{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ensemble Optimization for Robust Pulses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.419196Z",
     "start_time": "2020-03-22T05:01:27.400452Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:44.483473Z",
     "iopub.status.busy": "2024-06-03T14:25:44.483339Z",
     "iopub.status.idle": "2024-06-03T14:25:45.123828Z",
     "shell.execute_reply": "2024-06-03T14:25:45.123485Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.12.0\n",
      "IPython version      : 8.25.0\n",
      "\n",
      "matplotlib: 3.7.5\n",
      "krotov    : 1.3.0+dev\n",
      "numpy     : 1.26.4\n",
      "scipy     : 1.12.0\n",
      "sys       : 3.12.0 (main, Jun  3 2024, 09:08:56) [Clang 15.0.0 (clang-1500.3.9.4)]\n",
      "qutip     : 4.7.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "%load_ext watermark\n",
    "import sys\n",
    "import os\n",
    "import qutip\n",
    "import numpy as np\n",
    "import scipy\n",
    "import matplotlib\n",
    "import matplotlib.pylab as plt\n",
    "import krotov\n",
    "from qutip import Qobj\n",
    "import pickle\n",
    "\n",
    "%watermark -v --iversions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\newcommand{tr}[0]{\\operatorname{tr}}\n",
    "\\newcommand{diag}[0]{\\operatorname{diag}}\n",
    "\\newcommand{abs}[0]{\\operatorname{abs}}\n",
    "\\newcommand{pop}[0]{\\operatorname{pop}}\n",
    "\\newcommand{aux}[0]{\\text{aux}}\n",
    "\\newcommand{opt}[0]{\\text{opt}}\n",
    "\\newcommand{tgt}[0]{\\text{tgt}}\n",
    "\\newcommand{init}[0]{\\text{init}}\n",
    "\\newcommand{lab}[0]{\\text{lab}}\n",
    "\\newcommand{rwa}[0]{\\text{rwa}}\n",
    "\\newcommand{bra}[1]{\\langle#1\\vert}\n",
    "\\newcommand{ket}[1]{\\vert#1\\rangle}\n",
    "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n",
    "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n",
    "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2}\\mid{#2}\\vphantom{#1}\\right\\rangle}\n",
    "\\newcommand{ketbra}[2]{\\vert#1\\rangle\\!\\langle#2\\vert}\n",
    "\\newcommand{op}[1]{\\hat{#1}}\n",
    "\\newcommand{Op}[1]{\\hat{#1}}\n",
    "\\newcommand{dd}[0]{\\,\\text{d}}\n",
    "\\newcommand{Liouville}[0]{\\mathcal{L}}\n",
    "\\newcommand{DynMap}[0]{\\mathcal{E}}\n",
    "\\newcommand{identity}[0]{\\mathbf{1}}\n",
    "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n",
    "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n",
    "\\newcommand{avg}[1]{\\langle#1\\rangle}\n",
    "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n",
    "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n",
    "\\newcommand{Re}[0]{\\operatorname{Re}}\n",
    "\\newcommand{Im}[0]{\\operatorname{Im}}\n",
    "\\newcommand{toP}[0]{\\omega_{12}}\n",
    "\\newcommand{toS}[0]{\\omega_{23}}$\n",
    "\n",
    "This example revisits the [Optimization of a State-to-State Transfer in a\n",
    "Lambda System in the RWA](02_example_lambda_system_rwa_complex_pulse.ipynb),\n",
    "attempting to make the control pulses robustness with respect to variations in\n",
    "the pulse amplitude, through \"ensemble optimization\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Control objectives for population transfer in the Lambda system\n",
    "\n",
    "As in the original example, we define the Hamiltonian for a Lambda system in\n",
    "the rotating wave approximation, like this:\n",
    "\n",
    "![Lambda system considered in this notebook](energylevels.png)\n",
    "\n",
    "We set up the control fields and the Hamiltonian exactly as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.441078Z",
     "start_time": "2020-03-22T05:01:29.429149Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.145515Z",
     "iopub.status.busy": "2024-06-03T14:25:45.145298Z",
     "iopub.status.idle": "2024-06-03T14:25:45.147955Z",
     "shell.execute_reply": "2024-06-03T14:25:45.147686Z"
    }
   },
   "outputs": [],
   "source": [
    "def Omega_P1(t, args):\n",
    "    \"\"\"Guess for the real part of the pump pulse\"\"\"\n",
    "    Ω0 = 5.0\n",
    "    return Ω0 * krotov.shapes.blackman(t, t_start=2.0, t_stop=5.0)\n",
    "\n",
    "\n",
    "def Omega_P2(t, args):\n",
    "    \"\"\"Guess for the imaginary part of the pump pulse\"\"\"\n",
    "    return 0.0\n",
    "\n",
    "\n",
    "def Omega_S1(t, args):\n",
    "    \"\"\"Guess for the real part of the Stokes pulse\"\"\"\n",
    "    Ω0 = 5.0\n",
    "    return Ω0 * krotov.shapes.blackman(t, t_start=0.0, t_stop=3.0)\n",
    "\n",
    "\n",
    "def Omega_S2(t, args):\n",
    "    \"\"\"Guess for the imaginary part of the Stokes pulse\"\"\"\n",
    "    return 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.448554Z",
     "start_time": "2020-03-22T05:01:29.443630Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.149334Z",
     "iopub.status.busy": "2024-06-03T14:25:45.149232Z",
     "iopub.status.idle": "2024-06-03T14:25:45.151126Z",
     "shell.execute_reply": "2024-06-03T14:25:45.150878Z"
    }
   },
   "outputs": [],
   "source": [
    "tlist = np.linspace(0, 5, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.467163Z",
     "start_time": "2020-03-22T05:01:29.452425Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.152558Z",
     "iopub.status.busy": "2024-06-03T14:25:45.152452Z",
     "iopub.status.idle": "2024-06-03T14:25:45.155197Z",
     "shell.execute_reply": "2024-06-03T14:25:45.154961Z"
    }
   },
   "outputs": [],
   "source": [
    "def hamiltonian(E1=0.0, E2=10.0, E3=5.0, omega_P=9.5, omega_S=4.5):\n",
    "    \"\"\"Lambda-system Hamiltonian in the RWA\"\"\"\n",
    "\n",
    "    # detunings\n",
    "    ΔP = E1 + omega_P - E2\n",
    "    ΔS = E3 + omega_S - E2\n",
    "\n",
    "    H0 = Qobj([[ΔP, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, ΔS]])\n",
    "\n",
    "    HP_re = -0.5 * Qobj([[0.0, 1.0, 0.0], [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]])\n",
    "    HP_im = -0.5 * Qobj([[0.0, 1.0j, 0.0], [-1.0j, 0.0, 0.0], [0.0, 0.0, 0.0]])\n",
    "\n",
    "    HS_re = -0.5 * Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0]])\n",
    "    HS_im = -0.5 * Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0j], [0.0, -1.0j, 0.0]])\n",
    "\n",
    "    return [\n",
    "        H0,\n",
    "        [HP_re, Omega_P1],\n",
    "        [HP_im, Omega_P2],\n",
    "        [HS_re, Omega_S1],\n",
    "        [HS_im, Omega_S2],\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.480174Z",
     "start_time": "2020-03-22T05:01:29.470251Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.156516Z",
     "iopub.status.busy": "2024-06-03T14:25:45.156402Z",
     "iopub.status.idle": "2024-06-03T14:25:45.159010Z",
     "shell.execute_reply": "2024-06-03T14:25:45.158758Z"
    }
   },
   "outputs": [],
   "source": [
    "H = hamiltonian()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The control objective is the realization of a phase sensitive $\\ket{1}\n",
    "\\rightarrow \\ket{3}$ transition in the lab frame. Thus, in the rotating frame,\n",
    "we must take into account an additional phase factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.492615Z",
     "start_time": "2020-03-22T05:01:29.482710Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.160692Z",
     "iopub.status.busy": "2024-06-03T14:25:45.160580Z",
     "iopub.status.idle": "2024-06-03T14:25:45.162951Z",
     "shell.execute_reply": "2024-06-03T14:25:45.162706Z"
    }
   },
   "outputs": [],
   "source": [
    "ket1 = qutip.Qobj(np.array([1.0, 0.0, 0.0]))\n",
    "ket2 = qutip.Qobj(np.array([0.0, 1.0, 0.0]))\n",
    "ket3 = qutip.Qobj(np.array([0.0, 0.0, 1.0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.502476Z",
     "start_time": "2020-03-22T05:01:29.497857Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.164288Z",
     "iopub.status.busy": "2024-06-03T14:25:45.164176Z",
     "iopub.status.idle": "2024-06-03T14:25:45.165980Z",
     "shell.execute_reply": "2024-06-03T14:25:45.165714Z"
    }
   },
   "outputs": [],
   "source": [
    "def rwa_target_state(ket3, E2=10.0, omega_S=4.5, T=5):\n",
    "    return np.exp(1j * (E2 - omega_S) * T) * ket3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.511580Z",
     "start_time": "2020-03-22T05:01:29.505632Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.167760Z",
     "iopub.status.busy": "2024-06-03T14:25:45.167617Z",
     "iopub.status.idle": "2024-06-03T14:25:45.169516Z",
     "shell.execute_reply": "2024-06-03T14:25:45.169225Z"
    }
   },
   "outputs": [],
   "source": [
    "psi_target = rwa_target_state(ket3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.523688Z",
     "start_time": "2020-03-22T05:01:29.514140Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.171021Z",
     "iopub.status.busy": "2024-06-03T14:25:45.170916Z",
     "iopub.status.idle": "2024-06-03T14:25:45.174724Z",
     "shell.execute_reply": "2024-06-03T14:25:45.174447Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [H₀[3,3], [H₁[3,3], u₁(t)], [H₂[3,3], u₂(t)], [H₃[3,3], u₃(t)], [H₄[3,3], u₄(t)]]]]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective = krotov.Objective(initial_state=ket1, target=psi_target, H=H)\n",
    "objectives = [objective]\n",
    "objectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robustness to amplitude fluctuations\n",
    "\n",
    "A potential source of error is fluctuations in the pulse amplitude between\n",
    "different runs of the experiment. To account for this, the `hamiltonian`\n",
    "function above include a parameter `mu` that scales the pulse amplitudes by the\n",
    "given factor.\n",
    "\n",
    "We can analyze the result of the [Optimization of a State-to-State Transfer in\n",
    "a Lambda System in the RWA](02_example_lambda_system_rwa_complex_pulse.ipynb)\n",
    "with respect to such fluctuations. We load the earlier optimization result from\n",
    "disk, and verify that the optimized controls produce the $\\ket{1} \\rightarrow\n",
    "\\ket{3}$ transition as desired."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.532018Z",
     "start_time": "2020-03-22T05:01:29.525825Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.176475Z",
     "iopub.status.busy": "2024-06-03T14:25:45.176365Z",
     "iopub.status.idle": "2024-06-03T14:25:45.179752Z",
     "shell.execute_reply": "2024-06-03T14:25:45.179421Z"
    }
   },
   "outputs": [],
   "source": [
    "opt_result_unperturbed = krotov.result.Result.load(\n",
    "    'lambda_rwa_opt_result.dump', objectives=[objective]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.540217Z",
     "start_time": "2020-03-22T05:01:29.534230Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.181134Z",
     "iopub.status.busy": "2024-06-03T14:25:45.181022Z",
     "iopub.status.idle": "2024-06-03T14:25:45.183208Z",
     "shell.execute_reply": "2024-06-03T14:25:45.182945Z"
    }
   },
   "outputs": [],
   "source": [
    "proj1 = qutip.ket2dm(ket1)\n",
    "proj2 = qutip.ket2dm(ket2)\n",
    "proj3 = qutip.ket2dm(ket3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.860337Z",
     "start_time": "2020-03-22T05:01:29.542275Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.184598Z",
     "iopub.status.busy": "2024-06-03T14:25:45.184472Z",
     "iopub.status.idle": "2024-06-03T14:25:45.255102Z",
     "shell.execute_reply": "2024-06-03T14:25:45.254725Z"
    }
   },
   "outputs": [],
   "source": [
    "opt_unperturbed_dynamics = (\n",
    "    opt_result_unperturbed\n",
    "    .optimized_objectives[0]\n",
    "    .mesolve(tlist, e_ops=[proj1, proj2, proj3])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:29.874858Z",
     "start_time": "2020-03-22T05:01:29.862369Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.256920Z",
     "iopub.status.busy": "2024-06-03T14:25:45.256805Z",
     "iopub.status.idle": "2024-06-03T14:25:45.259119Z",
     "shell.execute_reply": "2024-06-03T14:25:45.258871Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_population(result):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(result.times, result.expect[0], label='1')\n",
    "    ax.plot(result.times, result.expect[1], label='2')\n",
    "    ax.plot(result.times, result.expect[2], label='3')\n",
    "    ax.legend()\n",
    "    ax.set_xlabel('time')\n",
    "    ax.set_ylabel('population')\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:30.119626Z",
     "start_time": "2020-03-22T05:01:29.879489Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.260666Z",
     "iopub.status.busy": "2024-06-03T14:25:45.260549Z",
     "iopub.status.idle": "2024-06-03T14:25:45.431491Z",
     "shell.execute_reply": "2024-06-03T14:25:45.427308Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8/zgL9i4AYEzrMRankdpOxY1IOVzXNQYvm8G6xOMkJGdaHUfEcl/t/opCZyGtI1rToW4Hq+NILafiRqQc6gf7cXlbs9l95ioNLJbazely8tn2zwC4vtX1GIZhcSKp7VTciJTT6ItjAfhqwyEKijWwWGqvFckrSMxKJNA7kCubXGl1HBEVNyLl1bdFPSJDfDmeW8QPCWlWxxGxzMlWm+HNhhPgHWBxGhEVNyLlZrcZjOoSA8Dnaw9anEbEGik5Kfx44EcArm95vcVpREwqbkQq4JoTxc2SHemkZeVbnEak6n2x8wucLifxkfE0D29udRwRQMWNSIU0rx9E50ZhOJwuvvrtkNVxRKpUkbOIL3aYu3+PbjXa4jQip6i4Eamga+NPdU25XC6L04hUnZ8O/kR6XjoRfhEMbDTQ6jgiJVTciFTQVR2i8fGysT01i81JWvNGao/Zu2YD5kBib7u3xWlETlFxI1JBof7eDG4XBcDnaw9YnEakaqTnpvPTwZ8AGNl8pMVpREpTcSPiBie7prTmjdQWX+/+GofLQcd6HWka1tTqOCKlqLgRcYM+zeuWrHmzZHu61XFEKpXL5WLOrjkAjGoxytowImeh4kbEDew2g+EdowH4er1mTYln+y3tN/Zl7sPfy5/BcYOtjiNyBhU3Im5ydaeGAHyfkEpWfpHFaUQqz8mBxIPjBhPoHWhxGpEzqbgRcZN20SE0qxdIQbGT77akWh1HpFLkFOWwcN9CQAOJpfqyvLh54403iIuLw8/Pj+7du7Nq1arznj916lRatWqFv78/sbGxPPTQQ+Tna2VYsZ5hGCWtN19tUNeUeKYFexeQV5xHXEgcnet3tjqOyFlZWtx8+umnTJw4kSeffJJ169bRsWNHBg8eTFra2TchnDFjBo899hhPPvkkCQkJvPfee3z66af87W9/q+LkImd3ctzNL7sOk55VYHEaEfc72SU1ssVIDMOwOI3I2Vla3Lz00kvceeedjB8/nrZt2/LWW28REBDA+++/f9bzf/31V3r37s2NN95IXFwcgwYNYsyYMedt7SkoKCAzM7PUh0hliasbSMdYczuG+ZuSrY4j4lZ7ju9hQ/oG7Iad4c2GWx1H5JwsK24KCwtZu3YtAweeWrLbZrMxcOBAli9fftbX9OrVi7Vr15YUM3v27GH+/PkMHTr0nPeZMmUKoaGhJR+xsbHu/UJEfufqE603X61PsjiJiHudbLXpG9OXuv51LU4jcm6WFTeHDx/G4XAQGRlZ6nhkZCQpKSlnfc2NN97IM888Q58+ffD29qZZs2b079//vN1SkyZNIiMjo+TjwAGtICuV66oODbAZsC7xOIlHcq2OI+IWRc4ivt79NaCBxFL9WT6guCyWLFnCs88+y5tvvsm6dev48ssvmTdvHn//+9/P+RpfX19CQkJKfYhUpvohfvRqZv5V+81GDSwWz7Ds4DKO5h+ljl8d+sb0tTqOyHlZVtzUrVsXu91OamrpKbOpqalERUWd9TVPPPEEt9xyC3fccQcXXXQRI0eO5Nlnn2XKlCk4nc6qiC1yQYZ3Mrum5vyWpJ3CxSPM3nlik8zmw/G2aZNMqd4sK258fHyIj49n8eLFJcecTieLFy+mZ8+eZ31Nbm4uNlvpyHa7HUBvIFKtXNE+Ch8vGzvTsklIzrI6jkiFpOWm8VOSuUnmiOYjrA0jcgEs7ZaaOHEi7777Lh9++CEJCQncfffd5OTkMH78eADGjh3LpEmTSs4fNmwY06ZNY+bMmezdu5dFixbxxBNPMGzYsJIiR6Q6CPHz5tJW9QENLJaa7+vdX+N0OelcvzNNQ7VJplR/XlbefPTo0aSnpzN58mRSUlLo1KkTCxYsKBlknJiYWKql5vHHH8cwDB5//HGSkpKoV68ew4YN45///KdVX4LIOV3dKZoFW1KYuzGZx4a01pogUiOdvkmmBhJLTWG4all/TmZmJqGhoWRkZGhwsVSq/CIH8X9fRE6hgy/u7kV843CrI4mU2drUtYxbMA5/L3+WXL+EAO8AqyNJLVWW9+8aNVtKpCbx87YzqJ05OP4bbccgNdSXO78E4Iq4K1TYSI2h4kakEg3r2ACAeZuScThrVSOpeIDswmwW7V8EwKgWoyxOI3LhVNyIVKI+zesR6u9NelYBK/cesTqOSJks2GduktkktAkd63W0Oo7IBVNxI1KJfLxsDGmvrimpmU6ubTOyuTbJlJpFxY1IJRt2Yq+pbzenUFisxSalZth1bBcbD2/EbtgZ1myY1XFEykTFjUgl69G0DnWDfDmeW8Qvuw5bHUfkgny5yxxI3C+mnzbJlBpHxY1IJbPbDK68SF1TUnMUOYqYu3suoIHEUjOpuBGpAie7pr7bmkp+kcPiNCLn9+OBHzlWcIx6/vXo07CP1XFEykzFjUgV6NIonOhQP7ILilmyPc3qOCLndbJLaniz4XjZLF3IXqRcVNyIVAGbzeCqE60332xItjiNyLml5KTwa9KvAIxsoe0WpGZScSNSRYZ1MIubxdtSyS4otjiNyNnN2TUHFy7iI+NpHNLY6jgi5aLiRqSKtG8YQlydAPKLnCxOSLU6jsgZnC5nySaZGkgsNZmKG5EqYhhGycBizZqS6mhVyiqSspMI8g7i8saXWx1HpNxU3IhUoeEnipulO9LJyC2yOI1IaSc3yRzSZAj+Xv4WpxEpPxU3IlWoRWQwraOCKXK4WLglxeo4IiUyCjJYvH8xoC4pqflU3IhUsZKuqY3qmpLqY96eeRQ6C2kZ3pJ2ddpZHUekQlTciFSxqzo0AOCXXYc5nF1gcRoR0+xd5iaZo1qM0iaZUuOpuBGpYo3rBNIxJhSnC77dpDVvxHpbj2xl29FteNu8ubLJlVbHEakwFTciFhimBf2kGjk5kPiyRpcR5hdmbRgRN1BxI2KBK090Ta3ad5TkjDyL00htlluUy9w92iRTPIuKGxELNAj1p1tcBADzNqr1Rqwzf+98copyaBzSmO4NulsdR8QtVNyIWGRYR7P1Rgv6iZU+2/4ZANe1vA6bobcE8Qz6SRaxyJCLGmAzYMPBDPYfybE6jtRCWw5vIeFoAt42b4Y3G251HBG3UXEjYpG6Qb70bl4XgLnqmhILfLbDbLUZFDeIcL9wi9OIuI+KGxELndwpXF1TUtUyCzP5du+3AFzf8nqL04i4l4obEQsNbheFt91gW0oWO1KzrI4jtcjc3XPJK86jeVhzOtfvbHUcEbdScSNiodAAby5pWQ+AuWq9kSricrmYtWMWYA4k1orE4mlU3IhY7NReU8m4XC6L00htsDZ1LbuO78Lfy59hzYZZHUfE7VTciFhsYJtI/Lxt7D2cw5ZDmVbHkVpgxrYZAAxtMpRgn2CL04i4n4obEYsF+npxWetIQAOLpfIdyj7E4sTFANzU5iaL04hUDhU3ItXAyQX95m5MxulU15RUnpnbZuJ0OeneoDstwltYHUekUqi4EakG+reqT5CvF0nH8/jtwDGr44iHyi3K5fOdnwNwc5ubLU4jUnlU3IhUA37edga1Pdk1pQX9pHLM3TOXrMIsYoNj6RfTz+o4IpVGxY1INXFy1tTcjck41DUlbuZyufgk4RMAxrQeo32kxKPpp1ukmujdvC5hAd4czi5g5Z4jVscRD7M8eTl7MvYQ4BXAiOYjrI4jUqlU3IhUEz5eNoa0jwLgm42aNSXudbLVZkTzEZr+LR5PxY1INXJyr6lvN6dQWOy0OI14ip3HdrLs4DIMDG5sc6PVcUQqnYobkWqke9M61A3y5XhuEb/sOmx1HPEQ07dMB2Bg44E0DmlsbRiRKqDiRqQasdsMrupgrnmjBf3EHZKzk5m/Zz4At7W/zeI0IlVDxY1INXNyQb+FW1LIL3JYnEZquo+2fkSxq5huUd1oX7e91XFEqoSKG5FqpnNsOA3D/MkpdLBwS4rVcaQGyyjI4IudXwBqtZHaRcWNSDVjsxlc06UhAJ+vPWhxGqnJZmybQV5xHq3CW9ErupfVcUSqjIobkWro2vhYAH7edZhDx/MsTiM1UVZhFv/d+l8Abr/odgzDsDiRSNVRcSNSDTWqE0D3JhG4XPDlOrXeSNl9kvAJWYVZNA1tyqDGg6yOI1KlVNyIVFPXxscAZteUy6XtGOTCZRVm8dHWjwC4q+Nd2G12ixOJVC0VNyLV1NCLGhDgY2ffkVzW7NdO4XLh1GojtZ2KG5FqKtDXiysvMqeFz1pzwOI0UlOo1UZExY1ItXaya2rexmRyC4stTiM1wQebP1CrjdR6Km5EqrFuTSJoXCeAnEIH8zdpzRs5v9Sc1JIZUvd3uV+tNlJrqbgRqcYMw+DaLmbrzWfqmpI/MG3DNPId+XSq14lLYy+1Oo6IZVTciFRz13aNwWbAqr1H2ZmaZXUcqaZ2H9/N7F2zAfhL179oXRup1VTciFRzDUL9uaxNJACfrEy0OI1UV1PXTcXpcnJp7KV0qt/J6jgillJxI1ID3NyjMQBfrDuogcVyhl+TfmXJgSXYDTsPxD9gdRwRy6m4EakB+javS6OIALLyi/lmwyGr40g1UuQoYsqqKQCMaT2GpqFNLU4kYj0VNyI1gM1mcGP3RoC6pqS0j7Z+xL7MfdTxq8M9ne6xOo5ItaDiRqSGuC4+Bh+7jY0HM9h48LjVcaQaSMlJ4e2NbwPmIOJgn2CLE4lUD5YXN2+88QZxcXH4+fnRvXt3Vq1add7zjx8/zoQJE2jQoAG+vr60bNmS+fPnV1FaEevUCfJl6EVRAHy8Yr/FacRqLpeL51c9T15xHl3qd+GqpldZHUmk2rC0uPn000+ZOHEiTz75JOvWraNjx44MHjyYtLS0s55fWFjI5Zdfzr59+/j888/Zvn077777Lg0bNqzi5CLWODmw+OsNh8jIK7I4jVhp4f6FfJ/4PV6GF3/r/jdN/RY5jZeVN3/ppZe48847GT9+PABvvfUW8+bN4/333+exxx474/z333+fo0eP8uuvv+Lt7Q1AXFzcee9RUFBAQUFByfPMzEz3fQEiVSy+cTitIoPZnprFrDUHuKOvBo/WRkfzj/LsimcBuLPDnbSKaGVxIqkqDoeDoiLP/cPGx8cHm63i7S6WFTeFhYWsXbuWSZMmlRyz2WwMHDiQ5cuXn/U1X3/9NT179mTChAl89dVX1KtXjxtvvJFHH30Uu/3sy4xPmTKFp59+ulK+BpGqZhgG43rHMenLTXzwyz7G9YrDy25577JUsSkrp3Cs4Bgtw1ty50V3Wh1HqoDL5SIlJYXjx49bHaVS2Ww2mjRpgo+PT4WuY1lxc/jwYRwOB5GRkaWOR0ZGsm3btrO+Zs+ePfzwww/cdNNNzJ8/n127dnHPPfdQVFTEk08+edbXTJo0iYkTJ5Y8z8zMJDY21n1fiEgVG9m5IS8s3E7S8TwWbknlyg4NrI4kVWjB3gUs2LcAu2Hn773/jrfd2+pIUgVOFjb169cnICDAI7shnU4nhw4dIjk5mUaNGlXoayxXcZOamsrDDz/M4sWLSUtLw+Vylfq8w+Eod6DzcTqd1K9fn3feeQe73U58fDxJSUm88MIL5yxufH198fX1rZQ8Ilbw87Zzc4/GvLp4J//5eY+Km1rkQNYBnl5utkTfftHttK3T1uJEUhUcDkdJYVOnTh2r41SqevXqcejQIYqLi0uGn5RHuYqbcePGkZiYyBNPPEGDBg3KVV3VrVsXu91OampqqeOpqalERUWd9TUNGjTA29u7VBdUmzZtSElJobCwsMLNWCI1xS09GvPWkt38lnictfuPEd843OpIUsmKHEU8svQRsouy6Vy/M3d3vNvqSFJFTo6xCQgIsDhJ5Tv5Pu5wOKq+uPn555/56aef6NSpU7lv7OPjQ3x8PIsXL2bEiBGA2TKzePFi7r333rO+pnfv3syYMQOn01ky4GjHjh00aNBAhY3UKvWCfRnROZrP1hzkvZ/3EN843upIUsmmrpvKliNbCPEJ4fm+z+Nls3Q+iFjAE7uifs9dX2O5RiLGxsae0RVVHhMnTuTdd9/lww8/JCEhgbvvvpucnJyS2VNjx44tNeD47rvv5ujRozzwwAPs2LGDefPm8eyzzzJhwoQKZxGpaW7vY86UWrA5hX2HcyxOI5Vp3p55fLT1IwD+0fsfNAhSV6TI+ZSruJk6dSqPPfYY+/btq9DNR48ezYsvvsjkyZPp1KkT69evZ8GCBSWDjBMTE0lOTi45PzY2loULF7J69Wo6dOjA/fffzwMPPHDWaeMinq5VVDD9W9XD6YK3lu62Oo5Uko3pG5n8y2QAxrcfz4BGAyxOJFL9Ga5yNMGEh4eTm5tLcXExAQEBZ/SLHT161G0B3S0zM5PQ0FAyMjIICQmxOo5Ihazdf5Rrpi3H226w5JEBNAzztzqSuFFKTgpj5o3hcN5h+sf0Z+qAqdhtZ1/2QjxXfn4+e/fupUmTJvj5+Vkdp1Kd72sty/t3uTptp06dWp6XiYibxTeOoGfTOizfc4R3lu7m6avbWx1J3CSjIIN7Ft/D4bzDtAhvwXP9nlNhIzXOsmXLeOGFF1i7di3JycnMnj27ZJxtZSpXcXPrrbe6O4eIlNN9lzZn+Z4j/G/1ASZc2pz6wZ79l11tkF2YzV2L7mLnsZ3U86/Ha5e+RqB3oNWxRMosJyeHjh07cttttzFq1Kgqu2+5h9s7HA7mzJlDQkICAO3atWP48OHnXClYRCpHz2Z16NIojHWJx3l32R7+70qtfVKT5RXnce8P97L5yGbCfMN4d9C7NAzS/nlSmsvlIq+octaU+yP+3vYLntU0ZMgQhgwZUsmJzlSu4mbXrl0MHTqUpKQkWrUy9zSZMmUKsbGxzJs3j2bNmrk1pIicm2EY3HdZC8Z/sJqPlu/n9j5NiQpV601NlFmYyX2L72Nd2jqCvYN5+/K3aRam36dyprwiB20nL7Tk3lufGUyAT/VeiqBcs6Xuv/9+mjVrxoEDB1i3bh3r1q0jMTGRJk2acP/997s7o4j8gf4t69G1cTgFxU5e/WGn1XGkHNJz0xm3YFxJYfPmwDe1ArFIOZWr9Fq6dCkrVqwgIiKi5FidOnV47rnn6N27t9vCiciFMQyDR4e05rq3lvPp6gPc0acJTesFWR1LLtCOYzu4/4f7ScpOop5/PaYNnKadvuW8/L3tbH1msGX3ru7KVdz4+vqSlZV1xvHs7GytFCxikYvjIri0dX1+2JbGvxft4I0bu1gdSS7Agr0LmPzrZPKK84gNjuXty98mNlib+8r5GYZR7buGrFSubqmrrrqKP/3pT6xcuRKXy4XL5WLFihXcddddDB8+3N0ZReQCPTK4FYYB8zYms+lghtVx5DwKHAU8v+p5Hln2CHnFefRo0INPhn6iwkbEDcpV3Lz66qs0a9aMnj174ufnh5+fH71796Z58+a88sor7s4oIheoTYMQRnQyZ9Y8M3eLW7ZJEffbcngL139zPR8nfAzAbe1v462BbxHupw1QxbNkZ2ezfv161q9fD8DevXtZv349iYmJlXrfcrVphYWF8dVXX7Fz5062bdsGmLtzN2/e3K3hRKTsHhncigWbU1i97xhfrT/EiM6aRlxdZBVm8faGt/k44WMcLgd1/OrwVK+n6B/b3+poIpVizZo1DBhwasuQiRMnAuZ6edOnT6+0+1aow65Fixa0aNHCXVlExA2iw/y599LmvLBwO8/OT2Bg20iCfNU3b6UiZxFzds3h9d9e52i+uT3NkLgh/K373wjzC7M2nEgl6t+/vyUtyBf8G2/ixIn8/e9/JzAwsKTyOpeXXnqpwsFEpPzu6NuEWWsOsO9ILq8t3smkoW2sjlQrFTgKmLNzDh9s+YCk7CQAmoQ24ZGuj9A3pq/F6UQ81wUXN7/99htFRUUlj0Wk+vL1sjN5WFtum76G937eyzXxMbSMDLY6Vq2xL2MfX+z8gq93f13SUhPhF8GdF93J6Naj8bZ5/8EVRKQiLri4+fHHH8/6WESqp0tbRzKwTSTfJ6TyyKwNfHF3L7zs5ZpDIBdgf+Z+FicuZvH+xWw8vLHkeFRgFOPbjWdUi1H4eWnlaJGqUK6O+Ntuu41XXnmF4ODSfwnm5ORw33338f7777slnIhUzD9HtmfV3iNsOJjBuz/t5e7+WsrfHYqdxSRmJbI+bT1rUtawJnUNyTnJJZ+3GTb6NOzDNS2uoV9MP7xsGvMkUpUMVzlG+tjtdpKTk6lfv36p44cPHyYqKori4mK3BXS3zMxMQkNDycjIICQkxOo4IpVu1poDPPL5RnzsNubd34cW6p76Q0WOIjIKM8gsyCQ1N5WUnBSSc5I5mHWQncd3suf4HgqdhaVe42V40TWqKwMbDeTSRpdSL6CeRenF0+Tn57N3716aNGmCn59nt/6d72sty/t3mf6cyMzMLFm0Lysrq9SNHQ4H8+fPP6PgERFrXRsfw7xNySzZns7DszYw665e+HjVzO4pl8tFZmEmKTkpZBRkkFmYaX4UZJJXnEeRs+jUh6OIQmchRc4iip3FFDmKKHYVm49PHPv947ziPDILzWv9EX8vf9pEtCE+Mp6uUV3pVK8TAd4BVfBdEJE/UqbiJiwsDMMwMAyDli1bnvF5wzB4+umn3RZORCrOMAymjLqIwS8vY8PBDP61YBuPX1W9N2R0uVyk5qaScCSBbUe3se3oNhKzEknOSSanKKdKMhgYBPkEUd+/PlFBUTQIbEB0YDTNwprRIrwFDYMaYjNqZpEo4unKVNz8+OOPuFwuLr30Ur744otSG2f6+PjQuHFjoqOj3R5SRCqmQag/L1zXkT//dy3/+Xkv3ZpEMKhdlNWxSskuzOanpJ9Yfmg5y5OXk5KTcs5zI/wiCPUNJcQnxPzwDSHAKwAfuw/eNm/zw+5d8tjL5nXGYy+b1xmP/ex+JdcL8g7Cbqv+GwSKyJnKVNxccsklgLl8cmxsLDab/moRqSkGt4vi9j5NeO/nvTw8awPzGoQQG2FtN4rD6WDpwaXM3TOXZQeXUeAoKPmcl+FF07CmtI5oTeuI1jQNbUp0UDQNAhto1pGInFe5hvA3btwYgNzcXBITEyksLD2wrkOHDhVPJiJu9+gVrVm7/xjrDxznT/9dy6y7elqyenFOUQ6zd87m44SPSxa3A4gLiaN/bH96NOhBl8gu+Hv5V3k2Ean5yvVbLT09nfHjx/Ptt9+e9fMOh6NCoUSkcvh42Xjjpi5c/fovJCRnct+Mdbw7tmuVrX9T5Cziix1fMG3DtJLF7cJ8wxjRfARDmwyldURrDMOokiwiUvmmTJnCl19+ybZt2/D396dXr148//zztGrVqlLvW67faA8++CDHjx9n5cqV+Pv7s2DBAj788ENatGjB119/7e6MIuJGDcP8+c+tXfHztvHj9nSe/mZrlez9siJ5BaO+GsU/V/6To/lHaRTciCd6PMF3137HX7r+hTZ12qiwEfEwS5cuZcKECaxYsYJFixZRVFTEoEGDyMmp3IkB5Wq5+eGHH/jqq6/o2rUrNpuNxo0bc/nllxMSEsKUKVO48sor3Z1TRNyoU2wYU0d35u5P1vLfFfupG+TLAwMrZxPc3KJcXl77MjO3zwQg3DecezrdwzUtr9E2BCLl5XJBUa419/YOgAv8Q2TBggWlnk+fPp369euzdu1a+vXrVxnpgHIWNzk5OSXr2YSHh5Oenk7Lli256KKLWLdunVsDikjluKJ9FI9f2Za/z93Ky9/vwGbAfZe5t8DZfnQ7E5dMJDErEYDRrUbzQJcHCPbRQoIiFVKUC89aNDv5b4fAJ7BcL83IyAAoNdu6MpSruGnVqhXbt28nLi6Ojh078vbbbxMXF8dbb71FgwYN3J1RRCrJ7X2aUORw8ty32/j3oh0YBkwY0Nwt3UOL9i/i/37+P/KK84gMiOSZ3s/QK7qXG1KLSE3kdDp58MEH6d27N+3bt6/Ue5WruHnggQdITjb3UXnyySe54oor+OSTT/Dx8WH69OnuzCcileyuS5rhcLp4YeF2XvxuB+lZBUwe1g67rXwFjsvl4p2N7/D6+tcB6NGgBy9e8iKhvqHujC1Su3kHmC0oVt27HCZMmMDmzZv5+eef3RzoTOUqbm6++eaSx/Hx8ezfv59t27bRqFEj6tat67ZwIlI1Jgxojo/dxj/nJ/Dh8v0kHc/j1TGdCfAp268Il8vFS2tfYvqW6QDc3OZm/tL1L9o4UsTdDKPcXUNWuPfee5k7dy7Lli0jJiam0u/nlvmfAQEBdOnSRYWNSA12Z7+mvHlTF3y9bHyfkMaoN39lV1rWBb/e5XLx/OrnSwqbx7o9xqPdHlVhI1KLuVwu7r33XmbPns0PP/xAkyZNquS+F/xbZ+LEiRd80ZdeeqlcYUTEWkMvakBkiB9//u8atqVkMey1X3j66nZcFx9z3nE4LpeLf63+F58kfALA5J6Tua7ldVUVW0SqqQkTJjBjxgy++uorgoODSUkxt1UJDQ3F37/yFum84OLmt99+u6DztE6FSM0W3zic+Q/0ZeKnG/h512H++vlGvtuSwlPD2xETfva+9v9u/S8fJ3wMwDO9nmFki5FVGVlEqqlp06YB0L9//1LHP/jgA8aNG1dp973g4ubHH3+stBAiUr3UD/bjo9u6MW3pbqZ+v4PvE9L4ZdcRHhjYgnG94vDzPrWh5Pf7v+fFNS8CMDF+ogobESlRFQuEno12vhSRs7LZDCYMaM78+/vSLS6CvCIHz327jf4vLOHjFfspLHay5fAWHvvpMVy4GN1qNOPajbM6tohI+WZLDRgw4LzdTz/88EO5A4lI9dIiMphP/9yDL9Yl8dJ32zmUkc/jczbz2o8bscdOpcBRQL+YfjzW7TF1S4tItVCu4qZTp06lnhcVFbF+/Xo2b97Mrbfe6o5cIlKNGIbBtfExDOvYgP+tTOT1JbvICP4P3o40nIUR5B0czfxNaQxsU7/M08dFRNytXL+FXn755bMef+qpp8jOzq5QIBGpvny97Izr3QRCf+Lfa7eCy4u8pBv5IT+LHxJ+w9fLRrcmEfRpXpeezerQKioYXy/7H19YRMSN3Pon1s0330y3bt148cUX3XlZEalGth/dziu/mX/gTOr+CJ0HX8XcjYeYuzGZ/Udy+WnnYX7aeRgAb7tBq6hgLmoYSrN6QTSKCKBRnQBiwgMI9LGrG0tEKoVbi5vly5fj5+fnzkuKSDVS7Cxm8q+TKXYWMyB2AGNaj8EwDNo0COHhQa3YlZbNTzsP8/Ouw/yWeIxjuUVsTspkc1LmGdfy9bJRJ9CHiCAfIgJ9Cfb1ws/bjr+PDX9vO/7edvx87Ph52fH1tuHrZcfXy4aPlw1fL/P5ycd+p30+2M8bfx+1FonUZuUqbkaNGlXqucvlIjk5mTVr1vDEE0+4JZiIVD8fbvmQrUe2EuwTzBM9nijV8mIYBi0ig2kRGcxtfZrgcrk4eCyPzUkZbDmUyd4jORw4msv+I7lk5BVRUOzkUEY+hzLy3Z7T39tORKAPEYE+1AnyITY8gEYRAcRGBNC8fiBN6gaVe+8sEan+ylXchIaW3gDPZrPRqlUrnnnmGQYNGuSWYCJSvezN2Mub698E4K8X/5V6AfXOe75hGMSeKCiGXNSg1OdyCoo5mlPIkZxCjmQXcCSnkNyCYvKLneQVOsgvcpBX5CCv0Py3sNhJQbHzxL8OCs72vMh87HRBXpGDpON5JB3PO2u2AB87bRuE0L5hKD2aRtCzaV1CA7zd840SEcuVq7j54IMP3J1DRKoxl8vF08ufptBZSO/o3lzd7OoKXS/Q14tAXy9iI8q3u/C5uFwusguKOZZTxNHcQo7mFJCWWcCBY7kkHs0j8UgOO1KzyS10sGb/MdbsP8b0X/dhM6BjbBhD2zfgyg4NiA6rvGXhRaTyVWjMzZo1a0hISACgbdu2xMfHuyWUiFQvC/ctZG3qWvzsfkzuObnaDgQ2DINgP2+C/bxpVOfshZPD6WJPejabD2WwPvE4P+86zO70HH5LPM5vicf55/wEujWJYGzPxgxuF4W3XWuditQ05SpuDh48yJgxY/jll18ICwsD4Pjx4/Tq1YuZM2dWyXbmIlI18orz+PfafwNw20W3ER0UbXGiirHbTo0NGtnZ/F2VnJHH9wlpzN1wiFX7jrJqr/kRGeLL7X2aMLZn6S0nROTCTJs2jWnTprFv3z4A2rVrx+TJkxkyZEil3rdcf5LccccdFBUVkZCQwNGjRzl69CgJCQk4nU7uuOMOd2cUEQtN3zKdlJwUGgQ28NjtFRqE+nNLj8Z8+ueeLH/sMu6/rAV1g3xJzSzg2fnb6PevH/nv8n0UOZxWRxWpUWJiYnjuuedYu3Yta9as4dJLL+Xqq69my5YtlXpfw1WOXa38/f359ddf6dy5c6nja9eupW/fvuTm5rotoLtlZmYSGhpKRkYGISEhVscRqdZSclIYNnsY+Y58Xuj3Alc0ucLqSFWmoNjBV78d4pXFO0sGJrdpEMJzoy6iY2yYteGkVsnPz2fv3r00adKkZLkVl8tFXvHZB8xXNn8v/wp1TUdERPDCCy9w++23n/G5s32tJ5Xl/btc3VKxsbEUFRWdcdzhcBAdXbObrEXklNd+e418Rz5d6ndhcNxgq+NUKV8vO9dfHMvVnaP5dPUBXlq0g4TkTEa8+QvjesXx6BWt1VUllskrzqP7jO6W3HvljSsJ8C77ZACHw8GsWbPIycmhZ8+elZDslHJ1S73wwgvcd999rFmzpuTYmjVreOCBB7Q6sYiH2JOxh7l75gLwcNeHq+0g4srm62VnbM84Fk+8hJGdG+JywQe/7GPkm7+y93CO1fFEqr1NmzYRFBSEr68vd911F7Nnz6Zt27aVes9ydUuFh4eTm5tLcXExXl5m48/Jx4GBgaXOPXr0qHuSuom6pUQuzF+X/pVv931L/9j+vHbpa1bHqTZ+3J7Gw59t4EhOIUG+Xvzr2g4M/d06PiLuVNO7pQoLC0lMTCQjI4PPP/+c//znPyxduvSsBY6l3VJTp04tz8tEpIbYfnQ73+77FoB7O91rcZrqZUCr+sx/oC/3/e83Vu09yj2frOPxK9twR9+mVkeTWsQwjHJ1DVnBx8eH5s2bAxAfH8/q1at55ZVXePvttyvtnuUqbm699VZ35xCRauTkSsSD4wbTKqKVxWmqn8gQP2bc0Z1/zEtg+q/7+Me8BJIz8vm/oW2waVsHkfNyOp0UFBRU6j3KvYifw+Fgzpw5JYv4tWvXjuHDh2O3a4CdSE229chWfjjwAzbDxj0d77E6TrXlZbfx5LC2RIf58ez8bbz3814y8or41zUdVOCInDBp0iSGDBlCo0aNyMrKYsaMGSxZsoSFCxdW6n3LVdzs2rWLoUOHkpSURKtW5l91U6ZMITY2lnnz5tGsWTO3hhSRqvP+5vcBuCLuCpqGqavlfAzD4E/9mhEZ4sfEzzbw+dqD+HrZ+MeI9rV2ALbI6dLS0hg7dizJycmEhobSoUMHFi5cyOWXX16p9y1XcXP//ffTrFkzVqxYQUREBABHjhzh5ptv5v7772fevHluDSkiVeNA5gEW7V8EwO0XnbkGhZzd1Z0aAvDgp+v5ZGUiPl42Jl/VVgWO1HrvvfeeJfctV3GzdOnSUoUNQJ06dXjuuefo3bu328KJSNWavmU6TpeTvg370jK8pdVxapSrOzWkoNjJXz/fyAe/7CMqxI8/X6JWbBErlGudG19fX7Kyss44np2djY+PT4VDiUjVO5x3mDm75gBwW/vbrA1TQ13fNZbJV5nTW59bsI1FW1MtTiRSO5WruLnqqqv405/+xMqVK3G5XLhcLlasWMFdd93F8OHD3Z1RRKrAjIQZFDoL6VCvA/GR8VbHqbHG947jpu6NcLnggZm/kZCcaXUkkVqnXMXNq6++SrNmzejZsyd+fn74+fnRq1cvmjdvziuvvFLm673xxhvExcXh5+dH9+7dWbVq1QW9bubMmRiGwYgRI8p8TxE5Jbcol5nbZwJmq43GipSfYRg8NbwdvZrVIbfQwR0friEj98ztakSk8pSruAkLC+Orr75ix44dzJo1i1mzZrFjxw5mz55NaGhoma716aefMnHiRJ588knWrVtHx44dGTx4MGlpaed93b59+3j44Yfp27dveb4EETnN3D1zySrMolFwIwbEDrA6To3nbbfx5k1daFwngKTjeTz6xUbKsRi8SClOp+fvSu+u/07Kvc7Ne++9x8svv8zOnTsBaNGiBQ8++CB33HFHma7z0ksvceeddzJ+/HgA3nrrLebNm8f777/PY489dtbXOBwObrrpJp5++ml++uknjh8/Xt4vQ6TWc7lc/G/b/wC4ofUN2Ixy/c0jvxMW4MNrYzpzzbRfWbAlhU9WJnJzj8ZWx5IayMfHB5vNxqFDh6hXrx4+Pj4e2brqcrlIT0/HMAy8vb0rdK1yFTeTJ0/mpZde4r777ivZ2XP58uU89NBDJCYm8swzz1zQdQoLC1m7di2TJk0qOWaz2Rg4cCDLly8/5+ueeeYZ6tevz+23385PP/103nsUFBSUWgkxM1P93yKnW52yml3Hd+Hv5c+I5iOsjuNROsSE8egVrfnHvAT+PncrXePCaR2lPe2kbGw2G02aNCE5OZlDhw5ZHadSGYZBTExMhRcELldxM23aNN59913GjBlTcmz48OF06NCB++6774KLm8OHD+NwOIiMjCx1PDIykm3btp31NT///DPvvfce69evv6B7TJkyhaeffvqCzhWpjU622gxvNpxgn2CL03ie23o34eddh1myPZ0HZ67nm/v64G1X65iUjY+PD40aNaK4uBiHw2F1nErj7e3tlp0OylXcFBUV0bVr1zOOx8fHU1xcXOFQ55KVlcUtt9zCu+++S926dS/oNZMmTWLixIklzzMzM4mNja2siCI1SnJ2Mj8c+AGAG1rdYHEaz2SzGbx4XUcuf2kp21KyeHvpbu69tIXVsaQGOtldU9Eum9qgXH8+3HLLLUybNu2M4++88w433XTTBV+nbt262O12UlNLrwWRmppKVFTUGefv3r2bffv2MWzYMLy8vPDy8uKjjz7i66+/xsvLi927d5/xGl9fX0JCQkp9iIjpsx2f4XQ56R7Vnebhza2O47HqBvny5LB2ALy6eBe70rItTiTi2So0oPi7776jR48eAKxcuZLExETGjh1bqqXkpZdeOuc1fHx8iI+PZ/HixSXTuZ1OJ4sXL+bee+894/zWrVuzadOmUscef/xxsrKyeOWVV9QiI1IGRc4ivtz5JWAOJJbKdXWnaOasT2LJ9nQe/WIjs/7cUxtsilSSchU3mzdvpkuXLgAlrSV169albt26bN68ueS8CxnNPXHiRG699Va6du1Kt27dmDp1Kjk5OSWzp8aOHUvDhg2ZMmUKfn5+tG/fvtTrw8LCAM44LiLnt+zgMo7mH6WOXx0uib3E6jgezzAM/jnyIga9tJS1+48xY5VmT4lUlnIVNz/++KPbAowePZr09HQmT55MSkoKnTp1YsGCBSWDjBMTE7HZNPhOxN1Ottpc3fxqvG3qw68KDcP8eXhwK57+Ziv//m47wzpEExqg772IuxmuWrayVGZmJqGhoWRkZGj8jdRaqTmpDPpiEE6Xk29GfENcaJzVkWqNYoeToa/+xI7UbMb3jisZiyMi51eW9281iYjUQl/t/gqny0l8ZLwKmyrmZbcx+SqzoPlo+X52pp65CbGIVIyKG5FaxulylnRJjWoxyuI0tVOfFnUZ1DYSh9PFM3O3amsGETdTcSNSy6xOWU1SdhJB3kFc3vhyq+PUWv93ZRt87DZ+2nmYZTsPWx1HxKOouBGpZb7Y+QUAVza9En8vf4vT1F6N6wRyS09zttSLC7er9UbEjVTciNQiGQUZLN6/GICRLUZanEbu6d+MQB87m5IyWLglxeo4Ih5DxY1ILfLt3m8pdBbSKrwVbSPaWh2n1qsT5MvtfZsC8OJ3O3A41Xoj4g4qbkRqkbl75gLmJpkXssimVL47+jYhLMCbXWnZzP4tyeo4Ih5BxY1ILXEg8wAb0jdgM2wMaTLE6jhyQoifN3df0gyAVxbvoNjhtDiRSM2n4kaklpi712y16dGgB/UC6lmcRk43tmccdQJ9OHA0j683HLI6jkiNp+JGpBZwuVzM3zMfgKuaXmVxGvk9fx87t/VpAsCbS3bj1NgbkQpRcSNSC2w5soV9mfvw9/LnskaXWR1HzuKWno0J9vNiV1o2323VzCmRilBxI1ILnBxIPCB2AAHeARankbMJ8fPm1p5xALz+4y6teyNSASpuRDxckbOIb/d+C6hLqrq7rU8T/L3tbE7KZOmOdKvjiNRYKm5EPNyKQys4mn+UCL8Iekb3tDqOnEdEoA83dm8EwDvL9licRqTmUnEj4uFOdkldEXcFXjYvi9PIHxnfOw67zeDX3UfYeijT6jgiNZKKGxEPllecx48HfgTMvaSk+osJD+CK9lEAvPfzXovTiNRMKm5EPNjPST+TV5xHw6CGXFT3IqvjyAW648S08K83JJGWmW9xGpGaR8WNiAdbtG8RAIMaD9J2CzVI50bhdGkURpHDxX9X7Lc6jkiNo+JGxEPlF+ez5OASAC5vfLm1YaTM7jixoebHK/aTX+SwOI1IzaLiRsRD/XLoF/KK82gQ2ID2ddtbHUfKaFDbSGLC/TmWW8TX67Ulg0hZqLgR8VCL9ptdUpc3vlxdUjWQl93GTd0bA/DxSnVNiZSFihsRD1TgKGDJgSWAuqRqsuu7xuBjt7HxYAYbDhy3Oo5IjaHiRsQDLT+0nJyiHOoH1KdDvQ5Wx5FyqhPky9CLzGnhH2tgscgFU3Ej4oFOdkkNajwIm6H/zGuym3uYXVPfbDxERm6RxWlEagb91hPxMIWOQn5MNBfuU5dUzRffOJzWUcHkFzn5fN1Bq+OI1AgqbkQ8zIrkFWQVZVHPvx6d6neyOo5UkGEYJa03n6zcr93CRS6AihsRD3OyS2pg44HqkvIQIzo3JNDHzp70HJbvPmJ1HJFqT7/5RDxIkbOIHxJ/ANQl5UmCfL0Y2aUhgFYsFrkAKm5EPMiq5FVkFmZSx68OXep3sTqOuNHJrqlFW1M5nF1gcRqR6k3FjYgHOb1Lym6zW5xG3Kl1VAgdY8ModrqYvS7J6jgi1ZqKGxEPUeQsYnHiYkBdUp7q+q4xAHy25oAGFouch4obEQ+xJmUNxwuOE+4bTnxkvNVxpBIM6xiNn7eNnWnZ/KYVi0XOScWNiIc42SV1WePL8LJ5WZxGKkOInzdD2zcAYNaaAxanEam+VNyIeIBiZ7G6pGqJ67rGAvDNhmRyC4stTiNSPam4EfEA61LXcTT/KKG+oVwcdbHVcaQSdW8SQaOIALILipm/KcXqOCLVkoobEQ/w3f7vALis0WV427wtTiOVyWYzSg0sFpEzqbgRqeEcTgff7/8eUJdUbXFNfAw2A1btPcrewzlWxxGpdlTciNRwv6X9xpH8IwT7BNM9qrvVcaQKNAj1p1/LeoAGFoucjYobkRru5CypS2MvxduuLqna4tp4s2vqq/WHcDq15o3I6VTciNRgTpezpEtqUNwgi9NIVRrYJpJgPy+Sjuexcu9Rq+OIVCsqbkRqsA3pG0jLSyPIO4geDXpYHUeqkJ+3nSsvMte8+XLdQYvTiFQvKm5EarDv9pmzpAbEDsDH7mNxGqlqo7qYXVPzNyWTV+iwOI1I9aHiRqSGcrqcJeNtNEuqduraOJzYCH9yCh18t1Vr3oicpOJGpIbadHgTqbmpBHoH0qthL6vjiAVsNoORnc3Wmy+1U7hICRU3IjXUon1mq80lMZfga/e1OI1YZWTnhgD8tDOdtMx8i9OIVA8qbkRqIJfLVdIlNaixZknVZk3qBtKlURhOF3y94ZDVcUSqBRU3IjXQliNbOJRzCH8vf3o37G11HLHYyYHFX6hrSgRQcSNSI53cS6pfTD/8vPwsTiNWu6pDA3zsNhKSM0lIzrQ6jojlVNyI1DAul6tkCri6pAQgLMCHS1vXB2D2b2q9EVFxI1LDJBxNICk7CT+7H30a9rE6jlQTo7qYA4tn/5ZEscNpcRoRa6m4EalhTg4k7hvTlwDvAIvTSHXRv1V9wgO8Sc8q4JfdR6yOI2IpFTciNYi6pORcfLxsDO8YDcBsbccgtZyKG5EaZMexHSRmJeJr96VvTF+r40g1M/LErKkFW1LILii2OI2IdVTciNQgC/ctBKB3dG8CvQMtTiPVTceYUJrWCyS/yMm3m5KtjiNiGRU3IjVEqYX74tQlJWcyDINrTrTeaNaU1GYqbkRqiO3HtrMvcx++dl/6x/a3Oo5UU1d3MsfdLN9zhKTjeRanEbFGtShu3njjDeLi4vDz86N79+6sWrXqnOe+++679O3bl/DwcMLDwxk4cOB5zxfxFCe7pPo27KsuKTmnmPAAejSNwOWCOWq9kVrK8uLm008/ZeLEiTz55JOsW7eOjh07MnjwYNLS0s56/pIlSxgzZgw//vgjy5cvJzY2lkGDBpGUpP+IxXO5XK6S4mZw3GCL00h1N+q0rimXy2VxGpGqZ7gs/snv3r07F198Ma+//joATqeT2NhY7rvvPh577LE/fL3D4SA8PJzXX3+dsWPH/uH5mZmZhIaGkpGRQUhISIXzi1SFrUe2MnruaPzsfiwdvVTr28h5ZeUX0fUf31NQ7OTre3vTISbM6kgiFVaW929LW24KCwtZu3YtAwcOLDlms9kYOHAgy5cvv6Br5ObmUlRURERExFk/X1BQQGZmZqkPkZqmpEtKC/fJBQj282ZwuygAvtRmmlILWVrcHD58GIfDQWRkZKnjkZGRpKSkXNA1Hn30UaKjo0sVSKebMmUKoaGhJR+xsbEVzi1SldQlJeVxcjuGrzccokjbMUgtY/mYm4p47rnnmDlzJrNnz8bP7+w7I0+aNImMjIySjwMHDlRxSpGK2XJkC0nZSfh7+dMvpp/VcaSG6NO8LnWDfDmaU8jS7elWxxGpUpYWN3Xr1sVut5OamlrqeGpqKlFRUed97Ysvvshzzz3Hd999R4cOHc55nq+vLyEhIaU+RGqSk602l8Rcgr+Xv8VppKbwstsYcWJauNa8kdrG0uLGx8eH+Ph4Fi9eXHLM6XSyePFievbsec7X/etf/+Lvf/87CxYsoGvXrlURVcQS6pKSihh5omtqUUIqGblFFqcRqTqWd0tNnDiRd999lw8//JCEhATuvvtucnJyGD9+PABjx45l0qRJJec///zzPPHEE7z//vvExcWRkpJCSkoK2dnZVn0JIpVm0+FNJOck4+/lT5+GfayOIzVM2wYhtI4KprDYyTxtxyC1iJfVAUaPHk16ejqTJ08mJSWFTp06sWDBgpJBxomJidhsp2qwadOmUVhYyLXXXlvqOk8++SRPPfVUVUYXcZ/07ZDwNez9CY7tg7zj4BvEgrBgsEP/8Hb42X2tTik1jGEYjOrSkGfnb2P2bwe5sXsjqyOJVAnL17mpalrnRqqVA6tgyRTY/cMZn3ICg2KjSfXy4pXUdC71j4G+f4EOo8FmeaOr1BCpmfn0nLIYpwuWPtKfxnW0urXUTDVmnRuRWqsgC755EN673CxsDDu0GARXvgTjF8CE1fx27VukenkRiJ3eRTY4shPm3AX/uRRSNlv9FUgNERniR+/mdQENLJbaQ8WNSFVLS4C3+sDaD8znnW6C+9bCTbPg4tuhcU+o15K5WTsAuLz5MHz/sg0GPgU+wXDoN3j3Ulj5DtSuhlcpp2u0HYPUMipuRKrSzu/hP5eb42pCG8Gt38CINyGiSanTCh2FJbOkrmp6FfiFQJ+H4P510PIKcBTAt4/A1/eBQ7Ng5PwGtYskwMfO/iO5rEs8ZnUckUpn+YBikVoj4RuYNR6cRdC4D4z+LwScfduQn5J+Iqswi/oB9ekaedpyB0H1YcxMWPEmfPc4/PZfyEyC0R+Dj8ZSyNkF+HgxpH0Dvlh3kC/WJREf5Q0H10DGQcg7Br5BEBQFMRdDUD2r44pUmIobkaqQMBdmjQNnMbS/Bka8BV4+5zx93p55AFzZ5ErsNnvpTxoG9JwAEc3g8/HmmJ0Zo+HGT1XgyDld27EujvUzGblhCa6N2zFcjrOfGNkeuoyFjjeAX2jVhhRxE82WEqls+3+Fj0aYXUkXXQ8jpoH93H9XZBZm0v/T/hQ5i/h82Oe0imh17msfWAX/HQWFWRDXF27+Arw0ZVxO43TAhv/h+vFZjMzTBhSHNoJ6rcA/DApzzK7StK2nPu8XCv3/Zo4Ds3tXdWqRM5Tl/VstNyKVKX0H/G+MWdi0uhJGvgW/b4n5nUX7FlHkLKJFeIvzFzYAsd3gltnw35Gw7yeYfRdc856miovp8E7zZyJpDQaQ5VOPd3IuIb3pSJ67/aozz885Alu+hFXvwOEdsOBRWP8xXPsB1G1R5fFFyku/AUUqS34mzLwR8o9DTDe45j9/WNgAzN0zFzgxkPhCxF4MN3wMNm/zjWnRExUILR5j/QxzVl7SGvANgUH/IPXW5bzmGMXnu20czi448zWBdaDbnXDPCrhqKvhHQMomePsS2PR5lX8JIuWl4kakMrhc8NU95to0IQ3hhhngE/CHL0vOTmZN6hoMDIY2GXrh92va35x1BbD8dVj5dvlyS83ndMDC/4M5d0NxPjQdAPcsh1730bxhPTrGhlHsdDF73XnWvLHZoet4uPtXaNIPinLgi9vh55e1/IDUCCpuRCrDL1PN2VF2H7j+owuegTJvrzmQ+OKoi4kKjCrbPTtcDwOfNh8vmAR7l5Xt9VLzFebA/24wC1yAfo/AzV9CaEzJKTdcHAvA/1Yn/vGaNyEN4JY50GOC+fz7p8yWQRU4Us2puBFxt/2/wuJnzMdD/gUxF7Zzvcvl4uvdXwNwZdMry3fv3g9AhxvA5TBnZx1PLN91pOYpyIJProOd34GXH1z7Plz6+Bnjr4Z1jCbAx86e9BzW7L+ANW9sdrjiWRg8xXz+62vw/ZMqcKRaU3Ej4k55x+HLP4HLCR1vhPhxF/zSDekb2JuxF38vfwY1HlS++xsGDJsKDTpB7hGYeRMU5pbvWlJz5GeYs+b2/2KOrxn7tbnkwFkE+XoxrEM0ADNXHbjwe/S8B4a+aD7+5RWzdVKkmlJxI+JO8x+GjAMQ3gSG/sssNi7Qlzu/BGBQ40EE+QSVP4O3v7moX0BdSNkICx4r/7Wk+ivINgubg6vALwzGfgWNup/3JaO7mV1T8zYdIjO/DCtcd7sTBj9rPv7+Kdj8Zfkyi1QyFTci7rLxM9g0y9wEc9S74Bt8wS/NKcphwb4FAIxqMariWcJi4dr3AAPWfaiZLp6quAA+vdmcEeUfbm7n0bDLH76sc2wYLSODyC9y8vX6Q2W7Z88J0P1u8/HsuyBxZTmCi1QuFTci7pCZDPMeNh9f8qg5PbsMFuxdQF5xHnEhcXSu39k9mZr2NweUAnzzABzZ7Z7rSvXgdJhdoHt+BO9AuOkLaNDhgl5qGAajL24EwMzV5RiXNfif5rpNjgKYOcbcxkGkGlFxI1JRLhfMfQgKMiC6C/T9S5kv8eUus3l/ZIuRGGXoyvpDlzwKjXtDYbY5wLj4LGubSM20YBJsnWPOyLvhE4iJL9PLR3ZuiI/dxuakTDYnZZTt3jY7XPMuNOhoju367Fb9bEm1ouJGpKI2fwE7vjUX0bv6jfNurXA2u4/vZmP6RuyGneHNhrs3m93LXDzQP8Icf/OdFvjzCKv/A6tOrGU06h1oNqDMl4gI9GFwe3O5gXK13vgEmssc+IWZ3WIL/6/s1xCpJCpuRCoi5zB8+1fzcb9HILJtmS/x+Q5zPEy/mH7U9a/rznSmkGgYeeKNcNXbsPVr999Dqs7uH2D+iZ+5y56EdiPLfakxJ9a8mb0uiayyDCw+KTzOHF8GsPpd2Dir3FlE3EnFjUhFzH/EbJaPbA99Hirzy3OLcpmzaw4Ao1uNdnO407QcBL3uNx9/fa/Wv6mp0nfAZ+PMdYw6jinXz9zpejarQ/P6QeQUOvjyfCsWn0/LQdDvRLE190E4uqdCmUTcQcWNSHklzDX3cjLscPXr4OVT5kvM3TOX7KJsGgU3omd0z0oIeZrLJkPDruaaKJ/fDo5y/KUu1sk9Cv8bbY7tiu0Bw14p01IDZ2MYBmN7Ngbgo+X7/njF4nPp/xg06mWO7friTv1sieVU3IiUR94xmDfRfNz7fogu+wwnl8vFzO0zAbPVxmZU8n+Odm9zerhvqLkmyo/PVu79xH2KC+GzsWarSFgjcx0jL1+3XHpk54YE+tjZnZ7Dr7uPlO8iNrs59sc31Bx/s/RfbskmUl4qbkTKY+HjkJ0KdVrAJeVbJG9t6lp2HtuJn92Pq5tf7eaA5xAeB8NfMR///LI5fkOqN5fLXBxy30/gEwRjPr3gvcouRLCfN9fEm3tPffjrvvJfKCwWhr1sPv7pRXMbEhGLqLgRKatdi2H9x4Bhdkd5+5XrMidbba5seiWhvqFuDPgH2o2E+PGAC778M2SnVd29pexWvGkuxGjYzP2iyjFo/Y/c0sPsmvo+IZWk43nlv1D7a8xtR1xOcw2evOPuCShSRipuRMqiIBu+edB83O1P0KhHuS6TmpPK4v2LARjTeoybwpXBFVOgflvISYPZfwans+ozyB/bsRC+e9x8POgf0HJwpdymRWQwvZrVwemCjyrSegPmtiPhceY2JPMfcUc8kTJTcSNSFj/8HTISIbSROUC3nD5J+IRiVzFd6nehVUQrNwa8QN7+ZiuAl7/ZNfXrK1WfQc4vdas58NvlhC5jocc9lXq72/s0AWDGysTyTQs/yTcYRv3HbGna9Jm5DpRIFVNxI3KhElfCyhPrxQybCr7l29wyqzCLz3Z8BsBt7W9zU7hyqN8GhjxvPl78dziwyrosUlp2ujkzqjAL4vrC0H9XeGbUHxnQqj7N6gWSVVDMp6vLsFv42cRefGrrj7kPQUY5p5mLlJOKG5ELUZRvrg+DCzrdBM0vK/elZu2YRU5RDs3DmtM3pq/7MpZHl7HQbpS5bsrnt2uMRHVQlA+f3mSuRRTR1FwFuBzLDJSVzWbwp35NAXj/570UOSrYVdnvEXM7kvwMmHOXuj6lSqm4EbkQP70Ih3dAUKS5aWA5FToK+XjrxwCMazeu8qd//xHDMFuhwhqb3W1f32fOzhFrOJ3w1T1wYCX4hZozowIiquz2V3dqSN0gXw5l5DN/U3LFLmb3Nlcv9g6Avctg5TT3hBS5ACpuRP5IyiZz2jTA0BfBP7zcl5q3Zx7peenUD6jP0CZD3RSwgvxC4doPwOYFCV/DmvetTlR7LXnWHKNi84Lr/wv1Wlbp7f287YzrZc6cenvpnvIv6ndS3ean/hj4/mlI3VLBhCIXRsWNyPk4iuGre8FZDG2GQ9vyb2xZ7Czm/c1m4TC27Vi87d7uSllxMfEw8Cnz8YJJkLTW0ji10voZsOwF8/GwV6DpJZbEuLlHY/y97WxNzmTJjvSKXzB+PLS8AhwF5urF2j1cqoCKG5HzWf46JK83WzeGvlihS83bM499mfsI8w3j2pbXuiefO/WYAK2Gmm9CM2/W+jdVae9P8PWJvb/6TITON1sWJSzAp2RLhqnf76x4641hwPDXIKAupG0xZxyKVDIVNyLnkroFfjzRpD74WQiOLPelihxFTNtgjjm4rf1tBHoHuiOhe9ls5u7hdVpA1iGYNU57BFWFtAT49GZwFkHbEXDpE1Yn4s5+TfH3trPhwHH3tN4E1TcLHIBfXzfH4IhUIhU3ImdTXGCu3usohJZDzBlSFTB712ySspOo41eHG1rf4KaQlcAvBG6YAT7BsP8XWPg3qxN5tmP74b8jIf84xFwMI98yi0yL1Q3y5RZ3tt4AtB4KXW4FXDD7bs3Mk0pl/X9FItXRkimQugkC6sDwVyu0xkiBo4C3N5rr49zZ4U78vfzdlbJy1GtpboIIsOodWPuhtXk8VXYa/HcEZCVDvTZw42fm4orVxJ/6NcXP2+a+1hswW0AjmkLmQXO/LJFKouJG5Pf2L4efp5qPh71iNqlXwMxtM0nLTSMqMIrrWl5X8XxVofVQ6H+i1WbuQ7Dze2vzeJr8DPj4mlO7fN/yZZVO+b4QdYN8GdszDoCXvtuB0+mG1hvfIHN6uGGHTbNg0+cVv6bIWai4ETldQZa519LJxfraDKvQ5Y7kHeHtDWarzV0d7sLHXvmLsbnNJX+FjmPMBf4+GwuHfrM6kWfIz4RProeUjRBYD26ZAyHRVqc6qz/1a0qQrxebkjL4aoObVhmO6Xra6sUTIeOge64rchoVNyInuVxmK8Xx/ebeUVc8V+FLvvbba2QVZdEmog0jmo+oeMaqZBgw7FVo2h+Kcsw35GP7rE5Vs+VnwMej4MAKcwbezV9AnWZWpzqnukG+3N3fzPfCgu3kFzncc+F+D0PDrlCQAbO1erG4n4obkZPWfWg2lRt2uOZdc3BtBWw5vIUvd34JwKTuk7Db7O5IWbW8fMzF5CIvMncQ//gac98jKbu8Y/DRCDi4GvzCYOzX0KCj1an+0O19mtAwzJ9DGfm89/Ne91zU7m2O6/IOgH0/nVrfR8RNVNyIgLkK8fy/mo8vmwyNelTock6Xk2dXPYsLF1c1vYrO9Tu7IaRF/ELgplkQGgtHdsFHwyHniNWpapacI/DR1XBoHfhHwK3fQHQnq1NdED9vO3+9wty5/s0fd5GWle+eC9dpBlf+23y8ZArsXOSe64qg4kbEnJL62a3m4nUtBkOv+yt8yS92fsHG9I34e/nzUPxDFc9otZAGMPYrCIqCtK3mG3XuUatT1QzH9sH7gyB5g7mQ3bi50KCD1anKZFiHaDrGhJJT6OC5+dvcd+FON0LX2wAXfHE7HHVTy5DUeipupHZzFMPnt8HR3RAS45Z1RpKzk/n3GvMv0gmdJlA/oGKzraqNOs3MN+bA+uY0+Q+HQ1aq1amqt0Pr4T+Xmy1eobEwfj5EtrM6VZnZbAZPDW+HYcCXvyWxzF1Tw8Ec2xZzsTke6dNboDDXfdeWWkvFjdRui56A3YvNvv8xMyo8HdflcvH0iqfJKcqhY72O3NzGumX0K0XdFqULnPcHmdOZ5UxbZsMHQ82xSpEXwe2LoF4rq1OVW+dG4dx6Ymr432ZvIrew2D0X9vKF6z8yZ46lboJvHtDO9FJhKm6k9lr7Iax403w88i23DO6csW0GvyT9go/Nh2d6P1MzBxH/kXqt4PaFEB5ndrm8N1jTxE/ndMD3T5nbVxTlQLNLzRabkAZWJ6uwhwe3omGYPweP5fHSdzvcd+GQaLhu+on1bz6DJRWfqSi1m4obqZ22zTOnfYO5WF3bqyt8yYQjCSXdUX/p+heahjat8DWrrYimcNt3EHViFtX7Q7QgG0Bmsrmdws8vm8973Q83zqrwzLvqIsjXi3+MbA/A+7/sZc0+N467iusDV534vi19Dn772H3XllpHxY3UPnt/glnjzcXpOt1kLlZXQRkFGTy89GGKnEUMiB3AmNZj3BC0mguOhHHzoMUgKM4zB4R+94Q5jqk22jYPpvWCvUvNbs5r3oNBfwe7l9XJ3GpAq/qM6twQpwsemLmejDw3bq4afyv0PbEtwzcPaGVsKTcVN1K7HFwL/xtjzoxqdaW5SF0F9o0CKHYW88jSR0jMSiQ6MJpnej2DUcFr1hh+oTBmJvSZaD7/9VX4YEjtmvWSc8TcCHLmjZB3FKI6wJ+WwkXXWp2s0jx9dTsaRQSQdDyPv325yT0ba5506eNw0fXgLIZPb4I9S913bak1VNxI7bHvF3MKc2EWxPWFa9+v8F/VLpeL51c9z/Lk5fh7+fPqpa8S5hfmnrw1hc0OA580x0z4hsDBVfBWX/jtE88eGOpywYaZ8MbFsGEGYEDPe+GO783NRz1YsJ83r47pjJfNYN6mZN79yY2Dyg0Drn4DWg6B4nz43w3mf7siZaDiRmqHXd+bq+ueLGzG/A+8/Sp82bc2vsXM7TMxMPhnn3/SKqLmzoapsHYj4a6foVFP8/v81T3w4TBI3251Mvfb/yv85zJzH7LcI1C/rTkbavA/zdk/tUCn2DAmD2sLwHPfbmPJ9jT3XdzLB67/EJpfDkW58Ml1sGeJ+64vHk/FjXi+dR/BjBvMcSEtBpur7foGV/iyH275kDfXm7OtHuv2GJc3vrzC16zxwhub43AGPgVe/ubS+tN6w4K/Qc5hq9NV3ME1MGO02fWWtBZ8gswVrf+8DGIvtjpdlbulR2NuuDgWpwsmfLKOjQePu+/iXr4w+mNoOsCcdfbxtbBxlvuuLx7NcLm1s7T6y8zMJDQ0lIyMDEJCPGMGg5yDoxgW/g1Wmbty0/4aGPGW+VdhBbhcLt7a+FZJYXNPp3u4u+PdFU3reY7tg28fhR0LzOc+QdDjHuhxd4XXE6pSTgfs/gGWv36q9cCwQfw46D8JgjxkkcZyKix2Mu6DVfy6+wgRgT589ueeNK8f5L4bFBeYLWRbZpvPBz4NvR+o8Fg5qXnK8v6t4kY80/ED5m7D+382nw/4P+j3SIV/IRY5ivjnyn/yxc4vALiv8338qcOfKprWc7lcsGsxLH4aUjaax7z8oeNo6H4X1G9jbb7zOZ5obqS6drr5GMDmBR1GQ5+HzAUNBYDsgmLGvLOCTUkZ1A3y5ZM7utMqquKtoyWcTvju/06tS9V2BAx/zWOm2MuFUXFzHipuPNzJQZ7f/hUKMsE7EEa9DW2GVfjSablp/HXZX1mbuhYDg0e7PcpNbW5yQ+hawOmEhK/hp3+fKnIAojubxUK7kRAcZV2+k47th21zYfOXkLTm1HG/UHPZgB53Q1gj6/JVY0eyC7j5vVUkJGcSFuDNe7deTHzjcPfeZOU7ZmusswgimpmD2GvYPl1SfipuzkPFjQdL327+4tt1Ym2MmG7mysN1mlXosi6Xix8Sf+Cp5U9xvOA4gd6B/Kvfv+gX088NoWsZl8scjLviTbO7ynnamjgNOppjouJ6Q8N4t4yL+sMsGQfg4GpzuvHepWZXWgnDXFiu4w3QbhT4BFRuHg+QkVvErR+sYv2B4/jYbUwZdRHXxMe49yYHVpurP2ceNFvSej8A/f7qlgkCUr2puDkPFTceKCsVfn4JVr1rLsxn84b+j0HvBys81ftA5gGeW/0cyw4uA6BNRBue7/c8TUKbuCF4LZdzGDZ/ARs/K91KAoBhzkBq2BnqtoQ6zc2PkGhz7E5ZuhcLcyEr2Sxcju011+BJ3Wzu0p137He3tUOjHma3R9urzYUKpUxyCoqZ+Nl6Fm4xN1W9Lj6GJ4e3I8jXjYsZ5hyBuQ+arYFg/mwM+ge0vEJjcTyYipvzUHHjQY7shl9fg/UzzEX5AFoNNX/JVbC1JiUnhQ+3fMhn2z+j0FmIl82Lce3GcXfHu/GxV2xAspxFdhrsXGRuYnpgNWQknvtcLz9zk0X/cPOxly/Yfcw3teICcBSa66PkHoPcw+ZU4nOxeZvjfuL6QNP+0LhX5bcY1QJOp4upi3fy2g87cbkgJtyfp4a1Y2BbNxeLCd/AvIchO8V8HtPNXASwST8VOR5Ixc15qLip4fIzzV9o6z+B/act7BXTDQZMMjcpLCeny8m61HXM3jWb+XvmU+wyu0x6NujJpO6T1FpTlbJS4MAqSN0CR3ad+Nhtrp9THl5+5kaf4U0goonZGhTdyWwdqiXr0lhh1d6jPPTpepKO5wHQt0VdHhzY0r1jcfIzzL28VrxlLvcAENkeut0JF10HPoHuu5dYqsYVN2+88QYvvPACKSkpdOzYkddee41u3bqd8/xZs2bxxBNPsG/fPlq0aMHzzz/P0KFDL+heKm5qmOJCSN0E+5fDzoXmeI2ScRoGtLjc7H5q3Ktcf6kVOApYl7qO5YeWs3DfQg7lHCr5XLeobtzW/jZ6RfeqPdspVHeFOWZ3Vs5hc6uD4vwTrTVFgMtswfHyBbuv2bITWAcC6pgrJ+t/Q0vkFBTz2g+7eO/nPRQ5zLebLo3CuOHiRlzZoQGB7uquykqBZS+aG26eLHK8A8zfEW2vNv/w8XfzAGepUjWquPn0008ZO3Ysb731Ft27d2fq1KnMmjWL7du3U7/+metH/Prrr/Tr148pU6Zw1VVXMWPGDJ5//nnWrVtH+/bt//B+Km6qKUexOS6i5K/0XXBoPSSvN9/ATle3pTnDpuMYCG14QZd3uVwcLzjOgawD7M/cz9YjW9l6ZCtbjmyh4GSXFhDkHcTljS/n2pbX0qGeZmGIuEvikVze+HEXX6w7SLHTfNvx97bTq1kd+raoS6/mdWlaNxAvewXXls07Zm79sfo/5hirEoa5i33j3ua/ke2gXivw9q/Y/aTK1Kjipnv37lx88cW8/vrrADidTmJjY7nvvvt47LHHzjh/9OjR5OTkMHfu3JJjPXr0oFOnTrz11lt/eL/KKm4KC7I4fGQ7uFy4cAGukn11zOeYnyv5dp/6fKnXQKlzXC7naY9PvO4s5+E87bwT1zz1+ORnnGfNVPLcdTK388THifufyGBmMT/vOuMcF5Rc33Xqc06HWZwU5eEqzjf/oirKx1WUZzYn5x3DlXfUfHwqVWm+wVCvDa6GXSC2O4Q2pNhZTIGjgILiAvId+RQ4CsgvNv/NK87jWP4xjhUc41j+MY7mHyUlJ4Xsouyz/m9X378+PaJ70C+mH5fEXIKfl2ZdiFSWtMx8vliXxGdrDrD3cE6pz/l62WgdFUzjOoE0CPUjKtSPyBA/AnzsBPh44e9tx9/Hjt1m4HKd+K3pMn83Ol3gdLlwOM2PYocT38ObCNs7j4gDiwjIPHP/Kxc2cv2jyPWLIscvkhzfSPK8gimwBZJvDyTfFkSB4UsRdoqx4cSO07DjMrxxGTYMXBg4zX9dpz3Ghe3E70vbyXNcrpLPAScemwzj5G8+o+Tz4DrV2Hi2X4wGmJsMnLiScfpVDVyGgWFQ8vzki1wnLurCMO9mGOe8BoZ57FzXOHl/jN99VYZBeEgwg3t2Pt+PQpmV5f3bjcPXy66wsJC1a9cyadKkkmM2m42BAweyfPnys75m+fLlTJw4sdSxwYMHM2fOnLOeX1BQQEHBqb/MMzMzKx78LBJ2zuXmtc9WyrU9mj/g7wf8QUHhTIQDiXBgToVuVz+gPo2CG9EqohVt67SlfZ32NAltom4nkSpSP8SPu/s3465LmrI1OZNlOw6zbEc6Gw4eJ7fQwYaDGWw4mOHGO14CXEI9jtHTlkBn205aGwdobUsk3MgmMO8QgXmHqOfGOwps82oDPVdYdn9Li5vDhw/jcDiIjCw9gj4yMpJt27ad9TUpKSlnPT8lJeWs50+ZMoWnn37aPYHPw2Z44ecsXV6f6+3SOM855/tcWV9jnPH/y5rHOFnIn/dKxunHjNLPzdeb1b1hGKc9toHNZk69tdnB8DKf/+56pxcdpx+3GTb8vPzwtfviZ/fD18u35LGflx9hvmFE+EUQ7hdOuF84kQGRNAxqqFYZkWrCMAzaRYfSLjqUu/s3w+l0sf9oLgnJmSQdyyM5I5+UzDzSswrILXSQV+ggr8hBbqEDp9PFyYYGm838zWAYBjYD7DYDL5vtxL8GthP/2m0h7LfFccA2lPk2A7sBdTlOpDOVus7D1HGkE+E8SoAzmwBXDv5O88PHVYjd5cCGA7urGJvLgc3lwMDJqbYYA5dhK2mncRnm7zInNlyGUXIcw8B5ji0dXaf9fnOd5fesq9Tv1VPtJLhOtgadPMN12nHz+anXnDh2tte4SrcqnbrOqfuVHDtxjuE6y31xYbggMNCNW3CUg6XFTVWYNGlSqZaezMxMYmNj3X6fi9pdx+p217n9uiIitYHNZtCkbiBN6mp2kydw/7ts2Vha3NStWxe73U5qamqp46mpqURFnX0p9qioqDKd7+vri6+vpnqKiIjUFhUcll4xPj4+xMfHs3jx4pJjTqeTxYsX07Nnz7O+pmfPnqXOB1i0aNE5zxcREZHaxfJuqYkTJ3LrrbfStWtXunXrxtSpU8nJyWH8+PEAjB07loYNGzJlyhQAHnjgAS655BL+/e9/c+WVVzJz5kzWrFnDO++8Y+WXISIiItWE5cXN6NGjSU9PZ/LkyaSkpNCpUycWLFhQMmg4MTERm+1UA1OvXr2YMWMGjz/+OH/7299o0aIFc+bMuaA1bkRERMTzWb7OTVXTIn4iIiI1T1nevy0dcyMiIiLibipuRERExKOouBERERGPouJGREREPIqKGxEREfEoKm5ERETEo6i4EREREY+i4kZEREQ8ioobERER8SiWb79Q1U4uyJyZmWlxEhEREblQJ9+3L2RjhVpX3GRlZQEQGxtrcRIREREpq6ysLEJDQ897Tq3bW8rpdHLo0CGCg4MxDMOt187MzCQ2NpYDBw5o36pKpO9z1dD3uWro+1x19L2uGpX1fXa5XGRlZREdHV1qQ+2zqXUtNzabjZiYmEq9R0hIiP7DqQL6PlcNfZ+rhr7PVUff66pRGd/nP2qxOUkDikVERMSjqLgRERERj6Lixo18fX158skn8fX1tTqKR9P3uWro+1w19H2uOvpeV43q8H2udQOKRURExLOp5UZEREQ8ioobERER8SgqbkRERMSjqLgRERERj6Lixk3eeOMN4uLi8PPzo3v37qxatcrqSB5n2bJlDBs2jOjoaAzDYM6cOVZH8khTpkzh4osvJjg4mPr16zNixAi2b99udSyPM23aNDp06FCy0FnPnj359ttvrY7l8Z577jkMw+DBBx+0OopHeeqppzAMo9RH69atLcuj4sYNPv30UyZOnMiTTz7JunXr6NixI4MHDyYtLc3qaB4lJyeHjh078sYbb1gdxaMtXbqUCRMmsGLFChYtWkRRURGDBg0iJyfH6mgeJSYmhueee461a9eyZs0aLr30Uq6++mq2bNlidTSPtXr1at5++206dOhgdRSP1K5dO5KTk0s+fv75Z8uyaCq4G3Tv3p2LL76Y119/HTD3r4qNjeW+++7jscceszidZzIMg9mzZzNixAiro3i89PR06tevz9KlS+nXr5/VcTxaREQEL7zwArfffrvVUTxOdnY2Xbp04c033+Qf//gHnTp1YurUqVbH8hhPPfUUc+bMYf369VZHAdRyU2GFhYWsXbuWgQMHlhyz2WwMHDiQ5cuXW5hMxD0yMjIA841XKofD4WDmzJnk5OTQs2dPq+N4pAkTJnDllVeW+l0t7rVz506io6Np2rQpN910E4mJiZZlqXUbZ7rb4cOHcTgcREZGljoeGRnJtm3bLEol4h5Op5MHH3yQ3r170759e6vjeJxNmzbRs2dP8vPzCQoKYvbs2bRt29bqWB5n5syZrFu3jtWrV1sdxWN1796d6dOn06pVK5KTk3n66afp27cvmzdvJjg4uMrzqLgRkXOaMGECmzdvtrTv3JO1atWK9evXk5GRweeff86tt97K0qVLVeC40YEDB3jggQdYtGgRfn5+VsfxWEOGDCl53KFDB7p3707jxo357LPPLOlmVXFTQXXr1sVut5OamlrqeGpqKlFRURalEqm4e++9l7lz57Js2TJiYmKsjuORfHx8aN68OQDx8fGsXr2aV155hbffftviZJ5j7dq1pKWl0aVLl5JjDoeDZcuW8frrr1NQUIDdbrcwoWcKCwujZcuW7Nq1y5L7a8xNBfn4+BAfH8/ixYtLjjmdThYvXqy+c6mRXC4X9957L7Nnz+aHH36gSZMmVkeqNZxOJwUFBVbH8CiXXXYZmzZtYv369SUfXbt25aabbmL9+vUqbCpJdnY2u3fvpkGDBpbcXy03bjBx4kRuvfVWunbtSrdu3Zg6dSo5OTmMHz/e6mgeJTs7u9RfAXv37mX9+vVERETQqFEjC5N5lgkTJjBjxgy++uorgoODSUlJASA0NBR/f3+L03mOSZMmMWTIEBo1akRWVhYzZsxgyZIlLFy40OpoHiU4OPiM8WKBgYHUqVNH48jc6OGHH2bYsGE0btyYQ4cO8eSTT2K32xkzZowleVTcuMHo0aNJT09n8uTJpKSk0KlTJxYsWHDGIGOpmDVr1jBgwICS5xMnTgTg1ltvZfr06Ral8jzTpk0DoH///qWOf/DBB4wbN67qA3motLQ0xo4dS3JyMqGhoXTo0IGFCxdy+eWXWx1NpMwOHjzImDFjOHLkCPXq1aNPnz6sWLGCevXqWZJH69yIiIiIR9GYGxEREfEoKm5ERETEo6i4EREREY+i4kZEREQ8ioobERER8SgqbkRERMSjqLgRERERj6LiRkRERDyKihsRqRGWLFmCYRgcP37c6igiUs1phWIRqZb69+9Pp06dmDp1KgCFhYUcPXqUyMhIDMOwNpyIVGvaW0pEagQfHx+ioqKsjiEiNYC6pUSk2hk3bhxLly7llVdewTAMDMNg+vTppbqlpk+fTlhYGHPnzqVVq1YEBARw7bXXkpuby4cffkhcXBzh4eHcf//9OByOkmsXFBTw8MMP07BhQwIDA+nevTtLliyx5gsVkUqhlhsRqXZeeeUVduzYQfv27XnmmWcA2LJlyxnn5ebm8uqrrzJz5kyysrIYNWoUI0eOJCwsjPnz57Nnzx6uueYaevfuzejRowG499572bp1KzNnziQ6OprZs2dzxRVXsGnTJlq0aFGlX6eIVA4VNyJS7YSGhuLj40NAQEBJV9S2bdvOOK+oqIhp06bRrFkzAK699lr++9//kpqaSlBQEG3btmXAgAH8+OOPjB49msTERD744AMSExOJjo4G4OGHH2bBggV88MEHPPvss1X3RYpIpVFxIyI1VkBAQElhAxAZGUlcXBxBQUGljqWlpQGwadMmHA4HLVu2LHWdgoIC6tSpUzWhRaTSqbgRkRrL29u71HPDMM56zOl0ApCdnY3dbmft2rXY7fZS551eEIlIzabiRkSqJR8fn1IDgd2hc+fOOBwO0tLS6Nu3r1uvLSLVh2ZLiUi1FBcXx8qVK9m3bx+HDx8uaX2piJYtW3LTTTcxduxYvvzyS/bu3cuqVauYMmUK8+bNc0NqEakOVNyISLX08MMPY7fbadu2LfXq1SMxMdEt1/3ggw8YO3Ysf/nLX2jVqhUjRoxg9erVNGrUyC3XFxHraYViERER8ShquRERERGPouJGREREPIqKGxEREfEoKm5ERETEo6i4EREREY+i4kZEREQ8ioobERER8SgqbkRERMSjqLgRERERj6LiRkRERDyKihsRERHxKP8P8A4CiiK+hIAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_population(opt_unperturbed_dynamics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "Now we can analyze how robust this control is for variations of ±20% of the\n",
    "pulse amplitude. Numerically, this is achieved by scaling the control\n",
    "Hamiltonians with a pre-factor $\\mu$.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:30.128652Z",
     "start_time": "2020-03-22T05:01:30.122273Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.435742Z",
     "iopub.status.busy": "2024-06-03T14:25:45.435519Z",
     "iopub.status.idle": "2024-06-03T14:25:45.439042Z",
     "shell.execute_reply": "2024-06-03T14:25:45.438751Z"
    }
   },
   "outputs": [],
   "source": [
    "def scale_control(H, *, mu):\n",
    "    \"\"\"Scale all control Hamiltonians by `mu`.\"\"\"\n",
    "    H_scaled = []\n",
    "    for spec in H:\n",
    "        if isinstance(spec, list):\n",
    "            H_scaled.append([mu * spec[0], spec[1]])\n",
    "        else:\n",
    "            H_scaled.append(spec)\n",
    "    return H_scaled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the analysis, we take the following sample of $\\mu$ values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:30.138078Z",
     "start_time": "2020-03-22T05:01:30.131210Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.444350Z",
     "iopub.status.busy": "2024-06-03T14:25:45.444208Z",
     "iopub.status.idle": "2024-06-03T14:25:45.451939Z",
     "shell.execute_reply": "2024-06-03T14:25:45.446690Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "mu_vals = np.linspace(0.75, 1.25, 33)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "We measure the success of the transfer via the \"population error\", i.e., the\n",
    "deviation from 1.0 of the population in state $\\ket{3}$ at final time $T$.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:30.153375Z",
     "start_time": "2020-03-22T05:01:30.144877Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.462713Z",
     "iopub.status.busy": "2024-06-03T14:25:45.462451Z",
     "iopub.status.idle": "2024-06-03T14:25:45.469328Z",
     "shell.execute_reply": "2024-06-03T14:25:45.468323Z"
    }
   },
   "outputs": [],
   "source": [
    "def pop_error(obj, mu):\n",
    "    res = obj.mesolve(tlist, H=scale_control(obj.H, mu=mu), e_ops=[proj3])\n",
    "    return 1 - res.expect[0][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:40.680753Z",
     "start_time": "2020-03-22T05:01:30.156668Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:45.473923Z",
     "iopub.status.busy": "2024-06-03T14:25:45.473631Z",
     "iopub.status.idle": "2024-06-03T14:25:47.602503Z",
     "shell.execute_reply": "2024-06-03T14:25:47.602171Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "def _f(mu):\n",
    "    return pop_error(opt_result_unperturbed.optimized_objectives[0], mu=mu)\n",
    "\n",
    "\n",
    "pop_errors_norobust = [_f(mu) for mu in mu_vals]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:40.693446Z",
     "start_time": "2020-03-22T05:01:40.684478Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.604288Z",
     "iopub.status.busy": "2024-06-03T14:25:47.604178Z",
     "iopub.status.idle": "2024-06-03T14:25:47.606958Z",
     "shell.execute_reply": "2024-06-03T14:25:47.606628Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_robustness(mu_vals, pop_errors, pop_errors0=None):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(mu_vals, pop_errors, label='1')\n",
    "    if pop_errors0 is not None:\n",
    "        ax.set_prop_cycle(None)  # reset colors\n",
    "        if isinstance(pop_errors0, list):\n",
    "            for (i, pop_errors_prev) in enumerate(pop_errors0):\n",
    "                ax.plot(\n",
    "                    mu_vals, pop_errors_prev, ls='dotted', label=(\"%d\" % (-i))\n",
    "                )\n",
    "        else:\n",
    "            ax.plot(mu_vals, pop_errors0, ls='dotted', label='0')\n",
    "    ax.set_xlabel(\"relative coupling strength\")\n",
    "    ax.set_ylabel(r\"$1 - \\vert \\langle \\Psi \\vert 3 \\rangle \\vert^2$\")\n",
    "    ax.axvspan(0.9, 1.1, alpha=0.25, color='red')\n",
    "    ax.set_yscale('log')\n",
    "    if pop_errors0 is not None:\n",
    "        ax.legend()\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:41.453727Z",
     "start_time": "2020-03-22T05:01:40.696343Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.608495Z",
     "iopub.status.busy": "2024-06-03T14:25:47.608382Z",
     "iopub.status.idle": "2024-06-03T14:25:47.795133Z",
     "shell.execute_reply": "2024-06-03T14:25:47.794824Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fOHXlhtSlERHV6nhGIUZ8dgB7z1+HrUKGD8Z2wcdPhsDRlksbmiIGJTJrcpmAqEGt8cOzvdCsqT0u55fh8S//xNcH0qDTcSqOiEyHKIr45o90PLn8ELKKKtDCowm2RvXFkz0CpC6N7oJBiSxC9+Zu2D6nP4Z38oFaK+Lt2GQ8szoe+SWVUpdGRARVhRozvzuOt7YlQaMTMaKzL36Z1RcdfJ2lLo3+AYMSWQwXBxt8Mb4b3h7dCUqFDHvOX8fwTw/gz5Q8qUsjIit25moRRn7+B3aczYGNXMCbj3bEsnFd4WRnI3VpdA8YlMiiCIKAf/dqjl9m9UVrL0dcK67E+G+O4KOd56HR6qQuj4isiCiKWH8kA499+Scu55ehWVN7bJrRB5F9giAIXGHbXDAokUVq7+OM/5vVD0+HBUAUgWV7UvCvrw4jV8XtT4io4ZVVaTDvh5N45afTqNLo8EB7L8TO6YfQgKZSl0Z1xKBEFsteKcd7j3XB5093hZOtAscuF2Lk53/gREah1KURkQW7mFuMUcsO4qcTVyGXCXj5ofZYObEHmjoopS6NjMCgRBZvZIgfts3ph7be+qm4p746jM0JV6Qui4gs0NYTV/HosoO4eK0EXk62WD81HDMHtuJmtmaMQYmsQnP3JtjyXF88GOyNKo0OL2w6iXdik9i3RET1Qq3V4X9bT2PuxkSUq7Xo29odsXP6I7ylu9Sl0X1iUCKr4WirwIp/d8fswa0BACsPpGPK6mMoKuNq3kRkvKIyNSatOorvDmdAEIA5g1tjzZRweDrZSl0a1QMGJbIqMpmAF4a2Q/S4brC3kWP/hesY/cVBbqxLREa5nF+Kx748iIMp+XBQyrFyQg/MG6rfLYAsA4MSWaURXXzx48zeaNbUHul5pRgTfRB7zl2TuiwiMiPHLhVgzBd/IvV6KXyc7bBpRm8MCfaWuiyqZwxKZLU6+rng51l9ERbkhuJKDaasjseXe1Mhitz6hIjubuuJqxi38ggKSqvQuZn+vaSjn4vUZVEDYFAiq+bhaIvvpobj6bBAiCLw/o5zmLsxERVqrdSlEZEJEkURS3ZdwNyNiajS6jCsozc2PtsL3s52UpdGDYRBiayeUiHDu2M64a1RHaGQCfg5MQtPrjiE7KJyqUsjIhNSodZizveJ+CzuIgDg2YiW+HJ8dzgoFRJXRg3J6oPSmDFj4OrqirFjx0pdCklIEARM6B2Etc+Ew9XBBqeuFGHk5weRcJmLUxIRkFdSiXErD+P/TmZBIRPw/uOdsXB4B66PZAWsPig9//zzWLNmjdRlkIno3codv8zqh/Y+TsgrqcTTXx3GD8cypS6LiCR0IbcYo6MP4njGDTjbKbDmmTA81TNQ6rKokVh9UBo4cCCcnJykLoNMSICbAzbP7INhHb1RpdVh/o+n8PFv59nkTWSF9l+4jse/+BNXCsvR3N0BP0X1RZ9WHlKXRY3IpIPS/v37MXLkSPj5+UEQBGzduvW220RHRyMoKAh2dnYIDw/H0aNHG79QsjhNbBX4cnx3zHmgDQDg899T8N+tZ6DVMSwRWYu1hy9jckw8iis1CAtyw0/P9UUrT0epy6JGZtIdaKWlpQgJCcGUKVPw2GOP3Xb9xo0bMW/ePCxfvhzh4eFYunQphg0bhvPnz8PLywsAEBoaCo1Gc9vP/vbbb/Dz86tTPZWVlaisrDR8r1Kp6viMyJzIZALmPdgWXk62ePXnM1h/JANFZWoseSoEtgq51OURUQPR6kS8E5uMbw+mAwAe69YM7z3Wmce9lTLpoDR8+HAMHz681uuXLFmCadOmYfLkyQCA5cuXIzY2Ft9++y0WLFgAAEhMTKy3et577z28+eab9XZ/ZB7+3as5mjrY4D8bExF7OhuqCjWW/7s7mtia9OFDREaoUGsxa/0J7E7OBQC8OLQtoga1hiCwadtamfTU291UVVUhISEBQ4YMMVwmk8kwZMgQHDp0qEEec+HChSgqKjJ8ZWayyddaPNLFD99O6gkHpRwHLuZh/NdHUFhaJXVZRFSPSis1mBITj93JubBVyLBsXFfMGtyGIcnKmW1QysvLg1arhbf3rcvFe3t7Iycn557vZ8iQIXjiiSewfft2+Pv73zVk2drawtnZ+ZYvsh7923hi3dRwNHWwQWLmDTzBtZaILIaqQo2J3x7Fn6n5aKKUY82UMDzSpW7tGWSZzDYo1Zfdu3fj+vXrKCsrw5UrV9C7d2+pSyIT1jXQFZue7Q0fZzukXCvB2C8PIe06N9QlMmeFpVUYv/IIEi4XwtlOge+mhiO8pbvUZZGJMNug5OHhAblcjtzc3Fsuz83NhY+Pj0RVkTVo4+2EH2f2RkuPJrh6oxxPLD+E01eKpC6LiIxwvbgS//rqME5fLYJbEyU2TO+FroGuUpdFJsRsg5JSqUT37t0RFxdnuEyn0yEuLo6jQtTg/F0dsGlGb3Ru5oL80io8vfIw/kzNk7osIqqD7KJyPLXiEM7nFsPLyRYbp/fixrZ0G5MOSiUlJUhMTDScuZaeno7ExERkZGQAAObNm4eVK1di9erVSE5OxsyZM1FaWmo4C66hREdHIzg4GD179mzQxyHT5u5oi/XTwtG7pTtKKjWY9G08dpy59/44IpJOZkEZnlxxCGl5pWjW1B4/PNsbbby5+DDdThBNeLnhvXv3YtCgQbddHhkZiZiYGADAsmXL8OGHHyInJwehoaH47LPPEB4e3ij1qVQquLi4oKioiI3dVqxCrcXz35/AzrO5kAnA4se64MmeAQ33gMXFQGws4OwMODg03OMQNYayMkClAkaMABppl4S06yUY//URZBdVoLm7A9ZNDYe/K48la1KXz2+TDkqmjkGJami0Ovz3pzPYWL0v3MLh7fFsRKuGeTAGJbIkjRyUzucUY/zXR5BXUonWXo5YNzUc3s52Df64ZFrq8vlt0lNvROZCIZdh8eOdMaM6HL336zm892sy94cjMiGnrxThqa8OIa+kEsG+ztg4vRdDEv0jBiWieiIIAhYMb49XHm4PAFixLw1v/l8SwxKRCUi4XIBxKw/jRpkaoQFNsWFaL7g72kpdFpkBBiWiejZ9QCt88HgXCAIQ8+clfLjzvNQlEVm1P1PyMOGbo/rNbVu44bup4XBxsJG6LDITDEpEDeDJngF4e3QnAMAXe1MRvSdF4oqIrNOe89cwOSYeZVVa9G/jgdWTw+DIfRqpDhiUjMDlAehejA9vjv+N6AAA+HDneXz7R7rEFRFZlx1ncjB9zTFUanQY0sELKyf2gL1SLnVZZGYYlIwQFRWFpKQkxMfHS10Kmbip/VviP0PaAgAWbUvC90czJK6IyDrsOXcNs9Yfh1orYkQXX3z57+6ws2FIorpjUCJqYHMeaI1nB7QEACz86TR+TrwqcUVEli3hciFmrkuARididKgfPvtXV9jI+XFHxuFvDlEDqzkb7t+9AiGKwLwfTmLnWa7gTdQQLuQWY0pMPCrUOgxq54kPnwiBXCZIXRaZMQYlokYgCAIWPdoJj3fzh1YnYvb6E9h34brUZRFZlKs3yjHxm6MoKleja2BTRI/vxpEkum/8DSJqJDKZgPcf74wRnX1RpdXh2bXHcCQtX+qyiCxCQWkVJnxzBDmqCrTxcsSqST3hoOTZbXT/GJSIGpFCLsMnT4VicHsvVKh1mBITj8TMG1KXRWTWSis1mBwTj7TrpfBzscOaZ8LQ1EEpdVlkIRiUiBqZUiHDF+O7oU8rd5RWaTHxmyNIylJJXRaRWarS6DDjuwSczLwBVwcbrHkmHL4u9lKXRRaEQckIXEeJ7pedjRwrJ/ZAt8CmUFVoMOGbI0i5ViJ1WURmRacT8eKmkzhwMQ/2NnJ8O6knWns5Sl0WWRgGJSNwHSWqD01sFVg1OQydmjkjv7QK//76CDILyqQui8gsiKKIRduS8MvJLChkApZP6I6uga5Sl0UWiEGJSEIu9jZYMyUcbbwckaOqwLivDyOnqELqsohM3hd7UxHz5yUAwMdPhiCirae0BZHFYlAikphbEyXWTQ1Hc3cHZBaUY/zXh5FXUil1WUQm6/ujGYbNpl97JBijQptJXBFZMgYlIhPg5WyHdVPD4edih9TrpZi25hgq1FqpyyIyOTvO5OCVn04DAKIGtcKUfi0krogsHYMSkYnwd3XAd1PD4WJvgxMZN/DKT6chiqLUZRGZjMNp+Zjz/QnoROBfPQPw4tB2UpdEVoBBiciEtPR0RPS4bpDLBGw5fhUrD6RJXRKRSTibVYRpq4+hSqPD0GBvvD26EwSBW5NQw2NQIjIx/dp44LVHggEA7/16DnvOXZO4IiJpZeSXIfLbeBRXahDWwg2fPd0VCm5NQo2Ev2lEJmhi7+Z4Oky/ie6cDSeQcq1Y6pKIJFFQWoUJ3x5BXkkl2vs4YeXEHrCzkUtdFlkRBiUjcMFJamiCIODNRzsirIUbiis1eGb1MRSWVkldFlGj0upEzNlwApfzyxDgZo81U8LgYm8jdVlkZRiUjMAFJ6kxKBUyLP93d/i72uNyfhmi1h+HWquTuiyiRvPxb+fxR4p+1e2vJ/aEl7Od1CWRFWJQIjJhbk2U+DqyB5oo5fgzNR9vbUuSuiSiRrHzbA6+2JsKAHh/bBe083GSuCKyVgxKRCauvY8zPnkqFIIArDl0GeuOZ0ldElGDSr1eghd+OAkAmNK3BR4N8ZO4IrJmDEpEZmBoRx/DmjGv70zFoWI2s5JlKq3UYMbaBJRUn+G28OH2UpdEVo5BichMPDewFR4N8YNGJ+K5S3bIKOdilGRZRFHE/B9P4eK1Eng722LZuK6w4TIAJDH+BhKZCUEQ8MHYLuji64hCrQzTzgIlGoYlshxfH0hH7Ols2MgFfDG+G7yc2LxN0mNQIjIjdjZyfDW2I7wUOpwvA+aeqoSO25yQBTh0+QYW7zgHAHj1kWB0b+4mcUVEegxKRGbGx9kWX7Uoh1IAdl/T4qOLaqlLIrov2VUCZm1JhlYn4rGuzTChV3OpSyIyYFAiMkOhTXT4sHo/0C/S1Pg5SyNtQURGqtSJmHnJHvllanTwdcY7YzpzDzcyKQxKRGZqlJeAmS30qxS/dKYSiTe0EldEVHdvpQKJZXK42Cmw4t/dYa/kGZ1kWhiUjMAtTMhUvNTWBkM85ajSAdNPVCKngit3k/n48aoa32UDAkQsHdUege4OUpdEdBsGJSNwCxMyFTJBwNIQW7R1FHCtUsTsk5XQsrmbzMAZlRb/Pavfv3CuTxUGtWbzNpkmBiUiM+eoELCymx0c5UB8oQ4r0tncTaatsErEjBOVqNQBD7gBs7254TOZLgYlIgvQ3EGG1zsoAQCfXFTjTBH7lcg0aUURz5+qxJVyEc0dBCxpD8jYu00mjEGJyEKMbabAcG851KJ+faUKLafgyPQsTVFjf54WdjJgeVc7uCiYksi0MSgRWQhBEPBuR1t42QpIKRWx+DynM8i07Lqmweep+qnhxZ1s0cGJH0Fk+vhbSmRBXJUCPuykn4KLydBg33Wur0SmIaNMh3mnKgEAkwIVGO2nkLgionvDoERkYSI8FYgM1H8IvXSmCoVVnIIjaelEEfPPVKJYA3RvKsMr7ZVSl0R0zxiUiCzQgnZKtG6iXzLglbOVELlkAEloXaYGhwt0sJcDn3SxhZLd22RGGJSILJC9XMDSLrZQCMCvuVps5hYnJJEr5TpDv9z8NkoEOvBjh8wLf2OJLFQnFzn+01q/xckbSVXILOOq3dS4RFHEwjOVKNUCPV1liGzOviQyPwxKRBZsRksb9HSVoUQL/OcUV+2mxrXxigYH8nWwlQEfdLKFjJvdkhliUCKyYHJBwJLOtnCUA8du6LA8jat2U+PIKtfh7XP6KbcX2yjRogk/bsg88TfXCNwUl8xJgIMMbwRXr9qdwlW7qeGJooiFZ6tQogW6usgwJYhTbmS+GJSMwE1xydw87qdftVsjAs+fqkQ5V+2mBvTjVQ325WmhlAEfdraFnFNuZMYYlIiswM2rdqdy1W5qQLkVOrxVPeX2n9Y2aO3Ijxkyb/wNJrISN6/avZqrdlMDEEUR/z1bBZUGCHGRYVqQjdQlEd03BiUiKxLhqcCk6lW7XzxThQKu2k316OdsLXZf18JG0J/lpuDCkmQBGJSIrEzNqt3XuWo31aNrlTq8kazfy21Oaxu044a3ZCH4m0xkZexuWrV7R64WP17lFBzdH1EU8WpSFW6ogY7OMsxowSk3shwMSkRWqJOLHPPaVK/anVyFDK7aTfdhW44WO3O1UAjAh52UsOGUG1kQBiUiK/VsCxuEucpQqgVePsMpODJOfpWI15P0U27PtbRBsLNc4oqI6heDEpGVkgsCPu5sC1sZcKhAhx25XIiS6u61pEoUqIH2jgJmteKUG1keBiUiKxbgIMOz1f0k75yvQgUXoqQ62JGjQWyOFnIB+KizLZScciMLxKBEZOVmtLCBr52AK+UiVl7iXnB0bwqrRPyvesptRgsbdHLhlBtZJgYlIivnoBCwoK1+Icov0tTIrmBjN/2zN5MrkVcFtHEUMKc1p9zIcjEoEREe9ZWjR1MZyrXA+9zehP7BrmsabM3WQgbgw062sOWUG1kwBiUigiAIeL2DEgKArdlaJBSysZvurEit36YEAKa1sEFoU065kWWrc1AqLy/H1atXb7v87Nmz9VIQEUmjs4scT/rrtzd5M7kKOi4XQHfwaUoVrlWKaOkg4D+cciMrUKeg9OOPP6JNmzYYMWIEunTpgiNHjhiumzBhQr0XR0SN68U2SjgpgFMqHVfspttklumwNkP/e/F6ByXs5JxyI8tXp6D09ttvIyEhAYmJiVi1ahWeeeYZrF+/HgCsarG66OhoBAcHo2fPnlKXQlSvPG0FzGmlb+z+4IIaxRrrOa7pn318sQpqEejrLsMAD065kXWoU1BSq9Xw9vYGAHTv3h379+/HihUrsGjRIgiC9fxlERUVhaSkJMTHx0tdClG9i2yuQAsHAXlVIpalcrkA0juj0mJrtr53bUFbpVW955N1q1NQ8vLywqlTpwzfu7m5YdeuXUhOTr7lciIyX0qZgFfb60eVvr2kRnoplwsg4P3z+tA80keOzlwziaxInYLS2rVr4eXldctlSqUSGzZswL59++q1MCKSziBPOSI85FCL+hW7ybr9kafFgXwtbATgpeo1t4isRZ2Ckr+/P3x8fO54Xd++feulICKSniDoR5UUArD7mhb789jYba10oojFF/RheXyAAoEOXFWGrAt/44nojlo7yhAZqF8uYFFyFdQ6NnZbo205WpxR6eAoB2a35mgSWR+FMT/UokULoxr55s6dizlz5hjzkEQkgTmtlfgpS4OUUhHfZWgwOYjr5liTKp2Ij6pHk55taQN3JRu4yfoYFZRiYmKMerCgoCCjfo6IpOFiI+DFtkq8crYKn6RUYZSfAm78sLQa6zM1yCgX4Wkr4JnmDMlknYwKShEREfVdBxGZqKf8FfguQ4OkYh2WXKzC2x1tpS6JGkGxRsRnKfrRpLmtbOCgYEAm61SvPUoFBQXQ6XgqMZElkVfvAwfoRxiSVNwHzhqsTFejQA20dBAMW9sQWaP7DkpJSUlYvHgx+vTpA09PT3h5eWHixInYvHkzSktL66NGIpJYuJscI3zk0AFYdK7Kqlbit0bXKnRYeUm/btL8tkrYyDiaRNbLqKB0/vx5vPDCC2jTpg169eqF+Ph4zJgxA7m5udi+fTuaN2+ORYsWwcPDA8OHD8eXX35Z33UTUSNb2E4JWxlwuECHHbkcVbJkn6aqUa4FurrIMMybi0uSdTMqKP35558oLS3FZ599hry8PGzevBkTJ06Eh4cHwsLC8NZbb+HkyZNITk7GQw89hC1bttR33UTUyPztZZjRQt/Q+875KlRoOapkiVJLdPj+in7drAXtuFUJkSByDN1oKpUKLi4uKCoqgrOzs9TlkLUoLgZiYwFnZ8DBoVEfulwrYvCBcmRXiHixjQ1mteK6OpZm5okK/JqrxQOecnzT3a7hH7CsDFCpgBEjACenhn88ItTt85sLThLRPbOXC1jYTh+OotPUyK7gyRuW5PgNLX7N1UIGfW8SEd1nUEpOTsaqVatw7tw5AMC5c+cwc+ZMTJkyBb///nu9FEhEpmWkjxw9XWUo1wIfXOA+cJZCFEUsrt7X7/FmCrRz4t/RRMB9BKUdO3YgNDQUL774Irp27YodO3ZgwIABSElJweXLlzF06FCGJSILJAgCXm+vH234OUuLS6UcVbIEv1/X4mihDrYy4D+tubgkUQ2jg9KiRYvw0ksvIT8/H6tWrcK4ceMwbdo07Nq1C3FxcXjppZewePHi+qyViExEJxc5Bnnqlwv4uvo0cjJfWlHE+9Wjg5Oa28DPnqNJRDWMPhrOnj2LSZMmAQCefPJJFBcXY+zYsYbrx48fj1OnTt13gURkmp6tPgNu01UN8ip5Tog523xVgwslIlxsgOdacjSJ6Gb39WdDzWmjMpkMdnZ2cHFxMVzn5OSEoqKi+6uOiExWuKsMIS4yVOqANRkcVTJXFVoRn6To//1mtVTCxYbLARDdzOigFBQUhIsXLxq+P3ToEAIDAw3fZ2RkwNfX9/6qIyKTJQiCYVRpTYYaZRqOKpmjmMtqZFeIaGYnYEIgtyoh+jujg9LMmTOh1f61Om+nTp2gUPx1kP36668YPHjw/VVHRCZtmLcczR0E3FADP1zVSF0O1dGNKhFfpOlHk+a1sYGdnKNJRH9n9J8PM2bMuOv17777rrF3TURmQi4ImBZkg/8lVWFluhr/DlBAwX3BzMYXaWqoNEB7RwGj/TiaRHQnPLWBiO7L2GYKuCuBqxUiYnO4B5y5uFquQ0x1b9nL7ZSQc6sSojtiUDJCdHQ0goOD0bNnT6lLIZKcnVzApOb6XqUV6WpwVyTz8FW6GlU6oJebDAM9uPEtUW2MGmtt0aKFURslzp07F3PmzDHmIU1KVFQUoqKiDHvFEFm7CQE2+CJNjaRiHf7I16E/P3hNWrFGxI/VPWWzWnLjW6K7MSooxcTEGPVgQUFBRv0cEZm2pkoB//JXYNVlDVakV6G/h73UJdFdbL6qQakWaNVEQF93TiwQ3Y1RQSkiIqK+6yAiM/dMkA3WZGjwR74OZ4q06OTCUSVTpBNFrLms702KDLThaBLRPzD6T4mMjAxkZGQgMzOTC0sSEfztZRjpow9HK9K5AKWp+iNfi7QyEY5y4LFmPNON6J/c14KTLVq0QFBQENzc3BAYGIg33ngDVVXcTZzIWk2vXoBye64WmWXcLNcUrb6s700a66+Ao4KjSUT/xOg/J/bs2QMAEEURWVlZOHbsGD766CPs2rULu3fvhr09exSIrE2wsxz93eU4kK/FN5fUeCPYVuqS6CYZZTr8fl2/hMPEQO7pRnQvjB5RioiIQEREBAYOHIhx48ZhyZIlOHv2LDIzM7Fo0aL6rJGIzMiM6k1Vv7+iQUEVlwowJWsz1BABDPCQo2UTNnET3QujjxSVSnXbl6urK1544QVs2rQJxcXFUKlU9VkrEZmBPm4ydHKWoUKn/2Am01CmEbHxin7abRL3dCO6Z0YfLU2bNr3r2RIuLi4QBOGW/eCIyPLVbJY7+2QlVl9WY3oLG9hzDzHJbc3WQKUBAu0FDPTkGYlE9+q+e5T+bseOHVi9ejU2bNhgdFFEZN6Ge8sRYC8gs1y/sOEE9sNISrxpSYCJgTaQcUkAontmdFC601pKpaWlmDt3LkaMGMG1loismEKm3yz3tWT9ZrlP+3OzXCkdKdThXIkIeznwhD+n3YjqwugjJiMjA4D+L5Xs7GwcP34cH3zwARQKBd599916K5CIzNMT/gp8klKFjHIRO3K1eMSXH9BSWV09mjTGTwEXGwZWorow+p0rKCjI0KMkiiJsbGwwduxYfPLJJ/D09Ky3AonIPNnLBUwMtMGnqWqsSFdjhI+cq0BLIKtch9+ucUkAImMZHZR+//13CIIAQRDg5OSEdu3awcHBoT5rIyIzN7G5DVakq3FapcOhAh36uLOJuLGty9RAKwK93GRo78QlAYjqyqiglJOTg969e8PW9t4Wk0tLS0PLli2NeSgiMmPuSgFP+iuwJkODFelqBqVGVqEVsSFTP+02iaNJREYx6s+LH3/8EW5ubhgzZgxWrVqF69ev33abI0eO4JVXXkHHjh0REhJy34USkXmaGmQDGYB9eVokF3Nbk8a0LUeDAjXgZydgiBdDKpExjApKs2bNwsmTJ9G/f3/ExMTA398f/fr1w7vvvotp06bB19cXo0ePxrVr17B48eI7Bikisg6BDjI8XL1Z7lfp3AuysYiiaNjXbXwAzzokMpYgiuJ97zGQn5+Pbdu2Yfv27QgKCsKoUaPQu3dvi2/cVKlUcHFxQVFREZydnaUuh6xFcTEQGws4OwNm0hd4ukiLkYcqIBeAfQPs4W/PXpmGdvyGFo8droBSBhwe6AA3pYm+H5eVASoVMGIE4OQkdTVkJery+V0v5+u6u7sjMjISkZGR9XF3RGRhOrvI0dddhoP5Onx7SY3XOnCz3IZWsyTAo74K0w1JRGaAf9YRUaN4tsVfm+Xe4Ga5DepapQ7bc/RLAkRyXzei+8KgRESNor+7HB2cZCjTAt9lcrPchrQhUwO1CHRrKkNnFzZxE90Po/7UaNGihVH9R3PnzsWcOXOMeUgiMnM1m+XOPVWJmMsazGhhwwbjBlClE7EuU9/EHcklAYjum1FBKSYmxqgHCwoKMurniMgyjPCRY1EykFcl4mC+FhGenBaqbztytbhWKcLTVsBwH44mEd0vo96luOEtERnDRibgYR8FvsvU4JdsBqWGsKa6iXucvwJKjtgR3Tf2KBFRo3q0enPc365pUKFlU3d9OqPS4tgNHRSCfu0kIrp/DEpE1Kh6uMrgZyegWAPsva6VuhyLUrPA5MM+cnjZ8e2dqD7wSCKiRiUTBIysHlX6OVsjcTWWo7BKNLyebOImqj/1GpQuXLgAjYZvfER0dyN99U3Gcde1KNZw+q0+fH9FjSod0MlZhm5N+TcwUX2p16OpQ4cOSEtLq8+7JCIL1NFJhpZNBFTpgN9y+cfV/dLoRHyXUTOapLD47aOIGlO9BqV62DaOiKyAIAiGpu5fstmndL/irmtxtUKEqw0M05pEVD84PktEkqgJSn/ka5HPLU3uS82+bv/yt4GdnKNJRPWJQYmIJNGyiQydnWXQisD2HE6/GetCsQ5/FuggA/Bv7utGVO8YlIhIMn9NvzEoGWvDFf1o0lBvOZrZ8y2dqL7xqCIiyTziK4cAIL5Qh6vlOqnLMTuiKGJnrr7Ha2wzjiYRNQQGJSKSjK+dDGGu+reh/+OoUp2dVumQVSHCQQ70c+e+bkQNwaqDUmZmJgYOHIjg4GB06dIFmzZtkrokIqvDs9+MVzOaNNBDziZuogZSr0Hp5Zdfhru7e33eZYNSKBRYunQpkpKS8Ntvv2Hu3LkoLS2Vuiwiq/KwjwIKAUgq1iGlhNNvdbGzeg2qYd6cdiNqKPUalN577z2zCkq+vr4IDQ0FAPj4+MDDwwMFBQXSFkVkZVyVAvp76KeN2NR971JLdEgpFaEQgIGenHYjaigmPfW2f/9+jBw5En5+fhAEAVu3br3tNtHR0QgKCoKdnR3Cw8Nx9OhRox4rISEBWq0WAQEB91k1EdXVqJvOfuPCtffmt2v6UNnbTQ4XG067ETUUkw5KpaWlCAkJQXR09B2v37hxI+bNm4fXX38dx48fR0hICIYNG4Zr164ZbhMaGopOnTrd9pWVlWW4TUFBASZOnIivvvqqwZ8TEd3uQS857GTApTIRp1WcfrsXNf1Jw7w5mkTUkEx6Ynv48OEYPnx4rdcvWbIE06ZNw+TJkwEAy5cvR2xsLL799lssWLAAAJCYmHjXx6isrMTo0aOxYMEC9OnT5x9vW1lZafhepVLd4zMhortpohDwgJccsTla/JKtQRcXfvjfTU6FDolFOggAhnrxtSJqSA02opSZmYkpU6Y01N2jqqoKCQkJGDJkiOEymUyGIUOG4NChQ/d0H6IoYtKkSRg8eDAmTJjwj7d/77334OLiYvjiNB1R/ak5+21bthY6Tr/d1a5r+tGkrk1l8LIz6YkBIrPXYEdYQUEBVq9e3VB3j7y8PGi1Wnh7e99yube3N3Jycu7pPg4ePIiNGzdi69atCA0NRWhoKE6fPl3r7RcuXIiioiLDV2Zm5n09ByL6y0BPOZwUQE6liKOFnH67m7/OduNoElFDM3rq7Zdffrnr9WlpacbedaPp168fdLp7f0O2tbWFra1tA1ZEZL1sZQKGeyvww1UNfs7SoJcbQ8CdFKlFHC7Qv28N9TLp7gkii2D0UTZ69GgIgnDXM1QEoeHOxPDw8IBcLkdubu4tl+fm5sLHx6fBHpeIGs6jvvqg9GuuBm8GK6GU8Wyuv/v9uhYaEWjrKKBFE067ETU0o48yX19fbNmyBTqd7o5fx48fr886b6NUKtG9e3fExcUZLtPpdIiLi0Pv3r0b9LGJqGH0dpfBQynghhr4I48rdd8JF5kkalxGB6Xu3bsjISGh1uv/abTpXpSUlCAxMdFw5lp6ejoSExORkZEBAJg3bx5WrlyJ1atXIzk5GTNnzkRpaanhLDgiMi9yQcAjPlx8sjYVWhH7qgPkMJ7tRtQojP6T5KWXXrrrdh+tW7fGnj17jL17AMCxY8cwaNAgw/fz5s0DAERGRiImJgZPPfUUrl+/jtdeew05OTkIDQ3Fjh07bmvwrm/R0dGIjo6GVsu/eInq26N+CsRkaPDbNS3KtSLsuYeZwf48Lcq1QDM7AR2dOe1G1BgEkcvgGk2lUsHFxQVFRUVwdnaWuhyyFsXFQGws4OwMODhIXU29E0URA/aXI7NcxOchthjpyymmGi+cqsTmLA0mNVfgjQ4WcmJJWRmgUgEjRgBOTlJXQ1aiLp/f/JOEiEyKIAiGcMTpt79odCLirlf3J/FsN6JGw6BERCanZvHJfde1KFJz0BsAjhbqcEMNuNoAPV351k3UWHi0EZHJae8kQztHAVUisCOXo0oA8Fv16zDESwEFl00gajQMSkRkkh7l9JuBKIr47Ro3wSWSAoMSEZmkmj6lQ/k6XKu07i1NTqt0yKoQ4SAH+rkzKBE1JgYlI0RHRyM4OBg9e/aUuhQiixXoIEOoiww6ALHZ1r0Ux2+5+ucf4SGHHZdLIGpUDEpGiIqKQlJSEuLj46UuhciijaoeVfrZyqffdl7jatxEUmFQIiKTNcJXDhmAxCIdMsqsc/otrVSHiyUiFAIwyJPTbkSNjUGJiEyWl60Mvd31b1P/Z6WjSjV7u/V2k8PFhtNuRI2NQYmITJq1n/22M5dnuxFJiUGJiEzaQ94KKAXgfImIc8XWNf2WU6FDYpH+OT/ITXCJJMGgREQmzcVGQER1b461jSrtql47qauLDN52fLsmkgKPPCIyeTdPv1nTPt41q3Fz2o1IOgxKRuA6SkSNa4iXHLYy4Eq5iNRS6whKRWoRhwr0025cFoBIOgxKRuA6SkSNy14uoFtT/dvVoQLrWHzy9+taaESgraOAFk34Vk0kFR59RGQWernpp58OW0lQ2pnLRSaJTAGDEhGZhZqgdKRAa/F9ShVaEfvy9IFwKM92I5IUgxIRmYXQpjLYyoC8Klh8n9KBfC3KtUAzOwGdnPk2TSQlHoFEZBZsZQK6W0mfUs0ikw96yyEIXI2bSEoMSkRkNqyhT0mjExFXswmuF/uTiKTGoEREZsMa+pSOFupQqAZcbYCernyLJpIaj0IiMhshVtCnVLPI5BAvBRQyTrsRSY1ByQhccJJIGpbepySKIn6r3rZkKFfjJjIJDEpG4IKTRNKx5D6lMyodsipEOMiB/u4MSkSmgEGJiMzKzUHJ0vqUas52i/CQw07OaTciU8CgRERmJaSpDHYyIL8KSLGwPqWd17gaN5GpYVAiIrNiKxPQvfpsMEuafksr1eFiiQiFAAzy5LQbkalgUCIis2OJfUo1Z7v1dpPBxYbTbkSmgkGJiMyOJfYp7a/e2+1BLjJJZFIYlIjI7HRxsaw+JY1ORGKRDgAQ7sZpNyJTwqBERGbn5j6lQ/nmP/12rliHMi3gpADaOHLajciUMCgRkVmypD6lYzf0o0ndmsoh4ya4RCaFQYmIzJIl9SklFOrDXg/u7UZkcnhUGoFbmBBJL6S6T6lADVwsMfOgVD2i1L0p+5OITA2DkhG4hQmR9JQywTACY87Tb1nl+m1L5II+/BGRaeFRSURmyxL6lI5XjyZ1cJKhiYL9SUSmhkGJiMyWJfQpHbuhD3ndm/LtmMgU8cgkIrPVxQL6lI4XVvcnubI/icgUMSgRkdm6uU/pkBlOv5VpRJwtrmnk5tsxkSnikUlEZs2c+5ROFumgFQFfOwHN7Pl2TGSKeGQSkVnrXR2UjhRooTOzPqWE6v6kbhxNIjJZPDqJyKx1dpHBXm6efUo16yf14PpJRCaLQYmIzJpSJqBHU/NbT0knioYVubtzRW4ik8Wjk4jMnjn2KaWWilBpAHu5fg0lIjJNPDqJyOz1MsM+pZrRpBAXGWxkXGiSyFQxKBGR2bu5T+mCmfQpHeP+bkRmgUHJCNwUl8i0mGOf0vHqEaUe7E8iMmk8Qo3ATXGJTI859SnlV4lIK9OPfHV14YgSkSljUCIii2BOfUrHq9dPauMooKmS/UlEpoxBiYgsQpfqPqVCM+hTOlbI/iQic8GgREQWwUYmGBZuNPXpt5oRJe7vRmT6eJQSkcXo5Wb6Dd2VOhEni6pHlFw5okRk6hiUiMhimEOf0lmVDlU6wM0GaOHA/iQiU8egREQW4+Y+pfMm2qeUUN2f1M1VDkFgUCIydQxKRGQxbulTyjfN6beE6v6kHuxPIjILPFKJyKL0dq/uUyo0vaAkiiISbrA/icicMCgRkUUx5T6lzHIR1ytF2AhAZ2e+/RKZAx6pRGRROjvL4CAHbphgn1LNaFInZxns5OxPIjIHDEpEZFFsZAJ6uJpmn9Kx6unA7tzfjchs8GglIotjWE/JxPqUakaUenBFbiKzwaBERBbHFPuUVGoR54trlgbgWy+RueDRSkQW5+Y+pXPV4URqiUVaiAAC7QV42fKtl8hc8GglIotzS59SgWkEJcNGuBxNIjIrPGKNEB0djeDgYPTs2VPqUoioFr1NbN+3vzbCZX8SkTlhUDJCVFQUkpKSEB8fL3UpRFQLQ59SofR9SlpRxAkuNElklhiUiMgidXKWoYkcKDKBPqVzxTqUagEnBdDWkesnEZkTBiUiskim1Kd0vHo0KdRFDjk3wiUyKwxKRGSxeplInxIXmiQyXzxqichimUqfEheaJDJfDEpEZLE639SnlCxRn1JuhQ5XykXIAIQ25VsukbnhUUtEFkshE9CtehQnvlCaoFQzmtTeSQZHBfuTiMwNgxIRWbTw6j6leIn2fWN/EpF545FLRBYtzLVm3zcdRAn6lNifRGTeGJSIyKJ1cZFBKQB5VSLSyxo3KFVoRZxVVW+Ey/4kIrPEI5eILJqdXDA0UTf29NvJIh00IuBlK8Dfnv1JROaIQYmILN7N02+NKaF6f7ceTWUQuNAkkVliUCIii9ezupH6aCOPKCVUn2nXjfu7EZktBiUisnjdXeWQAbhSLiKrvHFGlURRvGVEiYjME49eIrJ4jgoBnZxr+pQaJyilloq4oQZsZUCwM99qicwVj14isgo1029HGmn67Xj1aFKIiwxKGfuTiMwVgxIRWYUwt5oVuhsnKB2rHrnqzvWTiMwagxIRWYWe1Q3VF0tE5Fc1/HpKhv4krshNZNZ4BBORVXBTCmjjqJ8Ca+hRpcIqEaml+jDWlSNKRGaNQYmIrEbNekrxBQ0blGr6k1o2EeCmZH8SkTljUCIiq1ETlI428Jlv3N+NyHIwKBGR1Qhz07/lnVXpUKxpuD6lY9VTe93Zn0Rk9ngUE5HV8LWTIcBegA7A8QbqU1LrRJws4hlvRJaCQckI0dHRCA4ORs+ePaUuhYjqqKGn386qdKjUAU1t9D1KRGTeGJSMEBUVhaSkJMTHx0tdChHVUc30W0Od+VbTn9S9qRwyboRLZPYYlIjIqtSMKCXe0KFCW/99SjX9Sd24vxuRReCRTERWJchBgKetgCoRhl6i+lKiEbE3Tx+U+rizP4nIEjAoEZFVEQQBYa4NM/32a44G5VqghYOAUBe+vRJZAh7JRGR1aqbfjhTU74jS5iwNAODxZgoI7E8isggMSkRkdWo2yD1+QwuNrn76lDLLdDhcoIMAYIyfol7uk4ikx6BERFannaMAZwVQqgWSiutnVGlL9WhSH3cZmtnzrZXIUvBoJiKrIxME9KxZT6kept9EUTQEpcc5mkRkURiUiMgq1ayndKQeGrqP3dDhcpmIJnLgIW8GJSJLwqBERFapZkTpWKEWOvH++pR+vKofTXrYRwEHBZu4iSwJgxIRWaVOzjLYy4FCNZBSYnxQKteKiM3+62w3IrIsDEpEZJWUMsGwevb9TL/9lqtFiRbwt/9rfSYishw8qonIatVMv93PwpM1026P+Sm4txuRBWJQIiKrFXbTmW+iEX1K2RU6/JGvD1mcdiOyTAxKRGS1ujaVwUYAcipFZJbXPSj9lKWBCCDMVYbmDnw7JbJEPLKJyGrZywV0rt6T7Wgdp99EUcTmq2ziJrJ0DEpEZNXCjFx4MrFIh9RSEXYy/bIARGSZGJSIyKqFuxk3olQzmvSQtxxOXDuJyGIxKBGRVevWVA4BwKUyEdcq7m1UqVIn4v9yaqbdbBqwOiKSGoMSEVk1FxsBHZxqRpXuLSjFXdOiSA342Aro4863USJLxiOciKxeWB2n3wxrJzVTQM61k4gsGoMSEVk9Q0P3PYwoXa8UsS+veu0kPzZxE1k6BiUisno1K3SfL9bhRtXd11P6OUsDrQiEusjQypFvoUSWjkc5EVk9T1sBLZsIEAEcu1H79JsoivjxqhoA104ishYMSkRE+Gv6Lf4u029ni3U4VyJCKQCP+jIoEVkDBiUiIui3IQGAIwW1jyjVrJ30oLccLjZs4iayBgxKREQAwtz0I0pnVDqUaW7vU6rSifg5q3rtJDZxE1kNBiUiIgD+9jL42QnQiMCJotun3/Ze16JADXgoBQzwkEtQIRFJgUGJiKja3abfNlePJo3xk0Mh47QbkbVgUCIiqlYz/fb3hScLqkT8fq167SRuWUJkVRiUiIiq1Zz5duKGDlW6v/qUfsnWQC0CHZ1laO/Et00ia8IjnoioWqsmAtxsgEodcPqmPqWas93YxE1kfRiUiIiqCYJgmH47Uj39dqFYh9MqHRQCMIpBicjqMCgREd2k598Wnqxp4h7kKYe7kk3cRNaGQYmI6Cbh1We+HSvUokonYkvN2kncsoTIKll1ULpx4wZ69OiB0NBQdOrUCStXrpS6JCKSWAdnGRzlQLEGWJmuxvVKEa42wGBPrp1EZI2s+k8kJycn7N+/Hw4ODigtLUWnTp3w2GOPwd3dXerSiEgickFAd1c59uVp8XmqfgPcUb4KKLl2EpFVsuoRJblcDgcHBwBAZWUlRFGEKN6+dQERWZeahScrqk9847QbkfUy6aC0f/9+jBw5En5+fhAEAVu3br3tNtHR0QgKCoKdnR3Cw8Nx9OjROj3GjRs3EBISAn9/f7z00kvw8PCop+qJyFzVnPkGAG0dBXRyNum3SiJqQCZ99JeWliIkJATR0dF3vH7jxo2YN28eXn/9dRw/fhwhISEYNmwYrl27ZrhNTf/R37+ysrIAAE2bNsXJkyeRnp6O9evXIzc3t9Z6KisroVKpbvkiIsvTxUUGZfW74+PNFBAETrsRWSuTHk8ePnw4hg8fXuv1S5YswbRp0zB58mQAwPLlyxEbG4tvv/0WCxYsAAAkJibe02N5e3sjJCQEBw4cwNixY+94m/feew9vvvlm3Z4EEZkdW5mAZ5rb4M8CLZ7gliVEVs2kR5TupqqqCgkJCRgyZIjhMplMhiFDhuDQoUP3dB+5ubkoLi4GABQVFWH//v1o165drbdfuHAhioqKDF+ZmZn39ySIyGS93E6Jn3vbw41rJxFZNZMeUbqbvLw8aLVaeHt733K5t7c3zp07d0/3cfnyZUyfPt3QxD179mx07ty51tvb2trC1tb2vuomIiIi82G2Qak+hIWF3fPUHBEREVkfs5168/DwgFwuv635Ojc3Fz4+PhJVRURERJbEbIOSUqlE9+7dERcXZ7hMp9MhLi4OvXv3lrAyIiIishQmPfVWUlKClJQUw/fp6elITEyEm5sbAgMDMW/ePERGRqJHjx4ICwvD0qVLUVpaajgLrqFER0cjOjoaWq22QR+HiIiIpCWIJrwU9d69ezFo0KDbLo+MjERMTAwAYNmyZfjwww+Rk5OD0NBQfPbZZwgPD2+U+lQqFVxcXFBUVARnZ+dGeUwiFBcDsbGAszNQvbI8kdkqKwNUKmDECMDJSepqyErU5fPbpIOSqWNQIkkwKJElYVAiCdTl89tse5SIiIiIGhqDEhEREVEtGJSIiIiIasGgRERERFQLBiUjREdHIzg4GD179pS6FCIiImpADEpGiIqKQlJSEuLj46UuhYiIiBoQgxIRERFRLUx6ZW5TV7MElUqlkrgSsirFxfq1ZzQa/X+JzFlFBVBVpV9Licv6USOp+dy+l6UkGZTuQ3FxMQAgICBA4kqIiIioroqLi+Hi4nLX23Bl7vug0+mQlZUFJycnCIIgdTmSU6lUCAgIQGZmJlcqb0B8nRsHX+fGwde58fC1/osoiiguLoafnx9ksrt3IXFE6T7IZDL4+/tLXYbJcXZ2tvqDsDHwdW4cfJ0bB1/nxsPXWu+fRpJqsJmbiIiIqBYMSkRERES1YFCiemNra4vXX38dtra2Updi0fg6Nw6+zo2Dr3Pj4WttHDZzExEREdWCI0pEREREtWBQIiIiIqoFgxIRERFRLRiUiIiIiGrBoER1Eh0djaCgINjZ2SE8PBxHjx696+2XLl2Kdu3awd7eHgEBAfjPf/6DioqKRqrWfNXldVar1Vi0aBFatWoFOzs7hISEYMeOHY1YrXnav38/Ro4cCT8/PwiCgK1bt/7jz+zduxfdunWDra0tWrdujZiYmAav09zV9XXOzs7GuHHj0LZtW8hkMsydO7dR6jR3dX2dt2zZggcffBCenp5wdnZG7969sXPnzsYp1swwKNE927hxI+bNm4fXX38dx48fR0hICIYNG4Zr167d8fbr16/HggUL8PrrryM5ORnffPMNNm7ciFdeeaWRKzcvdX2d//e//2HFihX4/PPPkZSUhBkzZmDMmDE4ceJEI1duXkpLSxESEoLo6Oh7un16ejpGjBiBQYMGITExEXPnzsXUqVP54fIP6vo6V1ZWwtPTE//73/8QEhLSwNVZjrq+zvv378eDDz6I7du3IyEhAYMGDcLIkSP5vnEnItE9CgsLE6Oiogzfa7Va0c/PT3zvvffuePuoqChx8ODBt1w2b948sW/fvg1ap7mr6+vs6+srLlu27JbLHnvsMXH8+PENWqclASD+9NNPd73N/PnzxY4dO95y2VNPPSUOGzasASuzLPfyOt8sIiJCfP755xusHktV19e5RnBwsPjmm2/Wf0FmjiNKdE+qqqqQkJCAIUOGGC6TyWQYMmQIDh06dMef6dOnDxISEgzTRmlpadi+fTsefvjhRqnZHBnzOldWVsLOzu6Wy+zt7fHHH380aK3W5tChQ7f8uwDAsGHDav13ITInOp0OxcXFcHNzk7oUk8NNceme5OXlQavVwtvb+5bLvb29ce7cuTv+zLhx45CXl4d+/fpBFEVoNBrMmDGDU293YczrPGzYMCxZsgQDBgxAq1atEBcXhy1btkCr1TZGyVYjJyfnjv8uKpUK5eXlsLe3l6gyovv30UcfoaSkBE8++aTUpZgcjihRg9m7dy/effddfPHFFzh+/Di2bNmC2NhYvPXWW1KXZlE+/fRTtGnTBu3bt4dSqcSsWbMwefJkyGQ8vInon61fvx5vvvkmfvjhB3h5eUldjsnhiBLdEw8PD8jlcuTm5t5yeW5uLnx8fO74M6+++iomTJiAqVOnAgA6d+6M0tJSTJ8+Hf/973/5QX4HxrzOnp6e2Lp1KyoqKpCfnw8/Pz8sWLAALVu2bIySrYaPj88d/12cnZ05mkRm6/vvv8fUqVOxadOm26aWSY+fVHRPlEolunfvjri4OMNlOp0OcXFx6N279x1/pqys7LYwJJfLAQAitxi8I2Ne5xp2dnZo1qwZNBoNNm/ejFGjRjV0uVald+/et/y7AMCuXbv+8d+FyFRt2LABkydPxoYNGzBixAipyzFZHFGiezZv3jxERkaiR48eCAsLw9KlS1FaWorJkycDACZOnIhmzZrhvffeAwCMHDkSS5YsQdeuXREeHo6UlBS8+uqrGDlypCEw0e3q+jofOXIEV69eRWhoKK5evYo33ngDOp0O8+fPl/JpmLySkhKkpKQYvk9PT0diYiLc3NwQGBiIhQsX4urVq1izZg0AYMaMGVi2bBnmz5+PKVOm4Pfff8cPP/yA2NhYqZ6CWajr6wwAiYmJhp+9fv06EhMToVQqERwc3Njlm426vs7r169HZGQkPv30U4SHhyMnJweA/kQQFxcXSZ6DyZL6tDsyL59//rkYGBgoKpVKMSwsTDx8+LDhuoiICDEyMtLwvVqtFt944w2xVatWop2dnRgQECA+99xzYmFhYeMXbmbq8jrv3btX7NChg2hrayu6u7uLEyZMEK9evSpB1eZlz549IoDbvmpe28jISDEiIuK2nwkNDRWVSqXYsmVLcdWqVY1et7kx5nW+0+2bN2/e6LWbk7q+zhEREXe9Pf1FEEXOgRARERHdCXuUiIiIiGrBoERERERUCwYlIiIiolowKBERERHVgkGJiIiIqBYMSkRERES1YFAiIiIiqgWDEhEREVEtGJSIrNDAgQMxd+5ck7kfcyAIArZu3QoAuHTpEgRBMGy1QXf3xhtvIDQ0VOoyiIzCoERE/2jv3r0QBAE3bty45fItW7bgrbfekqYoCQUEBCA7OxudOnWSrAZTDWs3B0oiS8BNcYksSFVVFZRKZaM9npubW6M9limRy+Xw8fGRuox70ti/E0SWhiNKRGZs4MCBmDVrFubOnQsPDw8MGzYMAHDmzBkMHz4cjo6O8Pb2xoQJE5CXl1fr/axduxY9evSAk5MTfHx8MG7cOFy7dg2AfuRi0KBBAABXV1cIgoBJkyYZHr9m6u2VV15BeHj4bfcdEhKCRYsWGb7/+uuv0aFDB9jZ2aF9+/b44osv7vocdTodPvjgA7Ru3Rq2trYIDAzEO++8Y7j+9OnTGDx4MOzt7eHu7o7p06ejpKTkltfo79ODo0ePNjwHAAgKCsJbb72Fp59+Gk2aNEGzZs0QHR1da01/H82pGXGLi4tDjx494ODggD59+uD8+fO3/Nzbb78NLy8vODk5YerUqViwYMFdp6QKCwsxfvx4eHp6wt7eHm3atMGqVasAAC1atAAAdO3aFYIgYODAgQCASZMmYfTo0XjnnXfg5+eHdu3aAQAyMzPx5JNPomnTpnBzc8OoUaNw6dIlw2PV/NxHH30EX19fuLu7IyoqCmq12nCb7OxsjBgxAvb29mjRogXWr1+PoKAgLF261PA6AsCYMWMgCILh+xpr165FUFAQXFxc8K9//QvFxcW1PnciU8GgRGTmVq9eDaVSiYMHD2L58uW4ceMGBg8ejK5du+LYsWPYsWMHcnNz8eSTT9Z6H2q1Gm+99RZOnjyJrVu34tKlS4YgERAQgM2bNwMAzp8/j+zsbHz66ae33cf48eNx9OhRpKamGi47e/YsTp06hXHjxgEA1q1bh9deew3vvPMOkpOT8e677+LVV1/F6tWra61t4cKFWLx4MV599VUkJSVh/fr18Pb2BgCUlpZi2LBhcHV1RXx8PDZt2oTdu3dj1qxZdX4dP/zwQ4SEhODEiRNYsGABnn/+eezatatO9/Hf//4XH3/8MY4dOwaFQoEpU6YYrlu3bh3eeecdvP/++0hISEBgYCC+/PLLu95fzXP+9ddfkZycjC+//BIeHh4AgKNHjwIAdu/ejezsbGzZssXwc3FxcTh//jx27dqFbdu2Qa1WY9iwYXBycsKBAwdw8OBBODo64qGHHkJVVZXh5/bs2YPU1FTs2bMHq1evRkxMDGJiYgzXT5w4EVlZWdi7dy82b96Mr776yhCoASA+Ph4AsGrVKmRnZxu+B4DU1FRs3boV27Ztw7Zt27Bv3z4sXry4Tq8vkSREIjJbERERYteuXW+57K233hKHDh16y2WZmZkiAPH8+fOGn3v++edrvd/4+HgRgFhcXCyKoiju2bNHBCAWFhbe9vg3309ISIi4aNEiw/cLFy4Uw8PDDd+3atVKXL9+/W319u7d+451qFQq0dbWVly5cuUdr//qq69EV1dXsaSkxHBZbGysKJPJxJycnFqf66hRo8TIyEjD982bNxcfeuihW27z1FNPicOHDzd8D0D86aefRFEUxfT0dBGAeOLECVEU/3p9du/efUsdAMTy8nJRFEUxPDxcjIqKuuUx+vbtK4aEhNzxuYmiKI4cOVKcPHnyHa/7ew01IiMjRW9vb7GystJw2dq1a8V27dqJOp3OcFllZaVob28v7ty50/BzzZs3FzUajeE2TzzxhPjUU0+JoiiKycnJIgAxPj7ecP3FixdFAOInn3xyx9epxuuvvy46ODiIKpXKcNlLL710y+8GkaniiBKRmevevfst3588eRJ79uyBo6Oj4at9+/YAcMtoz80SEhIwcuRIBAYGwsnJCREREQCAjIyMOtUyfvx4rF+/HgAgiiI2bNiA8ePHA9CP/qSmpuKZZ565pba333671rqSk5NRWVmJBx54oNbrQ0JC0KRJE8Nlffv2hU6nu23a65/07t37tu+Tk5PrdB9dunQx/L+vry8AGEZczp8/j7CwsFtu//fv/27mzJn4/vvvERoaivnz5+PPP/+8pzo6d+58S1/SyZMnkZKSAicnJ8Pr7ubmhoqKilte+44dO0Iul9/yHG6uX6FQoFu3bobrW7duDVdX13uqKSgoCE5OTne8byJTxmZuIjN3c0gAgJKSEowcORLvv//+bbet+fC+Wc301bBhw7Bu3Tp4enoiIyMDw4YNu2Va5l48/fTTePnll3H8+HGUl5cjMzMTTz31lKEuAFi5cuVtvUw3fzjfzN7evk6PfycymQyiKN5y2c19N/XJxsbG8P+CIADQ91gZa/jw4bh8+TK2b9+OXbt24YEHHkBUVBQ++uiju/7cnX4nunfvjnXr1t12W09PzzvWD+ifw/3Uf7OGvG+ihsQRJSIL061bN5w9exZBQUFo3br1LV9//wAFgHPnziE/Px+LFy9G//790b59+9v+0q8ZndBqtXd9bH9/f0RERGDdunVYt24dHnzwQXh5eQEAvL294efnh7S0tNvqqmlM/rs2bdrA3t4ecXFxd7y+Q4cOOHnyJEpLSw2XHTx4EDKZzNDE7OnpiezsbMP1Wq0WZ86cue2+Dh8+fNv3HTp0uOvzrYt27drd0rMD4Lbv78TT0xORkZH47rvvsHTpUnz11VcA7v3fBND/Tly8eBFeXl63vfYuLi73XL9Go8GJEycMl6WkpKCwsPCW29nY2NxTTUTmgkGJyMJERUWhoKAATz/9NOLj45GamoqdO3di8uTJd/wACwwMhFKpxOeff460tDT88ssvt62N1Lx5cwiCgG3btuH69eu3nFX2d+PHj8f333+PTZs2Gabdarz55pt477338Nlnn+HChQs4ffo0Vq1ahSVLltzxvuzs7PDyyy9j/vz5WLNmDVJTU3H48GF88803hseys7NDZGQkzpw5gz179mD27NmYMGGCoeF78ODBiI2NRWxsLM6dO4eZM2feth4UoA9YH3zwAS5cuIDo6Ghs2rQJzz///F1f67qYPXs2vvnmG6xevRoXL17E22+/jVOnThlGnu7ktddew88//4yUlBScPXsW27ZtM4Q3Ly8v2NvbG5r1i4qKar2f8ePHw8PDA6NGjcKBAweQnp6OvXv3Ys6cObhy5co91d++fXsMGTIE06dPx9GjR3HixAlMnz4d9vb2tzyHoKAgxMXFIScn57YQRWSOGJSILIyfnx8OHjwIrVaLoUOHonPnzpg7dy6aNm0Kmez2Q97T0xMxMTHYtGkTgoODsXjx4tumdpo1a4Y333wTCxYsgLe3913PKhs7dizy8/NRVlaG0aNH33Ld1KlT8fXXX2PVqlXo3LkzIiIiEBMTU+uIEqA/8+uFF17Aa6+9hg4dOuCpp54yjHg5ODhg586dKCgoQM+ePTF27Fg88MADWLZsmeHnp0yZgsjISEycOBERERFo2bKlYbmDm73wwgs4duwYunbtirfffhtLliwxLLdQH8aPH4+FCxfixRdfRLdu3ZCeno5JkybBzs6u1p9RKpVYuHAhunTpggEDBkAul+P7778HACgUCnz22WdYsWIF/Pz8MGrUqFrvx8HBAfv370dgYCAee+wxdOjQAc888wwqKirg7Ox8z89hzZo18Pb2xoABAzBmzBhMmzYNTk5OtzyHjz/+GLt27UJAQAC6du16z/dNZKoE8e+T90REViYoKAhz585t9O1YHnzwQfj4+GDt2rWN+rj15cqVKwgICMDu3btrbbgnMnds5iYiagRlZWVYvnw5hg0bBrlcjg0bNmD37t11XqtJSr///jtKSkrQuXNnZGdnY/78+QgKCsKAAQOkLo2owTAoERE1AkEQsH37drzzzjuoqKhAu3btsHnzZgwZMkTq0u6ZWq3GK6+8grS0NDg5OaFPnz5Yt27dbWe0EVkSTr0RERER1YLN3ERERES1YFAiIiIiqgWDEhEREVEtGJSIiIiIasGgRERERFQLBiUiIiKiWjAoEREREdWCQYmIiIioFv8Po4DiCYjyyHgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_robustness(mu_vals, pop_errors_norobust)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows that as the pulse amplitude deviates from the optimal value, the\n",
    "error rises quickly: our previous optimization result is not robust.\n",
    "\n",
    "The highlighted region of ±10% is our \"region of interest\" within\n",
    "which we would like the control to be robust by applying optimal control."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting the ensemble objectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They central idea of optimizing for robustness is to take multiple copies of\n",
    "the Hamiltonian, sampling over the space of variations to which would\n",
    "like to be robust, and optimize over the average of this ensemble.\n",
    "\n",
    "Here, we sample 5 values of $\\mu$ (including the unperturbed $\\mu=1$) in the\n",
    "region of interest, $\\mu \\in [0.9, 1.1]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:41.462459Z",
     "start_time": "2020-03-22T05:01:41.456749Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.796847Z",
     "iopub.status.busy": "2024-06-03T14:25:47.796728Z",
     "iopub.status.idle": "2024-06-03T14:25:47.798557Z",
     "shell.execute_reply": "2024-06-03T14:25:47.798264Z"
    }
   },
   "outputs": [],
   "source": [
    "ensemble_mu = [0.9, 0.95, 1.0, 1.05, 1.1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The corresponding Hamiltonians are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:41.487262Z",
     "start_time": "2020-03-22T05:01:41.474312Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.800022Z",
     "iopub.status.busy": "2024-06-03T14:25:47.799922Z",
     "iopub.status.idle": "2024-06-03T14:25:47.802170Z",
     "shell.execute_reply": "2024-06-03T14:25:47.801873Z"
    }
   },
   "outputs": [],
   "source": [
    "ham_ensemble = [scale_control(objective.H, mu=mu) for mu in ensemble_mu]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `krotov.objectives.ensemble_objectives` extends the original objective of a\n",
    "single unperturbed state-to-state transition with one additional objective for\n",
    "each ensemble Hamiltonian for $\\mu \\neq 1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:41.504002Z",
     "start_time": "2020-03-22T05:01:41.492908Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.803857Z",
     "iopub.status.busy": "2024-06-03T14:25:47.803723Z",
     "iopub.status.idle": "2024-06-03T14:25:47.806284Z",
     "shell.execute_reply": "2024-06-03T14:25:47.806018Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [H₀[3,3], [H₅[3,3], u₁(t)], [H₆[3,3], u₂(t)], [H₇[3,3], u₃(t)], [H₈[3,3], u₄(t)]]],\n",
       " Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [H₀[3,3], [H₉[3,3], u₁(t)], [H₁₀[3,3], u₂(t)], [H₁₁[3,3], u₃(t)], [H₁₂[3,3], u₄(t)]]],\n",
       " Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [H₀[3,3], [H₁₃[3,3], u₁(t)], [H₁₄[3,3], u₂(t)], [H₁₅[3,3], u₃(t)], [H₁₆[3,3], u₄(t)]]],\n",
       " Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [H₀[3,3], [H₁₇[3,3], u₁(t)], [H₁₈[3,3], u₂(t)], [H₁₉[3,3], u₃(t)], [H₂₀[3,3], u₄(t)]]],\n",
       " Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [H₀[3,3], [H₂₁[3,3], u₁(t)], [H₂₂[3,3], u₂(t)], [H₂₃[3,3], u₃(t)], [H₂₄[3,3], u₄(t)]]]]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ensemble_objectives = krotov.objectives.ensemble_objectives(\n",
    "    objectives, ham_ensemble, keep_original_objectives=False,\n",
    ")\n",
    "ensemble_objectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is important that all five objectives reference the same four control\n",
    "pulses, as is the case here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the same update shape $S(t)$ and $\\lambda_a$ value as in the original optimization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:41.515808Z",
     "start_time": "2020-03-22T05:01:41.506536Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.807661Z",
     "iopub.status.busy": "2024-06-03T14:25:47.807536Z",
     "iopub.status.idle": "2024-06-03T14:25:47.809769Z",
     "shell.execute_reply": "2024-06-03T14:25:47.809484Z"
    }
   },
   "outputs": [],
   "source": [
    "def S(t):\n",
    "    \"\"\"Scales the Krotov methods update of the pulse value at the time t\"\"\"\n",
    "    return krotov.shapes.flattop(t, 0.0, 5, 0.3, func='sinsq')\n",
    "\n",
    "\n",
    "λ = 0.5\n",
    "\n",
    "pulse_options = {\n",
    "    H[1][1]: dict(lambda_a=λ, update_shape=S),\n",
    "    H[2][1]: dict(lambda_a=λ, update_shape=S),\n",
    "    H[3][1]: dict(lambda_a=λ, update_shape=S),\n",
    "    H[4][1]: dict(lambda_a=λ, update_shape=S),\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "It will be interesting to see how the optimization progresses for each\n",
    "individual element of the ensemble. Thus, we write an `info_hook` routine that\n",
    "prints out a tabular overview of $1 - \\Re\\Braket{\\Psi(T)}{3}_{\\Op{H}_i}$ for\n",
    "all $\\Op{H}_i$ in the ensemble, as well as their average (the total functional\n",
    "$J_T$ that is being minimized)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:41.526072Z",
     "start_time": "2020-03-22T05:01:41.518139Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.811207Z",
     "iopub.status.busy": "2024-06-03T14:25:47.811109Z",
     "iopub.status.idle": "2024-06-03T14:25:47.813402Z",
     "shell.execute_reply": "2024-06-03T14:25:47.813115Z"
    }
   },
   "outputs": [],
   "source": [
    "def print_J_T_per_target(**kwargs):\n",
    "    iteration = kwargs['iteration']\n",
    "    N = len(ensemble_mu)\n",
    "    if iteration == 0:\n",
    "        print(\n",
    "            \"iteration \"\n",
    "            + \"%11s \" % \"J_T(avg)\"\n",
    "            + \" \".join([(\"J_T(μ=%.2f)\" % μ) for μ in ensemble_mu])\n",
    "        )\n",
    "    J_T_vals = 1 - kwargs['tau_vals'].real\n",
    "    J_T = np.sum(J_T_vals) / N\n",
    "    print(\n",
    "        (\"%9d \" % iteration)\n",
    "        + (\"%11.2e \" % J_T)\n",
    "        + \" \".join([(\"%11.2e\" % v) for v in J_T_vals])\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll also want to look at the output of ``krotov.info_hooks.print_table``, but\n",
    "in order to keep the output orderly, we will write that information to a file\n",
    "`ensemble_opt.log`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:01:41.534779Z",
     "start_time": "2020-03-22T05:01:41.528504Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.814998Z",
     "iopub.status.busy": "2024-06-03T14:25:47.814872Z",
     "iopub.status.idle": "2024-06-03T14:25:47.816773Z",
     "shell.execute_reply": "2024-06-03T14:25:47.816511Z"
    }
   },
   "outputs": [],
   "source": [
    "log_fh = open(\"ensemble_opt.log\", \"w\", encoding=\"utf-8\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimization starts for the same guess pulses as the original [Optimization\n",
    "of a State-to-State Transfer in a Lambda System in the\n",
    "RWA](02_example_lambda_system_rwa_complex_pulse.ipynb). Generally, for a\n",
    "robustness ensemble optimization, this will yield better results than trying to\n",
    "take the optimized pulses for the unperturbed system as a guess.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:03.283073Z",
     "start_time": "2020-03-22T05:01:41.538943Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "16"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:25:47.818298Z",
     "iopub.status.busy": "2024-06-03T14:25:47.818156Z",
     "iopub.status.idle": "2024-06-03T14:27:32.197787Z",
     "shell.execute_reply": "2024-06-03T14:27:32.197474Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration    J_T(avg) J_T(μ=0.90) J_T(μ=0.95) J_T(μ=1.00) J_T(μ=1.05) J_T(μ=1.10)\n",
      "        0    1.01e+00    1.01e+00    1.01e+00    1.01e+00    1.01e+00    1.01e+00\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        1    6.79e-01    6.94e-01    6.83e-01    6.75e-01    6.71e-01    6.71e-01\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        2    4.14e-01    4.40e-01    4.20e-01    4.07e-01    4.00e-01    4.00e-01\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3    2.36e-01    2.68e-01    2.43e-01    2.27e-01    2.20e-01    2.23e-01\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        4    1.32e-01    1.63e-01    1.37e-01    1.21e-01    1.16e-01    1.22e-01\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        5    7.46e-02    1.04e-01    7.78e-02    6.29e-02    5.98e-02    6.86e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        6    4.46e-02    7.13e-02    4.58e-02    3.23e-02    3.12e-02    4.26e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        7    2.92e-02    5.32e-02    2.88e-02    1.66e-02    1.72e-02    3.04e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        8    2.14e-02    4.32e-02    1.96e-02    8.59e-03    1.04e-02    2.50e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        9    1.73e-02    3.74e-02    1.46e-02    4.48e-03    7.25e-03    2.28e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       10    1.52e-02    3.41e-02    1.19e-02    2.37e-03    5.83e-03    2.21e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       11    1.42e-02    3.20e-02    1.03e-02    1.29e-03    5.23e-03    2.20e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       12    1.36e-02    3.07e-02    9.36e-03    7.19e-04    5.00e-03    2.20e-02\n"
     ]
    }
   ],
   "source": [
    "opt_result = krotov.optimize_pulses(\n",
    "    ensemble_objectives,\n",
    "    pulse_options,\n",
    "    tlist,\n",
    "    propagator=krotov.propagators.expm,\n",
    "    chi_constructor=krotov.functionals.chis_re,\n",
    "    info_hook=krotov.info_hooks.chain(\n",
    "        print_J_T_per_target,\n",
    "        krotov.info_hooks.print_table(\n",
    "            J_T=krotov.functionals.J_T_re, out=log_fh\n",
    "        ),\n",
    "    ),\n",
    "    check_convergence=krotov.convergence.Or(\n",
    "        krotov.convergence.value_below(1e-3, name='J_T'),\n",
    "        krotov.convergence.check_monotonic_error,\n",
    "    ),\n",
    "    iter_stop=12,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After twelve iterations (which were sufficient to produce an error $<10^{-3}$\n",
    "in the original optimization), we find the average error over the ensemble to\n",
    "be still above $>10^{-2}$. However, the error for $\\mu = 1$ is only *slightly*\n",
    "larger than in the original optimization; the lack of success is entirely due\n",
    "to the large error for the other elements of the ensemble for $\\mu \\neq 1$.\n",
    "Achieving robustness is hard!\n",
    "\n",
    "We continue the optimization until the *average* error falls below $10^{-3}$:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:03.339376Z",
     "start_time": "2020-03-22T05:06:03.287117Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.199381Z",
     "iopub.status.busy": "2024-06-03T14:27:32.199290Z",
     "iopub.status.idle": "2024-06-03T14:27:32.204322Z",
     "shell.execute_reply": "2024-06-03T14:27:32.204085Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration    J_T(avg) J_T(μ=0.90) J_T(μ=0.95) J_T(μ=1.00) J_T(μ=1.05) J_T(μ=1.10)\n",
      "        0    1.36e-02    3.07e-02    9.36e-03    7.19e-04    5.00e-03    2.20e-02\n",
      "      ...\n",
      "      670    1.05e-03    2.80e-03    4.83e-04    1.10e-04    5.22e-04    1.34e-03\n",
      "      671    1.05e-03    2.78e-03    4.79e-04    1.10e-04    5.19e-04    1.33e-03\n",
      "      672    1.04e-03    2.77e-03    4.76e-04    1.10e-04    5.16e-04    1.33e-03\n",
      "      673    1.03e-03    2.75e-03    4.73e-04    1.11e-04    5.14e-04    1.32e-03\n",
      "      674    1.03e-03    2.74e-03    4.70e-04    1.11e-04    5.11e-04    1.31e-03\n",
      "      675    1.02e-03    2.72e-03    4.66e-04    1.11e-04    5.08e-04    1.30e-03\n",
      "      676    1.02e-03    2.71e-03    4.63e-04    1.12e-04    5.05e-04    1.29e-03\n",
      "      677    1.01e-03    2.69e-03    4.60e-04    1.12e-04    5.03e-04    1.28e-03\n",
      "      678    1.00e-03    2.68e-03    4.57e-04    1.12e-04    5.00e-04    1.27e-03\n",
      "      679    9.99e-04    2.66e-03    4.54e-04    1.13e-04    4.97e-04    1.26e-03\n"
     ]
    }
   ],
   "source": [
    "dumpfile = \"./ensemble_opt_result.dump\"\n",
    "if os.path.isfile(dumpfile):\n",
    "    opt_result = krotov.result.Result.load(dumpfile, objectives)\n",
    "    print_J_T_per_target(iteration=0, tau_vals=opt_result.tau_vals[12])\n",
    "    print(\"      ...\")\n",
    "    n_iters = len(opt_result.tau_vals)\n",
    "    for i in range(n_iters - 10, n_iters):\n",
    "        print_J_T_per_target(iteration=i, tau_vals=opt_result.tau_vals[i])\n",
    "else:\n",
    "    opt_result = krotov.optimize_pulses(\n",
    "        ensemble_objectives,\n",
    "        pulse_options,\n",
    "        tlist,\n",
    "        propagator=krotov.propagators.expm,\n",
    "        chi_constructor=krotov.functionals.chis_re,\n",
    "        info_hook=krotov.info_hooks.chain(\n",
    "            print_J_T_per_target,\n",
    "            krotov.info_hooks.print_table(\n",
    "                J_T=krotov.functionals.J_T_re, out=log_fh\n",
    "            ),\n",
    "        ),\n",
    "        check_convergence=krotov.convergence.Or(\n",
    "            krotov.convergence.value_below(1e-3, name='J_T'),\n",
    "            krotov.convergence.check_monotonic_error,\n",
    "        ),\n",
    "        iter_stop=1000,\n",
    "        continue_from=opt_result,\n",
    "    )\n",
    "    opt_result.dump(dumpfile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:03.357680Z",
     "start_time": "2020-03-22T05:06:03.349278Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.205591Z",
     "iopub.status.busy": "2024-06-03T14:27:32.205477Z",
     "iopub.status.idle": "2024-06-03T14:27:32.207655Z",
     "shell.execute_reply": "2024-06-03T14:27:32.207421Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Krotov Optimization Result\n",
       "--------------------------\n",
       "- Started at 2024-06-01 16:02:53\n",
       "- Number of objectives: 1\n",
       "- Number of iterations: 679\n",
       "- Reason for termination: Reached convergence: J_T < 0.001\n",
       "- Ended at 2024-06-01 18:17:38 (2:14:45)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:03.366547Z",
     "start_time": "2020-03-22T05:06:03.360976Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.208917Z",
     "iopub.status.busy": "2024-06-03T14:27:32.208835Z",
     "iopub.status.idle": "2024-06-03T14:27:32.210624Z",
     "shell.execute_reply": "2024-06-03T14:27:32.210397Z"
    }
   },
   "outputs": [],
   "source": [
    "log_fh.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even now, the ideal Hamiltonian ($\\mu = 1$) has the lowest error in the\n",
    "ensemble by a significant margin. However, notice that the error in the $J_T$\n",
    "for $\\mu = 1$ is actually rising, while the errors for values of $\\mu \\neq 1$\n",
    "are falling by a much larger value! This is a good thing: we sacrifice a little\n",
    "bit of fidelity in the unperturbed dynamics to an increase in robustness.\n",
    "\n",
    "The optimized \"robust\" pulse looks as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:04.274992Z",
     "start_time": "2020-03-22T05:06:03.369715Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.212020Z",
     "iopub.status.busy": "2024-06-03T14:27:32.211928Z",
     "iopub.status.idle": "2024-06-03T14:27:32.395371Z",
     "shell.execute_reply": "2024-06-03T14:27:32.395105Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pump pulse amplitude and phase:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stokes pulse amplitude and phase:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_pulse_amplitude_and_phase(pulse_real, pulse_imaginary, tlist):\n",
    "    ax1 = plt.subplot(211)\n",
    "    ax2 = plt.subplot(212)\n",
    "    amplitudes = [\n",
    "        np.sqrt(x * x + y * y) for x, y in zip(pulse_real, pulse_imaginary)\n",
    "    ]\n",
    "    phases = [\n",
    "        np.arctan2(y, x) / np.pi for x, y in zip(pulse_real, pulse_imaginary)\n",
    "    ]\n",
    "    ax1.plot(tlist, amplitudes)\n",
    "    ax1.set_xlabel('time')\n",
    "    ax1.set_ylabel('pulse amplitude')\n",
    "    ax2.plot(tlist, phases)\n",
    "    ax2.set_xlabel('time')\n",
    "    ax2.set_ylabel('pulse phase (π)')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "print(\"pump pulse amplitude and phase:\")\n",
    "plot_pulse_amplitude_and_phase(\n",
    "    opt_result.optimized_controls[0], opt_result.optimized_controls[1], tlist\n",
    ")\n",
    "print(\"Stokes pulse amplitude and phase:\")\n",
    "plot_pulse_amplitude_and_phase(\n",
    "    opt_result.optimized_controls[2], opt_result.optimized_controls[3], tlist\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and produces the dynamics (in the unperturbed system) shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:04.614894Z",
     "start_time": "2020-03-22T05:06:04.277559Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.396873Z",
     "iopub.status.busy": "2024-06-03T14:27:32.396752Z",
     "iopub.status.idle": "2024-06-03T14:27:32.479090Z",
     "shell.execute_reply": "2024-06-03T14:27:32.478761Z"
    }
   },
   "outputs": [],
   "source": [
    "opt_robust_dynamics = opt_result.optimized_objectives[0].mesolve(\n",
    "    tlist, e_ops=[proj1, proj2, proj3]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:04.825054Z",
     "start_time": "2020-03-22T05:06:04.616827Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.480926Z",
     "iopub.status.busy": "2024-06-03T14:27:32.480801Z",
     "iopub.status.idle": "2024-06-03T14:27:32.552270Z",
     "shell.execute_reply": "2024-06-03T14:27:32.551962Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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myu+HtC5HCGGFDp45yKilo9iQtgEnOyfe6vkWL8a+iIPeQevSxD9IuBECdffwiUPboNfB0r3pbEk6o3VJQggrYVbMfLv/W+5ddi+phamEuIfw/cDvGRY1TOvSxGVIuBHinNbBntwbGw7Am0sPYDbLysVCNHTZJdk8vvJx3t/xPhXmCvqG9WXO4Dm09mutdWmiGhJuhPib5/q3wN3Jnn1pBSzbl651OUIIjSiKwm/Hf+OOX+9gc/pmnO2cmRg3kal9puLt7K11eeIKJNwI8Td+7k482qspAB/8cQSjyaxxRUKIuna66DRPrHqCFze+SF55Hq19WzN36FxGtBiBTqfTujxxFSTcCPEPD/eKxM/NkRM5xczbcUrrcoQQdcRoMvLt/m8Zvng4f6X9haPekWc6PcOPg3+kqVdTrcsT10DCjRD/4O5kz9N9mwEwbdURSg0mjSsSQtS29afWc8evd/D+jvcprSilc0Bn5g+bz6MdHpXZUPWQvdYFCGGN7o0N538bTpCWV8r3W5J57MYorUsSQtSCpPwk3tv+HhvTNgLg6+zL+M7jGd5sOHqdvP+vr+RfTohLcLK3Y3y/5gB8sf4EZUZpvRHClhQYCnhn2zvcufhONqZtxF5vz9i2Y1l6+1LuaH6HBJt6Tv71hLiM2zuHEOLtQk5ROT9tS9G6HCGEBZjMJn4+/DNDFgzhh4M/UKFU0Du0N4tuW0R8l3hZadhGSLgR4jIc7PQ80Vvtjpq5LonyCmm9EaI+25Gxg5FLRvLGljc4W36WKK8oZvafySf9PqGJZxOtyxMWJGNuhKjGiC6hfLr6GBkFZczbcYr7u8sfQCHqm/SidD5I+IAVySsA8HD04KmOT3F3y7tlsLCNkpYbIarhZG/H/92kTgGdsfa4rHsjRD1Sbirn892fM2zRMFYkr0Cv03N3i7tZevtS7mt9nwQbGyYtN0Jcwahu4Uxfc5y0vFIW7kzj7q5hWpckhLiCxKxEJm6ayIn8EwDEBMbwQrcXaOXbSuPKRF2QlhshrsDZwY7/u1FtvZm+9hgm2XNKCKtVYizhnW3vMPr30ZzIP4Gfsx/v3vgu3wz4RoJNAyLhRoircF/3cHxcHTh5poQV+zO0LkcIcQn7z+xnxG8j+OHgDygoDIsaxuLhixkYOVC2TWhgJNwIcRVcHe154Nxg4i/WJ6Eo0nojhLVQFIUfD/7I/cvuJ6UwhSC3IGb0n8FbPd/Cy8lL6/KEBiTcCHGVHoiLwNFeT2JqHgknz2pdjhACKK0o5fl1zzNl2xQqzBX0C+/H/KHz6RnSU+vShIYk3Ahxlfw9nLijUwigtt4IIbSVVZLF2OVj+ePkH9jr7ZnQbQIf9f5IWmuEhBshrsUjvSIBWHkwkxM5xRpXI0TDdeTsEUYtHcX+M/vxdvLmf7f8j3tb3ytjawQg4UaIa9IswIO+rQJQFPhqo7TeCKGFfTn7GLt8LFklWUR5RTF78GxiAmO0LktYEQk3QlyjR3up08Ln7ThFbrFB42qEaFh2ZOzgkT8eocBQQLR/NN8N+o4wD1l7SlQl4UaIa9S9qS/tQjwprzDz/eaTWpcjRIOxK2sXT656kmJjMd2CuvHFzV/g6eipdVnCCmkebqZPn05ERATOzs7Exsaybdu2as+fOnUqLVu2xMXFhbCwMJ577jnKysrqqFohQKfTVbbe/LD1JIYK2ZJBiNp2OPcwT/35FKUVpfQI6cH0ftNxdXDVuixhpTQNN3PnziU+Pp5Jkyaxc+dOoqOjGTBgAFlZWZc8f/bs2bzwwgtMmjSJgwcP8tVXXzF37lxefPHFOq5cNHQD2wXj7+FEdmE5y2VRPyFq1cmCkzy28jEKjYV0DujMR70/wtneWeuyhBXTNNx8+OGHPProo4wdO5Y2bdrw+eef4+rqytdff33J8zdt2kSPHj249957iYiI4JZbbmHUqFHVtvaUl5dTUFBQ5UOI6+Vor+e+2HAAvt2UrG0xQtiws2VneXzl4+SW5dLKtxWf9PsEF3sXrcsSVk6zcGMwGEhISKB///4XitHr6d+/P5s3b77kY2644QYSEhIqw0xSUhLLli1j0KBBl73O5MmT8fLyqvwIC5OBZ8Iy7u0Wjr1eR8LJs+xLy9e6HCFsjtFk5Lm1z3Gq6BQh7iHM6D9DxtiIq6JZuMnJycFkMhEYGFjleGBgIBkZl27mv/fee3n99dfp2bMnDg4OREVF0bt372q7pSZMmEB+fn7lR2pqqkW/D9FwBXg6M6h9MCCtN0JYmqIovLn1TRIyE3BzcOPTvp/SyKWR1mWJekLzAcXXYu3atbz99tt89tln7Ny5kwULFrB06VLeeOONyz7GyckJT0/PKh9CWMqYGyIAWLz7tEwLF8KCZh+azYKjC9Dr9Lx343s082mmdUmiHtEs3DRq1Ag7OzsyMzOrHM/MzCQoKOiSj3nllVd44IEHeOSRR2jfvj233347b7/9NpMnT8Zslhkrou51DvemfYgXhgozc7dLq6AQlrAnew/v73gfgPiYeHqF9tK4IlHfaBZuHB0diYmJYdWqVZXHzGYzq1atIi4u7pKPKSkpQa+vWrKdnR2A7NIsNKHT6Spbb37YcpIKk4RsIa5HXlke/1r3LyrMFdzS5BZGtxmtdUmiHtK0Wyo+Pp4vv/ySb7/9loMHD/LEE09QXFzM2LFjARg9ejQTJkyoPH/o0KHMmDGDOXPmcOLECVauXMkrr7zC0KFDK0OOEHVtSIdgfN0cScsrZfWhSy9jIIS4MrNi5sWNL5JRnEETzya8dsNrsleUqBF7LS8+cuRIsrOzmThxIhkZGXTs2JHly5dXDjJOSUmp0lLz8ssvo9PpePnll0lLS8Pf35+hQ4fy1ltvafUtCIGzgx0juoQyc10Ss7elcEvbS3erCiGq9+PBH9mQtgEnOyc+uOkD3B3dtS5J1FM6pYH15xQUFODl5UV+fr4MLhYWk5xTTO/316LTwfp/9yHMV1ZOFeJaHD17lHuW3IPBbOCV7q9wd8u7tS5JWJlref2uV7OlhLBWEY3c6NmsEYoCc7anaF2OEPWKwWRgwoYJGMwGeoX0YkSLEVqXJOo5CTdCWMj5FYt/3nEKowwsFuKqTU+czuGzh/Fx8uH1Hq/LOBtx3STcCGEh/dsEVu439eeBzCs/QAhBQmYC3+z7BoBJcZNkoT5hERJuhLAQBzs9d3cJBWD2NumaEuJKSowlvLTxJRQUhjcbTr8m/bQuSdgICTdCWNA9XcPR6WDD0RxOninWuhwhrNqniZ+SVpRGsFsw/+36X63LETZEwo0QFhTm68qNzf0B+GmbrFgsxOXsyd7DDwd+AGBi3ESZ9i0sSsKNEBZ277mBxfMTUjFUyMBiIf7JaDIyadMkFBSGNh1Kz5CeWpckbIyEGyEsrF+rAAI9ncgpMvDHgUvvcC9EQ/a/ff/jWN4xfJ19+U/X/2hdjrBBEm6EsDB7Oz0ju4QBMHurDCwW4u+OnT3GF3u+AGBCtwl4O3trW5CwSRJuhKgFd3cNQ6eDTcfPkJpbonU5QlgFk9nEpM2TqDBX0Du0NwMiBmhdkrBREm6EqAWhPq70bKau1zFvhwwsFgLgp0M/sSd7D24ObrzU/SVZrE/UGgk3QtSSu891Tc1POIXJ3KC2cBPiImlFaXy862MA4mPiCXKTDWZF7ZFwI0QtublNIF4uDpzOL2PjsRytyxFCM4qi8Prm1ymtKCUmMIa7WtyldUnCxkm4EaKWODvYcXunEAB+lq4p0YD9evxXNp3ehJOdE6/GvYpeJy89onbJ/zAhatGIc9sxrNyfydlig8bVCFH3ckpzeHf7uwA8Ef0EEV4R2hYkGgQJN0LUoraNvWgX4onBZGZRYprW5QhR56Zsm0KBoYDWvq0Z03aM1uWIBkLCjRC17PzA4rnbU1EUGVgsGo41KWtYkbwCO50dr93wGvZ6e61LEg2EhBshatlt0SE42us5lFHIvrQCrcsRok4UGgp5c8ubAIxpO4bWfq01rkg0JBJuhKhlXq4O3NpWnfYqA4tFQ/FRwkdklWYR7hHOE9FPaF2OaGAk3AhRB853TS1KTKPMaNK4GiFq1/aM7cw7Mg+AV294FWd7Z40rEg2NhBsh6sANUX6EeLtQWFbBiv2ymaawXWUVZby2+TUA7mx+J12DumpckWiIJNwIUQf0el3ltPC526VrStiuGbtncLLgJP4u/sR3ide6HNFASbgRoo7cFRMqm2kKm7Yraxez9s8C4OXuL+Pp6KltQaLBknAjRB0J9XGlR5S6meYvO09pXI0QllViLOGljS9hVswMixpG3/C+WpckGjAJN0LUobti1K6pX3aewiybaQob8v6O90ktTCXILYgXur2gdTmigZNwI0QdGtA2CHcne1JzS9menKt1OUJYxIZTGypnR73Z4008HD00rkg0dBJuhKhDLo52DGqvrnkjXVPCFuSV5TFp0yQA7m99P7HBsRpXJISEGyHq3F0x6po3y/ZmUGKo0LgaIWrOrJh56a+XyC7NJtIrkvGdx2tdkhCAhBsh6lzXCB/CfV0pKpc1b0T99t3+71h/aj2Oekfeu/E9WaxPWA0JN0LUMZ1Oxx2dQwD4JUF2Chf10+7s3UzbOQ2A/3b7Ly19W2pckRAXSLgRQgN3dlZnTf11PIfTeaUaVyPEtTlTeobn1z1PhVLBrRG3MqLFCK1LEqIKCTdCaCDM15XYSF8UBRbuktYbUX8YTUbi18aTUZxBE88mTIqbhE6n07osIaqQcCOERu48v+ZNwikURda8EfXD5G2T2Zm1E3cHdz7u+zHuju5alyTERSTcCKGRQe2DcXGwIymnmJ0peVqXI8QVzT44m3lH5qFDxzs3vkNTr6ZalyTEJUm4EUIj7k72DGwna96I+mFF8gqmbJsCwPjO47kx9EaNKxLi8iTcCKGh811Tv+0+TZnRpHE1Qlza1vStTNgwAQWFu1vczUPtHtK6JCGqJeFGCA3FNfWjsZczhWUVrDyQqXU5QlxkT/Yexq8Zj9Fs5OYmN/Ni7IsygFhYPQk3QmhIr9dxR+cLm2kKYU12Zu7k0T8epdhYTGxQLFN6TcFOb6d1WUJckYQbITR2fkG/9UeyySwo07gaIVTb0rfx+J+PU1JRQregbnzc92Mc7Ry1LkuIqyLhRgiNNfV3J6aJD2YFFsmaN8IK/H7id5748wlKK0q5ofENfNrvU1wdXLUuS4irJuFGCCtw59+6pmTNG6EVRVGYsXsG/1n/HwxmA33C+vBx349xsXfRujQhromEGyGswOAOwTja6zmSWcTetHytyxENUJGhiP+s/w+fJX4GwJg2Y/io90c42TlpXJkQ107CjRBWwMvFgQFtz615kyADi0Xd2p+znxG/jWB58nLsdfZMjJvI812fl8HDot6ScCOElbjz3MDixbtPU14ha96I2mc0GZm5eyb3/34/p4pO0ditMbMGzpKNMEW9J+FGCCvRq7k/gZ5O5JUYWXMoS+tyhI3bk72HkUtH8mnip1SYK+gX3o+fh/5MtH+01qUJcd3stS5ACKGy0+sY3imEmeuSmJ+Qxq3tgrUuSdig9KJ0Ptn1CUuSlqCg4OPkw3+7/ZdBkYNkcT5hMyTcCGFF7uocysx1Saw9nEVOUTmN3GUwp7CMQkMhX+39iu8PfI/BbABgaNOh/Lvrv/Fx9tG4OiEsS8KNEFakeaAH0aFe7D6Vz+LE0zzcM1LrkkQ9l1Oaww8HfmDu4bkUGYsA6BLYhee7PE/bRm01rk6I2iHhRggrc1dMKLtP5TNvRyoP9YiQrgJRI2lFaXyz7xsWHVtEuakcgGbezRjfeTw3hd4k/6+ETZNwI4SVGRYdwhtLDnIoo5D9pwtoF+KldUminjArZramb2Xu4bmsSV2DWTED0KFRBx5u/zC9w3qj18k8EmH7JNwIYWW8XB24uW0gS/ekMz/hlIQbcUX55fn8evxXfj78M8kFyZXH44LjeKT9I3QN6iotNaJBkXAjhBUaERPK0j3pLEpMY8KgVjjZy2Jq4mIHzxxk7uG5LE1aSplJ3XTVzcGNYVHDGNlyJFHeURpXKIQ2JNwIYYXOr3mTWVDO6oNZDGwv08KFqrSilBXJK5h3ZB57svdUHm/m3YxRrUYxuOlg3BzcNKxQCO1JuBHCCtnpddzeKZTP1x1nfsIpCTeCw7mHmX9kPkuTllJoLATAXm/PzeE3M7LVSDoHdJauJyHOkXAjhJW6K0YNN2uPZJNVWEaAh7PWJYk6VmIsYXnycuYfmc/enL2Vx0PcQ7iz+Z3c3vx2Grk00rBCIayThBshrFSzAHc6hXuzKyWPRbvSeOxGGT/RUBw4c4BfjvzC0hNLKTYWA2Cvs6dPeB/uanEX3YO7y6wnIaqh+W/H9OnTiYiIwNnZmdjYWLZt21bt+Xl5eTz11FMEBwfj5OREixYtWLZsWR1VK0TdGhETBsD8hFMoiqJxNaI2FRuLmXdkHiOXjGTkkpH8fORnio3FhHmE8VzMc6wcsZIPe3/IDY1vkGAjxBVo2nIzd+5c4uPj+fzzz4mNjWXq1KkMGDCAw4cPExAQcNH5BoOBm2++mYCAAObPn09ISAgnT57E29u77osXog4MiQ7mtd/2cySziD2n8okO89a6JGFBiqKw/8x+5h+Zz7ITyyitKAXUsTT9w/tzV4u76BrUVcKMENdI03Dz4Ycf8uijjzJ27FgAPv/8c5YuXcrXX3/NCy+8cNH5X3/9Nbm5uWzatAkHBwcAIiIiqr1GeXk55eXllbcLCgos9w0IUcs8nR24tV0QixNPMz/hlIQbG5FVksWSpCX8euxXjucfrzwe4RnBXS3uYmjUUHydfTWsUFgrk8mE0WjUuoxa4+joiF5//WFep2jU1m0wGHB1dWX+/PkMHz688viYMWPIy8tj8eLFFz1m0KBB+Pr64urqyuLFi/H39+fee+/lv//9L3Z2l14H5NVXX+W111676Hh+fj6enp4W+36EqC0bjmbzwFfb8HS2Z9tL/XF2kDVv6qNyUzlrUtaw6PgiNp/eXLl6sJOdE/3C+3FXi7voEthFZjyJS1IUhYyMDPLy8rQupVbp9XoiIyNxdHS86L6CggK8vLyu6vVbs5abnJwcTCYTgYGBVY4HBgZy6NChSz4mKSmJ1atXc99997Fs2TKOHTvGk08+idFoZNKkSZd8zIQJE4iPj6+8XVBQQFhYmOW+ESFq2Q1RjWjs5czp/DL+PJjJkA6NtS5JXCWT2URCZgLLk5ezPHk5hYbCyvs6BXRiWNQwBkQMwMPRQ8MqRX1wPtgEBATg6upqkyHYbDZz+vRp0tPTCQ8Pv67vsUbhJjMzk+eff55Vq1aRlZV10UBHk8lU44KqYzabCQgI4IsvvsDOzo6YmBjS0tJ47733LhtunJyccHJyqpV6hKgLdnodd3QO5dM1x5ifcErCjZUzmU3szNrJiuQV/HnyT86Unam8L8gtiGFRwxgWNYwmnk00rFLUJyaTqTLY+Pn5aV1OrfL39+f06dNUVFRUDj+piRqFmwcffJCUlBReeeUVgoODa5SuGjVqhJ2dHZmZmVWOZ2ZmEhQUdMnHBAcH4+DgUKULqnXr1mRkZGAwGC7ZjCWELbgrRg03649kk5FfRpCXrHljTQwmAzsyd7AmZQ1/pvxJTmlO5X2ejp70b9KfgZED6RbUTQYHi2t2foyNq6urxpXUvvOv4yaTqe7DzcaNG9mwYQMdO3as8YUdHR2JiYlh1apVlWNuzGYzq1at4umnn77kY3r06MHs2bMxm82VA46OHDlCcHCwBBth0yIaudE1woftyWdZuCuNJ3rLmjdayynNYcOpDaw/tZ5NpzdRUlFSeZ+Howf9wvsxIGIAscGxOOhr/kdaiPNssSvqnyz1PdYo3ISFhVlkzY34+HjGjBlDly5d6NatG1OnTqW4uLhy9tTo0aMJCQlh8uTJADzxxBN8+umnjB8/nnHjxnH06FHefvttnnnmmeuuRQhrNyImjO3JZ5mXkMrjNzVtEH/orEmxsZidmTvZlrGNrelbOZh7sMr9jVwa0SukFzc3uZnuwd1xsJNAI4RWahRupk6dygsvvMDMmTOvOBW7OiNHjiQ7O5uJEyeSkZFBx44dWb58eeUg45SUlCpTwsLCwlixYgXPPfccHTp0ICQkhPHjx/Pf//63xjUIUV8M6hDMpF/3k5RdzK7UPDqH+2hdkk0rNhazN2cv29K3sS1jG/ty9mFSqo4nbOvXlptCb+LG0Btp7ddaupyEsBI1mgru4+NDSUkJFRUVuLq6XtQvlpuba7ECLe1appIJYW3if05kwc407ukaxpQ7O2hdjs0wK2aSC5LZk72H3dm72ZO9h2N5xyqna58X6h5Kt+BudAvqRmxwrOzrJOpEWVkZJ06cIDIyEmdn2x5vV933WutTwadOnVqThwkhrtM9XcNZsDONX3ef5uUhbXB3ku3haqLAUMDe7L1qmMnZzd7svRQYLl7gM9gtmC6BXega1JVuwd0IcQ/RoFoh6q/169fz3nvvkZCQQHp6OgsXLqyytl1tqdFfxjFjxli6DiHEVega4UOUvxvHs4v5NfE098aGa12S1TOZTSTlJ1W2yOzO3k1SftJF5znbOdO2UVs6+HcgulE0Hfw74O/qr0HFQtiO4uJioqOjeeihh7jjjjvq7Lo1fttnMplYtGgRBw+qg+ratm3LsGHDLrtSsBDi+ul0Ou7pGs5byw4yZ3uKhJtLyCvLY0/Ohe6lvTl7K3fW/rtwj3A1yPirQaa5T3OZ1STqDUVRKDXWzppyV+LiYHfVExoGDhzIwIEDa7mii9Uo3Bw7doxBgwaRlpZGy5YtAZg8eTJhYWEsXbqUqCiZpipEbbkzJpT3Vhxmz6l89qXl0y7ES+uSNHW27CzbM7azLUMd+Hsi/8RF57jau9K+UfvKMNPev73s3STqtVKjiTYTV2hy7QOvD8DV0bq7xGtU3TPPPENUVBRbtmzB11f9A3HmzBnuv/9+nnnmGZYuXWrRIoUQF/i6OXJL20CW7ElnzvYU3gxpr3VJdcpoMrI9czsbTm1gW8Y2jpw9ctE5EZ4RlUEm2j+aZt7NsNNLq7IQDUWNws26deuqBBsAPz8/pkyZQo8ePSxWnBDi0kZ1C2fJnnQW7zrNi4NaW/27qOtVYChgw6kNrE1dy8a0jRQZi6rc39ynOd2C1FlMnQM64+3srUmdQtQVFwc7Drw+QLNrW7sa/UV0cnKisLDwouNFRUWyUrAQdSCuqR/hvq6k5JawdE86I7rY3mawBpOBDac28FvSb6w/tR6j2Vh5n5+zH73DetO9cXe6BnbFz8W299sR4p90Op3Nv6m5HjX6yQwZMoTHHnuMr776im7dugGwdetWHn/8cYYNG2bRAoUQF9PrddzTLYx3lx/mp20pNhVuThacZM6hOfx6/Ncq07OjvKLoE96HPmF9aNeonSyYJ4S4rBqFm48//pgxY8YQFxdXuYBfRUUFw4YNY9q0aRYtUAhxaXfFhPLhH0fYmZLHkcxCWgR6aF1SjSmKwqbTm/jx4I9sSNtQeTzAJYDBTQczJGoILXxaaFihEKImioqKOHbsWOXtEydOkJiYiK+vL+HhtTfbs0bhxtvbm8WLF3P06FEOHToEqLtzN2vWzKLFCSEuL8DDmX6tA1ixP5OftqUwaWhbrUu6ZoqisCFtA58lfsb+M/sB0KGjV2gvRrUaRVxwnAwEFqIe27FjB3369Km8HR8fD6jr5c2aNavWrntdHXbNmzenefPmlqpFCHGNRnULZ8X+TBbsTOM/A1rh4lh/gsCW9C18svMT9uTsAcDF3oU7m9/JqFajCPeU9XuEsAW9e/e2yEbb1+qqw018fDxvvPEGbm5ulcnrcj788MPrLkwIcWW9mvsT6uPCqbOl/Lb7NHd3tf6xN6cKT/He9vdYnboaUFcGHtVqFA+2e1DWnhFCWMRVh5tdu3ZhNBorvxZCaM9Or+P+7k2Y8vshvt2czIguoVe9cmhdqzBX8PW+r/lizxeUm8qx09kxsuVIHu3wqGxAKYSwqKsON2vWrLnk10IIbY3sEsZHK4+w/3QBO1PyiGnio3VJFzl69igv//UyB84cACA2KJYXur1AMx8ZpyeEsLwazaV86KGHLrnOTXFxMQ899NB1FyWEuHo+bo4Mi24MwPebk7Ut5h8URWH2wdmMXDKSA2cO4Onoyds93+bLW76UYCOEqDU1CjfffvstpaWlFx0vLS3lu+++u+6ihBDXZnRcBABL96aTXViubTHnFBmKeH7d80zeNhmj2ciNoTey8LaFDI0aarVdZ0II23BNs6UKCgpQFAVFUSgsLMTZ2bnyPpPJxLJlywgICLB4kUKI6rUP9aJTuDe7UvKYsy2Fcf20ncWYUpDCU6ueIrkgGXudPf/q8i/ua32fhBohRJ24pnDj7e2NTqdDp9PRosXFC2rpdDpee+01ixUnhLh6o+OasCsljx+3pvBE7yjs7bRZwXdn5k7GrxlPXnkeQW5BvH/T+0T7R2tSixCiYbqmcLNmzRoURaFv37788ssvVTbOdHR0pEmTJjRu3NjiRQohrmxQ+2DeXHKQjIIyVh7IZGD74DqvYXnycl7c8CJGs5F2fu34pN8nMhNKCFHnrinc3HTTTYC6fHJYWBh6veztIoS1cLK3Y1S3cD5dc4xv/kqu83Cz+NhiXvnrFRQU+oX3Y3KvybjYu9RpDUIIATVcobhJkyYAlJSUkJKSgsFgqHJ/hw4drr8yIcQ1eyCuCTPXH2dbci6JqXl0DPOuk+vOPzKf1ze/joLCiBYjeCn2Jdk2QQihmRo1vWRnZzNkyBA8PDxo27YtnTp1qvIhhNBGoKczw6JDAPhyQ1KdXHP+kfm8tvk1FBTubXUvr3R/RYKNEAKAyZMn07VrVzw8PAgICGD48OEcPny41q9bo3Dz7LPPkpeXx9atW3FxcWH58uV8++23NG/enF9//dXSNQohrsEjvSIB+H1vOqm5JbV6rT9P/skbW94AYHSb0bzQ7QWZESWEqLRu3TqeeuoptmzZwsqVKzEajdxyyy0UFxfX6nVr1C21evVqFi9eTJcuXdDr9TRp0oSbb74ZT09PJk+ezODBgy1dpxDiKrUO9qRX80ZsOJrD13+dqLXdwrdnbOe/6/+LWTFzZ/M7eb7L8xJshKgrigLG2n3zclkOrnCVv+vLly+vcnvWrFkEBASQkJDAjTfeWBvVATUMN8XFxZXr2fj4+JCdnU2LFi1o3749O3futGiBQohr92ivpmw4msPc7ak8268FXq4OFn3+Y2eP8czqZzCYDfQN68vL3V+WYCNEXTKWwNsazU5+8TQ4utXoofn5+QBVZlvXhhp1S7Vs2bKyzyw6OpqZM2eSlpbG559/TnBw3U8/FUJU1at5I1oFeVBiMDF7W4pFnzu/PJ9n1jxDkbGIzgGdefemd7HX1+h9khCiATGbzTz77LP06NGDdu3a1eq1avQXafz48aSnpwMwadIkbr31Vn788UccHR2ZNWuWJesTQtSATqfjkV5NeX7ebmZtOsHDPSNxtL/+pRsqzBX8e92/SS1MJcQ9hKl9puJk52SBioUQ18TBVW1B0eraNfDUU0+xb98+Nm7caOGCLlajcHP//fdXfh0TE8PJkyc5dOgQ4eHhNGokC3YJYQ2GRTfm3eWHyCwoZ+GuU4zsGn7dzzk1YSqb0zfjYu/CtD7T8HG2vh3IhWgQdLoadw1p4emnn2bJkiWsX7+e0NDQWr+eRVbhc3V1pXPnzhJshLAijvZ6HruxKQDT1xynwmS+rudbm7qWbw98C8AbPd6gpW/L6y1RCGHjFEXh6aefZuHChaxevZrIyMg6ue5Vt9zEx8df9ZN++OGHNSpGCGFZ98aG89na46TklvDr7tPc0blm75gyizN55a9XALi/9f0MiBhgyTKFEDbqqaeeYvbs2SxevBgPDw8yMjIA8PLywsWl9lYwv+pws2vXrqs6T2ZMCGE9XB3tebhnJO+tOMyna45xW8cQ7PTX9jtqMpt4ceOL5JXn0dq3Nc/FPFdL1QohbM2MGTMA6N27d5Xj33zzDQ8++GCtXfeqw82aNWtqrQghRO0ZHdeEL9YnkZRdzLK96QyNvrbpo7P2z2JbxjZc7F1458Z3cLRzrKVKhRC2RlEUTa4rO18KYeM8nB0Y2yMCgE9XH8Nsvvo/Nkl5SUxPnA7AhG4TiPSqm/5yIYS4HjWaLdWnT59qu59Wr15d44KEEJY39oZIvtp4gsOZhfy25zS3dQy54mNMZhMTN03EaDbSM6Qnw5sNr/1ChRDCAmrUctOxY0eio6MrP9q0aYPBYGDnzp20b9/e0jUKIa6Tl6sD/3du5tSHK49gvIqZUz8d+ond2btxc3BjUtwkGU8nhKg3atRy89FHH13y+KuvvkpRUdF1FSSEqB1je0Qya1MyJ8+UMHd7Kvd3b3LZc08VnuLjXR8DEB8TT5BbUF2VKYQQ182iY27uv/9+vv76a0s+pRDCQtyc7Hm6TzMAPl51lDKj6bLnvrP9HUorSukS2IW7WtxVVyUKIYRFWDTcbN68GWdnZ0s+pRDCgkbFhhPi7UJWYTmzNiVf8pyNaRtZm7oWe509r3R/Bb1O5h0IIeqXGnVL3XHHHVVuK4pCeno6O3bs4JVXXrFIYUIIy3OytyP+5hb8a95upq8+xp2dQ/H3uLA3lNFk5J1t7wAwqvUomno31apUIYSosRq9JfPy8qry4evrS+/evVm2bBmTJk2ydI1CCAu6vVMI7UO8KCyv4IM/Dle574eDP5BckIyfsx9PRD+hUYVCCHF9atRy880331i6DiFEHdHrdbw6rA13ztjM3B3qwOJ2IV7klObw+e7PAXg25lk8HD00rlQIIWrmujrTd+zYwffff8/3339PQkKCpWoSQtSymCa+DItujKLA678dQFEUZu6eSUlFCe382jEsapjWJQohRI3VKNycOnWKXr160a1bN8aPH8/48ePp2rUrPXv25NSpU5auUQhRC14Y2ApnBz3bknP5ZtsO5h+ZD8BzMc/JIGIhhEXMmDGDDh064OnpiaenJ3Fxcfz++++1ft0a/QV75JFHMBqNHDx4kNzcXHJzczl48CBms5lHHnnE0jUKIWpBY28XnuqtTg2flvAJFUoFPRr3oFtwN40rE0LYitDQUKZMmUJCQgI7duygb9++3Hbbbezfv79Wr6tTarCrlYuLC5s2baJTp05VjickJNCrVy9KSkosVqClFRQU4OXlRX5+Pp6enlqXI4SmDBVmBnw2mxwvdYbUvKHzaOXbSuOqhBB/V1ZWxokTJ4iMjKxcbkVRFEorSjWpx8Xe5bpWLPf19eW9997j4Ycfvui+S32v513L63eNBhSHhYVhNBovOm4ymWjc+Np2HBZCaMfRXk9w5FpycsGY35Hc3Ebgq3VVQogrKa0oJXZ2rCbX3nrvVlwdXK/5cSaTiXnz5lFcXExcXFwtVHZBjbql3nvvPcaNG8eOHTsqj+3YsYPx48fz/vvvW6w4IUTt2pu9l725W9Ghpzz7ZiYs3EuJoULrsoQQNmTv3r24u7vj5OTE448/zsKFC2nTpk2tXrNG3VI+Pj6UlJRQUVGBvb3a+HP+azc3tyrn5ubmWqZSC5FuKSEueHrV06w7tY5BEUNZv6kf6flljOoWxuQ7OmhdmhDinPreLWUwGEhJSSE/P5/58+fzv//9j3Xr1l0y4GjaLTV16tSaPEwIYUUOnDnAulPr0Ov0PNnp/7gt1I37/reVn7al0rtlAAPaymaZQlgrnU5Xo64hLTg6OtKsmTp5ISYmhu3btzNt2jRmzpxZa9esUbgZM2aMpesQQtSxL/Z8AcCgyEE08WxCE094rFdTZq5P4oVf9tAxzJtAT9krTghhWWazmfLy8lq9Ro3CDagDgxYtWsTBgwcBaNu2LcOGDcPOzs5ixQkhasfh3MOsSlmFDh2Pdni08nj8LS3YeCyH/acLeHZOIt8/3A17O1nzRghRMxMmTGDgwIGEh4dTWFjI7NmzWbt2LStWrKjV69bor9axY8do3bo1o0ePZsGCBSxYsID777+ftm3bcvz4cUvXKISwsK/3fQ3ALRG30NTrwuaYTvZ2TLunE66OdmxOOsM7yw9pVaIQwgZkZWUxevRoWrZsSb9+/di+fTsrVqzg5ptvrtXr1qjl5plnniEqKootW7bg66vOGz1z5gz3338/zzzzDEuXLrVokUIIy0kvSmdFsvqu6eF2F68z0SzAnQ9GRPPEjzv5csMJ2oV4cVvHkLouUwhhA7766itNrlujlpt169bx7rvvVgYbAD8/P6ZMmcK6dessVpwQwvJ+OPgDJsVEbHAsrf1aX/Kcge2DebJ3FAD//WUP+9Ly67JEIYS4LjUKN05OThQWFl50vKioCEdHx+suSghROwoMBZV7SI1pU/3EgH/d0pKbWvhTZjTz4DfbOXmmuC5KFEKI61ajcDNkyBAee+wxtm7diqIoKIrCli1bePzxxxk2THYTFsJa/XLkF0oqSojyiqJnSM9qz7XT6/jk3k60DvYkp6icB77aRnZh7c5wEEIIS6hRuPn444+JiooiLi4OZ2dnnJ2dueGGG2jWrBnTpk275uebPn06ERERODs7Exsby7Zt267qcXPmzEGn0zF8+PBrvqYQDY3RZOSHgz8AMKbtmKtahMvT2YFvH+pKuK8rKbkljPl6G3klhtouVQghrkuNwo23tzeLFy/myJEjzJs3j3nz5nHkyBEWLlyIl5fXNT3X3LlziY+PZ9KkSezcuZPo6GgGDBhAVlZWtY9LTk7m+eefp1evXjX5FoRocFaeXElWSRaNXBoxuOngq35cgIcz3z/cjUbujhxIL+CeL7aQUyQtOELUNbPZrHUJta4GmyZcUo22XwB1BPRHH33E0aNHAWjevDnPPvssjzzyyDU9T2xsLF27duXTTz8F1H+8sLAwxo0bxwsvvHDJx5hMJm688UYeeughNmzYQF5eHosWLbqq68n2C6KhGvP7GHZm7eSJ6Cd4suOT1/z4I5mF3Pe/rWQXltPU343Zj3QnyEsW+ROitpnNZo4ePYqdnR3+/v44Ojpe167c1kpRFLKzsykpKaF58+YXrZtX69svTJw4kQ8//JBx48ZV7uy5efNmnnvuOVJSUnj99dev6nkMBgMJCQlMmDCh8pher6d///5s3rz5so97/fXXCQgI4OGHH2bDhg3VXqO8vLzKSogFBQVXVZsQtuRw7mF2Zu3EXmfPXS3uqtFztAj04Of/i+O+L7eQlF3MnTM28cXoGNo2vrbWWiHEtdHr9URGRpKens7p06e1LqdW6XQ6QkNDr3tB4BqFmxkzZvDll18yatSoymPDhg2jQ4cOjBs37qrDTU5ODiaTicDAwCrHAwMDOXTo0ouHbdy4ka+++orExMSrusbkyZN57bXXrupcIWzVnMNzAOgb3pcA14AaP09kIzd+fjyO0V9tIymnmLtmbOaDu6MZ1D7YUqXaFLNZIb2gjJQzJeSVGCgsr6DUYMLRXo+Lgx1eLg6E+boQ5uuKk72s7i4uz9HRkfDwcCoqKjCZTFqXU2scHBwsstNBjcKN0WikS5cuFx2PiYmhoqLiuou6nMLCQh544AG+/PJLGjVqdFWPmTBhAvHx8ZW3CwoKCAsLq60ShbA6hYZCliapC2ve0+qe636+UB9XFj7Zg6d/2smGozk8+eNOHruxKf+6pUWDfoEuKq9gX1o+u1Pz2HMqn8OZhaTklmCouPI4CUc7PW1DPLkhyo9b2wbTLsTTJrsdxPXR6XQ4ODjg4OCgdSlWr0bh5oEHHmDGjBl8+OGHVY5/8cUX3HfffVf9PI0aNcLOzo7MzMwqxzMzMwkKunhH4uPHj5OcnMzQoUMrj50fYGVvb8/hw4eJioqq8hgnJyecnJyuuiYhbM2vx3+ltKKUZt7N6BJ48ZuSmvBydeCbB7sy5fdD/G/jCb5Yn8T6I9lMvacjrYIaxli2UoOJhJNn+et4DpuO5bA3LR/zJUYw2ut1hPm60sjdEXcne1wd7SmvMFNmNHGm2EBqbglF5RXsSsljV0oe09ccp0WgO6PjIrgrJhRnh4YbGIWoqRoNKB43bhzfffcdYWFhdO/eHYCtW7eSkpLC6NGjq6TKfwagf4qNjaVbt2588skngBpWwsPDefrppy8aUFxWVsaxY8eqHHv55ZcpLCxk2rRptGjR4oqLCMqAYtGQKIrCsEXDSC5I5qXYlyzScvNPKw9k8sIvezhTbMDRTs/DvSJ5qk8z3J1qvC+vVTKazOw5lcemY2f463gOO0/mYTBVbZVp7OVMh1BvOoR50baxF00buRHs5Vzt5qOKopCSW8L25LOsOpjJmsNZlBnV5w32cubZ/s0ZEROGXi8tOaJhu5bX7xqFmz59+lzVeTqdjtWrV1d7zty5cxkzZgwzZ86kW7duTJ06lZ9//plDhw4RGBjI6NGjCQkJYfLkyZd8/IMPPiizpYS4jC3pW3j0j0dxtXdl1YhVuDu618p1sgvLmbBgD38eVJdwCPBw4vkBLbm9UwgO9XRXcbNZ4WBGAZuPn2HT8TNsTTpDsaHqWIdgL2duiGrEDVF+3NDMj2Avl+u+bn6pkfkJp/hqQxKn88sA6NLEhyl3dqBZQO38+wlRH9T6bKk1a9bUqLBLGTlyJNnZ2UycOJGMjAw6duzI8uXLKwcZp6SkoNfXzz+OQmht7qG5AAyNGlprwQbA38OJL0d34c+DWby59AAnz5Twn/l7+HjVUf7vpihG1IPuFUVROJ5dxKbjZ9h07AxbTpwhr8RY5RwfVwfiovwqA01kIzeLj43xcnHg4Z6R3Bcbznebk5n251F2nDzLkE828Obw9twVE2rR6wlhi2q8zk19JS03oqHIKc2h/7z+mBQTC4YtoLlP8zq5bnmFiW83JfPF+iRyitTVjD2d7bmtYwh3dwmzmsGyZUYT+9Ly1bEuqWfZnnz2ou0l3BztiG3qR1xTtWWmdZBnnXcPnTpbwoQFe9lwNAeA+7uH8+rQttV2dQlhi2q9W6o+k3AjGopv9n3Dhwkf0sG/Az8O+rHOr19qMPHzjlS+WJ9EWl5p5fEQbxdubhNI75b+xDTxwcO59md+FJQZOZJRyKGMQg5lFLA7NZ+D6QVU/GMEsJO9nq4RvsRF+REX5Uf7EC+r6FYzmxU+WX2MqauOoCjQv3UAn4zqjIujdbeGCWFJEm6qIeFGNASKonDb4ts4kX+CSXGTarxwnyWYzQqbjp9h7o5U/tifQfnfpkbrddAyyJN2jT2JCnAnyt+dyEZuBHg64eFkf1UtPIqiUGIwkVtsIKeonNN5ZaTklpCSW0JqbgkncoqrhKu/a+TuROdwbzqF+9A53JuO4d5WPZ19+b4Mxs/ZRXmFmW6Rvswa2xVXR9sauC3E5Ui4qYaEG9EQJGYl8sDvD+Bi78LqEatrdbzNtSg1mNh4LIc/D2SyKSmH1NxLhw5Q137xc3fEw9keR3s99no9DnY6KswK5UYz5RUmSg3qdOryq1hLJsjTmZZBHrQK9qBtYy86h3sT4u1iFV1k12JHci5jv9lOYXkFcU39+PrBrtKCIxqEWh9QLISwbguPLQTg5iY3W02wAXBxtOPmNoHc3EadMJBVUEbCybMcySzieLb6kZxTTLHBhMFkJj2/jPT8q3tuJ3s9fm6OBHu7EO7rSpiPuvJvEz83WgS64+1a/TIR9UWXCF++fbgbo7/axuakMzwzZxef3x+DnUwVF6KStNwIYWNKjCX0+bkPJRUlzLp1FjGBMVqXdM3UFplycosNFJZVYDSZMZoUjCYz9nodTg52OJ3bwsDXzRFfN0dcHe3qXSvM9dienMt9/9uKocLMIz0jeXlIG61LEqJWScuNEA3YiuQVlFSU0MSzCZ0DOmtdTo24ONoR6uhKqI+r1qVYra4Rvrw/IppnftrF/zaeoEkjNx7o3kTrsoSwCtpPAxBCWNT5LqnhzYY3qJaMhmhYdGOev6UFAJMW72NL0hmNKxLCOki4EcKGJOUnsStrF3qdnmFRw7QuR9SBp/o04/ZOIZgVGD9nFzlF5Vd+kBA2TsKNEDbkt+O/AdAzpCcBrgEaVyPqgk6n463b29EswJ3MgnKem5uI+VI7eArRgEi4EcJGKIrC7yd+B9TtFkTD4epoz2f3dcbZQc+GoznMWHdc65KE0JSEGyFsxO7s3aQVpeFq78pNoTdpXY6oYy0CPXjjtnYAfLTyCPvSrnIOvRA2SMKNEDZi2YllAPQN74uL/fXvTi3qnxFdwhjcIZgKs0L8z4mUV5iu/CAhbJCEGyFsQIW5ghXJKwAYFDlI42qElt64rR2N3B05klnEtD+Pal2OEJqQcCOEDdiWvo3csly8nbzp3ri71uUIDfm6OfLm8PYAfL7uOLtSzmpckRB1T8KNEDZg6YmlAAyIGICDvvZ32RbW7dZ2QQzv2BizAhMW7MVouvLeW0LYEgk3QtRzZRVlrEpZBcDAyIEaVyOsxaShbfFxdeBQRiHf/HVC63KEqFMSboSo5zakbaDYWEyQWxCdAjppXY6wEj5ujrw4qDUAH608yqmzJRpXJETdkXAjRD13fm2bgRED0evkV1pccFdMKN0ifSk1mnj11wNalyNEnZG/hELUY4WGQtalrgNgUFOZJSWq0ul0vDW8HfZ6HX8ezOSP/RlalyREnZBwI0Q9tjplNQazgaZeTWnp01LrcoQVah7owWM3NgXg1V/3U1xeoXFFQtQ+CTdC1GPnF+4bGDlQdgAXlzWub3NCfVw4nV/GjLWyNYOwfRJuhKinckpz2Jq+FZCF+0T1XBzteHlwGwC+2JBEaq4MLha2TcKNEPXUH8l/YFJMtPNrR7hnuNblCCs3oG0gPZr5Yagw8/ayg1qXI0StknAjRD11vktKBhKLq6HT6Zg4pC16Hfy+L4NNx3O0LkmIWiPhRoh66FThKXZn70aHjgERA7QuR9QTLYM8uL97EwBe/+0AFbJysbBREm6EqIeWJy8HoFtQNwJcAzSuRtQnz/VvgZeLunLxnO2pWpcjRK2QcCNEPSRdUqKmfNwcib+5BQAf/HGY/BKjxhUJYXkSboSoZ46ePcrRs0ex19vTL7yf1uWIeui+2HBaBLpztsTI1FVHtC5HCIuTcCNEPXN+u4VeIb3wcvLSuBpRH9nb6Zk0tC0A320+ydHMQo0rEsKyJNwIUY8oinKhS0rWthHXoUezRtzSJhCTWeH1JQdQFEXrkoSwGAk3QtQju7N3k1aUhou9CzeF3aR1OaKee2lwaxzt9Gw4msOqg1lalyOExUi4EaIeOd8l1Te8Ly72LhpXI+q7Jn5uPNIrEoA3lh6gvMKkcUVCWIaEGyHqiQpzReUUcOmSEpbyZJ9mBHg4cfJMCV9vTNa6HCEsQsKNEPXEtoxt5Jbl4u3kTVzjOK3LETbC3cmeFwa2AuDT1UfJKijTuCIhrp+EGyHqiWVJ6kDiW5rcgoPeQeNqhC0Z3jGEjmHeFBtMvLP8sNblCHHdJNwIUQ+Um8pZlbIKkIX7hOXp9TpeHaZODf9l5ykSU/O0LUiI6yThRoh6YMOpDRQZiwh0DaRTQCetyxE2qGOYN3d2DgXg1V/3YzbL1HBRf0m4EaIe+PvaNnqd/NqK2vHfW1vi5mhHYmoeixLTtC5HiBqTv5JCWLkiQxHrUtcBMDByoMbVCFsW4OnM032bAzDl90MUlVdoXJEQNSPhRggrtyplFQazgUivSFr5ttK6HGHjHuoZQRM/V7IKy/lszTGtyxGiRiTcCGHlzi/cNyhyEDqdTuNqhK1zsrfj5cFtAPjfhhMczy7SuCIhrp2EGyGs2JnSM2xJ3wLIwn2i7vRvHUCflv4YTGZeWbRP9p0S9Y6EGyGs2B8n/8CkmGjn145wz3CtyxENhE6n4/Xb2uFkr2fT8TMyuFjUOxJuhLBi5xfuk4HEoq6F+bryTD91cPGbSw6SX2LUuCIhrp6EGyGsVFpRGonZiejQcWvkrVqXIxqgR3s1pVmAO2eKDUxZfkjrcoS4ahJuhLBS5wcSdw3qSoBrgMbViIbI0V7PW8PbAfDTthQSTuZqXJEQV0fCjRBW6u8L9wmhldimftwVo65c/MIveykzmjSuSIgrk3AjhBU6evYoR88exV5vT/8m/bUuRzRwLw1qTSN3J45mFfHxqqNalyPEFUm4EcIKne+S6hnSEy8nL42rEQ2dj5sjb57rnpq5Pok9p/K0LUiIK5BwI4SVURSlsktqcORgjasRQnVruyCGRjfGZFb497w9lFdI95SwXhJuhLAyu7N3k1aUhqu9KzeG3qh1OUJUem1YW/zcHDmcWcinq2VrBmG9JNwIYWWWJC0BoH+T/rg6uGpcjRAX+P6te+qztcfZnZqnbUFCXIaEGyGsiNFkZHnycgAGN5UuKWF9BrYPZkiHYExmhWfnJlIsO4cLKyThRggr8tfpv8gvz6eRSyNig2K1LkeIS3preHsaezlzIqeY1387oHU5QlxEwo0QVuR8l9TAyIHY6e00rkaIS/NydeDDkR3R6WDujlR+35uudUlCVCHhRggrUWgoZG3qWgCGNB2iaS1CXEn3pn48cVMUAC8s2MvpvFKNKxLiAqsIN9OnTyciIgJnZ2diY2PZtm3bZc/98ssv6dWrFz4+Pvj4+NC/f/9qzxeivvjz5J+Um8pp6tWU1r6ttS5HiCt67uYWdAj1Ir/UyHNzE6kwmbUuSQjACsLN3LlziY+PZ9KkSezcuZPo6GgGDBhAVlbWJc9fu3Yto0aNYs2aNWzevJmwsDBuueUW0tLS6rhyISxr6YmlgNpqo9PpNK5GiCtzsNMz7Z5OuDnasfVELh+uPKJ1SUIAoFMURdGygNjYWLp27cqnn34KgNlsJiwsjHHjxvHCCy9c8fEmkwkfHx8+/fRTRo8efcXzCwoK8PLyIj8/H09Pz+uuXwhLyCzO5Ob5N6OgsPzO5YS4h2hdkhBXbcme0zw9excAX43pQr/WgRpXJGzRtbx+a9pyYzAYSEhIoH//C3vn6PV6+vfvz+bNm6/qOUpKSjAajfj6+l7y/vLycgoKCqp8CGFtfj/xOwoKnQM6S7AR9c6QDo158IYIAJ6bm0hqbom2BYkGT9Nwk5OTg8lkIjCwasoPDAwkIyPjqp7jv//9L40bN64SkP5u8uTJeHl5VX6EhYVdd91CWNr5WVKyto2or14c1JqOYd4UlFXwxI8Jsnu40JTmY26ux5QpU5gzZw4LFy7E2dn5kudMmDCB/Pz8yo/U1NQ6rlKI6h09e5TDZw9jr7dnQMQArcsRokYc7fVMv68zPq4O7Esr4I0lsv6N0I6m4aZRo0bY2dmRmZlZ5XhmZiZBQUHVPvb9999nypQp/PHHH3To0OGy5zk5OeHp6VnlQwhr8tvx3wDoFdJLdgAX9VqItwsfnVv/5setKSzYeUrrkkQDpWm4cXR0JCYmhlWrVlUeM5vNrFq1iri4uMs+7t133+WNN95g+fLldOnSpS5KFaJWGM1Gfj3+KwDDmw3XthghLKB3ywCe6dscgAkL9rL/dL7GFYmGSPNuqfj4eL788ku+/fZbDh48yBNPPEFxcTFjx44FYPTo0UyYMKHy/HfeeYdXXnmFr7/+moiICDIyMsjIyKCoqEirb0GIGtt4aiNnys7g6+xLr9BeWpcjhEWM79ec3i39Ka8w8/gPCeSVGLQuSTQwmoebkSNH8v777zNx4kQ6duxIYmIiy5cvrxxknJKSQnr6haW9Z8yYgcFg4K677iI4OLjy4/3339fqWxCixhYcWwDAsKhhOOgdNK5GCMvQ63VMHdmRMF8XUnNLeXZuImazpquOiAZG83Vu6pqscyOsRU5pDv3n9cekmFh822KaejfVuiQhLGr/6Xzu+GwT5RVmnunXnPibW2hdkqjH6s06N0I0ZL8d/w2TYiLaP1qCjbBJbRt7MfmO9gB8vOooqw5mXuERQliGhBshNKAoCguPLQTg9ma3a1yNELXnjs6hjI5rAsCzcxNJzinWuCLREEi4EUIDu7N3cyL/BC72LrK2jbB5Lw9uQ0wTHwrLKnj8hwRKDBValyRsnIQbITRwvtXmlia34O7ornE1QtQuR3s9n93XmUbuThzKKGTCgr00sOGeoo5JuBGijhUbi1l+YjkAtzeXLinRMAR6OjP93k7Y6XUsTjzNrE3JWpckbJiEGyHq2NKkpZRUlBDhGUHngM5alyNEnYlt6seLg1oD8NbSg2xPztW4ImGrJNwIUYcURWHO4TkAjGw5Ep1Op3FFQtSth3pEMDS6MRVmhSd/3ElWQZnWJQkbJOFGiDq0K2sXR88exdnOmWHNhmldjhB1TqfT8c6d7WkZ6EF2YTlP/rgTQ4VZ67KEjZFwI0QdOt9qM7jpYDwdZRFJ0TC5Otrz+QMxeDjZs+PkWd5edlDrkoSNkXAjRB3JKc1h5cmVANzd8m6NqxFCW5GN3PhoZEcAZm1KZuEu2UFcWI6EGyHqyKJji6gwV9ChUQfa+LUBRYHiM5CXCrlJcOY4lOapx4VoAPq3CWRc32aAuoP4gdMFGlckbIW91gUI0RAYzUbmHJwNwN0lBpjRE3KPg7Hk4pPtncEzBALbQlB7CImBJjeAg0sdVy1E7Xu2fwt2n8pn/ZFsHv8hgd+e7omXq2wiK66PbJwpRG0ym+HoHyzdPpUXTGn4VZj4IzUNx7+fY+8M+nPvMwxFl34eOycI7w5RfaDVUGjUrLYrF6LO5JUYGPLJRk6dLaVPS3++GtMVvV5mEoqqruX1W8KNELVBUeDQUljzFkrWAUY2DuKgkyNPGxz5vyaDILSr2jLjFQr2ThceZyyFoiw4ewIy9kH6bkjeCIWnqz5/YHtoOxza3g5+UXX6rQlRG/al5XPnDHUH8Wf7N+fZ/rKDuKhKwk01JNyIWnc6EZY8B6d3ArDdw5eHGrnjrHfkjxF/4uPsc23PpyiQcwSS1sKRFXBiHZj/tjdPcEfoeB+0vwtcfS31XQhR5+YnnOL5ebvR6eDrMV3p0ypA65KEFZFwUw0JN6LWGEth3Tvw18egmMDRHWIfZ5w5jbWn/+LuFnfzStwr13+dklw4tAT2L4Skdeq1AOwcoeVANehE9QM7GVIn6p+XF+3lhy0peDrb89u4njTxc9O6JGElJNxUQ8KNqBXZR+Dn0ZB9br2OtrfDwHdJNpUwbNEwFBR+Hf4rkV6Rlr1ucQ7snQ+JP0LGngvH3QOhw0g16AS0suw1hahFhgozI7/YzK6UPNo29uSXJ27A2cFO67KEFbiW12+ZCi7E9do7H77orQYb90AY+SOMmAXuAczaPwsFhZtCb7J8sAFwawTdH4fHN8DjG6H7k+DqB0WZsOlj+CwWvuwL275UW3yEsHLndxD3dXNk/+kC3loqC/yJayctN0LUlNkMf06ETZ+otyN6wV1fg7s6TuB00WkGLxxMhbmC7wd+T8eAjnVTV4UBjv4BibPh6IoL43P0DtBigNqi02JA1YHMQliZtYezePCb7QBMv7czgzsEa1yR0Nq1vH5Lp7wQNWEsg0WPq+NeAHrGQ5+Xqoxz+Xrf11SYK4gNiq27YANg7with6gfRdmw92fY/RNk7FXH6hxaAs7eatdZ9D0QFguygaewMr1bBvBE7yhmrD3Of3/ZQ9vGnkQ0qoPxN4qijp8zV4CjG+ilS6w+kpYbIa5VSS7MuRdSNqutIbdNh+iRVU7JLM5k4IKBGM1Gvh7wNV2DumpU7N+LOgB75sCen6Ew/cJxnwi1NafDSJlWLqxKhcnMPV9sYcfJs7Uz/qaiHE5sgJN/qbMbzyRBwSlQ/raRp4uv+nsRHK0uphnVF1yuccajsAgZUFwNCTfiuuSnwXe3wZmj4OQF9/wAkTdedNqUbVP48eCPxATGMOvWWXVfZ3XMJjixHvbMhQO/grH4wn3B0WqLTtvb1dAjhMbS80sZNG0DZ0uMjI5rwuu3tbu+JzSb4OhK2DtPXVrBUHhtj9c7qItpdnkYmt8Cehm6Wlck3FRDwo2osbMn4duhkHcSPEPhvnkQ2Oai07JKshi0YBDlpnK+uPkL4hrHaVDsVTIUw8ElaovO36eVAzTufCHoeIdpV6No8NYczmLsufE3n93XmUHtazD+pjQPEmbBjq8gL+XCcY9gdemEsK7g3wq8w8HJU+2OMhRDwWn1zUzqdnWtqey/DXD2aw43jFNnJcrSC7VOwk01JNyIGslNgm+HQX4q+ETCmN8u+4L/6qZX+eXoL3T078h3A79DV1/GsxTnwMFf1XFEyRurNs2HdlVDTpvb1FWVhahjU34/xOfrjuPhZM+SZ65h/ZvyItg6Qx34X5avHnPxgeh71VW+Q7pcW+tL9hHY9T0kfAvl557PvxUMeBua9bum70lcGwk31ZBwI65ZzjG1xabwNPg1U4ONZ+NLnpqUl8Ttv96OWTHz3cDv6BTQqY6LtZCiLDiwGPYvUscj8Lc/EyEx0Hqo7HEl6pTRZGbUufE37ULU8TdO9tWMvzGWwo6vYcOHUJKjHvNvDTc8De3uvP6NaMsLYed3sP59KD23zEKrITD4Q/AIvL7nFpck4aYaEm7ENck6BN8NU9eN8W8Fo3+t9g/XuNXjWJu6lr5hfZnWd1rd1VmbCjPUsTn7F0DKFqoEHf/WatBpPVTdwby+tFKJeul0XimDP1bH34yJa8Jrlxp/U2FQW1bWv39hTzbfptD7RWh3h+VnP5WehXXvwbaZ6gwrF18Y8qHa0iksSsJNNSTciKuWuV/tiirJgcB2MHqxumjeZezM3MmY5WOw09mx4LYFNPVqWofF1pHCTDi8FA7+pg5K/vseV95NLgSd0G4y0NKWGYohfQ+cTYaSM4ACDq5ql6VfM7Xrtpb+/dccymLsrEuMvzGb1JmAayer4+JAHRt303+g471g51Ar9VTK3A8L/09dcgHUbq/BH4Cja+1etwGRcFMNCTfiqqTvhu+Gq83NwdHwwKJqN6U0K2YeWPYAe3L2MKLFCCbGTayzUjVTehaO/KGO0zm2CipKL9znHggtB6lBJ6KXuvaOqN/KC9XwsG8BpGyqOibrn1x8IPwGiOgJrQZZfObd5N8PMnNdEh5O9ix9qjvhp5fChg/gzDH1BLcAuPF5iHmwbherrDDA+vdgw/vqzyegLYz8XpZYsBAJN9WQcCOuKC0Bvr9dHXwYEgP3LwAX72of8suRX3h186u42ruy5PYl+Lv6102t1sJQAsdXqS06h5dfGGgJ6pT5lreqQSeqn7yTrW8MxbB5uvpRlnfhuEew2lXr6qd29ZQXqbOQzhyrGnQBgjpA62Hq/wH/ltfdfWk0mRk9cy0RaUsY77SEIHOmeoeLD/QYD90eUxfg08qJDTD/ISjOAkcPGPENNL9Zu3pshISbaki4EdU6uRl+HKGufREWq073dvaq9iFny84ydNFQ8svz+XeXfzO67eg6KtZKVRggeYMadA4tVf/An2fvos4oaT1U3QJCFkOzbkdXwpJ4yD83ddqvGXQeDW2Gg0+TSz/GZFRbPpM3wrE/1QHpf2/l8Y1SW3NaDlJ/x65lDIzZDOm7IHE25t0/ozcUAFBs741b72eh6yPg5FGjb9XiCtJh/lh1sU+dHga+C90e1bqqek3CTTUk3IjLOr5GXXnYWKJ2pYyaA07uV3zYxL8msvDYQlr4tGDukLnY62W9i0pmE5zargadg79WXV9Eb3+u22KI+uEpewdZjQoD/DkJtnym3vYKg/6vqoNkr3VAbnEOHF6m/h9IWgsmw4X7XHzUgBPaBYKiwStEnYno4AYo6niegtPqeJaUzWr359/CcqlbKO/l9WG2qS8f3RfHwJqsf1ObKgyw5FlI/FG9HfsEDHhLtnSoIQk31ZBwIy7pyAqY+wCYyqFZfxj5w1VNFd2VtYvRv6stNXW6OWZ9pCiQsUddNPDQEsg6UPX+kC4XBiTLGAXtlOTCT/dA6lb1duzj0PeVqwr6V1RWoHZfHv5d/Z37ezfX1XJwgxa3QOcxEHkTk5cfZub6c+NvnulFuJ+VdXsqCmz8EFa9rt5uMVDtprreqegNkISbaki4ERfZvwh+eVid+dNqiLqz91UMQiwxlnD3krs5WXCSO5rfwWs3vFb7tdqSM8fVkHNwCZzaVvU+/9bqxp+thqgDumWKed3IS4Uf7oCcI+pYqdtnQKvBtXMtUwWkJ0LqNvXfP+cYFKRdWDMGQGcH7gHq2J7gDuqYrfC4KgPUjSYzI2duZmdKHh1CvZj3eFz1699oZf9CWPg4VJSpg63vnXPFLm9RlYSbaki4EVVs+xKW/RtQ1IW9bp951VNG39zyJnMPzyXANYAFwxbg5SR/qGqsIP3cFPMl6nidv08x9wpXX2BbD4Xw7tKkX1uyDsL3d6hrw3iGqAPpA1rVfR3GUnVDSzi3DcKVp5SnnVv/Jq/EyIM3RPDqsLa1XGQNJf+ltoqVF6jrQt2/QA1v4qpIuKmGhBsBqAMT/5wEmz5Wb8c8qK4sepUvnBtObeDJVU8CWP/+UfXN+Snmh35Tx1gYSy7c59oIWg5Ug07kTeDgrF2dtiT7CMwaBMXZaivJ/QvU8S/1yKqDmTz87Q4APhoZze2drHSbkPTd8MOd6s/aNwoeWHj5wdmiCgk31ZBwI6goh0VPwL5f1Nt9X4Fe/7rqro+zZWe589c7yS7N5r7W9/FCtxdqsdgGzlACSWvOTTH/veoYDUd3dXptqyHq7szO8vtcI7kn4JtBaotNUAd1scpq1nSyZu8uP8Rna4/jaK9n7mPd6RRupbPxzhxX19HKTwGPxmrA0aKVrJ6RcFMNCTcNXH4a/Dwa0naos3Vumw7R91z1wyvMFTz+5+NsTd9KpFckPw/5GWd7aT2oEyajOq344BJ1ivn5pfUB7BzVlpzWQ9Ww4+anXZ31ScFp+HqAOovNvxU8uKxe/+zMZoXHvt/Bnwez8Pdw4tenexDsZaUDdwtOq+tpZR9SZ43d/4u6rpa4LAk31ZBw04CdWA/zxqrbKTh7w93fQtPe1/QUH+74kG/2f4OLvQs/DvqR5j7Na6VUcQVmM5zepU4vP7Tkwsq0oIbWZjerobXFrdJ1dTllBWqLTeZede+lsb+DR5DWVV23ovIK7vxsE4czC2kf4sXP/xeHi6OVjtMqyYUf71IXDnV0h1E/QeSNWldltSTcVEPCTQNkMqpLoq9/HxSTOpDv7u/BN/KanmZ58nL+ve7fALx/0/sMiBhQG9WKa6UokH1YHaNz4Fd1uvl5zl7q2iwd7lEHI8usK5XJCLNHqtOy3QLgkT9tatxHam4Jt03/i9xiA4PaB/HJqM7Y6a303768SF1f68Q6sHOCEbPURQ7FRSTcVEPCTQOTcxQWPKq+y4cab2aXmJXIo388SpmpjLHtxhIfE18LxQqLyDoEe+ao+yAVpF047hOpDhzvdH+1G6DaPEWB356Bnd+pm10+uBRCOmtdlcVtTTrD/V9txWhSGB3XhNeGtUVnreHWWKZu13B4qTr9ffgMiB6pdVVWR8JNNSTcNBCGEtj4Efw1VV0R1dkLhnykTve+RsfOHmPM8jEUGAroGdKTT/p+IqsQ1wdmM5zcCLvnwIHFYChSj9s5QpvboMvDDbM1Z/37sPoNdUuAe2ars89s1JI9pxn30y4UBeJvbsEz/ay4G9lUAb8+Dbt/Um8Pel+2a/gHCTfVkHBj48xmOLBIneZ9fqn/qH4w7JMaTW1NK0pj9LLRZJVmEe0fzRc3f4Grg5WtgCquzFCs7ma946sLrXgAAW0g9v/UbquGMDZnzzxY8Ij6dQN58fx2UzKTft0PwNu3t+fe2HCNK6qG2QzLX4BtM9XbfV+GXs83vAB+GRJuqiHhxkaZzer+NWsnQ+Y+9ZhnCNw6Wd2NuAZ/HFIKUnj0j0c5XXyaZt7NmHXrLFmozxak7YQdX8Pe+Rd2r3YLgNjH1NacejoN+oqS/4Lvh6stmXFPq3scNRAf/HGYT1YfQ6+Dqfd0Ylh0Y61LujxFUf+OrXtHvR33NNzypgQcJNxUS8KNjSnNg8TZsP1LyE1Sjzl5Qvcnoccz4OhWo6c9cvYI/7fy/8gpzaGJZxO+uuUrAt0CLVe30F5pHuz6AbbMgIJT6jEHN+j8AMQ9Bd5W/A7/WmUfhq9uhrJ8NeyP+PaqVv61FYqi8OLCffy0LQW9Dj68uyPDO1n5IoWbP4MVE9SvOz0AQ6c1+NW5JdxUQ8KNDTAUw9GVsG++upKt6fxS7V7Q7RH1nc51vPvembmTcavHUWAooIVPC2bePJNGLg14AKqtMxnVLqtNH19o9dPbQ8f74Mbn63/IKcqC//VTu2lDu8GYXxvkpo1ms8KEBXuZuyMVvQ7eHxHNHZ2tdBXj83b9AL+OA8WsjhO748ur2vfOVkm4qYaEm3rIZFSn9x5fA0lr1d2KTYYL9we0UccOdBhZ45aa834+/DOTt06mQqmgg38HPuv3mXRFNRSKAsdXw1/T1Gm5AHoHdXZVr3+Bd5i29dWEoRhmDVbHGflEqlO+G/BMMbNZ4aVFe/lpWyo6Hbw8uA0P97y2JSHq3IFf1ZlUZiM06Qkjv7fdrtMrkHBTDQk3VkxRoOSMuiBbzlE10KTthIy9F1pnzvNuoq5f0v4uCGx33f3RpRWlvLPtHX45qm7JcGvErbx2w2syeLihOrlZHffw95DT+QG48d/gacXjNf7ObII598GR38HFVw02flFaV6U5s1nhtd/28+3mkwA80jOSFwe1Rm+t6+CA+sZu7gNgKAS/ZnDfPHXhxQZGwk01JNxYgYpydXxMzlE4cxRyjp37fLTq3kF/5+ylvmuJ6gNRfdVfbAsNsNuXs48JGyaQXJCMDh3jO4/noXYPWe+aGKLuJP+lhpzkDepte2fo+gj0jLfubQrMZnUtm13fqwvDjfkNwmO1rspqKIrC5+uSeGf5IQAGtgvivRHRuDtZ8RIPmQdg9t2QnwqufnDPTw3u31TCTTUk3NShklzIOaJ+ZB9Ww0vOEcg7qfYhX45XmPruJKCNurhY404WDTPnlVaU8uWeL/l639eYFBMBLgG80fMNbmh8g0WvI2zAiQ2w5i1I2azedvRQBx3HPWV9G3YqijqdeOvn6lo2I2ap4zXERRbtSuPf83djNClE+bsx84EuNAtw17qsyyvMUFeWTk9U12sa+A7EjG0wM6kk3FRDwk0tMFWooSV9t/qRsUfdDK7kzOUf4+SpBphGzdXP57/2jbrm1YOvlaIorEpZxbvb3yW9OB2AgREDean7SzK+RlyeosCxP2HV6xe2eHDxhZ7PqWO+rGGQrqKo9W38UL09fAZ0vFfbmqxcwsmzPPljApkF5bg52vHG8Hbc3inEeltuDcWw8HF1XzVQB74P/sA6/v/VMgk31ZBwYwF5qXBykzqwN323OsOkouzS53qFqaGlUYu/fTQH98A6f7ehKArbMrYxPXE6u7LUhdyC3YL5T9f/0L9J/zqtRdRjZjMcXAyr31K7UwE8guGm/6hTdu0ctKtrxYuwdYZ6e/AHaheauKLswnLG/bSTLUm5AAxoG8hbt7enkbuVzkxSFHXg+6rX1FbwoA7qRsA2Pg5Hwk01JNxcI0WBM8fh5F9qoDm5CfJTLj7P0V39BQvuoH4ObKu2xjhp38RrMptYd2od3x34joTMBAAc9Y6MbTeWh9s/jIu97b/jEbXAVKHuYbV2ijoOAsAnAvq8pG7zUZdrkpiMsPgp2DNXvX3rO9D98bq7vg2oMJmZuT6JqX8ewWhS8HF14N8DWjGya5j1brqZtE6dSVWSo/4NvnWKOrvPWludrpOEm2pIuLkCsxmy9l8IMic3QXFW1XN0dtC4I4THqWNigjuq00ytbFGw/PJ8Fh5dyJzDc0grUjdQdNA7MKLFCB5u/zABrgEaVyhsQkU5JMxSd54vzlaPBbRRl85vOaj2X2hKcuGXh9Vp7Hp7uO0z2XTxOhw4XUD8z4kcyigEoHWwJ68Mbk1clJ91dlXln4IFj6lvQAFaDYHBH4KH7S06KuGmGhJu/sFkVLuWzrfMpGxWVzH9OzsnCO0KTW5QP0K7WkWLzKWUGEtYd2ody5KWsfH0RirMFQB4OXlxR/M7uLfVvQS5BWlcpbBJ5UXqnkB/TbvwOxTSBfpNhKY31c41T++Cn8eog/TtXeDu76DFLbVzrQbEaDLzw5aTfLTyCAVl6t+QrhE+jOvbnF7NG1lfyDGb1EUoV7+lrofj5AX9J0LMQ1b3pvN6SLipRoMPN4ZiSEuAlC1qoEndBsaSquc4ukNY7Lkw00NtnbHiVTEzijPYkLaBDac2sCV9C6Xn9wsCWvm24p6W9zCo6SDpfhJ1o/Qs/PWxOlvp/O9W5E3qmJwmPSzTklNRDhs+UHf4Vkzquk/3/AhB7a//uUWl3GID0/48wk/bUjGY1BmeLQM9GNUtjNs7h+LlotH4qstJ36MuAXB+c9jGneHm1yDyRm3rshAJN9VocOGmKEsNMqlb1VaZ9N1wrjWjkosPhN9woWUmqAPYWed6D4qikFqYyq6sXZUfSflJVc4JdQ9lYORABkUOoplPM40qFQ1eYaYaQHZ8rb6bBghoC10fhnZ3qL9318psUne9X/U6nE1Wj7W5DYZMbbCr1taFzIIyvlifxOytKZQaTQA42evp3dKfQe2D6dsqAA9nKwk6ZhNs/0r9P2JQu9aI6ge9J0BYV21ru071LtxMnz6d9957j4yMDKKjo/nkk0/o1q3bZc+fN28er7zyCsnJyTRv3px33nmHQYMGXdW1bDrclBepq/mmJ8LpRDi1HXKPX3yeR2MI736hZca/lVU2XRpMBk7kn+DI2SMcPXuUI3lHOHjmILlluVXO0+v0dGjUgV6hvegZ0pPWvq2tr9lYNFx5KWrI2fPzhZYcvYO6GGXroerv4ZXWcco5qk79TZilPh+AexDc+rY6eFnUifxSI4t2pfHj1pMcySyqPG6n19E+xIu4KD/imvoRHeatfatOUZY6DmzHNxfCdUgX6P6EOi7HwVnb+mqgXoWbuXPnMnr0aD7//HNiY2OZOnUq8+bN4/DhwwQEXDzgc9OmTdx4441MnjyZIUOGMHv2bN555x127txJu3btrng9mwg3xrJzK/weUf/oZR9S193IOQpc4p8zoI0aZsLj1M9eYZqPpjcrZvLK8zhTeoYzZWfILskmrSiNU4WnOFV0irSiNDKLM1Eu8f046B1o69eWTgGd6BjQkZjAGFmfRli/8zvY7/oesg5Uvc8tAILaqZt0OnmqA4PL8qEgTe1qKDx94VwXH4h9Am54+rr3UhM1oygKB9IL+H1vBsv2pZOUXXzROSHeLrQO9qBlkAdhPq6E+rgS6uNCsLczTvZ1OJMu94Tafbn35wt78jl6QKtBashpckO92W+sXoWb2NhYunbtyqeffgqA2WwmLCyMcePG8cILL1x0/siRIykuLmbJkiWVx7p3707Hjh35/PPPr3i92go3hvJCcs4cRlHM6roDill9WVbM544pat84CorZDJhRzIr6WVEuHDcZwFiMYigGQ5HaGlNyBqUoE4qyUUqyoTib8/9s5//xKv8R3fzBvyX4t0TxbwmB7VCcPM6do1T5/PfcUHmfolzy3L//NzGajeqHSf1sMBkwmA2VXxtNRkorSikyFlFsLKbIWKR+bVC/zivP42zZWUyK6Yo/Vw8HD5r7NKe5T3Na+LSghU8LWvu1xsnOescACXFFWYdg/0J1hlN6YtWNYC9F7wCRvdT91NrdVesLXYprc+psCVuSctl8/AxbT5zh1NnSy56r04GXiwM+ro7nPqtfe7o44OSgx9neDmcHO5wd9Bc+29uh1+uw0+nQ60Gv02FXeVt37rZ6XK/TXfTeVYcO+5JsfA/9gO+hn3Aoyahyf7lnJGV+rTF4NsHgEYbJ2ReTgzuKkydmexcUnR50enQ6O/UVQacHdOe+n/OvJ0qV207OroQ2aW6JH2+lehNuDAYDrq6uzJ8/n+HDh1ceHzNmDHl5eSxevPiix4SHhxMfH8+zzz5beWzSpEksWrSI3bt3X3R+eXk55eUXNl0sKCggLCzM4uFm976fuD/hbYs9X0Ph7eSNn7MfjVwa0di9MSHuIYR6hFZ+9nO20umXQliKsUwNODlH1fVyDMXquDhnL/XNSmA7daCwlc5QFBfLLzVyKL2Ag+kFHM0qIi2vlFNnSzl1toQyYzVbz9QBHWY66Y4xxG4LPfV7aaFPq5XrHLJvTauXt1j0Oa8l3Gg6ajQnJweTyURgYNX5+IGBgRw6dOiSj8nIyLjk+RkZGZc8f/Lkybz22muWKbgaep09zuZzyfUS9+uu8PlCCj73tU6H7vznytR87rPe/tyJ5x5T+di/P1vV+y58qnqujks85h9h4p/H7fX2OOodcdA74Ginfnawc6hy29XeFTdHN9wd3HFzUD+7O7jj5uiGp6MnjVwa4ePsg4PeSgbhCaEVB+dz3cbdta5EWIiXiwOxTf2IbVp1c1VFUcgtNnCm2EBeiZGzJQbyStSvC8qMlBnNlBlN6ucKE+Xnvi6vMGEyK5gUdVdzk1nBrKgf6teo95sVLtVe8c8j6XTgC6UDXwAeShHtlCOEK2mEKJkEKVl4UowbxbgrJbhQju7cM+gxo0NBh4IeBeVvrx9/v4aCDrO9tmN6rHNKjAVNmDCB+Pj4ytvnW24srX3bEWxvO8LizyuEEMI26HQ6/Nyd8LPWbR0sqI3G19c03DRq1Ag7OzsyMzOrHM/MzCQo6NILrQUFBV3T+U5OTjg52f5/JCGEEEKoNJ3/6+joSExMDKtWrao8ZjabWbVqFXFxcZd8TFxcXJXzAVauXHnZ84UQQgjRsGjeLRUfH8+YMWPo0qUL3bp1Y+rUqRQXFzN27FgARo8eTUhICJMnTwZg/Pjx3HTTTXzwwQcMHjyYOXPmsGPHDr744gstvw0hhBBCWAnNw83IkSPJzs5m4sSJZGRk0LFjR5YvX145aDglJQX93xaYu+GGG5g9ezYvv/wyL774Is2bN2fRokVXtcaNEEIIIWyf5uvc1DWbWMRPCCGEaGCu5fXb+tbcF0IIIYS4DhJuhBBCCGFTJNwIIYQQwqZIuBFCCCGETZFwI4QQQgibIuFGCCGEEDZFwo0QQgghbIqEGyGEEELYFAk3QgghhLApmm+/UNfOL8hcUFCgcSVCCCGEuFrnX7evZmOFBhduCgsLAQgLC9O4EiGEEEJcq8LCQry8vKo9p8HtLWU2mzl9+jQeHh7odDqLPndBQQFhYWGkpqbKvlW1SH7OdUN+znVDfs51R37WdaO2fs6KolBYWEjjxo2rbKh9KQ2u5Uav1xMaGlqr1/D09JRfnDogP+e6IT/nuiE/57ojP+u6URs/5yu12JwnA4qFEEIIYVMk3AghhBDCpki4sSAnJycmTZqEk5OT1qXYNPk51w35OdcN+TnXHflZ1w1r+Dk3uAHFQgghhLBt0nIjhBBCCJsi4UYIIYQQNkXCjRBCCCFsioQbIYQQQtgUCTcWMn36dCIiInB2diY2NpZt27ZpXZLNWb9+PUOHDqVx48bodDoWLVqkdUk2afLkyXTt2hUPDw8CAgIYPnw4hw8f1rosmzNjxgw6dOhQudBZXFwcv//+u9Zl2bwpU6ag0+l49tlntS7Fprz66qvodLoqH61atdKsHgk3FjB37lzi4+OZNGkSO3fuJDo6mgEDBpCVlaV1aTaluLiY6Ohopk+frnUpNm3dunU89dRTbNmyhZUrV2I0GrnlllsoLi7WujSbEhoaypQpU0hISGDHjh307duX2267jf3792tdms3avn07M2fOpEOHDlqXYpPatm1Lenp65cfGjRs1q0WmgltAbGwsXbt25dNPPwXU/avCwsIYN24cL7zwgsbV2SadTsfChQsZPny41qXYvOzsbAICAli3bh033nij1uXYNF9fX9577z0efvhhrUuxOUVFRXTu3JnPPvuMN998k44dOzJ16lSty7IZr776KosWLSIxMVHrUgBpubluBoOBhIQE+vfvX3lMr9fTv39/Nm/erGFlQlhGfn4+oL7witphMpmYM2cOxcXFxMXFaV2OTXrqqacYPHhwlb/VwrKOHj1K48aNadq0Kffddx8pKSma1dLgNs60tJycHEwmE4GBgVWOBwYGcujQIY2qEsIyzGYzzz77LD169KBdu3Zal2Nz9u7dS1xcHGVlZbi7u7Nw4ULatGmjdVk2Z86cOezcuZPt27drXYrNio2NZdasWbRs2ZL09HRee+01evXqxb59+/Dw8KjzeiTcCCEu66mnnmLfvn2a9p3bspYtW5KYmEh+fj7z589nzJgxrFu3TgKOBaWmpjJ+/HhWrlyJs7Oz1uXYrIEDB1Z+3aFDB2JjY2nSpAk///yzJt2sEm6uU6NGjbCzsyMzM7PK8czMTIKCgjSqSojr9/TTT7NkyRLWr19PaGio1uXYJEdHR5o1awZATEwM27dvZ9q0acycOVPjymxHQkICWVlZdO7cufKYyWRi/fr1fPrpp5SXl2NnZ6dhhbbJ29ubFi1acOzYMU2uL2NurpOjoyMxMTGsWrWq8pjZbGbVqlXSdy7qJUVRePrpp1m4cCGrV68mMjJS65IaDLPZTHl5udZl2JR+/fqxd+9eEhMTKz+6dOnCfffdR2JiogSbWlJUVMTx48cJDg7W5PrScmMB8fHxjBkzhi5dutCtWzemTp1KcXExY8eO1bo0m1JUVFTlXcCJEydITEzE19eX8PBwDSuzLU899RSzZ89m8eLFeHh4kJGRAYCXlxcuLi4aV2c7JkyYwMCBAwkPD6ewsJDZs2ezdu1aVqxYoXVpNsXDw+Oi8WJubm74+fnJODILev755xk6dChNmjTh9OnTTJo0CTs7O0aNGqVJPRJuLGDkyJFkZ2czceJEMjIy6NixI8uXL79okLG4Pjt27KBPnz6Vt+Pj4wEYM2YMs2bN0qgq2zNjxgwAevfuXeX4N998w4MPPlj3BdmorKwsRo8eTXp6Ol5eXnTo0IEVK1Zw8803a12aENfs1KlTjBo1ijNnzuDv70/Pnj3ZsmUL/v7+mtQj69wIIYQQwqbImBshhBBC2BQJN0IIIYSwKRJuhBBCCGFTJNwIIYQQwqZIuBFCCCGETZFwI4QQQgibIuFGCCGEEDZFwo0QQgghbIqEGyFEvbB27Vp0Oh15eXlalyKEsHKyQrEQwir17t2bjh07MnXqVAAMBgO5ubkEBgai0+m0LU4IYdVkbykhRL3g6OhIUFCQ1mUIIeoB6ZYSQlidBx98kHXr1jFt2jR0Oh06nY5Zs2ZV6ZaaNWsW3t7eLFmyhJYtW+Lq6spdd91FSUkJ3377LREREfj4+PDMM89gMpkqn7u8vJznn3+ekJAQ3NzciI2NZe3atdp8o0KIWiEtN0IIqzNt2jSOHDlCu3bteP311wHYv3//ReeVlJTw8ccfM2fOHAoLC7njjju4/fbb8fb2ZtmyZSQlJXHnnXfSo0cPRo4cCcDTTz/NgQMHmDNnDo0bN2bhwoXceuut7N27l+bNm9fp9ymEqB0SboQQVsfLywtHR0dcXV0ru6IOHTp00XlGo5EZM2YQFRUFwF133cX3339PZmYm7u7utGnThj59+rBmzRpGjhxJSkoK33zzDSkpKTRu3BiA559/nuXLl/PNN9/w9ttv1903KYSoNRJuhBD1lqura2WwAQgMDCQiIgJ3d/cqx7KysgDYu3cvJpOJFi1aVHme8vJy/Pz86qZoIUStk3AjhKi3HBwcqtzW6XSXPGY2mwEoKirCzs6OhIQE7Ozsqpz390AkhKjfJNwIIaySo6NjlYHAltCpUydMJhNZWVn06tXLos8thLAeMltKCGGVIiIi2Lp1K8nJyeTk5FS2vlyPFi1acN999zF69GgWLFjAiRMn2LZtG5MnT2bp0qUWqFoIYQ0k3AghrNLzzz+PnZ0dbdq0wd/fn5SUFIs87zfffMPo0aP517/+RcuWLRk+fDjbt28nPDzcIs8vhNCerFAshBBCCJsiLTdCCCGEsCkSboQQQghhUyTcCCGEEMKmSLgRQgghhE2RcCOEEEIImyLhRgghhBA2RcKNEEIIIWyKhBshhBBC2BQJN0IIIYSwKRJuhBBCCGFTJNwIIYQQwqb8Pxl2SSpqLpkaAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_population(opt_robust_dynamics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robustness analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When comparing the robustness of the \"robust\" optimized pulse to that obtained\n",
    "from the original optimization for the unperturbed Hamiltonian, we should make\n",
    "sure that we have converged to a comparable error: We would like to avoid the\n",
    "suspicion that the ensemble error is below our threshold only because the error\n",
    "for $\\mu = 1$ is so much lower. Therefore, we continue the original unperturbed\n",
    "optimization for a few more iterations, until we reach the same error $\\approx\n",
    "1.13 \\times 10^{-4}$ that we found as the result of the ensemble optimization,\n",
    "looking at $\\mu=1$ only:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:04.832756Z",
     "start_time": "2020-03-22T05:06:04.827766Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.553941Z",
     "iopub.status.busy": "2024-06-03T14:27:32.553833Z",
     "iopub.status.idle": "2024-06-03T14:27:32.555755Z",
     "shell.execute_reply": "2024-06-03T14:27:32.555477Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J_T(μ=1) = 2.66e-03\n"
     ]
    }
   ],
   "source": [
    "print(\"J_T(μ=1) = %.2e\" % (1 - opt_result.tau_vals[-1][0].real))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:16.589810Z",
     "start_time": "2020-03-22T05:06:04.834702Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:32.557457Z",
     "iopub.status.busy": "2024-06-03T14:27:32.557323Z",
     "iopub.status.idle": "2024-06-03T14:27:38.444412Z",
     "shell.execute_reply": "2024-06-03T14:27:38.444160Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter.      J_T  ∫gₐ(ϵ₁)dt  ∫gₐ(ϵ₂)dt  ∫gₐ(ϵ₃)dt  ∫gₐ(ϵ₄)dt   ∑∫gₐ(t)dt          J       ΔJ_T         ΔJ  secs\n",
      "0     5.90e-04   0.00e+00   0.00e+00   0.00e+00   0.00e+00    0.00e+00   5.90e-04        n/a        n/a     0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13    3.24e-04   6.29e-05   9.90e-06   5.10e-05   9.21e-06    1.33e-04   4.57e-04  -2.66e-04  -1.33e-04     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14    1.83e-04   3.16e-05   7.05e-06   2.56e-05   6.48e-06    7.08e-05   2.53e-04  -1.42e-04  -7.08e-05     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15    1.06e-04   1.60e-05   5.02e-06   1.29e-05   4.56e-06    3.85e-05   1.44e-04  -7.70e-05  -3.85e-05     1\n"
     ]
    }
   ],
   "source": [
    "opt_result_unperturbed_cont = krotov.optimize_pulses(\n",
    "    [objective],\n",
    "    pulse_options,\n",
    "    tlist,\n",
    "    propagator=krotov.propagators.expm,\n",
    "    chi_constructor=krotov.functionals.chis_re,\n",
    "    info_hook=krotov.info_hooks.print_table(\n",
    "        J_T=krotov.functionals.J_T_re,\n",
    "        show_g_a_int_per_pulse=True,\n",
    "    ),\n",
    "    check_convergence=krotov.convergence.Or(\n",
    "        krotov.convergence.value_below(1.13e-4, name='J_T'),\n",
    "        krotov.convergence.check_monotonic_error,\n",
    "    ),\n",
    "    iter_stop=50,\n",
    "    continue_from=opt_result_unperturbed,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can compare the robustness of the optimized pulses from the original\n",
    "unperturbed optimization (label \"-1\"), the continued unperturbed optimization\n",
    "(label \"0\"), and the ensemble optimization (label \"1\"):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:25.330316Z",
     "start_time": "2020-03-22T05:06:16.592668Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:38.445976Z",
     "iopub.status.busy": "2024-06-03T14:27:38.445864Z",
     "iopub.status.idle": "2024-06-03T14:27:40.599983Z",
     "shell.execute_reply": "2024-06-03T14:27:40.599672Z"
    }
   },
   "outputs": [],
   "source": [
    "def _f(mu):\n",
    "    return pop_error(\n",
    "        opt_result_unperturbed_cont.optimized_objectives[0], mu=mu\n",
    "    )\n",
    "\n",
    "\n",
    "pop_errors_norobust_cont = [_f(mu) for mu in mu_vals]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:34.908457Z",
     "start_time": "2020-03-22T05:06:25.332449Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:40.601494Z",
     "iopub.status.busy": "2024-06-03T14:27:40.601404Z",
     "iopub.status.idle": "2024-06-03T14:27:42.952722Z",
     "shell.execute_reply": "2024-06-03T14:27:42.952404Z"
    }
   },
   "outputs": [],
   "source": [
    "def _f(mu):\n",
    "    return pop_error(opt_result.optimized_objectives[0], mu=mu)\n",
    "\n",
    "\n",
    "pop_errors_robust = [_f(mu) for mu in mu_vals]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-22T05:06:35.372866Z",
     "start_time": "2020-03-22T05:06:34.911667Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:27:42.954198Z",
     "iopub.status.busy": "2024-06-03T14:27:42.954102Z",
     "iopub.status.idle": "2024-06-03T14:27:43.121127Z",
     "shell.execute_reply": "2024-06-03T14:27:43.120859Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_robustness(\n",
    "    mu_vals,\n",
    "    pop_errors_robust,\n",
    "    pop_errors0=[pop_errors_norobust_cont, pop_errors_norobust],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that without the ensemble optimization, we only lower the error for\n",
    "exactly $\\mu = 1$: the more we converge, the less robust the result. In\n",
    "contrast, the ensemble optimization results in considerably lower errors (order\n",
    "of magnitude!) throughout the highlighted \"region of interest\" and beyond."
   ]
  }
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