examples/advanced_circuits_algorithms/Simons_Algorithm/Simons_Algorithm.ipynb

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    "# Simon's Algorithm\n",
    "\n",
    "**Abstract:** We study a quantum algorithm known as Simon's algorithm, which provided the first example of an exponential speedup over the best known classical algorithm by using a quantum computer to solve a particular problem. Originally published in 1994, Simon's algorithm was a precursor to Shor's well-known factoring algorithm, and it served as inspiration for many of the seminal works in quantum computation that followed.  \n",
    "\n",
    "This notebook is aimed at users with some basic knowledge of quantum computing and quantum circuits.\n",
    "\n",
    "### Table of Contents\n",
    "* [Simon's Problem Statement](#statement)\n",
    " * [Example for n=3](#example)\n",
    "* [Classical Complexity](#classicalcomplexity)\n",
    "* [Quantum Algorithm for Simon's Problem](#quantumalgorithm)\n",
    " * [Quantum Circuit](#circuit)\n",
    " * [Running Simon's Algorithm](#runningintro)\n",
    " * [Classical Post-Processing](#postprocessintro)\n",
    "* [Quantum Complexity](#quantumcomplexity)\n",
    "* [Implementing Simon's Algorithm in Amazon Braket](#implementation)\n",
    "* [References](#references)\n",
    "* [Appendix](#appendix)\n",
    " * [Implementing an Oracle Function](#oracleimplementation)\n",
    " * [Implementing the Classical Post-Processing](#appendixpostprocessing)"
   ]
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    "## Simon's Problem Statement: <a name=\"statement\"></a>\n",
    "\n",
    "Suppose we’re given a function $f:\\{0,1\\}^n \\rightarrow \\{0,1\\}^n$ that maps bit strings to bit strings along with the promise that\n",
    "$$\\forall x,y \\in \\{0,1\\}^n, \\quad f(x) = f(y) \\iff x=y\\oplus s,$$\n",
    "for some unknown $n$-bit string $s \\in \\{0,1\\}^n$, and where $\\oplus$ means bitwise addition modulo 2.\n",
    "\n",
    "Said another way, there exists an unknown string $s$ such that, $\\forall x, \\; f(x)=f(x\\oplus s)$. When $s$ is non-zero, the function is two-to-one as it maps *exactly* two inputs to every unique output.\n",
    "\n",
    "The goal of Simon's problem is to determine if $f$ is one-to-one, or two-to-one, or equivalently to find the secret string $s$.\n",
    "\n",
    "Since we're given the promise that $f(x)=f(y)\\implies x=y\\oplus s$, this means that $s=x\\oplus y$ whenever $f(x)=f(y)$. Thus, one way to solve this problem is to find two inputs to the function $f$ that produce the *same* output; $s$ is then the XOR of those two input strings. See [[1]](#References) for more details."
   ]
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    "<div class=\"alert alert-block alert-info\"><a name=\"example\"></a>\n",
    "<h3>Example for n=3:</h3>\n",
    "\n",
    "Consider the function $f:\\{0,1\\}^3\\to\\{0,1\\}^3$ defined by the truth table below.  \n",
    "<table>\n",
    "    <thead>\n",
    "        <tr>\n",
    "            <th><center>$$x$$</center></th>\n",
    "            <th><center>$$f(x)$$</center></th>\n",
    "        </tr>\n",
    "    </thead>\n",
    "    <tr>\n",
    "        <td><center>$$000$$</center></td>\n",
    "        <td><center>$$000$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$001$$</center></td>\n",
    "        <td><center>$$001$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$010$$</center></td>\n",
    "        <td><center>$$001$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$011$$</center></td>\n",
    "        <td><center>$$000$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$100$$</center></td>\n",
    "        <td><center>$$100$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$101$$</center></td>\n",
    "        <td><center>$$101$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$110$$</center></td>\n",
    "        <td><center>$$101$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$111$$</center></td>\n",
    "        <td><center>$$100$$</center></td>\n",
    "    </tr>\n",
    "</table>\n",
    "\n",
    "    \n",
    "    \n",
    "By inspection, we can see that $f$ satisfies the properties described in the statement of Simon's problem. In particular, note that each output $f(x)$ appears twice for two distinct inputs. We are given the promise that, for each of these two inputs $x$ and $y$ with the same output $f(x)=f(y)$, we have $x \\oplus s = y$ for a yet to be determined $s$, and therefore $x\\oplus y = s$.\n",
    "\n",
    "For concreteness, notice that the input strings $001$ and $010$ are both mapped by $f$ to the same output string $001$. Taking the bitwise XOR of $001$ and $010$ we obtain the secret string $s$:\n",
    "\n",
    "$$s=001 \\oplus 010 = 011$$\n",
    "\n",
    "Therefore, in this example, the secret string is $s = 011$.\n",
    "    \n",
    "    \n",
    "In this specific example, we also see that the string $000$ is mapped to itself. Since $x\\oplus y=s$ for two inputs $x$ and $y$ with the same output, we must have that $s$ is also mapped to $000$, since $s=000\\oplus s$. Indeed, we see that $011$ maps to $000$, as expected.\n",
    "</div>"
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    "\n",
    "## Classical Complexity<a name=\"classicalcomplexity\"></a>\n",
    "\n",
    "To solve Simon's problem classically, one needs to find two different inputs $x$ and $y$ for which $f(x)=f(y)$. As we saw above, one can then determine $s=x\\oplus y$. How hard is it to find two distinct inputs that map to the same output, given the function $f$ as a black box?  For $n$-bit strings, there are $2^n$ possible inputs. Thus, in the worst case, one would need to check at most $2^n$ different inputs to find a pair that maps to the same output; this provides an upper bound on the required query complexity.\n",
    "\n",
    "It turns out that a *lower* bound on the classical query complexity of Simon's algorithm can also be found: $\\Omega ({\\sqrt {2^{n}}})$. Proving this lower bound requires a little more work and is outside the scope of this notebook, so instead we will just provide some intuition.\n",
    "\n",
    "As mentioned above, the goal is to find a pair of input strings $x$ and $y$ that map to the *same* output string $f(x)=f(y)$ -- a collision. Finding a collision in a set is an instance of the well-known (generalized) birthday problem [[2]](#References): within a group of people, what is the probability that two of them share the same birthday? One can turn this problem around and ask \"how many people do we need in a room to ensure that the probability that at least two of them share a birthday is greater than some fixed number?\" This latter question gets to the heart of solving Simon's problem classically: how many queries to the function $f$ do we need to make to guarantee that we find a collision, with high probability? In the case of the birthday problem, we would need enough people in the room so that when we generate all possible pairings of people, we would have about 365 possible pairs. That way, we'd have a good chance that at least one of those pairs of people share a birthday. Using this intuition, we need to query $f$ enough times to generate a set of *pairs* with roughly the same size as the number of possible inputs ($2^n$). If we make $k$ queries to the function $f$, we can generate ${k \\choose 2}=\\frac{k(k-1)}{2}\\sim k^2$ pairs. Thus, we need to make $k$ queries such that ${k\\choose 2}\\gtrsim 2^n$ to have a high probability of generating a collision, and therefore, $k>\\Omega(\\sqrt{2^n})$."
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"
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   "source": [
    "## Quantum Algorithm for Simon's Problem<a name=\"quantumalgorithm\"></a>\n",
    "\n",
    "Simon's algorithm is a scheme for solving the problem above using exponentially fewer queries to the function $f$. In order for Simon's algorithm to work, one needs to be able to implement the unknown function $f$ using quantum logic. That is, given an input *quantum state* $|x\\rangle$, one needs a *unitary* $U_f$ satisfying\n",
    "$$U_f|x\\rangle |0\\rangle = |x\\rangle |f(x)\\rangle.$$\n",
    "This unitary is an *oracle* for $f$, and the goal is to query it as few times as possible to learn the secret string $s$.\n",
    "\n",
    "### Quantum Circuit<a name=\"circuit\"></a>\n",
    "\n",
    "Simon's algorithm involves both quantum and classical components. The quantum part of Simon's algorithm is used to query the oracle efficiently, while the classical component is used to process measurement results and determine the hidden string $s$. A circuit for the quantum component of Simon's algorithm is shown below.\n",
    "<div align=\"center\">\n",
    "<img src=\"quantum_circuit.png\", width=500>\n",
    "</div>\n",
    "\n",
    "For a function $f$ acting on $n$-bit strings, the circuit above acts on $2n$ qubits, as needed for the definition of $U_f$. Only the first $n$ qubits are measured; the remaining qubits are unused after the application of $U_f$.\n",
    "\n",
    "### Running Simon's Algorithm<a name=\"runningintro\"></a>\n",
    "To solve Simon's problem, one needs to run the quantum circuit above several times. After each run of the circuit, the measurements of the first $n$ qubits produce an output bit string, which we denote by $z$.\n",
    "\n",
    "An analysis of the circuit above shows that each output bit string $z$ satisfies the following condition:\n",
    "$$ z\\cdot s = 0 \\; \\mod{2}.$$\n",
    "\n",
    "Let us now analyze the above circuit step-by-step:\n",
    "1. Initialize all qubits in the $|0\\rangle$ state. That is, we start in the state $|0\\rangle^{\\otimes n} \\otimes |0\\rangle^{\\otimes n}$. We will use the shorthand $|0\\rangle^{\\otimes n}\\equiv |0^n\\rangle$\n",
    "2. Apply Hadamard gates to each of the first $n$ qubits, placing them in the equal superposition state: $$\\frac{1}{\\sqrt{2^n}}\\sum_{x \\in \\{0, 1\\}^n} |x\\rangle |0^n\\rangle$$.\n",
    "3. Apply the oracle $U_f$, which computes the function $f$ into the last $n$ qubits, giving the state $$\\frac{1}{\\sqrt{2^n}}\\sum_{x \\in \\{0, 1\\}^n} |x\\rangle |f(x)\\rangle$$\n",
    "4. Measure the last $n$ qubits, giving a random result $f(x)$. If $f$ is one-to-one, this output of $f$ corresponds to an input of $x$. If $f$ is two-to-one, the output of $f$ corresponds to an input of either either $x$ or $y = x \\oplus s$, where $x$ and $y$ are the two different inputs to $f$ that gave the *same* output $f(x)=f(y)$. Hence we are left with the first $n$ qubits in the state;\n",
    "    <center>A. $|x\\rangle$, &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&ensp; if $f$ is one-to-one;</center>\n",
    "    <center>B. $\\frac{1}{\\sqrt{2}} (|x\\rangle + |y\\rangle)$, where $x \\oplus y = s$,&emsp; if $f$ is two-to-one.</center> \n",
    "    Note that this step is not strictly necessary, since we do not need the measurement result, but we include it as it makes the analysis easier.\n",
    "5. Apply Hadamard gates to each of the first $n$ qubits. If $f$ is one-to-one, the state $|x\\rangle$ is mapped to $$H^{\\otimes n} |x\\rangle = \\frac{1}{\\sqrt{2^n}} \\sum_{z \\in \\{0, 1\\}^n} (-1)^{x \\cdot z}|z\\rangle,$$\n",
    "   where $x\\cdot z$ is the dot product between the two strings represented as vectors (modulo 2).\n",
    "   \n",
    "   Similarly, if $f$ is two-to-one, the state $\\frac{1}{\\sqrt{2}}(|x\\rangle + |y\\rangle)$ is mapped to $$\\frac{1}{\\sqrt{2^{n+1}}} \\sum_{z \\in \\{0, 1\\}^n} [(-1)^{x \\cdot z} + (-1)^{y \\cdot z}]|z\\rangle$$.\n",
    "6. Measure the first $n$ qubits.\n",
    "   1. If $f$ is one-to-one, measurements return a random bit string $z$ uniformly chosen from $\\{0,1\\}^n$.\n",
    "   2. If $f$ is two-to-one, measurements return a random bit string $z$ such that $x \\cdot z = y \\cdot z \\,\\mathrm{mod}\\, 2$, since otherwise the amplitude $(-1)^{x \\cdot z} + (-1)^{y \\cdot z}$ cancels out. Using the criterion for Simons problem (i.e,. $f(x)=f(y) \\implies x=y\\oplus s$), we find that\n",
    "\\begin{align*}\n",
    "x\\cdot z &= y\\cdot z & \\mod{2}\\\\\n",
    "x\\cdot z &= (x\\oplus s)\\cdot z &  \\mod{2}\\\\\n",
    "x\\cdot z &= x\\cdot z\\oplus s\\cdot z & \\mod{2}\\\\\n",
    "0 &= s\\cdot z &  \\mod{2}\n",
    "\\end{align*}\n",
    "   \n",
    "   \n",
    "   Thus, in both cases we obtain a random bit string $z$ such that $s \\cdot z = 0$.\n",
    "\n",
    "Therefore, each time we run the quantum circuit above, we find a bit string $z$ that is orthogonal to the secret string $s$. \n",
    "\n",
    "### Classical Post-Processing<a name=\"postprocessintro\"></a>\n",
    "From the measurement results $\\{z_1, \\dots, z_k\\}$, we can form a system of equations:\n",
    "$$ \\begin{aligned}z_{1}\\cdot s&=0\\mod{2}\\\\z_{2}\\cdot s&=0\\mod{2}\\\\&\\,\\,\\vdots \\\\z_{k}\\cdot s&=0\\mod{2}\\end{aligned}$$ \n",
    "\n",
    "There are $k$ equations and $n$ unknowns (the elements of $s$). If we run the quantum part enough times so that we find $n$ **independent** equations, then we can solve these equations (using, e.g., Gaussian elimination) to recover the secret string $s$. This is precisely the classical post-processing required: solve the system of equations found above to recover the string $s$. We refer the interested reader to the [Appendix](#Classical-post-processing) for details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Complexity<a name=\"quantumcomplexity\"></a>\n",
    "How many queries do we need to make to $U_f$ in the quantum case? Above we saw that we need to run the quantum part of the algorithm $k$ times to generate a system of equations. We need to find $n$ linearly independent equations for the system to be determined. Thus, we need at least $n$ queries to $U_f$ to find such a system. It is possible, however, that we will get the same measurement outcome on different runs of the quantum algorithm, so we would need to re-do those runs that do not produce distinct measurement outcomes. Fortunately, these repeated outcomes are unlikely, so we only need $O(n)$ queries to the oracle $U_f$.\n",
    "\n",
    "Comparing the quantum and classical algorithms, we saw that the classical algorithm requires at least $\\Omega(2^{0.5 n})$ queries to $f$, whereas the quantum algorithm requires only $O(n)$. Thus, we have established an *exponential* speedup by using the quantum algorithm above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing Simon's Algorithm in Amazon Braket<a name=\"implementation\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:55.620607Z",
     "start_time": "2023-08-29T21:32:53.083801Z"
    }
   },
   "outputs": [],
   "source": [
    "# Imports and Setup\n",
    "from braket.circuits import Circuit, circuit\n",
    "from braket.devices import LocalSimulator\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# Sets the device to run the circuit on\n",
    "device = LocalSimulator()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also import a method called `simons_oracle`, which generates a circuit implementing an example oracle function. The code for `simons_oracle` is defined in the `simons_utils.py` module, and it is shown in the [Appendix](#Implementing-an-oracle-function) for completeness. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:55.638392Z",
     "start_time": "2023-08-29T21:32:55.619670Z"
    }
   },
   "outputs": [],
   "source": [
    "# Import local utils\n",
    "from simons_utils import simons_oracle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now define the secret string, $s$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:55.642804Z",
     "start_time": "2023-08-29T21:32:55.625060Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The secret string is: 101011\n"
     ]
    }
   ],
   "source": [
    "s = '101011'\n",
    "\n",
    "# Other examples to try:\n",
    "# s = '011'\n",
    "# s = '00000'\n",
    "# s = '1'\n",
    "# Generate a random string of random length from 1 to 10:\n",
    "# s=\"\".join(str(np.random.randint(2)) for _ in range(np.random.randint(1,10)))\n",
    "\n",
    "print(\"The secret string is: \"+ s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Circuit Definition\n",
    "\n",
    "We now define the quantum circuit for Simon's algorithm:\n",
    "1. Apply Hadamard gates to the first $n$-qubits. \n",
    "\n",
    "\n",
    "2. Query the oracle (i.e., the $U_f$ gate). In this example, the oracle is defined dynamically, based on our chosen value of $s$. You can try experimenting with different values of $s$ (with differing lengths).\n",
    "\n",
    "\n",
    "3. Apply Hadamard gates to the first $n$-qubits.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:55.661390Z",
     "start_time": "2023-08-29T21:32:55.653732Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T   : |0|     1     | 2 |3|4|5|6|\n",
      "                                 \n",
      "q0  : -H-C-----------C---C-C-C-H-\n",
      "         |           |   | | |   \n",
      "q1  : -H-|-C---------|-H-|-|-|---\n",
      "         | |         |   | | |   \n",
      "q2  : -H-|-|-C-------|-H-|-|-|---\n",
      "         | | |       |   | | |   \n",
      "q3  : -H-|-|-|-C-----|-H-|-|-|---\n",
      "         | | | |     |   | | |   \n",
      "q4  : -H-|-|-|-|-C---|-H-|-|-|---\n",
      "         | | | | |   |   | | |   \n",
      "q5  : -H-|-|-|-|-|-C-|-H-|-|-|---\n",
      "         | | | | | | |   | | |   \n",
      "q6  : ---X-|-|-|-|-|-X---|-|-|---\n",
      "           | | | | |     | | |   \n",
      "q7  : -----X-|-|-|-|-----|-|-|---\n",
      "             | | | |     | | |   \n",
      "q8  : -------X-|-|-|-----X-|-|---\n",
      "               | | |       | |   \n",
      "q9  : ---------X-|-|-------|-|---\n",
      "                 | |       | |   \n",
      "q10 : -----------X-|-------X-|---\n",
      "                   |         |   \n",
      "q11 : -------------X---------X---\n",
      "\n",
      "T   : |0|     1     | 2 |3|4|5|6|\n"
     ]
    }
   ],
   "source": [
    "n = len(s)\n",
    "\n",
    "circ = Circuit()\n",
    "\n",
    "# Apply Hadamard gates to first n qubits\n",
    "circ.h(range(n)) \n",
    "\n",
    "# Now apply the Oracle for f\n",
    "circ.simons_oracle(s)\n",
    "\n",
    "# Apply Hadamard gates to the first n qubits\n",
    "circ.h(range(n)) \n",
    "\n",
    "\n",
    "print(circ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now run the circuit\n",
    "\n",
    "We need enough shots to obtain $n$ linearly independent bit strings in the output measurements. We have chosen `4n` shots in the example below, just to be on the safe side."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:55.748356Z",
     "start_time": "2023-08-29T21:32:55.710344Z"
    }
   },
   "outputs": [],
   "source": [
    "task = device.run(circ, shots=4*n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analyze the results\n",
    "\n",
    "We can retrieve the measurement results on all $2n$ qubits as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:56.031079Z",
     "start_time": "2023-08-29T21:32:55.748804Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = task.result()\n",
    "\n",
    "counts = result.measurement_counts\n",
    "plt.bar(counts.keys(), counts.values());\n",
    "plt.xlabel('bit strings');\n",
    "plt.ylabel('counts');\n",
    "plt.xticks(rotation=90)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Aggregate the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The measurements are performed on all $2n$ qubits, but we are only interested in the first $n$ qubits. Thus, we need to aggregate the results by ignoring the measurement outcomes on the last $n$ qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:56.314040Z",
     "start_time": "2023-08-29T21:32:56.031498Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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y8/NhZWUFAPj555/x2muvAQCaNGmCxMRE5VpHRERE9JRKFG6aNm2K+fPn4+DBg9i9eze6desGALhx4wZq166taAOJiIiInkaJws0333yDBQsWoGPHjujfvz98fX0BAFu3bjUeriIiIiJSQ8WSvKljx45ITU1Feno6atasaZw+fPhwVK1aVbHGERERET2tEu256dy5MzIyMkyCDQDUqlUL/fr1U6RhRERERCVRonCzb98+5OXlFZl+7949HDx48JkbRURERFRST3VY6sSJE8Z/nzlzBklJScbner0eO3bsQN26dZVrHREREdFTeqpw4+fnB51OB51Oh86dOxd5vXLlyvj2228VaxwRERHR03qqcHPp0iWICBo0aIDDhw/D3t7e+FqlSpVQp04dVKhQQfFGEhERET2ppwo3Li4uAACDwWCWxhARERE9qxJdCg4A58+fx969e5GSklIk7EyePPmZG0ZERERUEiUKN99//z1GjBgBOzs7ODo6QqfTGV/T6XQMN0RERKSaEoWbr776Cl9//TUmTJigdHuIiIiInkmJxrm5c+cO+vTpo3RbiIiIiJ5ZicJNnz59sGvXLqXbQkRERPTMSnRYqlGjRvj8889x6NAheHt7w9LS0uT10aNHK9I4IiIioqdVonCzcOFCVKtWDfv378f+/ftNXtPpdAw3REREpJoShZtLly4p3Q4iIiIiRZTonBsiIiKisqpEe26GDBny2NeXLFlSosYQERERPasShZs7d+6YPM/Pz8epU6dw9+7dYm+oSURERFRaShRuNm/eXGSawWDAiBEj0LBhw2duFBEREVFJKXbOjYWFBcaNG4eIiIgnfk94eDgCAgJQvXp11KlTByEhIYiPj//L961fvx5NmjSBtbU1vL29sX379mdpOhEREWmIoicUX7x4EQUFBU88//79+zFy5EgcOnQIu3fvRn5+Pl5++WVkZWU98j3R0dHo378/hg4diuPHjyMkJAQhISE4deqUEotAREREz7kSHZYaN26cyXMRQWJiIrZt24aBAwc+8efs2LHD5PmyZctQp04dHD16FO3bty/2PbNnz0a3bt0wfvx4AMCXX36J3bt3Y86cOZg/f/5TLgkRERFpTYnCzfHjx02eW1hYwN7eHjNmzPjLK6keJy0tDQBQq1atR84TExNTJFwFBwdjy5Ytxc6fm5uL3Nxc4/P09PQSt4+IiIjKvhKFm7179yrdDhgMBowdOxZt2rSBl5fXI+dLSkqCg4ODyTQHBwckJSUVO394eDjCwsIUbevjuE7cZtbPvzytp1k/n4jUp9Z6xNx1H1dbLeVxmcuDZzrn5ubNm/jll1/wyy+/4ObNm8/UkJEjR+LUqVNYs2bNM33OwyZNmoS0tDTjIyEhQdHPJyIiorKlRHtusrKy8MEHH2D58uUwGAwAgAoVKiA0NBTffvstqlSp8lSfN2rUKERGRuLAgQOoV6/eY+d1dHREcnKyybTk5GQ4OjoWO7+VlRWsrKyeqj1ERET0/CrRnptx48Zh//79+PHHH3H37l3cvXsXP/zwA/bv34+PPvroiT9HRDBq1Chs3rwZe/bsgZub21++JygoCFFRUSbTdu/ejaCgoKdeDiIiItKeEu252bhxIzZs2ICOHTsap/Xo0QOVK1dG3759MW/evCf6nJEjR2LVqlX44YcfUL16deN5M7a2tqhcuTIAIDQ0FHXr1kV4eDgAYMyYMejQoQNmzJiBnj17Ys2aNYiNjcXChQtLsihERESkMSXac5OdnV3kpF4AqFOnDrKzs5/4c+bNm4e0tDR07NgRTk5OxsfatWuN81y9ehWJiYnG561bt8aqVauwcOFC+Pr6YsOGDdiyZctjT0ImIiKi8qNEe26CgoIwZcoULF++HNbW1gCAnJwchIWFPdXhIRH5y3n27dtXZFqfPn3Qp0+fJ65DRERE5UeJws2sWbPQrVs31KtXD76+vgCA33//HVZWVti1a5eiDSQiIiJ6GiUKN97e3jh//jxWrlyJc+fOAQD69++PAQMGGM+VISIiIlJDicJNeHg4HBwcMGzYMJPpS5Yswc2bNzFhwgRFGkdERET0tEp0QvGCBQvQpEmTItObNm3K+zsRERGRqkoUbpKSkuDk5FRkur29vcmVTURERESlrUThxtnZGb/++muR6b/++iteeOGFZ24UERERUUmV6JybYcOGYezYscjPz0fnzp0BAFFRUfjkk0+eaoRiIiIiIqWVKNyMHz8et27dwvvvv4+8vDwAgLW1NSZMmIBJkyYp2kAiIiKip1GicKPT6fDNN9/g888/x9mzZ1G5cmU0btyYN6gkIiIi1ZUo3BSqVq0aAgIClGoLERER0TMr0QnFRERERGUVww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpiqrh5sCBA3j11VfxwgsvQKfTYcuWLY+df9++fdDpdEUeSUlJpdNgIiIiKvNUDTdZWVnw9fXF3Llzn+p98fHxSExMND7q1KljphYSERHR86aimsW7d++O7t27P/X76tSpgxo1aijfICIiInruPZfn3Pj5+cHJyQldu3bFr7/++th5c3NzkZ6ebvIgIiIi7Xquwo2TkxPmz5+PjRs3YuPGjXB2dkbHjh1x7NixR74nPDwctra2xoezs3MptpiIiIhKm6qHpZ6Wu7s73N3djc9bt26NixcvIiIiAv/73/+Kfc+kSZMwbtw44/P09HQGHCIiIg17rsJNcQIDA/HLL7888nUrKytYWVmVYouIiIhITc/VYanixMXFwcnJSe1mEBERURmh6p6bzMxMXLhwwfj80qVLiIuLQ61atVC/fn1MmjQJ169fx/LlywEAs2bNgpubG5o2bYp79+5h0aJF2LNnD3bt2qXWIhAREVEZo2q4iY2NRadOnYzPC8+NGThwIJYtW4bExERcvXrV+HpeXh4++ugjXL9+HVWqVIGPjw9+/vlnk88gIiKi8k3VcNOxY0eIyCNfX7ZsmcnzTz75BJ988omZW0VERETPs+f+nBsiIiKiBzHcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmMNwQERGRpjDcEBERkaYw3BAREZGmqBpuDhw4gFdffRUvvPACdDodtmzZ8pfv2bdvH5o1awYrKys0atQIy5YtM3s7iYiI6PmharjJysqCr68v5s6d+0TzX7p0CT179kSnTp0QFxeHsWPH4t1338XOnTvN3FIiIiJ6XlRUs3j37t3RvXv3J55//vz5cHNzw4wZMwAAHh4e+OWXXxAREYHg4GBzNZOIiIieI8/VOTcxMTHo0qWLybTg4GDExMQ88j25ublIT083eRAREZF2qbrn5mklJSXBwcHBZJqDgwPS09ORk5ODypUrF3lPeHg4wsLCSquJqnGduM3sNS5P66lKbbXqqln7UXXVxGVWXllcZrWUx++6PK47S8tzteemJCZNmoS0tDTjIyEhQe0mERERkRk9V3tuHB0dkZycbDItOTkZNjY2xe61AQArKytYWVmVRvOIiIioDHiu9twEBQUhKirKZNru3bsRFBSkUouIiIiorFE13GRmZiIuLg5xcXEA7l/qHRcXh6tXrwK4f0gpNDTUOP97772HP//8E5988gnOnTuH7777DuvWrcOHH36oRvOJiIioDFI13MTGxsLf3x/+/v4AgHHjxsHf3x+TJ08GACQmJhqDDgC4ublh27Zt2L17N3x9fTFjxgwsWrSIl4ETERGRkarn3HTs2BEi8sjXixt9uGPHjjh+/LgZW0VERETPs+fqnBsiIiKiv8JwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESaUibCzdy5c+Hq6gpra2u0bNkShw8ffuS8y5Ytg06nM3lYW1uXYmuJiIioLFM93Kxduxbjxo3DlClTcOzYMfj6+iI4OBgpKSmPfI+NjQ0SExONjytXrpRii4mIiKgsUz3czJw5E8OGDcPgwYPh6emJ+fPno0qVKliyZMkj36PT6eDo6Gh8ODg4lGKLiYiIqCxTNdzk5eXh6NGj6NKli3GahYUFunTpgpiYmEe+LzMzEy4uLnB2dkavXr1w+vTpR86bm5uL9PR0kwcRERFpl6rhJjU1FXq9vsieFwcHByQlJRX7Hnd3dyxZsgQ//PADVqxYAYPBgNatW+PatWvFzh8eHg5bW1vjw9nZWfHlICIiorJD9cNSTysoKAihoaHw8/NDhw4dsGnTJtjb22PBggXFzj9p0iSkpaUZHwkJCaXcYiIiIipNFdUsbmdnhwoVKiA5OdlkenJyMhwdHZ/oMywtLeHv748LFy4U+7qVlRWsrKyeua1ERET0fFB1z02lSpXQvHlzREVFGacZDAZERUUhKCjoiT5Dr9fj5MmTcHJyMlcziYiI6Dmi6p4bABg3bhwGDhyIFi1aIDAwELNmzUJWVhYGDx4MAAgNDUXdunURHh4OAJg6dSpatWqFRo0a4e7du5g+fTquXLmCd999V83FICIiojJC9XDTr18/3Lx5E5MnT0ZSUhL8/PywY8cO40nGV69ehYXF/+1gunPnDoYNG4akpCTUrFkTzZs3R3R0NDw9PdVaBCIiIipDVA83ADBq1CiMGjWq2Nf27dtn8jwiIgIRERGl0CoiIiJ6Hj13V0sRERERPQ7DDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpCsMNERERaQrDDREREWkKww0RERFpSpkIN3PnzoWrqyusra3RsmVLHD58+LHzr1+/Hk2aNIG1tTW8vb2xffv2UmopERERlXWqh5u1a9di3LhxmDJlCo4dOwZfX18EBwcjJSWl2Pmjo6PRv39/DB06FMePH0dISAhCQkJw6tSpUm45ERERlUWqh5uZM2di2LBhGDx4MDw9PTF//nxUqVIFS5YsKXb+2bNno1u3bhg/fjw8PDzw5ZdfolmzZpgzZ04pt5yIiIjKoopqFs/Ly8PRo0cxadIk4zQLCwt06dIFMTExxb4nJiYG48aNM5kWHByMLVu2FDt/bm4ucnNzjc/T0tIAAOnp6c/Y+uIZcrPN8rmFHtVuc9dVszaXufTqqlm7rNVVs7ZW66pZm8tcenUfV1uJzxSRv55ZVHT9+nUBINHR0SbTx48fL4GBgcW+x9LSUlatWmUybe7cuVKnTp1i558yZYoA4IMPPvjggw8+NPBISEj4y3yh6p6b0jBp0iSTPT0GgwG3b99G7dq1odPpVGzZ/RTq7OyMhIQE2NjYaL6umrW5zFxmrdbmMnOZtVz7QSKCjIwMvPDCC385r6rhxs7ODhUqVEBycrLJ9OTkZDg6Ohb7HkdHx6ea38rKClZWVibTatSoUfJGm4GNjY0qHUatumrW5jKXj9pc5vJRm8tcfmoXsrW1faL5VD2huFKlSmjevDmioqKM0wwGA6KiohAUFFTse4KCgkzmB4Ddu3c/cn4iIiIqX1Q/LDVu3DgMHDgQLVq0QGBgIGbNmoWsrCwMHjwYABAaGoq6desiPDwcADBmzBh06NABM2bMQM+ePbFmzRrExsZi4cKFai4GERERlRGqh5t+/frh5s2bmDx5MpKSkuDn54cdO3bAwcEBAHD16lVYWPzfDqbWrVtj1apV+Mc//oFPP/0UjRs3xpYtW+Dl5aXWIpSYlZUVpkyZUuSwmVbrqlmby1y6uMzar6tmbS5z6VKzdknpRJ7kmioiIiKi54Pqg/gRERERKYnhhoiIiDSF4YaIiIg0heGGiIiINIXhhoiIiDSF4YZIJbxQkYjIPBhuyii1NnwiAoPBUG7qFlKjduG9zQwGQ7kKOuXhdy5Pv2dZw++eAI5zU+YZDAbodLpSucmnXq9HhQoVSr22WnWLY87aBoMBR48eRXx8POLj4+Hm5obXXnsNdnZ2itd6FBFR/YaxhbT6Oz+sLH3n5pSYmIiUlBTcvn0b1tbW8Pb2RrVq1VRrj5r9S+sMBoPJ4LplEcNNGaHX6xEVFYXbt28jJSUF7u7u6NSpEypVqmT22tevX8fGjRvxxx9/4Pr16+jSpQv69etn9o2uWnWB+3e5jYyMxPXr15GYmIjAwECEhITA2trabDWnTp2KlStX4tatW/D29kZKSgqSkpLQtm1bfPDBB+jSpYvZaj+sNDe4anzXataOjY1F7dq14eLiYrIBKI3v/PLly6hZs+YT31xQKUuWLMHChQtx+PBh1KtXD/Xr14ednR3atWuHXr16oVGjRmZbfjXXneXd4wKk6qFeSHWZmZkSGhoqtra2UqdOHWnVqpX4+PhIy5YtJSwsTC5evCgiIgaDQfHa6enp0qlTJ6lbt6706tVL+vTpIy+88IJYWFhIt27d5MCBA4rXVLOuiEhGRob06tVLatasKX5+fhIcHCyurq7i4OAg7777rsTFxYmIst/3nTt3pHLlyrJ27VrJz8+Xq1evSkxMjHz33Xfy2muvib+/v6xbt06xeg/Lzc2VqKgouXHjRpHXzNGvCqnxXatZOy0tTerVqyevv/66zJw5Uw4ePCjJyclF5tu8ebMkJCQoVrewtru7uwwaNEg2bdokly9flnv37hWZb9++fcW2qaTu3LkjNWrUkMmTJ0tycrL88ssv8u9//1v69esngYGB0rt3b/nzzz8Vq/cgNded+fn5cu7cOcnOzi7ymjn/pvR6vWRkZJjt8x8nOztbwsPD5dChQ0VeKygoMOtyPy2GmzLgm2++EU9PT2OHiY2NleXLl8v7778vQUFB8tZbb8mdO3fMUnvatGni7+8vN2/eFJH7K6pLly7JqlWrJDg4WHx9fSUqKkozdUXuf98+Pj7yxx9/iIjIn3/+Kfv375dp06ZJx44d5aWXXpL4+HhFay5btky8vLxEr9ebTNfr9XLu3Dl57733xMrKSo4dO6Zo3ULfffed1KxZU0JDQ2X+/Ply+PDhIn0qNTVVFi9eLLm5uYrVVeO7VrP2ggULpFatWvLqq6+Ks7OzeHh4SGhoqCxevFiOHTsmaWlpkpSUJLVr15YjR44oWnvu3LlSpUoVad68ueh0OnF1dZUPP/xQ9uzZI0lJSVJQUCA3btyQhg0byokTJxSrO2fOHGnRokWR6ffu3ZOtW7eKr6+vNGjQQFJSUhSrWUjNdef8+fPlhRdekDFjxsjOnTvlxo0bkpeXZzLP3bt3ZevWrUWmP2tdT09PmT59usTHxxdZp4jcD30xMTFSUFCgWF0RkW+//VZ0Op20a9dO+vXrJ99++62cO3fOZJ5r167JRx99JFlZWYrWfloMN2VA27Zt5V//+leR6enp6bJ161apV6+e9OzZs9hO/Kx69eolo0ePLjJdr9fLpUuXpFevXtKkSRNJTU3VRF0RkS5dusjkyZOLTM/JyZHffvtNmjdvLoGBgYr+cR48eFDc3Nzkp59+KvZ1g8EgwcHB8s033yhW80Ht27eX9u3by8svvyx169YVPz8/ef/992XVqlVy5swZyc3NlcWLF4uLi4uiddX4rtWsPXr0aBk0aJCI3N+TMnfuXOnQoYO88MIL0qJFCxk3bpwMHjxY7OzsFKtZ6L333pP3339fRO4H1bCwMHF1dRWdTifNmzeXf/3rX/LJJ5+Ira2tonUXLlwo3t7ecvbsWRG5v0fjwXVVYmKiNG3aVNavX69oXRF1152tWrWS5s2bS5MmTUSn04m3t7eEhYVJTEyM3L59W0REFi9eLP7+/orWbd68uTRu3FicnZ3F0tJSOnfuLEuXLpXr168b51myZIm89NJLitYVEenZs6f07t1bvvzyS+ndu7cEBQVJu3btZOjQobJq1SpJSUmRxYsXi06nU7z202K4UVl+fr6MHTtWOnToYPyDeNjPP/8svr6+cvLkScXrf//99+Lq6iqXL18u9vXLly+Ln5+f7N69WxN1DQaDfP311+Lt7S2JiYnFzhMXFye+vr7F7notqezsbHnjjTckKChI1q5dK0lJSUVWuB07dpRPP/1UsZqFUlNTpX379rJ06VIRuf/dfv3119KiRQupW7eutGvXTj799FNxdXWVsWPHKlZXre9ardoGg0H27dsnCxYsKPI/5vj4eJk8ebK0aNFCdDpdsaHrWeTn58uGDRtk1qxZRWqfOHFChg8fLvb29mapffPmTWNYTkpKMk5/sH8HBQXJP//5T0XrqrnuvHnzprRp00Y2bdokIvd/3zFjxoidnZ1YWlpKx44dZe7cueLh4SGjRo1SrG5ycrIEBATI2rVrJS8vT3bt2iVvvfWWVK9eXWxsbKR///4SGRkp/v7+MmLECMXqitzfux4cHCxfffWViIjcvn1bIiMjZcKECdKjRw9p2bKlvPzyy1K9enWZMGGCorVLguGmDIiJiRF3d3eZOHGi8Rjxgy5fvixVq1aVK1euKF772rVr0q5dO2ndurUsXbpUzp8/b7IL9eLFi2Jtba34MXO16oqInDlzRvz8/KR///6yZ88euXPnjsmx4kuXLknlypUfGbxK6sKFC/Lqq6+Kvb29dO3aVebMmSPbtm2TXbt2SXh4uNSsWbPY3/9ZZWRkyIYNG2TXrl1FXjty5IiMHj1aGjRoIDqdTvFlVuu7Vqt2QUGBpKWlGf+dn59vUvPixYtSsWJFsyxvTk6O8Vya4mr/+eefYmFhYZb1yNq1a8XOzk4cHBzkk08+kZMnT0paWppcunRJNm7cKNWqVZMLFy4oXletdWdKSorMmzdPtm/fXuS1ffv2Se/evcXKykrxv6krV65IWFhYkbq3b9+W5cuXS8eOHcXS0tIsf8siImfPnpVffvmlyPTLly/LihUrpH///qLT6czSx54Wr5YqAwwGAxYtWoRJkybB0tISffv2xWuvvQZ7e3tcvnwZkZGRiI2NxfHjx81S//jx4/j6669x8uRJNGjQAAEBAbCzs0Nubi6ioqKQnZ2NAwcOKF43NjYW4eHhxrqBgYGlUhcAtm7dii+++ALXrl1Du3bt0KNHD9jb2yM1NRU7d+7E5cuX8dtvv5ml9u7du/Htt9/i119/hb29PQoKClCpUiV89tlnGDBggFlq5ufnQ6fToWLFitDr9QBgcvl9WFgYNm/ejLi4OMVrq/ldb9u2DZ9//jmuXbuG9u3bo3v37qVW+0GFq9mpU6di9uzZuH37tlnr6fV6WFhYQKfTGa9omTp1KubMmYObN2+apWZOTg6mT5+OFStW4MKFC6hXrx5q1KiBO3fuYMiQIQgLC1O8pl6vx/fff4/PPvus1NedGRkZqFChAqpUqQK9Xg8RQcWKFY2vh4WFYcuWLYrXvnXrFiwtLWFjY1PsFUljxozBwYMHcezYMUXrPkzu7xwxuSIwLCwM69atw+nTp81a+4moGKzoIXl5eTJjxgzx8vISnU4njRs3FgcHBwkJCVF8t31xtm3bJgMGDJDAwEBp2bKluLi4yIQJE8yyN+FBO3fulHfeeUcCAgJKta6IyMqVK6Vdu3bi4OAgPj4+4ujoKEOGDFF8N7Zer5f8/HyTafn5+bJnzx45ceKE3L17V9F6T9OuzMxMcXV1lbCwMLPWKq3vujirVq0ye+309HT5+eefZfv27UV+z8JDRRcuXJDDhw8rVrPQvXv35OzZsxIdHV3ktcKrWPbv3y979+5VtG5BQYHcvn3beOVZoRMnTsi8efNkzpw5cv78ecVPbH1Ybm6uTJs2TTw9PUWn08mLL75YquvOB68UKryayc3NTaZOnWrWug+f35STkyNubm7y9ddfm7XuwwwGg+Tk5EhQUJDZzht8WtxzUwYUl/pTUlJw6NAhuLq6okmTJmYbs6G42llZWbh27RoaN26s+CBY+fn5iI2Nxd69e1G/fn34+vrC29vbWPfy5cvw8PAwy+BbIoLz58/j0KFDqFOnDtq1a4eqVasCAO7cuYMTJ07Aw8MDtWvXNtmr8Sxu376NWrVqmUzLy8uDTqeDpaWlIjWexF8NuhUbGwsfHx/F+pka3/XDiuvbaWlpOH36NBo1aqRo7XXr1mH69Om4efMmsrOzcfv2bQQFBWHIkCEYPHiwIjUeZdeuXQgPD8eVK1cgIrh16xY6d+6MUaNGmXXspMOHD2PatGk4deoUqlWrhry8PLRr1w5Dhw5FixYtzFa3UEpKCk6dOgVra2u0bt3aOD0pKQnR0dFo2LAhPDw8zLLuTElJwZkzZ1C1alUEBAQYp8v/35uRn5+PyMhIvPLKK7CyslKs7r1793DlyhUYDAZ4eHgUqZuZmYlFixbh/fffV2wsJ3lg79CDewSLc/v2bdjY2Jj8zalGlUhFIiLGY/OFDAaD6PV6s5zZ/7CrV6+aPNfr9ZKbm1vkf1hKj1swaNAgsbOzk2bNmkmtWrXEwsJC/P395T//+Y+idYrz8ccfS82aNcXLy0uqVasmVlZW8vLLL8uPP/5otppvvPGGfP7557Jjx44il8IaDAYpKCgwXqpqjjEiirv8tjTGolDjuy5U3Pecm5tbZM+Zkuzs7GTq1KkSFRUl586dk59++klCQ0OlWrVq4uLiIj/88IOxLUpzcnKSMWPGyJo1a2THjh0yf/586dq1q1SuXFlat24tv/32m+I1RURcXV3l7bfflm+//VbmzZsn//jHPyQoKEjq1asnAwYMMF6Cbw7ffPON1K5dW5o2bSp2dnZSo0YNGThwoBw9etRsNR9Vu2bNmjJo0KAie6+UtnTpUnF2dhZPT09p2rSpeHl5yYQJE4p8z0pedl7o4RqF667ilJWxbhhuVLJ//34ZOnSorF+/Xs6dO1dksC29Xi85OTmSmZmpeO0ff/xRGjVqJCNHjpT169cbx5opVFBQIFlZWYqPD/Hf//5XGjZsKFFRUXLr1i3Jy8uTw4cPy+DBg6Vq1arSuHFjsw3et3z5cmnYsKHx+7548aKsX79eevbsKRUrVpT27dvL6dOnFa25YcMG0el0xsNtb7/9tsycOVOio6ONv2tubq40bty42JP0ntWuXbukS5cuMn36dDlw4ECxYTonJ6fI9Gelxndd6K+WWa/XS3Z2tqLLvGnTJnFxcSl2ZX/u3DkZMmSItGjRwuRSXaWsW7dOXFxcTDZoBoNB7t69Kzt37pQePXpI165d5datW4rWXbVqlbi5uZlcRp+TkyPx8fEyf/58adasmfTv398sl/ivWLFC3Nzc5LvvvpP9+/fLnj17ZPr06RIQECBVqlSRd95555FXyJmj9r///W8JDAyUKlWqyMCBAxUdILHQ6tWrxcXFRaZMmSLr1q2TxYsXy7hx48Tf318aN24sU6ZMUXR8qgdt3LhRKlasKD179pQ5c+YU6ceFh7ZPnDhRZoKNCMONajp37iw6nU7c3NykU6dOMmXKFNmxY4dcuXLF2EF27dolHTp0ULz2K6+8Im5ubiaX702cOFF+/vln4x/Ili1bxMLCQtG6vXv3No7DIWJ6qeiVK1fklVdekVdffVXRmoV69OjxyMuc9+/fL23atJEhQ4YoWnPkyJHyzjvvyJEjR+Q///mPvPLKK+Lv7y/t27eXv//977JkyRKJiIgQa2trResWCg4Olho1akhgYKC0bdtWhg4dKvPnz5fjx48b92Js27ZNXF1dFa2rxnddSI1ljoyMFG9vb7l06ZJxWuFeWJH7V5h4eHjI7NmzFatZaOXKlRIYGPjI8HLo0CFxdnaWNWvWKFp37ty50rlzZ8nJySn29V27domDg4Ps2bNH0boi98cv+uijj0ym6fV6SUpKkqVLl4q3t7fZLkVWq3aHDh2KfG5GRoYcP35cPv/8c3FxcZGZM2cqXldE5PXXXxd/f38JDQ0Vf39/8fDwkLfeekvWrl1rHJ05MjJSKlSoYJb6JVUGDoyVP1lZWUhNTcWKFSvg7OyMlStXYuXKlVi+fDl8fHzQsWNHBAQEYPr06ahTp46itbOzs5GamoqPP/4YXbp0QXR0NKKjo3Ho0CHs3bsXTk5OaN26NSIjI/HGG28oWrt58+aIjIw0PrewsEB+fj4AoH79+hg9ejRGjhyJqKgovPTSS4rVFRE0bdoUf/zxh8n0wqtI2rdvj5EjRyIsLAyxsbGKnC9gMBjw4osv4uLFi2jRogVatGiBDz74AEeOHMGPP/6IX3/9FceOHUNcXJxZrpAq7GMzZ86En58ftm3bhv379+PYsWNYv349vL290bJlS3z//fcm5ww8KzW+60JqLXPbtm2Rk5OD/v37Y/r06QgKCkKFChWM5yU0adIEXl5euHjxomI1C3Xo0AFjxozBsGHDMHXqVHh4eJicW9WyZUv4+fnh6NGj6Nevn2J1O3XqhPHjx2PixIkYP3486tata/J6165d4eXlhX379qFTp06K1TUYDHBzc0N6errJdAsLCzg4OGDQoEFIS0vDokWL8O6776JRo0bPfe2CggLY29sXOUevWrVq8PPzg5+fHwwGA1avXo0BAwYous3IycnB3bt3ERoair59++Ls2bM4fPgwfvvtN0ydOhXh4eFo164djhw5gtdff12xuopQO12VR5cvX5YRI0bI//73P+O0goICWb9+vbz++uvi7Ows7u7uotPpFD/T/9atWzJ58mSZP3++cZrBYJCjR49KRESE9O/fX1q2bCk6nU7xqzqOHz8u1atXlx49ehR7GObevXtSq1YtiY2NVbSuiMiePXtEp9PJsGHD5Pfffy/yenp6utSuXVuOHz+uWM28vDzjLuqHz/fIzc2V//3vf6LT6RQfhl/k/qiwH3/8sSxZssQ4Ta/Xy88//yxjx46VNm3aiK+vr+h0OsXPyVDjuxZRd5nPnz8vL7/8srRt21ZGjRolK1askFOnTonI/d36NWvWlF9//VXRmoUOHjworVq1kh49esiMGTNk3759xnFGDh48KLa2tmapvXLlSvH29pb+/fvLxo0b5cKFC8Y9SKdPnzZb3fXr14tOp5OpU6ea7C0rlJKSInZ2doreYkLt2t99951YWlrKf//732L30v35559Sp04dOXPmjKJ109PT5d///rcsXLjQZPrFixdl06ZNMnHiRGnfvr3odDqzrLefBcONCvR6vVy+fNnYSR8+Vnr37l3p06ePNGjQwGxtKDxG//BG9969ezJ69GhxdnY2S92YmBjp2rWr+Pv7S9++fSUiIkJOnz4tJ06ckIEDB0qjRo3MUlfk/kamVatW0qVLF/nkk09k7dq1cvXqVUlKSpIxY8YofuuB4jx4wvj8+fOlSpUqZquVmZlpPLfn4ZMMMzMzZciQIYofkiq0ceNGCQoKkq5du5bqd52VlVXqy1z4e/7+++8yYcIEadOmjQQGBoqXl5dUrVpV3NzcZPz48YrWfLCuXq+XqKgoefvtt6V+/fri4+MjnTp1kvr164urq6sMGzZM8doi9/9DtmHDBgkKChKdTiceHh7Sv39/adWqlTRs2FD69etnlroiIrNnzxY/Pz/p16+fzJs3Tw4ePCipqamSkZEhX3zxhdSrV09TtfPz8+Wjjz4ST09Pef/992Xnzp1y8eJFyczMlNzcXJk1a5Y4OTkpXrdQ4akSD59XVlBQIJMmTTJr7ZLipeAqkocGQSooKDDuzvb390ebNm0wZ84cxWsWdxnfg5cKt27dGgEBAZg9e7aitQtrnDp1CpGRkTh8+DASExNx6tQp5Obm4pVXXsHf//53BAcHK1q3UH5+Pg4dOoTVq1fj6NGjAIDr16/jxo0b6NKlC0aMGKHYrtW/umQSABYsWIDk5GRMnjxZkZrFefD3FhHo9XpjH/P29kaHDh3M0sf0ej0OHDiAtWvX4vfff4dOp8O1a9dw/fp1xb/rv/Lgb6H0Mhf3O6empuLXX39FamoqateuDScnJ7Rs2VKReg9LTU2FnZ2d8XlSUhK2bduGixcvon79+nB1dUWXLl0UvTS38BDjg8t8+fJlrFy5EqdOnUKjRo3g4eGBV155BTY2NorVLaxtYWGBrKwsbNu2DUuWLMGZM2fg5OQEg8GA06dPo1mzZhgxYoTih3vVql1YNy0tDcuWLcOcOXNw6dIlNGvWDPXq1UN0dDTq1auHv//97xg2bJhidYH/G3zy4fXYg+uV4OBgeHp6IiIiQtHaz4rhRgUGgwGZmZlF/vALO3FGRgZGjBiBr776Cq6urorWLty4PUpubi6mTZuGoUOHol69eorVLSgoKLKCTUlJwaVLl2BpaQlLS0s0bNgQVapUUaxmoZs3byIrKwv29vaoVKkSLC0tkZycjMOHDyM/Px92dnZo2rQpateurXjthwNsacnKykJOTg7s7OyK/c3v3buHjz/+GB9//LGifay4WlevXsWxY8dgMBjM+l3/Vd821zIX1tbr9ahYsWKp/NanTp3CihUrsGvXLly7dg0BAQHo0aMHQkJCipz/Yi4Gg8H4HzJzjVX0sOzsbOPfcqELFy5g9+7dyM7OhqurK1q0aAEXFxfN1BYRpKenw9bW1jgtLi4O69atQ1paGjw8PNC+fXt4eXkp3veKW28/KD8/H99//z169+4NBwcHRWs/K4abUrZ3714sXboU586dQ2ZmJoKDg/Hmm2+iTZs2pdoOg8EAAKW+0S0oKIDBYDDboIQPW7RoEZYuXYq4uDjodDoEBgaiS5cueO211+Dl5WWWmtOmTYOPjw86dOhgHLgOeLK9OUrYsGEDli1bZhz2vW3btujVqxc6deoEJycns9YuVPg7W1pamn15H1ZafXv06NEICAjAa6+9ZrLhKTxJ3tLS8pF7Sp9Vy5YtUbFiRQQHB6NOnTrYsWMHdu7ciSpVqmD48OH44osvYGVl9ZeDNz6t5cuXo0mTJvDx8TEZJO7BZTaXB/u1wWBA69at8frrryMkJATVqlUzW101az+4vUhPT0eXLl3Qr18/tGvXzmw1i1PcLVvKvNI+Dlae/fLLL+Lh4SHt27eXadOmyYQJE8TX11csLCykWbNmsnXrVrPVPn78uLz99tvy448/FjnP5sGhw5UWExMjbdu2leXLlxc5t6hw0ECDwSA3b95UvA179+6VunXryujRo+Xw4cOyZcsWeeutt8TJyUnq1KkjX375peI1Dx48KDqdTlq1aiWvvPKKTJ06VWJiYkzmyc7Olg8++MAsN5fbv3+/uLm5yZtvvilr166VOXPmSMeOHcXCwkIaNmxoPNn2wUuVlfC4/mXuAfTOnDkjEydOlIMHDxZ7ToA5+nbh7+zl5SXe3t4ydOhQ+emnn0zmyc7OliFDhig+ps/evXvFzs6uyBgyubm5Mnv2bKlXr5706dPnkZdpl9TBgwfFwsJCunTpIiNHjpRly5bJ2bNnTea5d++eTJ06VW7cuKFo7cf1a1dXV/n+++8VrVcWaj9ue+Hr62u8I7k5+vfj1tuFt3woXG+b+9YaJcVwU4reeOMNGTp0qMk0vV4vR44ckQEDBkjDhg2NHVZpoaGhYm1tLT4+PtK8eXP58MMPi9yH5tdff5V+/fop2llDQ0PF0tJSXFxcpFatWvLmm2/Kzp07Teb55ZdfJDg4WPEN4FtvvSXDhw8vMj0vL08iIiKkdu3aMmbMGEVrjh8/Xtq1ayczZsyQgQMHSrt27SQoKEj69u0r3377rcTHx8uhQ4dEp9NJenq6orVFRN58881iTyC9efOmfPzxx2Jvby8RERGK11WrfxXWrlq1qrRr10569+4tM2bMKHLPqOjoaBk+fLhiG4JPP/1UXnrpJVm1apVMmTJFunXrJh4eHhIQECATJkyQo0ePyuHDh83yO8+dO1f8/f0lNTVVRO6HmgdPnt62bZvUrl1b8dGgx4wZIwEBATJu3Djp0KGD+Pv7S/fu3WXChAmyefNmuXbtmsTExIhOp5OMjAxFa6vVr9Wsrfb2Qq31tlI4zk0pSk1Nha+vr/F54S7jFi1aYO7cuRg+fDjCw8PRvn17xc9JOHfuHD7++GN4eXkhNjYWsbGx2L59OxwcHNC9e3f06dPHeEKgkrseL126hM8//xxdunTBkSNHsG3bNvTv3x9VqlTBG2+8geHDh2PNmjVITExU/H4klpaWSE9PR15eHipVqoR79+6hQoUKsLS0xNixY2FhYYF58+YhPj4e7u7uitRMTU2Fu7s7xo0bh4KCAhw6dAgHDhzAsWPHsGrVKmzatAnnz59HcHAwqlevrkjNB+Xm5prcyyYvLw8WFhaws7PD9OnTISJYvHgxevfuDWdnZ8XqqtW/AODEiRMYMWIE7O3tcfToUWzcuBGbN29Gw4YN0alTJ3Tt2hXLly/HwYMHFTtElJWVBRcXF/Tr1w8WFhY4e/Ysjh8/jsOHDyM6OhqRkZG4cuUKunfvrvjv/Nprr2HatGlYvXo1Ro0aZTzEW7g+6dGjBzp16oQDBw7glVdeUazurVu30KZNG8yYMQO5ubnYsWMHtm3bhn379mHPnj1o0KABTp06hc6dOyt+qEatfq1mbTW3F2qutxWjcrgqVyIiIqRu3bpy4cIFk+mF/5v8888/pXHjxorfo+TPP/+Unj17yoIFC0Tk/uWyx48fl0WLFsmwYcOkZcuW0qRJE9HpdMZ74Cjh+vXrMnToUONu27y8PLl+/bpERUXJ5MmTJTAwUGrWrCk6nc4sh+R27NghderUkc2bN5tML/yfRmZmpjg7Oyt6y4fExMRi77x869YtiYyMlA8//FB0Op1s27ZNsZoPWrFihdjb2xcZo6jwENTNmzfFzc1N0fGT1OpfIvfvedOhQwdZunSpiIjxtgOfffaZvPLKK9KyZUvp0KGD6HQ62bJli2J1MzIyiv0OMzIyJDY2ViIiIszyOxeuK6ZNmybVqlWTbt26ybJly0wOA12+fFmcnZ1l3bp1itY+efKkbN++vcj0GzduyOLFi6V3795m69tq9Gu1a6u1vVB7va0UhptSlJKSIl27dhV3d3eZMmWKHDx40GSX9aZNm6RatWpmqZ2UlCQXL14sMv327dsSHR0t77zzjtja2ipeNzU1tchNOkXuH5u/fPmyfPzxx2apW3jfpLFjx4qlpaW0bdtWFixYYNyVf+fOHVm2bJnZvu/CNhQemy60detWqVq1qtnqZWRkyFtvvSW1atWS0NBQ2bRpk8k9wtasWWOWZVarf4ncH0AvPj6+yPTr16/Lhg0b5OWXX5YaNWqYpXahhw93bd26VaysrMxac+PGjfLmm29KQECABAUFSXBwsAwaNEh8fX2lTZs2ZqlZePhLr9cbz70o9OOPP5rtb1mtfl1Yu1+/fqVeW83thVrrbSXxaqlS9scff2DevHn45ZdfUKlSJTg7O6NKlSrIysrCmTNn0K1bN0yfPt2sbdDr9RARk92JISEhsLa2xpo1a8xaWx66eiQkJAQVK1bEhg0bzFYzMjISq1evxokTJ3Dz5k3Y29vDysoKWVlZGDx4MD755BOz1X6QwWDA+++/j9u3b2PdunVmq5ORkYGlS5fip59+QmpqKipUqIDq1atDRHD9+nX07dsXYWFhZqsPFP87l0b/elTfrlq1KlauXGnW2oVEBFOmTEFycjIWLFhg1loJCQn45ZdfcPr0aVy/fh3Xrl1DcHAw/va3v8HR0dGstQvJ/x/u4M0330R6ejp+/vlns9RRs19nZmZi2bJl2Lp1K1JTU1GpUqVSqV0WtheAOuvtZ8Vwo5KTJ08iMjIS586dw507d5CdnY2xY8eic+fOZhnrBbh/uebDl2oaDAakp6fjjTfewDfffKPoPXf+SmZmJj744AOMGTMGfn5+in/+g3+QiYmJOH36NBISEnDp0iXk5ORgyJAhaNy4saLHjPV6PXQ63SMvv9Xr9cjIyECNGjUUq/ko8fHxiI6OxuXLl3Ht2jXcu3cPI0eORPPmzU3OITC3u3fvqtK/RAS3bt1Cy5YtsXz5ckWHW/ir39lgMCArK8ss51UVFBQAQJF++/C5IUrJz8/HmTNnsG3bNtjY2MDf3x+urq5wcHBAxYoVjeMLFRQUIC0tzSxjGD1IzX5948YNHDhwAGfPnkVCQgJyc3NLpbYa24tHMfd6WykMN6Xgxo0bWL16NWJiYtCoUSP4+fmhZcuWcHNzg16vR3Z2tllWgsD9QabmzJmDY8eO4cUXX0SDBg3g7e2NgIAAk//Z5eTkoHLlyorXL2400weZa4VcWBsonbF8Tpw4AR8fH5NppTWuzYOK2/ApPdZJcf5qY5+dna34Srjw7+q3335D48aN0bRpU3h4eKBx48aoVq2ayYiyD4439Cx+++23IqMNFxQUwMLCwrjs5vq+i6udl5cHnU5n/E/LXw26VhIff/wxVq9ejTp16uD27dtISEhAgwYN0L9/f4wZM8ZkhGRzUaNfF647jx49ikaNGuHFF19Eq1at0LJlS7MGCjW3F4XUXG8rppQPg5U7ly5dkoCAAGnYsKH06dNH3N3dpUaNGuLp6SkfffRRsTdBU8rFixfFw8NDAgMDZfTo0fLSSy+Jt7e3NGvWTAYNGlTkBDmlLpNNTk6WH374ocglvw+Pq1I4DoeS4zQUV9tgMJicH6DX6+XevXuK1Tx//rxUrFhR2rRpI5MnTy5yGbLI/XMVfvvttyJjRighNTW1yA0K9Xq9yfgyBoNB8Uuwi6tbWOfB37SwrpK/c3F/VzVr1hRvb2/55JNP5ObNm0Xa9azOnTsnOp1O6tatK0OHDi1yAqnBYJDc3FzZunWrJCUlPXO9slD79OnTUr16ddm2bZvcuHHDeF+8yZMnS926dcXW1tZ4A2Clx1tRq1+LFL/u9PLyEl9fXwkNDTXLzW5F1N1eqLneNgeGGzP7+9//Lj179pSEhATjtEuXLsmUKVPE3t5eHB0dZceOHWap/d5778mrr75qcvLb9evX5bvvvhN/f3+xsbGRFStWKF535MiRotPpxM7OTgYOHFjsBvDSpUsyffp0RUOGWrW/+OILqV+/vrz33nvSunVrcXd3l+DgYJkzZ45cv35dREQSEhJEp9OZ9AOljB49WnQ6nbz44osyfvx4OXfunMnrBQUFcuXKFVm3bp2iG4K/qqvX6411lR4L46/+rpycnIqMy/GsvvzyS2natKlMnjxZ2rZtK7a2tvLiiy/K559/brxDdGJiouh0umJPxnwea3/11VfSvn174/MH+09mZqaMGTNGvL29JSUlRbGahdTq1yJ/ve6sXr26Wdadam4v1FxvmwPDjZm1bt1aZsyYISL3//f+4Eper9dLr169JCQkRESUT8LBwcESFhYmIvdXBA+vAN577z1p166d3Lt3T9HaLVu2lHHjxsl//vMfadOmjVSoUEHq168vEydONF5R88UXX0jDhg0Vq6lm7f79+8vYsWPl+vXrcvjwYfn222/lb3/7m/j7+4unp6cMGDBAQkJCxNPTU7GaD2rWrJkMGTJEJk6caFzxNmvWTGbOnCm3b98WEZGwsDBxc3PTRF0Rdf6uRowYIR988IGkpKRIQkKCREZGyrhx48TLy0uqV68ubdq0ka5du5rld1ar9saNG6VJkyYmo2nn5+cb90D+8ccf4uPjI/PmzVO0roi6/Uutdaea2ws119vmwHBjZpMnT5YWLVqYJN28vDzJzs4WEZGoqChp1KhRkUNESpg5c6a4ubmZXKKbm5trbEtcXJy4ubnJ/v37Fat57do1efPNN41jJKSnp0tsbKz84x//MI510qxZM6levbrio3qqUTs/P19WrFgh4eHhJtOTkpJk9+7d8s9//lNCQkJEp9OZZZj2y5cvS3BwsHGY9D/++EPWr18vw4YNk4YNG4qNjY0EBwdL7dq1ZebMmc993UKl/XdVUFAg27Ztk7lz55pMz8zMlLNnz8rq1atl4MCBotPpZPHixYrULAu1U1NTpUmTJuLp6SkbNmwo9n/sPj4+xjGOlKJ2/1Jj3Smi3vZCzfW2uTDcmNmRI0fE0dFRWrRoUexw6PHx8WJlZVXkPjFKuHjxovj5+UmDBg1k2bJlRV4/deqUWFpaKlo7KytLtm7dWuScAL1eL6mpqRIVFSWvvPKKVKhQwfgHq4XahR4cBr/Q6tWrRafTmeU3TktLk2XLlsm+fftMpt+9e1fi4uJk8eLF0q5dO8WXWa26hdT8uxIpeh6CyP1xXsz1O6tZ+/r169KvXz/x8fGRHj16yJQpU2Tfvn1y6dIlGTdunNSuXVsyMzMVral2/1Jj3SmiXr8uC+tOpfFqqVJw4cIFTJgwAbGxsahduzbatGmDHj16ID4+HqtXr4azs7PZxgvIyMjAxIkTsWbNGhQUFKBr167o1q0bTp06hX379sHb2xv/+9//zFIbKDo+AgC88847uHLlCg4cOGC2uqVV+1FXbDx4Bc348eNx5MgR7Nu3T5GajyIi0Ov1Ra6W6devH1JSUrB3715N1S3Nvyv5/2O5PO7qnLCwMERHR2Pnzp2K1CwLtQulpKRg+/bt+Pnnn3HlyhXEx8cjNTUVHTt2xLvvvou3337bLHUB9fqXWutONbcXhdRcbyuF4aaUZGVlISoqCnv27MGRI0dw8uRJ1K5dG0OHDsXf/vY3uLq6Kl6zcMN77949nDx5EgcOHMCePXtw9OhRNGjQAAMGDMAbb7wBJycnRWs+7hLCnJwc9OrVCyNGjMDrr7+uWF21aicnJ+PSpUuoVKkSRASurq4m43yICH744QfUrVu31MZ4ERHjb5+Tk4MOHTpg4sSJ6N27t+bqltbf1ZNcdrxv3z7Y29ujadOmitRUu3Zh37ayskLlypXRoEEDWFhY4OLFi8jOzkbVqlVhZ2eHWrVqKVbzcUqzf6mx7nxQaW8v1FxvmwvDjRlt374dd+7cgV6vh7OzMwIDA1G1alVkZ2ejQoUKyMjIKJUxIgo9OO5KWloabG1tS612ofz8fMTGxiIoKOi5r/39999j6dKlOHbsGCpWrAhPT080adIEbdq0Qc+ePVGvXj1F6jxOYR8rKCiAvb09WrZsaRKucnNz8fPPP6Nnz56aqPtgbTX+rp5kL4q5lGbth/u2u7s7PDw88NJLL+G1114z+0B9avav4pTGurOsbS8epOZ6u6QYbswgIyMD7733Hnbv3o2CggI4OTmhatWqqF27Nl5++WX06dPHuOFTeiCqgoIC3L59G3Xq1FHsM8tyXbVq37p1C40bN8bIkSMxbNgwpKenY/v27YiKisKFCxfg7e2NiIgIuLm5mWVgtYf72AsvvIBq1aqhdu3a6NixI/r27QsXFxdFa6pZt7japfF3defOHTRr1gy9e/fG4MGDTfaMPPi/3bNnz8LJyUnRkafVqv24vn3+/Hl4eXlh9uzZcHNzK/bwxbNQs3+ptQ4rj9uLUlE6p/aUL1999ZV4e3sb7zZ98uRJmT9/vgwYMEB8fHykT58+cvfuXbPUjoiIkBo1asioUaPkwIEDxZ54lpaWJtu3by/25Fdz142MjFR8IDs1as+ePVtatmxZ7Gt79uyRgIAA8fT0NBknQ0mP62O+vr7St29fs/Qxter+VW1z/V3Nnj1bdDqd+Pj4iE6nEw8PD/nXv/5lMlBeQkKC+Pn5FXvj0Oextpp9W83+pda683nYXphjvW1uDDdm0KZNG5k1a1aR6Xq9Xnbu3Cn169c3jlWgtMDAQGndurUEBASIhYWFNGnSRKZMmSInT540jtXw3XffPXLl9bzVVav2d999J02bNpWzZ8+KyP1ROx/84z979qy8+OKLsm7dOsVqPkitPqZm31aj9tChQ2X48OFy5coV+fXXX+WDDz4QZ2dnsbCwkA4dOsjq1atl1qxZUqVKFUXrqllbzb5dHted5XGZSwPDjcLy8vJk+PDh0qFDB0lNTRWR+2OhPDgI1I8//iheXl7FDtP/LFJSUqRt27bG4dDPnDkjkyZNEhcXF6lQoYK0adNG5s2bJ15eXjJ69Ojnvq6atW/evCne3t7y/vvvG4cjFzG9TDcoKEimT5+uWM1CavUxNfu2GrXv3bsnM2fOlH/+85/GaQUFBXLjxg3ZvHmz9OvXT+zs7ESn0xkHfFOKmrXV6tvlcd1ZHpe5tDDcmEFMTIw0atRI/vGPfxg77IMSEhKkatWqcu3aNUXr3rhxQ2bOnFlk2PmCggI5cOCADBo0SGxtbRW/DYBaddWqrdfrxWAwyMaNG6VevXpiY2Mjw4YNk2PHjhnbtGrVKqlWrZpxaHylqdXH1KqrVu179+4Zb6Hx8PgyeXl5sn37dtHpdGZZXjVqq923y9u6U6R8LnNpYLhRmMFgkLy8PFmwYIHUrl1batSoIcOHD5e9e/fKn3/+KZs2bZJBgwZJ8+bNzVI/OzvbOMhSccNzf/TRR+Lv76+ZumrWvnfvnpw+fVq+++47CQ4OlqpVq0q1atXE3d1dGjRoIJ9//rniNUXU62Nq9m01a9+4caPYjY6IyNSpU80y/L/atdXo2+Vx3Vkel7m0MNyY0Z07dyQiIkICAgLE0tJS7OzspF69evLaa69JTExMqbcnJydH3N3dZdq0aeWirjlq37x5U+bMmSMuLi7SrFkz6dKli/Tp00emT58uP//8s2zdulVmzZol8fHxpXLXXLX6mJp9uzRqF/7Orq6uEhAQIC+99JK88847sn79euPGQK/Xy4IFC4odSfZ5rF2W+nZ5XHeWx2U2J14KrqCcnBxUrlzZZJqIICcnB5mZmTh58iSqVauGli1blkrt4uZZt24d+vfvj0qVKj3XddWqPWTIEPz+++/o3r07qlWrhlu3buHChQu4fv06XFxcEBYWBk9Pz2eu8yhq9bGy1rfNXfvB37l69eq4desWzp49i4SEBDRu3Bjjxo0z25gfatVWs2+Xtf5V3Dylse7U+jKXKvVylfaMGzdONm7cKJcvX37kLeEL72ar9P98nqS2OS7dVKuuGrUNBoNUqVLF5H43BoNB/vjjD1m8eLEEBQWJu7u74if+PUitPlbW+7aStR/1O58/f16WLFkiQUFB4unpKadOnXrmWmWlttp9u6z3L7XWnVpb5tLEcKOQlStXik6nE0tLS3Fzc5MPP/xQ9uzZI0lJScYxEdLS0qRXr15y4sSJUqmdnJws+fn5InL/DsKvvvqqoisnteqqVfvUqVPi5eUlR44cKfb17Oxs8fHxkSlTpihS72Fq9bGy2LfNWVvN31mt2mouc1nsX2qtO7W8zKWN4UYhQ4cOlREjRsjFixflq6++EldXV+Nt4sPDw+XYsWOyZMkSqVixomZql7dlzs7Ols6dO0v79u3lzz//LPZ/UzNmzDDbyX/8nbX/O6tVW81lLm/9S826atcuTQw3CsjPz5evv/5aJk2aZDL9999/l+HDh4utra1Uq1ZNLC0tZfDgwZqoXR6XWUQkOjpa/Pz8pE2bNrJixQq5ceOG8STPe/fuSZ8+feTtt99WtKYIf+fSrq3W76xmbTXqlsf+VR6XWQ0MNwq5c+eOnDt3TkREcnNzi/zPZ8WKFaLT6SQuLk4ztcvjMouInDhxQvr06SPW1tZiZ2cnISEh8t5774mbm5sEBATI77//rnhNEf7O5eV3VrO2GnXLY/8qj8tc2pS9m185VqNGDeON6wrPLDcYDBARVKhQAdnZ2bC2toavr69mapfHZQYAb29vrFu3DikpKYiMjMSWLVtw+/ZtDB48GG+++SY8PDwUrwnwdy4vv7OatdWoWx77V3lc5tLGcGNGD969NSMjA2FhYZqvXZ6WuU6dOhgyZAiGDBmi+N16nxR/Z23/zmrVVrtvl6f+pXZdtWubC8e5KSX5+fmoUKGCKhtAtWqXx2VWE39n0qLy2L/K4zIrjeGGiIiINOX5jmZERERED2G4ISIiIk1huCEiIiJNYbghIiIiTWG4ISIiIk1huCEiRXTs2BFjx4597Dyurq6YNWtWqbSnOE/SRiJ6/nEQPyIqNUeOHEHVqlWNz3U6HTZv3oyQkJASf+bTfMamTZtgaWlZ4lpE9HxguCGiUmNvb69K3by8PFSqVAm1atVSpT4RlS4eliIixRQUFGDUqFGwtbWFnZ0dPv/8czw4TuiDh6VcXV0BAK+//jp0Op3x+cPy8vIwatQoODk5wdraGi4uLggPD3/sZ3zxxRfw8/PDokWL4ObmBmtrawBFD0u5urrin//8J4YMGYLq1aujfv36WLhwoUn96Oho+Pn5wdraGi1atMCWLVug0+kQFxcHALhz5w4GDBgAe3t7VK5cGY0bN8bSpUtL/iUS0TNjuCEixfz3v/9FxYoVcfjwYcyePRszZ87EokWLip33yJEjAIClS5ciMTHR+Pxh//nPf7B161asW7cO8fHxWLlypTHEPO4zLly4gI0bN2LTpk3GIFKcGTNmoEWLFjh+/Djef/99jBgxAvHx8QCA9PR0vPrqq/D29saxY8fw5ZdfYsKECSbv//zzz3HmzBn89NNPOHv2LObNmwc7O7sn+r6IyDx4WIqIFOPs7IyIiAjodDq4u7vj5MmTiIiIwLBhw4rMW3iIqkaNGnB0dHzkZ169ehWNGzdG27ZtodPp4OLi8kSfkZeXh+XLl//lobAePXrg/fffBwBMmDABERER2Lt3L9zd3bFq1SrodDp8//33sLa2hqenJ65fv26yPFevXoW/vz9atGgBAI/cA0VEpYd7bohIMa1atYJOpzM+DwoKwvnz56HX60v8mYMGDUJcXBzc3d0xevRo7Nq164ne5+Li8kTn+Pj4+Bj/rdPp4OjoiJSUFABAfHw8fHx8jIe1ACAwMNDk/SNGjMCaNWvg5+eHTz75BNHR0U/UPiIyH4YbIirTmjVrhkuXLuHLL79ETk4O+vbtizfffPMv3/fgVVmP8/DVUzqdDgaD4Ynb1717d1y5cgUffvghbty4gZdeegkff/zxE7+fiJTHcENEivntt99Mnh86dAiNGzdGhQoVip3f0tLyifbq2NjYoF+/fvj++++xdu1abNy4Ebdv336qzyiJwkNrubm5xmnFnRtkb2+PgQMHYsWKFZg1a1aRk5KJqHQx3BCRYq5evYpx48YhPj4eq1evxrfffosxY8Y8cn5XV1dERUUhKSkJd+7cKXaemTNnYvXq1Th37hz++OMPrF+/Ho6OjqhRo8YTf0ZJvf322zAYDBg+fDjOnj2LnTt34t///jcAGA+/TZ48GT/88AMuXLiA06dPIzIyEh4eHoq2g4ieDsMNESkmNDQUOTk5CAwMxMiRIzFmzBgMHz78kfPPmDEDu3fvhrOzM/z9/Yudp3r16vjXv/6FFi1aICAgAJcvX8b27dthYWHxxJ9RUjY2Nvjxxx8RFxcHPz8/fPbZZ5g8eTIAGM/DqVSpEiZNmgQfHx+0b98eFSpUwJo1axRtBxE9HZ08OAgFERE91sqVKzF48GCkpaWhcuXKajeHiIrBS8GJiB5j+fLlaNCgAerWrYvff/8dEyZMQN++fRlsiMowhhsiosdISkrC5MmTkZSUBCcnJ/Tp0wdff/212s0iosfgYSkiIiLSFJ5QTERERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESawnBDREREmsJwQ0RERJrCcENERESa8v8AKBThKxlUUycAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_results = {}\n",
    "for bitstring, count in result.measurement_counts.items():\n",
    "    # Only keep the outcomes on first n qubits\n",
    "    trunc_bitstring = bitstring[:n]\n",
    "    # Add the count to that of the of truncated bit string\n",
    "    new_results[trunc_bitstring] = new_results.get(trunc_bitstring, 0) + count\n",
    "\n",
    "plt.bar(new_results.keys(), new_results.values())\n",
    "plt.xlabel('bit strings');\n",
    "plt.ylabel('counts');\n",
    "plt.xticks(rotation=70)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In practice, we only need the measurement results (i.e., the bit strings, not the counts) from the first $n$ qubits. These measurement outcomes correspond to bit strings that satisfy the equations:\n",
    "$$ \\begin{aligned}z_{1}\\cdot s&=0\\mod{2}\\\\z_{2}\\cdot s&=0\\mod{2}\\\\&\\,\\,\\vdots \\\\z_n\\cdot s&=0\\mod{2}\\end{aligned}$$ \n",
    "\n",
    "With these $n$ linear equations in hand, we can use classical post-processing to solve for the unknown string $s$.\n",
    "\n",
    "Note that we may have too many bit strings in the above, since we ran the quantum task with $2n$ shots just to be safe. In this case, not all of the bit strings will be linearly independent. Moreover, the all-zeros string $0\\dots0$ may also be an outcome, but this bit string satisfies the equations above trivially, so we exclude it if needed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this stage, the quantum portion of Simon's algorithm is complete. Any remaining steps are just classical postprocessing, which we cover in the Appendix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References<a name=\"references\"></a>\n",
    "[1] Wikipedia: [Simon's Problem](https://en.wikipedia.org/wiki/Simon%27s_problem)\n",
    "\n",
    "[2] Wikipedia: [Birthday Problem](https://en.wikipedia.org/wiki/Birthday_problem)\n",
    "\n",
    "[3] Wikipedia: [Computing a kernel by Gaussian elimination](https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination)\n",
    "\n",
    "[4] StackExchange: [Sympy: Solving Matrices in a finite field](https://stackoverflow.com/questions/31190182/sympy-solving-matrices-in-a-finite-field)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appendix<a name=\"appendix\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing an Oracle Function<a name=\"oracleimplementation\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to run the algorithm, we will need a unitary function that we can use as an oracle to query the function $f$.\n",
    "\n",
    "There are many possible ways of implementing a function with the desired property that $f(x)=f(y) \\implies x=y\\oplus s$. We will pick one implementation that is commonly used in example code, and we will try to give some intuition for why this oracle works."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Classical Intuition Behind the Function $f$\n",
    "Generating a function that is one-to-one is conceptually straightforward, as any such function of the bit strings $\\{0,1\\}^n$ will just be a permutation of the inputs. Generating a two-to-one function is a little trickier, though there are many ways to do it. The goal is to define a function that splits the inputs into two groups, such that one element from each group maps to the same output (i.e., $x$ must be in one group, while $x\\oplus s$ must be in the other group.)\n",
    "\n",
    "We will implement one simple choice for $f$, in which we define the split based on the value of one of the bits in the string. In this way, exactly half of the inputs will have that bit with value $0$, while the other half will have that bit with value $1$. \n",
    "\n",
    "Our approach will be to choose a flag bit in the input bit strings that we will use to split the inputs. We then $\\mathrm{XOR}$ the input string with $s$ whenever the flag bit is $1$. With this definition, half of the input strings will be untouched, while half of the strings will be $\\mathrm{XOR}$'ed with $s$. Clearly, this function does nothing to the all-zeros string $0\\dots 0$, since any choice of the flag bit will always be $0$. Thus, we need to ensure that our definition also maps the string $s$ to the all-zeros string $0\\dots 0$. In other words, we need to ensure that our flag bit is $1$ when the input string is $s$. One way to ensure the function acts correctly on the input $s$ is to just define the flag bit to be the first bit in the string $s$ that is equal to $1$. For example, if $s=011$, we can choose the flag bit to be the second bit. Concretely:\n",
    "$$f(x) = \\left\\{\\begin{array}{lr}\n",
    "x, & \\text{if } x_j=0\\\\\n",
    "x\\oplus s, & \\text{if } x_j=1\\\\\n",
    "\\end{array}\\right\\},$$\n",
    "where $x_j$ is the $j^\\text{th}$ bit of $x$, and $j$ is the flag bit in $s$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    <h4>Example for n=3:</h4>\n",
    "\n",
    "We now revisit the example in the introduction. Suppose the secret string $s=011$. Since the first appearance of $1$ in $s$ occurs at the second bit, we will use the second bit in the input strings as our flag bit. We take the $\\mathrm{XOR}$ of the input with $s$ whenever the flag bit in the input is 1. This definition results in the following truth table:   \n",
    "\n",
    "<table>\n",
    "    <thead>\n",
    "        <tr>\n",
    "            <th><center>$$x$$</center></th>\n",
    "            <th><center>$$f(x)$$</center></th>\n",
    "        </tr>\n",
    "    </thead>\n",
    "    <tr>\n",
    "        <td><center>$$000$$</center></td>\n",
    "        <td><center>$$000$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$001$$</center></td>\n",
    "        <td><center>$$001$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$010$$</center></td>\n",
    "        <td><center>$$001$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$011$$</center></td>\n",
    "        <td><center>$$000$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$100$$</center></td>\n",
    "        <td><center>$$100$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$101$$</center></td>\n",
    "        <td><center>$$101$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$110$$</center></td>\n",
    "        <td><center>$$101$$</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>$$111$$</center></td>\n",
    "        <td><center>$$100$$</center></td>\n",
    "    </tr>\n",
    "</table>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We leave it as an exercise to the reader to verify that this definition works for any input string size (i.e., $n$ for inputs $\\{0,1\\}^n$, and that it is in fact two-to-one, rather than many-to-one. Note that the function defined in this way is not a general two-to-one function, but it is simple a choice that is easy to implement both classically and as a quantum circuit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Quantum Implementation of $U_f$\n",
    "We now define the unitary using the `@circuit.subroutine` functionality of the Amazon Braket SDK. The following code was imported from the `simons_utils.py` module, and is shown below for reference. \n",
    "\n",
    "In the quantum setting, we first copy the input register into some ancillary qubits:\n",
    "$$ |x\\rangle|0\\rangle\\mapsto |x\\rangle|x\\rangle.$$\n",
    "We then perform the quantum analog of $\\mathrm{XOR}$, which means we apply an $X$ gate to the $k^\\text{th}$ qubit whenever the $k^\\text{th}$ bit of $s$ is $1$. However, we only apply this $X$ gate when the flag qubit is also $|1\\rangle$. Thus, our $X$ gate becomes a $\\mathrm{CNOT}$ gate between the flag qubit on the input register, and the $k^\\text{th}$ qubit on the output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "from braket.circuits import Circuit, circuit\n",
    "\n",
    "@circuit.subroutine(register=True)\n",
    "def simons_oracle(secret_s: str):\n",
    "    \"\"\"\n",
    "    Quantum circuit implementing a particular oracle for Simon's problem. Details of this implementation are\n",
    "    explained in the Simons Algorithm demo notebook.\n",
    "\n",
    "    Args:\n",
    "        secret_s (str): secret string we wish to find\n",
    "    \"\"\"\n",
    "    # Find the index of the first 1 in s, to be used as the flag bit\n",
    "    flag_bit=secret_s.find('1')\n",
    "    \n",
    "    n=len(secret_s)\n",
    "    \n",
    "    circ = Circuit()\n",
    "    # First copy the first n qubits, so that |x>|0> -> |x>|x>\n",
    "    for i in range(n):\n",
    "        circ.cnot(i, i+n)\n",
    "    \n",
    "    # If flag_bit=-1, s is the all-zeros string, and we do nothing else.\n",
    "    if flag_bit != -1:\n",
    "        # Now apply the XOR with s whenever the flag bit is 1.\n",
    "        for index,bit_value in enumerate(secret_s):\n",
    "            \n",
    "            if bit_value not in ['0','1']:\n",
    "                raise Exception ('Incorrect char \\'' + bit_value + '\\' in secret string s:' + secret_s)\n",
    "                \n",
    "            # XOR with s whenever the flag bit is 1.\n",
    "            # In terms of gates, XOR means we apply an X gate only whenever the corresponding bit in s is 1.\n",
    "            # Applying this X only when the flag qubit is 1 means this is a CNOT gate.\n",
    "            if(bit_value == '1'):\n",
    "                circ.cnot(flag_bit,index+n)\n",
    "    return circ\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing the Classical Post-Processing<a name=\"appendixpostprocessing\"></a>\n",
    "\n",
    "We will now solve the system of linear equations above using Gaussian elimination. We first convert the results into matrix form, then we use `sympy`'s `Matrix.rref()` method to transform the matrix into reduced row echelon form. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:58.990918Z",
     "start_time": "2023-08-29T21:32:56.314378Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "\u001B[1m[\u001B[0m\u001B[34;49mnotice\u001B[0m\u001B[1;39;49m]\u001B[0m\u001B[39;49m A new release of pip available: \u001B[0m\u001B[31;49m22.3.1\u001B[0m\u001B[39;49m -> \u001B[0m\u001B[32;49m23.2.1\u001B[0m\r\n",
      "\u001B[1m[\u001B[0m\u001B[34;49mnotice\u001B[0m\u001B[1;39;49m]\u001B[0m\u001B[39;49m To update, run: \u001B[0m\u001B[32;49mpip install --upgrade pip\u001B[0m\r\n"
     ]
    }
   ],
   "source": [
    "from sympy import Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate a matrix from the bit string outputs. We first check that we have sufficiently many output strings to be able to solve the system of equations. If not: output and error and re-run the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:59.000368Z",
     "start_time": "2023-08-29T21:32:58.993059Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The result in matrix form is :\n",
      "[1, 0, 0, 0, 1, 0]\n",
      "[1, 1, 0, 1, 1, 0]\n",
      "[1, 1, 1, 1, 0, 0]\n",
      "[1, 1, 1, 0, 0, 0]\n",
      "[0, 0, 1, 1, 1, 0]\n",
      "[1, 0, 1, 0, 1, 1]\n",
      "[1, 0, 1, 1, 0, 0]\n",
      "[1, 0, 0, 1, 1, 0]\n",
      "[0, 1, 1, 1, 0, 1]\n",
      "[0, 1, 1, 0, 0, 1]\n",
      "[0, 0, 0, 1, 0, 0]\n",
      "[1, 0, 1, 0, 0, 0]\n",
      "[1, 1, 0, 0, 0, 1]\n",
      "[1, 0, 0, 0, 0, 1]\n",
      "[1, 1, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "if len(new_results.keys()) < len(s):\n",
    "    raise Exception ('System will be underdetermined. Minimum ' + str(n) + ' bistrings needed, but only '\n",
    "                     + str(len(new_results.keys())) +' returned. Please rerun Simon\\'s algorithm.')\n",
    "string_list = []\n",
    "\n",
    "for key in new_results.keys():\n",
    "#     if key!= \"0\"*n:\n",
    "    string_list.append( [ int(c) for c in key ] )\n",
    "    \n",
    "print('The result in matrix form is :')\n",
    "for a in string_list:\n",
    "    print (a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now solve the system $Ms=0$ by finding the kernel of $M$. We do this using Gaussian elimination on the augmented matrix $\\left[A|I\\right]$ to bring it to row echelon form. Converting the solution to numbers $\\mathrm{mod }\\,2$, we can then read off the solution from the last row of the reduced matrix. See [[3]](#References) and [[4]](#References) for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:32:59.021727Z",
     "start_time": "2023-08-29T21:32:59.013844Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Secret string: 101011\n",
      "Result string: 101011\n",
      "We found the correct answer.\n"
     ]
    }
   ],
   "source": [
    "M=Matrix(string_list).T\n",
    "\n",
    "# Construct the agumented matrix\n",
    "M_I = Matrix(np.hstack([M,np.eye(M.shape[0],dtype=int)]))\n",
    "\n",
    "# Perform row reduction, working modulo 2. We use the iszerofunc property of rref\n",
    "# to perform the Gaussian elimination over the finite field.\n",
    "M_I_rref = M_I.rref(iszerofunc=lambda x: x % 2==0)\n",
    "\n",
    "# In row reduced echelon form, we can end up with a solution outside of the finite field {0,1}.\n",
    "# Thus, we need to revert the matrix back to this field by treating fractions as a modular inverse.\n",
    "# Since the denominator will always be odd (i.e. 1 mod 2), it can be ignored.\n",
    "\n",
    "# Helper function to treat fractions as modular inverse:\n",
    "def mod2(x):\n",
    "    return x.as_numer_denom()[0] % 2\n",
    "\n",
    "# Apply our helper function to the matrix\n",
    "M_I_final = M_I_rref[0].applyfunc(mod2)\n",
    "\n",
    "# Extract the kernel of M from the remaining columns of the last row, when s is nonzero.\n",
    "if all(value == 0 for value in M_I_final[-1,:M.shape[1]]):\n",
    "    result_s=\"\".join(str(c) for c in M_I_final[-1,M.shape[1]:])\n",
    "\n",
    "# Otherwise, the sub-matrix will be full rank, so just set s=0...0\n",
    "else:\n",
    "    result_s='0'*M.shape[0]\n",
    "\n",
    "# Check whether result_s is equal to initial s:\n",
    "print ('Secret string: ' + s)\n",
    "print ('Result string: ' + result_s)\n",
    "if (result_s == s):\n",
    "    print ('We found the correct answer.')\n",
    "else:\n",
    "    print ('Error. The answer is wrong!')"
   ]
  }
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