Hamiltonian_simulation_Solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "### '''Installation'''\n",
    "# !pip install qiskit[visualization]==1.1.0\n",
    "# # Use the following if you are on MacOS/zsh\n",
    "# #!pip install 'qiskit[visualization]'==1.1.0\n",
    "# !pip install qiskit_aer\n",
    "# !pip install qiskit_ibm_runtime\n",
    "# !pip install matplotlib\n",
    "# !pip install pylatexenc\n",
    "# !pip install prototype-zne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1-D Schrodinger equation\n",
    " Schrodinger equation:\n",
    "$$-i\\hbar \\frac{d \\ket{\\psi}}{dt} = H \\ket{\\psi}  $$\n",
    "\n",
    "The Hamiltonian H of the system is:\n",
    "$$T+V = \\frac{p^2}{2m} + V$$\n",
    "where p is momentum operator, V is potential operator and K is Kinetic Energy operator.\n",
    "\n",
    "Its evolution is given by equation: $$|\\psi(x,t)\\rangle =  e^{-iHt} |\\psi(x,0)\\rangle$$\n",
    "\n",
    "The unitary operator is $U=e^{-iHt}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trotterization of Hamiltonian H\n",
    "\n",
    "T and V are non commuting operators, i,e $[T,V]\\neq 0$\n",
    "\n",
    "Hence, Hamiltonian H need to be decomposed using trotterization\n",
    "\n",
    "### Lie Trotter Method\n",
    "$$e^{i(A+B)n\\Delta t} \\approx (e^{iA\\Delta t} e^{iB\\Delta t})^n $$\n",
    "Lie-Trotter decomposition of H\n",
    "$$\n",
    "U =e^{-i\\hat{H}t} \\approx \\left(e^{-i\\hat{T}\\\\Delta t} e^{-\\hat{V}\\Delta t}\\right)^n\n",
    "$$\n",
    "\n",
    "\n",
    "<!-- <details>\n",
    "<summary>Lie-Trotter decomposition of H  </summary>\n",
    "\n",
    "inside text\n",
    "</details> -->\n",
    "\n",
    "### Suzuki Trotter Method\n",
    "$$e^{i(A+B)n\\Delta t} \\approx (e^{i\\frac{A}{2}\\Delta t} e^{iB\\Delta t} e^{i\\frac{A}{2}\\Delta t})^n $$\n",
    "Suzuki-Trotter decomposition of H\n",
    "\n",
    "$$e^{-i\\hat{H}t/\\hbar} \\approx  \\left( e^{-i\\hat{V} \\Delta t/2} e^{-iT\\Delta t} e^{-i\\hat{V} \\Delta t/2} \\right)^n\n",
    "$$\n",
    "<!-- <details>\n",
    "<summary> Suzuki-Trotter decomposition of H</summary>\n",
    "inside text\n",
    "</details> -->\n",
    "Since $\\hat{T}=\\frac{\\hat{p}^2 }{2m}$ which is in momentum space, for applying operator T, the  basis need to be transformed to momentum space and revert back to computation space after applying the gate. We can achieve by using Fourier Transform: Quantum Fourier transform for quantum computers. So the operation would become:\n",
    "\n",
    "$$e^{-i\\hat{V} \\Delta t/2} QFT e^{-iT\\Delta t} QFT_{inv} e^{-i\\hat{V} \\Delta t/2}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have $\\hat{T} = \\frac{\\hat{p}^2 }{2 }$(let m=1 for simplicity), we can write $\\hat{p}$ as :\n",
    "$$\n",
    "\\hat{p} = -\\sqrt{\\frac{1}{2^{2n-3} } \\frac{\\phi}{\\Delta t}} \\left(1 + \\sum_{j=1}^{n} 2^{n-j} \\hat{Z_j}\\right)\n",
    "$$\n",
    "\n",
    "The whole equation $e^{i\\hat{p}^2\\Delta t}$ becomes\n",
    "$$\n",
    "e^{i\\hat{p}^2\\Delta t} = exp\\left(\\frac{i\\phi}{2^{2n-3}} \\left(1 + \\sum_{j=1}^{n} 2^{n-j} \\hat{Z_{j}}\\right)^2\\right)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Free Particle: V=0\n",
    "$$U = QFT e^{-iT\\Delta t} QFT_{inv} $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import of required libraries and modules\n",
    "from math import pi\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit.visualization import plot_histogram, plot_distribution\n",
    "from qiskit.circuit.library import QFT\n",
    "from qiskit.primitives import StatevectorSampler,Sampler,Estimator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial wavefunction\n",
    "For now, We will be working on a Gaussian stationary wavefunction with no initial kinetic energy $k_0=0$:\n",
    "$$\\psi(x,t_{0}) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}\\left(\\frac{x-x_{0}}{\\sigma}\\right)^{2}} e^{i\\hbar k_{0}x}$$\n",
    "\n",
    "Since $k_0=0$, we can exclude the last term and $\\psi$ becomes:\n",
    "$$\\psi(x,t_{0}) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}\\left(\\frac{x-x_{0}}{\\sigma}\\right)^{2}}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Preparing the Gaussian-shaped histogram that will be used in the initialisation\n",
    "\n",
    "x = np.linspace(-4,4, num=64)\n",
    "x0=0\n",
    "\n",
    "\n",
    "'''wavefunction: guassian wavepacket'''\n",
    "pos=0\n",
    "unnormalized_wavefunction = (1/(np.sqrt(2*np.pi)*0.4)*np.exp(-(0.5*(x-x0)**2)/(0.016)))\n",
    "\n",
    "\n",
    "Normalisation_Constant = np.sqrt(np.sum(np.abs(unnormalized_wavefunction**2)))\n",
    "\n",
    "wavefunction = (unnormalized_wavefunction)/(Normalisation_Constant)\n",
    "\n",
    "\n",
    "plt.plot(x,wavefunction)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = StatevectorSampler()\n",
    "\n",
    "def initialization(qc,wavefunction,q_reg):\n",
    "\n",
    "    qc.initialize(wavefunction, q_reg)\n",
    "\n",
    "def apply_QFT(qc,q_reg):\n",
    "    qc.append(QFT(n),q_reg)\n",
    "\n",
    "\n",
    "def Time_Evolution(qc,n,q_reg,aux_reg):\n",
    "    # qc=QuantumCircuit(q_reg,aux_reg)\n",
    "    for i in range (n):\n",
    "        qc.p(phi/(2**(i+n-3)),q_reg[n-i-1])\n",
    "    for i in range (n):\n",
    "        for j in range (i+1,n):\n",
    "            qc.cx(q_reg[n-j-1], aux_reg[0])\n",
    "            qc.cx(q_reg[n-i-1], aux_reg[0])\n",
    "            qc.p(phi* (2**(2-i-j)), aux_reg[0]) \n",
    "            qc.cx(q_reg[n-i-1], aux_reg[0])\n",
    "            qc.cx(q_reg[n-j-1], aux_reg[0])\n",
    "            # qc.barrier()\n",
    "    # qc.to_gate()\n",
    "\n",
    "\n",
    "def apply_invQFT(qc,q_reg):\n",
    "    qc.append(QFT(n,inverse=True),q_reg)\n",
    "\n",
    "\n",
    "def display_histogram(qc,q_reg,clas_reg,plot=False,hist=True):\n",
    "    qc.measure(q_reg,clas_reg)\n",
    "    keys = range(0,2**n)\n",
    "    counts= {key: 0 for key in keys}\n",
    "    qc_counts= Sampler().run(qc, shots=1024).result().quasi_dists[0]\n",
    "    for key, value in qc_counts.items():\n",
    "        if key in counts:\n",
    "            counts[key] = value*100\n",
    "    keys = list(counts.keys())\n",
    "    values = list(counts.values())\n",
    "    if plot:\n",
    "        plt.plot(keys,values)\n",
    "    if hist:\n",
    "        display(plot_histogram(counts,bar_labels=False))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = 0.3  # function of time step\n",
    "n=6\n",
    "q_reg=QuantumRegister(6)\n",
    "aux_reg=QuantumRegister(1)\n",
    "clas_reg = ClassicalRegister(6)\n",
    "qc=QuantumCircuit(aux_reg,q_reg,clas_reg)\n",
    "initialization(qc,wavefunction,q_reg)\n",
    "\n",
    "initial_qc=qc.copy()\n",
    "display_histogram(initial_qc,q_reg,clas_reg)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">                                                                                                                                                                                                                                                                                                                      ┌───┐┌───┐┌────────┐┌───┐┌───┐┌───┐┌───┐┌────────┐┌───┐┌───┐┌───┐┌───┐┌─────────┐┌───┐┌───┐┌───┐┌───┐┌──────────┐┌───┐┌───┐┌───┐┌───┐┌───────────┐┌───┐┌───┐┌───┐┌───┐┌─────────┐┌───┐┌───┐┌───┐┌───┐┌──────────┐┌───┐┌───┐┌───┐┌───┐┌───────────┐┌───┐┌───┐┌───┐┌───┐┌────────────┐┌───┐┌───┐┌───┐┌───┐┌───────────┐┌───┐┌───┐┌───┐┌───┐┌────────────┐┌───┐┌───┐┌───┐┌───┐┌─────────────┐┌───┐┌───┐┌───┐┌───┐┌─────────────┐┌───┐┌───┐┌───┐┌───┐┌──────────────┐┌───┐┌───┐┌───┐┌───┐┌──────────────┐┌───┐┌───┐         \n",
       "  q1: ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤ X ├┤ X ├┤ P(0.6) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.3) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.15) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.075) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.15) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.075) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.01875) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.01875) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.009375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.009375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0046875) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0023437) ├┤ X ├┤ X ├─────────\n",
       "      ┌──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐┌──────┐┌──────────────┐└─┬─┘└─┬─┘└────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└───────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└───────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└───────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────────┘└─┬─┘└─┬─┘┌───────┐\n",
       "q0_0: ┤0                                                                                                                                                                                                                                                                                     ├┤0     ├┤ P(0.0011719) ├──┼────┼──────────────┼────┼────┼────┼──────────────┼────┼────┼────┼───────────────┼────┼────┼────┼────────────────┼────┼────■────┼─────────────────┼────■────┼────┼───────────────┼────┼────┼────┼────────────────┼────┼────┼────┼─────────────────┼────┼────■────┼──────────────────┼────■────┼────┼─────────────────┼────┼────┼────┼──────────────────┼────┼────■────┼───────────────────┼────■────┼────┼───────────────────┼────┼────■────┼────────────────────┼────■────■────┼────────────────────┼────■──┤0      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │├──────────────┤  │    │              │    │    │    │              │    │    │    │               │    │    │    │                │    │         │                 │         │    │               │    │    │    │                │    │    │    │                 │    │         │                  │         │    │                 │    │    │    │                  │    │         │                   │         │    │                   │    │         │                    │              │                    │       │       │\n",
       "q0_1: ┤1                                                                                                                                                                                                                                                                                     ├┤1     ├┤ P(0.0023437) ├──┼────┼──────────────┼────┼────┼────┼──────────────┼────┼────┼────┼───────────────┼────┼────■────┼────────────────┼────■─────────┼─────────────────┼─────────┼────┼───────────────┼────┼────┼────┼────────────────┼────┼────■────┼─────────────────┼────■─────────┼──────────────────┼─────────┼────┼─────────────────┼────┼────■────┼──────────────────┼────■─────────┼───────────────────┼─────────■────┼───────────────────┼────■─────────┼────────────────────┼──────────────■────────────────────■───────┤1      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │├──────────────┤  │    │              │    │    │    │              │    │    │    │               │    │         │                │              │                 │         │    │               │    │    │    │                │    │         │                 │              │                  │         │    │                 │    │         │                  │              │                   │              │                   │              │                    │                                           │       │\n",
       "q0_2: ┤2                                                                                                                                                                                                                                                                                     ├┤2     ├┤ P(0.0046875) ├──┼────┼──────────────┼────┼────┼────┼──────────────┼────┼────■────┼───────────────┼────■─────────┼────────────────┼──────────────┼─────────────────┼─────────┼────┼───────────────┼────┼────■────┼────────────────┼────■─────────┼─────────────────┼──────────────┼──────────────────┼─────────■────┼─────────────────┼────■─────────┼──────────────────┼──────────────┼───────────────────┼──────────────■───────────────────■──────────────■────────────────────■───────────────────────────────────────────┤2      ├\n",
       "      │  Initialize(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7.863e-09,4.4293e-07,1.5074e-05,0.00030995,0.0038505,0.028899,0.13104,0.35901,0.59422,0.59422,0.35901,0.13104,0.028899,0.0038505,0.00030995,1.5074e-05,4.4293e-07,7.863e-09,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0) ││  QFT │├─────────────┬┘  │    │              │    │    │    │              │    │         │               │              │                │              │                 │         │    │               │    │         │                │              │                 │              │                  │              │                 │              │                  │              │                   │                                                                                                                  │  IQFT │\n",
       "q0_3: ┤3                                                                                                                                                                                                                                                                                     ├┤3     ├┤ P(0.009375) ├───┼────┼──────────────┼────┼────■────┼──────────────┼────■─────────┼───────────────┼──────────────┼────────────────┼──────────────┼─────────────────┼─────────■────┼───────────────┼────■─────────┼────────────────┼──────────────┼─────────────────┼──────────────┼──────────────────┼──────────────■─────────────────■──────────────■──────────────────■──────────────■───────────────────■──────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤3      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │└┬────────────┤   │    │              │    │         │              │              │               │              │                │              │                 │              │               │              │                │              │                 │              │                  │                                                                                                                                                                                                                        │       │\n",
       "q0_4: ┤4                                                                                                                                                                                                                                                                                     ├┤4     ├─┤ P(0.01875) ├───■────┼──────────────┼────■─────────┼──────────────┼──────────────┼───────────────┼──────────────┼────────────────┼──────────────┼─────────────────┼──────────────■───────────────■──────────────■────────────────■──────────────■─────────────────■──────────────■──────────────────■────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤4      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │ ├───────────┬┘        │              │              │              │              │               │              │                │              │                 │                                                                                                                                                                                                                                                                                                                                                          │       │\n",
       "q0_5: ┤5                                                                                                                                                                                                                                                                                     ├┤5     ├─┤ P(0.0375) ├─────────■──────────────■──────────────■──────────────■──────────────■───────────────■──────────────■────────────────■──────────────■─────────────────■──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤5      ├\n",
       "      └──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘└──────┘ └───────────┘                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 └───────┘\n",
       "c0: 6/════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════\n",
       "                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              </pre>"
      ],
      "text/plain": [
       "                                                                                                                                                                                                                                                                                                                      ┌───┐┌───┐┌────────┐┌───┐┌───┐┌───┐┌───┐┌────────┐┌───┐┌───┐┌───┐┌───┐┌─────────┐┌───┐┌───┐┌───┐┌───┐┌──────────┐┌───┐┌───┐┌───┐┌───┐┌───────────┐┌───┐┌───┐┌───┐┌───┐┌─────────┐┌───┐┌───┐┌───┐┌───┐┌──────────┐┌───┐┌───┐┌───┐┌───┐┌───────────┐┌───┐┌───┐┌───┐┌───┐┌────────────┐┌───┐┌───┐┌───┐┌───┐┌───────────┐┌───┐┌───┐┌───┐┌───┐┌────────────┐┌───┐┌───┐┌───┐┌───┐┌─────────────┐┌───┐┌───┐┌───┐┌───┐┌─────────────┐┌───┐┌───┐┌───┐┌───┐┌──────────────┐┌───┐┌───┐┌───┐┌───┐┌──────────────┐┌───┐┌───┐         \n",
       "  q1: ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤ X ├┤ X ├┤ P(0.6) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.3) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.15) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.075) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.15) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.075) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.01875) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.01875) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.009375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.009375) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0046875) ├┤ X ├┤ X ├┤ X ├┤ X ├┤ P(0.0023437) ├┤ X ├┤ X ├─────────\n",
       "      ┌──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐┌──────┐┌──────────────┐└─┬─┘└─┬─┘└────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└───────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└───────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└───────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└─────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────────┘└─┬─┘└─┬─┘└─┬─┘└─┬─┘└──────────────┘└─┬─┘└─┬─┘┌───────┐\n",
       "q0_0: ┤0                                                                                                                                                                                                                                                                                     ├┤0     ├┤ P(0.0011719) ├──┼────┼──────────────┼────┼────┼────┼──────────────┼────┼────┼────┼───────────────┼────┼────┼────┼────────────────┼────┼────■────┼─────────────────┼────■────┼────┼───────────────┼────┼────┼────┼────────────────┼────┼────┼────┼─────────────────┼────┼────■────┼──────────────────┼────■────┼────┼─────────────────┼────┼────┼────┼──────────────────┼────┼────■────┼───────────────────┼────■────┼────┼───────────────────┼────┼────■────┼────────────────────┼────■────■────┼────────────────────┼────■──┤0      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │├──────────────┤  │    │              │    │    │    │              │    │    │    │               │    │    │    │                │    │         │                 │         │    │               │    │    │    │                │    │    │    │                 │    │         │                  │         │    │                 │    │    │    │                  │    │         │                   │         │    │                   │    │         │                    │              │                    │       │       │\n",
       "q0_1: ┤1                                                                                                                                                                                                                                                                                     ├┤1     ├┤ P(0.0023437) ├──┼────┼──────────────┼────┼────┼────┼──────────────┼────┼────┼────┼───────────────┼────┼────■────┼────────────────┼────■─────────┼─────────────────┼─────────┼────┼───────────────┼────┼────┼────┼────────────────┼────┼────■────┼─────────────────┼────■─────────┼──────────────────┼─────────┼────┼─────────────────┼────┼────■────┼──────────────────┼────■─────────┼───────────────────┼─────────■────┼───────────────────┼────■─────────┼────────────────────┼──────────────■────────────────────■───────┤1      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │├──────────────┤  │    │              │    │    │    │              │    │    │    │               │    │         │                │              │                 │         │    │               │    │    │    │                │    │         │                 │              │                  │         │    │                 │    │         │                  │              │                   │              │                   │              │                    │                                           │       │\n",
       "q0_2: ┤2                                                                                                                                                                                                                                                                                     ├┤2     ├┤ P(0.0046875) ├──┼────┼──────────────┼────┼────┼────┼──────────────┼────┼────■────┼───────────────┼────■─────────┼────────────────┼──────────────┼─────────────────┼─────────┼────┼───────────────┼────┼────■────┼────────────────┼────■─────────┼─────────────────┼──────────────┼──────────────────┼─────────■────┼─────────────────┼────■─────────┼──────────────────┼──────────────┼───────────────────┼──────────────■───────────────────■──────────────■────────────────────■───────────────────────────────────────────┤2      ├\n",
       "      │  Initialize(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7.863e-09,4.4293e-07,1.5074e-05,0.00030995,0.0038505,0.028899,0.13104,0.35901,0.59422,0.59422,0.35901,0.13104,0.028899,0.0038505,0.00030995,1.5074e-05,4.4293e-07,7.863e-09,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0) ││  QFT │├─────────────┬┘  │    │              │    │    │    │              │    │         │               │              │                │              │                 │         │    │               │    │         │                │              │                 │              │                  │              │                 │              │                  │              │                   │                                                                                                                  │  IQFT │\n",
       "q0_3: ┤3                                                                                                                                                                                                                                                                                     ├┤3     ├┤ P(0.009375) ├───┼────┼──────────────┼────┼────■────┼──────────────┼────■─────────┼───────────────┼──────────────┼────────────────┼──────────────┼─────────────────┼─────────■────┼───────────────┼────■─────────┼────────────────┼──────────────┼─────────────────┼──────────────┼──────────────────┼──────────────■─────────────────■──────────────■──────────────────■──────────────■───────────────────■──────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤3      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │└┬────────────┤   │    │              │    │         │              │              │               │              │                │              │                 │              │               │              │                │              │                 │              │                  │                                                                                                                                                                                                                        │       │\n",
       "q0_4: ┤4                                                                                                                                                                                                                                                                                     ├┤4     ├─┤ P(0.01875) ├───■────┼──────────────┼────■─────────┼──────────────┼──────────────┼───────────────┼──────────────┼────────────────┼──────────────┼─────────────────┼──────────────■───────────────■──────────────■────────────────■──────────────■─────────────────■──────────────■──────────────────■────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤4      ├\n",
       "      │                                                                                                                                                                                                                                                                                      ││      │ ├───────────┬┘        │              │              │              │              │               │              │                │              │                 │                                                                                                                                                                                                                                                                                                                                                          │       │\n",
       "q0_5: ┤5                                                                                                                                                                                                                                                                                     ├┤5     ├─┤ P(0.0375) ├─────────■──────────────■──────────────■──────────────■──────────────■───────────────■──────────────■────────────────■──────────────■─────────────────■──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤5      ├\n",
       "      └──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘└──────┘ └───────────┘                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 └───────┘\n",
       "c0: 6/════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════\n",
       "                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# write a code for first iteration: Initialization->QFT->KE operator->inverse QFT\n",
    "# initialization(qc,wavefunction,q_reg)\n",
    "apply_QFT(qc,q_reg)\n",
    "Time_Evolution(qc,n,q_reg,aux_reg)\n",
    "apply_invQFT(qc,q_reg)\n",
    "qc.draw(fold=-1)\n",
    "# iter1=qc.copy()\n",
    "# display_histogram(iter1,q_reg,clas_reg)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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okcydO/dJ2kdERERUYhUpSJ0/f15EHl4f5evrKyNHjpQRI0YUmE+r1YqTk5PY2dk9nVYSERERlUBFClJeXl7K/5ctWyaBgYEG04iIiIj+TYoUpPKKjo5+mu0golLEe+xGg8dJM9o/p5ZQXjwuRM+e6iCld+DAATl48KDcvHlTcnNzC9Q1Go1MmDDhSTdDREREVOKoDlLXr1+XLl26yJ49ewq9pxSDFBEREZVVqoNUTEyM7N69W1q0aCHR0dHi7u4u5uZPfIKLiIiIqNRQnXw2bNggISEhsm3bNt69nIiIiP6VVN/Z/P79+9K8eXOGKCIiIvrXUh2kAgICjN7VnIiIiOjfQnWQmjhxovz000+yb9++p9keIiIiolJD9TVSqamp0r59e4mIiJA+ffpIw4YNxcHBwei8/fr1U91AIiIiopJKdZDq37+/aDQaASBxcXESFxdX4HopAKLRaBikiIiIqExSHaSWLVv2NNtBREREVOrwT8QQERERqaT6YnMiIiKifzvVZ6SSk5Mfe15PT0+1myEiIiIqsVQHKW9v78e6GadGo5GcnBy1myEiIiIqsVQHqX79+hkNUhkZGfLHH3/I+fPnJSIiQry9vZ+kfUREREQlluogFRcXZ7IGQGbPni2zZs2SJUuWqN0EERERUYlWLBebazQaGT16tNStW1fefvvt4tgEERER0XNXrL/aCw4Olvj4+OLcBBEREdFzU6xB6uzZs7zQnIiIiMos1ddImaLT6eTy5csSFxcn69atk1atWj3tTRARERGVCKqDlJmZWaG3PwAgTk5OMnv2bLWbICIiIirRVAep5s2bGw1SZmZm4uTkJI0aNZIBAwaIs7PzEzWQiIiIqKRSHaR27NjxFJtBREREVPrwb+0RERERqfRULjbfs2ePHD16VG7duiUODg4SEBAgTZo0eRqrJiIiIiqxnihI7d27VwYMGCBnzpwRkYcXmOuvm6pRo4YsW7ZMwsLCnryVRERERCWQ6iB18uRJefHFF+XevXvywgsvSGRkpFSpUkVSU1Nl+/btsmXLFomKipJ9+/ZJnTp1nmabiYiIiEoE1UFq8uTJkpWVJZs2bZI2bdoY1N555x3ZvHmzdOrUSSZPnizffffdEzeUiIiIqKRRfbH5jh07pFu3bgVClF6bNm2kW7dusn37dtWNIyIiIirJVAepjIwM8fHxKXQeHx8fycjIULsJoz744APRaDQG//z8/Apd5ocffhA/Pz+xtraWevXqyaZNm55qm4iIiOjfSXWQcnNzk3379hU6z/79+8XNzU3tJkyqW7euXLlyRfm3e/duk/Pu3btXevXqJYMGDZIjR45Ily5dpEuXLnLixImn3i4iIiL6d1EdpDp16iQ7duyQCRMmyIMHDwxqDx48kIkTJ8r27dulc+fOT9zI/MzNzcXV1VX5V6lSJZPzzps3T9q0aSNvv/221K5dW6ZMmSINGzaU+fPnP/V2ERER0b+L6ovNJ0yYIBs2bJDp06fLwoULJSQkRFxcXCQtLU0OHjwoV69eFV9fX5kwYcLTbK+IiCQmJoqbm5tYW1tLWFiYxMbGiqenp9F5ExISJCYmxmBaVFSUrF27ttBtZGZmSmZmpvL41q1bIiKSnZ0t2dnZIvLwz+FotVrJzc0VnU6nzKufnpOTIwCU6VqtVszMzExO169Xz9z84eHJycl5rOkWFhai0+kkNzdXmabRaMTc3NzkdFNtZ5/Yp8L6ZEz+tueVd/3G/rRUdnb2c+/TszxOpvaNqZq+T/np+52/7abWXRbGXll8PrFPxd+n4qQ6SFWsWFH27dsnY8aMke+++87guiNra2sZMGCAzJw5UypUqPBUGqoXGhoqcXFxUqtWLbly5YpMmjRJmjVrJidOnBB7e/sC86empoqLi4vBNBcXF0lNTS10O7GxsTJp0qQC07ds2SK2trYiIuLp6SmBgYFy7NgxSU5OVuapVauW+Pn5yYEDB+Tq1avK9ICAAPHy8pJdu3bJ7du3lelhYWHi7OwsW7ZsMTjgkZGRYmNjU+Carnbt2sn9+/cNLuQ3NzeX9u3bS3p6uiQkJCjT7e3tpWXLlnLx4kU5evSoMr1y5coSHh4uiYmJcvr0aWU6+8Q+PU6fjDHsk+FLS971VK5cucCymzZtMujTS9+nKLXN/auVseNket+Yqun7lN/t27fz9cn0us3NzWXYb4bLzwvLKXVjryw+n9in4u3Tnj17pDhpkDe+qZSdnS2nTp1S7mzu5+cnFhYWT6N9j3Tz5k3x8vKSOXPmyKBBgwrULS0t5auvvpJevXop0z777DOZNGmSpKWlmVyvsTNSHh4ekp6eLg4ODiLCxM8+/Xv75DPO8MUzaUZ7g7bXmLDFoJ445UWDPlUf/0uBet4+VXtvs1I7O61NmTpOhe0bUzV9n7zHbjSon49tZ9D2wtZtql7axl5ZfD6xT8Xbp+vXr0vFihUlIyNDef9+mop8RmratGly9+5dmTRpkhKWLCwspF69eso8WVlZ8t5774m9vb2MHTv26bXWiPLly0vNmjWVu6vn5+rqWiAwpaWliaura6HrtbKyEisrqwLTLSwsCoRErVYrWq22wLymvgYxNd1U+CzKdDMzM6NfAZiabqrt7BP7VNh0Y0y1/XHWk7eevz/6x2XxOBXWnkfVRP73Nana45e3XlrGXll8PrFPz6dPT0uRLjbfunWrvP/++1KxYsVCn6CWlpZSsWJFee+994r9PlJ37tyRs2fPSpUqVYzWw8LCZNu2bQbTfv31V/7pGiIiInpiRQpSy5cvFycnJxk+fPgj5x02bJhUqFBBli1bprpxxowePVp27twpSUlJsnfvXnnppZdEq9UqX93169dPxo0bp8w/YsQI2bx5s8yePVtOnTolH3zwgRw6dOix+kBERERUmCKd79q7d6+0bt3a6Fde+VlZWUnr1q2f+kVely5dkl69esm1a9ekcuXK0rRpU9m3b59yAWtycrLBKcLw8HBZuXKljB8/Xt59912pUaOGrF27Vvz9/Z9qu4iIiOjfp0hBKiUlRXx9fR97fh8fH1m3bl2RG1WYR/3dvh07dhSY1r17d+nevftTbQcRERFRkb7aM3blfmH094YhIiIiKouKlHLc3NyK9KdVTpw4IVWrVi1yo4iIiIhKgyIFqWbNmkl8fLwkJSU9ct6kpCSJj4+X5s2bq20bERERUYlWpCA1bNgwyc7Olm7dukl6errJ+a5duybdu3eXnJwcGTp06BM3koiIiKgkKtLF5g0bNpSRI0fKxx9/LHXq1JH//Oc/EhkZKe7u7iIicvnyZdm2bZssWrRIrl69KjExMdKwYcNiaTgRERHR81bk233Onj1brK2t5cMPP5Rp06bJtGnTDOoARKvVyrhx42Tq1KlPraFEREREJU2Rg5RGo5Hp06fLoEGDZNmyZbJ3717lDwC7urpKkyZNpH///lKtWrWn3lgiIiKikkT1H6CpVq0azzgRERHRvxpv8kRERESkEoMUERERkUoMUkREREQqMUgRERERqcQgRURERKQSgxQRERGRSgxSRERERCoxSBERERGpxCBFREREpBKDFBEREZFKDFJEREREKjFIEREREanEIEVERESkEoMUERERkUoMUkREREQqMUgRERERqcQgRURERKQSgxQRERGRSubPuwFEVPJ4j91o8DhpRvvn1BIiopKNZ6SIiIiIVGKQIiIiIlKJQYqIiIhIJQYpIiIiIpUYpIiIiIhUYpAiIiIiUolBioiIiEglBikiIiIilRikiIiIiFRikCIiIiJSiUGKiIiISCUGKSIiIiKVGKSIiIiIVGKQIiIiIlKJQYqIiIhIJQYpIiIiIpUYpIiIiIhUYpAiIiIiUolBioiIiEglBikiIiIilRikiIiIiFRikCIiIiJSiUGKiIiISCUGKSIiIiKVGKSIiIiIVGKQIiIiIlKJQYqIiIhIJQYpIiIiIpUYpIiIiIhUYpAiIiIiUolBioiIiEglBikiIiIilRikiIiIiFQyf94NICIqCu+xGw0eJ81o/5xaYlxJbx8RPV08I0VERESkEoMUERERkUoMUkREREQqMUgRERERqcQgRURERKQSgxQRERGRSgxSRERERCoxSBERERGpxCBFREREpBKDFBEREZFKDFJEREREKjFIEREREalU6oJUbGysNGrUSOzt7cXZ2Vm6dOkip0+fLnSZuLg40Wg0Bv+sra2fUYuJiIiorCp1QWrnzp0ybNgw2bdvn/z666+SnZ0tL774oty9e7fQ5RwcHOTKlSvKvwsXLjyjFhMREVFZZf68G1BUmzdvNngcFxcnzs7OcvjwYWnevLnJ5TQajbi6uhZ384iIiOhfpNQFqfwyMjJERKRChQqFznfnzh3x8vISnU4nDRs2lOnTp0vdunVNzp+ZmSmZmZnK41u3bomISHZ2tmRnZ4uIiJmZmWi1WsnNzRWdTqfMq5+ek5MjAJTpWq1WzMzMTE7Xr1fP3Pzh4cnJyXms6RYWFqLT6SQ3N1eZptFoxNzc3OR0U21nn/7dfcpPX9f3yZj8bTe2vL5Pxup5+5RXbm6u0T7plbTjZEz+45S/76boa/o+5afvd/62P8669fWSNvbK4vOJfXr+fSpOpTpI6XQ6GTlypDRp0kT8/f1NzlerVi1ZunSp1K9fXzIyMuSjjz6S8PBwOXnypLi7uxtdJjY2ViZNmlRg+pYtW8TW1lZERDw9PSUwMFCOHTsmycnJBtvz8/OTAwcOyNWrV5XpAQEB4uXlJbt27ZLbt28r08PCwsTZ2Vm2bNlicMAjIyPFxsZGNm3aZNCGdu3ayf3792X79u3KNHNzc2nfvr2kp6dLQkKCMt3e3l5atmwpFy9elKNHjyrTK1euLOHh4ZKYmGhwjRn7xD79/5Ya9EXfN32fjDHsk/Hl9X3Kb9OmTQZ9yisxMTFfnwzXXdKOkzGGx8n0vjFV0/cpv9u3b+frk+l1GwvBmzZtKnFjryw+n9in59unPXv2SHHSwNhHvFJi6NCh8vPPP8vu3btNBiJjsrOzpXbt2tKrVy+ZMmWK0XmMnZHy8PCQ9PR0cXBwEBEmfvap7PapxoQtBo8Tp7xo0CefcYYvnkkz2hu03dTy+j5VH/9LgXrePlV7739f4Z+d1sagT/nXfWZqVIk6Tnnbrt83eY9TYfvGVE3fJ++xGw3q52PbGbS9sHWbqpe0sVcWn0/s0/Pt0/Xr16VixYqSkZGhvH8/TaX2jNTw4cNlw4YNsmvXriKFKJGHBzQwMFDOnDljch4rKyuxsrIyuqyFhYXBNK1WK1qttsC8pr4GMTU9/3rVTDczMzP6FYCp6abazj6xT0Wpi5hue1HXn78/+sel5TgZY+o4FdaeR9VE/vc1aVH7aqxe0sZeWXw+sU8lq09PS6n71R4AGT58uKxZs0bi4+PFx8enyOvIzc2V48ePS5UqVYqhhURERPRvUerOSA0bNkxWrlwp69atE3t7e0lNTRUREUdHR7GxsRERkX79+knVqlUlNjZWREQmT54sjRs3lurVq8vNmzflww8/lAsXLsjgwYOfWz+IiIio9Ct1Qerzzz8XEZEWLVoYTF+2bJn0799fRESSk5MNThPeuHFDhgwZIqmpqeLk5CRBQUGyd+9eqVOnzrNqNhEREZVBpS5IPc618Tt27DB4PHfuXJk7d24xtYiIiIj+rUrdNVJEREREJQWDFBEREZFKDFJEREREKjFIEREREanEIEVERESkEoMUERERkUoMUkREREQqMUgRERERqcQgRURERKQSgxQRERGRSqXuT8QQ0ZPzHrvR4HHSjPbPqSWlD/cdEeXFM1JEREREKjFIEREREanEIEVERESkEoMUERERkUoMUkREREQqMUgRERERqcQgRURERKQSgxQRERGRSgxSRERERCoxSBERERGpxCBFREREpBKDFBEREZFKDFJEREREKjFIEREREanEIEVERESkEoMUERERkUoMUkREREQqMUgRERERqcQgRURERKQSgxQRERGRSgxSRERERCoxSBERERGpxCBFREREpBKDFBEREZFKDFJEREREKjFIEREREanEIEVERESkEoMUERERkUoMUkREREQqMUgRERERqcQgRURERKQSgxQRERGRSubPuwFE9PR5j91o8DhpRvvn1JKS51H75t+877hviIqOZ6SIiIiIVGKQIiIiIlKJQYqIiIhIJQYpIiIiIpUYpIiIiIhUYpAiIiIiUolBioiIiEglBikiIiIilRikiIiIiFRikCIiIiJSiUGKiIiISCUGKSIiIiKVGKSIiIiIVGKQIiIiIlKJQYqIiIhIJQYpIiIiIpUYpIiIiIhUYpAiIiIiUolBioiIiEglBikiIiIilRikiIiIiFRikCIiIiJSiUGKiIiISCUGKSIiIiKVGKSIiIiIVGKQIiIiIlKJQYqIiIhIJQYpIiIiIpUYpIiIiIhUKrVBasGCBeLt7S3W1tYSGhoqBw4cKHT+H374Qfz8/MTa2lrq1asnmzZtekYtJSIiorKqVAap77//XmJiYmTixIny+++/S4MGDSQqKkr++ecfo/Pv3btXevXqJYMGDZIjR45Ily5dpEuXLnLixIln3HIiIiIqS0plkJozZ44MGTJEBgwYIHXq1JEvvvhCbG1tZenSpUbnnzdvnrRp00befvttqV27tkyZMkUaNmwo8+fPf8YtJyIiorLE/Hk3oKiysrLk8OHDMm7cOGWamZmZtG7dWhISEowuk5CQIDExMQbToqKiZO3atSa3k5mZKZmZmcrjjIwMERG5fv26ZGdnK9vVarWSm5srOp3OoD1arVZycnIEgDJdq9WKmZmZyen69eqZmz88PDk5OY813cLCQnQ6neTm5irTNBqNmJubm5xuqu3sU+nuky7znsE2b968adCn/PVr164ZPDZV1/cpf/3WrVsGbS9s/RqNxmjdoE956jdu3DA4TvmXvX79epGOU/7l9c9t/XFS03aD42Rk3+Q9ToWt31RN36cnabupet6x9yRtL8vPJ/apdPfp+vXrIiIGtacKpczly5chIti7d6/B9LfffhshISFGl7GwsMDKlSsNpi1YsADOzs4mtzNx4kSICP/xH//xH//xH/+VgX9nz5598hBiRKk7I/WsjBs3zuAs1s2bN8XLy0uSk5PF0dGxwPy3bt0SDw8PuXjxojg4ODzT+vPc9vOul+S2sW/sO/vOvrPvz7/vGRkZ4unpKRUqVChQexpKXZCqVKmSaLVaSUtLM5ielpYmrq6uRpdxdXUt0vwiIlZWVmJlZVVguqOjo9EDpefg4PDc6s9z28+7XpLb9qT1kty24q6X5LYVd70kt6246yW5bcVdL8ltK+56cW/bzKx4LgsvdRebW1paSlBQkGzbtk2ZptPpZNu2bRIWFmZ0mbCwMIP5RUR+/fVXk/MTERERPY5Sd0ZKRCQmJkaio6MlODhYQkJC5OOPP5a7d+/KgAEDRESkX79+UrVqVYmNjRURkREjRkhERITMnj1b2rdvL999950cOnRIFi1a9Dy7QURERKVcqQxSPXv2lKtXr8r7778vqampEhAQIJs3bxYXFxcREUlOTjY4hRceHi4rV66U8ePHy7vvvis1atSQtWvXir+//2Nv08rKSiZOnGj0677nXS/JbSvueklu25PWS3LbirtekttW3PWS3LbirpfkthV3vSS3rbjrz7ttT0oDFNfvAYmIiIjKtlJ3jRQRERFRScEgRURERKQSgxQRERGRSgxSRERERCoxSJVC/H0AERFRycAgpYL+D3mq8SQh6NatWyLy8A866uX9w41P6saNGyLyZG1MTEyUf/7552k1iUo4hnp61jjmqKRhkHpM6enpMn/+fPHx8ZFWrVpJVFSUfPDBB3LmzJnHfmLrdDrRaDTKX9HOH4Lu3LkjaWlpcuXKlQLLHjp0SPr06SPz5s2T/fv3y/3790Xk4S3vMzIyJCUlpcBfes/brqSkJPn555/l6tWrRtv2+++/y+DBg+X69esGQU3fzuTkZFm5cqXEx8eLTqczWHd6erosWLBAvL29JTo6WqKioqRPnz6yYsUKuXfP8K/F65d71i+Gj9pecbfncbdf3O0o7AOAmm3nHytFdfr06Sda/nE8yb4tznHzqA9Bz2pMPs8xV5Tt6+dTO+b0y6sdc0XZT0+6b4tr3D3vMZd3G8W5rWf9/sL7SD2mgQMHyh9//CFt27YVBwcHSU9Pl7/++ksuXrwofn5+8sEHH4iXl5fY2NgYXf7UqVPy8ccfS3x8vDRu3FgmTZokPj4+AkA0Go3Ex8dLbGysHDlyRJo2bSoLFy4UFxcXycrKEgsLCxk/frzExsZKy5YtJScnR2rXri2tW7eWa9euSUxMjDRr1kwCAwNl+vTpyjYByJUrV8TNzU1eeeUVsbCwkE8//VTKly8vFy9elEOHDom5ubm0b99eevbsKatXr5agoCCZO3euNG3aVAl+ixYtknnz5klmZqa4urrKp59+Kg0bNpTz58+Ll5eXDBo0SC5duiRt2rQRGxsbmT9/viQmJkrt2rWlZs2aMnXqVPHz8zO6X9S8OOr32ePUjc2bd5pOp3vk31/SHwNj6wEgiYmJkpmZKfXr1y90Pffu3RNbW9vH6kve/ZKWlibnz58XS0tLERHx8vKSihUrKvM+qg83b96UK1euSO3atQvUTp06JSkpKRIYGChOTk4GtatXr8r9+/elSpUqYmFhUWDZAwcOSEZGhrzwwgtGt7t9+3Y5dOiQDBo0yOgfC123bp28//77smTJEgkODlb6rd8f9+7dk23btsnx48fF399fOnXqVGAdV65ckcTERBERsbCwkGrVqomzs7PJfaH3qDGUf16dTidardbkPI8zjtRs29Tyly9fFktLy0f29VHj39T8xTnmREyPu6cx5g4fPiwDBw5UPea2bt0qJ06ceK5jTj9/SRl3xTnm8tbPnDkjp0+flgcPHoiVlZU0aNBAPDw8HquNly5dksuXL0vt2rUL/L09AHLw4EFJTEwUf39/adCgwWOt87GBHkmn08HW1hbbt283mJaYmIilS5ciPDwcdevWRXR0NFavXo2kpCQ8ePDAYB0hISFo0aIF3n33XQQHB8PLywvnz59X1lW9enX85z//wbfffgtvb298+eWXmDlzJl599VW88sor+Oyzz+Dj44N58+Zh6tSpaN68OUJDQ1G1alXUqlULWq0WGzZsAACcPn0a3bp1Q506ddCpUydMnjwZdnZ22LNnDwDgyy+/hJeXF2rXrg1vb2/UqFED5ubmWL16NTp06IDGjRvj+PHjStucnZ2xcOFC7Nu3D126dMGYMWMwZMgQBAUFoWrVqrCysjLYN/v27UNkZCRmzJiBOnXqIDIyEteuXcOGDRuwYsUKxMXFYePGjUhPT3/sY7Bz507s2bMHOp2uQO3OnTuIi4vDsmXLkJqaWqC+fft2HDlyBHfv3jW67gkTJhj0N7+YmBjExcXhzp07yrTMzEzl/127dkVISAj++usvo+s/fvw4YmJiMHjwYKxZs6ZAfc2aNVi6dCk++eQTrF+/Hv/8849SW7RoEcLCwmBlZQU7Ozs0atQIr776Kr744gtcvHgRAJCbm6u0Xf9/vbVr1yIqKgrly5dH5cqVsXjxYuTm5kKn0+HTTz9FQEAAzMzMYG9vj4MHDwIAHjx4gIsXL+Kll15CkyZNMGvWLBw8eFBp14EDB7B+/XqEhITgk08+UbaVlpaGxMRE/PPPP7h37x5atGiBwYMHIyMjAwCwYcMGzJ8/H1OmTMHPP/+Mxo0bw8LCAv7+/li/fn2B/fLWW2+hTp06cHFxgVarxbp163Dz5k0cPHgQmzZtwqeffooWLVrA3t4eGo0Grq6u6NSpEz788EOkpKQAAPbu3Ytt27Zh165dOHToEG7duqWsP/++yu/YsWM4ffq00ZpOp8NPP/2ErVu3Gq2fPHkSV65cQU5OjtH6Z599hnPnzinrym/8+PH44YcfDF5H8s7XrVs3dOzYEZcvXza6juTkZEybNg0TJ07EkSNHCqz/t99+w4YNG7Bx40YkJCTg5s2bSq04xxyAQsdd27Zt0aRJE8ycObNMjrm8+86U4hp3z3vMAYWPu48++ggNGjSApaUlqlatitDQULRu3Rpjx47F4cOHcfXqVZPPp+XLlyM0NBSWlpawsrLC1KlTkZWVpezr2NhY+Pv7w8rKChqNBlu3bkVmZiYuX76MQ4cOGbyeq8Eg9RhOnDgBf39/5Qmf37179+Dh4QERgYWFBXx8fDBq1CjEx8cjLS0NS5Ysgb+/P5KTk9G5c2fs27cPTZo0weuvvw4AWLp0KerWrYspU6YgJSUFmzZtgouLCxo3bozBgwcjIiICgYGBmD17Nvr27YucnBzcv38f69atg7m5OVxdXWFtbY2WLVsiPj4ejRo1QmhoKGbMmIG+ffvC3t4e9vb2uH37Nk6ePAlPT0989tlnOHz4MOLj49GyZUtYWFjgzJkzOHDgAMLCwlCuXDksWrQIy5Ytg5+fH7KzswEAf/75J6ysrPDKK69g+fLlGDhwICwsLLBhwwbliXXz5k04OzsjJycHN2/eROXKldG8eXNUrlwZTk5OqFu3LkJDQ9GuXTvExsbi0KFDAIw/ue/evYuYmBhUrlwZlpaWcHFxUcKITqfDrVu30KNHD7i4uKBcuXKoWrUqbty4gevXr2P//v3YvXs3bGxs0KlTJ7z77rtYv349/v77bwDAuHHjsGPHDlhYWODSpUvKNnft2oVff/0Ve/bswenTp2FnZ4dff/0VAHD27Fm88847GDhwIAYOHIiVK1dCo9GgXr16aNCggTKf3o0bNxAaGorAwEC0atUKFSpUQGJiIg4ePIjp06cjIiICPj4+8PHxgZOTE2xtbdG0aVNMmjQJJ0+ehJOTE9577z1cuHABx48fx8yZM/Hiiy/C19cXbdu2hbu7O9566y0lCOrl5uYiPT0dNWvWRPfu3bF69WpMmDABtWvXxvHjx3Ht2jVUqVIFs2fPxsWLF9GnTx9MmzYNffr0QdWqVREeHg43NzeUK1cOlSpVgoWFBVq1aoVVq1YhODgYQ4cOhUajQVJSEgBg1apVCAkJgbW1Nezt7dG1a1dYW1vj3Llz0Ol0GDFiBNzd3eHt7Y1mzZohODgYZmZm2L59O7p06QIHBwfMmzcPWVlZAIB//vkH9vb22LJlCwBgzpw5GDJkCIKDg+Hr64vAwEDY2Nhg5syZyMrKwokTJ1CzZk3UrVsXvr6+6Ny5MwYMGAA3NzdYW1vDxcUFTZo0wWuvvYbvvvsOt2/fVsaQ/l/e5/PkyZPh6+sLKysr+Pv747ffflPqt2/fxsCBA1GxYkVYWloiMDAQDx48UALon3/+CScnJ7z00kuYP38+jh8/juvXryv9SEhIgJ2dnUHoP3r0KP78809cunQJaWlpcHR0xLp16wAA165dw+zZszFx4kRMmTIFmzdvhkajgY+PD9q0aaOMZ72bN28iMjISvr6+8PX1RcWKFZGamorExESsWLECXbt2RbVq1ZQw4OPjg169euGrr75CSkoKnJycMH78+Kc+5vTH1dS40x8rGxubMjfm/vvf/yrhTj/WnuW4mzx5MmxtbZ/LmFu1ahV+/vlnDB8+vNBxV65cOeV4nDt3DsuXL8frr7+OsLAwhIeHo3Llyujbty82bNiAGzduKNu+du0avL29MW7cOHzzzTeYNWsWvL29sXPnTgAPw3blypUxf/58ZGdnY/To0Rg9ejSioqLg4eGBoKAgLFmyBE+CQeox3Lt3Dy1btkTz5s2VJ2l+ISEhqFy5Ms6ePYupU6fC29sbGo0GDRs2RO3atdG/f38sXboUWq0WALB582bUqFEDSUlJaNOmDfr06QONRgPg4RmSBg0aKJ9wjh49Ch8fH2zYsAG9evXCjBkzADw8k+Hh4QF/f380bdoUAwcOxJQpU9CpUydcuHBBadsXX3wBc3Nz/Pbbb/jqq6/Qvn17gz7Uq1cPnp6eWLBgAQAgKysLb7zxBmrVqoWuXbuia9euSrKfOHEigoODlWD1xx9/wN7eHhEREQCA7OxsTJkyBTVr1gQA5OTkoEGDBqhQoQJ27doF4OEZmi+++EJ58bSwsMCQIUOwa9euAmeNZs+ejYYNG2L06NG4fPky/vOf/yA0NBR37tyBTqfDjBkz0KhRI+zYsQM5OTno2LEjJk+eDGdnZ/j6+qJRo0awt7dHYGAg6tSpAw8PD3To0AEffPABNBoN+vbti4YNGwIAzp8/j+HDh6NcuXIwNzdH1apV0bBhQ6V++PBhtGjRAt7e3ujTpw86duyIqlWrws/PDxcuXEDz5s1RqVIlrFy5UtlfU6ZMQePGjXHv3j0AwPDhw9GnTx/Y2dnB19cXNjY2GDVqFABg06ZNqF69Ojp37oyaNWuicePGCAkJMTom4+Pj4enpCRFB3bp1odFoULt2bcyaNUt5sZw2bRqCg4MREBCAs2fP4vr16+jcuTO6dOmCadOmoWnTpsjKykK7du2wdOlSWFtbIzo6GuvWrUOnTp1gYWGB/v37Izc3F1u2bEHHjh1hbm4OjUaD6tWro1atWjh37hz279+PBg0aoHfv3vjjjz/w3XffwdPTE7a2trhz5w52794NDw8PbNu2DcDDT83h4eEQERw+fFgZ8z4+Ppg7dy4AYN68ecqYAh6GW41Gg/nz5+PIkSPo0KEDRATr1q1TPqV+8skneO211xAfH4/KlSujfPny+P7775GTk4N9+/ZhwoQJCA8Ph5OTE+zs7DBlyhQkJycb7Nfc3FzMnTsXQUFBGDlyJBISEtCtWze0bdsWOTk5yM3NxaxZs9CoUSNs3boVf//9N1q1aoXPPvsM1atXh4uLC5o2baocD1tbW9jb26Nnz55YsmQJrK2tMWTIEAQEBAAALl26hPfeew8uLi7QaDRwdnZGixYtEBwcrDy/2rRpgwoVKiAsLAzNmjWDj48P/P39sW/fPlSrVg2+vr7YvHmz8sY8depUhISEKGd8+/bti5EjR8LGxgZubm6ws7PD+++/DwBYsWIFnJ2dERISAldXV0RFRSE0NLRYxpy+3qRJE7Rr1w6pqan48ccfYW1tjX79+uGnn35CeHg4tFotEhMTy9SY8/LyQrNmzeDm5oZp06Y983Fnbm6uvCY/6zHXsGFDeHt7w8fHRzke+cdd27Zt0ahRI6Pj7uDBg6hTpw40Gg1CQ0OV1+YRI0Zg3759mDx5MsLDw5GcnIzq1avj2LFjGDJkCBo3bgwAmD59Opo0aYKIiAgkJyfjl19+gZmZGd5++23s2rVLCehHjx41uv3HwSD1mPbu3YuAgAA0adIEK1asQEpKivLmeOfOHfj7+6NOnToGy/zxxx8YNGgQzM3NYWlpCXNzcwwYMEAJIZGRkRg9ejT69OmDZs2aoWfPngCAxo0bK6FGp9MhKysLHTp0wKxZs7Bz5074+voiKSkJrVq1wrBhw9CwYUNUr14dnTp1goODA5YvXw7gYYjR6XRITU2Fvb09GjRogClTpqB79+7KqcyrV69Co9GgU6dOiImJUV4grl69ijfffBNarRY2NjYYPXo0pkyZAk9PT+VFWK927dowNzdHu3bt0KJFC1SpUgWrV69W6pUrV0Z4eHiBfZqbm4tatWrB0tIS5cuXh5mZGfz8/DBx4kQcP34cOTk58PPzQ+/evZUX95SUFNSrVw+TJ08GAPj5+eGNN95QXqi7du2KmjVr4ttvv8WBAwcQGhoKLy8vjBs3DgDw008/YcCAAXBycoKNjQ1sbW0RHR2NP/74A8OHD0eLFi3w3XffIScnB//9739hY2MDX19fAEB0dDT69u2rnM04c+YMbG1tUalSJVy7dg1ZWVkYPnw4vL29sWzZMgBA06ZN8cUXXyh97t27Nxo1aoTff/8dQUFBiIqKgqurq/KJvW/fvpg7dy7i4+Ph4OAAZ2dn5SvD+/fvG5yCfvnll+Ho6IjPPvsMe/bswZtvvgkPDw+YmZkhIiIC9evXR+fOnWFra6ssc+jQIbi5uSEwMBAff/wx/vvf/0Kr1SI6OhqtW7dW+nbjxg0EBQUhPDxcOXMKADNmzICHhwesra0hIoiIiEDv3r0xYMAAg68EfvjhB5ibm+Pjjz/GjBkz0Lt3b4Nj7+7ujuDgYMycORM6nQ7Xr1/HmDFjoNFoEB0djTFjxqB58+bK19+DBg1Chw4dlA8A48aNg6enJ0aNGqVMe/vtt9G2bVsAQLVq1eDg4FDgKxKdTgcfHx9otVo4OjpCo9GgcePGWLx4sdL3mjVronfv3njhhRcAPHwTrl69OhYuXAgAqFGjBt544w28+uqrAIBOnTrBx8cHn376KTZt2oRq1aqhRo0a+PjjjwEAcXFxiIyMhEajgYWFBcqVK4fRo0cjLS0No0aNQtOmTfHRRx/h8uXLmD9/PiwtLZXwHh0djR49eihB5dChQ7CysoKHhwcePHiAtLQ0dO/eHfXq1VO+Xg8NDTX4hN2jRw80aNAA8fHxqFu3LkJCQuDu7q68mffs2RNff/01Vq5cqZzVLY4xt3PnTkRGRqJ///7KB8r84y4lJQUVKlRA69aty9SY++abb2Bubg4nJyfUqFHjmY87EUGrVq2wadMmvP766890zP31119wcnKCk5MTLl26pHzIzDvu9K91+stPsrOzlfdJ/bGoWLEi5s+fj8uXL2PmzJmoV68eNBoN7O3t0bZtW4wfPx6Ojo4AHn4o9vLywqpVqxAVFYW+ffvC0tISAPDqq6+idevWyth58OABWrZsqexnNRikiuDYsWPo3r07rK2tUalSJXTp0gX/+c9/4OPjg8DAQOW0aGZmpsHp28OHD6N3797QaDQG3x2vXbsWFStWxL59+1CuXDns3r0bOp0OFy5cMHiBuH37NpydnZWvFpcvXw5fX19oNBocOHAAZ8+exdKlS9GrVy9EREQoqT//8o0bN0ajRo2g0WgwZswYHD58GA8ePMDChQtRvnx57N27t0Cf58yZAwcHB7i4uKBNmzaYNGkSgoODlbNlycnJqFSpEubNm4fevXvj1VdfVZ4MAHDkyBFYWFggMDBQ+bSSnZ2NnJwc/PPPP2jatCliYmLg7++PdevWYdy4cfDy8oJWq0VwcDBcXV1RvXp1/N///Z+yzsWLF8PHxweHDh1CzZo10ahRI+XN3sLCAt99950y7/bt2xEUFIT69esrLzAAUL16dbRp0wYiAo1Gg0mTJqFq1aoFvpobPnw4LC0tsWvXLrRv3x5fffWVUjt69Cisra0REhKiLJeamorXXnsNWq1WCXi9e/fGlStXcP/+fdja2mLVqlW4c+cOOnbsiFGjRqFx48ZK8KxQoQLWrl2rbLtcuXIYMmQI7t+/r2w3NzcXDx48wJw5c+Dp6YkPP/wQwMPgnJKSgjVr1uDll1+GlZUVRASTJk1SlgOAl156Cd7e3vj666/RokULvPXWW+jfv7/SB/3xadWqFWbPno169eph1qxZAB6+mH/44YcIDAxEvXr1EBYWhkqVKhW43uT27dvKG9fixYvx4osv4syZMwCAc+fOQavVIiIiAh988IHBcqtWrULdunXRvXt3eHp6YvDgwejVqxd8fHwwZswYpX379u2Dubk5unbtCuDhBx1HR0f88MMPuH//Pjp37owKFSpg5cqVAB6+WGZlZSE1NRWhoaHo168f6tatiyVLlqBfv36oWLEirKys8MILL8DNzQ3+/v544403lHZNnjwZAQEBOHnyJHx9fREaGoohQ4YAAKysrJTtAMDq1asREBAAPz8//PTTTwZjLiIiAiICEUFsbCyqVKmCn3/+2WAfdO7cGTY2Njh+/DiaNWtm8KHkjz/+gKWlJYKCgrB7924AwF9//YW2bdvC3NwckydPRlRUFEaNGqVc02dvb481a9YgIyMDkZGRylnlTZs2AQAcHR2V/7/88stwcHDA66+//lTHXI8ePdCtWze8+uqr8PPzw1tvvQUARsddREQE3NzcysyYAx6+Lnh7e8PT0xP79+/Hpk2bntm4059FdHd3h4jA0dHxmY05AMjIyEB4eDg8PDywefNmZUzkHXc9e/ZExYoV0bVrV4NrTfUnEr7++mt4e3tj6tSpBu1OSEiAv78/7OzsoNFoMHnyZOVkwJtvvolWrVrhnXfeQd26dRETEwMAGD16NOLj4wFAOT4vvPCCcmZSDQYpFfTXPXXs2BE9evTA5MmT8eeffxaYLzc3VzmoixYtgo2NjcFXapmZmWjbti3q1q0LDw8Pg2X18+Xm5mLZsmXw9PRUajk5OXj33XcxbNgw5ayYfn2nT582OG2cm5uLpUuXwsPDA7du3cLixYtRqVIlaDQaBAYGwsvLSzlNamz7+raHhobi/v37uHXrFlq2bIno6GiMHDkSgYGBaNeundH9dOPGDSxYsABRUVGoXr06xo8fb3CBeUpKCubMmYMVK1bAzs5OuU4pJycHu3btQufOnaHVaiEiuHjxotKmnJwcBAYG4q233lLOmp0/fx4XL17Em2++qXw9mJubi8TERHh6eiI+Ph61atXC1q1bcebMGVhaWmLz5s1o2bIlwsPDUaNGDdStW1e5mFYvISEB5cqVQ8+ePTF06FC8/PLLyidI/TVOdnZ2Bl+lAsCSJUtQq1YtdOzYEb6+vujYsSMiIiLg6+urvMB8/PHHcHFxgZWVFX755ReMGjUKlSpVUvb//v37UaVKFVSqVAnly5fH0KFDldPPKSkpWL58OWxtbZVP0HllZWVhwYIFEBHlU6B+/x05cgRubm5Yt24dLC0tkZiYiKSkJIOLYK9cuQJra2skJSVh+/btePnll7F+/XpYWlri1KlTuHXrFtasWYOBAweidevWynUleY+t/rS+RqOBRqPBgAEDsG3bNuzZswcTJkxAxYoVlbbr25ednY0VK1agUqVKypmzkSNH4quvvkJYWJjy5r5p0ybY2NjAxsYGlpaWcHd3V87oAg+vOxQRTJ8+3aBdZ86cwTvvvINly5bB0dERly9fRlZWFs6fP4/ly5cjPDxc+QSfd8zdunULPj4+GD9+PF555RVlzP3999/o06ePMuZ0Oh3++usv+Pj44JtvvoGPjw+OHz+Os2fPwtLSEqtXr4aPjw+Cg4PRoEEDBAQEIC0tzaCNP//8M+zs7DB8+HC89dZbGDRokHJW6IMPPkBkZCQcHBwKjLkJEyagZs2a6NatG1xcXDBw4EC0bdsWzs7OyhvHe++9h6pVq8LW1hbHjx/HlClT4OTkpHz637ZtGzw9PVGxYkVlzB05cgQ6nQ4pKSn46quvCh1z8+fPNzrmfv/9d1StWhXx8fGwsLDA2bNnkZubi6SkJIMLiJOTk2FjY4Nvv/0W3bp1w/r162FhYYFTp07h5s2bWL16NQYMGFDomAsMDFTGXP/+/bF161bs3bsX48ePR8WKFZULrk2NuYCAAGXMNW7cWBlzGzZsgI2NDaytrQsdc7GxsQbt0ul0OHPmDIYOHQpbW1ukpKQoAaE4xt3KlSsNxp25uTm8vb3RvHlz1K1bF/Xq1TM55t58880CY27ixInKmMv/lWTeMefq6opBgwYVGHM6nQ4jR45ULvK+ceNGgXEXHx8PX19f1KpVC1ZWVujWrRs2btyIixcv4ujRo/j0009hb2+P8+fPF7i0Ji0tDYsXL4ZGo8GFCxeU+tmzZ+Hh4YG1a9cqY06n0+HGjRsGr3WXL1+Gra2tcu2dGgxST+hRv8DQmz17tvIJC/hfUPnmm2+UMyLGrF69GmFhYQZnU4CHYSL/r0GM+eGHHxAQEKB8gtRLSkrCwoULsWjRImzfvt3gNKoxeQPQpUuX8H//938ICgrCpEmTkJiYaHK5ixcv4uLFi1i4cKHy4vzaa69h+/btOHfuHL799lv07dsXQUFBRq89GzBgAPz9/QFAedEDHl6bEBERgcmTJ8PHx8fkPpk9e7ay/OLFizFs2DD069cPERERyMnJwfXr1/HLL79gzJgxGDt2bIEg9dFHH6FatWoGgaBfv35YsWIF5syZgy5duqB58+bK/Po3hfv37+Pzzz+HiKBx48bo168ftm/fjvHjxyth7LfffoO/v7+y3mbNmuGbb75R1jVz5kz4+/sjLS0N06dPR8OGDWFpaQlHR0fUrl0bvr6+mDBhgsl9P2nSJGXf5G2fTqdD7969YW5ubnANln7/X7t2De+++y5CQkKU/owdOxYajQadO3dWjoF+/vT0dIPxce3aNYwdO1a55mLdunXo2bMnHBwcYGlpCV9fX9SuXRuff/65ybYnJCQoZy30P1oICwtD+fLlleA7dOhQ7N+/H2vWrMEvv/yivKn8888/GDNmDKpWrQpra2t4eHhg/PjxSExMVK73eu2119CgQYMC283KykLbtm1Rv359pY/6/r7//vto164dZs6cqezX+/fv48qVKwbryDvmJk2ahHfffReDBw9G8+bNkZ2djdTUVHz33Xfo2bMnBg8eXGDMzZ49G76+vnB3d1fGxsSJE7F7924sX74cPXv2VK7/0O8f4OEFvxMnToSIoFmzZmjSpAnWrFmDN954QznLcejQIdSqVUtZb8OGDbFo0SIAD88czJw5E/Xr18e1a9cwdepU+Pv7w8bGBuXKlUPNmjUNxpxOpzP42u/mzZsGz8e8+06n06Fbt24FxpxeRkYGrl27hvfeew8hISHIzc1FTEwMzMzM0KFDB2V86cfc1atXlbPiwMOvcsaNG6eMuTVr1uCll15ChQoVoNVqlV8p5x1zeV/zMjIyDMZcVlYW/vnnHzRr1gz29vYICQlRvlo7fPgwVq9ejQ0bNijfHOjHnJubm/I12HvvvaeMud27d2PQoEHKuMhPP+7q1aun9FN/tiTvuPP29gbw8GxX3v7rx03dunUBPBx348aNU8bd5cuX8dVXX6Fnz54YNGhQgUA0e/Zs+Pj4oGrVqgXG3MqVK9GjRw+DMaffd3nHXHh4OJo0aYK1a9di6NChypi7ePEi3njjDZQvXx6WlpbKh3j9uAOgjDvg4fVTERERsLKyQrly5VC9enXUqFEDc+bMUebXh2D9++/kyZOVkxF5992wYcOg0WgQFhZm0F/9cleuXME777xToF5UDFLPSN6fYual0+lw4MABk7cC0Ol0SEpKMjjzVBQ6nQ7nzp0z+On+02Is+BTmxo0bmDt3Lho1agQLCwtUqlQJ7u7u6NSpExISEgrMf//+fdSqVavAJ7zc3FzcvHkTQUFB0Gg0+PLLL41ub+/evQgODsZnn30GnU6HmzdvomvXrtBoNAaBRe/69esGx2jPnj1o0KCBcr3aL7/8gldeeQX29vaoWrUqfHx88Nprr5m87QHw8FNs3q9aT548CXd3dzg6OqJKlSoIDw/Ht99+i0OHDhnc9uDQoUMICQlRAvTdu3eRlJSEhIQErFy5EnPmzMHp06eVF4z8YysrKwsLFy5Uzn7lrefm5mLNmjUQEXzxxRcFflL8yy+/oE2bNgZfkV69ehXjx4/Hrl27lHWZGpObN29Gs2bNEBcXB+DhG/3t27eRmpqK+Ph4rF69GlevXjXa9rxvvvr9kTcozJ07F3369MH333+vnBnMb9++fRgxYgQ2bNiAY8eOYdSoUahZsybMzc3h6OgIV1dXhIeHY9u2bQXGcHp6OqpVq2Y0oCYlJcHPzw8iYvChKK89e/agfv36mDZtGoCHn3bbt28PjUaDr776ChkZGcjIyFD6mJaWZtD/3bt3o27duvj000+Rk5ODL7/8Eq1bt1bCjP7n9ps3bza6/du3b2PWrFnYuHGjMm379u1wcnKCm5sbPDw8UKdOHcyePRubNm1Svvo6ePAgmjVrBnd3d4waNUoJCLdv38bmzZsxa9Ys1KlTB+PGjUNCQoLBsdffHqBdu3bo2bMnPvroI6P1oKAgiAjeeecdg/r27dvRoUMH5YckK1asAPBwLAwbNgxxcXHo0KED5syZg927dxu8lt24cQMHDx5ESEgIfH19MXHiRIMfrJw6dQpLlixBUFAQpk6din379hltW/v27TFnzhxs2bLFYP3Jycl455134Obmhn79+uG3334rEB4vX76MHTt2YMyYMdiyZQuOHj2KkSNHwt/f32DMRUZGKq8FeY/5pUuXcOXKFdSqVUv5wJt3XO7fvx9+fn7QaDRGr+O5fPkydu7ciaCgIOW1Sn/7EhHB/PnzDebPG/z1bW/QoAHmz5+PrKwsLFq0CG3btoWNjQ3s7Ozg6uqKHj16GP119eXLl5Geno5PP/3UYMzt3r1bGXOenp4ICgrCt99+i4SEBGzcuFEJcufPn8f8+fPRoEEDzJs3z6CdV69eRVxcHMaNG1fgF6L6ZTds2ICUlBRs3LgRO3bsKFCfOXMmRETZL/n98ssvaNeundHb0hQFgxQVG2NvtDqdTgkFW7duxb59+0wue+/ePcTFxRm9x8e9e/cwbdo0aDQaZTt5n+C3b9/GggUL0LVrV4PrzVJSUrB48eICZxHytg94eEr9448/RlRUlMG1Inq7d+9W7qdijLF7VuW9PcTXX3+Njz76qMApduDhLSY6d+6s/Nz37NmzBvW//voLr7/+OmrUqIF+/foVuDeMvl69evUC9bzLRkVFKT9jzrvswIED4evra7Cs3smTJx+57YEDB8LHxwevvvqq6rbnr+uDR96+5V2//o1p27ZteOGFF+Dk5ITOnTsjLS0NOTk5+PPPP7FgwQIEBgaiXLly6Ny5s3IxrX58bdu2DS1atICtrS06depktK6/zYmpup+fHywsLAzWv2fPHkycOBFbtmxR2tahQwdlDOrH57Zt21CrVi3lhxv65a9fv47U1FR8/vnnCA0NRcWKFdGlSxej23/hhRdQvnx5tG/f3mCMx8XFoXbt2rC2tka7du2UcZednQ2dTod3330XGo1G+XXZ66+/jnXr1iEuLg52dnZKvVWrVoiIiMB//vMfrF69GosWLYKdnZ1yxrJly5aF1hs2bIjmzZsb1C0sLJR1h4WF4fXXX8eqVavw9ddfo1y5cnjnnXcKbHvVqlX48ssvDdbdtGlTpf7jjz9i8eLFRWp7/vV//vnnBsu3bNlS2Tc//PADFi5cCDs7O7Rp00b5MYue/ozzgQMH0LBhQ3Tp0qXA/Zn0Z5Tatm2LESNG4IMPPlDmyV8PDAyEmZmZ8lqXm5trUG/dujXatWtnsI2ffvoJ1atXx+jRo5Gf/rWrbdu2Sr/1r3PZ2dlITExEamoqGjdujOjoaINl87ctf9+Bh69/f//9N2rXro3g4GAlsOvpx27Pnj0RGRmJkSNHIjMzExcuXMDatWuxYcMG5ObmomfPnujbt69yu4Pk5GT8+OOPWL9+PXr06GGylnfZP/74Azk5OQXqeg8ePCjySYH8zJ/u7T2J/mf8+PHSpEkTCQoKEldXV7GyshKNRiO2trbyySefSJMmTaRy5cqSmZkplpaWBne+HT9+vAQEBEiLFi2M3u5//PjxEhQUJAkJCcqdffMuP3HiRAkKCpJZs2YZLFelShUZNGiQvPXWW1KvXj2JjIxU2pZ3HR988IEEBQXJ/Pnzjd6R98cff5T69etLixYtxMXFRaytrQ3qEyZMEH9/f2nZsqVS169n8uTJ0qRJE+nQoYM4ODgUuOtv//79xcbGRkaMGCFr166VyMhI2bFjh/j4+IiISHR0tNjY2Eh0dLRS37lzp3h5eRnU+/fvX6AeHR0tdnZ20qdPH9mwYYO88MILBZa1tbWVgQMHGmzb29tbREQGDBggtra2hW7b1tZWBg0aJGvXrpWWLVsaLP84bX/U+vP2rWXLlkodgLz++uvSunVrGThwoIwdO1Z++uknuXXrlhw/flxWrVolHTt2lDFjxsi4ceNk/fr1cv36dTl+/LhkZ2fL7t275aWXXpIhQ4bIe++9Z1DPysqSvXv3SqdOnaRKlSqyZMkSo8t37NhRYmJiZPr06Ur93Llzcv36dVm8eLG89NJLMnDgQBk3bpxs2LBBrl27JidOnFCW79Chg4waNUpmzJgh69evlxs3bsixY8ckJydH2f7IkSMLbX/e9aenp8uxY8dk/fr10q5dO5kwYYKyX9LT0+XkyZOSk5MjkZGR4u3tLSNGjJA7d+7Ili1b5MiRI3Lp0iXx8PAQe3t7cXd3l06dOsnt27cL1J2cnMTd3V06d+4st27dkl9//dWg7ujoKO7u7hIdHV1geTc3N3nw4IE0a9ZMzM3NlVpycrK4u7tLhQoVCt22vt69e3el/vvvvxe57abqDg4OSt/09aNHj8qlS5fE3d1dfv31V3njjTdEROSvv/6S999/X/7++2+pXr26BAYGyrFjx2Tx4sViZWUlp0+flvHjx8vJkyelevXq0qhRI/n1119l2rRp0qBBA0lMTDRaP3DggGRnZ0tycrLR+p49e8TX11eSkpJk/Pjx8ueff0r9+vXl3Llz0r59exERg23XqFFDgoODlWW9vb3lwoULMn78ePnrr7+kWrVq0qhRIzl06JB89tlnBZbP3/a89RMnTki1atUkNDRUEhMT5cCBA1KtWjVl35w4cUJq1KghjRo1kg0bNsivv/4qoaGhsmTJEpk2bZrY2NjIgwcPxMLCQpKTkyU+Pl7Kly8vX375pUybNk1sbW3l/v37cuHCBZk0aZI4Ojoa1B48eCAxMTGSnJws27Ztk/r16xeov/XWWzJp0iTp0aOH8tr/RJ4ohhGZoL/2K/8NSlNTU/HVV18pNVtbW7z66qvKzUuzs7OVZTUaDapWrWpwc9MnqaempiIzM/OJln/S9i1fvrzQvsfFxaFOnTqIiorC8ePHcefOHYObty5btgz+/v54//33kZKSUqR6XFwc/P39ce3aNcTGxuLMmTNPbd156xMmTHii5dXWTd3YNjQ0FM2aNYOtrS38/f1x+fLlAje9rVWrFqytrZUzdKbq+jNkpur6M2R5tz1gwACT9cdZfvDgwahZsyasra2VT/aPu3zjxo3RvHlzpe+XLl0yesNf/XWUxm746+fnh8aNG8PPzw9dunQplrqvry9cXFzw999/P/NtP0nd2M2QQ0JCEBsbi969e8POzg7lypXDvXv3cObMmQI3S9bX7969W2j9wYMHJuv29va4f/++QT02NhYhISEwMzNDz549cfLkycdaVt92/b3uypUrV2Dd+dtmrJ53eVN9098o+ubNm0ZvFN25c2flxy356zNnzkT58uVRu3Zt/PzzzyaX/euvv4yu+80330SdOnUKnClTi0GKisWgQYMwdOhQozcoDQ4ORvfu3TFjxgyYmZkZ1GJjY9GlSxdERkZCq9UWWPZp1Dt37lys6y+sHhwcjG7dupnse0REhPKzYv01RHlv3tqpUyf06tULGo2myPXWrVvjnXfewfbt26H/DPW01l0S6oXd2LZNmzYYNGgQfH198fPPPxe46W2TJk1Qvnx55Wfhpur6n2sbq+f9Wbma9T/p8qbqj+r7o274e+bMGSxatAj9+/cvlvrff/+NhQsXwtfX95lv+0nrj7oZcvXq1WFlZYXTp08/Uf3UqVNFXj4oKAgvvvgiKlWqhBEjRjzVdT+N+qNuFL1z507Y29tj+vTpBeqnTp1CUFAQgoOD0a9fvyItCzy8Li08PNzktVNFxSBFT112djamTZtW4LvzP/74A4MHD4aVlRUsLCxgYWGBAQMGKLXXXntN+WWXmZmZUisr9cfpu1arhZmZGfr376/sS+B/N299+eWX0aBBA/To0aNI9YiICOXC/V69eqFnz55Pbd0lpW7qxrb3799XLlDX39g2701v7927h169eiEoKEi5iLys1B/V90fd8Df/bVGKs/48t62m/qibId+9exf169eHtbU1AgICnmn99u3baNiwofKnp2xsbEpM2x7nRtHAw+vAKlWqBF9f3wL13NxcNG3aFG5ubggPDy/SsnqvvPKKcm+pJ8UgRcXixo0bOHXqFADDG5Tqa7NmzYJGo8HBgwcLXOi3cOFCiAiOHj1aYNnSXi+s7zqdDlOmTFGWzVvT37x148aNsLa2Vm7e+rj1NWvWoHz58pgwYQIcHR0N/obXk667pNRN3dhWp9MhOTkZhw4dgrOzMw4cOGBw01v9RfgVKlRQjklZqT+q70DhN/zVT8v7y87irD/PbRe1/qibIet0Ohw7dgyOjo6Iiop6pnWdToezZ8/iiy++gLW1NYKCgkpM2/QKu1F0dnY2duzYAQcHB4SGhhqtr1q1Cubm5qhdu3aRl92xYwfKly9v9NfiajBI0TNj7Aalj1Mr63VTtUfdvPVJ6sW57pJQ1yvsxraF1cp6vbCaqRv+Pov689z2k9QfdTPk51l3d3cvsW17nBtFF1YfOnSo6mXzn3F8EgxS9Fzkv0Hp49bKet1Y7VE3b32SenGuuyTU9Uzd2PZRtbJeV3vD3+KsP89tP426nqmbIZeEeklt26NuFF1Y/UmWfVIawMhvy4mKWXZ2tmi1WuXWBY9bK+v1wmoA5NChQ+Lr6ysVK1Z8qvXiXHdJqScnJ4uzs7PY2Ng8dq2s1x+1LKkHQJKSksTZ2Vns7OxKVL0kt600YpAiIiIiUsn4R2YiIiIieiQGKSIiIiKVGKSIiIiIVGKQIiIiIlKJQYqIiIhIJQYpIiIiIpUYpIiIiIhUYpAiIiIiUun/AaTUZdo/SnotAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def evolve(iter,wavefunction,n=6,plot=True,hist=True):\n",
    "    phi = 0.3  # function of time step\n",
    "    q_reg=QuantumRegister(6)\n",
    "    aux_reg=QuantumRegister(1)\n",
    "    clas_reg = ClassicalRegister(6)\n",
    "    qc=QuantumCircuit(aux_reg,q_reg,clas_reg)\n",
    "    initialization(qc,wavefunction,q_reg)\n",
    "    i=0\n",
    "    snaps=[]\n",
    "    for i in range(iter):\n",
    "        apply_QFT(qc,q_reg)\n",
    "        Time_Evolution(qc,n,q_reg,aux_reg)\n",
    "        apply_invQFT(qc,q_reg)\n",
    "        if i%2==0:\n",
    "            snaps.append(qc.copy())\n",
    "        i=i+1\n",
    "    for snap in snaps:\n",
    "        display_histogram(snap,q_reg,clas_reg,plot=plot,hist=hist)\n",
    "\n",
    "\n",
    "evolve(iter=10,wavefunction=wavefunction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets work on a gaussian wavefunction with initial kinetic energy, which means a wave that is travelling forward\n",
    "\n",
    "$$\\psi(x,t_{0}) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}\\left(\\frac{x-x_{0}}{\\sigma}\\right)^{2}} e^{i\\hbar k_{0}x}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "e:\\miniconda\\envs\\QGSS\\Lib\\site-packages\\matplotlib\\cbook.py:1762: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return math.isfinite(val)\n",
      "e:\\miniconda\\envs\\QGSS\\Lib\\site-packages\\matplotlib\\cbook.py:1398: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4,4, num=64)\n",
    "\n",
    "\n",
    "\n",
    "'''wavefunction: guassian wavepacket with moving forward(+ve x axis) in time'''\n",
    "x0=-2.25\n",
    "hk=-3\n",
    "unnormalized_wavefunction= (1/(np.sqrt(2*np.pi)*0.4)*np.exp(-(0.5*(x-x0)**2)/(0.016)))*np.exp(-3j*x)\n",
    "\n",
    "\n",
    "Normalisation_Constant = np.sqrt(np.sum(np.abs(unnormalized_wavefunction**2)))\n",
    "\n",
    "forward_wave = (unnormalized_wavefunction)/(Normalisation_Constant)\n",
    "\n",
    "\n",
    "plt.plot(x,forward_wave)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/5NLLLmo4FRGZiBQ+ZMyFMppNDcMY9ng1nIqITGwKHzLmRrLNFtTzISIy0Sl8yJgbyTZb0G4XEZGJTuFDxlyhF5VL8qWGjCl8iIhMRAofMuaSlY/hLiqXVO514SGKp69tLE9LRETGyfBDF0QOU2iElY9yj4Ofu7/PmR2boO1paFg4lqcnIiJFpsqHjLmRXFQOoLHjOd7ufAknJux9bixPTURExoHCh4y51FbbQioflsXUDT9M/7lr99iclIiIjBuFDxlzfdER7HbZsY7S/elqh9W1a6xOS0RExonCh4y5/kIrH5YFT94AwB6zHgCzQ5UPEZGJRuFDxlxfoeFj+1rY8wyWq4T/in3Yvk3LLiIiE47Ch4y5UCHLLpYFa+2qh7HsSl5zLQLA0bMfYpExP0cRESkehQ8Zc8mG0yG32m5/EvY8C64SeOs1hD01hCwPBhZ07y3SmYqISDEofMiYG7byYVmw9kb765M/BhVN+Erc7LXsvg861XQqIjKRKHzImEtfWC7PTLttT6SrHmd8FrCnnO616uz71fchIjKhKHzImBvywnJZVY+PQ0UTAOVeZ7ryofAhIjKhKHzImBvywnLbHrenmGZUPQB8XrfCh4jIBKXwIWMu74XlBlU9GlN3+VT5EBGZsBQ+ZMzl3e3y5uOw93lwlWZVPUA9HyIiE5nCh4y5dMPpgPDx1+/Yn0/JrnoA+Epc6cpHcD/EwmN9miIiUiQKHzLmQrkaTi0L9q23vz75Y4Me4/O4OIifiFECWBDQrA8RkYlC4UPGlGlauSsf0RCYUftrX8Ogx/lKXIDBQXeiIqKlFxGRCUPhQ8ZUOGamvs7q+Qh3258NB3h8gx5X7rVngrQ5k+FDg8ZERCYKhQ8ZU32RWOrrEldG+OhPhA9vBRjGoMf5EuFjv5GoiqjyISIyYSh8yJhKLrl4XQ4cjoyQkax8lFTmfFwyfOw1td1WRGSiUfiQMZV3m21/l/3Zmzt8JJdddpm19g0KHyIiE4bCh4ypvBeVSy67lPhzPi5Z+dgR06wPEZGJRuFDxlRqm+3Aysdwyy4ldvjYGq6xb9CsDxGRCUPhQ8ZUX74BY/0B+7M3T+UjcQXc1ng5lrvcvlGzPkREJgSFDxlT/cmeD7drwB1DL7uUe5NhxcCsnGF/qe22IiITgsKHjKnUReXyLbvkqXy4nA5K3PaPZ8Q33b6xU+FDRGQiUPiQMZVsOC0b1HCaWHbJ0/MB6abTUPk0+wY1nYqITAgKHzKm8jacDrPsAunw0Vs61b5B4UNEZEJQ+JAxlfeKtsMsu0B61kfAO8W+QeFDRGRCUPiQMdWX64q2UNCySzJ8dHoUPkREJhKFDxlT/dF8E06HnvMBUJEIH+3Ji8v1tEC0f9TPUUREikvhQ8ZU8sJyJQMrH+Gh53xAuvLRYfogY9ZHW18bd79+N+G4ho6JiByNFD5kTIWiJjBg2cU0IRy0vy5g2aU3YkL1LPvGrl3c9NJNfOPZb/CD9T8Yk3MWEZGxpfAhYyqUqHxkLbtEesCyQ8lQu10qEiPWe8JRqJpp39i1i13d9ryPe7fcS1tf2+iftIiIjCmFDxlTOXe7JHe6ONzgKsn72HJPMnzEM8LH7lTgiJgRbtl0y+iftIiIjCmFDxlToVy7XTKbTQ0j72OTI9Z7w7FU+LA6d2VVO+574z5ae1tH+axFRGQsKXzImOrLNWQstc02/5ILZC67pMNHMLCLUCwEwPG1x9vVj1dU/RAROZoofMiYyrnVtoABY5BuOM0MH23BfQBUeiu5Ztk1gKofIiJHmxGFjxtuuIFTTjmFiooKGhoauOSSS9iyZUvWMf39/axevZra2lp8Ph+rVq2itVW/GCar1IXl8i27DCE5Xr2nPwZV9m6X1kgXAA1lDZzadConNZxE1Iyq+iEichQZUfhYt24dq1ev5plnnuHPf/4z0WiU888/n97e3tQxn/vc53j44Ye59957WbduHc3NzVx66aWjfuJydEhdWC7RPApAf5f9eZhll9S1XSIxKK0Gj482px1iGsoaMAyD1SesBuzqR0tvy+ievIiIjAnX8IekPfbYY1l/vu2222hoaGD9+vWceeaZBAIBbrnlFu644w7OOeccAG699VYWLVrEM888w2mnnTZ6Zy5HhZwNp6lll6ErH6k5H+GY3ZhaNYvWyB4AGsvsqaenNJ3CssZlrG9dzy2bbuHLp315lL8DEREZbYfV8xEI2I2DNTU1AKxfv55oNMrKlStTxyxcuJCZM2fy9NNP53yOcDhMd3d31odMDNG4Scy0gIENp8Nf0RbSlY9gvz0rhKqZWZUPIKv68butv1P1Q0TkKHDI4cM0Ta655hrOOOMMjj/+eABaWlrweDxUVVVlHdvY2EhLS+5fCjfccAOVlZWpjxkzZhzqKckRJtnvAQO32g5/UTlIh49wzCQWN6FqJq0u+7Zk5QPs6sfJjScTNaP8atOvRunsRURkrBxy+Fi9ejWvvPIKd91112GdwHXXXUcgEEh97Nmz57CeT44cySUXl8PA48r4URvhbheA3sSgsYGVj6RPn/BpAO7fer+qHyIiR7hDCh9XXXUVjzzyCE8++STTp09P3d7U1EQkEqGrqyvr+NbWVpqamnI+l9frxe/3Z33IxNATjgLgKxnQWlTgsovH5UiFlmBixHqbyw4fmZUPsKsfpzSdouqHiMhRYEThw7IsrrrqKh544AGeeOIJ5syZk3X/smXLcLvdPP7446nbtmzZwu7du1mxYsXonLEcNboTvRo+74DwES5sq23mY3vDcSL+KXTkqXwAfGrppwD1foiIHOlGFD5Wr17N7bffzh133EFFRQUtLS20tLQQCtkTJysrK/n4xz/Otddey5NPPsn69eu58sorWbFihXa6TELJRtGKEnf2Hcmej2GWXSA9Yr0nHKPdWwaAx7SocngHHXtK0ymc2nQqMTPGna/feRhnLiIiY2lE4eOmm24iEAhw9tlnM2XKlNTH3XffnTrmBz/4Ae9+97tZtWoVZ555Jk1NTdx///2jfuJy5Av228suFYe47ALg89rBpSccozXeD0BDPIYR2Jvz+PNnnQ/AjsCOQzllEREpghHN+bAsa9hjSkpKWLNmDWvWrDnkk5KJIVn58A8MHyNadklfXC4UagegIR6Hrt1Qf+yg45PLMe197Yd62iIiMsZGFD5ERiJd+chYdonHINJjfz3MkDHIHrEecthj+htjcejalfP4hnI7fGRe+VZERI4sCh8yZtI9Hxk/ZuGMIXIFLLtkXlzuIHagsCsfecJHqR0+DvQfIGbGcDn0Iy4icqTRVW1lzAwZPtxl4HTneFQ2X8aI9WQ1oyGWWHbJoaakBqfhxLRMOvo7DuPsRURkrCh8yJjJudtlBDtdIGPZJRyjtS+57BLLGz6cDie1pbWAll5ERI5UCh8yZnLudhnBThfIXnZJhonGeP7KhxWLccr+MrwRS+FDROQIpQVxGTM5Kx8j2OkCmQ2nUdpiGT0f4XaI9IGnLOv4rvt+xxU/e5OVNRCY/SrMPOcwvwsRERltqnzImAmGc1U+RrjsknhsV6STqGk/X72z3L4zMPg6QKGXXgJgWgfM//dfEPjDHw7l1EVEZAyp8iFjJuecj0NcdumKHASP3VDqrvJD6yuJWR8Lso4Pb9sGwIEKqAvGaP63fye08SUaP//vGB4Pfd0RQj2RvK9X1VCG06VMLiIylhQ+ZMwEU9d2ybHsUnDDaWK8eswOH41ljWC67PDRuTPrWMuyiLz5JgA3vN/J+/dMZfmf9tD5P/9D/yuvUHrdDfzu5u1YZv5heU1z/az6wskFfociInIo9E88GROWZeVpOE0suxTc82EHl974QSARPioTV1Lu3pd1bKylBbOvD8vppLkWHjq3nOk/W4OjooLQhg28+uUfYJkWDpdBaYV70AdAy/ZuwqHYoX7bIiJSAFU+ZEyEYybRuF1hyB0+Cl12sSsf/VYnkBif7q2w7+xuzn7NN+0lF8fMacSdzbT2tVJx8TnM+d197P3MZ+kL2wFj/rQI51339kGv9evr/kFPZ5iOfT1MmV9V0PmJiMjIqfIhY6I7UfUwDCj35BgyVsBodYCKROUjSkb48E9LvMiA8LHNXnIpmT8fgGAkSCgWwjNzJrPvvANz3hL7wFefz/latdN9ABzY21PQuYmIyKFR+JAxke73cOFwGOk7+ke21TZZ+TAddsWksbwR/FPtOwcsu0QSzaZlxyyg1FUKpC8w5ygtJdo0FwBPW+7R7LXT7PBxcJ/Ch4jIWFL4kDGR3ukyYIT6iJdd7KqJ4bIfZ1c+kuGjGTKutJxcdimZPz91ddvkVFSAvpD92RPYTzwQGPRadQofIiJFofAhY6In13VdYMS7XbwuB26ngcOdqHyUZVQ+Yv3QZ1+/xbKs1DZbz7x0+EhWPizToqfL3mLr7e8ksnfvoNdKVz56h9wRIyIih0fhQ8ZEzp0uMOJlF8MwKCsxMZz9QKLy4fJCeb19QGLpJdbejtndDQ4HnjmzqS+170+OWO8LRjDjFlgm3kgX0b37Br1WVWMpTpeDaDhO98HQiL5fEREpnMKHjImco9VhxMsuAKUl9jKI11mKz21XJ7KWXiA138MzcyYOj8eukABtITt89HSE7edyhHFYJtEclQ+H00HNVHt66sG9vQWfn4iIjIzCh4yJ7lyVj1gY4nYIKHTZBaC01A4fVZ46DCPRvJra8WJXMJL9Hp758wCoL8uufAQ77MpJmdcEILpvcPgAqJ1mh48D6vsQERkzCh8yJoK5ej6SSy4YIwofLo/9uApXbfrGAZWPZL+Hd569zXZgz0dPpx0+yv32+eTq+QDteBERKQaFDxkTOUerpy4qVwGOwn/0HG47fJQ5M8PHgMpHYsaHN1H5SC67JHe7JJddKursq+Dm6vkAzfoQESkGhQ8ZEzkbTsMju6JtitMOHyVUpW/LCB+WZRHZmggf87KXXdr72u1R74nKh39aNQDRffbjBkput+1uDxHp15h1EZGxoPAhY2LoK9oWttMlKe7oAsBj1KRvzFh2iXd02HM7DAPPnDkAqd0uETNCIBygJ9HzUTW7ARwOrHCYWHv7oNcqrfBQVukBoKNZTaciImNB4UPGRDCcrHzkWHYZwU4XgAj2LA+nWZW+MSN8hBM7XdzTp+MotSebepweqr12laO1r5VgZ2LZpb4cV5O9JJNv6UXDxkRExpbCh4yJnA2nIxwwlnpY4qJyxDIqJsnwEe0j/Pom+2kTSy5JqSmnwTZC3faAMV+NF880+6q4+Xe8JMKH+j5ERMaEwoeMiZxzPlLLLoWHj7gZJ2R2AWDGMh7nLoVSexkm8torQLrZNCnZ99HSdhAAl9tBSbkb9/RE+Mi34yXZdKrKh4jImFD4kDGRu+F05D0fB/sPYmFiWQ4i4fLsOyvtptPwtu2APVY9U3LHy4H2LgB8NSUYhoF7uv24fNtt66anKx+5mlJFROTwKHzImMg952Pku12SQ8KsmI++iJl9Z2LHS3i3PetjYOUjuewSPGg3m/qqvQB4UpWP3D0fVY1lOJwGkf54ajiZiIiMHoUPGXWRmEk4ZgeFw112ae2153RYsUp6wwO2vvqnEgsbxAP2rhTv3LlZdyeXXfq6ElWYmhKAYZddnC4H1U2JMev7tONFRGS0KXzIqEsuuQD4vIe37JIcEmZG/QRzhI9Itx1u3FOn4ijPXpZJLrvEuu2R7MnKRyp8tLRgxXLP8kgvvQQLPlcRESmMwoeMuvR0UxdOh5G+47CWXXJVPqYRDtjhxjNgyQXSsz4cvfbcDl+i8uGqr8fweCAeJ9rSkvN1kzteDugCcyIio07hQ0Zdzn4PyJjzUXjlIx0+/PSG49l3+qcR7rZfwzug2RTSPR+ekF0RSS67GA4H7qn2Vt38O16Syy7a8SIiMtoUPmTUJZddspZc4JCWXZLhw4xW0hOOYZoZu0/804gEkuFj7qDHVpdU4zJc+ML2sLHksgsM3/eRrHwE2vqIRuI5jxERkUOj8CGjrnu4yscIll2SPR9WYsZHXzQjCPinEE70fHhnThn0WIfhYIp7Oh7Trngkl12AYbfblvk9lFa4sSyNWRcRGW0KHzLq0jM+Mna6WNaId7tYlpUKH8npppl9H/GwSSzkBMBT5x30eIDpzAbAWWrh9jhTtw+33dYwjPSkUy29iIiMKoUPGXU5ez6ifWAlqhYFLrv0RHsIxUIAlDlrsp4bILJtGwCu0jjOeFfO52gwE1e/9WU3qw637ALpSacasy4iMroUPmTU5R6tnlhyMZzgLivoeZL9HhWeCio89mMyKx/hRPjw+qPQnbuCUR2zm06jZX1Zt7sT13eJ5Lm+C+gCcyIiY0XhQ0ZdctnFnzXdNGPJxTByPGqw5JJLY1kjvsRzZYWPN+3w4amMQXdzzucoD1cB0Oftzro92fMRbz+A2Z97iml6u63GrIuIjCaFDxl1Q17RdiQDxnrT4aM8sXMmmFX5eBMArz+Wt/LhDSV2rbgPZN3urKpKDSWL7sv92Jop5RgOg3BfjN6ucMHnLSIiQ1P4kFHXEx7iiraHMGCsoawhtW03s/IRSVQ+vENUPpIDxg649mfdbl9gbpgx624H1U32cs8B9X2IiIwahQ8Zdd25rmjb32V/PoQZH5nhIxlszN5eos124PD4o3nDRzxo/4jvZ/eg+5LhI992W0A7XkRExoDCh4y6nA2n4cOrfJQPCB/h7dsBcNZU4fJaOZddTNOiP2Af3+5spjeaPa9juO22ALXTdIE5EZHRpvAhoy6Ys/Jx6BeVayxrHLTskmw29c5LXNMl3J1+jYS+QATLBJM4fZ7uVJhJSi+77Ml7DplNpyIiMjoUPmTU5Ww4TV3XZeTTTRvL0+GjJ/HckWSz6TELwJsINMHsvo6eTnsXS7ikF8uwaO9rz7o/PeU0f+WjbnoFAF2tfcSiGrMuIjIaFD5k1KXCh/fQl12i8Sgd/R3AwGUXOwCkttnOnwd++yJxA5degh12+IiX259T01ITPAUMGiuv8uAtd2GZFp37+/IeJyIihVP4kFEVjZuEEhWCw1l2aQ/ZVQq3w021txqf1x6Nnlp2SQ4Ymzc/I3xkN532dNjbYx0V9vkMWnaZZlc+zGCQeCCQ8zwMw9CwMRGRUabwIaOqJ2P8ue8wll0ym00Nw0g9V084hhkKpaoV3mPmQ2VihHpgQOUjsezirbSDSzLQJDnKynDW1gKF7XhR34eIyOhQ+JBRlVxyKXU7cTszfrxGuOzS0tcC2OEDoNyTDh+RHTvAsnBWV+OqqQF/InwMWHbpSSy7+Krti84NrHxAuu9jyB0v01X5EBEZTQofMqpyzviAES+7tPXaQaGxrBEga7x6esklsdMl37JLp73sUlNnN43mCh+eacP3fdRN15h1EZHRpPAhoyrnThc4rGUXIGvIWFazKeQNH8mG0/qG6qznzJTabjvEBeZqppSDAf09UULBaEHnLyIi+Sl8yKhKz/hwZ9+RWnYpsPIxIHxkDhmL7rGnlXpmz7YPzrHsEovE6e+xz2XGlCYA2vvaMS0z63XS223zhw+Xx5laugm0hwo6fxERyU/hQ0ZV+rouGZUP04Rw0P66wGWXzAFjABUZQ8ai7fZF4lz19fbBycpHfxdE7EmkySUXl9dJU009BgYxK0Znf2fW6xQy5RSgst6+xkugXdttRUQOl8KHjKrksos/s/IRCQKJXokCl112de8CYHqFHQ6SlQ/TguiBRPiorUs8ZyV47L6O5NJLcsmlotqLx+mhpqQGyLHdNrXssm/Ifo7K+lJAlQ8RkdGg8CGjKvdo9US/h9MLLu+wzxEIBzjYfxCAOZVzACjzODEM+/74Qfs+V11t+kEDBo0lp5tW1JQA6eWbgdtt3VOmgMOBFQ4Ta8++L1MqfLQpfIiIHC6FDxlVuUerj2yny47ADiAx2dRtX9jNMAx8HhcuM4bVbT9fckYHMKjpNJgYMJbs1UiGj4FTTg23G1eTvbQz1NKLKh8iIqNH4UNGVXcifPhyjVYvcMklGT7mVs7Nur3c66IqnJi14XLhrMwIMwOaTlMzPgZUPobcbjvEjpfKBjt8dCt8iIgcNoUPGVVDLrsUOGAsGT6SSy5J5V4n1f1246qrthbDkfHjm6x8BHIvu9SX2c2pAy8uB5lXt80fPvx1dvjo740S7tN2WxGRw6HwIaNq6GWXw6t8+ErcVIXT4SNLcsR6nmWX5K6ZgcsuUNh2W0+Ji1K/B9DSi4jI4VL4kFGVc85HeGQ9H9sD24HBlQ+f10l1YtnFWTcgfPjT4cOyrFTlI7nsUl+av/JR6HbbKvV9iIiMCoUPGVXprbaZlY8u+3MByy7heJi9PXYFYlDlw+vKqHzUZT8wY7dLuDdGLGIPExvYcDrklNMhKh8AfoUPEZFRofAhoyq97JJR+RjBbpfd3bsxLZMKdwV1pdkBo9zrorrfrny4BlU+EuEj1EGwze4xKa1w43LbV7RNLrt0hjuJxCNZD02Fj5YWrFiMfLTjRURkdCh8yKjK2XA6gmWXzCUXIznYIyGz8uEc2PNRUgVuewppT/N++xwSSy4Ald5KPA67Z2PgrA9XfT2GxwPxONGWlrznltzxEmjTlFMRkcOh8CGjJm5a9EbiwKHvdsm30wWGWXYxjFTfR7DFHkLmqy7JuNtI7XgZuPRiOBy4p9qVk6GWXirr7HCj7bYiIodH4UNGTfK6LpBv2WX48JGv2RQSyy7hPMsukFp66TlgBxRfTfY01cPt+0hWPnoDEaKJkCUiIiOn8CGjJrnk4nU58LgyfrRGsOyyM7ATGNxsCsMsu0Cq8tHTafd0ZC67wHDhY/jttiXlbrxldkVH1Q8RkUOn8CGjJmezKaQrH8Msu5iWOfSyixMqI3a/ReqKtpkSlY9gt32BuMxlF8i4vsthbLdV06mIyOFT+JBRk3ObLaR7PoZZdmnpbaE/3o/L4UpdzTaTPzHdNG44skerpw5ILLv02o2lg5ZdSnNf3wW03VZEpJgUPmTUJJddfAPDR4HLLsl+j1kVs3A5XIPu9/XZz9NTWpE9Wj2pcjqm5aA3YjeG5lt2yR0+ZgAQ2bFD221FRMaYwoeMmpyj1eNRiCa2pg6z7LK9yw4fc6sG93sAlCfCR6CkIvcT+KfSa9Zg4cDhNCir8GTdPaPCDhi7uncNemjJscfgrK4mHgjQ89e/5j3Hyno72Gi7rYjIoVP4kFGTmvHhzbHTBYYNHzu68/d7AJT0dAHQ4fHlfgL/NHri9hZcX5UHw5E9JyT5vAdCB+iOdGfdZ3g8VF5yCQBd99yb9xyTlY/uA6p8iIgcKoUPGTXduSof4US/h7scnIOXUjIlKx/5woenuwuAgx4flmUNPqC0miB234fPbwy62+fxpfo+ko2tmare908A9Pz1r0RbBy/NQHq7bfBgP/GYOcR3IyIi+Yw4fPz1r3/loosuYurUqRiGwYMPPph1v2VZfOUrX2HKlCmUlpaycuVKtm7dOlrnK0ewwx2tvrN7J5B7my2AM9AJ2JWPcK5f/IZBj8sOLr6yyOD7gTlV9v3JoJPJO3cupScvA9MkcP/9OR9f5vfg8jiwLDuAiIjIyI04fPT29rJ06VLWrFmT8/5vf/vb/PjHP+bmm2/m2Wefpby8nAsuuID+fv1FPdHlHK1e4E6Xrv4uOvo7AJjtn53zGKPTvr/L68saaJapx7Dndfi8PTnvn+O3w0dyiWegqn+yqx9d9/0OyxwccAzDUNOpiMhhGnH4uPDCC/nGN77Be9/73kH3WZbFD3/4Q/7jP/6Diy++mCVLlvCb3/yG5ubmQRUSmXhyNpyGC5vxkQwDU8qnUJa4RstA8YP22PTOEj+9+cKHac//qHB15Lw/2cy6oyt3+PBfcAGOigqi+/bR+/TTuY+pS4YPNZ2KiByKUe352LFjBy0tLaxcuTJ1W2VlJcuXL+fpPH+Rh8Nhuru7sz7k6JSsfPgPYdlluH4PgPjBAwB0en2poDNQT8x+nXIr9wXikks6+SofjtJSKi96NwBd992X85jKhsSOF1U+REQOyaiGj5bEFUEbGxuzbm9sbEzdN9ANN9xAZWVl6mPGjBmjeUpSRMmlkENZdkk2gObr9wCIHbArH13eivyVj5AdDHzxnTnvT4abPcE9ROK5+0Kq3vc+AIJ/eZxYx+AKipZdREQOz7jvdrnuuusIBAKpjz179oz3KckhytlwWuCyy1AXlAOwYjHiXV0AdJbk7vmIR01C/U4AfKHXcz5PfWk9PrcP0zLZ3b075zElixZRctxxEI0SeOj3g+5PbbdV+BAROSSjGj6ampoAaB2wTbG1tTV130Berxe/35/1IUennD0fhS67DBM+Yh0dYFmYhkHQU54zfPR0hQFwEqYk+Brk2I5rGEbqNZKvmUuy+tF1772DtvWmKh8HQphmji2/IiIypFENH3PmzKGpqYnHH388dVt3dzfPPvssK1asGM2XkiNQd67x6gUsu/TH+mnuaQbyL7skm01DZX5Mw0FvePAl7Xs67R1VPudBjFgf9B7I+VzJ8JFr1keS/93vwigtJbJ9O6ENG7Lu89WU4HAamDGL3kTgERGRwo04fPT09LBx40Y2btwI2E2mGzduZPfu3RiGwTXXXMM3vvENfv/737Np0yYuv/xypk6dyiWJ6ZEyMZmmlbvnIzlkbIhll13du7Cw8Hv81JTU5Dwm2e/R77MrKD3h6KBjejrtIODz2Bego2vwGHWgoMqH0+fDf+GF9tMMmHjqcBjpHS8asy4iMmIjDh8vvPACJ554IieeeCIA1157LSeeeCJf+cpXAPjCF77A1Vdfzb/+679yyimn0NPTw2OPPUZJSclQTytHud5ILLXKkXu3S1Xex2Y2mxrG4MmkALHETpeI336enqEqH2WJYNK5M+dzpXa8DFH5gPTE0+7HHiMeDGbdl95uq74PEZGRGnredQ5nn3127tHWCYZhcP3113P99dcf1onJ0SXZ7+F2GnhdGZk2dUXb/JWP4fo9IL3sEvNXA+Tc7dKbrHz4HRAib/hIvs7O7p2YlonDyJ3BS084Ac/8eUTe3Eb3I49Q/cEPpu6rbCiFVxU+REQOxbjvdpGJIXOnS1b1on/4ZZeCttm225UPs9pelunJMecjmAwfNYkqW55llxkVM3A5XIRiIVp6c28BBztIV6caT7Nnfmi7rYjIoVP4kFGRc7Q6FLTbpZDKRyxR+SAZPiI5Kh+J5k9ffZV9Q2fu8OFyuJhVMQsYfunF/573YLjd9G/eTOjVV1O3K3yIiBw6hQ8ZFTm32VrWsMsucTPOzsBOYOjKR3K6qbO2Fsi97JLq+ZiSGHKXp/IBhTWdAriqq6k47zz76TImnmaGj6GWIUVEZDCFDxkVyW22Fd6MZtNYPySniOZZdmnubSZiRvA4PEz1Tc37/MndLq46O3wMXHaJReOEgomtvjNm2jcG9oI5uDEVCttum1T1fnvppfvhRzAj9vfjry0FA2Lh9OuKiEhhFD5kVOSsfIS6El8Y4PHlfFzyl/+sylk4Hc68z59cdvHU2xeOGzhkLLnk4nI78DZOA4cbzBh078v5fIVWPgDKTj0Vh9+P2dNDZMdOAJxuBxXVdm+JttuKiIyMwoeMivSMj4zKx4E37M/Vs8CR+0etkGZTKx4n3tkJQGlj7vCRnPFRXu3FcLqgKnGNoDx9H6mr2xZQ+TAcDrxz7LAS2ZEOK371fYiIHBKFDxkVORtO2zbbnxuPz/u4grbZdnaCaYJhUF6fu+cjNWAsUY2gym4ozTtozG+/Xkd/B4HkILQheObaYSW8PR0+KhsUPkREDoXCh4yK5LKLPzN8tCZ2hzQszvu4grbZJpZcnNXV+MrtcDFwvHqq2bTaa99QnQgfeSofZe4ymsrt6w0VsvTimZuofGxPV0q040VE5NAofMioSIYPX67w0Zg7fFiWVdg22wP2ThdXXR0+r/38kbhJOJYOIOnKRyJ8DFP5gHT1o5ClF2+i8hHZofAhInK4FD5kVKSXXRI9H6YJ7YnL2udZdukMdxIIBzAwmO2fnfe546nwUUu5J92Umln9GLTsMkzlA9J9H9u7Cqh8zEksu+zYkdpaW1lfBkCgXQ2nIiIjofAho6J74G6Xzh0Q7QNXCdTkXlJJ/tKf6ptKiSv/tX+S22ydtXW4nA5K3XYAyez7GLTsUjXb/jxE5SN1jZfu4SsfnhnTweXC6usj1toKgL/OPudwb4z+Xm23FREplMKHjIrM8epAesmlfiHk2UJbyJILpHs+XIkBY+WJpZdgf2b4GLDskqx8BPdDtD/n86a22xZQ+TDcbjwz7fkhkUTTqafERZnfA0D3AS29iIgUSuFDRsWg3S6pnS7H5X1MIc2mkJ5umhww5vMmKh+JEeuxaJz+nsSAseSyS1ktuMvtrwN7cj5vMnzs69lHOB4e8hwAPInttuHMptPkjpc2hQ8RkUIpfMioGLTbpfUV+3MBO12GrXxkLLtAuqk1OesjWfVweRx4yxKvbxjD9n3UltRS4anAwkqNeB+KN7XjJWO7bZ2aTkVERkrhQw6bZVmDh4y1jl7lI7Xskqh8lHsS4SMReHozmk2zrqib2vGyM+fzGoYxsr6PVNNprlkfajoVESmUwocctr5InLhp7wCpKHFBpA86Er+g84SPQDhAc28zAPOq5g35/LHkskttctnFDh+9qcrHgGbTpAJ2vKSu8dJVyHbb5JTTnanbNOVURGTkFD7ksCWXXJwOw96J0v4aYEFZHfgacj7mtY7XAJjum06ltzLvc1umSbzDHq2eXHZJ9pUEQnafR0/iui6+qgHho4BZH8nKR0GDxhI9H7GWFuI9vUDmdluFDxGRQil8yGHrCaebTQ3DKGjJZfNB+5jFtfl7QgDiXV0Qj4Nh4KqpBmB6tf0Lf1eHvdTR05EIHzUDtuuOpPJRwKAxZ2Ulzjo7AEV27gTSg8b6AhGi4dxX0BURkWwKH3LYBs34KGCny6sH7K24w4WPWLu95OKsqsJw2/0kc+vtXSzb23uAdOWj/DAqHzu7dxI3hw8PAy8wV1LuTjW5qvohIlIYhQ85bKkZH95ks+nwO12SlY/j6vIHFBi8zRZgbr0PgG3t9tLHsD0foU7o7875/NN803A73ITjYfb37h/yXCD3Beaqm+wwdHBvcNjHi4iIwoeMguSMj9R1XYZZdgmEA+zt2QvAoppFQz536qJyiX4PSFc+2oNhgv3R9LJL9YBlF28FlNbYX+epfjgdTmb57ZBSWN/HbCD7AnONs/0AtO5U+BARKYTChxy2rBkfPW3QdwAw7OmmOSSrHjMqZgzZbArpGR/JnS7267ipr7CrHFubg6nR5oMqH1DYNV6S221HcoG5jMpHw5wKANp25a6uiIhINoUPOWxZF5VLLrnUzAVPWc7jC202hdzLLgBz6+zqx7bdXfb9mQPGMhVyddsRNJ0ml10iu3Zhxe0ekWTlo31PkHjMHPY5REQmO4UPOWzBzIbTAna6vHqwsGZTGDzdNCnZ97F3n910OmjAWNIoVz7cU6ZgeL1YkQjRZntOib+uFG+5CzNmcTBxPiIikp/Chxy2rPBRwE6XVLNp7dDNpjD4onJJ8xJ9H22tdtNpziUXGFHlo5CeD8PpxDN7NpBeejEMg8ZZib6PHVp6EREZjsKHHLbuXMsueXa6dPV3sa9nHwCLaoduNoWM6ab12ZWPeYnKR7BjwNVsByqg8jG7crZ9buEuOvo7hj0nz9zBF5hrSCy9qO9DRGR4Ch9y2FINp14D2rfYN+apfGzusKseMytm4vf4h33ueHLOx4DKR3LHS3Tg1WwHqpptf+7aBZaV85BSVylTy6cCBTadzhncdKodLyIihVP4kMOWbDhtjO2HWD+4y6A695VqR9JsapkmsQ67EuGqy658TK8uw+N0UGbnniGWXWYABkT7oPdA3teaU1X40ktq1kfGBeaSlY/Oll4iodiwzyEiMpkpfMhhS1Y+GkNv2jfULwRH7h+tEe10CQTs0eqAq6Ym6z6nw2BWbRl+024yzVv5cHnBb1c1Cpl0WtCOlxyzPsr8Hnw1XrCgbbeqHyIiQ1H4kMOWDB81PVvtG0ap2TR+ILHkUlmZGq2eaW59OT4rGT7yVD4g3XTauTPvISNpOvUmGk7jHR3EOjtTtyeXXtp2qu9DRGQoCh9y2HoSl7b3B96wb8gTPkbebJrYZjtgySVpbnUZZYWEj+rCr/GyrWvbsOflKC/HNWUKAJEdO1O3Nyh8iIgUROFDDotlWamej5LO1+0b8zWbJqoes/yzqPBUDPvcuaabZppVZi+1xB3gKc0xYCypavgdLwtrFuJyuGjpbSmw6TR5gblcY9YVPkREhqLwIYclHDOJxi3K6McVSPxybxh6p8vimuH7PSD/dNOkRpcdOHocVu4BY0kFVD7K3eWc0ngKAOv2rBv23FKTTjOaTutnVoABPZ1hegPhYZ9DRGSyUviQw5Kc8bHAsce+wdcI5bnDwqsHCp9sCvmnmyZVWvaPbydmauknpwIqHwBnzTgLgLV71w57brlmfXhKXNRMSQw/U/VDRCQvhQ85LMlm06Ueu5ejoGbTuuGbTSFjummeng+z137toMNiR3tv/idKVj4Ce8GM5z3s7BlnA7CxbSOBcGDIc8t1gTnIHDamHS8iIvkofMhhSYaP45yJ8JFnsmlnfyfNvfa1UBbW5L7a7UCxA+1A/mWXns5++xwMi+0HhrimSsUUcLjBjEJ3c97DpvmmMb9qPnErzt/2/W3Ic/MkB43t2YMViaRuV9+HiMjwFD7ksLQH7d6GBUZiSWOYZtPZ/tkFNZsCxFPLLnnCR5f92kGHxbahKh8OZ2LYGEP2fUC6+jFc34eroR5HWRnE40T27End3jDL/t7adnZj5ZmoKiIy2Sl8TCKmadHTObqNkJv2dgEW86zd9g3DhI9CttgmpS8ql3vZpSdxXZduh8X29mGuJlto38d0u+/jH/v+QdSM5j3OMIz0pNOMpZfaaT6cLgfhvhiBttDQ5yQiMkkpfEwS4b4ov/v2en7zf//B68/sH7Xn3bg3QANdlMe7wXBC3YKcx7160G42LWS4GNhbeNOj1fNVPuxll57hKh9Q0I4XgLfUvYWakhqC0SAvtr445LHJptPMWR9Ol4O6GfZF73SRORGR3BQ+JoH+3ii//9HGxFIArPvtFg42D1MpKIBlWby8t4tFjkTVo3YeuHOPOR/JWHUAMxCAqF15yLXsEo3ECScaTrsdFjsO9GCaQyxzFFj5cDqcvG3a2wBYu2ftkMfmazpV34eIyNAUPia4VPDYFaTE56ZpbiWxqMkff/EKkf7DuwDa7o4+uvqiLHbutW/Is+TS0d/B/l672rKoprBll+SSi8Pvx+HxDLq/N7F85PY6MR0G/VGT/d39+Z+wwMoHZPR97F03ZN9Gsuk08wJzoEmnIiLDGWIspBztksGjfbcdPC753ImUVni455vP0dnSx1/vfINzP7po6AFdQNyM88rBVwjFsnsYnnrzAM6ybVSVbyPcA958w8Uymk19Hl9B5z7cdNNgYqeLr9rLzAqL7e29bG/vYVpVae4nrJptfx6m8gFw+tTTcTvc7AnuYUdgB3Or5uY8zptcdtm+A8tKDzpLVj7ad/cQj5s4ncr4IiKZFD4mqMzgUVrh5uJrTqR2mv2L//x/OY4Hv7+BLc+2MPXYKhafMTXnc/RF+3jwzQe5/bXb2RPck/OYslnwU+AR/xR+XTOTmhzHjHTJBTKmm+YJH8nKh6/ay7xqVyJ89PK2Y+pzP2Gy8hHcD7GwfbXbPMrcZZzadCr/aP4Ha/euzRs+3LNmgcOBGQwSP3AAV7392pX1pXjLXIT7YnTs67Unn4qISIr+STYB9fdGeeiHG3IGD4Cpx1Sz/GL7F+pf73qDg/uy+z9aelv4/gvfZ+V9K7nhuRvYE9xDhbuCY6qPyfrwmNMw+xvxx012etys3n43fdG+QedzKOEjNd20Ps9Ol1Tlo4S59fZU0W1D7XgpqwV3OWBBV+4glamQLbcOjwf39OlA9qRTw2Gkttyq70NEZDCFjwkmGTwO7OnJGTySTjp/FjOPqyEeNXks0f+xqX0TX1j3Bd7xu3dw66u3EowEmeWfxZeXf5m/vO8v3P+e+1Mfd7/rPnq2fYZ37j6R2/e3UBU3eaVrK9euvZZoPHuL6kh3ugDEDiQrH/nCh135KK/2Mq/O/v62D7XjxTAy+j52Dvv6yS23G9s30tnfmfe49AXmBvR9zFLfh4hIPlp2mSD6e6Ns/nszLz+5l96usB08PncitVPTwSPe00No/XqsuAnAafMtDmyHrtY+7vjGvfzJ+Q02zzKIOw1ObTqVjyz+CGdOPxOHMTij7nnpSe5wfIVljq0QhTVli/mX+C7+0fwPvvLUV/jmW7+Jw3BwMHSQlt4WDIwRzvgY+qJyyfBRUV3C3Hp7h01Bsz7aNkPnzmFff4pvCguqF7Clcwt/2/c33jPvPTmP88ydC+vWZc36gHTTqSofIiKDKXwc5bpa+3j5iT289vR+YhE7VPiqvbz76qVZwcOyLPZ+8lP0vfBC1uMX+uey4cRr6D3QyMe2nEZF/CX8n13NwvM/mrsR9eA2ePzrzN38EDig3/BScuY1LDn9M3yvfQNXP3E1j2x/hNqSWv79lH9PN5tWzqbcXV7w9zXsdNPEskt5tZemevv7bA700xeJUebJ82NdXdh226SzZpzFls4trN2zdojwMXjWB0DjHDt8dO7vJdIfw1Oi/9VERJL0N+JRyLIsmrd2sfEve9i56QAkdoPWTitn6bkzOfaURpzu7GpF4KGH6HvhBQyvF++C9CCwJqCp6y/sr76AN455P6es3wlf/ja77vszjV/8AqUnnGAf2NcB674Nz/8KzCgmDu6JnUnH8n/n02+352K8bfrbuP6M6/ny37/Mrzf/mvqyevpjdkgYSb+HZZqEt20DwN3QkPOYnoyG05pyD9Vlbjr7ouw40MtxUytzP3FV4dttAc6efja/ePkXPNX8FNF4FLfTPeiYfLM+yiu9+Kq99HSGObAnyNRjqgt6TRGRyUDh4ygTj5k88tOX2Pt6ug9h1ltqWXruDKYvqM5ZrYh3d9P2ne8CUHfVauo+8YnUfVs6tvC137+fd7w+nVldx7Hz7M/ylse/SmjDBnZ+4INUvOMdNPzzeXie+CT0J670On8ln269mMfaa/nF3GOyXus9897DgdABfrD+B3z3he/SWNYIwOKawsNH71NPE927F0dFBWWnnDLo/mg4TrjPnlFSUW0vucyt97F+Vyfb2ocIH3XH2p93PwPxKOQIE5mOqzuOutI6DoQO8Hzr85w+9fRBxyRHrEebmzFDIRyl6a2+DbP89HS207pD4UNEJJMaTo8y6x/bxd7XO3G6HRx35jT++WvLeffqpcxYWJN3Xkf7j35M/OBBPHPmUHvFFanbLcviO89/B8swcZzZhsNl0Nbrw/uz+6hcdSkYBsHHHmPbR/+N1qcs+p0LsT70O/refzd/OmAvhyydUTXo9a487ko+vOjDALT2tQL2L/JCdd51JwCVF19sX7xtgOSSi7vEiafUzs9z6+wlnSH7PuaeBb5G6GmF1/8w7Hk4DAdnTj8TyL/rxVVdjbOqCiyL8JtvZt3XMFs7XkREclH4OIocbO5h/aM7ATj3ikWc/c8LqG4auo+if/NmOu+0f5k3/ed/YGRMC123dx3PtjyLx+Hh6jM/yVvOtLeNPr+2gynf+AZzHnyA8kVTwISON3zs+G03b3zwOrZdcSUf2vwY5wW3UWcNvlCdYRh8/pTPc+GcC+0/Y7CwZmFB32O0pYWeJ54EoPoDl+U8Jr3kkh7lPre+gB0vTjecdLn99fO/Kuh8krtehpp2mqzOdN1zb9btjZp0KiKSk8LHUcI0LZ78n9cx4xazl9Qxf1nuXohMlmnScv1/gWlSceE7KD89vWwQjUf53gvfA+Ajiz/CNN80ll04C7fXSfvuINtebKekMsrME19ixlkHKVsyH6OsDLOnB9eGF/jnLX/h2sdv4o3lp7Htne+i5RvfpO+FF7BMu+nVYTj45hnf5COLP8LnT/l8wc2mXffcC6ZJ2Smn4J0/P+cxmf0eSclZH9sPDLPjZdlHwXDAzr9B+xvDns9pU07D4/Cwr2cfb3a9mfOYmo/a1aTAQw+ltggD1M/ygwHBjn76uiPDvpaIyGSh8HGU2PTkXlp3dOMucXLWB48ddiQ6QOCBBwlt3IhRVkbjF7+Ydd89b9zDzu6d1JTU8C9v+RcASis8nHDeTACefWgb5kOfATOG7+3nMeueh1nw3LPMeeB+nnznlfxlxjL6GuzJqJHt2+m8/XZ2ffgjvHnW2bT81zfoe/55XDj4wilf4COLP1LQ92hFo3Tda1cPqj/4gbzH9WSMVk+alwwf7b1DXo+Fyulw7Dvsr1/472HPqcxdxvIpywG7+pFL6UknUbJ0CVYkQucdd6Zu95a6qG60l412v3pw2NcSEZksFD6OAt0HQjzzkL374/RL52ctN+QTDwRo+67dZFq/ejXupqbUfYFwgJ9t/BkAV514Vdb1Vk5YOYMSn5uuthCvb6sGbyW8034ew+WiZNEi7mg8me8t+yDh/76bY55+iulrfkrlJZfgqKgg1t5O529/y66PXM7Ws8+m5fr/Irx1a0HfZ/CJJ4m1t+Osq6Ni5coh3w8AX1U6fMysKcfpMOiLxGkZ6gJzACd/3P780h0QGTyRdaDktNN8V7k1DIPaKz8GQOcdd2CG0tfAmf0We0ja2t9uYZcCiIgIoPBxxLMsi7V3bCEWMZl6TBXHvTX3dVgGav/Rj4h3duKZP4+ay7MrDze/dDPdkW6OqT6GS+dfmnWfp8TFyWfZjZLP9VxG7JxvgH9K6v6DPWH2dtq/XI+fXomrupqKc89l6o03cOw//s6Mn99M5Xvfi8PvJ95+gM477mDHZR8gsmv47a3JRtOqVauyelMyxaJxdrxkL200zk3vavG4HMyssasMQ/Z9AMw7B6pn27t3XvndsOeVbDp9uf1l9gb35jym4ryVuKdPJ97VReDBB1O3L794LnOW1hGPmfzvTS+z6xUFEBERhY8j3JZnW9izuQOny8HbP7wQwzH8ckvolVfpvPMuAJr+4z8x3OktpTsDO7nrdfu+fz/533E6nNkPtiyOP/A1fI42es06NgXOyrr75b32dtt59eX4S7K3qhoeD76zzmLqDd/i2L//jRm/+Dklb3kLVl8fzV/8ElYslvecw9t30Pf0M+BwUP3+9+U9bvuGdsJ9MXw1XmYsyr6MXUE7XgAcDlh2pf31C7cMfSzQVN7E6VNPx8Litldvy3mM4XRSk9hJ1HHbr7HicQCcLgcXfOJ45p5Qjxmz+N+bX7Zns4iITGIKH0ewvu4If7/XXrI45d2zqWocvO10oN5wD7u++mWwLPzvehflpy3Puv/7679PzIpx5vQzc86tYMPtOHc9yamV9wP21t5wX/paLRv3dAG5t9hmMjwefGeeyfQf/gCHz0do40YO/ir/DpOuu+1A5DvrLNzTpuU9bvM/mgFYdPpUHAOCWPoCc8NUPgBO/DA4PdC8AfatH/bwZF/MA1sf4EAod3ioutSu+ER27aLnySdTtztdDs7/xHGpAPLozzcpgIjIpKbwcQT72z1vEO6NUTfDl2oEzcWMRIjs3UvwuWf4n2suxHp1CyEPXHnMWi564CI+8adP8B9//w++9ey3eHLPkzgNJ/+27N8GP1GwBf70ZQAWvPOtVE8pJ9wXY8Ofd6cOeWlvFwAnDBM+ktzTptH0n/8BQPtP1xB65dXB5x8K0fXAg8DQjaZdbX3s29IFBiw6fcqg+1PbbQ8UED7K62DxJfbXzw/feHpy48mcUH8CETPCbzb/JucxjvJyqj9gn//BW2/Lus/pTASQExVAREQUPo5QO15q580X2jAcBud8ZBFOZ/o/Vdd997HnqqvYseqfeOOtb2PLkqVsW3keey+/krOetH+h3fM2B/tLw+zs3skz+5/hoW0Pcefrdk/F+xe8n7lVcwe/6P9+3u6DmHICjtM/zWkX28e89PgeegNhLMtKLbssnV5V8Pfif897qLjgAojFaP7CFzD7sxtCu//3UczubtzTp1P+1rfmfZ7X/rEfgJmLa6moGdx0Oy8RPra1DbPsknRKovH0ld9BKP+Va8FuKk1WP+5+/W4C4UDO46o/9CFwuwmtX0/opZey7nM6HZz/L8cxLzOAvKwAIiKTj8LHEcaMm2x9oZW1v90C2LtP6mdWpO7vuv8B9v/Hf9Lzl8fpf/VV4om5EobHQ3uNk1dmGuy97K189bvP8Mh7H+GW82/hW2/9Fp858TNctuAyLltwGVefePXgF37ld/Da78Hhgot/Ck4Xc5bW0TjHTyxisv5/d7K3M0RHbwS302DhlIrBz5GHYRg0fe2rOOvriGzfTtv3v591f+dd9pJL1WXvx3Dk/pGMx01ee9oOH/mabpPLLs2BEP3R+PAnNmM5NB4PsRBsvHPYw8+cfibHVh9LX6wvFeQGcjc2UPnudwODqx9gB5Dz/uU45p2UDiDP/2EHoaDmgIjI5KFruxwhwn1RNv99Py+v3UNPhz1Eq6qxjFPfPSd1TP8bb9By/fX2fZddZvdHNDXimjKF3+57iO+u/x6NZVP5w6U/xev0Mqu0gln+WcO/+K6n4cFP21+fcQ00vQWwQ8OKS+bx4A828OrfmmmrceK2YPEUP16XM//z5eCqrmbqN7/Jnn/9P3T+5n+oOPtsyk8/ndArr9K/aROG203VqlX5T3HTQULdEUr9HmYtyX2l29pyD/4SF939MXYc6GXRFP/QJ2UYcPLH4A/X2jM/TvuUfVvew+3qxxf++gV++9pvuXzx5ZS5B/fh1Fz5UQIPPEDwT38ismcPnhkzsu53Oh2c9/HjgM1se7GN5x7ewfrHdrHg1EaWnDsj62rEIiITkSof4yzQ3sff7n6DX1/3FE/d/yY9HWFKK9yc/K7ZrPr8Mlwe+5e82dvLvms+h9XfT/kZZ9D01a9Qcc7bKVm8mFC5i1+9Yu/aWH3CarxO71Avma11M9x5GcT6YcE74ezrsu6etqCamYtrME2L1gd2c02glJWvR7nz+md5+Ccv8eTtr/P8H3bQ1Tr8vAzfmWdSlejpaL7u/xIPBFLbaysuuABXTU3ex27+e6LRdEVT1hJUJsMwChuznmnJ+8Hjg4NbYcdfhz38vFnnMaNiBl3hLn63Nfc23ZJjj7WXj0yTjl/n7g9JLsGc97HFNMyqIB412fyP/dx1/XM8/OON7H714NDD0kREjmIKH+OkvzfKY7/YxO1feYaXn9xLNBynZmo5b//IQi7/1uksv2guJT57K6tlWbRcfz2R7dtxNTQw9dv/L2t54tev/pqucBdzKudw0byLCj+Jrj1w+yq7z2PGabDqFnAOLoad8b5jqJ9ZQSzxko6YRUdzL7tfPcjmvzfz3MM7uO//vcDBfcP3WjR+/vN4Zs0i1tpK83X/l+5H7Au8DdVoGuzoT00IXXT60HNOkksvbxba9+GtgCWJa8gUsO3W5XDxsePtgWK3vXobkXju5ZLaj9lbebvuv594V1fOYxwOg2NPbeKfvnQy7/33k5h7Qj0YsHtzBw//5CXuvP45NaWKyISk8DEOLNPiz/+9mW0vtoMFM4+r4aLPLOUD/3kqi8+YisudvaQR+N3vCDz0e3A4mPa97+KqTS87HAgdSO2++MyJn8HlKHAlra8Dbr8Ugs1QvxA+eCd4cm/lrZlSzqVfXMbNtRF+VBnijKuO56LPLOXtH1nIKe+eQ90MH+G+GA//5CWCHUNPF3WUlTH12/8PnE56nngCq78f7zHHUHrSSXkf8/rT+7EsmHZs1bDbjRcnllpue2pH4QEk2Xj6+h+ge/+wh79n3ntoKG2gra+NR7Y/kvOYshUr8C5YgNXXR+fd9wz5fIZhMHV+FRd+8i18+PoVLDlnOm6vk879vfxhzcs889A2TFNVEBGZOBQ+xsGLf9rF7lcP4nQ7WPWFZVx09QnMXFyb83ot/VveoOW/vgFA/Wc/m7qCatIvX/4loViI42uP59yZ5xZ2ApE+uOP9cOAN8E+DD/8OyvIveQBsbeshFI3jKXGxZHE9MxfXsviMqZz67jlcfM2JVE8pp7crzMM/3kh/b3TI5ypdupS6//N/Un+u+uAH8l6rxjSt9GyPM4af7vrPy2eydHolnX1Rrvjv52gJDDNqHaDxOLvyY8bgxdzLJJk8Tg+XH2dfHfeWTbcQNwc3txqGkap+dN5++6AdPvlU1pfytvcfyxU3nsFbzravMrz+0V08/OONakoVkQlD4aPImrd28ezvdwBw5mXH0pQxInygeE8v+665Biscpvxtb6P2E/+Sdf/e4F7uecP+V/U1y64p6GJzxKNw70dh7/NQUgUfvt++2NowXkoMF1syvXLQcK+ScjcXXb0UX7WXzpY+/rDmJaKRoXeb1H3qk5S/7W14Fy6k8j0X5z1u72sd9HSE8Za5mHdS/bDnWeZx8d8fPYU5deXs6wpxxX8/RyA0dBgC0tWPp9fYDbjDeN+x76PSW8nu4G7+vOvPOY/xX3ghroYGYu3tbD3zLJq/dB3BtWuxIsOHCG+pizM/cCznfWwxLo+Dva93cs+3nqdlR+4tviIiRxOFjyIKBSP86VevYJkWxy5vZNEZgwdlJVmWRcvXvkZkxw5cjY2D+jwAfrbxZ8TMGCumrEhdeXVIlgUPXwNb/wiuEvjne6BhYUHnnhwulm+yaUVNCe++eineMhct27v50y9fwYybeZ/PcLuZ+ctfMPfBB3D6yvMel6x6HLu8adByVD61Pi+/+dip1Fd42dIa5BO/eWH4rbeLL7G33oYD8JuLYfNDQx5e5i7jQ4s+BMCvNv0qZ3Oo4fEw5Rv/hbO+DrO7m8CDD7L3k5/ijTPeSvMXv0TwiScxhwkiyZ6QqsYyejrDPPDdF9m0dq+aUUXkqKbwUSSWafGXWzfTG4hQ3VTGWR9ckLdSYVkWXXffQ/cjj4DTybTvfw9XdXXWMW90vpHqN/jsSZ8d/gTCPfD7q2Hj7WA44J9uhZkFBJaEl/YMP1ysdqqPd316CU63g52bDrL2t1sO65dkX3ckdRG5xQUsuWSaUVPGr688lQqvi+d2dHDNXRuJD9U34fLARx6EBe+CeBjuuQKeuXnI1/jnhf9MmauMLZ1b+Nu+v+U8xnfmmRyzdi2z/uc3VH/oQ7jq6zGDQQIPPcTeT3+araefQcu3vkVkz568r1M71cf7vnSyPZwsbvHXu97gL7dtJhouYJaJiMgRyLCOsH9CdXd3U1lZSSAQwO8fZk7DUeSFR3fy7EPbcbkd/NOXTqa61kXfc88R2bOHWEsr0ZYWYi0tRFtbibW0pErz9f92LXWf+MSg57v68atZu3ct5886n++d/b2hX3z7Ovj9VdCVGJP+np/ASZcXfO6hSJzjv/ZH4qbF09edw5TK0iGP3/FSO4/evAnLgmXvmMVpl8zLuj8ajtPT2U9PVxi3x0nDbP+gpRyADX/azVP3v0nDbD/v+9LJBZ9vpqe3HeSK/36OSNzkQ8tn8o1Ljh96ecqM25NekztfTr8aVl5vX4wuh++98D1ue/U2Tqg/gV9f+GscxtB53jJNQhs20P3YHwn+8Y/E2trsOxwOKs49h5qPfpTSk07KeY6WZbHxL3t4+oFtWKaF0+2gYWYFjXP8NM2tpGluJeVVI9hmLSIyikby+1vh4zDEoya7X+ugs6WXacdW0zCrIucvjX1vdPLQDzZgWbDipDiNrz9KcO06rL4hZmMYBpWXvpcp//Vfg5ZbNrRt4PJHL8dpOHng4geYUzkn93OEg/Dnr6Z/kVbOhPf8GOa9veDv0bIsHn55P5+5cwMNFV6e/b/nFtRbsvnvzTx5++sAzDuxnljUtANHZ5hwX/bVbcv8HuadWM+8ZQ1MmV+Fw2FgWRZ3fO1Zulr7ePuHF7I4z1TTQvzvpv2svuNFLAs+t/JYPrvymOG+afj7D+Dxr9t/Pn4VXHITuAb/Ym/va+eC311A1Iwyt3IuH178YS6aexElrsHj3we9jGnS+9TTdPz61/T+LV05KTn+eGo++lH8F5yfdUXipOatnfzl1tdy7izyVXtTQaRxjp/6GRU43SpwisjYOyLCx5o1a/jOd75DS0sLS5cu5Sc/+QmnnnrqsI870sNHMnC8ub6VnS8dINKfLn1X1JYw76QG5p/UQMNsO4j0tAW451svEOo3mNL+AotevTV1vGvqFEqPOw5X0xR7UmljE+4pTfbnhnoMjyd1bDQe5fWO13n5wMvcu+VetgW2seqYVXzt9K/lPtHta+GhqyGQqHac/HE47+v2XIthWJbFxj1d/OHl/Tz6Sgv7ukIAXHBcIz//SOEViBf+d0equXYgt9eJr9pLbyBCJJQOI2V+D3NPrKeqsYy/37MVl9fJlf/vDDwlhzeM93+e3sl/PmRf1O6flk1nxdxaTpxZxZy68vxh6qW74KHV9i6Y2W+Dy26H0qpBh933xn1894Xv0hu1B5tVeat4/4L384EFH6C+bPgmWYDwm2/S8evfEPj977HC9oRbV1MTlZdcjP8d78C7IHuZzrIsAm0hWnYEaNneTcv2AB37ehj4f7PDZSSqI+lAkuu6OCIih2vcw8fdd9/N5Zdfzs0338zy5cv54Q9/yL333suWLVtoaGgY8rFjFT7iMZPgwcK2O+bS2dLLmy+2DQoc5ZUe6mZWsG9LJ7FIusGyvNSiKbqdgx0WXf75lPfu5+T136akqY6Kd7yDkvPeTve8RuJWjnV7M4bZ28a23v281L2dlw9sYvPBzYTj4dQhZa4yHrrkIZrKm9KPsyzoaYW1N8L6RMipmgnv+SnMPWvI768nHGNLS5BHN2UHDoAyj5NzFzXyuZXHpCaIFsKyLF57aj/Bjn4qqkvwVXspr/biqy7BW2qHiXjMZM9rHWx7sY0dLx0YVBVZfMYU3v6RRQW/5lC+96ct/OSJN7Nuqy5zc+LMak6cUcVJs6pZOqMKnzcj6Gx7Eu7+CESCduVoyfvhuEvsa8JkhIGeSA/3b72fO16/g309+wBwGQ7eaZXzwe4g86efQcnxq2DOWXZ/SR6xjg4677qLzjvuTF23B8AzaxYV73gH/ndcgHfhwpyBKdIfo21HF82vtNC6N0Tbvn76ewbv9KmoLUlVmhpn+wuqZFmxGLEDB3A1NOS9/o6ITG7jHj6WL1/OKaecwk9/+lMATNNkxowZXH311XzpS18a8rFjFT66Wvv47VefGZXnKq/yMuuEavwLob++k65wF2YwjPl4K32vO+myZmBmjDh3mGHqHbfy2uIgmxqjtMaCdMSGH0c+UCUulnrrWFIxmwv885nd3wfd+6C7Of05c+LmKf8CK79O0PLSEuinOdBPSyDE/kA/+7v62d+d+HNXP8HwgKWQROB411umcPaCekoK3GlyOOIxk72vd/Lmi23s2NhOLGryT188mbrpo3OtE8uyWPdGO/948wAbdnfx8r4AkVj2jhzDgAWNFZw4s5qTZtqBZG5sG8Ydl0EwYwBZzTw7hCy+xL4WjmFAXwexzQ/x5OY7+E1oNxtLskNGVTxOkwmNpfU01i6gqekkGium0ljWSFN5Ew1lDTjx0trdz/72bvoe/wtVz/0V74vPQsauGPesmfgveAfOmmq7X6i1Jd031NYGcTvQWi4X0WnHEmw8jm7/bDod9QQiZVikw4av2svMpXWUz/fTV+GkNxynwe+l0Qzh3/Ya3Rs2cuDlN+jb3UnM8uB2RiifXUfd0gVUnbyM0iVLcFbm3y6e87+DadEXjNDTGaa3M4zhAF8inJb43EM2YpvBYKo/yuzrw9XQaFcNGxowXEfOpaosy6I70k1Lbwutfa2E42EayhpoLGukrrSu8GGAI3nNRECM7t9PrLUNR2kJrqYm3I2NOCorC9uKn0M8GLT70VpaMHt7cTU04G5MvOc5lgXHi2madHR3sWv/flpaD9DfH6G+rorpTU1Mb2zCU+RztUyLUE80tdwM9v9vvuoSSn1ujBx9bkmRUIyezjA9Xf2E+2KUV3rtf7xVeXG68of/eNSkNxC2/98K2CMKkv9vuV1k/Hy0gsOB//zzR/V7HtfwEYlEKCsr47777uOSSy5J3X7FFVfQ1dXFQw9lb2EMh8OEw+l/0Xd3dzNjxoxRDx8v/fXv/OO3XYf8eMMK4Yi9ihl9kbC1gxjpikVtEE7YblGS+Edm3OFm+4zFbJ95EjHvHP425yG217006Dm9polniHd/aizG0nCYJeEIS/vDzIrFGO6vDwuDFu8cbvV/kifDC9kf6KdnQLDIp7LUzVnH1vPOIgaOfOJxk3jUPOzllqFEYiab93fz4q5ONuzp4sVdnVkVn6TKUjenTfdyvvNFFnc9wTGBZ3BZ6TBw0DudgKeR2cGNODJ+Ltb653FrVS2bnAeJUsCsEaAk7qQi5sIXc+OLuXGZBp6IyfxdERZuDzNvdxjXMJtczMQPiSPHz1bc4aGjZhFt9SdyoPYtxDN6UxyxTjyRN3FHy7CclfR7q4m582+DdkeCeMOdGFaAuDuI5ci3tdrAdJQTNyoxHZWYRiUYeX62rCgOK4DTDOAwA7jivbgjFu6IiTtq4cizY8kC4m6DiNtB1GMQcxsw7P8toyuORdyw7M+YDPUXqxMDJwYuDByWgXFI52rhilr2+xO1cEXNvM9iGgZRj0HU4yDqNjCd+V/PYdrP5w4P/Z4DxFz2c0bG6z03vMQSP1OWowrDyN1wbVkmWN04rC6cZjcuK4gxBh0HpqMc06gknvo5z/P3lxXDYXXjNLtwWAEMK0bc4cc0qjAdlVhG/qVRwwzitLpwmAEcVi+mUY7pqCJuVGI58i+rO2N9lIS78PZ34g13YTg6ee+D3897/KEY1/DR3NzMtGnTeOqpp1ixYkXq9i984QusW7eOZ599Nuv4r33ta3z9618f9DyjHT6efew3+K+5YdSeL5euSoutx5i8cYzJ/noHYcNNzHJTEXdQFXNQFTOojjmoTnxdZhp0UMl+q5b9Vg0tVg37rRr2W7V0UIELk0ajkyYOMsXooMnoYKphf21Bzse1UU00x8WKK0vdTKksoamyhCmVpRlf239uqizJXm6YpNq6+3lxdycbdnfx4u5OXt4bIDygOlJOiHMdG3in81nOdmykxEgHi1fNWfwhvpxHzeXssJJzXCxwhHC6u1jgfpWFnldp9OyixxWlxeWk1emixeUkVMByRknY4qRtFidvtTAs6KiAA36Djgo4WGFw0A9d5favgKoeOxjXBC1qu6E2aFEbhNpu+7O/102gehFt9ScNCiKZTPqJuDuJunvwRPy4Y9U4yL90VBDLxBsJ4A0HsAyDsLeaiOfI6/GSo4872oM33IUzHibsrSLsqcJyjNM/pCwTT6Qbb7gLgLC3yv45H2ZXHIAr2oc33Ikr3k/Y4yfsrcJyDF+9cZhRvOEuPJFuYq5Swt4qYq7Bl6Uw4q18+pcfHPG3NJSjKnwUq/KxffNzPPftAuZh5OHAoBQXJZaTElyU4MSVGJNiut0Ejj2GjhmLCHobCXobCDsrhrw8+1gqcTlpqixhapUdKpr8JZQrWBySSMzk9Ra7OtLeEx50vzvey9zOpyiPdrC96nS6SmcU9sSWybTgS8zuXk+F26LM48TwQq8rQpcRoTXeR1s8RAw7+MRNi0jcJBozicTtr81D/F/XYRh4nA48DqgImVT0xCnttrA6ZmLFGnDXmPimOqmttKhyxXHGYvTF4vSFY1iAaVn0xA06oi56gwbWQQeOoBfDyv/zbli9OKxuHFbA/qAHg+xQZ+HENPyY+DEN+1+OcWcpEY+DmNcg4nEQ9TiwBpWrExWAxL/U7c/5B9yNFQcGThy4LLui4cKRs6IRwySORQyTmGF/faiiboOYx2G/N14HMZcx6O8dw0xUjpIVpIiJM57/NU1HokridRBxO4h5HZg53nNn1MKTfN6wOWTlZaw4rCheq4dyq4dyq5dyK4SX7NKgCfRRQtAoo88oJ+TwETXKGIsqjWGF0j/jVjcOghgDzsfCgUlF6mfcNPxYuHFgP8aZeKxBZMDjwKLMro4Yif9HKMdBT9b/WwZ99ndmQKjMSW+Fi77yMvpLqog5q3BGK3BFKvC4XXx+mDaIkRpJ+Bj130h1dXU4nU5aW1uzbm9tbaWpqWnQ8V6vF6937GcTzF18KnNvG35stkgmj8vBkulVLBliuBosA6DAK+tkWAyM7r88RESOBqPetu7xeFi2bBmPP/546jbTNHn88cezKiEiIiIyOY1JLf7aa6/liiuu4OSTT+bUU0/lhz/8Ib29vVx55ZVj8XIiIiJyFBmT8HHZZZfR3t7OV77yFVpaWjjhhBN47LHHaGxsHIuXExERkaOIxquLiIjIYRvJ72+NKhQREZGiUvgQERGRolL4EBERkaJS+BAREZGiUvgQERGRolL4EBERkaJS+BAREZGiUvgQERGRolL4EBERkaI64q6znhy42t3dPc5nIiIiIoVK/t4uZHD6ERc+gsEgADNmzBjnMxEREZGRCgaDVFZWDnnMEXdtF9M0aW5upqKiAsMwRvW5u7u7mTFjBnv27NF1YwbQezM0vT9D0/uTn96boen9ye9oe28syyIYDDJ16lQcjqG7Oo64yofD4WD69Olj+hp+v/+o+A85HvTeDE3vz9D0/uSn92Zoen/yO5rem+EqHklqOBUREZGiUvgQERGRoppU4cPr9fLVr34Vr9c73qdyxNF7MzS9P0PT+5Of3puh6f3JbyK/N0dcw6mIiIhMbJOq8iEiIiLjT+FDREREikrhQ0RERIpK4UNERESKatKEjzVr1jB79mxKSkpYvnw5zz333Hif0rj461//ykUXXcTUqVMxDIMHH3ww637LsvjKV77ClClTKC0tZeXKlWzdunV8TrbIbrjhBk455RQqKipoaGjgkksuYcuWLVnH9Pf3s3r1ampra/H5fKxatYrW1tZxOuPiuummm1iyZElq4NGKFSt49NFHU/dP5vdmoBtvvBHDMLjmmmtSt03m9+drX/sahmFkfSxcuDB1/2R+b5L27dvHhz/8YWprayktLeUtb3kLL7zwQur+ifZ386QIH3fffTfXXnstX/3qV3nxxRdZunQpF1xwAW1tbeN9akXX29vL0qVLWbNmTc77v/3tb/PjH/+Ym2++mWeffZby8nIuuOAC+vv7i3ymxbdu3TpWr17NM888w5///Gei0Sjnn38+vb29qWM+97nP8fDDD3Pvvfeybt06mpubufTSS8fxrItn+vTp3Hjjjaxfv54XXniBc845h4svvphXX30VmNzvTabnn3+en//85yxZsiTr9sn+/hx33HHs378/9fH3v/89dd9kf286Ozs544wzcLvdPProo2zevJnvfe97VFdXp46ZcH83W5PAqaeeaq1evTr153g8bk2dOtW64YYbxvGsxh9gPfDAA6k/m6ZpNTU1Wd/5zndSt3V1dVler9e68847x+EMx1dbW5sFWOvWrbMsy34v3G63de+996aOee211yzAevrpp8frNMdVdXW19atf/UrvTUIwGLSOOeYY689//rN11llnWZ/97Gcty9LPzle/+lVr6dKlOe+b7O+NZVnWF7/4Reutb31r3vsn4t/NE77yEYlEWL9+PStXrkzd5nA4WLlyJU8//fQ4ntmRZ8eOHbS0tGS9V5WVlSxfvnxSvleBQACAmpoaANavX080Gs16fxYuXMjMmTMn3fsTj8e566676O3tZcWKFXpvElavXs273vWurPcB9LMDsHXrVqZOncrcuXP50Ic+xO7duwG9NwC///3vOfnkk3nf+95HQ0MDJ554Ir/85S9T90/Ev5snfPg4cOAA8XicxsbGrNsbGxtpaWkZp7M6MiXfD71X9tWVr7nmGs444wyOP/54wH5/PB4PVVVVWcdOpvdn06ZN+Hw+vF4vn/zkJ3nggQdYvHix3hvgrrvu4sUXX+SGG24YdN9kf3+WL1/ObbfdxmOPPcZNN93Ejh07eNvb3kYwGJz07w3A9u3buemmmzjmmGP44x//yKc+9Sk+85nP8Otf/xqYmH83H3FXtRU5EqxevZpXXnkla11aYMGCBWzcuJFAIMB9993HFVdcwbp168b7tMbdnj17+OxnP8uf//xnSkpKxvt0jjgXXnhh6uslS5awfPlyZs2axT333ENpaek4ntmRwTRNTj75ZL71rW8BcOKJJ/LKK69w8803c8UVV4zz2Y2NCV/5qKurw+l0Duqcbm1tpampaZzO6siUfD8m+3t11VVX8cgjj/Dkk08yffr01O1NTU1EIhG6urqyjp9M74/H42H+/PksW7aMG264gaVLl/KjH/1o0r8369evp62tjZNOOgmXy4XL5WLdunX8+Mc/xuVy0djYOKnfn4Gqqqo49thjefPNNyf9zw7AlClTWLx4cdZtixYtSi1NTcS/myd8+PB4PCxbtozHH388dZtpmjz++OOsWLFiHM/syDNnzhyampqy3qvu7m6effbZSfFeWZbFVVddxQMPPMATTzzBnDlzsu5ftmwZbrc76/3ZsmULu3fvnhTvTy6maRIOhyf9e3PuueeyadMmNm7cmPo4+eST+dCHPpT6ejK/PwP19PSwbds2pkyZMul/dgDOOOOMQdv633jjDWbNmgVM0L+bx7vjtRjuuusuy+v1Wrfddpu1efNm61//9V+tqqoqq6WlZbxPreiCwaC1YcMGa8OGDRZgff/737c2bNhg7dq1y7Isy7rxxhutqqoq66GHHrJefvll6+KLL7bmzJljhUKhcT7zsfepT33KqqystNauXWvt378/9dHX15c65pOf/KQ1c+ZM64knnrBeeOEFa8WKFdaKFSvG8ayL50tf+pK1bt06a8eOHdbLL79sfelLX7IMw7D+9Kc/WZY1ud+bXDJ3u1jW5H5//u3f/s1au3attWPHDusf//iHtXLlSquurs5qa2uzLGtyvzeWZVnPPfec5XK5rG9+85vW1q1brd/+9rdWWVmZdfvtt6eOmWh/N0+K8GFZlvWTn/zEmjlzpuXxeKxTTz3VeuaZZ8b7lMbFk08+aQGDPq644grLsuwtXf/5n/9pNTY2Wl6v1zr33HOtLVu2jO9JF0mu9wWwbr311tQxoVDI+vSnP21VV1dbZWVl1nvf+15r//7943fSRfSxj33MmjVrluXxeKz6+nrr3HPPTQUPy5rc700uA8PHZH5/LrvsMmvKlCmWx+Oxpk2bZl122WXWm2++mbp/Mr83SQ8//LB1/PHHW16v11q4cKH1i1/8Iuv+ifZ3s2FZljU+NRcRERGZjCZ8z4eIiIgcWRQ+REREpKgUPkRERKSoFD5ERESkqBQ+REREpKgUPkRERKSoFD5ERESkqBQ+REREpKgUPkRERKSoFD5ERESkqBQ+REREpKgUPkRERKSo/j8Nib29pmte2AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evolve(iter=10,wavefunction=forward_wave,plot=True,hist=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<module 'qiskit.version' from 'e:\\\\miniconda\\\\envs\\\\QGSS\\\\Lib\\\\site-packages\\\\qiskit\\\\version.py'>\n"
     ]
    }
   ],
   "source": [
    "import qiskit.version as version\n",
    "print(version)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "QGSS",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}