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   "source": [
    "<div style=\"text-align: right\">Peter Norvig, 12 Feb 2016</div> \n",
    "\n",
    "# A Concrete Introduction to Probability (using Python)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "This notebook covers the basics of probability theory, with Python 3 implementations. (You should have some background in [probability](http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/pdf.html) and [Python](https://www.python.org/about/gettingstarted/).) \n",
    "\n",
    "\n",
    "In 1814, Pierre-Simon Laplace [wrote](https://en.wikipedia.org/wiki/Classical_definition_of_probability):\n",
    "\n",
    ">*Probability ... is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible ... when nothing leads us to expect that any one of these cases should occur more than any other.*\n",
    "\n",
    "![Laplace](https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG/180px-AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Pierre-Simon_Laplace\">Pierre-Simon Laplace</a><br>1814</center>\n",
    "\n",
    "\n",
    "Laplace really nailed it, way back then! If you want to untangle a probability problem, all you have to do is be methodical about defining exactly what the cases are, and then careful in counting the number of favorable and total cases. We'll start being methodical by defining some vocabulary:\n",
    "\n",
    "\n",
    "- **[Experiment](https://en.wikipedia.org/wiki/Experiment_(probability_theory%29):**\n",
    "  An occurrence with an uncertain outcome that we can observe.\n",
    "  <br>*For example, rolling a die.*\n",
    "- **[Outcome](https://en.wikipedia.org/wiki/Outcome_(probability%29):**\n",
    "  The result of an experiment; one particular state of the world. What Laplace calls a \"case.\"\n",
    "  <br>*For example:* `4`.\n",
    "- **[Sample Space](https://en.wikipedia.org/wiki/Sample_space):**\n",
    "  The set of all possible outcomes for the experiment. \n",
    "  <br>*For example,* `{1, 2, 3, 4, 5, 6}`.\n",
    "- **[Event](https://en.wikipedia.org/wiki/Event_(probability_theory%29):**\n",
    "  A subset of possible outcomes that together have some property we are interested in.\n",
    "  <br>*For example, the event \"even die roll\" is the set of outcomes* `{2, 4, 6}`. \n",
    "- **[Probability](https://en.wikipedia.org/wiki/Probability_theory):**\n",
    "  As Laplace said, the probability of an event with respect to a sample space is the number of favorable cases (outcomes from the sample space that are in the event) divided by the total number of cases in the sample space. (This assumes that all outcomes in the sample space are equally likely.) Since it is a ratio, probability will always be a number between 0 (representing an impossible event) and 1 (representing a certain event).\n",
    "<br>*For example, the probability of an even die roll is 3/6 = 1/2.*\n",
    "\n",
    "This notebook will develop all these concepts; I also have a [second part](http://nbviewer.jupyter.org/url/norvig.com/ipython/ProbabilityParadox.ipynb) that covers  paradoxes in Probability Theory."
   ]
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   "source": [
    "# Code for `P` \n",
    "\n",
    "`P` is the traditional name for the Probability function:"
   ]
  },
  {
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   "source": [
    "from fractions import Fraction\n",
    "\n",
    "def P(event, space): \n",
    "    \"The probability of an event, given a sample space of equiprobable outcomes.\"\n",
    "    return Fraction(len(event & space), \n",
    "                    len(space))"
   ]
  },
  {
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   "source": [
    "Read this as implementing Laplace's quote directly: *\"Probability is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.\"* \n",
    " \n",
    "\n",
    "# Warm-up Problem: Die Roll"
   ]
  },
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   "source": [
    "What's the probability of rolling an even number with a single six-sided fair die? \n",
    "\n",
    "We can define the sample space `D` and the event `even`, and compute the probability:"
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
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    {
     "data": {
      "text/plain": [
       "Fraction(1, 2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D    = {1, 2, 3, 4, 5, 6}\n",
    "even = {   2,    4,    6}\n",
    "\n",
    "P(even, D)"
   ]
  },
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   "source": [
    "It is good to confirm what we already knew.\n",
    "\n",
    "You may ask: Why does the definition of `P` use `len(event & space)` rather than `len(event)`? Because I don't want to count outcomes that were specified in `event` but aren't actually in the sample space. Consider:"
   ]
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   "cell_type": "code",
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    {
     "data": {
      "text/plain": [
       "Fraction(1, 2)"
      ]
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "even = {2, 4, 6, 8, 10, 12}\n",
    "\n",
    "P(even, D)"
   ]
  },
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   "source": [
    "Here, `len(event)` and `len(space)` are both 6, so if just divided, then `P` would be 1, which is not right.\n",
    "The favorable cases are the *intersection* of the event and the space, which in Python is `(event & space)`.\n",
    "Also note that I use `Fraction` rather than regular division because I want exact answers like 1/3, not 0.3333333333333333."
   ]
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   "source": [
    "\n",
    "\n",
    "# Urn Problems\n",
    "\n",
    "Around 1700, Jacob Bernoulli wrote about removing colored balls from an urn in his landmark treatise *[Ars Conjectandi](https://en.wikipedia.org/wiki/Ars_Conjectandi)*, and ever since then, explanations of probability have relied on [urn problems](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=probability%20ball%20urn). (You'd think the urns would be empty by now.) \n",
    "\n",
    "![Jacob Bernoulli](http://www2.stetson.edu/~efriedma/periodictable/jpg/Bernoulli-Jacob.jpg)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Jacob_Bernoulli\">Jacob Bernoulli</a><br>1700</center>\n",
    "\n",
    "For example, here is a three-part problem [adapted](http://mathforum.org/library/drmath/view/69151.html)  from mathforum.org:\n",
    "\n",
    "> An urn contains 23 balls: 8 white, 6 blue, and 9 red.  We select six balls at random (each possible selection is equally likely). What is the probability of each of these possible outcomes:\n",
    "\n",
    "> 1. all balls are red\n",
    "2. 3 are blue, 2 are white, and 1 is red\n",
    "3. exactly 4 balls are white\n",
    "\n",
    "So, an outcome is a set of 6 balls, and the sample space is the set of all possible 6 ball combinations. We'll solve each of the 3 parts using our `P` function, and also using basic arithmetic; that is, *counting*. Counting is a bit tricky because:\n",
    "- We have multiple balls of the same color. \n",
    "- An outcome is a *set* of balls, where order doesn't matter, not a *sequence*, where order matters.\n",
    "\n",
    "To account for the first issue, I'll have 8 different white balls labelled `'W1'` through `'W8'`, rather than having eight balls all labelled `'W'`.  That makes it clear that selecting `'W1'` is different from selecting `'W2'`.\n",
    "\n",
    "The second issue is handled automatically by the `P` function, but if I want to do calculations by hand, I will sometimes first count the number of *permutations* of balls, then get the number of *combinations* by dividing the number of permutations by *c*!, where *c* is the number of balls in a combination. For example, if I want to choose 2 white balls from the 8 available, there are 8 ways to choose a first white ball and 7 ways to choose a second, and therefore 8 &times; 7 = 56 permutations of two white balls. But there are only 56 / 2 = 28 combinations, because `(W1, W2)` is the same combination as `(W2, W1)`.\n",
    "\n",
    "We'll start by defining the contents of the urn:"
   ]
  },
  {
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   "execution_count": 4,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "{'B1',\n",
       " 'B2',\n",
       " 'B3',\n",
       " 'B4',\n",
       " 'B5',\n",
       " 'B6',\n",
       " 'R1',\n",
       " 'R2',\n",
       " 'R3',\n",
       " 'R4',\n",
       " 'R5',\n",
       " 'R6',\n",
       " 'R7',\n",
       " 'R8',\n",
       " 'R9',\n",
       " 'W1',\n",
       " 'W2',\n",
       " 'W3',\n",
       " 'W4',\n",
       " 'W5',\n",
       " 'W6',\n",
       " 'W7',\n",
       " 'W8'}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cross(A, B):\n",
    "    \"The set of ways of concatenating one item from collection A with one from B.\"\n",
    "    return {a + b \n",
    "            for a in A for b in B}\n",
    "\n",
    "urn = cross('W', '12345678') | cross('B', '123456') | cross('R', '123456789') \n",
    "\n",
    "urn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(urn)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Now we can define the sample space, `U6`, as the set of all 6-ball combinations.  We use `itertools.combinations` to generate the combinations, and then join each combination into a string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "100947"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import itertools\n",
    "\n",
    "def combos(items, n):\n",
    "    \"All combinations of n items; each combo as a concatenated str.\"\n",
    "    return {' '.join(combo) \n",
    "            for combo in itertools.combinations(items, n)}\n",
    "\n",
    "U6 = combos(urn, 6)\n",
    "\n",
    "len(U6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "new_sheet": false,
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   },
   "source": [
    "I don't want to print all 100,947 members of the sample space; let's just peek at a random sample of them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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    "new_sheet": false,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "['W3 R7 B1 B3 B5 B4',\n",
       " 'R1 R9 R8 W8 B4 B2',\n",
       " 'R7 W4 B3 B5 R4 W5',\n",
       " 'W1 W3 R4 R9 R6 R8',\n",
       " 'W3 B1 B5 R6 W8 B2',\n",
       " 'R1 R4 R9 R6 W5 R8',\n",
       " 'W1 W2 R7 R9 R6 R8',\n",
       " 'W3 R7 B1 W7 R6 B4',\n",
       " 'R7 B1 B5 W7 R4 B2',\n",
       " 'W3 B1 R4 R6 R8 B4']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "random.sample(U6, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Is 100,947 really the right number of ways of choosing 6 out of 23 items, or  \"23 choose 6\", as  mathematicians [call it](https://en.wikipedia.org/wiki/Combination)?  Well, we can choose any of 23 for the first item, any of 22 for the second, and so on down to 18 for the sixth. But we don't care about the ordering of the six items, so we divide the product by 6! (the number of permutations of 6 things) giving us:\n",
    "\n",
    "$$23 ~\\mbox{choose}~ 6 = \\frac{23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18}{6!} = 100947$$\n",
    "\n",
    "Note that $23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18 = 23! \\;/\\; 17!$, so, generalizing, we can write:\n",
    "\n",
    "$$n ~\\mbox{choose}~ c = \\frac{n!}{(n - c)! \\cdot c!}$$\n",
    "\n",
    "And we can translate that to code and verify that 23 choose 6 is 100,947:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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    "collapsed": true,
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   "outputs": [],
   "source": [
    "from math import factorial\n",
    "\n",
    "def choose(n, c):\n",
    "    \"Number of ways to choose c items from a list of n items.\"\n",
    "    return factorial(n) // (factorial(n - c) * factorial(c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "100947"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choose(23, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "new_sheet": false,
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   },
   "source": [
    "Now we're ready to answer the 4 problems: \n",
    "\n",
    "### Urn Problem 1: what's the probability of selecting 6 red balls? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(4, 4807)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "red6 = {s for s in U6 if s.count('R') == 6}\n",
    "\n",
    "P(red6, U6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "new_sheet": false,
    "run_control": {
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   },
   "source": [
    "Let's investigate a bit more. How many ways of getting 6 red balls are there?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "button": false,
    "new_sheet": false,
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "84"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(red6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "new_sheet": false,
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   },
   "source": [
    "Why are there 84 ways?  Because there are 9 red balls in the urn, and we are asking how many ways we can choose 6 of them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "84"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choose(9, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "new_sheet": false,
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   },
   "source": [
    "So the probabilty of 6 red balls is then just 9 choose 6 divided by the size of the sample space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
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    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(red6, U6) == Fraction(choose(9, 6), \n",
    "                        len(U6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
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   },
   "source": [
    "### Urn Problem 2: what is the probability of 3 blue, 2 white, and 1 red?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(240, 4807)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b3w2r1 = {s for s in U6 if\n",
    "          s.count('B') == 3 and s.count('W') == 2 and s.count('R') == 1}\n",
    "\n",
    "P(b3w2r1, U6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "We can get the same answer by counting how many ways we can choose 3 out of 6 blues, 2 out of 8 whites, and 1 out of 9 reds, and dividing by the number of possible selections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
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    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(b3w2r1, U6) == Fraction(choose(6, 3) * choose(8, 2) * choose(9, 1), \n",
    "                          len(U6))"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Here we don't need to divide by any factorials, because `choose` has already accounted for that. \n",
    "\n",
    "We can get the same answer by figuring: \"there are 6 ways to pick the first blue, 5 ways to pick the second blue, and 4 ways to pick the third; then 8 ways to pick the first white and 7 to pick the second; then 9 ways to pick a red. But the order `'B1, B2, B3'` should count as the same as `'B2, B3, B1'` and all the other orderings; so divide by 3! to account for the permutations of blues, by 2! to account for the permutations of whites, and by 100947 to get a probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
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    {
     "data": {
      "text/plain": [
       "True"
      ]
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     "execution_count": 16,
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   ],
   "source": [
    " P(b3w2r1, U6) == Fraction((6 * 5 * 4) * (8 * 7) * 9, \n",
    "                           factorial(3) * factorial(2) * len(U6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "### Urn Problem 3: What is the probability of exactly 4 white balls?\n",
    "\n",
    "We can interpret this as choosing 4 out of the 8 white balls, and 2 out of the 15 non-white balls. Then we can solve it the same three ways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(350, 4807)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w4 = {s for s in U6 if\n",
    "      s.count('W') == 4}\n",
    "\n",
    "P(w4, U6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(w4, U6) == Fraction(choose(8, 4) * choose(15, 2),\n",
    "                      len(U6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(w4, U6) == Fraction((8 * 7 * 6 * 5) * (15 * 14),\n",
    "                      factorial(4) * factorial(2) * len(U6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Random Walk\n",
    "\n",
    "We demonstrate in the sequel trajecorial and distributional properties of simple random walks. First we generate one trajectory of a simple random walk with $N$ steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import pylab\n",
    "\n",
    "def RandomWalk(N=100, d=2):\n",
    "    return numpy.cumsum(2*numpy.random.binomial(1,0.5,(N,d))-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CxTFGVzs2eDHSny2Gkc0ebczOo14wphgGOtuwZ4uWW5Cd94/BRsBbdypmCOp1\n/n542xwVWQheSKRx/tJCQy4AGxg1FipNMBzD1n43nAVkQwJ61jQRcNMu6/3pM+U+rhrsxuYqyn2I\nARAqjvHj2qbXirWGJQL1HQLaCBilIgN6Ja42h21JRNBQnxveNgeG+9zo04XIKlWVyhg5N+ICsIHf\n58HY9AIWk5UVhVtNHrvb7YTP24ahXu3+bO1zo9ftRL+3DQHFA5fdhi29br1+sRgAoUEJ6TIBbpcD\nAX3hK5nOIKhqLvJwARdZKI4Olx37hntxnb/fnNKw1h0wRufX+ftxvb8fgKFFU74HEDSNeON6cYEB\nL5i1qcpKkUpncGZyflXP6PpAP67z9wEArgv04/pAv7n9Jn8f7DZCQPHg9OR8VQrYSxioUHGCamyJ\ngJlRWjGkxjC8gossFM/3fv/N5nZgwIvD52eQ0ZUo37JdE5/7q1+/yjzG7/Pg4V+dx3wiVVZSWkiN\ngkhTSG1UjEXaYDiGyzZWpoj92PQCEunlInC5fOH+a8ztv3x39v58/M7Lze2P3rYLH7/r8qosspf9\nSySiXUT0iuVvlog+knPM24hoxnLMJ8s9r1CfMDNClhq6gSWZq6VXxBJWJ6B4cW5qHqcmY5oSZZ4p\nNjP8sUwvIKjGsKW3A+3OxhGBy8VQZK3kNEslcyO63c6qXd+yPQBmPg5gLwAQkR3AeQAP5zn058x8\nd7nnE+qbXJkA4wdxYmIOpydjeLse5SBUjoDiQYaBJ4+F9cd5DIBRFD0Sw5WD3Ws+l3WKqVFxuxwY\n7OmoqDxGvRY5Wo1K++K3AAgy85kKv6/QIBgjIaOT6O7QFr6eOqEimeaG7zzqEeOaPq7XL86n0rm1\n3w2i8uLLjSmmZriH2qJ45dYAgmoUPq/LzHhvFCptAO4D8K0Cz11PRIeI6DEiuqLQGxDRA0R0kIgO\nqqpa4eYJ600ojyscUDw4eHpK3278zqPeMKY0Dp6eQneHE/15ZDbanXYM9brLii+/MLuIhWS64WSg\n82EUaKnUQquWG9F43+2KGQAicgG4B8C/5Hn6ZQBbmXkPgC8A+EGh92Hmh5h5PzPvV5TlokpCfZNP\nJsCvl+IDGs9FbgQ8bQ5s6m5HhrWRbaHFQ7/iKcsDyGa6Nl5Hl0tA8VRYHiPakJFRlfQA7gTwMjMv\nqzzBzLPMHNW3HwXgJCJf7nFC45NPJsDo9Ps9jeciNwrWqmErHROKRNdcHSzr3TVeR5eLKQpXgXWA\nS/MJTMaIIBshAAAgAElEQVQSre0BALgfBaZ/iGgj6T0CEV2rn3eygucW6oR8MgHWMovC+lBM+Uq/\n4sFiMoMLs4trOkdQjaGz3QHF23gicLmYi+IVMACNnBtREQNARG4AtwH4vmXfh4joQ/rD3wBwmIgO\nAfg8gPu4GlkOQlnMLCTxjWdOg5kxn0jh6784hfQKo8f5RCqvTICRAt8MI8d6pZgC9mZZQn0q51sv\nnEV4TjMG33tpDGPTKytQhiLNo+S6oasNHpd9zQvBpyMxPHJIK92YG/jQSFTEADDzPDP3M/OMZd+D\nzPygvv1FZr6Cmfcw83XM/EwlziusLz/41Xn86SNH8PqFWfz48EV8+t9ex4v6Ym4+DCXK3Fjowd4O\nXDvSh5svkxDQ9eKG7f3YucGLa4YL1x22jnrPTc3j499/Dd954Rxm5pP44385hG88c3rFcwTDjVcH\nuBBEVJbkwkM/D+Ej3/4VFpNphNSYKePQaEgmsFAQq8CYtcjIdbq8wPLj87vCdhvhux+6fh1bKmwf\n6MTj/+2mFY/xeV3o1OsHjPiy93PUcp8LEY2ncHF2sSFHuYUIKB68eHp6Ta8NhqPI6HISQTWKEZ/b\nFHdrJCQnXyiI2emHo9kSjyvoqDeDTEAzQ0QI6KPebNnIrHFfaT78VIMmOq2EX/Hi/KUFzCdSJb/W\nCKcNhrXr14gLwIAYAGEFjOzGUCSWLfK+go56M8gENDuaOmvMotAaNQ3AWb0UYT4aeZ67EMZnOVVi\nboRR1wIAjk/M4ezkfEMuAANiAIQCGKUFAeDExTmcjmgLhCvNmTaDTECzE1C8uDi7iFfHtOW6WCKN\nZ4NaQN5KpQiDahR2G2G4v/HmuQthdNqlLgRbPaV/Px5GKtO4Ge5iAIS8GKOiwZ4OHJ+YQyKdwWBP\nR0Ed9WaSCWhmjCmc187PYLCnAwDw6lh2u9A0UEiNYai3oyqFyqvFSL9nTfIYhmc82NNhGtJGrY8g\nBkDIS6HSgoV01JtJJqCZsRrofGUjC42Gm1HJtd1px5bejpLlMYy6Fm/blVUqaNTvvRgAIS/BcBQ2\nyhavBiydRJ6F4FATzhE3I8P92WiV6wP98Li0Ef2Vg93Y2NWed4ovbXh3TVjJLaB41+QBDPe7sWtj\nJwCtNGdXu3M9mrfuiAEQ8hKMxDDc58Zlm7QveZ/HZcaY5+skjB9Ro46EWoU2hx1Dvdp0T0DxWrK0\nPQgM5FfIHL+0gHgq05S1nP0+L05FYiXJYxjeUDHJd/WOGAAhL8aCruJtQ2e7AwHFs0xH/fEjFy3Z\nkM0jE9DsBBQvHDbC1n63pRPzFlTINPIEmtIDGPBgIZleJo8RT6XxFz96HVOxBFLpDP76sWO4MLOA\nVDqD05NaQlwx+kv1jiSCCcswFnRv3OEDEeF33jyCIT3L0aqj/oWfjWJuMYl79mxuKpmAZufd+wbN\n0pz37NmMNocN3R1O+H0ezC2moEbjGOhsN483Fj2b1QMAtAGPsRAOAC+dnsZXfn4KAcWLKzZ348Gn\nguj3uHDb7g1mXYsNXW149zWD+LWrNtWq+WUjBkBYxnnd5TdGNn98+y7zuYDixb8cPIdMRiv9uJBM\nI55KIxiO4c3b82cIC/XF3Vdvxt1XbwYA3HzZgCnRYYzwg+HYEgMQVKPocTvRl6fOQKNjhIKG1Cje\nujO7qGvNfDfyWoJqFH41K7pHRPi7/7i3yi2uLDIFJCxjpfqmho76q+dnEEukkWHg9fHZppMJaEWM\n+52b7GdMBzajd2dMceaufRiPlybNxRq29GMhxAAIy1jpS250Egdev2ju++nRCf14MQCNzKaudnQ4\n7cuivEKR5RLfzYIhCrfM6Fk8gKxshpY13Ux1LWQKSFjGSi5/wDQA2bo/xnazjIpaFZuNNKkIS2do\nyB404wKwQUDx4JnRpeVJjEHQ2al52PSw2clYAi+dmW7oqJ9cxAMQlqGJW+UvLWjoqJ+YiJqlH09M\nNJ9MQKuSK5FsVgFrUg8AyMpjROOaKNxCIq3XtfAgw5oxMAY3J5tM7qSSNYFPE9FrRPQKER3M8zwR\n0eeJaJSIXiWifZU6t1BZtC98/i+54TID2dBBABjuczeVTECrElA8S+Q+zOnAJvcAgKziqeEB3bZ7\no3mMdVsMQGFuZua9zLw/z3N3Atih/z0A4MsVPrdQAWYXkwjPxVfUNgmY5QezsdDNPEJsJQKKd4nc\nhyF7MNzXvN6dWSktpy7CbbuzWfBv3emD0655xDIFtDbuBfCPrPEcgB4iatwA2ialmCgHawKMaQya\neITYShidm7EQbMgeOO3NO1s83O+GjbIGwKhrccVmTR4DAHZt6DTrXIgHkB8G8DgRvURED+R5fhDA\nOcvjMX2fUEeEisj6tE4B+cUDaCqMxKiQJQqmmTq8fLQ57Bjuc5uDH2tdC7/iQXeHFhDhVzxw2glb\nejtWecfGoZJRQDcw8zgRDQA4QETHmPlpy/P5goiXCXDoxuMBABgeHq5g84RiKMblv3GnD/dfO4y3\n7PDBZbfhP71pGLdcvqHg8ULj0OGyY7CnA0E1asoetMK9DVgWv611LT5wwzacv7QAIsL7rh/BNcO9\ncDSRN1QxA8DM4/r/MBE9DOBaAFYDMAZgyPJ4C4DxPO/zEICHAGD//v3FKzQJFaEYl7+r3Ym/+vWr\nzMd/+e6rCh4rNB5aKGgMY9MLSKa5qea8C+FXPPjFaASpdAanIjGz7vWtFsnsG7b7cMN2X62auC5U\nxJQRkYeIOo1tALcDOJxz2CMA3qdHA10HYIaZL1Ti/ELlaOT6pkJlMCSSR8OtI/EdULyIpzI4eGYa\nC8l0w5Z4LJVKeQAbADysx407APwzM/+YiD4EAMz8IIBHAdwFYBTAPIDfrdC5hQqRzjBOR+ZNbRih\nNTHkPp4NTZqPmx1/ToJjqwyCKmIAmDkEYE+e/Q9athnAH1bifML6MDY9j0Q60xIjPqEw1mzvZpI9\nWAnDyJlZ7S3iATTPaoZQNsYiWCuM+ITCGBFgZ6fmW2Yw0OdxocftxNmp+ZaqayEGQDAxYr9bxf0V\n8jPQ2WaWimyFBWBAz3DXQ5n9Tap8mg8xAIJJKBJFn8eF3ibUfReKh4gspSJbZzCQTXBsDaMHiAEQ\nLATDsZb68guFyY6GW+f74Fdaz+iJAWgBovEU3vPlZ3D4/AziqTTue+hZvHBqCpkM4/1ffwFPHgsD\naI2sT6E4rLWCWwVj8NNKWe1SD6AFOHJ+Bi+dmcZTJ1TYiPBcaApPHJvApu52PHVCxWBvB64Z7sFk\nLNFSIz6hML+5fwgdLjtGWkji+607Ffz323e2VBi0GIAWwKxoFI6aEg/BcGxJ6nvQFIFrnRGfUJiN\n3e34vRv9tW5GVWl32vHht++odTOqihiAFsAU9orEsNWieR4yt7N1T1vJ5ReEVkcMQAtgytxaPICz\nk/M4fnEOAKDOxfGrc5fgtBOGmkjpUBCElZFF4BYgqMZABMzFU3g+NAkiIJVhPHk8DCPc+aevT2Ck\n39NUSoeCIKyM/NqbnMVkGmPT89g33AsACM/FC27LArAgtBZiAJqcM5PzyDBwu0XW9jbL9tt2KnDY\nNDdAFoAFobUQA9DkGIu7N2z3ocOppfdfvaUbA52a1snOjZ3Yqof6yQKwILQWYgCanKAZ3eMxp3i2\nK15zO2Ap6yhZwILQWogBAPCpR47gj797qNbNWBeCagybu9vhdjmwfcCrKR12tmH7gBdOu1b6cfuA\nF0TiAQhCqyFhoACeOqFibjFV62asCyE1agp7ffS2nfiPbxwCEeEP3rYdt+3eCJfDhg/csA1vGO5F\nd4ezxq0VBKGalO0BENEQET1JREeJ6AgR/VGeY95GRDNE9Ir+98lyz1spEqkMzk7NIxKNY2YhWevm\nVBRmRlCNmYu7W/s9eHNAq2m6uacDN+1UAABKZ9uS2qeCILQGlfAAUgD+mJlf1usCv0REB5j59Zzj\nfs7Md1fgfBXl7FQM6YxWez6kRnGNHhbZDKhzcUTjKQnvFAQhL2V7AMx8gZlf1rfnABwFMFju+1aL\nUb0ICgBTGqFZGFVbp6i3IAilU9FFYCIaAXANgOfzPH09ER0ioseI6IpKnrccQhGtk7TbyIyYaRYM\ngTfxAARByEfFFoGJyAvgewA+wsyzOU+/DGArM0eJ6C4APwCQV3aPiB4A8AAADA8PV6p5BQmGY9jQ\n1QZvm6PpDEBIjcLtsmNjV3utmyIIQh1SEQ+AiJzQOv9vMvP3c59n5llmjurbjwJwEpEv33sx80PM\nvJ+Z9yuKUonmrUgoEjVj4ZttCshYAG6V+qaCIJRGJaKACMDXABxl5s8VOGajfhyI6Fr9vJPlnrtc\nmBnBsGYAAooXpydjSKUztW5WxQiGozL9IwhCQSoxBXQDgN8G8BoRvaLv+58AhgGAmR8E8BsAfp+I\nUgAWANzHzFyBcxcFM2MhmYbbtfTjRqIJzC5qUTLeNgeSacbY9AJGfB7MJ1Lm8QuJNNqdtqJH0vFU\nGnaimiprLiTSGJ9ZQEAZqlkbBEGobyoRBfQLZiZmvpqZ9+p/jzLzg3rnD2b+IjNfwcx7mPk6Zn6m\n/KYXz5PHw9j35wegzsWX7A9ZomSMLNigGkV4bhHXfPoAnjwWxuxiEtf+xU/xyKHxos/33q8+jz/7\n19wo2OpyKhIDsywAC4JQmJbIBH75zCUsJjM4emEWSmd2XcEaJeNtc+j7orDbCPFUBi+fnUZXhxNz\n8RR+dfYS7t27enRrKp3BoXMzmE+k1+fDFIkR3SQhoIIgFKIltIDM2rc5UT5BNYp2pw2buzvQ43bB\n53UhpMayNXTVaMHXFmJsegGJdAYhNYZMpmqzXMsIhrUiMNt84gEIgpCflvAACnXiITUKv88Lm66H\n7/d5EVSj5uNgOIbhvmxB9VLOtZBM48LsIgZ7alNiMahGMdjTgXZdAloQBCGXpvcA0hnG6cg8gOWZ\nvkE1tmSOPDDgQUjNFkg/NRnDaFirmzs+s4j5xOqCcdZzhGqYV2CEtwqCIBSi6Q3A2PQ8EukM2hy2\nJR6AUSrR2kkGFC8mYwm8NjaDNocNiVQGzwYn0ebQLlMxeQJBNWoeX6zXUGkyGUYwHBMDIAjCijS9\nATA67Rt3+DAxG8fcoqb4aZRKtHoAxnYskcaNO3zLtkOR4gzAni096GxzFHX8enBxdhELybREAAmC\nsCJNbwCMUb9RB/dUJLZkf64HYGCtm/v2yzaAqLgRfUiNITDggX/AWzNpCcPoiQcgCMJKtIQB6HU7\n8YatveZjIDs/bx0lb+l1w6Unb+0f6UOvWyuQsntzF7b0dqzaoU/HEpiMJeD3eRHweRAM18YDyBo3\n8QAEQShMCxgAbS58uM+jKX6GY+Z+o1Sigd1GGPG54bBppRKN5DC/4kGggFZQKp3BuSl9kdmIvR/w\nIDDgxcXZRUTj1a80FlKj6GzTSj8KgiAUoukNQEjVomFcDhu29rnNTjpoKZVo5crBbuza2Amn3Yar\nBrsx3OdGV7tTMwCR6LLY/u8eHMMtn30K07GEmT+gaQtpo+9TNRCYC6ox+AdEBE4QhJVp6jyAmfkk\nItGEOc3jV7RpGWZGSI3hPfuWZ/b+2T1XIJHSBOH+xzt24Q9uDpivXUxmMD6zgC29bvP4w+MzSKQz\nOBnWksZcdhu29LoR198jqEZx1Zbu9f6oSwiqUVzv76/qOQVBaDya2gMI5sghBBQvTk3GcGFGm5rJ\n5wF0tjvR79WmTjxtDgx0ti95j2W5BOHsmkIwHMOIzw27jbC13w0bVT8XIBZP4cLMYt7PJgiCYKW5\nDUDYmJPPzuUnUhn8/KSqPfYV30kGLGJxVkKWqKJQJGq+Z5vDjuE+tzktVC2MKCe/SEAIgrAKTW0A\nQpEYnHbCUK8mx2B04o8fmdAeDxTfSfq8LnS2O5Z4ALOLSVNh9PhEFGcn55e8p1+pfiioGQEkHoAg\nCKvQ1AYgGI5ia7/H1OU3onp+PhopuVQiESGQ06EbxsDb5sBzoUmkMrzEqwgoHpyKxJCuoihcUI3B\nRsDWfvfqBwuC0NI0twFQo0ti4fs8LvS6nUikMvArnpKjZPyKZ4kBMKaYbtqlmAvH1pG3X/Einspg\n/NJCOR+jJIJqFEN9brQ5RAROEISVqVRN4DuI6DgRjRLRx/I830ZE39Gff56IRipx3pVIpjM4OzVv\njvoNrAvCpRJQvJiYjZux/UE1CoeNcPOuAfOYJeJyBdYN1pOQKhpAgiAURyVqAtsBfAnAnQB2A7if\niHbnHPZBANPMvB3A3wH4m3LPuxrnpuaRTPOyztAMCS1hAdggGwlkRP7EMNzvxq4NnQAApbMNXe1O\ny/Hauaq1EJzJsC5xLQvAgiCsTiU8gGsBjDJziJkTAL4N4N6cY+4F8A19+38DuIXWOUspq4eztDM0\nPYASFoCzrzU6dEsymeI1jUruufo8LnR3OFf1ACLROI5fnCu5Pbmcv7SAeCojC8CCIBRFJQzAIIBz\nlsdj+r68xzBzCsAMgLyZSkT0ABEdJKKDqqquuVFBU+tnaWe4b2svnHbC1YM9Jb/ncL8W4x9SY0il\nMzgzqclJe9ocuGxjJ/YN9+Z+FgQUz6q5AJ/58TH81lefA3N5i8VGSKpMAQmCUAyVyATON5LP7cmK\nOUbbyfwQgIcAYP/+/WvuEYNqFD5vG7o7nEv2v3GkD6/+6TvQ4Sp9kTQb2x81Sz8ao/8ffvgGOGzL\n7WlA8eLfT6xsyI5fnEMkmsBULGEmoa0FY1FaZKAFQSiGSngAYwCGLI+3ABgvdAwROQB0A5iqwLkL\noi2G5u8I19L5G/h9etWwnCzjNocddttyO+dXvFDn4pjV6xDkYshSAMXVG1iJoBpFd4cT/R5XWe8j\nCEJrUAkD8CKAHUS0jYhcAO4D8EjOMY8AeL++/RsAfsblznesQlCNLpv+qQSBAS9CkRhOTBQnuWw8\nX6iamDoXx5wRVVRmBbGQXuJSROAEQSiGsg2APqf/YQA/AXAUwHeZ+QgRfZqI7tEP+xqAfiIaBfBR\nAMtCRSvJVCyB6fnkuujh+31ZOYl+jws97pVH28aCbKHO3RohVAkPQOb/BUEoloqogTLzowAezdn3\nScv2IoDfrMS5iiGkLq/2VSmMDv350NSyRd98DPdp9QWMKaNcjMXqXrezLA9gbjGJ8FxcDIAgCEXT\nlJnA+co9VgrjPVMZLmqx1Wm3YbjfXbA6WEiNocNpx3X+/rI8AGOKSRaABUEolqY0ACE1BpfDhkFd\nBK6S9Hlc6NFLRRZrYPy+wqJw2lqFB9sHvDg7NY94Kr2mdq2n0RMEoTlpSgMQVKPY1u/JG5VTCUpN\nJgsMeHBmch6pdGbZc8a8fUDxIp1hnJ2cX1ObQmoMdr2UpSAIQjE0qQGIrSnTt1gMqYVi5SQCiheJ\ndAZj0wvIZBjff3kM8VQai8k0zl9agF/xmFM3xqLwgdcnTKnpYgiqUWztc8PlaMpbKgjCOtB0vUUq\nncHE7OK6ToW8ZYcPOzd4saXIKSarhMRLZ6fx0e8ewo8PX8SpSAzM0OUkssJxMwtJ/Od/PIi//+Wp\notukhYDK9I8gCMXTdDWBHXYbXvvUO0x55vXg3r2DuHfv8nrChTA8hZAag7ddu+TBcNTMHA4oXnjb\nHNjQ1aYlmenz+aNFRgWlM4xTkRjetksp5WMIgtDiNJ0BAAC7jcrK9q00vR4X+j0uBNUoOg0DoMbM\nQjXbfIaYnLZYbEwDFSsjPTY9j0Q6IwvAgiCURFMagHrEr3iWegBqFA47YbCnwzRWfsWDH74ybnb8\nZ6fmkUxn4LSvPFNnKp+u47qHIAjNR9OtAdQrxujemN45FYnh5ER0iXRzQPFibjGFF05pMknJNOPc\n1OpRQaby6RpqHAiC0LqIAagSfsWDyVgCZ6bmsaGrDfFUBkcvzi4p3mJM4bx8dhobujRV0GKKyQTV\nqFbuUkTgBEEoATEAVcLo3JmBWy/fYG4vrSHsMfffoh+zWi0BQDMSUgVMEIRSEQNQJawLtLdfsdGy\nP9txb+7uQLtTuyXXDPXA520raiE4JCJwgiCsATEAVWJLbwecdi0zef/WXrNQjbXjttkI23xGlrHX\nXDheiZn5JCLRhCwAC4JQMmIAqoTDbsNIvwebutvhaXMgoHjgbXNgoHNpBTDDIwj4vObC8UoEI7IA\nLAjC2pAw0CryrmsGEdWLv7xzz2acjsSWFW+588pNSGcY3W4nAooH0/NJTMUS6CuwwGtISEsheEEQ\nSqUsA0BEfwvgnQASAIIAfpeZL+U57jSAOQBpAClm3l/OeRuVP7x5u7n9uzdsy3vMr129Cb929SYA\n2emhkBpFn6cv7/GhSAxOO2FoHZRPBUFobsqdAjoA4EpmvhrACQAfX+HYm5l5b6t2/mshYNEHKkQw\nHMXWfo+ZVSwIglAsZfUazPy4XhISAJ6DVhBeqBCDvR1wOWwr5gJoctKyACwIQulUctj4AQCPFXiO\nATxORC8R0QMVPGdTY7cRtvV7CuYCJNMZnJ2aFxVQQRDWxKprAET0UwAb8zz1CWb+oX7MJwCkAHyz\nwNvcwMzjRDQA4AARHWPmpwuc7wEADwDA8PBwER+huQkMeHD0wlze585NzSOZZskBEARhTaxqAJj5\n1pWeJ6L3A7gbwC3MzAXeY1z/HyaihwFcCyCvAWDmhwA8BAD79+/P+36thN/nxU+OTCCRyiwr9iJ1\ngAVBKIeypoCI6A4AfwLgHmbOq1pGRB4i6jS2AdwO4HA5520lAgMerVTk1PJ1ALMOsOQACIKwBspd\nA/gigE5o0zqvENGDAEBEm4noUf2YDQB+QUSHALwA4EfM/OMyz9syGAleo+H8BsDnbUO3XqReEASh\nFMrKA2Dm7QX2jwO4S98OAdhTznlaGWN6J6Rn/P6/TwWxe3MXbtyh6GUgZfpHEIS1IcHjdU5nuxMb\nutoQDMeQzjA+e+AE/unZMwCMEFCZ/hEEYW2IAWgA/D5NE+j89AISqQxCkRimYglMzyclB0AQhDUj\nBqABCAxouQCjqhYOemYyhuMXtW3xAARBWCtiABqAgOLF7GIKL5yaBqCVinzqhGo+JwiCsBbEADQA\nRqbvgdcvmvsOvH4RLocNgyICJwjCGhED0AAY8/xBNYadG7zm9rZ+D+w2WumlgiAIBRED0ABYS0Xu\n1UtFApIBLAhCeYgBaACWlIpUvGbHL/P/giCUgxiABiFg6fSNjl/qAAuCUA5SErJBMBaC/YoHpye1\njl/qAAuCUA5iABqE9+wbBDNjpN+Dd+7ZDDUaxxWbu2rdLEEQGhgqoOBcF+zfv58PHjxY62YIgiA0\nDET0UrGld2UNQBAEoUURAyAIgtCiiAEQBEFoUcQACIIgtCjlloT8FBGd16uBvUJEdxU47g4iOk5E\no0T0sXLOKQiCIFSGSoSB/h0z/z+FniQiO4AvAbgNwBiAF4noEWZ+vQLnFgRBENZINaaArgUwyswh\nZk4A+DaAe6twXkEQBGEFKmEAPkxErxLR14moN8/zgwDOWR6P6fsEQRCEGrLqFBAR/RTAxjxPfQLA\nlwH8OQDW/38WwAdy3yLPawtmnxHRAwAe0B9Giej4am0sgA9AZI2vXU+kXaVTr22TdpWGtKt01tK2\nrcUeuKoBYOZbi3kjIvoKgH/L89QYgCHL4y0Axlc430MAHirmnKu052Cx2XDVRNpVOvXaNmlXaUi7\nSme921ZuFNAmy8N3Azic57AXAewgom1E5AJwH4BHyjmvIAiCUD7lRgF9hoj2QpvSOQ3gvwAAEW0G\n8FVmvouZU0T0YQA/AWAH8HVmPlLmeQVBEIQyKcsAMPNvF9g/DuAuy+NHATxazrnWQNnTSOuEtKt0\n6rVt0q7SkHaVzrq2ra7VQAVBEIT1Q6QgBEEQWpSmMwD1IjtBRENE9CQRHSWiI0T0R/r+ouQzqtC+\n00T0mt6Gg/q+PiI6QEQn9f/58jrWs027LNflFSKaJaKP1OKa6XktYSI6bNmX9/qQxuf179yrRLSv\nBm37WyI6pp//YSLq0fePENGC5do9WOV2Fbx3RPRx/ZodJ6J3VLld37G06TQRvaLvr+b1KtRHVO97\nxsxN8wdtkTkIwA/ABeAQgN01assmAPv07U4AJwDsBvApAP+9Dq7VaQC+nH2fAfAxfftjAP6mxvfy\nIrSY5qpfMwBvBbAPwOHVrg+09a7HoOW8XAfg+Rq07XYADn37byxtG7EeV4N25b13+m/hEIA2ANv0\n3629Wu3Kef6zAD5Zg+tVqI+o2ves2TyAupGdYOYLzPyyvj0H4CjqPwP6XgDf0Le/AeBdNWzLLQCC\nzHymFidn5qcBTOXsLnR97gXwj6zxHICenBDpdW8bMz/OzCn94XPQ8m2qSoFrVoh7AXybmePMfArA\nKLTfb1XbRUQE4D8A+NZ6nHslVugjqvY9azYDUJeyE0Q0AuAaAM/ru1aTz6gGDOBxInqJtOxrANjA\nzBcA7csJYKBGbQO0fBHrj7Ierlmh61Nv37sPQBspGmwjol8R0VNEdGMN2pPv3tXLNbsRwAQzn7Ts\nq/r1yukjqvY9azYDUJLsRDUgIi+A7wH4CDPPQpPPCADYC+ACNPezFtzAzPsA3AngD4norTVqxzJI\nSxi8B8C/6Lvq5ZoVom6+d0T0CQApAN/Ud10AMMzM1wD4KIB/JqKuKjap0L2rl2t2P5YONKp+vfL0\nEQUPzbOvrGvWbAagJNmJ9YaInNBu7DeZ+fsAwMwTzJxm5gyAr2Cd3N7VYC1XA8wcBvCw3o4Jw6XU\n/4dr0TZoRullZp7Q21gX1wyFr09dfO+I6P0A7gbwW6xPGutTLJP69kvQ5tp3VqtNK9y7ml8zInIA\n+HUA3zH2Vft65esjUMXvWbMZgLqRndDnFr8G4Cgzf86yvxj5jPVum4eIOo1taAuIh6Fdq/frh70f\nwA+r3TadJaOyerhmOoWuzyMA3qdHaVwHYMZw4asFEd0B4E8A3MPM85b9Cmk1OUBEfgA7AISq2K5C\n98BrCl8AAAEBSURBVO4RAPcRURsRbdPb9UK12qVzK4BjzDxm7Kjm9SrUR6Ca37NqrHZX8w/aSvkJ\naJb7EzVsx1uguWevAnhF/7sLwD8BeE3f/wiATTVomx9aBMYhAEeM6wSgH8ATAE7q//tq0DY3gEkA\n3ZZ9Vb9m0AzQBQBJaCOvDxa6PtBc8y/p37nXAOyvQdtGoc0PG9+1B/Vj36Pf40MAXgbwziq3q+C9\ng6YoHARwHMCd1WyXvv8fAHwo59hqXq9CfUTVvmeSCSwIgtCiNNsUkCAIglAkYgAEQRBaFDEAgiAI\nLYoYAEEQhBZFDIAgCEKLIgZAEAShRREDIAiC0KKIARAEQWhR/n8HmIjyvvshzAAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b7b4e3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y=numpy.random.binomial(1,0.5,200)\n",
    "pylab.plot(numpy.cumsum(2*Y-1))\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JUbRtoFURqGfBAOz7yelW+U/t4OWHnMt7jv55n2b/yXl7NAF0anWL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\nhAgF1gghjpb3REmSZgOzAbp163ZxZZg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MpJXYSbdzT+xGHji2jtRHlMLw9dpnc8SrOZ4S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\njUajAf4fHBELX4rJGcgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b5b27390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def PlotRandomWalkXT(N=100,W=5):\n",
    "    \"\"\"\n",
    "    Plot X(t) for one-dimensional random walk W times\n",
    "    \"\"\"\n",
    "    for i in range(W):\n",
    "        X = RandomWalk(N,1)\n",
    "        pylab.plot(X)\n",
    "    \n",
    "    pylab.show()\n",
    "    \n",
    "PlotRandomWalkXT(10000,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the impressive roughess of the trajectories.\n",
    "\n",
    "Next we generate $W$ endpoints of a simple random walk with $N$ steps and draw a histogram of its distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b7b4dba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def Endpoints(W=10000, N=10):\n",
    "    return sum(2*numpy.random.binomial(1,0.5,(N,W))-1)\n",
    "\n",
    "def HistogramRandomWalk(W=10000, N=100, bins=50):\n",
    "    \n",
    "    sigma = numpy.sqrt(N)\n",
    "    X = Endpoints(W, N)[:]\n",
    "    pylab.hist(X, bins=bins,normed=1)\n",
    "    x = numpy.arange(-7*sigma,7*sigma,1/bins)\n",
    "    rho = (1/(numpy.sqrt(2*numpy.pi)*sigma))*numpy.exp(-x**2/(2*sigma**2))\n",
    "    pylab.plot(x, rho, \"k-\")\n",
    "    pylab.show()\n",
    "HistogramRandomWalk(W=1000, N=10, bins=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The fit to the bell shaped curve is actually quite good!\n",
    "\n",
    "Next we analyse some of many unexpected properties of random walks or random sequences. First we visualize two slightly different random walks: one random as sampled, the other one slightly modified which makes it unlikely in some respect. Which one is it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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i9GsM9GgZf/y0xvAc6WqD3VIqjpFIZ/EPz8xgaSOJu8Y8mBZE3DFK8379vfou\nkaAms+IXX38Ms1E6Hp/XiYcvLCOZySEYpgHRzjYb3nPLEZgIUVwv6hhUBSavq7Eb3G4SDIu0P35n\nK+4/PYDVeBrjvS64nXaEBBGnhzox3uvC+197FLeP9kCIpeT3xXB6qLNpxxGKiHjzhLdp+ytByXAp\n6pp47C7gll8A/HeXvmefwg36AUFbIMPajxou+NmYA7JJeuLHV2nBRTZFfY9lDPabmnQBjmoM+j2n\n9LfRziTNJoLjnlJxjCtCHJJE/w9X1xNIZfOq68DjxDd+sghJkpQbEAt2/uyZITqecS8gX+8+rxN5\nWZkpGBGVmelEXzv+29uLNCqhxhFCERF3jNYphHANCAn0JmoyEQz3OPCH99MvoLe9BX/809cDoIHr\nP3m3vGwxwWY2NVWYZF0uWNop9yAAWgna2l0qUmF3AT/15zv3udcA7nI5IBRoh0ZE2MwmHC1T7l4C\n62mxtQgsnqXL6RgQWy7/nibhtFsw0NFSMY87GBFhNRMMy+Pxe0vFMdj4tfnkiouk1wUxlcWKpvhn\naXMbiXRON6jL1gUjMSpaXCXw63XZ4bJb9p1gB41LGHfLWcwmHPc4lOrSphzDDtZLKAgB6lbZKZfO\nHoIb9ANCsMCgx3BMVkg3hFYe6/J39NfvIL5eV8VZH1V8dyrj8cviBqwTIKA+oWRyEh6/TCsbfR6X\nsj3bj3af9G+lM8Njbpof/2woilgqW9V1RQiBb5/1dGFxiVpTBX1NzujZyXoJAPQpU5g8UIHPSnCD\nfkAIRURYTARr8TTOzq3XNuMRAoBJ9r5NPqQu75LKiq9KP5RQUVk4W2a9R+g2dPwA1aD0uuzoaLMW\nbF+gtFQhVc5uMWO4x4HvySXvRmIRPs/+Sl1kcYlycYty+LxOLKwnlBa7jbKT9RIAgHgU2F4/UIHP\nSnCDfgBYFVNYi6dxh4/6CDcSmdpmPNEAMHQbYLbRk7/3OqC1a9cMur/XiWQmr8iIaUlmcphfS+jm\nvmtzy4MREbfLQdCNRKZg+x6HDV1t1gKDy5pBdes0gwKooduQc92NGHR/rxNRMVVTv/ZridJYrUZX\nh9/rgiQB003yowcjsR2rlwCgPmW6+QwdAEAIeYAQEiGEXNCs6yaEPEYICcq/u3b2MDmVYLPN+67r\nU9YZvlAliRru3pNAj5+u80zIque7NEOvkIo4E42XVGcO9zhgManFP7QrYAI3HulUZnpa3zDLXNGW\n89PCq/IdC3YEAAAgAElEQVT/I/b/62i1wmOg+dh+awEQKopLGKXZ45yuUyDFMNEyKYsHFCMz9H8C\ncG/Ruo8BeFySJD+Ax+XXnGsEm23d6XejzUbbiRpOWVSKLsZVP6NnjM5odkkHUWnSpVfNqTOTtJpN\nGHE7lL/NrsaRy0vw9zoVI12aK+5S9s9EKioFBLX510ZSM5UmXfvGoNcYZ5EZcbfBrLmZNkJd9RK1\nIgQAmwtoH6i+7QGg6rcpSdJTANaKVr8LwBfl5S8C+OkmHxenCnOrccyv0mKcUESEw0b9kD6vEyZC\nA3tlScWAhRfpsjZHV1sK7ZkAEqvUB2mUhReAlHyhL74EbG/Q5eVX1f2EL6lq6zJdDhvcTrUfyuLG\ntvJIH4qIuuPxedQZN/ONj3q01ZxFUmZeJ9YTGayKKUWkopIh0UqcGWGwsxUtVpMyBu33oyW8lcRU\nDZ0Zk5kcXpgpvvwaJ1jnzJjGF9rqzujRjme6XBxDkoArP9DX4Jz7EZCp0qpYe74JATpBOQQZLkD9\nPvReSZKWAUD+XTYpmRDyYULIWULIWUEQ6vw4TjH/6Wuv4D9//RUAclGOPJM8M9yNG4c6lcb/ujz/\nOeCBe6i/XFtFd/Q2wGwH+k+rVXRG3S7xVbrPF/8eyGwDD9xLi5XyeeCf3gH84JN0uy+9F/jeH5S8\nXZs98fvfOo+PfOkn8thiGO5xlIzH3+vErCyOEYqIIIQa9FtHuuCwmXGiv0iDUtH/FFWRigoGzed1\norPNijOyEHQ1TCaCUU1g9He+9gp+5+vnSrb7xEOX8Qv/+KKhfQLA188u4Gc/9xyurpevpK2VZCaH\nhbVEXdKBgBzErtOH/vWXruJnP/ccFtYS5QVS5n8M/PO7gNBjhevX54B/vA849y/lPyCfB774TuDJ\nT9DXLGXxkLDjhUWSJH0ewOcB4MyZM/ur2cUeRZIkTC5vwWQiSi/pO3w0IPjf33FCt1VsAeELgJSj\nJ3s0QAOgDjdw/I3Ax+YBawsAeR/CJDDyuuoHJVymnevCF4FoEMil6fLmPJDaosuJNeriCV8sebvf\n68L/PUeLfy4vxxAVU8jk8giGS5XgAbX4ZyYaRzASw5GuVrTazLjnVB/e+AfeEvV3NZCqZtNUijO0\n2Sz48X97C+wW43Mev9eJF2bW6PezEgMBCoqZAODy8hYWN7axlcygXS4Aq8SlZTqbnwrHcKSrdj1Y\nPa4INC5Rt9JUrxNPTEaQyeVrljS8LAuETIVjCEZi+vUS4Qvq77F71PWRS/L60vNHYesqkNyk22xv\nAOJKYZfFA069M/QwIaQfAOTfkeYdEqcaTJw5lsxiWohjZUv1Q5pNBLZqRkgrjltcdGGVS9fbBwGb\n0/gMnW0nBGhnO4DeLJTPmlS3WQ0BuUIFeZ/XWTCebJ7eqGZX42UNOqAWUrHZNpPJK6avvQVOu0VR\nWnLZqzeDarGaa2pt4PM6sbSZxLQgQkxlEUtlEYmp/V0yuTxmV6uLbmhhbolmBluVplx1FvP4vS5k\n8xLmVmvv6aItgJuOiPp+fOVcmjK2vmCbonMbKC35P8DUa9C/A+CD8vIHAXy7OYfDMYI28PaorDJj\n2B+aywKrVOGdnvST+jMYQmoLjLKLJxpUZ1Lrc8Cy7HbYXqdiAgDVdtyYK3g7my0+qlHNobNASXcm\nOepxghAgsBLDlWi86myTECK3uaUzQ19v85tBMb/9oxdVyTatr3luNYFMjj4dGK22VFo6NLM6Mxyr\nHmepgF5ev+HP1sgCBiOifr0ESzUsLmxTDHqFgjf2t+QGMPs0XeYzdBVCyFcAPAdgnBBylRDySwA+\nBeBthJAggLfJrzm7hHa2xuTBaurbkpNzpeeeoYa23AymltRFZviz20Do+/JKCZj8N3WbgirUwv0y\nI6EnfaY3Q2di1U8GIkhn84b8wayAKRSJ70hlIpvxFkq2xTTLhWmT1VgVU1iXc+Gb2T8lGBF14xJG\nYTfTWjN6WL0EAFxY3MTCWkL/e1Ce8IKFgVF2jiWiNGajh3YCcvk7gKUF6Dxa03HuZ4xkubxPkqR+\nSZKskiQdkSTpC5IkrUqS9BZJkvzy7+aH4TllCUVi6GqzwtViwYXFLdgsJgwZ7tsiz2C6jwPLNKha\ndgbjGaf9XJKbBvYboPsE6H7LLXcdKzwO9lEuO9o14+nvaMGFRepvLVfN6Pc6lW2M3ND8vU6Et1JU\nPHsHeocMd7fBaia4sLiFzjYr2lssBUaPGXeaJVI904W9d6SnDaFw8/qtV+psaYRWOaOqVjdQSDOe\nyZUY9eMXfw/b64AYpudMJk594oBcLzGlnkvlnhyLz0O3HzDVd+Paj/BK0X1IMCzC36uKPRx3O2A2\nWmnHZsYn7lfXlcsCUDJdKvgsAWrwY8uF+xx/O0DkC+n4m2guMAAcuZX654tm6IQQpa/IcbcD4310\nebCzFQ67fuxe+7huqJpTW226A8UsFrNJcWOMeV3w97qKDDoV3bjxSKeh2a1SMHZ9P2KpLMJbjfdb\nz+TymInGm6I0VesMPagZj7qfou+BnWsn3yW/ls+TrSXaME5Zr+N2YX1bjr8RsMtdMQ9RhgvADfq+\nQ5Ik6nv0OpWLoabCDCEAuAaAI2fo60pFF4pBr9Kki12EQ68FnFR7E33XqzMlz4ShoqVywgrlYNsw\nkYpq6PWDaTZsv6PyGIrFpkdloYzi5mJ6sPqCO+WWDs0IjM6tJpDN68clasHf68KVMuLb5Sgej4nQ\nQqUC2Ll24qfk10V+89E3U3FnvUmGGKGTC8+EWup/iAKiADfo+46omMbmdgb+Inkw4zsIyFWhrIio\nQtFF5zDNS68WGGUXm2dcowJTvFxUtCRMlRSOaMdjpLCHzeiNzjaZOAYTddgJWGCUfT+r8TRWxZTS\nf90vS9lJcr/1SgTlpmRsnHqVtLUSihS2Fq4Xn8eJVDZfU348U5Fi4xnR8+MLAcDSSmshHB713GJ+\ndc8Jes7qTTIKzsMJdfkQwQ36PuD81U289TM/xHo8XaBxqYj5VjJo2TTwuTcAU9+jBlSQxXK7jtFm\nXJUeSU1mOtNhs6QnPgF85zdLt4sGqOHvGpH3R2hfGO1FpZX78ozJ/tHFgt1ox6MYxgpjKycJVw6z\nXPzj8zobbwY1+wzwN3eolbEy/oIxqKmVTGzaX0VGTwsrGHM7behotVbd/jOPTeFj33i1ZP2Xn5/H\nL/zjCwAKq2obgbm7gmER8VQW9/75U3j+SplApYx2PJ1tVv3vLRoA3D753BsvnKEzkQrt+vP/Cjxw\nn9qTCJCrng+evJwRuGLRPuCpoIBQRMSri5uYl3N//V4X3E4bPn7/KbzlRAX1oNUgTR0MPQZ4J6gh\n9YwBZgvw3gfojKcSnjHgqix6Mflv1Jf5U39ROKsXAmrw6faP0IpTuxO49ZeBHh/g6gNu+gDQ0klf\nxwX1fZ1Dym5e73Mr47GaTPijd53CO28o34PDabfgL993E26qQQ7t4+86haYkK4a+D0Qu0hTNodco\nq992shcfv/8Ubj/eowhqhAQRcdm94vM6leZilWbcW8kMwlsp+L0uGl8w4LP+3sUVLG8m8cmfub4g\nJfP7l8N4MiAglswgJIgV4xJGUW5KgojONismV2J4Kijgtcd7yo5nZSupjOezP3safR06cn1CgJ4/\nADXKF/5VNdaecXreecaBV78KJLeAqUeB+R/R8zIaAOwd8vn2H4CWdnpeHiK4Qd8HKLm74Rjm1xJw\n2i3obbeDEIIP3jFS+c3anF7md2SzFuanrIRnArjwTXrxRINAPkMNslNzExECqk++a4T+AEB7P3D6\nfXS5rRu45YOFny9MAv63KruxmE0F4/nA7VXGBuD+G2trunSrwVL+qmhnjhqD3mI1K2MY6GhFm82s\nzGIBaghtFlPVfiiqAIc649fmtxeTzeVxRYgjnctDEFMF2qbsxjEtxMtW3tZKe4sVve12BMMiOlpp\n/MLIeNhn60oYpkRgcwHwsPNknPrExTD9P7OAKJt9R6eKzm9N35a2buCWDzU8zv0Gd7nsA9gFyaoi\njXYABFBYwan0hq7Br+gZByABwe9RYw4U+i/TcWBjvrZ9tnUDbe5d6+a4I2j/r2Vg/V2mBRHBsAi3\nk4pNA/QJq6JKU7jQAI56nFiT/fF6zK8lkM7lC94LANvpHK6u0z7zUysxxY/fDPxeF0KRmGLIK7mE\nim9QujA/uVsTewGoe0tbL8EmBJHLdJIBaKqeD5fPvBhu0Pc4+bykKPOEWHVdrVktAJ3lLDxPDalD\n/7FYF3YRlSsKigYBSLVfSLvYb73pZJLA+gxdrjIGpn8aKjKk/l4n5lYTSGd1OgqCujK09QUskFjO\naJYrWpoWRLD09R9MRZDK5puW4ePzOuVzkk445tYSSGX1lYxCEbF6vYS2URxQeu6xc6xzmMZ/Qo/R\nQjYAmH8OiEcOXVZLMdyg73EWN7axncmhzWbGxaUtCLFUbTMsIUDTvADq9601SNR9nErSBeXOd9a2\nIoNe5MYxCstUaFKxzK6yGqKNyKyOqgbd1+vEylYSl5e3CgK8Pq8Tubyk9HYpJhiOFdQXaH3WutvL\nBr3VataV2muzmfHkJI1dNKuoyud1Ip7O4ezsOtpsZjqeqH7WC9WFrVIvEQ0AJivQLRefufqoT5yd\ne+wcM1to0F05Jx1qdfIhC4IWww36HoddwG8a92Jb1nE0fEHmstT4+N9GX2cStYvlWmxy1V6CFgR5\nTxa6SoRJWkDEcs6N4pmQ/aP7sK8bG7//bbSbZLp8+iHLlU9m8rp58OX8zsGIWCDgPNDRAofNXHb7\n6YiI/o4WTPS7SsSwzSaC1/vcyvnDxLMbhY1hO5PDm8a9yufpjydWXZBaCAA9o4BZrilgAdBMorRe\ngq0H6PfAlrnLhbOXYf7QezXycoYvyPUZ6vf23017WgD1zWCK88m1s1J2EVr0tTnLwgo/qhUt7UWE\nAEBMwMQ76eto+UparRHTGnS1H0pppksincXixraujF55g8mKzQqzYYKRGIZ72nBygFZOejTi2Y2i\nPb67T/WWHQ/z41ftn6PnA9cWpGnjRmw7Z6+aFWNtAzqGcJjhBn2PE4zE4Hba8JpjNDujxWrCYJfB\nohhmeL0n1PStemYwBUVB49Qfv72ufkYj+6xgDPcsQoBm8vTfqL4uw1BXq9LOWFsAxpqL6RnoK0Ic\nklSaXz9axqCzoiVWPawVq6athdWq4mYFRAGgx2lXRLavG+zA0W798TA/fsUnSxaXKPaBa8+9gvWa\nSYZSFeoHTIfbpB3u0e8DWCMlr8sOl92C425nDX1bNIrn7EKpJ2ikvHessL9LNg2sXalvn8w/WssM\nXQgAl2ro1JzcoupMelJmjHyebpOKUX/+i1+gQhzFvPp1YH1WPQ73OPX1miwVDbrFbMJxtwMdrVa4\nnYVPMeVm3OUyQvxeF1a2kthKZgrWL21uI5HOFRSbhSIi0tk8ZlcTBet1A6KXvq2OIfAIlXADgOkn\n1BqE2WfpTxE+j1MRm2bdLMuNp2IwlsUliicH2nNPd72mKvSQB0QBbtD3NKxvi1/u3f3OGwdwn8b1\nUhUhQB9B7U5g/D7g2F3UkNbK8B30ojl2V2F/l7VpqnxUjxuHEDkwWkOmy9OfBr7xKyXiGGW58K/A\nw/8FWPpJ+W2uvki3ufBNOqaH/hNw7kuF26RiwDd/GXjub9S4hGec+np7fFXHcN91/XjnDf0lqaZ+\nrxNXhDiyucIbTjASg8VEMNzjKNkeKPVTq1JuLtU3HxExx8SzvS4ccztw09HO0vzvXBb4xi8Dz3yW\n3tC+9avAD+Ru2A9+FPj+H9Llh/8r8EipFvzdp3rx9uv7YTGb4OstPx6ziWCkp0L/9WhRhgvjyBka\ntxl9c+H6Hh9t9Oa/m/rWR+4Exou17A8fvLBoDyPEUogls8rj8id/5vradhANqDOb699Lf+qhYxD4\nyPN0OZ+nvTaEAK3EA+oPRHnGaUsCowiTqjhGz6iB7TXFP6zwSW+fbFs2nhJhBY3qEotLKLPCMVXQ\nowwffat+taLP60Q6l8fC+naB2EQwLGK4p61EeUo7+775aJeyXiu23NlqVTJdWMEPK2b61q/rSAmu\nz9D++MKk3Nxqgy6z+oLMNpDPUdcYMdHvX+PW+OU71WC4z6M/nlBExIjOeApgcYkeX+H6tm7g158r\n3d5iA375++rrD/1b6TaHED5D38MEjTyqlkPbt6WZmEzUV6nIy5H6y6vd4zR3WM/FUUw+X1hEYgSt\nsS6Hrlxe0fbaBlFKrjQL1k1Qt1O29ta2aqZLYSCR5qyXBr6HuqlRLJmhh0X0OGzodthoMZPXgZAg\nFohnl0Ur68bGuT6j6nbGBWDpHL2RZrdpVk8ZlCZiReMxVDvB4hJWnXYAHMNwg76HMVRdV47NBXoB\n7kQal2dcrTztGgasdXYurCUwurmgpqYZ9buXM9AF22iMvrI8VZgfz9wBsWVanAWoTz6ecer7XQ0Z\nOyYNernl6Wwec7LfuxizieC421Fi0ENCocH0eZwIhWMIRkRFPLssbMyZODD9OF2W8kVKU5q4RYX/\nZaXxVO0IyuISnIbgBn0PE4zE4GqxwFNFzFgXZSa5QwZ9c4H6phu5CI32WwdKUyWrkdwEYkvV98/2\ntbkALL5El1ObQGyldBsAuPwg0H4EsMsGShlD7VWvrhYr+tpbCkr1Z5nfu0xGCBXNUGfAkiQhGI4V\nGHR/rwtLm0m8srBhLFWQcek71Zcr/C+ddgv6O/THU3GGro1LcBqCG/Q9TDBMU87qEjPWZrg0G2bE\n12cbuwg7hkorT8vBZsn9NxrrAcPcM/2nqS84rVPByJpB9Z+mrzfm1OVo0Q2ErV+fKRxzj4/6futs\nY+DvLcobD1d2s/m9Tlxd38Z2mhYJCbEUtpLZgqc45mKZX0tUL+aJFo2t93o6nvUZWo1pbaPLzj6a\n811FvcpXnAdfZTzK52rjEpy64QZ9DzMtNNAZLxoAHF4aVGo22guvkYuQ+eONGENhko7n6O264hi6\n2wPAyfsBSLSNcDHM1XNSI53HltkxZbbpjct/N+35DhSO2dpKe4vU2WjM56XNu/Ky8k81v7dPFseY\nFgobYvk0Lo3iFgNlYXGW4Ttojx+A3jBZt0zvRKFryTNe9Wmq1vEA0AhT7MDk45DBDfoeZT2eRlRM\n1699uZOd51j+NdD4Z2jFCiohTKlFJDriGKXbT1ID7L9HfX8xzKCP3Ut7iADAyF1AiyY/njUfKyjO\nKjI8DTQa83mdSKRzWNqkTaaCkRiGutrQYtX3exenLiopixojzsSq2f7Loo2zKIU6RTULxVXC0amK\n/Xf8XlfJeKr78ZkwBTfojcIN+h6FBZZ8tTRSYj1FmEL6Tj3CsvxroPGL0DNOld1TFeTVtAIHSi91\nHQOaSdIUO4COv8dHj4+Y9WeWwiS9MbnH1PF4xlSJPKCw+Vg5FRzPGDX8RvPjNbAbNjPQoSoZIcM9\ntMGVdntXiwVeTZxFK1Zd0aCXU/jRXZZvpqktGhwuN57ewhsOrVQ1EBDtGFLjEpy64QZ9j6L4Ho1K\nhW3MA386Alz5IQ3opTZ3NsjUex3QeVTN3a4XI5kuyngmCsUxtEgS8Le3A0/9T/XvnnGar9wzWsag\nB6ghN1uBvuuAjqN0du7WaFYKk3J+9CgdMzGX3sQ8E9QHzCpJa0CbW57N5XElGq+Y1WSzmDDS06YE\nRpnuaHGc5UR/OwY7W9FeSTxbq8HZex1d9p6gAt8A0HuK+tQB+vdy/3vteDyl46mesjjJZ+dNghcW\n7VGCkRharWbjYsZLL9MCkYXnadoZsLMG/Z4/oZkkjaLNEhm8RX+bqOaR3NEDtPWU+qzjAs0HX/gx\nDYBuzAOn36++T++GIQSo0QKAuz+hjsczAbz8v4H4KjU23ccBix147a8Cx99QGpfQZuu4iwpjqtDt\nsKHHYUMwLGJhfRtpA/3K/V4XpjSiJ2/WUf/57+84ga3tTMn6AqIBKsTc1k0l29hN2jVAqy97T9L/\nxYceAoZeq5EOnCqt3JTpctjgdtYwHlZfMHJn5WPlGILP0PcoVFDXYVzMWJtzXaz8shO4epsTxOo6\nRv3XFXPFi8rC9XzW2gKZ1SLRDc8EsDpNe88wWDMotk/teJSnhkCh68rm0L/psNllnYHRUa9TKQQC\nqheS+bxUHCMSSyIqpnW397paCgKluggBdWwWO3D0tXTZbKGBUoAGrkdeT1s1ODxAa1fVwOiop4bx\nbM7Lfnw+Q28G3KDvUQz5HrUUF8i0dBbqfu5VzJbq/VCEAHWFsPG45R4w2uAcG//WVTWfXLkBjNOe\nM2tX1O3XpvWbQQGqcVm5QLer5g6wu2huer2pi14nguGY4kapOkPvpeIY378Ukd9fh+9ZibPUcNMn\nRA2MVjk+w+Mp1rnlNAQ36HuQWDKD5c1kfVJzq0GqteiZKOwfvZeplg7HZpJsPJ4J2nNEK46hNTKX\nH5RFN0bV/QOFn6H1HxfTfoSq4Ew9DOSzxoyNZ6zqzLUcfq8TW8ksnpteRV97C1yV/N5QUwAfvkCD\nk3WltrK4RK1Pce7q4/R7XQXjMeTH5z70psAN+h5kWqDZKoYv1HyOGvLWbiCbpB0E99MjrGeCFvVk\ntvX/zgKcyvZlDHSr7NueeUr2e8vtanv8AEhptaleMyhAzY+feUr+PAP/S88E9QVXy4/XgblGnpte\nNaRGxcQxnpterS3OoqXSDa0SngkgsQrEo2U3Yeftc9Or1c/hnayXOIRwg74HYc2NDPdw2ZijhvyE\nrKBjdFa5V/CMle+HEl8FEtHCmSQzQtpZuTBFpcjMNnn8mu1tbTTYV1z92VmhD41ngu4HMDZ7dI/R\nXjObC9W3LYIZ8Wy1EnmZVhsVx8jmpdriLFqUdMxaDTpTmirvXmLnraHx7GS9xCGEG/Q9SEgQYTOb\ncLSSQroW5oc8oal43E+Njirlluv1yXb1A/Z2dZa5vQ6IK7RvtpJPrqN8UzxDr3TTY4ar4ygNhjYy\nhiow8RLA+FOZIlhhNK21GGFSjkv01vY+A6mLHpcdrhYD49HWF3CaAjfoe5BQWMQxtwMWs8Gvh11c\nR26lPTeA/XWRVOqHUtyuFqC+dBYYBQoDa9WKf/I5TTOoCjNvbUDVCMpTQ+0GnRCiFJAZDXCyWXDV\nXi3lKI5LGKV9ELA5K964CCHq8VUy6LEVWqi0n54m9zjcoO9BQoJYvUL03JeBV75Kl4UANeStndRI\nWR1Ax5GdP9BmYbHT9EV2Y7r4LSoFB9CxWR00UKlFO+NWZvHj5SXLPBO0p/f6rLFmUGw/Rg16WzdN\n62NjOPdl4NxXSrebehT40V+VrGYz7ZIZ7eo08NDvlFShjsrbVeyRUgkhUF8gkt1Mq9y4ykreacdT\nrx+fUxZeWLTHSGZymF9L4KdPD1be8OnP0LL1G/89vbjYRXHmF2k/kv2S4cLQpsP96K+ArSXg1l+S\nxzZWKv7rGQfO/QsVxxACgKWF+slPvZvGFLwnS/cP0M9g7QEqGZLuY8DN/xG47j21jYE9LTzzWfrU\ncfp9hds8/3fAwgvA7R8p+I7ec8sROOwWRXRZ4cI3gBf/AbjlQ2oFJ4A3jnvwjhv6cftoj/HjY7C4\nRL0zY88EcOXJipv8zM1H0GazoMdZ1Pr5wjfpeG7+4O7USxwyuEHfYxhSSM+maE41MdFiGSGgVkWe\nevfuHGiz8YwBwUfV8aRjtHJTCOhXEWoDo0JAVnw30w6B7/670u1ZYy1hUjXolWaoJjNw//+qbQzu\nMeD8v9LvZ3WaGuxchrYWYAgBIC3S5mKap6jbjvfgtuM6xllbX6Ax6F5XC/76/TfXdnwM7RNNPXjG\ngFe+TL+flg7dTQyNZz/VS+wTuMtlj2FMIV0WZ85ngLlnqYHY74+tLKtk7llqzAFaILS1WKb4R5O6\naETtpqWDlrQLAfqjFalo5hhSm8Dcj+TvJ1tYzJTcUrtEGlZd0uiiNotGXR1KYNSA0lTJZ2vGU68f\nn1MWbtD3GKGICBNBgchuCVr/5WVZTWa/B5bYbPmyRh3n8oP0t57h6ThKxaqXXqbl44aLfwKqG6fZ\neHTGoA0eRjU92Y0Yw3yudh1VI5SLSxilFqUpLaxeApDbKuzQ93CI4QZ9j0EV0h2wW6r1j5ZnNczo\n7Xc/pGLQ5fEQk8ag6xhrVvwz+ZC8jYHxs0BqNLgzN0C2z8sPQvl+ClIlZQNITMaM4fosDeQ2oIik\ni+KiqvPy7xymveZrzehh9RLEBMz/uDE/PkcXbtD3GMGIqGQwlIWJM3cM0Q54rd2Aw707B7hT2J2a\n8XQBnhN02WyjBkQPz7jaAdCIQWfiGJnEzpSaO3upaycu0ABtx1Ch4Y4G6HgGzxgTxmbbDL+O9pTJ\nVemeaJRqOfjVMJkL00YNf65mPOx72+8TkT1GQwadEDJLCDlPCDlHCDnbrIM6rGRyecxW6YcNQO0A\nqBUfOAh+SD1hhR4/beBVaXuThZb6V91/k6TzykGIJt1RHkNxdWqPj7bsjVyuqPxDt5dvBifuL/XH\n10tyi4pnN+rq8NRj0DXjUfbDDXozacYM/U2SJJ2WJOlME/Z1qJlbjVcvl85lqR9Sm3N9UC4KbTGP\nkcIetg0TqTC6/2r7bYQSybagRkVJo7qU3FBnqeUQpmhV7NBr5NdNCIxGm9Td0DMhi2/Hjb9HCBSO\nx+bcX/US+wDuctlDMJWikmrBfB5YfoUub8xRIQutbNhBeWxlbhD3uDqDrGR4yxURlYOJYzBRh52g\nWLItm6SGj4lNa8dWbYbLlHyUlMsqbhpRADavlq5PbtLMKLZPoAkGfRyApAZtVy5UdwlFA4XjcfsP\nxpPlHqJRgy4B+B4h5CVCyIf1NiCEfJgQcpYQclYQqsxIDjksZXHUW5ThculbwOfuoheP9oIcvAUA\nAY4ckIcj7Xj6T9MWuIMVxtZ9jMYPahn/kVvpz05x5FYABBi4ubC/y2oIiuiGgX4okCQ6m/ZM0F4y\nnREcLIUAABi/SURBVEerz9Af/Cjw1feXrn/iE8AX7lZ7p1SKSxiF3UyjU8DmIvC5O2l1bDm0Orc2\nB1VHqvTdcuqi0cKi10mStEQI8QJ4jBAyKUnSU9oNJEn6PIDPA8CZM2eqOA0PN8GIiMHOVrTZir6W\n5Vfp75XztGwdoLOblnbgd0P7PyDK6LuucDz/eary2MxW4Dd/AthqyCd/7wONHWM1jt6mjmF7na4T\nJmmtAEANmqufHnOlwOjWYmF9gWeielbJyqu0P0ouWxh3WHmVZpTElmU/foW4hFG6j9PYBSsOkvL0\n/Cw7niVaX8CeTn7hYXpj4TSVhmbokiQtyb8jAL4F4DXNOKjDSjAi6leIKj1Lpugsp31QFWc+KMac\noR2PkbG1dtVmnGwOY90TG4Edd2sXzXyJTqFAbJoQVBf1KCr+cY8V+uOLSYm0dW8+o970AXlmrKnO\nbFYOvsVGjTrbp/aY9Sh29bS0A9aWxo+DU0DdBp0Q4iCEuNgygLsBXGjWgR02cnkJVwRRvx2q9oLh\nCun7C2a4hYAqNq2sryS7VxS89EzI/vg5/e0LesNr9huPqk8KSy8D63PNy/BhY2DGutITBzumgxLv\n2aM0MkPvBfAMIeQVAC8AeEiSpEeac1iHj6vrCaSy+dIZeiZJg2kAEJlU/aqc/QFr2CVMlmbZiGHV\n2BbDFJjYbF+pzixjNPUKmIqXJx9CgXh2o3gmaColc7VUGk80cDDqJfY4dRt0SZKuSJJ0o/xzSpKk\nTzTzwA4bag+XIn/waoj6JzuOAsJlWhTDy6X3D+4x6juOThU+WVXrh1Jc/MPeW86tEQ1Qn7azr3Cm\nzJ7uOo4Ci3KpSLNmyW5ZfHv5Fbp/oPp4eFbLjsLTFvcIwXJNudgFfFJbjMFn6PuGcsVMlQw083tr\nZ9KtnTSYWs5Noy1aKpihB2i+9+gb6Wtipn78ZqA9PnZ+VhwPn4jsNNyg7xGCYRFelx0drUUFMtEp\nGkybeIe6jhv0/UOBuLXGoHXKzcX0/M5xgRYeFbtGKglLKEVL43SWzMSqtcVMAE31ZH78RnHL4tsA\n4HtLhfHIfnx+3u443KDvEUKCqF8hKkwCXSNqL+w2N1dI3084PDTbBSh0uZjMgNunP6NVZPf0dFGn\nSlsGZJI0s4UVm2W3VbFq1lq4nDRfI1hbaU8hgAqKuP1lxiOv48H8HYcb9D2AJEmYjoj6PVyY79Hu\nou1OD0qZ/2GBEPr96YlNaxWOtCgGsNigy/74raXC9SzOUlC0FAC2N6h4tnZ9s42qZwKwy2LTxULc\nDD2hb86OwBWL9gArW0mIqSx8xYK/uQwt2R67l76+70/V2R5n//Dm36dNsYrxjAPnv05zyO2am3l0\nihYetQ8Uba+pMO3QSBRqFYjaB9V1rZ3q+9oHgXv/FJh4e3PGxLjrd2lrA0LoDef810rHIwT0x8Np\nOtyg7wFYD5eSHPS1IjHjE+/c5SPjNIWR1+uv15bPD2rk5FhAtDgjRDv79r1Fs31ALlryUTeIw6tW\ncALU0BIC3PZrzRmPliNn1NYLWt3WkvGM8QyXXYC7XPYALMOlJAddmXlx3+OBRGsAtbBAZjEON83l\nLg6MCgEaZ7G2yvvVFPxYWhrv22KUsuPhtRO7BTfoe4BQRERnmxU9xYrvPJh0sOk+pvZDYWyv0wKd\ncrESPT91saYqy3RhfVtMFdSvmknXMcBkLRqP7Mfn5/CuwA36HiAUicHvdYIUP5IKAap602wxY87e\nwGylbhJtYJQtlyv+8YxRg8kyXXJZGhTV3gDc41Ssev7HuxtEN1vk8Wh1VJvUf51jCG7QrzGSJCEY\nEUsrRAF55sVnNgca91ipTB1QeYa+vU5zuwGarpjPFOW7y8vp2O4b0mIlI6UpFz+PdwNu0K8xq/E0\nNhKZ0hz0fH7nxIw5ewfPBDXKmSR9LQRogU7n0TLbs54uk4W/9Qw6sPuGVHc8u+jHP+Rwg36NUVWK\nigz65jwtEOEzm4ONZ5zmkK8xRaEALTgq5/dWMmMC6vZA4ZMcE6sGdn9C4B7TGc8u+vEPOdyg18nF\nZx/CQvCVhvcTEsr1cOHFGIeCkhl3oPJ33j5Ac7oFjUFvP1IYZ2HFTEbFs5tJsRpTccCWs6Nwg14H\nUj6Pgcd+DcK3f7/hfYXCMThsZvR3FDX75xkuh4MeH80hF6ZkkYr5ygaQFfAoBn1S39/ueysw+hZj\n4tnNRBlPgApIb87zSckuwguL6mBNWEIPtrCVmKm+cRVCgghfr0snw2WKFojwvi0HG2sr9S8Lk8Cq\nLLhcLTPFMwGEHlfjLHqFS2/4L80/ViNYW2hOvBDQZLjwScluwWfodbASoq6WgdwSMulUQ/sKhsuo\nFJWbeXEOHiy33KibzTNOc7vD5+U4yx47T2odD6dpcINeB+LiRQCAleSwdOVi3fvZ3M4gEkuVVogq\niu977ELl7AyeMZpLHr4o+72PVd6euWQuP1j4eq/gLh7PLvvxDzHcoNdDRM0bXp19te7dKCpFxTP0\n2DKQ2uIzm8OCZ4Lmkk89Qn3Q1fze7EZ/6duFr/cK2vF0j+6+H/8Qww16HThi05gx0bza1PLluvcT\nisQA6PRwKdcPm3MwYd+z0acyrTjGXoyz1DoeTtPgBr0OelNziLafxDI8sK4F695PKCLCbjHhSFdb\n4R+4QvrhQpvJZOQ7Z+IYwN40mAXaqXvw+A4w3KDXyOaaAA/WkesZQ6RlBF2JK3XvKxgRcdzjhNlU\nnOEitz51ehs8Ws6+gImXAMYNIHPH7UWDaXfSHkQAdxvuMtyg18hy6BwAoGXgJLY7fBjMXkUum61r\nX8FwGZUi9qjK+0cfHlhqn1EDzWbye/Upjs3SeR3FrnKgDforn3ornv+rXwQAnP30z+DsZ94LAHj+\nf30Q5/4HVQF67nO/gYt/QvN4n/vi72H6j26i2/yfT2Hx42PI53IF+9xaoFktnmM3wuSdQAvJYGW+\njHBvBRLxGP7v9odwH54t/SNPWTx8eE/SjJAen7Hte0/K7zuxc8fUCL3yeNz+a30kh4oDW1iUz+Uw\ntv0KVtIRAMBI7CXkQPtJ9K+/iO7cGqR8Hj3Cj3E8E0I6lYRz6TmM5q5gcz0K68KzGJTCWL4aQv+w\nalzzkUkkJSv6jvoRW10EzgPCzHkMHj9V0/EtBl+Bn2ziVLooSyYeBRKr/FH1sPH63wbG71NFKqox\ndi/wc18qr4Z0rXndb9FjNDoeTlM4sDP0lYUQWkkag7lFrEUW4cYGerGKjegKBnLLcJJtRJZmMJBZ\ngIXksXzlIrypOQDUrdKdmAUACFfOF+y3dTOERcsQzBYL+n2nAQDJxdpz0Tfn6X49qdnCP/CA6OHE\n4a7NOJvMVJJwr7rlah0PpykcWIMuXKHVnDaSRejZbyjrp57+GiwkDwCYe/EhOMk2ACBy+Rn0YhUA\nsDnzMgZyiwCAxFKhsfYmZ7HuoIUSHV1uCOiCuY5Ml8wKzWVv2QgVHbhOO1QOh8MxwIE16NsaQ2yf\n+reqy7bgQ8pyy8xjsBHqOzdp9BvjsQ30Q0CmS/Vzhu3D6BCnaz6+lg16EyCJVVWsAKABUasD6DhS\n8z45HM7h5sAadFN0Clug+d0nEi8hKVmRliw4kXgJeYlAlFpxIvESAGALjrLL7aLagGtpmrpJWgZO\nKuvirlEMZBYg5fM1HV/P9iziJjnDpVjhhSukczicOjiwBr1DvIIFmw8rcMNGsrhqOYpF8yBsJItl\nkxcLtmOwkSzW4cJMy0nYSBYpyYqQ8wxshKYhTrXfgYHMnGKsN+aoQe8evl79IO+E4o83SiqZwEB+\nGbM9d9EVWgkyYYr7zzkcTl0cSIMu5fPoz85DbPch0jICANhwHMNaG216JLQcQ8w1CgBYtg5ju5Pm\nyi6aB5HqoWlgy/Ag238z2hHHauQqACAbvoyMZMaAJqPFOUiXI9PGxS6WrlyEheSxffSNgM2pthlN\nbgKxJe4/53A4dXEgDXp0ZR7tSADuMSTaqeHOdPuR7qI5scmOUeR7qBGPuY7D7KUGdN1xDPZ+atCF\nlhE4ZGO9woqJNkJYNA/AarMrn9XnuxEAEF+8ZPj41mbpTL9r+Hqap6uou3CFdA6HUz/7wqC/8I0/\nxwt/8fMVt1meC+C5f/ht5HM5hOXZsuPIKZi81Dja+0/BJhtrU+8JtMnGWnKPw3X0OgBAumsMPSM3\nAAASHb4SY+3ensVaa2Fr027PADbgBImWFhe98sTXcPbBz5WsTy9fRl4iGPTdIPeOlg15NcV3DofD\nqcC+MOi51WmcXnu4opjE7BMP4ParD2Au8BOIV2mGS9/xG3H0NT+FV1tuwfFb3oaRW+7Bqy23YOQ1\n78TI6Tfi1ZZbMfiad2Hk5GtxrvU2eG/9GQyOXoefOO5C5y3vgbvvKGJSKyAEFL83m+UziMmEZesw\nXLHSni4tP/o0jrz0ZyXrbetTWDZ50dLmpKXRsSXqbhEmAbOdK6RzOJy62BeVopbeE7At5TA3cxnD\n46d1t7Gu03zutdkLINEAtuBAT98QiMmEvo89oWzXo1m+4WPfV5ZP/9dHleWbf/dBZXnJOgzn1jSW\nps/jGJFg6St1h2y5RjG+9gSkfB7ERO+RzI/fjgTisQ04XJ3K9l2JWQgtxzAIqO6VaJDO1Ht8gHlf\nfC0cDmePsS9m6J2yS2RttnzgsStOZ8jplUtwxqaxZB1WjGsjbDqPozc9p/F731CyjeQeQydErAlL\nyjrFjw9gKaSW92czaRzJXUWyg/r2C1TfeQ8XDofTAPvCoA/4qBFNlhGTyGWzGMwuAABsa1PoT89h\ny1lFxssgefcY3NhAdvY55CSCwdHrSrZRgqfTquFmuqMAsDF/QVlenr0MG8nC1Cs3VeoaoW6WpXPA\nBldI53A49bMvDLrD1YmVCmISK/NBtJAM8hLBkPgqurGFfJNyuVsHqLE+JjyBZVMv9XsX4R2lwVPx\nqmq443J/l7xEkA2rNyJhhs70O1kuu8lMM10mHwIgcYV0DodTN/vCoANApGUEnXH94h1hhs6GA7aT\n8GINANA2UFv3w3J4jlNj7cUaoq36s37vwDGIcvCUQaIBbMKBBfORgn4tqWWaMdM/qnHdeMZpYBTg\nM3QOh1M3DRl0Qsi9hJAAISRECPlYsw5Kj0THKAazCyX9yQG12+HmyL3KOs/x60u2q4e+IR8SEs07\n32Z+7yKIyYQl6xAcW6rhdsWmsWwdxmrbMbi3Z5X1lrUgwuiBq0OjA8meJoiZiupyOBxOHdRt0Akh\nZgB/DeA+ACcBvI8QcrLyu+rH5J1AK0ljZb7U7WJeC0JAF7rGabvOhGRH7xGDQgHVPtdsxpKFNsqy\n9JYXE9h0HEev3H4XAPrSc9hyHke604+B/DKS23EAQKd4BRF7UVoiC4R2HwcstqYcN4fDOXw0MkN/\nDYCQJElXJElKA/gqgHc157BKaR+iwUhhhlZtRhZnkErSLJIOcRph+zAG/DSlcdEyBJPZ3LTP3nBQ\nV0vH0fKz/lzPGDxYx+Z6FOvCsuzHH4Ol/wTMRMLylQvI53IYzC4g3lF0s2EGnWe4cDicBmjEoA8C\nWNC8viqv2xGYmMT24iWkU0m0fv52/OT//DGkfB4DmQXEXaNwdXRjgQxgrbM5/nNGtu80tiWbkm2j\nR4uc6bIcOodluVK1beAUuuSbwNrseawshNBGUiDFfvLuUcDeDgzo59hzOByOERqpYNHr7yqVbETI\nhwF8GACOHj1a94d1dHsQRSdMq0EsXbmAEbINe+RVRJZm0Eu2AbnEv/VXH8WpNlfdn6PHze/5Xayu\n/Cz627vKbuM5dj3wNBBbuIh8LgOAZr90uvuRkwjSK5MQ2jowAMA1VHTDsdiAX38OaHM39bg5HM7h\nohGDfhXAkOb1EQBLxRtJkvR5AJ8HgDNnzpQY/FoI26iYxOrMeYwA6NmeQWT6FfRC7Xro7qv/plEO\nm72lQFdUj76j40hKVuTCl4F8Vvbjj4KYTLhq6oN9fQrbizTlccCnMxPnghYcDqdBGnG5vAjATwg5\nRgixAfj3AL7TnMPSR2wfxUBmHukVmvo3kFtGfJ761FkjrWuF2WLBouUIWrem4diaxqL1qFKpGm0d\nQdf/397dx1Z113Ecf3/aUgi0tCttGW1xUMa2wD+D1IVkD85oHJA5fEgMxkQSTRYXiRI1EUNi+Gd/\nTKN/LDEuWySbZk+aSeQPl02N0WSRaUGeJrACqxMoFMEJZjge9t0f53fZaXNv4dLe3zn38H0lzT39\ncZr7yfec++U83vPuMA2n3+QMs2nvvDnTrM65Yrruhm5ml4D1wCvAfuCXZlb905Kr0XUHrTpP+8hr\nAEzTZdre/j3v0EJHV09N3/pa/GdmP13/H2bue8NXTqQCnG9bTO/lo7SfG2Kk2b94yzlXG5O6Dt3M\nfmtmt5nZIjN7dKpCVTKrL7kq8vYL/2CUjivTI1P0vS2TdbFjMT02SjdnuNTx4R2fTXPvoFmXufXi\nEP9r9evMnXO1kX0XrMLNi5Jjzw0y3uq8n/dNNMg419qfcbJE6eEYADNS023hy8UaZJg/Xs45VyN1\n1dDndPfyDsmJRfUu40RDN8CUfW/LZJUejgHQ2f/hMf305Y4tfVN7SaVzzpXUVUNPHiaRXMUye/5S\nTs1IjkfP7KnZDapV6elfykVr5II1jbkqpmX2TZwguSRx7qJsT94654qrrho6cOXhzj233sn5tuTp\nQd05aZLTmqdzvLGHY419NE0bewv/6IwFnGVmTS6rdM45qJMnFqV1fOwRtu/pZ0X7HOZ9/GH+8loL\nK3rzcQwd4PRHv132BG3D3d/gwOgR7srByVvnXDHJbFL3+lRlYGDABgcHo72fc84VgaQdZjZwtfl8\nc9E55wrCG7pzzhWEN3TnnCsIb+jOOVcQ3tCdc64gvKE751xBeEN3zrmC8IbunHMFEfXGIkmngH9e\n5593Av+ewjhTJa+5IL/ZPFd18poL8putaLluMbOuq80UtaFPhqTBa7lTKra85oL8ZvNc1clrLshv\nths1lx9ycc65gvCG7pxzBVFPDf3JrANUkNdckN9snqs6ec0F+c12Q+aqm2PozjnnJlZPW+jOOecm\nUBcNXdJKSQclHZK0McMc8yX9UdJ+SW9I+mYY3yzpmKRd4Wd1BtmGJe0N7z8Yxjok/U7SUHi9KXKm\n21M12SXprKQNWdVL0hZJo5L2pcbK1kiJx8M6t0fS8si5fijpQHjvrZLaw/gCSedTtXsicq6Ky07S\n90K9Dkp6IHKuF1OZhiXtCuMx61WpP8Rbx8ws1z9AI3AY6Aeagd3AkoyyzAOWh+lW4E1gCbAZ+E7G\ndRoGOseN/QDYGKY3Ao9lvBxPALdkVS/gPmA5sO9qNQJWAy8DAlYAr0fO9SmgKUw/lsq1ID1fBvUq\nu+zC52A3MB1YGD6zjbFyjfv3HwHfz6BelfpDtHWsHrbQ7wIOmdkRM7sAvACsySKImY2Y2c4wfQ7Y\nD/RmkeUarQGeCdPPAJ/JMMsngMNmdr03lk2amf0ZODNuuFKN1gA/t8R2oF3SvFi5zOxVM7sUft0O\n9NXivavNNYE1wAtm9p6ZvQUcIvnsRs0lScAXgOdr8d4TmaA/RFvH6qGh9wL/Sv1+lBw0UUkLgGXA\n62Fofdht2hL70EZgwKuSdkh6OIzNNbMRSFY2oDuDXCVrGfshy7peJZVqlKf17iskW3IlCyX9XdKf\nJN2bQZ5yyy4v9boXOGlmQ6mx6PUa1x+irWP10NBVZizTS3MktQAvARvM7CzwU2ARcCcwQrLLF9vd\nZrYcWAV8XdJ9GWQoS1Iz8BDwqzCUh3pdTS7WO0mbgEvAs2FoBPiImS0DvgU8J2l2xEiVll0u6gV8\nkbEbDtHrVaY/VJy1zNikalYPDf0oMD/1ex9wPKMsSJpGsrCeNbNfA5jZSTO7bGbvA09Ro13NiZjZ\n8fA6CmwNGU6WduHC62jsXMEqYKeZnQwZM69XSqUaZb7eSVoHPAh8ycJB13BI43SY3kFyrPq2WJkm\nWHZ5qFcT8DngxdJY7HqV6w9EXMfqoaH/DVgsaWHY0lsLbMsiSDg+9zNgv5n9ODWePu71WWDf+L+t\nca5ZklpL0yQn1PaR1GldmG0d8JuYuVLGbDVlXa9xKtVoG/DlcCXCCuC/pd3mGCStBL4LPGRm76bG\nuyQ1hul+YDFwJGKuSstuG7BW0nRJC0Ouv8bKFXwSOGBmR0sDMetVqT8Qcx2LcfZ3Cs4eryY5Y3wY\n2JRhjntIdon2ALvCz2rgF8DeML4NmBc5Vz/JFQa7gTdKNQLmAH8AhsJrRwY1mwmcBtpSY5nUi+Q/\nlRHgIsnW0Vcr1Yhkd/gnYZ3bCwxEznWI5PhqaT17Isz7+bCMdwM7gU9HzlVx2QGbQr0OAqti5grj\nTwNfGzdvzHpV6g/R1jG/U9Q55wqiHg65OOecuwbe0J1zriC8oTvnXEF4Q3fOuYLwhu6ccwXhDd05\n5wrCG7pzzhWEN3TnnCuIDwDh5oeYs3pKxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b6032240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xrand = numpy.array([1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1,\n",
    "       1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,\n",
    "       0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1,\n",
    "       1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0,\n",
    "       1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0,\n",
    "       0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0,\n",
    "       1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,\n",
    "       1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1,\n",
    "       1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0])\n",
    "Xhumanrand = numpy.array([1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1,\n",
    "       1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1,\n",
    "       0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1,\n",
    "       1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0,\n",
    "       1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0,\n",
    "       0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0,\n",
    "       1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,\n",
    "       1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1,\n",
    "       1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0])\n",
    "pylab.plot(numpy.cumsum(2*Xrand-1))\n",
    "pylab.plot(numpy.cumsum(2*Xhumanrand-1))\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The phenomenon can be understood when one looks at distributions of longest runs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b5b3bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.96\n"
     ]
    }
   ],
   "source": [
    "def longestrun(walk):\n",
    "    y = 1\n",
    "    for i in range(2,4*int(numpy.log(len(walk))//1)):\n",
    "        for n in range(len(walk)-i):\n",
    "            if abs(walk[n+i]-walk[n])==i:\n",
    "                y = i\n",
    "                break\n",
    "    return y\n",
    "\n",
    "def longestrunhistogram(W,N):\n",
    "    z = []\n",
    "    for i in range(W):\n",
    "        helper = numpy.random.binomial(1,0.5,N)\n",
    "        walk = numpy.cumsum(2*helper-1)\n",
    "        z = z+[longestrun(walk)]\n",
    "    pylab.hist(numpy.array(z),bins=3*(max(z)-min(z)),normed=1)\n",
    "    pylab.show()\n",
    "    print(numpy.mean(z))\n",
    "longestrunhistogram(400,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4deD2i2PjWrthXcIYH3uXdLl35+o+CJypqvcMjA+e+/o14IHFf3YzJHlGkssvXmbhh28P\n8OSPe7gB+Otx5BvwpCOnrbJ+A5Zar2ngd7rfXHgJ8LWLL6E3S5LrgLcD+6vqGwPjE1n4vxRI8nxg\nN3BuM7N1t73UfTkNHMzCf9Szq8v3r5udD7gW+EJ1H1oI41m7pbqEcT72NvMnylvtC/hZFl4K3Qec\n6r5eCXwYuL8bnwauHFO+57PwGwmfA04DN3bjzwU+DTzYfX/OGNfw+4HHgWcNjI1t/Vh4knkE+DYL\nR0evX2q9WHhpfIyFI7v7gakxZJtl4dzrxcff+7q5r+7u888B9wK/Oqa1W/K+BG7s1u4ssG+zs3Xj\nfwa8cdHccazdUl0ytsee71CVpAZd0qdlJKlVlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUu\nSQ36P0+10HHQLdmRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b79bcdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "146.145\n"
     ]
    }
   ],
   "source": [
    "def hittingtime(level,walk):\n",
    "    y = len(walk)+1\n",
    "    for i in range(len(walk)):\n",
    "        if walk[i]==level:\n",
    "            y = i\n",
    "            break\n",
    "    return y\n",
    "\n",
    "def hittingtimehistogram(level,W,N):\n",
    "    z = []\n",
    "    for i in range(W):\n",
    "        helper = numpy.random.binomial(1,0.5,N)\n",
    "        walk = numpy.cumsum(2*helper-1)\n",
    "        z = z+[hittingtime(level,walk)+1]\n",
    "    pylab.hist(numpy.array(z),bins=max(z)-min(z)+1,normed=1)\n",
    "    pylab.show()\n",
    "    print(numpy.mean(z))\n",
    "hittingtimehistogram(10,4000,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7gSNV9WBVfR6Yp3dphXE2CZnfDvwWMPjkzV7g3dVzJ/DEJE9Zl3RLVNXXB4aP5/9zj21m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\nL+sCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b7a13080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.02472\n",
      "89.5638689216\n",
      "90.6864\n"
     ]
    }
   ],
   "source": [
    "def stoppedrandomwalk(level,walk):\n",
    "    for i in range(hittingtime(level,walk)+1,len(walk)):\n",
    "        walk[i]=walk[hittingtime(level,walk)]\n",
    "    return walk\n",
    "\n",
    "def stoppedrandomwalkhistogram(level,W,N):\n",
    "    z=[]\n",
    "    T=[]\n",
    "    for i in range(W):\n",
    "        helper = numpy.random.binomial(1,0.5,N)\n",
    "        walk = numpy.cumsum(2*helper-1)\n",
    "        z = z + [stoppedrandomwalk(level,walk)[-1]]\n",
    "        T = T + [hittingtime(level,walk)+1]\n",
    "    pylab.hist(numpy.array(z),bins=max(z)-min(z)+1,normed=1)\n",
    "    pylab.show()\n",
    "    print(numpy.mean(z))\n",
    "    print(numpy.var(z))\n",
    "    print(numpy.mean(T))\n",
    "    \n",
    "stoppedrandomwalkhistogram(5,50000,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jiMPKTCJJVzCCoih8d9TLVGxlTv/5SR/u8Mp1hd/wLtDuD72XS07fdD+Sb+OJ\nHEv654lYnP81NoOiKHT4w8wnpUw6JwOwQSpt48kkrY4aftTdRUWlGmzk/PPUGcZRxCQ1yTDNezYj\nKBpu9PYRCASYnJxcEZikpMzYDTW4FrsqGLUXUO7zotfrKTQF6AvmImv0atBv+hKYcrDPxMieT9CU\nv/wLtdtiImbScGnaz7dHpkk25OAosnC4Lp9ALMlVzzzPXevj25/9Mu3NO7EcPAiKQujMWTWvL0lY\nDhxgwr1AMi5T3uigrN6OKAqMdPvw+Xy88sortLW13fF6HiSL6ZxmaxZHc61MxhP0hqL8r7EZvuke\n4+JCiK1bt1JQUEB9ff269eNODHe242zcilavZ9tTH6Xh4DGMZgvbnnya2j37sObm3fG1W458iMKq\nWsoatlDZtIN4JMJEf+8djz+9aDHssHLErv7dW30BOoMR/kP/GH8zulx84I0n+K2eEf7fwcll++Oy\nzG/0DPOH7ve2glirz0+JQUd9lpGjDiv94RieaJz/4fHy7/tG6QlFedsXQAAOZQJ+BjZIwN9R30x2\nNMjphJF86Qb6CYiZrjN27TIoCtv6L6A36Mg25DM9P3ZH+eLkwAKJmISzwUFXMELEYKR0wcv5N15h\ns3mCeEKk43ofHPk9ePavCMeTTF2d4Sv6lVWwX6pUJ3D/oX8yPdI/4w+xryYPjShwqs/LyWhqwXBB\nj7GhAU1ODqG2NkJtbYgWC6amJka6fYhagdI6O3qTlqLqbEa6Z5f52q+3HFNRFE74Ahy0W9GKwrIg\n15pKI7T6AhQXF/P1r399mWnbw2B+apK5ifH0KP6Jz3yJp7/+OwDs+PgneeZ3v3HX11c27+DL/+XP\n0OkNlG9tQhDFu1ouLFoM77CZKTDo2GIx0erzp5cKbL0ttbI48j45F0Bakvq5tBAmKMlc9odYSNz5\niWI1krLC6Tl1wRJBEDiSMkQ74fPTOhtI9SPACZ+fZmsWDt2GsM3KcJ9siIAvajQ0hSfptRYTvXEc\n22wWkQI/g7Pj2OfmEK5dJzkzg6uiiqQQ4fy5C5jN5hV68JFuH6IoUFZvT6sfnL5pBk8fx2VWpYhn\nT51NH3/+5ixxSeZw3UrzrQ+V2dHEJF5dCBAzqfnsEz4/2SYdzc4cTveMcSVv0Wo5gKDRYN63j+CZ\nMwTPtGF+Yi+CToene5bi6hx0BvUczgYHM54gN3pVPf/c3BwXL15c9XoeFL2hKJPxRDotUGLUU282\n8tL0HFeuidr6AAAgAElEQVRSyz3eHuQeJkvXMr5fDFlmims33dFyQVEU3p71c9BuTVsMH3FYubgQ\n4tWUpUZXMMr0krTOYsD3JSQ6A5El+9X3TFLg9NzqE6534kogjD8ppwN9bZaBUoOO74/76Euljn48\nPUe7P5yprs2QZkMEfIAPZWtJaHW8niwm39ECWpCKFyhPuUGGzp6leXcjAJNTE6ta8o50z1JUnY3e\npKXV56fRbMQSlZhRsgkZsgka7Uz33JJOnuqbwagT2ela6TIoiiJVioZQKtjvsWRxfj5ESJI4VJuP\nf3qEuF7PYSHJQCTGcCSG+cABpJkZkuMTmPcfIDQfY3YsRHnjLV19RWMuCjLDI0PpEf3Y2Ni6Wgy3\nruKyeMRhpTMQQQaOpbZn4/c2Sn1QDHW0Y8svwF78YGr6KptamBocIOxf6YnkDscYiyWW5cSPOKwk\nFbgWjHAstf/EnPqeyamno6OOlP/SkhvjCV+AnbYsrJp7V/q8PetHBA6lKmfVUb6VKwH1Bnxsyd8n\nk7/PsMiGCfjPbt+LKMu8bj9IwcFfR0kI5DgmaXjqKTQOB8HTbbhqS9EqqiPg7emPsD/OjCdIeaOD\nYFLi4kKIo7k2rIqWOa2G4Zz96CsayJodJhhSv1Qn+7zsrcrFqFtdkfJUvqr11sQkfqeqiLiicG4+\nxOH6fPQ5ArpEnG9sUeWMJ3yBZZ455gMHGOlWqyfLG3LT+/PKLIjZISQpya5du7Db7atez4PkhM9P\nvdlIifHWmrTHUiNLm1bkd11FqlRz7uHLE6VkEk9XB66mlgemQlmUag53rkzrrGYxvDvbTFZKkvvr\n5QXk6bTp9M61YITZRJJPF9rZajWlb57eeILOYIQPpSbBW31+lHtQ+pzwBWixZZGzJFWz6HNfbNDx\na6k1a21akRbb2oz3Mmx8NkzAL8gtojzo5aJjK9ryXcTnirDbx6g+cgTz/v2EzpxBkWUK7WWggKt8\nuXzRsyS4ts0FSSrqlzo/z44sSszYjrB51y60SpLWkxfw+MIMzoQ4XHfnYrGv1hWDrFClaFQv/ZR0\nbmtpNtPOQjaNjrItN4cyo44TvgC6ggJ69vwWXbt/B31ZKa/+dJC4TiC31Mx/fb2X/+Mv2hBEgYSh\nFxSFCmd5OtAv9a25G52BMJUnO+gJRhgIR6k82cGlhRDj0TjVpzpXSPsWwmHOzMyzJbhc/78ntTTe\nIbuV7bYs7FpNujBrLZx7cYDn/+TiPQW51Zjo6yUeiaxI59zpetZCQVU1RquNoasr0zo/7BynMAbl\nJgMnv3+Dl/6sHb0octBuwaIR2ZVt5ojDysk5Vap5YvbWDeKYw8Zlfwh/UkoXax3NVZU+Y7EE/eHY\nmvrnSyS5Ggin0zmLHLRb0ApqW7uX/H204vrLMd/unWLrH/yE6UCUCzdn2fzNNxiefW/qowzrx4YJ\n+AB7s/RMWPMYnl/AG6vGlBUkLk9hObAfyecj2tPDgX0HyZ7bin9yuXRuuMuHyaojr8xCq89PlkZk\nd7aZD3/hs6CAP57NscNPkBQ0dL3zTrpy9tBdAn65zch/KirgO3tqMWpE9qakc6OjY4wXFpE1paYM\njjpsnJ4LEIkmmbZuwmupJRxKIExFuSEkmAnGebljnGtjCwzNhAjIfjThAINXbnDkyBG+8pWvYLGs\nzRTrlel5IrLCa94FXvMuEJEVXvbO8+asn5Ak8+Pp5SX6L1/vRtJoKexeHvyMGpHnm6v5jzWlaASB\nww4rJ1NSzXdDURT6L07hHQmwMB151+PvxmDHZQRRpHxL07L9d7qetSCKGiq2NjPUeQVlietpMJag\nRy9TMRIlFknSf3mKsRvzhP1x/ri2jH9uqkYvihx1WNP5+lafP7104BGHNZWvD3DCFyBXp2WrxZR+\nWljrzemUL4DCylRNtk7LPzdV8+8ri5f9fR4GL3dMEIglOXHDy6vXJogkJN7sfveK5QwPlw0V8D9R\npY7a/779GhMTahrE5zuNeb+aKgmdbqN6WwlGybGsYlWRFTw9PpwNDgRR4IQvwIEcC3pRpKA4F5OY\nzdjUCDabmbC9nOhQD6f6vJTmmKjKu/vj8i83lrLZoR5z1GHFHY7xvWtqJfDkgp6eCVVpEZRkftI7\nhZRUkGV480d9GBWBIa3M358dYmxeDYxvnu8kqdWhCfnpblMnn9c6uodbKYlWn//W9mwgvX3itqD9\n5sQM2kScrIsnScSW68h3ZZspTaV5jjisTMeTdIdWas1vZ34qTMCXsoq4Q+XwWhnqaKekbjOGrOV/\nhztdz1qpbN5BeGEe78hQet8b3dMktAJVEwmu/HSYWEids/B0z+I06tmRrfZhUQL5sneeS/5QOqDv\nsJmxaFQrjhO+AIcdVkRBoNxkoCbLkE73vButixJZW9aK3+23WykwqPNWS/8+64ksK5zuVwdAJ/u8\n6cLCU/0zd3tZhkfAhgr4R1xOTIk4x2cWiEat6PWlzPpOo83Lw7B5M6G2NvRGLcXV2csCjdcTIBpM\nUN6Qy2A4xnA0vixHW1JYTliaY37WT/6mbVgjM1zqGuRQXf495Y0XH8H/zmAjb2GeSSWbU/1eDtqt\naAT46dg8olZAqxfxnJ9GQWHWIvA3p1Xb4ZwsHe4rFwDQR2JM9nfe0/uzmDe2azW0+8O8sxDCrtXQ\nF47S6vNj12qYiCW4saRA6LJgoGJ6FCEaZbT7+rte29uz7z5KTVtFmLXpVNp7Ibwwz/TgwIp0TiIl\nWVztetZKRaoYa2nV7U8n5tBICtULMlff8oCwut1Fvl7HNouJ745606lBAJ0ocNBu5UdTc8wkkism\nwc/NB4ncwQ9nEVUi6+eQw4rmfVI52z3hZyYYJydLx1vdUwzNhsnJ0nHh5izRxMZfa+CDxIYK+FqN\nhkY5xkhOHo7cPPLzjzA3dw5ZjmM5cIDw1atIwSDOBgezo0FCC2rOdNFOwbnZkc5DL13ouXHbJhDg\n8tku9hzcB0BRcPiu+fvVWJTOxTRaDgR9bC62carPi02rYafNzDtSjJKaHErr7Qiygt8ksq+hgFhS\npirPzCe2FSMEphGlJKUV24kGPATvIUe9mDf+d5VFyEBCUfh3lao0NCor/K4rJRNN5Z27RseYsdo5\n4rCi1envajlQZNDRYDauSW0y0qVaRdTuLGS0bx4p8d4WixlKTareHvAv+0MEJXnF9dwLFruD/HLX\nsjz+O3Kc2jBUVecgJWQKyq1UbMnF0+NDkZc/RRzNtRGVFcypvH56v8NKNHXsYj2Dul89/sLC3eWZ\nPaEoU/Hk+0pqeSo1uv/NY7XEUrYfv/2kun1h8P6e4DI8WDZUwAf1SxTRG9HVbsJuP8gr0lH6Z9rV\nRcCTScIXLlDekEt25WluXlcD2Ej3LHlOC1k2PSd8AVwmPZVZtywKtu6qR1C09Pf1s6N5MxFLHtuU\nKfbV5DI15Kf/0spc5ezsLJcuqf718/PznD9/HoCDsurBf7TAzqG6fC4NzRGKJXnCZGLUKmJrsJNb\nZSVsHiGr3Ji+qRyqy+dAlR2jXiRLp6d+715A5tTLqp3vP18cwT1998B2whfAodPwlZJcLAIYUfhy\ncS7FBh0aAb5Q7KBKK/DKTdVk7se9anHXJzfVUNawhcF38Zg5aDVyYS6AP7Z88jGZSHDhxeeJhcMk\nExLjS6wikjGJiYF7z7MDdJ04iyHLSmFlNZ4eH8PX1aeFVl8gfT11WcZ0qmR2LEjP2buvNxz2x7ny\n0xFkWcHVvIOxGz3EoxH6pwJMmkX2Z2XhTKmmyhvVa4gEEng9y9/7xYB8wK6mBm/fv8ViSqdeAJ7I\nsWAQhVXTOhfmg7zunU9fGyy/WTwMFEXhuXNDjMyqCrXnL3ron0oVlN3wsrnYxqe3lyII4HSY+OKu\ncvRaMZ3eyfD+YMMF/M/Vq/nsmVIXw9pm/rfw83zHM0HW9mbErCyCp09jzQ9RvOsfmJz9DvFIkqmb\nfsobc4nJMmfmgyvUDzqdlhxTAV6/WgKvFJZjzDViRObci26O/10PifjyR9dTp07xyiuvMD8/z7lz\n53jjjTeYmpri470d1A8P8OGdzRyqzScuyZy/OUvdjPr6EaeBvqiHkHWIQmeQo/UFbCm18antpTgW\nBkGrJWYuxNy4CdDRdf4C0/4ov/eja3zr+PKFxJeyqAc/4rChF0V29F5m+412DKLAV0vy+FJRLjat\nhvKhXq4kBPzhMKf8EbJDfna6KnA17WBufBS/d/qObTgHe0gKAi9dWZ5qunn5Am3/9A90n35btYpI\nqFYRpfV2RI3wnvL4clLC092BoK1AEEVOfv8Grf+7F0VRaPX52WkzY9NqOOqwpq2D33l5kLef6yES\njN/xvNdOjnL2X9xMDszjampBlpJ4ujr51xvqdX+iKo+q5nzynBZqdxamg//t17DTZmZvtpmfKc5d\ntr/cZODj+dn8bMny/VkakT3Z5nSV7FK+6R7jt3tHSMpqOmfTbRLZh8HgTIhv/riLb58cYDoQ5f/+\nUSffOt5PMJbk8vAch+vysZv1fKaljC/vqcCk17Cn0pEJ+O8zNlzAr8ixscVioj0JpxfUIHo2aETQ\n68nau5dQ2xl8c6oNsaK7wkj3DLKsUN7g4OJCiLAkr1qoUuWqQhKitJ/pQtKLoNFw+pVWJtwLSEmZ\n8f5bo1RFUZat/rTUBqHmp6/z96//ELvDzk6XHZNOw6k+L8YeP+a4wkUlTv/IoHqeuBe7Wc8rv3mQ\nJmcOfdeugqLQLpdydmSBiN6JMD9Aa6/6hNHW70WSV5+gvB6MpPPG85MT7G59kQOtL+Ib8/DbrkL+\n+yYn8WiE/GvvIGm1vNjZRY85h+3JEKIoptMmd0vrmK+eR5eI8+bU8rz84muGOtoZ6Zq9ZRWxynzK\nWum72IUih5GSZYz1zbHgjRCaj+H2+LkWiKRH0kccVmKywllfgNFeHygw2nPn5Sc9qb6MdPkoqW9A\nazAweLWdE/NBbFGZPS47FruBL/yH3ThKzGTZ9OQ5LenXLaITBV5qqeUjedkr2vjulkp+rnSlt89R\nh42+cJSx6K0b0kw8ybVABH9SHYxcmA89knROeiK2z8vplL13m3uGtv4ZkrLCoTr1ev7755r41cNq\nbcmh2nz6p4OMz9+fEivDg2PDBXxYWuquBuFBuRhPcArzgf0kRkeZ8bwBgMYQoPPMCXQGDUVV2bT6\nAugEgf05KyWO2/dsAeCtt99K77t68TKypAZYz5KFSaampggG1Vxse3s7s7NqAOzv7SV67RrmgwcB\nMOo07K1ycLrPy3jvHNsSGk76AsTn1CeJoaEhkktcG8emphGTSS7PCvxL+xhjJieC7Oe1n14FYC6c\n4PrYyupQWFIwZLcuC9pLtz1d1ygdHUCbTPAXkwvE9EaO5auFXY7SMqy5+Qyuok0HSMRjTHdfwzl+\nk3bxlu+6oihpXxrP9U6Gr3tXWEUsnU9ZK92nzwEg6io4+6NbTzav9E+jcGsSeW+OBaMo8OrQDPGU\nd9HIHSaKo8EE00P+1DE+tDod5Y3buNlxhesGme1J7arVzOUNuUwOLBCP3F+l8WIgX7qgyqm5QHqJ\nuD+5OU5cUZbNLz0sFhU3Y/MR/v7cEADz4QR/fcJNll7DzoqVq6wtSpYzo/z3Dxsy4B9Nlbp3h6Ic\nyVaVDK+PdmI5cABFUPAFzpOTrQbduPIOZZvsaLQiJ3x+dmWbsWhXVs6WVRahx0xUWUBUdGhiccKE\n0OpFSmpzlgWRxRF9bW0t4+Pj6W3P6ChJUcSypKL2UF0+0akosXCSo7lWvIkkYYsJc76TeDyOx6Mu\n4DI/O0MEkbzU8oXXxhbQbN4KgHm4lyP1+QjCrZW1bqfV50/njQc7LpNdUIijpGxZAB/quIxJq6HG\nP8Nodh6CLPHJLZsBtXTf1dzCyPWOVa2DR7uvk0zE2UmcWUsOnamFZ3xjHgKzXqpadpGIRZnx9C2z\niihvVFMbt4+Q342JvmvojEVYHA6mhwNYc43Yi7I4uRDEodOwzapWVJs0Ik/kWDi9EEIQBZwNqiR3\nNammp9eHokDF1ly8IwHC/jiuphZuKCIRvcDRvNUDbXmjA1lWGL1xfwvXbzIbKTboluXx357149Bp\n2G7NoiMQwSQK7Ml+uJWzsaTEuYFZjtarAbxzdIHDdernrXN0gX3Vuei1K0NJXaGFIpsxPamb4dGz\nIQP+rmwz5lSp+29XVpGNqnvWl5ej7ClEEiOUln6aRLAKY1EP5Q0OpmIJuoLRu/qOFDrUVZwc5mLs\nxmwko448l0BlUx6+iWBaW+7ud1NQUMD27aq0z2azsXfvXiRFwVtZiXHrVmRZRpZlDtfl44qDjMyz\nm1TzM4+9gKeffgpRFNOpoUttp0AQ2LWzhTyLmr/99Ee3o2hyKI16+NT2UrYUWznVe8uCN5laazWQ\nsoo44rAiJRN4uq7hatqhTkr2dJGIq6ProavtlDdu44BFnbB2+WcpzL6VknA1tRCPhJlw31jx3gx1\ntKPV6fnZ/aqKaXHCd/GGcvBnvoogisiJ4eVWEaUWTDb9qmkdRVGQpVtzI3JKshicCxANjFBQ2Yiz\nQb15lDfmUtbo4JpJ4WC2BY0gpI8/4rAyqpHR1duo3VlAeCHO7JhaBSopSjr4j3T7MGRp2flRF7IA\nw92zuJpaGCyvA0Xhk5tXN6crqspGZ9Dc+RrktUkTBUHgsN3KqbkASVlBVhROzgU4bLfyZGo92idy\nLBg1D/dre2lojkhC4st7K9J1J89uL2FbqfrZuFPxoSAIHKrLU9M+7yI3zfBw2JABf7HU3aYV2Zlt\nYZdhhouxfCRZQjqcDzLkWPdw0fg5/s/8b2Cp0a5p3c/NjarPe011NVuaWkAQiGluUlCuI7bwbS68\n9BPmZ+YYGryJJpjEVeECRcBuKsLpdCLIAv2NBxE0Gr73ve/xxhtvUJlnZpPxNAuWE5Tbs7CHggw5\nitlaXY7T6Uw/LfT33kCQJZr27uNQXT56rcjeqlywV2OMj7K71Eq+zselKg03PNO0Pf8TvvWVz+Md\nmeRMyiriqMPK+I0eElHVisDV1EIyEWes+zpjN4aZn5rAVlDPM7VqAdsT+uU67/ItKevgqyvz+EMd\n7ZRubmRHdRU5gXmOe9WAevm10+iz8slzVmCyVYAyTG7prRGqIAqUb1ZX9ZJvm3/oOd3Kt3/ly0RD\nQW5e9fK3v3ua0EKMjrfOAjK1e3ZTkXpCKG9wEK+1EjKKNMU0BHxR/ubfnmK4a5Z9RnW0P1lvwbl5\ncZJ1lqSssPtcN3/t8aIoCp6uWco2OSh02XjuqWz+ZMpLTlEJQ+WbKJ2doTjHtOrnQqMVKa23M9I1\nu+LJ4epPXuE7X/95kvE7TxQv5WiulYWkxNVAmO5gBG88yRGHjWO56ufy2CNYiPxUnxedRmBvVS6H\nU0+SB2ryOVyv+vUcqr2zPPlQXT7+aJKO0femxMrwYNmQAR9IlbrXoBMFjuRaCWDl/FQXkYoAOo+A\n1HmTTvsOgoKVs5FeTvj85Ou1NFhW/1ID7D3azNG9H+NDz+xn/8cOI0gSc5EJ5qd6QYkx2H6Ok6+8\nCaJIZGSI+Yk4Ob5tGOfKmbnYjy6Rw4xeZn5+ntHRUbq6upgcGUc26UiaBCZn53DOTuDNthNMStTU\n1DA5OUkgEGAmGMKm16I3GPj9j27iB7+8hyy9lpaD+4AkYxc7uGHVEjVm8bdvX6L3zGlQElz5yWne\n9vnTevChjnZEjQZn4zbKNjei0ekY6myn4y11IjsaKWF3VSX/n0XiD47sX3b9RrMlZR28POD7Z6bx\njXlSTwASlWMzDOTlM+udJzh7E1l2EgsnkGQnUnya8MLyL395o4NoKIF3ZLlC5ca500SDAUaud+C+\nPE0iJjF8fZaBy5dB0LH16E6qtufzsa9tpXJbHtdTsdA5FGH42gzJuIz78jT6wSC2kESvXcBiN+Ao\nMTPS5aPdH2IsluDH03P4xkOEFuKUNzoYjycYsWs4a0gyuRBlIq+YipFupOTKlawWqWh0EJiNrrCK\nuHHuNKE5H2O93Xd87VIO2a2IqCm4pS6lLTYzz22tXKHueRic7POys8KB2aDlt47V8v1f2ku+1cCv\nHKriuV/cjesu1eYHavIQBTjZl6m6fT+wbgFfEIQ/FARhTBCEq6l/H1uvtlajzKhne6r0/GOl2wB4\nY6KXEIMYerXMnjnLpbDqNHh8xpd+dBbvUr0oiiKHn96NVqdFp9eTY9AxGwqni3P8M/0MuHtBlkjO\n3KT/4ii6RDY+T5zeN2+gizlIaKKcOaVq8kOhEK+/9DIIAmg0/O0/PE/F3BSyIHBmPpheGPzEW28h\nabRUVrgAKLAa2ZGaJNv99D5A5NqZs4wUqCOujkQE/7Sadhm+doUTvgD7U1YRg2krgix0BiNlm7cw\neLUdT9dVBNHG9JCAoih8cdcOss0rS/ddTduZGnQvsw5evAFUNu/A0+OjalImoTfw7X98EUgiaCto\n/+kIilK+7PhFnJsdILCs6jaZSDDSpco7h6624+lZVM/MMuvpxuKoRm80IIoClU35CKLAqYUQZREI\nXJ9Lp1c8XbN4uuaonZV4JxYlISuUN+YyMTDPca86QdsZiNDZpQak8gZH+mkvZBD543ODKKKAa7iX\nsd6eO342bskzb11DLBxivE9dOWuo893XyQWw67Q027JSi8sEaDAbKUzp9Z/Ky8awThbYd2LKH6V3\nMpBO29jNep6oVq/VYtBy8C6je4CcLD1NzpzMxO37hPX+9PyZoijNqX+vrXNbd6TEUki1OM7pBQkF\niWx5M+eGxojICjYhwpuRMnwJ6Z4flysrK5E1WnqvXEZvsoASIyCF0YbDCEqSa60XMJp1oMCNCQvm\niPr0cPnqRUwmddvjmwRJAkUhPj9O/ryPrFQBTlFREWazmSudauDbsW//ij5YcqwYbRVciUyS0Okx\nRcIMFeQiyxEE0cRw1MtINM7RXBuh+Tm8QzeXVaa6mlrwjXkIzvahM1UR9ifwjd/Z5XA16+ChjnYs\nuXk4Sp14un3UB+yIksRFKQho0Jsr6DjuQdDmY7Jlrwj4JquefKc1XfEMMNbbRTIWw2i1MdB+iUgg\njtGs4+YVN3JynrKG5mXnCKXmKZ4wGJmbDDPS5cNo1hFaiONun2af3khAkmn3hyhvcCAnFd6cnMOR\nsrZ+c3wOR4kZi93I2z4/OalF2H+si2GMy5TOTt41aGfnm8jONy27hpHrHSiyfEfnzTtx1GHlqj+c\ntuh+lCwG6nutKl/Kodp8OkbnmQutLa2VYf3YsCmd29lnidGn1BET88mt+whnbXb0AvxC7gJx9Oq6\nn/dYvbjzgKr0iRmy2P3JzyPrDCgGIwWOMkBLMjrI1iOlGLK0yIKWamsMrWJEliU2b95MYWEhigCm\nJCjxBKIgkDQ62G+30jrrRxRFqqurkRUFrZTEWb26531JXRODzipEKcn+0Sn81hx8OXnU7v0Eg84K\nQA0iw6tYEdzalth8YC/AsqB1O4VVNRgtt6SdsiQxcq0D17aW1GtnqdtURNnMNIPOarKyXTg3FSAl\nZApd2biaWhi+zYUS1JH15KCfWEraqKaetOx59nOE52dRZB+7PuEiEVF9hbYd27fs9WfmgyQUhY+W\nq6NPKSmz6xMudTsh8+HyXDSCKk8trskmZtbQk0jw86V5OLQaLpHA2eBILx34sYJsSoIySY3AlphI\nWV39XWsQQJ04HuubS1tFDF1tR28ysfPjzzLjGSbgW1ta46jDlra+eNSLl5zqnyHfamBz8Xvvx+H6\nfBRF1e1neLSsd8D/DUEQOgVB+J4gCCuXhXqIPFVQiixoGLJ8CuuBw1zc3ERLPMJnyjYBUG8Ik6df\nvu6n1/smPt+ZO56zpMKFTkqSNNtoPHIEHGrKYs+hQ2TZq5ATw1RsySPPNkcyehnXTidFuTbKnNdx\nuSrIsxhwlndSXFiMyaq+PUWFRRy0GRiOxumaHsXlUgN2Yc7KAp5FGg/vZdBZS7l3mi83q9cz5Grh\n4Bc+waCzhvxIBJfJwFBHOyZbNgWuW+6auWXl6E3ZgMjeZw+p+e27GJqJooaKbdvVoK0oTPTfIBYO\nUdncsiQPnktTPMl0fgmWxh0UbbZzqsFIboMd57YWWmu20+NeXhXsbHBwoVrP+S61ovUfJwJIW3ZT\nt2c/1+u24ysNUrerCDk5jEZnx9mw3CH0bV8AkyhyrMqBxW5AEAXq9xbjKFHzyw2NeeywmWn1/f/s\nvXd4W+l55v076CDAgsZOEGwgRVIkRapLJKcXT8a9xYnj2N5NNtnNxut8+ZJsdjfOOtl47W+d60ux\nEzuxEzuOxzW2E0/xFA0pqo0kSpRESuxgEwsIsAEE0c7ZPw4AEmIXKWnGw/u6eAk6OBUHeM77Ps/9\n3PcCKrWSmdp0JAEeNadxUKmlP1NF/j5TknXgYZXMVmrOSMVRU4/bNYB/dn3qpb3STCQkcrt/Vu4/\nuNaOvbqW4vpDAAxt4JO7EnWpKaSrlOgVyTo8dwP3QpAvvd63bkPenYhERf76VB8eX5CoKNHW66ax\nzLojc5na/AzS9eq9tM6bADsK+IIgvCIIwo01/t4FfBkoAeqAceD/rLOPXxME4ZIgCJfc7nv3hWjO\nqUNPkJvqh5gpKmEg387h3i7KTA5OKq/wlPJs0vqSJHLz1n+lp/ezG+7Xnp+HaExHYzCiyytAGRWp\nPlZHSX0DkjiDRu8ndPslIoEWjPttOKuGKSq6glocRyO24XB0UN+URmPTSRQBPzVmDXkjPwHguWsv\nYoiGUQR8HKg/sO45GPeXMW3J5rg+hacO7yNjbo7e4mr0mSZGcksoHOpHEkVcHe04ag4grMgDC4KA\nPv0gqbYGjOY0CirNjPfNrZKKWAlHbb2cHhoaxHWtHUFQYK+uS+TN7ZVmPlArP3gCzccYcOho2Z9C\nV6mO20UVnD7yOH/fN5S0T1+OlpfqDXxlwsONvlF+crCZV4oOEdSl8+JD7+GViixUWkAcJads/6pz\nejpRm6AAACAASURBVN07z0mTEZ1Syf6H8qk6mYtWr2J/cx7OI1kYMrQ8ZE6lY2ERTyiCK1+LPiji\nCAqUuSP49QrmcnSc8i5bB36sPBu7T+RDVTlb6jTOdWbIUhGdXmbGx5h3T+Gorcdqd2AwmTfVIopD\npRD4RJ6Vj+dZd5yz/+b5IT7/YjdvbFHE7NyAhy+81M0/Xxjm+tgcM4vhHaVzAJQKgZOlVlp73Ts2\nvNnDzrCjb5MkSY9JklS9xt+PJUmalCQpKkmSCHwVOLzOPr4iSdJBSZIO2mw7+2JtBK1KQ7PVxrlF\nY8JvtO7lF5CiUf40e5gjga8TjS53ey4sdBIOe/H7e1laur3ufo89+jgSMDAwwEJ0ibrDh1AqlTQ8\n0wTA8PUrzHjl4DbW04nWKBfxpsbbENSdAKgNfRw/fgSr9zah4R400y+QKU1wMapl/OZ10sb6qT1+\nct1zaJ2Vu3o/+dgRAPL1JkYsJl51zxFWqykYvErfpXYCC/M46hqStl2cDxEM1lL/zMcAKKy0yFIR\nPevT6BwrpINdVy+TXeZEZzQy3OnBlCPnwR+rKcWiVtGh0XAuKDNXLkSCnA3K6Y5zweQffuusXDdo\nV4T5zmX5c+k2mflR5wSSQsGgxUbv9auI0RANzzQnbTu4GMQVWJa0rn+ykOaPyBTa6uZ8Hv+47GX8\nkDkVCWiZWeCKKkLRZJjbN71Yb8jF29YFP6c8CxyIWQceK7bwxrP12C0pZDqKSUnP2DDga3Qqckoz\nGOnyJHL2cetFR009w9eubJmT/3vFOfyP0twtrbsRlrXptzaYWrl+a487RsFcLQOxXTQ7bUzOB+me\nvP82mHtYxr1k6eSs+O97gPXF1O8THjanMboU5uuj09jEKI5bnSx1dmIxNyGKS8zOXUys6/WeXvG6\nbd19FhYWolKpaGlpIRQKJSwHzbn5pNky6Xjx3/Ap5enwcNc5fH75YwhEWtBb5dSJx9uKoFDgqDmA\n61o7orqXGq5yU11Gz9VL5O+rRq3VrX0CyAqKmRoVlQZ5nXdkZYBS4LO9t1FJEvaxAVr+6evAcrCO\nI85+sccamHLK0lGpFQx3rp/WMZot2OwObp1pYWKgj6LaBsKhKON9c4kuWkXMVPv1GNsEoG3GxyvT\ncnB1pVlwzy9LO5+KyTzP6BX8m0pmpQS0Sv7WLZ9fRKXmW6++hkKpwl6VPMI/tYak9VqoTU3BrFby\nN8NTTEejVC1A15lxxJFFiiUlP5qa4erC4pr7ERSK5VSWuH4Tkb3SjGfMT9/lS5hy8kjPlCWaHbUH\nWPL7mOxfX+ButzHjDyX471tNp7TG6JPtw7M8f32c/XnpWIzaTbbaHI0xrZ29tM6Dxb3M4X9eEITr\ngiBcAx4G/ss9PNaWEB8BXvMFeMiShiAI+NraMJmOIAgavJ7WxLoeTyupxiq02mw8K5bfCbVajcPh\nYHx8HIVCQVGR3LQUH9W5R4cBcOyrZsF/GZBQRY+hNtxGoZJQRmoJBIZYXBzCUVuPpHSjSglR5R8h\nKOgYMIurgvRKRCWJVq/smhXPs/5KeTZEJQbDYQ5nGNFEBeYmh8h0lJCSnpG0/XCnB32qGluB/Nmo\n1EpynRmbCpoV1tbjHhoEScJRW8/tnlmiETHx4Ih/3p5whPFgmCetaQREkf5AkEaNgKhQ8pMbMs1x\nKSpybtbHI6lyvnrcbMY5Pg6SxKhRoNInooxEuKo2kFe+D40+mS76uneBQp2GIv3GCpJKQaDJlMo1\nnzzjeNiSluD+P2xJo9O3tKZ1YByO2noCC/NMDvavewx7lRlJijB260ZScbyw5gAIwrpaRPcCbX3T\nSBI8ti+TztvzuBc21isanwvQPbnAY/syiYqSTMfchHa5VeSk63FmGdeV/tjD/cE9C/iSJH1UkqT9\nkiTVSJL0TkmSNhYivw8o1Gsp1sujlUdyrOiqqvC3nUGpTCEj4yAerxzYI5EF5uavYLY0YTY34p05\ngyiu1o8RRfkHFOfL5+fno9PpEEMhpFggFBQS+miUhvd+CGPePArBSKH9N+XtIwL76/4HIM8oCmsO\nkFogp2feV/FhlFKE4ZLiVQYfoiQRio0yOxYWmYlEk0alVr0Gcyxl8rAljTRrmXz9tfKDI84iSVg7\n7pOtHeOwV1qYnVxkfjqQWP/O3Gv8nHTGVLJKShnu8qBUK8gtXX6grFR1/MPiXNSxB9J/qypGEwry\n6pT8ULkw5ycgSnyiKAtrTLr4cbUKu18+5mOpqZT6PAwWlFEYO+58TDYilJC0Tt1SYTF+TvsMOuoq\n5FGn0aTlqQK5aL6edSAkp7LWgyXPiEYzhRgJJ903fWoa2cWlW+bjxxEJr9/stRlae9yk69X8p0fk\n+x+3IYxExUQRNxIVE7IHcRXMTz3mxKiVCQwbeTZvF81OGxcHZ1gMyb+lYGTt9NZiYAlxg1nUnRCj\n0USqTIxGE3IcohhN6D5JorimBtTbDW8bWmYcj1hkO8EmUyqGkycIdHQQnZ/HYmmK5evHmZk5hyRF\nsJgbsZgbiUTmWVhI1ngPBMZoaa1nevoUZWXyD6qsrAzR76evqZnZ73yHvPIy9v1iH47jIfIqqkgt\n8CP68rGXHiEcUBNw2zDbatHpCvB4T2PIMGEpEwkvGHCWNVIaGaDXWoklRq2M489dk5y8cIuoJHHK\ns7AmpfSQQeb512g06ByVAEimUiYH5/nKf2nBPbLA9KiPwEI4aVQOJNIyw11eQksR/uH3z9B5OrmO\nkVdRhVqnp7DmAAqFkuFOL3llGag0y8Jzcau/coMOp0HHkXQDuVo1NelG9vlnaFelIIoip7zzaASB\nYxkGKmfdCKLILx7ZzzGNnKJ6Z1kmZZEoHnMWweJqvnxjFGfrDVrHZvh27yT+qEgJqwXv1sLD5jQE\nZImC/ApZj99ebeFwhhGjUkHzBtaBKekZZBaVbBjwBUFAZ7gNKMmrqE56z1HXwERvD0u+jV2t4vCM\njvBXv/qBDa0l14MkSbT2ujlZaqUmLx2LQZNIp3z8Hy7y6e/KCqu//dxVfu2b8qyjpddNVpqWqtw0\nTpZaSdWpOGDPWPcY20WTU/Z/uDDgZWw2QO0f/4xXbyabB83N+/jzT36Ur371W1ve7w8/9xle+Ksv\nAvDTv/gCP/qCTLR45at/zXf/538FoOVbX+effv+33/ZFY9Xmq/x84Xcc2bzTloFFo2KxsRHP3/wt\n/nPnsZxooo/P4fWeZn7+GkqlgfT0A0Sji4ACj+c06enLI7Zpz2uI4hJT7hep3Pcwv/Irv0J+fj7+\nM2eIzs4y/+JLaAtDaIwR9PsjLAX7UadEmL4CC0em6f+3fGof+zCCIGCxNDIx8WPC4Xn0tnmsGe8C\noClD4Kv+QkZ9kxSkZieO/RP3LMNLIa4tBHjdu0BtagqWOyiln3bm8No/XWLCaKY3uwqr8b10Daeg\nWZpCjEgMXHWjjCkcFlQmt+tnZKVgNGsZ6fJizNCy5A/Td3mK6qa8xDoqtZoP/dGfYTCZmfcEmJ1c\nTHo/jr+pciDGBH6/WFGAPyoiCAKNaTo6lOlcGR7mlHeJIxkGDEolT/SdYZ9LT+mj/53PWEw80u+l\nOi+dcFQeaf7Qp+LqvAe0Al/vm8AdioBCwjO8AOWb3/8srZp/OVBKpVGPRqXkPb9TT3qmHq1CwQ8O\nlJKtUW+4vaO2nos/+QHBRf8q4/Q4lhb6UajymJ0Mk1W0LNXhqKnn/A+eY/jGVZxH1y/Cx9F36TzR\nSISeN86QX1m96for0T25wOR8kCanFYVCoLHMSmvvNF5/iDN90+jUSuaXwrxyc5KoKDG3GKatd5rH\nK7MQBIHPvLOKaV8Q9S4KtR1ymNGpFbT0uBmdDbAUFnn++gSPrhCle+31s+iiAW5fOQ98dNN9BnwL\nDF/vQKlRE1z0M3D5DaLRCAHfAr0XzrLk9+Hzeug538bCtBvv7VEseQW7dk1vNbztRvgmtYrDMb17\nfU0NCqMRf1sbBoMTrSYLj/c0Hu9pTKZjKBQa1OoM0tJqEumeOOL5fq/nNJIkUVxcjEajwX9aLvAG\nLl9msu9H8mvlGBOT8uuJGxE6Xn6eJa+OfUefBMBibiIa9TM09DdIUog8u6xC8UyhLE38wtjy7GJs\nKUS3X1bl/NHUDO0L/jVzzjU56eRG5CLca2NzzGjtePsXGIo1VY10eRnp8iasHVdCEATsVRZGb3lx\nXZen+eN9s4SWkqfEWcWlGE3mhLRxwR0zBYDiFC2lKfJI3a7Xsi+mVfTuCrm4/fXeYbr9S7Knq9/H\nfM8NHi9zyPfKoOVdNTlERYmOnhlYinJ61kefJJ/HBV+AznAIYTbE+W1otRzNMJIWk8DOLk5HH1Mf\nrU1NScgYrIei2gYkUWT4Rsea7y94p1mYHkOhLlzVz5BTVo42xcDgGuJza8HVIY+81xKr2wzx0Xw8\nJdNcbsPrD/GV1gFECRZDUb50qp9gRCQiSny5pZ+5wDIFMztdR3Xe+r0fdwPZ/8FCa487iQ20ctR9\n66JMnDDMjDA7twV/5OtXkSSRSDDIhR99j0g4hCSKXPzJD1jyxzwpXvxXFqbl493NZ/nzhLddwF8J\nQa3GcOwovjY5SJstjUxPv8LS0igWc1NiPYu5ifn5a4TDMuNBFEPMzJ5HrTYTDE3i9/ck1vWdaUNp\nNiOFw8xFr6MIqACJ0dFvoNMWE1lU0/7CT0i12jDnynLLJtNRBEHFyOjXUSi0ZGTIDNZDtn2kM88p\n73IKIG6OYVGr+IexaaISazogCYJAU5mNl29OMjoTYEIPxvkInlEf+lQ1k655JvrnkqSKV8JeaSa0\nFOXWuQn0qWrEqLQuVXO404vRpMWUvXbuey1U5+dj8c3yI4U8Sn7YnJqQInDUJhepb4zNMbsYJmU2\nxJgGIjolipCIVycQ0CtJnQ9z7T617uc4K9Do9eumdeLLrfaqVR3LCqUS+/5aXNfaN00thAKL3O6+\niT4tnZnxMeamVvsmb4TWnmmcWUZy0uUHbFzz5mtnBknVqVArBb52ZhCNSoFBo+RrZwZ3jYK5EZrK\nbAxM+2npcWMxaHAvBLk5vhzYQ0O3WFLqUSLy6mtnN9iTDFdHO9oUAwqlivbnf4xSrUaj19P+/I9B\nENClpsmvQZb12GYN5ecNb+uAD2A42UhkfJzQwAAWcyNizGTcYmlMrCO/FhNdt7Nzl4lGFyku+hRA\nYvQfGh4mPDSM5ZOfRLRpCdtFbP7DqNVmRDFEZuYjpNmyiIbDCX42gEqVSnp6PaIYIiPjMEqlPCJW\nKpQc1rm5FJN2BpmCmaNV89FcC0FRIlWpoD5t7dRCk9NGKCIXvw4fy0OFfLzDv1AEEglrx7WQXyEX\ncqMRkQOPF6LSKNZk7kSjIqO3vNirLNvuxmwQl4golGRpVFQYdLg62tHoU8gpq0haL84Hf2+BBWIU\n13cbjBArNH+8POe+te4rVSoKqmpxdawdtF0dVzCYzJQ07GNycI4lf3LR1VFbj88zjXdsZMPjDHde\nR4xGOfHBX4rtd+uBajEU4Y1BbxLDxmqUc/OhiEhTmY2GQhOhiMiRIjPHS62EIiI1+RmYDPfWKzc+\n4whFRD71mFz7ivcI3OxxYQzOkH7kCcKCiu7LF9fdD8Td1Nop3F9HXkUl0XCY/H3V2KtriYbDZJeU\nUVJ/iGg4jCk3n4oTTYx23Uj4P7wd8bYP+HH3KX9bG2bzCZAEdEI2er2d+Zd+hu90G6mpNahUaXhi\n3Hyv5zSCoCI7+13oFQVM3voBQGKmYHzkYaSnZZmFzNL3yvsFLJYmiurkOkBRbXIDVHxGYbEkNxU9\nZE6PSTvfIByN0uJxczJNmUjjNJlTUSvWDrRxadoiq4EPPF1CBAlRq6DyZC7aFJVs7Viy9rRdq1eR\nXZwWO1creU7Tmtz8ycF5QkvRdR8cG+HxbHk0eUhY1s+xV9eiVCXXI1p73VTnpvOfagpAktAsRflf\nB4sgKqEIifzOYceute5PzS/xF6/2bmjYUVRXz7x7ipnxsaTlohhl+NoVHDX12KssSBKM3kqWYogz\nd9aiZ/ZeOJto2HJ1tKPW6qh++HFSrbZEwL/dc5Mbr7+yatu+qQX+vk32Qr4w4CUUFWkuT2bYxNM1\nTU4rzc7MxLL48p121G4FJTYDeRl6VAqBdx/IoyI7NXHfTp+Sfz8nH21myVpEZFhuUpybmuDCj76H\nJIr4Zryc+/63EaNRPKPD+LweCmPeDkDC50F+3ZB4XRT3fwgFGbvZec+v882Kt33AV+floSkqwne6\nDaWYQso5NcbTGqRolIk/+iMmP/c5FAoVZtMJvJ5WJEnC420lPb0BlcqI9lqUBXoJL0zjbzuDOj8f\njcNB5GgqyiU11tpnyc35ICbTcTIyDlL10GPkVVRRWJOs9piV9QukpR0g0/Zk0vKn8+Qmo5cmXJyZ\nuMa8qKZKPEd9moGHTKn8Us76+ugmg4YPH7bzsWOFGA0aprI1dBklFEoFNY8UsP/h/EThdi1UN+VR\nUp9JeqYee5WZOXeAOXey3vtIlxdBIZBfsX2ppHdVV2K/PcjBkVt4x0ZZmHavoqDOL4VpH56lyWnF\nkaanIqTgSYOBDJ2aelFFs0aHRqXctdb9b54f4osv93DRtb5mznoyC5P9fSz5fThqD5BdlIZGr0qS\nfAZIs2ZizitYta0kirz81b/i1D9+NbbvyxRU7UepUuOorWf4xlWikQht3/4Gr3z1rwgtJd+HL78+\nwGf/rYshj5wu0akVHHIkP4TfcyCPensGj+3L4hdqcjhgz+Dp/Tk8UZVFvT2Dd9XtvLN3MwiCwMdP\nOPilI3ZSdWqanDYuurz4gxFud17Br0mjprKU7Ko6DMFZOm/2c/n5H9P27X9kyjVAx8vPc/Z732L0\nZmdSN3P5sUZyyspxHj1B6aFj5Dgr2HeyGUddA3kVlVQ2PULBvv2y/8M2Zks/b3jbsXTWgqHxJLPf\n+S7+s2fJ+CdAMYX/kfNEZ2eJzs4Svn0bi6WJKfcLzMycxee7SUnx7xL1+VC0eKAaJi58k8Xz50l7\n57OAxIKmD2vWUyiUKszm45jNsrpjTmk5H/7j/73qHPT6Ag4d/P6q5bnGLEoVl2hbUBCRhhCkAkoW\n/w214uM8V1ey6bX9r/csd6UWPZrHt356k7HZgJzW2QTOw9k4D8vsIDnX38tIl4f05vzEOsOdHrIc\naWhTNi52roU0Qwq/O3CJxblZXLFi7p0B/2zfNFFRSoxIX3+qNvHe808sX1uz08ZPr4/TPblARfbd\nSwrHG4NaetwJ3fc7kZ6ZjSknF1dHO/VPvzOxfPDqZRAEmaqqVJBfYUr4565Mdzlq67n28guEQ0HU\nGrkvZHKwn8DCPIGFeYauX2VucoKGZ94NyLPB66++xPD1q4x130SMRhjpvE5Jg1zriVMwgURB9EiR\nBZ06mapalpXKD38zNtsE/uU3l+W2f/ibq6W37xX+XeOy8F2z08ZXWgdovTWB1j2AWHQAhULBieYT\n/Oz179HW0oa6Wxadc3W0J4K1q+MyU64BLPl20qzyzOQjf7Is1/WRz/5/idcf/uPPJ17nVVS9rQP+\n236ED8jm5sEg7r/4S3mBKDL1f5a/PL62NsxmOaff2/c5QM7rL164gLZbRAjBxPXnEBcXMTY24vPd\nJBSaxmJuXHWsu8FxY4hb0VxemddRTD+KxassBSc23/AOxKfsd5P6SM/Uk2rRJVg+AAFfiKnhhSRT\n8u3CUVvP9MgQnS2vYMrNJz0z2Te2pWcao3ZzPvhutO57/SGuj81taT+FNfWMdF5Psi50XWsnu6QM\nfar8wLFXmvHNBJkZX0zaNm4tuZJfvzIItfzT1xLrAdj3y9aSp5/7BmI0smr9m+MLiS7ab78xwsC0\n/76kZ3YDBx0m9Gol3/xxKxoxTFn9QQCqKorxa9KZvnyamdujANw628pEfy8AfZcuMHrzxqoC/2Zw\n1NbjGR1mfvrt2fG7F/CBlEOHEDQagjdvknLoEIq0NII3b6KrqkKVnY2/7Qw6XQ4GQxk+XxdqtQWj\ncR++tjaUGgN6txl/9jSoVKQcOYLHI+f6zbsU8B/LzEdEybCUzbEUmdHg9ayv77MeSjON5KTr7ioo\nxqmaY90zRGOF4JGbXpBYl+mzFcSDmntocNWPV5IkWnvcHC+xbMoH343W/dO9biQJnqzKomt8YymC\noroGOR8csy5c8vmY6O1JmqHEaap30jPzK6tRqTVJQdvV0U5mUQmpFhtu1wDpWdmYsuUUizbFQE5Z\nBW7XAGqtDvv+OoZWsE3io/snKuXzht3tkL2X0KqUHC02I43eRETgkZjPgUKhQGmvQDcvD2xKDx1j\netgFkkTpoaPM3B6VyQ819RvsfTXi92elgc/bCXsBH1Do9aQclIuoxuYmDMeOAWA4eRLDyRP4z51D\nikQSAVweuQv4T7eRcuQIJsMholmgPlmB0mjE423FaNyHVpu5K+fXnFOLHjln+478WjSazFV9AWsh\nGg0kvY5TNdv6phNFycAGMsh3wl5pJhyMMjEgj4KHO71oDSpsheubY4SjIuE1CqBRUSIYiSakg2F1\nOqff7WdsNrCq+Lge7mzd3y5ae6bJSFHzHx+WewROb6AwWVC5H6VKlaD5DcX44CsDUJpFjyk7JdGn\nEIdaoyVv33JqIbjoZ7z3VqzgKD/07gxk8eUFVfspaTjMzPhtZicnYuftpiI7lfc1yKm2vAw9Jbad\n6ejfTzQ5bdgDI/jS87Gal2dy5Q3yaF+TYaH+6WcBWcrjyHs+BIBKrSFvmw1p1oJCjCbzmy6tMzM+\ntmWj+51gL+DHYGiSWTKGxiaMTXJgNzY1Yjx5EnFhgcC1a1gtDwEykyY8NER4dBRD40myquQvYOQh\nG5GIj7m5y7uWzgFZ2rlBM4ERHydzarGYT+L1tiFJ6wfrqakXaT19iKXgBB5vGy2t9SwuDtJcbmNh\nKcLVkVl6Jheo+eOXOD+wvjLmSuSXm1AoZL13SZIY6fJi32dGsQ5LCOC3/vkKv/aNS6uW/+lPb/Ls\nX8qzlKK6BlRqDQX7klUwE81DWxTwWtm6v12slCKozpWlCDaaLah1OvIqKpNYNfJIPLndt6DSzFjv\nLJE7Hqxxa8n56SmGb3QgRqM4auspOiAHuaIDySyu4gOyiUpR3UEcMYaXq6MdfzDCRZeXZqeN4yUW\nNEoFzeW2HRmW3G8czdWSGZrG7Ey+/w8/fIKIoCSQWUZuTDSvsOYAWUUlGExm8qv2J2ogW4UgCBTW\n1jN8/WpCc+fNgB99/rP865//2T0/zl7RNgbTRz6CrrISXbkTbUkx6txcUhoaiM7NgUKBv60N64Hf\n4kDdNzCZjjLzrecAOf+vLihAe9tGsCLCzMx5JCmC2dK0yRG3hy/WHGUyMINGqcZsaWJ84ofMz18n\nPb1uzfUnp55HFAN4PC3Mz19DkkK4p1/lRMnHUAhyMNWoFISjEi/emOBo8eZpGY1eRXZJOsNdHsoO\nZbI4H1oly7ASi6EIr92aIipJzC+FSdPJhV1Jknjhxjjjc0v0u/00fuRXqXviGdS6ZAnolh43xVYD\nBeatNXStbN1/uGJ7s6t4HrzZaUOhEGhy2mjpcSOK0roPNEdtA63f+joL3mnZ3Wp/LQplcqHUXmXh\n2muj3O6dxV61/FkV1TXQ8s2/x9XRzuRAHxq9nlxnBQqFkvf/4Z9g31+btJ+s4lI+8N//F3kVlSiU\nStJsWbg62vEUNBCOSjQ7baTq1Hz/N45h3+Ln9WaBNNoNwHuefSRpucWURnfDrzAtpPL/qtR86DOf\nw5BhQlAoeP8ffnZdaYvN4Kitp/P1V5jo7yHXuW/H579TzE9P4b09Ss1jT93zY+2N8GNQaDQYDsus\nB0GlSqR1lOnp6Gtq8LWdQRAEzOYTCIIS/+nTqO12NHa7rIeT8ygzcxeY9rwmq2+mN2x0uG3DnprD\noUxZBM1iPgkIib6AOyFJ0USTmMfTmtD293paSU9RU1eQQUvvdEL7fDs5/YJKM9MjPm6dl9MJG/Hv\n43zwqChxtm95FtE75WN8TpaHaOlxk5KWTlZxsl/vUjjKhUHPtnLRK1v3t4t4HrxpBVfd6w/ReXt+\n3W3iKaj253+CzzO9KiUFkFuWgVK1umnNnFeA0WLFdbUdV8cVCqpqUarUMd39ujVH6PbqGpQqlSy9\nXXuAkc4OWm+Oo1craXDItNia/AwyUu5t89Ruw9XRjj41jYIy56r3Gg7Wcm06zNTCEpmOYgwZ8nVa\nCwpJtdxdV3Dh/joEQfGmSevEz2Ot789uYy/gbwGGkydZun6dyIzMzRZDIfxvvIHx5LIAlqyH42N8\n/F8wZRxFobh3Pzq12kRa6n686+Tx5xduEInMolZbmJ5+jaWlMdRqC7NzF4lGAzQ5bVwbneXy8AxW\no4aBaT8j3sU193Un4gH++uujWPIMGDLWn1K39LjRqhQYtaokx6V4QLYaNesG54suL0thcdtsk3jr\n/lavJ3Gu3XIePCtNnmXEpQhaeqbW3SZef7jygmxJudYPVq1RkluWvqppLe6XMND+BvPuyW3/2B11\nDYQCAW5cvcaxEgta1dbUQt9skESRoWtXKLzDejOO+P0/vQ2tpM2gT00ju6TszRPwr7ZjtFgx3wdR\nt72AvwUYT54AScJ/Vtb2CLS3IwUCGFYEfLP5OIKgRJJCu57OWQtmSyNzc1cJh+dWvScbtggUF/02\nkiQXgoqLPxXTALpAs9OGJMmF008/Luect2qBZytIlbV1ItKm7JzWXjdHiy0cK7HQ0r3cFNXS46Y0\n08gv1ORyYdDDUnh1LrW1x41GqeBI8fYon/ER+lavB8AfjHBpyJv0cLEatVTnpSVmQWshHrSjkQjm\nvALSrGunkexVFmYmFlnwLiUtL6qrT2i0bzfg26tqERRKNBO9NJXdW/2be4mpoUEW52bXvf7KnDR5\nYLCN+7kVFNbWM9HXS8D3YC0XxWiU4RsdFK2QWrmX2Av4W4Bu/34U6en42+Q0ie/0aVCrMRxZZEwy\n4AAAIABJREFUtulVqVJJS5OZFLtZsF0PshSDiHdGfggNj3ydhQWZIuj1tpKWup+srGcABSkpReRk\nvxeFQovH00pNfgYn8rs4nned9zfkk5eh33IaRFAIFOyTg3DBHfx7rz/EF166xVI4yoh3kQG3n6ZY\n6/7YbICBaT+BUJQLg95ES/9SWOSNQbkI/OXX++mbkoXiWnrcHCoykaLZXpkp3rrf0i1fz0WXl+9c\nHN5wm/MDHsJRaVX6qKnMRvvwDPNL65uQJFg1GwTsOD3zTraOvVpOLZhycsnIyl5r03WhTUlBlePA\nHhihuXx32GD3C0PXrtJ1+hRAUrfsWpClnW2c7p1GFHdPy76orh5JEhm+fnXX9nk3GO/tJrjovy/p\nHNgL+FuCoFRiOH4M/5kzSJKEv+0MKQcOoDAkF43y83+ZrKx3kpLiuOfnlJZWh0qVitfTytLSbXp7\n/wSX60uEw3PMzV3FbGlCrc4gP/+XKMj/VZRKHaaMI3i9p1EI8MuVP+RXKn+AWinQ5LRyps+zJn1y\nLVSezMVeZSa3JLkZ6ruXRvjrU/283u1OjMhWarW0dLu5MOiRBbycNo4Um9GoFLT2uOmd8vG/X7zF\nV1sHGJ8L0DPpu6vmIUGQC65n++Xr+cJL3fy3H93AH1yfqtna40avVnLQkSwP0eS0Ebmj/nAnig4c\npKByP1XNj667jjlHTn3dmdbRGY3UPfkM9U+/a4tXl4wxQyGZoWkyVfeezrebaPnW13jl775ENBLG\nda0d24rc/FqI11Nu3F49m71bZJc40RoMDzyt4+q4jCAosFevTb7YbewF/C3CePIkkakp/G1nCHZ3\nY2hcbWCRnfUs1VV/fl/OR6FQYTIdx+M9nTBZ986ciRVoxcQso9z5GfLzfxkAs6WJxcUBvN42NEyh\nFrz4/N00O234ghGuDK8tf3wn8pwmnv2tOpTq5K/PSo3z1h53gg9eYE6hyGqILZ9Gq1JwpMhMikbF\nYYc5sf7KbeHum4eanVZ8wQine920D80Qjkqc618/aLf0uDlabF6VB6+3mzBolBumE7QpBj74R39G\npqN43XUEQcBeaWbk1gziHQ/VRz7+69Q9+cwWr2wZoYjIuaCcyhl6wKPU7cA/O4PbNUB4KYCr4wq3\nu29uOrqN11N20wBdoVRSWF2H6+rlB+qC5epoJ6esHJ3ReF+Ot6OALwjCBwRB6BQEQRQE4eAd7/2B\nIAh9giB0C4Lw5Hr7eKvAcELWGpn6whcAkgq2DwoWcyPB4Dgjo/8IQCQyj2voy7H00uoRQ/wh0Ne3\nzPf1elo5XmpFqRB29INaDEW4FBMca+l2c7bPQ5PTmshLNjttnB/w8OqtSY4UL+u8NDmt9Ez6+P5l\nuX1+fG6Jr59xkZWmpTxr/YaujRC/ns+/2E0klgZYL2gPexZxeRbXnE1oVAqOl1pp7dm5KJu9ykIo\nEGHStTs54/bhGYYFM8qU1Ac+St0OVna4tj33Dbn/YJNu2a3UU+4GjroGfDNePCNDu7rfrWJxfo6J\ngb77ls6BnY/wbwDvBZLoIoIgVAIfBqqAp4AvCYLw1qQRxKDOzkZbVkawpwel1Yq2fAt+evcY5pik\nss93C6v1MUCBz3cLk+kECsXq3HdKSgk6bS4+fzd6vQODwYnH20qaTs2BgowdFcbOD3gIRUWers5m\nbDbAQjCSFESbnFaWwiJDnsWkImNcFO3WxAJPVWUnXjeV3X3zUJpOTb09g1sTCxg0Stneb52HWUvv\nxrOJJqeN0ZkAg9P+uzqXOPIrTAjCapmFu0VLjxuVUkFR7QGGrl1B2obp94PE4NXL6NPSyauoZHrY\nhVqrI69icy58U5mNy5vUU7aL9VRP7xeGrl8FSXrrBHxJkm5KktS9xlvvAp6TJCkoSdIg0AccXmO9\ntxTirBzjiRNrUsjuN/T6PFJSZMXM7Kx3kpZWA6xfNBYEAXPM2MViacRiaWJ2VjZzaXbauD42h8cn\n68f4gpFNR7WBUDQh0dDSLUvy/s4TMpdaqRA4vsI96Wix3AUK8NAKqQRnlpHsGBXyw4cLKM2Up7Y7\n1YKJd+ceK7HyaEUmLs8iQx45aPuDkUQBsKXbTb5JT5F17Sae5gQ9c2fpBJ1BTaYjbZUL1t2itcdN\nfaGJsvqDLM7NMuUaACC8tIQo7ryDVIxGCQdlVpEoRgkvLa1aR5IkQoGt01/jFExZQkLuUymorkGp\n2lxptdlpW9XPEcdSOJow+tkOUi1WLPl2BmMBf7vXs1MMdbSjM6aSVVK6+cq7hHsVtfKAlZY+o7Fl\nb2kYm2PyC033noWzVVgtDyEIKszmE1gsDwEClg1ooQl5CHMzFnMTkhRiZuYCTTGqZlvfNO6FIIf/\n9BV+2D627n5EUeKp/7+Vz78kP+9be6c5VmyhNDOVYpuBBrsp0VkLkKJRcaTYTL5JT4ltOV8pCAIP\nldvQq5UcKbLwcLkNlULYsdVevNP2oXJbgsXS2uPGF4xw/HOv8Y1zLjkP3j9Ns3P92YTdEqs/7EL+\n2F5lYWponiXfzkap7oUgnbfnaXbaKKyRWUKujnaikTB//9v/ngv/8t0dn+vr3/w7vvn7n0KSJM59\n/9t87dP/YZUUwfXXfsbf/sbHCCys35y2ElOuAQIL88kSEnUHN9lKRn2haVU/Rxwf//pFPvWduxND\nc9TWM3ark3BwiRunXt7W9ewEK926FIr7l/zYNOALgvCKIAg31vjbiFqw1q9nzeGiIAi/JgjCJUEQ\nLrndb27J0pQjR7D/4z+S9vTTD/pUEigq+i0ONnwftTqDQvu/42DD99Dp1jeysFofp/7At7BYHiI9\n/SAKhQ6Pt5XqvHRMKWpaYnrqi6EoL9xYX4K5a3yeIc8iL9wYZ9izyOC0PzEq/9rHDvHnH15dQ/jC\n+2v5xicOrwquv/dUBT/4jePoNUr+86Nl/PA3j+/Yaq86L53v/voxPnSoAIclhQKznpaeac71e5gL\nhHnhxgTtwzP4Q9FNZxNNZVbOD3jX7BfYDuyVZpBg5NbORvltfcsMKEOGiUxHCa5r7dzuuYV/dobe\nC5t7wW4ESZLovXCWmdujeEaH6b1wFp9nmvG+nqT1et84SygQ2LLyZKKjNKaH86HPfI79jzyxpW3V\nSsWqfg6QqcDnBz28dmvqru6Po7aeaDjMaNcNei6c2db17ATuoUH8szP3NZ0DWwj4kiQ9JklS9Rp/\nP95gs1FgZdtYPnB7nf1/RZKkg5IkHbTZ3tySroIgYDhy+E2RzolDLtDKolNKpZ709I31wQVBiJmm\nCyiVWkymI3g8rSgVAifLbLT2TPN6bDR7rn963alyfKQ14g3wj+dcwHIaxmGVufB3IjtdR7FtNRvB\nZNBQmStryKfq1NTkb6x9v1UcLjKjVioSKqHn+qd59aZsBn55aIYXro+jUggcX8foJI4mp41AOJoo\nSt8tMh1paFNUa1pFbgct3bIBeGWO/Jk5ag9wu/smPeflPpF4MLlbxK0DAW6c+hmeUbmPYWWuOxJa\n1vN3dWwtQA5evUxmUQkp6fL9zd9XvcrOciOs7OeIo61vGkmCpbDIRdf2H6R5+6pQqTX0XTq/7evZ\nCe6nnMJK3KvI9RPgw4IgaAVBKALKgDfu0bH2sANYzE0EAi4CgRGanTamfUFevDGOLVWLPxTl8tDa\ngaO1x40tVZZV+MY5F/kmPcXr5MHfDGh22vCHovygfRRbqpaIKPHPbwxTbzeRqts4hxyvP+y021MR\na1obiblg3Q1EUeJ07zSNZdaEqJujth4xGuXaKy8m+Ow7KUTGm6EMGSauvPjTxOuhFfscvdVJJBTE\nkGHCdW1tQ/eVCC4uJiSg7xZrGfi09rhJ06nk+3MXaTe1Rkt+ZTU3Tr2yrevZKYautWO1OzCa795L\n4m6wU1rmewRBGAWOAT8VBOElAEmSOoHvAl3Ai8B/lDbS8t3DA0Oc6ePxnk6wZ8JRif/8aBkqhbBm\nkPMFZQrme+vzcFhSEl2qb2ZJ3mMlFlQKgXBU4tebiknRKGWVyS1o7Ru0Kg46TLuSxy+oNOOfC+G9\nfXesn67xeTz+UNJ555bvQ63TI0Yj1D3xDCnpGTsL+NeuYM4roPx4E2I0gtFsoeaxpxjv70nkt11X\nL6NUqTjyng/in/HK5iQbYLhzWQL6bhHv54gX0OMGOY1OG4eKTHddWHfUNiBGI9u6np0gtBRg9GbX\nfR/dw85ZOv8iSVK+JElaSZKyJEl6csV7fypJUokkSeWSJL2w81Pdw71ASkoROl0eHk8LmWk6KrJl\n7vvT1dnUF64d5M71e4iIsiRvQl1yi5r1DwqpOjX1hfLo97F9WYk0zna09m9NLDA5v5qtsh3ExeeG\n7jKtEw9qjSvOW6lSY6+WGVpFBw7iqLl7qmY4uMTozRsU1dUnAlKCVSNJiSYvV0c7efuqKT18LPF/\ngOunfoZrjRy46+rlhAT0ThDv51gKR7k1scBUTNK62WmjZ9LH+FyAQCjKnz1/kxn/1jqQ49eZV1G1\n6nruBUY6ryNGI2+9gL+Htz4EQcBibmJm5jyiGOaTJ4v46NFCrEYtzU4bnbdXW/219rhJ0Sg5WGjm\ngwcLaHLaaHwLCHj96nEH7z2Qh8Nq4JePFvJ0dTZVuVszPG/aJXqm0aTDnGtYpauzVbT0uKnKTcNq\nTFYprX38HZQdOU6moxhHbT2BhXkmB/u3vf/RrhsJ68CCyv0UHTjI/keeILu0DJ3BiKujnQXPNJ7R\nYRy19aSarVgLCnF1tBMJhXjta39L27e/kbRPmZGyLAG9E8T7OS65ZpIMcuIDj9M907x8c5K/bR3g\nB+2jW9qnOS+fihPN1D31Cyuu5/KOznMjuDraUWm15FVU3bNjrIe9gL8HzJZGolEfc3NX+MDBAj77\nbtk2Lh7k7rT6a+11c6zYgkaloDovnW984jAG7ZvfS+cd+3P44odk9tBD5Zl8+ZcbNnTrWol9OanY\nUrW7Q8+sNHO7b5ZwcHtZzoWlMO1DM2uyiorqGnjnp/9rTE8/RtW8uv2g5epoT1gHqjQa3vv7nyHX\nuQ+FQil76Xa0M3iH4FlhjNo42HGZSCjI5GAfi/PLujcz47fvSgJ6LcTrKS09U7T0uCnPSiU7XUd5\nVipZadoEywxkqvBWIAgCz/zn36Xs0LEV19O1Zu/BbsDVcZmCyv2o1Dt7+N0N9gL+HjCbZGnnO31y\nq3LTsBiSNetd0365W/YtYpK9W1jpBxzdoWqjvdKCGJEY69kek+bsilTaRkhJzyCruDTht7sduDra\nya+sXtM60FFXj2/GS/vzP8ZoMmMtKASgqLaBaCTCmee+Ka8oSUnUxt1kpKRoVBwqMvFy1ySXXDOJ\nWsbK+xP/vl4YWFt6ezPEr2ek6/qOz/dOzE5OMDsxnmg8u9/YC/h7QKVKJT2tfpWhiixNa6V1hTTt\nShXMtxuanFZmF8NcG92ayNx6yClLR6Ve7YK1GVp73Bg0Surt6ytLxuGored2zy2Ci1svDs+7Zau9\n9QJzXPPGMzpM4Qr99ryKSlQaLZ7RYQqqatAZk/V9XB2X70oCej00ldlweRYJRcWkGkyT08ZcIMzU\nQpBn9ucQjIhcGLwLqmbseu5FHv9B0THj2Av4ewDktM7CQiehUPI0uMlpS7L6a+1xYzen4HgTUzDv\nFRrLbAgCCRGvYCRKILT9EaRKrSTXadpSHn/JL3flSpJES4+bYyVWNKrNf7aOmnokUWT4eseWz2s5\nGK09+oxLEcjrLAcslUZDQaWcBiyqa6Cw5gCujnYkUSQSDjPSdZ3CTQTStoP47FKnViRJWp8stRIn\niv0/T5YnpLe3i/j17FYeP7joTxTQXR2XSbNlYcpZvznyXmIv4O8BWNbf8cSkluNISNP2uglFRM72\nyyqYb0eYDRpq8tITs5zf/8F1PvyVc3e1L3ulmdnJReanA+uu4xnz8bXfbWPkppfBaT+jM4Et0UgB\ncpwVaPT6bY1SXR3tpFpsmPPy112nuP4QCqWKwv3JndRF9Yfkf+sacNTWszg3i3vYxditTiLBIEV1\nu5fCqMhOJSddx4kSa0J1FeQGvnq7iYrsVIqsBo4Ume+eqlnXwMz4beam1u823wpCgUW++p8+QfsL\nPyEaCTN84xpFdffH3WotvPkrbXu4L0hNrUatNuP1nCYn+92J5bZULVW5abT0uDlgz2AxFH3TUzDv\nJZqcNv76VB8eX5BXuiZZCEa4PRsgd43O4o1grzLD92C4y0t109oyU4MdbiRRYuCqm0G7LDXRvMXP\nXqlSYa+uTTQRbRZgopEIQ9evUn7s5IbrHn3fh6k40Yw+NZndVPPoU2QXl2G1O9DF3nN1tBNYmEep\nUlFQuX9L570VCILAP//7oxjXIAr85S8eQIw1TTWV2fjT52/e1f1ZqaRZ+/g77vpchzuvE/T76X3j\nLJlFJYSXAhQ+oHQO7I3w9xCDICgwm0/i8Z5GkpL5201OG+1DMzwflyLYobDZWxnNThuiBH91qo+F\nmIvWnSymrSAjK4VUs25DmYV4jn+4y0tr7zQOSwp2S8qWj+GorU/k5TfDeF83ocAijk1G4hqdfk2z\nF6VKRU6ZLBluNJmx2R24rl6W+foVlah1ui2f91ZQZDUkOr1XIjdDT75J/ozis6G7SeuYcvJIs2Uy\neHVnefw4U+p2zy26z7WhUCqxV9XuaJ87wV7A30MCFnMj4bCHBV9X0vLmmNXfc2+M0BBTLXy7oq4g\ng1Sdim+eG0KpELAYNHeVNhAEgYIqM6PdM0TXsJYMBiJMDMyTkq5h3h2gq8ezbWZUfJQ6tIW0zlBH\nO4JCgb16d4KRo66B0VudTA+7HhgjpSxTlt6+2/vjqK1npLMjYTR/N3Bda8doMiOJItdffZFc5z60\nKVt/aO829gL+HhIwx/L4Xs/ppOVxq7+IuNro++0GlVLBiRIrEVHiQEEGj+7LpK13OuELsB3YK82E\nl6JMDqz2ah295UUSJY6+Sx5N5wS2z4xKz8zGlJO3pTz+4NV2ckrL0Rl2x2rPUVufKFQ+KEaKIAg0\nO2Wq5t3cH0dtPaFAgPGeW3d1/JmJ28xNTnDw2feh0et3LC2xG9gL+HtIQKu1YTRW4vHKAX9urp2h\noa+gUSl4usLHs8UvJLlVvV2RkJOISUvML0XoGJ0jKkp87oVbuLbojpVfYUZQCAlTlH96rovv/1iW\nID5zehRBrcB5JBsxRUlRRMnRYgujt7xcOyWnaCYG5mj/mWzP5x5Z4OJPB1eJfjlq6xnpukEklCwz\nsOT3ceofvkJw0c/i/ByTg3046nYvGOWWV6LSajGYzFjtjl3b73bR5LSxsBShYxMq7Zde7+PKsNwX\n8bW2Qc71e7BX1yIoFAzeJVsn/qAtbjiUmDntBfw9vKlgMTcyN3eZSMTHoOtL9PX/b4JBN+8oepV3\nl75AUcbuODa9lfFkVRZNThvvrsvjZKkVhSBLHlwZnuFvWvoTctGbQatXkV2cxnCXl3BEZLJlnL5X\nRhFFkYnuWVzKKIIgMKwRcUSV6JQK3vi3Qc58r5dQIMKlF1yc+2E//rkgV18e5o1/HWRuKpn146ir\nJxIKMnqrM2l599lW2l/4CT3nz9wTqz2VWs3hd76fQ8++74GK6iXuT/f6aZ3bswE+/2I3X369n7nF\nMH/y0y7+4tVetCkGcp377pqP77p6mfSsbEzZudQ+8Qzlxxo3NLu/H9gL+HtIgtnSiCRF8HhamJk5\nD4DH24IqcgmAmZnTG23+toDFqOUbnziM3ZJCRoqG2oIMWnvciVzxdoqE9koz7uEFWluG0UkCqWH4\n15cGMEShWwjzes8U7eEllCIM3fAwMTCPKEoMdXoY65ZHpMOdnhUF3uQicMG+/ShVqlVBK/5/V0c7\nrquXZau94t212jv2/l+k4ZmNfJLuPdJT1NQVZNCygcxCvOh+tt/D6z1TiBJcGvLiD8oCZ1OD/SzO\nba/ZLhoJM9J5PVG/cNQc4Bc+9XsP3EtjL+DvIQkZ6Q0olSkMuv4SUZRHi8PDf0c4LAeUO+UX9iDT\n/66NzvLT6+MA9Lv9jM5szRvVXiWrdt58aTixrOsF+fWgSuTPnr/FsEpEUAic//EAUqzj+eJPXURC\ncl76yssjCdvEOz1z1TodeRVVSbo60UiE4RtyQ9bw9asMXbtCYc2B+2q1dz/R5JTvz3rqmfEHtS8Y\n4a9e6wNkifBz/Z5leuY2XbDGbt0kHFx64CmcO7EX8PeQBIVCg8l0DL+/F0FQY7M+jt/fC0Bm5juY\nmbmAKAY32cvbC00xquaA28+ztXIHZbwbdzPYClLRGdUI8xHm9AI+FaSFYEEN+fmp9E75yEjTklOS\nzsy4H7VOib3Kwsy4H4VSoLjOxsy4XDMobchkrGeGyB36MY66Bjyjwyx45HMa77lFKBCg/FgjS37f\nA7Hau5+I+zWf7lt9TyJRkbbeaZ6uzkapEOid8vFoRSZ6tZLWXjdZRSXoU9O2ndZxdVyOUTB3r/9g\nN7AX8PewCnG2TkbGQWyZTwGQmlpFTvZ7EMUAs7OXHuTpvelQm59Omk6mqn7ihIPcdN2W0zqCQiC7\nTLb8MxQaEXJkvroyV58oDjeWWeVGLSC/3IRjvzwryClNp/iAvI7Nnkr5kWwiIZHxvmTWz/IotT3x\nr6BQ0PiRjyEIcghw1GxsjflWRm1+Bul6deKehKMicwF5RtQxOsf8UoRnanKot8v34bHKLI6VWGjt\ncSfURwdjUhEAHt/ygGdsfGrNY/ZfuUxueSUafTIFc24xTHgNxlDX7fnEOd1L7AX8PayC1dIMCFgs\nD2Exn0QQVFgsD5ORcQRBUO+lde6ASqmguTwTi0FDTX4GTU4bZ/qm1/xhrwWfRZbJrT2cTXldJgD7\nGrJ4pEJ+/UhFJoXVcpAvrLbIrwUorLJirzSjUAgUVlvIdWagUAqrRNmsBYUYTWZcsSaiwauXyXVW\nkJ6ZTY6zgkxHyX232rufkP2arbT2yAbof/5yD499sYVwVKSlx41CkIu7D1dkohBi7KsyKy7PIkMe\nP4HMUpbm57jYfoNLLi8H//QV2odnuHD5Bv/8qU/yr8+fSjre8OgE3hEX8+bkAm0oIvLoF1/nL1/t\nXXWOv/mty/yX71y9p58D7Ekr7GEN6PV2Dh/6MQZDGQqFhsOHfoJeb0ep1JORcVDm6Zf+wYM+zTcV\n/uc7q5gLhFEqZO73cxdHuDoyyyGHedNt26UgFy0Rfv1IHgoBzlj0nDicg0Kh4Ef/8QS1+ekIgsAH\n/uAg1oJUFAqBD/7BIcy5BpQqBR/8w0Ok2fSoNUpySjMY6fLA+5YLsIIgUFhbT//F8/hmvEwN9nPi\nQx8F4NlP/R7iXThjvdXQXGbjp9fGuTWxwEudE7gXglwdmaW1x01tQQYZKRo+ebKIZqeNvAw9zeWZ\n8K9dtPa46YpkYgXOtZ7BX/EQkgQvd02ivd6CAolrZ9p49h0PJ4516lVZj6pdzEw6h8tDM0z7QrzU\nOcmnnyhPLB/2LOLyLPKrxx33/HPYqaftBwRB6BQEQRQE4eCK5Q5BEAKCIFyN/f3Nzk91D/cTqalV\nKBSyfovRWI5SKWuRWMyN+PzdBIOTD/L03nQwGTQJBdHjpVaUCmFLaR1Jkmjtm6Z8nwWVUoFCoaDx\naB6KGJujriAjQWvMLExLGLbY7KkoY6qZljwjao1ccLVXmvGM+fHNJNdZHLX1LPl9XPiX7yb+D2A0\nW0iz/vw308XTY99+Y5h+t1zz+NGVMa6Nzia0obQqJVW56QA4LCkUmPW09LhpGVnCrbHi7b6eoHe2\ndLuZ6ZH18qPDN5MemkPXLrOo0HPKrU7S448Xh7snFxifW6bPtsRYQvejqXGnKZ0bwHuBteb4/ZIk\n1cX+/sMOj7OHNwkSpueePXrmekjXy1TArQT8vikf43NLu/Zjj+f6R24m0zML99eBINDx8vPoU9PI\nKirZleO9VRB3xfrWBZkBlZ2m47mLI4jS2oE2bqhyqtvN7bklPOkODLOjDIx7yE7T0Tfmxjg/xqLa\niCE0z/Uumd0TjURRjvcxle5gKSJxybVsctPa4yY7Ta7RnF5R1G/pdpNv0lN0HyTHd2piflOSpO7d\nOpk9vPlhNFag0dj28viboKnMxrWxObybGGnHR327FfAteUZS0jSr8vj61DRySpxIokhhzYEHzgd/\nEGhyWomKErnpOj5yxE5UlEjXq6nNT19z/WanLeFu1vxoI0pE8gNj/O6T5RQExlAgYX/8/QCcbT0r\n/3uxA100QN3RI2iUioSU9tTCEl3j83z0WKFsxRhbHoqInOufptlpuy8NavfyrhcJgnBFEIQWQRAa\n7+Fx9nAfIZueN+L1nkGStm/+8XZBc3mMCriJkmZLj5vSTCN525TvXQ+CIGCvNDPS5U24lMWRW1ED\nQEF13Vqb/tyj2Snn1JuctoQu0clSKyrl2mHwWIkFlUKgxGbgfU+fJCSoqYje5j0H8nCGxwgpNHzo\nw+/Ep81gsksuuF5uk/0RnniiiYMOUyIFFB/RNzttNJbZaOuVrTLbh2fwh6L3TaNq04AvCMIrgiDc\nWONvoxa6ccAuSdIB4NPAPwuCkLbWioIg/JogCJcEQbjkdu/cIHoP9x5mcyORyCzzCzce9Km8abE/\nL52MFPWGfPylcJQ3Br277i9gr7IQXIwwNTSftFylrUShLkapeXulc+I4VGTiHfuz+cXDdvbnpfOu\nulx++Wjhuuun6tT8enMxv95cgl6nRWd34gyPIQjgjIyhK6xAp9WgKdyHbtrFYmCJmd7rLBizKcjN\npNlpo3tygYm5JVp73ViNGipz0miOWTF2jM7S0uOWJcdL7g9LatOAL0nSY5IkVa/x9+MNtglKkuSJ\nvb4M9APOddb9iiRJByVJOmiz/fwXj34eYDafBAQ8nr20znpQKgT+b3tvHh7Xdd73f87sgwFmuRdD\n7AABClwASaQoSlxEQJYlW/IqOfFWy43bpFXTOr84vyZN7Ki/2n3y5GmTNK6d2m4qp24LQdLVAAAg\nAElEQVRiW4lTx4sky7IlWbJALRRFyiTFfQFIAMR+72DH7Of3x50ZAMRCDHaS5/M88+DOmbu8c+fi\nvee+5z3fd/8txbSc758haJblYKtBLJle9gpiVds0EMwoodjfYcdV+Ai9rTfnxDm3w843Hr2T7VVB\nbDbBVz95B3uv4Wj/w4Nb+fiuKgDuu7+Z9LBB69tvkR6J8O77rcDFljvvwimT/OTZlygcukJhXSMw\nGaZ75VwfB84P0FQfxpa5LqxSmf20nOtnZ02IIo9zBb/5JCsS0hFChIUQ9sxyHVAPtK7EsRSrj8ul\n4S+6bUbRc8V07t0cpn8kxunukVk/bzk3gNthY0/d8vbuPIVONlQXTSuuEo8m6bloTchqP2XOeRNS\nzE02s6nlu9+a9v7d9+0lhY3Tz3wPG5Lb99wNWKUYNxS5eaKlFXMsnruxhzLzNZ4+2sXJruG8Za+X\nwlLTMj8ihOgE9gLPCiF+nvmoGTguhDgG/BPw21JKJbN4A6HpTQwNHSWRmKnlrrDI9vBa5ojjt5zv\n5+5abVpd1uWiulGnt204VwT9ytkI6bRk890ljA3GMLsXJuGsmCRYWkawpAyzq5NQeSWBDSVWe6CI\nsVAVhVGTuM1J836rvq8Qgqb6cC4NtGlK6O7e+mJaMzLaq1kydKlZOj+SUlZKKd1SyhIp5YOZ9h9I\nKRullNullDullM8sj7mK9YKuNQNpzMjra23KuqXE72FraVFu4C6dlvSPWOGUK4MTXOgbXbHeXXWD\nhpTQeSarqGnicNu5+0O1ufeK/MnWDKi9SntI32rp3cfCm/C4Xbn2bJnFWyv8FBe6Z7TrPheN5bMO\nb64IN19ulmJZ8Pt34HAUYao4/rw0bw7npHa/++Zlmv78JYzRWC5Hf6WyM0pq/bi8jpxccvspg8ot\nIQLhAkJlPms2riJv6nZa4ZranXdNa9/bvB+Aqtunl3NsuqUYl93Gu7dMn3W7vTKI5nPxri0bcpPp\nVgMlraBYFDabg1BoX6bouVzTIhfrmXs3h3mipZWDrQY/P9lDNJHmwPkBWs71UxbwUL9heUoKXo3N\nbqNqa4iOUyaDfeMMD0TZ8UA1YPX+T7xyhUQ8lZuhq1gYG7fv5NP/5StsuGri2l07G0j+wZ+y647G\nae0hn4tnf3c/Vdp0ETWH3caP/t0+ggUuVhPVw1csGl1rIhbrZmz8wlqbsm7ZtTGE12nnZyd6eKvN\nCq+8dKaPVy8M0Fy/spNtqho0RiMxjv2iI/ceLIefSqbpOp9fUQ+FFZcvqbtl1t9t713bcTpm9qHr\nS4pmHaep0X0EvKuTnZNFOXzFosnKLFxd9FwxidthZ0+dxg9/dYV4Kk15wMOz73QzEk2u+GSbbHGV\nkwe68Bd7CG6wepnl9UHsTtu0LB7FzYFy+IpF4/VWUFCwScksXIPsFH2P08bvvLueVFrmJHlXkiLN\nQ6i0AJmWOecP4HDZqagPzsjTV9z4KIevWBK61sTg4CFSqeham7Juyfbkd9fqPNBgDd7tqAoSKFj5\nx/nqBj3zd7pMc1WDRqRnnBEzSjya5JdPnmFsKEYykeKVvz/LsDFBOpXmwD+eI9KjUjhvFNSgrWJJ\naHoTHZ1/y+DgIXS9ea3NWZfUFvt4dHc172koYUORh3+1v5ZdG0Orcuxt+8sYHYxRuW26w69u0HmN\nC7SfNHC47FbYJ+wlVOrjRMsV3D4H1Q0ax1/uREpo/uSsE+UV1xnK4SuWRCi4G5vNhWEeUA5/DoQQ\n/OlHJmub/scPNqzasfXyQh567NYZ7aGyAgpDbtpPmThc1oN+xymTUSOaWyYzGbddpXDeMCiHr1gS\ndruXYOBuTFMN3F5PZFU1L7zdj91hZZx0XRhksG8cgL7LI0THkwAM9U0w1D9BILw8ip6KtUPF8BVL\nRtObGBs7TzTatdamKPKgqkEnPpFkYiTBlt2lpJOSUTPGlt2lAAz3T+SW1UStGwPl8BVLRs9WwVK9\n/OuKyq0hsunkd3+4FofTcgd3vq8Gj88aUL7tvkqKdM+MgipXI6VkNBKdsaxYXyiHr1gyPl89bnep\nyse/zvD4nJTdEmRDTRF+3UtVg0awpIBgSQE1t+kU+F2Eq4uobtDoPBshlZq72PnZN3v4zuNvMNQ/\nQduxAf7uj19noHN2lVDF2qFi+IolI4RA05ro7/8Z6XQSm01dVtcLD/7rW3NSye/+jW0k42lL5fET\nm4lPJLHZBNUNOicPdNHbOkR5/ezZRW3HBkinJZdPGPR3jICES8cNiiuLVvPrKK6B6uErlgVdbyaZ\nHGF45Nham6LIgwK/C1/AUnH0+JwUhqxlt9dBkWYV3K7YGkLYBJfnUNhMpdJ0nrY+az9l0HFyUrBN\nsb5QDl+xLGihewCbCuvcgLi9Dkrr/HPOzO1tGyYeTVGouWk/YTA2FKdQc9PTOkxsIrnK1irmQzl8\nxbLgdAbw+7ergdsblOoGnf72EcaH4zM+6zhlImyC3R+uI1tIa+8jm5BpyZWMHr9ifaAcvmLZ0LUm\nhoePkUiof/IbjepGa6Zux+mZvfz2kwYlG/3U7bBqtmrlPjbduQGnx67COusM5fAVy4Y101Zimq+t\ntSmKZSZcVYSn0DnDgU+MxulrH6G6UcPlcbDrAxu586Ea7HYblVtCtJ9U9XPXE8rhK5YNv/92HI6A\nCuvcgAiboGqbRscpE5medOAdpy0JhqxI210fqGXz3dZkrepGnREzymDv+JrYrJjJUouY/4UQ4owQ\n4rgQ4kdCiOCUz74ghLgghDgrhHhw6aYq1jtC2NG0ezCNA6pXdwNS3agxMZJgoHM019Zx0sTtcxCu\nmZl+mVXovNakLcXqsdQe/gvArVLK24FzwBcAhBANwCeBRuAh4BtCCFVL7SZA15qJxXsZGzu31qYo\nlpmqbVkHboV1pJS0nzKp2qbNWpfVX+wlsMGrCqavI5bk8KWUz0sps3lXB4HKzPLDwPeklDEpZRtw\nAbh7KcdSXB9omlXMOVsUJZEYJpEYmrFeKjVOPD6QWY4Si/WtnpGKReELuCmuKsw5cOPKKOPD8Vw4\nZzaqG3W6zkVIJlIrZld0LKHSPxfIcsbwfxN4LrNcAXRM+awz06a4wfF4yvD56jEMy+GfOPE7HDv+\n2Iz1zp37E9566yNImaa19cu8eej9pNMzU/4U64vqBo2ei0PEJ5I5x391cZWr108m0nRfmHnTXy5+\n8rVjPP83J1ds/zcS13T4QogXhRAnZnk9PGWdx4Ek8GS2aZZdzRrUFUI8JoQ4LIQ43N/fv5jvoFhn\n6Fozg4OHicX6iAweZGjoCPH45GO9lGn6B14kGutidPQM/QMvkEhEGBr61RparVgI1Q066bSk82yE\n9lMGeoUPX9A95/oVm0PYHGLF6ueODcXobRum86xJIrZyTxE3Ctd0+FLKB6SUt87yegpACPEZ4IPA\no3JypK4TqJqym0pgVu1cKeUTUspdUspd4fDKFnVWrA6a3oyUcVrbvoKUKaxUzVdzn4+MnCSRsG4A\nnVe+y8REO6DUNq8HSjcFcLrttB7tp/vC0LzhHACn2075LcEVG7jNzv5NJyVXzqn5H9diqVk6DwF/\nBHxYSjk19+pp4JNCCLcQohaoBw4t5ViK64dg4C5sNg9dXd/Hbi/E4QhOK5CSXfZ4Kujq+n5muRLT\nUMXQ1zt2h42KLSHOvdlDOiWpapw7nJOlqkHD7BpjNBJbdnvaT5l4i5w4nDY1OLwAlhrD/xpQBLwg\nhDgqhPhrACnlSeD/AqeAnwGflVZXT3ETYLe7CQXvBtJoob1o2j0Y5mSqpmEeoKiwkZINHwDSeD3V\nVJR/gpHRk8QyA7mK9Ut1g4aU4HDZKN8UXMD61lNAx+nlDevItKTjtEl1g07FlpCa1bsAlpqlc4uU\nskpKuSPz+u0pn/2plHKTlHKLlPK5+fajuPHQMvVtNb0ZXWsmHu9ndPQMyeQIQ0Nvo+lNaFpTbp3s\n8tTQj2J9kpVZqNgSwu68tgvRK3wUBFyL7oEPdI7wyyfPkE6lGewd5xffPk0ykaK/Y4ToaIKqBo2q\nBi1XinEqyXiKX3z7NEP946RSaV7+7hmMK6NzHOnGRwmXK1aEkpIPMTx8jA3hh5AyAYBptlBQUIuU\nSXStmUDgDsrKPkplxafw+epxOjVMo4Wy0kfW2HrFfATCBWy/v4qNt80fv8+SrZ+b1cyfLWd/Pt75\n5RVOvdrFlt2ltB4b4Mzr3Wy6I8xAh1VgpWqbRmzcusY6ThkE7q3Mbdtx2uTM690U+F1UN2icerUL\nm01w76e25GXDjYJy+IoVwe0q5tbGr+TeF/q2YBgtTEQ7sdt9BAJ3YLO5aNj2Z7l1dK0pE/pJI4RS\n/VjP7P9YfV7rVzfonHmjh77Lw5TWBha8nZQyl+HTfsrM1dZtP2Uy0DFCuLqIAr8Lb5EzV4rx1ikO\nP/tU0X7SyOUJtp8ykFIiRH43nhsB9V+lWBU0vZnBoSMMDLxEKLQXm801cx2tiUTCZGT01BpYqFhJ\nqrZpIMg7rBPpGbcGewWcO9SDcWUMBLQd7aendTg3ByD7FDG1FKM1E9gAAQMdo5w/3AsChgeiDPVN\nzHfYGxbl8BWrgq41IWWCWKwnV/T8ajQ9E8dXRVRuODyFTjbU+HM99IWSTbvctreM4QGrMPq2fWWM\nRmLItMyNJ4D1FJGIpuhttSZ5DfVNMDwQZdu+MgBGjMnlm1XfRzl8xaoQDO7CZvMCoGcc+9W4XcUU\nFjbkZBnS6WQuR18xnfHxy+ST+BaL9ZNMrk1R8fHxNsDK7ultGyY6lljwtu0nDYIlBTQ2WRP1CwIu\n7nhPNQBOj52Susnw0NWlGLNOfed7a/AWOQG47d5K/GHvkjJ6pqp/DvaOX1dCgcrhK1YFm82Nrjfj\n89Xj9VbPuZ6uNzM09DbJ5AidnX/HGwcfVDo7VxGNdnHwzffSeeXJa6+MFdo48vYnOH3m8RW2bCam\n+RpvHHyASORgLp2zc4FVsJLxFFfOD1LdqBGuKaIg4GLjbcUESwoIlhRQ06hjt0+6sKtLMXacMgiE\nvQRLCth4WzGFITfFlYXUNGhcORshlUjn/X06zpg8+cWDXDkboffSME9+8SBtx66fVGLl8BWrRsO2\nP2PnHd+ddx0r9JMkEjlI/8AvkDI+bdKWAgyjBSmTDPT/YkHrj49fZGLiMobxCun0wnvXy0H/wIsA\nDAy8REmtH5fXseDeddeFQVKJNNUNOjab4ONfuIv9H6tHCMFHfn8n931664xtsqUYRyNROs9GcjH+\n/R+v56Of32Xp+jfqJONpui8O5v19LmWce9s7A1w6bi1n/14PKIevWDUcjiJcruJ51wkEdmK3++jr\n+xlDQ0cAJblwNdnzMTh0iFTq2oOP2fVTqVGGho+uqG1Xk71ZG2YLNruNqq0hq4jKAsIg7SdN7A4b\n5ZutyV2+oBun21JZL/C7cHlnJhlmY/qHnmkjGU9T1Wiljro8DnwBS/OnYnMQm10sKo7fnnt6MHPL\n7Qv8PusB5fAV6wqbzUUotIee3qeQMonXU41pvppXvPpGJp1OEom8htdTTTodZ3Dw2oolptGCx12O\nEPZVla+YmOhgfLwNr6easbHzRKPdVDVojEZimN1j19y+/ZRJeX0Ap2vhpTSypRhPv9GNzS6o2Dxz\nJrDL46BsUyDvjKHhgQkGe8fxF3swu8bouzyMv9jD2ODCvs96QDl8xbrDyuKR2O0FbNz4WRKJCCMj\nSv4WYHj4KMnkCLW1/w82mzsnQz0XqVSUyOAhisPvwe/fkRsQXw2yTxabbvlDwOrtV2d63B3X6F2P\nmFEi3WNUXUOc7WqypRiRUHZLAJdn9qlG1Y06xpVRxoYWru+T7dHv/cgtVoOcXL5edHyUw1esO7Iy\nC6HQXoqL7wPErI6tveP/5MTXrlz5Bzo6vw1AT89TXLr8vwDo6/85ra1fmbHtSpBOxzl16g8ZGT2z\nrPud+n0sJ2qjuPh+gsG7J8M7g4c5c/aLM0ILg4NvkU5H0bUmdK2ZkZGTxOMGsfgAJ058jnjcIJEY\n5sTJ3yMa7V6yrZcufYOe3meAzJOFp4IN4Ydwu0osDSXNQ6i0YNZwSvspg9f+6TwweUOYT2t/LrJh\nnfmUPKsy+73Wjefwc5c4/1Zvbt1Czc2mnWF8QTfuAgd1d4QJlfnyTjddK5TDV6w7CgpqqK7+11RX\n/RYul05RUeOMOH46naC19Su0tn3VKqLS9lVaWy055rZL/4O2tq+SSkW5fOmvabv0dRKJ/Afo8mVw\n8DDdPT/gygKzZxbK1O9jmgcI+LfjdAbQtWbGxy8SjXbR0fG3XLny3RmlJU3zQCZMthtdt56cTPM1\nenufobfvJ/T1PUf/wPP09j5DT8+Pl2RnMjlGa9tfcenSN0inE5iRN9C0JoQQaHoTpvka6XSS6gad\nrvODJOPTw3RHX2jn6IsdDBsTtJ8y8AXdaOW+vO2o3R5m655StuwunXOd4opCvH7XvDr98WiSt37S\nxuHnLpFKpek4Ywm1CSHY/eE69jxch81mTfjqOj9EIr7+w47K4SvWJfW3fJ5QaDdgZe4MD/9qWh75\n0NCvSKVGicW66e17lni8n2RyiN6+nzI+3kY6HaO//+cMj7wDpDHN11bc5twA5TIWcZ+Y6JzyfZ5n\nePj4FGE660loYOBlzIj1/a4O2RhmC8HAXdjtBRQVNeJ0hjDMlimDqQdyE92WOjgeGTyIlAnGxs7R\n1/8zUqnR3CQ7XWsimRxiZOQ4VY0aqUSaK+cnb8KJeIqu89aEqfYTBp1nrAybxcgfuL0O7v8XDfMW\nZhEZR91xOkI6Pftv1XVukHRKYnaNcfHtPhLRVO7pYdu+spyEQ3WDRiqZpuv8yncqlopy+Ip1j6bf\ni5QpTPP1XJtptpC9fC9e/G+ZVjFl2cbF1i9jCajYViXTJxtuiUY7mJi4tEz7zDpwGxdb/xKQ6JmQ\nl6/gFtzuUi63P0EyOQzYps1Sjka7GRs7n7sxCGFHC92DYbxCJPImYCMSeQPDfBWwMTR0hGRy8UqS\n1rEnfxMh7GjaPgA07R7AhmEcoKI+iN1po2NK3Lvr/CCpZBoh4O3n24mNJ3Nhl5WiukEjOpagv332\nCWntp0yy95uDP25F2ASVW2faVJ75PitV1Ws5UQ5fse4J+HdgtxdO670a5gECgZ0UFNQRjXZS6NuC\n33870WgnHnc5Wmgf0WgnDkeQcPgBTHP5et2zEYv1MTp6mvLyj+XsWw5M88BV3yeA3387YOnH6Foz\n0WgnYKOs7NeIDL5FKjWe2xaYJmWh680kEibpdJTy8o+RSo2RTA5SXv6xzPyHNxZtq2G2oOvNuFwb\niEY78fvvwOEoAsDpDOH3345hHsDhslNeH5yWj99x0sTutFF/VwkjRhQhMvo7K8ikvs/sjrr9lEFV\ng44v4GLEiFJa58c9Syqow2Wnoj54zfGA9YBy+Ip1j83mRAvtxTRakFISjw8wMnICfYqOvnb1cqZX\nq2n3oOvvIhbrycW3x8cvk05b2RkTE52z5rLHYr0kEsMLtjHrXCsrPo3XW33N7JmFkE4nMM3X0fSm\nTPzd+j5CTKYpZsM7fv92Sko+hJTxTO/duum4XSX4fJsn19eyvX0XdbW/hxAOQFBb+7vY7QWLvlGN\nj19mYuIyutacewLJ/s1iheaOkUgMUt2gMTZ2kWHDujm1nzIorw9Su90qc7phox+Pz7koWxaKt8hF\nuKoo56hTGb19gKH+CYb6Jqhu1HJPGvMNIFc1aER6xhk21rcom3L4iusCTW8mGutifLw1F4/XtSbC\nxQ8AEC5+gHDx/bnlYv0+wEa4+IGc4zHMAyQSEd489BCXL3+TVGqCNw99gNbW/z7tWFJKjhz5JGfO\nLlyKwDAP4HIVU1i4FV27l0jkYO6msliGho9m4uD3ok/5PlPRQvdgs3kJF9+fKy1pmC2ZENhraHrT\ntDi4270Bv387mrYPt3sDoeAeAoGdeNylhEJ7M7N4838Syj1N6M2Eww8AguLid09bx7ppWeMp4U2D\n1D70Rc6d+HsrBbNnnOoGjaptIRwuG7Xb55+gt1xUN2r0tA0Tm0hy/KVO/uE/v8nYYCyXdVPTqFs3\nIQE1t81tU66q1zrv5Ss9fMV1QTYsYZgtjIycwOnUKCq6FSFs7Nv7Cl6vNYA2ffmXeDzlCCHw+eox\njQN43KWk03EGjJfw+28jlRplwHiJ+vo/zh1rbPwCE9F24gmTdDqBzTZ/T9Nyrq+i6/cihA1Nb6Lz\nyncYHDySi2EvBtNoycXBHY6i3PeZitPpZ+/eF3E5dWw2J6HQbkzzAMPDx0kmh2b0sgF2bP9W7inh\nttu+hpSWpoymNTEw8AsmJi5RUFCbl62GeQCPpwqvdyNe70b27f1l7nfIUlR0Ow6HH8M8QEFBHUJI\nIoO/pP3k+wDLaboLnDz6n/fi9a9s7z5LdYPOkecu03nG5NJxq0BL+ymD9lMmRbqHwAYvgQ1e/vmf\n7MVf7J1zP6GyAgpDbtpPmTmht/XIUouY/4UQ4owQ4rgQ4kdCiGCmfaMQYiJT5zZX61ahWCxebyUF\nBbUYxisYxgE0bX+uSMpUxzJ9uSLXu9W0JgaHDtHX/3MAhoeP09PzNGCpOU5MdOS2yw58plKjDA39\n6pq2jYycJJGIoGv3AhAK7kEI55InORlmC37/jlwcfOr3mYrHXZq7KWlaE+PjbRlhNZEZLJ2O0xnM\n7dPhKMLptBQnpz4J5UM6HScSeQM98zQhhJjh7AFsNgda6B5MYzJLSHqOcumdPgpDbkJlBQAUhtzT\nRNFWkpI6P06PnYtv99Nz0coSunR8epaQEGJeZw9T9PhPmzk9/vXIUs/qC8CtUsrbgXPAF6Z8dnG2\nWrcKxWLRtGZM81USCWPWnut86Foz6XScvr7n8HprAElP71OZ5elOzjCtCUNC2BfktK14/aRzdTh8\nBAN3Lkn0LR43GBk5OWftgLnIrt/T82P8/u04naEFb1tQsBGvtzrvegRDQ2+TSo0t6DfR9WZi8V4i\nkTdw2CqxOyfo7Xpr0SmYS8Vut1G1VeP84V7SaUkg7KX1WD+JWCo3K3ihVDXoxKMpetsWPvaz2iy1\niPnzUspk5u1BYOZtXaFYJiyHYsWXtTwdfjB4FzabG5DUVD+GwxEAJJUVj+LxVOQ0ZlKpKIODhwiH\n30vAvzOT/jk/htlCUVEjLtekg9D0ZkZHzxCL9eZlZxZrnELmBmsXSkFBHR5PBVPTN/NB05oxI2/k\nNf5gmAcQwkEotHcB+8/aJNlU9/tIKfCVnMxbQmE5qWqwpBgcbju7PrARJNhsgsotC79ZAlRts/T4\n13Mcfzmfm34TeG7K+1ohxK+EEK8IIfK/8hSKqwiFdiOEi8LCBtzucF7b2u0egsG7AdD1e3O98Wx2\nj+XkEgwOHiKdjqFrTWh6U0aKYIBYrI/j73yWeHy6FG4yOcLw8NEZPfHFhkeyGGYLTmeIoqLGvLYT\nQkzJVsr/307XmkinJxgcPEI6HefkyX/PyMhJpExz6vTnGRw8jJSSs2e/hJF5EjANK0U2GyaaD4+n\nDJ+vHpvNQ1nFg6TG6vGVnqRya37OdTnJZt9Ubg6y8dZiEFaoZzY1zvlwFzgp2ehf1/n41/xGQogX\ngdnmKD8upXwqs87jQBLIzinvBqqllIYQ4k7gx0KIRinljGcdIcRjwGMA1dVzF8ZQKOz2Am7Z9Ad4\nvVWL2r6m5t/g92/H4ymjuuq38HjK8RXcgq4109X1PYaGj2JkpAiCwbtxOkO0tn4Z03yNeNygv/9n\naKG9VFZ+OrdP03wdKVO59MgshYXbcLnCmMYByss+mpedUqYxzew4xcKVIrNUVf4GNpuTgH9H3tuG\nQtb4gxWOssJednsB5eUfp7v7+6RTE7hcOp1XvsNEtJ3Com2MjJ5kU93vL/gYtbWfIxbrwW53E95w\nL5Gxv8HuGgXWxun7i73c+VAN1Y0ankInuz9UR7jm2jev2ahu1Dj0kzYmRuN4C2fWbV5rrunwpZQP\nzPe5EOIzwAeB+2Umn0tKGQNimeUjQoiLwGbg8Cz7fwJ4AmDXrl3Xh6i0Ys2orv6tRW+rhfaiZcIO\ngcAOAgHLIWravox08CsYRgvBwN3Y7V6Kim7F6dQwjBbiCavXZpgHpjl8w3wFu71whnO1etr7MYxf\nImUqL8c9OnqGeHxgUSEZgMLCLWzZ/KVFbetwFBII7LRSOzPhM8M8gNtj1YI1I68RMO4AIBJ5k4F+\nq8BJPiG2kg3vyy1v2vYgh498E8N8ldKSDy3K5uVgzyObcsu73r9x0fupatA49EwbHadNNt81t5bP\nWrHULJ2HgD8CPiylHJ/SHhaZK1wIUQfUA61LOZZCsVI4HEX4/XfQ0/MU4+MXcnFzIWyW0zZbMrrz\nlhRBOh0HrHx90ziApu2bNXVT15pJJCIMj5zIy55sGCjfcYrlQtes8Yfe3p9gSUV00nXle4CNRCJC\ne/v/Bmyk01EuXfp6JkU2v9BTFr//dhyOwA1TuH5DjR+3zzFNNmI9sdQY/teAIuCFq9Ivm4HjQohj\nwD8Bvy2lXJ9nQKHAil1HY13AdEera00ZKYIYFeWfIJUaY2jobcAqHRiNdc3pmK1xApF30RHTaKGw\ncBtu94bFfZklkr3hxWLdVJR/AoBorCsjGyGIxrooK30EIVxEY13oWlMuRTZfrHkG92CssPTFamHL\n6PGv1ypYS83SuUVKWXV1+qWU8gdSykYp5XYp5U4p5TPLY65CsTJknZzbXYrPV59rzzpzm81FbZ0l\nRZDtgRuzaNVMxZJ2vjW3XjodZ2zswrx2JJNjDA4dWXQ4ZzkoLNyaK0VZUfEpvN6NAJSWPExR0a0A\nhMMPEgzuApb+JKJrzcTjfYyOnV3SftYL1Q0a48NxjCuLF6JbKZS0gkIBFBXdittdSnHxA1dJEYTx\n++9AC+3H7SomENiZCz+YRgsFBXWzTjLKYunHHCWRGKaj4//w5qEPEI31zLl+VpOq9dsAABEiSURB\nVGJ4rcI5YIWyiosfwOOpoLBwK+Hwe3A6NQKBOwiH34PdXkgotIdw+D3YbO5FZQNNJbv9apZfXEmy\nMgvrsQqWcvgKBZaTu/uuZ6i/5QszPtux/Vs0Nlp6O7rWxMjoSSYmOokMvnlNx6zpzUiZIhJ5nYGB\nl5EyiWm8Ouf6pnEAu72AYPDOpX2hJbK5/v/jrl0/Rggbm+r+X/bsfg6bzUVN9WPs3fMiDkchlRWP\nsm/vy7ivUZj+Wnjcpfh8m2+YYvW+oBu9wreoIukrjXL4CkUGl0vDbvfMaHc6/TgchcCkOmVr23+3\n8vWvMTEqK+3c2/dThoYtmYb5Zu8a5iuEgnsyk8TWDrvdg8tl5afbbO5ciMdmc+bmQAhhx+0uWZbj\n6VoTg4OHc9LO1ztVDTrdFwaJR5PXXnkVUQ5fociDosIGnE6Nnp4fW6UDg7vnXd9mc6Jp++jrexYp\nk3i9GzHNV5FyZjk8S2K4fckhkusRXb93mrTz9U51o0Y6Jek6t76qYCmHr1DkgRC23ICqVTpwflEt\nmBzUtNt91G78LMnkEMPD78xYb7aCJTcLgcCunLTzjUD5piAOl23dhXWUw1co8mSypuzCHHPWgYdC\neykuvg8QuXj1xdYv0939Q8DK+vF6qiko2LjsNq937HZ3TtoZIBI5yKlTf5iTbs4yOnqO4+98dtai\nNatJR+e3uXz5iRntvb3Pcv7Cf8XutFGxOTStqtd6QDl8hSJPwsUPUFHxKUpLH1nQ+l5vJbUbf5ea\nmsesUn9Ft2Ear5BMjnD58v/icvsTOYnhmzGckyUr7Twx0UFH57fp7vkBo6Nnpq3T1f1/6e//2aoU\npZ8LKdNcuvR12i59nXQ6Me2zy+3fpL39b4jHDaoaNIb6JhjqXz9VsJTDVyjyxOEoZOuWP8krO6Wu\n7nMEA1bmjaY3MzR8jL7+nyNlkrGx8/T2PpuRGL75wjlZsvUEBoyXcw796lKR2fdrGfoZHT1NPD5A\nKjXK8PCxXLslaX0CkJjma9Q0ZqtgrZ9evnL4CsUqY40BpGlt/UpOY+di619mJIb3rK1xa0hBQS0e\nTwWXLz9BKjU6ox5BNNrF+PjFjO7R2qVwGrlj26bZl5W0ztod2OClSPesqzi+cvgKxSqTrWIVi3Wj\n6/fhdpcSi3UTCNyZS/+8GclKO8di3Qhhp6zsYwwNvU0yOQZM9u4ryj/FRLSd8fFLa2KnYVrSF4HA\njmk3nqykdTj8YE5ttLpBo/NMhFRyfVTBUg5foVhlbDYHoZClx69rTbksnps5nJMlO6/B799OyYYP\nIGWCyOBBIKPa6S6lqupf5N4DRKPdxGL9M/YVjxtMTFxZVvuSyVGGMtIXmtbM8Mg7xOPmpKR16B50\n/V7i8QFGR89Q3aiTiKXoaR2ad7/tJw3MrrFltXU2lMNXKNaAcPg9COFE19/FhvB7AVsmg+fmRgvt\nw24vJFz8HoLBO7HZvBhGC+l0kkjkNXSt2SrF6KnOSTEcO/6vOHHyczP2dfr05/nV0U8vq4hZJHIQ\nKZNoenOuAptpvpqTtNb0ptyN2zAPULklhM0m5g3rSCl56TtnOPTMygsK51fSRaFQLAulJQ+jhe7B\n7Q7j9Vay/57X867idSPicBSxb+9LOByBTNHzvZhmC8PDR0kmR6alxPb0/JDx8cuMjp5BCDvJ5Eiu\n6lYqFcWMvEY6HWN8vBWfb9N8h10whpmRvgjciRB2HI4gpnmAaKwbsJ7S3O4NFBZuxTRa2Fjzbyip\ns6pg7X1kdhvM7jHGBmN519BdDKqHr1CsAUKIaQ5eOftJXC4dm83qi2p6ExMT7XReeRKwoYX2AVYo\nLJUap63tqwBImcKMvJ7bx+DgW7m6vMuZ0WMaLRnpC9cUaedXMYxXKCzcmpO01rQmBoeOkEyOUd2o\nM9AxyvhwfNZ9ZmvgVmVKLa4kyuErFIp1S3ZWc2/v0wT823E6A0C2FKODnt6ncLtKsNsLpw2gmplS\nlR5PZW4y11IZH7/ERLR92oS7rLTz4FVCerrWnBt/yNbM7Tg9e1in/aRBqLSAIm2mjtNyoxy+QqFY\nt3i9G/F4rBrGUx2tVYpxcl5DKLRnWhEVw2whGLiL4uJ3E4m8SSoVW7Itk/UPJh27pu/PLU9tz44/\nmMYBwlVFeIucs866TcRTdJ0fWpVwDiiHr1Ao1jFCiFzmztVZTNn3ut6MrjUTjXYyPt5GNNrF2Nj5\n3ABqOh1lcOitRR3/wsX/RlfX9wErnHO19IXHXUqhbws2mzdXEAYshVHrJvQKwiao3NHBuOO/kE6l\naD39Ki88/c9JxKN0nRsklUznngJWGjVoq1Ao1jVVlZ/Bbi/A779tWntZ2a8Ti/dQrN9HPG6lZZpm\nC3Z7AWDdELzeKoRwYRot6Nr+Gfuej2RyhPb2b+L11lBa+jCRwYOUlv7ajPXqNv0+sVjvDElrXW/G\nMF5mfPwyvsoXsKfeoLP1bdoufAdb4eu0nTlA75ka7E4b5fXBvGxbLMrhKxSKdY3Pt4n6Wz4/o93t\nDrNl85cA8Hqr8Xo35rJo3JmiKkIIgsFdGGYL9fxxXseNRN5AyiTj4xfp6X2aVGp81tKT4eL7Z90+\nu+6A8RIJeQSA9rbnSdoP4wC6O1/iyqmHqagP4nDZ87JtsSw5pCOE+BMhxPFMEfPnhRDlmXYhhPgr\nIcSFzOc7l26uQqFQzI6uNxGJHMQ0X0XT9udKVepaE2Nj54lGu/Pan2EeQAirT9x68ct5S19kxx/a\nL3+TVHoMmbYzlvwhDs8gMm1nPH6QSM/4qmTnZFmOGP5fSClvl1LuAH4C/KdM+/uA+szrMeB/LsOx\nFAqFYlZ07V7S6SjJ5PC0eL+uW6Jspjl3acmrkVJiGC3o+rtwu8uIxXvzlr7Ijj/E4r0IYceZeB8O\nj1UQxR59Py5/O3bP6g3YwjI4fCnl8JS3PiA7re1h4NvS4iAQFEKULfV4CoVCMRuh0G6EcAE2NO2e\nXLvPtxm3qySXj59MjjA2dgGAVGqc0dGzAKTTMUZGTgIwMXGJaLQTXWvKhWYWI32R3dbv30FZxQet\n449VsWnLo9bndecIlRYwMPAyI1dJQa8Ey5KlI4T4UyFEB/Aokz38CqBjymqdmbart31MCHFYCHG4\nv3+mHoZCoVAsBLu9AF1vIhS8G6dzchDUEmXbj2m+hpQpLlz8c946/BFSqShtbV/j0FsPk0gM0t7+\nLQ699QjRaFdOqE3XmwlveBAh7BQXvztvm0KhvZZURPi91G5tIhXz43U2U1m3k1QsQPEt5wA4c+Zx\nLl36+vKciHlY0KCtEOJFoHSWjx6XUj4lpXwceFwI8QXgd4AvAmKW9WeIWkgpnwCeANi1a9fyiV4o\nFIqbjlsbv8osbgZdb6a75wcMDx9jYOBlUqlxBgcPMWC8jJQJTPM1BoyXgTSG0WJVH/PWZAaDq9l/\nz8FcUfd8cDgKuWffKzgcRQhh5557XsTlLcRmt1NW8S4iQy2Mjp0lFu+ddUB4uVmQw5dSPrDA/f09\n8CyWw+8EqqZ8Vgl05WWdQqFQ5MFcNYatEI+gveNviWV0b7q6v8/YmNXD7u37KcPDRwEYGPgFkchB\nyss+mtt+Mc4+y9SnDZ9/Ml4f3nAvfQNPcenSNzI2rrzDX44snfopbz8MZANRTwO/kcnW2QMMSSnz\nGyZXKBSKZcDpDOH3305f37MA+Hz19PX9NLfc3/8zpEzh89UzYLxEOj2Rm/C1UmjafkDQ1/csPl89\nHs/KD3EuRwz/vwohTgghjgPvBbI6pT8FWoELwDeBf7cMx1IoFIpFkR10LSioo7zsYwC4XBuoqvqX\nANjthWyssdyUEE6Cwd0rao/LpVNU1DjNtpVmyROvpJS/Pke7BD671P0rFArFcqDpTbRd+h9o04rO\n7M85Wy20N5PCaSMYuBOHw7fiNulaEyMjJ1YlnANqpq1CobhJCPh3UFPzbykv+yhebw21G3+XDRse\nwuMpY9OmPyQU2oPTGWBz/eMUFm5bFZsqKj5FWiYIhVb2aSKLWM5qMEtl165d8vDhw2tthkKhUFxX\nCCGOSCl3XWs9pZapUCgUNwnK4SsUCsVNgnL4CoVCcZOgHL5CoVDcJCiHr1AoFDcJyuErFArFTYJy\n+AqFQnGToBy+QqFQ3CSsq4lXQoh+4PISdlEMDCyTOcuJsis/lF35s15tU3blx2LtqpFShq+10rpy\n+EtFCHF4IbPNVhtlV34ou/Jnvdqm7MqPlbZLhXQUCoXiJkE5fIVCobhJuNEc/hNrbcAcKLvyQ9mV\nP+vVNmVXfqyoXTdUDF+hUCgUc3Oj9fAVCoVCMQc3hMMXQjwkhDgrhLgghPj8GtpRJYR4WQhxWghx\nUgjxuUz7l4QQV4QQRzOv96+RfZeEEO9kbDicadOEEC8IIc5n/oZW2aYtU87LUSHEsBDi99binAkh\nviWE6BNCnJjSNuv5ydRq/qvMNXdcCLFzle36CyHEmcyxfySECGbaNwohJqact79eKbvmsW3O304I\n8YXMOTsrhHhwle36xyk2XRJCHM20r9o5m8dHrM51JqW8rl+AHbgI1AEu4BjQsEa2lAE7M8tFwDmg\nAfgS8Afr4FxdAoqvavtz4POZ5c8Df7bGv2UPULMW5wxoBnYCJ651foD3A88BAtgDvLnKdr0XcGSW\n/2yKXRunrrdG52zW3y7zv3AMcAO1mf9b+2rZddXnfwn8p9U+Z/P4iFW5zm6EHv7dwAUpZauUMg58\nD3h4LQyRUnZLKd/OLI8Ap4GKtbAlDx4G/i6z/HfAI2toy/3ARSnlUibfLRopZQtgXtU81/l5GPi2\ntDgIBIUQZatll5TyeSllMvP2IFC5Ese+FnOcs7l4GPielDImpWwDLmD9/66qXUIIAXwc+IeVOPZ8\nzOMjVuU6uxEcfgXQMeV9J+vAyQohNgJ3AG9mmn4n80j2rdUOm0xBAs8LIY4IIR7LtJVIKbvBuhiB\nDWtkG8Anmf5PuB7O2VznZz1dd7+J1QvMUiuE+JUQ4hUhxOpUx57JbL/dejlnTUCvlPL8lLZVP2dX\n+YhVuc5uBIcvZmlb09QjIUQh8APg96SUw8D/BDYBO4BurMfJteAeKeVO4H3AZ4UQzWtkxwyEEC7g\nw8D3M03r5ZzNxbq47oQQjwNJ4MlMUzdQLaW8A/j3wN8LIfyrbNZcv926OGfAP2N6x2LVz9ksPmLO\nVWdpW/Q5uxEcfidQNeV9JdC1RrYghHBi/ZBPSil/CCCl7JVSpqSUaeCbrNBj7LWQUnZl/vYBP8rY\n0Zt9RMz87VsL27BuQm9LKXszNq6Lc8bc52fNrzshxGeADwKPykzANxMuMTLLR7Di5JtX0655frv1\ncM4cwK8B/5htW+1zNpuPYJWusxvB4b8F1AshajO9xE8CT6+FIZnY4P8GTkspvzylfWrM7SPAiau3\nXQXbfEKIouwy1qDfCaxz9ZnMap8Bnlpt2zJM63Wth3OWYa7z8zTwG5ksij3AUPaRfDUQQjwE/BHw\nYSnl+JT2sBDCnlmuA+qB1tWyK3PcuX67p4FPCiHcQojajG2HVtM24AHgjJSyM9uwmudsLh/Bal1n\nqzEyvdIvrJHsc1h35sfX0I79WI9bx4Gjmdf7ge8A72TanwbK1sC2OqwMiWPAyex5AnTgF8D5zF9t\nDWwrAAwgMKVt1c8Z1g2nG0hg9ax+a67zg/Wo/fXMNfcOsGuV7bqAFdvNXmd/nVn31zO/7zHgbeBD\na3DO5vztgMcz5+ws8L7VtCvT/rfAb1+17qqds3l8xKpcZ2qmrUKhUNwk3AghHYVCoVAsAOXwFQqF\n4iZBOXyFQqG4SVAOX6FQKG4SlMNXKBSKmwTl8BUKheImQTl8hUKhuElQDl+hUChuEv5/V8I27hjK\nqk8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b58cb9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def stoppedrandomwalktrajectories(level,W,N):\n",
    "    for i in range(W):\n",
    "        helper = numpy.random.binomial(1,0.5,N)\n",
    "        walk = numpy.cumsum(2*helper-1)\n",
    "        pylab.plot(numpy.array(stoppedrandomwalk(level,walk)))\n",
    "    pylab.show()\n",
    "\n",
    "stoppedrandomwalktrajectories(5,10,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2j0yrpjW23WYYr+3ArwI3nW6b5niNygZmtH9tlXDv8wiEqeiu570PuK+q3jHUPnyt7FeA\ne1f+2w2u6+lJzjs9zeDDuHt58qMhrgL+bpp1DXnS0dSsx2uF1cZoEfit7lsNLwK+evr0ehqSXA68\nBdhbVV8fap/L4P9ZIMlzgd3AA1Osa7Vttwjsz+A/79nV1fUf06qrcxnw2eoeYgjTG6/VsoFZ7V8b\n/QnypH4YfLL8OQZ/dd86wzp+msGp093And3Py4EPAPd07YvABVOu67kMvqlwF3Ds9BgxePTyJ4H7\nu9/PnsGYfQ/wOPDMobaZjBeDPzCPAN9icOT02tXGiMFp86Fun7sHWJhyXScYXJM9vZ+9q+v7ym4b\n3wXcAfzylOtaddsBb+3G6zhwxTTr6tr/Enjdir5TGa81smEm+5d3qEpSg7bKZRlJ0hgMd0lqkOEu\nSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGvT/TCFh+9msn+oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b7a5af60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23.345\n"
     ]
    }
   ],
   "source": [
    "def firstreturn(walk):\n",
    "    y = len(walk)+1\n",
    "    for i in range(1,len(walk)):\n",
    "        if walk[i]==0:\n",
    "            y = i\n",
    "            break\n",
    "    return y\n",
    "\n",
    "def firstreturnhistogram(W,N):\n",
    "    z = []\n",
    "    for i in range(W):\n",
    "        helper = numpy.random.binomial(1,0.5,N)\n",
    "        walk = numpy.cumsum(2*helper-1)\n",
    "        z = z+[firstreturn(walk)]\n",
    "    pylab.hist(numpy.array(z),bins=max(z)-min(z)+1,normed=1)\n",
    "    pylab.show()\n",
    "    print(numpy.mean(z))\n",
    "firstreturnhistogram(400,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d15jZbUCpu5cA84EFZlZGfM9gZtPyZrYZGAzkmtmFwNnuvhb4OvAQUAD8Onh0m1DeAAD2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\nJKBAEBERQIEgIiIBBYKIiADw/wFsYV+0tjNjVAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b5a27c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def lastvisit(walk):\n",
    "    z = [0]\n",
    "    for i in range(1,len(walk)):\n",
    "        if walk[i]==0:\n",
    "            z = z + [i]\n",
    "    return max(z)\n",
    "\n",
    "def lastvisithistogram(W,N):\n",
    "    z = []\n",
    "    for i in range(W):\n",
    "        helper = numpy.random.binomial(1,0.5,N)\n",
    "        walk = numpy.cumsum(2*helper-1)\n",
    "        z = z+[lastvisit(walk)]\n",
    "    pylab.hist(numpy.array(z),bins=N,normed=1)\n",
    "    k = numpy.array(range(1,N-1))\n",
    "    rho = (1/numpy.pi*1/numpy.sqrt(k*(N-k)))\n",
    "    pylab.plot(k, rho, \"k-\")\n",
    "    pylab.show()\n",
    "lastvisithistogram(10000,500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is fascinating to understand the binary expansion of a real number $ \\alpha \\in [0,1] $ as independent Bernoulli random variables with respect to Lebesgue measure thereon. We shall visualize this Bernoulli sequence by the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PhyE8IiCZzmEo1Iy+TnvO0+thuDoSwnuTFONL8sw4Yr8EQOacT3POUwC+BuBzJoxryP99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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b5a81198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def randomwalk(alpha,N):\n",
    "    z=[]\n",
    "    beta = alpha\n",
    "    for i in range(N):\n",
    "        if 2*beta >= 1:\n",
    "            z = z + [1]\n",
    "            beta = beta - 0.5\n",
    "        else:\n",
    "            z = z + [0]\n",
    "        beta = 2*beta\n",
    "    walk = numpy.cumsum(2*numpy.array(z)-1)\n",
    "    pylab.plot(walk)\n",
    "    pylab.show()\n",
    "\n",
    "randomwalk(1/numpy.pi,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s0czISSUlMY6k+FjiY2NCvRkiImEVTLgPdMavf3QG0wYzWw4sB8jLywti1Z+U\nkRzP9PGpxMYYcTHW9zXW/zUmhtgYIzkhllEJsSTHx5KcGEf6qHjSR8UzOiGOjOR4xqclkRCnwBaR\nyBVMuJcDkwOmc4HKQ7QpN7M4IB2o7/9BzrkVwAqAoqKio+qyWXrCBJaeMOFovlVEJGoEc/i6Gig0\nsylmlgAsA1b2a7MS+Ir//eeAV73qbxcRkSCO3P196DcDL9J3KeSDzrlNZnY7UOycWwn8DnjYzErp\nO2JfFs6iRUTk8IK6zt059xzwXL95Pwp43wFcGdrSRETkaOmsoohIBFK4i4hEIIW7iEgEUriLiEQg\nhbuISAQyry5HN7MaYPdRfnsWYXi0wTCnbY4O2ubocCzbfJxzLnuwRp6F+7Ews2LnXJHXdQwlbXN0\n0DZHh6HYZnXLiIhEIIW7iEgEGqnhvsLrAjygbY4O2uboEPZtHpF97iIicngj9chdREQOY8SFu5md\nb2YlZlZqZrd6Xc/RMrPJZvaamW0xs01m9m3//Ewze8nMtvu/jvHPNzO727/d681sQcBnfcXffruZ\nfeVQ6xwuzCzWzNaa2bP+6Slm9p6//j/7Hy2NmSX6p0v9y/MDPuMH/vklZnaeN1sSHDPLMLMnzGyr\nf38vifT9bGb/2/97vdHMHjGzpEjbz2b2oJlVm9nGgHkh269mttDMNvi/524zG2hQpENzzo2YF32P\nHN4BFAAJwDpgltd1HeW25AAL/O9TgW3ALOBnwK3++bcCP/W/vxB4nr5RrxYD7/nnZwJl/q9j/O/H\neL19g2z7d4H/Ap71Tz8GLPO/vw/4mv/914H7/O+XAX/2v5/l3/eJwBT/70Ss19t1mO39I3Cj/30C\nkBHJ+5m+YTd3AqMC9u+1kbafgdOBBcDGgHkh26/A+8AS//c8D1xwRPV5/QM6wh/mEuDFgOkfAD/w\nuq4QbdtfgXOBEiDHPy8HKPG/vx+4OqB9iX/51cD9AfM/1m64vegbyesV4NPAs/5f3Fogrv8+pm8M\ngSX+93H+dtZ/vwe2G24vIM0fdNZvfsTuZ/5nTOVM/357FjgvEvczkN8v3EOyX/3LtgbM/1i7YF4j\nrVtmoMG6J3lUS8j4/wydD7wHjHfOVQH4v47zNzvUto+0n8mdwD8Avf7psUCjc87nnw6s/2MDrwMH\nB14fSdtcANQAv/d3RT1gZqOJ4P3snKsA/gPYA1TRt9/WENn7+aBQ7ddJ/vf95wdtpIV7UANxjyRm\nlgI8CXw6qn+gAAACJElEQVTHOXfgcE0HmOcOM3/YMbOLgWrn3JrA2QM0dYMsGzHbTN+R6ALgXufc\nfKCVvj/XD2XEb7O/n/ky+rpSJgKjgQsGaBpJ+3kwR7qNx7ztIy3cgxmse8Qws3j6gv1Pzrmn/LP3\nm1mOf3kOUO2ff6htH0k/k1OAS81sF/AofV0zdwIZ1jewOny8/o+2zT4+8PpI2uZyoNw5955/+gn6\nwj6S9/M5wE7nXI1zrht4CjiZyN7PB4Vqv5b73/efH7SRFu7BDNY9IvjPfP8O2OKcuyNgUeBg41+h\nry/+4Pwv+8+6Lwaa/H/2vQgsNbMx/iOmpf55w45z7gfOuVznXD59++5V59wXgdfoG1gdPrnNAw28\nvhJY5r/KYgpQSN/Jp2HHObcP2Gtm0/2zzgY2E8H7mb7umMVmluz/PT+4zRG7nwOEZL/6lzWb2WL/\nz/DLAZ8VHK9PSBzFCYwL6buyZAfwQ6/rOYbtOJW+P7PWAx/6XxfS19f4CrDd/zXT396Ae/zbvQEo\nCvis64FS/+s6r7ctyO0/k/+5WqaAvn+0pcDjQKJ/fpJ/utS/vCDg+3/o/1mUcIRXEXiwrScCxf59\n/TR9V0VE9H4G/gnYCmwEHqbvipeI2s/AI/SdU+im70j7hlDuV6DI//PbAfyafiflB3vpDlURkQg0\n0rplREQkCAp3EZEIpHAXEYlACncRkQikcBcRiUAKdxGRCKRwFxGJQAp3EZEI9P8B/KDM0+QK/dYA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b56ba7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n= 2000\n",
    "p =0.3\n",
    "W = 10**4\n",
    "Z = []\n",
    "bin = (0.5)**(1+np.array(range(n)))\n",
    "for i in range(W):\n",
    "    Y = numpy.random.binomial(1,p,n)\n",
    "    helper = numpy.sum(Y*bin)\n",
    "    Z = Z + [helper]\n",
    "\n",
    "Z.sort()\n",
    "pylab.plot(Z)\n",
    "pylab.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Revised Version of `P`, with more general events\n",
    "\n",
    "To calculate the probability of an even die roll, I originally said\n",
    "\n",
    "    even = {2, 4, 6}\n",
    "    \n",
    "But that's inelegant&mdash;I had to explicitly enumerate all the even numbers from one to six. If I ever wanted to deal with a twelve or twenty-sided die, I would have to go back and change  `even`.  I would prefer to define `even` once and for all like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def even(n): return n % 2 == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Now in order to make `P(even, D)` work, I'll have to modify `P` to accept an event as either\n",
    "a *set* of outcomes (as before), or a *predicate* over outcomes&mdash;a function that returns true for an outcome that is in the event:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def P(event, space): \n",
    "    \"\"\"The probability of an event, given a sample space of equiprobable outcomes.\n",
    "    event can be either a set of outcomes, or a predicate (true for outcomes in the event).\"\"\"\n",
    "    if is_predicate(event):\n",
    "        event = such_that(event, space)\n",
    "    return Fraction(len(event & space), len(space))\n",
    "\n",
    "is_predicate = callable\n",
    "\n",
    "def such_that(predicate, collection): \n",
    "    \"The subset of elements in the collection for which the predicate is true.\"\n",
    "    return {e for e in collection if predicate(e)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Here we see how `such_that`, the new `even` predicate, and the new `P` work:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2, 4, 6}"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "such_that(even, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(1, 2)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(even, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2, 4, 6, 8, 10, 12}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D12 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}\n",
    "\n",
    "such_that(even, D12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(1, 2)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(even, D12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Note: `such_that` is just like the built-in function `filter`, except `such_that` returns a set.\n",
    "\n",
    "We can now define more interesting events using predicates; for example we can determine the probability that the sum of a three-dice roll is prime (using a definition of `is_prime` that is efficient enough for small `n`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(73, 216)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D3 = {(d1, d2, d3) for d1 in D for d2 in D for d3 in D}\n",
    "\n",
    "def prime_sum(outcome): return is_prime(sum(outcome))\n",
    "\n",
    "def is_prime(n): return n > 1 and not any(n % i == 0 for i in range(2, n))\n",
    "\n",
    "P(prime_sum, D3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Card Problems\n",
    "\n",
    "Consider dealing a hand of five playing cards. We can define `deck` as a set of 52 cards, and `Hands` as the sample space of all combinations of 5 cards:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suits = 'SHDC'\n",
    "ranks = 'A23456789TJQK'\n",
    "deck  = cross(ranks, suits)\n",
    "len(deck)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['4H QS 6C 9C 2D',\n",
       " 'KC 6D AH 2S 9C',\n",
       " 'QC KS 7S TH 2H',\n",
       " 'TS 6D 2S JD 6C',\n",
       " '5D KD 7C 9C TC']"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hands = combos(deck, 5)\n",
    "\n",
    "assert len(Hands) == choose(52, 5)\n",
    "\n",
    "random.sample(Hands, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Now we can answer questions like the probability of being dealt a flush (5 cards of the same suit):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(33, 16660)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def flush(hand):\n",
    "    return any(hand.count(suit) == 5 for suit in suits)\n",
    "\n",
    "P(flush, Hands)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Or the probability of four of a kind:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(1, 4165)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def four_kind(hand):\n",
    "    return any(hand.count(rank) == 4 for rank in ranks)\n",
    "\n",
    "P(four_kind, Hands)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fermat and Pascal: Gambling, Triangles, and the Birth of Probability\n",
    "\n",
    "<table>\n",
    "<tr><td><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/9/98/Pierre_de_Fermat2.png/140px-Pierre_de_Fermat2.png\"><center><a href=\"https://en.wikipedia.org/wiki/Pierre_de_Fermat\">Pierre de Fermat</a><br>1654\n",
    "<td><img src=\"https://www.umass.edu/wsp/images/pascal.jpg\"><center><a href=\"https://en.wikipedia.org/wiki/Blaise_Pascal\">Blaise Pascal]</a><br>1654\n",
    "</table>\n",
    "\n",
    "Consider a gambling game consisting of tossing a coin. Player H wins the game if 10 heads come up, and T wins if 10 tails come up. If the game is interrupted when H has 8 heads and T has 7 tails, how should the pot of money (which happens to be 100 Francs) be split?\n",
    "In 1654, Blaise Pascal and Pierre de Fermat corresponded on this problem, with Fermat [writing](http://mathforum.org/isaac/problems/prob1.html):\n",
    "\n",
    ">Dearest Blaise,\n",
    "\n",
    ">As to the problem of how to divide the 100 Francs, I think I have found a solution that you will find to be fair. Seeing as I needed only two points to win the game, and you needed 3, I think we can establish that after four more tosses of the coin, the game would have been over. For, in those four tosses, if you did not get the necessary 3 points for your victory, this would imply that I had in fact gained the necessary 2 points for my victory. In a similar manner, if I had not achieved the necessary 2 points for my victory, this would imply that you had in fact achieved at least 3 points and had therefore won the game. Thus, I believe the following list of possible endings to the game is exhaustive. I have denoted 'heads' by an 'h', and tails by a 't.' I have starred the outcomes that indicate a win for myself.\n",
    "\n",
    "    h h h h *       h h h t *       h h t h *       h h t t *\n",
    "    h t h h *       h t h t *       h t t h *       h t t t\n",
    "    t h h h *       t h h t *       t h t h *       t h t t\n",
    "    t t h h *       t t h t         t t t h         t t t t\n",
    "\n",
    ">I think you will agree that all of these outcomes are equally likely. Thus I believe that we should divide the stakes by the ration 11:5 in my favor, that is, I should receive (11/16)*100 = 68.75 Francs, while you should receive 31.25 Francs.\n",
    "\n",
    ">I hope all is well in Paris,\n",
    "\n",
    ">Your friend and colleague,\n",
    "\n",
    ">Pierre\n",
    "\n",
    "Pascal agreed with this solution, and [replied](http://mathforum.org/isaac/problems/prob2.html) with a generalization that made use of his previous invention, Pascal's Triangle. There's even [a book](https://smile.amazon.com/Unfinished-Game-Pascal-Fermat-Seventeenth-Century/dp/0465018963?sa-no-redirect=1) about it.\n",
    "\n",
    "We can solve the problem with the tools we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def win_unfinished_game(Hneeds, Tneeds):\n",
    "    \"The probability that H will win the unfinished game, given the number of points needed by H and T to win.\"\n",
    "    def Hwins(outcome): return outcome.count('h') >= Hneeds\n",
    "    return P(Hwins, continuations(Hneeds, Tneeds))\n",
    "\n",
    "def continuations(Hneeds, Tneeds):\n",
    "    \"All continuations of a game where H needs `Hneeds` points to win and T needs `Tneeds`.\"\n",
    "    rounds = ['ht' for _ in range(Hneeds + Tneeds - 1)]\n",
    "    return set(itertools.product(*rounds))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{('h', 'h', 'h', 'h'),\n",
       " ('h', 'h', 'h', 't'),\n",
       " ('h', 'h', 't', 'h'),\n",
       " ('h', 'h', 't', 't'),\n",
       " ('h', 't', 'h', 'h'),\n",
       " ('h', 't', 'h', 't'),\n",
       " ('h', 't', 't', 'h'),\n",
       " ('h', 't', 't', 't'),\n",
       " ('t', 'h', 'h', 'h'),\n",
       " ('t', 'h', 'h', 't'),\n",
       " ('t', 'h', 't', 'h'),\n",
       " ('t', 'h', 't', 't'),\n",
       " ('t', 't', 'h', 'h'),\n",
       " ('t', 't', 'h', 't'),\n",
       " ('t', 't', 't', 'h'),\n",
       " ('t', 't', 't', 't')}"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "continuations(2, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(11, 16)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "win_unfinished_game(2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our answer agrees with Pascal and Fermat; we're in good company!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Non-Equiprobable Outcomes: Probability Distributions\n",
    "\n",
    "So far, we have made the assumption that every outcome in a sample space is equally likely. In real life, we often get outcomes that are not equiprobable. For example, the probability of a child being a girl is not exactly 1/2, and the probability is slightly different for a second child. An [article](http://people.kzoo.edu/barth/math105/moreboys.pdf) gives the following counts for two-child families in Denmark, where `GB` means a family where the first child is a girl and the second a boy:\n",
    "\n",
    "    GG: 121801    GB: 126840\n",
    "    BG: 127123    BB: 135138\n",
    "    \n",
    "We will introduce three more definitions:\n",
    "\n",
    "* [Frequency](https://en.wikipedia.org/wiki/Frequency_%28statistics%29): a number describing how often an outcome occurs. Can be a count like 121801, or a ratio like 0.515.\n",
    "\n",
    "* [Distribution](http://mathworld.wolfram.com/StatisticalDistribution.html): A mapping from outcome to frequency for each outcome in a sample space. \n",
    "\n",
    "* [Probability Distribution](https://en.wikipedia.org/wiki/Probability_distribution): A distribution that has been *normalized* so that the sum of the frequencies is 1.\n",
    "\n",
    "We define `ProbDist` to take the same kinds of arguments that `dict` does: either a mapping or an iterable of `(key, val)` pairs, and/or optional keyword arguments. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "class ProbDist(dict):\n",
    "    \"A Probability Distribution; an {outcome: probability} mapping.\"\n",
    "    def __init__(self, mapping=(), **kwargs):\n",
    "        self.update(mapping, **kwargs)\n",
    "        # Make probabilities sum to 1.0; assert no negative probabilities\n",
    "        total = sum(self.values())\n",
    "        for outcome in self:\n",
    "            self[outcome] = self[outcome] / total\n",
    "            assert self[outcome] >= 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "We also need to modify the functions `P` and `such_that` to accept either a sample space  or a probability distribution as the second argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def P(event, space): \n",
    "    \"\"\"The probability of an event, given a sample space of equiprobable outcomes. \n",
    "    event: a collection of outcomes, or a predicate that is true of outcomes in the event. \n",
    "    space: a set of outcomes or a probability distribution of {outcome: frequency} pairs.\"\"\"\n",
    "    if is_predicate(event):\n",
    "        event = such_that(event, space)\n",
    "    if isinstance(space, ProbDist):\n",
    "        return sum(space[o] for o in space if o in event)\n",
    "    else:\n",
    "        return Fraction(len(event & space), len(space))\n",
    "    \n",
    "def such_that(predicate, space): \n",
    "    \"\"\"The outcomes in the sample pace for which the predicate is true.\n",
    "    If space is a set, return a subset {outcome,...};\n",
    "    if space is a ProbDist, return a ProbDist {outcome: frequency,...};\n",
    "    in both cases only with outcomes where predicate(element) is true.\"\"\"\n",
    "    if isinstance(space, ProbDist):\n",
    "        return ProbDist({o:space[o] for o in space if predicate(o)})\n",
    "    else:\n",
    "        return {o for o in space if predicate(o)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Here is the probability distribution for Danish two-child families:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'BB': 0.2645086533229465,\n",
       " 'BG': 0.24882071317004043,\n",
       " 'GB': 0.24826679089140383,\n",
       " 'GG': 0.23840384261560926}"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DK = ProbDist(GG=121801, GB=126840,\n",
    "              BG=127123, BB=135138)\n",
    "DK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "And here are some predicates that will allow us to answer some questions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def first_girl(outcome):  return outcome[0] == 'G'\n",
    "def first_boy(outcome):   return outcome[0] == 'B'\n",
    "def second_girl(outcome): return outcome[1] == 'G'\n",
    "def second_boy(outcome):  return outcome[1] == 'B'\n",
    "def two_girls(outcome):   return outcome    == 'GG'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4866706335070131"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(first_girl, DK)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4872245557856497"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(second_girl, DK)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "The above says that the probability of a girl is somewhere between 48% and 49%, but that it is slightly different between the first or second child."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.4898669165584115, 0.48471942072973107)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(second_girl, such_that(first_girl, DK)), P(second_girl, such_that(first_boy, DK))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5101330834415885, 0.5152805792702689)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(second_boy, such_that(first_girl, DK)), P(second_boy, such_that(first_boy, DK))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "The above says that the sex of the second child is more likely to be the same as the first child, by about 1/2 a percentage point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# More Urn Problems: M&Ms and Bayes\n",
    "\n",
    "Here's another urn problem (or \"bag\" problem) [from](http://allendowney.blogspot.com/2011/10/my-favorite-bayess-theorem-problems.html) prolific Python/Probability author [Allen Downey ](http://allendowney.blogspot.com/):\n",
    "\n",
    "> The blue M&M was introduced in 1995.  Before then, the color mix in a bag of plain M&Ms was (30% Brown, 20% Yellow, 20% Red, 10% Green, 10% Orange, 10% Tan).  Afterward it was (24% Blue , 20% Green, 16% Orange, 14% Yellow, 13% Red, 13% Brown). \n",
    "A friend of mine has two bags of M&Ms, and he tells me that one is from 1994 and one from 1996.  He won't tell me which is which, but he gives me one M&M from each bag.  One is yellow and one is green.  What is the probability that the yellow M&M came from the 1994 bag?\n",
    "\n",
    "To solve this problem, we'll first represent probability distributions for each bag: `bag94` and `bag96`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "bag94 = ProbDist(brown=30, yellow=20, red=20, green=10, orange=10, tan=10)\n",
    "bag96 = ProbDist(blue=24, green=20, orange=16, yellow=14, red=13, brown=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Next, define `MM` as the joint distribution&mdash;the sample space for picking one M&M from each bag. The outcome `'yellow green'` means that a yellow M&M was selected from the 1994 bag and a green one from the 1996 bag."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'brown blue': 0.07199999999999997,\n",
       " 'brown brown': 0.038999999999999986,\n",
       " 'brown green': 0.05999999999999997,\n",
       " 'brown orange': 0.04799999999999998,\n",
       " 'brown red': 0.038999999999999986,\n",
       " 'brown yellow': 0.04199999999999998,\n",
       " 'green blue': 0.02399999999999999,\n",
       " 'green brown': 0.012999999999999996,\n",
       " 'green green': 0.019999999999999993,\n",
       " 'green orange': 0.015999999999999993,\n",
       " 'green red': 0.012999999999999996,\n",
       " 'green yellow': 0.013999999999999995,\n",
       " 'orange blue': 0.02399999999999999,\n",
       " 'orange brown': 0.012999999999999996,\n",
       " 'orange green': 0.019999999999999993,\n",
       " 'orange orange': 0.015999999999999993,\n",
       " 'orange red': 0.012999999999999996,\n",
       " 'orange yellow': 0.013999999999999995,\n",
       " 'red blue': 0.04799999999999998,\n",
       " 'red brown': 0.025999999999999992,\n",
       " 'red green': 0.03999999999999999,\n",
       " 'red orange': 0.03199999999999999,\n",
       " 'red red': 0.025999999999999992,\n",
       " 'red yellow': 0.02799999999999999,\n",
       " 'tan blue': 0.02399999999999999,\n",
       " 'tan brown': 0.012999999999999996,\n",
       " 'tan green': 0.019999999999999993,\n",
       " 'tan orange': 0.015999999999999993,\n",
       " 'tan red': 0.012999999999999996,\n",
       " 'tan yellow': 0.013999999999999995,\n",
       " 'yellow blue': 0.04799999999999998,\n",
       " 'yellow brown': 0.025999999999999992,\n",
       " 'yellow green': 0.03999999999999999,\n",
       " 'yellow orange': 0.03199999999999999,\n",
       " 'yellow red': 0.025999999999999992,\n",
       " 'yellow yellow': 0.02799999999999999}"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def joint(A, B, sep=''):\n",
    "    \"\"\"The joint distribution of two independent probability distributions. \n",
    "    Result is all entries of the form {a+sep+b: P(a)*P(b)}\"\"\"\n",
    "    return ProbDist({a + sep + b: A[a] * B[b]\n",
    "                    for a in A\n",
    "                    for b in B})\n",
    "\n",
    "MM = joint(bag94, bag96, ' ')\n",
    "MM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "First we'll look at the \"One is yellow and one is green\" part:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'green yellow': 0.25925925925925924, 'yellow green': 0.7407407407407408}"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def yellow_and_green(outcome): return 'yellow' in outcome and 'green' in outcome\n",
    "\n",
    "such_that(yellow_and_green, MM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Now we can answer the question: given that we got a yellow and a green (but don't know which comes from which bag), what is the probability that the yellow came from the 1994 bag?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7407407407407408"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def yellow94(outcome): return outcome.startswith('yellow')\n",
    "\n",
    "P(yellow94, such_that(yellow_and_green, MM))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "So there is a 74% chance that the yellow comes from the 1994 bag.\n",
    "\n",
    "Answering this question was straightforward: just like all the other probability problems, we simply create a sample space, and use `P` to pick out the probability of the event in question, given what we know about the outcome.\n",
    "But in a sense it is curious that we were able to solve this problem with the same methodology as the others: this problem comes from a section titled **My favorite Bayes's Theorem Problems**, so one would expect that we'd need to invoke Bayes Theorem to solve it.  The computation above shows that that is not necessary. \n",
    "\n",
    "![Bayes](http://img1.ph.126.net/xKZAzeOv_mI8a4Lwq7PHmw==/2547911489202312541.jpg)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Thomas_Bayes\">Rev. Thomas Bayes</a><br>1701-1761\n",
    "</center>\n",
    "\n",
    "Of course, we *could* solve it using Bayes Theorem. Why is Bayes Theorem recommended? Because we are asked about the probability of an event given the evidence, which is not immediately available; however the probability of the evidence given the event is.  \n",
    "\n",
    "Before we see the colors of the M&Ms, there are two hypotheses, `A` and `B`, both with equal probability:\n",
    "\n",
    "    A: first M&M from 94 bag, second from 96 bag\n",
    "    B: first M&M from 96 bag, second from 94 bag\n",
    "    P(A) = P(B) = 0.5\n",
    "    \n",
    "Then we get some evidence:\n",
    "    \n",
    "    E: first M&M yellow, second green\n",
    "    \n",
    "We want to know the probability of hypothesis `A`, given the evidence:\n",
    "    \n",
    "    P(A | E)\n",
    "    \n",
    "That's not easy to calculate (except by enumerating the sample space). But Bayes Theorem says:\n",
    "    \n",
    "    P(A | E) = P(E | A) * P(A) / P(E)\n",
    "    \n",
    "The quantities on the right-hand-side are easier to calculate:\n",
    "    \n",
    "    P(E | A) = 0.20 * 0.20 = 0.04\n",
    "    P(E | B) = 0.10 * 0.14 = 0.014\n",
    "    P(A)     = 0.5\n",
    "    P(B)     = 0.5\n",
    "    P(E)     = P(E | A) * P(A) + P(E | B) * P(B) \n",
    "             = 0.04     * 0.5  + 0.014    * 0.5   =   0.027\n",
    "    \n",
    "And we can get a final answer:\n",
    "    \n",
    "    P(A | E) = P(E | A) * P(A) / P(E) \n",
    "             = 0.04     * 0.5  / 0.027 \n",
    "             = 0.7407407407\n",
    "             \n",
    "You have a choice: Bayes Theorem allows you to do less calculation at the cost of more algebra; that is a great trade-off if you are working with pencil and paper. Enumerating the state space allows you to do less algebra at the cost of more calculation; often a good trade-off if you have a computer. But regardless of the approach you use, it is important to understand Bayes theorem and how it works.\n",
    "\n",
    "There is one important question that Allen Downey does not address: *would you  eat twenty-year-old M&Ms*?\n",
    "&#128552;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Newton's Answer to a Problem by Pepys\n",
    "\n",
    "<table>\n",
    "<tr><td><img src=\"http://scienceworld.wolfram.com/biography/pics/Newton.jpg\"><center><a href=\"https://en.wikipedia.org/wiki/Isaac_Newton\">Isaac Newton</a><br>1693</center>\n",
    "<td><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Samuel_Pepys_portrait.jpg/148px-Samuel_Pepys_portrait.jpg\"><center><a href=\"https://en.wikipedia.org/wiki/Samuel_Pepys\">Samuel Pepys</a><br>1693</center>\n",
    "</table>\n",
    "\n",
    "[This paper](http://fermatslibrary.com/s/isaac-newton-as-a-probabilist) explains how  Samuel Pepys wrote to Isaac Newton in 1693 to pose the problem:\n",
    "\n",
    "> Which of the following three propositions has the greatest chance of success? \n",
    "  1. Six fair dice are tossed independently and at least one “6” appears. \n",
    "  2. Twelve fair dice are tossed independently and at least two “6”s appear. \n",
    "  3. Eighteen fair dice are tossed independently and at least three “6”s appear.\n",
    "  \n",
    "Newton was able to answer the question correctly (although his reasoning was not quite right); let's see how we can do. Since we're only interested in whether a die comes up as \"6\" or not, we can define a single die and the joint distribution over *n* dice as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "die = ProbDist({'6':1/6, '-':5/6})\n",
    "\n",
    "def dice(n, die):\n",
    "    \"Joint probability from tossing n dice.\"\n",
    "    if n == 1:\n",
    "        return die\n",
    "    else:\n",
    "        return joint(die, dice(n - 1, die))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'---': 0.5787037037037037,\n",
       " '--6': 0.11574074074074073,\n",
       " '-6-': 0.11574074074074073,\n",
       " '-66': 0.023148148148148143,\n",
       " '6--': 0.11574074074074073,\n",
       " '6-6': 0.023148148148148143,\n",
       " '66-': 0.023148148148148143,\n",
       " '666': 0.0046296296296296285}"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice(3, die)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to determine which proposition is more likely to have the required number of sixes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def at_least(k, result): return lambda s: s.count(result) >= k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6651020233196159"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(at_least(1, '6'), dice(6, die))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6186673737323101"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(at_least(2, '6'), dice(12, die))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5973456859477544"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(at_least(3, '6'), dice(18, die))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reach the same conclusion Newton did, that the best chance is rolling six dice."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<hr>\n",
    "\n",
    "# Simulation\n",
    "\n",
    "Sometimes it is inconvenient to explicitly define a sample space. Perhaps the sample space is infinite, or perhaps it is just very large and complicated, and we feel more confident in writing a program to *simulate* one pass through all the complications, rather than try to *enumerate* the complete sample space. *Random sampling* from the simulation\n",
    "can give an accurate estimate of the probability.\n",
    "\n",
    "# Simulating Monopoly\n",
    "\n",
    "![](http://buckwolf.org/a.abcnews.com/images/Entertainment/ho_hop_go_050111_t.jpg)<center>[Mr. Monopoly](https://en.wikipedia.org/wiki/Rich_Uncle_Pennybags)<br>1940&mdash;\n",
    "\n",
    "Consider [problem 84](https://projecteuler.net/problem=84) from the excellent [Project Euler](https://projecteuler.net), which asks for the probability that a player in the game Monopoly ends a roll on each of the squares on the board.  To answer this we need to take into account die rolls, chance and community chest cards, and going to jail (from the \"go to jail\" space, from a card, or from rolling doubles three times in a row). We do not need to take into account anything about buying or selling properties or exchanging money or winning or losing the game, because these don't change a player's location. We will assume that a player in jail will always pay to get out of jail immediately. \n",
    "\n",
    "A game of Monopoly can go on forever, so the sample space is infinite. But even if we limit the sample space to say, 1000 rolls, there are $21^{1000}$ such sequences of rolls (and even more possibilities when we consider drawing cards). So it is infeasible to explicitly represent the sample space.\n",
    "\n",
    "But it is fairly straightforward to implement a simulation and run it for, say, 400,000 rolls (so the average square will be landed on 10,000 times).  Here is the code for a simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
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    "collapsed": true,
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   "outputs": [],
   "source": [
    "from collections import Counter, deque\n",
    "import random\n",
    "\n",
    "# The board: a list of the names of the 40 squares\n",
    "# As specified by https://projecteuler.net/problem=84\n",
    "board = \"\"\"GO   A1 CC1 A2  T1 R1 B1  CH1 B2 B3\n",
    "           JAIL C1 U1  C2  C3 R2 D1  CC2 D2 D3 \n",
    "           FP   E1 CH2 E2  E3 R3 F1  F2  U2 F3 \n",
    "           G2J  G1 G2  CC3 G3 R4 CH3 H1  T2 H2\"\"\".split()\n",
    "\n",
    "def monopoly(steps):\n",
    "    \"\"\"Simulate given number of steps of Monopoly game, \n",
    "    yielding the number of the current square after each step.\"\"\"\n",
    "    goto(0) # start at GO\n",
    "    CC_deck = Deck('GO JAIL' + 14 * ' ?')\n",
    "    CH_deck = Deck('GO JAIL C1 E3 H2 R1 R R U -3' + 6 * ' ?')\n",
    "    doubles = 0\n",
    "    jail = board.index('JAIL')\n",
    "    for _ in range(steps):\n",
    "        d1, d2 = random.randint(1, 6), random.randint(1, 6)\n",
    "        goto(here + d1 + d2)\n",
    "        doubles = (doubles + 1) if (d1 == d2) else 0\n",
    "        if doubles == 3 or board[here] == 'G2J':  \n",
    "            goto(jail)\n",
    "        elif board[here].startswith('CC'):\n",
    "            do_card(CC_deck)\n",
    "        elif board[here].startswith('CH'):\n",
    "            do_card(CH_deck)\n",
    "        yield here         \n",
    "\n",
    "def goto(square):\n",
    "    \"Update the global variable 'here' to be square.\"\n",
    "    global here\n",
    "    here = square % len(board)\n",
    "                   \n",
    "def Deck(names):\n",
    "    \"Make a shuffled deck of cards, given a space-delimited string.\"\n",
    "    cards = names.split()\n",
    "    random.shuffle(cards)\n",
    "    return deque(cards)         \n",
    "\n",
    "def do_card(deck):\n",
    "    \"Take the top card from deck and do what it says.\"\n",
    "    global here\n",
    "    card = deck[0]             # The top card\n",
    "    deck.rotate(-1)            # Move top card to bottom of deck\n",
    "    if card == 'R' or card == 'U': \n",
    "        while not board[here].startswith(card):\n",
    "            goto(here + 1)     # Advance to next railroad or utility\n",
    "    elif card == '-3':\n",
    "        goto(here - 3)         # Go back 3 spaces\n",
    "    elif card != '?':\n",
    "        goto(board.index(card))# Go to destination named on card"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "And the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
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   "source": [
    "results = list(monopoly(400000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
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   },
   "source": [
    "I'll show a histogram of the squares, with a dotted red line at the average:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c62fe898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.hist(results, bins=40)\n",
    "avg = len(results) / 40\n",
    "plt.plot([0, 39], [avg, avg], 'r--');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Another way to see the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A1': 0.0215675,\n",
       " 'A2': 0.02176,\n",
       " 'B1': 0.02244,\n",
       " 'B2': 0.0235225,\n",
       " 'B3': 0.0227275,\n",
       " 'C1': 0.027135,\n",
       " 'C2': 0.0237975,\n",
       " 'C3': 0.02486,\n",
       " 'CC1': 0.0188075,\n",
       " 'CC2': 0.02623,\n",
       " 'CC3': 0.0237175,\n",
       " 'CH1': 0.008725,\n",
       " 'CH2': 0.01035,\n",
       " 'CH3': 0.008745,\n",
       " 'D1': 0.027495,\n",
       " 'D2': 0.0290075,\n",
       " 'D3': 0.03107,\n",
       " 'E1': 0.0288625,\n",
       " 'E2': 0.0268675,\n",
       " 'E3': 0.0317075,\n",
       " 'F1': 0.027145,\n",
       " 'F2': 0.026925,\n",
       " 'F3': 0.0256775,\n",
       " 'FP': 0.0287325,\n",
       " 'G1': 0.0274025,\n",
       " 'G2': 0.0262425,\n",
       " 'G3': 0.02464,\n",
       " 'GO': 0.031025,\n",
       " 'H1': 0.0220425,\n",
       " 'H2': 0.0262425,\n",
       " 'JAIL': 0.0619275,\n",
       " 'R1': 0.0296175,\n",
       " 'R2': 0.0289175,\n",
       " 'R3': 0.0306475,\n",
       " 'R4': 0.024315,\n",
       " 'T1': 0.023195,\n",
       " 'T2': 0.021615,\n",
       " 'U1': 0.0263625,\n",
       " 'U2': 0.0279325}"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ProbDist(Counter(board[i] for i in results))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "There is one square far above average: `JAIL`, at a little over 6%. There are four squares far below average: the three chance squares, `CH1`, `CH2`, and `CH3`, at around 1% (because 10 of the 16 chance cards send the player away from the square), and the \"Go to Jail\" square, square number 30 on the plot, which has a frequency of 0 because you can't end a turn there. The other squares are around 2% to 3% each, which you would expect, because 100% / 40 = 2.5%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Central Limit Theorem / Strength in Numbers Theorem\n",
    "\n",
    "So far, we have talked of an *outcome* as being a single state of the world. But it can be useful to break that state of the world down into components. We call these components **random variables**. For example, when we consider an experiment in which we roll two dice and observe their sum, we could model the situation with two random variables, one for each die. (Our representation of outcomes has been doing that implicitly all along, when we concatenate two parts of a string, but the concept of a random variable makes it official.)\n",
    "\n",
    "The **Central Limit Theorem** states that if you have a collection of random variables and sum them up, then the larger the collection, the closer the sum will be to a *normal distribution* (also called a *Gaussian distribution* or a *bell-shaped curve*). The theorem applies in all but a few pathological cases. \n",
    "\n",
    "As an example, let's take 5 random variables reprsenting the per-game scores of 5 basketball players, and then sum them together to form the team score. Each random variable/player is represented as a function; calling the function returns a single sample from the distribution:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from random import gauss, triangular, choice, vonmisesvariate, uniform\n",
    "\n",
    "def SC(): return posint(gauss(15.1, 3) + 3 * triangular(1, 4, 13)) # 30.1\n",
    "def KT(): return posint(gauss(10.2, 3) + 3 * triangular(1, 3.5, 9)) # 22.1\n",
    "def DG(): return posint(vonmisesvariate(30, 2) * 3.08) # 14.0\n",
    "def HB(): return posint(gauss(6.7, 1.5) if choice((True, False)) else gauss(16.7, 2.5)) # 11.7\n",
    "def OT(): return posint(triangular(5, 17, 25) + uniform(0, 30) + gauss(6, 3)) # 37.0\n",
    "\n",
    "def posint(x): \"Positive integer\"; return max(0, int(round(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is a function to sample a random variable *k* times, show a histogram of the results, and return the mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statistics import mean\n",
    "\n",
    "def repeated_hist(rv, bins=10, k=100000):\n",
    "    \"Repeat rv() k times and make a histogram of the results.\"\n",
    "    samples = [rv() for _ in range(k)]\n",
    "    plt.hist(samples, bins=bins)\n",
    "    return mean(samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two top-scoring players have scoring distributions that are slightly skewed from normal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.12879"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bgUuBS4DtR0NDkjQeo9wU/n8kWXtMeTPwc219J/AI8Jutfk+7MfyjSVYkObe13V1VhwGS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b7bb6358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(SC, bins=range(60))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.14294"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aIZOHgL3AFuDfgOeq6kDrMk2vuRuAjwE/b+uvY3prgcGdBf4pyY52VwGY3tfam4B9wOfa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\nBya17d0Q7AGqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c673a358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(KT, bins=range(60))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next two players have bi-modal distributions; some games they score a lot, some games not:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.00997"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eqnqxqp6id4/p80bplyRpNKMeOXwC+BDwk7b+SuD5qjrS1qeBVW15FXAQoG1/obX/f/UB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c654c828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(DG, bins=range(60))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.72097"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gSeoYDpKkjuEgSeoYDpKkjuEgSeoYDpKkjuEgSep4E9wKtdJveDvZ+LwzXFoa7jlIkjqG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\ns+QlcPAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c654cdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(HB, bins=range(60))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fifth \"player\" (actually the sum of all the other players on the team) looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36.28666"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3yZoz8PqSpBHM93sABfxFkgL+U1VtBy6sqsMAVXU4ydtb27XA80OPnWq1w8NPmGQbgz0E\nLrroonl2TwvBY/6l1Wm+AXB5VR1qH/J7k3znNG0zTa1eVxiEyHaA8fHx190vSVoY85oCqqpD7foI\n8BVgM/DCiamddn2kNZ8C1g89fB1waD6vL0mauzkHQJK3JHnbidvAVcCTwG5ga2u2Fbi/3d4NfDgD\nlwEvn5gqkiQtvvlMAV0IfGVwdCdvAP60qv48yWPAvUluBL4PfLC138PgENBJBoeBfmQery1Jmqc5\nB0BVfRd49zT1/w1cOU29gJvm+nqSpIXlN4ElqVOeDlqSlthSfWPYPQBJ6pR7AJK0iJbTFysNAL3G\ncnpzSjqznAKSpE4ZAJLUKQNAkjplAEhSpwwASeqURwF1zCN+pL65ByBJnTIAJKlTBoAkdcoAkKRO\nuQjcCRd8JZ3MPQBJ6pQBIEmdcgpoFXK6R9Io3AOQpE4ZAJLUqUWfAkqyBfgMcBbwx1V1x2L3YbVw\nqkfSfCzqHkCSs4DPAtcAlwAfSnLJYvZBkjSw2HsAm4HJqvouQJJdwHXAU4vcjxXHv/YlLbTFDoC1\nwPND21PApYvch2XFD3ZJS2WxAyDT1Oo1DZJtwLa2+eMkz8zj9S4AfjCPxy8nq2kssLrGs5rGAo5n\nWcinpi2POpa/M8prLHYATAHrh7bXAYeGG1TVdmD7QrxYkomqGl+I51pqq2kssLrGs5rGAo5nOVvo\nsSz2YaCPARuTXJzkjcANwO5F7oMkiUXeA6iq40luBh5kcBjojqo6uJh9kCQNLPr3AKpqD7BnkV5u\nQaaSlonVNBZYXeNZTWMBx7OcLehYUlUzt5IkrTqeCkKSOrUqAyDJliTPJJlMcstS92e2kuxIciTJ\nk0O185PsTfJsuz5vKfs4qiTrkzyU5OkkB5N8tNVX6njelOTRJN9q4/mdVr84ySNtPF9sBzmsCEnO\nSvLNJA+07ZU8lueSfDvJgSQTrbYi32sASc5Ncl+S77T/Q7+0kONZdQGwSk438Tlgy0m1W4B9VbUR\n2Ne2V4LjwMer6p3AZcBN7d9jpY7nFeCKqno3sAnYkuQy4FPAnW08LwI3LmEfZ+ujwNND2yt5LAC/\nXFWbhg6XXKnvNRicN+3Pq+oXgXcz+HdauPFU1aq6AL8EPDi0fStw61L3aw7j2AA8ObT9DLCm3V4D\nPLPUfZzjuO4HPrAaxgP8LeBxBt9m/wHwhlZ/zXtwOV8YfBdnH3AF8ACDL2uuyLG0/j4HXHBSbUW+\n14C/DXyPtlZ7Jsaz6vYAmP50E2uXqC8L6cKqOgzQrt++xP2ZtSQbgPcAj7CCx9OmTA4AR4C9wF8B\nL1XV8dZkJb3n/gD4V8D/bds/w8odCwzOLPAXSfa3swrAyn2v/SxwFPiTNkX3x0newgKOZzUGwIyn\nm9DiS/JW4EvAx6rqh0vdn/moqlerahODv543A++crtni9mr2kvwKcKSq9g+Xp2m67Mcy5PKqei+D\nKeCbkvyjpe7QPLwBeC9wV1W9B/g/LPD01WoMgBlPN7FCvZBkDUC7PrLE/RlZkrMZfPh/vqq+3Mor\ndjwnVNVLwNcYrG2cm+TE92pWynvucuCfJnkO2MVgGugPWJljAaCqDrXrI8BXGAT0Sn2vTQFTVfVI\n276PQSAs2HhWYwCs1tNN7Aa2tttbGcylL3tJAtwNPF1Vnx66a6WOZyzJue32m4H3M1iYewj4tdZs\nRYynqm6tqnVVtYHB/5OvVtU/ZwWOBSDJW5K87cRt4CrgSVboe62q/hfwfJK/20pXMjh1/sKNZ6kX\nOs7Q4sm1wP9gMDf7b5a6P3Po/xeAw8DfMPgr4EYGc7P7gGfb9flL3c8Rx/IPGUwhPAEcaJdrV/B4\n/j7wzTaeJ4F/1+o/CzwKTAJ/Bpyz1H2d5bjeBzywksfS+v2tdjl44v/+Sn2vtb5vAiba++2/AOct\n5Hj8JrAkdWo1TgFJkkZgAEhSpwwASeqUASBJnTIAJKlTBoAkdcoAkKROGQCS1Kn/B3UfkYB2+tz7\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77b7bd2518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(OT, bins=range(60))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define the team score to be the sum of the five players, and look at the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "114.23839"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lyfGtniTXJplOcl+SsybX88VzgDH5iyTfbdv95STHDa27vI3JI0kumEyvF9dMYzK07k+S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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c63538d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def GSW(): return SC() + KT() + DG() + HB() + OT()\n",
    "\n",
    "repeated_hist(GSW, bins=range(70, 160, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sure enough, this looks very much like a normal distribution. The Central Limit Theorem appears to hold in this case. But I have to say \"Central Limit\" is not a very evocative name, so I propose we re-name this as the **Strength in Numbers Theorem**, to indicate the fact that if you have a lot of numbers, you tend to get the expected result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Conclusion\n",
    "\n",
    "We've had an interesting tour and met some giants of the field: Laplace, Bernoulli, Fermat, Pascal, Bayes, Newton, ... even Mr. Monopoly and The Count.\n",
    "\n",
    "![The Count](http://img2.oncoloring.com/count-dracula-number-thir_518b77b54ba6c-p.gif)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Count_von_Count\">The Count</a><br>1972&mdash;</center>\n",
    "\n",
    "The conclusion is: be explicit about what the problem says, and then methodical about defining the sample space, and finally be careful in counting the number of outcomes in the numerator and denominator. Easy as 1-2-3. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "# Appendix: Continuous Sample Spaces\n",
    "\n",
    "Everything up to here has been about discrete, finite sample spaces, where we can *enumerate* all the possible outcomes. \n",
    "\n",
    "But I was asked about *continuous* sample spaces, such as the space of real numbers. The principles are the same: probability is still the ratio of the favorable cases to all the cases, but now instead of *counting* cases, we have to (in general) compute integrals to compare the sizes of cases. \n",
    "Here we will cover a simple example, which we first solve approximately by simulation, and then exactly by calculation.\n",
    "\n",
    "## The Hot New Game Show Problem: Simulation\n",
    "\n",
    "Oliver Roeder posed [this problem](http://fivethirtyeight.com/features/can-you-win-this-hot-new-game-show/) in the 538 *Riddler* blog:\n",
    "\n",
    ">Two players go on a hot new game show called *Higher Number Wins.* The two go into separate booths, and each presses a button, and a random number between zero and one appears on a screen. (At this point, neither knows the other’s number, but they do know the numbers are chosen from a standard uniform distribution.) They can choose to keep that first number, or to press the button again to discard the first number and get a second random number, which they must keep. Then, they come out of their booths and see the final number for each player on the wall. The lavish grand prize — a case full of gold bullion — is awarded to the player who kept the higher number. Which number is the optimal cutoff for players to discard their first number and choose another? Put another way, within which range should they choose to keep the first number, and within which range should they reject it and try their luck with a second number?\n",
    "\n",
    "We'll use this notation:\n",
    "- **A**, **B**: the two players.\n",
    "- *A*, *B*: the cutoff values they choose: the lower bound of the range of first numbers they will accept.\n",
    "- *a*, *b*: the actual random numbers that appear on the screen.\n",
    "\n",
    "For example, if player **A** chooses a cutoff of *A* = 0.6, that means that **A** would accept any first number greater than 0.6, and reject any number below that cutoff. The question is: What cutoff, *A*, should player **A** choose to maximize the chance of winning, that is, maximize P(*a* > *b*)?\n",
    "\n",
    "First, simulate the number that a player with a given cutoff gets (note that `random.random()` returns a float sampled uniformly from the interval [0..1]):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def number(cutoff):\n",
    "    \"Play the game with given cutoff, returning the first or second random number.\"\n",
    "    first = random.random()\n",
    "    return first if first > cutoff else random.random()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4383135592153289"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "number(.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now compare the numbers returned with a cutoff of *A* versus a cutoff of *B*, and repeat for a large number of trials; this gives us an estimate of the probability that cutoff *A* is better than cutoff *B*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Pwin(A, B, trials=30000):\n",
    "    \"The probability that cutoff A wins against cutoff B.\"\n",
    "    Awins = sum(number(A) > number(B) \n",
    "                for _ in range(trials))\n",
    "    return Awins / trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4970333333333333"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pwin(.5, .6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now define a function, `top`, that considers a collection of possible cutoffs, estimate the probability for each cutoff playing against each other cutoff, and returns a list with the `N` top cutoffs (the ones that defeated the most number of opponent cutoffs), and the number of opponents they defeat: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def top(N, cutoffs):\n",
    "    \"Return the N best cutoffs and the number of opponent cutoffs they beat.\"\n",
    "    winners = Counter(A if Pwin(A, B) > 0.5 else B\n",
    "                      for (A, B) in itertools.combinations(cutoffs, 2))\n",
    "    return winners.most_common(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 34.5 s, sys: 0 ns, total: 34.5 s\n",
      "Wall time: 34.6 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(0.62000000000000011, 46),\n",
       " (0.60000000000000009, 45),\n",
       " (0.59000000000000008, 44),\n",
       " (0.57000000000000006, 43),\n",
       " (0.6100000000000001, 42)]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import arange\n",
    "\n",
    "%time top(5, arange(0.50, 0.99, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a good idea of the top cutoffs, but they are close to each other, so we can't quite be sure which is best, only that the best is somewhere around 0.60. We could get a better estimate by increasing the number of trials, but that would consume more time.\n",
    "\n",
    "## The Hot New Game Show Problem: Exact Calculation\n",
    "\n",
    "More promising is the possibility of making `Pwin(A, B)` an exact calculation. But before we get to `Pwin(A, B)`, let's solve a simpler problem: assume that both players **A** and **B** have chosen a cutoff, and have each received a number above the cutoff. What is the probability that **A** gets the higher number? We'll call this `Phigher(A, B)`. We can think of this as a two-dimensional sample space of points in the (*a*, *b*) plane, where *a* ranges from the cutoff *A* to 1 and *b* ranges from the cutoff B to 1. Here is a diagram of that two-dimensional sample space, with the cutoffs *A*=0.5 and *B*=0.6:\n",
    "\n",
    "<img src=\"http://norvig.com/ipython/probability2da.jpg\" width=413>\n",
    "\n",
    "The total area of the sample space is 0.5 &times; 0.4 = 0.20, and in general it is (1 - *A*) &middot; (1 - *B*). What about the favorable cases, where **A** beats **B**? That corresponds to the shaded triangle below:\n",
    "\n",
    "<img src=\"http://norvig.com/ipython/probability2d.jpg\" width=413>\n",
    "\n",
    "The area of a triangle is 1/2 the base times the height, or in this case, 0.4<sup>2</sup> / 2 = 0.08, and in general, (1 - *B*)<sup>2</sup> / 2. So in general we have:\n",
    "\n",
    "    Phigher(A, B) = favorable / total\n",
    "    favorable     = ((1 - B) ** 2) / 2 \n",
    "    total         = (1 - A) * (1 - B)\n",
    "    Phigher(A, B) = (((1 - B) ** 2) / 2) / ((1 - A) * (1 - B))\n",
    "    Phigher(A, B) = (1 - B) / (2 * (1 - A))\n",
    "    \n",
    "And in this specific case we have:\n",
    "\n",
    "     A = 0.5; B = 0.6\n",
    "     favorable         = 0.4 ** 2 / 2 = 0.08\n",
    "     total             = 0.5 * 0.4    = 0.20\n",
    "     Phigher(0.5, 0.6) = 0.08 / 0.20  = 0.4\n",
    "\n",
    "But note that this only works when the cutoff *A* &le; *B*; when *A* > *B*, we need to reverse things. That gives us the code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Phigher(A, B):\n",
    "    \"Probability that a sample from [A..1] is higher than one from [B..1].\"\n",
    "    if A <= B:\n",
    "        return (1 - B) / (2 * (1 - A))\n",
    "    else:\n",
    "        return 1 - Phigher(B, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phigher(0.5, 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're now ready to tackle the full game. There are four cases to consider, depending on whether **A** and **B** gets a first number that is above or below their cutoff choices:\n",
    "\n",
    "| first *a* | first *b* | P(*a*, *b*) | P(A wins &vert; *a*, *b*) |  Comment |\n",
    "|:-----:|:-----:| ----------- | ------------- | ------------ |\n",
    "| *a* > *A* | *b* > *B* | (1 - *A*) &middot; (1 - *B*) | Phigher(*A*, *B*) | Both above cutoff; both keep first numbers |\n",
    "| *a* < *A* | *b* < *B* | *A* &middot; *B* | Phigher(0, 0)  | Both below cutoff, both get new numbers from [0..1] |\n",
    "| *a* > *A* | *b* < *B* | (1 - *A*) &middot;  *B* | Phigher(*A*, 0) | **A** keeps number; **B** gets new number from [0..1] |\n",
    "| *a* < *A* | *b* > *B* | *A* &middot; (1 - *B*) | Phigher(0, *B*) | **A** gets new number from [0..1]; **B** keeps number |\n",
    "\n",
    "For example, the first row of this table says that the event of both first numbers being above their respective cutoffs has probability (1 - *A*) &middot; (1 - *B*), and if this does occur, then the probability of **A** winning is Phigher(*A*, *B*).\n",
    "We're ready to replace the old simulation-based `Pwin` with a new calculation-based version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Pwin(A, B):\n",
    "    \"With what probability does cutoff A win against cutoff B?\"\n",
    "    return ((1-A) * (1-B) * Phigher(A, B)  # both above cutoff\n",
    "            + A * B       * Phigher(0, 0)  # both below cutoff\n",
    "            + (1-A) * B   * Phigher(A, 0)  # A above, B below\n",
    "            + A * (1-B)   * Phigher(0, B)) # A below, B above"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That was a lot of algebra. Let's define a few tests to check for obvious errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ok'"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def test():\n",
    "    assert Phigher(0.5, 0.5) == Phigher(0.7, 0.7) == Phigher(0, 0) == 0.5\n",
    "    assert Pwin(0.5, 0.5) == Pwin(0.7, 0.7) == 0.5\n",
    "    assert Phigher(.6, .5) == 0.6\n",
    "    assert Phigher(.5, .6) == 0.4\n",
    "    return 'ok'\n",
    "\n",
    "test()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the calculation with our new, exact `Pwin`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.62000000000000011, 48),\n",
       " (0.6100000000000001, 47),\n",
       " (0.60000000000000009, 46),\n",
       " (0.59000000000000008, 45),\n",
       " (0.63000000000000012, 44)]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(5, arange(0.50, 0.99, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is good to see that the simulation and the exact calculation are in rough agreement; that gives me more confidence in both of them. We see here that 0.62 defeats all the other cutoffs, and 0.61 defeats all cutoffs except 0.62. The great thing about the exact calculation code is that it runs fast, regardless of how much accuracy we want. We can zero in on the range around 0.6:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.6180000000000001, 199),\n",
       " (0.6170000000000001, 198),\n",
       " (0.6160000000000001, 197),\n",
       " (0.61900000000000011, 196),\n",
       " (0.6150000000000001, 195),\n",
       " (0.6140000000000001, 194),\n",
       " (0.6130000000000001, 193),\n",
       " (0.62000000000000011, 192),\n",
       " (0.6120000000000001, 191),\n",
       " (0.6110000000000001, 190)]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, arange(0.500, 0.700, 0.001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This says 0.618 is best, better than 0.620. We can get even more accuracy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.61802999999999531, 200),\n",
       " (0.61801999999999535, 199),\n",
       " (0.61803999999999526, 198),\n",
       " (0.6180099999999954, 197),\n",
       " (0.61799999999999544, 196)]"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(5, arange(0.61700, 0.61900, 0.00001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So 0.61803 is best. Does that number [look familiar](https://en.wikipedia.org/wiki/Golden_ratio)? Can you prove that it is what I think it is?\n",
    "\n",
    "To understand the strategic possibilities, it is helpful to draw a 3D plot of `Pwin(A, B)` for values of *A* and *B* between 0 and 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0fz8LOp2uInzk4qgcOZKLI4/HoxgzchLaRQydpuEiQN8tZUgMdTiSJKFQKKBY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5XrTRY2UiztZFnbL5IsVtEJkpj74rCbmXE/M+N+fHYLdrN8kRr2qHUaUyGXZrDrrgo0wUTAQauD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HdGbRh1GimF96HfxeNOtpBKIeB3DbHfIV73vQ7WjqIICOi0WgrlChq1ikq9gVajQqtRoVOr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\nUhBJZkhl248/oYbitHroE7+3exJivNdBMHa2Ri+hXVURBOi1mzBoV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L5G+DQy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\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EglwOAsEQikWRyodMEvlf28Li7I7RjmJJpFpDRowtuL1oLJcBiCTcly7mlQ1Pa5GfxwMA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\nyKcxDBEREZFP+39EsMaQOW6uJgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c5eaae80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
    "\n",
    "def map2(fn, A, B):\n",
    "    \"Map fn to corresponding elements of 2D arrays A and B.\"\n",
    "    return [list(map(fn, Arow, Brow))\n",
    "            for (Arow, Brow) in zip(A, B)]\n",
    "\n",
    "cutoffs = arange(0.00, 1.00, 0.02)\n",
    "A, B = np.meshgrid(cutoffs, cutoffs)\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "ax = fig.add_subplot(1, 1, 1, projection='3d')\n",
    "ax.set_xlabel('A')\n",
    "ax.set_ylabel('B')\n",
    "ax.set_zlabel('Pwin(A, B)')\n",
    "ax.plot_surface(A, B, map2(Pwin, A, B));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does this [Pringle of Probability](http://fivethirtyeight.com/features/should-you-shoot-free-throws-underhand/) show us? The highest win percentage for **A**, the peak of the surface, occurs when *A* is around 0.5 and *B* is 0 or 1. We can confirm that, finding the maximum `Pwin(A, B)` for many different cutoff values of `A` and `B`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cutoffs = (set(arange(0.00,    1.00,    0.01)) | \n",
    "           set(arange(0.500,   0.700,   0.001)) | \n",
    "           set(arange(0.61700, 0.61900, 0.00001)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.625, 0.5, 0.0]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max([Pwin(A, B), A, B]\n",
    "    for A in cutoffs for B in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So **A** could win 62.5% of the time if only **B** would chose a cutoff of 0. But, unfortunately for **A**, a rational player **B** is not going to do that. We can ask what happens if the game is changed so that player **A** has to declare a cutoff first, and then player **B** gets to respond with a cutoff, with full knowledge of **A**'s choice. In other words, what cutoff should **A** choose to maximize `Pwin(A, B)`, given that **B** is going to take that knowledge and pick a cutoff that minimizes `Pwin(A, B)`? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5, 0.61802999999999531, 0.61802999999999531]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(min([Pwin(A, B), A, B] for B in cutoffs)\n",
    "    for A in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And what if we run it the other way around, where **B** chooses a cutoff first, and then **A** responds?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5, 0.61802999999999531, 0.61802999999999531]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(max([Pwin(A, B), A, B] for A in cutoffs)\n",
    "    for B in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In both cases, the rational choice for both players in a cutoff of 0.61803, which corresponds to the  \"saddle point\" in the middle of the plot. This is a *stable equilibrium*; consider fixing *B* = 0.61803, and notice that if *A* changes to any other value, we slip off the saddle to the right or left, resulting in a worse win probability for **A**. Similarly, if we fix *A* = 0.61803, then if *B* changes to another value, we ride up the saddle to a higher win percentage for **A**, which is worse for **B**. So neither player will want to move from the saddle point.\n",
    "\n",
    "The moral for continuous spaces is the same as for discrete spaces: be careful about defining your space; count/measure carefully, and let your code take care of the rest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Calculating the value of $\\pi$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are evaluating by a Monte Carlo method the integral\n",
    "$$\n",
    "\\int_0^1 \\int_0^1 4 \\mathbb{1}_{x^2+y^2 < 1} dx dy .\n",
    "$$\n",
    "We therefore consider indepdent samples of the random variable $ \\mathbb{1}_{x^2+y^2 < 1} $ on the probability space $ [0,1] \\times [0,1] $. The expectation of the random variable is $ \\pi $, whereas its variance is $ \\pi(4-\\pi) $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Number of random points for Monte Carlo estimate of Pi?\n",
      ">10000\n",
      "\n",
      "Number of Samples for Monte Carlo estimate of Pi?\n",
      ">10000\n",
      "\n",
      "--------------\n",
      "\n",
      "Approximate value for pi: 3.1184\n",
      "Difference to exact value of pi: -0.023192653589793277\n",
      "Percent Error: (approx-exact)/exact*100: -0.7382450924467182%\n",
      "Execution Time: 2.5958142280578613 seconds\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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J5cxwv0Q6EvGO9VKGXNU1MhIRX3yP64j9rAwb8thCzGM0ivSVcAsB+JEFdzMt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\nOzo6OhYQXbl3dHR0LCD+H+LkoOc8UvkDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f58e52938d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YUM66L/uu5YbaHzAiWCFat+E5uZyDANgarNBiwTK+OFeXMVDTLQAyslyDca91\nGX5cuf785douoGNfrGPqgmHDnh1/I71xnrzLKsFrVVCst/kfbp/LD4Av8uaFg6OBA+7eFvR3bX/n\nvAXjDwblh9M8nwrUA/8e7PZaYmal5OhydvdtwHeBN0jeKfggsJLcXsZdZWq5Tgq6uw/vt1wLgFT7\nv4b9aU7Wzxvp0fv8D5vPxcz+Dtjt7iu7Dk5R1NOMGzbzTPJX7XnA/3P3c4EjJHcN9GZYz3Owz3s+\nyd02E4FSYF6Korm0jPtjoPMZev5zLQDqgCld+icD27PUloyw1DfS22VmE4LxE4DdwfDe5n84fS7v\nBi4zs83Ar0juBvoBUGlmx65c79r+znkLxlcA+xhe81wH1Ln7sduk308yEHJ1Oc8BNrl7vbu3Ar8D\n3kVuL+OuMrVc64Lu7sP7LdcC4HlgWnA2QZzkAaOlWW7TCQuO6Ke6kd5S4NiZAAtIHhs4Nvz64GyC\nWcDBYBPzUeCDZjYy+PX1wWDYkOPuN7v7ZHevIbn8/uTu1wFPAFcFxbrP87HP4qqgvAfDrwnOIJkK\nTCN5wGzIcfedwFYze2sw6CKSD0zK1eX8BjDLzEqC7/ix+c3ZZdxNRpZrMO6wmc0KPsfru0yrf7J9\ngGQQDrhcSvJsmQ0kn1mQ9TaFmJcLSG7SvQy8GPxdSnL/53JgXfA6KihvwB3BvK8CEl2m9XFgffD3\nX7M9b/2c//fz5llAp5L8514P/AYoDIYXBf3rg/Gndnn/LcFnsZYBnh2RhXk9B6gNlvXvSZ7tkbPL\nGfgX4DWSj5W9l+SZPDm3jIFfkjzO0UryF/uNmVyuQCL4DDcAt9PtRIJ0f7oSWEQkonJtF5CIiPST\nAkBEJKIUACIiEaUAEBGJKAWAiEhEKQBERCJKASAiElEKABGRiPr/yzHPZu9RL6EAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f58e0fe4e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f58e0f2c7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as numpy\n",
    "import matplotlib.pyplot as plt\n",
    "import time as time\n",
    "\n",
    "# input total number of random points and number of samples for the histogram\n",
    "total_random_points = int(input(\"\\nNumber of random points for Monte Carlo estimate of Pi?\\n>\"))\n",
    "W = int(input(\"\\nNumber of Samples for Monte Carlo estimate of Pi?\\n>\"))\n",
    "\n",
    "# start time of calculation\n",
    "start_time = time.time()\n",
    "\n",
    "# number of random points inside unit cicrle and total random points\n",
    "inside_circle = 0\n",
    "\n",
    "# create empty x and y arrays for eventual scatter plot of generated random points\n",
    "x_plot_array = numpy.empty(shape=(1,total_random_points))\n",
    "y_plot_array = numpy.empty(shape=(1,total_random_points))\n",
    "pi_approx = numpy.empty(shape=(1,total_random_points))\n",
    "\n",
    "\n",
    "# generate random points and count points inside unit circle\n",
    "# top right quadrant of unit cicrle only\n",
    "for i in range(0, total_random_points):\n",
    "    # print(f'\\nIteration: {i + 1}')\n",
    "    # generate random x, y in range [0, 1]\n",
    "    x = numpy.random.rand()\n",
    "    x_plot_array[0,i] = x\n",
    "    #numpy.append(x_plot_array, [x])\n",
    "    #print(f'{x_plot_array}')\n",
    "    # print(f'x value: {x}')\n",
    "    y = numpy.random.rand()\n",
    "    y_plot_array[0,i] = y\n",
    "    #numpy.append(y_plot_array, [y])\n",
    "    #print(f'{y_plot_array}')\n",
    "    # print(f'y value: {y}')\n",
    "    # calc x^2 and y^2 values\n",
    "    x_squared = x**2\n",
    "    y_squared = y**2\n",
    "    # count if inside unit circle, top right quadrant only\n",
    "    if numpy.sqrt(x_squared + y_squared) < 1.0:\n",
    "        inside_circle += 1\n",
    "    # print(f'Points inside circle {inside_circle}')\n",
    "    # print(f'Number of random points {i+1}')\n",
    "    # calc approximate pi value\n",
    "    pi_approx[0,i] = inside_circle / (i+1) * 4\n",
    "    #numpy.append(pi_approx,[inside_circle / (i+1) * 4])\n",
    "    # print(f'Approximate value for pi: {pi_approx}')\n",
    "\n",
    "pi_approx_sample = numpy.empty(shape=(1,W))\n",
    "for j in range(W):\n",
    "    x = numpy.random.rand(total_random_points)\n",
    "    y = numpy.random.rand(total_random_points)\n",
    "    x_squared = x**2\n",
    "    y_squared = y**2\n",
    "    pi_approx_sample[0,j] = 4*numpy.mean((x_squared+y_squared < 1.0))\n",
    "                           \n",
    "# final numeric output for pi estimate\n",
    "print (\"\\n--------------\")\n",
    "print (f\"\\nApproximate value for pi: {pi_approx[0,-1]}\")\n",
    "print (f\"Difference to exact value of pi: {pi_approx[0,-1]-numpy.pi}\")\n",
    "print (f\"Percent Error: (approx-exact)/exact*100: {(pi_approx[0,-1]-numpy.pi)/numpy.pi*100}%\")\n",
    "print (f\"Execution Time: {time.time() - start_time} seconds\\n\")\n",
    "\n",
    "# plot output of random points and circle, top right quadrant only\n",
    "random_points_plot = plt.scatter(x_plot_array, y_plot_array, color='blue', s=.1)\n",
    "circle_plot = plt.Circle( ( 0, 0 ), 1, color='red', linewidth=2, fill=False)\n",
    "\n",
    "ax1 = plt.gca()\n",
    "ax1.cla()\n",
    "\n",
    "ax1.add_artist(random_points_plot)\n",
    "ax1.add_artist(circle_plot)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(pi_approx[0,1:]-numpy.pi)\n",
    "plt.show()\n",
    "\n",
    "plt.hist(pi_approx_sample[0,:]-numpy.pi,bins=int(numpy.sqrt(total_random_points)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does a quicker MC implementation look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Number of random points for Monte Carlo estimate of Pi?\n",
      ">1000000\n",
      "\n",
      "Number of Samples for Monte Carlo estimate of Pi?\n",
      ">10\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd370346630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as numpy\n",
    "import matplotlib.pyplot as plt\n",
    "import time as time\n",
    "\n",
    "# input total number of random points and number of samples for the histogram\n",
    "total_random_points = int(input(\"\\nNumber of random points for Monte Carlo estimate of Pi?\\n>\"))\n",
    "W = int(input(\"\\nNumber of Samples for Monte Carlo estimate of Pi?\\n>\"))\n",
    "\n",
    "# create empty x and y arrays for eventual scatter plot of generated random points\n",
    "x_plot_array = numpy.empty(shape=(1,total_random_points))\n",
    "y_plot_array = numpy.empty(shape=(1,total_random_points))\n",
    "\n",
    "pi_approx_sample = numpy.empty(shape=(1,W))\n",
    "for j in range(W):\n",
    "    x = numpy.random.rand(total_random_points)\n",
    "    y = numpy.random.rand(total_random_points)\n",
    "    x_squared = x**2\n",
    "    y_squared = y**2\n",
    "    pi_approx_sample[0,j] = 4*numpy.mean((x_squared+y_squared < 1.0))\n",
    "                           \n",
    "\n",
    "plt.hist(pi_approx_sample[0,:]-numpy.pi,bins=int(numpy.sqrt(total_random_points)))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}