Grover Search of Sudoku.ipynb

{
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   "id": "88b805a9",
   "metadata": {},
   "source": [
    "## Programming Assignment 2 - Solving sudoku in quantum\n",
    "\n",
    "In this assignment, we will look at how to use Grover's algorithm to solve a real world problem.\n",
    "\n",
    "Disclaimer : Recall from Lab 1 that we saw how to create and run jupyter (.ipynb) notebooks using IBM Quantum Lab. For this assignment, please continue using the same to avoid any installation issues.\\\n",
    "You can upload and download notebooks in IBM Quantum Lab."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e088f176",
   "metadata": {},
   "source": [
    "Fill in your details in the below cell. \\\n",
    "Your Name :  Soham Chatterjee \\\n",
    "ID : BMC202175 \n",
    "\n",
    "Rename the notebook with your ID as a suffix before submitting in the moodle page."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bf69e47",
   "metadata": {},
   "source": [
    "## Problem Statement \n",
    "\n",
    "Consider a 2×2 binary sudoku, with two simple rules:\n",
    "* No column may contain the same value twice\n",
    "* No row may contain the same value twice\n",
    "\n",
    "Assigning each square in the sudoku to a variable: Construct a quantum circuit to output the solution for this sudoku.\n",
    "<div align=\"center\">\n",
    "\n",
    "| __v0__ | __v1__ |\n",
    "| :---: | :---: | \n",
    "| __v2__ | __v3__ |\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8be6c381",
   "metadata": {},
   "source": [
    "Mathematically, we simply need solve a boolean function that checks whether the state of our variable bits is a valid solution. Since we need to check down both columns and across both rows, there are 4 constraints all of which need to be satisfied:\n",
    "\n",
    "* v0 ≠ v1   # check along top row\n",
    "* v2 ≠ v3   # check along bottom row\n",
    "* v0 ≠ v2   # check down left column\n",
    "* v1 ≠ v3   # check down right column"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f42bc22",
   "metadata": {},
   "source": [
    "## Expected output\n",
    "\n",
    "Set of assignments to the binary variables v0,v1,v2 and v3 such that the above conditions are satisfied.\n",
    "\n",
    "In this assignment, we will try to find such an assignment (or set of assignments if there are more than 1) using Grover's algorithm. \n",
    "\n",
    "To help you solve this, the assignment is broken down into individual parts. You need to write the code wherever marked."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "03dd3786-0ec5-4c07-9e82-c0e74ae69cad",
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   "source": [
    "# Importing standard Qiskit libraries\n",
    "from qiskit import QuantumCircuit, transpile, Aer, execute\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from ibm_quantum_widgets import *\n",
    "\n",
    "# qiskit-ibmq-provider has been deprecated.\n",
    "# Please see the Migration Guides in https://ibm.biz/provider_migration_guide for more detail.\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Estimator, Session, Options\n",
    "\n",
    "# Loading your IBM Quantum account(s)\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "backend = Aer.get_backend('qasm_simulator') \n",
    "\n",
    "# Invoke a primitive. For more details see https://qiskit.org/documentation/partners/qiskit_ibm_runtime/tutorials.html\n",
    "# result = Sampler(\"ibmq_qasm_simulator\").run(circuits).result()\n",
    "\n",
    "from qiskit.providers.fake_provider import FakeGuadalupe, FakeKolkata\n",
    "from qiskit_aer import AerSimulator\n",
    "from qiskit_aer.noise import NoiseModel"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53f79929-c023-4f96-b365-151f8f4fce19",
   "metadata": {},
   "source": [
    "## Create logical gates with the help of quantum gates\n",
    "\n",
    "### NOT gate\n",
    "\n",
    "The NOT gate flips the value of a bit and, as was mentioned before, an X gate can be considered a NOT gate. The truth table for a NOT gate looks like this:\n",
    "\n",
    "| Input | Output |\n",
    "| --- | --- |\n",
    "| 1 | 0 |\n",
    "| 0 | 1 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fd6565d5-2660-4e70-8b70-a99b1519b346",
   "metadata": {
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   "outputs": [
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SkvWx6upq5OXlYfny5TAYDE6ZD/cVqbc8LsaGhgakpaVZf11p2LBhCA4OhslkQmVlJRRFQV1dHQYMGNDnc6mrb8TGbTthkWUs/bc/8iQ/3ZLHXYETEBCATz/9FNu3b8fkyZPR0tKCb7/9FhqNBjNmzMD27dvh7+/f80Aq4NU2ZAuPWzOK5NMvinH86+/wyLwUxkg9Yox9rPVaG/Q+3q6eBrkBxkgkCI/bZyRyV4yRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQjJFIEIyRSBCMkUgQ/wc4ZO+kQpfUiQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 269.064x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_gate=QuantumCircuit(1,1) # Create a quantum circuit with 1 qubit and 1 classical bit\n",
    "not_gate.x(0)\n",
    "not_gate.measure(0,0)\n",
    "not_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10028d6e-13c0-4bf1-8ae3-47e4560ed3b1",
   "metadata": {},
   "source": [
    "### AND gate\n",
    "\n",
    "The output of an AND is true if and only if both inputs are true. The truth table for an AND Gate looks like this:\n",
    "\n",
    "| A (Input) | B (Input) | Output |\n",
    "| --- | --- | --- |\n",
    "| 0 | 0 | 0 | \n",
    "| 0 | 1 | 0 |\n",
    "| 1 | 0 | 0 |\n",
    "| 1 | 1 | 1 |\n",
    "\n",
    "With a Toffoli gate, we can get the result of an AND gate by interpreting the two control bits as the input bits and the target bit as the output bit."
   ]
  },
  {
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   "outputs": [
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     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 287.496x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "and_gate=QuantumCircuit(3,1) # Create a quantum circuit with 3 qubits and 1 classical bit\n",
    "and_gate.ccx(0,1,2)\n",
    "and_gate.measure(2,0)\n",
    "and_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc338fde-c2bc-4ce6-9b14-8955aebeea40",
   "metadata": {},
   "source": [
    "### OR gate\n",
    "\n",
    "An OR gate returns true if at least one of the input gates is true.\n",
    "The truth table for an OR Gate looks like this:\n",
    "\n",
    "| A (Input) | B (Input) | Output |\n",
    "| --- | --- | --- |\n",
    "| 0 | 0 | 0 | \n",
    "| 0 | 1 | 1 |\n",
    "| 1 | 0 | 1 |\n",
    "| 1 | 1 | 1 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4ca564cf-c21b-4905-a46d-717e50469add",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 454.719x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "or_gate=QuantumCircuit(3,1) # Create a quantum circuit with 3 qubits and 1 classical bit\n",
    "or_gate.cx(1,2)\n",
    "or_gate.cx(0,2)\n",
    "or_gate.ccx(0,1,2)\n",
    "or_gate.measure(2,0)\n",
    "or_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bba5e944-d53a-4ff2-832b-073ee6e02e70",
   "metadata": {},
   "source": [
    "### XOR gate\n",
    "\n",
    "A XOR gate returns true if both of the inputs are not equal.\n",
    "The truth table for an XOR Gate looks like this:\n",
    "\n",
    "| A (Input) | B (Input) | Output |\n",
    "| --- | --- | --- |\n",
    "| 0 | 0 | 0 | \n",
    "| 0 | 1 | 1 |\n",
    "| 1 | 0 | 1 |\n",
    "| 1 | 1 | 0 |\n",
    "\n",
    "Do you see a relation between XOR and the sudoku problem?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ac55011c-59d1-404f-8180-212b10ae2edc",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 371.107x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xor_gate=QuantumCircuit(3,1) # Create a quantum circuit with 3 qubits and 1 classical bit\n",
    "xor_gate.cx(0,2)\n",
    "xor_gate.cx(1,2)\n",
    "xor_gate.measure(2,0)\n",
    "xor_gate.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "368fc772-c6a5-4dfe-bdb0-1f4d632a8834",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Create a quantum circuit that satisfies the boolean constraints of the sudoku problem described above\n",
    "\n",
    "Hint : A quantum circuit with 9 qubits will work for this, 4 for the variables, 4 to encode truth value of each constraint and one qubit for the output which is a conjunction of the four constraints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1e65ba6f-7926-4bb5-9ecb-a21b90342008",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 872.774x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code here\n",
    "myxor_gate=QuantumCircuit(3) # Create a quantum circuit with 3 qubits and 1 classical bit\n",
    "myxor_gate.cx(0,2)\n",
    "myxor_gate.cx(1,2)\n",
    "sudokucheck = QuantumCircuit(9)\n",
    "\n",
    "sudokucheck = sudokucheck.compose(myxor_gate,[0,1,5]) # Check if v_0 = v_1\n",
    "\n",
    "sudokucheck = sudokucheck.compose(myxor_gate,[2,3,6]) # Check if v_2 = v_3\n",
    "\n",
    "sudokucheck = sudokucheck.compose(myxor_gate,[0,2,7]) # Check if v_0 = v_2\n",
    "\n",
    "sudokucheck = sudokucheck.compose(myxor_gate,[1,3,8]) # Check if v_1 = v_3\n",
    "\n",
    "sudokucheck.mct([5,6,7,8],4) # Take the AND of all the upper results\n",
    "\n",
    "\n",
    "sudokucheck.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "922d3ec1-e8fa-4e39-9561-03fcbdb78998",
   "metadata": {},
   "source": [
    "## Phase Kickback\n",
    "\n",
    "During the Grover's algorithm, we have seen how the information of the function $f(x)$ is transferred to the sign/phase by considering the output qubit to be in $|-\\rangle$ state. \\\n",
    "This trick is usually referred to as \"Phase Kickback\", where the information of the function is passed back from the output qubit onto the state as phase"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0c8d924-6094-40cb-b787-a7d244da0d2f",
   "metadata": {},
   "source": [
    "## Initialize the output qubit in the above circuit to $|-\\rangle$ to realize Phase Kickback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5ec6d24c-02d4-4d27-b953-103a2999b526",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1040x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code here\n",
    "oracle = QuantumCircuit(9)\n",
    "oracle.x(4)\n",
    "oracle.h(4)\n",
    "oracle = oracle.compose(sudokucheck, [0,1,2,3,4,5,6,7,8])\n",
    "oracle.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57848e1a-7667-4d95-9e6a-6a13b7321159",
   "metadata": {},
   "source": [
    "## Uncomputation\n",
    "\n",
    "Upon keen observation, the final result we want to find is the assignment to the input variables that satisfy the constraints right? \\\n",
    "Compare this with the usual Grover's algorithm with a black box. We see that in addition to the input qubits (the first 4) and the output qubit (the last qubit) in the usual Grover oracle, we used 3 more qubits to construct the oracle. \\\n",
    "Now, these additional qubits we used for clauses needs to be reversed (or uncomputed) so that the oracle is coherent with the usual Grover's oracle. \\\n",
    "What happens if these are left unchanged?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1e66bb1-4b86-4bbc-a248-130694db767b",
   "metadata": {},
   "source": [
    "## Append the Quantum Circuit that uncomputes the values of the clause qubits so that they are taken back to their initial configuration i.e., $|0000\\rangle$\n",
    "\n",
    "Hint : Every unitary is invertible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5a6a45ce-ecea-471c-becb-d73b247665b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1876.11x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code here\n",
    "uncompute = QuantumCircuit(9)\n",
    "uncompute = uncompute.compose(oracle, [0,1,2,3,4,5,6,7,8])\n",
    "\n",
    "uncompute = uncompute.compose(myxor_gate,[1,3,8])\n",
    "uncompute = uncompute.compose(myxor_gate,[0,2,7])\n",
    "uncompute = uncompute.compose(myxor_gate,[2,3,6])\n",
    "uncompute = uncompute.compose(myxor_gate,[0,1,5])\n",
    "uncompute.h(4)\n",
    "uncompute.x(4)\n",
    "uncompute.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac4f747c-cce2-46a7-b81c-815b72d640a2",
   "metadata": {},
   "source": [
    "## Diffuser operator\n",
    "\n",
    "One of the key operators used in Grover's algorithm is the construction of the Diffuser operator. Recall that the diffuser operator has the following structure\n",
    "\n",
    "$$G = I-2|\\psi\\rangle\\langle\\psi|$$\n",
    "\n",
    "where $|\\psi\\rangle$ is a uniform superposition on the possible assignments which in our case all possible binary strings of length 4\n",
    "\n",
    "Hints : \n",
    "* Recall that $G$ can be re-written as $$G = H^{\\otimes n} (I-2|0\\rangle\\langle 0|) H^{\\otimes n}$$\n",
    "* Use phase kickback idea for the middle part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "562d7b7b-ba25-4fb6-b4b6-01cd9b1769ac",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 705.552x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write a code to construct the diffuser operator for the problem\n",
    "def diffuser_operator(n):\n",
    "    diffuse = QuantumCircuit(n)\n",
    "    controlbit = []      # This will help to list all the control bits for \n",
    "    for i in range(n):\n",
    "        diffuse.h(i)     # First layer of hadamard gates\n",
    "        diffuse.x(i)     # Layer of X gates\n",
    "        if i>0:\n",
    "            controlbit.append(i) \n",
    "    diffuse.h(0)\n",
    "    diffuse.mcx(control_qubits=controlbit, target_qubit=[0])   # applied C^nX\n",
    "    diffuse.h(0)\n",
    "    for i in range(n):\n",
    "        diffuse.x(i)     # The second last layer of X gates    \n",
    "        diffuse.h(i)     # The last layer of hadamard gates\n",
    "    return diffuse\n",
    "    \n",
    "n = 4\n",
    "diffuser_circuit = diffuser_operator(4)\n",
    "diffuser_circuit.draw('mpl')\n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "892ffa0d-0020-4367-953e-7aed5d1b9abc",
   "metadata": {},
   "source": [
    "## Putting it altogether\n",
    "\n",
    "With all the pieces in place, we are finally ready to solve for the satisfying assignment using Grover's algorithm. \n",
    "\n",
    "Assemble the oracle circuit and the diffuser and repeat them for $\\lfloor \\frac{\\pi}{4}.\\sqrt{N}\\rfloor$ times which would be the final circuit where recall that $N$ is the total number of possible assignments\n",
    "\n",
    "Don't forget to measure the assignment qubits (the first 4 qubits) at the end 😉"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a077805f-414c-443b-a3df-258db72397e7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FF15gxowZlJWVsXHjRnr06MEDDzzA/PnzWbNmDXBsomvUqFEtzsW1atUqRo0alZXYpfYa2R8GJJmXvXAspGGkAkkdxPQxya3ftyuMq8pMLJKk7JsyDCqTSFoVR+D8kZmLR1J2lRTBtCSbME4bBL1TmKdDHV/sV78mvmo14euvJTRw4OHPQ5EIkS/fBrEo0W/dSzwez2GUkqS2KiqFTt1yt30TXVk2atQonnzySfbt28e+fftYsmQJN954I/X19WzcuJFwOMzYsWOPKnPJJZewcOFCqqs/6Kq/ZMkS1q9fz6WXXprtXZBSEg7BP5wPvdr4kDJjQuKNP0n5Y/TJ8Ikz2rZu9wq48fxEDwBJUn7oXAafPx/K2jDtYiQM10+Fft0yHZWkbLpwDEwe2rZ1h/aGa87ObDzKjfjmzcR+8jNCo0YS/tQnj1keGjyI8LWziK94k9jjT+QgQklSKnqdkpvtVvaC0g74YkwoXoCvayxZsoSzzz6bU089lbfeeuuoZXv37mXcuHH06tWLf//3f6ehoYE5c+bQu3dvXnrpJcLh7LQCBm0c4rkzcQziDmh/Azz2Cry+GWItXOndK+Dj4+HMNj78SAqeZRvh969D3f5jl4VCiV5cnzoTugZvnmdJUhvU7IZfLYX177a8vKp74sWIUzrgW5mS2i8eh2dXwXOrof7QsctLIjD5FLjstEQvsI4kaO0ikN62kXTP0ZUNuy6YXvBzdNk+Jilb6nfCSw+lVvb9Oboa9iU/R9fIC6FqYmrbbcmRc3Tt37+fioqKlOopyK/eFStWAMcOWwjQpUsXFixYwK233srVV19NUVERl1xyCffee2/WklxSulSWJd7O3XMAlqyHZ1ZCUzQxNM1nPwSj+oGntZTfTh8MEwfB2zWJpPcrG6A5lnj4+udLEglvSVL+6tcNvjgdavck7gdfeDvx70BJBP73hYk5Wh2+WspfoVCiZ9f5I2H5ZnhrW+J3cyzR4/PfrkhtLi9JkpRbFT2gxyDYuSl724wUQ9/R2dteMkx0teCUU07hySefzGZIUkZ1LYePjoNFa2HPwcSDzJiTcx2VpGwJh2BU/8TP6m2J74GyYpNcklRI+naFy09P9PTdcxA6lcDgXrmOSlK2FEVg0pDEz9rtie+B0iKTXJIkBdmwD8HSzYke3Nkw9Fwo6qD3DgXZl+NEiS5JkiRJkiRJkqSOqktfGHxWdrbV9WQYeHp2tpWKguzRtWDBglyHIEmSJEmSJEmSlLIhU2DHBti7ve1lGuuP/n0iRaUw+mMQ6sDdpgoy0SVJkiRJkiRJkhRk4QhM/BS8+guo39m2Mi8/0vb6I8Uw8ZOJOcE6sg6cg5MkSZIkSZIkSVJrSsrhjKuhS5/01ltcBqd/GrqdnN56M8FElyRJkiRJkiRJUkCVlMOka2Dw2RAKtb++XqfA2Z+Frv3bX1c2OHShJEmSJEmSJElSgIWLYNhUOGkYrP0z7NqSfB3l3RPzfvUdlZ6EWbaY6JIkSZIkSZIkScoDXfrCGTOhfgdUL4e6d+DgntbXL+4E3QdA1QToPjBYCa73meiSJEmSJEmSJEnKIxU94dSPJH6aDsLed6FhL6x9DpoboagMzv4MlHYOZnLrSM7RJUmSJEmSJEmSlKeKO0HPQXDyOIiUJD6LFEFZl+AnucBElyRJkiRJkiRJkgLKRJckSZIkSZIkSZICyUSXJEmSJEmSJEmSAslElyRJkiRJkiRJkgKpKNcBqGUlEZg7M9dRtF1JJNcRSJIkSZKkfBG0dhFIb9tIeTjCrgump6/CLCgPp7dxqNDPAUlS25no6qBCISj1ryNJkiRJkgpQobeLhEIhKiIFfADwHJAktZ1DF0qSJEmSJEmSJCmQTHRJkiRJkiRJkiQpkEx0SZIkSZIkSZIkKZBMdEmSJEmSJEmSJCmQTHRJkiRJkiRJkiQpkEx0SZIkSZIkSZIkKZBMdEmSJEmSJEmSJCmQTHRJkiRJkiRJkiQpkEx0SZIkSZIkSZIkKZBMdEmSJEmSJEmSJCmQTHRJkiRJkiRJkiQpkEx0SZIkSZIkSZIkKZBMdEmSJEmSJEmSJCmQTHRJkiRJkiRJkiQpkEx0SZIkSZIkSZIkKZBMdEmSJEmSJEmSJCmQTHRJkiRJkiRJkiQpkEx0SZIkSZIkSZIkKZCKch2AWhaPQ2M011G0XUkEQqFcRyFJkiRJkiQFX9DaBiH97YPxeJwDseAchPJwhJANpFJOmOjqoBqjcMe8XEfRdnNnQqlnkyRJkiRJktRuQWsbhPS3Dx6IRem+4Jn0VZhhuy6YTkXEBlIpFxy6UJIkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgVQQia66ujrmzJnDsGHDKCsrY8CAAdx6663U19dzww03EAqFuP/++3MdpiRJkiRJkiRJkpKQ94mu5cuXM27cOL75zW9SW1vL6NGjaWpq4r777mPmzJmsXr0agIkTJ+Y20AypXvU83702xKvz72l1ne9eG+K391ySxagkZduBQ7BoLcxfDk8uh4VrYH9DrqOSlC3xOGx4D/64Ap54DZ5aAWtqE59LhaJmN/xpZeIa+MMb8MYWiMZyHZUkScqW7Xvh2SPuBZZvhuZorqPKPNsGIfrQwzR99OPEnvrjMcvi8TjNX76DphmXEd+wMfvBSVm0713YsBiaDyX+P9oM8Tx5JirKdQCZVFdXx6WXXkptbS233347d955J507dwbg7rvv5o477qCoqIhQKMT48eNzHK0kpd+eA/D7N2DZRmj6mxv4x1+F0wbBxeOhR2VOwpOUBcs2wrOrYOuuY5ed1AWmjYKzT4FQKOuhSVmxphaeXgHr3z12WddOMHUEXDAaInn/CqAkSYVp/buJe4E1tccu61IGU4bD9DFQFMl+bMqO8HWziC1eQvSBBwmdcTqh3r0OL4v9+nHib6wg/PefJTRkcO6ClDKo7p1EgmvPtqM/b26ART+EAafBwDMgFOBnogCHfmK33HIL1dXV3Hzzzdxzzz2Hk1wAc+bMYcKECTQ3NzN48GC6dOmSw0glKf3e3Qv3Pg1L1h+b5AJojsHSDfCdpxNvuUvKP79/HX66qOUkFyS+J+Ytgf9Zau8u5acl6+G/n205yQWw5yDMfx1+9OfCeKNbkqRCs2wjfO9PLSe5APY2JJJgDzwHh5qzGpqyKFRcTNHs26Ghgei3v3P48/iWamIP/5TQyFMJf/pTuQtQyqDNy2D5r49Ncr2vYS+s/TOseBJiAX4myttE1+rVq5k3bx69evXirrvuanGdM844A4AJEyYc/uz9xNjkyZMpLS0l5OvNkgKo/lDiRn33gROvu7cBvr8A9h3MfFySsmfhGvjjm21b98W1ieEMpXyyehv8YjG0JYe7ahs8ujjjIUmSpCxatx0eeRFibbgZWLsdHlnky1/5LDR8GOGrryL+6jJi8/9APBolevc9EI8TmX07oYhd+pR/tr8Naxa0bd1318DbbVy3I8rbRNejjz5KLBZj1qxZVFa2PCZXp06dgKMTXevWreOxxx6jb9++nHnmmVmJNRuaGw9wcF9diz+S8s/idbBjf9vX33MQFq7NXDySsqs5Ck+9kVyZBasS8/lJ+SAeT/TUSqat6tWN9nCWJCmf/OGNtiW53reiGjbvyFw8uWbbIIRnXQNDhxJ98IfEvvd94m+vIfzZzxAaUJXr0KS0i8dh/cLkymx9HQ7uyUw8mZa3c3QtWJBIP06bNq3Vdaqrq4GjE10f/vCHqampAeBrX/saixYtymCU2bP4sTtZ/NiduQ5DUhbEYvDiuuTLvbQWPjrWOUqkfPD6ZtifZNKqKQovb4DzR2YmJimbNu+A6p3Jl1u0Bq6cnP54JElSdtXsbn3o4uNZuBYG9TrxekFk2yCEiooomn0bzV/8ErEn5xMaO4bwJ6/IdVhSRuzcDAdamcbgeLa+DsM+nP54Mi1vE12bNm0CYNCgQS0ub25uPpzEOjLRFQ7nZwvv2Gk3MvysT7e47DffmJ7laCRlUvWu5HpzvW9vA2x4D4b1SX9MkrLr9S0plttsokv54fXNqZVbvsVElyRJ+SDVe4HXN8OsKemNpaOwbfCvKiqguBiamwmdOYlQnrYFS++uSa3c9jUmujqU+vp6AA4ebHnSmXnz5lFXV0fnzp0ZMmRIRmOZNGkStbWtzHrZikhxJz7x9fSNI9at73AGjr0wbfX9rRHDhxNtcoKfju7jX11Kedd+1NTWUFWVP0Nz6mh9RpzPh254JKWys66/ka1v/j7NEakj8XugMJx306/oPfTspMu9sWo9VX9/XgYikrLrjCvvYciZVyddbt+BKFVVLb8oly/8d0CS3wMqBBMv+w+Gnfu5pMs1NsPAwacQa879mN5BaxuE9LcPxktK4IHvpa++eJzot+6F5iYYOIDYz39B+LwPE+rfLy31jxg+glBjY1rqktrrCzMe4MzhM5IuV1e7m6qqsRmIqGWxWOzwf0+dOpXXXnstpXryNtHVt29fdu3axbJly5gy5ehXMWpqapg9ezYA48ePJxQKZTSW2tpatm7dmlSZotLyDEWTGdtqttF86ECuw9AJRKPRw7+TPScVHKEuqf9t39u+zXMjz/k9UBgO1u9LqVzDgf2eF8oLI/akMEYH0Nx0KO+vAf8dkOT3gArBkN2pT7ZVvXkj8XjsxCtmWNDaBiED7YNlpRSnrzZijz9B/PU3CH/uesJTzqb5C18k+q17idwzNy3tw9tqtkFD7pOkEsDefbtTKneoqSFn9wfbt29PuWzeJrouvPBCVq9ezdy5c5k+fTojRowAYOnSpVx33XXU1SUmWpw4cWLGY+nbt2/SZSLFnTIQSeb079ffHl0BEIlEDv8++eSTcxyNMqU0vpd4LEooHGlzmXg8TigUoji6y3Mjz/k9UBgO7dmUUrmDuzZ4XigvRPen9mC27721eX8N+O+AJL8HVAhiB7alVG7vu2vpn6bePe0VtLZBSH/7YLykhPfSVdfWrcQeepjQqSMIX3UloUiE8LWziP34J8Qef4LIJy5v9zb69+tvjy51GLsOpjanQe3u9Vm9P4jFYtTU1ADQp0/q86nkbaJrzpw5/PznP2fLli2MGTOGkSNH0tDQwLp167j44osZPHgwTz/99FHzc2XKK6+8knSZQ81wx7wMBJMha9aupTRvz6b8ceevYc9B6Ne3H9XV1bkORxn0oz/DiiT+xKFQiFP7wnfeWJS5oNQh+D1QGGr3wDeeTL7c3V++gmHfvCLt8UjZdqAx8X3XFE2u3D9+agI/vSO/vxv9d0CS3wMqBIeaE+d6Q1Ny5a6/eDgP/VPHuC6C1jYI6W8frI82033BM+2uJx6LEf3mtyEWIzL7NkJ/TfiHr7qS+KIXiT30MOGzJrd7CMM1a9dQEbGBVB3Dof2w8AeQbAfVmf94Lrd8N3vfg/X19VRWVgKwcOHClOvJ29n2qqqqeOGFF5gxYwZlZWVs3LiRHj168MADDzB//nzWrEnMxpaNRJckZdvUEdkpI6lj6tsVhif5IlTfrnDKSZmJR8q28hKYlOQ0vOUlcPrgjIQjSZKyrLQIzjoluTIlRXDm0MzEo9yK/erXxFetJnz9tYQGDjz8eSgSIfLl2yAWJfqte4nH4zmMUkqv0ko4Kcm2vpIK6D08M/FkWt4mugBGjRrFk08+yb59+9i3bx9LlizhxhtvpL6+no0bNxIOhxk7NnsTq0lStpzaD6aNavv65w6HsVWZi0dS9l1zNnQpa9u6ZcVw/VTI8LSlUlZddhr069q2dcMh+MxUHKFAkqQ88vEJMKBH29YNAdedk3jxRfklvnkzsZ/8jNCokYQ/9cljlocGDyJ87SziK94k9vgTOYhQypxTL4BO3dq2bjgC4y9N/A6ignyUW7lyJfF4nBEjRlBefuzEjr/61a8AWLVq1VH/P3jwYCZNmpS9QNOgavT53PrI8d9GONFyScF02WlQFIZnVh5/vfNGwuWn28At5ZselfDF6fDA81C3r/X1unaCz58P/bplKTApSzqVwBcuhB/+GTbWtb5eaRF89kMwsmNMxyFJktKktAj+8QL48Quwdnvr6xVH4LpzYdyA7MWWTYXeNhgaOJDi+b897jqRa2YSuWZmliKSsqekHCZdDct/DfvebX29ojKYcDl0C/BL8AWZ6FqxYgXQ+rCFn/70p1v8/+uvv56HH344o7FJUrqEQjBjIkwaCi+uhSXrjx6ffOqIxE/fNr7tLil4eneBf54Bb2yBRWth/RE3tpEQXHUWnDYoMUyLlI8qy+CWj8LbNbBwDazaCu8344RDcNnpMHkIlJfmNExJkpQh5aXwvz8Ca2oT98MrquH90elCIbh0YmKIwwrvBSTlqdJKmHwt1L0D1cthx8YPloXCMGIa9BsNRQH/HizIZo0TJbocj1VSPunTBT5xBlxxemIy3r0NieHMrjwz15FJyoaiSGLeodMHQ3MU/v1x2NeQSAAkO2+BFEThEIzqn/iJxuBrv0lcA53L4PyRuY5OkiRlWiiUGN7/1H5/cy9QCheMznV0kpR5oTD0Hpb4iUVh4Q+gsT7R42vAabmOLj3yeo6u1pwo0SVJ+SgU+mB4QocplApTUSTR6C8VqkjYa0CSpEJ25L2Az8WSClE4kp/ffwXZo2vBggW5DkGSJEmSJEmSJEntVJA9uiRJkiRJkiRJkhR8JrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEgmuiRJkiRJkiRJkhRIJrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEgmuiRJkiRJkiRJkhRIJrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEgmuiRJkiRJkiRJkhRIJrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEhFuQ5ALSuJwNyZuY6i7UoiuY5AkiRJkiRJyg9BaxuE9LcPlocj7LpgenorzaDysA2kUq6Y6OqgQiEo9a8jSZIkSZIkFRzbBiEUClERKfCDIKlNHLpQkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFUlOsA1LJ4HBqjuY6i7UoiEArlOgpJkiRJkiQp+ILWNgjpbx+Mx+MciAXnIJSHI4RsIJVywkRXB9UYhTvm5TqKtps7E0o9myRJkiRJkqR2C1rbIKS/ffBALEr3Bc+kr8IM23XBdCoiNpBKueDQhZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQqkgkh01dXVMWfOHIYNG0ZZWRkDBgzg1ltvpb6+nhtuuIFQKMT999+f6zAzonrV83z32hCvzr+n1XW+e22I395zSRajkrIvHoc9B2H7HthVD9FYriOSlG2NzVC3D97dC/WHch2NJEnKtqYo7NgP270XUIGKxmDn/sRz8d6Diedk5T/bBiH60MM0ffTjxJ764zHL4vE4zV++g6YZlxHfsDH7wUlZFI/Dof0Qi33w//miKNcBZNry5cu5+OKLqa2tpaKigtGjR7Nt2zbuu+8+1q9fz86dOwGYOHFibgOVlBGNzbBsIyxcA9W7Pvi8SyeYMizx0608Z+FJyoKa3YnvgFc2wKHmDz4f2Q/OHQ6jT4ZIQbz6I0lSYdq+BxathZffgYamDz4f3gemjoCxVd4LKL/tPgAvroXF62BvwwefD+gB546A0wdBSd63EKqQha+bRWzxEqIPPEjojNMJ9e51eFns148Tf2MF4b//LKEhg3MXpJRB0UaofQuql8O+dz/4vPEArF8EJ4+Hss45Cy8t8vqfsbq6Oi699FJqa2u5/fbbufPOO+ncOfEXu/vuu7njjjsoKioiFAoxfvz4HEcrKd3e2wsPPAd1+49dtvcgPL0Cnl0F150DEwZmPz5JmRWPwzMr4fevt7z8rZrEz/A+8LkPQ3lJduOTJEmZ9/xq+O0yaOmF5bXbEz+De8E/nAeVZVkPT8q41zfDzxZBcwujmmzZCb9YDM+uhJumQa+AN3JKrQkVF1M0+3aab/knot/+DkV3fR2A+JZqYg//lNDIUwl/+lM5jlLKjPqdsPwxOLinhYVx2PASbFoKY2fAScOzHl7a5PU7S7fccgvV1dXcfPPN3HPPPYeTXABz5sxhwoQJNDc3M3jwYLp06ZLDSCWl2+4DcP+fWk5yHak5Cg+/ACursxOXpOz503GSXEdaux0efC7RA1SSJOWPP78Fj7eS5DrSxjr4/nNwqOkEK0oB82Z14nm3pSTXkd7bl3h+3n0gO3FJuRAaPozw1VcRf3UZsfl/IB6NEr37HojHicy+nVAkkusQpbRr2AvLftlKkusIsWZ44wmoeyc7cWVC3ia6Vq9ezbx58+jVqxd33XVXi+ucccYZAEyYMOHwZ7/61a/41Kc+xaBBgygvL2fkyJH8y7/8C/v3n6C1vINrbjzAwX11Lf5I+eixpYk5udoiDvy/l2zklvJJ7R6Y34Yk1/s21CXe+JYkSflhx/5EkqutqnfCH9/MXDxSth1qTjzntnX6ld0H4DevZDQk5ZhtgxCedQ0MHUr0wR8S+973ib+9hvBnP0NoQFWuQ5My4q1nE3NytUkcVv4eogF98Sdvhy589NFHicVizJo1i8rKyhbX6dSpE3B0ouuee+5h4MCB/Od//idVVVUsX76cf//3f+fPf/4zf/nLXwiHg5kbXPzYnSx+7M5chyFlxa56eHNrcmUONMJrm+CsUzITk6TsWrgm+TIvroOPjHGODkmS8sGLa5OfYH3xerhoPBT7Ur/ywLKNcLAxuTIrqhMJL+exzk+2DUKoqIii2bfR/MUvEXtyPqGxYwh/8opchyVlxME9yffQamqA7W9D/7GZiSmT8jbRtWDBAgCmTZvW6jrV1Ymxyo5MdP3ud7+jd+/eh///vPPOo3fv3syaNYuFCxfy4Q9/OEMRZ9bYaTcy/KxPt7jsN9+YnuVopMxasj75h1pINHKb6JKCrykKS1Pobr/7AKzelpiQXpIkBVcslkhaJav+EKzYAqcPTntIUta9tC75MrF44nn6Y+PSH49yz7bBv6qogOJiaG4mdOYkQgHt1CCdyLY3aXu33iNsfcNEV4eyadMmAAYNGtTi8ubmZhYtWgQcneg6Msn1vkmTJgGwdWuSXUSOKF9bW5tUmUhxJz7x9bUpba8l3foOZ+DYC9NW398aMXw40aY2jhOnnPn4V5dS3rUfNbU1VFWdmetwMubMmfcx6PRPJl1uzcYdVFVNOPGKAVYo54BaVwjnQKdu/ZnxlZdTKvvFL3+NtQt/mOaIOpZCOAek4yn0a6DQ91+FobhTNy7/WmrjEM75t7t5a8F9aY6oY/F7oDBcdueblJR3S7rcf//4f7jhl/+U/oA6kKBcA0FrG4T0tw/GS0rgge+lr754nOi37oXmJhg4gNjPf0H4vA8T6t8vLfWPGD6CUGOSXSmlDLnpovuZMvKKpMttXvsen6g6Lf0BtSIW+2AiyalTp/Laa6+lVE/eJrrq6+sBOHiw5S/XefPmUVdXR+fOnRkyZMhx63ruuecAGDVqVEqx1NbWJp0kKyoNVj/xbTXbaD7krKUdXTQaPfw71cRtEIw7lOJNRbgor48LFM45oNYVwjnQpbEk5bL79h/I2+PyvkI4B6TjKfRroND3X4WhvEvqk0vUH2jI+2vD74HCEA+l1kvl0KGmvD8vgnINBK1tEDLQPlhWSnH6aiP2+BPEX3+D8OeuJzzlbJq/8EWi37qXyD1zCYVC7a5/W802aDiUhkil9mtMsX00FIrk7Ltx+/btKZfN20RX37592bVrF8uWLWPKlClHLaupqWH27NkAjB8//rhfZFu3buVf//Vfueiii5g4cWLKsSQrUtwppW3lSv9+/e3RFQCRSOTw75NPPjnH0WROOJbaTVVj/Y68Pi5QOOeAWlcI50BRaQnxWCylIShKw415e1zeVwjngHQ8hX4NFPr+qzCEIsXEmhsJFyX/8ktJ6FDeXxt+DxSGpvqdlHbqknS5cLQ+78+LoFwDQWsbhPS3D8ZLSngvXXVt3UrsoYcJnTqC8FVXEopECF87i9iPf0Ls8SeIfOLydm+jf7/+9uhSh9EUT619dH9DdttHY7EYNTU1APTp0yflevI20XXhhReyevVq5s6dy/Tp0xkxYgQAS5cu5brrrqOurg7guMmr/fv3c/nll1NSUsJDDz2UciyvvPJK0mUONcMd81LeZNatWbuW0rw9m/LHnb+GPQehX99+h+eoy0cb3oPv/jH5cldeMJQffSl/jwsUzjmg1hXKOfDg87AyyReQiiPwzP98h/LS72QipA6jUM4BqTWFfg0U+v6rcPxkIby2Kbky4RD87qf/H106/X+ZCaqD8HugMMxfDs+sTL7c//365xn0/c+nPZ6OJCjXQNDaBiH97YP10Wa6L3im3fXEYzGi3/w2xGJEZt9G6K/JzvBVVxJf9CKxhx4mfNbkdg9huGbtGioiNpCqY9i9FV55NPlyUy8ZTvV/Zu+7sb6+nsrKSgAWLlyYcj15O9venDlz6NmzJ1u2bGHMmDGMGzeO4cOHM3nyZIYOHcoFF1wAHD0/15EOHjzIpZdeyoYNG/jjH/9Iv37pGatVUuYN7gUnd0+uTDgEU4ZlJh5J2Xfu8OTLnDEYykvTHookScqBqSncC0wYCF2C14FCatE5wyHZkdgG9ICBPTMTj5RLsV/9mviq1YSvv5bQwIGHPw9FIkS+fBvEokS/dS/xeDyHUUrp1bU/VPZOrkwoBCePz0w8mZa3ia6qqipeeOEFZsyYQVlZGRs3bqRHjx488MADzJ8/nzVr1gAtJ7qampq48soreeWVV/jDH/7A6NGjsx2+pHYIheCy0xLJq7Y6fxR0C97w15JaMbI/nJrEOyoVpXDhmMzFI0mSsmvoSTCuqu3rlxXDx8ZlLh4p27pXwPkj275+OASXnpZ8ckzq6OKbNxP7yc8IjRpJ+FOfPGZ5aPAgwtfOIr7iTWKPP5GDCKXMCIVg+HlAEt/rg86E0sqMhZRRed2XctSoUTz55JPHfL5//342btxIOBxm7NixRy2LxWLMmjWLZ599lt///vdMnjw5W+FmRNXo87n1keO/jXCi5VIQndoPZk2B//cSxE5wip99ClwyMSthScqScAg+96HEEIbr3z3+uhWlcOP50KtzNiKTJEnZEArBdefCj/4Cb9ccf92yYvj8edC3a3Zik7Ll0tPgQCMsWX/89SLhxPPziOSnmFcAFHrbYGjgQIrn//a460SumUnkmplZikjKnp6DYczFsOopiMeOv+7J4+GUD2UlrIzI60RXa1auXEk8HmfEiBGUlx/dheMLX/gC//M//8M///M/U15ezuLFiw8vO+WUU+jdO8n+fpJy5owh0LMzPLsS3twKf9sDvao7fHgknDnEt9akfFRWDP94ATz/FixaC7vqj15eEkl8T3xktEkuSZLyUUlR4mWWv7wNi9ZA3f6jlxdF4PRB8JEx0KdLTkKUMiocgqvPgqG9E9fB1l1HLw+FEj0fLxidmAJAkpR/+o2GTt1g08vw3nrgb9pHO/eBgadD39HBbh8tyETXihUrgJaHLfzDH/4AwDe+8Q2+8Y1vHLXsxz/+MZ/97GczHp+k9BncC244L9HA/VYN/PZVaGhO9OC4/eJgf4FLOrGiSGJIwgtGwdu1iYnpG5qgUzH86xVQXpLrCCVJUiZFwjBtFJw3EtbWwo9f+OBe4P9cnngukPJZKARnnQKTh8KmHfD9BR9cA3dc4hD+klQIuvWHbldAw17YsRHWPA/RRijuBJOvzY/2URNdf2Pjxo1ZjkZSNnSvgCnD4Kk3EomuonB+fIlLaptwGEb1h9KixIN9SZFJLkmSCkk4lBje/Mh7AZNcKiShUOJF0COvAZNcklRYyrokhih858VEoiscyZ/20XCuA8iF4yW6JEmSJEmSJEmSFAwF2aNrwYIFuQ5BkiRJkiRJkiRJ7VSQPbokSZIkSZIkSZIUfCa6JEmSJEmSJEmSFEgmuiRJkiRJkiRJkhRIJrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEgmuiRJkiRJkiRJkhRIJrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEgmuiRJkiRJkiRJkhRIJrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEhFuQ5ALSuJwNyZuY6i7UoiuY5AkiRJkiRJyg9BaxuE9LcPlocj7LpgenorzaDysA2kUq6Y6OqgQiEo9a8jSZIkSZIkFRzbBiEUClERKfCDIKlNHLpQkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBVJTrANSyeBwao7mOou1KIhAK5ToKSZIkSZIkSQq+oLUPQ3rbiOPxOAdiwToA5eEIIRvJc8JEVwfVGIU75uU6irabOxNKPZskSZIkSZIkqd2C1j4M6W0jPhCL0n3BM+mpLEt2XTCdioiN5Lng0IWSJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQqkgkh01dXVMWfOHIYNG0ZZWRkDBgzg1ltvpb6+nhtuuIFQKMT999+f6zAlSZIkSZIkSZKUhKJcB5Bpy5cv5+KLL6a2tpaKigpGjx7Ntm3buO+++1i/fj07d+4EYOLEibkNNEOqVz3PY/85janXfJMzZny5xXW+e22IwRNncPmXn8xydJKUHbvq4cW1sGkHHGqGTsUwsj9MHgLlpbmOTlKmxWKwahu8sgH2HIQQ0LMznH0KDO0NoVCuI5SkzGqOwhtb4LVNsL8BwmE4qQucMwwG9Mx1dJIkZd7eg7B4PazfDg3NUFYEw/rA2cOgc1muo8ss24ch+tDDxH7xSyK3fYnwRR89alk8Hic6+5+Jr15N0f33ERoyODdBZljzIdi2Ena8A40HPvjs4G7o1C2XkaVHXie66urquPTSS6mtreX222/nzjvvpHPnzgDcfffd3HHHHRQVFREKhRg/fnyOo5UkpduBRvjlEnh9C8TjRy97qwbmL4epI+CSiRApiD7OUuF5Ywv85hXYdeDoz995D5a+A/26wsyzYXCv3MQnSZm2eD08uTyR4DrS+nfhpXUwsCf83RTo2zUn4UmSlFGNzfDYK4mX3qKxo5e9XQtPrYDJQ+GTk6A4kpsYlXnh62YRW7yE6AMPEjrjdEK9P3gAjP36ceJvrCD895/NyyRXPAbrF8GWZRBtOnpZtAkW/RB6D4NRH4OSTrmJMR3yulnvlltuobq6mptvvpl77rnncJILYM6cOUyYMIHm5mYGDx5Mly5dchipJCnd6g/Bf/0Rlm8+Nsn1vqYoPLcafrLw2BteScG3ZD38+C/HJrmOVLMHvvcnWFObvbgkKVv+tBJ+sfjYJNeRNu+A7z4N1TuzF5ckSdnQ2Az/vSDxXNDaM380lnjx4/sLEusrP4WKiymafTs0NBD99ncOfx7fUk3s4Z8SGnkq4U9/KncBZkg8Dm/+HjYuOTbJdaT31sErj0JjffZiS7e8TXStXr2aefPm0atXL+66664W1znjjDMAmDBhwuHPXnjhBS688EL69etHaWkpVVVVzJw5k9WrV2clbklSevxsUaIBuy3e2AJ/eCOz8UjKrk11MG8JtJLnPkpTFB76C+w+TkJMkoJm5dZET662ONgEDz4PDcdpAJEkKWj+ZylseK9t665/F379SmbjUW6Fhg8jfPVVxF9dRmz+H4hHo0TvvgficSKzbycUyb8ufRsWw/a32rbugZ3wxu9af1m8o8vboQsfffRRYrEYs2bNorKyssV1OnVK9MU7MtG1a9cuxo0bx0033cRJJ51EdXU1d911F1OmTOHNN9+kqqoqK/GnW3PjAQ7uq8t1GJKUFVt3JYYmTMbCNTB9DJQWZyYmSdn1/FsQS+IGvaEp8SbnxY5mLSlPLFiV3Pp7DsKrG+DcEZmJR5KkbNp9IPHvWjJefgc+PgG6BHj4tuOxfRjCs64h9tISog/+kPD6d4i/vYbwjf9AaEAw2/yPJ9qcGK4wGburYW8tdO2XmZgyKW8TXQsWLABg2rRpra5TXV0NHJ3ouuyyy7jsssuOWu/MM8/k1FNP5bHHHuPWW2/NQLSZt/ixO1n82J25DkOSsmLRmuTLNDTBsk0wZVj645GUXXsPwuubky/30lr46Fjn7JMUfDW7E2+mJ2vhWjhnOIRCaQ9JkqSsemldci++QWL9xevgo+MyE1Ou2T4MoaIiimbfRvMXv0TsyfmExo4h/Mkrch1WRrz7NjQdTL5c9XITXR3Kpk2bABg0aFCLy5ubm1m0aBFwdKKrJT179gSgqCi4h2vstBsZftanW1z2m29Mz3I0kpRZa7enVm5NrYkuKR+8817yD7UAextg+x7o3z39MUlSNqV6L1SzOzHPaWVZWsORJCnr1qY4B++a7fmb6LJ9+K8qKqC4GJqbCZ05iVA4P9903JnCy5/tKZdrwc3cnEB9fWLmtIMHW05bzps3j7q6Ojp37syQIUOOWR6NRonFYmzatImvfOUr9O3bl6uuuiqlWCZNmkRtbXLfrpHiTnzi62tT2l5LuvUdzsCxF6atvr81YvhwoqmkiJVVH//qUsq79qOmtoaqqjNzHU5OFPoxKJT9v+T/LKOs80lJl/v9U8/yL1dfn4GIOo5COQdaU+j7D4VxDAZPmsmkT38rpbIXX3IFOzY5OH8+K4Rr4HgKff8LxchpX2TsRXekVPaMyedQH9QWjjbwGvAYFDr//h6DQnHhrX+kW//RSZd7+dXXqfrsjAxElLygtQ9DetuI4yUl8MD30lLX4TrjcaLfuheam2DgAGI//wXh8z5MqH96ujCNGD6CUGNjWupqr5tn/IBJwz+edLlddXuoqhqTgYhaFovFDv/31KlTee2111KqJ28TXX379mXXrl0sW7aMKVOmHLWspqaG2bNnAzB+/HhCLYzLcN555x3u8TVs2DAWLFhA7969U4qltraWrVu3JlWmqLQ8pW3lyraabTQfcgb3ji4ajR7+new5mS8K/RgUyv43HNibUqJr3566vD4uUDjnQGsKff+hMI5BedWWlMtuq95AXZ4eFyUUwjVwPIW+/4Wi93vbUi67ZdM6Du59L43RdCxeAx6DQuff32NQKA7s30W3VMrt29VhzougtQ9DmtuIy0pJ9zTqscefIP76G4Q/dz3hKWfT/IUvEv3WvUTumdtijiBZ22q2QcOhNETafjv3pHY/V39wX86uge3bUxyWgDxOdF144YWsXr2auXPnMn36dEaMSMyou3TpUq677jrq6hIT702cOLHF8j/60Y/YvXs3GzZs4Jvf/CYf/ehHWbRoEQMHDkw6lr59+yZdJlIcrFkP+/frb4+uAIhEIod/n3zyyTmOJjcK/RgUyv7v3vIq3fokPwZh/fY38/q4QOGcA60p9P2HwjgG8X0biMeihMKRpMod2r+DTqH9eXtclFAI18DxFPr+F4qmnW8DibeWk2m02fvuOnp0LoHO+XtueA14DAqdf3+PQaHYu3U5/Uecm3S5fduWd5jzImjtw5DeNuJ4SQnpfPUmvnUrsYceJnTqCMJXXUkoEiF87SxiP/4JscefIPKJy9u9jf79+neYHl3Vu95Mqdw721/N6jUQi8WoqakBoE+fPinXk7eJrjlz5vDzn/+cLVu2MGbMGEaOHElDQwPr1q3j4osvZvDgwTz99NOtzs916qmnAnDWWWdx0UUXMXjwYO6++27uv//+pGN55ZXkh7851Ax3zEu6WM6sWbuW0rw9m/LHnb+GPQehX99+VFdX5zqcnCj0Y1Ao+795B3z7qeTKlBTBU4/8B51K/iMzQXUQhXIOtKbQ9x8K5xg89Bd4I8mOXR+f3JP/3rg+MwGpwyiUa6A1hb7/heTep2FTXXJvJl9/8TAe+qf8Pi+8BjwGhc6/v8egUOzYD1//LSQzdW84BPPu/xLdyr+UqbCSErT2YUhvG3F9tJnuC55JS13xWIzoN78NsRiR2bcR+mvCO3zVlcQXvUjsoYcJnzW53UMYrlm7hopIx2gkjzbBC9+H5iQ7mP3vOy/nXx5sf9Kvrerr66msrARg4cKFKdeTnzOtAVVVVbzwwgvMmDGDsrIyNm7cSI8ePXjggQeYP38+a9asAWg10XWkbt26MWzYMNatW5fpsCVJaTCwJ5yS5MiFU4ZBp5LMxCMp+84bCck07xZH4NzhGQtHkrLuglHJrV9RCmcOzUwskiRlW89KmJDkwFynDYJuwRstUG0Q+9Wvia9aTfj6awkdMWJbKBIh8uXbIBYl+q17iceTSY12bJFiqJqYXJkufaFbx+jQmLS8TXQBjBo1iieffJJ9+/axb98+lixZwo033kh9fT0bN24kHA4zduzYE9bz7rvv8vbbb3PKKadkIWpJUjp8dir06ty2dU/tC5dOzGg4krLslJPgE5Patm4knPjO6FGZ2ZgkKZsmDITpbZxHvKQI/uE8KPelH0lSHrn6bKjq3rZ1B/SAqyZnNh7lRnzzZmI/+RmhUSMJf+qTxywPDR5E+NpZxFe8SezxJ3IQYeYMPRd6tfFFprLOMP5ySMNUZTnRMfrRZdnKlSuJx+OMGDGC8vKj0/TXXnstw4YNY+LEiXTr1o21a9dy7733UlRUxD/90z/lKOLUVY0+n1sfOX4m+kTLJSmIOneCWz8Kj7wIb9e0vE44BJOHwpVnQlFyU/lICoAPnwqdiuHxZVDfynAN3SvgmrNhRPJTqkpSh/fxCVBRBk+9AQ1NLa9zUhe47txEA58kSfmkrBhung6PLoY3Nrc8jGGIxMshV58NpcXZjjA7Cr19ODRwIMXzf3vcdSLXzCRyzcwsRZQ94XAiebXmOdj6BsRjLa/XfQCMnQGlAX75syATXStWrABaHrbw7LPP5qc//Snf/e53aWhoYMCAAUybNo2vfvWrDBo0KNuhSpLaoXMZ/OMFULMbFq2Fl9ZCNA6REEwfmxiusKvDEkh57cyhMHEQvL4Zlm6AtbUQi0NRGD73IRjVP3HzL0n5KBSC80fClFPglY3w2iZ4593E92BxBD5/PgzvE9w3dyVJOpGy4sR9f90+eHEt/PmtD9oFzhuVGL68Z4Ab96UTCUdg5IUwZApsWwF170BzQ2Jow859E8Mbdu6d6yjbz0TX37j55pu5+eabsx2SJCmD+nVL9NpasSUx6XBlGVw0PtdRScqW4ghMGpL4eX/y8YpSGFOV68gkKTtKixMNeecO/+B7sLzE3qySpMLRqzNcdjq8uvGDdoHLTst1VFL2lFbAkLMTP/moIN9fPV6iS5IkSZIkSZIkScFQkD26FixYkOsQJEmSJEmSJEmS1E4F2aNLkiRJkiRJkiRJwWeiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFkokuSJEmSJEmSJEmBZKJLkiRJkiRJkiRJgWSiS5IkSZIkSZIkSYFUlOsA1LKSCMydmeso2q4kkusIJEmSJEmSJCk/BK19GNLbRlwejrDrgunpqzALysM2kueKia4OKhSCUv86kiRJkiRJklRwCr19OBQKUREp4AOgpDh0oSRJkiRJkiRJkgLJRJckSZIkSZIkSZICyUSXJEmSJEmSJEmSAslElyRJkiRJkiRJkgLJRJckSZIkSZIkSZICyUSXJEmSJEmSJEmSAslElyRJkiRJkiRJkgLJRJckSZIkSZIkSZICyUSXJEmSJEmSJEmSAslElyRJkiRJkiRJkgLJRJckSZIkSZIkSZICyUSXJEmSJEmSJEmSAslElyRJkiRJkiRJkgLJRJckSZIkSZIkSZICyUSXJEmSJEmSJEmSAslElyRJkiRJkiRJkgLJRJckSZIkSZIkSZICyUSXJEmSJEmSJEmSAqko1wGoZfF4nAOxaK7DaLPycIRQKJS2+uJxaAzO7gNQEoE0HgJJkiSpoAXtmcDnASm9gtYuAulvG1Fh8xpQ0O6FwPsh5Y6Jrg7qQCxK9wXP5DqMNtt1wXQqIuk7nRqjcMe8tFWXFXNnQqlXlCRJkpQWQXsm8HlASq+gtYtA+ttGVNi8BhS0eyHwfki549CFkiRJkiRJkiRJCiQTXZIkSZIkSZIkSQokE12SJEmSJEmSJEkKJBNdkiRJkiRJkiRJCiSnhpMkSZIKQLQJmg9BPAbhCBSXQyiU66gkSZIkSWofE12SJElSHmpuhO1vwa5q2FcL9TuPXh4phs59Ej8nDYNuVSa+JEmSJEnBY6JLkiRJyiMHdsPmV6BmFUQbW18v2gS7qxM/W16Fip5QNRFOHp/o8SVJkiRJUhCY6JIkSZLyQDwOW5bBuhcg1px8+fod8PazsPV1GH0xdOmT/hglSZIkSUq3cK4DkCRJktQ+jfXw6i9gzXOpJbmOtL8Olj4CGxYnkmeSJEmSJHVk9uiSJEmSAqxhHyz7JRzYlb4643FYvxAaD8KI8527S5IkSZLUcdmjS5IkSQqopgZ47VfpTXIdacur8M6LmalbkiRJkqR0MNElSZIkBdTbzybm1sqkDS/Bzs2Z3YYkSZIkSaky0SVJkiQF0LvroHZ1cmUmXwtTb0r8Tsaqp6C5MbkykiRJkiRlQ94nuurq6pgzZw7Dhg2jrKyMAQMGcOutt1JfX88NN9xAKBTi/vvvz3WYGRN96GGaPvpxYk/98Zhl8Xic5i/fQdOMy4hv2Jj94LKgetXzfPfaEK/Ov6fVdb57bYjf3nNJFqOSJElqn1gzvP2n5MuVVEBZ58TvZDTshQ2Lk9+elGs+D0gq9HYRyWtA3g+pEOR1omv58uWMGzeOb37zm9TW1jJ69Giampq47777mDlzJqtXJ16BnThxYm4DzaDwdbNg8CCiDzxI/L26o5bFfv048TdWEL7uWkJDBucmQEmSJCXt3bVwaH92t7ntDYg2ZXebkiS1l+0iKnReA5IKQd4muurq6rj00kupra3l9ttvp6amhmXLllFbW8vcuXOZP38+S5cuJRQKMX78+FyHmzGh4mKKZt8ODQ1Ev/2dw5/Ht1QTe/inhEaeSvjTn8pdgJIkSUpa9fLsb7OpAbavyf52JUlqD9tFVOi8BiQVgrxNdN1yyy1UV1dz8803c88999C5c+fDy+bMmcOECRNobm5m8ODBdOnSJYeRZl5o+DDCV19F/NVlxOb/gXg0SvTueyAeJzL7dkKRSK5DlCRJUhs17IXdW3Oz7WTnBJMkqSOwXUSFzmtAUr4rynUAmbB69WrmzZtHr169uOuuu1pc54wzzuD1119nwoQJrdZz8cUX89RTT3HnnXfyta99LUPRZkd41jXEXlpC9MEfEl7/DvG31xC+8R8IDajKdWhZ0dx4gIP76k68oiRJUge3tza3247HIRTKXQxSKnwekFTo7SKS14C8H1I+y8tE16OPPkosFmPWrFlUVla2uE6nTp0AWk10/fKXv2T58uWZCjHrQkVFFM2+jeYvfonYk/MJjR1D+JNX5DqsrFn82J0sfuzOXIchSZLUbnu3527bzQ3QsAc6dctdDFIqfB6QVOjtIpLXgLwfUj7Ly0TXggULAJg2bVqr61RXVwMtJ7r27t3Ll770Je655x6uvfbazASZCxUVUFwMzc2EzpxEKJy3I1ceY+y0Gxl+1qdbXPabb0zPcjSSJEmpq9+Z++2b6FLQ+DwgCSjodhEJ8BoocN4PKZ/lZaJr06ZNAAwaNKjF5c3NzSxatAhoOdH1L//yL4wYMYJZs2alJdE1adIkamuTG2MmXlICD3yv3ds+XF88TvRb90JzEwwcQOznvyB83ocJ9e+XlvpHDB9BqLExLXUBRIo78Ymvr01bfd36Dmfg2AvTVl9LRgwfTrTpYEa30V4f/+pSyrv2o6a2hqqqM3MdTk4U+jFw/wt7/8FjUOj7Dx6DfNj/2694hHGDz29x2eRroaSi9bKlFR/8nnrT8bfTWA8vP3Ls55+/4SaWrp3ftmA7oHw4B9ojSPufzmcCnwc+EKRzIBMKff8hOMcgaO0ikP62kUwIyt8/k4JyDLwGMiMof3+wfVSFIRaLHf7vqVOn8tprr6VUT14muurr6wE4eLDli2revHnU1dXRuXNnhgwZctSyV155hQcffJBXX301bfHU1taydWuSM4aXlVKctggg9vgTxF9/g/Dnric85Wyav/BFot+6l8g9cwmlYZKFbTXboOFQGiJNKCotT1td2bKtZhvNhw7kOozjikajh38nfU7miUI/Bu5/Ye8/eAwKff/BY5AP+3+wofUHx5IKKOt84jpC4bat15K6HXWBPXaQH+dAewRp/4P2TBCE5wEI1jmQCYW+/xCgYxCwdhFIf9tIJgTm759BgTkGXgMZEZi/P8G7F4Lg3A+pY9q+PfVx+vMy0dW3b1927drFsmXLmDJlylHLampqmD17NgDjx48/6os8Go1y0003cfPNNzNmzJi0xpOseEkJ76Vp+/GtW4k99DChU0cQvupKQpEI4WtnEfvxT4g9/gSRT1ze7m3079c/7T26gqZ/v/4d/o2FSCRy+PfJJ5+c42hyo9CPgftf2PsPHoNC33/wGOTD/sfDTa0ua6w/ftnSikSSKx6DQydYt7W6yitLA3vsID/OgfYI0v4H7ZkgCM8DEKxzIBMKff8hOMcgaO0ikP62kUwIyt8/k4JyDLwGMiMof38I3r0QBOd+SB1HLBajpqYGgD59+qRcT14mui688EJWr17N3LlzmT59OiNGjABg6dKlXHfdddTV1QEwceLEo8rdf//9bN++na997WtpjeeVV15Jukx9tJnuC55p97bjsRjRb34bYjEis28j9Ncv8/BVVxJf9CKxhx4mfNbkdndTXrN2DRWR9J1Oh5rhjnlpqy4r1qxdS2kHv6Lu/DXsOQj9+vY7PE9doSn0Y+D+F/b+g8eg0PcfPAb5sP/vvATvLGp5WUtDDR5p6k2JnlyH6mHhA6lt/4lnfn54CMQgyodzoD2CtP9BeyYIwvMABOscyIRC338IzjEIWrsIpL9tJBOC8vfPpKAcA6+BzAjK3x+Cdy8EwbkfUsdRX19PZWUlAAsXLky5nryccXDOnDn07NmTLVu2MGbMGMaNG8fw4cOZPHkyQ4cO5YILLgCOnp+rrq6Of/3Xf+Xf/u3faG5uZvfu3ezevRuAhoYGdu/efdR4kUER+9Wvia9aTfj6awkNHHj481AkQuTLt0EsSvRb9xKPx3MYpSRJktqqS+ovubVbaSWBTnJJkgqP7SIqdF4DkgpBXia6qqqqeOGFF5gxYwZlZWVs3LiRHj168MADDzB//nzWrFkDHJ3oqq6uZt++fdx0001079798A/A3Llz6d69O5s3b87J/qQqvnkzsZ/8jNCokYQ/9cljlocGDyJ87SziK94k9vgTOYhQkiRJyerSF0jPNArJbzt9c5VLkpRxtouo0HkNSCoUeduRcNSoUTz55JPHfL5//342btxIOBxm7Nixhz8fNmwYzz333DHrT5s2jeuvv57PfvazKc21lUuhgQMpnv/b464TuWYmkWtmZimi7KsafT63PnL8N1JOtFySJKkjKSmH3qfAe+uyv+3+Y0+8jtSR+DwgFTbbRVTovAYE3g+pMORtoqs1K1euJB6PM2LECMrLyw9/XllZyfnnn99imcGDB7e6TJIkScq2qonZT3SVdYFeQ7K7TUmSJEmSTiQvhy48nhUrVgBHD1soSZIkBUmPQVDZK7vbHHgGhAru6UGSJEmS1NEVXI+uZBNdTsQoSZKkjiYUgtEXwdL/B9m4Xe3SF6pOy/x2JEmSJElKVsG9k2mPLkmSJOWDLn1h0OTkyjTWQ8O+xO+2CkdgzMUQLrgnB0mSJElSEBRcj64FCxbkOgRJkiQpLYaeA/u2w46NbVv/5UeS38boi6CiZ/LlJEmSJEnKBt/LlCRJkgIqHIHxlyfm7MqEUR+DvqMyU7ckSZIkSelgokuSJEkKsEgxTPwEVKVxZO7iTjDhCjh5XPrqlCRJkiQpEwpu6EJJkiQp34SLYOR0OGkErHoaGvamXlefU+HUj0BJefrikyRJkiQpU0x0SZIkSXmixyCY8lmofQu2vAb732tbuVA4kSQbMBG6VWUyQkmSJEmS0stElyRJkpRHIiVw8njoPw721sLu6sTvfe/CgV1/XSkEXftC5z7QpQ/0HAqlFTkNW5IkSZKklJjokiRJkvJQKARd+yV+3vfC9+HQ/kRS68xZuYtNkiRJkqR0Cec6AEmSJEmSJEmSJCkVJrokSZIkSZIkSZIUSCa6JEmSJEmSJEmSFEgmuiRJkiRJkiRJkhRIJrokSZIkSZIkSZIUSEW5DkAtKw9H2HXB9FyH0Wbl4Uha6yuJwNyZaa0y40rSewgkSZKkgha0ZwKfB6T0Clq7CKS/bUSFzWtAQbsXAu+HlDsmujqoUChERaRw/zyhEJQW7u5LkiRJBc9nAqmwFXq7iOQ1IO+FpLZz6EJJkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAVSUa4DkJQ5Bxth8w7YshO27oL6Q4nP6w/BY6/AgB6Jn75dIRTKbazKjD0HYNMOqN4JNbuPPgfmL4eqHjCwJ3SvyGWUkiRJkjIhGoNtuxLPhFt2wu4DsP+vzwQHGuHPbyWeCat6QIktRMpD8TjU7vngGtix7+hr4NmVMKBn4jroVJLbWCVJqfM2Rsoz8XgisbFwDSzfBM2xY9dpjsELb3/w/yd1gXOHw5lDodwbu8CLxmDl1sQ5sKa25XWaY/DMyg/+f1gfmDocxg2AiH19JUmSpEDbcwBeWpf42XOw5XWaovCbVxP/XVYMk4cmngv7dM1enFKmHDgEL2+ARWvgvX0tr9MUhd8tT/x3URhOG5y4Bgb19GVgSQoaE11SHqnbB/OWwNrtyZV7d2/iAWf+cpgxET50KoS9qQuktbXwiyWwY39y5dZtT/x0L4erzoJR/TMTnyRJkqTMaYrCH96A51dDLN72cg1N8Je3Ez+nD4JPToLKsszFKWVKLJY4j3//OjRG216uOQZL30n8DO8DV58NPSszF6ckKb1MdEl5IB6HRWvhidegsTn1ehr/+kbf65vh76ZAr87pi1GZdagZfrcMFq5tXz27DsADz8HZp8AVZyTe7JQkSZLU8W2qg//3UuJFxvZYtgnWbIerJsP4AemJTcqG9/bBz1+CDe+1r56122HufLjstEQPL3t3SVLH5wBVUsDF4vA/S+FXS9uX5DrSO+/BvU/Dlh3pqU+ZdeAQ/Pez7U9yHWnxerj/T7C/IX11SpIkScqMN6vhv55pf5Lrffsb4KG/wHOr01OflGmbd8B3nm5/kut9jc2JdpbHlibXO1KSlBsmuqQAi8fhVy/Di2lMcLyv/hD83wWwdVf661b6NDTB95+DjXXpr7t6Z+IcOHAo/XVLkiRJSo9VWxNJqZbmZ26v3y4z2aWOr3on/N9nE+0Y6bZwLfx6aaL9RZLUcZnokgLshTXw4rrM1X+wEX7wHBxozNw21D6/WJx4cy1Ttu2Cn73oTb0kSZLUEb23F378QmZ7nPx2Gazelrn6pfY4cAgefD7xEmimLFwLC9dkrn5JUvs5R5cUUO/tg9+9llyZ2y6CLp1g70H49lNtK7PnIDz+amLOLnUsr22C5ZuTK5PKObB6G7z8Dpx1SvIxSpIkScqMWBweXQxN0eTKpfJMMG8J3DEDOpUkH6eUSb95NdFukYxUroHfvQaj+juXuSR1VAXRo6uuro45c+YwbNgwysrKGDBgALfeeiv19fXccMMNhEIh7r///lyHKbVZPJ7oyZPsA02XTtCtPPE7GS+/4xt8HU39ocR44clK9RxI5eFBktTx2ENXkvLHwjWJ+ZWTlcozwe4D8ESSL1pKmbZqKyzdkHy5VK6Bxmgi4eu9lCR1THnfo2v58uVcfPHF1NbWUlFRwejRo9m2bRv33Xcf69evZ+fOnQBMnDgxt4FKSdjwHqx/N7vb/NPKxNtL6hheXJuZ8cdb09AEC9+GGROzt01JUnpEm6D2Ldi6HBrrE58d2g9v/h6qJkLXfhAK5TJCSVKyojF4dmV2t7lkPVw0DrqWZ3e7UmueyfI1sHZ7Yn7sIb2zu11J0onldY+uuro6Lr30Umpra7n99tupqalh2bJl1NbWMnfuXObPn8/SpUsJhUKMHz8+1+FKbZaLsaHXvws1u7O/XR0rFkskurLtpfXQnGQvQklSbu3aAgt/AKufhr3bj15Wuwpe+Tksfwyas/jyhCSp/d6szv6IC7E4vJTBOaKlZGzdlXgJONsWOVeXJHVIeZ3ouuWWW6iurubmm2/mnnvuoXPnDwbSnTNnDhMmTKC5uZnBgwfTpUuXHEYqtV39IXh9S262/aIPNR3CWzWw60D2t7u/IfFALUkKhl1bYNmvoOkEDaE7NsKy/0n0/JIkBUOuEk4vrXPoNnUMuboGXtsMB3xBSJI6nLxNdK1evZp58+bRq1cv7rrrrhbXOeOMMwCYMGHC4c+ef/55QqHQMT8ObaiOYlNdYpiKXHgny8MlqmXZHrbyqG3n4I05SVLyok3wxhMQb2NP3L21sO6FzMYkSUqPWCy1ubnSYc9B2LE/N9uWjpSr5+JoDDbtyM22JUmty9s5uh599FFisRizZs2isrKyxXU6dUrMOnlkout93/ve9zj99NMP/39FRUVmApWStGVn7rZdsxuaolAcyV0MguocngPV3tBLUiBsf/vEPbn+1rY34ZSpUFSSmZgkSenx7j5obM7d9rfshF6dT7yelCmNzbB9T+62X73TOcwlqaPJ20TXggULAJg2bVqr61RXJ8bgainRNXr0aM4+++zMBCe1w9Zdudt2LJ5Idg3smbsYBNU5PAe27koMVRIK5S4GSdKJVS9Pvky0Eba/BSc7da0kdWhbc/jiGyQa+U8blNsYVNhq9yTaJ3Illy+fSpJalreJrk2bNgEwaFDLd1/Nzc0sWrQIaDnRlU6TJk2itrY2o9tQ4Tjvxv+h9ylTWlx220XQpVPrZbuUffD7a584/nb2HoRvP3Xs51dceQ3vrg3u2EYf/+pSyrv2o6a2hqqqM3MdTko+ddcmQuGWu9Wl6xxo7e/fGIVBQ04h1hzMQcnz4e/fXoV+DAp9/8FjUCj7/+DN6yguKku63H/d/WMeef5fMxBRx1Eo50BrCn3/5TmQD/t/ypTPctoVX29x2YmeB6D9zwQP/vgR/vHSf25jtOpo8uEa6DPifD50wyMtLsvGNfDMcwv517+7uo3RqqPJh2tAyiex2Adz9EydOpXXXnstpXryNtFVX18PwMGDLY/ZMm/ePOrq6ujcuTNDhgw5ZvnMmTOpq6ujZ8+eXHbZZXzjG9+gV69eKcVSW1vL1q1bUyor/a2m5tYn2+jSCbqVn7iOcLht67Vk1649gT6fo9Ho4d+B3I9QqNUkF2TnHKjd/i5NDcEcmD/wf/80KPRjUOj7Dx6DQtj/UCiUUpILoOlQ/h6X9xXCOXA8hb7/8hzIh/3vva/1e/G2Pg9A6s8EBxsaA3vslB/XQEnv3a0uy8Y10NQcC+yxU35cA1K+2r59e8pl8zbR1bdvX3bt2sWyZcuYMuXo3i81NTXMnj0bgPHjxxM6Ygyurl27Mnv2bD784Q9TWVnJSy+9xF133cXixYt55ZVXKCtLvtGgb9++7dsZ6QhFx5kfa+8J5uLoUpa4kYvFYG/D8ddtra5uXSs5+eSTj1+4A4tEIod/B3U/Ys2NhFuZQCVd58Dx6unTuyfxWNc2RNrx5MPfv70K/RgU+v6Dx6BQ9n9/w24qy7olXS4eacrr4wKFcw60ptD3X54D+bD/nStb765youcBaP8zQWlxOLDHTvlxDXTrWtnqsmxcA0XheGCPnfLjGpDySSwWo6amBoA+ffqkXE8oHo/ncFTbzLnlllv4r//6LwYMGMCf/vQnRowYAcDSpUu57rrreOedd2hqauILX/gC999//3Hr+t3vfsdll13GQw89xOc+97lshC+16heLYfH61Mp+7ROJt5V2H4Cv/Sa1Ov71cujZ+j1lh3fnr2HPQejaCf79k7mOJjX/+Tt4d29qZdt7DnQrP/Gwlx1ZPvz926vQj0Gh7z94DApl/1c+BTVvJl9u0t9BtzyfXL1QzoHWFPr+y3MgH/Z/9TZ44LnUy7f3meCy0+CC0alvX7mVD9dA3T74+hOpl2/vNXDOMLjqrNS3r9zKh2tAyif19fVUViYam/fv309FRUVK9YTTGVRHMmfOHHr27MmWLVsYM2YM48aNY/jw4UyePJmhQ4dywQUXAG2bn+uSSy6hoqKCV155JdNhSyc0oEfutl1eAj1S+65RGuXyHKjK4bYlSW03YGLyZSp7Q9d+aQ9FkpRmuXwe6Ajbl3pWQqeWBznJigE9c7dtSVLL8jbRVVVVxQsvvMCMGTMoKytj48aN9OjRgwceeID58+ezZs0aoG2JrvcdOcShlCu5vKEa0AO8DHIvl8kmH2olKRi69IVepyRXZui5/jsvSUFQWQbdU5xvNx18+U25FgpBVffcbd9rQJI6nrydowtg1KhRPPnkk8d8vn//fjZu3Eg4HGbs2LEnrOeJJ56gvr6eyZMnZyJMKSlV3RMPNbsOZH/b4wZkf5s61rgq+O2y3G1bkhQMY2fA8sdgdxvm2B5xAZw0LPMxSZLSY9wA+Mvb2d/u8D657UkjvW/8AFi7Pfvb7VEBJ3fL/nYlSceX14mu1qxcuZJ4PM6IESMoLz/6Nahrr72WoUOHcvrpp1NZWclLL73E3XffzcSJE7n66qtzFLH0gXAYzhkO81/P7nZLi2DSkOxuUy3r1RlG9oO3arK73aG9oX8O35qTJCWnqARO+zS8swi2roDmFiZb73wSDD0HepvkkqRAOXdEbhJdU0dkf5tSSyYNgd8th8bm7G73nOGJdhlJUsdSkF/NK1asAFoetnDMmDH85je/4TOf+QwXX3wxDz30EJ///Od5/vnnKSnxtSV1DGcPg0iWr94zh0JZcXa3qdZ9KAcPmD7USlLwRIpg+HnwoZtg9EUQ+eu/5ZFiOHMWTL7OJJckBVGfLjCib3a32bUTjHWEB3UQnUqy/zJuURjOTnJoaElSdpjo+htf+cpXWLFiBXv37qWpqYkNGzbw7W9/m65du2Y7TKlVncvgYycedTNtKkrhY+Oytz2d2OiTE726smVob5g4KHvbkySlV6QY+o+FotLE/xeVQtd+zsklSUF2xenZfQHyE2dk/4VL6XguGgflWXwn/WPjEnPkSZI6noK8RTleoksKio+Myd4EqFeemUiuqeMIhWDmWYkhJTOtOALXTIGwjaGSJElSh9G/O3w0Sy9AThzoi2/qeLp0gk+dmZ1tDegBF4zOzrYkSckryETXggULiMfjzJgxI9ehSCmLhGHWlOSGE9x7EHYfSPxuq0lDEg816ni6V8BVk5Mrk8o58MlJ0LtzctuRJEmSlHkXjoEhvZMrk+wzQffy7CUTpGSdPgjOGJxcmWSvgbJimHWOPRolqSPLQl8ASZnSrxt8/nx44Lm2TcD67aeSq3/MyXDN2Q5r1JGdMQT2H4LfvNq29ZM9B2ZMgCnO3SJJkiR1SJFw4pnw/z4L1TvbViaZZ4IuneB/f8QRPtRxhUKJdouDjbBqW9vKJHMNlBTBjedDX2c0kaQOzXcRpIA75aTEg0dlaXrrnTQE/v7DvrEUBOeNTPTsSufQguFQYgz+6VmcC06SJElS8spLEs+Ep5yU3np7d4ZbpkPvLumtV0q3okii/SLZnl0nUlmauLaGpvnakiSlnz26pDwwuBf88yXwq6WwfHP76iovSczJddoge3IFyTnDYVAv+PlLsHVX++rq2xX+bgoM7Jme2CRJkiRlVnkJfOEj8Oe34fevQ1M09bpCwIdOhUsmJnqzSEFQFIFrz4HR/eGxV+BAY/vqmzgw0TZSaW9GSQoEb1mkPFFZBp/9ELy+GZ5Z2fZhK95XEkkMg3fx+MTwFAqek7vDbRfBn9+Cv7ydGHM8GV07wbkj4IJRiYcESZIkScERDsO0UTD6ZPjD6/DGFojFk6tjRF/42Lj09w6TsiEUSrRrDO8Lf3gDXt0AjUkmfQf0SMx9N8G5yiUpUEx0SXlmwkAYPwA274CX1sE778F7e6Gl55uyYqjqkVj/zCHQqSTr4SrNImG4YHRiOMNVW2HpBthUB3tamWS3S6dEz60zh8DYKoeqlCRJkoKuT5fES5B7DsLidYl5i7btarmXVzgEfbvB8D6JUSL6OEyh8kCXTjDzLLj0NFj6TiLpW70TDrUwt3mIxPCcp5yUmJ/akU0kKZhMdEl5KBRKDGM3qFfi/xuaEg82BxohGoPiCPTqnPhJ57xO6jgiYRg3IPEDsPcg1OyGxuZE0rO0KDFEYdfyXEYpSZIkKVO6dkr0zvrYuMRz4PY9iVEfmqJQFE6MCtKvm8MTKn+VlyReAj1vZKJ3Y92+xE9TNPHMXF4C/bsnXgKWJAWbtzNSASgrdvLUQtelk0NSSpIkSYUqEk406PfvnutIpNwIh+CkLokfSVL+cZAqSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSZIkSZIkSZIkBZKJLkmSJEmSJEmSJAWSiS5JkiRJkiRJkiQFkokuSXmvKQqb6mD5ZmhsTnzWHIX6Q7mNS9lzoBHW1n7w92+Kwsa6D/5fkiRJkvJZ/SFY8zfPRJt3JH5LheBQE6x/9+hr4J13E59LCr6iXAcgSZmw+wC8uBZWboWa3RCLH728vhH+5VfQsxJOOQnOHQ6DeuUkVGVI9U5YtBbWboe6fUcvO9AI33kawiHo2xVGnwznDIMelbmJVZIkSZLSKR6HTTsSz8Xr34Ud+49efqARvv1U4pmoXzcYWwVThkG38pyEK2VE7Z7ENfBWDby3F45sGjrQCPc9AyHgpC4wsj+cMxz6dMlVtJLaw0SXpLyyfS/MXw5vVh+b3GrJjv2Jn5ffgQE94GPjEjf4Cq7V2+CpFYlefCcSi8O23YmfZ1cmEl4zJkD/7pmOUpIkSZIyY8UWePrNxMt/JxKLw9ZdiZ9n3oRxVTBjYqLhXwqqDe/B719PvPh6InESbUnb98Kf34IRfeHjE2CwL0NLgWKiS1JeiMXg+bcSNzLNsdTq2LITfvhnOGMwfHISVJSmNURl2MFGeHwZLFmfWvk4iR6Ab9UkEp4fGQ0RB/iVJEmSFBD1h+CxpbBsU2rlY3F4fQus2pZo6D/vVAj7TKQAaWxOtAv9+a2je28lY01tIkE2bSRcPAGKI2kNUVKGmOiSFHgHG+FHf4F1bXhTpy1e3Zi4qbnxfKjqkZ46lVm1e+CBBbDrQPvrisYSN8artsLnzzfhKUmSJKnjq94JP3gO9ja0v66mKPx2WeKZ6IbzoKy4/XVKmbarHr6/INEzq73icViwOjFizE0XOKSnFAS+lyEp0A42wv99Nn1JrvftPQj3/ynRy0sdW81u+K9n0pPkOtLGusQ5UH8ovfVKkiRJUjpt3pF4dklHkutIa7cnnrcbmtJbr5RuO/fDfX9MT5LrSDV7EvXuqk9vvZLSz0SXpMCKxhJDDWYqGdXQlHgb6G8n7VXHsecA/PeCzCWjanYn3opsjmamfkmSJElqjx374YHnMpeM2rwDfvTnxHQBUkd0sDHRLpDul1/ft7M+Ub8JX6ljc+hCSYH13GpY/25yZW67CLp0SvTY+vZTJ16//hD8YjH840cgHEotTmVGPA7zliT+lm2V7N8fYNMOeGYlXDw+tTglSZIkKRNicfj5S8m9+JfKM9Ha7Yk5sS8YnVqcUiY9vgze29f29VO5Bt7dC08sg6vOSi1GSZmX9z266urqmDNnDsOGDaOsrIwBAwZw6623Ul9fzw033EAoFOL+++/PdZiSklS7B/7wRvLlunRKjK3cpVPby6zdDi+uTX5byqylGxKTJCcjlb8/wDNvJsa8lyRJkqSOYtGa5F/+TPWZ6Pevw/Y9yZWRMm31NliyPrkyqV4DL66Dt2uSKyMpe/I60bV8+XLGjRvHN7/5TWpraxk9ejRNTU3cd999zJw5k9WrVwMwceLE3AYqKWm/ey0xdGG2PLkcDjVnb3s6vuYoPPFa9rYXiycmY5akoGo+BFteg6aGD/5/5+ZE71hJkhQ8h5pg/uvZ215zDH63PHvbk04kHoffvJrdbT7+qvfPUkeVt4muuro6Lr30Umpra7n99tupqalh2bJl1NbWMnfuXObPn8/SpUsJhUKMH+94VFKQ7NgPq7Zmd5sNTbBsY3a3qda9vgX2p3mi5RNZuz3Rk1CSgiTaCG89Cy98H95+FmJ/fWkj2gTLfgkv/Ri2v5XbGCVJUvJe2Zj9OYNWboVd9dndptSatdsTQwpmU80eeOe97G5TUtvkbaLrlltuobq6mptvvpl77rmHzp07H142Z84cJkyYQHNzM4MHD6ZLly45jFRSsl5aB7l4gWbhGt/c6SgWrcnNdh3CUlKQNB+CV38J1a8lElstObATVjwJG1/ObmySJCl18XhunonicZ+J1HHkql1gYY62K+n48jLRtXr1aubNm0evXr246667WlznjDPOAGDChAnHLPvNb37DOeecQ0VFBV27duXcc89l5cqVGY1ZUtu9WZ2b7W7dBbsP5Gbb+kD9ody9QbUiR+eeJCUrHocVv4O9tW1bf91fYPvbmY1JkiSlx6562LY7N9vO1fO4dKRoLPk5u9NlZTXEsjiVhqS2yctE16OPPkosFmPWrFlUVla2uE6nTokZB/820XXfffdx1VVXMXXqVJ544gkeffRRLrzwQg4ePJjxuCWd2KGm3E6Au2Vn7rathFz+DXbVJxJtktTR7a2BHRuTK/POS/ZcliQpCHL5TFS7Fxqdv1o5VrsHmqK52XZjFN7dl5ttS2pdUa4DyIQFCxYAMG3atFbXqa5OvIJyZKJr/fr1zJ49m3vvvZebb7758Ocf//jHMxSppGRt3ZWbYQvfV70Txg/IYQBiy44cb38njOyX2xgk6US2LE++TH0d7N4K3avSHo4kSUqjXCa64vHEc/mQ3rmLQcr1S8hbdkDfrrmNQdLR8rJH16ZNmwAYNGhQi8ubm5tZtGgRcHSi66GHHqK4uJjPf/7zmQ9SUkp25nji2x37c7t9eQ5IUlvUrU+x3Lr0xiFJktIv188kuX4mk3bm+BrY4TUgdTh52aOrvj7xbdPacIPz5s2jrq6Ozp07M2TIkMOfv/jii5x66qk88sgjfP3rX2fLli0MHz6cf/u3f+Oaa65JOZ5JkyZRW9vGCRIkHdfgM69m0pX3tLjstougS6fjl+9S9sHvr32i9fX2HoRvP3Xs57/93Xy+MvOmNkarTJj06W8zeNJVLS470TnQ1r8/tH4O/Mv/uZN1i37Uxmg7no9/dSnlXftRU1tDVdWZuQ4n6wp9/8FjUAj7HyLEj7+0JaWyP334UX587ew0R9SxFMI5cDyFvv/yHCj0/Vd+mHLdg5w89uIWl2XjmeiWL93Gpld+2cZopfQbd/FXOfX8/93ismxcA/d+5z7+4em72xitpOOJHTHp3dSpU3nttddSqicvE119+/Zl165dLFu2jClTphy1rKamhtmzEw/v48ePJxQKHbVs69atfOUrX2Hu3LkMGDCAH/3oR/zd3/0dvXv35sILL0wpntraWrZu3Zr6Dkk6rMvQ91pf1gm6lbetnnC47eseqX7/Xq/nHBu5f2+ry9p6DqT69wfYtfO9QJ8D0Wj08O8g70eqCn3/wWNQKPt/qOkgpcUnePujBTt3B/s7ri0K5RxoTaHvvzwHCn3/lR/q61ufICgbz0Q76t71+lFODdyzq9Vl2bgG9uze6TUgZcD27dtTLpuXia4LL7yQ1atXM3fuXKZPn86IESMAWLp0Kddddx11dXUATJw48ahysViM/fv387Of/YwrrrgCgI985COsWrWK//iP/0g50dW3b9+U90XS0cpLWp+ha2/LnTiP0qUscTMTi8HehtbXa62uSPwQJ5988ok3pIwpih9qddmJzoG2/v2PV1en4nigz4FIJHL4d5D3I1WFvv/gMSiU/d/83kqG95+UdLmdBzbl9XGBwjkHWlPo+y/PgULff+WHSKz1B59sPBNVloa8fpRTpZHmVpdl4xooi8S8BqQ0icVi1NTUANCnT5+U6wnF4/HWW40Dqrq6mokTJ7Jjxw6KiooYOXIkDQ0NrFu3josvvphYLMbTTz/ND37wg6Pm4zr77LNZsmQJ+/bto7Ky8vDnt99+Ow8//DA7duzIxe5IOsKeA3Dnb1Iv/7VPJN7Y2X0AvpZCPdecDWedkvr21X7LNsJPF6VWtr1/f4B/uQx6d06tbEdw569hz0Ho2gn+/ZO5jib7Cn3/wWNQKPtfswpW/j65MkWl8KH/BZHizMTUURTKOdCaQt9/eQ4U+v4rP7y0DuYtSa1sOp6J/uOT0Dn5juNS2qzdDt/7U2pl03EN3DIdhp6UWllJR6uvrz+ci9m/fz8VFRUp1RNOZ1AdRVVVFS+88AIzZsygrKyMjRs30qNHDx544AHmz5/PmjVrAJgwYcJR5caMGdNqnQ0NJ0jxS8qKruUfjKecCwN65G7bShjQM3fbLiuGXpUnXk+Scu2kEVCS5PPByePzP8klSVI+yOVzaddOJrmUe1Xdc7ftUAhOtm1I6nDyMtEFMGrUKJ588kn27dvHvn37WLJkCTfeeCP19fVs3LiRcDjM2LFjjypz+eWXA/DHP/7x8GexWIxnnnmGM890klqpozgl9V6s7VJRCn265mbb+kCvysTDVS6cclLiplaSOrpIEUy4AsJtHKi8WxUMPTejIUmSpDTp1w3KS3Kz7WE5eh6XjtSpJHfJrgE9oDQvJwOSgi1vE12tWblyJfF4nOHDh1NefvSMg5deeikf+tCHuPHGG3nwwQd5+umnmTlzJitXruTf/u3fchSxpL91zrDcbPfsUyBScN+aHU8oBFOG52bb5+Rou5KUiq794IyZUHqCnqi9h8Npn0wkxyRJUscXCeduSP1cPY9Lf8t2AUlHKrgm2xUrVgDHDlsIEAqFeOKJJ/jUpz7FV7/6VS677DI2bdrE73//ey644IJshyqpFcP6wEldsrvNEN7MdCRTToFwlntWda+AUf2yu01Jaq+u/eDcz8PYSxK9tg4LJYYqPOszMOFyiOTorXBJkpSaXDyf9u3qvETqOCYNzn7Pqk4lcPqg7G5TUtuY6Pob3bp144EHHuC9997j0KFDvPzyy3zsYx/LZoiSTiA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      "text/plain": [
       "<Figure size 2210.55x3628.72 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code here to put all the pieces together as a single circuit\n",
    "\n",
    "# pi/4 x sqrt{2^4}=pi/4 which is approximately 3. So we will apply the operator = uncompute + diffuser_operator 3 times\n",
    "grover_search = QuantumCircuit(9,4)\n",
    "for i in range(4):\n",
    "    grover_search.h(i)\n",
    "for i in range(3):\n",
    "    grover_search = grover_search.compose(uncompute, [0,1,2,3,4,5,6,7,8]) # apply the uncompute operator\n",
    "    grover_search = grover_search.compose(diffuser_circuit, [0,1,2,3])    # then apply the diffuser operator\n",
    "grover_search.measure([0,1,2,3],[0,1,2,3])\n",
    "grover_search.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a126992-e0dd-462c-88fd-5306582d4978",
   "metadata": {},
   "source": [
    "## Simulate using Aer Simulator\n",
    "\n",
    "Now, since we have the circuit lets first perform an ideal simulation to find out if there are any satisfying assignment to our problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a5c45e80-130f-404d-8035-66891226d86c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write a code to run the final circuit and plot the results to see if there are any satisfying assignments\n",
    "result = execute(grover_search, backend).result() \n",
    "counts = result.get_counts(grover_search)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b1ba4e59-4c97-469c-98aa-75606ef8126b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# List down the satisfying assignments and verify for yourself if they are correct"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49bbb8cf-af57-4d5a-b329-5011dc50620a",
   "metadata": {},
   "source": [
    "Final satisfying assignments are $$v_0=0, v_1=1, v_2=1, v_3=0$$ and $$v_0=1, v_1=0, v_2=0, v_3=1$$ \n",
    "With these twwo assignments we have \n",
    "- $v_0\\neq v_1$ and $v_0\\neq v_2$\n",
    "- $ v_3\\neq v_1$ and $v_3\\neq v_2$\n",
    "\n",
    "Hence these are indeed satisfying assignments"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d053797-4abf-48f2-bb4c-8cc8059c965e",
   "metadata": {},
   "source": [
    "## Noisy simulation\n",
    "\n",
    "Let's now use our knowledge of transpilation and noisy simulations to see what the results may look like on a noisy backend.\n",
    "\n",
    "Plot the result while running the above circuit on two fake backends\n",
    "1. FakeGuadalupe (16 qubits)\n",
    "2. FakeKolkata (27 qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d88ee5a5-03ac-4592-a6bd-94b16a72abb5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code here\n",
    "fake_kolkata = FakeKolkata()           \n",
    "fake_guadalupe = FakeGuadalupe()\n",
    "\n",
    "fake_kolkata_noisemodel = NoiseModel.from_backend(fake_kolkata)  # Created a noisemodel from FakeKolkata backend\n",
    "fake_guadalupe_noisemodel = NoiseModel.from_backend(fake_guadalupe)  # Created a noisemodel from FakeGuadalupe backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "14036d9a-a5cf-491e-b5cb-dfe8dc988652",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulate with fakekoklkata backend\n",
    "simulate_fake_kolkata = AerSimulator(noise_model = fake_kolkata_noisemodel) \n",
    "fake_kolkata_circ= transpile(grover_search,simulate_fake_kolkata)\n",
    "fake_kolkata_counts = simulate_fake_kolkata.run(fake_kolkata_circ,shots=1000).result().get_counts()\n",
    "plot_histogram(fake_kolkata_counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6202c8f4-7c92-4d9c-8b55-a50bc8f82a51",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulate with fakeguadalupe bakcend\n",
    "simulate_fake_guadalupe = AerSimulator(noise_model = fake_guadalupe_noisemodel)\n",
    "fake_guadalupe_circ= transpile(grover_search,simulate_fake_guadalupe)\n",
    "fake_guadalupe_counts = simulate_fake_guadalupe.run(fake_guadalupe_circ,shots=1000).result().get_counts()\n",
    "plot_histogram(fake_guadalupe_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe0d99d4-b139-4f2f-acd6-02b425f9cc13",
   "metadata": {},
   "source": [
    "## Optional : Optimizations\n",
    "\n",
    "Explore how the results change with different optimizations we discussed during transpilation lecture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "39e1f7a2-8ea1-46d7-a028-1aacc4ba4c0b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Write your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca4b4385",
   "metadata": {},
   "source": [
    "**Credits: Similar exerise was carried out during the ACM Winter School at IIT Madras, December 2022**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acb3366c",
   "metadata": {},
   "source": [
    "### Resources for more advanced problem\n",
    "\n",
    "https://www.classiq.io/insights/competition-results-kakuro"
   ]
  }
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