Quantum Teleportation.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "<div class=\"container-fluid\" style=\"background: #1BA39C; margin: wide\">\n",
    "    <div style=\"text-align: center; padding: 50px\">\n",
    "        <img src=\"https://www.qubitbyqubit.org/prod/images/index/qubit_logo_singleQ_white%202.svg\" width=\"100px\" height=\"50px\">\n",
    "        <h1 style=\"color: white; text-align: center;\">Quantum Challenge Notebook 1</h1>\n",
    "        <h3 style=\"color:lightgrey\">Quantum Teleportation</h3>\n",
    "        <h4 style=\"color:lightgrey\">Anastasiia Andriievska | 2022</h4>\n",
    "    </div>\n",
    "</div>\n",
    "\n",
    "<!-- Note for future, it would be nice to put the QxQ logo in here via github cdn -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a3c302f5-e4fe-47c1-ae8e-69f16e3fce92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Libraries imported successfully!\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, Aer, execute\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.extensions import Initialize\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "print(\"Libraries imported successfully!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08f07cc1-befe-4ac1-a856-824361deeb05",
   "metadata": {},
   "source": [
    "# In this programming challenge we will code a Quantum Teleportation protocol!\n",
    "\n",
    "Before we get ahead of ourselves, let's clarify what we mean by *teleportation*.\n",
    "\n",
    "I'm sure that when I say teleportation, you may be thinking of something like this:\n",
    "\n",
    "<img src=\"https://media2.giphy.com/media/3o7TKLzBYFrRWcXk9q/200.gif\" width=\"200\" align=\"center\">\n",
    "\n",
    "But unfortunetly this is not a physical kind of teleportation, instead we are teleporting a *State* - which is more like teleporting information. So it's more along the lines of:\n",
    "\n",
    "<img src=\"https://hips.hearstapps.com/pop.h-cdn.co/assets/17/11/768x384/landscape-1489615804-teleportation-1.gif?resize=640:*\" width=\"200\" align=\"center\">\n",
    "\n",
    "*(That's schrodingers cat and it's representing a quantum state)* **If you're interested in where I got that gif, you should check out <a href=\"https://www.youtube.com/watch?v=DxQK1WDYI_k\">this video on teleportation by minute physics.</a>**\n",
    "\n",
    "\n",
    "\n",
    "### This challenge will have two sections: A <b>Learning Section</b> and a <b>Coding Section</b>\n",
    "\n",
    "Using our good friends Alice, Bob, and Charlie we will transfer the quantum state $|\\Psi \\rangle$ from Alice to Bob by only sending two classical bits of information.\n",
    "\n",
    "There are a few new `Qiskit` things we will need to learn for this challenge:\n",
    "\n",
    "1. Creating circuits with registers\n",
    "2. Classical-quantum conditional gates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "383c898b-630a-45b6-b391-56a4aefa99a3",
   "metadata": {
    "tags": []
   },
   "source": [
    "---\n",
    "<h2 style=\"text-align: center; color: darkblue\"> Learning Section</h2>\n",
    "\n",
    "---\n",
    "\n",
    "## 1. Using Registers\n",
    "\n",
    "In `Qiskit` a register is collection of either qubits or classical bits, these registers can then be used to create a normal `QuantumCircuit`. This is useful if we want to give specific labels or use more advanced gates like classical-quantum conditional gates. \n",
    "\n",
    "Here's an example:\n",
    "`QuantumRegister(3, name='quantum_register')` will create a quantum register of 3 qubits each with the label name `\"quantum_register\"`.\n",
    "\n",
    "<div class=\"alert alert-info\"><b><i>N.B.</i></b> There is some strange behaviour with what you can put in the labels, they have to be <b>lower case</b> and only quanutm registers can have <b>spaces</b>. Why is this the case? 🤷🏼‍♂️ That's qiskit for you! </div>\n",
    "\n",
    "#### Let's try out an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0578e3c5-bce7-45f7-8cd3-667ce949697a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 288.623x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(3,name='quantum_register')\n",
    "qc = QuantumCircuit(qr)\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ce72852-9497-4bbc-b804-5c16ad5ac81b",
   "metadata": {},
   "source": [
    "#### We can do the same thing with classical registers too!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "77d715c6-ddbe-419e-8d6a-c2a928fdcb1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288.623x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(3,name='quantum_register')\n",
    "cr = ClassicalRegister(3,name='classical_register')\n",
    "qc = QuantumCircuit(qr, cr)\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f641b7a9-f43b-49e8-a4c9-519cf855c234",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\"><b><i>N.B.</i></b> Notice that when a register is made with multiple bits at once, <b>Qiskit</b> enumerates all qubits on seperate lines and squashes all classical bits into a single line. This is perfectly normal behaviour!</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8347a52f-0bd9-4bbc-a674-4d02459ec85b",
   "metadata": {},
   "source": [
    "#### Sometimes we need each register to have a unique name\n",
    "To do this we need to make each register seperately:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d5016c29-e4f9-44f7-b96a-373a59c13d21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 207.714x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_a = QuantumRegister(1, name='quantum_a')\n",
    "q_b = QuantumRegister(1, name='quanutm_b')\n",
    "\n",
    "c_a = ClassicalRegister(1, name=\"classical_a\")\n",
    "c_b = ClassicalRegister(1, name=\"classical_b\")\n",
    "qc = QuantumCircuit(q_a, q_b, c_a, c_b)\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d169be0f-e1b8-42b3-8f10-a3f380439903",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 2. Using Classical-Quantum Conditional Gates\n",
    "\n",
    "In order to complete the teleportation, Bob needs to apply different gates to his qubit depending on which classical bits Alice sends.\n",
    "\n",
    "We can build this into our circuit with a classical-quantum conditional gate. As the name suggests, these quantum gates are controlled by the classical registers. Think of them as operating with the logic:\n",
    "\n",
    "```\n",
    "if classical_0 == 1:\n",
    "    apply X gate\n",
    "```\n",
    "\n",
    "In `Qiskit` classical-quantum conditional gates use the syntax: \n",
    "`QuantumCircuit.A(B).c_if(C, D)`\n",
    "\n",
    "Where:\n",
    "\n",
    "- A = gate type\n",
    "- B = target qubit\n",
    "- C = classical control register\n",
    "- D = desired activation value\n",
    "\n",
    "That's a little confusing so lets look at an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "797b6c3d-0e73-4159-b790-84e74164488e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.652x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First we make our registers\n",
    "q_0 = QuantumRegister(1, name='q0')\n",
    "q_1 = QuantumRegister(1, name='q1')\n",
    "c_0 = ClassicalRegister(1, name='c0')\n",
    "c_1 = ClassicalRegister(1, name='c1')\n",
    "# Next we make a quantum circuit\n",
    "qc = QuantumCircuit(q_0, q_1, c_0, c_1)\n",
    "# Now we apply the classical-quantum conditional gate\n",
    "qc.x(0).c_if(c_0, 1)\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f24de4bc-c5be-42a2-9193-78d6f0ab82cf",
   "metadata": {},
   "source": [
    "In this circuit, we created 2 quantum registers and 2 classical registers. We then created added an X gate to qubit `0` and made it conditional on the classical register `c_0` being in the `1` state.\n",
    "\n",
    "<div class=\"alert alert-info\"><b><i>N.B.</i></b> Notice that the variable names and the labels are different. This is to make it clear that we are passing the <b>variable name</b> into our conditional gate and not the <b>label name</b></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eac930d-b3f9-48c0-8bb7-2082c9a6551b",
   "metadata": {},
   "source": [
    "---\n",
    "<h2 style=\"text-align: center; color: darkblue\"> The Protocol</h2>\n",
    "\n",
    "---\n",
    "In this experiment we are going to imagine we have three people, Alice, Bob, and Charlie. Alice has a state $|\\Psi \\rangle$ that she wants to send to Bob. In order to help send her state, Charlie provides Alice and Bob each with an entangled pair of qubits. In the experiement, Alice initially has qubit $Q_0$ (this qubit is in the state $|\\Psi\\rangle$ that she wants to send Bob), and Charlie distributes $Q_1$ and $Q_2$ to Alice and Bob respectively. \n",
    "\n",
    "Using teleportation we can show the state $|\\Psi \\rangle$ (which is stored on Alice's Qubit $Q_0$) is teleported from qubit $Q_0$ to qubit $Q_2$ on the same circuit. Unlike a swap operation, $Q_2$ and $Q_0$ never have a quantum gate directly connecting them - the only information transfered are two classical bits through the $C_0$ and $C_1$ registers.\n",
    "\n",
    "Confused? Let me clarify:\n",
    "\n",
    "Alice starts with $Q_0$,\n",
    "\n",
    "Charlie creates and entagled pair: $Q_1$ and $Q_2$\n",
    "\n",
    "Charlie then distritbutes $Q_1$ to Alice and $Q_2$ to Bob\n",
    "\n",
    "At this point our teleportation circuit is prepared!\n",
    "\n",
    "In order for Alice to send the state $|\\Psi \\rangle$ of $Q_0$, she only needs to send two classical bits of data to Bob and Bob will be able to completely recreate the state $|\\Psi \\rangle$ on his $Q_2$!\n",
    "\n",
    "Amazing! But there's two more key parts we need to figure out: Alice needs to know what two classical bits to send to Bob, and Bob needs to know how to interpret those classical bits as intructions to recreate $|\\Psi \\rangle$.\n",
    "\n",
    "# Alice, Bob, and Charlie steps:\n",
    "\n",
    "Charlie needs to make an entangled pair - we are going to create the $|\\beta_{00}\\rangle$ state between the $q_1$ and $q_2$ qubits, where:\n",
    "\n",
    "$$\n",
    "| \\beta_{00} \\rangle = \\frac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle\n",
    "$$\n",
    "\n",
    "Alice is now going to apply a CNOT gate with $Q_0$ as control and $Q_1$ as target as well as a hadamard to $Q_0$.\n",
    "\n",
    "Then Alice will measure the $Q_0$ and $Q_1$ qubits and send the classical values to Bob via the classical register.\n",
    "\n",
    "Now with only two bits of classical information, Bob can completely recreate the state of $| \\Psi \\rangle$ on his end!\n",
    "\n",
    "To do this he can follow the following format:\n",
    "\n",
    "**If the first classical bit is 1, Bob applies a Z gate, if the second classical bit is 1 he applies an X gate.**\n",
    "\n",
    "00 = Nothing\n",
    "\n",
    "01 = $X$ gate\n",
    "\n",
    "10 = $Z$ gate\n",
    "\n",
    "11 = $Z$ and $X$ gate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c94edc55-6897-4789-9906-dfb6e99fbe86",
   "metadata": {
    "tags": []
   },
   "source": [
    "---\n",
    "<h2 style=\"text-align: center; color: darkblue\"> Coding Section</h2>\n",
    "\n",
    "---\n",
    "\n",
    "## Here are all the necessary functions:\n",
    "1. A function that creates the registers and places them into a circuit\n",
    "2. A function that initializes a given State that Alice wants to send (we've completed this for you)\n",
    "3. A function that creates a bell pair\n",
    "4. A function that prepares Alices gate\n",
    "5. A function that measures Alices qubits and places their output on the classical register (this is to mimic sending them along a classical line)\n",
    "6. A function that applies gates on Bobs qubit depending on the output of the classical register.\n",
    "\n",
    "---\n",
    "\n",
    "As you go through, try to keep all arguments and returns the same so as to avoid bugs!\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a19bc8bd-9a36-4c4c-a13b-17a4cd9f5078",
   "metadata": {},
   "source": [
    "## Crash course on functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8058e9c-f696-4909-bbf1-a9b1edad73fe",
   "metadata": {},
   "source": [
    "In the course we learned how to use pre-created functions. To implement teleportation we need to level up, and learn how to create our own functions! Learning how to create functions makes your code easier to read and edit, as you will see. \n",
    "We use the `def` keyword to create functions. The syntax for creating your own functions is as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "544ba03f-e917-4067-a106-16b38d873539",
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_function_name(input1,input2):\n",
    "    # Function code goes here\n",
    "    return  # variable names go here\n",
    "## return is an optional statement we use to allow our functions to produce outputs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3189b37a-84e2-467c-bbe2-674fde9e44d4",
   "metadata": {},
   "source": [
    "As an example, suppose you wanted to create a function to multiply two numbers. You want the function to return the result of multiplying the two numbers. You would first create this function as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "36aa23ea-e891-4ccc-b834-badd701ba361",
   "metadata": {},
   "outputs": [],
   "source": [
    "def multiply_two_numbers(num1, num2):  # Using the def keyword to create the function, and naming it multiply_two_numbers.\n",
    "    # It has two inputs – the two numbers num1 and num2.\n",
    "    ans = num1*num2  # Calculating the answer when the two numbers are multiplied.\n",
    "    return ans  # Returning the answer."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4165d108-4d16-464b-ac8f-86ed5459feeb",
   "metadata": {},
   "source": [
    "Next, we can use or call this function as shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2d30ade1-6f5a-4d37-a92e-43b5ef9aacac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "950\n"
     ]
    }
   ],
   "source": [
    "num1 = 25\n",
    "num2 = 38\n",
    "result = multiply_two_numbers(num1,num2)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5252676-ca3d-40e2-980d-85542b2aa55f",
   "metadata": {},
   "source": [
    "As you can see, we get the result of multiplying the two numbers! \n",
    "\n",
    "Now, the function we just created above is a VERY roundabout way of doing the very simple task of multiplying two numbers. However, as we will see in this notebook, we can create functions to do actually useful tasks as we implement quantum teleportation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdd0d738-11e5-41dd-97ab-7f94cb77a2dc",
   "metadata": {},
   "source": [
    "Now, let's implement all the functions required for Teleportation:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d9f7729-0b9a-49a8-86d0-3f6976255cfc",
   "metadata": {},
   "source": [
    "## 1. Create the registers and circuit\n",
    "Using the walkthrough in the learning section, create a `QuantumCircuit` called `qc` with the following registers:\n",
    "1. A QuantumRegister with variable name `alice_0` with a single qubit and the `name=` keyword argument set to `\"alice_0\"`.\n",
    "2. A QuantumRegister with variable name `alice_1` with a single qubit and the `name=` keyword argument set to `\"alice_1\"`.\n",
    "3. A QuantumRegister with variable name `bob` with a single qubit and the `name=` keyword argument set to `\"bob\"`.\n",
    "4. A ClassicalRegister with variable name `c_0` with a single bit and the `name=` keyword argument set to `\"c_0\"`.\n",
    "4. A ClassicalRegister with variable name `c_1` with a single bit and the `name=` keyword argument set to `\"c_1\"`.\n",
    "\n",
    "<div class=\"alert alert-danger\"><b><i>🚨</i></b> The variable names and <code>name=</code> keyword argument of the classical registers must be <code>c_0</code> and <code>c_1</code> and also passed into the return tuple!</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1a3683b7-e213-4d65-8280-7b0a1487fd07",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_registers_and_circuit():\n",
    "    # First we make our registers\n",
    "    alice_0 = QuantumRegister(1, name='alice_0')\n",
    "    alice_1 = QuantumRegister(1, name='alice_1')\n",
    "    bob = QuantumRegister(1, name='bob')\n",
    "    c_0 = ClassicalRegister(1, name='c_0')\n",
    "    c_1 = ClassicalRegister(1, name='c_1')\n",
    "    # Next we make a quantum circuit.\n",
    "    qc = QuantumCircuit(alice_0, alice_1, bob, c_0, c_1)\n",
    "    return (qc, c_0, c_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e65ac66-1d38-445d-99ae-ee3327f7d43b",
   "metadata": {},
   "source": [
    "## 2. Alice Initializes the Psi state\n",
    "This is unusual, but we are essentially making a function that hard-codes a quanutum state because we are using a simulator we can bend the rules a little bit! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "03547730-90d7-45da-b8b0-c5470ca499aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def alice_initialise_psi(psi):\n",
    "    # First we make our state Psi into a initialisation gate.\n",
    "    init_gate = Initialize(psi)\n",
    "    init_gate.label = \"Alice's State\"\n",
    "\n",
    "    # Alice's Makes a State to send to Bob.\n",
    "    qc.append(init_gate, [0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cf1f599-d522-4ee4-af58-7f53703bec83",
   "metadata": {},
   "source": [
    "## 3. Create a Bell pair\n",
    "Create a $|\\beta_{00}\\rangle$ bell state between `qubit_one` and `qubit_two`. \n",
    "\n",
    "**Do not return anything! The qc object that is passed in will be altered by the function.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "53eabb6e-369b-4608-a1af-1707848c2311",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_bell_pair(qc, qubit_one, qubit_two):\n",
    "    qc.h(qubit_one)\n",
    "    qc.cx(qubit_one, qubit_two)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8f43beb-6086-47b6-8555-983774dfe877",
   "metadata": {},
   "source": [
    "## 4. Prepare Alices Qubits\n",
    "\n",
    "\n",
    "Apply a **CNOT** gate to the `QuantumCircuit` with `qubit_zero` as the control and `qubit_one` as the target.\n",
    "\n",
    "Next, apply an H gate to Alice's `qubit_zero`.\n",
    "\n",
    "**Do not return anything! The qc object that is passed in will be altered by the function.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3173b9df-c033-4fd6-9bae-891f4e0365d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def alice_gates(qc, qubit_zero, qubit_one):\n",
    "    qc.cx(qubit_zero, qubit_one)\n",
    "    qc.h(qubit_zero)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b917e33c-f40a-4951-8105-6ec86d6ad0cc",
   "metadata": {},
   "source": [
    "## 5. Measure Alices qubits and Send the Results on the Classical Register\n",
    "\n",
    "Now Alice needs to measure her qubits and send the results over to Bob via the Classical channel\n",
    "\n",
    "1. Measure qubit 0 to the classical bit 0 \n",
    "2. Measure qubit 1 to the classical bit 1\n",
    "\n",
    "**Do not return anything! The qc object that is passed in will be altered by the function.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9874dca4-c3d4-4fbf-bf4d-e6e6e70cdb17",
   "metadata": {},
   "outputs": [],
   "source": [
    "def measure_and_send(qc, qubit_zero, qubit_one, classical_zero, classical_one):\n",
    "    \"\"\"Measures qubits 0 & 1 and 'sends' the results to Bob\"\"\"\n",
    "    qc.measure(qubit_zero, classical_zero)\n",
    "    qc.measure(qubit_one, classical_one)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "445aff81-2b4f-49fa-a96d-54a1b3082d81",
   "metadata": {},
   "source": [
    "## 6. Apply gates to Bob's Qubits\n",
    "\n",
    "This is when we have to use the classical-conditional quantum gates described in the learning section above.\n",
    "\n",
    "1. Apply a classical-conditional gate with:\n",
    "- gate type = Z\n",
    "- target qubit = qubit_two\n",
    "- classical control register = crz\n",
    "- desired activation value = 1\n",
    "\n",
    "2. Apply a classical-conditional gate with:\n",
    "- gate type = X\n",
    "- target qubit = qubit_two\n",
    "- classical control register = crx\n",
    "- desired activation value = 1\n",
    "\n",
    "**Do not return anything! The qc object that is passed in will be altered by the function.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4b16618a-bbd9-46bd-bcc2-e307c95706ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bob_gates(qc, qubit_two, crz, crx):\n",
    "    qc.z(qubit_two).c_if(crz, 1)\n",
    "    qc.x(qubit_two).c_if(crx, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54b4c196-b2a5-48f3-88cd-a885eb8de424",
   "metadata": {},
   "source": [
    "# Test your Teleportation Sequence!\n",
    "Now that you have completed each step of the protocol as a function, we can test it out by trying to have Alice send the $| \\Psi \\rangle$ state that we've created for you:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9b946a84-664e-4fbc-b991-b3982c79b6e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "psi = np.array([0.5533920757991503+0.3043529040180291j, 0.6147796854942953+0.4724113234904887j])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9aac821-f092-40e7-a1f2-a986399475cf",
   "metadata": {},
   "source": [
    "Let's visualize Alice's statevector on a Bloch sphere!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e025dc2e-9747-4b65-a46b-e06bd49ba4f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "psi_s = Statevector(psi)\n",
    "display(psi_s.draw(output = 'bloch', title=\"Psi State\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b3132ff-0020-4cb4-8e94-2352ae3dabaf",
   "metadata": {
    "tags": []
   },
   "source": [
    "We are going to run this on the `statevector_simulator` because it allows us to take `snapshots` which are like a view into the statevector at any moment along the circuit.\n",
    "\n",
    "## 1. Create the Circuit\n",
    "Each of the registers should be named including two sepereate classical registers.\n",
    "\n",
    "The `snapshots` should look like a vertical gray bar. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "00763de9-b412-490f-92fb-7cf6b4b1686b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1095.95x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make sure you return the QuantumCircuit and both classical registers as a tuple!\n",
    "# e.g. return (qc, c_0, c_1)\n",
    "qc, c_0, c_1 = create_registers_and_circuit()\n",
    "\n",
    "# Alice intializes a quantum state\n",
    "alice_initialise_psi(psi)\n",
    "\n",
    "# Use a snapshot to record the initial statevector (this is for checking after)\n",
    "qc.snapshot('1')\n",
    "\n",
    "# Charlie creates the Bell pair\n",
    "create_bell_pair(qc, 1, 2)\n",
    "qc.barrier()\n",
    "\n",
    "# Alice does gate prep\n",
    "alice_gates(qc, 0, 1)\n",
    "qc.barrier()\n",
    "\n",
    "# Alice measures her state and sends to Bob\n",
    "measure_and_send(qc, 0, 1, 0, 1)\n",
    "qc.barrier()\n",
    "\n",
    "# Bob decodes the classical bits and re-creates Psi\n",
    "bob_gates(qc, 2, c_0, c_1)\n",
    "\n",
    "# Use snapshot to record the final statevector  (this is for checking after)\n",
    "qc.snapshot('2')  \n",
    "\n",
    "# Draw it!\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "037132df-648f-402d-ac9b-3ae2e0c90293",
   "metadata": {},
   "source": [
    "## 2. Run it on the Statevector Simulator\n",
    "Like normal, we will run our circuit on a simulator and pull the results out of the return object.\n",
    "\n",
    "<div class=\"alert alert-info\"><b><i>N.B.</i></b>\n",
    "    Notice that we are not calling <code>get counts</code> here, instead we are going to read the snapshots and directly check if the state has been teleported across the circuit!\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5c856502-915e-46da-b41e-221ba5725c64",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Execute the circuit on the simulated backend.\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result = execute(qc, backend).result()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2983988-2d9b-4cfa-9464-8601813c0dba",
   "metadata": {},
   "source": [
    "## 3. Check if it's Worked!\n",
    "\n",
    "We made a function called `check_same_state`, by passing the simulation `result` object, it can pull out the statevectors from the snapshots!\n",
    "\n",
    "It will tell you Alice's and Bob's state and check if they are close enough to be the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6875a0a1-7730-4aea-a403-07b268d2c85c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Alice's state: 0.5534+0.3044j 0.6148+0.4724j\n"
     ]
    },
    {
     "data": {
      "image/png": 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ao0GjVqNer0ee1w8Csvk8g0NDDAwPs2PHDvbt27dhsDcZa+nWrvrkBq4P9Xqd+elpSktLtBwn8npCCEzDWL7olUf0fD/0hL4PhkEqkSCdSmHbdtgipoyy88uSQUCpXMYPAgaLRTAMhJRUazUajQaWaXLuwgUuX75MPpulMDhIJpXCTqVIpVJYVnjv9jyPRqOB4zg0m01mZmZwg4BDhw7x8KOPkkgkPsJP745E17vchnF+RGg6DrNTU8zNzEReKZVMkrRtEpaFZVmYpolpGBjqR0qJ7/uRsfq+j9Ns4jSbBMoLppJJUskkwliZ22s1m5QqFXKZDKlUKtyGlFy+dIlTp0/jNBrs3LmTHTt2kMlkwrA6Flq7rosfBASxH9/38YKASqXC1NWrOM0mO3bs4MGHH2Zy82ZS6fSGR10/Nozzo4SUEsdxqCwtUS2VWFpcDL2VZZHP58mm0yQSCRKW1XYx+0EQJXV8Xw0DEyLyomrjNJU3cz0PAWQzGZLJJEJKEAIpJaVKBbfVYnBgACEEs7OzvPHGG2QyGYZHRxkaHianjFLT/nQoa5ompmmG+43vGyIjdT2P+YUFzp07hx8E7N27l4GBAYZGRxkZHSWfz2Pb9kfwaX/ssWGcNxtSSprNJpVKhfLCAq7jIIMA13VpeR5p2yaXzeIFAZ7nLf8ob6UNwzDNMEyVEtM0MQwDQSjKZZgmCcsKQ1ohcD0vTPj4PgnLIpfNhqGulMwtLGAnEiQSCd57912mZ2e55+BBCsUi1WoVz/cZKBYjr22ZJpZlYRhGZKxC7duXksD3EbDCM/pBwFtvvcXUzAwH9u9HmCZCCLLZLCNjY4yMjVEoFDY8am9sGOfNgud51Ot1youLOLUango7W60WS+UyrVYLK5EIw0/Ci1v/tkwzWgtKWA4hlTEEy8ODQuhyCWBZFknbJplMEkiJ73kIwyCjQstSpUK5XOb4sWOMjIywa/fu0ABNEyklru8zMjS0LG2i96M8ddBxbegwW6rXiNhvAZw+c4ZTJ0/y6KFDZHM5qvU69XodO5WiODjI+MQEQ0NDG2vUldgwzhsNx3Eol8vUSiUqS0u0ms0wRJQSwzBwHAfLsijkcmGCxTQxLSv8rX6klGFo2uFVPLXWFLoson4Hvk/LdWk2m7jqd0CY/HE9D7fVIlDlk+mpKTzX5e59+xgcHCRp21ESyfM8KrUa+UyGRCIRekghwpDWMKI17KoG2v4EGAZT167x+tGjPPHYY4yMjhIEAbV6nUq1SiAl2UKB8YkJJiYmNsgPy9gwzhuFRqNBuVxmamqKyvw8fhBgWxamYZBKpUinUpHnyedyXdddOrvqqlAR9bd+XHa0fsHyWk/GvKrv+7RaLZxWC7fVotFsMjM3x4ULFwiAPbt2MVAokM1mSdl2ZIRBEFCqVEilUqS6HZ8yUgChbybKaA1YsQ6NY2pqijffeIPPfO5z4TpYPd5sNilXKjRdl8HRUSYnJzc8aYgN4/ywaDQaLCwsMDs7S2lxEUtK0qkUuUyGdDpNKp3GMk3cVotSpYJt22QzmSj860QQBPg9jFB7yfjaVH8ZuuwCYKr1nZQSt9lkfmGBk6dOsW3bNk588AEP338/QRAgVHInnU6TzWTIZjIslUokLIt8LheF1L4iPXgqSRQEAZ66IcThB0G4TrWs8Makj0M9//bbb9NoNHj00Uej9+iyT7PZZLFUIplOMzQywtDQEIVC4ZNspBvGeb3wPI/p6Wmmp6epVavYUlLI5ykWCqTT6bbXyiBgqVRCSkmxWFw1CaINTid/XN/Hc92QA6sztYRJIiuRCMNh7b0MA9M0oxqk5/tMT03xwZkzPPTQQ2TTaf7km9/kuc9+lpbrgmEQKEKC53lI5T1T6TSTIyOYqqbZRmoAAiFCIoQ2XGWsvu/TVGE8AEJgWVZUFkIInv/2t9m1cyfbd+5ccfUJoFKr4UtJJpdjYGiIYrFIPp//JCaOup7wBkNoFUgpmZqa4vKlSzi1GulEgolikUKxiB2/y6vyhRCCSr1OoIy350UmBDIIaLoufswzQng3NA2DZDJJQhmkoULRuMf0fZ9arRYanhBcuXyZK5cv8+lnn41CTlMICoUCVfW6dDbL8PAwTqNB3XFYWFhgaXGRVrNJLptlsFAgoUJcqc7LkBIpBMI0MUwTgCShl02nUmFJxXXxVGml0WhE53jPvffy2quvMjA0tKxfpJyBBHLZLI6iJFZKJarDwwyNjFAsFqO67CcZG8bZA+VymZMnTtCoVEglEmweH2ewUEAocgAs3+508sRR1Lt0KhXWCLvA9TxarVbUISKlxLKsMGGUSEThYdystTfTYaNm6wAkUylOvP8+5XKZT3/mMySTSZaWlrBjyZZcLkejXqfhOEgpyWYyZLJZ0uk05XIZ0zCoNRpUq1Uy6TSDyjhkLBPbK8IyldGmCA0uUKUh1/MwDIMdO3fy+uuv88ihQySTSZKJBKZhRCFZyraxCgXKitRQXlpiaGSEkbExBlR99pOKDePsQBAEXLp0iQvnzpEAtk5OMjw4GD6nyAHdan0ADcdBqKQQsdf4vk+z1aLZbEYXeTKZJK0pcqqWqPevoT2lEdtOpVolCAKSqRSpZJJXX30VKSWHDx/GNAxc5YH1+k0bdDqTQRgGddXJks/nsUyTZDJJMZ9nMAgoV6tUq1UuT0+TSiQYGBggl8lgCEGwfFBRxlZDxH4bpoltWeHNQUry+/dz9epVSktL5AsFGo4TPZ8wTYRhYCUS5PN5qFZxGg3mpqZYWlxky9atjE1M9LzR3enYMM4YHMfh1MmTLM3Pk0+n2b5lCwnbXi7IQ9fEDkCz1cL3fTKZTJQNdZpNWupxCA0mmUxGrCAZa+3qRHxfUh2bNv58LodlWbzx5pv4vs9TTz4ZeW9PdaqY6hh0GUbfNIQQVOt1avV6VMrwpcSybYYHBykWClSqVSqVCjOzs8ybJsVikWwmEyV0AnXTiDjB8eOOfz5CYFoWB+6+m3PnzvHEU0+FN6lWi1a1imEYYXlHhfD5XI5ypYLn+xiuy9nTpymXy+zas+cTmSzaME5CbzU7O8uFM2fwHIfJ4WEmxsejtaGhLvRukGq92VBhJlJSqVQiD2ZZFplMhqRtr/C2QtHkPLXtyFB1mUIlY6q1Gr7vYycSZLJZDCF4//33KS0tcfiZZ9p4ta7vh2vD2GMiRv+zbZtMEIQeVEUCUS8oYUa1WChQyOep1GpUKhXm5+eZX1igWCiQy+Wiz8LQ3S+sNNJo38CWrVs5rkLvocFB0qlUWKNttWiom46mMmYzGWr1Oq1Wi3Qmw8y1a1RKJfYdPBh6108QPvHG6TgOF86fp7K4iOH7bNuyJcqyBr4fGmaX9ZYOOYUQuK5LrVaLvKEhxMqukVinSSe0lzMAHyKP2Ww2qTcaICXZbJakStacP3uWixcv8uyzz0adIxraiFccr9q3EIJUKoUfBDiOE66R0+m2tjPtGQu5HIVcjlq9zlKpxPzCAnMLCwwNDpLNZPC1QcbOr5uRmobB3r17OXXyJI8//viyx0wk8BWTqtls0nJdZBCQTCZptlo4jkMmnabRaPDOG2+wd98+xiYm+vhW7wx8oo1zaWmJC+fOETSbZGybosoUam9idDEoHSLqC9BxHGbn53Fdl0HlFexEom2NJjq2ET2lfgvFp/WDAFSSqFav4yraX8SXBa5du8bxEyd45pln2jKaEsKSh0owdUIAMua5M+l05OVTrtu2LUPdZKLXZjLYySSVSoWlpSXm5+epVKsMDQ1hW1a0Do0fi16naiL+jh07OHniBJVymbxSlxdCYAmBqTprNE9YJ7v8IKDRaJDN5ahUKpw+cYJquczWHTuirPKdjE+shtDi4iIXz5zBDgIGcjnyuVxY/lDPt2VLITIuoUjlTrPJ4tISZZWgGRoaopDLYSUSBMoIeiWO4ojvT6iLvFQu47ZaZDIZ8rlcZJgLi4scPXqUJ594glwu13Z8AqJyTDfj7DwnIQSZTIaEZVGrVleMANTH7alSiVTr6YmJCQaLRbxWi2tXr7JYKnUN+aOQmdDIhBDs2rWrqyq9EALDMLAti2KhEK1vgyCg1mjQbDbD7pkgYHpqitPvv0+tWl31c70T8Ik0zvn5eS6fPYstBIOqK6NQKCxnBTu8gFS8UQg95eLSEtV6PSwhpFJkFEMoKj30WH9F24sZbxzNVotKtYppGAwMDIThpvJilUqFl44c4ZFDhxgcGmp7n1DH6ymObr/ZTSEEuVwOQwhq9XrEmQ2kjIgG+nU61DYMg+LAAJOTk+SyWSrlMlempsLwuwf02nTL1q1cvXYtKiG1xRI6Mw0kbJtCPk9BrTHnFxZoui7JRALXdXEaDc6dPs3SwkJf5/lxxSfOOGdnZrh67hy2EExOTOD6fpgttKwoewosd14IgRQiNMpSiWqthmGaFBVDKPD9iMS+mo+UxMLYLiGu4zjhtoWgkM9jqYyu9iBHjhzh4IEDYaIqvt3YRe6pY1kNnXsWhkEqk0EGAYuqgybw/eVIge7eP5FIMDo6ytjoKJZhMDs3x8zsbOS9uyGbzZLNZllYWAiPWzGOpEqESYjKSoYQJG2b8dFRkskkpXI5zPK6blivDQIunTvH9NWrq57vxxmfKOOcmZ5m+sIFbNNk8+bNtFotkDJcf6E8pGLEaE/RarUoLS2FhqMymUXFA9XKAbZtr2qYGrqg34l6o0G1ViOhPLjRYWBvv/02o6Oj7Ny1q42/Gl/naVqd7nSJPL5m5MSM2FdUvIg/6/tkslmkWuN1O27dI9qJTCbD5MQEA8UizVaLK9PTlHqEugCbN23i6rVrbY9por821mi/ihI4WCySjpEqSuUytUYDhGD66lWuXrzYdV8fd3xijHNmZobpS5dI2jabJycxDINmq4Vt25imudw3qUJTqaQ4yqoep7m0iUQiutBbap3WqwbX5i17PF+tViMBrlwut8JLXbp4kYX5eR64//7osWidGnutr7yd9px6/RroWqryVLpsog1bJ70syyKdTuN6Hs1Wa8WxagPtdh6GYTA4MMCmiQkytk2pXGZqZqarF920aRNTMePsNPdIDkUdqyAkbNiqFDVQKGAYBuVSKZJ7mZuZYW56usuRfbzxiTDOmZkZrl28SCaRYHJiIsyMKjJ3IpEIDROi0kiz1WKpVKLleWTTaQaKRWzbbvNUglCjJ2qY7kCvdaVGICXlchmn1SKjOkU6DbNarfL222/z6GOPRcT0tn3E/q+7W7ody2oQsVJRSrF26vV6G/E+/trVzimRSDA+Ps7I8DCB73O1y1q0oMpU5XI5WmMun5BsZ0ip8wqCIIpuXM+jkM9jmCbNZpNarYaUkmtXrlDqMrn744w73jir1SpTFy+StW3GJyaizKdOSpiqFKCbmivVKpVqNVxXqq4TwzDCC1hfnKouqUPaTkhWTwp5QUC5VMLzPPK53IrOFgg9yKuvvMLd+/f3HCcfDzN95aUMY+2vtJPFE60vhSCrssPVWm0lc0mH+x3c307kcjnGx8awLYvZuTkWO4b6bt60iat6rahrpD3qydGuDYOESgiZpomdSJBOp/F9n3KlQqvV4vL589Tr9TXP/+OCO9o4Pc/jyvnzWMD42Fh04Ur1HOoLhzBTurS0RMt1yabTFBX3VIemnQkf13WRUrYV/PVrV7twPd+nUi4TQJsAViex/NixYyRTKXbv2tXXufpqvdkvUVzEbjSw3NxtGEY4KrDH+jO2gSiT3A3JZJLxsbEoozs1PR2FuZObNjHdGYZqmuFq27TtsEFdffamaUY14FqtRrVa5ezJk3eMgd7Rxnnt0iVcx2FsdDRMlMSe050fvud19ZbxxIsg/KDiF77uxYz6IGOv7QUtKSmBQj7ftlaNH9v01BSXLl3ikUce6cnl7UzO+EGwrpC2c90a31oikSCVSoWsndi6set6cxVjMi2L0ZERhgYHcT2Pq9PTOI7D4OAg5Y6kUZy/3JkQi7an9I90A4FmY2m1iWazSblc5oP336d+B9RB71jjnJ+epjY/T7FL2KgV7lzXZaGLt4TuxtaZgDFFu5jzaobpBwGVcjkyzLaSRyxB4zgOrx89yqFHHllVVjJuDlq+RJdddDZWolTzOhg8cUQSKR3Pp9JpLMuiphqie0KVe1ZDoVBgfHQUyzSZmp2lWquRzeUol8vh8Xccn4hRIzuRSiajyEdTBwMpo3qz7/ssLi3x/rvvfuyJCnckfa9WKrFw7RqGZTGo2r3iXFgpJY1Gg1q9TkGVRlYzSmKPaQNwfT96z1qBZCBlGMpKudIw9bYVyf7o66+zbetWCsViKN6lMq1atkQfY6CyrhBmjeuNBr7nhZ0rhEYpgXIsSRLVblnWKtIN0sIwSFhWSBgwDAwhsJNJWiqqKObzq8pirBaOAqRSKSbHxphbWKBUKmGnUiwuLlIoFqPzattex+enDTWRSCAIlyGdCSpLhbm1ep1ytcp7b7/Nwfvvb2NTfZxwxxmnW6sxd+UKru+zeXIySjZEzcqKbeN5HknbDnsq+zBMOp6Tvo/Zh3qcNkxfhmJfplK+03NQvCAI1RB8n5mZGUrlMvvuvptqrRbuRy73dGpFBAEYlrXsOQDb86JkTtQcrTzKirporA6qFeV9lSBDDT+KUwKr1SpNx8FOJKJQ3jSMUJ1eSacguo+EiMO0LMbHxigtLTGdTnPpyhUmJyd70g3D0xNhY0DM8A3DCGVXgqDNawvDQAYB2UyGhuNQr9U4/vbbHLj3XnKKz/txwh1lnH6jwYJK3492qLoJIcJmZdUvmM/nMS2LplIuWCsD2bYfzwt1fVZZ4wVS4roupVIp2ke1Wl3hXfToBSMIOH3qFPc/8ECkoxMZY0d417kN3QmSiYXvUVP3GnIfOqGVy2ajz0t7ahkEoVqCEHi+j2VZEdfWVUYcZXrjoyRE2MfZK0FVKBYZHx/n2LFjTM/OMjo8vKYyvB5lqMP3hPru2gxbrUEload2XZdqrcbxd97h7nvvpdAr632b4o4xTr9ep1mtUiqXSafT5PL5Ns0dz/MoVypRaGkphk9N9UqudveOQ693pGFEF1Tg+yHjRmkBua6L7/s06nVczyObzbbNQtHSHmbsrv/2O+8wOjrK5k2b1n3ugbpgrwtdEkLaW2EYWMDgwADlSgXDMMgpY9ddMFqtT09Fc7UHVjANAys2C0YvC8ZHR3ldheDTc3OMj4ysaaCCZeJHNpOJ9tW1T1YI0uk09XqdSq3G++++y9333ENRaxl9DHBHGKffbOI5DuVKBT8IGB4cjEgFsEwoNxTDxLIsfN8nmUy2rT3X8py6O8X1PALfD1XvPC/6GyVBqVXxEskkw8PDa4pVlctlzp47x+c++9nrO39Fprge9FN6sSyLZDKJ02y28YijeSod+47fqDzPw2m1IJZhTVgWpmVhJxJhc3WjwczcHCMjI101dDWCIKDVbGInk9iWFW2/17mbhkEmm6Ver1Ot1Th1/Dj3Pfzwx0bM+mOfrQ18H69eD0silUrYBmXb0Yk5jkOlUsFSvFjLspbrkSKc5+F5XtRD2Aue8oTlSoUFNZTIaTTC5mDVRTEwNMTQwEC0BtNK72vhzTff5MD+/V3JCGuev2LVXK/n7Ozz7IV0Oo0hBI0+aoimiirS6TS5XI6CEhOzbTvU9fU8GvU62WyWubk58qquOjMzs+r3UFP7zqqeWaArkymCCrEz6TSmYVCuVDjx3ns9eb+3Gz7WnjMIArxqFaSMtGfGBwaixERVNe7aSkBKe4l4TS1p2zRtm3qjga3U72A5fNVKeZoep8O0TDodtjR1XNgNNcMyk073dYe+dPkyLddlV59kg871ps50Xq8Ilk4wraFfHKo7ZDJUq1VarttVbaHLwS7PdVE1StRnEqjEjZb2zGazLCwucvHKFUaHh1dktZtKrTCjGFsACcvCdd0wZ9Bj/6iyWSabpV6rMTc3x9lTp9hz991rH/8txsfbOBsNpOo7rFQq4Rg8xSIpVyo0Wy1SyWTb2PRuDJ5cJsNSuUypUiGdSkWhqmbNmJZFJka+9n0/7MTvMEztEexkMpwaDVEo1w2e5/HOO+/w6KOP9hVedttKELtpXC/WyrJqpGwbxzSjUYZGl2PWWeBANVjrElHnZ6WZSK1Wi3wuh+d52LYdNijMztJwHLJqjgtS0nTdKLzWsCwL1/NC9fnVzl8lijLpNPVGg/MXLpAtFJi8jvX9R4mPbVjrOw6+Ip6Xy+VwnJ1a7Ou7ezaTaev0iBQNOr2PooKVFc3McZxIbGpgYIBiPh9q0apkhmSlMQRBQFUnTbLZ6PGoDNIl63rs+HEmJiYYHh7u76S7GLluiL7usFbzZdfwnBrZTAaplCCWD0vJZer+zFiSRkCb1m8cmoUEoaFls1m2bdvGQKFAo9GIWulmFxaioVDxkDShykndwtS2valjMUyTTCaDaRicPH6cmipX3a74WBqn7/v49TpCiHBallprJm07Um7LZTJt4U6nMLMkFIEulUqUSiU816VYKJDJZCKFg2QyucI76JarNkOTkprKBHdr+4rI4qo8YhgGlXKZixcvcs/Bg/3PvOjiqQLlNT60+HKf7zd1cqjRoKW8ViBXjgts33R3FlFKJZnatm+ajI6MkM/lqNfrOM1mpDTRcBxKlQrVWi0iwOtrQDfFx7HCQFUIn1GE+feUtOjtio+dcfq+j1+rRRdTuVzGDwIGBwaoOw6O44STvtLptgtOX7y69rW4tEStViOQknQmw+DAQDiVeXAw0vFxuvQ1+qoZO36x1RsNmp5HLpvte+33/vvvs3///mgKVy8aHbHHuz3nB0FPLuq6sIpx6f5VnXyy1bQyZzVifAe61WtT6XTXBJChCe1C0Gg0SKmEWz6XI5FI0FLfYblcjqasQfvF3G1KGxDNmUmnUlSqVU69/37f5/BR42NnnNJxQNPYpKRer4dd8lKG6z012QtoU73ThIDFpSWazWY4XSufD7V6UqlI+9U0zWjac61Wo6L6BaP9K8+pPWpLaa9qKcx+sLi4yPziIrt27lwOK7Vn1WSIjos56NGCprtRPjQUC0fzXNsatYndNEQ4GjCt1PLW43lWGGcySbPDOP0giJYl42NjFPN5FpeWcFotTNMkk04vD5AyjLDLp1qlWqtF69yI3rjKcdiJBLZtc+XSJaY7lBluF3ysjNN3XQJ1lxQQzRtJJJNUa7VQRjLOoxThWPZSqURJ3WUzykvm1F04Dh36moZBIZcjnUpF06m1Ol18HLvv+1SrVRLqoukXx48f5+59+7oKinX2S2qPE58vol+nDakt9BbLIs+R7IrskC2JGWDb4/pzIBYS9gh37WQSwzBWbyvrgvj607btUKtW7a/VaoUsqiAgm82SyWQYHRnBMk3m5+ejljMhBLZtk8/lyBcKWIkEjpr9Wa/XI0WL7gew/HgqmcQ0TU6eOLGq9tGtwsfKOIOOu2y9VgvXPcp75HO56KJ2XZdyuRwSE2JGmYp5yTg6Q0ahsnuFXC4s1VSrlJWSu6E4nNVqNSwD5HJ9r9kWFhYolcts3759eV99vG+FWLMiwq9Q24utrduysOr82gxP7bubp14LhhCkk0k8NUO0X8RbwgzTJJFIUFUzWuqNRtijmcuRUIwt0zQZGR5GALNzcys8YsI0SSWTZFKpkNKnJEsbjoPs4dX1+ZqGQTqTwW21+OD06TXLSR81PjbG6bsuMnbnRISj1QPfj0JUQ3nKJeUpPd8nm8lEYs+9DKhzalgciUSCgWKRjCqxlMtlGmoil+/75GOCz/3g2LFj3H333esKRXtdMjoJc93Uvbad9Hlhxl6XTCYxDWN5FEWf0DcPz/OwE4modSybzbYJaGvYts3w0BCB768w0LiuUUaRHmzLotVqUanVaNTrKwxaxn5bav157fJlFhcX13UeNxsfH+NU7BD9RTiNBpVymVQqFc3CrNZqlEqlNk+pG6d7YTXD1BCKpzkwMICdTFKv15lbWAgVzddhGHNzc9RqNbZv29a5g9Xf2MNwojLKDZrC1Q8ZoTPJllIzOvv1nlKG4xeqtVpIqTQMbLUcSazCb06nUgwMDOB5XpvsiQ779dAmCNlM+Ww2JCl4HlUlY9LtHCC8AZuGwcVz56LSzu2Aj4VxBq4btjJpSMnCwgJuEDAxNoYfhNOkHcchmUqFnjJmlFGmsEs3B/QXVoLSUk0kMEwzpLMRyjRW9Je/xoV97Phx9u/ff2M8HWFySoevNwTrDG0hZFhZhrGqqDSEa3VNpazX6+G6UrF9LNWjuRbyuRy5bDaiUWpoLnOnR82k02EGXa2Nq9VqxPSKDFSdcyqVorS4yPz8/G0T3n4sGEK+Guajw1mn0aBWq5FR9K9Ws4kwzVD6o0fGVAgRjknoYKus98Ju1OsYhsHoyAhCCJxmk2azSVUNMkomk9iJxIouF80b3bp164ptrnUx9Hre/xCc2l5Yq2m62+uTqRR1VXtsk15RbXOe54U0Pbk8KDiRSETr5V5lj24YKBbxfJ9SuYylSAWGEMtG1wHTMMjlcjSbTRrNJtVKJaxhd1wnhtKTmpmaYmBggIzK+N9K3PbG6bdaSJX4QFHnKtUqzVaLbC4X9kqm023lkF6IKyF0o/GtBafVoqmG/mijSKdS0Ug7p9mkqWqtOqOYTCQwLYtjx46xf//+vjyTJuK3mk0cx6GuJlk7zSaeakcL1EBeHcoFisaoWTpuq0UA/MEf/AGGalPTLVu6dc1Qf/tBQCqVIpfNhjcXNVgoqYgYa1EDk0q/p+E4kRdzVeucvqnaajZp51rb7MEe6gUhBCNDQ0zPzrKwuIgR0xzu1j6mofWJ9Wepp6vFj8e2bUqLiywuLq65HPoocNsbZ6C8JkpxXGf2fM8jrWpelmn2ly1VYWAgZTT9qu/jkJJarYZpWV3bmhKJRCQ47bpuSJhXXnV+fp5mq8XIyEgUflXVgNqyCosbjhMatpImSSaTpFIp7GSSpG2TTCbD+qtaHxmK45pMJiNKmmEYkUqBEILf/Q//geeee26531L3Xiqld61YX1XNA67rRllTfSy6JpxKpcLjsW2y2Sz5QoF8Pk8um41kRGoqvLeU0duJBAnVidLrQl+N89wLQghGh4eZmplhdm6OQUXbDIKgZ6JNiLABPJfN0nLdaPxFW31aSmzLYurqVYrF4i2XN7mtjTNotaJ1FYQtQzVVGkmkUmGKfR28UM0hNYRAGkb7OnYNaDZRZpWsb7iL0GPatk2j0WBxaYnTp0+TSiY5cuRIGP55Hrlcjpyabja5aVN08adSqTYFgV7FdF9p36YzGVJdul/itcTVIKVkqVQinU5H24lP29YJHB0R1BS7au7cOarVasTI0vTJTCbD2NgYAwMDfY3p03VPzVvuF4ZhMFAoMDs/T6VSCcXBVzFOUMavbhqW8qINxyFQkQNCkEgkKC0tsbS0FIbMN3jZsB7c9sapa1KtZpPFhYWQ26k8ScQA6tcDyo6RC/p9axh3S01hzqRSXUcVQHhBLy4uMjc/z8L8PHNzcwjDIJ1O4zQa7Nq1KxKQTiQSYYN2sDzROjyM0BCikHMVAbG4zuyHQdczF4JA8WZ1CC0Mg6RaK2q5D8uywrEWzSZ1ZbSLpRJT09NUq1VSqRTDIyMMDw0xPDzc1rYX7Soe1vZ5o9U3j1Q6TT6XY0kRTPrph9VEfAhLN/VGI1weKEkWIQQpFd4WCgUKt1B76LY1ziAIwrqmELitFrOzsyAEI8PDXL12bbl1aD2hacfr27pVurQ1QRjOVpWKQjqdDlXfCPsL5+fnmZ+bY35+nlK5TD6XY3BoiC1bt3L/Aw+QSaV4/Y03mJyY4K69e7ueY7Q+U8bajGV9o7VxjDCv/++5Lq7rEvg+rj4XnZ2OnacfU+mLhhlpZpBSrW84TnRj0O1e8QSLlhK1EwlIpTCgzbtnVC15ctMmSuUyCTV3RY+sn52d5dSpU7RaLYaGhxkeHGR4ZIShoaG2jLoBqxLo9THHX1EoFKg3GlSq1VCku09FiOjY0+lQn1et3zNqHVqv1ajVamTXwZe+0bhtjVMqupzXajE3P08QBIyNj0c1rYRlrcswo1axLu8ROsyFFUZabzQIpCSbyTA1NcW5c+eYX1jAjV1oBw4eZGhgYEWGttlqceXyZZ577rmuh2QoxQAzkSAZMwa9JvR8H9/zooSHryZXS2XEzWazZxlCX8C6wN/7Y5Gh8l4iERp/rKivE0fxRJtuCet1PknbjkLdfD5PPp9nx44d4efRbLKwsMDc3Bzvvftu2CDvedRrNexkksGBgUhBrxOa59vpeQ3DYGhwkEq1ylK53DeNMqrpShlGYYYRhu31OqlkkkBlmavVau9xGDcZt7Vxep7H4tISge8zPDxMUq3jpJTXN3Z8jbUiEBqpuviq9Trnz55lYXGRxYUFCsUixYEB7t+6lcmJiTUTGOfPn2dycnJtRYSOi11nVi3TRHabxSJlyCW2LApKyEw/rn/r/2fUgKQ4V1f/1kYnhIjWjBp+B99Wo40S2AVJ2w7naLZaK847mUwyOTnJ5OQknufx6quvMjc3h23bvPbaa/iex+TkJOPj44yNjYU8YXUzWq0Ga9s2uUwGR5W04v20PdFBb7QTiUiGpeq6Yfml0aCu+kz7FYC7kbgtjTMIAvxmM9RLbbXI5/PLU6ZcF1/KrkmQntAXWR/r00a9zrVr17h8+TIzc3MMDQ2xY9s2Dj3yCMlUiqVSaSXPtds5SMkHH3zA448/3v9xdh52j8d1SSjRpZ4avVedc2c9rxO96oNrGWEvmJYVjkzoYpwajuPw0ksvMTAwQKFY5O79+xkeHqZSqXD16lVOnDjBS6+8wvjoKJObNjExMbGmgFkul4ta/VLJZF/GpFX6ogltlkU6m40I9I1ajWw+T10JwH3UuC2N0282qVWruM0m6VQqHKyjjKrZaoW6qOtZB2ij7GGYruty8cIFzp8/T8NxmJiYYMeOHdx94AD5QgFbTZmGMIxy+6CqXb16NewTVYrzq6FX4X+1ul3g+x9KmmTNY6K7cfZjsMlkEldlpTspeeVymSNHjrBr1y7uuusuvv6Nb0SvyeVy7L3rLvbu3Uu9VuPqtWtcuniRN958k9HhYXbs3MnE5OSKBnjdJlYsFimVSswvLDA6MnJdyTLTNMmkUjQch7m5OUYnJ2k0GhvGCSpkm5/HC4IwMxtTZEdKPM/rP8SIZQFXXFRSsri4yLmzZ7ly9Spj4+Pce++9jCjmz+LSUpS508cV1eL6yCieOXOGPXv29HmY6zNMUNIqN7JI3uWC77tE1QHNVXUch0SsVjgzM8Prr7/Offfdx5YtWwDwlDaQTkTp40hnMuzYuZMdO3fiex5Xrlzh5KlTvPXWW+zYsYMdO3a0s3hkOM6xUCyypCaRF/L5Pk+9/eaYSCTwgwDXdZm+do3R8XFaatDyR4nbzjhL8/O4Ssnbg3ZpSSHwXPe6PiR96Xmuy6VLlzh79iye57Fzxw4+/9xzbSGY02gQBAH52Jer121mbE3aC4ulEpVqlcnJyf6OrYvnXG0Peh12sxUQrvf1msZYbzSidr7z58/z/vvv89hjj7VpJjWbTYTRPv9UbST6XEzLYtv27Wzbvp1yqcS5c+f41re+xdDwMLt27mRsfDw6tlw2G3J4q1VSSpStH+h9xQcJB0HAzNQU2XyeRqPxyTbOpuPQUh9qS80yMU2zrRTgBwGpfi/K2Be+VC5z+tQpLl++zMjYGPfcc0+UdGh7SxBQV+pyXdc5sSSKLkt04oMPPmDXzp19h53r9U9Rw/cN9JzdtrRenm0ctsratlotzp49y9WrV/nU00+Ha0OW67SuahvrBsMwwqHAsfMsFIvc/8AD3HPPPVy6fJljx4/z1ltvRUuRVCrF4MAArdlZFpaWmBgbW/NY44QPPeoeQmpmtVbj6uXLZLPZUHj8I6T03VbGWVlawhIiGlLTNucjNmCnrxKKMsxKpcLx999nZmaGHTt28LnPfY7UKun2huMQSEm+B/FZr8WiEDdeKyX0BFeuXuX7Pv/5tY9RwQA624JXSzppg7kRa87VOnO6rTv7NVVD6fu++cYbNF2Xpw8fDgchdZSMTNOMbni9ttOt9mlaVhTeLi0tceLkSV588UV279rF3r17KeRyLJZK1Or1SLZmLQjDQMSOTzfclysVSqUSQ0NDH6la/G1jnI1Gg6DVIpVKhZxR7TU1TDMUUJZy7R5KKak1Grz//vtcu3qVPbt389CDD66aFILltqakbfdc1+p9d64J9f8uX77MxNhY9CWutXYM39zhvVepyerjjB/Lh8FaciTr3p467qbj8Nprr2EYBo8eOtTVO7pqvbkahFjZSdSJYqHA/rvvJti7lzNnzvDHf/In7N69m0KxSLlcJh1rVOhx0G3ePA7TNLFtm9nZWUZHRz95ximlpLK0hC0EgSq0r5iOpetdrN6E6jQaHD95kssXL7Jr1y6e+77vw1YXwKrS/RDxLFejgRnECthdLpgLFy+yP6Ym3mmYkaeKPd4tdFw1GaQ/hxthUKt4zn7odN0mnlUrFV46coRNmzezddu2no3YrutircXoUeyk1Xi30ZS1bJaHH344ipbOnD3L+Ph42CjfJ5GgGwlCT4hbWFhoYzXdbNwWzdb1ep3AdUkqetwKr6k83mofiuu6vPvOO/zxH/8xhhB8/vOf5+CBA5FhRtvpAT8IcBqNiHjeEzqM7XLRVqpV6rVauJbt+fbu57GaMnwndFbzRpCy9R67HVPnI5odpBNSbX+rn/n5eb7z4ovs3buXgwcPYts2vsoVdMLrUmrphjVryrR3teTzeR579FGeevJJqpUK33vpJc6ePdszJJe0j+jofJ1WRJyZnv5IhahvueeUUlIplUiZJp7ymm0Z2piH0uFeZzg3PTXF0TfeYGxsjM99/vM9KVyrFdb1gJ6eczcUtEF0WwddunSJzVu2rPvOagjVCK4Q6PPUx9tB0I9Per4RiCvx9XpOl5BWu4FcuXKFt99+m4cffphxlUG1EwkaQoQi0B0hYUMpV6wJdSPq6T17NAEUi0Uef+IJzp07x9nz57l8+TIPP/xwWDePn2PHdo0O7ymlJJ1KsbiwwMLCwkfWSnbLjdPzPPA8kqkUNbXWNDq9poJOt+tHXNflnXfeYXZ2lkceeYTRkZHVd9YjTPN8n2azSTKVWrM8oZMwge9D7K4vgYsXL/LII4+sfgz9QLaPM4igyeyqSyQeInd2dkjaie7xc5dChP2s+jzoXddse3yVG8KpU6c4e/YsTz31VBsXVQ+6bam5NXE06vW+J6sJet9cI03fLseXtG1GR0fJ5nJUymW+/e1vs3//fnbt3t2W3OvcV8DyZy+EGpQcBCwsLLCtUwPqJuGWG2ez2UTELiZ7jQW3IPzCp6enOXr0KBMTE3zmM5/pKzzqBa1cvpbXBJWEEWKF51xcXCSQsi9G0GroK7SVcsUIhjZPqg0qblix7Yr4/9fwwFHJaJVjefOtt1hcXOTZZ57pmgnX+rSdAtj1er1/vV/lPbuFx2upIBRUnXJsbIxNmzbxxhtvcOXKFR56+OGeIxo7vSci7NMtLy19ZISEW77mbDYa2CqkbRvl3oM14wUB7x07xtGjR3n44Yd58MEHw3pkH2Fet1f4QUCz2WyTHll1GyLUOw06kksXL11iWxd9oPVCsLbBSClvnEjYGl6x7dGO78TzPI689BJOo8Hhw4d7lqi0XlCroxe27jg3RKtHJ+d6JcgSiQTZbJZGs0kymeTw4cOMjY/zja9/nTNnzvS8IXY+aicSYcP/R7TuvKXGKaWk1WximSZeq9XeBtblg56fm+ONo0dZXFjggfvvD5kmXTxDT3TZZlP1Mq6HSN95Bw+k5NLFi2z9MOFOR720FyIvESvpdH1drI+z7XHaQ7l+UlDRa2Ofn9No8OKLL5JOp3niiSdWLYloDaFWx0j69YS1akPdxw7GiAO9UFC6xiXVQrd7zx4OP/ssFy9e5MiRI5Gif7QrOrLhUoZzWpS43EeBW2qcrVYLQ6sAwHJIq+t8MczOzHD06FHGx8eZmJjg1OnTfO1rX+Oll1/m7Jkza0ozdoWU4XDdZHJdVLhOxbiZmRnSmUx/rUo9oC+DrsYSSwT5vt8mIaJ/r/gRos0Qu62tdI9keAAd3NqO/8dJEaVSiedfeIGtW7fyoK4frwHbthHQNlulrhQU14Ueme61og09EcB13VAEW0ryuRzPPPss6UyGF198ceVgpo6lgu53nZ+bu27m1HpwS9ecvu8j1AWnBZiAFV/ApYsXefuddzj06KM4jQa5YpEHikVazSbT09Ncm5ri+Pvvk0qlIuMdGh5ekxjeVJ3/62o/g2UuqMLFixc/VEgbL4D3lInU2Vu13xtR4+wkUcQvN9n+wujYpqenef3oUR544AG2bN7ck8LYiYTq7NFDcAMZzvjsZ53fecxGx5q/WxN2N+Sy2WiEoG6lE8D999/P6VOneP6FF3jiyScpqg4UnWSKz5JJqDmua+kV3Qjc8oSQkBLX85YNpCPrqLOATz/9NMVCgfMXLoR8S0JPu2XrVrZs3Rpp+ExNT/Peu+9SqVYZGxtjYmIiLER3uQgcx8FUeqXrgc7Y+oqLefXqVe65554136eTXl0vpFiWdbXL7IaOYIDI6FeDNtyz585x/PhxHn/8cYaHhpa9h86ir0asUAkVx3GQqVSolpBMrkrd631A7YkuPwjW/A515JBJp6lWq23dTUII7tq3j3QqxXe/8x0effRRRkdHwzcaRjjVTp+jaVJXZbebjVtrnEGA57qYltWe/VIf/ltvv83c3BzPPPNMtDYxDYNAM05iNDfDMEIhqaEhDu7fj+M4TM3MMD09zbvvvksmk2FiYoKRsTGGBgaiEQL98i7jECpTKoOAa1NTXTmXvXxJT4lI2tP3vaA9642qc/ZFLwTee+89Ll++zOHDh1fW+VYhZujSlwRsy8IR4TybRr1+3cmg+JAmHZav5sUClj+3bCZDrVajVq9HHlJj6/btpNJpXn31VR64//6wZi0lOpYRhNef02zeuNGLq+DWG6fnYSsua9Q2JCWvHz1KvV7nmcOH2+6KpmXhdaS4V/xfERl2bNvGjm3bCGQ4vmFqaoq33nyTRqPB4OAgxWKR3bt3r/uwtef0pOTq1atMbtrUk87XNzSHdA3IG+w5Jasbuu95HH39daq1Gs8+++y6owwdDUCoNGCqTpN6vb5qA8JaiFq8tHF2mxzHSuZVIpHATiSoNxrkc7kVn+Po2BhPPvkkL738Ml4QsH3btrCsoufSGEakR3yzyym31DgDzwspXDFRX4DTp09TLpU4/Mwzy6UVBdM0Q2l/Vsk0dhTUDRGq9o0MD7P/wAGq1Spnz51jcWGBr589Sz6XY1yFv4ODg70vVpVo0ReG57pcm5pi/4EDH544vlY9UUGvr26k5+x17E3H4eWXXyaTyfD0009fl2xJG4QgYVk4rRblcjnUN9LHse5NhTczL2Y0ccS9aieyuRzNhQUcxyGbyazYd3FggKeefJLvfOc75PN5BgcHo+WG7uetlMtt/b43A7fUOD2VkElYVvQBTU1Pc/r0aT796U+vMEwIjbOzxtgVqzBeDCGYnJzkgCKoz83PR6SGVqvFxPh4KDI1Ph7VUKPShDIMwzBYXFiIBJU/LOLJntXQj37RetDLc1arVY5873ts3ryZAwcPRjKaHxaWZUGzyVK5zJYtW9rOua1Hdq2bj6b0+f6K2nAgV6cZ6qG5tUaDTDbb9TrJFwo8+OCDvPLyy3z62WeXHYgQSCE+knLKLTVOobyAvuDKlQqvv/46TzzxRM/6l6VmY/i+v3Zo18FJDf+ryicxmuDY2BhjY2Pce++91Go1pq5d48KlSxw9epRiscj4xAQTExNtaxTLNJmamWFCd+F/RAhuIAEB6GoI83NzvPLKKxw4eDCStZQ3yFNrQkK5VKJ44EDHocQMVT+2yraE4tsaphkZtd9H5tYwDLKZDOVqlVar1TNU1zq8L7/8Mp96+mmAKBm5ouxyE3DLjFN3NFiWhed5CMPgyJEj3HPwIMNDQz3fpw3K9zyMfmP+2JfVchx8Kcn0GGGQzmTYuXMnO3ftIggCZmdnmZqa4pWXX8YPgrBUMz5OLp9nbnaWBx54YF3nvRr6Sc7c8BS+bG8kuHTpEu+8/TaPPPII4xMT0eM3KozWyRzHcVYlkHf1qCtfhJQyjKbWmSjLZrNUqlVq9fqq7WR379tHuVTirbfe4oEHHsDzfSzLusM9p5L6TyaTuK7LG2++ybiSmlgNphpa5AUB60xNAOAq9b6Iixvj9UZQX7BhGIyrEJf776darYbC0ufPMzc3h9NqMTc3RzKZ7DpqYD3oN2uqjzNezO+mV6svVrfVImq5o53MLdTnaCsS/amTJzl37hxPf+pTFNRwoNhOrvvcOuE4Dtlcrr/wlS6Gqj8D1bZ2Pbcq0zRJp1LUHYcgn+8djQjBww8/zPMvvMAHH3zAxORkmLG9oz2nGlJkJ5NMT01RrVT60nhN2jaGov2tt4AtgyDUJkqlolLIei65XC7Hnj172LNnDx988AGnz5yhptZmQFRTHR0bW7cIsVQ3K52B1HpJMggiJo/WZU3a9gq6WSd0PbS2Rk2uWq1imWZUGz506BCWbdNwnHAMgxAR2f9GoV6vk8tm25OBfUKXRALCnIVQYyquBxk1K6XeaKzK7jIti0cfeYQXvvtdhoaHsSwrHPmolO1vFm6ZceqLK2XbfHDmDHft29eXJo5pmliWRdNxYJ0y+U3XDRNQMS2bNmbMOsohc3NzbN60ie3bt0dzQaanpvjgzBlee/11hoaGmFBspVwsqyelJFCj9/RIPk//3UUxQBuHDmWTtk1aTSMDFcZprxj7v/YueSWopfdNzMtCyG89eeIEpmXxyKFDmKaJqz6nOKQMZUlNw8BQA4ys2IzP9aCi5sq46zHOGIVRw1M3LD16cb3Q4tP6ZrEaCsUio6OjnL9wgb1794KUNFVz/s3CLTNOfSFOTU9jCMHgwECY7OgjS5dMpdbN0pCE7WkQUsniNLko+dCnYQZBwPTMDI899liUgNATqfbedReu6zIzM8PUtWucPHUK0zAYGRlhcHiYYqHQxuM1DANL3XCw7SgTrH/H4fs+rhreu5aWjb6IzVU8eK1W49333mNocJCHH364be2pDTlQnlt372jyRtDx+WmjNdWNZLWZqeVKha1bt4bZ37VuiGrZ0Y2i53ledNOKxmms00gz6TQlNbNltWhHy6i+9PLLbN+2jVQ6va6RhdeDW2acnuLTHjt2jPvuvx8I62prdilIGfbVqTmdayVHdBbPU5OgU8oAuqkJiM739cDCwgLZTIZMJhMZPCxPDfM8j1w+z85Mhh27dlFT+jPnz5+nUqkwMjTExMQEE5OTUVJEDy9a7eLSz9yI5MzS0hJHjhxhy5Yt7LvrrhXqEtoLm4aBCVhSYsU4xVJlzPUQXl+deysWkejRDJb6rY1wqVTi3nvvDQ09CLqWzKSUEATRDXOFFpOKOmzbxhAiup7WAwHhEqdSwWk2ya0y2sJRbYVbN2/m3Llz7N+//841Tl8V8LPZLJMTE9Tq9ahDpFd4qy/OZDKJoWhUveh3siN882J8XAjT8KslOVYz1KmpKSYmJjAUkbtarUYXKKieT9MklUqRsCyGBgej7vlWsxl61elpTpw8STKZZGJigtGREYZiYstdz6mHHMd6MTU1xdHXX+fe++6jUCj0v71Y7VgI0dXT6PDX8zx8z8PxPFA3MMs0w88oCMiqmSSe67b18LY1sa9ibLrmailCvWG0j6/vR3NXEvZomoYR9pr2CG1d1Siesm3u3r+fb3zjG2zfvv3ONE697rpw/jyPHDoEhCoEjuPQWG1xrj5s27YxCMPUbsa5IvtK2J4moI3s3G8IFL9EgiDg0tWr7L/rLirVKk6jgSFENCJee4meE7FiZH0pw5EQ01NTvHf8OOVSiZGRkWWyfkcUcSPEpM+eOcOJkyd54oknKBSL4cj5frbXR8+kPrZEIhHVDqUMRwx6nofn+yzMz5PN5ahWq7itVrjuVLXP9cDzPCTLnFpDiHAymkJXCZcY4o8lk0lqSnlxBdNIynA+j2qQsIAtW7dy4eJFnrgTjdPzPGr1Oq7nMaRkPQzDIKWmQHtrTIkyDQM7mWwLKSFmlJ3JDIhU/TTWlN+IQc/NaLVaNByHeqVCLp8nqdhDmXQ6moq8HgghGBoaYnBwkLv27cNxHK5duxZ21rz3Hul0erkFLl77vQ7jlFLy3nvvMXXtGs8cPkxW9Tbq41jz/eveI9G2rUQiksA8d+4cAwMDYU+slDSqVQQhOSFhWeG80T6Ox1NLmui1mszS8V5dF+70cnGj1fpVLddd0T6op15nYzfK0ZERjh071lbOuhm4JcYZBAHz8/Ph0KDY4+lkkpbjUKvVyBcKKzrR47Btu20wbLwnshNaHqOTqLxae1agyjVNNScUwptCU5Hm9U3FVeFs9GULEWki9Wus0UWSTLJt2za2bdu23AI3NcXb77xDvV5nZHiY4sAAqWRyXQoCvufx+uuv02w2Q/J6bDgTq3wGncd3veWUuMbP4uIiO3ftIpPJhFlWVQrxPC+8WTQaJCyLhGqG6CojGquRawhYEdqGhyzakkmdQmgQZsCFEKFcTWybnueFSh06W66YbNlcjqYaUXkzccvC2oX5ebZt3tz2hQvDCEOeSoVatUoul1v+UDu2kUwmCQjvbPYaqXRtnJ3e2OgS8ni+j9Ns0mo2o7Apk0qFF4tpcu3qVUZ0rx9h5rehPHj8Lt7JlRWobPBqZIM4Wd8wGB4eZnh4mIMHD9JwHC5dusT09DRnPviAXC4XEiQmJhgcGOi5bozI69ksn/rUp9oyxf12uOgoQ5MYen3S+uYUSZjGv1tlJPMLCxxSSxnLsrBNk4Rth/q2KhvtuS5uvY4hBHYyiZ1ItCWs9M2y8/tcbami68faY8c/a9M0sS2rLRLzfZ+GIhrE5Tv1UOGhoSEuXrrEXTEB8RuNW+Y55+bmePjBB1c8Z6lJwlXVcxetPzuI7Hrd6ag7bS9EIW23cEltU0pJy/NoOg6u5yHU9rsNYZ2bn2fnzp3Lx5tIIJpNfM9bUbbomg3uuIDajFgRI7oZbzqVYvOmTYyPjZHL51lQZP0333gDR80U1ROh4x7lhRdeYMuWLew/cGBlxrNfj6iZR8pIo2Sbeq5tu7K3TGWpVCKTTkfrUSFCNXff8xB6vW5ZyFQKz3VpqUK/4zjYiUSYLFRicFGHSOfnuwq0Z9UElDhSqVRUUjEMg3qjQSAlWbVciRoOlKD3yOgoly9eXGOPHw63xDjn5uYwTXOFuK++Kydsm3QQ0Gg0aBhGGMJ1CWtN06RWr6/auuO6brTNTki1j2arhR8EmIZBJpUK9Wu7hVMy7At9+OGHo8e08XpdjLMXuoZq4RPthIgORCoIQjAyMsLI6CgHDx6k3mgwPTXF5StXOPXiG2yftzFySewE3PXQvmXyetxwpIw6bUTHc3HjE8RarzpDRr2tPjE/P89gB286YVmhpk98u0KQsG0Sypu21Bj7lmrM19HSipufEKt6T41uBJRkMhmVVAShnm8mnQ5rzrH3BlJiAGOjo7z1zjt90y6vB7fEOBcWFigWCqve6VKpFIHvhzQyw2hbLwaEF0w2k2GxXF613ul6HkKxSDR0Z0qj0QglLiyLdCbTNsG6G8qVColEos0zaf1Y1/O43hE38UupM9SOr4u16l70mHpdOp1mx86dbLUGaP32DDTqBEGNxzLwaupdZmdn2TQ+zsj4ePg5dmHb6O3ror8mqEN7uLieLHcnZufmmIiR6SEMKbUxdBNZM02TdDodjoXUnrReR6ZSJG17RUdJX8cXPx9UScW2MQ2DSqVCJp1uH8thGFEjvFSeM5/PU6/VQgriehvQ+8QtW3P2bBiOha/pTIYgCKhVq8hcjqRth5IT6v0ZJdhUazQo9Ohw8Fw3MiCpkjx1x0EGAVYiQT6d7ntC9KIaZNOJRCIRNYCvF53rH8nKNZ3+O1DenS6vQUq8r7yNcMJ5loaAQt3gmS33MlV0OXfhAq+/8QYDAwNRBthSUqTdRkus8KQdy4rrOc/5uTkOHjzY9rhuZPB7GKeGMIzopugqNk+t0cBSk+m6ERlWO5bo/7HHpJTUGw0GisWeSyWtLm9oquRN8ppwq2VKusCAZc0WIcL1p5TUajU81w2lLdQHkkylQm5krdbVOCXhF5my7bAMUq+H4atpksnnI05mT8W7DszOz3clClgq1FqTsRSjqkkARY1bsQbt+fbeIZT3+mXkucUVj6cH8+zaOciu3bvxfZ+5uTmmpqZ4+aWX8KRkZHiYrVu2MDY2tiIs12tK7U3DA+xeslgt8w1ELVadjemGYUQMn378T0tNNs9ls7Rcl6bjUK3VSFhWKAx+HcYSqOWNhDAzG6cxhi+Izq1bLfRm4ZZ5zn7vwsIwyOVy1BsNGo0Gnu+TzWaj7F02ne4Z2uridz0IMJpNDMMgl822jXyIEjJ9fKkLc3Ps3rVrxeMJy0KwXHuLnWj4i/YLffUT7u2hehlnq+7Q+Ldvrgiry1nJ0LZi9LdpmsstcPfdx9TMDAtzc5w5e5bXFVlfy7Xkc7n2G0n8nHrUiFcz0Pn5eYY7Smfh6YZsKrePmmHg+yFTR3UVJW0bO5Gg2WrRbDapVKskE4mwBNOnAfm+H4anQUAum424wzqX0LmVm7nG7MStM87YmqYfpFIphGFQr9epVCrkcjkM0ySTzbLUJbSVhCP5arUahXyeTCYTLvq7ZGxFh0h0N7RcNxSF6pJ8inpMXZekbUchUj/oO1CMrfniqNdqXPjyC+ysrby4j98ledrs3aeYSacp7NjBgYMH8TyPWUUr/OCDDzCEiAx1eHh4+aazxoXZacj6eOfn57suCSCMPFpKsma1C18vHeIhpxCClCq3NFVdutlqkVTUydXgui71eh1JqGkrpQwphfEbRXy9qcox620HvF7csrB2VW8V8x4yCPBVnJ+0bSzDoFqtUq5UyGYy0ZcQD239IKBaq1GtVknYNkODg6veSfthCy2oTGM8pIkboKWEx9LrpHSJeMhIb8/TreyxtLjI68+/xJOnVq53jXvGmRu+vOq+dYIJQgOZ3LSJyU2bQErK5TJTU1OcOnWKxYUFhkdGorVqX2P71LHqiGF6ZobHdu5c/qw76oxCrTtXu/DdVguzR4uaobL6CdumVqtRr9exE4nIy8bPGcKG72azGS2donBYhdjdoBsTdPh/s/3nLTHOYrHI2Uql550yWndqZknsOdOyyBcK1KpVqtVqxJYpVyoEUuK6btRgnEgkQoW3G7BGWFhYYGhwsO2mEjfOhFp3rndN0q/nlB2e89q1a7xx9ChPzQ1itGbaX2wIEn/+Hvhub+OMs3ZWQAgKxSKFYpG79u2j2WwyMz3N1PQ0J0+eRAgR1VWHh4fXLCFVqlUC36dQKKzorJEQJaZWM07f9wmkDCmTq8AyTfL5PLVajZbr4qmSiPb8mlzg+X60To1/BpZp4iqSQ+d6UxutaZrUazVSse3eDNwS45ycnOQb5TL1apVsjxplW8tQR4hoGAb5QoGG49B0nJBZ0moxMzMT0b5SqdS6QpBu48bjWCqXmZyc7LleTtg2RqOB67pr9lqueSx0ydjGapxnz5zh5MmTPLX7flL/5eiK95tP70BsKqx4vGOD4b76WD8lEgk2b9nC5i1bQErmFxa4du0ax48fp1KtMqrI+mPj412VCKenphgbH2/3YPHzFeF0udW4qlG9uo/v0xCCdDqNlUjQqNej8QuSkDEF4TLJ7mLolmWFtU4VzsY/HU1QMIVgZnaWu/btu/OytZZlURgYYGZujp2rGecaJ55WH3ClXKbeaFCt19m9cye5XK4nZW89iBfjy0tL3HXXXT1fayqO6HqNs5vn7Fark4Rh1bFjx5idm+Pw4cMkvvwOQdCxhbRF4k/fvaZHjhMaVj2+zhuREAwMDlIcGODu/ftDrzozE3bWvPceqXQ6UoAYGhrCME2mpqbaWFVdThjDNMPOoS5RCYTG2Suk7b7JUCfKzOWoVCrMLy4iCEfSr5bVtSyLoNEIGV+KT6uPx1f9oxDOY336Boq7dT2Wm7r1HjBNk/HJSa72+NJ0EbyvrK4IZTyK+TxL5TK1ej2USlR3vX7DDiHEspdW60A9HiFQa9i1xo1Hs0DWk9HrM3HkeR7Hjh0jCAKefeYZjFMLuMemV7zO+sI+KKTW3O6HIbO3dXQkk2zdupWtW7ciY/Nq3n33XWq1GiOjo8zNzXHfffetuk1DkSviJRv92Wshr/VIgug1rC6RaC/ZuUzqhB5DqSVZdAbaj4W0ATC/sMCuLpn7G4lbZpybN2/m1e98hydZubDubJTuBd/zqKr62aZNmxBC0Go2aagE0Xr1XQSKfaRJEurxml5frHHXTiQSNBxnXayRbuUH0RHKO47DS0eOkEylePyxx0iYFs5/PLZyY8MZrM/0d8F0rmF7vk4xYtqOr8drhWEwNDzM0PAwBw4coOk4nDhxAsuyeP7558lms6EGsFbWj32epmmGc0liZAR9k9a9m/1GQYGSVNH82FQqRVYJijUaDWpqTks372lZFkKGyhk2y99F1NxtmiyVSmQLBYrr1LBaL26JcQohKBaLND0vFBeOnWQ8YRAnJHTC8zyq1WooEJzLYRoG+XyeUrlMNpOhUq3SaLVYWloinU53L6PEENfM6XydLt2shYRlYQiB67p9GWfPu3jMMCvlMkeOHGHT5s1s2bIlnBXz3QtwtbzibYn/6iAk+vtKI1WFtTznh1hTJVMpfN/nrrvuYvfu3cwvLDA9NcVbb70VjYHXa1XTNEENJe7snGk1m+Fnq7Sfeh2RHwS0mk1arRa+lBimSVZNLJdShnxcoNFohLNB41laBVNROD3XhXQ6uolpvSIhBFNTU6sucW4UblkpJZFIsGv3bk68/z6PxSQx27xlrMYUh+u61Gq1iDyv1yG5fJ6qmr+Yz2axlMqeTq2nUinSql6qdhYOmdX6MyKUguz019VKhUKfczEsy4qyfWtitQtfSmbn5njt1Vc5eM89jI+P4zgOwvHw/uD9lZvaNYT58Ob+9svymvNGZLJ7Qkqmp6fZvWcPQomcjYyMcPCee2jU60xNT3P16lXeevttcrkcgwMDjClpUX2DbCklQDuZXE7QiPbuHc/3Q6N0XQJlhGm1NuzUZdKqC/V6nVq12nb9QHizMgyjrZyi65tJ28b1PM6fO8ef+rN/9uZ9bgq3zDhN02T/gQO8+uKLYZliaKgrX7QTvu+HhmlZ5LLZNi+XtG1S6TSVcplcPk86mcRKJPDUNOOGYhmlUinS2pN28CO7JWNK5XLPAnonNM+2rxFxvcJ2Ibh0+TLvvP12OCtybAxHZRn9Pz4NleaKtyR+8N51ebmICHITs42lUgkhRNeoI1LW37mTwPeZn5/nwqVLvPX223iuGzGZdFN2G3dWLTs836fpOLR0c4PqC43PT9X5hzh0W2KtXqder4eMs9jnEPV8Kuhp4qZlcerUqbAePDl5Yz+sLrilxilMk/379/Pue+9x+PDhlReraG9alopjK4RYYZgahWIxml6sZfatRIJ8IhEmCByHer1Oo9HATibDzoZYN0rneg/CsHb7Gkr0GnYiQY2Q09uXMmDnY1Jy8uTJaGBwQYf8UiKXHLxvnlnxHuPQFoxd/d08ov0EwfoztQr9GvRUlxJKNximyejYGKl0mj179mAA09PTXLhwgfmFBQqFQjhcamKCQj6P73k0W63Qu2kan1Lh63ISXfdpmiaZdJpavU7DccjElSU6GF4t140y8WfOnuW/+vN/vq/z/7C4pcYppWT79u2cOX2a6WvXGJ2YWJkcYTlrWq/VCIKAfEwhoRPpVIpkIkGpXF6RwDENI2wHSiZxms2IJWIIQTKZxFaGGh9rrild/Y57M5SkhdtqrTnOvpMdFAQBb775JuVymc985jNtPaiBlHjfPgNeRy3QMkn8ufaBQP0goA8j6zOT3AvXrl1j3zqUAjQBIFcosDOXY2x8nFarhdNocE3Nq/F8PxySPDLCxORkm7ZPJ7T8Sc/9WVZ0LbRMc7ktUSw3Y2u502QqxYljx9iyZQvDa6gk3ijc0jUnhBfdwYMHefe99/jM2NjKMeQqMeQ0GrieRzqdXpORkslkKKnapy6Kx7OTpmmGurPpNC0l3FVvNGioMfTaSE1VkDYMo2vBuhdStk21Xl+TLRQnWLiuyyuvvIJlWTz99NNYlhVJbQIEFxaRx2ZWbMP67G7E8Opq5V333QeT6cOYZl3RJ8diki5rIcrSqtKJo3p509ksO3ftYufOnbRcNxqEfPzYMQYHB6MMcD6fX9H/uhaSySS+7+M4TiSGHZXVWJ5M0Gw0uHj5Ms8999yHJpn0i1tqnIZh4Po+k5s2cfLkSU6fPs1d+/ateK3neTQcZ0Wjcy8kbZtkMhnKYmQyq4ZnSdsmadtkM5mo477RaFCXEtMwKPeZqe12bi3Va9gT6rhq9TovHTnC6Ogo991330qur5S4Xzu1MkuZT2J94fqyhjIIEKv1T17XVpdx6dIlJjdtWlfCyVC1yapadrQch3Q2S9I0w3WnuimPDA9z1969IVl/bo7pqSm+dyYM9zUBYmR0tG/CQiqdpqomjmndKqESSS1FfnjzzTfZvWcPqWSyf27xh8QtM04hBLZt02o0SCcSPPrYY3zrm98kn8+H5GsNKanX6wjD6HtIrZSSfC5HtV4Pa1p9KNUZhkFKzSDR0hiNRoOFxUVMy2KpVFqWb1SzQnrBNM1wAvdaxknINHn55ZfZu3cve/bsiR6PlA6EwH/9CsHlpRUWY/3ZA5C+vi78tcLatXzOWooDly9f5t57713zOPzYnJhms0mjVguTeL5PNpdbNUtuWRaTExNMKnWFcqXC1NQUp0+f5pVXXmFoaIhRVa7plMSJwxCCbCZDrV6n6TgIIcJBSZ6HlJJTp05BELDvrrvCuumd7jkhDCkq1WrE/nj8iSd46cgRDj/zTFT7bLluKEnSIwHUDX4QkMvnabZazM/Pk9myZV3HpaUxkqkUly5dIp/Ph8bWbEYaM6YWGVYG23lsyUSCqjr2XoZ89epVjr7xBg89+CCb4jckBSEE0vVwf/8YsvPUNxewnty2rvPS0NpBH6ppuEviTKNSLtNsNhkeGVnxXHxkhasufpQXTyQSJFOpcIyDkqFZDwr5PIV8nrti82ouX7nCyVOnsCwrmlg+2sWrGoYRTQ/TN52W63LlyhVmZ2d55plnohxG6gZMMu8Ht9w4S4YRDsK1LIaHhrj//vs58r3v8enPfIakosNZarHez8g+3b1gWRaDg4PMzs5SLpcpFNYggneBEIJmq0WxUAindSl+pb6wHMdBqjutZZqheLLymrqe1my1uo4qPHPmDMeOH+epJ59kUGngdjkAvG+ehfk6MtvuOBN//h7o1au5Bvrh1a61XltNseHixYts2rw5ZNaomSa++swC9R0ahFl0PU9Frze1cHebhs91IGFZoVrhxASB70ctcCdPnuSVV19ldGQkWqtmMplwfEYySdV1o/ELs7OznD17lmcOHw5zJKoGerM0gzrx0egt9ICWQtRylABbt25l2/btvPS971FvNKLOd+gvhe95HqgyQTabJZVKsVgqXddcC0E4CVuvc4UQUcdLPpdjcHCQYqEQGZ/jOFRqNUrlMqVyGafRYKlUwnEcXOVFpZS88847nD13jk8/+2xvwwRkpYX3RyeXj0fTYQ+OYx6IjbtfxZCMWC0zoiRq7u9qoek6MrX6pqUzq5cuXWJoeJhSuUy1UqFer9NU5Qj92eWLxVBUzbbbGEERj/Z6Q8ceXUzFYpF9+/Zx+PBhvvCFL7B161YW5uf59re/zTe+/nXefvtt5ufnw0Sc71OpVDh+7BiPPPIIGR0SS7lCmBzgn//zf44Qgl/+5V/uekgn1Uycw4cPr+tUbrmGUDKdprW42LY2279/P+VSiaNHj3LfffctlxSEWFF+iEOPq5MsZ/4GBwaYmp5mcWlp1XH2veCorvpu0MZqWRZpRfXylZSGHmxUrdUoqwG1vu/z/vHj+EHAo4cOYRgGzVYrFCBTWjqRgLOUeH9wDBxVChAgAlSv5sGVxtPZxaL+jot3RY+pm0QU2umbXoywr7OemqygtY70MF9PCUBr6RCpXlsplwmkpFgoLHtFNcdzTciwH1d/rteFTsMUyxPl9PnbiQRbtmxhy5YtSClZWlpiamqKY8eOUalUQmHzRoO79u1jVGWbtURmvksE9tRTTwHw8ssvdz2kv/k3/ya+7/Mv/+W/XNep3HrjTCZpCIEf020RwP0PPMCRI0d4+513eOLxx9uEiLvd7bVRdn45yVQq5NoqCt56Q5L1TNCOGysQtSZZiQRIyctvvEEum2X/3XeHqoL1+so7vQqdxFwN97XzGMnQY7oWIEF+ahvBWBap6GVaxbCfqELzhz3fj4yMIEAq49KCY3qsn5TL07X1DUM3wWtj1SG8qWZzXjx/nq1btoRj5deJplrPX3fY2G0dHPu727UjgMHBQQYHB9m/fz9zs7O89PLLJCyL7du2xTYTGvhglxrnQw89RDqd5pVXXlnx3O/8zu/w9a9/nZ/+6Z9eszOnE7eFcUpVLLYsq+2O/cADD3Du3Dmef/55nnrqqTBbK1aOOpAdf0P7+mxwcJBGo8H8wgIT4+P0C61vm0ql1tcGpqDXJ6VSiXfeeYft27dztyrKS4h0c4KgfbR8EAQ4XzuJLwKCRPjimg2JtIHx9GZEeSXpPTpnZaiBMsRSqRR6vPCEQO1X906uaGaXy320uiYstPcTIhrzLoSI1o9xBtflK1ciT7IeSNVJYnZJrvW9jS6NBPHz08/HrxQRm68yPTXFa6+/zuYtW0jHsrvR8QjRdRmSSCQ4dOgQL774IteuXYuofbVajb/zd/4OY2Nj/MIv/MK6z+eWG6cQAjuVolWtLg/nkTJqu3rooYf44IMP+Na3vsWTTz7J0NBQG2tINyFrdPOqWtpkcWkpJCb0OQTI80IN2EQicd2zGEvlMq8fPco9Bw6wY+fOtgZuHVauUA08No3x9vzyOQnwLcg8s4vc2ABxAbG2G5MOPSEyHC0BIlhec+qQNq2yjhHpHyLjW+t84/vVBjE7N4dt26Fy3zrRVDeqdCqF01zJHV4Tasmz4mHaO510r66Atpv8Bx98wMmTJ3nwwQfD/atliB6mJKUkk8tF09I68dRTT/Hiiy/y0ksv8QM/8AMA/MIv/AKXL1/my1/+8nW1l91y4wTI5HKUqlVaqtXKV2FVSpHT9+7dSzab5bvf+x4PPvAAW7duDdvJlJeJo9d6dKBYpFarMT8/T2rTpr7KCE01zRhUgbzHHJNO6C/8/IULvPvuu9xz8GDb8CP1ou7vDSTu777b9piQYBVSJJ/a2fPi6IRea3arDbueh5VIdE1uxI9/NXQzhLPnzrFjx46IeCD0cazF4Q0Cmo6zvCRoNtelxbRazXXFo+omFARBJE3z9jvvMDM9zaeeeoqAcHKcoWaypGLbHlgleaejhVdeeYUf+IEf4MSJE/zKr/wKTzzxBD/8wz/c13l04rYwzlQqRdmyaKqBNVHXeSwpsGnTJjKZDEeOHKFarXL3vn2r3907LwghGBgYYHZ2lkq1SrGP0orjOMszPVVI19Ooov+E67QTJ05w8eLFiIrnNJvhnA2dcOlxwfrfPU/QpVfT/PRuROLGiEnpaVu90I9xdr7CcRxmp6d5MCbdIVleE3dTldfQ0730CI71jnxY7bW9lBUNVbd+9dVXkVLy7LPPhh7T9zFVzTPo0DRaLaH45JNPIoSIkkI/9VM/he/7/Pqv//p1h+m3tJSiIYQgm88vjytXU6S0IrvGwMAAn/70p5mamuLbL7xAtVJZubFV1obZbJZMOs3iwkJf4xP0ejN+nJ1ftA4xA1UC8H2fo0ePMjU1xbPPPEOhUAhLMTJsGo4f54pDb7i4/+n4isfF7kGMfSsL+tcLqbzGh0HnZ3zu3Dk2bd7cNZmj13r6J37uge/TbDbDpJLKWnfmFFY9jrXOo8d2rly+zNe//nWy2SxPPvEEgcq06wFJ+tqLZrOaJvlVQlOdUDp69Chf+cpX+OY3v8mP//iP82CXSXr94rYwToBMoYAQIvQw6uLpZmLpdJrDhw+zefNmnn/hBd4/frzv0BZgeHgYyzSZmZlZc13VbDZXqMPrD0yvuQL1A6Gu6ne/9z18z+Pw4cNRCUZnNJ1Wa9Vjc//oFLJLr6b55+/tOyO7FiISwA3s4wyk5Pz5831r6miVC6SkqeagpmK15FXrr+0bWncuoFGv89LLL/PesWM8+uij3Hf//ZEqn2VZUUSRsKywF1QdR3GVkFbjU5/6FLVajR//8R9nZGSEL33pS+s6tk7cNsZpGAZ2JoPbakW6NRK6rleEEOzetYvPffazlMplvvH1rzM/Nwcsp7x7wbQshoaH8X2fxaWlVY/J87yV3ShC4McyrBr1Wo3nX3iBYqHAo48+uiJsTKpO/l4qCcF8He8bH6x43Hp0K9bO9ddneyGSJ7kBCgj67Kempkil0+tKekiIJE1t246OR39zq4XB0b67ZGdXQF0LQRBw5oMP+Ma3vkUhn+ezn/lMRC9stlqR1pCnykpxwwRWjC7sBr3urFar/OIv/uKqBJN+cFusOTXS+TzNep1mqxVmyXq8Tt8t0+k0Tzz+OFeuXuXlV15hcnKS3bt3r/mFZbNZGvV6pBrfi5wel8KIZ0iNjjXU4sICL738Mvv27WP37t1dt6U7VZqOg53LrfCg3u+9t7JXM2Fi/Vf3RKHZjfB10ZCoHsa5nrWezn6ePXuWXatJX3bbD9BwHIRpkk4moVM3eI3j6NYU331HYTnpzTffBODw00+3EwmU7pCe9+ortprm2ep9deMJd0IrSR46dIi/8lf+ytrHtgZuG88JYGcyJJLJ0HvGygNxdLujbt60ieeeew4hBN9Rtaa1vrih4WGSiQQzs7P4vbxZjFkS368uS0BIXj/y0ks8+OCDPQ0T9fpkMonveWGfZnzddXYB77WV6uzW5/ZgDKW7Rg/Xi8hzdn2y/xkv+vW1Wo2lpaVQcHodaDWbBDojr6IMQ5Vx+t33mvtotXj33Xd58TvfYcuWLRx+5pk2w5RSUlOj5XVYrbPL8bB/dGysZ2Y7jn/2z/4ZhmF8qCRQHLeV5xRCkM7nKS8tRTQuvbZb62QTlsWDDzzA2Ogox48f59z58+y76y6279jRc7bGyPAwU9PTzC0uMt6lKVizZLoVtwVw+oMPOH36NE+uRl6PIZlMhir1SiVBb7v1799Z+VkUUiRUr6bUIlU3aM0JdKXT9e2Nlt/A2XPnwtLWOsLkIAjCJnbTbFN70MsYg97Z7H7gOA6nT5/m3IULTIyN8ZnPfGa5hh5Ds9nE9/22kR1us7liSbJp69Y19/mVr3yFP/iDP+Anf/InOXTo0HUfexy3lXECJHO5cN6lKj10Mjp6jUzQF9bg0BAPPfQQvu9z4uRJ3j9xgrv27mXnzp0rFBSSqRTFYpHFpSWq1WrUVK0L+X4QdB3KGgQB77z7LjMzMzzzzDN995kahkHCsmg1m1GJxn/9MsG5hRWvTfzZ/YhUQp/cMmn9Q0JLf3a72a3DLMNt+T4XLlxYN6G7rrxVVzKI5hazds9oJ2r1OqdPneLipUts2bKFz37602F/bpdtuK4bJvyU/lAgQ96w6/ttLWGDw8M9m+0vXrzIV77yFc6cOcNv/uZvcvDgQf7pP/2nfR/vWrjtjNMwDLLFIo2pKWrVaqjdE6OfrepFhYh67gaHhnjqqadYWlrixIkTnDh5kr179rB79+62Qv5AsYjjOMwtLpJMJsP6lqK+ySBAdCSEPM/j1ddew/c8nn3mmYhy2C9SqRRupUKz1SKBgft7K8Whjc1FzKd2RH9rj3IjQqXV5EnWa5yXL19moFhcl1KE67r4nkcymexJho/T5YQQPW/IGpVqlVMnT3Ll2jW2b9vG5z73uSiP4Hd5b6CU4E3TDKmZ6vGWmseSVM3eAFtj/NpO/NEf/RE/+7M/y8DAAF/84hf5F//iX/R9o+4Ht51xAuSGhijNz1NXMpaaSO6zdtuYnpUZsToGBnj88ceplMucOHmSr/3RH7F71y527d4dfoFCMDI8zLVr15ienWU81ogbdISzDaW8XigWefCxxyK5/n4nYwMRSdxxHMT3riHn6ytf81/fizBie+4nK9knfCkxu3nNda43tUrgffffv673NJQu0GpyM51HoTnAcUFpCSwtLXHq1ClmZmbYtWsX3/f5z7eFyaCYXXEetpRtnjt+PWn5UT1WI18orJoI+rEf+zF+7Md+bO0Tv07clsaZsG1SuRzNajUaWCvozwh0+NfJgskXChw6dIh6rcaJU6f4+te/ztDgINu2bWPTpk0MDA4yNzfH/MICo+oLkVJGd/dSqcSRI0fYsWMHd99993KPJKw5oawT6VSK1rU56l8/sWLUunnPBOb+sb63tV4Evo/VxTDWG0JevXqVRCIRtVT1A6fZRAZB2B+5FqUvfiw6pBehGPTFixe5ePEinuexa9cuHnjgga7kB6Eol23HoKbSZTKZNs8thKDZbEZcWt/3153kutG4LY0TwrWnq6Y9NRsNkul0SMhWWqW9EK2nelxomWyWhx58kPvvu49r165x8eJFXj96lE2bNjE0NES9XmepVGKgWAz5nUIwPTPDa6++yn333ce2LmHOaqoA3ZBIJAheOIcrvXbjNEQoDt375Naxl5XQyaBunnM9kFJy4sQJ9nURY+sFz/OWSxZr9Gq2RUdS4noeV69c4eKFCyyUSmyanOSBBx5geHi4ZySlbzbxWS+u6sZJJpNtxixY1jLKZjIhUyiZDNUcbiFuW+NMZTI0bBtBeMe1dMe8+tB7fSmGYUSv6axHxmGaJlu2bGHz5s006nUuXb7M+fPnqVarDAwOsmf3bmQQML+wwPHjx3nsscd6egmh9tsvW0VerWAcuYqfAs8CS1VyrKd3Ykz2p497PdDe/cNS96anp5GEc1bXIgtArKapykn9QAYBU9eucfHSJaamphgeGWHnrl08MTGx5vG30f/UdeKrIUaWaXY9Bs3vTdo2nu8zOj7eV/nkZuK2Nc5kMomwbQzXJYBQNj+XW06M9LgohKpRxXVyel1A+s6aSqXYu2cPe/fsYalU4sSJE7zy2mu4rRaGYfDwQw8xtIaQ8Hqyi83ffQe7KXFscJKQ8wjnav6Z/au/8cN6Tv2ZdLm4+76xSMmJkyfZt45BPk6jQdBRsugGt9VidnaWS5cucW16mmw2y9YtW7jv3nvbDEqyzBDqeoyxY4XQ0OuNBkKI8Bhin6P+n25TMy0LpGSyz86lm4nb1jgNwyBbKFBdWCClSistxyHRx53X6MjwGZqD2XFxB10mVg0Uizxy6BBT167x5ptvkrBtTp8+zRtvvMHI6CjjY2OMjo1RVFzgOLoZp/vCWbxXLiGKKRLP7kS6Af570wgByRY0UuCZkP5T+xH57ucW9Wj6fiiYFWvODmQ4Nk+XH/RrtbpBaWkpPG81TqDpOJFqgW6aNkwz6uVcC3Nzc7Qch82bN/dl0K7r0nJdbDW3Jo7A91mYn2d6ZoaZ2Vkq5TJDg4Pki0Uef/TRnsrqmkDfbztaTQl8Z7PZtiFW8e9Ph9ye57F1xw4GBgbWPLebjdvWOAFyuRz1apXA80hYFjXHIa/JyfqD7Xb37OItDcNYfkxd2L2+VsswGBsbY3h4mEBKHnn4YfwgYHZmhumZGT44cwbP8xgbG2NsbIzxsbHwjky7p3ZfuUjz/3oz2q73+mVILX/kdguaSWhNpMl/epk03qlF5DSbVKvVUKWwI4lhKOOCduYSiv5oK7IDUoZj8dSNy1UEi2htpt9vGJGCoDbiOE6eOMFeNW59rRghUB7LMIyQgSMlS6USszMzzMzMMDc3R75QYGx0lHsOHGBIrSFLpdKa61Jo/071MqatJi4ltXo9TABls226RG2G2WrhBQE5y6IwOMjI6OgtD2nhNjdOwzDIFQqUFxbI2jatVotKpRJ6Ld1b2eXuaare0E50o+L1gp1IkM/nWVhYYHpmhomJCTZv3sxmlSSo1+vMzMwwNTXFu+++i51IMDQ0RHFggGKhQKFQIHjjysoNK8EufQR2C4LP76YVeEjHjdrm2lQGZCj1mUmnSdh2aJTK6/WC9mrxQr+UkkQiEcmE6ptAQLgm06JkrpKH1Aarm6ArlQqVapVtmjGzyvJCShnKklYqNB2HSrnM/Pw8CdtmbHSUHTt3cujQoRVZVn2j6LdrRsuldN4s9OhHnZlNxA2zYxsV1XqYyWaZmJzsey7OzcZtbZwQktRrtRpN1yWXz1NaWqKsDBTVXkRHyGpZFg60jeH7pf/lf+G9d9/lJ3/qpzj0yCPRayXwr//Nv+E73/kOf+b7v5//9i/8hei5XDZLuVzG9Tzm5uba5n5kMhl27NjBjh07kFJSKpdZWlqiVCpx7do1FhcXeeisS1FKELCS3yPxTZBDKeqb0zjz82RURlory5tKWd51XRACO5mM1kTXg0C2C0lrQbIA2phQuj9Va81qnd5jx46xbfv2SLFCw/M8SqUS5VIp/AzKZcqlEpZlUSgUKA4MsHXrVu69//41JWJkjxvuaq83WMkiqzUaeNowO28ALBuo7/s0FGNrfPNmcrncR6ZLuxZue+MUQpDP51laWCAAsvk81Wo1mjYtYtlZ7Un0hebFjPMv/nf/Hf/PY8f43d/9XR5++OHozvyVr3yF73znO3zm059uM0wIRY8RgsFikcVSibn5eUa6rIOEEAwUi9HIQQgNoXr0T2CxDFInJySBELRsaCYlnikQNQfxW2/jPLeTzN5MOEHtJiUiutU4uyVWtLCXaZrYySSB73Px0iWq1SoTExOcPn2aZqNBtVajUq3SbDbJFwoU83mKg4NMTk5iJRKk0+munNZuiLLrmvvbp3Hqm43OMWgyu+/7JFOp7vXP8CSRUlKpVhHA2MQEhULhtvGa8DEwTghbwxrpNI16nYxpkslkwsnEjQY5rcinGST6whIiHN2m1g7btm3jiSef5MUXX+R73/0uTx8+zFe/+lX+y9e+xuOPPsqP/uiPrtivnUzSajYZGBiIvONMEDAyMrLmxWMIgXD96I7um9BMClqaLtuEVENiuRJjqcni757gu49/QDPwSCWTZFQrWzqdxk4mEUAlkwn/bxhYSgtWq6WbsZ/OcNdXIxCaqtnb87wwueR5+FLiKcFr13XDAcP1OnXHodloUFfT3YSUpLNZFhcXw8FP+Tz5QoGd6TSZbDaakSkJ+xkNWHNOTBxRMkuH82sZpyIm6MYITfGsqzVmWkUh8e3H36sz9fV6HTuRYNOWLeTz+evXy70JuH2OZBUIEUoSzvl+qJ6XSIRzFR0HU4jw7hwvsYhQK7ZzNuMP/uAP8tJLL/F7v//7OM0m//7f/3vuve8+fuInfqKrsdmJRNTTNzg4iBAiTGjMzTHah4FKx8MzoJkKdWcFYYbWbgGuDsUECMhV4fF9D5DZPhJRzBw1ibumxuktqGRTNPxH/QSx//tKA0equut/+I//EVDDipVRmyqppg1ZD2ZKqM91YHCQiVSKdCpFKp1menqas2fP8uyzz7adnxaWbjabtFotms0mruuG6+N8vi8ucGfNOkpOrfZe9ZyM/gyXN7VaLQxlFeUzzg6Kk+l1zqFWr9PyPHbt3Us+n1/3NLmbjY+FcUIYvgwNDTE7PU210SCfzRKoi1gAdjod9igqAzVNM5QFiX35g4ODfOELX+AP/uAP+M3f/E327dvH3/mZn+l5t9Qj5DUGBgZACJaWlpiZmWFsbKyngQZSUsejlQNDQtKBpBv+H8Dv4BXZGIiRbDibJZ9vW5u5rku1ViOXzbbNNe0GXUZxfZ/f//3f54tf/CKGELRcl3qtFg1l0q9da/3q+T7Hjx/v2gYVTxb5vs/S0lJYzBcCV6lIrGpk+ruJH4PygqsyfzoeC4KARr0eGWZCdZnoY4yMvSMZWC6XyWQybNm69bqkK282bqtm67VgWRaDw8NI06Req5HJZLAsi7rj4LnuMsFZiHDyF0RKfvpLia8p/tpf+2thyrxHWcC27chzagwUiwwODNBstZiemelqJE6zydLiIi18ks3QK6Zby4YZIvaHbWL/tcfIDBZByhW6rZ0XaiQS3QWCsFdTy6vom4dWkmsrrPfh2U6fPs3g4GDXmmP8GLTHHBocJJ1O01Tln9UmS3fL9garec4udWTf86L9aMMEIpK83pbWTtKo12o4zSa79uyJoqLbDR8r44RwHTMwMkLL92nU6+SyWQwhqFWr+K4bCW6Zyjj1xSGBl44c4bd/+7eju+Qf/dEfRdvt9uUkEomoxBBHsVhkZGiIVqvF1NRUZKCBDEfU1+p1hCdDo2x2GmW0x/Df3UOk/qfPYt4/GXqhRIKm43TtQYyHceu9lCLRtDg7Zg2v6TgOH3zwAffcc0/3F6j3t5rNsDcykSCTzZLLZskqJk690Yi6PXq9v/0h2V6v1ccaW7JotFotqrUaANlcbsVMG92gviJ0DgJm5+fJDwywd+/eDzXN7GbiY2ecEJITcgMDNJtNaorWJ4SgWqtF8pMB4TpLG+dbb77Jv/43/4YtW7bwi7/4i0xOTvL888+HkiYanRcEkM1kohajOPL5PCPDw7iex7WpKZrNJqVSCdd1SadS5MwU1moEGssk8YP3kvq7hxFjy2udjFo/O/F9drlxrPdO73fp41yrIHP8+HG2b9/ee/CsEHiuS12xjuKZ2UQiQSGfx1ZLg1q1utyCp8slXRDXbVreTbvYm5QySlyZpklONejHjyv66fTMvh9K0/g+DzzwwEc2Qv568LE0ToChsTFyxSJuq0WtViOby2GZJrV6HUetQy3LouW6HH//fX7tV3+VoaEh/t7f+3vk83n+6x/8QYIg4N/+23/bvmH9pSrkCwUqPWaT5HM5RkdGaDWbnLtwgZbnkcvlwvkvXSQuo11sHyT9P30a6/N7V8zYNBQx23XdqOG36zbW/oja0FVIehXPWSqXuXLt2qqdJ77nUa/XMQ2DbLqL1pHismaUGkG1Wl0RhXTC8/0VoXf8KIMgoK5uwolkkmw2u6J2G8m6dNn2UqlEtVpl6/btXTuMbid8bI0ToDg6Si6fJwgCqtVqNO+x4TjUajXsZJKpa9f4tV/7NSzb5u///b8fcSYPPfoou3bu5I033uDkyZMrN64uikKxSKmHcUKY0U2n02FavlaLPLXYUgCj82KFxJ87SPofPIuY7K04r5vA6/X2Ruzrox4sE/z7XW9K4O2332b/vn09aWy+71Or1UAIcnHOahfYyWRYvwWqiufaa7+Brk133CRBrS/VZ5xKp6Nm6fjcmCAIuqofuCohVqtWySv+9O2Oj7VxmokEuaGhMAUuJdVKhWQyGTYzt1pcunSJL3/5y9i2zT/82Z9lbGwsGl0H8N8o0sFv//Zvd92+EILiKp6z1WqFN4V0mu3bt5OwLKZnZihXKmFp4i89BPqizdik/odnsP/U3QhzdZU5YRhk0ulICCsK87qQBfpBNN4its/VumfOnj2L73ns6qEmqMcX+lK2k8l7QIhQPkaXKnoZqCbwG6a54lyj9aWU4foyJpAWnU8PZlGz2QwH+DabWGo41o2UE7lZ+NiUUnrBzmQIPC9ccyrmUCadjlqD/v4/+AfRF6qhs50HDhzgt37rt1bdfqFQ4MTJkyuSCl7cc6g17/j4OHNzcywtLdFqtRh6chv2p3YQ1JoY2Y61jVy939ROJqNJ0Z3k8/UiarLuoOh1M+16o8Hx48d55plnuhq/lJJ6vY4MAnJqXHtPSLk8Yk+RQ3KKjlmr18PPLfZyX9EwTcX60sfuOA5uq4VpWW0tX3paWvxGE+9GkkFAQ00VN9T6eMeePWzdvr2PT+3W42PtOTVsdSfVw3H1XTKtitENx4lCxHgmUM83Wc2L5PN56rVaWz1OylCv1Q+CyDAhvPjHxsYo5vM06nWmpqfDiVWdhhk7htWIDHoeqU5IdR5lv+tOX6lHtAlndXmdBN544w327NnTlcYWKDK5pxg4a0486zAcCPMA2UwmGoEQnYsudwRB1GXTarWoVKu4arp43EtHZPfOhI8yTle911MJuqbjMDQ2xoGDB1c/5tsId4RxGoaBXSxiWBa5XI5sNhvdNTWJfGlpiVq93tbtEfEyFetGT3COw7IsUqlUGFKpdZCj7sadyQhQPFtVFwx8n6mpqd6lBH38PQzUME3SSjbDdd2uCZx+Qls/CMIhQTGP0w0XL17EcRzu6tJIrUNZz/PC7ph+yOE99mMlEiRVFrfleaF3ZbncEwQBtWqVRr2OIQS5fH45q7oKvU+HufVajbpS18vlcuGs10yGg/fcsy5K4a3GHWGcELaJpRWDx04myRcKIcNHzeKwTJNatUq5UmkrjGvqVyRgrRIK8Qu4oNedKhPYUENvVrtAs9ksY2NjWIYRrkNXSSpBbwNNJpMk1AjBbomOfhDEvBHQ1WicZpN33303bArouOEEQUC1VsP3PDLZ7Nq9jn10zaRSqWg8hf6sdQeMzuqmFG83Op4eobhGo9GgUqngel5YzspmcV0Xp9Vi1+7d6xIjux1wxxgnhAmidLEIIux3zKqCuGlZ4fpOecdKpRKum2JeVBup/js+1i+fz1MqlQA1gTkI+uq2SCaTjI+Pk06lWCqVmJ6dxVXJmW4hWS8vmFVrs0Z9pYwmEMl2xH/CJ5YVFCJtpR7vf/PNN9mxffsKBQBtmFIpCWjmUXdehWj/vQqEasCWKI6u51GtVHBdF9M0o5tA202rx/FrllCj0cAwTQqFAqlUKmQp1Wrs2L277wlotxPuKOMEsJJJUrF5GAnbJp/Pk8nnabZaYROxlDiOQ1ldDBF6cDpHRkaYmp4OxYhV4ds0zb7WfKZpMj4+zkCxSMtxuHbtWtTc2/n+bswYWK59ep5HUx2/ZkL5KpTr/NE+1lcZUDM+NStWpJfAlStXqFYq3L2/XcPI931q1SrS98nGeL36s1o+8O7Z5BXo+HwTtg2+T6lUorS0hC9ltCyJJ5p6fc6+51FXTQFeq0U6naaQz2MaBs1mk0qtxo49e9i7d+9t1W3SL+444wRIpFLYhUJ0MRqGwdDgIIViMRpaJKUMO/QV3U4nGGD5YtDvHx0dpVQq0Wg08IOARDK5IpG01tqvWCwyOTmJnUiwuLTEtenprrzTyEA7LnQ7mUQomqLrectzQXuUDzT8OKe2CzOn0Wjw9ltv8dAjj7Q1XPu+H4ayKtPd9eLW2+ojjI1YPuq1vsrCNlWbGoYRdsF0WRN2bt33vKhTx1Pq8Zl8PmoPdFstSpUK23bs4K677rotJEeuBx+/20mfSKbTCClplMthb6UIG6KXIArNms1mmJRotWg1m2EopTop4l7MNE1GlfcsFAqR8HD8YovkNehoZYohkUgwMT5OpVKJFBOKAwORbIiGgCgxAkQ3gqQay16t1Sjk88tG2UW8TENnak3DCGuuMUMKfJ9XXnmFu/bti0aqaz5yTdUU82pZ0AnZhSSw8kUy+pwCNVnNCwKa6vOWsKzuABjqe2nv14mdi+fhNJt4ashVMpUiqW6UGm6rxeLSElt27uSuVUgUHwfcscYJYQ0UoF4qYQiBrfoVded+Kp1e7plU5RfbtsO1ldLqgdDIJiYnmZqaYqBY7Jm80ReV/hHKaOKvFkJQKBTIZDLMzM6GdLJajZGhobYp2lGZJ/Y+IQQZVSes1+uhcnr4ZNc1LITGaem6Ycfzb7/zDplMhr179kSPua4blW5yKkTsdp4rvKX24LEmAMMw8FUSJwiCqO9TArZlRUT1UqlE03XJZ7MrW8KkjBrF40Zp2zaWYRCwvH73fZ/FUolN27axb9++j1VmthvuyLA2DjuTIZXP4ysZyawaBdDQnNBslsGhIQYHBzFNk3qjwezcHHNzczQajeiCn5yYYG5uLpoluRoELPeWwrKEpZThcajs6djYGEODg/i+z9TMDEtLSwSqeXoFg0ZtK5FIkEylcJWCukavwNIPAowunu/ChQvMzc7y8EMPRUbVaDQirmyxUCDRRVUhgGWWlYoWdAkq3soWqfqpBvmyHt5kWeRzOTJqXWkYRhim+35b6Bz4fpQX0EJdyVSKfD5PKpXCNAwCEY5NCJQ3nl9YYHzzZvbdfffHggG0Fu5oz6mRUmum2tISSEkmnaZWr0c9iKZhkM1kSKdSuK5LrVaj4TjMzs5i2za5XI6M4u1WSiXyelQgqxMBoud08iXGAdUeJpvNkkomWVhcZHFpiaVyOWy2zmRChT29nxhVLaWSQw2tQavobt3CQalqnHGUSiXee+89Dj/9NFYigZQyXF8GAUnbJh3nrCrPHyesR2GqPg9djmK5b9b3/WjZAERRS1zGU98UfN+Plh4t9R6dG7ASCWytBSTaJ61p1la5UqHleWxXA6puN0WD68UnwjgBrFSK/MgI9VIJOwioK9ZQfL1nmCa2UBOofZ96vU61WmV+YYGlUonBgQGmpqejGRpR4og1jLSjHADtRADTshgZGSFZrbK0uMjC4iLlSoVCoUBWewDFoNFN0+lUioqq2xby+bBXM7ZPXQrqpLi1XJeXXnqJew4eJJvP02q1IvZUOpOJkirR8anfuv2ujSnFcgJLqqjAVWt4XZONG2Xc2DV90A8Cmq6LZZqUK5WQ1qhG89m2HTGCuiXJfNdlbmGBTC7H/n372LZt28cyK9sLd86Z9AHDssgND+NUKqGsRqlEpVoNOybUl6/rnaZpRroyzWaTSqVCOpPh3NmzXJuaIpNOk1ad9213c3obarc+RR28BkEQcoLTaWq1GqVSiYX5ecqlEsViEQPwdOJHGVw2k6FWrVKv1UJWVOd+NEUwxoR64+hRxsbH2bZ9O81mMxxFKATZTtFlVnphLUcSNUSjxMMU00dnn03TDD+bRCLatyEEQcwLe56Hp+RXnEaDfC4XDrJVIxL1McQ1f+J11Kq6MY2MjbF7zx7Gxm7eZLZbhU+UcWqk8nmsZJJASkqlEpVaLUpGAMt3aHUxpVSKP5PJcOHCBRYXF/E8j3K5jGlZpJLJsF3NsqJhS2shnmzqZCRls1nSmQz1Wo1yqcT8wgJSSmzbDj29uoFYlhUOfFJqedkuxAhDjV2QUvLuu+/iNJs88sgjIUfW80IxLhVCx9FrDSuUkTVbLbxWC9fzIhHoVDKJnUgsh66xNXdTGaPnecvyl4aB53nYts3w0NAKo4wSazGjlEHA4uIirgpj9+zZc0esL7vhE2mcAJZtM7ptG/LSJcpLS9SEIK0oZV1btIQglU6zZ88erl69yl1799JwHBpKJa9Wr2NZVpSF1BepaVlheaVHPVIAdHT/65JMTiVOatUqCyq0llIyUCySUuvCZCKBTKVwmk0a0M5cUhGAHtk3OzPD4088EZZJgGQqRUrJbvaCXhsGSl6z5Xk06vUw0URIJLATicjragK7pxJbXsyjCiGiKV+WZREEAaVqNexu0Swu9Tm13RxU2NxsNFhaXCRTKLB3/362bNlyR4Wxnbhzz6wPGIbBxPbtSCGoLi5iiOURdUZ8rQMgJaZhsGXzZk6cOhWOChwYIK+I1a1mk4bSeHWWljBUoslUkpNxOUqdpdTo2m2iQ1IRimrbts3s3Bye6zI3Px9lmjPZbDg6Xa3dhBCkUqkogWMlEpw5c4aLFy/yyCOP4HpeFBJb2st3oRHq0NNXxqXXkNrAUqlUxOLRbV1amrNzPa2nk3dq6laqVaTrkhkcbFfJWz4QpJS0HCcstzSbTGzZwp69exlZZeL0nYJPtHFqTGzdypQQVBYWEIaBnUiEyRQhwulbsVplOp1m9/btnHj/fR5/8sk2echMNhsaqhrS6ilxsJaafaKHDpmGgWmaWJaFFCLsR1WGLEyzrY6qDdW0LHLZLJl0mpbnhST+cplypRJllC3DCJX7dJZXSq5cvszp06d56KGHsCyLZDJJKpVa4aml8oyuypTGpSVNFRHoG0qz1aLZakUZVQ3TNMMbkdLG1SF1HHqvnkq4JWw7rO/Gz1l5UG2UrVYL0zS5/6GH2L5z5y0fzfdRYcM4USSDLVuQQG1xEZlOk7TtqHwhwxchhCBh22zbvp1vP/88tWo1lOggZMwIwjqkXscFQbAsAK09kDJYz3VpAr4qJWiSQTSWLz6iT7GFPM8LeylTKTLpdFj2qdep1WrMz89H6nqe62KpwcPHjx8PO/+z2TAEhqh+q2uEnu+Dyu7q49Ai1Kg1sfbEUkpaqgRlJ5OYaiqZ0aUmql9vaDZRzKPWajXcVouBwcGIlK+fd5pNSqphXRgGIyMjPHjo0DLp4hMCscaw17VJk3cQgiBgdmqKytwclmWRzmZXsDR0l8ebb72F63k8GhuKFH+NLi90Zj3jRqb7NBuNxnIHiWo4jl4fo8DVazVSySQJNfZAc2UDKWm1WjQajZCO2GyysLTE3Pw8u3buZHBwcMXazBACYRihN1c3AkuF29rQzNjNQXt2RCgYveKc1XG21XZ7XFue53F1ehrDMBhRY/+iURCNRrRGzefzjE9MsHf//ttmuNBNQtdl/4bnjMEwDMYmJ0lls8xfu0alXA5bzjQrSF1wpmmyZ/duvv3CC1y5epVNmzaFT6vtaHpb29+oRI9hhHNFWDbgRjodtrOpWmG8RhlN/AoCWo4TenDDCL26MgYBZFTI2nQcLlcqVEolTCFIqJEShgjHVqRTKZIq8aWPTXtLbaxx6NKQJkJ4sntP5Qqv2cMwpZTh2tnzKOTzlMvlKMEkpSRhWRTUHJbN27YxoT7bTyI2PGcPtFotZq5dwymXSSWTK/RNJXDu3Dneefddnn3mmUhSJE7b66elDMLQtlNZPl7O0VgqlbAMI+rvBEIpEDVgt9lscu7cOaanpjhw4ADZXI5GoxHR7SJSgkp8JZPJcBJXbD25apeLlFHLWt+IMaM8zwupkQsLJCwrJDyoElFaNVZbpkkun2frzp2k+pxQdgeg6we+YZyrIAgC5ufnKc/PYyjdnHifYSAlr736KtVGg8cefTQKvbSn0WutTg+6Yj/QVv/rhWqtBkFAvlhcJoSr4UEyCDhx8iStVosHH3yQIAjI5fM4jQZOsxkRAxzHCQ3ZcSJdXAnRulHPBU2ohJWVSEStZIHOCPc4PilE+0xPlRTTibF6o0G1UsFKJBgdGYnkLfVnapomE5s3MzY5ueZ3c4dhwzivF9VqlcX5eVpqlmNSFdshpMN961vfYtPkJDt37Yo6S3SWVa/FIrU7sdyOFg93PTVVGimXp3bHt0GohOA4DplsNswG+z6m8nJvvvkm6WyWRx5+OBwHARFHVivjG4YRjq9QXFw9IUwbULQW1scRXzcrD61LKlKxlaQKr/X6t63HlTDTa5lmNEjJTCTYvGlT203OMAwGR0aY2LSprTPnE4QN4/wwCNQsx9LCAo1KBYIg4n+WSyWef+EF7n/gAQYHBlaUKtZCnCUkw51F60kIDaGpNHIbSlLSsiwStk2jXufV115j27Zt7FdKBqWlpRWDY11VfoGQgbRCOS92HUhluJ7r4gVBVBYKPI8gfqNpPwkgLCsllL6SZVnRvE6t/jA8PBwZpjAMhkdGGNu06bYei/ARYMM4bwS0xMni/Dz1Ugl8HyuR4Nq1axw7dox77rmHYrEYTUBbz3b12lCXKzzXDdupAjUxKwj41vPP84d/+If80pe+xPTMDJcvX+aBBx9k8+bNYSa11aJerZKNz8dUns0PAurVKp7vc/HiRf7pP/tn/Pc//MM897nPtXfN+H64llX71C1ha41S6ESr1YpKPYZpUlAqeoZhMDQ6ytjk5CfdKDU2srU3AkJnPbdsoTk6ytLCAvVymeGREQ4cOMC7777Ljh07GBkZifi4beJhsWSRJOzu1/XQlpowrVUDpMoMJ2MtU0iJAXznu99lx+7dfPbznydp27zyyiscf/99pqammJmaYmp6mieffJKf+ImfiJI8hhBkFZF/y9atTE5O8vabb/K5z362feKYYYDqQb0e+Go0hVY8SCaTZHM5cvk8QyMjDI2MfKwVCj4qbBjnh0AymWR8chImJ2m1WoxOTlIYGODll17CaTYZHRmhVCph23bYvRJ/c0cdUBMINM1Ns4hEzIM5jQbT09OYpsm999/Pvpi+7O//3u9x6fJlRkdHyeRyMD3dfrBqTajpfQnbZt++fbz99tvMzs4yPDQUtnWpfYWHuOx5fcViWoHY2jhQx9hstSKCQyaTYXLrVsYnJ8l1EareQG9sGOcNgm3b2KOjDI6OsnnnTn7vd34Hp9Fg69atmKZJ4PvYyeQKj9FphCsytlKyOD/PmfPnuXblCpbi6Q4PDra95i/90A+F/Z/ZLFevXeNL/+SfrDzIWILKNAwefPBBvvfd73L8/fe59557MA0DW5H2O+l9PcsrIpQcdZpNWs1mVJNNZTIMDQ+zY+dO7I+5XMitwoZx3gQMDg3xl370R3n99dd57bXXGMrl2L5tG4OWheM4oSHb9oo5IwKizgy32eTCpUucP3eOwPfZsXMn937f9/Ff/vAPI05uXG/n4IEDVKrVsFtklTpl+EvNitm/n0BK3n37bR579FGajkOjXqeButkkk1im2bXEI6UM+zhV25iu02bzeYZHRxkeHSWfz39ieLA3AxvGeZNg2zZPPvkkjz32GMePH+flI0cQnhcJeaVTKdKZTDhlW8pI6lGT2ZeWlhgfH+eB++9neGRkRfbXV2R6DZ1VTadSYfInnmCiPeOg9X7sZJJ77rmHt995JyTFF4tR7VSrEuoElaWICjqT23CcsKyipEILAwOMjI8zODTUdUzFBtaPDeO8yTBNk3vvvZd77rmHixcvMjU1xcL8PFfn5ymfOUOtViOthK/zuRyFQoFNW7ZEmc1ukFLitlptjzmOE1ID1WxPM2bMnX5UE/WRkocffpg333iD999/n3vuuWe5wyYIaLkujuNEow79IMBUHnVwdJR8oUC+UIgigfgEsA18eGwY50cEIQTbt29ne8f4Oc/zcFTTdq1SoeU4uI4TKg0oRTpTk9HVe1rNZtjMHIQDcf0gwFUzYfr1WAahgT74wAMgBK+/9hoHDx6MCPm+kh5J2DZDxSLZfJ6c0uxNqezxhiHeXGwY5y2GpSaj5XI5RkZGaCqObLPZpFGrUV1aoq68pBACLwgICGuICwsLZPN5HKVYn7DtiD+rs6W6e0WXRWRMplP6PmYiwf79+zn+/vuUymWEEGRyOYojI9GQ2mQyuWGMtwAbxnkbQZc5tBiyVPxZV2nvuK5LzfM4d/kyqXweTwiWyuVoyFBTcWwbzSapTAbDNKnWasvdJqoJ24wxeBK2zQcXLuD6Pvvvvz8cmZhIrD4UdwMfCTaM8zaGUC1fnb2MZ8+fZ+uOHYyNjUVTubRWkJSSq3NzvHX8ODv37WPPgQPLLWGxhm79nnPnzvG9l17iH/7Df9h1YO4Gbh02jPNjCsMweoonJ5NJyuUynuetaXBf/epXAfjiF794w49xAx8OG/nuTzi++tWvMjk5+f9v745xJILDMIy/B5jCDTSuIFpROYNK4SAO4BJuQKHQS7RcQJQavUayxSSbzM7sTrXrW55fopFIvuaJPwL5vn/0KPiCM+dJVFWlqqokScuySJL6vleappLu/xgtiuLhmHVd1XWdsizjZo9BxHkSwzCoLMuHfdM0aZomSZLruk9xNk2jfd9Z0hrFsvYk8jz/vCH0apvn+emYuq51u90URdHfD4y3iPOitm1T27aK45h3Ko0izosax1Ge5ylJkqNHwTe45ryoIAg0DMPRY+AHxPnPhGEoSXIc59A58Pv4hhBwvJfPsbjmBIwiTsAo4gSMIk7AKOIEjCJOwCjiBIwiTsAo4gSMIk7AKOIEjCJOwKh3b6XwYRngIJw5AaOIEzCKOAGjiBMwijgBo4gTMOoDIiryUh7auGsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bob's state: 0.5534+0.3044j 0.6148+0.4724j\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[92mState Successfully Teleported! Good Job!\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "def check_same_state(result):\n",
    "    # A little extra style\n",
    "    def green(string):\n",
    "        return ('\\033[92m' + string + '\\033[0m')\n",
    "    def red(string):\n",
    "        return ('\\033[91m' + string + '\\033[0m')\n",
    "    try:\n",
    "        # Put our snapshots into a list\n",
    "        snapshots = result.data()['snapshots']['statevector']\n",
    "\n",
    "        # Get Alice's state:\n",
    "        alice_state = snapshots['1']\n",
    "\n",
    "        # Get Bob's final state:\n",
    "        bob_state = snapshots['2']\n",
    "\n",
    "        a = alice_state[0][:2]\n",
    "        b = [c for c in bob_state[0] if c != 0]\n",
    "        # Account for a single state in bob's statevector\n",
    "        if len(b) < 2: b.append(bob_state[0][1])\n",
    "        \n",
    "        # print(\"Psi state: \", psi[0], psi[1])\n",
    "        print(f\"Alice's state: {a[0]:.4f} {a[1]:.4f}\")\n",
    "        plt.close(\"all\")\n",
    "        display(Statevector(a).draw(output = 'bloch', title=\"Alice's State\"))\n",
    "        print(f\"Bob's state: {b[0]:.4f} {b[1]:.4f}\")\n",
    "        plt.close(\"all\")\n",
    "        display(Statevector(b).draw(output = 'bloch', title=\"Bob's State\"))\n",
    "        # For simplicity I am rounding and summing to check for equality\n",
    "        \n",
    "        if np.round(a[0]+a[1], 5) == np.round(b[0]+ b[1], 5):\n",
    "            print(green(\"State Successfully Teleported! Good Job!\"))\n",
    "        else:\n",
    "            print(red(\"Bob did not get the same state as Alice! Check your code and try again!\"))\n",
    "    except:\n",
    "        print(red(\"Error: Something went wrong while running the checker function! Check your code and try again!\"))\n",
    "\n",
    "# Check if it's the same state\n",
    "check_same_state(result)"
   ]
  },
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   "metadata": {
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   "source": [
    "---\n",
    "<h2 style=\"text-align: center; color: darkblue\"> Well Done! </h2>\n",
    "\n",
    "---\n",
    "\n",
    "<img src=\"https://thumbs.gfycat.com/LikableUnfortunateCaecilian-size_restricted.gif\" width=\"500\" align=\"center\">\n",
    "\n",
    "\n",
    "# That was hard! Well done for getting to the end! \n",
    "\n",
    "---\n",
    "### After you successfully impelement teleportation, try changing Alice's state $|\\Psi\\rangle$, and see if it is successfully teleported every time! When you change this state, make sure that the state you are using is normalized.\n"
   ]
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    "## Do you want to learn more about teleportation? \n",
    "\n",
    "Why does Alice use the exact gates she does? Why does Bob use either an X gate, or a Z gate, or both?\n",
    "\n",
    "Check out the <a href=\"https://qiskit.org/textbook/ch-algorithms/teleportation.html\"> Qiskit textook page on teleportation to learn the math behind the protocol! "
   ]
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       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.21.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.10.4</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.19.2</td></tr><tr><td><code>qiskit</code></td><td>0.37.0</td></tr><tr><td><code>qiskit-nature</code></td><td>0.4.2</td></tr><tr><td><code>qiskit-finance</code></td><td>0.3.3</td></tr><tr><td><code>qiskit-optimization</code></td><td>0.4.0</td></tr><tr><td><code>qiskit-machine-learning</code></td><td>0.4.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.8.13</td></tr><tr><td>Python compiler</td><td>GCC 10.3.0</td></tr><tr><td>Python build</td><td>default, Mar 25 2022 06:04:10</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>31.211315155029297</td></tr><tr><td colspan='2'>Tue Jul 19 01:05:10 2022 UTC</td></tr></table>"
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    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table"
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    "### © 2022 The Coding School\n",
    "\n",
    "**All rights reserved**"
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