memory_neighbors.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "17df5f1b",
   "metadata": {},
   "source": [
    "Playing with my son memory, I noted, that there is usually somewhere a directly neighboring pair in the tile area. (Directly neighboring is defined as neighboring on a edge, not just over a corner. )\n",
    "\n",
    "Why are there those pair? Is it just because of not perfect mixing? Or is it normal? As a scientist I know that no repetation at all is often unlikely and that small patterns can appear by chance. In contrast, my wife thought that there should be usually no neighbors. \n",
    "\n",
    "To solve that I use now python for calclulations, first I import the libraries. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e13c9104",
   "metadata": {},
   "outputs": [],
   "source": [
    "#importing the necessary libraries\n",
    "import numpy as np\n",
    "import logging\n",
    "import time\n",
    "import calendar\n",
    "import itertools\n",
    "import math\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.pyplot import figure\n",
    "import matplotlib.cm as cm\n",
    "%matplotlib inline\n",
    "\n",
    "import seaborn as sns\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10337ea9",
   "metadata": {},
   "source": [
    "Now let's define the needed functions. \n",
    "\n",
    "First a function which creates a ordered memory sequence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4c942ca5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#creates ordered numbers array\n",
    "def ord_memory(n_pair):\n",
    "    lis=[]\n",
    "    for i in range(n_pair):\n",
    "        lis.append(i)\n",
    "        lis.append(i)\n",
    "        arr=np.asarray(lis)\n",
    "    return(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73def5b7",
   "metadata": {},
   "source": [
    "Then a function which creates a random sequence of x memory pairs (which are here just numbers)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "159208a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_1d(n_pair):\n",
    "    #this shuffle function is used\n",
    "    d = np.random.default_rng()\n",
    "    #the previos function is used as inout\n",
    "    arr=ord_memory(n_pair)\n",
    "    #shuffle\n",
    "    d.shuffle(arr)   \n",
    "    return(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ecfe098",
   "metadata": {},
   "source": [
    "Then a function which for x memory pairs calculate the most compact (Most similar to a square) rectangle. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fb5016e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#This function gets the most compact rectangle for a number of pairs\n",
    "def fac(n_pair):\n",
    "    #factors to output\n",
    "    xar=np.zeros(2,dtype=int)\n",
    "    #run until square root reached\n",
    "    for i in range(int(np.sqrt(2*n_pair))):\n",
    "        #execute if no rest in division, if yes pair  overwritten with more similar ones if possible\n",
    "        if 2*n_pair/(i+1)%1==0:\n",
    "            xar[0]=1+i\n",
    "            xar[1]=2*n_pair/xar[0]\n",
    "    return xar        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17957640",
   "metadata": {},
   "source": [
    "The number of pairs in the memory game of my son is 12. Now the created functions are applied, to create a memory tiling. Then it is visualized in the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fc514035",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f8928360f10>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_pair=12\n",
    "xar=fac(n_pair)\n",
    "shuf=random_1d(n_pair)\n",
    "reord=shuf.reshape(xar[0], xar[1])\n",
    "plt.axis('off')\n",
    "plt.imshow(reord,cmap=cm.jet, interpolation='nearest')\n",
    "#add pictures of real memory at some point"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e71cafa9",
   "metadata": {},
   "source": [
    "Since some neighbors have the same colors, there are neighbors as many random draws but not in all."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da0a7556",
   "metadata": {},
   "source": [
    "The most straight forward way is to just count the possible pairs.  That I do below for the smallest possible memory of two pairs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f6b806c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f88aac801c0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mem2a=[[2,2],[1,1]]\n",
    "mem2b=[[2,1],[2,1]]\n",
    "mem2c=[[1,2],[2,1]]\n",
    "mem2d=[[2,1],[1,2]]\n",
    "mem2e=[[1,2],[1,2]]\n",
    "mem2f=[[1,1],[2,2]]\n",
    "com=np.zeros((8,5))\n",
    "com[0:2,0:2]=mem2a\n",
    "com[3:5,0:2]=mem2b\n",
    "com[6:8,0:2]=mem2c\n",
    "com[0:2,3:5]=mem2d\n",
    "com[3:5,3:5]=mem2e\n",
    "com[6:8,3:5]=mem2f\n",
    "plt.axis('off')\n",
    "plt.title(\"6 options for two pairs\")\n",
    "plt.imshow(1-com.T,cmap=cm.gray, interpolation='nearest')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19877887",
   "metadata": {},
   "source": [
    "There are six possibilities. 4 of 6 have neighboring pairs, only 2 of 6, a third has not. \n",
    "\n",
    "The number of total options follows from the following consideration:\n",
    "4 options can draw for the first location. Multiplied on that are then three options for the second location and then two to for the third while only one option remains for the last location. (This operation of multiplying a number by all number equal or smaller than itself is the factorial of a number.) That results into 24 options, as true for 4 different option. However, because in this case we have two identical pairs, they are equavalent and thus the result is divided twice by 2. (Mathematical that is 2 to to the power of 2.)\n",
    "\n",
    "As equation it is: N!/(2)^(N/2) for draw options, which for a number of pairs is:  (2*P)!/2^P\n",
    "\n",
    "For two pairs it is: (4 *3 *2)/2^2=24/4=6\n",
    "\n",
    "That means already for 3 pairs, it are much more: 6 *5 *4 *3 *2/2^3=90 possibilities.\n",
    "\n",
    "Thus  already for three pairs there are a lot of posisbilities. While that still can be counted by a man, it is proon to errors\n",
    "and thus we construct a program. \n",
    "\n",
    "First, a helper function which converts to tuples to list. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3a4caf7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#convert tuple of tuple to list of list \n",
    "def tuple_to_list(t):\n",
    "    return [list(x) for x in t]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4eaca377",
   "metadata": {},
   "source": [
    "Then a function which selects from all permutations the unique one. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b325273d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#not ideal from memory usuage since first are created, also not fast \n",
    "#for 4 , 5 seconds \n",
    "#5 are 3628800 in total uniques are   takes hours at least \n",
    "#get unique permutations for a number of memory pairs\n",
    "def uniqper(pairs):\n",
    "    start_time=time.time()\n",
    "    #create two vectors of length\n",
    "    arra = np.arange(pairs)\n",
    "    arrb = np.arange(pairs)\n",
    "    #combine them\n",
    "    arr=np.concatenate((arra,arrb))\n",
    "    #convert to list\n",
    "    lista=arr\n",
    "\n",
    "    #get permutaations\n",
    "    a=list(itertools.permutations(lista))\n",
    "    #convert to list\n",
    "    lista=tuple_to_list(a)\n",
    "    #fill first element which is never a duplication\n",
    "    listb=[lista[0]]\n",
    "    c=1\n",
    "    print(f\"all permutations are {len(lista)}\")\n",
    "    for i in range(1,len(lista)):\n",
    "        x=0\n",
    "        j=0\n",
    "        #check for equality in while loop should make it faster\n",
    "        while x==0 and j<len(listb):\n",
    "            if lista[i]==listb[j]:\n",
    "                x=1\n",
    "            j+=1    \n",
    "        if x==0:\n",
    "            listb.append(lista[i])\n",
    "            c+=1\n",
    "    print(f\"unique permutations are {c}\") \n",
    "    bar=np.array(listb) \n",
    "    stop_time=time.time()\n",
    "    print(f\"run time is {stop_time-start_time} s\")\n",
    "    return bar"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06c60e5c",
   "metadata": {},
   "source": [
    "We now run the program to get the permutations of 3 pairs and siaplay then the options. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8beede6b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "all permutations are 720\n",
      "unique permutations are 90\n",
      "run time is 0.006837368011474609 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f88aac50f70>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_pair=3\n",
    "res=uniqper(n_pair)\n",
    "xar=fac(n_pair)\n",
    "mem=np.zeros((44,25))\n",
    "for i in range(15):\n",
    "    for j in range(6):\n",
    "        res2=res[j+i*6]\n",
    "        reord=res2.reshape(xar[0], xar[1])+1\n",
    "        mem[i*3:2+3*i,4*j:3+4*j]=reord\n",
    "plt.axis('off')\n",
    "plt.title(\"90 options for three pairs\")\n",
    "plt.imshow(1-mem.T,cmap=cm.gray, interpolation='nearest')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28634930",
   "metadata": {},
   "source": [
    "As visible the number of permutations is too latrge that man cxan reliable count the fraction. \n",
    "\n",
    "Therefore another function is constructed which determines whether a tile was neighboring pair. \n",
    "It does not ensure that there are only unique pairs in it. The problem isnthat ensuring that needs\n",
    "more time than checking for neighbors while it does not change the result since duplicates just increase the number of all patterns with the same factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "35c830b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#function which determine whether there is no\n",
    "#neighboring pair in a tiling (identical numbers neighbors in a numpy array) \n",
    "#input is a 2D array\n",
    "def check_nopairs_tiling(array):\n",
    "    #bollean paramter for existance of no neighboring pairs\n",
    "    c=False\n",
    "    #dimnsion of array\n",
    "    axis1=array.shape[0]\n",
    "    axis2=array.shape[1]\n",
    "    #number od pairs\n",
    "    n_pair=int(axis1*axis2/2)\n",
    "    #for more than 2 pairs\n",
    "    #subtract by one shifted in both axis\n",
    "    if n_pair>2:\n",
    "        x1=np.min(abs(array[0:axis1-1,:]-array[1:axis1,:]))\n",
    "        #create dummy only changed if second operation needed\n",
    "        x2=0\n",
    "        #only done if no macth in first part\n",
    "        if x1>0:\n",
    "            x2=np.min(abs(array[:,0:axis2-1]-array[:,1:axis2]))\n",
    "        #enarge counter by one if no match \n",
    "            if x1>0 and x2>0:\n",
    "                c=True\n",
    "    if n_pair==2:\n",
    "            #special case for two pairs\n",
    "            if array[0,0]!=array[0,1] and array[0,0]!=array[1,0]:\n",
    "                c=True\n",
    "    #return whether there are no no neighboring pairs                                               \n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "a4d64198",
   "metadata": {},
   "outputs": [],
   "source": [
    "#function to determine fraction of no neighboring tilings among all tilings\n",
    "def prob_all_perm(n_pair):\n",
    "    print(str(n_pair)+\" pairs\")\n",
    "    #time for knowing run_time\n",
    "    start_time=time.time()\n",
    "    list_pairs=ord_memory(n_pair)\n",
    "    #permute list\n",
    "    perm_object=list(itertools.permutations(list_pairs))\n",
    "    #convert permutation object to list\n",
    "    list_permutations=tuple_to_list(perm_object)\n",
    "    #convert to array, each row is one to be tested case\n",
    "    arr=np.array(list_permutations)\n",
    "    #dimensions of reordering to tile\n",
    "    dim=fac(n_pair)\n",
    "    print(f\"number of permutations {arr.shape[0]}\")\n",
    "    #number of cases with no neighbors\n",
    "    no_neighbor=0\n",
    "    for i in range(arr.shape[0]):\n",
    "        #reorder to tile\n",
    "        array=arr[i].reshape(dim[0], dim[1])\n",
    "        #function to determing whether there are no neighboring pairs\n",
    "        c=check_nopairs_tiling(array)\n",
    "        no_neighbor+=c\n",
    "    stop_time=time.time()\n",
    "    print(f\"run time is {round(stop_time-start_time,4)} sec\")\n",
    "    print(f\"no neighbor in tile to {round(no_neighbor/arr.shape[0]*100,2)} % \")  \n",
    "    return no_neighbor/arr.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2cd7df47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 pairs\n",
      "number of permutations 24\n",
      "run time is 0.0002 sec\n",
      "no neighbor in tile to 33.33 % \n",
      "3 pairs\n",
      "number of permutations 720\n",
      "run time is 0.0177 sec\n",
      "no neighbor in tile to 13.33 % \n",
      "4 pairs\n",
      "number of permutations 40320\n",
      "run time is 0.559 sec\n",
      "no neighbor in tile to 20.0 % \n",
      "5 pairs\n",
      "number of permutations 3628800\n",
      "run time is 47.7704 sec\n",
      "no neighbor in tile to 19.68 % \n"
     ]
    }
   ],
   "source": [
    "res=np.zeros((2,4))\n",
    "for i in range(res.shape[1]):\n",
    "    npair=2+i\n",
    "    res[0,i]=npair\n",
    "    res[1,i]=prob_all_perm(npair)\n",
    "np.savetxt(\"probabilities_all_permutations.txt\", res) \n",
    "#6 pairs fails because of storage problem, would also take long "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1c3032f",
   "metadata": {},
   "source": [
    "It is visisble in the printed numbers that clearly less 50% have no pairs in a tiling. While there is a lot variation between 2 and 4 pairs, the fraction is then more stable, but 2 is a too small range to be certain about a trend. \n",
    "\n",
    "Already 5 pairs takes long to run on a laptop and 6 does not work. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "69dbaad3",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_perm_prob=np.loadtxt(\"probabilities_all_permutations.txt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15a7b9f5",
   "metadata": {},
   "source": [
    "As shown even with a laptop it is not possible to test also options to get the probablities.\n",
    "\n",
    "Therefor, I use in the following two approximations to get probabilities. \n",
    "\n",
    "The first calculates it from the number of pairs and how the are tiled. It assumes that each pairs is independent of each other. It determines first the number of corner, edge and inner tile because the number of neighbors depends on that. The number of neighbors need to me divided by two since otherwise each neighborship is counted twice.  \n",
    "By this number is then the probability of single tile taken to the power.\n",
    "The probablity is how likely it is that for a single neighbordhio they are not a pair. Just one of the 2*pairs is a problem, given that one of the N is already excluyded it is the tile considered, the probability is (2 * N-2)/(2*N-1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d5ed09b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#analytic probability\n",
    "def ana_prob(n_pair):\n",
    "    #dimeniosn of the tile\n",
    "    xar=fac(n_pair)\n",
    "    #number of corner\n",
    "    corn_num=4\n",
    "    #inner tile\n",
    "    inner_num=(xar[0]-2)*(xar[1]-2)\n",
    "    #rest is number of edge \n",
    "    edge_num=xar[0]*xar[1]-inner_num-corn_num\n",
    "    #get number of neighbors, divide by two since it work both ways \n",
    "    n_neigh=(inner_num*4+edge_num*3+corn_num*2)/2\n",
    "    #excluding the current one there 2_n-1 in the denominator, in the numertator it is 1 less more\n",
    "    prob=((2*n_pair-2)/(2*n_pair-1))**(n_neigh)\n",
    "    return xar[0],  xar[1], prob        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23688b99",
   "metadata": {},
   "source": [
    "We calculate that for up to 12 pairs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2ac09b7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "nn=int(12)-1\n",
    "res_ana=np.zeros((4,nn))\n",
    "for i in range(nn):\n",
    "    res_ana[0,i]=i+2\n",
    "    a,b,c=ana_prob(i+2)\n",
    "    res_ana[1,i]=a\n",
    "    res_ana[2,i]=b\n",
    "    res_ana[3,i]=c        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd0d73be",
   "metadata": {},
   "source": [
    "We compare the this way obtained answer with the probabilities obtained when checking all permutations in the plot below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a1f420fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '% of having no neighboring pair')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res_ana[0],res_ana[3]*100,'o',ms=5,color='red', label='analytic approximation')  \n",
    "plt.plot(all_perm_prob[0],all_perm_prob[1]*100,'o',ms=5,color='blue', label='checking all permutations')  \n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"number of pairs\")\n",
    "plt.ylabel(\"% of having no neighboring pair\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ffd8395",
   "metadata": {},
   "source": [
    "For 2 and 3 the resukts are rather different, then they get more similar. The high probbaility for 2 pairs is because when there is one pair then there is also a second pair. Because the number of pairs is constant there then relatively many cases without pairs occur then. In essnetnce the different pairs are not fully independent. \n",
    "\n",
    "While its is expected that this problem is smaller for a larger number of pairs, we also use another way for getting a probability, randomly drawing numbers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "8136eee0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#parameters: number_of_pairs, number of random draws\n",
    "#the neighbor counting is the same as above should be another function\n",
    "def count_rand_pairb(pairs,draws):\n",
    "    #convert to integer\n",
    "    pairs=int(pairs)\n",
    "    #function for getting dimensions of tiled area\n",
    "    dim=fac(pairs)\n",
    "    #counter for no_pair cases\n",
    "    counter=0\n",
    "    #do the number of random draws\n",
    "    for i in range(draws):\n",
    "        #shuffle the pairs\n",
    "        shuf=random_1d(pairs)\n",
    "        #reorder into tiling\n",
    "        reord=shuf.reshape(dim[0], dim[1])\n",
    "        #application of function which check whethers the assumption that there are no pairs is correct\n",
    "        no_pair=check_nopairs_tiling(reord)  \n",
    "        counter+=no_pair                  \n",
    "    return counter/draws "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65d3d35e",
   "metadata": {},
   "source": [
    "We run that for up two 12 pairs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "9324eb31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "75.37630438804626\n"
     ]
    }
   ],
   "source": [
    "time_start = time.time()\n",
    "nn=11\n",
    "res3=np.zeros((2,nn))\n",
    "for i in range(nn):\n",
    "    print(i+2)\n",
    "    res3[0,i]=i+2\n",
    "    res3[1,i]=count_rand_pairb(res3[0,i],100000)\n",
    "time_stop = time.time()    \n",
    "print(time_stop-time_start)\n",
    "np.savetxt('random_2_to12_its100000.txt',res3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8330fdb6",
   "metadata": {},
   "source": [
    "By comoarsion with up to 5 draws it is possible to see how many draws are needed that random effect are not anymore cause large effects. More than 10000 are needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "a8485f2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.       3.       4.       5.       6.       7.       8.       9.\n",
      "  10.      11.      12.     ]\n",
      " [ 0.33306  0.13348  0.20239  0.19568  0.17591  0.20661  0.17452  0.18082\n",
      "   0.17405  0.21434  0.1743 ]]\n",
      "[[ 2.          3.          4.          5.          6.          7.\n",
      "   8.          9.         10.         11.         12.        ]\n",
      " [ 2.          2.          2.          2.          3.          2.\n",
      "   4.          3.          4.          2.          4.        ]\n",
      " [ 2.          3.          4.          5.          4.          7.\n",
      "   4.          6.          5.         11.          6.        ]\n",
      " [ 0.19753086  0.2097152   0.21405832  0.21628042  0.19784467  0.21853449\n",
      "   0.19093372  0.19458917  0.18710527  0.22035947  0.1846733 ]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '% of having no neighboring pair')"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res3=np.loadtxt('random_2_to12_its100000.txt')\n",
    "print(res3)\n",
    "print(res_ana)\n",
    "plt.plot(res_ana[0],res_ana[3]*100,'o',ms=5,color='red', label='analytic approximation')   \n",
    "plt.plot(res3[0],res3[1]*100,'o',ms=5,color='black', label='checking random permutations')\n",
    "plt.plot(all_perm_prob[0],all_perm_prob[1]*100,'*',ms=5,color='cyan', label='checking all permutations') \n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"number of pairs\")\n",
    "plt.ylabel(\"% of having no neighboring pair\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16f81d8a",
   "metadata": {},
   "source": [
    "Overall it is visisble that the anlytic method overestimate the number of no pairs slightly, by about 1%. Both agree that a no pairs is unlikely. For 12 it happens with about 17.4% probability that corresponds to about once is six games.   \n",
    "\n",
    "\n",
    "In both method it is visible that no pair is more likely for some numbers like 7 and 11. Those numbers are prime numbers which means the rectangle is elongated to 2 times the prime number. Since then there no inner tile there then less neighbors and thus no pairs is more likely. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78e2b30e",
   "metadata": {},
   "source": [
    "Below is more, is mainly on larger numbers of pairs. Not clear whether needed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e6c7cc2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "nn=int(999)\n",
    "res3=np.zeros((2,nn))\n",
    "current_GMT = time.gmtime(1)\n",
    "\n",
    "time_start = time.time()\n",
    "for i in range(nn):\n",
    "    print(i)\n",
    "    res3[0,i]=i+1\n",
    "    res3[1,i]=count_rand_pairb(res3[0,i],100)\n",
    "time_stop = time.time()    \n",
    "print(time_stop-time_start)\n",
    "#np.savetxt('random_1_to1000_its10000.txt',res3)\n",
    "#7.6 previous code \n",
    "#4.3 with c stop on first level \n",
    "#2.9 when using only one sided \n",
    "#2.6 only checking wither larger is in frame\n",
    "#without checking for exist before one loop less 0.88\n",
    "#more C conditions 0.85 (used 100 up to n=100 apirs)\n",
    "#shufted array only execute second part about 0.78\n",
    "#1059.5 1_to1000_its10000 1060  seems faster for larger numbers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba8e9032",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3d6cd4d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1000.0)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#is slow now\n",
    "#results look good, for very small appoximation is less good \n",
    "res2=np.loadtxt('random_upto100_its10000.txt')\n",
    "res3=np.loadtxt('random_1_to1000_its10000.txt')\n",
    "plt.plot(res3[0],res3[1],'o',ms=8,color='blue',label='Monte Carlo') \n",
    "plt.plot(res[0],res[3],'x',ms=10,color='red',label='analytic approximation')  \n",
    "#plt.plot(res2[0],res2[1],'o',ms=5,color='blue',label='Monte Carlo 10000')  \n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"number of pairs\")\n",
    "plt.ylabel(\"probablity of perfectly mixed\")\n",
    "plt.xlim(0,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6c708916",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 100.0)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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88cdCCCHefPNN0bhxY3H9+nXz81988YXQarUiLy9Pcj1y7wt3n795w14iIqqRzp41RiQpQhifd6dmzZph+PDh2LhxI4QQGD58OIKCgqzmOX36NMrKynD33Xebp9WtWxfR0dHIysqymrdLly7m35s3bw4AuHTpkt0+Uj/++COuX7+Opk2bWk3/888/cfr0acnXCCGg0Wgcbpter8crr7yCDz74ABcvXkRpaSlKSkrg7+9vNV/Pnj1ll5OVlYWuXbuifv365ml33303DAYDTp48iZCQEIdlqUoMTUREVCNFRAD2zv8ajfF5d5s4caK5qWnNmjWVWlbdunXNv5uCjcFgsDv/9evX0bx5c6Snp1d4ztTMZuvOO+9EYWEhcnNzzcFMyrJly7By5UqsWLECnTt3Rv369TFz5swKnb0tw1BNwD5NRERUI02cKF/TNGmS+8swbNgwlJaWoqysTLIjdNu2bc19fkzKyspw4MABdOzYUfF6fHx8oNfrrab16NEDeXl5qFOnDiIjI60etjVeJn/961/h4+ODpUuXSj5fUFAAANi7dy9GjBiBf/zjH+jatSvatGmD7OxsxeU16dChA3788UcUFxebp+3duxdarRbt2rVTvTx3Y2giIqIaKSoKWL8e0GoBnc765/r1QGSk+8ug0+mQlZWFEydOQKfTVXi+fv36ePLJJ/Hss89i586dOHHiBP75z3/ixo0bmKQi1UVERODMmTM4evQorly5gpKSEsTExKBfv34YOXIkvvnmG5w9exY//PADXnjhBRw8eFByOeHh4fj3v/+NlStXYtKkSfj+++/x22+/Ye/evXjiiSewaNEiAEBUVBR27dqFH374AVlZWXjiiSeQn5+vev+MGTMGfn5+GD9+PI4fP47du3dj+vTpGDt2rNc1zQFsniMiohpswgRgwABjSDp71tgkN2lS1QQmk4CAANnnFy9eDIPBgLFjx+KPP/5Ar1698PXXX6Nx48aK1/HYY49h+/btuPfee1FQUIDU1FRMmDABX375JV544QXEx8fj8uXLCA0NxT333CMbSJ566inceeedePXVV/HII4/gzz//REREBB588EEkJCQAAF588UX8+uuviI2Nhb+/P6ZMmYKRI0eisLBQcZkBwN/fH19//TVmzJiB3r17w9/fH4899hiWL1+uajlVRSOEvcrL2quoqAiBgYEoLCx0+GYnIiL3uHnzJs6cOYPWrVvDz8/P08UhLyH3vnD3+ZvNc0REREQKMDQRERERKcDQRERERKQAQxMRERGRAl4RmtasWYOIiAj4+fmhT58+Fe5dY2n79u3o1asXGjVqhPr166Nbt2549913reYRQmDevHlo3rw56tWrh5iYGORUxW2tiYjI5Xi9Elny5PvB46Fp27ZtSEhIwPz583H48GF07doVsbGxuHTpkuT8TZo0wQsvvICMjAz89NNPiI+PR3x8PL7++mvzPEuXLsXrr7+OdevWITMzE/Xr10dsbCxu3rxZVZtFRESVZBoB+8aNGx4uCXkT0/vBcoT0quLxIQf69OmD3r17Y/Xq1QCMQ8KHh4dj+vTpSExMVLSMHj16YPjw4Vi0aBGEEAgLC8MzzzyD2bNnAwAKCwsREhKCjRs3Ii4uzuHyOOQAEZF3yM3NRUFBAYKDg+Hv76/ovmhUMwkhcOPGDVy6dAmNGjWSvM2Lu8/fHh3csrS0FIcOHcLcuXPN07RaLWJiYpCRkeHw9UIIfPfddzh58iSWLFkCADhz5gzy8vIQExNjni8wMBB9+vRBRkaGZGgqKSlBSUmJ+e+ioqLKbBYREblIaGgoANhtfaDap1GjRub3RVXzaGi6cuUK9Hp9hZFJQ0JC8Msvv9h9XWFhIVq0aIGSkhLodDq88cYb+Mtf/gIAyMvLMy/Ddpmm52ylpKRg4cKFldkUIiJyA41Gg+bNmyM4OBhlZWWeLg55WN26dSVvR1NVquVtVBo2bIijR4/i+vXrSEtLQ0JCAtq0aYPBgwc7tby5c+eah4YHjDVN4eHhLiotERFVlk6n8+jJkgjwcGgKCgqCTqercJO//Px82ao3rVaLyPIbB3Xr1g1ZWVlISUnB4MGDza/Lz8+3au/Mz89Ht27dJJfn6+sLX1/fSm4NERER1WQevXrOx8cHPXv2RFpamnmawWBAWloa+vXrp3g5BoPB3CepdevWCA0NtVpmUVERMjMzVS2TiIiIyJLHm+cSEhIwfvx49OrVC9HR0VixYgWKi4sRHx8PABg3bhxatGiBlJQUAMb+R7169ULbtm1RUlKCL7/8Eu+++y7Wrl0LwNj+PXPmTLz00kuIiopC69atkZSUhLCwMIwcOdJTm0lERETVnMdD06hRo3D58mXMmzcPeXl56NatG3bu3GnuyH3u3DlotbcrxIqLi/HUU0/hwoULqFevHtq3b4/33nsPo0aNMs8zZ84cFBcXY8qUKSgoKMCAAQOwc+dO3iWbiIiInObxcZq8EcdpIiIiqn7cff72+IjgRERERNUBQxMRERGRAgxNRERERAowNBEREREpwNBEREREpABDExEREZECDE1ERERECjA0ERERESnA0ERERESkAEMTERERkQIMTUREREQKMDQRERERKcDQRERERKQAQxMRERGRAgxNRERERAowNBEREREpwNBEREREpABDExEREZECDE1ERERECjA0ERERESnA0ERERESkAEMTERERkQIMTUREREQKMDQRERERKcDQRERERKRAHSUzJSQkKF7g8uXLnS4MERERkbdSFJqOHDli9ffhw4dx69YttGvXDgCQnZ0NnU6Hnj17ur6ERERERF5AUWjavXu3+ffly5ejYcOG2LRpExo3bgwA+N///of4+HgMHDjQPaUkIiIi8jCNEEKoeUGLFi3wzTff4K677rKafvz4cdx33334/fffXVpATygqKkJgYCAKCwsREBDg6eIQERGRAu4+f6vuCF5UVITLly9XmH758mX88ccfLikUERERkbdRHZoeeeQRxMfHY/v27bhw4QIuXLiAjz76CJMmTcKjjz7qjjISEREReZyiPk2W1q1bh9mzZ+Pxxx9HWVmZcSF16mDSpElYtmyZywtIRERE5A1U92kyKS4uxunTpwEAbdu2Rf369V1aME9inyYiIqLqx+v6NJnk5uYiNzcXUVFRqF+/PpzMXkRERETVgurQdPXqVQwdOhR33nknHnjgAeTm5gIAJk2ahGeeecblBSQiIiLyBqpD06xZs1C3bl2cO3cO/v7+5umjRo3Czp07XVo4IiIiIm+huiP4N998g6+//hp33HGH1fSoqCj89ttvLisYERERkTdRXdNUXFxsVcNkcu3aNfj6+rqkUERERETeRnVoGjhwIN555x3z3xqNBgaDAUuXLsW9997r0sIREREReQvVoWnp0qV48803cf/996O0tBRz5sxBp06d8N///hdLlixxqhBr1qxBREQE/Pz80KdPH+zfv9/uvG+99RYGDhyIxo0bo3HjxoiJiakw/4QJE6DRaKwew4YNc6psRERERIAToalTp07Izs7GgAEDMGLECBQXF+PRRx/FkSNH0LZtW9UF2LZtGxISEjB//nwcPnwYXbt2RWxsLC5duiQ5f3p6OkaPHo3du3cjIyMD4eHhuO+++3Dx4kWr+YYNG2YeFiE3NxdbtmxRXTYiIiIiE9WDW968eRN+fn6Sz+Xm5qJ58+aqCtCnTx/07t0bq1evBgAYDAaEh4dj+vTpSExMdPh6vV6Pxo0bY/Xq1Rg3bhwAY01TQUEBduzYoaosJhzckoiIqPrxusEte/TogaNHj1aY/tFHH6FLly6qllVaWopDhw4hJibmdoG0WsTExCAjI0PRMm7cuIGysjI0adLEanp6ejqCg4PRrl07PPnkk7h69ardZZSUlKCoqMjqQURERGRJdWgaPHgw+vbta+6/VFxcjAkTJmDs2LF4/vnnVS3rypUr0Ov1CAkJsZoeEhKCvLw8Rct47rnnEBYWZhW8hg0bhnfeeQdpaWlYsmQJvv/+e9x///3Q6/WSy0hJSUFgYKD5ER4ermo7iIiIqOZTPU7TG2+8geHDh2Py5Mn4/PPPkZubiwYNGmD//v3o1KmTO8po1+LFi7F161akp6dbNRnGxcWZf+/cuTO6dOmCtm3bIj09HUOHDq2wnLlz5yIhIcH8d1FREYMTERERWVEdmgDg/vvvx6OPPoq1a9eiTp06+Oyzz5wKTEFBQdDpdMjPz7eanp+fj9DQUNnXvvrqq1i8eDG+/fZbh82Cbdq0QVBQEE6dOiUZmnx9fTnGFBEREclS3Tx3+vRp9OvXD59//jm+/vprzJkzBw8//DDmzJmDsrIyVcvy8fFBz549kZaWZp5mMBiQlpaGfv362X3d0qVLsWjRIuzcuRO9evVyuJ4LFy7g6tWrqjupExEREZmoDk3dunVD69at8eOPP+Ivf/kLXnrpJezevRvbt29HdHS06gIkJCTgrbfewqZNm5CVlYUnn3wSxcXFiI+PBwCMGzcOc+fONc+/ZMkSJCUlYcOGDYiIiEBeXh7y8vJw/fp1AMD169fx7LPPYt++fTh79izS0tIwYsQIREZGIjY2VnX5iIiIiAAn+zSNHTvWalr//v1x5MgRzJw5U3UBRo0ahcuXL2PevHnIy8tDt27dsHPnTnPn8HPnzkGrvZ3t1q5di9LSUvz1r3+1Ws78+fOxYMEC6HQ6/PTTT9i0aRMKCgoQFhaG++67D4sWLWITHBERETlN9ThNtQHHaSIiIqp+3H3+VlTT9Omnn+L+++9H3bp18emnn9qdT6PR4KGHHnJZ4YiIiIi8haKaJq1Wi7y8PAQHB1s1lVVYmEZjdyyk6oQ1TURERNWPV9Q0GQwGyd+JiIiIagvVV88RERER1UZODW554MAB7N69G5cuXapQ87R8+XKXFIyIiIjIm6gOTa+88gpefPFFtGvXDiEhIdBoNObnLH8nIiIiqklUh6aVK1diw4YNmDBhghuKQ0REROSdVPdp0mq1uPvuu91RFiIiIiKvpTo0zZo1C2vWrHFHWYiIiIi8lurmudmzZ2P48OFo27YtOnbsiLp161o9v337dpcVjoiIiMhbqA5NTz/9NHbv3o17770XTZs2ZedvIiIiqhVUh6ZNmzbho48+wvDhw91RHiIiIiKvpDo0NWnSBG3btnVHWYiIqBrJyQE2bADOngUiIoCJE4GoKE+Xish9VIemBQsWYP78+UhNTYW/v787ykRUafwwB7BgAaDTAUlJyl+zaBGg1xtf68yyLOeztyyl61SzXqXLU8rb1+vq/exE2VJTgcmTAY0GEML4c+lSYP16wDwijSuOrSe2VU35lK7XE+8pT72PlXLHPi4rc1HhpKm+eu7111/HV199hZCQEHTu3Bk9evSwelAttmCB8Q2tZr5Fi5T9c8rNZ7Pe1FSgfXtg2TLggw+MP9u3BzZuVLg8pTy1vUrpdMC8ecrKaFrnvHnG1zm7LNN8Q4faX5bSdbp6G9Tw9vW6ej+rLFtOjjEwGQzG85flz0mTgFOnFKzTm7dVTfmUrtcT7ylPvY+Vcsc+fuUV15VPilBpwYIFso+aoLCwUAAQhYWFni6K8+bPFyI5Wd18ycnGvx2xN19yshCA4/Wa5hsyRN389uazeD47Wwit1vin7UOrFSInR0U5HanE9mZnC5GYKERcnPFndrYTy3VHGeXmU7os03YOGVJ1ZVMzn1Levl5X72cVZUscuEfodNL/ZzqdEIkD97h233liW9Usz5vfy556Hyvl4vIVPv+8W8/fqkNTbVAjQpMXBBhZbjqxuuzDXCkntnfDBmOA0+msf6amqlieK8uoZp1Kl+Xo/aR2O125DWp4+3pdvZ8Vli0Om4VWo5f+cqLRizhsdurYSn6Z8OS2KlludXgve+p9rJTS94CC8rn7/M3QJMEjoUlpzZAlRzVD3loz4MYTq0s/zJVSsb3ZiJQtXw7auueDy14ZnfmwVLosV67THcurKev1QPkSB+4ROpRJfzlBmfHLiRrJyWIDJgitRm/9ZUKjF6kY79Ftdct6PbEdntp3Sil9DzjA0OQBHglNrv62onS+qq4ZcPMHvss/zJVSuB0eK59UGSvzYZmcLLIRKRIH7jF+Ixy4R2QjUnL7Fc3niW2oSeut4vJlZ4vy8G+weR8bjOE/x9nl2f5fSCzP24+FiuW59H/DW9epkKr3gAyGJg9w6U5XU4NkGWBcUYPkaP6qrhmogg98V3+Yq6JgO+Li7H0wlNeExbmxfJZl8vGp1Af+hg3G8upQJrS4Zfyp0RubGJ2YT43sGatFIl4RcdqtIhGviOwZq51fmBou2nduW28Vly811XRsS4UWZZU6tomJQr5ZPdHmBR46Fq5877njf8Mb16mU6veAHQxNHuDSna42ADhqKqtGAcbq9VX4ge/KD3PVHGyHqz4YKsVUNh8fp16uqLO9ivnUMPcHs/zQ14qq+9Cv5L5z+3qruHw5OUIkapeIOGwWidolTn8piYuTf69Ifpmo4m115XvPHf8b3rhONZx6D0jwutD03XffuaMcXsXlO11tU5q9prJqGGCys60/VK2uErPlwg9BV32YO0VmOzz+weWCY6s0+Lk6INrfd4Yq2XfeXsPlkfK56LPC22uaXP3e88SXJ6/4wlYF5fO60OTj4yPatGkjFi1aJM6dO+eOMnmc0ztdrilOrmbH9Dq5Gh4XtNtXdYBRVRXs6g9BL25K8VhNmIveU0qbGF3dFJmYKITOzvJ0Gr1bP/Q3jPzE+B7W6I21DRq90OKWSH1kh/tWKoTiPigeKZ+nmtU90KfJ1e89TzTTe7xrgAOu6lrhdaHp8uXLYvny5aJr166iTp064r777hPbtm0TJSUl7iifRzi90x3989r7Z3dUs+SCE39VBxiPduz0YEdRpZ2jc9DWaj63XTVnsU7Z95iKdSvtzO7qTu9xnY8JLW5Jf+ijTMR1PqZqeUplz1htZ70GocUtkTNjlVvWK5KVXU3kkfK5of9jKsYrvnoue8Zq68vSZ6x26/+4q997nrggxKMXoSih9D3ggNeFJkuHDh0S06ZNE02bNhVNmzYV06dPF0ePHnVV2TymUjtdaXCy7LskN78LanzUBhhXXF2h+B/UDR++Ll2eivV67SXTasO8g2UpGjbB1cMrJCeLRLwi/20fr7h+/3lwvUr3c5WXz5XvJ5v5c3Ksx+ixGoy2/LNyw8hPpMc5e2SHe/6HXP0eUHpsXXzMPDbcicLyKXoPKCifV4cmIYS4ePGimD9/vvD19RX169cXOp1ODBgwQBw/ftwV5fOISu90RwfYFJRMDbiOPnwq219ARYBxxTgZIlnheEk1aABEpSe4Ki+fzTLtjkSuZN0W86SmygzQafGFQHY+pdtrUbsg2x9sxirX7r/y9cZ1PibfQbXzMbes1+FAra3eN5YvOK3qyqfymLlsvvL3VHbfsR55D7jsvaf0f8iVnwWeWKeT5XPFfF45Inhpaan48MMPxf333y/q1Kkj+vbtK9566y1x/fp1cebMGTFmzBjRoUMHV5e1yigKTY6GEpA6wMnJQgwebB2Y7NUg2b6+EjUvSgOMS76JqPzArym32qjy7VVRNtOyZEcid7RuieeU1ArY/eaodHttnpf90FeyPKUslqOog6ob1it7NZHF/61sLYgry+epLzEW76kq21aJ8lX6vaf0f0hm/spuQ5Wss5Llq9T8ycmiEPCu0GRqjmvSpImYMWOGOHasYltubm6u0Gg0LimgJygKTSq/mZt/tzyh2KtBsrdsJ99gSk/oia3er9wtSCzKJ3uVmNKaF6Xb7ep/PKWcOMFVabCzCPaKr9pLTpYeI8wT9zK0s17ZD30165Xjyn3n5Hplw5pGb64hzp6x2v6XHVeWz9V3LXDiPRXX+Zjstpo7M7v4WJhU6r3njrs+OOKJdarhhveU19U0DRkyRGzevFncvHnT7jxlZWUiPT29UgXzJMXNc2qCk21gsleD5OpvZyoCjGyNlOkDSW79Nv8Adr+Zjfi4wolV9ga2FvNJ8tQHgxMnOJcECSd4++XG3s5hLYMbqBmewhPl8wS+j8kRr+/TVBOp2ulKQ47pv1quBskmUFWq/4kTASZx4B7HVd+m9Ss8oTv8ZiYUNBtVAx4ff8kBVw0cV5speS+7mpow5InyVTVv/z8jz3N3aNIIIQQc+PTTTx3NYvbwww8rntdbFRUVITAwEIWFhQgICHD8gkWLgHnzgORkICmp4nQA0OkAvR4YMgRIS6u4jKFDge++Mz+fmgpMngxoNMaPBNPP9euBCRNk1inj1Cnj68+eBSIigEmTgMjI28/n5ADt2wMGQ8XXarXAyZPW87uCJ9bpLhs3Gvep3WPmQXPnAsuWGd+CtnQ64NlngZSUqi8XOebo/7a28eb/M/I81edvtRQlK41G0UOr1bol2VU1p5KqvWY2yxokuT4t8+ffvkLE0ZUaruxDYaOqq/lrWnW7t37b5zd0qkm89f+MPI/Ncx5Q6cEtTR28lfRhkliGoitE3KgqP5DYbFR1aku/FyKqvdwdmuqorZl65513MGrUKPj6+lpNLy0txdatWzFu3DiX1IBVS0lJwEsvAaWlxr+Tk43tIYMH325CM/00NdvZNq0lJeHsh8chjkuvQghjNb07RUZWXVNNRISxel2KRmN8nlxjwgRgwAA29RAROUt1aIqPj8ewYcMQHBxsNf2PP/5AfHx87Q5NixbdDkwmCxZUnM9BcIoY3gmaEwAk+p/UtCAxcSKwdKn0c0IYT+rkOlUZiImIahrVoUkIAY1E1cCFCxcQGBjokkJVS5advpOTjT/t1SZZTpOYpzYFiagoY82HvY6drAUhIiJvoTg0de/eHRqNBhqNBkOHDkWdOrdfqtfrcebMGQwbNswthfR6psA0eLDx6jfLkKQkONlc0lTbggSbjYiIqDpQHJpGjhwJADh69ChiY2PRoEED83M+Pj6IiIjAY4895vICej25S/8d9V+yNw21L0iw2YiIiLye2p7jGzdulB0N3BmrV68WrVq1Er6+viI6OlpkZmbanffNN98UAwYMEI0aNRKNGjUSQ4cOrTC/wWAQSUlJIjQ0VPj5+YmhQ4eK7ApDTNtXofe9vRGn5a6EsxwOwHY+bx/anoiIqBpy99VzWrUhq2PHjjh69GiF6ZmZmTh48KDq0LZt2zYkJCRg/vz5OHz4MLp27YrY2FhcunRJcv709HSMHj0au3fvRkZGBsLDw3Hffffh4sWL5nmWLl2K119/HevWrUNmZibq16+P2NhY3Lx5U3X5ABhH/5s3z1irZCJXw2R6Tqcz/p2UZJyvfBk5Bc0wd14djO5yHHPnGgd4lGW7PCIiIqp6alNW7969xYcfflhh+kcffSSio6NVp7bo6GgxdepU8996vV6EhYWJlJQURa+/deuWaNiwodi0aZMQwljLFBoaKpYtW2aep6CgQPj6+ootW7YoWqZkUlVaW+Sg9mnDwx8bx8jR6IUWt4w/5cbKqeq7ThMREVVTXjdO04kTJ9CjR48K07t3744TJ06oWlZpaSkOHTqEuXPnmqdptVrExMQgIyND0TJu3LiBsrIyNGnSBABw5swZ5OXlISYmxjxPYGAg+vTpg4yMDMTFxakqo5lt/ySpoQQkap9ycoANG4z9kgICkvD256ZbhpRX8gkAQmDSJA0GDLDpsyRVm7VggbHGSeGtU8zL0euly0xERESKqA5Nvr6+yM/PR5s2baym5+bmWl1Rp8SVK1eg1+sREhJiNT0kJAS//PKLomU899xzCAsLM4ekvLw88zJsl2l6zlZJSQlKSkrMfxcVFUmvTK5jt0TAsb1/nOlRkQYaYcD69drbnaHtNf+Zmgpt12+P5XKIiIjIaapD03333Ye5c+fik08+MY/LVFBQgOeffx5/+ctfXF5AOYsXL8bWrVuRnp4OPz8/p5eTkpKChQsXKptZKjjZqWGaPFn6RrRShDDg7BcngJROlb8iz8SJm/oSERGRNNWh6dVXX8U999yDVq1aoXv37gCMwxCEhITg3XffVbWsoKAg6HQ65OfnW03Pz89HaGiow3IsXrwY3377Lbp06WKebnpdfn4+mjdvbrXMbt26SS5r7ty5SEhIMP9dVFSE8PBw+yu3DC6m26bYBJMNG+zfHkSKRqNFxLHPAN+eksuzu37Lvy0xMBEREbmU6qvnWrRogZ9++glLly5Fx44d0bNnT6xcuRLHjh2TDxoSfHx80LNnT6SlpZmnGQwGpKWloV+/fnZft3TpUixatAg7d+5Er169rJ5r3bo1QkNDrZZZVFSEzMxMu8v09fVFQECA1cOhpCTAx8cYcHx8KgSTs2ftNcVJExotJtV913p5CxZYX7Fnu36LK/LMFi0C7r2XgYmIiMjFVNc0AUD9+vUxZcoUlxQgISEB48ePR69evRAdHY0VK1aguLgY8fHxAIBx48ahRYsWSCnv7LNkyRLMmzcPmzdvRkREhLmfUoMGDdCgQQNoNBrMnDkTL730EqKiotC6dWskJSUhLCzMPECnS5juM2cKTosWWQUUuRvRAsbnTA8hgPUjPkHkx1nWy3PUf8m2xsnydwYmIiIi13Lmkrt33nlH3H333aJ58+bi7NmzQgghli9fLnbs2OHUJXyrVq0SLVu2FD4+PiI6Olrs27fP/NygQYPE+PHjzX+3atVKoPyaM8vHfIuBH02DW4aEhAhfX18xdOhQcfLkScXlcXjJou0wABLDAmRnC6HVWnb/vv3QaIR44gkh4uKESEwUImfGKvvLUzLkgGke04PDExARUS3k7iEHVIemN954QwQFBYmXXnpJ+Pn5idOnTwshhEhNTRWDBw92eQE9QXan2wsxEtNTU43BSaez/mk1JpOS5TkKToMH3w5MPj7KNpIjjBMRUQ3jdaGpQ4cO4uOPPxZCCNGgQQNzaDp27Jho2rSpSwvnKXZ3uqPwIvF8To6xNslcq5Tj5PIchSvAmMqU1DRxwEwiIqqBvC40+fn5mZvkLENTdna28PPzc23pPETRiOD2uHM+e82CgBBDhlj/VBHsiIiIagKvC00dOnQw912yDE2vv/666N69u2tL5yEVdrraoOFEjZTi5Zl+9/Gp2IfJ9Jy94GRqxlMTmNiMR0RE1YTX3UYlISEBU6dOxc2bNyGEwP79+7FlyxakpKTg7bffdknndK+j16u7Gs00n17v+uUtWHB7bCjAejmWV9MNGVJxAM70dGXrM+Fo4kRERGaqQ9PkyZNRr149vPjii7hx4wYef/xxhIWFYeXKlc7f183bOXPPNrlAVJnlmYY6cDSfZXBKTwe+++52+JEbxsB0bzvTfErCHe9tR0REtYCi0PTpp5/i/vvvR926dQEAY8aMwZgxY3Djxg1cv34dwcHBbi0klTPV/ADyAcgyOOl0xsA0ZIj1PPaCk+XYUHKBSSpcKSk/wxUREVVTikLTI488gry8PDRr1gw6nQ65ubkIDg6Gv78//P393V1GAm4HpsGDlQWgpKTbzXg6HTBwoPVz9l6nlNJwZVt+NvUREVE1pSg0NWvWDPv27cNDDz0EIQQ0am6qRpXnzA18bUcsN9UKyb3ONtiYntPrja9XE64sa5VceR88Uw2Xs2UhIiJylpLe4vPnzxcajUZotVqHj5rA3b3vVXHl0ARSy7C9Gs9yHntX4zkaP0rtiOZquPpKxvnz1ZeNVxQSEXklrxlyICsrS3z22WdCo9GIjRs3ih07dkg+agKvCU3OBgSFI5abmQKT1GjitsFJajgDeyHJXWNCuXIsLFeHMFdjqCMiUsxrQpMQxnu6TZgwQfzxxx9uKYy38JrQpPaEaTqh27udjVytkFRNk+08phHHhwyxP4+7A5Pctqh53pl5PTEwaG2qWfPmshFRteBVoUmv14u6deuK7OxstxTGW3hNaFLD3c14plBl71YtlqHJMoApPRFazqf0RGhvEE9nwo2rByR1pdpSs+bNZXMHV4fE2hQ6vX1ba9Ox9bKyeVVoEkKIjh07ioyMDHeUxWtUu9Dk7mY829oouT5Otk19ak/4jm4D42j+ypxI7b3WG07OrFlzbj5v5uqQKPF8drb1vS+tvu9W533o7QHb1cfCm7fXy8rmdaHp008/FQMGDBDHjh1zR3m8gjeHJsl/PHc249mrjTKFFctaJdtwpTbIWPabEjLbZbO87BmrRSJeEXHarSIRr4js6DHSy1eyn2zLqjTEVQVXhrrqXLNWnU/2tlwdEi3m27BBCK3WWDls+TM1VcXyvJm3B2xXHwtv3l4vKpvXhaZGjRoJHx8fodVqhZ+fn2jcuLHVoybw1tBk7x8vJUXmG4wttW9uuZO0qanOx8d+uFIanKRqjuRqvcqnmfcJyoQWt4w/NXrjh1Flt12uD5enJCeLbESKxIF7jMd74B6RjchK1axlz1ht/f6ZsdrzJ1RvrvVzNYttkvxS5MQ3+WxECq1Gb/4XtnxoNXqRg7Y1Yx96e8B29bHw5u119fvYSV4XmjZu3Cj7qAm8MTRlZxvDgdQ/nun8XuEbjC01b1q50CTE7XBjChZKTnBKT4T2arpsa5js7hOD8cNoxqoK+zBx4B4Rh83GsGEbLpOTb7ezm7ZLp3O8r6rQhg3GD1pFIVHJ8kZ+YlyORm98/2j0QotbIvWRHS4tt1NcGRC9XXKy2IAJxmNr+b+s0YtUjFe9zYkD9wgdyqQ/K1AmEgfucc92eIKXB2yXHwtv3l4Xv4+d4XWhqTbwRGiSbe8WxmmW+cTRQ6sVIifHZiUSzVMOvxFYBgkT21ohuXDlbA2UVFiymS8x0XiSl/4wuiUS8UrFGimdReiwDBuW64uIsA6ESkOmmztdygVnyePt9PIMTi3P1VwdEL1ZdrawUxtR/gVA5bGIi7O3POP0uDj3bIfHqK3ZrkJuORZeur2ufh87wytD06lTp8QLL7wg4uLiRH5+vhBCiC+//FIcP37cpYXzlKoOTbLt3eXi4uRrmqRqnhITnVivxDcCq2Bl+W3fMszI9f2x9w8uN8yB1Hw288Z1Pia0uCX9YYQyERecJgSMzU8Oa6RMy7YMgvaaCB1tn5vIBWclx9vdy3MlVwdEb1ebjq27VOjbOGO1p4skhHDjsVD6OVqFvOF953WhKT09XdSrV0/ExMQIHx8fcfr0aSGEECkpKeKxxx5zeQE9oSpDk9KTgzM1TXLfYBw2bZWv124NzSM7rIOFqRZLaXCSG1DTkuV8NrVPiXjFfrW3Rm+saRoyxDif3Rqpsts1UpYd0aVquuTGpzJtlzNDJ5jmc9BR3dXfWOWCuKP3j7t5w4dvVXL1sahtoVOyb6PWTjeFKubWY6H0c7SKeMNniteFpr59+4rXXntNCCFEgwYNzKEpMzNTtGjRwrWl85CqDE1KTw6O+jSpPbEoWa/sP3sl+gwp/kYo9U3KonZLtoOlVphrkOKC0+RrpLBZutO3ZSCyvbLP9nnbaWqHTlBQq+XqvhGyzZsavUeDSW1rXnJHSExNNX3RKRValNXY5k1vb2YWwk3HgjVNkrwuNNWvX1/8+uuvQgjr0HTmzBnh6+vr2tJ5SFWGJjXJPDXVujlNLkQ5+rBQsl65fwCtVoi+fW/Pl5LioM9QOcUdj+016Vk2n/n4VNgnFZo2zTVS0qFJp9GLRM3i2//VQqY50l5NlC2pgGVr/nzHt6Sx2R/ZiCwPfwbpECt3FY5ErVf2jNV2lmcQWtyqEIrlluVqtaojs7DsCyJxLJztC5KcLHLQ1qojfY25as6CN4d/M1cfC6/v0+TC97FKXheaWrRoIfbu3SuEsA5N27dvF23atHFt6TzEG2uaTHJyrDtuL17suD+Us+t11I9Ko3EU3qy/6d0+SUvMZ3mSdhAcbGupbPeJ7T9m9ozV9v+Rccv44VW+MzaM/ES+n5dtnydbSmua5IKVvQ9EQKQ+sqO8+aHU+NN0vEd8rG6E9PJpqU2fsQ6xpuVZNr86WparJbvxknkvG73Ych2pGO+6q46UXGBRQzjs29jZw2MKuvpYlL/OW4cKcen72AleF5qeeeYZMWDAAJGbmysaNmwocnJyxJ49e0SbNm3EggUL3FHGKueNfZrkOAoNzq5XbT8q2eBnqvGR+0ZY3gfJ3j++uZaqvBZLzeXx5hoplFlXj2O8ObjYD3UWJ2o7ndKFEMq//SkJVlI1a+VNeDloKxJbvW9uBs3JkVmmXBNi+fScGauMQbTzMev3j6PtcUcAsViHbC1iJU84il/nqpAht68s1mH1vzxwj8iZvtL1Za5JwUnp54qnttXVx6J8fskvd3JfdqqCvfex6TOlit53XheaSkpKxOTJk0WdOnWERqMRdevWFVqtVvzjH/8Qt27dckcZq1xVXz3nsInJCY6GMFCyXrX9qOwFsLjOx4QAjN8IZYKa6Wo3qdoXxbVUMszhoLyWKgdtrb6t9e1rv5pfqxWiLzKMQUW7pOK3OqXfJtVUq9uEG8XLGjLEfsd822VKldO2M7u9gGf5GiW1MU6cQGS/ENgrsyO2+8nZ8qohsSzZPoBq3ifOlNmdJ7Cqqs2zqHGR/QJoeXVsVXLTMfPK7fWG9105rwtNJr/99pv44osvxLZt22rcDXw9MU6TM7VF9igZwkDpem2DlUajLjRZftOTbRKUq2lyxbdJ2xM8UGEQNvltMwgN9NbjBZm+1akdOsFRsLKdrua1jmqxBg92HNJsX6ukRkxu+6X6b0mdWB1deWiaJjWfkkBmuTxH/c7c8eFusUyrMags3oOytWhuqrVw+QmsKsph8xolfRurNEi4eh9YPK+oS4fce6gyTc1SY/2ZLuwpr6mWHTRYybZWkteGJiGEMBgMwmAwuKosXsMbRwRXyh2Xt1oGq759VQ59YHGVneKr8Sz/ycr/wRzWUpXXZsme2C0C0+1+TupCoGWI0mr0Iqduh9uhRuaYJGqX3K6lkvqOIVez4OiyYtvX2gsESj6sbIOTo75ZSkKTRHlkP2ilyilxDFWHT3vBcvBg++uS20/OnHySK9lfS2693tRfy901DxLb6vCLp7u2VWH5HFJ4bOX6mmo0QnToYHERy7SV1suvbFixWYY5/Nv2iUx1sE43HguvDE1vv/22uOuuu4SPj4/w8fERd911l3jrrbdcXTaPqc6hyd2XfFb2di6qmiJd8e3KzslWXX+tilerARZjPMnUNKka1VqqRspRLZW91yrp22SPaV5H996zE0YlO6dalMdcE1reJ830gWu3lkXpNNvpUjVc9gKUaZpcSDSduCyWIdUMnj1tpfWtXyxPXKJ6XBmopHnfIVfXjLmIS7bNgxx9dpku0HHbDZotv3jKfUH3ULOo14WmpKQkUb9+fZGYmCg++eQT8cknn4jExETRoEEDkZSU5I4yVrnqHJqqYnAxe8Fn8WJlTYyKmyItvl0prkGTqKUy/9Mq/LZm/uDR6IUGUlfdla/XNMaTndoPp24pYG8wT6ntkXut5fzOjONieo29W8lIlMXhcBKytSwG6VoWuW12FJxat7YOfY7mNz0chUTL8GfzLVujEUIDg2xIlr3ay91jUCmoAanQvK/R2w/6jpZnL/DKNRO7kZquC95Kblwqe+8plw81keyaDvjuCLBeF5qCgoLE5s2bK0zfvHmzaNq0qUsK5WnVOTRV1eBiruyDZY/tP5Sq4RUcBAyHY1DdcV7EYbPoe8d5+X5YA/dUqG0xrVN1jYJtyFEYViRfa3remRGDnai1UjrAoKp9orSZTGoeU5ktg5PcsuRuPG27Lsh/y5YN9o5ONlL/o5Vp6rF9rdT+sv1yYi/USn05UXuMbGv23K2yX7y8VIW+pjDYDU3uqr2s7FAP7gqwXheaAgMDJTt+nzx5UgQGBrqiTB5XnUNTTbl9gr1/KKW1WY5ONA5vI1P+zUxRGJA6KQwZIuKwWX5Ua1MtlbCzDHsnFkc1UBZlkAxScsprg6yalxDpcFlKw7rcSN8alIkOzS5VHFRUQZllt9+imVGyOa3vWGP/Ks0W49hfUuu1OT5ywcfuPigP2LcDl8QgpVL/o2qbVqTeS3LByeJv2VBrrxnccn/bCxummiU1gckV4cVy25QM1tv5mPr71im9EbqLt83yi2uHDvb/r5yuvXTwGVqZQUXdeZ7yutA0bdo0MWvWrArTn3nmGfHUU0+5pFCeVp1DkxDuGcKgKlVV8LO7n0Z8bPVhYZ5PozeO8VTeHJOSYjNyuKnvSvnJOrHV+/JBwlRLZVkL4uiEZ2IbDOzVtDhqmrJZpu0VhVYD05k2RqLWSmmzsHx/DIkrFFMVHkxHNW06neS2aWBsgtXhllWTYgrmVAyOFvtO7lu25D7ALauQbD1IqYLbaigNTkpCktS08r9lg75W5oILR1cj2ozkb5dEvzGH7NWq2Wyr3MUkVu89yz52cuuwU9vmsHnT0bY5UbOYOHCPutpLJRyU8/bntMSgwQ4+p93ZIuKVoSkgIEDcddddYtKkSWLSpEmiU6dOIiAgwByoTI/qqrqHJiGqpvnMXary/kVK95PtAJBWt42xDFymYQiGDHF8b7wc4fjWLHIfXI6uklPTGTzZwVVdNiOnS9Y0KfjWqXbsL1UhWaZP1+1b0FQ8WUpPk++XJLe90vuvTPQNOG4VwlTfVsPRyVZJyJZ4b2XPWG0eL6ov9srfckiqn4qjAG9Zc2p6KGgCVV3L6GD71dYOOqpJlvrfst9sa5DuHC0VkJQcZ5tL+G//7yqsvZRbnoqySA4aLPHF05ZL+t7aCZdeF5oGDx6s6HHvvfe6o7xVoiaEpurMG+6UXYHSvhE2QyekjvjYfq2fbbOGg2/KkmHKtklEpunF0bISB+6x33xhOuljs0hs9X6Fmhc197GzvXmpXGd7xSHZtqapPLSaQknfO87bbXZyJsDJfcu2N80qhCm536Lcdqo90VrMY3mF4wNR2VbB8PYxVHg/QqXvN9vQ4SjcKQlNKr9kyL1H7b73LPssmsh8WVHdOVrt8ZTZ36mpQlntpdTgtbbDbkitc/DgitPnzxc5ff9h1bydM2OVdPkt1qv4i7FcLaKdfeR1oak2YGjyLG+4U7Yry6f0lgKS/W1M0yz7Wrjwg9byd/krCg3mKwrNJ33TvaTKl5H6yA752jeL9VvWsnRodqlyV5PZbt+QIcamOIt78xkHLpU+OSp92B5bqW/Zt6+eM564tCizs147TRjOBCclrylneYWj/X1SHvJMVwXilvF4d1iirKy2AdZesJELPK6uVStne+9G2atjbfsdWi7bTq2aU52jnfm/tfO31S2WWr0vXXsptQ1K9qfUuuWuUJUpr6IvnkreDxJfHhmaPIChybO8vTO7O6qWpTq+azTGR4W+ERJV306PymvxDVPt2FXmDvMWH2Z2mztlTjaVGrdI4oPZflNc5R5SAa7CrXlmrDLug/LBTPsiQ/0XADXBSUUnfzVNo1roRV/svb1dff+hLqjZBKYKXwhM43fJnRTVfjmQmEdq3LActDUfM2NzpJNXc0qUIzFRyDdv2vvCpyQUqAxQptdZXdhh+myQqi1zdAxsy2IbmOReI1FOqxpny1HxTV+ylL4fbLal8PnnGZqqGkOT53lzZ3ZX14RVtp+Pw1F57bEJUmrLYW5uUHjStvdBLdsfQ26MGTsfyHLNjMqb0ypxErW40jAOm52rRVMSDFQOJ6EmFGu1QsRpt1ovX2lQs6yZgIKby0qdIB3tY5W1ahXGDSvfhuy6He289wxCg1viiV4H5a/mTLa+2nRKr4P2m6kdfeGzF/T6jrX+v1G6T5KTb9e4Wt6ux/JG5bAJtY5qtE2vMd1zSsXAt1L/J1b9+mxr4S1eI1k+m2WZfhYCDE1VjaHJO3hrZ3ZX14Spq+GxDmauLovttz+5+/FpNXpjc4OamhHLPli23zrNJ7Yy6yuYlNRCWPytppnRfPVceS2e/eY0mwCn8FtvYqv3K1eL5qiDroqaJkcDulqX7VaF0e6V3g4oG5HmWs/bIcLO+9N0GyIlIcwltWoWNaTly0t9ZIdVH7vb7wv5iwGEkB7xXwPj/02FztGpUiW1WZ6doJfS9k2rGs0KoUFinygaXDdZ4opZU7g0Nb9XOLYpxveAZrH8YJQ2wcmqxsvUL1JBLVWF0G27T0y16+XhsvCeexiaqhpDEzniypowNScz08lGySX85rFn7I0VY0fO9Nu3AZG716Bkh00pCptezCG5/NukVadjuW+uwvrWJXJlttonA/eInOkrbzexYbNIHLhHfhBViW/BFcpoEZxuNxWqrEWT42Tti/Ir/so7fff9h3n5VjUW9kKE5XzlJ325vmS2TYDZ0WPsF96FtWpWYbV83+XMWGUOhFM0byr6IiL3hUUDvXgCa62abR1xNNK31b7XSvQVVLMPdLc/E+wGK8uO/0rfA7Ysg4/t7aRsg5nU/7W5877UPjFUGCoktcMS76hp6t69u7h27ZoQQoiFCxeK4uJitxTGWzA0kRKuqgmrTE2TotvBVCLUuaQmS+rKFyW337ANYaZpDvqDydUyyXa+tvjAdtg3y1EItAhOdvtupEq8zhF7TTimPkIyy5G/esxwu4nX1Om7fHnZ2cLuicuyxkJuyAp7x0NTfkwq3HJH6vi4qFatQrOo5TH18VE8YrvaYKYo1KrtUygTxpT0vZTdBlPzu4MhO+zeEqqc3M3RbWv9bPeRuqE9jO+lw3Xu9Hxo8vPzE+fPnxdCCKHVakV+fr7LCrB69WrRqlUr4evrK6Kjo0VmZqbdeY8fPy4effRR0apVKwFA/Pvf/64wz/z58wXKk6bp0a5dO1VlYmiiqlSZPk1qA5fTTXYuqlVzNfl9Z7Duy2GvzEoHVLSt7bJ3j0PbGqfkZGMIKx8LKXHgHutjoDQ42WuusHeVosRrrZqiyveLRiPEA3eeNJbNslak/DUOmxhbvW+cT7YvmcKTnu2wBrbNOgpHilc1WrVNEFZ6b0C50e21uCUdzGTKrbbG2dGo20pqmuTWqdEI0QE/l1/Q8IPTzcwOy6EtD+gqB821t09mYZ7nQ1Pfvn1FTEyMWLBggdBoNOLZZ58VCxculHyosXXrVuHj4yM2bNggfv75Z/HPf/5TNGrUyG4o279/v5g9e7bYsmWLCA0NtRua7rrrLpGbm2t+XL58WVW5GJqoqkkFkwpXz0mc+FV33nZyyAZv7V8m2zwJvfEegmrKLNfMqHSsGKlRo+Xmd7Rei9c5dWd5m7CntPOtEOL27YDsXkZfPtL5kCEqT3B2OttbjmUk1d/GsiOzk7Vqts1OlvtGQEFILA8ITt9bUq45TeWAqXL3d7vd9CaxD8prh5SO0K96aAYLDsMlNjt1eybJoIcycWfT054PTb/88osYNWqU6NWrl9BqtaJTp06iW7duFR7du3dXtfLo6GgxdepU8996vV6EhYWJlJQUh69t1aqV3dDUtWtXVeWwxdBEniAVTJSElQo375TrvK310OCgbuLxgVArczNdNfOXn1AUXbkp1//LUfCzFyLkam0U1jRpYHA4mKlWe/tWLbIj1Cu4qlKqVs2qRk5qrCWl/dAcjfhvr3xyHbfVDr5pb4R2i3WlYrxs6JQLVlIhyu77TmoQ0HIOw2Wr9+3uG/lBZKWDHuBl4zRpNBqXNM+VlJQInU4nPv74Y6vp48aNEw8//LDD18uFJn9/f9G8eXPRunVr8fjjj4vffvtNdlk3b94UhYWF5sf58+cZmqhasQxXijtv1wDePhCqS1gEHcUh0U7/L0fLN7/WdIPdZOU3rZYLEeaO0Z2POX5/lp+AHfYtkjpR25x4LS9qsPrSITdO0ZAht0fyl7qas7L91aSmWwY9i/VqoTfva6njLVmzaLMO2cF1hwypEKw0ksNw2A8rlu8Bqe2y/74w3L49k0xncPOApOXHQG7UeuNPLwtNrnLx4kUBQPzwww9W05999lkRHR3t8PX2QtOXX34pPvjgA/Hjjz+KnTt3in79+omWLVuKoqIiu8uS6gfF0ETVlbcPDupKtWlbhajCkGgTpBT1a0uWuW2QxYCsDkeDLj+JxnU+Jn/z4DghX6tmj0SfM6nXSl7NKdVfzV4ws1yXXHOsbdCzuc+l+WpOqQAntQ6l+8Ei/Fluawf8LNOhv7zJzl4/QTvbZfX+MV1FZ7ryTq785b/nzFhldSwWt/lPeZAqK6+9tAxQXhiaTp06JaZNmyaGDh0qhg4dKqZPny5OnTqlahnuCk22/ve//4mAgADx9ttv252HNU1U03hz521Xq03b6smQqPjm1k40KUuFK5fcn0yKVJ8zpVdzyvVXc/Rae8/ZBhyJssgOx2G5DhcER9l7UGqN93GUvKDBwXapuhhCqo+dbbg03fMuOE106GD5f+FloWnnzp3Cx8dHREdHi1mzZolZs2aJ6Oho4evrK7755hvFy3FX85yUXr16iUQVX8HYp4lqAm/tvO0OtWlba0pIdHTMakUtoqv7xClZnlRAcaI5VjacqbjBruR22YYme+GyPPRZBz0vC03dunUTzz33XIXpzz33nFMdwadNm2b+W6/XixYtWlSqI7itP/74QzRu3FisXLlScbkYmojIm9WWkFhTAqJXUTBuWoX9brrvZarFa9Re0KA0INo2zzmqCazQb8q952+NEEJABT8/Pxw7dgxRUVFW07Ozs9GlSxfcvHlT8bK2bduG8ePH4z//+Q+io6OxYsUKfPDBB/jll18QEhKCcePGoUWLFkhJSQEAlJaW4sSJEwCABx54AGPGjMGYMWPQoEEDREZGAgBmz56Nhx56CK1atcLvv/+O+fPn4+jRozhx4gSaNWumqFxFRUUIDAxEYWEhAgICFG8PERG51qlTwPr1wNmzQEQEMGkSUP5xT27ksf2+YAGg0wFJScpfs2gRNh7qjEmfjQRQBIPBjedvtSnrjjvuEB988EGF6du2bRPh4eGqU9uqVatEy5YtzU1++/btMz83aNAgMX78ePPfZ86ckeywPWjQIPM8o0aNEs2bNxc+Pj6iRYsWYtSoUar7W7GmiYiIqHrJyRFi1iwvq2lKTk7Gv//9byQmJqJ///4AgL1792LJkiVISEhAkpp06KVY00RERFT9uPv8rTo0CSGwYsUKvPbaa/j9998BAGFhYXj22Wfx9NNPQ6PRuLyQVc3ZnZ6TA2zYcLs6c+JEwKYVk4iIiNzE60KTpT/++AMA0LBhQ5cVyBs4s9NTU4HJkwGNxtgVzfRz/XpgwgT3lpeIiIjcH5q0lXlxw4YNa1xgckZOjjEwGQyAXm/9c9IkY4c6IiIiqt4qFZrIaMMGY82SFI3GWNtERERE1RtDkwucPWtsipMihPF5IiIiqt4YmlwgIkK+pikioipLQ0RERO6gOjT9+uuv7ihHtTZxonxN06RJVVseIiIicj3VoSkyMhL33nsv3nvvPVWjf9dkUVHGfktarXEgU8uf69dz9FoiIqKaQHVoOnz4MLp06YKEhASEhobiiSeewP79+91RtmplwgTg5Eng2WeBv//d+PPkSQ43QEREVFM4PU7TrVu38Omnn2Ljxo3YuXMn7rzzTkycOBFjx45VfI83b8URwYmIiKofrx2nqU6dOnj00Ufx4YcfYsmSJTh16hRmz56N8PBwjBs3Drm5ua4sJxEREZFHOR2aDh48iKeeegrNmzfH8uXLMXv2bJw+fRq7du3C77//jhEjRriynEREREQeVUftC5YvX47U1FScPHkSDzzwAN555x088MAD0GqN+at169bYuHEjInidPREREdUgqkPT2rVrMXHiREyYMAHNmzeXnCc4OBjrOQw2ERER1SCqO4KfPXsWLVu2NNcsmQghcP78ebRs2dKlBfQEdgQnIiKqfryuI3jbtm1x5cqVCtOvXbuG1q1bu6RQRERERN5GdWiyVzF1/fp1+Pn5VbpARERERN5IcZ+mhIQEAIBGo8G8efPg7+9vfk6v1yMzMxPdunVzeQGJiIiIvIHi0HTkyBEAxpqmY8eOwcfHx/ycj48PunbtitmzZ7u+hEREREReQHFo2r17NwAgPj4eK1euZAdpIiIiqlVUDzmQmprqjnIQEREReTVFoenRRx/Fxo0bERAQgEcffVR23u3bt7ukYERERETeRFFoCgwMhEajMf9OREREVNuoHtyyNuDglkRERNWP1w1uSURERFQbKWqe6969u7l5zpHDhw9XqkBERERE3khRaBo5cqSbi0FERETk3dinSQL7NBEREVU/7j5/qx6nyeTgwYPIysoCAHTs2BE9e/Z0WaGIiIiIvI3q0HThwgWMHj0ae/fuRaNGjQAABQUF6N+/P7Zu3Yo77rjD1WUkIiIi8jjVV89NnjwZZWVlyMrKwrVr13Dt2jVkZWXBYDBg8uTJ7igjERERkcep7tNUr149/PDDD+jevbvV9EOHDmHgwIG4ceOGSwvoCezTREREVP143ThN4eHhKCsrqzBdr9cjLCzMJYUiIiIi8jaqQ9OyZcswffp0HDx40Dzt4MGDmDFjBl599VWXFo6IiIjIWyhqnmvcuLHV4JbFxcW4desW6tQx9iM3/V6/fn1cu3bNfaWtImyeIyIiqn68YsiBFStWuHzFRERERNWJotA0fvx4d5eDiIiIyKs5PbglANy8eROlpaVW09icRURERDWR6o7gxcXFmDZtGoKDg1G/fn00btzY6kFERERUE6kOTXPmzMF3332HtWvXwtfXF2+//TYWLlyIsLAwvPPOO6oLsGbNGkRERMDPzw99+vTB/v377c77888/47HHHkNERAQ0Go3dvlZqlklERESkhOrQ9Nlnn+GNN97AY489hjp16mDgwIF48cUX8corr+D9999Xtaxt27YhISEB8+fPx+HDh9G1a1fExsbi0qVLkvPfuHEDbdq0weLFixEaGuqSZRIREREpoTo0Xbt2DW3atAFg7L9kGmJgwIAB+O9//6tqWcuXL8c///lPxMfHo2PHjli3bh38/f2xYcMGyfl79+6NZcuWIS4uDr6+vi5ZJhEREZESqkNTmzZtcObMGQBA+/bt8cEHHwAw1kCZbuCrRGlpKQ4dOoSYmJjbhdFqERMTg4yMDLXFqtQyS0pKUFRUZPUgIiIisqQ6NMXHx+PHH38EACQmJmLNmjXw8/PDrFmz8OyzzypezpUrV6DX6xESEmI1PSQkBHl5eWqLVallpqSkIDAw0PwIDw93av1ERERUc6kecmDWrFnm32NiYpCVlYXDhw8jMjISXbp0cWnhqsrcuXORkJBg/ruoqIjBiYiIiKxUapwmAIiIiEBERITq1wUFBUGn0yE/P99qen5+vt1O3u5apq+vr90+UkRERESAE81zAJCWloYHH3wQbdu2Rdu2bfHggw/i22+/VbUMHx8f9OzZE2lpaeZpBoMBaWlp6NevnzPFcssyiYiIiAAnQtMbb7yBYcOGoWHDhpgxYwZmzJiBgIAAPPDAA1izZo2qZSUkJOCtt97Cpk2bkJWVhSeffBLFxcWIj48HAIwbNw5z5841z19aWoqjR4/i6NGjKC0txcWLF3H06FGcOnVK8TKJiIiInCJUatGihVi1alWF6atXrxZhYWFqFydWrVolWrZsKXx8fER0dLTYt2+f+blBgwaJ8ePHm/8+c+aMAFDhMWjQIMXLVKKwsFAAEIWFhaq3h4iIiDzD3edvjRBCqAlZDRo0wNGjRxEZGWk1PScnB927d8f169ddk+Y8qKioCIGBgSgsLOS99IiIiKoJd5+/VTfPPfzww/j4448rTP/kk0/w4IMPuqRQRERERN5G0dVzr7/+uvn3jh074uWXX0Z6erq5c/W+ffuwd+9ePPPMM+4pJREREZGHKWqea926tbKFaTT49ddfK10oT2PzHBERUfXj7vO3opom021TiIiIiGorp8ZpMhFCQGU/ciIiIqJqyanQ9M4776Bz586oV68e6tWrhy5duuDdd991ddmIiIiIvIbq26gsX74cSUlJmDZtGu6++24AwJ49e/Cvf/0LV65csbo3HREREVFNoXqcptatW2PhwoUYN26c1fRNmzZhwYIFNaL/EzuCExERVT9eN05Tbm4u+vfvX2F6//79kZub65JCEREREXkb1aEpMjISH3zwQYXp27ZtQ1RUlEsKRURERORtVPdpWrhwIUaNGoX//ve/5j5Ne/fuRVpammSYIiIiIqoJVNc0PfbYY9i/fz+CgoKwY8cO7NixA0FBQdi/fz8eeeQRd5SRiIiIyONU1TSVlZXhiSeeQFJSEt577z13lYmIiIjI66iqaapbty4++ugjd5WFiIiIyGupbp4bOXIkduzY4YaiEBEREXkv1R3Bo6KikJycjL1796Jnz56oX7++1fNPP/20ywpHRERE5C2cGtzS7sI0Gvz666+VLpSncXBLIiKi6sfd52/VNU01YcRvIiIiIrWcumGviRACKiuqiIiIiKolp0LT+vXr0alTJ/j5+cHPzw+dOnXC22+/7eqyEREREXkN1c1z8+bNw/LlyzF9+nT069cPAJCRkYFZs2bh3LlzSE5OdnkhiYiIiDxNdUfwZs2a4fXXX8fo0aOtpm/ZsgXTp0/HlStXXFpAT2BHcCIiourH3edv1c1zZWVl6NWrV4XpPXv2xK1bt1xSKCIiIiJvozo0jR07FmvXrq0w/c0338SYMWNcUigiIiIib6O6TxNg7Aj+zTffoG/fvgCAzMxMnDt3DuPGjUNCQoJ5vuXLl7umlEREREQepjo0HT9+HD169AAAnD59GgAQFBSEoKAgHD9+3DyfRqNxURGJiIiIPE91aNq9e7c7ykFERETk1So1uCURERFRbcHQRERERKQAQxMRERGRAgxNRERERAowNBEREREpwNBEREREpABDExEREZECDE1ERERECjA0ERERESnA0ERERESkAEMTERERkQIMTUREREQKeEVoWrNmDSIiIuDn54c+ffpg//79svN/+OGHaN++Pfz8/NC5c2d8+eWXVs9PmDABGo3G6jFs2DB3bgIRERHVcB4PTdu2bUNCQgLmz5+Pw4cPo2vXroiNjcWlS5ck5//hhx8wevRoTJo0CUeOHMHIkSMxcuRIHD9+3Gq+YcOGITc31/zYsmVLVWwOERER1VAaIYTwZAH69OmD3r17Y/Xq1QAAg8GA8PBwTJ8+HYmJiRXmHzVqFIqLi/H555+bp/Xt2xfdunXDunXrABhrmgoKCrBjxw6nylRUVITAwEAUFhYiICDAqWUQERFR1XL3+dujNU2lpaU4dOgQYmJizNO0Wi1iYmKQkZEh+ZqMjAyr+QEgNja2wvzp6ekIDg5Gu3bt8OSTT+Lq1at2y1FSUoKioiKrBxEREZElj4amK1euQK/XIyQkxGp6SEgI8vLyJF+Tl5fncP5hw4bhnXfeQVpaGpYsWYLvv/8e999/P/R6veQyU1JSEBgYaH6Eh4dXcsuIiIiopqnj6QK4Q1xcnPn3zp07o0uXLmjbti3S09MxdOjQCvPPnTsXCQkJ5r+LiooYnIiIiMiKR2uagoKCoNPpkJ+fbzU9Pz8foaGhkq8JDQ1VNT8AtGnTBkFBQTh16pTk876+vggICLB6EBEREVnyaGjy8fFBz549kZaWZp5mMBiQlpaGfv36Sb6mX79+VvMDwK5du+zODwAXLlzA1atX0bx5c9cUnIiIiGodjw85kJCQgLfeegubNm1CVlYWnnzySRQXFyM+Ph4AMG7cOMydO9c8/4wZM7Bz50689tpr+OWXX7BgwQIcPHgQ06ZNAwBcv34dzz77LPbt24ezZ88iLS0NI0aMQGRkJGJjYz2yjURERFT9ebxP06hRo3D58mXMmzcPeXl56NatG3bu3Gnu7H3u3DlotbezXf/+/bF582a8+OKLeP755xEVFYUdO3agU6dOAACdToeffvoJmzZtQkFBAcLCwnDfffdh0aJF8PX19cg2EhERUfXn8XGavBHHaSIiIqp+avQ4TURERETVBUMTERERkQIMTUREREQKMDQRERERKcDQRERERKQAQxMRERGRAgxNRERERAowNBEREREpwNBEREREpABDExEREZECDE1ERERECjA0ERERESnA0ERERESkAEMTERERkQIMTUREREQKMDQRERERKcDQRERERKQAQxMRERGRAgxNRERERAowNBEREREpwNBEREREpABDExEREZECDE1ERERECjA0ERERESnA0ERERESkAEMTERERkQIMTUREREQKMDQRERERKcDQRERERKQAQxMRERGRAgxNRERERAowNBEREREpwNBEREREpABDExEREZECDE1ERERECjA0ERERESnA0OQKixYBCxZ4uhRERETkRgxNlbVoETBvHqDTebokRERE5EYMTXKWLJF/3hSYkpOBpKSqKRMRERF5hFeEpjVr1iAiIgJ+fn7o06cP9u/fLzv/hx9+iPbt28PPzw+dO3fGl19+afW8EALz5s1D8+bNUa9ePcTExCAnJ0d9wV55BVi0CDk5wNy5wOjRxp85OWBgIiIiqmU8Hpq2bduGhIQEzJ8/H4cPH0bXrl0RGxuLS5cuSc7/ww8/YPTo0Zg0aRKOHDmCkSNHYuTIkTh+/Lh5nqVLl+L111/HunXrkJmZifr16yM2NhY3b95UV7jnn0fqvF/Rvp0By5YBH3wALFsGtG9nwMZ5pxmYiIiIahGNEEJ4sgB9+vRB7969sXr1agCAwWBAeHg4pk+fjsTExArzjxo1CsXFxfj888/N0/r27Ytu3bph3bp1EEIgLCwMzzzzDGbPng0AKCwsREhICDZu3Ii4uDiHZSoqKkJgYCAOHy5Er54NYBC22VJAqxE4ma1FZKTz205ERESuYzp/FxYWIiAgwOXL92hNU2lpKQ4dOoSYmBjzNK1Wi5iYGGRkZEi+JiMjw2p+AIiNjTXPf+bMGeTl5VnNExgYiD59+thdZklJCYqKiqweAPDuu4BGK7WLNNBotVi/Xs3WEhERUXXm0dB05coV6PV6hISEWE0PCQlBXl6e5Gvy8vJk5zf9VLPMlJQUBAYGmh/h4eEAgHPnAHv1cEIAZ8/Kbh4RERHVIB7v0+QN5s6di8LCQvPj/PnzAICWLQGNRvo1Gg0QEVF1ZSQiIiLP8mhoCgoKgk6nQ35+vtX0/Px8hIaGSr4mNDRUdn7TTzXL9PX1RUBAgNUDAMaOBYTBAMC2uklAGAyYNEnJVhIREVFN4NHQ5OPjg549eyItLc08zWAwIC0tDf369ZN8Tb9+/azmB4Bdu3aZ52/dujVCQ0Ot5ikqKkJmZqbdZdrT9v+WYL2YCK1GQKcDtFrjGJZajcB6MRGRWxapWh4RERFVX3U8XYCEhASMHz8evXr1QnR0NFasWIHi4mLEx8cDAMaNG4cWLVogJSUFADBjxgwMGjQIr732GoYPH46tW7fi4MGDePPNNwEAGo0GM2fOxEsvvYSoqCi0bt0aSUlJCAsLw8iRI9UV7pVXMCE5GQNGGzt9nz1rbJKbNEmLyC1tjeM0ARx2gIiIqBbweGgaNWoULl++jHnz5iEvLw/dunXDzp07zR25z507B63FFWz9+/fH5s2b8eKLL+L5559HVFQUduzYgU6dOpnnmTNnDoqLizFlyhQUFBRgwIAB2LlzJ/z8/NQV7vnngaQkRAIoz2y3mYISgxMREVGt4PFxmryRqnEeODI4ERGRV3D3OE0er2mq9kxBSa/3bDmIiIjIrRiaXIE1TERERDUex2kiIiIiUoChiYiIiEgBhiYiIiIiBRiaiIiIiBRgaCIiIiJSgKGJiIiISAGGJiIiIiIFOE6TBNMg6UVFRR4uCRERESllOm+762YnDE0Srl69CgAIDw/3cEmIiIhIratXryIwMNDly2VoktCkSRMAxpsFu2Onk3JFRUUIDw/H+fPn3XIfIVKOx8K78Hh4Dx4L71FYWIiWLVuaz+OuxtAkQas1dvUKDAzkP4CXCAgI4LHwEjwW3oXHw3vwWHgP03nc5ct1y1KJiIiIahiGJiIiIiIFGJok+Pr6Yv78+fD19fV0UWo9HgvvwWPhXXg8vAePhfdw97HQCHddl0dERERUg7CmiYiIiEgBhiYiIiIiBRiaiIiIiBRgaCIiIiJSgKFJwpo1axAREQE/Pz/06dMH+/fv93SRarSUlBT07t0bDRs2RHBwMEaOHImTJ09azXPz5k1MnToVTZs2RYMGDfDYY48hPz/fQyWuPRYvXgyNRoOZM2eap/FYVK2LFy/iH//4B5o2bYp69eqhc+fOOHjwoPl5IQTmzZuH5s2bo169eoiJiUFOTo4HS1wz6fV6JCUloXXr1qhXrx7atm2LRYsWWd3jjMfCPf773//ioYceQlhYGDQaDXbs2GH1vJL9fu3aNYwZMwYBAQFo1KgRJk2ahOvXr6suC0OTjW3btiEhIQHz58/H4cOH0bVrV8TGxuLSpUueLlqN9f3332Pq1KnYt28fdu3ahbKyMtx3330oLi42zzNr1ix89tln+PDDD/H999/j999/x6OPPurBUtd8Bw4cwH/+8x906dLFajqPRdX53//+h7vvvht169bFV199hRMnTuC1115D48aNzfMsXboUr7/+OtatW4fMzEzUr18fsbGxuHnzpgdLXvMsWbIEa9euxerVq5GVlYUlS5Zg6dKlWLVqlXkeHgv3KC4uRteuXbFmzRrJ55Xs9zFjxuDnn3/Grl278Pnnn+O///0vpkyZor4wgqxER0eLqVOnmv/W6/UiLCxMpKSkeLBUtculS5cEAPH9998LIYQoKCgQdevWFR9++KF5nqysLAFAZGRkeKqYNdoff/whoqKixK5du8SgQYPEjBkzhBA8FlXtueeeEwMGDLD7vMFgEKGhoWLZsmXmaQUFBcLX11ds2bKlKopYawwfPlxMnDjRatqjjz4qxowZI4TgsagqAMTHH39s/lvJfj9x4oQAIA4cOGCe56uvvhIajUZcvHhR1fpZ02ShtLQUhw4dQkxMjHmaVqtFTEwMMjIyPFiy2qWwsBDA7RsnHzp0CGVlZVbHpX379mjZsiWPi5tMnToVw4cPt9rnAI9FVfv000/Rq1cv/O1vf0NwcDC6d++Ot956y/z8mTNnkJeXZ3U8AgMD0adPHx4PF+vfvz/S0tKQnZ0NAPjxxx+xZ88e3H///QB4LDxFyX7PyMhAo0aN0KtXL/M8MTEx0Gq1yMzMVLU+3rDXwpUrV6DX6xESEmI1PSQkBL/88ouHSlW7GAwGzJw5E3fffTc6deoEAMjLy4OPjw8aNWpkNW9ISAjy8vI8UMqabevWrTh8+DAOHDhQ4Tkei6r166+/Yu3atUhISMDzzz+PAwcO4Omnn4aPjw/Gjx9v3udSn1k8Hq6VmJiIoqIitG/fHjqdDnq9Hi+//DLGjBkDADwWHqJkv+fl5SE4ONjq+Tp16qBJkyaqjw1DE3mVqVOn4vjx49izZ4+ni1IrnT9/HjNmzMCuXbvg5+fn6eLUegaDAb169cIrr7wCAOjevTuOHz+OdevWYfz48R4uXe3ywQcf4P3338fmzZtx11134ejRo5g5cybCwsJ4LGoRNs9ZCAoKgk6nq3AlUH5+PkJDQz1Uqtpj2rRp+Pzzz7F7927ccccd5umhoaEoLS1FQUGB1fw8Lq536NAhXLp0CT169ECdOnVQp04dfP/993j99ddRp04dhISE8FhUoebNm6Njx45W0zp06IBz584BgHmf8zPL/Z599lkkJiYiLi4OnTt3xtixYzFr1iykpKQA4LHwFCX7PTQ0tMLFXLdu3cK1a9dUHxuGJgs+Pj7o2bMn0tLSzNMMBgPS0tLQr18/D5asZhNCYNq0afj444/x3XffoXXr1lbP9+zZE3Xr1rU6LidPnsS5c+d4XFxs6NChOHbsGI4ePWp+9OrVC2PGjDH/zmNRde6+++4Kw29kZ2ejVatWAIDWrVsjNDTU6ngUFRUhMzOTx8PFbty4Aa3W+pSp0+lgMBgA8Fh4ipL93q9fPxQUFODQoUPmeb777jsYDAb06dNH3Qor1Y29Btq6davw9fUVGzduFCdOnBBTpkwRjRo1Enl5eZ4uWo315JNPisDAQJGeni5yc3PNjxs3bpjn+de//iVatmwpvvvuO3Hw4EHRr18/0a9fPw+WuvawvHpOCB6LqrR//35Rp04d8fLLL4ucnBzx/vvvC39/f/Hee++Z51m8eLFo1KiR+OSTT8RPP/0kRowYIVq3bi3+/PNPD5a85hk/frxo0aKF+Pzzz8WZM2fE9u3bRVBQkJgzZ455Hh4L9/jjjz/EkSNHxJEjRwQAsXz5cnHkyBHx22+/CSGU7fdhw4aJ7t27i8zMTLFnzx4RFRUlRo8erbosDE0SVq1aJVq2bCl8fHxEdHS02Ldvn6eLVKMBkHykpqaa5/nzzz/FU089JRo3biz8/f3FI488InJzcz1X6FrENjTxWFStzz77THTq1En4+vqK9u3bizfffNPqeYPBIJKSkkRISIjw9fUVQ4cOFSdPnvRQaWuuoqIiMWPGDNGyZUvh5+cn2rRpI1544QVRUlJinofHwj12794teY4YP368EELZfr969aoYPXq0aNCggQgICBDx8fHijz/+UF0WjRAWw5kSERERkST2aSIiIiJSgKGJiIiISAGGJiIiIiIFGJqIiIiIFGBoIiIiIlKAoYmIiIhIAYYmIiIiIgUYmojIKw0ePBgzZ870dDHMhBCYMmUKmjRpAo1Gg6NHj7ptXREREVixYoXblk9Ezqnj6QIQEVUHO3fuxMaNG5Geno42bdogKCjIbes6cOAA6tev77blE5FzGJqIqNbQ6/XQaDQVbryqxOnTp9G8eXP079/fDSWz1qxZM9nny8rKULduXbeXg4issXmOiOwaPHgwnn76acyZMwdNmjRBaGgoFixYYH7+7NmzFZqqCgoKoNFokJ6eDgBIT0+HRqPB119/je7du6NevXoYMmQILl26hK+++godOnRAQEAAHn/8cdy4ccNq/bdu3cK0adMQGBiIoKAgJCUlwfLOTyUlJZg9ezZatGiB+vXro0+fPub1AsDGjRvRqFEjfPrpp+jYsSN8fX1x7tw5yW39/vvvER0dDV9fXzRv3hyJiYm4desWAGDChAmYPn06zp07B41Gg4iICMllmNa3Y8cOREVFwc/PD7GxsTh//rx5ntOnT2PEiBEICQlBgwYN0Lt3b3z77bdWy7FtntNoNFi7di0efvhh1K9fHy+//DL+97//YcyYMWjWrBnq1auHqKgopKamSpaLiFyDoYmIZG3atAn169dHZmYmli5diuTkZOzatUv1chYsWIDVq1fjhx9+wPnz5/H3v/8dK1aswObNm/HFF1/gm2++wapVqyqsu06dOti/fz9WrlyJ5cuX4+233zY/P23aNGRkZGDr1q346aef8Le//Q3Dhg1DTk6OeZ4bN25gyZIlePvtt/Hzzz8jODi4QtkuXryIBx54AL1798aPP/6ItWvXYv369XjppZcAACtXrkRycjLuuOMO5Obm4sCBA3a388aNG3j55ZfxzjvvYO/evSgoKEBcXJz5+evXr+OBBx5AWloajhw5gmHDhuGhhx6yG+Ys998jjzyCY8eOYeLEiUhKSsKJEyfw1VdfISsrC2vXrnVrkyERAajs3YeJqOYaNGiQGDBggNW03r17i+eee04IIcSZM2cEAHHkyBHz8//73/8EALF7924hxO07lH/77bfmeVJSUgQAcfr0afO0J554QsTGxlqtu0OHDsJgMJinPffcc6JDhw5CCCF+++03odPpxMWLF63KN3ToUDF37lwhhBCpqakCgDh69Kjsdj7//POiXbt2Vutas2aNaNCggdDr9UIIIf7973+LVq1ayS7HtL59+/aZp2VlZQkAIjMz0+7r7rrrLrFq1Srz361atRL//ve/zX8DEDNnzrR6zUMPPSTi4+Nly0NErsWaJiKS1aVLF6u/mzdvjkuXLlVqOSEhIfD390ebNm2sptkut2/fvtBoNOa/+/Xrh5ycHOj1ehw7dgx6vR533nknGjRoYH58//33OH36tPk1Pj4+FbbBVlZWFvr162e1rrvvvhvXr1/HhQsXVG1nnTp10Lt3b/Pf7du3R6NGjZCVlQXAWNM0e/ZsdOjQAY0aNUKDBg2QlZXlsKapV69eVn8/+eST2Lp1K7p164Y5c+bghx9+UFVOIlKPHcGJSJZth2ONRgODwQAA5g7VwqKfUVlZmcPlaDQa2eUqcf36deh0Ohw6dAg6nc7quQYNGph/r1evnlUY8rTZs2dj165dePXVVxEZGYl69erhr3/9K0pLS2VfZ3s13f3334/ffvsNX375JXbt2oWhQ4di6tSpePXVV91ZfKJajTVNROQ001Veubm55mmuHL8oMzPT6u99+/YhKioKOp0O3bt3h16vx6VLlxAZGWn1CA0NVbWeDh06ICMjwyr87d27Fw0bNsQdd9yhalm3bt3CwYMHzX+fPHkSBQUF6NChg3m5EyZMwCOPPILOnTsjNDQUZ8+eVbUOk2bNmmH8+PF47733sGLFCrz55ptOLYeIlGFoIiKn1atXD3379sXixYuRlZWF77//Hi+++KLLln/u3DkkJCTg5MmT2LJlC1atWoUZM2YAAO68806MGTMG48aNw/bt23HmzBns378fKSkp+OKLL1St56mnnsL58+cxffp0/PLLL/jkk08wf/58JCQkqB6eoG7dupg+fToyMzNx6NAhTJgwAX379kV0dDQAICoqCtu3b8fRo0fx448/4vHHH1dVw2Yyb948fPLJJzh16hR+/vlnfP755+ZgRkTuwdBERJWyYcMG3Lp1Cz179sTMmTPNV5y5wrhx4/Dnn38iOjoaU6dOxYwZMzBlyhTz86mpqRg3bhyeeeYZtGvXDiNHjsSBAwfQsmVLVetp0aIFvvzyS+zfvx9du3bFv/71L0yaNMmpAOjv74/nnnsOjz/+OO6++240aNAA27ZtMz+/fPlyNG7cGP3798dDDz2E2NhY9OjRQ/V6fHx8MHfuXHTp0gX33HMPdDodtm7dqno5RKScRljWRxMRkdM2btyImTNnoqCgwNNFISI3YE0TERERkQIMTUREREQKsHmOiIiISAHWNBEREREpwNBEREREpABDExEREZECDE1ERERECjA0ERERESnA0ERERESkAEMTERERkQIMTUREREQKMDQRERERKfD/AaknjQFLEXIZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res[0],res[3],'x',ms=10,color='red',label='analytic')  \n",
    "plt.plot(res3[0],res3[1],'o',ms=5,color='blue',label='Monte Carlo') \n",
    "#plt.plot(res2[0],res2[1],'o',ms=5,color='blue',label='Monte Carlo 10000')  \n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"number of pairs\")\n",
    "plt.ylabel(\"probablity of perfectly mixed\")\n",
    "plt.xlim(0,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1d59829a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9995687119214739\n",
      "0.03360270579623273\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(res2[1,1:100]/res3[1,1:100]))\n",
    "print(np.std(res2[1,1:100]/res3[1,1:100]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "cdc33cc1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_6405/3383112364.py:1: RuntimeWarning: invalid value encountered in divide\n",
      "  plt.plot(res3[0],res[3,0:999]/res3[1],'o',ms=8,color='blue',label='analytic/Monte Carlo')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 1000.0)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res3[0],res[3,0:999]/res3[1],'o',ms=8,color='blue',label='analytic/Monte Carlo') \n",
    "#plt.plot(res2[0],res2[1],'o',ms=5,color='blue',label='Monte Carlo 10000')  \n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"number of pairs\")\n",
    "plt.ylabel(\"probablity of perfectly mixed\")\n",
    "plt.xlim(0,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "7e56473d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_6405/4121775268.py:1: RuntimeWarning: invalid value encountered in divide\n",
      "  plt.plot(res3[0],res[3,0:999]/res3[1],'o',ms=8,color='blue',label='analytic/Monte Carlo')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.9, 1.1)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res3[0],res[3,0:999]/res3[1],'o',ms=8,color='blue',label='analytic/Monte Carlo') \n",
    "#plt.plot(res2[0],res2[1],'o',ms=5,color='blue',label='Monte Carlo 10000')  \n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"number of pairs\")\n",
    "plt.ylabel(\"probablity of perfectly mixed\")\n",
    "plt.xlim(50,1000)\n",
    "plt.ylim(0.9,1.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d509e27",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}