{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "# Table of Contents\n", "

1  Exploring different doubling tricks for different kinds of regret bounds
1.1  What do we want?
1.2  Dependencies
1.3  Defining the functions $f$
1.3.1  Cheating with a \"safe\" log
1.3.2  Geometric sequences
1.3.3  Exponential sequences
1.3.4  Generic function $f$
1.3.5  Some specific case of intermediate sequences
1.4  Defining the sequences and last term
1.4.1  Sequence $f \\mapsto (T_i)_i$
1.4.2  Last term operator $T \\mapsto L_T$
1.4.3  Helper for the plot
1.5  Plotting what we want
1.5.1  Plotting the values of the sequences
1.5.2  Plotting the ratio for our upper-bound
1.6  Results
1.6.1  Values of the doubling sequences
1.6.2  Bound in $R_T \\leq \\mathcal{O}(\\log(T))$
1.6.3  Bound in $R_T \\leq \\mathcal{O}(\\sqrt{T})$
1.6.4  Bound in $R_T \\leq \\mathcal{O}(\\sqrt{T \\log(T)})$
1.6.5  A last weird bound in $R_T \\leq \\mathcal{O}(T^{2/3} \\log(T))$ (just to try)
1.7  Conclusions
1.7.1  About geometric sequences
1.7.2  About exponential sequences
1.7.3  About intermediate sequences
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring different doubling tricks for different kinds of regret bounds\n", "\n", "- Author: [Lilian Besson](https://perso.crans.org/besson/) and [Emilie Kaufmann](http://chercheurs.lille.inria.fr/ekaufman/),\n", "- License: [MIT License](https://lbesson.mit-license.org/).\n", "- Date: 19 September 2018." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What do we want?\n", "\n", "This notebooks studies and plot the ratio between a sum like the following\n", "$$ \\sum_{i=0}^{L_T} (T_i - T_{i-1})^\\gamma \\ln(T_i - T_{i-1})^\\delta $$\n", "and the quantity $T^\\gamma (\\ln(T))^\\delta$, where $T \\in\\mathbb{N}$ is a time horizon of some multi-armed bandit problem, and $\\gamma,\\delta \\geq 0$ but not simultaneously zero.\n", "\n", "The successive horizon (in a [doubling trick scheme](https://hal.inria.fr/hal-01736357/)) are defined by $\\forall i\\in\\mathbb{N},\\; T_i := \\lfloor \\exp(\\alpha \\times \\exp(f(i))) \\rfloor$, for some function $f: i \\mapsto f(i)$.\n", "\n", "We study a generic form of functions $f$, with parameters $c,d,e \\geq 0$: $f(i) = c (i^d) (\\log(i))^e$.\n", "\n", "- $d, e = 0, 1$ corresponds to the geometric doubling trick, with $T_i = \\mathcal{O}(2^i)$,\n", "- $d, e = 1, 0$ corresponds to the exponential doubling trick, with $T_i = \\mathcal{O}(2^{2^i})$,\n", "- we are curious about intermediate sequences, that grow faster than any geometric scheme but slower than any exponential scheme. Mathematically, it corresponds to the generic case of $0 < d < 1$ and $e \\geq 0$.\n", "\n", "Moreover, we are especially interested in these two cases:\n", "- $\\gamma, \\delta = 0, 1$ for bounds in regret like $R_T(\\mathcal{A}) = \\mathcal{O}(\\log T)$ (stochastic problem and problem dependent bounds),\n", "- $\\gamma, \\delta = 1/2, 0$ for bounds in regret like $R_T(\\mathcal{A}) = \\mathcal{O}(\\sqrt{T})$ (stochastic problem and worst-case bounds, ie \"minimax bounds\", or adversarial regret).\n", "\n", "To conclude these quick explanation, the notation $L_T$ is the \"last term operator\", for a fixed increasing sequence $(T_i)_{i\\in\\mathbb{N})$:\n", "\n", "$$ L_T = \\min\\{ i \\in\\mathbb{N}, T_{i-1} < T \\leq T_{i} \\}.$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> For more details, please check [this page on SMPyBandits documentation](https://smpybandits.github.io/DoublingTrick.html) or this article: [[What the Doubling Trick Can or Can’t Do for Multi-Armed Bandits, Lilian Besson and Emilie Kaufmann, 2018]](https://hal.inria.fr/hal-01736357)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Dependencies\n", "Here we import some code." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: watermark in ./venv3/lib/python3.6/site-packages (1.7.0)\n", "Requirement already satisfied: ipython in ./venv3/lib/python3.6/site-packages (from watermark) (7.1.1)\n", "Requirement already satisfied: pexpect; sys_platform != \"win32\" in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.6.0)\n", "Requirement already satisfied: prompt-toolkit<2.1.0,>=2.0.0 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (2.0.7)\n", "Requirement already satisfied: setuptools>=18.5 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (40.6.2)\n", "Requirement already satisfied: pygments in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (2.2.0)\n", "Requirement already satisfied: pickleshare in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.7.5)\n", "Requirement already satisfied: decorator in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.3.0)\n", "Requirement already satisfied: jedi>=0.10 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.13.1)\n", "Requirement already satisfied: traitlets>=4.2 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.3.2)\n", "Requirement already satisfied: backcall in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.1.0)\n", "Requirement already satisfied: ptyprocess>=0.5 in ./venv3/lib/python3.6/site-packages (from pexpect; sys_platform != \"win32\"->ipython->watermark) (0.6.0)\n", "Requirement already satisfied: six>=1.9.0 in ./venv3/lib/python3.6/site-packages (from prompt-toolkit<2.1.0,>=2.0.0->ipython->watermark) (1.11.0)\n", "Requirement already satisfied: wcwidth in ./venv3/lib/python3.6/site-packages (from prompt-toolkit<2.1.0,>=2.0.0->ipython->watermark) (0.1.7)\n", "Requirement already satisfied: parso>=0.3.0 in ./venv3/lib/python3.6/site-packages (from jedi>=0.10->ipython->watermark) (0.3.1)\n", "Requirement already satisfied: ipython-genutils in ./venv3/lib/python3.6/site-packages (from traitlets>=4.2->ipython->watermark) (0.2.0)\n", "Lilian Besson and Emilie Kaufmann \n", "\n", "CPython 3.6.6\n", "IPython 7.1.1\n", "\n", "numpy 1.15.4\n", "matplotlib 3.0.2\n", "seaborn 0.9.0\n", "\n", "compiler : GCC 8.0.1 20180414 (experimental) [trunk revision 259383\n", "system : Linux\n", "release : 4.15.0-38-generic\n", "machine : x86_64\n", "processor : x86_64\n", "CPU cores : 4\n", "interpreter: 64bit\n" ] } ], "source": [ "!pip install watermark\n", "%load_ext watermark\n", "%watermark -v -m -p numpy,matplotlib,seaborn -a \"Lilian Besson and Emilie Kaufmann\"" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from __future__ import division, print_function # Python 2 compatibility\n", "\n", "__author__ = \"Lilian Besson and Emilie Kaufmann\"\n", "\n", "import numpy as np\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "mpl.rcParams['figure.figsize'] = (16, 9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Change here if needed, use 128 bits floats instead of 64 bits." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "_f = np.float\n", "_f = np.float128" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Defining the functions $f$\n", "\n", "Let's start by defining the functions.\n", "\n", "This is some experimental code to plot some doubling sequences and check numerically some inequalities : like controlling a sum $\\Sigma_i=0^n u_i$ by a constant times to last term $u_n$ and controlling the last term $u_{L_T}$ as a function of $T$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#: The constant c in front of the function f.\n", "constant_c_for_the_functions_f = _f(1.0)\n", "constant_c_for_the_functions_f = _f(0.1)\n", "constant_c_for_the_functions_f = _f(0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We recall that we are interested by sequences $(T_i)_i$ that grows about $$T_i = \\mathcal{O}(\\exp(\\alpha \\exp(f(i)),$$ and $$f(i) = c \\, i^d \\, (\\log i)^e, \\forall i\\in\\mathbb{N}$$\n", "for $c > 0, d \\geq 0, e \\geq 0$ and $d, e$ not zero simultaneously." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cheating with a \"safe\" log\n", "I don't want to have $\\log(T_i - T_{i-1}) = -\\infty$ if $T_i = T_{i-1}$ but I want $\\log(0) = 0$. Let's hack it!" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def mylog(x):\n", " res = np.log(x)\n", " if np.shape(res):\n", " res[np.isinf(res)] = _f(0.0)\n", " else:\n", " if np.isinf(res):\n", " res = _f(0.0)\n", " return res" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Geometric sequences\n", "\n", "$$ f(i) = \\log(i) \\Leftrightarrow T_i = \\mathcal{O}(2^i). $$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def function_f__for_geometric_sequences(i, c=constant_c_for_the_functions_f):\n", " r\"\"\" For the *geometric* doubling sequences, :math:`f(i) = c \\times \\log(i)`.\"\"\"\n", " if i <= 0: return _f(0.0)\n", " return c * mylog(i)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exponential sequences\n", "\n", "$$ f(i) = i \\Leftrightarrow T_i = \\mathcal{O}(2^{2^i}). $$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def function_f__for_exponential_sequences(i, c=constant_c_for_the_functions_f):\n", " r\"\"\" For the *exponential* doubling sequences, :math:`f(i) = c \\times i`.\"\"\"\n", " return c * i" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generic function $f$\n", "\n", "As soon as $0 < d < 1$, no matter the value of $e$, $T_i$ will essentially **faster than any geometric sequence** and **slower than any exponential sequence**." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def function_f__for_generic_sequences(i, c=constant_c_for_the_functions_f, d=_f(0.5), e=_f(0.0)):\n", " r\"\"\" For a certain *generic* family of doubling sequences, :math:`f(i) = c \\times i^{d} \\times (\\log(i))^{e}`.\n", "\n", " - ``d, e = 0, 1`` gives :func:`function_f__for_geometric_sequences`,\n", " - ``d, e = 1, 0`` gives :func:`function_f__for_geometric_sequences`,\n", " - ``d, e = 0.5, 0`` gives an intermediate sequence, growing faster than any geometric sequence and slower than any exponential sequence,\n", " - any other combination has not been studied yet.\n", "\n", " .. warning:: ``d`` should most probably be smaller than 1.\n", " \"\"\"\n", " i = float(i)\n", " if i <= 0: return _f(0.0)\n", " if e == 0:\n", " assert d > 0, \"Error: invalid value of d = {} for function_f__for_generic_sequences, cannot be <= 0.\".format(d) # DEBUG\n", " return c * (i ** d)\n", " assert e > 0, \"Error: invalid value of e = {} for function_f__for_generic_sequences, cannot be <= 0.\".format(e) # DEBUG\n", " if d == 0:\n", " return c * ((mylog(i)) ** e)\n", " return c * (i ** d) * ((mylog(i)) ** e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Some specific case of intermediate sequences\n", "\n", "Analytically (mathematically) we started to study $f(i) = \\sqrt{i}$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def function_f__for_intermediate_sequences(i):\n", " return function_f__for_generic_sequences(i, c=constant_c_for_the_functions_f, d=_f(0.5), e=_f(0.0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And empirically, I'm curious about other sequences, including $f(i) = i^{1/3}$, $f(i) = i^{2/3}$ and $f(i) = \\sqrt{i} \\sqrt{\\log(i)}$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def function_f__for_intermediate2_sequences(i):\n", " return function_f__for_generic_sequences(i, c=constant_c_for_the_functions_f, d=_f(0.3333), e=_f(0.0))\n", "\n", "def function_f__for_intermediate3_sequences(i):\n", " return function_f__for_generic_sequences(i, c=constant_c_for_the_functions_f, d=_f(0.6667), e=_f(0.0))\n", "\n", "def function_f__for_intermediate4_sequences(i):\n", " return function_f__for_generic_sequences(i, c=constant_c_for_the_functions_f, d=_f(0.5), e=_f(0.5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Defining the sequences and last term" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "#: Value of the parameter :math:`\\alpha` for the :func:`Ti_from_f` function.\n", "alpha_for_Ti = _f(0.1)\n", "alpha_for_Ti = _f(1.0)\n", "alpha_for_Ti = _f(0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sequence $f \\mapsto (T_i)_i$\n", "We need to define a function that take $f$ and give the corresponding sequence $(T_i)$, given as a function $Ti: i \\mapsto T_i$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def Ti_from_f(f, alpha=alpha_for_Ti, *args, **kwargs):\n", " r\"\"\" For any non-negative and increasing function :math:`f: i \\mapsto f(i)`, the corresponding sequence is defined by:\n", "\n", " .. math:: \\forall i\\in\\mathbb{N},\\; T_i := \\lfloor \\exp(\\alpha \\times \\exp(f(i))) \\rfloor.\n", "\n", " .. warning:: :math:`f(i)` can need other parameters, see the examples above. They can be given as ``*args`` or ``**kwargs`` to :func:`Ti_from_f`.\n", "\n", " .. warning:: it should be computed otherwise, I should give :math:`i \\mapsto \\exp(f(i))` instead of :math:`f: i \\mapsto f(i)`. I need to try as much as possible to reduce the risk of overflow errors!\n", " \"\"\"\n", " # WARNING don't forget the floor!\n", " def Ti(i):\n", " this_Ti = np.floor(np.exp(alpha * np.exp(f(float(i), *args, **kwargs))))\n", " if not (np.isinf(this_Ti) or np.isnan(this_Ti)):\n", " this_Ti = int(this_Ti)\n", " # print(\" For f = {}, i = {} gives Ti = {}\".format(f, i, this_Ti)) # DEBUG\n", " return this_Ti\n", " return Ti" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Last term operator $T \\mapsto L_T$\n", "Then we can define the \"last term operator\", by a naive search (and not an analytic derivation).\n", "I don't care if this is not efficient, it works and at least we are sure that $L_T$ satisfies its definition." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def last_term_operator_LT(Ti, max_i=10000):\n", " r\"\"\" For a certain function representing a doubling sequence, :math:`T: i \\mapsto T_i`, this :func:`last_term_operator_LT` function returns the function :math:`L: T \\mapsto L_T`, defined as:\n", "\n", " .. math:: \\forall T\\in\\mathbb{N},\\; L_T := \\min\\{ i \\in\\mathbb{N},\\; T \\leq T_i \\}.\n", "\n", " :math:`L_T` is the only integer which satisfies :math:`T_{L_T - 1} < T \\leq T_{L_T}`.\n", " \"\"\"\n", " def LT(T, max_i=max_i):\n", " i = 0\n", " while Ti(i) < T: # very naive loop!\n", " i += 1\n", " if i >= max_i:\n", " raise ValueError(\"LT(T={T}) was unable to find a i <= {max_i} such that T_i >= T.\".format(T, max_i)) # DEBUG\n", " assert Ti(i - 1) < T <= Ti(i), \"Error: i = {} was computed as LT for T = {} and Ti = {} but does not satisfy T_(i-1) < T <= T(i)\".format(i, T, Ti) # DEBUG\n", " # print(\" For LT: i = {} was computed as LT for T = {} and Ti = {} and satisfies T(i-1) = {} < T <= T(i) = {}\".format(i, T, Ti, Ti(i-1), Ti(i))) # DEBUG\n", " return i\n", " return LT" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Helper for the plot" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def markers_colors(nb):\n", " \"\"\"Make unique markers and colors for nb plots.\"\"\"\n", " allmarkers = ['o', 'D', 'v', 'p', '<', 's', '^', '*', 'h', '>']\n", " longlist = allmarkers * (1 + int(nb / float(len(allmarkers)))) # Cycle the good number of time\n", " markers = longlist[:nb] # Truncate\n", " colors = sns.hls_palette(nb + 1)[:nb]\n", " return markers, colors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Plotting what we want\n", "\n", "By default, we will study the following doubling sequences:\n", "\n", "- **Geometric** doubling with $d=0, e=1$,\n", "- Intermediate doubling with $d=1/2, e=0$ (the one I'm excited about), \n", "- Intermediate doubling with $d=1/3, e=0$,\n", "- Intermediate doubling with $d=2/3, e=0$,\n", "- Intermediate doubling with $d=1/2, e=1/2$,\n", "- **Exponential** doubling with $d=1, e=0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the values of the sequences\n", "\n", "First, we want to check how much do these sequences increase." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def plot_doubling_sequences(\n", " i_min=1, i_max=30,\n", " list_of_f=(\n", " function_f__for_geometric_sequences,\n", " function_f__for_intermediate_sequences,\n", " function_f__for_intermediate2_sequences,\n", " function_f__for_intermediate3_sequences,\n", " function_f__for_intermediate4_sequences,\n", " function_f__for_exponential_sequences,\n", " ),\n", " label_of_f=(\n", " \"Geometric doubling (d=0, e=1)\",\n", " \"Intermediate doubling (d=1/2, e=0)\",\n", " \"Intermediate doubling (d=1/3, e=0)\",\n", " \"Intermediate doubling (d=2/3, e=0)\",\n", " \"Intermediate doubling (d=1/2, e=1/2)\",\n", " \"Exponential doubling (d=1, e=0)\",\n", " ),\n", " *args, **kwargs\n", " ):\n", " r\"\"\" Display a plot to illustrate the values of the :math:`T_i` as a function of :math:`i` for some i.\n", "\n", " - Can accept many functions f (and labels).\n", " \"\"\"\n", " markers, colors = markers_colors(len(list_of_f))\n", " fig = plt.figure()\n", "\n", " i_s = np.arange(i_min, i_max, dtype=np.float128)\n", " # now for each function f\n", " for num_f, (f, la) in enumerate(zip(list_of_f, label_of_f)):\n", " print(\"\\n\\nThe {}th function is referred to as {} and is {}\".format(num_f, la, f)) # DEBUG\n", " Ti = Ti_from_f(f)\n", " values_of_Ti = [Ti(i) for i in i_s]\n", " plt.plot(i_s, values_of_Ti, label=la, lw=4, ms=7, color=colors[num_f], marker=markers[num_f])\n", "\n", " plt.legend()\n", " plt.xlabel(r\"Value of the time horizon $i = {},...,{}$\".format(i_min, i_max))\n", " plt.title(r\"Comparison of the values of $T_i$\")\n", " plt.show()\n", " # return fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the ratio for our upper-bound" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def plot_quality_first_upper_bound(\n", " Tmin=2, Tmax=int(1e8), nbTs=100,\n", " gamma=_f(0.0), delta=_f(1.0), # XXX bound in RT <= log(T)\n", " # gamma=_f(0.5), delta=_f(0.0), # XXX bound in RT <= sqrt(T)\n", " # gamma=_f(0.5), delta=_f(0.5), # XXX bound in RT <= sqrt(T * log(T))\n", " # gamma=_f(0.66667), delta=_f(1.0), # XXX another weird bound in RT <= T^2/3 * log(T)\n", " list_of_f=(\n", " function_f__for_geometric_sequences,\n", " function_f__for_intermediate_sequences,\n", " function_f__for_intermediate2_sequences,\n", " function_f__for_intermediate3_sequences,\n", " function_f__for_intermediate4_sequences,\n", " function_f__for_exponential_sequences,\n", " ),\n", " label_of_f=(\n", " \"Geometric doubling (d=0, e=1)\",\n", " \"Intermediate doubling (d=1/2, e=0)\",\n", " \"Intermediate doubling (d=1/3, e=0)\",\n", " \"Intermediate doubling (d=2/3, e=0)\",\n", " \"Intermediate doubling (d=1/2, e=1/2)\",\n", " \"Exponential doubling (d=1, e=0)\",\n", " ),\n", " show_Ti_m_Tim1=True,\n", " *args, **kwargs\n", " ):\n", " r\"\"\" Display a plot to compare numerically between the following sum :math:`S` and the upper-bound we hope to have, :math:`T^{\\gamma} (\\log T)^{\\delta}`, as a function of :math:`T` for some values between :math:`T_{\\min}` and :math:`T_{\\max}`:\n", "\n", " .. math:: S := \\sum_{i=0}^{L_T} (T_i - T_{i-1})^{\\gamma} (\\log (T_i - T_{i-1}))^{\\delta}.\n", "\n", " - Can accept many functions f (and labels).\n", " - Can use :math:`T_i` instead of :math:`T_i - T_{i-1}` if ``show_Ti_m_Tim1=False`` (default is to use the smaller possible bound, with difference of sequence lengths, :math:`T_i - T_{i-1}`).\n", "\n", " .. warning:: This is still ON GOING WORK.\n", " \"\"\"\n", " markers, colors = markers_colors(len(list_of_f))\n", " fig = plt.figure()\n", "\n", " Ts = np.floor(np.linspace(_f(Tmin), _f(Tmax), num=nbTs, dtype=np.float128))\n", " the_bound_we_want = (Ts ** gamma) * (mylog(Ts) ** delta)\n", "\n", " # now for each function f\n", " for num_f, (f, la) in enumerate(zip(list_of_f, label_of_f)):\n", " print(\"\\n\\nThe {}th function is referred to as {} and is {}\".format(num_f, la, f)) # DEBUG\n", " Ti = Ti_from_f(f)\n", " LT = last_term_operator_LT(Ti)\n", " the_sum_we_have = np.zeros_like(Ts, dtype=np.float128)\n", " for j, Tj in enumerate(Ts):\n", " LTj = LT(Tj)\n", " if show_Ti_m_Tim1:\n", " the_sum_we_have[j] = sum(\n", " ((Ti(i)-Ti(i-1)) ** gamma) * (mylog((Ti(i)-Ti(i-1))) ** delta)\n", " for i in range(1, LTj + 1)\n", " )\n", " else:\n", " the_sum_we_have[j] = sum(\n", " (Ti(i) ** gamma) * (mylog(Ti(i)) ** delta)\n", " for i in range(0, LTj + 1)\n", " )\n", " # print(\"For j = {}, Tj = {}, gives LTj = {}, and the value of the sum from i=0 to LTj is = \\n{}.\".format(j, Tj, LTj, the_sum_we_have[j])) # DEBUG\n", " plt.plot(Ts, the_sum_we_have / the_bound_we_want, label=la, lw=4, ms=4, color=colors[num_f], marker=markers[num_f])\n", "\n", " plt.legend()\n", " plt.xlabel(r\"Value of the time horizon $T = {},...,{}$\".format(Tmin, Tmax))\n", " str_of_Tj_or_dTj = \"T_i - T_{i-1}\" if show_Ti_m_Tim1 else \"T_i\"\n", " plt.title(r\"Ratio of the sum $\\sum_{i=0}^{L_T} (%s)^{\\gamma} (\\log(%s))^{\\delta}$ and the upper-bound $T^{\\gamma} \\log(T)^{\\delta}$, for $\\gamma=%.3g$, $\\delta=%.3g$.\" % (str_of_Tj_or_dTj, str_of_Tj_or_dTj, gamma, delta)) # DEBUG\n", " plt.show()\n", " # return fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Values of the doubling sequences\n", "We check that the exponential sequence is growing WAY faster than all the others." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n", "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/lilian/ownCloud/owncloud.crans.org/Crans/These_2016-17/src/SMPyBandits/notebooks/venv3/lib/python3.6/site-packages/ipykernel_launcher.py:12: RuntimeWarning: overflow encountered in exp\n", " if sys.path[0] == '':\n" ] }, { "ename": "OverflowError", "evalue": "int too large to convert to float", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mOverflowError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in 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"\u001b[0;32m/tmp/SMPyBandits/notebooks/venv3/lib/python3.6/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36masarray\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m 499\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 500\u001b[0m \"\"\"\n\u001b[0;32m--> 501\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 502\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 503\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mOverflowError\u001b[0m: int too large to convert to float" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_doubling_sequences()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And without this faster sequence, just for the first $10$ first sequences:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n", "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_doubling_sequences(\n", " i_max=10,\n", " list_of_f=(\n", " function_f__for_geometric_sequences,\n", " function_f__for_intermediate_sequences,\n", " function_f__for_intermediate2_sequences,\n", " function_f__for_intermediate3_sequences,\n", " function_f__for_intermediate4_sequences,\n", " ),\n", " label_of_f=(\n", " \"Geometric doubling (d=0, e=1)\",\n", " \"Intermediate doubling (d=1/2, e=0)\",\n", " \"Intermediate doubling (d=1/3, e=0)\",\n", " \"Intermediate doubling (d=2/3, e=0)\",\n", " \"Intermediate doubling (d=1/2, e=1/2)\",\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And for the three slower sequences, an interesting observation is that the \"intermediate\" sequence with $f(i) = i^{1/3}$ is comparable to $f(i) = \\log(i)$ (geometric one) for small values!" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n", "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_doubling_sequences(\n", " i_max=14,\n", " list_of_f=(\n", " function_f__for_geometric_sequences,\n", " function_f__for_intermediate_sequences,\n", " function_f__for_intermediate2_sequences,\n", " ),\n", " label_of_f=(\n", " \"Geometric doubling (d=0, e=1)\",\n", " \"Intermediate doubling (d=1/2, e=0)\",\n", " \"Intermediate doubling (d=1/3, e=0)\",\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bound in $R_T \\leq \\mathcal{O}(\\log(T))$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "gamma, delta = (_f(0.0), _f(1.0))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/lilian/ownCloud/owncloud.crans.org/Crans/These_2016-17/src/SMPyBandits/notebooks/venv3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log\n", " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(Tmax=int(1e3), gamma=gamma, delta=delta, show_Ti_m_Tim1=True)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n", "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(gamma=gamma, delta=delta, show_Ti_m_Tim1=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conclusion:\n", "- geometric sequences **cannot** be used to conserve a logarithmic regret bound (as we proved),\n", "- exponential sequences **can** be used to conserve such bounds (as we proved, also),\n", "- and we conjecture that all other sequences (ie as soon as $d > 0$ ie $f(i) >> \\log(i)$) can be used too." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bound in $R_T \\leq \\mathcal{O}(\\sqrt{T})$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "gamma, delta = (_f(0.5), _f(0.0))" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/lilian/ownCloud/owncloud.crans.org/Crans/These_2016-17/src/SMPyBandits/notebooks/venv3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log\n", " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(gamma=gamma, delta=delta, show_Ti_m_Tim1=True)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n", "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(gamma=gamma, delta=delta, show_Ti_m_Tim1=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conclusion:\n", "- geometric sequences **can** be used to conserve a minimax (worst case) regret bound in $R_T = \\mathcal{O}(\\sqrt{T})$ (as we proved).\n", " > But the proof has to be careful and use a smart bound on $T_i - T_{i-1} \\leq \\text{cste} \\times b^{i-1}$ and not with a $b^i$ (see difference between first and second plot)\n", "- exponential sequences **can** be used to conserve such bounds (as we conjectured but did not proved, also),\n", "- and we conjecture that all other sequences (ie as soon as $d > 0$ ie $f(i) >> \\log(i)$) can be used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bound in $R_T \\leq \\mathcal{O}(\\sqrt{T \\log(T)})$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "gamma, delta = (_f(0.5), _f(0.5))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/lilian/ownCloud/owncloud.crans.org/Crans/These_2016-17/src/SMPyBandits/notebooks/venv3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log\n", " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(gamma=gamma, delta=delta, show_Ti_m_Tim1=True)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n", "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(gamma=gamma, delta=delta, show_Ti_m_Tim1=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conclusion:\n", "- geometric sequences **can** be used to conserve a minimax (worst case) regret bound in $R_T = \\mathcal{O}(\\sqrt{T \\log(T)})$ (as we proved).\n", " > But the proof has to be careful and use a smart bound on $T_i - T_{i-1} \\leq \\text{cste} \\times b^{i-1}$ and not with a $b^i$ (see difference between first and second plot)\n", "- exponential sequences **can** be used to conserve such bounds (as we conjectured but did not proved, also),\n", "- and we conjecture that all other sequences (ie as soon as $d > 0$ ie $f(i) >> \\log(i)$) can be used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A last weird bound in $R_T \\leq \\mathcal{O}(T^{2/3} \\log(T))$ (just to try)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "gamma, delta = (_f(0.66667), _f(1.0))" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/lilian/ownCloud/owncloud.crans.org/Crans/These_2016-17/src/SMPyBandits/notebooks/venv3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log\n", " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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bKbXJwl97M1lEAb9W5SfE8MF8UOWK4T7n2lCpjFrOHwxtH6e1rtirVZG5NgCsH3/GdROB/8bwHv8Ww4+uso+csZR3Xe9/fbyH5trX3jY3seOzxNq2pe9BGIbnZ07F8MPakrr6LChl65x/F8OEO5cxTEgVYWt9Nethidny7ficrdZnWTXen1Jmj98qlFndc9bu87UMe4/5h6jacV3T7z0wBK4dMVykqC1zgBYYPkfeA2Zrrc+BqQfz/5VJuwLDPc0XMUxgdQrDvdX2rp8BfKDNTMKF9fbcBJzEMNHWMeP/w+3fRauWYLhI/RKG4+cO9yY5q7j/QtQ7ZXlkiBBCNCxluMdxiJ3Ju2qtr5jJ48/Aj1rrtTbKegIYorVeUeWK2qFi/srwfFBzPQwh2vB4prLbRgKrtdbJZZYdBf677DIrZdvVBnbkcxTYpLXeVtW867p9zZVhbxvb275VafNfGqXUFSBcW5jp29Z6UTcqnrNV/Syw55hXhtmMTwPe2vK9ubVOGR6bNExrPbm+yqwPDdWeQtwPpPtfCNFoWbnHsSp52HuF2Bs4azNV9ZXL3xg4Da9uZlpr/yqkrdZVcqXU4xiu6mdi6InypsJ9VI2ofSuVUZM2Nte+VWlzIRqCrXO2qp8F9hzzxh7UXlWraa3wou5nFq93DdieQjR6MlRYCCEM+mJ9UpQGyV8p9QkwCtislAqr7UrZ0APDlf+bwP8FJmmtr1czr7pu32qV0cDtK0Rtq81ztrHrS91fDBNCNCIyVFgI0egopeYBn9k7O6xS6i/AYOAK8KwMrxJCCCGE+HmRHlchRKNTlUeaKMMs0J211sOACxge+C6EEEIIIX5GJHAVQjQ6VXxsymAMM4mC4V4ueydzEkIIIYQQ9wmZnEkI0ahUfKSJUsoNM8+5497MsO2A0nu4bgEP1HklhRBCCCFEvWrU97i6urpqDw+Phq6GEKIe3b59m9zcXNzd3e1K/+OPP+Lo6Ej79u3Jzc0lKyuLhx9+uI5rKYQQQgghakNiYmKm1trNVrpG3ePq4eHBiRMnGroaQoh6tHbtWjw8PBg/fjwAGRkZTJ5c+TF9O3fu5MEHHyQpKYk1a9YQFRXFn//8Z7p27UpoaGh9V1sIIYQQQlSDUuo7e9I16sBVCPHLc/bsWYKDg02v3dzciIuLs5je19eXjh07MmzYMB5++GFeeOGFeqilEEIIIYSoT416qLCfn5+WHlchhBBCCCGE+HlSSiVqrf1spZNZhYUQQgghhBBCNGoyVFgIIYQQQvwiFBYWcu3aNe7evdvQVRHiF6d58+Z06dKFpk2bVmt7CVyFEEIIIcQvwrVr12jdujUeHh4opRq6OkL8YmitycrK4tq1a3Tt2rVaechQYSGEEEII8Ytw9+5d2rdvL0GrEPVMKUX79u1rNNpBAlchhBBCCPGLIUGrEA2jpueeBK5CCCGEEELUk//85z8888wzdOvWjQEDBhAQEMCHH37YIHWJi4vjyy+/tLj+o48+4vXXX6/TOjg7O1d7Ww8PDzIzMystX7ZsGatXrwbglVde4eDBg9UuoyytNU888QS3b9+2WqY9Vq5ciaenJz169OCzzz6rlfqZk5WVRVBQEM7OzsybN6/cupEjR3Ljxo06K7u2yT2uQgghhBBC1AOtNePHj2fGjBm8++67AHz33Xd89NFHDVKfuLg4nJ2dGTx4cKV1RUVFBAcHl3u2+v3o1VdfrbW8PvnkE3x8fGjTpk2N8klJSWHnzp2cO3eO9PR0Ro4cycWLF3F0dKylmt7TvHlzVqxYQXJyMsnJyeXW/e53v2Pjxo386U9/qvVy64IErkIIIYQQ4hclNSykTvP3jNxpdvm///1vnJycmDVrlmnZI488wu9//3sAiouLeemll4iLiyM/P5+5c+fyP//zP2itefHFF9m/fz9KKZYsWcLUqVOJi4tj6dKluLi4cPbsWaZMmULfvn158803uXPnDjExMXTv3p2MjAxmzZrF999/D8DatWvp3LkzmzZtwtHRkR07drB+/Xq2bNlC8+bNOXXqFEOGDMHb25sTJ07w1ltv8Z///IdZs2Zx+fJlAN5++22zAa8t3377Lc888ww5OTmMGzfOtNzaPq5evZqPP/4YgHnz5uHn50dYWBgAb7zxBvv376dFixa8++67eHp6lisvLCyMsWPHMmnSJDw8PJgxYwb//Oc/KSwsZPfu3fTs2ZOMjAyeeeYZ0tPTCQgI4PPPPycxMRFXV9dyeUVHRzNz5kzT69dee41//OMfdOjQgYceeogBAwbY1Qb79u0jJCSEZs2a0bVrVzw9PTl27BgBAQEWt0lMTOT5558nJycHV1dXIiMjcXd3t1lWq1atGDp0KKmpqZXWBQcHM2zYsPsmcJWhwkIIIYQQQtSDc+fO0b9/f4vrt2zZQtu2bTl+/DjHjx9n8+bNfPvtt3zwwQckJSVx+vRpDh48yOLFi7l+/ToAp0+fZtOmTZw/f57t27dz8eJFjh07Rnh4OOvXrwdgwYIFLFq0iOPHj7N3717Cw8Px8PBg1qxZLFq0iKSkJIYNGwYYZl7+8ssvWbNmTbm6zZ8/n8cff5zTp09z8uRJvLy8qtUGCxYsYPbs2Zw9e7Zc4GVtH61p27YtZ8+eZd68eSxcuNBmeldXV06ePMns2bNNQ3uXL1/OE088wblz55g0aZIpwK8oISHBFJwmJiayc+dOkpKS+OSTTzh+/Lgp3apVq/D19a30N3/+fADS0tJ46KGHTOm7dOlCWlqaxToXFhby+9//nj179pCYmMizzz5rCjZtlWVNu3btyM/PJysry2baxkB6XIUQQgghhGgAc+fOJT4+HicnJ44fP86BAwc4c+YMe/bsAeDWrVtcunSJ+Ph4QkNDcXR0pGPHjjz++OMcP36cNm3a8Nhjj5kCwO7duzNq1CgA+vbtS2xsLAAHDx4kJSXFVO7t27fJyckxW6fJkyebHbL673//m6ioKAAcHR1p27ZttfY5ISGBvXv3Aoahqn/4wx8ArO6jNaGhoaZ/Fy1aZLP8iRMnAjBgwAA++OADU9ml9xmPHj2adu3amd32p59+onXr1gAcPnyYCRMm0LJlS4ByQ6oXL17M4sWLbdbFXl9//TXJyck8+eSTgKFnvvQ9r2lZHTp0ID09nfbt29dKXeuSBK5CCCGEEELUAy8vL1PQBrBhwwYyMzPx8/MDDMNl169fz1NPPVVuu/3791vMs1mzZqb/Ozg4mF47ODhQVFQEQElJCUeOHKF58+Y269iqVSv7d6iaqjK7bJMmTSgpKTG9rvg4lbJ52ZNvafs4Ojqa2qeqdXFwsD5oddWqVURHR1daHhgYyLp16+jcuTNXr141Lb927RqdO3e2mJ/WGi8vL7766qsql2XL3bt3adGihc10jYEMFRZCCCGEEL8onpE77fp75I03adqpCzg40LRTFx554027trPkiSee4O7du7z99tumZXl5eab/P/XUU7z99tsUFhYCcPHiRXJzcxk2bBi7du2iuLiYjIwMDh06xMCBA+3e31GjRpmGDQMkJSUB0Lp1a7Kzs+3KY8SIEaZ6FxcXc+vWLbvLL2vIkCHs3Gloo7IBl6V9fOSRR0hJSSE/P5+bN2/yr3/9q1x+u3btMv1r7R5RW3V6//33AThw4IDFmXZ79Ohhusc3MDCQmJgY7ty5Q3Z2Nv/85z9N6RYvXkxSUlKlv9JAMjg4mJ07d5Kfn8+3337LpUuXTO/niBEjKg0b7tGjBxkZGabAtbCwkHPnztlVljVaa3744Qc8PDyq0FoNR3pchRBCCCGEMKNph4488mf7H3Fii1KKmJgYFi1axBtvvIGbmxutWrXiL3/5CwDh4eFcuXKF/v37o7XGzc2NmJgYJkyYwFdffYWPjw9KKd544w0efPBBLly4YFe569atY+7cuXh7e1NUVERgYCCbNm3iN7/5DZMmTWLfvn3lAltz3nzzTWbOnMmWLVtwdHTk7bffrlag+Oabb/LMM8/wl7/8pdzkTJb2EWDKlCn06dOHrl270q9fv3L53bhxA29vb5o1a8Z7771X5foALF26lNDQULZv305AQAAPPvigaUhwWWPGjCEuLg5PT0/69+/P1KlT8fHxoUOHDjz22GN2l+fl5cWUKVPo3bs3TZo0YcOGDTg6OlJSUkJqaioPPPBAufROTk7s2bOH+fPnc+vWLYqKili4cKHd9xl7eHhw+/ZtCgoKiImJ4cCBA/Tu3ZvExEQGDRpEkyb3R0iotNYNXQeL/Pz89IkTJxq6GkIIIYQQ4mfg/Pnz9OrVq6GrIRqZ/Px8HB0dadKkCV999RWzZ8829UqXdf36daZPn87nn39eJ/VITk5m69atlSbGqisLFiwgODiYESNG1Et5YP4cVEolaq39bG17f4TXQgghhBBCCFEHvv/+e6ZMmUJJSQlOTk5s3rzZbDp3d3eee+45bt++XeNnuZrTp0+fegtaS8urz6C1piRwFaIW5N8poaRY08K59h8cLYQQQggh6s6vfvUrTp06ZVfaKVOm1HFt6s9zzz3X0FWoEglchaihNf99mbu592a7a9XWkQV/69qANRJCCCGEEOLnRWYVFqKGygatALm3ihuoJkIIIYQQQvw8SeAqhBBCCCGEEKJRk8BViDpwK6OwoasghBBCCCHEz4YErkLUkDJzFiUeqN5DuYUQQgjx8+bs7Gwzzdq1a8nLy6uH2lgWGRnJvHnzANi0aRNRUVFW08fExJCSklKjMj08PMjMzKzWtsOHD8fcYzSruh9VMWnSJC5fvmy1THuMHj0aFxcXxo4dW2ndzp07ee2114iOjsbb25u+ffsyePBgTp8+XaO627Jy5Uo8PT3p0aMHn332GQAFBQUEBgZSVFRUp2VbIoGrEDXU1rXyHGenY29TmF9iJrUQQggh7icF+emkf/sGBfnp9VZmdQLX4uK6m2Nj1qxZTJ8+3Wqa2ghc65o9+2Gvc+fOUVxcTLdu3Wqc1+LFi9m+fbvZdfv372f06NF07dqVL774grNnz/Lyyy8zc+bMGpdrSUpKCjt37uTcuXN8+umnzJkzh+LiYpycnBgxYgS7du2qs7KtkVmFhaihEjPfE3dySjiXkI3vE23rv0JCCCGEsCr1dEiVt/n+9km703r67LSZJi4ujmXLluHq6kpycjIDBgxgx44drF+/nvT0dIKCgnB1dSU2NpYDBw6wdOlS8vPz6d69O9u2bcPZ2RkPDw+mTp3K559/zosvvsimTZvo168fhw8fJjc3l6ioKFauXMnZs2eZOnUqERERAOzYsYN169ZRUFCAv78/GzduxNHRkW3btrFy5UpcXFzw8fGhWbNmACxbtgxnZ2deeOEFNm/ezDvvvENBQQGenp5s376dpKQkPvroI7744gsiIiLYu3cvAHPnziUjI4OWLVuyefNmevbsWa4NsrKyCA0NJS0tjYCAALTWpnVr1qxh69atAISHh7Nw4UKuXLnC2LFjSU5OBmD16tXk5OSwbNkyALZv3054eDhFRUVs3bqVgQMHliuv7H4MHz4cf39/YmNjuXnzJlu2bGHYsGHk5eURFhZGcnIyPXr0ID09nQ0bNuDn51cur+joaMaNG2d6bant7DFixAji4uIqLddak5SURP/+/VFKmZYPGjSIa9eu2cw3MTGR559/npycHFxdXYmMjMTd3d3mdvv27SMkJIRmzZrRtWtXPD09OXbsGAEBAYwfP54//vGPTJs2ze79qy3S4ypEDRUXa7PLT3x6q9wHsBBCCCFEWadOnWLt2rWkpKRw+fJlEhISmD9/Pp06dSI2NpbY2FgyMzOJiIjg4MGDnDx5Ej8/P9asWWPKo3379pw8eZKQEEMw7uTkxIkTJ5g1axbjxo1jw4YNJCcnExkZSVZWFufPn2fXrl0kJCSQlJSEo6Mj0dHRXL9+naVLl5KQkEB8fLzF3tOJEydy/PhxTp8+Ta9evdiyZQuDBw8mODiYVatWkZSURPfu3Zk5cybr168nMTGR1atXM2fOnEp5LV++nKFDh3Lu3DkmTJjA999/DxgCrm3btnH06FGOHDnC5s2b7XrOal5eHklJSWzcuJFnn33WZvqioiKOHTvG2rVrWb58OQAbN26kXbt2pKSksGJn15WVAAAgAElEQVTFChITE81um5CQwIABAwCstl10dDS+vr6V/iZNmmSzfqdOncLHx6dc0AqwZcsWnn76aavbFhYW8vvf/549e/aQmJjIs88+y5/+9CcAVq1aZbZO8+fPByAtLY2HHnrIlFeXLl1IS0sDoE+fPhw/ftxm3euC9LgKUUMlFgLXH78v4Pvzd3mkd4t6rpEQQggh7gcDBw6kS5cuAPj6+nLlyhWGDh1aLs2RI0dISUlhyJAhgOE+w4CAANP6qVOnlksfHBwMQN++ffHy8jL1sHXr1o2rV68SHx9PYmIijz32GAB37tyhQ4cOHD16lOHDh+Pm5mbK9+LFi5XqnJyczJIlS7h58yY5OTk89dRTldLk5OTw5ZdfMnnyZNOy/Pz8SukOHTrEBx98AMCYMWNo164dAPHx8UyYMIFWrVoBhmD58OHDpn2zJDQ0FIDAwEBu377NzZs3raafOHEiAAMGDODKlSumshcsWAAYgjRvb2+z216/ft3UVtbabtq0adXunfz0008rBaixsbFs2bKF+Ph4q9t+/fXXJCcn8+STTwKGoeSlx8LixYtZvHhxterk6OiIk5MT2dnZtG7dulp5VJcErkLUkLmhwqVOfHpTAlchhBBCmFV2OKmjo6PZSW+01jz55JO89957ZvMoDe4q5ung4FAufwcHB4qKitBaM2PGDFauXFluu5iYGLvqHBYWRkxMDD4+PkRGRpod4lpSUoKLiwtJSUl25WmvJk2aUFJybw6Ru3fvlltfsWey4uuKStvHUttb06JFi0rlmxMdHc2qVasqLff09GTPnj1Wtz1w4IBp2DXAmTNnCA8PZ//+/bRv397qtlprvLy8+OqrryqtW7VqFdHR0ZWWBwYGsm7dOjp37szVq1dNy69du0bnzp1Nr/Pz82nevLnV8uuCBK5C1JClHleAiydyuZVZSFvXpvVYIyGEEEJYY889qGCYmOnapVcoKc7FwbEVXX71Kk7NOtVx7aB169ZkZ2fj6urKoEGDmDt3LqmpqXh6epKbm0taWhqPPvpotfIeMWIE48aNY9GiRXTo0IGffvqJ7Oxs/P39WbBgAVlZWbRp04bdu3fj4+NTafvs7Gzc3d0pLCwkOjraFNCU1hmgTZs2dO3ald27dzN58mS01pw5c6ZSfoGBgbz77rssWbKE/fv3c+PGDQCGDRtGWFgYL730ElprPvzwQ7Zv307Hjh358ccfycrKwtnZmY8//pjRo0eb8tu1axdBQUHEx8fTtm1b2rat+lwjQ4YM4f333ycoKIiUlBTOnj1rNl2vXr1ITU3Fw8PDattVt8f11q1bFBUVmQLU77//nokTJ7J9+/ZK7/2IESOIiooqF1z26NGDjIwMvvrqKwICAigsLOTixYt4eXnZ7HENDg7mmWee4fnnnyc9PZ1Lly6Z7hfOysrC1dWVpk3r/7etBK5C1FBxUfnA9QH3pvx03fAcV10CJz+/RVCoa0NUTQghhBA14NSsE11+9SqZ6Ttw7fTbeglaAWbOnMno0aNN97pGRkYSGhpqGm4bERFR7cC1d+/eREREMGrUKEpKSmjatCkbNmxg0KBBLFu2jICAAFxcXPD19TW7/YoVK/D398fNzQ1/f39TsBoSEsJzzz3HunXr2LNnD9HR0cyePZuIiAgKCwsJCQmpFLguXbqU0NBQvLy8GDx4MA8//DAA/fv3JywszBQshYeH069fPwBeeeUVBg4cSOfOnStN9tS8eXP69etHYWGhaWKnqpozZw4zZsygd+/e9OzZEy8vL7MB8JgxY4iLi2PkyJG4u7vb1XaWDBs2jAsXLpCTk0OXLl3YsmUL2dnZjBw50pTm1VdfJSsry3SvcJMmTThx4gQlJSWkpqbywAMPlMvTycmJPXv2MH/+fFMQvHDhQry8vGzWx8vLiylTptC7d2+aNGnChg0bcHR0BAxDlceMGVOl/astytbkMUqph4AooCOggXe01m8qpR4AdgEewBVgitb6hjL0yb8J/BrIA8K01ieNec0AlhizjtBa/8Na2X5+ftrc85iEaCy01qwM/abcstH/7canWzJMr1u0dmDeBg+aOslcaEIIIURDOn/+PL169WroaohGrLi4mMLCQpo3b84333zDyJEj+frrr3FyciqX7s6dOwQFBZGQkGAK6mpTeHg44eHhDBo0yGq65ORktm7dWm7Crro0ceJEXn/99WpfODF3DiqlErXWfhY2MbGnx7UI+L9a65NKqdZAolLqcyAM+JfW+nWl1EvAS8AfgKeBXxn//IG3AX9joLsU8MMQACcqpT7SWt+wcz+FaHQqXvdRCvoMa03czizu5hruwbiTXUJKQg4+QW0aoIZCCCGEEMJeeXl5BAUFUVhYiNaajRs3VgpawXCP6/Lly0lLSzP1FNemv//973al69OnT70FrQUFBYwfP77aQWtN2QxctdbXgevG/2crpc4DnYFxwHBjsn8AcRgC13FAlDZ05R5RSrkopdyNaT/XWv8EYAx+RwPm7zQX4j5QUmGYsEMThVNzB3yC2nD043sz2Z347Cbew1vbnCRACCGEEEI0nNatW2PviE9zMyr/nDk5OTF9+vQGK79KYxeVUh5AP+Ao0NEY1AL8gGEoMRiC2qtlNrtmXGZpecUyZiqlTiilTmRkZFRcLUSjUlxhRuHSkSIDRrWFMjHqf64UcPWC7ZnnhBBCCCGEEJXZHbgqpZyBvcBCrfXtsuuMvavWb5a1k9b6Ha21n9bar/RZSEI0VhVnFHZwNESrLh2a8uiA8tPTn/jsVr3VSwghhBBCiJ8TuwJXpVRTDEFrtNb6A+Pi/xiHAGP890fj8jTgoTKbdzEus7RciPuWpcAVYMBT5Weg+/pYDrczC+ulXkIIIYQQQvyc2AxcjbMEbwHOa63L3vn7ETDD+P8ZwL4yy6crg0HALeOQ4s+AUUqpdkqpdsAo4zIh7lslFYYKO5SZVM6jTwtcu9y7mV+XwMmDtxFCCCGEEEJUjT09rkOA3wFPKKWSjH+/Bl4HnlRKXQJGGl8DfAJcBlKBzcAcAOOkTCuA48a/V0snahLiflXxGa5le1yVUvhV6HX9MuYGa//n23qpmxBCCCEaH2dnZ5tp1q5dS15eXj3UxrLIyEjmzZsHwKZNm4iKirKaPiYmhpSUlBqV6eHhQWZmZrW2HT58uNlJlaq6H1UxadIkLl++bLVMe4wePRoXFxfGjh1bad3OnTt57bXX2LdvH97e3vj6+uLn50d8fHyN6m6N1pr58+fj6emJt7c3J0+eBCAjI4PRo0fXWbm22DOrcDzlppkpZ4SZ9BqYayGvrUD1ngYsRCNUUlI+cHV0LH+q9BnWutwzXQHyblXophVCCCGEKGPt2rX89re/pWXLlnZvU1xcXCfPEwWYNWuWzTQxMTGMHTuW3r1710kdaoM9+2Gvc+fOUVxcTLdu3Wqc1+LFi8nLy+Nvf/tbpXX79+9n/vz59OjRg+DgYJRSnDlzhilTpnDhwoUal23O/v37uXTpEpcuXeLo0aPMnj2bo0eP4ubmhru7OwkJCQwZMqROyrbGnue4CiEssDZUGMCpuflBDSUlGgcHeTSOEEII0RBeTA2p0/zf8NxpM01cXBzLli3D1dWV5ORkBgwYwI4dO1i/fj3p6ekEBQXh6upKbGwsBw4cYOnSpeTn59O9e3e2bduGs7MzHh4eTJ06lc8//5wXX3yRTZs20a9fPw4fPkxubi5RUVGsXLmSs2fPMnXqVCIiIgDYsWMH69ato6CgAH9/fzZu3IijoyPbtm1j5cqVuLi44OPjQ7NmzQBYtmwZzs7OvPDCC2zevJl33nmHgoICPD092b59O0lJSXz00Ud88cUXREREsHfvXgDmzp1LRkYGLVu2ZPPmzfTs2bNcG2RlZREaGkpaWhoBAQEY+r8M1qxZw9athv6u8PBwFi5cyJUrVxg7dizJyckArF69mpycHJYtWwbA9u3bCQ8Pp6ioiK1btzJw4MBy5ZXdj+HDh+Pv709sbCw3b95ky5YtDBs2jLy8PMLCwkhOTqZHjx6kp6ezYcMG/Pz8yuUVHR3NuHHjTK8ttZ09RowYQVxcXKXlWmuSkpLo379/uUcq5ubm2vWIRUvHjS379u1j+vTpKKUYNGgQN2/e5Pr167i7uzN+/Hiio6MbJHCt0uNwhBDlmXuOqz0uHMmpi+oIIYQQ4j5y6tQp1q5dS0pKCpcvXyYhIYH58+fTqVMnYmNjiY2NJTMzk4iICA4ePMjJkyfx8/NjzZp70860b9+ekydPEhJiCMadnJw4ceIEs2bNYty4cWzYsIHk5GQiIyPJysri/Pnz7Nq1i4SEBJKSknB0dCQ6Oprr16+zdOlSEhISiI+Ptzjsd+LEiRw/fpzTp0/Tq1cvtmzZwuDBgwkODmbVqlUkJSXRvXt3Zs6cyfr160lMTGT16tXMmTOnUl7Lly9n6NChnDt3jgkTJvD9998DkJiYyLZt2zh69ChHjhxh8+bNnDp1ymZ75uXlkZSUxMaNG3n22Wdtpi8qKuLYsWOsXbuW5cuXA7Bx40batWtHSkoKK1asIDEx0ey2CQkJDBgwAMBq20VHR+Pr61vpb9KkSTbrd+rUKXx8fExB6ocffkjPnj0ZM2aMKai3xNpxs2jRIrN1ev11w52faWlpPPTQvTl1u3TpQlqaYU5dPz8/Dh8+bLPudUF6XIWogeKKswqb6UVt1daR3ArDg7/cd4NeAc52XS0TQgghxM/TwIED6dKlCwC+vr5cuXKFoUOHlktz5MgRUlJSTD1cBQUFBAQEmNZPnTq1XPrg4GAA+vbti5eXF+7u7gB069aNq1evEh8fT2JiIo899hgAd+7coUOHDhw9epThw4dT+jjKqVOncvHixUp1Tk5OZsmSJdy8eZOcnByeeuqpSmlycnL48ssvmTx5smlZfn5+pXSHDh3igw8MDywZM2YM7dq1AyA+Pp4JEybQqpXh0YITJ07k8OHDpn2zJDQ0FIDAwEBu377NzZs3raafOHEiAAMGDODKlSumshcsWABAnz598Pb2Nrvt9evXTW1lre2mTZvGtGnTrNbDkk8//ZSnn37a9HrChAlMmDCBQ4cO8fLLL3Pw4EGL21o7bv76179Wqz4AHTp0ID09vdrb14QErkLUQMWhwuZuLVnwt65kpRfwt//7velpxz9+V8DlpDy692tVeQMhhBBC/CKUHU7q6OhIUVFRpTRaa5588knee+89s3mUBncV83RwcCiXv4ODA0VFRWitmTFjBitXriy3XUxMjF11DgsLIyYmBh8fHyIjI80OcS0pKcHFxYWkpCS78rRXkyZNKCkpMb2+e/duufUVOwRsdRCUto+ltremRYsWlco3Jzo6mlWrVlVa7unpyZ49e6xue+DAAdOw67ICAwO5fPkymZmZuLq6mt3W2nGzaNEiYmNjKy0PCQnhpZdeonPnzly9etW0/Nq1a3Tu3BkwtHmLFi2s1ruuSOAqRA1Ueo6rhaHC7Ts50XNgKy4czTUtS4i5IYGrEEII0QDsuQe11O2iG0T/8Ca/fXAhrZu41GGt7mndujXZ2dm4uroyaNAg5s6dS2pqKp6enuTm5pKWlsajjz5arbxHjBjBuHHjWLRoER06dOCnn34iOzsbf39/FixYQFZWFm3atGH37t34+PhU2j47Oxt3d3cKCwuJjo42BTSldQZo06YNXbt2Zffu3UyePBmtNWfOnKmUX2BgIO+++y5Llixh//793LhxA4Bhw4YRFhbGSy+9hNaaDz/8kO3bt9OxY0d+/PFHsrKycHZ25uOPPy43y+2uXbsICgoiPj6etm3b0rZt+ac72GPIkCG8//77BAUFkZKSwtmzZ82m69WrF6mpqXh4eFhtu+r2uN66dYuioiLat28PQGpqKt27d0cpxcmTJ8nPzzet69mzZ6WJmqwdN7Z6XIODg3nrrbcICQnh6NGjtG3b1tRzf/HiRfr06VPl/akNErgKUQOVhgo7Wr6yN3h8u3KB67Wv73L1wh0e6tkwV62EEEIIYVubJu2Y3WVZvZY5c+ZMRo8ebbrXNTIyktDQUNNw24iIiGoHrr179yYiIoJRo0ZRUlJC06ZN2bBhA4MGDWLZsmUEBATg4uKCr6+v2e1XrFiBv78/bm5u+Pv7m4LVkJAQnnvuOdatW8eePXuIjo5m9uzZREREUFhYSEhISKXAdenSpYSGhuLl5cXgwYN5+OGHAejfvz9hYWGmyZXCw8Pp168fAK+88goDBw6kc+fOlSZ7at68Of369aOwsNDmPaCWzJkzhxkzZtC7d2969uyJl5eX2QB4zJgxxMXFMXLkSNzd3e1qO0uGDRvGhQsXyMnJoUuXLmzZsoXs7GxGjhxpSrN3716ioqJo2rQpLVq0YNeuXSilyMzMLDepVSk3N7dqHze//vWv+eSTT/D09KRly5Zs27bNtC42NpYxY8ZUaf9qizK3o42Fn5+fNvc8JiEai2/P5PHen++N8/fo24Jn/tTZYvr3/pzGt2fumF5379eSqX/oVKd1FEIIIYTB+fPn6dWrV0NXQzRixcXFFBYW0rx5c7755htGjhzJ119/jZOTU7l0d+7cISgoiISEhDp5DFF4eDjh4eEMGjTIarqPP/6Yy5cvM3/+/FqvgzmBgYHs27fPdD9yVZk7B5VSiVprPwubmEiPqxA1ULHHteJzXCsaPK5ducD1m1N5/OdKPh097J8yXQghhBBC1I28vDyCgoIoLCxEa83GjRsrBa1guMd1+fLlpKWlmXqKa9Pf//53u9KNHTu21su2JCMjg+eff77aQWtNSeAqRA1UusfVRuD6cO8WdP5Vc9Iu3buZ/8t9N5iw4ME6qZ8QQgghhLBf69atsXfEp7kZlX/O3NzcGD9+fIOVL89xFaIGiitMQOdgY6SIUorB48tfpbpwJIeffiio5ZoJIYQQQgjx8yGBqxA1UFJStR5XAM9+LXF76N6QE63hyEfWnzMmhBBCCCHEL5kErkLUQElR1e5xBVAOisHjyve6nj10m+yfqvb8MCGEEEIIIX4pJHAVogZKisu/drDzrvFeAc64dLiXuLgIjv6v9LoKIYQQQghhjgSuQtRApcmZHGz3uIJhSPGg35TvdT118BZ52cUWthBCCCHEz4Gzs7PNNGvXriUvL68eamNZZGQk8+bNA2DTpk1ERUVZTR8TE0NKSkqNyvTw8CAzM7Na2w4fPtzspEpV3Y+qmDRpEpcvX7Zapi1JSUkEBATg5eWFt7c3u3btKrd+586dvPbaa+zbtw9vb298fX3x8/MjPj6+VvbBHK018+fPx9PTE29vb06ePAkYZhUePXp0nZVriwSuQtRAxcfhODSxL3AF8H68Na1c7s3mVJivSfzsVq3VTQghhBD3p+oErsXFdXfxe9asWUyfPt1qmtoIXOuaPfthr3PnzlFcXEy3bt1qlE/Lli2Jiori3LlzfPrppyxcuJCbN++Nwtu/fz+jR49mxIgRnD59mqSkJLZu3Up4eHhNd8Gi/fv3c+nSJS5dusQ777zD7NmzAcOswu7u7iQkJNRZ2dbI43CEqIGKQ4Wr8vzpJk4O+I9x4d/RWaZlh/f8xOE9P9GqrSML/ta1lmophBBCiLJCUnfXaf47PSfbTBMXF8eyZctwdXUlOTmZAQMGsGPHDtavX096ejpBQUG4uroSGxvLgQMHWLp0Kfn5+XTv3p1t27bh7OyMh4cHU6dO5fPPP+fFF19k06ZN9OvXj8OHD5Obm0tUVBQrV67k7NmzTJ06lYiICAB27NjBunXrKCgowN/fn40bN+Lo6Mi2bdtYuXIlLi4u+Pj40KyZ4Tnzy5Ytw9nZmRdeeIHNmzfzzjvvUFBQgKenJ9u3bycpKYmPPvqIL774goiICPbu3QvA3LlzycjIoGXLlmzevJmePXuWa4OsrCxCQ0NJS0sjICAAre91CKxZs4atW7cCEB4ezsKFC7ly5Qpjx44lOTkZgNWrV5OTk8OyZcsA2L59O+Hh4RQVFbF161YGDhxYrryy+zF8+HD8/f2JjY3l5s2bbNmyhWHDhpGXl0dYWBjJycn06NGD9PR0NmzYgJ+fX7m8oqOjGTdunOm1pbaz5dFHHzX9v1OnTnTo0IGMjAxcXFzQWpOUlET//v1R6l7nSG5ubrnXllg6bmzZt28f06dPRynFoEGDuHnzJtevX8fd3Z3x48cTHR3NkCFD7Nq/2iQ9rkLUQHWHCpfqN7ItzVtVPg1zb8mQYSGEEOLn7tSpU6xdu5aUlBQuX75MQkIC8+fPp1OnTsTGxhIbG0tmZiYREREcPHiQkydP4ufnx5o1a0x5tG/fnpMnTxISEgKAk5MTJ06cYNasWYwbN44NGzaQnJxMZGQkWVlZnD9/nl27dpGQkEBSUhKOjo5ER0dz/fp1li5dSkJCAvHx8RZ7TydOnMjx48c5ffo0vXr1YsuWLQwePJjg4GBWrVpFUlIS3bt3Z+bMmaxfv57ExERWr17NnDlzKuW1fPlyhg4dyrlz55gwYQLff/89AImJiWzbto2jR49y5MgRNm/ezKlTp2y2Z15eHklJSWzcuJFnn33WZvqioiKOHTvG2rVrWb58OQAbN26kXbt2pKSksGLFChITE81um5CQwIABAwCstl10dDS+vr6V/iZNmlQpz2PHjlFQUED37t0Bw/Hh4+NjClI//PBDevbsyZgxY0xBvSXWjptFixaZrdPrr78OQFpaGg899JApry5dupCWlgaAn58fhw8fttm2dUF6XIWogUqBaxXPqGYtHBgwqi0JH96oxVoJIYQQ4n4wcOBAunTpAoCvry9Xrlxh6NCh5dIcOXKElJQUUw9XQUEBAQEBpvVTp04tlz44OBiAvn374uXlhbu7OwDdunXj6tWrxMfHk5iYyGOPPQbAnTt36NChA0ePHmX48OG4ubmZ8r148WKlOicnJ7NkyRJu3rxJTk4OTz31VKU0OTk5fPnll0yefK/nOT8/v1K6Q4cO8cEHHwAwZswY2rUzzP8RHx/PhAkTaNWqFWAIlg8fPmzaN0tCQ0MBCAwM5Pbt2+WG3JozceJEAAYMGMCVK1dMZS9YsACAPn364O3tbXbb69evm9rKWttNmzaNadOmWa1HaX6/+93v+Mc//oGDg6FT49NPP+Xpp582pZkwYQITJkzg0KFDvPzyyxw8eNBiftaOm7/+9a8262NJhw4dSE9Pr/b2NSGBqxA1UPF2Enue41rRY792kcBVCCGE+AUqO5zU0dGRoqLKj8bTWvPkk0/y3nvvmc2jNLirmKeDg0O5/B0cHCgqKkJrzYwZM1i5cmW57WJiYuyqc1hYGDExMfj4+BAZGUlcXFylNCUlJbi4uJCUlGRXnvZq0qQJJSUlptd3794tt77i8Flbw2lL28dS21vTokWLSuWbEx0dzapVqyot9/T0ZM+ePQDcvn2bMWPG8NprrzFo0CBTmgMHDpiGXZcVGBjI5cuXyczMxNXV1Wy51o6bRYsWERsbW2l5SEgIL730Ep07d+bq1aum5deuXaNz586Aoc1btGhhY6/rhgSuQtRAdZ7jWlHL1o40baYozC+fV152MS1bV+GmWSGEEELYxZ57UAFyiwvYnnmauyVFNHdowu9cfWjl6FTHtYPWrVuTnZ2Nq6srgwYNYu7cuaSmpuLp6Ulubi5paWnl7o2sihEjRjBu3DgWLVpEhw4d+Omnn8jOzsbf358FCxaQlZVFmzZt2L17Nz4+PpW2z87Oxt3dncLCQqKjo00BTWmdAdq0aUPXrl3ZvXs3kydPRmvNmTNnKuUXGBjIu+++y5IlS9i/fz83bhgu5A8bNoywsDBeeukltNZ8+OGHbN++nY4dO/Ljjz+SlZWFs7MzH3/8cblZbnft2kVQUBDx8fG0bduWtm3bVrl9hgwZwvvvv09QUBApKSmcPXvWbLpevXqRmpqKh4eH1baz1eNaUFDAhAkTmD59ernhw7du3aKoqIj27dsDkJqaSvfu3VFKcfLkSfLz803revbsyYULF8rla+24sdXjGhwczFtvvUVISAhHjx6lbdu2pp77ixcv0qdPHxutWDckcBWiBioNFa5mnDn/7a5snH+FOzn3riIe+egGT0wzfxVNCCGEEHWvlaMTszo+Vu/lzpw5k9GjR5vudY2MjCQ0NNQ03DYiIqLagWvv3r2JiIhg1KhRlJSU0LRpUzZs2MCgQYNYtmwZAQEBuLi44Ovra3b7FStW4O/vj5ubG/7+/qZgNSQkhOeee45169axZ88eoqOjmT17NhERERQWFhISElIpcF26dCmhoaF4eXkxePBgHn74YQD69+9PWFiYaXKl8PBw+vXrB8Arr7zCwIED6dy5c6XJnpo3b06/fv0oLCy0eQ+oJXPmzGHGjBn07t2bnj174uXlZTYAHjNmDHFxcYwcORJ3d3e72s6c999/n0OHDpGVlUVkZCRgeJxOamoqI0eONKXbu3cvUVFRNG3alBYtWrBr1y6UUmRmZpab1KqUm5tbtY+bX//613zyySd4enrSsmVLtm3bZloXGxvLmDFj7N6/2qTM7Whj4efnp809j0mIxuJf2zM5+r/37p94Ylr7Ss9ntdeRf94oN8NwEyfFnDcfwbmdXF8SQgghasP58+fp1atXQ1dDNGLFxcUUFhbSvHlzvvnmG0aOHMnXX3+Nk1P5nvY7d+4QFBREQkICjlV5rISdwsPDCQ8PLzd02JyPP/6Yy5cvM3/+/FqvgzmBgYHs27fPdD9yVZk7B5VSiVprPwubmMgvYiFqoNJzXKsxVLjUgFFtOfq/N8m9abhxtqhAk/DhDZ561q1GdRRCCCGEEPbJy8sjKCiIwsJCtNZs3LixUtAKhntcly9fTlpamqmnuDb9/e9/tyvd2LFja71sSzIyMnj++eerHbTWlASuQtRAbQ0VBmjazIGhEx/gs60ZpmWn/nUL/7EuuHRoWv2MhRBCCCGEXXEs9VsAACAASURBVFq3bo29Iz7Nzaj8c+bm5sb48eMbrHx5jqsQNVBSYVbh6kzOVJbvE21o63bvelJJMcTv/alGeQohhBBCCHG/k8BViBqo/BzXmgWujk0UwyY9UG7Z2UPZZKYV1ChfIYQQQggh7mcSuApRAxXvca1pjytAn2Gtad/p3tBgreHwbul1FUIIIYQQv1wSuApRAyUVnlWtamFSOQcHReCU9uWWnT+Sww/f5tc8cyGEEEIIIe5DErgKUQMlJbXf4wrQc2ArOno0K7fs0PtZFlILIYQQ4n7h7OxsM83atWvJy8urh9pYFhkZybx58wDYtGkTUVFRVtPHxMSQkpJSozI9PDzIzMys1rbDhw83O6lSVfejKiZNmsTly5etlmmP0aNH4+LiYnaG4J07d/Laa68RHR2Nt7c3ffv2ZfDgwZw+fbpGdbcmKyuLoKAgnJ2dze7H66+/TnR0NGvWrKF37954e3szYsQIvvvuO8Aw+/Do0aNrvV4SuApRA5VnFa6dwFU5KB6fWv5e19RTeVz7+k6t5C+EEEKIxqs6gWtxcbHtRNU0a9Yspk+fbjVNbQSudc2e/bDXuXPnKC4uplu3bjXOa/HixWzfvt3suv379zN69Gi6du3KF198wdmzZ3n55ZeZOXNmjcu1pHnz5qxYsYLVq1ebXf/ZZ58xatQo+vXrx4kTJzhz5gyTJk3ixRdfBAyzD7u7u5OQkFCr9ZLH4QhRA8UVhgrX5vOnu/u2pEuP5lz7+q5pWdzOLKa90hmlaidAFkIIIX6JQv6eWqf57wz3tJkmLi6OZcuW4erqSnJyMgMGDGDHjh2sX7+e9PR0goKCcHV1JTY2lgMHDrB06VLy8/Pp3r0727Ztw9nZGQ8PD6ZOncrnn3/Oiy++yKZNm+jXrx+HDx8mNzeXqKgoVq5cydmzZ5k6dSoREREA7Nixg3Xr1lFQUIC/vz8bN27E0dGRbdu2sXLlSlxcXPDx8aFZM8Por/+fvfsOj7pM9z/++c6k90ASCIEQehURUEABBXWta8H1CLpHxQVsu4ie9be661l1l3U966qIHQQRxYq9oyuIIFKlg5RQQyAhvScz8/39ETJkSsoM6Xm/rotL5/mWeTKQzNy57+d+HnnkEUVEROiPf/yj5s2bp7lz56q8vFy9e/fW66+/rk2bNumTTz7R999/r1mzZun999+XJN19993KzMxUWFiY5s2bp/79+7u8BllZWZo8ebLS0tI0evRomeaphMBTTz2lBQsWSJKmTp2qmTNn6sCBA7ryyiu1bds2SdK///1vFRYW6pFHHpEkvf7665o6dapsNpsWLFigc845x+X5qn8dF1xwgUaOHKlly5YpNzdX8+fP19ixY1VcXKxbb71V27ZtU79+/XT06FE9//zzGjFihMu9Fi9erKuvvtr5uKbXrj4uvPBCLV++3GPcNE1t2rRJw4YNc/nsN2rUKB05cqTO+27YsEH33XefCgsLFRcXp4ULFyoxMbHO68LDwzVmzBjt3ev5fZKfn6/y8nLFx8dr/PjxLnN64403nI+vueYaLV68WOedd16dz1dfZFyB0+BeKtxQGVdJMgxD59/gutb10M5S/XPyPj1z+/4Gex4AANA8fv75Z82ePVs7duxQamqqVq1apRkzZqhLly5atmyZli1bphMnTmjWrFn69ttvtXHjRo0YMUJPPfWU8x4dO3bUxo0bNWnSJElSUFCQ1q9frzvuuENXX321nn/+eW3btk0LFy5UVlaWdu7cqXfeeUerVq3Spk2bZLVatXjxYqWnp+vhhx/WqlWrtHLlyhqzpxMnTtS6deu0efNmDRgwQPPnz9e5556rq666Sk888YQ2bdqkXr16afr06Xr22We1YcMG/fvf/9Zdd93lca9HH31UY8aM0fbt23Xttdfq0KFDkioDrldffVVr1qzRTz/9pHnz5unnn3+u8/UsLi7Wpk2b9MILL+i2226r83ybzaa1a9dq9uzZevTRRyVJL7zwgmJjY7Vjxw79/e9/14YNG7xeu2rVKg0fPlySan3tFi9erKFDh3r8+c1vflPn/H7++WedeeaZHgmL+fPn67LLLqv12oqKCv3hD3/QkiVLtGHDBt122236y1/+Ikl64oknvM5pxowZdc7p22+/1YUXXugx7j6nESNG6Icffqjzfr4g4wqcBofNPXBt2Pt3HxiqHkNCtX+La4lwUV7jlQMBAICmcc4556hr166SpKFDh+rAgQMaM2aMyzk//fSTduzY4cxclZeXa/To0c7jN9xwg8v5V111lSTpjDPO0KBBg5wZtp49e+rw4cNauXKlNmzYoLPPPluSVFJSooSEBK1Zs0YXXHCB4uPjnffdvXu3x5y3bdumhx56SLm5uSosLNQll1zicU5hYaF+/PFHXX/99c6xsjLPJpMrVqzQBx98IEm64oorFBsbK0lauXKlrr32WoWHh0uqDJZ/+OEH59dWk8mTJ0uSxo0bp/z8fOXm5tZ6/sSJEyVJw4cP14EDB5zPfc8990iSBg8erCFDhni9Nj093fla1fba3XTTTbrppptqnUdNvvrqK48AddmyZZo/f75WrlxZ67W//PKLtm3bposvvlhSZSl51b+F+++/X/fff7/fc5oyZYrL2BtvvKH169fr+++/d44lJCTo6NGjfj1HTQhcgdPgcIsfT3cfV28uuKGj9m+puxwEAAC0LtXLSa1Wq2w2m8c5pmnq4osv1ltvveX1HlXBnfs9LRaLy/0tFotsNptM09Qtt9yif/7zny7XffTRR/Wa86233qqPPvpIZ555phYuXOi1xNXhcCgmJkabNm2q1z3rKyAgQA6Hw/m4tLTU5bh7ZrKupVVVr09Nr31tQkNDPZ7fm8WLF+uJJ57wGO/du7eWLFlS67VLly51ll1L0pYtWzR16lR9+eWX6tixYy1XVv67GTRokFavXu1x7IknntDixYs9xseNG6c5c+bUet+1a9fqxRdfdD7+9ttv9Y9//EPff/+9y7+30tJShYaG1novXxG4AqfBfR9Xi6XhA9fEXiFex8tKHAoOpdofAABf1WcNanW5xTa9/3O2dh8v1f9NTG6kWZ0SGRmpgoICxcXFadSoUbr77ru1d+9e9e7dW0VFRUpLS1Pfvn39uveFF16oq6++Wvfee68SEhKUnZ2tgoICjRw5Uvfcc4+ysrIUFRWl9957T2eeeabH9QUFBUpMTFRFRYUWL16spKQklzlLUlRUlHr06KH33ntP119/vUzT1JYtWzzuN27cOL355pt66KGH9OWXXyonJ0eSNHbsWN1666164IEHZJqmPvzwQ73++uvq1KmTMjIylJWVpYiICH322Wcu3WvfeecdjR8/XitXrlR0dLSio6N9fn3OO+88vfvuuxo/frx27NihrVu3ej1vwIAB2rt3r1JSUmp97fzNuObl5clmszkD1EOHDmnixIl6/fXXPf7uL7zwQi1atMj5dyFJ/fr1U2ZmplavXq3Ro0eroqJCu3fv1qBBg/zOuG7fvl39+/eX9WRTl59//lm33367vvrqKyUkJLicu3v3bg0ePNjn56gNgStwGtwzrtZG+o4KjbSopMDhMrb6oxxdMLn237YBAIDTFxMWoN+dl1D3iQ1k+vTpuvTSS51rXRcuXKjJkyc7y21nzZrld+A6cOBAzZo1S7/61a/kcDgUGBio559/XqNGjdIjjzyi0aNHKyYmRkOHDvV6/d///neNHDlS8fHxGjlypDNYnTRpkqZNm6Y5c+ZoyZIlWrx4se68807NmjVLFRUVmjRpkkfg+vDDD2vy5MkaNGiQzj33XCUnV/5SYNiwYbr11ludzZWmTp2qs846S5L017/+Veecc46SkpI8mj2FhITorLPOUkVFhbOxk6/uuusu3XLLLRo4cKD69++vQYMGeQ2Ar7jiCi1fvlwXXXSREhMT6/Xa1WTs2LHatWuXCgsL1bVrV82fP18FBQW66KKLnOf87W9/U1ZWlnOtcEBAgNavXy+Hw6G9e/eqQwfX3SiCgoK0ZMkSzZgxwxkEz5w5U4MGDarXnFJSUpyNmD766CMtXbrU2eG4yv3336/CwkJnSXhycrI++eQTSZUlzVdccYVPr0NdjOrdu1qaESNGmN72YwJainn3H1Lm4XLn46n/6qaE5Pp3kfPF9+9kadWHOc7H1kBDtz+ZrJiEwEZ5PgAA2pqdO3dqwIABzT0NtGB2u10VFRUKCQnRvn37dNFFF+mXX35RUFCQy3klJSUaP368Vq1a5cxANqSpU6dq6tSpGjVqVK3nbdu2TQsWLHBp2NVYLr74Yi1atKhenYnHjRunjz/+2LluuYq370HDMDaYpunattkLMq7AafAoFW7ArsLuRl8dq83L81WYU5nmtVeY+m7xCU28t+4fHgAAAKhbcXGxxo8fr4qKCpmmqRdeeMEjaJUq17g++uijSktLc2aKG9Irr7xSr/MGDx7cJEGrJH3zzTf1Oi8zM1P33XefR9B6ughcgdPQ2F2FqwsKsWj85I769IUM59iuNUU6tLNEyQMadvE7AABAexQZGan6Vnx666gMKT4+Xtdcc02D35fOLsBpcLguO5W1ETOukjR4TKQSe7qWIn/z2gmP/WQBAACAtoTAFTgNjiYsFZYkw2LoolviXMaOHyjT1hUFjfq8AAAAQHMicAVOg70JS4WrdOsXqgGjI1zGlr+dpbISRw1XAAAAAK0bgStwGky3WLGxM65VJtzYUQGBp56rKNeu1R/l1HIFAAAA0HoRuAKnwT3jag1omsA1Oj5QI6+McRlb80WucjMqmuT5AQCAf6xWq4YOHer88/jjjzf3lGo0e/ZsFRcXOx9ffvnlys3NrfWalJQUnThxot7PsXz5cl155ZV+ze/AgQMaPHiw12MXXHCBs8lSfeZdX+np6TXOt/pz1mXFihUaNmyYAgICtGTJkgaZW01M09SMGTPUu3dvDRkyRBs3bpRU2f23+r6sLR2BK3AamnqNa3Wjr45VROyp2mR7hanv3sxqsucHAAC+Cw0N1aZNm5x/HnjggeaeUo3cA9cvvvhCMTExtVzRMjXkvJ966ilNmzbttO+TnJyshQsX6sYbb2yAWdXuyy+/1J49e7Rnzx7NnTtXd955p6TK7r+JiYlatWpVo8+hIbAdDnAa7HbXx02xxrVKUIhFF0zqqM9erLY9zk+FemzSXoVHW3XPyz2abjIAALQij03a26j3//PbvX06Py8vT+ecc44++eQT9evXT5MnT9aECRM0bdo0RUREaNq0aVq6dKk6d+6st99+W/Hx8dq0aZPuuOMOFRcXq1evXlqwYIFiY2N1wQUXaOTIkVq2bJlyc3M1f/58jR07Vna7XQ888ICWL1+usrIy3X333br99tu1fPlyPfLII4qLi9O2bds0fPhwvfHGG3r22Wd19OhRjR8/XnFxcVq2bJlSUlK0fv16xcXF6ZprrtHhw4dVWlqqe+65R9OnT6/31/vVV19p5syZCgsL05gxY5zj2dnZuu2225SamqqwsDDNnTtXQ4YM0SOPPKKIiAj98Y9/lFS5d+lnn30mSbLZbLrpppu0ceNGDRo0SIsWLVJYWJjL81XNu7CwUJdddpnGjBmjH3/8UUlJSfr4448VGhqqdevW6Xe/+50sFosuvvhiffnll9q2bZvH3N9//33NmjVLklRSUqIpU6Zo8+bN6t+/v0pKSur9GqSkpEiSLJb65xGXLl2qhx9+WGVlZerVq5deffVVRURE1Hndxx9/rJtvvlmGYWjUqFHKzc1Venq6EhMTdc0112jx4sU677zz6j2P5kLGFfCT6TCl6glXQ7JYmi7jKklnjPXcHkeSivLsXs4GAADNraSkxKVU+J133lF0dLSee+453XrrrXr77beVk5PjzOoVFRVpxIgR2r59u84//3w9+uijkqSbb75Z//d//6ctW7bojDPOcI5LlcHc2rVrNXv2bOf4/PnzFR0drXXr1mndunWaN2+e9u/fL0n6+eefNXv2bO3YsUOpqalatWqVZsyYoS5dumjZsmVatmyZx9exYMECbdiwQevXr9ecOXOUlVW/qq/S0lJNmzZNn376qTZs2KBjx445jz388MM666yztGXLFj322GO6+eab67zfL7/8orvuuks7d+5UVFSUXnjhhVrP37Nnj+6++25t375dMTExev/99yVJU6ZM0csvv6xNmzbJavWeidi/f79iY2MVHFz52evFF19UWFiYdu7cqUcffVQbNmxwnnvDDTe4/D1X/Vm0aFGdX5M3J06c0KxZs/Ttt99q48aNGjFihJ566ilJ0r333uv1uarK0NPS0tStWzfnvbp27aq0tDRJ0ogRI/TDDz/4NaemRsYV8JN7trWGn3GNqmp7nNcfTmv6JwcAAD6rKhV2d/HFF+u9997T3Xffrc2bNzvHLRaLbrjhBknSb3/7W02cOFF5eXnKzc3V+eefL0m65ZZbdP311zuvmThxoiRp+PDhOnDggKTKbN2WLVuc6ynz8vK0Z88eBQUF6ZxzzlHXrl0lSUOHDtWBAwdcMqHezJkzRx9++KEk6fDhw9qzZ486duxY59e/a9cu9ejRQ3369HF+TXPnzpUkrVy50hlITpgwQVlZWcrPz6/1ft26dXNmC3/7299qzpw5zsysNz169NDQoUMlnXp9cnNzVVBQoNGjR0uSbrzxRmdGt7r09HTFx8c7H69YsUIzZsyQJA0ZMkRDhgxxHnvnnXdqfyF89NNPP2nHjh3Or7W8vNw536efftrv+yYkJOjo0aMNMsfGRuAK+Kk517dW161fqNfx/BMViooLbOLZAAAAfzgcDu3cuVNhYWHKyclxBpLuDKPuzxtVGUGr1SqbzSapskHPs88+q0suucTl3OXLlzvPd7+mJsuXL9e3336r1atXKywsTBdccIFKS0vrnJe/AgIC5HCc2sqh+nO5vx51vT7uX6sv5b2hoaH1/jpvuOEG/fLLLx7j9913X70yye5M09TFF1+st956y+PYvffe6zUrPmnSJD3wwANKSkrS4cOHneNHjhxRUlKSpMrXMjTU+2fJlobAFfBTSwlcJSksyqLifNe9eZa+dkK/+Z/EZpoRAAAtV33XoD5z+36X5TeN2UPi6aef1oABA/TYY49pypQpWr16tQIDA+VwOLRkyRJNmjRJb775psaMGaPo6GjFxsbqhx9+0NixY/X66687s681ueSSS/Tiiy9qwoQJCgwM1O7du53BS00iIyNVUFCguLg4l/G8vDzFxsYqLCxMu3bt0k8//VTvr7N///46cOCA9u3bp169erkEYmPHjtXixYv1v//7v1q+fLni4uIUFRWllJQUZwZ048aNzhJnSTp06JBWr16t0aNHO18fX8XExCgyMlJr1qzRyJEj9fbbb3s9r2/fvs4MtiSNGzdOb775piZMmKBt27Zpy5YtzmOnk3Ht37+/du3a5TI2atQo3X333dq7d6969+6toqIipaWlqW/fvnVmXK+66io999xzmjRpktasWaPo6GglJlZ+Rty9e3eNnZlbGgJXwE/N2ZjJ3cy5PbXxmzx9NT/TObZ7XZF2ry9U3xF1L9oHAACeGiNIrVrjWuXSSy/VlClT9Morr2jt2rWKjIzUuHHjNGvWLD366KMKDw/X2rVrNWvWLCUkJDgDotdee83ZnKlnz5569dVXa33eqVOn6sCBAxo2bJhM01R8fLw++uijWq+ZPn26Lr30Uuda1+pzfumllzRgwAD169dPo0aNqvfXHxISorlz5+qKK65QWFiYxo4dq4KCAknSI488ottuu01DhgxRWFiYXnvtNUnSddddp0WLFmnQoEEaOXKk+vbt67xfv3799Pzzz+u2227TwIEDnR1zfTV//nxNmzZNFotF559/vqKjoz3OCQ8PV69evZzB45133qkpU6ZowIABGjBggIYPH17v51u3bp2uvfZa5eTk6NNPP9XDDz+s7du368SJEzJN0+P8+Ph4LVy4UJMnT1ZZWZkkadasWS6vRU0uv/xyffHFF+rdu7fCwsJc/q0sW7ZMV1xxRb3n3ZwMby9MSzFixAizvnshAU2tINumZ+864HwcEWvVjBebr5Ov6TC16OEjSttT5hyL7BCg6U8mKziUPmwAAOzcuVMDBgxo7mn4JCIiQoWFhc09jTavsLDQ2aH38ccfV3p6up555hmP8z788ENt2LDB2Vm4oX322WdKTU11rp1tbOPGjdPHH3+s2NjYJnk+b9+DhmFsME1zRF3XknEF/ORRKtzEHYXdGRZDl01N0PwHD8s8WTVckG3TD+9l6aKb42u/GAAAoB37/PPP9c9//lM2m03du3fXwoULvZ537bXX1ruDsj+uvPLKRru3u8zMTN13331NFrSeLgJXwE+OFlQqXCWhe7BGXhGjnz7NdY6t+zJPg8dGqXMPz21zAABAy0a2tWnccMMNzu7NdZk6dWojz6ZpxMfH65prrmnuadQb9YOAn+zuGdeA5s24VhlzXQdFx536nZRpSl/Oy5DD0XKXBQAAAAC1IXAF/OReKmxtxq7C1QWFWHTJba6lwempZdq4NK+ZZgQAQMvRkvu7AG3Z6X7vEbgCfvLcDqeZJuJF72Hh6j8y3GVs+TtZKsiufV82AADaspCQEGVlZRG8Ak3MNE1lZWUpJCTE73uwxhXwk+ca15aRca1y8S3xSt1SrPKSyjfn8hJT37yWqYn3srcrAKB96tq1q44cOaLMzMy6TwbQoEJCQtS1a1e/rydwBfzkvsa1pZQKV4nsEKALbuiopQtPOMd2rSnS3o1F6j0svJYrAQBomwIDA9WjR/NtXQfAf5QKA35y2FwDV6MFlQpXGfaraCX2dO0m/O6/0jV7+v5mmhEAAADgOwJXwE8Oh+vjlpZxlSr3lr1sWoLHeHG+3cvZAAAAQMtE4Ar4yT3j2tLWuFapaf/W1M1FTTwTAAAAwD8EroCf7G5JS2srWzH++csZKi0i8woAAICWj8AV8JP7djiGpWVmXCUpPNpzAW5Btl3fvHbCy9kAAABAy0LgCvjJPXBtiWtcq9zzcg/9+e3eGn1VjMv41hUF2r2ekmEAAAC0bASugJ889nFtBaXCY6/vqLiuQS5jX87LUHEBJcMAAABouQhcAT+57+NqacGlwlUCAg39+q4EGdW+84vy7Pp6ARuxAwAAoOUicAX85FEqHNDyA1dJSuwZovOujXUZ27m6UDt/KmymGQEAAAC1I3AF/ORRKuzZ/6jFOu/aDuqU4loy/NX8DBXm2pppRgAAAEDNCFwBP9lbyT6u3lgDDP36rk4uwXZJgUNfzc+UaZo1XwgAAAA0AwJXwE/upcKtKXCVpITkYI39TQeXsd3rirR9JSXDAAAAaFkIXAE/ORyuj62tqFS4yuirYtWlV7DL2CfPH9fT01KbaUYAAACAJwJXwE+OVlwqXMViNXTlXZ08xksKHB4ZZQAAAKC5ELgCfvLYDqcVBq6SFJcU5HV85QfZTTwTAAAAwDsCV8BPnmtcm2kijWTVBzk6uKOkuacBAAAAELgC/nLfDqe17OPqTXi0Z9RtmtInzx1TcYHdyxUAAABA0yFwBfzU2rsKV3fPyz3057d7a9KDXVzGC7Lt+vyl42yRAwAAgGZF4Ar4ye6WiLS0ge+mnmeGadSvY1zG9mwo1vqv85ppRgAAAACBK+A3j4xrKy4Vru78Gzp6bJHz3RsndGx/WTPNCAAAAO0dgSvgJ/fA1dqKS4WrswYYunpGZwWHnvrxYLdJH805pvJSRy1XAgAAAI2DwBXwk8Pm+rgtdRWO7RSoy6bFu4xlp1do6auZzTQjAAAAtGcEroCf2so+rjUZeG6kzhwf5TK25fsCbVtZ0EwzAgAAQHtF4Ar4qS11Fa7JxbfEqWNSoMvYJ88d12OT9uqZ2/c306wAAADQ3hC4An7y3Me1eebRmIJCLLr2ns6yBnoG5UV57O8KAACApkHgCvjJI+NqaXsZV0lKSA7WRf8d5/UY+7sCAACgKRC4An5qD6XCVYZdHOV1fO0XuU08EwAAALRHBK6An+xulbKWNlgqXMUwDIVFebZN/m5xlg5sL26GGQEAAKA9IXAF/NRW93Gtycy5PXTH7GQFh536sWE6pI+eOa78ExXNODMAAAC0dQSugJ8ctvZTKlylQ+cgXf37Ti5jxfl2ffD0MdkqWO8KAACAxkHgCvjJ4XB9bPGspG2Teg8L19jfdHAZO7qvTEsXZjbTjAAAANDWEbgCfrK3s1Lh6sZMjFXvYWEuY5v+k69N3+U104wAAADQlhG4An5yLxU22lHgalgMXXV3J8V2CnQZ/3pBpo7uLW2mWQEAAKCtInAF/ORw6ypsbSelwlVCwq267n86KzD4VMBut0kLHzqixybt1TO372/G2QEAAKAtIXAF/NSe9nGtSUJysC6/PcHrsaI8u9dxAAAAwFcEroCfPNa4BrS/wFWSBp0bqXOuiPF6zDTpNAwAAIDTR+AK+Mm9VNhox99NE27s6HV81Yc5TTwTAAAAtEXt+KM2cHrcS4Xba8ZVqiyTDovy/HGy4t1s7Vhd0AwzAgAAQFtC4Ar4iTWurmbO7ak7nk5WaITrj5XPXshQ2h46DQMAAMB/BK6An+xupcKWdtZV2JsOiUGaeF+iy2thqzD13r/TlZdZ0XwTAwAAQKtWZ+BqGMYCwzAyDMPYVm3sEcMw0gzD2HTyz+XVjj1oGMZewzB+MQzjkmrjl54c22sYxgMN/6UATct9H1drO8+4Vuk+MFSXT3ftNFycZ9e7/0pXWbGjmWYFAACA1qw+GdeFki71Mv60aZpDT/75QpIMwxgoaZKkQSevecEwDKthGFZJz0u6TNJASZNPngu0SqbDlHvD3PbcnMndkPOjdO7VsS5jmYfL9dGcYx4l1gAAAEBd6vyobZrmCknZ9bzf1ZLeNk2zzDTN/ZL2Sjrn5J+9pmmmmqZZLuntk+cC+A4eBgAAIABJREFUrZLDLXFosUqGQca1uvNv6KD+I8NdxvZtKta3r59ophkBAACgtTqdHNHvDcPYcrKUuCq1kiTpcLVzjpwcq2ncg2EY0w3DWG8YxvrMzMzTmB7QeOw2GjPVxbAY+vVdnZTYK9hlfP1XeXps0l49c/v+ZpoZAAAAWht/A9cXJfWSNFRSuqQnG2pCpmnONU1zhGmaI+Lj4xvqtkCDcjhY31ofgcEWXf/HREV1DPA4VpRn93IFAAAA4MmvwNU0zeOmadpN03RImqfKUmBJSpPUrdqpXU+O1TQOtEoOm+tji2dchpMiYgN0/f9L9Hps/9biJp4NAAAAWiO/AlfDMKp/Cr1WUlXH4U8kTTIMI9gwjB6S+khaK2mdpD6GYfQwDCNIlQ2cPvF/2kDz8tjD1ULGtTadugd7HX//yXQd288erwAAAKhdfbbDeUvSakn9DMM4YhjG7yT9yzCMrYZhbJE0XtK9kmSa5nZJ70raIekrSXefzMzaJP1e0teSdkp69+S5QKtkdw9cKRWuU3i050a35aWm3n48XdnHypthRgAAAGgtDNN9T48WZMSIEeb69eubexqAh5zjFXrxnoPOxzEJAbprTkrzTagVWfNZjv7zRpbLWExCgG5+tKsiYqm5BgAAaE8Mw9hgmuaIus5j50nADx6lwmRc623klbEa9esYl7HcDJvefvyoSotp2AQAAABPBK6AHygVPj3jJ3fUGeMiXcYyDpZryRPpspU7argKAAAA7RWBK+AHj67Cnss3UQvDYujy6QnqfVaYy/ihnaX66NnjHtsNAQAAoH0jcAX8wD6up88aYOjamZ2V1Me14/DudUV6/MZ9eub2/c00MwAAALQ0BK6AHxw2SoUbQmCwRdf/vy7qmBTocawoz66W3DwOAAAATYfAFfCD3a2HEKXC/guLtGryg128Hlv2ZhbBKwAAAAhcAX/QVbhhRcV5Zlwl6adPc7Xivewmng0AAABaGgJXwA/ugas1gMD1dIVHe09br/ogR6s+JHgFAABozwKaewJAa+RwLxXmV0Cn7Z6Xe0iSju0v1eK/H1VZ8altcb5/J1vWAEOjfh3bXNMDAABAM+LjNuAHj31cybg2mM49QjTpwS4KCnV9Tb9bnKV1X+U206wAAADQnAhcAT+wxrVxJfUJ0Q1/6qLAYNfX9ZuFJ/Tzt3nNNCsAAAA0FwJXwA/upcJWugo3uG79Q3X9/0tUQKBr8PrlK5l6bNJe9nkFAABoRwhcAT+wj2vTSBkUpt/8sbOsXlbjF+XZPQcBAADQJhG4An5wOAhcm0rPM8M18d5Er8c2LKVsGAAAoD0gcAX8YLe5PrZQKtyo+gwP9zr+9YJMrfk8p4lnAwAAgKZG4Ar4geZMTa+mfV7/83oW+7wCAAC0cezjCvjBPXClOVPjq9rndd+mIr3/5DHZKk79HXz/TrYqyk2d/18dZBj8EgEAAKCtIeMK+MG9qzAZ16bTa2i4/utPiR5b5fz4YY7+80aWTNOs4UoAAAC0VgSugB/s7qXCAQSuTSllcJgm/bmLgkJdX/e1n+fq61dPyHQQvAIAALQllAoDfvBY48qvgJpct36huvEvSXr7n0dVWuRwjm9cmqeNJ7sNh0dbnSXGAAAAaL34uA34weHWVdhKxrVZdOkdopv+N0mhkd5/lLHXKwAAQNtA4Ar4gX1cW45OKcH67V+TFB7jvUNWaTHBKwAAQGtH4Ar4wW5zD1ybaSKQJMV3qwxevXnj0TQV5ti8HgMAAEDrQOAK+IGuwi1Pxy5BXkuGMw6Wa9HDR5R9rLwZZgUAAICGQOAK+MG9VNhK4Noi3Duvp2bO66GkPsEu47kZNi36a5rSU0ubaWYAAAA4HQSugB8cHqXCBK4tRVikVZP/kqReZ4W5jBfn27X4b2nav7W4mWYGAAAAfxG4An6we5QKN8884F1QiEW/+Z9EnTEu0mW8vNTUO48f1Y7VBc00MwAAAPiDwBXwg/s+rpQKtzzWAENX3pmgUb+OcRl32KWPnjmuxybt1TO372+m2QEAAMAXBK6AH9wDVwv7uLZIhmFowk1xuvC/O3o9XpRn9/i7BAAAQMtD4Ar4wbOrcPPMA/Uz8opYXXV3J6/H3v1XusqKHU08IwAAAPiCwBXwg90942oh49rSDR4b6XU8dXOxFj18RHmZFU08IwAAANQXgSvgB481rgHNNBH4JDzae2o883C5Fj50REf3sV0OAABAS8THbcAPnqXCZFxbg3te7iFJKsy16b0n0pW+r8x5rCjPrjceTdNVv++k/udENNcUAQAA4AUZV8APdvZxbdUiYgL0278mqd854S7jtnJTHzx1TD99miPTpGkTAABAS0HgCvjBo6swzZlancBgiybO7OyxXY4kfbc4S/+cvE+z2S4HAACgRSBwBfzgcGtCyz6urZNhqdwu57Jp8TK8/DQszrOrINvW9BMDAACACwJXwA8O91Jh9nFt1c66MFqTHuzi9dirfzmstD00bQIAAGhOBK6AHzy3w2mmiaDB9DgjzOt4YY5dbzx6RJu+y2/iGQEAAKAKH7cBP9BVuG2qabscu036Ym6Gvl6Q6dGYCwAAAI2P7XAAP3ju40rg2hZUbZfjcJj6/u0srf4k1+X4hqV5yjxcpmvvTVR4FB25AAAAmgqBK+AHj67C1C60KRaLofE3xikhJVifv5QhW/mpv+9DO0v1zPTKbsPh0VZnsAsAAIDGw8dtwA9291JhMq5t0qBzI3XL37oqOs777/iK8uzs9woAANAECFwBP5ge+7gSuLZVnVKCdetj3ZQ8MNTr8U9fyFB5qcPrMQAAADQMAlfAD+5dhdnHtW0Lj7Jq8p+9b5ez7YcCLXzoiE6klTfxrAAAANoPAlfADw6b62MLfXraPGuAUWPX4RNHyrXwL4e1/ceCJp4VAABA+0BzJsAPHvu4knFtF6oaMZ1IK9f7T6UrK63Ceay81NTHc47ryK5SXfjfcQoI5N8EAABAQyHjCvjINE2Zbksaybi2L3FJQZryj24aNCbC49iGpXl6/ZEjys2o8HIlAAAA/EHgCvjI4dZR2LBIhkF2rb0JCrHoqrs76dKp8bK61a6k7yvTCzMO6snbUptncgAAAG0MgSvgI/c9XGnM1H4ZhqFhF0Xr5r91VUyC58qLsmKHvphL12EAAIDTReAK+Mg942phpXi7l9gzRFMe6+b12Kbv8vXqnw/r+MGyJp4VAABA20HgCviIrXDgTWhEzQuds45WaOFfDmvtF7kyTbPG8wAAAOAdgSvgI/dSYYPAFSfVtF2OJNlt0reLTujdf6WrKM9W43kAAADwRJEj4COHzT3j2kwTQYtTtV2OJJWXOvTNwkxtXu66t+u+n4v1yp8O66q7OqnHkLCmniIAAECrROAK+MjhsRUOGVd4Cgqx6Io7OqnHmWH6cl6myopP/cMpyrXrrceOSpLCoqyaObdHTbcBAACAKBUGfGZ3y7gSuKI2A0dH6nePd1PXviFejxfn23V0b2kTzwoAAKB1IXAFfOS+xtVCqTDqEJMQqN8+nKQx18V6Pf7aX4/o+3ezPH4pAgAAgEoEroCP3LfDoasw6sNiNTTu+o5ej5kOadUHOVr40BFlHmbbHAAAAHcEroCPPDKuAQSuqL/aOg8fP1CmBX8+ojWf5cjhIPsKAABQheZMgI/c93G18Osf+KB65+G9Pxfp85czVJR7Ko1vrzD1nzey9J83siRVBrrVrwEAAGiP+MgN+Mi9VJjmTPBX77PCNe2JZA0YFVHjOUV5drKvAACg3SNwBXzkXipspVQYpyEs0qprZ3bW1TM6KSTc+4/kRX9l7SsAAGjfCFwBH9FVGI1h0LmRmvZEstdjR/eWaf4Dh7Xy/Ww6DwMAgHaJwBXwkd3m+phSYTSUyA4BNTZvctilFe9l69U/H1Z6Kvu+AgCA9oXmTICPPEqFCVzRgKoaMRXm2PTVgkztXlfkcjzjULkWPnREo66M0ZjfdFBgEL9/BAAAbR+feAAfORyujykVRmOIiA3Qdfd11rUzOyvMLQtrOqTVn+TqiZtT9dTvUptphgAAAE2HwBXwkcPmvsaVjCsah2EYGjAqQtP/nazBYyK9nlNa5NBHc46pMNfm9TgAAEBbQOAK+MhjH1cCVzSysEirrvp9J/3XnxK9Ht/xY6Fevu+QNizNk8nWOQAAoA0icAV85L6Pq5VSYTSR3meF13isrNihrxdk6rW/HtHxg2ydAwAA2hYCV8BHHtvhsI8rmlBNXYerHN1bpgUPHtZ/Xj+h8lJHrecCAAC0FnQVBnzkUSpsIXBF06nqOixV/hJl/dd5WvFulspLT/27NB3Sms9ztebzXAWHWXTf/B4yDP6dAgCA1ouMK+Ajj4wrpcJoJharoXMuj9H0J7ur3zney4jLih1a/Lc0ZRyifBgAALReBK6AjzzWuFIqjGYW1TFA192XqOvv99686dDOUs1/4LCWLsxUaZHd6zkAAAAtGYEr4COPjCulwmgh+gyvuXmT6ZDWf5Wnl+49pE3f5dN9GAAAtCqscQV8ZHffx5XvIrQg4dFWFeXVnFUtzrfri7kZ+mJuhvP86utmAQAAWiI+cgM+ci8VZh9XtCTVg1DTNLVnQ7G+XZSp3Ayb1/OL8uzKO1Gh6LjAppoiAACAzygVBnzkXipsJXBFC2UYhvqOCNf0fydr3PUdFBDk/d/qy/ce0vfvZLF9DgAAaLEIXAEf0VUYrU1AkEVjruug259M9nrcVmFq1Yc5enHmQW1eli8H618BAEALQ+AK+MhOqTBaqej4QIVH1/yblqJcuz5/OUOv/vmwDmwvbsKZAQAA1I41roCPPDOuBK5oParWwDocprYsz9f372R7NHM6fqBcb/79qPMxDZwAAEBzI+MK+MizOVPzzAM4HRaLoaETonXH7O4695pYWQNr/gVMUZ5d+VnemzsBAAA0BQJXwEc0Z0JbEhxq0QWTOuqOp5I18NyIGs97aeZBLXvzhEqLat5qBwAAoLEQuAI+8tzHlcAVrV90fKCumdFZt/y9q9fjtgpTqz/J1QszDmrNZzmyldOBGAAANB0CV8BHDrfP65QKoy1J6hNSawOn0iKH/vNGll6695C2LKcDMQAAaBo0ZwJ8RHMmtHXOBk52U5uX5WvFkmwV5bqWCOdn2fTZSxn67KUMBYdZdN8rPWRY+F4AAACNg4wr4COHjTWuaB8sVkNnXRStO2d31/k3dFBwqPe3jLJih+Y/eFh7NhTJNMnAAgCAhkfgCviIUmG0N0EhFp13bQfd+Ux3nX1ZtNdzMg6W670n0vXaQ0e0f0sxASwAAGhQBK6AjzyaM5FxRTsRFmXVxbfE13rO0X1leuuxo3rjb2k6tLOkiWYGAADaOta4Aj5ijSvau/Boq4ryat8W5/DOUr3xaJokKSTcovvm92yKqQEAgDaKwBXwkec+rs00EaCZVDVvqpJxsEwrlmRr97oir+eXFjn0xt/SNOa6WHUfGCrD4Jc9AADANwSugI8cbokm9nFFe5fQPVi/+Z9EHd1XqhXvZit1c7HHOYd2lOjNHSXq1j9EY67roJTBBLAAAKD+WOMK+MjuXirMFiCAJKlLrxBNerBLrecc3lWqt/5xVK8/nKbUzTRxAgAA9UPGFfCRZ8a1eeYBtFT1WQN7ZHep3v7nUUliH1gAAFAnPnIDPmIfV6B27mtgj/xSopUf5HgtIZYq94Gde/8hnXt1rAaeGykr5fcAAMANpcKAjxwOugoDvujaL1STHuyiW/7eVb3OCvN6TlZahT59IUMvzTyo9V/nqqLc4fU8AADQPhG4Aj6y21wfW+gqDNRLUp8Q3fCn2tfA5p2waemrJ/T8Hw7qx4+yVVpce8kxAABoHygVBnzkuR0OGVfAF/VZA1ucZ9fyt7O1/O1sBQYZuv2pZEXFBTbRDAEAQEtD4Ar4iFJh4PS4r4HNOV6hnz7N0ZbvC2Sv8OwyXFFu6oV7Dmrg6EiNvDJGnVKCm2qqAACghSBwBXzkoFQYaFCxnQJ12dQEjb2ug9Z+kaufPs31OMdhl7atLNC2lQVKOSNUo66MVY8h7AULAEB7QeAK+MhjH1cyrkCDiIgN0ISb4rwGrtUd2FqiA1tLXMbCo60emVwAANB21NmcyTCMBYZhZBiGsa3aWAfDML4xDGPPyf/Gnhw3DMOYYxjGXsMwthiGMazaNbecPH+PYRi3NM6XAzQ+jzWubN0BNKjwaNcyBqMebQSL8uwqyrPVfSIAAGiV6pNxXSjpOUmLqo09IOk/pmk+bhjGAycf/0nSZZL6nPwzUtKLkkYahtFB0sOSRkgyJW0wDOMT0zRzGuoLAZqCaZpyuPWUsdCbG2hQ7plT02Fq78/F+unTHB3eVVrjdc/9/qAGnRehsy+LUafurIMFAKAtqTNwNU1zhWEYKW7DV0u64OT/vyZpuSoD16slLTJN05T0k2EYMYZhJJ489xvTNLMlyTCMbyRdKumt0/4KgCZkum0taRiSYSHjCjQmw2Koz/Bw9RkerrQ9pVrzWY52rSnyOM9eYWrL8gJtWV6g7oNCdfZlMeo9LEwWvkcBAGj1/F3j2sk0zfST/39MUqeT/58k6XC1846cHKtp3INhGNMlTZek5ORkP6cHNA6P9a2UCQNNKqlPiCbem6inp6WqpMBR43kHt5fo4PZT62DDoiyaObdnU0wRAAA0gtNuzmSapmkYhuf+Bf7fb66kuZI0YsSIBrsv0BDcy4StdBQGmsW98yqD0NJiu7YsL9D6r3KVm1HzGtfifIc+fzlDw38Vrc49KCMGAKC18TdwPW4YRqJpmuknS4EzTo6nSepW7byuJ8fSdKq0uGp8uZ/PDTQb98ZMdBQGmldImFXnXB6jEZdGa8+GIq37Mk+HdpR4PXfzsnxtXpavrn1DNPxX0eo/KoLmagAAtBL+Bq6fSLpF0uMn//txtfHfG4bxtiqbM+WdDG6/lvRYVfdhSb+S9KD/0waah91G4Aq0RBaLoX5nR6jf2RE6fqBM8x84XOO5R3aX6sjuUn383HHnGNvpAADQstVnO5y3JK2W1M8wjCOGYfxOlQHrxYZh7JF00cnHkvSFpFRJeyXNk3SXJJ1syvR3SetO/vlbVaMmoDXx6ChMqTDQ4nRKCfbYUqcuRXl27dlQJIeDFSoAALRE9ekqPLmGQxd6OdeUdHcN91kgaYFPswNaGI89XMm4Ai1S9eypw2Fq78Yirf86Twe2ei8jlqT3nkhXVMcADZ0QpTPHRymyw2m3gQAAAA2Ed2XAB6xxBVofi8VQ3xER6jsiQifSyrXxmzyt/yrP67n5WTateC9bP7yfrT7DwzXsoij1OCOMba8AAGhmBK6AD+yUCgOtWlxSkH51a7x2/Fio4nx7jeeZDmn3uiLtXle5X2xgsKHbn0xWVFxgU00VAABUQ+AK+MAj40pHUqBVmjm3spTYNE2l7yvTxm/ztOPHQtnKva9xrSgz9fwfDqrnmWE6c0KU+gwLpyMxAABNiMAV8AFrXIG2xTAMdekdoi69Q3TRf8dp6w8F+vnbfJ04Uu5xrmlK+zYVa9+mYoVFW3XG2EidOT5KcUlBzTBzAADaFwJXwAceXYXr7MsNoLUICbfq7EtjNOKSaP1z8r5azy3Os2vNZ7la81muJCko1NDvn09RSBjrBwAAaAx87AZ84LGPK6WCQJtjGIbHdjp1/ZKqvMTUnNsP6ONnj2n/1mK21QEAoIGRcQV84P5hlK7CQNtUfTudKsf2l2rTd/navqpQZcUOj+O2ClPbVxVq+6pCRXUM0OBxkRoyLlIdEiklBgDgdBG4Aj5w2Fwf01UYaD869wjRpb8L0YW/jdMTt6TWem5+lk0/fpijHz/McY6FRVk0c27Pxp4mAABtEqXCgA9ozgQgMNjiUUps1ONHQXG+Q0ueTNeutYWyVVBKDACAL8i4Aj6wu2+HQ+AKtEvupcSmw9TBHSXa8n2Bdq2peVudqr1hQ8It6j8qQmeMjVTXfiEy6hP5AgDQjhG4Aj7w6CpMqTAASYbFUMrgMKUMDtMlU+K1a02hPn85o8bzS4sc2vSffG36T75zLDTContfoZQYAABvKBUGfOBeKkzGFYC74DCLzhwf5VFOXJeSQofm3X9Iqz7MVm5GRSPNDgCA1omMK+AD1rgCqK/q5cSmaSp9X5m2/lCgHT8WqKTAsyuxJGUeLtf372Tr+3eyldQnWAPPjdSA0RGKiOHtGgDQvvFOCPjAo1SY7yAA9WAYhrr0DlGX3iG66L/jlLq5WO89kV7rNWl7ypS2p0zfvHZCkhQUaujOZ1IUHsUaBQBA+8PHbsAHHs2ZLGRcAfjGGmCoz/BwhUdbVZRnr/uCk8pLTM25Y79SBoVqwOgI9T07QmGRBLEAgPaBwBXwgcPmFrgGELgC8I97Z+KifLt2/VSo7asKdOSXUq/XmA5p/9YS7d9aoq/mZyplcFhlEDsiXKERBLEAgLaLwBXwgXupsJXPiQAaSHiUVcN/Fa3hv4pWXmaFnv/DwVrPd9il1M3FSt1crM9VuXThkinx6nt2BOXEAIA2h8AV8IHDQVdhAI0vOj7Qo5TYsFRmXGvisElfzsvUV69kKnlgqPqPjFC/s8MVEctbPQCg9ePdDPCB3b1UmKQGgEbiXkosSZlHyrXrp0LtWF2grDTvW+aYpnRwe4kObi/R1wsyneOhkRbdO499YgEArRP7uAI+8OgqTMYVQBOK7xqksb/poOn/Tvb52pICh+Y/cEg/LMlWxsEymaZZ90UAALQQZFwBH7h3FWYfVwDNwTAMj1LiwGBDsZ0ClXGovMbrjh8o1/ED2fphSbZiEgLU7+wI9T0nXEl9QuiSDgBo0QhcAR+Y7tvhUCoMoJl4KyWWpOz0cu1aW6Tlb2XVen1uhk1rPs/Vms9znWPBYRbNeDFFgcEUZAEAWhbemQAf2CkVBtDCdUgM0rlXxyo82vffrJUVO/T01P1674mj2vRdngpzbY0wQwAAfEfGFfCBwyPjSuAKoGXy2Cc2z6Y9G4q1e12h9m8tlr2GmNRWYWrPhmLt2VAsKdPlWHi0tcZMLwAAjYnAFfCBe+BqDSBwBdA6hEcHaOiEKA2dEKWyEof2bSrSR88c9+keRXl2fTU/Q73PClf3waEKDKJwCwDQNAhcAR94dBXmMxuAVig41KKBoyP1zcITrnvFGpXb6dRm4zf52vhNvgKCDKUMDlXvYeHqfVa4ojrykQIA0Hh4lwF84LGPKxlXAK2Ye9mvaZrKPFSu3RuKtGdDkdL3ldV4ra3c1N6Nxdq78VRJcWCwof/6Uxd17RtCRQoAoEERuAI+8CgVZo0rgDbEMAwldA9WQvdgjZnYQbOnpaq4wFHv6yvKTC3+W5qCQy1KOSNUvYaGq9fQMEV24OMGAOD08E4C+MC9VNhgOxwAbdjMeT2d/19R7tCh7SXa83Ox9m4sUv6JmjsOl5U49MvaIv2ytshlPCTcohkv9VBAIL/0AwD4hsAV8IGdjCuAdiowyKJeZ4Wr11nhMqfEKfNwuV75f4d9ukdpkUNPT01V90Gh6jkkTD3PDFNs50AZBj9LAQC1I3AFfMB2OABwsqQ4OVjh0VaX5k4BgYaCwiwqzrPXeG1FWfW1sa7CoiyaObenl6sAAO0dgSvgA/dSYSulwgDaMW97upoOU8f2l2nfpmKteC/bp/sV5zv02v8eVsoZYepxRpiS+tDkCQBQicAV8AEZVwConWExlNgrRIm9QrRhaZ5LRlaGpDq220nbU6a0PWVa9UGOgkIMJQ8MVY8zwpRyRpjikigrBoD2isAV8IH7GlcLGVcAqJHX7XYOlyt1c7FSNxfrwLaSWq8vL/UsK7YGGrrsd/FKGRyqqLjARpk3AKDlIXAFfOBwa6LJPq4AUH9Va2MTkoM16texmj19v4rza14P6429wtRnL2VIkjp0DlT3waFKGRym7oNCFRbJbxMBoK0icAV84HDQVRgAGsrMua4Z2YJsm/ZvLdb+rcU6sLXEtczYi+xjFco+VqGfv813jgUEGbpmRmclDwhRSDiBLAC0FQSugA8817g200QAoA2K7BCgIedHacj5UZVlxYfK9cqffNtyx1Zuasm/02UYUqceweo+MFTdB4WqW/9QBYdaGmnmAIDGRuAK+MDuXipMxhUAGoVhGEro7rnlTmCwoU4pwTq6t9Sj03t1pikdSy3TsdQyrfks1+X6a+/prK79QxQSxm8fAaC1IHAFfEBXYQBoWt623JGk8lKHDu0s0bv/l+7T/SrKTL37r1MZ2eQBoUoeEKpu/UMUGkEgCwAtFYEr4ANKhQGgZQgKsaj3WeEeGdmAIEMxCYE6caS81uurZ2TXfn4qIxsQZOjKOxOU3D9UEbF8TAKAloKfyIAP3MvSaM4EAM2rpoxsUZ5NB3eU6KNnjvt0P1u56bwmtnOgkvuHqFv/yjWyMZ0C2EcWAJoJgSvgA899XPkAAwAtUXh0gAaOjtQ3C0/4lZGVpJxjFco5VqHNywucY9ZAacKNcerWP0QJycG8DwBAEyFwBXzgUSrMPq4A0KLVmJHNt+vwzhJ98PQxn+5nr5C+ee2EJCkoxFCXPiHq1i9UXfuFKKlPiIJC6FwMAI2BwBXwgXupsIXPJwDQKoVHWdV/ZIRn1+IgQ/HJQTq2v6zWrsWSVF5q6sDWEh3YWuIyHhBk6IrpCeraL0RRcZQXA0BDIHAFfOCecbWScQWAVq22rsVpe0r11j+O+nxPW7mpj5+rXCcbEWtV174h6to3VEl9Q9QpJVgBgbx3AICvCFwBH9htrHEFgPYgKMSiHmeEeWRkg0IMpZwRpiO/lKo4v46UrKTCHLt2rSnSrjVFzjGLVRpxSbSS+oYqqU+IojrycQwA6sJPSsAHDofrY7bDAYC2raaMrGmayjlWocO/lOrzlzJ8uqfDLq39Ik/6Ik+SZBiV2/NUCYu2amYNzwsA7RUr9IB6cjhMqXoQscdNAAAgAElEQVTC1ZAsFjKuANAeGYahDolBOvOCKIVHu/4WMzDYUPKAEAUE1e89wnQt5lFxnl0LHjysr+ZnaOuKfGUdLZfpML1fDADtBBlXoJ4cbmXCVrKtAADVnJW120wdP1imhX854vM9j+0v07H9Zdr4Tb7HseAwi25/KlkRMXyMA9B+8BMPqCfPMmGyrQCAmlkDDHXpFeKxTjY4zKKh46OUtrdU6allslf4lk0tK3Zozh0HFNUxQIm9gtWld4i69ApW554hCg6lmA5A20TgCtQTjZkAAP6oKSMrVb63PHPHfpUWOmo8pyb5WTblZ9n0y9oil3FroKEJN3ZUYq9gdeoerMBgglkArR+BK1BP7lvh0JgJAHC6rAGG7nulp8tYUb5d6XtLlba3VEf3lmr/lpIarvbOXmHqm9dOSJIMixTfNUiJvUKU2DNYnXsGK6FbkAKCCGYBtC4ErkA9uW9Ezx6uAIDGEB5lVe9h4eo9LFyS9Mzt+11KjS3Wyk7Edlvd9zIdUsahcmUcKtfmZafGLRbpjPOj1LlHsBJ7BishmWAWQMtG4ArUk0fGlY7CAIAm4K3U2FZhKvNQmY7uK9PXCzJ9vqfDIW1elu8SzFYXEmHR759LUVAIwSyAloHAFagnO6XCAIAWIiDQqCz/7RWile9nu2Rkg0IM9TorXMdSy5RzvMKv+5cWOvTklFR16BKozj2CK/+kBKtTSrBCwnkDBND0CFyBenIvFbZQKgwAaAFqa/5UUmjXsdQyvfXYUZ/va5pSVlqFstIqtH1locsxa4B03rUd1OlkMBvZwSrD4H0RQOMhcAXqyXMfV96gAQAtW2iEVT2GhHlsyRMSbtGoX8coPbVyv9i8zHosmK3GbpNWvJd9asCQVO1tMjTConte7kEHfgANhsAVqCeHg1JhAEDrVFtWVpJmT09Vcf6pLXkMS2Vjp3pz24q2pNChJ25NVXy3IHVKDlJC98rMbEJyEKXGAPxC4ArUk3v3Rn6LDABoK2bO7ekxVlpsV8bBch3bX6ZvF53w+Z72ClPHUst0LLVMUoHLMWuANPLXserUvTKYje0cSNNDALUicAXqyb2rMKXCAIC2LCTMquQBoUoeEKrVH+e4NoAKNTR4TKSOHyhTxqFyVZSZtdzJk90m/fhhjvNxQJAhh9106ScRFmXxGlADaJ8IXIF68tgOh0onAEA7UVupscNh6pnb96ukoFptsdua17rYyj1PLs536Jk79iuhW5DikyszswnJQYpLYs9ZoD0icAXqyaOrMBlXAABksRi6d55nZrQw16aMg+U6frBMy97M8uveRbl27c8t0f6tJR7HrAHS6KtjFd8tWPHdgtShcyDvzUAbRuAK1JPnPq68OQIAUJOImABFxASo55lhWvt5rkep8dAJ0co4WKbjB8tcs7X1ZLdJK9/PqfF4cJhFtz3WTTEJATJYPwu0egSuQD15rHHluwcAgHqprdTYNE0V5dk1938OqbTI9wC2JmXFDr0486ACggzFJQUpvluQ4roGKb5r5X+j4whogdaEj95APbmXCvNmBwDA6TMMQxExAbpvvmu5scNuKvtYhTIOVTaAqt7MyRe2clPH9lfuV+uuc89gxSVVC2iTghSdEECHY6AFInAF6sm9VJiuwgAANB6LtTJTGpcUpIGjpc3f5XuUG595QZQyj5Qr83C5inLttdzNu1Pb9XiyBkrnXdNBHZOCFJcUqA6JQbIG8N4PNBcCV6CeHDa3Na589wAA0GRqKzeWpNnTU1Wcf6rU2GKVgkMtKin0r/zYXiGteC/b+dg42cjYrHa7kAiL7p6TouAwuhwDjY2P3kA9Odze98i4AgDQcnjb87Vq/Wzm4XK99Y+jp3V/00v8W1ro0JO3pSoi1qqOXSqzwx27BKpjUpA6JgYqsmOADIPPC0BDIHAF6skj40rgCgBAi1a1fjYiJkDh0VaXUuOw/9/efUdJcpb3Hv89nWdmd2dz3tVKWmVhIyQULLIkghAW2GCDLaJAYEBCyNjG93KPOfblXGOb5HvI4YJsTDBJAiRQQIAIEopIWoXVauNsmp0cO9Z7/6ia6TQzXTs7W9278/2cM2e663mr6qmemp5+5n3rrUUxvfq61erpyqtnb14P3j406/2M9Jc00j+uXVvqb9uzalPaL2bXprR0bVLL1qS0dE1SqQy9tMDhoHAFQqq/HU6TEgEAAIdtuqHGm85ulyQ99bvRKa+h7dmbV09XQcN9xVnt9+DOnA7unPo62lhcevYlnVq2Jqmla/zidtFyJocCpkLhCoRUO6swPa4AABw/Gl1Dmxv39Olrdypbcc2sxSSz+s8IYXkl6cHbBqeNJ9Oml75lhZYGhW37ojhDjzFvUbgCIdXex5XCFQCA+SPdFtMNX6q/jrZUdOo/WFDvvry++7EDc7rPQs7px5/vnjGnN/zPtVqyOqm2BQwFw/GNwhUIqbZwjfP3AQCAeS+eKN+2Z6rraF9z/Rr17curd19ev7tl+t7V2ciNe/rqh7okSW0LY1q6Oqklq1P+9zVJLV2V1JLVSWU6+NCCYx+FKxBSiaHCAABgBtMNNz7hzDZJ0pZfj1QVtun2mC66con69ufVt6+grq3ZWe97fNjT3uGc9j5dfz3tZFG7KqUlq/1idklQ1LYtiDH8GMcEClcgpPr7uPImDwAAwmt0He2n3rmjqrBNpk2bz+lQ34G8+vYXVMi5Gdae3kxFrSStPintF7KrKoraVUktWMI1tWgdFK5ASJ5XU7gyiz0AAJhDMxW2zjl96podGhsuTw4VT0hLVqfUf7CgUmF2Ra0kHdie04HtUxe1FpM2n9OuxSvLBe3iVUl1rkgqkaSoRXQoXIGQvJpZ8OP0uAIAgIiYma7/Yv3kUJL/z/WhnqI+c92uulg8IZVmdycfSZLzpKcfGJs2HotLz3r+Qi1eldTilcnJArdtIUOQMbcoXIGQ6u/jypsxAABovljMtHhlsm5yqI7OuK797CYN9RTVf7Cg/gMF/eTLh+Z0315J+v3Ph6eNxxPSuS/tVOfKpJasTKpzZVKLVySUTDN0DYeHwhUIyfOqnzNUGAAAtJLphhpP9ISe+Czp7u/0Vc98vDCm17x/jQaCwvY3N/XPaU6lomacTTmelC545RItXplQ5wo/z0XLEoxsQx0KVyAkJmcCAADHukYzH//+50NVhW1mQUwve9sKv7A9WNAjM/SuzkapIP3mBzMXy8m06WVvXaHOFQktXpnUwqUJRr7NQxSuQEj193HlDRMAABxfGs18/MxDY9W39OmI6YWvW6qB7oIGuovaev/onOdUyDn96HPd08YnCttFKxJavMIvbOmxPf5QuAIh1V/j2qREAAAAmuRwb+mTbo/pwlct1kB3UQPdBe3aMj7nOYUpbC9943J1rkho0fKkOlcklExxzdexhsIVCMkrVT9niAoAAEC1wy1sU22m816+WINBj+3AoYJGB0ozbOHwFXJOt35p+kmpEinTi16/TJ3LE35xu4xZkVsRhSsQUu1QYQpXAACAw9OosJWkT75zh8Yqittk2rT5OR1+cdtTrIrNhWLe6Y4be6aNJ1Kmi65cos5lCS1aHnwtTShBr22kKFyBkOquceW3BwAAYM5d36C4/eQ1OzQ2VF/YDvUUNHCoOOc9tsW8093/3Tdjm0TK9ILXLfWL2mV+r+2CJXHFYnR0zBU+egMh1Q0V5o0IAAAgctd/oUFhO0WP7WnnL9BgT0FDh4oa7CnOeU7FvNPPvt47bTyelM572eKgqE1oYfC9Y1FcxmfKUChcgZDqJ2fiTQYAAKDVNOqxrb3ONpkxnf28hRo8VNRQb1E9Xfk5z6lUkO790cC08VhcOv2CBeWidinFbS0KVyCk+vu4NikRAAAAzNphTyCVMT3nsk4N9hQ11FPUUG9Bw31zOxzZK0mP/2Zk2riZtO6UjBYuTWjh0rgWLksEjxNauCQxL24BxEdvIKTaocLcxxUAAOD4E2YCqal6bZ/1gkUa7i1oqLeogzvnttfWOalra3bGNu2dcS1cktCiZXEtCIrZRUFxu2h5QsvWpuY0p6hRuAIhMaswAAAApNnd9ufCK5ZoqK+o4d6innl4bM5zGhssaWywpIM7p453dMZDFeWtisIVCKlUdx/X5uQBAACA1na4hW2mI6ZL3rhcw71FDfUV9fCdQ3Oe0+gc30YoahSuQEh1t8OhxxUAAACz0Kiwffr+0apCs21hTK+5frWGe4sa7i/p59+Yfgbj4xWFKxBS3azCx/kF8AAAAGiORoXtfbcMVBW2HZ1xvfUj6/2hyH0lDfcVdceNPUc7zUhRuAIhubr7uDYnDwAAAMxv0xW2i5YnJx//9qb+uuL2WEbhCoTEfVwBAABwrDiWJ2KaCn1GQEh117gyVBgAAACIBIUrEFLtfVyN3x4AAAAgEnz0BkKixxUAAABojiMqXM1sp5k9amYPm9n9wbKlZna7mT0dfF8SLDcz+3cz22Zmj5jZc+biAIColIpc4woAAAA0w1z0uL7YOfds59x5wfMPSrrTOXeKpDuD55L0CkmnBF/XSPrsHOwbiEz9fVyblAgAAAAwzxyNocJXSvpa8Phrkl5dsfxG57tH0mIzW3MU9g8cFbXXuNLjCgAAAETjSAtXJ+k2M3vAzK4Jlq1yzu0PHh+QtCp4vE7Snop1u4JlQMtznpOr7nBlciYAAAAgIkd6H9fnOef2mtlKSbeb2ZOVQeecMzM3zbpTCgrgayRp48aNR5geMDdKdb2tkhk9rgAAAEAUjqjPyDm3N/jeLen7ks6XdHBiCHDwvTtovlfShorV1wfLarf5Befcec6581asWHEk6QFzpvb6VoYJAwAAANGZdeFqZh1mtnDisaSXSnpM0s2S3hw0e7Okm4LHN0t6UzC78IWSBiuGFAMtrX5iJgpXAAAAICpHMlR4laTvB8MlE5L+yzn3EzO7T9K3zexqSbsk/VnQ/hZJl0vaJmlM0luPYN9ApOqGCh/pIHsAAAAAoc3647dzbrukP5xiea+kS6ZY7iS9Z7b7A5rJ4x6uAAAAQNMwLyoQgufVFK4xClcAAAAgKhSuQAhesfp5nKHCAAAAQGQoXIEQSswqDAAAADQNhSsQArfDAQAAAJqHwhUIwaudVTjenDwAAACA+YjCFQiB+7gCAAAAzUPhCoTANa4AAABA81C4AiEwVBgAAABoHgpXIAQmZwIAAACah8IVCMEr1lzjmqBwBQAAAKJC4QqEUGKoMAAAANA0FK5ACJ7HUGEAAACgWShcgRBqhwpTuAIAAADRoXAFQqidVTjOUGEAAAAgMhSuQAjMKgwAAAA0D4UrEEKJwhUAAABoGgpXIITaocLMKgwAAABEh8IVCKHEfVwBAACApqFwBUJwtbfD4TcHAAAAiAwfv4EQSnVDhelxBQAAAKJC4QqEUHcfV4YKAwAAAJGhcAVCqJtVmN8cAAAAIDJ8/AZCcDVDhZmcCQAAAIgOhSsQAvdxBQAAAJqHwhUIwaspXOMUrgAAAEBkKFyBELyaocIWb04eAAAAwHxE4QqEUDtUmB5XAAAAIDoUrkAItUOFucYVAAAAiA6FKxCCV6x+HmOoMAAAABAZClcgBM9jqDAAAADQLBSuQAilYs1QYe7jCgAAAESGwhUIoXZWYYYKAwAAANGhcAVCqB0qHIvR4woAAABEhcIVCMGrGSocTzQpEQAAAGAeonAFQijVDRWmxxUAAACICoUrEAL3cQUAAACah8IVCKG+cG1SIgAAAMA8ROEKhFA7qzD3cQUAAACiQ+EKhFCq7XHlPq4AAABAZChcgRBqZxWO8ZsDAAAARIaP30AInlf9nMmZAAAAgOhQuAIh1N/HlcIVAAAAiAqFKxBC3TWu9LgCAAAAkaFwBUKoHyrcnDwAAACA+YjCFQihbnImelwBAACAyFC4AiF4NUOFuY8rAAAAEB0KVyCEUqn6OUOFAQAAgOhQuAIh1Pa4MlQYAAAAiA6FK9CAc06OyZkAAACApqFwBRrwphgmbEaPKwAAABAVCleggVLtjMIxilYAAAAgShSuQAOeV1O4JpqUCAAAADBPUbgCDXjF6ufcCgcAAACIFoUr0EDtjMJG4QoAAABEisIVaKC2cI0zozAAAAAQKQpXoIFS3azC9LgCAAAAUaJwBRqo73GlcAUAAACiROEKNFCqu8a1SYkAAAAA8xSFK9CAqxkqTI8rAAAAEC0KV6CB2h7XWILCFQAAAIgShSvQgFesKVz5rQEAAAAixUdwoAHPq37OrMIAAABAtChcgQZKNT2ucYYKAwAAAJGicAUaqL0dToxZhQEAAIBIUbgCDXg1swozVBgAAACIFoUr0EBtjyu3wwEAAACiReEKNFB3OxyGCgMAAACRonAFGmCoMAAAANBcFK5AA3X3caVwBQAAACJF4Qo04Hm117g2KREAAABgnqJwBRooFaufx7iPKwAAABApCleggbr7uMYoXAEAAIAoUbgCDdQOFWZWYQAAACBaFK5AA17NUOE4Q4UBAACASFG4Ag3U38eVwhUAAACIEoUr0EDdNa4MFQYAAAAiReEKNOCVqp/T4woAAABEi8IVaKC2xzVO4QoAAABEisIVaKBUZKgwAAAA0EwUrkADnlf9nKHCAAAAQLQoXIEG6idnonAFAAAAokThCjTg1QwVjiealAgAAAAwT1G4Ag2UamcVjtHjCgAAAESJwhVooG6ocILCFQAAAIgShSvQQP01rk1KBAAAAJinKFyBBrzaocJMzgQAAABEisIVaKBU0+Map3AFAAAAIkXhCjTAUGEAAACguShcgQYYKgwAAAA0F4Ur0ECpWNvjSuEKAAAARInCFWjAebXXuDYpEQAAAGCeonAFGijVDhXmPq4AAABApChcgQa8IrMKAwAAAM1E4Qo0UHs7HGOoMAAAABApClegAVczVJgeVwAAACBaFK5AA7U9rswqDAAAAESLwhVowKsrXJuUCAAAADBPUbgCDXgMFQYAAACaisL1KHLOqVQzIy2OPfU9rhSuAAAAaH25oqcdPTn1jRabncoRS0S9QzN7uaRPSYpL+pJz7p+jzuFo8Dynvv0FHdiRU9e2UT18+0h1T505da4qKN3mKZ1xSqY9xdNZlTJ71B5bq3QirXjCUyrhlEyUlEw4JeNO8dSgcskHtdD9gZJapFjMTX7JnLzYoMYz92pB4QIl1Sm56iKraIMaSd2jjvz5inuLlDVp0EoainsaijkNxMc0nNyndHGt4i6juEwmKeYm/qsxrkJypzKFE5Tw2hWTZM4pNtFOktOY8qmnlcmdqqRrkznJpMnteLER5dJPqS17moqFhRrOJzVcSGmokNJQIanBQkyjLqfh3FLlSwltaB9VTFLMnL8dKygfG1b/2GqNlZI6fcFQsG8/LisoFx/QwZENGimmdc7C/sn9mzn/OGI5jcX6tHf4JA0VMvqjzl5ZsL5JUiyrQmqfMvm1inkpmZWPIZddo8r/8dxy668UT02s62QmuVhWufQuteU2KuZl/B/5RH6SFBtXtm2HMtlNFXE/Pxe09WLjyrVtV2bsRMVde7C+TbZ1sXHl2p9WZmyz4p4flyQLduLZaBA/RbHJuJuMu9iYxju2qm10s+JeRzm3IM9SfFTZjq1qGz1VcddRFZs8z+OjyrY/qbax0xQvdshZOe5vY0TZjifVNnqaEqWOYLlNtvHioxpf8LjaRs5UvNTh52iV2x/RWMfjah89Q/Fix+R2XZCLlxjR+IIn1DZyhuKlBcFPxSbzNJlKsRGNL3pMbUNnT+agYBsmp2JiWNlFW9Q2dJYSpQWTOUqSOamUGFa2c4vaBs9SLIhXv07DGuvcovahsxUvLiinHzwoJYY1Fuw/Xlwwud1KpcSIxhc9qrahZ0228ffggvhoRbyj4hUM1o+PaLzzUbUNzrD+ZHyK9RP160+sO3kc8WGNL96itoGzFC8tmPghTL5e/jYeU9tgzesQtCjFRzS++DG1DZytePBzqHwZatevXrsiPnC2YsWOqribzHFE44u3KDNwlrJaoP6EqS9p6k9KvUnTjnannlRMy/KeOouxqnPVkzSY8NSbiml53tPigpXfD+T/tAeSnnpSMa3Ie1qSj1XFJakv6ak7HdPKnKdlFXFn/vukk9Sb8nQwHdfqXKmqzcQL0pPytD8T15psSSsm4m4yrJ60p72ZmNZlPa3IxYL33Imz3qk75bS3LaZ1455W5qzuv9HdaU9dbXGtHy9pVTZWES8fyYGMpz1tMW0YL2lNNlZ1jE7SgbSn3e1xnTBW0ups9TG4QkFdbkRdq5Zow8F+rbcFiiWT/h6cv/6+tpJ2tCd04lhR68bjVe89XqGgPW5Eu1cv1cYDfdpgCxSvWF+SvEJBu92wdq1Zpk37e7XRFk62kSSXLyjfu1danZcdSCq1bL1iyVQ5Xsgr39MlrclL+5JKLd/g5zjx3pjPK9e7R1pTkFXGJ16nfF653t3SmmI5nkqp8lfGy+eV79ktrc1L+1JKr9goS6Y08b7hFfLKHfLjtjep9IoTZKlU+XXMF5Q7tFNal5d1pZRecYK/D1Xk2L1Lbn1esa6k0is2VcTNjx/cIbchL+tKKr3iRMXSqcn3PQU55rp3SOsLUldSmZUnlnNwfg7Z7u2yDXlpT1KZlSdX5ejl88od3C5tyMl2p5RedZJiqXRFjjnlDm6X25iT7Ur78XT5GLxcTrnu7XIb87JdSWVW+dv3j8CCfeSUPfiMbGNetiulzOqTZcE+TJLL5ZQ9uE3uhLxsZ1qZ1Scrlk6Xz5V8Ttn926RNOWlnWpk1mydzdHLy8jnlDmyT25SX7Uwps3pz9THkcsoeeNqP70ipbc2piqXT5V+G4DiyB7ZKJ+ZkO9LKrD6lOodcTuMHnpadmJNtTyu9JohXvA7Z/f762pFWZs0piqUzFa9TVtn9W+VOysu2+zlYuvy5wsvllN23Ve7knOyZlNrWnDaZo03sf/9TciflFHsm7ccz5WOUJC+b0/i+p2QnZ6VnMmpbe7pimfIxlLI5je97UtqclW3LKLOuvI+JHMf3PSl3ct7PYe3p9TnsfVJuc062La32YPvV+/fjsafTalt3+uRrMPE6lXJZjXc9KTslKz2d8dtkMuV4Nqvs3ifkNvvx9vV+fOJnXcplla3IoWofLsix6wm5U7OyrWm1rTuz7ucwvvdx6dTclHH/fMlqvOtx6dSs9FRGbRvOVDydmTwKLzeu8T1BfGtGbevPlAXH4OT8n3XX40EOGWXWT6xffg0m40+l1b7hLFmqHHf5rMb2bJFOy8meTCu+/g80GFuq3mK7egtt6iu2q7eQ0VCpTTLTmuI+JZeu17/82Uk6VpmrKXSO6s7M4pK2SrpMUpek+yS9wTn3+FTtzzvvPHf//fdHll9Yvf3d+vydD2i8Oy2vp03xng6l+jKKFZvbge2CImDiQ5155T8GE/FiOnhkUjJrdfH8gokSQUqPmsxVx7OdXvmPvaS2wVhVG8+cxpeWK/a2vrhiVXFprFOT22gf8IvbyvjokvLzjv76+MjS8vMFfVPEl5Xzk6SFvfVthpeXny/sqY8PrSg/7+yu/rBaSEpPvFBAA1O9t04sq+m1r61sJ5tW/TLXxK3cJlYznl1BzAUlRrwyHpQ9zvyTXSrHp9qHF7RN1P6ndqJ6jPnxZFHVxxysNxkvTHGMMX/7XkxK5ac4hmD9qnjlPmJ+u2Lcb5ua4r/JTjXxKV7rYtzfR3qqHGcRr/15OkmFhN8mU3ucIeKSlA/ibdOsPxnPTRNPTh+fzCHpv97tU7TxGsVduPW9GeL5GeJh2tTGa38OnvnxUkzqyE6x/hHGJf88ywVtFky1DQXxuLRgfOp9HM14ZY7FuLRwhm1MG5eUSwXxsWnWDxlfNEV8ok12hjbNjkv+78x4SiolpEWjU2+jleOSfy6Mp6RiQuqcahuSxtP+6zBl3I5ufK73sXia+NgRxCX/dRrLBG1GptnGUYwX49Jwu+Q1moTF//v/zbdvbtAuemb2gHPuvIbtIi5cL5L0Yefcy4Lnfy9Jzrn/M1X7Vi1c77/3ad32idpPeJhPHrm02RkAAAAAh+fGN7YrlV7b7DSqhC1co+4iXCdpT8XzrmDZMWXz5lTjRgAAAADQVK7iS+rZ959NzeZIRH6NayNmdo2kayRp48aNTc5mamND35L0J3XLi0lpfKE0vkha1iXFi9WxHc+WEgUpUfC0YUv9/wwGV5UU80xWkqxk6his79UtpPzRT+bVjP5DtFb3+t+d/CFhI21SduL6DZNW9JfblmLSaMYfGjURXzZYXl/yh7aNpaR8RZvFw+VtTAxbyldcd7WoYriIF/OHdhUS5fjC0fK48YkhdMWKeEfFELCJeClejrdnq0dVTgxnrGyTyVVvoxgMV5yIp/PlbTj561bGU4WaeMwfPjoRrxye6oLjnBx6bsEvmdW0qbwCr3IYbeXwWZWXmVe9vmriUw75rYwDAAC0gLYxWceorH1M1j4m156X1+75Q8Z3rdKigYSWr72q2VnOWtSF615JGyqerw+WTXLOfUHSFyR/qHB0qYXn/8Drr3lIvukxrWpboKVtCxUvjOvewh4dsoQS3WvUllutf3vlKrWnpGTc6f/+1SGNj5THontpp7/7aKdKzuTJyZP09WsHla9oU0o7/eknYyo5J8/zdMcHPRVGElXxiz/i5EoxlUrSQ/+7pNJYxfopp9f8r8WSk0qe020fHVBhPFYVf+n1GXlOcp7Trz6TVbEynnR6/rsSkpyc58+afP9XSipmy228pNMFb0vLnzoppoe+NqJSTfwv/ia4SNU5fe+TfcpX7CPV5unKa4NJppx006eHquMZT696d4cmhrj/6LNjymcr4yVd/s62oNZwck669YtZ5bPl1yGZKekVV/sFopP0ky/nVaiIewmnV73dJsuV279aqo6nnb586QbJYjLF1XNgq24c+YX2uHbFd2xWZsg60aIAABJHSURBVGyj/uny0+SC6W5692/RfwzfpT2uQ/EdJysztkH/cPkmlacckvoOPKGvj/5OXV6H4jtOUnpsvT50xZpgri2nvu6t+ubo/drrdSi242Rlxtbpg1csn1y/v/tpfXvsIe312hXfcbLSo2v1d1csCTJw6j+0Td8Ze1R7vbbJ+AeuWDA5Ic9AzzZ9d2xLVfyGV6Ynty9Jg73b9b2xx7XPa/dzHF2r970yOP+cNNi7Qz8Yf1L7gm2kRlfrusvLr9tg707dNP6U9lfEr31FMIGBcxrq360fjj8dxE9SanS13vNyN5njUN8e/Si7Tfu9NsV2nKT06Bq95/KUZHGZxWUW00DPTt08+qAOTLQZW6f3vmrJ5HEMHtqmm0cf0IFgH+mxdXr3FZ2aOIiBnmf0o9GHg/iJSo+t1V9dsWjyJzXY84x+PPrIZDw1tlbveuWCyVepv2eHbhl9RAe9NsV3nqj06Fq94xVtqjTYu1O3jj3mt9l1olKjq3X1yzKTOQ7179RPx54I4puUHl2tt7y0PKnFYP8u3TH25GQ8NbZKb75s4nx2Gu7frTvHt+pgqU3x3ScoNbpKb7wsOfk6Dvfv0c/Gn1a358eToyt11aXxqvp8eKBLPxvfpkNexm8ztlJ/8RKbzHFkYK/uym5XTymj2J4TlBpboT9/cXn9kcF9+sX4DvV4GcX2bFRqbIVe92I3uY/Rwf36RXaHeksZxbr8+GtfWP4HwsjQft2d3eXH92xQcmyFXvsir2ruudGhA/pVdpf6Siklu9YrM75af3dZeZKnXO92dfV+U3cl2xXbfZF682fpry9tL8f7dmpvz7f081S7bNdF6iucWR3v3am9vd/SXal2xYL4DZe0Tb735Pt3aW/vf+vnyXbFdl+o3sKZev9LMlU55vp3al/vd/WLVLtiuy9QX/5MXf+SVEUOu7Wv73v6RbJdsT0XqC9/hq57cTme79+tfX3f1y+T7YrtOb8unuvbrf39ftz2nK/+/Bm6/pLFchaXKa5s7y7t7flasP5z1V88Wze8dIMqf9jjh57Rnu4v6+7URJuzdP1l5YFQ2Z5t6ur+f+V44Sy977I1k/FCvle7uj6vu11M8X0Xqr9wpq578crJfWR7tmtvz9d0d7JDsa7z1F84U++7dHXF+j3avfeLutvFFdt3gQYKZ+q9L6qYhEBSsdCj3V1f1q9cTLH9QZsXLpuMD+cO6nvdv9a+UlKJ/SconV9bFR/Jduv7h36jfcWkEgc2KpVbq2tfuLRi/UP6QRCPH9iodG6t3vvCpZM/65Fcj37Q8xvtL6aC+Gq95wUVkzFMtDl0j/aXkpNt3v38xVXxm3ru1f5iUvGDfvyvnt85GR/N9eimnvuC+Ia6+EiuRzdPxA9sUDq/Wu+6uCKe9+MHSuX4Oy9eVJXjaL5HN/fcr/2lpBIH/H2883kLK/bRqx/23q/9xaQSQQ7XPK/8OzWa69UPex+siK/SOy6uiOd79aOKeCq3Stf8UXlitZF8n37c+6C//4MblMqt1Dv+qHritdF8n37c+1BVm7dXtPHjD+tAMal493qlcyv19osq9lHo1S29v6+KX31Re8X6vbql75Gq+NsurI7f2l8br34PH8336da+R/3X+uB6pfMrqtqM5vt1a+U+8iv01gsyVfGf9D86GU/Vxfv00/7HyvFcffwnA4/pYEX8LRekq7b/07p49UjB0Xy/ftr/uA6Wkop3r1Mqt0JvPr/cZqwwc3w036/bBirjy6eIP+HncMiPv+m5FdvP9+u2wer4G59bneNYvl+3Dz6hA8WUEofWBm2SFfsY0B0h4/HutUrnl+uq88qfmccKg7p94AkdLPnxVH653lgRH80P6o7BJ4NjrI9Xt0kp3r1Gqdp95Ad0x+BT1fFz4xXxQd0xVB3/y5r4nZPxIIfndvifPy2usfyAbut7QAdLCaV6V2pBab3+7U/OrMqxf3yPPr/n+9qdlDaetEPvOuG1LTdM+LA45yL7kl8ob5d0oqSUpN9LOmu69ueee65rVR9/+1PuI3/+9OTXP71pa12bXHav27v9oy6X3TvlNhrF52IbRzveCjmQIzm2Ug7kSI6tlAM5kmMr5UCOrRFvhRzIsXVybAWS7nchaslIJ2eSJDO7XNIn5d8O5yvOuY9M17ZVJ2eakM/tU8++/9TytVcd2/+9AAAAAIAmCDs5U+TXuDrnbpF0S9T7PRpS6bVae+LfNjsNAAAAADiuNffGowAAAAAANEDhCgAAAABoaRSuAAAAAICWRuEKAAAAAGhpFK4AAAAAgJZG4QoAAAAAaGkUrgAAAACAlkbhCgAAAABoaRSuAAAAAICWRuEKAAAAAGhpFK4AAAAAgJZG4QoAAAAAaGkUrgAAAACAlkbhCgAAAABoaRSuAAAAAICWRuEKAAAAAGhpFK4AAAAAgJZmzrlm5zAtMzskaVez82hguaSeZieBeY/zEK2CcxGtgPMQrYDzEK2i1c/FE5xzKxo1aunC9VhgZvc7585rdh6Y3zgP0So4F9EKOA/RCjgP0SqOl3ORocIAAAAAgJZG4QoAAAAAaGkUrkfuC81OABDnIVoH5yJaAechWgHnIVrFcXEuco0rAAAAAKCl0eMKAAAAAGhpFK4hmdnLzewpM9tmZh+cIp42s28F8XvNbFP0WeJ4F+I8vMHMHjezR8zsTjM7oRl54vjW6DysaPenZubM7JifyRCtKcy5aGZ/FrwvbjGz/4o6Rxz/Qvxt3mhmd5nZQ8Hf58ubkSeOb2b2FTPrNrPHpombmf17cJ4+YmbPiTrHI0XhGoKZxSV9WtIrJJ0p6Q1mdmZNs6sl9TvnNkv6hKSPRpsljnchz8OHJJ3nnPsDSd+R9C/RZonjXcjzUGa2UNL7JN0bbYaYL8Kci2Z2iqS/l3Sxc+4sSddHniiOayHfEz8k6dvOuXMkvV7SZ6LNEvPEVyW9fIb4KySdEnxdI+mzEeQ0pyhcwzlf0jbn3HbnXF7SNyVdWdPmSklfCx5/R9IlZmYR5ojjX8Pz0Dl3l3NuLHh6j6T1EeeI41+Y90NJ+if5/8DLRpkc5pUw5+I7JH3aOdcvSc657ohzxPEvzHnoJC0KHndK2hdhfpgnnHO/lNQ3Q5MrJd3ofPdIWmxma6LJbm5QuIazTtKeiuddwbIp2zjnipIGJS2LJDvMF2HOw0pXS7r1qGaE+ajheRgMP9rgnPtxlIlh3gnznniqpFPN7Ndmdo+ZzdQbAcxGmPPww5KuMrMuSbdIujaa1IAqh/s5suUkmp0AgLlnZldJOk/SC5udC+YXM4tJ+riktzQ5FUDyP+ecIulF8keg/NLMnuWcG2hqVphv3iDpq865j5nZRZL+w8zOds55zU4MOJbQ4xrOXkkbKp6vD5ZN2cbMEvKHgvRGkh3mizDnoczsUkn/U9IfO+dyEeWG+aPRebhQ0tmSfm5mOyVdKOlmJmjCURDmPbFL0s3OuYJzboekrfILWWCuhDkPr5b0bUlyzv1WUkbS8kiyA8pCfY5sZRSu4dwn6RQzO9HMUvIvrL+5ps3Nkt4cPH6tpJ85bpKLudXwPDSzcyR9Xn7RyrVcOBpmPA+dc4POueXOuU3OuU3yr7X+Y+fc/c1JF8exMH+bfyC/t1Vmtlz+0OHtUSaJ416Y83C3pEskyczOkF+4Hoo0S8A/L98UzC58oaRB59z+Zid1OBgqHIJzrmhm75X0U0lxSV9xzm0xs3+UdL9z7mZJX5Y/9GOb/AujX9+8jHE8Cnke/qukBZL+O5gbbLdz7o+bljSOOyHPQ+CoC3ku/lTSS83scUklSX/jnGM0FOZMyPPwryV90czeL3+iprfQuYG5ZmbfkP+PuuXB9dT/ICkpSc65z8m/vvpySdskjUl6a3MynT3j9wYAAAAA0MoYKgwAAAAAaGkUrgAAAACAlkbhCgAAAABoaRSuAAAAAICWRuEKAAAAADhsZvYVM+s2s8dCtN1oZneZ2UNm9oiZXX44+6JwBQAAAADMxlclvTxk2w9J+rZz7hz5tw79zOHsiMIVAAAAAHDYnHO/lNRXuczMTjazn5jZA2Z2t5mdPtFc0qLgcaekfYezLwpXADgGBUNtXlaz7Hoz++wM64xEkNd1ZvaEmX29ZvliM3t3xfNNYYYVTbOPqm0Fy34zu4xn3M+sc6zZzpznFmz37Wb2cPDlVTz+xCy2tSE4px43sy1m9r6jkXODHKYcbmZmLzezp8xsm5l9sNHyqNaZzbYAYJ74gqRrnXPnSvqAyj2rH5Z0lZl1SbpF0rWHs1Fzzs1lkgCACJjZNZIucs69tWLZPZL+Nvjv51TrjDjnFhzlvJ6UdKlzrqtm+SZJP3LOnT3V88Pcx6zXjXI/Zmby/856c5nXFPtZJ+k3zrkTjmAbayStcc49aGYLJT0g6dXOucfnKs8QObxA0oikGyvOk7ikrZIuk9Ql6T5Jb5D01FTLnXOPR7HObLYV5WsJAFGq/HtpZgskHZL/Pjkh7Zw7w8xukP938WNmdpGkL0s6O+zfSXpcAeDY9B1JrzSzlDT5R2OtpLvN7AfB8JwtQYFbpbYn0cw+YGYfrnh+lZn9Lui9+3zwQbx2GzeY2WPB1/XBss9JOknSrWb2/ppV/lnSycE2/zVYFjezLwZ53mZmbSH3X7etid7k4NieNLOvmtlWM/u6mV1qZr82s6fN7PzDOc4Zcqw7/or9P2VmN0p6TNIGMxsxs3dV9IjuMLO7GryWm8zvua7b9xTOlvToNLFQnHP7nXMPBo+HJT0had2RbHMWOdQNN5N0vqRtzrntzrm8pG9KunKG5VGtM5ttAcB8EJM04Jx7dsXXGUHsaknfliTn3G8lZSQtP5wNAwCOMc65Pkm/k/SKYNHr5U944CS9LRiec56k68xsWdjtmtkZkv5c0sXOuWdLKkn6y5o250p6q6QLJF0o6R1mdo5z7l3yr1d5sXOudrjqByU9E/wB+5tg2SmSPu2cO0vSgKQ/DbP/abZVabOkj0k6Pfj6C0nPkz9c6X+EPc4Zcpzy+GvW+Yxz7izn3C5Jcs59LtjPc+X3wn18ptdyun1PkZ8kPUt+kVzH/GuLHp7i69JptjXxT5BzJN07XZsIrZO0p+J5V7BsuuVRrTObbQHAcc85NyRph5m9TvJHH5nZHwbh3ZIuCZafIb9wPRR224k5zhUAEJ1vyC9Ybwq+Xx0sv87MXhM83iC/AOoNuc1LJJ0r6T5/pKvaJHXXtHmepO8750Ylycy+J+n5kh46zPx3OOceDh4/IGmTpMUh9h9mu48GuW2RdKdzzpnZo8E+pHDHOV2OyzTz8e9yzt0zTW6fkvQz59wPg+fTvZY3T7PvqZwt6fapAs6550+zzpSCIV7flXR98OEDAIBpmdk3JL1I0nLzr139B/n/CP6smX1IUlL+yJPfS/prSV8MRmU5SW9xh3HdKoUrABy7bpL0CTN7jqR259wDZvYiSZfKv/51zMx+Lv8/mpWKqh5xUxk3SV9zzv390Ut7Uq7icUl+8TgX+6/crlfx3FP5717Y/UyVYyOjUy00s7dIOkHSe0Ns43D2/SxJU07IZGZ3S1o4RegDzrk7atom5RetX3fOfS9kjkfbXvn/fJmwPlg23fKo1pnNtgDguOOce8M0obpb5ATX+l88230xVBgAjlHOuRFJd0n6ivzeV8mfXr4/KFpPlz/8tNZBSSvNbJmZpSVdURG7U9JrzWylJJnZUjOrnfTnbkmvNrN2M+uQ9Jpg2UyGNXUBVSvM/sNu60j3M53DPv5gSPAHJF1VMwnFbF7Lyu3G5PeoPzFV3Dn3/JrrjCa+aotWkz9JxhPOuY/XxO40fwKoOXMY27xP0ilmdqL513O/Xn5v9HTLo1pnNtsCABwBClcAOLZ9Q9Ifqly4/kRSwsyekD+JUd2QVedcQdI/yr9G9nZJT1bEHpd/g/DbzOyRIL6mZv0H5d9w/Hfyr4P8knNuxmHCzrleSb8OJiD61xnahdl/qG01yKfhfmZY97CPX34v61JJdwXXmH7pCLZVabOkrmASoCNxsaQ3SnpJxXWwlweF8WbV36PvFjNbO8tl023zG5J+K+k0M+sys6udc0X5r91P5Rfn33bObZluuSRFsc5sttX4RwAAmAm3wwEAAFMys7PlT/Z1QytvEwBw/KNwBQAAAAC0NIYKAwAAAABaGoUrAAAAAKClUbgCAAAAAFoahSsAAAAAoKVRuAIAAAAAWhqFKwAAAACgpVG4AgAAAABaGoUrAAAAAKCl/X8fsZ2LkORt/AAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(gamma=gamma, delta=delta, show_Ti_m_Tim1=True)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "The 0th function is referred to as Geometric doubling (d=0, e=1) and is \n", "\n", "\n", "The 1th function is referred to as Intermediate doubling (d=1/2, e=0) and is \n", "\n", "\n", "The 2th function is referred to as Intermediate doubling (d=1/3, e=0) and is \n", "\n", "\n", "The 3th function is referred to as Intermediate doubling (d=2/3, e=0) and is \n", "\n", "\n", "The 4th function is referred to as Intermediate doubling (d=1/2, e=1/2) and is \n", "\n", "\n", "The 5th function is referred to as Exponential doubling (d=1, e=0) and is \n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_quality_first_upper_bound(gamma=gamma, delta=delta, show_Ti_m_Tim1=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conclusion:\n", "- geometric sequences **can** be used to conserve a minimax (worst case) regret bound in $R_T = \\mathcal{O}(T^{\\gamma} (\\log(T))^{\\delta})$ (as we proved in the generic case)\n", " > But the proof has to be careful and use a smart bound on $T_i - T_{i-1} \\leq \\text{cste} \\times b^{i-1}$ and not with a $b^i$ (see difference between first and second plot)\n", "- exponential sequences **can** be used to conserve such bounds (as we conjectured but did not proved, also),\n", "- and we conjecture that all other sequences (ie as soon as $d > 0$ ie $f(i) >> \\log(i)$) can be used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Conclusions\n", "\n", "The take home messages are the following:\n", "\n", "### About geometric sequences\n", "- We can see that bounding $T_i - T_{i-1}$ by $T_i$ usually is strongly sub-optimal for the geometric sequences, as we saw it in our paper, but works fine for the other sequences.\n", "- We could check that (numerically) a geometric sequence grows too slowly to preserve a logarithmic bound $R_T \\leq \\mathcal{O}(\\log(T))$ (first plot), as we proved.\n", "\n", "### About exponential sequences\n", "- They work perfectly fine to preserve logarithmic regret bound, as we proved.\n", "- And as we conjectured, they (seem to) work perfectly fine too to preserve minimax (worst case) regret bound, even if we failed to prove it completely so far.\n", "\n", "### About intermediate sequences\n", "- They (seem to) work perfectly fine to preserve logarithmic regret bound, as we started to prove it (work in progress).\n", "- And as we conjectured, they (seem to) work perfectly fine too to preserve minimax (worst case) regret bound, as we started to prove it (work in progress).\n", "\n", "That's it for today!" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" }, "toc": { "colors": { "hover_highlight": "#DAA520", "running_highlight": "#FF0000", "selected_highlight": "#FFD700" }, "moveMenuLeft": true, "nav_menu": { "height": "485.125px", "width": "252px" }, "navigate_menu": true, "number_sections": true, "sideBar": false, "threshold": 4, "toc_cell": true, "toc_position": { "height": "421.667px", "left": "997.646px", "right": "20px", "top": "103px", "width": "263.135px" }, "toc_section_display": "none", "toc_window_display": true }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }