example_higher_pauli_weight_mixer.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### IMPORTs & HELPER FUNCTIONs"
   ]
  },
  {
   "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_qulacs_exact import quantum_mcmc_exact\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",
    "from scipy.linalg import expm\n",
    "from qulacs.gate import DenseMatrix, SparseMatrix\n",
    "from qulacs import QuantumState\n",
    "from qumcmc.quantum_mcmc_routines_qulacs import quantum_enhanced_mcmc\n",
    "from qumcmc.quantum_mcmc_qulacs_2 import quantum_enhanced_mcmc_2\n",
    "from qumcmc.quantum_mcmc_routines_qulacs_exact import quantum_mcmc_exact\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "### BAS dataset energy model\n",
    "### 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']\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",
    "        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": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# hebbing learning\n",
    "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": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def define_random_spin_ising_model(n_spins:int,seed_val:int):\n",
    "    # define the model # seed 4\n",
    "    np.random.seed(seed_val)#(610358)# should always be in the same cell!  ## best seed -> 610358\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",
    "    # defining h\n",
    "    h = np.round(np.random.uniform(low= -1, high = 1, size= (n_spins)), decimals=2)\n",
    "    # instantiate the model\n",
    "    model = IsingEnergyFunction(J, h, name= 'my_model')\n",
    "    return model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXPERIMENTs"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate Instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# \n",
    "gridsize=3\n",
    "bas=bas_dataset(grid_size=gridsize)\n",
    "bas.dataset.sort()\n",
    "# considering only stripes dataset\n",
    "wt=hebbing_learning(bas.bas_dict['bars'])\n",
    "\n",
    "# creating ising model for the bas stripes only dataset\n",
    "n_spins=gridsize*gridsize\n",
    "shape_of_J=(n_spins,n_spins)\n",
    "J=-1*wt\n",
    "h=np.zeros(n_spins)\n",
    "model=IsingEnergyFunction(J,h,name=f'ising model BAS {n_spins}X{n_spins} bars only')\n",
    "#model.model_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ###\n",
    "# model=define_random_spin_ising_model(n_spins=10,seed_val=1)\n",
    "# #model.model_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n",
      "     MODEL : ising model BAS 9X9 bars only |  beta : 1.5\n",
      "=============================================\n",
      "Num Most Probable States : 6\n",
      "Entropy : 2.5849625007211547\n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta=1.5\n",
    "## run exact sampling over all possible configurations \n",
    "exact_sampled_model = Exact_Sampling(model, beta)\n",
    "\n",
    "## get distribution from the model\n",
    "bpd=exact_sampled_model.boltzmann_pd\n",
    "exact_sampled_model.sampling_summary()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run MCMC Chains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_different_chains=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed_val_list=list(range(1,num_different_chains+1))\n",
    "list_labels_bas=['cl','local','Q-MCMC:pauli_wt_1','Q-MCMC:pauli_wt_3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 2: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 3: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 4: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 5: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 6: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 7: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 8: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 9: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}, 10: {'cl': 0, 'local': 0, 'Q-MCMC:pauli_wt_1': 0, 'Q-MCMC:pauli_wt_3': 0}}\n"
     ]
    }
   ],
   "source": [
    "init_val_keys=dict(zip(list_labels_bas,[0,0,0,0]))\n",
    "list_init_val_keys=[init_val_keys.copy() for i in range(1,num_different_chains+1)]\n",
    "dict_mcmc_bas_gridsize_3=dict(zip(seed_val_list,list_init_val_keys))\n",
    "print(dict_mcmc_bas_gridsize_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  0111010001 with energy: -0.4089999999999998\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:27<00:00, 549.74it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  1001000110 with energy: 0.705000000000001\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:28<00:00, 529.12it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  1010111000 with energy: -3.3569999999999998\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:29<00:00, 511.74it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  0001100111 with energy: 1.2410000000000008\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:29<00:00, 505.00it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  1011100001 with energy: -6.563000000000001\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:30<00:00, 486.77it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  1001110101 with energy: -3.165\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:30<00:00, 490.13it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  1110111100 with energy: -2.269\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:30<00:00, 492.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  0001010011 with energy: 0.21099999999999997\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:31<00:00, 479.55it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  1000001001 with energy: -10.835\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:31<00:00, 476.11it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  0001010001 with energy: 2.9849999999999994\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 15000/15000 [00:31<00:00, 481.31it/s]\n"
     ]
    }
   ],
   "source": [
    "### case of mismatched hamiltonian\n",
    "import random\n",
    "n_spins=10\n",
    "model=define_random_spin_ising_model(n_spins=n_spins,seed_val=1)# data for presentation.\n",
    "beta=1.5\n",
    "## run exact sampling over all possible configurations \n",
    "exact_sampled_model = Exact_Sampling(model, beta)\n",
    "\n",
    "## get distribution from the model\n",
    "bpd=exact_sampled_model.boltzmann_pd\n",
    "#exact_sampled_model.sampling_summary()\n",
    "\n",
    "\n",
    "random_indices=random.sample(range(0,7),k=5)\n",
    "J_pert=model.get_J\n",
    "for j in random_indices:\n",
    "    J_pert[j,j+1]=-1*J_pert[j,j+1]\n",
    "h_pert=model.get_h\n",
    "model_pert=IsingEnergyFunction(J_pert,h_pert,name=f'perturbed {n_spins}X{n_spins}')\n",
    "\n",
    "# run mcmc for perturbed case\n",
    "num_different_chains=10\n",
    "seed_val_list=list(range(1,num_different_chains+1))\n",
    "list_labels_bas=['Q-MCMC perturbed:pauli_wt_1']\n",
    "init_val_keys=dict(zip(list_labels_bas,[0]))\n",
    "list_init_val_keys=[init_val_keys.copy() for i in range(1,num_different_chains+1)]\n",
    "dict_perturbed=dict(zip(seed_val_list,list_init_val_keys))\n",
    "\n",
    "# quantum 1: single qubit pauli\n",
    "for seed_val in range(1,num_different_chains+1):\n",
    "    steps = 15000\n",
    "    #list_labels.append('QMCMC; pauli_wt-1; gamma range=(0.2,0.6)')\n",
    "    qamcmc_chain_1 =quantum_enhanced_mcmc_2(\n",
    "        n_hops=steps,\n",
    "        model=model_pert,\n",
    "        temperature=1/beta,\n",
    "        verbose=True,\n",
    "        name= 'Q-MCMC perturbed:pauli_wt_1',\n",
    "        gamma_range=(0.1,0.4)\n",
    "    )\n",
    "    #qumcm1_statistic = get_trajectory_statistics(qamcmc_chain_1, exact_sampled_model, verbose= False)\n",
    "    dict_perturbed[seed_val]['Q-MCMC perturbed:pauli_wt_1']=qamcmc_chain_1\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 2: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 3: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 4: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 5: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 6: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 7: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 8: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 9: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}, 10: {'Q-MCMC perturbed:pauli_wt_1': MCMCChain()}}\n"
     ]
    }
   ],
   "source": [
    "print(dict_perturbed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 2: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 3: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 4: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 5: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 6: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 7: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 8: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 9: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}, 10: {'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}}\n"
     ]
    }
   ],
   "source": [
    "name='dict_ising_model_num_spins_10_beta_1.5_seed_1_with_pert.pkl'\n",
    "with open(name,'rb') as f:\n",
    "    dict_mcmc_bas_gridsize_3=pickle.load(f)\n",
    "print(dict_mcmc_bas_gridsize_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i in range(1,11):\n",
    "#     dict_mcmc_bas_gridsize_3[i]['Q-MCMC-pert']=dict_perturbed[i]['Q-MCMC:pauli_wt_1']\n",
    "\n",
    "# dict_mcmc_bas_gridsize_3\n",
    "# done"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# list_labels=['cl',\n",
    "#                 'QMCMC; pauli_wt-1; gamma range=(0.1,0.4)',\n",
    "#                 'QMCMC; pauli_wt-2; gamma range=(0.1,0.4)','local']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "for seed_val in range(1,num_different_chains+1):\n",
    "    # classical uniform\n",
    "    steps=15000\n",
    "    #list_labels.append('classical uniform strategy')\n",
    "    cl_chain =classical_mcmc(\n",
    "        n_hops=steps,\n",
    "        model=model,\n",
    "        temperature=1/beta\n",
    "    )\n",
    "    cl_statistic = get_trajectory_statistics(cl_chain, exact_sampled_model, verbose= False)\n",
    "    dict_mcmc_bas_gridsize_3[seed_val]['cl']=cl_chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[17], line 5\u001b[0m\n\u001b[1;32m      3\u001b[0m steps\u001b[39m=\u001b[39m\u001b[39m15000\u001b[39m\n\u001b[1;32m      4\u001b[0m \u001b[39m#list_labels.append('classical uniform strategy')\u001b[39;00m\n\u001b[0;32m----> 5\u001b[0m cl_chain \u001b[39m=\u001b[39mclassical_mcmc(\n\u001b[1;32m      6\u001b[0m     n_hops\u001b[39m=\u001b[39;49msteps,\n\u001b[1;32m      7\u001b[0m     model\u001b[39m=\u001b[39;49mmodel,\n\u001b[1;32m      8\u001b[0m     temperature\u001b[39m=\u001b[39;49m\u001b[39m1\u001b[39;49m\u001b[39m/\u001b[39;49mbeta,\n\u001b[1;32m      9\u001b[0m     method\u001b[39m=\u001b[39;49m\u001b[39m'\u001b[39;49m\u001b[39mlocal\u001b[39;49m\u001b[39m'\u001b[39;49m\n\u001b[1;32m     10\u001b[0m )\n\u001b[1;32m     11\u001b[0m cl_statistic \u001b[39m=\u001b[39m get_trajectory_statistics(cl_chain, exact_sampled_model, verbose\u001b[39m=\u001b[39m \u001b[39mFalse\u001b[39;00m)\n\u001b[1;32m     12\u001b[0m dict_mcmc_bas_gridsize_3[seed_val][\u001b[39m'\u001b[39m\u001b[39mlocal\u001b[39m\u001b[39m'\u001b[39m]\u001b[39m=\u001b[39mcl_chain\n",
      "File \u001b[0;32m~/Documents/QBMS/quMCMC/qumcmc/classical_mcmc_routines.py:91\u001b[0m, in \u001b[0;36mclassical_mcmc\u001b[0;34m(n_hops, model, initial_state, temperature, verbose, method, local_flips)\u001b[0m\n\u001b[1;32m     89\u001b[0m     s_prime \u001b[39m=\u001b[39m get_random_state(num_spins)\n\u001b[1;32m     90\u001b[0m \u001b[39melif\u001b[39;00m method \u001b[39m==\u001b[39m \u001b[39m'\u001b[39m\u001b[39mlocal\u001b[39m\u001b[39m'\u001b[39m :\n\u001b[0;32m---> 91\u001b[0m     rbstr \u001b[39m=\u001b[39m random_bstr(num_spins, num_flips)\n\u001b[1;32m     92\u001b[0m     s_prime \u001b[39m=\u001b[39m xor_strings(current_state\u001b[39m.\u001b[39mbitstring, rbstr)\n\u001b[1;32m     94\u001b[0m \u001b[39m# accept/reject s_prime\u001b[39;00m\n",
      "File \u001b[0;32m~/Documents/QBMS/quMCMC/qumcmc/basic_utils.py:377\u001b[0m, in \u001b[0;36mrandom_bstr\u001b[0;34m(n, k)\u001b[0m\n\u001b[1;32m    375\u001b[0m \u001b[39massert\u001b[39;00m n \u001b[39m>\u001b[39m\u001b[39m=\u001b[39m k\n\u001b[1;32m    376\u001b[0m s \u001b[39m=\u001b[39m \u001b[39m'\u001b[39m\u001b[39m1\u001b[39m\u001b[39m'\u001b[39m\u001b[39m*\u001b[39mk \u001b[39m+\u001b[39m \u001b[39m'\u001b[39m\u001b[39m0\u001b[39m\u001b[39m'\u001b[39m\u001b[39m*\u001b[39m(n\u001b[39m-\u001b[39mk)\n\u001b[0;32m--> 377\u001b[0m perm \u001b[39m=\u001b[39m \u001b[39mlist\u001b[39;49m(permutations(s))\n\u001b[1;32m    378\u001b[0m r \u001b[39m=\u001b[39m perm[np\u001b[39m.\u001b[39mrandom\u001b[39m.\u001b[39mrandint(\u001b[39m0\u001b[39m, \u001b[39mlen\u001b[39m(perm))]\n\u001b[1;32m    379\u001b[0m rnd_str \u001b[39m=\u001b[39m \u001b[39m'\u001b[39m\u001b[39m'\u001b[39m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "for seed_val in range(1,num_different_chains+1):\n",
    "    # classical local\n",
    "    steps=15000\n",
    "    #list_labels.append('classical uniform strategy')\n",
    "    cl_chain =classical_mcmc(\n",
    "        n_hops=steps,\n",
    "        model=model,\n",
    "        temperature=1/beta,\n",
    "        method='local'\n",
    "    )\n",
    "    cl_statistic = get_trajectory_statistics(cl_chain, exact_sampled_model, verbose= False)\n",
    "    dict_mcmc_bas_gridsize_3[seed_val]['local']=cl_chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting with:  011000101 with energy: -16.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "runnning quantum MCMC steps . ..: 100%|██████████| 100/100 [00:00<00:00, 187.61it/s]\n"
     ]
    }
   ],
   "source": [
    "qmcmc_trial =quantum_enhanced_mcmc_2(\n",
    "    n_hops=100,\n",
    "    model=model,\n",
    "    temperature=1/beta,\n",
    "    verbose=True,\n",
    "    name= 'Q-MCMC:pauli_wt_1',\n",
    "    gamma_range=(0.1,0.4),\n",
    "    mixer= {'alternate': {1: 0.5, 2: 0.5}}\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# quantum 1: single qubit pauli\n",
    "for seed_val in range(1,num_different_chains+1):\n",
    "    steps = 15000\n",
    "    #list_labels.append('QMCMC; pauli_wt-1; gamma range=(0.2,0.6)')\n",
    "    qamcmc_chain_1 =quantum_enhanced_mcmc_2(\n",
    "        n_hops=steps,\n",
    "        model=model,\n",
    "        temperature=1/beta,\n",
    "        verbose=True,\n",
    "        name= 'Q-MCMC:pauli_wt_1',\n",
    "        gamma_range=(0.1,0.4)\n",
    "    )\n",
    "    qumcm1_statistic = get_trajectory_statistics(qamcmc_chain_1, exact_sampled_model, verbose= False)\n",
    "    dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC:pauli_wt_1']=qamcmc_chain_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for seed_val in range(1,num_different_chains+1):\n",
    "# quantum 2: \n",
    "    steps = 15000\n",
    "    #list_labels.append('QMCMC; pauli_wt-2; gamma range=(0.2,0.6)')\n",
    "    qamcmc_chain_2 =quantum_enhanced_mcmc_2(\n",
    "        n_hops=steps,\n",
    "        model=model,\n",
    "        temperature=1/beta,\n",
    "        verbose=True,\n",
    "        pauli_weight_x_mixer=3,\n",
    "        name='Q-MCMC:pauli_wt_3',\n",
    "        gamma_range=(0.1,0.4)\n",
    "    )\n",
    "    dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC:pauli_wt_3']=qamcmc_chain_2\n",
    "    qumcm2_statistic = get_trajectory_statistics(qamcmc_chain_2, exact_sampled_model, verbose= False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# name=f'''dict_simulations_BAS_bars_dataset_3x3.pkl'''\n",
    "#with open(name,'wb') as f:\n",
    "#         pickle.dump(dict_mcmc_bas_gridsize_3,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### plotting related"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this function would be useful for plotting curves\n",
    "def plot_with_error_band(xval:list,y_list_of_list:list,label:str,\n",
    "                            std_dev_multiplicative_factor:int=1,\n",
    "                            alpha_for_plot:float=0.5):\n",
    "\n",
    "    curve_of_mean_value=np.mean(y_list_of_list,axis=0)\n",
    "    standard_dev_band=np.std(y_list_of_list,axis=0)\n",
    "    plt.plot(xval,curve_of_mean_value,\"-\",label=label)\n",
    "    plt.fill_between(xval,\n",
    "                        curve_of_mean_value-standard_dev_band* std_dev_multiplicative_factor,\n",
    "                        curve_of_mean_value+standard_dev_band* std_dev_multiplicative_factor,\n",
    "                        alpha=alpha_for_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#list_labels_bas=['cl']#['cl',  'Q-MCMC:pauli_wt_1', 'Q-MCMC:pauli_wt_3','local']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'cl': MCMCChain(), 'local': MCMCChain(), 'Q-MCMC': MCMCChain(), 'Q-MCMC-pert': MCMCChain()}\n"
     ]
    }
   ],
   "source": [
    "print(dict_mcmc_bas_gridsize_3[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10/10 [00:53<00:00,  5.39s/it]\n"
     ]
    }
   ],
   "source": [
    "# KL divergence\n",
    "list_kl_cl_bas_gridsize_3=[]\n",
    "list_kl_qmcmc_pauli1_bas_gridsize_3=[]\n",
    "list_kl_qmcmc_pauli3_bas_gridsize_3=[]\n",
    "list_kl_local=[]\n",
    "list_kl_pert=[]\n",
    "for seed_val in tqdm(range(1,num_different_chains+1)):\n",
    "    cl_chain=dict_mcmc_bas_gridsize_3[seed_val]['cl']\n",
    "    local_chain=dict_mcmc_bas_gridsize_3[seed_val]['local']\n",
    "    qamcmc_chain_1=dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC']\n",
    "    #qamcmc_chain_2=dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC:pauli_wt_3']\n",
    "    q_pert=dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC-pert']\n",
    "    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)\n",
    "    kldiv_local= calculate_running_kl_divergence(exact_sampled_model.boltzmann_pd, local_chain)\n",
    "    kl_pert=calculate_running_kl_divergence(exact_sampled_model.boltzmann_pd, q_pert)\n",
    "    #\n",
    "    list_kl_cl_bas_gridsize_3.append(kldiv_c)\n",
    "    list_kl_qmcmc_pauli1_bas_gridsize_3.append(kldiv_q1)\n",
    "    #list_kl_qmcmc_pauli3_bas_gridsize_3.append(kldiv_q2)\n",
    "    list_kl_local.append(kldiv_local)\n",
    "    list_kl_pert.append(kl_pert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=list(range(0,15000+1))\n",
    "plt.figure(figsize=(12,8))\n",
    "plot_with_error_band(x,list_kl_cl_bas_gridsize_3,label='classical uniform')\n",
    "#plot_with_error_band(x,list_kl_local,label='local')\n",
    "plot_with_error_band(x,list_kl_qmcmc_pauli1_bas_gridsize_3,label='Q-MCMC:pauli_wt_1')\n",
    "#plot_with_error_band(x,list_kl_qmcmc_pauli3_bas_gridsize_3,label='Q-MCMC:pauli_wt_3')\n",
    "plot_with_error_band(x,list_kl_pert,label='Q-pert')\n",
    "plt.xlabel(\"iterations \")\n",
    "plt.ylabel(\"KL divergence\")\n",
    "plt.yscale('log')\n",
    "plt.legend()\n",
    "# plt.savefig(\"KL_BAS_3X3_bars_only.pdf\")\n",
    "# plt.savefig(\"KL_BAS_3X3_bars_only.jpeg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'cl': MCMCChain(),\n",
       " 'local': MCMCChain(),\n",
       " 'Q-MCMC': MCMCChain(),\n",
       " 'Q-MCMC-pert': MCMCChain()}"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict_mcmc_bas_gridsize_3[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  4%|▍         | 674/15000 [00:00<00:02, 6667.88it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 15000/15000 [00:24<00:00, 616.86it/s]\n",
      "100%|██████████| 15000/15000 [00:37<00:00, 399.28it/s]\n",
      "100%|██████████| 15000/15000 [00:30<00:00, 484.61it/s]\n",
      "100%|██████████| 15000/15000 [00:36<00:00, 410.86it/s]\n",
      "100%|██████████| 15000/15000 [00:23<00:00, 642.14it/s]\n",
      "100%|██████████| 15000/15000 [00:32<00:00, 456.19it/s]\n",
      "100%|██████████| 15000/15000 [00:28<00:00, 521.40it/s]\n",
      "100%|██████████| 15000/15000 [00:37<00:00, 396.84it/s]\n",
      "100%|██████████| 15000/15000 [00:23<00:00, 632.40it/s]\n",
      "100%|██████████| 15000/15000 [00:29<00:00, 507.76it/s]\n",
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     ]
    }
   ],
   "source": [
    "list_mag_cl_bas_gridsize_3=[]\n",
    "list_mag_qmcmc_pauli1_bas_gridsize_3=[]\n",
    "list_mag_qmcmc_pauli3_bas_gridsize_3=[]\n",
    "list_mag_local=[]\n",
    "list_mag_pert=[]\n",
    "magnetization_model = exact_sampled_model.get_observable_expectation(magnetization_of_state)\n",
    "\n",
    "for seed_val in range(1,num_different_chains+1):\n",
    "    cl_chain=dict_mcmc_bas_gridsize_3[seed_val]['cl']\n",
    "    local_chain=dict_mcmc_bas_gridsize_3[seed_val]['local']\n",
    "    qamcmc_chain_1=dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC']\n",
    "    #qamcmc_chain_2=dict_mcmc_bas_gridsize_3[seed_val][list_labels_bas[3]]\n",
    "    q_pert=dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC-pert']\n",
    "    \n",
    "    mag_c = calculate_runnning_magnetisation(cl_chain)\n",
    "    mag_q1 = calculate_runnning_magnetisation(qamcmc_chain_1)\n",
    "    #mag_q2 = calculate_runnning_magnetisation(qamcmc_chain_2)\n",
    "    mag_local= calculate_runnning_magnetisation(local_chain)\n",
    "    mag_pert =  calculate_runnning_magnetisation(q_pert)\n",
    "    #\n",
    "    list_mag_cl_bas_gridsize_3.append(mag_c)\n",
    "    list_mag_qmcmc_pauli1_bas_gridsize_3.append(mag_q1)\n",
    "    #list_mag_qmcmc_pauli3_bas_gridsize_3.append(mag_q2)\n",
    "    list_mag_local.append(mag_local)\n",
    "    list_mag_pert.append(mag_pert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Lc9FFF7F+/XruueceoijijDPO2OOyM8UREfMsCIIgCIIwk7z0pS/l1ltvJYoidu7cyU9/+lPOO+88XvWqV/GVr3wli2lOwzZGR0eZN28eQRDwjW98Y5/bX7x4MY88Eg9t8Z3vfKcljvfBBx/k+eefR2vNrbfeykte8hLOP/98fvKTn7B7926CIOC2227Llh8eHmbBggUAfPWrX82md3R0MDo6mn1+9atfzRe+8IXscxpO0cxzzz3HkiVLeO9738uVV17Jo48+Omk7ExkeHqanp4dischTTz3F/fffn81zXTc7tle84hXcfvvt7NixIzt3GzZs4Nxzz+UnP/kJg4ODhGHIv//7v7ds/3d+53d4y1vewjve8Y49n9AZRMRzO8gIg4IgCIJwTHP11VezYsUKVq5cyctf/nI+/elPM3fuXC6//HKuuOIKVq9ezapVq7I0dH/1V3/F+eefz0UXXcSLXvSifW7/ne98Jz/5yU9YuXIlv/jFL1qc3HPPPZcbb7yRZcuWcdJJJ3H11Vczb948Pvaxj3HhhRdy0UUXsWzZsmz5j33sY1x33XWcc845zJo1K5v++te/njvuuCPrMPj5z3+ehx9+mBUrVrB8+XJuuummSeX6t3/7N8444wxWrVrF448/zu/8zu/Q19fHRRddxBlnnMEHP/jBSetcfvnlhGHIsmXL+PCHP8wFF1yQzXvXu97FihUreOtb38ry5cv5+Mc/zqtf/WpWrFjBq171KrZu3cqCBQv4yEc+wnnnncdFF13E4sWL6erqyrbx1re+lcHBQa6//vp9nteZQJmjSBiuXr3aPPzww4d/x6EPjnf49ysIgiAIxzBr165tEYXHI/fccw+f+cxn+N73vjfTRTmspLHXYRhy9dVX87u/+7tcffXVANx+++18+9vf5utf//phK89U16JS6hFjzOqJy0rMsyAIgiAIgnBY+djHPsZdd91FrVbj1a9+NVdddRUQx3P/4Ac/4D/+4z9mtoB7QZzndhDnWRAEQRCmHXGehSOF/XGeJeZZEARBEARBENpExHNbHD3uvCAIgiAIgnDoEPEsCIIgCIIgCG0i4lkQBEEQBEEQ2kTEsyAIgiAIxzWbNm3iyiuvZOnSpSxZsoQbb7yRer0+abmbb74ZpRR33XVXNu3OO+9EKcXtt98OQBAEfPjDH2bp0qWcffbZXHjhhfzgBz8A4oFSXvrSl7Zsc9WqVS2j6D344INcfPHFnHbaaZx11ln8/u//fjZAi3BkIOJZEARBEITjFmMM11xzDVdddRXr1q1j3bp1VKtVPvShD025/Jlnnsktt9ySff7mN7/JypUrs8//63/9L7Zu3crjjz/OL3/5S+68886W0fpGR0fZuHEjEGd4aGb79u1cd911fOpTn+I3v/kNv/rVr7j88sv3OtqfcPgR8SwIgiAIwnHL3XffTT6fz4aCtm2bz372s3zta19jbGxs0vIvfelLefDBBwmCgLGxMZ555hlWrVoFQKVS4Utf+hJf+MIXyOVyAMyZM4c3vvGN2fpvfOMbufXWW4FYeDePovcP//APvP3tb+fCCy/Mpr3hDW9gzpw5037cwoEjg6S0w1GUC1sQBEEQjkY+9eCneGrgqWnd5ot6X8Sfnvene13miSee4JxzzmmZ1tnZyeLFi1uEcYpSile+8pX88Ic/ZHh4mCuuuILnn38egGeeeYZFixbR2dm5x/1de+21vOMd7+ADH/gA3/3ud/nGN76RjaT3+OOP8/a3v/0AjlQ4nIjzLAiCIAiCsB+8+c1v5pZbbuGWW25pcY7boa+vj56eHm655RaWLVtGsVg8RKUUDhXiPAuCIAiCMOPsyyE+VCxfvjzr7JcyMjLCtm3buPfee7nhhhsAWoaLPu+883jssccoFouceuqp2fRTTjmFF154gZGRkb26z29605t4z3vew80339wy/fTTT+eRRx7hyiuvPPgDEw4Z4jwLgiAIgnDc8opXvIJKpcLXvvY1AKIo4k/+5E+48cYbec973sOaNWtYs2YN8+fPb1nvk5/8JJ/4xCdaphWLRX7v936P973vffi+D8DOnTu57bbbWpa7+uqr+dCHPsRll13WMv3GG2/kq1/9Kg888EA27Vvf+hbbt2+ftuMVDh4Rz4IgCIIgHLcopbjjjju4/fbbWbp0KX19fViWxZ/92Z/tdb3XvOY1XHrppZOmf/zjH6e/v5/ly5dzxhln8LrXvW6SC93R0cGf/umf4nley/Q5c+Zwyy238IEPfIDTTjuNZcuW8cMf/pCOjo6DP1Bh2lDmKOoMt3r1avPwww8f/h0HVXALh3+/giAIgnAMs3btWpYtWzbTxWjhvvvu4/rrr+eOO+7g7LPPnuniCIeJqa5FpdQjxpjVE5eVmGdBEARBEISEF7/4xWzYsGGmiyEcwUjYhiAIgiAIgiC0iYhnQRAEQRAEQWgTEc+CIAiCIAiC0CYingVBEARBEAShTUQ8C4IgCIIgCEKbiHhuh6MonZ8gCIIgCPvHpk2buPLKK1m6dClLlizhxhtvpF6vT1ru5ptvRinFXXfdlU278847UUploxQGQcCHP/xhli5dytlnn82FF17ID37wAwAWL17MS1/60pZtrlq1ijPOOCP7/OCDD3LxxRdz2mmncdZZZ/H7v//7VCqVaT/mNWvWtIyaKLSPiGdBEARBEI5bjDFcc801XHXVVaxbt45169ZRrVb50Ic+NOXyZ555Jrfcckv2+Zvf/CYrV67MPv+v//W/2Lp1K48//ji//OUvufPOOxkdHc3mj46OsnHjRiDOLdzM9u3bue666/jUpz7Fb37zG371q19x+eWXt6w/HYRhKOL5IBDxLAiCIAjCccvdd99NPp/nHe94BwC2bfPZz36Wr33ta4yNjU1a/qUvfSkPPvggQRAwNjbGM888w6pVqwCoVCp86Utf4gtf+AK5XA6IRw184xvfmK3/xje+kVtvvRWIhff111+fzfuHf/gH3v72t3PhhRdm097whjcwZ86cSeVYvHgxH/rQhzjzzDM577zzeOaZZ4B4OPBrr72Wc889l3PPPZd7770XgI997GO87W1v46KLLuJtb3sbf/7nf86tt97KqlWrsvII7SGDpAiCIAiCMONs+8QnqK99alq3mVv2IuZ+5CN7XeaJJ57gnHPOaZnW2dnJ4sWLW4RxilKKV77ylfzwhz9keHiYK664gueffx6AZ555hkWLFk0ajruZa6+9lne84x184AMf4Lvf/S7f+MY3+PrXvw7A448/ztvf/va2j6+rq4vHHnuMr33ta/zxH/8x3/ve93jf+97H+9//fl7ykpfwwgsvcNlll2UO95NPPsnPf/5zCoUCN998Mw8//DB///d/3/b+hBgRz20hMc+CIAiCIMS8+c1v5vOf/zzDw8P8zd/8DZ/4xCfaXrevr4+enh5uueUWli1bRrFYPOBypK719ddfz/vf/34A7rrrLp588slsmZGRkcxBv+KKKygUCge8PyFGxLMgCIIgCDPOvhziQ8Xy5cuzzn4pIyMjbNu2jXvvvZcbbrgBoCU++LzzzuOxxx6jWCxy6qmnZtNPOeUUXnjhBUZGRvbqPr/pTW/iPe95DzfffHPL9NNPP51HHnmEK6+8ctI6l112Gdu3b2f16tX80z/9ExC74Cnpe601999/P/l8ftI2SqXSHssktI/EPAuCIAiCcNzyile8gkqlwte+9jUAoijiT/7kT7jxxht5z3vew5o1a1izZg3z589vWe+Tn/zkJMe5WCzye7/3e7zvfe/D930gjkG+7bbbWpa7+uqr+dCHPsRll13WMv3GG2/kq1/9Kg888EA27Vvf+hbbt2/nhz/8IWvWrMmEM5DFKt96661ZnPSrX/1qvvCFL2TLrFmzZsrj7ujomPaOiMcLIp4FQRAEQThuUUpxxx13cPvtt7N06VL6+vqwLIs/+7M/2+t6r3nNa7j00ksnTf/4xz9Of38/y5cv54wzzuB1r3vdJBe6o6ODP/3TP8XzvJbpc+bM4ZZbbuEDH/gAp512GsuWLeOHP/whHR0dU5ZhcHCQFStW8Hd/93d89rOfBeDzn/88Dz/8MCtWrGD58uXcdNNNU6576aWX8uSTT0qHwQNAmaMoh/Hq1avNww8/fPh37I+DJ00dgiAIgjCdrF27lmXLls10MVq47777uP7667njjjs4++yzZ7o4e2Tx4sU8/PDDzJo1a6aLckww1bWolHrEGLN64rIS89wOR1EFQxAEQRCEA+fFL34xGzZsmOliCEcwIp4FQRAEQRCOMtavXz/TRThukZhnQRAEQRAEQWgTEc+CIAiCIAiC0CYinttCYp4FQRAEQRCEGRTPSqm8UupBpdSvlVJPKKX+90yVRRAEQRAEQRDaYSad5zrwcmPMSmAVcLlS6oIZLM8eOZrS+QmCIAiCcGi45557uO+++w5qG+VyeZpKI8wUMyaeTcxY8tFN/kSlCoIgCIJwRDId4lk4+pnRmGellK2UWgPsAP7bGPPAFMu8Syn1sFLq4Z07dx72MsaIphcEQRCEY5WrrrqKc845h9NPP50vfvGLAPznf/4nZ599NitXruQVr3gF69ev56abbuKzn/0sq1at4mc/+xk33HADt99+e7ad1FUeGxvjFa94BWeffTZnnnkm3/72t2fkuIRDw4zmeTbGRMAqpVQ3cIdS6gxjzOMTlvki8EWIRxg8/KWMx0hRM7FjQRAEQTiOeNM//mLStNetmMfbLlxM1Y+44SsPTpr/hnNO4LrVCxkY9/nDf3mkZd6tf3BhW/v953/+Z3p7e6lWq5x77rlceeWVvPOd7+SnP/0pJ510EgMDA/T29vLud7+bcrnMBz7wAQC+/OUvT7m9fD7PHXfcQWdnJ7t27eKCCy7giiuuQClRE8cCR8QgKcaYIaXUj4HLgcf3tfzhRhsjaUkEQRAE4Rjl85//PHfccQcAGzdu5Itf/CIXX3wxJ510EgC9vb37tT1jDB/5yEf46U9/imVZbN68me3btzN37txpL7tw+Jkx8ayU6geCRDgXgFcBn5qp8uyNIDJHRi1DEARBEI5h9uYUFzx7r/N7S17bTnMz99xzD3fddRe/+MUvKBaLXHLJJaxatYqnnnpqn+s6joPWGgCtNb7vA/CNb3yDnTt38sgjj+C6LosXL6ZWq+132YQjk5k0VOcBP1ZKPQo8RBzz/L0ZLM8eCSM900UQBEEQBOEQMDw8TE9PD8Vikaeeeor777+fWq3GT3/6U55//nkABgYGAOjo6GB0dDRbd/HixTzySBwq8p3vfIcgCLJtzp49G9d1+fGPf8yGDRsO81EJh5IZM1SNMY8CZ83U/vcH6S4oCIIgCMcml19+OTfddBPLli3jtNNO44ILLqC/v58vfvGLXHPNNWitmT17Nv/93//N61//et7whjfw7W9/my984Qu8853v5Morr2TlypVcfvnllEolAN761rfy+te/njPPPJPVq1fzohe9aIaPUphO1NGUw3j16tXm4YcfPuz7HR7YRVfvrMO+X0EQBEE4llm7di3Lli2b6WIIwpTXolLqEWPM6onLSj+4tjh6KhiCIAiCIAjCoUPEcxvoo8idFwRBEARBEA4dIp7bIO1JKwiCIAiCIBzfiHhuA3GeBUEQBOHQcDT1vRKOTfb3GhTx3A7yuxYEQRCEaSefz7N7924R0MKMYYxh9+7d5PP5tteRsT/awIh6FgRBEIRp54QTTmDTpk3s3LlzposiHMfk83lOOOGEtpcX8dwWIp4FQRAEYbpxXTcbAlsQjhYkbKMdpDlJEARBEARBQMRzW4h2FgRBEARBEEDEc1soCdsQBEEQBEEQEPHcHmI9C4IgCIIgCIh4bguRzoIgCIIgCAKIeG4Tkc+CIAiCIAiCiOf2kLANQRAEQRAEARHPgiAIgiAIgtA2Ip7bQIYNFQRBEARBEEDEc5uIeBYEQRAEQRBEPLeFSGdBEARBEAQBRDy3h4RtCIIgCIIgCIh4bg8Rz4IgCIIgCAIinttExLMgCIIgCIIg4lkQBEEQBEEQ2kbEcxtIqjpBEARBEAQBRDwLgiAIgiAIQtuIeG4HcZ4FQRAEQRAERDwLgiAIgiAIQtuIeG6D/TGetRaXWhAEQRAE4VhFxHM77Id6fmj9wCEsiCAIgiAIgjCTODNdgKOD9sRzLYh4fMsIXUWX32wb5UVzOzltbschLpsgCIIgCIJwuBDx3AZ7S1UXaYNtKQB+s20UrQ0/e3oXACO1AZb0l3BtMfgFQRAEQRCOBUTVtcWexfO2kRoQxzo/uXWkZV7Nj3h009ChLJggCIIgCIJwGBHx3AZ7cp7H6iGD4z4Az+4cY6wWTlpmzcZhdo7WD2n5BEEQBEEQhMODiOe2mFo8D477VPyIqh/x0PrBKZfR2vAfj21luBJk0362bie/emGQ0Vow5TqCIAiCIAjCkYnEPLfBnpzn3eM+I9WAO9dsZrw+2XVO8UPNd369mZNnl+nMuzy1dRSAh9cPsqCnwOK+Egt6CnQV3AMqXxBpnt05xtLZHVn89c7ROp5jHfA2BUEQBEEQhMmIeG6LPTvP63ePt5XJrhZontg8Mmn65sEqmwerAMzq8OguegCM1kKMMRgDXQWXC5b0UfDsSev7oeY/n9jG9uEaT20d5cKT+1i3fYy1Sfz1nK4887vynDa3g468CGlBEARBEISDQcRzG5g9DHyyc7Q+rSN37xr12TXqT7mf53aNM6vscf5JfcztygOxcP7B41vZMVLPlvvOmi0t624frrF9uMaajUOcc2IPZy3qmb4CC4IgCIIgHGdIzHNbTFbIWhtGDmPMstaGHSN1fvD4Vp7cMoIxhruf2p4J531hTBwm8tim4UNcUkEQBEEQhGMXcZ7bYCp3ecwPp9V1bpcwMtz7zC5++cIgVT/a7/Xvf243eddi6RwZvEUQBEEQBGF/Eee5LSar5KnS0h1ODkQ4pzwq7rMgCIIgCMIBMWPiWSm1UCn1Y6XUk0qpJ5RS75upsuyLKZ3nvWTXONIZGPfZMVqb6WIIgiAIgiAcdcyk8xwCf2KMWQ5cALxHKbV8BsuzR4zRk6Yd7Tman9gyOfOHIAiCIAiCsHdmTDwbY7YaY36ZvB8F1gILZqo8e2OqPM8jMxy2cbA8s32MTYOVmS6GIAiCIAjCUcUREfOslFoMnAU8MMNFmZqpxHP16HaeAe59ZhdBNNlVFwRBEARBEKZmxrNtKKXKwL8Df2yMmRRLoJR6F/AugEWLFh3m0sXoCeI5iDS7xibnYz7aGKmG3PGrzSzuK9FZcFjQXWh7IJVtwzWe2THGrA6P0+Z0oJQ6xKUVBEEQBEGYeWZUPCulXGLh/A1jzLemWsYY80XgiwCrV6+egeRwTHKed43V0XsYOOVoY7gS8OvKUPZ5dmeOxX0lTuwr0lVwW0TxeD3kqW2jPLNjlJFqErayNc7ecfaiHk7uL4mIFgRBEAThmGbGxLOKVdaXgbXGmL+dqXK0xQSdfDBp4o50dozU2TFS58HnB7AtRVfBpZx3MAY2DVamzDwyXAn48VM7+OUGlxULu1g6uwPbEhEtCIIgCMKxx0w6zxcBbwMeU0qtSaZ9xBjzHzNXpD3Rqhjr4fERJxxpw8C4z8B4eyEqw9WAnz29i4fWD3LanA6Wzi7TU/IOcSkFQRAEQRAOHzMmno0xPweOCnvS0CqWjxfxfKDU/Ihfbxzi1xuH6C15LJ5VYn53nr5SDs85IvqoCoIgCIIgHBAz3mHwqGBCrIIv4rltUuf6lxviz+W8Q0/RZVFviSX9JfKuPbMFFARBEARB2A9EPLeDmRi2cezGPB9qxmohY7WQjQNVfvHcbhZ0FzhldonFfSUcW1xpQRAEQRCObEQ8HwDiPE8PWhs2DlTYOFDBc3azamE3p8/vFBEtCIIgCMIRi4jnNpiYYELE8/Tjh5oHnx/gsc3DrDihixfN7ZT4aEEQBEEQjjhEPLeBMdJh8HBR9SMeeG6ARzYMsqi3yIvmdbKguzDTxRIEQRAEQQBEPLeFkg6Dh50wMjy3c5zndo7TVXBZubCbpbPLWJI/WhAEQRCEGUTaxQ+AerR/4tmJqhTrOw5RaY59hqsBP316J999dAu1QDprCoIgCIIwc4h4bgPDwTnPs4cfo6uyYTqLdFyyY6TOnb/azPO7xtk9VsdMNdyhIAiCIAjCIUTCNtqhSaSFkUbr9kXbiTt/TGd1IzW3+xAU7PhjtBZy15PbAeguurz8RbPpK+dmuFSHET2h4mZZ8fXpj4MOoDYCQTVZNgRlxa9Wkk87rEHog+3G60V1yHVCsQ/Kc8CWW4IgCIIg7A15UrZBs1T29yNkwwkrdFY3ApAPhnDDMQKnPM2lO34ZqgT8x2Nbec2Z85h1NArosR0wvCkWt0EVIh/qI4351aFY9OowFs1GxwK5GZU0HpnpiMNXYDlQ6IFiL5RmQaEXch3xZ0EQBEEQRDy3Q3OHwf0J2SgEgy2fS/UdDIl4nlZqgea7v97Cq0+fe+Rm5TAG6qMwuB7COozvgJEtsQt80Nuezs6rJhbn4zviv51Ns2wPyrNjlzrXAfmu2K223djJVk0dOS0boiAW9m4RvOI0llEQBEEQZhYRz20Ri2c/1PvlPBfrO1s+d1Q3M1RaAoAd1eiurCeyXIZKJ09fUY9Dwsjwg8e2ct5Jvaw4oXumixML5NGtMLgBTAQDzzVCKY5WIj92yQ8ErwT57vi1PhoL61wHdM4Drww6it11k7jrYS0OP4nq4BSaQklUvJ6y4m11zI1FvCAIgiAcRkQ8t4ExhiCKhXMQtRnvbAzd48+1TOqqvkAw9Eu2dZ/NrNG1zB55DIBifRdbes+f7mK3RS4YJrTyRPZRGPbQhDHwwHMD1EPNuYsPYYhBWE/CLBLX2B+D6iAElfivMghj25k8tM5xjD8e/zVT2QWDzx/8tp18HF7idSRhJj3g5GKnXFnxeyff6owLgiAIwkEg4rkdjCHSBm0MYZvO86zRJ/GisZZpykT0jzyOG45nsdAAfWO/Ybh4IuP5udNa7H0xZ+hXzB55jMjyGCydzFh+Hlo5+E75qI3NXvPCED1Fl1Nmd+z/ykE1DqdIwysKPXEIQnUIgnEY3T455liYWcJawxHfuYdlLDcOMcl3xkLayYPjNTpKOrl4GeksKQiCILSBPC3aIhbPRkPQpnjuG3t6j/O6K5Mdt3Jt62EVz/MHHqRv7CkAbO0za3Qts0bXZvNrbjdVbxZDxcXU3G682jDFoa1E+Rx+eRYd1Y0ooOL1UXO7qbtdlOo76axupFjfia19BktLqHm9+HYRlIVvlzDWob/kfvL0Lko5h3ldbcRAh/U4vGLXb2LRLBx76ADGtsV/e8PJxxUmtwhuPhbXXil2sXOdcUXKK8Vie6YI63HYi+3FFYCUKIzd9TT0RUfx57RDqbIaoUPKisNwIj+Zr+KKg1tq3eZMoZOOsbYnLQaCIByRiHhuA6MNkYmd53bCNkq17Xjh6H7to1zbynbOOtAi7hEnrBA6SYctYygEAyzc9TNy4ciUy6uxGqpapzS6jXIQMbv+36h6AE2VhmhOD9G8nvjBlnPTNZkYqjB3+FctnwO7xIb+S6h6fdN1eFOiteG/ntjOb62YIguHX4HqQCyYB9fH7wUBYhd7dOu+l7Nzsci0c5Arg1uIL30dxvONbsRre8U4TtvoeBnLSsJIrIbI1UHc6VIHcXhLWIPKQJJlJSLuyJm8Tsnk394BY7lxJcF2E5EdxOVwi/HvPU1/qJLjSJczJo7vt5x4G5ikXEBYTY5VNwR9KoqjMJ6vo2SZMBb1zcdmOY3tpftItxGF8XdhufE8ZYGyW8+HshvvTbKfpPyBgQCXwFiEWhFpQxhFhGGA8atEWhMahYlCjNFoA5HtEalccuxxmQwWGovAzqOx48vBKDTxYYdRRGAUNfIEVo7I8jDKwTIRtq7jKk3RMZQtn4JnY3fOIVfqxsmVsC2FpcBSCpW8Nr+3LYUxJtmniS8XE49PoA1ZalVt4s9R8jnnWLi2Rd61KHg2OafpPCWkLa6RNoTaEEUGQ/wcjHT8XqHwHItc8ufYMnyEcOwj4rktDDoR0O04zx1NIRntUvR34URVQrsNtzSK6HxuLWGxTGXB4ikXUSZiwcAv6Bl/jrrTRWjncaNxvHAs2wZBhFWpY/Iexrawtw5gbxuccnvN2NsHsbcPglLo7hIm76G7y5iCC7YNe7h5uvURTtn0HcbKJzCaX8BIYSGR5eDoOnWns+GSTQN+qPner7fwyiUFTsjXoD4WC+Vtj01rhgptDJa4Y8cXUT3+YzSO3Z5xpjG+XgeJmJ+QCaZF0B5OTEuolDGGKIriVx2LwTCsoIOQKNBERqPDKHmf3LcVaBShMXFqc+JOxkEYobVBGYNxbHDtaXG607vYZCnaHumZrgJG2YRWDt/pILCL1K0iASUqxX58rxNjuY0VjWktvzFgNFYQoMIAKwpRUYTKXiMUBm07GNsGZWG5DrbnooAwjAhDjdIRxnEwthNfaek+lIVRKqkQKbTjgmVhWbGYdiyFAjzHIu/aibi2ybkW+eTVseJtxQI9fjUGiEKM1hgDOgwJgyD5zjRBvU7gh5jAR/sBOgwhijAmPvfadbE8D8dzyVmGnALbsbAx2AqUAW1ZaNtBKwtjWWjLBi8HnodlqfgYbItSzqGcc7Ljybs2tnVk3++NMajkOzLGoMfHMbUaJoor6ybSEAbxd1UuY3d0oFx3n9tEa7CsbNvHOyKe26Ep5rkt57m+p+DLvdNR3cJgeR+ZN7Sm99EHKezcSpTLU5s1F53LT1ps3uBD9CQdFnPhMPnh7ajRKqoeYI1WUWPTkP3BGKzBWIzbWxMH17IwxdjtNbaF8sPYgAo1yg8ARU9pI52zOpk3pzt24ogfEpFyqXk9jOYXUMnNouZ2o639a0ZWOqS7soFybQud1Y1sfj4k11+mv6O9pnZtDCO1kJFqkKUldGyFnQxGUgsjaoGm5kdExqCAnpJHXzlHZ97BbdN1MZFG+yHRaPI9GEM0VsMYcDryKCd+kCvHxi7nMJHG1ENMpFG2hQFMLYjPraVQlgW2heXYWPnJN0KjNSbUGD/EGINdyqOOoIdAqONzeaQ8mIwxWWuLShy55ofS/qKDEBNEKNvCyrkYbQCDiUz8PRiTVTqn++GUfffNx6N1Uob4WjRhFF8bsTWJ0TpZzqD9EBOEmDC+ZjEGy3NitzOKtx2Xm+S9yX7XzURaEwSaIBFlYahjt5T4XqEhE8RKazAGY9toS8VlC6P4HEZRbK1aKnH8D6wyPOXDLzlm4zmYgofJefH3YluYVDM2DZJlLIXSBmPH9wcVRPF1Y1sYN75ulCEbaMuk13dyP1GRjpePdHzMyflXYZRNz0WaEgai+JrJsCyMVoROHq1ctHLQyiFyPLTy0MZCWw5a2RjlYNSByvn2MUrF5UoGZTIKwnIX44USY5aFFYaoKECFIVYUt6bEYj4ON4rnhy3pYdslbX9JX4Pkb2xvK011DLaNURbGUhg7buUw6WBUgIPGSVoDXMfGsRRucu+1HQfbc7AsGyfnkvM8PJskbadDpA2Rie93kTEYo1BJhcWzLXKuDVFEFIQEyZ8fROgwjI/L99FBAFpjOzaOAleBo0NsHYHvE0U6bikgrgBp3Wh1UIrsPuvaFq4dVxJy5SJusQhGY/y4+maMgTDC6OT3lp5nxwbbxiqWsDvKmPS6BbAUVqGIVSzEQttx4m8k+a0q14mFulLxPSiMMH4dEwSYIG1pAxOG6FoN4/uYIKDzssuwCkdWKloRz+2QNNdpDaG/j9y8RpOfkN+5XTpqm/YpnruefozCzrhp2a2NsvBndzC24CSGTjoT16pjR3XmDf+Sgr8bADVew3l++/SI5XbQOtvX1BLAxGUar8GmXejOIibvoSKNY1m4c4YpFxpN56GVp+b1MJafR9XtZTw/p+UhkPcH6KpsoFTfQS4YxjIhlgmb9gbP7hzj+V3jOLaFNhrPtnHt+ObRVXDxHIsg0gxVAoaqPmG7GVWS7Q+M+wyM+yhgVkeOE3qK5JxW8WDCiKjiEw6P428bIhgYO7QJOdIHvR03b5swat2fAqvgYTk2xphYcEcaXQ/RQRQ/2B0b5Vi4fR04HQWsvBsLMGNQroPlOVjFXIsI9yNNmDTpRsYQRbFASpuaURBFmnqos4pIPdDUw/imqZJm6O6Cy6yOuEIylbOfCtlUGGYiL9KgQNcC9Hg9vjkbkwkvE0TxclrHFY1CXDlr3k5U9eMbeXK+0uMziWBTjh0/hJJKDNpgdCyClWtj5VyUa6OUQtd8wuEKpvma2keUhXJtLM/B6Spi5ZPyhVEi4uPjTB9WRhtMFKEsq/EQM6bxPUYN0XwoaWna14ZQxw/wOAyiEfZ2sLRcCfvxO22b9Dqs+ajaTLntbaI1CnDDCZls6lMvbrCJLA9t2Q2xbXlElotWLlEisnXiZh+I2FbGQOJqp9gDO8ntsTfvkUfsyKfln/oaiJK/Y6f7+DB2IqQ9xybnxM9Hz7HwbAvXseLns62wwgjCiKjuEw0emNbZXw7HPWx/EfHcBlrrpOZmcIY3YOk9O6JFf1eLeNuPndC14Qk853T87llTLmKPj1La+Bx2VKXo76JU3wEYZg08ht74Y6I5XTjPbwfXxhRysUM0MNoyvPgRRaQz5zrF3j6IntVJ1N+F6Szi6Brl2lbKtVhQa+US2nkMClv7OHpflZm4uq2NwQ8jCEL06Aj18TqqHjCkyByu1P2zjUFV/cQ1V7HzFEbZtlTy3uQ9dCkPuaTZU2sGNmoGOgp0W5Cv++SCEDeM0LXDfJtNvnKzp0F9DOiKTzo3Gp18Hk0Q7XFeirIVYd5jNNCM1MLMmYztDTt28GwLHDtz4gBUpOPzG4SoIMJNBDuJUB2JNMOOjeU6FPMOedsip8ANw1go+mG8rD7wa1sDjOy7Umma96FN7IJOtRxALdjr+WosuJfZQUQURETje1BBbZLGvJq0KRyyGNgoEbuZ4E1CHLQ2rXUs1XhVKFQSa2un4cw6dpSnQxgLhxZFhKOr0LYOsRJhHbvWkeVisDFKxSJbWWjLw2BhlBU73Ml8bTk0AliEo4EoMlSjiKof7XW51OCwLLBQadQOjh0L7bxrNQyqRHw7dtyfwA9j46QeRNQjjR/orMIdGYOt4u3aloWdxvdbiuVRxJHlO4t4bg/T6DRBfQQvdKh5U+cSTh3f/SKMcJ7egjUyzskbv86G1VdTWXBiS/xazh9k4UPfxh0fpOjvYuIT2BoaxRpKOin6AWp8GkavmwmMwdo5jLVzGOO5cfOn56DCCOM6mLyHNbcb8hMqL0EYd2wMNdZ4DVWpo8Zr8XqJ+6rCKH7aT5Plq8aq2Htw9EeTPwDXsih6Nh0FF/sIihdLBRPEZ8QknYwgFUoNpy8udmyZRknWGT9xkP2wUQGaeHQHc7QqCDHVOuMjkHprllIUPZuCa5Nz7SPqfBpMcg5bw0+tRHg2Lwe0LEuyriYW67qpA5gxybLGxPObxHDz92YSYayJMwPpabjOM01ssv+EIxWdXSjx5+YLzIDCTJoGE5YxpmWa1RRy0mLCNP/uFHGohhP3dzFWrKaMcrIQDmNbSehILLJRKrlerSRcJQlbScJwrMhPQjlU3EVFa5QxaGMly5i4ImsUGIVKsssYZYGlkrALq2ma1Zhn2XE4kONmcdom6cjaHMOdvW9B7fWj2dsdT034MHHbJj5GFUUoHTXi0nW0x9CktsJbtMYKg3g72b6bytscjmQ0Kopa4uMxpmk/yb0r7bCbnl+lMJZFoBR+87m0Gue0+btRjZtafMwYnHQ/pmFWpvOH+soUfveGfR/rYUTEc1skYRvGoP0Ktt5zDuRifT86EIUR7tqNqFoQd+ADiv5O5q/5IeEL3Ww867UU9RCl8a3MfuEh3B2bD/ZAjiriGGlQ1diBS2819rYBTCmPKeXjH6Deu8Ouwr3XpA81gdYM1zSj9ZC+kkfRm/6fXXqzCSOTidoocRI1ZtKpaRbKRxPaGMbqIWP1uHXHsWJXw0Jh2wrXVihix8NOQombXdYUK6kMZO6sNskzRWXPtJazk4pX0zjXUeriJlkH9oRq+v9oPOfCAaKTeGadxDYnsX8qjQFs/pzFPZtsvWy61o3109joyDSmp/s4gt1/A40YdVIxP43bV3HFXh25p+CoJKuEpGQ3x1joo2Phe6gZ3b2FeSKej0IShy7SBhNUsfWeY+FiV3jfqGode/2OKR3irsoGqGygd/MTKAcIDiAM5BhHjdeOOnddG8POsTqOFcTpoVwb27ZwLdUS1xtqTTWI8EPdZBTFjm+YNJGrJi8z9oqOz6dGqDVZZMoRGoBomv4/JsncTtWI525yljJXU7d+BhJbXmVuJRNfm9EmjqdNW5C0RoUawijrYKcyEaqnPuVTCcyJtSRIHFOVdHw0EJlGh75JAtg0BG0UxWUI9UGJ2WzfduzoYSfuqa0wrgP5RNTYibtnx65eXCtMnT4aPcTS70Y1vUKT09qY1vI5rWQ2N0NlpylppUrc4vh7SDuPJeclnZf0lWj5Tq3UCVbZ+/hz07FYDceyca20zqfZIW5x1vdw/aXfYahj00qnx2HAqCzVoMHCkLiq8QnBKJtYLiZlIXFWs8pxUt70c5pBasKloFJ3P31tcrqNbWfuePaqrMnO9VRMsYxRCuO4cWhheo6y77G1NcGkLQVOIwPLPskcYt3iJqetBQ2h3fjcuEYnO/2trnb8+uL3/d6+y3GYEfHcBiZxmrQx6NDHUlOLWTuqt5ffuebjPr6hJXfyVCgTHrGCQDhwQq0Zq+vMPYUkX6uK6/BhG9kD9u51CsIEzESx1ywiYjGqoqghgJoFaTo/jBLx2uiYiDEt2SemtcjQIqJVm52GTBJGkKEmvJmkO9TkaU0iOS5Hk5BtEnup8DOuAzkL4ySZOdIQhkT0YqlGSEO2btO2WkTyVOECRy5H1H2oubIwgYnl3Fe5G5J4b7Rzr7aTcBUHbcVx4Y0MKM0CvbFXraxMhBtlZesbbLRlARaxhWKyI8nCclTq8CdZcJJQnEkOsTFYJsIyYdIGl1YONMr4MEnmJBXkbDuGtEIRx7vHAt9YKul0ujfhnYjtzFpQZAM2ZefUahxbbgYHptoDIp7bwOgoSf9CLJ6dqcVzPhhqY2MG99lt+xTOwvFFFuMlzBzGQBChkk6M+GHjffqaNqebJiGaulkmSVmWpitMmzUnOWG0xpGmTmvqIKbiy7Xj1+bllEpErm7Zlpq47aRDpvLjHLj725xtFHEnT9sGJy6P8RyMkwPHaqSYbHYNUyetxU2i6TMN91AlLSfNbmAqxI1uma60iR2opBw4dixSraZzlU6zG67VtJB+T0eRmBWOLBQRykRYJtiPzppHP0Y5RMptct8NFhGWDpuymbRJfRTomvYyHgwintvBgAnrRHiY0MeypraDc22IZ2vnMGq0Ms0FPDCMgYAQTzlZgoRJVe2ajz0whjUwijVaxeRcdHcJ3VHElPOYvLvvB0sqSupBLDA6CvIwEuLrwg9RtSAeqCLpHIqbjCjXLKCaBBbGZO5o3JGmufmWxquhRQDH2T1icUwYNZpxIx3P30tsvFGqIWaVariOSsWC102aVcOkOVjR1GGGluZl0+yOKRqiMY11DcK4w2uSEiomPiBlaAjs5ibrFpEal02X8+A5cZlbnNIJ7mcqSu1EgDr2Ued+HjKOu3OgWkJBVKT3EDaY/MCUmjoUZtqL1VTBbLlmrbhSG0ZZRfGIJnWF0/Se6bmzrUbLA/H8bOAeknOcrpNW2qMI6gGNjp40skK17rRxf0gr2M0tIXaSCcm1G+c3ne80jQaaldXOwoNM83HYTZVoSzVaXVRcZhVEsUk06Tdl4vum1kmoCFlGq7QDqTjPRzGqNkTk9UPk40RTZ1hoJ7+zvXPqYbEPJ2PGp4LPOD4BETnjxq/YzDdd2AasoTGc57ZjD8V5DoznoDsKqFqA89z2Rrxt8mNPBxVI07ulD3hVqcdp35r2bxwb3VsmXDgL3V2a3gdUEGZp5uK/IC5Pzo2FmWU1mqQNmIKH7sjHN4RmoghVaWwncxU9J8764dngOI0b2v5gTFPMZtJLPMk3HN8k99LcpU3igiaiM8lC0iKmLCspXxsjpplke/XG+VJpHuFU6DlJs7StsptZ1nLnJu5kOsBHes4zkZqEA0S6EXcYJvur+YesyX/KQ00HrvDieD7jJg8A24qPw3Ua85PPpNNs68gQUhPjRoVjGxXHOCuTuu8NoWPS+09TxSkVM1lYTiK60vt0VsFqdktcO74/us7Uoyw2D4KRhsQ0L5POT3/zzS0radnSNJVpyE8ampaK4vS+l4W2xKKuOe1lW0wYsCPtZNnSgqBUXE4/bMnwEa9vklYMuyEg03tbNFWLSNMxQEMspgIynZek6zwspDHm6fEeIfcuk9vHKIZ7eA8kg60cWRx5JToCMYAa20bY3YcJA1y7IZ6dsELv+Dp2l0+lo7plLxsxWLtGZtx1HjRVdk4Yc6meBFYHfkB1/W56t1awQ41xHYJT5hH1llvd4jDCGquixupYY9X4ZlQPUFUfk/cabl49wHQUiOb2xDf8nBufh4Ex7J0j5HYMowseuqcci0cVC2tTyrfWWsOoEe9owBRzDbEZRvH2BkaxRqqokcp+9+I2EDvo6ah+9URAtrOuk8ZpGdC0itamcpukpq6MBj+a1JnIJA8QZeKbTHyjMY1e+M298ds9rngIrCxVX0vv/PSBFelD2kM9c4ns5LtUsYDV5TymvzMeGj7vxuUJE9fVj7KH7lQdyRpN+E7jOExzeATZw9J4TuJm23uvlBwtHAEPQaENUjevOQzHboS/tIiaZvfOJNdszj28gmtvxAl99z3fsRv35ZliYlmTck3EeA6UJou0vTFx2SM2yM6yjo173RGOiOc2MX6FWqCxdNAyMEfv+NPMGX6UXDCCF+15IFB76yD2CzsOR1GnZNz4bGOUqCnoygo13dur5KoRXjWkY3cdSxuGZhcY7s8zOqtAv91Jl5rQZOLY6O4ydJf3N3IJgGhuD0GksbcNYu8awd4xvN/p5GKnxEaN17Mmf91RIDppDrqjgMk54CVus46FvAqSntXNQ+dW6rHorvrZsL+6oxA70sVc7EI2O9ZB2Gj+98NG81Iax5lOIxb5pCMN6obz0XA/k4djpFHj9az3uKr6cYiLUq2dkGyr8VBOHrDGsWMXpckVUToJh6gHWdN/c3N/5sgkjlT2sPYcjOfG5y4VpZr4vPhhJtwzIQxJk2niLicuWSZYU/fmMHHEPsyEoxsrCSdqEcJxiEt2nZNW1OLfUdb8LgjCMYmI5zYxYZ1qEFI0QUvYRj6IwzC6K8/veeUowt5yAIOnAHUTksOZHIs8Bb6JiNCM42MAD5sqAQrFCHVMIpxtP6L/hXF6t1RwA41WEORtRvrzbF/cQb3UuCy2MwKmgy6VP6Dy7xHbIlrQR7Sgr9FhCDIHO0sHZUwjZjMVbKNVrNEqKgiJ+jrQfR2xmN+TULPjsIOpxJUp5dH97XdEOBIF2iEtk00s1vPe1OfvUO5bOLZojs9GJU3LB3kFNQ3O0eg0aGex5C0dKzNB29Q60dyKkYYvpLGmaUz4PpqbBUE4/hDx3Cb2+HYCaycAblRB6YB8MIwb7tltBlCDY7hPb96vThVbzAg2ViZ487jMN504E3IuVk3AABU8HCI0I+w773HHrhoL1w7hBJqxnhzrl3RQ6dx7p7/tjJEzDnl1iC4XpbLxfk0xFzu2e6PnwBxv4SjHpC+GIKkIemr/m7UDE1EjJGi6inwifCJsFDZW8hdn09YYLBQhmgiNjRUPyoKFg5XVawu48ac05nGf4eYGdaSFYVhpXLibdCZKxGnSOhHYcYU+JMJWNtqxCFxFaCKCwCcgBB2nXlS2jWM78XKejbFUdlric2kwYYgVaJxQkwsVxcgmH1moMMLWCpXG22cdM53WTo3SPC0Iwgwg4rkNDAarNkBILJ5t7XPSzruJLI/C3joJ+iHuc9vaFs47zBij1FtCKwBqBOxinLl0EBjNKDVG8bNY5XH2PGgLgB1oisM+3dur9G6rUi07PHdWH7Vyu46KYTPDnGC68HAOe9ilNoY6YSZTIgw1Akp4uNhJZkzVljsvHAKmEIomjTlOPqskk2j6HaZCNERTJ8QnbjUxgJVlHY2FazzPZC0nzTjGxsPGSQStxhCik2vCysIf0+lBsp+DO1xFkLcJ3XjrVppKTdUwGBwNoWth5XJ4jkPeB68SQRiio4iapQlsQ2AZHGNRCC1cLDSa0GhMEBChUShc7ESsx8ejgNAyRBi0AqUUllHklIOrbGxNXMl2XUzBw3YctIrPN66DpRSO7SUhCDbGVoSOoupq6rahZmtqhHG/MCwiNBUCxk113+duX41TU90G7eRvD7hJFcbDpkN55HCwsdDJsBXGxC1sGpMNR+5g4SXrWU1/QFbpSa8VBXhJFWiiOXGwtFM50sa0DJB0rJKm4UyPNR5q3mS/9wiNg4UBAiLqSZLh9LtO7wfpvSHCEKHRTa86mR4QZfcXD5s8Li4WbnKfSH9XHva0n/vINO5h+9q2MXF5fULC5F5okpupTvI3Nx9Peozp7TY9JxD/vl1s3KTin44DEKGT89s4h3bye4KkASbZbnrOouSznayXGga65ZwbtNHZMTb30Uy/Nycpi2r6Hq1k33mc7N6mk3MQJNtOz0O6vwjD0qjOnsd1nhlEPLeJ1oawMpx9LtW3730FY3Cf2jh1mh8TX+yOsuIhlZOLdogae2rGHKFG3cTu2FQiYiq8Ssjc50bp3lFFGdAKdiwqse3kzkaKmTaJ0GxgMP6BGps+ihTUgTVnhkbv80FVMyHj+GgMI9SJpvCadzHe8tk1jQdm84O0mzzliXHbxzmRiW/KGkOVAI3Jbmo2ViY005t6RCyq0vMaTegbnTNOdt7r+3GNHiwhEeEhaIcwShHkbGolh3rRIfRsIicRzYmLun84QJvXoDHYgY7TzdlJdgBtspRU2mlX5AW0jrJUb2PfbW76MJG2DviEjJk2yn8Q2CZubUhbEDwVp0y0sWLTgLgSlrZaREYn92My8dcs5DQGZWKhlkvEfCoEa4SZQFBGNYl6yBGHmNWTSkwqxtIKKJAJJJ2Uz8bCUVbScqJwsOkgRw4HnQiQKgH15DfcLDZDE+Eoi8aYpcm5NxEBGpt0KA6Dg01ROdk+VVLCRgU33mbdhNQJswpxWm7LqJbPM45hUktSTjmJJdPqCaSiMu4KorN7oEmOvyF+YxxjkWtqm4rFYXw+UmF41HOYelGG+shraxbx3A7GYIzBi9oYPTDBGhxDVaa+2Q9SjYWfUTikTZnpbXLP1NsZbtAYvFrE7OfH6N1aQduKXSeUGO7PU+n0MPbB1bQDosQZiFhserD3WbsmS4sX30zjG02vKeCj6SZPHocaYbJcsF8VhIllm4hPvP+yyTGXjgN2GtJ48hAd15r3EC6QuuQONnYb7sPhQJv4wVkhYBw/qc1P7427doBDYYauTeQqlAbHj7DazCZikhG5UhFrtzv6HArtKCLHws/bhJ5FkIsFcZCzCF0bbSu0O4PhAEoRea3XV3qcRppXDhnx7yIO4QH2WwhMdf8xiavmTx6urWWZqElM1fay7F45GOGyH+sOH8R+9JEimptIv/f0+5uuSlpsPOy9VVg4ejmqxPNzO8d50z/+omXa61bM420XLqbqR9zwlQcnrfOGc07gutULGRj3+cN/eWTS/N++4ERev3I+W4aqvP/WNZPmv/OlS5gVRqwf9/jcswUsfVrL/Gtmb+XM8gjrqwW+unVRNt0ar0FhOW+tr+FFeidPWf18I7cKY6DaJDReX7+H+Xon6+xF3O2dP2n/19Tuot8M8qS9hJ9550ya/6baD+g2Y/zaOZUHrRXkKyGWZeBkCJZbXO9/n5zn87CznEfc0yet/47qHXiE/MJdyaPOqZPm/0H1NgB+6p7DWmdJy7wcmr+o3o2F4g5vJY/Z85qaXSBvKvxO7ftoNP/pvYQN9ryW9bvMGG+u/QCA7+YuYYvV3zK/Xw9yTf0uAL6VeyU7rZ6W+fP1Tl5fvweAW/KvYViViRwrExpzczu4oOuXuPWImwdfTt3kcSKypqTToy1c6z9KiObThVcTJO5S6oycHq7n4uAR6kTcVLi2Zd8KxapwHS8OHiXC5YuFKyY5KquDJ3lx+DSBKvFP+ctbXCQbxWXh07wk3MAuVeTv8hdNOvdX+Gs5N9rEZtXJTfnJ18Yb/MdYGW3jeauHf/ZWZ3tOnY3X1X/BIr2Zp6xZ/Gfu0knrT+e1d7+7ctL83659l5Kp8ZB3Bg/nTscokr/YUX31oh9jeYa1A0t5fuREAKyokT/19Qv+Cysy/HL8DDZUTkDpJETCUign4rIT7wFgzc4z2DI2F5Wkq7NCTdHUuLL03/gFh59VVrM1mJOkvYvLVnIrvGzBfQDcv+0cBsZ6aM7g2OmN8JL58f3k51vOY8TvbDm23vwgF8yN7yc/2fxixoNiy/zZhV2snrMGgB9tfCn1qNV1nl/axqr+xwH44YZLiUyrWF5Y3syZs9YC8B/rXznp3J7UuYFlvesItc1/vTD5u13a/RxLu5+jFua4e9NLJ81/Uc86lnRtYCwo8tPNL540/4y+tSzq2MxwvYN7t06+NlbOepz5pa3srHXz4PbVQKP51wBn9j/M/OIAQ5W5/GrnWZPWP3/uI/TlB9k8Npdf7zpj0vyL5j1AV26UF0YX8PjuZZPmX7zgPspuheeGT+SpwaWT5r/8hJ+Rd+qsG1rCuqElk+a/etGPcayo5dpr5rWL4/vOY7uWsXFsQcs8W0VcduKPgfja2zw+F2MUxlhoFI6KWN73G+qRx3PDJzLqd6CTecbEQw67dogfuYTabqkQqWT7RbeKrSIqYQFt4mAFleSUzNk+/YVdWMqwbbyf0Dgt6xecKnOKO1EYXhhdQGTslipXhzfG3OIOwPDs8GJAoZTGwmApzfzSNk7vewpgymtnYXkzp3StpxZ52bWRls9SmlMPw7W3oLyN3bUeHtg2+b50zuw1zCnuYntlFo/sWDVp/tF47aUet60iXr7oRxgMj+48k+2V+S3PHM+uccEJd2MwPLZjNQPV2U3rQ84ZY8WCuzDAU9suYqQ+q2nPhoI3xKnz7sYAT2+9lIrfQ/NTrZjbwaK592AwPLf5tfhhuWltKBW2MHf2TzDAhk1XEUWFlvIXixvo778XBWx44Y0Y49Ds73eWn6G/7yEsFM9ueHM2/T//+V4Wdi48LHrvlcvn8OzOMT7yrccmzW/mqBLPM0YYEWqDpdtz11QQNpKuT2Aqd+JAcAKNHWi6dtVYuHOQbeVRinMCjIJ6wSZyLbSlCJVF7hBV9nUSygGwmyqVCe6jSZY5lBilGJmVp6Yd6sqNm7kT6gWX8d5YtFRDl3rkoJLk9gCbbcPjQZWOwRp1wkneaVWFDJahVs4TVu1MnKWj3cVOdISPQqfJkpvOtcFQJ2Cc2qTvXaHYYcbYYIYYxxAY3dJBTWMYMBVeMEPsQlEzYdasmsb97TYVnjW72WosqkkzcDMV6i0VtenGxI/MxmdLNcSxo9g2r5Ocm2eHLlMfmXyr0U4cVdsyzW50Hg0K8Tq6ZiUdxiBK5rXKAeIc4YkbrW2buu2we2F8Yw+3OxjdvmNrEhdwzPiESfylnzVKx/MHTZUnzHZCNAOmQr2pRHHc5jCYTSgUQ1QneYmbzAi+2YiDxRh1DG7WpG8wrGeQEbMBg2GYWiOuP9n+s2aAHeY56sZikAvSU5BdAU+a7WwwzxCYAgM0BEYa1rSOXewyGwlNJ6NJOEdzTOWvzBaeM88Rmj6GWNFUMYvn/5znsXiGiHnUWT7pHD7EJmxeIKKCz6mT4o/Xmh3kzHZGk47RafnT0IXtZpzAjFMzQRKbPDGo4MAxgDYabXRLdxRjVCZyN43Noxbm2F7pZ9Qvo41CY6GNhTFw2zOvIVQR9bCA1i5xknENSqNUwMC4hbIqhKaCUQ5KmSTRiMK2qnT2PoKrYHDoTPygOz46A2Dh2DW6ShsIlaY6ehImKiTXXRJfSpXtagBjFDW6k2OIo9SNsagHHqOj/ZioQKjzk1orxsMC26q9KMvH6DQvsyHtvDAQnMTjQyeBdokTJTdVy5VhZ73MLweWgrbA5Casb9jl51gzNAfbChj3C4kw1yilUcrwnA/DtYBIV6mYMKsUpFvZaIYZNdsZN/Xkt9FImALwqN7Bumgj1ajGoKll66X8ItqKG27CjwLGzItIz076/y/C3eT8AWpBiWEdkYx0Ep8nY3H3SAnL8qhWe6j78fgDCg3KoND8aMzguD41v0ZFh41jT47j7nArHnWqUR9jxk9+u43j+0W0BWMCBvUsxsyclvsKGO7QT6CBmukhNN0T+pMEfJsnAagzj4julu9WUeG/WJfMP5mIzgnzx7mPFwCosQJNR+u1wThjbEnmV9CUWubXqFJlF4r4+WImdHTQ1DGMoiAJEWrc39Npw8R9Q8IkjKWZMXw0Y+gkTDDDHwYWciShTJud2Y4EVq9ebR5++OHDvt81370Zf2RD1ulhX7iPPj9lyEbVBGxi5IBCEprp2FXjpF8PZL+pyFLUyg7j3R47TixPavI9nASeTeRYBHkbrxpS6fLwCw7aUtSSFHi5akh5oE7H7noStLJnjFL4eTuOPy3H4tgONXZg0BYMzSkS5g/ueL3xgOJogLbibfsFJ95nfs8j9CltyI0HQCwYg6QMhZEgEXKxi2qHmlwlpDAW4FWifR7vTFEvOkSOReimYQxx2EKQSzqWWHHcbeTEw01r24qXSfNBw2EbwCPuJxBHU+Zw9topKw2jGU9Ch8bwGaHeEs/d/Le/4SxxfGkc/5nGd6adWBsR4tDs3jSiS1UWWx5/UuRxsijJVDCmMbVxMFPceSft/JR2lGzubEnLflQiq+JKWRx21TjWLDYXRQEn6Xxp0xzHahmL9F8aT+uknZNMvH8HC1tZ5JJwpUCF+ATUifAJqSeVkBphFr7VnKlEAX7TuZgKJzluN+kQmB5TFr9rGnGpaTyvSc5ZJq+muFQa4jMlPeuxmMLYjW9NhaAC2h1ZSBmy/h1p2Q4nzddIeo2m8blHOkY7YJzYndQOxrjJd6GyV2Os+DtqmoaxMFiZKFYqSr63MH5vNb3Ppiev1j7MLWOBdjHGwWgvLpN2k7I5yY0/QFk+Svlg+fG2rSA+Fu2CcVtftYfROYzOJduwSCtCkByfiauWJjtWq/UcZMsl77NzYyd/Fga7dRnTtFy6TSwspfGsEM8KyFkhOSsiZ4fk7YCc7ZOz67hWXGmY/HMyTY8Bk/2SQu0QaYfA2ASRS6DTP4dAu0TaxlIaS2lsFWFb8Wv6+dIzXs4HXnv2QV1PB4pS6hFjzOqJ08V5bgdt2hbO1IM9xjrvpnLQwtmpRyx6coha2eHZs2fh+JrQs4gOYYzmaG+e4f489aKD6+vM/SuOBjj1iJH+PEbFwrNedPYpooKCw1hvnsF5AT3bKnTsikW0n4+d4dCzqJZdxnty1EruQcdp7wu/5OKX9q/zo7EUtY7Jo2mlTvdUWKHGrUc4dY3rR9l359QjunfUsLRGW2rKuF8/7xC6Vhaj6xccamWH0I0rKXaU9FzXhtC18GoRxREftx5hh/EQtH7ewVhJaISBIGdR6fSolV3C3EFUQA5ANEcmdhZcbHxCBqhmmWaCps6KQeLup4IvyGRijItFyXhZr+24w2KYdIGcWqyU8TKRmEvEavOfPeHz3uZPR6o5bXTW8Wvi9oyBeuRRi/JUwzyBdvEjD1+7BJFLZGwiEzuikbFbXn1jYUwi0xOxp2JZgZc85IwBX3vUI4+hKH6NjIM26ZIHjyJ2HC00ljJZiIBScTO0Y0XYKsSzIvJWFcsZQ9kVLLsCzhiRCggJiVRIqAJ85TNq+bEsTgSJNk4iPGKxYLL3DiYVVcRi1lIGR2kcK8S2fBwrjP9UhD3hvWWFKCt2wNIMBPF336i8uNn1YLdcJy4W1oRUemmWieZMAs3v0wqNSSoXaae8ZueymUaXvbhV00/6pASJSE4zOaSVCQtFDhsPJ8vM0NwikDqCQVJxiitercuk5W10l0sc9QmtC41sMcm2jUMYeQRRjiDK40d5alGOIMpRC3No42ApQ1pVsRWZoJr0l1xLU063DJaKsJJrPv5NxN9DfK0lf1aEZwU4VpgtG2fAaHwvaSU269BpqZYRDI2ByFiE2iE0TvyqHYLm12S6MSpugUiu/ZZXDFgkLR9WUsaGgHSsCEvVG9OtvRsxCrCT35WlTNyqQnw/MKj4920sfO1SjzzqUW4Prx5jfo7dyefITI9kdKwA1wrwrADXCrGtKBbYxkLr+J6W3tsibTP+xAAfeO207HraEPHcDnsIwZgKa2Tq4bdDo6kcbOcBY1j45BAqMmw4o4fIPbSiuV502HJKV9Z8DrS42sOF1stnfwVYveSy7eQudpyo4yb3QyySZxrtWNQdi3pp8rxdi5LYMaVQkSZXidBW/DnI7z27Q32KlIP1ssvorOkb2MYYkz2QawTZg7qePEZTFzFtfvSJqBJkmQmaU4kFRIzvIZzESh64DVFiU8ClM3mfChU3SbU0Sj0bFCh90Pck+RJSRzSHQxGPMh5FXOxpTkl2IETGoh7mqEY5amGeWpRnPChSCQvJa5HxoEg1zO9TxNoqQqWOjdJY2WssMAyAIZMC8efGo9ezfQpOje7cCF4iJpvFrqWSJvfG2i2eU7q9dLpBJQ9pklcrDnswVvLgtrKHeaTjh2T84LTxwzJR0E2o7WS6HYvdRNA6iSPmWlH2AHatsOk1jKc7Ia4K8OwA16onrz620nup66V58w5dZh6lVJIRg+waPm6If6Dg1okzvwzPbHmmQKm0ZaXd5UkqYj4cB50DQ21Tj7y4MjDBd7aIQ5qspLrRmK7wLE1OaQq2Jq9CCmgKkU9Bh9hGg/HBRFgmwtIRxgRgAjAhjtGcv/LNwOS+HzOJiOd2mCrd3B5QY60DlaSDWO2ckFbtQOgYqNM5UGfz0k7q++mU7i/Vssfm07r2Iy1We2ij2F7pZ0elnyB5YEbGptMbZXZhJ7MKA5kLcKSRuqVpyiYblcXD+kSM4zNKnVHq1IlamtDTNHBFXLrIM4sSueZBZ5qe6Ma2GCiH7KbCKHU8HMZMnXGCzAmJ01jFt6gCbiPNUuKmNpOmj6snQtZvcqhKeBRws+2mgjU9lmpT0/v+fis5HApJPs9UzMaNjzlOJEcRl4A4xVcPBbrIHxHZSdpBG5UI3RLjQSJ0o3ziPNmEJmmm1LELbClNqF1qUY56lCPQU/9+Xcun5FYoOlUWlLZScKoUnBoFp0beruHZAZ7tJ2Ix2IcYFAThcJDmIw8ntIy1S+psQyMnfjq9Oe+9i42rLLQhyb+ssjSDaYtHuo00lzWAMRrHaBwT4uoQx4QoHWAZHzsRsB5gGY2r42VcE+GYCNtE2DrCMiG2SV9DLB3GYteEDfc8qalnLSVKoYlH/LR1gK19bO3v1TWfCv3Lr8DL3r/f5/VQIuK5DVSbabCg1XmumIBBKsw2HYy2MfrfXjGGuc+OUs/b7D5hCutymhiaXWRoTgG/sOd434loo5Km5dhFC7SLNqrFUQLYNj6HzeNzCZJOKoq4+clC4+vY7fGsOvPL2zihvIUTSlsputU97nff5YpjPNN4zL3RHPufCuIasYAdosYwtaxj1d6wUVl+1eYOfFUCBqm2dILwjJ35eC42neTwsBmmzvCE68VCUcZLlo7FuEmaYwepodETYmwnkyaoT//yOAxRZQfjkAQUpTG/6XGUydGXLJs29RZw8bCT/LXx7boRQxkLZPcQDEBwOAkih7GgxFhQYjx5HQuK2edKWJjkCNsqzJogXRUmIQCxC6yxyNl1unIj5Ow6+fQvEcV5p07JqeDaYfYgTQeNIGlyT+OoHSxK5HCVm1VI8sl3EsdM25STAYTSAQ4gdvyrBMlDvlERTNMXFnAp4BKik9SGsaM/bvwslCaXhLvEeYXTONp0sBE7qcapbL8j1Kma4OBb3Y5A0u+pgEtOxaEQ6W8rdi9Vdj5c4oFc0vOQtsjUs/CkiDDJG938q0lHugRwVPxNxr800xI+ZCDpvBzPDU3amTnaaxx5KrrSzsoKlYV67OvYs1AjyN5DGuufhgk17ge5JJuRQiUpThvd+KzsvUquI4v0XpKev/RqT7eRtnLFoSbpq87OX/O5wxg0IZgQ1xgsoxMhqMFoUI1wHG3SVKnxQEXKGDwUHha2SVpfTJKdhDh3dXyvi3sdYBodf+NnUBwfHJ+zeLj4uI1DYcfRGtgq3g+JTG48eye08KRHbuIQFVvXsaM6jvaxdR1H17GjGo6uY5kgEbhhInD3H42Ntmy0chp/VvrqESoHY9nJmVBJA1T63Zq4kz0RGENk5YgsL/sL7QKhlcOodPs2WtkYK33vJPNslv/WjTJISjNKqX8GXgfsMMZMzhlzpNBu2EYQoqqxwKqbkB2M4ROykaGDLkLXjhrF0YAXlnfv9wANBqjjESiHDtMaVqItxVhPjnrRoVZ2qXZOjuOdiDaK9SOLeGrwFIbq3dSiHFP2xJlA0alwUucGFpa3MK+0Dc9uCMlKkGdbZTabx+ezaWwe65MUPr25ARaUtzKnuJP+wm4KTiwqR0w8ymIFn1pS34/DCkJ84hCZNPuHAsomRxd5usiRx2UscVbT9VMnVzFxABAo4dFFnhPoopjcwtOewh4OuUQ0FBPxsbc42NBohqmyPcnBkUYz+oQMU2cUnxIuK5nHLIp0kcdPRIvVRgUgfSCnpA+aHE5bI6ilg/a4+xnP6xyFTdD1yGOw3sVwvZNhv5MRv4MxPxbKaWUuRaEpueOU3QpzS9vpcCv0uT6z3IBetxa/JmFHcaiJk8WTpgLYwsJTNrWmASTG8LGxKdBJnl7yuNNa6bCavpcczqRWibY42OKoeNCjCj4DVBg0VTQmHhGReGTF9HcQC+1gWvKQxyMNOpkbZ6OwVdrB0uARDwaUSrIcTjZIUD4RwumIhnEnu4i4Y2XiMx7A99Sxt5AQBUqHsfDRAQqNMsl5SDLJKNOIXY9jceIMEMnqpOItlmRx4FKgA3x8AuPjGEMOhYsTS38rFamxIEtdw8DoJEeQTkSlwjEKB7CNxjJRtt8sU0WKiQANJsKB5BhSIdV4nwX5mPg4LROi0qb7pvdTTbNMEoeu4vABk9zb4leVbLNp/aOgg+SBorFiYWp7hFae0MpTdzvRym0IXeWgLZdIuclr/Fkrl8hyE5EadyrUVjxNKweOgBA3ANzCTJdgEjPtPN8M/D3wtRkux17ROmzrAdLsOu9gPEuMf7AjoCltmPvcCNWSw+DcfV9EdVwecFewzjmRIdXJkNVBkIwGuDRcz8v9Bzgp2ky96LD51G6GvYjNjLCTnU2jGMYjzpXwOJk++lWJSpjnN4On8NTgUqphkQ53lMWdLzQ5aHVydh3P9uOOH0mMoq002iiKTnWPZnbRrbGk6wWWdL2AMbC73sXGsdlsrvbyZKXAWr8HhrvoKG3AKa+l5jTFy6XZALSLbTyKtqFflSjikcNO0uPUGaTKpiTOTiVObhmPHgrJSFzxg6mIm3Uk66e0xwFRDgRHWfRRoo/2Ww8K+4h5TVFKJe7Xgf+sLdUYuvVYIdIWu2u9bKvMZkdlFqNBmfGg2CKQbRXR4Y3S4Y4zr7ibHrdOv1en3w2Y64Z0OnWKyskcNC+7JiygOOV+90RexSINoHc/1z1aSY+5l+Le76VN88JEwMVJ4OLOeiE6drMJsFHZ0MtpJpBcEibkYE1rJSQW4PsOlVMmipumozqOjh1AJ6ph6xq2DrBMgK1DlImbvN2ogheO4YVjOLqGZY68kdSmgyytpYpj4I1KI+hj4WuU1eI0pm5kaHkNRzJ5TZeD+HyrTIzrRKCbWAim62FP2K7dEIvKwWSub+LuqrQyoFreG5W2BFlJWszkvqwmVB7SCnOTe9zSRyAR+PH5oMm1TTu1pmn/WrbWNC09hxaR5SUi9+ht5TtamVHxbIz5qVJq8UyWoR0iE7Ulnu1tQ0DsOlf3t5nSGLq315i9fpTItXhi4SK+s/Al7KKH31r3ACsqW3l2Ze+kH0mIxa+cZTzrLGJpuIFI2fy3dyGjVpm50U7m6l2cFj1Hpx7HVy73uyv5x+KbuMh6kP6lv+JpazObGMYQZyEo4NJFDgNUjWErFTaqYYqDF7Fz62vR2CwobWH5vAc4obxlWn+zVROwnkE2MMRorp7122mWF6FR1GsnEOy6mKh6IibswIRdLduxVMTJnetZ0LUebSx63QrLc8NYKh6K1ieadofveCfUdtbhDcg6q6kJGRZSdNLTO80c0frqEUROkhdXY1uaolOl6FTiVEnKp5sxiqpGqCxqeNSMR4iNbzxGgzIjfgcjfgfD9U7GglL2oOv3xliQq1IobaXLrTA/V+HEXJ0+1yen4taDllj0w9CJTJgaR1mUpzjv3RyAC2V0i1BNHUlb17F1kIkp1eTmpkIsazBP3NE0btNJmsyz5nJdxzb77h/TEIAWgV3Ed8pUvFlZM3Zk54hU7Aa2CiqaRCc0xF3yvlmkqbQDJ/F2ErEVb9NKjtFkrnAjVKDR8bOFdETPVIhmTfVN4i4rY7KvZJ9k2xaEY4eZdp6PCtpJU6eGx1GjsfM8vp/C2Q40i54YpHN3HW1BUHc4/7FnWPHkCxSieFs/n3cmnzvxOlaFT/Fb9XuwgKftE/n3/KsYtuJE6GvceDSk+dF23jb+XRbprZP2tYoHuGXhXNZ0bMCyhrC0S7m2DGv4HKq1eYxFHkHSk7Ye5UH55OffSqX7XmblX2C+AwXHZwTDON1TPtzaITRxXKXBMESNrYyykWEMhlmUOIHOJM6tEQ5hocgphxE1i7BznK7++3GsCJJ0QbalqQQFnhh4Ec8MLWHd8Mmt51nFaajmFbeztPs5FpS3HlTnxOF6BxvHFjDidxDp2Anpyo0wt7iDWYXd097xsYhHSESXylPAZdTEsdGHOndsc+e4saDY0kluPIyn1aODz+yh0MxjN0ucLZxsbWchO5jDAN2M08E4vYzSrcboVHuOgw+MTR0XH5dAOWjbwbg2rgLPNtiJ02O0grqF8RWMxusaZRMpl9DOEVm5pEnTI8qaMeP3cbOmR5TM11Z8G7V0BJgm8TBFv4FEmJlpbM04mrF0gBuNkwtGcaNx3KiCres0C8GGkNVNhlzDhYvdu0YkrB3VcHUVJ6rhRFXcqIobVZocvAMnbe4OrfgaCa0cvlMmsnNN07z41c4RWXlCK0do55tcwiOkKVwQhAPmiBfPSql3Ae8CWLRo0T6WPkRozb5asq3hRsjGntJwNaO0wa1F+Hmbk9bspjAasPnUTh5YdBpfKV7N25/5Ty4eeoQR12OkN8cz/f0s1Fu51zubAauLTj3GA95KZke7+N3Kv3NytJHdVjcBNnP1LuwJD4qneur8elaV57t8tLWdgj+XsW2vpza0mjEcyu4YHd4Y3bkRHBWHqXR5I/TlB+jOezxLP+vzW3m2qcPbOnZxgVnEHMptxf/5JuJZdrOO3dQnjLnmYrOEHk5lFmW1d0E+qzA4aVraoNqVG+XF8x7inNlr2FmdhWcFiQtZJjI29SjHC6MnsH70RMruGCtnPc7S7ufaErqRsdg2PptNY/MT0RxXWvJ2DduKMEZlgt1RAXOKu5mbH2JRocLc/DBFb4hhqm2J3QIu81UnneSp4NNJnh41wXFTccVuLGnGHqLGOD5Dptr2IAjGQC3KNQRxmHaKa4jkqTrHeZZPyR2n5FaYVdhN2RlPskRUUIrW1GRaUdAhHaZOXzTC4miAflOn21TIm1FKpkqnrlMOx7Cbym1Q1J0OQruAbxWoqH62WYt5VhUZo0SFHLaJyCkfj7gHuEdAWdUpqgDLhLhJ8zhodNKRB6Ozpt602RdAaZ+cHkma2P22XMR9nl9Sty5u6rV0iIXORJdvl5KONC46E+RuEo/oNGI5sbJpWjlZTGIjpjGObzRYh87lMyYWuuEoto4r9ZYO8cLRRPQGKCIsncamhg2H1zT1tG+KRW33HBtougbVhDlNMcCoRKwWCOwCdbeT8dwcAqcUn2+njG+XiSwHg01ke0TKwyJCGd0aWtDSbJ/sVxxUQRBg5kcYTMI2vtdOh8GZGmHwga98GuNOnb85xX3iBdRoBWPgGXazt8FQrFCz5Fe7KY0EpPlp15/Rw9PzTuAfitfTo0f4g8q/UZwiQ8ePvPP5kXchAOcFj/La+k/xJg3+Cxs6fNb0V9lSjvs+D+U1XXWbPreDZdYcispDG4UfueRsv+1ngjaNgSh+znpGqONhcxI9zKUDF5sQTR9FxvHZrQcJoyG2K5+tdtzseKLOMdcUmBUZXBMxLzQsCTVaOQy4JTble/CtQ1evi4zFxtEFPLprObtqsyi7o5zU+QJd3ihld4yyN07JqWBbmmqYZ+PoAjaOzWfz+DxC7WKriHmlbSwsb+aE8hZ6vVrcGUvZuGEXg5X5PDfew28qZTbWC1mC/oIVcmK+woL8GB35AfrzgyzJBfQkx5p2WrSx6FMHHgsbGsWGOmzVITuikNHQZTT0GA5zjAeFLIdwLcol+TonZo2IYmHsVDKBXHIrlJNp3W6Ngq3JYVNQcZYHGwtPh3TUd9FT38Xc+hC9/jD5qIYb1SZ12NHKJrALhFaB0M4T2gXqTgc1t4u600XN68Z3OmbWoW1ppg+wtJ+IwInvg+yYUCrrAJV2+FJJ5yplTCKA7SyEwA3HsY2fbcfW/kF1bjKopFOQk8VCNsdUNsdvRlbcwcgoq0XoNsRtU6crojh2dw9iN91vGhagJ/SYb7j0XkvsaWAXCO0idacD3ykR2CUiK83G0+hqKaJVEI5fzrjifZQ7e2Zk3zLC4EGwz/qFMajxWOjG+XD38vAzhoVrhyiOBuxYVMIODWM9HtvmdPP1whV4JuB3q9+aUjgDvMJ/gJf5D6GxcAl4tsvHNgovUtw/r8KuQshgLiKyoBAq5voFAlexKCiw1JuNZTXEiKUMeWf/QkwspZI+3B4vNyezmRE2MczT7OI37MqWs5Me7VgwS0ecGgS8ogKvGR3iTH/v+wyx2OmV2e2WWFeczdrSPEJr+kSUrTSLOzdyYsdGNo3N57Hdy3h897IJItJQsGtUozygKDnjnN61iRd17GRVaZyuZOSwArMpqKaORC7QNcrLuuJYgFArNtXzrK+VeLZaYn21yM8H51A384FYIPS6PnO9OnO8Ot2OT2QshkKHHX6O0FjkrYg0wYrCkLfiOOK8FZG34tRMcXwxPFct8ptKB4GZ3DTsKk2349Pr+iwu1Ol0xqlZFZQ9SsEdo8et0elWKTsBRRXno04zDrhYRHhY5OjSEYX6AF44iheOUvR3UartoBA0hoyv22UquX6G8vNjF9AqxA6yU2Y8N5vInr4BXA4ZykKrWPDtuy1pGndrIiwdJNkFkkwKRmObeFqcfmri+3idOP9q0EhPlWU10Fmcaxo64ug6RX83oNGqqce9sgksryGEkzjXyMrFlRu3k8jKJZ29bHynTGAXpj0c4cjM9i4IgjDzqeq+CVwCzFJKbQL+whjz5Zks01SYptyRExk3Ps54HSsKsbFa8vhORefOGt07amw9uYMdizuAOG/nvxUuZ0B18q7qbXSZsb1uw0GzrVjnvxeN8UJn47GeDxULR11OHvLoDBx65i7AHILBVHqCcU6t7MDTIeWoRl9QIdIBa3MO45ZDBc1jHpxVq/GiKMevepaxo9BBraj4r1KdtfUBLGMYt3PULIeq7VGzHDwdMdsfZUl1F/3+KItqg5wxvpXLdz/JrzoW8nDniQy505edQClY2LGFxR3bKJkCuwKbStCJH3Yy5OcZDUrMdyMu6BzmlJyPbaUdatrPOOlYhsWFKosLVS7piSsX2sAOP8fztSJb6gW2+Tm21fM8MtLNSBQPUdtlh8zy6uStiJpuBOFoFDuCeMS2qrap63hUJ41CG5iXq/HK3h2cmK/QYYcUbE2HHdDlhHTY4V4MPC/562yZ6objFPwdlGvb6KhtoVTfjhe1tsL4domx3Bx2d5zGeG521kwuHBhG2US2fZA5egRBEIRDxUxn27h+JvffNnuxnh832zl12DDOOJ3kk8EFctyVu5Bzg8eZp3e1bGfu86PUig47TmwIsLu8F7PWOZkranezONqyz+JsLPt887QhFIrXPN9Bp29RcTRLRjzKgY22FBuX9VDPTa9w7g3Gef3ORzmxNpBNq1ouA26RcTvH8sBQ0HV8ZbM6zPNk+UR+WJjd0uQ67uR4ypk35fZ9y2XMyfNcsT+eYAwn1gY4d2Q9Fww/z4uHn2Or18kzxdk8XZzN5lz3ATXn2ljMV510k6eHAvnUObaBPEAIjCV/KdOYe1fB3Fydubk60Bq/rU3Sb/4wt1IrE5L3hyj4uyn6uynWd1Kub8eLGiNjVtxehosnUvH6qXq91N1O6k4H2tp3bnBBEARBOFaQsI020MmIQBOpmYBRatRHfcKkYXc38Kny71NXOR5yz+Q9lX9lrt4NQMfuOoWxkBeWd2fq6CHndO7OXcBq/zEuDNZMuf9IGXYUQraUA57r9Hmm26fLt3nb2m46gtaS+XmHLUu78IvT+9WeXNnBNTt+hUHxo97TeKy8gDE7hz6UPceVYkOhjw2FPjrCGmeObebU8e1cNPQsLx16hl1uie1eJ+O2x4BbYsAtsSXXRdXyshRPEA9yMld10EEOC0U3hbYGDJkJ9nP8m71jTJxrNqpkGQfcsIKjq1mu2Vw4SsEfIB8MNcWYKqpuD8PFRYznZlP1+hjLzTk6Qi0EQRAE4RAj4rkNzB6i73aZcTSG8dFhbCK24/DZ0u9QVzleXr+fB9wV3Ja/jP9R+SY2hlkbxwk8i8E5cdaE39iLuSP/KpaG67m6/qMpvc0NHT7fO2mEoXwc+1gMFCt35bl0Y5lC1CoAx3pybFvSiXamTxgqo7lg+HleMfAUO7wO/m3O6mkNnWiXUSfPfd0nc1/3yeSigGXjWzl9fCtz/BHKYZ38hI5MgXII7Bw1t49qIgCrXi+29inXt+OG8ZDUvtOROKjxX2gXjorOSfFIZLUs1jUfDCfxx7FrnAuHcaPqHtNz6azDVpmK18fu8qnZOaq6PZhD2GFTEARBEI5m5AnZFq0CpGZC8srBX7+J3CyFHcbRiU87ixmxOnhT9QecFa5lnt7JNwqv527vAq7dfDedA3W2LukASzGmCtyafw1z9C5+u/rdlhRdKY/11fjeSSOUAouXbC7SVbc5c3ce20wWd9Wyy5ZTug7cujSGE+qDlJK80j1BhX5/lKXVnZSjOmuLc7lz9kqCI0BU1W2XNZ2LWNO5iG4KdJGjqH2W+iHd/iC2ruEkI3wV6zvpHvrlpAwGoYpDDRzT2nkxUg6+U0YrJxkGNh6s23c64qwQSYqxwCkneV297C8d6jTufJXGRxsK/gDxkLFxHmCd5A7WysUyYSxkLReDih3iMM5360bjeGEFN4oHdnCjapa31jZTd2ELrRwVbxaDpSUEdpHQLhLYRQK7kLwWCe285JoVBEEQhANk5pXQUUBzOr/ARGximI4auNuHmT/UEKtPOydSMDVWhk8BcGa4jrODJ/ixex6/u+6/2Fnq4oETT+VZbyFPOKdQVx5vrv6A3IS+/L5l+O9Fo6yZXePEEZc3rOsiH+1Z7NRKLptP7T6oNv+XDa7jZUPrWqaNWx4v5Ht4tOMEni7OaQmFmGlmqzIL6aJPJR3TLKg5sK24eNKyykTkgmEK/gBG2Yzm5xPZcS5pO6qRC0fIBaPkwhG8cIRcOIoyOkuphTHkwhHywRC2ruOF49My4EK7+MkoZKFdpOr1ElqFJMVXPitjze1Osh6UjgrnXBAEQRCOVkQ8t0Fz2MYodTaaIdxKhRPQuPV0GVhnL+aUcEPLMMTX1P6b1QO/obc6yl+edwO/6Gqks35N/afMSeKhU+qW5p/OGGAor1mxM89r1nfgTOE0p9RKLptO60a7B+4kvjQRzr8uL+D+rpOwMAw5RaqWOyNCrIcipaQT36ip4xNRTSoY/arEIroborkNjLKpeb3UvN5J8yI7T8XOU8nNbnt7yiQ5b7WfDO8bD/5gpXl/kxRjqcCuut2AyvLupvl8bROglZMMExw74KGdJ7BL+HaRwCkR2gUZjU4QjnIspcg5Fp5j4dgK21LYysKyFI5SKKu5o3AyRLYxRNpgDFiWSoarj7eV3pZDbQginfVpN4as50I2LXnf/BkTd07WyT5CbQi1JowkQeC+SL+DaIbHyDhasJTCc6w4zW02enzjvQEibQi0IlDpCJ0eoZVD2x6hscA+8jqli3huh6YfiU9EQESp1ppIaofVy4hVZqm/oWV6seLzmt88QL1gc0HnQ8ytbeWkaDO7VDfLoudalh3MRXx3SRzf/Or1ZVbvKKD2kuVhuL/A9pM6DkrgXjj0LJcOPs2vywv4Tv/KGXWXHSxOUbNYSFdjxMLkRRuDdYQ4qkbZBE6JAEnHJghCjG0p8q5N3rHIuTZ51yLn2OQci5xjtTUK60yjjcEPNYGORbVOhHUQxcJaqVj4OEph26mQVxhjCKJ4OT/U+JEmiAxhpAmjdsZUnTlUUrEpenb8/SXfm2tb2JbKWp5tS2EplaQsjQWfH2pCbbIKSvOxamMIQkOgk5pLIhhtFW8nrTAZ4tlam+w5Z9sKx1I4VlIGWudblsJWcZmUalSslFJZJSx9XmpjiItgsn2ly6dE6fdtkvfGZPsLo/gaSCtaUfIeGtLDsWy8fAG32ImTK+E6Dq5j4zkWrm2DZYPtgpMHywWvBG4hfrW9+M87/H2pDgYRz23Q/NP3k+yrXrW1g9oGewEAJ4WbsmleJeS0B3YChhdO72GOGWROEKcmm81Ay/oGw50nD7OrEPHKDWXO3bH3C6lWcg9aOK8a2cirBp7iidK8GRXOeRz6VIlTmYW7B5f1SBHOgnA4cWxFPhVgbirE4lcge4jZlsoe7kolD+NE0IQ6ETHJq58InDB5ENbDiDAyuLZFKWdTcJ2ktU1R9CwUCte2cG2VCUAFRJk40AShJtDxdoMoEWCRzsp3tOPaFvnk/OddO3HSwLFiJznnWLj20d+PwFJJBWAat6mNoR7q+C+IqAWaih9SDTR+2H4281QcWhYoVIuItBJBayuVOfsQ/xBMclyWFc+3LYVn23iOSsTdgX1vtqUoeEd+q2DD8d3zM9RtPgxlx6I21wG5TnDzYOdi8esWwfHAcuI/JwduKZ52nCHieX+IImqmDspQHG6NU95gz6Ooq8wyQ0AsnJes2Y0Bnj5/9j5Txz3VU2dLOeR1z3Wwcldhr8saFFtP7jwo4Xza+DZet+tRni3M4o7Zq6YUzi42/aqET8QuM94y7wTVxYipM7KHkRD3hUJRxGW2KnMyfSKOheOazLV0LYquQynnUMzZeAcqyFQ8yqfb5rPdGHNgzmhu77NrQcRoLaTiR/hRLJyqfnREiGrbUuQSd8xzYkHl2mlFwYqdP7tRKREODEspCq5NwbWh0Dr2QJS42pCEpjTNazQ+qhYnVWgDJx+LXycXi1xlxaLYycWOr5OPp9teLI6dfPw+nS/sExHPbRA32yhUPcSMjXDCjiG8eqvz/II1j0V6a/zjN4bFjw1gh4b1K3vbyrn80NwqvTWbM3ftu84/2pcjKBz4V7e4uotrd/yKLblu/m3OOS25mj1slqg+5lDGQmVO8BZGGMenizw2ij5VIiBiJ+M8bwYYp/1hvot4nKXmU1LHX21VOH5InbJUKFpKUfTsRBQ3XMy8O/Ou5aEKKYiPb7KCrwVR4kZGVH3NuB8yVgvbFtUtLqRS2ElztZUIXc9RmUOfuoM6Hqkc1z44x1GYPuIWkyPfvT0iSN1ey4ldYK8cO8FuHvJdyedC8l5CCg81bSkwpdQ1wKeA2ST3LcAYYzr3uuIxQyye8UM6n91NfUJ2jAp5dtp9nFVfC0DHQGMwlLHefVgzwO58yMaOgJe/UMLax0h2Ril2LWx/eOiJnDm6iSt3/ppdbpl/nXtuS+q5Eh7nqoV4U4ROzFeTv2pX2cynk35KrGUH28zoPvd/kuoVp1k4JlBAzrUpenbmYDYL4uaYQxDnrJmGqG44kcYY/CRO1koqHZFpdHazbUXescQJFo5sLBdsB5xCEs/rTAhzKDY5v268TOoOp66vsuI44WbBLNf8EUW79uWngdcbY9YeysIcqRiSDmthRDQhX7CPw3fylwKwONoMQP+GMfycxdCc9po/HppTxdJwxu59u84js/KEuQOoqRvD6pENXL77SdYX+rh99tnUmnqwdpLnbLVgSuG8L1xls4J5nEY/2xljjDqbzDAQp5Qr4OJiU8Zjtjpw4S8IM4VKXWMvbn4u5x1KnpN1HtobIvTaI+64pbJ4bkGYMZQNucTZTcVtFvObb4Q3WE4scp1C/Nl24z/hmKdd8bz9eBXO0AjbGA7HiSb0G77bu4A17jIu8h/hpGgzhRGfjkGfLad0Ytp4sD7ZW+OROVVW7sxPGmp7UjlQDM7d/x6pHWGVq3esYXFtgGcK/dw+52z8Jsf5HHUCferge7rmlMMiujHG4CmbXor0TsN2BeFwk3NsOgsO5VwSf+zZIoIF4WjF9lqFbyqEvXKSBSKXdJDraGR/kN+7sBfaFc8PK6VuBe4E6ulEY8y3DkWhjkQ0htGogmlyntc4L+Ke3HmcETzN6+s/AaBnWxVtKXYv2LdoHHMjvn/SKCeMuly+vmPfy/fm2oqfBnB1yHkj6zm5spO59REsDN+ZdSZrOhZmNwWF4mTVNy3CuRmlFKcwa1q3KQiHkpxj05F36Mg7dBbcuHOTIAhHHk7Swc0tJCnQPEDFqc5yHbELnCsnwthLOsNJ9y5hemn3iuoEKsCrm6YZ4PgQz2ly+ag1rc6z9kIAXu3fm00rDfmMd7noNpoe7144TqQMr39u7wOhpAzObS8M5KTqLl6381F6wioDTpEXCr38V99yBtwSNhYFXE5QXfRToqCkiUk4/lBAMefQXfToK3kUj4KUU4JwbKEacb2pIHa8ON4X1dr5LdcZf851SFiEcETQlng2xrzjUBfkSMdgMLo13nnQ6mRhtJXZOs7dbIWawljAjhP3HterMfxo0RiPzarx4i1Feuv7/hrqBYdax96zU5TCGpcMPs05oxvZ7RT57rxLsYpLGaBKHxYr6cLh6EjWLwjTjWNbzCp5dBZcOgsOjiWxtYJw8KgkFMJr5AF2i0lKtEI8z8knKdEKYFnHbW5g4dih3WwbJwBfAC5KJv0MeJ8xZtOe1zq20BiMbnWeB61OFkTbs8/FkQBlYLx77zeFX/XXeHBulZOGXV6ypb2UMkN7iXXORz4XDz3DWSMbcU3IL7pO4onesznDXgRAn4yEJxzH5F2buV15+su5tjr4CcJxje3FjrBXjl1fpxCHRKS5gL1S7Ag7+aSz3L4zSgnCsUa7YRtfAf4VuC75/NvJtFcdikIdeWg0YCLdNEUxpDo5Q6/LppWGfAww3tUQz8NeRKcfO1ybygFDuYj/OjGOc77+N917HX4725dlMdI3dSaO5bVxXrv9AfJRjRfKJ7K95yVUvW5OQ1w14filnHPoKXp0Fl3Kni2tLYLgFqA4CwrdcfiD5SbiNwmZyJVjR1jigwVhn7T7K+k3xnyl6fPNSqk/PgTlOeLYOFDh9za8mP+xcC0nNo1bP6pKRMqmN0nJBlAaqlMrO1m885O9Ne44ZQSAvqrN7kLsXBdCxZXPdk4pnIOcTaXTIz8W4Bcc6gWHkf48xm5d1kLxkkqVi7f9FN/t4LF5V1PNzwFA8lsIxxOubVH04rzBpZxNV8GTdGfC8YGTj51gr5SESiSDZqRxxNngGcU4XEIQhGmhXfG8Wyn128A3k8/XA7sPTZGOLB7bHIvj+4f6ObHJeR6wugDo0bE4tgNNechn58JGiMRverLEJOwuRFywtUh/xWbJiEd5D2npdp1QZnRWPh4Oay9NzKdGeS7a8SOqXh9PLngDkb3vHNGCcDSSucbGUMo5FDyboudQysU5l2WkOOGYx3JjxzjfDaVZ8V+xL3aQBUE47LQrnn+XOOb5s8S5J+4DjqtOhEqBikzmPA+r+KbVnYyq17WjijJkA6NoDM93+py5K8/l6zuwDdhmonusWV7cyq6gzLagi20ndcbCGfYqnEvG5ZU7H8Y2Ps/MfY0IZ+GwoQBvwmh6QaQZr4eM+1GSE/3gyTk2vSWPnpJHR64xvLLELAvHJMqOXeJib+wU5zuh0BO/lwwTgnDE0W62jQ3AFYe4LEckqRYwAE3O84iKHeZOPQbGMGvTONWSQ7Ujvsk93+VTdQ1Lhj08PfmB3+HUeEnXM3RZNQB+WjyFp2fP2WtZCricQi9njjxNb2U9z8+6hKrXd/AHKQh7wLEV5ZxLZ96hI+9Syu15sBBtDJGO/7SBUBu0NoRaE2pDFBnC5HO8bGMdbcCxFOWcQ3fRpaswWSzYopuFo51cZyyQc52NjnelWbGjLHH5gnDUsFfxrJT6kDHm00qpLwCTLCVjzHsPWcmOQFSzeLZKuCYgh09uPKQwFrLptK7sBnjPCeOUfYuThyZn3lAYzu95HkdF3Du8hFldY1xceYat4138pjR3yn0vq9d42egGuiobyIWjDJROZnvXqkNynMcStqXoL+fIuTaurRivR2wfqaGnySE91vAcm3LOpiMfC+ZSrv3OQ5ZSWLZCxhcRjluUlYjibij1x0K52NfIWiFxx4JwTLCvJ2M6JPfDh7ogRyqNQA3TIp5HVZlOM44CunbF7vFwfxw+Me5otpVCLtlYohBNvlnO7hhlFuPc3n8Wu02Z4Tl53jr4INfs+BVfmf9ituW6smUdHfHygac4f2QDkeUxXFjI5p7z2NmxXJyKfWArxfJ5nS0CcFYZ5nTmeHbnOKO1YFr2k3Ns5nTmKLgOth23VlSDiCDShJGhFkT4oaaYiNKCG7u3Q9WAMNIEkWasHuGH0b53dpAooJDEC9fD+Hou5xw6ci7lvMQPC0Jb5DpicZwO5JHvjsMs8l1xBgtBEI5p9iqejTHfTd5WjDG3Nc9TSl03xSrHHEr7XG49yI7oRJRuDdvoSEI2+jaNM97pEiaxmes7fQAWj8Suc6dd5fyO54k9Z8h7AYN2gbWleZglsQC+1VvN722+l9/ffC9DToExO8eAW+K0yjYKOmRb10o29l1EZElOzX3RVXBxbYvZnfkpndO8a7N8XgebBqtsHqoe8H4UMLerwAk9hUmxuFOFHUykI99atqofMVQNGKsFRAbyroU2hnqgqYexyI70vh1zx7YwxuDZFoY4HCJ2kl06CrYMDiIcv3jlOEzCLcZxxGnqNh1CFCSdW+z4M4DR8R80Urrlu+KMFoIgHLe02yb7/wG3tTHtmOO0J7/Ab3n/xF+ZP2iJWxm2OlgYbaM4EuDVNYPzGgni1vXUKQaKeePx6T0lv5M+t0JkFKM6z4BX4j9nnY5pco7HnDxfWfBizhl5gTPHNjPHH2FRfZBnC/0M9byUoHji4Trko5a8a3PqnI62hlpWSrGwt0jOtXh+5/jkmKR90F30OLG3SGEah3UueHa8va49P5iNMdRCjdaGQBuCUOOHmkoQYgz0FD36yt4e45IF4bjB/f/bu/MoydKzvvPf595Yc8/at66uUqtXNb2pEOoWBrQgQHDUIOMDBg/CYMvAMGAwhxFoDjbjM8d45LGNBg+4h8XDIIRnZGQ0bFrYEZaQEGqptbTUWlq9d/VW1bXlEvHOH/dmZlR1ZcXNyoyMrIzv55w4eeNG5M0337rd+cs3n/d9x4pgPL4Hpg/CxN6ifEKS1qlfzfM3Aa8DDkbE23pemgIWB9mwraJ95lEAxtNKwDpHg2eyGb5y4T7GThSjzE8dLP6nvBiJz83Mc+PTTbJyHefdjed5fH6SPz1xHccPT50XtHudrLX5kx3X86ez1xJAnrocyHdzfewe6Pe4HYw1aty4f3LNZQd7Jlu06zW+cPwUZxf6l03sGG9wYKbNxBpqgTdSRNC2qHhAghdM7cgbxZq5nXnodl74+lo1JooRz7PPru86201joih7GN9VjPxGFPXDnYWi//N6cS4r/6KT14vXo+e/98W5omRifHcxIc/NPiQNSL//uzxKUe/8euBves4/D/zYoBq1FUVKLG2R8mhehNkDnSdpP7/AQiNjsVUEmqfai8zniWtOFCUb9VhkJj/LfXMH6Ea2XBd9KSmKP7fXo8FRdgzmG9pGptt1rt07cdnlCJOtGrccmuaJ5+d4+NkzLHZeGJDGGjWO7hp/QamFtqjIVrYPzmpFMGtOFUuAZbVyAle5wUTqruys1juR9GKj952FIrh1u5A6RaBOneJaAAtnYf50cc1aswx8tSIQQrHNMcD8GXjuy8V7O/PQmYNTT8Lp4ytlAleiyMrvNyv6KStDb2NiZRe7xjjkzfLfqFkEZkeEJV1B+tU83wvcGxG/mVLamNlVV5h03nHxQ+3B/AAAB7pP0jq9yLmJlfrWp1vF6OXOc0XX7qqfIgKOL0xwakdzeffBKm6OvTRie48ydqPGqdZ+zjZmqXXmqHXnmD7zIN3IyVL/P27snWpx9c6xdZcpRAT7plrsmmjy6HNneezEOVJK1PLg8I4xdk803eJ5K8ibMHNV8Sf4+lgRhpeCa61ZhrIA4vJWNuj3b7y03m6WAdkL199tThSPfhpjsOeGF55fnIfnHytC9HKQDlg4A3PPF7W4EbBwjnWPgl+uxnj5y0a9mDg3uR8m95Xn28NpkyRtoqrDaEci4l8BNwHLQ6cppRcNpFVbSJQjUUurbiyS8Z7m3wFgsnOa1ukFnjq0MmrydKsDCWbPFaF3d/0U3RQc70zyzIHqoytHYwc7Y3uNxizk4yzmLZoLJ3l64lqenryRrDXO1bsmaUexrFwQzC92eH6uw+KzX2b8+MeYOPfYC66VRXB45xj7pjZ24k4tWwnLT5w8x8HZtitQDFN7tghn47tg+qpi6a/trNaA2auLx6UsnIVzJ4qR7+5i8Zg/VYxkn322GNlePFt87C5SOWhHBpQlE93FYhS53i6WW5s5XPzi0p5d73cpSVe0quH514B/TrHD4CspdhcciUSRLvj43+q3AXDn/MdonV4k67K8MQoUZRszcxn1cjfB3fVTPLM4xjN7xpkfq9bdu2Kca2PXBn0Hwzdfm+TJqZt5dvya5RrFdiPnpYdmuOGSdcr7OX3udp65/wOMH/8YY/Ugy4JOWVaxkZP1LtRu5BzZtb1+ebkiNCdh9mgRlif3b/+wfLnq7eqjvN3OSqhOnWJZtVoTzp2EM08Vo9tL6xI3Lj4fQ5K0omp4bqeU/igiotxt8F9ExN8APzPAtm0pS9sOf6x+A1d3HuHuuT9m7GQxWfDM1MpGKI+NL7D/dBGmM7rsqJ3ms2f3cHrvCzdLWc12qnM+3dzLF/Z8/XkTe24+OM1XHpmlVmFEd7zVYPzWV8KJ6+DxTxR1op25QTZZm6U9C1MHYOpQEZob40UZhjZWlhf9emHfNsZhav9w2iRJV7Cq4XkuIjLgcxHxw8AjQIXCvu2jW04XfCqb5aULnwJg7OQCnVow3855urXI56fnea7V5Y4ni27dWT9NHoknF6c4O1ktPN8eB5mN7VE32I0aD+28azk41/Lga6/bzYt2X8atM32weHQ78NTn4It/Vky00pVl6gDsvLaokZ3YM+zWSJK0ZlXD848CY8CPAP8SeBXwxkE1aivqpC7naDIXTWa7JwAYOzHP6akGRPB/3vwMS5sJHjpVjDzvb5ygm4JP791LyvtPNpuhze4rtM45RU6k85d6e2zmpSzUJoFiw4/X3LSX/dPr/MUgy4uJVu0Z+OwfFpOotEVFUQowtb+Y4De535FlSdIVr1J4Til9uDw8FRHfD0yklE4Orllbx4kz8xwCFro1TpcjwmPpLNlil9bpRU7safPo+AK9u3AfLMPzweZzPNSY5cn90xe58gvtjSttMD94dvwoT0/eyLnaFI3OaXY9/xmaCyc5V5/i7M6buOvwDIdmxxhv5JXKNCqb3Ad3vBGefgAe+pDr5m4ZUUx2m74Kdl/v6guSpG2nUniOiN8EfgDoAB8GpiLi51NKbx1k47aCE3NFrfM8dc5EsbLDeDpH++QCAdx/MPFrL3mWrAs3PNtk95kaGUGzvcB0fo6/mqq+IMmeK6QS5umJ63hm4jo6WZOF2spI+Vw2wyM7Xs5YM+em/VN8w8HpjQ3MF4qAXdfCjhfBk5+CJz5ZLO+lzZfVYe9LYP+tji5Lkra1qmUbN6WUTkbEdwN/ALyZYtOUbR+ePzT+Ku4688c81t1JLc4CMJbO0T5dLHv99tvOAsGeszW+7fMrI8xHdz5FmoP7x/dV+joTNGlHvf8bh+zx6ds5Pv0VF31tolXjrmt2cnjH2OauiZzlsO8risfx++HJT8OJhxnaOrijZGxXUUaz56ZiBQdJkra5quG5HhF14FuBX0gpLUTEaCSTpRCY0vLI81g6S22uSzdgoZEBiVc9tDJqXM873DL3KB+ZupqTtWp/tp6JjV2veBDmalMcn3rJRV+7Yf8kX3V0J401bAIzELuvLx4nH4NH/xae+fxw27Mdje0sRpl3vtid4SRJI6dqeP6PwJeAe4E/j4irgZGoeYal8ExPeD5Hfb7DYiPjTCNx16NjHD25sprG3umTZCQ+Onm48lfZwdZfX/Wx2WPnLTkH0KxnfM21u7femshT+4vHc1+GL/0lnHl62C268rVm4Oq7YOc1w26JJElDU3XC4NuAt/WcejAiXjmYJm0xZVgMEmeiTaQuLc5Rm+8y18xIsbKbYCFxTfM4T8U4TzQmK3+ZWbb2xKoTY0d4vn1o+XkEHNk5zle9aAeTrS1cbjJzGG79+3DqSXjwL+Hko8XIaUpw9plht+4KEbD/Fjh85wu3o5YkacRcMjxHxD9IKf1GRPz4Km/5twNo05byulv2w/vgqs4TfDoO005zZEBtvsvJsQASM3Mr4Xmmdpb9iyf5vV03r5R89DFJk2ZU/SPA5puvTfLQjjsBqOfBjfuneMnBaSaaW7fN54mAyb3wkjcUS9stTWg78wx8+YOWdlzKruvhwO0wsXvYLZEkaUvol36W/hZ/sSHUddc8R8Q3Aj8P5MAvp5R+br3X3GhHdxffejud40y0GaOYNFif73ByV40Lw/PV48+wGBn3jR+o/DX2RfUR6mF4fPp28nqDmw9Oc8uhaZq1wW2LPVAR568EMbYDbnhdUR/9pb+EU48Pr21bzdQBOPI1hmZJki5wyfCcUvqP5eH7U0of6H0tIl6xni8cETnwH4CvBx4GPhwR704pfWo9191oRTOLyucz0WIsnYOUqM13eW4CIsHU/Eod8J7GSb7Y2sncGv68fYCtubTXfG2CZ/e+gutefCM37JukVb9CQ3M/U/vhlr8HT3wKHv7r0d54pT0LV70cdr142C2RJGlLqvp39/8duKPCubV4GfBASukLABHxW8DdwJYKz1m2UnpxOtpMp+fJF7pEgqcnYXouIysnFWZ0meUsn2pWH3XeGWNbrmSjkzU5t/Mmrrr5FXz1/p3n9cG2tvemYqWOxz4GnYVio4+8Ac8/Vix/d/rJYbdwcMZ2wr5biiXnsiGvmCJJ0hbWr+b5TuAuYPcFdc9TFKUW63EQeKjn+cPAV63zmhuvnDB4f+0oj7GH/QvHqc13ATg+mZieX+nC6dpZMhKPN6qPJF/FzIY2dz2enH0p04dv4tZDs8zM7hh2c4Yjy+HgS88/N7G7mDDXWSgmHj7xyWKy4bkT0JkfTjvXLSCrFTs1HrgNZo8Mu0GSJF0R+g15NoCJ8n29hbkngW8fVKN6RcSbgDcBHD5cfem3jbI06noma0MXWmmeehmen5hKTPaUbEw2zgHwZM8qG23qnGVh1etvhSXqannG/p3T3P61X0+zufXXmx6avA7TB4sHQLdbjEY/9+ViZ8POPDz/BHRX//feNJEVazA3p2DqYPELQN4sar7r40X992ZuZCNJ0jbRr+b5z4A/i4j/lFJ6MCLGUkpnNuhrPwJc1fP8UHnuwjbcA9wDcOzYsU3fmGWl5rn40s/G5PLI8xNTiYPzKwPw9YkuKcGz9ZVA/OLYyRkW+Hx64TrDU7SoxXD/RL53qsXhHWPkB28Hg/PaZFkxcjvZs4tkZ6EYmX7uQTjxCKRuEboHPUIdeRGM2ztgz41FYK41+n+eJElak6rFtgci4g8oRqEPR8StwD9JKf3QOr72h4FrI+IoRWj+TuC71nG9wSjDbVaG5xs6X6Q23wHgmQm44fhK+B1rzHOi06bbE4inaLGXSR7mBHMsnnfp3TG8jUUCOLxjnP0zZWDefcPQ2rKt5PWiDOLAbbA4B0QRYk88UoxSn3oSTj1RlHysSUBzohg9Ht9VhOT2DNTHilKTsZ3FR0mSNFBVw/O/B74BeDdASuneiPia9XzhlNJiRPww8B6K+ulfTSl9cj3XHIhYmgyYuHHhAV628Alq88XW3KfbMFGWbZwbrzPFOZ7r2Y47IxijTkTwcg7z1+mh5RKOfTHJUTa3rniiWWOyVWe8mTPVrtPIy5A/vtslyQah1lw57i33gGKN6ac+W+x82FkoJiV2F4sR5Ik9xeYutVZxjeZk8W/kBiWSJA1d5WUeUkoPxfk1kp31fvGU0u8Dv7/e6wxUKko0dnCSU+QElLsLBimCyYVitO/5HU1mFs7wwNhKCB2jwVKfNaPGzezjw6mYI7mbcbJNqjkN4PDOcfZPr1KWse8rNqUd6jG2Aw6/fOV5SkWIttRCkqQtrWrB7UMRcReQIqIeET8BfHqA7do67v8DAP6n+m9QT0XZRW2hw9lW0XWT8xlnphqc2t1ksjPHs7WVeuexOH+kcDba7CpLNTZjO+4ADs62ueWqmdWDc61V7CKn4YowOEuSdAWoGp5/APjvKZaXewS4rXy+/d34egB+dfGbqLMUnrucLrPoxELGMwfGmUnFzoPP1lfqmCd4YRi6nt3cEvtpxWD/BN+q59x0cJqrZsdoX2pzk903QL611pmWJEnaqiqlppTSU8B3D7gtW9PYLACPpp3LI8/5QuLUjmB8IchTsNDM2LFwGmB55Dkn48hFaprHo8H4RUL1xQSwY7xBPc944uS5SvuhZxEc3jnG3skm0a8spNaCA7dXaoskSZIqhueI2A38Y+BI7+eklL5vMM3aQsqVM/LoLo885wtdTrYzJspl6hYbObtOnALgqUYx8jxFc13L0LXqOTcdmFqe1LdzssnpuUUefvYsi52iDjvPgul2nQjodKGWBQdn2rQbFVZdyOpw3TcUKzhIkiSpkqp/r/8d4C+A97MBEwWvKOU6zxldailBStQWu5xoB5MLGZ1aRsqCXQunOJm3mM+Kcoz2OssyDs22V1bDACabNSabNcYbNT5//BR7p1rsmihGpS/jmyqC88zmbzojSZJ0JasansdSSv/jQFuyVWVL4TlRp0PWSUSCpyYTO8/mzLeK13ctnOKpxsoobtXSjItpN2rsmmhe9LXJVo3brpq57GsD8OJXw46j67uGJEnSCKo6bPm7EfG6gbZkq1oq26BLPS2SLxYlEyfGYN+ZOgutHFJi1/wpjtc3JjwfnBngTn87ry12oJMkSdKaVQ3PP0oRoM9GxMmIeD4iTg6yYVtGT9lGnUUmOnMAnGrBP258hjfGf+PA3AmaqcPxxuTyp01x8ZHjfhq1nB3jA1qybHw3XPOqwVxbkiRpBFRdbWOy/7u2qZ6yjUgLfHX783yZXdTqicOLiwTwjx79AACPNqcBmKZ92UvR7ZlsDmbzlN03wjWvdAtnSZKkdai62sYdFzl9AngwpXL9tu2qDLI5Xdpxlk65HffhfJ5Pn9rH7olT7O6e4rlam8cbUwBMxeWNOgewe/LyPvfSF87h6jsNzpIkSetUdcLg/wHcAXyifP4VwH3AdET8YErpvYNo3JbQU7Yxm52iM1eE51Z9kc+e3c97D9/Eyxa+xMcnDy4H7Wb1Xc/PMz1Wp1m7/OXtVnXgdmiM93+fJEmSLqlqynsU+P6U0icBIuIm4H8GfhL4bWD7hudytDanS5t5FueXwnOXc90GZ5oN3j91/gS8yw3Pq62wsXYB+2+Fib0wuRcaruUsSZK0EaqmvOuWgjNASulTEXFDSukLfXexu9LFSnhOkXFuIWM+h7nFMRLBYuOFI8WtywjPWQSzYxswUXDqIBz5apjYs/5rSZIk6TxVU94nI+IXgd8qn38H8KmIaAILA2nZVpGtlG1clR7n3ELGqTY8dXYHe+vZcqlGr/ZlhOfpdp08W+cvImM74frXQX2AS91JkiSNsKop73uBHwL+afn8A8BPUATnV254q7aScuT5us6XqEWXhfmc0y1oL2YXHXXOiMsq21j38nT7b4WrvgpqA5hwKEmSJKD6UnVngf+tfFzo1Ia2aKvJioD8os7DnKbJ4kLG6SaMLRZbc19oR4yRx9om/eVZrC88t2fh6le4moYkSdKAVV2q7lrgXwE3Acs1ASmlFw2oXVtKlyBI5NGluxicmwhai0GndX6Zxc4YY4y1r++8e7K1vpKN677J4CxJkrQJqg6R/hrwi8AiRZnGrwO/MahGbTWJjCygFl3SQnCuAY1OsNBYCawZwQGmmKW95uvvXc/azjuvhfGdl//5kiRJqqxqeG6nlP4IiJTSgymlfwF88+CatbWkcuS5Fh1iMTjbgFYn6NRXum+aNrsYZxdrW095slWn3bjMUeOsBkdecXmfK0mSpDWrOrNtLiIy4HMR8cPAI8AILR7cU7YxnzFXh9lunFfzvDcmqMfaQ/DuyXXUOu+4Bpqju3O6JEnSZqs68vyjwBjwI8BLgf8OeOOgGrXVFCPPxVrP+SLM14Mg6NRW6pR3Mbbm60asc6Lg7usv/3MlSZK0ZlVX2/hweXgK+IeDa87WdPLLTWgn8rEune5KaO7mxe8e4zQYi/ND8MGZNo+eOEdKadXrTrfr1LLL3I67PQuzV1/e50qSJOmyXDI8R8S7L/V6Sun1G9ucrenJv5qEPNF87TnmgYX6UnguPl4fu897/47xBlftGGOyVef+x0+yWnyeGVv7yhzL9tzY/z2SJEnaUP1Gnu8EHgLeAXwI2OZ7cb9QWlwsDjpB1ili8HwNSCyPQO+4oGRj33Sxmt/MWJ2juyf4wvFiKew8CzrdlSg93brc8Bywy5INSZKkzdYvPO8Dvh74+8B3Ab8HvCOl9MlBN2yrOPH//e7y8VJ4XqxlsFCUbbSokfVs0Z1HMNFc6dY9k0063cRCp8uBmRYPPn2GZ07PU8uyta+ykTdh93XQmobmCM3XlCRJ2iIuGZ5TSh3gD4E/jIgmRYj+04j42ZTSL2xGA4et88zTy8f5cniGtBCkPGhc0IUTrfPDNMD+6eV9Zbhm9wQHpjs8e2a+eiMig4PH4OAdkK+j1EOSJEnr0nfCYBmav5kiOB8B3ga8a7DN2jq6c3PLx7G4FJ5jud65dsFW3FMVSjHajZx2o+JmKvUxOPq1sOvFFVssSZKkQek3YfDXgZuB3wd+NqV036a0aivpdJcPoxx57tSylfB8wWp/k+2qS2evIm/Armuhs1isqLH3JdBY+zJ4kiRJ2nj9kt4/AE5TrPP8I7FSjhBASilNDbBtW0LqLC4fR6f42Mm5aHgOYLyxjvDcnISXvAFa275bJUmSrkj9ap4vcxHibaRn5JmF8lTPyHOdlUl/rUaNPFvjgiSt6aKmGeDmvwv1iuUckiRJ2nTrrDHY/lK3s3I8H3RZqnkuAm/vyPP4WlfPIOCaV8PEXlg8Z3CWJEna4gzP/fSMPHfnM860isC8NPLc6Bl5HltreL76Tpg+WBznLj0nSZK01VmW0UfvyPPiXPB8G/KeDVKaPb9/jK2l3jlvwr5bNqydkiRJGjzDcz+LveE55/k21LtByi5S81xfQ3ceuM01myVJkq4whuc+Hnzui8vHC3MZJ8eCWjdesNpGRNCsVe3OgD03bnRTJUmSNGCG5z5St6fmeS7jxDjUukGnnDBYL7uwWcuIqLjSxsE7imXpJEmSdEVxwmA/KS0fducynm9DLfWu81yUbbTqFSYLRgYH7oBDXzmQpkqSJGmwDM9r0Q2eb6+UbWTE8vbcrSolG5P7ihU2JEmSdEWybKOfnpFngFPtomyjW8uWJwvOjDWYHW/0v9b4nkG0UJIkSZvEkec+LqxiPtWGfd2gkwc1MrIIrt0zUW1nwdkjg2iiJEmSNokjz/2cP/DMqVZQ6xY1zzVyJloVt+SeOgAzVw2mjZIkSdoUQwnPEfH3IuKTEdGNiGPDaENVcbGyjVTUPNciq7628+T+AbROkiRJm2lYI8/3AW8A/nxIX/+ynWoVm6R084waGY284pbcY7sG2zBJkiQN3FBqnlNKnwaqr4s8TC8o24C8G6Sy5rlRdWOU9syGN02SJEmby5rnfnrKNhZzWKgHWbk8XTHyXKULA9qzA2qgJEmSNsvARp4j4v3Avou89JaU0u+s4TpvAt4EcPjw4Q1qXXW9Y+NzjeJZXv7OkZNRzyuMnremIa8PoHWSJEnaTAMLzyml12zQde4B7gE4duxY6vP2jdcz8nymVQTlyFa25q5UtuGosyRJ0rZg2UY/PXH9TKvorqxcmq4RNepVyjaak4NomSRJkjbZsJaq+7aIeBi4E/i9iHjPMNpRSc/I81wD8i6kcuS5nVccuG+MD6JlkiRJ2mTDWm3jXcC7hvG112ph347l405WbM2dypHndlZxmbrGxCCaJkmSpE1m2UYfT3/Xa/jg9eVEwU46LzyP1Rx5liRJGiWG5z5SLeNPbinCcq0DtQTdMjyP1yquoNGaGlTzJEmStIkMz310U5fT5SobjflEvRuksteq1TwHNJwwKEmStB0Mpeb5SpJS4gv74MPXBh+8tUEj9dQ8VynbaE1B5u8okiRJ24HhuY9EYrEWvPXbc46eCOopIM+okVHLKmyQMrZr8I2UJEnSpnBItI/Us1TdQkYZnoMaWbU1nq13liRJ2jYMz3106S4fL2ZFzXPkQY28Wnh2mTpJkqRtw/DcR+/I83yeaHWDyDMakVPLK5RtOPIsSZK0bRie++gNz+fyRKuTEXnQpEYeFcJze0f/90iSJOmKYHjuo7ds41zeZayTQZ4xRp2834TB6augPTPYBkqSJGnTGJ776KaV8NzNYHoxJ8uDqbxx6U9sz8KNrx9w6yRJkrSZDM999JZtAMws5EQtYzzrE553vMj1nSVJkrYZ010fifPD8+RCTp5n3LqvTy3z9KEBtkqSJEnD4CYpffSWbUCxznOtnjFbb67+SbNHYOrgYBsmSZKkTefI8xrVUtCo1chWW2kjMrjm1ZDlm9swSZIkDZzhuY8XjDx3g3p2iQH78T3QGBtwqyRJkjQMhuc+Lqx5riXIL7WzYHt2wC2SJEnSsBie+7hw5LmWgiwu0W2OOkuSJG1bThjs48Kl6mrdIKtdKjxPDLhFkiRJGhZHnvvoHXmOVHRYdqnJgE3DsyRJ0nZleO6jt+a51g2CuHTNc2NyE1olSZKkYTA899FbtlErD3NHniVJkkaS4bmP80aeU5AiyFbbdjurQb29SS2TJEnSZjM899Fb81zvBmRBbbVua4xvUqskSZI0DIbnPl4w8pwF+Wq7CxqeJUmStjXDcx+9Nc/NTpAyqK22zrPL1EmSJG1rhuc+ess2Wt0MIqjHKhMGrXeWJEna1gzPfUz0jCa3OxkpC+qrdVvd3QUlSZK2M8NzH2+86Y3Lx61uQFi2IUmSNKoMz33U8zrXzu8AoNktRp5XD89OGJQkSdrODM8VfK7xDAAn6h1SuFSdJEnSqDI8r0GegAyXqpMkSRpRhucKvuPUTQDsnasXOwxykfCc1aDW3OSWSZIkaTMZnit4yfxuXvfwFHc9MwEZZEsjz+N7Vt7kMnWSJEnbnuG5gpyMu45PMNbJzh95PvjSlVINV9qQJEna9gzPa7W02kZkMLkXGpPF+ebUcNslSZKkgTM8V1UONqeAIGD39dCchLHZ4oXm5PDaJkmSpE1heK5oeYpgBDkBkweK5+0yPLcceZYkSdruDM8VLU0STFEeL40077im+NiaGU7DJEmStGkMzxVEz7rOKStHnmut4kR7pjh2jWdJkqRtrzbsBlwJMlip28iiGHnuXdN55zWutiFJkjQChjLyHBFvjYjPRMTHI+JdETEzjHZUFivZOWXlUnW96zofvgtyfw+RJEna7oZVtvE+4OaU0i3AZ4GfGlI71ixlkGc1yOsrJ+ut4TVIkiRJm2Yo4Tml9N6U0mL59IPAoWG0o6qI4lEch7sJSpIkjaitMGHw+4A/WO3FiHhTRHwkIj5y/PjxTWzWKu3JMzdEkSRJGlEDK9SNiPcD+y7y0ltSSr9TvuctwCLw9tWuk1K6B7gH4NixY2kATe0reo8jYGLvMJohSZKkIRtYeE4pveZSr0fE9wLfArw6pTSUUFxdFLsKUobnwy8fcnskSZI0DENZIiIivhH4SeBrU0pnhtGGtYiIlZrnRvv8yYKSJEkaGcOqef4FYBJ4X0R8LCJ+aUjtqOS8so2m6zlLkiSNqqGMPKeUXjyMr3u5IoOlupKoN4baFkmSJA3PVlhtY8s7b+Q5NzxLkiSNKsNzFfV8+TBq7iQoSZI0qgzPFaRaTipnDEbNyYKSJEmjyvBcRZaR8qXwbNmGJEnSqDI8V5DlQaoVXRUuUydJkjSyDM+VBCkrRp6zRnPIbZEkSdKwGJ4riIzl8JzqThiUJEkaVYbnCiLLlsNz1C3bkCRJGlWG5yoylnsqc5MUSZKkkWV4riCirHmOcMKgJEnSCDM8VxBZBlHUPWeR9/8ESZIkbUuG5woiglSOPmeZEwYlSZJGleG5iiwgC7r1jMgdeZYkSRpVhucqmjVSQKeZk4Ujz5IkSaPK8FxFowYRdBsZWeaEQUmSpFHlMGoFRc0zpFpGlttlkiRJo8qR5wryLIMIUp6RW7YhSZI0sgzPFWQEKS8e4cizJEnSyDI8VxBRbM+9MFl3nWdJkqQRZniupBh1XhxrkIVdJkmSNKpMghVkASkPus06ETHs5kiSJGlIDM8VRASdRg55TmaXSZIkjSyTYAVBsbsgEWSZXSZJkjSqTIIVRLlBCpERWLYhSZI0qgzPFRRL1WVARu5qG5IkSSPL8FxRt1aUbUiSJGl0GZ4rCIA8IMKRZ0mSpBFmeF6LCNd5liRJGmEmwQpq+dJoc4bzBSVJkkaX4XktwgmDkiRJo8zwXMHyYHOES9VJkiSNMMPzWkTm9tySJEkjzPBcxVJedsKgJEnSSDMJVpBltaUjMrtMkiRpZJkEK4ilSYJZWLYhSZI0wgzPFSyHZzInDEqSJI0ww3MFy6PNEeSZS9VJkiSNKsNzFXmj+OhkQUmSpJFmGqwglkabI3eTFEmSpBFmeK4glkacs8yl6iRJkkbYUJJgRPzLiPh4RHwsIt4bEQeG0Y6qVmqe3SRFkiRplA1rGPWtKaVbUkq3Ab8L/MyQ2lHN0mhz5K7zLEmSNMKGkgRTSid7no4DaRjtqGypzrnetmxDkiRphNX6v2UwIuJ/Ab4HOAG8cljtqKYs1ai3LduQJEkaYQMbRo2I90fEfRd53A2QUnpLSukq4O3AD1/iOm+KiI9ExEeOHz8+qOZeUmRZUboRbpIiSZI0ygY28pxSek3Ft74d+H3gn69ynXuAewCOHTs2lPKOyHIol6uzbEOSJGl0DWu1jWt7nt4NfGYY7agqsgyy4vcMyzYkSZJG17Bqnn8uIq4HusCDwA8MqR0VZTC+B8BNUiRJkkbYUMJzSunvDuPrXq7IcxjbAVi2IUmSNMpMghVEYwxqLScLSpIkjTjDcwXRGocsJ88s2ZAkSRplhucqsjqAI8+SJEkjzvBcQZQrbVjvLEmSNNpMgxVEuMazJEmSDM9r4jJ1kiRJo83wXMFSpXMjbwy1HZIkSRouw3MFS7sK1rJh7SkjSZKkrcDwXEGUtc6GZ0mSpNFmeK6kHHkOw7MkSdIoMzyvQT2vD7sJkiRJGiLDcwVlyTPtWnu4DZEkSdJQGZ4rWFqizvAsSZI02gzPFeRlrbMTBiVJkkab4bmCzNU2JEmShOG5IlfbkCRJkuG5kqycMZhnbs8tSZI0ygzPFSxtkpLZXZIkSSPNNFjBUs3z0jbdkiRJGk2G5wqWQrMTBiVJkkab4bmCKCcMLq33LEmSpNFkeF4DR54lSZJGm+G5gsiKbnLkWZIkabQZnitYKttYmjgoSZKk0WQarGBpwqAjz5IkSaPN8LwGjjxLkiSNNtNgBcurbbjDoCRJ0kgzPFcQBPWsPuxmSJIkacgMzxVkkdGqtYbdDEmSJA2Z4bmCiGC6MT3sZkiSJGnIDM8VtevtYTdBkiRJQ2Z4rqhdMzxLkiSNOsNzRa3cmmdJkqRRZ3iuyAmDkiRJMjxXNNmYHHYTJEmSNGSG54rcXVCSJEkmwooyu0qSJGnkmQgriohhN0GSJElDZniuKI982E2QJEnSkBmeK7LmWZIkSSbCigzPkiRJGmoijIh/FhEpInYNsx1VuM6zJEmShhaeI+Iq4LXAl4fVBkmSJGkthjny/O+AnwTSENsgSZIkVTaU8BwRdwOPpJTurfDeN0XERyLiI8ePH9+E1kmSJEkXVxvUhSPi/cC+i7z0FuCnKUo2+kop3QPcA3Ds2DFHqSVJkjQ0AwvPKaXXXOx8RHwFcBS4t9x45BDw0Yh4WUrp8UG1R5IkSVqvgYXn1aSUPgHsWXoeEV8CjqWUntrstkiSJElr4eLFkiRJUkWbPvJ8oZTSkWG3QZIkSarCkWdJkiSpIsOzJEmSVJHhWZIkSarI8CxJkiRVZHiWJEmSKjI8S5IkSRUZniVJkqSKDM+SJElSRYZnSZIkqSLDsyRJklSR4VmSJEmqKFJKw25DZRFxHHhwCF96F/DUEL7udmM/rp99uH724frZh+tnH66ffbgx7MfVXZ1S2n3hySsqPA9LRHwkpXRs2O240tmP62cfrp99uH724frZh+tnH24M+3HtLNuQJEmSKjI8S5IkSRUZnqu5Z9gN2Cbsx/WzD9fPPlw/+3D97MP1sw83hv24RtY8S5IkSRU58ixJkiRVZHjuIyK+MSLuj4gHIuLNw27PVhIRV0XEn0TEpyLikxHxo+X5HRHxvoj4XPlxtjwfEfG2si8/HhF39FzrjeX7PxcRbxzW9zQsEZFHxN9GxO+Wz49GxIfKvvrPEdEozzfL5w+Urx/pucZPlefvj4hvGNK3MhQRMRMR74yIz0TEpyPiTu/DtYmIHyv/O74vIt4RES3vw/4i4lcj4smIuK/n3IbdexHx0oj4RPk5b4uI2NzvcPBW6cO3lv89fzwi3hURMz2vXfQeW+3n9Wr38XZysT7see2fRUSKiF3lc+/D9Uop+VjlAeTA54EXAQ3gXuCmYbdrqzyA/cAd5fEk8FngJuB/Bd5cnn8z8K/L49cBfwAE8HLgQ+X5HcAXyo+z5fHssL+/Te7LHwd+E/jd8vn/A3xnefxLwA+Wxz8E/FJ5/J3Afy6PbyrvzyZwtLxv82F/X5vYf/8X8I/K4wYw4324pv47CHwRaPfcf9/rfVip774GuAO4r+fcht17wF+X743yc79p2N/zJvXha4Faefyve/rwovcYl/h5vdp9vJ0eF+vD8vxVwHso9sjY5X24MQ9Hni/tZcADKaUvpJTmgd8C7h5ym7aMlNJjKaWPlsfPA5+m+CF8N0WYofz4reXx3cCvp8IHgZmI2A98A/C+lNIzKaVngfcB37h538lwRcQh4JuBXy6fB/Aq4J3lWy7sw6W+fSfw6vL9dwO/lVKaSyl9EXiA4v7d9iJimuIHx68ApJTmU0rP4X24VjWgHRE1YAx4DO/DvlJKfw48c8HpDbn3ytemUkofTEWC+fWea20bF+vDlNJ7U0qL5dMPAofK49XusYv+vO7z/9NtY5X7EODfAT8J9E5w8z5cJ8PzpR0EHup5/nB5Thco/2x7O/AhYG9K6bHypceBveXxav056v387yn+59Ytn+8Enuv5wdHbH8t9Vb5+onz/KPfhUeA48GtRlL78ckSM431YWUrpEeDfAF+mCM0ngL/B+/BybdS9d7A8vvD8qPk+itFOWHsfXur/p9taRNwNPJJSuveCl7wP18nwrHWLiAngvwD/NKV0sve18rdUl3RZRUR8C/BkSulvht2WK1iN4s+Vv5hSuh04TfGn8mXeh5dW1uTeTfGLyAFgnNEadR8Y7731iYi3AIvA24fdlitJRIwBPw38zLDbsh0Zni/tEYp6oSWHynMqRUSdIji/PaX02+XpJ8o/81B+fLI8v1p/jnI/vwJ4fUR8ieLPjK8Cfp7iz2i18j29/bHcV+Xr08DTjHYfPgw8nFL6UPn8nRRh2vuwutcAX0wpHU8pLQC/TXFveh9eno269x5hpVyh9/xIiIjvBb4F+O7ylxBYex8+zer38XZ2DcUvw/eWP18OAR+NiH14H66b4fnSPgxcW87UbVBMjHn3kNu0ZZS1ZL8CfDql9G97Xno3sDRL943A7/Sc/55ypu/LgRPlnzbfA7w2ImbLEbDXlue2vZTST6WUDqWUjlDcX3+cUvpu4E+Aby/fdmEfLvXtt5fvT+X574xiFYSjwLUUEzy2vZTS48BDEXF9eerVwKfwPlyLLwMvj4ix8r/rpT70Prw8G3Lvla+djIiXl/8u39NzrW0tIr6Ropzt9SmlMz0vrXaPXfTndXlfrnYfb1sppU+klPaklI6UP18eppjg/zjeh+s36BmJV/qDYlbqZylm8b5l2O3ZSg/gqyn+HPlx4GPl43UUNWZ/BHwOeD+wo3x/AP+h7MtPAMd6rvV9FBM/HgD+4bC/tyH159exstrGiyh+IDwA/L9AszzfKp8/UL7+op7Pf0vZt/czYjOhgduAj5T34n+lmCnufbi2PvxZ4DPAfcD/TbGagfdh/357B0Wd+AJFQPn+jbz3gGPlv8nngV+g3NxsOz1W6cMHKOpvl362/FK/e4xVfl6vdh9vp8fF+vCC17/Eymob3ofrfLjDoCRJklSRZRuSJElSRYZnSZIkqSLDsyRJklSR4VmSJEmqyPAsSZIkVWR4lqQtICJOlR+PRMR3bfC1f/qC53+1kdeXpFFieJakreUIsKbw3LN72mrOC88ppbvW2CZJUsnwLElby88BfyciPhYRPxYReUS8NSI+HBEfj4h/AhARXxcRfxER76bYDZCI+K8R8TcR8cmIeFN57ueAdnm9t5fnlka5o7z2fRHxiYj4jp5r/2lEvDMiPhMRby93FiMifi4iPlW25d9seu9I0pD1G62QJG2uNwM/kVL6FoAyBJ9IKX1lRDSBD0TEe8v33gHcnFL6Yvn8+1JKz0REG/hwRPyXlNKbI+KHU0q3XeRrvYFid8ZbgV3l5/x5+drtwEuAR4EPAK+IiE8D3wbckFJKETGzsd+6JG19jjxL0tb2WuB7IuJjwIcotn6+tnztr3uCM8CPRMS9wAeBq3ret5qvBt6RUuqklJ4A/gz4yp5rP5xS6lJsj3wEOAGcA34lIt4AnFnn9yZJVxzDsyRtbQH8Dyml28rH0ZTS0sjz6eU3RXwd8BrgzpTSrcDfAq11fN25nuMOUEspLQIvA94JfAvwh+u4viRdkQzPkrS1PA9M9jx/D/CDEVEHiIjrImL8Ip83DTybUjoTETcAL+95bWHp8y/wF8B3lHXVu4GvAf56tYZFxAQwnVL6feDHKMo9JGmkWPMsSVvLx4FOWX7xn4CfpyiZ+Gg5ae848K0X+bw/BH6grEu+n6J0Y8k9wMcj4qMppe/uOf8u4E7gXiABP5lSerwM3xczCfxORLQoRsR//LK+Q0m6gkVKadhtkCRJkq4Ilm1IkiRJFRmeJUmSpIoMz5IkSVJFhmdJkiSpIsOzJEmSVJHhWZIkSarI8CxJkiRVZHiWJEmSKvr/AX35ir7f0wyRAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(figsize=(12,8))\n",
    "\n",
    "# These are in unitless percentages of the figure size. (0,0 is bottom left)\n",
    "left, bottom, width, height = [0.55, 0.2, 0.25, 0.25]\n",
    "#ax2 = fig.add_axes([left, bottom, width, height])\n",
    "\n",
    "x=list(range(0,15000))\n",
    "\n",
    "# ax1 figure\n",
    "mean_mag_cl=np.mean(list_mag_cl_bas_gridsize_3,axis=0);std_cl=np.std(list_mag_cl_bas_gridsize_3,axis=0)\n",
    "ax1.plot(x,mean_mag_cl,label='classical- uniform update')\n",
    "ax1.fill_between(x,mean_mag_cl-std_cl,mean_mag_cl+std_cl,alpha=0.45)\n",
    "\n",
    "mean_mag_local=np.mean(list_mag_local,axis=0)\n",
    "std_local=np.std(list_mag_local,axis=0)\n",
    "ax1.plot(x,mean_mag_local,label='local update strategy')\n",
    "ax1.fill_between(x,mean_mag_local-std_local,mean_mag_local+std_local,alpha=0.45)\n",
    "\n",
    "\n",
    "mean_mag_qmcmc1=np.mean(list_mag_qmcmc_pauli1_bas_gridsize_3,axis=0)\n",
    "std_q1=np.std(list_mag_qmcmc_pauli1_bas_gridsize_3,axis=0)\n",
    "ax1.plot(x,mean_mag_qmcmc1,label='Q-MCMC')#list_labels_bas[2])\n",
    "ax1.fill_between(x,mean_mag_qmcmc1-std_q1,mean_mag_qmcmc1+std_q1,alpha=0.45)\n",
    "\n",
    "mean_mag_pert=np.mean(list_mag_pert,axis=0)\n",
    "std_qpert=np.std(list_mag_pert,axis=0)\n",
    "ax1.plot(x,mean_mag_pert,label='Q-MCMC-pert')\n",
    "ax1.fill_between(x,mean_mag_pert-std_qpert,mean_mag_pert+std_qpert,alpha=0.45)\n",
    "\n",
    "# mean_mag_qmcmc2=np.mean(list_mag_qmcmc_pauli3_bas_gridsize_3,axis=0)\n",
    "# std_q2=np.std(list_mag_qmcmc_pauli3_bas_gridsize_3,axis=0)\n",
    "# ax1.plot(x,mean_mag_qmcmc2,label=list_labels_bas[3])\n",
    "# ax1.fill_between(x,mean_mag_qmcmc2-std_q2,mean_mag_qmcmc2+std_q2,alpha=0.5)\n",
    "\n",
    "\n",
    "\n",
    "ax1.axhline(magnetization_model, label= 'actual',linestyle='--')\n",
    "ax1.legend()\n",
    "ax1.set_xlabel(\"Iterations\")\n",
    "ax1.set_ylabel(\"Magnetisation\")\n",
    "\n",
    "\n",
    "# ax1.axhline(magnetization_model, label= 'actual',linestyle='--')\n",
    "# ax1.legend()\n",
    "# ax1.set_xlabel(\"Iterations\")\n",
    "# ax1.set_ylabel(\"Magnetisation\")\n",
    "\n",
    "#ax2 figure\n",
    "# ax2.plot(x,mean_mag_cl,label=list_labels_bas[0])\n",
    "# ax2.fill_between(x,mean_mag_cl-std_cl,mean_mag_cl+std_cl,alpha=0.5)\n",
    "# ax2.plot(x,mean_mag_cl,label='local')##\n",
    "# ax2.fill_between(x,mean_mag_local-std_local,mean_mag_cl+std_local,alpha=0.5)###\n",
    "# # ax2.plot(x,mean_mag_qmcmc1,label=list_labels_bas[1])\n",
    "# # ax2.fill_between(x,mean_mag_qmcmc1-std_q1,mean_mag_qmcmc1+std_q1,alpha=0.5)\n",
    "# ax2.plot(x,mean_mag_qmcmc2,label=list_labels_bas[2])\n",
    "# ax2.fill_between(x,mean_mag_qmcmc2-std_q2,mean_mag_qmcmc2+std_q2,alpha=0.5)\n",
    "# ax2.axhline(magnetization_model, label= 'actual',linestyle='--')\n",
    "# ax2.set_xlim([10000,14000])\n",
    "# ax2.set_ylim([2,0])\n",
    "# ax2.set_xlabel(\"Iterations\")\n",
    "# ax2.set_ylabel(\"Magnetisation\")\n",
    "\n",
    "fig.savefig(f\"Magnetisation_10_spins_for_presentation_with_pert.pdf\")# done\n",
    "#fig.savefig(f\"Magnetisation_BAS_{gridsize}_bars_only.jpeg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "check=dict_mcmc_bas_gridsize_3[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "list_keys=list(dict_mcmc_bas_gridsize_3[1].keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plt.figure(figsize=(15,10))\n",
    "# labels=['classical- uniform update','local','Q-MCMC','Q-MCMC-pert']\n",
    "# for i in range(0,4):\n",
    "#     a=dict_mcmc_bas_gridsize_3[1][list_keys[i]]\n",
    "#     plt.subplot(2,2,i+1)\n",
    "#     xval=list(range(1000,2000))\n",
    "#     plt.plot(xval,a.markov_chain[1000:2000],label=labels[i])\n",
    "#     # plt.plot(a.markov_chain,label=labels[i])\n",
    "#     plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# magnetisation\n",
    "# magnetization_model = exact_sampled_model.get_observable_expectation(magnetization_of_state)\n",
    "# magnetization_c = calculate_runnning_magnetisation(cl_chain)\n",
    "# magnetization_q1 = calculate_runnning_magnetisation(qamcmc_chain_1)\n",
    "# magnetization_q2 = calculate_runnning_magnetisation(qamcmc_chain_2)\n",
    "\n",
    "# plt.figure(figsize=(10,8))\n",
    "# plt.plot(magnetization_c, label= list_labels[0])\n",
    "# plt.plot(magnetization_q1, label= list_labels[1])\n",
    "# plt.plot(magnetization_q2, label= list_labels[2])\n",
    "# plt.axhline(magnetization_model, label= 'original',linestyle='--')\n",
    "# plt.xlabel(\"iterations\")\n",
    "# plt.ylabel(\"magnetisation\")\n",
    "# plt.legend()\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['cl', 'local', 'Q-MCMC', 'Q-MCMC-pert']"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_keys=list(dict_mcmc_bas_gridsize_3[1].keys())\n",
    "list_keys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x1080 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### plots\n",
    "\n",
    "# acceptance probability\n",
    "plt.figure(1,figsize=(20,15))\n",
    "for seed_val in range(1,num_different_chains+1):\n",
    "    cl_chain=dict_mcmc_bas_gridsize_3[seed_val][list_keys[0]]\n",
    "    local_chain=dict_mcmc_bas_gridsize_3[seed_val]['local']\n",
    "    qamcmc_chain_1=dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC']\n",
    "    q_pert=dict_mcmc_bas_gridsize_3[seed_val]['Q-MCMC-pert']\n",
    "    #qamcmc_chain_2=dict_mcmc_bas_gridsize_3[seed_val][list_labels_bas[3]]\n",
    "    \n",
    "    cl_statistics=get_trajectory_statistics(cl_chain,exact_sampled_model)\n",
    "    qumcm1_statistics=get_trajectory_statistics(qamcmc_chain_1,exact_sampled_model)\n",
    "    local_statistics=get_trajectory_statistics(local_chain,exact_sampled_model)\n",
    "    qpert_statistics=get_trajectory_statistics(q_pert,exact_sampled_model)\n",
    "    #qumcm2_statistic=get_trajectory_statistics(qamcmc_chain_2,exact_sampled_model)\n",
    "    \n",
    "    plt.subplot(5,2,seed_val)\n",
    "    plt.hist(np.log10(cl_statistics['acceptance_prob']),\n",
    "            label= 'uniform' ,alpha= 0.5, \n",
    "            bins= 50,density=True)\n",
    "    plt.hist(np.log10(local_statistics['acceptance_prob']),\n",
    "            label= 'local' ,alpha= 0.5, \n",
    "            bins= 50,density=True)\n",
    "    plt.hist(np.log10(qumcm1_statistics['acceptance_prob']),\n",
    "                label='Q-MCMC' , alpha= 0.5, bins= 50,density=True)\n",
    "    # plt.hist(np.log10(qumcm2_statistic['acceptance_prob']), label= list_labels_bas[3] , alpha= 0.5, bins= 40,density=True)\n",
    "    plt.hist(np.log10(qpert_statistics['acceptance_prob']), label= 'Q-MCMC-pert', alpha= 0.5, bins= 50,density=True)\n",
    "    if seed_val==9 or seed_val==10:\n",
    "        plt.xlabel(\"log(Acceptance Rate)\")\n",
    "    plt.legend()\n",
    "plt.savefig(\"Acceptance_rate_plot_10_spins_for_presentation_with_pert.pdf\")\n",
    "plt.savefig(\"Acceptance_rate_plot_for_presentation_with_pert.jpeg\")\n",
    "plt.show()\n",
    "\n",
    "# # energy plot\n",
    "    # plt.figure(2,figsize=(10,10))\n",
    "    # plt.hist(cl_statistic['energy'],label= list_labels[0] ,alpha= 0.8, bins= 20)\n",
    "    # plt.hist(qumcm1_statistic['energy'],\n",
    "    #             label=list_labels[1]  , alpha= 0.8, bins= 20)\n",
    "    # plt.hist(qumcm2_statistic['energy'],\n",
    "    #             label= list_labels[2] , alpha= 0.8, bins= 20)\n",
    "    # plt.xlabel(\"Energy-Difference Statistics\")\n",
    "    # plt.legend()\n",
    "    # plt.show()\n",
    "\n",
    "# # Hamming distance\n",
    "    #plt.figure(1,figsize=(10,10))\n",
    "    # plt.subplot(5,2,seed_val)\n",
    "    # plt.hist(cl_statistic['hamming'],label= list_labels_bas[0] ,alpha= 0.8, bins= 20)\n",
    "    # plt.hist(qumcm1_statistic['hamming'],\n",
    "    #             label= list_labels_bas[1] , alpha= 0.8, bins= 20)\n",
    "    # plt.hist(qumcm2_statistic['hamming'],\n",
    "    #             label= list_labels_bas[2] , alpha= 0.8, bins= 20)\n",
    "    # plt.xlabel(\"Hamming-Distance Statistics\")\n",
    "    # plt.legend()\n",
    "    # plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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",
    "#                         ]\n",
    "# plot_multiple_bargraphs(distributions_to_plot, ['exact']+list_labels, \n",
    "#                                                 list_normalise= [False, False, False,False], \n",
    "#                                                 plot_first_few=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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