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Introduction to The Mathematical Theory of Communication, part II
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| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:15.652217Z", | |
| "end_time": "2021-02-24T14:33:15.664222Z" | |
| }, | |
| "slideshow": { | |
| "slide_type": "skip" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "from IPython.core.display import display, HTML\nfrom IPython.display import Image\ndisplay(HTML(\"\"\"<style>\n.prompt_container { display: none !important; }\n.prompt { display: none !important; }\n.run_this_cell { display: none !important; }\n</style>\"\"\"))", | |
| "execution_count": 1, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<IPython.core.display.HTML object>", | |
| "text/html": "<style>\n.prompt_container { display: none !important; }\n.prompt { display: none !important; }\n.run_this_cell { display: none !important; }\n</style>" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# A (The) Mathemathical Theory of Communication\n\nhttp://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "## Introduction" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Why Shannon's article is cool" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- Introduces a full size research field\n- A time window to first half of the XX century\n- Technology changed, results still apply\n- Strong content, light style" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "## Reminders" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# What is communication?" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "center" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Reproduce at one point a message selected at another point.\n" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Shannon_communication_system.svg/2880px-Shannon_communication_system.svg.png\">" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Quantifying information on a channel" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- Communication: reproduce at one point a message **selected** at another point.\n- Information should depend on the *possibilities*, e.g. the set of messages one can choose from\n - `Yes` or `No`: Minimal quantity of information\n - A book: more information (how many monkeys to write Shakespeare?)" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Quantifying information on a channel" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- Information should be a monotonic function of the possible number of messages $N$ that *could* have been sent.\n- Proposition: $I = \\log_2(N)$" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "fragment" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- Why the $\\log$?\n - Adding one bit in a memory doubles the possible states\n - Two punched cards square the number of possible messages\n - $\\log$ simplifies a lot the maths" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "fragment" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- Why the $\\log_2$?\n - Minimal amount of information ($N=2$) is 1 (*bit*).\n - the $2$ is omitted from now on." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Capacity of a channel" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "How much information can we transmit per unit of time?\n\n$$C = \\lim_{t\\rightarrow\\infty}\\frac{\\log(N(t))}{t}$$" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Quantifying information" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- We started with *Information=possibilities*\n- Natural language suggests we could say *Information=possibilities+rules*\n- Shannon proposes something more powerful: *Information=possibilities+probabilities*\n- Interest: statiscal properties may be exploited\n - In Morse, the shortest letter (dot) is *E*, the most frequent English letter\n - Telegraph companies developped short custom sequences for common phrasings (greetings/anniversaries)\n - Seed to Huffman-like compression" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Sources" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- A *source* generates messages, one symbol after the other\n- By considering all messages that a source *may* have sent, along with the probabilities of occurence, we can see a source as a stochastic symbol generator\n- Real life messages come from natural written language (NL). The underlying stochastic process is almost impossible to properly define, not to say compute\n- Shannon thesis: relatively simple artificial stochastic processes can provide a reasonable approximation of NL...\n- ...and they can be computed and analyzed!" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Markov sources" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- Consider a finite set of $n$ states\n- For each set $i$, \n - $p_i(j)$: probability to go to state $j$\n - $p_i(s)$: probability to output symbol $s$\n - right example: states and symbols are identified\n- This defines a Markov source" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "<img src=\"http://www.lincs.fr/wp-content/uploads/2020/06/markov.png\">" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Entropy of a probability distribution" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "center" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- Remind: information should mix possibilities and probabilities\n- Consider a distribution $p = p_1, \\ldots, p_n$\n- We would like a measure $H(p)$ that verifies:\n - $H$ is continous\n - $H$ is monotonic: if $p_1 = 1/n_1, \\ldots, 1/n_1$ and $p_2 = 1/n_2, \\ldots, 1/n_2$ with $n_1<n_2$, then $H(p_1)<H(p_2)$\n - $H$ is *associative*, i.e. for example $H(1/2,1/3,1/6) = H(1/2,1/2) + 1/2H(2/3, 1/3)$\n" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Entropy of a probability distribution" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Theorem: The only $H$ that checks continuity, monotonicity and associativity is of the form\n$$H=-K\\sum_i p_i\\log(p_i)$$\n\nNote: the name *entropy* and variable $H$ are inherited from statistical mechanics / thermodynamics. They discovered the formula first." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Example: entropy of biased coin" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- A coin outputs $0$ with probability $p$ and $1$ with probability $1-p$\n- Entropy: $(p-1)\\log(1-p)-p\\log(p)$" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:15.674263Z", | |
| "end_time": "2021-02-24T14:33:16.224330Z" | |
| }, | |
| "cell_style": "split", | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "from matplotlib import pyplot as plt\nimport numpy as np\np = np.linspace(0.001,.999)\nplt.plot(p, (p-1)*np.log2(1-p)-p*np.log2(p))\nplt.xlim([0,1])\nplt.ylim([0,1])\nplt.show()", | |
| "execution_count": 2, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 1 Axes>", | |
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\n" | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Properties of entropy" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- $H=0$ iff $p_i=\\delta_{i_0}^i$ for some $i_0$ (certainty).\n- For fixed $n$, $\\max(H)=\\log(n)$, reached uniquely for the uniform distribution.\n- If $x$ and $y$ are two events (distributions living in the same universe), $\\max(H(x), H(y))\\leq H(x, y)\\leq H(x)+H(y)$\n - l.h.s. is reached when $x$ and $y$ are fully correlated (knowing one is knowing the other)\n - r.h.s. is reached when $x$ and $y$ are independent ($p(i,j)=p(i)p(j)$)\n- Any smoothing/averaging/convolution of the distribution increases the entropy" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Conditional entropy" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "For $x$ and $y$, the conditional entropy of $y$ (w.r.t $x$) is the weighted average of the entropy of $y$ when $x$ is known.\n\n$$H_x(y) = \\sum_i p_i \\sum_j -p_i(j)\\log(p_i(j)) = -\\sum_{i, j} p(i, j)\\log(p_i(j))$$\n\nProperties:\n- $H(x, y) = H(x)+H_x(y)$\n- $H_x(y)\\leq H(y)$ (equality iff independence)" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-06-09T12:51:52.476578Z", | |
| "start_time": "2020-06-09T12:51:52.465985Z" | |
| }, | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Entropy of a Markov source" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- Remind: $n$ states, $p_i(j)$, $p_i(s)$, $P_i$.\n- Each state has a symbol entropy $H_i$\n- Entropy of the source: $H=\\sum_iP_iH_i = -\\sum_{i, s}P_ip_i(s)\\log(p_i(s))$\n- Unit: bits per symbol produced\n- Can be converted into bits per second" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2020-06-09T12:51:52.476578Z", | |
| "start_time": "2020-06-09T12:51:52.465985Z" | |
| }, | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Links between entropy of a Markov source and produced messages" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*It is possible for most purposes to treat the long sequences [of length $N$] as though there were just $2^{HN}$ of them, each with a probability $2^{-HN}$*" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Transducers" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- Transduction (encoding/decoding at transmitter/receiver) is modeled by a device with internal memory (finite).\n- When a new input symbol $x_n$ is fed to a transducer in state $\\alpha_n$, two deterministic operations are performed:\n - An output symbol $y_n=f(x_n, \\alpha_n)$ is produced;\n - A new state $\\alpha_{n+1}=g(x_n, \\alpha_n)$ is set.\n - A transducer is *non-singular* is there exists an *inverse* transducer that can recover the input from the output." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Transducers" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Theorem: *The output of a finite state transducer driven by a finite state statistical source is a finite\nstate statistical source, with entropy (per unit time) less than or equal to that of the input. If the transducer\nis non-singular they are equal.*\n\nProof:\n- trivial for stateless (one state) transducers\n- multi-state: sum over the product-state space\n\nInterpretation: the best thing a transducer can do is not to destroy information" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "## The fundamental theorem for a noiseless channel" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The fundamental theorem for a noiseless channel" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*Let a source have entropy $H$ (bits per symbol) and a channel have a capacity $C$ (bits per second). Then it is possible to encode the output of the source in such a way as to transmit at the average rate $\\frac C H -\\epsilon$ symbols per second over the channel where $\\epsilon$ is arbitrarily small. It is not possible to transmit at an average rate greater than $\\frac C H$.*" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The fundamental theorem for a noiseless channel: Easy part" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Assume a transmission at rate $m$.\n\n$$m H = H'$$\n\n- $H$: entropy (bits per symbol)\n- $H'$: entropy (bits per second)\n- $m$: rate (symbol per second)\n\n$H'\\leq C$ (otherwise entropy at output will be bigger than entropy at input)\n\n$$\\Rightarrow m\\leq \\frac{C}{H}$$" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The fundamental theorem for a noiseless channel: proof #1" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*It is possible for most purposes to treat the long sequences [of length $N$] as though there were just $2^{HN}$ of them, each with a probability $2^{-HN}$*" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Recipe: separate the possible messages of length $N$ ($N$ may have to be big)\n- the most probable ones ($2^{HN}$ messages)\n- the unlikely ones" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The fundamental theorem for a noiseless channel: proof #1" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Choose a timeframe $T = N(\\frac{H}{C}+\\lambda)$; during that timeframe, the channel can express $2^{CT}=2^{HN+\\lambda CN}$ messages.\n- Inject the most probable source messages to the channel messages\n- Choose a spare remaining channel messages to act as a *switch encoding message*\n- Encode the unlikely source messages (almost) as stupidely as you want, there impact on the transmission rate will arbitrarily negligeable if $N$ is large enough." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Remarks on proof #1" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- Not very practical (no guideline on the injection or how to separate likely/unlikely messages)\n- The rate is average (you have always the -low- possibility to have a big sequence of unlikely messages)" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The fundamental theorem for a noiseless channel: proof #2" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2021-02-16T14:19:54.754745Z", | |
| "start_time": "2021-02-16T14:19:54.744858Z" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Sketch:\n- Encode messages in bits\n- Less bits for most probable messages\n- If channel does not use bits, make conversion" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The fundamental theorem for a noiseless channel: proof #2" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*This method of encoding is substantially the same as one found independently by R. M. Fano. His\nmethod is to arrange the messages of length N in order of decreasing probability. Divide this series into two\ngroups of as nearly equal probability as possible. If the message is in the first group its first binary digit\nwill be 0, otherwise 1. The groups are similarly divided into subsets of nearly equal probability and the\nparticular subset determines the second binary digit. This process is continued until each subset contains\nonly one message. It is easily seen that apart from minor differences (generally in the last digit) this amounts\nto the same thing as the arithmetic process described above.*" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The fundamental theorem for a noiseless channel: proof #2" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2021-02-16T14:23:27.325997Z", | |
| "start_time": "2021-02-16T14:23:27.182673Z" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Deep link to compression\n\n- Shannon paper (1948)\n- Fano (1949)\n- Huffman (1951)" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Interpretation" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*The transducer which does the encoding should match the source to the channel in a statistical\nsense. The source as seen from the channel through the transducer should have the same statistical structure as the source which maximizes the entropy in the channel. [...] although an exact match is not in general possible, we can approximate it as closely as desired.*" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Example" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Imagine a source that produces the symbols A, B, C, D with the following probabilities:\n- A: 1/2\n- B: 1/4\n- C: 1/8\n- D: 1/8" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- How fast can we transmit the source?\n- How to transmit this source over a binary channel?\n- How to transmit this source over a ABCD channel?" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Formula" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.226330Z", | |
| "end_time": "2021-02-24T14:33:16.241374Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "def H(p):\n return -np.sum(p*np.log2(p))\nh = H([1/2, 1/4, 1/8, 1/8])\nprint(f\"Entropy is {h:.2f} (bits per symbol)\")", | |
| "execution_count": 3, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Entropy is 1.75 (bits per symbol)\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Interpretation: \n- Entropy says that each letter (A, B, C, D) produced by the source should require, in average, 1.75 bits.\n- Straight encoding requires two bits per symbol. We can potentially save 1/8 ( (2-7/4)/2 ).\n- Shannon says we can get arbitrarily close to that." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The source" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.243366Z", | |
| "end_time": "2021-02-24T14:33:16.263334Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "import numpy as np\ndef generate_letter():\n r = np.random.randint(8)\n if r < 4:\n return \"A\"\n if r<6:\n return \"B\"\n if r==6:\n return \"C\"\n return \"D\"\n\ndef generate_sequence(N=100):\n return \"\".join([generate_letter() for _ in range(N)])", | |
| "execution_count": 4, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The source" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.265331Z", | |
| "end_time": "2021-02-24T14:33:16.275332Z" | |
| }, | |
| "cell_style": "split", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "seq = generate_sequence(300)\nseq", | |
| "execution_count": 5, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 5, | |
| "data": { | |
| "text/plain": "'CBCCACBAABBDABCAAAABBADBAAAAAACABACDBADAADBDDAACABCABAADBABBBBAACDAAAAABAAABCAABAAACBDABACAABDAABBABBCBBABCABBCACDDBACAAABCCBADAAAADAAAAACBAAABDADBABDAAABABAABABAAAAAACBAADADCABBAADCABDCCDDABBAACCBBABADACABCBBBABABABBBAACDABAADBAAAADBACACAAAAAAACAAAAAAAABBCAAAAAADAACBCAADADACABBADACAAABDDBABAAABBBCB'" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.277334Z", | |
| "end_time": "2021-02-24T14:33:16.375366Z" | |
| }, | |
| "cell_style": "split", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "from collections import Counter\nseq = generate_sequence(30000)\nCounter([c for c in seq])", | |
| "execution_count": 6, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 6, | |
| "data": { | |
| "text/plain": "Counter({'A': 15196, 'C': 3731, 'B': 7389, 'D': 3684})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Encode as a binary channel: Shannon tree" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2021-02-16T23:12:25.139420Z", | |
| "start_time": "2021-02-16T23:12:25.134358Z" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- Try to make most probable messages short to encode\n- In this toy example, equivalent to Fano/Huffman" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Encode as a binary channel" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.377334Z", | |
| "end_time": "2021-02-24T14:33:16.387334Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "binary_encoding = {'A': '0', 'B': '10', 'C': '110', 'D': '111'}\ndef encode_sequence(seq):\n return \"\".join(binary_encoding[c] for c in seq)\nencoded = encode_sequence(seq)\nCounter([c for c in encoded])", | |
| "execution_count": 7, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 7, | |
| "data": { | |
| "text/plain": "Counter({'0': 26316, '1': 25903})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.389332Z", | |
| "end_time": "2021-02-24T14:33:16.396331Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "print(f\"Number of bits per symbol required: {len(encoded)/len(seq):.2f}\")\nprint(f\"Theoretical value for large sequences: {h}\")", | |
| "execution_count": 8, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Number of bits per symbol required: 1.74\nTheoretical value for large sequences: 1.75\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Checking consistency" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.400332Z", | |
| "end_time": "2021-02-24T14:33:16.406388Z" | |
| }, | |
| "cell_style": "split", | |
| "hide_input": false, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "def decode_sequence(encoded):\n results = []\n i = 0\n n = len(encoded)\n while i<n:\n if encoded[i]=='0':\n results.append('A')\n i += 1\n elif i+1==n:\n i+=1\n elif encoded[i+1]=='0':\n results.append('B')\n i += 2\n elif encoded[i+2]=='0':\n results.append('C')\n i += 3\n else:\n results.append('D')\n i += 3\n return \"\".join(results)", | |
| "execution_count": 9, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.408374Z", | |
| "end_time": "2021-02-24T14:33:16.421335Z" | |
| }, | |
| "cell_style": "split", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "seq == decode_sequence(encoded)", | |
| "execution_count": 10, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 10, | |
| "data": { | |
| "text/plain": "True" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Encode as a letter channel (compression)" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.423339Z", | |
| "end_time": "2021-02-24T14:33:16.429331Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "letter_encoding = {'00': 'A', '01': 'B', '10': 'C', '11': 'D'}\ndef compress(seq):\n enc = encode_sequence(seq)\n if len(enc) % 2:\n enc = enc+\"1\"\n return \"\".join(letter_encoding[enc[2*i:2*(i+1)]] for i in range(len(enc)//2)) ", | |
| "execution_count": 11, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.431366Z", | |
| "end_time": "2021-02-24T14:33:16.458388Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "c_seq = compress(seq)\nprint(f\"Compressed sized: {100*len(c_seq)/len(seq):.1f}%\")\nprint(f\"Prediction: {100*h/2:.1f}%\")\nCounter(compress(seq))", | |
| "execution_count": 12, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Compressed sized: 87.0%\nPrediction: 87.5%\n", | |
| "name": "stdout" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 12, | |
| "data": { | |
| "text/plain": "Counter({'A': 6611, 'B': 6427, 'C': 6667, 'D': 6405})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Uncompress" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.460331Z", | |
| "end_time": "2021-02-24T14:33:16.466375Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "letter_decoding = {v: k for k, v in letter_encoding.items()}\ndef uncompress(c_seq):\n binary_sequence = \"\".join([letter_decoding[c] for c in c_seq])\n return decode_sequence(binary_sequence)", | |
| "execution_count": 13, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.468331Z", | |
| "end_time": "2021-02-24T14:33:16.485331Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "uncompress(c_seq) == seq", | |
| "execution_count": 14, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 14, | |
| "data": { | |
| "text/plain": "True" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Misfitted source" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.486328Z", | |
| "end_time": "2021-02-24T14:33:16.492331Z" | |
| }, | |
| "trusted": true, | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "code", | |
| "source": "import numpy as np\ndef generate_letter():\n r = np.random.randint(8)\n if r < 3:\n return \"A\"\n if r<6:\n return \"B\"\n if r==6:\n return \"C\"\n return \"D\"\n\ndef generate_sequence(N=100):\n return \"\".join([generate_letter() for _ in range(N)])", | |
| "execution_count": 15, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.494368Z", | |
| "end_time": "2021-02-24T14:33:16.599392Z" | |
| }, | |
| "cell_style": "split", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "from collections import Counter\nseq = generate_sequence(30000)\nCounter([c for c in seq])", | |
| "execution_count": 16, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 16, | |
| "data": { | |
| "text/plain": "Counter({'B': 11093, 'A': 11281, 'C': 3822, 'D': 3804})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.600331Z", | |
| "end_time": "2021-02-24T14:33:16.604331Z" | |
| }, | |
| "trusted": true, | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "code", | |
| "source": "h = H([3/8, 3/8, 1/8, 1/8])\nprint(f\"Entropy is {h:.2f} (bits per symbol)\")", | |
| "execution_count": 17, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Entropy is 1.81 (bits per symbol)\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Misfitted source" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.606329Z", | |
| "end_time": "2021-02-24T14:33:16.621336Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "encoded = encode_sequence(seq)\nCounter([c for c in encoded])", | |
| "execution_count": 18, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 18, | |
| "data": { | |
| "text/plain": "Counter({'1': 30149, '0': 26196})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.623334Z", | |
| "end_time": "2021-02-24T14:33:16.630341Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "print(f\"Number of bits per symbol required: {len(encoded)/len(seq):.2f}\")\nprint(f\"Theoretical value for large sequences: {h:.2f}\")", | |
| "execution_count": 19, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Number of bits per symbol required: 1.88\nTheoretical value for large sequences: 1.81\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.632330Z", | |
| "end_time": "2021-02-24T14:33:16.662329Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "c_seq = compress(seq)\nprint(f\"Compressed sized: {100*len(c_seq)/len(seq):.1f}%\")\nprint(f\"Optimal compression: {100*h/2:.1f}%\")\nCounter(compress(seq))", | |
| "execution_count": 20, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Compressed sized: 93.9%\nOptimal compression: 90.6%\n", | |
| "name": "stdout" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 20, | |
| "data": { | |
| "text/plain": "Counter({'C': 8087, 'A': 4949, 'D': 6926, 'B': 8211})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Misfitted source" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.663334Z", | |
| "end_time": "2021-02-24T14:33:16.668331Z" | |
| }, | |
| "trusted": true, | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "code", | |
| "source": "import numpy as np\ndef generate_letter():\n r = np.random.randint(8)\n if r < 2:\n return \"A\"\n if r<4:\n return \"B\"\n if r<6:\n return \"C\"\n return \"D\"\n\ndef generate_sequence(N=100):\n return \"\".join([generate_letter() for _ in range(N)])", | |
| "execution_count": 21, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.670328Z", | |
| "end_time": "2021-02-24T14:33:16.779409Z" | |
| }, | |
| "cell_style": "split", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "from collections import Counter\nseq = generate_sequence(30000)\nCounter([c for c in seq])", | |
| "execution_count": 22, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 22, | |
| "data": { | |
| "text/plain": "Counter({'C': 7357, 'A': 7557, 'D': 7586, 'B': 7500})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.781331Z", | |
| "end_time": "2021-02-24T14:33:16.785331Z" | |
| }, | |
| "trusted": true, | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "code", | |
| "source": "h = H([1/4]*4)\nprint(f\"Entropy is {h:.2f} (bits per symbol)\")", | |
| "execution_count": 23, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Entropy is 2.00 (bits per symbol)\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Misfitted source" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.790329Z", | |
| "end_time": "2021-02-24T14:33:16.808385Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "encoded = encode_sequence(seq)\nCounter([c for c in encoded])", | |
| "execution_count": 24, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 24, | |
| "data": { | |
| "text/plain": "Counter({'1': 44972, '0': 22414})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.811389Z", | |
| "end_time": "2021-02-24T14:33:16.817329Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "print(f\"Number of bits per symbol required: {len(encoded)/len(seq):.2f}\")\nprint(f\"Theoretical value for large sequences: {h}\")", | |
| "execution_count": 25, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Number of bits per symbol required: 2.25\nTheoretical value for large sequences: 2.0\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.819398Z", | |
| "end_time": "2021-02-24T14:33:16.852331Z" | |
| }, | |
| "cell_style": "center", | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "c_seq = compress(seq)\nprint(f\"Compressed sized: {100*len(c_seq)/len(seq):.1f}%\")\nprint(f\"Optimal compression: {100*h/2}%\")\nCounter(compress(seq))", | |
| "execution_count": 26, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "Compressed sized: 112.3%\nOptimal compression: 100.0%\n", | |
| "name": "stdout" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 26, | |
| "data": { | |
| "text/plain": "Counter({'D': 14114, 'B': 8513, 'C': 8231, 'A': 2835})" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Side reflexion on compression" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Most compression softwares rely on two estimators:\n- A priori assumption on the source structure (e.g. English text)\n- Live estimates (on-the-fly, two-passes encoding)\n\nTrue story: MP3 is preferred for most people, but classical music users prefer ogg. Why?" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "## The noisy channel" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# The noisy channel" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- Noise can be deterministic (distortion) or random. Distortion is *easy*.\n- Shannon assumes the received signal is a function of two stochastic process, the sent signal and the noise.\n\n$$E=f(S, N)$$\n\n- General model: noise can be a Markov source, $p_{\\alpha, i}(\\beta, j)$\n- Stateless version: $p_i(j)$ (noiseless version was $p_i(j)=\\delta(i, j)$)\n- There will situations where the original signal cannot be recovered. Can that be controlled?" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Entropies: $H(x, y)=H(x)+H_x(y) = H(y)+H_y(x)$" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Equivocation example" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "A good example to understand the issue:\n- You have binary source of maximal entropy (0s and 1s, i.i.d., $p(0)=p(1)=1/2$)\n- You have 1% of i.i.d. errors: $p:=p_0(1)=p_1(0)=0.01$\n- How much information can you get in the end?" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "fragment" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Hint: if you ignore the source and send random bits, $p_i(j)=1/2$ for all." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Equivocation formula " | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*Evidently the proper correction to apply to the amount of information transmitted is the amount of this\ninformation which is missing in the received signal, or alternatively the uncertainty when we have received\na signal of what was actually sent.*" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "$$R = H(x) - H_y(x)$$\n\n$H_y(x)$ is a measure of ambiguity." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Interpretation of effective rate" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "$$R = H (x) - H_y(x) = H(y) - H_x(y) = H (x) + H (y) - H(x, y) $$" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*The first defining expression has already been interpreted as the amount of information sent less the uncertainty of what was sent. The second measures the amount received less the part of this which is due to noise.\nThe third is the sum of the two amounts less the joint entropy and therefore in a sense is the number of bits\nper second common to the two. Thus all three expressions have a certain intuitive significance.*" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Equivocation in the example" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "center" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- If I see 0, it was 0 with probability (1-p) and 1 with probability p.\n- Uncertainty of 0 is $H_{y=0}(x)=-(p\\log(p)+(1-p)\\log(1-p))$\n- Same for 1, so $H_{y}(x)=-(p\\log(p)+(1-p)\\log(1-p))$" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.854330Z", | |
| "end_time": "2021-02-24T14:33:16.956368Z" | |
| }, | |
| "cell_style": "split", | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "from matplotlib import pyplot as plt\np = np.linspace(0.001,.999)\nplt.plot(p, 1 - ((p-1)*np.log2(1-p)-p*np.log2(p)))\nplt.xlim([0,1])\nplt.ylim([0,1])\nplt.xlabel('Noise')\nplt.ylabel('Relative rate')\nplt.show()", | |
| "execution_count": 27, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 1 Axes>", | |
| "image/png": 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\n" | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.957373Z", | |
| "end_time": "2021-02-24T14:33:16.960335Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "p = 4/100\nh = H([p, 1-p])\nprint(f\"With error {100*p:.1f}%, equivocation is {100*h:.1f}%.\")", | |
| "execution_count": 28, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "With error 4.0%, equivocation is 24.2%.\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Correction channel" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Experience of thought:\n- one observer sees sent and received signals\n- she can send an *erratum*\n- what is the quantity of information required in the *erratum*" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.961328Z", | |
| "end_time": "2021-02-24T14:33:16.982368Z" | |
| }, | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Image(filename='correction_channel.PNG') ", | |
| "execution_count": 29, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 29, | |
| "data": { | |
| "image/png": 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pP/FuTsycObui72XeQ5Niy/KqwNZY+4S7OrdM/8x/+rzYeaez+w5W75Eu3vUtbbzLcJ8tx7tT4q9zno3L939/tJVXmrXGynv9PJ7sY8FWo8W7Bfvst8cvcqjYFfb7r3g15ZN783eHxqqtg2OryQ/Ha9d+Jlbu+vm0rBD7Xf7KgL/XVPGuYm/G7w5dNVoHbxWTH34trv3MyuV/INCywn5xef+WIAIAixHvAAAAaApzbj8u1uz6oHpQa4w96uYKz9/Uk4545e7fxp0v9/BB9Pzn4vwJw8rhZFD7tvG9f6auOQvMvu6QbueNaomVP3tdzCpd1qM08a7j+fjRR4ckz7N1zTjujso/vE8T7zqe/1F8dEhySMTWNY+Lyh+qH/HujUtjv30urCCWzInbj1szCZitY+Oom/u/V0THK3H3b++MnnaL3mUc77LcZ7vHu+Iu9OY9yTkpi1M6L2Vvp95rvHjXuUmf+UHs0G2fL4zYOy5NU+86XoiffWy5aBm5R1z0Yuft5twdX1q3rXR/hRi2ww+inz+islrEu44XfhYfW64lRu5xUSx82l+KddtKj1EYFjv84J8Vr+4FAJZMvAMAAKAJvBt3n7B2EmkKy8Sel7xeuqzKXrs09hre7dxdqxwZN/SzBy04V1x76Tl3Tuvqx8RtvX2+niLezX1oUowvx4VCtG8yMe5L0Scqj3dz46FJ42NI+Rxg7bHJxPt6WRG4uPTxbvZNn491dq8g3r17d5ywdrfDGy6zZ9Rqt+hdxvEuy3128XjXad5Tl8Z+nftx1/MvtK0eB/36hSVGn0aMdzFvenxjs/bydhjUslJ89neVHzpz3vRJscXg1lj1sN+VwmVxNd9W5dV8hfaN4tSuDdZP1Y9382L6pC1icOuqcdjvSrl13iPx7a2Sw7G2b3Rq+ecMAPSfeAcAAMDSb/6T8b1tu32QXrVDxL3X3Lu6fSDeOe3jvx2P9nHYvyWaMzUOHpVElUHtH45zn+mlwlQY7zpevTVO3mLZJI4M2zROvj3did4qi3cd8eqtJ8cWyyaRcNimJ0e6h0oX7zpevye+tu1yMXS3vuPd/Ce/F9t2D00Djmb9lW28y3Sf7SHeFfebN+78amxe3m8GRcuoHeK7f+v5B9+Q8S5mxzUHjVrknJJbn/lY6bK+zI5bjl4jWts26HzcZEcormrbbUTXNmmNsUdc3/uqxj5UPd7NviWOXqO182f51Uiedke88LPdYkRXvG8dG0dcP5BnDQAUiXcAAAAs/eb8MT73vpbSh96d075tfPfJ3pYi9d/sKz4Rw8rnuhoUg3e6IF7qb1GYe9ciK8MGta0bJ97TS0ToK97NnxkPT/1m7LveMslKmDHbx1d+/3ykbTV9xbv5Mx+Oqd/cN9ZbphQbCu0xZvuvxO+fT/tIi8W79vfHNnvuHXvvvdjs9fHYZfsPxPtHLFyxNbiCeDfnj5+L95UP8Tgo2rf9btRot+hDtvEu0322x3hX9G488fO94n2tSfgdPO7ouL6Hc6Y1Zrx7N+79yvrJ+f8GtcYax95euqx3HTN+GZ9YviWGfficxfbHmXH1QWOSc8iN2isu6fcPqvN7rGq864gZv/xELN8yLD58zpOLrpKceXUcNKbr929LjNrrkv7vXwDAAuIdAAAAS7+3L499h3ZbDTR4QkwpnpCpBl69cLcY3PU4nTNk94ui30difPe+OHXDrvNcdU7r2Pj8Tb18wL5IvGuJ0dt8Ok448YQ47qjD4oA9tosNxwyNlmKkKbTHqPU+GodMuiIefK1/tWqRuNEyOrb59Alx4gnHxVGHHRB7bLdhjBnasiAeFdpHxXofPSQmXfFg9O+hFot3g9eOCZ8+JA45ZNH5zMEHxL47j4/Vhi983Eri3duX7xtDu0erCVMWnKer/rKNd5nus0uMd506Xo9bv7RJt7DYEmP2+Gk8vtj1GjPezYuHv7lleb9dcP6/w68vXdab+fH49z4UQ1tWiP0uf+U93887d34x1i6fQ25IbPvdx/p9Drmqxrv5j8f3PtT5+2WF/eLy9wTWdzr377XLIbMwZNv47mP9fdYAQJF4BwAAwNLv7V/GPovEu53igpdrU2nevHTPGNL1OJ0zeOefxoz+PtS798fEjbuHkDXj+Dsrj3crbLFvfPazh8bhR/xHjF+xa+VLIYZu8bW4r/LTb/Vo0Xi3Qmyx72fjs4ceHkf8x/hYsWs1W2FobPG1+2JgD5XusJnz/nVDfGmLZWNIJfHul/ssGu92uiBqtFv0Idt4l+k+21u8K3r3sbhg92S1WfF8lZufcle8Wbq4qFHj3UPf2KxbvGuN9x99S+myXsy5J04a1xatqx8dN88ufa27eX+PSVu2l3+2beNOij/18/yE1Yx3c+45Kca1tcbqR98cPT/tSbFle9fv4LYYd9Kfop9PGwDoJN4BAACw9JtzXRxSjled075tfO+ftVn5Mef3h8ZK3Q/FuM134on+PtS7d8eX1ukWQtq3isn/6OXOlnjYzI544Yr9kxhRGBabnfqngZ0va5G40e2wmR0vxBX7jy2HqMKwzeLUPw3kkdLFu6K3fnNgrPKxCg6bed0hSWjsnPZtvxc12i36kG28y3Sf7Svedep49cY4bsOh5e+n0Pb+OOCK58orzhoz3s2NO45fs/wzLZ7zbrNvTC9dtmQzrz4oxrR0Xvfrf+vc83vSEc9dsHMM74rOLe+LQ67tnjIrV714VzqcZ/tm8fW/LeGwuB3PxQU7Dy//DFved0j082kDAJ3EOwAAAJZ+86bHpM3bSx+iFz+oXiOOu2NAdWSJ5j92ZmzVXnqczmld47i4vb8PNefa+PTySXRsWeHgmPp26bKe9HbOu45X4rrD14r20of+hcHrx/G3vFG6ML0lxrtOHa9cF4ev1bU6qBCD1z8++v9Q6ePd/KfPiQl79h3v5k2fFJsv9rOq0W7Rh2zjXab7bAXxrmjOwz+MXUZ3u9+R28eZDyxc49WY8e71uGTPrnNLdk5hudjvij5q1fxnOrfFslEY+sH4xj1PxTPPPNPz/O1HsfvI5FyAy33swnihH994teLd/GfOjwnLFmLoB78R9zzVw/Mtzd9+tHuM7IqOndvjYxe+ULWfFwDkjXgHAABAE3gnrj/ifd0OvTckdjy/Rh8cz709jlujK6ANisKQneKCf/XvkYoRavtyVCnEMrv+NHq9q97iXaeOmbfE8esPLke19rUOj+vec36qyvQW7zofKWbecnysP7gUGArtsdbh10X/Hip9vIt5/4jfTX2o78N1vnN9HPG+JAgVhuwY5/enggxYtvEu0322wnhX3Kdm/P7zMa5rnypG4fWOjN/N6GjMeDfnljj6/d236Yfj3Kd7X8747gOnxyblQ0tWPoXB4+NbDy9hxVsvqhPv3o0HTt+k/I8CKp/On9/4b0U/njYA0Em8AwAAoCm8de1nYkz50ICFGLnvZX2uzOqfd+KWL6yeHC6vZcU46Jr+HTZy1jUHxQrl88eNiI9d+GLvcaKPeFc060+nxWbDugJBa4w94Mr+rdrpNd4VzYo/nbZZDOv6UL91bBxwZX+CaT/iXcXeims/0/18aiNj38terVoAqlzG8S7LfbbieFf0Tjx09oTk/ge1xOjdpsTf/9x48W7OnV+Mtdu6nmchhm5/Th+HZH0rrj9ibLR2PtbRv7k/HnzwwV7n/muOjQ27nUNu7ePv6Nw66VQl3r11fRzR+Tunbf2j4zf39/xck7k/rjl2wyT0ta0dx99RtRczAOSKeAcAAEBzeOeu+NJ6ybm4CsN3iZ88P4CP+jtej5dnzCn9YVHz/jYptiivEGqJMZ+5Nt4qXVa52XHDkcm541pX+1xc39c5oiqIdxFz4sFvbxsjuj5Ab1kp9rzo6fL5wyrVd7zrNOfB+Pa2SURqWWnPuKiP1UfvVYV4N+/FePD+56KnNPHOXV+K9bpFluG7/CQGtlu8HEvYLXqRdbzLcJ9NFe86dbwU1x6+bhKACsNio113jNVbGyjedbwaV31q5SQKt4yO/f5rRq/PreNfF8fHR7bEsjv+KCp6iXQdYrP0GC0rHRhXvV66rEIDj3cd8a+LPx4jW5aNHX9U2e+QrkNsLnjMzv1spQOvipRPGwDoJN4BAADQJDrihUv3idHlVUFtsc4Xbo6+2kLPZsd9kz8WHz/n0dKfF9Pxevz+8NWjtRQYCsvtFj99Ll206pjxX7HfiqVDOraMjr1/8VzfH45XFO86vftonDdhVDkutIyaEOf9I0Wc6FRRvOv07qPnxYRRXYembIlRE86LdA810HjXES9e8onY7tS/9LwtOl6IS/cZXd4WhbZ14gs392+viNn3xeSPfTzOeTTtsQCzj3eZ7bNp413R7AfirA8n++/CaZx4N+uuk2LDbof3HP6h78Tfe7155z7+7a1icOvK8elrZpa+1reZVx8cK5d/ny0bE6Y8myrCDzjezXskvr3V4Ghd+dNR+dOeGVcfnITNwrITYsqz6fYzAEC8AwAAoJnMfyYu3fd95UhSaF8rPnvNiylXnc2Nx3/xyfjAzufGw7181t3x2h/j6HFd55drjdUPu67yw3R2zIybjx23cHVRoT1W+9SV8XwlT3KxeLfRaUuId53mP31R7LlSV1QrxPBtJsV9s0sXVmDRuLFRnLaEeNf5SPH0RXvGSuXIMDy2mXRfVP5QA4t3Ha9fH59bZ+M45S9Lrifzn7k09n1f13Yrngvws3HNiymDwtzH4xef/EDsfO7DPa7w6131491V+6eMd50y2Wf7E+86dbz4mzhkrfby99go8W7+i9fEoeskz6tl+Qlxbm+/KIrevjWOWbO1cxt8Ne5N83Of86c4eVzXauLO/XbTM+LBFNtwoPHu7VuPiTVb22KDr96bap+f86eTY1zXatfOfWXTMx5c4u8pAKBn4h0AAABNpeP12+OrWyZho7DMRnHYZY/G26XLe/dm3P+jfWLcRkfE1H/1nQnmPPrT2Hvswg/yC62rxt4/ezT6PqLirHjgBx+LVVoLMajQGivvck48UNmT63zAP8RhY7qCXFusd9KfevlQvCNeuPKAJFAUBse4I38XL1dYP+b84bDkHIJt68VJf+rl4/eOF+LKA5LDKRYGj4sjf/dyhaFlXjz09c2SeDfyU3F1pfGueIjFQ9eKIRucEr20u04d8frtX40tRySrpZbZ6LC47NEKN/yb98eP9hkXGx0xNSrYLXowN245uvvhJr8Qtw4o3r0dl+87tLyPt2/5zXikwsWAdd9n5z8d52zfHm3rnhj3pCw4b//1m7HtyK79vbrxrrh/l4NzhfFuzj9/HUdu0u1QliO2iBNv6Gs/74jnf75HjGoZEtt9/8mU/5CguGJvfHII0c6f1yHXVn4Qyrm3HJ28/ltXiy+k2ek6no+f7zEqWoZsF99/MmXoLq7YG58EztZVD4kUTxsA6CTeAQAA0HQ6Xrk9Jk1YJfnQu2VEjNvzlLjk7ufi7R4/aZ8bL/3l8pi457ox5gNHxdXPVF4Z5jxxRRy52cgFh4krtI+N3SbdEM8uoYZ0zHwwLvnC1rFiMYJ0PqeND700Hk2xGq7jlQtjt6FJgBp1wFUxq3RZjzpeiesOX6vbdhgVHzzttnilzwLSEa9cuFsM7bpdYVQccFWvj9T5UNfF4d1WSrWM+mCcdtsrFcSWuXHrF96fhL8he8TFlXzQP/9f8ccvbx2jWtpig1OWcMjMRXR+T7dPigmrdHuOI8bFnqdcEnc/93bPz3PuS/GXyyfGnuuOiQ8cdXWk2C0W80b8cp8k+hSGfyIu7+eROxeY/2R8d9v2hT+bzmld49i4PUWXqec+G+/+OU5ery0Kow6MqysNfmXz47krPxWrtxX3+WrGu46Y8bNdY0jX/t1XvJv7Qtw55XMxfoXW0s+wEMPW2S/OnfZ6n8+nY+Yf48i1Or//9s3iG9PTHm61c/P96aRFztk4ZLOJcW+F2/+NX+4Ty5Zfw8PjExXvdB0x849Hxlqd2719s29E+qf9bvzppPWibcFzLj72kNhs4r0pVuMCAOIdAAAAzWnev+L2cw6J8Sslsaa4amj42E1i+z32j0OO+Hx8/sjD4qB9JsSWa4yM9mGrx4Qv/Vc80nuj6tnsJ2LqGXvHuJGtUSi0xPA1tosDvjQ5plz8X/Gb31wRF//4O/GVQybE+it0PpfOy0est0ecetU/eg9vi+t4Ne44ZXzyYXzntIzeNc77ex9F5I1b4/gNug6VWNwGQ2Ot3U+Ly6a9EEta4Nbx6h1xyvgkNhXPZTd61/Oi74c6PjYonwtsUBSGrhW7n3ZZTHthiY8Usx65MPYrHwq0+PyWiY0//b247OrfxnXXXbfo/HZqXHX5RfHDbx0f+2y6QrQVt0XbBnFKiuMxzvvX7XHOIeNjpfZuz7N1eIzdZPvYY/9D4ojPfz6OPOyg2GfClrHGyPYYtvqE+NJ/PZLuZ7WIjnjzvjPjo+XzAnZOy4qx23kPV7gadHHz4qWbTogPDEmef3FV1X/8/OF4K03Zqsc+G3PjmV99ZkEEGtSycuz103/0I+C8FX/+2tYxolC9ePee/btlRKz/sSPixK9/N86/6PK4aupv49qrr4xLpkyOLx+2e2y28pBytBuyylZx0Leujccr+OHNf/3BuGC/1RbG886f+a7nPpTuZ9T5Cv3HD3eJ5btWCBanczus+6kL48GZva+G63jzvjjzo93PG9gSK+52Xjzc5/OeH68/eEHst9rC35stK+4a5z70Vrrt/s4/4oe7LN/tsTtfY4PXjU9d+GD08bQBgBLxDgAAgOY2+9m467Kz4oSDdottNlo9Ri83LNpbW6N92IhY8f0bxgd3OzhO/P6VMe2Fvg8e2Jf5rz8Sf7jg9PjcPh+OTdcaE8sNbY/W1vYYutxKscbG28Weh50a5183PV5NsZLlzetPjd123D42X2O5hbGq2wfiCz8UHx3jtv5ITNh7cty9hNVXs/58Wmw+rFvsKU6hJYaNGRfbn3FH6XxWb8b1p+4WO26/eayxXFu3cNc1hRg8elxs/ZEJsffku0u3Wdys+PNpm8ewxZ5noWVYjBm3fZxxR+lW794X5+4/IbbbfI0YuWBV1aLXTzNpz6XWZfazd8VlZ50QB+22TWy0+uhYbtjCn9WwESvG+zf8YOx28Inx/SunRb93i7l3x+S9J8QO49eJ5buFwvIUBseK642PHSb8R3y/92N+LtDx0m/ihF13jA994P0xvLgK7j331xYj19g8tpuwf5x7X+UbpBb77PxnfhlH7fKR+OBGq8Swlm7PtTAkRo/bqvN7TvccO+8wLvuPtWPXAcW7hfv3hA9vEWuO7Gn/7j6FaGnr3BeGj4r3rblhjN9x3zjsxDPj4hv+Hq9UtMJxZlx79Eax0pDCoo9TaI1lVh4X4/c7L/7W6/Z8N/585sdii7VXiME9vOaLz691mVVio92/s9jhYufG3ZP3jgk7jI91lu/2jxa63W7wiuvF+B0mxH98v4fVqjOvjaM3WimGFBbdvwqty8TK48bHfuf9LXp/2n+OMz+2Ray9Qrd/LNB9it//KhvF7t/5S+kGAMCSiHcAAAAAAADQIMQ7AAAAAAAAaBDiHQAAAAAAADQI8Q4AAAAAAAAahHgHAAAAAAAADUK8AwAAAAAAgAYh3gEAAAAAAECDEO8AAAAAAACgQYh3AAAAAAAA0CDEOwAAAAAAAGgQ4h0AAAAAAAA0CPEOAAAAAAAAGoR4BwAAAAAAAA1CvAMAAAAAAIAGId4BAAAAAABAgxDvAAAAAAAAoEGIdwAAANCk3n777dh///3jzDPPjL///e+lrwIAAI1MvAMAAIAm9t///d8xaNCgBbP66qvHscceGzfddFPMnTu3dA0AAKCRiHcAAADQ5D7/+c+XA17XLLvssvGJT3wiLr300njllVdK1wQAALIm3gEAAECT+9///d9YbbXV3hPwuqZQKMQ222zj8JoAANAAxDsAAADIge6Hz+xrHF4TAACyI94BAABATvR0+My+xuE1AQCgvsQ7AAAAyIm+Dp/Z1zi8JgAA1J54BwAAADmS5vCZfY3DawIAQPWJdwAAAJAz/Tl8Zl/j8JoAAFAd4h0AAADkzEAPn9nXOLwmAAD0n3gHAAA0hOIH/Jdccokxpk5z8skn9xjeajErrLBC7LjjjnHiiSfGhRdeuMjzuOKKKxb5szHGGHPXXXeV/oYIkE/iHQAA0BDOOuusHj/0N8Y092y88cY9ft0YY0x+5+CDDy79DREgn8Q7AACgIYh3xuRzNtpoox6/bowxJr8j3gF5J94BAAANYfF4d9BBBxljajh77rlntLa2LvK6q+WMGDEi1l9//dhpp53iwAMPLD+P448/fpHnZYwxJp/T/b8Z4h2Qd+IdAADQELrHu5NOOqn0VaAW/r//7/+Lj3zkI4t8UFrtaWtrW3Ceu/POOy/++c9/lh4ZAHpWPNdd139DxDsg78Q7AACgIYh3UD9Tpkwpv96qOcsvv/yCD1x//etfxxtvvFF6NADom3gHkBDvAACAhiDeQX08/fTTscwyy5RfbwOdcePGxVe+8pW4++67Y968eaVHAYB0xDuAhHgHAAA0BPEOaq8ah8vsOhzmD37wA4fDBKBqxDuAhHgHAAA0BPEOaq+/h8t0OEwAak28A0iIdwAAQEMQ76C20h4u0+EwAagn8Q4gId4BAAANQbyD2qnkcJkOhwlAlsQ7gIR4BwAANATxDmrnxz/+cfn11X1GjRrlcJgANATxDiAh3gEAAA1BvIPaWPxwmV2Hw7zrrrscDhOAhiHeASTEOwAAoCGId1B9xcNl7rTTTvHRj37U4TABaGjiHUBCvAMAABqCeAfV98477zgcJgBLBfEOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQAADUG8AwDIL/EOICHeAQDQVC6//PL4yU9+YpbC2Wuvvcof2EyYMKHH65jGn4suuqj0agQAqJx4B5AQ7wAAaCqrrbZa+U2/Mab+M2zYsNKrEQCgcuIdQEK8AwCgqYh3xmQ74h0A0B/iHUBCvAMAoKl0j3cf+tCH4ogjjjDG1Hj23nvv8utOvAMA+kO8A0iIdwAANJXu8e6JJ54ofRWopf/5n/8pv+7EOwCgP8Q7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4BwBAUxHvoP7EOwBgoMQ7gIR4B5ChBx54IK6//npjjDFVnNGjR5ff9It3UB/d493gwYN7fG0aY4zp/0ybNq30Gxeal3gHkBDvADK01157lf9iaowxpvoj3kF9dI93xhhjqj8f+tCHSr9xoXmJdwAJ8Q4gA4899lh88IMfjFGjRi3yhswYY0x1R7yD+hDvjDGm9lN8D3nvvfeWfvNC8xHvABLiHUAG7rvvvvJfSJdddtnYeeedjTHGVGmGDBlS/h0r3kF9dI93LS0tPb42jTHG9G+6fr8W54Ybbij95oXmI94BJMQ7gAx0j3ebbrpp6asAVMNqq61W/h0r3kF9dI93w4YNK30VgGrYcccdy79jxTuamXgHkBDvADIg3gHUjngH9SfeAdSOeEdeiHcACfEOIAPiHUDtiHdQf+IdQO2Id+SFeAeQEO8AMiDeAdSOeAf1J94B1I54R16IdwAJ8Q4gA+IdQO2Id1B/4h1A7Yh35IV4B5AQ7wAyIN4B1I54B/Un3gHUjnhHXoh3AAnxDiAD4h1A7Yh3UH/iHUDtiHfkhXgHkBDvADIg3gHUjngH9SfeAdSOeEdeiHcACfEOIAPiHUDtiHdQf+IdQO2Idyztnn766dL/611/4t2bb74Zr7/+eulPAM1DvAPIgHgHUDviHdSfeAdQO+IdS7u99947vv/978f8+fNLX+lZ2nhXfD2st956MXfu3NJXAJqHeAeQAfEOoHbEO6g/8Q6gdsQ7lnZTpkxZsP9us8028fjjj5e++l6VxrviartDDz10wfX23Xff0lcBmot4B5AB8Q6gdsQ7qD/xDqB2xDuWds8++2x5Hx4yZMgSV+FVEu+Kr4FVV121fL3ibQCakXgHkAHxDqB2xDuoP/EOoHbEO5rBxhtvXN6Pi9PTKrze4l331XZdUygUYsaMGaVrADQX8Q4gA+IdQO2Id1B/4h1A7Yh3NIOJEyeW9+OuWXwV3pLi3eKr7bqmGAABmpV4B5AB8Q6gdsQ7qD/xDqB2xDuawb333lvejxefrlV4i8e74mq7ww47bJHrdp/JkyeX7h2g+Yh3ABkQ7wBqR7yD+hPvAGpHvKMZdHR0xOjRo8v78uJTXIX3yU9+svznj3zkIz2utus+06dPL907QPMR7wAyIN4B1I54B/Un3gHUjnhHs1j8nHUDmeLf+QGamXgHkAHxDqB2xDuoP/EOoHbEO5rF1KlTy/vyQOfYY48t3StAcxLvADIg3gHUjngH9SfeAdSOeEezmDVrVgwePLi8Pw9kbrrpptK9AjQn8Q4gA+IdQO2Id1B/4h1A7Yh3NJNdd921vD/3d5ZddtmYO3du6R4BmpN4B5AB8Q6gdsQ7qD/xDqB2xDuayZQpU8r7c39n3333Ld0bQPMS7wAyIN4B1I54B/Un3gHUjnhHM3n22WfL+3N/55JLLindG0DzEu8AMiDeAdSOeAf1J94B1I54R7PZeOONy/t02ikUCjFjxozSPQE0L/EOIAPiHUDtiHdQf+IdQO2IdzSbiRMnlvfptLP11luX7gWguYl3ABkQ7wBqR7yD+hPvAGpHvKPZ3HvvveV9Ou1Mnjy5dC8AzU28A8iAeAdQO+Id1J94B1A74h3NpqOjI0aPHl3er9PM9OnTS/cC0NzEO4AMiHcAtSPeQf2JdwC1I97RjA499NDyfl3pFP+eD5AX4h1ABsQ7gNoR76D+xDuA2hHvaEZTp04t79eVzrHHHlu6NUDzE+8AMiDeAdSOeAf1J94B1I54RzOaNWtWDB48uLxvVzI33nhj6dYAzU+8A8iAeAdQO+Id1J94B1A74h3Natdddy3v233NMsssE3PmzCndEqD5iXcAGRDvAGpHvIP6E+8Aake8o1n9+Mc/Lu/bfc2+++5buhVAPoh3ABkQ7wBqR7yD+hPvAGpHvKNZPfvss+V9u6+55JJLSrcCyAfxDiAD4h1A7Yh3UH/iHUDtiHc0s4033ri8fy9pCoVCzJgxo3QLgHwQ7wAyIN4B1I54B/Un3gHUjnhHM5s4cWJ5/17SbL311qVrA+SHeAeQAfEOoHbEO6g/8Q6gdsQ7mtm9995b3r+XNJMnTy5dGyA/xDuADIh3ALUj3kH9iXcAtSPe0cw6OjpipZVWKu/jPc306dNL1wbID/EOIAPiHUDtiHdQf+IdQO2IdzS7Qw89tLyPLz7Fv9sD5JF4B5AB8Q6gdsQ7qD/xDqB2xDua3dSpU8v7+OJzzDHHlK4FkC/iHUAGxDuA2hHvoP7EO4DaEe9odrNmzYrBgweX9/Puc+ONN5auBZAv4h1ABsQ7gNoR76D+xDuA2hHvyINdd921vJ93zTLLLBNz5swpXQMgX8Q7gAyIdwC1I95B/Yl3ALUj3pEHP/7xj8v7edfsu+++pUsB8ke8A8iAeAdQO+Id1J94B1A74h158Oyzz5b386655JJLSpcC5I94B5AB8Q6gdsQ7qD/xDqB2xDvyYtVVVy3v68WZMWNG6RKA/BHvADIg3gHUjngH9SfeAdSOeEde7LHHHuV9fYUVVih9FSCfxDuADIh3ALUj3kH9iXcAtSPekRcTJ04s7+s+KwHyTrwDyIB4B1A74h3Un3gHUDviHXlx8cUXl/f13XffvfRVgHwS7wAyIN4B1I54B/Un3gHUjnhHXlxyySXlff3ggw8ufRUgn8Q7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDviHdSfeAdQO+IdeSHeASTEO4AMiHcAtSPeQf2JdwC1I96RF+IdQEK8A8iAeAdQO+Id1J94B1A74h15Id4BJMQ7gAyIdwC1I95B/Yl3ALUj3pEX4h1AQrwDyIB4B1A74h3Un3gHUDviHXkh3gEkxDuADIh3ALUj3kH9iXcAtSPekRfiHUBCvAPIgHgHUDvd411x1l9/fWNMjWfFFVcsv+bEO4DqEu/IC/EOICHeAWRAvAOoncXjnTGmviPeAVSXeEdeiHcACfEOIAPiHUDtiHfGZDviHUB1iXfkhXgHkBDvADIg3gHUzqOPPhr/5//8H2NMRjN9+vTSqxGAahDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAS5k5M+Lvt10Tl114fpw9eVJMOusH8ZNLfhXX3/tMzOooXadSs/4SF3/ttDjttL5mYkw8/Yz4+qRvx3fOnRIXX/G7uOOh5+Ot+aX76bd58ebT0+K6S6cs+F6+WfxeLv1N3Pr3l2NO6RpFs+//r/jlX2aV/rSYeU/GtWdN7OE5p5+v/ecDizxu2ez74pI+ttPEiafHGV/7Rnxz8nfj3Ck/j19ec1NMe2xGz/e3iHfjb7/8Wo/3ucicfm7c8HxvG3x+PHXd9+L0nm7bOad/73fxdNfNl/ptBkBWxDvyQrwDSIh3ABkQ7wCWBu/GS9N+EV/Zd8sYO7w1CoXBsdz71ohxm2wWm66/eqw4rPi1lhi2ymbx8S/+LP788rzS7frw7kvx93vuiJuvuTBO23OdGFpY+N+DBVNojWXGjIvxO+wWe33iP+I/9ts7PvaR8bHeSkOjZcH1CjFkzCbxsS/8IG58anbpDiv39iNXxMm7rRsjWgqdj1WItiHDY9nBLVEoPfbwsVvGnkd+Lc6dclYc8oHlY5efvBw9tsmOmfHkvXfGbddfGT84ZvtYua3z/krfQ6FtxVh3y/ExfnxPs0Vstsm4WH3FYdFa+r4HT5gSL/b0IPNejoeL22nqz+P0vdeNYd2304IpREv70BgxckQM7Xz8Bd9DcYrfx+rbxSFnXR9Pv1O6r/foiJcf/H388twvxR7rLZvctjSFwavHhGPOjAuvuiOeeLO3OtsRMx/5Y1w8+cjYYezg5H5ahse4vU6OH13395jZdfOlfpsBkBXxjrwQ7wAS4h1ABsQ7gMbW8fq9cd7+42J4SyEKw9aIXb98cdz+5BuxyBqsOTPioevOjs9tMybaC4VoHbVpHDzlvnijt9azuDl/ipPHtZX/m9A27ssx7d3SZd11zIqnb/9pHPfh93U+1sLrtozYKD576T8qXDHVES/94YTYYmRLDCosG+v/x7fjmgdfjgWdZv478dpTf45fnfX5mLDmMt1C1uDYeUnxrruOl+Oi3ZMAVhh1cEztMwDNjn/+7tT48Iot0b7VmfFYX6sJ5/4lvrpBt+20zpEx9anX4p2u2737ejxxxy/ilN3XSoJVoTVW2Pa0uOWV3r+Djpl3xVc2H9bt+26NVT/3x85nmM67D38zxrcXH3dIbHjcjfFabw+7lG8zAOpLvCMvxDuAhHgHkAHxDqBxvf3QT+KT6xZjTiFax+wU37n3jd4D1rwX4g8nbBkjWjp/r7csF5t/4Tfx1NzSZX2aHb/+5IhyxGlb/6txb0/xrsu7z8ZvDhsXQ0qxpdC+Rhz86xf7DGzzHvthTBhVDHeDY8PjbopXl3SDtx+JSw9ZvxRzKox38W5M+/K4aCt9D5WFqKKOeP6nu8WojU6Nv/b2PS8wO646YLlkO208Me7vMXLOiFtO3jKGd8WoQS2x/M7nx2N9LIp88/eHxdjW5DajP/Pb1PFu/jPnxvbthWhf/+S4p8/vf+nfZgDUj3hHXoh3AAnxDiAD4h1AY5r76AWxxyqtC4JHYdjmceo9b5Uu6cP85+PyT64arcXf7YXBsc5nr4peT5VWNiduOHKVaCn9N6HPeFc0+944ddPkEI2t7z8irn+zdFmP3ohrP7PygsdoWfGA+PXM0peXZN5TcdFeYzqvX2m8mxd/n7RFtJeeT+UhKqLj1Utinw2Pidv6jJ1z4sbu22lJIapo7oPx9c27H8JyTHzqqtd7/z7efTC+9oH2ZJuudlTcXOH3sFBHvPTzj8XwllGx58V9x9Sm2GYA1I14R16IdwAJ8Q4gA+IdQAN66444eeOhCwNGoT02OOnuVKuv5j9/UXx8+ZaFv99bRsWO5z4SfS6Oirlx81FjF0a/zqko3kVHPH/+jsm58jofa/9f91Lv5vwxjnjfwufVvuU345EKVlTNf/x78aGhQyqOd498a3y/QlTMfy6uOevn8WCf3/Ni26m3EBXz4+lzto/B3VaSrXDw1Hi7dGnPFq5oG1HepistiFcVm/9M/GjHYdE69sj446zS13rVDNsMgHoR78gL8Q4gId4BZEC8A2g0c+LeUzcpx4vC8J3jgufSrjuaHbcds2Y5lrSM2jl+/FSfJybrR7zrvNVdX4y1yod5bI9NTn8gltjkXvt57Dak9JyKK+8qaVId/4qf7DIqdql1vKtYmhDVee0bj4xVi4cxLV2/fftz4um+fhRv/i4OXbW1dJtCLLvjD/u+Tcm86ZNi8/a22PCUv1YQbIuaZJsBUBfiHXkh3gEkxDuADIh3AI2l46VLY+/iOeEW/G4uxPA9LoqX+3HMwLl3nxDrtC38/T5oUGusdextfaze62e8u+2YWL0c79piw1PvW3I0evuq2H+5wsLrFgbHuM/9Nl7sM8rMj39M3j52r1m8mxMzZ86u4L67pAxRNx/V7Rx2g2LwR38Uz/f5YO/GfadtHO1dAbd9wzjlL5WcvPCduP24taJt6PZx9pOV1q5m2WYA1IN4R16IdwAJ8Q4gA+IdQCOZH8+dPyGGlQ8Z2B7bfu+fnV/th9nXxSGjuyLgoGhZ+bNxXa+HUexPvJsf//z+h5JDHBaGx16Xvla6rAcdz8WPd1omOZ9ZYWiste/34+4ZvX+H8x65Jn51XyUHTuxHiHrj0thvnwvj1YrjUJoQ1RHP/+ijMaT882yNNY+7o/Me+jb/mSkxYXgpdA5qiVUO+W28UbpsiWb+Jj61UmuM2vvSFMG3ebYZALUn3pEX4h1AQrwDyIB4B9BIXotL9xqexK2WVeLIG+aULktp/tNxzvbt5d/xg1pXj2Nu6y2B9CPezbozThjXXn6+LaP3jyv7KDpv3HBUrN3WFaWKU4j2lbeLY39xf7w24EMjpg9Rs2/6fKyze41C1NyHYtL4IeXtU2jfJCbe12cRLXkjpn7mfdHSddsFh0/tbQMVz5W3a4xoHRuH/+Gt0tcq0UzbDIBaE+/IC/EOICHeAWRAvANoIHPvii+u1XWus85pHx/ffnSJZ5Drw5yYevCoJAQOao8Pn/tM6bKepIx3bz8SF+2/VnJox9aVY8+fP1nBKsE340/f2DZGdTun2YIptMdKWx0W59z8TPR51MYlSheiOl6/J7627XIxdLcahKiOV+PWk7eIZcurEofFpiff3vfquW7m3vvV2KArdHZun03PeGDJhySd90h8e/zgzp/bV+LeVMvUmmubAVBb4h15Id4BJMQ7gAyIdwANZPYV8Ylh3ValDd4pLnip4kKymLlx1wlrl4NJ8Xx06554T+myniwaWFrH7htn/+Gu+OtD/4gnnno6nnn6n/HY3++Lu66/MqZ8/fDYcc3k8JeF4ePiwB8/EBWv9+p4I/76w/1i3e7fa9cUlok1d/5S/OKvr/TjcKGLhaj298c2e+4de++92Oz18dhl+w/E+0e0LvgeBlc1RM2PmQ9PjW/uu14s0xU228fE9l/5fTyftsPOfyrO+2iynVvHHhFLWlQ35+4TY722IbHt9x5Pud2abJsBUFPiHXkh3gEkxDuADIh3AA3k1Qtjt8ELfycvmCG7x0Wvly5L7d2479QNo63rvga1xtjP31S6rCeLBpaKptAWK21zbFzxj9ml+0ijI96cflkc/+FVyqv3uk+hbcXY4pAfxJ3/WuJasx4sFqIGrx0TPn1IHHLIovOZgw+IfXceH6sNbxlwiGoZvU18+oQT44TjjorDDtgjtttwTAxtKUbJQrSPWi8+esikuOLB1/oRIhd6/TefijFdqxQLy8XuF77QueUW90Zc+5n3RevIPeMXqWNv820zAGpHvCMvxDuAhHgHkAHxDqCBvHlp7Dlk4e/kBTN45/jpjLQxpsu7cf/EjReJd2sef2fpsp4sGlhax34izv79bXHXtL/G/Q88EPf/5c9x543XxH/+6BtxzH5bx9hlFkacYnBpHbFW7HjU+XH3S/1YJtUxMx78zxNjp9WHlVeYJVOIthW3jmN/9URUdua/dIeAnPevG+JLWywbQwYSolbYIvb97Gfj0MOPiP8Yv2JyjrqhW8TX7uv/AUDL5twTJ41rK2+P9i0mxfTFNnPHvy6KPZZrjVUO/V3lqx/LmnCbAVAz4h15Id4BJMQ7gAyIdwANZM7v49CVWsq/lwe1bxPfeaK/64/ejbu/tE63eNceW03+R+myniwaWPo6593cF++Ic/cfl5yfrBiW3r93XPD3fsaXt5+M308+IDZdfuFhGcvboHMKbavGXj/7R+cz7Eu6EFX01m8OjFU+Vp1DQHa8cEXsP7brnIWFGLbZqfGnWQsv67/58cTZ28ewru3culp8/sa3S5cVzY/HvvPBGNI2Lk7+c6qT3ZU04zYDoFbEO/JCvANIiHcAGRDvABrI/MfizK3ay7+XB7WuEcfd3p8gUzQnrv308uVVTYNaVoiDp3aPPotLF+8WmP9SXHv4Ot0Oe1mIIRt/Ne7pz1E0S+bNmBY/PfpD8b72Rc+HV1h22/jOw32t7EsfouY/fU5M2LM6Iap4KNBXrjs81up67oXBsf7xt8QbpUv7q+PVK+OTK3ZF3ZYYtdclUT465txp8ZX122LIB78Tj/Wr8zbnNgOgNsQ78kK8A0iIdwAZEO8AGsncuP24NcqRY1BhSOx0wb96OMdZBeY/Hedsn4TAwjK7xk//1ds99SPedep45crYv/tqwcKo2PeyV0uX9ldHvDrtB/GJNQd3W4XXGqsecX3p8iVJH6Ji3j/id1Mfir6ulugtRHXqmBm3HL9+DC4FzUL7WnH4da/072dY9k7c+cVkFWVh8Fbx7UcWhsy3fn94rNq6XOxxUT/3k6bdZgDUgnhHXoh3AAnxDiAD4h1AY3nnli/E6q0Lfy8XV1mteNA10a+jCM66Jg5aoSuqFWLExy6MF3utIf2Ld50PFFd/aoVkhV/nc17lyCV8mDdvenxr96PiDxVWn3ef+Fl8fEwSBlvXPqF0yZL0I0Sl1keIKpr1pzhts+Qcfq1jD4grXxhYipr/2Hfig0O7ViO2xprH3BazO16OS/ceFa3v+0xc2++las27zQCoPvGOvBDvABLiHUAGxDuABjPvbzFpi2TFWcuYz8S1b5UuS2H2DUfG2K4I2LpafO76N0uXLEl/4928eOD0jcvxZ0Eo3P+q0mWLmfdQfH3LTeOUv1Z0x53mxaOTt0pWZI38VOnrS1KFEDXvxXjw/uc6t8aSVBCiOs158Nux7Yiu2NYSK+15UTzd39MXFnXMiF9+IjkMasvyn4hLp30/th/aFuudeHfMKV0tvSbeZgBUnXhHXoh3AAnxDiAD4h1Ao+mI139/eKze2nUOsOVit58+F6kaRseM+K/9ViyFnpYYvfcv4rk+76C/8W5u3HbM6uXbDRrUFuNO/nPpssUU490HhsYmpz8QfZ29rsu7d58Qa5ciZOsax5W+uiQDDVEd8eIln4jtTv1LLPlbryxEdT7zePS8CTGqpbRdWkbFhPP+0cv99m32bcfEml1BttAe719jbLQN3iomP1rp1uxJc28zAKpLvCMvxDuAhHgHkAHxDqABdbwWfzx6XHnFWevqh8V1r1Z6CMGOmHnzsTGuvRj/CtG+2qfiyucrSX/9jHdzpsVX1m8r/7dkUOtacdztS6g/C+Jde7SO/XRcU+H38/a1n47RC2JOS6x08DWlry7JwEJUx+vXx+fW2ThO+Utv3/hi22mj05YQojrNfzou2nOl8mq5wvBtYtJ9s0sX9sO8R2LyVkO6nQewECN2+1kM7OiSTb7NAKgq8Y68EO8AEuIdQAbEO4AGNefR+OneY6O9GPAKrbHq3j+LRys4NuKsB34QH1ulNQqDCtG68i5xzgNvly7py5z4/aFJNKks3s2OByZvH8t1rZQa1BLL7/aTeGpJrbAU74rfzyp7nB/T+3pq85+Li/ZcuIKwMHTz+Np9fW2AefHQ1zdLQtTIT8XVlYaojpfi2kPXiiEbnBK9dqjO7fSHw8Yk22m9k+JPvVy/44Ur44CxraXtU4jB446M373c39rWES9dsle3lWlj4uBrZpYu669m32YAVJN4R16IdwAJ8Q4gA+IdQAOb80RcceRmMbIYawrtMXa3SXHDs0sIWB0z48FLvhBbr1gMdy0xYuND49JHU6xY6ng5frJzsqqrz3j3ztPx+9MnxPvaus5RVogh63wmftXb8Tm74l3x+oWWGPWBQ+IHNz0Vs3rqMu88Gb85ZosY0fm9F1pXip1/8FD03ZTmxq1feH95hVdhyB5x8euli3oz/1/xxy9vHaNa2mKDU3o7/GOnjlfiwt2GlrdTYdQBcdWs0mU96ohXrjs81lqwErJ4m87v+4OnxW2v9DNGvX1jfH71hWGrbZ0T4q7+n+yuJAfbDICqEe/IC/EOICHeAWRAvANodLPjialnxN7jRkZroRAtw9eI7Q74UkyecnH8129+E1dc/OP4zlcOiQnrrxDtxctHrBd7nHpV/KPXOLK4+fHK7V+JLZfpiiWDOu9nXOx66PEx8awfxYWXXB6/uvra+O01v4r//Mn34rQj94otV0lizKDCMrHWHt+IG57v49xrpXjXvtyYGLNcexRKqwpHrLV97HfE8fHVSWfGdyZ/PU7+3F4xfsH9d34/ozaPIy97JPpeP9gRsx65MPYrr9ha+Lw2/vT34rKrfxvXXXfdovPbqXHV5RfFD791fOyz6QrRVnwubRvEKX/tLUN1xKt3nBLjl02206CW0bHreX/v4/m9Ebcev0H5MKjF0Dl0rd3jtMumxQspDlG50LyYPmmLzp/14Bj/zYc7/zQQedlmAFSLeEdeiHcACfEOIAPiHcBSYv7r8cgfLojTP7dPfHjTtWLMckOjvbU12ocuFyutsXFst+dhcer518X0V1PknNd/F1/ZbcfYfvM1YrnyCrolT6HQEq3tQ2LZkaNj7Dobx9YTPhFHfPWc+NVfXoq5pbvs1byH4hsf3S8ueakjouPtePHBG+Oys78ah+21XWy8xphYbmh7tLYNiRErjo0NttsnPv+t/4r7X+nj+3n3vjh3/wmxXef3MLKC76G3advglOixQ715fZza23YqDI7R47aOj0zYOybfvYQtMevPcdrmw5LguWAK0TJsTIzb/oy4o6INuFDHiz+PPVbdNX7yfD9XouVwmwFQHeIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAa6x7sNN9yw9FUAAABY1A477FB+/yje0czEO4CEeAeQge7x7v3vf3/pqwAAALCo4tFaut4/inc0M/EOICHeAWTgv//7v8t/IR05cmTpqwAAALCoVVddtfz+sRg3oFmJdwAJ8Q4gA9/85jfLfyFtaWmJf//736VLAAAAIDFkyJDy+8ejjz669FVoPuIdQEK8A8jAzjvvXP4LaXHuuOOO0iUAAACw0PTp0xd577j55puXLoHmI94BJMQ7gDorrrJbZpllFnkDdtJJJ5UuBQAAgIUmT568yHvH1tbW+N///d/SpdBcxDuAhHgHUGe33377Im++irPOOuuULgUAAICFtt566/e8f7zmmmtKl0JzEe8AEuIdQJ0VV9l1f+PVNY8//njpGgAAAOTdjBkzolAovOe946GHHlq6BjQX8Q4gId4B1FlxlV33N15dc84555SuAQAAQN51DxndZ/To0dHR0VG6FjQP8Q4gId4B1FFxdV33N13dZ4cddihdCwAAgLzbd999e3zvWJxp06aVrgXNQ7wDSIh3AHV09tlnL/KGq/sUTzw+c+bM0jUBAADIqzlz5sQyyyzT43vH4px22mmla0LzEO8AEuIdQB19+MMfXuQN1+JzxRVXlK4JAABAXt144409vmfsmo022qh0TWge4h1AQrwDqJPiqrri6rrub7gWnwMPPLB0bQAAAPLq2GOP7fE9Y/d59tlnS9eG5iDeASTEO4A6Ka6q6/5Gq6cZOXJk/Pvf/y7dAgAAgDxabbXVenzP2H2mTJlSujY0B/EOICHeAdRJcVVd9zdaS5o77rijdAsAAADyZvr06T2+V1x8dtlll9ItoDmIdwAJ8Q6gDoqr6Yqr6rq/0VrSnHTSSaVbAQAAkDeTJ0/u8b3i4tPe3h6zZs0q3QqWfuIdQEK8A6iD4mq67m+yept11lmndCsAAADyZptttunxvWJPM3Xq1NKtYOkn3gEkxDuAOiiupuv+Bquvefzxx0u3BAAAIC9mzJgRhUKhx/eJPc2hhx5auiUs/cQ7gIR4B1AHxdV03d9g9TVnn3126ZYAAADkRfd4UcmMHj06Ojo6SreGpZt4B5AQ7wBqrLiKrvubq0pmhx12KN0aAACAvNh33317fI/Y20ybNq10a1i6iXcACfEOoMaKq+i6v7GqZFpbW2PmzJmlewAAAKDZzZkzJ5Zddtke3yP2NqeddlrpHmDpJt4BJMQ7gBorrqLr/saq0rniiitK9wAAAECzu+mmm3p8b9jXbLzxxqV7gKWbeAeQEO8Aaqi4eq64iq77G6tK58ADDyzdCwAAAM3u2GOP7fG9YSXz7LPPlu4Fll7iHUBCvAOooeLque5vqNLMyJEj49///nfpngAAAGhmq622Wo/vDSuZKVOmlO4Fll7iHUBCvAOooeLque5vqNLOHXfcUbonAAAAmtX06dN7fE9Y6eyyyy6le4Kll3gHkBDvAGqkuGquuHqu+xuqtHPSSSeV7g0AAIBmNXny5B7fE1Y67e3tMWvWrNK9wdJJvANIiHcANVJcNdf9zVR/Zp111indGwAAAM1qm2226fE9YZqZOnVq6d5g6STeASTEO4AaKa6a6/5Gqr/z+OOPl+4RAACAZjNjxowoFAo9vh9MM4ceemjpHmHpJN4BJMQ7gBoprprr/kaqv3P22WeX7hEAAIBm0z1YDGRGjx4dHR0dpXuFpY94B5AQ7wBqoLharvubqIHMhz/84dK9AgAA0Gz23XffHt8L9memTZtWuldY+oh3AAnxDqAGiqvlur+BGsi0trbGzJkzS/cMAABAs5gzZ04su+yyPb4X7M+cdtpppXuGpY94B5AQ7wBqYIcddljkDVT3KZ7LYP/99y//ed11140PfOADi1xn8bniiitK9wwAAECzuOmmm3p8D9g16623XmyxxRblPx9wwAEL/oFn9+t0n4033rh0z7D0Ee8AEuIdQJUVV8kt6c3U2muvHXfffXfcd9995a9tuumm8e9//zsmTZoUbW1ti1y/aw488MDSvQMAANAsjj322B7fA7a0tMTJJ58c/+///b/Ycccdy1+/4YYb4sEHH1wQ6bpfv/s8++yzpXuHpYt4B5AQ7wCqrLhKrvsbp+IUV9t98YtfjNmzZy+4zuLxrstDDz3U4yq85ZZbbkHgAwAAoHmsttpq73n/V1xt1/3cdYvHu6K5c+fG6aef3uM/HJ0yZcqC68DSRrwDSIh3AFVWXCXX/Y1T12q77pYU74qWtArv9ttvL10DAACApd306dMXec/XfbVddz3Fuy49rcLbZZddSpfC0kW8A0iIdwBVVAxvI0eOXPAXzcVX23XXW7zrsvgqvJNOOql0CQAAAEu7yZMnl9/vLb7arrve4l3R4qvw2tvbY9asWaVLYekh3gEkxDuAKrrjjjsW/CWzp9V23VUS74q6r8JbZ511Sl8FAABgabfNNtsscbVdd33Fuy7dV+FNnTq19FVYeoh3AAnxDqCKvvzlLy9xtV13lca7Ll2r8B5//PHSVwAAAFhazZgxI9Zff/0lrrbrrtJ4V9S1Cu9zn/tc6Suw9BDvABLiHUAVPf3006X/17u08a6ouArvxRdfLP0JAACApdXLL7/c62q77tLEuy7PPPNM6f/B0kO8A0iIdwAZ6E+8AwAAIH/6E+9gaSTeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gIR4B5AB8Q4AAIBKiHfkhXgHkBDvADIg3gEAAFAJ8Y68EO8AEuIdQAbEOwAAACoh3pEX4h1AQrwDyIB4BwAAQCXEO/JCvANIiHcAGRDvAAAAqIR4R16IdwAJ8Q4gA+IdAAAAlRDvyAvxDiAh3gFkQLwDAACgEuIdeSHeASTEO4AMiHcAAABUQrwjL8Q7gERTxrvbb789br31VmNMRjNt2rTSq5ElEe/SmTlzZo/7mjGmfvPEE0+UXpEAzeOZZ57p8XeeMaZ+88orr5RekSyJeJfO/fff3+O+Zhp/Tj755PK+Xtzve7qOWTpm/vz5pVck0F9NGe/a29vLv+iNMfWftdZaq/RqZEnEu3SK/yij+z5mjKn/HHfccaVXJEDzmDRpUo+/84wx9Zurr7669IpkScS7dLbeeutF9jFjTP1n1qxZpVck0F/inTGm6iPe9U28S0e8Myb7Ee+AZiTeGZP9iHd9E+/SEe+MyX7EOxi4po93G220UWy33XbGmBrPcsstV37diXd9E+/SWTze9bQPGmOqP91fd+Id0IwWj3c9/S40xlR/ur/uxLu+iXfpLB7vetoHjTHVn+6vO/EOBq7p492bb75Z+ipQS48++mj5dSfe9U28S6d7vNt2221LXwVq7Zxzzim/9sQ7oBl1j3ennXZa6atAre25557l15541zfxLp3u8e6uu+4qfRWotdbW1vJrT7yDgRPvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId4BzU68g2yId+mId+mId5AN8Q6qS7wDqkK8S0e8S0e8g2yId0CzE+8gG+JdOuJdOuIdZEO8g+oS74CqEO/SEe/SEe8gG+Id0OzEO8iGeJeOeJeOeAfZEO+gusQ7oCrEu3TEu3TEO8iGeAc0O/EOsiHepSPepSPeQTbEO6gu8Q6oCvEuHfEuHfEOsiHeAc1OvINsiHfpiHfpiHeQDfEOqku8A6pCvEtHvEtHvINsiHdAsxPvIBviXTriXTriHWRDvIPqEu+AqhDv0hHv0hHvIBviHdDsxDvIhniXjniXjngH2RDvoLrEO6AqxLt0xLt0xDvIhngHNDvxDrIh3qUj3qUj3kE2xDuoLvEOqArxLh3xLh3xDrIh3gHNTryDbIh36Yh36Yh3kA3xDqpLvAOqQrxLR7xLR7yDbIh3QLMT7yAb4l064l064h1kQ7yD6hLvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId4BzU68g2yId+mId+mId5AN8Q6qS7wDqkK8S0e8S0e8g2yId0CzE+8gG+JdOuJdOuIdZEO8g+oS74CqEO/SEe/SEe8gG+Id0OzEO8iGeJeOeJeOeAfZEO+gusQ7oCrEu3TEu3TEO8iGeAc0O/EOsiHepSPepSPeQTbEO6gu8Q6oCvEuHfEuHfEOsiHeAc1OvINsiHfpiHfpiHeQDfEOqku8A6pCvEtHvEtHvINsiHdAsxPvIBviXTriXTriHWRDvIPqEu+AqhDv0hHv0hHvIBviHdDsxDvIhniXjniXjngH2RDvoLrEO6AqxLt0xLt0xDvIhngHNDvxDrIh3qUj3qUj3kE2xDuoLvEOqArxLh3xLh3xDrIh3gHNTryDbIh36Yh36Yh3kA3xDqpLvAOqQrxLR7xLR7yDbIh3QLMT7yAb4l064l064h1kQ7yD6hLvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId4BzU68g2yId+mId+mId5AN8Q6qS7wDqkK8S0e8S0e8g2yId0CzE+8gG+JdOuJdOuIdZEO8g+oS74CqEO/SEe/SEe8gG+Id0OzEO8iGeJeOeJeOeAfZEO+gusQ7oCrEu3TEu3TEO8iGeAc0O/EOsiHepSPepSPeQTbEO6gu8Q6oCvEuHfEuHfEOsiHeAc1OvINsiHfpiHfpiHeQDfEOqku8A6pCvEtHvEtHvINsiHdAsxPvIBviXTriXTriHWRDvIPqEu+AqhDv0hHv0hHvIBviHdDsxDvIhniXjniXjngH2RDvoLrEO6AqxLt0xLt0xDvIhngHNDvxDrIh3qUj3qUj3kE2xDuoLvEOqArxLh3xLh3xDrIh3gHNTryDbIh36Yh36Yh3kA3xDqpLvAOqQrxLR7xLR7yDbIh3QLMT7yAb4l064l064h1kQ7yD6hLvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId4BzU68g2yId+mId+mId5AN8Q6qS7wDqkK8S0e8S0e8g2yId0CzE+8gG+JdOuJdOuIdZEO8g+oS74CqEO/SEe/SEe8gG+Id0OzEO8iGeJeOeJeOeAfZEO+gusQ7oCrEu3TEu3TEO8iGeAc0O/EOsiHepSPepSPeQTbEO6gu8Q6oCvEuHfEuHfEOsiHeAc1OvINsiHfpiHfpiHeQDfEOqku8A6pCvEtHvEtHvINsiHdAsxPvIBviXTriXTriHWRDvIPqEu+AqhDv0hHv0hHvIBviHdDsxDvIhniXjniXjngH2RDvoLrEO6AqxLt0xLt0xDvIhngHNDvxDrIh3qUj3qUj3kE2xDuoLvEOqArxLh3xLh3xDrIh3gHNTryDbIh36Yh36Yh3kA3xDqpLvAOqQrxLR7xLR7yDbIh3QLMT7yAb4l064l064h1kQ7yD6hLvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId4BzU68g2yId+mId+mId5AN8Q6qS7wDqkK8S0e8S0e8g2yId0CzE+8gG+JdOuJdOuIdZEO8g+oS74CqEO/SEe/SEe8gG+Id0OzEO8iGeJeOeJeOeAfZEO+gusQ7oCrEu3TEu3TEO8iGeAc0O/EOsiHepSPepSPeQTbEO6gu8Q6oCvEuHfEuHfEOsiHeAc1OvINsiHfpiHfpiHeQDfEOqku8A6pCvEtHvEtHvINsiHdAsxPvIBviXTriXTriHWRDvIPqEu+AqhDv0hHv0hHvIBviHdDsxDvIhniXjniXjngH2RDvoLrEO6AqxLt0xLt0xDvIhngHNDvxDrIh3qUj3qUj3kE2xDuoLvEOqArxLh3xLh3xDrIh3gHNTryDbIh36Yh36Yh3kA3xDqpLvAOqQrxLR7xLR7yDbIh3QLMT7yAb4l064l064h1kQ7yD6hLvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId4BzU68g2yId+mId+mId5AN8Q6qS7wDqkK8S0e8S0e8g2yId0CzE+8gG+JdOuJdOuIdZEO8g+oS74CqEO/SEe/SEe8gG+Id0OzEO8iGeJeOeJeOeAfZEO+gusQ7oCrEu3TEu3TEO8iGeAc0O/EOsiHepSPepSPeQTbEO6gu8Q6oCvEuHfEuHfEOsiHeAc1OvINsiHfpiHfpiHeQDfEOqku8A6pCvEtHvEtHvINsiHdAsxPvIBviXTriXTriHWRDvIPqEu+AqhDv0hHv0hHvIBviHdDsxDvIhniXjniXjngH2RDvoLrEO6AqxLt0xLt0xDvIhngHNDvxDrIh3qUj3qUj3kE2xDuoLvEOqArxLh3xLh3xDrIh3gHNTryDbIh36Yh36Yh3kA3xDqpLvAOqQrxLR7xLR7yDbIh3QLMT7yAb4l064l064h1kQ7yD6hLvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId4BzU68g2yId+mId+mId5AN8Q6qS7wDqkK8S0e8S0e8g2yId0CzE+8gG+JdOuJdOuIdZEO8g+oS74CqEO/SEe/SEe8gG+Id0OzEO8iGeJeOeJeOeAfZEO+gusQ7oCrEu3TEu3TEO8iGeAc0O/EOsiHepSPepSPeQTbEO6gu8Q6oCvEuHfEuHfEOsiHeAc1OvINsiHfpiHfpiHeQDfEOqku8A6pCvEtHvEtHvINsiHdAsxPvIBviXTriXTriHWRDvIPqEu+AqhDv0hHv0hHvIBviHdDsxDvIhniXjniXjngH2RDvoLrEO6AqxLt0xLt0xDvIhngHNDvxDrIh3qUj3qUj3kE2xDuoLvEOqArxLh3xLh3xDrIh3gHNTryDbIh36Yh36Yh3kA3xDqpLvAOqQrxLR7xLR7yDbIh3QLMT7yAb4l064l064h1kQ7yD6hLvgKoQ79IR79IR7yAb4h3Q7MQ7yIZ4l454l454B9kQ76C6xDugKsS7dMS7dMQ7yIZ4BzQ78Q6yId6lI96lI95BNsQ7qC7xDqgK8S4d8S4d8Q6yId41p2effTauvfZab6ihk3gH2WjEeHf33XcvmPnz55e+0jgaMd4V36P9+c9/bsjtJd5BNvIa76ZNmxZ33HFHzJs3r/QVqA7xDqgK8S4d8S4d8Q6yId41r1133TUGDx684H9//OMfx3PPPVe6BPJFvINsNGK8+5//+Z8YM2ZMLL/88vHpT386rrrqqob5TKkR491LL70Uo0aNihVXXDE++9nPxjXXXBP/+7//W7o0W+IdZCOv8a7434pVV101Ro4cGZ/61KfiyiuvjJkzZ5Yuhf4T74CqEO/SEe/SEe8gG+Jd83rhhRdiueWWK/98i7PJJpvE6aefHn/5y1+io6OjdE1obuIdZKNRD5tZXJne9byK09bWtiCcnXfeefF//+//LV2r/hr1sJm//OUvF9lexc/jdtlllzj//PPjmWeeKV2r/sQ7yEaeD5tZ/N3c9b0Xp7gtPvKRjyx4T/3EE0+UrgXpiHdAVYh36Yh36Yh3kA3xrrldfPHF5Z/v4rPSSivFYYcd5vCaND3xDrLRyOe8O/DAA8vPbfFZf/3146tf/WrdD6/ZyOe822uvvRbZRt1no402WvC7tXhIuXr+wyDxDrKR93PeFd8/dX3/i8+6664bJ598ctx5550Or0nFxDugKsS7dMS7dMQ7yIZ41/yKh83s+hkvaYqH19xtt90cXpOmJN5BNho53nUdPrPr+S1p6nl4zUaOd12Hz+y+bXqa0aNH1+3wmuIdZCPv8a7r8Jld22BJU/yd6fCaVEK8A6pCvEtHvEtHvINsiHfNr6fDZ/Y1Dq9JMxHvIBuNHO+KFj98Zl9T68NrNnK8K1r88Jl9Ta0PryneQTbyHu+KFj98Zl/j8Jr0RrwDqkK8S0e8S0e8g2yId/lw0UUXlX/OacfhNVnaiXeQjUaPd0W9HT6zr6n24TUbPd4Vdf+Zpp1qH15TvINsiHcLHXrooeXtkHYcXpPuxDugKsS7dMS7dMQ7yIZ4lx+VHD6zr+k6vOYFF1wQzz//fOmeobGJd5CNpSHeVXr4zL6mGofXXBriXaWHz+xrqnF4TfEOsiHeLVTp4TP7GofXRLwDqkK8S0e8S0e8g2yId/nRn8Nn9jUOr8nSQLyDbCwN8a4o7eEz+5ri4TUnTJiQ+vCaS0O8K0p7+My+puvwmlOmTIlnn3229Ch9E+8gG+JdIu3hM/uarsNrnnvuufHkk0+WHoVmJ94BVSHepSPepSPeQTbEu3wZyOEz+5ri4TUPP/zwBR+Cvv3226VHhOyJd5CNpSXeFQ3k8Jl9TdfhNe+5555eD6+5tMS7ooEcPrOvqfTwmuIdZEO8W9RADp/Z16y33noOr5kD4h1QFeJdOuJdOuIdZEO8y59qHD6zr3F4TRqJeAfZWJriXbUOn9nXrLDCCks8vObSFO+qdfjMvqZ4eM3iB+NTp059TyQQ7yAb4t2iqnX4zL6m+Dv3oIMOil/96lfxxhtvlB6dZiDeAVXRPd4Vp3g4ELPk6f4XGtur7+m+rcQ7qJ/u8a5QKPT4+jTNNYv/96leU9y/io9dnJ6elzG1mu77oXgH9dM93rW0tPT4+mykKT7H7r8v6jHF/zYWH7f438bi/+/6uu3V83TfXt2/Lt5B/XR//fl7/cLJ4vdhcbp+HxafQ/EfNLB0Eu+Aqlg83hlTqxHvoH66xztjjGn2Ee+gfmp5aEVjuo94B/WzeDw3jTHjxo0r/YRY2oh3QFWId6ZeI95B/Yh3xpg8jXgH9SPemXqNeAf1I9415my++ealnxBLG/EOqIru8a54rP633nrLmKrNb3/72/L+Jd5B/XSPd0ceeWSPr0/TXLPXXnuVf+a1nOIbyIkTJ8bdd9+94O/rPT0XY+oxJ554Ynm/FO+gfrrHu8suu6zH12ejzIsvvhhjx44tP99aTfGcsDvttFOce+658cj/3959QEdVLWDfZ1pCqKEI0juCSA0iApaIgoCAeOGCiiIidixXEYQrKCAqWK8FQRALShUULHxIUxFBXCBYwCUo8NEXoC+QN2Ql8z3fmWRawmQyM5mZEyf/31p7uWQy7cw5e5+9n7P32bEj4Gf5J5Q//vgj9350gb5jNEtycnLuPXRffPFF/fLLL/k+g2uWiefvCO+A+PEP7/7f//f/zXdclsbiugdow4YNvdskVsWVhbjujfrss8/qxx9/POdznD592v0L4Z+G8A5AVPiHd40aNXL/KxAdq1ev9u5fhHdA/PiHd/fee6/7X5Go5s+f7/29o11SUlJyg8GZM2fmdmKBkmLChAne/ZTwDogf//Bu4cKF7n8tmVwXMHk+a7RLjRo1NHz4cC1dujRhBleHDBkS8LtGo5x//vm644479MknnygjI8P9judy3d/J8xzCOyB+/MO7U6dOuf+19Lr//vu92yPaxXWRxK233qrFixezrRMY4R2AqCC8QywR3gHmILwrPY4cOaJq1ap5f+9olNq1a+vOO+/UihUr9H//7/91vxNQshDeAeb4p4R3K1eu9H7OaJU2bdpo3Lhx+u677+R0Ot3vlBj8V0yJVmnfvn1uXf3999/r//v//j/3OwVHeAeYg/DOx1X3WCwW7/aIRmnVqlXu6iUbNmxIuPYDgRHeAYgKwjvEEuEdYA7Cu9JjwIAB3t860uLqnKalpWnixIn64YcfQh5gA8xEeAeY458Q3v2f//N/VK9ePe/njLS4lnfs2bOnXnvtNe3du9f96onn+PHjuTMJA22DcErZsmXVu3dvzZgxI3fZvUgQ3gHmILzLc+bMGTVu3Ni7LSItruWUr776ar3yyiu5SxKj9CG8AxAVhHeIJcI7wByEd6VDcZbLZDlM/NMR3gHm+CeEd8VZLtOzHKZrJlppuddQcZbLDHU5zFAR3gHmILzLU5zlMv2Xw3RdRILSjfAOQFQQ3iGWCO8AcxDeJb6jR4+GvVwmy2EikRDeAeYo6eFdJMtlJvJymEWJZLnMSJbDDBXhHWAOwjtp/fr1YS+XyXKYKAzhHYCoILxDLBHeAeYgvEt8N9xwg/c3LqywHCYSGeEdYI6SHN6FulxmaVkOsyiu5TJr1qwZcBv5l2gshxkqwjvAHKU9vAt1uUyWw0SoCO8ARAXhHWKJ8A4wB+FdYgu2XCbLYaK0ILwDzFGSw7tgy2WWxuUwixJsucxoL4cZKsI7wBylPbwLtlwmy2EiEoR3AKKC8A6xRHgHmIPwLnEFWi7Tsxzm8uXLWQ4TpQbhHWCOkhreBVous3Xr1qV2OcyiBFou07Uc5hNPPBGT5TBDRXgHmKM0h3eBlst0LYfpOr9kOUxEivAOQFQQ3iGWCO8AcxDeJS7XcpmuzmWHDh1YDhOlGuEdYI6SGN55lst0LWfGcphF8yyXGc/lMENFeAeYo7SGd57lMl2ZhGc5zD179rgfBSJHeAcgKgjvEEuEd4A5CO8Sk6sj6VoO88CBA+5/AUovwjvAHCUxvFu1ahXLYYbhs88+08cffxzX5TBDRXgHmKO0hneuembRokUsh4moI7wDEBWEd4glwjvAHIR3ABId4R1gjpJ8zzv88xHeAeYo7fe8A6KN8A5AVBDeIZYI7wBzEN4BSHSEd4A5CO8QS4R3gDkI74DoIrwDEBWEd4glwjvAHIR3ABId4R1gDsI7xBLhHWAOwjsgugjvAEQF4R1iifAOMAfhHYBER3gHmIPwDrFEeAeYg/AOiC7COwBRQXiHWCK8A8xBeAcg0RHeAeYgvEMsEd4B5iC8A6KL8A5AVBDeIZYI7wBzEN4BSHSEd4A5CO8QS4R3gDkI74DoIrwDEBWEd4glwjvAHIR3ABId4R1gDsI7xBLhHWAOwjsgugjvAEQF4R1iifAOMAfhHYBER3gHmIPwDrFEeAeYg/AOiC7COwBRQXiHWCK8A8xBeAcg0RHeAeYgvEMsEd4B5iC8A6KL8A5AVBDeIZYI7wBzEN4BSHSEd4A5CO8QS4R3gDkI74DoIrwDEBWEd4glwjvAHIR3ABId4R1gDsI7xBLhHWAOwjsgugjvAEQF4R1iifAOMAfhHYBER3gHmIPwLv6efPJJWSyW3G0+ZMgQ978mJsI7wByEd0B0Ed4BiArCO8QS4R1gDsI7AImO8A4wB+FdfJ08eVI1a9b0hneuksgI7wBzEN4B0UV4ByAqCO8QS4R3gDkI7wAkOsI7wByEd/F17Nix3G3tCe/Kly/vfiQxEd4B5iC8A6KL8A5AVBDeIZYI7wBzEN4BSHSEd4A5CO/i6/3338/d1p7w7vXXX3c/kpgI7wBzEN4B0UV4ByAqCO8QS4R3gDkI7wAkOsI7wByEd/H173//O3dbu8K7SpUq6fPPP3c/kpgI7wBzEN4B0UV4ByAqSmt4d2rjLI0fMyZ3sCd/eVzPfrxHOe6/i1TWjg/15NhArz9WT7y3Tdnuv0t0hHeAOQjvACQ6wjvAHIR38eUf3rVq1cr9r4mL8A4wR6kM705t1KzxgcbtxujxZz/WnuIPDOrDJ8cGfP2xT7ynbaVlYLCUIrwDEBWlNbzLPvqrNq79RHMn36IOVayyuLeBq9ga3aMvz7j/MBLO41owuIasfq9pKddM/cfN1JIv1ujrn4/K6f7TREd4B5iD8A5AoiO8A8xBeBc/e/bsUYsWLXK3tSu8c9V7iY7wDjBHqQzvso/q141r9cncybqlQxVZLXnfP7fYGume4g0M6viCwaph9XtNSzk16z9OM5d8oTVf/6yjpWVgsJQivAMQFSyb6dTReQNV3b9Btaaq7+yDEQdsObum67JyefckyCsOXfT498pyP16aEN4B5iC8A5DoCO8AcxDexc/69eu997pz/df1/4mO8A4wR2lfNtN5dJ4GVrd6t0GZMlal9p2tg5EPDGr6ZeXyTRRwXPS4vi+NA4OlFOEdgKggvDMa6YP/U3qSr0EtU8aipPYTtDWiKeyZ+urB5rJ7X8sollTduDjD/XjpQngHmIPwDkCiI7wDzEF4Fz/+4d0111xTKgbUCe8Ac5T6e945D+p/6UnebeAqlqT2mhDZwKAyv3pQze2+13KNM6beuFilc2SwdCK8AxAVhHeGjHkakGJVuerVVcEzA89WR7d9En495LlaJ6ladVX2e62RX5x1/0XpQngHmIPwDkCiI7wDzEF4Fz933HGHN7xbvny5+18TG+EdYI5SH94pQ/MGpMharrqqV/DMwLOpzm2fKOyRQedRzRtYXdakaqpe2e+1Rn6h0jkyWDoR3gGICsI7Q8YHuqG8TTWHPKYRDT0nLBZV7P6q/gjrBrU5+vXZLkqx1dANo0f4rrKx1dWdKwnvCO+A+CG8A5DoCO8AcyR0eHdqo2aNH5NbpxQsjz/7sfaE1TcMIGuHPnxybMDXH/vEe9pWYIJHq1atvOHdsWPH3P+a2AjvAHMQ3mXogxvKy1ZziB4b0VA297awVOyuV8MbGFTOr8+qS4pNNW4YrRHN7e7talPdO1cS3pUihHcAooLwzuAJ74Yv0w9TOinZfZNai6OlRm8Mo2nNWKv7m9hlb/GI1q/9D+GdgfAOMAfhHYBER3gHmCOhw7vso/p141p9MneybulQRVZ3vzC32Brpni/PuP8wEk4dXzBYNfzvtW4pp2b9x2nmki+05uufdbTAvZU84d2DDz4opzPSGy/9sxDeAeYgvPOEd8O17Icp6pScd+FEGYtDLUdvDCN0y9Da+5vIbm+hR9av1X8I70otwjsAUUF4Z/CGd8uVceQ9DajmmdZuVY3BC3QspH6SU4ffHaCqtgpKf3m3MjcQ3rkQ3gHmILwDkOgI7wBzlJZlMz23Q/B8V1ffMLXvbB2MNEPL2aXpl5WTxft6ZeS46HF9n+V+vIDPP/9clSpVkt1u14svvuj+18RHeAeYg/DOF94tzzii9wZUk9W9Paw1BmtBaAODch5+VwOq2lQh/WXtztxAeFeKEd4BiArCO4NfeJdpNNjrHmgqu3ubWFK66rmdIUyRz/5ZUzoly1ZrqJaclLII73IR3gHmILwDkOgI7wBzlJp73jkP6n/pSd7v6iqWpPaasLXA2pYhyvzqQV//MLdYlHrjYqP3Gdjrr7+e+3c1atRw/0vpQHgHmIPwzi+8yzT+b90Dauqpsy0p6vrcThU9Mpitn12redlqaWjewCDhXSlGeAcgKgjvDPnCO9dFkdPULcU9Rb6MXU3uW1Nop8rjzKq71cjm0EVjN8t18SThXR7CO8AchHcAEh3hHWCOUhPeGT3AeQNSZC1XXdUreGbg2VTntk8U9miV86jmDawua1I1Va/s91ojvyh0INcT3vXu3dv9L6UD4R1gDsK7/OGda7b0tG4p3tnS9ib3aU3RA4O6u5FNjovGanPewCDhXSlGeAcgKgjvDAXCOzmPa8HgGr4p8lX66e1DQabIOw9pTr9U2Spdo9f/zPs7wrs8hHeAOQjvACQ6wjvAHKUpvMsbyB2ix0Y0lM39nS0Vu+vVP0JYmcVPzq/PqkuKTTVuGK0RIQ7kNm3aVBUqVNCqVavc/1I6EN4B5iC8KxDeFbxPqbWK+r19yPjXwjh1aE4/pdoq6ZrX/8z7O8K7Uo3wDkBUEN4ZCoZ3hrMbHlELu+cGtUlKm/ijClsgJXv7U0pLtqmO8fy/3f9GeJeH8A4wB+EdgERHeAeYo/SFd8O17Icp6pTs6Rs61HL0xjAGYDO09v4msttb6JH1a0MeyHX9zZVXXun+v9KD8A4wB+FdwfDOcHaDHmlhd8++sygpbaJ+LHxgUE+lJctWx3i+b2CQ8K4UI7wDEBWEd4YA4Z1y9ujl9AreKfK2uiO0wtMA53Nan4+sL5ujnZ7wu/8B4V0ewjvAHIR3ABId4R1gjtIY3i3POKL3BlTzrcxSY7AWHAuyMosf5+F3NaCqTRXSX9buTAZyi0J4B5iD8C5AeKcc7Xk5XRUsedvFNbY3IvDAoE5/PlL1bQ61e2Kr78J/wrtSjfAOQFQQ3hkChXeGkx/doto2dyNt8Zv67sd5YJZ6p9qU2nuWDvg9SHiXh/AOMAfhHYBER3gHmKNUhndGJzFj3QNq6unfWVLU9bmdKnrxzGz9PKWTkm21NHTJSQZyQ0B4B5iD8C5QeGc4+ZFuqe3ZNhZVuuZ1ue+W4+M8oFm9U2VL7a1Z+QcGqfNLMcI7AFFBeGcoJLxT1mY93trhnSLvaDVG37luOuuVrW0T2stha6A7vzjt/rc8hHd5CO8AcxDeAUh0hHeAOUpreKecXZrWLcW7Mou9yX1ak5H3l4U6s0p3N7LJcdFYbXb1IxnILRLhHWAOwrtCwjtlafPjreVwz76zOFppTP6BQWVvm6D2Dpsa3PmF8o0MUueXaoR3AKKC8M5QWHgnp/a+0UOVPFPkrefrxkXH3Y8ZTq3QiLo2JXecpB0F1r0mvMtDeAeYg/AOQKIjvAPMUWrDO6NveHzBYNWw5n33MtYq6vf2oXNWZvFx6tCcfkq1+a3gwkBukQjvAHMQ3hUW3hm1+d431KOS+76nZaw6/8ZF8o0MntKKEXVlS+6oSecODFLnl2KEdwCigvDOUGh4Z/h7hW6v65siX+6y6dqVuz6KU/tm9FQlWxX1n3tup43wLg/hHWAOwjsAiY7wDjBH6Q3vDGc36JEWdu/KLElpE/VjgbFar+zteiotWbY6xvM9t0hiILdIhHeAOQjvCg/vpL+14va6srm3j6XcZZqeNzAo574Z6lnJpir95+rQuQOD1PmlGOEdgKggvDMEC+9yl8bsoCTP7Dt7U41al2E0wls0vo1D9saBl0shvMtDeAeYg/AOQKIjvAPMUarDO+Voz8vpquDpGxr9vBErPMlcfqc/H6n6NofaPbHV6FG6MZBbJMI7wByEd8HCu7ylMTskeWbf2dV01DrjGVnaMr6NHPbGui/wwCB1filGeAcgKgjvDEHDO8l5YLauS7W6t5NVVa+fq11Lh6mOLUWXPvNrwBuVE97lIbwDzEF4ByDREd4B5ijd4Z3h5Ee6pbZvZZZK17yuPwvOtnAe0KzeqbKl9tasA34PMpBbJMI7wByEd8HDO1e9Pvu6VFnd28ha9XrN3bVUw+rYlHLpM/o18MAgdX4pRngHICoI7wxFhHfSaa26q6FvinxSc7W70GjUqw/UvKMFe2p5CO/yEN4B5iC8A5DoCO8Ac5T68E5Z2vx4azncs+8sjlYa812W+7E8rhka7R02NbjzC6Mn6YeB3CIR3gHmILwrIrwznF51lxra8rZRGUuSmre7UOVt1TVw3tHA9z+lzi/VCO8ARAXhnaHI8M7ogP00RZ2SPVPkXcWu5g99VejfE97lIbwDzEF4ByDREd4B5iC8k5x731CPSp6+oVXn37hIx92PSae0YkRd2ZI7atKOAjfEYyC3SIR3gDkI74oO75T9k6Z0Snbf9zSv2Js/pK8KHxikzi/FCO8ARAXhneHUXPVNtqrKTR8VGsbJeUTvDajmnSJvKXe5nv8t0Lz4PGfX3a9GnityrDU1vNDWP7ER3gHmILwDkOgI7wBzEN65/K0Vt9f1rcxS7jJN35XXN3Tum6GelWyq0n+uDhWcisFAbpEI7wBzEN6d0ty+ybJWuUkfFT4wqCPvDVA1a952KmMpp8uf/y3grXRynV2n+xt5tqs16IQBJB7COwBRQXgn5ex8Wpc4yijpqld1MPAqmLky1o1S09zZdEaje+NCv6srz3Xqw4Gq7LmRuaWses486n6kdCG8A8xBeAcg0RHeAeYgvMvjWhqzQ5Jn9p1dTUetM56RpS3j28hhb6z71mS4/9IP4V2RCO8Ac5T68C5np56+xKEySVfp1eADgxrVNK8et9a8UQuDDwxqYGVPO2FR2Z4zVTpHBksnwjsAUVHqw7vsQ/r8/tZKtpSRpWIXTfwuSN2Ts0vTuqXI4mip0RuDdLNO/aBp3X2z9FxhX+XLJmlzKazWCO8AcxDeAUh0hHeAOQjv3JwHNPu6VG+fz1r1es3dtVTD6tiUcukz+jXQVAzCuyIR3gHmKN3hXbYOfX6/WrtulWOpqC4Tv1Phw3c52jWtm1IsDrUcvTFIHX5KP0zr7pulZxRr5cs0qTQODJZShHcAoqK0hnfHlz2iHld2Udt6FWXzzJAzisWRqsYduim95xNadU4r7NSx+YPV+Or/6Y9zOmNZ2jB1gNIvS1Ozakn51sDOKxY5qjRRWrd09ZqwutR00gjvAHMQ3gFIdIR3gDkI73xOr7pLDT23SrAkqXm7C1XeVl0D5x01eo4BEN4VifAOMEepDO+OL9MjPa5Ul7b1VNHmmSHnqs8dSm3cQd3Se+qJcwcG5Tw2X4MbX63/nTswaFTzUzUg/TKlNaumJL+xRk+xOKqoSVo3pfeaoNU0AAmN8A5AVLBsJmKJ8A4wB+EdgERHeAeYg/DOT/ZPmtIpOd+Fm/bmD+mrwv6e8K5IhHeAObjnHRBdhHcAooLwDrFEeAeYg/AOQKIjvAPMUXrCu1Oa2zdZ1io36aPCwjg5deS9Ab5l0SzldPnzvynQipm5zq7T/Y08A+RW1Ry+XIW+dClFeAeYg/AOiC7COwBRQXiHWCK8A8xBeAcg0RHeAeYoNeFdzk49fYlDZZKu0qsHAy6CmSdjnUY1zZtNZ615oxYed/97IKc+1MDKnqXZLCrbc6aOuh9CHsI7wByEd0B0Ed4BiArCO8QS4R1gDsI7AImO8A4wR+kI77J16PP71TrZojKWiuoy8TsVPkKVo13TuinF4lDL0RuDLIN5Sj9M6+6bpWcUa+XLNGkzY1/+CO8AcxDeAdFFeAcgKgjvEEuEd4A5CO8AJDrCO8AcCR3eHV+mR3pcqS5t66mizTNDzigWh1Ibd1C39J56YtW58Zzz2HwNbny1/vfHuQtmZm2YqgHplymtWTUlWdyv51csjipqktZN6b0maDU3wCO8A0xCeAdEF+EdgKggvEMsEd4B5iC8A5DoCO8Ac5See97BDIR3gDkI74DoIrwDEBWEd4glwjvAHIR3ABId4R1gDsI7xBLhHWAOwjsgugjvAEQF4R1iifAOMAfhHYBER3gHmIPwDrFEeAeYg/AOiC7COwBRQXiHWCK8A8xBeAcg0RHeAeYgvEMsEd4B5iC8A6KL8A5AVBDeIZYI7wBzEN4BSHSEd4A5CO8QS4R3gDkI74DoIrwDEBWEd4glwjvAHIR3ABId4R1gDsI7xBLhHWAOwjsgugjvAEQF4R1iifAOMAfhHYBER3gHmIPwDrFEeAeYg/AOiC7COwBRQXiHWCK8A8xBeAcg0RHeAeYgvEMsEd4B5iC8A6KL8A5AVBDeIZYI7wBzEN4BSHSEd4A5CO8QS4R3gDkI74DoIrwDEBWEd4glwjvAHIR3ABId4R1gDsI7xBLhHWAOwjsgugjvAEQF4R1iifAOMAfhHYBER3gHmIPwDrFEeAeYg/AOiC7COwBRQXiHWCK8A8xBeAcg0RHeAeYgvEMsEd4B5iC8A6KL8A5AVBDeIZYI7wBzEN4BSHSEd4A5CO8QS4R3gDkI74DoIrwDEBWEd4glwjvAHIR3ABId4R1gDsI7xBLhHWAOwjsgugjvAEQF4R1iifAOMAfhHYBER3gHmIPwDrFEeAeYg/AOiC7COwBRQXiHWCK8A8xBeAcg0RHeAeY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X94XvKl4Za+5TE+8+Y1G57q9qX6Gfw6mjM3ooyfi7sg2v1Zi3v9QPu/bq0FHfPnvok5FqYHO/nq2h7lx+yPvYsaOHtW/XZn06a4yuyx3ws6v5I98q/8eMx3v4OA/N1LWuY8v9/VNvXFx0m3vmNy17rJuqWR3qOPkX7/FVmJJzXAKAieLYX4lH3e6V8buWjr1a9VyD4xa7qrT+l8bNXq1dJ/OfpDhP79OmhVN1e5faSrJVVJ0mdVTRZpGj2/QiZt/Ho0+UoTX3NZHd/du4LgDq/uq+os9nTqzTI+38L1CxqfbtK4JeFBVI1vaJSnO43jdZLe/9rMCsi4LisT3OauOjLXzbw95EIxb/rmO+nVXHd67RW6OvVSNvoGCRrWpnjVl5pMjtBsRaxu9LNfbqerl9MYu9ilr/a5xmu8a+8g/U6PS+TVo49XZ1qZ0kW8U6alKnomwWh7pN3xNaHRivMbZ4HpOJ2lYZrxyL8Tvn0RnqkWTsZ2Ub6toxb+vLH3Zp76Gjvr7ZoU80soHN/R1tanjnch3yPHbsqA7v26XNn87SmOua5dbr9uaPKMhwR5h9V7esP7Xk7jaq4Pm9XPtGrX56K7zBBKPL/awuTbLIWnWgPih6MMHHeVLfz7hN7XMvSDba/RoXa+iT72rdbwW2vfF/J3//Wh9MGqqLz08ytnmq6jY4T2XtjTVqXf75eADyEN7FTbZ+eTE9d6aZJaml7v38aKGN6+kdczT0AncHIZzw7vRWvfavvCtoXDMurnr6WwU/V8jWvk9GqUNF1+CqVZXa3aUFv4dYWTqP6I1rktyNgtH4NHtY34QwgJpfltY/YHSgbI10/9pQ3veM5g+q5O042VuN1eZA7+k8rJUPd/BrtKyq0v1l/RJem5X7OqvGdTVOGFydVJvOu2ysPt1X1Jd06uiG59Tbc6WMo7XGbQn+xlkb/qPmnoY5xI6Zi3Pv6+qReqEe+y7sDQ9EV85uTeuanBs0/RZwdz+rtfc38oV3jUcp8HmZU4c/uUPNk+vprlVB6oQz8zWokqcDYFersZsDhhbOwyv1cAe/MMxaRd1f/qXAyWMxZKzV/U3cnR7refr3/HDObgPL2TtPg+p6TvyNYqmgjuM3KJzVk8+uvFN1bQ51evrXIjs62b+8qHTXTD1Lklre+3m+mWv5nN6hOUMvcHfeQgvvXBes/C/d1064iiWpvSZsjewXyPzqQV9dmVtC7Py5nHxLvZI9z7OrxaMbCw26jF9Bu6d1VbKrsxN4h9bZtferkTdYK7yj4Tz8ie5onqx6d60qsDRIPN7DT9YG/ae5p4MexnZz7tXrPVJ14WPfBdlebiXluAQAU8WxvxKPut3gPLxK47pWy1s1xnaeLhv7qYruEh3Vhud6e2e6OVqPUxFdorj0iU6+1UvJudvLKPYWenRjKFtA+uvjYarjaZON36r6zR+FHd7l7Jmursb2cFzwsL4K4avFY3ucmT9IlTz7oL2VxgbeWXV45cPqUMHTxpeRtUp3vRx25xqIFmOfXDVOXau5VgmxyHbeZRr76b4i6zPn0Q16rncd9wpSDrUet6Xo8894jrEZ4ndMJl5b5fqssRq/y9k9TV2Ta6nfW78F3mfOrtX9jXzhXeNR6wL3y4zP+MkdzZVc7y4FG+4Ir+/qJ2ev5g2q6x13cW3vCh3Ha0N4gwm6s65Njk5P69dQU9Os3/XB7a3y9hOLQ/V6P6Ovjhb95JzDazW5h/uYNNq5ISG2c0BpQ3gXLyeX6OaaeQ14tUEfyn9RjkCyf5+p62oYfx9qeHf2J73aq1beNGlLito99pVCWy44R3vf/Zdq53ZGLEpqcovmB1233yND8wdW9Db2jg5PBl4bOqhsbf1vWzkcbfWE70ZFQWTqsxG18qZwG6XQEwyXs1v033b+S5PU0OD5oU0Zz3NS68emuU9SLCqfNlZfhbGqQub253VVFeP3s9XX3V8GP1nL/nGC2ruuwnR9zjA6Zq5O8ex+LYt8fSDmsn/UhI6dNLHQSiDU8M7gPKiZvRvolqVBVmjP/EwjarnqU9frFR4SuJzd8l+1S/Lr2NQYrPkhLUVZFKeOfThI1b1LOBr1RPor+iPUE9zCOPfr5YKBl6Ohhi4MfbmQrI2P6gK7a4mRA0U856SW3Fwzt061VhukD4tumDTzuhrG34cY3hntxLwBKbKWq67qFTy/l011bvtEf7n/ImRGfTdvYHVZk6qpumuWoOe1Rn5ReGDlL+ND/cvbwXWo46SfgwSb2fpxQkd1mhjo/jx5Qg3WXPvJwZm91eCWpUYL5i8e7+HHdYy2d7i/fxidZuO1j87up5Z3f1n0di4RxyUAmC2O/ZV41O0n12tsmvuCC0t5pY39KsDyl4XJ1Pbnr1IV41zJVv9uFdVliUefKOPDf/kGoR0dNennEE/csrZofBvfMma2eiP1RVhjjEZb/WZPVbCmqs+s0M7p4rE9Mj8boVqec9lCgwKXs9ry33ZK8my7MlbVGDxfNN0ww8n1Y5XmPq+3lE/T2PAGavT8VVWMOtqm+kXVgXEfY4vnMZlgbVWMx+9c9XHHThMLH/MMNbwzOA/OVO8GtyjYcEd4fVd/Tu1/OV1Jnt/KVSwONRy6UCHfbSdrox69wK6k9Fd0IJTn5OzV/KFN3PuiTef3eV0h37rfJWOrnrvSdUwm6Zo3mNUNBEJ4FyeZK4br/NxG2KEOQQbrfHL06zOXqmxyKOHd31rzcCuVdTdUjhYPaX04lwIale3M3q7K0vV8q1KvnK4dhTXcXhlaNDjV24A70iYp/OWJXYOX7eVwdNDE7aE8+ay+GFnHGwAEPcEwtp9rVoP/yUxV4yThtPvR4IzO1fwhquO+Z4Al5WI9ubXo04X8cvTHjF6qYiv66pHsHU/mLaHi+pzhdMyM9/hz0RS9uaXIHwuIrawNGt3zocIDOePYDTm8M/brnVPTNej9IJXY2S80so7n5Dh4SJA3K9C/s1HVOMZCqwmCyvldL1yRfwlHi6ON/vtD2BVhfu7wzlK2nO++JUaxVrlS07aFdhactekxtbQn6apXDwY/+c1coeHu5Y8dHYJ0Rvzk/PqMLi2bHHJ498EN5WWrOUSPjWjo/f0tFbvr1TBTzpxfn1WXFJtq3DBaI7xXbtpU986VIXTmDBkLNKiirwPUaUqwWYlZ2jC6px4qfCcNI1gzPvvOqUof9H6BK/Tj8R5+snfoybRIOs3Ga/+5SFPe3FL4MeZREo5LADBdvPorhljX7c6Dmj/E+C7uPmbKxU8q/C7RH5rRq4psqUNUVBcnHn2ijAWDVNGzvR2dNCXkaQVO7X29h++51vNyB69DlrNHL12ZIludEVoR4gyIeGyPs1+M9M0oDBoUGK/qmnnif+FN1RtF0414cx6cryHG+WbuOaQlRRc/uTW0voCfnD9mqFcVm1KHBKszzRhji+cxmUBtVRzG77I2jFbPhwoP5MIJ74yOm6amD1Kw4Y7w+q7+3OGdpazKee8baBRrFV05bVvhF3r6y9qkx1ralXTVqyHc7iJTW6d2y701lOt9bPWGakkE90PI+e0VXVXZobSnfgphrBwofQjv4uTYmz3cS3TkzbwL5VTfeeA1XZ16dZHhXea3j+kiT6NtqaDur/4ZwqBqfme+vFsNPScJ1lR1/9/vRTQOJT28M/76sxGq7blqyfUZu07T7hBaPOfRj3RrPV/DW2fYsjCuMPVz9juNvaiCrp0VfDpL5B0zoIRw/q0/du4PchIeTnhnvNyxXdp5JMjBGk5IYLz3ZyNqe68qdJ38dp22O8ST38Kd/e4xtXTY1ejfw5XuXSrQpvojvwh7GaV83OGdvcV9evXxTqrkrcMsSm5xjz4LfoOUXCGHd8feVA/3chy5M+9Ca5j02tWpujqs8G64lv0wRZ1ybyJvvJ/FoZajNxbeoTlHhrH/NJHd3kKPrF/rt+xKrMI7p/7+Y6f2B6mKwwnWjB1au3YeKfB+8XgPP8XoNIesBByXAGC++PRXcsW0bnfq6Ee3qp63HaqjYcsi6hEZ50xjdVGFa1VElygufaLIwzvDX8t0a21PO2dR+StfDPm3yt42Qe2M88aWo0Nc/s0Qj+0RTlBg7KwaUdszw94ojq6aFvLOCkSB86g+urWer09ZZ5giq5bO6ruxF6nCtbMKXRHLnDG2eB6TidJWuXaL2I/fOf/+QzuDd9xCD++MPenYrp0KNtxR7PDO6Dff9+rj6lTJt39Yklvons+OFb0fhxHeZf04RZ099zM09vFrZ/wZYX8uQ1892EJN718bZLsBpRfhXZycnj/Qu3a1Jam5bv9of9GVWs7PmtT12uDhnfOg5vRN9Q6AWSr00sxQ75Hn7+x6jfLcu8kotkb36MugI9D/gPDO/8THKElXvKS9RW6abG2d0MF3VVFRA6ZB5Wj3C9111XPBT9Ii6ZhlnjihMxH8zIA5wgvvihRmSOBfb7ju13bFS3vD7nzl95eW3VpbtqSOmrT9mHfpSdfrW6sO0LsRXG3m5Q3vRuu7zD/07sC6snuvcrSp5nVvalcR1WXI4d3p+RroCR4tSWp++0faX3TDpJ8nddW1YYZ3yzOO6L0B1XzbqcZgLQghiHRxHn5XA6raVCH9Ze3O9L9nQqzCu6KFFaxFKKrvEUmnOfOEToTT0Jh+XAJASRCP/opbLOv27K2a0ME3Q7pY5245u/VC96v03O/BW9549ImKFd4ZrdqmMa3c98sy+t2Olhq9MZSNkqHV9zaSvWxXPbcr9PeLx/YILyjwb+eNknSFXgp5ZwWKL3vrBHXwzjQrKiAJLmf3C+p+1XMKWC2ZNsYWz2MyQdoqE8bvAgorvAtBFMK70d9l6o93B6qu3fM6xj5Y8zq9WfRgQmjhnfOA3u5f1Xuc2OqO0KfFmI2d/fN0Dbh3eWizA4FShvAuTpx//k9XlfNVmpayjdT/2fU6HLQGztaORR9oU5AKMOfPl5We4ntdR+dn9FvYLY3LGS0dWt1b8Zax1tQtS4Ot6VHSwzun9r50hZL9Br0b3rum6AY0c7Xubeg7AbLVGakvitF6OI+s10drgw9yh98xO6k5A/ppxtFQz5YAs5kY3jn36qUrkn1LRtga6t41xTqVlnPfG+pZyarKvWbmrh2fuf4BNbW7X9+Sosue/y3yYMg/vHN9qb++8t1rJvf18+43E+x+CyGHd84/9b+r/Jb+tJRVo/7Pan3whsmosxbpg2ANk5dfeGfUoxnr8m+nrs/tDGE7ZevnKZ2UbKuloUtOGl+O8C4iEXSaT84ZoH4zjoYeqJl8XAJAyRCH/opHDOv2zNX3+maMGJ/LdY/ZyLtETh1Z/5HWFjH4HY8+UfHCO6PvvecVpXvvQ2RVraEfFT3D48QCDT7PptS+cxTO+H88tkc4QYFz70u6wrOKglFsDe8VTTfiJ1Or7/Utw++aDTyyeAM1Wv/R2oDHpHljbPE8JhOjrTJj/C6gEhneuX7Qv/SV916Aeds/936AwQcTQgrvsn+cmC9Mr3PH50X+rgAiQ3gXNyf16cjGfjMojGJxqGaXe/TW5mMRDyIem3OdX0VsdCBGfBphxypvHWuH57MZlW/wG/iW8PDu7FZNSPMNDFocF2nspsJPfDyy1o9SY29H1aJyfWaHtMRpcYTdMTvzue5oci3hHf5BzAvvzm6doDRvp8Yix0VjFUJVEES2thn1VpKttoYtc5/1Gh2Spzp6rk433uPCx/KCt0gUDO8M2b/P0QDj+3rrM3t9DflwX6HtRsjhneHkpyPV2O9qvNzPX7OL7nlrs45F2jB55Q/vlLNL07qleL+Hvcl9WlPUGf6ZVbrb6Ai5frfc+p7wLjJhd5rP6PM7mujaGIV30T8uAaCkiH1/xStmdXuW1o9q7Bskt5RTn9mx7hG5vk7s+0TFDe9cffrFN5/vNyOnu179M9hruO6Vd40q2urotk+CjZaeKx7bI/Sg4Ky2TkjzDd5bHLpo7KbCL9IBoi1rvUY19oU0lnJ9FKtqybwxtngek4nQVpkzfhdQiQ3vDNm/a84A47f27it21R/yofYV9oIhhXfZ+v7xi3z7tqWirn83sqW1ARSN8C6e/vpaT3T2Tb/3FIvjPHUcNk1f7CnihPwcZ7XOb0DcVakX5wafmYtvVKr3JKWMHN2ma0+hLUQJDu+cR7Xq4fYq722cUtT64dVFXxVpNIe7numc7+Sq2I1uCMLqmDmP66vxnVWpbA/CO/yDmBPeOY+u0sPty/s6Gimt9fDqYp5UnlmpOxvYZG/xqL71fgen9r3RwzcYZKuj4cuDX1VZqADhnev1T659VO0868kbxZp6mab+ELiuCCe8c12N9/UTnZXqdw+D3GJ0AM/rOEzTvthTROcqmALhnfFpji8YrBqe97JWUb+3g13Z6NShOf2Uaquka15332eC8C4yYXWajd/pq/HqXKmsesQgvIvJcQkAJUas+yt+YlW35+zSM509r2uUGLVzBcWjT1T88M74hb99VC08Fz4Z50utx31f+IC58Rs9lWac113wiN95Y2jisT1CCwqcOrrqYbX3nodalNL6YdF0I55ydj2jzp7jwSjF7k8WyswxtngekwnQVpk0fhdQSQ7vDM6Ta/VoO1//y3V/usum/hD4dwglvMvZree6+J0nFDFLFEDxEN7FmfPkd3pxQFOl+DXgnmIp11DdH3hL3wW9c6m/M3r/et8sBtc9Y0IbrA3s7Dr/q1aMBrzpg/qq0Pq3JIZ3OTqxfbEm9m+mcu7ta3HUUNdHPtbekD5bplbc7ruS0tVIdp66q1gDvKHI3zFzqG6nPurbt2+Bcp16X91VbepWzLtiJonwDv8kcQ7vck5o++KJ6t/MsySkRY4aXfXIx3sj7njlcerwO9erijVF3aYVqBtOLNSQGp4bQluVet3sIm/wHFDA8M4lSzvfvE7n23ydtKTmd2p5gPvrhRfeGZwn9d2LA9TUb3kYb7GUU8PuD+it745EUBcWDO8MZzfokRZ27++SlDZRPxb2o2Rv11NpybLVMZ7vuVid8C4yBTrNjrqd1Oecdqavrut9tbq2qauKuftZUnTDu5gdlwBQksS6v+InVnV75grdfr7nnMYojs6aGsa92iIVjz5RNMI75fyuF67wLTvuOk8pbFJd5voH1cyerM7PhH/eEY/tUVRQkHNiuxZP7K9mntt/GJ+jRtdH9HHYOytQPJkrbtf5fhcbOjpPVWyqJTPH2OJ5TCZAW2XS+F1AJTy8c8na+aauO99vNZ+k5rpz+ZFzt3Eo4V3mx7r1PL/zhKQr9GIY91s8sf8P7dmzJ0j5QwdOBjlQgFKG8M4Mzr+0be596lbL4XdS4CkW2au119Dn1+pAkXXVUc3okeT33GRdOzPySeJ5A76+z2Krc4c+L7TFMT+8s1bvpJtGPahR947UsEG91KVlDZW1uho444QgtZmuGDpB728JZ0nS03q3f9l8J2rpr+yP+EQtVPk7ZklqnH6Thg4dmr/cfKMG9e+utHoVZI2gYwaYK5bhnVXVO92kUQ+O0r0jh2lQry5qWaNs3nFidGZSm12hoRPe15birwFp9GF+1TOXGq9ddYDePSc0yzC+Y2PZ3d/RktxZU3+J4D0LDe8MzuNa9cBFfhd/WFWj1+v6tcDfhR3e5XLqr21zdV+3WnJ4X99XLPZqaj/0ea0tumHyEyC8M2rkPUaHwrsUja2uRqwIPOJ1+vORqm9zqN0TW33hDuFdZAp0mpMap+umgu3M0Jt146D+6p5WTxVy29LihHdxPC4BoESJdX/FT6zq9tPvqn9ZT5tplKR0veK6yW+MxaNPFJXwzpBvJQFLJV07Y1+AbXpSS24+X7bKffRWBFd0xWN75AsKrNXV6aZRenDUvRo5bJB6dWmpGmWtuX1jiyNVza4Yqgnvb4nCsupA+E6/219lPceuUZLSX8m993j0mTnGFs9jMgHaKpPG7wL6B4R3rseOr3pAF/ldsGut0UuvnzuYUHR4d2KWeiV7trtRkrrrtVBv6pqzS+89NFj90tuqtv+5hrtYKzTUpdfdqMeX7HU/AQDhnYmcJ7bo7QevUv2Asx3sqnbxPfpgZ7DVtf/SnD7Jfs9LUvfXD0fcWGVtHqtW/icWDe/T2kJbnBIQ3lVtr/633KJbbxuuG9Kq+e49ULa9xm8KsqxIoU7rnX75G/+rXo3gZrVhyt8xK2JJlOwD+vSB9iqfTHiHf5LYhndV2/fXLbfcqtuG36C0ap4rwCwq2368IqoKCpH51UNqbrep/p1f6Iz73/xl/zhBHRye+tyu5g99Hf79EYKFdy5Zv+jVa2v4rjC0lFO70euM1sAnsvDOzXlCW95+UFfV97/i1FNcF5dcrHs+2Bni9woU3hlOfqRbant+P4sqXfO6/iz4QZ0HNKt3qmypvTXrgN+DhHeRKdBpDr5cTbYOfPqA2pdPLlZ4F6/jEgBKllj3V/zEqm4//Y765QvvrtKroQ7KFUM8+kTRCu+Mk0I95D0fscjRfoK2FejOOg/MVK9KNtW6dZnCu9tdnnhsj/xBQVW173+Lbrn1Ng2/IU3VvOFkWbUfvynIvgXE3ul3+uUP7656VbGplswcY4vnMZkAbZVJ43cB/SPCO5cs/fLqtb6LT4zfo1y70VqXfzCh6PDu2Ez19A/vHF303O7w29O/vhmrNL/xcIujtR7dEOHtR4AERnhXApze9bEmDWqtKt7l0DzFInvt6/TGz4VV+5n6+Nbz8k0T7/T0zogHJLPWP6AmficWjo6T9HOhL5apxTcWP7zbNqFdbnj35I7wwzv/qf3Ofe9roHfQ0KKUto/p67Dr/EwtHeo7UXFtz87P/FasAd5QhNUxc/l7gf5dqyfhHf5B4rVsplP73h/o6/BYUtT2sa8VndO/E1o4pIasjrb67w+F1FfOP/Vq9wreetF6/lAt8T8RDkVR4Z3BefQz3dvS11Gx2Otq0Pt/euuqYoV3Hqd36eNJg9S6im9pDU+x2Gvrujd+DqFDUkh4Z/xamx9v7Z3hZ3G00pgCXzZ72wS1d9jU4M4vjG6ZH8K7yITVaXb5Wwv+XUs9Iw7v4nVcAkBJE+v+ip9Y1e2ZSzXUe9GFURyd9cxvse4RxadPFLXwzjiL2PlcV99qCLZ6uuMz/zOWHP3y9CVKtjfXw99E1n7HY3sUukSfc5/eH+jbjy0pbfVYsXZWoHgylw71hVdGcXR+RrGplswcY4vnMZkAbZVJ43cB/WPCO4PzqD67t6UvDLfYVXfQ+/rT8wahhHcZCzU41W/82t5MD31dyPsFk7NTT3fy7Bt5y8pG8jJAoiO8KzGydXjD67rz0vMLLFlmUfnOTyvwxDSjUzC5Y74btDa4d3XEjUTmkptUxXtCZFVVo1HNN2iaT6aW3VLd21C6rjYs9L5FhcrS5rGtZHdcoqd3htIUFX6C4Wqkjiy9TY08s14sSbrgvpXh3UjXEya6Xz9ve64pXqMbgrA7Zjm7NS29D+Ed/kHieM875xEtva2RLxhKukD3rSz+HfVz9rys9PIWlb3kCX31e8E12X3lh5euVWXviXAlo9MRaBmlIEII71wyt7+oq6v7Btaslbtq8vd58wGjEt65ZR/eoNfvvFTne2cUurdr+c56usgZ04WFd8bX3PuGelTyvKZV59+4SL4FaU5pxYi6siV31KSCF3YQ3kUm7E5zjnZPS1efqIR3hhgdlwBQ8sS6v+InVnV79jZNaOcbTCtja6B718S6RxSfPlH0wjvj1zw6T//yhpwF7nfsusfvBXYlX/K0IllF3SUe26PQoMDgPLJUtzXy3ObDoqQL7hNNN8ziurCvned4MIqtwb2KTbVk5hhbPI/JBGirTBq/C+ifFN65ZG7Xi1f7xnPLWCur6+Tv81YXCiW8M84Tnmjrd55gSVGvWUfdD4bjmN7s6Zvp6ug4OeI2E0hkhHcljfOoNjx/vRomeSpqo9hqa/jywE382dX3qoGncTcawmSjgvVfYSx0rgayq6/hs5TTNa8fCNJYntXKO+v6Gvvmj+jbIG1DYGe1zjWgn3SlXg5pwfJgJxgG5wmtvO8CJXkGBx2NdNvSADdgDSJj+XC/GyEb2/PKl7Uvou0ZurA7ZsZJys/LFmtrUX8GlBhxDO8MzhMrdd8FSd6OjaPRbVp6zj3qwpGl7x+/KOC94IIXo1OV9mQhF18UIsTwznVifvjjO9Tc21YY79VshJYddkY1vMvj1NENz+v6hp5t6io21R6+3P14YQoP71xXVK643deGWMpdpunuu847981Qz0o2Vek/99zlcAjvIhN2p9l4ys/LtDichibuxyUAlESx7694xaxuz9Dy4ef7BvUsybry5TAvRopAPPpE0QzvXNtp7f1NfPc7Tuqop9wXHf398W2qbaukXjOD9aeDi8f2CBYUuM7/Tqy8Txd4zjUtDjW6baloumGKjOUafr7vwkVL8pV6OUYDNeaNscXzmEyEtsq1W8R//C6gf1p4Z3Ae/lh3NPf17y1JzTRi2WE5QwnvlKlVd9Xz7j+uYLr6zUuCBtOBndRbvfzCu0umKqR5HUApQ3gXJ9nbntS1Iz8pspHKk6Wdb/T2W4c4r/IPKGOl7qrvaSTKyFptiBZFNKX9lBYNqertpFkq9tSMoIFaljaNudDbWbFWvVkfhXYTJD8ZWjg4VdYK/9KHgW4gdY4iTjBcTn2tMW1992qy1RmkeeG03n8v0c01/E4KK/fX3BjPcAu/Ywb808Q3vHM59fUYtfWun25TnUHzIj+R/9voLBrvZ7/gTi3YvEVbtgQrm7Xonpa+oM/eWPetCeOYDjm8c8nQ1ufSVdXvas7qPV7Rj9+EGN5lb9OT147UJyF+vKydb6i3X/3o+h2DCxbeud5+gjp4w0e7mhrtXIbxS24Z30aOwrYb4V1kIug0hy3exyUAlEhx6K94xLBu/3vJzfnuiVO5/1zFetGPePSJohveSTm/PK1LvPcHtKnh3V/qjPOQ5vRNle38m7WkGDPV4rE9ggcFLqf09Zi2fsuD1tGgebEPcoFz/a0lN/vf97uy+s8NY4WIcJg2xhbPYzIx2iozxu8C+geGdy4ZW59TelXf9rNW76FXfvwmhPDOeO6a+9TYs6+6nhvJLUMI74CQEN7FSfbW/6pD61AGY92yf9Kkjr4r1CsPXuR+oKBs/TChvfeKmDLWGrp5SQS3xD7zqUZ4B91sqnf7cgWvd5069Fp3Jbkr2TJJl+uFP8NsJLN/1iSjEQ94ohBQCCcYhswtT6mzt6Gz6rw+MxX6vVMztO6BZt5Qsoylgq5+bW8xTgqdOn7osILlmsXvmGVr/5bN+jP6Y8dAlMQ/vHNdDbblqc6+ARrreeozc3cEgY1TB2b1VmVreV35UmjP9yyxmff5jDro3/P9loQsQljhncF5UEtua+oLCy0puvCaK1XfFkp4t1X/7dA6pBP7PNn6aVJH3xWYlQe7/70wwcM7OQ9o9nWp3g6tter1mrtrqYYZv23Kpc8o4Hga4V1kotBpzt6/RZuDNTRxPS4BoKSKR3/FLZZ1e8Y6PdDM094abX6Fq/Xa3mIMiDqP69Dh4Fd6xqNPFO3wTs7Deuf6Kr5zmSrXa86GZ9W1rF3NHlwftA9YlHhsj6KDAkPmFj3VuaJ3AN96Xh/NDHtnBYovY90Daua9f5xFFa5+TcWrlg4pcLVk1hhbPI/JBGmrTBi/C+gfGt65/v7gktvU1HuLDItSLrxGV9a3FRneKedXTetW3rsfum4Z0uP1P8Pc9oR3QCgI7+LEFd61KXuRHv8+1PXTsrR+VGN3Y5q3dnNhnMc/1m1G5eoJ+ir1eN13s9GQOHX4vQHeGwBbq/fVWyG8QNbXD/lOnqzVddPi8C5Hcu79n9JTjBOAoUtDnF4d2gmGa9v99EK6Uj1Xi1pTlf7CzwEGEQNz7pujft57SVlkb3KXvgj7CpI8ZzZNUs/e0/RTkJ+9uB0z5/7Zur7LY9oY6hcE4s6M8M6Q9ZNeSPcLh1LT9cLPYR4oRmfjqY5JstW8SYtOuP+tSCe08Maavqssy6frlT9CrJTDDe9cznyvKd183zOvhBjetSmrix7/3uiihiZr/SjvFXaue00EV0R4Zzi96i419HRQLUlq3u5ClbdV18B5hVxJS3gXmeJ2mo39cvb1XfRYsIYmnsclAJRY8emv5Ipp3e7Uvjn9VN3z+Sx2NbnriyIHngM7o02Teqr3tJ/c/x9YPPpEUQ/vDGe+vNvvXMahug3qyJ7UUZOCdQBDEI/tEVJQYMj66QWlp3r6x1alpr8gmm7EnXOf5vTz3afLYm+iuyIfqNGknr01rZDj1Kwxtvgdk4nSVrl2i/iO3wX0jw3vXM7o+yndfL+xuxQZ3hnObBirtt7Z567xgRFaEdaMc8I7IBSEd3GSG945bKpz06IQlxw5rSU3uU9MrOfpxkXBWh+njq2403fvI1t9DVsa+hICzhNf6J7meTe+tTjqafC8vaE1DFmbNKaV54a5Vp038IMwllM5qVX3NpfDVku3fBRqy1rgBOPCMYWcYBhydmtmn/N8J3YVOmnCppDW5jTkaM+c/jrfrxPW6JZF2h9mI3L217f0rzbdNX178Ga7WB0z53Etv72JWo3eGN4JFBBXsQ3vLhxTSEhgyNk9U33O853MV+g0QSFXBYbTq1wDMna1ePTbsE7AM79+WM09FzcYdUjrcVtCO0YjCe8Mzv0LNNR7A3NXCTW8c8hW5yYtCrHyPr3kJvdAnlHn31jYjHCPosM71yzzKZ2S/T63Ubc3f0hfFfb3EYd38zWQ8M79/cPtNDt1fPntatJqdPCLROJ4XAJAyRWv/ooh1nV7zh7N6X++97u47nl0y6L9YbafZ/XrW/9Sm+7TVUSXKC59ooz5A6Me3rl+h0kd/c9lLKrY441iLwsdj+2RPyi4UGMK31m1e2YfnecNcyuo04RNoulGvOXsmaP+53vON133UL5Fi8IfqNFb/2qj7tO3B+lHmDPGFr9jMoHaKmNbxHP8LqCoh3eR9l0jCe8Mzv1aMLRRvnv8hxLeufr7Pzxzuap490Nj2w9bcu596wtFeAeEgvAuTvLCO6Ohs9VSr5e3FTnTLOfPmepTzTWwZVHZduO1qch525n66fW+qpM73dkiW+2+euOnECZ7n/pez/esJZtRSVtsNXX1tO/DuMmoU4cXD1U9W16jYnE00a2hdOicJ/TtM9eols2qKle9rF9DvqolU58M861zbm/2kL4O0h45983TIO9AokVJzUdoWaitiNHhWf1oB1/nzlJOFw6bq59C3Dh/bX5J/ZpfqOGLi75JuWvfaOvtmFXW4IWhnsq4prjfqkbJRsMcdEQVMNtZrbzT1zmw1btLq4pzNpv5iYZ517a3q9lDXwcZmHBq37xBvk6Qa3bXiGWhnVA69+rNXqmyJnfRs7vCPIs0OilPGZ0Uz0COrfZQLQll7UyjczStq0P2pg/qqzAP69PfTVTnyp7tEnp4V8ZiU61eL2tb0Q2T0XGrllsHW8q20/giG6ZTmts3WdYqNwW5J6pTR/yuSnXVtZc//1vh7cjZdX4dI6tqDl8e2rImp99Vf+9VgQ51mLgj5NmGgZxdeadvn7LV013F2qEDi+p7uH7rtr5Oc+XBC0PuNDsPLtGtjZLVoqiLROJ1XAJAiRbH/koc6nbn8dV6tINveTZLuQs1bO5PIfYX/9Lml/qp+YXDtfhA0d8pHn2i0+/2V1lveNdBE3cUb3ZcHuP9Z1/nNzOlhm4MfbmGQsVje2R+Msx3b0N7Mz0UfGfVvEG+83lLUnONWHbIeDcgnpw6vvpRdfAGGxaVu3CY5oY+UKOX+jXXhcMXq+hqKf5jbPE7JhOrrYrn+F1AZ1fqTu/2saneXauKF95F3HfN0e5pXeWwN9WD4Q8maGLnyt59IrTwzuA8qpWjO+abndlpzJc6EtKGJLwDQkF4Fyee8M5VIVmMyqzN0Of1+e+nAjYMGbsW6O72FY1K0zhBOK+7nt8aatOWqZ3vj1Db3MFbixx1emjCp38UMrDp1Ikts3XXxdVyTyqsFVvp1jk/hX/1nPOE1o27xFtRW8o2Vt+nluu3gI3kGf25bqYe7F7f6DRZVP6iu7Q0hI6cl/OIZvQo6+s8pg7S/KArdTp1ZOltauRdv9mq1EvG6MvQWpHc91s9IV21/J5fsXkfjZ69Xn+eDvwaZw9u1Ltj+6hpjTYauXBP8BMMt7Or7lJd7wBmsnrNCmmEXwdW/EcXp1pzZ+iQ3aFkO6l3+vnWQ7dUuF7vRriUhYvzyAz18J7MWpQ6aL6CVwVHtPQ2vyvJjDr4kiJPKI06csUINbIbdWnbJ7Qt7LGdLH39kP/6+8lqO/bbouvYrG/0cDO7Ub/9WwtD7eV55ejPeYNV3/jMYYV3uZ/PqB/bDNXzn/+uU4GelLFLC+5ur4pGXW+xnafuz28tutOVs1NPX2K8ftJVejXo3a7XaVTTvNl01po3amGwKvDUhxpY2ffbl+05U0fdDwWTs2uqOnsGwIwOVYN7VherQ3XynX4q7+0cVtD1xdmhCxHV9zi7SnfV9XW4k3vNCuk+jDkHVug/F6fK6rp6s4iGJj7HJQCUcPHsr8ShbndxHlmtCem1/OrrimreZ7Rmr/9TgbtEZ3Vw47sa26eparQZqYV7QuuoxL5PlKNdUzvLkbu9jGJroHtWR+nim9Of6Y76eb+FvckorQvpyqLgYr89jH1vRg9fmGlJ1aDgO6uxLyzVbX4rPVhTL9GYL48EP98Eos7Yd1dPUHotv32xYnP1GT1b6/88HXh/PHtQG98dqz5Na6jNyIUKsVoyxHOMLY7HZAK2Va7vFI/xu4BOvqN+3nveW1Th+ncjXGY6T+R91yx983Az2Y1959/hDyYo5895GlzfnrtfhBze5fpbW16/SS0ruS/ktJRVw94TtGxX8M+QdWi9HungCXbzwrtwr5kGSgPCuzjJC+8cqlSjhioZjYmrMrTYKqpR1wEaft+jmjD5aU3678O6/bo01XINfrkGUtuN0Nwd4Ve4Z3Yu1ri+zVXZZryPtYIadBmkBya9olnvLdCC92fpf08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| |
| "text/plain": "<IPython.core.display.Image object>" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Correction channel" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*If the correction channel has a capacity equal to $H_y(x)$ it is possible to so encode the\ncorrection data as to send it over this channel and correct all but an arbitrarily small fraction $\\epsilon$ of the errors.\nThis is not possible if the channel capacity is less than $H_y(x)$.*\n\nInterpretation: Equivocation $H_y(x)$ is both noise and information (useless information about the noise process). To counter it, the same amount of information is required." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Correction channel in the example" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "center" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Reminder:\n- you have binary source of maximal entropy (0s and 1s, i.i.d., $p(0)=p(1)=1/2$)\n- you have 1% of i.i.d. errors: $p:=p_0(1)=p_1(0)=0.01$\n- What type of correction could you use and how much information would it cost?" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Correction channel in the example" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "center", | |
| "slideshow": { | |
| "slide_type": "fragment" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "Answer:\n- Send complete report: 1 for success, 0 for failure\n- Entropy of the correction: $-(p\\log(p)+(1-p)\\log(1-p))=H_y(x)$\n- That means the erratum can be compressed to the uncertainty.\n- e.g. if p=1%, 8% of correction is required\n- Exercice: a simple compression when p is small?" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Capacity of a noisy channel" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2021-02-17T08:42:09.778957Z", | |
| "start_time": "2021-02-17T08:42:09.773965Z" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "*The capacity C of a noisy channel should be the maximum possible rate of transmission, i.e., the rate\nwhen the source is properly matched to the channel. We therefore define the channel capacity by*" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": " $$C=\\max_x(H(x)-H_y(x))$$\n" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "You need to find a source statiscal structure that achieves the best trade-off between throughput and uncertainty (and use a transducer that transforms the original signal into that source)." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Shannon theorem on a noisy channel" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*Let a discrete channel have the capacity $C$ and a discrete source the entropy per second $H$.\nIf $H \\leq C$ there exists a coding system such that the output of the source can be transmitted over the channel\nwith an arbitrarily small frequency of errors (or an arbitrarily small equivocation). If $H > C$ it is possible\nto encode the source so that the equivocation is less than $H- C +\\epsilon$ where $\\epsilon$ is arbitrarily small. There is no\nmethod of encoding which gives an equivocation less than $H-C$.*" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Interpretation: no matter the actual amount of noise, if we are in the feasibility region, the probability of error in the transmission can be made arbitrarily small **without paying any additional bandwidth cost**: if I can transmit at 1Mbits with 1% chance of error, I can transmit at 1 Mbits with 0.0001% error." | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Feasibility region" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.984368Z", | |
| "end_time": "2021-02-24T14:33:16.989368Z" | |
| }, | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Image(\"feasible_region.PNG\")", | |
| "execution_count": 30, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 30, | |
| "data": { | |
| "image/png": 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| |
| "text/plain": "<IPython.core.display.Image object>" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Proof by picture" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:16.991329Z", | |
| "end_time": "2021-02-24T14:33:16.999367Z" | |
| }, | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Image(\"sop_noise_thm.PNG\")", | |
| "execution_count": 31, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 31, | |
| "data": { | |
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lGHimS5dO9erV09SpU3Xw4EH7SAAAACQnBKAAAABAtAsXLmjp0qXq0qWLbr/9dsfA09S9996rPn36aNWqVfrrr7/sowEAAJBcEYACAADglrV9+3aNHTtW1atXV0hIiGPgGRoaqsaNG2v69Ok6evSofSQAAABuFgSgAAAAuGX88ccfWrhwoTp06KDbbrvNMfB0uVwqVaqUBgwYoDVr1igqKso+GgAAADcjAlAAAAD4tZ9++kkvv/yyKleuLLfb7Rh6ZsmSRS1atNCcOXN04sQJ+0gAAAD4AwJQAAAA+JXTp09r3rx5atOmjXLmzOkYeAYEBKh8+fIaMmSINmzYII/HYx8NAAAAf0MACgAAgJva33//re+//15Dhw61Qs3AwEDH0DNHjhx68sknrXD01KlT9tEAAADwdwSgAAAAuOmYZepmufoTTzyhrFmzOgaeQUFBeuCBB6zl7z/++KMVlAIAAODWQwAKAACAZM80Ilq7dq0GDhyo0qVLW0vYnULPPHny6KmnnrIaHZmGRwAAAAABKAAAAJKlo0ePavr06WrSpIkyZszoGHgGBwerWrVqGjt2rLZt22YfCQAAAPyDABQAAADJQmRkpL7++mu9+OKLuvfee+VyuRxDzwIFCujpp5/W0qVLdeHCBftoAAAAwBkBKAAgWdm3b5/69u2rBg0a6JFHHlGjRo2s/fvMfn8A/M+hQ4c0depU1a9fX+nTp3cMPFOmTGn9Pnj99de1a9cu+0jAv3k8Hn388cdW467HHnvMKvNvE/yb7wEAAN8RgAIAkoWNGzeqdu3aXvf1CwkJUcuWLfXrr7/aRwC4GUVEROiLL77Qs88+q+LFizu+300VKVJEzzzzjJYtW6Y///zTPhrwfybcfO2113T77bc7vjdMmVnQ48aNIwgFAMBHBKAAgCRnlrymSZPG8SIvduXMmZMZYMBNZu/evZo4caL1Rw5v73XzdfP9SZMmWbcHbkUm0Gzbtq3je8SpzIxQQlAAAOJHAAoASFIJCT9jihAUSN7MjE0zc9PM4CxcuLDj+9jUnXfeac0ENTNCw8PD7aOBW9Pff/+doPAzpghBAQCIHwEoACDJmIYnuXLlcrygi68qVapkjwIgOTB/lDDLds1enWbPTqf3rdnj0+z1+dZbb1l7fwL4x4cffuj4vvGl3n//fXsUAADghAAUAJBkPvjgA8cLOV9r8+bN9kgA/mum+/qSJUusbuxmP0Kn96ipEiVKWF3dzWzvv/76yz4aQGyVK1d2fA/5UhUrVrRHAQAATghAAQBJ5oEHHnC8kPO1nnrqKXskAP+Fbdu2acyYMapWrZqCg4Md35cZM2ZUkyZNNGPGDB09etQ+EkBctm7d6vh+Skj99NNP9mgAACA2AlAAQJIw+/05XcAlpPLly2ePBuBGOHv2rBYsWGD9sSFPnjyO70OXy6XSpUtr4MCBWrt2raKiouyjAfjq1VdfdXx/JaTMHycAAIAzAlAAQJI4duyY4wVcQsrsJwgg8ZgmLD/++KNefvlla4Z2UFCQ43sva9aseuKJJzRnzhydOHHCPhrA9TANjLp16+b4XktI9e3b1x4RAADERgAKAEgSp06dcryAS0hlyZLFHg3A9TLvRdNAxXSSzpEjh+N7LTAwUOXLl9fQoUP1/fff03EaSCAzM3rfvn36/PPPNWnSJPXq1Ut16tRRsWLFFBIS4vi+S2i99NJL9tkAAEBsBKAAgCRhApQ0adI4XsT5Wqa5CoCEMe+9DRs2aMiQISpXrpwVbjq9v3LmzKk2bdpYzcpOnz5tHw3Am8jISO3Zs0efffaZJkyYoB49eqhWrVoqUqSI1z1zE7Pefvtt+54AAIDYCEABAEmmc+fOjhdxvtZrr71mjwQgLsePH9fs2bPVokULa+a00/vJLHc3XahHjhxpNVMxy+EBXO2vv/7S7t279cknn+j111+3lq4/+uijKlSokNctI5zK7J2bO3duPfjgg9Yeu4MHD1bKlCkdb+tLmT8onjlzxr6XAAAgNgJQAECS2b59u+OFnC9lLvZMgxYA1zLLbdesWaMBAwaoVKlSVtji9D667bbb1KFDBy1cuFB//PGHfTRwazNN+nbu3KmlS5dazYm6dOmihx56SAUKFPA6Y9qpAgIClDdvXlWrVk0dO3a0mhR99NFH2rZtm/7880/7bP94+umnHcfxpcz4AADAOwJQAECSql27tuPFXHz17LPP2iMAMI4cOaJp06apcePGypgxo+P7xizDrV69ul555RXrDxDArSosLMx6DyxevFhjx45Vp06drPdGvnz5rODS6f3jVCYQzZ8/vxWQmgBz3LhxWrJkiXbs2GEFqQmxa9cupUqVyvE8cZWZOWrOBwAAvCMABQAkqQsXLljdpp0u6ryV6T5tZrgBtzKzFHfVqlXq06eP7rnnHsf3iqnbb7/dmsFmZrOZ9xtwq7h48aK2bNlizXAePXq0NdvZLDnPkyeP11nRTmWWthcsWFCPPPKIunbtam2/YpbAm8AyIiLCPlvi+PLLLxMUgprwc8WKFfbRAADAGwJQAECSM6GM2XvQ6eIudhF+4lZ28OBBvfnmm6pXr57SpUvn+B4x4YnZk/CNN96w9ioE/Nn58+etPWvnz5+vl19+We3atbM+T3LlypWgkNPtdqtw4cKqWbOmnnnmGY0fP17Lli3TL7/8Yv2x4b9kQtDUqVM73s8ry7zXCT8BAPANASgAIFkwnak//vhja4ZN7ItWc2HatGlTrV692r41cGswS2hNwNG7d28VK1bsqvfFlWW6TJuO06b7tNPegsDNzOxPu2nTJs2bN0/Dhw9XmzZtVKlSJWXPnt3x/eCtQkJCVLRoUWvrlZ49e2rixIn6/PPPtXfv3mT3h7UTJ05oxIgR1j69sR+HmcFqvmduAwAAfEMACgBIdvbt22ddlJpli1988YWOHTtmfwfwf7/++qsmTJigxx57zGr2FTv8MGW+XqdOHU2ePNl6vwA3O9PB/Pvvv9fcuXM1dOhQtWrVSuXLl1fWrFkd3wPeyiwJL168uB5//HFrr+gpU6ZYnyP79++3/tB2szHB7HfffWdtYWH2FjX/ZhUEAAAJRwAKAACQhMyMzU8//VTdu3dXoUKFHEMdU3fddZeee+45a3lsYu87CPwXTp48qXXr1mnOnDl66aWXrC1N7r//fmXKlMnxNe+tzPLwu+++W/Xr19fzzz+vqVOnauXKlTp06JD+/vtv+2wAAAD/IAAFAAD4j/3888969dVX9fDDD1sz1pxCnvTp06tBgwZ6++239dtvv9lHAsnb8ePHtXbtWs2aNUsDBw5Us2bNVLp0aWXMmNHxde6t0qZNq3vvvVcNGzbUiy++qHfeeUdff/21Dh8+TMgJAAASjAAUAADgBjONWhYvXqzOnTsrf/78joGP2fu2RIkS6tu3r7755htFRkbaRwPJi9mW5Ntvv9X06dPVr18/NWnSRPfdd58V2ju9tr2Vub05zhxvxjHjmb2e2fYEAAAkNgJQAACAG2Dr1q0aM2aMqlatquDgYMcAyCz9NQ2+Zs6cSeiDZMPMsDQzLc2MSzPz0szANDMxzYxMMzPT6bXsrUJDQ60ZoGYmqJkRamaGmhmiZqYoAADAf4UAFAAAIBGcPXtW8+fPV/v27ZU7d27HMCggIEBlypTRoEGDaGaCJGVCTrNnptk70+yhafbSNHtqmr01zR6bTq9fb2WCfLOXp9nT0+ztafb4NHt9mj0/AQAAkgMCUAAAgOtgAqQffvhBI0aMUKVKlRQUFOQYDmXLlk0tW7bUe++9p//973/20cCNZ7qem+7npgu66YZuuqKb7uimS7q3vWe9lenGbrqym+7sQ4YMsbq1m67tp0+fts8GAACQfBGAAgAA+MjMaDPBT+vWrZU9e3bHoCgwMFAVKlTQsGHDtHHjRhq24IYys4j37t2rzz//XBMnTlTPnj1Vu3ZtFS1aVCEhIY6vUW9lXtMVK1ZUmzZtNHz4cM2bN0+bNm2yZjcDAADczAhAAQAAvDAz6NavX6/BgwdbS3zNEnan4ChXrlxq27atPvjgA2bEIdGZhli//PKLli1bpvHjx+uZZ55RzZo1VbhwYbnd7mtej97KNNoyr9XKlSurXbt2evnll61tG3766SerURcAAIC/IgAFAAC4gmnOYhq1NG/eXFmyZHEMkkzoVKVKFY0aNUqbN2+2jwSu319//aVdu3bpk08+0WuvvaauXbvqkUceUcGCBb1ur+BUJuTMkyePHnzwQXXo0EGjR4/WwoULtWXLFl28eNE+GwAAwK2FABQAANzSzBLi1atXq3///rrvvvusAMkpWMqbN686duyojz76SOfOnbOPBnwXHh6uHTt2aMmSJRo3bpyefvppPfTQQ8qfP7+1dYLT686pzEzkfPnyqXr16urUqZPGjh2rxYsXa/v27QoLC7PPBgAAgBgEoAAA4JZz5MgRvfPOO2rUqJFCQ0MdQyazf2KNGjWsoMqEVoAv/vzzT23bts0KyseMGWOF5tWqVbMCdG9bKDiVCUQLFChgBaRdunTRq6++qqVLl2rnzp1WkAoAAADfEYACAAC/Z5YXr1y5Ui+88ILuvvtux8DJlFlubJYef/zxx7pw4YJ9NHA189owWx8sWLDA2gbhqaeespac586d2+sMYqcyS9sLFSqkRx99VN26ddPrr7+uTz/9VLt377ZeswAAAEgcBKAAAMAvHThwQFOmTFHdunWVLl06xwAqVapUVjMZ01jGNJkBYphtDn788Ud9+OGHVrMg0+TqgQceUM6cOR1fS97K7BdbpEgR1apVSz169NCECRP02Wefac+ePVZzIwAAANx4BKAAAMAvmGXBn3/+uXr16qWiRYs6hlGmzPd69uyp5cuXs1/iLe7s2bPatGmT3n//fQ0bNkxPPvmkKlasqOzZszu+dryV2S6hWLFiqlOnjvX6mzRpkvVa3Ldvn7XHLAAAAJIWASgAALhp/frrr9aMOjO7LnXq1I7hVNq0afX4449bs0H3799vH4lbxenTp7Vhwwa99957GjJkiFq2bKly5cp57fDvrcxs4TvvvNOaUfzcc8/pzTff1JdffmnNNPZ4PPbZAAAAkBwRgAIAgJvGxYsX9cknn1j7JZr9Op2CKlN33XWXnn/+eX311VeKiIiwj4a/+t///qd169Zp9uzZGjRokFq0aKGyZcsqU6ZMjq8Pb2VC9HvuuUcNGjSw9ot96623rL1jf/vtN/3999/22QAAAHCzIQAFAADJmul6bTpgm27YKVOmdAyuMmTIoIYNG1qd3Q8fPmwfCX/y+++/a82aNZo5c6YGDBigpk2bqlSpUl67+HsrMyO4RIkSatSokV588UVNmzZN33zzjY4cOWKfCQAAAP6GABQAACQrpvnMRx99pE6dOilfvnyOIZbptF2yZEn169dP3377Lc1k/MTRo0etn6cJJfv27avGjRtbP+f06dM7vg68lbm9CUdNSNq/f3/NmDFDq1evtkJUAAAA3HoIQAEAQJLbsmWLRo8erQcffNDqmu0UamXOnFnNmjXTrFmzCLJuUmYZuVlOvmrVKr399tvq06ePNXPXLDtPkyaN48/dW2XMmFFlypRR8+bNNXDgQGv5+3fffacTJ07YZwMAAAAuIQAFAAD/uTNnzujDDz9Uu3btlDt3bseAKyAgwNrH8aWXXrL2d6TRzM3BhJwHDx609l81jYJMw6B69epZ+7J6a1TlrUzoff/991uNiwYPHqx3331X69ev16lTp+yzAQAAAPEjAAUAADecCcU2bdqk4cOHq2LFigoKCnIMvLJly6ZWrVpZHbtNYxskTyaM3rdvn1asWKHJkyerd+/eVqf9YsWKed2n1VuZn3mFChXUunVrDR06VHPnztXGjRutkBwAAABIDASgAADghjh58qQVZJpA04RcTuFXYGCgFYiaYNQEpHTaTj6ioqL066+/avny5Zo4caJ69Oihxx57THfccYeCg4Mdf57eKkeOHKpUqZLatm2rESNG6IMPPtAPP/ygP/74wz4bAAAAcOMQgAIAgERhZgWapepmybpZum6WsDuFYbly5bKWvs+fP59ZfknMNI/65Zdf9Omnn+qNN95Q9+7dVbNmTRUqVMjrXqxOZZpSma0MqlSpovbt22vkyJHWz3fz5s26cOGCfTYAAAAgaRCAAgCA62aaEZmmRKY5kdmv0SkcM0GaaW5kmhyZZkf4b0VEROjnn3/Wxx9/rNdee01dunTRww8/rNtvv93rVgROZULO2267TVWrVlXHjh01ZswYLVq0SFu3btXFixftswEAAADJDwEoAADwmZkx+O2336pfv34qWbKkFYo5hWX58uVTp06d9NFHH+ncuXP20bhRwsPDtWPHDi1evFivvPKKOnfurBo1alg/B28zcZ3K3DZ//vzWsWYMM5YZ04wdFhZmnw0AAAC4uRCAAgCAOB0+fFhvv/22GjZsqAwZMjgGZyEhIXrooYf06quvaufOnfaRSEx//vmnNdvSzLo0sy87dOhgzcY0szITEnKafVfN7E8zC9TMBjWzQs3sUDNL1MwWBQAAAPwNASgAALiKCcG++uorPf/887rrrrscQzRTBQsWVLdu3fTJJ5+wBDqRmP0yzb6ZZv9Ms4+m2U/T7Ktp9k31NtvWqczS9sKFC1v7eZp9Pc3+nmafT7Pf519//WWfDQAAALg1EIACAAAdOHBAU6ZM0eOPP660adM6hmqpU6dWrVq1NGHCBO3Zs8c+EglltgQwHdBNJ3TTEb1NmzZWh3TTKd3pefdWphO76chuOrObDu2mU7vp2G46t5utCgAAAABcQgAKAMAtyOznaMKynj17WiGaU8BmqmjRourVq5c+//xz9oBMgLNnz2rjxo2aO3euhg4dqtatW6tChQrKli2b4/PsrczWAsWKFbOC6d69e2vy5MlasWKF9u/fb3XdBwAAABA/AlAAAG4RZvnz+PHjrWXRZjanU+CWLl061a1bV2+++aY1KxTenTp1SuvXr9e7776rwYMHq2XLlrr//vu9dsP3VqlSpbK2GqhXr56ee+45TZ061dqC4ODBg4ScAAAAQCIgAAUAwE+ZfTlNc5uuXbta+3U6hW+m7r77br3wwgtauXIl+0PGcuLECX333XeaPXu2Bg4cqObNm6tMmTLKmDGj43PprdKkSaN77rnHaiTVp08fq6nUqlWr9Ntvv+nvv/+2zwYAAADgRiAABQDAj+zYsUPjxo1TjRo1rOXTTmFcaGioGjVqpHfeecfq8H6r+/3337V69WrNmDFD/fv3V9OmTXXfffd57Xjvrczs2ZIlS6px48bq27evpk+frm+//VZHjx61zwQAAAAgKRCAAgBwEzMNdRYtWqSOHTsqX758jsGc6R5uAj0T7pmg71ZskHPkyBF98803mjZtml588UUrAC5RooQVWjo9Z97KhKKlSpVSs2bNNGDAAM2cOVNr1qyxQlQAAAAAyRMBKAAAN5nNmzdr1KhRqlKlitxut2NQZ/ahNMu1zdLt48eP20f6L7OM3CwnN8v433rrLWtJf4MGDazl/Wb5udNz5K0yZcqksmXLqkWLFho0aJD1HK5bt07/+9//7LMBAAAAuJkQgAIAkMydOXNGH374odq2batcuXI5hnYBAQFWAx7TjMc05vHH5jnmMZnGTF9++aXVpOnZZ5+1GjbdeeedViMhp+fFW2XJkkXlypVTq1atNGTIEL333nvasGGD1dgIAAAAgH8hAAUAIJkxsxk3btyoYcOGqUKFCgoMDHQM8bJnz67WrVtr7ty5OnnypH30zS0qKkr79u3T559/rkmTJqlXr16qU6eOihUr5nVPU29lnp+KFSvqySeftJ7L999/X5s2bdLZs2ftswEAAAC4FRCAAgCQDJjl1e+++65atmypbNmyOQZ6QUFBqlSpkkaMGKEffvjhpu0ebvYg3bNnjz777DNNmDBBzzzzjGrVqqUiRYooODjY8bF7q5w5c+qBBx6wZse+/PLL1kzZH3/80dobFQAAAAAMAlAAAJKAWc793XffWXtMlilTxlrC7hTw5c6dW+3bt9f8+fNvqpmLf/31l3bv3q1PPvlEr7/+urp166ZHH31UhQoVsoJcp8fqVKaBk3kOHnzwQT311FPW3qcLFizQli1bdOHCBftsAAAAAOAdASgAAP8R0yncdA1v2rSp1WjHKfAzMyCrVq2qMWPGaOvWrfaRyVN4eLh27typpUuX6tVXX1WXLl300EMPqUCBAl6X7TuVCX/z5s2ratWqWd3sx44dq48++kjbtm3Tn3/+aZ8NAAAAAK4PASgAADeIWer9zTffqG/fvipRooQ1m9EpAMyXL586d+6sxYsX6/z58/bRyUNYWJi2b99u3TcTTHbq1EnVq1e37rO3WatOZQLR/PnzWwHp008/rXHjxmnJkiXasWOHFaQCAAAAwI1CAAoAQCL67bff9Pbbb6tBgwbKkCGDYxiYMmVKPfzww3rttdf0888/20cmnYsXL1pLyhcuXKjRo0erQ4cO1pLzPHnyeA1tncosbS9YsKAeeeQRde3a1Vr6bpbA79q1SxEREfbZAAAAAOC/RQAKAMC/YIK9L7/8Us8995zuvPNOx2DQlNn7snv37vr000+twPG/ZmaW/vTTT9ZeoqZZULt27VS5cmXlypXL8f56K7fbrcKFC1tNi0zzovHjx2vZsmX65ZdfrH0/AQAAACC5IQAFACCB9u3bp0mTJqlOnTpKmzatY1CYOnVqPfbYY5o4caJ+/fVX+8gb648//tCmTZs0b948DR8+XG3atFHFihWVPXt2x/vorUJCQlS0aFHVrl1bPXv2tB7D559/rr179yoqKso+GwAAAADcHAhAAQCIh9kH87PPPlOPHj1UpEgRx9DQVLFixdS7d2+tWLHihu1reebMGX3//feaO3euhgwZolatWql8+fLKmjWr433yVmYZfvHixVW3bl09++yzmjJlir744gvt37/f6lAPAAAAAP6CABQAAAe7d+/WG2+8oUcffVSpUqVyDBHTpUunevXq6c0339SBAwfsI/+9kydPat26dZozZ45eeuklPfHEEypbtqzXzvHeysxCvfvuu1W/fn09//zzmjp1qlauXKlDhw7p77//ts8GAAAAAP6NABQAgGgXLlzQ0qVL1aVLF91+++2OgaKpe+65R3369NGqVav+1Z6Xx48f19q1azVr1iwNGDBAzZo1U+nSpZUxY0bH83orswT/3nvvVcOGDfXiiy/qnXfe0ddff63Dhw8TcgIAAABANAJQAECy8vvvv2vkyJF68skn1ahRI6tZj9mD8ty5c/YtEs/27dv1yiuvqHr16ta+l04BY2hoqBo3bqxp06bpyJEj9pG+OXbsmL799ltNnz5d/fr1U5MmTXTfffcpffr0jufyVub25jhzvBnHjLd69WprfACA/zJ/0DIN9MwfyUyZf5uvAQCAhCEABQAkCyaMbNGihYKDgx1DQLPc3MzO/O233+wjEs40CVq4cKE6dOig2267zfE8LpdLpUqVsmZlrlmzJs6mP2aGpZlpaS5GzcxLMwPTzMQ0MzK9NUfyViZoNTNAzQXuwIEDrZmhZoaomSkKALi1mD+6mRUHTp8Xpsz2Jm+//bZ9awAAEB8CUABAktuwYYMyZMjgeJEXu/Lly2c16vHVTz/9ZM0orVy5stxut+OYWbJkscLX2bNnXxM4mpDT7Jlp9s40e2iavTTNnprm4tPssek0nrcye3jef//91p6eZm9Ps8fn+vXrrT0/AQAwnnnmGcfPEKfq2rWrfRQAAIgLASgAIEklJPyMqbhC0NOnT2vevHlq06aNcubM6Xh8QECAypUrZ3VRN+ePjIy0xjNd0E03dNMV/fHHH7e6pJtu6U5jeCvTjd10ZTfd2YcOHWp1azdd2839AgAgLgkJP2OKEBQAgPgRgAIAkoxZXp43b17HC7r4qlq1atYYZoamCRhN2GiCx8DAQMfbm1meDzzwgNq2bWvdtmfPnqpdu7aKFi3qddm9t8qePbsqVapkhazDhw+3AtcffvjBWmIPAMD1WLx4seNnji9ltncBAADeEYACAJLMokWLHC/kfC0TYJoZl07fi11BQUGOX3cqsw9orly5rGXzpgmTWUI/f/58azn9+fPn7XsPAEDiMQ35nD6TfKkHH3zQHgUAADghAAUAJBkzi9PpQu6/KBNy5smTR1WrVrWaIo0ePdqaQbNlyxZdvHjRvocAANx4P//8s+NnVULKNBMEAADOCEABAEkiIiLC8QLuRpQJOwsXLqyaNWta+6uNHz9en376qb766iuKoiiKSvJ6+umnHT+/ElKvvPKK/QkLAABiIwAFACSJ33//3fECjqIoiqKohFe/fv3sT1gAABAbASgAIEmcPHnS8QKOoiiKoqiE16BBg+xPWAAAEBsBKAAgSXg8HqVKlcrxIi6xy2kJ/EcffaQlS5ZQFEVRVJJX165dHT+/ElJTpkyxP2EBAEBsBKAAgCRjOqw7XcT5Wg8//LCefPJJVaxYUdmzZ3e8jbcKCQlR0aJFVadOHfXq1UuTJk3S559/rr179yoqKsq+hwAA3HinTp36V38UTJkypbWyAgAAOCMABQAkmR9//NHxQs6XMheK5oLxSufOnbPG/PDDD/Xyyy9bAesDDzygnDlzOo7hrYKDg1WkSBHVqlXr8ozRzz77THv27FFkZKR9NgAAEk/79u0dP5N8qTZt2tijAAAAJwSgAIAkVaNGDceLufiqS5cu9gi+uXDhgrZs2aKFCxdq1KhReuqpp/Tggw8qT5481hJ5p3M4VVBQkAoWLKhHHnlE3bp10+uvv65PPvlEu3bt0l9//WWfDQCAhNm6dav1Bzinz564yu1266effrJHAQAATghAAQBJ6syZMypdurTjRZ23qlu3bqKGjX/++ae2bdtm7Qs6duxYderUSdWqVVPevHkVEBDgeB+cKjAwUAUKFNBDDz2kp59+WuPGjdPSpUu1c+dOhYeH22cDAMCZ+cxISAhqws/FixfbRwMAAG8IQAEASc6EoGXKlHG8uItdiR1+xscElybANE0qTKBpgk0TcJqg0wSeTvfRqUyQagLV6tWrWwGrCVpN4GqC17CwMPtsAIBbna8hKOEnAAC+IwAFACQLJtScO3euKlSocM1FnlmibvbjXLZsmf7++2/7iKQXERFhLX03S+DNUnizJN4sjTdL5M1S+diPw1uZx2eW4psl+WZp/ujRo62l+mbJ/sWLF+2zAQBuFYcOHVLfvn2VJUuWaz4zzNdefPFFHTx40L41AACIDwEoACDZMfugzZ8/XzNmzNCiRYuszuw3G9MsyTRNMqGtaaJkmimZENc0VzKzdmJf0MZVpolT5cqVraZOprmTafJkmj2dP3/ePhsAwB+ZVQiff/653n33Xc2ZM0fLly9n1QAAANeBABQAgP9YVFSUFeqai9pJkyapZ8+eql27tooWLaqQkBDHENRbZc+eXRUrVtSTTz6pYcOGad68edq0aZP++OMP+2wAAAAAcGsjAAUAIBnxeDw6cOCAvvjiC02ZMkXPPvuste9p8eLFlTJlSscQ1FuZZZLly5dXq1atNGTIEL333nvasGGDTp8+bZ8NAAAAAPwfASgAADcJs/+p2Rdu5cqVeuutt/T888+rfv36uvvuu5U6dWrHENRbZcqUSWXLllWLFi300ksvWUsr161bp//973/22QAAAADAPxCAAgDgJ44cOaKvv/5a77zzjtUgo1GjRrr33nuVNm1axxDUW4WGhqp06dJq1qyZBgwYoJkzZ2rNmjU6fvy4fSYAAAAAuHkQgAIAcAs4duyYVq9ebTWW6tevn5o0aaL77rtP6dOndwxBvZW5fcmSJdW4cWNrnOnTp+vbb7/V0aNH7TMBAAAAQPJCAAoAwC3OzOxcu3atZs2apYEDB6p58+bWDFAzE9QpBPVWZqapmXHasGFD9enTR2+//bY1I/Xw4cPW8n0AAAAASAoEoAAAwKuTJ09q/fr11h6hZq/QJ554Qvfff78yZ87sGIJ6K7NH6V133aV69epZe5dOnTpVX331lQ4ePEg4CgAAAOCGIgAFAADXxXST//777zV37lwNHTpUrVu3trrOZ82a1TEE9Vamu73pcv/444+rd+/emjx5stUFf//+/VZXfAAAAAD4NwhAAQBAovvjjz/0ww8/aN68eRo+fLjatGmjSpUqKUeOHI4hqLcKDg7WHXfcoccee0w9e/bUxIkTtXz5cv3666+KioqyzwYAAAAA3hGAAgCA/9T58+f1008/af78+Ro5cqTatWunypUrK1euXHK5XI5BqFO53W4VLlxYNWvWVPfu3fXGG29o2bJl+uWXXxQZGWmfDQAAAMCtjgAUAAAkGxcvXtTWrVu1cOFCjR49Wh06dFDVqlWVJ0+eBIWjQUFBuv322/Xwww+ra9eueu211/Txxx/r559/VkREhH02AAAAALcCAlAAAHBTCAsL0/bt27V48WK98sor6tSpk6pXr658+fIpICDAMQh1KnPb/Pnzq0aNGurcubM11pIlS7Rjxw6Fh4fbZwMAAADgLwhAAQDATc/M6jSzO5cuXapXX31VXbp0sWZ/FihQQIGBgY5BqFOZcPS2226zZp127NhRY8aM0aJFi6xZqX/++ad9NgAAAAA3EwJQAADg1/766y/t3r1bn376qbVPaLdu3fToo4+qUKFC1lJ5pyDUqcwS/Ny5c6tKlSpq3769tX/pggULtHnzZl24cME+GwAAAIDkhgAUAADcskyzJNNR/rPPPtOECRPUo0cPq+N8kSJFrCZLTkGotzId7k2n+7Zt22rEiBH64IMPrE74586ds88GAAAAICkQgAIAADiIiorSvn37tGLFCk2ePFm9evVSnTp1VKxYMYWEhDiGoN4qW7ZsqlChglq3bq2hQ4fq/fff18aNG3X27Fn7bAAAAABuFAJQAACABPJ4PDpw4IC+/PJLvfnmm3ruuedUr1493XnnnUqVKpVjCOqtMmfOrHLlyqlly5YaPHiw3n33Xa1fv16nTp2yzwYAAADg3yAABQAASER///23fvvtN61atUpvvfWWXnjhBTVo0ED33HOP0qRJ4xiCequMGTOqTJkyat68uQYOHKjZs2fru+++04kTJ+yzAQAAAIgPASgAAMB/6MiRI/rmm280bdo09e3bV40bN1aJEiWULl06xxDUW2XIkEGlSpVS06ZN1b9/f82YMUOrV6/W77//bp8JAAAAgEEACgAAkEyY8HLNmjVWmGlCTRNumpDThJ1OIai3MmGqCVUbNWqkF1980QpbTehqwlcAAADgVkMACgAAcBMwy97N8nezDH7QoEHWsnizPN4sk3cKQb2VWYZvluObZflmeb5Zpr9y5Upr2b5Zvg8AAAD4GwJQAACAm5xpmLRhwwargZJppGQaKpnGSqbBklMI6q1MAyfTyKlu3bpWYyfT4Mk0ejINn0zjJwAAAOBmRAAKAADgx86cOaONGzfq/fff17Bhw9S6dWtVqFBB2bJlcwxBvVVISIiKFSumOnXqqFevXpo0aZI+//xz7du3T1FRUfbZAAAAgOSHABQAAOAWde7cOf3444/64IMPNGLECLVt21YPPPCAcuTI4RiCeqvg4GAVKVJEtWrVUo8ePTRhwgR99tln2rNnjyIjI+2zAQAAAEmDABQAAADXuHDhgjZv3qwFCxZo1KhRat++vapUqaLcuXPL5XI5BqFOFRQUpEKFCunRRx9Vt27d9Prrr+uTTz7R7t279ddff9lnAwAAAG4cAlAAAAAkyMWLF7V161YtWrRIY8aMUceOHVWtWjXddtttCQpHAwMDVaBAAT300EPq0qWLXn31VS1dulQ7d+5UeHi4fTYAAADg3yEABQAAQKIJCwvTjh07tGTJEr3yyivq3LmzatSoofz58ysgIMAxCHUqc9t8+fKpevXq6tSpk8aOHavFixdr+/bt1jkAAAAAXxGAAgAA4D8RERGhn3/+WR9//LFee+01de3aVY888ohuv/12azaoUxDqVGaWaZ48efTggw+qQ4cOGj16tBYuXKgtW7ZYs1MBAACAKxGAAgAAIMmZ/UB/+eUXLVu2TG+88Ya6d++umjVrqnDhwnK73Y5BqLfKlSuXKleurHbt2unll1/W/Pnz9dNPP+n8+fP22QAAAHArIQAFAABAsmY6yf/6669avny5Jk6cqJ49e+qxxx7THXfcYXWgdwpBvVX27NlVsWJFtWnTRsOHD9e8efO0adMm/fHHH/bZAAAA4G8IQAEAAHDT8ng82r9/v7744gtNnjxZvXv31uOPP67ixYsrZcqUjiGot8qaNavKly+vVq1aaciQIXrvvff0/fff68yZM/bZAAAAcDMiAAUAAIBfMuHowYMH9dVXX2nq1Kl6/vnnVa9ePd11111KlSqVYwjqrTJlyqSyZcvqiSee0EsvvaQ5c+Zo3bp1OnnypH02AAAAJFcEoAAAALjl/P333zp8+LC+/vprvf322+rTp48aNmyoe++9V2nSpHEMQb1VxowZVbp0aTVr1kwDBgzQrFmztHbtWh0/ftw+GwAAAJISASgAAAAQy9GjR/Xtt99q+vTp6tevnxo3bqySJUsqXbp0jiGot0qfPr11XJMmTaxxzHhm3GPHjtlnAgAAwI1GAAoAAAAkgJnZuWbNGs2cOdOa8WlmfpoZoBkyZHAMQb1V2rRprRmnZuapmYH6zjvvWDNSzcxUM0MVAAAAiYMAFAAAAEgk//vf/6y9Qc0eoWav0BYtWlh7h5o9RJ1CUG+VOnVqa6/S+vXrW3uXmj1MzV6mhw4dIhwFAABIIAJQAAAA4D9w+vRpbdiwweoub7rMm27zput8lixZHENQb2W625su96bbvel6P2XKFKsLvumGbxo/AQAA4GoEoAAAAEASO3v2rDZt2qR58+Zp+PDhevLJJ1WxYkVlz57dMQT1VsHBwbrjjjtUu3Zt9ezZUxMnTtTy5cu1d+9eRUVF2WcDAAC4tRCAAgAAAMnYuXPn9OOPP+rDDz/Uyy+/rHbt2umBBx5Qzpw5HUNQb+V2u1W4cGHVrFlT3bt31/jx47Vs2TL98ssvioyMtM8GAADgfwhAAQAAgJvUhQsXtGXLFi1cuFCjRo3SU089pQcffFB58uSRy+VyDEKdKigoSAULFtQjjzyirl276rXXXtPHH3+sXbt2KSIiwj4bAADAzYkAFAAAAPBDf/75p7Zt26aPPvpIY8eOVadOnVStWjXlzZtXAQEBjkGoUwUGBip//vyqUaOGOnfurHHjxmnJkiXasWOHwsPD7bMBAAAkXwSgAAAAwC3GBJc7d+7U0qVLrUDz6aef1kMPPaQCBQpYgadTEOpUJkg1gaoJVjt27KgxY8Zo0aJFVvBqAlgAAIDkgAAUAAAAwGVmybtZ+v7JJ5/o9ddfV7du3ayl8WaJvFkq7xSEOpVZgp87d25VqVLFWppvlugvWLBAmzdvtpbuAwAA/FcIQAEAAAD4xDRL2rNnj9U8yTRReuaZZ1SrVi0VKVLEarLkFIR6K9PEyTRzatu2rUaMGKEPPvjAavZkmj4BAAAkJgJQAAAAAP9aVFSU9u7dq88//1yTJk1Sr169VLt2bRUtWlQhISGOIai3ypYtmypUqKDWrVtr2LBhev/997Vx40adPXvWPhsAAIDvCEABAAAA3FAej0cHDhzQF198oSlTpujZZ59V3bp1deeddyplypSOIai3ypIli8qVK6eWLVtq8ODBevfdd7VhwwadPn3aPhsAAMDVCEABAMmKmd0zceJEde/eXe3atVOPHj00a9YshYWF2bcAAPiTv//+W4cOHdLKlSv11ltv6fnnn1f9+vV19913K3Xq1I4hqLfKmDGjypQpoxYtWmjQoEGaPXu2vvvuO504ccI+283FbAnQr18/q8GUKfPvH374wf4uAADwFQEoACBZ+PXXX9WpUyelSZPG8aLWzPjp06ePjh8/bh8BALgVHDlyRF9//bXeeecdvfjii2rUqJFKlCihtGnTOn5eeKvQ0FCVKlVKTZs2Vf/+/TVz5kytWbNGv//+u32m5OPDDz+0tgBwehymypcvr3nz5tm3BgAA8SEABQAkua1bt1oBp9NFXuwyjTaOHj1qHwkAuJUdO3ZMq1ev1owZM6zZkU2aNNF9992n9OnTO36GeKt06dJZoWrjxo3Vt29fTZs2Td98840Vvv7XTDjrdB+dygTCAAAgfgSgAIAklZDwM6YIQYGkZYKhKlWq2P/7d8w4ZjwgsZll72vXrrW2URk4cKCaN29uLY83M0GdPlu8lVmZcM8996hBgwZ64YUXrGX6q1at0m+//WYt309MCQk/Y4oQFACA+BGAAgCSjGmKUahQIccLuvjq0UcftUcB/FvUhZM6dvSoFfpfW8d0+qrtcT26eOqYw+3sOnZcZyPsm14nM9vOhJbm/ZsYzDhmPDOu78J05vc4HmdcdeyULibOXcdN7OTJk1q/fr3VQOmll17SE088ofvvv1+ZM2d2/MzxVqlSpbIaOdWrV0/PPfec3nzzTX355ZdWw6eEvkc+++wzx3P4Uh9//LE9CgAAcEIACgBIMp988onjhZwv5XK59Msvv9gjAf7KoyPfTNfYl7rqofwhcsW8B1xByla6hfqMnKzle6Ps20bznNC6d8dp6DO1VCiV65/3TEB6Fa3TXUPGvat1J64//TOz6dxutyIjI+2vJA4znhnXjO+LqJ3DVdb9z3OROlMu5bu9kArlzawQl/m6S6mzFbD+wFKwwG3Knj5YAdbXUyjwto5aTk81xMF0k//+++81d+5cDR06VK1bt7b23MyaNes/7ykfynS3L1asmOrUqaNevXpp8uTJWrFihfbt26eoqCvet7aaNWs6juNLPfzww/YoAADACQEoACDJmFmcThdyvpbpEA/cGjz6fXINBVuvfZfSlB+uzXGGeGc1o06qS4Gpy607uq7QqUSY9RgSEqKlS5fa/0tcZlwzfvw8OjKphlK5c+nBZ6Zq5Z4ziomSzsxtpNCA6McceJs6rbjiCfKc187pTZQ3MFC523+ii/aXgYT6448/rC7sH3zwgYYPH642bdqoUqVKypEjxzWfUXFVcHCwtZ3LY489Zn2WmY71TrfztcwfBXfv3m3fSwAAEBsBKAAgSfz111/WBZvThZyvdfvtt9ujAf4uSjuHl5XbvPYDMqvx+6fsr3vhOaDXqgRb7xNX6qp6Y/+1s80SavTo0dYS4RvJjG/OE7czeq9xEdWZsktXr+a/qKVtcyog+jEHZGmh+efsL8eI+EbPFM6tJxeft78AJK7z58/rp59+0vz58zVy5Ei1b99elStXVq5cuf71550vNW7cOPueAACA2AhAAQBJ4vjx444XcAmpDBky2KMB/u6kZtZNb83oDAhtpPdO21/25vx8Nc8cEP0+cSmkymvanwizP00jmMGDB9v/uzHM+OY8cbr4qbo1HqufY2e6EV+r++2B1mNOV2e6TthfvixitZ6t0FoLYgejwH/g4sWLVtO/hQsXWiF/hw4dVLVqVd12222JFo6aLvgAAMAZASgAIEn873//c7yAS0hlypTJHg3wc+cXqmXWS4Fmusfe0e/xBJphyzsqT6B5n7hVeuj2y0vEr5eZWWbec2aG241kxjfniWsmW8TaQeo29ZBiPwWRm/rrbrMvqCtEVV8/cM33dWaO2refpzP2f4HkIiwsTF26dLFe+/+mTKd7AADgjAAUAJAkTAMIs9+f00Wcr1W8eHF7NMC/ha3opNtMoOlKrRqTDl8b7l0lQqt7FVaQeZ+471Lf7/99w6LQ0FCVKFHC/t+NZc5jzudVZLjCr0l0o7R7VHkFm0ZH7tIaut0h8vVEKCw8EabCAjeA6R7v9DmXkJo0aZI9GgAAiI0AFACQZFq2bOl4EedrDRs2zB4J8GcRWtO7iBVoulJW0av74pnPGfmjBtzjtt4jQYV66JurN8pMMLNs1yzRHTJkiP0VLyJOac+6jzXztXFasNMhdI3cr2XjBmrYnE06E0cOac5jzmfO6zPPYU2qcanpU1DR5/Xdv3zMwH/txIkT/+qPgqap0u+//26PBgAAYiMABQAkmfXr1zteyPlS5mLP7CMKJGcRJ3Zo5cJZemvCG5r41mwtXLlNx8Ptb/oqcosGlTSBpkvuciO1K578M+rnl3W/2+wpGKjcTy1TnM3ifWD25TTvuQULFthfuZrn4Pvq8kBR5UgdeKnrvDlv+090wf5+jLAlbZTN6tCeR08ti/3df5jzmPMlaL/RU7NVP8Olx3xbx+X/+jEDSaFVq1bWa/96qkWLFvYoAADACQEoACBJVapUyfFiLr5q166dPQKQ/EQeXK6Xm9+nrFYQeeVr1yV3prvVYNAi7bpo3zgeUb+OUcVgM06QCraZrq9Xr9bqOOrjF8srxCwFD8iqlgv//Z6dMQGoV+e3aMm06Zo2YYDqF7FnYRZ85pqZp5FbRqhcGvM43Ko45lf7q87M+RISgJ7/qNWlcDUgi1pc0/4duDn88MMPCgw0jbyu/J0Rf5ljvv/+e3sUAADghAAUAJCkzLK/u+66y/Gizls99NBDVtMIIDk6v/FV1crjtmdDeilXoLJUfFHLj8W3J6VHRyY/rNRWoJlZRR+oanWO9l4VVSTUNEtKIVdoA805ZQ/zL+TIkcMazxdnP2iqzAFmqf5jmnZNp3qPTm+bozZFs6jJvLhDSnM+c17fhOvLLvkUaB5zujqafk37d+Dm8f777ycoBDW3fffdd+2jAQCANwSgAIAkl5AQlPATyZnn5MfqUMiEny65s9yph1p2U9+XBmvgcx1Uv2yeS0Hm5ddzgEKrjNbmOJfEn9Ls+hkuz6r8Or69LS8s1pPZL3WLT1vzLcWbr/rA7MdpyhfWbFXTid1bI6Lzn6lTqWaae9L+vxcJOaci1qtP8SDrMYc8+LoO0OcINzlfQ1DCTwAAfEcACgBIFi5evGh1wb377rsdL/TMUvl58+YpMvLfd7QGbowIbeh7t9wBGVW267vads0kxwv6+f2nVTL9pRmaVrky6KGJe+V1W8/zC9Uyq7l9oHK1+0TxrZoPX9lNBaxu8SlV9fUD8XSL902CwsiL89Q4vUspAguo28rYyW6kdoyupvL91iu+bVATcs6oHcNVxoSuKdwqPXS79+cSuIn8/PPP6tq1q9KmTfvP7wu7zNe6dOminTt32rcGAADxIQAFACQ7a9as0fTp0zV+/HjNnDlTW7Zssb8DJGMXl6tj3vQq1fdbnbW/dC2Pfl/SXoUu7w3qkrvscO30ktqFreik20ygGZBRTeZ5H/WSSH3f9y65o8d1ue/Xyz8nThQYE7r4JHyluhUItILdph9cHddGHXhb9ct21qfXLI2/lu/n9OjgG1WV0sysDSqq52j/Dj/zxx9/aP78+ZoyZYomT55s/dt8DQAAJAwBKAAAQCKIWN1Ld5bqrw3xTW/0HNOs+pkUYId8rjT1NcdxS8wIreldREHmNmkf09u/xzOfM2qXXi53ae9R970D9VMiTZZOUAAatV1DS5uO9cGqPvHoPzNQPUc0t0V5tV98wqdZqb6f84SmP57OesyBt3XUcnbHAAAAgAMCUAAAgERwemFvdX3viE8B3+k59ZU+Zj/Q4Bqa7BRuRm7RoJImTDR7W76m/fEM7Dk8UdVTXeoWX6T3Gl09FzJcJ3Z8rQ8nD1GPnpO14fLkzLP6ccbzerLtEH16xPkECVoCr5Oa+mhI9H1wq+SgzbqUwXp0ZF5rVe6wRCd8eXKi+XzOc/PVIovZIiBAmZvPF/3fAQAA4IQAFAAA4D8Wsf4FFQuyZ4Cmb6z3L9jfuILVUCjYBJq+7W15anZ9ZTChamBedf7i6mmonuOL1bf+I7o/XxoFuNKq2htm39HzWj/8AWUMiD7GYcl6jIQFoGH6qFVmBaQIVN7OX1h7fUYdmKmmD3bTZ6d8TD+j+XrOsM86KI+152la1X7nuE/hMwAAAG49BKAAAAD/scjv++ouq3FPCrlLD9W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| |
| "text/plain": "<IPython.core.display.Image object>" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Reflexion about robustness/efficiency trade-off" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*An approximation to the ideal would have the property that if the signal is altered in a reasonable way\nby the noise, the original can still be recovered. In other words the alteration will not in general bring it\ncloser to another reasonable signal than the original. This is accomplished at the cost of a certain amount of\nredundancy in the coding. The redundancy must be introduced in the proper way to combat the particular\nnoise structure involved. However, any redundancy in the source will usually help if it is utilized at the\nreceiving point. In particular, if the source already has a certain redundancy and no attempt is made to\neliminate it in matching to the channel, this redundancy will help combat noise. For example, in a noiseless\ntelegraph channel one could save about 50% in time by proper encoding of the messages. This is not done\nand most of the redundancy of English remains in the channel symbols. This has the advantage, however,\nof allowing considerable noise in the channel. A sizable fraction of the letters can be received incorrectly\nand still reconstructed by the context. In fact this is probably not a bad approximation to the ideal in many\ncases, since the statistical structure of English is rather involved and the reasonable English sequences are\nnot too far (in the sense required for the theorem) from a random selection.*" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Generalization of the first noise example" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Generic case:\n- all $x$ input symbols have the same output probability values ($p_i$)\n- all $y$ output symbols have the same input probabilities values ($q_i$)\n\n$$C = \\max(H(x)-H_y(x)) = \\log(x) + \\sum(q_i\\log(q_i))$$\n\n$$C = \\max(H(y)-H_x(y)) = \\log(y) + \\sum(p_i\\log(p_i))$$\n\n" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.000332Z", | |
| "end_time": "2021-02-24T14:33:17.005391Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "def C(y, p):\n return np.log2(y)+np.sum( p*np.log2(p) )", | |
| "execution_count": 32, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Quizz" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.007335Z", | |
| "end_time": "2021-02-24T14:33:17.014343Z" | |
| }, | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Image('4X4.PNG')", | |
| "execution_count": 33, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 33, | |
| "data": { | |
| "image/png": 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mnRN7TtfUqVPNLBLZtGkTzU/hCEIXEEKUH73lRuiybuEjYTlVQ9RsDBkyxN5muWcgEtuxY0eX5qf33XefWQJkjtAFhFiq8uPo0aN1jynKj7lxI3SNGTNGr2/u3LlmxjmLFy+2t1dOBkdi8c1Pv/71r5slQHYIXUBEpCo/XnLJJerxxx+n/JgFp0PXhg0bVL9+/fT6tm7damadsXPnTh20rO2VIznoTtp10PwUTiN0ARGUqvw4c+ZMyo8ZcDp0NTU16XVNmDBBH610Uk1Njb2t6fT+iiJpfnrhhRfa3yean8IphC4gwig/OsPJ0LVnzx79fZd1yU2qnSRHOq3tlGCNxKZPn25/n2h+CicRugBolB+z52Tosu6fOGjQILVt2zYzm7v58+fb2zhjxgwzi3h33HGH/X064YQTaH4KRxG6AHRD+TEzToYuObol66moqDAzubN6cg0ePFgfxUFi0vzU+jlK89Pf/va3ZgngDEIXgB5RfkyPU6FLvt9yHpesR87rcsKiRYv0+uTI2ZYtW8ws4sU2P+3fv7/69a9/bZYAziF0AUgL5ceeORW65EpFWYdcuShXMOZKOtnL+uSG1ps3bzaziBff/PSxxx4zSwBnEboAZCxZ+fHoo4+OXPnRqdAlPblkHdKjK1fLli3T65IwIaECiUnLDPmdtX5+ND+FmwhdALJG+fF9ToQu6Tov3edlHdKNPhctLS16PYWFhfrEfCT25ptvqpKSEvtnR/NTuI3QBcARUn78zne+o04++WT7TcwaYS8/OhG65P6K1jrkvovZamtr0+uQEuX69evNLOLFNz+trq42SwD3ELoAOE7KWddee62+Asx6U7OGVX50utO6l1atWqWvMpSvQz5WVVXZX9+wYcO6LJOP6bDOvyotLTUzmZOTwa3tkEAhnz/dESU0P0W+ELoAuObAgQNqxYoVatKkSUnLj3KPuyCZPXu23v5evXp1+5qsYS2Tj+mQIy3y+NraWjOTufr6+i7bkMmIkvjmp++++65ZAriL0AXAE2EqPzoduqQBZ0FBgX68lAezRehKjeanyCdCFwDPhb38mCm5B6KEMzmpW841gjusEq4Mmp8iHwhdAPImrOXHTMj3oLKyUoeuxsZGMwunycUJND9FvhG6APhCVK9+lHYa8jVKe4f29nYzCyfJkdXDDz9cf59pfop8InQB8J1U5Ue52i4s5ceGhgb9dRUXF5sZOInmp/ATQhcA30pVfpQrz773ve8FtvwoDVGtdhN1dXVmFk6Jb37K9xj5RugCEAjJyo99+/ZVF198sfrpT38aqPJjZ2en3n4516i1tdXMwgk0P4UfEboABE5Yyo/Nzc16m4uKiswMnCDB+4ILLrB/J+RCBZqfwg8IXQACK+jlRwmHsp01NTVmBk6YNm2a/TsgV8DS/BR+QegCEApBLD/KtkmriKamJjODXN1+++32z12an8rvBeAXhC4AoROU8mN5eXnWN8hGdzQ/hd8RugCEVtivfsS/0PwUQUDoAhAJ6ZYfOeE6eJ577rkuzU/l5wj4EaELQOREqflq2NH8FEFC6AIQWVJ+lP5Y0l7AKk3FDsqP/kbzUwQNoQsA/umNN95Q99xzjzrllFO6BC8ZlB/9R5qfnnXWWfbP6IorrjBLAP8idAFAnOeff17NmDEjaflxy5Yt5tHwGs1PEVSELgDoAeVHf7r66qvtnwHNTxEkhC4ASEOq8qP023rsscc44uIymp8iyAhdAJAhq/w4ePDgLuFLxlFHHUX50SUPPvig/X2W7/2rr75qlgDBQOgCgCxRfvTOk08+aTe4lean69evN0uA4CB0AYADKD+6h+anCAtCFwA4LFX58YYbbqD8mKbXXntNf8+s79/9999vlgDBQ+gCAJekKj+edtppav78+brJJ7qT78uJJ55of7++8Y1vmCVAMBG6AMADlB8zQ/NThBGhCwA8RvkxOZqfIqwIXQCQJ5QfE6P5KcKK0AUAPkD58X3f/OY37a/7ox/9KM1PESqELgDwmaiWH2l+irAjdAGAT0Wp/EjzU0QBoQsAAiDM5cf45qePP/64WQKEC6ELAAJm8+bN6rrrrktafnzxxRfNo/2N5qeIEkIXEHFyhKS8vNz8D0Ei5ce2tjZ14YUXBrL8SPNTRA2hC4iwpqYm1atXL/2Gh2D785//rL773e+qkSNH2iHGGn4sP0rz0zPPPNPexi9/+ctmCRBe7GmBCKupqdFveDfeeKOZQRj4vfwY3/z03HPPpfkpIoHQBfhcXV2dPkrhhqKiIv2m19zcbGZSmzNnjv1maY3x48er9vZ28wj4Rary46mnnqoaGho8Lz9OnTrV3gaanyJKCF2AT61YsUINHz5c9e7d25XQJa0IrDfizs5OM9uztWvXJnzjtoZcdVZRUWEeDb9JVX6cPHmyevTRR10/4kTzU0QZoQvwiXnz5ukxduxY3afI6lkkw43QJUfQZN1VVVXq4MGDZjaxdevW6Tdma3ukHGmNsrIye17GxIkTzbPgV8nKj//+7/+urr/+elfKjzQ/RdQRugCfsE5otz7GDjdCV3FxsV63lJdSkRsOW9si5apY+/bt03PWchly1AT+52X5cdWqVTQ/ReQRugCfsMLWuHHj1LRp09SCBQvsNz+nQ5ecf1VYWKjX3dHRYWYT27hxo70dLS0tZrY7WWY9ToY8D8HhZvnx2Wefpfkp8E+ELsAndu3apYdcSi+kS7f1pud06GpsbNQhT45gydGOZCZNmqS3YdSoUWamZ/IYa5vr6+vNLILGyfJjfPNTaVMCRBWhC/Apt0KXhLqSkhIdumbNmmVme2Yd+UgnRMljrG0eOHCgmUVQ5Vp+lKNnsc1Pb731VrMEiCZCF+BTboUu6/yrgoICtXv3bjPbMyk/yuNTlSHF8uXL7W2WgfDItPxI81OgO/aKgE+5Fbpqa2v1Oqurq81MagsXLjT/Ss3aZhkIp1Tlx2uvvVZ95CMfsedofgq8j70i4FNuha7S0lK9ziVLlpgZ50g4s7ZZBsItVfnRGr///e/NM4BoY68I+JQboWv16tX2Ordv325mnRN7Tpd0HUd0SPlRzu+yfv6xw8vmq4CfEboAn3IjdFm38JkyZUrKhqjZGDJkiL3NS5cuNbOIigceeMD++fc03Gy+CvgdoQvwKTdC15gxY/T65s6da2acs3jxYnt7hw4damYRFbHNT6UH3IYNG3x770cgXwhdgE85HbrkTbBfv356fVu3bjWzzti5c6cOWtb27tixwyxBFKTT/NQqP0rQsn5PrEH5EVFB6AJ8yunQJU0pZV0TJkxQ+/fvN7POqKmpsbc1nd5fCI9smp++8MILusQopUbredaQObkyUh4DhA2hC/ApJ0PXnj171OjRo/W65CbVTpKbdFvbOXPmTDOLKMi1+akc1ZKjW3KUK1H5UXqCUX5EmBC6AJ9yMnRZ908cNGiQ2rZtm5nN3fz58+1tnDFjhplFFMQ3P73yyivNkuxQfkQUELoAn3IydMnRLVlPRUWFmcmd1ZNLGmROnz7dzCIK/vGPf9j35JRx3nnnORqGKD8irAhdgE85Fbrk/C05j0vW49TNhhctWqTXJ0fOtmzZYmYRFVdddZX9uynNdt99912zxFnplB/l1kRylAwIAkIX4FNOhS65UlHWIVcuyhWMuZJO9rI+uaG13A4G0WL1epPx0Y9+VL3xxhtmibuSlR8lkElbCmlPQfkRfkboAnzKqdAlPblkHdKjK1fLli3T6xowYIDatGmTmUVUxDY/lTKfG3c1SAflRwQVoQvwKSdCl3Sdl+7zsg45QpGLlpYWvR5pfCkn5iNaEjU/zTfKjwgaQhfgU06ELjkSYa1D7ruYLSnbyDqkRLl+/Xozi6iQ5qcStOR3QILXypUrzRL/oPyIICB0AT4hRxLkKkPpdSUfq6qq7DeNYcOGdVmWbj8s6/wrOdk5W2vWrLG3o6ysTH/+dAeC73e/+12X5qdyEYXfUX6EXxG6AJ+YPXu2flPo1atXtzcKa1jL5GM6qqur9eNra2vNTObq6+u7bEMmA8EmR48k8Fs/T/ldCBLKj/Ab9oqATzgdunbv3q0KCgr046Wski1CVzT97W9/U2eccYb9s8y1+Wm+UX6EH7BXBEJK7oEo4aykpER3DwfSJc1Pzz//fDuUSPNTmQsLyo/IF0IXEEIHDhxQlZWVOnQ1NjaaWSA9sc1PTz/9dH3UK4zkqNZjjz2mL1SRWw3Fhi8ZlB/hNEIXEEIdHR36TUOuOGtvbzezQGq33XabHTqKi4s9a36ab3JTbbmXKOVHuInQBYSQnLtivWkC6Vq8eLEdNKTMlq/mp/lG+RFuIXQBISMNUa12E3V1dWYWSM6PzU/zjfIjnEboAkKms7NTvyFISaS1tdXMAj2TOwz4vflpvlnlx9NOO61L8LJeaxdccIF+vcn5lEBPCF1AyDQ3N+s3gqKiIjMD9Eyan8aW0YLQ/DTfXnzxRXXDDTd0aRprjcGDB6sZM2ZwM3gkROiC415++WXdxfynP/2pevrpp9W7775rlsAL0gledv41NTVmBkgs6M1P8y1V+fGUU05R99xzT84XI+zbt0/96le/Uo8//rh68skndehDMBG64Ij9+/erH/7wh/ry8vgdz8CBA/WJp6+++qp5NNwk33NpFdHU1GRmgO7im58S0nPjRvnxD3/4g/rqV7+qjjzyyG7rlEB3//33h7adR1gRupCznTt36qvk4ncK8UOCwLx588yz4Jby8vKsb5CNaAh789N8c6L8+MADD6hDDjmk2/Pjx7HHHqu2bdtmngW/I3QhJxK4TjjhhIQ7g54GwQvIr6g0P823bMuPErh69+7d7fE9jaOPPprgFRCELmRNSorpHOFKNB566CGzFgBeimrz03xLt/woV45mErisccwxx6g9e/aYzwa/InQhaz/60Y8SvvjTGfIXHgBv0fzUH5KVHyWAxc+lO6QpMvyN0IWsnXnmmQlf+OmOX/7yl2ZNANz2xBNPdGl+Kr25kF+pyo+ZDrm5vTRHhn8RupCVV155JeGLPpPx+c9/Xr399tsMBsPl8dRTT3V57f34xz9O+DhG/oYcdfzUpz7V5eeUzZDWEvAvQhey8rOf/SzhC57BYDAY+RsPP/yw2UvDjwhdyIqUKhK94BkMBoORv7FkyRKzl4YfEbqQlXXr1iV8wWcyhg4dqm699VYGg+HCuOmmm7q95hI9juGfceqpp3b7mWU65Bwx+BehC1nZu3evGjRoUMIXfbpDGv/JCaSyk5ATSgE4QxqdTpw40X6tyb9pfup/cq5d7D4y01FQUKDeeustszb4EaELWUv0l3S2Qy6dlkuot2zZYtYOIFtySx/rtUXz0+CQWwRJo9PYfWMm44orrjBrgl8RupC1HTt2ZNXET0ZlZaW68MILE/akkeaB0kRQmgkCyMx//dd/2a8luZk1zU+DRcqMsfvDTMamTZvMWuBXhC7kZMGCBQlf/MnGyJEj7UPgf/7zn9V3v/tdPRf/OOlbQ/kRSN8PfvAD+/UjzU9/97vfmSUIinfffVeNGTOmy74wnSFhG/5H6ELOMglesYErntwA9rrrrtM3hI1/nlV+lE7OALqj+Wl4SPD69Kc/3W0/2NOor683z4TfEbrgiEceeUSNGjUq4Q5BxhFHHKGuueaatE7ylPMa2traeiw/yhU+crsLyo/A+yRgSdCS14cELwlgCDYJXjfffHPSC5ZGjBihHnzwQfMMBAGhC4565pln1NSpU9V5552nzj77bHXJJZeoxsZG9c4775hHZCZV+XHy5Mnq0UcfpfyIyJJO5lJKtF4XUmJEeMiV4vIznTJlipowYYI+H1ZOmP/FL35hHoEgIXQhMJKVH+VN5/rrr6f8iEiRk+SLi4vt1wHn9QD+RuhC4FB+BJRuAyHtIKzf+6uuusosAeBXhC4EGuVHRBHNT4FgInQhNCg/Iipim5+eccYZND8FAoLQhdCh/Igwo/kpEFyELoQa5UeECc1PgWAjdCEyKD8iyGh+CgQfoQuRQ/kRQUPzUyAcCF2INCk/SsCSoBUfvig/wg/im58uXrzYLAEQNIQuwHjhhRd0iTH2Dc4alB+RD/HNT2+77TazBEAQEbqAOHJUS45uyVEuyo/IF5qfAuFD6AKSoPyIfJBGp3L/Uut37fzzz6f5KRAChC4gTZQf4ZUrr7zS/t2i+SkQHoQuIEOUH+Gm+vp6+3dJmp/K0VYA4UDoAnJA+RFOWrRokf37c9RRR9H8FAgZQhfgkFTlR2nMKo8BElm5cqXd/PTwww9Xzz77rFkCICwIXYDDUpUf5ZZEcmsiykawbNiwoUvz01WrVpklAMKE0AW4KFn5UQKZdMWX7viUH6NLmp/G3pqK5qdAeBG6AI9QfkQ8mp8C0ULoAjxG+RGC5qdA9BC6gDyi/BhNND8FoonQBfgE5cfooPkpEE2ELsBn5KjWY489pi666CLd6ys2fMmg/BhsND8FoovQBfiYdLWfP38+5ceQoPkpEG2ELiAgKD8GG81PARC6gICh/Bg8ND8FIAhdQIBZ5cfTTjutW/ii/OgPr776apfmpw888IBZAiBqCF1ASLz44ovqhhtu0OcKxYYvGZQf80Oan370ox+1fw5z5swxSwBEEaELCBnKj/7w7rvvqtLSUvv7PnXqVLMEQFQRuoAQS1V+vOCCC1Rra6s6cOCAeQacIMH33HPPtb/XkyZNovkpAEIXEBXJyo9yztGMGTPU5s2bzaORiy9/+cv29/bMM8+k+SkAjdAFREyq8uMpp5yi7rnnHn0+EjJ366232t/LE088kTIuABuhC4gwyo/Oampqsr9/ckTxtddeM0sAgNAFwKD8mJvHH3+c5qcAkiJ0AeiC8mPm1q9fr/r376+/PzQ/BdATQheAHlF+TI3mpwDSRegCQk6OWJWXl5v/ZY/yY3evv/46zU8BpI3QBYSYnNjdq1cvHQicQvnxfTQ/BZApQhcQYjU1NToQ3HjjjWbGWVEtP9L8FEA2CF1AHtXV1ekjRm4pKirSoaC5udnMJCflMStIWGP8+PGqvb3dPKJnW7Zs0eEuCuXH+Oane/fuNUsAoGeELiAPVqxYoYYPH6569+7tWuiSI0xytEmCQWdnp5lNbO3atfZjE41DDjlEVVRUmEcnJ0eBfvrTn6qLL744lOVHmp8CyBahC/DAvHnz9Bg7dqxuLWD1c5LhVuiSo2iy/qqqKnXw4EEz2926deu6hCM5WmWNsrIye17GxIkTzbPS89Zbb6nvfe97atSoUV3WIyOI5UeanwLIBaEL8IB1Mrv1MXa4FbqKi4v1+hsaGsxMYpWVlfa2tLW1mdn37du3T89Zy2VMnjzZLM1MOuXH559/3jzaf6T5qRzxk+2V5qfPPfecWQIA6SF0AR6wwta4cePUtGnT1IIFC+zA4UboknOwCgsL9fo7OjrMbHcbN260t6OlpcXMdifLrMfJkOdlK4jlx/jmp08++aRZAgDpI3QBHti1a5ce1gnXcpTEChluhK7GxkYd9OQoVrLSnVx1J9sg5b9UYkuE9fX1ZjY3QSg/xjc/ffDBB80SAMgMoQvIAzdDlwS7kpISHbpmzZplZhMbOXKk3oZ0QpQ8xtrmgQMHmlnn+LH8GN/89Jvf/KZZAgCZI3QBeeBm6LLOwSooKFC7d+82s4lJ6VEem6wEaVm+fLm9zTLckk758Tvf+Y7r5cf45qdXX321WQIA2SF0AXngZuiqra3V662urjYzyS1cuND8KzVrm2V4IVX5Ucqj0n7D6fIjzU8BuIHQBeSBm6HLOjqzZMkSM+MMCWfWNsvwWrLy45FHHqmuvfZatWnTJvPo3FxxxRX2uml+CsAphC4gD9wKXatXr7bXu337djPrjNhzuvJ5n0G3y4/f+MY37HVJ81O51REAOIHQBeSBW6HLuo3PlClTkjZEzcaQIUPsbV66dKmZzS+ny4/333+//XyanwJwGqELyAO3QteYMWP0OufOnWtmnLF48WJ7e4cOHWpm/cUqPx599NH2tlojnfIjzU8BuI3QBeSBG6Frw4YNql+/fnqdW7duNbO527lzpw5a1vbu2LHDLPGnbMqPND8F4AVCF5AHboQu676AEyZMUPv37zezuaupqbG3NVXfL79Jp/woRwU/8IEP2PM0PwXgFkIXkAdOh649e/ao0aNH6/VJic0pcpNuaztnzpxpZoMpWfnRGnJ0DADcQugC8sDp0GXdQ3HQoEFq27ZtZjY38+fPt7dRusGHhVV+POecc+yvL3Z41XwVQPQQuoA8cDp0yREcWVdFRYWZyY3Vk0tuvzN9+nQzGx7xzU8TDTebrwKIJkIXkAdOhi45f0vO45J1yXlduVq0aJFelxw1k5JcGMU2Pz3rrLN081O5+EBKqNle/QgAqRC6gDxwMnRJWJD1yJWLcgVjLqSLvaxLbmi9efNmMxsuqZqfyu1+pH3EJZdcktd7PwIIH0IXkAdOhi65+k7WIz26crFs2TK9ngEDBoT2iE5s81M5opWq+alc/bhgwQL7IoXYQfkRQKYIXUAeOBW6pOu8dJ+X9Ug3+my1tLTodRQWFuqT8sNITp7PpflpqvLjNddck/E6AUQLoQvIA6dCl9xf0VqP3HcxG21tbfr5Up6UJqFhFNv8VI5Q5dL8NLb8eNhhh9nff2ucfPLJlB8BJEToAjywatUqfYWhHCmRj1VVVfab9LBhw7osy6QflnUOVmlpqZnJzJo1a+ztKCsr058/3REUv/3tb/VVmNbX6WTzU8qPADJB6AI8MHv2bP1G3KtXr25vztawlsnHdFVXV+vn1NbWmpnM1NfXd9mGTEYQvP766+qEE06wt/mb3/ymWeI8yo8AUiF0AR5wI3Tt3r1bFRQU6OdIiTAbYQ5d7777bpcjUNOmTTNL3JVO+VE6/UsgBBAthC4goOQ+iBLQSkpKdJ8p/Is0P62srLSDzgUXXKDee+89s9Q7ycqPcmPt888/Xy1fvpzyIxARhC4ggORNWkKFhK7GxkYzC4tVdpVhNT/NN8qPAAhdQAB1dHToN2tp8dDe3m5mIerq6uwwI0cB45uf5hvlRyC6CF1AADU0NOg36OLiYjMDcd9999nhRY4o7dixwyzxJ8qPQLQQuoCAkYaoVssJOaqD98U2Pw1iV33Kj0D4EbqAgOns7NRvxNIHqrW11cxG269//esuzU+zbRTrB5QfgfAidAEB09zcrN98i4qKzEy0SfNTORJkhRJpGBsWlB+BcCF0AQEj3eDlTbempsbMRFd889Pbb7/dLAkfyo9A8BG6gICRN1lpFdHU1GRmoilfzU/zTcqPK1eu1Dc6p/wIBAuhCwiY8vLynG6SHQbxzU8vvPDCvDQ/zTdpHSJ92uTem7HBSwblR8B/CF0AAsePzU/z7aWXXlI33XSTOuaYY7qELxmUHwF/IHQBCBS/Nz/NN8qPgH8RugAERtCan+ZbqvLjxIkT1SOPPKL2799vngHATYQuAIHw2GOPBbr5ab4lKz9+6EMfUrW1terZZ581jwbgBkIX4CNygrycKI+u4pufrlmzxixBplKVH0866SR19913q927d5tnAHAKoQvwCWkBIa0g5I0P/xLm5qf5RvkR8BZ7d8AnpNmpvNlJ81O8T462RKX5ab5RfgTcR+gC0iRXzbnZH0tu6yNvcHKbn3TMmTOn25vj+PHjVXt7u3lEsL3zzjtq1KhR9tc2ffp0swRuovwIuIfQBaSwYsUKNXz4cNW7d2/XQpfcuFrOVZI3NbmhdTJr1661H5toyMnmFRUV5tHBJM1PzznnHPtrimrz03yj/Ag4i9AFxJEeRjLGjh2rT96WNxfrjcat0GX1nqqqqlIHDx40s92tW7dO9e3b194eKUVao6yszJ6XIW+IQfWlL33J/jrk66L5af5RfgRyR+gC4lgns1sfY4dboau4uFivv6GhwcwkFnvrm7a2NjP7vn379uk5a7mMyZMnm6XB8fWvf93e/o997GPqrbfeMkvgB5QfgewRuoA4VtgaN26cvonyggUL7DcUN0KXnINVWFio1y/lnJ5s3LjR3o6WlhYz250ssx4nQ54XFDQ/DRbKj0BmCF1AnF27dulhlbTkfnXWG4kboUvetCToyVGsZDcmnjRpkt4GObk8ldgT0Ovr682sv9H8NNhefvlldfPNN1N+BJIgdAEpuBm6JNjJ/QMldM2aNcvMJjZy5Ei9DemEKHmMtc0DBw40s/71zDPP0Pw0JKT8+MQTT6hLL72U8iMQh9AFpOBm6LLOwSooKEj5JiSlHHlsshKkZfny5fY2y/Cz+OanP/zhD80SBB3lR6ArQheQgpuhS0oust7q6mozk9zChQvNv1KztlmGX8U3P73jjjvMEoQN5UeA0AWk5Gboso4AOH1rGwln1jbL8COan0ZTqvLjiBEj1F133UX5EaFE6AJScCt0rV692l7v9u3bzawzYs/pmjp1qpn1D5qfQkj58fvf/746/fTT7d8Fa0j58bzzzqP8iFAhdAEpuBW6rNv4SL+jZA1RszFkyBB7m5cuXWpm/YPmp4hnlR+PPfZY+3fDGpQfERaELiAFt0LXmDFj9Drnzp1rZpyxePFie3uHDh1qZv2D5qdIhvIjwozQBaTgRujasGGD6tevn17n1q1bzWzudu7cqYOWtb1+ay5677332tsmJ1T//ve/N0uA7tIpP0ozYMqPCApCF5CCG6GrqalJr2/ChAmOvmHU1NTY25qq75fXHn300S7NT59//nmzBEgtWflx0KBB6itf+Uqg7r6AaCJ0ASk4Hbr27NmjRo8erdcnN6p2ityk29rOmTNnmll/oPkpnEL5EUFG6AJScDp0WfdQlL/Ot23bZmZzM3/+fHsbZ8yYYWb94ZVXXqH5KVxB+RFBQ+gCUnA6dMnRLVlXRUWFmcmN1ZNr8ODBvut1JUcbYs8xo/kp3EL5EUFA6AJScDJ0yV/cch6XrEvO68rVokWL7DeVLVu2mFl/iG9+Km96gNsoP8LPCF1ACk6GLrlSUdYjVy7KFYy5kC72si65ofXmzZvNrD9I81M5kmd93yZPnkzzU3iO8iP8htAFpOBk6JKeXLIe6dGVi2XLlun1yFWAmzZtMrP+8cUvftH+nn3yk59UnZ2dZgmQH5Qf4QeELiAFp0KXdJ2X7vOyHulGny35y1zWUVhY6Ms3idmzZ9vfL5qfwm/SLT/u2rXLPANwDqELSMGp0CX3V7TWI/ddzEZbW5t+vpQn169fb2b9g+anCJK3335bX4hyxhln2L+31qD8CDcQuoA4q1at0lcYSq8r+VhVVWXviIcNG9ZlWSb9sKxzsEpLS81MZqS3lbUdcr9C+fzpDi/Q/BRB9pvf/EbdcsstlB/hKkIXEMcqj/Xq1avbztca1jL5mK7q6mr9HLlxbzbq6+u7bEMmw23S/LSgoEB/Lml++tRTT5klQLBQfoSbCF1AHDdCl1yeboUSKRFmw6+hS5qffuhDH9KfR74fS5cuNUuAYKP8CKcRugAPyH0QJZCUlJSovXv3mtngi29+euedd5olQLikKj9KY+Jc28Ag/AhdgMsOHDigKisrdehqbGw0s8EnzU9PO+00+42H5qeIAik/ynmfl112mb6gJTZ8yfjEJz6hW8NQfkQihC44ThoSvvTSS7p/1GuvvRb5ppjy/ZCdsbR4aG9vN7PBRvNTIHn5US4qOffcc9VPfvITtW/fPvOM7MmVwHJxitx54s9//rOZRdAQuuCYn//85/rN17qCzRonnHCCuvvuu3X4iKKGhgb9fSguLjYzwUfzU6ArN8qPcjR5wYIF6uMf/3iX9clRczl6Lif8S/8/BAehCzmT5pdnnXVWl51CotG/f3/dST1KZIdotZyoq6szs8FG81OgZ06VHyVQHXHEEd2eHz9OPvlk9ac//ck8C35H6EJO5A331FNPTbgzSDTkKFiUgpccAZKvW9ootLa2mtngklKK9bOk+SmQXLblRwlcidpV9DROPPFEgldAELqQNfmLbtSoUQl3AsmG7GxkpxIFzc3N+msuKioyM8EV3/zUbzfZBvws3fKj9LzLJHBZQ4JXmK6MDitCF7ImR24SvfjTGVKOjALpBi9fb01NjZkJJpqfAs5IVX48/PDDu82lOxYtWmQ+C/yK0IWsnX322Qlf+OkOuadh2MnXKSe9NjU1mZngofkp4I5k5cdshpzqAX8jdCEr0goi0Ys+kzFt2jSztvAqLy/P6SbZ+UbzU8AbUn5M54KkVOPZZ581a4QfEbqQFWkPkegFn8no3bu3vqKR4c+R6GeW6HEMBsOZEd9uJ5shJ+bDvwhdyMrKlSsTvuAZDAaDkb+xZMkSs5eGHxG6kJW1a9cmfMFnMo477jh15ZVXMnw44n9Wl19+ecLHMRgM54ZcgRj/2st0yFXG8C9CF7KyZ8+enK6ykSGH06+55ppInFAfJF/72tfsn5F0wqb5KeANueAmdh+Z6ZAri//4xz+atcGPCF3ImpwIn+iFn82Qrsrz5s1Tr7/+ulk78oHmp0D+/O1vf1Mf/OAHu+wbMxmXXnqpWRP8itCFrMlNrRO98NMZZ555piotLe02f+ihh6rzzz9fLV++XB04cMB8Jnihra3NPpFXbj9C81PAe1Zvv2zG008/bdYCvyJ0ISex9+FLd0gLgp07d+rnS3C76aab9FGV+McdeeSRlB89sm7dOpqfAj7w5ptvqhEjRnTbH6YaU6dONWuAnxG6kLPYc4BSDQlcf/jDH8wz/0W6NMsVkVOmTEl4CwzKj+6h+SngL2+88UZGwUsCl9xcH/5H6IIj5s+fr4YMGZJwhyBDylbSJDRR4IrX0dGhGhsbeyw/Tpw4UT3yyCNq//795hnI1q5du7o0P/3Wt75llgDIJwlen//851Xfvn277ANjx1FHHaVuv/12AleAELrgGDlaJWFIQtEpp5yiSkpK9LlbciTMKidmKln5UY7O1NbW0oE5S++884467bTT7O+nfC8B+IvcFeK2225TZWVl+mrik046SVVUVKgf/ehH/OEZQIQuBEKq8qPsiO6++269g0JqcpGC7Lit758chXzvvffMUgCAGwhdCBzKj7n7whe+YH/PPvWpT6nOzk6zBADgFkIXAo3yY+ZofgoA+UHoQihQfkzP97//fft7cuyxx6Z1YQMAwBmELoQO5cfEpPlp79699feB5qcA4D1CF0KN8uP74puf/uxnPzNLAABeIXQhEqJcfty2bVuX5qdyqTkAwHuELkROlMqP0vz0Ix/5iP310fwUAPKH0IVIe/nll9XNN98cyvLjX//6V3XqqafaX4/cxxIAkD+ELuCfpPz4xBNPqEsvvTQU5UdpfvrZz37W3n6anwJA/hG6gDhSfpTWCqeffnqX4CUjKOVHmp8CgP8QuoAkglh+nDVrlr2N0vxUQiQAIP8IXUAaglJ+pPkpAPgXoQvIkF/Lj62trTQ/BQAfI3QBObDKj3JUKT6AeVl+/NWvfkXzUwDwOUIX4IBU5ccRI0aou+66y5XyozQ/HTRokP48ND8FAP8idAEOS1V+PO+881RLS4sj5cf45qff/va3zRIAgN8QugAXJSs/ytGpr3zlK2rjxo3m0Zmh+SkABAuhC/CA0+VHaX76mc98xn7+xRdfTPNTAPA5QhfgMSfKj1VVVfZzaH4KAMFA6ALyKJvyI81PASCYCF2AD6Rbfqyrq7PnaH4KAMFC6AJ85u2331YLFy5UZ5xxRpfgFT82bNhgngEACAJCF+Bjv/nNb9Qtt9ySMHTlevUjouuiiy5S5eXl5n8AvELoAnxOgtcHPvCBhMHLGm42X0W4NDU16Sa68nsDwFu86gAfS9T8NFn50enmqwifmpoa/bty4403mhkAXiF0AT4V3/z02muvNUv+xSo/utF8FfkhF0tI+c8tRUVF+vejubnZzCQ3Z86cbr9b48ePV+3t7eYRANJF6AJ8KNPmp3L146pVq9Rll12m+vXr1+UNUoZVfpQjZ/CnFStWqOHDh6vevXu7FrpaW1v1DdHldyJVb7e1a9faj000DjnkEFVRUWEeDSAdhC7Ah2Kbn37605/OqPkp5cdgmDdvnh5jx45V/fv31z8b6+fkVuiyWo7I79fBgwfNbHfr1q1Tffv2tbdHSpHWKCsrs+dlTJw40TwLQCqELsBnvvrVr9pvaHLkI5fmp6nKj9OnT6f1RJ5YJ7NbH2OHW6GruLhYr7+hocHMJFZZWWlvS1tbm5l93759+/SctVzG5MmTzVIAyRC6AB9pbGy038gkKO3cudMsyU2q8uMnPvEJyo8es8LWuHHj1LRp09SCBQvsn4cboUvOwSosLNTrTxbk5RxAazvkiGhPZJn1OBmcOwikRugCfELO6ZHzeeQN7IgjjlAvvPCCWeIsyo/+IAFXxt69e/X/n3vuOfvn4EbokkAvQU+OYsk5gz2ZNGmS3oZRo0aZmZ7JY6xtrq+vN7MAekLoAnxATlq2jkDJuTT//d//bZa4i/Kjf7gZuiTYlZSU6NAl9+5MZuTIkXob0glR8hhrmwcOHGhmAfSE0AXkmQQfCTjyxiVvij/+8Y/NEu+kU36cO3cu5UcXuRm6rHOwCgoKUjbQldKjPDadcwmXL19ub7MMAMnxKgHy6E9/+pM6/vjj7TctCTb5lqz8KG0Czj33XPWTn/xEn1AN57gZumpra/V6q6urzUxy8vNPl7XNMgAkx6sEyBNpfmqVcmQkan6ab5QfveNm6CotLdXrXbJkiZlxhoQza5tlAEiOVwmQB/HNTy+55JKkzU/zjfKj+9wKXatXr7bXu337djPrjNhzuqZOnWpmAfSE0AV4TJpSXn755fablTQ/DVKpjvKjO9wKXdZtfKZMmZK0IWo2hgwZYm/z0qVLzSyAnhC6AI852fw03yg/Oset0DVmzBi9TqfPF1y8eLG9vUOHDjWzAJIhdAEeim2AKTcedqr5ab5JafTJJ59U//Ef/0H5MUtuhC4JvNbPY+vWrWY2d/J7K0HL2t4dO3aYJQCSIXQBHvGq+Wm+Sfnx3nvvpfyYITdCV1NTk17fhAkTHG12W1NTY29rqr5fAP6F0AV4IF/NT/ON8mP6nA5de/bsUaNHj9brkxtVO0Vu0m1t58yZM80sgHQQugCXxTc/XbZsmVkSHZQfU3M6dFn3UJTfvW3btpnZ3MyfP9/exhkzZphZAOkidAEu8mPz03yzyo9nnnmm/X2xRpTLj06HLjm6JeuqqKgwM7mxenINHjxYH6EEkDlCF+CS+OanHBnoTo7AyNWcclGB9X2yRtTKj06GLjl/S87jknXJeV25WrRokf0z2bJli5kFkClCF+ACaX5qvenJ8Hvz03yj/Ohs6JIrFWU98r3MNbRKF3tZl9zQevPmzWYWQDYIXYDD4pufSp8krtRL31/+8pek5cfKykrV3Nwcuu+pk6FLAqqsR373ciHnH8p6BgwYoDZt2mRmAWSL0AU4TK7Ws9485QiNnMOE7CQrP37wgx9U06ZNU+vXrzePDjanQpeEfuk+L+uRbvTZamlp0esoLCzUJ+UDyB2hC3BQWJuf5luq8qN09v/2t7+tL1wIKqdCl9xf0VqP3HcxG21tbfr58r0OS6gF/IDQBc/IG0l5ebn5X/jENj/9wAc+oF588UWzBE4KS/lRbiAuVxhKryv5WFVVZX8dw4YN67Isk35Y1jlYpaWlZiYza9assbejrKxMf/50B4DkCF3whFxBJT2qZEceRvHNT3/+85+bJXBTkMuPs2fP1ttpvS4SDWuZfExXdXW1fk5tba2ZyUx9fX2XbchkAEiOVwk8Yd02JIx/DdP8NP+CWH50I3Tt3r1bFRQU6OdIiTAbhC7APbxKYKurq8v5qqmeWEcipOyTDjkBOH6HPn78eNXe3m4e4Q/xzU/vuususwT5EtWrH4XcB1ECWklJidq7d6+ZBeAXhC7oc5HkSICcj+RG6GptbVV9+vTRb3qdnZ1mNjEp01mPTTTkTdOpDtu5kuanp5xyir1tND/1nyhd/Si94SRQSuhqbGw0swD8hNAVQXLDWhljx45V/fv3V4ceeqj9RuRG6JIjaLJuOVFYLmfvybp16/T5UNa2xJ6gKyf0WvMyJk6caJ6VH/HNT+USfZqf+lcUrn7s6OjQX4u0ePDbEWEA7yN0RVDseSKxbzwy3AhdxcXFet0NDQ1mJjH5K93ajvjzUaQUZF3Gbo3Jkyebpd6i+WmwhbX8KK8v+Rrk9QbAnwhdEWSFrXHjxunySmxvKadDl/zFLX95y7rlL/GeSPNFaxukKWNPrIaN1shH00aan4bHK6+8os+DGjJkSJffKxlBKj/KHwJWywk5sgzAnwhdEST3r5NhnWjr5O1H4sm5JRLy5OiBlOR6MmnSJP35R40aZWZ6Jo+xtleutPLS9773Pftz0/w0PKT8KI1EP/e5z9lX/8UOv5cf5VxJ2U45H1LOoQTgT4QuuBa6JNTJVVQSuuRoQjIjR47Unz+dEBV7SbvchNcry5cvp/lpBEj58b777lNnnXWW/XtmDb+WH2V7ZPvkDwEA/kXogmuhyzoHS44cSP+gZKyTgJOVIC0SfqztleEFmp9GU1DKj3KxiWyT9MMD4F+ELrgWuqQjtqxTOmSnY+HCheZfqVnbK8NtL7/8cpfmpw899JBZgqhIVX78+Mc/rr71rW/lrfxo/W7KnR8A+BehC66FLrn3m6xT7gXnJAln1vbKcBPNTxEvVfnxnHPO8bz8KPc0dfp8TADOI3TBldAlRwWsdW7fvt3MOiP2nK6pU6eaWeft2bOnS/PT6667ziwB3heWqx8BeIPQBVdCl3UbH2kamqwhajZi3+CWLl1qZp2VqPmp018HwsPv5UcA/kDogiuhSxqGyvrmzp1rZpyxePFie1uHDh1qZp1F81PkIp3y48MPP8zvFBBBhC44Hro2bNhgX+m3detWM5s76YklQcva1h07dpglzrr55pvtz0HzU+QiVfnx6quvVr/+9a/NowGEHaELjocuuYJK1iXluf3795vZ3Mnl8NZ2pur7la345qf/+7//a5YA2Uu3/PjHP/7RPANAGBG64GjokpPPR48erdclvYOcIjfotrZx5syZZtZZND+FFyg/AtFF6IKjocu6h6L0tdq2bZuZzc38+fPt7ZsxY4aZddbTTz/dpfnpL37xC7MEcA/lRyBaCF1wNHRZnbErKirMTG6snlyDBw9W06dPN7POkuan8gYnn4fmp8gHyo9ANBC64FjokvO3rDYLTnTGXrRokV6XHDXbsmWLmXWWvIl9+MMftr/+u+++2ywB8oPyIxBehC44FrrkSkVZh5Tp5ArGXEgXe1mX3NB68+bNZtZZND+F31F+BMKF0AXHQpf05JJ1SF+rXCxbtkyvZ8CAAWrTpk1m1lnS/PTss8+2v+5LL72U5qfwLcqPQDgQuuBI6JLAIl3bZR3SjT5bLS0teh2FhYX6pHw3yLZ+/vOft7/msWPHUqpBYMgR2vvvv1+VlZXZv8PWoPwI+BuhC46ELrm/orUO+Ys8G21tbfr5Up508351ND9FWEj58Wtf+5o67rjj7N9pa0hpnvIj4C+ErghatWqVvspQ+l3Jx6qqKntHPWzYsC7L0u2JZZ2DVVpaamYys2bNGnsb5C94+dzpjkzEtp+Q82RofoowkPKjvIb+8z//k/Ij4GOErgiaPXu23hFLe4T4nbM1rGXyMR3V1dX68bW1tWYmM/X19V0+fyYjXfHNT926IhLIJ8qPgH8RuiLI6dC1e/du+69rKRFmw+3QRfNTRFGq8uPUqVPVM888Yx4NwG2ELuRMLmmXcFZSUqL27t1rZv0jvvmp/JUPREmq8uPHPvYxdeedd1J+BFxG6EJOpPVCZWWlDjONjY1m1j9ofgp0lar8KHeTkLsydHZ2mmcAcAqhCznp6OjQO2tp8dDe3m5m/SG++en1119vlgAQv/3tbyk/Ah4idCEnDQ0NegddXFxsZvyB5qdA+ig/At4gdCFrEmKsdhN1dXVmNv9ofgpkj/Ij4B5CF7ImO13ZEffp00e1traa2fy76aab7DeJESNG0PwUyBLlR8BZhC5krbm5We98i4qKzEz+0fwUcB7lR8AZhC5kTbrByw63pqbGzOTXI488QvNTwGWUH4HsEbqQNdnJSquIpqYmM5M/v/zlL2l+CniM8iOQGUIXslZeXp71DbKd9NJLL9H8FMgjKT8+9dRT+gIWyo9AzwhdCLT45qfz5s0zSwDkg5Qf5eg35UegO0IXAkt27ieffLK9Q6f5KeAvlB+BrghdCKT9+/er8ePH2zvwyy67jOangE+lW378v//7P/MMIJwIXQgcCVdy6bq1w6b5KRAcVvnxk5/8ZJfgJUOuPv7sZz+rli1bRvkRoUToQuDQ/BQIByk/zp49m/IjIoPQhUCx7vUog+anQDhQfkRUELoQGDQ/BcKP8iPCjNCFQIhtfnrYYYfR/BSIgFTlx6uuukqtW7fOPBrwP0IXfI/mp0C0pSo/lpSUqDvuuIPyI3yP0AVfk+ansX/l0vwUiDbKjwgyQhd8i+anAJJ59dVXeyw/ynmflB/hN4Qu+BLNTwGki/IjgoLQBd+Jb346btw4mp8CSAvlR/gZoQu+M3PmTHsnKc1P//KXv5glAJA+yo/wG0IXfIXmpwCcFlt+7N+/f5fwJYPyI7xC6IJvtLS02M1PpQcPzU8BOI3yI/KJ0AVfaG9v101PZccnH//nf/7HLAEAd0j58etf/7r68Ic/3C2AUX6EGwhdyLv45qfNzc1mCQC4Ty7e+dnPfqYuv/xyyo9wFaELeSU7sdiTXO+55x6zBAC8R/kRbiJ0IW/im5/ecMMNZgkA5B/lRziN0IW8oPkpgKBIVX488cQT1e23387V1kiJ0AXPyQ7sc5/7nL3DkuanEsIAwO/++te/qkWLFqlPfepTXYKXDCk/fuYzn1E//vGP1d69e80zgH8hdMFxEqqkoenrr7+eMEzR/BRAGKQqP9bU1Khf/epX5tG5+fvf/67eeOMN1dHRQVUgwAhdcMwrr7yirrnmGnXEEUd02fnICakPPfSQOnDggPrud79rz8sJ9FwNBCDo3Co//uMf/1Ctra3q7LPP1ld2W+uTzyGB7oUXXjCPRFAQupAzOYx+8cUXd9kpJBrS8NR6jPx769atZg0AEA5OlR/Xr1+vjj/++G7riB8VFRVUCwKE0IWcyI5jwoQJCXcGPY0+ffrQ/BRA6GVbfpTAJcvjn9PTOOOMMwheAUHoQk6kZ02inUCyIaHLqfMcAMDvMik/yu3PMglc1jj99NP1KRzwN0IXsiY3kE304k9nyCF2AIiaVOXHo48+utt8uuPhhx82nwV+RehC1i644IKEL/x0hpzbtW3bNrMmAIie7du391h+zGZIkIO/EbqQFbnqUP4qS/TCT3dcf/31Zm0AEF1W+fGUU05JuK/MZEh5Ev5F6EJW5ET4RC/4TIac2zBs2DAGg8Fg/HMMGDAg4b4yk/HII4+YvTT8iNCFrKxcuTLhC57BYDAY+RsPPvig2UvDjwhdyMovf/nLhC/4TMbgwYNVZWUlg8FgMP45ioqKEu4rMxnSTBX+RehCVt5880112GGHJXzRpzvq6urM2gAADQ0NCfeV6Q45z/a1114za4MfEbqQtS984QsJX/jpjEMPPZRbAAFADGlwWlhYmHCfmc4477zzzJrgV4QuZG3jxo0JX/jpjEsuucSsBQBgufrqqxPuM9MZq1atMmuBXxG6kJMrrrgi4Ys/2ZBzuV5++WWzBgCAZefOnVn17brwwgt16wn4G6ELOXnvvfdUdXV1wp1AoiGB68UXXzTPBgDE+93vfpdR8JLAxS2AgoHQhZxJ8LrlllvU4YcfnnCHYA25KSuBCwBSk+A1bty4hPtSa/Tr109Nnz6dwBUghC44Zs+ePfrqm1NPPVUdeeSROoQdd9xx6otf/KI+/wsAkBnpMD916lR1/PHHqyOOOEINGjRIjRgxQn3729/WV5EjWAhdAAAAHiB0AQAAeIDQBQAA4AFCFwAAgAcIXQAAAB4gdAEAAHiA0AUAAOABQhcAxLnoootUeXm5+R8AOIPQBQAxmpqaVK9evXTHbwBwEnsVAIhRU1OjA9eNN95oZgDAGYQuAIFSV1eny39uKSoq0qGrubnZzCQ3Z84c+1541hg/frxqb283jwCA9xG6AATCihUr1PDhw1Xv3r1dC12tra2qT58+Ojh1dnaa2cTWrl1rPzbROOSQQ1RFRYV5NAAQugD41Lx58/QYO3as6t+/vzr00EPtQONW6JKjaLL+qqoqdfDgQTPb3bp161Tfvn3t7ZFSpDXKysrseRkTJ040zwIQdYQuAL5kncxufYwdboWu4uJivf6GhgYzk1hlZaW9LW1tbWb2ffv27dNz1nIZkydPNksBRBmhC4AvWWFr3Lhxatq0aWrBggV2iHEjdMk5WIWFhXr9HR0dZra7jRs32tvR0tJiZruTZdbjZMjzAEQboQuAL+3atUuPvXv36v8/99xzdoBxI3Q1NjbqoCdHsQ4cOGBmu5s0aZLehlGjRpmZnsljrG2ur683swCiitAFIBDcDF0S7EpKSnTomjVrlplNbOTIkWmHKHmMtc0DBw40swCiitAFIBDcDF3WOVgFBQVq9+7dZjYxKT3KY5OVIC3Lly+3t1kGgGhjLwAgENwMXbW1tXq91dXVZia5hQsXmn+lZm2zDADRxl4AQCC4GbpKS0v1epcsWWJmnCHhzNpmGQCijb0AgEBwK3StXr3aXu/27dvNrDNiz+maOnWqmQUQVYQuAIHgVuiybuMzZcqUpA1RszFkyBB7m5cuXWpmAUQVoQtAILgVusaMGaPXOXfuXDPjjMWLF9vbO3ToUDMLIMoIXQACwY3QtWHDBtWvXz+9zq1bt5rZ3O3cuVMHLWt7d+zYYZYAiDJCF4BAcCN0NTU16fVNmDBB7d+/38zmrqamxt7WVH2/AEQHoQtAIDgduvbs2aNGjx6t1yc3qnaK3KTb2s6ZM2eaWQAgdAEICKdDl3UPxUGDBqlt27aZ2dzMnz/f3sYZM2aYWQB4H6ELQCA4Hbrk6Jasq6KiwszkxurJNXjwYDV9+nQzCwD/QugCEAhOhi45f0vO45J1yXlduVq0aJFelxw127Jli5kFgK4IXQACwcnQJVcqynrkykW5gjEX0sVe1iU3tN68ebOZBYDuCF0AAsHJ0CU9uWQ90qMrF8uWLdPrGTBggNq0aZOZBYDECF0AAsGp0CVd56X7vKxHutFnq6WlRa+jsLBQn5QPAKkQugAEglOhS+6vaK1H7ruYjba2Nv18KU+uX7/ezAJAcoQuAL60atUqfYWh9LqSj1VVVXZYGjZsWJdlmfTDss7BKi0tNTOZWbNmjb0dZWVl+vOnOwBEG6ELgC/Nnj1bB5tevXrZISd+WMvkY7qqq6v1c2pra81MZurr67tsQyYDQLSxFwDgS26Ert27d6uCggL9HCkRZoPQBSBb7AUARIbcB1ECWklJidq7d6+ZBQBvELoARMKBAwdUZWWlDl2NjY1mFgC8Q+gCEAkdHR26xCctHtrb280sAHiH0AUgEhoaGnToKi4uNjMA4C1CF4DQk4aoVsuJuro6MwsA3iJ0AQi9zs5OHbj69OmjWltbzSwAeIvQBSD0mpubdegqKioyMwDgPUIXgNCTbvASumpqaswMAHiP0AUg9CRwSauIpqYmMwMA3iN0AQi98vLynG6SDQBOIHQBAAB4gNAFAADgAUIXAACABwhdAAAAHiB0AQAAeIDQBQAA4AFCFwAAgAcIXQAAAB4gdAEAAHiA0AUAAOABQhcAAIAHCF0AAAAeIHQBAAB4gNAFAADgAUIXAACABwhdAAAAHiB0AQAAeIDQBQAA4AFCFwAAgAcIXQAAAB4gdAEAAHiA0AUAAOABQhcAAIAHCF0AAAAeIHQBAAB4gNAFAADgAUIXAACABwhdAAAAHiB0AQAAeIDQBQAA4AFCFwAAgOuU+n8JKl51XNf0jwAAAABJRU5ErkJggg==\n", | |
| "text/plain": "<IPython.core.display.Image object>" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.015393Z", | |
| "end_time": "2021-02-24T14:33:17.022333Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "C(4, [.5, .5])", | |
| "execution_count": 34, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 34, | |
| "data": { | |
| "text/plain": "1.0" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Quizz" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.024355Z", | |
| "end_time": "2021-02-24T14:33:17.037389Z" | |
| }, | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Image('2x4.PNG')", | |
| "execution_count": 35, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 35, | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": "<IPython.core.display.Image object>" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.062332Z", | |
| "end_time": "2021-02-24T14:33:17.069330Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "C(4, [1/3, 1/3, 1/6, 1/6])", | |
| "execution_count": 36, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 36, | |
| "data": { | |
| "text/plain": "0.08170416594551067" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.046330Z", | |
| "end_time": "2021-02-24T14:33:17.053328Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "C(2, [2/3, 1/3])", | |
| "execution_count": 37, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 37, | |
| "data": { | |
| "text/plain": "0.08170416594551044" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Quizz" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.054328Z", | |
| "end_time": "2021-02-24T14:33:17.060329Z" | |
| }, | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Image('3X3.PNG')", | |
| "execution_count": 38, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 38, | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": "<IPython.core.display.Image object>" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.062332Z", | |
| "end_time": "2021-02-24T14:33:17.069330Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "C(3, [1/2, 1/3, 1/6])", | |
| "execution_count": 39, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 39, | |
| "data": { | |
| "text/plain": "0.1258145836939113" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Example of efficient coding" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*The following example, although somewhat unrealistic, is a case in which exact matching to a noisy channel\nis possible. There are two channel symbols, 0 and 1, and the noise affects them in blocks of seven symbols.\nA block of seven is either transmitted without error, or exactly one symbol of the seven is incorrect. These\neight possibilities are equally likely. We have*\n\n\n$$C = \\max(H (y) - H_x(y)) = 7 + 8/8 \\log(1/8) = 4 \\text{ bits per block.}$$" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Example of efficient coding: Hamming solution" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "*Let a block of seven symbols be $X_1$, $X_2$, ..., $X_7$. Of these $X_3$, $X_5$, $X_6$, and $X_7$ are message symbols and chosen arbitrarily by the source. The other three are redundant and calculated as follows:*\n\n- $X_4$ is chosen to make $\\alpha := X_4 + X_5 + X_6 + X_7$ even (binary pattern $1xx$);\n- $X_2$ is chosen to make $\\beta := X_2 + X_3 + X_6 + X_7$ even (binary pattern $x1x$);\n- $X_1$ is chosen to make $\\gamma := X_1 + X_3 + X_5 + X_7$ even (binary pattern $xx1$);\n\n\n*When a block of seven is received $\\alpha$, $\\beta$, and $\\gamma$ are calculated and if even called zero, if odd called one. The binary number $\\alpha\\beta\\gamma$ then gives the subscript of the $X_i$ that is incorrect (if 0 there was no error).*" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Three symbols example" | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split", | |
| "ExecuteTime": { | |
| "start_time": "2021-02-24T14:33:17.070330Z", | |
| "end_time": "2021-02-24T14:33:17.076366Z" | |
| }, | |
| "hide_input": true, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Image('three_symbols.PNG')", | |
| "execution_count": 40, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 40, | |
| "data": { | |
| "image/png": 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| |
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| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "cell_style": "split" | |
| }, | |
| "cell_type": "markdown", | |
| "source": "- Channel is made of three symbols (A, B, and C)\n- A is always properly transmitted ($p_A(A)=1$)\n- $p_B(B)=p_C(C):=p$, $p_B(C)=p_C(B)=1-p:=q$\n- What is the capacity of the channel?\n- What should be the shape of the source?" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Three symbols example" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "- The source can be described by $p(A), p(B), p(C)$\n- Symmetry argument: $p(A):=P$, $p(B)=p(C)=Q$ ($P+2Q=1$)\n- Entropy of the source: $H(x)=-P\\log(P)-2Q\\log(Q)$\n- Equivocation: $H_y(x)=2Q\\alpha$, with $\\alpha=-p\\log(p)-q\\log(q)$ \n- We need to maximize $C=-P\\log(P)-2Q\\log(Q)-2Q\\alpha$" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "subslide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# Three symbols example" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Solution:\n$$P=\\frac{\\beta}{\\beta+2}, Q = \\frac{1}{\\beta+2}, C=\\log(\\frac{\\beta+2}{\\beta})\\text{, with }\\beta=2^\\alpha$$\n\nSanity check:\n- Certainty: $p=1$, $\\alpha=0$, $\\beta=1$, $P=Q=1/3$, $C=\\log(3)$ (perfect three symbols channel)\n- Chaos: $p=1/2$, $\\alpha=1$, $\\beta=2$, $P=1/2$, $Q=1/4$, $C=\\log(2)=1$ (perfect two symbols channel)" | |
| }, | |
| { | |
| "metadata": { | |
| "slideshow": { | |
| "slide_type": "slide" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "# That's all, folks!\n\n<img src=\"https://journals.openedition.org/bibnum/docannexe/image/1190/img-2.jpg\">" | |
| } | |
| ], | |
| "metadata": { | |
| "_draft": { | |
| "nbviewer_url": "https://gist.github.com/9513082d753016073fb9138ccd5cbe6d" | |
| }, | |
| "celltoolbar": "Slideshow", | |
| "gist": { | |
| "id": "9513082d753016073fb9138ccd5cbe6d", | |
| "data": { | |
| "description": "Introduction to The Mathematical Theory of Communication, part II", | |
| "public": true | |
| } | |
| }, | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3", | |
| "language": "python" | |
| }, | |
| "language_info": { | |
| "name": "python", | |
| "version": "3.7.7", | |
| "mimetype": "text/x-python", | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "pygments_lexer": "ipython3", | |
| "nbconvert_exporter": "python", | |
| "file_extension": ".py" | |
| }, | |
| "toc": { | |
| "nav_menu": {}, | |
| "number_sections": true, | |
| "sideBar": true, | |
| "skip_h1_title": true, | |
| "base_numbering": 1, | |
| "title_cell": "Table of Contents", | |
| "title_sidebar": "Contents", | |
| "toc_cell": false, | |
| "toc_position": {}, | |
| "toc_section_display": true, | |
| "toc_window_display": false | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 4 | |
| } |
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