ZV3DFGlrefPmTVpbW7NSpUopoqgUaVdZ09c3VantpUuXUl9fn1WqVOGrV68U/gzSQyqVcunSpTQ2NmbJkiV55coVhWXExcXRy8uL9vb2fPnypdp0UydXr16lUCjk9OnTta1KrifHGgaSbNeuHcuUKaP2G/fz589pa2tLb2/vbP0E/l9OnTpFKysrlixZUuXGKZqiaNGiHDBggFJzPT09Wbdu3VSvJyQk8OjRoxw0aBBLlSqlUlvL27dv08bGhhUqVEizBwH5s11lnz59KBaJqKcnTtWuMqOezxEREbS3t6e9vT0jIiLke+MZ8PnzZ7Zq1YoAGBwcrFSDI6lUys6dO9PAwIAXLlxQWSdNEhISQlNTU7UaVh2pydGGIbkJjDp7BMfExNDFxYUFChRQ+Hw2O3D//n06OTkxX758PHPmjLbVSUW7du2U7rWwbNkyCgQCPn78mG/evOGKFSvYsmVLtbW1vHfvHu3s7FiuXLlM80Q+f/5MANy4caPC/TNev35Nb29vlf0Op0+fZsGCBWlubs5///1XaTmzZs0iAK5Zs0ZpGVnF58+faW1tzfbt22tblVxNjjYMiYmJtLa25h9//KEWeVKplG3atKGxsbFS2/HswocPH1i1alUaGBhw48aN2lYnBbNmzaKBgYHC58QSiYQnTpygvr4+8+fPr/a2llFRUbS3t2fp0qXleiB48OABASjdvexXv0OPHj0U+jwSExM5btw4CoVC+vj4qORnO3jwIIVCIQcPHqy0jKxm2bJlBMCTJ09qW5VcS442DCTZr18/2tnZpYgmUZYJEybIfY6d3YmLi2NAQAABMDQ0NNv4Sc6ePUsAvHjxYqZjv3z5wn///TdFW0t9fX0aGhpy+fLlasv+fvjwIR0dHVmyZEm5e2CcP3+eAFR+gFDU7/D06VNZRNW4ceNU6uYWFRVFCwsL+vv7q+X7k1VIJBK6u7uzQoUKGu9m97uS4w3DhQsXCEDlcNJt27YRAMeOHasexbIBUqmUY8aMIQB27dqVCQkJ2laJsbGx1NPT47x581Jdk0qlvH37NqdNm5ZuW8vk37e6SqI8efKEBQsWpJOTk0JO17179xIAnz17prIO586do729PfPnz8+zZ8+mO+7ff/+lubk5CxYsyFOnTqm05tevX1m6dGmWKFGCnz9/VkmWNrhw4QIFAkGaf0c6VCfHGwapVMqSJUsyKChIaRnXr1+niYkJW7Rokav6LSezcuVK6unp0c/PTys1b/6Lm5sbO3ToQPJnjsLevXsVamvp6urKBg0aqKzHs2fPWKRIERYtWjTdsNX0WLNmDQGorQVrst9BT0+PS5YsSXHt+/fv7NatGwGwZcuWCteb+i8SiYSNGjVi3rx5effuXZVkaZNu3brR3Nw8x9UNywnkeMNAkn///TdNTEyUish49+4dCxcuTGdnZ6Xm5xSOHj1Kc3Nzli1bNst6CKdHhw4daGtrq3Rby8WLF1MoFKr0tP7ixQsWK1aMhQsXVuqMftasWTQ0NFR6/bT4r98hLi6OV69eZalSpWhkZMSwsDC1HAmOGDGCAoGAe/bsUYPW2uP9+/e0sLBgcHCwtlXJdeQKw/Dw4UMCYHh4uELz4uPjWa1aNVpbW2v9ZpkV3L59m0WKFKGtrW2WhiUmJiby5MmTHDZsGMuXL08ABEBvb29OnTqVt27dUuiGFx0dTRMTE44bN04pfV69esUSJUqwQIECfPz4sVIyRo8eTQcHB6XmZsbSpUupp6fHwoULU19fn87Ozrx9+7ZaZG/YsIEAOGXKFLXI0zbz58+nQCDg+fPnta1KriJXGAaS9Pb2pr+/v9zjpVIpe/ToQT09PZXPa3MSb9++paenJ42MjLht2zaNrfP+/XuuWbOGbdu2pYWFBQHQ2tqaHTp04D///EMAPHDggNLyg4ODWaBAAYWdpm/evGGpUqXo4OCgUq5H7969WaFCBaXnZ8S7d+/o7e1NADQ2NuaxY8fUIjcyMpJGRkYMDAzMNsEIqpKUlMSKFSuycuXKufIYWFvkGsOwaNEiCoVCvnnzRq7x8+fPJwAuXbpUw5plP378+MGWLVtSIBBw5syZarlJSKVSXr58mX///Tc9PT0pEAgIgK6urhwzZgzPnz8v++JKJBKam5tz/PjxSq+XHBWkyHHIu3fvWKZMGebPn5/3799Xem2SbNu2LX19fVWSkRYHDx6knZ0dra2tuXbtWvr4+FBPT4+LFy9WSe6bN29YoEABurm5ZXpUl9M4ffo0AWRJLarfhVxjGD5+/Eg9PT256hodOXKEIpGI/fv317xi2RSJRMJhw4YRAHv37q1U2F90dDS3bt3K4OBg2tvbEwDz5MnDFi1acNmyZRmGX9apU4cNGzZUWn+pVEpnZ2c2bdpUrvHv379n+fLlaWtrqxaHa+3atdmyZUuV5SQTHx/PIUOGEABr164t++zi4+PZu3dvAmD37t2VysSPj4+nt7c37ezs+OLFC7XpnJ0ICgqilZVVti0Hk9PINYaBJJs2bUpXV9cMxzx48ICWlpasXbu2Lgaa5JIlSygSiVi/fn1GR0dnOv7+/fv8559/6OfnR319fQJgyZIl+ccff/DIkSNyJ2qNHj2a1tbWKu1W5s2bR5FIlGn8/8ePH1mxYkVaW1vz1q1bSq/3Ky4uLuzRo4daZEVFRdHNzY16enqcNm1amkciy5Yto76+Pr28vBQKq5VKpQwODqa+vr5aSnBkV169esU8efKwT58+2lYlV5CrDMOWLVsIIF1H3devX1mmTBkWL15c5ZC/3MSBAweYJ08eOjs7pwrbjIuL48GDB9m/f386OTnJkszq1q3LOXPmKH1On1xp9dGjR0rr/fnzZxoZGXHixIkZjnF1daWVlRVv3Lih9Fr/pVChQhwxYoRKMqRSKVetWkVTU1MWL14806S/8+fP08HBgXZ2dnKXO5k7dy4BcMWKFSrpmhOYMWMGhUJhjq5akF3IVYYhNjaW5ubmHDlyZKprSUlJbNiwIfPmzcs7d+5oQbvszY0bN1igQAHa29vzwIEDDAsLY9OmTWlqakoAdHR0ZPfu3bljxw61hPUmV1pdv369SnI6duzIIkWKpPmU/eXLF7q7u9PS0pJXr15VaZ3/YmpqyhkzZig9/+vXr7LM9I4dO8q1WyN/5jvI63dIPjJVtmhhTiMhIYGlS5emt7d3rnGua4tcZRjIn0kvhQsXTnWjGD58OAUCAffu3aslzbIvSUlJPHv2LPv16yfLKxAIBPT29uakSZN47do1jXzRihQpwoEDB6ok48yZM2lmvkdHR9PLy4vm5uYZVjtVhvj4eALgypUrlZofERHBIkWKME+ePAqHWCev36dPHwJgt27d0vQ7PHz48Lc8Mj18+HCOKQiYncl1huHkyZOpCmwld3+aNm2aFjXLXnz8+JHr169n+/btmS9fPgKgpaUl27RpQ1dXVwqFQs6fP1+jOrRt25ZVqlRRSYZUKmWZMmXYqlUr2Wvfvn2jj48P8+bNq5F8jVevXhEAd+3apdC8pKQkTpo0iSKRiB4eHko1LPqV5cuXp+l3iI6OZrly5VisWLHf0hnbqlUr2tnZKVVhV8dPcp1hkEgkLFSoELt3707yZ00VAwODbNeqMKtRpK1lUlKSrD3kwIEDNVZg7Z9//qGhoaHKNZz++ecf6unp8e3bt/z+/TurV6/OPHnyaMzZeuPGDQLIsK7Rf3nx4gV9fX0pEAg4YsQItdWt+q/fQSKRsGnTpsyTJ4/aHO05jadPn9LY2JiDBg3Stio5llxnGMifKf/m5uZ89OgR8+fPT09Pz2zXqjArULatZTJz586lUChk06ZNNVIuJLnS6qVLl1SS8+HDBxoYGHDChAmsWbMmTU1NNdqL4vjx4wTAe/fuyTV+x44dtLKyor29PY8ePap2fd68ecOqVatST0+PDRo0oEAg4M6dO9W+Tk5i4sSJFIvFv61xVJVcaRhu374ta+fo4ODwW3V7UrWt5X/ZtWsXTUxM6ObmJndJann58eMHxWKxWo6skvtoGBsba7xOf3L0W3od3pL58eOHzBfQpEmTTMerQnx8PP39/QmAlStXzlGdBzVBXFwcixcvzlq1av3WJwXKkisNg1QqpaWlJYVCocpPo9kddba1TI/Lly/T3t6eBQsWVGvIJ/mzUmrHjh1VkhEXF0d3d3cC4D///KMWvTJiyZIlFAgEGR6x3bx5k+XKlaOhoSHnz5+v8ZvT1atXaWxsTHd3d+rr69PT0zPb9m7OKpI7PKrS3e53JVcahilTphAAxWJxrnS+aaKtZWY8f/6cFSpUYN68eVXuffErvXv3ZqlSpZSeHx8fz4YNG9LQ0JAODg5s166d2nRLj9DQUFpYWKR5TSqVcsGCBTQ0NGTZsmXVbkjT4t27dyxUqBBdXFwYExPDCxcuKJzvkFtp1KgRCxQokKsrJ2uCXGcYdu3aRYFAwP79+1MoFHLRokXaVkllJBIJL1y4wLFjx9LNzU3tbS3lJTo6mvXq1aNYLFZbXZpVq1YRgFLNYhISEtikSRPq6+tz//79nDZtGvX19TV6ZEOSgwcPZvHixVO9/uHDBzZt2lRWZiQrahIlVwi2sbFJUYb8V7/DokWLftvjlAcPHtDAwCDN3CYd6ZOrDMPNmzeZJ08eNmnShBKJhP7+/vTx8dG2WkqRVltLMzMztm7dmqtWrZKrL7EmSExMlPUMGD58uMoG6e7du0p14EtISGCLFi2op6cnK6T37t076unpcebMmSrplBmdO3emh4dHiteOHTtGBwcHWlpacvv27Rpd/1d69uxJPT09nj59OtW1hIQEhoSEEACDg4N/W7/D6NGjqa+vz6ioKG2rkmPINYbhw4cPLFq0KMuVKyfLIk3OX1Cl7EJWIU9by+ySqCSVSjljxgwKBAK2atVKpSdjiURCMzMz/v3333LPSUxMZJs2bSgWi1NF37Ru3ZqlS5fW6BNy48aNWb9+fZI/b74jR46kQCBgjRo1FO4EpwoLFy6Uq6roihUraGBgQA8Pj1xbRC8jYmJiWKhQIbV0/ftdyBWGISEhgTVr1qSVlVUKI/D9+3eamJhwwoQJWtQufWJjYxVua5md2Lp1K42MjOjl5aVSe8XatWuzUaNGco1NSkpiQEAARSIRt27dmur6oUOHCECjPTa8vb0ZFBTER48e0dPTkyKRiBMnTtRYvkdaHD9+nGKxmCEhIXKNv3DhAh0dHWlnZ5fm7iK3s3XrVqWSEn9XcoVhCAkJoVgsTrOhSVBQEEuWLJltzlifPn3KhQsXKt3WMrtx/vx52tjYsGjRokrXoBo1ahRtbGwy/R0lJSWxQ4cOFIlE3LRpU5pjJBIJixYtKusprQlKlSrFevXqMW/evCxSpEiWVy19/Pgx8+XLR19fX4US5d68ecNq1apRT0+PCxcuzDbfiaxAKpWyTp06LFq06G+Z06QoOd4wLF68mAC4cOHCNK8fOHCAADKtXKkp0mprKRKJWL16daXaWmZHHj9+zDJlytDCwkKpbmO7du0igAzbbEokEnbp0oVCoTDTwnuTJk2ioaGhRirofvv2jYaGhgTAdu3a8cuXL2pfIyO+f//OChUqsEiRIko52RMSEti3b9/f0u9w9+5d6unpKXRs+buSow3DiRMnKBaL2bt373THJCYm0s7OLkub8mTU1nLjxo1KReBkdz5//sxatWpRT0+Pq1atUmju27dvCYAbNmxI87pEImH37t0pEAjkKo72+vVrisVizp07VyE9MuPSpUssXrw4AWilxIpUKmXLli1pamqqchjs7+p3GDp0KI2MjLL9Ma22ybGGQZHt9MCBA2ljY6Mx560ibS1zMwkJCezSpQsBcOzYsQrdOAsXLpxmpVWpVMrevXtTIBAo1FOgWbNmLF++vFpu3hKJhNOmTaOenh6dnZ0JgBs3blRZrqKMHz+eANQW9ZTsd7C1tf1t+p5HR0fT3t6ezZs317Yq2ZocaRi+ffvG8uXLs2jRonJtpy9fvkwAai25HR0dzW3btinV1jI3I5VKOWnSJAJg+/bt5T6qaNOmDb29vVPJ6tevn1L9fPft20cAPHfunELz/svr169Zp04dAuCQIUNk5VYOHz6sklxF2bZtGwGo1Cc7Ld6+fctq1apRLBZzwYIFOf5YUx7WrVtHADxw4IC2Vcm25DjDkFw90tTUlDdv3pRrTnJp5oCAAJXWVldby9+BDRs20MDAgNWqVZMr+3zmzJkpKq1KpVL+8ccfBKBUkmJSUhILFizILl26KDw3mT179tDa2pq2traym8j58+cJIEu7hF2/fp2mpqZs2bKlRm7cv/odunbtmuv9DlKplNWqVWPJkiV139l0yHGGYdSoUUpVj5w0aRKNjIzk7pRFaq6t5e/C6dOnaWVlxRIlSmSaXJTccCcyMpJSqZRDhw4lAM6bN0/p9cePH09jY2OFS4TExcXJyo7Xr18/RTLh3r17CSBFlrEmef/+PYsUKUJnZ2eNl3VYuXLlb+N3uHbtGkUiEadOnaptVbIl2c4wZHQWv2HDBgJgaGiownKfPn1KAJk6Rl++fKnxtpa/E1FRUSxRogTz5cuXYfz8r5VWR44cqZaCeM+fP6dQKEw3Yi0t7ty5w4oVK1JfX5+zZs1K9YS+Zs0aAmBMTIxKuslDQkICfX19mS9fvixzll68ePG38Tv069ePpqamud4IKoPWDUNkZCRDQkLo6uIiKxNtYGBAVxcXhoSEyNoyRkZG0sjIiAEBAUpvp6tXr87atWuneC25reXIkSNZsWJFAqBQKNR4W8vfiQ8fPrBatWo0MDBIN/KIJF1cXGTO3enTp6tl7UaNGtHFxSXTcVKplEuXLqWxsTFLliyZ7lHRrFmzaGhoqBbdMiM5P+fEiRNZsl4yv/odsqIyrLb4/Pkzra2tVT5izo1ozTBERUXRt0YNAqCDjTU71vfjzP49uHTEQM7s34Md6/vRwcaaAOhdpQrt7Ozo5uamUgJYWFgYhUIhb926lWZby8DAQIaHh2u8CNvvSFxcHNu3b08AnDhxYpo3m+TS2crsCNNj586dmTYD+vz5M1u1aiWL7c9oVzh69Gg6ODioTb/0CAsLyzA/R9MkJCTIHP9dunTJtUlhy5cvJ4AsN77ZHa0YhvDwcBoZGbGogz23hI5mwqk9lEbsT/WTcGoPt4SOZiE7G4qEQqXPm5PbWo4ZM4YCgUAWTppWW0sdmkMqlXLs2LGym82vYcaTJ08mAAJQa9JYYmIiHRwc2KNHjzSvnz59mgULFqS5ublcdft79+7NChUqqE2/tDh16hT19PTYs2dPja4jD6tWraKBgQHd3d1z5ZGLRCKhh4cHy5cvn21qkWUHstwwhIeHUyAQMMi/Fr8d3Z6mQfjvz7ej29nevxYFAgHDw8PlWie9tpb29vZ0dHTM0mJnOlKyatUqWTOhz58/c/r06bJS1QB46NAhta43evRo5smTh9++fZO9lpiYyHHjxlEoFNLHx4dPnz6VS1abNm3o6+urVv1+5enTp7SxsWG1atWyTcTMpUuXWKBAgVzrd7h48SIFAgHnzJmjbVWyDVlqGO7fv08jIyMG+ddi0pm9chmF5J+kM3sZ5F+LRkZG6Ua4yNPWcvv27QSQJQ1UdKTPsWPHaG5uTjs7OwLgiBEjmJSURDMzM7UXPXzy5AkFAgGXLl1K8ufN18fHh0KhkOPGjVPoSdHPz48tW7ZUq37JxMTEsFKlSixUqJBKRQk1wdu3b1m9evVc63fo3r07zczMtFbOPruRpYbBt0YNFnO0T7FTmD8khOWLFWYeY2PmMTamZ7lS3DPz73R3DkUd7OlbowbJ/7W1HDx4MEuXLi1XW8v4+HhaWlpy2LBhWfnWdaTBqFGjZDu55EQ0Pz8/uSutKoK/vz89PDz477//0tzcnAUKFFDq6bdSpUrpHkupglQqlfWtvnr1qtrlq4Nf/Q6dO3fOVX6H9+/f08LCQqW8l9xElhmGS5cuEQC3hI5OcbPfMXUcd88Yz7sbl/LuxqX8s2Nb6onFvBG+KE3jsDn0582kVq1aSre17NWrFx0dHX+LMhXZlUWLFhEAe/ToQS8vLxoZGXHr1q0cOXIkbW1t1f5EmpztCoAtW7ZUusBewYIFOWLECLXqRlKWLb5582a1y1Y3q1atoqGhId3d3XPVkeyCBQvUki2fG8gywxASEkJHW5t0Hc2//ljkMWXYnwPSdUjbWprT1tZW6baWyclUylQC1aE6S5cuJQD27duXUqmUP378YKtWrSgQCNi5c2cCUGvc/tWrV1mqVCkCoK+vr0pGx8TEhDNmzFCbbuTPyCmBQMAxY8aoVa4mSfY72NjY8OTJk9pWRy0kJSWxYsWKdHV1/e2DUYTIIiLOnkUt1woQi0XpjpFIJNhw6Dhi4uLhVb50mmPEYhHqerihgKMjRo8eDRcXFwiFir0NLy8vFC1aFGvWrFFong7VWbVqFbp164ZevXph9uzZEAgEMDIywoYNGzBs2DCsWLECAHD27FmV1yKJOXPmwN3dHQYGBggODsbly5cRGxurlLz4+HjExMTAyspKZd2SuX37NgIDA9G0aVOMHTtWbXI1jaurKyIjI1GmTBnUrFkTCxYsAEltq6USIpEI8+bNQ2RkJJYvX65tdbRLVlkgAwMDzuzfI81dwLU1C2liZEiRSEgzUxPunjE+wx3FjH7daWBgoJI+Y8aMYd68eXNcY5yczNq1aykQCNitW7d0d3nJ8fuFCxdWqHzJf3n37h0bNGhAAOzfvz9jY2P54MEDubLf0+Ply5dq7QL28eNHFitWjOXKlUsRMZWTSEhIYP/+/XOV36FDhw60srKSq8ZXbiVLdgxSqRTx8fHIa2Kc5vWShRxxZdUCRITNQs9mDdDp7xm4/fhpuvLMTE0QHx8PqVSqtE6BgYGIjo7G7t27lZahQ342btyIDh06oFOnTli0aFG6u7zg4GBUq1YNz58/h4+PD168eKHwWocOHUKFChVw4cIF7NmzB7NmzYKhoSGKFSuGWrVqYcmSJUq9h48fPwKAWnYMSUlJaNOmDT5//owdO3bA1NRUZZnaQE9PD7NmzcLq1auxfv16VKtWTanfWXZiypQpSEhIwOjRo7WtitbIEsMgFAphYGCA6JgfaV7X19ND8QL2cCtdAqG9u8C5eBHM3rg9XXlfv8fAwMBA4SOkXylRogTc3d11x0lZwObNmxEYGIjAwECEhYVl+ntr0qQJxGIxvnz5Ag8PD1y5ckWudRISEjB06FDUqVMH5cuXx7Vr11C/fv0UY7p3744zZ87g9u3bCr8PdRqGIUOG4NixY/j3339RtGhRleVpm6CgIJw+fRpv376Fq6srTp06pW2VlMbOzg5//fUXFi1aJPffXm4jy3wM5cqWxbWoh3KNJYGExMR0r1+LeoTy5cqprFP79u2xb98+fPjwQWVZOtJm+/btaNeuHdq0aYMVK1ZAJErfx5SMh4cH4uPjERYWBnt7e1StWjXTnd2DBw/g7e2NWbNmYdq0adi/fz/y58+falyTJk2QL18+hIWFKfxe1GUYVq5ciVmzZmHWrFmoWbOmSrKyE66urrh06ZLM7zB//vwc63cICQlB6dKlERISkmPfgypkmWHwqlIFhy9dQ1KSJMXrIxauwKmrN/Hk9RvcePAYIxetxPEr1xFQN+0vTFKSBEcir8HTy0tlndq2bQuS2LRpk8qydKRm165daN26NZo3b45Vq1bJZRQAwMXFBWKxGI8ePcLx48fh5+eHJk2aYN68eanGksTq1atRqVIlfPnyBWfPnsXgwYPT3ZUYGBigU6dOWL16NeLi4hR6Px8/foRAIIC5ublC834lIiICPXr0QHBwMPr06aO0nOyKtbU1Dh06hJCQEISEhKBr164Kf87ZAT09PcydOxdnz57F2rVrta1O1pNVzozIyMg08xg6N6zDQnY21NfTo7WFGWu5VeSB2ZPSdTwn5zEkV11VlQYNGtDLy0stsnT8j71791JfX58tWrTItPVqWri4uLBTp04kf4YRJjft6d+/vyyU8OvXrwwICCAAduzYUW5n9d27dwlA7vIqyUyaNImWlpaKvZFfePHiBe3s7Ojj45Ntyl1oktWrV9PQ0JCVK1fOsv4V6qZNmza0tbVVuKdHTifLM5+LOtjLXSMps8xndbB+/XoCyLSRjA75OXDgAA0MDNikSROlb4A9e/ZkmTJlUrw2f/58CoVCNm7cmMeOHWPRokWZJ08ehW/w5M8S7DUU/DsaNGgQnZycFF6L/Nlvws3NjQUKFPityi5ERkayYMGCtLGxyZEVTJ8/f05jY+M0+5HnZrLsKAkAloSF4fWnz+g9da7CEUVSqRQ9p8zBy/cfsESJ8+H0aNy4MfLkyYPw8HC1yfydOXLkCJo0aQI/Pz9s3LgR+vr6Ssnx8PDAnTt3EB0dLXutd+/e2LZtG/bv3w9fX1+YmZnh6tWrCAgIUFh+t27dcPz4cdy/f1/uOR8/flTKv0AS3bp1w61bt7Bjxw7Y2NgoLCOn4uLigkuXLqFs2bKoVasW5s2bl6PO7B3/P19qzpw5uHXrlrbVyTKy1DAUL14cy5Ytw9oDR9H57xmIiZXv7DEmNg6d/p6BdQePIT4hAcuXL1cpVPVXjI2N0aJFC6xduzZH/cFmR44fP45GjRqhRo0a2Lx5MwwMDJSW5eHhAZK4ePGi7LWXL19i1qxZSEhIgKmpKT58+ICYmBil5Ldo0QIWFhZYunSp3HM+ffqklGGYNm0awsPDsWLFClSqVEnh+Tkda2trHDx4EH379kXfvn3RpUuXHOV3GDhwIIoWLYq+ffv+PvcIbWxTfu3HsDl0VIb9GDaHjmIhO1uKhEIuWLCA06dPp0AgYPPmzdXWZvPw4cMEwIiICLXI+x05efIkTUxMWLt2bbUkDUokEpqZmXHixIkkyR07dtDKyor29vY8evQonz9/TmdnZ+bJk4cHDhxQao3+/fvT2tpa7uMub29vdujQQaE19uzZQ4FAoJH6SjmRNWvW0NDQkG5ubjnK77Bv3z4C4MaNG7WtSpaQbTq4dajnxxn9unPpiIGc0a87O9T7Xwc3H29vWllZsWbNmkxKSuKOHTtoYmJCFxcXtTQPSUpKooODA/v06aOGd/b7cebMGZqamtLX11etvZD9/PzYoEED9unThwDYpEmTFN31oqOjWb9+fYpEIi5ZskRh+Tdv3iQAbtq0Sa7xpUqVUuis+c6dO8ybNy8bNWqkK9j4CznV79CkSRM6Ojrm2Cx1Rcg2PZ/dXF1T9Hx2c3VN0fP52LFjFAqFHDVqFEnyypUrdHR0pL29vVoilIYMGUIrKyulImh+Z86dO8c8efKwWrVqatvBJdOtWzeKxWIaGhqm2wMgMTFR1uBn6NChCt+Aq1SpQj8/P7nGWltby90r4vPnzyxRogTLlCnz20W0yMO7d+/o6+tLsVjMOXPm5Ij+Do8ePaKBgQH//PNPbauicbRuGP5LRl/s5NLEe/fuJUm+evWKlStXprGxMbds2aLSuteuXSMA7ty5UyU5vxMXL16kmZkZvb291foUJZVKuWDBAurr6xMADx48mOn4mTNnUiAQsGXLlgodZa1cuZIA+PDhw0zXEIlEcvVgTkpKor+/Py0sLHTRbhmQmJjIgQMHysKNc0KdpbFjx1JPT4/37t3TtioaJdsZhoyQSCSsX78+LS0tZa0Yf/z4wdatW8uayKvy5FG+fHm2bt1aXermai5fvkxzc3N6enqqVOzuv3z48IFNmzaV3SwUOerZtm0bjYyM6OnpKXdIaExMDM3MzDJ9Cvz8+bPcugwePJhCoTBTg6bjJ2vXrs0xfocfP36wcOHC9Pf3zxG7HGXJUYaB/HnjKFiwID08PGROQ4lEwjFjxhAAO3TowLi4OKVkT506lYaGhmptRp8buXr1Ki0tLVm5cmW1flbHjh2jg4MDLS0tuW3bNpJkoUKFOGjQILllXLhwgba2tixSpAhv374t15w+ffrQzs4uw2PE5MqsR44cyVDW6tWrCYCzZs2SW2cdPx80ChUqRGtrax4/flzb6mTItm3bCIA7duzQtioaI8cZBpI8f/489fT02K9fvxSvr127lgYGBvTx8eH79+8Vlvv8+XMKBAIuX75cXarmOm7cuMF8+fLRxcWFnz9/VovMhIQEjhw5kgKBgDVq1EjRFax169b08fFRSN6TJ09YtmxZmpub8+jRo5mOv3r1KgFw69at6Y45f/48AWTYdvP8+fM0MDBg586dc/XTpKZ4//49a9asme39DlKplHXr1mWRIkVybdn+HGkYSHLu3Llpbu3Pnj1LGxsbFilShLdu3VJYbs2aNenr66suNXMVt2/fpo2NDStWrKi2WvWPHj2ip6cnRSIRJ06cmKpz1vTp02lkZMTExESF5H758oV+fn7U09PjypUrMx3v7u7OevXqpXt97969BJBuK8uXL1/S3t6eXl5eSu9YdaT0O3To0CHb3njv3r1LPT09/vXXX9pWRSPkWMOQ3Dw9T548qRxBjx8/Zrly5Zg3b17u379fIbkrVqygQCDI9medWc3du3dpZ2fH8uXLK7UbS4t169Yxb968LFKkSLo5JKdOnSIAXrlyRWH5CQkJ7Nq1KwFw9OjRGT6BhoWFUSAQyHxX/2XNmjUEkOaNKjY2lu7u7nRwcODr168V1lNHatauXUsjIyO6urpm2+/isGHDaGhoyMePH2tbFbWTYw0D+TOOvWTJkixfvnyq+PmvX7/KYtznzZsnt8yvX7/S0NCQU6ZMUbe6OZaoqCja29uzTJkyaqnz8+3bN3bq1IkA2K5duwz9FDExMRSJRFy0aJFSa0mlUoaGhhIAAwIC0n2a//btG01NTdPtuzxr1iwaGRmlKb9Dhw40NDTkxYsXldJRR9pkd7/Dt2/faG9vz2bNmmlbFbWTow0D+fPM28jIiJ07d051LSkpiQMGDCAAhoSEyH0c0aZNG5YrVy7bnnFmJQ8fPqSjoyNLlSrFN2/eqCzv0qVLdHJyoomJCVeuXCnXZ1ypUqU0f7+KsHHjRhoYGLBq1aopkuR+pXv37nR0dEzxd5IcPj169Gg6OjqmmjNjxgylKrXqkI9kv4NIJOLs2bOz3XcyuQinoicT2Z0cbxhIctWqVQTAZcuWpXl90aJFFIlErFu3rlxRNLt3787U0fg78PjxYxYsWJAlSpTgq1evVJIlkUg4bdo06unp0dXVlffv35d7blqVVpXhzJkzzJcvH52cnNLML7h48SIBsGHDhnR1cUmRcGlrY0MrK6sUyZT79++nUCjk0KFDVdZNR/okJibKyq5nN7+DVCpl9erVWaJEiVxVSj1XGAaSDA4OpqGhYbo380OHDtHc3JxlypTJNJkpISGB+fLl4+DBgzWhao7g6dOnLFy4MIsVK6Zy2ZHXr1+zTp06BMDBgwcr/AVavnw5BQKBWjKIHzx4wJIlS9LKyoqnTp2Svf5riRY7K0t2rO/Hmf17cOmIgZzZvwc71vejnZUFAdC3Rg3Z31P9+vVTOcx1aIbkGmuurq7p+oK0wfXr1ykSiXLV8XOuMQw/fvxgxYoV6eTklO4N5O7duyxevDjz5cuX4qaQFiEhIbS3t/8tv/TPnz9nsWLFWKRIEZUdf3v37qWNjQ1tbW2VLnZ369YtuXII5OXjx4+sXr069fX1uW7duhRFHbeEjs6wqOOW0NEs6pCfIpGI+fPn1+W8ZDG/+h2OHTumbXVk9O/fnyYmJmqp3ZYdyDWGgfz51Jc3b162bNky3bPIDx8+yG4Kq1evTlfWuXPnCICHDh3SlLrZkpcvX9LJyYkFCxZUKdoiLi5O5t+pX7++Sk5riUTCvHnzctKkSUrLSEu/oKAgAqBAIGCQfy25G0h9O7qdgXVrUiAQ6HwLWuD9+/esVatWtvI7fP78mTY2NmzXrp22VVELucowkOSWLVsyzTyNj49nly5dCIAjRoxIsz6TVCqlk5MTO3bsqEFtsxevX79mqVKl6OjomOlxW0bcuXOHFStWpL6+PmfNmqWWL26tWrXYpEkTleX8yr1796ivp8fAujWZdGavQt0Ek87sZZB/LRoZGenqIWmBxMREDho0KFv5HVasWEEA2TKCSlFynWEgyT/++INisZhnz55Nd4xUKuW0adMoEAjYokWLNMtF//XXXzQ1NVVrKensytu3b1mmTBna29srfaOTSqVcunQpjY2NWbJkSaVyD9JjxIgRtLOzU+vToW+NGizmmHmr2Yk9f4bW9mvdVOOtZnUoRvIxoIuLi9b9DhKJhF5eXixXrpzCCZnZjSzt4JZVTJ48Ge7u7mjdujU+fPiQ5hiBQIDBgwdj27Zt2LdvH6pVq4ZXr16lGBMYGIjv379jx44dWaG21vjw4QP8/Pzw6dMnHDt2DMWLF1dYxpcvX9CmTRsEBwcjICAAkZGRqFixotp0dHd3x5s3b/DixQu1yIuMjMSx48cxtU9XmBgZpjvu4u17CNuxDxWKF0l1zcTIEFNDuuDY8eO4fPmyWvTSoRgBAQE4e/YsPn78CFdXVxw/flxrugiFQsybNw+3bt3C/PnztaaHOsiVhkFPTw8bN25EXFwc2rdvn2Eb0CZNmuD06dN4+/Yt3N3dU3zBixUrhipVqmDt2rVZobZW+PTpE/z8/PD27VscPXoUJUqUUFjGmTNn4OzsjEOHDuHff/9FWFgYTExM1Kqnh4cHAOD8+fNqkbdy5Uo42tqgkY9numO+/4hF+3FTsWR4f1jkMU1zTGMfLzjYWGPFihVq0UuH4lSsWBGXLl2Cs7Mz/Pz8MHv2bK214HRxcUGPHj0wZswYvH37Vis6qINcaRiAn028w8PDcfDgQUyaNCnDsZUqVcKFCxdgb2+PqlWrYtu2bbJr7du3x4EDB/Du3TtNq5zlfP78GbVr18bLly9x9OhRlC5dWqH5SUlJ+Ouvv1CtWjUULFgQ165dQ8uWLTWiq52dHQoWLKg2wxBx9ixquVaAWCxKd0zI9PmoX8Udfu4u6Y4Ri0Wo5eqMcxERatFLh3Lky5cP+/fvx8CBAzFgwAB07NgRsbGxWtFlwoQJEIvFGD58uFbWVwe51jAAQJ06dTBmzBiMGTMGR44cyXBs/vz5cfz4cTRo0ADNmzfHlClTQBKtW7eGUCjEhg0bskjrrOHr16+oW7cunjx5giNHjqBs2bIKzX/27Blq1qyJ8ePHY/To0Th27BgKFiyoIW1/4uHhoTbDcPPWLTg7FUv3+oZDx3H53gOE9uqcqSxnp6K4cfOmWvTSoTxisRjTpk3DunXrsHnzZvj4+ODZs2dZroeVlRUmTZqElStXIiKHPjDkasMAAKNHj0atWrUQEBCQyofwX4yNjbFhwwaMHj0aw4cPR+fOnWFqaor69evnquOk6Oho+Pv748GDBzh8+DAqVKig0PwtW7bA2dkZT548wfHjxzFu3DiIxWINafs/PDw8EBkZiaSkJJXkSKVSxMfHI6+JcZrXn799jwH/LMKacUNhaKCfqTwzUxPEx8dneGSpI+to164dzp49i0+fPsHV1RXHjh3Lch2Cg4Ph4uKCkJAQSCSSLF9fZbTt/c4K3r17RwcHB/r4+Mjd03nt2rXU19dn1apVuWzZMgLg3bt3Nayp5vn27Ru9vb1pZmbGS5cuKTQ3JiaG3bp1IwC2bNmSnz590pCWaXPy5Em1lSoxMDDgzP490oxC2jr5Z9MnkUgo+8H/5zuIREImnk6ZADejX3caGBio4R3qUCcfPnyQ5Tv8888/WZ7vcPbsWQJQugCkNsn1OwYAsLa2xsaNGxEREYGRI0fKNScwMBDHjh3D3bt3MWHCBJiYmOT4XUNMTAwaNGiAGzdu4ODBg3B1dZV77rVr1+Dm5oa1a9ciLCwMmzZtgoWFhQa1TY2rqytEIpFajpPKlS2La1EP07xWy60irq9dhCurFsh+3Eo7IbCuL66sWgCRKKVf4lrUI9jZ2uLevXtac3rqSI2VlZXM7zBw4EB06NAhS/0OXl5e6NSpE0aMGIGPHz9m2brq4LcwDADg7e2NqVOnYtq0aXKHn1apUgUXLlyAsbExEhMTERYWlmO/+D9+/ECjRo1w+fJl7N+/H+7u7nLNI4k5c+bA3d0d+vr6iIyMRHBwMAQCgYY1To2xsTHKly+vkmH49OkTlixZgtdv3mD/uUtISkq9zc9jYoxyxQqn+DExNIRl3rwoV6xwirFJSRIcvBCJ5y9eoFSpUihWrBh69+6NnTt34vv370rrqUM9JPsd1q9fjy1btsDb2xtPnz7NsvUnT56MpKQkjBo1KsvWVAe/jWEAgIEDB6JZs2bo2LEjHj16JNecwoUL4+zZs6hUqRLevn2LIUOGaFhL9RMbG4smTZrgwoUL2LdvH7y8vOSa9/79ezRq1Aj9+/dHr169cO7cOYUjl9SNMg7oHz9+YOPGjWjSpAns7OzQq1cvFChQAG8/fcGu0+dU0mfn6Qi8+fgZJ0+exO7du9GgQQMcOnQITZo0gaWlJWrVqoVp06bhxo0bOfahIjfQtm1bRERE4PPnz3Bzc8syv4OtrS3Gjx+PxYsX56xcF+2eZGU9nz9/ZtGiReni4sLY2Fi558XHx9PU1JQA2Ldv3xyT2RgbG0t/f38aGRkplKp/8OBB2tnZ0dramnv27NGghoohb6XVxMRE7tu3j0FBQbLfm7u7O2fPni3rsuZbowaLOmSe+ZxRzaT0Mp+joqI4d+5cNmjQgEZGRgRABwcHdu3alf/++6/a+mXrUIwPHz7Qz88vS/0OiYmJLFeuHL28vNIsv5Md+e0MA/mzQqOBgQF79uyp0Lzhw4fT2NiYIpGI/v7+2b6yZlxcHBs0aEBDQ0O5K5PGx8dzyJAhBEA/Pz+V+zCom5s3bxIAjx49muqaVCrl2bNn2adPH1pbWxMAS5YsyfHjx6dZ5iMqKopGRkYM8q+l0VpJsbGxPHToEP/44w+WKVPm/x3bInp7e3PChAm8dOlSjrlh5AYSExNlf+OBgYFZUvLm2LFjBCBX//HswG9pGEhyyZIlBMC1a9fKPSe5/PO4ceNoZmbGsmXL8tGjRxrUUnni4+PZpEkTGhgYyF3uOioqim5ubhSLxZw6dWq2vFklJSUxT548DA0Nlb128+ZNjhgxgoULFyYA2tvbc9CgQYyMjMz0iXDdunVKVVcN8q9FgUDAdevWKfwenj59ysWLF7NZs2bMkycPAdDGxoZBQUEMDw9XW09tHRmzfv16GhkZsVKlSnzy5InG12vbti1tbGyy/QMl+RsbBqlUyqCgIBobG/PWrVtyz6tUqRJbtGjBO3fusFixYsyXLx9Pnz6tQU0VJyEhgc2bN6e+vj737t0r15zVq1fT1NSUxYsXz/a9i2vWrMk6depwypQprFChAgHQ3NycwcHBPHr0qMI9NH7tx7A5dFSG/Rg2h45iUQd7GhkZKWUU/ktCQgJPnDjB4cOHs2LFirKw2MqVK3PMmDE8e/bsb9kTJKu4evUqixQpQisrK7X1+0iP58+f08TEhAMGDNDoOurgtzUMJPn9+3eWLVuWpUuX5rdv3+SaM2PGDOrr6/PTp0/88OEDq1WrRn19fa5Zs0bD2spHYmIiW7VqRT09Pe7atSvT8V+/fmVgYCABsGPHjoyOjs4CLZXjw4cPXLhwIQsUKEAANDQ0ZOvWrbl9+3bGxcWpJPvXDm4ONtbsUM+PM/p159IRAzmjX3d2qOdHB5ufx1M1fX01Vmr71atXXLFiBdu0aUMLi58d4ywsLNi6dWuuWLEi2x3t5QY+fPjA2rVrUyQScebMmRr1O0yePJkikYg3btzQ2Brq4Lc2DOTP3gGmpqYMCAiQ6w/i1atXFAqFXLJkCcmfRzadO3cmAI4cOVKrxy9JSUls164dxWIxt23blun4c+fOsWjRosyTJ0+2bTjz/ft3rlu3jg0bNqRYLKZQKGSlSpUIQKGdnrxERkYyJCSEbq6uFAl/JrYJBQIWL1aMISEhKXo+a5qkpCRGRERwzJgxdHd3p0AgIAA6Oztz2LBhPH78uNwJmzoyJqv8DnFxcSxRogRr1KiRLRoMpcdvbxjIn2eNALhw4UK5xtepU4fVqlWT/V8qlXLKlCkUCARs2bKlVvo3JCUlMSgoiCKRiJs3b8507KRJkygWi+nh4aFSUx5NkJCQwD179jAwMJAmJiYEQE9PT86ZM4dv3rzhq1evCCDT96kq5cuXl+2mNH3MIA/v37/nunXrGBQURBsbGwJgnjx52LRpUy5atChLzslzOxs2bKCxsTErVqyoUgfDjNi/fz8BcMOGDRqRrw50huH/6dOnD/X19eUqE7F69WoCSPWHs23bNhobG9PNzY0vX77UkKapkUgk7Ny5M4VCYaZ/bC9evKCvry8FAgFHjBiRbZ44JRIJT58+zd69ezNfvnwEwNKlS3PChAlpGq4CBQpwyJAhGtWpUKFC7NSpk9rKcKgTiUTCyMhITpw4kT4+PhSJRLLPbODAgTx48KBC4dg6/kdW+B2aNm1KBwcHuY+wsxqdYfh/4uLiWLlyZRYuXDjTGkDfvn2jsbExJ06cmOra5cuX6eDgQAcHB16+fFlT6sqQSCQMDg6mUCjM9Dhox44dtLKyor29fZrhntrgxo0bHD58OAsVKkQAdHR05JAhQ3jlypUMt9otW7ZMsWvTBBYWFrJjwufPn2t0LVX5/PkzN2/ezK5du9LBwYEAaGRkxPr163Pu3Lm69qMKkux3EAqFnDFjhtqPfR49ekRDQ0MOHz5crXLVhc4w/MLjx49pYWHBRo0aZeorCAwMZKlSpdL8g3n58iXd3NxobGws11m/skilUvbq1YsCgYCrVq1Kd9yPHz/Yp08fAmDjxo21Hg755MkThoaGsnz58jLnavfu3Xn8+HG5fTTTpk2jsbGxxhINpVIpRSKRbMeQHXoKy4tUKuWNGzc4bdo01qxZk3p6egTAYsWKsU+fPty9eze/f/+ubTWzPUlJSRw6dKjG/A7jxo2jnp4e7927p1a56kBnGP7D7t27CYBTpkzJcNy+ffsIIN2jp5iYGLZs2ZICgYCTJ09W+xOHVCpl3759CYDLli1Ld9zNmzdZrlw5GhgYcP78+VpzeL1//54LFiygj4+P7Gm2bdu23LlzJ+Pj4xWWd+LECQLgtWvXNKDtT6c3AAYFBdHIyEgja2QV3759486dO9mrVy9Zroe+vj79/Pw4ffp03rp1K1s7QrWNpvwOP378YOHChVm3bt1s9/nrDEMaDB8+nCKRiCdOnEh3TGJiIm1tbTOMSZZIJBw1ahQBsHPnzkrdANNCKpVywIABBMDFixenO2bhwoU0NDRk2bJlef36dbWsrQjfvn1jeHg4GzRoQLFYTJFIxHr16nHNmjUqh8V+//6dIpFIFh2mbl6+fEkAbNOmDR0dHTWyhjaQSqW8d+8eZ8+eTX9/fxoaGhIACxQowG7dunHLli2Zlhv5Hbl27ZrM73D48GG1yd2+fTsBcPv27WqTqQ50hiENEhMTWb16debPn59v3rxJd9yAAQNoa2ub6XHGmjVrqK+vz2rVqql8jCOVSmVhdfPnz09zzIcPH9i0aVMCYK9evbL0GCQhIYG7du1iu3btaGxsTACsUqUK582bx7dv36p1LWdnZ3bt2lWtMpO5c+cOAbBp06Z0dnbWyBrZgR8/fnD//v0cMGAAS5YsSQAUi8WsVq0aJ02alKmv53fi48ePrFOnjlr9DlKplPXq1WPhwoWz1XGlzjCkw6tXr2hra8uaNWumm3l66dIlAuD+/fszlXf69GlaW1uzWLFivHPnjlI6SaVS/vnnnwTA2bNnpznm2LFjdHBwoKWlpUb9G78ikUh48uRJ9uzZk1ZWVgTAMmXKcOLEiRotGdK9e3eWK1dOI7LPnz9PAKxbty5r1qypkTWyI48ePeLChQvZuHFjWaiwnZ0dO3bsyPXr1/Pjx4/aVlGrJCUlcdiwYQTAgIAAtfgd7t+/T319fY4dO1Z1BdWEzjBkwLFjxygUCjlq1Kg0r0ulUpYqVYqBgYFyyXv8+DHLli1LMzMzHjp0SGF9xoz52VlsxowZqa4lJCRw5MiRFAgErFGjhsajaKRSKa9du8Zhw4axYMGCsuOIYcOG8dq1a1nylLls2TIKBAKNZGsfPHiQAOjt7c1WrVqpXX5OID4+nkePHuXQoUNlgQJCoZCenp4cN24cz50799uW69i4caNa/Q5//vknDQwMsk1Okc4wZMKkSZMIIN2aQxMnTqSxsbHc8chfv35lvXr1KBKJ5E6oI8nx48en6xR/9OgRPT09KRKJOHHiRI1+WR8/fsyJEyeybNmyBEBLS0v27NmTJ0+ezPKs7xs3bhAAjx07pnbZmzdvJgBWqFBB4Sq8uZUXL15w2bJlbNWqFc3MzAiAVlZWbNeuHVetWpXhsWtu5Nq1ayxatKha/A7fv3+no6MjmzRpoh7lVERnGDJBIpGwfv36tLS05NOnT1Ndf/z4MQEoVCspMTGR/fr1IwD269cvUx9FsnFKK29i3bp1zJs3L4sUKcKIiAi5dVCEd+/ecd68eaxSpQoB0NjYmO3atePu3bvV5lBXhqSkJJqamnLy5Mlql718+XICYMGCBTly5Ei1y8/pJCYm8vTp0xw1ahTd3NwIgADo4uLCESNG8OTJkzmmZ4kq/Op3mD59uko75Y0bN2b4EJqV6AyDHHz8+JGFChWih4dHmjfCqlWrsk6dOgrLXbBggSxSJ71IkGnTpslKff/Kt2/fZDH27dq1U3sp3+joaK5Zs0a2uxGJRKxfvz7Dw8OzVbamr68vmzVrpna5//zzD42NjWliYsKZM2eqXX5u4+3bt1yzZg0DAwNlmetmZmZs0aIFw8LCsn2CoCr86ndo166d0n4HqVRKX19fOjk5qVwUUlV0hkFOzp8/Tz09Pfbv3z/VtcWLF1MoFCpV+fLgwYPp9nb4559/CICjRo1K8SRy6dIlOjk50cTEhCtXrlTbeX58fDx37tzJtm3byrqO+fj4cMGCBXz37p1a1lA3w4cPp729vdrl/vXXX7SzsyOADJMHdaRGIpHwwoULHD9+PKtUqULh/xcjLFeuHAcPHszDhw9r/canCZL9Ds7OzkoHXdy8eZMikShFvxFtoDMMCjB37lwC4KZNm1K8/unTJ+rr6yv9ZHn79m0WLVqU1tbWPHPmTIq1hg8fLrvxSyQSTp8+nXp6enR1dVVLxqREIuGJEyfYvXt3WZnn8uXLMzQ0VGNFxNTJtm3bNFKy4o8//mCxYsUIgLt371ar7N+Njx8/cuPGjezcuTPz589PADQxMWGjRo04f/78bONwVQfXr19n0aJFaWlpqVSACUkOHDiQxsbGWt1l6QyDAkilUrZp04Z58uRJdVNu3rw5K1WqpLTs9+/fs2rVqtTX15fV5xk0aJDMKLx+/Zp16tQhAA4ePFils32pVMorV65wyJAhdHR0JAAWKlSIf/75p1YS4VQhORFty5YtapUbHBwsc7BrynfzOyKVSnn16lVOnjyZNWrUoFgsJgCWKFGC/fr14969e7VSnVidfPz4kXXr1lXa7/Dlyxfa2tqyTZs2GtIwc3SGQUGio6NZsmRJli9fPsUf8NatWwmAN2/eVFp2XFyczMHr7u4uiy7au3cvbWxsaGtrK3ebzrR4+PAhJ0yYIOs7nC9fPvbu3ZunT5/Olm085cXR0ZFDhw5Vq8zWrVvTxcWFAHj//n21ytbxP75+/cpt27axR48esrBnQ0ND1q1bl//88w/v3LmTIxPskpKSOHz4cKX9DqtWrUq3t3lWoDMMSnDjxg0aGRmxc+fOstfi4uJoYWHBP//8U2m5K1asIAB6eXlRIBCwefPmsuJ39evXVypz+O3bt5w7dy69vLxkW/jAwEDu2bMn25TcVpUWLVqwevXqapVZt25denh4EMBvn9SVVUilUt6+fZszZ85knTp1aGBgQAAsXLgwe/bsye3bt2frDoNpsWnTJqX8DhKJhFWqVGHZsmW18j3VGQYlSbbovxawS37qUebpe82aNRQIBOzRowclEgnnzJlDoVBIgUDAv/76S6GnpujoaK5atYp169alSCSiWCxmw4YNuX79+lxZVXPq1Kk0MTFRa/6Gl5eXzHGak3dTOZmYmBju2bOHffv2pZOTEwFQT0+PNWrU4JQpU7IskVJVrl+/zmLFiinsd7h8+TIFAgH/+ecfzSmXDjrDoALBwcE0NDSUNXE5deoUAfD48eOyMfLcVNatW0ehUMiuXbsyKSmJS5cupbGxMQsVKkQbGxs6OjryypUrGcqIi4vj9u3b2bp1a1lhtKpVq3LRokX88OGDSu8zu6OJSqtly5ZllSpVaGVlpTaZOlTjwYMHnDdvHhs2bCirw2Vvb88uXbpw06ZNmfZR0SafPn2S+R2mTZsmt0Hr1asX8+bNy9evX2tYw5ToDIMK/PjxgxUrVqSTkxO/fv1KqVTK/Pnzs0yZMnR1cZFthQ0MDOjq4pJmz+BNmzZRKBSyY8eO/PjxI1u1akUADA4O5vfv3/ny5Uu6urrSxMQkVQVGiUTCY8eOsVu3brKIImdnZ06ZMiXNZLzcyrdv3ygUChkWFqY2mY6OjvT09GSJEiXUJlOH+oiLi+OhQ4c4aNAgWZCAUChklSpV+Pfff/PixYvZbqeXlJQkq3Umr9/h48ePtLKyYseOHTWv4C/oDIOKPHjwgHnz5qW/vz99a9QgANpaWrBjfT/O7N+DS0cM5Mz+Pdixvh8dbKwJgL41ajAqKopbtmyhSCRiYGAgT5w4wYIFC9Lc3Jz//vtvijV+7e0wZcoURkZGctCgQbJOXYULF+aIESNUcnzndCpUqMDg4GC1ycubNy/d3Nzo5eWlNpk6NMezZ8+4ZMkSNm/enHnz5iUAWltbs3379ly7dm22ysP5999/aWJiIrffYfHixQQgC2XPCgQkCR0qMXDgQMyZMxsF7Wwxo283NPLxhFgsSjUuKUmCXafPYci8ZXj54QMSE5PQsmVLlC5dGn///Te8vLwQHh6OQoUKpZobFRWF4OBgnDx5EgCQL18+tG3bFgEBAfD09IRAIND4+8zOdO/eHefOncP169dVliWVSiEWi1G+fHkULFgQu3btUoOGOrKKxMREnDt3Dvv27cP+/ftx5coVCAQCuLq6ol69evD394e7uzvEYrHWdLx58yaaNm2Kz58/Y8OGDahdu3a6YyUSCTw8PCCVSnHx4kWIRKnvLWony0xQLiU8PJwCgYDt/Wvx29HtlEbsz/Tn29HtDKxbk4L/j98WCoUcO3Zsqtoyr1+/5uzZs2XRMaampvT29pbVy8/tvgNFWLp0KYVCoVrKdXz9+lUWW5/VW3gd6uf169dcuXIl27ZtS0tLSwKgubk5W7VqxeXLl/Ply5da0evTp0/09/enUCjk1KlTM/Q7REREEIBChTdVQWcYVOD+/fs0MjJikH8tJp3ZK7vxT+zZiW6lnWhqbERrCzM2qebFOxvCUhiHpDN7GVi3JkVCIdetWyeT+fXrV65cuVJWmEtPT4+NGzfmhg0bZGeSp0+fZr58+VTq7ZDbUGel1efPnxMAHR0d+ccff6iunI5sQ1JSEiMiIjh27Fh6eHhQIBDIqugOHTqUx44dy9LCkL/6Hdq2bZth1GDnzp1paWmZJQ+EOsOgAr41arCYo32qnUJdD1cuH/UHb4Qv4pXVC9igijsL2tmkGvft6HYWdcjP6tWqcdu2bWzZsiUNDQ1lPRWWLFmSbgz9o0ePWKZMGaV7O+Q2kiutZtarWx5u3rwpe6pMq6KtjtzDhw8fuG7dOnbo0IE2NjaynXmTJk24aNEiPnnyJEv0SPY7VKhQIV2/w5s3b2hmZsYePXpoXB+dYVCS5O5tW0JHZ3p09Hbvhp9hrAumpbq2OXSUrGRxpUqVOG3aND579kwuHb58+UJ/f3+FezvkVmrUqMHmzZurLOfs2bOyKJdFixapQTMdOQGJRMLLly9z4sSJrFq1KkUiEQGwVKlSHDBgAA8cOMDY2FiNrX/jxg1ZvsPBgwfTHDN79mwKBAJeunRJY3qQpFDzXozcycqVK+Foa4NGPp6Zjv36/QcAwDJvnlTXGvt4IX8+SwQEBODy5csYPHgwChQoIJcOZmZm2LVrF3r37o1evXphwIABkEgkir2RXISHhwfOnz+vspzo6GgAP53QVlZWKsvTkTMQCoWoVKkSRowYgZMnT+Ljx4/YsmULfHx8sHnzZtStWxeWlpaoX78+5syZg6ioKFCNsTvlypXDxYsX4e7uDn9/f0ydOjWV/N69e6Ns2bLo06cPpFKp2tb+LzrDoCQRZ8+ilmuFNKOPfoUkBs1ZDB/nsihXrHCq62KxCLUru+D+vXtK6SEWizFnzhzMnz8f8+bNQ+PGjWU3tt8NDw8PvHz5Ei9fvlRJztevX2X/1hmG3xczMzM0b94cYWFhePbsGW7evInx48cjISEBQ4YMQYkSJVC8eHH06dMHu3btwvfv31Ve08LCArt378bw4cMxbNgwtGvXDjExMbLrYrEY8+fPx/nz57Fq1ao0ZajDYOgMg5LcvHULzk7FMh0XMn0+rj94jHXjh6c7xtmpKG7cvKmSPr1798bevXtx+vRpeHt748mTJyrJy4l4eHgAgMq7hl8Nq84w6AAAgUCAsmXLYvDgwTh8+DA+fvyIXbt2wd/fH/v27UPjxo1hZWUFPz8/TJ8+Hbdu3VJ6NyESiTBx4kRs3rwZu3fvRpUqVfDo0SPZ9WrVqiEgIADDhg3Dly9fcPnyZfTt2xdurq4wNDSESCSCoaEh3Fxd0bdvX1y+fFlhHXSGQQmkUini4+OR18Q4w3F9ZyzArtPncHT+VDjaWKc7zszUBPHx8Spb+jp16iAiIgI/fvyAu7s7zp49q5K8nIa9vT0cHBxw4cIFleRER0fDyMgIgM4w6EgbU1NTNGzYEPPnz8fDhw9x//59TJ8+Hfr6+hg9ejTKlSuHggULolu3bti6dWuKXai8tGjRAufPn8ePHz/g5uaGQ4cOya5NmzYNMTExcK5QAa6urti2aSPK2VkitGcnLB0xEKE9O6GcnSW2bdoIV1dX1PT1xYMHD+ReW3sZHjkYoVAIAwMDRMf8SPM6SfSdsQDbT5zFsQVTUcTeLkN5X7/HwMDAAEKh6na6TJkyOH/+PJo3b46aNWti+fLlCAgIUFluTkEdfoavX7/C0NAQsbGxOsOgI1MEAgGcnJzg5OSEvn37IjY2FqdOncL+/fuxb98+LF26FCKRCFWqVIG/vz/q1asHZ2dnub7vZcuWxYULFxAYGAh/f3+EhoZiyJAhOH78OJISE4GEeGwJHS1XUm2FChWwbNkytGvXLtN1dTsGJSlXtiyuRT1M81qf6fMRfuAowv8ahjzGRnjz8RPefPyE2Lj4NMdfi3qE8uXKqU23fPny4dChQ2jbti0CAwMxZswYjTqqshMeHh64dOmSSk746Oho6Ovrw9jYGIaGhmrUTsfvgJGREerUqYOZM2fizp07ePz4MebPnw8rKyuEhobCxcUF9vb26NixI9avX4+PHz9mKM/CwgK7du2S+R28vLzQvn17tK5VDbfWL0GzGt7p+jrFYhGa1fDGtTUL0LJ6FQQGBmLdunWZvgddSQwl6du3L7Zt2ojHW1am+qUIvfzTnLN81B/o1KBOiteSkiQo0qITmrVug7lz56pVR5KYOnUqhg8fjtatW2PlypWyI5LcyokTJ1CjRg1cv34d5cuXV0pGly5dcPDgQQiFQjx79kzNGur4nUlISMDZs2dlu4nr169DIBDIIpH8/f1RuXLldMtezJs3D/3790e7OjWwavRghU4ZpFIpOv89A5tPnMX169dRvHjxdMfqDIOSXL58Ga6urtgSOhrNangrLWfr8dNo+ecEREZGwsXFRY0a/o9t27ahffv2KFeuHLZv3478+fNrZJ3swPfv32FmZobFixcjODhYKRktW7bE+fPnkS9fPly5ckXNGurQ8T9evXqFAwcOYN++fTh06BC+fPkCS0tL1KlTB/7+/qhbty7s7P53FF3T1xdPH9zHtdULYGKUcje7YMsuTA/fjNcfP6FskUL4Z0BPVK2Y8iQiJjYOzkG9UcipBI4eO5auXrqjJCVxcXGBb40aGDJvGWJi45SSERMbh0Gzl0AkEmL16tUaCzNt1qwZTp06hRcvXsDd3R1Xr17VyDrZAVNTU9m5rLIk/x50/gUdmsbe3h6dO3fGpk2b8P79e5w5cwZ9+vTBgwcP0KlTJ+TPnx8uLi4YMWIEwsLCcOz4cUzr0zWVUdh4+AQGzlqMEZ3a4vKq+fBxLof6f4zCszfvUowzMTLE1JAuOHb8eIbRSjrDoAJLwsLw+tNn9J46V+EzfKlUit5T5+Ld128YNGgwwsLCUKpUKWzcuFGtSTPJuLi44MKFC7C1tYWPjw927typ9jWyC6o6oL9+/apLbtOR5YjFYlSpUgXjx4/HxYsX8fbtW6xduxZly5bF0qVL0b17d9hZWqSZVPvP+q3o0qgughvXQ+nCBTFrYE8UsLHGwq27U41t7OMFBxtrrFixIl1ddIZBBYoXL45ly5Zh7YGj6Pz3DLl3DjGxcej89wysPXAUy5Ytw5QpU3Dnzh14enqibdu2qFu3Lu7fv692fR0cHHDy5En4+/ujadOmmD59ukaMkLbx8PDAzZs3lU44io6ORmJios4w6NAqNjY2CAwMxJo1a/DmzRuULlUKdT1dU/k0ExITEXkvCnXcUx5F1/ZwQcSNO6nkisUi1HJ1xrmIiHTX1hkGFWnXrh3Wrl2LzSfOwjmoN7YeP42kpLQjYpKSJNh6/DScg3pj84mzCA8Pl4WOFSxYEFu3bsXu3bsRFRWF8uXLY8yYMYiNjVWrvsbGxti0aRP+/PNPDBkyBN26dUNCQoJa19A2ybXrIyMjlZofHR2N+Ph4nWHQkW0QCoV49Phxmkm1H75EQyKRwtbSIsXrthYWePPpU5ryMkuq1eUxqIGAgAC4u7uje7duaPnnBDjYWKOWqzOcnYrCzNQEX7/H4FrUIxyJvIaX796jpq8vDixZkmZUQIMGDeDr64tJkyZh8uTJCA8Px7x581CvXj216SsUCjFx4kSUKlUKwcHBePDgAbZs2ZJrboRlypSBiYkJLly4gOrVqys8/+vXr7odg45shTxJtf/t1UUQAqTdwOvXpNq0Ipt0OwY1Ubx4cRw9dgyRkZFo1roNbr/7jBGLVyF40j8YsXgVbr/7jGat2yAyMhJHjh7NMFTM2NgYEyZMwI0bN1C4cGHUr18fLVu2xPPnz9Wqc1BQEI4cOYJbt27B09MT95Ss15TdEIlEcHNzU8rPIJFIEBMTg4SEBFhaWmpAOx06FCejpNp85nkhEgnx5uPnFK+/+/wl1S4imcySanWGQc24uLhg7ty5uHjpEuLi4iCRSBAXF4eLly5h7ty5CoWklixZEocPH8a6detw5swZlC5dGtOnT0diYqLa9PXx8cH58+ehr68PT09PHDlyRG2ytYmyDmhdnSQd2Y2vX79iw4YNyGNqmmZSrb6eHlxLOuHQxZSh1YcvXIFX+dJpyswsqVZnGDSMqmUuBAIB2rVrh7t376JLly4YNmwYXFxccObMGTVpCBQtWhRnz56Fu7s76tati8WLF6tNtrbw8PDAixcv8OrVK4Xm6QyDjuzA69evsXjxYvj7+8Pa2hrt2rWDQCjEwQtX0vRhDmzXHMt27sfyXQdw58kzDJy1GM/evkPPZg1SjU1KkuBI5DV4enmlu77OMOQQzMzMMGfOHFy8eBHGxsbw8fFBly5d8OHDB7XJ37NnD3r16oWePXti4MCBObq3g7KVVnWGQYe2uH//PqZMmQIvLy/Y29ujT58+SExMxIwZM/D06VPs378frz98xK7T51LNbeNXHf8M6IG/l4ejUoc+OHX1BvbM+BuF8tumGrvzdARevnuPzp07p6uLLvM5ByKRSLB06VIMHz4cQqEQkydPRteuXdVShA8A5s+fj/79+8Pf3x/r169HnjypGwzlBBwdHREUFITQ0FC555w+fRpVq1YFAHz8+FHnZ9ChMaRSKS5duoTt27dj+/btuHPnDoyMjODv749mzZqhQYMGqf7+avr64mnUfVxbkzrzWR50mc+5GJFIhB49euDevXto1KgRunfvDm9vb7VlNPfp0wd79uzBqVOn4O3tjadPn6pFblbj7u6u9I5BKBTC3NxcA1rp+J1JSEjAoUOH0KdPHxQsWBAeHh5YsmQJPD09sWPHDnz48AFbt25FUFBQmg8l6kiqff3pM5aEhWU4VmcYcjA2NjZYuXIlTpw4gW/fvsHV1RUDBgxQS2mNunXrIiIiAt+/f4e7uzvOnUu9fc3ueHh44OLFiwodiSV/dubm5mrbgen4vfn+/Ts2b96M9u3bw8bGBnXq1MGePXvQqlUrHD9+HG/evMHy5cvRuHFjGBtn3ONFXUm1GUVFAgA02lFaR5aRkJDAqVOn0tjYmPnz5+eGDRsolUpVlvvu3Tv6+PjQwMCA69atU4OmWcexY8cIgDdu3JB7zqJFiwiAJUqU0KBmOnI7b9++ZVhYGBs0aEADAwMCoLOzM8eOHcsrV66o/N0MDw+nkZERizrYc3PoKCac2kNpxP5UPwmn9nBz6CgWdbCnkZGR3N9hnWHIZTx9+pTNmjUjANauXZv37t1TWWZcXBw7dOhAABwzZoxaDE5W8O3bNwqFQi5dulTuOVOnTqW+vj69vLw0qJmO3MiDBw84ffp0+vj4UCAQUCgUslq1avznn3/46NEjta8XFRVF3xo1CIAONtbsUM+PM/p159IRAzmjX3d2qOdHBxtrAmBNX19GRUXJLVtnGHIpu3fvZpEiRaivr8/Ro0fzx48fKsmTSqUMDQ0lALZp00ZleVlF+fLl2b17d7nHjxo1ikZGRmzYsKEGtdKRG5BKpYyMjOTo0aNZvnx5AqCBgQEbNWrE5cuX8927d1miR2RkJENCQujm6irbnRgYGNDN1ZUhISGMjIxUWKbOMORiYmJiOGrUKOrp6bFo0aLcu3evyjK3bNlCIyMjuru78/Xr12rQUrN07dqVzs7Oco/v27cvjY2N2bFjR43ppCPnkvh/7d19WFR1mwfw7wwjECghMhCu4uIDjymYCV4MgiaQsiwSgWKKLblQaomW5uJLa156kWGi6eVbNIjiW2IijC9EJpAolpFoCK4okKGkggaOIC8yc+79o5WNQBSYYWC4P/85c+bMl0vr5pzf+d13YyNlZmbS+++/T7a2tgSAzM3NKTQ0lA4fPkzV1dW6jkhqtbrT5+DVNT1mYmKCqKgojbbWmDJlSrPZDnl5eRpMrHkymQz5+fl4+PDhMx3/4MEDEBHvYWBNamtrkZKSglmzZsHa2hre3t5ITk5GQEAA0tPTUVFRgT179mDKlCno27evruNq5KEJLgy9gKZba7i4uCAnJwdSqRQeHh44duyYhhNrTns7rSqVSqhUKi4Mvdy9e/eQkJCAwMBAWFpaYsqUKcjNzcV7772H8+fP48aNG9iyZQteffVV9OnTR9dxNa/zFy6sJ7l//z4tWLCAxGIxOTk50ZkzZzp8rpqaGpoyZQqJRCJav359t1yUVqlUZGpqSuvWrXum4728vEgkElFsbKyWk7Hu5vr167Rp0yby9PQksVhMIpGI3N3dKSYmhq5du6breF2KC0MvlZubS66urgSAwsLCOrxQplarafny5QSA3n77bWpoaNBw0s6bMGECBQcHP9OxL7/8MgGgQ4cOaTkV0zVBECgvL49Wr15No0ePJgBkaGhIfn5+JJfLe8QamrZwYejFVCoVxcbGkrm5OVlYWJBcLu/wwtXu3bupT58+5OnpSX/88YeGk3ZOZGQkDR48+JmOHTJkCAGgzMxMLadiuqBSqej06dO0aNEisrOzIwBkZmZGISEhdPDgQVIqlbqO2C1wYWBUXl5Os2bNIgDk5uZGFy9e7NB5Tp8+TQMGDCAHBweN7J/QlKSkJAJAt27deuqxFhYWBIDy8vK6IBnrCrW1tXT06FEKDw8nS0tLAkA2Njb07rvv0okTJ7rlVa6ucWFgTbKyssjR0ZHEYjF98MEHHfrtqbi4mIYPH079+/enjIwMLaRsv5s3bxIASklJeeqxhoaGBIDKysq0H4xpTWVlJe3du5emTp1KpqamBICGDRtGy5Yto3PnzmnkkU59xoWBNaOJ1hr3798nHx8fkkgkJJfLtZS0fQYOHEjLli1r85hHjx4RAAJAdXV1XZSMacrNmzdp69atNHHiRJJIJASAZDIZRUdH05UrV3Qdr0fhwsBa1dnWGo2NjRQREUEA6MMPPySVSqWlpM8mKCiIvL292zzm3r17TbtGWfcnCAJdvnyZ1qxZQ2PGjCEAJJFIyMfHh7Zv385XfZ3AhYG1qbOtNbZs2UJisZj8/f3pwYMHWkr5dNHR0dSvX782C1RJSQkBIKlU2oXJWHuo1Wo6e/YsRUZGkoODAwGgvn370rRp02j//v1UVVWl64h6gQsDe6rOttZIS0sjMzMzGjlyJP32229aStm2zMxMAkAFBQVPPObixYvcWbUbqq+vp2+++YbmzJlD1tbWBICsrKxo9uzZlJqayrf9tIB3PrOn+mtrDTs7u3a31vD19dX5bIcxY8ZAJBK1Objn8SwG3vWse0qlEomJiZgxYwakUin8/PyQkZGB0NBQZGdn49atW5DL5fDz84OxcfsnmbG2cWFgz2zYsGE4efIkDhw40O7WGiNGjMBPP/0EBwcHeHp6IjExsQsS/79+/frB0dGxzcKgVCoBAFKptKtisb+4ffs2vvzyS/j6+kIqlSIkJATFxcVYsmQJ8vPzUVRUhJiYGHh4eMDAwEDXcfUaFwbWLiKRCDNmzEBhYSHCw8OxdOlSODs7Izs7+6mflUqlyMjIwPTp0xESEoJVq1aBunDkuEwmQ05OzhPff3zFYG3dcoA6046rV6/is88+w9ixYzFw4EBERESgsbERGzZsQGlpKc6fP48VK1bAyckJIpFI13F7DS4MrEOef/55bN68GT///DNMTEwwfvx4hIeH4+7du21+zsjICAkJCfj000+xevVqzJw5E3V1dV2S2dXVFfn5+aitrW31/ceFwcrKqkvy9EaCICAnJwcfffQRRowYgRdffBGrV6+GjY0N9uzZg4qKCmRkZGDBggWwtbXVddxeiwsD6xRnZ2f88MMPiI2NRUpKCoYNG4a4uLg2B5WLRCIsX74cSUlJOHLkCLy8vHDnzh2tZ5XJZFCr1U/stPr4VpKlpaXWs/Qmjx49wsmTJxEREQFbW1vIZDLI5XK4ubnhyJEjuHfvHpKTkxEaGgoLCwtdx2XgwsA0wMDAAHPnzsXVq1cREBCAOXPmwMPDA7/88kubn5s6dSrOnDmDmzdvwtXVFZcuXdJqTkdHR5iYmDxxnaGyshIALz5rQk1NDZKSkvDmm2/CysoKPj4+SE1NxbRp03Dq1CncuXMHO3fuREBAAExMTHQdl/0NFwamMVZWVkhISEBWVhaqq6vh4uKChQsXNt2iac1fZzu4u7trdbaDRCLBmDFjnlgYKioqAHBh6KiKigrs2LED/v7+sLS0xLRp03D58mUsXLgQFy9exPXr17Fx40ZMmDABEolE13FZW3T9vCzTT+1trVFTU0NBQUEkEolow4YNWpvtEBkZSba2tq2+N3nyZAJA586d08p366Pi4mJav349jRs3jkQiEYnFYnrllVdo48aN9Ouvv+o6HusgLgxMq9rTWkOtVtOyZcsIAM2ePZsePXqk8TyHDh0iAK322nd3dycAVFRUpPHv1ReCIFBubi59/PHH5OTkRADI2NiYAgICaOfOnR2e68G6Fy4MrEu0p7XGrl27qE+fPuTt7a3x2Q43btwgAKRQKFq8N2LECAJAlZWVGv3Onq6xsZEyMzNpwYIFNHjwYAJA5ubmFBoaSocPH6aamhpdR2QaxoWBdZn2tNbIysrSymwHQRDIxsaGli9f3uK9wYMHk0gk4pbM9OffVXJyMr311ltNMyoGDRpE8+fPp/T0dK1czbHuQ0TUhTuMGMOfm5oiIiKQkZGBqVOnYuPGjRg8eHCL40pKSuDv74/y8nIcPnwYXl5eGvn+oKAgVFdXIz09vdnrAwYMQF1d3RP3Oei7e/fu4fjx41AoFPjuu+9QV1cHR0dHBAYGIigoCM7OzrzJrLfQdWVivZMgCHTgwAF64YUXyNTUlGJiYlr9LbSqqoomTZpEEomE4uLiNPLd0dHRZGZm1uLKwNjYmCwtLTXyHT3F9evXadOmTeTp6UlisZhEIhF5eHhQTEwMXbt2TdfxmI5wYWA6df/+fXr//fdJLBaTk5MTnTlzpsUxjY2NNG/ePAJAixcv7vRsh4yMDAJAly9fbva6WCymoUOHdurc3Z0gCJSXl0erVq2il19+mQCQoaEh+fn5kVwub3VRnvU+XBhYt5Cbm0uurq4EgMLCwlp9ukVTsx2USiWJRCLauXNn02v19fUEgEaPHt3h83ZXKpWKsrKyaNGiRWRnZ0cAyMzMjEJCQujgwYMdGuHK9BsXBtZtqNVqio2NJXNzc+rfvz/J5fIWt3vS0tKoX79+9NJLL1FpaWmHv8vR0ZHmzp3b9Ofy8nIC8NQpbz1FbW0tHT16lMLDw8nS0pIAkI2NDb377rt04sQJamho0HVE1o3xzmfWbYjF4qe21ng82+HBgwdwdXVts412W/7eafXx7uye3CepqqoK+/btQ3BwMKRSKQICAnD27Fm88847OHfuHMrKyvDFF1/Ax8cHhoaGuo7LujEuDKzbeVprDUdHR+Tk5MDe3h4TJkzo0GwHmUyGS5cuNT2B1FNnMZSVlWHbtm2YOHEirKysEBoairKyMqxYsQJXrlxBYWEhoqOjIZPJIBbzf+7sGen6koWxtrTVWqO+vp5CQ0MJAK1atapdbTQej/F8vNidnp5OACgqKkorP4emCIJABQUF9Mknn9CYMWMIAEkkEvLx8aHt27dTWVmZriMyPcCFgfUIT2qtIQgCrVmzhgBQSEjIM8//bWxsJBMTE1q/fj0REe3du5cAUHx8vNZ+ho5Sq9V09uxZioyMJAcHBwJAffv2pWnTptH+/fupqqpK1xGZnuFrS9Yj2NraIjk5GcePH0dxcTFGjhyJlStXor6+Hh999BEOHToEhUIBLy8vlJeXP/V8EokELi4uTWsUt27dAgAMGjRIqz/Hs2poaEBaWhrmzp2LgQMHwsPDA7t374anpydSU1Nx9+5dfP3115g5cybMzc11HZfpGS4MrEeZPHkyCgoKsGTJEqxduxZOTk5IS0tDcHAwTp8+jdLS0qZJbU/z1wXox8XExsZGq/nbolQqkZiYiOnTp0MqlcLPzw8ZGRkIDQ1FdnY2bt26BblcDj8/PxgbG+ssJ9N/XBhYj2NiYoKoqCjk5+fDzs4Ofn5+CA4OhrW1NXJycmBhYQF3d3ekpqa2eR6ZTIbS0lKUl5c3jSTt6lkMt2/fRmxsLHx9fSGVShESEoKSkhIsWbIE+fn5KCoqQkxMDDw8PGBgYNCl2Vgvput7WYx1RmutNSorKykwMJDEYjF9/vnnT1yUPn78OAEgB/t/kIGBAQEgIyMjcnF2pvnz51Nubq5WMhcWFtLatWvJzc2NAJCBgQF5e3vT5s2bO7U3gzFN4SZ6TC8olUqsXLkSW7duxYgRI7Bt2zZ88803+OyzzzBnzhxs3boVffr0AQAUFxdjzuzZ+P7UKVhb9IevmwtGOfwDZqYmePCwFnlFJUg/n4ffK+7Cy9MT8rg42NvbdzibIAg4f/48FAoFUlJSUFhYiOeeew6+vr4ICgrC5MmTedYx61a4MDC9cuHCBbz33nvIyclBWFgYRo8ejcWLF2P8+PFISkpCWloa3nnnHdhY9EfM/Lfx2jg3SCQtb9GoVGocyz6HyK3xuF1Zhfj4eISEhDxzjkePHiErKwsKhQJHjhzB77//jgEDBiAgIACBgYGYOHEizzpm3RYXBqZ3BEHAjh07sGzZMgBAeHg4du3aBUNDQ5SXl+M//s0b25csgOlzT1/AfVhXj3nrtmDfiUzs27cPM2fOfOKx1dXV+Pbbb6FQKJCamgqlUokhQ4YgKCgIgYGB8PDw4FnHrEfgwsD0VkVFBZYuXYqEhAQMHz4c165exYxJnti98r8gFouhUqmxKn4vvjrxPe78UQUbSwvM8puEFWEhzXYJC4KAsKgNSMr6AZcuXWp2W6m8vBzHjh2DQqFAeno6GhoaMGrUKAQGBiIwMBCjRo3iGQasx+HCwPTemTNnMNnPDxZ9TVDwlbzpSmFNwgFsSkxBwseL4Th0CM5fKUL4ms8RNWcWPpge2OwcD+vqMSp0HoY4/BNxO3ZAoVBAoVDg7NmzEIlEGDduHIKCgvD666/Dzs5OBz8lY5rD17VM75mYmKC6pgYJ/72o2e2jc/lXEDDeDZM9ZACAf7V5AYknTyG38FqLc5g+Z4x188MRvPwT2Nvbw9jYGD4+PoiPj4e/v3+P67HEWFu4MDC9l5CQgEHWVnhtnFuz1z1GOeLLlFRcu1GGf9oOQl7Rr8jOu4yNC+e2ep6AcWPxwgALjHaV4dChQzA1Ne2K+Ix1OS4MTO/9+MMPeNXlpRZPHy0NfQPKmocYPmM2DMRiqAUBn8ydhRCf1mdLSyQG8HF1xv9UVHBRYHqNCwPTewWXL+PN8f/Z4vWD6VnYfyIT+1cvhaPdEPxSVIJFm77EQMsBmDV5UqvnGuUwFAczd2s5MWO6xYWB6TVBENDQ0AAz05Z7BpZs3YGloW9gxiRPAMBIezuU3qnA2j0Hn1gYnu9rioaGBgiCwPMNmN7if9lMr4nFYhgZGeHBw9oW79XWN7T4n7uBWAyhjQf1lDUPYWRkxEWB6TW+YmB6z8nREXlFJS1ef22cDJ8mJMLWWgrHoUNw8WoJNiamIMzf54nnyiv6FSOdnLQZlzGd48LA9N5Yd3ekfH0QKpW62QL05g/n4WP5HkSs34aKyvsYKB2AOYH/jpXhb7Z6HpVKjYzcPAS9Mb2rojOmE7zBjem9CxcuwMXFBYejP0aQp0eHz5N8KhvByz9Bbm4unJ2dNZiQse6FCwPrFby9vFBadA15e7c/U4+kv/vrzufM77/XQkLGug9eQWO9gjwuDrcrqzBv3RYIgtCuzwqCgHnrtuB2ZRXkcXFaSshY98GFgfUK9vb2iI+Px74TmQiL2oCHdfXP9LmHdfUIi9qAfScyER8f36m5DIz1FHwrifUqX331VdM8hnXzwxEwbuwT5zEczf4RS7bu7NA8BsZ6Mi4MrNf56wS3f7GS4lWXURjlMBTP9zWFsuYh8op+RUbunxPcvL288KVczlcKrFfhwsB6rQsXLmDXrl049+OPyC8oQENDA4yMjDDSyQluY8ciLCyMnz5ivRIXBsb+D7e5YOxPXBgYY4w1w78eMcYYa4YLA2OMsWa4MDDGGGuGCwNjjLFm/hebql/TNBQMhwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Graphics object consisting of 34 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 6 6\n"
     ]
    }
   ],
   "source": [
    "# c=3\n",
    "k1=graphs.CompleteGraph(3)\n",
    "k2=graphs.CompleteGraph(3)\n",
    "k2.relabel([3,4,5])\n",
    "k3=graphs.CompleteGraph(3)\n",
    "k3.relabel([6,7,8])\n",
    "k12=k1.union(k2)\n",
    "f3=k12.union(k3)\n",
    "f3.add_edges([(0,3),(3,6),(6,0)])\n",
    "show(f3)\n",
    "f3c=f3.complement()\n",
    "show(f3c)\n",
    "print(3, 3^2-3, Zplus(f3c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4baf2f5d-843e-4264-970d-841959746e7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 45 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 12 12\n"
     ]
    }
   ],
   "source": [
    "# c=4\n",
    "k1=graphs.CompleteGraph(4)\n",
    "k2=graphs.CompleteGraph(4)\n",
    "k2.relabel([4,5,6,7])\n",
    "k3=graphs.CompleteGraph(4)\n",
    "k3.relabel([8,9,10,11])\n",
    "k4=graphs.CompleteGraph(4)\n",
    "k4.relabel([12,13,14,15])\n",
    "k12=k1.union(k2)\n",
    "K123=k12.union(k3)\n",
    "f4=K123.union(k4)\n",
    "f4.add_edges([(0,4),(4,8),(8,12),(12,0)])\n",
    "show(f4)\n",
    "f4c=f4.complement()\n",
    "print(4, 4^2-4, Zplus(f4c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c6ad9a43-7eaa-4945-8c5f-59b3ebbc8b52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 81 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k1=graphs.CompleteGraph(5)\n",
    "k2=graphs.CompleteGraph(5)\n",
    "k2.relabel([5,6,7,8,9])\n",
    "k3=graphs.CompleteGraph(5)\n",
    "k3.relabel([10,11,12,13,14])\n",
    "k4=graphs.CompleteGraph(5)\n",
    "k4.relabel([15,16,17,18,19])\n",
    "k5=graphs.CompleteGraph(5)\n",
    "k5.relabel([20,21,22,23,24,25])\n",
    "k12=k1.union(k2)\n",
    "k123=k12.union(k3)\n",
    "k1234=k123.union(k4)\n",
    "f5=k1234.union(k5)\n",
    "f5.add_edges([(0,5),(5,10),(10,15),{15,20},(20,0)])\n",
    "show(f5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "425c2aff-6a30-4b7f-91fe-7782b9408a31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 20 20\n"
     ]
    }
   ],
   "source": [
    "f5c=f5.complement()\n",
    "print(5, 5^2-5, Zplus(f5c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4dfb271-e1a1-4bd0-be35-ced620f9b6e4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "94e674a3-75c3-4cd9-bba8-b9fda38b7744",
   "metadata": {},
   "outputs": [],
   "source": [
    "####################################\n",
    "# Power domination, propagation, and throttling\n",
    "####################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2a8af4a5-68d7-40f5-87e3-35efda38f804",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F- Power dominating set functions\n",
    "# by Brian Wissman\n",
    "# input: a graph G and a subset of its vertices V\n",
    "# output: true/false depending if V is a power dominating set of G\n",
    "def isPowerDominatingSet(G,V):  \n",
    "    N=[]\n",
    "    for i in V:\n",
    "        N+=G.neighbors(i)\n",
    "    NVert=uniq(N+list(V))\n",
    "   \n",
    "    A=zerosgame(G,NVert)\n",
    "    if len(A)==G.order():\n",
    "        return True\n",
    "    else:\n",
    "        return False\n",
    "# input: a graph G\n",
    "# output: a power dominating set of G that achieves the power domination number\n",
    "def minPowerDominatingSet(G):\n",
    "    V = G.vertices()\n",
    "    for i in range(1,len(V)+1):\n",
    "        S = subsets(V,i)\n",
    "        for s in S:\n",
    "            if isPowerDominatingSet(G,s):\n",
    "                return s\n",
    "                \n",
    "# input: a graph G\n",
    "# output: the power domination number of G, gamma_P(G)\n",
    "def PowerDom(G):\n",
    "    V = G.vertices()\n",
    "    for i in range(1,len(V)+1):\n",
    "        S = subsets(V,i)\n",
    "        for s in S:\n",
    "            if isPowerDominatingSet(G,s):\n",
    "                p=len(s)\n",
    "                return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ec9bc6c2-2392-4f53-a6e6-84b7e50f70ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-15 All power dominating sets of size k\n",
    "#  \n",
    "# input: a graph G and a positive integer k \n",
    "# output: a list of all power dominating sets G of size k\n",
    "def PDsets(G,k):\n",
    "    ord=G.order()\n",
    "    V = G.vertices()\n",
    "    S = subsets(V,k)\n",
    "    PDS=[]\n",
    "    for s in S:\n",
    "        if isPowerDominatingSet(G,s):\n",
    "            PDS.append(s)\n",
    "    return PDS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "473f7389-da72-4110-9f33-a407bc96279b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F-16 Functions for power propagation time\n",
    "# function to compute closed neighborhood N[S] \n",
    "# input: a graph G and a list S of vertices \n",
    "# output: set N[S] \n",
    "def nhbd(G,S):\n",
    "    NS=set(S)\n",
    "    for x in S:\n",
    "        nx=G.neighbors(x)\n",
    "        NS=NS.union(set(nx))\n",
    "    return NS   \n",
    "# function to compute ppt(G,S) = power propagation time of a set S\n",
    "# input: a graph G and a subset S of vertices \n",
    "# output: ppt(G,S) \n",
    "def pptS(G,S):\n",
    "    ord=G.order()\n",
    "    V = G.vertices()\n",
    "    NS=nhbd(G,S)\n",
    "    ptNS=ptz(G,NS)\n",
    "    if ptNS>-1:\n",
    "        ptNS=ptNS+1\n",
    "    return ptNS\n",
    "# function to compute ppt(G,k) = minimum power propagation time over sets of size k\n",
    "# input: a graph G and a positive integer k \n",
    "# output: ppt(G,k) \n",
    "def pptk(G,k):\n",
    "    ord=G.order()\n",
    "    V = G.vertices()\n",
    "    S = subsets(V,k)\n",
    "    ptm = -1\n",
    "    for s in S:\n",
    "        ptms=pptS(G,s)\n",
    "        if (ptm < 0):\n",
    "            ptm=ptms\n",
    "        if (ptms >= 0) and (ptms < ptm):\n",
    "            ptm=ptms\n",
    "    return ptm\n",
    "    \n",
    "# function to compute ppt(G) = ppt(G,gamma_P(G))\n",
    "# input: a graph G and a positive integer k \n",
    "# output: ppt(G) \n",
    "def ppt(G):\n",
    "    return pptk(G,PowerDom(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "102efe13-5335-4cb2-aa02-8767c0e360eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute domination number of graph g\n",
    "def dom(g):\n",
    "    gds=g.dominating_set()\n",
    "    ds=len(gds)\n",
    "    return ds "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "897f7211-d625-457b-b40d-bfa731a97423",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function for product-x power throttling number\n",
    "#\n",
    "# This function computes th_pd^x(G) by minimizing th_pd^x(G,k) over k in {1,2,...,2/3gamma(G),gamma(G)} \n",
    "# To run on all graphs first comment out the print statements\n",
    "# Note differences to previous- checks gamma and stops when gamma/2 is reached rather then at ko when ptx(g,ko)=1\n",
    "#\n",
    "# input: a graph g\n",
    "# output: product throttling number th_pd^x(g) and least k such that th_pd^x(g) = th_pd^x(g,k)\n",
    "def thpdx(g):\n",
    "    nn=g.order()\n",
    "    saveko=PowerDom(g)\n",
    "    savept=pptk(g,saveko)\n",
    "    saveth=saveko*(1+savept)\n",
    "    gam=dom(g)\n",
    "#    print(saveko, savept, saveth)\n",
    "    for ko in [saveko+1..2*gam/3]: \n",
    "        ptko=pptk(g,ko)\n",
    "#        print(ko, ptko, ko*(1+ptko))\n",
    "        if ko*(1+ptko)<saveth:\n",
    "            saveko=ko\n",
    "            savept=ptko\n",
    "            saveth=saveko*(1+savept)\n",
    "    if 2*gam<saveko*(1+savept):\n",
    "        saveko=gam\n",
    "        savept=1\n",
    "    if nn<saveko*(1+savept):\n",
    "        saveko=nn\n",
    "        savept=0\n",
    "    return saveko*(1+savept), saveko \n",
    "       \t\n",
    "# Function for product-* power throttling number\n",
    "#\n",
    "# This function computes th_+^*(G) by minimizing th_+^*(G,k)\n",
    "# Note differences to previous- checks gamma and stops when gamma/2 is reached rather then at ko when ptx(g,ko)=1\n",
    "# To run on all graphs first comment out the print statements\n",
    "#\n",
    "# input: a graph G\n",
    "# output: product throttling number th_pd^*(G) and k such that th_pd^*(G) = th_pd^*(G,k)\n",
    "#         if th_pd^*(G)=gamma(G) then k=gamma(G) is returned; otherwise least k is returned\n",
    "def thpda(g):\n",
    "    nn=g.order()\n",
    "    gam=dom(g)\n",
    "    saveko=gam\n",
    "    savept=1\n",
    "    kmin=PowerDom(g)\n",
    "    for ko in [kmin..gam/2]:\n",
    "        ptko=pptk(g,ko)\n",
    "        if ko*ptko<saveko*savept:\n",
    "           saveko=ko\n",
    "           savept=ptko\n",
    "        if saveko*savept <= gam/2:\n",
    "            return saveko*savept, saveko\n",
    "    return saveko*savept, saveko "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "b8bb412c-8f3a-48fe-9a10-528b01876a9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# F- Functions for power dom throttling number\n",
    "# This function computes th_pd(G) by minimizing thpdk(G,k)\n",
    "# input: a graph g\n",
    "# output: PSD throttling number thp(g) \n",
    "def thpd(g):\n",
    "    pdg=PowerDom(g)\n",
    "    t=pptk(g,pdg)\n",
    "    thpdg=nn\n",
    "    for k in [pdg..dom(g)]:\n",
    "        pptkg=pptk(g,k)\n",
    "        if k+pptkg<thpdg:\n",
    "            thpdg=k+pptkg\n",
    "    return thpdg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ff2673c-7ed3-49a6-a33e-a694d8e9cc03",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Theorem 4.10: check thpdx(K_3 box K_3)\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "19fcf42b-b826-4ef6-a749-15a27e864665",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Graphics object consisting of 28 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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AYG1tDX9/fwwcOBCWlpZYsGCBSPtj+QWbBy8COtrb413cCzw8UHQla1moyEpWFvkjJycHFhYWsLKyQnBwcIXaePjwIZo2bYp///0XLVu2FLLCoixbtgwLFixAYGAgBg4cKPL+5B02RCMCfHbvRkJSMsZ5b4FAICjXtQKBAGNWb0b85y9Y/M8/IlLIIgvs3LkTb9++xapVqyrchqhj8P9l3rx5cHFxwbBhw3D37l2x9CnPsAYvAurUqQNfX18cvHAVHkvXIT0zq0zXpWdmYdjStQi4cBVq6upwcnLCjRs3RKyWRRr5+fMnli5dCg8PD1haWla4HXGFaPLhcDjw9f1VFrt37974+PGjWPqVV1iDFxEuLi44ePAgjl+7hYauo3EyPKLYiVfg14TqyfAINBk6Diev3UKDBg0gEAhgYmKCjh07YseOHezEFEshvL29kZ6ejn8q+ZQnboMHAFVVVZw+fRqKioro3bs3MjKKphWzCAd2klWEuLq6QllZGYMHDYLTnGUwNtBHJ+smaFLXHFoa6khJS8fDuNe4Ev0QH78moqO9PS74+MDQ0BAODg549OgR+vXrh3HjxuH+/fvYsmULuy0aCz59+oT169dj8uTJMDY2rlRbosyDLw1DQ0MEBwejTZs2GDZsGI4ePcqu9xAFxCJSBgwYQHXq1KHbt2+Tl5cX2VhbE4/HIwDE4/HIxtqavLy8KDo6utB1P3/+pDZt2pCWlhYtWLCAlJWVydbWlj59+sTQnbBICp6enqSrq0s/fvyodFvHjx8nAJSUlCQEZeXn1KlTBIAWLFjASP+yDmvwIiQuLo44HA7t3LmzyDE+n//H61NSUsjW1pa0tbVp3759ZGRkREZGRhQVFSUKuSxSQGxsLHG5XNqwYYNQ2gsICCAAlJ6eLpT2KsLKlSsJAAUEBDCmQVZhDV6EjB07lvT19SkjI6PCbfz48YNatmxJOjo6dOHCBbK1tSVlZWXy8/MTnlAWqaFPnz5Us2ZNysrKEkp7e/fuJQCUl5cnlPYqgkAgoKFDhxKPx2MHL0KGNXgR8fXrV1JRUaElS5ZUuq3k5GRq0aIFVa1alW7fvk0jR44kADRx4kTKyckRgloWaSAiIkLoI93t27eTgoKC0NqrKFlZWWRnZ0fVqlWj+Ph4puXIDOyshojYtm0buFwuxo0bV+m2tLW1cfHiRdSqVQsODg6YMGECtm3bhu3bt6Nbt2749u2bEBSzSDJEhBkzZqB58+YYPHiw0NrNzs6WiF2XeDweTp06BRUVFfTq1QtpaWlMS5IJWIMXARkZGdi6dStGjBghtE058k3e1NQUnTp1wl9//YUrV67gyZMnsLGxwYMHD4TSD4tkcvr0aURGRmL16tVCzTYR1nZ9wsDAwAAhISF49eoVhg4dWu5FgixFYQ1eBOzbtw/JycmYOnWqUNutWrUqLl++XJAfr6enh7t370JXVxd2dnY4cuSIUPtjkQzy8vIwZ84cdO3aFZ07dxZq21lZWRJj8ADQqFEjHD58GEFBQZg3bx7TcqQe1uCFDJ/Px/r16+Hk5IRatWoJvf18k69evTo6duyIjIwMREREoH///nBxccGsWbMK9mxlkQ18fX3x4sULrF69WuhtS0qI5nd69uyJNWvWYNWqVfD392dajnTD9CSArHHs2DECQHfu3BFpP1+/fqWGDRuSoaEhPXv2jAQCAa1du5a4XC51796dsbxmFuGSlpZGhoaGNGTIEJG0P3XqVGrQoIFI2q4MAoGARowYQcrKyhQREcG0HKmFHcELESLCmjVr0KFDB9jY2Ii0L319fVy5cgW6urqwt7dHXFwcpk2bhvPnzxdUBoyNjRWpBhbRs379eiQlJWHp0qUiaV+SYvC/w+FwsGPHDrRu3Rr9+vXD27dvmZYklbAGL0Ru3LiB27dvY8aMGWLpz8DAAFeuXIG2tjbs7e3x8uVLdOnSBXfu3IGKigpatWqFoKAgsWhhET5fv36Ft7c3vLy8ULNmTZH0IWkx+N9RVlbGiRMnoKGhgV69eiE1NZVpSVIHa/BCZM2aNbCysoKDg4PY+qxWrRquXr0KTU1N2Nvb49WrV6hduzYiIyPRtWtX9O3bF//88w+bkSCFLF26FAoKCpg7d67I+pDEGPzv6Onp4cyZM4iPj4erqys7v1RemI4RyQoxMTEEgLEVpp8+faJ69epRjRo16NWrV0T0qxzC0qVLicPhUN++fennz5+MaGMpP3FxcaSoqEirVq0SaT8DBw6kLl26iLQPYXDu3Dnicrk0ffp0pqVIFazBC4kRI0aQkZERZWdnM6bh48ePVLduXTI1NaU3b94UvB8cHExVqlQhS0tLiouLY0wfS9lxdnYmExOTSpW5KAu9e/emnj17irQPYbFx40YCQL6+vkxLkRrYEI0Q+PTpEw4ePIhJkyZBWVmZMR1GRkYICwuDkpIS7O3t8e7dOwBAr169cPv2beTl5aFFixY4f/48YxpZ/sydO3cQGBiIJUuWQFVVVaR9SXIM/r9MnDgRo0ePxpgxY3D9+nWm5UgFrMELgc2bN4PH42H06NFMS4GxsTHCwsLA5XJhb2+P9+/fAwAaNGiAf//9F3Z2dujRowe8vb3ZTUQkECLCzJkz0bBhQ7i7u4u8P0mPwf8Oh8PBli1b0K5dO/Tv3x+vX79mWpLEwxp8JUlNTcXOnTsxevRoaGlpMS0HAFCjRg2E/f9m3R06dMCHDx8A/Cp3EBwcjNmzZ2PWrFlwc3Njd9ORMEJDQxEeHo5Vq1ZBQUFB5P1JappkSSgpKeHYsWPQ0dFBz549kZKSwrQkiYY1+Eqye/dupKenY9KkSUxLKYSpqSnCwsLA5/Nhb29fsPelgoICli9fjsDAQAQFBaFNmzYFoRwWZuHz+Zg1axbat28PR0dHsfQpbQYP/FrNfebMGXz69AmDBg1CXl4e05IkFtbgK0Fubi42btwIV1dXmJiYMC2nCGZmZggLC0NOTg46duyIhISEgmMDBw5EZGQkUlJSYGNjg/DwcOaEsgAADhw4gCdPnsDb2xscDkcsfUpTDP536tevj2PHjuHy5cuYPn0603IkFtbgK8HRo0fx/v17if6A1apVC2FhYcjIyIC9vT0+f/5ccKxx48a4c+cOmjRpgs6dO2PLli1sXJ4hMjMzsWDBAgwcOBAtW7YUW7/SFIP/L126dMHmzZuxadMm7Nq1i2k5kgnDWTxSi0AgoMaNG1P37t2ZllIm4uLiyNjYmBo0aECfP38udCw3N5emTJlCAMjDw4MyMzMZUim/rF69mhQVFcWexmpsbEyLFi0Sa5/CZvz48aSoqEhXrlxhWorEwRp8Bblw4QIBkKoP1YsXL8jIyIgsLS3py5cvRY7v37+feDwetWrVij5+/MiAQvnk+/fvpK2tTePHjxd737q6urRixQqx9ytMcnNzqXPnzqSjo0MvXrxgWo5EwYZoKsiaNWvQvHlz2NvbMy2lzNStWxdXr15FUlISOnXqhMTExELH3d3dERERgY8fP8La2hqRkZEMKZUvVqxYgby8PCxcuFDsfUvjJOt/UVRURGBgIAwMDNCzZ08kJyczLUliYA2+Aty/fx+XL1/GjBkzxDYZJizq16+PsLAwJCYmolOnTkW2+7OxscHdu3dRu3ZttG/fHnv27GFIqXzw7t07bNmyBTNmzICBgYHY+5fmGPzv6OjoICQkBImJiXB2dkZubi7TkiQDph8hpBFXV1eqWbMm5ebmMi2lwsTGxpKBgQE1adKEvn37VuR4dnY2jRkzhgDQuHHjGC3BIMsMHTqUqlWrRqmpqWLvm8/nEwDas2eP2PsWFVevXiVFRUVGwl2SCGvw5eTt27ekoKBAmzZtYlpKpXny5Anp6+tTs2bN6Pv378Wes2vXLlJSUqJ27doVG7dnqTgPHjwgDodDO3bsYKT/jIwMAkAHDhxgpH9R4ePjQwBo69atTEthHNbgy8nkyZNJR0eHkRGXKHj06BHp6emRtbV1ibtARUREULVq1ahGjRp09+5dMSuUXbp160b16tWjnJwcRvpPTk4mAHTs2DFG+hclkydPJgUFBbp48SLTUhiFNfhykJSUROrq6jRv3jympQiVBw8ekK6uLtnY2FBycnKx57x//55atGhBKioqdPDgQfEKlEEuX75MAOjEiROMafj8+TMBoODgYMY0iIrc3FxycHAgLS0tevr0KdNyGIM1+HKwYsUK4vF4RfLIZYH79+9T1apVqWXLlvTjx49iz8nMzCR3d3cCQNOmTZPqOQgm4fP51Lx5c7K1tSWBQMCYjnfv3hEAunDhAmMaRMmPHz/I0tKSateuXew8kzzAGnwZyczMJENDQ/L09GRaisiIjo4mbW1tat26NaWkpBR7jkAgoI0bN5KCggJ16dKlxNg9S8kEBAQQALpx4wajOp4/f04AKDw8nFEdouTVq1ekq6tLHTp0kMtEAdbgy8ju3buJw+HQs2fPmJYiUu7evUva2tpkZ2dX6g5Qly9fJl1dXTI3N6dHjx6JUaF0k5WVRTVr1qTevXszLYUePXpEACgqKoppKSLl2rVrpKSkRJ6enow+MTEBa/BlgM/nU/369alv375MSxELt2/fJi0tLWrbtm2pk8mvX7+mxo0bk7q6Oh0/flyMCqWXDRs2EJfLpZiYGKal0J07dwgA3b9/n2kpIsfX15cA0MaNG5mWIlZYgy8DQUFBBIBu3rzJtBSxERUVRZqamtSuXbtSTT4tLY2cnZ0JAM2fP5/4fL4YVUoXP378IF1dXRo5ciTTUojoV3YUAIqNjWVailiYPn06cblcOnfuHNNSxAZr8GWgbdu2ZGdnx7QMsXPr1i3S0NCg9u3bU1paWonnCQQCWrlyJXE4HOrVq1eJ8Xt5Z86cOaSqqioxdX7yM3nyN2mXdfLy8qhXr15UpUoVevLkCdNyxAJr8H8gMjKSANCpU6eYlsIIERERpKGhQfb29pSenl7quWfPniUtLS1q0KCBzM9VlJcPHz6QqqoqzZ07l2kpBZw9e5YASMwPjjj4+fMnNWrUiGrVqkWJiYlMyxE5bC2aP7BmzRrUq1cPvXv3ZloKI7Rp0wahoaG4ffs2+vTpg8zMzBLPdXR0xO3btwEALVu2xNmzZ8UlU+JZtGgR1NTUMHPmTKalFJCdnQ0AUl9srDxUqVIFISEhSE9PR//+/ZGTk8O0JNHC9C+MJPPixQvicDi0a9cupqUwzrVr10hNTY26dOlCGRkZpZ6bkpJCvXv3Jg6HQ8uXL5e7zIX/EhMTQ1wuV+Im+A4dOkQAZGZVdnm4efMmKSsrk4eHh0x/PlmDL4UxY8aQgYEBuwHG/xMWFkaqqqrUrVu3P/5N+Hw+LVy4kACQk5OTXJpIPr169aJatWpRVlYW01IK4efnRwAYK5XANP7+/gSA1qxZw7QUkcEafAl8+fKFVFRUaOnSpUxLkSiuXLlCKioq5OjoWCbDOnHiBKmrq1OjRo3o9evXYlAoWVy/fp0A0KFDh5iWUoSdO3cSl8uV6RHsn5gzZw5xOByZLNdAxBp8iSxcuJDU1NTkdolzaVy6dIlUVFSoR48eZTL5x48fk7m5OVWtWpUuX74sBoWSgUAgoNatW5O1tbVEpo9u2rSJVFVVmZbBKHw+n/r27UsaGhr08OFDpuUIHXaStRgyMjKwbds2/P3339DV1WVajsTRuXNnBAUF4fLlyxg4cOAfJ6oaNmyIO3fuwMbGBt26dcPGjRvlYnPvkydPIioqCqtXrwaXK3lftaysLLmaYC0OLpeLAwcOoE6dOujVqxe+fPnCtCThwvQvjCSydetW4nK5chlSKA+hoaGkrKxMffv2LVMcNzc3l6ZPn04AaOjQoX+crJVmcnJyqG7dutStWzempZTIkiVLqFq1akzLkAji4+OpWrVqZGdnJ1NzbqzB/4e8vDwyNzenQYMGMS1FKjh79iwpKytT//79yzxZFxAQQCoqKmRjY0Px8fEiVsgM27dvJw6HQw8ePGBaSonMmzePzMzMmJYhMURFRRGPx6OhQ4fKzLwEa/D/ITAwkACwG1uUg5CQEFJSUiInJ6cym3x0dDSZmpqSgYEB41UVhU1qaipVq1aNhg4dyrSUUpk+fTrVq1ePaRkSxeHDhwkArVy5kmkpQoE1+N8QCATUokULsre3Z1qK1BEUFERKSkrk7Oxc5jrxX758ob/++ouUlJRo586dIlYoPhYvXkzKysr09u1bpqWUipeXFzVq1IhpGRJHfnrvyZMnmZZSaViD/42wsDACQKGhoUxLkUpOnTpFioqK5OLiUmaTz8nJofHjxxMAGjVqlNTX7P78+TOpq6vTtGnTmJbyRzw9PalFixZMy5A4+Hw+DRw4kNTU1OjevXtMy6kUrMH/hqOjIzVq1Ehm4m9McPz4cVJQUCA3NzfKy8sr83V79uwhZWVlatOmDSUkJIhQoWgZN24caWtrS8VGKO7u7tS2bVumZUgk6enpZG1tTSYmJvTp0yem5VQYycvdYoiYmBicO3cO06dPB4fDYVqO1DJgwAAcPnwYR44cgYeHB/h8fpmu+/vvvxEeHo7Xr1/DxsYGd+7cEbFS4RMXFwcfHx/MmTMHVatWZVrOH2HTJEtGTU0NQUFBEAgE6Nu3b6k1mCQZ1uD/n7Vr18LY2BiDBw9mWorUM3DgQAQEBCAgIAAjR46EQCAo03W2tra4e/cuTExM0K5dO+zfv1/ESoXL3LlzYWhoiAkTJjAtpUxkZ2ezBl8KxsbGCAoKwuPHjzFixAjpXLvB9COEJPDhwwdSUlKS6ZoUTHDo0CHicrk0YsSIcq3kzMrKohEjRhAAmjRpklRs7h0VFUUAyM/Pj2kpZaZ79+7Uv39/pmVIPPmZdUuWLGFaSrlhDZ6IZs6cSZqamuxGFSLgwIEDxOFwaOTIkeUyeYFAQFu3biVFRUXq2LGjRNfuFggE9Ndff1GjRo3KNe/ANPb29uTi4sK0DKlgyZIlBIACAwOZllIu5N7gU1JSSFNTk2bMmMG0FJll//79xOFwaPTo0eWuyRIeHk56enpUs2ZNiV00FBISQgDo7NmzTEspF7a2tjR8+HCmZUgFAoGABg8eTKqqqnTnzh2m5ZQZuTf4tWvXkpKSEn348IFpKTKNn58fcTgcGjt2bLmzlN6+fUvNmjUjNTU1Onr0qIgUVoy8vDyysrKiDh06SF32VfPmzWn06NFMy5AaMjIyqFWrVmRkZCQ1fiHXBp+Tk0MmJiY0bNgwpqXIBfk723t5eZXbDNPT08nFxYUA0OzZsyUmFJJ/T7dv32ZaSrmxsrKiSZMmMS1DqkhISKAaNWqQtbX1H7ewlATk2uDzC/4/fvyYaSlyg4+PDwGgiRMnltvkBQIBrVmzhrhcLjk4OFBycrJoRJaR9PR0MjY2JmdnZ0Z1VJQ6derQzJkzmZYhddy/f5/U1NTIyclJIstA/47cGrxAIKBGjRqRg4MD01Lkjp07dxIAmjJlSoXCGufPnydtbW2qW7cuxcbGikBh2Vi5ciUpKipSXFwcYxoqg4mJCS1YsIBpGVLJqVOnCIDE//3k1uDPnz9PAOjq1atMS5FLtm3bRgBo+vTpFTL5uLg4srKyoipVqlBQUJAIFJbOt2/fSEtLi7y8vMTet7DQ19enZcuWMS1Dalm5ciUBoICAAKallIjcGnynTp3I2tpa6ibGZIktW7YQAJo5c2aF/h1+/vxJ/fr1K8hRLs/jcmUfradMmUIaGhr05cuXSrXDJJqamrR27VqmZUgtAoGAhg4dSjwej6KiopiWUyxyafDR0dEEgI4cOcK0FLln48aNBIDmzJlTIZPn8/n0zz//EADq378//fz5s9jzoqOjycvLi6ybNycej0cAiMfjkXXz5uTl5UXR0dFl7vPNmzekrKwslQtffofH49GWLVuYliHVZGVlkZ2dHVWrVk0i9zaQS4N3cXGhmjVrSsUKSXlg/fr1BIDmz59f4Seq06dPk4aGBllZWRWKicfFxZF9hw4EgIwN9GmYY2daP2k07Zk7hdZPGk3DHDuTsYE+ASD7Dh3KFE93c3MjQ0NDSktLq5BWSUAgEBAA8vHxYVqK1PPlyxcyNTWlJk2aUGpqKtNyCiF3Bv/mzRtSUFBgRy4Sxpo1awgALVq0qMJtxMTEUN26dUlbW5suXLhAAQEBpKqqSubGRnRi5QLKuXGWBJHni7xybpylEysXkLmxEamqqtKhQ4dK7OPevXsEgHbt2lVhnZJAVlYWAaD9+/czLUUmePjwIWloaFDfvn0lKrNG7gx+4sSJVLVqVakefckqq1evJgD0zz//VLiN5ORkcnBwIA6HQxwOh4Z270SpV08Xa+z/faVePU1Du3ciDodT4sRZly5dqEGDBlL/9JeSkkIAJG7hmDQTHBxMHA6H5syZw7SUAhTFUdBMUkhKSsKePXswbdo0qKurMy2H5T/MnDkTfD4fc+fOhYKCAubNm1fuNrS1tbF+/XpcuXwZAzu2g9+CaeByy1Y0VV1VBX4LpgEARo4ciZYtW6JOnToFxy9duoRLly7h1KlTUFSU7q9OVlYWALDVJIVIr1694O3tjRkzZsDCwgJDhw5lWpJ8lQvesWMHBAIBvLy8mJbCUgJz5szB0qVLMX/+fKxatapCbYwbOxY1qulj56yJJZr7yv1HwLXtjskbdhZ6n8vlYvvMCaheVQejPD0L3hcIBJg1axbs7OzQp0+fCumSJLKzswGwBi9spk2bhhEjRmDkyJG4desW03Ig3cOQcpCVlYUtW7Zg2LBhMDAwYFoOSynMnz8ffD4fc+bMAZfLxcyZM8t8bXR0NMLCw3Fi5QKoq6oUe86d2OfYHRSKxnVqFXtcXVUF3l4j4DRnGe7du4fmzZvj8OHDuH//Pm7evCkTG8KwBi8aOBwOduzYgZcvX6Jv3764c+cOzMzMGNMjNyP4AwcO4OvXr5g2bRrTUljKwKJFi7Bw4ULMmjUL69atK/N1+/btg0k1A/Rq27rY42kZmRiy2Bs+sydBp4pGie30bmsLYwN9+Pn5ITs7G/Pnz0ffvn1hZ2dX7nuRRPINXkWl+B9BloqjrKyMEydOQENDAz179kRqaipjWuTC4AUCAdatW4e+ffuibt26TMthKSOLFy/GvHnzMH36dGzYsKFM10TeuoVO1o2hqKhQ7HGvtdvgaNcSnVs2L7UdRUUFdLJugqjISGzfvh3v37/HypUry30Pkgobgxctenp6OHPmDOLj4+Hq6lrmrSuFjVwYfEhICJ4/f44ZM2YwLYWlHHA4HCxduhSzZ8/G1KlTsXnz5j9e8yQmBk3q1i722JFL4bj3/CVWjvUoU/9N6prj8ZPHWLZsGf7++280aNCgXPolGTZEI3osLS1x5MgRnDt3DrNnz2ZEg1zE4NesWYM2bdrA1taWaSks5YTD4WDFihUQCASYNGkSuFxuiZPkAoEA2dnZ0FRXK3Ls/ZdETN6wExc2rYAKT7lMfWtpqCM7OwfZ2UmIjIxEz549Ub169WJfhoaGUFYuW7uSABuiEQ8ODg5Yv349Jk+eDAsLC4wYMUKs/cu8wUdGRuLmzZs4ffo001JYKgiHw8GqVavA5/MxYcIEKCgoYOzYsUXO43K54PF4+JmeUeRY9LM4fE3+ARuP//048PkCXH/wBNtOBCPrWggUFAqHdVLS0sHlcNC2XTtYWFggISEBDx8+xPnz5/H582fk5eUVOl9XV7dY8zcyMir0/9XUiv4AiRt2BC8+Jk6ciNjYWIwZMwZ16tTBX3/9Jba+Zd7g16xZg/r166NXr15MS2GpBBwOB2vWrAGfz8e4ceOgoKCAUaNGFTmvoZUVHsa9KvJ+J5umeHSwcErkiOXr0MCsBmYOcS5i7gDwMO41lJSVEBISAk1NzULHBAIBvn//joSEBCQkJODTp08F/52QkICXL1/ixo0bSEhIKIh356OpqVnik8DvLy0tLZFl7LAxePHB4XCwdetWvHjxAv3798ft27dhbm4ulr5l2uBfvHiB06dPY9euXWVe7MIiuXA4HKxfvx4CgQCjR48Gl8vFyJEjC51Tv0EDXLhwHnl5/EITrVXU1dCwds1C56qrqKCqpmaR9wEgL4+PC//eRatWrYuYO/DraUFfXx/6+vpo3LhxiZqJCCkpKYXM//cfhU+fPiE6OhoJCQlFsi1UVVXL9EOgq6tb7s83O4IXL0pKSjh+/Dhat26NXr164datW9DS0hJ5vzJt8OvXr4eBgYFErChjEQ4cDgcbN24En8+Hp6cnuFwuRowYgXfv3mHx4sU4fPgwiAghEVHo16FNhfsJjojEl6QfCPL2rrRebW1taGtrw8LCotRz09PTi/0hyH89e/YMnz59QlJSUqHrlJSUUK1atRJDQvkvAwODghW4bAxe/Ojq6iIkJAStW7fG4MGDERISIvIV0RwiIpH2wBBfv36FqakpFixYUKEl7yySDRFh/Pjx2LFjBzp37oxr165BR0cH8+fPx4njx/H+1Us8PLC9xMVOpZGemQUrF09o6hng8ZMnIlBfObKzs/H58+dSfwwSEhLw9etXCASCgus4HA4MDAxQvXp15OXl4cmTJ5g7d27BD0L+/xoaGrIjexFy6dIlODg4YMKECX9M/xUIBJWKPsjsCH7r1q1QVFQsdjKORfr58eMHtLW1oaioiMuXL8PJyQl+fn7Q0NCAg4MDGjdujHHeW8pViwb49YUa470Zn74l4dL1CBHeQcXh8XgwMzP74wrJvLw8JCYmFjtHkL8i98CBA/j8+TNyc3MLXVu1atUyhYc0NEpeLMZSPF26dMHmzZsxfvx4WFhYFJpLunfvHvz8/BB56xaexMQgOzsbPB4PDa2sYGtnBw8PDzRvXvoajt+RyRF8eno6TE1NMXToUGzcuJFpOSxCJD09HZs3b4a3tzdycnIwceJEfPz4EQcPHsSBAwfg5uYGADh8+DDc3NwwpFtHbJ85oUwj+fTMLIzx3oyA81cxb948LFu2TNS3wxhr167F0qVLkZKSAoFAgKSkpGLnCP77XmZmZqF2NDQ0SgwJ/f7S1taWiRIPwsTLywu7du3CxYsXUaNGDYzy9ERYeDiMDfTR2aYJmtStDU11NfxMz8DDuFe4fPchPn5NhH2HDvDZvbtQIbySkMkR/N69e5GSkoIpU6YwLYVFSGRnZ2P37t1YtmwZkpKSMHr0aMybNw+GhoYQCARQUlKCu7s7uFwuXFxc4OLiAiLCyJEjcfPxU3h7jUDvtrbFrnDNy+MjOCISM7b64l3CZ1StWlWmzR349ffMj79zuVzo6elBT08PjRo1KvEaIsLPnz9LDQvdv38fCQkJ+PnzZ6FrVVRUYGho+McUUj09PblJiNi4cSOeP3+OXr16gc/nw0i3Kk6sXIBebVuX+DkNiYjCjK2+aNy4MXx9feHi4lJqHzJn8Hl5eVi/fj2cnZ0ZLfLDIhz4fD4OHDiAxYsX4/3793B3d8eiRYtQs2bNgnO4XC52794NPp+PIUOGgMvlYtCgQXB1dUXLli0xytMTTnOWwdhAH52sm6BJXXNoaagjJS0dD+Ne40r0r5FRg/r1IRAkICkpCXv37hX7ohRxkpWVVe44O4fDgZaWFrS0tP64qjcjI6PUH4Lr168jISEB3759K3SdoqJioQnjkl7VqlWDkpJSue9bklBUVISzszMuX74Mt+4dsXPmxFKfNBUVFdCvQxt0bWWNcd5b4ObmBiKCq6trydeIQjiTnDhxAm/fvsXJkyeZlsJSCYgIJ0+exIIFC/D06VMMGDAAoaGhJWaicLlc+Pr6QiAQwM3NDVwuFwMHDkSdOnVwNSysILYZFRmJo1f3F8Q2GzVsiH7Og+Ds7AwnJycMGzYMysrKGD9+PJo3b46mTZuK98bFRP79iwo1NTXUrl0btWsXXzYin5ycnFInjO/evYuEhAR8+fKlyISxvr5+meYJJDVTKC4uDpMmTcKQ7p2wT4j7FvyOTMXgiQgtWrSAtrY2Ll++zLQclgpARLh06RLmzp2L6OhodOvWDcuWLYONjU2Zrufz+XB3d8fRo0cRGBiI/v37F3vef7MTFi9ejFWrVuHFixcwMDCAnZ0dfv78iejoaLHkK4ubSZMm4cqVK3gigVlCxcHn8wsmjEubI/j8+TNycnIKXautrV1qWCj/VaVKFbHeU0d7e8S/fIEH/v/L9lq5/whOXbuJZ+8+QJWnDLtGllg1bgTqm9Uocn16ZhaaDB0Hs7r1cDUsrNg+ZGoEHx4ejujoaJw/f55pKSwV4NatW5g7dy6uXbsGOzs7hIeHo3379uVqQ0FBAfv374dAIMCgQYNw7Ngx9O3bt8h5v5v758+fsXbtWkycOBGmpqYAgGPHjsHa2hoeHh44ceKEzE0Q/h6DlwYUFBRgaGgIQ0NDNGvWrMTziKjYCeP817t37xAVFYWEhARkZBQuaaGurl7qk0D+D4OOjk6lPw8l7Vtw/f5jjBvQCy0s6iGPL8D8nfvQbfI8xBzyKRK+KW7fgv8iUyN4R0dHfPz4EQ8ePJC5L6Qs8/DhQ8ybNw9nz55FkyZNsHz5cjg6Olbq3zAvLw9ubm44deoUjh8/jt69e5d47rhx43DkyBG8evUKOjo6Be8HBQWhb9++WLduHaZOnVphLZLI8OHDERcXh5s3bzIthRGICKmpqX9cS/Dp0yekpKQUupbH4xU7Yfzfl76+frElMABgwoQJOH0sEK+P+5VY2hoAEpN/oJrjYIRvX4O/mhWdAM/L46PWgOHo5zwIW7ZsKXJcZkbwT548QWhoKPz9/VlzlxJevHiBRYsW4ciRI6hTpw4OHz4MZ2dnoWRRKCoq4uDBg3B1dYWTkxNOnjyJnj17FqvBx8cHq1atKmTuANCnTx/MmDEDM2fORMuWLdG2bdtK65IURB2Dl3Q4HA40NTWhqamJ+vXrl3puZmZmqT8CERERSEhIQGJiYqHrFBQUYGBgUGxI6HxoaKn7FuSTkvbrKaOqZvHho9/3LSj2PmVlBD98+HBcuXIFr1+/lvrZdVnn/fv3WLJkCfz8/FC9enUsWrQIw4YNE8m/W25uLgYPHowzZ87g1KlTcHR0LHTcyckJd+7cwfPnz4sNWeTm5qJTp0549eoV7t+/LzPbPfbv3x+ZmZkIDQ1lWorMkJubiy9fvpQ4P5D/+vLlC0ggwNqJozB5cL8S2yMi9J25GMmpabi+s+RdzTYcPom5u/YXKWoHyMgI/uPHjzh06BBWrlzJmrsEk5iYiJUrV2L79u2oUqUK1qxZg7Fjx4o0FqykpFTwZNC/f3+cPn0a3bt3BwBERUXhxIkT2L9/f4kalJSUcOTIETRv3hyurq64cOFCiY/d0oS0xeClASUlJZiYmMDExKTU83Jzc6GsrFzsvgW/47V2Gx69fIMbu0rfsvLXvgXZxZY1kIkVBZs2bYKqqio8PT2ZlsJSDCkpKVi4cCHMzc2xZ88ezJ07F69fv8aUKVPEYjLKysoIDAxE165d0bdvX1y8eBFEhJkzZ6Jx48YFq19LwsjICIcPH0ZYWBj++ecfkesVBxXJg2cRDkpKSiXuW5DPhHXbERIRhavbvGFioF9qeylp6eDxeMWGNqV+BP/z50/s2rULY8aMKbasKwtzZGRkYNu2bVi1ahUyMjIwYcIEzJo1C7q6umLXoqysjGPHjmHAgAHo06cP5s6dixs3biA0NLRMI3J7e3ssW7YMc+fOha2tLRwcHMSgWnTIewyeaUrat4CIMGHddpy+dgth271Ry8jwj209jHuNRg0bFntM6kfwPj4+yMzMxKRJk5iWwvL/5OTkYMeOHahTpw7mzp0LZ2dnvHr1Ct7e3oyYez48Hg8nTpxA+/btsWjRIjRr1gzdunUr8/WzZs1Cjx49MGTIEMTHx4tQqehhQzTMkD8gjX//Huej7iIvr/Bm3OPXbkPAhasI+GcWqqip4vP3JHz+noTMrOxi28vL4+NK9EO0LmE7Uqk2+JycHGzcuBFubm4wMjJiWo7cw+fzcfDgQVhYWGD8+PHo1KkTnj17hh07dkjMvw+Px0Pfvn1BRIiNjcW1a9fKfC2Xy4W/vz+qVKmCgQMHFllQI02wI3jxQUS4c+cOPD09YWRkhHHjxsHCwgJfkn4gJCKq0Lk7T55BSlo67MfPhFFP14LX0SvFf06DIyLx8WsiPDyK30heqrNo/P39MWzYMDx58gRWVlZMy5FbiAjBwcGYP38+njx5gr59+2Lp0qVoWMJjI5NkZGSgbt26aNOmDX78+IGbN28iNDS0XPtk3r17F23atMHo0aOxefNmEaoVHfXq1UOfPn2wZs0apqXILCkpKTh06BB8fHzw4MEDmJqaYuTIkfDw8ICJiQk62tvjXdyLSu1b8KeVrFI7gicirFmzBj169GDNnUGuXLmC1q1bo2/fvqhWrRqioqJw6tQpiTR34NeEfGJiIlatWoWgoCDY2trC0dERERFlr/1uY2ODjRs3YsuWLThy5IgI1YoOdgQvGogI//77L/7++28YGRlhwoQJqFmzJs6dO4fXr19jwYIFBVk2Prt3IyEpGeO8txSqs1MWBAIBxnlvQUJSMnx27y5VkFRy7tw5AkDh4eFMS5FLoqKiqFOnTgSAWrZsSZcvX2Za0h9JTEwkTU1NmjhxYsF76enpZG9vTxoaGnTz5s0ytyUQCMjV1ZXU1dUpNjZWFHJFSrVq1Wjp0qVMy5AZkpOTacuWLdSoUSMCQGZmZrRs2TL6+PFjqdcdOnSIOBwODe3eiVKvniZB5Pk/vlKvnqah3TsRh8OhQ4cOldq+1Bq8vb09tWjRggQCAdNS5IrHjx9Tnz59CABZWVnR6dOnpebfYPLkyVSlShX6+vVroffT0tKoffv2VKVKFYqMjCxze6mpqWRhYUGWlpaUlpYmbLkiRUtLi7y9vZmWIdUIBAK6efMmDRs2jFRVVUlRUZH69+9P58+fJz6fX+Z2AgICSFVVlcyNjej4yvmUc+Nsscaec+MsHV85n8yNjUhVVfWP5k4kpQZ/9+5dAkCBgYFMS5EbXr58SUOGDCEOh0Pm5uZ08OBBysvLY1pWmXn9+jUpKSnRsmXLij2emppK7dq1I01NTfr333/L3G5sbCypq6uTm5ub1PzQERGpqKjQpk2bmJYhlSQlJdGmTZvIysqKAJC5uTmtWLGCPn36VOE24+LiyL5DBwJA1fWqkrtDZ1o3cRTtmTuF1k0cRe4OncnYQJ8AUEd7e4qLiytTu1Jp8IMGDSJzc3OpMhhp5cOHDzRmzBhSVFSk6tWr044dOyg7O5tpWeXG1dWVqlevXupIOzU1ldq0aUNaWlp0586dMrcdEBBAAGjnzp3CkCpyBAIBcTgcqdErCQgEArpx4wYNHTqUVFRUSFFRkQYOHEiXLl0q12j9T0RHR5OJiQnpVq1KPB6PABCPxyMba2vy8vKi6OjocrUndQb/+vVr4nK5tHXrVqalyDTfvn2j6dOnk4qKClWtWpW8vb0pPT2daVkVIjo6mgCQj4/PH8/9+fMn2drakra2Nt29e7fMfYwbN46UlZXLdQ1T5OTkEADat28f01Iknm/fvtGGDRvIwsKCAFDt2rVp9erV9PnzZ5H1aWhoSPPnzyciqvSPh9QZ/IQJE0hXV1dqzUbS+fnzJ/3zzz9UpUoV0tDQoIULF9KPHz+YllUpOnfuTA0aNKDc3NwynZ+SkkKtW7cmHR0dunfvXpmuycrKohYtWlDNmjUpKSmpMnJFzs+fPwkAHT58mGkpEolAIKBr166Rm5sb8Xg8UlJSokGDBtGVK1eEOlovju/fvwv130aqDP7bt2+kpqZGCxcuZFqKzJGZmUnr168nPT094vF4NGXKlCKTkdLIhQsXCACdPn26XNf9+PGDWrZsSVWrVqUHDx6U6Zq3b9+Sjo4O9ezZU+RGUBkSExMJAJ08eZJpKRJFYmIirVu3jurXr08AqG7durRmzRqxfg+uX79OAOjRo0dCaU+qDH7p0qWkoqIiE8YjKeTk5JCPjw+ZmJiQgoICeXp6Unx8PNOyhAKfz6emTZtSmzZtKjQBmpycTDY2NqSrq0sPHz4s0zVnz54lALRq1apy9ycuPnz4QADo7NmzTEthHIFAQGFhYeTi4kLKysqkrKxMLi4uFBYWxsik+c6dO0lBQYGysrKE0p7UGHxmZiYZGBjQmDFjmJYiE/D5fDp8+DDVrVuXANDgwYPp+fPnTMsSKgcOHCAA5cpv/y9JSUnUvHlz0tPTo8ePH5fpmnnz5hGXy6WwsLAK9ytKXr16RQDoypUrTEthjK9fv9KaNWsKPv/169endevWUWJiIqO6JkyYQPXr1xdae1Jj8Lt27SIOh0MvXrxgWopUIxAIKCQkhBo3bkwAqEePHnT//n2mZQmdzMxMMjMzo379+lW6re/fv1PTpk1JX1+fnjx58sfz8/LyqGPHjlStWrVKpc6JipiYGAJAERERTEsRK3w+ny5fvkzOzs6kpKREPB6P3Nzc6Nq1axKT4tqxY0fq37+/0NqTCoPn8/lUr149od64PBIeHk52dnYEgP766y+Z/oKvW7eOFBQU6NmzZ0Jp79u3b9SkSRMyMDAo08rVz58/U/Xq1al9+/ZlntwVF/fu3SMA5UoFlWY+f/5Mq1atotq1axMAsrCwoA0bNtC3b9+YllaEatWq0YIFC4TWnlQY/KlTpwhAuVYZsvyPu3fvUteuXQkAWVtb04ULFyRmxCIKkpOTqWrVqjR69GihtpuYmEiNGjWiatWq0dOnT/94/vXr10lBQYFmzZolVB2VJTIyUqgTeZIIn8+nixcvkpOTEykqKpKKigoNHTqUbty4IbGf/W/fvhEAOnLkiNDalAqDt7Ozo3bt2jEtQ+qIjY2lAQMGEABq0KABHT9+XGI/3MJk1qxZpKamJpLwyNevX6lhw4ZUvXr1Ms1ZrFmzhgBQUFCQ0LVUlLCwMAIgk+HOhIQEWrFiBdWqVaugnMbmzZslPnWV6H8ZNGWd6ykLEm/wN2/eJAAUHBzMtBSp4c2bNzRs2DDicrlkZmZG+/btk5tVv/Hx8aSioiLUx9z/8uXLF7K0tCQjI6M/mqRAIKC+ffuStrY2vXr1SmSaysP58+cJAL17945pKUKBz+fT+fPnqX///qSoqEiqqqo0fPhwunXrllQNaHbs2CHUDBoiKTD4vn37UoMGDSQ6r1hSSEhIIC8vL1JSUqJq1arRli1bhPphkQY8PDxIX1+ffv78KdJ+Pn/+TA0aNCBjY+M/1gVJTk4mc3Nzat68OWVmZopUV1kICgoiACJdjSkOPn78SMuWLaOaNWsSAGrUqBFt3bqVkpOTmZZWIby8vKhBgwZCbVOiDf7Zs2fE4XBoz549TEuRaJKSkmj27NmkpqZG2tratHLlSqmrbigMHj9+TFwul7Zs2SKW/j59+kT169cnExOTP47O7927RzweT+jzAhUhMDCQAEjlCuW8vDw6d+4c9e3blxQUFEhNTY1GjBhBUVFRUjVaLw57e3saMGCAUNuUaIP39PQkQ0NDuRuFlpXU1FRavnw5aWlpkZqaGs2dO1cqYo2iokePHlS7dm2xFkP7+PEj1a1bl0xNTenNmzelnrt7924CQP7+/uIRVwL+/v4EQCKeJsrK+/fv6Z9//iFTU1MCQE2aNKHt27dL5Y9USRgYGAh9lb7EGvznz5+Jx+PRihUrmJYicWRlZdGmTZvIwMCAlJWVaeLEiVL/uF1ZwsPDCQAdPXpU7H1/+PCB6tSpQ2ZmZvT27dsSzxMIBDR8+HBSU1MT6kRaecn/oZH0sGdeXh6FhIRQr169iMvlkrq6Oo0cOZJu374t9aP1/5JfPkLYn1+JNfh58+aRurq6XI9I/0tubi7t3buXTE1NicvlkoeHR6mGIi8IBAJq2bIloxvAvH//nszNzalWrVqlTl6mp6dTo0aNqH79+iKfJyiJrVu3kpKSEiN9l4X4+HhatGgRmZiYEABq3rw57dy5k1JSUpiWJjKuXbtGAMq0kK48SKTBp6amko6ODk2ePJlpKRIBn8+nwMDAgiJITk5OZcrDlhfyY8pMlwZ49+4d1apVi8zNzUut5/P8+XOqUqUKOTs7M/KDtG7dOqpSpYrY+y2N3NxcCgoKoh49ehCXyyUNDQ0aNWqUVJRfFgbbt28nRUVFoYcXJdLgN23aRAoKCnI/OhUIBBQaGkrNmzcnANS9e3e5+cCXlZycHKpTpw45OjoyLYWIflWUrFmzJtWuXZs+fPhQ4nnHjh0jAGKbEP6d5cuXk56entj7LY63b9/SggULyMjIiACQjY0N+fj4MPZ0wxTjx48nCwsLobcrcQafm5tLNWvWJFdXV6alMMqNGzeoXbt2BIDatGlD165dY1qSRLJ161bicDgStSrzzZs3ZGpqSnXr1i110+XJkyeTkpISRUVFiVEd0cKFC8nY2Fisff5OTk4OnTp1ihwcHIjD4VCVKlVo7NixZa69L4t06NCBnJychN6uxBn84cOHCYBMFsAqC/fu3SNHR0cCQE2bNqWzZ8/K3ISSsPj58yfp6+vT8OHDmZZShFevXlGNGjWoXr16Ja6ozc7OJltbW6pRo4ZYqxjOmjWLzM3NxdZfPq9fv6Z58+ZR9erVCQC1atWKfH19KTU1VexaJA0DAwNatGiR0NuVKIMXCATUvHlz6ty5M9NSxM7z58/J2dmZAFC9evXo6NGjEp/lwDQLFy4kFRUVia1f//LlSzIxMaEGDRpQQkJCsefEx8eTnp4edevWTWz/3pMnTyZLS0ux9JWTk0MnTpygbt26EYfDIU1NTRo/fnyZN1GRB/IzaAIDA4XetkQZ/JUrVwgAXbhwgWkpYuPdu3f0999/k4KCAtWoUYP27NkjcdUHJZGEhARSV1enmTNnMi2lVOLi4sjIyIgsLS3py5cvxZ5z4cIF4nA4tGTJErFoGjNmDDVr1kykfbx69YrmzJlD1apVIwBka2tLfn5+crkA70/kp/gKO4OGSMIMvnv37tSkSRO5CEl8+fKFJk+eTMrKyqSvr08bN26UqoUnTDNmzBjS0dGRijTa58+fU/Xq1cnKyqrE3cgWL15MHA6HLl26JHI9Hh4e1Lp1a6G3m52dTYGBgdSlSxcCQFpaWjRhwgSJmh+RRLZt2yaSDBoiCTL4R48eEQA6cOAA01JEyo8fP2j+/Pmkrq5OmpqatHTpUrnLGKgsz549IwUFBVq7di3TUsrM06dPydDQkBo1alRsvD0vL4+6du1Kenp69P79e5FqcXV1pfbt2wutvbi4OJo5cybp6+sXJAXs37+f0tPThdaHLDNu3DiRhcwkxuDd3d2pRo0alJOTw7QUkZCenk6rV68mHR0dUlVVpZkzZ9L379+ZliWV9O/fn0xNTaXuiSc2NpaqVatGjRs3LnazicTERDIxMSE7OzuRfg/69+9P3bp1q1QbWVlZdOTIEerYsSMBIB0dHZo0aZJIwgyyTocOHWjgwIEiaVsiDP79+/ekqKhI69evZ1qK0MnOzqZt27aRoaEhKSoq0rhx40pNnWMpnVu3bklEPZeKEhMTQ/r6+tS0adNif+AjIyNJUVGRpk6dKjINPXr0oN69e1fo2ufPn9P06dNJT0+vYGewAwcOUEZGhpBVyg/6+vq0ePFikbQtEQY/ffp00tLSkqlQRV5eHvn7+1OtWrWIw+HQ0KFDJaYeuLQiEAiobdu21KRJE6nOMHr8+DHp6elRs2bNip1D2LRpEwGgEydOiKT/zp07l2vEmJWVRYcOHaIOHToQAKpatSpNnTq1TFsXspTO169fRZZBQyQBBv/jxw+qUqUKzZ49m2kpQkEgENDJkyfJ0tKSAFC/fv3Yx1YhkV/H/Pz580xLqTSPHj0iXV1dsra2LlK/XCAQ0MCBA0lTU1Mkuy61a9eOhgwZ8sfznj59SlOnTiVdXV0CQB06dKBDhw5JXWhMksnfXSsmJkYk7TNu8KtXryZlZWWJ3H2+PAgEArp06RK1aNGCAFDnzp3p33//ZVqWzJCbm0sWFhbUqVMnmcmyevDgAVWtWpVatGhRpOxtSkoK1atXjxo3biz08EeLFi1o5MiRxR7LzMykgwcP0l9//UUASE9Pj6ZPny60zctZCpNf+E1Ucy6MGnx2djYZGRnRiBEjmJRRaSIjI8ne3r5gdd6VK1eYliRz5Je4lbVaPPfu3SMdHR1q1apVkWqJjx49IlVVVaF/Pxo3bkzjx48v9F5MTAxNnjyZdHR0CAB17NiRjhw5wu7FIGLGjRtHVlZWImufUYP38/MjAFIby3v06BH17t2bAFDDhg0pKChIZkaXkkR6ejoZGRmRi4sL01JEwt27d0lbW5tsbW2LzEPt37+fAJCvr6/Q+qtfvz5NnTqVMjIyyN/fn9q0aUMASF9fn2bOnCmTm3FLKu3btydnZ2eRtc+YwQsEArKysqKePXsyJaHCxMXFkaurK3E4HKpduzYFBARI9aSfpLN8+XJSUlKi169fMy1FZNy5c4e0tLSoTZs2RUze09OTVFRUhFafydjYmGxsbEhbW7sgnBgYGCjWnbBYfqGnpyeyDBoiBg3+7NmzBECqqiR++PCBRo8eTYqKimRkZES7du2S2bx9SSExMZE0NTVp0qRJTEsROf/++y9pampSu3btChXgyszMpGbNmlHt2rUrvEVdeno6+fn5ka2tLQEgdXV1mj17Nr18+VJY8lnKyZcvXwgAHTt2TGR9MGbwHTp0oJYtW0pFSCMxMZGmTZtGKioqpKurS2vXrmXzfsXEpEmTSFNTU6zVFpkkMjKSqlSpQn/99Vehui0vX74kLS0t6tevX7m+Mw8fPqTx48eTlpYWAaCuXbuShoYGLV++XBTyWcrB1atXRR6iZsTg79y5I/JfLmGQkpJCixcvpipVqpCGhgYtWrRIprcNkzRevXpFSkpKcmdGN2/eJA0NDbK3ty+03P/06dMEgNatW1fq9WlpaeTr60utWrUiAGRoaEhz584tCHGpqanRhg0bRHkLLGVA1Bk0RAwZvLOzM9WuXZvy8vKY6P6PZGRk0Nq1a0lXV5d4PB5NmzZNbkaQkoSLiwsZGRnJZU2TGzdukLq6OnXs2LHQ/c+YMYMUFBToxo0bRa65f/8+jR07lqpUqUIcDoccHBzo1KlTRQxEQUGBduzYIfJ7YCmdsWPHUsOGDUXah9gN/tWrV8Tlcmnbtm3i7vqP5OTk0K5du8jY2JgUFBRo1KhRIi/8xFI8d+/eJQC0e/dupqUwxrVr10hNTY06d+5cEBLMzc2ldu3akZGREX358oVSU1Np9+7dBesvjIyMaMGCBSVud5mbm0sAaO/eveK8FZZi+Ouvv0SaQUPEgMF7eXmRnp6eRI3K+Hw+BQQEUO3atYnD4ZCrqyvFxcUxLUtuEQgE1KlTJ7KwsJD72vjh4eGkpqZGXbt2LVhB+unTJ9LV1SVjY2NSV1cnLpdLPXr0oKCgoD/+vdLS0ggABQQEiEM+SwkIBALS1dWlf/75R6T9iNXgv337RmpqaiJNCyoPAoGAgoODqVGjRgSAevXqRQ8fPmRaltxz/vx5AkBBQUFMS5EIrl69SqqqqtSlSxfaunUrWVtbE4CCYl/v3r0rc1vfv38nAHT8+HERKmb5E58/fxbLvwMXYmT79u0gIowfP16c3RZLWFgY7Ozs0Lt3b+jq6uLWrVsIDg5G48aNmZYm1/D5fMycORNt27ZFr169mJbDOEQEDQ0NdOjQAZcuXYKXlxcMDQ0REhKCZcuW4fr164iJiSlze1lZWQAAFRUVUUlmKQOxsbEAACsrK5H2IzaDz8zMxJYtW+Dh4QE9PT1xdVuEO3fuoGvXrujYsSPy8vJw8eJFXL16Fba2toxpYvkfAQEBePToEby9vcHhcJiWwxgpKSnYsWMHmjdvjpYtW+LJkydwd3eHsrIyuFwuunbtijlz5qBHjx4YMmQI4uPjy9RudnY2AIDH44lSPssfiImJgZKSEurUqSPajkT6fPAbO3fuJC6Xy9jCipiYGOrXrx8BIEtLSzp58qRU5ODLE5mZmWRqakr9+/dnWgojCAQCioqKohEjRpCamhopKChQnz596OzZswUZZ+fPnycej0d9+vSh7Oxs+v79O5mZmVHLli3LtBL16dOnBICuX78u6tthKYUxY8aIPIOGSEwx+Ly8PKpbty45OTmJo7tCvH79mtzd3YnD4VDNmjVp//79EpueKe+sWbOGFBQU5K5yYXJyMm3dupUaN25MAMjMzIyWLVtW4sYw586dI2VlZerXrx/l5OTQnTt3SFlZmby8vP7Y14MHDwgAW+mUYdq1a0eDBg0SeT9iMfgTJ06I/UP16dMnGjduHCkpKZGhoSFt27aNrbUhwSQlJZGOjg6NGTOGaSliQSAQ0K1bt2j48OGkqqpKCgoK1L9/fzp//nyZBiAhISGkpKREAwYMoJycHNq+fTsBoMOHD5d6XVRUFAFgkwkYRCAQUNWqVWnJkiUi70vkBi8QCKh169b0119/iborIvqVJTBr1ixSVVUlHR0dWrVqlUSlZLIUz4wZM0hdXZ0SEhKYliJSkpKSaPPmzdSwYUMCQLVq1aIVK1ZUaD+E4OBgUlJSooEDB1JOTg65urqSurp6qUvfr127RgDk7ilJkkhISBDpjl2/I3KDv3HjBgGgkJAQkfaTmppKy5YtIy0tLVJXV6f58+cX2SmHRTJ59+4d8Xg8WrhwIdNSRIJAIKCIiAhyd3cnFRUVUlRUJCcnJ7p48WKlq5CePn2aFBUVafDgwZScnEwWFhZkaWlZqI7N71y8eJEA0Js3byrVL0vFuXLlith+ZEVu8L179yYLCwuRldPNzMykjRs3kr6+PikrK9OkSZPo8+fPIumLRTQMGzaMDAwMZGpPXqJfT5MbN24s2L6xdu3atGrVKqF/Pk+cOEEKCgrk6upKjx8/JnV1dXJzcys2iSAkJIQASP0OatLM5s2bSVlZWSyL+ERq8Pkz9sLcrCCf3Nxc8vX1pRo1ahCXy6URI0aUa8EHi2Tw8OFD4nA4tHXrVqalCAWBQEDXr1+nIUOGEI/HIyUlJXJ2dqbLly+LdM+AY8eOkYKCAg0ZMoQOHDhAAGjnzp1ERBQdHU1eXl5k3bw5KSkpEQDi8ZTJunlz8vLyoujoaJHpYinK6NGjqVGjRmLpS6QGP3LkSKpevbpQt/3i8/l09OhRqlevHgEgZ2dnNp4oxTg4OFCdOnWkvq5+YmIirVu3jho0aEAAqE6dOuTt7U1fvnwRm4ajR4+SgoICDRs2jMaOHUtKSkpkY/Nr1auxgT4Nc+xM6yeNpj1zp9D6SaNpmGNnMjbQJwBk36EDW55DTLRt25YGDx4slr5EZvAJCQmkrKxMK1euFEp7AoGAzp49S02bNiUA5ODgQPfu3RNK2yzMkF8POzAwkGkpFUIgEFBYWBi5uLiQsrIyKSsr0+DBg+nq1auMrbE4fPgwcblcatu2LSkqKJCpoQGdWLmAcm6cJUHk+SKvnBtn6cTKBWRubESqqqp06NAhRnTLCwKBgHR0dGjp0qVi6U9kBj937lzS0NAQykTn9evXqW3btgSA2rZtyy7SkAH4fD7Z2NhIzaYvv/P161das2ZNwVNkvXr1aO3atfT161empRHRr42cAdCQ7h0p9erpYo39v6/Uq6dpaPdOxOFw2EJkIiQ/g+bkyZNi6U9RFKtj09LSsGPHDnh6ekJbW7vC7dy7dw/z5s3D+fPn0axZM5w7dw7du3eX6yXsssKxY8dw9+5dhIeHS8W/p0AgQHh4OHx8fHDy5ElwuVw4OTlh9+7daNeuncTcQ1xcHPz8/DCkeyfsWzANXG7ZqpGoq6rAb8E0AMDIkSPRsmVL0S+jl0Py6waJugZNAaL41di4cSMpKChUeNLz6dOnNHDgQAJA9evXp8DAQHZTaxkiOzubzM3NqUePHkxL+SNfvnyh1atXU506dQgAWVhY0IYNG+jbt29MSysW+w4dqLaJUZGR+8K/3QoqUOa/qlXVKXYkb25sRPYdOjB9KzLJpk2bxJZBQySkEbxAICgYKeTl5WHDhg1wcXGBqalpudp59+4dlixZgn379sHY2Bi+vr5wd3eHoqJIHjRYGGLXrl14+/YtgoKCmJZSLAKBAFevXoWPjw9Onz4NLpcLZ2dn+Pn5oU2bNhIzWv8v0dHRCAsPx4mVC6CuWrRapJW5GS5tXlnw/xWKGd2rq6rA22sEnOYsw71799C8eXORapY3YmJi0KBBA7F5WoV6uXfvHvz8/BB56xaexMQgOzsbPB4PDa2soKunh3fv3pXry/vlyxesWLECO3fuhLa2NjZs2IDRo0ezFe9kkJ8/f2LJkiUYNmwYGjZsyLScQnz+/Bn79u3D7t278fr1a1haWmLt2rUYMmQIqlatyrS8P7Jv3z6YVDNAr7atiz2uqKAAQ90/30fvtrYwNtCHn58fa/BCJiYmRnzhGZTT4F++fIlRnp4ICw+HsYE+Ots0gVu74dBUV8PP9Aw8jHuF81F3AABTJk+Gz+7dpcbxfvz4gbVr12Ljxo1QVFTEokWLMHHiRGhoaFTurlgkljVr1iAtLQ1LlixhWgqAX6P1S5cuwcfHB8HBwVBUVMSgQYNw4MAB2NraSuxovTgib91CJ+vGUFRUKPZ43PuPMO7lCp6SElpZNcDyMcNhbly9yHmKigroZN0EUZGRopYsVxARYmNj4eDgILY+y2zwhw4dwsiRI1G9qg5OrFyAXm1bF/tBysvjIyQiCjO2+qJx48bw9fWFi4tLoXPS09OxZcsWrF69GtnZ2Zg0aRJmzJghFaMkloqTkJCA9evXY9KkSTAxMWFUy6dPn+Dn54c9e/bg7du3aNSoETZs2AA3Nzfo6Ogwqq2iPImJgVu74cUea2XVAPsXzkC9Gsb4kpSM5fsOo82oqXhyaBd0tTSLnN+krjmOXt0vYsXyxefPn5GcnCx5I/hDhw5hyJAhGNKtI7bPnFBsfK+gQUUF9OvQBl1bWWOc9xa4ubmBiODq6oqcnBzs3r0by5Ytw/fv3zFq1CjMmzcP1asXHUWwyB6LFy+GiooKZs+ezUj/fD4fFy9ehI+PD0JCQqCsrIzBgwdj1KhRaNWqlVSN1v+LQCBAdnY2NNXVij3uYNui4L8boRZsG1mijpMH9p+7hKkuA4qcr6Whjuzs7ELzayyVIz+DxtLSUmx9/tHg4+LiMHLkSAzp1hF+lUi7+vDhA3bs2IH4+HgMHToUixYtQq1atSqnnkVqePbsGXx9feHt7V2p1NmK8PHjR+zduxd79uxBfHw8mjRpgi1btsDV1RVaWlpi1SIquFwueDwefqZnlOl8dVUVNKpdE3HvPxV7PCUtHTwejzV3IRITEwMej4fatWuLrc8/GvzoUaNgpKuD7TMn/JYpw8di3wM4dCEMn78no7peVQxz7IL5Hi6FPhBcLhfbZ07A9QePMXfOHPTp2xdnz54V6y8Yi2QwZ84cmJiYiG0/Xj6fj/Pnz8PHxwdnzpyBqqoqXFxcMGrUKNjY2Ej1aL0kGlpZ4WHcqzKdm52Tg6dv36Ntk+Inuh/GvUYjCZsEl3byM2gUFIqfIxEFpRp8SWlXqw8GYtepc9i3YBqszM1w92kcRixfDy0NdUwa1LdQG+qqKlg3aRSc5izDvHnzWHOXQ27evInTp0/jwIEDIs+Mev/+Pfbu3QtfX1+8f/8ezZo1w/bt2+Hi4gJNzaKxZlnC1s4OpwKPIi+PX2R+bPrm3ejVthVMDQ3wNfkHlvsdxs/0DAxz7Fyknbw8Pq5EP0Q/50Hiki4XxMbGijX+DvzB4EtKu4p6/BS927VGjzatAAA1qxviyKVwRD97UWw7bNqV/EJEmDlzJpo2bQpXV1eR9JGXl4fQ0FD4+Pjg3LlzUFNTg6urK0aNGgVra2uR9CmJeHh4YOvWrQiJiEK/Dm0KHfuY+A2ui1bh24+f0NfWQuuGDRC5ZwPMqlcr0k5wRCQ+fk2Eh4eHuKTLPESEmJgYODo6irXfUg2+pLSrNk2ssOvUWbyI/4B6piZ4GPcaEQ9jsGHy6OI7YdOu5JagoCDcunULFy5cEHo8Nz4+Hr6+vvD19cXHjx9hY2ODnTt3YvDgwahSpYpQ+5IGmjdvDvsOHTBjqy+6trIu9NR9eOmcMrWRnpmFmVv3wr5DB3YwJkQSEhLw48cPsUcwSjX4ktKuZg11RkpaOiwGe0KBywVfIMCy0cPg0tW+xLbYtCv5Iy8vD3PmzEHnzp3RtWtXobV59uxZ+Pj4IDQ0FBoaGnBzc4OnpydrSAB8du9G48aNMc57S7mSIoBfmTjjvLcgISkZF3bvFqFK+UPsNWj+nxINvrS0q6OXryHgwlUE/DMLVrXM8CDuFaZs3AUjPV0M69Gl2Pby064uXLiAatWqwcDAAHp6elBWVhbe3bAwyn9T6vbu3Ytnz54hICCg0m2/ffsWe/bswd69e5GQkICWLVti9+7dGDRoELsw7jfq1KkDX1/fX+nJAHb8Ia05n/TMLIxZvRmHLoYhICCALTQmZGJiYqCiogJzc3Ox9luiwZeWdjVz6x7MGuqMwV06AAAa1amFd5+/YpX/0RINPiUtHVwOB927dy/0vpaWFvT19cv8UlVVrcTtsgiT0kpW2LRogePHj8PV1bXCI+vc3FyEhITAx8cHFy9eRJUqVTBkyBB4enqiadOmwr0ZGcLFxQVEhOHDhuH6g8dYP2kUere1LXFhYnBEJGZs8cW7z58BQOwmJA/ExsaKPYMG+EOIpqS0q4ys7CKPfgpcLgREJbb1MO41mjZtiuMnTiAxMbHE1+PHjwv+Oy0trUg76urqpf4AGBgYFPr/6urqMpkSxyRlKVkRfOI4vn//jjevX+Ply5flGhG+fv26YLT+5csXtG7dGr6+vnB2doa6uroI70x2MDMzQ25eHtS1q8JpzjIYG+ijk3UTNKlrDi0NdaSkpeNh3GtciX6Ij18T0dHeHv0Gu2D9+vXo2bMnnj59Cj09PaZvQ2YQdw2afEo1+JLSrnq1bYUV+47AtJo+rMzNcP/5K2w4cgoePYuPs/6edlWrVq0yL3DKzMws9ccgMTERL168wM2bN5GYmIiUlJQibaioqJTrCUFLS4v9QSgFYZas+J2cnBwEBwfDx8cHly5dgpaWFtzd3eHp6YlGjRqJ8pZkDj6fj4kTJ8LGxgb//vsvHjx4AD8/P0RFRuLo1f0FT1qNGjZEP+dB8PDwQPPmzQsyPS5evIj+/fsjPDycXegkBPL/rj169BB73xyikofd9+7dg7W1NU6sXFAo7So1PQMLfPxx+votfE36ASN9XQzu0h4LR7hBWUmpSDsnwyPgNGcZoqOjRToRlpOTg2/fvhX7Q/D169ci7yUlJRVpQ0lJCXp6en98Msh/6ejoyM2XoDwlK/JJz8zCOO8tOHjhKg4ePFgkVfLly5fYs2cP/Pz88PXrV7Rp0wajRo2Ck5MT1NSKX3bPUjp79uyBp6cnbt26BVtb2yLHSys/kJKSAktLS3z69AkLFiyQmKJw0szHjx9hYmKC06dPo0+fPmLtu1SDB4CO9vZ4F/cCDw9sL9MX+r+kZ2ahydBxMKtbD1fDwiosVBTk5eXh+/fvf3xKyH99+/YNAoGgUBsKCgrQ1dUt8xOCrq6uVNa3j4uLQ5MmTeDU3q5C2RkeS9fh+LVbePToEUxNTXH69Gn4+PjgypUr0NbWxrBhw+Dp6cnIY6ws8ePHD9StWxcODg7w9/evUBuPHj2CtbU18vLycPHiRXTpUvy8GkvZuHjxIrp164a4uDixT17/0eBfvnyJxo0bC+WLLe0z8wKBAMnJycU+DZT0ysvLK9QGh8OBjo5OqU8Fv78kJdOoo7094l++wAP///3Q7zh5BjtPnsHbhK8AACtzUywY4VaosFU+6ZlZaDx0LASKSsjI+BV6a9euHUaNGoUBAwawk+dCYsqUKdi9ezdevHgBIyOjCrfj5+eHESNGQENDA0+fPmW8+qc0s3HjRsyZMwdpaWlin2T9o8EDwOHDh+Hm5lbuR/Mx3ptx6MKvtKvS4q+yChEhJSWl1B+A//5YZGdnF2mH6Uyj6Oho2NjYFAnVhdyIgoICF3VMfhnJ/nOXsTbgOO7t3wor85pF2skP1bm6umL+/PmwsLAQqk55JzY2Fk2aNMHSpUuFUrFz2LBh8Pf3R+PGjXH37l0oFRN+Zfkznp6eiI6Oxr1798Ted5kMHig8uebtNeKPaVczt/riXcIX1DA1xePHj9lc5TJAREhLSyvz00FiYiLS09OLtKOhoVGuH4Q/ZRpNmDABp48F4vVxvxI3k8hHt6sTvL1G4u/e3Yscy8vjo9aA4ejnPAhbtmwp/x+IpUSICN26dcPr168LqhZWlqysLDRr1gzPnj3D2LFjsX37diEolT/s7Oxgbm6OgwcPir3vMgeDXV1d0bJlS4zy9Cxz2tXGHbvg5uYGZ2fngt1yWEqGw+GgSpUqqFKlSplzkTMyMvDt27dSw0bPnj3DjRs3kJiYiJ8/fxZp40+ZRudDQ0vdKQj4lblx7OoNpGdlw7ZR8SNztmSF6AgODsalS5cQHBwstIJuKioqCA0NhZWVFXbs2IGOHTvCyclJKG3LC/kZNL169WKk/zKP4H8nf4FLVGQkHj95UijtqrWtbUHaFQBcunQJjo6OGD58OHx8fNgURIbJzs4uMdOouLBRcnIyuBwO1k4chcmD+xVp7/HLN7AbNQVZOTnQUFVFwD+z4GjXssT+Nxw+ibm79iMrK0uUtylXZGVlwcrKCnXr1kVoaKjQv2Pnzp1Djx49wOPx8PjxY9StW1eo7csyHz58QI0aNRAUFITevXuLvf8KDambN29eKN2xtLSrLl26YM+ePRg+fDjMzMwwf/78iillEQo8Hg/GxsYwNjYu0/nZ2dlQUVEpcaeg+mYmuL9/O36kpeFEWASGL12H8O3esKxlVuz57E5BwmfDhg2Ij4/H2bNnRTKAcnR0xKxZs7B69Wp069YNMTEx7KR4GYmNjQUg/ho0+QjlG/anL+qwYcOwZMkSLFiwAPv3swXHpAkej1fqTkHKSkqoU8MINhb1sHLcCDSpUwubjp4usT12pyDh8vHjRyxfvhwTJ05EgwYNRNbP8uXLYWdnhzdv3mD48OEi60fWyP8xZGr3OrF9y+bPn4+RI0di5MiRuHTpkri6ZREC5dkpiAjIyc0t8Ti7U5BwmTVrFtTV1bFw4UKR9qOgoICgoCBUrVoVgYGB8PHxEWl/skJMTAwsLCwYG9CIrVcOh4Pt27ejS5cuGDBgAB4+fCiurlkqia2dHS7ffYi8PH6h9+fu8MONB0/wNuEzHr98g3k79yH8/iO4dutYbDv5JStaF7O6kqX83Lx5EwEBAVixYoVY9pbV09NDaGgouFwuxo0bhwcPHoi8T2knJiaG0V3sxPqzoqSkhMDAQNStWxeOjo54//69OLtnqSAeHh74+DURIRFRhd7/kpQM93+80WCQJzpPnI3bMc8QumEZurQsvhwFu1OQ8Pi93ow4/54tW7bEhg0bwOfz0a1bt2LrP7H8gogY2abvdyqURVNZPn/+DFtbW6irqyMiIgLa2trilsBSTmS5ZIU08qd6M6KEiNCvXz8EBQWhU6dOuHTpEpsdVwzv37+HqakpgoODGUuTZCQwZGhoiNDQUHz69An9+vUrdvUmi2Ths3s3EpKSMc57S5F6PH/i952CfNidgirNjx8/MHfuXAwZMkTs5g78CrcGBATA1NQUV65cwcqVK8WuQRpgOoMGYMjgAaBBgwYICgpCZGQkRowYUW7TYBEv+TsFHbxwFR5L1yE9s2x57OmZWfBYug4HL1yFr6+v1NcjkgT++ecfZGRkYPXq1YxpUFdXx6VLl6CsrIx58+bhxo0bjGmRVPIzaGrWrMmYBkZz1dq1a4cDBw7g0KFDmDdvHpNSWMqAi4sLDh48iOPXbqHJ0HE4GR5RZOI1n7w8Pk6GR6DJ0HE4fu2W3NYjEjZPnz7F1q1bMX/+/EoVExMG9erVK1h+37NnT3z9+pVRPZIG0xk0AEMx+P+yfv16TJs2Ddu3b8fYsWOZlsPyB/67o9OfSlbs8vFhR+5CgIjQvXt3vHr1Smj1ZoTB2LFjsXPnTjRv3hy3b98We8VESaV169aoV69ehcs2CwWSAAQCAU2cOJG4XC4FBQUxLYeljERHR5OXlxfZWFuTkpISASAej0c21tbk5eVF0dHRTEuUKYKCggiAxH1HcnNzqXHjxgSApkyZwrQciUAgEFCVKlVo1apVjOqQCIMnIsrLy6P+/fuTqqoq/fvvv0zLYSkngYGBBICSk5OZliKTZGZmkrm5OXXr1o0EAgHTcorw6dMn0tDQIAAUEhLCtBzGiY+Pl4i/hcSsF1dQUMDBgwfRrFkz9OzZE69elW3lJItkkJ/qmpyczKwQGSW/3szGjRslMiWxevXqCAkJAYfDwcCBAxEfH8+0JEaJiYkBwGwGDcDwJOt/UVVVRVBQEHR0dNC9e3ckJiYyLYmljOjo6ABgDV4U5NebmTBhgkjrzVSWDh06YPHixcjKykKnTp2Qk5PDtCTGiImJgZqaGszMii+6Jy4kyuCB/y2H/vnzJ3r37o2MjOKLXLFIFqzBi478ejOLFi1iWsofWbBgAezt7fHy5Uv8/fffTMthDEnIoAEk0OABwNzcHGfOnMGjR4/g5uYGPr/4VDwWySHf4H/8+MGsEBnj1q1bYq03U1k4HA5OnToFAwMDHDx4UG6rx8bExDAengEk1OABoEWLFjh69CiCg4MxefJkEPPZnCylkG8+7AheeOTXm7G2tpaq+j1aWlq4dOkSFBQUMHLkyIIVnfICSUANmnwk1uCBX4sntm/fjq1bt2LdunVMy2EpBQUFBWhpabEGL0T8/PwQHR2NzZs3M/6oX14aN26MnTt3Ii8vD507dy5272BZ5f3790hLS2MNviyMHj0ac+fOxYwZM3D06FGm5bCUgo6ODmvwQuL3ejN2dnZMy6kQI0eOxODBg5GQkAAnJye5eQrPz6BhskxwPhJv8ACwbNkyDBkyBO7u7rh+/TrTclhKQFtbmzV4IbFkyRLG680Ig3379sHc3Bznz5/H+vXrmZYjFiQlgwaQEoPncDjw9fVF27Zt0adPH7mL6UkL7AheODx9+hRbtmzBvHnzGK83U1l4PB7CwsKgoqKCGTNm4M6dO0xLEjn5m3xIQliNeQVlRFlZGSdPnkSNGjXg4OCAT58+MS2J5T+wBl95iAiTJ0+GmZkZpkyZwrQcoWBqaopjx46BiNC1a1eZ/4xIygQrIEUGD/yanT937hz4fD569OiB1NRUpiWx/IaOjg6bJllJQkJCcPHiRaxfvx4qKuXfWEVS6dmzJ6ZMmYIfP36ge/fuMlseXJIyaAApM3gAMDExwblz5/D69WsMHDgQuaVs8MwiXtgRfOXIysrClClT0LVrV8Z2ABIla9euhY2NDW7fvo25c+cyLUckxMfHIy0tTSImWAEpNHjgVwrWyZMnceXKFYwZM0ZuZuclHdbgK4ek15upLFwuF+fPn4eWlhZWr16NixcvMi1J6EhKDZp8pNLgAaBTp07Yu3cv9u7diyVLljAthwX/M3j2B7f8/F5vxsLCgmk5IkNXVxcXLlwAh8NB3759kZCQwLQkoRITEwN1dXWYmpoyLQWAFBs8AAwdOhTLly/H4sWL4efnx7QcuUdHRwd8Ph9paWlMS5E6Zs+eDTU1NSxcuJBpKSKnVatW8Pb2RmZmJuzt7ZGXl8e0JKERGxsrMRk0gJQbPADMmTMHo0aNwqhRo3DhwgWm5cg1bMnginHr1i0cPHgQK1euLPgbyjrTpk1D9+7d8fz5c4wePZppOUJDUmrQ5CP1Bs/hcLBt2zZ069YNTk5OuH//PtOS5Ba2omT5EQgEUllvprJwOBycOHEC1atXx969e3H48GGmJVUagUBQMIKXFKTe4AFAUVERR44cQYMGDdCjRw+8e/eOaUlyCWvw5Uea681UFjU1NYSHh0NRURHDhg2T+k1+4uPjkZ6ezo7gRYGGhgbOnDkDFRUVODg4sCbDAGzJ4PLx48cPzJkzB25ublJbb6ay1KtXD/v27UNubi7at2+PrKwspiVVGEnLoAFkyOABoFq1aggNDcWXL1/Qr18/ZGdnMy1JrmBj8OVDVurNVBY3NzcMGzYMHz9+hLOzM9NyKkxsbCw0NDQkJoMGkDGDB4D69esjODgYUVFRGD58uMyumJNElJSUoKGhwRp8Gfi93oyxsTHTchhnz549qFevHkJCQrBlyxam5VSI/Bo0krSGQeYMHgDatGmDgIAAHD16FLNnz2ZajlzBLnb6M/n1ZkxNTWWm3kxlUVRURHh4OFRVVTF58mSpTJaQtAwaQEYNHgAGDBiADRs2YM2aNdi2bRvTcuQGtmTwn8mvN7NhwwaZqjdTWapXr47g4GAIBAJ06tRJqmpNSWIGDSDDBg8AkyZNwpQpUzBhwgScPn2aaTlyATuCL53s7GxMnTpVZuvNVJbOnTtjzpw5SE5ORvfu3aVmVfS7d++QkZHBjuDFzdq1azFgwAC4uLggKiqKaTkyD2vwpbNhwwa8e/dOZuvNCIPly5ejdevWuHXrFhYtWsS0nDKRv0cFa/Bihsvl4sCBA7CxsUGvXr0QFxfHtCSZhi0ZXDIfP37EsmXLZL7eTGXhcDi4cOECdHR0sHTpUoSFhTEt6Y/ExMSgSpUqqFGjBtNSCiHzBg8AKioqCAoKgq6uLhwcHPD161emJcks7Ai+ZOSp3kxl0dTUxNWrV8HlctGzZ08kJiYyLalUJDGDBpATgweAqlWrIjQ0FGlpaejVqxcyMjKYliSTsAZfPPn1ZlasWCE39WYqS9OmTbFx40ZkZGSgffv2Ep3ynG/wkobcGDwA1KpVC2fOnEFMTAxcXFzA5/OZliRzsCWDi5Jfb6Z58+ZyVW9GGEyYMAG9e/fG06dPMXbsWKblFItAIMDTp08lLv4OyJnBA4CNjQ0CAwNx9uxZTJw4kTUiIaOjo4OcnBxkZmYyLUVi+L3ejIKCAtNypI5jx47B2NgYPj4+OHHiBNNyivD27VuJzKAB5NDgAcDR0RE7duzA9u3bsWbNGqblyBRsuYLCpKSkYO7cuXBzc0ObNm2YliOVKCsrIyIiAkpKSnBxcZG4YoKSmkEDyKnBA4Cnpyfmz5+PWbNmyUSpUkmBrShZmCVLliA9PV3u681Ulpo1a+Lw4cPIzc1F27ZtJWov5vwMGhMTE6alFEFuDR749eVzd3fHsGHDEB4ezrQcmYA1+P/x9OlTbN68ma03IyQGDBiA0aNH48OHDxg0aBDTcgqQ1AwaQM4NnsPhYPfu3Wjfvj369u1bUO6TpeKwJYN/QUSYMmUKW29GyGzfvh2WlpY4deoUdu7cybQcAJJZgyYfuTZ44Fd878SJEzAzM4ODgwM+ffrEtCSphh3B/+LMmTO4cOEC1q9fz9abESJcLhfXr1+Hmpoaxo8fjydPnjCqR5IzaADW4AH8WlRx7tw5EBEcHR3x8+dPpiVJLTweD6qqqnJt8NnZ2ZgyZQq6du2K3r17My1H5tDV1S34vrZv357RjK23b98iMzOTNXhJx9jYGKGhoXj79i2cnJwkahJH2pD3xU5svRnR0759eyxcuBBJSUno1q0bYzokcRen32EN/jcaNmyIU6dOITw8HJ6enmyOfAWR55LBnz59wrJly+Dl5cXWmxExixYtQrt27XDjxg38888/jGiIiYmBpqamxE6iswb/H+zt7bFv3z7s378fixcvZlqOVCLPI/hZs2ZBTU1NaqogSjP5RcmqVq2Kf/75Bzdu3BC7BknOoAEARaYFSCKurq6Ij4/HnDlzYGpqir///ptpSVKFvBp8ZGQkDh48iN27d7P1ZsSEqqoqbty4gcaNG6N79+74+PGjWP/2MTExaN68udj6Ky/sCL4EZs2ahbFjx2L06NEIDQ1lWo5UIY8lg9l6M8xhaWmJbdu2ISMjA23bthVbaJXP50t0Bg3AGnyJcDgcbN68GY6Ojhg4cCDu3bvHtCSpQR5H8Pv27cPdu3fZejMMMXr0aAwYMAAxMTEYP368WPp8+/YtsrKyWIOXVhQVFXH48GFYWlrC0dERb9++ZVqSVCBvBp+SkoI5c+aw9WYY5siRIzA1NcWOHTvEskVnfgaNJJYJzoc1+D+grq6OM2fOQF1dHQ4ODkhKSmJaksQjbwbP1puRDBQVFREZGQllZWUMGjQIHz9+FGl/kp5BA7AGXyYMDAwQGhqKxMRE9O3bF1lZWUxLkmh0dHSQmZmJ7OxspqWInGfPnmHz5s2YO3euRH/R5QUjIyMcO3YMOTk5sLW1FemeD/klCiQ1gwZgDb7M1KtXDyEhIbhz5w6GDRsm0bvLMI28lAwmIkyePBmmpqaYOnUq03JY/p/evXvDy8sL79+/F2lRstjYWImOvwOswZcLW1tbHDp0CMeOHcPMmTOZliOxyEs9GrbejOSyefNmNGrUCCdOnICPj4/Q25eGDBqANfhy069fP2zatAnr1q3D5s2bmZYjkciDwefXm+nSpQtbb0YC4XA4iIiIgIaGBsaNG4enT58Ktf03b94gKytLoidYAXahU4WYMGEC3r17h8mTJ8PExAT9+/dnWpJEIQ8lg/PrzYSEhEh0DFae0dTUxMWLF9GmTRu0bdsWHz9+FNqTlqTXoMmHHcFXEG9vbwwcOBBubm64desW03IkClkfwbP1ZqQHW1tbLFu2TOhFyWJiYqClpQUjIyOhtSkKWIOvIFwuF/v370fLli3Ru3dvvHjxgmlJEoOqqiqUlZVl1uBnz57N1puRIubOnYsOHTrg+vXrWLp0qVDazJ9glfSnN9bgK4GKigpOnToFAwMDODg44OvXr0xLkgg4HI7M5sJHRkbiwIEDWL58OVtvRoo4f/489PT0sGjRIty8ebPS7UnyLk6/wxp8JalatSpCQ0ORkZGBnj17Ij09nWlJEoEslgz+vd7MiBEjmJbDUg54PB4iIiLA5XLRrVu3Sm3qw+fz8ezZM9bg5QUzMzOcPXsWsbGxGDx4MPLy8piWxDiyOIJn681IN/Xr14ePjw/S09PRpk2bChcle/36tVRk0ACswQuN5s2b4/jx4wgNDYWXl5fcbxYiawafX2/G1dWVrTcjxYwYMQKDBg3CkydPMGHChAq1IS0ZNABr8EKle/fu8PHxwa5du7Bq1Sqm5TCKrJUMzq834+3tzbQUlkpy6NAh1KxZE9u2bUNwcHC5r4+NjYW2tjaqV68uAnXChTV4ITNixAgsXLgQc+fORUBAANNyGEOWRvBsvRnZgsvlIjIyEjweDwMHDkRCQkK5rpeGGjT5sAYvAhYvXozhw4fDw8MDV69eZVoOI8iKwbP1ZmQTQ0NDnDx5Ejk5OWjVqlW5aktJSwYNwBq8SOBwOPDx8YG9vT369euHx48fMy1J7MiKwbP1ZmQXR0dHTJ48Ge/fv4ezs3OZrsnPoJGGCVaANXiRoaSkhGPHjsHc3ByOjo748OED05LEio6ODtLS0pCbm8u0lArD1puRfTZs2ICmTZvixIkT2L179x/Pf/XqFbKzs9kRPMuvWhhnz54Fl8tFjx49kJKSwrQksZG/CEiaJ1o3btyIt2/fYuPGjVIRb2WpGBEREahSpQrGjh2LZ8+elXpubGwsAOnIoAFYgxc5RkZGOHfuHN69e4cBAwYgJyeHaUliQdrr0Xz69AlLly6Fl5eX1DyOs1QMdXV1XL58GQKBAG3atCn1O/r48WPo6OjA0NBQjAorDmvwYsDKygqnT5/GjRs3MHLkSLnIkZd2g589ezZUVVWxePFipqWwiIGWLVti1apVSEpKQteuXQvev3fvHiZMmAAba2uoqKhg4cKF+JmSghY2NpgwYQLu3bvHoOo/wyF5cBsJ4ciRI3BxccG8efOwbNkypuWIlPj4eJiZmeH8+fNCreInDqKiomBrawsfHx94enoyLYdFjHTu3BlXrlzB5MmT8fDBA4SFh8PYQB+dbZqgSd3a0FRXw8/0DDyMe4XLdx/i49dE2HfoAJ/du1GnTh2m5ReBNXgx4+3tjVmzZmHXrl0YNWoU03JERmpqKjQ1NXH48GEMHjyYaTllRiAQoFWrVuDz+bhz5w5bkkDOyMvLQ9WqVZGengYzQ0OsnTASvdq2hqJi0c9BXh4fIRFRmLHVFwlJyfD19YWLiwsDqkuG3fBDzMyYMQPx8fEYN24cjI2N0aNHD6YliQQNDQ0oKChIXYgmv95MREQEa+5ySGBgINLS0uDa1R47Z02EumrJqbGKigro16ENurayxjjvLXBzcwMRwdXVVYyKS4cdwTMAn8/HgAEDcOnSJVy7dg02NjZMSxIJ+vr6mDJlCubOncu0lDKRkpKCevXqoXPnznK9ClleiYuLQ5MmTeDU3g5+C6aBy/01Rfnx6zfM3u6L0Mi7yMzOQT1TY+yZOwXWDeoWXCsQCOCxdB2OX7uFR48eSUy4hp1kZQAFBQUcOnQIjRo1Qo8ePfDmzRumJYkEaSsZvHTpUqSlpWH16tVMS2FhgNGjRsFIVwfbZ04oMPfkn6loO3oqlBQVcW79MsQc3oW1EzyhraFe6Foul4vtMyegelUdjJKgeRvW4BlCTU0NISEh0NTUhIODA75//860JKEjTatZnz17hk2bNmHevHkwMTFhWg6LmImOjkZYeDi8x/9dKCyz+uAx1Kimj73zp6GlVX3UrG6ITi2aobZJ0a361FVV4O01AmHh4RKTXcMaPIPo6+sjNDQU379/R58+fZCZmcm0JKEiLQZPRJgyZQpbb0aO2bdvH0yqGaBX29aF3g+5EQXrBvXgPHcZqjkOQnP38dgdFFpiO73b2sLYQB9+fn6illwmWINnmDp16uDMmTO4d+8ehg4dWq6iR5KOtJQMPnv2LM6fP49169ax9WbklMhbt9DJunGRbJnXnxKw89QZ1KlhjPMblmN0P0dMWr8D/ucuF9uOoqICOlk3QVRkpDhk/xHW4CWAVq1a4fDhwzh16hSmTZvGtByhIQ0j+OzsbEyePBmdO3dGnz59mJbDwhBPYmLQpG7tIu8LBITm9epgxVgPNKtfB6P79cDIPt2x89SZEttqUtccj588EaXcMsMavITQp08fbN68GRs3bsTGjRuZliMUpMHg8+vNbNq0ia03I6cIBAJkZ2dDU12tyLHqelVhUcu00HsWNU0R/zmxxPa0NNSRnZ0tEU/jbB68BDF+/HjEx8dj6tSpMDExgZOTE9OSKoWkG3xCQgKWLVvG1puRc7hcLng8Hn6mZxQ51qaRJV7EF64E+yL+I8wMDUpsLyUtHTweryATh0mYV8BSiJUrV2LQoEEYMmQIIiIimJZTKXR0dJCSkgI+n8+0lGKZPXs2VFRU2Hozcszjx48xffp0cAA8jHtV5Pjkwf0Q9eQZVuw7gpfvP+HQhTDsDjqHcU69SmzzYdxrNGrYUISqyw47gpcwuFwu9u3bh4SEBPTp0we3bt1C/fr1mZZVIfJLBqekpKBq1arMivkPUVFR8Pf3h4+PT4FOFvngy5cvOHToEPz9/fHgwQPo6emhXv36uHTnAfLy+IUmWltY1sfJVQsxd4cflvoFoFZ1Q2yYPAZu3ToW23ZeHh9Xoh+in/Mgcd1OqbArWSWUHz9+oE2bNsjIyEBkZKTUlCf9nStXrqBz5854+fIlatcuOoHFFAKBAK1bt0ZeXh5bb0ZOyMzMRHBwMPz9/XHhwgUoKCigV69ecHd3R/fu3fHkyRNYW1vjxMoF6NehTYX7ORkeAac5yxAdHY3mzZsL8Q4qBhuikVC0tbURGhqK7Oxs9OzZE2lpaUxLKjeSWjJ4//79uHPnDjZv3syauwxDRIiIiMCoUaNQvXp1DB48GMnJydi6dSsSEhJw/Phx9O7dG8rKymjevDnsO3TAjK2+SM/MqlB/6ZlZmLl1L+w7dJAIcwdYg5doTE1Nce7cOTx//hyDBg1CXl4e05LKRb7BS1IufEpKCmbPng1XV1e0bduWaTksIuDVq1dYvHgxateujXbt2uHixYuYMGECXrx4gVu3bmHMmDHFhgx9du9GQlIyxnlvKXcGjEAgwDjvLUhISoZPGbb+ExdsDF7Cyd8vskePHhg3bhx27dolNel8kjiCZ+vNyCY/fvxAYGAg/P39cfPmTVSpUgUDBw6En58f2rVrV6aMljp16sDX1xdubm4AgO0zJ5RaTTKf9MwsjPPegoMXriIgIEBiCo0BrMFLBV27dsXu3bvh4eEBMzMzzJs3j2lJZUJTUxMcDkdiDD6/3szixYvZejMyQG5uLi5evAh/f38EBQUhNzcXXbt2xaFDh9CnTx+oqRXNa/8TLi4uICKMHDkSNx8/hbfXCPRua1tiPfjgiEjM3LoXCUnJCAgIYOvBs1SM4cOHIz4+HvPnz0eNGjXg7u7OtKQ/wuVyJaaiZH69mRo1asjUamF5g4jw4MED+Pv749ChQ/j69SsaNmyIZcuWwdXVFUZGRYuAlRdXV1e0bNkSozw94TRnGYwN9NHJugma1DWHloY6UtLS8TDuNa5E/9rRqaO9PS74+EjUyL0AYpEaBAIB/f3336SoqEiXLl1iWk6ZqFWrFs2aNYtpGRQSEkIA6NSpU0xLYakAHz9+pDVr1lDDhg0JABkYGNCUKVPo/v37JBAIRNZvdHQ0eXl5kY21NfF4PAJAPB6PbKytycvLi6Kjo0XWtzBg0ySljNzcXPTu3Rs3b95EREQEGjduzLSkUrG2toaNjQ127drFmIbs7Gw0bNgQNWvWxMWLF6VmDkPeycjIwOnTp+Hv749Lly5BSUkJffv2hbu7O7p27QpFRfEHIAQCgUSsUC0rbIhGylBSUkJgYCDat28PR0dHREZGokaNGkzLKhFJKFewceNGvHnzBkFBQay5SzgCgQDXr1+Hv78/jh8/jtTUVLRt2xY7d+7EwIEDGV+UJk3mDrALnaSWhIQE2NraokqVKrhx4wbjH/ySGDhwIFJSUnDx4kVG+k9ISEC9evXw999/y0wRN1nkxYsX8Pf3x4EDBxAfHw9zc3O4u7tjyJAhErVITtpgR/BSSvXq1REaGgo7Ozv0798f58+fh7KyMtOyiqCjo4O3b98y1j9bb0ZySUpKwtGjR+Hv74+oqChoaWnB2dkZ7u7uaNOmDfu0JQRYg5diLCwsEBwcjM6dO2PEiBE4cOCAxH0pmAzR5Neb2bVrl8Q+4cgbOTk5CA0Nhb+/P86cOQM+n4/u3bvj6NGj6NWrF1RVVZmWKFOwBi/ltGvXDv7+/hg8eDBMTU2xYsUKpiUVgimDFwgEmDhxIpo1a4a///5b7P2z/A8iQnR0NPz9/XH48GF8+/YNzZo1w+rVq+Hi4oJq1aoxLVFmYQ1eBhg0aBA+fPiA6dOnw9TUFGPGjGFaUgH52/aJO/sgv97MjRs32HozDPHhwwccPHgQ/v7+ePr0KQwNDTF8+HC4u7ujUaNGTMuTC1iDlxGmTp2Kd+/eYfz48TA2NkavXiXXqxYn2traEAgESE1NhZaWllj6TElJwZw5c+Di4sLWmxEzaWlpOHXqFPz9/XHlyhWoqKigX79+2LBhAzp16sRIaqM8w/61ZQQOh4MNGzbgw4cPGDx4MMLCwtCyZUumZRWqRyMug1+6dClSU1Ph7e0tlv7kHT6fj/DwcPj7++PEiRNIT09H+/bt4evriwEDBkBTU5NpiXKLdCV1spSKgoICAgIC0KRJE/Ts2ROvXhXdoUbciLvg2PPnz7Fp0ybMnTuXrTcjYp4+fYo5c+agZs2a6Ny5MyIjIzF79my8efMG4eHh8PDwYM2dYdg8eBnk27dvsLOzAwDcunULenp6jGl5+fIl6tati6tXr8Le3l6kfRERHB0d8fz5c8TGxkJF5c+VAFnKx7dv33DkyBHs378fd+/ehY6ODgYPHgx3d3e0atVK4rK45B02RCOD6OnpITQ0FLa2tujduzeuXLnCWPqZOEfwZ8+exfnz53Hy5EnW3IVIdnY2zp49C39/f5w9exYA4OjoWFDGmsfjMayQpSTYEbwMc/v2bXTo0AHdu3fHsWPHGMkm4fP5UFRUxJ49e0SarsjWmxEuRITbt29j//79OHLkCJKTk2FjYwN3d3cMHjwY+vr6TEtkKQPsCF6GadmyJY4ePYq+ffti6tSp2Lhxo9iNT0FBAZqamiIfwW/atImtNyME3r17V5Da+OLFCxgbG2P06NEYOnQoLC0tmZbHUk5Yg5dxevXqhW3btmHs2LEwMzPD1KlTxa5B1DXhExISsHTpUowfP541oQrw8+dPnDhxAv7+/ggPD4e6ujoGDBiA7du3o0OHDuw6AimGNXg5YMyYMXj37h2mTZsGExMTODs7i7V/Ua9mZevNlB8+n48rV65g//79OHXqFLKystCxY0fs378f/fv3h4aGBtMSWYQAa/BywvLly/H+/XsMHToUhoaG+Ouvv8TWtygN/t9//y2oN5M/octSMk+ePIG/vz8OHjyIhIQENGjQAAsXLoSbm5tEl51mqRjsJKsckZOTg+7du+P+/fu4desWLCwsxNJv//79kZmZidDQUKG2KxAI0Lp1a+Tl5eHOnTtsKKEEvn79ikOHDsHf3x/379+Hrq4uXFxc4O7uDhsbG3bOQoZhR/ByhLKyMk6ePIm2bdvCwcEBkZGRqF69usj71dHRwadPn4TeLltvpmSysrIQEhICf39/hIaGgsvlolevXli0aBEcHBwksrQ0i/BhV7LKGdra2ggNDUVubi569uyJ1NRUkfcpihDNz58/2Xoz/4GIcPPmTYwePRqGhoZwdnbGt2/fsGXLFiQkJODEiRPo06cPa+5yBDuCl0Nq1KiB0NBQtG3bFs7OzggODoaSkpLI+hOFwbP1Zv7H69evC1IbX716BVNTU3h5ecHd3R316tVjWh4Lg7AGL6c0btwYJ0+ehIODA8aOHYvdu3eLLBabb/BEJJQ+nj9/jo0bN2LRokVyW28mJSUFx44dg7+/P27cuAENDQ0MHDgQe/bswV9//SV1e4eyiAbW4OWYzp07w9fXF8OGDYOZmRkWLFggkn60tbWRl5eH9PR0oaTfTZkyBTVq1MD06dOFoE56yMvLw8WLF+Hv74+goCDk5OSgc+fOCAgIQN++faGmpsa0RBYJgzV4Ocfd3R3x8fFYsGABatSogeHDhwu9j9/r0VTW4M+ePYvQ0FC5qjfz8OFD+Pv7IyAgAF++fIGVlRWWLFkCV1dXGBsbMy2PRYJhDZ4F8+bNQ3x8PDw9PWFkZISuXbsKtf3fDb4yudbZ2dmYMmUKOnXqhL59+wpJnWSSkJBQkNr46NEj6Ovrw83NDe7u7mjatCmb2shSJliDZwGHw8H27dvx8eNHDBgwADdu3EDTpk2F1n6+wf/48aNS7WzatAmvX7/GqVOnZNLgMjMzERQUhP379+PixYtQUlJC7969sWLFCnTt2lWkE+Essgk7E8MCAFBUVMTRo0dRv359ODo6Ij4+XmhtC6Nk8O/1ZqysrIQljXEEAgGuX7+OkSNHwtDQEC4uLkhNTcWOHTuQkJCAwMBA9OjRgzV3lgrBrmRlKcTnz59ha2sLNTU1RERECGX5f25uLpSVleHn51fhGP/w4cNx5swZxMXFyURJgri4OBw4cAAHDhzA27dvUatWLbi7u2PIkCGoU6cO0/JYZAQ2RMNSCENDQ4SGhsLOzg79+vXDhQsXKr2hg5KSEtTV1Ss8gv/333+xf/9+qa83k5ycjKNHj8Lf3x+RkZHQ1NSEs7Mz3N3d0bZtW5kMO7EwCxuiYSlCgwYNEBwcjKioKHh4eEAgEFS6zYqWDBYIBJgwYQKaNWsm0g1DREVubi5CQkIwcOBAGBoawsvLCzo6Ojhy5Ag+f/6M3bt3o127dqy5s4gEdgTPUixt27bFwYMH4ezsDFNTU6xatapS7VV0Nau/vz/u3LmD69evS029GSLCvXv34O/vj8OHDyMxMRFNmzbFqlWr4OLiAkNDQ6YlssgJrMGzlIiTkxPWrVuHqVOnokaNGhg/fnyF26qIwf/8+ROzZ8/G4MGD0a5duwr3LS4+fvyIgIAA+Pv7IyYmBoaGhnB3d4e7uzsaN27MtDwWOYQ1eJZSmTJlCuLj4zFx4kSYmJigT58+FWpHR0en3GmS0lBvJj09HadOnYK/vz8uX74MHo+Hfv36Ye3atejcuTMUFdmvGAtzsJ8+lj+ybt06vH//Hi4uLggLC0OrVq3K3YaOjg7i4uLKfP7z58+xadMmLFy4UOI2ohAIBAgPD4e/vz+OHz+O9PR0/PXXX9i9ezecnJygpaXFtEQWFgBsmiRLGcnMzETnzp3x4sULREZGljuVb8qUKbhw4QJiY2PLdL6joyOePn2K2NhYqKqqVkSy0Hn27FlBauP79+9Rp06dgtTGWrVqMS2PhaUI7AiepUyoqqoiODgYdnZ2cHBwwK1bt6Cvr1/m68sTg/+93gzT5v79+3ccOXIE/v7+uH37NrS1tTF48GC4u7ujdevWbPYLi0TDjuBZysWbN2/QunVr1KpVC1evXi1zBcMtW7ZgxowZyMrKKvW8nJwcNGzYEKamprh06RIjBpqTk4Nz585h//79OHv2LIgIDg4OGDZsGHr06CE3Rc5YpB82D56lXNSqVQtnz57F48eP4erqCj6fX6brtLW1kZ2djczMzFLPy683s2nTJrGaOxHh9u3b8PLyQvXq1dGvXz+8f/8ea9euxcePHxEcHIwBAwaw5s4iVbAhGpZyY2Njg8DAQPTu3RuTJk3Cli1b/mjGv9ejKSnskpCQgCVLloi13kx8fHzBbkjPnz+HkZERPD09MXToUJmqecMin7AGz1IhevTogR07dmD06NEwMzPDjBkzSj3/d4M3MjIq9pw5c+aAx+Nh8eLFwpZbiNTUVJw8eRL+/v4ICwuDqqoq+vfvjy1btqBjx45Ss6CKheVPsAbPUmFGjRqF+Ph4zJw5EzVq1MDgwYNLPPdPJYPz683s3LlTJPVm+Hw+rl69Cn9/f5w8eRKZmZmwt7eHn58f+vfvjypVqgi9TxYWpmEnWVkqBRFh2LBhOHr0KC5evIj27dsXe15CQgKMjIwQEhKCnj17FjomEAjQunVr5Obm4u7du0IdQcfExMDf3x8HDx7Ep0+fUL9+fQwbNgxubm4wNTUVWj8sLJIIO4JnqRQcDgd79uzBp0+f0LdvX9y8eROWlpZFzssflX///r3IMWHXm0lMTMThw4fh7++P6OhoVK1aFS4uLnB3d0eLFi3Y1EYWuYEdwbMIhZSUFLRr1w4pKSmIjIwsiLPfu3cPfn5+iLx1C/fv34eACDweDw2trGBrZ4eBAwfC2dkZ9vb2OHz4cIX7z8rKwpkzZ+Dv74/Q0FBwOBz07NkT7u7ucHR0hLKysrBulYVFamANnkVofPjwAa1bt4a+vj78/PwwdcoUhIWHw9hAH51tmqBJ3drQVFfDz/QMPIx7hct3H+Lj10QoKSriytWr5S4oRkSIioqCv78/jhw5gh8/fqBVq1Zwd3fHoEGD8H/t3VFMW1UcBvAvXZO6lLgoOuIQjbM1hHVrKC5QxGEZLlnilpHUGCBtvZP5AMQXEs0epg8s0aAkZJhF21RJHTyhJNvTEgYbIZSZNaO0S7S3jLhkUpkBa+jodd3Fh2UkWnFFTjG03+/13nv6Pw/9enJ6zj2FhYVZ6inR1sCAJ6FCoRAqKytx794feK6oCJ+2v4MjNVXQatOnXlKp+7gwPomOMx788lscXq8XjY2Nj/yM2dnZ1aWN0WgUJSUlcDgccDgcKC0tzUa3iLYkzsGTUKFQCMlkEk2HbPjig/eg3772xiCtdhsaXnsFhyor0NrVi+bmZqysrKCpqSnt3ng8jsHBQfh8PoyNjaGgoAB2ux1utxu1tbXQaLhnj+jvOIInYWRZhtlshr22Gl+f6lhX6KqqCqmzG4NXJjA9PQ2DwYBUKoXh4WH4fD4MDQ1BURTU19fD6XSioaEBer0+i70h2voY8CRMnc2GW9EIpnxn/zJyH7sewmf9gwj8KGPu1wV898mHOFZbnfZ8YjkJs6MVT+0qxqsHDqC/vx+xWAxlZWWrSxuLi4s3s0tEWxqnaEiIQCCA0cuX8e3Hp9KmZRLJJPYZX8Dbb7wO+8nTa7ah3/4YutqPw37yNCKyDJfLBafTifLyci5tJPoPGPAkRF9fH54t2okjNVVp1w5b9+OwdX9G7RytsWLX04U49uZb6OnpEVwlUX7hP1MkhH9iAgcr9v3japn10Gq3of7lcnx/9aqgyojyFwOehAjfuAGz8UUhbZmNuxEKh4W0RZTPGPC0YaqqQlEUPK7P7PCPR9lRoIeiKFBVVUh7RPmKAU8bptFooNPp8HvirpD24ksJ6HQ6rm0n2iB+g0gI0549CMozQtoKyjex12QS0hZRPmPAkxDW6moMXwsilUo/wm/p7jKmIjOYijz4AZj9OYapyAxuxebT7k2l7uNSIIgqqzXrNRPlOgY8CSFJEm7P38GF8cm0a9d+iMDiaoPF1QYA6DjjhsXVho88vrR7z4/7cXv+DiRJynrNRLmOO1lJmDqbDT/JEQS/Ofuv76BZy8OdrM8bX8LI6GgWKiTKLxzBkzBujwdzC4to7epd9woYVVXR2tWLuYVFuD2eLFVIlF8Y8CSMwWCA1+vFuYsjkDq7kVhOZvRcYjkJqbMb5y6OwOv1wmAwZLlSovzAKRoSbmBgAC0tLXjmySfQ1X4cR2usa74P/vy4H+9//hXmFhYzfh88EWWGAU9ZEY1G8e6JE6snOh2sMMNs3I0dBXrElxIIyjdxKfDgRKc6mw1fut0cuRMJxoCnrHp4Juuk349QOAxFUaDT6bDXZEKV1QpJkmCxWP7vMolyEgOeNpWqqtyhSrRJGPBERDmKQykiohzFgCciylEMeCKiHMWAJyLKUX8CXSTwDHu5P1AAAAAASUVORK5CYII=",
      "text/plain": [
       "Graphics object consisting of 28 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 2)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(6, 2)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g=graphs.CompleteGraph(3)\n",
    "g2=graphs.CompleteGraph(3)\n",
    "g2.relabel([3,4,5])\n",
    "h=g.cartesian_product(g2)\n",
    "h.relabel()\n",
    "show(h)\n",
    "hc=h.complement()\n",
    "show(hc)\n",
    "print(thpdx(h))\n",
    "thpdx(hc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "98970866-a72b-4f01-b7c0-762ba1e96722",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h.is_isomorphic(hc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "795f78f7-e6cd-4944-bae5-971f46981d9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Remark 4.11: Test for grapha having (gamms(G)+1)(gamma(G^c)+1)> 2n\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "c9764804-ec20-4b2e-99f9-1e2214a62d22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 7 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 8 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 9 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "10\n",
      "11\n"
     ]
    }
   ],
   "source": [
    "# Number of vertices:\n",
    "nn=4\n",
    "k=0\n",
    "for g in graphs(nn):\n",
    "    gc=g.complement()\n",
    "    domg=dom(g)\n",
    "    domgc=dom(gc)\n",
    "    thyg=min(domg+1,nn)\n",
    "    thygc=min(domgc+1,nn)\n",
    "    k=k+1\n",
    "    print(k)\n",
    "    if thyg*thygc>2*nn:\n",
    "        show(g)\n",
    "        print(thyg, thygc)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "adacba91-a07a-44ff-89a0-d1e642c4c483",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 10.3",
   "language": "sage",
   "name": "sagemath-10.3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}