reference/qis/teleportation_superdensecoding.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "<img src=\"../../images/QISKit.gif\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"250 px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*Quantum Teleportation and Superdense Coding*_ \n",
    "\n",
    "\n",
    "The latest version of this notebook is available on https://github.com/QISKit/qiskit-tutorial.\n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Anna Phan, Jay Gambetta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "In [superposition and entanglement](superposition_and_entanglement.ipynb), we introduced you to the quantum concept of entanglement, in particular, the maximally entangled quantum state $|\\psi\\rangle = (|00\\rangle + |11\\rangle)$. In [entanglement revisited](entanglement_revisited.ipynb), we explored this state in detail, running various experiments to compare quantum mechanics to hidden variable models. In this notebook, we will explore how this state can be used in two quantum communication protocols:\n",
    "* [Teleportation](#teleportation), where a qubit state is transmitted using two classical bits; and\n",
    "* [Superdense Coding](#superdensecoding), where two classical bits are transmitted using one qubit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "try:\n",
    "    sys.path.append(\"../../\") # go to parent dir\n",
    "    import Qconfig\n",
    "    qx_config = {\n",
    "        \"APItoken\": Qconfig.APItoken,\n",
    "        \"url\": Qconfig.config['url']}\n",
    "except:\n",
    "    qx_config = {\n",
    "        \"APItoken\":\"YOUR_TOKEN_HERE\",\n",
    "        \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# useful additional packages \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from pprint import pprint\n",
    "\n",
    "# importing the QISKit\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit import QuantumProgram\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram, circuit_drawer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _Quantum Teleportation_<a id='teleportation'></a>\n",
    "\n",
    "Quantum teleportation is a protocol to transmit quantum states from one location to another, assisted by a previously shared entangled state and a classical communication channel. It was devised by Charles H. Bennett (IBM), Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters in [1993](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895). It was first demonstrated with photons in [1997](http://www.nature.com/nature/journal/v390/n6660/abs/390575a0.html), and has since been realised in [atoms](http://www.nature.com/nphys/journal/v9/n7/abs/nphys2631.html), [ions](http://www.nature.com/nature/journal/v429/n6993/full/nature02570.html, http://www.nature.com/nature/journal/v429/n6993/full/nature02608.html), [electrons](http://science.sciencemag.org/content/345/6196/532) and [superconducting circuits](http://www.nature.com/nature/journal/v500/n7462/full/nature12422.html). The [record](http://www.nature.com/nature/journal/v489/n7415/full/nature11472.html) distance for quantum teleportation is 143 km via satellite, set in 2012.\n",
    "\n",
    "<img src=\"../../images/teleportation.png\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"600 px\" align=\"center\">\n",
    "\n",
    "As illustrated above, the protocol starts out with a shared entangled state between the sender (Alice) and the receiver (Bob):\n",
    "$$|\\psi\\rangle_{AB} = \\frac{1}{\\sqrt{2}}(|0\\rangle_A \\otimes |0\\rangle_B + |1\\rangle_A \\otimes |1\\rangle_B)$$\n",
    "The first qubit, denoted by subscript $A$, belongs to Alice, and the second qubit, $B$, belongs to Bob.\n",
    "\n",
    "Alice has a quantum state that she wants to convey to Bob:\n",
    "$$|\\psi\\rangle_{C} = \\alpha|0\\rangle_C + \\beta|1\\rangle_C$$\n",
    "\n",
    "At this point, Alice has two quantum states ($C$, the one she wants to teleport, and $A$, one of the entangled pair), and Bob has one quantum state. The total state of the system is given by:\n",
    "$$|\\psi\\rangle_{AB} \\otimes |\\psi\\rangle_C = \\frac{1}{\\sqrt{2}}(|0\\rangle_A \\otimes |0\\rangle_B + |1\\rangle_A \\otimes |1\\rangle_B) \\otimes (\\alpha|0_C\\rangle + \\beta|1_C\\rangle)$$\n",
    "or, in the Bell basis:\n",
    "$$|\\psi\\rangle_{AB} \\otimes |\\psi\\rangle_C = \\frac{1}{2}[\n",
    "|\\Phi^+\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B + \\beta|1\\rangle_B) + \n",
    "|\\Phi^-\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B - \\beta|1\\rangle_B) + \\\\\n",
    "|\\Psi^+\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B + \\beta|1\\rangle_B) + \n",
    "|\\Psi^-\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B - \\beta|1\\rangle_B) ]$$\n",
    "where:\n",
    "$$|0\\rangle \\otimes |0\\rangle = \\frac{1}{\\sqrt{2}}(|\\Phi^+\\rangle + |\\Phi^-\\rangle), \n",
    "|0\\rangle \\otimes |1\\rangle = \\frac{1}{\\sqrt{2}}(|\\Psi^+\\rangle + |\\Psi^-\\rangle)\\\\\n",
    "|1\\rangle \\otimes |0\\rangle = \\frac{1}{\\sqrt{2}}(|\\Psi^+\\rangle - |\\Psi^-\\rangle), \n",
    "|1\\rangle \\otimes |1\\rangle = \\frac{1}{\\sqrt{2}}(|\\Phi^+\\rangle - |\\Phi^-\\rangle).$$\n",
    "\n",
    "Alice now measures her two quantum states, $A$ and $C$, in the Bell basis. This will collapse the three state system into the one of the following four states with equal probability, with the corresponding measurement outcomes:\n",
    "- **00**: $|\\Phi^+\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B + \\beta|1\\rangle_B)$\n",
    "- **01**: $|\\Phi^-\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B - \\beta|1\\rangle_B)$\n",
    "- **10**: $|\\Psi^+\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B + \\beta|1\\rangle_B)$ \n",
    "- **11**: $|\\Psi^-\\rangle_{AC}\\otimes(\\alpha|0\\rangle_B - \\beta|1\\rangle_B)$\n",
    "\n",
    "Alice now sends the results of her measurements to Bob. Using this information, he performs one of the following transformations on his quantum state to transform it to the desired state $\\alpha|0\\rangle_B - \\beta|1\\rangle_B$:\n",
    "- If he receives **00**, he applies $I = \\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix}$\n",
    "- If he receives **01**, he applies $X = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}$ \n",
    "- If he receives **10**, he applies $Z = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix}$\n",
    "- If he receives **11**, he applies $XZ = \\begin{pmatrix} 0 & -1 \\\\ 1 & 0 \\end{pmatrix}$ \n",
    "\n",
    "Transmission (teleportation) of $|\\psi\\rangle = \\alpha|0\\rangle + \\beta|1\\rangle$ is thus achieved. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall from [superposition and entanglement](superposition_and_entanglement.ipynb) and [entanglement revisited](entanglement_revisited.ipynb) that the steps to make the shared entangled state $|\\psi\\rangle = \\frac{1}{\\sqrt{2}}(|0_A 0_B\\rangle + |1_A 1_B\\rangle)$ are:\n",
    "1. Start with an initial state $|0_A 0_B\\rangle$\n",
    "2. Apply $H = \\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}$ on $q_A$ \n",
    "3. Then a $CNOT = \\begin{pmatrix} 1 & 0 & 0 & 0\\\\ 0 & 0 & 0 & 1\\\\0& 0& 1 & 0\\\\0 & 1 & 0 & 0 \\end{pmatrix}$ from $q_A$ to $q_B$\n",
    "\n",
    "With $q_A = q_1$ and $q_B = q_2$, this looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.cx.CnotGate at 0x10c7fdfd0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating registers\n",
    "tq = QuantumRegister('tq', 3)\n",
    "tc0 = ClassicalRegister('tc0', 1)\n",
    "tc1 = ClassicalRegister('tc1', 1)\n",
    "tc2 = ClassicalRegister('tc2', 1)\n",
    "\n",
    "# Quantum circuit to make the shared entangled state \n",
    "teleport = QuantumCircuit(tq, tc0,tc1,tc2)\n",
    "teleport.h(tq[1])\n",
    "teleport.cx(tq[1], tq[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alice then prepares her quantum state to be teleported, $|\\psi\\rangle_{C} = \\alpha|0\\rangle_C + \\beta|1\\rangle_C$. In this experiment, $\\alpha = \\cos(\\frac{\\theta}{2})$ and $\\beta = \\sin(\\frac{\\theta}{2})$ where $\\theta = \\frac{\\pi}{4}$. This state can be created by applying a rotation around the y axis:\n",
    "$R_y(\\theta)$ on $q_C$\n",
    "\n",
    "With $q_C = q_0$, this looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.ry.RYGate at 0x107d55dd8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teleport.ry(np.pi/4,tq[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alice now applies $CNOT$ to her two quantum states $q_A(q_1)$ and $q_C(q_0)$, followed by an $H$, to entangle them and project them into the Bell basis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.barrier.Barrier at 0x10c7fd978>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teleport.cx(tq[0], tq[1])\n",
    "teleport.h(tq[0])\n",
    "teleport.barrier()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "She now measures her two quantum states $q_A(q_1)$ and $q_C(q_0)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._measure.Measure at 0x10c7fda20>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teleport.measure(tq[0], tc0[0])\n",
    "teleport.measure(tq[1], tc1[0])\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the results of these measurements, Bob has to apply an $X$ or $Z$, or both, to his quantum state $q_B(q_2)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.x.XGate at 0x10c7fdc50>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teleport.z(tq[2]).c_if(tc0, 1)\n",
    "teleport.x(tq[2]).c_if(tc1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "His state is now the same as the state Alice prepared earlier, which can be verified by measurement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._measure.Measure at 0x10c7fdb00>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teleport.measure(tq[2], tc2[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=1165x486 at 0x10C8B6978>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(teleport)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now create and execute the quantum circuits on the simulator (so we don't have to wait in queue for a device) and plot the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "circuits = ['teleport']\n",
    "\n",
    "backend = 'local_qasm_simulator' # run on simulator so we don't have to wait in the device queue\n",
    "shots = 10000 # the number of shots in the experiment \n",
    "Q_program = QuantumProgram()\n",
    "Q_program.add_circuit('teleport',teleport)\n",
    "result = Q_program.execute(circuits, backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We must manipulate the data to understand the results better, first only plotting the results of Alice's measurement:  \n",
    "\n",
    "Note each classical register is seperated by a space, and the order is c2 c1 c0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10db7b240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = result.get_counts('teleport')\n",
    "alice = {}\n",
    "alice['00'] = data['0 0 0'] + data['1 0 0']\n",
    "alice['10'] = data['0 1 0'] + data['1 1 0']\n",
    "alice['01'] = data['0 0 1'] + data['1 0 1']\n",
    "alice['11'] = data['0 1 1'] + data['1 1 1']\n",
    "plot_histogram(alice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the probabilities are roughly equal.  \n",
    "\n",
    "Now, manipulate the data to plot the result of Bob's measurement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10db79fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bob = {}\n",
    "bob['0'] = data['0 0 0'] + data['0 1 0'] +  data['0 0 1'] + data['0 1 1']\n",
    "bob['1'] = data['1 0 0'] + data['1 1 0'] +  data['1 0 1'] + data['1 1 1']\n",
    "plot_histogram(bob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, $|\\alpha|^2 = |\\cos(\\frac{\\pi}{8})|^2 \\approx 0.854$ (the probability of measuring 0) and $|\\beta|^2 = |\\sin(\\frac{\\pi}{8})|^2 \\approx 0.146$ (the probability of measuring 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _Quantum Superdense Coding_<a id='superdensecoding'></a>\n",
    "\n",
    "Quantum superdense coding is the dual protocol of quantum teleportation, whereby two classical bits of information are transmitted using only one qubit and a previously shared entangled state. It was devised by Charles Bennett (IBM) and Stephen Wiesner in [1992](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.2881). \n",
    "\n",
    "<img src=\"../../images/superdensecoding.png\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"600 px\" align=\"center\">\n",
    "\n",
    "As illustrated above, and as in quantum teleportation, the protocol starts out with a shared entangled state between the sender (Alice) and the receiver (Bob):\n",
    "$$|\\psi\\rangle_{AB} = \\frac{1}{\\sqrt{2}}(|0\\rangle_A \\otimes |0\\rangle_B + |1\\rangle_A \\otimes |1\\rangle_B)$$\n",
    "The first qubit, denoted by subscript $A$, belongs to Alice, and the second qubit, $B$, belongs to Bob.\n",
    "\n",
    "Alice wants to send a two bit message to Bob, 00, 01, 10, or 11.  She performs a single qubit operation on her qubit which transforms the entangled state according to which message she wants to send:\n",
    "- For a message of **00**: Alice applies $I = \\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix}$. The resultant state would be $|\\psi_{00}\\rangle = \\frac{1}{\\sqrt{2}}(|0_A 0_B\\rangle + |1_A 1_B\\rangle)$\n",
    "- For a message of **01**: Alice applies $X = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}$. The resultant state would be $|\\psi_{01}\\rangle = \\frac{1}{\\sqrt{2}}(|1_A 0_B\\rangle + |0_A 1_B\\rangle)$  \n",
    "- For a message of **10**: Alice applies $Z = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix}$. The resultant state would be $|\\psi_{10}\\rangle = \\frac{1}{\\sqrt{2}}(|0_A 0_B\\rangle - |1_A 1_B\\rangle)$ \n",
    "- For a message of **11**: Alice applies $XZ = \\begin{pmatrix} 0 & -1 \\\\ 1 & 0 \\end{pmatrix}$. The resultant state would be $|\\psi_{11}\\rangle = \\frac{1}{\\sqrt{2}}(- |1_A 0_B\\rangle + |0_A 1_B\\rangle $\n",
    "\n",
    "The key to superdense coding is that these four states, $|\\psi_{00}\\rangle, |\\psi_{01}\\rangle, |\\psi_{10}\\rangle, |\\psi_{11}\\rangle$ (otherwise known as the [Bell states](https://en.wikipedia.org/wiki/Bell_state)), are orthonormal and are hence distinguishable by a quantum measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.cx.CnotGate at 0x10c980f28>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating registers\n",
    "sdq = QuantumRegister(\"sdq\", 2)\n",
    "sdc = ClassicalRegister(\"sdc\", 2)\n",
    "\n",
    "# Quantum circuit to make the shared entangled state \n",
    "superdense = QuantumCircuit(sdq, sdc)\n",
    "superdense.h(sdq[0])\n",
    "superdense.cx(sdq[0], sdq[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alice now needs to decide what two bit message she wants to transmit to Bob, ($00$, $01$, $10$, or $11$), and perform the corresponding to transformation ($I$, $X$, $Z$ or $XZ$ respectively) to her qubit $q_A$ ($q_0$). In this case, she encodes $11$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.extensions.standard.barrier.Barrier at 0x10dc06a20>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For 00, do nothing\n",
    "\n",
    "# For 01, apply $X$\n",
    "#shared.x(q[0])\n",
    "\n",
    "# For 01, apply $Z$\n",
    "#shared.z(q[0])\n",
    "\n",
    "# For 11, apply $XZ$\n",
    "superdense.z(sdq[0]) \n",
    "superdense.x(sdq[0])\n",
    "superdense.barrier()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bob now needs to 'decode' the message that Alice sent him. Since measurement in QISKit is only possible in the standard computational basis, he does this by:\n",
    "1. Applying a $CNOT$ from $q_A$ to $q_B$\n",
    "2. Then a $H$ on $q_A$ \n",
    "3. And measuring $q_A$ and $q_B$\n",
    "\n",
    "Recalling that $q_A = q_0$ and $q_B = q_1$, this looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._measure.Measure at 0x10de20eb8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "superdense.cx(sdq[0], sdq[1])\n",
    "superdense.h(sdq[0])\n",
    "superdense.measure(sdq[0], sdc[0])\n",
    "superdense.measure(sdq[1], sdc[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FRER8/fqV36Pu3bsnlOW8JQGNRps6dWppaSn20MjI6OrVq+1/tkk3e3t74sSmx48fYxtKSkqxsbG2trYkxSUEMvINl6mrloSAguoyi6eREGw2+/3799j2x48fORwO72s2xsTEYJ1fCCFbW9vDhw9zOZb7yj3Xr1+Pj4/HtjU1NWNjY7lUL3Jzc8PnIbVp6smTJ5MmTWpoaEAIKSkp2djYqKiovHnzpr6+vra21t/f/+jRo3zVGzI3Nx85cmRSUtLZs2fXrFnD+4E919evXwsKCvCHvXv3fvPmDe+HP3jwAN9WUFAgzuiUTPh0lm4c2NPruWAWLVqEZxJqamrXrl1rU6BHRmzdurXNDEUqlRoVFTVq1CjyghICWfiGy9pVSxJAQXVZxlN+SaVS8YpCFRUVixYt2rNnT5eVKTF//vknvn38+HHuFfK49z4QV2Y7ePCgiYkJl6bq6uo6bKqxsTEwMBBLLn19fY8cOWJgYIAQam5uXrdu3dGjRzkczurVqz08PPiquxsUFJSUlHTq1CkZyS+JtwEQQsRFXPhlZ2fX2f1sCcFms58/f969Y4nz1Xqu7du344sIUCiUs2fP2tnZkRsSWaytrWfOnHnhwgX8mYMHD86YMYPEkAQnI99wmbpqSQIoqC7jeJ3JNWzYsKdPn2LbkZGR58+fd3d3HzFixMiRI93d3dXV1Ts8KiUlBb9sjRo1ivuAFSaT+fr1a2xbQ0Nj8ODBxFdfvHiBBzBkyBBs7W8u8CLtffr0sbCwwJ/ftm1bUVERQmj06NGXLl3CO/hUVVX/+ecfKpV65MgRGo22ZMkS/HS8mD59+sqVKzMyMt6+fWtjY8P7gTzat2/f0aNHWSyWgO1g5Zw+f/4sYDvEXwIC6nY3U0lJCUJo7dq1mzdvFlYwHWKxWMQ5p3xJTk4W9QpyTU1NCCG851rorly5Qrz3sGPHDn9/f+GeAnsLOTk5gn9W2NrQ7SugCQuLxcJ+nWLk5eWJcz6EC1uIcvv27YcOHRLRKTAS/g3Hhvx2o/u+DUm4amE97HFxcQJ+aFj5FOwPR9Sampry/lNcXFxTU9Pc3NzU1FRXV9fS0qKsrNy7d29lZeVevXr17t3byMjI3Nzc3NzczMwsOjo6MzOzf//+ohuni133Vq1aRZxp10M1NDQ0NDTo6Oh0uUJNj6Crq8vr/PGbN2921q+toqKybNmynJyc9kdhv10wXc7zJZZDHz9+fJtXiVN//v77b+5NEUfJEJui0Wh9+vRBCFEolA5nPtbW1vbr1w87kK+S6QwGQ0dHByH05MkT3o/inXBLwEyYMEHAeLy9vfHWFBUVe/GjTfWWyMjI7sVgZGQkxM+kp9PX1xfw/2mHXr9+TZzM1705s10SejHF/Px8UcTJ4XCWLFnS5lzY5EVR6NEDOoWud+/eAn6eknDVWr58uRA/E3l5eQE/kw4xmczU1NT9+/dPnTqVOHeWX1i3p7+//6NHjzqsBiM4vmaDAHGiUCi83r+cOHHiX3/9tWbNmvY/c2k02rFjxyIjIyMiIubOnUt8KSEhAd8eO3Ys91PgdxxRR53jeOU5hFCXNwyIfT3Epi5fvoxV6PTx8enwLqOGhgbW+48QioqK+v3337mfCHfr1q3y8nIjI6MRI0bweAhfLl68yKXiMe/++uuvyMhIAcdZcwhreCKE/vnnn0WLFvF++OvXr4kBdPtOwJAhQ4qKin777TcfH5/utcAjJpM5YsQIDqGuMu9sbW35LfvCrwcPHgQHB3NZcKXbysvL/fz88HskLi4uJ06cEPpZEELYGBULCwtiv3P3eHh4tLS0qKioCCOutsLCwtrUpkAInT59OiQkZODAgUI/nb29fUZGxvr160VdZlLCv+GvXr1atmyZgHPzJeSqhf27M3HiROKi9t1QXFwcEBCgoaEhSCNtVFZWxsTE3Lhx4/Hjx/X19cSXDAwMLCwsLCwsjI2N+/btq6ampqam1rt3bzU1taampsbGRhqN1tDQUF9f//Hjx/z8/Pz8/IKCAqwbITY2NjY2VklJydnZ2dfXd+bMmUIss2BlZVVaWrpz585x48YJq02ytLa2lpeXS81AAg0NDT4qna5YsWLChAn79++PiopqbGxs8yqdTg8KCrKysnJ0dMSeaWlpwScEmJqaYrf3uOAyuae2tjYjIwPb1tHR6fLGFTG/JDZ19+5dbIP4Q7aNMWPGYPnltWvXeM8vsX93Fy5cyO9qtjxSU1PDP1hBYCt0CSgvLw9fvATxX6eDOApKQ0Nj0KBB3QsD+6hNTU2F8slwN2TIkMzMzG4c6O7uLurwPn36hP77NISITqf7+/tjXbQIIUNDw9jY2PYlw4RIRUVF8M9KRH+ACKGjR49u27YN27a2tlZRUcGub0wmc9u2baJYwQvrMhowYICMf8Oxf24E/D8rIVctjJaWloAfGpZZ8j7RloumpqbY2NgLFy7cvXsXX7VEW1vb09PTy8vL3d3d0tKyw4qEXJSUlAwaNKi5ufnHH3+srq5OSkoqKip68uTJkydPfv75Zzc3t1mzZs2YMaPLrKBL2Ldi4MCBYvgbAfzi7y/W3Nz88OHD1dXVjx8//v333318fIjzdRgMxr59+/CHZWVl+HhBPT29LhvnMrmHOLaMl6aePXuGbzs7O+Pb+FB0Lr8+8XGfOTk5eKk/7srLy2/cuEGhUGRk5SvipVZdXZ2viVCo3f9ooVwiRa3bIw4DAgKEGoj4LF26FP+dpqqqGhcXx8ufnrSKjY1dsWIFtq2np3fz5s1ffvkFf/Xs2bN4hY0eSuq/4TJ41erShw8fvv/+ex0dnblz5964cYPJZLq5uR08eDAzM7O8vPzy5cs//vijo6Mjv8klQigkJKS5uXnMmDEHDx6MiooqLCwsLCw8ceLEhAkT5OTknj59umrVKkNDw5kzZ/as+laAL935RaigoODh4RESEnLr1q2SkhLi0EDid4U4CBIb9chFU1NTVlYWtm1sbNzmZ01ZWRm+3eUfNovFwvtBjIyM8Dt2ra2t+fn52DaXuefGxsbYTRoWi8XjD/qoqCgmkzl69GhTU1Ne9u/piJdaJycnfu8riGFdeKFbvnx5N27d2djYdDksRDLt3r07KioK26ZQKKdPn5bl2nVPnjyZPXs29mtZTU3t+vXrRkZGfn5+eI7CYrG2bt1KaoyCkvpvuAxetbhIT0+fP3++paXlP//809TUZGVlFRYWlpub+/Tp0x9//HHIkCGCJNAdFlQ3MjIKCgq6fft2eXl5ZGTklClTOBxOdHS0s7Ozh4cHtvqdMN4ZkCCC9iVpa2tfvHgRv4tJ7DfHa6qj/60W1KG0tDT8Zmf7v15sTigGzxE78+7dO+KIsQ5j4HJbnkql4kOpsJ7HLmHDj4KCgnjZWQoIcqltaGggDiTtKWtgDBgwoBuVp/bu3Su67lrRiY+PJ87MCwsL6+n1dwSRlZXl5+eHdWXIycn9+++/WKpNoVCIkw4vXrzYvf5lCSH133AZvGp16PXr1+PHj3dwcIiKimKz2f7+/snJyVlZWb/++is22Vdw3Auqa2lpzZ8/Pz4+PjMzc+nSpUpKSk+fPvXz87Ozs8MHsAHpIIRLg5qaGj7FzNraGn+eOIY3Ly+P+68T7pXViSNeGxoa8DFhHcIWq23fFDazByGkqKjI/ZqIl1tqP8y0vefPn2dnZ2toaBAX9pBidDqdWJSY30ttSkoKsXZMD7pSb9++ffTo0bzvHxYWxmWYr8R69+5dYGAg/v9oxowZW7ZsITckEn3+/HnChAn4uL1Dhw5NmTIFfzUwMBCbmYQQYrPZv/76q/gjFCIp/obL7FWLqKamZvXq1c7Ozvfv31dUVJw3b97bt2+vXr0q3DmpvBdUHzx48LFjx4qKisLCwrS0tN6+fTthwgRfX98PHz4IMR5Aoq7zSzwt6ww2tALbJo6xNTQ0lJf///OHKioqkpKSOmuhtLSUWOCt/V9vm+lm+/fv76ypT58+EcuwE5si5pedHY7p8HZsZ7Cbl7NnzxbRlFVJk56e3traij/k904A8YdE+4EQkkxeXv7KlSs89gZu3LixJ65XUVlZ6evri9d3dHR0PH36tHQMNeuGmpoaHx8fvFjsTz/99MMPPxB3UFRUXLt2Lf7w8uXL6enp4oxQuKT4Gy6zVy0Mm80+evSohYXFoUOH2Gz2woULP336dObMmSFDhgj3RN0oqN6/f/9ff/21oKAgODhYSUnp+vXrQ4cO/eWXX8RT2hOIVBf5ZWpq6uDBgy9fvtzZDnQ6feXKldhvOwqFQuwjlpOTI9YAWrt2bXNzc/sWsrOzPT098VuS8vLy7W+qa2hoEO+MHjlyBJ9OTpSVleXp6YkP1qRSqcSmeM8v8R2IhZQ71NzcjK1rIjud48RLrYGBAb/lx3r0MKY+ffrcvn17y5YtbYrhEQ0YMCA6OnrXrl09Li1jMBjTpk3DF9DT09OLi4vj8k6lW0tLi5+fH97lPX369N27d7ffbdmyZfjgcg6H04NSrg5J6zdclq9aBQUFHh4e3333XVVVlaOjY3Jy8qlTp0RUNvLYsWPdK6iurq6+c+fOt2/fTpkypaWlZceOHXZ2dsR6UqAn6iK/jIiIqKiomD59+rBhw8LDw4nd3EwmMzEx0dnZ+fr169gzK1asaFO1YfXq1fj269evR44cSRxgUVlZGRoa6uTk9PHjR/xJGxubDi9txDsHdDrd3d393Llz+E/SioqKbdu2OTo6Ymu6YKytrXv16oU/xPNL/K5qZ/AduswvL126VF9fb21tTZylLt0EvNRyXwJU8snLy2/dujU/P3/Hjh3Ozs74V0VdXX3ixInHjx/Pzc3toaMVv//+e7yTQVlZOTY2Fu/8lTVsNnvOnDlPnjzBHo4YMSIqKqrDdEpdXR2fV44QunbtWk+fD9vmG4535vTob7jMXrUuXbrk4ODw7Nmzvn37Hj169OXLl8OHDxfRuRoaGrACXjt27OhsST/uLCws4uPjb968aWZm9uHDB3d39z179sC8nx6My/o9TU1NvXv3brO/mpqaiYkJPska5+7u3tjY2KYFOp3e/neSvr6+m5sb3uVNpVKJydny5cs7LNPf0NDQfhI6VrJ16NCh2D/zVCqVeMd08eLFxBZiYmKw5zU1NbkvCYAPQtq8eTP3Pb28vBBC+/bt476b5AgODkYIhYSEdLsF4hjwnTt38nVsm3UpHz9+3O0wOBzOpEmTEA/rQolUaGgoQmj16tUkxoB9sceNGydII3/++Sfxf8358+eFFR4vHj16hBCytbUVvCns12lJSYkgjXz33Xf4R2FmZvb161cuO5eXlxMvhhMnThTk1EQLFixACB04cEBYDXbDgQMHEEKBgYEkxoANqbezs+t2C5Jz1fr777+F8nnm5eUhhPr169fZDjQa7ccff8Ri9vLy+vz5s4Bn7NKmTZsQQlZWVgwGQ8Cm6uvr582bhwU/duxYLn/O48ePRwhFR0cLeEYgCtzuXzIYjICAgDa/2puamgoKCgoLC4m1IadPn3779u32VbIUFRVPnz7d5n5haWlpcnIyNmTT2to6OTmZWHm/sx+XvXr1ioyMbDMvh06np6SkvHv3jslkDhky5MmTJ8TBQ22awu9lEgfidPbGsY326TXRhw8fkpKSFBQU2qxaJMWqq6uJ8/cFqVEsJycnNSVvuhxxIeHu3Lnz008/4Q9DQ0NFvWCMJNu+ffs///yDbfft2/fWrVv4mrEd6t+/P3ElmFu3bhHr70qHLvt8JJkMXrWKi4tdXV0PHTokJyf366+/PnjwQNR9ESUlJdhPkf379wv+bVFXVz9z5syZM2fU1dUfPHjg6OiYlpYmhCiBeHHLLzU0NE6fPp2VlbV+/XozM7P2OygrK0+dOvXOnTsxMTHEnmii8ePHJyYm4kXLMXJyct7e3thweFdXV+LlmEvnhZ+f3507d9rUUJCTkxszZszly5czMjJGjBjBZZFJ/I49sXBSh/AElPvqW6dOneJwOFOmTOnfvz/3BqUGsZ+ISqU6OTl1+/DOBkIAMcvJyZk5cyZeHSwgIEDAlet6tBMnTuDz5ZWUlOLi4iwsLLo86qeffpKTk8Mfbt68WVTxAf7J2lUrKyvL3d09IyPD0NAwISEhLCyM+OUUEbyguhBX6503b15aWtqwYcPKyspGjRpFXCMa9Ahd/86wtLTcu3fv3r17v3z5kpWVVVVV1djYqK2traura2Vl1VlaSeTh4ZGTk5OSkpKbm8tisYyMjJycnIgHJiYm8hjuuHHjcnNzX7x4gf0e1dfXd3FxwZtisVivXr3CtlVUVIhTghAhv2QymSwWi8ufXHV1NbbBJb9ks9mRkZFIlmb2oP+91FpZWfE7yKZHD5OXStXV1b6+vnhpWDs7u84GGsqC+Pj45cuXY9sUCuXMmTPu7u68HDhw4MDp06djU/0QQg8ePEhKSho5cqSoAgX8kKmr1suXLydPnlxZWTl06NBbt27hpQNFqsOC6kJhYWHx+PHjmTNnXr9+fcqUKUeOHFmyZIlwTwFEh4/72Hp6eoIsEOfs7CyUSTAUCmX48OEdDlJ+9+4dXond0dGxzV164mWluLi4syV8WCwWXm6JS3559+7dz58/6+rqCvHnmuQT5FLLZrOJUx961jB5qcRkMmfMmIF3HVKp1KCgoHv37nE4HDabjf2XqM0zeDuqqqr4YKme69mzZ8T7uLt27fr22295Pzw4OBjPLxFCmzdvxgaVAtLJzlXr+vXrM2fObG5u9vLyiouL497/JkRYQfXFixeLYvCAqqrq1atXly9ffvLkyWXLllVVVWGzCIDk68Gjatrj0jmOEDIwMFBUVMT6vt+/f99ZfllUVISPv9TW1u7sXCdOnEAILViwoEePTOKXIPMos7KyiPVEJf9OgNQLDg5OSEjAH7LZbGLBB96NHj26p+eXOTk5vr6++K/T7777jrg2Dy8cHBzGjx9/79497GFSUtL9+/eJI8sBWWTkqlVUVPTNN98wGIxvvvnm3Llz3Vjts3t4L6jebfLy8hEREQYGBtu3b//555+nTZsmrKWGgEj1jKW9eMR9ESBFRUW8nGxubm5njeCLBygpKQ0dOrTDfaqqqq5du4YQWrhwoQDx9jAfP36srKzEHwpSo7hXr1742s2AFK2trUeOHBFKUxJ+U6dLpaWlPj4+VVVV2MOJEydik3z51ea2CozClASyc9XS0tLy8PBYv359dHS02JLLbhRU7x4KhbJt27azZ89u2LChs3tDQNJIVX7J/f4lQgjvoCdeNdp4/fo1tuHg4NDZvOCzZ8+2tra6u7tbWlp2P9yehvihqaiodJZ883K4s7NzT1m2WFq9efMGv10noB6dX9bV1U2cOBEfEuPg4BAdHd29+RBjx44lzh15/vz5zZs3hRMl6C7ZuWr16tUrISFh7969YpjNg+t2QfXuCQwM3L17t0z1GfZokvvXwi8ajfbu3TtsW1tbu8OfOHhZ4Js3b3b2jyu+WJG/v39n58LWhCQWJZEFs2bNwutaNTc38/tH/s8//+CHE7tlASmcnZ2FVeTsm2++IfvddJ+GhsabN2/w9/Lq1Ste5ix2JiUlhfjJYCVaAYngqiU6ghdUB9JNevLL169fM5lMbLuzGypjxozBpihVV1djAyjbeP78OfaDVU5Obv78+R02kpaWlpGRoaamxtfwfwAAAEBqXLlypaysbOjQobJ2qwXwSHryyy47xxFCcnJy+BipLVu2tFnEvLGx8fvvv+dwOAihOXPmdDZZHrt5OWPGDPjFBgAAQDb5+Pj88MMPUVFR4uyRBz2IdOaXXAZxr1q1ytPTEyFUU1Pj7e0dGxtLp9ObmpoSEhKGDx+enp6OENLR0WmzXB6upaXl/PnzSMbKXgIAAABEOjo64eHh9vb2ZAcCJJT0jJNtMxC7s92oVGpkZKS3t3d+fn55eXlAQACVSqVQKHjdOy0trZiYmL59+3Z4+NWrV2tra83NzbEkFQAAAAAAtCFV9y9r/6OlpcVlT1NT09TU1OnTp2PrlLDZbDy5dHNze/bsGZfcEesch5uXAAAAAACdkVdTU0MIYf/t0fhaq0BDQyMmJubDhw8XL17Mz89nsVgDBw708fHhXh2trq4uMTGRy9QfAAAAAAAg7+vrq6ysLJsFS83MzDZt2sT7/r169Ro7dqyrq6uBgYHoogIAAAAA6NHkt2/fvn37drLD6Bnk5OTu3LlDdhQAAAAAABJNesZfAgAAAAAASQD5JQAAAAAAECbILwEAAAAAgDBBfgkAAAAAAIRJeuqrA15glT5zcnJiYmLIjkVQX758QQhh63nKMuwTKC8v77n/T7OzsxFCDAZD8KawT+P69euampqCt0augoIChBCbzSY7EIlQW1vbc7/huNevXyMhfdUBkHCQX8qWtLQ0hNDVq1evXr1KdizCkZWVRXYIJMvJyUEIvX379ttvvyU7FoEUFxcL3khLSwtCaPny5YI3JSHevHlDdggkKyoqQggVFhb29G84LiMjg+wQABA5yC9ly48//piTk2NiYiIFFfWrqqqqq6sXLFhAdiAkmzt37smTJ/v06dOvXz+yY+kmNpv9/v17Pz8/wZuaMmXKmzdvBg0aJHhTpKurq/vy5ct3331HdiAkmzx5soWFhZKSkq6uLtmxCIpOp+fn569cuVLAdphMJkKopqbGzMxMGHHxh06nV1ZWamlpqaioMJnM8vJyDQ2NXr16iT8SrBerurpawHYuXbq0YMGC3r17q6qqCiOunqqiokJHRyc/P18orUF+KVv8/f39/f3JjgIIk6mp6adPn8iOQlJcu3aN7BCAkGlpaeXm5pIdhWRRUlJCCLFYrI8fP5IVA5bbYSoqKioqKsiKRE5OTsAW4uPjm5ubm5ubhRJPj9bY2Nja2qqoqCh4U5BfAgAAAD2Jqanpq1ev6uvrSblrePTo0ePHjwcGBq5du/bmzZtbtmzx9PT8888/xR9Ja2srjUYbM2aMgO3Y2toihKZOnbp582ZhxNUjtbS0eHh4CLFByC8BAACAHsbBwYGsU+vp6SGEdHR0HB0dscl5Ghoajo6OZMUjLP369ZOCd9FtQr99C/WJAAAAAACAMEF+CQAAAAAAhAnySwAAAAAAIEyQXwIAAAAAAGGC/BIAAAAAAAgT9fTp08uWLcOWDQRd+umnn06ePEl2FAAAAAAAHSCxFikRNTw8/Pjx44WFhWRH0gPU1NTs37//hx9+KCsrIzsWAAAAAID/cebMGV1d3b1795IdCKLW1tYihGpqasiOpAfQ1NR0d3en0+lRUVFkxwIAAAAA8H8aGxt//vlnDoejoaFBdiwSPP4yMzPT6j8hISFkh/P/BQUFIYROnTpFdiAAAAAAAP9nz549X758sbS0XLRoEdmxSHB+mZycnPMffX19ssP5/2bMmKGmppadnf3ixQuyYwEAAAAAQAih0tLSffv2IYT27NkjL0/+6oySm1++fPkS33ZxcSExEqJevXp9++23CCGY5SPjGhsbMzIyioqKEEJFRUUZGRmNjY1kBwWA0NBotHfv3n369Akh9OXLlzdv3tTV1ZEdFACgU7/88ktTU9OoUaOmTJlCdiwISXJ+id8gVFRUtLe3JzWW/4Hddv73339pNBrZsQCxqq2tPXXqVGBgoLGxsbq6up2dHTYS9+LFi3Z2durq6kZGRnPmzDl58iQ2rBmAnqWxsfH8+fMLFy40MzNTU1OzsbE5ePAgQuju3bv29vZ9+vTR19efMWPGP//88/XrV7KDBQD8n4yMjDNnzlCpVEmY2YOR0PyyqakpKysL27a3t1dSUiI3HiJPT08LC4v6+vorV66QHQsQk4yMjLlz5+rp6QUFBZ0/fx67bWlgYKCpqYkQ6tOnj4GBAUKouLj4woULixcv1tPTmzNnTnp6OrlhA8Cj3NzcpUuX6unpBQYGRkZGfvz4kcPh6OrqamtrI4TU1dUNDQ2pVOqXL18uXbr0/fffGxgYBAQEPHv2jOzAAQAIIbRhwwYWizVv3jxHR0eyY/n/JDS/TEtLw0tySk7nOA67hQmzfGRBSUnJzJkz7e3tz50719LS4uTk9Ntvvz19+rShoeHz588//PADQmjp0qWfP39ubGxMTk7esWOHs7NzS0vLhQsXhg0b9u23337+/JnsNwFApyorK5csWWJlZRUREdHY2Dh06NCwsLCHDx/W1dV9+fJl06ZNCKFp06YVFxc3NTW9fPlyz549np6eTCYzNjbWzc1t0qRJ+fn5ZL8JAGTarVu37t69q6Kism3bNrJj+T8Sml8SZ8+4urqSGEmH5s+fLycnl5CQUFBQQHYsQITOnDljZWUVHR0tJyc3f/78t2/fpqSkhIaGurm59erVq83OampqI0aM2LRp08uXLzMzMxcuXCgvLx8TE2NlZXX69GkywgegC3FxcZaWlidOnEAITZ8+PSUl5e3bt7/++quXl1fv3r3b7KysrOzs7PzTTz8lJSXl5eX98MMPysrKt27dwrrRORwOGe8AAFnHYrGCg4MRQuvWrTMyMiI7nP8jofklcXKPBOaXBgYG3t7eHA4nMjKS7FiASDCZzGXLli1YsKChoWHUqFFv3ryJjIwcOnQoj4cPGTLk1KlTGRkZY8aMaWxsXLRo0ZIlS5hMpkhjBoB3HA7n559/DggIqKqqcnJyevHiRUxMjJOTE4+Hm5mZhYeH5+Tk+Pn5tbS0rFmzZsaMGTAkHQDxO3ny5Nu3b7W1tTdu3Eh2LP9D0vNLTU1Nc3NzcoPpEFYI8/Tp0/CrXfrQ6fRp06YdP35cXl5+165dCQkJQ4YM6UY7lpaW9+/f37t3r4KCwokTJ/z9/VtaWoQeLQD8YrFYixYt2rVrF4VC2bRp07Nnz3jPLImMjY3j4uIiIiJUVFQuX748YcKE+vp6oUcLAOhMY2NjWFgYQmjbtm3t+xzIJYn5ZVlZGTZ/AiHk4uJCoVDIjadDfn5+ffv2LSgoSExMJDsWIExsNnv+/PnXrl1TVVW9du3axo0bBfkGUiiU9evX3759u3fv3jdu3Jg5cybcxQSkW7duXWRkpKKi4rlz53bs2CFgqbzFixc/evRIW1v78ePHU6dOhR9RAIgNXlB9yZIlZMfSliTmlxLeOY5RVFQMDAxEMMtH6mzatCk6OlpFReX27dsTJ04USptjxoy5desWlrBKzmJUQDbt27fv0KFD2ODgWbNmCaVNZ2fnhIQETU3Nhw8ffvfdd0JpEwDAnaQVVG9DEvNL4uQeCZw8jsNmkV++fBm6hKTG7du3d+/eTaFQzp8/7+npKcSW3dzcLly4QKFQ9u3bd+PGDSG2DADvXr58if3COXLkiJ+fnxBbHjp0aFxcnIKCQmRkJAxMB0AMJK2gehuSmF9K5so97dnb2zs4ONBotIsXL5IdCxCCpqam7777jsPhrF+/3t/fX+jt+/n5bdy4kcPhfPfdd7DYDxA/JpO5ZMkSBoOxYMECUfSmeXp6/vHHHwihtWvXVlRUCL19AABOAguqt9HNG6oZGRlxcXF5eXllZWVVVVXa2tqGhoaGhoaurq7e3t5ycnLcD8/Ly3v48GF2djadTh8wYICLi4uXlxd2FIfDSUlJwXYbOHAgVt2Xi+bm5tu3b2dnZ5eUlJiYmFhbW0+YMAG7UYxNAcbm3xgZGW3durV7b5aLoKCgVatWnTx5cunSpUJvHIjZrl27CgsLLSwsfvvtNxGdYtu2bXFxcTk5OX/88ceOHTtEdBYAOnTkyJG3b9/q6upiq/KIwtq1ay9duvT8+fNffvnl2LFjIjoLAAArqL5gwQLJKajeFjY7OzU1lcObBw8ecK/SYmBgEBoa2tra2uHhmZmZAQEBVGrb+6aGhoa7du1iMBjZ2dn4k7Nnz+YSSX19fXBwsJaWVpumjI2Nz507x+FwXr16hT85b948Ht8gX6qqqrC1hbKyskTRPhCb2tpaDQ0NhFB8fDzvR4WGhiKENmzYwPshN2/eRAj17t27urqa/zAB6KaWlhZslamTJ0/yftSff/6JEFq4cCHvh6SkpFAoFAUFhcLCQv7DBD3Ali1bEELr1q3jcDjYGrlTpkwhOyiBYLcAFy9eTHYgvML+HVFRURHiX1lTUxOWL9HpdKE0yF//+ObNm8eOHfvu3Tsu+5SUlMTHxysoKLR/KSoqytnZ+erVq2w2u81Lnz9/Dg4O9vLyiomJwZ/k0jn+8uVLe3v7Xbt2VVdXt3mpsLAwMDAwLCxMDEXatbS0pk6dihCCAto93YkTJ+rq6oYNGzZ58mSRnmjixInOzs719fUREREiPREARNHR0SUlJaampnPnzhXpiZycnCZOnMhgMP7++2+RnggA2SSxBdXb4CO/3L9/P95vaGho+PPPP587d+769etHjx4NDQ2dOXNmnz59sFc77CzevXv3/Pnzm5ub8Wf09fWnTp26atWqOXPmGBsbI4SSk5OxH0aYzpLCGzdueHh4fPz4EX9GTk7O3t7e39/f1dVVUVERIbRt2zbioATRjePECmGeOXMG6s70aGfOnEEIrVy5Ugz1sFauXIngNwkQL2zOzXfffdfhj3/hwr7h586dw5f5BQAIi8QWVG+Lx/7xjx8/KisrY4dMmjSpsbGx/T50Oj0qKsrW1rZ9x19UVBTxn+0hQ4Zcv36dyWTiOzAYjJ07dxL3UVBQoNFo7c+SkJCAR4IQUlJSCg0NLS4uxnd49eoVlq3iFBUVhXW/tz0Wi2VoaIj47FcFEiUvLw8hpKKiUldXx9eB3egf53A4DQ0NqqqqCKGcnBy+DgSge6qrq+Xk5CgUyufPn/k6sBv94xwOh8Fg6OjoIIQeP37M14GgR4D+cRI1NDTo6ekhhI4cOSLclknrHw8PD8eq5srLyx8/flxNTa39PoqKinPnzn3z5o2mpibx+dzc3CVLlnD+W+dm6dKlr169mjx5MnEakLy8fHBw8IYNG/BnbG1tiXkkpqysbMaMGXj9XktLy/T09N9++w3L8DAODg5teh7t7e2xm5qdef78+aBBg9LS0rjs0xkqlbpgwQIEhTB7MqxIvru7u3jWP+jVq5eHhwd+XgBE7dGjRywWy9bWFhuCKWry8vLjxo1D8A0HQNgkuaB6G7zml/fu3cM2nJyc9PX1eT8Bh8NZtmwZnU7HHi5ZsuTo0aPYnJj27O3t8e0OO8eXLVtWVVWFbdvZ2SUlJVlaWrbfbdy4ccRJSFw6xxsaGvbs2ePl5ZWXl9ftDu6FCxcihOLj4ysrK7vXAiAXVrJAuAUvufPy8kL/W4oLANGBbzgAUkDCC6q3wVN+yWaz379/j21//PiRw8+K2zExMY8ePcK2bW1tDx8+zGV8G/eVe65fvx4fH49ta2pqxsbGcqle5Obm1mFTzc3Nubm5z549i4iIWLJkiaGh4caNG1tbW3l/R+2Zm5uPHDmSwWCcPXtWkHYAWbCvd/cWGe8eKysrhFBubq7YzghkGXzDAZACmzdvluSC6m3wlF9SqVS8olBFRcWiRYu+fv3K4wmw4TuY48ePcx9azr2y+s6dO/HtgwcPmpiYcGmqrq6uw6YuXLgwePBgNze3pUuXnjhxQlhL72CzfKCLvIcqKSlBCHH/RgmXqakpQqi4uFhsZwSyDL7hAPR0GRkZkZGRklxQvQ2Kubl5fn5+amoq9xKdHh4eT58+xR8qKCi4u7uPGDFi5MiR7u7u6urqHR6VkpKC53ajRo3iPhaHyWT27t2bRqMhhDQ0NGpqaoh3Ol+8eDF8+HBse8iQIW/fvm1fRJPIzMwMm2Dep0+f6upqvKkTJ05goxaoVKqLi4ubm9v+/fuxl54/f97tMkZNTU26urqNjY0ZGRk2Njbda4SL3bt3Hzt2jK87xyRqbm6uqanR1tbmPuxVcnz69InD4QwYMIDfqbXV1dW1tbV9+vRpX4eVOwaDUVxcTKFQsH+GJVxdXV1TU5OOjk6XSyfIiB73gRQWFrJYLD09PRUVFb4OrKurq6qqUldX73KpizbYbHZBQQFCyNTUVAw1GQTHZDIrKirU1dU7++cM4GpqampqatTV1VtbW5WVlevq6lRVVXV1dcmOq/uw7/n48ePv3r0r6nOVlpbm5ubm5eXl5eWVl5c3NTXV1dU1NDQ0NTUxGIxevXqpq6srKyurq6v36dPHzMzM3Nwc+++0adPu3r07f/58Ea2/2tzcjE2tEcrfrLa2Nq/zx2/evNnZ+VRUVJYtW9bhTFhsoVsMVvOcC2I59PHjx7d5lTj15++//+beVHl5eWdN5eTkXLx4MSEhobKyksPhlJWV4Xs+f/6ce7Nc4PMlnzx50u1GuPD19RXwfzYAAAAAOjNs2DBR/PNdV1d3/fr1jRs3jhgxolevXoJEKCcnt3Xr1vT0dBaLJfQ4GxoahPVJIoSoVCqv40MnTpz4119/rVmzpv0kGBqNduzYscjIyIiIiDaVexMSEvDtsWPHcj8Fviwk6qhz/M6dO/h2l8nW8+fPO2tq8ODBgwcP5n54N9y6dau8vNzIyGjEiBFCbxwhdPHixezsbE4PuX/JZrNLSkoGDBhAdiC8mjx5cnl5+YULFywsLPg68PDhwydPnpw/f/6PP/7I14EfP3789ttv+/Xrd/v2bb4OJEVra2tVVRVWFAOgHviBzJ07Nycn5/Dhw/xWAj5//vz+/ft9fX3DwsL4OrC6utrb21teXp54NZZwpaWl2traYqgP2tMdPXr0+PHjgYGB06dPz8jICAsL8/T0JI6F63HOnj174MAB4gxjwb158+bff/+9d+8elg7izyspKZmZmQ0aNMjCwsLQ0FBNTa137969e/dWU1NTVFSsr69vamqi0Wj19fVVVVX5/yktLUUIsVissLCwsLCwPn36eHp6Tps2zd/fH1t5TnB4n/CzZ88E/yvQ0tLiY/7RihUrJkyYsH///qioqMbGxjav0un0oKAgKysrvJ+9paUlNTUV2zY1NcVu73HBZXJPbW1tRkYGtq2jo9NlwXriFU1EK/e0ceLECYTQwoULuffad5uKisqwYcNE0bKIODs7kx0CHwwMDMrLyzU1NfldyBXLMHR0dPg9sKamBiGkr68vuUvHAilibGyck5Ojrq7O7/ft8ePHCKG+ffvye+CbN28QQtra2j3oG96DQiUXft3z9/fHkgENDY0e/ek9fPgQISSUgRyfPn26cOHC+fPnMzMzsWcoFIq1tbWXl9fIkSNdXFyMjY35zROOHz++bNmyPn36rF+//uXLl0+fPq2uro6Pj4+Pj1dWVp40adLs2bMnT57M7+iXzgwbNkwoY9v4e5Pm5uaHDx+urq5+/Pjx77//7uPjQ0xyGQwGNnMeU1ZWhufsvPzQ5zK5B8vceW/q2bNn+LYYEp3y8vIbN25QKBSsUBHocQYNGoT+m2MrHti8Wuy8AIgafMMBECkOh3Pr1q0xY8aYmZmFhoZmZmaqqanNmTPn8uXLFRUV7969Cw8PnzlzpqmpKb/JZWNjI9Z78Mcff/zyyy/Xrl37+vVrRkbGzp077ezsWlparly5MmPGDD09veDgYGKyRLru3GxTUFDw8PAICQm5detWSUkJcb1m/IYlQog4CBJfOrIzTU1NWVlZ2LaxsXGbm53EUZJd/sJgsVh4V7uRkZEYBh1HRUUxmczRo0f3iLkaoD1bW1v0v7e9RQ07F3ZeAEQN+6a9ePFCbGeEbziQEUwm89y5c/b29pMmTUpMTJSXl580adLZs2fLy8vPnTv3zTff9OvXT5D22xdUp1KpNjY2wcHB6enp2dnZYWFhgwcPrqur2717t6mp6aJFi/Bbp+QStDNXW1v74sWL+F1MYr85XlMd/W+1oA6lpaXhNzvb92hjk8ox+fn53Jt69+4dvsyR6JYdJzp58iT6r0QR6IlGjRqFEEpMTGSz2WI4HYfDwYYmjx49WgynAwD7hj99+hRf/EzU7t+/j+AbDqQah8M5ffq0ubn53LlzMzIy+vTpExISUlRUdOPGjcDAwA6XOeRXlwXVLS0tf/3115ycnLt3744fP761tfX06dM2NjYBAQEfPnwQPABBCGGwoJqaGr48o7W1Nf48cRHwvLw87nNTuFdWJ84UaWho4F5TDRtI0VlTQvf8+fPs7GwNDY1vvvlG1OcCIuLs7KytrV1WVkb88ojO48ePS0pK+vbtK57BwQCYm5sPGjSoubk5Li5ODKfLzs7OyMhQVlYeM2aMGE4HgPi9fv3aw8Nj0aJFhYWFOjo6YWFhnz59+v3334XbZcp7QXWsuFJ6evq8efPk5eVjY2OtrKxWr14t3FnhfOk6v6ytreW+Q2FhYWFhIbZNHOFraGiIp9sVFRVJSUmdtVBaWnro0CH8YfubjsRUFSGEV6xs79OnT8Qy7GK4f4ndvJw9e7awhtYC8ZOXl581axZCqM3K9SKCnWXmzJkwUxWIDVbcQ5zfcF9fX2HNbAVAclRWVi5fvtzJySk5OVlTU/PQoUNFRUW//vprl+MA+dWNgup2dnZnzpzJysry9fVlMBiHDh2ysrI6f/48KcVnusgvU1NTBw8efPny5c52oNPpK1euxHoVKRQKsY9YTk6OWGl87dq1zc3N7VvIzs729PTEb0nKy8u3nyitoaFBvDN65MgRfDo5UVZWlqenJz5Yk0qlinrOdXNz88WLFxF0jvd8y5cvp1Kp0dHRXQ7AEBA2u5BCoSxfvlykJwKAKCgoSElJ6f79+6JeE7yysvLYsWMIoe+++06kJwJA/K5du2ZpaYl9w5csWfL+/ftVq1aJaCWRDRs2sFisuXPn8js339zc/Nq1a7du3Ro8eHBJSUlgYKCfn19lZaUoguSii/wyIiKioqJi+vTpw4YNCw8PJ3ZzM5nMxMREZ2fn69evY8+sWLGizWzB1atX49uvX78eOXIksTh+ZWVlaGiok5MTttAOxsbGRlVVtX0kP/zwA75Np9Pd3d3PnTuHrxteUVGxbds2R0dHbBk0jLW1tYC1TLt06dKl+vp6a2vrnlWOB7RnbW09depUFou1ceNGkZ5o48aNTCbT19cXpj4AcTIwMFiwYAFC6KeffhLpzYwtW7Y0NjaOGDECOseBNKHT6atXr/b396+qqnJ2dn7+/Pnx48f5XdeKd7du3bp7966Kisr27du714KPj8/bt2/37t2rqqp6/fp1Ozs7YklyceCyfk9TU1Pv3r3b7K+mpmZiYmJsbKysrEx83t3dvbGxsU0LdDpdX1+/TQv6+vpubm54lzeVSiUmZ8uXL++ssnz7m89KSkrOzs5Dhw7FOuKxSVX4q4sXL+6yYL2A6/d4eXkhhPbt28fvgUAC5eTkKCkpIYSuXr3K4yGhoaEIoQ0bNvC4f3x8PEJIUVExKyurm1EC0F2lpaXYJR1bbJYXWNHshQsX8rh/cnKynJwchUJ5+vRpd8MEkm7Lli0IoXXr1nE4nKioKITQlClTyA5KIFgHNJec4f379w4ODgghCoXy448/tra2ijQeJpOJJTOhoaGCt5adnY2VjseCp9PpHe6GT4zubAd+cbt/yWAwAgIC2tQDampqKigoKCwsJM5DnD59+u3bt9vPllJUVDx9+nSbSU+lpaXJycnYkE1ra+vk5ORx48bhr3Y246FXr17YQATik3Q6PSUl5d27d0wmc8iQIU+ePCGuEiTqyRMfPnxISkpSUFBos2oR6KEGDx4cHByMEFq8eHFRUZHQ2y8uLl60aBFCaMOGDVZWVkJvHwDu9PT0duzYgRBas2aNKCqYVFdXz5o1i8ViLV261M3NTejtA0CKuLg4R0fH169f6+np3bt37+DBg6IeOn/y5Mm3b99qa2sLpT/N0tLy2bNnK1euRAgdOnTI29u7y3k1QsEtv9TQ0Dh9+nRWVtb69evNzMza76CsrDx16tQ7d+7ExMR01hM9fvz4xMTENksyysnJeXt7X758OT093dXVlVgOnUtS6Ofnd+fOHeyGK7GpMWPGXL58OSMjY8SIEdwXmRSuU6dOcTicKVOm9O/fX6QnAmKzefNmDw+P6urqSZMmVVdXC7Hl+vp6bASMi4sL9usfAPFbsWKFv79/c3Ozj48P90Ic/KLRaP7+/kVFRYMGDeJ9OgIAEi4iImLatGmNjY0TJkxIT0/vcqVrweEF1bdt29a+D7l7lJWV//rrr9jYWC0trUePHnl6en7+/FkoLXPR9fqQlpaWe/fu3bt375cvX7KysqqqqhobG7W1tXV1da2srHgZ4Ojh4ZGTk5OSkpKbm8tisYyMjJycnIgHJiYm8hjuuHHjcnNzX7x4gU3C0NfXd3FxwZtisVivXr3CtlVUVIhTgoSOzWZHRkYimNkjXeTl5S9evOjm5paZmenj43Pz5k0BS+NiqqqqpkyZkp6ePmDAgMuXL4toMDgAXaJQKCdPnszLy8vMzJwwYcKdO3eI1d+6rbGxcdq0aY8fP+7Xr9+1a9fU1dUFbxMA0u3atSskJITD4axYseLQoUMiWv+5jfYF1YXFz8/vyZMnEydOfPfunaur682bN+3s7IR7CiI+1h/X09PjZW3Gzjg7OwtlEgyFQhk+fPjw4cPbv/Tu3Tu8Erujo2OHxUiF5e7du58/f9bV1fXx8RHdWYD46evr37lzZ9SoUSkpKe7u7leuXBHwh0p2dvY333yTk5PTv3//27dv48ViASCFpqbm7du3R44cmZ2d7e7ufunSJQG7egoLC6dNm5aWlta7d+/r16+36a0CoCdis9mrV6/++++/EULbt2//5ZdfxHPeLguqC8jKyio5OXnixIkZGRmjR4+Oi4vz9PQU+lkw4kjGxUacneMnTpxACC1YsECkWSwgxeDBg588eWJmZpabm+vi4hIeHo4vLsUXNpt95MgRZ2fnnJycgQMHPnnyZMiQIUKPFgB+GRoaPn361M7Orri42NPT848//mAwGN1oh8PhnD171sHBIS0tTVdX99GjR7BkAJAO//zzz99//y0nJ3fs2DGxJZeIn4Lq3aavr5+UlDR69OiamhqRFhGTqvyS+yJAQlRVVXXt2jWE0MKFC0V3FkAiMzOzly9f+vr6Njc3r1y50sXF5fr16xx+qrrcvHnT1dX1hx9+aGpqmjx58suXLy0sLEQXMAB80dPTe/Lkydy5c1tbWzdt2mRnZxcdHc3X+qiPHj0aNWrUvHnzampqRo4cmZqais1RBUAKODg4uLq6XrlyZenSpWI7aTcKqnePhobGrVu3Nm/evHnzZtGdRaryS7Hdvzx79mxra6u7u7ulpaXozgLIpaWlFRcXFxER0a9fv1evXvn6+g4dOnT37t25ublcjsrNzd29e/fQoUMnT56cmprat2/fY8eOxcfH9+3bV2yRA8CLXr16RUVFXbx40cDAIDs7e+bMmYMGDdq2bRv3qeUFBQWHDh1ycnIaNWpUUlKSurr6/v37Hzx4YGBgILbIARC1ESNGPH/+3M/PT5wn7XZB9W5QUlLatm0btnCdiEhP3y6NRnv37h22ra2tbWJiIrpzYWtCYrVmgBSjUCiLFy8OCAg4cODAX3/9lZWVFRwcHBwcbGBgYGdnN2jQoNTUVITQkydP1q5dm5eX9+bNG3xSnoaGxsqVK9euXQuZJZBk33777cSJE//+++8DBw58+PAhLCwsLCxMR0fH3t5+0KBB2K+pV69erVu37uPHj2/evCkoKMAOVFVVXbZs2caNGwUZlw8AwAheUF3SSE9++fr1ayaTiW2L9OZlWlpaRkaGmprat99+K7qzAMmhpaW1bdu24ODgK1euXLhwISkpqaSkpKSk5ObNm9gOz549w2tsqaqqjhw5ctasWdOmTRP18lEACIW6unpISMjatWvj4+PPnz+fkJBQXl5+586dO3fuYDtkZGTgS/IqKSm5ubnNmjVrxowZmpqa5EUNgFTB1pxcu3atkZER2bEIh/Tkl2LrHMduXs6YMQNqcMgUNTW1efPmzZs3r7W19dWrV1lZWZ8+fSoqKnr58qWzs7OxsbGpqemQIUOGDRsG5YdAT6SsrDxjxowZM2Ywmcz09PSsrKz8/PwvX748ffrU1tbWzMzMxMTEysrK0dFRRUWF7GABkDbr1q0zNzfftGkT2YEIjXTml1wm93z9+vXw4cP4w8bGRnw7IiLi9u3b+MNZs2a1L7TR0tJy/vx5BGUvZZiiomJnFbIAkALy8vJOTk5OTk5kBwKADPH09BRdqSBSSE9+SZw8zqXQZkVFxa+//trhSxEREcSH9vb27fPLq1ev1tbWmpubS9n3AAAAAABAWKQnvyTev9TQ0BDRWbDOcbh5CQAAAADQGXk1NTWEEPbfHo3HnNLa2pqvKoZEdXV1iYmJcnJy8+fP714LAAAAAABST97X11dZWVmk1XykRq9evcaOHevq6gqV3gAAAAAAOiO/fft2qSm2JGpycnJ4wQ4AAAAAANAhqVq/BwAAAAAAkA7ySwAAAAAAIEyQXwIAAAAAAGGC/BIAAAAAAAgT5JcAAAAAAECYIL8EAAAAAADCJD3r9wAAAAAA8Ku0tBQhFB0dnZiYKP6z19bWNjc36+rqUqnUxsbGurq6/v37KygoiDmMbi890xnILwEAAAAg6xoaGhoaGsg6e0FBAb5dXFxMVhhUKlVeXjiZIeSXAAAAAJBd+/btmzBhgqamJpVKwqDBOXPm5ObmHjt2bNiwYT///PP9+/dDQ0MDAgLEH0ldXd2AAQOE9SFAfgkAAAAAmebt7U3WqVVUVBBCgwYNcnR01NTURAgZGxs7OjqSFY+wwPweAAAAAAAgTJBfAgAAAAAAYYL8EgAAAAAACBPklwAAAAAAQJggvwQAAAAAAMIE+SUAAAAAABAmyC8BAAAAAIAwQX4JAAAAAACEScrzy8zMTKv/hISEkB0OAAAAAID0k/L1e5KTk3NycrBtfX19coMBAAAAAJAFUn7/8uXLl/i2i4sLiZEAAAAAAMgIKc8vX7x4gW0oKira29uTGgsAAAAAgEyQ5vyyqakpKysL27a3t1dSUiI3HgAAAAAAWSDN+WVaWhqLxcK2oXMcAAAAAEA8pDm/xDvHEUKurq4kRgIAAAAAIDukOb8kTu6B/BIAAAAAQDxkIr/U1NQ0NzcnNxgAAAAAABkhtfllWVlZUVERtu3i4kKhUMiNBwAAAABARkhtfgmd4wAAAAAApJDa/JI4uQcmjwMAAAAAiI3U5pewcg8AAAAAACnIXH88IyMjLi4uLy+vrKysqqpKW1vb0NDQ0NDQ1dXV29tbTk6O++F5eXkPHz7Mzs6m0+kDBgxwcXHx8vLCjuJwOCkpKdhuAwcO1NbW7jKYoqKimJiY3NzcgoKCiooKNTU1bW1tOzu7KVOmODk5Cf5mAQAAAABkBDn5ZUJCwurVq9+9e9fZDgYGBgsXLgwLC1NQUGj/alZW1i+//BIXF8dms4nPGxoarlq1at26dfn5+XV1ddiTXQ6+TExM/OOPPx48eNCmNYRQbGzs1q1bHR0d9+3b5+XlxdN7AwAAAACQbST0j2/evHns2LFckkuEUElJSXx8fIfJZVRUlLOz89WrV9ung58/fw4ODvby8oqJicGf5NI5XldXt2zZsrFjx967d699a7i0tLRRo0bhS00CAAAAAAAuxH3/cv/+/b/99hu2bWhoOHfuXBsbGw0NjZKSkqKiovz8/Dt37tTW1iKEli5d2v7w3bt3BwcHE5/R19d3dnY2MjKqqqp6+vRpYWFhcnJycnIyvkNn9y9LSkrGjh37/v17/JmRI0fa2tqamJgwmcyKiorU1NSnT59iK0xaW1sPGTJE0DcPAAAAACADxJpffvr0KTQ0FNueNGlSdHS0mppam31aW1ujo6P37NkTGBjY5qWzZ8/+/PPP+MMhQ4bs3r3bx8cHH6nJZDL37dsXEhLC4XCwZxQUFBwcHNpHUlhYOGbMmI8fP2IP/f39f//9dysrqza7FRcX79mzJzw8fMmSJcTnmUzmhQsXrl69mpeX19jYaGJiMnXq1Llz5/br14/3TwMAAAAAQCqJNb8MDw9vaWlBCMnLyx8/frx9cokQUlRUnDt37ty5c9s8n5ubu2TJEjxxXLp06V9//aWkpETcR15ePjg4uLq6evfu3dgztra2ysrKbZqi0+n+/v54crl79+4NGzZ0GPCAAQMOHToUGBhIXP7n9evX06ZN+/TpE/5MQUHBw4cPt27dGhkZ6efn19XHAAAAAAAgzcQ6/vLevXvYhpOTk76+Pu8HcjicZcuW0el07OGSJUuOHj3aJrnE2dvb49sddo5v3LgxPT0d2968eXNnySWxkb59+2LbT5488fLywpJLJSUlJycnT0/P3r17I4Rqa2v9/f2PHz/O+/sCAAAAAJA+FPyOoKix2WxVVVUsR+zfv39ZWRnvazZGR0fPnDkT27a1tU1NTe1w6g9m7dq1Bw4cwLYjIyPnz59PfDUlJQWf8ePu7v748WPew2hsbLS2tsaWnfT19T1y5IiBgQFCqLm5ed26dUePHkUIqaiopKWlte9qF1BISAjWfo/Q2tpKo9HU1NTk5cksgCUGDAajublZVVWVyxdSCtBotNbWVnV1dSpVaivm8kV2PhAmk9nU1KSioqKoqEh2LKLFZrMbGhqUlJTad3mBNmg0WktLi6KiIpPJVFBQoNPpCgoKvXr1Ijuunqq+vp7FYikpKTEYDDk5OQaDoaqq2tkdtJ5CU1MTccRIRUUFP/eCBQsqKip4PHD48OH4gS9evOC+s5ubG75zdnZ2m1cnTZqEvUShUNLS0viKH7/TOXr0aDqd3ubV77//HnvVzc2Nr2Z5MWvWLJF/HQAAAAAABKakpCS++5cIIQ8Pj6dPn+IPFRQU3N3dR4wYMXLkSHd3d3V19Q6PIt5xHDVqVGJiIpdTMJnM3r1702g0hJCGhkZNTQ3x9uSbN2/w3vPRo0cnJCTwHnxLS4uenl5tbS2FQnnz5o2NjU2bHerq6szNzSsrKxFCWVlZwr2FyWKxPn/+jE1m7xHq6+uxYQNSTxbeKYvFamlp6XDAtGySqQ9EFr7hmMbGRlVVVam/Jy24AwcO/PXXX4sXL165cmVCQsL69evHjBkDY8O6bcqUKdnZ2efOnRs6dGhISMjNmzd37NjR028qaWpqirX7MjQ0dPLkyXhGy2AwHj58+PDhwz/++ENFRWXevHnr1q0bPHhwm6OuXr2Kb3dYtIjo7du3WHKJEHJxcWnT933p0iV8e+HChXwFf/nyZaxwko+PT/vkEiGkoaGxaNGiPXv2IISioqJ+//13vtrnTk5OztjYWIgNAgAAAN1gZ2eHELKxsbG3t6+vr6dQKJaWlgMHDiQ7rp4KG3xiYGBga2uL/WrV1taWgs9TrPcvEULh4eFr1qxhMpkdvqqkpBQREdFm8vjw4cNfvHiBbZeVleno6HBp/9ixY8uXL8e2Q0ND8VqbGDs7u4yMDGy7uLjY0NCQ98gXLFhw5swZhNCff/65Zs2aDve5ffv2xIkTEULW1tbcC8jz68iRIydPnhTz/6xuq6+vLysrMzIykvqRTM3NzZ8/fzYwMJDuW1mVlZW1tbWmpqZdrtoqI2TnA2lpaSkuLtbR0ZH6W5gMBqOwsFBLS0tLS4vsWHoAbIQY9t1QVlZWUFDgfSYDaCMrK4tGo+np6TU3N1MolNraWmNj455e7rBfv35iHX+JycvL+/777zsbC6ygoJCamorvTKPR8Cu4qalpl40vXrwYb+ratWvEl7DSSBhdXV1+w8ZLFCUnJ3e2D17zSE5Ojkaj8XsKLiZMmCCSrwAAAAAAgLCJ+/4ljsFgvHjx4vHjx0lJSQ8ePGAwGPhLs2fPPn/+PLZdUFBgamqKbbu5uRGHb3bI1tb27du32Habm53EphwcHF69esV7tK2trfhkrtLSUj09vQ53Y7PZampqWCKbmprq6OjI+ym4q62txWYjCatBkWIymR8+fBg0aJDU/6LlcDi5ubkWFhbSPWarubm5vLwc//MBTU1NFRUVsvCBYN9wMzMzqa8FgRD68OGDvr4+cR4q4EKmvhsitXz58o8fP/7+++99+/Y9d+5cUlLS2rVr8bnIPVS/fv1I+1ooKCh4eHh4eHiEhIR8/fp10aJFN27cwF5KTU3FdysvL8e3+/Tpw73NpqYmfJVwY2PjNj3pFRUV+Da/fw91dXX4NpcOeiqVOnDgQCyGT58+CTG/7NOnz9ixY4XVGhCi8ePHkx0CACIkO9/wcePGkR1CDyM73w2RwiY3u7m5eXl53b9/HyFkZWUlBd9Gibjpoq2tffHiRbyCYGNjI/4SXlMd/W+S16G0tDR8hnX7yurE+el4RzaPsJk9CCFFRUXud6rwsxDfBQAAAACA7JCI/BIhpKamhs+2sba2xp8nTprOy8vj3kH88uVLfLt9fmloaIgP5ayqqqqqquI9PGJ+yX3PDrNkAAAAAADZIab8Es/POlNYWFhYWIhtE7uVDQ0N8b7sioqKpKSkzlooLS09dOgQ/hAvmYlTV1d3cHDAHx48eLDLsPFlJHnPL/EdGhoaumwfAAAAAED6iCO/TE1NHTx48OXLlzvbgU6nr1y5ks1mI4QoFEpQUBD+kpycHLHY5Nq1a5ubm9u3kJ2d7enpWVxcjD2Ul5cfNmxY+92Ia0Xu3buXSwmhDx8+zJkzx8fHB3uI55ddDtzEd4D8EgAAAACySRz5ZUREREVFxfTp04cNGxYeHk7s5mYymYmJic7OztevX8eeWbFixaBBg4iHr169Gt9+/fr1yJEj7969iz9TWVkZGhrq5OREHFJpY2OjqqraPpKgoKABAwZg2zQazcXF5eDBg2VlZdgzra2tHz9+jIiImDx5spWV1YULF/T19bGX8HnQxHnuHcJ3gCl1AAAAAJBNIs+BmpubL1y4gG2/fv165cqVCCE1NTVtbW0Oh1NeXk4sS+nu7r5z5842LcyePXvTpk2lpaXYw7S0tAkTJujr65uYmJSUlGC96lQq1dnZOSUlBdunfec4Rk1NLSoqavz48VgWSKPR1qxZs2bNmn79+snLy5eXl7cZ34kPCcWrdba2tnJ/v3h+KfXliAEAAAAAOiTy+5cMBiMgIKBNHcSmpqaCgoLCwkJicjl9+vTbt2+3XwdFUVHx9OnTbW4HlpaWJicnY8mltbV1cnIycTJ/+8k9OC8vr9jY2DZnqaysLCsrIyaX+vr6O3fujIqKwh7is8KJ89k7hCegGhoa3PcEAAAAAJBKIs8vNTQ0Tp8+nZWVtX79ejMzs/Y7KCsrT5069c6dOzExMZ0t6jN+/PjExMQ2S5PLycl5e3tfvnw5PT3d1dX12bNn+Etc8kuE0KRJk3JychYuXNj+dMrKyqNGjTpx4sSnT5+Cg4PxHBHPL5lMJl4CqUPV1dX4G+eyGwAAAACAtBLTGEFLS8u9e/fu3bv3y5cvWVlZVVVVjY2N2traurq6VlZWnaWVRB4eHjk5OSkpKbm5uSwWy8jIyMnJiXhgYmIi7/EYGhqeOnXqyJEjKSkppaWlNBqtX79+Ojo6tra2+Do9RMTamcXFxSYmJh02y2Kx8FnwkF8CAAAAQDaJew6Knp5eZ4sr8sLZ2dnZ2VlYwSgrK3t6evKyp4GBgaKiItb3/f79+87yy6KiInz8pba2tpDCBAAAAADoSSSlvrqEU1RUHDJkCLadm5vb2W4fPnzANpSUlIYOHSqOyAAAAAAAJAzkl7zC75sSVwlq4/Xr19iGg4NDl5XYAQAAAACkEuSXvJoxYwa2cfPmTRqN1uE+eA15f39/8UQFAAAAACBpIL/k1ZgxY7CRo9XV1SdOnGi/w/Pnz7Fbm3JycsSFggAAAAAAZArkl7ySk5MLDg7Gtrds2ZKRkUF8tbGx8fvvv8cqaM6ZM0eQOUwAAAAAAD0a5Jd8WLVqFTbfvKamxtvbOzY2lk6nNzU1JSQkDB8+PD09HSGko6Pz559/khwoAAAAAAB5YI1sPlCp1MjISG9v7/z8/PLy8oCAACqVSqFQ8IrrWlpaMTExffv2JTdOAAAAAAASwf1L/piamqampk6fPh1b8ZLNZuPJpZub27Nnz3gsqAkAAAAAIK3g/iXfNDQ0YmJiPnz4cPHixfz8fBaLNXDgQB8fH+6LUgIAAAAAyAjIL7vJzMxs06ZNZEcBAAAAACBxoH8cAAAAAAAIE+SXAAAAAABAmCC/BAAAAAAAwgT5JQAAAAAAECbILwEAAAAAgDBBfgkAAAAAAIQJ8ksAAAAAACBMkF8CAAAAAABhgvwSAAAAAAAIE+SXAAAAAABAmCC/BAAAAAAAwgT5JQAAAAAAECbILwEAAAAAgDBBfgkAAAAAAIQJ8ksAAAAAACBMkF8CAAAAAABhgvwSAAAAAAAIE+SXAAAAAABAmCC/BAAAAAAAwgT5JQAAAAAAECYpzy8zMzOt/hMSEkJ2OAAAAAAA0k+e7ABEKzk5OScnB9vW19cnNxgAAAAAAFkg5fcvX758iW+7uLiQGAkAAAAAgIyQ8vzyxYsX2IaioqK9vT2psQAAAAAAyARpzi+bmpqysrKwbXt7eyUlJXLjAQAAAACQBdKcX6alpbFYLGwbOscBAAAAAMRDmvNLvHMcIeTq6kpiJAAAAAAAskOa80vi5B7ILwEAAAAAxEMm8ktNTU1zc3NygwEAAAAAkBFSm1+WlZUVFRVh2y4uLhQKhdx4AAAAAABkhNTml9A5DgAAAABACqnNL4mTe2DyOAAAAACA2Ehtfgkr9wAAAAAAkILM9cczMjLi4uLy8vLKysqqqqq0tbUNDQ0NDQ1dXV29vb3l5OS4H56Xl/fw4cPs7Gw6nT5gwAAXFxcvLy/sKA6Hk5KSgu02cOBAbW3tLoMpKiqKiYnJzc0tKCioqKhQU1PT1ta2s7ObMmWKk5OT4G8WAAAAAEBGkJNfJiQkrF69+t27d53tYGBgsHDhwrCwMAUFhfavZmVl/fLLL3FxcWw2m/i8oaHhqlWr1q1bl5+fX1dXhz3Z5eDLxMTEP/7448GDB21aQwjFxsZu3brV0dFx3759Xl5ePL03AAAAAADZRkL/+ObNm8eOHcsluUQIlZSUxMfHd5hcRkVFOTs7X716tX06+Pnz5+DgYC8vr5iYGPxJLp3jdXV1y5YtGzt27L1799q3hktLSxs1ahS+1CQAAAAAAOBC3Pcv9+/f/9tvv2HbhoaGc+fOtbGx0dDQKCkpKSoqys/Pv3PnTm1tLUJo6dKl7Q/fvXt3cHAw8Rl9fX1nZ2cjI6OqqqqnT58WFhYmJycnJyfjO3R2/7KkpGTs2LHv37/Hnxk5cqStra2JiQmTyayoqEhNTX369Cm2wqS1tfWQIUMEffMAAAAAALKAI0YfP35UVlbGzjtp0qTGxsb2+9Dp9KioKFtb2+rq6jYvRUVFEctYDhky5Pr160wmE9+BwWDs3LmTuI+CggKNRmt/loKCgoEDB+K7+fv7Z2Vltd+tqKho1apVVCr1zz//7OxNPXv2zMLCIjU1lccPAQAAAAAAY2dnhxB6+PAhh8OZMWMGQujYsWNkByUEYu0fDw8Pb2lpQQjJy8sfP35cTU2t/T6Kiopz58598+aNpqYm8fnc3NwlS5ZwOBzs4dKlS1+9ejV58mTiNCB5efng4OANGzbgz9ja2uIZLY5Op/v7+3/8+BF7uHv37qtXr1pZWbUPZsCAAYcOHUpOTp43b177VxsaGvbs2ePl5ZWXl8dkMnn5BAAAAAAApJ5Y+8fv3buHbTg5Oenr6/N+IIfDWbZsGZ1Oxx4uWbLk6NGjnS3JY29vj2932Dm+cePG9PR0bHvz5s3EfLRDeCPNzc2fP3+uqqrKzMx8/vx5TExMfX097+8CAAAAAEAWUPA7gqLGZrNVVVWxHLF///5lZWW8r9kYHR09c+ZMbNvW1jY1NbXDqT+YtWvXHjhwANuOjIycP38+8dWUlBR8xo+7u/vjx495D+PEiRNLlizp8KXnz5+LdJWgjRs3RkREiK594WptbaXRaGpqavLyZBbAEgMGg9Hc3KyqqsrlCykFaDRaa2ururo6lSq1FXP5IjsfCJPJbGpqUlFRUVRUJDsW0WKz2Q0NDUpKSu27vECHZOe7IWr19fUsFktJSYnBYMjJyTEYDFVVVSUlJbLjEoiGhoZYx1+qqKjg516wYEFFRQWPBw4fPhw/8MWLF9x3dnNzw3fOzs5u8+qkSZOwlygUSlpaGl/x4xkelUodPnz4unXr8BM9f/6cr6b4NWfOHNF+FwAAAAAAhEFJSUl89y8RQh4eHk+fPsUfKigouLu7jxgxYuTIke7u7urq6h0eRbzjOGrUqMTERC6nYDKZvXv3ptFoCCENDY2amhri7ck3b97gveejR49OSEjgK/7379+/efNGW1vb1ta2b9++5eXlurq62Euivn/JZrM/f/7cg0Z5Ynf1yI5CHGThnbLZ7NbWVrivg5OpD0QWvuEYGo2mrKzMe48WkJ3vhkhNmTIlOzv73LlzdnZ2GzduvHnz5o4dO2bNmkV2XALp27evWLsvQ0NDJ0+ejGe0DAbj4cOHDx8+/OOPP1RUVObNm7du3brBgwe3Oerq1av4dodFi4jevn2LJZcIIRcXlzZXikuXLuHbCxcu5Df+wYMHtw9PPKhUqpGRESmnBgAAAICIDB48OD8/39XV1czMzNra+tatW87OzsQSNz2UWO9fIoTCw8PXrFnT2X04JSWliIiIuXPnEp8cPnz4ixcvsO2ysjIdHR0u7R87dmz58uXYdmhoKF5rE2NnZ5eRkYFtFxcXGxoadu9dYMR5/zI8PPzUqVOia1+46uvry8rKjIyMpP4GT1NTU0lJiYGBQYfFEKRGZWVlTU3NwIEDu1y1VUbIzgfS0tJSVFSkq6vbu3dvsmMRLQaDUVBQ0LdvXy0tLbJj6Rlk57shamw2m8Vi1dfXV1dXm5iYcDgcKRjSqqWlJdbxl5i8vLzvv/++V69eHcakoKBArCVJo9HwK7ipqWmXjS9evBhv6tq1a8SXsNJIGF1dXcHfSFlZGd6gqMdf+vj4iOY7AAAAAAAgZCRM7zU3Nz98+PDBgwdfvHjx+PHjpKSkBw8eMBgM7FUGg7Fv377z589jD8vKyrAVdBBCenp6XTb+8uVLfLvNypBfvnzBt3lpSqL8+++/aWlpXBaxlChMJrOgoMDc3JzsQESOw+Hk5+ebm5tL95it5ubmr1+/Ghsbkx2IpJCpDyQ/P9/ExETqa0EghD59+qSnpyf1vS5CJDvfDTFoaWkpKyszMTEhOxDh6N+/P2lfCwUFBQ8PDw8Pj5CQkK9fvy5atOjGjRvYS6mpqfhu5eXl+HafPn24t9nU1ISvEm5sbNymJ72iogLf7nF/DxoaGmPGjCE7CtCB8ePHkx0CACI0btw4skMAEgq+G4ALiSjepq2tffHiRbyCYGNjI/4SXlMdIVRXV8e9nbS0NPxmZ/vRkMT56fjiPQAAAAAAQLgkIr9ECKmpqeGzbaytrfHniT1QeXl5HK6zkYid4+3zS0NDQ3woZ1VVVVVVlYAxAwAAAACA9sSUX9bW1nLfobCwsLCwENt2dHTEnzc0NMT7sisqKpKSkjprobS09NChQ/jDNoMvEULq6uoODg74w4MHD3YZNr6MJAAAAAAA4JE48svU1NTBgwdfvny5sx3odPrKlSuxySsUCiUoKAh/SU5OzsbGBn+4du3a5ubm9i1kZ2d7enoWFxdjD+Xl5YcNG9Z+N+JakXv37n337l1nIX348GHOnDkwaxsAAAAAgF/iyC8jIiIqKiqmT58+bNiw8PBwYjc3k8lMTEx0dna+fv069syKFSsGDRpEPHz16tX49uvXr0eOHHn37l38mcrKytDQUCcnJ+KQShsbmw4XFQgKChowYAC2TaPRXFxcDh48iJcZam1t/fjxY0RExOTJk62srC5cuKCvry+E9w8AAAAAIEtEXl+9ublZT0+vvr6e+KSampq2tjaHwykvLyeWpXR3d79z506bUtWtra2mpqalpaXEJ/X19U1MTEpKSrBedSqV6ujomJKSgr26fPnyf/75p8N4Hj16NH78eLwcEqZfv37y8vLl5eVtPg1fX99r16519tbEWV8dAAAAAKCnEPn9SwaDERAQ0KY6YFNTU0FBQWFhITG5nD59+u3bt9uvg6KoqHj69Ok2FYVKS0uTk5Ox5NLa2jo5OZlYKIFLqufl5RUbG9vmLJWVlWVlZcTkUl9ff+fOnVFRUXy8VQAAAAAAIIb8UkND4/Tp01lZWevXrzczM2u/g7Ky8tSpU+/cuRMTE9PZoj7jx49PTExss/a3nJyct7f35cuX09PTXV1dnz17hr/E/VbipEmTcnJyFi5c2P50ysrKo0aNOnHixKdPn4KDgzU0NHh9nwAAAAAAACEk/vXHv3z5kpWVVVVV1djYqK2traura2Vl1Vla2V5KSkpubi6LxTIyMnJycuL9wA61tLSkpKSUlpbSaLR+/frp6OjY2toqKSnxeDj0jwMAAAAAtCfu/FKaQH4JAAAAANCepNRXBwAAAAAA0gHySwAAAAAAIEyQXwIAAAAAAGGC/BIAAAAAAAgT5JcAAAAAAECY5LveBfzn69evhw8fxh82Njbi2xEREbdv38Yfzpo1q021TgAAAAAAGQH1ifiQmZk5dOhQXvaMjY2dOnWqqOMBAAAAAJBA0D8OAAAAAACE6f8BhZQrAKthcbsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=885x262 at 0x10DC50668>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(superdense)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now create, execute the quantum circuits, and plot the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10db7ec50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuits = [\"superdense\"]\n",
    "\n",
    "backend = 'local_qasm_simulator' # run on simulator so we don't have to wait in the device queue\n",
    "shots = 1000 # the number of shots in the experiment \n",
    "Q_program.add_circuit('superdense',superdense)\n",
    "result = Q_program.execute(circuits, backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)\n",
    "\n",
    "plot_histogram(result.get_counts(\"superdense\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The state with the highest probability should match the message that Alice encoded earlier ($11$). Mathematically:\n",
    "- For a message of **00**: Bob received $|\\psi_{00}\\rangle = \\frac{1}{\\sqrt{2}}(|0_A 0_B\\rangle + |1_A 1_B\\rangle)$. Applying $CNOT$ gives: $\\frac{1}{\\sqrt{2}}(|0_A 0_B\\rangle + |1_A 0_B\\rangle)$. Applying $H$ on $q_A$ results in: $\\frac{1}{\\sqrt{2}}\\frac{1}{\\sqrt{2}}[(|0_A\\rangle + |1_A\\rangle)|0_B\\rangle + (|0_A\\rangle - |1_A\\rangle)|0_B\\rangle] = |0_A 0_B\\rangle$ \n",
    "- For a message of **01**: Bob received $|\\psi_{01}\\rangle = \\frac{1}{\\sqrt{2}}(|1_A 0_B\\rangle + |0_A 1_B\\rangle)$. Applying $CNOT$ gives: $\\frac{1}{\\sqrt{2}}(|0_A 1_B\\rangle)+ |1_A 1_B\\rangle$. Applying $H$ on $q_A$ results in: $\\frac{1}{\\sqrt{2}}\\frac{1}{\\sqrt{2}}[(|0_A\\rangle + |1_A\\rangle)|1_B\\rangle + (|0_A\\rangle - |1_A\\rangle)|1_B\\rangle + (|0_A\\rangle + |1_A\\rangle)|1_B\\rangle] = |0_A 1_B\\rangle$ \n",
    "- For a message of **10**: Bob received $|\\psi_{10}\\rangle = \\frac{1}{\\sqrt{2}}(|0_A 0_B\\rangle - |1_A 1_B\\rangle)$. Applying $CNOT$ gives: $\\frac{1}{\\sqrt{2}}(|0_A 0_B\\rangle - |1_A 0_B\\rangle)$. Applying $H$ on $q_A$ results in: $\\frac{1}{\\sqrt{2}}\\frac{1}{\\sqrt{2}}[(|0_A\\rangle + |1_A\\rangle)|0_B\\rangle - (|0_A\\rangle - |1_A\\rangle)|0_B\\rangle] = |1_A 0_B\\rangle$ \n",
    "- For a message of **11**: Bob received $|\\psi_{11}\\rangle = \\frac{1}{\\sqrt{2}}(- |1_A 0_B\\rangle + |0_A 1_B\\rangle $. Applying $CNOT$ gives: $\\frac{1}{\\sqrt{2}}(|0_A 1_B\\rangle - |1_A 1_B\\rangle)$. Applying $H$ on $q_A$ results in: $\\frac{1}{\\sqrt{2}}\\frac{1}{\\sqrt{2}}[(|0_A\\rangle + |1_A\\rangle)|1_B\\rangle - (|0_A\\rangle - |1_A\\rangle)|1_B\\rangle] = |1_A 1_B\\rangle$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h2>Version information</h2>\n",
       "<p>Please note that this tutorial is targeted to the <b>stable</b> version of the QISKit. The following versions of the packages are recommended:</p>\n",
       "<table>\n",
       "<tr><th>Package</th><th colspan=\"2\">Version</th></tr>\n",
       "<tr><td>QISKit</td><td> 0.4.10</td></tr>\n",
       "<tr><td>IBMQuantumExperience</td><td>&gt;= 1.8.26</td></tr>\n",
       "<tr><td>numpy</td><td>&gt;= 1.13, &lt; 1.14</td></tr>\n",
       "<tr><td>scipy</td><td>&gt;= 0.19, &lt; 0.20</td></tr>\n",
       "<tr><td>matplotlib</td><td>&gt;= 2.0, &lt; 2.1</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run \"../../version.ipynb\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}