Correlation functions and local order parameters Spin 0.5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we want to check if there is any local order parameter for us to define the phase transition in our Kitaev ladder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the model file we designed\n",
    "\"\"\"\n",
    "    Here we want to clarify that the 'kitaev_ladder_snake1.py' file\n",
    "    is different from the 'kitaev_ladder_snake.py' in that the *1 file \n",
    "    uses the original representation of xyz,\n",
    "    i.e. Jz stands for the sigmazsigmaz interactions which starts from\n",
    "    the first pair of neighbors; Jx being the second pair; and Jy being\n",
    "    the third-nearest-neighbors.\n",
    "    \n",
    "    The purpose of designing so many different 1D correspondences is \n",
    "    to serve for different phases.\n",
    "    For example, when the Jx interaction is very weak, the optimal \n",
    "    choice is to make Jx as the third-nearest neighbors; when Jy is \n",
    "    weak the similar case holds.\n",
    "\"\"\"\n",
    "from kitaev_ladder_snake1 import run_atomic, save_after_run, finite_scaling, load_data, fDMRG_KL\n",
    "\n",
    "# the folder name for storing data\n",
    "folder_prefix = 'snake/'\n",
    "\n",
    "# generate the function for running and storing the data in the folder we want\n",
    "run_save = save_after_run(run_atomic, folder_prefix=folder_prefix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.random import rand\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import optimize\n",
    "\n",
    "import scipy.sparse as sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# naming function for the png of finite scaling\n",
    "def naming(Jx, Jy, Jz, L):\n",
    "    return f\"_Jx_{Jx}_Jy_{Jy}_Jz_{Jz}_L_{L}.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The spectra of two candidates can be given by\n",
    "\n",
    "$$\\epsilon(k) = \\pm\\sqrt{(J_z + (J_x + D J_y)\\cos k)^2 + (J_x - D J_y)^2\\sin^2k}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## True Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate as integrate\n",
    "\n",
    "def e_k_sorted(k, Jx, Jy, Jz, D):\n",
    "    Jp = Jx + D*Jy\n",
    "    J2 = Jx**2 + Jy**2 + Jz**2 # J square\n",
    "    return np.sqrt(J2 + 2 * Jz * Jp * np.cos(k) + 2 * D * Jx * Jy * np.cos(2*k))\n",
    "\n",
    "def E_sorted(Jx, Jy, Jz, D):\n",
    "    assert D==1 or D==-1\n",
    "    e_k_D_sorted_func = lambda k:e_k_sorted(k, Jx, Jy, Jz, D)\n",
    "    return integrate.quad(e_k_D_sorted_func, -np.pi, np.pi)[0] * -1 / (16*np.pi)\n",
    "\n",
    "def E_true(Jx, Jy, Jz):\n",
    "    D_true = 1 if Jy*Jx < 0 else -1\n",
    "    E_true = E_sorted(Jx, Jy, Jz, D_true)\n",
    "    return E_true\n",
    "\n",
    "def E_false(Jx, Jy, Jz):\n",
    "    D_true = -1 if Jy*Jx < 0 else 1\n",
    "    E_true = E_sorted(Jx, Jy, Jz, D_true)\n",
    "    return E_true"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## X Region"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose a typical gapped point living in the $X$ region, i.e.\n",
    "$$ J_x - J_y > |{J_z}|$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'L'=4 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=1.902113032590307 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.6180339887498948 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  8 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 408\n",
      "Energy = -0.2490359920946497, S = nan, norm_err = 3.8e-07\n",
      "Current memory usage 209.1 MB, time elapsed: 3.3 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 5.5753e-06, max_E_trunc = 5.4850e-06\n",
      "MPS bond dimensions: [8, 8, 8, 8, 8, 8, 8, 8]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 648\n",
      "Energy = -0.2490359906770747, S = nan, norm_err = 6.2e-08\n",
      "Current memory usage 209.1 MB, time elapsed: 6.5 s\n",
      "Delta E = 1.4176e-10, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 5.5179e-06, max_E_trunc = 5.4856e-06\n",
      "MPS bond dimensions: [8, 8, 8, 8, 8, 8, 8, 8]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 888\n",
      "Energy = -0.2490359900233692, S = 0.7779607770863237, norm_err = 5.1e-15\n",
      "Current memory usage 209.1 MB, time elapsed: 8.4 s\n",
      "Delta E = 6.5371e-11, Delta S = nan (per sweep)\n",
      "max_trunc_err = 2.7534e-06, max_E_trunc = 5.4857e-06\n",
      "MPS bond dimensions: [8, 8, 8, 8, 8, 8, 8, 8]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 1128\n",
      "Energy = -0.2490359900234402, S = 0.7779607770863268, norm_err = 3.2e-15\n",
      "Current memory usage 209.1 MB, time elapsed: 10.4 s\n",
      "Delta E = -7.1054e-15, Delta S = 3.1086e-16 (per sweep)\n",
      "max_trunc_err = 2.7534e-06, max_E_trunc = 5.4857e-06\n",
      "MPS bond dimensions: [8, 8, 8, 8, 8, 8, 8, 8]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 1128, maximum chi = 8\n",
      "================================================================================\n",
      "Before the canonicalization:\n",
      "Bond dim =  [8, 8, 8, 8, 8, 8, 8, 8]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000036-2.256454054487297e-16j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [8, 8, 8, 8, 8, 8, 8, 8]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=8 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n",
      "Reading 'L'=4 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=1.902113032590307 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.6180339887498948 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  16 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['P_tol'] for config lanczos_params\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 408\n",
      "Energy = -0.2490400520507476, S = nan, norm_err = 3.6e-09\n",
      "Current memory usage 209.9 MB, time elapsed: 5.0 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 4.4882e-09, max_E_trunc = 5.5508e-09\n",
      "MPS bond dimensions: [16, 16, 16, 16, 16, 16, 16, 16]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 648\n",
      "Energy = -0.2490400544638156, S = nan, norm_err = 3.9e-09\n",
      "Current memory usage 209.9 MB, time elapsed: 8.4 s\n",
      "Delta E = -2.4131e-10, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 3.0399e-09, max_E_trunc = 4.6808e-09\n",
      "MPS bond dimensions: [16, 16, 16, 16, 16, 16, 16, 16]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 888\n",
      "Energy = -0.2490400549327045, S = 0.7784885084379021, norm_err = 5.9e-15\n",
      "Current memory usage 209.9 MB, time elapsed: 10.5 s\n",
      "Delta E = -4.6889e-11, Delta S = nan (per sweep)\n",
      "max_trunc_err = 1.4619e-09, max_E_trunc = 4.6614e-09\n",
      "MPS bond dimensions: [16, 16, 16, 16, 16, 16, 16, 16]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 1128\n",
      "Energy = -0.2490400549307630, S = 0.7784885502617369, norm_err = 1.1e-14\n",
      "Current memory usage 209.9 MB, time elapsed: 12.8 s\n",
      "Delta E = 1.9416e-13, Delta S = 4.1824e-09 (per sweep)\n",
      "max_trunc_err = 1.4705e-09, max_E_trunc = 4.6743e-09\n",
      "MPS bond dimensions: [16, 16, 16, 16, 16, 16, 16, 16]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 1128, maximum chi = 16\n",
      "================================================================================\n",
      "Before the canonicalization:\n",
      "Bond dim =  [16, 16, 16, 16, 16, 16, 16, 16]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000038+1.962134882448155e-16j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [16, 16, 16, 16, 16, 16, 16, 16]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=16 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n",
      "Reading 'L'=4 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=1.902113032590307 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.6180339887498948 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  32 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 408\n",
      "Energy = -0.2490400578889567, S = nan, norm_err = 3.6e-11\n",
      "Current memory usage 211.0 MB, time elapsed: 5.3 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 1.9400e-12, max_E_trunc = 3.4532e-12\n",
      "MPS bond dimensions: [32, 32, 32, 32, 32, 32, 32, 32]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 648\n",
      "Energy = -0.2490400578912197, S = nan, norm_err = 2.5e-11\n",
      "Current memory usage 211.0 MB, time elapsed: 9.8 s\n",
      "Delta E = -2.2631e-13, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 1.2834e-12, max_E_trunc = 2.1600e-12\n",
      "MPS bond dimensions: [32, 32, 32, 32, 32, 32, 32, 32]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 888\n",
      "Energy = -0.2490400578921879, S = 0.7784899583162601, norm_err = 1.0e-12\n",
      "Current memory usage 211.0 MB, time elapsed: 12.6 s\n",
      "Delta E = -9.6811e-14, Delta S = nan (per sweep)\n",
      "max_trunc_err = 3.0359e-13, max_E_trunc = 2.1316e-12\n",
      "MPS bond dimensions: [32, 32, 32, 32, 32, 32, 32, 32]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 1128\n",
      "Energy = -0.2490400578920173, S = 0.7784899582813022, norm_err = 6.9e-15\n",
      "Current memory usage 211.0 MB, time elapsed: 15.3 s\n",
      "Delta E = 1.7053e-14, Delta S = -3.4958e-12 (per sweep)\n",
      "max_trunc_err = 3.1474e-13, max_E_trunc = 2.1032e-12\n",
      "MPS bond dimensions: [32, 32, 32, 32, 32, 32, 32, 32]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 1128, maximum chi = 32\n",
      "================================================================================\n",
      "Before the canonicalization:\n",
      "Bond dim =  [32, 32, 32, 32, 32, 32, 32, 32]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000073+2.2811613820142253e-16j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [32, 32, 32, 32, 32, 32, 32, 32]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=32 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n",
      "Reading 'L'=4 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=1.902113032590307 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.6180339887498948 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  64 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 408\n",
      "Energy = -0.2490400578927998, S = nan, norm_err = 3.3e-12\n",
      "Current memory usage 211.2 MB, time elapsed: 6.3 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 3.1024e-16, max_E_trunc = 1.4211e-13\n",
      "MPS bond dimensions: [63, 64, 48, 64, 64, 64, 63, 64]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 648\n",
      "Energy = -0.2490400578928060, S = nan, norm_err = 6.0e-13\n",
      "Current memory usage 211.2 MB, time elapsed: 12.8 s\n",
      "Delta E = -6.2172e-16, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 2.4656e-16, max_E_trunc = 2.5580e-13\n",
      "MPS bond dimensions: [63, 64, 46, 64, 63, 64, 64, 64]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 888\n",
      "Energy = -0.2490400578927687, S = 0.7784899589489715, norm_err = 2.0e-13\n",
      "Current memory usage 211.2 MB, time elapsed: 17.9 s\n",
      "Delta E = 3.7303e-15, Delta S = nan (per sweep)\n",
      "max_trunc_err = 2.0417e-17, max_E_trunc = 5.4001e-13\n",
      "MPS bond dimensions: [64, 64, 62, 64, 62, 64, 62, 64]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 1128\n",
      "Energy = -0.2490400578927705, S = 0.7784899589502626, norm_err = 5.9e-15\n",
      "Current memory usage 211.2 MB, time elapsed: 21.7 s\n",
      "Delta E = -1.7764e-16, Delta S = 1.2911e-13 (per sweep)\n",
      "max_trunc_err = 2.0890e-17, max_E_trunc = 5.6843e-13\n",
      "MPS bond dimensions: [62, 64, 62, 64, 62, 64, 62, 64]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 1128, maximum chi = 64\n",
      "================================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2275: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(i1, Gl, Wr)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2296: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(j1, Gl, Wr_list[j1 % L])\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before the canonicalization:\n",
      "Bond dim =  [38, 48, 38, 48, 38, 49, 38, 48]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000042-3.2408727241813596e-16j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [38, 48, 38, 48, 38, 49, 38, 48]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=64 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n",
      "Reading 'L'=4 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=1.902113032590307 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.6180339887498948 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  128 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 408\n",
      "Energy = -0.2490400578927741, S = nan, norm_err = 3.4e-12\n",
      "Current memory usage 213.7 MB, time elapsed: 8.5 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 1.2820e-19, max_E_trunc = 1.1369e-13\n",
      "MPS bond dimensions: [69, 75, 49, 80, 110, 124, 109, 81]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 648\n",
      "Energy = -0.2490400578928185, S = nan, norm_err = 9.0e-13\n",
      "Current memory usage 219.2 MB, time elapsed: 22.6 s\n",
      "Delta E = -4.4409e-15, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 1.3196e-19, max_E_trunc = 3.1264e-13\n",
      "MPS bond dimensions: [59, 74, 46, 80, 104, 127, 105, 81]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 888\n",
      "Energy = -0.2490400578927705, S = 0.7784899589503094, norm_err = 4.0e-14\n",
      "Current memory usage 219.2 MB, time elapsed: 28.7 s\n",
      "Delta E = 4.7962e-15, Delta S = nan (per sweep)\n",
      "max_trunc_err = 4.5689e-20, max_E_trunc = 3.6948e-13\n",
      "MPS bond dimensions: [66, 90, 66, 90, 66, 90, 66, 90]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 1128\n",
      "Energy = -0.2490400578927918, S = 0.7784899589503238, norm_err = 1.0e-14\n",
      "Current memory usage 219.2 MB, time elapsed: 34.1 s\n",
      "Delta E = -2.1316e-15, Delta S = 1.4433e-15 (per sweep)\n",
      "max_trunc_err = 4.6543e-20, max_E_trunc = 4.5475e-13\n",
      "MPS bond dimensions: [66, 90, 66, 90, 66, 90, 66, 90]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 1128, maximum chi = 90\n",
      "================================================================================\n",
      "Before the canonicalization:\n",
      "Bond dim =  [38, 48, 38, 48, 38, 48, 38, 48]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000095-9.415368919197361e-17j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [38, 48, 38, 48, 38, 48, 38, 48]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=128 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2275: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(i1, Gl, Wr)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2119: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  self.canonical_form_infinite(renormalize)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2296: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(j1, Gl, Wr_list[j1 % L])\n"
     ]
    }
   ],
   "source": [
    "# set the region to be the circle `r = x**2 + y**2 = 2, z=.5`\n",
    "\n",
    "r = 2\n",
    "theta = np.pi * 9 / 90\n",
    "Jx = r*np.cos(theta)\n",
    "Jy = r*np.sin(theta)\n",
    "Jz = .5\n",
    "\n",
    "chi_list = [2**k for k in range(3, 8)]\n",
    "initial_psi = None\n",
    "\n",
    "for chi in chi_list:\n",
    "    result = run_atomic(Jx=Jx, Jy=Jy, Jz=Jz, chi=chi, initial_psi=initial_psi, L=4, bc='periodic', bc_MPS='infinite')\n",
    "    psi = result['psi']\n",
    "    initial_psi = psi.copy()\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation of the Ground State"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our theoretical energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.abs(result['energy'] - E_true(Jx, Jy, Jz)) < 1e-10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our local symmetries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm: <psi|psi> = 1.0\n",
      "Local Symmetry: W0 = 1.0\n",
      "Local Symmetry: W1 = 1.0\n",
      "Local Symmetry: W2 = 1.0\n",
      "Local Symmetry: W3 = 1.0\n",
      "Local Symmetry: W4 = 1.0\n",
      "Local Symmetry: W5 = 1.0\n",
      "Local Symmetry: W6 = 1.0\n",
      "Local Symmetry: W7 = 1.0\n",
      "Local Symmetry: W8 = 1.0\n",
      "Local Symmetry: W9 = 1.0\n"
     ]
    }
   ],
   "source": [
    "psi = result['psi']\n",
    "k=0\n",
    "print(\"Norm: <psi|psi> = %.1f\" % psi.norm)\n",
    "for k in range(20):\n",
    "    if k % 2 == 0:\n",
    "        print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sx', k), ('Sy', k+1), ('Sy', k+2), ('Sx', k+3)])))\n",
    "#     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Local Operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "site_left = [0]\n",
    "site_right = 20\n",
    "xticks=range(site_right)\n",
    "for op in ops:\n",
    "    cf_list = 4*psi.correlation_function(op, op, site_left, site_right, opstr=op)[0, :]\n",
    "    plt.plot(xticks, np.abs(cf_list), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n",
    "\n",
    "site_left = [1]\n",
    "site_right = 20\n",
    "xticks=range(site_right)\n",
    "for op in ops:\n",
    "    cf_list = 4*psi.correlation_function(op, op, site_left, site_right, opstr=op)[0, :]\n",
    "    plt.plot(xticks, np.abs(cf_list), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q: solvability?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Double Local Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try the 'double local operators'.\n",
    "\n",
    "That is, we used two local, neighboring operators combined together as our observed quantity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_local_op(psi, op='Sx', i0=1, d=1):\n",
    "    return psi.expectation_value_term(term=[(op, i0), (op, i0+1), (op, i0+d*2), (op, i0+d*2+1)])*16\n",
    "def double_local_op_corr_func(psi, op='Sx', i0=1, dN=9):\n",
    "    return [double_local_op(psi, op=op, i0=i0, d=d) for d in range(dN)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0000000000000056, 0.9125260097711534, 0.9275264577254282, 0.8991795018519586, 0.8987500110560571, 0.8979157884722947, 0.8978199467305463, 0.897752973978285, 0.8977370482520552, 0.8977288996478081, 0.8977262039899874, 0.897724963872422, 0.8977244834650054, 0.8977242687493526, 0.8977241787437947, 0.8977241385163728, 0.8977241209169525, 0.897724112977994, 0.8977241094134902, 0.8977241077876146]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']\n",
    "N=20\n",
    "\n",
    "xticks=range(1, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, double_local_op_corr_func(psi, op=op, i0=1, dN=N), label=op)\n",
    "print(double_local_op_corr_func(psi, op='Sx', i0=1, dN=N))\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n",
    "\n",
    "xticks=range(0, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, double_local_op_corr_func(psi, op=op, i0=0, dN=N), label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22691338311389625\n"
     ]
    }
   ],
   "source": [
    "Jp = Jx + Jy\n",
    "Jm = Jx - Jy\n",
    "ratio = Jp / Jm\n",
    "Delta = np.sqrt(ratio) * (1 - (Jz / Jm)**2)**(1/4) / (2 * (1 + ratio))\n",
    "print(Delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_local_op(psi, op='Sx', i0=1, d=1):\n",
    "    return psi.expectation_value_term(term=[(op, i0), (op, i0+1), (op, i0+d*2), (op, i0+d*2+1)])*16\n",
    "def double_local_op_corr_func(psi, op='Sx', i0=1, dN=9):\n",
    "    return [double_local_op(psi, op=op, i0=i0, d=d) for d in range(dN)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-local operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nonlocal_op(psi, op='Sx', i0=1, end=11):\n",
    "    if end==i0:\n",
    "        return 1.0\n",
    "    return psi.expectation_value_term(term=[(op, i) for i in range(i0, end)])*(2**(end-i0))\n",
    "def nonlocal_op_corr_func(psi, op='Sx', i0=1, N=20):\n",
    "    return [nonlocal_op(psi, op=op, i0=i0, end=i0+2*d) for d in range(N)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']\n",
    "N=20\n",
    "\n",
    "xticks=range(1, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, np.abs(nonlocal_op_corr_func(psi, op=op, i0=1, N=N)), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.ylim(top=1.1)\n",
    "plt.show()\n",
    "\n",
    "xticks=range(0, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, np.abs(nonlocal_op_corr_func(psi, op=op, i0=0, N=N)), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.ylim(top=1.1)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Double Local Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try other sort of 'double local operators'.\n",
    "\n",
    "That is, we used two local, neighboring operators combined together as our |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_local_op_diff(psi, op1='Sx', op2='Sz', i0=1, d0=1, d=1):\n",
    "    return psi.expectation_value_term(term=[(op1, i0), (op2, i0+d0), (op1, i0+d*2), (op2, i0+d0+d*2)])*16\n",
    "def double_local_op_diff_corr_func(psi, op1='Sx', op2='Sz', i0=1, d0=1, dN=9):\n",
    "    return [double_local_op_diff(psi, op1=op1, op2=op2, i0=i0, d0=d0, d=d) for d in range(dN)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Fzx0OpMPuakc6HM5zHQ6k3e78kQ5nud1e2JYDHJdu3iCLrzAq/jaWOF7q/fW0KsnDMel+bxwPt8u5hlTT1VTyrrtwFCYu3f630GT87tP2HWGtsXX7a5nl/bp3Z/b8+XTo04d+vXox7K676NOjB0E6HW+//DKP/eUvTBo7loz0dMbfdx92u5264eG07tWL23v14t7YWO7u1w8NsOiNNxj55z/z1ssvs3HLFn78z39cr831eu12HGYzqcnJhAQFobFYcFgsNAgNJeXMGRx5eXy+di3/9HAzlBuaNuXzd94hKTGRqIgIV9uN6tQhKTHRra/i/GnKFOa/8gp9evTghblzQUoceXkkJSVxU+fOl9qKjCTp9Gkc7drRf+RIcnLdN3XOmT6dfjffjMbkcB1bsmQJw4cPL/d34S01OOHnAyEk5Vg9lttMWgLzHB7Lrkf09eoSNmI4YfjmF6+o+Rw9ehRT69bOJ8fDoMDzMuWKogkNQ1fUvgdMwIFff3XpkcdMnerSI9/dujVrdu5kyuuvc+jQIUyFtsyNP/7o0iNPnzePX86eZcaMGdzYujVjDx3igSefZOfOnQQXmycvQhscjKFhQ4wtWiD0etdrN/n5oTEaMbVuzfipUxk/dWqZMesiIrCbza5zdRERGPz9L72PpcjKyiIrP5/Y0aMBGD95Mv/bvRtT69ZoQ0LQN2jgOlcbEoKxUSNMrVuzw0ttzOzZs9HpdOUK366EGpvwgx3ZQH3SRIjHcptJj5/FyteL/sl9j//l2ganUFxr7nyzSrpVeuSK65GXL1/OunXr2Lx5s8/u01EjV+kABJMDQBae9QoOg/O2a+fi916zmBSK2kR8fDwJCQmu5570yJ9//jkTJkzAarWSkpLCgQMHPNYvrkf+85//XO6qleJ6ZMBNj3zw4EG3n6K6gwYNYuPGjWRkZJCRkcHGjRsZNGgQ4NQjl75FYXE9MuCmR16xYgVms5mTJ0+66ZE9xVGU7NevX8/cuXNZu3Yt/v6++2ZWY0f4kcY8yINM6Tnh2wz+QAYGi4+WOykUihLk5OTwzDPPkJmZiU6no2XLlixatIjff/+djz/+mD179hAUFMStt97K66+/zoQJE5g6dSopKSmYTCYiIyP54IMPuHDhAs8//zybN2+mcePGPP3000yePLncJZNz585lxIgRvPzyy3Tt2pVHH33Uq5jDw8N55ZVXiImJAZxLPcPDwwGIi4ujQYMGbucsXbqUCRMm4O/v7/pwAOjQoQMPPfQQ7du3R6fTsXDhQrRardv5nnj66acxm83ExsYCzgu3H3zwgVfnlkeN1CMD/LR+EQ9/34gWNySy6bEJaDQlb4m2+M/3cfPGePb1rc+YD7dWNlyF4rpD6ZF9h9IjX+e0aRmNMAhyzIGYze5zfo6AOgDovNArKBSK2o3SI1/nGAMi0eoEeRY/CgrOuJVHxz4E4LVeQaFQKKo7NTbhG0Ii0WslZrMes9k94d/UbxDZfqA1e69XUCgUiupMjU34OlMgBhzYLFoKClI81sn1B32+3WOZQqFQ1DRqbMLXaDT4SSsOC6RfOO6xTr6fwFQBvYJCoVBUR2pswgcIoADhgF9PH/NYbvEX+JV/DxSFQqGoMdTohB8ondn8jM3ksdxq0hKkEr5CcdVQeuSK6ZFfeeUV13s2cOBAUlI8T0tfMWVpNK/kB7gDiAeOAc97KG8CbAV+BuKAuy7XZmX1yFJKOWrWfNl0+jo5bcVEj+Wfj+4mj7RpK//z/puV7kuhuN5QeuTqq0fOyspyPV6wYIGcONFzDrtSPXKlR/jCeTuphcCdQHvgYSFE+1LVXgb+I6XsCowA3q9sv94QzEUALtjDsdvd19s7jE69QsbvB69FOApFreLMmTNERERgLPx3FhERQcOGDcnKyqJNmzbEx8cD8PDDD/PRRx9x/vx5goKCCCy821tgYCDNmzfHZrMRExPjcty88MILvPTSS279jRs3jtWrVyOlZMuWLQwbNgyARx55hK+//tqrmDds2EBsbCzh4eGEhYURGxvL+vXryz1n//79dO7cmV69erFw4ULX8TVr1jBixAiMRiPNmzenZcuWbmqGsggODnY9zs3N9ZlLxxdqhR7AMSnlCQAhxArgXuBIsTqSSzrsEMBH30/Kp57xIuRChiWMgoIzBATcUKLcqVdIR2/NuhbhKBRVxtw9c/kt/Tefttk2vC3Te0wvs3zgwIHMmjWL1q1bM2DAAIYPH07fvn0JCQnhvffeY9y4cUyePJmMjAz+9Kc/YbfbqVevHs2bN6d///7cf//9DB48GJ1Ox7Jlyxg2bBjvvPMO69evL3dqKC0tjdDQUJdPPioqiuTkZODy8rTk5GQaN27sOl783LIYP3487777Ln379mXatGmu48nJyfTs2dNjW97I01566SU++eQTQkJC2LrVNzYAXyT8RkBisedJwE2l6swANgohngECgAE+6PeyDGgTwZJdkGUOwWx2T/hWXQAAequayFcofE1gYCD79+936ZGHDx/u0iPHxsayatUqJk2axKFDhwCnWXP9+vUuPfKUKVPYv38/M2bMoEOHDowZM4bBgwezc+dODAZDmf1KD7qYohHyqFGjylUNl3euJ7KyssjMzKRv374AjBkzhu++++6ybW3btq3MNouYPXs2s2fPZs6cObz33nvMnDnzsudcDl8kfE/vRulX+jCwTEr5lhCiF/CpEKKjlLKEkF4I8TjwOECTJk0qHVjjhs0Qeg3ZlgCPu20dgXWBeLRKr6Co4ZQ3Er+aKD1yxfXIRYwcOZK7777bJwnfF6t0koDGxZ5H4T5l8yjwHwAp5U6c90aIKN2QlHKRlLK7lLJ7ZGRkpQMz+NVx6hXMJgo87LaNGTIaB6A1e38FX6FQeIfSI1dcj1z8fVu7di1t27b1+n0vD1+M8PcCrYQQzYFknBdlR5aq8wfQH1gmhGiHM+Gn+qDvcjEGRKLXnMViMWD2sNu2S89b2e0PugKlV1AofI3SI1dcj/z8888THx+PRqOhadOmPlEjg4/0yEKIu4B/AlpgiZRythBiFs7lQWsLV+18BATinO55Tkq5sbw2K6tHBsi7kESvDw9y0aLhy/tW0rWr+x/IllvakRskGPzdEQ8tKBTVF6VH9h01RY/skxugSCm/Bb4tdezVYo+PAL190deVYAyOwE9aybQYyL6Y5LFOgZ/AqPQKCoWiHJQeuRqgNZgIIB8hISm3wONVc4ufwF8t0lEoFLWAGp3wAQJlLgBnbHWx2dyvitv8dATlwXlfbV1WKBSK65Qan/CDpTPJn7PU9ejFtxkNGGywaeWH1zo0hUKhuKbU+IQfgnP5Vqo5wqMX31647Tsn0be7EBUKheJ6o8Yn/Pp+GUChXsHDCN+u9wfAYL54TeNSKBSKa02NT/i9moAUkGkOwexht61F7xQ16ZReQaHwOdVRj3zHHXcQGhrKPffc4/U5xSmSv0HFVcs//vgjN954IzqdzrUpzBf4ZFnm9UxU3UYIvYYccyAFZg/TNgGRwFGlV1AofMzOnTtZt24dBw4cwGg0cuHChXITb1JSErNnz+bAgQOEhISQk5NDaqr3+zNnzZrlejx9+nSmTJnCiBEjeOKJJ1i8eDFPPvmkV+1MmzaNvLw8Pvywctf10tPTmTlzJvv27UMIQbdu3RgyZAhhYWGXPbdJkyYsW7aMefPmVSqG0tT4Eb7BEF6oV/Dz6NPp/dCfcAjQmq1VEJ1CUXOpjnpkgP79+xMUFOR1/ZMnT9KrVy9iYmJ45ZVXXMcrolouolmzZkRHR6PR+DZF1/gRvsEUgV4jsVj0HlfptOvSnV1+oCtQCV9Rczn7xhuYj/p2YYKxXVvqv/himeXVUY9cESZPnsyTTz7J2LFjS/jwy1MtDx8+3PWBV5xnn32WsWPHVigOb6j5CT+gDiaRTaZFg7ngrEe7XW4A6AscZbSgUCgqQnXUI1eEHTt28MUXXwBOPfL06dMvG8fKlSt9GoO31PyEHxiBiTSkxYjFYcNqTcNgKCnqLPATmPKUXkFRcylvJH41qW565IriSZFcnmpZjfCvEsbASALlQYQ0csFah4KCM24J3+KnITTDXkURKhQ1kyLbY6tWrQDPeuQ33niDCRMmsHPnTlJTUzl79iw33nijW/3ieuR77rmHPXv2EBoa6rHf4nrkESNGuOmRKzrCf+GFF+jRowdDhw4tcbx3796sWLGC0aNHl9AjDxo0iBdffJGMDOfS8I0bNzJnzhyg6kb4Nf+ibVAdl14hxdLI825bk1bpFRQKH5OTk8MjjzxC+/btiY6O5siRI8yYMcOlR37rrbfo06ePS49stVqZOnUqbdu2pUuXLqxcuZIFCxa49MiLFy+mdevWLj1yecydO5f58+fTsmVL0tLSvNYjg/PmJA8++CCbN28mKiqKDRs2AM5vGPXr13erv2DBAhYuXEhMTAxZWZdul1pctRwTE1NCtXw59u7dS1RUFKtWrWLixIl06NDB6/jLwyd65KuBL/TIRYydNY8f89oxrNs6JvfsSePGj5QoXzE2hs57cjgwYSijnnvDJ30qFFWN0iP7lkGDBrmS//XCleqRa/wIHyBEOPUK582RnnfbFi4byzt77JrGpVAoqg/XW7KvCLUi4TcKPA9Aen4dj7ttbYV6Bb3Z3aapUCgUNYVakfB7NEhHCsgqCKHA7D5Pb9U7N1norLnXOjSFQqG4ZtSKhF8npD7CoCHHEuhxt60m1HmfSq2l4FqHplAoFNeMWpHwdbowtFpBgdWIxXIeKUsuwYwd8zR2AVqz94IlhUKhqG7UioRv0Idj0EgsVi1S2jGbz5cob9yyLdn+oCuwVVGECoVCcfWpFQlfbwrDKGzYC3U5ntbi5waAIV/pFRQKX6L0yBXTI8+fP9+1f6F///6cPn26QrGUplYkfINfHfykBWmV2KTG4zy+2U9gyr8+9yQoFNWR4nrkuLg4Nm3aVEImVpoiPfL27duJi4tj165dREdHe93frFmzGDBgAHBJj5yQkEBYWBiLFy/2up1p06bx6aefel2/LIr0yLt372bPnj3MnDnTtev2cnTt2pV9+/YRFxfHsGHDeO655yodD9SShG8MiCSQfISE89a6HtfiW/w0+Kt7oCgUPkPpkSuuR7799tvx93cuF+/ZsydJSUlex1MeNd6lA4UJXx4CwkjMi/K8Ft+kIyjXzvmUFOoWipYUiprCtv/8zoXEHJ+2GdE4kD4PtS6zXOmRfaNHXrx4MXfeeWeFYitNrUj4hpBIQqTznrVn8xqWsdtWj85h5tulbzPuJfc/CIVCcWUoPXLl9cj//ve/2bdvHz/88INPYvVJwhdC3AEsALTAx1LKNz3UeQiYAUjgkJRypC/69gadKZBgjXPuLDW/LgUF7qMDu8EE5GC9cPJahaVQXDPKG4lfTZQe+XvX8yvVI2/atInZs2fzww8/uKbFKkulE74QQgssBGKBJGCvEGKtlPJIsTqtgBeA3lLKDCFE3cr2eyVoNBqahJyGnN5kmMM8rtKxGgr1Chbffu1VKGorSo9ccT3yzz//zMSJE1m/fj116/ouXfriom0P4JiU8oSU0gKsAO4tVedPwEIpZQaAlPI815hOkX8gNZBtCcZiuYDDYS5RbjU4L9LolV5BofAJSo9ccT3ytGnTyMnJ4cEHH6RLly4MGTLE6/jLo9J6ZCHEMOAOKeVjhc/HADdJKZ8uVudr4HegN85pnxlSynIvV/tSjwywe939DN/7J0L9C3grZio399qKn18TV/nS16bQ87P1HLopkBHL9/qsX4WiqlB6ZN+i9MiF7Xs4VvpTRAe0Am4DHgY+FkK4fR8TQjwuhNgnhNiXmprqg9CKBaAJQacVFNidF3tKr8Uf8PBEbBrQmtXNzBUKhTvXW7KvCL5I+ElA8d0UUUBpJWUSsEZKaZVSngTicX4AlEBKuUhK2V1K2T0yMtIHoV1CrwlFr5FYbc6XXHqljtIrKBSKmo4vEv5eoJUQorkQwgCMANaWqvM1cDuAECICaA2c8EHfXqPXhWEqrlfwsBY/LwD0Sq+gUChqKJVO+FJKG/A0sAE4CvxHSnlYCDFLCFF0pWEDkCaEOAJsBaZJKdMq2/eVYDDWwQ8L0urALkRVMe0AACAASURBVIM9rsUvUHoFhUJRg/HJOnwp5bfAt6WOvVrssQSeLfypEvSmcAJlPgITp7IaUi/Cg17BpKHOBbuHsxUKhaL6UytcOuAUqAVK5xr7pBzPu22degVIPPbbtQ5PoVAorjq1JuEbAy7pFc4V1KOgwP1Whw6jAa2EjZ+9f63DUyhqJEqPXDE98gcffECnTp3o0qULt9xyC0eOHLn8SV5QK1w6AMagSEJ0zh1vaeYIbLYs7PY8tFp/Vx2b0QRkI9OTqyhKhaLmUFyPbDQauXDhQrmJt0iPfODAAUJCQsjJyeFKlmfPmjXL9bhIjzxixAieeOIJFi9ezJNPPulVO9OmTSMvL48PP/zQ6749UaRH3rdvH0IIunXrxpAhQwgLC7vsuSNHjuSJJ54AYO3atTz77LNemzbLo/aM8IMjaFrnKACZlhDAfS2+vUivYFN6BYWisig9csX1yMHBwa7Hubm5Hl09FaHWjPC1BhOtIuORpwU5NucfVIH5DAEBLVx1LAbnm6yzKDG+omaxddkizp/27Urouk1v4PZxj5dZrvTIldMjL1y4kPnz52OxWNiyZUuFYitNrUn4AMGmUDR6QZ7dBLivxdfXbQb8gtZccO2DUyhqGEqPXDk98qRJk5g0aRL/93//x+uvv35F1wDKolYlfJ0MQasVmB06QLit1Llr7F84++l/0Zq9v8CjUFQHyhuJX02UHvl71/Mr1SMXMWLECK+vP1yO2pXwCcGgkRTYBQZ9hNsIv27DhiT4g65ArcVXKCqL0iNXXI+ckJDget+++eYb1+PKUqsSvl6EYsJGnk2HUV/P41r8PH8wFCi9gkJRWXJycnjmmWfIzMxEp9PRsmVLFi1a5NIj79mzh6CgIJceecKECUydOpWUlBRMJhORkZF88MEHLj3y5s2bady4sUuPXN4Ux9y5cxkxYgQvv/wyXbt2vWI98m+//UZOTg5RUVEsXryYQYMG8csvv3jUFC9YsICRI0eyYMECHnjgAdfx4npk4Ir0yO+99x6bNm1Cr9cTFhbmk+kc8IEe+Wrhaz0ywK8bpjNxbwxJOX4s7f9v/ILS6dWzpAHvv3e0xz9X0n/bUZ/2rVBca5Qe2bcoPXI1Q28IK9QrwK/JBszmFLcLK1Y/DQFqkY5CoSjF9ZbsK0KtSvgGQzhBONfYJ+bWwW7Pw2a7WKKOzaQnKA+OHvTttwuFQqGoampXwjdFECydtyC7YI4A3L34dqMejYTtXyy55vEpFArF1aR2JfyAOoTq0gHIsDm3N5deqWM3+AEgsstf+qVQKBTVjdqV8AMjaBLpNGFm2Qr1CqVG+FZ9oV7Bkn1tg1MoFIqrTK1K+MbASDq1OIzUCnKlP0LoMJeyZlqNhXoFq7pyq1Aoaha1KuEbguqAFGh0gnypx2io6zbC92vo3OCgNZurIkSFokZRHfXIFVUaA5w6dYqOHTu6ns+ZM4eWLVvSpk2bK1rls2rVKjp06IBGo8GXy9Nr1cYrjVaL1hqETicwSy1GUwM3Y+agkU9xZukXSq+gUFSS6qhHrozSuDRHjhxhxYoVHD58mJSUFAYMGMDvv/+OVqu97LkdO3bkyy+/ZOLEiVfcb3nUqhE+gM4RhF44sDnAqKuH2eyuV8gOAH2+rYoiVChqBr7SIx8/ftylWwCndqBbt25u/flCj1wRpfH+/fvp3LkzvXr1KmHLXLNmDSNGjMBoNNK8eXNatmzJnj17vIqjXbt2tGnTxqu6V0KtGuEDaB0h+AkbeVYdBlEPs3kTUjoQ4tJnX74/GAquzx3ICkVFyPzvcSwpuT5t09AwgNDBLcos95UeuUWLFoSEhHDw4EG6dOnC0qVLGTduXJn9VkaPXJ7SuCzGjx/Pu+++S9++fZk2bZrreHJyMj179vTYVp8+fcjOdl8YMm/ePAYMGFBuf5Wh1iV8vQjBT5rBpiU52YI0WrBY0zEaIlx1CvwEAdkq4SsUlcGXeuTHHnuMpUuXMn/+fFauXFnuSLkyeuTyzvVEVlYWmZmZ9O3bF3Dqkb/77rvLtrVt27Yy27ya1L6ErwklUOYD/uw5lk1MBzAXpJRI+FY/DQHnlDFTUXMobyR+NfGVHvmBBx5g5syZ9OvXj27dulGnTp0y+6yMHrk8pbEnpJRlfiBERUWRmJhYoq2iOKpqhF/75vB1YQRKp14hJd+5BLP0Sh2bSU9gPhxRegWFosLEx8eTkJDgeu5Jj/z5558zYcIErFYrKSkpHDhwwGN9k8nEoEGDePLJJxk/fny5/RbXIwNueuSDBw+6/RTVHTRoEBs3biQjI4OMjAw2btzIoEGDABg7dqzbN4vQ0FBCQkLYvn07QAk98pAhQ1ixYgVms5mTJ0+SkJBAjx49AOcI31McVzPZQy0c4Rv04YSQCTQlzVrWbls9GlnAjlUf0b6LR+mcQqG4DL7SIxcxatQovvzySwYOHHjZviuqRy5PaRwXF0eDBg3czlm6dCkTJkzA39/f9eEA0KFDBx566CHat2+PTqdj4cKFXq3QAfjqq6945plnSE1N5e6776ZLly4+kbfVKj0ywKldy3h3y698cfF2Ogac46995hEVNYZWLV9w1fn3xNvo9sM5fhrYlkff+crnMSgU14KapkeeN28eWVlZvPbaa9e874sXL/Loo4+yatWqa953eVSJHlkIcYcQIl4IcUwI8Xw59YYJIaQQosqGzQa/OtxQ/xcAskUARmN9t7X4Lr2CLeeax6dQKNwZOnQon3zyCZMnT66S/oODg6+7ZF8RKj2lI4TQAguBWCAJ2CuEWCulPFKqXhDwZ6D8rXZXGWNAJG2bHUMeF+QJEyZjA7e1+DaDc25fa1F6BYXieuCrr9Q3bV/gixF+D+CYlPKElNICrADu9VDvNeDvQIEP+qwwxoBIADR6DfnoPe62Db4hGlB6BYVCUbPwRcJvBCQWe55UeMyFEKIr0FhKuc4H/VUKQ4gz4eu0YHFoMBrqY7Gcx+G4tLP29vvHYdaB1mytqjAVCoXC5/gi4XtahOq6EiycW1jfBv562YaEeFwIsU8Ise9KHBpXgs4UiLDrMQgHVjsYRT2ktGOxnHfVcekVCpReQaFQ1Bx8kfCTgMbFnkcBxZ3DQUBH4HshxCmgJ7DW04VbKeUiKWV3KWX3yMhIH4TmjkajQWsLwiRsSJsDvc3ZT+m1+Pn+YMi/PlcwKRQKRUXwRcLfC7QSQjQXQhiAEcDaokIpZZaUMkJK2UxK2QzYBQyRUlbZriadIxh/aQab5Oe4PwD3tfgFfgKTSvgKRaVQeuSK6ZGnTZtG27ZtiY6OZujQoWRmZl5RHGVR6YQvpbQBTwMbgKPAf6SUh4UQs4QQQyrb/tVAJ0MIxLkCZ1fCWcDDna9MWgJ965pSKGoVxfXIcXFxbNq0qYSYrDRFeuTt27cTFxfHrl27iI6O9rq/WbNmuXaqFumRExISCAsLY/HixV61UaRH3r17N3v27GHmzJlkZGR4HUNxiuuR169fz1NPPYXd7p2yJTY2ll9//ZW4uDhat27NnDlzKhRDaXyyDl9K+a2UsrWUsoWUcnbhsVellGs91L2tKkf3ADpNCEGFeoVzViNabaDbSh27SUdAPuzeUvndbQpFbUTpkSuuRx44cKDL9tmzZ0+SkpK8Ou9y1Dq1AjgFasFkAZCpCcBkcl+Lbzca0FBA3P/+w039BnlqRqGoNnz33XecPXvWp23Wr1+fO++8s8xypUf2jR55yZIlDB8+vNwYvKV2JnxdGKF65yqgiwR63G1rN/gBFxG5aVUQoUJR/VF65MrrkWfPno1Opys35iuhViZ8g7EOrRtshswB5Ah/TMYG5OQcLVHHaghw1rUqvYKi+lPeSPxqovTIFdcjL1++nHXr1rF58+ZyP3SuhFqnRwbQm8Jp0TgJqRPkCSNGU0Mslgs4HJd21loL9Qo6S35VhalQVGuUHrnieuT169czd+5c1q5di7+//5W87eVSO0f4fnUgGzQ6DQXoMRmdylOz+Rx+fk0ACGvZBTiIxlKlJgiFotqi9MgV1yM//fTTmM1mYmNjAeeF2+LvRUWpdXpkgIyTP3Pg5DCe2OG8or7z8QAOHR7HjV0/Iyzs0kWWnzu143hbPcNWxV2VOBSKq4nSI/uOmqJHrpUjfGOQc3etUeMg16rBYHPe3rD0hdvsANAVqFsdKhRVzdChQzl+/Dhbtmypkv6VHrkaYwx2JngTVrJtenTmwjtfldYr+IFR7bZVKKocpUf2DbXyoq3WYEJj88NfmhE2yZZtO9Drw9x225r9lV5BoVDUHGplwgfQ2oIIlIV6hT/iMRrdvfhKr6BQKGoStTbh62QIQTjXwaY6tB5329qMegILYPsG77ZlKxQKxfVM7U34hBAiLwKQqQn0OMJ3GA0AHP7ee2OfQqFQXK/U2oSvF6GEFekVRCAmYwNstizs9kv3sXXqFUCfm14lMSoU1R2lR66YHvmVV15xvWcDBw4kJSXl8id5Qe1N+NpQ2jT8GYAc/DGZnBsqio/yrXqnXkFnUXoFheJKUXrkiuuRp02bRlxcHAcPHuSee+5h1qxZFYqhNLU34RvCaNo4CYr0CsaihH/pk9RqLNQrWJVeQaG4UpQeueJ65ODgYNfj3Nxcn7l0auU6fACDIRzMIHQaCqQOo6FIr3BphF+vU2/45me0ZnNZzSgU1YLff3+N7FKCwMoSFNiO1q1fKbNc6ZErp0d+6aWX+OSTTwgJCWHr1q3lxuAttXaEbzA5N1/ptWCRGvT2cECUmNK5d9wk8g2gLbBWUZQKRfWlSI+8aNEiIiMjGT58OMuWLQOcd3Tq1KkTkyZN4uOPPwYu6ZFXr15N69atmTJlCjNmzABw6ZHtdjsrV65k5MiRZfZ7OT1yefI0X+iRvYnjcvI0cF7/SExMZNSoUbz33ntlxnAl1N4RfkAdyAKDxkGuVUAeGAyRbpuvsgNAb1Z6BUX1pryR+NVE6ZErrkcuYuTIkdx9993MnDmzzDi8pfaO8AOdI3w/rDisEnu2xbkWv8Bdr2DIc1RFiApFtUbpkSuuRy7+vq1du5a2bdt69Z5fjlo7wjcGOgVq/rIAYdfxzZZvaHVzA3JzE0rUs/gJgjOUXkGhuFKUHrnieuTnn3+e+Ph4NBoNTZs29YkaGWqpHhnAYbez9fs2zP/pJQ7n1mWk/0HGPSxJSVlJ31vjXF/TVg+LplmCle6HfHvBS6G42ig9su9QeuRqjkarRWsNIkhmA3W5gB6TsQ52ex4220X0+hAA7EYdAWYrW9aspN+9vrmRsEKhuDKUHtk31No5fACdI4hgsgDIJBBj0earYhduHYVriI/t+ObaB6hQKACnHjkuLo6IiIiqDqVaU6sTvtYRQoTBqU0o0isAJS7c2gr1Ctr8zGsfoEKhUPiQWp3w9SKE6AbOufkc4YfJ5FwyVWK3rd65689gVXoFhUJRvfFJwhdC3CGEiBdCHBNCPO+h/FkhxBEhRJwQYrMQoqkv+q0sOk0o9eudB50gXxgxGCIQQldiSsfm59zirFV6BYVCUc2pdMIXQmiBhcCdQHvgYSFE+1LVfga6SymjgdXA3yvbry/Q68Kw67LR6DXkSx3YBUZjvRJTOs26O9fFKr2CQqGo7vhihN8DOCalPCGltAArgHuLV5BSbpVSFnmHdwFRPui30hj04aBxoNOAVWqw51icXvxiI/yBD40jzwjaAlsVRqpQVE+qox75jjvuIDQ0lHvuucfrc4pTJH+DiquWf/zxR2688UZ0Op1rU5gv8MWyzEZAYrHnScBN5dR/FPjOB/1WGr0pDPLAKOzkWDU4sq2YTA24mHWoRL0cf9AXKL2CQnElFNcjG41GLly4UG7iLdIjHzhwgJCQEHJyckhNTfW6v+IK4SI98ogRI3jiiSdYvHgxTz75pFftTJs2jby8PD788EOv+/ZEkWp53759CCHo1q0bQ4YMISws7LLnNmnShGXLljFv3rxKxVAaX4zwPYkkPO7mEkKMBroD7jILZ/njQoh9Qoh9V/KLrigGP6ePw09YcdgK9QrGBhSYz+JwXPrDzPcHY753eoUjm/7G6d2fXpV4FYrqRHXUIwP079+foKAgr+ufPHmSXr16ERMTwyuvXHIWVUS1XESzZs2Ijo5Go/HtuhpfjPCTgOJ3NYgC3G7PIoQYALwE9JVSepwQl1IuAhaBc6etD2IrF2NAJKQV6RX0fLH5K+4ceTOn/1hEcvLnNG78CABmPw2haZdP+JbcTM7wOYa0SBo7Rvn8l6VQVJRXEpL4Nce3Cw86BvrxWquyZ2erox65IkyePJknn3ySsWPHlvDhl6daHj58uOsDrzjPPvssY8eOrVAc3uCLhL8XaCWEaA4kAyOAEu5SIURX4EPgDinleR/06ROMAU6fTqDMA4I4nH6OUeGPEhbWi5On3qVBg/vR6YKw+mkJzL18wr+QsA00diyms2Se3E94i5ir/AoUiuuXIj3ytm3b2Lp1K8OHD+fNN99k3LhxxMbGsmrVKiZNmsShQ84p1CI98t69e9m8eTNTpkxh//79zJgxw6VHnj9/PitXriz3RiKX0yOPGjXKp69zx44dfPHFF4BTjzx9+vTLxrFy5UqfxuAtlU74UkqbEOJpYAOgBZZIKQ8LIWYB+6SUa3FO4QQCqwpf8B9SyiGV7buyGEKcCT9YZgP1uCCMCCFo2fJ59u69l1OnP6Bli2nYjTr8LVa+/exD7ho1scz20s9tR2h1SBycObFGJXzFdUN5I/GrSXXTI1cUT4rk8lTL1XmEj5TyW+DbUsdeLfZ4gNtJ1wE6UyDCridYOPUKGTjvYRsc1JH69e4jMXEpUY1GYTcagXwSf94G5ST8LNt+/K1tEUJLmtiCw+FQ0zqKWkuR7bFVq1aAZz3yG2+8wYQJE9i5cyepqamcPXvWNV9flh75cvenLa5HHjFihJseuaIj/BdeeIEePXowdOjQEsd79+7NihUrGD16dAk98qBBg3jxxRdd98TduHEjc+bMAapuhF+rs5FGo0FrCyJC69QmZItLy6luuOFZQHL8xHzseqdewWDOKrOtgszz5Jr+4GX/yawKfAyr6RyZJ/eXqJOabab3m1tYc7D8W6YpFDWBnJwcHnnkEdq3b090dDRHjhxhxowZLj3yW2+9RZ8+fVx6ZKvVytSpU2nbti1dunRh5cqVLFiwwNXeqFGjEEJ4rUeeP38+LVu2JC0tzWs9MjhvTvLggw+yefNmoqKi2LBhAwC//PIL9evXd6u/YMECFi5cSExMDFlZl3JEcdVyTExMCdXy5di7dy9RUVGsWrWKiRMn0qFDB6/jL49aq0cuYsc3/TmfHs5fDo8jKjCfHS8Pc5UdOzaX0398ROJ3N3DTfxPZd1sDxnzg2daXtG8VH1z8Hx+LpzAJwTu2R2gh76ZD7GxXnZe//oV/7/qD1vUC2fCXW312Y2KFwhNKj+xbBg0a5Er+1wtKj3yF6GQI9cNyEXoN+RhL3LKsadMnSTmziuDmFwDQWspe5ZB8YTerDQ/TzKTnVIGVHfbRhNq/cE3rHDufw+d7EmkeEcDv53L46XgavVsq859C4Q1VrUcGrrtkXxFq9ZQOgE4Tgk2ThUYnKECLLHb/Wr0+mGbNJhHYzDnlU55e4TNNGJkijHfbN6NXaAAbDH0oMF0g48ReAOau/w0/vZbPHruJ8AADS3ecuqqvS6GoSSg9sm+o9QlfrwnFpr2IXiuxODTYs0vuBIxqNIrAsKbkmkBXYPXYxukzp1mj60dfzhETEsBjUZGcxcgBRw/OnljDnpPp/O/IOZ68rQUNQ/0Y2aMJm387xx9peR7bUygUiquBSvi6MBz6PAw4sNsljlIJX6Mx0KLFNHL8JXqzZ5/OmwnHsKFnegPnBZlBdUKIMunZxIOk2bYy+5vD1A82MaF3cwBG92yKVgg+2Xnqar40hUKhKEGtT/gGo3M9r7+w4rBKLpw661anbuSdFASAMV9it5ecx/89t4A1tjAGOLbQpZVzOZlOIxjfKJJftc04bvIj8+Kv/HVga/wMzhsY1w8xcWenBqzcl0huGR8iCoVC4WtqfcLXm5yjcn9ZgHBINh/a5lZHCIHZpMEvF/5IXFKi7PXjKRgxM9acgKbYHelHNgjHJGC9vJuBUXHcf2PJjS/jbm5GdoGNLw8kXYVXpVAoFO7U+oRfJFALlM47Wh256Nn8YDXpCMwTnD69CIvFuWrnp4wcNqZdZAhf0DS4c4n6YXodHdGzQ9xKu4h4RCmf3I1NQomOCmHZT6dwOK7PpbEKRWVReuSK6ZHnz5/v2r/Qv39/Tp8+XaFYSlPrE36RTyeoMOFfwOSxnt2ox88C5ou5nDj5Lg4pmXk8mXqYuYNviGx6W4n6WXlWTu49i03o+cF0IxnHS/6hCyEY37sZx1Nz2X7sgu9fmEJRxRTXI8fFxbFp06YSMrHSFOmRt2/fTlxcHLt27SI6Otrr/mbNmsWAAc5N/UV65ISEBMLCwi67O7c406ZN49NPK2+8LdIj7969mz179jBz5kzXrtvL0bVrV/bt20dcXBzDhg3jueeeq3Q8oBI+xiDnMq9geRGATE2Ax3r2QsVrZnwEKSmf89/EgxzKzmeU+Qf8LP4ERZW8ydfC74+Rl15AV6OW/3EHSSf/69bmXZ0aEBFoZNlPp3z4ihSK6wOlR664Hvn222/H398fgJ49e5KU5Jup31q/8coY7Bzh1/W7CPlwsZheoThOvUIG+UmhaGLyOH1iHu0DXqG7eSXBji4lnDmJ6Xks23GK+7tGMbB1Ex75xc56mUGnUm4do07LqJuasGBzAicv5NI8wvOHjUJRWWb+9zBHUi76tM32DYP52+Cyt/wrPbJv9MiLFy/mzjvvrFBspan1CV9rMKGx+dG7cR7L0yEXP4/1LAbnJ74u38y5kNF0SP+QlsafkYZMwky9StR9a2M8QsDUQa2pG2yiIWa+1ffhseO7qNPq5hJ1R/VswvvfH2P5T6eYMcQ3vgyF4npA6ZErr0f+97//zb59+/jhhx98EmutT/gAWlsQkSFmhF5DnjAgHRKhKem5sQc4L+5qLfm8frEfszVfEJb2HhYgsvntrnq/JGXx9cEUnrqtBQ1CnB8ej0bV5bUkIz+e3MDQUgm/bpCJe6Ibsnp/En8d2Jogk/7qvlhFraS8kfjVROmRv3c9v1I98qZNm5g9ezY//PCDa1qsstT6OXxw+nSsjkynXkHqcOS676jtHPsQABqzhQt2HQ2bTsbCWbTWYAIbtACcn+hvfHuU8AADT9zWwnXu6GaNMUkLK0UQDof7jVTG3dyMHLONL/arJZqKmkN8fDwJCQmu5570yJ9//jkTJkzAarWSkpLCgQMHPNYvrkceP358uf0W1yMDbnrkgwcPuv14k+xfeOEFvvrqK7fjRXpkwE2PvHHjRjIyMsjIyGDjxo0MGjQIcI7wPcVRlOx//vlnJk6cyNq1a6lbt+5lY/MWlfABHSHYhFOvYHUIN70CwE39BpHtBzqzleH1w+na+AGQAqm14nA4HTtb48+z80Qak/u3IrjYSD1Er+NuXRbbtTEkxO90a7tz41C6Ngll+c7Taommosag9MgV1yNPmzaNnJwcHnzwQbp06cKQIb65X1St1yMD/PztRLLFQZ4+8CoXLRqOjrwJvzbuv5itvduRHSKI+eoghsSfOfiH806OrVq9TMOGj3Dngm3YHJKNU25Fry35WXr4/Dn6Hz7DOFscb8a639FmzcFkJq84yNJxMdze1nef6Irai9Ij+5aaoEdWI3xArw3FpruIn7QgrQ7STrvrFQ5ezCPfT2DKlzQwGkhL/BGAkMDunDz5Hqv3/UbC+Rym39HGLdkDdKhbj672E6zRNsFss7uV39WpAfWCjSytxBLNwxtfZPe6oVhyMyvchkJxPTJ06FA++eQTJk+eXGUxXG/JviKohA/oDWFIrYUAChAO2Hhwa4lyWbjJyuIn8CsUXGbm7sGYH0WbdjOw2bI4/Pu7dG8axqAO7l/5ihhjkmSIUFb+utc9Bq2G0Tc15cffUzl2PueKX8P5o1s5q1tJjn8cP3//GHZr2SpnhaK6ofTIvkElfMBgcE7fFOkVfssvuV75f2kX2ZmZi9VPS2Ae2C0F5BgPE6y9kaCgdmTI/vSuv4XpA0KwZ5qxX/S8jXto9G3Uk2dYmuY5oT98UxMMWg3Lr3CUb7fkE3/yVY5ZenFUM5tsv5+J+9+f3S4Qrz2Uwg61q1ehqLWohA8YTM5RQxCFegVxaQmUzSF57XgKLfyMOIwGTFZY9e6rSK2Z8IjenDudyYEd/dEJgfj575ydu5czb+wm5fVdXFj6K1kbTpH3ywVs6QWYgsIZYv2Vo5oI9mdku8UREWhkcOeGfHEgiax8z+59T/z+4zwOmsKYbfwrr8u2/J+cz3nT9/y2eYarzqe7TvPnz39m9OLdfLzthMc1wgqFomaj1uEDhoA6kAUhDufIPotLO17/70waCXlmlnZsRobRCOSSk5xItPYJNDmNsOb8wlM04HzyHWQ0/i+N7xmHv2iNNTkHa0ouBQmJUDjQFiYdjwZ2JiQgh+0XDhN9ayd0kf4l1vyP792MLw4ksWpfIo/1ueGysWclHWYHO5jPTJr6m4itE8L7iZBkf5tJ2hcwbmvAr0FDeHXNr/RvWxeDTsPr3xzleGous+7t4PF6g0KhqJmohA8YAp0j/Hr+ZqdeodCnk221sfKXZKZeFPTYeIZvDf5AOjpLDv7pHbA0D+Sf8Wdo2qU+Tz8wi527dpAcsJiuXT51bcSQVgfWs7lYUnKwpuRgTtTzQGIu+tOSc/sPIPQa9A0C0DcMxNAwkFb1/bm3YSjfbzvN6OaRaIo+DDwMyB0OBz/tWM5XpheJ0Rl4u1l9Ig06uteRzDvlYJnjbUaLhWzeaeHuhjHMHdQOvU5Dp0ATn+w6zeSzOcwe2olgfz0IAQLnT2WoxI3Z1T3dvLwR3QAAIABJREFUfYt0SKTdfd+H4vpAVMFgSy3LBAoyz7PjQC+MWeMYtedGGgUW8N+m7cg4loGpwPkPRhti4Lszf6fXxiPs71uPLvf35O0zD7DnZDo/PHc74QEGEhOX83vCLJo2eRy9oQ5IB1I6AOf/JRKknfiEb9kpo+mh1dHMDvZcM/ZcC9jtSEBILRq7HuEo+VPymMHDMT1CanBlbdevVhT+t1hGLVV2iaJzRalSUaq8jPNlJRJ+pT9tqpLrL/bMwSG0adKySmN4851/sGLNKrQaLRqNhoVv/pMeXWPKrL9sxae88/FChBA4HA5mPvcqQwbd7VVfM+e9zi039aZ/n9s5+ccpxkwaT3pmBl07dmHpgkUYDAav2rln9FD2/LyPm2N68vWyVV6dU5zwNg1Ijz8DwKerPmPOO86dvS/8eRpjHizUOggwNCpb0PbBBx+wcOFCtFotgYGBLFq0iPbt27vVu9JlmWqEDxiC6oAUhAfZnHoFDOQnZbO1jhZLkxAm3tICbbgJ+0uX9Aqphq5s/u08z93RhvAA5x9So0YPc+bsV5z+Y1H5/ekFt3ASiYZUvRbhp4UIAVIDUiKlFbu0IMT1+WGsqB6E+31IQXDV/RPfs+cQ675fww/b/43RaCAtLQOLxUpB8CmP9ZOTzzJn4Rx+/HElISFB5OTkceFCepn1SzN91mgACjjF8/+YyhPPPMSwYXfyl7+8xqKv3+axx4Z71c7Tzw4nP/9eli5d7XXfJRAOCoJPkZ6exWsLXuf771cghKBv3+EMuL8TYWHBgMBAxzKbGDlyJE888QQAa9eu5dlnn/XatFkePvlrEELcASwAtMDHUso3S5UbgU+AbkAaMFxKecoXffsCjVaL1hqEVWag1QrMUsc/72vIyrPpbLupFTo/50XcmCGjcXy5DY3ZwruHw2kYonHdpxac97+N6f4FdnseIBBCA2hK/V9gzc1k4a6JzNW+yHttm/D/7N13eBTl+jfw72zJpm16r5teSQKhCiIgiBLAUMQIrxRBkF5OFDy/I3gQFTzSpKhEuliOAcFDVQQDCFIChEAahCSQQtqmt23z/pFsDEl2s9nsEkjuz3XtRbI7M8+zA9z77Mwz35no0PIir21n7mLDb0k4trAfPG34UCjqGh4SlEurEX39IsSMAO9aMQh2coRCXv86y8pQVFmHnRfug8th8P8GuuNYYTHSJQoEKVIw3iUchibmAAAWLEqqpPjhahbElRJEhDgizNUCyuE72ziMb/iTffx3hUKOoowLuKPIwx2mB8oYC9iyRXBj0uEhLYe9SRiMHQKRmFuByxliVNXJ4GljgkAnM3jbmYLHafqVtmMfbmwH1+9Y40/nB3NlpRkEAvtOa7+4WApbW3uYmdUnRjo51felrKwcgwa9jIMH98HX1xtvvjkHQ4YMQq9eoTAzM4e1tQe4XC4EAsDa2gPp6ZmYMmUW/vqr/uYm9+7dx5tvzsGlS7891t6sWYswatQIjBs3GufPX8O33+4Gj8fDtGnTsGbN55g/f5FG/R458lXExf0JDsdAo/2XkZGF6dPnQiaTY8SIoQAYCAT2OHfuTwwfPgyOjr4AgOHDhyEuLhGvvz6+zW2amZk1/lxVVdVqVo82OlzwGYbhAtgGYASAbABXGYb5hWXZpCaLzQRQwrKsN8MwUQDWAdDs4/YJ4SnqCz6fy0KiYPBdXjFmuthAZPT3jJ2w/oNx2Rjg18pwPVuC9a+FwpDPfWw7DMMFj6c+S9vA1BID67hwMsxDzEMjTLC3bPEX+kY/d3xx5h72XS7EJ+N6ND5fI1fg7RtXcZPph48UV/Bi2LzH1ssrq8H8by+hRuqG/84ZAG87U4T5sFgeH4+NlaNw/uEd7O/3CizN6j9k3AB4iKSYf+A6Fv2vCHMGe+K9l/3B5aj/B1aeew8xCd/gR8EkPOCKIBJwMcrOGr8VleJujQRcvgyhkhsIunsLD+/ZQMEbiyAXa/xwKw8FV+pgKuDhpSB7RIY54zkva/C0PJ5ZI85FbtJR3K1IgaOBDexse8LKox8Ewr8/RCUyBQoqauFgZqh1O8+i5ORkCAQNV22fWAE8StRtAw49gFfWqnw5IuI1fPrpZvToMeixeGQ7Ozts2/YlZs/+BxYvXozy8hrMm/cPyOVyODg4w9+/32PxyIGBdrCwsEZyci7CwsJw4MAmzJgx6+/31oDLNQSfb47KSi4sLCxhYlIfmObpGYK8vEIIBHYah6cZGFiCwxG0aKM17703C/PmLWoSj8xAILBDQUElRCLfxm24u/ugoKASAoGdRuFp27Ztw4YNGyCRSHDmzJk2+6EJXYzw+wK4x7LsfQBgGOYHAK8CaFrwXwXwYcPPsQC2MgzDsE/RCQSuwhwylEHAyFEr58KUx8FS0eMXUUkqS1BlDPBr5Qh0NMO4ns5at2dvPQovVf8Peypn43p5NcLNH8/CtzIxQGSYMw5dz8bykf4wN+ZDqmDxdmI6rkv5WCTdi6lDHv/PJq6S4M2dV1BWI8X3b/eHt119tj+Pw2B9n95w/essPqv2x6grV/Bj/0Fwa7jRhJkhH7un98Hqo0n4+tx93C+qwqbXw2AiaPnPQyaXY/fFI9gh5eOhYRTcmVps9XNFpL0VeBwG77rZYf3lTOzLysdt22BcN+wDw6Aa9FHchDdfiLNLXkVCXh0O38zBiduPcOh6TsN0VEe8GuaMUBfzNkczeQ9T8Me9P3FFUoI7fGvcQxCqDfuCYeWwKyqAU9EhOMhKYVYnR02FAHdzTPBAbA8uhw+RjTG87UzhZWva+KenrQmMDTT/r6CQy1FemImsR+nIKs9DXm0Z+BwerA1MYGtoAXszG5gL7VHFtUZBLYuiijoYC3iwNObD0tgA5sZ8CAW8Do/aFHI5pFUlAFjwjMzA5esmUVFXKB65Y/HI8+fPx/z58/Hdd99hzZo17bpFoiq6KPjOAB42+T0bQD9Vy7AsK2MYpgyANYCn5iogPmOOWmTDCBKUSgQwOJeNwedapleuNWZg94jFW6fn4dDpjrXZG0BvnEcGgIxWXu/T8PityXehyIYHABze2rfFOu80/Jk6F2g+fnAB8EXDz1c2A83/y4QA+BwA7gAn1JyrsgSwvNlzTe8n5A/gExXrnsA6APWjhMd6fxm4h/qHJvgABjY82qIqaksKIKXh0RHKoF4pgNyGR3NVAAo72E57eURvgpjXMEvH+01AH+dv795pc5EQZ1uE/L9J8LCxwA/79mDswD5QKBRIvB4PAZ+PjBtXYFzzd+iYt6UJvCeORV8/Tyx8/wMsmvIahoYGYNW//g99/L3Rw88HjPgRxOLHI1DqyktRmfcQnJJ8lBQXoyA5ATweD0k3bsLWwgziu3fw0y9HsfWb3S366OHuhj1bNjb+Xp6dAWlVBcQavD9WIUfJvSTweDyUV1YCrALiu3dgwQP+jL/VuI30O4kY2K8PxHfvYObif+BeRmaLbc2fMRVR48ZCweXAyrP+JG1UVBTmzp3bZj80oYuC39owpflHmybLgGGY2QBmA4Cbm1vHe9YOPI4FZEwSvGVZKDAMQCsJyQCANFcHmFbkwaZI9kT7R0h7cRQAX9Z5X6LvZmSAYTjwFtVHHN+5kww3R0fwZSy27N4Hf08PfLh4ERa//wFOf/ctikpKkF9UhLCG2SjJd1Ial+dzDfDic8/h3VUfYetH/271fXFYFlw5CwM5MLhvHxw7/ismjnoF/z14BKOHDgVfxmLyqAhMHqVi1k+TbfLkAMM+vv8+3LAJ4SE9MGb4i4+t1r9nTxz55Tiixo7Bz4ePAg3rvdT/OXy8fjMqi+uzrf64cBH/XrwYfBmLfes/V73jZEB6ZkZjwT927Bh8fHza3uEa0EXBzwbQ9M7ELmg5yFEuk80wDA+AOQBx8w2xLLsDwA6gflqmDvqmMT7PEnKmAvs+WPzYbQib+vPYMPB6m6PfTt0cT8u6vB8Xq77EMmYblrg7YLmnY4tlTt5+hJmX0iD3NsNY6Xm8we7EgH6/wtCi/rigTK7AvAPX8WtSPjZMCsX4Xi5ttqtQKHDu1HtYJeiFVCYQyz0csMTd/rFDDEmPyhF19BaKHQWQG/PhwmbhdckfmOk3FVYePVFVJ8P+v7IQc+4+iqskGORtg8XDfdBH1Hb8a2bqJXyfcRa/GzjjDnqAZTgINuLChMfHzYpq1DVcAG7DFsCbTYNJZRmElUIUlnjjZi4gb4iQ9rU3Rbi7JXq5WaK3yAoia+M2D5PIJLVIz0jArUdpSK0VI53DIptrgWoYwwolsJHXwErOwlTBBVdmiKpaE+SVClEtt4KDuTEczAzhYN7wMDOEvZkh7MwEEPC4attt3PdyGSpK8vFInIuCiiIUVpeiQlYLE64AZgJjmAtMYSQQgsM1hZxrikqFMSRyFiYCHkwEXJgY8GAi4MFUwIMhn6P2/SYnJ0PYSlomy7JgFXIoFAooWDkYhgMOUz/JgOHUTy5gWRYsW38ynAFTf5lGOw9BsdV1WLBwIUpLS8Hj8eDt7Y0dO3YgTyzG/v8dxZUrVyAUCnHqRgI2HzyMt956C6v+vQa5ubkwNDSEra0tvtq5C0Kv+ntLzFi4CEf/iEPkrNngclvub765JYxc3CAMCMb6L79CVFQUPv7ya/Ts2RPz/+8DjW8i8vzzzyMlJQWVlZUIGPEydu7ciZEjRyI17xEmvjUTwoDHZ9ds27kLkydPxo7YQ5gwYQLA4UAYEAwhgJWrV2PY/5sGAFj10UdwH6DJd1Jg31cxmLrkPfD5fFhaWurkcA6gg3n4DQU8DcCLAHIAXAUwmWXZO02WmQ+gB8uy7zSctB3Psuwkddt9kvPwAeDuHxvxQLEVg3pfhsCsZUBTTckjXLwxEM54G/7DVuikTUlVKS5c7I8tzH+QZuiB+AGBMGx2UvGrBwX4MD0XfpVZ+MBkGbyNP4Co/3QAgELB4r2DtxAbn41VYwIxo8mMobbIZVJcPjUdG4364DwzBBPsLbHezxU8hsHB/BJszsrH/Zo6OMsfYgLzA9xK7BA15hPUgo99lzLxzfkMiKskeN7HBkuG+yDcXbOc76ZKsxJw7c5OnBQw+IsZCBYc+CAZ/rJM9JIJEWg/CFV2g3AsuQy/JuXD0tgAvUWW6OVuiV6uljA31s3dwerKiyCpFMPYzgNcXte54xjFI+tWV4hH7vAIv+GY/AIAp1A/LXMXy7J3GIZZDeAay7K/ANgJYD/DMPdQP7KP6mi7usY3tASqgbqKolYLftG9PwAANi7P66xNAxMLCCXheJH3Iy5Jo3GkoBSvO/5dOP/7SIwP03MRoJBhscG/wK3qAbch9WfwWZbFx8eTERufjSXDfdpV7AGAy+Ojz7CvsOTMa3AS5OHH/Ddwr7oWZTI5Mmsk8GZLsZT9Gn2lmYgrnot/3bbGydJbuJNbhpJqKYb42WLRiz7o5Wap9fu3cA/FcPcv0C83DZm3vgYLFnYuL8PW773HTkD6uTpg2Ut+WrfTFoGZTat/5+TpMW7cOKSnp+tstoo2nrZirw2dzMNnWfY4gOPNnlvZ5OdaAK/poi19MTCyri/4lYWoP+34OHHRn+BwDWHp2fJEaUfY27wC/6pV8OLJ8U12ISY51E/RPFVUhqUpDzDIwhQLc9agRiDBH1VvY2jD4aZtZ+9h54UMTH9OhMUvand8j28kRK/n9kBxaQIceUX4unIhPPjAirrdCDY4Cuu6EQgafAJDTMxhc/Ye1v+WhqF+dlj0ok/DfH3dEDr5oofTep1tj3Q9rd1akLQfXWnbQGBiCxQDkqriVl8vZ2/AVNpD51/5HYJH497FNYiQXcEXsgG4UlYFGcti9p1M9DA1xifsHTw0Po+Mgtfww20OFldJcOxWLj7/NQ3jejpj5ejADk3vM7J0QFjYLshvRaFX7VxwpSXgMobwNv8MLsMmNC63YJgP3hrk0a7pi4SQp0v3uQqlDQITWwCApLZlwa8syITEMA8WJs1nm3acgYkFzCS9Ea7YBwseF6vTczEtMQPuhgLs9bHFo/xPIKhxxdBB0aiTKbDo+xtY+csdDA+ww2cTQ/4OV+sAoZMfenh/CT6nEmaSMPTrcxwu4RNaLEfFnpBnG/0PbmBgXl/wpXUtC35R+h8AAGu3wXpp2872FZRVrkSkQSX2lMvhYsjHj2GeKPjjX5AKihDitAu2LjYY6G2NC/eK0M/DClsn99JptLG1d38MdrsKroGhzrZJCHm60Ai/Ac/QFIycD4m0pMVrJSWXwJUKYeEeppe2HYLHgJHz8XLJL4hysMJ/Q71h8PAGCniHYFM3Crb+LwAA3n8lAG/0dcU303q3iHTQBSr2hHRtVPAbcDgccGVCSGWPF3yFQoFy5gaEslBwWpn7qwsGxmYwk/QG8Cs2+DrB3YCDlNR/gSs1h/+gfzcuF+xsjk/Hh0Bo2HWmDpKu7eOPP0ZQUBBCQkIQFhaGy5cvq11+165d6NGjB0JCQhAcHIwjR45o1M4vv/yCtWvro0bq6urw+uuvw9vbG/369UNmZqbG/Y2Pj0ePHj3g7e2NRYsWtfvOcCKRCEVF9QECJ0+ehJ+fH7y9vRv7pomUlBQMGDAAAoEAn3+u5gItLdAhnSZ4CjPIUPbYc5V5aZAJimHB76/Xtu1sR6Gs8hKKUuNQVnALtUb34SNc81gIGCHPkkuXLuHo0aO4fv06BAIBioqKIJG0fr9nAMjOzsbHH3+M69evw9zcHJWVlSgs1CyQYuzYsRg7diwAYOfOnbC0tMS9e/fwww8/YPny5Rpl1wDA3LlzsWPHDvTv3x+jRo3CyZMn8corr2i0blNyuRzz58/Hb7/9BhcXF/Tp0wdjx45tNdO+OSsrK3zxxRc4fPhwm8u2F43wm+Cx5pCi9LHnCjPOAgBsPF7Qa9sOwaPByA2QlbETD6UxEFaHwyX8qQoUJaRd8vLyYGNj03iFq42NDZycnFBWVgY/P7/GtMg33ngDMTExKCgogFAohGlDqJ+pqSk8PDyQm1ufkql8cLlcZGVlPdbWnj17sGDBAgDAkSNHMG1a/dWtEydOxO+//67RSD0vLw/l5eUYMGAAGIbB1KlT2yy6xcXFeOmll9CzZ0/MmTOnsZ0rV67A29sbnp6eMDAwQFRUlMbfVuzs7NCnTx/w+br/Jk8j/CZ4HHNIkP/Yc6Vll8HjWEHo1HJuvi4pD+uUGV0EIzdAYPinKiMeCGmvdVfWIUXc0Zi4x/lb+WN53+Yxen976aWXsHr1avj6+j4Wj2xubo6tW7di+vTpWLx4MUpKSvD2229DLpfD3t4eHh4ej8UjOzk54ebNmwDqI4Pj4uLg7u6ust2cnBy4utanvfB4PJibm6O4uBjFxcV4/fXWB1F//PEHcnJy4OLydzSJi4sLcnJy1O6Df//73xg0aBBWrlyJY8eOYceOHS36oNyW8nDW0qVLcfbs2RbbioqKwooVurmKXxUq+E3wORaQMeWNvyvkclRwE2Cm6P1Eiq+9XQTKKi7ChT8Lpo5eem+PEH3SZTwyUB9D/M033+D8+fNq21UVS+zn59f4wdGe9dQ5d+4cDh06BACIiIiApaVlm9vauHFji9eeFCr4TfB5llBwqiGX1oHLF6D84S3IDcphZfTcE2nfuddr4CdbwS7gxbYXJqQd1I3E9YnL5WLIkCEYMmQIevTogb1792L69OlQKBRITk6GkZERxGJx48iaYRj07dsXffv2xYgRIzBjxgx8+OGHyMvLw8yZM/HLL780HvJRxcXFBQ8fPoSLiwtkMhnKyspgZWWF1NRUtSN8FxcXZGf/HYmenZ0NJyenNt9jax8Kyj60ti0a4T8lDATWgBSQVBTDyMoJhVlxAAAbL/0ev1ficLlwCFaV3k7IsyU1NRUcDqcx2vfmzZuNh2I2btyIgIAAfPLJJ3jrrbdw6dIlFBYW4tGjR+jVq9djy0ulUkyaNAnr1q2Dr69vm+2OHTsWe/fuxYABAxAbG4thw4ZpNMK3sLCAUCjEX3/9hX79+mHfvn1YuHAhAGDr1q0A0HieQGnw4ME4cOAA/vWvf+HEiRMoKamf5denTx/cvXsXGRkZcHZ2xg8//IDvvvuu8b13Fir4TfANrQApUFdeACMrJ5RWXoYB4wBTO8/O7hohz5zKykosbCUeOS0tDd98801jPPLgwYOxZs0avPXWW4iOjn48Hvmrr3Dx4kVcvXoVq1atwqpVqwAAx48fVzn6njlzJt588014e3vDysoKP/zwg8Z9/vLLLzF9+nTU1NTglVdeaZyhk5KSgoEDW0Ybr1q1Cm+88QZ69eqFF154ofE+HjweD1u3bsXIkSMhl8vx1ltvISgoSKM+PHr0CL1790Z5eTk4HA42bdqEpKSkx+5zq60OxyPry5OORwaAR7d/xZ2CuQi2/xo2fi/g3JmesJIPQegrW59oPwjRha4Wj9yZRo8ejUOHDsHAwKCzu/KYJx6P3JU05unUFKM04yoUvBpYWjyZ4/eEkKfX0aNHO7sLOkEFvwmBsD4TXVIjRnVF/V1mbb2HdGKPCCFEd6jgNyEwawhQk4hRVhsPAVxhZNX2WXpCCHkW0JU9TXANDMGRGaFOko8qg2SY81o9DEYIIc8kGuE3w5UJUcpcAsuVwMpasxsOE0LIs4BG+M3wWHPIBGKAZWDj82Tm3xNCyJNABb8ZHswBAEa1XpRUSUgHUTxy++ORDxw4gJCQEISEhOC5555rjJ7QCZZln8pHeHg42xmuH5vNnv7dk7196v1OaZ8QXUlKSurU9i9evMj279+fra2tZVmWZQsLC9mcnByVyz98+JD19PRkS0tLWZZl2YqKCvb+/fvtbnfbtm3snDlzWJZl2e+//56dNGmSxuv26dOHvXjxIqtQKNiXX36ZPX78eLvadnd3ZwsLC1mZTMZ6enqy6enpbF1dHRsSEsLeuXNHo238+eefrFgsZlmWZY8fP8727dtX5bKt/R0DuMaqqKs0wm+Gz7UAAFg5PN/JPSHk2UbxyNrFIz/33HONIWz9+/d/LN+no+ikbTMmQj9wy81g4zOos7tCiM48+uQT1CXrNh5ZEOAPh3/+U+XrFI/c8XjknTt3anUDFlWo4Dfj8dxbcJO9CS6PbiNISEdQPHLr29I0PO3s2bPYuXMnLly4oNHymqCC3woq9qSrUTcS1yeKR265LU1G+Ldu3cKsWbNw4sQJWFtbt9kHTVHBJ4ToBcUjaxeP/ODBA4wfPx779+/X6P22R4cKPsMwVgB+BCACkAlgEsuyJc2WCQPwJQAzAHIAH7Msq9kdhQkhzyyKR9YuHnn16tUoLi7GvHnzGrelq+TgDsUjMwzzGQAxy7JrGYZZAcCSZdnlzZbxBcCyLHuXYRgnAPEAAliWLW1lk406Ix6ZkK6E4pF1p6vEI3d0WuarAPY2/LwXQGTzBViWTWNZ9m7Dz7kACgDYdrBdQgh5Yo4ePfrUFXttdLTg27MsmwcADX/aqVuYYZi+AAwApKt4fTbDMNcYhrlWWFjYwa4RQghpqs1j+AzDnAbg0MpL/9eehhiGcQSwH8A0lmUVrS3DsuwOADuA+kM67dk+IYQQ9dos+CzLDlf1GsMw+QzDOLIsm9dQ0AtULGcG4BiAf7Es+5fWvSWEEKK1jk7L/AXANABrG/5sce0wwzAGAH4GsI9l2Z803XB8fHwRwzBZbS+pkg2Aog6sr0/UN+1Q39rht99+6yGXy2VyuZzH5XJlnd2f1lDftKPs26NHj3iBgYGJzV5WeRlyRwv+WgD/ZRhmJoAHAF4DAIZhegN4h2XZWQAmARgMwJphmOkN601nWVb1hFgALMt26MQuwzDXVJ2p7mzUN+1Q39onISEhMzg4uOj27dsBwcHByZ3dn9ZQ37Sj7JtcLrdpz7+7Dp20ZVm2mGXZF1mW9Wn4U9zw/LWGYg+WZb9lWZbPsmxYk4faYk8I6RqWL1/u4O3tHeTr6xvo7+8feObMGRN1y2/atMna19c30NfXN9DHxyfo22+/tdCknQMHDpj/85//dACAmpoaJiIiwtPNzS04JCTEPzU1VePpNefPnzf29fUNdHNzC/74448NFIpWTzeq5Ozs3CMvL48HALGxsWYikSjYzc0tWNk3TXz77bcWyv0VHBwccOrUKfWXFrcDXWlLCNGL06dPm5w6dcoiMTExycjIiM3Ly+PV1dWpDKdJT0/nr1+/3vHmzZvJ1tbW8rKyMo6yeLZlypQpZQDKAGDz5s025ubmsgcPHtzesWOH5bJly1yOHTt2X5PtzJs3z3379u1Zw4YNq3r++efDYmNjzSZNmlSu0RtuQiaTYenSpW6nTp1K8/T0lIaGhgZMmDChNDw8vLatdceMGVM+efLkUg6Hg8uXLxtFRUV5ZmRk3GlvH1rTleORd3R2B9SgvmmH+qYFGxubTpnjnJOTw7eyspIZGRmxAODo6CgTiUTS4uJirkgkCk5ISBDY2NgUjhkzxmP9+vU2eXl5fBMTE4W5ubkcAMzNzRX+/v6SzMxMvr+/f6DyweVyw9PS0h4btX/xxRfWU6dOdQOAo0ePWrz11lvFADBjxoySixcvCjUZqWdlZfErKys5w4cPr+JwOHjttddKDh8+bKlunUePHnEHDhzoExAQEDh58mR35YWsf/zxh4m7u3tdYGCgxNDQkB0/frw4NjZWo28r5ubmCg6nvjRXVFRwWsvq0fbvtMuO8BumeD6VqG/aob5px8HBoej3fcmu4pxKY11u18rZtPrFqQEPVb0eGRlZ/umnnzqJRKLgQYMGlb/xxhviiIiISmtra/nGjRsfTJs2zWPevHn5paWlvH/84x9FMpkMNjY2UldX1x4DBw6sGD9+fMnkyZPLRCKRNCUlJQkAPv30U9vz588LfX19Jarazc/PN/Dw8JAAAJ/Ph6mpqTw/P59XUFDAff31171aW+fChQupWVlZfEdHR6nyOX9//+IjR46oPRSzYsUKpwEDBlR+/vlnQj81AAAgAElEQVTneT/88IP5999/bwMADx8+NHB2dm7so4uLi+Ty5cumADBz5kzXP//8U9h8W+PHjxd/8sknjwBg3759FqtWrXIWi8X8gwcP3m2+rIODg1YTBLpswSeEdC5zc3PF7du3k06ePCn8/fffhdOmTfNauXJl9qJFi4rHjRtX/t///tfyvffec4+Pj78D1GfGnDt37m5cXJzxr7/+arZixQrXa9eumWzYsCEXAH799VeTffv22f71119qg/1VRBOzoaGhdcoPjnasp/Y9/vXXX8JDhw7dA4CoqKiyOXPmyNX1AQB27typ8kNSaerUqaVTp04tPXHihOnKlSudhw8fntbWOpqggk9IN6BuJK5PPB4Po0ePrhg9enRFSEhIzf79+60XLVpULJfLkZaWZigQCBRFRUU8Ly8vKQBwOBwMHTq0eujQodWvvPJK+axZs0QbNmzIzcrK4s+ZM0d05MiRe+bm5mqPzzg4OEgyMjIMvLy8pFKpFJWVlVw7Ozt5QkKCQN0IXyQSSfPy8hqz0bOysgwcHBykrS3flPLwS1Nubm6SnJycxsNO2dnZBk5OTlJAsxG+0iuvvFI5a9YsQV5eHs/R0bHDU0S7XMFnGOZlAJsBcAF8w7Ks5ncP1jOGYTIBVKA+NVTW2dP4GIbZBWA0gAKWZYMbnmszAbWT+vUhgLcBKI9d/pNl2eNPsl8N/XAFsA/1V58rAOxgWXbzU7LfHuvbhQsXzAAUPXz40Km4uNiGx+PJAMDJySnHysqqTN/9SUhIEHA4HPTo0aNOLpczFy9edLW1tWUSExOD9u/fL/H19a398MMP82fMmOG/f/9+aXV1dQ2AvOeff74aAK5du2bs7OwsqaurY8aPH+/50Ucf5YSEhNS11W5ERETprl27rIcPH161e/duywEDBlRwOByoGuHL5XImJSXFn2VZxtjYWBAbG+s+fvz4rH379rlERUUxt2/fNvn22295xsbGxStXrnzsFlj9+/ev2LVrl/Vnn32W99///tesvLycCwAvvPBCVWZmpmFKSoqBSCSSHjp0yOrAgQP3gbZH+Ldv3xYEBgbWcTgcXLhwwVgqlTJ2dnay27dvB/L5fImfn9+9mpoag/v373sWFBQIGIb5EcCbLMuqPMyl1KUKPsMwXADbAIwAkA3gKsMwv7Asq/JrXCcYyrLs03KBzh4AW1FfJJRWAPi9SQLqCgDLW1n3SfcLADayLPv5E+5LczIA/2BZ9jrDMEIA8QzD/AZgOjp/vz3Wt+rqanFVVZUhANja2uY7OzvnP8nOlJeXcxctWuRWXl7O5XK5rEgkqtq7d29Wfn4+76effgo8d+7c3draWtu+fftWfPvtt9WRkZEG7777rmdhYSErEAhYKysraUxMzIPTp0+b3L5922TNmjVOa9ascQKAkydP3hWJRK2OvhcvXlw0YcIEDzc3t2Bzc3P5jz/+2Gp2lxKHw2H9/PxSeTyeYtu2bSazZs3yXbp0qfmgQYPkr7/+eq6dnV1Jbm6u28CBA2uar7t27drcCRMmeAYGBgYMGDCg0tHRsfHcwfr16x+8/PLLvnK5HJMnTy7q3bt3mzN0AOD777+3/PHHH615PB5raGio2L9///38/Hx7gUBQo1AouACQnZ3tYmdnly+TybgASgDMRH0MvVodikd+2jAMMwDAhyzLjmz4/X0AYFn2007tWIOGEX7vp6jgg2EYEYCjTUbSqQCGNInL+INlWb+noF8fAqh8Cgr+YxiGOYL6D6eteAr2W1Nnz56tDgsLy66srDTlcDjyJ13wVZHL5Zzk5GQ/Nze3B+np6d6hoaEJHA4H5eXlJrm5uU7+/v4tTlJ2Rt8KCgpsLSwsymxsbEqGDh3qfeLEiXRDQ8MnXjDr6ur49+/f93B0dMzLz8+39/X1vXfz5s3Q0NDQhMTERJuwsLA30KTuqdPVpmU6A2j6dSm74bmnBQvgV4Zh4hmGmd3ZnVGhXQmoT9gChmFuMQyzi2EYtdPlnoSGD6WeAC7jKdtvDMOIpFKpgVAorASAoqIiu8TExMD09HSRVCrldkafWJbF7du3AxMSEkKFQmG5kZFRHZfLlSuPgRsYGEikUmmnZBA375uZmVkVAOTm5jonJiYG7t69u66z4pGzsrJcXVxcGu+9KJPJeE33G9pR57pawW/tlPrT9BVmIMuyvQC8AmA+wzCDO7tDz5AvAXgBCAOQB2B9Z3aGYRhTAAcBLGFZtt0X5uiTsm9mZmZiHo+nsLe3LwgJCUkMDg5O4vP50gcPHrh2Ur8QHBycFBIScqu6utqkurrasJXFOuX/a/O+VVVVGbq6uub06NHjdlBQULJMJuPm5ORofLWsrojFYnMejycTCoXVyudUHJXRaL91tYKfDaDpP2YXALmd1JcWGm4AA5ZlC1AfKNe3c3vUqvyGQxLKSOtWE1CfNJZl81mWlTdEa8egE/cdwzB81Bf7AyzLHmp4+qnYb037ZmRkVA0ABgYGMoZhwDAM7OzsCqurq9XGG+gbj8eTm5qaVlRWVprI5XKu8qIoiURiwOfz25wV8yT6Vlpaai4QCKQMw4DD4bA2NjbFnbHfKioqTMvLyy0SEhJ6ZGZmelZWVgofPHjg2nS/oR11rqsV/KsAfBiG8WhI6YxCfaJnp2MYxqThJB8YhjEB8BKA253bq1YpE1ABFQmonUFZTBuMQyftO6Z+YvZOAMksy25o8lKn7zdVfaurq2ucaigWiy0MDQ1bnHzUN4lEwms4wQi5XM5UVFSYGRkZ1ZqYmFQUFxdbAkBRUZG1ubm52lufPsm+Kfcby7IoLS3tlP3m7u6eExYWdis0NDRRJBLdNzU1rfD29s5out/Qjn9vXWqWDsuyMoZhFgA4hfppmbtYltVJBoUO2AP4ueFCDh6A71iWPdmZHWIY5nsAQwDYMAyTDWAVVCSgPgX9GsIwTBjqv7pmApjzpPvVYCCANwEkMgyjDAH8J56C/da8b7/99puTWCyWisViq5qaGiOg/ji5SCTqSOy4ViQSCT8zM9Oj4XAEY2FhIbaysiozMjKquX//vldeXp6zoaFhtb29/ROf0KCqb8nJyb4ymYwHgDEyMqrujP2miqura/b9+/e9CgoKDABYo/6Dvk1dapYOIeRvCQkJmaGhoU/NjDCiewkJCTahoaEiTZfvaod0CCFPkWctHnnhwoXODg4OIcbGxj01Xaepvn37+p07d84YeDxqefr06a6aRi0/evSI269fP19jY+OeykA4XelSh3QIIU+PZzEeOTIysjQ6OrogICAgWKM3qUbTqOUhQ4b4aBq1bGxszK5evTo3ISHB6Pbt20Yd7UdTNMInhOiFJvHIAPC0xCMDwIsvvljl7u6u8UyhyspKZvTo0Z6+vr6BERERnrW1tQzQMmp5ypQpxW1FLSuZmZkpRo4cWWloaNi+u69ogEb4hHQDp77c5Fr0MEun8cg2ru7VI+cu6TLxyDY2NvL27oPPP//czsjISJGWlpZ0+fJlo4EDBwYC9QW/adSyu7u7RBnM9sEHH9j/9NNP1s231b9//4o9e/boNeSOCj4hRC+etXhkbVy4cMF00aJFBQDQr1+/Gl9f32o1fQAAfPTRR/kfffRRp8RcUMEnpBtQNxLXp2cpHlmbET7Qema+uqhlGuETQrqcpvHIAHDjxg0jFxcXCQCsXr3a3tfXt/bjjz/OmTlzpig+Pj4lLy+Pl52dzR80aNATjUfWxL59+ywuX75ssm3btsfikQcNGlT57bffWo0ZM6bi6tWrhmlpacYA4O7uLjUxMVH8/vvvJkOHDq06cOCA9fz58wsAGuETQrqgVuKR6/bu3Zt169Ytwf79+23i4+OTLS0tFbGxsRUrVqxwnDt3blF0dLRLfn4+/0nGIzf1zjvvuPz8889WtbW1HHt7+5ApU6YUbdiwIffevXsCMzOzFt8AoqOjC6Kiojx8fX0Dg4KCqnv06FGlfG379u1ZM2fO9KitrWWGDh1a/tprr2l8DwJnZ+celZWVXKlUypw6dcri+PHjaZrcAL0tdOEVIV0UXXilO6+++qrHl19++dDJyanDd53SpfZeeEUjfEIIacORI0cyOrsPukDz8AkhpJuggk8IId0EFXxCCOkmqOATQkg3QQWfEEK6CSr4hBC9oXjk9scj//zzz2ZBQUEBDXP7A3755RehNn1pDU3LJIToBcUjaxePbGdnJz127Ng9kUgkvXr1qmFERIRvQUHBrY72B6ARPiFETygeWbt45IEDB9YoryIODw+vlUgknJqaGpUflO1BI3xCugFxbJqr9FGVTuOR+Q4m1VYTfSkeWY/xyHv37rUMDAysVn5odhQVfEKIXlA8cos+ANA8PO3atWuGK1eudD558uRdXfWXCj4h3YC6kbg+UTxyvfbGI6enp/MnTpzovXPnzoygoKA2E0I1RQWfEKIXFI+sXTxyUVERd9SoUT4ffvhh9ksvvVSlajlt0ElbQohelJeXc6dOnerh5eUV5OvrG5iSkmK0bt26XGU88vbt2x++/PLLlf37969YsWKFo0QiYaKjo108PDyC/P39A2NjYy23bt36sGk8svLEbWZmJl9Vu4sXLy4qKSnhubm5BW/ZssXh888/z9a0z++8846Lvb19iDIeedmyZU4AoC4euaqqiuvr6xv4ySefODSPR37nnXdE7u7uwSKRqE7TeOTPPvvM7sGDB4K1a9c2vt+cnBydDM4pHpmQLorikXWH4pEJIaSboHhkQgghzxQq+IQQ0k1QwSeEkG6CCj4hhHQTVPAJIaSboIJPCNEbikdufzzy2bNnjZXz7/38/AL37dun0T7QBE3LJIToBcUjaxeP3Lt379rExMQkPp+PrKwsfs+ePQPfeOONUj5f5bVmGqMRPiFELygeWbt4ZKFQqFAW95qaGqa1rB5t0QifkG7g8OHDrgUFBTqNR7azs6uOjIykeGQ9xCOfOXPGZPbs2aLc3FyDr776KkMXo3uACj4hRE8oHrlFHwBoFo88bNiwqnv37t25fv264bRp0zwmTpxYZmxs3OEcHCr4hHQD6kbi+kTxyPXaG4+s1KtXr1pjY2P5tWvXjAYPHlytTf+aooJPCNELikfWLh45JSXFwMvLS8Ln85GWlmaQkZFh6OPjo/IQVntQwSeE6EV5eTl30aJFbuXl5Vwul8uKRKK6vXv3ZinjkePj45MtLS0VsbGxFStWrHCcO3duUXR0tEt+fj5fIBCwVlZW0piYmAdN45HXrFnjBAAnT568q7zva3OLFy8umjBhgoebm1uwubm5/Mcff0zXtM/vvPOOy88//2yljEeeMmVK0YYNG3LVxSNHRUV5+Pr6BgYFBVU3j0eeOXOmR21tLTN06NByTeORf//9d9PRo0c78ng8lsPhsOvXr3/g6Oiok5ROikcmpIuieGTdoXhkQgjpJigemRBCyDOFCj4hhHQTVPAJIaSboIJPCCHdBBV8QgjpJqjgE0L05knFIwPAkiVLnA4fPiwE6i9eCgkJ8Xd3dw9uGmqmiS1btli7u7sHu7u7B2/ZsqXFFbHqpKamGvj4+AQpf3///fcd3NzcgkUiUfDBgwfNNN3Orl27LL29vYM4HE64Mm5ZF2haJiFEL55kPDIAbNq0KVf587Jly1wWLFiQP3v27JLJkye7bd682Wb58uWFbW0jPz+fu27dOqf4+PgkDoeDnj17BkZFRZXa2tq2O3YhPj7e8NChQ1apqal3srKy+CNGjPB99dVXb/N4bb+lsLCwmoMHD957++23Re1tVx0a4RNC9EJVPPKRI0eEI0aMaMy0+fnnn81eeuklL1XxyFKpFMHBwQFHjx4VAsD8+fOdFy5c6Ny8vQkTJoh2795tqVAocOnSJeGMGTNKAOCtt94q/t///qfRN4XDhw+bDx48uNze3l5ua2srHzx4cPmhQ4fM1a1z/vx5Yz8/v8CwsDD/DRs22Cmfj42NtRg/frzYyMiI9ff3l7i7u9f98ccfar/hKPXq1as2NDS0zRiJ9qIRPiHdQFLycteqyjSdxiObmPpWBwasa3c88pgxYyqWLFnilpuby3NycpLt2rXLevr06UX9+/evbi0emc/nY8+ePRmTJk3ykkqlD8+cOWN+48aNZFXt5ufn84RCoVwZKSwSiST5+fkGAPDll19abd682aH5OiKRqPbkyZP3c3Jy+Mq8HwBwdnaW5OTkqM0mnjlzpmjjxo0PIiIiKufMmeOifD4nJ8egf//+lcrfnZycJA8fPjQAUBUeHu5XVVXFbb6ttWvXPoyMjKxQ115HUMEnhOiFunjkSZMmFcfExFjNnz+/+Pr166aHDh3KUBeP3Lt379pJkyYVR0VFeZ85cybZ0NBQZSaMqnhkAJg7d6547ty54nauq/I9FhcXcysqKrgRERGVQP23iTNnzpi31Y/4+PhUlRvVIyr4hHQD6kbi+qQqHnnu3LnFERER3oaGhuyYMWNKlKNxVfHIAHDnzh0joVAob4gdrlHVpoODg6yiooIrlUrB5/ORmZlpYGdnJwXaHuG7uLhI4+LihMrnc3JyDF544QWVI26WZVV+ILi4uChH9ACA3NxcAxcXFykA0AifENKlqItHFolEUnt7e+n69esdT5w4kQYAmZmZ/NbikQFg7969FmKxmHfmzJmUsWPH+gwZMiRZVX49h8NB//79K3bv3m05e/bskl27dlmPHj26FGh7hB8ZGVm2evVq58LCQi4AxMXFmW3cuDEbAMaNGydatGhRwdChQxtz6W1sbOSmpqbyU6dOmY4cObJyz549VsrXJkyYUDplyhTPlStX5mdlZfEzMzMNhwwZUgXQCJ8Q0sWoikdWvh4VFVW8bds2Xnh4eC0ASCQSprV45Ly8PN6qVatcTp8+nert7S2dNWtWwezZs10PHTqUqart9evXZ7/++utea9ascQ4KCqpevHixRqmh9vb28nfffTc3PDw8AADee++9XHt7ezkAJCcnG7u6uraIZN65c2fmrFmzREZGRophw4Y13qS8d+/etZGRkWJfX98gLpeLDRs2ZGkyQweoz99/99133UpKSnjjxo3zCQgIqL5w4cJdjVZWg+KRCeminvZ45KlTp7r17NmzeunSpU9tH5XEYjFnypQpohMnTtzv7L40RfHIhJCnXlBQUICRkZHi66+/7pRzC+1lZWWleNqKvTao4BNCnrg7d+6onFZJ9IcuvCKEkG6CCj4hhHQTVPAJIaSboIJPCCHdBBV8QojeUDyydvHIc+bMcfHw8Ajy9fUNHDFihFdRUVGLq3K1QQWfEKIXTeOR09LSks6ePZvm6ekpUbW8Mh750qVLqWlpaUnXrl1L7t27d7Wq5ZvbtGlTrjKWQBmPnJWVddvc3Fy2efNmG022oYxHvnLlSvK1a9eS161b56S86ra9msYjnzx5Mm3JkiVuMplMo3VHjhxZnpaWdictLS3J29u79oMPPmgRB6ENKviEEL2geGTt45HHjx9frswXGjBgQFVOTo5BG6tohObhE9INLEl+4JpSVavTeGR/E8PqTQFuFI+s53jkPXv22EycOFFl/k97UMEnhOgFxSN3PB55+fLlDlwul33nnXeo4BNCNKNuJK5PFI+sfTzyli1brE+dOmVx/vz5NA5HN0ffqeATQvSC4pG1j0eOjY0127Rpk8P58+dThUKhou29rRkq+IQQvaB4ZO3jkZctW+YmkUg4w4YN8wWAXr16VX733XcPNFpZDYpHJqSLonhk3aF4ZEII0RLFI3cOKviEkCeO4pE7B114RQgh3QQVfEII6Sao4BNCSDdBBZ8QQroJKviEEL2heGTt4pEXL17spNxnAwcO9MnMzFSb56MpmodPSBfV2fPwT58+bRIdHe166dKlVCMjIzYvL49XV1fHiESiFhcvAfXxyEOGDPG7efNmsrW1tbysrIyTl5fH8/f3VxmprMqoUaM8IyMjS2bPnl0yefJkt9DQ0Jrly5cXtrVefn4+Nzw8PDA+Pj6Jw+GgZ8+egTdu3EiytbVt9are5lJTUw1Gjx7tc/fu3Tvx8fGGkydP9rx582ZyVlYWf8SIEb4ZGRm3Nbn4SiwWc6ysrBQAsGbNGrukpCTD1i68au88fBrhE0L0guKRtY9HVhZ7AKiqquKoC3BrD5qHT0g38G5sgmvaowqdxiP7Ogir/zMxlOKR9RSPvHDhQueffvrJWigUyuPi4jRK12wLFXxCiF5QPHLH4pG3bNmSs2XLlpz333/f4T//+Y/dxo0bc9tapy1U8AnpBtSNxPWJ4pG1j0dWmjFjhjgiIsJHFwWfjuETQvQiISFBkJiYKFD+rioe+e233y4C6uORL1y40HjYSVU8cnR0tJu6m3o3jUcGgObxyCkpKUnNHydPnrwP1Mcjx8XFmRUWFnILCwu5cXFxZpGRkWVAfTzy2bNnHzss1jQeGQCaxyMfOnTIqqamhklJSTFoHo/cWj+Uxb7pfvvpp58svLy8VH7AtQeN8AkhekHxyNrHI0dHR7vcv3/fkGEY1sXFRbJz586sttdqG03LJKSL6uxpmW2heOSOo3hkQshTj+KROwcVfELIE0fxyJ2DTtoSQkg3QQWfEEK6CSr4hBDSTVDBJ4SQboIKPiFEb57FeOTnn3/eRygUhg0dOtRb03WaMjY27qn8Wduo5RMnTpgGBgYG8Hi8cOUFZLpAs3QIIXpx+vRpk1OnTlkkJiYmNY1HVrV8eno6f/369Y7N45E1bW/Tpk2N0QPLli1zWbBgQb4yHnnz5s02msQjA0B0dPSjqqoqTkxMjK2mbbcmPz+fu27dOqemUctRUVGlmkQte3p6Snbv3p25du1a+470oTka4RNC9OJZjEcGgFdffbXCzMxM0faS9VJSUgzCwsL8g4ODAxYvXuykfF6bqGUlPz8/Sb9+/Wo4HN2WaBrhE9IdHJ7vioIkncYjwy6wGpHbulQ8sja7Yd68eW6zZs0qXLBgQfGnn37a+K1AXdRyRESEZ3p6umHzbS1YsCB/wYIFxdr0QxNU8AkhevEsxiNr4/r166YnTpxIB4A5c+YUf/TRRy5q+gEAOHbsWKdctUsFn5DuQM1IXJ+etXhkbd8nh8NpUd3VRS3TCJ8Q0qUkJCQIOBwOevToUQeojkc+ceJEGlAfj5ydnc0fNGhQNaA6Hnns2LE+Q4YMSbaxsWn15GfTeOTZs2eXNI9H1naEP3/+fOd+/fpVTZ06tbTp87169aqMiYmxmjdvnjgmJqZxJk5kZGTZ6tWrnQsLC7kAEBcXZ7Zx48ZsoPNG+HTSlhCiF+Xl5dypU6d6eHl5Bfn6+gampKQYrVu3rnEmTVRUVLGjo6OkeTyyh4dHkL+/f2BsbKzl1q1bHyrjkffu3ZsZEhJSp4xHVtf2+vXrs7ds2eLg5uYWXFJSwtM0HhmovznJm2++6Xnp0iUze3v7kIMHD5oBQFJSkpGTk1OLeOTt27c/2LFjh11wcHBAWVlZY05/06jl8PDwgKZRy22Ji4sztre3Dzl+/Ljl0qVL3b29vYM07b86FI9MSBdF8ci6NWjQIJ8LFy7c7ex+NEXxyISQp96zFo8MAE9bsdcGFXxCyBNH8cidg47hE0JIN0EFnxBCugkq+IQQ0k1QwSeEkG6CCj4hRG8oHlm7eOQPP/zQXnn9woABA3zT0tIMtOlLc1TwCSF60TQeOS0tLens2bNpnp6eElXLK+ORL126lJqWlpZ07dq15N69e1dr2t6mTZtyIyMjK4C/45GzsrJum5ubyzZv3myj6Xaio6Mfff311xmaLq+KMh75ypUrydeuXUtet26dk/Kq27aEh4dX37x5MzktLS0pMjKyZOnSpS4d7Q9ABZ8QoicUj6x9PPKYMWMqhEKhAgAGDRpUmZeXp5MRPs3DJ6Qb+ODPD1zvldzTaTyyt6V39UcDP6J4ZD3HI3/99de2w4cPL9Omb81RwSeE6AXFI3c8Hnn79u1WCQkJxl9//XWqLvpKBZ+QbkDdSFyfKB5Z+3jkw4cPCz///HPH8+fPpyoPi3UUFXxCiF5QPLL28ch//vmn0cKFC92PHz9+19nZWaZNf1tDJ20JIXpB8cjaxyO/++67rtXV1dzXXnvNy9/fP3DYsGFaTRFtjuKRCemiKB5ZtygemRBCtEDxyJ2DCj4h5ImjeOTOQcfwCSGkm6CCTwgh3QQVfEII6Sao4BNCSDdBBZ8QojcUj6xdPPJnn31mq9xn4eHhfvHx8S2uytUGzcMnpIvq7Hn4p0+fNomOjna9dOlSqpGREZuXl8erq6tjRCJRi4uXgPp45CFDhvjdvHkz2draWl5WVsbJy8vj+fv7q4xUVmXUqFGekZGRJbNnzy6ZPHmyW2hoaM3y5csLNVn3yJEjwqqqKk5MTIzt2bNn77W3bWNj457V1dU38vPzueHh4YHx8fFJHA4HPXv2DLxx40aSra1tmxdficVijpWVlQIADhw4YP7VV1/ZnT9/vsW00PbOw6cRPiFELygeWft4ZGWxB4DKykquMnSto2gePiHdQO4//8+17u5dncYjC3x8qp0++ZjikfUUj/zpp5/abt++3V4qlXJ+++03SsskhDy9KB65Y/HI77//fuH7779f+NVXX1mtWrXK8dChQ5kd7SsVfEK6AXUjcX2ieGTt45GV3n77bfG7777rpm3fmqKCTwjRC4pH1j4eOTExUaDcbz/++KO5u7t7nTZ9bo4KPiFEL8rLy7mLFi1yKy8v53K5XFYkEtXt3bs3S/l6VFRU8bZt23jN45Hz8/P5AoGAtbKyksbExDxQxiOfPn061dvbW6qMR1Z3iGP9+vXZr7/+uteaNWucg4KCqtsbj3z//n3Dmpoarr29fcj27dszJ0yYUJ6UlGQ0bty40ubLb9++/UFUVJTn9u3b7ceOHVuifL5pPDIAtCceecOGDXbnz5834/F4rLm5uWzPnj0dvqk6QNMyCemyOntaZlsoHrnjKB6ZECuaFFYAACAASURBVPLUo3jkzkEFnxDyxFE8cuegC68IIaSboIJPCCHdBBV8QgjpJqjgE0JIN0EFnxCiN89iPLK2kcYAkJqaauDj4xOk/P399993cHNzCxaJRMEHDx4003Q7u3btsvT29g7icDjh586d01kGEs3SIYToxenTp01OnTplkZiYmNQ0HlnV8unp6fz169c7No9H1rS9TZs25Sp/XrZsmcuCBQvylfHImzdvttEkHjk/P5+7bt06p6aRxlFRUaWaRBo3Fx8fb3jo0CGr1NTUO1lZWfwRI0b4vvrqq7d5vLbfUlhYWM3Bgwfvvf3226L2tqsOjfAJIXqhq3jkO3fuCAIDAwOUyycmJgqCgoICmreni3hkbSKNz58/b+zn5xcYFhbmv2HDBjvl87GxsRbjx48XGxkZsf7+/hJ3d/e6P/74Q+03HKVevXrVhoaG6iROoSka4RPSDfy+L9lVnFOp03hkK2fT6henBug9HjkoKKhOKBTKL168aPTcc8/VfP311zaTJ08uVtVuR+KR1UUaqzJz5kzRxo0bH0RERFTOmTPHRfl8Tk6OQf/+/SuVvzs5OUkePnxoAKAqPDzcr6qqitt8W2vXrn0YGRlZoa69jqCCTwjRC13GI0+fPr0oJibGpm/fvg+PHDliefXqVZUXbnUkHlldpHFriouLuRUVFdyIiIhKoP7bxJkzZ8zb6kd8fLxO8u3biwo+Id2AupG4PukqHnnatGkl69atc/rhhx8qevToUe3g4KDymHpH4pHVRRq3hmVZlR8ILi4uyhE9ACA3N9fAxcVFCtQHtNEInxDSZegyHtnY2Jh94YUXypYtW+a2devWTHXtdiQeWV2k8bhx40SLFi0qGDp0aLVyeRsbG7mpqan81KlTpiNHjqzcs2ePlfK1CRMmlE6ZMsVz5cqV+VlZWfzMzEzDIUOGVAE0wieEdDG6ikdWLj916lTxiRMnLMePH1/eVtvaxiOrizROTk42dnV1bXED9p07d2bOmjVLZGRkpBg2bFhj33r37l0bGRkp9vX1DeJyudiwYUOWJjN0AGDfvn0W7777rltJSQlv3LhxPgEBAdW6CG+jeGRCuqiuFo+8cuVK+7KyMu7mzZtz215at8RiMWfKlCmiEydOaH1XLH2geGRCyFOvvfHII0aM8MrKyhLExcWl6btvrbGyslI8bcVeG1TwCSFPXHvjkX/77bd0ffWlO6ELrwghpJuggk8IId0EFXxCCOkmqOATQkg3QQWfEKI3FI+sXTzynDlzXDw8PIJ8fX0DR4wY4VVUVNTiqlxtUMEnhOhF03jktLS0pLNnz6Z5enpKVC2vjEe+dOlSalpaWtK1a9eSe/fuXa1q+eY2bdqUq4wlUMYjZ2Vl3TY3N5dt3rzZRpNtKOORr1y5knzt2rXkdevWOSmvum2vpvHIJ0+eTFuyZImbTCbTaN2RI0eWp6Wl3UlLS0vy9vau/eCDD1rEQWiDCj4hRC8oHln7eOTx48eXK/OFBgwYUJWTk2PQxioaoXn4hHQDp77c5Fr0MEun8cg2ru7VI+cuoXhkPccj79mzx2bixIkq83/agwo+IUQvKB654/HIy5cvd+Byuew777xDBZ8Qohl1I3F9onhk7eORt2zZYn3q1CmL8+fPp3E4ujn6TgWfEKIXFI+sfTxybGys2aZNmxzOnz+fKhQKFeqWbQ8q+IQQvaB4ZO3jkZctW+YmkUg4w4YN8wWAXr16VX733XcP2lqvLRSPTEgXRfHIukPxyIQQoiWKR+4cVPAJIU8cxSN3DrrwihBCugkq+IQQ0k1QwSeEkG6CCj4hhHQTVPAJIXpD8cjaxSMvXrzYSbnPBg4c6JOZmak2z0dTNA+fkC6qs+fhnz592iQ6Otr10qVLqUZGRmxeXh6vrq6OEYlELS5eAurjkYcMGeJ38+bNZGtra3lZWRknLy+P5+/vrzJSWZVRo0Z5RkZGlsyePbtk8uTJbqGhoTXLly8vbGu9/Px8bnh4eGB8fHwSh8NBz549A2/cuJFka2urMsqhqdTUVIPRo0f73L179058fLzh5MmTPW/evJmclZXFHzFihG9GRsZtTS6+EovFHCsrKwUArFmzxi4pKcmwtQuv2jsPn0b4hBC9oHhk7eORlcUeAKqqqjjqAtzag+bhE9INiGPTXKWPqnQaj8x3MKm2muhL8ch6ikdeuHCh808//WQtFArlcXFxGqVrtoVG+IQQvVDGI2/dujXL1tZWNm3aNK8vvvjCmsPhQBmPXFRUxL1+/brpa6+9VqaMR/7uu+/SfXx8alesWOG6bNkyJwBQxiPLZDIcOXLEcubMmSoLflvxyCkpKUnNHydPnryvZl2V77G1eGRN+hEfH5/aWj+aZuFv2bIl59GjR7cmTpxY/J///Meuxca0QCN8QroBdSNxfaJ4ZO3jkZVmzJghjoiI8Nm4cWOHM4So4BNC9ILikbWPR05MTBQo99tPP/1k4eXlVaNueU1RwSeE6AXFI2sfjxwdHe1y//59Q4ZhWBcXF8nOnTuz2l6rbTQtk5AuqrOnZbaF4pE7juKRCSFPPYpH7hxU8AkhTxzFI3cOmpZJCCHdBBV8QgjpJqjgE0JIN0EFnxBCugkq+IQQvXkW45Gff/55H6FQGDZ06FBvTddpytjYuKfyZ22jlk+cOGEaGBgYwOPxwnfv3m2pTT9aQ7N0CCF6cfr0aZNTp05ZJCYmJjWNR1a1fHp6On/9+vWOzeORNW1v06ZNjfPzly1b5rJgwYJ8ZTzy5s2bbTSJRwaA6OjoR1VVVZyYmBhbTdtuTX5+PnfdunVOTaOWo6KiSjWJWvb09JTs3r07c+3atfYd6UNzNMInhOjFsxiPDACvvvpqhZmZmaLtJeulpKQYhIWF+QcHBwcsXrzYSfm8NlHLSn5+fpJ+/frVcDi6LdE0wiekGzh8+LBrQUGBTuOR7ezsqiMjI7tUPLI2+2HevHlus2bNKlywYEHxp59+2vitQF3UckREhGd6erph820tWLAgf8GCBSrfW0dRwSeE6IUyHvnkyZPC33//XTht2jSvlStXZi9atKhYGY88f/784uvXr5seOnQoQxmPHBcXZ/zrr7+arVixwvXatWsmGzZsyFXGI/ft2/fhkSNHLK9evarywq224pHVhadp4/r166YnTpxIB4A5c+YUf/TRRy5q+gEAOHbsWKdctUsFn5BuQN1IXJ+etXhkbd8nh8NpUd3VRS3TCJ8Q0qU8i/HI6syfP9+5X79+VVOnTi1t+nyvXr0qY2JirObNmyeOiYlpnImjLmq5s0b4dNKWEKIX5eXl3KlTp3p4eXkF+fr6BqakpBitW7eucSZNVFRUsaOjo6R5PLKHh0eQv79/YGxsrOXWrVsbv5lMnTpVDACaxiNv2bLFwc3NLbikpISnaTwyUH9zkjfffNPz0qVLZvb29iEHDx40A4CkpCQjJyenFvHI27dvf7Bjxw674ODggLKyssabmjSNWg4PDw9oGrXclri4OGN7e/uQ48ePWy5dutTd29s7SNP+q/P/27v3uKbuPP/jH3LBEAWU+0WScIuQIEq1KsWtYm2rIlMq2lLcpVa6Qi9qde2j1q3UqR3WuuijrquWaaWV4lgt3upYZVpLR7HKiLUqxRhQbnIVASGES7j8/nDij0UIOSGnlJz38/GYP4oJ+ZJ5PD755uScV5BHBrBQyCOb18yZM/1zcnIKh+OxB4I8MgD87o20PDIR0e9t2JsCAx8AfnPIIw8PHMMHAOAIDHwAAI7AwAcA4AgMfAAAjsDABwDWII9sWh5506ZNrvrrF0JDQ+VqtdralLX0hYEPAKzonUdWq9UF2dnZah8fn46Bbq/PI1+4cOGmWq0uyMvLuzF16lStsY/38ccfV0ZFRTUT/f88cmlpab69vX3njh07nIz9PevWratOTU0tNvb2A9Hnkf/xj3/cyMvLu/HRRx956K+6HcyUKVO0v/zyyw21Wl0QFRXVsGbNmvFDXQ8RBj4AsAR5ZNPzyJGRkc22trbdREQzZ87UVFVVmWWHj/PwATig4MY7Xi0atVnzyKPHyLWKwI+QR2Y5j5yamuo8d+7c+6asrS8MfABgBfLIQ88j79692+Hq1avi1NTUm+ZYKwY+AAcY2omzCXlk0/PIx44ds01JSXE/d+7cTf1hsaHCwAcAViCPbHoe+fz58zYrV66Ufvvtt4Wenp6dpqy3P/jQFgBYgTyy6Xnkt99+20ur1fKXLFniGxAQoJgzZ45Jp4j2hTwygIVCHtm8kEcGADAB8sjDAwMfAH5zyCMPDxzDBwDgCAx8AACOwMAHAOAIDHwAAI7AwAcA1iCPbFoeeevWrc7652zKlCkTLl++/MhVuabAefgAFmq4z8P//vvvR69bt87rwoULN21sbHqqqqoE7e3tVjKZ7JGLl4ge5JFnz5494Zdffrnh6OjYdf/+fV5VVZUgICBgwKTyQBYsWOATFRXVsGLFiobY2FjJpEmTWt955527xtz3+PHjti0tLbxPP/3UOTs7u4jpY4vF4hCtVnulpqaGP2XKFMXly5cLeDwehYSEKK5cuVLg7Ow86MVX9fX1PAcHh24iov3799t/8sknLufOnXvktFCm5+Fjhw8ArEAe2fQ8sn7YExFpNBq+Pro2VDgPH4AD3rpR5qVqaTNrHjlgtEj7caAEeWSW8sj/9V//5bx7925XnU7H++6771DLBIDfL+SRh5ZHfvfdd+++++67dz/55BOH999/3/3IkSMlQ10rBj4ABxjaibMJeWTT88h6//7v/17/9ttvS0xdW28Y+ADACuSRTc8jX79+fZT+eTt48KC9VCptN2XNfWHgAwArmpqa+KtWrZI0NTXx+Xx+j0wma9+3b1+p/t9jYmLu7dq1S9A3j1xTUyMcNWpUj4ODg+7TTz8t098+Li6u/tSpU+OMzSO/+OKLvh9++KGnUqnUMs0j3759W9Ta2sp3dXUN3r17d0l0dHRTQUGBzfPPP9/Y9/a7d+8ui4mJ8dm9e7frH/7whwb9z3vnkYmImOSRt2/f7nLu3Dk7gUDQY29v3/nFF18M+UvViXBaJoDFGu7TMgeDPPLQIY8MAL97yCMPDwx8APjNIY88PHDhFQAAR2DgAwBwBAY+AABHYOADAHAEBj4AsOa3yiPv37/ffsOGDW5ERK2trVYRERE+EokkKDg4OODmzZvWxq733LlzYrlcrpBIJEHLli3z6u42uqFGRESenp4Tq6qqBEREmZmZdjKZLEgikQTp12aMK1euiCZPnhxgbW39WFJSkiujBQwCZ+kAACu+//770VlZWWOvX79e0DuPPNDtb926Jdy2bZt73zyyMY+1dOnS+0R0n4hox44dTvb29p1lZWX5f/7zn8etXbt2vDHtGiKi119/Xbp79+7SOXPmtMyePds/MzPT7oUXXhj0Qq++Ojs7ac2aNZKsrCy1j4+PbtKkSYHR0dGN+ovMDHFxcencsWNHWWZm5jimjzsY7PABgBXmyiOXlJQIAwICFPr/8fn8KWq1+v/s2v/nf/7HMS4uTkJE9Ne//nXs8uXL7xERvfLKKw0//fSTrTE79dLSUqFGo+HNnTu3hcfj0dKlS+8dO3bM4NCtrq7mh4WF+QcGBipiY2Ol+gtZf/zxx9FSqbRdoVB0iESinkWLFtVnZmYa9W7F09Ozc9asWVqhUGj2q2KxwwfggLczr3qpq5vNmkeWu9lq/3vxJNbzyDKZTKdSqQqIHiSDz507ZyuXywf8UpSamhprb2/vDiIioVBIY8aM6aqpqRHU1tbyX3zxRd/+7pOTk3OztLRU6O7u/vDLWaRSaUdVVZXQ0HOwfv16j9DQUE1KSkrVV199ZX/gwAEnIqLy8nJrfQeIiGj8+PEdubm5Y4iI4uPjvc6fP2/b93ctWrSoPjk5udrQ4w0VBj4AsMKceWQior/97W+j09PTnS9evKgy9LgD5ZEnTZrUrn/hYHA/g3/jxYsXbY8cOVJERBQTE3M/ISGhy9AaiIj27t07LOVSIgx8AE4wtBNnk7nyyKWlpcKEhATZ8ePHi+zt7Q0en3Fzc+soLi629vX11el0OtJoNHwXF5euq1evjjK0w5fJZLreO/rS0lJrNze3fr+OsTce79Ej4xKJpKOiouLhYac7d+5Ye3h46IiwwwcAC2SuPHJ7e7vVokWLfDZv3lwRHBw8aCY4IiKiMS0tzXHu3Lktn3/++bjQ0NBmHo9Hg+3wnZycukaPHt195syZ0eHh4S379+93fOONN2qJiJKTk52JiDZs2PB/vhd3xowZzWlpaY5bt26tOnTokF1TUxOfiGjWrFktJSUlIpVKZS2TyXRHjhxx2L9//20i7PABwAKZK4/8/fffj87Pzx/94Ycfenz44YceRESnT58uHOjL0FevXl0XHR3tLZFIguzt7bsOHjxodIdn9+7dpfHx8d5tbW1W4eHhTUuWLLlPRKRSqWzCwsI0fW+/ZcuWyujoaB+FQhEYGhqqcXd3f/jZwbZt28rmzZsn7+rqotjY2LqpU6cOeoYOEVFZWZng8ccfV7S0tPCtrKx6UlNTXW/cuJHf+3tuTYU8MoCFsrQ88nAKDw/3O3Xq1C2RSPS7GpjIIwPA7x7TPPJwy87OLhruNZgDBj4A/OaY5pHBPHDhFQAAR2DgAwBwBAY+AABHYOADAHAEBj4AsAZ5ZOZ55D179jjon4OQkJCACxcu2DBahAE4SwcAWIE8sml5ZD8/v/bz58/fdHZ27jp06JBdQkKC9Nq1awb7QcbCDh8AWIE8sml55KeffrrF2dm5i4goPDy8pbq62uh3KIPBDh+AC4694UW1BWbNI5OLQktRu5BHZjGPvHPnTqfw8PD7htbABAY+ALACeeRH10BkfDztxIkTthkZGU4//fSTWQ7nEGHgA3CDgZ04m5BHfoBpHjk3N9fm9ddfl548ebLQzc2ta7A1GAsDHwBYgTyyaXnkwsJC6yVLlvimpaUVG/P3MoGBDwCsQB7ZtDzye++9597Y2ChYuXKllIhIIBD05Ofnm6U9hDwygIVCHtl8kEcGADAR8sjDAwMfAH5zyCMPD1x4BQDAERj4AAAcgYEPAMARGPgAAByBgQ8ArEEemXkeOSMjY6z++QoKCgrMysoaw2gRBuAsHQBgBfLIpuWRIyMjm2JjYxt5PB7l5ubaxMTE+BQXF//KdA39wQ4fAFiBPLJpeWR7e/tufZ+nubmZN1jAjQns8AE4YOP5jV5FDUVmzSP7jfPTbg7bjDwyC3nk9PT0se+//75nfX298PDhw4WG1sAEBj4AsAJ55EfXQGRcHjkuLq4xLi6u8dSpU2OSkpI8586dqx7sPsbAwAfgAEM7cTYhj/wA0zyy3vz58zWvvvrqqKqqKoG7u3vnYGsZDAY+ALACeWTT8sj5+fmjFApFO4/Ho5ycHLFOp7NydXUd8rAnwsAHAJYgj2xaHvnAgQPjDh486CgQCHpEIlH3l19+ebu/dxGmQB4ZwEIhj2w+yCMDAJgIeeThgYEPAL855JGHBy68AgDgCAx8AACOwMAHAOAIDHwAAI7AwAcA1oy0PPLKlSs93dzcgsVicYix9+lt2rRpE86ePSsmMj21XF1dzZ8+fbpcLBaH6INw5oKzdACAFSMxjxwVFdW4bt262sDAwCCj/kgDTE0ti8Xing8++KDy6tWrNvn5+TZDXUdv2OEDACtGWh6ZiOipp55qkUqlg/Zz9DQajdXChQt95HK5IiIiwqetrc2KyLTUsp6dnV33s88+qxGJRMy+fcUI2OEDcEDlhv/0ai8sNGseeZS/v9Yj+U8Wk0d2cnLqYvocpKSkuNjY2HSr1eqC3Nxcm7CwMAXRg4E/UGp548aNrl9//bVj3981Y8aM5i+++ILVC9Ew8AGAFSMtj2yKnJycMatWraolIpo+fXqrXC7XGlgDERFt3ry5ZvPmzTXmXIexMPABOMDQTpxNIymPbMoOn6j/Zr6h1DJ2+ABgcUZaHtmQ9PT0sbm5uaN37dpV0fvnM2fO1GRkZDhERkY2X7p0SaRWq8VERFKpVDdQahk7fACwOCMxj5yYmDj+6NGjDm1tbTxXV9fgpUuX1m3fvr2yqKholJ2d3SPvANatW1cbExPjLZfLFUqlUjtx4sQW/b8NlFo2hqen50SNRsPX6XRWWVlZY7/99lu1MV+APhjkkQEsFPLI5vPcc89579mzp9zDw8MsX0RiLsgjA8Dv3kjLIx8/frx4uNdgDhj4APCbQx55eODCKwAAjsDABwDgCAx8AACOwMAHAOAIDHwAYA3yyMzzyEePHrVTKpWB/zy3P/Cbb76xNWUt/cFZOgDACuSRTcsju7i46E6ePFkkk8l0ly5dEkVERMhra2uvDXU9RNjhAwBLkEc2LY8cFhbWqr+KeMqUKW0dHR281tbWAV8omcAOH4ADzqTf8Kqv0Jg1j+zgOUb7VFwg8sgs5pH37ds3TqFQaPUvmkOFgQ8ArEAe+ZE1EJHx8bS8vDxRUlKS5+nTpwvNtV4MfAAOMLQTZxPyyA8wzSPfunVLuHjxYr+9e/cWK5XKQQuhxsLABwBWII9sWh65rq6Ov2DBAv9NmzbdeeaZZ1oGup0p8KEtALCiqamJHxcX5+3r66uUy+UKlUpl89FHH1Xq/z0mJuaeu7t7R988sre3tzIgIECRmZk57n//93/Le+eR9R/clpSUCAd63NWrV9c1NDQIJBJJ0M6dO91SUlLuGLvmxMTE8a6ursH6PPLatWs9iIgM5ZFbWlr4crlckZyc7NY3j5yYmCiTSqVBMpms3dg88tatW13KyspGbdmy5eHfW1FRYZbNOfLIABYKeWTzQR4ZAMBEyCMPDwx8APjNIY88PHAMHwCAIzDwAQA4AgMfAIAjMPABADgCAx8AWIM8MvM8cnZ2tlh//v2ECRMU6enpRj0HxsBZOgDACuSRTcsjT506te369esFQqGQSktLhSEhIYqXXnqpUZ+fGArs8AGAFcgjm5ZHtrW17dYP99bWVqv+Wj2mwg4fgAOy9nzsVVdeatY8spOXVPvsa28hj8xCHvmHH34YvWLFClllZaX1J598UmyO3T0RBj4AsAR55EfWQETG5ZHnzJnTUlRU9OvPP/8sevnll70XL158XywWD7mDg4EPwAGGduJsQh75AaZ5ZL3HHnusTSwWd+Xl5dk8+eSTWlPW1xsGPgCwAnlk0/LIKpXK2tfXt0MoFJJarbYuLi4W+fv7D3gIiwkMfABgRVNTE3/VqlWSpqYmPp/P75HJZO379u0r1f97TEzMvV27dgn65pFramqEo0aN6nFwcNB9+umnZb3zyB9++KEHEdHp06cL9d/72tfq1avroqOjvSUSSZC9vX3XwYMHbxm75sTExPFHjx510OeRly5dWrd9+/ZKQ3nkmJgYb7lcrlAqldq+eeT4+HjvtrY2q/Dw8CZj88hnzpwZs3DhQneBQNDD4/F6tm3bVubu7m6WSifyyAAWCnlk80EeGQDARMgjDw8MfAD4zSGPPDxw4RUAAEdg4AMAcAQGPgAAR2DgAwBwBAY+ALCGSR75zJkzo4ODgwMCAgIUPj4+yrVr13oY+zjmyiObmjTW8/T0nKgvfGZmZtrJZLIgiUQSpF+bMa5cuSKaPHlygLW19WNJSUmujBYwCJylAwCsYJpHjo+P9z5w4MCt0NDQ1s7OTrp69arI2McyVx7Z1KRxX52dnbRmzRpJVlaW2sfHRzdp0qTA6OjoRv1FZoa4uLh07tixoywzM9OouiYT2OEDACsGyiOfPXv24Rd8yOVyhZWV1RQiovr6eoFEItERPWjw6IfjsmXLvNatW+dORHT48GG7qVOnTujq+r8XvZojj2xK0ri6upofFhbmHxgYqIiNjZXqL2T98ccfR0ul0naFQtEhEol6Fi1aVJ+ZmWnUF5l4enp2zpo1SysUCs1+VSx2+AAcUJ+p9tJVt5g1jyx0G611WCxnnEd+8skntfqmTUJCwvjw8PAmIqIVK1bUBAYGBk2fPr35mWeeuf/GG2/cE4vFPTt37qwICQkJnDVrluY//uM/JCdPnizk8/kDrsvUPLKhpPFA1q9f7xEaGqpJSUmp+uqrr+wPHDjgRERUXl5u7enp+bB/M378+I7c3NwxRETx8fFe58+ft+37uxYtWlSfnJxcbejxhgoDHwBYYSiPTET02Wefjbt27Zr43LlzaiKilJSUqldeeaX+r3/9q92hQ4ccv/76a8d//OMfN21tbbv37NlTMn/+/IA//vGP5Uql0mBAzdQ8sqGk8UAuXrxoe+TIkSIiopiYmPsJCQldhtZARLR3795hu7oYAx+AAwztxNk0UB45Ly9PlJyc7JGTk3NTIPj/Y0ipVLYrlcq7a9euvevo6Di5urqa7+bm1vXLL7/Y2Nvbd1ZWVg76TSCm5pENJY0N4fEePTIukUg6KioqHn5YfOfOHWsPDw8dEXb4AGCBBsoj37t3jx8bG+vz+eefF/eOkX311Vf2L7zwwn0ej0fXr18X8fn8Hicnpy61Wm29a9cut8uXLxfMmzfP/4cffmicM2dOy0CPa2oe2cnJqWugpHFycrIzEdGGDRvu9r7PjBkzmtPS0hy3bt1adejQIbumpiY+EdGsWbNaSkpKRCqVylomk+mOHDnisH///ttE2OEDgAUaKI/8l7/8ZWxlZeWohIQEmf62KpWqICMjw3H9+vVeIpGoWyAQ9Hz22WfFPB6Pli1bJvvTn/5ULpPJdJ9++mlJfHy87Jdffrkx0DdADSWPPFDSWKVS2YSFhWn63n7Lli2V0dHRPgqFIjA0NFTj7u7+8LODbdu2lc2bN0/e1dVFsbGxdVOnTh30DB0iorKyMsHjjz+uaGlp4VtZWfWkpqa63rhxI9/BwYHZOaL9QB4ZwEL93vPII0l4eLjfqVOnbolEot/VwEQeGQDAzLKzs4uGew3mgPPwAQA4AgMfeok+VAAAH+BJREFUAIAjMPABADgCAx8AgCMw8AEAOAIDHwBYgzwy8zzynj17HORyuUIulytCQkICLly4YMNoEQbgtEwAYAXyyKblkf38/NrPnz9/09nZuevQoUN2CQkJ0mvXrqmYrqE/2OEDACuQRzYtj/z000+3ODs7dxERhYeHt1RXVxv9DmUw2OEDcMCxY8e8amtrzZpHdnFx0UZFRSGPzGIeeefOnU7h4eH3Da2BCQx8AGAF8siProHI+HjaiRMnbDMyMpx++uknsxzOIcLAB+AEQztxNiGP/ADTPHJubq7N66+/Lj158mShm5tbV9/bmgoDHwBYgTyyaXnkwsJC6yVLlvimpaUVBwcHG3w3wxQGPgCwAnlk0/LI7733nntjY6Ng5cqVUiIigUDQk5+ff8PYv8EQ5JEBLBTyyOaDPDIAAEcgjwwAACMKBj4AAEdg4AMAcAQGPgAAR2DgAwBwBAY+ALAGeWTmeeSMjIyx+ucrKCgoMCsrawyjRRiA0zIBgBXII5uWR46MjGyKjY1t5PF4lJubaxMTE+NTXFz8K9M19Ac7fABgBfLIpuWR7e3tu/V9nubmZt5gATcmsMMH4ICCG+94tWjUZs0jjx4j1yoCP0IemYU8cnp6+tj333/fs76+Xnj48OFCQ2tgAgMfAFiBPPKjayAyLo8cFxfXGBcX13jq1KkxSUlJnnPnzlUPdh9jYOADcIChnTibkEd+gGkeWW/+/PmaV199dVRVVZXA3d29s+99mMLABwBWII9sWh45Pz9/lEKhaOfxeJSTkyPW6XRWrq6uQx72RBj4AMAS5JFNyyMfOHBg3MGDBx0FAkGPSCTq/vLLL2/39y7CFMgjA1go5JHNB3lkAACOQB4ZAABGFAx8AACOwMAHAOAIDHwAAI7AwAcA4AgMfABgzUjLI69cudLTzc0tWCwWhxh7n96mTZs24ezZs2Ii01PL1dXV/OnTp8vFYnGIPghnLjgtEwBYMRLzyFFRUY3r1q2rDQwMDDL2sQdiampZLBb3fPDBB5VXr161yc/PtxnqOnrDDh8AWDHS8shERE899VSLVCodtJ+jp9ForBYuXOgjl8sVERERPm1tbVZEpqWW9ezs7LqfffZZjUgkYvbtK0bADh+AA966Uealamkzax45YLRI+3GgxGLyyE5OTl39/ZshKSkpLjY2Nt1qtbogNzfXJiwsTEH0YOAPlFreuHGj69dff+3Y93fNmDGj+YsvvmA1coeBDwCsGGl5ZFPk5OSMWbVqVS0R0fTp01vlcrnWwBqIiGjz5s01mzdvrjHnOoyFgQ/AAYZ24mwaSXlkU3b4RP038w2llrHDBwCLM9LyyIakp6ePzc3NHb1r166K3j+fOXOmJiMjwyEyMrL50qVLIrX6wbeKSaVS3UCpZezwAcDijMQ8cmJi4vijR486tLW18VxdXYOXLl1at3379sqioqJRdnZ2j7wDWLduXW1MTIy3XC5XKJVK7cSJEx++EA2UWjaGp6fnRI1Gw9fpdFZZWVljv/32W7UxX4A+GOSRASwU8sjm89xzz3nv2bOnvPc7kt8D5JEBAMzs+PHjxcO9BnPAefgAAByBgQ8AwBEY+AAAHIGBDwDAERj4AAAcgYEPAKxBHpl5Hvno0aN2SqUy8J/n9gd+8803tqaspT84LRMAWIE8sml5ZBcXF93JkyeLZDKZ7tKlS6KIiAh5bW3ttaGuhwg7fABgCfLIpuWRw8LCWmUymY6IaMqUKW0dHR281tbWAV8omcAOH4AD3s686qWubjZrHlnuZqv978WTkEdmMY+8b9++cQqFQqt/0RwqDHwAYAXyyI+sgYiMj6fl5eWJkpKSPE+fPl1orvVi4ANwgKGdOJuQR36AaR751q1bwsWLF/vt3bu3eLAXOCYw8AGAFcgjm5ZHrqur4y9YsMB/06ZNd5555pkB/05T4ENbAGBFU1MTPy4uztvX11cpl8sVKpXK5qOPPqrsnUfWf3hLRJSRkeHo4+MTFBAQoIiLi/MeKI+cmJgo1Wq1A36IuXr16rqGhgaBRCIJ2rlzp1tKSsodY9ecmJg43tXVNVifR9afGmooj9zS0sKXy+WK5ORkt7555MTERJlUKg2SyWTtxuaRt27d6lJWVjZqy5YtHvrnp6Kiwiybc+SRASwU8sjmgzwyAABHII8MAAAjCgY+AABHYOADAHAEBj4AAEdg4AMAcAQGPgCwBnlk5nnk7Ozsh3G5CRMmKNLT08easpb+4LRMAGAF8sim5ZGnTp3adv369QKhUEilpaXCkJAQxUsvvdQoFA5alRgUdvgAwArkkU3LI9va2nbrh3tra6tVf60eU2GHD8AFx97wotoCs+aRyUWhpahdyCOzkEf+4YcfRq9YsUJWWVlp/cknnxSbY3dPhIEPACxBHvmRNRCRcXnkOXPmtBQVFf36888/i15++WXvxYsX3xeLxUPu4GDgA3CBgZ04m5BHfoBpHlnvscceaxOLxV15eXk2Tz75pNaU9fWGgQ8ArEAe2bQ8skqlsvb19e0QCoWkVquti4uLRf7+/h2mrLsvDHwAYEVTUxN/1apVkqamJj6fz++RyWTt+/btK+2dR9bfVqVSFWRkZDiuX7/eSyQSdQsEgp6B8sjx8fGyX3755cZAhzhWr15dFx0d7S2RSILs7e27Dh48eMvYNScmJo4/evSogz6PvHTp0rrt27dXGsojx8TEeMvlcoVSqdT2zSPHx8d7t7W1WYWHhzcZm0c+c+bMmIULF7oLBIIeHo/Xs23btjJ3d3ezVDqRRwawUMgjmw/yyAAAHIE8MgAAjCgY+AAAHIGBDwDAERj4AAAcgYEPAMARGPgAwJqRlkc2NWms5+npObGqqkpARJSZmWknk8mCJBJJkH5txrhy5Ypo8uTJAdbW1o8lJSW5MlrAIHBaJgCwYiTmkU1NGvfV2dlJa9askWRlZal9fHx0kyZNCoyOjm7UF0ANcXFx6dyxY0dZZmamUXVNJrDDBwBWmCOP3NXVRVKpNKiyslJARNTV1UUSiSRIv4vWM0ce2ZSkcXV1NT8sLMw/MDBQERsbK9VfyPrjjz+Olkql7QqFokMkEvUsWrSoPjMz06gvMvH09OycNWuWVigUmv2qWOzwAThg4/mNXkUNRWbNI/uN89NuDtvMeh558eLF9z777DOHpKSk2uPHj9sFBga2GkoNmJpHNpQ0Hsj69es9QkNDNSkpKVVfffWV/YEDB5yIiMrLy609PT0f9m/Gjx/fkZubO4aIKD4+3uv8+fO2fX/XokWL6pOTk6sNPd5QYeADACvMlUd+7bXX6v7whz/4JSUl1aalpTktW7bMYC7C1DyyoaTxQC5evGh75MiRIiKimJiY+wkJCV2G1kBEtHfv3mEplxJh4ANwgqGdOJvMkUf28/PTOTk5dX7zzTe2V65cGX3s2DGDx+NNzSMbShobwuM9emRcIpF0VFRUPPyw+M6dO9YeHh46IuzwAcACmSuPTES0fPnyu6+++qp3dHT0vd4vEP0xNY/s5OTUNVDSODk52ZmIaMOGDXd732fGjBnNaWlpjlu3bq06dOiQXVNTE5+IaNasWS0lJSUilUplLZPJdEeOHHHYv3//bSLs8AHAApkjj6wf7i+99NL9N998k79ixYp7gz3uUPLIAyWNVSqVTVhYmKbv7bds2VIZHR3to1AoAkNDQzXu7u4PPzvYtm1b2bx58+RdXV0UGxtbN3Xq1EHP0CEiKisrEzz++OOKlpYWvpWVVU9qaqrrjRs38h0cHJidI9oP5JEBLJQl5ZHPnj0rXrNmjdfly5dvDsfjh4eH+506deqWSCT6XQ1M5JEBwKJs2LDB7YsvvnD+/PPPhy1RnJ2dXTRcj21O2OEDWChL2uFD/5ju8HHhFQAAR2DgAwBwBAY+AABHYOADAHAEBj4AsAZ5ZOZ55D179jjI5XKFXC5XhISEBFy4cMGG0SIMwGmZAMAK5JFNyyP7+fm1nz9//qazs3PXoUOH7BISEqTXrl1TMV1Df7DDBwBWII9sWh756aefbnF2du4iIgoPD2+prq42+h3KYLDDB+CAyg3/6dVeWGjWPPIof3+tR/KfkEdmMY+8c+dOp/Dw8PuG1sAEBj4AsAJ55EfXQGR8PO3EiRO2GRkZTj/99JNZDucQYeADcIKhnTibkEd+gGkeOTc31+b111+Xnjx5stDNza1rsDUYCwMfAFiBPLJpeeTCwkLrJUuW+KalpRUHBwe3G/xjGcLABwBWII9sWh75vffec29sbBSsXLlSSkQkEAh68vPzbxj7NxiCeBqAhbKkeBryyP1DHhkALAryyOaDHT6AhbKkHT70D3lkAADoFwY+AABHYOADAHAEBj4AAEdg4AMAa5BHZp5HzsjIGKt/voKCggKzsrLGMFqEATgtEwBYgTyyaXnkyMjIptjY2EYej0e5ubk2MTExPsXFxb8yXUN/sMMHAFYgj2xaHtne3r5b3+dpbm7mDRZwYwI7fAAOOJN+w6u+QmPWPLKD5xjtU3GByCOzkEdOT08f+/7773vW19cLDx8+XGhoDUxg4AMAK5BHfnQNRMblkePi4hrj4uIaT506NSYpKclz7ty56sHuYwwMfAAOMLQTZxPyyA8wzSPrzZ8/X/Pqq6+OqqqqEhh6V2MsDHwAYAXyyKblkfPz80cpFIp2Ho9HOTk5Yp1OZ+Xq6jrkYU+EgQ8ALEEe2bQ88oEDB8YdPHjQUSAQ9IhEou4vv/zydn/vIkyBeBqAhbKkeBryyP1DHhkALAryyOaDHT6AhbKkHT70D3lkAADoFwY+AABHYOADAHAEBj4AAEdg4AMAa0ZaHnnlypWebm5uwWKxOMTY+/Q2bdq0CWfPnhUTmZ5arq6u5k+fPl0uFotD9EE4c8FpmQDAipGYR46Kimpct25dbWBgYJCxjz0QU1PLYrG454MPPqi8evWqTX5+vs1Q19EbdvgAwIqRlkcmInrqqadapFLpoP0cPY1GY7Vw4UIfuVyuiIiI8Glra7MiMi21rGdnZ9f97LPPakQiEbNvXzECdvgAHJC152OvuvJSs+aRnbyk2mdfe8ti8sj6bg8TKSkpLjY2Nt1qtbogNzfXJiwsTEH0YOAPlFreuHGj69dff+3Y93fNmDGj+YsvvmA1coeBDwCsGGl5ZFPk5OSMWbVqVS0R0fTp01vlcrnWwBqIiGjz5s01mzdvrjHnOoyFgQ/AAYZ24mwaSXlkU3b4RP038w2llrHDBwCLM9LyyIakp6ePzc3NHb1r166K3j+fOXOmJiMjwyEyMrL50qVLIrVaLSYikkqluoFSy9jhA4DFGYl55MTExPFHjx51aGtr47m6ugYvXbq0bvv27ZVFRUWj7OzsHnkHsG7dutqYmBhvuVyuUCqV2okTJ7bo/22g1LIxPD09J2o0Gr5Op7PKysoa++2336qN+QL0wSCeBmChLCmeNtx55Oeee857z5495b3fkfweII8MABbl95BHPn78+LA9tjlhhw9goSxphw/9Qx4ZAAD6hYEPAMARGPgAAByBgQ8AwBEY+ADAGuSRmeeRjx49aqdUKgP/eW5/4DfffGNrylr6g9MyAYAVyCOblkd2cXHRnTx5skgmk+kuXbokioiIkNfW1l4b6nqIsMMHAJYgj2xaHjksLKxVJpPpiIimTJnS1tHRwWttbR3whZIJ7PABOKA+U+2lq24xax5Z6DZa67BYjjwyi3nkffv2jVMoFFr9i+ZQYeADACuQR35kDURkfDwtLy9PlJSU5Hn69OlCc60XAx+AAwztxNmEPPIDTPPIt27dEi5evNhv7969xUqlst2UdfUHAx8AWIE8sml55Lq6Ov6CBQv8N23adOeZZ55pGeh2psCHtgDAiqamJn5cXJy3r6+vUi6XK1Qqlc1HH31U2TuPrP/wlogoIyPD0cfHJyggIEARFxfn3TePrNVqjc4jNzQ0CCQSSdDOnTvdUlJS7hi75sTExPGurq7B+jyy/tRQQ3nklpYWvlwuVyQnJ7v1zSMnJibKpFJpkEwmazc2j7x161aXsrKyUVu2bPHQPz8VFRVm2ZwjngZgoSwpnoY8cv+QRwYAi4I8svlghw9goSxphw/9Qx4ZAAD6hYEPAMARGPgAAByBgQ8AwBEY+ADAGuSRmeeRs7OzH8blJkyYoEhPTx9rylr6g9MyAYAVyCOblkeeOnVq2/Xr1wuEQiGVlpYKQ0JCFC+99FKjUCgc7K6Dwg4fAFiBPLJpeWRbW9tu/XBvbW216q/VYyrs8AE44NixY161tbVmzSO7uLhoo6KikEdmIY/8ww8/jF6xYoWssrLS+pNPPik2x+6eCAMfAFiCPPIjayAi4/LIc+bMaSkqKvr1559/Fr388sveixcvvi8Wi4d8lSwGPgAHGNqJswl55AeY5pH1HnvssTaxWNyVl5dn8+STT2pNWV9vGPgAwArkkU3LI6tUKmtfX98OoVBIarXauri4WOTv799hyrr7wsAHAFY0NTXxV61aJWlqauLz+fwemUzWvm/fvtLeeWT9bVUqVUFGRobj+vXrvUQiUbdAIOjpm0d+8803jc4jR0dHe0skkiB7e/uugwcP3jJ2zYmJieOPHj3qoM8jL126tG779u2VhvLIMTEx3nK5XKFUKrV988jx8fHebW1tVuHh4U3G5pHPnDkzZuHChe4CgaCHx+P1bNu2rczQZxZMIJ4GYKEsKZ6GPHL/kEcGAIuCPLL5YIcPYKEsaYcP/UMeGQAA+oWBDwDAERj4AAAcgYEPAMARGPgAwJrfIo9cUlIinDdvno/+v9999103iUQSJJPJgg4fPmxn7Fpramr4TzzxhL9UKg164okn/O/evcs39r5ERNHR0bLPP/98HNGDi6eCg4MDpFJpUO+omjH+5V/+xd/W1nZyeHi4H5PHNwYGPgCwonceWa1WF2RnZ6t9fHwGvGI0Pj7eOzU1tVSlUhWo1epfly5dWm/M48hkMt3p06dvExFdvnxZdOTIEYebN2/+evr0afVbb70l6ew07tT5999/33327NnNpaWl+bNnz25OSkpyM+qO/Vi7du34N998s6a0tDTf3t6+c8eOHU7G3nfdunXVqamprJwGioEPAKwwRx6ZiGjWrFl++tvb2tpO3rlz5//p0Ny8edPa399fSUSUmZk5dtGiRfU2NjY9AQEBHVKptP3HH38c8F1Fb6dPnx6bkJBwj4goISHh3qlTpwzmjLu7uykuLk7i6+urnD17tl9dXZ1A//MLFy7YvvLKKw1ERMuXL7934sQJo7/E5Lnnnmu2s7MzrufMEC68AuCAghvveLVo1GbNI48eI9cqAj9iPY/897//vYjowTdIxcfHy2JjYxsHesyKigrrGTNmaPT/7eHh0VFeXm5NRC1TpkyZ0NLS8shhmi1btpRHRUU137t3T6Bv4UulUl19fb3B+fjll1+OLSoqGnXz5s1f79y5I5w4caJy2bJl92pqagS2trZd+qSxTCbrqKmpsSYi2rNnj8OOHTseeecgk8na9O9S2ISBDwCsMFcemYioqqpKsGzZMu+vvvrqlqOj44BVy4HSyERE5s4y/P3vf7d94YUX6gUCAclkMl1oaGjzYGt47bXX6l977TWjDlWxAQMfgAMM7cTZZI48spOTU1d0dLTPO++8U/n444+3GXq88ePH63f0RERUWVlpPX78eB0R0WA7fEdHx87S0lKhVCrVlZaWCh0cHAY9+N9fGtnNza2zubmZr9PpSCgUUklJibWLi4uOaPh3+DiGDwCsuHr16qjr16+P0v+3MXlk/VcR9s4jv/HGG+MVCoV2xYoVDYM9ZnR0dOORI0ccWltbrVQqlXVJSYlo9uzZLUQPdvgqlaqg7/+ioqKaiYieffbZxtTUVEciotTUVMd58+Y1Ej34UvHnn39e1vexZs2a1fz11187dHZ2UmlpqfDixYu2REQ8Ho9mzJjRrD9jJy0tzXHhwoWNRA92+P2t4bcY9kTY4QMAS8yVR/7zn//s6ufn1xYQEGBHRLRx48aKf35p+SOmTp3aFhUVVS+Xy5V8Pp+2b99eOlg/X++Pf/xj1fPPP+8rlUqdPDw8Oo4dO3aLiKikpGSU/oPn3v7t3/6t8cyZM3YTJkxQent7t02bNq1Z/2/btm278+KLL/p++OGHnkqlUrt69Wqjm0ZTpkyZcPv2bVFrayvf1dU1ePfu3SXR0dGDfvm5MRBPA7BQiKeZR0JCwvjly5ffmz59eutwr6Uv5JEBAMwoNTX1znCvwVxwDB8AgCMw8AEAOAIDHwCAIzDwAQA4AgMfAIAjMPABgDXIIzPLI//00082kydPDtA/Z59++qnBgBtTGPgAwArkkZnnkceMGdP95ZdfFhcVFf36t7/9rXDDhg1edXV1jF54DMHABwBWII/MPI8cHBzcPnHixHaiBy9kDg4OnVVVVWa7XgoXXgFwwFs3yrxULW1mzSMHjBZpPw6UII/MUh45OztbrNPprBQKRbuhdTCBgQ8ArEAe+dE1GJtHLi0tFb7yyis+e/fuLebzzXZEBwMfgAsM7cTZhDwy8zxyfX09b/78+X5JSUkVTz31VMtga2ACx/ABgBXIIzPPI7e1tVlFRET4xcTE3Fu+fPmgfy9T2OEDACuQR2aeR05LSxt36dKlMQ0NDYK//OUvTv/8WfETTzxhllIn8sgAFgp5ZPNAHhkAgCOQRwYAgBEHAx8AgCMw8AEAOAIDHwCAIzDwAQA4AgMfAFiDPDKzPLJarbZWKpWBAQEBCj8/P+XWrVudmaxhMBj4AMAK5JGZ55ElEokuLy9PpVKpCi5fvnxjx44dbiUlJUJT19EXBj4AsAJ5ZOZ5ZJFI1KN/vlpbW630qQlzwYVXABzwduZVL3V1s1nzyHI3W+1/L56EPLKZ88hFRUXCBQsW+JeXl49KSkq6I5PJdIbWwQQGPgCwAnnkR9dgTB7Zz89Pp1arC0pKSoSRkZF+//qv/9rg5eVl3HGpQWDgA3CAoZ04m5BHZp5H7vUz3YQJE1q///77h4eHhgrH8AGAFcgjM88j37p1S6jRaKyIiO7evcvPy8sbo1QqDb7IMYEdPgCwAnlk5nnka9eu2bzzzjvjraysqKenh958883qadOmma3SiTwygIVCHtk8kEcGAOAI5JEBAGDEwcAHAOAIDHwAAI7AwAcA4AgMfAAAjsDABwDWjKQ8clpa2jg/Pz8lj8ebcvbsWcbdobVr13okJSW5Eg0ttbxkyRKZg4PDJH0Qzpww8AGAFSMtjzx58uTWw4cPF02dOlUz+K0NG0pqefny5XXffPNN4VDX0B8MfABgxUjLIz/22GNtkyZNamfyN77zzjtuMpks6IknnpAXFhY+zEgwTS33Nn/+fI2zs7NZYml94cIrAC449oYX1RaYNY9MLgotRe2ymDwy0z//3Llz4qNHjzpcv369QKfT0eTJkxUhISFaIqKBUssnTpywffvtt736/i4bG5vuK1euqJiugSkMfABghaXnkbOzs8csWLCg0dbWtpuI6JlnnhnwhUgvMjKyOTIyssCc62ACAx+ACwzsxNk0kvLIpvx9/eWRiYgGSi0P9w4fx/ABgBUjLY88kOLiYmFoaKi878/nzJmjOXny5FiNRmPV0NDA++677x5+jeFAqeXIyMjm/tbwWwx7IuzwAYAlIy2PnJ6ePvbtt9+WNDQ0CJ5//nn/wMBAbU5OTmF5ebmQz+c/cqxo5syZ2ueff74+KChI6enp2T5t2rSHnx0MlFo2RmRkpPfFixdtGxoaBK6ursHr16+vXLNmjVmqp8gjA1go5JHNIzk52VkqlXYM9CIznJBHBgAwow0bNtwd7jWYC47hAwBwBAY+AABHYOADAHAEBj4AAEdg4AMAcAQGPgCwBnlkZnnkoqIi4fTp0+U+Pj5KPz8/5ebNm12YrsMQDHwAYAXyyMzzyEKhkLZt23bn9u3bv166dOnG3r17XS5fviwa6nr0MPABgBXIIzPPI0ulUt3MmTO1RETjxo3r9vX1bS0rK7Me7H7GwoVXAByw8fxGr6KGIrPmkf3G+Wk3h21GHpmlPPLNmzetCwoKxLNmzRryOw49DHwAYAXyyI8yNo98//593qJFi3y3bNlS7uDg0G2O9RJh4ANwgqGdOJuQR2aeR25vb7eKiIjwXbJkSf3LL7886IsIEziGDwCsQB6ZeR65u7ubYmJipHK5vG3Tpk01g/29TGGHDwCsQB6ZeR75u+++G3Ps2DFHf3//1oCAAMU/f1fFiy++aJZSJ/LIABYKeWTzQB4ZAIAjkEcGAIARBwMfAIAjMPABADgCAx8AgCMw8AEAOAIDHwBYgzwyszyyVqu1mjhxYuCECRMUfn5+yjVr1hj1HBgLAx8AWIE8MvM8skgk6snJybl58+bNgl9//bXgzJkzdmfOnDGq9mkMDHwAYAXyyMzzyDwej+zt7buJiDo6Oqw6OzutBur1mAIXXgFwQOWG//RqLyw0ax55lL+/1iP5T8gjmzmP3NnZSUFBQYqysrJRL7/8cu2cOXNamK5tIBj4AMAK5JEfZUweWSAQkEqlKqirq+NHRET4Xrp0STRYJdRYGPgAHGBoJ84m5JGZ55H1nJycumbOnNl84sQJe3MNfBzDBwBWII/MPI9cWVkpqKur4xMRaTQaqx9//NEuMDDQLMOeCDt8AGAJ8sjM88jl5eXCZcuWeXd1dVFPT4/Vc889V//SSy+ZrdKJPDKAhUIe2TyQRwYA4AjkkQEAYMTBwAcA4AgMfADL1d3d3W2+yzThd+Wf/992M7kPBj6A5cq/e/euPYa+5enu7ra6e/euPRHlM7kfPrQFsFCdnZ2vVldXf1ZdXR1E2NxZmm4iyu/s7HyVyZ1wWiYAAEfgVR8AgCMw8AEAOAIDHwCAIzDwAQA4AgMfAIAj/h9tX9AbIdX38gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ops1 = [\n",
    "    'Sx', \n",
    "    'Sy', \n",
    "    'Sz',\n",
    "       ]\n",
    "ops2 = [\n",
    "    'Sx', \n",
    "    'Sy', \n",
    "    'Sz',\n",
    "]\n",
    "i0_list = [0, 1]\n",
    "d0_list = [1, 2, 3]\n",
    "\n",
    "\n",
    "N = 20\n",
    "\n",
    "for op1 in ops1:\n",
    "    for op2 in ops2:\n",
    "        for i0 in i0_list:\n",
    "            for d0 in d0_list:\n",
    "                xticks=range(i0, 2*N, 2)\n",
    "                plt.plot(\n",
    "                    xticks, \n",
    "                    double_local_op_diff_corr_func(\n",
    "                        psi, \n",
    "                        op1=op1, op2=op2, i0=i0, d0=d0, dN=N), \n",
    "                    label=op1+op2+f' i0={i0}, d0={d0}')\n",
    "                \n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22691338311389625\n"
     ]
    }
   ],
   "source": [
    "Jp = Jx + Jy\n",
    "Jm = Jx - Jy\n",
    "ratio = Jp / Jm\n",
    "Delta = np.sqrt(ratio) * (1 - (Jz / Jm)**2)**(1/4) / (2 * (1 + ratio))\n",
    "print(Delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Triple Local Operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('Sx', 'Sy', 'Sz'), ('Sx', 'Sz', 'Sy'), ('Sy', 'Sx', 'Sz'), ('Sy', 'Sz', 'Sx'), ('Sz', 'Sx', 'Sy'), ('Sz', 'Sy', 'Sx')]\n",
      "[(0, 1, 2), (0, 1, 3), (0, 2, 1), (0, 2, 3), (0, 3, 1), (0, 3, 2), (1, 0, 2), (1, 0, 3), (1, 2, 0), (1, 2, 3), (1, 3, 0), (1, 3, 2), (2, 0, 1), (2, 0, 3), (2, 1, 0), (2, 1, 3), (2, 3, 0), (2, 3, 1), (3, 0, 1), (3, 0, 2), (3, 1, 0), (3, 1, 2), (3, 2, 0), (3, 2, 1)]\n"
     ]
    }
   ],
   "source": [
    "from itertools import permutations, product\n",
    "print(list(permutations(ops)))\n",
    "i0s = [0, 1, 2, 3]\n",
    "print(list(permutations(i0s, 3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multiple_local_op_diff(psi, ops=['Sx', 'Sy', 'Sz'], i0s=[0, 1, 2], d=1):\n",
    "    return psi.expectation_value_term(term=[(op, i0) for op, i0 in zip(ops, i0s)] + [(op, i0+d) for op, i0 in zip(ops, i0s)])*(2**(2*len(ops)))\n",
    "def multiple_local_op_diff_corr_func(psi, ops=['Sx', 'Sy', 'Sz'], i0s=[0, 1, 2], dN=20):\n",
    "    return [multiple_local_op_diff(psi, ops=ops, i0s=i0s, d=d) for d in range(dN)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ops_input in list(product(ops, ops, ops)):\n",
    "    for i0s_input in list(permutations(i0s, 3)):\n",
    "        plt.plot(multiple_local_op_diff_corr_func(psi, ops=ops_input, i0s=i0s_input))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quartic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Sx', 'Sy', 'Sy', 'Sx')\n",
      "('Sx', 'Sz', 'Sz', 'Sx')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f746eb92590>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ops_input in list(product(ops, ops, ops, ops)):\n",
    "    corr_values = multiple_local_op_diff_corr_func(psi, ops=ops_input, i0s=i0s)\n",
    "    plt.plot(corr_values,label=f'{ops_input}')\n",
    "    if np.average(corr_values) > .25:\n",
    "        print(ops_input)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Sx', 'Sy', 'Sy', 'Sx')\n",
      "('Sx', 'Sz', 'Sz', 'Sx')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f746e4a4810>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ops_input in list(product(ops, ops, ops, ops)):\n",
    "    corr_values = multiple_local_op_diff_corr_func(psi, ops=ops_input, i0s=i0s)\n",
    "    if np.average(corr_values) > .25:\n",
    "        print(ops_input)\n",
    "        plt.plot(corr_values,label=f'{ops_input}')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hmmm, XZZX? Interesting. It is indeed not commutable with the Hamiltonian, but still commutable with the global symmetries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Z region"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose a typical gapped point living in the central region, i.e.\n",
    "$$ -|{J_z}| < J_x - J_y < |{J_z}|$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'L'=8 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=1 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=1 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=1 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  128 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 816\n",
      "Energy = -0.2097012464827843, S = nan, norm_err = 9.5e-13\n",
      "Current memory usage 522.9 MB, time elapsed: 30.6 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 7.1491e-18, max_E_trunc = 1.4211e-13\n",
      "MPS bond dimensions: [98, 112, 66, 124, 124, 128, 123, 128, 123, 128, 120, 128, 121, 128, 124, 123]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 1296\n",
      "Energy = -0.2097012464828101, S = nan, norm_err = 7.8e-13\n",
      "Current memory usage 522.9 MB, time elapsed: 69.4 s\n",
      "Delta E = -2.5757e-15, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 4.0512e-18, max_E_trunc = 2.8422e-13\n",
      "MPS bond dimensions: [92, 105, 67, 121, 128, 126, 124, 128, 124, 128, 121, 128, 125, 128, 122, 116]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 1776\n",
      "Energy = -0.2097012464828083, S = 1.2232332305847287, norm_err = 9.0e-15\n",
      "Current memory usage 522.9 MB, time elapsed: 86.1 s\n",
      "Delta E = 1.7764e-16, Delta S = nan (per sweep)\n",
      "max_trunc_err = 3.9042e-19, max_E_trunc = 4.5475e-13\n",
      "MPS bond dimensions: [96, 128, 96, 128, 96, 128, 96, 128, 96, 128, 96, 128, 96, 128, 96, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 2256\n",
      "Energy = -0.2097012464827568, S = 1.2232332305847415, norm_err = 6.3e-15\n",
      "Current memory usage 522.9 MB, time elapsed: 102.2 s\n",
      "Delta E = 5.1514e-15, Delta S = 1.2879e-15 (per sweep)\n",
      "max_trunc_err = 4.3602e-19, max_E_trunc = 6.8212e-13\n",
      "MPS bond dimensions: [96, 128, 96, 128, 96, 128, 96, 128, 96, 128, 96, 128, 96, 128, 96, 128]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 2256, maximum chi = 128\n",
      "================================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2119: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  self.canonical_form_infinite(renormalize)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2269: UserWarning: Although we renormalized the TransferMatrix, the largest eigenvalue is not 1\n",
      "  warnings.warn(\"Although we renormalized the TransferMatrix, \"\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2275: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(i1, Gl, Wr)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2119: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  self.canonical_form_infinite(renormalize)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2296: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(j1, Gl, Wr_list[j1 % L])\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before the canonicalization:\n",
      "Bond dim =  [28, 46, 48, 76, 48, 76, 48, 76, 49, 76, 48, 76, 48, 76, 48, 46]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000016+2.1528189387415297e-17j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [28, 46, 48, 76, 48, 76, 48, 76, 49, 76, 48, 76, 48, 76, 48, 46]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=128 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n"
     ]
    }
   ],
   "source": [
    "# set the region to be the circle `r = x**2 + y**2 = 2, z=.5`\n",
    "\n",
    "Jx = 1\n",
    "Jy = 1\n",
    "Jz = 1\n",
    "\n",
    "result = run_atomic(Jx=Jx, Jy=Jy, Jz=Jz, L=8, chi=128, bc='periodic', bc_MPS='infinite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi = result['psi']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation of the Ground State"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our theoretical energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.abs(result['energy'] - E_true(Jx, Jy, Jz)) < 1e-10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our local symmetries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm: <psi|psi> = 1.0\n",
      "Local Symmetry: W0 = 1.0\n",
      "Local Symmetry: W1 = 1.0\n",
      "Local Symmetry: W2 = 1.0\n",
      "Local Symmetry: W3 = 1.0\n",
      "Local Symmetry: W4 = 1.0\n",
      "Local Symmetry: W5 = 1.0\n",
      "Local Symmetry: W6 = 1.0\n",
      "Local Symmetry: W7 = 0.0\n",
      "Local Symmetry: W8 = 1.0\n",
      "Local Symmetry: W9 = 1.0\n"
     ]
    }
   ],
   "source": [
    "k=0\n",
    "print(\"Norm: <psi|psi> = %.1f\" % psi.norm)\n",
    "for k in range(20):\n",
    "    if k % 2 == 0:\n",
    "        print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sx', k), ('Sy', k+1), ('Sy', k+2), ('Sx', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sy', k), ('Sx', k+1), ('Sx', k+2), ('Sy', k+3)])))\n",
    "#     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Local Operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "site_left = [0]\n",
    "site_right = 20\n",
    "xticks=range(site_right)\n",
    "for op in ops:\n",
    "    cf_list = 4*psi.correlation_function(op, op, site_left, site_right, opstr=op)[0, :]\n",
    "    plt.plot(xticks, np.abs(cf_list), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n",
    "\n",
    "site_left = [1]\n",
    "site_right = 20\n",
    "xticks=range(site_right)\n",
    "for op in ops:\n",
    "    cf_list = 4*psi.correlation_function(op, op, site_left, site_right, opstr=op)[0, :]\n",
    "    plt.plot(xticks, np.abs(cf_list), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Double Local Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try the 'double local operators'.\n",
    "\n",
    "That is, we used two local, neighboring operators combined together as our |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_local_op(psi, op='Sx', i0=1, d=1):\n",
    "    return psi.expectation_value_term(term=[(op, i0), (op, i0+1), (op, i0+d*2), (op, i0+d*2+1)])*16\n",
    "def double_local_op_corr_func(psi, op='Sx', i0=1, dN=9):\n",
    "    return [double_local_op(psi, op=op, i0=i0, d=d) for d in range(dN)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']\n",
    "N=20\n",
    "\n",
    "xticks=range(1, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, double_local_op_corr_func(psi, op=op, i0=1, dN=N), label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n",
    "\n",
    "xticks=range(0, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, double_local_op_corr_func(psi, op=op, i0=0, dN=N), label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-local operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nonlocal_op(psi, op='Sx', i0=1, end=11):\n",
    "    if end==i0:\n",
    "        return 1.0\n",
    "    return psi.expectation_value_term(term=[(op, i) for i in range(i0, end)])*(2**(end-i0))\n",
    "def nonlocal_op_corr_func(psi, op='Sx', i0=1, N=20):\n",
    "    return [nonlocal_op(psi, op=op, i0=i0, end=i0+2*d) for d in range(N)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']\n",
    "N=20\n",
    "\n",
    "xticks=range(1, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, np.abs(nonlocal_op_corr_func(psi, op=op, i0=1, N=N)), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.ylim(top=1.1)\n",
    "plt.show()\n",
    "\n",
    "xticks=range(0, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, np.abs(nonlocal_op_corr_func(psi, op=op, i0=0, N=N)), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.ylim(top=1.1)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Large Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose a typical gapped point living in the large $Z$ limit, e.g.\n",
    "$$ J_x^2 + J_y^2 = 0.1$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'L'=8 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=0.09950041652780259 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.009983341664682815 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=1 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  128 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 816\n",
      "Energy = 0.1371278591078502, S = nan, norm_err = 1.5e-01\n",
      "Current memory usage 522.9 MB, time elapsed: 68.3 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 4.8341e-10, max_E_trunc = -9.5213e-13\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 1296\n",
      "Energy = 0.3198556878029666, S = nan, norm_err = 2.2e-01\n",
      "Current memory usage 522.9 MB, time elapsed: 147.9 s\n",
      "Delta E = 1.8273e-02, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 3.5508e-10, max_E_trunc = -8.3276e-12\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 1776\n",
      "Energy = -0.0983175582116784, S = 1.2202778202775277, norm_err = 2.2e-02\n",
      "Current memory usage 522.9 MB, time elapsed: 215.5 s\n",
      "Delta E = -4.1817e-02, Delta S = nan (per sweep)\n",
      "max_trunc_err = 1.6588e-10, max_E_trunc = -2.1316e-11\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 2256\n",
      "Energy = 0.2440959195914099, S = 3.5115369335485473, norm_err = 1.1e-01\n",
      "Current memory usage 522.9 MB, time elapsed: 283.8 s\n",
      "Delta E = 3.4241e-02, Delta S = 2.2913e-01 (per sweep)\n",
      "max_trunc_err = 2.3030e-10, max_E_trunc = -6.7644e-12\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 50, age = 2736\n",
      "Energy = 0.0894229989191295, S = 1.8230668976189277, norm_err = 1.5e-01\n",
      "Current memory usage 522.9 MB, time elapsed: 350.2 s\n",
      "Delta E = -1.5467e-02, Delta S = -1.6885e-01 (per sweep)\n",
      "max_trunc_err = 1.1270e-10, max_E_trunc = -2.6773e-11\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 60, age = 3216\n",
      "Energy = -0.0622001516426884, S = 1.2535168294326415, norm_err = 4.9e-02\n",
      "Current memory usage 522.9 MB, time elapsed: 416.6 s\n",
      "Delta E = -1.5162e-02, Delta S = -5.6955e-02 (per sweep)\n",
      "max_trunc_err = 7.8563e-11, max_E_trunc = -1.2506e-11\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 70, age = 3696\n",
      "Energy = -0.1253563752516325, S = 0.9723681281294451, norm_err = 4.2e-07\n",
      "Current memory usage 522.9 MB, time elapsed: 482.9 s\n",
      "Delta E = -6.3156e-03, Delta S = -2.8115e-02 (per sweep)\n",
      "max_trunc_err = 3.6215e-11, max_E_trunc = -5.6843e-13\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 80, age = 4176\n",
      "Energy = -0.1253601626208720, S = 0.9706681695530515, norm_err = 4.4e-06\n",
      "Current memory usage 522.9 MB, time elapsed: 549.3 s\n",
      "Delta E = -3.7874e-07, Delta S = -1.7000e-04 (per sweep)\n",
      "max_trunc_err = 8.8354e-11, max_E_trunc = -2.0862e-11\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 90, age = 4656\n",
      "Energy = -0.1253733035710027, S = 1.0382774933755339, norm_err = 3.0e-08\n",
      "Current memory usage 522.9 MB, time elapsed: 615.7 s\n",
      "Delta E = -1.3141e-06, Delta S = 6.7609e-03 (per sweep)\n",
      "max_trunc_err = 8.0390e-11, max_E_trunc = -2.7285e-12\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 100, age = 5136\n",
      "Energy = -0.1253730443813659, S = 1.0375279816913725, norm_err = 1.5e-08\n",
      "Current memory usage 522.9 MB, time elapsed: 684.4 s\n",
      "Delta E = 2.5919e-08, Delta S = -7.4951e-05 (per sweep)\n",
      "max_trunc_err = 2.4158e-11, max_E_trunc = 1.1369e-12\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "================================================================================\n",
      "DMRG finished after 100 sweeps.\n",
      "total size = 5136, maximum chi = 128\n",
      "================================================================================\n",
      "Before the canonicalization:\n",
      "Bond dim =  [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000167+6.319709941973472e-16j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=128 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n"
     ]
    }
   ],
   "source": [
    "# set the region to be the circle `r = x**2 + y**2 = 2, z=.5`\n",
    "r = 0.1\n",
    "theta = .1\n",
    "Jx = r * np.cos(theta)\n",
    "Jy = r * np.sin(theta)\n",
    "Jz = 1\n",
    "\n",
    "result = run_atomic(Jx=Jx, Jy=Jy, Jz=Jz, L=8, chi=128, bc='periodic', bc_MPS='infinite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi = result['psi']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation of the Ground State"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our theoretical energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4487843093269337e-06"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(result['energy'] - E_true(Jx, Jy, Jz))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our local symmetries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm: <psi|psi> = 1.0\n",
      "Local Symmetry: W0 = 1.0\n",
      "Local Symmetry: W1 = 1.0\n",
      "Local Symmetry: W2 = 1.0\n",
      "Local Symmetry: W3 = 1.0\n",
      "Local Symmetry: W4 = 1.0\n",
      "Local Symmetry: W5 = 1.0\n",
      "Local Symmetry: W6 = 1.0\n",
      "Local Symmetry: W7 = 1.0\n",
      "Local Symmetry: W8 = 1.0\n",
      "Local Symmetry: W9 = 1.0\n"
     ]
    }
   ],
   "source": [
    "k=0\n",
    "print(\"Norm: <psi|psi> = %.1f\" % psi.norm)\n",
    "for k in range(20):\n",
    "    if k % 2 == 0:\n",
    "        print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sx', k), ('Sy', k+1), ('Sy', k+2), ('Sx', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sy', k), ('Sx', k+1), ('Sx', k+2), ('Sy', k+3)])))\n",
    "#     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Local Operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "site_left = [0]\n",
    "site_right = 20\n",
    "xticks=range(site_right)\n",
    "for op in ops:\n",
    "    cf_list = 4*psi.correlation_function(op, op, site_left, site_right, opstr=op)[0, :]\n",
    "    plt.plot(xticks, np.abs(cf_list), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n",
    "\n",
    "site_left = [1]\n",
    "site_right = 20\n",
    "xticks=range(site_right)\n",
    "for op in ops:\n",
    "    cf_list = 4*psi.correlation_function(op, op, site_left, site_right, opstr=op)[0, :]\n",
    "    plt.plot(xticks, np.abs(cf_list), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Double Local Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try the 'double local operators'.\n",
    "\n",
    "That is, we used two local, neighboring operators combined together as our |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_local_op(psi, op='Sx', i0=1, d=1):\n",
    "    return psi.expectation_value_term(term=[(op, i0), (op, i0+1), (op, i0+d*2), (op, i0+d*2+1)])*16\n",
    "def double_local_op_corr_func(psi, op='Sx', i0=1, dN=9):\n",
    "    return [double_local_op(psi, op=op, i0=i0, d=d) for d in range(dN)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']\n",
    "N=20\n",
    "\n",
    "xticks=range(1, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, double_local_op_corr_func(psi, op=op, i0=1, dN=N), label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n",
    "\n",
    "xticks=range(0, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, double_local_op_corr_func(psi, op=op, i0=0, dN=N), label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-local operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nonlocal_op(psi, op='Sx', i0=1, end=11):\n",
    "    if end==i0:\n",
    "        return 1.0\n",
    "    return psi.expectation_value_term(term=[(op, i) for i in range(i0, end)])*(2**(end-i0))\n",
    "def nonlocal_op_corr_func(psi, op='Sx', i0=1, N=20):\n",
    "    return [nonlocal_op(psi, op=op, i0=i0, end=i0+2*d) for d in range(N)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ops = ['Sx', 'Sy', 'Sz']\n",
    "N=20\n",
    "\n",
    "xticks=range(1, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, np.abs(nonlocal_op_corr_func(psi, op=op, i0=1, N=N)), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.ylim(top=1.1)\n",
    "plt.show()\n",
    "\n",
    "xticks=range(0, 2*N, 2)\n",
    "for op in ops:\n",
    "    plt.plot(xticks, np.abs(nonlocal_op_corr_func(psi, op=op, i0=0, N=N)), '-', label=op)\n",
    "plt.legend()\n",
    "plt.xticks(xticks)\n",
    "plt.ylim(top=1.1)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'L'=8 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=-1.902113032590307 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.6180339887498948 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  128 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 10, age = 816\n",
      "Energy = -0.2472012973842528, S = nan, norm_err = 9.1e-04\n",
      "Current memory usage 522.9 MB, time elapsed: 69.6 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 1.4074e-11, max_E_trunc = 1.1369e-13\n",
      "MPS bond dimensions: [128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 20, age = 1296\n",
      "Energy = -0.2490400578897169, S = nan, norm_err = 2.1e-11\n",
      "Current memory usage 522.9 MB, time elapsed: 136.1 s\n",
      "Delta E = -1.8388e-04, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 8.0555e-16, max_E_trunc = 3.4106e-13\n",
      "MPS bond dimensions: [68, 75, 51, 95, 126, 128, 124, 126, 125, 127, 128, 128, 128, 126, 125, 92]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 30, age = 1776\n",
      "Energy = -0.2490400578927900, S = nan, norm_err = 7.0e-13\n",
      "Current memory usage 522.9 MB, time elapsed: 164.8 s\n",
      "Delta E = -3.0731e-13, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 1.4040e-19, max_E_trunc = 5.6843e-13\n",
      "MPS bond dimensions: [58, 70, 47, 82, 98, 125, 108, 124, 114, 126, 108, 128, 108, 125, 98, 78]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 40, age = 2256\n",
      "Energy = -0.2490400578927563, S = 0.7784899589503622, norm_err = 5.5e-15\n",
      "Current memory usage 522.9 MB, time elapsed: 177.2 s\n",
      "Delta E = 3.3751e-15, Delta S = nan (per sweep)\n",
      "max_trunc_err = 4.5755e-20, max_E_trunc = 1.3642e-12\n",
      "MPS bond dimensions: [66, 90, 66, 90, 66, 90, 66, 90, 66, 90, 66, 90, 66, 90, 66, 90]\n",
      "Updating environment\n",
      ".....\n",
      "================================================================================\n",
      "sweep 50, age = 2736\n",
      "Energy = -0.2490400578927066, S = 0.7784899589503850, norm_err = 8.4e-15\n",
      "Current memory usage 522.9 MB, time elapsed: 186.9 s\n",
      "Delta E = 4.9738e-15, Delta S = 2.2760e-15 (per sweep)\n",
      "max_trunc_err = 4.6617e-20, max_E_trunc = 1.7053e-12\n",
      "MPS bond dimensions: [66, 90, 66, 90, 66, 90, 66, 90, 66, 90, 66, 90, 66, 90, 66, 90]\n",
      "================================================================================\n",
      "DMRG finished after 50 sweeps.\n",
      "total size = 2736, maximum chi = 90\n",
      "================================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2275: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(i1, Gl, Wr)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2119: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  self.canonical_form_infinite(renormalize)\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/networks/mps.py:2296: UserWarning: canonical_form_infinite: project to smaller bond dimension\n",
      "  Gl, Wr = self._canonical_form_correct_left(j1, Gl, Wr_list[j1 % L])\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before the canonicalization:\n",
      "Bond dim =  [38, 49, 38, 48, 38, 48, 38, 48, 38, 48, 38, 48, 38, 48, 38, 48]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000147-1.3576921704955207e-16j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [38, 49, 38, 48, 38, 48, 38, 48, 38, 48, 38, 48, 38, 48, 38, 48]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=128 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n"
     ]
    }
   ],
   "source": [
    "# set the region to be the circle `r = x**2 + y**2 = 2, z=.5`\n",
    "\n",
    "r = 2\n",
    "theta = np.pi * 9 / 90\n",
    "Jx = -r*np.cos(theta)\n",
    "Jy = r*np.sin(theta)\n",
    "Jz = .5\n",
    "\n",
    "result = run_atomic(Jx=Jx, Jy=Jy, Jz=Jz, L=8, chi=128, bc='periodic', bc_MPS='infinite')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation of the Ground State"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our theoretical energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.130407375655068e-14"
      ]
     },
     "execution_count": 416,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi = result['psi']\n",
    "np.abs(result['energy'] - E_true(Jx, Jy, Jz))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.24904005789277786\n",
      "-0.2476191661911536\n"
     ]
    }
   ],
   "source": [
    "print(E_true(Jx, Jy, Jz))\n",
    "print(E_false(Jx, Jy, Jz))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test with our local symmetries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm: <psi|psi> = 1.0\n",
      "Local Symmetry: W0 = -1.0\n",
      "Local Symmetry: W1 = -1.0\n",
      "Local Symmetry: W2 = -1.0\n",
      "Local Symmetry: W3 = -1.0\n",
      "Local Symmetry: W4 = -1.0\n",
      "Local Symmetry: W5 = -1.0\n",
      "Local Symmetry: W6 = -1.0\n",
      "Local Symmetry: W7 = -1.0\n",
      "Local Symmetry: W8 = -1.0\n",
      "Local Symmetry: W9 = -1.0\n"
     ]
    }
   ],
   "source": [
    "psi = result['psi']\n",
    "print(\"Norm: <psi|psi> = %.1f\" % psi.norm)\n",
    "for k in range(20):\n",
    "    if k % 2 == 0:\n",
    "        print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sx', k), ('Sy', k+1), ('Sy', k+2), ('Sx', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sx', k), ('Sz', k+1), ('Sz', k+2), ('Sx', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sz', k), ('Sy', k+1), ('Sy', k+2), ('Sz', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sy', k), ('Sx', k+1), ('Sx', k+2), ('Sy', k+3)])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'L'=8 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'conserve'=None for config KitaevLadderSnakeCompactModel\n",
      "Reading 'S'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc'='periodic' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'bc_MPS'='finite' for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jx'=-1.902113032590307 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jy'=0.6180339887498948 for config KitaevLadderSnakeCompactModel\n",
      "Reading 'Jz'=0.5 for config KitaevLadderSnakeCompactModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  128 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n",
      "================================================================================\n",
      "sweep 10, age = 16\n",
      "Energy = -3.9926303769879272, S = nan, norm_err = 1.2e-09\n",
      "Current memory usage 522.9 MB, time elapsed: 6.1 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 5.6183e-20, max_E_trunc = 7.9936e-15\n",
      "MPS bond dimensions: [2, 4, 8, 12, 22, 36, 47, 50, 39, 26, 21, 12, 8, 4, 2]\n",
      "================================================================================\n",
      "sweep 20, age = 16\n",
      "Energy = -3.9926303769879183, S = nan, norm_err = 4.9e-13\n",
      "Current memory usage 522.9 MB, time elapsed: 11.1 s\n",
      "Delta E = 8.8818e-16, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 5.2717e-20, max_E_trunc = 8.4377e-15\n",
      "MPS bond dimensions: [2, 4, 8, 13, 22, 28, 40, 48, 38, 23, 19, 11, 8, 4, 2]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "================================================================================\n",
      "sweep 30, age = 16\n",
      "Energy = -3.9926303769879183, S = 1.3761035672628337, norm_err = 2.7e-13\n",
      "Current memory usage 522.9 MB, time elapsed: 13.8 s\n",
      "Delta E = 0.0000e+00, Delta S = nan (per sweep)\n",
      "max_trunc_err = 2.9468e-28, max_E_trunc = 8.8818e-15\n",
      "MPS bond dimensions: [2, 4, 8, 8, 16, 16, 32, 32, 32, 16, 16, 8, 8, 4, 2]\n",
      "================================================================================\n",
      "sweep 40, age = 16\n",
      "Energy = -3.9926303769879290, S = 1.3761035672628339, norm_err = 1.8e-12\n",
      "Current memory usage 522.9 MB, time elapsed: 17.1 s\n",
      "Delta E = -1.0658e-15, Delta S = 2.2204e-17 (per sweep)\n",
      "max_trunc_err = 4.8261e-28, max_E_trunc = 9.3259e-15\n",
      "MPS bond dimensions: [2, 4, 8, 8, 16, 16, 32, 32, 32, 16, 16, 8, 8, 4, 2]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 16, maximum chi = 32\n",
      "================================================================================\n",
      "Before the canonicalization:\n",
      "Bond dim =  [2, 4, 8, 8, 16, 16, 32, 32, 32, 16, 16, 8, 8, 4, 2]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  (1.0000000000000007+0j)\n",
      "After the canonicalization:\n",
      "Bond dim =  [2, 4, 8, 8, 16, 16, 32, 32, 32, 16, 16, 8, 8, 4, 2]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=128 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['start_env'] for config TwoSiteDMRGEngine\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    }
   ],
   "source": [
    "# set the region to be the circle `r = x**2 + y**2 = 2, z=.5`\n",
    "\n",
    "r = 2\n",
    "theta = np.pi * 9 / 90\n",
    "Jx = -r*np.cos(theta)\n",
    "Jy = r*np.sin(theta)\n",
    "Jz = .5\n",
    "\n",
    "result = run_atomic(Jx=Jx, Jy=Jy, Jz=Jz, L=8, chi=128, bc='periodic', bc_MPS='finite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm: <psi|psi> = 1.0\n",
      "Local Symmetry: W0 = -1.0\n",
      "Local Symmetry: W1 = -1.0\n",
      "Local Symmetry: W2 = -1.0\n",
      "Local Symmetry: W3 = -1.0\n",
      "Local Symmetry: W4 = -1.0\n",
      "Local Symmetry: W5 = -1.0\n",
      "Local Symmetry: W6 = -1.0\n"
     ]
    }
   ],
   "source": [
    "psi = result['psi']\n",
    "print(\"Norm: <psi|psi> = %.1f\" % psi.norm)\n",
    "for k in range(14):\n",
    "    if k % 2 == 0:\n",
    "        print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sx', k), ('Sy', k+1), ('Sy', k+2), ('Sx', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sx', k), ('Sz', k+1), ('Sz', k+2), ('Sx', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sz', k), ('Sy', k+1), ('Sy', k+2), ('Sz', k+3)])))\n",
    "#         print(r\"Local Symmetry: W%d = %.1f\" % (k//2, 16*psi.expectation_value_term(term=[('Sy', k), ('Sx', k+1), ('Sx', k+2), ('Sy', k+3)])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary & Plotting\n",
    "\n",
    "In this section we will summarize over the previous conclusions and then implement some with plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test\n",
    "\n",
    "In this subsection we want to test the usage of plt: how to plot the lattice with matplotlib.pyplot and highlight part of the points to indicate our local operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Circle at 0x7fdc47d32ed0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAABFCAYAAADpejX1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAADhElEQVR4nO3dvYtcZRiG8etJTCojaUXsFLSxsBAGFBaLgFhY2fkX+NGJmEosRCy0U0SwsBBLAxY2IisEU6rYWQVBLMQuiCTBx2KOOoHNNvueW+bd6wfDMtlhr7xb3HPYr6nuRpKUceb//g9I0mni6EpSkKMrSUGOriQFObqSFOToSlKQoytJQY6uJAU5upIU5OhKUpCjK0lBjq4kBTm6khTk6EpSkKMrSUGOriQFObqSFLTK6FbVpqouV9VmjY9/mnozny3dm/ls6d7MZ1u9191Db8AG+AO4vbzdjG6clt7MZ/Nzub+9mc+W6K1xpXsAnAfOAueW+2uauZdszd5LtmbvJVvT9dYY3UPgJttniVvL/TXN3Eu2Zu8lW7P3kq3perVcTg+1fB3kADjs7mvDA6eoN/PZ0r2Zz5buzXy2tXurjK4k6Wj+yJgkBTm6khTk6EpSkKMrSUGOriQFObqSFOToSlKQoytJQY6uJAU5upIU5OhKUpCjK0lBjq4kBTm6khTk6EpSkKMrSUGOriQFrfQS7NxTxX1Vjrok7Ro2ilVUFc9U8QXbly3+BbhRxSdVPDGqI0n7bMjoLle0HwHvAVeAi91cAB4EfgQ+r+LVES1J2mdDXpiyireAJ4Fnu7lxxPsfAL4B3ujm0xMHJWlPnXh0q7gIXAce7ebXYx73FPAx8Eg3f50oKkl7asSXF14Avtwd3KraVNXl5bXj/3EV+JPta8kPdZfeapK9mc+W7s18tnRv5rOt3uvuE92gP4B+6b/7bNh+I+328naz89j3oV8+afPO/t17a9ySvZnP5udyf3szny3RG3Gl20Dt3D8AzgNngXPceWV7Znn8SMf11pDsJVuz95Kt2XvJ1nS9EaP7A/D0zv1D4CbbZ4lby32qqOVx3w9o7jqyt6JkL9mavZdszd5LtqbrjfhG2r3Az8Dj3Vzf/ltt2D47HHb3teVxl4B3gce6x17tHtVbU7I389nSvZnPlu7NfLa1e6N+ZOx14HngUje/H/H+h4GvgVe6uXLioCTtqVG/kfYO8BXwXRWvVXF/FeeqeKiKt4FvgTcdXEmn3ZAr3X8/2PbXfV8EngMuAL8BnwEfdvPTsJAk7amhoytJOp5/BUySghxdSQpydCUpyNGVpCBHV5KCHF1JCnJ0JSnI0ZWkIEdXkoIcXUkKcnQlKcjRlaQgR1eSghxdSQr6GxKobpnHt/qmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First part: plot the lattice one by one\n",
    "\n",
    "# create the list to store all the coordinates of lattice points\n",
    "point_list = [(x, y) for x in range(1, 13) for y in [1, 2]]\n",
    "\n",
    "# plot all the points one by one\n",
    "for x, y in point_list:\n",
    "    plt.plot(x, y, '.', c='black')\n",
    "    pass\n",
    "\n",
    "plt.axis('scaled')\n",
    "plt.ylim((.5,2.5))\n",
    "plt.box(False)\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "\n",
    "c1 = plt.Circle((1,1), .2, color='b', fill=False)\n",
    "plt.gcf().gca().add_artist(c1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perturbation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What kinds of perturbation:\n",
    "1. pure `Jz`: spin pairs (dimers) up or down \n",
    "    consider the interactions between the pairs.\n",
    "    \n",
    "Corr. len.\n",
    "    "
   ]
  }
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