" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Python implementation of [the Exponential Integral](https://en.wikipedia.org/wiki/Exponential_integral) function\n", "\n", "This small notebook is a [Python 3](https://www.python.org/) implementation of the Exponential Integral function, $Ei(x)$, defined like this:\n", "\n", "$$\\forall x\\in\\mathbb{R}\\setminus\\{0\\},\\;\\; \\mathrm{Ei}(x) := \\int_{-\\infty}^x \\frac{\\mathrm{e}^u}{u} \\; \\mathrm{d}u.$$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "scrolled": true }, "outputs": [], "source": [ "import seaborn as sns\n", "sns.set(context=\"notebook\", style=\"darkgrid\", palette=\"hls\", font=\"sans-serif\", font_scale=1.4)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "import matplotlib as mpl\n", "mpl.rcParams['figure.figsize'] = (19.80, 10.80)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two implementations\n", "As one can show mathematically, there is another equivalent definition (the one used on Wikipedia):\n", "\n", "$$\\forall x\\in\\mathbb{R}\\setminus\\{0\\},\\;\\; \\mathrm{Ei}(x) := - \\int_{-x}^{\\infty} \\frac{\\mathrm{e}^{-t}}{t} \\; \\mathrm{d}t.$$\n", "\n", "Numerically, we will avoid the issue in $0$ by integrating up-to $-\\varepsilon$ instead of $0^-$ and from $\\varepsilon$ instead of $0^+$, for a some small $\\varepsilon$ (*e.g.*, $\\varepsilon=10^{-7}$), and from $-M$ for a large value $M\\in\\mathbb{R}$ (*e.g.*, $M=10000$), instead of $-\\infty$.\n", "\n", "We use the [scipy.integrate.quad](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html) function." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import quad # need only 1 function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First definition is the simplest:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "@np.vectorize\n", "def Ei(x, minfloat=1e-7, maxfloat=10000):\n", " \"\"\"Ei integral function.\"\"\"\n", " minfloat = min(np.abs(x), minfloat)\n", " maxfloat = max(np.abs(x), maxfloat)\n", " def f(t):\n", " return np.exp(t) / t\n", " if x > 0:\n", " return (quad(f, -maxfloat, -minfloat)[0] + quad(f, minfloat, x)[0])\n", " else:\n", " return quad(f, -maxfloat, x)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The other definition is very similar:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "@np.vectorize\n", "def Ei_2(x, minfloat=1e-7, maxfloat=10000):\n", " \"\"\"Ei integral function.\"\"\"\n", " minfloat = min(np.abs(x), minfloat)\n", " maxfloat = max(np.abs(x), maxfloat)\n", " def f(t):\n", " return np.exp(-t) / t\n", " if x > 0:\n", " return -1.0 * (quad(f, -x, -minfloat)[0] + quad(f, minfloat, maxfloat)[0])\n", " else:\n", " return -1.0 * quad(f, -x, maxfloat)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Checking the two versions\n", "We can quickly check that the two are equal:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "from numpy.linalg import norm" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "X = np.linspace(-1, 1, 1000) # 1000 points\n", "Y = Ei(X)\n", "Y_2 = Ei_2(X)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Two versions of Ei(x) are indeed equal for 1000 values.\n" ] } ], "source": [ "assert np.allclose(Y, Y_2)\n", "print(f\"Two versions of Ei(x) are indeed equal for {len(X)} values.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compare which is fastest to evaluate:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.72 s ± 176 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n", "1.62 s ± 18.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" ] } ], "source": [ "%timeit Y = Ei(X)\n", "%timeit Y_2 = Ei_2(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They both take about the same time, but the second implementation seems (slightly) faster." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison with [scipy.special.expi](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.expi.html#scipy.special.expi)\n", "\n", "The $\\mathrm{Ei}$ function is also implemented as [scipy.special.expi](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.expi.html#scipy.special.expi):" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "from scipy.special import expi" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "Y_3 = expi(X)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(Y, Y_3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference is not too large:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.0000000611197777e-07" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.max(np.abs(Y - Y_3))" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Our version of Ei(x) is the same as the one in scipy.special.expi (1000 values).\n" ] } ], "source": [ "assert np.allclose(Y, Y_3, rtol=1e-6, atol=1e-6)\n", "print(f\"Our version of Ei(x) is the same as the one in scipy.special.expi ({len(X)} values).\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Special values\n", "We can compute some special values, like $\\mathrm{Ei}(1)$ and solving (numerically) $\\mathrm{Ei}(x)=0$." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(1.89511762)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ei(1)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import root" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fjac: array([[-1.]])\n", " fun: array([-3.55271368e-15])\n", " message: 'The solution converged.'\n", " nfev: 9\n", " qtf: array([-2.78710388e-12])\n", " r: array([-3.89621516])\n", " status: 1\n", " success: True\n", " x: array([0.37250746])" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res = root(Ei, x0=1)\n", "res" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The approximate solution to Ei(x)=0 is x0 = 0.37250746211322744 (for which Ei(x)=[-3.55271368e-15])...\n" ] } ], "source": [ "print(f\"The approximate solution to Ei(x)=0 is x0 = {res.x[0]} (for which Ei(x)={res.fun})...\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Limits" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that $\\mathrm{Ei}(x)\\to0$ for $x\\to-\\infty$ and $\\mathrm{Ei}(x)\\to+\\infty$ for $x\\to\\infty$:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For x = -1, Ei(x) = -0.219 : it goes to 0 quite fast!\n", "For x = -112, Ei(x) = -1.17e-54 : it goes to 0 quite fast!\n", "For x = -223, Ei(x) = -4.27e-103 : it goes to 0 quite fast!\n", "For x = -334, Ei(x) = -2e-151 : it goes to 0 quite fast!\n", "For x = -445, Ei(x) = -1.05e-199 : it goes to 0 quite fast!\n", "For x = -556, Ei(x) = -5.85e-248 : it goes to 0 quite fast!\n", "For x = -667, Ei(x) = -3.39e-296 : it goes to 0 quite fast!\n", "For x = -778, Ei(x) = -0 : it goes to 0 quite fast!\n", "For x = -889, Ei(x) = -0 : it goes to 0 quite fast!\n", "For x = -1e+03, Ei(x) = -0 : it goes to 0 quite fast!\n" ] } ], "source": [ "for x in -np.linspace(1, 1000, 10):\n", " print(f\"For x = {x:>6.3g}, Ei(x) = {Ei(x):>10.3g} : it goes to 0 quite fast!\")" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For x = 1, Ei(x) = 1.9 : it goes to +oo quite fast!\n", "For x = 101, Ei(x) = 6.46e+41 : it goes to +oo quite fast!\n", "For x = 201, Ei(x) = 7.66e+84 : it goes to +oo quite fast!\n", "For x = 301, Ei(x) = 1.21e+128 : it goes to +oo quite fast!\n", "For x = 400, Ei(x) = 2.15e+171 : it goes to +oo quite fast!\n", "For x = 500, Ei(x) = 4.09e+214 : it goes to +oo quite fast!\n", "For x = 600, Ei(x) = 8.08e+257 : it goes to +oo quite fast!\n", "For x = 700, Ei(x) = 1.64e+301 : it goes to +oo quite fast!\n", "For x = 800, Ei(x) = inf : it goes to +oo quite fast!\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:7: RuntimeWarning: overflow encountered in exp\n", " import sys\n", "/usr/local/lib/python3.6/dist-packages/numpy/lib/function_base.py:2831: RuntimeWarning: invalid value encountered in ? (vectorized)\n", " outputs = ufunc(*inputs)\n" ] } ], "source": [ "for x in np.linspace(1, 800, 9):\n", " print(f\"For x = {x:>6.3g}, Ei(x) = {Ei(x):>10.3g} : it goes to +oo quite fast!\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that $\\mathrm{Ei}(x)\\to-\\infty$ for $x\\to0^-$ and $x\\to0^+$:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For x = -0.1 --> 0^-, Ei(x) = -1.82 : it doesn't go to -oo numerically!\n", "For x = -0.000774 --> 0^-, Ei(x) = -6.59 : it doesn't go to -oo numerically!\n", "For x = -5.99e-06 --> 0^-, Ei(x) = -11.4 : it doesn't go to -oo numerically!\n", "For x = -4.64e-08 --> 0^-, Ei(x) = -16.3 : it doesn't go to -oo numerically!\n", "For x = -3.59e-10 --> 0^-, Ei(x) = -21.2 : it doesn't go to -oo numerically!\n", "For x = -2.78e-12 --> 0^-, Ei(x) = -26 : it doesn't go to -oo numerically!\n", "For x = -2.15e-14 --> 0^-, Ei(x) = -30.8 : it doesn't go to -oo numerically!\n", "For x = -1.67e-16 --> 0^-, Ei(x) = -31.9 : it doesn't go to -oo numerically!\n", "For x = -1.29e-18 --> 0^-, Ei(x) = -31.9 : it doesn't go to -oo numerically!\n", "For x = -1e-20 --> 0^-, Ei(x) = -31.9 : it doesn't go to -oo numerically!\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/scipy/integrate/quadpack.py:364: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n", " If increasing the limit yields no improvement it is advised to analyze \n", " the integrand in order to determine the difficulties. If the position of a \n", " local difficulty can be determined (singularity, discontinuity) one will \n", " probably gain from splitting up the interval and calling the integrator \n", " on the subranges. Perhaps a special-purpose integrator should be used.\n", " warnings.warn(msg, IntegrationWarning)\n" ] } ], "source": [ "for x in -1/np.logspace(1, 20, 10):\n", " print(f\"For x = {x:>10.3g} --> 0^-, Ei(x) = {Ei(x):>5.3g} : it doesn't go to -oo numerically!\")" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For x = 0.1 --> 0^+, Ei(x) = -1.62 : it doesn't go to -oo numerically!\n", "For x = 0.000774 --> 0^+, Ei(x) = -6.59 : it doesn't go to -oo numerically!\n", "For x = 5.99e-06 --> 0^+, Ei(x) = -11.4 : it doesn't go to -oo numerically!\n", "For x = 4.64e-08 --> 0^+, Ei(x) = -16.3 : it doesn't go to -oo numerically!\n", "For x = 3.59e-10 --> 0^+, Ei(x) = -21.2 : it doesn't go to -oo numerically!\n", "For x = 2.78e-12 --> 0^+, Ei(x) = -26 : it doesn't go to -oo numerically!\n", "For x = 2.15e-14 --> 0^+, Ei(x) = -30.8 : it doesn't go to -oo numerically!\n", "For x = 1.67e-16 --> 0^+, Ei(x) = -31.9 : it doesn't go to -oo numerically!\n", "For x = 1.29e-18 --> 0^+, Ei(x) = -31.9 : it doesn't go to -oo numerically!\n", "For x = 1e-20 --> 0^+, Ei(x) = -31.9 : it doesn't go to -oo numerically!\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/scipy/integrate/quadpack.py:364: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n", " If increasing the limit yields no improvement it is advised to analyze \n", " the integrand in order to determine the difficulties. If the position of a \n", " local difficulty can be determined (singularity, discontinuity) one will \n", " probably gain from splitting up the interval and calling the integrator \n", " on the subranges. Perhaps a special-purpose integrator should be used.\n", " warnings.warn(msg, IntegrationWarning)\n" ] } ], "source": [ "for x in 1/np.logspace(1, 20, 10):\n", " print(f\"For x = {x:>8.3g} --> 0^+, Ei(x) = {Ei(x):>5.3g} : it doesn't go to -oo numerically!\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots\n", "And we can plot the $Ei(x)$ function, from $-1$ to $1$." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0.5,1,'The function $Ei(x)$ on $[-1,1]$')" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0.5,0,'$x$')" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0,0.5,'$y$')" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X, Y, 'b')\n", "plt.title(\"The function $Ei(x)$ on $[-1,1]$\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Checking some inequalities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check that $\\forall x\\in\\mathbb{R}, \\mathrm{Ei}(x) \\leq \\mathrm{e}^x$:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.alltrue(Y <= np.exp(X))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check a tighter inequality, $\\forall x\\in\\mathbb{R}, \\mathrm{Ei}(x) \\leq \\mathrm{Ei}(-1) + (\\mathrm{e}^x - \\mathrm{e}) + (\\mathrm{e} - \\frac{1}{\\mathrm{e}})$.\n", "\n", "It is indeed tighter, as the constant on the right-hand side is non-negative:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.5872633755669625" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ei(-1) + (-np.exp(1)) + (np.exp(1) - np.exp(-1))" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "upper_bound = np.exp(X) + (Ei(-1) + (-np.exp(1)) + (np.exp(1) - np.exp(-1)))\n", "np.alltrue(Y <= upper_bound)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0.5,1,'The function $Ei(x)$ and upper-bound $e^x$ and $e^x + Ei(-1) - 1/e$')" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0.5,0,'$x$')" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0,0.5,'$y$')" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X, Y, 'b')\n", "plt.plot(X, np.exp(X), 'r--')\n", "plt.plot(X, np.exp(X) + (Ei(-1) + (-np.exp(1)) + (np.exp(1) - np.exp(-1))), 'g--')\n", "plt.title(\"The function $Ei(x)$ and upper-bound $e^x$ and $e^x + Ei(-1) - 1/e$\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check a tighter inequality, $\\forall t\\geq1, \\forall x\\geq1, \\mathrm{Ei}(x) \\leq \\mathrm{Ei}(t) + \\frac{\\mathrm{e}^x - \\mathrm{e}^{t}}{t}$." ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.8231642121030913" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "2.6367399306227393" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "13.473133012157838" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = np.exp(1)\n", "upper_bound_cst = lambda t: Ei(t) - np.exp(t)/t\n", "upper_bound_t = lambda t, X: Ei(t) + (np.exp(X) - np.exp(t))/t\n", "\n", "upper_bound_cst(1)\n", "upper_bound_cst(e)\n", "upper_bound_cst(2*e)" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "True" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "True" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_4 = np.linspace(1, 2*e, 1000)\n", "Y_4 = Ei(X_4)\n", "\n", "def check_upper_bound(t):\n", " upper_bound_4 = upper_bound_t(t, X_4)\n", " return np.alltrue(Y_4 <= upper_bound_4)\n", "\n", "check_upper_bound(1)\n", "check_upper_bound(e)\n", "check_upper_bound(2*e)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [], "source": [ "def see_upper_bound(t, xmax, onlylast=False):\n", " X_4 = np.linspace(1, xmax, 1000)\n", " Y_4 = Ei(X_4)\n", " \n", " plt.plot(X_4, Y_4, 'b', label='Ei(x)')\n", " upper_bound_4 = upper_bound_t(t, X_4)\n", " plt.plot(X_4, upper_bound_4, 'y--', label='$Ei(t) + (e^x - e^t)/t$ for t = %.3g' % t)\n", " if not onlylast:\n", " plt.plot(X_4, np.exp(X_4), 'r--', label='$e^x$')\n", " plt.plot(X_4, np.exp(X_4) + (Ei(-1) + (-np.exp(1)) + (np.exp(1) - np.exp(-1))), 'g--', label='$e^x + Ei(-1) - 1/e$')\n", " plt.title(\"The function $Ei(x)$ and upper-bounds $e^x$ and $e^x + Ei(-1) - 1/e$ and $Ei(t) + (e^x - e^t)/t$ for t = %.3g\" % t)\n", " else:\n", " plt.title(\"The function $Ei(x)$ and upper-bound $Ei(t) + (e^x - e^t)/t$ for t = %.3g\" % t)\n", " plt.legend()\n", " plt.xlabel(\"$x$\")\n", " plt.ylabel(\"$y$\")\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = 1\n", "see_upper_bound(t, 2*e)" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "image/png": 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MRnGm5eDBg3JxcVGbNm3k4+OTZr1Dhw5JksWngJhMJouf6d27tz788EPt27dPK1asSHMi0bQ+f7+4uDjNmjVLX375pS5evGj2Xv78+S1+Jr39kvyfoHsvGJNZKrOXBx980Ox1UFCQ8uXLl+oJiBnVu3Llis395P5jkJiYmOo/NPny5TO7NcSaOGxtr7Zw5DG8c+eONm/erJs3b6Y5N0l6/ccatrZba845zrrNO3fuVPfu3VOV79q1S998841Z2fLly82eupXM2nOSlPZ5ydI5ZceOHXr++ecz3Ib0YrNWeue07IxDujs3zdatW/Xiiy+mlNmjDThbu7ZHu5FSH7tDhw7JZDKl+5/1jL7D7NEvLK3LkX3ZHu3UnvHdv48ttWvJuuOVkcx8p9nrIQD3y5cvn0Mm97948aL69++vgIAARUREGPpgGMCRSCgBuVhav2aZTCYlJSVJktq0aZPmryblypXL1HrTGjGUmJhosTy9OJ1JZuOMjIxUsWLFMrwAj4yMVEhIiNlcFsn3/8fExFj8zPz585WUlCQXF5d05+KIiYmRh4dHhheWkyZN0vr169W1a1fVqFFDgYGBcnV11VtvvZXmdjr6+NnanuwpM/3k3lEFknT27NlUT4eyx39i05KZ/eXIY3jy5EndvHlTQ4YMUc2aNS3Wyey5Jpmt7dbRbdaR22zp1/Rp06YpJCREffr0SVXXEmvPScl17z0vpXdOKl26tFWPEZf+/U9jZqV3TsvOOKS7SYuYmBg98sgjKWX2aAPO1q6z0m6ktNtO8mim9BIUGX2H2aNfWIrPkX3ZHu3UnvHdv48ttWvJuuPlCPd/t9rLnTt3FB0dbVXd+38MSktsbKz69u2r2NhYrVq1yqbJ/YGchoQSkEcFBQXJz89PCQkJdv9lJjAw0OJ/Ns6cOZOp5QUFBcnf31+HDx9Ot54tt74FBQXJx8dHx44dS/Xe0aNHJcnikP7MiIyMNLsVIL169/+amzyR5KlTp1I9inrZsmVatWqVxowZo1mzZmnu3LmaOXOmxWWfOnXKqklBv/vuOz311FMaM2aMWXl0dHTKxbYtgoKC5O3trePHj6d6z1KZJZlpTydOnDD75TN5pNH9xzSjevboJyEhIan+o3P/hbg1cVjbXh3R/7JyDJOfVle6dGmHPeLd2dqtI7fZ0q/p+fLlU0hIiNXrsvaclFz33vNSeuek4OBgs6d6OVJ657TsjEO6+1j1UqVKmY3ysUcbcLZ2nZV2I6XddiIjI1WgQAGLD31IltF3mD36haX4HNmX7dFO7Rnf/fvYUruWrDteGXHkNZit0yDs2rXL4ug2S6z5MSguLk4DBgzQ8ePHtXTp0iz/YAI4u6zfNA4gR3Jzc1PLli31448/psyLcC9LT3Cx1gMPPKDY2Fiz5SY/kS0zXF1d1aJFC23ZskV79uxJ9X7yr6/Jv5qmNZrnXm5ubmrSpIk2b96sf/75J6X82rVr+vzzzxUeHp7p24fudenSJV26dCnDZI7JZNKRI0cUGhpqVl65cmV5eXlp3759ZuU//vijpk+frgEDBqh79+7q2rWrNmzYoKioKIvL//vvv1WjRo0M43Vzc0v1a/bXX3+tCxcuZPjZtJbXuHFjbd682SyhcezYMW3dutWqZWSmPa1cudJsO1asWCFJqX5pzaiePfqJl5eXGjZsaPZ3/2gya+Kwtr3au/9l9RgWL15cLi4u2rhxY6r3kpKSdPXq1UzFdX+MztRus2ObM8vac5Jk+byU1jkpu1l7TssOyY9Vv5c92oAzteusthsp7bZz9uxZFS1aNN1lZsfxthSfM/dlyb7x3b+PLbVrybrjlRFHXoPZci0o/Tu6zZq/jEZlJSYm6uWXX9bu3bs1a9YspzlHAY7ECCUgD3vllVf0+++/q2PHjnruuedUvnx5RUdH6+DBg9q0aZP++uuvTC23devWmjFjhgYPHqxu3brp9u3bWr16dboTO2dk+PDh2rZtm7p166aOHTuqXLlyunTpkjZt2qQ5c+aoRIkSKY/6nTlzptq2bSsPDw/Vr19fwcHBFpf58ssva+vWrerSpYu6dOkiLy8vffzxx4qNjdWoUaMyFef9kv9Tf+3aNX3xxRep3i9btqzCw8P1zz//6ObNm6l+0fX09FSTJk20bds2DR8+XJK0f/9+vfLKK2rZsqVefvllSVLPnj21fPlyzZ49W++9957ZMvbt26dr166lTCydnmbNmunzzz+Xv7+/ypcvrwMHDujbb7/N0twFQ4YM0S+//KLnn39enTt3VlJSklauXKmyZcumDJ1PT2ba0/nz59W3b181bdpUBw8e1Mcff6zGjRunmmPCmnqO6ie2xmFte3VE/8vKMQwODlbbtm315Zdfqk+fPmratKlMJpNOnTqlTZs2ady4cWratGmm4krmbO02O7Y5s6w9J0myeF6ydE6yh5UrVyomJiZlYuXffvtNCQkJku5OUh8QEJBS15ZzmqPjiomJ0eHDh/X666+bfc4ebcCZ2nVW242UdtspUaKEtm7dqoULF6pw4cIqXbq0qlatmvJ+dh1vS/E5c1+2Z3z37+PTp09bbNdSxsfLWo66BrP1WtCecyhNmzZNP/30k5o2bWqxr7Rr184u6wGcCQklIA8LDg7WunXrNG/ePP34449as2aN8uXLpzJlymTpy7xAgQKaM2eOpk2bpnfeeUclSpTQ8OHDdeLEiUz/h7ZQoUJat26dZs2apW+++UYxMTEqVKiQGjdunDL0v0qVKhoxYoQ++ugjjR49WklJSVq+fHmaFxFly5bV6tWrNXPmTC1atEgmk0nh4eGaPHmy6tSpk+ntv1fyRfjnn3+uzz//PNX7Y8eOVXh4eMoEppZ+/Wrfvr0GDhyokydPysPDQwMGDFBoaKimT5+eMrS7QIEC6ty5s5YsWaJDhw6Z/TL87bffqmjRolZdMI0ZM0bu7u7asGGDbt68qfDwcC1atEjvvPNOprY/eZsWL16sqVOnKiIiQkWKFNHgwYN18eJFqxJKmWlP7777rubPn693331XLi4ueu655yy2aWvqOaqf2BqHte3VEf0vq8dwypQpCg0N1RdffKEZM2bIy8tLxYsXV9u2bVW7du1MxXQvZ2y3jt7mzLL2nCQpzfPSvecke02Uu2TJErNJ87du3ZoyaubJJ580SyjZck5zdFw///yzfH19LR7TrLYBZ2rX9mg3kuW2079/fx0/flzz58/XjRs3NGLECLMERXYeb0vxOWtfTmaP+O7fx//973/TbNcZHS9rOeoazNZrQXtK7iebN2/W5s2bU71PQgm5kYvJ2Wa9BQCYSUpKUps2bdS0aVO9+uqrNn02Li5OzZo1U9++fdWzZ0/HBOhEZs+erTlz5mjr1q0KCQnJcj0AqWXlnJRVznZO69evnzw9PTVnzhyjQ8kRbG072X28jWzbRrG0j2nXAKzFHEoA4ORcXV01dOhQrV692uo5AZJ98skn8vDwUJcuXRwUHYC8JivnpKxytnNanTp11KtXL6PDyDFsbTvZfbyNbNtGsbSPadcArMUIJQBArsEIJQAAACB7MEIJAAAAAAAANmGEEgAAAAAAAGzCCCUAAAAAAADYhIQSAAAAAAAAbOJudABGuHgx1ugQ7KJAAV9dvXrT6DCAPI1+CDgH+iJgPPohYDz6IRwhJCTAYjkjlHIwd3c3o0MA8jz6IeAc6IuA8eiHgPHoh8hOJJQAAAAAAABgExJKAAAAAAAAsAkJJQAAAAAAANiEhBIAAAAAAABsQkIJAAAAAAAANiGhBAAAAAAAAJuQUAIAAAAAAIBNSCgBAAAAAADAJiSUAAAAAAAAYBMSSgAAAAAAALAJCSUAAAAAAADYhIRSHvHss2310UcrzMp27dqhTp2eUWJiolXLiIo6oqeeaqVbt245IkQAAAAAAJBDuBsdAOxjypQ39e23X6cqr1QpXAsXLtOiRcvl4+Nj9t68ebPUo0dvubm5WbWOsmXLqXLlcK1du0o9e75gl7gBAAAAAEDOQ0IpF6ldu67GjZtoVubh4SFJKlCggFn5X3/t0YkTJ9SsWXOb1tG69ZN6++0p6tq1p9zdaT4AAAAAAORF3PKWi3h6eio4uKDZX2BgPkmpb3nbtOk71apVR15e3pIkk8mkl18epKFDB8lkMkmSbt68qU6dntbMmdNTPle3bn3FxsZo164d2bhlAAAAAADAmTDEJANvvumlr77K3t3Utm2C3nwzzqHr2LNnt9noJBcXF40dO0E9enTS6tUr1KVLd7333jtyd/fQ4MFDU+p5eHioXLlQ7d69U3Xq1HNojAAAAAAAwDmRUMpFfvttu1q0aGJW9vTTz2nQoJdS1T1//qwKFgwxKytYMEQjR47TG2+M1o0bN7Rp03dauPDDlFFM99Y7d+6M/TcAAAAAAADkCCSUMvDmm3EOHy1kL9Wq1dBrr40xK/P3D7BYNy4uTp6enqnKH3roEbVo8bg+/HCxBg16SeXLh6aq4+Xlpbi4nLFPAAAAAACA/ZFQykW8vb1VokRJq+rmy5dfsbGxqcrj4uJ04MB+ubm56dSpkxY/GxMTo6JFi2YpVgAAAAAAkHMxKXceFRoapuPHj6YqnzdvluLj4/Wf/8zVhg1faevWn1PVOXYsSqGhFbIjTAAAAAAA4IRIKOUid+7c0eXLl8z+rl69arFu3br1tXfvHrOy7du36YsvPtW4cZNUs2Zt9e7dT9OmTdbly5dS6pw9e0YXL15Q3br1HbotAAAAAADAeZFQykX+/PN3tWv3uNlf797PW6z72GOtdfLkCR09GiVJunr1qqZOnagePfqocuVwSVLXrj1VqlRpvfXWRJlMJknSDz9sVJ069VWkCLe8AQAAAACQV7mYkjMFecjFi6nnDsqJQkICsrQt778/W9euXdXo0eOtqn/nzh116vS03nxziqpWrZ7p9QK5SVb7IQD7oC8CxqMfAsajH8IRQkIsP+yLEUp5WPfuvVSsWHElJiZaVf/cubPq3r03ySQAAAAAAPI4nvKWh/n5+atHjz5W13/ggQf1wAMPOjAiAAAAAAByNv8RL8lUIEg3Xntd8vQ0OhyHYYQSAAAAAACAHbie/Ec//P6hov7cIHl4GB2OQzFCCQAAAAAAwA5cli1Q7ydNSvI/qb1J8fJ0Y4QSAAAAAAAA0nLrlr78c7Eu+UldKvfK1ckkiYQSAAAAAABAlnl9uk5zw2/K1eSintX7Gx2Ow5FQAgAAAAAAyKI/3M7oz+JSy6JN9UBg7n+gFQklAAAAAACALPrsgRuSpD51XzY4kuzBpNwAAAAAAABZkZSk8Q0m6vHST6hukXpGR5MtGKEEAAAAAACQSa7nziqoRiX5LF+qekXry8XFxeiQsgUJpTxm4MDe2r9/nyRp6tSJWrt2lcERAQAAAACQc7kuW6hxlc4oynTJ6FCyFbe85TE9eryglSuXqVq16nJ1dVXHjs8bHRIAAAAAADlTXJw2bF+oqS2lKw+e1ySj48lGjFDKY+rXb6jz589p+/ZtGjFilNHhAAAAAACQY3l9+ZnmVoqVi0nqVXOQ0eFkK0Yo5TIXL17Q/PlztH37NiUlJapWrToaMWKUgoKCJUkHDuxXbGyMihQpKnd3Dj8AAAAAAJliMunAxzO1vanUPKSJyuQra3RE2YoRSrnImTOn1bt3V4WEFNK8eR9o9uwFio6O1jvvTJV0N9k0bdpkzZr1vs6dO6OjR48YHDEAAAAAADmT+55der9ApCSpT92hBkeT/RiiYoWgWuEWy28Oekm3+/STJAUM6iuP37anqhNfq7ZiFy6TJHmvWCbf92ZYXNaV7TslT0+5HT6kxPKhmYpzxoypatOmnfr3fzGlrEePPhoz5jXFxd3WuHGjNGzYqypWrLi6du2lZcsWa+LEqZlaFwAAAAAAedmZ8sW1uoa7ynkXU9MHmhsdTrYjoZRLnDt3Vr///qv27NmlTz5Zk1KemJgkb29veXl5a/78JSnlzZo1V7Nmea/BAwAAAABgD/FJ8Xoq9DnVL9pQri557wYwEkpWuLJjX4Z1YuctyrDO7W49dbtbz3TrZHZ00pEjh+Tn56fFi1emes/d3SNTywQAAAAAAKl5frdBJUPDNOfRBUaHYhgSSrmEm5uVE4UWAAAgAElEQVS7bt++raCgYPn6+hodDgAAAAAAudONG9Lw/srv6q0ruw9IefSBV3lvTFYuVblyFQUEBGjSpPE6dOigTp8+pT/++FUzZ05XUlKS0eEBAAAAAJAreK39SI+0j9aj/byVkIezKnl403OXwMBAzZgRoRs3ruullwaoZ88umjNnlgoVKiRXVw4zAAAAAABZlpSkP798V7uLSvkerCR317w5OknilrdcpUKFSoqImG90GAAAAAAA5Eqem3/Q7JKnJUn96g43OBpjMXQFAAAAAADACmc/nKkvKkg1/CuoTpG6RodjKBJKAAAAAAAAGUlI0NzQqzK5SH3rj5CLi4vRERmKW94AAAAAAAAykOAqrS8Zo8KmInqy7NNGh2M4EkoAAAAAAADpSUqSu6u7fun0mw5fOyRPN0+jIzIct7wBAAAAAACkw2fOe8r35OMqcOqCahWuY3Q4ToERSgAAAAAAAGmJj9dv387RcfdYtQwKlJfR8TgJRigBAAAAAACkweubLzUl/JJeaBWnqKRLRofjNEgoAQAAAAAAWGIy6fBHb2tzaemh4LqqFFzZ6IicBgklAAAAAAAAC9x/+1Vz8x2QJPWrN8LgaJwLCSUAAAAAAAALri1/T6uqSOW8Sqj5gy2NDsepkFACAAAAAACwIKJTOd1xl/rVGy5XF1Io9+IpbwAAAAAAABaEF6utxlcfUoewLkaH4nRIr+UxAwf21v79+yRJU6dO1Nq1q7I9hpkzp2v06FdSXsfExKht28d0+vQph61z7NiRWr16pcOWDwAAAADIPVwuX5b3quV6skQrfdrua/l6+BodktNhhFIe06PHC1q5cpmqVasuV1dXdez4vF2XP3ToQO3Y8Ueq8vr1G2rGjAhJUt++A+Xu/m/TW7FiqRo0aKTixUtkap27d+/U6tUrFBl5UJcuXdTrr7+h1q3bmtXp1auvBg/up7Ztn5K/v3+m1pOV9Sd755235OnppaFDmcwNAAAAAJyV57KFSpw1Vd5xcbrdu6/R4TglRijlMfXrN9T58+e0ffs2jRgxyqrPTJnyphYvXmBV3cjIg+rXb5C++OI7s78JE95KqRMYGChf37vZ3du3b+urrz7XE0+0s31j/ufWrZsqU6achg4dIS8vL4t1ypYtp2LFimvjxg2ZXk9W1i9JJpNJW7duUZMmD9s9BgAAAACAndy+re83z1XJ4dLHde07ICE3IaGUy1y8eEGTJo1X69aP6vHHH9GYMa/qypXLKe8fOLBfsbEx8vPzNxslZA+nT5/S9euxql69poKDC5r9+fnd7YQXLpxX48a1deLEcUnS9u1b5eLioqpVq2V6vQ0aNFb//i+qadPmcnVNu0k3bvyQfvhhY6bXk9X1HziwX/Hx8apatbqkjI8VAAAAACD7eX+yVv8Jj9F1T6li8VpGh+O0SCjlImfOnFbv3l0VElJI8+Z9oNmzFyg6OlrvvDNV0t0ExrRpkzVr1vs6d+6Mjh49Ytf1Hzx4QG5ubgoNrZBmnSNHDsvb21slSz4gSdqzZ7fCwirIxcXFrrFYUrFiZR04sF9xcbcdvi5LfvnlZzVo0Eju7u4ZHisAAAAAgAGSkrT7k3f0fw9IjxV5ROULhBodkdNiDiUr1FoRbrF8UPWX1KdKv7v//qGvfju7PfVnC9fWwseWSZJW/L1M7+2YYXFZ27vslKebpw5fPZTpBjtjxlS1adNO/fu/mFLWo0cfjRnzmuLibmvcuFEaNuxVFStWXF279tKyZYs1caL9EhiRkQeUmJiotm1bmJXXq9dQkydPlyQdPhypMmXKpYzkOX/+rAoWDLFbDOkpWDBECQkJunTpUqbna8qKX375WX37DpCU/rECAAAAABjD88fvNavEP5KkgfVeNTga50ZCKZc4d+6sfv/9V+3Zs0uffLImpTwxMUne3t7y8vLW/PlLUsqbNWuuZs2aW1zW8uVLtGLF0pTXd+7ckYuLi9as+fcpaTNmRKhatRpmnzt06KAeeaSZBgwYYlaefLubdHeEUvny/ybM4uLiVKBAkFn9hQvnafnyJUpPRMR81axZO90690ue38jSCCVHrTPZqVMndebMadWt2yDDYwUAAAAAMMZR02V9VkGq5h+mhsUaGx2OUyOhZIUd3fZlWGde80UZ1ulWqae6VeqZbp3Mjk46cuSQ/Pz8tHjxylTvubt72LSsp55qr2bN/h1l9P77EQoJKaRnn+2UUhYSknpU0aFDkerRo7dKlCiZ5rIPHz6kTp26pLzOly+/YmNjzep06NBFLVu2TjfGwoWLZLgd94uJiZEk5c9fINV7jlpnsi1b/qvatevIx8dHO3b8brdjBQAAAACwnw2Fo5V0RBrY4LVsmZolJyOhlEu4ubnr9u3bCgoKTnmCWmYFBuZTYGC+lNe+vn4KCAhMN1F05sxpxcREq3z5sDTr3Lp1S2fOnFK5cv/WKV8+TN9++5VZvfz58yt//vxZ2ALLjh07opCQQgoKCk71nqPWmWzr1p/VqlUbSfY9VgAAAAAAO7l9W/2qDVKDYo1UIaiS0dE4PSblziUqV66igIAATZo0XocOHdTp06f0xx+/aubM6UpKSnL4+iMjD0iSgoML6vLlS2Z/CQkJkqSoqMOSpHLlyqd8rl69Bjpx4riio69let03b97U4cOROnw4UklJSTp//pwOH47UuXPnzOrt2bNbdevWz/R6Mrv+q1evav/+v9SoURNJxh8rAAAAAIA511MnFVwlVD7vz1GVkGrycOPukYwwQimXCAwM1IwZEZo3L0IvvTRAiYlJKlasuJo3fyzdR9nbS2TkQUnS888/a1bu4uKiDRt+UkBAgI4cOaQSJUqazRNUtmw5VaxYWT/88L3at++QqXUfPPi3XnppQMrrxYsXaPHiBWrVqo3GjHlT0t25mrZs2ayZM+dkah1ZWf+2bVtUsWLllJFRRh8rAAAAAIA510VzNbjxNXUJuK6077vBvVxMJpPJ6CCy28WLsRlXygFCQgJyxbb8+uv/adasGVq5cp3c3Nwcso716z/W1q0/6z//meuQ5adn1KjhqlKlmp5/vke2rxuOl1v6IZDT0RcB49EPAePRDzPH5dpVfdk1VH1ax2lg+CBNeGia0SE5lZCQAIvljFCC4erXb6iTJzvo4sULKlKkqEPW4e7urmHDjHnkY5Uq1dS8eUtD1g0AAAAASJ/Xsg80s3ac3E2u6lvjRaPDyTFIKMEpPPdcp4wrZUG7ds84dPnpYWQSAAAAADipW7f00/ez9HcbqUOZp1UiIO2HUcEcE7YAAAAAAIA8yfPnzXqnaowk6cU6xtzVklORUAIAAAAAAHnSL9WCtO0BqUXRpqoYXMnocHIUbnkDAAAAAAB5UsmAkupbZYCeLGfcNCk5FQklAAAAAACQt5hM8ntroh548ilNafK20dHkSNzyBgAAAAAA8hSPX37W0dUz5fPeDKNDybFIKAEAAAAAgDzl8sKpqtFf6vxYjNGh5FgklAAAAAAAQJ7hvmeX5rpsV4Kb1LTqc0aHk2ORUAIAAAAAAHnGrfff0cJaUjH3YLUP7WB0ODkWCSUAAAAAAJAnuB47qsWXv9ENT6lfnWHydPM0OqQci4QSkAWnT5/S1q0/Gx0GAAAAAMAKN73cFPGQt/K5+Kp75V5Gh5OjkVACsuDXX/9Px44dMzoMAAAAAIAVDntck4t/gHrVGCR/zwCjw8nRSCghRxs4sLf2798nSZo6daLWrl2VbevetWuHPvhgvr755gv16tVFt27dyrZ1AwAAAABs43o0SlUKVtWObvv0Us1hRoeT45FQymNmzpyu0aNfSXkdExOjtm0f0+nTp9L93NixI7V69UqHxWVtHPfr0eMFrVy5TGvWrJSrq6s6dnzeQRGmVqNGLZUtW07/+c9cLV36kXx8fByyn5KSkvT221PUuvWjaty4tnbu/NOuywcAAACA3M4lJloFHntE+Z57St7u3oxOsgN3owOAfQ0dOlA7dvyRqrx+/YaaMSNCffsOlLv7v4d9xYqlatCgkYoXL2FWf+7cWYqKOqx3350jSerVq68GD+6ntm2fkr+/v93jTiuOjNSv31ALF87T9u3bNHPmbLvHlZHz58+raNFiKa8z2k/vvPOWPD29NHToCEmp97Ml27dv04YNX2n27AUqVqy4AgPz2S3+wYP7qUyZsho+fKTdlmnJihVL9fPPm/XPPyfk6emhSpWqaMCAF1WmTDmHrhcAAAAAJMl7yUI92SZaD5X1EjMn2QcjlHKZyMiD6tdvkL744juzvwkT3pIkBQYGytfXV5J0+/ZtffXV53riiXaplnPgwH5VrFg55XXZsuVUrFhxbdy4wao4pkx5U4sXL7CqbnpxZOTAgf2KjY2Rn5+/WaIsO1y4cF4FCxY0K0tvP5lMJm3dukVNmjycUnb/frbk9OmTCg4uqCpVqik4uKA8PDxsjjU+Pt7mz9jTrl079PTTz2r+/MWaNWu+3Nzc9PLLLyomJtrQuAAAAADkATdvavPG9/RNqPRbWS+jo8k1GKGUi5w+fUrXr8eqevWaCg4umOr9CxfO65lnntCqVZ/owQdLafv2rXJxcVHVqtVS6sTHx6tFiyZKSEjQ7t079eGHi1WqVGmtXLlOjRs/pB9+2Kj27TvYNW5LcUjSxYsXNH/+HG3fvk1JSYmqVauORowYpaCg4JT3p02brFmz3tfYsa/p6NEjdh/xkl4M586dtbif09pPBw7sV3x8vKpWrZ7ufr7XlClv6ttvv/7fcmurSJGi+uSTr3Tnzh29//5s/fDDRt24cV3lyoXqxRdfVrVq1SXdHXlUqlRpeXv76LvvvlaRIsX0wQfLUy179+6d2r17pz799O5616370mzElb3cPwJr3LiJevzxR7R37x41bvyQ3dcHAAAAAMm8VyzV1OqxkqSh9UYbHE3uQULJCocOhVssDw5+ScHB/SRJp0711c2b21PV8fGprZIll0mSrlxZpkuXZlhcVrlyO+Xq6qm4uEPy8grNVJwHDx6Qm5ubQkMrWHz/yJHD8vb2VsmSD0iS9uzZrbCwCnJxcUmp4+bmpvnzl+qFF7pp4cJlKly4iDw8PCVJFStW1ocfLlZc3G15eXlnKkZLLMVx5sxp9e/fS0888aTmzftA8fF3NGvWTL3zzlRNnTpDcXG3NW7cKA0b9qqKFSuurl17admyxZo4card4soohjJlyunMmdPq3r2jJkyYqtKly0hKez/98svPatCgkdzd3ZWUlJTmfr7X0KGvqEiRovrmmy+1aNGHcnV1kyTNmxehzZs3afTo8SpWrLjWrl2lV14ZotWrP0sZNbVx47d68smnNXfuBzKZTBaXffLkP3rggQfVv/+LkqT8+QtY3BfLly/RihVL091fM2ZEqFq1GlbsWenmzZtKSkpSQECgVfUBAAAAIFPi4vTb5zO0va3UqngLVQyuZHREuQYJpVwkMvKAEhMT1bZtC7PyevUaavLk6Tp8OFJlypSTq+vdOx3Pnz+rggVDzOq6urrq8uVL8vX1U8WKlc2SPAULhighIUGXLl2yea6j9FiKY8aMqWrTpl1KokOSevToozFjXpMkeXl5a/78JSnvNWvWXM2aNbdbTNbE4O/vryVLUk/AndZ++uWXn9W37wBJ6e/ne/n7+8vHx1eurq4po6Fu3bqlzz//RCNHjlXDho0lSa+8Mlo7dvyhTz/9WP36DZIkFStWTEOGpP3kAn//u7cJent7Wxxpda+nnmqvZs1apFsnJCQk3ffvNWvWDJUvH6rw8CpWfwYAAAAAbOUWdeTf0Un1GZ1kTySUrBAaui/DOiVKLMqwTlBQTwUF9Uy3TmZHJ0nSoUMH9cgjzTRgwBCzcj+/u5NDHzlyWOXL/7v8uLg4FSgQlGo5hw9Hqly58qmSHF5eXv/73O1Un7l/BMudO3fk4uKiNWv+TbikNYLl/jjOnTur33//VXv27NInn6xJKU9MTJK3t20joxYunKfly5ekWyciYr5q1qxtVpaVGCztp1OnTurMmdOqW7dBSlla+zkjp0+fUkJCgqpWrZ5S5ubmpvDwqjp+/FhKWVhYRZuWm57AwHx2mwx89ux3tXfvbs2b94Hc3NzsskwAAAAAsGRXSLx+KnlHDxdpopqFa2f8AVgt2xNKCxYs0Pfff69jx47J09NT1atX1/DhwxUa+m+iw2Qyac6cOVq7dq1iYmJUrVo1jR8/XuXLl0+pEx0drcmTJ+unn36SJDVr1kzjxo1TYGDevYXm0KFI9ejRWyVKlLT4/uHDh9SpU5eU1/ny5VdsbKyFepEKDQ1LVR4TEyPJ8m1R949gef/9CIWEFNKzz3ZKKUtrBMv9cRw5ckh+fn5avDj16B93d9smpO7QoYtatmydbp3ChYukKstKDJb205Yt/1Xt2nXk4+OTUpbWfs6Ke3NTtibf0mOvW94iImbqxx+/V0TEAruOcgMAAAAAS8ILVtXyVmtU2Lew0aHkOtmeUPr999/VpUsXValSRSaTSREREerVq5e++eYb5c+fX5K0aNEiLVmyRNOmTVPp0qU1d+5c9erVS999913Ko9hHjBihs2fP6oMPPpAkjR07Vq+99prmz5+f3ZvkFM6cOa2YmGiVL285QXHr1i2dOXNK5cr9+3758mH69tuvUtU9cuSw6tdvlKr82LEjCgkplDIp9r3uH8Hi6+ungIDANJNb97o/Djc3d92+fVtBQcEpT6TLrPz586e0K1tkJQZL+2nr1p/VqlUbs3pp7eeMFC9eQh4eHtq7d3dKUiYxMVH79u1VixaP27QsDw8PJSUlZVjPHre8vffeDP300yZFRMzXgw+WsiVMAAAAALBNUpLydXxad1q01OP/mxYE9uWa3StcvHix2rdvr9DQUIWFhentt9/WlStXtHPnTkl3RyctX75c/fr1U8uWLRUaGqrp06frxo0b+vrru0+7ioqK0i+//KKJEyeqRo0aqlGjhiZMmKDNmzfr6NGj2b1JTiEy8oAkKTi4oC5fvmT2l5CQoKiow5KkcuX+HeVVr14DnThxXNHR18yWlZiYqBMnjuvSpYtmI4f27NmtunXr2z32++OoXLmKAgICNGnSeB06dFCnT5/SH3/8qpkzp1uV/LCHrMRw/366evWq9u//S40aNTGrl9Z+zoiPj4+eeupZzZ8/W9u3b9Xx48c0Y8Y0Xb16RU8//ZxN21mkSDH9/fd+nT17RteuXUtz2wID86lEiZLp/qU3UfvMmdO1YcNXeuONyQoICEhpmzdv3rQpXgAAAACwhud3G/Tx1c26sD/1w7NgH9meULrfjRs3lJSUlHKr2qlTp3Tx4kU1avTvyA1vb2/VqVNHu3btkiTt2rVLvr6+qlmzZkqdWrVqydfXN6VOXhMZeVCS9Pzzz6pdu8dT/p56qpVu3bqlI0cOqUSJkma3QZUtW04VK1bWDz98b7asfv0G6ccfv9fTT7fWggV3H/ceFxenLVs2q23bp+0e+/1xBAYGasaMCN24cV0vvTRAPXt20Zw5s1SoUKGUCcUdLbMxWNpP27ZtUcWKlVON7LK0n601cOAQNWv2mN56a6J69eqiqKjDmjFjdsoT3qzVuXNXeXh4qGvX59SmTXOdP3/Ops9b67PP1unmzRsaOnSgWftcvXqFQ9YHAAAAIA8zmXT6g8nq8ZTUoU6U0dHkWi4mS88Tz0ZDhw7ViRMntH79erm5uWnnzp3q3LmzNm/erGLFiqXUGz16tC5cuKDFixdr/vz5WrdunX788UezZT366KPq0KGD+vfvn+46ExIS5e7OZMCStGXLFk2ZMkUbNmxId4LkVatW6ccff9SSJelPcO3oOJydpf00cOBA1axZU3379jUwMgAAAADIIzZt0gtzHtPimtLHz36s5yrbdicHrGPoU96mTp2qHTt2aPXq1dmaRLh6NXfcZhMSEqCLF62/VcqSihVrqF27Z/X331EqUqRomvVu3UrQiy8Oy/L6shqHs7O0n8LCKqtBg0cctu9gLHv0QwBZR18EjEc/BIxHP7wrZuoYLW8slfd5QE0KtmCfZFFISIDFcsMSSm+99ZY2bNigDz/8UCVL/jtxc/LEvpcuXTIboXT58uWU23kKFiyoK1euyGQypTxy3WQy6cqVKzbf8gPpuec6ZVinXbtnnCIOZ2dpPz3/fA8DIgEAAACAvMd9905FeP2heDdpSIPRcnPNuXfAODtD5lCaPHmyvvnmG3344YcqW7as2XslSpRQSEiI/u///i+lLC4uTn/++adq1Lj7SPIaNWro5s2bZvMl7dq1Szdv3kypAwAAAAAA8paz5UtoUQNPlfAqrPblOxgdTq6W7SOUJkyYoC+++EJz585VYGCgLl68KEny9fWVn5+fXFxc1L17dy1YsEBlypRRqVKl9P7778vX11dt2tx97HrZsmXVpEkTvfHGG5o4caIk6Y033lDTpk1VpkyZ7N4kAAAAAADgBG4n3dajpVupSYmH5eHmYXQ4uVq2T8odFhZmsXzw4MEaMmSIpLu3r82ZM0dr165VdHS0qlWrpvHjxys0NDSlfnR0tCZNmqSffvpJktSsWTONHz8+5Wlx6ckt909yfyxgPPoh4Bzoi4Dx6IeA8fJ6P/T+cInuPPa4kooWy7gyrJbWHEqGP+XNCLmlg+X1kwXgDOiHgHOgLwLGox8CxsvL/dB9724lPPmQ8tV6RNHrvzQ6nFwlrYSSIXMoAQAAAAAA2Evcfyar3EtSn/aGPsw+TyGhBAAAAAAAciy3v/Zq/o3vFeMtla34sNHh5BkklAAAAAAAQI4VP2uK3qsvFXQLVM/wF4wOJ88goQQAAAAAAHIkt/37tPDat4r2lgbWGSE/Dz+jQ8ozuLkQAAAAAADkSDEeifrPQx4KcvNWryp9jQ4nT2GEEgAAAAAAyJF2+F7VbW93Daw9XP4e/kaHk6cwQgkAAAAAAOQ4rieO66EHH9GfXffJx8PH6HDyHEYoAQAAAACAHMUt8qCC6lWX3xtjFOIbwugkA5BQAgAAAAAAOUrSrLf0aLckfVnVy+hQ8iwSSgAAAAAAIMdwO3xIi89+rs2lpV0PeBodTp5FQgkAAAAAAOQYpvemamZDKdDFV32rDjA6nDyLhBIAAAAAAMgR3A4f0tLTn+qin9S35mDl88pvdEh5FgklAAAAAACQI8Tt/UNvNzIpwMVH/aoNMjqcPI2EEgAAAAAAyBGWlo/RRT+pX82XVMA7yOhw8jR3owMAAAAAAADIkMmk7pV7y83VXe3LP2d0NHkeI5QAAAAAAIBTc/9rjwo80kD+//ereof3Ze4kJ0BCCQAAAAAAOLU7MyfovQJ/60b8DaNDwf+QUAIAAAAAAE7LfeefmnfzB736mLQ4KMrocPA/JJQAAAAAAIDTuv3um/pPAynEPb+6V+5tdDj4HxJKAAAAAADAKbn//ptmJ25RrJc0pN5r8vPwMzok/A8JJQAAAAAA4JSufzhbEfWkIh5B6lG5j9Hh4B4klAAAAAAAgFOa1qmkbnhKQ+uPlo+7j9Hh4B7uRgcAAAAAAABgSdNSj+no9eN6vmIPo0PBfUgoAQAAAAAAp+Kx7Re57/hDD/fpr4dbNTU6HFjALW8AAAAAAMB5mEy6/vbrujL7TblHHTY6GqSBhBIAAAAAAHAant9t0FtBe1RuqIu2F4ozOhykgYQSAAAAAABwDomJOj97nBbVlEr6lVCNQrWMjghpIKEEAAAAAACcgten6zSp5BEluEkjG0+QuytTPzsrEkoAAAAAAMB48fE6tuBNraoqhQeGqV25Z4yOCOkgoQQAAAAAAIzn7q7Xu5eQyUUa3XiSXF1IWTgzxo4BAAAAAADDxSclyLvog6p/3V3NH2xpdDjIAAklAAAAAABgKM8fv5draAXNb7FYdxLvyMXFxeiQkAESSgAAAAAAwDAu0dekl/oov6uPruzcL08PT6NDghVIKAEAAAAAAMN4z52lZk9Fq0CxQlrqKnkYHRCswgxXAAAAAADAEC4XLmjj5tn6o7jkU7qiPNxIJ+UUJJQAAAAAAIAhvN6brnGN78hNrhrV8A2jw4ENSCgBAAAAAIBs5/rPCa3fuUQHQqTOYV1UNn95o0OCDUgoAQAAAACAbBenRL3xuJe85K4RdV83OhzYiEm5AQAAAABAtvvL64qu+LmpZ6X+Kh5QwuhwYCMSSgAAAAAAIFu5/bVXNavU1h9d98rNhZunciKOGgAAAAAAyDYeW7eowKON5TttkoJ9gpXfu4DRISETSCgBAAAAAIDskZSk2OmjVLO/9FVdEkk5GQklAAAAAACQLby+/ExvFdyn3UWlU4V9jQ4HWUBCCQAAAAAAON6dOzo1e6wW1ZLK+ZXS8xW7Gx0RsoCEEgAAAAAAcDifDxdrbKXTSnSVxjSZIndXnhOWk5FQAgAAAAAADvdr0nF9VlGqE1xLrUu3MTocZBEJJQAAAAAA4HDzy1yWJL3x0DS5uLgYHA2yivFlAAAAAADAYVxiY2Ty9lFEs/fVPvQ51S1az+iQYAeMUAIAAAAAAA7j98YYFWhSV16nz6j5gy2NDgd2QkIJAAAAAAA4hFvkQa3dt1yTakQrJiSf0eHAjrjlDQAAAAAAOMZbYzT6UZNiA2P1nClO/kbHA7thhBIAAAAAALA7j+3bNPfGJp0LkAbUfFmFfQsbHRLsiIQSAAAAAACwL5NJN6aO1NuNpBD3/HqxxktGRwQ7I6EEAAAAAADsyvXcWU0pdVzXvaThDcbK3zPA6JBgZ8yhBAAAAAAA7OpUgEmLKt5Uab9S6l6pl9HhwAFIKAEAAAAAAPu5c0fF/Itr3ZNfKMmUJA83D6MjggNwyxsAAAAAALALl/PnFVQrXN6LF6hR8SZqUuJho0OCg5BQAgAAAAAAduH99iSNqnpOx3TN6FDgYCSUAAAAAABAlrnt36fVf6/QjEbS9FLHjQ4HDkZCCQAAAAAAZI3JJNOE18m+iMcAACAASURBVDSuqUm+Ll4aVX+80RHBwUgoAQAAAACALPH8YaPedd2q8/7S4NojVMSvqNEhwcFIKAEAAAAAgCw5+8sXmtlQKuoVooHVhxgdDrIBCSUAAAAAAJAlbzycpDh3aUzjyfLz8DM6HGQDd6MDAAAAAAAAOVRSkuTqqtF1x6mEfwk9G9rR6IiQTRihBAAAAAAAMsVvwjgF9O+lEvE+GlVvnFxdSDPkFYxQAgAAAAAANnM9GqUtP82TqUBB1fblNre8hoQSAAAAAACwmfvksRr4eKLOFLisPxOvqoh4sltewlg0AAAAAABgE49fftb8q9/oeAHphWoDVcSPZFJeQ0IJAAAAAABYLyFB1ycN15SHpCD3fBpW+1WjI4IBuOUNAAAAAABYzX33Tr1WJkqxXtLbDd9UPq/8RocEAzBCCQAAAAAAWO2Pkm5aVjVJlfNXVLdKPY0OBwZhhBIAAAAAALCOyaSKwZU1pt4bqle0gdxc3YyOCAZhhBIAAAAAAMiQ+197lP/RJvLftUdDa41Q/WINjQ4JBiKhBAAAAAAA0mcyKWn8cM3z26v469eMjgZOgIQSAAAAAABIl9fn6zXN9w+93EpaFBRldDhwAiSUAAAAAABA2m7c0Kn/jNKs+tIDPsXUrXIvoyOCEyChBAAAAAAA0uQbMVOv1LqgeDdpwsPvyMfdx+iQ4ARIKAEAAAAAAMvi4/XjjlX6trz0UNGH1Lp0G6MjgpMgoQQAAAAAACyKd5VebuctN7lpysMz5OLiYnRIcBLuRgcAAAAAAACckMkkDzcPTf5/9u47Oqo68f//607NJJOeECAh9CZdRURApIMdFESRJoIgYMEFdVFQUCmKqGBHRQUVVOyKu5a1sSqurH0VkRoIqaSSNnN/f/j58P34UxeFkPfM5Pk4h3OWJMRn2Fz35LXve6fPEv2n8D9qm9TOdBFCCIMSAAAAAAD4paoqJYw4UxXDz9egSVM0qNlQ00UIMdzyBgAAAAAAfsH34H16LPCxcn74zHQKQhSDEgAAAAAAOMSRtUefr7tVl50ljT3xJ9M5CFEMSgAAAAAA4BDvvGs1fUClJOmGPrcarkGoYlACAAAAAACSJPc7b+mhvFf0dZo0pt1YdW/Yw3QSQhSDEgAAAAAAkCTlbXxG80+TEl1xuqHnAtM5CGEMSgAAAAAAQJJ0/WBLpV5pbq+FSvYlm85BCHOZDgAAAAAAAIbV1Egul/7S/Tql+hro4uPGmy5CiOOEEgAAAAAA9VzcJRfLP2umWnjTdXOvW+WwmAvw3/EdAgAAAABAPebZ+LrW7XtdHxf+W/J6TecgTHDLGwAAAAAA9VV5uQpum6VpIyS/f7c2Byrkc/lMVyEMMCgBAAAAAFBPRd+zTJd12atyj7Sk922MSfjDuOUNAAAAAIB6yPnTj3rv9eV6ob3Uo8FJGtX2QtNJCCMMSgAAAAAA1EM1H3+gKwbXyCmHlvS7W5ZlmU5CGGFQAgAAAACgHrqvfYm2JUmXdp6m45I7mM5BmOEZSgAAAAAA1Cfl5ZLXqwkdJ6kicFBTOk8zXYQwxAklAAAAAADqEf+N1ynhzEGKzS/WNSdeq1hPnOkkhCEGJQAAAAAA6gnXx//UK5+v1gONs1SdmGg6B2GMW94AAAAAAKgPqqpUOXe6pp8ulccW6tTqfDX2ppuuQphiUAIAAAAAoB6IXnmXZrb4UXkx0k0n36jGfsYkHDlueQMAAAAAIMI5f/pRnz6/RI91kzomduBB3DhqDEoAAAAAAES46t07NPX0oCxZWtZ/pVwObljC0WFQAgAAAAAgwq1P268fEgOa1GmKuqWdYDoHEYBJEgAAAACACGUdKJRsWxe0vUg+l0/9MweaTkKE4IQSAAAAAAARKmb+XCX16i7XD9/rnFYjFOuJM52ECMGgBAAAAABABHJ/9IGe+W6NJp8eUH5GiukcRBgjg9LmzZs1depU9enTR23bttWGDRt+8f7rrrtObdu2/cWvUaNG/eJjqqqqtHDhQvXo0UNdu3bV1KlTlZ2dXZdfBgAAAAAAoamiQuU3TNc1Q6T1rQ6qLFhhuggRxsigVF5erjZt2mju3LmKior6zY855ZRT9OGHHx769dBDD/3i/bfeeqvefPNN3XnnnVq7dq3Kysp02WWXKRAI1MWXAAAAAABAyIq+c6mubbNDhT7pup7zlR6bYToJEcbIoNS3b1/NmjVLQ4cOlcPx2wkej0epqamHfiUkJBx6X0lJiZ5//nnNmTNHvXr1UocOHbR06VJ9//332rRpU119GQAAAAAAhBzXV1/o/dfv1JouUpfkzprU6TLTSYhAIfsMpX/961/q2bOnhgwZohtuuEH5+fmH3vf111+rurpavXv3PvS2Ro0aqWXLltqyZYuJXAAAAAAAQkKxK6ip57rkklPLB9wvp8NpOgkRyGU64Lf06dNHgwYNUkZGhrKysnTXXXdp/Pjx2rBhgzwej/Ly8uR0OpWYmPiLP5ecnKy8vLzDfv7ExGi5XJFxQaWmxppOAOo9rkMgNHAtAuZxHQLmpabG6tXCYmXFBHR97+vVr/0pppMQoUJyUDrjjDMO/ee2bduqQ4cO6t+/v/7xj39o8ODBR/35CwvLj/pzhILU1Fjl5paYzgDqNa5DIDRwLQLmcR0C5qUeyFbh7v3q0amv3hr5gVoltua6xFH7vf+zIGRvefu/0tLSlJaWph07dkiSUlJSFAgEVFhY+IuPy8/PV0oKL4UIAAAAAKhngkFVXTJesUP6yvnD9+qQ0lFep9d0FSJYWAxKBQUFysnJUYMGDSRJHTt2lNvt1kcffXToY7Kzs7Vt2zZ169bNVCYAAAAAAEZEPfaw5nv/qVOujtfORtGmc1APGLnlraysTLt27ZIkBYNB7d27V999953i4+MVHx+vlStXavDgwUpNTVVWVpbuvPNOJSUlaeDAgZKk2NhYnXfeebr99tuVnJyshIQELVq0SG3bttUpp3B/KAAAAACg/nDs3qUfHrpRt4+V0v0xSohKPPwfAo6SkUHp66+/1rhx4w79fsWKFVqxYoWGDx+um266ST/88INefPFFlZSUKDU1VT169NBdd90lv99/6M/MnTtXLpdLV199tSoqKtSzZ08tXbpUTmdkPGwbAAAAAIDDsm1FzZ6pSwdXKOCQlg24V363//B/DjhKlm3btumIuhYpDyXjwYeAeVyHQGjgWgTM4zoEzPA+v14rn7pUcwdIl3SdqMWn3G06CRHm9x7KHZKv8gYAAAAAAA7vm+4tdHO2Q2neZC0bcqeq2XVRR8LiodwAAAAAAODX9jnKFBedrCX97lZCVILpHNQjnFACAAAAACDMeF57RVZZqfqMHK1Px/xbfs9v35YEHCsMSgAAAAAAhBErJ0dF86fLV1ohR5++8jdqbDoJ9RCDEgAAAAAA4cK2FTPnKp3f/4C+bebXW7FSI9NNqJd4hhIAAAAAAGHC+/x6PZz/qt5rJp3YrK8axjAnwQwGJQAAAAAAwoAje5/2LZ2l6wZKSe4E3X7a3bIsy3QW6ilueQMAAAAAIAy4Vz+kS/qX6KBbuqffXWoQ3cB0EuoxTigBAAAAABAGlg9J0KZM6ZyWw3VOqxGmc1DPcUIJAAAAAIBQFghITqcGNB2ij/Z+qMWn3mm6CGBQAgAAAAAgZNm24seMVE3b9mp7w01ae8azposASQxKAAAAAACErKgnV+vp/LfUfk+xmrv4ER6hg+9GAAAAAABCkGPXTm1fcZ2mjJUaxO7WJ8EauZ1u01mAJB7KDQAAAABA6AkGFTXrck0cclBVLmlxv7sYkxBSGJQAAAAAAAgxvlUPaJn1gT5vLI1uO0aDmw0znQT8AoMSAAAAAAAh5ou8L7XwVKmxr6EW9l5kOgf4FQYlAAAAAABCzLzOOapxSssH3K94b4LpHOBXGJQAAAAAAAgRrs2fSLathwY9pnsHPKR+mQNMJwG/iUEJAAAAAIAQ4P54k+LOHCT/X65SnDdeI9uONp0E/C4GJQAAAAAADLNKilU961J1mSY9Naix6RzgsFymAwAAAAAAqO9i5s7R+G579E0DaVsKZz8Q+vguBQAAAADAIM+rL2vDN0/p2Q5S9wYnaebxV5tOAg6LQQkAAAAAAEOsgnwV3jRd08+QYpzRunfQw3I5uJkIoY9BCQAAAAAAQwIJCRo3pYGKoqRbT71dzeKbm04C/hBmTwAAAAAADCmuKlZNgwYa5m2rC9tdbDoH+MMYlAAAAAAAqGPOrT/It+oB6cYF2nD2qzpYUy7LskxnAX8Yt7wBAAAAAFCXKivlmTZBX/x9lTwfvi+nwym/J9Z0FfCnMCgBAAAAAFCHYm6Zrxsaf61TJkkvtbVN5wBHhEEJAAAAAIA64nnrTb37zn26+2SpdUJr9c3oZzoJOCIMSgAAAAAA1AHH/myVXneZJgyXPJZbDwxZrWh3tOks4IjwUG4AAAAAAOqA88P3NOG0AuVFS7f2ukUdUzqZTgKOGIMSAAAAAAB14JF25XprvzSo6RBd2mmq6RzgqDAoAQAAAABwDDmy9iiY1lDnt7lA24t+0vRuV8qyLNNZwFFhUAIAAAAA4FgpLVX8eWcp2CBNev4VzT9loekioFbwUG4AAAAAAI6R2L/O1sz22/RgryjZLs50IHIwKAEAAAAAcAx4X3hOG75Zqwe6S482L1BNsMZ0ElBrGJQAAAAAAKhljh3blbPwCk09U4pxRuuBIY/J7XSbzgJqDeftAAAAAACoTYGAfJeN1xlDS1XilVb0vVMt4luargJqFSeUAAAAAACoTU6n/npxhj7JkEa0HqlRbS80XQTUOk4oAQAAAABQiwLBgH5IkZo7Wuj2vstlWZbpJKDWcUIJAAAAAIBa4Ni5Q7HTp8hVXKzVQ9fqleF/U6wnznQWcEwwKAEAAAAAcLSqquS7bLw2ffaMPG//XZZlqUF0A9NVwDHDoAQAAAAAwFGKWThPC5K2aMB4aU3HoOkc4JhjUAIAAAAA4Ch4Xn9V7719n5b0lprHNtfQ5qebTgKOOQYlAAAAAACOkGPnDhXNnaqxIySP5daqoU/w3CTUC7zKGwAAAAAAR+qLz3XR0BLlR0tL+ixRp9QupouAOsGgBAAAAADAEVrVIl8f7bF1TssRmtBhkukcoM4wKAEAAAAA8Ce5tvxLNe2O09j2E1RSWaxLOk2WZVmms4A6wzOUAAAAAAD4E5w/bpX//LOUMOpcuR0uXXnCNTw3CfUOgxIAAAAAAH9UWZmiLh2j/ueXatHIxrJN9wCGcMsbAAAAAAB/hG0r9porNLvpf/RhUymtkdN0EWAMJ5QAAAAAAPgDoh59SM9vfVYre0jtE9vrjtPu5rlJqLcYlAAAAAAAOAxr/37tWPlXTTlbinX59eiwNYpxx5jOAoxhUAIAAAAA4DCKEqI0fHqqyt3SPQMfVMuE1qaTAKN4hhIAAAAAAL8nEJBsWy6HW92a9dGwmEY6o8VZpqsA4xiUAAAAAAD4HTGLFsr1+WeyHlqtewc8JJvXdQMkccsbAAAAAAC/yfPGa/r05Tv1hO87yeOWZVlyWPwYDUicUAIAAAAA4FecP/2o4uun6IIxUoG/QJ3tfDVXvOksIGQwKAEAAAAA8H9YpSXyTbhQZw0tUU6MdGuv29Q8voXpLCCkMCgBAAAAAPC/bFuxM6bqmhbfa1OmNKL1+bq001TTVUDIYVACAAAAAOB/WZYeHpSie4uk9knH6Y7T7pFlWaargJDD08QAAAAAAPgftm1rY3K+ErwJenzY0/K7/aaTgJDEoAQAAAAAqPecW39Q7PQpcpSVatXgx/XGeW+rWXxz01lAyGJQAgAAAADUa1ZxkbwTLtBHnz0j9wfvy+lwqmVCa9NZQEhjUAIAAAAA1F/BoPzTJumqdts0cLy0oU3AdBEQFhiUAAAAAAD1VvTSW7W68G9adYLUKaWz+mcONJ0EhAUGJQAAAABAveR55SV9/tztmnm6lOxN0uphTynaHW06CwgLLtMBAAAAAACYsK/gJ51/gSXb4dCqoU+qSWym6SQgbDAoAQAAAADqpaXNdyunzNatvW9Tr/Q+pnOAsMItbwAAAACA+qOyUr577pQqK7Ww12Kt6P+ALu001XQVEHYOe0KptLRUfr+/LloAAAAAADh2bFuxs69SzhtrlVxdLV1zrS5od5HpKiAsHfaE0pAhQ/Tss8/Ktu266AEAAAAA4Jjw3XuPXv9irVpdaemxwQ1N5wBh7bCD0oQJE7R48WINHz5cmzdvrosmAAAAAABqlefNN/TDwzdq7AhLHrdPHRodbzoJEci2A6YT6sxhB6XJkydr48aNat++vcaNG6crrrhCWVlZddEGAAAAAMBRc377jcqumahzLrRU7rZ176BV6pjSyXQWIoxt29qz51JlZ98o2w6azjnm/tBDuVNTU7Vo0SKtW7dO+/fv1+mnn67ly5ervLz8WPcBAAAAAHBUAh+/rxFnl2tPnK25Pebr9BZnmk5CBMrNvU3Fxc/r4MFPZdvVpnOOuT/1Km+dO3fWunXrtGDBAr3wwgsaMmSIXnjhhWPVBgAAAADAUVvcMV+fZEjnt7lAVxw/y3QOItCBA88oN3eJ3O5matLkKTkcXtNJx9xhX+XtfxUUFOjLL7889KuiokLFxcW6/vrrtXbtWi1YsEDHHXfcsWwFAAAAAOCPsW15X9qgyrPO1cxuV0u2ratOmC3LskyXIcKUlf1Te/fOkMORoKZNn5PLlWw6qU4cdlC66qqr9OWXX2rfvn2ybVtpaWnq2rWrpk2bpq5duyoxMVErVqzQqFGjdPvtt2vYsGF10Q0AAAAAwO/yrVguLb1JMV9+Ic1boOt63Gg6CRGoqmq3du8eLdsOKjPzCXm9bUwn1ZnDDkr79u3ToEGD1LVrV3Xr1k0NG/76pRWXLVumzMxMLVu2jEEJAAAAAGCU98XntXXVTRo0y6ElpzbV2aaDELHc7saKj79AUVGd5PefZjqnTh12UFq3bt0f+kT9+vXTAw88cNRBAAAAAAAcKdcnH+vAXy/TGRMsFUTZciWlmU5CBLLtoCzLIctyqlGjpaZzjPhTD+X+b9q2bcugBAAAAAAwxvHTNlmTL9CZI6u0z2/rplNu5RXdUOtsO6Ddu8cpN3e5bNs2nWNMrQ1KXq9Xffv2ra1PBwAAAADAn+LY+KpGDyzUV2nSxI6XamqX6aaTEIGys/+qkpKXVVb2tqQa0znG/OFXeQMAAAAAIJTddmKZ3pQ0qOkQ3dp7Ka/ohlqXn3+fCgrul9fbTk2arJFluU0nGVNrJ5QAAAAAAKhzti3PKy9Jtq3JnadqQodJenDwY3I5OD+B2lVc/Iqys6+Xy5WmzMzn5HQmmE4yikEJAAAAABC2opfcIvfUsfKtWK7EqCQt7btcfrffdBYiTEXF19qzZ5Isy6fMzPXyeDJNJxnHoAQAAAAACEvep9foy/W3q/kshzYOaGE6BxHM42mt+PgRatLkMfl83UznhATOAAIAAAAAwo77vXeVc8tMnT3RUmG0pUBsjOkkRCDbDsiynHI4vEpP55Xt/y9OKAEAAAAAworrqy9UM/UinTE6oLxoW0tOvVP9MweZzkKECQRKtX37IBUWPm46JSQxKAEAAAAAwkrwpfU655wy/ZAszeh2lcZ1mGg6CREmGKzS7t0X6+DBz1Re/qls2zadFHIYlAAAAAAAYWV2n4PalCmNaH2+bjj5JtM5iDC2HdTevZerrOwd+f1D1bjx3bIsy3RWyOEZSgAAAACA0FdWJu/G11R53ihdfeJsWZalm3vdJofFOQnUrv37b1BR0Xr5fCepSZPVsiymk9/C3woAAAAAILTV1Cjusok6+P5GeV0uNTxnhBafusx0FSLQgQNPKz9/pbzetsrMXC+HI9p0UshiygUAAAAAhC7bln/2VVqbu1FtZrn1SfcM00WIYHFxZyshYayaNn1BLleS6ZyQxgklAAAAAEDIil56m9759AlNuVCKi4qR35doOgkRKBAokdMZK4cjRunp95rOCQucUAIAAAAAhKSoxx/V188s0ahRljzuKK0581m1SmxtOgsRprz8M23d2knFxS+bTgkrnFACAAAAAIQe29aOz17TGRdbqnBbenzI4+resIfpKkSYiorvtGvXeQoEiiQ5TeeEFU4oAQAAAABCji1pYt9C5fts3XHa3RrSbJjpJESYqqrt2rnzHAUChWrceKXi4s4wnRRWOKEEAAAAAAgZrn9/LucP36ty1IW6d9DDenfXW7r4uPGmsxBhqqv3aceOc1RTk62GDRcpMfFi00lhh0EJAAAAABASnD98L/fFw3Wgqki+7j3UonlLtejU0nQWIlB29vWqrt6h1NRrlZw83XROWGJQAgAAAAAY59i9S77R5+i8QYX6qk2iXk5xK8N0FCJWo0Z3Kjr6JCUlTTOdErZ4hhIAAAAAwCgrN1exI8/WpB579UZrqW2TE9UgOs10FiJMMFihiorvJEkuV5KSky+XZVmGq8IXgxIAAAAAwBiruEhxo4fr6nY/6elO0kkNT9YjQ56Ux+kxnYYIYtvV2rNnorZvH6iKiq9M50QEbnkDAAAAABhjO5y6+fgi3ddcOi65o9aesV7R7mjTWYggth1UVtblKil5TTEx/eTxtDGdFBEYlAAAAAAAxmRbJVrRpkDNfM217qwXFO9NMJ2ECGLbtvbt+4uKitbJ5+uuJk3WyuHwms6KCAxKAAAAAIC6FQjIP2umqk4/Sw2HDNOL576uOG+80nhuEmqRbdvav3+uCgtXyevtqKZNn5PT6TedFTEYlAAAAAAAdScYlP+aK7Tp4zU6LusHuQYPVafULqarEIECgUIVF78sr7etmjV7SU5noumkiGLkodybN2/W1KlT1adPH7Vt21YbNmz4xftt29aKFSvUu3dvde7cWWPHjtXWrVt/8TFFRUWaPXu2TjjhBJ1wwgmaPXu2iouL6/LLAAAAAAD8GbYt/9w5eu/TJzVsrKUzR1bJNt2EiOVyJalZszfUtOkrcrlSTedEHCODUnl5udq0aaO5c+cqKirqV+9/+OGH9eijj+rGG2/Uc889p6SkJE2cOFGlpaWHPuaaa67Rt99+q1WrVmnVqlX69ttvNWfOnLr8MgAAAAAAf5RtK2bBPH3y9kMaPtqS0+3Rjb1v5WXbUesKClapsvLnQykeTxO53Q0NF0UmI4NS3759NWvWLA0dOlQOxy8TbNvWE088oSlTpmjIkCFq06aNlixZorKyMr366quSpG3btumDDz7QggUL1K1bN3Xr1k0333yz3n33Xf30008mviQAAAAAwH8R9dgqffHS3TpzjKWgx6XVw55Wr/Q+prMQYfLz79e+fbOUlTVZts35t2PJyKD03+zZs0e5ubnq1avXobdFRUWpe/fu2rJliyRpy5Ytio6O1vHHH3/oY0444QRFR0cf+hgAAAAAQOj49NTWGjrBpQqPQw8PeUL9MweaTkKEKSh4VNnZ18rlaqj09FWcfjvGQu6h3Lm5uZKklJSUX7w9OTlZOTk5kqS8vDwlJSX94pvDsiwlJSUpLy/vsP+MxMRouVzOWqw2JzU11nQCUO9xHQKhgWsRMI/rEL8pP19KTlblAaeqo9xac86jGt1xtOmqiFVfr8N9+1Zr376r5HanqmvXdxQT0950UsQLuUGpLhQWlptOqBWpqbHKzS0xnQHUa1yHQGjgWgTM4zrEb4la+4RibrpBRWufVfeT+mjzxV+pQXQDvleOkfp6HRYVPa89ey6R05mozMyXVF6eofLy+vf3cKz83kgZcre8pab+/OT1//9Jo/z8/EOnllJSUlRQUPCL+yFt21ZBQcGvTjYBAAAAAOqe97l1yl0wQ+OHlqs0xi1JahDdwHAVIpHH01oeTzM1bfqSoqI6ms6pN0JuUMrIyFBqaqo2bdp06G2VlZX67LPP1K1bN0lSt27dVF5e/ovnJW3ZskXl5eWHPgYAAAAAYIb3+fUqun6KBkywtKZ9lV73bDOdhAgUDFZJkny+zmrV6l/y+boaLqpfjNzyVlZWpl27dkmSgsGg9u7dq++++07x8fFq3Lixxo0bpwcffFAtWrRQs2bNdP/99ys6OlpnnnmmJKlly5bq06eP5s+frwULFkiS5s+fr379+qlFixYmviQAAAAAgCTvhmdVdN1k9Z9gaUd8UNeeNFcjWo80nYUIc+DA08rLW66mTV+R250my6qXT/QxyrINvI7eJ598onHjxv3q7cOHD9fixYtl27ZWrlypdevWqaioSF26dNG8efPUpk2bQx9bVFSkhQsX6p133pEk9e/fX/PmzVNcXNxh//mRck9pfb0/FgglXIdAaOBaBMzjOoQkqbJSB4ccrwGDsvRjYlBXn/AXXXfSjbzaVh2pL9fhgQNPKStrmpzOeDVt+op8vi6mkyLa7z1DycigZFqkXGD15V8WQCjjOgRCA9ciYB7XISSpMlCp09Z017ayHbrq+L/o+h6MSXWpPlyHBw6sVVbW5f8zJr3MbW514PcGJc6EAQAAAACOiue1VxRo107elq0186TZ2lG0nTEJta6wcI327p3OmBQiGJQAAAAAAEfM8/ILqrx6ouIatVTJe5/qovZjTSchAtXU5Co7e7aczoT/GZO4zc00BiUAAAAAwBHxvPKiyq6ZqH4TbXVola77LMlpOgoRyeVKVZMmT8vpTJLP19l0DiQ5TAcAAAAAAMKP55UXVTZrgvqPk35IspXetKscFj9ionYVFW1QIFAsSfL7T2NMCiFc7QAAAACAP8X70gaVXz1BA8ZJ3ycHNb3rlbrx5Jt5ZhJqVV7ePdqzZ4L27p1uOgW/gUEJAAAAAPCn7MpIUL9LHPpPclCXd71C83ouYExCrbFtWzk5i7V//w1yuRqrQYN5ppPwGxiUAAAAAAB/TEWFJOk17zZ9n1CjGd2u0vyeCxmTUGt+HpNuUm7ubXK7m6p5jMrI9AAAIABJREFU843yelubzsJv4KHcAAAAAIDD8j14r6KeXK0DG17TJR0nq3VCG/VOP5UxCbVq//6/Kj//Xnk8rdSs2Styu9NNJ+F3cEIJAAAAAPBf+e5Zrqy7rtctrbJkFR2QJPXJ6MuYhFoXFdVNUVGd1Lz5RsakEMcJJQAAAADAb7NtRd+xWNsfX6SBkxzaH12qE2LydLLamC5DBLHtGtl2QA6HVwkJoxQfP0KWxVwR6vhvCAAAAADwa7atmNsW6Pt1yzToEofyo4Ja1OcOndz4FNNliCDBYIX27JkkyVaTJo/LstyMSWGCW94AAAAAAL/i3L5NX7+0Qv0nOlQQZevO01ZoUqcpprMQQQKBEu3aNVIlJa8oEChSMFhpOgl/ArMfAAAAAOBXtiZbGnSJU2XBGq0c8KBGth1tOgkRpKYmX7t2naeDBz9XbOwZysh4TA5HlOks/AmcUAIAAAAA/KyiQtG3LZBVWqJmcc11XvuL9ODgRxmTUKuqq7O0Y8dQHTz4uRISxqhJkycZk8IQJ5QAAAAAAFJpqeLHX6Rt3/1DTQMBld14s5b2XW66ChGotPRtVVZ+r+TkGUpLu0WWxVmXcMSgBAAAAAD1nFVYoPiLztfj9me6bLq06JSGmmg6ChErMXGcPJ5Wio7uKcuyTOfgCDEDAgAAAEA95tifrYRzT9fd3s80+WwpISpJ3dJ7mM5ChCkr+1D79s2RbduSpJiYUxiTwhwnlAAAAACgvqqqUty5wzS/6TbddqrUKKax1p/1otomtTNdhghSXPy69uwZLymohISL5fN1Np2EWsCgBAAAAAD1VNDt0rTJGXqkYpuax7fQs2e9pMy4pqazEEEOHFirrKwZsiyvMjOfZkyKINzyBgAAAAD1jPO7b6XKSgXtoLIaxui45I56efibjEmoNbZtKzd3mbKypsnpjFWzZi/L7x9oOgu1iBNKAAAAAFCPeN7+m/yTxqp60DCVPLxaDw1ercpAheK9CabTEEFKS/+unJyb5XZnKDPzeUVFtTedhFrGCSUAAAAAqCe8z6xV4NJRGnhBpZ4a1FiSFOWKYkxCrfP7B6lBg/lq3vwtxqQIxaAEAAAAAJHOtuW7e5mKb5imUydK/2ga1GuJ+01XIcLU1OSroGCVJMmyLKWmXiO3u7HhKhwr3PIGAAAAABEu5oZrtf3FBzR0ilN7/AFd2uky3dJ7ieksRJCqqp3auXOEqqq2yu1uotjYIaaTcIwxKAEAAABAhPswI6gLJjt0wBPQDSffrJndrpJlWaazECEOHvxCu3adr5qa/UpOvlJ+/yDTSagDDEoAAAAAEIGskmLZvmjJ5dLSJttVutuhFf3u0wXtLjKdhghSWvqOdu++WMFgmRo2XKLk5Gmmk1BHGJQAAAAAIMI49u1V/OgRqj6xh0rvuEsPDHpEX+V9qd7pp5pOQwQpL/9MO3eeL8tyqkmTJxQXd47pJNQhHsoNAAAAABHE+cP3ij99gG5J+1Z/i8uWbFvx3gTGJNQ6n+94JSSMUdOmLzEm1UOcUAIAAACACOH+8H1FXzJGU08t0iPHSx2S9+hti5MEqD3BYIVKS/+uuLizZFkOpaevMJ0EQ/j3CgAAAABEAO8za+W8+FyNOKNYjxwvdUntpnVnvSCHxY99qB01NXnaufNs7d49RiUlb5rOgWGcUAIAAACACLB/55caNcHWvxvYOq1Jfz065En5PbGmsxAhKit/0M6d56u6eofi4s5TTExf00kwjKkaAAAAAMJVVZUUDEqSruy8W/9uENDY4yZo7enPMiah1pSWvqeffhqo6uodSk29VhkZj8rhiDKdBcM4oQQAAAAAYcgqLFDchDGq7tFT5X+dp6V9l+vUjNN0ScfJsizLdB4iRFnZJu3cOVyWZSk9/UElJFxoOgkhgkEJAAAAAMKM46dtih8zUo8k/KjWOS51CgSUFp2mSZ2mmE5DhImO7q64uLOVlDRZMTG9TOcghDAoAQAAAEAYcX3ysWLHX6DrTizUslOkNonZes+SnKbDEDGCwTKVlX2k2NjBsiy3mjRZbToJIYhnKAEAAABAmPC+8Jw8o8/UBYN+HpNaJbTWmtPXy+lgTkLtqKrare3bh2rXrlEqK9tkOgchjBNKAAAAABAmCj57RxdcXKNPG0m9GvfRY0PXKCEq0XQWIkR5+cfatWuMAoFcJSZOlM93oukkhDBOKAEAAABAKKuokGxbknTpydn6tFFQo9peqHVnvcCYhFpTWPikduw4Q4FAgRo1WqZGje6Sw+ExnYUQxqAEAAAAACHKsWe3EocNkO+BeyVJt516h27suUAr+j8gj5Mf9lE7Dhx4Rnv3TpfD4VfTpi8qKYlXCsThMSgBAAAAQAhyffqJEgb31bKEr/R11qeSbat5fAvN7HYVP+yjVsXFna34+FFq0eJd+f19TecgTDAoAQAAAECI8T6zVt5Rp2vsafm6bpB01fH7ZZuOQkSprPxexcUvSZIcjmhlZKySx9PCcBXCCQ/lBgAAAIBQEQwqZuF8HXjibp07zqnNDW2dmHaSHhn6JKeSUGtKSjZqz55Jsu0qtW59otzudNNJCEOcUAIAAACAUGFZ2nLga3Wf5tTmhgFd0PYivXDua2oQ3cB0GSKAbQeVk7NEu3ZdINuuVnr6fYxJOGKcUAIAAAAAw6y8PNkpKQrYQV1y4m7tKwpqfs9bdHnXmZxMQq0IBA4oK+sylZS8Ibe7iZo0WSOfr5vpLIQxTigBAAAAgEGev72hpB5d5X1mrZwOpx4cslprTl+n6d2uYExCrdm//2aVlLyhmJh+atHifcYkHDVOKAEAAACACcGgopctUfWKRRp7lkN/sQqUIalDSkd1SOloug4RJi1tnjyepkpOninLcprOQQRgUAIAAACAOmYVFyl2xmX68V+v69xpLv0YXyNf451aZDoMEcO2a7R//zxFR/dSXNwZcjoTlZJyleksRBAGJQAAAACoQ4792Yo/93S96P1REy5zqsxVoyu6zdL1PW40nYYIUVOTq927J6i8/AOVl3+s2NjTuX0StY5BCQAAAADqUHVSkq4/LaA7mkjRriit6n+fzm413HQWIkR5+Wbt3j1ONTVZio09S+np9zMm4ZjgodwAAAAAcKwFAnJ/8J4kKa+6UKvblKp5fAu9cd7bjEmoFbZtKyvrXu3YMUw1NfvUoMFNatJkjZzOONNpiFCcUAIAAACAY8jKz1fc9Mmy/vGWytc+p7QBg7XuzA3KjGuqeG+C6TxEjID2739KDkesMjJWye8fYDoIEY4TSgAAAABwjLg++1SJA/vo+Zy31G62T7uPy5QkdUrtwpiEWlFTUyBJsiyXOnRYr5YtP2RMQp1gUAIAAACA2mbb8j18v3wjhuqKLnt00flSTpxLW4M5pssQIWzbVmHh49q6taPKyjZJkrzedLnd6YbLUF9wyxsAAAAA1LKop9co7/ZrNWqiS5vTpPZJx+mRIU+qVWJr02mIAMFgmfbuvVpFRc/I6UxQMFhmOgn1EIMSAAAAANSyv/dspEtnelXorNQFbS/SklPvVLQ72nQWIkBFxX+0Z884VVb+Rz7fCcrIWC2Pp6npLNRDDEoAAAAAUAu8z6yVVVGhigmT1CihqZz+WC3vsUwXtR/Ly7ajVpSV/VM7dw6XbZcrKWma0tIWyuHwmM5CPcWgBAAAAABH4+BB+efOUdGLjyu/UYLSzh+lVomttfnirxTjjjFdhwji83VWVFRHpaTMVFzcOaZzUM8xKAEAAADAEXL+uFVxkydoU+lXumC6S77kWL3tteSXGJNQKw4e/LeqqnYoPv5cORwxat7875x4Q0jgVd4AAAAA4Ah41z2l+IF9tCzhK/WfYCk32taErtMU42JIwtGz7aDy8lZq+/YB2rt3mmpq8iWJMQkhgxNKAAAAAPBn2bYK33tZI0dW6m/NpUYxjfTQ4NXq0ehk02WIADU1ucrKmqrS0r/L6UxVRsaDcrmSTWcBv8CgBAAAAAB/kGPPbgUzmsiWNPK0/dqcF9DAzMG6Z8ADSvGlmM5DBCgtfVdZWVNUU7Nffv8Apac/KJergeks4Fe45Q0AAAAADse25XvoPiWd3E3eF56TZVla0Hepbj7lNq05Yz1jEmpNfv79CgQKlJZ2qzIzn2dMQsjihBIAAAAA/BdWQb5ir7xc2R+/oZEXubU4ukqNJZ2Q1l0npHU3nYcIUFOTf+iWtvT0+1RdvUs+3/GGq4D/jhNKAAAAAPA73P/8SIn9eunVXW+o6wyXNjar1tPJu01nIULYtq2Cgse0dWtHlZT8TZLkcqUwJiEscEIJAAAAAH6De9OH8ow6QzMGSw+cKPlcbt3V525d2O5i02mIADU1OcrKmqHS0o1yOBJk21Wmk4A/hUEJAAAAAH7Dd21TNGVWnL6OKlL7pA56aPBjapvUznQWIkBJyRvKypquQCBPMTF9lZ7+gNzudNNZwJ/CLW8AAAAAIEm2rajHH1X08tslSTHeOGXFOzS+wyRtPP8dxiTUiuLiV7Rr1wUKBkuUlnabmjZ9iTEJYYkTSgAAAADqPSs3V7GzZih/0xvanRGvlpOmqFFcY3144WdKjU41nYcI4vcPUXz8hUpJuVJRUceZzgGOGIMSAAAAgHrN89abir3icr2QmqspV7jkjY3SB14pTmJMwlGz7Wrl5i6VwxGvlJQZcjg8ysh40HQWcNQYlAAAAADUT8Gg/HPnqObJhzTpDIdWd5GinC7NOWmOYj1xpusQASoqvlFW1lRVVHwhj6eFkpImy+Hwms4CagWDEgAAAID6yeHQp859mjTTrW2x1eqU0kX3D1ylNkltTZchzNl2jfLylis3d7Fsu1oJCRerYcPbGJMQUXgoNwAAAID6o6pK3mfWSratoB3UjI7b9VNsjWZ2u1pvnPc2YxKOWiBQqp9+GqCcnIVyOpOVmble6en3yelMMJ0G1CpOKAEAAACoF5zffK24GZep7Mev5HU4VDnqQq0c9LAKKwrUK72P6TxECKfTL6+3lbzedmrUaLGczkTTScAxwQklAAAAAJGtpkbRd92huCGnann8V8qc49ZXPVtLko5L7sCYhKNWWblVOTlLDv0+Pf0BZWQ8yJiEiMYJJQAAAAARy7n1B8XOvEw7dvxL4ye69c9GUqovUTmOcrUxHYewZ9sB5effr5ycBbLtCvn9/RQdfZIsy206DTjmGJQAAAAARCznR+/rQde/NGeGUwcd1Tq31Qgt6rNMyb5k02kIcxUV32rv3hk6ePAzOZ0patx4laKjTzKdBdQZBiUAAAAAEcX5048KNGgo+f1a0rFAi8qlRG+c7j71Tp3b+jzTeYgAubnLlJt7m2y7WvHx56thw6VyuVJMZwF1imcoAQAAAIgMNTXyrbhLCaf1VMzihZKkcR0maXS7MXr/wk8Zk1BrLMspp7OBMjPXKyPjUcYk1EsMSgAAAADCnvPrr5QwbIByVs7T4DFBPdfp55sxkn3Juqf//UqLTjNciHAWCJQoN3epgsFKSVJy8gy1avWJYmOHGi4DzGFQAgAAABC+KisVvXih4oacqnt9W9RpplNvN6nWxtRC02WIECUlf9O2bT2Uk3OLCgtXSZIsyyWnM85wGWAWz1ACAAAAELZc332jHU/erksv9ejjtICSouJ1R+8lOq/1KNNpCHM1NfnKzr5WRUXrJbmUkjJbiYmTTGcBIYNBCQAAAEB4KSuTo6RYwYaN9HHDGp073aUqVWl4q/N0S++lSo1ONV2IMFdc/Kr27p2pQCBfPt/xatx4paKiOprOAkIKgxIAAACAsOF+/x+KnXWFAhkZKtrwqro2OF79mw/RRe3Gamjz003nIUI4HD4FgweVlnabkpOnybKcppOAkMOgBAAAACDkWXl58t80V/aGp3V9f0uero10ZSAgl9utJ4Y9bToPYS4YLFde3p1KTJwotztdfv8AtWnzjVyuZNNpQMhiUAIAAAAQuoJBRT29RjELbtQ/Egp12ZVe/RhbqVYJeZrqCMprug9hr6TkTe3bN1vV1TtUU5Onxo3vkiTGJOAwGJQAAAAAhCzrQKHKlv5V0waWa20HyWFV67LO03XdSTfI62ROwpGrrs5SdvZ1Ki5+SZJLyclXKjX1WtNZQNhgUAIAAAAQWg4elHPHdgXaH6c8n3TK5bYKAzXqktpNd/S9S10adDNdiDBXXPy6srIuVTBYqujok9Wo0XJFRXUwnQWEFQYlAAAAACHD/c5bir12luyqSh346DMl+5M14rgL1SK+pS7pOEVOBw9HxtGLijpOTmeCGjZcooSEMbIsh+kkIOwwKAEAAAAwzrE/WzE3Xqfgaxs09zRL353YQg9bDlmSFvW5w3Qewlx1dbb275+nhIQx8vv7yuNpptatv5BluU2nAWGLQQkAAACAOTU18j32sKKX3Ka/NSjS5Vd5tT2mUk1iq5VrlamBYkwXIowFg1UqKHhAublLFAyWSArI7+8rSYxJwFFiUAIAAABgjmUp74XVmnNGuZ5tKzmtGs3oepWuOfFaxbgZk3DkSkvf0r5916qqaqucziQ1anSXEhPHm84CIgaDEgAAAIA65di3V67Nn6jq7OGqUkA9z8tTdmW1Tkjrrjv63q0OKR1NJyLMFRU9qz17JklyKDHxUjVocINcriTTWUBEYVACAAAAUDeqquR78D7FLFuiAleVHJ27ytOsuWb3vFEOOXRh+4vl4OHIOELBYLksyy3Lcis29kzFx5+vlJSrFRXVyXQaEJEYlAAAAAAcc+5335Z/7hztyduqsSPc+nfreL3fOE1RksYeN8F0HsKYbdsqLn5e+/fPV3LydCUnXy6Hw6eMjEdNpwERjUEJAAAAwLFTU6O4yRNkv/mybutladFFTlU4qnVSWisVVBWqsSfadCHCWHn5p8rOvl4HD26WZXkUDJabTgLqDQYlAAAAAMeOy6XXGhRq9tVe/RRTqVRfsu44ZaFGthkty7JM1yFMVVXt0v7981Vc/LwkKS7uXKWl3SSPp4XhMqD+4AZlAAAAALUnGJR3/dPyXzVdklQTrNF1nfdpp79GU7vM0MdjPteothcyJuGoVFR8peLi5xUV1U3Nmr2pJk2eYExCSPjmG4dmzfLq7LN9KikxXXNscUIJAAAAQK1wffKx/Ddeq9L/bNGm5m51336NXM1baMXAhxTtjlG7pPamExGmbDugwsInFRs7TG53mmJjT1dm5nPy+wfK4kHuMKymRtq40aVVq9zatOnnmaVdu4AifTdnUAIAAABwVBy7dkozFsr/3Ho9eKJ00188Kvc69M9UrxpLOj7tRNOJCGOlpe8oO3uuKiu/UUXFJDVuvFyWZSk2drDpNNRzBQXSmjUePfaYW1lZPw+bp51Wo8mTqzRgQECOCN86GZQAAAAAHLnKSiUO7a+NCbm6+uoo/Se2Qn63V7NPnKNkX4rpOoSxgwe/VE7OTSotfUuSpYSEi5WaOsd0FqBvvnHokUfceu45tyoqLEVH27rkkipNmlSt1q2DpvPqDIMSAAAAgD8nEJBjb5aCTTJV4bQ15MoUvRXIlcOq0rj2l+jak+YqNTrVdCXCWH7+A8rO/nk8ionpq7S0W+TzdTFchfrst25ra9o0qEsvrdSFF1YrLs5woAEMSgAAAAD+GNuW552/K2bBfFnlZSr4cLOivFHyNm2tAXZj3dB9oTqkdDRdiTAVCJTI6YyVJPn9/RUV1U1pafMUE9Ofh7jDmOxsS2vWuLVmjVt79/58D1vfvv/vtjan03CgQQxKAAAAAA7L9e/PFbNgnoIfv6/lJ0nfDWmppQfLZXu9unfAQ8ps1EB5eaWmMxGGgsEy5effp7y8u9W06QZFR58kr7eNWrT4B0MSjLBt6YMPnFq92q2NG12qqbHk99uaOPHn29ratKk/t7X9NwxKAAAAAH6XdaBQ/mtnyf3i81rbWbrhL1HaHVWhBG++ZnmqlCYp2h3ND/7402y7WoWFTyo3d5FqavbL6UxWTU32offzPYW6duCA9Mwzbj3+uEfbtv18GqlDh4AmTKjWeedVy+83HBhiGJQAAAAA/K5gjF/v5H+s66/06cuEg/I6bU3vdKWuPH6WEqISTechTBUXv6r9++epqupHWVa0UlPnKDn5Cjmd9fBBNDBuyxaHVq/26MUXXTp40JLXa2vkyGpNmFClE08Mim3ztzEoAQAAAPh/yssV/dB9sl1uHZxxpQpqinX+oHxVBCo1qu2Fuu6kG5QR28R0JcLcwYOfq6pquxITJyk19Tq53Wmmk1DPlJdLL7zg1urVbn3xxc8PQmrWLKjx4ys1enSNkpNtw4WhLyQHpRUrVmjlypW/eFtKSoo++ugjSZJt21q5cqXWrVun4uJidenSRfPmzVPr1q1N5AIAAADhr7paUU89qehlS7SrYp9ymjdUi8suV7IvWXecdo/aJ3dQx5ROpisRhmzbVlnZOzpw4Cmlpz8ky3IqJWWmEhLGyOttaToP9cw33zi0dq1b69e7VVxsyeGwNWxYtSZMqFbfvgE5HKYLw0dIDkqS1Lx5cz355JOHfu/8P49Of/jhh/Xoo49q8eLFat68ue69915NnDhRGzdulJ+bGgEAAIA/LhCQd8Ozill6mwpzd+jGfk7df6JTLRLi9K7TIaekkW1Hm65EmCor+0g5OQtVXr5JkpSYOEExMX3kdCbK6eSWSdSN0lJpwwa31q51a8uWn7eFtLSgJk+u0tix1WrcmNNIRyJkByWXy6XU1NRfvd22bT3xxBOaMmWKhgwZIklasmSJevbsqVdffVWjR/M/dgAAAMAf5fpii+xZU3RTb4fuGu9WqaNambFNdWX3OTwUGUesvHyzcnJuUVnZu5Kk2NhhSk2dK5+vs+Ey1Be2LX322c+nkV580a3y8p9PIw0ZUqMxY6o0cGBArpBdRMJDyP717d69W71795bH41GXLl00a9YsNWnSRHv27FFubq569ep16GOjoqLUvXt3bdmyhUEJAAAA+G9sW+5331agWXMFW7TU501cGnm9T4U6qBRfsq47/hqN7zhJXqfXdCnClG0HtGfPJFVX71BMTD81aHCDoqO7m85CPZGfb+m551xau9at//zn59NImZlBjRlTpdGjq9WoEaeRaktIDkqdO3fWokWL1KJFCxUUFOj+++/X6NGj9eqrryo3N1fSz89U+r+Sk5OVk5Pzhz5/YmK0XC7n4T8wDKSmxppOAOo9rkMgNHAtAn/ABx9Ic+eq8v9j777j46jv/I+/pmzf1a567+5NNgYXcLdpxoSOAyQEQnoPHORSL/0SkktyufzIkeSSXLgQTEkMgQChuYAB4957lS1bvW6fmd8fs1ohTDHNq/J5Ph6TXWlnRp+xtRJ+5/P9zJrVWNdcjfsvDzArexqVRaO5fdy1fGH6F/A5fe/49PI+HL46O9cRjR6koOAaADTtLjTNSyg0N8OVDT/D8X1omvDss/C738Hf/gbxODidsHQpfOxjsGCBiqq6AAnK30sDMlCaO7f/D526ujoWLVrE8uXLqaure9fnb2sLv+tzDAT5+QGamroyXYYQw5q8D4UYGOS9KMSb0zesw3fnD1FXPM2f6uDbd7j56JgCPpt63zx5xUoURSHcYRLmnb2X5H04PIXDa2lqupPu7n+iaSFMcxaa5gdmYZrI98QZNtzeh0ePKjzwgIN773Vw5Ig9TXv0aIMbbkhwzTV9d2praclklYPfG4WUAzJQei2fz8eIESM4dOgQixYtAqC5uZmSkpL0Pi0tLad0LQkhhBBCCDHcuf/nbnxfu50HxsE3b/Ow1xfBpVlE8kLpfWRWkni7enpepKnpx/T0PAuA1zuL/PyvoKrvvMNNiNPR0wOPPaazbJmD1avtSMPrtbj++jg33JDg7LNN5EfamTEoAqVYLMbBgweZPn06ZWVl5Ofns2bNGiZNmpR+fd26ddxxxx0ZrlQIIYQQQojM07ZuwZgwERSFp8/K4Ru3+djh70FXE9w45qPcevbtlPhLM12mGKQikY0cOmTfIMnnm0d+/h34fLMyXJUYykwTXn5Z4777HDzyiE5Pj50YzZiR5IMfTHDppUkCw2+lX8YNyEDpxz/+MfPnz6e4uJjW1lbuuusuwuEwV1xxBYqicOONN3L33XdTU1NDVVUVv/71r/F6vSxZsiTTpQshhBBCCJEx+ssv4fvpv+NY+Rwd9z1EYsH5xHOz2R2Icu2o67jt7K9QHazJdJlikLEsi56elTid1Tidlbjdk8nN/QJZWUvwemdkujwxhB0+rHD//Q6WLetb0lZebvKpT8W59toE1dUyYDuTBmSgdOLECW699Vba29vJzs5m8uTJ3H///ZSW2v8vysc//nFisRjf/e536ejooK6ujt///vf4/f4MVy6EEEIIIcSZ53hpDd6f/Ajt+RXcPx5+dJuPe3xJioH55QtZ+6HNlAcqMl2mGGQsy6Sr63Gam39GJPIKodCHKS39fyiKQlHR9zNdnhiiurvh0Ud17rvPwZo1fUvali5N8MEPJpg500BVM1ykAECxLGvYRXpDZUjZcBu4JsRAJO9DIQYGeS+K4SzwiZtwPPxX7psA37vIy25fGE3R+M8Fd3Ht6OvOWB3yPhw6TDNOR8cDtLT8glhsNwCBwCXk59+BxzMlw9WJNzNY34fJJKxapfHQQw4ee0wnHLaXtJ13XpKlSxMsWZJE+kcyZ1AP5RZCCCGEEEKkWBbq8WOYpWUA/GWSyo9GednjDaOrcT40+iN8ceptVGZVZbZOMWg1Nn6blpZfATqh0PXk5n4Jt3tMpssSQ4xlwcaNKg895GD5cp2mJrvtqKLCZOlSe0lbZeWw638ZVCRQEkIIIYQQYjAwDFx/X47nlz9HbWmmde1mcLl4dBQcOBDnw2Nu4otn3UZFVmWmKxWDTDLZQmfn38nJuQmA7OybsSyD3NzP4XSWZ7Y4MeQcOKDw0EMOHnrIwYEDdoiUk2Ny882FAxyYAAAgAElEQVRxrroqwTnnyF3aBgsJlIQQQgghhBjIYjHcD9yH51e/IHZ0P/9vqsL6BeX8vKsLy+Xi6zO/zddm/JsESeJtSyTqaW7+FW1tf8Sywrhco/D5zsXlGklx8Y8zXZ4YQhobFR5+WOehhxxs2KAB4PFYXHFFgquuSjB/voHDkeEixdsmgZIQQgghhBADlHr4EKFLL6SzvYF/n6nxyxtcNGsxvHozt7vjFIMM2xZvWySyhZaW/0dHxwNAEl0vJS/vW3g8dZkuTQwh3d3w+OM6Dz7oYNUqDcNQUFWL+fOTXHVVgsWLZS7SYCeBkhBCCCGEEAOI0tYKgJWdQ2tBFj9cZPGbGgfdaoKgK8CtE7/Ixyd+mlxPboYrFYORacY4fPhSDKMNp3MUeXlfJhi8BlV1Zro0MQREo/DsszoPP6zz5JN9w7WnTDG46qoEl12WpLBQ5iINFRIoCSGEEEIIMQCoRw7j+e2v8dzzv0RuuoWeb38fFIW7x3bjd+RyW93n+Mj4m/E7X/9uO0K8HtOM0N6+DE0LEgxegaq6KCz8Ibqei99/AYoi918X7048DitWaCxf7uCJJ3S6u+0Qqbra5Kqr7LlItbUSIg1FEigJIYQQQgiRQfqGdXh+/Stcf1/OlnyTH13hYWFZK5cBIXc2D37gYcbnTsStuzNdqhhEkslGWlt/S2vr7zCMFlyusWRlXY6iKGRn35Dp8sQgl0jA6tV2iPT44zodHXaIVF5u8pGPJLj88gSTJslw7aFOAiUhhBBCCCEyxHvnD/H+9Ec8MQJ++kk/zxZ2AxHC5T1cltpnauE5mSxRDDKx2F6am39BR8cyLCuOpoXIy7uNnJxPoMi/7sW7kEzCCy9oPPywzmOPOWhrs7+fiotNPvhBO0Q66ywJkYYTCZSEEEIIIYQ4U8JhnKtWEL9oMQAPn+XjB7f72OHrAbqZXTqXT0/+HAsrLshsnWJQsSwrHRZFo1tob78Hp7OG3NzPEgpdj6r6MlyhGKwMA156SWP5cp3HHtNpbraXSBYUmHzsY/ZMpHPOMVBl5eSwJIGSEEIIIYQQ7zOlqQnP73+D5w+/JdnRivH0GozxE2guzWXPvhhX1V7LZyZ/non5cpctcfoMo422tv+jvf1PVFU9jq7nkZV1GRUVy1LzkbRMlygGoUTC7kR67DGdxx/XaWy006K8PJObbopz+eVJpk830OTba9iTQEkIIYQQQoj3ibZtK57/uRv3g8s44I3xs3kuHproY022lwBw5ahrmFM2j9JAWaZLFYNINLqd1tbf0N6+DMsKoygeIpH1BAIXoig6gcDFmS5RDDLRKKxcqfHoow6efFKnvd3ueMvNNfnQh+JcdlmS884z0CVBEK8i3w5CCCGEEEK8H7q7CS1ZxAt5EX5+nZflVQoWMcr8BezX25kMuDSXhEnitJlmnCNHrqKnZyUADkclOTkfIxT6MLqek+HqxGDT3Q3PPGMvZXvqKZ2eHjtEKioyueWWBJdckmTGDAmRxBuTbw0hhBBCCCHeA0prC+7/+xPGyFHEL76Ebhcs+ko2W6wIEGZy/hQ+PfnzXFp7Oboq/xkuTk8y2YJpduF0VqGqThTFic83n5ycTxAIXCTL2sTb0t4OTz5ph0jPPacTi9khUmWlfXe2JUvswdoyE0mcDvlNJoQQQgghxLuQXtb20P0cc0aJTJ1K6OJL8Dv8BEtGcql7Gh+b+ElmFJ8rd9kSp8WyLMLhNbS1/Z7OzocJBC6mvPweAMrL70VVXRmuUAwmJ04oPPGEHSK98IJGMmn/HBo92uCSS5IsWZJk/Hi5O5t4+yRQEkIIIYQQ4h1wrFqB92d34ljzPGvK4T+XevlrtcpVNdX8KrXPskv/Jt1I4rQZRhvt7X+hre0PxGK7AXA6R+H1zk7vI2GSeCuWBTt2qDz5pM6TT+ps3NjXxVZXZ7BkSZLFi5OMHGlmsEoxFMhvNyGEEEIIIU5XTw/47FuwJw7t5S89z/Oft/nZGOgGwozLncDsqkXp3SVMEm9HS8tdNDX9GEVxEgxeTXb2LXi90tkm3loiAS++qLFqFSxf7uPIEXvNmqZZzJ6d5KKLklx4YZKKCivDlYqhRH7DCSGEEEII8WZME8eqFXj++D841qymZcMO8Pv5fvUhfnkFqEqYJdWX8bGJn2RmyXnyj39xWgyjg46O++nq+icVFctQFJXs7I+gqn5CoRvQ9bxMlygGuM5OePZZnSee0Hn6aZ3OTvtnTyCgcPnlCS66KMmCBUlCoQwXKoYsCZSEEEIIIYR4HUpLC+77/oz7T79HOXSAx0fCI5fm8O/H6jFHj+GGSbdg6To3TbiF8kBFpssVg4BlWUSjG2ht/SMdHQ9gWWFAJxrdisdTh8NRRl7eFzNdphjAjh5V+Oc/dR5/XGfNmr55SGVlJtdem2DpUidjx3bjdGa4UDEsSKAkhBBCCCHEa6jH6smZPpkTzjg/n6bzm+u91DvCQCvXZIeZDFQHa/jmzO9kulQxSCQS9Rw+fA2x2HYAHI5KsrNvIhT6EA5HYYarEwNVMgnr12s884zGU0/pbN/efx5S71K23qHa+flOmpoyWLAYViRQEkIIIYQQw57S1YnrgWUkZpyLMW48J7KdfPyzBfw9eJwkSXwONx8ZdQs3jr+ZiXmTMl2uGAQsK0l39zO43ZNwOIrR9WJMs4esrMsIhW7E71+Iosi92cWpmpsVnntO45lndJ59Vqe93e5CcjotFiyw5yFdcEGSkhKZhyQySwIlIYQQQggxPFkWjpfW4P7zn3D9fTmtREhecz3qT/+bkCvE6qIoo7zjuGn8LVw96lr8zkCmKxaDQCy2j/b2P9Pefi/JZAP5+V+noOArKIrGiBHrUFVZiyT6M03YulXl6aftWUgbNqhYlh0ilZaafOADCc4/P8msWUbvPQGEGBAkUBJCCCGEEMOO+/e/xfObu9AO7GdlFfzuah8P1mh8bVIFnwacmpNnrnmeIl+xDNkWp6W9/T7a2v5IOLwGAFUNkp19C1lZi9P7SJgkenV2wsqVOk89pfPMMxpNTX13ZZsxw2DRIoNFi5KMGWMvZRNiIJJASQghhBBCDH2JBGrDccyKSgBOHtjAssrD/H6pnwOubqCH2tAIcguq04cU+0syVKwYDCzLxDDa0PVcADo7HyEcXoPPN49Q6ENkZV2KqnoyXKUYKCwLtm9Xee45O0Bau7ZvoHZensnSpXYX0ty5SYLBDBcrxGmSQEkIIYQQQgxZ2r69uO+9B9f9f8HKy6ftuRdAUfjklKM8W5LEq5ssrb2eG8beyPTimdKNJN5SLLab9vb76Oi4H5drLJWVDwJQWPhtior+HaezMsMVioGisVFh5UqNFSt0Vqzo60JSFIspU0wWLUqyaFGSSZNMVBmnJQYhCZSEEEIIIcSQonR14nz0ETz33oPj5RfZmQe/m+mia3QuP4jHweXis9NvZ3HHVVwx8ioCzqxMlywGuGSyiY6OB2hvX0Y0uhEAVQ3gcJRgWRaKouByjcpwlSLTYjFYu1bjuefsEGnbtr47suXnm1xzTYJ585LMm2eQny8DtcXgJ4GSEEIIIYQY/CyL3kEjzn8+gXr7Z7hnPPz2S1m8FOoEYhR6W/mWDi5gdtlcZpfNzWjJYmCzLDN9F7b29ns5efKbgIbffwGh0AcJBBajqt7MFikyyrJg716VFSvsAGnNGo1wuO+ObLNnJ5k/3w6Qxo2TLiQx9EigJIQQQgghBi1t+zbc9/8F12OP0Pb0KqxQNn8bp/GZrzoIKwkUuphfvpAbxt7IhdWLcWmuTJcsBjDLMujpeZ6OjmWEw2sYMeIVFMVBMHht6vFqdL0g02WKDGppUXjhhb4upGPH+lKi0aMN5s0zmDcvycyZBl7JG8UQJ4GSEEIIIYQYVNSTJ3A99ADu+/+CvmMb2wrggbNcfGHnNqyZsxlfOpXCUDlXj1rKdWM+RFmgPNMliwHMsiwikbV0dDxEZ+ffSCZPAuBwlBGPH8LlGonDUUxu7mcyXKnIhO5ueOkljVWrdFav1ti+vW8ZW3a2xWWXJZg/P8ncuQalpbKMTQwvEigJIYQQQohBQ2lsJGfyWBrdBr+tU/nT7Vls8tlL2iaWJZkLVGZV8dL1G2XAtnhDvXOPACKRdRw8eD4AmpZNdvZNBIPX4PWel17yJoaPWAzWr9dYtUpj9WqdjRvV9N3YXC6LWbOSzJ5tMHdukro6E017ixMKMYRJoCSEEEIIIQamRALnimdw/fVBoh++icS5s2gKqHz4thKe8h7DwERXw1xYcTHXjr6O6cUz04dKmCReTyy2h46OB+noeIiKintxuUbj8UwlJ+eT+P2L8Pnmo6rOTJcpziDDgC1bVFavtjuQ1q7ViETsnx+qajF5ssns2XaIdM45Bh5PhgsWYgCRQEkIIYQQQgwchoHjpTW4/vogrkeXY7W3saIKKot8BM+dRbYrm835BhO9dVw7+jouH3k1eZ68TFctBrB4/DAdHX+ls/MhotEtACiKm2h0Gy7XaBRFpbj4JxmuUpwplgV79qg8/7zdhbRmjU5HR18APWaMwezZBrNnJzn3XIMsuQmkEG9IAiUhhBBCCDFghJacj75+HS+Xwb3zPdw/3stJLcxXp5XyZUBTNVYsXUO2OyfTpYoBrHdJm2lG2bdvOpYVRlEcBAIXk5V1FYHAxWhaINNlijPANGHXLpUXX9RYs0bjxRc1mpv7ljJWVJgsWZJg9myDWbMMCgpkDpIQp0sCJSGEEEIIkRHa7l24/vYAZnEp0Y98FIDvXOTlzxf5OeToBiLkuHO4seaDzCtfmD5OwiTxWpZlEYvtorPzYTo7HyY399NkZ9+IqrrJz/8XdD2fQOBSdF2+d4Y6w4AdO1TWrLEDpJdf1mht7QuQiopMrrwywaxZdhdSZaUESEK8UxIoCSGEEEKIM0bbsxvX35fjemQ5+s7t7M+GjvGjKU8FShtHBWmqh6url3LlyKuZW7YAh+bIcNVioIpEttDZuZzOzoeJx/cCoChOEonj6X3y8/8lU+WJMyCZhG3b1FT3kc5LL2n9lrCVlZksXJjg3HMNZs5MUl1tISPWhHhvSKAkhBBCCCHOCN83/xXv3XdxJAgPTtC477YgrwQ6WFRaxr2pfX44+05Crmy8Dm9GaxUDk2VZmGZ3erlaQ8OtRCJrURQPWVmXkZX1Afz+C9E0GXwzVCUSsHmzypo1Oi++aHcgdXf3JUSVlSaLFyeZOdOegVRRIR1IQrxfJFASQgghhBDvLctC27YV16PLUVta6f7pLwD4y0SVu/8lxCv+dsBAU7qZX7aQK0YtTR9a4i/NUNFioDLNOOHwarq6/kFn5z/w+xdSWvorAPLzb8eyovj9i1BVX4YrFe+Hzk5Yt84Ojtau1diwoe8ubAA1NSaXX55g5kyDc881KC2VAEmIM0UCJSGEEEII8e5ZFvqWTbgeWY7r78vRDh1kXw7sLvUwLfxD8Ho5MrKQDS1dzCmdz6W1l7G4+lLyvfmZrlwMUF1dT9Le/he6u5/GNDsBUNUQqupP7xMIXJip8sT7wLKgvl5h7dq+AGnnThXLsgMkRbEYM8Zk2jQ7PDr3XIPCQgmQhMgUCZSEEEIIIcQ7Y1n0DiNx/+kPBG7/Ertz4f7JDh5cGmSLp4M8t5ctbic68KGxN3LdmA+R68nNbN1iQIrHj5BMNuD1Tgegp2clnZ1/xeGoJBS6gaysS/B6Z6IoMlNrqOgdoP3qAOn48b4B2h6PxcyZBtOnG0ybZnD22QbBYAYLFkL0I4GSEEIIIYQ4feEwzlUrcD7+KI6XX6Rt9VpwOHhikpfv/GuQ7e4OIIFDDXN++YVcWns5pmUCEHJnZ7Z2MaBYlkU0uomurn/Q1fUPotGtuFxjGDFiLQA5OZ8gFLoel2s8ikxRHhK6u2Hjxr7waN26/vOP8vJMFi9OpAOkiRNNnM4MFiyEeFMSKAkhhBBCiDeldLTjfPwxXI8/hnPFM5jRCGvKYdU4P58+fAhjxEg8RVXs80W5qOISLq25jAurLibLJa0E4vW1t/+Zkye/TzJ5DLDvzOb3n08gsBjLMlEUFaezKrNFinfFNGH/fpV161TWrdNYv15j1y4V0+wLkEaMsLuPegMkuQObEIOLBEpCCCGEEOIU6pHDmOUVoChoB/aj3/ZpnqiBv12dxWPV0KxGgG4W5kEtcE7RNHbefAC/M5Dp0sUAE4vto7v7nyQSxykq+j4AiuLFssIEg0sJBC7B71+YvnObGJza2uzuo97waMMGjY6OvnTI47GYNs1g6lR7BtI55xjk5cn8IyEGMwmUhBBCCCEEGAb6hnU4n34S1xP/QN+5g9aVL2GMHceawjjXfN1BhATQSYG3kA9XfZDF1ZdQFqgAQFVUCZMEAKYZJRx+ga6uJ+nu/ifx+IHUKzr5+V9B0wJkZS0hK+sDKIqW0VrFO5NMws6dKuvXa6lNZd++/n+XNTUmF1yQZOpUe/bR2LEmDhl/JcSQIoGSEEIIIcQwppw8if8738D53NOoLS3sz4bl4zUe/nI2f4y0EADG5U+kNm8sC8oXcXHNJUwpmIqqqG95bjF8GEYbYAeK7e1/pqHhywCoaoBA4AMEAhfg95+f7kKSwdqDh2XB8eMKmzZpbNxoh0gbN2qEw33dR36/xZw5Sc4+2w6Ppkwxyc2V7iMhhjoJlIQQQgghhgvLQtu1E+dTTxJdej1WYSFxv4cXtv6NR+c4+MfYLPY4OwEDhXZeyunhfMDv8PPstc9nunoxgJhmDz09z9Pd/Sw9Pc+SSDRQUNAEQCBwIfH45/H7L8DrnYmqylTlwaSlRWHTJpWNG7V0iNTU1BcgK4rFmDEmU6fay9emTjUYOdJEk2YzIYYdCZSEEEIIIYaycBjnC6twPvUkzqf/iVZ/lBN+cOQEsT70UZqtbhZdFwfieHUvF5Ut5oKqi7mg6mIKvAWZrl4MMOHwyzQ2fo9w+EUsKwHY85B8vlkkEs1AAIejjKKiH2S2UHFaurpg82YtFR6pbN6sceRI/+7D0lL7zmtTpphMnmxw1lkGAVndKoRAAiUhhBBCiKHFsuxNVaG7m7wJI7EiPawvhkcnunj0+hAbvO0smxJiPlDsL+EbM77NxLw6Zpach1t3Z/oKxACRSBynu/s5IpG1FBf/AkVRUBQnPT2rcLun4PcvwO9fgMczDVV14XIFgK5Mly3eQCQC27apbNqkpTaVfftULKtv6VpursnChUkmTzaYMsWgrs6ksFCWrgkhXp8ESkIIIYQQg5zS3oZj9Uqczz2Dc8WzdH//x8QXL6HbBbd9vIAngydpVMNADF01mFU8Bz2Ymz7+C2fdmrHaxcBhL2N7Ib2MLRbblX4tJ+dTuN1jcbvrGD36ALqel8FKxVsJh2HHDpUtW7R0iLRrl0oy2X/u0XnnGanwyKSuzqC83EJR3uTEQgjxKhIoCSGEEEIMRskk3p/difO5Z9A3rsfAZG0pPDnBxSWNW6lmCT7dxzNlcSzTz3WVV7Ko8kLmlc8n4MzKdPViADDNKNHoJrzeGQCEw69w5MjVACiKB7//fPz+Bfh8C3G5Rqc+r0qYNMB0dMC2bRpbtqhs3aqxdavK3r0qptmXDLndFpMnm6muIztAqq01UWW2vhDiXZBASQghhBBiEFCPHsG54lkSZ0/DGDsOdJ2GJ/7MM+56nvhENs8V9tChxIAY8QkatwKKovDolf+kxF8qd2UTWFaCSGQDPT0r6elZTTj8EpYVY9SonTgcpXi908nLuxWfbz5e7wxU1ZXpksVrNDYqbNtmdx5t3Wo/Hj7c/73t81lMm2YwcaLJxIkGkyaZjBxp4pAb6wkh3mMSKAkhhBBCDEBKawuOF57HuXoFjtUr0ffvo9sJ8c98AW3s90maSc5a2kqXYQGtVGRVcXn5QuaVL2B26Zz0ecoC5Zm7CJFRlmWhpNYv9fS8yJEjV2KaPenX3e6J+Hx93yuq6qGw8NtnukzxOiwLjh5V0p1HvY8nTvQPj3JyTObOTaaDo0mTDKqqLOk8EkKcERIoCSGEEEIMBN3dKKaBlRUEyyJ7zgxoOsmGYnh6tJMnP5DDmmAHPxjv5yZAV3W+cPa/4HcGmF+xkOqsmnR4IIYny0oSjW4lHF5DT88LhMMvMnLkJjQtiMs1CoejDK93Nn7/XLzeWeh67lufVLzvenpg1y6VHTs0tm9X2b7dft7V1f/9XFxscsEFfeHRxIkGpaUy80gIkTkSKAkhhBBCZEI0imP9K/Yw7dUr0Teup+cb3yHymc9jAdd8Modn1fbUMrY40Epd/hR8RVXpU3xx6m0ZKl4MJNHodk6e/Cbh8MuYZt9d1hyOKhKJI2jaRHQ9lxEjXslglcKyoL5eSQdGvY8HDij97rSmqha1tSYLFpiMH293HU2YYFJQIHdbE0IMLBIoCSGEEEKcSZZF1keux7niGYhGOZgNT9coPHNzNpcFjnI+9uyjE+U5hLojfKBsHueVzmZO2XzyPDIMeTgzjC4ikbX09KwhEnmFiooHUFUXquqlu/tpnM6R+HxX4fWei9d7Lk5nRaZLHrbCYbvraPt2jR07+rqOOjv7txMFgxYzZxqMG2eHR+PGGYwebeL1ZqhwIYR4GyRQEkIIIYR4P0SjODZtwPHiCzhefIHo1UuJXXsdFrAseIhnl7p5rtzBEb0LsOcgBavg/NThf77kAfwOf8bKFwNDPH6A1tbfEQ6vIRLZDBipVxRisZ14PJNxOKoYPXoful6QyVKHpWQSDh5U2bWrb3ujrqOaGpP5881UeGQwfrxJSYksWRNCDF4SKAkhhBBCvIe8//FjHKtW4NiwDiUW41gAVlVC1e4CRnAdiqLwo/Msdra2E3KFuKT0A8wqncOcsnmMCI1Mn0fCpOHFskzi8b2Ewy8TiWykuPg/UBQVw+iipeVXKIoDj+dsfL7z8Hpn4vVOR9NCgN3RJmHS+8s04fBhhd27VXbt0tLh0b59KvG4dB0JIYYnCZSEEEIIId4BpaMdx8sv4nhxDfH5C0nMmQdA/ZpHeCG6lZXXZbO6zMVBvROAT9Xl8d3UsT+YfSdZzizG505EU7XMXIDIuHj8EB0d9xMOryUSWYthtKdfy8n5BG73WNzuCVRVPYbHczaq6slgtcODZcHx48qrOo40du9W2bNHJRzuHxx5vRbjx5uMHm0yZozBmDEmY8aYFBdL15EQYniQQEkIIYQQ4jQ5H/lbOkTSt28Fy2JXHjjiTQRTgdL5lzRzNArQRtAV4sLii5lRfB4LKhalzzOrdM7rnl8MTZZlkUgcIhx+mVhsJ4WF3wEgkainsfH7ADid1fj9F+H1TsfrnYbLNQoARdHw+WZnrPahyrLgxAmFPXtUdu+2t5077fDotXdXc7ksRoww04FRb3hUXm6hqhm6ACGEGAAkUBJCCCGEeK1kEn37VvRXXiY5bQbJSZMBcN/5fXZ27mVlrcbKT+WwOj9CsxrmK5NL6b3f2mfOuRXLsphRch5jc8ZJB9IwFY8foKPjYSKRdUQiL5NMNqZfy8n5OA5HGR7PWZSX34vXO02WrL1Pkkk4dEhhzx6NffvsTqO9e+2tu7t/cKRpdnBkdxzZj2PHGlRVWejyryYhhDiF/GgUQgghhDBNnM89jb72JRyvrLXnH4XDdLgg8pnP40gFSqM/0sHhBNiDkVso8ZVyVckS6kqnpU91y8RPZuQSRGaYZpxYbBuRyHoSifp091E0uovGxn8DQNdLyMq6Aq93Gh7PdHS9EABV9ZKVtSRjtQ8lPT2wb19fWLRnjz3f6MABlUSif3DkcFjU1pqMHGlvo0fbW22ticuVoQsQQohBSAIlIYQQQgwvloV2YB/6K2tJnj0NY8RIUBR8X/4ch2MneKECnr8ymxfLXWx3tfOD8T4+ljp00ZjLiSQizCg5l5kl51ERqESRYSnDTiSynvb2+4hE1hONbsGy4qlXFPLybkXTgni9MygvvwePZyoOR1lG6x0qLAuam5V+nUa9wVF9/alrzwIBi0mT+oKjkSMNRo0yqaiQjiMhhHgvyI9SIYQQQgxtySTOZ59C37Aex8b16BvXo7a3E9Uh9tVvwudvx8Si9rNJjvTekZ02PLqHcwtmkVcyOn2qf5/904xcgjjzLMsimWwgEtlIJLIe0+yiuPgnAMRie2ltvRtFceByTcDjOQuP52w8nqmoagAAXc8hK+uyTF7CoNXTAwcP2t1F+/f3bQcOqLS1nRrgFhWZzJ6dZNSovvBo1CiTggIZji2EEO8nCZSEEEIIMXSEwzi2bELfsJ7YxZdgVteAquL/1C0cdnSzthRevCCLlytz2ehr5z8maCwFVEVlavVczsLinKLpnFM0nfG5E3FojkxfkTjDOjv/TlvbH4hENmMYTenPK4qboqIfoigO/P7zqa5+Brd7IqrqzmC1g1ciAUeOKKcERvv3qzQ0nNpt5HBYVFaaTJ9uh0UjRpjpACkQyMAFCCGEkEBJCCGEEINYOIz7bw/Czi1kv/Ai2q4dKIZBiweSXgdq9aeIW0lKbldptHoP6kRTNCbmTcJZXJE+1d0X/CEjlyDOLMsyicf3E41uJhLZTDS6GU3Lprz8fwFIJBro7n4ah6MCr/dSPJ66VPfRFBTFDhh1PRddz83kZQwKpgkNDUq/wKg3NDp8WMEwTm0fKiszmTMnSW2tmd5qauw7qskyNSGEGFjkx7IQQgghBj7TRDuwH33LJvTNm4h8/FOYZeWgqmhf/SIv5hm8XKXz0i0hXilIcEDv5I+TPCwGnJqTuoqZ+Bw+phSczVmFZzMxbxJehzfTVyXeZ5aVxDA60fUcAE6e/B6trf+NaXb128/jOTv9PBS6lmDwKgmMTlMyCceOKRw6pNLSAlu2uDh0yP744EGVSOTU0Cgvz2TqVIPaWns4dnW1mX70eDJwEUIIId4RCZSEEEIIMSApjY14/+tn6Js3oW/dgtrTTRJwigwAACAASURBVFKFXXmQVzcerex62olQ8q+QBOz/bSHkCjG/YCGevL5ByH++5IEMXYU4U5LJVmKx7USjW4lGtxONbiMW20kgcBHl5X8CQFX9OByluN11uN11eDyTcbsnomnB9Hk0LZSpSxiwolE4fFjtFxQdOmRvR44oJJOvDo2cAHi9FiNG9HUYvbrbKCR/xEIIMSRIoCSEEEKIzEkm0fbstjuPtmzCsXkTHX+8Fys/n6QG+5bfxboShXWXBVlflstWbycREjwwMZu5QMidzfnVFzMyv4YxWRM5q/BsqrNq5M5rQ5hlGakla1txOMrweqcDUF9/Mz09z6X3UxQnLtdYnM7a9Ofy8r5Efv6Xz3jNg0FHB+mQyA6NlPTz48dPnWkEdqdRXZ1JVZW91dW5yMnpoarKIj9fBmILIcRQJ4GSEEIIIc6MWAxcLgC0bVsJ3P5F9O3bUKJR4hpsz4d1pQqX7t2Olj+Pw3oXMz4NYAHt6KrO6OyxTMqvIztUnD7t/158L/n5AZqaul73y4rBr7X1D0Qi69JdR5YVBSAUujEdKAWDV6U6jibgck3A5RqRnnnUazgHjbGYvTTt8GGVo0ftzqIjR1SOHLE7j1pbTw2NFMWipMRi1qxkKjSyqK7uC5BeOww7P99FU5N5hq5ICCFEpkmgJIQQQoj3lmWhNhxH374Vffs2tO3b0LdvRTt8iOa9R8Hr5aQrzv3aBtZdG2JDiY/t7nbiGIDFk7UBpgDVWTXcPOFjjM0ZT13+ZMbmjsetyx21hiLD6CYW25XadhCL7SQ7+2aysj4AQHv7/xKJbEh3Hdmh0Xh8vpnpc2Rn35ip8gcEw4Djx+2Q6OhROziyAyOFo0dVGhoULOvUQM3hsKiosDjrrGQ6KLJDI4vychO3vOWEEEK8AQmUhBBCCPHOxWJoe3ajNRwjfsHFALgeXEbWZz+BBZzww+Yi2FTpZvv8ED9raQJvJceCCp9ebAKtuDQX43PrmJg3mbqCyZQGygG7m+THc36WuWsT7znTDBOL7cbprEHTglhWgr17p5JIHDplX49nWjpQKir6Carqf92uo+HCsqCxUeHw4d7QqH+X0bFjr51lZFNVu8to5kyD8nKLigqTigqTykr7eWGhhaZl4IKEEEIMehIoCSGEEOK0aTt34Hz26b7uo727UZJJDK+H1v3HQdNYVW7y8y/nsSUrTLMSTh0ZBaJ8LitJDTAmdzw/n/crJhVMZkz2WBza8AwJhjLD6KKr6x+prqOdRKM7SCQOAxbl5feRlbUYRXGg64U4ndW4XGNS3UdjcblG9xuO7fWek7kLOUPicWhoUDh2TKW+XqG+3g6J6uvtj48eVYlGX3/JXkGByeTJZjosqqiww6LycpPSUgun8wxfjBBCiGFBAiUhhBBC9KM0N6Pv3om2awf6zp1YXi893/0hAM5VzxG78xusLYKN5Q42nRtkc4FFpxteSSZB04iXlfJssJmKrCouzp3A+NwJjM+byPjcCVRkVQLg0lzcMG54L1Ea7CzLwjBaiMX2EIvtIR63H0tLf4Ou52CaPRw79vH0/pqWi9c7C7d7DA5HSfrzNTVPZaL8M8qyoLOTdDjUPyyyn5848fpL0gBCIYtRo/qHRZWVJuXl9rI0j+cMX5AQQgiBBEpCCCHEsKV0tKP09GCWlALgvfOHeP74P6jNTQB0OWFzAXQV5TEZO1D6Se0JvvuV3jMkgBY8uocxOWMJqwZeYHrxTPbdcpQsV/CUrykGH8tKEo8fIpGox++fB0B390rq62/EMNpO2T8e34euT0PXCyku/jku10hcrrHoev4ZrvzMSSbhxIlTu4qOHbM/PnpUpbv79cMiTbOXpM2YYVBaalFWZlJWZj+WllqUlpr4/Wf4goQQQojTIIGSEEIIMQzomzeib9uKtntXqvtoJ1rDcaKXXUnXb/8IwLPaQVbNibGtPJ/tWVGOavZd00aHclmdOs+4UXNYFN2Z7jganzeRmmAtmto3hMWpOXFqssZmsIpENtDZ+Wi66yge349lJQCdceNOppep2R1HM3E6R+FyjU4FRyPRtGzAnoGVk3NLZi/mPZBIwMmTCsePKzQ0qBw/rnD8uD3kuvfxxAkFw3j9wCgQsLuIysrscOjVYVF5ucwwEkIIMXhJoCSEEEIMBaaJeqwebe9u9L170PbsIT5/IfEl9lBj33e/BWtWsicXtufDlnMCbKvIZ0JeB19KneLv07L5racTgEJvEXNyzmZszljG501Mf5kFFeezoOL8M3114j1iGB3E4/uJx/cTi+1PPT+ApuVQWfkAAJHIZpqbfwqAqgZxu+twuUbhdI7CsuIoigO3ewwjR27I5KW8J2Ixe27RqUFR3+caG994KZqmWRQXW0yZYqZCI/OULqOsrDN8UUIIIcQZIoGSEEIIMZhEo2gH9mMWF2Nl54BlEVpyAfr2rShhewB2uxu25YHf2U1hKlC6ekmYfyxUMTBTJ+oCuuiu6PuH8o3jP8qS2ssYnTOGHHfuGb4w8V4xjE7i8QPp4MjprCEYvBqAhoY76Oj4y2uO0PF4pqY/CgQuxOV6DKdzFLpegKK8fpgy0HV328vQeoOhUx8VmpvVNzze6bTDohkzDIqLLUpKTEpKrH7P8/Kku0gIIcTwJYGSEEIIMVB1d+N+cBnagf1o+/ei79mNeuQwimXReddviV29FAu4q/IEO8d42FnoY7cvzEmlB4AvTCrmG6lT5ddOZmqzxqjs0YzJGcuY3HGMzhlLgacg/eVG54w589co3rbeYdjx+EEcjmIcjjIA6us/Snf3Sgyjqd/+gcDidKAUCJyPpgVxOmtxuWpxOmtxOMpRlL7/JHQ4SvoNzR5oenrsJWgnTqipx/7PT55UOXFCoafnjYMwj8eeWzR2bDIdEL02NMrNtRikWZoQQghxRkigJIQQQmSCZaE2nrTDot5t/z60g/vpuGcZZoV9NzT9a19mXw7szoOdY73suDCXXbkW3wg2MQd7Ts3PZloc6WpBQaE8q5KFoXMZkT2KWRUL0l/uR3P+I0MXKt4J04yiKBqK4sCyEpw8+S3i8UPE44dJJA5hmt0AFBZ+l7y8L6WO6UHT/Hg8dTidNTidtangqC8oDAavTodLA00k8vpB0YkT9rKz3o+7ut485cnLM6mqMikqsigqsmcUlZb2D42CQSQsEkIIId4lCZSEEEKI94tlobS0pAKjfWgnGgh/6V8AcKx8jtC1lwMQ0+BANuzNhT1FTq6p34+3opJGNUzBN159wjAQxqW5OFYWSn/2lwv+myxXkJpgLV6H98xdn3jXkslWurufTIVFh0gk7MdksoGqqifw+c4FdNra/g/T7EBV/TgcVTid9vbqpWrl5fcNuOVplgXt7dDUpNLYqKS3pqa+TqLeEKmj481rz8mxZxTZQVFfWFRYaD8vKrLIz7dwyjx4IYQQ4oyQQEkIIYR4N5JJ1OPHULq6MMZPAMD594fx/tfP0A4cQO3ssHdT4VgAfB/7JJY/wKYCkx98OZ99/jhHtE5MrNQJ44yv8XM2kO/JZ0HFIkr95dSGRjAqexQjQqMoD1T0u6vauaWzzvBFi9NhGG1Eo7tIJI6QSBxNbUdIJOqpqXkeVXWRTDZy7NgnX3WUisNRjs83B0Wx/44VRaG6+gl0vQhNy3nD0OhMhUmWZS87s8Mhlaam/kFRY6P6qucKicSb1xUKWRQXm0ye/MZBUUGBhct1Ri5PCCGEEKdJAiUhhBDirSSToNu/Mp1/fxjnyufQDh9EO3wItf4oSjJJcux42la+CMDenoO85NnK3sUB9hbmszeQ4JDeCSgc0TX7l29BEU8Hm8j3FDAtNJOaYC01oVqqg7XUhkYAdkBw35K/ZuaaxZsyzeirQqKjxON2aKSqbkpKfglAZ+ejHD/+2VOO1bRskslGnM5ynM4qiot/ke44sucZOU45xu0e/75fUyRCOgR6vY6i3qCouVkhHH7zkMjlskOgSZNM8vNN8vPtj3sfCwpMCgrs0Mjjed8vTQghhBDvAwmUhBBCiBTHS2vQ9u6xg6LDh9AOHUQ7fJDYpVfQ/R//CUDXmiepf/b/OJAN+8f42L8gxIEchWyvye9S53lurJc7LkwCbQDkuHOoC06lJlhLWEmQhT0Ae//H6gk45Z7iA41lmRhGM4nEsdRWTyJRj8s1muzsDwNw4sQdtLX98ZRjNS0vHSh5PGeRl/dlHI7y1FaBw1GGpgXS+6uqm5ycj74v15FMQkuLHQA1NyunPG9qsu9y1vv5t5pNpOt2IDRihJkOhfoCot6wyH4tEJAZRUIIIcRQJ4GSEEKIoc800fbvQz16BO3oEbT6o/bz+qOEP/kZ4pfas4x83/hXjB2bOBy0ZxrtK9DZf1GAscUNXJk61W3T27m/vPfEPUAPCgqT8svSX25u1SJ+7fkd1cEaaoK1hNzZp5Skq7qESRlgWQbJZBOJRD3J5PF0aBQILE7NK4IDB+YSjW4+5Vi//6J0oOT1nodlJXE4ylJBUTlOZzm63vd94HaPx+3+zntWu2lCW1v/cMgOhU4Ni5qbVdra3jrR0XX7bmbl5a8Nh8zXBEUW2dkWqvqeXY4QQgghBjkJlIQQQgx6Skc76tGjdlBUfwQt9bz7W9/FrKyCeJyc884G7AHYR4JwKASHshXqjk6jGjtQmv/BCGviClZ6npHdZbS42pEOlM6fcDU5+VVUBaupyqqiMquKskAFLq1vwEt1sIbqYM0Zu35hs6wkyWQjicSxVFhUTyJxnNzcz+FwFGOaYXbuLMP+e+1P07LTgZLPNxunsxpdL8HhKMXhKEkFRtXp/UOhpYRCS99VvbGYHRC1tvZtLS19j68NjlpbFUzzzUMiRbHIybE7hcaNs8OivDx7632en2+Rl2eSm2sRDCIhkRBCCCHeEQmUhBBCDGzRKGrDcbTjx1B7t6ZGer7/Y8Bephb6wEXp3buccCAEh4Mwcc9VeCqriOgW079WyGFHNyeVnled3OJbM/P5XOqjsuqpnNtVQGUqKKoM2o9VWX3h0GUjruSyEVcizhw7KGoimWwgkThBMnmCZLIBw2ijuPinALS3r2bHjrmQDgP7BAIX4nAUo6pefL7ZaFo2DkdJv8DI6RyR3r+o6Idvu8Z4/PXDod7P9QZFbW19z7u7T29NWDBoB0E1NUY6HHr19urQKCfHQtPe+pxCCCGEEO+WBEpCCCEypzcsajiOeqweteE4ls9H9Bb7rlee3/4a/9e/kt7dVKDRBw1+KP/K17ECWezMNvjR5ws47Dc44gzTpkTS+z8yLo8ZgFtzsy8rQcCZz6zAVMoC5ZT5yykPVHBO0fT0/v+18L/P2KULW9/ysxOpsKiBZPIEul5EQcHXAGhu/jmNjd973eMLC7+HqnpwuUrwes9F1wtTy9DssEjXS3C5xqb3r6p6+C1r6g2H3iwMeu3HbzV/qJfLZYc+lZUmOTl2GJSdbaWf5+TYH786LHI6T+vUQgghhBBnlARKQggh3nuWhdLdhXryJOqJBns7fgxj7Dji59vdRIHPfRL3/X9JH9IbFnWMqiYnFSg9nd/FfZ8q4GiWxTF3jONqDwkMFBSOOnWcQDI/j0dyG/HqXsoCFUwJlFPmr6A8UE5JwJ5noygKO24+gKrI2p4zqbt7ZaqbqIlkspFk8iSG0UggcBk5OTcBcOzYZ+nufuKUY93uSelAye2uIyvrSnS9CIejGF0vSj9XFDtt8Xhqqa5+vN85IhFob7eDn/6P/T//2n16ek4vHHI67QCovNzsFwa9Ohx67eb1yrBqIYQQQgwNEigJIYR4e3p60E42oJ44YQdFqdAodvW1JCfWAZA9Ywr6wQPpQ0wFmrwQufJqfKlA6fcju1j1OmHR5ICbf6aOOziqkGXHG1EVlUJvEZP8oynxl1LiLyWuGDiBEaGR7Lj5ALnuXJQ3+Ze6hEnvnGUZGEYrup4PQDLZTHv7vamQyN4Mww6NSkt/i98/D4D6+pswjJZTzud0jkw/DwQW43TWpIKiQnS9GIfDDozsrw2KcgFwIc3NrxcOKbS3QzgMJ096+r0WjZ5+cuP322FQTY1JKGQRCr1xKNS7+XwSDgkhhBBi+JJASQghhC0WQ204jnriRCow6guLun/0U6ysIGr9UXLPGp8+xALaPHA8AIERpXhTgdJXL3ayTy3guN+iwRnjRCos+nilgx+kjn1hYjbLdr06LBpFib+MMTl9y5Murb2M+eULKfQVoauv/ytLV3XyPHnv15/KkGRZJobRjmG0kEw2A+DzzQSgp2c1bW3/SzLZnAqKGlP7mIwZcxxN82MY7Zw8+Y1+51RVP7pegGUl0p/Lz/8qiqKhqgXEYgX09BTS1VXI3r1+1q1T6OxUaG//OJ2dCh0dfVt7u0JHB+lgKJk8vdRGUTSCQQiFLMaOtYOh7GwrHRD1Pu97JP2aw/He/NkKIYQQQgwXEigJIcQwoB3Yh7Z7N2pTI2rjydRjI5ZDp+s3fwTA9fijZH3iZsAOijpdUB+ww6Jx9Z9HGzeJkwGVT3zWDopOuOI0qD3EUnfM+u+J3vSd0B4ZbbGnrRFd1e2wyDeKYl8p4ytnpWu6Y9rXuP2cr75pWBR0hQi6Qu/XH8uQkkicTHUJtWAYzSSTzRhGM273FLKyFgPQ0PCvdHQ8gGG0Akb6WJdrLCNGvJw6z1E6Ou4HQFUD6HoBHk8tUMCxY3E6O1U6OyuJx++js7OQ1tYimpsLaW/3pQIh0sFQZ+eXaW8//eHTvTStL/Spqnq9IMg6JSwaOdJPPN4tA6mFEEIIIc4QCZSEEGKwiUbtdUAeDwCu5Q+h7d9nh0RNTaiNJ1GaGknMmUf3nT8HwP2H3+G9+y5imj2n6IQfTvohGvAyN3XaFfk9/OT2fBrcCRq0HsL0dZqsLfJSBbg9Af6a34imaBR4Cxnnq6XQV0yRt4jyor7OonsWLyPgzCLHnfOGS81K/KXvx5/OoGeakdTysmIURcUw2unoWI5htGIYbalHu7OosPDf8PlmA3DgwBySyYZTzpedfRNO52K6uhQ6O3WSyRDJ5Aji8TxisVzC4Xza2yu55x4XnZ0QDl9NInE+DQ35NDf7UsEQr7ldvQ9Y+qbXkZVlEQxaVFWZBINW6mP7jmW9W1aWHQYFg337B4PvbClZTg40Nb29Y4QQQgghxDsngZIQQmRaJILa0oza0ozS0kxi2kzw+yEcxv/1O+zXmu3X1OZm1K5Ouu78OdGbbgFAu/uXtO7dyEk/nPRBQ0Dh5CgvFZ79XJT6Et+pa+M333bTTrTfl87z+NjRW0Z5MS/4msn3FjDCV0WRt8gOi3xFeN1ZAPgdAbbetJc8dx6a+satINXBmvf6T2nQMc14KgBq6xcGKYqTUMgOY7q6nqK5+Rf9Xrcs++9o9OiDqGounZ2dNDR84ZTzW5bOY481sX+/k64uhXHjrsM0I3R05NPSkk9TUx6Njfns319LfX0gddR/prY3kwvk4vXa4U5xscno0X2hTyhk9Qt/Xh0S9b7u9yOdQkIIIYQQQ5wESkII8V7r6bGXlbW2pEKiFjsQSsQJ33oHAI4XVhP44mfsz4d7+h3e+szzGBMnkdRVNqz6E40+aPQrNI32cnKmi5PBAj7oa2B2av/p17SxvV9OZAE9XFTtSwdKntrxFCU3MdFbSL4nn3xvAQXeQgq9hemj5pTN59inWt5w+RnYd0t79TFDnWnGMM0ODKMdXS9E04IAtLX9H8nkidQcog5M034MBC4kN/ezGAYcOfJpwuEHTjlnLDaSDRv+f3t3HiZFea99/Fvd1VXV2+wDCqIgy7ggCm4kiBhfkmiOelRiQoCThBgVD+FVDAYxMUajuMSokahRY+ISRc2rQg5gctSELCrixokYd1BBQAZm6727uur80T2Dk0HeTIy2w9yf66qruqufrvpRM6VwX88yg44Og5qaFEce+WdyuWrS6TqSydEkErW0tdUzY0aETZtimOYIJk26m46OehKJOtrb6+noqCeZrAHe343nx12vIhGfeLwU8AwcCMOHu1RVld7HYnS9jsd94nG6Xr+/t5DmFBIRERGRXVGgJCLyQYpFjLY2sC38WKmHh/XIcoLr12G0tRJoaYF0B9VbtuIeMo7U9y8FIPrjq4j89PodpzFgewTaqixq554PhsGb/jZ+M6aF5lqH5niU5gg02y7bzBxL7Q6GA3nD46jTO89SColKGzQNj3YFSp/Z/2SakhtpDA+gMTKQAZEBNIYb2adqWFcNs8f+X2aP7dnL5f12FST1Vb7vd6385rpbyeVeoVhs7wqCisVWPK+dAQMup1CwaW9/m+3bT8Pz2oB2DCPTda6//W0xb799CsmkwXHHXUU8/naP6y1dOpLrrouRThucfPLRHHwwdHTU0dFRX97q2L59EM8+6wAQDE7F97+C55nl9z5VVXSFO3vvXSQeDxKPf5khQzpDIspBULYcDJVWKHt/QGTufj9KEREREfmE0V85RWT35/sYyQRGSwuB1haM1tbyvoXcqafh19ZBJkP1zOldQZHR2kqgvQ2A5GVXkjnzPwFwbvoJqb+uoiUM28OloGh7GGq3pjiyfLlfjEqx+DuNbLdcmoM5Wo0MPj7VQYvXy23eGlrLpYclupVZZVVTHx5Iuq40vCwSinDeoedTbddSH66nIdxAvdPAgMhAGsKNXd/7/qcu/UhvX6Xl8+vKvYASFIsdeF4HxWIHweCB+P5EUimDROKnuO5KisUEvt8BdBAIdJBKjeCPf/wLyaTBXns9ytFHn73Ta0ye/AOamxuoq6vnF79oJpmsIZkcTCJRW35dy/Ll+/LKKzYAzz57M75vkEyWPnfdGqCacNhixAiPWMwnnZ7Fiy+eRSxW6hU0bJhPLFYKfM4+O1MOf0qBUFVVlljMJxLRMvQiIiIi0jcoUBKRvqFYxOhoL/UYMk28IXsDYK5+mtDqVQTa2zDa2jA62gi0lYKg9vsfBsD6/aNUf+WL3U7nAykL/LFjofYICqEgDzU/Tks0yLYDHLZXW2yPN9ISCTC9biufK3/vqFNbePb4nuVN3ruee8uv3x0xkKdatlHn1FHv7MWocAP14QYawo34lAYpjWk4mP930m+oc0pBUZ1TjxW0epz3giMv+vD3rgKKxQSuuxXPS1EoJMlk2slmk2SzCXK500mlAmQyG4hELsXz2oEEhtFBMFja/vCHO3nttc+SShmcc85kotFtPa7x0ENzWLSotHrZBRe8zOc//zt8P0A6XUUqVUU6vRfr14/guutKIdCIEUeybt3FJJM1pFI1FIs1eF41UMPQobUccIBLLNbA4sWbicf9riAoGvVpaPCZPx/i8XT5+NHlfWkC6dJ8QYXyJiIiIiKy+1OgJCIfD98v7Q0DXBfz+ecItLditLdjtJdCIKO9nfzx/0bhUxMAiJ81k9Czz2C0tRFIdHSdKnf8CXTcWYpvjN8/QuZn19IahlYH2hxoDUMubPEF3wfD4IWqNNfPGcB2x2e7VaTFzNNqZMhTZGVNngPKdX1lig+4QLJb6YcMjXYFSkc0HUdD+0jq7DpqnTr2qt8DqxjtNgn17LHncM64b+9y0uoap5aj9zrmw93TfwHfLwIGhhGgUID29hfIZJJks0lyuRS5XJJCIUEicQQtLRNIpQwaGq4hGl2FYSQJBJKYZgLTTLF580HceusyUik46qifM336eTu95gknnE42G2HIELjrrnu7jmcyUZLJatLpBh57zOL550uT+AwdejrhcI5CoQrXrcbz4nheFYnEKI4/vkAkAs3NP+bBB6/DcSLE46U5zWMxn/3391m6tDMEGkksNo9YzMdx/r4nkMIgEREREZHeUKAkIv8wY9s2Aps3EUgmMDo6MBIdGB2loCf7jTMAMJ9/lsi1V2N0dBBIJMpt2jESCVpXPkWxaT8oFKg94bPAjp5CrU5piw2MESsHSovDr7P+kFba4hatsQG0hQ1abY/D4km+W67p+wdtY9F3etYaMUO8VU4MOgY3srR+KwA1dg01diODnVIgZNaUho6FgiF+NOl64lacWruOOqeOGqeWOqeOWCjedd4ffPqybtdpbIzT3Nx96JodtP/5m/wBPC9PJpMinU6TyaTJZm2y2aGk0wa53N/w/f/BdVO4bppiMYPnpfG8AqtXX006DZHIWiZOPAfTTBAKJbGsJLadwLbTLFjwR557biKFgsEjjxyH45TmDTIMcJzStnTphdx++2QALrnkeY4+ejkA2WyYdDpOR0eMjRurefHFANEovPPOaJ544usUi3E8L4bnVQFVGEacmTN9wuEc0ehgnn/+FWy7inA4TiRS+m59vc9NN/lEo0kiEZ9I5Lu7WDGsczbyznuuUEhERERE5OOgQElkd1csEnj7LQKpJEYqVZpLKJnESCYpHPkpiiNHARBZeCnmG6+Xg6JSAGR0dJD/3HEkr11UavOTa4jcclPXqX0gE4JEQxWBcqC0teVt1m74Le0OtDfYtA+zaI+FaI/UMS+/nUYgFSzy6YtqaQvkaTMyuHhd57x8rMUZ5dc3Hx3mmS3dwxoDg+q9dwQ8B46axAnBdmrsGqrs6m77zgmZxw08jJdnrqfGrtllr6GvHfiNf+oWe55PoVAgm7XIZg3S6SSZzNvkcmny+Qy5XBrXTVMopNiy5WQSiVqy2QIjRnyX0iTbaQwjTSCQJhhM8ec/z+bJJ6eSShnMnXsco0f/AdN0u13z6aeP44ILHgFgxozfcvrpOx8ad+aZ1+L7AUaN8pk69QkymRiZTJyOjmpyub0oFGLU1NiMGeMRifg899x5mKaB70cxjDiBQBTTjLP//qO47ros0ahPNLqItrYbiUYjVFWZ7LGHTzTqc8wxMGdOZ++u8eXtg+TL+0HlvQ8U/5nbLyIiIiIiFaBASeSTwvfBdelcqzvw1nqCm97dEQClUhjJJL5t7+gNtOopIjf9pBwQdW/X+sen8PYagtHWLxFRywAAFRNJREFURv34sT0u5wagcMU1UA6U/rrmN2zf9BodNrRFTdobbdpjIUY2vMtJ5e/85IAEiy+sJ2G6tBt5EkYOF48BwQBry22eH+Yw7cudV8mVt5JpAyM0AuFQhETcptZqZJ9y+FNt11BtV7PfkMO72l/8qcvIFbPdQqK4VUXACHS1OXXkaZw68rQefz7PK5DJQDYLmUyQdHobm3MbywFPlkIhi+tmaWs7lERiX7JZqK+/DdPciOdlgAyQxTAybNgwnj/96VwyGYOjjrqaI464A9PMYFkZLCuNZWVoa2tkypT3ABg//o9cccUJWBZYVmn4VadLLhnPG2/sSSAQ4vHHF/Wou1gMkMmcwpYtAcJhn7a2fdmwIYHrRikWo3heBN+P4HmjOeusPJGIz4ABn+WNN+oJBiOEQhFCoSiWFcG2wzz2WJpIBMLhUUQibUQiBtbfTdU0ZQpAuvxufo+adujs/VP1/ju9i/YiIiIiIrK7UqAk0lv5PEY6hZFOl7cU7oEHQTCIkejAWrGs22ed++y0/8A9uBTsxL/5NYJvv9U9BEolyc74Oskf/wSAyKLrCN99R9dlCwFI2JDeaxB2OVDa8t5rvPLWChI2JCImiQEWHdEQyXCIc7KtVDGE1pDLSfMbSQY9kkGXRMAlZeTJUOCGfTuYWj7/mf8eYG1759Xc8gYn7BvtCpS2DhvI+mSeuBVngLUnw60qquwq6p2Grjr3GzCGy4+6ingoRpUVIW7ZxE2bqGnRGN6H9nbIZoMsPfpO8vk0+XyOQiFHPp/FdXOk1oZZ/GeTTMYgHt9EJPIcbV4O389RGt6UI5EYyPLli8hmYdiwZRx//IXlgCdNKFQKekzT5YtffJft2wdRV7eZBx88HMMA2y5tne6883YeeeQAAH7+858zfPhfe/zIN20K8Kc/mQSDPmPHZnCcdgqFMMlkI8ViGNcNk802cNxxBcJh2GOPIbz66ln4fpRAIIJhRDHNCMFghAULGrDtUsiTy/0FxwnjOBEikQjRaIRw2OL66w2uv76zp8+PdvHL2BnWHVDedsZ/32stHyYiIiIiIv8aCpRk9+J5kMmUEgOz9OsdfGltKdjJZDCyGYxMBtJpiqOacA8t9YaxF/+K0HPP7giAUkmMdJri3vuQuPnnADj33EXs/HMxXLfHZbe9sh6/rh6jtZX4nFlkzdK8QKnQjn3juAOIlgOlh1Or2BbbRmKPzgDIIhFu4IhBLXypfM6Lx7Xz62HVJIwCSSNPrhzwDLU8VpfbPDHK4YxyImQaLqbhYgXADMDUOpMqIOhEaBmwjXgoTKMVJmbGiJg2kYCNGavizTcNMhmD6YOPJjh4KCHfxMQkRJCgD4XMKH72sxDZrMGeNYdz67CXKPXcyREIZAkENhEIrOe000zSaYu6ujzz5n0P0yuU8p/yFDd54KsL/otVq04A4MEHv0pd3XsEg6UVshyn1G7lym+xaNH/AWD+/N9z3HF39rjfGzeO4LHHSj9fy3KJRJopFMKk0zW47iBc18HzwkyYUMR1C8RiYV5++ZtABMNwMIwwgUAY0wxz4onjOOmkDOEwxGKLSKcLhEIOtu3gOA6OE2bGjAhnnpkodx47v7yVvH8OpS9+sXM+n2HsOgjqHNo1ZhdtREREREREPrkUKMlHz3VLw7k6h3K98zaB1hbIZDEyaYxsFiObwauto3DMsQCEnnoC6/FHofPzTDkIymXpuOfXYBgE//YS1V+fBuXvG5kMRq7UY6Pt10spTPoMADUnf4FAe1u3kjwDEmedDeVAafMTv6H1yd92C4CSDkTz7/HZ8nf+Et/EillVZG2DvA05yycX8sibHouK7cSp541QK+fdAAGjFOqYRnkLwJQRrfxb+VyPfi1P0C9gGgVCAbANiAZgo7+RVauCZLNg1if59rAMlhEkZFiEAjamAV6xwA9/aJHLGVgNAR49NogZ7Dn3zCVzc7z+SpRMNsKv7jYIBtPsGNZU8otfpPnPu0vjsa64YgOHj/9tj/O8+OIEvv/9UtozZcpmjji8NG9PsRggnw+Tz9vk8w5PP+2RzwfYe+9q3nzzUIpFh2LRplh08DwHz7MZOnQANTUFbBteeeXbWFaOQMAmEHAIBm2CQZuRI0dxww0ZHAei0Xm0tp6Bbds4jo1tO9i2xbhxDuvWJQiHIRj8PLBup796J50EpUQrCFy70zYlnSFhz6GBIiIiIiIi0pMCpd1deV4eI5eFbA4jl8XIZfGdMN6gwQAEX3+N4Po3IZcrhTe5HORyEAiQnfnNUpvXXiX8y9u62pDPl8+ZIXHltfjDR0CxSHzyWHBzUMzhF8p7zyV/1gUUzr4QAPOyb8Crz+AHwQ+CV977Iw6GcqDU8vLDtG+8lbwFeQsKNZAfAG4IjshnMewwG903WH72RjzLoBgy8ELgmQ6+6XOA9Qz7UQqUfnpLDtsyMQIehgEBwyMQgI7EXxi/ziCfN3hqykvs/81S8OMYEDNgTwM2ZzZx550h8nloq9nMlCktO73NF1ydJvGeg2vVcvncnf8obvyVy+zFMXI5uPH2Gpr22d6jzZ+e2JOTvhcB4PTTD+dzMx7FdU0KBZtCwaJQsEmlqlm0qDRma+TIQ9hv0OG4rkU+b+O6FoWChefZbHx7IOk0OI7B44/PxTCCGIYF2BiGhWFYxONHMmNGHseBTGY+q1d/E9O0MM0QphkiFLKJxWq4444MjuPjOP9BLjcV23aIRoPU15c6gzmOz7p1HqaZBBqA/97pPfja12DHqlyzPvj3tivg2WcXbURERERERKRSFCj1UX7Lu7x908m4bg68Ar5XAN/F911io8/BPK40JKfjmhHkg81d4U3nFvEPpOqspwBoXzWPVmtl6TMTPKcU8hhugH0pBUrN7/2GLSfd2vV9AkAQjCDs0fIY9cNHUDTgqUVvYexkmpb2d//Age0Xks0avDDjNYbU92yzru0N+C+TXA6a61/j6Dk7PgsA5RFRXHBxgGzGoVhrcvZpO18i/OrFHmtmR0vhzZ15GsNFih64voHrBXCLAZ5+ZSDnfqXUO2fmBeOoPyRLsWjiuqHyZtG8bTBXfrd05QMO+TKhU7bh5sMUC2EKuQhuwaZYDPG7h0fR0REiFBpBffhqwMT3QxjGju29jYczYoSHbcPvV9zDk06WYNDuCm9M0yYQiDN3bq4c0ixg1arv4jgBHMfvCm7icVi+PFVezr0J234U24ZwuNTGskrLvc+eDaUVxAAu3sVvU+c8PON20aYz4AmVN+g+N4+IiIiIiIj0JwqU+qh0voW3Jr2608+MjS9wAKWRZms/laC6tmebF7Y0U/VEkFwOttQ1c8DeUPS7b2nX54ErS0Or8tUOn/50+bNC93Y/vG8vti2IkM35TP9hefHvvzvXEytH8NSM0lLvx188jL32fhnXDVEshii6FkU3RPPG/Xn82jAAQydO5emjihQLDoV8GLfgUMyHcfMRnlkcw3NDWLFj+Z9Xb8DNxShmo7j5GIYXJ1CMk08MwzSgqgou/U4SywpiWaXVrRwHLMvHsmDatHxpJa7WB/jrk37XhM22Xfp8j6jPzTdnyt+biGVN7Pr8/fs5c8C2E+VAZxaBQM97Xv7JlfcfNIEy7FhOHUpz7WgpdREREREREflkMXzf73fdDDon0O3LfnDVezyz98gewU3Rh9ZHrqFl5XkUiwYN544mOPCl7m2KBvmXTqPwwP2lk33qxzD2F+A63bdsDTx0T6lN/Wtw2M96tnEdgq//O7Y7AMfx8ff9b6yAjRW0sQIOTtDBCYaJBGqJhqJdPWgcx+9aUr3z9Y6QphT4lIKf97fdcez9bTtfmyY77R0l8lF6/6TcIlI5ehZFKk/PoUjl6TmUj0JjY3ynxxUo9VGnTQ3wl8wdmNiEDBvLcAgZDnbQJpbdn5i/J7YNXmwjtgVOyCYccgiHbCKOiWV1D2/+Ppzp7KHT2ZunZ9Cz41gwWOm7IVI5+p+2yCeDnkWRytNzKFJ5eg7lo/BBgVKfH/J2zz33cPvtt9Pc3MzIkSO58MILOeywwypd1kfu1/d5NDbO3sV/LDLl/d9PVqQhVCIiIiIiIiLy4XzgTC99wYoVK1i4cCGzZs1iyZIljB07ljPOOINNmzZVujQRERERERERkd1Wnw6UfvnLX3LKKafwpS99ieHDh3PRRRfR2NjI4sWLK12aiIiIiIiIiMhuq88GSvl8npdeeokJEyZ0Oz5hwgReeOGFClUlIiIiIiIiIrL767NzKLW2tlIsFmloaOh2vL6+nieffHKX362tjWCau8dM0h80OZaIfHz0HIp8MuhZFKk8PYcilafnUD4ufTZQ+jBaW9OVLuFfQjP4i1SenkORTwY9iyKVp+dQpPL0HMpH4YNCyj475K22tpZgMMi2bdu6Hd++fTuNjY0VqkpEREREREREZPfXZwMly7I48MADewxve/LJJxk7dmyFqhIRERERERER2f316SFvM2fO5Dvf+Q5jxoxh3LhxLF68mK1btzJ16tRKlyYiIiIiIiIistvq04HSF77wBVpbW7n55pvZunUro0aN4tZbb2Xw4MGVLk1EREREREREZLfVpwMlgOnTpzN9+vRKlyEiIiIiIiIi0m/02TmURERERERERESkMhQoiYiIiIiIiIhIryhQEhERERERERGRXlGgJCIiIiIiIiIivaJASUREREREREREekWBkoiIiIiIiIiI9IoCJRERERERERER6RUFSiIiIiIiIiIi0isKlEREREREREREpFcUKImIiIiIiIiISK8oUBIRERERERERkV5RoCQiIiIiIiIiIr2iQElERERERERERHpFgZKIiIiIiIiIiPSKAiUREREREREREekVw/d9v9JFiIiIiIiIiIhI36EeSiIiIiIiIiIi0isKlEREREREREREpFcUKImIiIiIiIiISK8oUBIRERERERERkV5RoCQiIiIiIiIiIr2iQElERERERERERHpFgZKIiIiIiIiIiPSKAqU+5plnnmHWrFlMnDiRpqYmHnrooUqXJNLv3HLLLUyZMoVx48Yxfvx4Zs2axWuvvVbpskT6lXvuuYcTTzyRcePGMW7cOL785S+zcuXKSpcl0q/dcsstNDU1cemll1a6FJF+ZdGiRTQ1NXXbJkyYUOmypB8wK12A9E46nWbUqFGcfPLJzJ8/v9LliPRLq1evZtq0aRx00EH4vs8NN9zAzJkzWb58OTU1NZUuT6RfGDhwIPPmzWPo0KF4nseSJUuYPXs2Dz74IPvtt1+lyxPpd9asWcP9999PU1NTpUsR6ZeGDRvG3Xff3fU+GAxWsBrpLxQo9TGTJk1i0qRJACxYsKDC1Yj0T7fffnu391dffTWHHXYYzz//PMcee2yFqhLpXyZPntzt/dy5c1m8eDFr1qxRoCTyMUskEsybN4+FCxdy4403VrockX7JNE0aGxsrXYb0MxryJiLyIaVSKTzPo6qqqtKliPRLxWKR5cuXk06nGTt2bKXLEel3LrroIj7/+c8zfvz4Spci0m9t2LCBo446imOPPZa5c+eyYcOGSpck/YB6KImIfEiXX345+++/v/4hK/Ixe/XVV5k6dSq5XI5IJMJPf/pTDbcR+Zg98MADvPPOO/zoRz+qdCki/daYMWO44oor2HfffWlpaeHmm29m6tSpLFu2jNra2kqXJ7sxBUoiIh/CFVdcwXPPPcfixYs1Vl3kYzZs2DCWLFlCIpHgd7/7HfPnz+fuu+9m1KhRlS5NpF9Yt24d1157Lffeey+hUKjS5Yj0W51TonQ6+OCDmTx5MkuWLGHmzJkVqkr6AwVKIiL/pIULF7JixQruvPNOhgwZUulyRPody7LYZ599ABg9ejQvvvgid9xxBwsXLqxwZSL9w5o1a2htbeWEE07oOlYsFnnmmWe47777WLNmDZZlVbBCkf4pGo0yYsQI3nrrrUqXIrs5BUoiIv+Eyy67jEceeYS77rqL4cOHV7ocEQE8zyOfz1e6DJF+Y/LkyYwePbrbsQULFjB06FDOOuss9VoSqZBcLsf69es58sgjK12K7OYUKPUxqVSKd955Byj9xXnTpk28/PLLVFdXM2jQoApXJ9I/XHLJJSxdupQbb7yRqqoqmpubAYhEIkSj0QpXJ9I/XHPNNRxzzDHssccepFIpli1bxurVq7nlllsqXZpIv1FVVdVjQYpIJEJ1dbWGnop8jK666io+85nPsOeee9LS0sJNN91EOp3mlFNOqXRpsptToNTHrF27lq9+9atd7xctWsSiRYs45ZRTuPLKKytYmUj/ce+99wLw9a9/vdvxb33rW8yZM6cCFYn0P9u2beP888+nubmZeDxOU1MTt912GxMnTqx0aSIiIh+rLVu2cN5559HW1kZtbS2HHHIIDzzwAIMHD650abKbM3zf9ytdhIiIiIiIiIiI9B2BShcgIiIiIiIiIiJ9iwIlERERERERERHpFQVKIiIiIiIiIiLSKwqURERERERERESkVxQoiYiIiIiIiIhIryhQEhERERERERGRXlGgJCIiIiIiIiIivaJASUREREREREREekWBkoiIiIiIiIiI9IoCJREREZEKWLt2LU1NTTz88MNdxxKJBCeeeCLTpk0jl8tVsDoRERGRXTN83/crXYSIiIhIfzR79mzeeOMNVqxYged5nHnmmWzevJn77ruPmpqaSpcnIiIi8oHMShcgIiIi0l/NmTOHk08+mWXLlrFq1SpeffVV7r//foVJIiIi8omnHkoiIiIiFXTuueeycuVKAO666y7GjBlT2YJERERE/gGaQ0lERESkgvbZZx8ymQzTp09XmCQiIiJ9hgIlERERkQpZtmwZt912GwcddBBLly4lm81WuiQRERGRf4gCJREREZEKWL16NRdccAHz5s3jhhtuoK2tjXvvvbfSZYmIiIj8QxQoiYiIiHzM3nzzTWbPns1pp53GN77xDQYNGsSpp57KbbfdRjqdrnR5IiIiIv9fCpREREREPkbNzc2cccYZHHrooXzve9/rOj5r1iwSiQR33XVXBasTERER+cdolTcREREREREREekV9VASEREREREREZFeUaAkIiIiIiIiIiK9okBJRERERERERER6RYGSiIiIiIiIiIj0igIlERERERERERHpFQVKIiIiIiIiIiLSKwqURERERERERESkVxQoiYiIiIiIiIhIryhQEhERERERERGRXvlfwBL6XrsXuvAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = 2\n", "see_upper_bound(t, 2*e)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = e\n", "see_upper_bound(t, 2*e)" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = 2*e\n", "see_upper_bound(t, t, onlylast=True)" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "image/png": 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nyZ2fgdlszlCcKFeunM0lXo7kcHa8OiO/P0NHzwHJufPg5MmTslgsWX5Zz2rsZzbDJCQkRN98841NW3YzTO7cV0pKinbt2qXExMRM11bK6udGVn777TcNGjTIob72cud1tjuPcVpamvbt26e///3vNu2OfF7Zycm5kJuF0rNSrly5PLvRwTfffKOpU6fq22+/tebt1KmTfHx8tGDBAvXq1cvuOZFX7r77bj388MP697//rdTU1EJ1h0EAJQsFJQAoJDK7TbbFYlF6erokqXv37nriiSfs9qtbt26O9pvZjCGz2Wy3PauchUlOc4aGhqpq1arZfpEODQ1VQECAzbo0t9bxiIuLs/uahQsXKj09XSaTybreiT1xcXFyd3fP9kvim2++qa+++kqDBw9WUFCQypYtKxcXF73zzjuZvs/8/vycHU95KSfnyZ2L5169ejXDHZccKU7kVE6OV35/ho6eA7f6Onoe3JrNlFWBIquxb2+GyYwZMxQQEKBRo0Zl6JsZe/kuXbqkxMREjR8/3mY2yO1y+jO2Vq1aNpcoZuVWkeV2eZ3tzmMcEhKiuLg4PfTQQzb9HPm88kN2C1rnVEpKimJjYx3qe2cR+U6rV69Ww4YNMxS/OnXqpPnz5+vgwYP5WlCSpMqVKys1NVUJCQmZ/gEBAPIbBSUAKAL8/PxUunRppaWl5fmt5MuWLWu3AHLlypUcbc/Pz08+Pj46depUlv2cufTNz89PXl5eOnfuXIbnbq2HkleLoIaGhtpc0pNVvzu/MNxaEDYsLMzm1tuStHz5cq1atUqvvPKKPvnkE82bN0+zZs2yu+2wsDCHFvjdvn27Hn/8cb3yyis27bGxsdYvzc7w8/OTp6enzp8/n+E5e2325GQ8XbhwwWYGw62ZRnd+ptn1y4vzJCAgIEPR4s4v1I7kcHS85sf5l9vP0NFz4FZfR8+D0NBQ+fr62l0s/pasxr69GSblypVTQECAU5+3vXy37tJXq1atPP8Z6+/vb3MXPGfldbY7j/EPP/ygmjVrZpjB5sjnlZ38/Nnt7OXTISEhebaGUmRkpM3lgbfcKgQXRAE9LCzMoT88AEB+sv8nLgBAoeLq6qouXbro+++/t65vcjt7d2Jy1F133aXr16/bbPfWHdlywsXFRZ07d9aePXt0+PDhDM/fmkVxa/ZDZrN5bufq6qr27dtr165dunjxorU9JiZGmzZtUmBgYI4vH7pdZGSkIiMjsy3mWCwWnT59WvXr17dpb9y4sTw8PHTkyBGb9u+//14zZ87U008/raFDh2rw4MH69ttvdebMGbvbP3bsmIKCgrLN6+rqmmFWytatWxUeHp7tazPbXrt27bRr1y6bgsa5c+e0b98+h7aRk/G0cuVKm/fxxRdfSFKGGRPZ9cuL88TDw0P333+/zb87Z5M5ksPR8ZrX519uP0NHzwHJ+fPg6tWrqlKlSpbbdHTs54a9fNWqVZPJZNKOHTsy9E9PT1d0dHS+ZspKXme78xjv3r1bDz74YIZ+jnxe2cnPn93O/A6R/jfDzZF/2c3KqlWrlkJDQzP84eTWAuiNGze2tiUlJenMmTM5/j1t73UnTpzQf/7zH91///1277oHAAWFn0AAUEQ8//zz+u9//6t+/frpySefVL169RQbG6sTJ05o586d+uOPP3K03a5du+qDDz7QuHHjNGTIEN24cUNffvlllgs7Z2fSpEn68ccfNWTIEPXr109169ZVZGSkdu7cqblz56p69erWW3bPmjVLPXr0kLu7u9q0aSN/f3+72/znP/+pffv2aeDAgRo4cKA8PDy0bt06Xb9+XS+99FKOct7p1pf6mJgYbd68OcPzderUUWBgoC5evKjExMQMMzNKlSql9u3b68cff9SkSZMkSUePHtXzzz+vLl266J///Kckafjw4VqxYoXmzJmjjz/+2GYbR44cUUxMjHVh6ax07NhRmzZtko+Pj+rVq6fjx49r27ZtuVqDZPz48dq7d68GDRqkAQMGKD09XStXrlSdOnWsl8BkJSfj6a+//tLo0aPVoUMHnThxQuvWrVO7du0yrBfjSL/8Ok+czeHoeM2P8y83n6Gj54Akp84DSapevbr27dunTz/9VJUqVVKtWrVs7lDlzNjPDXv5/P391aNHD3399dcaNWqUOnToIIvForCwMO3cuVOvvvqqOnTokK+5MpOX2e48xpcvX9apU6f08ssvZ+ib3eflqPz62e3s75C8XEPpqaee0t69ezV48GANHjxYFSpU0M8//6zt27erXbt2NgW733//XUOHDtW4ceM0fvx4a/vKlSsVFxdnXWj+l19+UVpamqSbC/2XKVNG0s3j5+npqaCgIPn7++v06dNat26dPDw8sr1rKQDkNwpKAFBE+Pv7a/369Zo/f76+//57rVmzRuXKlVPt2rVz9Z9yX19fzZ07VzNmzND777+v6tWra9KkSbpw4UKOv9BWrFhR69ev1yeffKJvvvlGcXFxqlixotq1a2e9FKtJkyZ67rnntHr1ak2ZMkXp6elasWJFpl8G6tSpoy+//FKzZs3S4sWLZbFYFBgYqLfeekutWrXK8fu/3a0v05s2bdKmTZsyPD916lQFBgZaFyK291fsJ554Qs8884wuXbokd3d3Pf3006pfv75mzpxpvUTD19dXAwYM0NKlS3Xy5EmbGR7btm1TlSpVHPri88orr8jNzU3ffvutEhMTFRgYqMWLF+v999/P0fu/9Z6WLFmid999V7Nnz1blypU1btw4RUREOFRQysl4+vDDD7Vw4UJ9+OGHMplMevLJJ+2OaUf65dd54mwOR8drfpx/ufkMHT0HJDl8HtwqcI4dO1bnz5/XwoULlZCQoOeee86mQOHM2M8te/nefvtt1a9fX5s3b9YHH3wgDw8PVatWTT169FDLli3zPVNW8irbncf4hx9+kLe3t91tZPd5OSq/fnY7+zskL7Vs2VJr167V3LlztX79ekVFRalixYoaPXq0xo0b59A2li5danPjgX379llnEfbs2dNaUOrUqZO2bNmi5cuXKz4+Xr6+vurUqZPGjRuXrzdLAABHmCyFbRVVAACKsPT0dHXv3l0dOnRw+q/HycnJ6tixo0aPHq3hw4fnT8BCZM6cOZo7d6727dungICAXPdD4eHseVDQYz8352lRZe8YjxkzRqVKldLcuXONDQcAKJJYQwkAgDzk4uKiCRMm6Msvv3R4bY9bNmzYIHd3dw0cODCf0gEFw9nzoKDHfm7O06LK3jFu1aqVRowYYWAqAEBRxgwlAABgCGYoAQAAFF3MUAIAAAAAAIBTmKEEAAAAAAAApzBDCQAAAAAAAE6hoAQAAAAAAACnuBkdwAgREdeNjpAnfH29FR2daHQMFBGMFziLMQNnMF7gDMYLnMWYgTMYL3AG4yVrAQFlMn2OGUpFmJubq9ERUIQwXuAsxgycwXiBMxgvcBZjBs5gvMAZjJeco6AEAAAAAAAAp1BQAgAAAAAAgFMoKAEAAAAAAMApFJQAAAAAAADgFApKAAAAAAAAcAoFJQAAAAAAADiFghIAAAAAAACcQkEJAAAAAAAATqGgBAAAAAAAAKdQUAIAAAAAAIBTKCgBAAAAAADAKRSUSoi//a2HVq/+wqYtJOQ39e/fR2az2aFtnDlzWo8//piSkpLyIyIAAAAAACgi3IwOgLzx9tuva9u2rRna77knUJ9+ulyLF6+Ql5eXzXPz53+iYcNGytXV1aF91KlTV40bB2rt2lUaPvypPMkNAAAAAACKHgpKxUjLlq316qvTbdrc3d0lSb6+vjbtf/xxWBcuXFDHjp2c2kfXrj313ntva/Dg4XJzY/gAAAAAAFAScclbMVKqVCn5+1ew+Ve2bDlJGS9527lzu4KDW8nDw1OSZLFY9M9/PqsJE56VxWKRJCUmJqp//96aNWum9XWtW7fR9etxCgn5rQDfGQAAAAAAKEyYYpKN11/30JYtBXuYevRI0+uvJ+frPg4fPmQzO8lkMmnq1Dc0bFh/ffnlFxo4cKg+/vh9ubm5a9y4CdZ+7u7uqlu3vg4dOqhWre7N14wAAAAAAKBwoqBUjPzyy3517tzepq137yf17LP/yND3r7+uqkKFAJu2ChUC9OKLr2ratClKSEjQzp3b9emnn1tnMd3e788/r+T9GwAAAAAAAEUCBaVsvP56cr7PFsorzZoF6YUXXrFp8/EpY7dvcnKySpUqlaH9gQceUufOj+rzz5fo2Wf/oXr16mfo4+HhoeTkonFMAAAAAABA3qOgVIx4enqqevUaDvUtV668rl+/nqE9OTlZx48flaurq8LCLtl9bVxcnKpUqZKrrAAAAAAAoOhiUe4Sqn79Bjp//myG9vnzP1Fqaqo++mievv12i/bt252hz7lzZ1S/fsOCiAkAAAAAAAohCkrFSEpKiq5di7T5Fx0dbbdv69Zt9Pvvh23a9u//UZs3b9Srr76pFi1aauTIMZox4y1duxZp7XP16hVFRISrdes2+fpeAAAAAABA4UVBqRg5cOC/6tXrUZt/I0cOstv3kUe66tKlCzp79owkKTo6Wu++O13Dho1S48aBkqTBg4erZs1aeued6bJYLJKk777boVat2qhyZS55AwAAAACgpDJZblUKSpCIiIxrBxVFAQFlcvVeFiyYo5iYaE2Z8ppD/VNSUtS/f2+9/vrbatq0eY73C2Pkdryg5GHMwBmMFziD8QJnMWbgDMYLnMF4yVpAgP0bfUkGzFCaM2eOGjRoYPOvbdu21uctFovmzJmjdu3aqWnTphoyZIhOnTpls43Y2FhNnjxZwcHBCg4O1uTJkxUXF1fQb6XIGzp0hKpWrSaz2exQ/z//vKqhQ0dSTAIAAAAAIBNnz5q0fbur0THynSF3eatVq5a++OIL62NX1/8d6MWLF2vp0qWaMWOGatWqpXnz5mnEiBHavn27fHx8JEnPPfecrl69qs8++0ySNHXqVL3wwgtauHBhwb6RIq50aR8NGzbK4f533XW37rrr7nxMBAAAAABA0bZ37z909GgNde78nFxdTUbHyTeGrKHk5uamgIAA6z8/Pz9JN2cnrVixQmPGjFGXLl1Uv359zZw5UwkJCdq6dask6cyZM9q7d6+mT5+uoKAgBQUF6Y033tCuXbt09mzGu5YBAAAAAAAUhPDwSAUFfa4HHviuWBeTJIMKSpcuXVK7du3UsWNHTZw4UZcuXZIkhYWFKSIiwuYSOE9PT7Vq1UohISGSpJCQEHl7e6tFixbWPsHBwfL29rb2AQAAAAAAKGgHD+6Qq2u6zObuRkfJdwV+yVvTpk317rvvqnbt2oqKitKCBQvUv39/bd26VREREZKkChUq2LzG399f4eHhkqTIyEj5+fnJZPpfpc9kMsnPz0+RkZFyhK+vt9zcisf1jFktkAXcifECZzFm4AzGC5zBeIGzGDNwBuMFzsjL8ZKS8q0kqW3bvxX7cVjgBaUHH3zQ5nGzZs3UqVMnbdq0Sc2aNSuQDNHRiQWyn/zGavRwBuMFzmLMwBmMFziD8QJnMWbgDMYLnJGX4yU+Pl41avxbly83VuPGlYvFOCxUd3m7U+nSpVW3bl2dP39eAQEBkpRhptG1a9ess5YqVKigqKgoWSwW6/MWi0VRUVEZZjYBAAAAAAAUhJ9+itDZs00UH9/D6CgFwvCCUnJyss6dO6eAgABVr15dAQEB+umnn2yeP3DggIKCgiRJQUFBSkxMtFkvKSQkRImJidY+AAAAAAAABWnLlkZ65plfVbPmy0ZHKRAFfsnbzJkz1aFDB1WpUkVRUVGaP3++EhMT1bt3b5lMJg0dOlSLFi1S7dq1VbNmTS1YsEDe3t7q3v3mglZ16tRR+/btNW3aNE2fPl2SNG3aNHXo0EG1a9cu6LcDAAAAAABKuLQ0aedOV1WunK7mzY1OUzAKvKD0559/atKkSYqJiZGvr6+aN2+udevWqVq1apKk0aNHKzk5WdOnT1dsbKyaNWumpUuXysfHx7qNWbNm6c0339SoUaMkSR07dtRrr71W0G8FJdzly2E6d+6M2rV7MPvOAAAAAIBi67ffftXQoRskjZGLSx2j4xQIk+X2xYhKiOKwMJbEYnNG++qrdUpMTNSQIcOBMDsiAAAgAElEQVSNjuIQxgucxZiBMxgvcAbjBc5izMAZjBc4I6/Gy7/+9ZLq15+v6OitatfugTxIVjgU6kW5gZx65pmROnr0iCTp3Xena+3aVQW275CQ3/TZZwv1zTebNWLEQCUlJRXYvgEAAAAAhUd6ukX+/lsUH19eLVveZ3ScAkNBqQSZNWumpkx53vo4Li5OPXo8osuXw7J83dSpL+rLL1fmWy5Hc9xp2LCntHLlcq1Zs1IuLi7q129QPiXMKCgoWHXq1NVHH83TsmWr5eXllS/HKT09Xe+997a6dn1Y7dq11MGDB/J0+wAAAACA3Dly5A/5+19SWFhXeXq6Gx2nwBT4GkrIPxMmPKPffvs1Q3ubNvfrgw9ma/ToZ+Tm9r+P/Isvlum++9qqWrXqNv3nzftEZ86c0ocfzpUkjRgxWuPGjVGPHo/brGWVVzLLkZ02be7Xp5/O1/79P2rWrDl5nis7f/31l6pUqWp9nN1xev/9d1SqlIcmTHhOUsbjbM/+/T/q22+3aM6cRapatZrKli2XZ/nHjRuj2rXraNKkF/Nsm/aYzWYtXfqp/v3vbbp2LVL+/hXUufOjGjlyjM14vNOhQwf15ZdfKDT0hCIjI/Tyy9PUtavt7TeXLFmkZcsW27T5+fnr66935Mt7AQAAAIA7nT79jRo0kHx9uxsdpUBRUCpGQkNPaMyYZ9WtW0+bdk9PT0lS2bJlrW03btzQli2bNHPmRxm2c/z4UTVrFmR9XKdOXVWtWk07dnyrJ57om22Ot99+XZUrV9GoUWOz7ZtVjuwcP35U16/HqXLlKlkWJvJDePhfqlChgk1bVsfJYrFo3749mjbtLWvbncfZnsuXL8nfv4KaNGmW46ypqalydzeuSr5q1efauHG9XnnlddWpU1dnzpzSW2+9rlKlSmn48KcyfV1SUqJq166rRx/tprfempZpv7vuultz5iyyPnZxcc3D9AAAAACQNR+fr5WS4qFWrR4yOkqBoqBUTFy+HKb4+Otq3ryF/P0rZHg+PPwv9enTTatWbdDdd9fU/v37ZDKZ1LTp/woVqamp6ty5vdLS0nTo0EF9/vkS1axZSytXrle7dg/ou+92OFRQcoa9HJIUERGuhQvnav/+H5WeblZwcCs999xL8vPztz4/Y8Zb+uSTBZo69QWdPXtatWvXzdNsWWX488+rdo9zZsfp+PGjSk1NVdOmzbM8zrd7++3XtW3b1v/fbktVrlxFGzZsUUpKihYsmKPvvtuhhIR41a1bX3//+z/VrNnNe1OOGzdGNWvWkqenl7Zv36rKlavqs89WZNj2oUMHdejQQW3ceHO/69d/bTPjKq8cOfK72rZtb12YrkqVqmrX7gEdO3Yky9fdd1873XdfO0nSO++8kWk/V1dXu58FAAAAAOS3kyfT9MsvHVS79v0KCsr7K3oKM9ZQKiZOnDguV1dX1a/f0O7zp0+fkqenp2rUuEuSdPjwITVo0FAmk8nax9XVVQsXLpMkffrpcm3evF3z5y+RJDVq1FjHjx9VcvKNPM1tL8eVK5c1cuRgBQRU1Pz5n2nOnEWKjY3V+++/K0lKTr6hV199SRMnTlbVqtU0ePAILV++JE9zZZehdu26unLlsoYO7adz585aX5fZcdq7d7fuu6+t3NzcsjzOt5sw4XmNGDFaFStW0ubN27V48c2i0Pz5s/Wf//xbU6a8pqVLV6lOnbp6/vnxioyMtL52x45tslgsmjfvM02dmrEYM2HC8woMbKquXXto8+bt2rx5uypWrGT3WKxYsVSdO7fP8t/hwyGZHssmTZrr4MEDunDhvCTp3LmzOnjwgNq0aZvpa5xx5cpl9er1qJ58sqemTZvi9FpcAAAAAJBT27Z5a86cOXJ3/8ToKAWOGUoOOHky0G67v/8/5O8/RpIUFjZaiYn7M/Tx8mqpGjWWS5KiopYrMvIDu9uqW/egXFxKKTn5pDw86judMTT0uMxms3r06GzTfu+99+utt2bq1KlQ1a5dVy4uN2uIf/11VRUqBNj0dXFx0bVrkfL2Lq1GjRrbFHkqVAhQWlqaIiMjnV7rKCv2cnzwwbvq3r2Xxo79u7Vt2LBReuWVFyRJHh6eWrhwqfW5jh07qWPHTnmWyZEMPj4+Wro04wLcmR2nvXt3a/TopyVlfZxv5+PjIy8vb7m4uFhn4CQlJWnTpg168cWpuv/+m7N3nn9+in777Vdt3LhOY8Y8K0mqWrWqxo+fmOn78/HxkZubmzw9PbOd3fP440+oY8fOWfYJCAjI9LnBg4cpMTFBgwc/KRcXF5nNZg0dOlJ9+jyZ5TYdcc89gXr55dd19901FR0dpc8/X6JnnhmlL75Yq3Llyud6+wAAAACQlW++cZObm0WPPJJmdJQCR0GpmDh58oQeeqijnn56vE176dI3p9ydPn1K9er9r1CVnJwsX1+/DNs5dSpUdevWy1Dk8PDw+P/XZZyhtGLFUn3xxTLr45SUFJlMJq1Z87+CywcfzLa7XtCdOf7886r++9+fdfhwiDZsWGNtN5vTrWtBOerTT+drxYqlWfaZPXuhWrRoadOWmwz2jlNY2CVduXJZrVv/7/aRmR3n7Fy+HKa0tDQ1bdrc2ubq6qrAwKY6f/6cta1Bg0ZObTcrZcuWy9Vi4N9//2/t2PGtpk17S7Vq1dGpU6H65JNZqlq1qrp3fzxX2e67z3aWU+PGTdS3by9t27ZV/fsPztW2AQAAACArFy9e0LPPDtHhw8+rfPme2b+gmKGg5ID69bNe60WSqldfnG0fP7/h8vMbnmWfnMxOkqSTJ0M1bNhIVa9ew+7zp06dVP/+A62Py5Urr+vXr9vpF6r69RtkaI+Li5MklS/vm+G5O2ewLFgwWwEBFfW3v/W3tmU2g+XOHKdPn1Tp0qW1ZEnG2T9ubs4tLN2370B16dI1yz6VKlXO0JabDPaO0549P6hly1by8vKytmV2nHPj9tqUs8W3rNxZMLQns4KhdPMSvf79B6tTpy6Sbi5e/uefV/XFF8tzXVC6k7e3t2rVqq2wsEt5ul0AAAAAuNPvv29VvXqH5O4ea3QUQ1BQKgauXLmsuLhY1atnv0CRlJSkK1fCVLfu/56vV6+Btm3bkqHv6dOn7K5tc+7caQUEVLQuin27O2eweHuXVpkyZTMtbt3uzhyurm66ceOG/Pz85e3tne3rs1K+fHmVL+/8ZU+5yWDvOO3bt1uPPWZ7+8jMjnN2qlWrLnd3d/3++yHrJXVms1lHjvyuzp0fdWpb7u7uSk9Pz7Zfbi95u3HjhlxdbZdrc3V1VXq6xbGgTkhOTtbFi+czzDoDAAAAgLzm4rJZZrOLWrR4zOgohmBR7mIgNPS4JMnfv4KuXYu0+ZeWlqYzZ05JkurWrWd9zb333qcLF84rNjbGZltms1kXLpxXZGSEzcyhw4cPqXXrNnme/c4cjRs3UZkyZfTmm6/p5MkTunw5TL/++rNmzZrpUPEjL+Qmw53HKTo6WkeP/qG2bdvb9MvsOGfHy8tLjz/+Ny1cOEf79+/T+fPn9MEHMxQdHaXevZ1bk6hy5ao6duyorl69opiYmEzfW9my5VS9eo0s/3l4ZD4jqm3b9lq58nP99NM+Xb16Rbt379Latav0wAMPWft89dVaDRz4hM3rEhMTdepUqE6dClV6err++utPnToVqj///NPaZ+7cjxUS8puuXLmso0eP6NVXX1RS0o0MBTwAAAAAyEtXr17V3Xf/rPPn26tKlZJ512lmKBUDoaEnJEmDBv3Npt1kMunbb/+j06dPqnr1GjaXQdWpU1eNGjXWd9/92+YW92PGPKsFC+Zo7dpV6tWrj55/foqSk5O1Z88uzZo1N8+z35mjbNmy+uCD2Zo/f7b+8Y+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = 3*e\n", "see_upper_bound(t, t, onlylast=True)" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "image/png": 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Xq1at1KpVK73xxhvatGmTTpw4IUn6/vvvlZKSopkzZ6phw4bq0aOHRo4cqaVLlzLbCQAAAACAcubatX4aMWKfYmOfkKen0WnKB8OKTtOmTVP37t3Vvn17i/bIyEhFR0erY8eO5jY3Nze1bdtWYWFhkqSwsDB5eHiodevW5j5t2rSRh4eHuc/evXsVFBQkNzc3c5/g4GBFRUUpMjKyKJ8aAAAAAAAoYTZtctaJE811112+RkcpNwxZSHzlypU6c+aM3n///RzboqOjJUl+fn4W7b6+voqKipIkxcTEyMfHRw43rPrl4OAgHx8fxcTEmPtUq1bN4hjZx4yJiVGtWrVyzVelioecnZ0K8cwA2/j7c/8wYCvGC2AbxgpgO8YLYJuyNFaSk8N1+PBVSa3Ur5+b/P3d8t0Ht67Yi04nTpzQBx98oK+++kouLi7F/fA2iYtLNjoCyjB//0qKjk40OgZQKjBeANswVgDbMV4A25S1sRIZOVP9+y/V0aNbVKVKC/13vgvsIK/iZLEXnfbu3au4uDj17t3b3JaZmaldu3ZpxYoV5nWbYmJiVKNGDXOfy5cvm2cq+fn5KTY2ViaTyTzbyWQyKTY21qLP5cuXLR47exbUzbOoAAAAAABA2WQyZSku7iclJvqqTp02cnBgEfHiUuxrOnXt2lXr1q3T2rVrzV+BgYF64IEHtHbtWtWpU0f+/v7avn27eZ/U1FTt3r1brVq1kiS1atVKycnJ5vWbpOvrPCUnJ5v7tGzZUrt371Zqaqq5z/bt21W1alUFBAQU07MFAAAAAABGSknZI0fHiwoN7a2uXflgseJU7EUnLy8vNWzY0OLLw8ND3t7eatiwoRwcHDR06FAtXrxYv/zyiyIiIjRp0iR5eHiYZ0fVq1dPnTp10muvvaawsDCFhYXptddeU+fOnVW3bl1JUp8+feTu7q5JkyYpIiJCv/zyixYtWqRhw4ZZrAUFAAAAAADKrsTEHyVJu3Y9qA4dMg1OU74YspB4fkaOHKnU1FRNnz5d8fHxatGihUJCQuR5w2cazp49W2+++aZGjBghSerSpYteffVV8/ZKlSopJCRE06dPV9++feXt7a3hw4dr2LBhxf58AAAAAACAMWJjf1Jamqvc3LrI3d3oNOWLg8lkYm7ZTcrSYmkoecragnxAUWK8ALZhrAC2Y7wAtikrYyUj47IOHmyh3buD5eCwRsOHpxsdqcwpUQuJAwAAAAAAFAdnZ1/Nnn1Bu3Zd0YYNLCBe3Ip9TScAAAAAAIDicO2atHmzu/z8qun227nRq7hRdAIAAAAAAGVOZuYV7dmzRBUrntd997GAuBEoOgEAAAAAgDInKelXeXuPU48eS9WjB7fWGYGiEwAAAAAAKHMSEn6QJB082FtBQcx0MgJFJwAAAAAAUKaYTOmKj/9VFy/+Q/Xr3yFnPkbNEBSdAAAAAABAmXL16hY5OMRr+/YH1aMHs5yMQtEJAAAAAACUKQkJ6yRJ27c/onvvZT0no1B0AgAAAAAAZUpSUoIuX75NXl4dVKmS0WnKL4pOAAAAAACgTNm2bZkGDjyp++83Okn5RtEJAAAAAACUKRs2OCs93U3338+tdUai6AQAAAAAAMoEk8mkM2cmKi3tZzVtmqlatUxGRyrX+NBAAAAAAABQJly7tk+JiZ/onnsSlZLSzeg45R4znQAAAAAAQJmQkPC9JGnLlkfVvTu31hmNohMAAAAAACgTEhLWKTXVTadO3a8WLbKMjlPuUXQCAAAAAAClXmpquNLSwrVzZw/dc4+rHKl4GI6XAAAAAAAAlHoJCeskcWtdSULRCQAAAAAAlHpOTr6KjGymvXsfUKdOmUbHgSg6AQAAAACAMuDKleEaMmS/Wrf2kru70WkgUXQCAAAAAABlwI8/OkuSevZMNzgJslF0AgAAAAAApVpk5D8lTZOjY5buv59b60oKik4AAAAAAKDUSk+/pPj4VfLx2aEOHbLk52cyOhL+i6ITAAAAAAAotRITv5dk0pYtj6pXLz61riSh6AQAAAAAAEqt+PhvZTI5aPPm/2fvzuOjqrUnOVwAACAASURBVO/9j7/PbJlMEgJZCEsCsojlXmVV6wJVaBW1Yt1FQSq4Qd2LIJQKAipu6FWwyq6gyCZSxd5K73X50VIXbFwqFhRkCSDJZE9mMts5vz+4pk3ZAiRzJsnr+Vc95ztnPnngFx959/P9nGt08cWETomE0AkAAAAAADRJkcg+BQIb9eWXA9SxYzvl5nK0LpEQOgEAAAAAgCapouL3kiy99961HK1LQIROAAAAAACgSUpO7qe//32kPvjgakKnBOSyuwAAAAAAAIDjc6YeeGCwOnQw1aNHwO5i8G/odAIAAAAAAE2OaYb1/vsuBQKGLrkkKsOwuyL8OzqdAAAAAABAk7Njx8/lciXJ4fhfjtYlKDqdAAAAAABAkxIO71Yw+JH8frdychzq08e0uyQcAqETAAAAAABoUioq1kqS/ud/rtXFF0flIN1ISPyxAAAAAACAJqWiYo1M06kNG67gaF0CI3QCAAAAAABNRji8Q8Hgp/r73wfJ4cjS2WfH7C4Jh0HoBAAAAAAAmowfjta9884wXXhhVG63zQXhsAidAAAAAABAk9G69Y3atOl3+vOfL9ell0bsLgdH4LK7AAAAAAAAgPpyOjP13HO3y7IMnX9+ld3l4AjodAIAAAAAAE1CKLRF+fk12r3boSFDokpKsrsiHAmdTgAAAAAAIOFZlqVdu26QZZXL6SzQZZdxtC7R0ekEAAAAAAASXk3N5wqHv9Hnn5+n5GSXzj+ft9YlOkInAAAAAACQ8MrLV0qS3npruIYMicrrtbkgHBWhEwAAAAAASGiWFVN5+WqFw2300UcX67LLonaXhHogdAIAAAAAAAmtuvrPika/11/+crW8XrcGDSJ0agoInQAAAAAAQEKrrv5AkvT73w/XhRdytK6pIHQCAAAAAAAJLSdniv7nfzbpiy8GauhQupyaCkInAAAAAACQ0CxLeuWVvvL5DA0eTOjUVBA6AQAAAACAhFVa+oq+/DJfO3cauvDCqJKT7a4I9eWyuwAAAAAAAIBDicXKtW/ffaqu7irpK47WNTF0OgEAAAAAgIRUUfGmLCuk9euHy+eTfvpTQqemhNAJAAAAAAAkpPLyVZKk11+/gaN1TRChEwAAAAAASDiRyD5VV38gv/9sff99F/3iF3Q5NTWETgAAAAAAIOGUl6+UZGnduuFKS7M4WtcEEToBAAAAAICEY1kRmWZbrVlzvS65JCqv1+6KcKwInQAAAAAAQMLJzr5fy5btUGVlhq64ImJ3OTgOhE4AAAAAACDhRKPS73+fpKwsUz/5SczucnAcCJ0AAAAAAEDCMM2Qduz4hT75ZIX8foeGDo3K5bK7KhwPQicAAAAAAJAwqqreUXX1e9qx4ytJ0hVXMEC8qSJ0AgAAAAAACaOsbJkkacGCm9Shg6kzz+RoXVNF6AQAAAAAABJCNFqkysr1CoV668sve+vyy6NykFw0WfzRAQAAAACAhFBevlJSVB9+OFKSdOWVvLWuKSN0AgAAAAAACaGs7DVJLr3wwgh17WrqtNNMu0vCCSB0AgAAAAAAtrMsUxkZY+X3j9f+/W11xRURGYbdVeFE8NJBAAAAAABgO8NwqE2b4Zo/P1mSdOWVvLWuqaPTCQAAAAAA2MqyoorFKlRaKr33nlOnnhrTySdztK6pI3QCAAAAAAC2qqr6k7ZsOVl/+csKRSKGLr+cLqfmgNAJAAAAAADYqrT0ZVlWUG+91VuGYenqq3lrXXNA6AQAAAAAAGwTiexTZeU7cjj66o03ztCAATF16GDZXRYaAKETAAAAAACwTVnZMkkxffnlaEnSNdfQ5dRcEDoBAAAAAABbWJapsrIlMoxkvfDCcCUnW/r5z5nn1FwQOgEAAAAAAFvU1OQrHP5O0eiV+uqrNrrooqjS0uyuCg3FZXcBAAAAAACgZUpO7q/u3Tdp1iyvJI7WNTeETgAAAAAAwDYORw8tXZqirCxT558fs7scNCCO1wEAAAAAgLirqnpPgcCHevddh4qLHbryyqhctMY0K/xxAgAAAACAuLIsS99//xuFw1u1bt0OSSkcrWuG6HQCAAAAAABxFQx+qlDoK3m9P9fate118skx9epl2l0WGhihEwAAAAAAiKuysiWSpC+/HK1QyNA110RlGDYXhQZH6AQAAAAAAOImFqtSeflqud15eumlCyVJV13F0brmiNAJAAAAAADETUXF6zLNKhnGCP3lL0k655yo8vIsu8tCIyB0AgAAAAAAcWNZYblcbfXOOzdLkq65JmpzRWgsvL0OAAAAAADETUbGrUpPH6URI9Ll81n6xS84Wtdc0ekEAAAAAADi6qOPkrRzp0OXXhpVaqrd1aCxEDoBAAAAAIBGF42WaNu2ASorW6HXXnNLkq6/ni6n5ozQCQAAAAAANLqysmWqqflCgUCh3nrLpU6dTJ19dszustCICJ0AAAAAAECjsixTpaULZRhJ2rBhpAIBQ8OGReQglWjW+OMFAAAAAACNqrr6A4XD29Sq1ZV65ZV2MgxL113H0brmjtAJAAAAAAA0qpKShZKkYPAWffSRSwMGxJSXZ9lcFRoboRMAAAAAAGg0kcheVVa+La+3l1auPEcSA8RbCpfdBQAAAAAAgObL5cpWbu4iSclaudKjtDRLl1wStbssxEHcO51effVVDR06VP369VO/fv103XXX6f3336+9b1mWZs+erQEDBqhXr1668cYb9c0339R5Rnl5ucaPH6/+/furf//+Gj9+vCoqKuqs2bJli0aMGKFevXpp4MCBmjNnjiyL1j0AAAAAAOLJMNxKT79Cn376c+3b59Dll0fk89ldFeIh7qFTTk6O7r//fr3xxht6/fXXddZZZ+mOO+7QP/7xD0nS/PnztWjRIj344INavXq1MjIyNGrUKFVVVdU+Y9y4cdq8ebMWLFigBQsWaPPmzZowYULt/aqqKo0ePVqZmZlavXq1Jk+erIULF2rx4sXx/nEBAAAAAGixQqEtikb9kqTXXnNL4mhdSxL30OlnP/uZzjvvPHXu3FldunTRfffdp5SUFH322WeyLEtLlizRbbfdpiFDhqhHjx56/PHHVV1drXXr1kmStm3bpg0bNmj69Onq27ev+vbtq2nTpum9997T9u3bJUlvvvmmgsGgHn/8cfXo0UMXXXSRbr31Vi1evJhuJwAAAAAA4mTv3nu1det/yO8v0n//t0snnxxT//6m3WUhTmwdJB6LxfT2228rEAiob9++KigoUFFRkc4999zaNV6vV2eccYby8/MlSfn5+fL5fOrXr1/tmv79+8vn89Wu+eyzz3T66afL6/XWrhkwYIAKCwtVUFAQp58OAAAAAICWKxj8QoHAX5SScq7Wru2gcNjQsGFRGYbdlSFebBkkvmXLFg0bNkyhUEg+n09z5szRKaecor/97W+SpKysrDrrMzMzVVhYKEny+/3KyMiQ8S//lhqGoYyMDPn9/to1OTk5dZ7xwzP9fr/y8vKOWF+bNj65XM4T+yGBI8jOTrO7BKDJYL8A9cNeAeqP/QLUz4nulX/8Y6Ek6aSTfq3XXvPK5ZLuuCNJ2dlJDVEemgBbQqcuXbpo7dq1qqys1DvvvKMHHnhAS5cutaOUQyotDdhdApqx7Ow0FRVV2l0G0CSwX4D6Ya8A9cd+AernRPdKNOrX/v3L5PF00yefDNSXX0pDh0bkcNSoqKgBC4XtjhRO2nK8zuPxqHPnzjr11FM1btw49ezZUy+99JKys7MlqbZj6QfFxcW1nUpZWVkqKSmpM5vJsiyVlJTUWVNcXFznGT8889+7qAAAAAAAQMMqLV0sywopI+N2vfLKgc6mESMYIN7S2DrT6QemaSocDis3N1fZ2dnauHFj7b1QKKRNmzapb9++kqS+ffsqEAjUzm+SDsx5+mEulCT16dNHmzZtUigUql2zceNGtW3bVrm5uXH6qQAAAAAAaJnC4Z1yONLlct2gtWvd6tTJ1HnnxewuC3EW99Dpqaee0qZNm1RQUKAtW7Zo1qxZ+vjjjzV06FAZhqGRI0dq/vz5Wr9+vbZu3aqJEyfK5/Pp0ksvlSR169ZNAwcO1NSpU5Wfn6/8/HxNnTpVgwYNUteuXSVJQ4cOVXJysiZOnKitW7dq/fr1mjdvnkaNGlVnFhQAAAAAAGh4HTvOUY8eX+iNNzIVCBgaPjwiR0K0vSCe4j7Tye/3a/z48SoqKlJaWppOOeUUzZ8/XwMHDpQk3XrrrQqFQpo+fbrKy8vVu3dvLVq0SKmpqbXPmDVrlmbMmKGbb75ZkjR48GBNmTKl9n5aWpoWLVqk6dOn66qrrlJ6erpGjx6tUaNGxfeHBQAAAACghXI62+iVV9xyOi1dfz1H61oiw/rX4UiQJAYLolExvBKoP/YLUD/sFaD+2C9A/RzvXgkGP1VR0TPKzp6grVv76IILUnTRRREtWVLTCFUiESTcIHEAAAAAAND8FBe/qMrKNxWL+bV0qVuSNHIkXU4tFaETAAAAAAA4YZHIflVUrFFS0imyrEFas8atjh1NDRrEAPGWitAJAAAAAACcsJKSebKsiDIyxujNNz2qqjJ0ww0ROZ12Vwa7EDoBAAAAAIATYprVKi1dIKczU61bX69XXnHL4bB0ww0crWvJCJ0AAAAAAMAJKS19VbFYqTIybtHXX6fq00+dGjw4po4deXdZS+ayuwAAAAAAANC0tWp1maLR75WRcZuefPLAAPEbb6TLqaUjdAIAAAAAACfE7W6nnJwpqqyUVq1yKzfX1IUXRu0uCzbjeB0AAAAAADgulmWpquoDWZYpSVq50q1AwNDIkQwQB6ETAAAAAAA4TsHgR9q5c6j27Rsny5Jeesktt5sB4jiA0AkAAAAAABwXv/9ZSVJ6+jX661+d2rLFqaFDo2rblgHiIHQCAAAAAADHIRT6RpWVf1By8uny+c7W4sUHBojfdBNdTjiA0AkAAAAAAByz4uLnJVnKzLxbhYUOvf22Sz17xvTjH8fsLg0JgtAJAAAAAAAck2i0SGVly+R2n6RWrYbqlVfcikYNjRoVkWHYXR0SBaETAAAAAAA4JuHwDrlc2crM/JViMaeWLHErNdXS1VdztA7/5LK7AAAAAAAA0LT4fGfo5JM/k2WZ+sMfXNq3z6HRo8NKTbW7MiQSQicAAAAAAFBvlmXJMAwZhluGIQaI47A4XgcAAAAAAOrFNIPatu1sFRf/TpL07beGNmxw6ZxzovrRj0ybq0OiIXQCAAAAAAD1Ulb2ikKhzYpG/ZKkBQs8kqRRo+hywsGOGjpVVVXFow4AAAAAAJDALCsiv/9ZGUayMjPHqrxcWr7crQ4dTF1ySdTu8pCAjho6DRkyRKtWrZJlWfGoBwAAAAAAJKDy8lWKRHapTZtfyuXK1muvuRUIGBo9OiK32+7qkIiOGjrddNNNeuyxx3TFFVfok08+iUdNAAAAAAAggViWqaKipyW5lJl5l2KxA0frkpMtjRgRtrs8JKijhk633nqr/vjHP6pnz54aOXKk7r77bu3ZsycetQEAAAAAgARQXf2ewuGtat16mDyePK1f79KuXQ5dfXVEGRl2V4dEVa9B4tnZ2Zo5c6ZWrFih/fv365JLLtEzzzyjQCDQ2PUBAAAAAACbpaQMVufOv1d29v2SpPnzD5ynu+UWBojj8I7p7XW9evXSihUrNH36dL3xxhsaMmSI3njjjcaqDQAAAAAAJADDMJSaOkgeT1d99ZVDf/6zSwMHRtWzp2l3aUhg9Q6dSkpK9P777+u5557TW2+9pZqaGhUVFWnSpEm6+uqrtXnz5sasEwAAAAAAxJllWSoqekrh8M7aawsWHOhyuu02ZjnhyFxHW3Dvvffqiy++0L59+2RZlnJyctSnTx+NHTtWffr0UZs2bTR79mxde+21evLJJ3XxxRfHo24AAAAAANDIqqvfVWHhdAWDn6lTp1dUXGzo9dfdOukkUxdcELO7PCS4o4ZO+/bt0wUXXKA+ffqob9++ateu3UFrZs2apU6dOmnWrFmETgAAAAAANAOWZamwcKYkKTt7vCRp6VK3amoM3XJLSI5jGtiDluioodOKFSvq9aBBgwbpxRdfPOGCAAAAAACA/aqr31Uw+LHS0i5VcnJvRSLS4sVupaZauv56Bojj6BoslzzllFMInQAAAAAAaAbqdjk9IElat86lffscuv76iNLS7KwOTUWDhU5JSUk677zzGupxAAAAAADAJqWlf6rT5WRZ0u9+55FhWLrlFgaIo36OerwOAAAAAAC0LF5vV6WnX6fMzDslSX/9q1Off+7UpZdG1KWLZXN1aCoInQAAAAAAQB0+X3fl5s6v/efnn/dIkn71K7qcUH/MmgcAAAAAAJIOzHIKBj+rc23LFof+9CeXzjwzqtNPN22qDE0RoRMAAAAAAJAkVVX9j7Zv/4l27JhWe+3FF92SpF/9ijfW4dgQOgEAAAAAAFmWqcLCGZKkrKzLJUn79xtatcqtrl1NDRkStbM8NEGETgAAAAAAQBUVb6qm5jO1anWVUlN7S5IWLXIrHDY0ZkxYTqfNBaLJIXQCAAAAAKCFs6yoCgsfluRU27aTJUnV1dLixR5lZpq69lqO1uHYEToBAAAAANDClZUtVzi8VW3ajFRSUndJ0vLlbpWVGbrppoh8PpsLRJNE6AQAAAAAQAtnmgE5ndnKzp4gSYrFpBde8CgpydLo0XQ54fgQOgEAAAAA0MJlZt6mHj02y+3uKElas0batcuha6+NKDvbsrk6NFWETgAAAAAAtFCmWSPLOtDJ5HAkSZIsS5o5UzIMS2PHhu0sD00coRMAAAAAAC1UcfFsffvtGaqp+ar22nvvOZWfLw0dGlX37nQ54fi57C4AAAAAAADEXzRaIr//ORmGS253p9rrzz3nkSTdcw9dTjgxdDoBAAAAANAC+f1PyzTLlZU1Tk5nmiTpk08c2rjRpSFDpNNOM22uEE0doRMAAAAAAC1MOLxTJSUvyu3upIyMW2qvP/fcgblOkybZVRmaE0InAAAAAABamMLCabKssNq2nSKHwytJ2rzZoXfecemMM2L6yU9sLhDNAqETAAAAAAAtSCxWpWDwc3m9fZWefnXt9X/OcgrJMOyqDs0Jg8QBAAAAAGhBnM5Ude/+oaLR/TKMA70oO3YYWrvWpZ49Y7rggpjNFaK5oNMJAAAAAIAWwrIODAc3DLfc7tza688/75FpGrr77jBdTmgwhE4AAAAAALQAlhXR9u2DVFT0VJ3r+/cbWr7crc6dTf3iF1GbqkNzROgEAAAAAEALUFr6smpq8hWJ7Klz/Xe/8ygUMnTnnWG5GMKDBkToBAAAAABAMxeLVaiw8FE5HKlq23ZS7fWiIkMvveRWhw6mhg2L2FghmiNCJwAAAAAAmjm//2nFYn5lZd0rl6tt7fUXXnArGDR0111hJSXZWCCaJUInAAAAAACasXB4u4qL58jtzlVm5p2114uLDS1a5FG7dqaGD6fLCQ2P0AkAAAAAgGasvPz3sqywcnJmyOHw1V5/4QW3AoEDXU5er40FotliRBgAAAAAAM1YdvZ9Skk5R8nJZ9ZeKymRFi70qG1bUyNG0OWExkGnEwAAAAAAzZBlWbX/2+f7sQzDqP3nuXM9qq4+8Ma65GQ7qkNLQOgEAAAAAEAzVFIyT7t336RI5Ps610tLpfnzPcrONjVyJF1OaDwcrwMAAAAAoJmJRotVWPiIJEuGUfdX/7lzPaqqMnT//SH5fIf+PNAQ6HQCAAAAAKCZKSx8WKZZprZtJ8rlyqq9Xl5+oMspK8vUL39JlxMaF6ETAAAAAADNSE3NlyotXSyPp4cyMm6rc2/uXI8qKw2NHRtRSopNBaLFIHQCAAAAAKCZsCxTe/f+WpKp9u0fk2G4a++VlEgvvnigy2nUqLB9RaLFIHQCAAAAAKCZCIU2q6bmc6WlXabU1J/VuTdnzoFZTvfcE1Zqqk0FokVhkDgAAAAAAM2E13uqunf/WIbhqXN9/35DCxd61L49s5wQP4ROAAAAAAA0A5ZlyjAc8nhOOujes896FAwamj49JK83/rWhZeJ4HQAAAAAATVwg8LG2bTtXgcDHB90rKDC0ZIlbnTubuuEGupwQP4ROAAAAAAA0YZYV1b594xQKfSXLih50/+mnPQqHDY0fH5LbfYgHAI2E0AkAAAAAgCaspGSBamo+V+vWNygl5Zw697ZvN/Taa2716BHTVVcdHEgBjYnQCQAAAACAJioS+V6FhQ/L4WitnJwZB91/8skkxWKGHnggLKfThgLRojFIHAAAAACAJur77yfKNCvUvv0zcrmy69z7xz8cWrPGpVNPjennP6fLCfFHpxMAAAAAAE1QNFqiYPBvSk4+U23a3HTQ/Ucf9ciyDE2aFJKD3/5hAzqdAAAAAABoglyuDHXv/lfFYqUyjLpn5z780Kk//tGts86K6mc/i9lUIVo6QicAAAAAAJqYWKxCTmcrORwpcjhS6tyzLGn69CRJ0oMPhmQYdlQIcLwOAAAAAIAmJRD4UFu3/qfKy9cc8v4f/uDSpk1O/fznEZ1xhhnn6oB/InQCAAAAAKCJMM2Q9uy5U6ZZIbe740H3o1HpkUc8cjotTZ4csqFC4J8InQAAAAAAaCL8/lkKh7cqI+NW+Xw/Puj+smVuffutU8OHR9S9u2VDhcA/EToBAAAAANAE1NR8Lb9/llyujmrbdupB96urpSef9MjnszR+fNiGCoG6CJ0AAAAAAEhwlhXV3r1jZVkRdejwtJzOtIPWzJvn0f79Do0ZE1ZODl1OsB+hEwAAAAAACc40K+V0tlF6+jClpV180P3iYkOzZ3uUmWnqjjvockJicNldAAAAAAAAODKns406dVojyzr0cPBZszyqqjI0aVJIaQc3QQG2oNMJAAAAAIAEZVkRBQIfSpIMw5DD4T1ozTffOLR4sVtdupj65S8j8S4ROCxCJwAAAAAAElRR0VP67rsLVVa28rBrpk1LUixmaOrUkDyeOBYHHAWhEwAAAAAACSgY/FxFRU/K5eqotLQhh1zzwQdOrV/v0rnnRnXxxdE4VwgcGaETAAAAAAAJxjRD2rNnjKSoOnacI6cz/aA1sZg0ZUqSDMPS9OkhGUb86wSOhNAJAAAAAIAEU1T0mEKhr9SmzSilpv70kGtefdWtr792atiwqE47zYxzhcDREToBAAAAAJBAAoGP5fc/Lbf7JOXkPHzINZWV0mOPeeTzWfrNbw79RjvAbi67CwAAAAAAAP/k9fZWZuZdatVqqJzOtEOuefZZj/x+hyZODCknx4pzhUD9xL3Tae7cubrqqqvUr18/nXXWWRozZoy2bt1aZ41lWZo9e7YGDBigXr166cYbb9Q333xTZ015ebnGjx+v/v37q3///ho/frwqKirqrNmyZYtGjBihXr16aeDAgZozZ44si80IAAAAAEhcDkeS2rV7WD7fjw95f9cuQ3PnetSxo6mxY8Nxrg6ov7iHTh9//LFuuOEGLV++XC+//LKcTqdGjRqlsrKy2jXz58/XokWL9OCDD2r16tXKyMjQqFGjVFVVVbtm3Lhx2rx5sxYsWKAFCxZo8+bNmjBhQu39qqoqjR49WpmZmVq9erUmT56shQsXavHixXH9eQEAAAAAqI/y8tfl98+RZR15PtNDDyUpFDI0eXJIyclxKg44DnE/Xrdw4cI6//zEE0/o9NNP19/+9jcNHjxYlmVpyZIluu222zRkyIFXQj7++OM6++yztW7dOg0bNkzbtm3Thg0btGzZMvXt21eSNG3aNA0fPlzbt29X165d9eabbyoYDOrxxx+X1+tVjx49tH37di1evFijRo2SwVh/AAAAAECCCId3ae/eeyXFlJ5+udzu3EOu++ADp9atc+uMM2K66qpofIsEjpHtg8Srq6tlmqZatWolSSooKFBRUZHOPffc2jVer1dnnHGG8vPzJUn5+fny+Xzq169f7Zr+/fvL5/PVrvnss890+umny+v11q4ZMGCACgsLVVBQEI8fDQAAAACAo7KsmPbsuU2mWa527Z44bOAUiUiTJyfJMCzNnFkjeimQ6GwfJP7II4+oZ8+etR1LRUVFkqSsrKw66zIzM1VYWChJ8vv9ysjIqNOtZBiGMjIy5Pf7a9fk5OTUecYPz/T7/crLyztsTW3a+ORyOU/wJwMOLzv70MMAARyM/QLUD3sFqD/2CxLNzp2PKhDYqKysK3XyyWMOezLn6aelrVulMWOkn/40pdHrYq/gRNkaOs2cOVOffvqpXnvtNTmdiRPylJYG7C4BzVh2dpqKiirtLgNoEtgvQP2wV4D6Y78g0VRX/1U7dkyRy9VBmZmz5PdXHXLd/v2Gpk5NUZs20r33Vun/+jUaDXsF9XWkcNK243WPPvqo3n77bb388st1uo6ys7MlqbZj6QfFxcW1nUpZWVkqKSmp8yY6y7JUUlJSZ01xcXGdZ/zwzH/vogIAAAAAwA6VlW9JknJzF8nlyjzsuhkzklRVZWjixJAyMuJVHXBibAmdHn744drAqVu3bnXu5ebmKjs7Wxs3bqy9FgqFtGnTptojeH379lUgEKid3yQdmPMUCARq1/Tp00ebNm1SKBSqXbNx40a1bdtWubmHPh8LAAAAAEA85eQ8om7d/p9SUs457JqPP3Zo5Uq3Tj01ppEjI3GsDjgxcQ+dpk2bpjVr1uipp55Sq1atVFRUpKKiIlVXV0s6MJtp5MiRmj9/vtavX6+tW7dq4sSJ8vl8uvTSSyVJ3bp108CBAzV16lTl5+crPz9fU6dO1aBBg9S1a1dJ0tChQ5WcnKyJEydq69atWr9+vebNm8eb6wAAAAAAtguFvpF04Hdgr/e0w66LxaRJkw68IGvmzJASaDINcFSG9a9n1OLglFNOOeT1O++8U3fddZekA0fl5syZoxUrVqi8vFy9e/fWlClT1KNHj9r15eXlmjFjht59911J0uDBzZWGBQAAIABJREFUgzVlypTat+BJ0pYtWzR9+nR98cUXSk9P17Bhw3THHXccNXTi3CoaE2ejgfpjvwD1w14B6o/9gkQQCGzSd99dqKysu5STM+2Ia196ya0JE7y65pqInn++Jk4VsldQf0ea6RT30KkpYGOhMfGXN1B/7BegftgrQP2xX2C3WKxM27YNVCSyS507/16pqecfdm1hoaFzz01RLCb99a/VysmJ36/v7BXU15FCJ1vfXgcAAAAAQEthWZb27PmVIpGdys6ecMTASZIeeihJ5eWGZs6siWvgBDQU295eBwAAAABAS+L3/5cqK9cpJeUnys6eeMS1GzY4tXq1W717x3TTTQwPR9NE6AQAAAAAQCMLBvNVWDhNLlcH5eYulmEc/uBRKCRNmOCVw2HpqadqGB6OJovjdQAAAAAANDKvt7eysycqNXWwXK7sI66dM8ejbdscuvXWsHr3NuNUIdDwCJ0AAAAAAGgklmXJMAwZhkNt2x75SJ0kbd9u6L/+y6OcHFMTJ4biUCHQeDheBwAAAABAI9m3b5z2758uy4odda1lSRMnehUKGXrkkZDSDv9SMKBJIHQCAAAAAKARlJW9qtLSBaqqekeWdfSupbVrXXr/fZcGD45q6NBoHCoEGhehEwAAAAAADSwQ+Fh7994jh6O18vKWyuHwHXF9SYk0eXKSkpMtPfZYjQwjToUCjYjQCQAAAACABhSJ7NHu3cNlWVHl5S2Wx9P1qJ+ZMsUrv9+hCRNCOukkKw5VAo2PQeIAAAAAADQQ0wxq164bFI3uV7t2jyk19adH/cy77zq1cqVbffrEdPvtkThUCcQHoRMAAAAAAA3EMFzy+U6X13uqMjLGHnV9VZV0//1euVyWnnmmRi5+S0czwr/OAAAAAAA0EMNwq337WbKsmIx6DGZ69NEkFRQ4dN99If3nf5pxqBCIH2Y6AQAAAABwgior/1t+/xxZ1oF5TIbhPOpnPv7YoYUL3Tr55Jjuuy/c2CUCcUenEwAAAAAAJyAY/FwFBaNlWaZatbpUHs9JR/1MKCT9+tdeSdLTT4fk9TZykYANCJ0AAAAAADhOkcge7dp1rUwzoLy8V+oVOEnSM894tHWrUzffHNaPfxxr3CIBmxA6AQAAAABwHGKxCu3ceY2i0X3KyXlErVoNrdfn8vMdevZZj3JzTU2eHGrkKgH7MNMJAAAAAIBjZFlRFRTcpFDo72rT5mZlZt5Zr8/V1Eh33eVVLGbo2WdrlJrayIUCNiJ0AgAAAADgGFlWTE5na6WmXqD27Z+s15vqJOmJJw4cqxs9OqyBAzlWh+aN43UAAAAAABwjhyNJHTsukGWFZBj1+9X6k08c+t3vPDrpJFMPPsixOjR/dDoBAAAAAFBPZWWvqbR0iSTJMBxyOJLr9blAQLrrrmRZlvTcczVKSWnMKoHEQKcTAAAAAAD1UFn5jvbs+ZWczjSlpf1cLldmvT/76KNJ2r7doTFjwjrrLI7VoWWg0wkAAAAAgKMIBD7W7t2/lGG41anTymMKnDZudGrePI9OPjmmSZM4VoeWg04nAAAAAACOIBTaol27rpFlhdSp0zL5fGfV+7Pl5dKdd3rlcFh67rkaJdfvNB7QLNDpBAAAAADAYUQie7Vjx+WKxUrVocMcpaVdfEyff+ABrwoKHLrvvrD69zcbqUogMdHpBAAAAADAYTid6fJ6eyol5Xa1aTP8mD67erVLa9a41b9/TOPGhRupQiBxEToBAAAAAPBvLMuSYRhyOFLUqdMqHetBoV27DD3wgFcpKZZ+97ugXPz2jRaI43UAAAAAAPwL06zWzp2/UEXFW5Ikw3DKMIx6fz4WOzDHqbLS0MyZNerSxWqsUoGERugEAAAAAMD/Mc2gdu0apurq91VR8fvjesbs2R59+KFLQ4dGdN110QauEGg6CJ0AAAAAAJBkmiHt3j1C1dUfKC3tUnXs+MIxPyM/36EnnvCofXtTTz1Vo2NokAKaHUInAAAAAECLZ1kRFRSMUlXVn5Sa+jPl5i6WYbiP6RlVVdLYscmKxaQ5c2rUpk0jFQs0EYROAAAAAIAWr7Bwpior1ykl5Tzl5b0qhyPpmJ/x298maft2h371q4gGDow1QpVA08L8fAAAAABAi5eZeadisTK1azdDDkfyMX9+1SqXli3zqFevmCZODDVChUDTQ6cTAAAAAKBFsqyoamq+liS5XBnq0OFpORwpx/ycb75xaPx4r9LSLM2fH1TSsTdJAc0SoRMAAAAAoMU5MMNptL777qcKBj877ucEg9Itt3gVCBh65pkadeliNWCVQNNG6AQAAAAAaFEOvKVupCoq1srr7S2Pp/txP+u3v03S1187NWpUWJddFm3AKoGmj5lOAAAAAIAWwzRrtHv3CFVVrVdKyvnq1Om14zpSJ0mvv+7S0qUenXpqTNOmMccJ+HeETgAAAACAFsE0A9q163pVV7+n1NSfKi9v2XENDZekbdsM3X+/V6mplhYsCMrrbeBigWaA0AkAAAAA0CLEYuUKh79TaupFystbIofj+JKimhrplluSVV1taN68oLp2ZY4TcCiETgAAAACAZs2yLBmGIbe7vbp0eUdOZ6YcDs9xP2/y5CR99ZVTv/xlWJdfzhwn4HAYJA4AAAAAaLbC4Z367rsLFQptlSS53e1PKHB69VV37RynGTOY4wQcCaETAAAAAKBZqqnZrO++u1DB4EeqrPzjCT8vP9+hiROT1Lq1pcWLmeMEHA3H6wAAAAAAzU4g8JF27bpGsViZcnIeVVbWnSf0PL/f0OjRyQqHpZdfDqpzZ+Y4AUdD6AQAAAAAaFYqK/+k3btvlGWF1LHjC2rdevgJPS8alW6/3as9exz6zW9CGjw41kCVAs0boRMAAAAAoNkwzRrt3Xu3pJjy8l5Vq1aXnPAzH3kkSRs2uHTRRRHdfXf4xIsEWghCJwAAAABAs+FweNWp06syzZBSUs4+4ee9+aZLzz/vUbdupubMqZGDychAvbFdAAAAAABNmmmGtG/feEUiBZKk5OR+DRI4bdni0N13e+XzWXrppaBatTrhRwItCp1OAAAAAIAmKxot1u7dwxUIbJRpBtWx45wGeW5pqTRyZLICAUMLFwZ1yilmgzwXaEkInQAAAAAATVI4vF07d16tcPhbtWp1pdq3f6pBnhuJSLfckqzvvnPonntCGjo02iDPBVoajtcBAAAAAJqc6uoN2r59sMLhb5WVdZ9ycxfJ4fA2yLMnTz4wOPziiyOaNInB4cDxotMJAAAAANCkmGa1du++SbFYhdq3f04ZGTc12LMXLnTrpZc8+s//jOn55xkcDpwIQicAAAAAQJPicKQoN3eRDMOtlJRzGuy5H3zg1G9/m6SsLFNLlgSVmtpgjwZaJDJbAAAAAEDCi0aLVFBws6JRvyQpNfW8Bg2ctm0zdMstyXI6pZdeCiovz2qwZwMtFaETAAAAACChBYOfa/v281VevkqlpYsb/PllZdKIET6VlxuaNatGZ57Jm+qAhsDxOgAAAABAwiotfVX79t0ny6pR27YPKivr/gZ9fjgs3XxzsrZtc+jOO0O67jreVAc0FEInAAAAAEDCMc0a7ds3XmVlL8vhSFde3stKS7u4Qb/DsqRx47zasMGliy6KaPJk3lQHNCRCJwAAAABAwolEdqq8fJW83t7Ky1sij6dLg3/HE094tGKFW/36xfTiizVyOhv8K4AWjdAJAAAAAJAwTDMohyNZSUmn6KSTfi+vt5ccjuQG/55ly1yaNStJnTubWro0KJ+vwb8CaPEYJA4AAAAAsJ1lRbR//0Pavv18xWJVkiSf78eNEji9+65T48Z5lZFhavnygLKzeVMd0BjodAIAAAAA2Coc3qGCgpsVDH4ij6eLotH9cjpTG+W7vvzSoZtvTpbLJS1ZElS3bgROQGMhdAIAAAAA2Ka8fLX27r1Xplmh9PRr1L79M3I6WzXKdxUUGLrhhmQFAtKCBTU680yzUb4HwAGETgAAAAAAW+zfP11+/1NyOFLUseOLSk+/XoZhNMp3lZRI11+frP37HZo+vUZDh0Yb5XsA/BOhEwAAAADAFqmpF6i6+n117DhPSUndG+17qqqk4cN92rLFqdtvD2vMmEijfReAf2KQOAAAAAAgLiwrqqKipxUO75QkpaScrS5d/rdRA6dQSBo1KlmffurUdddFNG1aqNG+C0BddDoBAAAAABpdKPSN9uy5XcHgJtXUfKG8vJckqdGO00lSLCbdcYdXH3zg0kUXRfTMMzVy0HoBxA2hEwAAAACg0ViWqZKSudq//yFZVlDp6deqffsn4/C90oQJSXrzTbfOPjuquXNr5OI3YCCu2HIAAAAAgEYRiezRnj1jVF39gZzODLVvP1fp6ZfH5bsffdSjpUs9Ou20mJYuDSo5OS5fC+BfEDoBAAAAABpNMPiZ0tIuVvv2z8ntzonLdz7/vFvPPpukrl1NLV8eVKtWcflaAP+G0AkAAAAA0GBCoW8Ui5XI5/ux3O6O6tbt/8ntPqlRZzf9q4UL3Zo2zav27U2tWhVQdrYVl+8FcDBGqAEAAAAATphlRVRU9JS2bTtHBQWjZZpBSZLH0yVugdOSJW5NmuRVdrap118PKC+PwAmwE51OAAAAAIATEgz+TXv33qWami/lcuWoXbuZcjjiO0Rp+XKXxo9PUmamqddfD6p7dwInwG6ETgAAAACA42Ka1dq/f4pKShZKMtW69S/Vrt0MOZ2t41rH66+7dM89XqWnS6tWBfWjH5lx/X4Ah0boBAAAAAA4LobhUXX1n+XxdFeHDk8rJeUnca/hrbdcuvNOr9LSpFWrAjr1VAInIFEQOgEAAAAA6q2m5ivV1Hyh1q2vl2G41anTSrlc7eVweOJey3//t0u33+5VcrK0YkVAvXsTOAGJhNAJAAAAAHBUsViFCgsfVUnJXBmGWykpg+V258jj6WxLPevWuXTbbV55PNKyZUH170/gBCQaQicAAAAAwGFZVkxlZctUWDhd0eh+eTxd1K7dU3K7c2yrae1al8aO9crrPRA4nXVWzLZaABweoRMAAAAA4JBMs1rffTdENTVfyDCSlZ39G2Vl3SuHw2tbTStXunT33V6lpEjLlwd0xhl0OAGJitAJAAAAAFCHZVkyDEMOR4o8nu7yek9V27ZT5HZ3sLWuZctcuu8+r1q1klauDKhvXwInIJEROgEAAAAAJEnRaImKih5XNPq98vJeliTl5i6UYThtrkxavNitBx7wKiPD1KpVQZ12GoETkOgInQAAAACghTPNgIqLX5Tf/18yzTK53ScpFiuV09kmIQKnefPc+u1vvcrKMvX660H17EngBDQFhE4AAAAA0EKZZlhlZS+rqOgJRaP75XS2Vk7Ow8rIuF0OR5Ld5cmypCef9Oipp5KUk2NqzZqgTj6ZwAloKgidAAAAAKCFMs0yff/9gzIMQ1lZ45WVdZecztZ2lyVJMk1p8uQkLVzoUefOplauDKhLF8vusgAcA0InAAAAAGghLMtSZeUf5HD4lJo6SC5XW+XlvaTk5H5yudraXV6tcFi6+26v1qxxq2fPmFauDConh8AJaGoInQAAAACgmbMsU5WV61RU9IRqar5QUtJ/qFu3v8owDKWlXWR3eXUEAtLNNyfrf//XpTPPjOqVV4JqnRjNVwCOEaETAAAAADRTlhVTRcVaFRU9qVBosyRD6elXKzv7ARmGYXd5Bykrk4YP9+mTT5z66U+jWrgwKJ/P7qoAHC9CJwAAAABopsrLV2nPntskOZWePkzZ2fcrKamH3WUd0t69hq6/Pllff+3UlVdGNHt2jdxuu6sCcCIInQAAAACgmTDNGpWVLVd6+hVyOtPVqtUVqqn5XG3a3KKkpG52l3dYf/+7Q8OHJ2vfPoduuSWshx8OyeGwuyoAJ4rQCQAAAACauGi0RKWlC1RcPFexWJFMs1xZWffI4UhSu3Yz7S7viN5/36nRo5NVVWXooYdqNHZsRAl48g/AcSB0AgAAAIAmKhzeqeLiOSotXSrLCsjhSFdW1q+Vnn6d3aXVy/LlLv361145ndKCBUFddlnU7pIANCBbGhY/+eQTjRkzRgMHDtQpp5yiNWvW1LlvWZZmz56tAQMGqFevXrrxxhv1zTff1FlTXl6u8ePHq3///urfv7/Gjx+vioqKOmu2bNmiESNGqFevXho4cKDmzJkjy+I1mwAAAACah71771BJyVw5nW2Uk/OoevTYrJych+R2t7O7tCOyLOnJJz26++5kpaVJq1YROAHNkS2hUyAQUI8ePTR58mR5vd6D7s+fP1+LFi3Sgw8+qNWrVysjI0OjRo1SVVVV7Zpx48Zp8+bNWrBggRYsWKDNmzdrwoQJtferqqo0evRoZWZmavXq1Zo8ebIWLlyoxYsXx+VnBAAAAICGZJohlZUtU2HhY7XXsrMnqWPHuerR4wtlZd0ppzPNxgrrJxyW7rnHqyefTFKnTqbefrtaZ50Vs7ssAI3AluN15513ns477zxJ0qRJk+rcsyxLS5Ys0W233aYhQ4ZIkh5//HGdffbZWrdunYYNG6Zt27Zpw4YNWrZsmfr27StJmjZtmoYPH67t27era9euevPNNxUMBvX444/L6/WqR48e2r59uxYvXqxRo0Yl5OtBAQAAAODfRSJ7VFKyUKWlLykW88swvMrMHCunM10pKedKOtfuEuvN7zc0erRXH37oUp8+Mb3ySlBt23IaBWiuEu59AAUFBSoqKtK55/7zL06v16szzjhD+fn5kqT8/Hz5fD7169evdk3//v3l8/lq13z22Wc6/fTT63RSDRgwQIWFhSooKIjTTwMAAAAAxycU+la7d/9SW7eeKr//KUkxZWbeq+7dP5HTmW53ecfs668duuginz780KXLLoto7doAgRPQzCXcIPGioiJJUlZWVp3rmZmZKiwslCT5/X5lZGTU6VYyDEMZGRny+/21a3Jycuo844dn+v1+5eXlHbaGNm18crmcJ/7DAIeRnZ34bc9AomC/APXDXgHqL5H3Szjsl9udIcNwKBhsrW+/XauUlF7Kzb1LbdteL6fTZ3eJx2XdOun666WqKumhh6QpU9wyDLfdZeEoEnmvoGlIuNApEZSWBuwuAc1Ydnaaiooq7S4DaBLYL0D9sFeA+kvE/WJZpqqrP1Bp6cuqrHxLnTqtUmrqYElZ6tbtQyUl/UiGYaikJCYpsWo/GsuSnn/erRkzkuT1SgsW1Oiyy6L6v14BJLBE3CtITEcKJxMudMrOzpZ0oBupQ4cOtdeLi4trO5WysrJUUlIiy7Jqu50sy1JJSUmdNcXFxXWe/UMX1L93UQEAAABAvEUi+1RW9opKS5cqEtkhSUpK+pEsK1K7xuvtaVN1Jy4YlCZM8GrFCrfatTO1dGlQvXubdpcFII4SbqZTbm6usrOztXHjxtproVBImzZtqh0a3rdvXwUCgdr5TdKBOU+BQKB2TZ8+fbRp0yaFQqHaNRs3blTbtm2Vm5sbp58GAAAAAA5mWZa++26ICgtnKBotVOvWI9Sly5/UrdtHSksbYnd5J2z3bkNDh/q0YoVbffvGtH59gMAJaIFs6XSqrq7Wrl27JEmmaWrv3r36+uuvlZ6erg4dOmjkyJGaO3euunbtqpNOOkkvvPCCfD6fLr30UklSt27dNHDgQE2dOlXTp0+XJE2dOlWDBg1S165dJUlDhw7V888/r4kTJ2rs2LHasWOH5s2bpzvvvJM31wEAAACIG8uKqbp6g8rLlysp6T+UlXW3DMNQVtZ9kiylp18tp7OV3WU2mPffd2rMGK9KShy64YawHnsspH95vxOAFsSwLCvurwv46KOPNHLkyIOuX3HFFXrsscdkWZbmzJmjFStWqLy8XL1799aUKVPUo0eP2rXl5eWaMWOG3n33XUnS4MGDNWXKFLVq9c+/rLds2aLp06friy++UHp6uoYNG6Y77rjjqKET51bRmDgbDdQf+wWoH/YKUH/x3C81NZtVVrZc5eUrFY3ulSSlpJyvk056My7fH2+WJc2e7dGjj3rkdEozZ4Z0440R8f/5N038twX1daSZTraETomOjYXGxF/eQP2xX4D6Ya8A9Rev/fL995NVXDxbkuRwpCs9/Qqlpw+Tz3eWDCPhppycsKoq6e67vVq3zq327U0tXBjU6adznK4p478tqK8mNUgcAAAAAJqSUOgbVVS8oUhknzp0eEaSlJIyQOHwd0pPv1ZpaRfJ4Wi+58s2b3bo1lu9+uYbp845J6p582rUti29Df+/vTuPk6Os9z3+raqu7p6eLZOZyTpZyEoISYSgEjmAhJyLAY4sCheIKHAvGA9yReSAKIGrh02OoCgcDIsoSAA5omAMnnMRBA4Y9p2QAFnNNjPJ7D29VdX9o7p7utOTBZikZiaf9+tVr66u56mqX/csSX/nqacAEDoBAAAAwEfieZ6SyZXq6Pij2tv/oETiLUmSYcQ0fPgPZVmVqqycr8rK+QFXund5nnT//ba+972IEglDX/96SlddlZRtB10ZgP6C0AkAAAAAdsPzvPzcsG1tS7Rx4zckSYYRVmXlfFVVnaLKyvmyrJ1fZjKYdHZKl14a1SOP2Kqu9rR4cbfmz88EXRaAfobQCQAAAAB64bpxdXY+qY6OPykef14TJ74o04yovPzzqqo6SZWVx2eDpiFBl7pPvfWWqfPPL9Pq1aZmz3Z0xx3dGjOGy+kAlCJ0AgAAAICsTGab2tsfVWfnf6qz8yl5XkKSFAoNVyq1RtHogbLt0Roz5r6AK933PE/61a9sXXVVRMmkoW9+M6krrkhxOR2AnSJ0AgAAALDfct2E4vHlKi8/WoZhKJ3eqM2bL5YkRSIHqrLyBFVWHq+ystmD8q5ze6q11b+c7rHHbA0d6uqee7o1b54TdFkA+jlCJwAAAAD7DX8S8A/V2fn/1Nn5hLq6npXndWvixOcUjc5QNDpDI0feooqKoxUOTwi63H7hmWcsXXRRVJs3m/rsZzNavDihUaO4nA7A7hE6AQAAANgvJJPva/nyU5VMrstvi0SmqaJinkyzQpJkGIaGDj03qBL7lURCuvbaiBYvDisU8nTFFUlddFFKIT5FAthD/LoAAAAAMKhkMs3q6npWXV3PqKvraY0b93uFw+Nk22PleRlVVn5RFRXzVFFxrMLhMUGX2y+9/bapCy+MasUKS5MmOfr3f0/oU59ygy4LwABD6AQAAABgwMtkmtTU9GN1dT2rZPLt/HbTrFAq9YHC4XEyzYjmzNmg5ubOACvt31xXuv12W9dfH1EqZejcc1O6+uqkYrGgKwMwEBE6AQAAABgwPM9TKvW+4vHlisf/puHDr1EoVCvDCGv79l/IMCIqLz9G5eVHqrz8KJWVHSLD6Lm9mmEYAVbfv61da+jb347quedCqq93dcstTBYO4JMhdAIAAADQr2UyzWptvT8bNC2X42zLt1VWnqiqqhNkWdWaMOFJRSIHyzQjAVY78Liu9Mtf2rrmmojicUPz56d1001J1dUxWTiAT4bQCQAAAEC/4HmuUqn31d39suLxVzR8+A9lWRXyvKS2bl0kSbLtsaqomKtYbI5isTmKRKbl9y8rmx1U6QPW6tWGvvWtqF54IaSaGk833dStU0/NiAFhAPoCoRMAAACAwKRS69XS8kt1d7+i7u7X5Lrt+bbq6i+pvPwI2fZojRlzv8rKDpFtNwRY7eDhONLixbZuuCGiRMLQiSemdcMNSQ0bxugmAH2H0AkAAADAXuWPYFqtROJNJRJvKZF4W2PHLpFh2HLduJqbb5YkhcNTVFZ2gsrKZisWm61IZEb+GFVV/xRU+YPOypWmLr44qldesVRX5+rWWxP64hczQZcFYBAidAIAAADQZzzPkWFYkqSurufV2Ph/lUi8LdctvmNcMvmBotFpikSmaNy4R1VWdogsa0gQJe83EgnpllvC+vnPw0qlDJ16alrXXptUbS2jmwDsHYROAAAAAD4yz3OUSq1RMvmeksl3lUisUDK5Qo6zTVOmrJJhGDIMS/H4i4pEpiganalodJai0RmKRmcoFKqVJBmGqYqKYwJ+NYPf009buuyyqNasMTVypKvrr0/o+OMZ3QRg7yJ0AgAAALBTnucqnd6gZPJduW5S1dUnS5Kam3+mxsari/qaZoUikQPluu2yrGqVlc3WtGmbZJqxIEqHpMZGQ1ddFdEjj9gyTU9f/3pKl1+eVEVF0JUB2B8QOgEAAACQ57kyDFOS1Nb2e3V0/EnJ5PtKpd7PXxpn2+PzoVMs9llVV5+hSGRa9jK5abLtMfljSJJhhGQYfOQIgutK991n65prImprM/SpTzn68Y8TmjnTDbo0APsR/gUAAAAA9iOp1Holk+8plfogGyp9oGTyA5WXH6mGhjskSd3dr6mt7bcyjIjC4YkFwdL0/HHKyz+n8vLPBfUysAtvvGHqu9/1JwqvrPR0/fUJnXNOWpYVdGUA9jeETgAAAMAg4jhtSqXWKp1eq1TKXyor/4cqK+dLkjZu/N+Kx5cX7WPbDbKsyvzz2tqFGjr0vOzIJZKKgaKpydD114d1//22PM/QSSel9a//mtSIEUwUDiAYhE4AAADAAOK63UqnNyqd/rvS6XWqqJgn2x4tz/O0atVUZTJbSvYxzbJ86DRkyAKVlx+rSGSywuFJikQmyjTLi/rb9qh98lrQN9Jp6e67bf34xxG1txuaNs3RNdckdeSRTtClAdjPEToBAAAA/YTnucpkGpVOb1A6/XdVVX1RhmEplVqjDRvOUTq9QY7TXLRPQ8O9qq4eLcMwFI0eLGmmwuHxsu3xCocPUDg8XuHw+Hz/mpqv7dPXhL3rqacsLVoU0apVloYM8S+l+9rX0grxSQ9AP8CvIgAAAGAfcN2EMpktymS2yHUTqqj4vCSps/NpNTXdqHR6gzKZjfK8dH6fKVNWyrZHyjSrlEyukG03KBoyIfYNAAAgAElEQVSdIdtukG2Plm2PVVnZ7Hz/ceMe2dcvCwH58ENDP/hBRH/+s39XunPOSenyy1OqreVSOgD9B6ETAAAA8Am4brcymaZ8oGRZdfkJtpubf6bW1iXKZDbLcVry+9h2g6ZMeTe7f5fi8WcVCo1QNDpLtj0mHyqZZlSSZFlDNW3aVhmGse9fIPqVxkZDN90U1r332nIcQ3PmZHTttUkdfDB3pQPQ/xA6AQAAAAU8z5PjbFcm0yTHacwGSk3KZBpVWTlfsdinJUlr156s7u4X5bqdRftXVZ2aD50cp0Xp9CbZth8ohUIjZNsjZdsN+f4VFfM0bVqTTDOy05oIm9DVJf3iF2HdemtYXV2GJkxwtWhRQscfnxHfHgD6K0InAAAADFqe58h1O2VZ1ZKkdHqTurqeUibTIsfZLsdpyS7bNXr07bLt0XLdNq1ceUCvxwuFavOhk2VVKhw+QJZVr1CoTqHQiOxopYPz/YcNW6Thw6/eZY2mGe6jV4vBKJORHnzQ1o9+FNbWrabq6lwtWpTU2WenZdtBVwcAu0boBAAAgH7PcTrluq1ynHY5Tptct02O06ZQaIQqKo6WJLW23q+2tt9nw6Tc0ibLqtOBB34oSUok3tbGjd/o9Rzp9ObsJW3Vqqo6WZZVq1CoLhsq+UskMiXff8yY+3Zbt2GYffDqsT/yPGnZspBuuCGslSstlZV5uuSSpC68MKXKyqCrA4A9Q+gEAACAvcYfadQl1+3MLh1ynE7FYp+RaZbJdeNqbv5pNkhqL3qsq/u2qqtPlSStXTtficQbJcevrDwxHzolk6vV2flfMgxbljVUodBIRSLTFQoNy/ePRmdo1Kify7KG7rDU5EccGYahMWPu3QfvDlDK86Qnn7R0ww0RvfGGJdP0dNZZ/iThI0cySTiAgYXQCQAAAEUcpyUbFMXzIZHrdioUGq5Y7DBJUnv7nxSP/3e2rSMbKHXJNCs0btzD2T5LtWHDWb2eY9KklxSJTJVkqKnphpJ206yQ42zPP6+oOFaRyBSZZpUsa4gsq1qmWa1IZGK+T13dxaqru1imWbHTOZBse6Rqar72cd8aYK/67/+2dP31Eb30kiVJOvnktP7lX1KaPJlJwgEMTIROAAAA/ZznOfK8hFw3Ic9LZteTMgwzG9xIqdQaxeMvyHW75XlxuW53NjSKa9iwK2VZFcpkmrRx49fzbYX9Ro78cX5U0erV85RKvV9SR3X16YrF7pIkdXU9o+3bby/pY9tj8uuh0DDFYv8g06yQZVXINAsXf44lw4hq/PilMs1qWVZV/tEwiv+bOnz4/93t+2RZXHOEgemll0zdcENEzz7rf99/4QtpXX55StOnEzYBGNgInQAAAHbghzyp7JKR56VkGFb+Mq10eqvS6XXyvHRBP3+9quoUGYahTKZJra0P9BIWpVRbu1DR6HRJ0vr1X5HjNMp1/XbPS8p1k6qp+YqGDfu+JGnjxgvU1vZwSZ2RyIGaNOlFSVI8/jdt3Liw19dTV/dNWVaFJKmz8wlJhkwzJsMok2nGFArVFoU8lZVfUCZzqEwzlg2IymWalYpGp+X71Nb+s4YMOSPbXpl9jBXNYRSLfUYHHLBsl++1YRgqLz9qd18SYFD6298s3XxzWE8/7f/8HXNMRpdfntShhxI2ARgcCJ0AAMDH5nmuPC8jKSPPy2QvazLleY7S6Y3Z7U42kPH72fZYhUJ1kqR4/AU5TpskJxvu+P1suyF/y/murr8pkXgte5zcudIyjLDq6y+VJCWTq7Rt2y+yx0kXhUAjRlyrcHiCPM/TmjXH5kOkwj51dRerttafXHrt2pPV1fVkyWuNxY7UAQf8SZLU1vaQtm69stf3ZNq0E2UYYWUyjTvtU1k5Px86dXe/pExmqwwjKtOMyDCiMoyICv+bFo3OlOO0lvSx7VH5PmVln9HIkT+TaZZlw6IyGUa5TLNMllUvSbKsOk2btjW7/87vsT5ixLU7bcsJh8dJGrfbfgCKeZ701FOWfvrTsJYv93/Ojzwyo3/5l5QOP9wJuDoA6FuETgCAPeZ5nqTixd8mGUYoP8LBdROS3KJ2yZNh2DLNaLZPV/ZD/47HNBUK1UqSMplOpVIbssfKHc9/DIcPkGGE5HlpJZOrCtrc7HFc2fb4/LG6u1+X68Z3OI6rUGi4otGDJEmJxHtKp9eWHMswbFVWzpfk392qq+vZovPkXkNl5fEKhWrlea5aWn5ZchzPc1VePkdlZbMlSW1tDyuVWpvt48jzHEmuwuHx+TlnOjufUkfH0vxx/D6OPM/V6NG3yzBMpVJrtWXLlZKckj7Dhi3Kz8Gzbt1pcpxt2XYvf87q6tNVX3+JJGnz5u+qo+OPRceQHIXDEzVhwl8kSa2tv9WmTd/IBkDFk9pOmbJCtj1amUyz3n//YPVm1KjbVFNztiRp06ZvK5l8u6RPVdWp+dCpo2OZtm27paSPaVbnQ6d0epNaWu7q9Xx1dZcoHJ4gwzCUSLwjw7BkGLYMIyzDCGfDmcKAZ4akTFEfw7AViRyY71NWdpjq6r6d7yPZBf39MMe2x2rs2IeyAc+OYdHIgvfsHUnWLkOgurpvqa7uWzttl6RIZJIikUm77GMYhgyjbJd9AOwdriv953+G9JOfhPX66/6cTf/4jxldfHFSn/40I5sADE6EToNYR8d/qq3tkV7bRo++TYYRUiq1QY2NP+y1T23tRSormynJ/1Dguu0lfSoq5mrIkAWSpO3b71JX13MlfWx7pEaMuE6S/9fq7dsX93q+kSN/rFCoTo7Trk2bLipo6flAU1NzrioqjpEkbdlypdLpdSXHKSv7jOrq/P1bWx9Qe/vSkj6mGVVDw92SpETiHTU2XtNrTcOH/1CRyGRJ0vr1Z8n/QFesuvrLqq4+TZLU2Hi9urtfLekTiUzViBH+OZqbH9O6dbeVvDZJGjPmfplmVOn037Vp0/8paOnpV19/uWKxwyVJf//7+cpkmkrOV1l5XP4v9s3Nt6qz8/+V9AmFhqmh4U5JUlfXf6up6Ue9vAPS6NG/kG2Plut2ad2603vtU1v7DVVVnSgp9wHyvZI+sdhn8/NxtLTcp9bW+0tem2GENX78HyX5t7TevPmSnnfA6+k3cuSPVVY2S5K0du2J2YCj2JAhZ2no0PMkSVu3Xp0NCYpFIlM1erQ/H0l7+2Nqbr55h3P5j+PHL5VlVSmd3qj160/fISTx+w0f/q+qrPwf2ZpOVjq9oahd8lRVdZKGD/+BJKmx8Rq1tj5Y1O55nkKhYZo48WlJ/iUwPbf19grOKx1wwJ8ViUyR6ya0atXUbLuKzjls2FWqrb0gX1M8vrykpvLyYzRu3G8lSU1NNxX8LBS+RkPTp7dJkhKJV7V69TEl76UkjRv3B1VUzJUkrVw5Ra7bWtKntvb/5H8WNm68UO3tpb+jIpGDNWnS89maHtL77//vXs83Zcr7su3hymQa9eGHc3rtM3r0LzRkyFnZ813Q6/dmdfXpamjww4qWll9p+/Z/L+ljWbU68MA1kqRE4i1t3Nh7TRMmPJsPuQq/fwsNG/aDfOjU0nKfurr+WtInFjsyHzolEm9q+/Y7d/L6bpVkynU71NHxWK99HKfn1vCJxFtynGb5AYclyZRh+PsXM7LhiZXta+ZHJkmSZdUoGv1UNmi0s31C2cW/+5dpxlRdfWZ+e0+f4vCmtnahMplt2TZLkt8nHD4g32fIkDMUi31mh+OEsqOBfGVlh2nixBcKAqVcAGTLNHvm+TnooK29vk+FRoz41932KS//XD4U2xnLqsyHlbuy49xFAAaXTEZautQPm1assGQYnk48Ma1vfzulGTMImwAMbvwvZxBLJt9TW9sDvbb5H1Qk121TW9tDvfaprv6SJD906uj4ozKZxpI+ljU0HzrF4y+pvf13JX3C4cn50CmdXt/rh0zJD3gkyfNSam//fa99ysvn5te7up7u9dbJUs9fipPJ99TR8ceSHoUfQBxnmzo6/tTr+erqvp1f7+j4s6RMSZ9o9FP59e7uV9TZ+V8lfRyn58N3IrG21z7ZnpIk141n59woVVNzbn49Hn8+G24UC4fH59eTyZXq6nqqpI9t91wSkck0qavr6V7P57rdkvz5TeLx0uBGkqqqTsqvJxJvqLv75ZI+llWVX0+n1yse/1tBq/81K/wA6bqdisdf2uEoRr4tp7v7DXlevOR8mczn8+up1DolEm/1UrlZ0H+7Eol31fP9Y2RHHRjZ0RyS52WUSq0vaO+pyfN6gi//Vt+t+f1z/T0vle/TEyDl+pjZEQiFv5ZDMs2KomP01GXmt4VCI3tpL55Q17bHKBJp8XsZPccr/F6x7REqKzusqD1XW/4dMysL5l4xChY/iMipqPh89utU3Cc34bEklZUdKs9LFtRtSTKKJiEuK5us6uozsiOocrX471VuxJRplmvo0PPzbf6x/PXCcKOm5lxlMs0F75/fN3eJk+Rf8uSPQMkdJ/e16RkZEo0epJEjbyk6T66vbTfk35uGhl8W1ZtbL3wPhg+/Wo7zLeWCnVwYlJtgWfID1IqKeQV9zHwYlPtnPBKZpqlT1+SPUdin8Htq6tTS0G1HI0feoJEjS+8kVqiy8h9VWfmPu+xjWZVqaOj9jwyFamq+uts+0ej0oq9T7+erkGVN22UfANiXOjulBx6wtXhxWOvXmzJNT1/+clrf+lZKU6cSNgHYPxhe4fABSJKamnb8i+/A5Dht2XkyStn2GBmGIddNyXFKwyTJ/8u+afoftNLpLfIvDylmmjFZ1pDs+VrkusmSPv7Eq/5cEq7bLcdpL2jrCYgsq1aGYcnzXDnOth2Pkj1feb4mx2nJXvax4/nsfMDh37WndBSMJIVCQyVJnpeW63b12sefmySUPV+bej78F54vItOM5F+ff0nKjn1MmWZMklRbG1VTU+HrMwr6lckwjOwcKTu+l7lgxs5+mFSv73fufP7oA/V6+UtPv1wfd6d9ch+Yd/erYleXhQAfV3195aD5nQzsTfysAHtub/+8bNli6K67bP3612G1tRmKRj2dfnpa//zPKU2YwEcvDBz824I9VV+/87vHMtJpELOsallW9S77mGZYptmwyz6SPwJi9+erkWXtuo8/uemu55LwL+Oo36Pz7Y4/kWpsN+ez88HZrs+36/fSP9/u58kwTVumWb6bmopHVuz8WJHd9tmTyzYK7zS08z6ESgAAADvz7rumbr89rEceCSmdNlRX5+qyy1I655y06uoImwDsnwidAAAAAOBjcF3pySct3XlnWE895X+0mjTJ0Te+kdaXv5xWGfP2A9jPEToBAAAAwEfQ0uLP1/SrX4W1dq0/YvyIIzL6xjdSmjfPkbn7QeQAsF8gdAIAAACAPfDWW6buucfW735nq7vbn69pwYKUzjsvzZ3oAKAXhE4AAAAAsBPJpLRsWUh3323rxRf9j09jx7o677ykzjwzrZrdTzMKAPstQicAAAAA2MGqVaZ+8xtbDz8c0rZt/vVyc+dm9L/+V0pz5zq7vYEOAIDQCQAAAAAkSfG49NhjIf3mNz2jmmprXS1cmNI556Q0YQJ3oQOAj4LQCQAAAMB+7c03/VFNv/udrY4OQ5J09NEZnX12Wscdl1EkEnCBADBAEToBAAAA2O9s2WLod78L6eGHbb37rn+t3IgRrs4/P6Uzz0xr3DhGNQHAJ0XoBAAAAGC/0NUl/dd/SXfdVaZnnrHkuoZs29P8+WktWJDW3LmOQnxCAoA+w69UAAAAAIOW40jPPWfp4YdtLV0aUleXJIU0e7aj005L6+ST0xo6NOgqAWBwInQCAAAAMKh4nvTaa6YefdTWo4+GtGmTf/e5sWNdXXKJoRNO6GRScADYBwidAAAAAAx4nudPCP7ooyE99pit9ev9oKmqytPZZ6d02mkZffazjoYNq1RTE4ETAOwLhE4AAAAABiTPk955xw+aHn3U1tq1ftBUUeHpy1/2L507+miHu88BQEAInQAAAAAMGK4rvf66qccfD2npUlsffugHTbGYp1NOSeukkzKaOzejaDTgQgEAhE4AAAAA+rdUyp8M/PHHQ/rzn0PassUPmsrKPH3xi37QdOyxGcViARcKAChC6AQAAACg3+nokP7yl5AefzykJ54IqaPDkCTV1Hj6n/8zrfnzM/r85wmaAKA/I3QCAAAAEDjPkz780NATT4T0l7+E9Le/WUql/KBpzBhXZ52V1he+4E8GHuJTDAAMCPy6BgAAABCIeFx6/nlLf/mLP5pp3Toz33bwwY7mz89o/vyMpk93ZRgBFgoA+FgInQAAAADsM2vWGHryST9keu45S4mEnyZVVHg68cS0jj3W0dy5GY0c6QVcKQDgkyJ0AgAAALDXbNtm6LnnLD3zjKVnnglp7dqe0UzTpjk69tiM5s1z9OlPO7LtAAsFAPQ5QicAAAAAfSYel5Yvt/TssyE984ylt9825Xn+aKaqKk/z56c1b54/mmn0aEYzAcBgRugEAAAA4GNLJqXXX7f03HOWnn3W0ksv9UwAHg57OuIIR0cd5ejIIzOaNctlEnAA2I/wKx8AAADAHuvqkl5+2dLy5f7yyis98zIZhqeZM10deWRGRx3l6DOfcRSLBVwwACAwhE4AAAAAdqq1VXrhBUvLl4e0fLmlN94wlcn0hEwHHeRqzhxHc+Y4OuKIjIYODbhgAEC/QegEAAAAQJLkef7d5V5+2dLLL1t68UVLK1b0zMkUCnmaNcvVnDkZzZnjj2Sqrg64aABAv0XoBAAAAOynOjqkV1/1L5F7+WVLr75qavv2nrvLRaOePvc5R4cf7o9kmj3bUXl5gAUDAAYUQicAAABgP5DJSKtWmXrtNUuvvGLq5ZctrVzZM4pJksaOdfX5z6c1e7YfME2f7ioSCbBoAMCARugEAAAADDKZjLRypak33zT1xhuW3njD0rvvmuru7gmYYjF/FJMfMLmaPdvRsGFegFUDAAYbQicAAABgAEunpffeM/Xmm5befNN/fOcdM39HOcmfi+nAA13NmuVo1ixXhx3m6MADXYX4NAAA2Iv4ZwYAAAAYILZvl9591x+15C/+RN/JZE/AZNs9AdPMmf7jtGmuotEACwcA7JcInQAAAIB+JpWSPvjALAqX3n3X1JYtZlG/cLj3gIl5mAAA/QGhEwAAABCQdFpau9bUypWm3n/f1KpVplas8NfTaaOo76hRrubNy+iggxwddJCr6dNdTZjgyrYDKh4AgN0gdAIAAAD2su5uf+RSLljKLWvWlIZLsZinGTPcfLh00EGupk1zVFMTUPEAAHxMhE4AAABAH3BdafNmQ6tXm/nlgw/8cGn9ekOeVxwuVVZ6mjnT1eTJrqZMcTRlir8+dqwnywroRQAA0IcInQAAAIA95HnSli1+sLRmjanVq3vW16411d1tlOxTV+dqzhxHkye7mjo1FzK5GjHCk1HaHQCAQYPQCQAAACiQTEobNxpat87U+vX+KCU/YPKDpXi8NCkqL/c0aZI/x9KECa4OOMB/nDTJ1dChAbwIAAD6AUInAAAA7FcyGWnTJiMfKPmPpjZs8Ne3bCm9FE7y51rKhUk94ZKnCRNc1dczagkAgB0ROgEAAGBQ6eiQNm40tWmToU2bTG3c6D/mQqWNGw05TmlCZJqeRo/2NGeOo7FjPY0d62rMGFfjxnkaP97V8OEESwAAfBSETgAAABgwOjuVD5I2bzaKwqVNm/znnZ07T4aGD3d16KGuxo7NLT3h0ujRnmx7H74YAAAGOUInAAAABK6rS9q61VBjo6mtW42Cxcxu9wOl9vadB0rV1V4+PBo50n8cNcrVqFGeRo/2n0ej+/BFAQCwnyN0AgAAwF7hulJLi6HmZqMkSGpsLA6VdjU6SZKqqvwAafZsP0AaNaowUPJDpoqKffTCAADAHiF0AgAAwB7xPKmtTWpuNtTcbKq52dC2bUb2ec/6tm2GmpoMbd9uyHV3HSbV1fmXuQ0f7mWXnvVhw/znw4Z5isX20YsEAAB9htAJAABgP+S6Unu7tH27odZWQy0t/tLaauS3bd9eGiZlMrufSbu62lNdnaeJEx3V1nqqrfV6DZXq65lDCQCAwYzQCQAAYABLp6XmZmnNGkNtbT3hUS5AKnzes11qbd39KKScigo/RJo1y1V9vau6Oj9IKnzMLUOHegqH9/KLBgAAAwKhEwAAQEA8z59Au6PDD4za26X2dkPt7f5zf3vxNn+9Z1s8nguOdj+hUSjkqabGD4cmT3ZVU+OppkYaMsQPiwofc+u1tUy+DQAAPh5CJwAAgI/AcfygqLPTyC69r++qT1eXHyi1t0uOs2ejjXJCIU9VVZ6qqqRhw1xVV3uqrw8pEkmrqqonNPIDpeKlvFwyPtrpAAAAPjZCJwAAMOh4ntTdLXV3G4rHpXjcUHe3/xiP+9u7unbc3nufHYOjnpFFH51peqqo8C9Xq693NXGiP/+RHyL5S3W1CtY9VVb623LrsVhpcFRfX6mmpsQnfNcAAAD6FqETAADY6zzPn3somfTDnGRSSiQMJRLKLkZJm/9cSiaNfJ/Cx1w4tGNYlHvueX0zpCcW81Re7odFw4e7qqjoCY4qKvzRQ7n1wu0VFVJlZc++FRWeysoYaQQAAPYfhE4AAAxSnielUrnFUCrlhz659cLtflvp9mRSSqeN7H6l/dPp4tBox2CocNueTlr9UUUi/uifsjL/srJRozyVlfnbYjE/6InFep6Xbi/uk9u3vNzfbll7pWwAAIBBb9CHTvfff7/uvvtuNTU1afLkyfre976nww47LOiyAAADgOdJmYw/Qsd/NPLP/W1GQZvf3tNW3D/3vLB/JuMHOIX77+x8hfsX9t1VeJRO7/shNdGoP+l0JOI/VlV5ika9/HN/8RSJ9PTt2ccPfHZs858XH7uszA+FolEpNOj/NwMAADAwDer/pi1btkzXXXedrr76as2ePVtLlizR+eefrz/96U8aNWpU0OUBwF7leZLr+ovj9Kz3PDfkOH6/XHtxP6Noe2k/4yMdP5PxHx3HKFjf9fZIROroiOyw3dhhv9x6b9uNXs6zs+2l599bI3P6gmV5sm0pHJbC4Z5gprraUzjs5beHw/77aNt+n8LtflvPcSKRnu25Y9p24fbi/QrXc6ERl44BAAAgZ1CHTvfcc49OOeUUnX766ZKkRYsW6dlnn9UDDzyg73znOwFXhyB5Xs+y4/NdtRU+730/Y7f7pVJSc7PxMc/3cffb3esrrXtP35fcei5s8NeN/LZcv5429dJmlLS5rn/s3vbL9e/t2IXHLW4zdtG2s/2MHV5XaU2lbcZuXmvxo+MYJWFO8fOeGnoPd4ydhkJ9NZ9N8MIfe0/b9mRZ/uVRoZAf1BQ+t21lR8p4+Ta/n983t27b/hIKednH4uc927yd9rVtr2C/nr6hkB/c7Mmxe45FuAMAAID+b9CGTqlUSu+8847OO++8ou1HHHGEXnvttYCq2ne2bjV0ySVRtbYWhwm5x48Suuys3d++8xBkd8fd2baettJj77hf4fM9O19/+ZRWEXQBCJhheDIMP9AwTf8x99zf5sk0e9pyj7bd0+7v4xW15/bJtfc8LzzOzs+da+9tv57n3k726zl3b/uFQrlwRzuEOzvb7qm+vlwdHV1F+/es7/q4phn0VxkAAADYvw3a0KmlpUWO46iurq5oe21trZ5//vld7ltTE1MoNLBnDW1ull55RWpr8z8U5v4inlvfcdmbbab50fYLslbaPl5bLlQo/HoXPu7ptsHeVvizIBm7+SneXfv+pDzoAoABob6+MugSgAGDnxdgz/Czgk9q0IZOn0RLSzzoEj6xujrpvfeCrgK9qa+vVFNTR9BloI/kLmnD3sHPC7Bn+FkB9hw/L8Ce4WcFe2pX4eSgvfigpqZGlmWpubm5aPu2bdtUX18fUFUAAAAAAAD7h0EbOoXDYU2fPr3kUrrnn39ehxxySEBVAQAAAAAA7B8G9eV15557ri677DLNnDlThx56qB544AE1NjbqjDPOCLo0AAAAAACAQW1Qh07HH3+8WlpadPvtt6uxsVFTpkzRHXfcodGjRwddGgAAAAAAwKA2qEMnSVqwYIEWLFgQdBkAAAAAAAD7lUE7pxMAAAAAAACCQ+gEAAAAAACAPkfoBAAAAAAAgD5H6AQAAAAAAIA+R+gEAAAAAACAPkfoBAAAAAAAgD5H6AQAAAAAAIA+R+gEAAAAAACAPkfoBAAAAAAAgD5H6AQAAAAAAIA+R+gEAAAAAACAPkfoBAAAAAAAgD5H6AQAAAAAAIA+R+gEAAAAAACAPkfoBAAAAAAAgD5H6AQAAAAAAIA+R+gEAAAAAACAPkfoBAAAAAAAgD5H6AQAAAAAAIA+R+gEAAAAAACAPmd4nucFXQQAAAAAAAAGF0Y6AQAAAAAAoM8ROgEAAAAAAKDPEToBAAAAAACgzxE6AQAAAAAAoM8ROgEAAAAAAKDPEToBAAAAAACgzxE6AQAAAAAAoM8ROgH7wOLFi/WlL31Jhx56qA4//HAtXLhQq1atCrosoN9bvHixpk6dqh/+8IdBlwL0S42Njbr88st1+OGHa8aMGTr++OP14osvBl0W0K84jqOf/vSnmjt3rmbMmKG5c+fqJz/5iTKZTNClAYF76aWXtHDhQh155JGaOnWqHnnkkaJ2z/P085//XP/wD/+gmTNn6uyzz9b7778fULUYiAidgH3gxRdf1FlnnaUHH3xQv/71r2VZls4991y1trYGXRrQb73++ut66KGHNHXq1KBLAfql9vZ2nXnmmfI8T3fccYeWLVumRYsWqba2NujSgH7lzjvv1JIlS3TllVfq8ccf1/e//30tWbJEixcvDro0IHDxeFxTpkzR97//fUWj0ZL2O++8U7/85S+1aNEi/cd//IeGDh2qc889V52dnQFUi4EoFHQBwP7g7rvvLnp+44036mhZEiMAAAZLSURBVLDDDtOrr76quXPnBlQV0H91dHTo0ksv1XXXXafbbrst6HKAfumuu+5SfX29brzxxvy2MWPGBFgR0D+99tprOuaYY/L/52poaNDcuXP15ptvBlw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = 4*e\n", "see_upper_bound(t, t, onlylast=True)" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.114501550751474" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "2.3504023872876028" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "8.230413924956927" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "I = lambda t: Ei(t) - Ei(-t)\n", "I(1)\n", "e - 1/e\n", "assert I(1) < e - 1/e\n", "I(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Other plots" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0.5,1,'The function $Ei(x)$ on $[0, e^2]$')" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0.5,0,'$x$')" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "Text(0,0.5,'$y$')" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.linspace(1e-3, 2*e, 1000) # 1000 points\n", "Y = Ei(X)\n", "plt.plot(X, Y, 'b')\n", "plt.title(\"The function $Ei(x)$ on $[0, e^2]$\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "That's it, see [this page](https://en.wikipedia.org/wiki/Exponential_integral) or [this one](http://mathworld.wolfram.com/ExponentialIntegral.html) for more details on this function $\\mathrm{Ei}(x)$." ] } ], "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": "3.6.3" }, "toc": { "colors": { "hover_highlight": "#DAA520", "running_highlight": 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