tutorial-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Imports**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## import essential modules \n",
    "import qumcmc \n",
    "from qumcmc.basic_utils import *\n",
    "# from qumcmc.energy_models import IsingEnergyFunction\n",
    "from qumcmc.energy_models import IsingEnergyFunction, Exact_Sampling\n",
    "\n",
    "from qumcmc.classical_mcmc_routines import classical_mcmc\n",
    "from qumcmc.quantum_mcmc_routines_qulacs import quantum_enhanced_mcmc     #for Qulacs Simulator backend (** Faster )\n",
    "# from qumcmc.quantum_mcmc_routines_qiskit import quantum_enhanced_mcmc   #for qiskit Aer's Simulator backend \n",
    "\n",
    "from qumcmc.trajectory_processing import calculate_running_js_divergence, calculate_running_kl_divergence, calculate_runnning_magnetisation, get_trajectory_statistics\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Define the Energy Model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "### class to generate BAS dataset of arbitrary gridsize.\n",
    "from itertools import permutations, product\n",
    "class bas_dataset:\n",
    "    def __init__(self, grid_size:int):\n",
    "        self.grid_size=grid_size\n",
    "        all_combn=[''.join(p) for p in product('01',repeat=self.grid_size)]\n",
    "        all_combn.sort(key=lambda s: s.count('1'))\n",
    "        all_combn.pop(0);all_combn.pop(-1)\n",
    "        self.__all_combn=all_combn\n",
    "        self.bas_dict=self.bars_and_stripes_dataset()\n",
    "        self.dataset= self.bas_dict['stripes']+self.bas_dict['bars'] + self.bas_dict.get(\"both\", [])\n",
    "    \n",
    "    def vertical_stripes(self):\n",
    "        vert_stripes=[j*self.grid_size for j in self.__all_combn]\n",
    "        return vert_stripes\n",
    "\n",
    "    def horizontal_bars(self):\n",
    "        hor_bars=[]\n",
    "        for l in self.__all_combn:\n",
    "            st=\"\"\n",
    "            for j in l:\n",
    "                st=st+j*self.grid_size\n",
    "            hor_bars.append(st)\n",
    "        return hor_bars\n",
    "\n",
    "    def bars_and_stripes_dataset(self):\n",
    "        bas_dict={'stripes':self.vertical_stripes(),\n",
    "                  'bars':self.horizontal_bars(),\n",
    "                  # \"both\": [\"0\"*self.grid_size*self.grid_size, \"1\"*self.grid_size*self.grid_size]\n",
    "                 }\n",
    "        return bas_dict\n",
    "\n",
    "    ### create matrix of bitstring: meant for plotting\n",
    "    def bit_string_to_2d_matrix(self,bitstring, array_shape:int):\n",
    "        len_bs=len(bitstring)\n",
    "        list_bs_int=[eval(i) for i in list(bitstring)]\n",
    "        arr_bs=np.reshape(list_bs_int,(array_shape, array_shape))\n",
    "        return arr_bs\n",
    "\n",
    "    ### plot pixels\n",
    "    def draw_pixelplot(self,bitstring:str,array_shape:int):\n",
    "        im_array=self.bit_string_to_2d_matrix(bitstring,array_shape)\n",
    "        plt.title(f\"pixel plot for bitstring: {bitstring}\")\n",
    "        pixel_plot=plt.imshow(im_array,cmap='Greens',interpolation='nearest')\n",
    "        plt.colorbar(pixel_plot)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hebbing_learning(list_bas_state:list):\n",
    "    size=len(list_bas_state[0])\n",
    "    wts=0\n",
    "    for i in list_bas_state:\n",
    "        arr=np.array([-1 if elem == \"0\" else 1 for elem in i])\n",
    "        array=np.reshape(arr,(size,1));array_t=np.transpose(array)\n",
    "        wts+=array@array_t\n",
    "    wts=wts-len(list_bas_state)*np.identity(size)\n",
    "    return wts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "gridsize=3\n",
    "bas=bas_dataset(grid_size=gridsize)\n",
    "wt=hebbing_learning(bas.dataset)\n",
    "# np.shape(wt);wt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the model\n",
    "np.random.seed(610358)# should always be in the same cell!  ## best seed -> 610358\n",
    "n_spins = gridsize*gridsize\n",
    "\n",
    "## construct problem Hamiltonian ##\n",
    "shape_of_J=(n_spins,n_spins)\n",
    "\n",
    "## defining J matrix (mutual 1-1 interaction)\n",
    "# J =  np.round(np.random.choice([+1, 0, -1], size=(n_spins, n_spins)), decimals=2) \n",
    "# J =  np.random.uniform(low= -2, high= 2, size= shape_of_J )\n",
    "# J = 0.5 * (J + J.transpose() )\n",
    "# J = np.round( J - np.diag(np.diag(J)) , decimals= 3)\n",
    "\n",
    "#evaluating J for BAS dataset\n",
    "J=-1*wt   #np.array([[0,0,0,4],[0,0,4,0],[0,4,0,0],[4,0,0,0]])\n",
    "# defining h\n",
    "#h = np.round(0.5 * np.random.randn(n_spins), decimals=2)\n",
    "#h = np.round(np.random.uniform(low= -1, high = 1, size= (n_spins)), decimals=2)\n",
    "h=np.zeros(np.shape(J)[0])\n",
    "# instantiate the model\n",
    "#model = IsingEnergyFunction(J, h, name= 'my_model')\n",
    "model=IsingEnergyFunction(J,h,name=f\"BAS data of gridsize {np.shape(J)[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0., -4., -4., -4.,  4.,  4., -4.,  4.,  4.],\n",
       "       [-4., -0., -4.,  4., -4.,  4.,  4., -4.,  4.],\n",
       "       [-4., -4., -0.,  4.,  4., -4.,  4.,  4., -4.],\n",
       "       [-4.,  4.,  4., -0., -4., -4., -4.,  4.,  4.],\n",
       "       [ 4., -4.,  4., -4., -0., -4.,  4., -4.,  4.],\n",
       "       [ 4.,  4., -4., -4., -4., -0.,  4.,  4., -4.],\n",
       "       [-4.,  4.,  4., -4.,  4.,  4., -0., -4., -4.],\n",
       "       [ 4., -4.,  4.,  4., -4.,  4., -4., -0., -4.],\n",
       "       [ 4.,  4., -4.,  4.,  4., -4., -4., -4., -0.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.get_J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n",
      "            MODEL : BAS data of gridsize 9\n",
      "=============================================\n",
      "Non-zero Interactions (J) : 36 / 36\n",
      "Non-zero Bias (h) : 0 / 9\n",
      "---------------------------------------------\n",
      "Average Interaction Strength <|J|> :  3.5555555555555554\n",
      "Average Bias Strength <|h|>:  0.0\n",
      "alpha :  0.125\n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.model_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## checking qulacs fn_qc_h1 term.\n",
    "# from qulacs.gate import Pauli,X\n",
    "# gate_x=X(2)\n",
    "# print(\"gate_x:\")\n",
    "# print(gate_x.get_matrix())\n",
    "# target_list=[2]\n",
    "# pauli_index=[1]\n",
    "# gate_2=Pauli(target_list,pauli_index)\n",
    "# print(\"gate_2\")\n",
    "# print(gate_2.get_matrix())\n",
    "# # these two are the same thing\n",
    "# multi_x_gate=Pauli([0,1],[2,1])\n",
    "# print(\"multi_x_gate\")\n",
    "# print(multi_x_gate.get_matrix())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Exact Analysis**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "## set current beta\n",
    "beta = 1#1.100209\n",
    "\n",
    "## run exact sampling over all possible configurations \n",
    "exact_sampled_model = Exact_Sampling(model, beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(['000000111',\n",
       "  '000111000',\n",
       "  '000111111',\n",
       "  '001001001',\n",
       "  '010010010',\n",
       "  '011011011',\n",
       "  '100100100',\n",
       "  '101101101',\n",
       "  '110110110',\n",
       "  '111000000',\n",
       "  '111000111',\n",
       "  '111111000'],\n",
       " 12)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bas.dataset.sort()\n",
    "bas.dataset,len(bas.dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n",
      "     MODEL : BAS data of gridsize 9 |  beta : 1\n",
      "=============================================\n",
      "Num Most Probable States : 102\n",
      "Entropy : 3.5849606926186035\n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1700x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## get the distribution from model\n",
    "bpd = exact_sampled_model.boltzmann_pd\n",
    "\n",
    "## exact sampling summary\n",
    "plt.figure(figsize=(17,10))\n",
    "\n",
    "exact_sampled_model.sampling_summary(show_threshold=1e-10)\n",
    "plt.yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Run Classical MCMC**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'000000111'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_state = bas.dataset[0]\n",
    "initial_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "steps = 10000\n",
    "cl_chain =classical_mcmc(\n",
    "    n_hops=steps,\n",
    "    model=model,\n",
    "    initial_state=initial_state,\n",
    "    # return_last_n_states=10,\n",
    "    temperature=1/beta,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "cl_statistic = get_trajectory_statistics(cl_chain, exact_sampled_model, verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Run Quantum Enhaned MCMC**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "steps = 10000\n",
    "qamcmc_chain_1 = quantum_enhanced_mcmc(\n",
    "    n_hops=steps,\n",
    "    initial_state=initial_state,\n",
    "    model=model,\n",
    "    temperature=1/beta\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "steps =10000\n",
    "qamcmc_chain_2 = quantum_enhanced_mcmc(\n",
    "    n_hops=steps,\n",
    "    initial_state=initial_state,\n",
    "    model=model,\n",
    "    temperature=1/beta,single_qubit_mixer=False, pauli_index_list=[1]*gridsize,\n",
    "    gamma_range= (0.01,0.1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "qumcm1_statistic = get_trajectory_statistics(qamcmc_chain_1, exact_sampled_model, verbose= False)\n",
    "qumcm2_statistic = get_trajectory_statistics(qamcmc_chain_2, exact_sampled_model, verbose= False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
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       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
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       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
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       " MCMCState(bitstring='0011', accepted=True),\n",
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       " MCMCState(bitstring='0011', accepted=True),\n",
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       " MCMCState(bitstring='0011', accepted=True),\n",
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       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " MCMCState(bitstring='0011', accepted=True),\n",
       " ...]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qamcmc_chain_1.states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Sampled Distributions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distributions_to_plot = [exact_sampled_model.boltzmann_pd, cl_chain.get_accepted_dict(normalize= True), \n",
    "                        qamcmc_chain_1.get_accepted_dict(normalize= True),qamcmc_chain_2.get_accepted_dict(normalize= True) ]\n",
    "plot_multiple_bargraphs(distributions_to_plot, ['Exact Distribution', 'Classical-Uniform', 'Quantum-Xi','Quantum-XiXi+1'], list_normalise= [False, False, False,False], plot_first_few=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({'000000111': 0.1040895910408959,\n",
       "         '011011011': 0.09319068093190681,\n",
       "         '001001001': 0.11768823117688232,\n",
       "         '101101101': 0.0836916308369163,\n",
       "         '111111000': 0.0695930406959304,\n",
       "         '111000111': 0.08999100089991001,\n",
       "         '111000000': 0.0608939106089391,\n",
       "         '010010010': 0.0932906709329067,\n",
       "         '100100100': 0.0898910108989101,\n",
       "         '000111000': 0.08339166083391661,\n",
       "         '110110110': 0.047995200479952004,\n",
       "         '000111111': 0.06629337066293371})"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qamcmc_chain_2.get_accepted_dict(normalize= True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qumcmc.prob_dist import kl_divergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'000000111': 0.08333326299889905,\n",
       " '000111000': 0.08333326299889905,\n",
       " '000111111': 0.08333326299889905,\n",
       " '001001001': 0.08333326299889905,\n",
       " '010010010': 0.08333326299889905,\n",
       " '011011011': 0.08333326299889905,\n",
       " '100100100': 0.08333326299889905,\n",
       " '101101101': 0.08333326299889905,\n",
       " '110110110': 0.08333326299889905,\n",
       " '111000000': 0.08333326299889905,\n",
       " '111000111': 0.08333326299889905,\n",
       " '111111000': 0.08333326299889905,\n",
       " '000001111': 9.377923311507073e-09,\n",
       " '000010111': 9.377923311507073e-09,\n",
       " '000011011': 9.377923311507073e-09,\n",
       " '000011111': 9.377923311507073e-09,\n",
       " '000100111': 9.377923311507073e-09,\n",
       " '000101101': 9.377923311507073e-09,\n",
       " '000101111': 9.377923311507073e-09,\n",
       " '000110110': 9.377923311507073e-09,\n",
       " '000110111': 9.377923311507073e-09,\n",
       " '000111001': 9.377923311507073e-09,\n",
       " '000111010': 9.377923311507073e-09,\n",
       " '000111011': 9.377923311507073e-09,\n",
       " '000111100': 9.377923311507073e-09,\n",
       " '000111101': 9.377923311507073e-09,\n",
       " '000111110': 9.377923311507073e-09,\n",
       " '001000111': 9.377923311507073e-09,\n",
       " '001001011': 9.377923311507073e-09,\n",
       " '001001101': 9.377923311507073e-09,\n",
       " '001001111': 9.377923311507073e-09,\n",
       " '001011001': 9.377923311507073e-09,\n",
       " '001011011': 9.377923311507073e-09,\n",
       " '001101001': 9.377923311507073e-09,\n",
       " '001101101': 9.377923311507073e-09,\n",
       " '001111000': 9.377923311507073e-09,\n",
       " '001111001': 9.377923311507073e-09,\n",
       " '010000111': 9.377923311507073e-09,\n",
       " '010010011': 9.377923311507073e-09,\n",
       " '010010110': 9.377923311507073e-09,\n",
       " '010010111': 9.377923311507073e-09,\n",
       " '010011010': 9.377923311507073e-09,\n",
       " '010011011': 9.377923311507073e-09,\n",
       " '010110010': 9.377923311507073e-09,\n",
       " '010110110': 9.377923311507073e-09,\n",
       " '010111000': 9.377923311507073e-09,\n",
       " '010111010': 9.377923311507073e-09,\n",
       " '011000011': 9.377923311507073e-09,\n",
       " '011000111': 9.377923311507073e-09,\n",
       " '011001001': 9.377923311507073e-09,\n",
       " '011001011': 9.377923311507073e-09,\n",
       " '011010010': 9.377923311507073e-09,\n",
       " '011010011': 9.377923311507073e-09,\n",
       " '011011000': 9.377923311507073e-09,\n",
       " '011011001': 9.377923311507073e-09,\n",
       " '011011010': 9.377923311507073e-09,\n",
       " '011111000': 9.377923311507073e-09,\n",
       " '100000111': 9.377923311507073e-09,\n",
       " '100100101': 9.377923311507073e-09,\n",
       " '100100110': 9.377923311507073e-09,\n",
       " '100100111': 9.377923311507073e-09,\n",
       " '100101100': 9.377923311507073e-09,\n",
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       " '110111011': 1.3365079474258814e-29,\n",
       " '110111101': 1.3365079474258814e-29,\n",
       " '111001110': 1.3365079474258814e-29,\n",
       " '111010101': 1.3365079474258814e-29,\n",
       " '111011100': 1.3365079474258814e-29,\n",
       " '111011101': 1.3365079474258814e-29,\n",
       " '111011110': 1.3365079474258814e-29,\n",
       " '111100011': 1.3365079474258814e-29,\n",
       " '111101010': 1.3365079474258814e-29,\n",
       " '111101011': 1.3365079474258814e-29,\n",
       " '111101110': 1.3365079474258814e-29,\n",
       " '111110001': 1.3365079474258814e-29,\n",
       " '111110011': 1.3365079474258814e-29,\n",
       " '111110101': 1.3365079474258814e-29,\n",
       " '001001110': 1.5040415537724992e-36,\n",
       " '001010101': 1.5040415537724992e-36,\n",
       " '001010110': 1.5040415537724992e-36,\n",
       " '001011100': 1.5040415537724992e-36,\n",
       " '001011110': 1.5040415537724992e-36,\n",
       " '001100011': 1.5040415537724992e-36,\n",
       " '001100110': 1.5040415537724992e-36,\n",
       " '001101010': 1.5040415537724992e-36,\n",
       " '001101110': 1.5040415537724992e-36,\n",
       " '001110001': 1.5040415537724992e-36,\n",
       " '001110010': 1.5040415537724992e-36,\n",
       " '001110011': 1.5040415537724992e-36,\n",
       " '001110100': 1.5040415537724992e-36,\n",
       " '001110101': 1.5040415537724992e-36,\n",
       " '001110110': 1.5040415537724992e-36,\n",
       " '010001101': 1.5040415537724992e-36,\n",
       " '010001110': 1.5040415537724992e-36,\n",
       " '010010101': 1.5040415537724992e-36,\n",
       " '010011100': 1.5040415537724992e-36,\n",
       " '010011101': 1.5040415537724992e-36,\n",
       " '010100011': 1.5040415537724992e-36,\n",
       " '010100101': 1.5040415537724992e-36,\n",
       " '010101001': 1.5040415537724992e-36,\n",
       " '010101010': 1.5040415537724992e-36,\n",
       " '010101011': 1.5040415537724992e-36,\n",
       " '010101100': 1.5040415537724992e-36,\n",
       " '010101101': 1.5040415537724992e-36,\n",
       " '010101110': 1.5040415537724992e-36,\n",
       " '010110001': 1.5040415537724992e-36,\n",
       " '010110101': 1.5040415537724992e-36,\n",
       " '011001100': 1.5040415537724992e-36,\n",
       " '011001110': 1.5040415537724992e-36,\n",
       " '011010100': 1.5040415537724992e-36,\n",
       " '011010101': 1.5040415537724992e-36,\n",
       " '011011100': 1.5040415537724992e-36,\n",
       " '011100001': 1.5040415537724992e-36,\n",
       " '011100010': 1.5040415537724992e-36,\n",
       " '011100011': 1.5040415537724992e-36,\n",
       " '011100100': 1.5040415537724992e-36,\n",
       " '011100101': 1.5040415537724992e-36,\n",
       " '011100110': 1.5040415537724992e-36,\n",
       " '011101010': 1.5040415537724992e-36,\n",
       " '011101100': 1.5040415537724992e-36,\n",
       " '011110001': 1.5040415537724992e-36,\n",
       " '011110100': 1.5040415537724992e-36,\n",
       " '100001011': 1.5040415537724992e-36,\n",
       " '100001110': 1.5040415537724992e-36,\n",
       " '100010011': 1.5040415537724992e-36,\n",
       " '100010101': 1.5040415537724992e-36,\n",
       " '100011001': 1.5040415537724992e-36,\n",
       " '100011010': 1.5040415537724992e-36,\n",
       " '100011011': 1.5040415537724992e-36,\n",
       " '100011100': 1.5040415537724992e-36,\n",
       " '100011101': 1.5040415537724992e-36,\n",
       " '100011110': 1.5040415537724992e-36,\n",
       " '100100011': 1.5040415537724992e-36,\n",
       " '100101010': 1.5040415537724992e-36,\n",
       " '100101011': 1.5040415537724992e-36,\n",
       " '100110001': 1.5040415537724992e-36,\n",
       " '100110011': 1.5040415537724992e-36,\n",
       " '101001010': 1.5040415537724992e-36,\n",
       " '101001110': 1.5040415537724992e-36,\n",
       " '101010001': 1.5040415537724992e-36,\n",
       " '101010010': 1.5040415537724992e-36,\n",
       " '101010011': 1.5040415537724992e-36,\n",
       " '101010100': 1.5040415537724992e-36,\n",
       " '101010101': 1.5040415537724992e-36,\n",
       " '101010110': 1.5040415537724992e-36,\n",
       " '101011010': 1.5040415537724992e-36,\n",
       " '101011100': 1.5040415537724992e-36,\n",
       " '101100010': 1.5040415537724992e-36,\n",
       " '101100011': 1.5040415537724992e-36,\n",
       " '101101010': 1.5040415537724992e-36,\n",
       " '101110001': 1.5040415537724992e-36,\n",
       " '101110010': 1.5040415537724992e-36,\n",
       " '110001001': 1.5040415537724992e-36,\n",
       " '110001010': 1.5040415537724992e-36,\n",
       " '110001011': 1.5040415537724992e-36,\n",
       " '110001100': 1.5040415537724992e-36,\n",
       " '110001101': 1.5040415537724992e-36,\n",
       " '110001110': 1.5040415537724992e-36,\n",
       " '110010001': 1.5040415537724992e-36,\n",
       " '110010101': 1.5040415537724992e-36,\n",
       " '110011001': 1.5040415537724992e-36,\n",
       " '110011100': 1.5040415537724992e-36,\n",
       " '110100001': 1.5040415537724992e-36,\n",
       " '110100011': 1.5040415537724992e-36,\n",
       " '110101001': 1.5040415537724992e-36,\n",
       " '110101010': 1.5040415537724992e-36,\n",
       " '110110001': 1.5040415537724992e-36,\n",
       " '001010100': 1.6925757903881418e-43,\n",
       " '001100010': 1.6925757903881418e-43,\n",
       " '010001100': 1.6925757903881418e-43,\n",
       " '010100001': 1.6925757903881418e-43,\n",
       " '011101110': 1.6925757903881418e-43,\n",
       " '011110101': 1.6925757903881418e-43,\n",
       " '100001010': 1.6925757903881418e-43,\n",
       " '100010001': 1.6925757903881418e-43,\n",
       " '101011110': 1.6925757903881418e-43,\n",
       " '101110011': 1.6925757903881418e-43,\n",
       " '110011101': 1.6925757903881418e-43,\n",
       " '110101011': 1.6925757903881418e-43}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exact_sampled_model.boltzmann_pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02704417245715795"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kl_divergence(exact_sampled_model.boltzmann_pd, qamcmc_chain_2.get_accepted_dict(normalize= True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Proposition Strategy Analysis**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we analyse the main adavnatge of the Quantum Enhanced MCMC routine, which is to propose transitions which are are more likely to be accepted when compared to usual classical proposition strategies. In the subsequent plots we compare statistics of all proposed transitions with respect to the *Acceptance-Probabilities* , *Energy-Difference*, and the *Hamming-Distance*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Acceptance-Probabilities**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G/QMVoY+gIjWtj6Smxsvnq/iKL46EVRPbthUIkH8BAACAow0DcwAAAACAhzgShrAlJibq/fc/re5mAAAAALUKR8IAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDjI4IAAAAwDWGYcg0DVdqu1XXbRwJqyaGYcjnM6vln2HUzs5anl27dmrhwvnau3dPdTfFcTfcMEY33zy5upvhmEcffVDDh59zxGXuu+8eDR06QPv37y81fffuNA0a1FePP/5IcFqfPt31wgtLJUnFxcW64opLdMMNY2TbpW+Cvm7du+rTp7s++OA9SdJnn32qPn2667vvvqnS81m8+BlNnny9/vCH/o7UAwAgEhmGoZi4KMlvuvLPMkzlFRTXus+3HAmrBoZhKKmOIQWKqqcBvihl5arMh9XaaNeunXr22afVu/fpql+/QXU3B1U0btwEvffeWj3xxCO67ba7g9Mffvg+JSUl6ZprxganzZv3rBo3biJJ8vv9uummW3XDDddq5coVOvvscyVJubm5euSR+9Wv3xnq3ft0SVL79h00b96zatmydZXa+s9//l1NmzZT9+499e67/65SLQAAIpVpGioKWFr29vdKz8x3vH79lFiNHHy8alkGI4RVB9MsCWD733tZxdn7PN22PzFVdU+/SKYZpUCg9ocwRJakpCSNHz9JM2feqaFDz9FJJ3XXunXv6r331mrOnAcVFxcXXPaEEzqXWrdr124aOvQcPfnko+rdu69SUlL09NNPKScnR5Mn/zm4XHx8Qpl1f++ee+6SJP3f/9112GVeeeV1maapzz77lBAGAEAF0jPzlbYv1/G6tS18HcTpiNWoOHufijJ2e/qvKqHvtdf+oeHDz9GAAb01adJ1+u67b9SnT3etXLkiuMyhp4gdtHz5C+rTp3vwcV5enh566F5deukFGjCgt4YPP0f33z9LOTk5pdYbPvwcPfTQvXrlleW68MI/avDgfrr11puCp6p99tmnmjhxnCRp9Ogr1KdP9+B2Vq5coT59uisjI6NUzSuvHBn8gC2VfNi+/PKL9cknH2vUqBE688zeuuGGMdq1a6eysjJ1++3TdNZZ/XTxxefpX/96O6T9tHLlil9rnabzzx+i+fOfUCAQKDW/T5/u+uGH73TTTRM1cGAfjRgxTG+++Xq59d55Z40uvfQCDRp0uiZOHKcdO34uNf+pp+bqiisu0aBBp+v884fozjuna+/evaWWOXhqY0W1CgsLtWDBk7roovN0xhm9NGzY0FL7S5I2btygiRPHaeDAPho8uJ/uuGO69u8v3a/27t2jW265UQMG9Nb55w/RX//6XEj7TpL+8IezddJJ3fXAA7OVmZmhRx65X6ef3l99+vQrtVx5fe366yfKMAw9+eSj+u67b/X3vy/X6NHj1KBBw+AyTp2OaJq8fQIAgPBwJAwh+eCD9369XuccDRhwlr7//lvdfvu0sGrl5+fLsiyNGXO9UlLqavfuNC1Zski33nqT5s6dX2rZ999fp59/3q4pU25RZmaGHnvsIT3yyH26++7Zat++g6ZMuUUPPXSvpk+/Uy1atAqrPfv2pevxxx/RFVdcLb/fr0ceeUAzZtymmJhYdet2ks4993y99tqrmjHjdnXq1Dl4Clx5li17Xk89NVcXXzxSN9wwWdu2bdOCBU/Ksixdd92EUsvOmHG7zjnnfI0YMVKvvfaqZs26W8cf30mtWv12mtymTT9o//6lGjdugiwroLlzH9aMGbdr/vxng8vs379Pl19+lerXb6CMjP1atuyvuuGGMXr++eXy+/2VqnXbbTdr/fpPdPnlV6lTp87KyNivtWvfCc7fuHGDJkwYq1NP7a27756t/Pw8Pf30U5o27aZSdaZNu0l79qRp6tRblZCQoOeff067d6fJ5/OF9JpMnTpNo0ZdqtGjr1B2drYmT54a0nrJySm67rqJmj17hj7/fL3atm2nCy+8OKR1AQAAvEIIQ0iee26hunY9UdOn3ylJOuWUXiosLNTixc9UulbdunU1deqtwcfFxcVq0uQYXX/9aP30049q0aJlqeXnzHlI0dHRkkquAVu69FlZlqX4+IRgYGnTpq06dOgY1nPLysrS3LkL1KZNW0klR3Eefvh+/elPo3TllaMlSR06dNK6de9o3bp3dfHFl5ZbJzf3gBYuXKCRI6/Q2LHjJUk9epyqqCi/5s59WCNHXq7k5JTg8hdccLEuuOAiSdIJJ3TVf/7zvt5991/BbUpSTk62Fi36q+rWrSup5CjirFl3a/fuNDVs2EiSgq+JJAUCAZ1wQhcNGzZUn332qXr2PDXkWp988pE+/PB93XnnTA0a9Ifgeof+f968x9Whw/GaNev+4AWwxx13nEaOvEj/+c/76tWrjz766EN99903evTRp3TyyT0kSSee2F0XXHC2kpKSQnpNWrRopbPOGqI33nhNY8Zcr0aNGoe0niQNHXqOlixZpB07ftYdd/wlpOAXCARKXSN58P/FxcXBaSWD6YQWIgEAAI6EEIYKBQIBff/9t7r++omlpvfvPyCsECZJq1a9oZde+qt+/nm78vLygtO3b/+pVAjr1u2kYACTpFat2qi4uFj79+9TvXr1w9r279Wv3yAYwCSpefOS7Xfv3jM4LTExMXjU7nC++mqD8vJydcYZA0p9eO/e/RQVFBRoy5bNOvHEk4PTDw1IcXFxaty4ifbs2V2q5rHHHhcMTZKCoXP37t3BEPaf/3yg555bqK1bN+vAgQPBZbdv/7HUNiqq9emnnyg2NlYDBw4u9/nl5+frq6++1Pjxk0qdXtm8eQs1bNhI3377jXr16qNvvtmohISEYACTpISEBHXv3lM//PDdYfffofbv36d1696VYRj6/PP1uuKKq0NaT5I+/fS/2rHj5+C6nTt3rXCdSZOu0xdffFZm+qpVbwT/363bSXr88QUhtwMAAOBwCGGoUEbGfgUCAdWtm1pqempq6mHWOLK1a9/RzJl36txzh2nMmOuVlJSi9PS9mj59qgoLC0otm5CQUOpxVFSUpJJrl5zy+20cPIUvMTGxzLZ/375DZWZmSJKuvvqycuf/PsAlJJSu7/dHlXle5bVBUrAd3377taZNm6LTT++nyy4bpZSUVBmGobFjr1RBQeVqZWVlql69+ocd4jU7O0uBQECPPfaQHnvsocM+v/T0vUpJqVtmfmX6y+OPPyy/36+77pqlO++8Vf/619saMOCsCtcrLCzUgw/OUY8ep6hDh4567rmFGjToD2rS5JgjrnfzzdOVm/vbxcKLFj0tSbr66muD0+rUqRNy+wEAAI6EEIYKpaTUlc/nKzP4wr59ZQf5iI6OVnFx6aH3s7OzSz1+5501atfuON188/8Fp33++XoHW6zg0bOybclydDuHSkwsOdXunnvuV6NGjcrMrygIhGPduneVkJCgGTPmBAeK+OWXXWHVSkpKVnr6Xtm2XW4QS0hIlGEYuvzyq9S3b//gdJ/PVCBgBU+1rFevvjIy9pdZv7z+Up7PPvtUb731pm677W4NGDBI69b9W3PnPqxevXqrTp34I667dOmz2r07TQ888JgaNGigNWve1sMP36/77nv4iOv9/nrC5ORkSQr7FFcAAIAjYXgvVMjn8+m44zpo3bp3S01/991/lVm2QYOG+vHHraWmffLJx6UeFxQUyO+PKjXt7bdXhdW2g0dzfn/Up0GDkhC0bdtvbdm2besRTyesqhNO6KLY2Fjt2ZOmDh06lvl36PVgTikoyJff7y8Vmt5++82wanXv3lP5+fn6979Xlzs/Li5OJ5zQWT/+uLXU8zr++JKfB0Pm8cd3Uk5Ojtav/yS4bk5Ojj799L8VtqGoqEgPPDBbJ53UXX/4w9mSpAkTpig3N1dPPz3viOv+9NOP+utfn9Nll12pZs2aKyYmVpMnT9WHH75Xpu8CAABUJ46EISSjRl2tadNu0qxZdwdHR3zrrZVlluvff4BefvlFdejQSS1atNTbb68sc51Tjx6n6KGH7tXixc+oU6fO+uijD7R+fcUf0MvTvHlL+Xw+vfHGP+Xz+eT3+9ShQ0d16nSCGjZspLlzH9LYsTfowIEcPf/8c8EjHG5ITEzUNdeM05NPztXu3bt14okny+fzaefOn/Xee+t0zz33KTY21tFt9uhxipYvf1EPP3yf+vY9Qxs3bij3dQm1Vq9evTV79gzt2PGzOnY8QVlZWXr33X9pxozZkqTrr5+kSZOu0x133KoBA85SYmKi0tP36OOPPwre1+vUU0/Tccd10IwZt2ncuAlKTEzU0qWLFR9/5KNYkvT884u1a9dOzZnzYHBa/foNNHr0OD3xxCMaOvSPateufbnrPvjgHDVq1FiXXXZlcFrv3qfr9NP769FHH1CPHqeUus9YVX3++XplZOzX1q1bJEnr13+iXbt2qkmTYziCBgAAjogQVo38ieFdU1Ud2+zTp5+mTr1VS5Ys0po1b6tjx066++5ZGjPmylLLXXnlaO3fv0/PPvu0TNPQuedeoIsuaq/HH38kuMx5512gnTt36G9/e0kvvLBUPXueqjvvvEdjx5auFYqUlBTdeOPNeuGFJXrrrZUKBAJ6//1P5ff7NWvWA3rwwdm6/fZb1KxZc02YMKVUO9xw6aWXqUGDBnrppb/qlVdekt/vV9OmzXTaaaeXGi7eKb169dF1103QK68s18qVK9S5c1fdd98juvTSC8KqN3PmfXr22af1z3/+XYsWLVBqaj316HFKcH7nzl315JPPaOHC+Zo9+24VFRWpYcNGOvnkHmrWrLmkklEE58x5UA88MFv33z9biYmJGj78Eu3bt0/vvffuYbf988/btXTpYo0ceUWZ0wMvvPBivfnmCj3wwBzNm7eozOmSq1a9ofXrP9EjjzxZaiAXSZo0aaouv/wiPfvs02UGl6mKhQvnlxrM46mn5kqShgz54xFv8gwAAGDYh47LjLAEApb27TtQZnpRUaHS03epXr0mior67YOhYRhKqmNIgaIy63jCF6WsXFuhvPR+v6niYqvcednZ2Roy5AxNn36nhg49x+lWopY4Uh9BaYd7T4hkfr+punXjtX//AfoJyqB/oCL0kdrP5zMlv6knXv5SaftyK16hkhrXq6MJF58oBQIqLAxUvILLUlPjS55zBTgSVg1s21ZWrmSaURUv7AKrILQABgAAAMB5hLBqYtu2AgGCEAAAAHC0IYQhbImJiXr//U+ruxkAAABArcIQ9QAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihFUTw5BM06iWf4bh/PPZtWun+vTprnfeWeN88SNYuHC+Bg063fG6K1euUJ8+3ZWRkeF47cPp06e7XnhhaalpTz75qM47b7BOP72HHn30Qc/aAgAAAPdws+ZqYBiS7S9WbqCgWrYf54+RUeyXbVfL5h11zjnn67TT+lR3Mxwxb96zaty4SfDxJ598rBdeWKqJE6eoY8cTVL9+g2psHQAAAJxCCKsGhmEoN1Cgz3d8pfziQk+3HeuP1olNOyveiJIdASmsYcNGatiwUXU3wxEnnNC51OOfftomSRo+fIRMs2oHrQsK8hUTE1ulGgAAAHAGIawa5RcXKq8ov7qbEbKNGzdo4cL5+vrrjbJtW61atdaYMdepR49Ty13+zTdf12uv/UPbtm2Vbds69th2uv76ierY8YTgMrt3p2nu3If1xRef6cCBHNWrV1+nn95PEyfeFNL8hQvna9my57V69XvBmtnZ2Xrmmae0bt27ysjYr/r1G2jAgLM0btwNkqQPP3xfy5e/oP/9b5MKCwvVsmUrXXPNWJ166mmV2h8rV67QrFl36/XX1yglJSU4/corR6pdu+P0f/93lyTpnnvu0nfffaMbb7xZc+c+pO3bf1Lr1m100023qkOH44Pr9enTXddfP0kjR16uG24Yoy+++EyS1LdvT0nSY4/N00knddfmzf/TE088og0bvpDP51OPHqfohhumqHHjxqVqjR17g7Kzs7Rq1RvKy8vT6tXrNHz4OTrttD5q1qy5li37q7Kzs9W//5n685+n68cft+qhh+7Vpk0/qHXrNpo27Q61bXtspfYJAAAAKkYIQ0g2bPhCkyZdp06dOuuWW25TYmKivvvuG6Wl/XLYdX75ZZf+8Iez1bRpMxUVFWnNmrd0ww1jtHjxi2rRoqUkaebMO7V37x5NnjxVdeumKi3tF33//bfBGhXN/73CwkJNmjROu3bt0lVXXau2bY/V7t1p2rDhi+Ayu3btUO/efXXppZfLNA199NGH+vOfJ+nRR5/SSSd1r/rOKse+fel69NEH9Kc/XamEhATNn/+4pk+fquXL/ym/v+yv4U03TdOKFf/Q8uUvat68ZyVJrVu3VlraLxo//lo1bdpMt9/+FxUWFmjBgqc0YcIYPffci6pTJz5Y429/e1EdO3bWtGm3KxAoDk5///11at26rf7851u1c+cOzZ37sPz+KH399QZdcsmflJqaqqeemqvbb79Fzz//cpWPwgEAAKA0QhhC8tRTj6lp0+Z69NGn5PP5JEk9e5Z/BOygq666Nvh/y7LUo8cp+vbbr/Xmm69r7NjxkqRvv/1aY8eO14ABZwWXHTLkj8H/VzT/91atekM//PC95s1bpBNO6FLuOhdeeEmpdp14Yndt3bpFr732D9dCWFZWlubOXaA2bdpKkmJjYzVx4jh9/fVGde3arczyrVu3CV4fduhpiosWLVAgUKyHH35cSUnJkqTjjuugyy67SCtXrtDw4SOCyyYmJmvWrPtllDMSy5w5DyoqKkqS9Pnn67VixT/0wAOPBY8GWpatW265UZs3/0/t2h3nzE4AAACAJEIYQpCfn6+vv96osWPHBwNYKLZt26r585/Qxo0btH//vuD07dt/DP7/uOM66MUXn5fP51ePHqeoWbPmpWpUNP/31q//r1q1al0qgP3e7t1pWrDgSX366X+Vnr43eG1c+/bHH3adqqpfv0EwgEklIUuS9uxJq1SdL7/8Qied1D0YwCSpZctWOvbYdtqw4ctSIezUU08rN4B163ZSMIBJUvPmLWWapk4+ucch01pIKtlXhDAAAABncZ4RKpSdnSXLsio1Ol9u7gFNmXKD0tJ2acKEG/XEE8/omWeW6Nhjj1Nh4W+Dkdx992ydfHIPLVjwpEaMGKaRIy/U2rX/Dnn+72VmZqpevcO307IsTZs2RRs2fKHRo8fqscfm6ZlnlujUU09TYaF7o1UmJCSUeuz3l4SgQ/dFKLKzs5SaWq/M9Lp16ykrK7PUtNTU1BDb4ldMTEypYHbw/27uEwAAgKMVR8JQoYSERJmmqb1794S8zsaNX2n37jTde+/DpY6kHDiQI6lh8HH9+vU1ffqdsixL33//rZ57bqHuuONWvfDCK2ratFmF838vOTlZmzf/77Dt+vnn7frhh+81e/YDOv30/sHpBQWVDxvR0dGSpOLiolLTs7OzKl0rVElJSaWOKh60f3+6mjdv+bupLtwQDgAAAFXGkTBUKC4uTp06ddaqVW8oEAiEtE5BQcmoj4ceXfnqqy+1a9fOcpc3TVPHH99J1157vQKBgHbs+LlS8w/q3v0Ubdu2VV9/vfEw7SoJWwePREklA4h89dWXIT2vQzVoUDI0/rZtW4PTtm3bqt27K3eKYWV06dJN69d/oqys34LeTz9t0+bN/1OXLl1d2y4AAACcw5GwahTrj6412xw3boImTRqnyZOv17BhFykxMVE//PCdkpNT9Mc/nldm+U6dOisuro4eeuheXXbZldqzZ7cWLpyvBg1+OwqWk5OjKVNu0ODBQ9WiRUsVFxfpb39broSERB13XIcK55dn8OCh+sc/XtbNN0/SVVddqzZtjtWePbv1xRef65Zb/k8tW7ZSw4aNNG/e47IsS3l5uWXaFapOnU5Qw4aNNHfuQxo79gYdOJCj559/TsnJyRWvHKaLLx6pN95YoSlTbtAVV1ytwsICPf30U2rUqLGGDj3Hte0CAADAOYSwamDbtuL8MTqxaeeKF3ZBnC9GdnHlbtTctWs3zZ07X08//ZRmzbpLpulT69ZtdO2115W7fGpqPf3lL3P0xBOPaNq0m9S8eQv9+c/T9de/PhdcJjo6Wm3bHqtXXnlJaWm/KCYmVh06HK+HH35cKSkpKiwsPOL88kRHR+uRR57SggVPaunSZ5WVlaUGDRpq4MDBwfn33HOfHnroXt1++zQ1bNhIo0Zdrc8++1TfffdNpfaJ3+/XrFkP6MEHZ+v2229Rs2bNNWHCFD3++COVqlMZjRo11uOPL9ATTzyiGTNuk2n61KNHT02YMKXU8PQAAACouQz74NBwCFsgYGnfvgNlphcVFSo9fZfq1WuiqKjSR6AMQ+WOXOcF27YV6qvu95sqLrbcbRBqNfpI6I70nhCp/H5TdevGa//+A/QTlEH/QEXoI7Wfz2dKflNPvPyl0vblOl6/cb06mnDxiVIgoMLC0C6bcVNqanzJc64AR8KqiW1L5F8AAADg6FOjQtiPP/6ohQsX6ssvv9SmTZvUpk0bvf7660dc5+OPP9YVV1xR7rzWrVtr1apVR1xu6NChevjhh6veeAAAAAAIQY0KYZs2bdLatWvVtWtXWZYV0pGiTp066aWXXio1LScnR9dee6369u1bZvnZs2erTZs2wcd169atesMBAAAAIEQ1KoSdeeaZGjhwoCRp2rRp2rix/GHGD5WQkKBu3bqVmvb3v/9dlmXpj3/8Y5nl27Vrp86dq2dADAAAAACoUfcJM01nmvP666+rVatW6tKliyP1qoprvwBIvBcAAIASNepImBP27t2rjz76SNddV/7Q6WPGjFFGRoYaNGigs88+W5MmTVJsbGyVt+v3lw2QpllyQ+DCwgJFR8dUeRteOzh4o2Eo5NEUcXShj1ROYWHJzcJjYqIc+9Kppjs4QlQoI0Xh6EP/QEXoI7WfaRqyZPw6MrgbWygp6vOZ8vtrz4eRiAthK1euVCAQKHMqYmJiokaPHq0ePXooJiZGH330kRYtWqQtW7Zo/vz5VdqmaRqqW7f8ezQVFKRq//4M+XyGYmJidLCj1BaB6h/pEzUcfSQUtgoKCpSbm6l69VJVr15SdTfIc0lJcdXdBNRg9A9UhD5Su2XmFMhnmvK7EKZ9Zsln64SEqh9U8VLEhbAVK1aoU6dOat26danpHTt2VMeOHYOPe/XqpYYNG2rGjBnasGFDlU5dtCxbWVnl3/cgNjZJcXFFyszcF3b96mOUfHth2ZJqzzcL8BJ9pDLi4xMVG5uk/fvL3lcwUvl8ppKS4pSVladAgHv8oDT6BypCH6n9TNOQZZgKWJaKXXgNA1bJ54+cnHwVFVX/N8NJSXFH333CfvrpJ23YsEG33nprSMsPGTJEM2bM0MaNG6t8/diRbiCYmJiq+PgUBQLFVdqG13w+Q8nJdZSZmatAgA/YKIs+Ejqfzy/TNH/dT0ffvgoELG60isOif6Ai9JHaq+Rmzfav98h1YwslRWtbH4moELZixQqZpqmhQ4dWd1PKME1Tphld3c2oFL/fVGxsrPLyArWqU8M79BEAAIDKi6irHN944w317NlTDRs2DHl5SQxZDwAAAMAzNepIWF5entauXStJ2rFjh3JycrRq1SpJUs+ePZWamqpRo0Zp586dWr16dal1v/nmG23evFlXXXVVubWnTp2qli1bqmPHjsGBORYvXqyBAwcSwgAAAAB4pkaFsPT0dE2aNKnUtIOPlyxZolNOOUWWZSlQznBsK1asUHR0tAYPHlxu7Xbt2mnFihVatGiRioqK1LRpU40bN05jxoxx/okAAAAAwGEYNncPrbJAwNK+fZE32pnfb6pu3Xjt33+A631QLvoIKkIfwZHQP1AR+kjtVzIwh6knXv5SafvKH028KhrXq6MJF58oBQIqLKz+0RFTU+NDGh0xoq4JAwAAAICajhAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeMhf3Q0AAAAAaivDMGSahmv1LcuWbduu1Uf1IIQBAAAAYTAMQzFxUSoKWK5tI8ZnqiCviCAWYQhhAAAAQBhM01BRwNKyt79Xema+4/XrJcdqxFntZZqGAgFCWCQhhAEAAABVkJ6Zr7R9udXdDNQiDMwBAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeMhf3Q041I8//qiFCxfqyy+/1KZNm9SmTRu9/vrrFa535plnaseOHWWmb9iwQTExMcHHaWlpmjlzpt5//31FRUVp0KBBuvXWW5WQkODo8wAAAACAw6lRIWzTpk1au3atunbtKsuyZNt2yOsOHjxYV199dalp0dHRwf8XFRVp9OjRkqQHH3xQ+fn5uvfee3XTTTdp/vz5zjwBAAAAAKhAjQphZ555pgYOHChJmjZtmjZu3BjyuvXr11e3bt0OO/+tt97Spk2btHLlSrVp00aSlJSUpGuuuUYbNmxQly5dqtR2AAAAAAhFjbomzDTda866devUvn37YACTpN69eyslJUVr1651bbsAAAAAcKgaFcKqYsWKFTrhhBN04okn6tprr9X3339fav6WLVtKBTBJMgxDrVu31pYtW7xsKgAAAICjWI06HTFcZ555prp06aJjjjlG27dv17x58zRy5Ei9+uqrat68uSQpKytLiYmJZdZNTk5WZmZmldvg90dMng3y+cxSP4Hfo4+gIvQRHAn9AxWp6X3ENA1ZMmQYkmE4X98wJEOGTJ8hw6iZ+6Aibu8jqaSoz2fK7w99PInqFhEh7Lbbbgv+v3v37urdu7eGDBmihQsX6q677nJ9+6ZpqG7deNe3U12SkuKquwmo4egjqAh9BEdC/0BFanIfycwpkM805XchKPpMU6ZpKDmhjuO1veTuPioJYQkJsY7XdlNEhLDfa9iwoU4++WR9/fXXwWlJSUnKyckps2xmZqaaNGlSpe1Zlq2srNwq1aiJfD5TSUlxysrKUyBgVXdzUAPRR1AR+giOhP6BitT0PmKahizDVMCyVOxC+wKWJcuylZmZK8uqPUd5DuX+PirZLzk5+SoqCjhev7KSkuJCOnIbkSGsPG3atNEPP/xQappt29q6dat69+5d5frFxTXvjcEpgYAV0c8PVUcfQUXoIzgS+gcqUlP7iM9nSn5bti1V4s5KIbNtyZatQMCukSE0FG7vI6mkaE3tI4dTO08urUBaWprWr1+vzp07B6f17dtX3333nbZt2xac9p///EcZGRnq169fNbQSAAAAwNGoRh0Jy8vLCw4Xv2PHDuXk5GjVqlWSpJ49eyo1NVWjRo3Szp07tXr1aknS66+/rnfeeUf9+vVTw4YNtX37di1YsEA+n09XXXVVsPbgwYM1f/58TZgwQVOmTFFeXp7uu+8+9e/fn3uEAQAAAPBMjQph6enpmjRpUqlpBx8vWbJEp5xyiizLUiDw2/mezZo10+7duzVr1ixlZ2crMTFRp556qiZOnBgcGVGSoqKi9Mwzz2jmzJmaMmWK/H6/Bg0apOnTp3vz5AAAAABANSyENWvWrMz9vX5v6dKlpR5369atzLTDadSokebOnRt2+wAAAACgqiLymjAAAAAAqKkIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIf81d0AAAAAHL0Mw5BpGuXOOzjdNA35fOEdO7AsW7Zth90+wA2EMAAAAFQLwzAUExelooBV7nxLhjJzCmQZpuQPL0jF+EwV5BURxFCjEMIAAABQLUzTUFHA0rK3v1d6Zn6Z+YYh+UxTActSOBmqXnKsRpzVXqZpKBAghKHmIIQBAACgWqVn5ittX26Z6YYh+X2migPhhTCgpmJgDgAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPCQv7obcKgff/xRCxcu1JdffqlNmzapTZs2ev3114+4zu7du7V48WJ98MEH+umnn5SYmKgePXpoypQpatq0aXC5jz/+WFdccUWZ9YcOHaqHH37Y8ecCAAAAAOWpUSFs06ZNWrt2rbp27SrLsmTbdoXrfP3111q9erUuvPBCde3aVfv379dTTz2liy66SK+//rpSU1NLLT979my1adMm+Lhu3bqOPw8AAAAAOJwaFcLOPPNMDRw4UJI0bdo0bdy4scJ1Tj75ZL355pvy+397KieddJL69++vV199VVdffXWp5du1a6fOnTs723AAAAAACFGNCmGmWflL1JKSkspMa9y4sVJTU7V7924nmgUAAAAAjqlRIcwpW7duVXp6utq2bVtm3pgxY5SRkaEGDRro7LPP1qRJkxQbG1vlbfr9kTfGic9nlvoJ/B59BBWhj+BI6B8wTUOWDBmGZBhl5xsyfvtpVHyZSpn1jZJ1TZ8hw3C+n1XU/qpyu/1ecHsf6dc+4vOZ8vsr30eqS8SFMNu2NXPmTDVs2FBnn312cHpiYqJGjx6tHj16KCYmRh999JEWLVqkLVu2aP78+VXapmkaqls3vqpNr7GSkuKquwmo4egjqAh9BEdC/zi6ZeYUyGea8h8hjPt8hg5+2K4Mn2nKNA0lJ9SpQguPLJT2h8uL9nvB3X1U0i8SEqp+UMVLERfC5s6dq48++kjPPPOM6tT5rcN27NhRHTt2DD7u1auXGjZsqBkzZmjDhg3q0qVL2Nu0LFtZWblVandN5POZSkqKU1ZWngIBq7qbgxqIPoKK0EdwJPQPmKYhyzAVsCwVl9MHDBny+QwFArZsVf4oR8CyZFm2MjNzZVnOHyWpqP1V5Xb7veD+PirZLzk5+SoqCjhev7KSkuJCOrofUSFs+fLleuKJJ3TPPfeoV69eFS4/ZMgQzZgxQxs3bqxSCJOk4uLI/eMRCFgR/fxQdfQRVIQ+giOhfxy9fD5T8tuybancQbENW5IhW3b58ytg25ItW4GA7UrQr7D9VeR2+73g9j7Sr+G8tr2P1M6TS8uxevVq3XXXXZo4caKGDx9e3c0BAAAAgHJFRAj7+OOPNWXKFF100UUaP358yOu98cYbksSQ9QAAAAA8U6NOR8zLy9PatWslSTt27FBOTo5WrVolSerZs6dSU1M1atQo7dy5U6tXr5Ykbd68WePHj1erVq103nnn6YsvvgjWS01NVYsWLSRJU6dOVcuWLdWxY8fgwByLFy/WwIEDCWEAAAAAPFOjQlh6eromTZpUatrBx0uWLNEpp5wiy7IUCPx20d2XX36p7OxsZWdn69JLLy217rBhwzRnzhxJJTdpXrFihRYtWqSioiI1bdpU48aN05gxY1x+VgAAAADwmxoVwpo1a6bvv//+iMssXbq01OMLLrhAF1xwQYW1x44dq7Fjx1apfQAAAABQVRFxTRgAAAAA1BaEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEP+cFbKyclRdna2mjRpEpyWlpamZcuWqbCwUIMHD1aXLl0cayQAAAAARIqwQtgdd9yhn3/+WcuXL5dUEsouueQS/fLLLzJNU0uWLNEzzzyjU045xdHGAgAAAEBtF9bpiOvXr1f//v2Dj//5z39q9+7dWrZsmf773/+qffv2euqpp5xqIwAAAABEjLBC2P79+9WoUaPg43//+986+eST1a1bNyUkJOj888/Xd99951gjAQAAACBShBXCkpKStHfvXklSfn6+1q9fr969ewfn+3w+5efnO9NCAAAAAIggYV0TduKJJ+qFF15QmzZt9N5776mgoEADBgwIzt+2bVupI2UAAAAAgBJhHQmbOnWq/H6/JkyYoOXLl+vKK69Uu3btJEmBQECrVq1Sjx49HG0oAAAAAESCsI6EtWzZUqtWrdLmzZuVkJCgZs2aBefl5eXp9ttv1/HHH+9YIwEAAAAgUoQVwl599VV1795dHTp0KDMvISFBHTp00CeffKKmTZtWuYEAAACoHoZhyDQN1+qbpiFL7tUHaqqwTke89dZb9fnnnx92/oYNG3TrrbeG3SgAAABUL8MwFBMXJflNV/8ZhohhOOqEdSTMtu0jzs/NzZXP5wurQQAAAKh+pmmoKGBp2dvfKz3TnVGv2zZL1pBerV2pDdRkIYew7777rtS9vz799FMFAoEyy2VlZWnZsmVq3ZpfKAAAgNouPTNfaftyXaldLznWlbpATRdyCFuzZo0ef/xxSSWHp1966SW99NJL5S6blJSke++915kWAgAAAEAECTmEXXzxxerfv79s29ZFF12kiRMnqm/fvqWWMQxDcXFxatGihfz+sM50BAAAAICIFnJSatiwoRo2bChJWrJkidq2bat69eq51jAAAAAAiERhHa7q2bOn0+0AAAAAgKNC2OcMvvfee/rb3/6m7du3Kysrq8yIiYZhaM2aNVVuIAAAAABEkrBC2DPPPKMHH3xQ9erVU5cuXdS+fXun2wUAAAAAESmsELZkyRKdeuqpWrBggaKiopxuEwAAAABELDOclbKysjR48GACGAAAAABUUlghrHPnztq6davTbQEAAACAiBdWCLvrrru0evVqrVixwun2AAAAAEBEC+uasMmTJ6u4uFg333yz7rrrLjVu3FimWTrPGYah1157zZFGAgAAAECkCCuEpaSkKCUlRS1btnS6PQAAAAAQ0cIKYUuXLnW6HQAAAABwVAjrmjAAAAAAQHjCOhL2ySefhLRcjx49wikPAAAAABErrBB2+eWXyzCMCpf79ttvwykPAAAAABErrBC2ZMmSMtMCgYB27Nih5cuXy7Is3XTTTVVuHAAAAABEmrBCWM+ePQ8774ILLtDIkSP13//+V7169Qq7YQAAAAAQiRwfmMM0TZ199tl6+eWXnS4NAAAAALWeK6MjZmZmKjs7243SAAAAAFCrhXU64s6dO8udnpWVpU8//VQLFy5U9+7dq9QwAAAAAIhEYYWwM88887CjI9q2rW7duunuu++uUsMAAAAAIBKFFcJmzZpVJoQZhqGkpCS1aNFCxx57rCONAwAAAIBIE1YIu+CCC5xuBwAAAAAcFcIKYYf63//+px07dkiSmjZtylEwAAAAADiCsEPYmjVrNGfOnGAAO6hZs2aaNm2aBgwYUOXGAQAAAECkCSuErV27VhMnTtQxxxyjG2+8UW3btpUkbd68WcuXL9eECRM0b9489e3b19HGAgAAAEBtF1YIe/LJJ9W+fXv99a9/VZ06dYLTBwwYoMsuu0wjR47UE088QQgDAAAAgN8J62bN33//vc4///xSAeygOnXqaNiwYfr++++r3DgAAAAAiDRhhbCYmBhlZmYedn5mZqZiYmLCbhQAAAAARKqwQtgpp5yiJUuW6PPPPy8z78svv9TSpUvVq1evKjcOAAAAACJNWNeE/fnPf9aIESM0cuRIdenSRa1bt5Ykbd26VRs2bFC9evU0depURxsKAAAAAJEgrCNhzZs312uvvabLL79cmZmZWrlypVauXKnMzExdccUV+uc//6lmzZo53VYAAAAAqPXCvk9YvXr1NH36dE2fPt3J9gAAAABARKvUkbAvvvhCX3311RGX+eqrr/Tll19WqVEAAAAAEKlCDmEfffSRLr30Um3duvWIy23dulUjRozQp59+WuXGAQAAAECkCTmELVu2TJ06ddK55557xOXOPfdcde7cWS+++GKVGwcAAAAAkSbkELZ+/XoNGjQopGUHDhyoTz75JOxGAQAAAECkCjmE7d+/Xw0aNAhp2fr162vfvn1hNwoAAAAAIlXIISwhIUF79+4Nadm9e/cqISEh7EYBAAAAQKQKOYR17txZq1atCmnZVatW6YQTTgi7UQAAAAAQqUIOYRdffLG++eYb3XvvvbJtu9xlbNvWvffeq2+//VaXXHKJY40EAAAAgEgR8s2aBw0apGHDhunZZ5/Ve++9pz/+8Y9q166d4uPjdeDAAf3www9644039L///U/nn39+yIN4AAAAAMDRJOQQJkmzZ8/WscceqwULFuiRRx6RYRjBebZtKzk5WTfddJNGjx7teEMBAAAAIBJUKoRJ0jXXXKPLLrtM69ev1+bNm5WTk6OEhAS1adNGJ598smJjY91oJwAAAABEhEqHMEmKiYnRaaedptNOO83p9gAAAABARAt5YA4AAAAAQNURwgAAAADAQ4QwAAAAAPBQjQphP/74o+644w6dd9556tixo/74xz+GtJ5t21qwYIH69++vLl266JJLLtEXX3xRZrm0tDRNmDBBJ554onr27Kn/+7//U05OjsPPAgAAOMEwDPl8pmv/Dh3lGQC8VKNC2KZNm7R27Vq1bNlSbdu2DXm9p59+Wo899piuvPJKzZ8/Xw0aNNDVV1+t7du3B5cpKirS6NGjtW3bNj344IO666679P777+umm25y46kAAIAqMAxDMXFRkt907V9MXBRBDEC1CGt0RLeceeaZGjhwoCRp2rRp2rhxY4XrFBQUaP78+br66qt15ZVXSpJOPvlk/eEPf9DChQt11113SZLeeustbdq0SStXrlSbNm0kSUlJSbrmmmu0YcMGdenSxZXnBAAAKs80DRUFLC17+3ulZ+Y7Xr9ecqxGnNVepmkoELAdrw8ARxJSCDvzzDMr/U2RYRhas2ZNpdYxzcofmPvss8+Uk5OjIUOGBKdFR0dr0KBBWr16dXDaunXr1L59+2AAk6TevXsrJSVFa9euJYQBAFADpWfmK21fbnU3AwAcFVII69mzZ5kQtnHjRm3atEnHHnusWrduLUnaunWr/ve//6ldu3Y64YQTnG9tObZs2SJJpcKVJLVt21bPPfec8vPzFRsbqy1btpRZxjAMtW7dOlijKvz+GnVmpyN8PrPUT+D36COoCH0ER3Kk/mGahiwZMgzJjTMGDUMyZMj0GTIM+md53H4NpEPqHmYbhozffhqVP2Lp9utMP62Y+/2opKjPZ8rvrz1HtUMKYXPmzCn1eM2aNVqzZo2effZZ9erVq9S8Dz74QJMnT9akSZOca+URZGVlKTo6WjExMaWmJyUlybZtZWZmKjY2VllZWUpMTCyzfnJysjIzM6vUBtM0VLdufJVq1GRJSXHV3QTUcPQRVIQ+giM5XP/IzCmQzzTldyHE+0xTpmkoOaGO47UjiZuvgfTrWVCGKtyGz2fo4IftyvDidaafVszdfVTSLxISYh2v7aawrgl79NFHddlll5UJYFLJKX5/+tOf9Oijjwav74p0lmUrKyvyTpXw+UwlJcUpKytPgYBV3c1BDUQfQUXoIziSI/UP0zRkGaYClqViF/pOwLJkWbYyM3NlWbXn23Mvuf0aSJJlWZKtw27DkCGfr+S6PVuVf53cfp3ppxVzfx+V7JecnHwVFQUcr19ZSUlxIZ39EVYI+/HHH5WSknLY+SkpKfrpp5/CKV1pSUlJKiwsVEFBQamjYVlZWTIMQ8nJycHlyhuOPjMzU02aNKlyO4qLI/fDRSBgRfTzQ9XRR1AR+giOpLz+4fOZkt+WbUu2C589bVuyZSsQsPmC4DDcfg2kQ+oebhuGLcmQLTusNrj9OtNPK+Z+PyopWtv+zoR1TLBFixb6+9//rgMHDpSZl5OTo1deeUXNmzevcuNCcfA6r61bt5aavmXLFh1zzDGKjY0NLvf7a79s29bWrVvLXCsGAAAAAG4J60jY5MmTNXHiRA0ZMkTDhg1Ty5YtJZUcIfvHP/6h9PR0Pfroo4429HBOOukkJSQk6M0331SHDh0kldwT7O2331bfvn2Dy/Xt21evvfaatm3bplatWkmS/vOf/ygjI0P9+vXzpK0AAAAAEFYIGzhwoBYsWKAHHnhA8+fPLzXv+OOP1z333KPTTz+90nXz8vK0du1aSdKOHTuUk5OjVatWSSoZoTE1NVWjRo3Szp07g8PPx8TEaOzYsZo7d65SU1N13HHH6cUXX1RGRoauueaaYO3Bgwdr/vz5mjBhgqZMmaK8vDzdd9996t+/P8PTAwAAAPBM2Ddr7tOnj/r06aM9e/Zo586dkqRjjjlGDRo0CLsx6enpZUZVPPh4yZIlOuWUU2RZlgKB0hfdXXvttbJtW4sWLdK+fft0/PHHa+HChaVOiYyKitIzzzyjmTNnasqUKfL7/Ro0aJCmT58ednsBAAAAoLLCDmEHNWjQoErB61DNmjXT999/f8Rlli5dWmaaYRgaO3asxo4de8R1GzVqpLlz51apjQAAAABQFWEP1r9z507dcccdGjx4sHr27KlPPvlEkrRv3z7NnDlT33zzjWONBAAAAIBIEVYI+9///qdhw4bpzTffVLNmzZSdna3i4mJJUmpqqtavX6/nn3/e0YYCAAAAQCQI63TE+++/X4mJiVq+fLkk6bTTTis1v1+/fnrzzTer3joAAAAAiDBhhbBPPvlE48ePV2pqqvbv319m/jHHHKO0tLQqNw4A4A7DKLme1i22Hd6NVQEAOBqEFcJs2w7eBLk8+/btU3R0dNiNAgC4xzAk21+s3ECBa9uI88fIKK7y2E8AAESksP5CduzYUWvXrtWf/vSnMvOKi4v1xhtvqGvXrlVuHADAeYZhKDdQoM93fKX84kLH68f6o3Vi086KN6Icrw0AQCQIK4SNGTNG48aN05133qmzzz5bUsk9vj788EPNmzdPW7Zs0R133OFoQwEAzsovLlReUX51NwMAgKNOWCGsX79+mj17tmbNmhUcnOPPf/6zbNtWQkKC7r33XvXo0cPRhgIAAABAJAj7hP3zzz9fZ511lj788ENt27ZNlmWpRYsW6tOnjxISEpxsIwAAAABEjCpdNV2nTh0NHDjQqbYAAAAAQMQL62bNAwYM0CWXXKItW7aUO3/NmjUaMGBAlRoGAAAAAJEorBC2Y8cOff3117rooou0Zs2aMvNzc3O1c+fOKjcOAAAAACJNWCFMkm699Vb16NFDEyZM0COPPOJgkwAAAAAgcoUdwpKSkjRv3jyNHz9eCxYs0JgxY5Sdne1k2wAAAAAg4oQdwg664YYbNG/ePH355ZcaPny4Nm3a5ES7AAAAACAiVTmESVLfvn31t7/9TXFxcbr44ov1r3/9y4myAAAAABBxHAlhktS8eXO99NJLOuuss/TWW285VRYAAAAAIkpY9wlbsmSJ2rZtW2Z6TEyM7r33Xg0ZMkT79++vcuMAAAAAINKEFcJ69ux5xPn9+/cPpywAAAAARLyQQtirr74qSTrvvPNkGEbwcUXOP//8MJsFAAAAAJEppBA2bdo0GYahoUOHKjo6WtOmTatwHcMwCGEAAAAA8DshhbCDox1GR0eXegwAAAAAqJyQQljTpk2P+BgAAAAAEBrHhqgHAAAAAFQspCNhV1xxRaULG4ah5557rtLrAYh8hlHyHuEW27Zl266VBwAAqJKQQpgdxqeZcNYBEPkMQ7L9xcoNFLi2jTh/jIxiP0EMAADUSCGFsKVLl7rdDgBHCcMwlBso0Oc7vlJ+caHj9WP90TqxaWfFG1F8GQQAAGqksG7WDABVlV9cqLyi/OpuBgAAgOeqHMJycnKUk5Mjy7LKzDvmmGOqWh4AAAAAIkrYIeyFF17Q4sWLtX379sMu8+2334ZbHgAAAAAiUlhD1L/44ouaMWOGWrRoocmTJ8u2bY0aNUpjxoxR/fr11aFDB91zzz1OtxUAAAAAar2wQtjzzz+vPn366JlnntHFF18sSerXr59uvPFGrVy5UgcOHFBGRoaT7QQAAACAiBBWCPvpp590xhlnSJKioqIkSUVFRZKkxMREDR8+XC+88IJDTQQAAACAyBFWCEtMTFQgEJAkJSQkKC4uTr/88ktwfnx8vPbu3etMCwEAAAAggoQVwtq1a6fvvvsu+Lhr16568cUXlZaWpl27dumll15Sq1atnGojAAAAAESMsELYueeeq02bNqmwsORGqxMmTNDmzZvVv39/nXnmmdq6dasmT57sZDsBAAAAICKENUT9hRdeqAsvvDD4+OSTT9Ybb7yhf//73/L5fOrdu7dat27tWCMBAAAAIFJU+WbNBzVv3lyjRo1yqhwAAAAARKQqhzDLspSdnS3btsvMS0lJqWp5AADKZRiGTNNwrb5l2eX+bQMAoKrCCmFFRUV6+umn9corr+iXX36RZVnlLvftt99WqXEAAJTHMAwl1TGkQJF7G/FFKStXBDEAgOPCCmF33HGHXn31VXXt2lUDBw5UYmKi0+0CAOCwTLMkgO1/72UVZ+9zvL4/MVV1T79IphmlQIAQBgBwVlghbNWqVTrvvPM0Z84cp9sDAEDIirP3qShjd3U3AwCASglriPq4uDh17drV6bYAAAAAQMQLK4SdffbZevfddx1uCgAAAABEvrBOR/zzn/+s6dOna+zYsbrwwgvVuHFj+Xy+Mst16tSpyg0EAAAAgEgSVggrLCyUbdtat26d1q1bV2a+bdsyDIPREQEAAADgd8IKYdOnT9eaNWs0dOhQde3aldERAQCoYdy+j5rEvdQAIFxhhbD3339fl112maZPn+50ewAAQBV5ch81iXupAUCYwgphCQkJatmypdNtAQAADnD7PmoS91IDgKoIK4RdfPHFev311zVixIhyB+QAAADVj/uoAUDNFFYIa9u2rf71r39p2LBhGjZs2GFHRzzrrLOq3EAAAAAAiCRhhbAbb7wx+P9777233GUYHREAAAAAygorhC1ZssTpdgAAAADAUaHSIaygoEDfffedjj/+ePXo0cONNgEAAABAxDIru0JMTIweeOABbd261Y32AAAAAEBEq3QIk6R27dppx44dTrcFAAAAACJeWCHsxhtv1LJly/Thhx863R4AAAAAiGhhDczx/PPPKyUlRddcc42aNWumZs2aKSYmptQyhmHoqaeecqSRAAAAABApwgphP/zwgySpSZMmCgQC+vHHH8ssYxhG1VoGAAAAABEorBD273//2+l2AAAAAMBRIawQBgAAgOpnGIZM052zj0zTkCXObALcUKUQ9t///lfvvvuudu7cKUk65phj1L9/f/Xs2dORxgEAAKB8hmEoJi5KRQHLnQ2YhgxbxDDABWGFsMLCQt10001as2aNbNtWUlKSJCkrK0vPPvusBg0apAcffFBRUVGONhYAAAAlTNNQUcDSsre/V3pmvuP12zZL1pBerR2vCyDMEPbEE09o9erVuvrqq3X11Verfv36kqT09HQtWrRICxcu1BNPPKHJkyc72VYAAAD8TnpmvtL25Tpet15yrOM1AZQIK4StWLFCw4YN080331xqer169fTnP/9Z6enpeu211whhgAsMw93RR23blm27Vh4hcvN1NoySU4xQvdy+lgcAUHOFFcL27NmjLl26HHZ+ly5d9MYbb4TdKADlMwzJ9hcrN1Dg2jbi/DEyiv0EsWrk9utsypRtWlzoUY0Mw1BSHUMKFLmzAdOUye8wANRYYYWwxo0b67///a8uvfTScud/8sknaty4cZUaBqAswzCUGyjQ5zu+Un5xoeP1Y/3ROrFpZ8UbUbJJYdXG7dc5OTZB7Ru1lUEKqzamWRLA9r/3soqz9zleP6Zxa6WcfJbjdQEAzggrhJ1//vmaO3euEhMTdeWVV6ply5YyDEPbtm3Tc889p1WrVmnChAlOtxXAr/KLC5VX5PxF2KhZ3HqdY/0xjtdEeIqz96koY7fjdf2JqY7XBAA4J6wQNm7cOG3fvl3Lly/Xyy+/LNM0JUmWZcm2bQ0bNkzjxo1ztKEAAAAAEAnCCmE+n09z5szRlVdeqXXr1mnHjh2SpKZNm6pv377q0KGDo40EAAAAgEhRpZs1d+jQgcAFAAAAAJVgVncDAAAAAOBoEvKRsHPOOadShQ3D0GuvvVbpBgEAAABAJAs5hKWkpIS03N69e7V161ZXbyYLAAAAALVVyCFs6dKlR5y/Z88ePf3003rppZfk8/l07rnnVrlxAAAAABBpqjQwh1Ry5GvBggVavny5iouLdc455+i6665TixYtnGgfAAAAAESUsEPYwSNfh4av66+/Xs2bN3eyfQAAAAAQUSodwvbs2aMFCxbo5ZdfVnFxsc4991xdd911hC8AAAAACEHIIWz37t3B8BUIBHTeeedp3LhxhC8AAAAAqISQQ9igQYNUWFio448/XmPHjlWzZs2UlZWlr7/++rDrdOrUyZFGAgAAAECkCDmEFRQUSJK++eYbTZ48+YjL2rYtwzD07bffVqlxAAAAABBpQg5hs2fPdrMdAAAAAHBUCDmEDRs2zM12AAAAlGIYUr3kWFdq10uOlWFItivVAeDIqnyfMAAAAKcZhqF4v61LTm8qy7Icr2+apuL9tg4UG47XBoCKEMIAoJIMo+QDonv1DRl8PX9UMGPj5auT6HzdmDjHa3rNMCQFCpW+7iUd2LfH8frxqQ2UOOQyGUa047UBoCKEMACoBMOQbH+xcgMFrm3DlCnbtCS+oI9YhiHlGZYK2p4gqzDf8fp2fLJiZcmIqv0BoyAjXXnpaY7X9Zum4zUBIFQ1LoRt3rxZM2fO1Oeff674+Hidd955mjx5sqKjD/+H5OOPP9YVV1xR7rzWrVtr1apVR1xu6NChevjhh515AgAimmEYyg0U6PMdXym/uNCVbSTHJqh9o7YySGERzFBecYE++/kLHchy/ihPYr1m6tWolQxflOO1AQBVV6NCWGZmpkaNGqVWrVpp7ty5SktL05w5c5Sfn6877rjjsOt16tRJL730UqlpOTk5uvbaa9W3b98yy8+ePVtt2rQJPq5bt65zTwLAUSG/uFB5Rc4fwZCkWH+MK3VR8+QXHFBeXpbjdaMKch2vCQBwTo0KYcuWLdOBAwf0+OOPKyUlRZIUCAR09913a+zYsWrUqFG56yUkJKhbt26lpv3973+XZVn64x//WGb5du3aqXPnzk43HwAAAAAqVKNOiF63bp169eoVDGCSNGTIEFmWpQ8++KBStV5//XW1atVKXbp0cbiVAAAAABC+GnUkbMuWLbrwwgtLTUtKSlKDBg20ZcuWkOvs3btXH330ka677rpy548ZM0YZGRlq0KCBzj77bE2aNEmxsVW7D4nfX6PyrCN8PrPUT1Q/wzBkWpJpGjJN568XMk1DpiH5TFOmWfHwfOH0kZr2HCrL7fZLJbUNQzJMubaP3K7/22tQUt/p9xHT/O2KObcGqjQk+XyGDMP590CfT5L123bc5OJAnlXeR0d6D/H5jJLrIg2X9pEhGTLk8xmy7dr5d840DVn69ffZhZ0UrOlS/VC2cfA3vaQvVP493fj1dTZd+l324jVws/1ecHsfHXyH8PlM+f21Z2jhGhXCsrKylJSUVGZ6cnKyMjMzQ66zcuVKBQKBMqciJiYmavTo0erRo4diYmL00UcfadGiRdqyZYvmz58fdrtN01DduvFhr1/TJSXV/qGOI0nhgTzFxEbJ9jt/35wYf5SiY6KUEl+nUutVto/UxOdQGW62X5KiY/wyTUMxMVGyfc5vw+365b0GbryPBA4UyeczZft8jtf2+UoCZHKie/0oLyOz5HYELozSd/AWCj6fKZ8L++dgbaf20eH6R1FO4a8fvp3/5Hbww31iYu3+G5eZUyCfacrvwhempmlKv36h4kb9ymzD5zMUThw/+GVQcoJ7v8tuvgZetN8L7u6jkn6RkODOjd3dUqNCmFNWrFihTp06qXXr1qWmd+zYUR07dgw+7tWrlxo2bKgZM2Zow4YNYZ+6aFm2srIi7yJon89UUlKcsrLyFAi482ETlWMYhgqtIhXkFym/yPmR+YwoU4UFRcooypVth3YkrLJ9pKY9h0rXd7n9khSnYlmWrYKCIuUXOr8Nt+sb0aas4iIV5WRKsmUahizblpx8OUxThm0rELAUCAQcLFzCCFiyLFs5mbmyLOf7kc9nyJZk27ZsF25EfLDvu7V/JGf20ZHeQ/x+U7GGZMuWXPhdtn/tkNnZeSourp1/40zTkGWYCliWil34O21ZlmTLtfqhbOPg0cpAwA6+ZpURsEr6aaZLv8tuvwZut98L7u+jkv2Sk5OvoiJ33u8qIykpLqSzP2pUCEtKSlJ2dnaZ6ZmZmUpOTg6pxk8//aQNGzbo1ltvDWn5IUOGaMaMGdq4cWOVrh+rrW/goQgErIh+frVJySH9kuDvxpuxZdmy7JLXvDL1K9NHaupzCJXb7devtW1bsi25to/crG+XpAtlfLxChXt3yOczHf8iJ6Zxa6WcfNZv23OBLSkQsF36EsoX/FLf7Y9Vbu0fybl9VN57iGEYsv0l4d2Vp2CXBLFAwK61f+N8PlPy//r77MJOCtZ0qX5I2zBsSYZs2WG1wT7kdXbjd9mL18DN9nvB7X108B2itn1erVEhrE2bNmWu/crOztaePXtKDSl/JCtWrJBpmho6dKgbTQQAhKg4J0PFmbtl+3wKBAKO/vH1J6Y6VwwAAI/VqCv8+vbtqw8//FBZWb/dM2XVqlUyTVO9e/cOqcYbb7yhnj17qmHDhiEvL4kh6wEAAAB4okYdCRsxYoSWLl2q8ePHa+zYsUpLS9N9992nESNGlLpH2KhRo7Rz506tXr261PrffPONNm/erKuuuqrc+lOnTlXLli3VsWPH4MAcixcv1sCBAwlhAAAAADxRo0JYcnKynnvuOf3lL3/R+PHjFR8fr+HDh+vGG28stZxllX+h8YoVKxQdHa3BgweXW79du3ZasWKFFi1apKKiIjVt2lTjxo3TmDFjXHk+AAAAAPB7NSqESVLbtm21ePHiIy6zdOnScqffcsstuuWWWw673tixYzV27NiqNA8AAAAAqqRGXRMGAAAAAJGOEAYAAAAAHiKEAQAAAICHatw1YQAAAJHCMAyZpuFK7ZKbx7tTG4C7CGEAAAAuMAxDMXFRKgpY7mzANGTYIoYBtRAhDACAw3DrKIbBp+ajgmkaKgpYWvb290rPzHe8fttmyRrSq7XjdQG4jxAGAMDvGFHRyjMs5dhZsl2o77NNybAl0+dCddQ06Zn5StuX63jdesmxjtcE4A1CGAAAv2P4opRXXKDPd36tvMICx+un1ElUh0atZRiMjwUARyNCGAAAh5FfXKi8IudPI4sr5ggGABzN+AoOAAAAADzEkTAAABCe4MAl4X2ne3DQE9M05POZZeYxfgmASEUIAwAAlWbGxsvn86mOXSiFOb6IISlwoEh1TFv273OcaZYMv+7SPbYAoDoRwgAAQKWZUTGyA8Xa//7LKs7aF3Ydn89UoJz7aMU0aa2Uk86SyXj+ACIQIQwAAIStOGufijJ2h7WuYUi2z6dAICD7d/cC8CemOtA6AKiZGJgDAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAAD/mruwEAANRUhiEZpuFKXQDA0YsQBgDA75gxdSTDkF+Wok3L8fo+wxY5DACOXoQwAAB+x4yKlmXbKtjxvXKz9zhev07j46Qm7R2vCwCoHQhhAAAchlWUr0D+Acfr2sWFjtcEANQeDMwBAAAAAB4ihAEAAACAhwhhAAAAAOAhrgkDAABHJUOSaRry+dz5Tto0DVmMgwmgHIQwAABw1Cm5/5sh2zTd+zRkGjJsEcMAlEEIAwAARx3z1ztmr/xgi/73c6Yr22jbLFlDerV2pTaA2o0QBgAAjloZ2QVK25frSu16ybGu1AVQ+zEwBwAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhBuYAACCCGR6Mjx7+NozgT8OwHWoNANR8hDAAACKVIfdSmHHIzypsI2BZv9b6XQ1urgUgghHCAEQcwzBkyJDpwgnXhlFy81WgNjiQV6z9Lg2/Xr9+sepJysktUla42zAkQ4Zs2dLvfq8O1geASEQIAxBRoky//D5TB4qzf/+ZzhGmTNmmxbf0qBUsy1ZRwHKldsCygz/D3UbJATBDsu0yv68H67vKMJSSGKNGqXVcKZ+SGOPJ6aCoXobh3j3h6iXHlvyKuFId1YkQBiCi+Eyf8osL9NXO75RXVOB4/eTYBLVv1FYGKQyo1Xxx8TJNn4ac1EBFXVJd2UaU36d4v6X4uChX6qP6GYaheL+tS05vKsty/gsP0zQV77d1oJi/OZGGEAYgIuUXFyqvKN/xurH+GMdrAvCeLzpWdqBI6euWK2tvmivbSKrfSPGD/6TYaJ8r9VH9DENSoFDp617SgX17HK8fn9pAiUMuk2FEO14b1YsQBgAAjloFmenKS3cnhMVE8THraFGQ4U4/8rtxcTNqBF5ZAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwEMP2AAAA1FIHbxTsxs18udk04B5CGAAAQC0UF+NXvN/SxS7dKJibTQPuIYQBAADUQjHRPilQ5NqNgrnZNOAeQhgAAEAt5taNgrnZNOAeBuYAAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPMewNAAAAymcYSkmMUaPUOq6U54bQOFoRwgAAAFCGLy5epunTkJMaqKhLqivb4IbQOFoRwgAAQI3lj0tQVHyS43V9se4c2YkkvuhY2YEipa9brqy9zt+HTOKG0Dh6EcIAAECNY/qjlSdLOr6r4lq1c7y+lVRXebJkRsU4XjvSFGS6czNoiRtC4+hFzwcAADWO4fcrt7hAn23/Qhn7fnG8fmrjVurXtI1MP6fBAfAeIQwAANRYeQU5OpCb5XjdOgUHHK8JAKFiiHoAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBD/upuAACgfIYhGabhfF0XagIAgNARwgCgpjEMmabkNy1Fm5bj5f2GJZPzIAAAqDaEMACoYQxDkmwV7tqs3IxdjtePq99KOqbDr9sBAABeq3EhbPPmzZo5c6Y+//xzxcfH67zzztPkyZMVHR19xPXOPPNM7dixo8z0DRs2KCYmJvg4LS1NM2fO1Pvvv6+oqCgNGjRIt956qxISEhx/LgBQFVZRgQL5B1ypCwAAqk+NCmGZmZkaNWqUWrVqpblz5yotLU1z5sxRfn6+7rjjjgrXHzx4sK6++upS0w4Nb0VFRRo9erQk6cEHH1R+fr7uvfde3XTTTZo/f76zTwYA4DozNl6+OonO142Ok/MnggIAUKJGhbBly5bpwIEDevzxx5WSkiJJCgQCuvvuuzV27Fg1atToiOvXr19f3bp1O+z8t956S5s2bdLKlSvVpk0bSVJSUpKuueYabdiwQV26dHHqqQAAXGT4o5QnSwVtT5BVmO94/byk+jJkS6bP8doAANSoELZu3Tr16tUrGMAkaciQIbrzzjv1wQcf6IILLqhy/fbt2wcDmCT17t1bKSkpWrt2LSEMAGoJw+dXbnGBPvv5Cx3I2uN4/fpNjlOneo1kGIxgAgBwXo0KYVu2bNGFF15YalpSUpIaNGigLVu2VLj+ihUrtHz5ckVFRal79+6aOnWq2rdvX6r+oQFMkgzDUOvWrUOqDwCoWfILDigvL8vxugWFeY7XBADgoBoVwrKyspSUlFRmenJysjIzM4+47plnnqkuXbromGOO0fbt2zVv3jyNHDlSr776qpo3bx6sn5hY9tqBUOpXxO+PvG9LfT6z1E9UP8MwZFqSaRoyXbjXk2kaMg3JZ5oyTbvC5cPpI148h5L7a6lW1pekQ8u6OYChYbi0jw5t/69DMJb8rLhPhcPtQR5rdX3DxfrGbz+d2EaZGg7XP+wGvdpHLmzEOAr2kfHrAoYMyaj8e4hhlKxr+gxXjmz7fMavbXPvNTBkyOczZNu18/OYaRqy9OvfThc7qs9nyu935++MG2pUCKuK2267Lfj/7t27q3fv3hoyZIgWLlyou+66y9Vtm6ahunXjXd1GdUpKiqvuJuAQhQfyFBMbJdvv/LABMf4oRcdEKSW+TqXWq2wfcfM5RMf4ZZqGYmKiZPtqX31Jior2y1DJTZUNF27oZfz6YSE6JkqWG/vIHyVDkukzFfi1/abDz8M0TVkqCXfu7KNfP/i59hp4VL/kgeP1g7Wd2kY56ztav7xNulz/0G2Ypim/C19omr+GCsOllFeT9pHPZxyydOhKvlQ0lJxQub9rlVGUU+jia1BSMzGxdn8Wy8wpkM+l3wPfr9/8JSTEOl7bTTUqhCUlJSk7O7vM9MzMTCUnJ1eqVsOGDXXyySfr66+/LlU/Jyen3PpNmjSpfIN/ZVm2srJyw16/pvL5TCUlxSkrK0+BAOOE1QSGYajQKlJBfpHyiwqdrx9lqrCgSBlFubLt0I6EVbaPuP0c4lQsy7JVUFCk/EIX6hvFsm1bVmGBrCLnB4SQJMss+UNiW7Zsy/nfPdsuOSZV6NI+MqNN2ZKsgCXLskoCk2WF1KdCZf26X2zbrX1U0lb3XgOP6pc8cLx+sLYT2zCMctd3rP5huF3/0G1YlqViF/6OWvavvweyI3YfHTwKFAjYJc+zkgKWJcuylZmZK8ty/jn4/aZiDTdfg5Ka2dl5Ki6unZ/FTNOQZZgKuPR7EPj1dc3JyVdRUcDx+pWVlBQX0hlCNSqEtWnTpsy1WdnZ2dqzZ0+Za7nCrf/DDz+UmmbbtrZu3arevXtXqXZt/cUIRSBgRfTzq01KDumXBH83/phYli3LLnnNK1O/Mn3Ei+dg25JtyZX6JX9jbRXs2qwDLtxIWZLiGh8nNSm5ntXNEyts2519dGjJYBiwbbc+w7m6j2p9fdvF+od8Qg93G4ceNyhTw4H6R+R2/d9vw4WN2EfDPjJsSYZshfceUvKlk61AwHblC2XDMGT7bVdfg4Ptr62fxXw+U/L/+rfZxY5a2z6v1qiTS/v27asPP/xQWVm/XWS9atUqmaZZ6ZCUlpam9evXq3PnzqXqf/fdd9q2bVtw2n/+8x9lZGSoX79+VW4/gKPHwRspu/HPLnb+6BQAAKg5atSRsBEjRmjp0qUaP368xo4dq7S0NN13330aMWJEqXuEjRo1Sjt37tTq1aslSa+//rreeecd9evXTw0bNtT27du1YMEC+Xw+XXXVVcH1Bg8erPnz52vChAmaMmWK8vLydN9996l///4MTw8AAADAEzUqhCUnJ+u5557TX/7yF40fP17x8fEaPny4brzxxlLLWZalQOC3cz6bNWum3bt3a9asWcrOzlZiYqJOPfVUTZw4MTgyoiRFRUXpmWee0cyZMzVlyhT5/X4NGjRI06dP9+w5AgAAADi61agQJklt27bV4sWLj7jM0qVLSz3u1q1bmWmH06hRI82dOzfc5gEAAABAldSoa8IAAAAAINLVuCNhAABvlNx02oX72rh9d2MAkcUwlJIYo0apZe/lZRgl9/oKWFZYI+vVS44tuQuCA80EnEQIA4CjjOHzl9x7x7AUbTo/nK/fsGWIDz0AKuaLi5dp+jTkpAYq6pJa/kKHuZdcKEzTVLzf1oFivh1CzUIIA4CjjGH6JNkq/GWzcvc7f68zM7WZ1OIkx+sCiDy+6FjZgSKlr1uurL1ph1kq/K914lMbKHHIZTKM6LDbCLiBEAYARymrsOReZ06ziwocrwkgshVkpisvvWwIM6TgkbBwYpjfZPgD1Ez0TAAAAADwECEMAAAAADxECAMAAAAAD3FNGAAACJs/LkFR8UlhrXuk6318MXFVbRoA1FiEMAAAUGmmP1p5sqTjuyquVbuwahw6aPjvQ5iV2lDFsmWYfFQBEHl4ZwMAAJVm+P3KLS7QZ9u/UMa+X8KrIR32SNgxLTqqW8MmMhjdDkAEIoQBAICw5RXk6EBuVljrHimEFRTmVrVpAFBj8fUSAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAh7hPGAAAgFsMQymJMWqUWsfx0knx0Y7XBOANQhgAAIALfHHxMk2fhpzUQEVdUh2vHxMTLUO2TNNwvDYAdxHCAAAAXOCLjpUdKFL6uuXK2pvmeP16rdurzmlDZRiEMKC2IYQBAAC4qCAzXXnpzoewwvqNHK8JwBsMzAEAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB5idEQApRiGIUOGzBC+ojk4LLJhGCHfp8YwDBl2VVqI2sCQITOmjnxxiTJ9PikQkJMvuxkdJ8vBepHIkCFfbLyi4pNcqe+LiXOlLo5O/riEcvuqIUmGIdl2WO8h/riEqjYNcAUhDEBQlOmX32fqQHF2SH/sTEsqPJCnQqso5A/EpkzZpvXrX1ZEoih/tOQzld/yOFkNj5FhGrKt8D5AHU5eUn0ZsiXT52DVyHHwNbCP7aC4xse4sg0rtaGKZcsw+SiB8Jn+aOXJko7vqrhW7crMP/RPRTjvIWZsXEl9oIbhnRNAkM/0Kb+4QF/t/E55RQUVLm+ahmJio1SQXyTLCu3PY3Jsgto3aiuDFBaxfL4o5RcX6LOfv9SB/TtlmKZsy3I0hNVvcpw61Wskw+Cs+vIcfA3W//yF9u/+2ZVtHNOio7o1bCIjlMPmwGEYfr9yiwv02fYvlLHvl7LzpSodCUuu20hntO6oOCO2qk0FHEUIA1BGfnGh8oryK1zONA3Zfkv5RYUhh7BYf0xVm4daIr/ggPLyslwJYQWFeQ5Wi1z5Bbk6kJvlSu2CwlxX6uLolFeQU25frWoIi64TX9WmAa7g6ysAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQoyMCiEiGIRkh3kC6snUBAEDoDEOql+zObQLqJceWDKDpSnX3EMIARBbDkGlKftNStOn8DTp9hs0dzgAACJFhGIr327rk9KayLOf/Lps+U3FmQHm17I8zIQxARCk5UmWrcNdm5Wbscrx+ncbHSU3aO14XR69a9rkBACrFMCQFCpW+7iUd2LfH8frxqQ2UNORyGUa047XdRAgDEJGsogIF8g84XtcuLnS8Jo5ihjjHFcBRoSAjXXnpaY7X9ftq5xAXhDAAAKpJUbGlA3lFjtetG3D+lB8AgHMIYQAAVBPblgKW85eT27XtCnUAOMrUzuN3AAAAAFBLEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAP+au7AQAAAKi5/HEJiopPcqW2LybOlbpATUcIAwAAQBmmP1p5sqTjuyquVTtXtmGlNlSxbBkmH0lxdKHHAwAAoAzD71ducYE+2/6FMvb94so2jmnRUd0aNpFhcoUMji6EMAAAABxWXkGODuRmuVK7oDDXlbpATcfXDgAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHCGEAAAAA4CFCGAAAAAB4iBAGAAAAAB4ihAEAAACAhwhhAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUIYAAAAAHjIX90N+L3Nmzdr5syZ+vzzzxUfH6/zzjtPkydPVnR09GHX2b17txYvXqwPPvhAP/30kxITE9WjRw9NmTJFTZs2DS738ccf64orriiz/tChQ/Xwww+78nwAAAAA4FA1KoRlZmZq1KhRatWqlebOnau0tDTNmTNH+fn5uuOOOw673tdff63Vq1frwgsvVNeuXbV//3499dRTuuiii/T6668rNTW11PKzZ89WmzZtgo/r1q3r2nMCAAAAgEPVqBC2bNkyHThwQI8//rhSUlIkSYFAQHfffbfGjh2rRo0albveySefrDfffFN+/29P56STTlL//v316quv6uqrry61fLt27dS5c2fXngcAAAAAHE6NCmHr1q1Tr169ggFMkoYMGaI777xTH3zwgS644IJy10tKSiozrXHjxkpNTdXu3bvdai5QLsOQDMNwqbYhw3alNADAJf64BEXFl/2sUlW+2DqO1wTc4tbvgT8uwfGaXqhRIWzLli268MILS01LSkpSgwYNtGXLlkrV2rp1q9LT09W2bdsy88aMGaOMjAw1aNBAZ599tiZNmqTY2Ngqtd3vj7wxTnw+s9RPhCbgK1Jecb4rtU3DlAxbpmnINJ0PeqZplIRIUyHVN35dxjCNkEf5qew2KuvQku5EYe/qe7EN15/DwS8kDEOG7c43CLV9H7lS34vfA4e3UaaG28/B+O2nW/vIjIpWnizp+K6q06qd4/Wt5LrKkyUzOqbW7qPKvM5VaYPPZ7jyWc3nM2T8uoPceg0MGfL5DNl27fw85vMZypcls1M31cnPc7y+GRunPAXkM81a9Xm8RoWwrKysco9qJScnKzMzM+Q6tm1r5syZatiwoc4+++zg9MTERI0ePVo9evRQTEyMPvroIy1atEhbtmzR/Pnzw263aRqqWzc+7PVruqSkuOpuQq2y+0C6vk77XgWBQsdrJ0YnqG1qC8XERsn2W47Xj47xyzQNxcREyfaFXj8mJsr1bYQqKtovQyXB0DCdfzM+eJTTrfpebMPT+gf/X3KI2J1t1OZ9VPLA+fqH/nTryLyT2yhnfbefgxf7yPT7lVtcoM9//kIZ+9Icr5/auKX6HtNGPn9Urd1HIW8j7O2XrJeQ4N5nmaKcwl+DmBuvQUnNxMTa/Vnsl4wMfbb9S2VlOP97kJTSSGe07qjGKamKj49xvL5balQIc8rcuXP10Ucf6ZlnnlGdOr8dqu/YsaM6duwYfNyrVy81bNhQM2bM0IYNG9SlS5ewtmdZtrKycqvc7prG5zOVlBSnrKw8BQLOf1iORIZhqNAqUtaBA8orcv5omBFnykqxVVBQpPxC50NenIplWaHXN34NUwUFRbKt0I5yVHYblVXHKJYtybZs2Zbz/db+9WiOW/W92Ian9W1bhmGUTHPwSFjE7KOSB87XP/SnS0cgHduGYZS7vtvPwct9lFuQowMHQv8yOVRxBQd+204t30dH3MZh+khltpCTk6eiIud/l/1+U7GGZMvZ97iD7F/bn52dp+Li2vlZLCqq5IusvIJsV34PouJKPuvn5haooKDY8fqVlZQUF9JZZDUqhCUlJSk7O7vM9MzMTCUnJ4dUY/ny5XriiSd0zz33qFevXhUuP2TIEM2YMUMbN24MO4RJqrW/GKEIBKyIfn5OMk1DlkqCuRViKKkMy7Jl25JtqUbUP/gWY1fi+br+HA4p6fblc15cnlfrn4NtBz9AubWt2r6PXKnvxe+BA9s49LhBmRpuP4dDPv27vo/c2kZtr3/oNlT+No7YRyohELBd+SxjGIZsv+3qa2DLdq39Xjj00gM3308tq3Z9Xq1RJ062adOmzLVf2dnZ2rNnT6kh5Q9n9erVuuuuuzRx4kQNHz7crWYCAAAAQNhqVAjr27evPvzwQ2VlZQWnrVq1SqZpqnfv3kdc9+OPP9aUKVN00UUXafz48SFv84033pAkhqwHAAAA4IkadTriiBEjtHTpUo0fP15jx45VWlqa7rvvPo0YMaLUPcJGjRqlnTt3avXq1ZKkzZs3a/z48WrVqpXOO+88ffHFF8FlU1NT1aJFC0nS1KlT1bJlS3Xs2DE4MMfixYs1cOBAQhgAAAAAT9SoEJacnKznnntOf/nLXzR+/HjFx8dr+PDhuvHGG0stZ1mWAoFA8PGXX36p7OxsZWdn69JLLy217LBhwzRnzhxJJTdpXrFihRYtWqSioiI1bdpU48aN05gxY9x/cgAAAACgGhbCJKlt27ZavHjxEZdZunRpqccXXHDBYW/kfKixY8dq7NixVWkeAAAAAFRJjbomDAAAAAAiXY07Egbg6GAYJfcZc6MuAABATUYIA+Atw5BpSn7TUrTp/P08fIYtchgAAKjJCGEAPFVypMpW4a7Nys3Y5Xj9Oo2Pk5q0d7wuAACAUwhhAKqFVVSgQP4Bx+vaxYWO1wQAAHASA3MAAAAAgIcIYQAAAADgIUIYAAAAAHiIEAYAAAAAHiKEAQAAAICHGB0RAAAclQwZ8sXGKyo+yZX6vpg4V+oCqP0IYQAA4KgT5Y+WfKbsYzsorvExrmzDSm2oYtkyTD5uASiNdwUAAHDU8fuilF9coPU/f6H9u392ZRvHtOiobg2byDC5+gNAaYQwAABw1MovyNWB3CxXahcU5rpSF0Dtx1czAAAAAOAhQhgAAAAAeIgQBgAAAAAeIoQBAAAAgIcIYQAAAADgIUZHBADgCIzqbgAAIOIQwgAAOBxDkkEMAwA4ixAGAMBhFBVbOpBX5HjdugHL8ZoAgNqDEAYAwGHYthSwbFfqAgCOXgzMAQAAAAAeIoQBAAAAgIc4HREAUKsxbAYAoLYhhAEAai9GLwQA1EKEMABArcXohQCA2ogQBgCotRi9EABQGzEwBwAAAAB4iCNhAAAAtZQhQ77YeEXFJzle2xcT53jNSOWPS3DlNfDHJTheEzUDIQwAAKAWivJHSz5T9rEdFNf4GMfrW6kNVSxbhsnHxSPJkyWzUzfF5ec5XtuMjVOeuEY1EvFbBQAAUAv5fVHKLy7Q+p+/0P7dPzte/5gWHdWtYRMZJlevHI5hSHnFBfps+xfK3J/meP3kuo10RuuOijNiHa+N6kUIAwAAqMXyC3J1IDfL8boFhbmO14xUeQU5rrwG0XXiHa+JmoGvNgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwECEMAAAAADxECAMAAAAADxHCAAAAAMBDhDAAAAAA8BAhDAAAAAA8RAgDAAAAAA8RwgAAAADAQ4QwAAAAAPAQIQwAAAAAPEQIAwAAAAAPEcIAAAAAwEOEMAAAAADwkL+6GwAAiGRG8Kchu1pbAgBATUEIAwC4wyj5Z9v2r1nMqGAFAACODoQwAIAriootHcgrcqV23YDlSl0AALxACAMAuMK2JcuyJcOQbNvRkxFtzmwEANRiDMwBAAAAAB4ihAEAAACAhzgdEZViGJJhuHlxvS33L953bxuGYcjgNCkAAAAcASEMITMMyfYXKzdQ4FJ9Q7FRUcovLHRtIGu3t2HKlG1aDAIHAACAwyKEIWSGYSg3UKDPd3yl/OJCx+snxyaofaO2+mrnd8orcifoub2Ng/UNUhgAAAAOgxCGSssvLlReUb7jdWP9Ma7W92IbB+sDAAAAh/P/7d15XFTV/z/w1wxrgIP7hiJizkgBghlGICrigpqauSZoSYaWVpaPJC3C5aPFRz8a0EfJJc0Mo8wFF4SyQg1tMcU0TUAU9COZKJvA4Mz5/eF37s9xWHUYttfz8eCh98y5555z7+Ew77nnnuHCHERERERERCbEIIyIiIiIiMiEGIQRERERERGZEJ8JIyJqxriEDBERkekxCCMiaq5kuPvdE0RERGRSDMKIiJqp8jtaFJeUG73cVhqt0cskIiJqShiEERE1U0IAGq3xv7Zc1NW3rRMRETURDMKI6oBMBsjkxp/mpSuzoZQvk8mkf2U1XOaHs9+IiIiouWMQRmRMMhnkcsBcroWl3PhTsszlWpg1oPJlAIRaAwsZIGoYXJnJBBeDICIiomaNQRiREd29yyOg/l8Gbt/6n9HLt+moBDr1gvpaBm7fbBjly2QyiFrMP7t7DNWDVpGIiIio0WMQRlQHtOVl0JQWG71ccUd9t3x1wyhfBkAml0NotahpGKY7BhEREVFzxS9rJiIiIiIiMqEGF4RlZGTgxRdfhIeHB3x8fBAZGQm1uvpPzoUQ+OSTTzBw4EC4u7tj0qRJOHnypEG+3NxczJ07F56envDy8sKiRYtQVFRUBy0hIiIiIiIy1KCCsPz8fEyfPh3l5eWIjo7GvHnzEB8fjw8++KDafdevX4+oqCi88MILiI2NRbt27TBjxgxkZ2dLecrLy/HSSy8hKysLq1atQkREBI4cOYK33nqrLptFREREREQkaVDPhG3fvh3FxcWIiYlBy5YtAQAajQaLFy9GaGgoOnToUOF+ZWVliI2NxYwZM/DCCy8AAJ544gkMHz4cGzduREREBADg4MGDuHDhAvbv3w9nZ2cAgEKhQEhICNLS0uDu7l7XTSSiJoSrPBIREdGDaFB3wlJSUuDt7S0FYAAQGBgIrVaLo0ePVrrfiRMnUFRUhMDAQCnN0tISQ4YMQUpKil75KpVKCsAAwMfHBy1btsSPP/5o3MYQUdMmw/99oVod/BAREVGTJhO1WVu6jnl7e+O5557D/Pnz9dL79++PMWPGGKTrbNu2DUuWLEFaWhqsrKyk9Pj4eISHh+PkyZOwtrbG+PHj0bVrV6xevVpv/8mTJ6NTp04G6TUlhIBW2zBOo3Hfv8kgl8v+r21326cVWpRpyoE66DYymQwWZhZQ11H5pjiGTC6HhdwcavVtCK3G6OXLzSxgaWGNskZavimOYcrytXV0jszMzGFp8Yhp2qAxfvlm5v+//nVRvimOwfLr/xiNvXxTHKOxl2+KY8jkclhb2UIuMwNqvI5vrY4ArdCgtKwYQmv87++s+/qbgunOUUMIa+RyGWQ1eEPeoKYjFhQUQKFQGKTb29sjPz+/yv0sLS31AjDg7lRDIQTy8/NhbW2NgoICtGjRotblV0cmk8HMrOl+ei2Xy6CbeCWHHOZmddttLOq4fFMcw+IRw35sTOaNvHxTHKOxl2+KYzT28k1xDJZf/8do7OWb4hiNvXxTHaOuJpHLYQ47G/s6KVtf432vyXNkqEFNRyQiIiIiImrqGlQQplAoUFhYaJCen58Pe/vKo2eFQgG1Wo2ysjK99IKCAshkMmlfhUJR4XL01ZVPRERERERkLA0qCHN2dkZmZqZeWmFhIa5fv663mEZF+wHAxYsX9dIzMzPRuXNnWFtbV1q+EAIXL16ssnwiIiIiIiJjaVBBmJ+fH3766ScUFBRIaYmJiZDL5fDx8al0vz59+sDOzg4HDhyQ0srLy5GUlAQ/Pz+98s+dO4esrCwpLTU1Fbdu3cKAAQOM2xgiIiIiIqIKNKjVEfPz8zFy5Eh0794doaGhyM3NxQcffIBnnnkG4eHhUr7p06fj6tWrSE5OltI++eQTREdHY/78+VAqlYiLi8ORI0ewe/dudO3aFcDdwGzcuHEAgDfffBMlJSWIjIyESqVCbGysaRtLRERERETNUoMKwgAgIyMDS5cuxe+//w5bW1uMGTMG8+bNg6WlpZQnODgYV65cwaFDh6Q0IQQ++eQTfPHFF8jLy4OLiwveeecdeHp66pWfm5uLZcuW4ciRIzA3N8eQIUOwcOFC2NnZmayNRERERETUfDW4IIyIiIiIiKgpa1DPhBERERERETV1DMKIiIiIiIhMiEEYERERERGRCTEIIyIiIiIiMiEGYURERERERCbEIIyIiIiIiMiEGIQRAECj0WD9+vWYOnUq+vXrBy8vLwQHB+PXX3+tdt+cnByoVCqDn4kTJ5qg5mQqD9NHAKCwsBALFy6El5cXPD098dprr+Hvv/+u41qTqR09ehRvvfUWAgICoFKpsGTJkhrtx3Gk+XjQPgJwHGlODh06hNGjR8PNzQ3Dhg3Djh07qt2H40jTk5GRgRdffBEeHh7w8fFBZGQk1Gp1tfvpvj944MCBcHd3x6RJk3Dy5Mm6r3AtmNd3BahhKC0txSeffIJnn30WM2fOhFwuR3x8PKZNm4aNGzfC29u72jLefPNN9OvXT9q2tbWtyyqTiT1sH3njjTeQnp6OiIgIWFlZYc2aNZg5cyZ27NgBc3MORU3F4cOHce7cOTz55JPIz8+v9f4cR5q+h+kjHEeah19//RVz5szB+PHjsXDhQhw7dgyLFi2Cra0thg8fXu3+HEeahvz8fEyfPh1OTk6Ijo5Gbm4uPvjgA5SWliI8PLzKfdevX4+oqCjMnz8fKpUK27Ztw4wZM7B792507drVRC2ohiASQty5c0fcunXLIG348OEiNDS0yn2zs7OFUqkUBw4cqMsqUj17mD5y4sQJoVQqxeHDh6W0jIwMoVKpxL59++qkvlQ/NBqN9P9BgwaJxYsX12g/jiPNx4P2EY4jzceMGTPEpEmT9NLefPNNERgYWOV+HEealnXr1gkPDw9x8+ZNKW379u3CxcVFXLt2rdL9SktLRZ8+fcSqVauktLKyMjFo0CDx/vvv12GNa4fTEQkAYGZmBnt7e4M0lUrFqR4E4OH6SEpKChQKBXx8fKQ0Z2dnuLi4ICUlpU7qS/VDLuefFarag/YRjiPNg1qtxvHjxw3ueI0YMQIZGRnIycmpp5qRqaWkpMDb2xstW7aU0gIDA6HVanH06NFK9ztx4gSKiooQGBgopVlaWmLIkCENaqzgX0uq1J07d3Dq1Ck4OzvXKH9ERARcXFzg7e2Nd999F7du3arbClK9q2kfyczMRPfu3SGTyfTSnZ2dkZmZWZdVpEaG4whVhuNI83D58mWUl5cb/F3p0aMHANToWnMcaRoyMzMN+oFCoUC7du2q7Ae61yrqQ1evXkVpaanxK/sAOIGaKrVhwwbk5ubihRdeqDKfpaUlpkyZAl9fXygUCpw6dQrr1q3DH3/8ga+++goWFhamqTCZXE37SEFBAVq0aGGQbm9vjz/++KOOakeNCccRqg7HkeZB95ygQqHQS9dtV/UcIceRpqWgoMCgHwB3f+er6gcFBQWwtLSElZWVXrpCoYAQAvn5+bC2tjZ6fWuLQVgTVlhYWKOphF27doWlpaVe2tGjRxEdHY1XXnkFrq6uVe7fvn17RERESNteXl7o2bMnQkNDkZycjBEjRjxQ/anumaqPUOP1MH2kNjiONF6m6iPUeNWmjzwMjiPUmDAIa8ISExPx7rvvVptv//790m1+ADhz5gzmzp2LUaNGYc6cOQ907AEDBsDGxgZnzpzhoNeAmaqPKBQKXLt2zSA9Pz/f4DkzalgetI8YA8eRxsFUfYTjSONVmz6iu5aFhYV6rxUUFABAra81x5HGS6FQGPQDoPrfeYVCAbVajbKyMr27YQUFBZDJZA1mvGAQ1oRNmDABEyZMqNU+ly5dwsyZM+Hp6Ylly5bVUc2ooTBVH3F2dkZqaiqEEHrPc1y8eBFKpbJWxyfTepA+Qs2LqfoIx5HGqzZ9RK1Ww8LCApmZmejfv7+UXtlzPtR0VfS8Z2FhIa5fv15lP9C9dvHiRfTq1UtKz8zMROfOnRvEVESAC3PQPf7++2/MmDEDnTp1QlRU1EPNnf7+++9x+/ZtuLm5GbGGVN8etI/4+fkhPz8fqampUtrFixdx9uxZ+Pn51VV1qZHjOEL34jjSPFhaWqJfv344ePCgXrruTmqXLl1qVR7HkcbLz88PP/30k3QXFLh7V1Uul+utknq/Pn36wM7ODgcOHJDSysvLkZSU1KDGCt4JIwB3v4h35syZuHnzJhYtWoQLFy5Ir1laWuKxxx6Tth977DGMHTsWy5cvBwB88MEHkMlk8PDwgEKhQFpaGmJjY+Hq6oqAgACTt4XqxsP0EU9PT/j6+mLhwoVYsGABrKyssHr1aqhUKgwdOtTkbaG6c+XKFZw+fRoAUFJSgsuXLyMxMREA9Jac5jjSfD1oH+E40nzMnj0b06ZNQ0REBAIDA3H8+HHs3bsXq1ev1svHcaRpmzx5MrZu3YpXX30VoaGhyM3NRWRkJCZPnowOHTpI+aZPn46rV68iOTkZAGBlZYXQ0FBER0ejdevWUCqViIuLw61btxASElJfzTHAIIwAAP/88w/OnTsH4O7gdy8HBwccOnRI2tZoNNBqtdJ2jx49EBcXh/j4eJSWlqJDhw4YP348XnvtNZibs4s1FQ/TRwBgzZo1WLFiBcLDw3Hnzh34+vri3XffZR9pYo4fP4533nlH2j58+DAOHz4MADh//ryUznGk+XrQPgJwHGku+vbti+joaKxZswZff/01OnfujGXLlul97xPAcaSps7e3x5YtW7B06VK8+uqrsLW1xfjx4zFv3jy9fFqtFhqNRi9t5syZEEJg06ZNyMvLg4uLCzZu3PjQi78Yk0wIIeq7EkRERERERM0FnwkjIiIiIiIyIQZhREREREREJsQgjIiIiIiIyIQYhBEREREREZkQgzAiIiIiIiITYhBGRERERERkQgzCiIiIiIiITIhBGBERERERkQkxCCMioiYjJycHKpUKGzduNFqZ0dHRUKlUyMvLqzavv78/wsLCpO3jx49DpVLh+PHjUlpYWBj8/f1rdWxT0p3De+vcUAQHByM4OLjOj3P/dSQiMjYGYUTUZG3btg0qlQoTJkyo76rUWnp6OqKjo5GTk1PfVTEKXTCh++nduzdGjBiB1atXo6ioqL6rV69KSkoQHR3dIIMeqjuZmZlYvnw5Jk+eDDc3N6hUqip/37/77js8++yzcHNzw8CBAxEVFYU7d+6YsMZEZEwMwoioyUpISICDgwPS0tJw6dKl+q5OraSnpyMmJgZXrlyp76oYVUREBCIjIxEWFgZnZ2esW7cOL730EoQQ9V01o0hMTMTSpUurzLN06VIkJiZK2yUlJYiJicHPP/9skHf27NlIS0szej2p/p08eRJbt25FcXExevToUWXeH3/8Ea+++ipatGiB9957DwEBAVi7dm21fY2IGi7z+q4AEVFdyM7Oxu+//46YmBiEh4cjISEBc+bMqe9qNXvDhg1D69atAQBTpkzB3LlzkZSUhJMnT8LT07PCfUpKSvDII4+YspoPzNLSsto8FhYWNS7P3Nwc5ub8U90U+fv745dffoGdnR02btyIP//8s9K8kZGRUKlU2LRpk9QfbG1tERsbi2nTplUbxBFRw8M7YUTUJCUkJMDe3h4DBgzAsGHDkJCQUGG+goICLF++HP7+/nB1dYWfnx/efvttved/ysrKEB0djWHDhsHNzQ2+vr6YM2cOLl++LOXRarXYvHkzRo4cCTc3Nzz99NMIDw9Hfn6+3vH8/f0RGhqKI0eOYMyYMXBzc8OIESOQlJQk5fnmm2/w+uuvAwCmTZsmTeHTTVf79ttv8fLLL8PX1xeurq4ICAjAxx9/DI1Go3es4OBgjBo1Cunp6QgODkbv3r3Rv39/rF+/3uA8GLONtfHUU08BgDQNS1fnP/74A1OnTkXv3r3xn//8BwBw48YNLFy4EE8//TTc3NwwevRo7Ny5s9KyN2/ejEGDBsHd3R1BQUH466+/9F4/d+4cwsLCMHjwYLi5ucHHxwfvvPMObt68WWF5N2/exOuvv44+ffqgX79+WLZsGcrKyvTy1ORZonufCcvJyYG3tzcAICYmRrrW0dHRACp/Jmz37t0YN24c3N3d4eXlhXnz5uF///ufXp6srCzMnTsXPj4+cHNzg5+fH+bNm4fCwsIq61cbp0+fRkhICPr16wd3d3f4+/vjnXfe0cuj1WqxZcsWPPPMM3Bzc8NTTz2FkJAQnD59WsqzY8cOTJs2Dd7e3nB1dcWIESPwxRdf1KgOarUaUVFRGDJkCFxdXTFgwABERkZCrVbr5cvLy0NGRgZKSkoeqK3Z2dl47bXX4OXlhd69e2PixIn44YcfDPJduXIFs2bNgoeHB7y9vbF8+XIcPnzY4Dm7li1bws7OrtrjpqenIz09HRMnTtQLyJ9//nkIIXDw4MEHag8R1S9+vEZETVJCQgKGDBkCS0tLjBo1CnFxcUhLS4O7u7uUp7i4GFOnTkVGRgaee+45PPbYY7h58yYOHTqE3NxctG7dGhqNBqGhoUhNTcXIkSMxbdo0FBcX4+jRo/jrr7/g6OgIAAgPD8fOnTsxbtw4BAcHIycnB9u2bcPZs2cRFxend/cjKysL8+bNw+TJk/Hss89ix44deP3117Fhwwb4+PjgySefRHBwMLZu3YpZs2bB2dkZAKRPu3fu3AkbGxu8+OKLsLGxwbFjxxAVFYWioiIsWLBA7zzk5+fjpZdewpAhQxAYGIiDBw9i5cqVUCqVGDBgAADUSRtrShfktWzZUkq7desWZs6ciZEjR2L06NFo06YNSktLERwcjMuXL2Pq1Kno0qULEhMTERYWhoKCAkyfPl2v3F27dqG4uBjPP/88ysrKsHXrVkyfPh0JCQlo27YtAOCnn35CdnY2xo0bh3bt2uHChQuIj49Heno64uPjIZPJ9Mp844034ODggLfeekuaSlZQUIDIyMhat1undevWiIiIQEREBIYMGYIhQ4YAQJWLcaxduxYfffQRAgMDMX78eOTl5eHzzz/H1KlTsWvXLigUCqjVaoSEhECtViMoKAht27ZFbm4ufvjhBxQUFKBFixYPXGedGzduICQkBK1atcLLL78MhUKBnJwcJCcn6+VbtGgRvvnmG/j5+WH8+PHQaDT49ddfcerUKbi5uQEA4uLi0LNnT/j7+8Pc3Bzff/89Fi9eDCEEpk6dWmkdtFotZs+ejd9++w0TJ05Ejx498Ndff2HLli3IysrCf//7Xynvtm3bEBMTg88++wz9+vWrVVv/+ecfTJ48GSUlJQgODkarVq2wc+dOzJ49WwoAAeD27duYPn06rl+/jmnTpqFt27bYu3fvQz3vd/bsWQCQzpVOhw4d0LFjxyrvoBFRAyaIiJqY06dPC6VSKY4ePSqEEEKr1Qo/Pz+xbNkyvXwfffSRUCqVIikpyaAMrVYrhBDi66+/FkqlUnz66aeV5vnll1+EUqkUe/bs0Xs9JSXFIH3QoEFCqVSKgwcPSmmFhYXCx8dHjB07Vko7cOCAUCqV4tixYwbHLSkpMUh77733RO/evUVZWZmUFhQUJJRKpdi5c6eUVlZWJnx8fMTcuXOlNGO3sSJRUVFCqVSKzMxMcePGDZGdnS22b98uXF1dxdNPPy1u376tV+e4uDi9/Tdv3iyUSqXYvXu3lKZWq8WkSZOEh4eHKCwsFEIIkZ2dLZRKpXB3dxfXrl2T8p46dUoolUqxfPlyKa2i87h3716hVCrFL7/8YlD3WbNm6eWNiIgQSqVS/Pnnn1LaoEGDxIIFC6TtY8eOGVzHBQsWiEGDBknbN27cEEqlUkRFRVV63nRycnKEi4uLWLt2rV6+8+fPi8cee0xKP3v2rFAqleLAgQMGZVZHdw4r6nv3Sk5OFkqlUqSlpVWaJzU1VSiVSrF06VKD13R9S4iKr8WMGTPE4MGD9dKCgoJEUFCQtL1r1y7Rq1cvveslhBBxcXFCqVSK3377TUrTncvq2iWE4XX817/+ZdAvioqKhL+/vxg0aJDQaDRCCCE2bdoklEqlSE5OlvKVlpaK4cOHV3nsDRs2CKVSKbKzsyt97erVqwavPffcc2LixInVtoeIGh5ORySiJkd3t0P3abdMJsOIESOwf/9+vSl7SUlJ6NWrl/Qp9r10d0GSkpLQqlUrBAUFVZonMTERLVq0gI+PD/Ly8qSfxx9/HDY2Ngafgrdv317vmHZ2dhg7dizOnj2L69evV9s+a2tr6f9FRUXIy8tD3759UVJSgszMTL28NjY2GDNmjLRtaWkJNzc3ZGdn650HY7exMsOHD4e3tzcGDx6M8PBwdOvWDbGxsXrPfFlaWmLcuHF6+6WkpKBdu3YYNWqUlGZhYYHg4GDcvn0bv/zyi17+gIAAdOjQQdp2d3dH79698eOPP0pp957HsrIy5OXloXfv3gCAM2fOGNT9/jsyuvOVkpJSo7YbQ3JyMrRaLQIDA/WuQ9u2bdGtWzfpOuimuR05cuSBp99VR3c37YcffkB5eXmFeZKSkiCTySp8HvPeO433XovCwkLk5eXBy8sL2dnZVU6fTExMRI8ePeDs7Kx3PnTTXO/tl3PnzsX58+drfRcMuLswhru7O/r27Sul2draYtKkSbhy5QrS09MBAIcPH0aHDh0wePBgKZ+VlRUmTpxY62PqlJaWAqj4eUMrKyvpdSJqXDgdkYiaFI1Gg3379qFfv356yz27u7tj06ZNSE1Nha+vL4C7U+GGDh1aZXmXL19G9+7dq1wc4dKlSygsLJSe7bnfjRs39La7detmMNXNyckJwN3nSdq1a1dlnS5cuIA1a9bg2LFjBsu73/+GtWPHjgbHsre3x/nz56XtumhjZaKjo2FnZwdzc3N07NhRmup4rw4dOhi84bxy5Qq6desGuVz/s0PdFM2rV6/qpXfr1s2gXCcnJxw4cEDavnXrFmJiYrB//36D+lf0xv/+Mh0dHSGXy036NQJZWVkQQlTab3XXsGvXrnjxxRfx6aefIiEhAX379oW/vz9Gjx5tlKmIAODl5YVhw4YhJiYGmzdvhpeXFwICAvDMM89I1+/y5cto37693nTTivz222+Ijo7GyZMnDYLGwsLCSut86dIlZGRkPHS/rM7Vq1elAP1euqnCV69ehVKpxJUrV+Do6GjwO1dRP68pXYB6/zNuwN0PD+4NYImo8WAQRkRNyrFjx3D9+nXs27cP+/btM3g9ISFBCsKMRavVok2bNli5cmWFr+tWAzSGgoICBAUFwc7ODq+99hocHR1hZWWFM2fOYOXKldBqtXr5zczMjHJcY7Wxb9++1eY11ZvKN954A7///jtCQkLg4uICGxsbaLXaGi+Zf/8bbVPQarWQyWRYv359hdfWxsZG+n9YWBieffZZfPfddzh69CiWLVuG2NhYxMfHo2PHjg9dF5lMhqioKJw8eRLff/89Dh8+jIULF+LTTz/Fl19+CVtb2xqVc/nyZbzwwgtwdnZGWFgYOnXqBAsLC/z444/YvHmzQZ++l1arhVKpNFgMRMcY7axvug9lrl+/jk6dOum9dv36db3nXImo8WAQRkRNSkJCAtq0aYPw8HCD15KTk5GcnIzFixfD2toajo6OuHDhQpXlOTo64tSpUygvL6904QlHR0ekpqaiT58+NQogLl26BCGE3pv4rKwsAICDgwOAyt/g//zzz9IdnCeffFJKf5i7MXXRRmNzcHDA+fPnodVq9e6G6aZfdu7cWS9/Rd8Ll5WVJZ3f/Px8pKamYu7cuXpT5XTXoSKXLl1C165d9ba1Wi26dOnyQG3SqU0w5+joCCEEunTpgu7du1ebX7fa4iuvvIITJ05gypQpiIuLw7x58x6myno8PDzg4eGBefPmISEhAfPnz8f+/fsxYcIEODo64siRI7h161ald8MOHToEtVqNtWvX6l3HmkxxdXR0xLlz5+Dt7V2nQXHnzp1x8eJFg/T7+5+DgwPS09MNfr/vXWW0tlxcXADcXYny3oArNzcX165de6ipjkRUf/hMGBE1GaWlpUhKSsLAgQMxfPhwg5+pU6eiuLgYhw4dAgAMHToU586dM1jNDYB0J2To0KG4efMmtm3bVmmewMBAaDQavZXYdO7cuYOCggK9tL///lvvmEVFRdi1axdcXFykT711z0jdPy1OF4Dce6dGrVbXeDnvitRFG43Nz88P169fx/79+/WOu3XrVtjY2OgFpMDdZfxzc3Ol7bS0NJw6dQp+fn4AKr9DuGXLlkrrcP/5+fzzz6W6PQzdta7JORw6dCjMzMwQExNjcLdOCCEtr19UVIQ7d+7ova5UKiGXyyuc1vYg8vPzDeqgCxh0xxg6dCiEEIiJiTHYX7ev7lrcW1ZhYSF27NhRbR0CAwORm5uL+Ph4g9dKS0tx+/ZtafthlqgfMGAA0tLS8Pvvv0tpt2/fRnx8PBwcHPDoo48CAHx9fZGbm4vvvvtOyldWVlZh/WqqZ8+ecHZ2Rnx8vN4zrXFxcZDJZBg+fPgDl01E9Yd3woioyTh06BCKi4ul72C6n4eHB1q3bo09e/ZgxIgRCAkJwcGDB/H666/jueeew+OPP478/HwcOnQIixcvRq9evTB27Fjs2rULK1asQFpaGp544gmUlJQgNTUVU6ZMQUBAALy8vDBp0iTExsbizz//hI+PDywsLJCVlYXExEQsWrRI742Sk5MTFi1ahNOnT6NNmzbYsWMHbty4gRUrVkh5XFxcYGZmhvXr16OwsBCWlpZ46qmn4OnpCXt7e4SFhSE4OBgymQy7d++u0fS5ytRFG41t0qRJ+PLLLxEWFoYzZ87AwcEBBw8exIkTJ7Bw4UKD71tydHTElClTMGXKFKjVanz22Wdo2bIlXnrpJQB3F6548sknsWHDBpSXl6NDhw44evRolXcUc3JyMGvWLPTv3x8nT57Enj17MGrUKPTq1euh2mZtbY1HH30UBw4cgJOTE1q2bImePXtCqVQa5HV0dMQbb7yBVatW4cqVKwgICICtrS1ycnLw7bffYuLEiQgJCcGxY8ewZMkSDB8+HE5OTtBoNNi9ezfMzMwwbNiwh6qvzs6dOxEXF4eAgAA4OjqiuLgY8fHxsLOzkwLTp556CmPGjMHWrVtx6dIl9O/fH1qtFr/99hv69euHoKAgqS/NmjULkydPRnFxMb766iu0adOm2oVqxowZgwMHDuD999/H8ePH0adPH2g0GmRmZiIxMREbNmyQlnZ/mCXqX375Zezbtw8zZ85EcHAw7O3tsWvXLuTk5CA6Olr6cGTSpEn4/PPP8dZbb2HatGlo164dEhISYGVlBUD/rmdhYSG2bt0KADhx4oRUxxYtWkChUOgtlPP2229j9uzZmDFjBkaOHIm//voL27Ztw4QJE/hFzUSNFIMwImoy9uzZAysrK/j4+FT4ulwux8CBA5GQkICbN2+iVatW2LZtG6Kjo5GcnIydO3eiTZs28Pb2llbW0wVCa9euxd69e5GUlISWLVuiT58+et/ltGTJEri6umL79u1YvXo1zMzM4ODggNGjR6NPnz569XBycsJ7772HyMhIXLx4EV26dMHq1avRv39/KU+7du2wePFixMbGYtGiRdBoNNKbx3Xr1uHDDz/EmjVroFAoMHr0aHh7eyMkJOSBzltdtNHYrK2tsXXrVqxcuRI7d+5EUVERunfvjhUrVhispAjcDSzlcjm2bNmCGzduwN3dHe+99x7at28v5Vm1ahWWLl2KL774AkII+Pj4YP369XrX4V5r1qzBRx99hFWrVsHc3BxBQUF4++23jdK+ZcuWYenSpVixYgXKy8sxZ86cCoMw4G5A4OTkhM2bN+Pjjz8GcPfZJx8fH+kDCJVKBV9fX3z//ffIzc3FI488ApVKhfXr18PDw8Modfby8sLp06exf/9+/PPPP2jRogXc3d2xcuVKvWmbK1asgEqlwtdff43IyEi0aNECrq6u8PT0BHB3cYuoqCisWbMGH374Idq2bYspU6agdevWWLhwYZV1kMvl+Pjjj7F582bs3r0bycnJeOSRR9ClSxcEBwfXaMpmTbRt2xbbt2/Hv//9b3z++ecoKyuDSqXCunXrMHDgQCmfra0ttmzZgmXLluGzzz6DjY0Nxo4dC09PT8ydO1cKxoC7dxI/+ugjveNs2rQJwN1pjfcGYYMGDUJMTAxiYmKwdOlStG7dGqGhoXj11VeN0j4iMj2ZeJiPT4mIqFb8/f3Rs2dPxMbG1ndViCqUk5ODwYMHP9AdI6rY5s2bsWLFCqSkpOh9dQIRNV98JoyIiIjISO7/3q6ysjJ8+eWXcHJyYgBGRBJORyQiIiIykjlz5qBz587o1asXioqKsGfPHmRmZlb69Q5E1DwxCCMiIiIyEl9fX3z99ddISEiARqPBo48+itWrV2PEiBH1XTUiakD4TBgREREREZEJ8ZkwIiIiIiIiE2IQRkREREREZEIMwoiIiIiIiEyIQRgREREREZEJMQgjIiIiIiIyIQZhREREREREJsQgjIiIiIiIyIQYhBEREREREZnQ/wMXZYlvfm0DOgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "bins = np.linspace(np.log10(np.min([np.min(qumcm1_statistic['acceptance_prob']),\n",
    "                                    np.min(qumcm2_statistic['acceptance_prob']),\n",
    "                                    np.min(cl_statistic['acceptance_prob'])]))-0.1, 0, num=30)\n",
    "\n",
    "plt.hist(np.log10(qumcm1_statistic['acceptance_prob']),label= 'quantum enhanced Xi' , alpha= 0.8, bins= bins, density=True)\n",
    "plt.hist(np.log10(qumcm2_statistic['acceptance_prob']),label= 'quantum enhanced XiXi+1' , alpha= 0.8, bins= bins, density=True)\n",
    "plt.hist(np.log10(cl_statistic['acceptance_prob']),label= 'classical uniform' ,alpha= 0.5, bins= bins, density=True)\n",
    "\n",
    "\n",
    "# plt.xscale(\"log\")\n",
    "\n",
    "plt.xlabel(\"Acceptance Probabilities | scale: log10\")\n",
    "plt.ylabel(\"Normalized Counts\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot depicts that the *Acceptance-Probability* for the *quantum-enhanced* sampling is skewed towards unity, whereas for the *classical-uniform* sampling it is barely close to unity for most of th cases leading to a large rejection rate of the proposed moves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Energy-Difference**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "bins = np.linspace(0, np.max(cl_statistic['energy'])+0.1, num=30)\n",
    "\n",
    "plt.hist(qumcm1_statistic['energy'],label= 'quantum enhanced Xi' , alpha= 0.8, bins= bins)\n",
    "plt.hist(qumcm2_statistic['energy'],label= 'quantum enhanced XiXi+1' , alpha= 0.8, bins= bins)\n",
    "plt.hist(cl_statistic['energy'],label= 'classical uniform' ,alpha= 0.5, bins= bins)\n",
    "\n",
    "\n",
    "# plt.xscale(\"log\")\n",
    "\n",
    "plt.xlabel(\"Energy-Difference Statistics\")\n",
    "# plt.ylabel(\"Hamming Distance\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows that the *Energy-Difference* of the propose transitions is low for the case of *quantum-enhanced* transitions compared to the *classical-uniform* sampling, this also explains the trend in *Acceptance-Probability* as it is directly dependent on the former.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hamming-Distance**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "bins = np.arange(0, n_spins+1)\n",
    "\n",
    "\n",
    "plt.bar(*np.unique(qumcm1_statistic['hamming'], return_counts=True),label= 'quantum enhanced Xi' , alpha= 0.8)\n",
    "plt.bar(*np.unique(qumcm2_statistic['hamming'], return_counts=True),label= 'quantum enhanced XiXi+1' , alpha= 0.8)\n",
    "plt.bar(*np.unique(cl_statistic['hamming'], return_counts=True),label= 'classical uniform' ,alpha= 0.5)\n",
    "\n",
    "\n",
    "# plt.xscale(\"log\")\n",
    "\n",
    "plt.xlabel(\"Hamming-Distance Statistics\")\n",
    "# plt.ylabel(\"Hamming Distance\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### **Convergence Analysis**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### KL Divergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "kldiv_c = calculate_running_kl_divergence(exact_sampled_model.boltzmann_pd, cl_chain)\n",
    "kldiv_q1 = calculate_running_kl_divergence(exact_sampled_model.boltzmann_pd, qamcmc_chain_1)\n",
    "kldiv_q2 = calculate_running_kl_divergence(exact_sampled_model.boltzmann_pd, qamcmc_chain_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(kldiv_c, label= 'classical-uniform')\n",
    "plt.plot(kldiv_q1, label= 'quantum-enhanced Xi')\n",
    "plt.plot(kldiv_q2, label= 'quantum-enhanced more X_i terms')\n",
    "plt.xlabel(\"iterations \")\n",
    "plt.ylabel(\"KL divergence\")\n",
    "plt.yscale('log')\n",
    "# plt.xscale(\"log\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  },
  "vscode": {
   "interpreter": {
    "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}