Chapter 3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The quantum harmonic oscillator: brief remarks\n",
    "\n",
    "The Hamiltonian of the quantum harmonic oscillator in the energy eigenbasis is defined as\n",
    "$$\n",
    "\\hat{H} = \\omega \\hat{a}^\\dagger \\hat{a} \\, ,\n",
    "$$\n",
    "where $\\omega$ is the resonance frequency and $\\hat{a}$ is the bosonic annihilation operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims=[[120], [120]], shape=(120, 120), type='oper', dtype=Dia, isherm=True$$\\left(\\begin{array}{cc}0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 2 & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 3.000 & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 4 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 115.000 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 116.000 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 117 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 118 & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & 119.000\\end{array}\\right)$$"
      ],
      "text/plain": [
       "Quantum object: dims=[[120], [120]], shape=(120, 120), type='oper', dtype=Dia, isherm=True\n",
       "Qobj data =\n",
       "[[  0.   0.   0. ...   0.   0.   0.]\n",
       " [  0.   1.   0. ...   0.   0.   0.]\n",
       " [  0.   0.   2. ...   0.   0.   0.]\n",
       " ...\n",
       " [  0.   0.   0. ... 117.   0.   0.]\n",
       " [  0.   0.   0. ...   0. 118.   0.]\n",
       " [  0.   0.   0. ...   0.   0. 119.]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 120 # Hilbert space cutoff\n",
    "w = 1 # Resonance frequency of the harmonic oscillator\n",
    "\n",
    "a = destroy(N)\n",
    "\n",
    "# The Hamiltonian\n",
    "H = w * a.dag() * a\n",
    "\n",
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Passing in the position basis\n",
    "\n",
    "We can also express the system in the position basis (eigenstates of the position operator $\\hat{x}$), rather than the energy basis. In this way, the position and momentum operators are expressed as ($\\hbar = 1$):\n",
    "\n",
    "$$\n",
    "\\hat{x} = \\frac{1}{\\sqrt{2 m \\omega}} \\left( \\hat{a} + \\hat{a}^\\dagger \\right)\n",
    "$$\n",
    "$$\n",
    "\\hat{p} = i \\sqrt{\\frac{m \\omega}{2}} \\left( \\hat{a}^\\dagger - \\hat{a} \\right) \\, .\n",
    "$$\n",
    "\n",
    "We first check that\n",
    "$$\n",
    "\\left[ \\hat{x}, \\hat{p} \\right] = i\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims=[[120], [120]], shape=(120, 120), type='oper', dtype=Dia, isherm=False$$\\left(\\begin{array}{cc}1j & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 1j & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1.000j & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1j & 0 & \\cdots & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1j & \\cdots & 0 & 0 & 0 & 0 & 0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 1j & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 1j & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 1.000j & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 1.000j & 0\\\\0 & 0 & 0 & 0 & 0 & \\cdots & 0 & 0 & 0 & 0 & -119.000j\\end{array}\\right)$$"
      ],
      "text/plain": [
       "Quantum object: dims=[[120], [120]], shape=(120, 120), type='oper', dtype=Dia, isherm=False\n",
       "Qobj data =\n",
       "[[0.  +1.j 0.  +0.j 0.  +0.j ... 0.  +0.j 0.  +0.j 0.  +0.j]\n",
       " [0.  +0.j 0.  +1.j 0.  +0.j ... 0.  +0.j 0.  +0.j 0.  +0.j]\n",
       " [0.  +0.j 0.  +0.j 0.  +1.j ... 0.  +0.j 0.  +0.j 0.  +0.j]\n",
       " ...\n",
       " [0.  +0.j 0.  +0.j 0.  +0.j ... 0.  +1.j 0.  +0.j 0.  +0.j]\n",
       " [0.  +0.j 0.  +0.j 0.  +0.j ... 0.  +0.j 0.  +1.j 0.  +0.j]\n",
       " [0.  +0.j 0.  +0.j 0.  +0.j ... 0.  +0.j 0.  +0.j 0.-119.j]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 0.5\n",
    "\n",
    "x = (a + a.dag()) / np.sqrt(2 * m * w)\n",
    "y = - 1j * (a - a.dag()) * np.sqrt(m * w / 2)\n",
    "\n",
    "commutator(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now numerically diagonalize the position operator $\\hat{x}$, such that $\\hat{U}^\\dagger \\hat{x} \\hat{U}$ is diagonal. Then we plot the eigenstates of the quantum harmonic oscillator in the new basis, obtained with\n",
    "$$\n",
    "\\vert \\phi_n (x) \\rangle = \\hat{U}^\\dagger \\vert \\psi_n \\rangle\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 5.0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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dGz2Veuf6q9NMTDn1/WvwsGsb4xMcw14CwtUOnVptOFCS62AWkxU1pS2oKmq0L7rQhKba/tc3iiRCaKK87F1UfjT33TmOHj2K1NRUbvvTTz/F9ddf3+tjzCYr8g9XIWtvOaqLm7o9RqYUI3FGKOKnaKCJdt8BOaZWC0qy6pB/uBolWXWwWnpvFfQLUSJ8jB9XB6jwcn6ZgKnVgsKjNchJ7z3h8AtRImFGCBKmh0Lt5371Y1aLDaWn6pF/uBpFx2p67G4F2K7D0VPY6fX8QlROianwWA3MvcTkH6ZC/GQNRk8Jhm+wcthiGi6MjUH5aS1y9lcg/2hN7ydWU4KRMDMEwdHOr+NnbAzqyltQlssmIuWntX2WTnj5y7mTkaBI9014W3VmnMmuw6m/K3A2p6HbY8QSIeKnBiNlXjg0Ue77t7oKXaORG/tTdlqLpgGseioSCxE4St0p8fUOdK3V2SjJHSTGxqBFa0RjjQGN1XrUlrLz29WdbRnQABG/kI5nRj7wD6d1q3vDMAwmTJiAEydOAAAWLVqEP/74o9+Pry5pQva+cuQdrOxxIJ9cLUFUcgCixgUgcqy/y3fRcN3dR6pQcqKuxxHGAOAdpOBGc4ePcb3BBk21BuTau457+rIVCICIJH8kzghBzMQgSFy4Bd5mtaEsV4vTR6pQeLT3VlMfjQKjpwQjfrIGAeHObzW1mK04k1WP00eqUHy8tteBroGj1FzC6+rjALTVeuSmVyI3vRLN9d03OAiEAkQm+yNxRiiixwe41Aw03MCiXLaGviJfC3MvLf/eQQpu/vHACNcuN2lrxS45UYfiE7WoLGzqsaTJL0SJ5HnhSJge0u8eptzcXGzYsAE33HADEhMTHRm6xzK0mNjpyooa2R7o4qZ+9Sy0kask9vIGL/iHqeETpIB3kKLXUrfhREluLyxmK1tTWGNgk9laA3e7qc4w4EEhCm9pe0JrX6mEr//x7mz9+vV46KGHAAACgQBFRUWIiooa0HMYDRbkHahE1t4y1Jf3PKeiQChAWLwPolICET0+AL7BSpf40bCY7N3dR/ru7m5rgRvuVkFH6jQI6HBVj62eUrkI8ZM1SJgZitA4H97/39isNtSUtqAiX4sK+0pLPXW1AuwIZ7bF1rXqX81GK4pP1CL/iL1HoJcTp4BwFULjfREW74vQeF+XaGU3GiwoOFKNnPQKVOR3X8cJsLEnzgzF6KnBLnfC1xOr2d76fqTv1neu3GSyBv5hrjF+w2K2oixPi5LjtSjOqut1JhehSIC4VA1S5oUhNH7gc58/8sgjeOkldoWz+fPnY9euXR474Gy4MAyDxhoDt3pqVXETakqbB5z/yFUSeAcp4GO/eAe231b6SIftvTnik9xWnRlNtfYktqZDEltrQIvW2K8C7e6IJUIERXnZk1ofBMd4Q+0nc4kvGXdXWVmJiIgIWK3sl/szzzyDxx57bFDP1ZZMZe0rQ/Gx2l67kAF2UE70uEBEjQtA+Gg/p5aSWM02nDlZh/wj1Sg6Vttra45vsBLx9u5ud6+ltJisKDxWg9z9lSg9Vd/jmu/eQQqMSvJHQJgK/mEqBISpIVcPbyu82WRFVVETt1JfZVFTryccgPvVUppaLSg6xia8Z7Lr+hwg6x0o75D0+gz7iaHNxqCpxoC68hbUl+tQW9qCkuyeE3O5WoIx09g6b1c6sRgMrrb7SDWKj/f+neAXouQGFPqHOfdkt6XBiJKsWhSfqMPZnPo+p8P0C1EicWYoEmeGDnqmFavVisjISJSXlwMAVq9ejY0bNw7quUhnVrMNtWUt9nFGjagu7n11tr6IJUJ4n5P4egcp4BPI1sAPpe7Xo5Jcq9UGo86CVp0ZRp0ZrTozWrvZNurZ2811rQOewLs7QrEAvhplp5GIAWEql1hFzFMtX74cv/76KwBg9OjRyM3NHfKPldViQ0W+FsVZdSg5Udfnh1YsE2FUoh+b9KYEQOXr+JYgrmbySDWKMnuv4/QJUiB+CtuF7CqtNo6m0xq5cob+LF2t9JZyCa9/OJv8+oeqBj1IpVVnRkVBIypOa1Gezy493Z9ZUTxlTlqj3ozCzFrkH+n/3L0KLwlC49iEdyhLpjIMg5YGI+rLdWxCW8ZeN1Tq+5yRQigSIHpcIBJnhiAyJcAjS8IsJitKsuu4hLe3RHK466tt9jmAS7LYMoTa0pZejxeKBQgf44eolABEjwuAT9DQY9q+fTvOP/98bvu3337DhRdeOOTnJd1r1Zm5lt6q4ibUnGnu11R5fREIALW/HEpvKeQqCeQqCWQqMXf73G2ZSgKpXMT9/rl9kvvKP79GkDoSRp25z1a4oZAqxF2a2Nua3mn1Juf77rvvcOWVV3Lbe/fuxdy5cx36GtoqPfclXX5a22cyExTphahxAYhOCYQmygsWiw0mgwXmVitMrRaYDBaYWq0wt7LX7D72mjvmnH1GvaXXwWPsdE9sHae7t0oNBMMwqC5pRu7+CuQdrhpQzRjAlgkEhKngH662t/yq4Res7NIy31zfyrbS5jeiIl/ba2lLRyKJECEx3giN90VEoh9C43097juitcWM4iz2s1GR39jvlhyJTISQWG+utTc4xrvLzCaGZhPqynWoL29hr8vY2wP9jtdEeSFhRihGT9VAoR45cy+bjVZ2AGo/6vSlCjGkclH7tVwMibzDbQV73XaMRNZ2bId9chEsJhvOZNehJKsOZ7Lr+pwWTekjRXRKAKLGBSIi0c/hsyOsXr0a3377LQAgJCQEpaWlEIupPNCZzEZr155y+3ZLXavDF7hpIxAKILcnvtVNZ/DAa6vdN8ldt+pjhPpHO+Q5Vb4yeyIr79BcroRPkAIyleOmjCFD19raivDwcGg0GqxZswbXX389fH19h+31TK0WlJ6qZwdIZNXB0NTHGaoAgy516YunjKR2FKvZhmJ7V2h9WQvqK3T9Wh3wXAKhAL4aBfzD1BCJBajIb+xxoNK5ZEoxQuN82MRttC+CIr1cfmodR9M3mdprkfO1qC1t7rG0pCOhSABNlBf8Q1VorG1FfXnLoFcXU/nKEBCmQlCkF0ZPC3b7Uh1HMLVaUHKiDqcPV+FMdn2fM64MGwGgifJG9LgARI8LZAfFDdOJX2VlJUaNGgWLhT35Xbt2LVebS1yDzWpDS4Ox2wS4qcbQa+nNQFTUF+O5727x3GV9RWIh5CoxZN00bat8ZFzdh3eg3OPmSfVkcrkchw8fRnR0tFOSPKlcjLhJ7FyljI1BTWkzio/XoiSrDtUl3Swr6eAEt62OM36yhpdpjVyZSCLk/t8A7MwnTXUG1JXpUN+hNVBbqe+15YCxMWio1Pdr3ki1nwyh8b4IjWO74P1DVW5bguAoSm8p4lI1iEtl/z+YWi2oLGzkBuBVFTd1W1ZgszKoLGxCZWH30/t1R6YSIyBMzbXGt5WhOHJeZ08hlbNzTY+eGgyTwYKi4/b6aiesqCeRixA51h9RKWxJl7NWMvzf//7HJbgAcPvttzvldUn/CUVCeAeyveOjkjrfxzAMDM3t46Waag1obTGjVW9Ga4u95NS+bdRbHP5761ItuZ+9+ivGJo2FTNmWxIohV0vYbbUEYomQEgIyrHSNRpRksd10pSfr+zwDFYoEbFefQtTeLagQQyoTQdKxG1DOdgP6h6rYxHaEJ1FDZbXYoK3W2xNfHerK2OS3qdbQ55ekX4jS3r3OttZ6ypKXzmQ121B9ptle/qFFZUFjn2MixDL2/d9xMKF/uApK7+EbjT1SGPVmnM1lV1vjSqYMlnPKp6xcmZWp1cJ+t/XxWfENVtrLtgIQGu/r9B4Nq9WK2NhYnDlzBgBw/vnn4/fff3dqDMR5bDYGJoOlQxLMJr5t2zk5J3Hj2ovdtyU39bwoJCdH8x0GGcFUPjKMnR2GsbPDYDXbUFHYCH2jkUtS2xJaNnkV0+IePBGJhfbWv85d2GajFQ2VOnvLL5v4WkxWaKK8uRkC+Fgkw9OIJEK2pCPOB6nnR4GxsXOksjW9WjTVtcI7UIGAcLZGOiBMBS9/OZ3cDROZUsL1fvQXY2NgNlm5cQMdE2KrxQZNpDfvC4Vs3bqVS3ABYM2aNTxGQ4abUCjgeum7o441AGsH9pwuleQS0hHDMLy28IgkQkQk+PH2+mTgJDIRNFHe0ER58x3KiCIQChAQrkZAuBrjFkTwHQ7pB4FQwJ2sA645r/C7777L3Y6IiMCyZct4jIa4I2qGIi6FYRjs378f119/Pa6++mq+wyGEEMKD4uJibN26ldu+7bbbaEYFMmD0jiEu5a233sI///lPAIBQKMR///tfREZG8hwVIYQQZ9q1axfahgyJRCLceuutPEdE3BG15BKXcumll3JLNdpsNnz44Yc8R0QIIcTZbr75ZuTn52Pt2rW49dZbERYWxndIxA1RkktcSkREBC6++GJu+6OPPoLZPLh5NgkhhLivuLg4vPTSS3jvvff4DoW4KUpyicvpOIK2srISmzdv5jEaQgghhLgjSnKJy1m6dCni4uK47Y4jbAkhhBBC+oOSXOJyhEIh7rjjDm57165dyM3N5TEiQgghzpCRkQGTqY+l1gnpJ0pyiUu68cYbIZW2T9pPNVmEEOLZdDodFi5ciFGjRuHRRx9FeXk53yERN0dJLnFJQUFBWLVqFbe9YcMGGAwGHiMihBAynDZu3IimpiZUV1fjhRde6LTaGSGDQUkucVkdB6BptVp88803PEZDCCFkOHUcfzFx4kRMnz6dx2iIJ6Akl7isWbNmYdy4cdw2DUAjhBDPdOjQIRw5coTbXrNmDa/LuhPPQEkucVkCgQB33nknAEAikSA2Nhatra08R0UIIcTROo678PLywjXXXMNjNMRT0LK+xKX94x//QFNTE2666SYEBwfzHQ4hhBAHa2howNdff81tX3fddVCr1TxGRDwFJbnEpXl7e+ORRx7hOwxCCCHD5LPPPus0sLitB4+QoaJyBUIIIYTwgmGYTqUKs2fP7jQWg5ChoCSXEEIIIbxIS0tDTk4Ot91xVh1ChoqSXOJWmpub8d577+Hw4cN8h0IIIWSIOs6aExgYiCuuuILHaIinoSSXuI1169YhLCwMa9aswauvvsp3OIQQQoagqqoKP/74I7d90003QSaT8RgR8TSU5BK3YTQa0dLSAgD4/vvvUV1dzXNEhBBCBsvX1xeffvop5s6dC4FAgDvuuIPvkIiHcViS+9FHH0EgENC0H2TYdPwCNJvN+OSTT3iMhhBCyFDIZDJcc8012Lt3LwoLCxEXF8d3SMTDOCTJLSsrw0MPPYSwsDBHPB0h3Ro9ejSWLFnCbb///vuw2Ww8RkQIIcQRoqOj+Q6BeCCHJLl33nkn5s2bh6VLlzri6QjpUceRt0VFRdi2bRuP0RBCCCHEVQ05yf3iiy+QlpaGd955xxHxENKrSy65pFOPQcf5FQkhhLg+hmH4DoGMEENKcqurq3H//ffjxRdfREREhKNiIqRHYrEYt912G7f9yy+/4MyZMzxGRAghZCAef/xxXHTRRdiyZQusVivf4RAPNqQk96677kJCQsKAJm+urq5GdnZ2p0t+fv5QwiAjzG233QaRSAQAsNls+PDDD3mOiBBCSH+YTCZ8+OGH2Lp1Ky655BJa/IEMq0EnuT/88AO2bNmCDz/8EAKBoN+Pe+edd5CSktLpsnLlysGGQUag8PBwXHzxxdz2Rx99BLPZzGNEhBBC+uOnn37qNP3j6tWreYyGeLpBJbktLS24++67ce+99yIsLAxarRZarRYmkwkAoNVqodPpun3sXXfdhaysrE6XTZs2DfoPICNTx7P/yspKbN68mcdoCCGE9EfHFc5Gjx6NhQsX8hgN8XTiwTyotrYWVVVVWL9+PdavX9/lfj8/P6xYsaLb5FWj0UCj0QzmZQnhLFmyBHFxcSgoKAAAbNq0iZaDJIQQF3by5EmkpaVx23feeSeEQlqTigyfQSW5ISEh2L17d5f9L774ItLS0rB161YEBgYOOThCeiIUCnH33Xdj9+7dWLNmDc4//3y+QyKEENKLjrPhyOVy3HjjjfwFQ0aEQSW5crkcCxYs6LJ/w4YNEIlE3d5HiKM98MADeOCBB/gOgxBCSB90Oh0+++wzbnv16tXw9/fnMSIyElA/ASGEEEKG1caNG9HY2Mht33nnnTxGQ0aKQbXk9mTDhg3YsGGDI5+SjBAMw8BaWwvGxkAgFAAiESAQQCASAUIRt08gsN8nFA5oVg9CCCH86TjgbOLEiZg+fToA+8IQVisYmw2w2djb5+xjrFaAYSBUqSFSq/j6E4gbcmiSS0h/2IxGGE/nw5hzCq2nctCamwNjTi5sLS0DeyJ7wisQCtmkVyiEDYBQIoFQLodi/HgoZ86AasZMSGOiKSkmhJBhZmttheHoUej2p0N3IB3mkjOwmEx4t7kZwtFjIAQgNZqQkzIOGMRCEJKICMiTEiFLSIQ8KRHyxESIw8Lo+510i5JcMqws9fUw5uSwyWxODow5p2AsLBrUl1sXDANYLGhbILLt2gbA1tiI5h070LxjBwBAHBwM1YzpUM6YCdXMGZCEhAz99QkhZIRjLBa0ZmVBl54O3f50GI4eBWOfTrSNAIDavoAPALbFdpDMZ8/CfPYsmnfs5PYJvb0hT0iALCkR8sQkNgmOi4NAKh306xDPQEkucQjGZoOppIRNaHNy0ZpzCsZTObB0mPSbT5aqKjRu/hmNm38GAEijorhWXuX0aRD7+fEcISGEuD7GZoPx9Gno7Umt/tAh2HqYF99ZbE1N0B86BP2hQ+07xWLI4uIgT0y0J7+JkCUk0Hf9CENJLhkUS10d9AcOQH/4MFpPnkJrXh4YvX5gTyIWQxYby3U9ycaMgVAhZ+uvbAxgs4Jpu7bXZHW6z2oDGLZe67MNG5C2Zw9EAORSGZ7714OwHs2E4cSJbluNTSUlMJWUQLvxGwCALCkJqhkz2NbeKVMgVFHdFyGEMAwDc2kpm9AeSIcu/QCs9fV9Pk7k6wvljBlQTJwAoVwBo9mEg4cOY3RiAsLCw9mxFiK21Kyt3KzXfQIBLFVVnRtRamp6DsBigTE3F8bcXKDDYkHi0FDIExMhH5cC1YwZUIwbB4FE4oh/KuKCBAzDMH0fNryys7ORkpKCrKwsJCcn8x0O6Ya1pQX6g4fYL7n96TDm5Q3o8UIvL3t3UhL7BZOUCGl8PIQO6k46duwYJk6cyG2/+eabuOeee9i4Dx2CPv0AdOnp7BdeX8RiKMaPt5c3zIBi4kSHxUkIIa7OXF0N/YEDbGKbng5zeXmfjxEqlVBMnQKVvSRMNmYMm6QOI0tdnb0Mrq0k7hRMRcUDKocTKJVQTpnMxj1jOmSJicMeNxmcweSKlOSSbtmMRm7wgD49HYasrH5/cUjCw9troxITIEtMgiR8+AcGzJo1C/v37wcAJCcn48SJE11e01JXB/3Bg+ygiPR0mM+c6fN5hUolvJcvh99VqyEfO3ZYYieEED7ZWlvRvG0bGjZ+A8PRo30eL5BIoJg4kSv7UoxLcYkWUVtrK4yn89nW3pxcLgnub0mFyNcXyunTuUYOaTQNWnYVlOSSQes0eCD9AAwZGV0GD3RHGh0NxaRJkCfZi/0TEiDy9nZCxF19/vnnuP7667ntvXv3Yu7cub0+xlxWBp29lVeXvh/Wmtpej5ePHw+/1avhfdGFECoUDombsBiLBfrDh9G8Yyf0RzPAGE3sABWbrX0qIcbGlqu0TTN0zv3sMZ3vF6pUUM2aBa+lS6CePx8itZrvP9UjGQsK0LxjJ5p37kRrbi7AMGxyIBS2T//XqRtaCAgFEAh6v18cFAT1/PnwWrIU0ohwvv9Mj2MsKoL2m2/R+NNPsHaYx7YLoRDy5GQu+VOmprrNdyBjs8FcVobWU6dgzMmBITsbhiMZ/ZrRRxwSAtV09m+mQcv8oiSX9NtgBw+IQ0KgmjEDyhnToZrhWh/41tZWhIeHo95eL3b11Vfjq6++6vfjGYaBqbDQ3sq7H/qDh2Braur2WKGXF3xWroTf6ishi493SPwjka21Fbq//0bzjp1o2b0bVq12WF9PIJFAOXMGvJYsgdfixRAHBAzr63kyhmHQeuIEl9iaioqG/TVlY5PgtWQJvJcuhTQ+nlrYBokxmdC8axcaNn4DfXp6j8dJ4+O4bnzl1KkQ+fj0+zUqKyvx0Ucf4ZZbbkFoaKgjwnYoxmJBa3Y2N9WZIeMoGKOxz8fRoGX+UJJLesRYLGjNzYUh4yj0GUegP3BwQIMHVG1JbVSUS/+wPPTQQ1i/fj0AQCKRoKioCOHhg2v9YaxWtJ44Ae2PP6Hxl196HFinmDIZfquvgtf551Htbj9Ym5vRsicNzTt3omXfvoEPWHQUoRCK1ElswkuthP3SsbW9+Y8/YKms5C0WaVQUvJYugdeSJZCPH091lP1gOnsW2m+/g/aHH2Ctq+v2GGl8HPd9JtFoBv1aTz31FJ5++mmIxWJcdtll+PLLLyEWu+5Yd7ZEL5Nt4Eg/0OOg5XPJkpKgmjYVikmpUKROGtK/GekdJbmEY9PpYDh2DPqMozBkHIEh8xhs/UgmhEollFOncl0zzhg84Ej5+fkYM2YM2t7Wa9euxUsvvTTk57W2tKBpyxY0bPymx8FrIj8/+Fx2KfyuvBLSqKghv6YnsdTWovmPXWjeuRO69HTAbO7xWJGfH9QLF0ISGsp2Z9tHWHO3BUL7aGt71zZ3u7tjBTDmF6B5xw6YCgt7jbGtldBryRLIRo926ZM5ZxpIa7tAIoFy1ky2LMTLy15Kwtiv7TOjMPbykrbZUWy2c2ZTaT+WsZhhOJoJ/eHDvSYcYo0GXksWw2vJEiinTnWJ2lBXwVgsaNm7Fw0bN0K37092fvFzCCQSeJ1/PvyuWg3F5MlDfu/r9XpERUWhtpYt/7rooovw66+/Duk5nc3a0gL94cPQ70+H7sABGHNy+vU4yahRUKZOgiJ1MpSpkyCNi3Or31BXRknuCGauqoIhI4NNao8cYWvi+nEWKpBIoJg0CaqZM9iZBFJcY/DAUFx++eX48ccfAQDe3t4oLS2Ft4PqhBmGQeuxY2jY+A2atm7tsXtLNWsWfFevhteihW7/7zlYJvuE7c07drADWXr5qhGHhXLd0IrUVHY5ZwczFhZy8bRmZfV6rCQqEt5Ll47YVsKBtLYLlUqoF8yH15IlUM2bNyw1z5aGBrTs2s2eJP31V6/jBYQ+PvBasABeS5dANXu229SNOpq5qgra77+H9rvve2xxl0RGwm/1avhcdqlDu93fffdd3HXXXdz2rl27sHDhQoc9Px8s9fXsjBPpB6BL3w9zSd+DlgH2/aicOBGKyWzSKx83DkKZbJij9UyU5I4QjM0GY36+PanNgOFIBsxlZf16rEAigXzcOCgnT4Zq5gwoUlMhlMuHOWLn2r9/P2bNmsVtr1+/Hg8++KDDX8eq1aJx82Y0bPymx3pEUVAgfK+4An6rVkESFubwGFwJwzAw5p1mV5rbubPPlg9pfBzbcrp0KeRjxzq15dRcUYHmnX+geedOdgL5XlZgGimthANubV+8iE1sZ8506o+2TadDy74/2QR8z55eBw8JFAqo58xhBx0uWMDboFhnYWw26P76Gw3fbETL7j3dN3SIRPBavBh+V62GcsYMh5/AWa1WJCYmIj8/HwCQmpqKw4cPe1zPiLm8HLr0A+x88RkZMJeW9utxAokE8uRkKCanQpmaCkVqKtX19hMluR6IYRhY6+rYpDbzGPRHM2A4mtnjgKhziXx8oEhNhXIy+2GSJyePiLPIOXPmIC8vD/fccw/uuusuBAYGDttrMQwD/cFD0H6zEU07dnafHAiFUM+bB98rLveo1iXGaoXh2DEuYexrSjb5hPHtJQExMU6KsncDbiVctAhe558H1axZbl+Dba6sRPP2HWjavg2GIxn9am33WrIEytRUCFygvpIxmaA7cIBtod+1C9baXmZHEYuhmjYN6iWL4bV4MSTBwc4LdJiZSkvRtPV3aL/7rsdkSxwaCr8rV8HnssshCR6+utEff/wRl19+Obf91Vdf4eqrrx6213MV5upqGDKOwnA0A/ojGWg9darf025KY2LYpHdSKuTJYyGNjva4xidHoCTXjTE2GywVFTAWFMBYUAhTYQGM+QUwFhbC1tu0LueQREVCOSmVO0uUxsSMuK5WACgqKkJISAgUTk4mLXV10P74I7TffAvz2bPdHiOQyaCaORPqRQuhXrDA7QYq2IxG6PbvR8sff6B51+4eB7AAAEQiKKdN5ZIjV08srC066P7cx9af7tnT64wjQrUa6oUL4X3+eVDNmeM2P0qms2Vo3r4dzdu2wXDsWK/Hcq3tS5ZCnuzc1vaBYqxWGDIzudkeevr8tZGPHw+vxYvhtWQxpLGxLv23nYux2dB6/Diad+1Gy+7dMJ4+3f2BAgHU8+fD96rVUM+dOyxlQOfqOF95ZGQkCgoKXHrA2XCx6fUwHD/O9bYaMjP7v/yxQABJRARkcXGQxsVCFhsHWXwcpHFxI3oKREpy3QBjscB0phTGgnyYCgphLCyAKb8AxqIiMAbDwJ5MLIZ87FgoJ02ynwVOgjgoaHgCJwPSr25DO/m4cfBatBDqRYvYgX4u+GNrbWpCS1oamnf+0WeNpkAmg8reRey1YAFEvr7OC9SBbCYT9Onp3EwCvc1GIlAqoZ4/D97nnQf1vHkutyy0qbgYTdu2o3n7drRmZ/d6rHx8h9b2WNdobR8ohmFgzM3larD7WqFRGh0NryWLoV68GIoJE1yyYcCm10O3fz+ad+1Cy560Xk8uuTKpK66AZJCzywzG33//jdmzZ3Pbr732Gu6//36nvb4rY6xWGPPyuKRXn5ExqNlJxBoNm/DGxkEWFwtpXBxkcXEQ+fu75G+HI1GS6yIYkwmW+npYamphOlMCk7111liQD1PJmV5r3XojVKuhmDSJG7mpGD/OY7q9PVnbAJDGH37sc3lMcVgovBYugnrRQqimToWAx+5wc2Ul+4O68w/oDh4ELJYej2UH+8yHevFiqOfMgVCpdGKkw4+xWmE4ehRN27ejefuOXn+cBDIZ1PPmwuu889g6UC8vJ0bazpifj6Zt29C8fUfvy1kLBFBOngyv88+H19IlLjX3taOYzpzhShoMGb2XZYiCAuG1cBG8liyGcsYMXktSzFXVaNmzBy27dkGXnt77PK4iEVTTp/M64PXSSy/Fpk2bAAC+vr44c+YMvHh6/7sDc3k5NwOS/kgGezI2yJRM5OvLJryxsVwSLAkNgTgwEEIfH49IgCnJHUaM1QprQwMstbWw1NbBUlsDa20tLDW1sNTV2ffXwFpT2/uqMf0g9PaGLDaW7aaIi+fO1iRhYS7ZwuAudDodVDy2sLEDs/LQsmsXmnfvQevx470eL1SpoJo7F16LFkI1d+6wD05gGAamggK2vvaPP9B64kSvx4tDQtju3qVLoJw82WMHZJ2rrau4afsONG/f3mu3uEAiYVdbO/98eC1aOKyt2m2tl03btqF52/bep0wTiaCaPg1e553HLooxgnqALLW1aN69mz15+/tvML00OghVKqjnz2NP3ubNG/YTFq4FetcutOza3ecsIEK1Gqq5c+C1aBHUc+fy2muSl5eHxMREbvrGRx55BC+88AJv8bgjm14PY1ERTIWFMOYXsGWLBYUwlZT0u763WxIJxAEBEAcGspegQIgCAiAODOK2xQEBEAUGQahSumxCTEluLxibDTa9AYxBD5teD5vBwF7r9LC17dPrwRgMsGq1bPJaa7/U1cJaV9/rCOzBEAUFsrU2HbocpLGxEAcFueybzB0VFxfj//7v//Dxxx/j77//xrhx4/gOCQA7UKFlzx607N7D/tj21kojFEKZmgr1okVQL1wwpEFb3LK3VisYswXG03nsSPWdf7Bfpr2QjR5tH7izxOVrNJ2BYRi0njyJ5m1sjWuv/35iMVTTp8Pr/PPgtWQJxP7+jnn9rCw0b9+Opm3bex/4J5FANXMGW1KxeDGN6EaHGuydf6AlLQ225uaeD5ZI2P9/S+wJr68vIBZDIBINqdbVZjJBf/CQ/eR3NywVFb0eLwkPh3rhQngtWgjllCm89vZ0dOedd+L9998HwC7EU1xcjDAPn1HGWRiTCaYzZ9p7hAsKYSwshKmwsF+rtA2EQKFgE9+AADYZDgyEOCAQIi81BAoFhEoVhEoFhEole1GwtwX2bYFUOmy/C26f5Ka/9x4Sw8LBWCxgLGbAYgFjtti3e99nazXCZtCD4RJXA5e42gyGgde7OpAkPLxz8bg9sR3IEolkcHQ6HUJDQ9Fs//G64YYbsGHDBn6D6obNYGAHc+3ejebde3ofJQ52tSeRnx+bqFotgMWetFrM7bc77bewnx2rdWAtAgIBFJMmtQ/QoUUuesRNobZ9O5q3b4PxdH7vD3BErwzD9Nq9KZBKoZozB97nnwf1woUeP4XWUDAmE3SHDrEDKnf+AUt1df8fLBB0TnjFYgjs2xCLIBB1uC2WtN8WCGHMy+tzoR75hPHwWrgQ6oWLIBvjeguVMAyD5cuX47fffgMA3HTTTfjf//7Hc1Sej7FaYS4vh7GggCuLZK8Lep1ab1iJROckvx0TYna/QCplPx8Ssf2zIuG2BeKe9+WcLcOMO+9w3yR3c3QMRrvL9FZicafmf1GQvRsgwN7039YtoNF4XH2iu7n77rvxzjvvABj6Ur/OwNhsaD1xgu1S3bW7z0EzjtbWxa5eshheCxdCPIzTr3kyY2Eh28K6fTuMJ0857XUFCgXU8+bB67ylUM9fAJHatQbBuQPGZmNbyO2lO6aCAqe+vkAuZz+DCxfAa8ECtyknOXz4MF555RU8/vjjLlt6OBK0TT1qaSupbCunrK1r76GurYW1dujllc502mjEiuIiSnIHQyCRcE3uIi+v9rqVwMD2upVANqkVBQZC5OND9bFuYriW+nUW09kytOzejZbdu6A7eKjXAWCDJfTygnrBAngtXgzVnDmUGDmYqbSUKynoqxZ7MIRKJduFff55UM+dSwNSHcxYWISWXWwLryEzc1heQxQUCK8FC6FeuBCqmTPo/yFxCpvJ1DkhrqttH29Uy445stbWwqrXgdGzPeSDHRw3VJ6R5CqVbBO1/QKJpNM227zddZ9AKuu+abzttn1/e01J+z6hQjFiBs2MVFdccQV++OEHAI5f6teZrM3N0P35JwyZmWBsjP0zIAJE9i5Rsb2rVNRhv1jS6zFCtRcUKckuU9vn6czl5TAcP8GWkziAyNcXyilTRsQiL67AXF0N4+nT7IA1qxWMxQpYLVyNO2O1cPsZS/sxbPmQpcNttpRI5OsL9by5kKekUMMJcXkMw4AxGtvLQfX2MtGOJaL6tts6MNz+9vu5UtNOpac97bMAZjMYiwWnW1vdO8k9ceIEUlJS+A6HeKD09HTMnDmT2x6upX4JIYQQ4nhZx49j3IQJA0pyXeq00dWK6YnnmDFjRqdJyv/v//4P5kHOV0wIIQRIS0vD5s2bYXPwzEOEdGcws5i4VJJLyHB6+OGHudulpaX49ttveYyGEELc27///W+sXLkSSUlJ9H1KXBIluWTEuPjiizFmzBhu+5VXXoELVOsQQojb+euvv7B//34A7EIQFX3M70sIHyjJJSOGUCjEv/71L247MzMTf/zxB48REUKIe3rllVe4276+vrjlllt4jIaQ7lGSS0aU6667DkEd5pzs+EVNCCGkb3l5edi8eTO3vWbNGqjVah4jIqR7lOSSEUWhUODee+8FAFx44YVYu3YtzxERQoh7efXVV7lSL6lUyn2nEuJqxHwHQIiz3X333bj00ktpujpCCBmg6urqTkuj/+Mf/0BoaCh/ARHSC0pyyYjj7+8Pf39/vsMghBC38/bbb8NoNHLbHcc5EOJqqFyBEEIIIX3S6/V4++23ue1ly5Zh7NixPEZESO8oySUE7FKFFotjllklhBBPtGHDBtTV1XHbDz30EI/RENI3SnLJiGaxWPDNN99g2rRpeOONN/gOhxBCXJLVasWrr77KbU+ZMgXz58/nMSJC+kY1uWREu+6667Bx40YAQFVVFe69915IJBKeoyKEENeSl5eH+vp6bvuhhx6CQCDgMSJC+kYtuWREu/rqq7nbtNQvIYR0LykpCaWlpXjjjTewcOFCXH755XyHREifKMklI9ry5cuRkJDAbb/88su01C8hhHRDpVLh3nvvxa5duyAWU0cwcX2U5JIR7dylfo8dO0ZL/RJCCCEegJJcMuJdd9110Gg03PbLL7/MYzSEEEIIcQRKcsmIJ5fLOy1LuX37dhw/fpzHiAghxDX88MMPOHv2LN9hEDIolOQSAmDNmjVQKpXc9iuvvMJjNIQQwr+qqipce+21iImJwQ033IDCwkK+QyJkQCjJJQRAQEAAbr75Zm7766+/ptYLQsiI1raEr8ViwWeffdZpOV9C3AEluYTYPfDAAxAK2Y+ExWLB66+/znNEhBDCD51O12kJ3+XLlyMpKYnHiAgZuEEluZmZmVi2bBkiIyOhUCjg7++PmTNn4osvvnB0fIQ4TWxsbKe5H99//300NjbyGBEhhPBjw4YNXRZ/IMTdDCrJ1Wq1GDVqFJ5//nn89ttv+OyzzxAdHY3rrrsOzz77rKNjJMRp2qYT02g0WLt2La3oQwgZcbpbwnfevHk8RkTI4AxqNucFCxZgwYIFnfYtX74cRUVF+OCDD/DYY485IjZCnG769On46aefcMEFF0Aul/MdDiGEON1PP/3UaZDZww8/TCf8xC05tCY3MDCQVkEhbm/lypWU4BJCRiSGYTrNFR4dHY3LLruMx4gIGbwhZaQ2mw02mw0NDQ347rvvsG3bNrz11lu9Pqa6uho1NTWd9uXn5w8lDEIIIYQ4wJ9//omDBw9y2w888AA1XhG3NaR37l133YX3338fACCVSvHGG2/gjjvu6PUx77zzDp5++umhvCwhTscwDHXXEUI8Xsc5wv38/DpNrUiIuxlSkvvoo4/i1ltvRXV1NbZs2YJ77rkHOp2u11GYd911F1atWtVpX35+PlauXDmUUAgZFkVFRfi///s/FBUV4eeff+Y7HEIIGTZZWVmdvufWrFkDtVrNY0SEDM2QktzIyEhERkYCAC666CIAwL///W/ccMMNCAoK6vYxGo0GGo1mKC9LiFP8+OOPWLVqFWw2GwBg9+7dWLhwIc9REULI8NixYwd3WyaT4Z577uExGkKGzqEDz6ZNmwaLxUJL/xGPsHjxYvj4+HDbjz/+OBiG4TEiQggZPg888AAyMzOxYsUKrFmzBqGhoXyHRMiQODTJ3b17N4RCIWJjYx35tITwwsfHB2vXruW2//rrL2zfvp3HiAghZHhNmDABmzZtwvr16/kOhZAhG1S5wu233w5vb29MmzYNwcHBqK2txXfffYdvvvkGDz/8cI+lCoS4m3vuuQevvvoqNyPI448/jvPOO6/HQWgMw8BoNaLV0gqDxQCD1cDdNlqM8Ff4I84nDhKRxJl/BiHEgzW0NiBfmw8rY4VCrIBcJIdCrGBvi+WQi+WQCAf2ndO2xDkh7mxQSe7MmTPxySef4NNPP4VWq4VarcaECRPw+eef4x//+IejYyTE6fRmPU7Vn0J2bTYW/WcR9qXvg0AqQKW0Eld8fQW8/L245LXV0opWa/ttBr2XNIiFYoz2HY1E/0Qk+idibMBYjPEbA6VE6aS/jhDijhiGQaWuEqfqTyGnPgen6k7hVP0pVOmr+nysWCiGQtSe9LYlwApR52RYIVZAJVEh1icWKYEpiPKOglBACS9xTwLGBYoMs7OzkZKSgqysLCQnJ/MdDhlhTFYT8hrykFWbhazaLGTXZaOwsRA2xua0GAQQIMo7Ckn+SUgKSEKifyKS/JPgK/d1WgyEENdhtVlR0lyCnLocNqG1J7Zao9apcaglaiQHJCM5MBnJAclICUxBqCqUplQkTjeYXJFmeCYjitVmRWFjIZfMZtVmIa8hD2abmde4GDAobipGcVMxthZv5faHqELY1l7/sWziG5CEYGUw/cAQ4kFMVhPytflc62xOfQ5yG3JhsBj4Dg0t5hYcqDyAA5UHuH3+cn8u4U0JTEFyQDICFAE8RklI9yjJJR6LYRiUNpeyLbR1Wciuzcap+lMD+uFQiBWI8YmBQqRA+r506Jv0sBlt8FX54oZrboBSqoRcxHbzKcVKtstPJIdC0rUuTiqU4mzLWbZFxt46k9uQC6PV2OPrV+oqUamrxJ7SPdw+X5kvkvyTMCd8DpbFLqMfF0LcDMMwOFZzDL8U/oJjNceQr82HxWYZ0HNoFBokBiRyvT6J/olQSVTdjgfg9p1TXnW66DR++uUnCGVCCKVCjB47GmFRYahvrUdJU0mPr13fWo99Zfuwr2wfty9EFYKUgBQkByZzia+X1GvQ/0aEOAIlucRjmG1mZNVmIb08HUerjyK7LhtNpqZ+P14ilCDBL4H7kk4JSEGMTwxEQhEA4IPSD7gV/cpQhvBp4bjmmmsGFKOv3BcpgSnctsVmQXFjcXuNnT0BbjY39/gcWqMW+yv2Y3/Ffrx25DXMiZiDlfErMS98Hg1oI8SFVeoq8UvhL9icvxnFTcX9flykVyTXk9NWyx+oCBxSLAzDYM69c1D+dzkAwN/fHz8W/Qhvb28AQLOpGSfrTnI9Xtm12SjXlff6t1XqKrHzzE5uX7R3NFICUzA1ZCpmhM5AmDpsSDETMlBUk0vclo2x4XTDaaRXpONAxQEcqToCvUXfr8cKBULE+cYhJcDe3RaYjDG+Y3pNEs1mMxISElBUVAQAGDNmDE6dOuXwUcgMw6CspQw59Tk4WXcSOfVsq2+NoabXx/nJ/LAsdhlWxK9Aon+iQ2MijlHWUoa9Z/fiVN0pWBmrQ57TW+qNGaEzMC10GhRihUOekzhOq6UVu87swuaCzdhfvr/XgakigQixvrFsbb69dTbBP2FYWkR///13XHjhhdz2Cy+8gEceeaTXx9QZ6pBdl81eatnkt661rt+vOcprFKaHTmffryHT4Cf3G3T8ZOQZTK5ISS5xK2ebz+JAxQGkV6TjYOVB1LfW9+txUd5RXA1ZckAyEv0TBzWbwYYNG3DTTTdh+fLl+M9//oNJkyYN+DkGq9ZQy9Xr7a/Yj0OVh3o8NsEvASviV+CimIuonIFHZpsZR6uOYl/ZPuw9uxeFjcO3UI5UKMXU0KmYFz4P8yLmIcIrYthei/SurRxhc8Fm/F70O1rMLd0e5yX1wtKopRgXOA5J/kmI94uHTCRzSnzTpk3D4cOHAQBBQUEoLCwc8BK+DMOgSl/VadBudl02mk0990R1lOifiBmhMzA9dDpSNak0wwzpFSW5xOPUt9bjYMVBpFekI70iHWUtZX0+Ri1RY0rwFEzQTEByQDLGBoyFj8ynz8f1h8ViQWZmJqZMmeKQ5xuKspYy/FzwMzbnb+7x30UsEGNuxFysiF9B5QxOUmuoxb6zbL3i/vL9PSY4wy3GJwbzwudhbsRcpGpS6f+9E/SnHEEoEGJW2CysiF+BhaMWOiWpPdfmzZuxcuVKbvvVV1/FAw884JDntjG29rEQtVk4UnUEOfU5/ZpacULQBK6lNyUwZcBz+xLPRkkucXt6sx6Hqw7jQMUBHKg4gNyG3D4fIxFKMEkziftyHBswFmLhyCk3tzE2HKk6gs35m7G9ZHuPA+uonGF42BgbsmqzuNbak3Unez1eKBAiJTAFvjLfIb82wzDIa8jrc55UlUSFWWGzMDd8LuaEz0GQkhbscZT+liPE+MRgZfxKLI9dDo1S4+Qo29lsNkyaNAnHjx8HAISFhSE/Px8KxfCVumhbtThUdQjp5ek4UHmg10FtbZRiJaaETMH0kOmYETYDo31H06wyIxwlucTtNJuacazmGDKqMnCk6giO1xyHhel9lLEAAowNGIvpodMxPXQ6JmkmUS2ind6sx46SHdhcsJnKGYZRo7ER+8v3Y+/Zvfir/K8+y2Z8Zb6YEz4Hc8PnYnb4bIf1LADtie6+sn3Yd3YfMmsy+5zjOck/CfMi2FbelIAUbnAl6Z+O5Qjbirb1OFDUS+qFi2Iuwoq4FUgJTHGJJO27777DlVdeyW2/9dZbuPvuu50aQ0VLBTuWovIA0svT+1XX6y/3x7SQaUgNTkWqJhXxvvH0vh1hKMklLq9SV4mMqgxkVGfgaPVRnG443Wc3FsCO0m1rqZ0aMtWhScJQWa1WFBQUYMyYMXyH0snZ5rPYUrAFmwv6Wc4QMY+6B3vAMAzytfnYe3Yv9p7di2M1x/ocOJbkn4S5EXMxN3wuxgWOc9oPcqOxEX+X/419Z/fhz7I/0WBs6PV4P5kfm4BHsAm4t9TbKXG6oypdFbYUbumzHGFm2EysjFuJhZH8lCP0xGq1Yty4cTh16hQAYNSoUTh9+jRkMv5iZBgGBdoCLuE9VHUIOrOuz8epJWpM0EzApKBJSA1ORUpgCjV2eDhKcolLsdqsyNfm42j1Ue5Soavo12ODFEFcUjs9dDpCVCHDHO3A2Ww2fP/993jyySfR2NiIgoKCYe3yG6z+ljP4y/3Zcoa4FUjwT3BylK6poqUCvxb9il8Lf0W+Nr/XY5ViJWaGzcS8iHmYEz6H1y7pNlabFVl1Wdh3li2lOFV/qtfjJUIJ5kfMx/LY5ZgbMRdSkdRJkbouo9WI3aW7sSl/E/aX7++xlTzGJwYr4lZgeexyBKuCnRxl/3z55Zf4xz/+wW1/8MEHuO2223iMqCuLzYLsumyutCGzOrNfi/WIBWKMDRiLSZpJmBQ8CZM0k+Av93dCxMRZKMklvGq1tCKrNgtHq48iozoDx6qP9Trfa0cB8gBM0kzClJApmBk6EzE+MS7RtdebHTt24LzzzuO2169fjwcffJDHiPqmN+uxvWQ7NudvxuGqwz0el+SfhJXxK7EsdplLtZo7Q5OpCTuKd+CXwl96/TcC2B6Gtm7/yZrJLj+4q0Zfgz/L/sS+sn34u/zvXlvMvKReOC/qPCyPXY7U4FQIBY6dKs+VMQyDk3Un8VP+T9hatLXH+ba9JF64MOZCrIhfgXGB41z+O+ubb77Bgw8+iPLycsTGxiInJwcSiWu/Zw0WA45WHUV6ZToyqjKQXZfd74Uzor2j2aRXw7b2RnpFuvz/I9IzSnKJ09gYG8qay5DXkIfMmkxkVGfgZN3JAX35pAansl8+mlSM8hrldl8+DMNg+vTpOHSIrX0d7DQ8fCltLsXPBT/j5/yfe5zkXSKUYOGohVgRvwKzwmZ57IA+k9WEfWf34ZfCX5B2Nq3HliOpUIqpIVMxN2Iu5oXPwyjvUU6O1HHMVjMyqjPYVt6yvShqLOrx2FBVKJbFLsPy2OWI841zYpTOVWuoxa+Fv2JT/qYeW+4FEGBW2CysjF+JBaMWQC6WOznKoTEYDHj//fcRERGBK664gu9wBqzV0orsumy2MaUqA5nVmf1uTPGX+yNVk4qJmokYFzgOcb5xI+4k3p1RkksczmqzorylHPnafBQ0FqBAy16KGovQam3t13OIBWKMDRzLfbl4UjfSYCZUdzU2xoZDlYewOX8zdpTs6PH/q0ahwfK45VgRvwKxPrFOjtLxbIwNGVUZ+LXoV2wr3tbj3J5tNZbLY5dj0ahFHjuXZ1FjEX4tZEszzrac7fG4JP8kLItdhgtjLnSJkoyhMtvM2Ht2Lzblb8KfZ//sceBrlHcUNzuCK5ZPjVQ2xsaWxVUd5cZ69LcsDmBL42J9YxHvG4843zjE+cRR8uuiKMklg2a1WVHWUsYmsYNMZtu0DQhI1bAttZ48IIBhGMyZMwd///03AHZpzKKiIm5pTHfTYmrBtuJt2JS/CZk1mT0eNz5oPFbGr8QF0Re43fr0BdoC/FL4C34t/LXXH8PkgGQsj12OC2IuGPISqu6kbeaAXwp/wbbibdAatd0eJ4AA00OnY3nsciyOXAy11D16MNrk1udiU/4m/Fb0W4+zYyjFSlwQcwFWxq/ExKCJbtfbNFJV6iq5lt6j1UeR15DXrwHOHQUqAhHnG4d433jE+rQnwZT88oeSXNInnVmHan01ihqLUNhYiHxtPgq1hShsLITRahzUcwYrgzuVHoy0qV127dqFxYsXc9tPP/00nnjiCR4jcozixmJsLtiMnwt+RrW+uttj5CI5Fkctxsr4lZgWMs1l6zar9dXYWrQVvxb+2uvgq3B1OJbHLsey2GWI8YlxYoSuyWw146/yv/BL4S/YU7qnx+8IuUiOBaMWYHnscswKn+Wys3Q0Ghu5coTe3gfTQqZhZfxKLI5c7LEt9yNJx6kqj1YfxYnaE4P+vWtLfttafON84xCuDkeAIsBl3/eegpLcEYphGOjMOtQYalCjr+n+2n5bb9EP+nX85f6I843rdFYb5xvnMaUHQ7Fw4ULs2bMHAODj44OioiL4+XnGuuxWmxXpFenYlL8Ju87sgslm6va4UFUolkQtwWjf0Yj1jUWsTywvrbw2xoYqXRV3Ipd2Ng0HKw/2OCreR+aDC6IvwPLY5ZgQNIFa63rQYmrBzjM78UvhLzhYcbDHljE/mR/Oiz4PE4ImIMYnBtHe0by08toYGyp0FVyP1LGaY9hTuqfHeutwdThWxK3AxXEXe9SSyO+++y4OHTqExx9/HDExdOIGsDM4lDaXolDLNvS09WAWNRb1ayaH7ggggJ/cDxqlBoGKQGiUGgQpgtiLsv2akuHBoyTXQ1hsFujMOujNeujMOugsOuhMOtQb63tMYnuaFmow/OX+nbpoYn1jKZntw59//om5c+dy2+vWrcOzzz7LY0TDo9HYiK1FW7E5fzOy6rL6PL6t3i3WJxZxPnGI9Y1FjE8MAuQBQ04mjVYjSppKuGS2qLEIxY3FKG4q7vPzIBPJuJbH2WGzXX5WBFdTpavC1qKt+KXwl36tSqhRaNiE1ycaMT4xiPGJQaxPLIKVwUN+H5htZpQ2l6JIW4SCxgIUNhaiUFvYr/eBXCTH0qilWBm/ElNCprhsT8Rg6fV6xMXFobKyEmKxGM899xzWrl3Ld1guy2Kz4GzzWS7pbevpLGos6vHkfqDakuFzk9+2hNhb5g2lRAmVWAWVhL0oxAo6+QYlucOKYRhYbBaYbeb2i9Xc53artRUt5pb2hNV+0Zv1aDG3sLctne8bbDfKQAXIA7gkti2pjfONg5/cM1ogne3888/H9u3bAQBqtRqFhYUICvLc5VNPN5zG5vzN2FK4pc8Vv87lI/NBrE9s+8WeCIeoQjolGgzDoMHYgKLGoi6XspayAdXZCSDAtJBpWBa7DEuilrhdLbGrOt1wmh2wVvQrKnWVA3qsQqxAtHc0l/S2JcCR3pFdFlFotbSiuKkYhdpCrtWtUFuIkuaSfs/q0maSZhJWxq/EeVHnuV0t8UCsX78eDz30ELf9888/4+KLL+YxIvdksVlQ1lLGJb352nzuZMpRyW9vhAIhlGIlm/xKVGwCLFVxiXDbfrVE3X6MRAWZSAaxUAyJUMJdxEIxJCJJp30dt0UCkcsm1G6f5N684WYExAQADMC0/ccwnX7I2ra5a/ZgMGBgZaxgGAY2xsZeYIPVZgWDDvs6XLjj0Xl/x2TWYrPAbDX3udSsKxEKhAiQB7R3mZx7tqgMQrgqHL5yX75D9SgHDx7E9OnTue2HHnoIL7/8Mo8ROYfZZsZfZX/ht6LfkFOfg9Km0kF/XhRiBWJ8YhChjmBrx5uK0GhsHHRsKokK8b7xWBK5BBfGXOiyk/R7grZFR34t/BWHKg/hbMvZPpcX7olQIES4Opyriy7UFg74pKYjL6kXYn1iMS1kGi6JuwTRPtGDeh530tLSgpiYGNTW1gIApk2bhvT0dJdNYNxR2+xDVfqqbssD265bzC18h9pvAgi6JL5ioRhCgRAigQhCgbDLRQBBl/sEAgGXMLddC8E+BwTs67S9nkAg4K7b9gFo388+AHVFdfjfjf9z3yQ3/rl4yMPda85BZxIKhAiUByJQGQiNQtPjtb/cf0QN/HIll1xyCbZs2QIAbjPZuqOZrWz3cUFjATeosbCxEMWNxQOeqaO/QlQhiPGO4VoC2y5BiiD6UeeJyWrCmaYzKGrq2go/lLEBvQlSBHEtwrG+7SUyjiiPcTcvvPACHn30UW5727ZtnRavIc6jN+tRa6jtcdxMtaEatfrafs/3O1K1lrUif13+gJJcz5zZ3YUIIGivr+mme+Hci1KshFqqhkrc9Ri1RE3Jq4v7z3/+g/T0dKxduxZ33XXXiEtwAUAikrDlB76xQFT7fhtjQ3lLOdfNV9ho73bWFvXry10ilCDKO6pLIhvjHUMj4F2QVCRFvF884v3iO+1nGIZrpW+rd2xLhHuaxaMjAQQIU4dxpS5xvnFcUustdc+p+xytsbGxUy/SnDlzsHTpUh4jGtmUEiUiJZGI9I7s9bhWS+fyxk6ljpZzyhzPKYHkSiHt5Y/OKnt0dS6V5E4NmYrAUYEDar5uO0YItnm8rUm9bV93TeudmtiFIu6xHZvWpSJp7zUs5zTn97btaYMZSM8mTpyI0tJSyGSyvg8eYYQCISK8IhDhFYF5EfO4/QzDoNZQyya9WnbgUIWuAkGKoE6JbJg6jE7yPIBAIECwKhjBqmDMCJ3R6T6dWYfixuL2gYRNxQDYFRLbZnaJ9on22Hm3HeX//u//0NDQwG0/88wzI64l2x3JxXJ2BT0HvL07jSHqZrxQr/efs89kNXFln13KQu2loTYbe80wbOlox/sZMFzpaNvjAXQqN+1PeWqttRb56H4lwp64VLmCKw88I4QQQlxdfX09YmJi0NTUBABYtGgR/vjjD56jImToBpMrUhMjIYQQ4iHWr1/PJbgA24pLyEhFSS4hw6ykpASffvop32EQQjxcTU0NXn/9dW77ggsuwKxZs3iMiBB+UZJLyDCpqqrCXXfdhdGjR+OWW25Bfv7AaokIIWQg/vvf/0Kn03Hb//nPf3iMhhD+UZJLyDDR6XT48MMPYTabYbVa8fTTT/MdEiHEg11//fW49NJLAbDTGU6dOpXniAjhFyW5hAyT2NhY3HTTTdz2l19+iVOnTvEYESHEk40bNw4//vgjjhw5gv/+9798h0MI7yjJJWQYPfbYY5BKpQDY6VCeeuopfgMihHi81NRUJCQk8B0GIbyjJJeQYRQZGYnbb7+d2/72229x7NgxHiMihBBCRgZKcgkZZo8++ijk8vblqh988EG4wPTUhBAPUFZWBr1+eJZJJsTdUZJLyDALDQ3FP//5T257165d+Omnn3iMiBDiCRiGwXXXXYfExER89913dPJMyDkoySXECdatW4eQkBBu+8EHH4TBYOAxIkKIu/vhhx+we/dulJaW4sorr8S7777Ld0iEuBRKcglxAm9vb7z00kvcdklJCV5++WUeIyKEuDO9Xo9//etf3HZISAiuu+46HiMixPVQkkuIk/zjH//AjBkzuO0XXngBJSUlPEZECHFX//3vf3HmzBlu+6WXXoKXlxePERHieijJJcRJhEIh3njjDW778ssvh0wm4zEiQog7Kikp6dQzNGPGDPzjH//gMSJCXJOY7wAIGUmmTp2K559/HvPmzcPs2bP5DocQ4oYeeughtLa2AgAEAgHeeOMNCIXUZkXIuSjJJcTJ/v3vf/MdAiHETe3atQvff/89t33zzTfT8r2E9IBO/QghhBA3YLFYOk1H6O3tjeeff57HiAhxbZTkEuICWlpaoNVq+Q6DEOLC3n33XWRnZ3PbTz31FDQaDY8REeLaKMklhEcMw+Crr75CQkICHnnkEb7DIYS4qJqaGjzxxBPcdlJSEu655x4eIyLE9VGSSwiPHnvsMVx77bUoLy/HBx98gKNHj/IdEiHEBVVUVCA4OJjbfv311yGRSHiMiBDXN6gkd9euXbj55puRmJgIlUqF8PBwrFixAkeOHHF0fIR4tJtvvhlSqRQA26r7z3/+k5bmJIR0MX78eBw/fhzr16/H9ddfj6VLl/IdEiEub1BJ7rvvvovi4mLcd999+O233/D666+juroaM2bMwK5duxwdIyEeKy4uDg899BC3/eeff2Ljxo08RkQIcVVSqRQPPvggPv30U75DIcQtCJhBNBtVV1d3KXZvaWlBfHw8UlJSsHPnzgE9X3Z2NlJSUpCVlYXk5OSBhkOIW2tpaUFiYiLKysoAAOHh4cjJyYFareY5MkIIIcQ1DCZXHFRLbnejOdVqNcaOHYvS0tLBPCUhI5ZarcbLL7/MbZeVleGFF17gMSJCiCuwWCxUvkTIEDhs4FljYyMyMjKoJZaQQbjqqqswZ84cbvuVV15BQUEBjxERQvj2xBNP4KKLLkJubi7foRDilhyW5N59993Q6XRYt25dr8dVV1cjOzu70yU/P99RYRDilgQCAd58801uaU6TyYR//etfPEdFCOFLfn4+1q9fj99//x0pKSn44IMP+A6JELfjkCT38ccfx5dffonXXnsNkydP7vXYd955BykpKZ0uK1eudEQYhLi1iRMn4vbbb+e2N2/ejG3btvEYESGELw8++CBMJhMAwGazYfr06TxHRIj7GXKS+/TTT+PZZ5/Fc88916+Jqe+66y5kZWV1umzatGmoYRDiEZ555hn4+flx2/fddx/3Q0cIGRl+//13bNmyhdu+4447MGHCBB4jIsQ9iYfy4KeffhpPPfUUnnrqKTz66KP9eoxGo6FlCAnpQWBgIJ555hnuhFEsFqO8vBzR0dH8BMQwAGMDbFb2mmm7btvHdN4n9wWkSn5iJaQnDAPo6wCrCRCIAIEQEIoAgaB9m9sntO8TsBcnM5lMuP/++7ltPz8/PPPMM06PgxBPMOgk95lnnsFTTz2Fxx57DE8++aQjYyJkRLvjjjvw7bff4oorrsCaNWsgFg/pXLQdwwCNZ4Hqk0BVFlB1EqjKBprLAZutcxLbltRigCO7BUIgMAEImwiETgBCJwIh4wAZTYdGnIRhgMZSoOIYUJ4JVGSyt3U1A3+utuS3U2IsBMRyIHA0EJwMaMYCwSmAJskh7/M333yz00CzZ599FgEBAUN+XkJGokH9eq5fvx5PPPEELrjgAixbtgzp6emd7p8xY4ZDgiNkJBKLxdizZw8EQ2lFam0Cqk+xyWy1PZmtOgkYGx0XaHcYG1Bzir0c+9q+U8AmBKET7cnvRDbxlXsPbyzE8zEMoC3pnMyWZwKGegc9v/3kD5bO+41NgK4aKPmr836/aECTzCa/wfbk1z+WTY77obKyEk8//TS3PX78+E51+oSQgRlUkttWK/T777/j999/73I/zetHyND0O8G1WoD6gs4ts9XZgPbM8AY4IAxQm8deTnzbvjsgnk14Qye0t/zKffgKkrg6hgHqC9lEtiLTntgeA1q1PAfWQUMxe8n9tX2fWA4EJdoT3w4tv+qgLg//97//jebmZm77jTfecFxPDiEj0KA+PXv27HFwGISQvjA2G6AtgaAoDThzgE1sa3IBq3HgT6YMsP/o2luaRNLuaxI7bXe8X9B1HwT2JCSTTT4qTwBmfc8x1OWzl6zv2/f5xbS39sYvZuPjoS6SuACzATi9Ayg9YE9sjw+8J8I7vP1EKnQCoPDtWl9+bqlOpxr0c7ft1watvackG6jNZWt9e2JptX8mMjvvVwWxn8GQ8UDMPByukWLDhg3c3atXr8b8+fMH9vcSQjoZ1LK+jkbL+hLSg+ZKoGgvGo5uhvHUdoTIBzjTgkgGaBLtXahj7S1JyYBaM/zJo83Ktt52qo08Dph1/X8OzVhg/JXAuFWAT8RwRUpchc0KFP8JHP8WOLkZMDX3/Zg2PpFA6Hj7SdIkNqntprXU4axm9mStKtvek2LvUWkc2OqfFhuQftaCP4qs+LNMhP9tP45R0XHDFDQh7mcwuSIluYS4EoOW/ZEvSgOK9gI1Of1/rG8k2/LZsUvUPxYQuVB3p80K1BV07m6uONaPZEYARM9hE96kS9gWOeI5qrKBYxuBE9+zAyH74hvV3uLfNsBR5WKDs9pae6uz22viq0+y9bz9IVYAUTOBmHlAzHz27+xnbS8hnmgwuaIL/foRMgKZ9EBpOlCYxia2FcfsA116ZmMEEIZPBMInt7fMapLcYyCXUAQEjWEv469k99lsHcocMtnk9+xhwGLo8EAGKN7HXn59CEi4ABi/GohfCoilzv87yNA1lrGlKse/ZUtveuITCURM7jBwcQKg8Ov5eFeh8GWT1KiZ7fvaZn6oapvhJAso2Q+0VHZ9vMUAFOxiLwBbrx49l014Y+cDgWOolIeQPlCSS4gzWc1A2RF7UrsXOHuw93o+u2KdHD9nNWJXkRV/lwuw79D7SEhIcELATiAUAoHx7GXcFew+YwuQ8ytw/BugcHfnxN9qZLuyT25mk53ky9iEd9Q0+tF3da2NwKkt7P/Xon3ocYo6ZSCQcjkwYTUQluo5/18FArbHxTeSPVED2MS3No870WWK9kLQXWtvayOQ8wt7AQB1CNvKGzufvfaNdN7fQYiboHIFQoaTzca21hSlsT9iJX/3rybVJxKInQfELABi5iKrpBYTJ06E1WoFAFxwwQX47bffhjbNmLtorgKyfmATo3MH73TkG8Umu+OvZKcsI67BYgIK/mD//+VuZQdidUesABKXsf8P4xYCIolz43QVNivbo1O0l/3eKNl/Tq9GD/xi2pPe6HnOqUcmxImoJpcQvjEMW3NaZC8/KNrXvzk7lYEdWmXms/NtnpPA3nfffXjjjTe47S1btmD58uUO/gNcXE0u2719/FugsZdp0sJS2WQp5TJ2kB1xLoYBzh5iE9usH3v+DAiE7Pt9/GogaTkg83JunO7AYmTLd9pOlMsOAzZL34/TJLd/n0TNco9yJkJ6QUkuIXxoKm8vPyhKA5rK+n6M1IsdSNWW2GrG9tkl29DQgDFjxqC2thYAEBcXhxMnTkChUDjir3AvNhs7tdTxb4Dsn3qeK1UgAuIWAZOuBRIuAsQyp4Y54mhLgcwv2YVAGop7Pi5kPJvYjrsC8ApxWniuZMuWLThw4AD+/e9/Q6VS9f+BxhbgzH6gcA/7nVN5An2uTCgQAeGpbMIbMw8YNR2QyIcSPiFOR0kuIc6gr2cHQLUltnWn+36MSAZETrePlF4AhE0a1KwHH374YacVkB544AG8+uqrA34ej2IxsvOpHv8GyPu95xpnhT8w4Wog9Tp2oB5xDIsRyP0NyPjcPkiqh58Un1HsVHDjrxzx//51dXVISUlBZWUlIiIi8Oabb2LlypWDezJ9ffsJdtFedjqzvojlbKIbMw+IXcAO6nOlWVgI6QYluYQMB2MLcCYdKNrDJrb9ajkRsl3mbd2Fo6YBkqG3uFqtVsyePRsHDhxgX0YgwO7du2nS+DaGBnZA2vFvuy652lH4FDbZTbmcusgHq/oUm9ge+7rncgSZD5C8km21jZzJDjIkWL16Nb79tn31v08++QQ33nijY568saw96S1M69+UbDJvIGp2+yC2fvQsEeJslOQSMlRtS4eWHQHKMtjr8oz+18C1lR9EzRq2JWpzcnIwadIktLayA3iio6Nx/PhxeHlRstaJ9gxw4jvg6Bfs/9PuSFRA8qVswjtqOv2w98XYzA4CzPicrQ3tjkAEjD4PmHgNe03d4p188803uOqqq7jt5cuX4+effx6eQaTcGIE9bMJbvI89EeyLKoj9PIRNYqcqDJtEc1MT3lGSS8hANVd2TWhb+7l0qF90+5yV0XOdOsDp9ddfx/333w8ACAoKwm+//YYpU6Y47fXdCsOwrboZn7OtvD2NVA8cA0y6ji1poJHp7RiGrX/O+Jytf+5pdhD/WPbfb+I1I7bOti8VFRVISUlBfT3b8h0QEICsrCyEhDjp38tmA6pOsC29A5ntBQAC4u0Jbyp7HTKOTmCIU1GSS0hvWhvZhQbKjtgT2qP9GyTWRh3cvvpQzDzAL2rYQu2LzWbD4sWL4efnh/feew8aDc0g0C8GLbsAQcbnPU9HJhQDYy4AUq8H4haP3FrFlhq2FOHo5+w8rt0RK4CxK9iW8KjZ1BLeC4ZhsHz5cvz222/cvm+//RarVq3iLyiLiT2xb1uMpvQgYDP377FCMbsYTcfENyiBVmUjw4aSXELamFvZ+Wk7ttD29EPdk4DR7Bd3+GQ2qQ1KcKkf8ZaWFqhUqpExV+5wqDzBJrvHv+l5dgavMLZlctI/AP8Yp4bHC5sVyP8DOPoZO6dtT2U6oRPtNc1XUDd2P3300Ue47bbbuO2rr74aX331FY8RdcOkZ2duKPmb/c4sy+j5s9EdiYpdlS48tT3x9Y10qe9N4r4oySUji83GtsTWF7A1l3UFQH0Ru11X0P8WCYBNZsJT7Rf7EqL04z0ymFvZVaQyPmNbs3oSM48dQOVpq0tZzWyvRt42IPOrngcqyX3Zvz/1OrarmvRbUVERxo8fj5aWFgBAaGgosrKy4O/vz3NkfeDGKGTYk94j7EIVPS3o0R2FP7s4i38s4B/HniwGxLHbwzRugXimweSKI7QfjriN3hLZ+iJ2ideBkvkA4ZPaW2nDUgHvUMfHzpOamhoEBVFNab9J5Ox8reOuYN9TmV8CR7/smuwV7WUvALu6WvRc+1zHcwGfCOfHPVhWM1u2U7yPvZw50HtdZsw8IPUGIHE51WAOgs1mw0033cQluADbquvyCS7AtsAGxLGX8fayCquZnVmjY9lX9cnOS293ZKhna7pLD3S9TxnIJrsBcZQAk2FBSS7hl83KjvbV1bCDwBqK7Ilsof0yyES2jUgGhI7vnND6x3rkVEbNzc3417/+hR9//BEnTpxAaKjnJO5O4x8DLHoMWPDv3rvttSVAZgmQ+QW77RfNJrzR89hrn3Cnh94jq4WtPy7ex67Adya978FGXmHsAhoTrx0ZZRrD6PXXX0daWnsPwW233YaLLrqIx4iGSCRhv1NDxwNTbmL3mXRAxfEOiW9G74uBtNHXspezB7ve1ykBjmUvvlGAKpCd/UGqojII0idKcoljMQxbw6WrYxPXtou+43at/VLDnuX31AIwEGJ5+xdh2xdj6ER2vkexdOjP7+Lq6uowdepUFBUVAWB/SLds2UL1uoMlFAFjzmMvLTXA8Y1s7W7lie6PbyhmL0fbkt4YtoW3rbXXO8xZkduT2mP2lto/2RpLU0vfj5Oq7avDXQfEL6YBRA5SXV3N3Y6JicH69et5jGaYSFVA1Ez20kZXxya71Sc798I1ne3fc/aWAAPsoEdVYHvSq+xwWxXU9T7qhRiRqCaXsCwmtnXHpGfPys069tqkZ38gzfpzbuvaL/o6NmnV25PXgdTCDkR3iWxbnZdXqEe2zg7E1VdfjY0bN3LbH330EW655RYeI/JA+np2OrIiewJZnd2/x/nH2Vt625JeB7ayWy1A5fH2pLZkP2Bq7vtxEntiEm1PxkMnjNyZJIbZnj17cMstt+CTTz7BvHnz+A6HX2YDe0LI9di1laIV9j8BHgypV+fEV+7DJucSJXuCJ1V2vi1VsZ8Rqcp+n6r9+BH+W8MX9x94lrYZyYmjB/4EXf4Epof7BrKfsd9m7HczHe5nzrk+9/hzr232C8N2z3PbbRcre1/bdrfH2NguU6uZTSKt5qHdNhvsyWoLm7wOV2I6UGKFPXGN6ZzE+sdSItuH+vp6pKSkoKKiAgCgVqtx4sQJREdH8xuYJ9PVASV/ssll8Z9sq1V/+EU7puaQYdiEwdjU97ESFRA5w15HPM+e1EqGHgPpF7PZDImE/r17xVcCPFCStoTYnviKpOxnSSRlp1YTSQChxL5vgLcFQvYiFLXfFgjZRVYEQrZEo9djOtwvEAAQdCjrEJyzz77/3H1cB+C5x3fYz908t7ewp/t6e0z/ZOecRsr8FW6c5K5RIVlDXWQeR+bNnj0rAzt0I51zrezQzUSJ7KD99ttvWLZsGbc9f/587Nq1C0L6N3WOlhq2pbct6a05xV8sEmV7Uhs9l121ipJa4q7MBqClqnO5W1v5m762azmcqzTcEIfJrrYi5V0dza5AhoFY0XMXjtK/a6La1i1EtVBOddFFF+HWW2/FRx99BABIS0vDG2+8wa2ORoaZOghIXsleAHvS26GltyZn+F5brOia1I6AenRX09rairq6OoSHu9DgQ08gUbA9IH7RfR/LMOziPz0lwLoadonqc0vz2m73Zxl34haoJddVdOpy6KF7oq0bZChdIW3dKRJF5+4WrjZJ1X2dEg1CcRvNzc0YP348iouLAQByuRxHjx5FYmIiv4ERoKWaTXarstiyJEeQ+wBRs9iZQyip5d3atWvx4Ycf4q233sI111xDgz/dkcXUdfzJuWNROm5bTY4rJWSs7eWNPZUwgve0jReDacl1rSQ37efB1eQCvdeFDOp+dFOnMtC6Fvu1sKfktUPdDH0REgdKS0vDwoUL0fbxnjp1Kv7++2+IxdR5Q8hw+fPPPzFv3jzuc7du3To8++yzPEdFPE7HBLjXsTz2cUFtj+nveKIux3fz+p139HJ/b/cNTHZO3oBrcl3rFy8gFtBQaxMhQzV//nzcf//9eO211wAAhw4dwosvvojHHnuM58gI8UwtLS244YYbuARXJpPh6quv5jkq4pEEAraxDCOsh7Vm4L1fNBqFEA/13HPPISkpidt++umncezYMR4jIsRzPfzwwygsLOS2n332WZoSkxCeUZJLiIdSKBT47LPPIBKxZ/v33HMPxowZw3NUhHiebdu24b333uO258yZgwceeIDHiAghgKuVKxBCHGrKlCl47bXXkJKSgoULF/IdDiEep6GhATfffDO3rVKpsGHDBu7kkhDCH0pyCfFw9957L98hEOKx7r33XpSXl3Pbr7zyCuLi4niMiBDShsoVCCGEkEH44Ycf8OWXX3Lb559/Pu644w4eIyKEdERJLiEjUFlZGd5//32+wyDEbVVVVeHOO+/ktn19ffHxxx/TvLiEuBBKcgkZQRiGwVdffYWUlBTceeed2LFjB98hEeKW7rvvPtTW1nLbb731Fq1yRoiLoSSXkBGkqqoKt99+O7RaLQDgpptu4m4TQvrvqaeewtSpUwEAl19+Oa655hqeIyKEnIuSXEJGkJCQELzyyivcdllZGf75z3/yGBEh7ikxMRF///03XnrpJbz77rtUpkCIC6Ikl5AR5o477sD555/PbX/++ef48ccfeYyIEPckFouxdu1aBAUF8R0KIaQblOQSMsIIBAJ8/PHH8PX15fbdfPPNyMvL4y8oQgghxMEoySVkBAoPD8dbb73FbTc2NuLiiy+m+lxCevD9999jzZo1MJlMfIdCCOknSnIJGaGuvfbaTlMg5eXl4aqrroLVauUxKkJcT2ZmJm644Qa89957WLp0KWpqavgOiRDSD5TkEjKCvf7665g/fz63vW3bNvy///f/eIyIENdSXV2NFStWQK/XAwD27t2LtLQ0nqMihPQHJbmEjGBSqRTfffcdoqOjuX3r16/Hp59+yl9QhLgIk8mEyy+/HGfOnOH2PfLII7jiiit4jIoQ0l+U5BIywgUFBWHz5s1QqVQAAG9vb2g0Gp6jIoRfDMPg7rvvxp9//sntW758OZ599lkeoyKEDAQluYQQjB8/Hp9//jnGjBmDAwcO4MILL+Q7JEJ49fbbb+Ojjz7itpOSkvDll19CJBLxGBUhZCDEfAdACHENl156KZYtWwapVMp3KITw6o8//sD999/Pbfv5+eHnn3+Gt7c3f0ERQgaMklxCCIcSXOcwmKywMYxDnksqFkIiok45RykoKMCqVau4WUZEIhG+/fZbxMfH8xwZIWSgBp3kNjc345lnnkFmZiaOHj2K2tpaPPnkk3jqqaccGB4hhG9btmxBQUFBp5Yt0juTxYYyrQGl9Xqcqde3XzfocaZOj6ZWi8NeSygAQn0UGOWvQKS/EqP8lIgMUGKUvxKR/koEqKS05Gw/NTU14ZJLLkFDQwO379VXX8WSJUt4jIoQMliDTnLr6urwwQcfYMKECVi5cmWn2iVCiPtjGAYvvvgi1q1bBwCIj4/H8uXLeY7KNTAMg9oWE0ob7AlsXXsSW1pvQEWjATbHNNT2ycYAZVoDyrQGpBfWd7lfIRGxya896W1LhiP9lYjwU0IhpRrTNi+++CJOnjzJbd9yyy249957eYyIEDIUg05yo6Ki0NDQAIFAgNraWkpyCfEwOTk5ePLJJ8HYu9WvueYapKenY+zYsTxH5lw1zUYcKalHxhktCmt0XKuswewei2YYzFbkVjUjt6q52/uDvGRc0psY4oUp0f4YF+4DqXjklUA8+eSTqKysxCeffILZs2fj7bffplZwQtzYoJNc+uAT4tmSkpLw3nvv4ZZbbgHAlihdcsklOHjwIPz9/XmObngwDIPCWh0OF9fjUHEDDhfXo7hOP6TnVEpFGOXX3pIa6a9AmK8CEgclkU0GM5d4s6URBpQ3GtDfkt+aZqM9kW/vopeJhZgwyhdTovwwNdofqVF+8FFIHBKvK5PJZPj4448xY8YMrFixAjKZjO+QCCFD4PSBZ9XV1V2WRMzPz3d2GISQfrj55ptx7NgxvPHGGwDYQTlXXnklfv/9d4jF7j9u1WSxIau8kUtqj5Q0oF5nGtBzCARAmIvVxJosNpRrDR0SX3s9cL0eJXV6NPdRE2y02HCwqB4Hi+oBFEAgABKCvTAl2g9TovwxJdoP4b4Kj2zsEAgEuP322/kOgxDiAE7/lXrnnXfw9NNPO/tlCSGDtH79epw8eRI7d+4EwE6v9K9//Quvv/46z5ENXKPBjIwzDThS3IBDxfXILNXCaLH167Gj/BVIDvVBVEDHVlklwnwVLte1LxULER2oQnSgqtv7G/Xm9oFw9kS4qEaHY2e10Ju6lmEwDJBT2YycymZ8kc6u/hXqI8eUaH9MjfbD5Cg/JIZ4QyR0r6S3rq4O3t7ekEg8v5WakJHI6UnuXXfdhVWrVnXal5+fj5UrVzo7FEJIP4jFYnzzzTeYNm0aCgoKAABvvPEGxo0bh1tvvZXn6HpX1dSK9MI6HLYntblVzf3qxhcKgLFh3lyr5ZQof4T4yIc/YCfxUUowTumDcRE+nfZbrDacqmjGoeJ6HClpwMHietQ0G7t9jorGVmw5Vo4tx8oBAF4yMSZF+WFqlB+mRPsjNcoXMrHrDmprbW3FsmXLoFAo8N133yEwMJDvkAghDub0JFej0dCSoYS4GX9/f/z888+YMWMGmpvZAUx33XUXEhMTMWfOHJ6ja2e22pBR0oDduTXYk1uNnMruB1udSyERYVKkL9cyOSnSD2qZ+5djDJRYJMS4CDb5vXlODBiGQWm9AYeK63G4hC3pyK9u6faxzUYL9ubVYG8eW46mlIowKy4A8xM0WDAmCKP8lc78U3rFMAzuvPNOHDhwAAAwdepUbN++HaNHj+Y5MkKII428b3FCyKCMHTsWX331FS655BIwDAOz2YzLLrsMhw8fRmRkJG9xVTW1Ii23Brtzq/Hn6Vo0G/uegzZQLcPUaD8uqU0K9aYFFbohEAgQGcDWGF8+OQIA0KAz4UhJAw6V1ONwcQOOn9XCbO3aPK43WbHzVDV2nqoGAMRr1FgwJggLEjSYGuPHayvva6+9hk8//ZTb9vLyQmhoKG/xEEKGByW5hJB+W758OV544QU88sgjAICamhpcf/312L17t9MGIVmsNmSc0WJ3bjX25NbgVEVTn4+JC1JharQ/pkT7Y0qUH6IClB45aMoZ/FRSLBkbjCVjgwEArWYrjp9tZFt77WUO3S12kV/dgvzqFnz0Z5G9lTcQCxKCsCAhCBF+zmvl3bZtGx5++GFuOyAgAJs3b4ZarXZaDIQQ5xhSkrt161bodDqu+/LkyZP4/vvvAQAXXXQRlErX6Z4ihDjG2rVrcfz4cXz11VeIj4/Hu+++O+wJY1tr7Z68auw7Xdvn7AA+CgnmjQnCgjFBmDcmCEFeNBXUcJFLRJgW449pMey0cjYbg6zyRuyxl4wcLdV2qYNmW3mrsPNUFQBgtEZtT3g1mBrtP2wD+fLy8rB69WrYbOxgQ7FYjO+//x4xMTHD8nqEEH4JGGbwC6hHR0ejpKSk2/uKiooQHR3dr+fJzs5GSkoKsrKykJycPNhwCCFOYjAY8Oijj+Lxxx8fljlzLVYbjpZqsTuHba092Y/W2nHhPlzL4IQIX4ip/MAlNOhM2Hu6Bmm5NUjLq0FdH1O0qaQizIoP5JLecF+FQ+LQarWYMWMGcnNzuX3vvvsu7rzzToc8PyFkeA0mVxxSS25xcfFQHk4IcVMKhQKvvfaaQ5+zutneWptbg32na7rt8u7IWy5mW2sTNJg3JhAaL8+Z/cCT+KmkWDExHCsmhsNmY3CizN7Km1eNzG5aeXUmK3acrMKOk2wr75hgNRYkaLAgIQhTogbXymu1WnH11Vd3SnDXrFlDCS4hHo5qcgkhDsMwDM6cOYOoqKg+j7XaGGSWNmB3DpvwZJX13VqbEu6NBWPYhGfiKGqtdTdCoQATRvliwihf3LdkNOp1Juw7zZ7YpOXVdLsQR15VC/KqWvDB3kKoZWLMjg/gkt5Qn75beRmGwYMPPojff/+d27dgwQK3nOeZEDIwlOQSQhyCYRisXbsWH374IbZt24bp06d3Oaa2xWivrWWnmmo0mHt9Tm+5GHPttbXzE4KotdbD+HfTyts2oPDY2a6tvC1GC7ZlV2FbNtvKmxjixSW8k6P8usyQwTAM7r//fm7FPoAts/vuu+9oAQhCRgBKcgkhQ8YwDB577DG88sorAIClS5fit99+w8xZs3HsrJYbhHT8bGOfz5Uc5s3VY06i1toRo2Mr7/1LxqBeZ8LePPZ9s/d0bbetvG2rsL2XVgAvmRhzRgdiYYIG8xOCEOwth0AgQHBwMHe8Wq3Gzz//TAs/EDJCUJJLCHGItllWhApv2Eal4or1vyJwWyNaem+shZdcjLmjA9kWuTFB0HhTay1hW3lXTgrHyknhsNoYHO94slTW2KWVt9lowdasSmzNqgQAjA1lT5aWXnMnWo0mvP5/r2Hbtm0YN24cD38NIYQPlOQSQoak1WxFZqkWMRffjUnyGagTeEEgYFtfe0pwE0O8sDCRTWpTu+lmJqQjkVCASZHsSnQPLB2D2hajvZW3BntP10Cr7/pGO1nRhJMVTXhnTwG85TNx2folKBaGIaRWR/MkEzJCUJJLCBmQVrMVR89okV5YhwNFdcg4o4XJws47CqEPuksd5CJgQWIIFiSwtbX9GTBESE8C1TJclhqBy1Ij7AMYtdiTW43dOdXIKu86gLGp1YLd+Y3YnX8CABDiLceMWH9Mjw3AjNgARFPSS4hHoiSXENKrVrMVGWcakF5YjwOFdTha2iGp7YWpphiGwiMwFBwGU1OA/37zNS6ZNtkJEZORRCQUYHKUH8aFqvD3+49CcCof/379MxyrsWJfXvdT0VU2tWJTZjk2ZZYDAIK9ZZgewya8M2L9EROooqSXEA9ASS4hpJNWsxUZJQ1IL6xDemE9Mku1MFn7Tmq95WJMjw3AQvto9w3vvIZ1//uEu//yyy/Hxo0bcfnllw9n+GQEMhqNWLVqFbZs2QIAePmuK5CWlgbN6onILGWXgN6bV4vs8kbYuln+qKrJiJ+PlePnY2zSq/GS2Vt5/TEjNgCxlPQS4pYoySVkhDOY2lpq65BeWIdjpY39Smp9FBJMi/HnWr8SQ7whErYnAo8++iikUikefvhhAIDFYsHq1avx+eef4+qrrx62v4eMLAaDAZdddlmneXBbW1uh0+kgFgkxJdofU6L98fD5QFOrGYeL65FeWI/0wjpklXWf9FY3G7HlWDm22JPeIC8ZpnPv9QDEBVHSS4g7oCSXkBHEYLIip7IJ2eXs5WR5I05WNMFs7Xt1bx+FpNMPfWKIF4TC3n/oH3roIUilUtx3330A2JWnXnnlFaxatQpiMX39kKHR6XRYsWIF/vjjD25fVFQUdu/ejZiYmC7He8slWJQYjEWJ7LRiTa1mHCluP8E70UPSW9NsxC/HK/DL8QoAQKBainHhPkgO80FymDfGhnkj0p/qeglxNfQrQ4iH0upN9kS2Cdnljcgub0JBTUu3P+Ld8VV2TmoTgvtOarvzz3/+E1KpFGvWrEFycjJ+//13SnDJkDU3N2P58uXYu3cvty82Nha7du3q14p7AJv0LkzUYGGihn3OVjMOdyjVySprhLWbD0xtiwm7c2uwO7eG2+clEyMpzBvJYd5c8huvUdPMIYTwiH5pCHFzDMOgorHV3jrbyCW2ZVrDgJ7HTymxD77xx4y4AIzRDC6p7c6dd94Jf39/zJ8/H0FBQQ55TjJyNTY24qKLLsLff//N7RszZgx27dqF8PDwQT+vl1yChQkaLExgk94Wo6VTecOJHpJegJ2n92BRPQ4W1XP7pGIhEoK9uNbe5DBvJIV6Qymln15CnIE+aYS4CYZhoNWbcaZej+I6XadW2oZu5gntjVQkxJgQNZJDfZAS7o1pMQEYrVE7LKntzpVXXtntfoZhqJuX9FtDQwMuuOACHDx4kNs3duxY7Ny5E6GhoQ59LbVMbF82uHPSe/SMliv3KW9s7fHxJosNJ8oacaKsfaU/gQCICVRxrb0JIV6I9Fciwk8BmVjk0PgJGekoySXEhbSarTjbYEBpvR6lDXqcqbNf1xtwtl6PZmPX6ZD60rEbdWwo25Uar1FDKua/G5VhGNx///0YNWoUHnroIb7DIS6urq4OS5cuxdGjR7l948aNw86dO6HRaIb99c9NegGgQWfCyYr2XpTs8iYU9lIWxDBAYY0OhTU6bmAbwCa/Id5yjPJTYpS/EqP8FYj0VyLSn90OUsuG9SSUEE9ESS4hTmSzMahqbkVpvQFn6vVsMtuW0NbrUdVkHNLzB3nJ7DWB7XWBo/yULvnjyDAMHn74YbzxxhsA2Gmg1q1bx3NUxJVt2bKlU4I7adIk7NixAwEBAbzF5KeSYnZ8IGbHB3L7DCYrTlV2GNxZ3oRTlc29zi/NMEBFYysqGltxsLi+y/0ysRARfgou6WVbf9uSYAW85JJh+fsIcWeU5BIyRHqTBXUtJjToTajTmVDfYkK9zoR6PXu7TmdCvc6Iep0J5Y2t/VpIoT+iA5RIDvPhav3GhnlD4yV3yHM7Q05ODt58801u+7HHHoPJZMJTTz1F5QukWzfeeCPKy8uxbt06TJ06Fdu2bYOfnx/fYXWhkIqQGumH1Mj22CxWGwpqdB1afNnkt7vFKrpjtLCPL6jRdXu/n1KCYG85/FVS+KukCFBJ4We/9lfJuP3+Kin8lBKIaUAcGQEoySUjntXGQG+yQG+yQm+yQmdsu81eNxnM9kSVvdTpTGjgbhvRanZM0noutUzMdlue03ozyl+BCD8l5BL3rt9LSkrCpk2bcOmll8JoZFuw//Of/8BkMuH555+nRJd069FHH0VwcDCuuOIK+Pj48B1Ov4lFQiSEeCEhxAuXpbL7GIZBvc7E9uq0lSnV6+3bepRrW3sc6HauBr2537X5AgE7JaC/Sgp/pT0pVrclwTL4qyRQScVQycRQSEVQScVQSkVQSkVQycSQiYX0+SRugZJcwgubjYGVYWC1MWAYcLctVhvMVgZmqw0mqw1mqw1mC9N+234xWZjO21YGZkv7ttFi65So6oxWGMwW6IzWLgmt0UEtqwMlFgoQ7qfoUoM3yt4F6auUePwPyYUXXohffvkFl1xyCQwGdjaIF198EUajEevXr/f4v58Mzi233MJ3CA4hEAgQoJYhQC3DpMiuLdIWqw0Vja1caVNbMnymXo+z9XrU6UyDel2GAbR6M7R6MwrRfctwb4QCQNkh8VVKxVDJRFBIxVDZt5VSEZQyERQSEaRiIaQiISTcRdD5dqf72fuk4vbttvtEIgFEAgFEQgGEAgGEAnZZZ/qeID1xqST33z+egO+BgX/gGKafE386WW9hMej+zp4e03F/22M77+t8o+PzM0znYxiGvZdh7Pvs2zaGTTjb9rf9u3L7OzwWjH2//X6bjW0RtTHsxWrrmsCy96HfLRPuSiIS2LsE21pHZGzXoVKKEB8Z1yIb4i2nLkMAS5YswdatW7Fs2TLodOzn/7XXXoNer8cbb7wBqVTKc4SED6dOncKaNWuwYcMGREdH8x0OL8Qiof0EWNnt/S1GC85yA1QNqGsxcr1N9fYepzqdCY2Ggc2+0hcbw752yyAGwg4HgQAQCeyJr9B+254Ii7hrdr+A28eeZAgAQAAIAAgFAggEgADsNfvcbce27xfYX1Rov90xyRZ0iInd7pCAC7o/puNxPeXrveXxnV6jn4/h02BPSrRlhQN+jEsluYeL6yHVefEdBiGdKKUirsbN/5w6ty771FJ4ycTUsjBA8+fPx7Zt23DhhReiubkZAPD+++/jyJEj+PrrrxEfH89zhMRZGIbBxx9/jH/+858wGAxYtGgR0tLSMGrUKL5DczlqmRiJId5IDPHu9Tiz1YYGfXvJFVd6dc74gbYEWas3weJGjREMA1gYBgADWPmOhgwXU03XAZl9cakkl5CBknbo7pKIhNy2VCzs0nWmknXoRrN3rynPqTVTSNhrlVQEhf04kQvOTOCJZs+ejZ07d+K8885DYyM7r+jhw4eRmpqKd999F9deey3PEZLh1tjYiDvuuAPffPMNt6+oqAgvvfQS3nrrLR4jc28SkRAaL3m/B6YyDFsipjdaoTdboTdaoGsr/zJaoTNZYDBZ2X1GS9djTNb248xWWKxMh1Kz9pI0d0qkiXtyqST3gpRgBI6K4DuMHpv+B/VcvXUx9Hhf310PPXWJCLp0h3R+ro7HC7iuFnu3jaCb/WC7ZGDv1ul4jLDD47qrkxIKBR26kNjuIqHg3C4k9vi2Y9larI71WvbEtcM+qUgIsUgAMdVieZxp06Zh//79uPLKK5GVlQWAXb517969lOR6uAMHDuDqq69GUVFRp/0PPvggXnjhBZ6iGpkEAgFkYhFkYhGGc+4Km42B2WZPei22DmMxmA4Jceek2GYvhbMyDBiGgdXGlsTZbO2lcjb7/t7K55hOZXhsiZ/NvtFxX9sxNvsNrmyv4350X2rYVvLXXipovz6n5PDc+7t5ph7/DftT4jhUPZVXOlttaSs+GeBjXCrJ/dd5iUhOTuY7DEIIj5KSknDw4EE8+OCDeO+995CcnIzXXnuN77DIMLHZbHj55Zfx2GOPwWJpr/EMCgrCp59+igsvvJDH6MhwEgoFkAlFkIkByPiOhri67Gyxeye5hBACAAqFAu+++y6WLFmChIQEKJXdD7wh7q2yshLXX389duzY0Wn/4sWL8fnnnzt8mV5CyMhCQ7sJIS7r8ssvR0pKSpf9VVVVuPnmm1FXV8dDVMQRtm/fjgkTJnRKcEUiEZ5//nls27aNElxCyJBRkksIcSs2mw033HADPvnkE0yYMAFpaWl8h0QGyGAw4Oabb0Z1dTW3LyoqCnv37sW///1viETuvdAJIcQ1UJJLCHErb7/9NrZt2wYAKCsrw6JFi/DUU091quckrk2hUOCzzz7jBo5eccUVyMzMxKxZs3iOjBDiSSjJJYS4lauuugoXXXQRt22z2fD0009j0aJFKC0t5TEyMhCLFi3C008/jffffx/ffvstfH19+Q6JEOJhKMklhLiVoKAg/PLLL3j11VchkUi4/fv27cPEiROxefNmHqMj59LpdPjss8+6ve/xxx/H7bffTlMBEkKGBSW5hBC3IxAI8MADD2D//v2dVkOrr6/HypUrce+996K1tZXHCAkAHD9+HFOmTMENN9yAjRs38h0OIWSEoSSXEOK2Jk+ejIyMDFx33XWd9r/11luYMWMGcnJyeIpsZGMYBm+//TamTZvG/T+4/fbbUVg48LXnCSFksCjJJYS4NS8vL3z22Wf49NNPoVKpuP3Hjh3DrFmz0NTUxGN0I099fT0uvfRS3HPPPTAajdz+lJQUmjWBEOJUlOQSQjzC9ddfj4yMDEyaNInb98QTT8Db25vHqEaOpqYmvPDCC0hISOhUFy0QCPDoo48iLS0NUVFRPEZICBlpaMUzQojHGDNmDPbv349HHnkE+fn5uO+++7oc09jYCG9vbxrs5CANDQ1444038Prrr6OhoaHTfaGhofjiiy+waNEinqIjhIxklOQSQjyKTCbDa6+9BovF0m0ie91116GsrAyPPfYYVqxYAaGQOrQG66OPPsKDDz6I5ubmLvctW7YMn3zyCYKCgniIjBBCqFyBEOKhxOKu5/CZmZnYsmULMjIycNlll2HChAn45ptvYLVaeYjQ/YWGhnZJcOfNm4cdO3Zgy5YtlOASQnhFSS4hZMR46623Om1nZWXhqquuQnJyMj777DNaNa0XNputy76LLroIqampAIClS5ciLS0NaWlpWLJkCZWDEEJ4R0kuIWTEePPNN/Hmm28iIiKi0/7c3FzccMMNSEhIwEcffQSTycRThK6nqKgId955Jy644IIu9wkEArz55ptIT0/H9u3bMW/ePB4iJISQ7lGSSwgZMRQKBe655x7k5+fjgw8+QExMTKf7CwsLcdtttyE+Ph5vv/32iF5Q4vTp07jpppswevRovP/++9ixYwf27t3b5bhZs2Zh+vTpPERICCG9oySXEDLiyGQy3HbbbcjNzcWGDRswZsyYTveXlpbinnvuwWOPPcZThPw5efIkrr32WiQmJmLDhg2d6pWfe+45HiMjhJCBoSSXEDJiSSQS3HDDDTh58iS+/vprJCcnc/eJxWLcc889PEbnXJmZmbjiiiuQkpKCr776qlMNrkgkwvXXX4833niDxwgJIWRgaAoxQsiIJxKJcNVVV+HKK6/Epk2b8Oyzz2LixImIjo7ucuztt98OjUaD+fPnY+bMmVCr1c4P2EEyMjLw9ttvIy0tDQUFBV3ul0gkuPHGG/HII48gNjaWhwgJIWTwBp3ktrS04LHHHsO3336L+vp6JCYm4pFHHsFVV13lyPgIIcRphEIhLrvsMlx66aXQ6/Vd7m9qasLHH38Mm82G5557DmKxGJMnT8a8efMwf/58zJ49G76+vs4PvA8Mw8BkMkEmk3XaX1NTg//9739djpfJZLj11luxdu1aREZGOitMQghxqEEnuZdddhkOHTqEF198EWPGjMFXX32Fq6++GjabDddcc40jYySEEKcSCARQqVRd9v/111+duvEtFgsOHDiAAwcO4OWXX4ZAIMDEiRMxb9487hIYGOjM0AGw031lZWVh79693OXee+/FunXrOh03a9YsCIVC7m9SKpW488478dBDDyE0NNTpcRNCiCMNKsn97bffsGPHDi6xBYCFCxeipKQEDz/8MFavXg2RSOTQQAkhhG/e3t647LLLsHfvXtTW1na5n2EYHD16FEePHsXrr78OAMjLy8Po0aOHNS6LxYLMzEzs3bsXaWlp2LdvX5cldvfu3dslyfXy8sLVV18NPz8/zJ8/H4sWLYK/v/+wxkoIIc4yqCT3p59+glqtxqpVqzrtv+mmm3DNNdfgwIEDmDVrlkMCJIQQVzF79mzMnj0bDMPg1KlTXCtpWloaysvLuxwfGBiI+Pj4Lvs//fRTZGRk9Pt1r732WkybNq3TvqysLHzwwQc4ffo0/vrrr26X1u3or7/+gsVi6bIS3BdffNHvOAghxJ0MKsnNyspCUlJSly/L8ePHc/dTkksI8VQCgQBjx47F2LFjceedd4JhGBQWFiItLY1LeouLizF37txuV/7673//i5MnT/b79VJTU7skucXFxXjzzTd7fZxEIsG0adO4mmFCCBlJBpXk1tXVdTvStq2bq66ursfHVldXo6amptO+ti/7/Pz8wYRDCCEuYfr06Zg+fToefvhhVFRUwGAwIDs7u9Mx9fX1A0pwAaCsrKzL85SUlHQ5TiqVYuLEiZg8eTKmTJmC8ePHQ6FQcPfn5uYO6HUJIcRVtOWIRqOx/w9iBmH06NHMBRdc0GV/eXk5A4B54YUXenzsk08+yQCgC13oQhe60IUudKELXQZ02bRpU7/z1UG15AYEBHTbWltfXw8AvQ5cuOuuu7rU8jY1NSEvLw/jxo3rMsXNSJGfn4+VK1di06ZN3dbwkZGD3gsEoPcBYdH7gAD0PgDYFtzS0tIBlV4NKskdN24cvv766y6DGE6cOAEASElJ6fGxGo0GGo2my/6ZM2cOJhSPEx8f32nVJTJy0XuBAPQ+ICx6HxCA3gepqakDOn5Qy/peeumlaGlpwQ8//NBp/6effoqwsDBMnz59ME9LCCGEEEKIQwyqJffCCy/E0qVLsWbNGjQ1NSE+Ph5ff/01fv/9d3zxxRc0Ry4hhBBCCOHVoFc8+/HHH7Fu3To88cQT3LK+X3/9NS3rSwghhBBCeDfoJFetVuP111/nVvUhQxMUFIQnn3wSQUFBfIdCeEbvBQLQ+4Cw6H1AAHofDJaAYRiG7yAIIYQQQghxpEENPCOEEEIIIcSVUZJLCCGEEEI8DiW5hBBCCCHE41CSSwghhBBCPA4luW7io48+gkAggFqt5jsU4kS7du3CzTffjMTERKhUKoSHh2PFihU4cuQI36GRYdLS0oL7778fYWFhkMvlmDhxIjZu3Mh3WMSJ6HNPekK5wMDQ7ApuoKysDMnJyVCpVGhsbERLSwvfIREnWbVqFerq6rBq1SqMHTsWNTU1WL9+PQ4fPoxt27Zh0aJFfIdIHOy8887DoUOH8OKLL2LMmDH46quv8NFHH+HLL7/ENddcw3d4xAnoc0+6Q7nAwFGS6wYuvvhiCAQC+Pv74/vvv6c39ghSXV0NjUbTaV9LSwvi4+ORkpKCnTt38hQZGQ6//fYbli1bhq+++gpXX301t/+8885DdnY2zpw5QytKjgD0uSfdoVxg4KhcwcV98cUXSEtLwzvvvMN3KIQH5/7QAexCLGPHjkVpaSkPEZHh9NNPP0GtVmPVqlWd9t90000oLy/HgQMHeIqMOBN97sm5KBcYHEpyXVh1dTXuv/9+vPjii4iIiOA7HOIiGhsbkZGRgeTkZL5DIQ6WlZWFpKQkiMWdF6McP348dz8ZmehzP3JRLjB4lOS6sLvuugsJCQlYs2YN36EQF3L33XdDp9Nh3bp1fIdCHKyurg7+/v5d9rftq6urc3ZIxEXQ537kolxg8CjJdYI9e/ZAIBD065KZmQkA+OGHH7BlyxZ8+OGHEAgE/P4BxCEG8z441+OPP44vv/wSr732GiZPnuzcP4A4RW+fd/ouGJnocz9yUS4wNOK+DyFDlZCQgA8//LBfx0ZGRqKlpQV333037r33XoSFhUGr1QIATCYTAECr1UIikUClUg1XyGQYDPR9cK6nn34azz77LJ577jncc889jg6PuICAgIBuW2vr6+sBoNtWXuLZ6HM/clEu4AAMcTlFRUUMgF4vK1as4DtM4kRPPfUUA4B56qmn+A6FDKPbbruNUavVjNls7rT/66+/ZgAwf/31F0+RET7Q535ko1xg6GgKMRfU2tqK9PT0LvtffPFFpKWlYevWrQgMDERKSgoP0RFne+aZZ/DEE0/gsccewzPPPMN3OGQYbd26FRdddBE2btyI1atXc/svvPBCHD9+nKYQG0Hoc08oFxg6SnLdyI033khz440w69evx0MPPYQLLrgATz75ZJf7Z8yYwUNUZDidd955OHz4MF566SXEx8fj66+/xocffogvvvgC1157Ld/hESegzz3pDeUC/Uc1uYS4sC1btgAAfv/9d/z+++9d7qdzVM/z448/Yt26dXjiiSdQX1+PxMREfP3117jqqqv4Do04CX3uCXEMasklhBBCCCEeh6YQI4QQQgghHoeSXEIIIYQQ4nEoySWEEEIIIR6HklxCCCGEEOJxKMklhBBCCCEeh5JcQgghhBDicSjJJYQQQgghHoeSXEIIIYQQ4nEoySWEEEIIIR6HklxCCCGEEOJxKMklhBBCCCEeh5JcQgghhBDicSjJJYQQF1FRUQG1Wo2rrrqq0/5ffvkFEokE69at4ykyQghxP5TkEkKIiwgNDcXatWvx7bff4siRIwCAPXv2YNWqVVizZg2ee+45niMkhBD3IWAYhuE7CEIIISy9Xo/Ro0cjKSkJL7zwAhYvXowrrrgCH3/8MQQCAd/hEUKI26AklxBCXMwnn3yCm2++GSqVCsuWLcNXX30FkUjEd1iEEOJWqFyBEEJczJgxYwAAAoEAGzZsoASXEEIGgZJcQghxIZmZmVi+fDlmz56NlpYW/O9//+M7JEIIcUtUrkAIIS4iNzcX8+bNw+TJk7F582asWrUKf/31F/Lz8+Hj48N3eIQQ4laoJZcQQlxAcXExlixZgoSEBPzwww+QSCR48cUX0dDQgOeff57v8AghxO1QSy4hhPCsoqICc+fOhY+PD3bv3g1vb2/uvttvvx2fffYZcnJyEB0dzV+QhBDiZijJJYQQQgghHofKFQghhBBCiMehJJcQQgghhHgcSnIJIYQQQojHoSSXEEIIIYR4HEpyCSGEEEKIx6EklxBCCCGEeBxKcgkhhBBCiMehJJcQQgghhHgcSnIJIYQQQojHoSSXEEIIIYR4HEpyCSGEEEKIx6EklxBCCCGEeBxKcgkhhBBCiMf5/zrVqenTOZRoAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "E, T = x.eigenstates()\n",
    "\n",
    "U = np.zeros((N, N)).astype(np.complex128)\n",
    "for i in range(N):\n",
    "    U[:,i] = T[i].full().flatten()\n",
    "\n",
    "U = Qobj(U)\n",
    "\n",
    "xlist = ( U.dag() * x * U ).diag()\n",
    "dx = xlist[1] - xlist[0]\n",
    "\n",
    "# Harmonic potential\n",
    "V = w**2 / 2 * xlist**2\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(xlist, V, color=\"black\", ls=\"--\", lw=2)\n",
    "for i in range(5):\n",
    "    factor = 5 # The purpose of this factor is to only make more visible the states\n",
    "    ax.plot(xlist, factor * np.abs( (U.dag() * fock(N, i)).full() )**2 + i * w + w/2, lw=2)\n",
    "\n",
    "ax.set_xlabel(r\"$x$\")\n",
    "ax.set_xlim(-5, 5)\n",
    "ax.set_ylim(0, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Closed Dynamics: The $\\text{Schr\\\"{o}dinger}$ equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 3 # Coherence of the initial state\n",
    "\n",
    "# We start from a coherent state the most classic-like state\n",
    "psi0 = coherent(N, alpha)\n",
    "\n",
    "# List of the times for the time evolution\n",
    "tlist = np.linspace(0, 2 * 2*np.pi/w, 100)\n",
    "\n",
    "e_ops = [H, a + a.dag()]\n",
    "\n",
    "sol = sesolve(H, psi0, tlist, e_ops)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the expectation values\n",
    "\n",
    "We can access to the expectation values with the command `sol.expect[i]`, where `i` is the index of the $i$-th operator for which we want to calculate te expectation value as a function of time. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.7468247855685135, 16.0)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(tlist, sol.expect[0], label=r\"$\\langle \\hat{H} \\rangle$\", lw=2)\n",
    "ax.plot(tlist, sol.expect[1], label=r\"$\\langle \\hat{a} + \\hat{a}^\\dagger \\rangle$\", lw=2)\n",
    "ax.legend()\n",
    "ax.set_xlabel(r\"$t$\")\n",
    "ax.set_xlim(tlist[0], tlist[-1])\n",
    "ax.set_ylim(None, 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Access directly to the evolution of the state\n",
    "\n",
    "We can also access directly to the wavefunction at each `tlist`. This can be done by simply calling `sol.states` to the solver without the `e_ops` operators.\n",
    "\n",
    "To check this feature, let's see if after $10$ cycles we get still the initial state, by calculating the fidelity\n",
    "$$\n",
    "\\langle \\psi \\left(t = 10 T\\right) \\vert \\psi \\left( t = 0 \\right) \\rangle\n",
    "$$\n",
    "where $T = \\frac{2 \\pi}{\\omega}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.999999999991156-6.853074431693678e-07j)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = sesolve(H, psi0, tlist)\n",
    "\n",
    "sol.states[0].dag() * sol.states[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then switch to the position eigenbasis. Thus, we need to diagonalize the position operator. This in general involves the _Laguerre_ functions, but here we limit ourselves to numerically diagonalize the position operator.\n",
    "\n",
    "We now show the wavefunctions in the position basis at three different times: $t_0$, $t_1$ and $t_2$, with\n",
    "$$\n",
    "t_0 = 0 \\, , \\quad t_1 = \\frac{\\pi}{\\omega} \\, , \\quad t_2 = \\frac{2 \\pi}{\\omega} \\, ,\n",
    "$$\n",
    "showing the exact periodicity of thi system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 120.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx_t0 = 0\n",
    "idx_t1 = np.where(tlist >= np.pi/w)[0][0]\n",
    "idx_t2 = np.where(tlist >= 2*np.pi/w)[0][0]\n",
    "\n",
    "psi0_x = U.dag() * sol.states[idx_t0]\n",
    "psi1_x = U.dag() * sol.states[idx_t1]\n",
    "psi2_x = U.dag() * sol.states[idx_t2]\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(xlist, 700 * np.abs(psi0_x.full())**2, label=r\"$\\vert \\langle \\psi (t_0) \\vert \\psi (t_0) \\rangle \\vert^2$\", lw=2)\n",
    "ax.plot(xlist, 700 * np.abs(psi1_x.full())**2, label=r\"$\\vert \\langle \\psi (t_1) \\vert \\psi (t_1) \\rangle \\vert^2$\", ls=\"--\", lw=2)\n",
    "ax.plot(xlist, 700 * np.abs(psi2_x.full())**2, label=r\"$\\vert \\langle \\psi (t_2) \\vert \\psi (t_2) \\rangle \\vert^2$\", ls=\"-.\", lw=2)\n",
    "ax.plot(xlist, V, color=\"black\", ls=\"--\")\n",
    "ax.legend()\n",
    "ax.set_xlabel(r\"$x$\")\n",
    "ax.set_xlim(xlist[0], xlist[-1])\n",
    "ax.set_ylim(0, 120)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also export an animation, showing more easily the time evolution of the state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "line, = ax.plot(xlist, 700 * np.abs(psi0_x.full())**2, lw=2)\n",
    "ax.plot(xlist, V, color=\"black\", ls=\"--\")\n",
    "ax.set_xlabel(r\"$x$\")\n",
    "ax.set_xlim(xlist[0], xlist[-1])\n",
    "ax.set_ylim(0, 120)\n",
    "\n",
    "plt.close(fig) # Otherwise the static figure also appears\n",
    "\n",
    "def update(frame):\n",
    "    psi_t = U.dag() * sol.states[frame]\n",
    "    line.set_ydata( 700 * np.abs(psi_t.full())**2 )\n",
    "    return line,\n",
    "\n",
    "fps = 25\n",
    "ani = FuncAnimation(fig, update, frames=len(tlist), blit=True, interval=1000 / fps)\n",
    "\n",
    "HTML(ani.to_html5_video())\n",
    "# HTML(ani.to_jshtml())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:red\">**Exercise!**</span>\n",
    "\n",
    "<ins>*What happens if we start from the following superposition state?*</ins>\n",
    "$$\n",
    "\\vert \\psi (0) \\rangle = \\frac{1}{\\sqrt{2}} \\left( \\vert 2 \\rangle + \\vert 5 \\rangle \\right)\n",
    "$$\n",
    "<ins>*Write a code that generates the animation of the wavefunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code here...\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution:\n",
    "psi0 = (fock(N, 2) + fock(N, 5)).unit()\n",
    "\n",
    "# List of the times for the time evolution\n",
    "tlist = np.linspace(0, 2 * 2*np.pi/w, 100)\n",
    "\n",
    "sol = sesolve(H, psi0, tlist)\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "line, = ax.plot(xlist, 700 * np.abs(psi0_x.full())**2, lw=2)\n",
    "ax.plot(xlist, V, color=\"black\", ls=\"--\")\n",
    "ax.set_xlabel(r\"$x$\")\n",
    "ax.set_xlim(xlist[0], xlist[-1])\n",
    "ax.set_ylim(0, 120)\n",
    "\n",
    "plt.close(fig) # Otherwise the static figure also appears\n",
    "\n",
    "def update(frame):\n",
    "    psi_t = U.dag() * sol.states[frame]\n",
    "    line.set_ydata( 700 * np.abs(psi_t.full())**2 )\n",
    "    return line,\n",
    "\n",
    "fps = 25\n",
    "ani = FuncAnimation(fig, update, frames=len(tlist), blit=True, interval=1000 / fps)\n",
    "\n",
    "# HTML(ani.to_jshtml())\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Open Dynamics: The Master Equation\n",
    "\n",
    "In contrast to the closed case, open quantum systems interact with their environment, leading to non-unitary evolution described by the Master equation:\n",
    "\n",
    "$$\n",
    "\\frac{d \\hat{\\rho}}{dt} = -\\frac{i}{\\hbar}[\\hat{H}, \\hat{\\rho}] + \\sum_k \\left( \\hat{L}_k \\hat{\\rho} \\hat{L}_k^\\dagger - \\frac{1}{2} \\{\\hat{L}_k^\\dagger \\hat{L}_k, \\hat{\\rho}\\} \\right)\n",
    "$$\n",
    "\n",
    "Here, $\\hat{\\rho}$ represents the density matrix of the system, $\\hat{L}_k$ are the Lindblad operators representing different dissipation processes. and $\\{\\hat{A}, \\hat{B} \\} = \\hat{A} \\hat{B} + \\hat{B} \\hat{A}$ is the anti-commutator between the operators $\\hat{A}$ and $\\hat{B}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5.074499442383836, 16.0)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gamma = 0.2 # Decay rate\n",
    "\n",
    "psi0 = coherent(N, alpha)\n",
    "\n",
    "c_ops = [np.sqrt(gamma) * a]\n",
    "\n",
    "tlist = np.linspace(0, 6 * 2*np.pi, 100)\n",
    "\n",
    "sol = mesolve(H, psi0, tlist, c_ops, e_ops)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(tlist, sol.expect[0], label=r\"$\\langle \\hat{H} \\rangle$\", lw=2)\n",
    "ax.plot(tlist, sol.expect[1], label=r\"$\\langle \\hat{a} + \\hat{a}^\\dagger \\rangle$\", lw=2)\n",
    "ax.legend()\n",
    "ax.set_xlabel(r\"$t$\")\n",
    "ax.set_xlim(tlist[0], tlist[-1])\n",
    "ax.set_ylim(None, 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Driven Dissipative Harmonic Oscillator\n",
    "\n",
    "The driven dissipative harmonic oscillator is a foundational concept in quantum optics, illustrating how quantum systems interact with external forces and their environment. This section begins with the time-dependent Hamiltonian, transitions to a time-independent form via a unitary transformation, and delves into the significance of this transition.\n",
    "\n",
    "### Initial Time-Dependent Hamiltonian\n",
    "\n",
    "The Hamiltonian for a driven harmonic oscillator, subject to a time-dependent external driving force, is expressed as:\n",
    "\n",
    "$$\n",
    "\\hat{H}(t) = \\hbar \\omega \\hat{a}^\\dagger \\hat{a} + \\left( F(t) \\hat{a}^\\dagger + F^*(t) \\hat{a} \\right)\n",
    "$$\n",
    "\n",
    "where $F(t) = Fe^{i\\omega_d t}$ represents the time-dependent drive with $F$ being the drive strength and $\\omega_d$ the drive frequency.\n",
    "\n",
    "This Hamiltonian encapsulates the energy dynamics of the system under natural oscillations and external driving forces.\n",
    "\n",
    "### Transition to a Time-independent Hamiltonian\n",
    "\n",
    "To simplify the analysis, a transition to a rotating frame matching the drive frequency is performed through a unitary transformation $\\hat{U}(t)$:\n",
    "\n",
    "$$\n",
    "\\hat{U}(t) = e^{-i\\omega_d \\hat{a}^\\dagger \\hat{a} t}\n",
    "$$\n",
    "\n",
    "The time-independent Hamiltonian in the rotating frame, $\\hat{H}'$, is derived using:\n",
    "\n",
    "$$\n",
    "\\hat{H}' = \\hat{U}^\\dagger(t) \\hat{H}(t) \\hat{U}(t) - i\\hbar \\hat{U}^\\dagger(t) \\frac{\\partial \\hat{U}(t)}{\\partial t}\n",
    "$$\n",
    "\n",
    "Upon substitution and simplification, the transformed Hamiltonian becomes:\n",
    "\n",
    "$$\n",
    "\\hat{H}' = \\hbar(\\omega - \\omega_d) \\hat{a}^\\dagger \\hat{a} + (F \\hat{a}^\\dagger + F^* \\hat{a})\n",
    "$$\n",
    "\n",
    "This Hamiltonian, now free of explicit time dependence, facilitates the application of quantum mechanical principles for the analysis of system dynamics. In particular, it includes a term for detuning between the natural frequency of the oscillator and the drive frequency, as well as the drive interaction in the rotating frame.\n",
    "\n",
    "Notice that the dissipator term (Linblad term) in the master equation is invariant under this transformation!\n",
    "You can now rewrite the master equation like:\n",
    "$$\n",
    "\\partial_t \\hat{\\rho} = -i[\\hat{H}', \\hat{\\rho}] + \\gamma\\left(  \\hat{a} \\hat{\\rho} \\hat{a}^{\\dagger} - \\frac{1}{2}\\lbrace{\\hat{a}^{\\dagger} \\hat{a}, \\hat{\\rho}\\rbrace} \\right)\n",
    "$$\n",
    "\n",
    "### Steady state\n",
    "In a driven-dissipative quantum system is fundamental the concept of steady-state. The steady-state is a density matrix (so a mixed state!) $\\hat{\\rho}_{ss}$ for which\n",
    "$$\n",
    "\\partial_t \\hat{\\rho}_{ss} = 0.\n",
    "$$\n",
    "\n",
    "In our simple example above this stae can be obtained by computing the kernel (in linear algebra meaning, i.e. the zeros) of the operator defined by \n",
    "$$\n",
    "\\mathcal{L}[\\hat{\\rho}] = -i[\\hat{H}', \\hat{\\rho}] + \\gamma\\left(  \\hat{a} \\hat{\\rho} \\hat{a}^{\\dagger} - \\frac{1}{2}\\lbrace{\\hat{a}^{\\dagger} \\hat{a}, \\hat{\\rho}\\rbrace} \\right) \n",
    "$$\n",
    "Notice that $\\mathcal{L}$ is an operator-valued operator, so it takes as an input an operator and gives as output an operator. Often people call these object \"super-operators\" (mathematically I think it can be also called a tensor).\n",
    "Anyway a useful way to deal with superoperators is to flatten them into a matrix. Under the same operatio the density matrix is flatten into a vector.\n",
    "Then one can diagonalize $\\mathcal{L}$ and find the steady state. Indeed there is mathematical proof that any \"standard\" Linblad dissipators have a single eigenvalue which is zero, always. (There are more pathological cases in which there exists multiple zeros eigenvalues, but this case are either trivial or either super complicated, so we skip them).\n",
    "Finding the zero eigenvalue corresponds to find the steady state.\n",
    "You do not have to bether, QuTip does it for you with the function \"mesolve\".\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims=[[30], [30]], shape=(30, 30), type='oper', dtype=Dense, isherm=True$$\\left(\\begin{array}{cc}0.527 & 0.422j & -0.239 & -0.110j & 0.044 & \\cdots & 0 & -7.936\\times10^{ -17 } & 0 & 1.846\\times10^{ -18 } & 0\\\\-0.422j & 0.337 & 0.191j & -0.088 & -0.035j & \\cdots & 4.046\\times10^{ -16 } & 0 & -9.774\\times10^{ -18 } & 0 & 2.147\\times10^{ -19 }\\\\-0.239 & -0.191j & 0.108 & 0.050j & -0.020 & \\cdots & 0 & 3.591\\times10^{ -17 } & 0 & -8.355\\times10^{ -19 } & 0\\\\0.110j & -0.088 & -0.050j & 0.023 & 0.009j & \\cdots & -1.057\\times10^{ -16 } & 0 & 2.554\\times10^{ -18 } & 0 & -5.609\\times10^{ -20 }\\\\0.044 & 0.035j & -0.020 & -0.009j & 0.004 & \\cdots & 0 & -6.635\\times10^{ -18 } & 0 & 1.544\\times10^{ -19 } & 0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0 & 4.046\\times10^{ -16 } & 0 & -1.057\\times10^{ -16 } & 0 & \\cdots & -1.206\\times10^{ -25 } & 0 & -3.723\\times10^{ -24 } & 0 & 1.791\\times10^{ -22 }\\\\-7.936\\times10^{ -17 } & 0 & 3.591\\times10^{ -17 } & 0 & -6.635\\times10^{ -18 } & \\cdots & 0 & -5.655\\times10^{ -26 } & 0 & -5.488\\times10^{ -24 } & 0\\\\0 & -9.774\\times10^{ -18 } & 0 & 2.554\\times10^{ -18 } & 0 & \\cdots & -3.723\\times10^{ -24 } & 0 & 4.185\\times10^{ -26 } & 0 & -1.038\\times10^{ -24 }\\\\1.846\\times10^{ -18 } & 0 & -8.355\\times10^{ -19 } & 0 & 1.544\\times10^{ -19 } & \\cdots & 0 & -5.488\\times10^{ -24 } & 0 & 6.285\\times10^{ -26 } & 0\\\\0 & 2.147\\times10^{ -19 } & 0 & -5.609\\times10^{ -20 } & 0 & \\cdots & 1.791\\times10^{ -22 } & 0 & -1.038\\times10^{ -24 } & 0 & 1.203\\times10^{ -26 }\\end{array}\\right)$$"
      ],
      "text/plain": [
       "Quantum object: dims=[[30], [30]], shape=(30, 30), type='oper', dtype=Dense, isherm=True\n",
       "Qobj data =\n",
       "[[ 5.27292424e-01+0.00000000e+00j  0.00000000e+00+4.21833939e-01j\n",
       "  -2.38625311e-01+0.00000000e+00j  0.00000000e+00-1.10216310e-01j\n",
       "   4.40865240e-02+0.00000000e+00j  0.00000000e+00+1.57728743e-02j\n",
       "  -5.15139919e-03+0.00000000e+00j  0.00000000e+00-1.55763670e-03j\n",
       "   4.40566190e-04+0.00000000e+00j  0.00000000e+00+1.17484317e-04j\n",
       "  -2.97214426e-05+0.00000000e+00j  0.00000000e+00-7.16908170e-06j\n",
       "   1.65562850e-06+0.00000000e+00j  0.00000000e+00+3.67350981e-07j\n",
       "  -7.85429436e-08+0.00000000e+00j  0.00000000e+00-1.62237607e-08j\n",
       "   3.24475213e-09+0.00000000e+00j  0.00000000e+00+6.29574389e-10j\n",
       "  -1.18713685e-10+0.00000000e+00j  0.00000000e+00-2.17878298e-11j\n",
       "   3.89752548e-12+0.00000000e+00j  0.00000000e+00+6.80407830e-13j\n",
       "  -1.16050749e-13+0.00000000e+00j  0.00000000e+00-1.93586032e-14j\n",
       "   3.16124667e-15+0.00000000e+00j  0.00000000e+00+5.05799463e-16j\n",
       "  -7.93563258e-17+0.00000000e+00j  0.00000000e+00-1.22175628e-17j\n",
       "   1.84621069e-18+0.00000000e+00j  0.00000000e+00+2.68344097e-19j]\n",
       " [ 0.00000000e+00-4.21833939e-01j  3.37467151e-01+0.00000000e+00j\n",
       "   0.00000000e+00+1.90900249e-01j -8.81730481e-02+0.00000000e+00j\n",
       "   0.00000000e+00-3.52692192e-02j  1.26182995e-02+0.00000000e+00j\n",
       "   0.00000000e+00+4.12111935e-03j -1.24610936e-03+0.00000000e+00j\n",
       "   0.00000000e+00-3.52452952e-04j  9.39874540e-05+0.00000000e+00j\n",
       "   0.00000000e+00+2.37771541e-05j -5.73526536e-06+0.00000000e+00j\n",
       "   0.00000000e+00-1.32450280e-06j  2.93880785e-07+0.00000000e+00j\n",
       "   0.00000000e+00+6.28343549e-08j -1.29790085e-08+0.00000000e+00j\n",
       "   0.00000000e+00-2.59580171e-09j  5.03659511e-10+0.00000000e+00j\n",
       "   0.00000000e+00+9.49709483e-11j -1.74302638e-11+0.00000000e+00j\n",
       "   0.00000000e+00-3.11802038e-12j  5.44326264e-13+0.00000000e+00j\n",
       "   0.00000000e+00+9.28405995e-14j -1.54868826e-14+0.00000000e+00j\n",
       "   0.00000000e+00-2.52899733e-15j  4.04639570e-16+0.00000000e+00j\n",
       "   0.00000000e+00+6.34850606e-17j -9.77405020e-18+0.00000000e+00j\n",
       "   0.00000000e+00-1.47696855e-18j  2.14675278e-19+0.00000000e+00j]\n",
       " [-2.38625311e-01+0.00000000e+00j  0.00000000e+00-1.90900249e-01j\n",
       "   1.07989488e-01+0.00000000e+00j  0.00000000e+00+4.98782082e-02j\n",
       "  -1.99512833e-02+0.00000000e+00j  0.00000000e+00-7.13798810e-03j\n",
       "   2.33125715e-03+0.00000000e+00j  0.00000000e+00+7.04905905e-04j\n",
       "  -1.99377498e-04+0.00000000e+00j  0.00000000e+00-5.31673328e-05j\n",
       "   1.34503895e-05+0.00000000e+00j  0.00000000e+00+3.24435602e-06j\n",
       "  -7.49251929e-07+0.00000000e+00j  0.00000000e+00-1.66244077e-07j\n",
       "   3.55444787e-08+0.00000000e+00j  0.00000000e+00+7.34203596e-09j\n",
       "  -1.46840719e-09+0.00000000e+00j  0.00000000e+00-2.84912845e-10j\n",
       "   5.37236812e-11+0.00000000e+00j  0.00000000e+00+9.86004620e-12j\n",
       "  -1.76381869e-12+0.00000000e+00j  0.00000000e+00-3.07917434e-13j\n",
       "   5.25185740e-14+0.00000000e+00j  0.00000000e+00+8.76070374e-15j\n",
       "  -1.43061693e-15+0.00000000e+00j  0.00000000e+00-2.28898707e-16j\n",
       "   3.59125735e-17+0.00000000e+00j  0.00000000e+00+5.52903774e-18j\n",
       "  -8.35499581e-19+0.00000000e+00j  0.00000000e+00-1.21438676e-19j]\n",
       " [ 0.00000000e+00+1.10216310e-01j -8.81730481e-02+0.00000000e+00j\n",
       "   0.00000000e+00-4.98782082e-02j  2.30377575e-02+0.00000000e+00j\n",
       "   0.00000000e+00+9.21510301e-03j -3.29689548e-03+0.00000000e+00j\n",
       "   0.00000000e+00-1.07676156e-03j  3.25582091e-04+0.00000000e+00j\n",
       "   0.00000000e+00+9.20885218e-05j -2.45569391e-05+0.00000000e+00j\n",
       "   0.00000000e+00-6.21246880e-06j  1.49850386e-06+0.00000000e+00j\n",
       "   0.00000000e+00+3.46064642e-07j -7.67848500e-08+0.00000000e+00j\n",
       "   0.00000000e+00-1.64172915e-08j  3.39114115e-09+0.00000000e+00j\n",
       "   0.00000000e+00+6.78228230e-10j -1.31595606e-10+0.00000000e+00j\n",
       "   0.00000000e+00-2.48139055e-11j  4.55416026e-12+0.00000000e+00j\n",
       "   0.00000000e+00+8.14672954e-13j -1.42220971e-13+0.00000000e+00j\n",
       "   0.00000000e+00-2.42572903e-14j  4.04639573e-15+0.00000000e+00j\n",
       "   0.00000000e+00+6.60773656e-16j -1.05723784e-16+0.00000000e+00j\n",
       "   0.00000000e+00-1.65873072e-17j  2.55375314e-18+0.00000000e+00j\n",
       "   0.00000000e+00+3.85900726e-19j -5.60901217e-20+0.00000000e+00j]\n",
       " [ 4.40865240e-02+0.00000000e+00j  0.00000000e+00+3.52692192e-02j\n",
       "  -1.99512833e-02+0.00000000e+00j  0.00000000e+00-9.21510301e-03j\n",
       "   3.68604121e-03+0.00000000e+00j  0.00000000e+00+1.31875819e-03j\n",
       "  -4.30704622e-04+0.00000000e+00j  0.00000000e+00-1.30232836e-04j\n",
       "   3.68354087e-05+0.00000000e+00j  0.00000000e+00+9.82277565e-06j\n",
       "  -2.48498752e-06+0.00000000e+00j  0.00000000e+00-5.99401543e-07j\n",
       "   1.38425857e-07+0.00000000e+00j  0.00000000e+00+3.07139400e-08j\n",
       "  -6.56691660e-09+0.00000000e+00j  0.00000000e+00-1.35645646e-09j\n",
       "   2.71291292e-10+0.00000000e+00j  0.00000000e+00+5.26382424e-11j\n",
       "  -9.92556218e-12+0.00000000e+00j  0.00000000e+00-1.82166411e-12j\n",
       "   3.25869182e-13+0.00000000e+00j  0.00000000e+00+5.68883883e-14j\n",
       "  -9.70291610e-15+0.00000000e+00j  0.00000000e+00-1.61855829e-15j\n",
       "   2.64309462e-16+0.00000000e+00j  0.00000000e+00+4.22895137e-17j\n",
       "  -6.63492287e-18+0.00000000e+00j  0.00000000e+00-1.02150126e-18j\n",
       "   1.54360291e-19+0.00000000e+00j  0.00000000e+00+2.24360487e-20j]\n",
       " [ 0.00000000e+00-1.57728743e-02j  1.26182995e-02+0.00000000e+00j\n",
       "   0.00000000e+00+7.13798810e-03j -3.29689548e-03+0.00000000e+00j\n",
       "   0.00000000e+00-1.31875819e-03j  4.71813274e-04+0.00000000e+00j\n",
       "   0.00000000e+00+1.54093570e-04j -4.65935160e-05+0.00000000e+00j\n",
       "   0.00000000e+00-1.31786365e-05j  3.51430305e-06+0.00000000e+00j\n",
       "   0.00000000e+00+8.89056163e-07j -2.14448415e-07+0.00000000e+00j\n",
       "   0.00000000e+00-4.95247401e-08j  1.09885532e-08+0.00000000e+00j\n",
       "   0.00000000e+00+2.34945151e-09j -4.85300616e-10+0.00000000e+00j\n",
       "   0.00000000e+00-9.70601233e-11j  1.88324301e-11+0.00000000e+00j\n",
       "   0.00000000e+00+3.55107708e-12j -6.51738363e-13+0.00000000e+00j\n",
       "   0.00000000e+00-1.16586503e-13j  2.03530085e-14+0.00000000e+00j\n",
       "   0.00000000e+00+3.47142080e-15j -5.79073019e-16+0.00000000e+00j\n",
       "   0.00000000e+00-9.45622280e-17j  1.51299564e-17+0.00000000e+00j\n",
       "   0.00000000e+00+2.37378217e-18j -3.65463400e-19+0.00000000e+00j\n",
       "   0.00000000e+00-5.52256164e-20j  8.02696481e-21+0.00000000e+00j]\n",
       " [-5.15139919e-03+0.00000000e+00j  0.00000000e+00-4.12111935e-03j\n",
       "   2.33125715e-03+0.00000000e+00j  0.00000000e+00+1.07676156e-03j\n",
       "  -4.30704622e-04+0.00000000e+00j  0.00000000e+00-1.54093570e-04j\n",
       "   5.03267493e-05+0.00000000e+00j  0.00000000e+00+1.52173786e-05j\n",
       "  -4.30412464e-06+0.00000000e+00j  0.00000000e+00-1.14776657e-06j\n",
       "   2.90364527e-07+0.00000000e+00j  0.00000000e+00+7.00385592e-08j\n",
       "  -1.61747124e-08+0.00000000e+00j  0.00000000e+00-3.58884646e-09j\n",
       "   7.67327649e-10+0.00000000e+00j  0.00000000e+00+1.58498518e-10j\n",
       "  -3.16997035e-11+0.00000000e+00j  0.00000000e+00-6.15064592e-12j\n",
       "   1.15977692e-12+0.00000000e+00j  0.00000000e+00+2.12856858e-13j\n",
       "  -3.80769923e-14+0.00000000e+00j  0.00000000e+00-6.64726475e-15j\n",
       "   1.13376128e-15+0.00000000e+00j  0.00000000e+00+1.89124456e-16j\n",
       "  -3.08838943e-17+0.00000000e+00j  0.00000000e+00-4.94142306e-18j\n",
       "   7.75274011e-19+0.00000000e+00j  0.00000000e+00+1.19359847e-19j\n",
       "  -1.80366108e-20+0.00000000e+00j  0.00000000e+00-2.62159573e-21j]\n",
       " [ 0.00000000e+00+1.55763670e-03j -1.24610936e-03+0.00000000e+00j\n",
       "   0.00000000e+00-7.04905905e-04j  3.25582091e-04+0.00000000e+00j\n",
       "   0.00000000e+00+1.30232836e-04j -4.65935160e-05+0.00000000e+00j\n",
       "   0.00000000e+00-1.52173786e-05j  4.60130279e-06+0.00000000e+00j\n",
       "   0.00000000e+00+1.30144496e-06j -3.47051990e-07+0.00000000e+00j\n",
       "   0.00000000e+00-8.77979803e-08j  2.11776697e-08+0.00000000e+00j\n",
       "   0.00000000e+00+4.89077331e-09j -1.08516516e-09+0.00000000e+00j\n",
       "   0.00000000e+00-2.32018072e-10j  4.79254468e-11+0.00000000e+00j\n",
       "   0.00000000e+00+9.58508937e-12j -1.85978051e-12+0.00000000e+00j\n",
       "   0.00000000e+00-3.50683577e-13j  6.43618641e-14+0.00000000e+00j\n",
       "   0.00000000e+00+1.15134003e-14j -2.00994393e-15+0.00000000e+00j\n",
       "   0.00000000e+00-3.42817189e-16j  5.71858602e-17+0.00000000e+00j\n",
       "   0.00000000e+00+9.33841187e-18j -1.49414589e-18+0.00000000e+00j\n",
       "   0.00000000e+00-2.34420826e-19j  3.60910252e-20+0.00000000e+00j\n",
       "   0.00000000e+00+5.45375847e-21j -7.92696038e-22+0.00000000e+00j]\n",
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       "  -4.30412464e-06+0.00000000e+00j  0.00000000e+00-1.30144496e-06j\n",
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       "   1.38331958e-09+0.00000000e+00j  0.00000000e+00+3.06931053e-10j\n",
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       "  -9.91882923e-14+0.00000000e+00j  0.00000000e+00-1.82042840e-14j\n",
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       "   1.54255584e-21+0.00000000e+00j  0.00000000e+00+2.24208297e-22j]\n",
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       "   0.00000000e+00-4.11348221e-22j  5.97888789e-23+0.00000000e+00j]\n",
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       "  -2.48498752e-06+0.00000000e+00j  0.00000000e+00-8.89056163e-07j\n",
       "   2.90364527e-07+0.00000000e+00j  0.00000000e+00+8.77979803e-08j\n",
       "  -2.48330189e-08+0.00000000e+00j  0.00000000e+00-6.62213837e-09j\n",
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       "  -9.33213998e-11+0.00000000e+00j  0.00000000e+00-2.07061591e-11j\n",
       "   4.42716310e-12+0.00000000e+00j  0.00000000e+00+9.14463901e-13j\n",
       "  -1.82892431e-13+0.00000000e+00j  0.00000000e+00-3.54864620e-14j\n",
       "   6.69140212e-15+0.00000000e+00j  0.00000000e+00+1.22809215e-15j\n",
       "  -2.19688028e-16+0.00000000e+00j  0.00000000e+00-3.83519176e-17j\n",
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       "  -1.78187284e-19+0.00000000e+00j  0.00000000e+00-2.85099697e-20j\n",
       "   4.47301110e-21+0.00000000e+00j  0.00000000e+00+6.88657062e-22j\n",
       "  -1.04063797e-22+0.00000000e+00j  0.00000000e+00-1.51255237e-23j]\n",
       " [ 0.00000000e+00+7.16908170e-06j -5.73526536e-06+0.00000000e+00j\n",
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       "   0.00000000e+00+5.99401543e-07j -2.14448415e-07+0.00000000e+00j\n",
       "   0.00000000e+00-7.00385592e-08j  2.11776697e-08+0.00000000e+00j\n",
       "   0.00000000e+00+5.98994953e-09j -1.59731988e-09+0.00000000e+00j\n",
       "   0.00000000e+00-4.04093511e-10j  9.74709956e-11+0.00000000e+00j\n",
       "   0.00000000e+00+2.25099626e-11j -4.99452096e-12+0.00000000e+00j\n",
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       "   9.92835744e-21+0.00000000e+00j  0.00000000e+00+2.21915047e-21j\n",
       "  -5.77911142e-22+0.00000000e+00j  0.00000000e+00-8.76269214e-22j\n",
       "   4.13449100e-21+0.00000000e+00j  0.00000000e+00+1.01711977e-19j\n",
       "   2.64174879e-19+0.00000000e+00j  0.00000000e+00+2.39130353e-20j\n",
       "  -2.02052868e-21+0.00000000e+00j  0.00000000e+00-1.66150205e-22j\n",
       "   1.35568772e-23+0.00000000e+00j  0.00000000e+00+1.11520715e-24j\n",
       "  -1.82112566e-25+0.00000000e+00j  0.00000000e+00-7.53784349e-25j\n",
       "   4.26237455e-24+0.00000000e+00j  0.00000000e+00-5.22203421e-23j\n",
       "   9.73971504e-22+0.00000000e+00j  0.00000000e+00+2.35379980e-21j]\n",
       " [ 0.00000000e+00-5.05799463e-16j  4.04639570e-16+0.00000000e+00j\n",
       "   0.00000000e+00+2.28898707e-16j -1.05723784e-16+0.00000000e+00j\n",
       "   0.00000000e+00-4.22895137e-17j  1.51299564e-17+0.00000000e+00j\n",
       "   0.00000000e+00+4.94142306e-18j -1.49414589e-18+0.00000000e+00j\n",
       "   0.00000000e+00-4.22608274e-19j  1.12695538e-19+0.00000000e+00j\n",
       "   0.00000000e+00+2.85099697e-20j -6.87691720e-21+0.00000000e+00j\n",
       "   0.00000000e+00-1.58853575e-21j  3.54971572e-22+0.00000000e+00j\n",
       "   0.00000000e+00+9.12972911e-23j -1.07747690e-22+0.00000000e+00j\n",
       "   0.00000000e+00-6.99204937e-22j  8.80340059e-21+0.00000000e+00j\n",
       "   0.00000000e+00+7.52357920e-20j  1.25083509e-19+0.00000000e+00j\n",
       "   0.00000000e+00+1.35814838e-20j -1.25957188e-21+0.00000000e+00j\n",
       "   0.00000000e+00-1.09025780e-22j  9.10840363e-24+0.00000000e+00j\n",
       "   0.00000000e+00+7.53784349e-25j -1.20605496e-25+0.00000000e+00j\n",
       "   0.00000000e+00-3.60442700e-25j -3.72324609e-24+0.00000000e+00j\n",
       "   0.00000000e+00-7.29521083e-23j  1.79145433e-22+0.00000000e+00j]\n",
       " [-7.93563258e-17+0.00000000e+00j  0.00000000e+00-6.34850606e-17j\n",
       "   3.59125735e-17+0.00000000e+00j  0.00000000e+00+1.65873072e-17j\n",
       "  -6.63492287e-18+0.00000000e+00j  0.00000000e+00-2.37378217e-18j\n",
       "   7.75274011e-19+0.00000000e+00j  0.00000000e+00+2.34420826e-19j\n",
       "  -6.63042221e-20+0.00000000e+00j  0.00000000e+00-1.76811257e-20j\n",
       "   4.47301110e-21+0.00000000e+00j  0.00000000e+00+1.07893931e-21j\n",
       "  -2.49224960e-22+0.00000000e+00j  0.00000000e+00-5.56182410e-23j\n",
       "   1.39013451e-23+0.00000000e+00j  0.00000000e+00+1.46076203e-23j\n",
       "  -6.91064200e-23+0.00000000e+00j  0.00000000e+00-9.77569087e-22j\n",
       "   5.08325091e-21+0.00000000e+00j  0.00000000e+00+8.13682807e-20j\n",
       "   3.30206031e-21+0.00000000e+00j  0.00000000e+00+3.71597615e-21j\n",
       "  -4.81937403e-22+0.00000000e+00j  0.00000000e+00-4.79373578e-23j\n",
       "   4.26237455e-24+0.00000000e+00j  0.00000000e+00+3.60442700e-25j\n",
       "  -5.65509034e-26+0.00000000e+00j  0.00000000e+00+2.71849457e-25j\n",
       "  -5.48813046e-24+0.00000000e+00j  0.00000000e+00-1.36381921e-23j]\n",
       " [ 0.00000000e+00+1.22175628e-17j -9.77405020e-18+0.00000000e+00j\n",
       "   0.00000000e+00-5.52903774e-18j  2.55375314e-18+0.00000000e+00j\n",
       "   0.00000000e+00+1.02150126e-18j -3.65463400e-19-0.00000000e+00j\n",
       "   0.00000000e+00-1.19359847e-19j  3.60910252e-20+0.00000000e+00j\n",
       "   0.00000000e+00+1.02080834e-20j -2.72215557e-21+0.00000000e+00j\n",
       "   0.00000000e+00-6.88657062e-22j  1.66111455e-22+0.00000000e+00j\n",
       "   0.00000000e+00+3.83686603e-23j -8.55210824e-24+0.00000000e+00j\n",
       "   0.00000000e+00-2.04176318e-24j  1.76143651e-24+0.00000000e+00j\n",
       "   0.00000000e+00+8.29405343e-24j -7.61400376e-23+0.00000000e+00j\n",
       "   0.00000000e+00-5.32223976e-22j  4.40175982e-21+0.00000000e+00j\n",
       "   0.00000000e+00+1.12389453e-19j -1.69619584e-19+0.00000000e+00j\n",
       "   0.00000000e+00-1.11988581e-20j  7.54903212e-22+0.00000000e+00j\n",
       "   0.00000000e+00+5.22203421e-23j -3.72324609e-24+0.00000000e+00j\n",
       "   0.00000000e+00-2.71849457e-25j  4.18539618e-26+0.00000000e+00j\n",
       "   0.00000000e+00+4.15732801e-25j -1.03823683e-24+0.00000000e+00j]\n",
       " [ 1.84621069e-18+0.00000000e+00j  0.00000000e+00+1.47696855e-18j\n",
       "  -8.35499581e-19+0.00000000e+00j  0.00000000e+00-3.85900726e-19j\n",
       "   1.54360291e-19+0.00000000e+00j  0.00000000e+00+5.52256164e-20j\n",
       "  -1.80366108e-20+0.00000000e+00j  0.00000000e+00-5.45375847e-21j\n",
       "   1.54255584e-21+0.00000000e+00j  0.00000000e+00+4.11348221e-22j\n",
       "  -1.04063797e-22+0.00000000e+00j  0.00000000e+00-2.51012557e-23j\n",
       "   5.79761798e-24+0.00000000e+00j  0.00000000e+00+1.29038675e-24j\n",
       "  -2.97632260e-25-0.00000000e+00j  0.00000000e+00-1.71850774e-25j\n",
       "   8.07896091e-25+0.00000000e+00j  0.00000000e+00+7.29472978e-24j\n",
       "  -2.44195173e-23+0.00000000e+00j  0.00000000e+00-3.90498803e-22j\n",
       "   5.62309065e-21+0.00000000e+00j  0.00000000e+00+7.12066758e-20j\n",
       "  -1.76228886e-19+0.00000000e+00j  0.00000000e+00-1.30666169e-20j\n",
       "   9.73971504e-22+0.00000000e+00j  0.00000000e+00+7.29521083e-23j\n",
       "  -5.48813046e-24+0.00000000e+00j  0.00000000e+00-4.15732801e-25j\n",
       "   6.28528916e-26+0.00000000e+00j  0.00000000e+00+8.09480370e-26j]\n",
       " [ 0.00000000e+00-2.68344097e-19j  2.14675278e-19+0.00000000e+00j\n",
       "   0.00000000e+00+1.21438676e-19j -5.60901217e-20+0.00000000e+00j\n",
       "   0.00000000e+00-2.24360487e-20j  8.02696481e-21+0.00000000e+00j\n",
       "   0.00000000e+00+2.62159573e-21j -7.92696038e-22-0.00000000e+00j\n",
       "   0.00000000e+00-2.24208297e-22j  5.97888789e-23+0.00000000e+00j\n",
       "   0.00000000e+00+1.51255237e-23j -3.64842305e-24+0.00000000e+00j\n",
       "   0.00000000e+00-8.42623447e-25j  1.87262568e-25+0.00000000e+00j\n",
       "   0.00000000e+00+4.16346311e-26j -1.69403569e-26-0.00000000e+00j\n",
       "   0.00000000e+00-3.87438358e-26j  5.43055276e-25+0.00000000e+00j\n",
       "   0.00000000e+00+1.93685708e-24j -4.59215960e-24+0.00000000e+00j\n",
       "   0.00000000e+00-4.10500355e-22j  1.12571188e-21+0.00000000e+00j\n",
       "   0.00000000e+00+6.71547806e-20j -3.09431724e-20+0.00000000e+00j\n",
       "   0.00000000e+00-2.35379980e-21j  1.79145433e-22+0.00000000e+00j\n",
       "   0.00000000e+00+1.36381921e-23j -1.03823683e-24+0.00000000e+00j\n",
       "   0.00000000e+00-8.09480370e-26j  1.20253385e-26+0.00000000e+00j]]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# System parameters\n",
    "N = 30  # Number of Fock states\n",
    "omc = 1.  # main frequency\n",
    "gamma = 0.1  # Dissipation rate\n",
    "F = 0.04  # Drive strength\n",
    "omF = 1. #Drive frequency\n",
    "# Operators\n",
    "a = destroy(N)\n",
    "\n",
    "H = omc * a.dag() * a\n",
    "\n",
    "Hdriven = H - omF * a.dag() * a + F*(a+a.dag()) # Driven Hamiltonian in the rotating frame\n",
    "\n",
    "c_ops = [np.sqrt(gamma)*a] #given jump operators (in this case only 'a')\n",
    "rho_ss = steadystate(Hdriven, c_ops) #Steady state of the master equation for a given H \n",
    "rho_ss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do we do with the steady state? Well, we can compute steady state quantities.\n",
    "Think about what's happening: your harmonic oscillator represents a single electric field mode of a Fabry-Perot cavity and you are illuminating this cavity with a laser (the drive). Photons can enter and exit the cavity because of the dissipations (or losses) in the mirrors, which are non completely reflective but semi-transparent.\n",
    "You keep the laser shining its light from outside on one of the mirrors, while you collect the light escaping from the other mirror. After a while the system is going to be in the steady state.\n",
    "\n",
    "You can perform measurements on the output light of your cavity. For instance you collect this light in an interferometer and measure the $g^{(2)}(\\tau)$ as a function of the time delay $\\tau$ in the arms of the interferometer.\n",
    "\n",
    "All this abstract operation can be put in a numerical framework using the theory + the truncation procedure to represent fields, operators and states as matrices and vectors (basically using QuTip).\n",
    "\n",
    "Here below you find the normalized $g^{(2)}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "taus = np.linspace(0., 40., 200)\n",
    "G2 = correlation_3op_1t(Hdriven, rho_ss, taus, c_ops, a.dag(), a.dag()*a, a)\n",
    "avgNph = expect(a.dag()*a, rho_ss)\n",
    "g2 = G2/(avgNph**2.)\n",
    "\n",
    "# plot the spectrum\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "ax.plot(taus, np.abs(g2), 'r--', lw=2)\n",
    "ax.set_xlabel('$\\tau$')\n",
    "ax.set_ylabel('g$^{(2)}$')\n",
    "plt.axis( [0, 40, 0, 2] )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:red\">**Exercise!**</span>\n",
    "\n",
    "<ins>*Let's consider that the environmet is a temperature $T$. It means that our cavity is sourronded by a thermal ensemble of photons, like as it is embedded inside a black-body.\n",
    "If you go back on your quantum optics course (or look at Gardiner-Zoller 'quantum noise' book, or, even better to Cohen-Tannoudji 'Atom-Photon interactions' book) you find that the master equation is modified to*</ins>\n",
    "$$\n",
    "    \\mathcal{L}[\\hat{\\rho}] = -i[\\hat{H}', \\hat{\\rho}] + \\gamma(1+N_{\\rm th}(T))\\left(  \\hat{a} \\hat{\\rho} \\hat{a}^{\\dagger} - \\frac{1}{2}\\lbrace{\\hat{a}^{\\dagger} \\hat{a}, \\hat{\\rho}\\rbrace} \\right) + \\gamma N_{\\rm th}(T)\\left(  \\hat{a}^{\\dagger} \\hat{\\rho} \\hat{a} - \\frac{1}{2}\\lbrace{\\hat{a} \\hat{a}^{\\dagger}, \\hat{\\rho}\\rbrace} \\right) \n",
    "$$\n",
    "<ins>*where $N_{\\rm th}(T)= 1/( \\exp[\\omega/(k_b T)] - 1)$ is the Bose-Einstein distribution of the harmonic oscillator.*</ins>\n",
    "\n",
    "<ins>*The first Linblad dissipator term is only rescaled by the factor $(1+N_{\\rm th}(T))$, but the real novelty is the appearence of a new term, still in the Linblad form, scaled by $N_{\\rm th}(T)$. This last term has the annihilation and creation operators swapped, and thus is not a dissipator term but rather a pumping term. It pumps thermal photons into the system. The fact that the dissipator is proportional to $(1+N_{\\rm th}(T))$ and the thermal absorption is proportional to $N_{\\rm th}(T)$ ensures the correct thermalization in the steady state, and it is nothing else than a fancy rewriting of the good old A,B Einstein coefficient for spontaneous emission, stimulated emission and absorption.*</ins>\n",
    "\n",
    "<ins>*Rewrite the exercise above in the new framework.*</ins>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code here...\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution:\n",
    "\n",
    "# System parameters\n",
    "N = 30  # Number of Fock states\n",
    "omc = 1.  # main frequency\n",
    "gamma = 0.1  # Dissipation rate\n",
    "F = 0.04  # Drive strength\n",
    "omF = 1. #Drive frequency\n",
    "# Operators\n",
    "a = destroy(N)\n",
    "\n",
    "H = omc * a.dag() * a\n",
    "\n",
    "Hdriven = H - omF * a.dag() * a + F*(a+a.dag()) # Driven Hamiltonian of the Kerr oscillator in the rotating frame\n",
    "\n",
    "T = 2 # I set the temperature (k_b=1 We stay in units where Bolzmann constant is 1 )\n",
    "\n",
    "Nth = 1./( np.exp(omc/T) - 1.)\n",
    "\n",
    "c_ops = [np.sqrt(gamma*(1. + Nth))*a, np.sqrt(gamma*Nth)*a.dag() ] #given jump operators (in this case only 'a')\n",
    "rho_ss = steadystate(Hdriven, c_ops) #Steady state of the master equation for a given H \n",
    "\n",
    "taus = np.linspace(0., 40., 200)\n",
    "G2 = correlation_3op_1t(Hdriven, rho_ss, taus, c_ops, a.dag(), a.dag()*a, a)\n",
    "avgNph = expect(a.dag()*a, rho_ss)\n",
    "g2 = G2/(avgNph**2.)\n",
    "\n",
    "# plot the spectrum\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "ax.plot(taus, np.abs(g2), 'r--', lw=2)\n",
    "ax.set_xlabel('$\\tau$')\n",
    "ax.set_ylabel('g$^{(2)}$')\n",
    "plt.axis( [0, 40, 0, 2] )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time-dependent case\n",
    "Here we take a quick look to what happens if you cannot use the trick of the rotating frame. Solving for steady states is not so easy anymore and you have to deal with the full quantum time evolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0%. Run time:   0.00s. Est. time left: 00:00:00:00\n",
      "Total run time:   0.26s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 150.0)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# System parameters\n",
    "N = 50  # Number of Fock states\n",
    "omega = 1  # Frequency of the oscillator\n",
    "gamma = 0.05  # Dissipation rate\n",
    "F = 0.1  # Drive strength\n",
    "omega_d = 0.99  # Drive frequency\n",
    "\n",
    "# Time-dependent drive function\n",
    "def drive1(t, args):\n",
    "    return F * np.exp(-1j * omega_d * t)\n",
    "\n",
    "def drive2(t, args):\n",
    "    return F * np.exp(1j * omega_d * t)\n",
    "\n",
    "# Operators\n",
    "a = destroy(N)\n",
    "H0 = omega * a.dag() * a # Hamiltonian of the harmonic oscillator\n",
    "\n",
    "# Time-dependent Hamiltonian\n",
    "H = [H0, [a.dag(), drive1], [a, drive2]]\n",
    "\n",
    "# Initial state\n",
    "psi0 = basis(N, 0)\n",
    "\n",
    "# Collapse operators\n",
    "c_ops = [np.sqrt(gamma) * a]\n",
    "\n",
    "# Time points\n",
    "times = np.linspace(0, 150, 1000)\n",
    "\n",
    "# Solving the dynamics with mesolve\n",
    "result_me_td = mesolve(H, psi0, times, c_ops, [a.dag() * a, a.dag() + a])\n",
    "\n",
    "# Solving the dynamics with mcsolve\n",
    "result_mc_td = mcsolve(H, psi0, times, c_ops, [a.dag() * a, a.dag() + a], ntraj=1)\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(times, result_me_td.expect[0], label=r\"$\\langle \\hat{a}^\\dagger \\hat{a} \\rangle_\\mathrm{ME}$\", lw=2)\n",
    "ax.plot(times, result_me_td.expect[1], label=r\"$\\langle \\hat{a}^\\dagger + \\hat{a} \\rangle_\\mathrm{ME}$\", lw=2)\n",
    "ax.plot(times, result_mc_td.expect[0], label=r\"$\\langle \\hat{a}^\\dagger \\hat{a} \\rangle_\\mathrm{MC}$\", ls=\"--\", lw=2)\n",
    "ax.plot(times, result_mc_td.expect[1], label=r\"$\\langle \\hat{a}^\\dagger + \\hat{a} \\rangle_\\mathrm{MC}$\", ls=\"--\", lw=2)\n",
    "ax.legend()\n",
    "ax.set_xlabel(r\"$t$\")\n",
    "ax.set_xlim(times[0], times[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Trajectories: The Monte Carlo Method\n",
    "(Very advanced stuff!)\n",
    "\n",
    "The Monte Carlo quantum trajectories approach simulates open quantum system dynamics by randomly sampling trajectories of the system's state vector. Each trajectory evolves according to a non-Hermitian effective matrix\n",
    "\n",
    "$$\n",
    "\\hat{H}_\\mathrm{eff} = \\hat{H} - \\frac{i \\hbar}{2} \\sum_k \\hat{L}_k^\\dagger \\hat{L}_k\n",
    "$$\n",
    "\n",
    "Here, the strictly negative non-Hermitian portion gives rise to a reduction in the norm of the wave function. The probability for a quantum junp to occur is then\n",
    "\n",
    "$$\n",
    "\\delta p = \\delta t \\sum_k \\langle \\psi (t) \\vert \\hat{L}_k^\\dagger \\hat{L}_k \\vert \\psi (t) \\rangle\n",
    "$$\n",
    "\n",
    "Let's consider the fock state $\\vert n \\rangle$ as the initial state. In this case, the action of the quantum jump is trivial: it makes a jump into the next fock state, losing energy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0%. Run time:   0.00s. Est. time left: 00:00:00:00\n",
      "Total run time:   0.01s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.25000000000000017, 6.0)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "psi0 = fock(N, 5)\n",
    "\n",
    "H = omega * a.dag() * a\n",
    "\n",
    "c_ops = [np.sqrt(gamma) * a]\n",
    "\n",
    "e_ops = [H, a + a.dag()]\n",
    "\n",
    "tlist = np.linspace(0, 5 / gamma, 100)\n",
    "\n",
    "# We perform only one quantum trajectory\n",
    "sol = mcsolve(H, psi0, tlist, c_ops, e_ops, ntraj=1)\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(tlist, sol.expect[0], label=r\"$\\langle \\hat{H} \\rangle$\", lw=2)\n",
    "ax.plot(tlist, sol.expect[1], label=r\"$\\langle \\hat{a} + \\hat{a}^\\dagger \\rangle$\", lw=2)\n",
    "ax.legend()\n",
    "ax.set_xlabel(r\"$t$\")\n",
    "ax.set_xlim(tlist[0], tlist[-1])\n",
    "ax.set_ylim(None, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, if by performing a large number of trajectories and averaging among them, we get the same results as the master equation case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0%. Run time:   0.05s. Est. time left: 00:00:00:00\n",
      "20.0%. Run time:   0.11s. Est. time left: 00:00:00:00\n",
      "30.0%. Run time:   0.17s. Est. time left: 00:00:00:00\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.0%. Run time:   0.22s. Est. time left: 00:00:00:00\n",
      "50.0%. Run time:   0.28s. Est. time left: 00:00:00:00\n",
      "60.0%. Run time:   0.34s. Est. time left: 00:00:00:00\n",
      "70.0%. Run time:   0.39s. Est. time left: 00:00:00:00\n",
      "80.0%. Run time:   0.45s. Est. time left: 00:00:00:00\n",
      "90.0%. Run time:   0.51s. Est. time left: 00:00:00:00\n",
      "100.0%. Run time:   0.57s. Est. time left: 00:00:00:00\n",
      "Total run time:   0.57s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.2146261637028203, 6.0)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol_mc = mcsolve(H, psi0, tlist, c_ops, e_ops, ntraj=100)\n",
    "sol_me = mesolve(H, psi0, tlist, c_ops, e_ops)\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(tlist, sol_mc.expect[0], label=r\"$\\langle \\hat{H} \\rangle_\\mathrm{MC}$\", lw=2)\n",
    "ax.plot(tlist, sol_me.expect[0], label=r\"$\\langle \\hat{H} \\rangle_\\mathrm{ME}$\", ls=\"--\", lw=2)\n",
    "ax.legend()\n",
    "ax.set_xlabel(r\"$t$\")\n",
    "ax.set_xlim(tlist[0], tlist[-1])\n",
    "ax.set_ylim(None, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Here we take a look at the thermalization of the harmonic oscillator:\n",
    "the bath is set at a temperature $T$ (given in units of $\\hbar\\omega/k_b$ and it can thus also provide energy to the system, rather than just absorbing it.\n",
    "To include such a process we need to add a new jump operator, that can create an energy quantum in the harmonic oscillator (or a photon, in quantum optics language). Again, like in master equations, the dependence from the temperature enters in the coefficient of the loss/gain jump operators, for which losses enters with a factor $1+n_{\\rm th}(T)$ while gain takes $n_{\\rm th}(T)$. Notice that those are nothing else than the Einstein A,B coefficient for spontaneous/stimulated emission and absorption. This structure ensures the detailed balance in the steady state, that leads to correct thermalization when the system reaches the steady state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0%. Run time:   0.56s. Est. time left: 00:00:00:05\n",
      "20.0%. Run time:   1.17s. Est. time left: 00:00:00:04\n",
      "30.0%. Run time:   1.62s. Est. time left: 00:00:00:03\n",
      "40.0%. Run time:   2.19s. Est. time left: 00:00:00:03\n",
      "50.0%. Run time:   2.75s. Est. time left: 00:00:00:02\n",
      "60.0%. Run time:   3.35s. Est. time left: 00:00:00:02\n",
      "70.0%. Run time:   3.88s. Est. time left: 00:00:00:01\n",
      "80.0%. Run time:   4.39s. Est. time left: 00:00:00:01\n",
      "90.0%. Run time:   4.85s. Est. time left: 00:00:00:00\n",
      "100.0%. Run time:   5.32s. Est. time left: 00:00:00:00\n",
      "Total run time:   5.36s\n",
      "100.0%. Run time:   0.00s. Est. time left: 00:00:00:00\n",
      "Total run time:   0.03s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 94.24777960769379)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A2L9/P6BO0NG67bbbMJvNHHfccR6fx9Njrlq1itraWrfavRkMBoes8ocffsjhw4fJzc3V3T9//nzuvPNOli5dyt69e+nXr59utbuYmBimT5/Ohg0byM/P15UueMLdMcXGxnLcccexbNkyHn/88Y7z1dfX88EHH3htXLGxsUyePJl3332Xxx9/vKMkxWKx8Morr9C/f39GjBjRra/VmYceeoiFCxfypz/9yeXEvjlz5vDf//6Xd955RzfR66WXXiInJ4fJkyd3a19nupPV9uR1peXJz2ratGm89dZbPPLII51+GHE2fl/9TLv7Whs4cCC33HILX3zxBd99953H5xUi5Gkzw9oAWFsmYd1PguFeq9vBcF1dHQ899BAbN25kw4YNHbOVFy5c6LDv+vXr+d3vfsePP/6IyWTitNNO4/HHH/fKqmh91ezZs3nxxRcpLi4mKyuL8ePHExMTw3333YfBYKCpqYn//ve/FBQUAHQrGPb0mMuXL2fixIkMGDCgy2Off/75LF26lLy8PPLz81m3bh1/+9vfnF5+TkpKYs6cOSxdupTq6mruuusujEZ9hc/ixYs5+eSTOeWUU1iwYAGDBw+mrq6OgoICVqxY4bBwRE/H9OCDD3Leeedx1llncdttt9He3s7f/vY34uLiOsoAvDGuP//5z8yYMYPp06dz1113ERERwZIlS9i6dSuvv/56j+turZ544gnuv/9+zj77bM477zyHWuYpU6YAcM455zBjxgwWLFhAbW0tubm5vP7663z88ce88sorur7BnuzrzLhx6h+jxYsXc9VVVxEeHt5pNwjw7Gdoz92f1d///ndOPvlkJk+ezL333ktubi4lJSW8//77/Pvf/yY+Pr7T8fvqZ+rO+Gtqapg+fTqXXnopeXl5xMfHs3bt2o7uKEL0OdrMsLY0IioRkgerNcXW/cZ2Xb8vQpTSTfv27VMSExOVqVOnKtdff70CKA888IDDfjt27FDi4+OVU045Rfnwww+Vd955RxkzZoySk5OjlJaWenzerVu3KoCydetWp4/v2bNH2bNnj8fHDTWNjY1KTEyM8p///Kfjvg8++EDJy8tTIiMjldGjRyuLFy9WHn74YcVoNCp1dXXdOo+7x7RYLEq/fv2UBx980K3jVlVVKdddd52SkZGhxMTEKCeffLLyzTffKNOmTVOmTZvmsP+nn36qAAqg7Nq1y+kx9+3bp1x77bVKv379lPDwcCU9PV058cQTlYcffli33wMPPKAASllZWY/G9N577ynjxo1TIiIilIEDByqPPfaYcuuttyrJycndGpcr33zzjXLaaacpsbGxSnR0tDJlyhRlxYoVbn1NL774ogIo+/bt6/Qc06ZN6/j+OvunVVdXp9x6661KVlaWEhERoeTn5yuvv/660+N6sq8zv//975WcnBzFaDQqgLJ69WqXX6uiePYztH5vCgsLO+5z92e1fft2Zd68eUpqamrHz//qq69Wmpubuxy/ovTsZ6odu/3PtavxNzc3KzfeeKOSn5+vJCQkKNHR0crIkSOVBx54QGloaOj0Z9FX3ltFH1JXoigPJNj+7fhA//j/Lrc99vLswIxRdEtXsaI9g6IoSjeDaEC9LFleXk56errTzPBFF13E6tWr2bNnT0e7n/379zN8+HDuuOMO/vKXv3h03m3btjF27Fi2bt3KmDFjHB7fu3cvQJ/IOs+ZM4e2tjbdpflAWbt2LccffzybNm3q6CPb17S1tTFhwgT69evHp59+GujhiC4sXryY22+/nbq6Ol1nB+FcX3pvFX1Ewefwiibbe/tWSNJc2fzqb7D6YfV2TBrcXQBeuhonfKurWNFet8sk3LmUZzab+eCDD7jyyis7AmGAQYMGMX36dN577z2Pg2FhM2vWLBYsWEB9fX3A/5gvX76cwYMH96lA+LrrrmPGjBlkZ2dTXFzMs88+y44dO1i8eHGghyY6UVNTww8//MDSpUsZO3ZswH93gopigfpSdeZ8XCaE9ZlpJX3PzpWw+Q1ob+18v6RBcNKtkJDjn3H5k7ZEIioJEu3KqbQ1xI3lUFfUO78PwrcT6Pbs2UNTU5PTACk/P5/PPvuM5uZmoqKinD6/tLSUsrIy3X3WelUBV199NVdffXWghwHAww8/zMMPPxzoYfhVXV0dd911F2VlZYSHh3PssceycuVKzjjjjEAPTXRiw4YNzJkzp2MFOKHRcPQPPoDSDkkDAzse4RtVhfDmlWBxs8d07WG4+P98OqSAsF95zj7Jl5XvuL8Ew72ST4Nha79MZ/1EU1JSUBSFqqoql300lyxZ4tbKS0IEwptvvhnoIYhuOPXUUz3qUNGntNRqbtcFbhzCt/Z97X4gDLBnNVgsYOxlSxPUaFokpjmZnBufBbHp0HA0KVe0GUac5Z+xCb/yyzWw7q5CddNNNzFv3jzdfQUFBcyePdtbQxNCCAHqsrRtmg8J7a3QbpZSid5IWx4QkwbDTnPcp6kKCj5Tb7fWQdU+SB3mn/H5S71moZn4LMfHDQY1O7znC3W7eJN/xiX8zqfvctbVsFytQmUwGDpthJ+RkUFGRoavhieEEMLK0gYWs/4+cxOE9Y7+7EJDWx4wfAbMedZxn8ZK+OsQ/XN6UzCsKGp9vFWc44qigFo+YQ2Gi2RZ5t7Kp9c8hg0bRnR0dMeKU1pbtmwhNzfXZb2wEEIIP2pzUjri7D4R2iwWKNlq27avi7WKSYFETc24/bLFoa65BszNtm1nmWHQL75RvR+aqn06LBEYPg2GTSYTM2fO5N1336WuzlZ/duDAAVavXi1N3oUQIlg4DYYb/T8O4VuVe6G13rad3UkHIO1jvS0rqs0KA8S5uAqdNV6/XeyY3BOhr0dlEh999BENDQ0dge727dt5++23ATj33HOJiYlh0aJFTJo0ifPPP597772X5uZm7r//ftLS0vh//+//9fwrEEII0XPOAl/JDPc+9nWv9ssO2z+282gf+96WGdbWC4PrMomUoRARZ/sAUbwFhpzi27EJv+tRMLxgwQL279/fsf3WW2/x1ltvAbBv3z4GDx5MXl4eX375Jffccw8XXnihbjnm9PT0no1eCCGEdzgLfM3NvbOLQF+mzfAmDVKXHXZFW0JRXwJ1JRDvImgMNdrMsMGodo1wxmiEzLFw8OgS9b3tQ4EAehgMFxYWurXfxIkT+fzzz3tyKiGEEL5iMbtefMHcBBGx/h2P8B1tMNdZiYSzx4u39KJguMR2OyYNjGGu983OtwXDva1cRAA+rhkWQggRAjorh5BSid5DUfTBnH09rL2EfhCtWSegN7UWq9O2VesiwNeWkpTthLZm1/uKkCTBsBBC9HXagNdgBFO088dEaKsrVpcVtuoqM2ww9N5JdO60VbPSloso7VC63TdjEgEjwbAQQvR12oDXFA0R2mBYOkr0Gvb1rq7aqun20WRFe1O9rHYCXVfBcMYoMGqqSnvT90EAEgwL4Oqrr2bp0qWBHoYQIlC0AW94NJhiNI81q5fXRejTZnZj01331tXSllJU7oXmWtf7hhJPMsOmSEgfZduW9mq9jgTDvdSePXuIjY1l6tSpKF78Q+ar4wohAsRi0S8+EB6t/rPtoH9chC5tzW/WOLUMoiv2pRQl27w7pkDRTqDrKhiG3lsuIgAJhnslRVG49tprueOOO2hoaOBf//qX0/3mzJlDXFwcr776KjfeeCNxcXH8/e9/7/FxhRAhxGxXExweYxcMI3XDvYVu8pwbJRIAqbnqa8KqN5QImFuhscK27U6HDO33q2QrWNq9Py4RMBIMh7AVK1aQl5dHfX297v5//vOfhIeH8+CDD/Lmm2/y2GOPsXfvXofnv/fee9TX13PZZZfx7LPPUl9fz5133unyfJ0d9y9/+Qtnnnmmd79AIYTv6QJdA4RHqW2mwiJd7CNCUlO1upywVVeT56yMYZA5xrbdG7KiDWX6bXcyw9ra6bZGqNjj3TGJgJJgOIS98cYbZGVlERcXp7v/tttu4/PPP8doNDJs2DAOHz7M0KFDe3y+zo57/PHH89lnnzkNurtr6dKlGAwGt/tZB8t5vv/+exYuXEh1dbVXjqfl6++JL8cugpRu8lyU2k0C9NlhmUQX+kq26re7aqum21cTOPeG9mrurj6nZb9SX2/IkIsOEgyHKLPZzMqVK5k9e3aghwLAKaecQkpKCsuWLfPaMc877zx++OEHsrOzvXZMf/j+++9ZtGiRTwJKX39PfDl2EaS0wbA2AA63a68mcwRCmzajGxGnLjPsLm0gWLpTLTMIZdrJc+BeMByVAMlDbNtFveBDgeggwXCI+vrrr6mqquJXv/pVoIcCgMlk4rzzzmP58uVeO2Z6ejpTpkwhMjKy651DVGOjZxm3UP2eePp1Cj9RFH3NsC4Y1tSJKu0SDIc6bSYzc6xnS2xrSyosberCE6FMu+BGeCxExrneV0v7fZCOEr2KBMMhavny5YwbN86h/OGnn37i4osvZvDgwURHR5ORkcGcOXPYs6f79U3uHnPWrFl89913VFRUuDiSTVlZGTfccAMDBgwgMjKS9PR0TjrpJN2y3c5KAhYuXIjBYGDbtm3Mnz+fxMREMjMzufbaa6mpqdGdY/ny5eTn5xMZGcnQoUNZvHhxx/O7snv3bi699FIyMjKIjIxk1KhRPP30010+b+HChdx9990ADBkyBIPBgMFg4Msvv+w49/r167nwwgtJTk5m2LBhABQUFHDNNdcwfPhwYmJi6NevHzNnzmTLFv0brqsyCXfHu3PnTubPn09mZiaRkZEMHDiQK6+8kpaWlk7HbvXtt99y+umnEx8fT0xMDCeeeCIffvihw/fA2df5zTffYDAYeP311x3G9fLLL2MwGFi7dm2X32PhReYWUCy2bW0AbD+JTjH7Z0zCN3ST58a53s+ZjDFg0CxXHOolAtrMsCfLS+vKRTbLB8RexNT1LiIYvf/++1x++eUO92/cuJHx48dz6aWXkpyczMGDB3n00UeZO3cumzZ177KOu8c866yzMJlMfPDBB1x11VWdHvOKK65g/fr1PPLII4wYMYLq6mrWr1/vViANcMEFF3DxxRdz3XXXsWXLFn7/+98D8MILLwDw8ccfM3fuXKZOncobb7yB2Wzm8ccfp6SkpLPDArB9+3ZOPPFEBg4cyBNPPEFWVhaffPIJt956K+Xl5TzwwAMun3v99ddTWVnJU089xbvvvttRzjB69OiOoHLu3Llccskl3HjjjTQ0NABw5MgRUlNTeeyxx0hPT6eyspKXXnqJyZMns2HDBkaOHNnj8W7atImTTz6ZtLQ0HnzwQYYPH05RURHvv/8+ra2tnY4d4KuvvmLGjBnk5+fz/PPPExkZyZIlS5g5cyavv/46F198sW5c9l/nKaecwjHHHMPTTz/N/Pnzdfv+61//YtKkSUyaNKnLn4/wIvtaYG0AHBYOxnA1Ewjq7PkwRChqa9Znc92dPGcVHgXpI20rrxVthmO8Nzy/87StmlW2ps66sQJqj0BiP++NSwRM3wmG25qhal+gR6GXPER9k/HQpk2bKCwsZNasWQ6P3XDDDR23LRYLFouF5uZmrr/+eqqrq0lKSnJ4TlRUFOHh4S7P5+4x4+LiOP3001m+fHmXwfB3333H9ddfz69//euO+5x9Pa5cd911HVnMM844g4KCAl544QWef/55DAYD999/P/369eOTTz4hIiICgLPPPpvBgwd3eew777yT+Ph4vv32WxISEgCYMWMGLS0tPPbYY9x6660kJyc7fW7//v0ZOHAgAMccc4zT81111VUsWrRId9/UqVOZOnVqx3Z7ezvnnXceY8aM4d///nenLe/cHe+dd96JyWTip59+Ij09veP5l112GQDx8fGdjv3ee+8lOTmZL7/8smPS5vnnn8+ECRO46667uOiii3RZd2df56233so111zDxo0bmTBhAgBr165l7dq1vPTSSy6/RuEj2nrhsAi1c4BWeDS0aIJhEZpKt6ulLlbutlXTysq3BcMhnxnWBsMZ7j/P2SQ6CYZ7hb4TDFftgyVTAj0KvZt+VJd59NDq1auJi4tj4sSJuvsVReGdd95hyZIl7Ny5k+Li4o6FMYxGI9HR0c4Ox7PPPuvyXJ4ec/r06TzyyCNdfg3HH388S5cuJTU1lTPOOIOJEyd2GpDbs6+Vzs/Pp7m5mdLSUuLi4vj555+55ZZbOgJhUIP1mTNndrraXnNzM1988QULFiwgJiYGs9l2afjcc8/lX//6Fz/++CPnnHOO22O1d8EFFzjcZzab+etf/8orr7xCQUEBbW1tHY/t2LGjx+OdNm0aX331Fdddd50uEHZXQ0MDa9asYcGCBbruJWFhYVxxxRXcc889/PLLL+Tl5XX6dc6fP5977rmHp59+mv/+978APPXUU6SnpztklkUnFAXqjkCLvq0iBiNEJ0NsmvPn1ZdCc7Xt8q65xfaYfVmE9b6WoyuOKRIMhyxtfavR1K2/O2SNg83/U28f+hn+e7rrfeOzYOrdkDPB8/M409YMXyyCxko47Y+QNLBnx9MFw26swmcVnwWxGdBwtMxi5e/g68fV2+HRMPk3MGpmz8YmAkJqhkPQpEmTqK+v55dfftHdf8MNNzB//nxGjx7NkiVL+Oabb1i7di3jx48nNze3W5OuPD3m2rVr3brU/cYbb3DVVVfx3HPPccIJJ5CSksKVV15JcXFxl88FSE1N1W1bx9HU1ERVVRWKopCZ6Xj5y9l9WhUVFZjNZp566inCw8N1/84991wAysvL3RqjK846Qdx5553cd999zJ49mxUrVrBmzZqO73NTk+ser+6Ot6qqivb2dvr379+tMVu/p87GnpOT0zGWrr7OyMhIfvOb3/Daa69RXV1NWVkZb775Jtdff33ITQoMqOZqNbBta9T/a62HmoPO+wK3NkDtYfV/6/7aAFdbL+zsPsUC7SHeRaCv0rZVSx+lLi/sKftJdId/dv1v5wew/Oaej9tq7X/hxyVqML6q62RLl+q6mRkG/feh5oDtay78Bt75tfTkDlF9JzPci5xwwglkZGSwfPnyjkzcL7/8wnPPPcdf//rXjvIBUAOhbdu2cdFFF3l8Hk+P2drayscff8yjjz7a5bHT0tJ48sknefLJJzlw4ADvv/8+9957L6WlpXz88ccej1UrOTkZg8HgtD64q2A7OTm5I9t5883O38yHDBni9H53OZvA98orr3DllVc6fO/Ky8udlrZ4Ot6YmBjCwsI4dOhQt8acnJyM0WikqKjI4bEjR44A6s9Uy9VExQULFvDYY4/xwgsv0NzcjNls5sYbb+zWuPqsrlpbtdY7Znpb6jp/TlSi4332QZP8oQ9NNZrf+7Tc7h2j33EQnw11ju8BTpVsVTO5MSndO5/W3q80x+3hctCK0v2aYVAzvwWfO3/M3KR2qkjp2d8I4X99JxhOHqKWJQST5O79whiNRs4//3yWLVvGPffcA8D+/erKQtbJTla33XYbZrOZ4447zuPzeHrMVatWUVtb63G7t4EDB3LLLbfwxRdf8N1333k8TnuxsbEcd9xxLFu2jMcff7yjVKK+vp4PPvig0+fGxMQwffp0NmzYQH5+vq7Mwl3aLLW7DAaDQ2b0ww8/5PDhw+Tmuv7j5cl4p02bxltvvcUjjzziELh2NfbY2FgmT57Mu+++y+OPP95RHmOxWHjllVfo378/I0aMcOtrzc7OZt68eSxZsoTW1lZmzpzZUass3KTtAGEIg5hUaKqyTXZzFrTq6oMjbcGvAYhMcF4mYbQrXTI392jYIkC6WxagFREDV74PW99Wry4409YIP79g2y7eDENP7d75tLQ1ys3VPTtWcw20a8qD4j38fhxzhdqn+cgG2/E2/J/3xicCou8Ew+FR3auTClKzZ8/mxRdfpLi4mKysLMaPH09MTAz33XcfBoOBpqYm/vvf/1JQUADQrWDY02MuX76ciRMnMmDAgE6PW1NTw/Tp07n00kvJy8sjPj6etWvXdnSA8IYHH3yQ8847j7POOovbbruN9vZ2/va3vxEXF0dlZWWnz128eDEnn3wyp5xyCgsWLGDw4MHU1dVRUFDAihUrWLVqVafPHzduXMdxrrrqKsLDwzvtBgHqRLSlS5eSl5dHfn4+69at429/+5tbZQ3ujvfvf/87J598MpMnT+bee+8lNzeXkpIS3n//ff79738THx/vcuzx8fH8+c9/ZsaMGUyfPp277rqLiIgIlixZwtatW3n99dfdallnddtttzF58mQAXnzxRbefJ47SBsOmCHUSj9KuznAH5yvGae+LSnRv4o8xDDVadlJjLEKHtpWYp2UBWukjYPofXD9uscCWt2115kVeCIbrSvTBfHON633dUW93xdDT74cxDMZdqP4DaKiwC4Z7OD4REFIzHKLOOOMMoqOjWbFiBaDWwr755ps0NTUxd+5c7r//fs4991yuueYajEYjxxzjeR8cT46pKAorVqxwqyNEVFQUkydP5v/+7/+47LLLOOecc3juuee45557OiZV9dTZZ5/NO++8Q0VFBRdffDF33nknc+bMYdasWZ2WHYCaCV+/fj1jx47lT3/6E2eeeSbXXXcdb7/9Nqef3smkkaNOPfVUfv/737NixQpOPvlkJk2axLp16zp9zuLFi7n88sv585//zMyZM3n//fd59913O/oQ29MGnu6Od/z48fz0009MnDiR3//+95x99tncc889REZGdmSUOxv7tGnTWLVqFbGxsVx99dVccskl1NTU8P7773s8+e34449n8ODBjBo1yq3vqbCjyww7Wz65Wb+Pxayv93WWBXbGYFAnXGmPK0KLfVmAp5lQTxiN+o4L3ug6YX+MltqedTZxCIZ7+P2IStBvSzAckgyKElpdo7dt28bYsWPZunUrY8aMcXh87969AA6LUfRGc+bMoa2trctL//6wdu1ajj/+eDZt2kR+fjfa9vhBW1sbEyZMoF+/fnz66aeBHk63LF68mNtvv526ujpdV4dQs3nzZsaPH8/TTz/NTTfdFOjhhJ7q/Wo9JkBkPKTmqpeuy3fZ9knPswW9LfVQsVvz2Cj32zqW/QJtjeytskD1QYaeNNsrX4Lwk8ZK+KumJO/ydyD3DN+d76N7Yc0z6u20kXDLTz073tePw6qH9PfdU6h2TemOzW/Bu9ertw1GuK/csaWgpx7JgbajpSO/egqOvbJnxxM91lWsaK/vlEn0QrNmzWLBggXU19cHPDBavnw5gwcPDqpA+LrrrmPGjBlkZ2dTXFzMs88+y44dO1i8eHGgh+axmpoafvjhB5YuXcrYsWMD/vPurj179rB//37+8Ic/kJ2dzdVXXx3oIYUmiyaHYc0Mm+yC27ZGWzCsLZEwGD3rJqCtG5aa4dDj7UxoV7TdFip2Q2ujWm/cXc6WPW6q7n4wrP1+xKT1PBAGiE6yBcNN1T0/nvA7KZMIYVdffTVNTU1BERg9/PDD7NsXXIua1NXVcdddd3WUDbS3t7Ny5UrOOMOHWREf2bBhA3PmzCEiIiKkF6d46KGHmDFjBvX19bz11lvExPTgj2Rf5qxMwhimD4i1E+a0t03RavmDu8I0OROpGQ49DsGwh90TPKVd0EOx2Bbq6C5npRY9KUWo13QU8mQp5s5oO7FImURIksyw6LXefPPNQA/Ba0499VSPulMEq6VLl3a66Ilwk7NgGNRA15q9dRUMu1svbCWZ4dCm7alr7TziS+kj1W4l1o4NRZugv+cTuAForoXKvU7u70kwrJ1MKMGwUElmWAghQo2rYDhCO4muSZ08pVj0QaynwbBkhkOb/dLDRh//2Q8L13du6skkOu1iIVo9aV/mjTZz9nTBcLV3jin8SoJhIYQINbpgWFPyYNIEukq72kGirZmO1mjQs8ywpU2tARWhwz4Y9gdtR4miHgTDrp7bk+xrT1afcyUqyXZbMsMhSYJhIYQINa4yw/ZLKrc1OfYcNnmaGbZbeMO+BlUEN19kQruSPd52u3Q7tJu7dxxXWeUelUn0YPU5V6RMIuRJMCyEEKHGVTAcZtJnctsa7SbPRXl+mdxoN7VEW3Mpgl9AMsOaSXTmZn3LP094OzNsboUmzaJLMoFOHCXBsBBChBwnrdWswu3qhnWT57rRveNocN1xRu1sfBH86nyQCe1K5hjUlQuPctYerSvmVijb6fyx7rYva7D7IOet70d0ku22tFYLSb0uGDYYDJjNZkJsLREhhHCfq8ww6APetiYw96CTBIDRiIKRdnM7RnOTZIZDjb9Wn9OKjFMXgrHqziS6sh1qjbpVrCar3d3sa52P2sxJZjjk9bpgOC4ujvb2doqKijCbu1mnJIQQwcraIcKqs8ywpU2/bzeCYUVRKG0y0N5cR2TDIakZDiXmFn13A3+VSYB+8Y2iTZ4/X1siYQiDQSfYtrsbcPqq57I2GDY3SdeVENTr+gwnJyfT2NhITU0NNTU1mEwmjEYjBk+azAshRLBSFGjWBLgNpRBWZdu2tEOLxfF5AE0lYCjz4FQK7e3ttNfVEH3kezL3vQvxF3Vz4MLv/L36nFZWPmx9R71dvFl93Xryd1ibTU4fqQ9cvREMh8eqGWxv0AbDoPZHjkv3zrGFX/S6YNhkMjFw4EDq6uqora2lra1NSiaEEL1Hexvs/dK2PegkfcbPYITC7/SXmEEtnxhxlkenMhgMREREEFm1mcytT2Fsb5EyiVBi/7PyZ2ZY216tuQaqD0DyIPefr80MZ+V7p5evrmTEi/XT2tZqoI5PguGQ4pdgeMOGDSxatIiffvqJ6upqBg4cyKWXXspdd93lk+VYDQYDCQkJJCQkeP3YQggRUDWH4bUHbdvjP4WBQ/X7fPsZ7Ptaf9+omTB0QffO+csR24piMoEudNTZ/az8NYEO9O3VQM30uhsMWyz6BTey89XMspU3MsPe/F44ZIalbjjU+LxmePv27Zx44okUFhby5JNP8sEHH3DJJZfw4IMPMn/+fF+fXgghepc2u2W5ndUBa1tbdXafu7SBg2SGQ4c2+ItMgAjvJ59cik2D+BzbticdJar2QWu9bdshM+yFCXQ+DYarvXds4Rc+zwy/9tprNDc388477zBs2DAATjvtNIqKivjPf/5DVVUVycnJvh6GEEL0DvaLaDhrl+brYNjSDsaw7h9P+EcgegxrZedD3RH1ticr0dlPuMsaB02auvi2RrX1minCs/H4KjMcmYDaSu5o9lraq4Ucn2eGw8PVHpWJifpPTklJSRiNRiIiPHwxCyFEX2Zu1m+HRznuk+0k8HV2n7u09ZVKOzRWut5XBI9ArD6npf0A5kl7Ne2+SYPUPr7eKEXQXtXw5ocDoxGiNGWZUiYRcnyeGb7qqqt48sknWbBgAX/5y19IT0/nq6++4t///jc333wzsbGxvh6CEEL0Hu5khlOHq6vNWQPnmDSIz+7+Oe2zaPUltglC5lb48A6o2g8zFkG/id0/T0+1NsCK29W65rMfO7r4Qx/mq+DPXdoPYLWH4R/jdGtxuNRQ4XgM7cIWoAacnkxSUxR9vbu3ey5HJdqCYAmGQ47Pg+HBgwfzww8/MGfOnI4yCYBbb72VJ598stPnlpaWUlambwNUUFDgi2EKIURocKdmOMykBoKH16nb2fmetbWy5xAMFwNj1dsbXoYNr6i3P70PrlnZ/fP01E//hS1vqrc/+QNcuTxwYwkGdT4M/tyh7SgBUHOgG8c4Ggz3NDPcWAntrbZtb08mlIU3QprPg+HCwkJmzpxJZmYmb7/9Nunp6axZs4aHH36Y+vp6nn/+eZfPXbJkCYsWLfL1EIUQInTYZ4ZNTsokAMbNswXD4+b17JzRyeqyzNZ2bdqM4/7vbbdLt/fsPD114Afb7YM/SW1zoDPDSYOg//Fw6KfuPd9ogtGz1dsOwXCVw+6dKt2m304Z6ny/7tK2V5MJdCHH58HwvffeS21tLRs3buwoiZg6dSppaWlce+21XHnllUybNs3pc2+66SbmzdO/iRcUFDB79mxfD1sIIYJTm6ZmODzGdcb3+BvUP/hh4TDk1J6d02BQM2m1h9RtbcZR2yWgqUpdfcsU2bPzdZd2LG2NUFGgLtjQFymK7yaMuctggEvfgB0r9BPg3GEMg6HTIX2Euh1p1yrV0+yrdgJfRDwkD/Hs+V2RzHBI83kwvHHjRkaPHu1QGzxp0iQAtm7d6jIYzsjIICMjAJ9mhRAiWGkzw66ywqAGEx4ustGpeE0wbM04tjZA+W79fvWlkDTAe+d1V0OFWpeqVbyl7wbDTVX6hVcCEQwDxKTAxKt6fhxjGEQmQks363K1k/KyxqqT3rxJlxmWYDjU+LybRE5ODtu2baO+vl53/w8/qJez+vfv7+shCCFE76GtGXY2ec5XdO3VjmaGS7bR0U6q47EA9SEu3uR4n32Lrr4kkAtu+EpPsq/aqwY9aTPoimSGQ5rPM8O33347s2fPZsaMGdxxxx2kpaXx448/8uc//5nRo0dzzjnn+HoIQgjRe+iCYSeT53xFW3NqDXidBZvaS/P+5KyPrSftvHob+59DICbQeVtUIljjTE96+bY1Qdkvtu2etBl0RdvtQvoMhxyfZ4Z/9atf8cUXX5CQkMBtt93G+eefz0svvcRvfvMbvv76a+kzLIQQnjAHKhjWBFPWQMtZsBmo5ZqdjaVos34Z375Em6E3hEF0SuDG4i3dzb6Wblf7Y1vZd7nwBskMhzSfZ4YBpk+fzvTp0/1xKiGE6N2CITNsXdbW2RK7ASuTcDKWpkq1jjixD5bjaT+UxGV4v0Y2ELTZV08CTu1VA2M4pI/y2pA62AfDitKzdobCr3rBb4cQQvQh2gl0/gyGtZfZW+vUP/glTlqp2deq+oOziXxWniwD3Jvo2qr1gnphsAs4q91/nvaqQUae58s4u0M7NkubYwtEEdQkGBZCiFASDBPoAAq/hfYWx/0CkRm2n8hn0PQWdpYx7gu0H0p6ZTDsQWZYN3luvPfGo6XtJgFSKhFiJBgWQohQEgxlEgC7P3W+XyBqhrUT+cIiYchU23ZfnUSnnUAX34eDYUv70Q9LR/li8hz0fIU8EVASDAshRCjRBsMmfwbDdgHV7s+d7xeIzLA24M0cDTnH2LalTKIXZYaTbLfdDTYrCvQlC75oqwYSDIc4CYaFECKUBCozbIrUByPWBThAnZRkVV/i/w4O2oA3K1+f/as5AI2V/h1PMKjv5WUSTdXuvc7sPwxljvHqkDpoJ/eBtFcLMRIMCyFEKAnUBDpw3at20Am22+2tni+92xPtbVC6w7adne+Y/etrdcNtzfrMZG8Mhi1t+g+GrmgXY0kZClEJrvftifAYMGoadElmOKRIMCyEEKEkUBPowLFu2Gr4mfptf5ZKlO/ST+TLGg/JQyAi3nZfX6sbtl9wozcGw+BewGl/1cBXDAbpNRzCJBgWQohQolt0I8q/53YVVOWeod/25yQ6bbBjMKqXwY1G/cIKfa1u2P7DSG+ZQGdfitBVwKko+qsCvpo8ZyXBcMiSYFgIIUJJQDPDToKqhH6QNkINRK38mRnWZn1TcyHi6PdEG/j0tTIJ+w8jvTYzXN35/rWH1YVXrHzVVs1KN8Gv2rfnEl4lwbAQQoSSQE2gA+dBVVY+GMMgNt12nz8X3nB1GVx7u3yXe/WlvYW2TCIy0f+vE1/xtEzC/oqAL5Zh1uruoiAi4CQYFkKIUKEodhPo/JwZdjaBzpqB1QbK9jWrvtLZZXBt4KO0O18tr7fStVVzUecdiiLi9AuqdBUMa68axGX6vlxEyiRClgTDQggRKtrbQLHYtv2eGXYSWGU5C4b9VCZRvR9aNEGHNhucnqdv+abtKtDb9cbV58BxklpX7cv8NXnOypOxiaAiwbAQQoQKbVYYwBQEE+is2Vht1s1fE+gcLoNrAh5TBGSMcr1vb6b9MNJbJs9ZeZJ99efkOdBP8JPMcEiRYFgIIUKFfd1roCfQRSVB4gDHx/yVGdZeBk/oB7Gp+sd1k+j6UjDcSzPD4H5dbmOluuCKlb8zwxIMhxRT17uIkNPaAG9dDfu+ATQr9JgiYeLVMOPBAA1MCNEj9plhf5dJRCdDWIS6sAaodbkGg3o7TlNP3NUEOks7LFsAh9bCGQth9Kyuz60o8NE9sOl/tr7C1nGA82Anazzwinq7ZBu0myGsD/zZ641LMVu5m3217yDij8ywBMMhSzLDvdG6l2D3p2o/UnOz7V9zDXy3GIr6UO2cEL2JuVm/7e/MsMGgD3qzNa2qtPXEzdVg1iyEYW/Xx7D5DajcCx/d6965D66Bn/6t1ghb39O09dPOgh3tfeZmqNrn3rlCmcWin8DY24JhdzPD2isBEfGQNNhXI7LRtVarUX8WIiRIMNwbHfqpi8fX+mccQgjvciiT8HPNMMC4C9T/DWEw4VLb/fZBV2elEuW7bbfrjkBLfdfnPdjJ+5oxHMZd5Hh/8hD9du2Rrs8T6pqqwGK2bfembhLgfvZVN3lunLoQi69pg2EUaK3z/TmFV/SB60V9kPZNYMQ5MPpX8PXjULnH8XEhROhwKJPwc2YY4PQHIHcGJPaH5EG2++0natWXQNIA58ewD5QbSiEyrvPzajN9GaPhxN+qtw1GGHSS83PFpqmPWzPI/lwMJFDs29o5a4cXytwNhrWvF3+USIDzPsj294mgJMFwb9NSZwt6AcbOhfyL4MAPtvv70kQSIXoTh8xwABZTMBhg8EmO9ztkhjvpNWzfbaKuBFKGdn5e7Yf4IdP0WWlXrIuBWMfiz2WiA6W3rj5nZV+K4Exbk7rQipU/Js+B54uCiKAhZRK9Tck2/bb1TUD7ZlCyXZ1IIoQILfbBsCmIVhaLiFVrM606m0Rnn6HtapGO1kao0JRWeJLp05YJ+GsxkEDSfm+NJohOCdxYfMGdXr4l27uuJ/cF7eQ+kF7DIUSC4d5Gmz0xRUPacPW2dqJLe4v+U7MQIjRog+GwSP/UQXpCF3h2UpJgHyh3FaSW2gU3nmT6dF0u+kAwrP3exmYE32ukp7SZ4ZZa55PUtAushEVA2kifDwuAyAT9tmSGQ0Yv+y0RujeBzDHqZULrbQya/aRUQoiQo1uKOYiywlba+tTOShI8zQxrO+CERUK6B8FNIJaJDqTeuhSzlTYzrFig1cnkS21SKD1PXYDFH8Kj9AvhSDAcMiQY7m2KXEwaiIiF1Fzn+wkhQoM2MxyIyXNdcScz3NakX0IZug5SdZPnRkFYuOt97cUHYDGQQNJ+L3vb5DlwLEVw1l4tEJPnrNxt/SaCigTDvYm5FUp32Lazxukf76urMQnRW5i1wXAQZobdycI6u7+r8gX7NlndHlNfmECn7THcyzPD4Jh9bTfr585kjcev3JngJ4KOBMO9SfkvYGmzbdu/CWTZBcOKghAihLSFUDDsKsB1lp3tLDPcblZrhq2yPQxutAFhU1Xni4H0BrpguBdmhrsKhisK9IvTBDQzLMFwqJBguDfRZk8MYZA5Wv+49k2huQaqDyCECCGhFAzXlzj/wO2sy0RnwXDFbn1w42mbLPuAsLeXStT18cyw7qqn4eh8GT+SYDgkSTDcm2jfBNJGOP6xtP8jIqUSQoSWoJ9ApwmGLW1qJtaes8C3oQws7c6PWdTD4MY+IOzNwbB9PXZvrBkOj1YnUVrZty/TTrZMGQqR8fiVtqZZWquFDAmGexNXk+esYtMgPsf5/kKI4Bf0E+jcWHjD2X2KBRornB9T+6E9Nbfrleq6M6bewv5r620Lblh1ln0N5OQ5kMxwiJJguLewWKB4i23b1aVEmUQnROgKpTIJ8KwkwtUiHdpMX3eCm8g4iNAE0L15Ep191rs3lkmA64BTUewmW0owLNwjwXBvUV0IrXW2bVd/NLRvDpIZFiK0aIPhYFp9ziomVZ2vYOWsJMGTiXWKov/Q7mknCSt3FwMJdX09M1xzSN/OTDLDwk0SDPcW9oFt5ljn+2nfHOqOQEO578YkhPCuYM8MG8MgNt227W6ZhKv7qw/oA4ruZvq0k+h6c5mENrsemRicrxFv0NblaoNf+6ud/m6rBnat1ar9f37RLRIM9xbaN4HEgRDjYj16mUQnROgK9gl0YLfIhbNg2EVm1ln5grb0Czxvq2alzQz35iWZtd/b+F6aFQbX2VdtUig+G+I0H8z8RTu21nq1NaAIehIM9xZdTZ6zShqo/2WVUgkhQoe2xVgwTqCDzhfesFigwVUw7OR+7Yf1+Bx1EnB3xPeRzLD2A0VvLZEA18GwN0pqesq+9VtLbWDGITzit2D422+/5dxzzyU5OZno6GiGDx/OQw895K/T937Fbk4aMBgcF98QQoQGXWY4KnDj6Ixu4Q27bG9TJVg0mTLtxDZnE+jc/ZDf5Zi0NcO9ORjWfKDorZPnQF+KoG1fFujJc+AYDDtrLyiCjl+C4ddee41p06aRmJjIyy+/zMqVK7nnnntQZAU076gr0b/Bd/VHQybRCRGagr21Gthlhu2yvfYBrzZ711VmuCeZPvua4d76t0f7/e2Nq89ZOcsMN1ZC7SHb/YGYPAf6emaQSXQhwuTrExw+fJgbbriB3/zmNyxZsqTj/unTp/v61H2HfV1dV5+ItW8SFQXQ2gARsd4flxDCu4J9Ah10XiZhv501Dg784PyxhgqoPazZtyeZYc2Y2lvViU3Ryd0/XrDqM5lhJ8Gww+S5QGWGk/TbEgyHBJ8Hw8899xwNDQ3cc889vj5V31Ws6cMZnQIJOa73Bbs3CQUOrYWcY9VNUxSYIrw+RCF6DYsFjAGabhEKmWHtxK3mamhrtpV0aIM1ownS82zb9sGw9n0NvFcmAerVNPtguKVeXfyjM5HxaqlZMLKvx+6Nq89Z6Sap1amlCId+tt0XmQDJg/0+rI5za9UVQ/PRuuHwGAjzedglusHnP5Wvv/6alJQUdu7cyaxZs9i6dSspKSnMnTuXv/71ryQkJHR9ENE5+7q6rt6s00aoy1m2t6jbL8+yPRaZAGc+BBOv9vowhQhp5hZ45QL19+2sR+DYK/x7/vY2dYljK1MI1AyDGqAlDVRv20/wis+2bbfWqwGpdYU57RWvqERIGtT9MdkHhvUlkHE0EG9thP+bAwd/7Po4KUPhktdtzw0m9vXYvTkzbF+K8JfB+u2scYH70BJmgoh4W9//ZTfaHotJhVlLYOTZgRmbcMnn6Y3Dhw/T2NjIvHnzuPjii/n888+5++67efnllzn33HM7rRsuLS1l27Ztun8FBQW+HnLoKd1hu+1OXV2YCTLHOH+spRY+X9R7a+qE6K4dK6DwG2ipgU//qGbi/EmbFYbgzQzbB8M1mjpO+8v4nS2VbD8ZqifBTUwqGDR/7rTn2fiqe4EwQOVe+OFf3R+HL/WVBTeg6xKXQJVIWLkaX2MFfPGgf8ci3OLzzLDFYqG5uZkHHniAe++9F4BTTz2ViIgIbr/9dr744gvOOOMMp89dsmQJixYt8vUQQ5920oS7l4Ym/wbe+43zx5oqoaUOoiRrL0SHqn2228016nbqMP+d3yEYDtKa4cQBatba2gaueCsMOlG9bT/By74Xbn2p7XvqboccdxjDIDbDlpnWBo6H13t2rKrCno3FV+wnJ/bmCXSZ49QSm7Kdjo+FRcJx1/h/TFrjLoRv/+78sdLtMk8nCPk8GE5NTWX37t2cddZZuvvPOeccbr/9dtavX+8yGL7pppuYN2+e7r6CggJmz57tq+GGnrYmNVNl5e4b4PhLYOAUdQIdqG/wH/4/2+P1JRIMC6Flv1hD0Sb/BsPmEAmGrVeeDq9Tt7VBrX1mONZuUQRrkNraAOW7bfd7o2dsnItgWFuOkXe+80Bq0xuw5U3H5wYT+3rs3jhB0CrMBL9epX6QsZb7AWCAnGNcLzrlL6ffD6N/pWaCAWqPwPu/PfqgAiXbYcCkgA1POPJ5MJyfn8+PPzpegrKWRxg7mYiSkZFBRkYvrnvyhp5cGksebMsk1xY5BsNpw3s6OiF6D4cJXpth7Fz/nT9UyiRAzeQ6DYbtaoZNkWrQZu3Fav0el2wDNKVa3miTFZ9lG4v1g425Bco0ZWbDz4RcJ8mZyn0hEAxrxhWXGbhJnv4SEQtDTgn0KJwzHA3Krdrb4MO7bIF78SYJhoOMz39bLrjgAgA++ugj3f0rV64EYMqUKb4eQu9mn63q7qSJ2HRAU5MXrG/4QgSKfR9cf/fo1i64AcG76Abog9fSHWowAM6XC7bvAQxq1t0qLFKd9NtTzhbeKN2hn3TmKujWJhmaa9QOGcFGFwxLEimohIVD5mjbtvT3Dzo+zwyfeeaZzJw5kwcffBCLxcKUKVP4+eefWbRoEeeffz4nn3yyr4fQu3lr0kSYSV3qtKFM3bYPsoXo6+rtajKLN6sTTf01az3UMsNW7a1qbWfKMP3StNb3qrgMW3bW+r6jLV3IHK0GEz3lrP+xNmttNEH6qK6fa31+cg+6W/iCLhjuxfXCoSprHBzZoN6WlV+Djl+uo7zxxhvcfvvt/Oc//+Gcc87hmWee4Y477uDtt9/2x+l7N+0bYFRiz7JFnTXLF6IvUxTHzHBDmX9/T+yzkcFaMwyQMVrfvaF4i5MP7kcDtngnmWFvTp6zP5/2PNoMXdpI1++f9plWZ6vlBVqdZIaDmvZ1XLLddrVEBAW/BMPR0dE89thjHDhwgLa2Nvbv38+jjz5KZGSkP07fu3kzGyDBsBDOtdQ5limAfy932p/fFMTBcESMvrShaLNjAGkN2OzLF9rb1GDBylvL6mrP01Sl1gsX2/Vod/lc+8xwsfP9Asm+ZlgEl+zxttvtLVC+K3BjEQ56eYV9H+DNOjEJhoVwzlUm0H6VNF/SlkkYw4N/JSttJqx4s2MAGeeiZrh8l75DgLcyw/YLb9QVq23f3DlPRIx+ZbFgfH/Ujsm+ZZ0IvMwx6OblaEuBRMBJMBzq6ryYDdC+gUrNsBA2rjKBgcoMB3O9sJU201q8Rd8HV1vSpX3faiiz1VUCYHC9QJCn7JMFB36Atgbn43X6fG2yIMjKJFobnddji+AREavv0CST6IKKBMOhTpcNkDIJIXzC1e+DPyfCmDU1w8FcL2yl7Q3cUgsHf7Jta99rtEGqYoG9X9q204Z7b3EC+wCx4HP9dle9jLXPt1/gItAa7EtQZAJdULK/WiKChgTDoc6+iX1PaJ/fWCEF/kJYucoEVhWqrbb8QZcZDoVg2C7TuucL221tYGn/Ib5As583l9WNiIWIeOfnSR6sZqs7o6ttDrLMsLdabArf0n7gsnajEUFBguFQZrHoMwI9nkCnfb5ia7MmRF+nzQRGxOkf09ad+pK2ZjgUguGYFHVpZivrwhrgOjMM6nLwVt6aPOfsXNrzuLPCna7rRZBlhr3VYlP4lvb13FwD1fsDNxahI8FwKGuq1DeM9+YEOpBSCSGstJnA/sfpa3b9dbkz1IJhcJ3Z1QaWUUnqwhqePL+7XJWSZY13fr9WMGeGvdliU/iO/etM6oaDhgTDocy+bs2bE+hAJtEJYaXNBMbnQOZY27a//qDpguEQmEAHnazopgksDQbX713eDoZdJQzcyUDrul6UqlfmgoW0VQsNsamQ0M+2LXXDQUOC4VBmn7nt6QS6iDj9H1nJDAuhsq/Nzw7ARJiQzAy7KD+wL+ly1gosoZ8aPHiTq1Iyd4JubSBtadOXfQSaNjEiwXBwy7LrsiKCggTDoUwbrBrDITq5Z8czGIL7UqAQgWLftUX7B61sp7qAg69pJ9CZQuQyuKsg0z5D6yyA83ZW2Nl5AWLT3Usk2O8TTMkC3Yc1CYaDmvaDtJRJBA0JhkOZ/aUxg8H1vu6KC+JJIkIEQrsZGspt23EZ+oynxQylO3w/jlAsk0js7/xDun3A5ixI9fbkOWfnBTXodue9M5hXoZMyidChfe+oO6J/bxEBI8FwKPNmWzVnxwmmzIcQgdJQBmhaIMVlQsZoMITZ7vNHqUSotVYDNch0luG1z7I6K1/wRWbYWTmGu0F3dAoYNav+BdOVM1l9LnTYv66L/LiKpXBJguFQ5os6Me0fKZlAJ4STZYSz1Nn66Xm2+/xxuVO36EaIZIbBMdh0VtIV0MywG23VAIxGiA3CZIHFImUSoSRpoNpBxUom0QUFCYZDmfYN0FvZAMkMC6FnnwG0/o74exJdKE6gA8dMmLOSLvtMcVSSvkextzjNQLvRVq3j+Zr3x2BJFjRWgNJu25ZgOLgZDPoPYFI3HBRMXe8igla9DzLD9u2DFMU7tci+0HY0UyY9NYUvaT8UhsdA5NFVzLLyYdPr6u3irWBpB2OY4/O7q7lGvyqarkwihF7zDsGwkyyw/X1Z43zzvhOTopa3WIPHiDhIGer+8+OzoOjobV8lCywWqNrn/v4VBfptCYaDX/Z4KPxGvS2Z4aAgwXAo88WlMe1xzE3QUtv1MqWBcOBHeHUeYIAr3lUXQhDCF7QZwLgMW5Cmze60NUDlPkjL7fn5FAXeugq2L4exF8AFz6vnDMUJdABpw8EUrb6fgPP3Kvv7sj3I1nrCGKZ2j7AmEjLHquUP7vL1lbP6MvjvaVBzoPvHkGA4+Gk/IFbsgZZ6iIxzvb/wOSmTCFWtjWqgauW1YNguQxNMk0S0vv2H+vW31MB3TwZ6NKI3czVT377WtNhLE2GKNqmBMMDWd6Bkm3o7VMskjGH671ViP8d9YjPUWmIrXwXDoHa46O55tD9/XwTD617sWSAcHtPzFpvC93TvHQqU7wrYUIRKguFQ5au16O1r9+xXuQsWRzZqbstsXOFDrsqRopMgaZBt21u1f0UbnW+HamYY4OQ7ICxCvco08WrHx00RMGWBejt9FIya6buxTFlgG8vk33j2XF8Hw9r3NY8Z4MRbPct0i8BIsquHD9akUx8iZRKhyv6Xx1sT6GLSAAMdraSCcRJdfak+QKk5AI2Vaj2gEN7WWTlSdj5U71dve6v2zz6oLtoM49uhXbOwR6gsumGVdy7cvUfNEkfEOt/nzIfghFvUMgZfBnTjLoRhp6n1wqYIz56r/fk316gfULyZpde+hiZeA8dd6/5zY9MgIcd7YxG+ExkP4bFqeRUEV8/qPkqC4VBl/8sT66U+w2Em9Y9Rw9EAIBiDYWcZuOItMHSa/8cier/OerhmjYcdK9TbRZu9M+HUPqgu3qzPCkPoZYYBohK63sdfPXK7+8HZYRW6Ukge5HxfTzVWQs1B2/bQU33TXk4Eh7gM20RJyQwHnFxPCVXaX56oJO/OLvf1pcCecpaBkzXehS8oit0EOieZYavG8p6XFVnabTXCVsVb9Z0kILRqhnsThzkVXnx/tH9fk0C4d9P19JfMcKBJMByqfLHgRsfxtDOmg/ATq9NgWNrTCB9oqbN1QQDH3zWHSXQ9fB1W7HEMfFvroHS7/r5QzAz3Bg5LMnsxGNZe8YpMgKTB3ju2CD7S0z+oSDAcqurt2j15U7B/YnVWJiGNy4UvdDVRNT77aJ39UT19HboKpg+s0W+HUp/h3iQ8GiI1rSa9mhnWXN3KGicT4Xq7YL8C28fIb1uo0q0+52RVpZ4I5sxwSx1U7nG8v3yXY12lED3VVTBsMNitRNfDziZFLp5/0D4YljKJgPHVKnTaD0L2C5WI3keC4aAiwXCo8sXqcx3H065CF2SZ4eKtzu9X2qFku/PHhOgu3ZURgzq51J42cPFVZvjQWv22lEkEjjb54K0gprVR32vWvvxG9D7av9t1Jer8BBEwEgyHKl+sPtdxPE3mo7EC2tu8e/ye0F5KNEWp/UI7HpNSCeFl2t+z2DS124o9bWa4ej80VXfvXIqif31rL8drF9gByQwHki9qPUu3g2Kxbcvkud5P+6GqvUVt1ScCRoLhUGRp93EwbHe8hjLvHr8ntJehM8dAep7mMQmGhZe5Wn1OK8tuFbMSF1cvulJ7RP3waTXuQtf7miQYDpg4H2SGteUxYRH69zXRO4XKaq99hATDoaixUi0LsPLlBDoIrkl0RXZ1ddlevEQthD13guGUoWoDfavuvg7tP8wdc5nz/QxhEBbu/DHhe76YU6H92WeMkp9vXxBn37M6iP7O9kESDIci+18aX06gg+D5xGpuhdIdtu3sfH29Zsk2NWsuhLe4EwwbjZA11rbd3SsU2iA6NgNyjoVoJ4tDhMf0fGEP0X32NcMWi+t93aXrJCElEn1CbBoYNCFYsPyd7aMkGA5FXc1w7ynrUpEd5wuST6xlO8GiqV/OGq//w2FugvLd/h+X6L3qOll9Tssbk+i0QXR2vmOnCiupFw4sbbLAYoamqp4dr92sX2gle7zrfUXvYQzTt2UMpiuwfZAEw6FI+wnSGA7Ryd4/RzC2V9NmTwxG9XJi1ljA4HwfIXrKncww6IPW8l+grdnzczlrreWsq4AEw4HlsPBGD4OYit1g1rxeJDPcd8RLe7VgIcFwKLJffc4Xl0yDsQeiNlhIGwERMWoWO2WoZp8e9nkVwqq9TT+hrbPafG0AYzFD2Q7X+zrTVAXVB2zb1uDafnIeSDAcaA61nj18f9RdSTCoE4NF3xCMf2f7KAmGQ5Guk4SXJ89ZaT+xBsvlG/vJc1YyiU74QkMZoOn9aR8EaWWMAqOm7Zqnr0P7KxrW17eUSQSf6GT9z7qnV860H/JTh0FkXM+OJ0KHLzqTiG6RYDgUaS/LeXvynJXuE2sQlElYLPqAQRskaC8lF2+W5uXCOzypzTdF9qzNnzZ4joiH5CHq7dRcxwU2ZMGNwDIa7RZM6GGyQNtWTUok+pZgLEfsowISDD/33HMYDAbi4uQTcLf4IzOsC4aDIDNctQ9a62zb2j8a2kvJTVVQc8h/4xK9l/1Su51NoIOeTaLT1QuPVQMuUCfZ2F82l8xw4HkriFEUx4mTou/w5ocq0SN+D4YPHz7MXXfdRU5Ojr9P3XvoJvX4KTMc6GyrfaZNmw22/wMii28Ib9D+noXHQEQXH961r8OSrZ61+XNVAuRs2xTl/nGFb3grWVBzUL/ymGSG+xbtB+ymSrV9qAgIvwfDN954I1OnTmXGjBn+PnXvoc1Y+axmWBNkm5sDv1SktkQicSDEaPqvxmXoPxRIRwnhDfarPHY1UVUbyLQ1QuVe987T1gTlu2zb9h/u7LelTCLwvFVGZn8FQdqq9S0Oq71KqUSgmLrexXteeeUVvvrqK7Zv386f/vQnf56692ht0JcLeLvHcMdxnSy8EZ3km3MB1ByG6v2uH9//ve22s3ZT2fmw+2iGpvBb2/6GMPUPTLhk04SH6u26tnRFu/AGwLZlMPikrp9XuVe/oqRDZtju9S5lEoGnfT1U79e/P3li9ye22/E56kIMou9waNNXAon9AzOWPs5vwXBpaSm33347jz32GP37u/fDLi0tpaysTHdfQUGBL4YXOuwn9fhjAp31vOkjfHOuDa/A8lvQzdzvjLO6uqxxsPtT9XbhN/DiObbHYjPgph8hNrXHQxV9SL2HV2CiEiF5MFQVqturH/b8nMZw/UQ8gIwx6oc6a8AsmeHA017erj6gf7/pLmcf8kXArT9QxZtrD5IUE8GEAYnk908iOzEKgzdamtr/nbWfpyD8xm/B8E033cTIkSNZsGCB289ZsmQJixYt8uGoQpC2Fyn4LjMcm64ubKEcXWrUl21fvv8XbgfCADnHOLnvWNf7N5TC5jfghJs8Hprow+o1H8Td/T3LOdYWDHdH5hgwRejvC4+CzNG28h/JHgZe0mDvH9PZ+5oImMZWM49/sosXv9/nMGUmPT6SiQOTOWdcFqePyiQuspuhVGScutprW4O6Le3VAsYvwfA777zDihUr2LBhg0efpm666SbmzZunu6+goIDZs2d7eYQhRFtjFpkACf18cx7rUpHWGiZf/ZK2Nakrdrkr9wz1n70RZ8PQU2Hvl86fJ5PqhKe0dfLurvJ48h2w/7vu/b5EJsL0Pzh/bPqf4L0b1Ksc4y/x/NjCu4ZNh6HTYe9q7xwvNRcmXe+dY/VxiqJQ0dDKntJ69pSpQebpozLITHC/VO77PeXc+84WDlQ2On28rK6Fj7cV8/G2YiJNRk7Ly+DssVkkRIXTYrbQ1q7+y0yIYlz/RBKiwl2fLD7TNr9A2qsFjM+D4fr6em6++WZ++9vfkpOTQ3V1NQCtreqsyerqasLDw4mNjXV4bkZGBhkZPpogFqq0k8OyxtlaMPlCfKYtGPZV25eS7bbsM8CV70P6SOf7hkXoJ87pHjPBlcuhoQIsbep9qx+B9S+rt2UxDuGp5mrb7ahE956TnQ937ji6YIeHopPVfsXOjDwb7t6jXq0xhnl+bOFdxjC4cpn+/abbDGoZji9WEu1Dvt9TzpLVe9hyuIaaJv3PJPx9AzPH53D9yUMZnZMAQHFNM98VlLNmXwXl9a20tVtoMVtobmtn8yH9hPEIk5H0uEgOVzc5nLfFbOGjrcV8tNX138ih6bGM75/EMQOTOC0vg/7JmlKnOG0w7N/2aoqisLe8gZ8LKzlc3czYnAROHZlBhMn9uKLF3M6hqiYOVjZysKqJMIOB/snRDEyJIScp2qNjBZLPg+Hy8nJKSkp44okneOKJJxweT05OZtasWSxbtszXQ+kdijtpweRtcZnA0eDbV59Ytcsnh0XAwBMcLxN7QlsX3P94WzBcthPammUinXCfNjPsbjAMaqDki1r+sE6yS0KnpLaZtYWVrN1XydrCKvaVN3DaqAzuO280WYlefA8IkXkIlQ2tvLH2ICW1zYzKjmf8gCSGZ8QTZuw8AC+ra6GmqY1+SdFERwTnh7C65jb+/NFOXltzwOU+be0K764/zLvrDzNpcDKVDa0dWeOuTByUzF8vzGdYehxldS1sPlTNhgPVfLKtmN2l9W4dY29ZA3vLGnhvw2HuX76NMTkJnDUmizPHZDIyLpOOn4Ld31lzu4XKhlbqWsw0tJipbzbT2NpOhMlIXJSJuEj1X1JMODER7oVzheUNrP6llB/3VvBzYRUVDfp2bskx4cwcn8PcY/szrl8iDa3qeRtazJTUtrCnrL7j396yBoprm112XjUaYEhaLL87O4+zxvhofpOX+DwYzsrKYvVqx0tJjz32GF999RUfffQRaWlSA+eW1sbOWzB5mz/WTddmbNPzehYI29NOSFHaoXQ79OuktlgIK3Or2h7NypNgWHRbY6uZA5WNHKhQs0wHKxtptyhkJkSSmRBFVmIUmQnqv4QoU0fZXXNbO2v2VbJ6Zylf7SpjX7ljoPPh5iK++qWMu88ayeVTBnUZCPYG7RaF/609wF8//sUhWxodHsbYfgkMSYtlYEoMA1JiyE6MprC8gZ8KK/m5sJLCCtvvQFpcJANT1IzfSblpnDMuu/u1sm6wWNQIy9jJz2n1L6X84d0tFNU0O308wmSkrd2iC9bWFla5df7o8DB+d/ZIrjxhcMdrJT0+ktNHZXL6qEzuOmskvxTX8cHmI3ywucjhNWcyGjBbnEeJ247Usu1ILX//bBcPRzZz+dEvsfhwIa9++gt7yuopKK2nsLyR1naL02PYi48ykZVg+/1IjYsgOSaC1NgIoiPCWLe/yuXvhlZVYxsv/7Cfl3/opLuTmywK7ClrYMEr63jxmuOZNiK9x8f0FZ8Hw1FRUZx66qkO9y9dupSwsDCnjwkXSu1KCnw9+9gfwbAvV1/KGAVGE1jMtnNJMOxTiqJ4Z5Z1oLXU6rd92VZQUFrXzGMf7eT9jUdcBhD2osPDyEqMIjkmnB1FdTS1db3ISX2LmQfe38Z7Gw5z3clDaGw1U9XYRlVDK5HhYfxqfA65Gd5bGVVRFIprm9lT2tCRTWtsbefUkemcNy7bp78rmw5Wc9/yrQ6X/K2a2tpZW1jldnBYXt9CeX0L6w9Us2zjEe5bvpWzx2Qx99j+nJSb5vDhorqxlR/3VvBtQTn7yhsYnhHPtScNYWBq591QqhtbefzTX1i24Qgt5nYy4qPITIgkKzGKKFMYlY2tVDW0UtHQyqEqfdlCdHgYv546lAkDEslNj6dfcjQHKxt54bt9vPXzIaevkbyseEZlJxBpMhJhMhIeZiQlNoJfjc9hQErnYx2ZFc/IrJH8vzNHUtfchtFgIMJkxHT0e1FY0cjmQ9VsPKj+23SwGvuX9xFzIhy96GOuLeapVd3rmFXXbKauud7tbLWW0QBJMRFUNvRs0Y+YiDAsikJzmz6Atyhwy2vree+mk7z6+9WZNjc/RFj5tc+w6KEiu5IC+xZM3ubrYLjdDCXbbNtZXm44b4qE9FFQcrTUQxbj8Imm1nY+3FLEG2sPsPlQDaflZfCHc0d1+YckqDVV67clM+wT5nYL//fjfv7+6S7qWswePbeprZ195Q3s62SfIWmxHDcomWazhRWbjnTcv/FgNb99fYPD/k+vLuCSSQO4/YwRpMe7qN/uhMWi8EtJHT/urWDN3krW7KugqtGxpvjtdYd4Y/hBHp49lkGpjvNleqKt3cJfP97Jc986dkEYlBrDoaom2t38wNGZ5jYLyzYeYdnGI4SHGUiOiSAlVs1G1reY2XqkRnf+7woqePmHQmaOz2HBqcPIy0rQHc9iUXh73SEe+3inLig7XN3ktFbX3onDUvnLBfkO7zuD02J5cNZY7pwxgtd+OsD6/VWkxkZy0vA0Thia2q2fszPxTibJDUmLZUhaLLMmqBPdKxta+XxHCZ9uK+Gb3WW0mC2UYXtvSacatbOSbxMKJqOBYwcmM3loCpMGp3DMwCRiI0ysLazk3fWH+XBLEfUufh9jIsIYlh7HsPRYhqbHMTgtlgFHa4RTYtUru+X1rRyobOSrX0r559Hgvq7ZzPUvrWXZzSeRFOPFK8BHNbSY2Xiwmp/2VfLz/kp+/HlT10/SCFgwvHTpUpYuXRqo04cmbTCXMcr3NYTaXpqNFeqlY2+WMVQUqKvbWfmi7CM73xYMyyS6biuqaeLDzeobZFykidhIEzERYawtrGT5hiO6QOajrcWs/qWUW6bn8uupQ4k0BWetYafsV1yUYLhH6lvMvL/xCIerGwkPO5qBMxp5d8NhdhTVOn1OUkw4A1NiCA8zUlzTTGldM23tnQdx6fGRnDoinWkj0zl+SAoZ8bb64IuPG8Afl21hf4XzDgGglhW8uuYAyzYc5oapw5g/eQDpcZEuM7gWi8LO4qPB774K1uyrpNpJ8OvMN7vLOfMfX3Pr6cO5YepQwsMcJxqV17fw36/38tWuMo4bnMzN03PJTnS96EpZXQu3vLaeNfsqdfcPSo1h4a/GMH1kBk2t7Ww7UsPGg9XsLK5TJz5VNlJ0tPbTYIBRWQlMGpzMpCEp9E+O4Ui1WrJyoLKR9QeqHX5mbe0KpXUtlNa1dPo1WxRYvvEIyzce4bhByeQkRXcE0F/tKmX9gWq3vnda8ZEm/nDeKC6ZNKDTTHtSTAQ3nZrr8fG9KSU2gouOG8BFxw2gsdXM+v3VNG+vgqOfyyINZkYnK2RmZKgBZ0Ycg1JjSIwO76gPjokw0Wq2UNfSRkNLO/UtbZTXt1JS20xJbTPFNS2U1jVT1dhKVUMblQ2tNLW1kx4fyfSR6UwfmcFJw9OcdriYPDSVyUNTWfirMfy4t4LG1nZiI8OIj1Lf85OiI8iIj+y0dAXU38P0+EgmDkqmqrGN//tRLbkorGjk5tfWs/Sa452+3t1RVtfCG2sPsOVwjfr1Hb1SUNXYqsu6t7pxpUhLMsOhxJ+T58DJUpFlkOjFVm66dmcGtceqt2XlA6+qt0u2gqVdZuN7oNVs4flv9/HPL3a7dRnaqrnNwuOf7uKd9Ye5ZXoug9NiyUyIJCM+igiTEYtFobGtnfpmM01t7USajMQefbPvrJbzcHUTb649yNe7yxjXL5G7zhrZedui7tJ2kgCISvL+OfqINXsruOvtTRys7Dq7d35+Nr+ZOozBaTEOmTaLRaGqsZVizR/94tpmyutbyEmM4tSRGYzOTnD5h/rk4Wl8cvtUnlq1m5e/309di5mocCOpsZEkRoezq6Suo0SjobWdf3y+i398vovo8DAGHK2VjYkwqROZjv47XN3kdvBrzagV1zZTdjRobDFb+Nsnv/DG2oOcNSaT6SMzOG5wCjVNbfzn6z288uOBjt+7ncV1vPnzIa6cMogFpw4jNU6f0Vx/oIoFr6yjpNYWkEaajNw8PZcbpg4lKlx934uOCOO4wSkcN1jfmafF3E5pbQtJMeEO3/sJA5J02zuKanlvw2He23C442txZWBKDMPSY/lmd7muBObn/VWw33WJxvSR6ZwzLpuyuhaKa5oprm2mrd1CSkwEybFqFjo9PpLT8jJIi/NOdtefYiJMnDw8DeLyO4JhgJXXjnDdUemo6IgwEmPcf99rMbcTEWZ0uywnOiKM6Xne6eR1/8zR7Cmr5/s9FYB6hWDRim08NGusR2VCvxTX8fy3e1m24YjbddSekGA4VNiXFPhjDXunS0V6MRjWln2kDIXIeO8d20pbV93WCBV7fLeSXi/zfUE59y3f6vas65GZ8eRmxvHh5qKO+/aVN/D/3tJfroqJCKOx1XVgHR0eRmZCJHlZCYzKTmBUdjxmi8IbR4Ng66XXDQeq+fKXMp6afwzj7f5Y95guM2xQe3oLQJ2strawknaLwoCUGPonRzvN/je3tfO3T37hhe8cL9fbG5auXso+Kdf1ZGqj0UBqXCSpcZGMyelepj4qPIy7z8rjzhkjaTG362bgF5Y38NdPdrJyi769VVNbO7tK6tlV4n4tZniYgWMGJDNlaAoTB6cwIjOOrAR11bLa5jb++vFOXl1zoOP7cqCykf9+s4//frOP2Igw2p3UXYL64fS5b/fx+k8HOHdcdkeA22Ju570Nh3WZ86FpsTx7xURGZLr3vhppCnO7tEn9vUzgd2eNZN3+Kg5VNVHV2EqlNUNngWMHJXHisLSOYx6qauS5b/bxv7UHnH5tVv2Soln4qzGcMSqjd8w/6IrDKnTFXQbDngrk1bnwMCNLLjuWWU9/13FV5pUfD1Be18pf5+V3msxQFIVvdpfz3Lf7+HqXe+0qk2LCOW5QCv3yjDz4gvvjlGA4VFTs1pcUBCIz7O26YV9OnrOyn2RYvFmC4S60mNv5w7tbeWf9IYfHBqfG0NjaTkOLmYbWduIjTZw7LptLjh/AhAFJGAwGrju5ivuXb2XrYeeXvzsLhEENPgorGimsaOTjbZ333TxQ2cgFz3zP784eyfUnD8VggKKaZnYU1VLb3MbxQ1Lpl+T6srJVQWk9L3y3jzV7K4iLNHGJcTPzjz7WFh7H9sO16uXc2AhiI8K89ke6vL6FN9Ye5O11h2hqbWfhr8Zw9tjgbEF0qKqRV9cc4I21B3U1nQYDZMZHkZ0URXxUOPGRJmIj1dnr9h+k+iVFExlupNVsodVsIS7KxLyJA7ju5CF+7UcaZjQ4tKIanBbLkssmsv5AFX9eucPtiWUAEWFGJgxMYsrQVKYMSeGYgckuW5ElRIXz8OxxzDmmP394dwu/lNTpHm9w8vuR3z+RLYdtNbgNre28tc7x99NqxuhMnrhovG+ummiYwozqpXU39u2frJZq3HJaLm+vO8TesnoqG9qobGihqrENowHOy89hwbRhQdvGzSdi0+xWe+19C28kxUTw/FXHMefp7ztK6j7eVsyO4lqWXHasw4fb5rZ23t94hOe+3evyQ+hJuakMSYvVXSkYnZ3AsPQ4jEYD27Zt40EPxijBcKjQTf7yUUmBPV8uFako+hpeXwX3UQmQPASqjk6zKdoE4y70zbl6gea2dn7zf+v4yu5TeF5WPA/NHsskzaVVi0XBYMAhMDx2YDLLbz6Z19bs5z/f7HXr8rgnwowGBiRHd7R9MlsUHl25k/+tPUhFfauuhZTJaODCif25eXquQ9ZLURR+2FPBc9/uY9VO/R+gE8KKOmZ4l7RGMuvp7zoeS4gyceHEAdw0fZhbl2eb29rZX9GIRZMerWps5a2fD/Hh5iLdJb+bX1vP05cew9ljs93/hviQud3CNwXlvLbmAF/sKHGYCQ/qr3JxrXoZ25UIk5HfnTWSa08a0mW9YaAdOzCZt248kQMVjeyraDi6mIBaV9tqVoiLDFNLeqJMJEaHM2FAEscOTO7I0rpr4qBkVvz2ZD7dXsyqHaV8uavMYTb/maMzufX04Yztl8jO4lqe+HQXn213/T5sMMBdZ45kwbRhQft9TouL5MZpwwI9jOBhDIPYdNvfVz8vvOEvuRnxvHjNJBa8ur6jtGZ/RSNzlnzPraflEmEyUlzTQkltc8dCKPYiTUYunNifa08ewrB073alkGA4VGhLClKHqYGqP2iXiqzzYjBcc0hfl+nLnsnZ+bZgWDpKuNTYaub6l37uqO0CdXLKnWeO4IopgzDZTXjo7I9tmNHAFScM5ooTBnfUIhbXNlNc00xDi7mjPjguykR0eBgt5nbqW9Qa4rrmNvZVNLCjqI6dRbUdk3IGpERzyaSBXDixP2lxkSxZXcA/Pt/VEaDtdVLOYbYo/O9o5vWCY/szYWDS0WVa1cvermapJxhsk6xqFP1s/9pmMy98t4831h7gupOHcP3UoboMnLndwubDNXxfUM53BRWs21/ldo1bu0Xhltc28MzlRmaMzux03+a2dlraLB7VDrpr+5Fa3l1/iGUbj1Be33lNaFfG90/kiYvGk5vhgzIoHxqYGtNlG7CeijAZOT8/h/Pzc2i3KGw5XMPXu8potyicOSZTlzHLy0rgv1cex4YDVbz0faFDb93UuAgunzKIE4dJ3/6QE5ehCYZ91MY0CBw3OIUPbz2Z217fyA971b8zrWZ1fkln0uMjueqEQVw6eVBHxwpvk2A4VPh78pyVbqlIL/6SFtt1dvB2WzXdsfNh+3Lbea1TpkWH+hYz1764lp8KbbPQB6bE8Or1k3vcIs1ai9jd45TXt9DQYmZAcowuAP/t6cOZMiyV217fwBEXTfetzBaFN34+yBs/H3S5T0SYkZnjc4iNDGPU7nY4enWuVnHe+qqhtZ1/rirg5R/3k5se1zGrubqprcsaWXvHDExiw9GZ9GaLwk2vruM/VxznMInFunrU6l/K+HFvBW3tFm6cNozfnTWyx6UbpbXNLN94hHfWH2JncZ3TfcKMBs4cnckVJwxiRGZ8xxKsBysbKatrUSeWNZtpaDVjURROy8vkqhMcP0gJR2FGAxMGJDlMVrN3zMBkjhmY7J9BCf+Iy6JjtVdvJp2CUEZ8FK9cP5knP9/VZU/lvKx4rj9lKDPHZ/u87lmC4VBgX1Lg65XntOI0f4y9GQxrv574bIjz4co02smGjRVQe8S7EwFDTEOLmTX7KiitbekI4L4tqNC1SxqaFstrv57i3aVruyktLtJlOcKkwSmsvO0Unl5dQEV9KyOONtAflR1PY0s7/1pdwHsbDnfaVzUlNoIrpgzi8imDbD1H34qEo/NVj8sbzFdnn0plQyvl9a289fNBPtVcqq5ubFNnxnsoPtLEhcf154opgxiaHseL3+1j0YrtgNqq6jevrOOcsVnUNLVR1dhGaW2z05W2nvlyD+0Whd+fk+dRQNzYauZgZRPbi2pYtuEI3+wuc1oGAZCVEMW84/pz6eSButZeaXGREpgJ0VP+WOAqiIQZDfy/M0cycVAy976zhZK6ZtLj1IVVMuKj6JcUxYzRWZyUm+q3SZQSDIeCmoP6kgK/ZoY1k3l8lRn29Up6zibR9cFgeGdxLa/+eID3Nhx22VAdYERmHK9cP1nXozWYJcVE8MfzRjs+EA+PzxvPLdNz+dfqAj7YfASLRW2En5uhNo3Py07gtLwMx3pPTTeJ8NhkBqXGdiyOMGN0JhsPVvP4J7/wbUG5y3HFRoRx/JAUTspNY9LgFGI1S9caDDh0YbjmpCGY2xUeWbkDUC8fLt94xOG4zvzn672YjAbu7iRDXFzTzP/9WMj3eyo4WNnotCZPKzo8jHPGqiuMnTAstU8sXyxEQGh7+vfCCXSunDoygx9+fxoWhYC/v0gwHArs61z9Ggz7ITPs668nPgtiM6Ch1Hbukef49pxBormtnZVbinh1zQHWuZG9HJ2dwCvXT/ZZXVYgDE6L5fF54/nrBfkouPmmq22t5qTH8IQBSbxy/WS+Lyjn423FKArqjOaYcJJjI+ifHEN+/0SPG8v/eupQWtvV3rOuhBkNTByUzOQhKbzw7b6O7gNLvtxDeJiRO2bou6VsPVzD89/uY8Wmrpc6NhjUlbzmHtOfs8dm6QJ4IYSP6DLDvXMCnSsGg4GwIPicLe90ocCfJQX24jWZ4boS79TbNlZCraYtkD/KPrLzoeBz9bZ9vXIvtLesntfWHODt9YdcLgoQHR5GytGWNMmxEUwYkMR1Jw8hMdrHKxsGiEez67VXYjpZfe7E3DRO7KQ3bnfcPD2XpJhwlm880vEzUpe6DWdYehwn5qZ1/Iymjkjnqhd+6mhXt/iL3fy4twJTmEFdparZ7LL+V2t4Rhxzju3H7An9yHGjFZ0Qwou0SaemKjC3gCn0FhIJZRIMh4JATZ4D/SfW9hY1Yxad1LNjOkye88PXlNX7g2FFUfhyVxn//XqvriOEVlS4kVnj+3HZlIHk90/y7wBDiS4z7P+lmC+bPIjLJg/qcr9Jg1N4/qpJXLP0p46FDOyX4tUyGOCMUZlMGpzMwJQY+ierExt76wcgIUJCnF1v8fpSSBoQmLH0URIMh4JATZ4D5wtv9DQY1n49kQmQPLhnx3OH9vtWfUD99B3dOyb+tFsUVm4p4pkv97C9yPlCFyMy47hs8iBmH9NPAp+uKIo+GO7p693HThiWynNXTuLal9bSanbewi0mIoyLjhvANScN7qh9FkIEiTi7pY8lGPY7CYaDnX1JQSAzw6AGwz1dKtJ+8pw/Zovaf9+Kt8CQqb4/rw/tLavn0+0l/O+nAx0LUGhFhBk5d1wWl00ZxHGDkvvG0qbe0NYE7ZrJZQHIDHvq5OFp/O+GKfzvpwOYLQoRYUYiTEYiwowMTI1h1gT5ECRE0HL4O9u36oaDgQTDwc7+kr6/M8O+WCrSn5PnrJKHQEQ8tNbZxuDLYLipCgq/A4vrrg2A+sEiY1SXh1MUhfL6VgpK6/m2oIxPt5Wwu9T5MpXp8ZFcc9JgLpk0sFdNhPMbbVYYQiIYBnXltGOlzZkQoScyDiLioPXoe3ofaK8WbCQYDna6koJESOq6jtCr7JeKrOvhJ9bWRqjYbdv2V3BvNELWWDjwg7rty7rhhnJ4aqJ+ElZnZi2BYy5zuHvLoRpeX3uAHUW17Cmtp7a588B6YEoMv5k2lAuO7e/x0rBCI0SDYSFECIvLhEprMNx32qsFCwmGg502cMwcE5iV07y5VGTpdluWGfxb9pGVrwmGfbgs87b33A+EAda9qAuGNx+qZvHnu/liZ9dviOFhBk4YlsYFx/bjvHHZstKXNzgEw0kBGYYQog+Jy4DKPeptCYb9ToLhYKddmjFQC0Vol4rsaTBctMl2Oyyy5/XHntBmoct+UWtDw33QRkr7Nbqh9fAW/rx8M7FRkWwvqmVVF0FwbEQYp47M4MwxmUzPyyAhSmpBvcr+g4xkhoUQvqb90G3/gVz4nATDwU4bfNoX2fuLN5eK1JYnZIyCMD8GctostNKuZqn7TfT6aZoObsAaYr8fNoM3Mu9kYEoMqXGRbDhQxdr9lUyw7OTNyIcAiFCa+frHH9mjOH7YiYkI47xx2YzMimdYRhy56XH0S4r2rGeu8Iz2D5EhDCKk+4IQwse0H7olGPY7CYaDXVAEw9pV6Hp4+abIj8sw20vPA2M4WNpsY/FiMNzYauafn+7gjrKdcDRWXdM8gO/2VvHdXu3qbwa2o6/9HmPYrwuGYyLCuOrEwfz6lKEyCc7f7HsMSxcOIYSvaVs4SjDsdxIMBzOLRR98BioY1q1C14MJdO1mNRtrlT2++8fqDlMEZOTZ6oW9MImurd1CaV0LWw5V89AHO4iv+YV7I20T3bZZBjt9Xj0xHDRkM0ApAuC0pGJ+CY/HYIDT8jK4XoLgwGmqtt0O8h7DQoheQjLDASXBcDBrrFAv51vZN+b2F91SkZVgblUDS09V7AZzs23b3z2TAbLGa4Jh9yfRKYrC4eom1hZWsrawii2HaiiqaaaioQVFse13gbGw47YFI2ecOp2hNRYOVTZRXNvMwJQYTh2ZzvS8DPqvngzblwEwO6uc2VeGdt/jXsPNpZiFEMJrdMFwdcCG0VdJMBzM7Otz47Oc7+dr9ktFNpRCYn/Pj6MtkcCgdsfwt+x82Hj0dsk2sLSr7eNcKKpp4unVBXyxo5SimmaX+1mN0QTDxrTh3HJWJwF/1riOYJiizerKZ3JJPvACvBSzEKIPksxwQEkwHMzsg+FgqBkGdVzdCYa1ZQmpuWqjcX/TZqPbGqGiwGlHi7rmNp79ag/Pf7uP5jbnS9zaS42N4LyEMrCWB3fVQ1lbJtJUCbWHu/d9Fd6lC4aTAjYMIUQfon2vMTdDWzOERwVsOH2NBMPBTBsMG8MhOkCrSzksFdnNSXTalmP+njxnZZ+NLtrcEQxbLAqFFQ18tauMf60qoKKh1ckBYHhGHMcNTmZoWhyZiVFkJaj/chIjMP3tWtuOXZWB2D9etFmC4WAgZRJCCH+zf69prpFg2I8kGA5m9p0kAnUJ3X6pyO5MolMUfWbY38tKW0UlQMpQqNwLwIHtP/Dsnjy2H6nll+I6mtranT5t1oQczs/PYeKgZNcT2yr3QUutbburrzE+U/25Wn/OxVsg71xPvyLhbVImIYTwN2fBcHyArgb3QRIMBzPtghuBmjynPX9PloqsPqAPMtycPGexKFQ0tFJS20x5fQsRYUZiI03ERpqIizSRHBtOpMl5zW95fQu7iuuIizIxND2OuEj15d6eOY4wazC87Udeazvd5flPHJbKH84dxdh+bgRF9t0p3Pkas/Kh4DPnzxeBIcGwEMLf7DvXSN2wX0kwHMy0meFATZ6zisvqyKZS343MsH3nBhdt1aoaWvl8RwmfbS9h25FaSuuaaWtXnO4LYDTAwJQYhqXHMSwjjqSYcLYdqWXTwWoOVTXpT5kYxdD0WKYcjuW3R+8bbdwPKHQ0Bj5qTE4Cd505klNHpmNwNyOvnSCYOABiUrp+TrYmGC6SYDgoaP8ISWs1IYQ/OMsMC7+RYDiY1QdZZtiqO5lhbdYzPgdi0wBotyjsKKplzb5KPttezE/7KrG4jn0dWBQorGiksKKRL7pYxrioppmimmZMxgFwtNIhxVDP2Lh6RueNYlR2gvovK4HEmG6sjFfcjQVFtPvVHIDGSveCaOEbFotMoBNC+F9EPGpS5ugfQGmv5lcSDAczXTAc6MywpnapOzXDmqxnfcpolq7azU+FVazfX0V9i7mTJ3qf/UIY782NI3y0FxYA0a2u52ZNtP1+xVtg6LSej0V0T2s9KJruIVImIYTwB6NRndNi/TAuwbBfSTAczHSrzwU4M6wt5O9GZthStAnj0dsv7Inj77/s6nT/0dkJnD4qg0GpsWq3hsRI0uOiMFssNLS0U99ipq65jSM1TRSU1rOntIE9ZfVUNbaSmxHH+AFJjO+fxLh+iTS0mjse31NWT3T4AFoL0oloKgMgvHQrjD7f469Jp75UXz7i7gTB5CFqRqC1Tt0u3izBcCDZX5qUYFgI4S9RSZpgWMok/EmC4WDV2qjvTBCoHsPOzl9f4vYCEbXNbTy78id+V3ek4z5nSxRHhBk5ZmASZ47J4szRmQxIiXF5zNRutCfOy0rQ3/HKBO/W6nZn8hyo2YCscXDg+6PHcX9VPOED9tkYKZMQQviLLLwRMBIMB6tgWX3OSlum0d6iBg1d9D3+aV8ld7yxkcG1P3XU6AJsUwYTaTJywrBUJg1OYdLgFPL7JxIV7nolOK/TTlzzRgCqDaijkz3rF5ydbwuGZRJdYElmWAgRKNr3m6bqgA2jL5JgOFg5rD4XRBPoQC0LcBEMt7VbePLzXTzz5R4sCpwXVtjxWJ0hlhtmnsqsY/qTGN2NSWreos3cemPiWrFdvbAnPaG1YynfBW1NEB7d/bGI7pNgWAgRKJIZDhhj17v0zKpVq7j22mvJy8sjNjaWfv36MWvWLNatW+frU4e2YFmK2co+M+1iEt36A1Vc+Mz3PL16T0dXiDHG/R2Pxw06hitPHBLYQBgca3p7mh0u6kYnCWf7K+1Qsr1nYxHdp/0DZIqSFaCEEP6jbeUowbBf+TwYfuaZZygsLOS2225j5cqVLF68mNLSUqZMmcKqVat8ffrQpZ2kFpUEpsiADQWAmFQwaF4umvGZ2y2s3FLE3CXfMXfJ92w6ZPsljggzMi2+qGPb4G4tra8lDT7ayuaonix40VIHlXts2y56KLuUnqcut90xlk2u9xW+pb00KVlhIYQ/aecoSDDsVz4vk3j66afJyNBfYj/77LPJzc3l0Ucf5bTTTvP1EEKTNvMa6KwwgDEMYtNtGeuj/7+z7hD/+HyXwwIXACMy41g8dyRJLxba7gyWYNh+4lpPanVLtum3Pf0aTRGQMcoWkMskusCR1eeEEIGiK5OoDtgw+iKfB8P2gTBAXFwco0eP5uDBg74+fejSrT4XBMEwqEF5RzBczD+/2M3fP3NskRYfZeLKEwbx29OGE1W8jo4m4uB+yzF/0E5c60lmWBtIm6IhbXj3xmIdg68n0bXUwa5PoKmq8/2ik2HEWRAZ3/l+vlZVCHtWgaXddp8xDIZOh5Qh3j2XBMNCiECRzHDABGQCXU1NDevXr+8yK1xaWkpZWZnuvoKCAl8OLXjoFtwIomD4qG27Cvj7IX0gPCAlmmtPGsK84wYQF3n0paUNMsMiIW2EP0bqHm9NXNOWNWSOUQM1j8cyHnhFvV2yTQ38unOcrigKvD4fCr9xb/9BJ8HVH3o2IdCbao/AkhOhrcHxMVM03LIWkgZ473zabIy0VRNC+JP9BDo3W5iKngtIMHzzzTfT0NDAH//4x073W7JkCYsWLfLTqIJMMAbDCTkdN1tLd3fcjjQZeeyCcfxqfD/CjHa/uNosZ+ZoCAvwxDktbZZasagT1/pP9Pw42q+xu5lv7fPMTVC+GzLyunesztQedj8QBtj/HdQc8m7A6YkdHzgPhEH9Pu1YASfc5L3zSWZYCBEo2vccixlaGyCyG431hcf8Hgzfd999vPrqqzz11FNMnNh54HHTTTcxb9483X0FBQXMnj3bhyMMEnXBFwy3pOZhncaXZziAEQuR4eE8f9VxnJib5vxJ9i3HgknaSAiLgPZWdbt4k+fBsLkVSnfYtj3tJGGVOQbduvTFm30TDNuXYMSkHj2vlgKNFbbN4s2BC4a1WXdjuPrHoqVW8zPzckmJBMNCiECxf89prpFg2E/8GgwvWrSIhx9+mEceeYRbbrmly/0zMjKc1hz3epZ2aNCUhwQwGG5qbeeLnSV8sKmI2l9aeO3oKyba0MrYyFLuu2YOkwa76M/b3qZvE9bdQNFXTBFqJ4ee1OqW7QRLm207y8NOElaR8ZAy1NaVomgT5F/UvWN1Rhs8xmXBXb843++JPKg72gWkaDPknef9sbhD+zM59go4/x+w8m746T+Oj3uDBMNCiEDRtlYD9f0osV9AhtLX+C0YXrRoEQsXLmThwoX84Q9/8NdpQ1Njpdpv1ioAE+jqmtv41+oC/u+H/TS2qmOJZYDuFfPPU8MY7CoQBrUOt73Ftu1pyzF/0E5c606WUdv5wRCmloL0ZCzWYNhXHSXc7YeclW8Lhr2dfXWXQ9Y9X/8/qB9G2pq91w9Y21rN/g+TEEL4krPMsPALn/cZBnjooYdYuHAhf/rTn3jggQf8ccrQVm+3oIUfM8MWi8Kbaw8y/fGv+PdXezsCYYAGotlnsY1lcFsXkxl1AZ3haClAkNFmcku2QbvZs+drA8W0ET1bOU4b5BVvVidPeFuxm/XN2kA5UEtEO2TdrcGw3SIlpV5cpEQyw0KIQHEIhqsDMoy+yOeZ4SeeeIL777+fs88+m/POO48ff/xR9/iUKVN8PYTQE6DV534urGThim1sPVzr8NiQtFjOz88mtXgS7P1AvbOrIEn7eNpwiIj14mi9RDdxrRkqCjyr1fXG5Dlnz2+q8v7EtcZKqNG0M+yshls7ltpDPV+uujtcZd0zRoHRpE4wse7X79ien6/dDK11tm0JhoUQ/hQeo39vk8yw3/g8GF6xYgUAH3/8MR9//LHD44ovsl+hTjt5zhiu9nv1oerGVh77aCf/W+vY9/nEYan87uw8xvdPxGAwwDfH2oJha/bSVeuXYJ48Z5U5lm5PXLNY9AFbT79G++d7e+KafelFp5lhJ2MZeqr3xuIOV1l3UySkj4KSLY779USL3YdAaa0mhPAng0F932ksV7clGPYbn5dJfPnllyiK4vKfcMK+rZqP+gwqisLyjYc54+9fOQTCA1Ni+PcVE3n1+slMGJCkBsKgLyuwZi+dH9z9S/KBFBkHqcNs20UeLIVctU+fSezpBMG4DHVSW8dYvFyeoP15RCaoS1K7kjwYIjWZ0UCUSnSWdddue2ts9pckJTMshPA3+17Dwi8C0mdYdKG+1HbbB5PnWs0Wvi0o48XvCvlmd7nusejwMH57ei7XnTyESJOTRR/sg5LiLc6zl9X79b/IwdZJQitrnFoeAZ5lGe339cbXmJ0Pu4s9H4s77CfPGTv5LGwwqPvs/9Y3Y+lKV1n3rHzgVfV2yVbvLFJi/4dHgmEhhL9p33e0E3qFT0kwHIy0E+i8VC/cblH4fk85KzYd4ZNtJdQ0tTnsM31kOg/OGsuAlBjXB7JmL+s1AVveuY772V+S727LMX/Iyodt76m3i7e4v+qP9mtMHOidmtqsfNj9qePxvaHYLhjuciyaYNjfmeGusu7a7bZGqNgD6T1c3dAhGE7q2fGEEMJT2i42khn2GwmGg5E2M9zDYLjVbGHZhsMs+bKAwopGp/ukx0fywMzRnDcu21YO0Rlt9tJVkKS9P6EfxKZ6OHI/6u7ENW9OnnN2nJqD3pu41taktrqzcqe+WTuWit3Q2ggRnXxQ8iaHD1OdBMOgBvo9DYbtszCSGRZC+JuuTKI6YMPoayQYDkZ1Pc8MN7e189bPB3n2q70crm5yuk92YhSzJvRjwanDSIz2YJnkrHGa7KWLYDgUJs9Z2Wet3Z245ouv0VcT10q2q0tOW7kTvGvHoljUFmb9j+v5WNyh/d46y7pHJUDyEDWDbN1/3IU9O6c2CxMRB2Hy9iiE8DOpGQ4IebcPRrrMsGcr8DW2mnltzQH+8/VeSutaHB5Pi4vkvHFZnD8+h4kDkzEauzE5L8uN7KUvsqa+EpcO8dmerbhWV6Kf6OitmuikQerkNmtngyIvBcPaZY3Djq6815X0kRAWaVs4pWiT/4Jhd14/2fm2YNgbZRzSY1gIEWiSGQ4ICYaDTWuDvlYyPsv1vhp1zW28/MN+nv92H5UNrQ6P52bEccv0XM7Pz8YU1sMmIg6T6OwCtoZyqDti2w7myXNWWeM8W3HNfh9vBfxG49Fa3e/cH4s7tMFixigIc+NKQFi4um/RRu+OxR3uZN2z8mH7ctv+7tZ6u6L9wyP1wkKIQNC+90hm2G8kGA42biy4oSgK24tq2X6klh1FdewoqmXL4RrqWxxXTxudncBvT8vlrDFZ3csCO5M0WJ+9LN6iD4bt25MFe5kE6CeuuZNl1H6N0SlqXbQ3x2INhr01cc3TyXPafa3BsL8m0bmbdde+rhoroPYIJPbg5yCZYSFEoEmZREBIMBxstCUS4BAMl9W18Jv/+5n1B6o7PcyEAUncenou00dmuDcpzhP22Uv7IEk7+SkqCZIGevf8vuDpimvarzE737u9oL09ca3drC41beVJZ4/s8bDh/9TbpdvVY/m6ltbdxUGctfmTYFgIEcp0wXCt2mayszaYwivkOxxstJPnQFczfLi6iYv+/UOngfDkISm8ev1k3rvpRE7Ly/R+IGylzcrZXz63z0L6agze5GziWmd8OUHQ2cS1nqgoUJeatvKkpEM7FnOzGpz7WrGbWff4LIjV1NT3tIxDgmEhRKDpSrQUx5UxhU9IZjjYaDPDUUnq0rPA3rJ6Ln9uDUdqbEFNmNHA0LRYRmUnMCo7gROGpTJhQJJ/xqm9dF2+S5+91E1+CuL+wlrWFddajgZEnU1ca66Fyr22bW9/jekj1Ulu7Udrv3s6cU0XJBqOLkHtpswx6JarLtqs1hH7kv3kuc4+TGXnQ8HnR5/nweqBzmhbq2l7fQohhL/Yv/c018j7kR9IMBxstAtuHJ08t6OoliueX0N5vW1i3Mm5aTxz+bHER3nQEs2bsp1kL/sfBy31ttXcIDTqhcGzFddKtuq3vT1BsGPi2qaux+IObZCYOkxdgtpdkXGQmmvLCBdvhvEX92w8XfEk656lCYYlMyyECHX27z1SN+wXUiYRbDQTh2rCkvnje1uY9+wPukB4xuhMnrvquMAFwqC25gqLsG1bA66SbXRkESE0OklYacfa2WQx7WPhMWqw6PWxaILAnk5c6+7kOWfP6Wn2tSv2Wfcug2HN2KoPqIumdPvcEgwLIQLMIRiuDsgw+hoJhoNMU1VRx+1Vh428uuaArkvE7Ak5LLnsWKLCwwIxPBtr9tLKOulJG3iZoiCth6uC+ZOziWvOaCd4ZY4Bow9+FtrSC+vEte5QFP14u5Op135frMtV+4p2op/9uZ2xL1Ep3up8P3dIMCyECDTJDAeElEkEWtFm2PUxra0t/FxYydBDG4g+WiJZpiTpdr18ykAe/NVY77VI66msfFumcM8XsOoR2LPK9njG6NBaxct+4tqnf4SYNMf99n7p/Dm+Gou5GT75g+1NMmkgjJ0LEbFdH6fmkD5b2p1+yNqxNFfDp39SM+K+oA3c3cm6Jw+BiHhbb+7vn4J9X3t+XsUCZs1KjdJnWAgRCKZIMEXb3o8kGPaLEIpUeqHqAyjPz8BgbiYCOBHUuUpHlSmJJMeEc/bYbOYc04/jh3TS6isQtG23qg/A13+1ezxE6oWt7Fdc+/mFrp/jq6/RfuLaT//WP35kPZz/j66PY19H60lbNSv77OsP//L8GN3hTtbdaISssXDgB3V79yfqv56SzLAQIlCiEqFegmF/kjKJALBYFDYdrOazZS9h0La8snP+WWfx0x/P4M9zxwVfIAww6MQuHj/ZP+PwlrBwGHC8B08wwMAuvgfdFRkHOce4fnzbMvfKFbT1xvHZ6tLTnopNg7SRnj+vpwad5N39PJE8yPvHFEIId2g/jGu73AifkcywHx2ubuK/X+/l463FFNc285jp546fQL0SxSElnZiIMNITY4keO5Pxp8wK7h69mWPgnL/CxtdsbcAADEa1LdnYuQEbWred+zf4fKGa6e6MKRKOuRzSfVgTff4/YNVD6spqAG2NUFWo3m6qhNrDkNi/82P0dPKc1aynYfUjjisk+kr2eDj5dvf2PelWdSntIxt6ft6wCBg/PzQWihFC9E7aVmqSGfYLCYb9oKyuhSVfFvDqjwdobbd03D/GWNhx+wvTVCJm/5Ozx2b5bqEMX5j8G/Vfb5ExCi59I9CjUOVMgMvfsW3XlcATmuC7aHPXwXCRB23KOjNgEly5rPvP96WoRJi9JNCjEEII75Almf1OgmEva2ptp7KxlaqGVioaWvlpXwUvfldIY2u7bj8TZkYaDnVsnzvjLMLHZft7uCKUxGeqy3Nbs7PFWyDvXNf7N1aqS0tbhVoNtxBC9EUSDPudBMM9VFrXzPcFFXxXUM73eyo4XN3U6f4GA/xqfA6XDa4j4mNbu6zw/hN8PFLRK2TlQ8Fn6m1Ploy2PlcIIURw03azkT7DfiHBcDdYLAorNh/hmS/3sLO4zu3nnT0mizvPHMGIzHi1ztbKYFTbkAnRlaxxtmC4q8U4tI9HJqhLTgshhAhukhn2OwmGPfTDngoeXbmDLYfde4GajAZOHp7GHWeMYPyAJNsD2kAldThE+Khvq+hdtKUONQfUUogYF51G7CfPhVItuhBC9FUSDPudBMNuqG8xs35/FS99X8gXO0ud7jM8I46TctOYNDiFrMRIkmMiSImNICEq3PkiGdpARWo5hbvsSx2Kt8DQac739dbkOSGEEP4jrdX8ToJhJ9otCl/vKuPr3WWsLaxk+5FaLE5auvZLiuaW03I5PS+DjIQo909gsfR8iVzRN9mvuOYqGG5tVJeUtpIPXEIIERq0rdXaGqC9Te2DL3xGgmGNxlYzb687xAvf7qOwotHlfvFRJm6ZnstVJw4mKryLFbKcqS6EllrbtgQqwl1Go1rycOB7ddvVJLrS7eoSw1bygUsIIUKD/QqYzbUQmxqYsfQREgwDByoa+d/aA7y65gA1TW0u90uJjWDuMf24eXouybER3T+h/cQnCVSEJ7LzbcGwq0l0RZtst8Mi1KWmhRBCBD+HYLhagmEf67PBcE1TGyu3FPHu+kOsLaxyuk9mQiQn56YzaXAyk4akMDQt1jsLYmhLJBIHuJ4AJYQz2pXkyndBWxOER+v30WaMM0bJJTYhhAgVzoJh4VN9LhjeeriG577Zy8qtxbSaLU73ye+fyPWnDOWcsVmEhxm9P4himdgkekD7mlHaoWQ79J+o30cmzwkhRGjS9hkG6SjhB30iGLZYFL7YWcpz3+xlzb5Kp/uYjAbOGJXJdacM4bhByb5dErnIruWVEJ5IzwNjOFiOlvQUb9YHw+1mtWbYKnu8f8cnhBCi+yIT9NsSDPtcrw+Gv99Tzp+WbWVvWYPTx8cPSGLuMf2YOT6HlJ7UAburvhTqi23bMnlOeMoUoZY+WK8w2E+iq9gN5mbbtmSGhRAidISZ9F2DJBj2uV4bDDe1tvPXT3by4neFDo/FRoRx0aQBXDZ5ILkZ8f4dmEyeE96QnW8Lgu1fU7ptA2SO8duwhBBCeEF0ki0Yll7DPtcrg+H1B6q4681N7C3XZ4OzE6O45qTBXDxpIInRAZpQVKyZ5R+dDIn9AzMOEdq0H6JKtoGlHYxH2/xpM8WpwyAyzr9jE0II0TNRiVBzUL0tmWGf61XB8NbDNbz8QyFvrzukWyQjKtzIPWfncfmUQb6ZEOcJ+8U2ZIlc0R3aYNjcBOW7ISNP3da2VZMrD0IIEXpkSWa/8ktkWF9fz+23305OTg5RUVFMmDCB//3vf145dou5nWUbDjNnyXec/9S3vPmzPhA+ZmASK289hWtOGhL4QBj0l7ClXlh0V9ZYQPNByvohS1H0H7jkNSaEEKFHgmG/8ktmeO7cuaxdu5bHHnuMESNG8NprrzF//nwsFguXXnppt46pKArLNx7msY92UlTT7PB4eJiBO2aM4IZThmIKhiAYoKUOKvfYtrNklr/opsh4SBlqez0Vb4L8eeplNW1PSskMCyFE6NG2V5M+wz7n82B45cqVfPbZZx0BMMD06dPZv38/d999NxdffDFhYZ4vaXzHGxvZ3ZbscH9MRBhzj+3HNScNYVh6kNVKFm/Vb0tbNdET2fm2YLjIxWQ6CYaFECL0SGbYr3weDL/33nvExcUxb9483f3XXHMNl156KWvWrOHEE0/0+LgzSl/gmnRbL76E6HBGZMQzOC2GCKMRfujx0L2vQpMVNkVD2vDAjUWEvqxxsO099fbhdfD+repkOqv4bIhLD8zYhBBCdJ82GC7frb6/C/cdqPBod58Hw1u3bmXUqFGYTPpT5efndzzuKhguLS2lrKxMd19BQQEA54X9xBiTJqPcBhw++i8UZI6xzf4Xoju0ZTat9bD+JbvHJSsshBAhSZcZrnZ8fxedK233aHefB8MVFRUMHTrU4f6UlJSOx11ZsmQJixYt8tnYAmroqYEegQh1/SfqG7PbGzbdv+MRQgjhHWkjAj2CPsUvE+g6W9q4s8duuukmh/KKgoICZs+eTUvWRBiU6OKZQS47H06+PdCjEKEuOhkuWgprX1Azw1r9J8Fx1wVkWEIIIXpo2GlwxiLY+yUolkCPJvRE1AFfur27z4Ph1NRUp9nfyspKwJYhdiYjI4OMjAynj0VesATGyMpaoo/LPUP9J4QQovcwGtWkmSTOumfbNvjjWLd393nPsXHjxrFjxw7MZrPu/i1b1F6oY8e6P1ghhBBCCCG8yefB8Jw5c6ivr+edd97R3f/SSy+Rk5PD5MmTfT0EIYQQQgghnPJ5mcQ555zDjBkzWLBgAbW1teTm5vL666/z8ccf88orr3Srx7AQQgghhBDe4JcJdO+++y5//OMfuf/++6msrCQvL4/XX3+dSy65xB+nF0IIIYQQwim/BMNxcXEsXryYxYsX++N0QgghhBBCuMXnNcNCCCGEEEIEKwmGhRBCCCFEnyXBsBBCCCGE6LMkGBZCCCGEEH2WXybQeVNLSwugLssshBBCCCGEljVGtMaMXQm5YNi6ct3s2bMDOxAhhBBCCBG0Dh48yLHHHtvlfiEXDI8YMQKAN998k9GjRwd4NCJYFRQUMHv2bJYtW0Zubm6ghyOClLxOhDvkdSLcJa+V4NDS0sLBgweZNm2aW/uHXDCckJAAwOjRoxkzZkyARyOCXW5urrxORJfkdSLcIa8T4S55rQSeOxlhK5lAJ4QQQggh+iwJhoUQQgghRJ8lwbAQQgghhOizQi4YTk9P54EHHiA9PT3QQxFBTF4nwh3yOhHukNeJcJe8VkKTQVEUJdCDEEIIIYQQIhBCLjMshBBCCCGEt0gwLIQQQggh+iwJhoUQQgghRJ8lwbAQQgghhOizQiYYrq+v5/bbbycnJ4eoqCgmTJjA//73v0APSwTIqlWruPbaa8nLyyM2NpZ+/foxa9Ys1q1b57Dv+vXrOeOMM4iLiyMpKYm5c+eyd+/eAIxaBNpzzz2HwWAgLi7O4TF5nYhvv/2Wc889l+TkZKKjoxk+fDgPPfSQbh95nfRtGzZsYPbs2eTk5BATE0NeXh4PPvggjY2Nuv3kdRJaQiYYnjt3Li+99BIPPPAAH330EZMmTWL+/Pm89tprgR6aCIBnnnmGwsJCbrvtNlauXMnixYspLS1lypQprFq1qmO/nTt3cuqpp9La2sqbb77JCy+8wK5duzjllFMoKysL4Fcg/O3w4cPcdddd5OTkODwmrxPx2muvMW3aNBITE3n55ZdZuXIl99xzD9qGS/I66du2b9/OiSeeSGFhIU8++SQffPABl1xyCQ8++CDz58/v2E9eJyFICQEffvihAiivvfaa7v4ZM2YoOTk5itlsDtDIRKCUlJQ43FdXV6dkZmYqp59+esd98+bNU9LS0pSampqO+woLC5Xw8HDld7/7nV/GKoLD+eefr8ycOVO56qqrlNjYWN1j8jrp2w4dOqTExsYqCxYs6HQ/eZ30bX/84x8VQCkoKNDdf8MNNyiAUllZqSiKvE5CUUhkht977z3i4uKYN2+e7v5rrrmGI0eOsGbNmgCNTARKRkaGw31xcXGMHj2agwcPAmA2m/nggw+44IILSEhI6Nhv0KBBTJ8+nffee89v4xWB9corr/DVV1+xZMkSh8fkdSKee+45GhoauOeee1zuI68TER4eDkBiYqLu/qSkJIxGIxEREfI6CVEhEQxv3bqVUaNGYTKZdPfn5+d3PC5ETU0N69evZ8yYMQDs2bOHpqamjteJVn5+PgUFBTQ3N/t7mMLPSktLuf3223nsscfo37+/w+PyOhFff/01KSkp7Ny5kwkTJmAymcjIyODGG2+ktrYWkNeJgKuuuoqkpCQWLFjA3r17qaur44MPPuDf//43N998M7GxsfI6CVEhEQxXVFSQkpLicL/1voqKCn8PSQShm2++mYaGBv74xz8CtteFq9eOoihUVVX5dYzC/2666SZGjhzJggULnD4urxNx+PBhGhsbmTdvHhdffDGff/45d999Ny+//DLnnnsuiqLI60QwePBgfvjhB7Zu3cqwYcNISEhg5syZXHXVVSxevBiQ95NQZep6l+BgMBi69ZjoG+677z5effVVnnrqKSZOnKh7TF47fdc777zDihUr2LBhQ5c/a3md9F0Wi4Xm5mYeeOAB7r33XgBOPfVUIiIiuP322/niiy+IiYkB5HXSlxUWFjJz5kwyMzN5++23SU9PZ82aNTz88MPU19fz/PPPd+wrr5PQEhLBcGpqqtPsb2VlJeD8E5joOxYtWsTDDz/MI488wi233NJxf2pqKuD8ykFlZSUGg4GkpCR/DVP4WX19PTfffDO//e1vycnJobq6GoDW1lYAqqurCQ8Pl9eJIDU1ld27d3PWWWfp7j/nnHO4/fbbWb9+PbNmzQLkddKX3XvvvdTW1rJx40ZiY2MBmDp1KmlpaVx77bVceeWVZGVlAfI6CTUhUSYxbtw4duzYgdls1t2/ZcsWAMaOHRuIYYkgsGjRIhYuXMjChQv5wx/+oHts2LBhREdHd7xOtLZs2UJubi5RUVH+Gqrws/LyckpKSnjiiSdITk7u+Pf666/T0NBAcnIyl112mbxOhNP6TqCjrZrRaJTXiWDjxo2MHj26IxC2mjRpEkBH+YS8TkJPSATDc+bMob6+nnfeeUd3/0svvUROTg6TJ08O0MhEID300EMsXLiQP/3pTzzwwAMOj5tMJmbOnMm7775LXV1dx/0HDhxg9erVzJ0715/DFX6WlZXF6tWrHf6dddZZREVFsXr1ah5++GF5nQguuOACAD766CPd/StXrgRgypQp8joR5OTksG3bNurr63X3//DDDwD0799fXiehKpB93TwxY8YMJTk5WfnPf/6jrFq1Svn1r3+tAMorr7wS6KGJAHj88ccVQDn77LOVH374weGf1Y4dO5S4uDhl6tSpysqVK5V3331XGTt2rJKTk6OUlpYG8CsQgeKsz7C8TsTMmTOVyMhI5aGHHlI+++wz5c9//rMSFRWlnH/++R37yOukb1u+fLliMBiUKVOmKG+88YbyxRdfKI888ogSFxenjB49WmlpaVEURV4noShkguG6ujrl1ltvVbKyspSIiAglPz9fef311wM9LBEg06ZNUwCX/7R+/vln5fTTT1diYmKUhIQEZfbs2Q5N00Xf4SwYVhR5nfR1jY2Nyj333KMMGDBAMZlMysCBA5Xf//73SnNzs24/eZ30batWrVLOPPNMJSsrS4mOjlZGjBih/L//9/+U8vJy3X7yOgktBkXRrDUphBBCCCFEHxISNcNCCCGEEEL4ggTDQgghhBCiz5JgWAghhBBC9FkSDAshhBBCiD5LgmEhhBBCCNFnSTAshBBCCCH6LAmGhRBCCCFEnyXBsBBCCCGE6LMkGBZCCCGEEH2WBMNCCCGEEKLPkmBYCCFCmKIoPPjgg3z11VeBHooQQoQkCYaFECKE7dq1iwceeICioqJAD0UIIUKSBMNCCBHC1q1bB8DEiRMDPBIhhAhNBkVRlEAPQgghhOcmTpzI+vXrdffFxcVRW1uLwWAI0KiEECK0SDAshBAhat26ddx4441YLBaefvppAKKjoxk/fnyARyaEEKFDgmEhhAhhmZmZXHLJJSxevDjQQxFCiJAkNcNCCBGiDh48SGlpqdQLCyFED0gwLIQQIUomzwkhRM9JMCyEECFq3bp1xMTEkJeXF+ihCCFEyJJgWAghQtTmzZvJy8sjLCws0EMRQoiQJcGwEEKEqKSkJPbs2cPy5cv58ccf2b9/f6CHJIQQIUeCYSGECFEPPPAAEyZM4LLLLuOEE07gnXfeCfSQhBAi5EhrNSGEEEII0WdJZlgIIYQQQvRZEgwLIYQQQog+S4JhIYQQQgjRZ0kwLIQQQggh+iwJhoUQQgghRJ8lwbAQQgghhOizJBgWQgghhBB9lgTDQgghhBCiz5JgWAghhBBC9FkSDAshhBBCiD5LgmEhhBBCCNFnSTAshBBCCCH6LAmGhRBCCCFEn/X/AdL4NGQ33/ZHAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "psi0 = fock(N, 0)\n",
    "\n",
    "T = 4\n",
    "NTh = 1./(np.exp(w/T)-1)\n",
    "c_ops = [np.sqrt(gamma*(1+NTh)) * a, np.sqrt(gamma*(NTh)) * a.dag()]\n",
    "e_ops = [H, a.dag()*a]\n",
    "\n",
    "tlist = np.linspace(0, 15 * 2*np.pi, 150)\n",
    "n_tot_traj = 200\n",
    "sol_tot = mcsolve(H, psi0, tlist, c_ops, e_ops, ntraj=n_tot_traj)\n",
    "sol_1 = mcsolve(H, psi0, tlist, c_ops, e_ops, ntraj=1)\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120, figsize=(7, 3))\n",
    "\n",
    "ax.plot(tlist, sol_tot.expect[1], label=r\"$\\langle \\hat{a}^\\dagger\\hat{a} \\rangle$ average on %d trajectories \" % (n_tot_traj), lw=2)\n",
    "ax.plot(tlist, sol_1.expect[1], label=r\"$\\langle \\hat{a}^\\dagger\\hat{a} \\rangle$ single trajectory\", lw=2)\n",
    "ax.legend()\n",
    "ax.set_xlabel(r\"$t$\")\n",
    "ax.set_xlim(tlist[0], tlist[-1])\n",
    "#ax.set_ylim(None, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}