diff --git a/hack/LIHEDP_notebooks/Airy.ipynb b/hack/LIHEDP_notebooks/Airy.ipynb
new file mode 100644
index 0000000..530bd8e
--- /dev/null
+++ b/hack/LIHEDP_notebooks/Airy.ipynb
@@ -0,0 +1,1316 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Import useful modules"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from scipy import constants as sc\n",
+ "from scipy import special as ssp\n",
+ "import matplotlib.pyplot as plt\n",
+ "import matplotlib"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def sciprint(a):\n",
+ " print(f\"{a:0.2g}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# The Stokes equation & the Airy functions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## The Airy functions (maths)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The Stokes equation is most commonly written:\n",
+ "\n",
+ "$$\n",
+ "y'' - xy = 0\n",
+ "$$\n",
+ "\n",
+ "and has for solutions: \n",
+ "\n",
+ "$$\n",
+ "y(x) = \\alpha A_i(x) + \\beta B_i(x)\n",
+ "$$\n",
+ "\n",
+ "where $A_i(x)$ and $B_i(x)$ are the Airy functions, and $a$ and $b$ are constants that we can find by using the boundary conditions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from scipy import special\n",
+ "x = np.linspace(-15, 5, 201)\n",
+ "ai, aip, bi, bip = special.airy(x)\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "plt.plot(x, ai, 'r', label='Ai(x)')\n",
+ "plt.plot(x, bi, 'b--', label='Bi(x)')\n",
+ "plt.ylim(-0.5, 1.0)\n",
+ "plt.xlabel(\"x\", fontsize=18)\n",
+ "plt.ylabel(\"Airy functions\", fontsize=18)\n",
+ "plt.grid()\n",
+ "plt.legend(loc='upper left')\n",
+ "\n",
+ "\n",
+ "plt.axvline(-1, color=\"black\")\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note:** The maximum of $A_i(x)$ can be found at $x = -1$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## The electric field (physics)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have\n",
+ "$$\n",
+ "\\boxed{\n",
+ "\\frac{d^2 E_0}{dx^2} + k_0^2 \\left( \\frac{x}{L} \\right) E_0 = 0\n",
+ "}\n",
+ "$$\n",
+ "\n",
+ "which can rewrite in the common form of the Stokes equation:\n",
+ "$$\n",
+ "\\boxed{\n",
+ "\\frac{d^2 E_0}{d \\xi^2} - \\xi E_0 = 0 \\ \\ \\ \\text{ with } \\xi = - k_0^{2/3} L^{-1/3} x\n",
+ "}\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Therefore, we have\n",
+ "\n",
+ "$$\n",
+ "\\boxed{\n",
+ "E_0 = \\alpha A_i(\\xi) + \\beta B_i(\\xi)\n",
+ "}\n",
+ "$$\n",
+ "or, more directly:\n",
+ "$$\n",
+ "\\boxed{\n",
+ "E_0 = \\alpha A_i(- k_0^{2/3} L^{-1/3} x) + \\beta B_i(- k_0^{2/3} L^{-1/3} x)\n",
+ "}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Let us see what this looks like"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#free space\n",
+ "lambda_0 = 0.2\n",
+ "L = 5\n",
+ "\n",
+ "k0 = 2*sc.pi / lambda_0\n",
+ "\n",
+ "xmax = L\n",
+ "xmin = -5\n",
+ "N = int(20*(xmax-xmin)*k0) #number of points (this formula gives you enough points per period)\n",
+ "x = np.linspace(xmax, xmin, N)\n",
+ "\n",
+ "xi = -k0**(2/3)*L**(-1/3)*x \n",
+ "Ai, _, Bi, _ = ssp.airy(xi)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "\n",
+ "ax.plot(x/L, Ai, 'r', label='Ai(x)')\n",
+ "ax.plot(x/L, Bi, 'b--', label='Bi(x)')\n",
+ "ax.set_ylim([-0.5, 1.0])\n",
+ "ax.set_xlim([xmax/L, xmin/L])\n",
+ "\n",
+ "plt.axvline(L**1/3 * k0**(-2/3) / L, color=\"black\")\n",
+ "\n",
+ "plt.axvline(0, color=\"firebrick\")\n",
+ "plt.text(-0.05, 0.6, 'critical surface, where ne=nc', color=\"firebrick\")\n",
+ "\n",
+ "plt.xlabel(\"x/L\", fontsize=18)\n",
+ "plt.legend(loc='upper left')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note:** The maximum of $A_i(\\xi)$ can be found at $\\xi_{max} = -1$.\n",
+ "\n",
+ "This corresponds to $-k_0^{2/3} L^{-1/3} x_{max} = 1$, _i.e._ $\\boxed{x_{max} = L^{1/3} k_0^{-2/3}}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Finding $\\alpha$ and $\\beta$: Boundary conditions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Finding $\\beta$: avoiding non-physical results"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "\n",
+ "ax.plot(x/L, Ai, 'r', label='Ai(x)')\n",
+ "ax.plot(x/L, Bi, 'b--', label='Bi(x)')\n",
+ "# ax.set_ylim([-0.5, 1.0])\n",
+ "ax.set_xlim([xmax/L, xmin/L])\n",
+ "\n",
+ "plt.xlabel(\"x/L\", fontsize=18)\n",
+ "plt.legend(loc='upper left')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Clearly, we should have: $\\beta = 0$.\n",
+ "\n",
+ "Otherwise the electric field would go to infinity around the critical density.\n",
+ "\n",
+ "This leaves us with:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "\n",
+ "ax.plot(x/L, Ai, 'r', label='Ai(x)')\n",
+ "ax.set_ylim([-0.5, 1.0])\n",
+ "ax.set_xlim([xmax/L, xmin/L])\n",
+ "\n",
+ "plt.xlabel(\"x/L\", fontsize=18)\n",
+ "plt.legend(loc='upper left')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Finding $\\alpha$: the boundary with free space"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Remember how we got here: $n_e = n_C \\left(1 -\\frac{x}{L} \\right)$\n",
+ "\n",
+ "From this, we can define \"free space\" as $x \\geq L$.\n",
+ "\n",
+ "Therefore, we need to match a free wave with our Airy solution, at $x = L$.\n",
+ "\n",
+ "We can define our free wave as:\n",
+ "\n",
+ "$$E_0(x \\geq L) = \\tilde{E_0}_{FS} e^{-i (k_0 x + \\phi)}$$\n",
+ "\n",
+ "We will just consider the real part of this:\n",
+ "\n",
+ "$$E_0(x \\geq L) = \\tilde{E_0}_{FS} \\cos\\left( k_0 x + \\phi \\right)$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We want:\n",
+ "\n",
+ "$$\n",
+ "\\tilde{E_0}_{FS} \\cos\\left( k_0 L + \\phi \\right) = \\alpha A_i(- k_0^{2/3} L^{-1/3} L)\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkAAAAHACAYAAABKwtdzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAgAElEQVR4nOxdeZxcRbX+bvcsPXv2yUIIAzGQR0jARCAJkU3DLiogChhke8QIiGyKqBBAo8hDRB4RFIhAMAEUxWdYIhIIBDCEhEUCYUnIwiRDttl7err7vj9u33tr7+pOZtL2nO/3i3371q1Tp+oO1tffOVXluK7rgkAgEAgEAqEPIbKnHSAQCAQCgUDobRABIhAIBAKB0OdABIhAIBAIBEKfAxEgAoFAIBAIfQ5EgAgEAoFAIPQ5EAEiEAgEAoHQ50AEiEAgEAgEQp8DESACgUAgEAh9DkSACAQCgUAg9DkQASIQCAQCgdDn0KME6IUXXsApp5yC4cOHw3Ec/OUvf8la5/nnn8fEiRMRi8Ww77774re//W1PukggEAgEAqEPokcJUHt7OyZMmIA777zT6vm1a9fixBNPxLRp07By5Ur88Ic/xGWXXYY//elPPekmgUAgEAiEPgantw5DdRwHjz/+OL785S9rn/n+97+PJ554AqtXrw7uzZw5E2+88QZefvnl3nCTQCAQCARCH0DJnnaAxcsvv4zp06dz94477jjce++96O7uRmlpqVSnq6sLXV1dwfd0Oo3t27dj4MCBcBynx30mEAgEAoGw63BdF62trRg+fDgikZ5PUS4oArR582bU19dz9+rr65FMJrF161YMGzZMqjNnzhzMnj27t1wkEAgEAoHQg9iwYQP22muvHm+noAgQAEm18SN0OjXn2muvxRVXXBF8b25uxt57743/nvs0fnnW4cH9ZCqNg29cDAC44xuH4JgDhgRlly9YiX+sbgIAvD37OM7+uOufBgBMHNUffzj/0OD+6sZmnPHbVwAAL37/aPSrLAvKDrrhafiBRZ29q48bg3OnNAT3b33mPcx7aZ2xzsgBFXjyu58P7m9pjuPY254HAPz9siMwamBVUHbCr1/Ahu2dRnvnThmFq487ILi/cPl63PR/q411xLL2riQO+9mzAID7zv0cDt13QFB2ycMrsOS9rUZ7X/yvIfjVmYcE95ev3Y7z5i0HALz6w2NRVV4i1RHtpdMuxs9+BgDw868ehJMnDA/K5ixajfmvrjf6cMCwGjw2c0pw/+Nt7TjpjhcBAM9ddSQG18SCsi/8zxJsbuky2rvk6NGYedR+wf0l7zXhkodXYtzwWiy4eDIIBAKBIKOlpQUjR45ETU1Nr7RXUARo6NCh2Lx5M3evqakJJSUlGDhwoLJOeXk5ysvLpftOWQVqa2uD780d3YiUVwIA6mprubLSiqqgjL0PILhfUVXNlZXsSAZlZRXVqK0NJ0mnrBI+XWPruK7LtFPHlcUqq7P6UBqr5Mqa4hHBh/CPpiRWhUi5Y7RXWVXD9ykWjkNVdQ2iEUeq4zi8va7WrqCsppa3FymvQqS8w+hDeSU/rrGqRFAWq6xGbVWZVEe019YVvouqmpqc321prIofh3a2rBq1tWG7KKtEpDwq2WPfrfi34pS1IVJeidq6WskHAoFAIPDorfSVgtoHaPLkyVi8eDF375lnnsGkSZOU+T8mdKfS3Pe2RDL8IoxtMpU9D7wkyg9Vazy0J7alQ7w7fK5UsJdIZrfBEhIA6Ejofei2sCf+kbHfdH0S/e5MpILrVJofx3h3CtlQIsR52Tq248r6INqzsVFWwtfpYOzFk3wfEhp73czfUGmJeowqywrq9waBQCD0afQoAWpra8OqVauwatUqAN4y91WrVmH9ei8kce2112LGjBnB8zNnzsTHH3+MK664AqtXr8Z9992He++9F1dddVXObYsTHztJioTHhmyWCuSDJTPJtN1CunaGsJRE1KG+XMBO1LZkIck8J/abJUS6PolD1dEd9kkkByIhsgHbJx3ZEJFmxi6ZFoigBbkV+8SSMJHE6cgy2640Rpn3XlEWzeoLgUAgEHoHPfqT9LXXXsPRRx8dfPdzdc4991zMmzcPjY2NARkCgIaGBixatAjf+9738L//+78YPnw47rjjDpx22mk5t50QJipukpQm1tzlNrM9NdjJUyQYLPlwXVcpAYpTL0swxIleJyGypCIiESDWV3WfRB9Y5UpUsWxkTNEeSyRsyItXh30XwjhY1Bdb6UqyxNKOLLM+SGOUGcvyaEEJrgQCgdCn0aME6KijjjIqG/PmzZPuHXnkkXj99dd3uW0xBMROjN1pF6lUCt3d3QCA/uXAiBrv13k8Hufq+fdry1yuzEl1B2VdXV2Ix0ulOqK9rq54UOaku7my6tJ0UNba3smFZfz7gysiXJ1UdyIoSya6uLIhlREgJfepsyv0uzKa5spKkQrKOjrjiEXCMfTvl0Qcrk4y0RWUpZMJrmxQzGJcS9PacY13xhGPR6U6or1EnB1X3od+zLtt7+jkwoj+/QHlfJ/SzLimuvlxHVETRWupK/kQ7wzrlDsprqwESYyoiaJfuTwOuwulpaWIRklhIhAIBFv02kaIvYWWlhbU1dXh5Fufxt+uDPcUentTM07+zYtwAPzujP0wojLs9ra2LnRmQlp79a/g7G3c4a2kipVGMKg6TLbuSCSxvd0jUENqyjnC4tcR7SXTaWxu9lYQ1VWUoiYW8s+dHd1o6/JCJcP7xRBhpAbfXmnUQT2TbB3vTmFrWwIAMKi6DLHScALc3BwPVAnWh3TaxSfN3iRcEytBXUVI3NriSezs9Po0rC7GkQXfBwfACMZeIplGU6vXpwFVpVyey6etXehKmse1siyKAUyic3tXEjs6chzXVDpYmdW/spRbObajI4H2Lk/RGdEvxqlSvr2ykgiG1ITvtjORwrZ2b1wHV5ehnBnXxp2d8Lk060Mq7aIxM651FSWoiYXj2hrvRnNnElXlUfRnVgvubvTr1w9Dhw6l/a8IBMJ/JPz5u7m5uVcWjBRtVqYYPfHDRV8dW4UBJUkMGTIMlZWVcBwHZTs6AvKxT30NN4EkKloAeBP1yAHhMvPmjgRKWrwJb+SASm7i9+sAQMPQ8CUmulNIb2sHAAyqKcfAqnDSbWqJY0eHN+mOGlLNJfP69kqjETQMrg7ut8W7EdnpTeLD+1Vwk677aVuQF8T6kEylkfy0DQAwoKqMW+K9vT2BslavT3sPqkJZSTjx+z44cNAwNFxt1pFIAtu9lV71tTFuO4CS7e1BTg/rg+u6SFS0AgCqy0swon+4ympHewKlvg8DKlFhMa5dzLgOqYmhP0OoKps7A1I3akg1oopxLS+NYh9mC4GWzgSiGTKzV/8KVJWH45pqakMqLY9rdyqNVGZcB1aXc2R5a1sXytu6UFdRiqF1PBHcHXBdFx0dHWhq8rZyUO2XRSAQCAQeRUuA0kKOTTLtoqLEwbH7VmPgoEHcsvqSshSclDcxxmK8SuCUeBNhtLQEsVhIFjpSETgl3kRYVh5DjFEdIiXxIA+ErYNoCk6JNxmXlpZzZaVxF04iU6c8xq06832IlES4Ol1uFE5JKuNDOWIxZsl4aQKOk5Z86E6l4ZQkMv3mfSjpBt8nRvnwfXAEe0l0wylJMj6EE3+0NAknnZR8cF0XTklXxodSrqws6cDpVI+r74Nojx1Xr0+hDyWdaTjd3vss14xrtCTK2YunhXfLEMtIaQLplDyukSQzrsK7LUkATomLUmG8dycqKjxi1dTUhCFDhlA4jEAgELKgaLMyU66cBN0vFkFp1EFpTP8rnK1mig664B4USnNP/nUNZXojrurS7IGpIYuGjX4b6rNjaWomn3gs3+6uR3Rt+2SopSzq6chUZaWnpPm5bQQCgUDQo2gJkEhekik3s+rJgYmgWBMRV3mZxSe7OtpJVz2vaqDuoy3/2R2pYdzKNs62vg5PQG1b0hPBfIil7XuyrePuBlJmA8r9IRAIBHsULQES96BJcwqEQdnRzGTSER1cHcGIjfxinKjtJsy8VCOWLIglvUbq9IRFqGXng6lGHqoWX5iHD5oqxE8IBAKhcFC8BEiYhWw35etRBcj0zRDOsjJoWccc4svDB0X1JUuWwHEctDTvzNk2S/5eXrYMBx10EEpLS/HlL39ZX8egGumIiW14c9dDcnmOJYFAIBB6FEVLgMQkaI4A5ZXXYSrhv+l+6OejsADAIw/eh8kHjER3Mtx1ua2tDUP6VeFbXz2Bs7d06VI4joO1H77PtNuD+TeK6ylTpqCxsRE1tXWMD5btMIXXfv9qHHzwwVi7dq1yzyh1dbse5k1uNRVt8pBIACIQCITCQdESIJMCZAr9GHObucfswlkGA3ofBBw6ZRo62tvw7zdWBveWLl2KIfX1+PebK9HZ2REYXLJkCYYPH46G/T6T3YXdoVQoBq+srCzv/WhYa2vXfoRjjjkGe+21F/r166do2kUymbQOvVlwFKkorzwknQ8UAyMQCISCQdESIOFIKIkQ6dBbITDrSdt1sc9+n8Hg+mFYvmxpcH/JkiU44aRTsNeoBrzx2r+COkuWLMkcP+LdeOCe/8X48eNRVVWFkSNH4rJLLkFHu7dfTUtLMyoqKvDUU09x7f/jyb9hyIA6tLV5z23atAlXf/t8HDFuH3z+oH1x6qmnYt26ddo++SGw5p07AAB/feRhDBo4AE8//TTGjh2L/nW1+PY5p+PTLZuV/d+0YT0mjOyP7du24fzzz4fjOJg3bx6Wv/wiJozsj5eWPItJkyahvLwcS5cuBVwXSxY/ia+feBQa6vtj3333xezZszPkyPOqtaUZs2bOxJAhQ1BbW4tjv3As3nvnLQAKZcYFuhMJ/OxHV+O/9huFWCyGffbZB3PmzAkemTCyP+bOnYsTTjgBFRUVGDvmM3jm//7CDcT3v/99jBkzBqNHDMSJUw/GLTfPllZoPfHEE5g0aRJisRgGDRqEr371q0FZIpHANddcgxEjRqCqqgqHHXYYlixZohwzAoFAIOSGoiVAYs4PpwAJBKMjkUK82/vXkehGRyIZ/AvvJ4V/YZ3OREpZR6rX1c3V0Yem5PufmzwVrzIE6LnnnsOUaZ/HpMOmBMQokUjg5ZdfxtFHHx3Ui0QiuP32X+Ptt9/GH/7wBzy/5Dn86qfXAwBqaupw0kknYf78+cFYAMCTf3kMJ518Cqqrq9HR0YGjjz4alVVVuP/Rv2Pen59EdXU1jj/+eCQSCX7QDayuo6MDt956Kx588EE8+8/nsPmTjbjt5h8r1ZKhw0fg2RXvora2FrfffjsaGxtx5plnBs/c/rPrMWfOHKxevRrjx4/H4sXP4LrvXoyzzrsYz73yOu6++27MmzcPP/3pT4N+XfKtM7Fl82YsWrQIK1aswCGHHIL//vqX0bxjh+SrC+Dh++7G84ufxO//8BDee+89PPTQQ9hnn32453784x/jtNNOwxtvvIEzv3EWfnDJhfjo/feCPtXU1GDevHn458srcM0Nc/DQH+7Hr371q6D+3//+d3z1q1/FSSedhJUrV+LZZz1i5+O8887DSy+9hAULFuDNN9/EGWecgeOPPx7vv/8+CAQCgbBrKN6NEC2ToDu7UzjxjqXKsp7GOzceF+wgrSVDmS+TJh+BW2dfh2Qyic7OTqxcuRKTpx6BrS2d+OP9d8MF8Morr6CzsxNHH300fGpyzoXfxoHD6xCNOGhoaMCPb7gBl37nO7juZ/8DFy7OPvtszJgxAx0dHXABtLW2YOmzz+ChBQsBAAsWLEAkEsENv7wDjuPAAXD//fejX79+WLJkCT439Si138L37u5u/Pa3v8V+++2Hru4Uvn7uhbj717+UkpFduIhGoxg0pB5wHNTV1WHo0KHcM7Ou/CG++MUvBt9v/cXPcf6sy/GlM76BQdXlGH7wf+Gmm27CNddcg3O/cxX+tWwpPnj3HSz552bUVXt75dxyyy/x2J8ex+JFf8U3v3WB5HnjJxuxd8N+OHzKVAyqiWHUqFHeO/sk3I369NNPx4UXXggA+MkNs/Hk08/gj/ffg4m3/wYA8KMf/QgAsGF7B6oGDsO2TWvxyCOP4JprrgEA/PSnP8XXv/51zJ49O7A5YcIEAMCHH36IP/7xj9i4cSOGDx8OALjqqqvw1FNP4f7778fPfvYzEAgEAiF/FC8BMilAvbQvy+5AqABNQ0dHO5YvX44dO3ZgzJgxGDRoCCYdPhXXXT4T7W3tWLJkCfbee2/su+++eHezN1H/a9lSXHHPHVi9+h20tLQgmUwiHo+jo6MddRX9cNJJJ6GkpARPPPEEpk7/Ev6x6G+orK7GsV/wCMaKFSvwwQcfYPIBIwOfIo53qOeHH36ISQwB0joPb5O+/fbbL7g9aMhQbN/6aV5j8l/jD+a+r1r5Ola89hp+95vb4DheSCuV8g4k7ezowOq3VqGjvR0jhg7h6nV2dmLDx2uVbp96xlm4+Kyv4LBDDsJJJ56Ak08+GdOnT+eeO3zy5LCOC0z47OfwbiasBgCPPfYYbr/9dqx5/320tbUjnUpy59usWrUKF110kbKPr7/+OlzXxZgxY7j7XV1d3C7mBAKBQMgPRUuAbJfBV5RG8X+XHuGdaQVg9JDq4AiIrmQK72/x8mAqy0qw7+DwvKjNzXFsbfOOcxjRrxL9q8LjEv69qTmY+8eNCFdCtXR2Y33m3Kz+lWWoYI6a0CVi+1/2btgXQ4ePwHPPPYcdO3bgyCOPBOBi0JB6jBg5Cq++sgzPPfccjjnmmKDaJxvX45IZX8PFMy/GzTffhAEDBuDZ557HrJn/jWR3Eq7rJSyffvrpePjhhzF1+pfw5F8fw3GnfAXREu9PI51OY+LEifjxrXMBePsh7Z85C2zw4MFIWW5CWFpaypU5jqNcim6TqlVRWcV9T6fT+PaVP8Cxx5+CfpVlGFoXHjfhxGJIp9MYNGQonn32WcQyilt3Ko0Pm9pQU1cHCS4w9qAJWLRsFf796gv410vP42tf+xq+8IUv4MY77lN3MPPFcZxAjfPVnR/M/jncsgq89PQT+O2dvw77UaHfkTydTiMajWLFihXSsRbV1dWaWgQCgUCwRd8hQIYNDmOl0SBkVllWEhCgaKYMAGKlUe7A04qyaFBWURbhytjTwytKo8FqqO6Uy9nTrZLSrUI6bMo0LFmyBDt27MDVV18dPDfp8Kl47tnFeOWVV3DeeecFz7/z5iqkUkn88pe3oqzU8++hhxdI7Z199tmYPn063lv9DpYvW4rvXPXDwInPfvazWLhwIQYMGoTqmlo4joPRDKnbliGBsud6pS3f7QB0mHDwIVj34QfYu2FfDKwq4w5X/ejTNowdNwHbPt2CaEkJRo8eDcA7xb67qkXpg/+9uqYWXz7tDFz0rXNw+umn4/jjj8cVs29FdZ23Iu3VV1/Bt751blDnzZWv4YADDwJc4KWXXsKoUaNw3XXXYf22duzs7MbCDeu5dsaPH49nn32We2c+DjnkEKRSKTQ1NWHatGm7PkgEAoFA4FC0SdDGfYAsoUtMBvKdxPVP6krY+4dOnYYXX3wRq1atwpFHHhn4MPHwKXjoD/cjHo9nVoB59fYa1YBkMok777wTH330ER588EHc+7t7pDaOPPJI1NfX47KZ52P4Xntj/Gc/F5SdffbZGDRoEL57wdl4/dVl2Lh+HZ5//nl897vfxcaNG/PchXkXtxAQcPUPfoj/+9MCzL3t53h39TtYvXo1Fi5cGOTgHD7tKIz/7Odw5hmn4emnn8a6devw8rKXcOctN3NbCwQ+uMCDv7sLT/71T3h/zXtYs2YNHn30UQwdOhS1deFy/Mceewz33Xcf1qxZg5/eOBtvr1qBr3/rIrhwMXr0aKxfvx4LFizAurUfYf59d2PR357g2rn++uvxxz/+Eddffz1Wr16Nt956C7fccgsAYMyYMUF+1p///GesXbsWy5cvxy9+8QssWrQoj1EiEAgEAouiJUApYSY1ESCbXZiNoZk89pSRVz/p95HxcdjUaejs7MTo0aNRX18f3J90+FS0tbZiv/32w8iRYa7OAQcehKt+8lPc+stbMG7cOMyfPx/X33ST1I7jOPjGN76B1W+/hRO/cgZXVllZieeWPI9hI/bCFf89A18++jCcf/756Ozs5PJZVI7bkDqZNOVOgY794nTccf8CvLL0OZz8hc/j8MMPx2233YZRo0bBzfTvfx94BFOPmIbzzz8fY8aMwTnnnI1NG9dj4ODBSuZWWVWF++f+Gl88cgo+97nPYd26dVi0aBEikfA/mZ9cfwMWLFiA8ePH44/zH8LP7rgH+405AABw6qmn4nvf+x4uueQSnHjUFLzx2qu48vvXcq0cddRRePTRR/HEE0/g4IMPxjHHHINXX301KL///vsxY8YMXHnlldh///3xpS99Ca+++ir3jgkEAoGQHxx3d5x6WUBoaWlBXV0d9r3yMXx462nB/QdeXoe7//kubjh6CMaM3hejhoS/5NdsaUW8OwUA+MyQalRkwlmdiSTeb/JygGKlUYyprwnqbNrRiW3tfg5QBQZWlwdlb24Mj4AYN7wOEe8UVuzsSAQ5QP0qyrD3QD5U09bl5SHtO6gK1TEvZyaRTAcJzWXRCA4YFpKOzc1xNLXGAQD1tTHU14a5L+80tiCZ8jZDGjusFqVRb+JujXdj7dZ2AEBNrBQNg8J8mo+3taO509unZtSAStRVlgEAkul0sPop4jhcXtOnrV1obO4EAG8FVr8wr2XN5lbEk964jqmvCcJ/7V1JfPhpmFs1ekiY07JxRwe2tyeyjutBI+qCEOKO9gQ27Ahzq0YOCMf1w6Y2tGfyu/YbXI2qcu/dxrtTWLOlFQBQXhIN8poAoLG5E5+2eu92aF0MQ2qYcf2kBcl0GhNG9sdjf/oTTsvs29Pc2Y2Pt3njWhsrxT7MuK7b2o6WeDdG9K/AwKqwP7sb8Xgca9euRUNDA2KxWPYKBAKBUEDw5+/m5mb5B3YPoGgVIHEZfDJlkF+gLjKLPtkVG7NtU4DNrsS0+7CuI6bzsPLZNTlfz3VP6RW4XR2hvMQl48DytrP759BhGAQCgVAwKFoClMtp8FYTo2mTmzxCYKYHrcNmBv929UBPg2ltmbwKTB1aNB1eqrVt9MnaQ7UPOeR37cpYEv0hEAiEwkHRrgIDvERoP/xkfRq8bqIWn9NcKywinPr0uUY2+TKmwnwOAd0tsU+TD1qGZqnmZGNAmWE151bpyuwUQZ2Db2zYgQOGqiVabX4XMSACgUAoGBStAgTwS991y+DtYUkwTGEly3ZtE7HtyZGFcX114/3ctZcs9fN4Tab+5UMsbVUpYwhSAeI/BAKBUDgobgKkO//Lsr5tnd2SWqKxYp23kkd4zRi607EXAwnbHen0rqYxW+KVD7GRbdspdbqxlI/38EAEiEAgEAoHRU2AuLwfywScvMIkBpVHO1EblAq9ymBbJz/1xeY5c5hLj3wSrLOHFmXbORrJHfnEEIkBEQgEQsGhqAlQPvk8utl0tygQhjIdK+jJ+TvfJ12tPJQ78hkTzwc7K3aKTQ7tWuRT6c0RAyIQCIRCQVETIH7lFwNb1cKycHeTlHwkG2sf8lBsbCvlkh9k1+7urm9HLLXExjqJy+4xAoFAIOw5FDUBYuch0zL4niQztnknNmXGvCHTPjSa/snLv3MnOkaepG1X74O2HdtcHBO076J3GAvpPwQCgVA4KG4ClGaud7uyoMtByU+m0RZZ1ln24gtwHAc7d+7kyn743Ytxyy/mWNv+n5t+jJ//5Ps5hKZsnbVgQ7sBuzsdyH5PoJ4LWxIIBAJh96OoCZA2BCbApDTY1MkntGJLbMTrZcuWIRqN4vjjj+fqTDz0cDQ2NqKuLjymYs3qt7H02Wcwc9Z3svuTwbe+fRn++sjD+HjdWhtXs9rL1YY1rEmURcv5dnB3xx0JBAKB0GvoMwQoHwlIR3KMz4mhmrxkB/39++67D5deeilefPFFbNq4ISgqKyvD0KFDg/Ox4AIL5v0eXzz5VNTU1GgMyhg4aDAmf/5ozLv391p/7LuU/UkjacpDMTOtrsvHB9ua5tBi3g0QCAQCoYdQ1ASIzwHKvU6P5gblUdbR0YZHHnkE3/72t3HyySfj0YcfCspeXsqHwNLpNJ75+19w1BdPCAy+++672GtwPyx6/NGg3p///GfEYjG89dZbQbtHffEEPP7YQjsP81CyTMgn/ykf23klQe+qcUoCIhAIhIJBURMgXeIzT3JcOB3twT+0twHt7cE/voy5z5a1tWvruO1sWVtY1t5uSDBRz6BPPfE49t9/f+y///4455xz8MjDDwaKh1jjvdVvo7W5GQeOPyQoO+CAAzD7pz/Hz350FT7ZuB6bGxtx0UUX4ec//zkOOuigoO64gz+LTRs34uOPP1b6oU3nsWQV9iFHS9XNdN+CmORTJycfMiD+QyAQCIWDoj4LzCoC1tGBA0YPVxbVAjhIWQLsrblfYqgzOPMvQFsbUFXl+cfc1l3/ZeGDOPfsswEAxx9/PNrb2/Hqi8/j8GlHSW19smE9otEoBgziWsT5F12Mv/3977juuzNRXl6OiRMn4rvf/S73zJChwwAA69atw6hRo/ZYBsuupvYYq1hvDb7rGdsUASMQCITCQ1ETIFYBSnNkqMCnJIV76z58H2+veh1f/9tfAQAlJSU45cun4S8LH5IIkOu66Ip3orSsHI7jSOZm33onTj1yEiKRCN7597+5vCEAKI9VAAA6Ojps3cvaD33SuJgvY2dd+1RexEif3WzLjWwT3AkEAoFQGChqAsT/yNfMSpWVWP3+J0imvTXzI/tXol9lGQCgubMb67e3AwAijoMDh4crrD7e2o6Wrm4AwMCqcgzv55GG7lQa725uCZ4bPbgGFWVRAEBTaxxbWuIAgIqSKEZXVlp0wvt4fMGDSCaT2GuvvZj+uSgpLUXLzp1S7/oNGIh4Zwe6EwlJ/lrzztvo7OiAE4lg8+bNGD6cV8Badu4AAAwezKtHu4RdPYw2z1wj6/wg1w2IoG1oK9cQGIFAIBAKB0VNgNKaSZeboBwHbmUV3AwBcqsqgQwBQqQbbjxTx3GCcCXhJ8YAACAASURBVBUAuJ2AG/UIkFtZBlRlyEwqDbcyFdqvqgTKMsOcisJNemTILY0CjjorRFRLkskk/vanhbjyxzdjxulfQiTi1dvc3IkLZ5yFv//lERw8fjxXa/8DvUDch++/h/2HHx7c37F9O358xXdw4aVXYsfWJpx99tl4/fXXUVFREbT7wXurUVpaigMPPFDpnzafx9CPfBSbvKJURuSeOL0bImABKAeIQCAQCgdFnQRtLzpkj2Xks2rLVCaTBb2zL/zjabQ078RXvn4ODhw3DuMy//YfeyC+eOKX8PiCh6Q6AwYOwtiDJmDl8pe5oisvvxRDh4/ARZddhe9f/zO4rourrrqKq/v6v17GYZOnoqKiQuPrrmF3cAp9pMyQOL0bE5pNyPfAWAKBQCD0HoqaAHE5QGk9wdBOyHlMmHnVMTznAnh84YM4/IgjUVNbJz33hRO/hPf+/RbefnOVVP+0s87FoscfC+4/8MAD+MczT+Gnv/4tSkpKEKusxPz58/H73/8eixYtCp578q9/wtnnnmdwXKOs9WhulZ2+1JvpXbar2cIi0oAIBAKhUNArBOiuu+5CQ0MDYrEYJk6ciKVLlxqfnz9/PiZMmIDKykoMGzYM5513HrZt25ZzuzrOkw8RsZV5pGl6N0zIv7l/Ae78wyPKxsYeNAFvbNiBC2ddCtd10a9fv6D4S6d/A59uacSrr7wCAJgxYwY+3rwNoxr2C56ZOHEiurq6cOKJJwIAXnj2aUSjUZx86le0/ugSmk2wPRMtr3eTR7smg7scetPdJ/5DIBAIBYMeJ0ALFy7E5Zdfjuuuuw4rV67EtGnTcMIJJ2D9+vXK51988UXMmDEDF1xwAf7973/j0UcfxfLly3HhhRfm3DarSNgTkdyDIXlxHMPMbzwg1KaxYDVXDDf/6rfYtnWrph25YmdHB2b/z52IlpRA+6QlQdjlHCCD7ZzbEZ+zjVJlGa9s7bAg/kMgEAiFgx4nQLfddhsuuOACXHjhhRg7dixuv/12jBw5EnPnzlU+/8orr2CfffbBZZddhoaGBhxxxBG4+OKL8dprr+XcdtqSVOh+/WseyTy3a1kjuyNSY3OK+aTJU3H8SSer2xVJgAscd8pXMP6QSbvBO1vYxSNNUbge8cOioXyUMAKBQCAUBnqUACUSCaxYsQLTp0/n7k+fPh3Lli1T1pkyZQo2btyIRYsWwXVdbNmyBY899hhOOukk5fNdXV1oaWnh/vnQKUD5J97mXtO2XR0xsQ0R7Y7+6WDtQ9Yb8m2zr3Z5W9z9PJnS7k2C3h1WCAQCgdCT6FECtHXrVqRSKdTX13P36+vrsXnzZmWdKVOmYP78+TjzzDODAz779euH3/zmN8rn58yZg7q6uuDfyJEjgzLt5oe2SdCWMNffRWayW+ZOXaimF+NPJjKjIZa7RyVj27F8cBfboUVgBAKBUPjolSRoR9jvht10TsQ777yDyy67DD/5yU+wYsUKPPXUU1i7di1mzpypfP7aa69Fc3Nz8G/DhvCEdPH8L48QuejNMJXe9m7OKTI3lrP13grR7ZZ286iUDxeyzhvaQyj4Hc4JBAKhgNCjGyEOGjQI0WhUUnuampokVcjHnDlzMHXqVFx99dUAgPHjx6OqqgrTpk3DzTffjGHDhnHPl5eXo7y8XGkrs7chAG/y2hlPozvlIpXoyqs/LjSJrAYVZHfnidjlKFm2mkcisPjVOgE5HyEsn/BhXtTGUMM6qzr7cz2dBO0fXVJaWtrDLREIBMJ/PnqUAJWVlWHixIlYvHgxvvKVcFn14sWLceqppyrrdHR0oKSEdysazeyenOMvXP4sMBedSRfPftSGr8Q+xba6GCorK+E4DtLJRGC7uyuCeIl3nYgn4CYTgY14ZzzYhTnZ3QU36e34nEykEY97YlqiO8XVSXRFEYf3XHeiKyhLpyOIx+PBc6nuRLAbdXfCgV+U6OrmfYjHkS6JZNrtgptMZuqnEY9745RMpwUfIohHPNsJxoeU48g+BH0C4nGvr/FEkrPX1RmHk4oyPnRn7KUQj4fvTvLBH9cuflw743FEMopgihnX7oQbjGuXMK7xrjiibgnjQ6ZPLj+u6W7m3RrGtTMeR2k0wvggj2siKY5rFHFHfrepiCP7kE6jqyuOiLv7/5NzXRcdHR1oampCv379gv9eCAQCgaBHjx+FccUVV+Cb3/wmJk2ahMmTJ+Oee+7B+vXrg5DWtddei02bNuGBBx4AAJxyyim46KKLMHfuXBx33HFobGzE5ZdfjkMPPVQ6syobVKrDn1e3Y3BVOQZWNwVlTTs7g2cTFaXYGfOGpSORxPb27uC50o5YELr7tLULXUmPVLSVRdG10zs+ozuVRlNLqDClW8oQK/UmpObObrTGvYm1JOLAaY+FPjTHkcokLcVjJWit8H7Fd3ansK0tnHQj7eUoiXgT9ba2LnR2ez7ESiPo3ukpYem0i6bmcAJONpehMnMeWWu8G82dng8RByjtqAie29ISR3fK86GjvATtlZ4PiWQaTa1hn5y28oAsbG9PoCPhkYCykgjSLaEa17SjM7hOVJZiZ7k3ru1dSezoUI9rU2sXEplxbS+LIr5DPa5uSxnKM+O6s6MbbV3MuLYx47qzM8gF66ooQXMsM66JFLa1h+MabY8hmiG3W9u6EM+Ma2tpBInMuCbTaTQ1hz6kWspQUaoe15J2Zlyb40imXaC1HGUlPRd17tevH4YOHdpj9gkEAqGY0OME6Mwzz8S2bdtw4403orGxEePGjcOiRYswatQoAEBjYyO3J9C3vvUttLa24s4778SVV16Jfv364ZhjjsEvfvGLnNvmcoBc/x7wzw0JXP2VMeju9ibhmb963pugAMw8cj+cMdZLpH7q7Ub88rn3Ahv/d+kRqMic6/XrBSvx1qZmAMDnxwzG9afsDwD4eFs7bvjr8qDOz756EMY2DAQA3P3Ch3hk+ScAgMHV5Vhw8eTguavuegk7Oz1/zjlsFM47ogEAsHTNp7jhuX8Hzz10wWEYljl49d7H38bLH3l7/Ewc1R+3nH4AAKClM4H//ku4yu6HJ47FsQ1eyHH+qx/jvhc9H0qjETx1+eeD5266/1/4eLsXRvnywcNx6bGeD29v2okbngh3mp57zkQ01NcAABYuWo3Fqz0yOaa+BnPP8XxIpV1c+OfngzqXHfMZnHrACADAorc+wf88tyYoW3TZtIDM3PLQCqzZ0goA+OLYevzgRM+HtVv5cb31jAk4YO/+AIA7//k+Hl/p+VBfG8PDF40Nnrv0jqXo7PYI2vlHNODssd7f3fNrmnDjc+8Ezz1y8WQMrPaIztzH3sCKj70DYQ9tGIA5X/X61LizEzf85dWgzuwvHYgjGrwDYx96eR3uX+aNa1V5CZ645IjguWvvfhmftnVh7tkT0TC0Bj2B0tJSUn4IBAIhB/TKYaizZs3CrFmzlGXz5s2T7l166aW49NJLd7ld3SqwtOuF1fwJY1NrKiBA8XQUsZinICTcEmxqDQ82LS2PIZZRMbbF3aBsZxeCOtHSbq5O2ikNyjqSkaAs6aSC+wDQ2J7G9navrD0VCcpSEd6HkrLyoGxHV+jDPnE3bCcV4ep0oyQoi6ejQVlpNM350NQZ2mvpDn1wo2WcPSdaFpQ1dztB2YDa0IdkKs3VibvhuHYJ41pWHkMso1BtZXxo7naCOk5Jgh/XSDiurYwPEPr0SVsqUKg6mXFNolQ7rtvjCMq2xdl3y/cp6YTj2p4Kx7Um4XA+bG5PY3NrCpHSMu4+gUAgEPYc+sxZYK6GDInPcXWgf441obsv24P2OVfTbj72xP6x9tgz0dIGH0x94v3TjZ3ettEeLH3QJEib3i1fRxgjzftkx8tUR+e3qh6BQCAQ9jyKmgDZkgrtqibxOWZVmZ4MiT4wZSbyoakjEwn22o58cKvhmPuptDhRq6/FCT2t6S9/ra8jE0umTGPPSARtx9/wnA25leuo29G9s4hm6wcCgUAg9D6KmgDlOkF5dQxEQlNmntx1io3wnIYcyURC9xxrm/fbROqgKTMqNhZ9MvlgVp507ZjImt1zPMmxtGdQ1nT2ZLLmfRL/IRAIhMJBURMg/a9/w0RoIB96ImGpLtnazkut0vdJF+Iz1TOGi7T1oQW/E7dJAdKRD96eDREUnTVto8CFunaZEKudIAJEIBAIhYOiJkC6fB7TxMrCHHaxU2xsw1TQ+CSrVTaExWBbKEprysz5N9knftucHfWN7Pa042V6Z5r7kjsaX63VM02ZQ+fBEwgEQsGgzxAgdlYy58vk/ovfHC7S+CZIFfpwil6h0tcXfNCxBcG+PmlcsKdRVUxKk31StaaOIbTIK3B6tco+WV39d2MMgVn4ECH+QyAQCAWDoiZANr/kTROmTBbU11LYRWMvnxwZXT6Jd61WoYxJxkb/dHUM9myVK66+3l4+yc22ipkxT0r7bk1kWe2fjlxRCIxAIBAKB32GANmEr8TnjJMu1BNjviEY/YQuEjSdSmPnt60yY8xDsgi92S5Hl+xxdezsmXK6tOSKd0Gv7nF+GuoYxjj8SgyIQCAQCgVFTYD0kzt7bSIihkk3rX7ORGyM++Tks//NbiEfUMJMmtRl5n2A1L6K9rQ5TqI9ra/Qw0RSoC4zheF0f0c6FYoUIAKBQCgc9B0CpLtvqUaY7JkndzuVQDdx2+aqmHNs9P7pfbUja9pxZQiiCNNGjbv6nmxXw4mdsll9lhb6ZLtizf9K+wARCARC4aCoCZA+BKZ+BtCHYOR6diEYW9s6dcKsKDHXafUzok/2YRyN47AjCFLekGaZucmeSdXK592a8pr0CqG+jilEpxpzoj8EAoFQOChqAqRfBcbeNoWL9JOk7r6tAmRUQQz2XM3sbJqoje1qxkKnxEg+aDQlswpl559t8rZuHHJbiaZ2yHaFn5FsUQiMQCAQCg5FTYB0kzs0ZEP1nYVOmbElTTa7BYv2JPWFIyl2E7Vt8q/NaizbOrmQj3y2F7AKb/JVjLlC2hV1ln8PcltyGYXACAQCoXBQ1ATIJrwjEwKmzDTpakM1dvaMOzJr2hTt2a5wMitP6ud0qopcR0MEDT6YzkHbncTSnDdkp4TZ7qJtm1RNIBAIhMJAkRMg9lo9mcoTl0nFYJ9jrq2VALXKkLc9CyVG/G5WvGzJh46s6exmIx/ZCYytYmPePFHvn00ekS251dkjAYhAIBAKB0VNgHQTqzHEYVA+9ARBb09HEEz+2drTkiZj2Ebvg82p7La+ms8Ps7NnIjNa24Z27M+Ay25bZUNnz790iAERCARCwaC4CZDu2pBjY85VURu0P2xU8M9V+CP6kIdaInbKbE9tW3fUhGhDf4QHVyWv5HLTSjStvTzIo/is/rw1k6Jk6FPmmo7CIBAIhMJBURMgG5XGuCOzkUhAfW1SNzT2THXyWYpvq9iI9ayVFM0eP/ls4CjWs92xW8dh8yGPqmdVz+W0a7iCJNJhqAQCgVA4KHICFF5rN84z1hHKtLs/s/b0KoGsYmT3QXRCf3q7topZqdA0tau7MO+O88jM5DG7rxJh0bw/2R5736CE5dhfioARCARC4aCoCZDNyirzfjym0A/XEPuQoY7anu3OyOKzugnYeH6YZC+8tt+1Wt2WrcJiVqF0apDod3ZfzeeH6e3Z7Pgt+mr2z1eACAQCgVAoKHICxF7riIOpjqFMQyrkMEn2tky7QhvVHJYsGHeCNpWpHbQNZ+natT0TzeSfzdgZr8U6mmtTW+ajUdTXOnuUBE0gEAiFg6ImQPls2Gd7UrxWdZAkoOzKhynXyLhM3/pAVpM6lNu1yV6+Z6zpV6LZjYMu18eoNImFFkpWOq1/TwrpT7JB/IdAIBAKB0VOgMJr7VRlqbBIZRbXJh/YMjm0orenUzhs65iSifW7IRtIk6F/LEx5Tbpvtu9J1yfb1WaiDXsiqLcdJriHBcR/CAQCoXBQ5ARI96veoEbY5qpYqEvyc7ZKBeuP4J+lQqK1Z6lq5XeAqqmvan9s7ZmX76vtmfy2D8NZqloaEsvepxAYgUAgFA6KmgDpNqqzz/OxK7NdMaVfBaYnTbaHphpJmEHHcDXP6fKdTGXWRMtgjyMpTIhPXHpv3qdIdTfbe9eRZdYuX8mG+LJ3aR8gAoFAKBwUOQEKr20OMvW+s/VNxETdTi4hNZ0CZB9Syz5pS3XEsnT2yd42RGciglx9S9JpGFZj4rkuBGY+FFbXrqUSprHHPkP7ABEIBELhoKgJkDZnB+pr8Y6JSGiXghvUHFnFUPtga0+bhyTYg4HwaR7j1ReTWqKpb3t+mOiTPgynZ006omOb7+T5pFHWDKvrjGefQUFuif8QCARCwaCoCVDKhiyIkyc74RlWZ+kUCJHkmENJ/kRt8MFSLTHvf2NrT0PqjPk8OmWNb8cULuJtq+3ZKjacLdP7y4Ec6eyZSFigQjF1KARGIBAIhYOiJkDcBGUbfrJOgpZtefVzsae+bz41PjvhMNWxVV/Mq9ey1xFrceNvOa75hCM5ewaSI8KGIJvDkWp7bB1KgiYQCITCQVETIJ1Kw343h7kMBnUJwyb1RTSnmaiNS/FZhUnbbg4KEPec2lmTAqTrUz5kweSPbTiSfVZ8f7wiqFeHbNux2XWaI0DKFggEAoGwJ1DcBEjPCZhVOqbJXVQxQljtMSTak/JOfFsGHwyEReuPQfmwzc0xkw99YxpOJ+TVWBIJE2mCHroNJvVqlaHvRvUsu39sfRKACAQCoXBQ5ARIPZEBhvCTQd7QEQnb86d0xESrDCmQ195Gtrk0tqROU58tM+9GrbenvTa8Jx1JlIfRjtRpiZLUjqt+DiHJY21FiAERCARCwaC4CRBzrcuLkVcDsXUMZIatY1BfdLZZe6adlkW1xCZPR6rD1VfTj9yIm55Y5rO034ZMGlUy0Ye0f9/gg8xmlGXWdbQhNJNWRSAQCIQ9haImQOYk2synVCe7siCWmVYrmTc1tPABIjThGUM4hiVEtrlQuv5JbVmqL/ns6mxSoXQbJrL2zUTQ4B9XZmonu3/sfRKACAQCoXBQ1ATIHBbiP8X76jo6pUJd33tOfc3ay4Vg6ENWlsQNQpmGCNqGrHR77ZiUNfu8puzk0bvWjx8Loz3NezKuhjMUqv6+aCNEAoFAKBwUNQFiofvFb3vQp1imC3+YQzUan3aHWmJQu8xEIvs4iANhm/NkXUdDJMxEUE/4dGeBGVUy7mG1r8ZQpa6MuU37ABEIBELhoKgJkIkUaLiHdmM/8WGdamGypz2bTHnXr29nz4poqfxLZ2/HtKOyDppUI7V/mnaNeT4W9kyr+OzDm4Z2LAgadxQGxcAIBAKhYFDcBMi4hFmtEpjYiM15YrkoSjanlkvLzLXXekWEq69TgISO87tRi+RD31YYUtMrQ7bJ5Sq7ah/U9kxHeNgqddYH02oIGnuX6A+BQCAUDoqaANnsjWM+LsEwSRps83WyT5K5hc00ColBLbFaim9SREQfNLbZtk377BjVIQuFS/yus2faTsA0rjar/cTvOrLF2iUBiEAgEAoHvUKA7rrrLjQ0NCAWi2HixIlYunSp8fmuri5cd911GDVqFMrLy7Hffvvhvvvuy7ldcwglM1Ebz+4SyrhrdYgorxVTQjv5nFnFkxJ9HWsCZMqxSavbZdvOZUdsXdKxcVw115wP0n3DuLLXWmIp1LGwxylAxIAIBAKhYFDS0w0sXLgQl19+Oe666y5MnToVd999N0444QS888472HvvvZV1vva1r2HLli249957MXr0aDQ1NSGZTObcNkdSNEQnl1CNfsIzkAUjmZFVAvE5+72IsoeEvDpqxca8a7KBfGjGKDeyoFZqbM8w06lQ5iM8TCqZ+to0DuI3MQeIuA+BQCAUFnqcAN1222244IILcOGFFwIAbr/9djz99NOYO3cu5syZIz3/1FNP4fnnn8dHH32EAQMGAAD22WefvNo2/XrXrhTS1DeV5XXWFli1xNAOhDJNWzbHMojPmXwwbeBndQSEUQnTjYO+jthQfqpW9jritf0RI5qyzCfxHwKBQCgs9GgILJFIYMWKFZg+fTp3f/r06Vi2bJmyzhNPPIFJkybhlltuwYgRIzBmzBhcddVV6OzsVD7f1dWFlpYW7p8Psyri3+ft2R8pYakSGMgCAqXC0I6BHKksivWz2tMpNtwzOfinJXU2SpjBB00IU3wOUG9CKPtgqawZVCg+DKq259+lYzAIBAKhsNCjCtDWrVuRSqVQX1/P3a+vr8fmzZuVdT766CO8+OKLiMViePzxx7F161bMmjUL27dvV+YBzZkzB7Nnz1baMogYVqGfvFQCyQd9oS4MZxuqUSXeOo5j9FtHoUyhNnNek5q1GJUrSx90YyzZ19TLRbHhn1OTtVzymvxHKQRGIBAIhYleSYIWkz/9iVqFdDoNx3Ewf/58HHrooTjxxBNx2223Yd68eUoV6Nprr0Vzc3Pwb8OGDWE7rF3bSVLwU1umey4XFUPwReWrNFEbJmRdn+zykAztSEUW6ks+PojtGOrY7FOUC6HK55y3XMJwtAs0gUAgFBZ6VAEaNGgQotGopPY0NTVJqpCPYcOGYcSIEairqwvujR07Fq7rYuPGjfjMZz7DPV9eXo7y8nKlLasJSqiT1wosk2JjOIdLO1Fzz9iFatjvJvVFSwpyIizqa9ZMTmqODRnNQSULk6BFe67yWvZP/ZycrG16FwKpI/5DIBAIBYUeVYDKysowceJELF68mLu/ePFiTJkyRVln6tSp+OSTT9DW1hbcW7NmDSKRCPbaa6+c2rdRKnI6ZVyTx8IrTaIPrG01mZF9U/sjtZVW29MlW5vaMi8z19vTrZSTFZvs9kx5PrrkbVNbuYQ3dfbsk6DVbfn36RgMAoFAKCz0eAjsiiuuwO9//3vcd999WL16Nb73ve9h/fr1mDlzJgAvhDVjxozg+bPOOgsDBw7Eeeedh3feeQcvvPACrr76apx//vmoqKjIqW2bfWRyCa3oVyvZhWp0yowcfjL5kLs9qwRkwZZ5zxxTmfyM5K3OBwPZk/J8djGpWoQuqTrfzRjFUCCFwAgEAqGw0OPL4M8880xs27YNN954IxobGzFu3DgsWrQIo0aNAgA0NjZi/fr1wfPV1dVYvHgxLr30UkyaNAkDBw7E1772Ndx88825N27IzQnVE/20aDuxmtQNY+hHE7SytSfnG6ntGUNgwTMmtcTggwB9SE3vg3YpvmHDRVOfbFb4mZQ/HVcz78lkJtiUBE0gEAiFhR4nQAAwa9YszJo1S1k2b9486d4BBxwghc3ygYErBDArLOpasraRXY1QFYY5QDnYM/lhMfGL0C4ZN4Z+TETCzdzX15G98X1Qk4hsPshQ2zOHFtV9MnBoIRyp9s+3S/yHQCAQCgtFfRaYScXQboRoUlgCgmGaWA2TuIWfgDyZ8s9mVzFyyZdBUEdNZJhHrOyFApA9+Uhr/GZNGPOatO9Jay5LUrVoz1UWGPPFBB9oHyACgUAoLBQ3AeJ+1QtlWjJjIBjiyp6wQHXJtSNes/ZNykduZ4tZKCm6MgNpyilR3Ip8CGWad2FWgPQ+6BK72UrGMKYupGaZFK/0gfgPgUAgFBSKmgCZVx5ZhH5Ee2m+rmhLrC+WaRUbTfgkmz1b8sH5kFaXyeKLpQ8aEmZSlLLtmqyqI6tQBnKrIao8sVTXMflhUqh0dfz7xH8IBAKhsFDUBMislnjI6/R2k7qRi4oRfOausJjsycpHdnu5LJ03EQndSezG0KLqGdEHQ86PpNik1fb474b+WvvHEkGNauQLQBQCIxAIhIJCcRMgm+TkPJQAEdmOp8hmLxeFxWZHZRE2ao4xxGRQc8Re6cbVrFy53KeN38ZxZail1gcNQ1ONoU2oUqeE+U/RPkAEAoFQWChqAgTjJC49wt0H7PcOMifQ6n2QQioKG7pnvOfMqkNwnwl76dQcE9kzkyN1mXE7ACnkZ9FOLoqNKz8j+ZBFscndP7MPpAARCARCYaGoCZAh6qJNlE0bZrUwF0SeJXUqhlF10OTL8N9zUTH8D5OSoo7vmFevGexBDV2ukcmejpx5/oll+j5pCYvJnvHdatphrrOdNUf0h0AgEAoLRU2AuI30NBOocZLUJRkr2tKlqNjk8+iIjNI/o0KVmcQl8qG3l8/hpTYrxHIhM2HOjv5lGJf2QyxTk1Gbpf3Kd6sjaBahymAfIFKACHsKH34I/O53wM6de9oTAqGg0CsbIe4pmH6hB5OuUIeb3MVQjf+pyROJwMltvxqFn6KvZoImlOnIh0Woxky0DPa0hMqefPjfc9mU0hiG07VjU0fBgPIKgWU+/b8h4j+EPYIdO4DDDgO2bQMefxxYtGhPe0QgFAyKWgEyT1DqiRoWk64qL0c3gep2GObt2YdWbMiR+awydVu6bQJUZXb2BN848qFuK9+doPW7UasVMqXfGh84/wz2RAdpJ2hCQeCJJzzyAwBPPgmsXbtn/SEQCgjFTYCMq4jU962OS1AQIN1eNtwcqauTi7IQ+G2aqLUuaFUWk8oj5ULpiwwrujS22UIDyRFhVqF09tT+sGVKBUi0q7Cn32jT+yQFiLBH8NRT/HdSgAiEAMVNgLhJSa2+5JLgq9sRmLWXW1K1usBmqbsxVGNUczR1DKqRHD60UaH4+yYf9JsxqttU+aSqabJnezQKe8+oahn+jgA6CoOwh/DGG97nlCne5yuv7DlfCIQCQ5ETIHYSF8o0SdDcknGNNJNTnojm2uSDKVykm4xt7elDNQa/TX2ytcepJWp1yHzkhr0PNqfB60UoFbnVqVp6IijuGk70h9DrSCSA99/3rmfM8D5ff33P+UMgFBiKmwCx17aTJFdHXaZcKq2kJOYVU36VXDZPDP3Wx2p0CouyLUWb3nf5GZU9HdExHq6qIWhqYqkhqqY+aX1g6+fig3xPtJFNCaNVYIRex5o1i8ss+AAAIABJREFUQDIJ1NYCp57q3Xv3XaCjY8/6RSAUCIqbAJkUBF2irE24SNGWjpgYJ37FM6J9nepg8sEUHrI/vDQ7YVG1JU784n3xmrWhVLV0feLerUhubVQtdR3V2OnKTONg6hOB0Cv44APvc//9gaFDgYEDPWnSV4UIhD6O4iZApklc+FQ9pw3vGJQK45Jxy4nanC8jPyPaN+bfaMpM45CXmiP5zdZRkyYxz4ctM9vT+JADuTXd15E6E70RfYgU9X9phILExo3e5957e5+f+Yz3SQSIQABQ5ATIasM+g/KhP+hTpRJY2MvjCAj5BHITCfPb1NvLFqoR76tgUnN02wsYfTApVppBMvqgGSOjApTezeMqEGKHsoAIvQ2fAO21l/fpE6A1a/aMPwRCgaGoCZBrmiU1E7XNKejK+VpDjkTSo7Zn8MEw8dvbc5XX7LNmlUdPZkSHdCex8+NqR0bZejolTOlflnZUbenGjr1nIlT6vZy8K0oBIvQ6dASIFCACAUCREyB5GgonIv2vetPEr1cJxGXU/unfdpvvZffbt2fKVdFO1Ap/pXHIQYUyEqogR4mf+HM5NkJlzyYMF8nSJ6tQoEoBEp5xhHfBPqOzR/yH0OsQCdCYMd4nESACAUCREyBVHou/H4uo5oiEQLzm7GZqRyMOc8+vw5cZFSVhog5JDtcYZ8+klkh5J4Y+heOgJh+8C4I9zXMq/6IO7zcgEwm/TLnDtmaMVD6EY56dCEp9UhBi0V5wX9EnN0ufaB8gQq9DJEANDd7nunV7xB0CodDQZwiQRDLS/MQfFYgRVyaQj7QwuXv3eDUnYpj4A3uCuhG2Iyssvj1VSEg3iYskR9VfMWRlUmxU/olkS6yj9EEYP/GoCdEW2yfTGDnCO0wb7KU1fWLtyoqSmkRz/kkEmyQgwh6A6wKbNnnXw4d7nyNHep+Njd7yeAKhj6OoCZDqPCtx8gp+oSt+7cvKjDBJMpOarFT4hfqJX0dYVPvLSIoN46dMqPg+qcJZ/qokUQkzTe4qUicTE78dl2tHpYRFBGYi2lLaU6ovmXoioZL8Vr1b9d8DIBMqG5IYEQmVbwsEQi+iowOIx73rIUO8z/p6oLTU+9XzySd7zjcCoUBQ1ASIm8SlX/z+fXUohL3WTYQRR54MRdVINfHL+Tfi5K5QbDQqFF+PtycSAlNbupAQZ89IEtXkI6roE5jx4/3mbXFtCe9P1aeAOIn2Ivz7Yx+SwmZM7pLvha8WiqoRZ00Yc1OfCIQeh38AalkZUFXlXUciYThs/fo94xeBUEAobgJkoaT4UJGFtGZS8+Ewi5slRcmkEoiEyvdBodhoVQcVAeLdM+fLWEzUYlK1jmgpfTAoSuK4yiEwRW6V0I5SUZKSk13NfTk3RzxA1YFMWqTwIUdUPch5SCGhIhB6DVu3ep+DBvF/fH4YbMOG3veJQCgwFDcBUuS+iJGpMFRjEd4RcnYch1GHBCKhVIBc9YQsqVBMH+RcFblvsj1wfVIlVQeESpOHpOqTmKTNjpWYS2MzrqIyIxIZ1p6NUpctV0ulaulWBTqOI632ksloaE9eISbYoyAYoTfhE6CBA/n7RIAIhABFTYCgmCR1q8BU4SeJLAgTvwMwChAfQjHm0mhWdIn5I2ytqKBUsI+I9iQyo1K1BHIkKizsvaBPAhFkvQwJFf9pSpzWrdpic4NEZS0kaDnYMyUta8hthAmBSblaBqVOTqr27pMCROhV+CGwQYP4+0SACIQARU2ATCEKnWLDT5ICmVEk10pJuQYyI+WqgJ8klSvRgglUPVEr7TH+yX0S+iuSOoX6Iq16E4gWb08kH3y7rD1x7JQqlLBKzZSILeVqicRNRViEPoXk1lGQZZ6Mqla2yeFNXxkiBkToRbAhMBb+sRiUA0QgFDcB4iddIYQikYXMfS6soS7jVoEJYRJT3lC2iV+5Ei3zGfVXbQlqhO8G7x/fjilpWVxVpt7bCEr/OBVKWtnGT/zKEJhILAXfOP9Ee0z/JbIlEjeFaqRbOh88oXi3slIHCRGJJIbmCIReg68AiSEwPwnaXyJPIPRhFDcBUvziF5Ne5Q0S9YqNGI7hQmAS+YDWnqiKmEmYSKhk8qHb/0YkTXyZRQhMIDOy36Fh3XJylVoCjX9iO1xZQGb87zKZkRO7eXuqjRZF0hTkBkFP6kzvSSLYQm4QgdAr0ClAw4Z5n42NvesPgVCAKG4C5H8aQjXSaiWjUsGXRCKONLFJ4RiDPatcFZ9s6cI7jnqVk7ZPosqiCVmxbUghOoGUsPXCUKBAtJgz0aRx1fkG+R2KuVCcPeVyd/ZdyEqYRAQZH6QtDjTqmbJMIJZEgAi9Cp0C5BOgLVuAVKp3fSIQCgxFTYCMoZrMd9O+PfJSad6eUiWQJlZ5ppaXu/MqFBSTuy7B15vcdcqHmhB49Xj7yiXogj3dfkhcW0KelGri121qqCRAkj1Fn3TkQ1Kh2CpmH9h9gERVS02WNX9Hij4RCD0O3SqwIUO8P+5UKiRJBEIfRVEToCCxlbklL4P3PiMRoRIQzHBi6CcIgTmOtApMPtYiNKc7j0zenZlVFtT2uDQkKUdJsOfq7Vlt8ge1PdZPceL37Rp3YRb6K21VAIUyo+qTFKKzeBfpLD5ApeYI9kJz2j4FuUYgEHoRO3d6n/378/dLS8OwGIXBCH0cRU2AVMdGyMm/wn1DaAWuPEk6jvCLPwOFmKMnEoJSoToKQ15mHhIMmYTx9ngSJpQp7IXPqv1ThsAkIpG5rxoHSVmT72v3KVIoKbqjP6SxU5Imvg5HbsXQYuCfbE+nDgWPkAJE6E20tHifdXVyGeUBEQgAip0AKRQg3YaCpvwb8Rc/G34Kk6B5sqUMZ+kmSWkytp+o4ag28xP7JNsTN+xD0CfZX2lTQ4GUqPobKiJ6JSwqOM4pdaHDXJk6r4m3Z3MwrUjqRFuOI+dx6Q6mZT3U7fJN9IfQq2hu9j5ra+UyIkAEAoA+QoDYiVobLlL+qleTD05Z0ITHlHvFaIiJTuVhy8KJmidapjwksa+cPWnnZv4+64eOSLB+ao/3UCzF9yH2V7nDtuC3aasA6egKTQjTZI8lLL417U7QKnvC35HpRHoCocdgowBt3tx7/hAIBYiiJkCqJGjd+VPqoyu8T3GVVdpEPnySY0yq5u1b5Q0Jq6nUybrqPnETNXwfBLKgCIHJK+X4tvkkaN5fUyK2TML4+94Gk2IbAplRvCd9LpRJWVPXYUNgvAd2O2yr7BEIvYLubqCz07tWKUBDh3qfpAAR+jiKmgDJmoNeqVCHn9R1WFvhvMaTLZWiBM3EL/rG1pPsCV54PqiVGXUCskj41OoGa0e7VxJLLLMe78Ha1dhjwnN+cDEgnX7SsqSehYalMj9p2UDCdPa87QX0BE2yJ/rgCn0CgdBL8NUfgEJgBIIBxU2AVEpFll/o/CQpTNSKEFMYJgFXXz1JqlURcWLl2hLtCaoRO7Hq7KnUEu0xFMpl8N6ntNJLST7EvoreqbYX4NtxmI7J9tTvgvVPS1hkLmrYt8eRQmC6kCjnu8W7JRB6FH7+T2UlUFIilxMBIhAA9BIBuuuuu9DQ0IBYLIaJEydi6dKlVvVeeukllJSU4OCDD86zZX7iAuQJWdw1WZm0LB0CGpIP+TR4l6/D2EsLk6R0fIYi/0YKPwm+KU8tD8JwUpeYiV+wl/nklsEHpEBDPhi74maDZhLG9zckYUyfhGfDd6H22ysTCZp4nyVh6jFiSZhyzyGmDn/ECP93JPaJJCBCr8GU/wNQDhCBkEGPE6CFCxfi8ssvx3XXXYeVK1di2rRpOOGEE7A+y2F8zc3NmDFjBo499ti82zYm61qFNdTkyLQPkByyYv1R2xPrsM9KK7BEpULRJ3kZvDxRS6RAIGdsmeyffz+0GxWIhIl8yCSMt+eowk9+O0KfVORW3KfIlAQtHTHChuE0eU2q7QVEeyIZJf5D6DWYVoABvAIkxuEJhD6EHidAt912Gy644AJceOGFGDt2LG6//XaMHDkSc+fONda7+OKLcdZZZ2Hy5Ml5ty1OXACr5oD7tDk4VLSnWiqtm1jZtsQVYmzYRXxWN/HzPvC1TGE93R5BynO4hDoiCWMTvOWdoH2ywNtivwT9VZA6MaFZSwQZw9LeRn5fFQwoeO9in9Khb/L2ArzfKmVNTHZW5VYRCD2KbAqQnwTd0QG0tvaOTwRCAaJHCVAikcCKFSswffp07v706dOxbNkybb37778fH374Ia6//vqsbXR1daGlpYX750OcwAHVqh9Xed+r55MMXZ6IQiXQhIvYa13YjAuBSf7xk646XOT7p++T6sgLIJz4eR94GqbL8wGyn0ivGlf5kNlwvEVlDaI9hQ/SXkS+b4otCSCOqzB2DsJEbN+SvNJLVtbkfaYE3wiEnkY2BaiqCqip8a4pD4jQh9GjBGjr1q1IpVKor6/n7tfX12OzJv78/vvv4wc/+AHmz5+PElUCn4A5c+agrq4u+Ddy5MigTJi/Aej34IlG5EkyVF/47+EePDL50B1rwa9WEu357SjCT5nvoRrBd0q1Zw6EPinDT34eS9pChdKEd7j8JF0ulIUSlhYyyJW5Vb7fYpiLebch/+HHPHh/HAkT7EnqWfY9o1jo7YXviUDoFfgESKcAAaEKtGVLz/tDIBQoeiUJWg4LuMp9UVKpFM466yzMnj0bY8aMsbJ97bXXorm5Ofi3YcOGsJ3gM5z5xOMmwpwPWakQiYQ4EfLhJ77MtFpJCqlBP0mKGxSKpIQ9CiM81yu7CiWvRONVI/ZZKWFYobDwWgnTjioRWwgLiTw1orCnO0eNC4EZTnZnbXj19WMECORW4Z/Oni4k6lAWEKG34KvgOgUICAkQJUIT+jCySyy7gEGDBiEajUpqT1NTk6QKAUBraytee+01rFy5EpdccgkAIJ1Ow3VdlJSU4JlnnsExxxzD1SkvL0d5ebmyfZVKoDuHSxkuynyKIRR+otbl0qgVDM8H9SSpWgavC9UEITCoTnaX7YV21aEa0Z7rqvvLfuc3hOTtByqPzaGwBmIpnZcmkhyW3ErjqiZNJnvszs1ZE+YVxFJPsEEg9A5yUYCIABH6MHpUASorK8PEiROxePFi7v7ixYsxZcoU6fna2lq89dZbWLVqVfBv5syZ2H///bFq1SocdthhObUvKhiAIvdFUlhcpoxXReRf9YoNCgPlQ1B5GB/EZF31MRQC+ZCObAgnVl24SJmrkvmU82JCBcMRHpYnfp6UsD7o1Beb0+D5I0tEIsHbg+CDqk/h2EF6Vjq8VAqBOUFik27XcI5QZT7FvyMx74tAMGLDBiCR2DUbpAARCFboUQUIAK644gp885vfxKRJkzB58mTcc889WL9+PWbOnAnAC2Ft2rQJDzzwACKRCMaNG8fVHzJkCGKxmHTfBuJECOiTXo2/6qVzs0IGJE7U4YaCvC9cInawDJ4nMxGWACkUCbYvoZ+q0+B5e0rlw0DqnIwEJIV+hOQXlkyJmUNSAjlk6FQy9Q7bvJIi+ubV4/uiJJaZ8KuUm6NQ6sT8Lil0x5E6wT+FskYgGPGPfwDHHw8ccgjwr3/lLxuSAkQgWKHHCdCZZ56Jbdu24cYbb0RjYyPGjRuHRYsWYdSoUQCAxsbGrHsC5QtV/o2cKOt93/WdmwXVQUO02DJZLQnbFvfgiQozP1snW7KuagNAkdRx5EPygSd10nYAUPgAcHV4YqnxgSEROvIhh+4UyppgTwwtsvOKNqznqBQlgwKk+JsQ+0QgGPHYY0AqBbz2GrB2LbDvvvnZ8RUgf6WXCkSACISeJ0AAMGvWLMyaNUtZNm/ePGPdG264ATfccENe7Yrkg52ExKRX9dJm79O4VFqjzEiTJ6sAiRO1cN/GHjdRC3lIcjtMvyHaA2cPRkJlytkRSIGUf8OSMMGe5JviSAmJjCrGVUFM2L5y9iRCJRPigJBmGQfWro5YEv8hZMWbb4bX776bPwFqb/c+q6v1zxABIhCK+yww6aBPKJKJ0/zEanMaPLiJn382nAiF+xwB4p/VKRUmez4cOApVy7fH22C/mPKaAkIVVPHJlpoAKVUjv68RxbjqEsUDRcmRxlwkH/6+RVCNq6AOseFIaYdt6b0riGXQN7Edliyr7en2XSIQJGzcGF5/8EH+dtravE8iQASCEUVNgMRf+2xuiTRRK+YnXdJrmNfhMBMbP7FKp60bVyspfBAmUNPp7SIxkRQWE/kQE4aZ+FNAFoKT2CHUUShhAvkQVRRVf9XHiKhDXfKRG6FhXZK26ow18b1LihvTJ+0ml2GXFORIsEf8h2CC6/JkZNOm/G35ClBVlf4ZnwA1NXlhNwKhD6KoCVCY2Mr+queKrPJ55FVWsr20MLPqTgVn2xIVIOUqMNGe4INqzxwxV4WdqnXHWhjzb8TcF2lyd2TVSCAfxhCYqJI5imMopDr8O+L6JPSaC4FpiGWoDOnrQOyToMZx/kH0jxgQwYAdO4Du7vD7p5/mb8uGAA0e7P3HnkoB27bl3xaB8B+MoiZAEomAozh/KkMkmJGQQyg8keAm/iyrysJ2QtjkAIn7yOiOwvD84P2VwkWc+sL3SUzEdhxVIm/GniYBmVeAzOQRTKluDx4HLFHVjxHbnqlPyuRywZ5IRtV5SHwd5RYHNuoegSBCDEXtCgGyCYGVlgKDBqnbJhD6CIqbAAkTKxx5YhXVCK+Mry/uI6OcqIVwkXh8Bheqkez59xUqlDa0wk7UvOOyyhO2LYd++PAOl1PkinXU6oaKNMk5NowPUn/19iQioTlry6/H9lcMR7KQQlOCPQdyrg+beM7aUJFR8b1TCIxghEhCmpryt2WjAAGUB0To8yhqAiQrIvLkBcUkqVMJlOdziTkkUE/86hAYryCoT2LXqFCMLXmlFW+PJQlSyE+hAIVhPd4/7d5BityqIFyk8iHwXW2PzdWSQlZCO9zmiVBDmVyeNbfKkciMKqeItcWWyavAiAERDNi5k/+erwKUSgHxuHdNBIhAMKKoCZArfHcYzUYX1gBMeSd8JY58ZFEqWGd0OSSmVWDiaiqbPXN0q6w4/zLfudPlNflLpnBRNr/ZvurPKlMoa5oQmFAlQ27V/eXVPd5eVFuH3V5AV4e/r7IHxRgRihx33w0cdRTw8cf2dfzNCxsavM/t2/Nru6MjvDaFwAAiQIQ+j+ImQEGIQg4XiWXKSVJMlBXKefIhTtSCLWaaNJ2pJS5pZyd4rh2fsCCslDVhmFOhRHsK8qHN5xHVDTvy4UMmVL6a47ejt6f1wVFtB8D3lb0n71QtKzY6FcqU4G46N47QB5BOAzNnAs8/D9x5p309f/PCkSPD7+IvJBv4+T+OA8Ri5meJABH6OIqbAPmfnGLjl2WfJMPJlb/v5/nwhMV/RiBNwYQb2tclLXM5SqKSoknIZY+hEMNC0l5EoQuKQ0X9diCH9QR7qvO+xHBbcAyFanVdFnvKjQtZ/yC/W89tvk+q3CpVWJT9rgoFysSSt8UvxeefTacZBwnFj08+Ca/fe8++nkiAXDfM5ckFbP5PNtJNBIjQx1HUBMifhTilArqJX6VUZCZqbfKv4jR4YRJXhZ+ksEvgn7yqTDrXSzVRS3lIfJ9EpcnkH0uoRPJmo4RJBIMjH7xd0w7bYaI4rw5FBQbEKnhy8rasQonESd7jSTFGQn9V+yv5kMcIQZ8IfQAffhheb9liX88nQEOHAtGod+2HxXKBzS7QPogAEfo4ipoAifky7DEPME7U6vCFTBbkkJVfx5Qnol1mzqoOGoVKnKgdpX+Z7hpCYBKpY4QK/eosnmEEuzGbthfglDW1PXnPIwVRFYig+I5UK/wCkqPIrfIhrpRj37m0tF/4WxHJlNI/hapFKGKwuzmz19ngE6C6uvAUd/9eLvBDYNkSoAEiQIQ+j6ImQFJuCUwhK6aeEL7QTZLm3Be+HV5Z4J9lc5R0qoh80KdvSz6JXeyTqGBw/okqlCL0A02fWJKjJ24q9UUYc0HNYfNveOqoCoGFRFCXs8OdYi8pR+o6vKrFPyOHFuVxFVK4aB+g/2Tccw9w7712z+7YEV5v2aKWCVXw1Z7a2l0jQLZL4AEiQIQ+j145DHVPIfz/nnAilEJWmSeUE3XmUyISinBRmA+CoC3OB1blCXJIeH8dRsbQKQiqcJEc+sn4rVGGWP98sEnBfltiLo3Oniq5XLm0XzPm4hQRicgkTNwOQOWDpKwF7bD31ARNfOdsIrZ/V06Y59+50h5D0Aj/gVi9Grj4Yu/6yCOB0aPNz7MEKJXyVmXZkBGf7NTWeioQ0HshsB07gK4uoLw89/YIhP9gFLcCJE6Swf+wSoo4qTEhM3GSFOxx+wqB/9RvGugETshKhT7xVjpSgvFNFy4KiQw/6QPsrskC0YJCzWEIJFvHB5e7JI6D4ngP3SaJoQ+OgkiA65OKyATEMq1XobQ7bAt/D+Go6ombFGJV2uP9JvyH4e23w+s33sj+PEuAVN912BMhsP79vR2hgV3beJFA+A9FURMgeeNC+dws007Q0n41QjkXqtEoHyoSJq5ECxUENvRjtscuGYdgT6ewcKEazY7KajVHsCeoMqYkaFX+jUTqFPaQhcz4+UesEhYQS6G/3BlrolKnIVoRx1SmDonyZYJ/xH8KC65rF5766KPwesOG7M+LhEfc4FAHlQLU0yEwxwHq671rCoMR+iCKmgD5sEkY5nKAgsnVg7hsnT1aQ96F2YO4caFpLyJV8q+kOhhOl9eRIzHHhv3/ezF5O8zzUSlUQjsQ78srsMTVa8o+aewBkIhqSGbAgcuFMpFE0Z4wRmKeD8vqxFCqFBINksFle2H+GTGggkFnJ/DZzwKHHcYfQKoCu6zd5oT2fAmQKgdoV0JgNgQIoDwgQp9GURMgmWDIRzaol0prVAwFIciWq+JX4lUotVKhVod4eypVRj6JXVSusisV/CaEah90yeCe7/pcGgT3/HEV/BPsRZg8JNE/0QfjAaoK8iHlhWl8YO1J+V0alYcrE30g/lM4ePllYNUqYPly79MEloTYkJl8CRB7gKlPXthdnW2RSw4QQASI0KdR3ARIMQmJ85AqR0Oc2MT8m3CSDNlC1j1u2IlaykMK64gJyLpkXbWiJBAJTYgJYJfBi/45kqLkQ3cSO+sDhD6ZQmDycnLGnn9PkfPE1cl8mlbQqUid6IMP5bgK/klEkBknObQYvndCL2D5cl61UWHtWvW1CiyBsSEzompjmwPkk53KSu8fkN9GiLnkAAFEgAh9GsVNgISJ3yMfamLChcDg1/M+9ZsGsgqQSGZ4WyoSZmUPvD2BDyhDahB8UB7Iqlvaz4ThfIhkRlREOPIR1sr44Ah3wk/t0n62nkAk9Ds3y/v2sOOgU+qMB7JqzgLTbSHAlgV9FogboQexfDlw6KHA0UfL7J0Fm/Cbba8eltDYkBmftAwZ4n36hMSEdDo8wLSyMiQvu7oTtA2IABH6MIqaAImrlSJcErQcdvGhmkC9+/ynUiXwJ2qNSsCFdyRFCcFMLRKniKBC+R8O2BAYHxYSVR52ptYnVWfP51GGkXyylTHkJymrj6HQkA/GXhiq5D9FEub7wKtGfHuOozi0Frw9F4I9INiNOuhtFjWOKxP6SvxnF9HdDaxfb37mn//0PtesMe/CzBKgbKQmVwXIV3IGD/Y+bUiMT34AngBRCIxA6FEUNQFSqS9iYqsqBCYulY5qEpBVp8HLEzVviw+ByT7oQmc6e9xSfE2fjLkqogoVDpFiR2xw31nFRiQf6p2gfbsa/9j3JNiRwk+Bj4wPOntA1hBYsKqMU+rUIUTTIbO6ECYRoF3EJZcAo0YBTz2lf6axMbw2KTu5EKBcc4BEBciGALFEp6KCQmAEQi+hqAmQGD7xJmpNLg0Mk6RmObRfT2jMq6NRgIxJ0GwujahQicm//sojRcKwavm319fwWtpXKDQn7+mjmfh51UhNPqI8m+GgT9JW9UmoI7SjTGIPzcmr68Q+QdUnZO7xjtuciabqE0GDxkbgj39kz1aRcc893udvfqN/hiUzpgl9+/bwOhupYcttVmXlowB1dnqfZWXeOWC7QwEiAkQgZEVx7wSd+WQntWxHQLjMTfkXP1+XnyR9e3zIw0S0pFwaJvtG3tSQtxf4Df1qJXH/G3bDPp1qpAoFBuEiQ9Ky7jR4cSNE7lBY4UgJ1b5CIukMzfFqnCoJmnt/utCiJgzH0hV5jNT3TeoeHYVhwNe/DrzwgkdgZs2Sy9ml6q2teju2ZIXNyzEpQK7L28lGZrq7Q1/zUYB85WdXFKBdCYG5LkmVhD6FolaAVHkYIvkIJy/DbsbCpMsvvTaHwJRJy7w5IafIVvmQ+yRO7uz/l6VdXoARdzNWK2G8PV0eDRcCU4QJg+66wrERwl5JLFkQT4OXV2DxdQAFGWWISZAQ7m+sKPigGjvx74HNKWK/KxOnpTrom/jkE2DCBOCmm/TPvPCC9/noo+rybdvCa1Nysy0BYomF6bl4nFelOjvNKhWr2OSiAIkEaHcoQL6tbPA3QuzosEvYJhCKCEVNgNLiRM2EQkL4E7VhRZA4UWdqRpiZX7vHjd8Kq0JpQiiqQ0X9CVtath74EOYNidnOopqjVliEUI1CSZGTlgXyqAiB+QbZ1XVpQYUSz9QKCZX+zDZ5JZq+T0GXFO9dzK2S9xVytP01hcC0CmOxhsDWrQNmzvQ+VbjtNuDNN4Gf/ERdnkiE16mU+plPPw2vTQoQq+aYQlssKTGRDD80le2eaCsS8Y6ZyGZfrCcSoHwUIN8/WwJUXR2qRRQGI/QxFDUBUm2IJy6V9n/QsZOkbqIWV4eZQmryuVmKidqCSEhKhahqQUFmFGEXl/UbjCIhqS/ySeySCiX4r/QBfltsCIxXocTNHcGSGYlY6nwI+yr3KSSC8so2wZ4gLHDnsgl9022Mqfr7Yvv0H4nWVuCXv9SbGUKWAAAgAElEQVSfFTVzJnD33cAZZ6jLWfVGRQbYch1YAmQiNvkoQCaS4fsbjcr3THZzXcruk5aKirC+bd1stmxAeUCEPoriJkCmcFFAMJiwBjOvsROiePSBMgQmtKldZh78jyLPB7J/0NjjQzViWyoFiFXCDKEasARNsKc5P4zLsRHqcDnQLj+ucp4U0yfBBym3SiAsqhAmt0LMt6fIHWLrKEOiElHlbbFHo2QLYRYcXBf4wx+AJUvU5T/6EXDNNV6ejgpPP+19vvaaupxVdVRL07duDa916g57vzcJkE8mqqqAWCz78z45qqrKjQDtzhCY77Pvrw2IABH6KPoGAcp85865Ep4RlRl2ftXmvjjyL/5wY0W/HVnBkFck+QblhGZZfREUFqZPYoguKiUg+7YgKxWBPTbHhfdPPKaDHTtTyI8lDHZ75iiOwkjzfVKREuldhFKdfpWatCGkSqkTx0Fti1fcBHK0J/HBB8D/s/ftwZZdZZ2/fbqTTgjkYp4QSEhQhEgQZgKBMMUgCuGploMFFNqA8pDCyACiw0OnAjNlyiq1ggqCiEWhyDCO+BpT0YygUhWCAySDOpmIM2IA04RH6AZiOt337Pljn7XX73utvfc553bfPllfVbPv3Wuvb31rnxPW7/5+37fWVVf5h2vecAPwkpcAz362n9/yy7/cXT/ykeXG5oorb3xmgCLQwkDg4ME4D4flqTFMzdBzzKaMATTLMkDrTIKuDFC1aqNtowFQMk6GjaQQKV9IYBAv7h6jlNo0aCrIOzSOJgoi9mVK+X66x/ktFuRQG+Q9DRb0SewpDo6LMJ2To6T86XdHc4qBoGxnYOklQY/2R2urYYeSBGbkzTSOldo0a7Rj9va3Ay9+scypSfb61wNveQvwEz9h2/7hH7rrXXf5h33u27daXAxwPADE9yJ2R4MULw9nPgeOHo37JLvnHllVNobRGbs54W5igCoAqlZt0DYaAHmnt5ekEAYMolopYBakBKbBRxoH4j5g84ZKVWWRpCbZF9+fPomdQojLzGcQUiBbo1bx0u7R3vEe81ZKV+Gmhk3jxOcDQY4xAqOzEf5sgnvMGpUqx6KzykZLYAcO+Ad0ti3wnOd0FVW6Wmc+7zYKfN/7gP/+323fP/zD7uq1MUPDclQyBhVeTKXftX8PAGl2x/MxBgBp4BclK2tAcs898RwZTIxhZdadA8Rl9WNsezs/XwFQtWqDttEAyJMuTNIrswSLW/O2FezGHsO+LPq4DNCCJYiqixqvIin7MzKT8mcZFpvPk0xLMqUDWTPgYwYovw9vTlwdFs6JxzISmIxB+Iskq1A285LBmXUbkK3G+DNxy/fDQMtUqfHL+cxnOsDCyb3JnvpU4NJLgb/5G3n/9tuBP/mTrqLqxhtlG/spLWJeXggnN3sJyZzDo4GCBiYeY8FAxANA3D6fA4cP22c0iPDG0QAoYk88QBI960lgUxmgVarAxvZPxkdqVABUrdqgbTYA0iwPvDyRzvRf/D5TIVdPjyXQZ2B5C66WY/pxPH8E3sTcegaDq58kC6VPYpd5SBDzdzcUHGK1FtemcfbtQWZYmNXiGUesCINRqM8w2nDRBaMOCIMCM9H2AlI2S9f8ubN5fbRD0eW7vquTrF7/euEH99wD/N3fdV+iP/9z2cZARS9UfPq5BjH8HfPkMWZ9ho6F0ABGS1YeuOAxhwCQ9zswDmhp4DQEgLa28pc2YmlWYYAS2GRQEpkGQGlH6KHxonhTzGOtAqBq91LbbADkLEJ6fSrtPpwsToIek7QsrSkwLLxGztVgEaDivBN7ThhLejkJugMsEkl4AA2BP8ueZcji5d/I6jpi1gJWxj8TLcWnYqDYLEjM82UZDhRHvMEkfVIKWMrzzWjLBGLCLEikTgmwXHutiLdYMl6qcOI2DWIYGOjTXfU4ekwtv2gAM1Wa8jbaG+NjGQlsCADd977DoMbLARqbMzQFAGkJrGnyz1MYID5Sw/usI6sAqNq91DYaAOmTxGVpM8R18cDiXiTVyKtIekXuK/soKYRoAs2woHH8GeZDsVq86KaxnJPYW+4DB7j1IMwrkZf+tLzjHcg6J/TB70IwQIE/Bk0mNyeornPn1L+j+NDaOIHcS4JObQwsVbl9IOu5ZJfe+I/ZGA0WGNiUgIheoId292UwofsOsTMaIA1JUx4YWBcDNDYHiEFKAkBjJLAESEqAJrWdemoGQEePlvOodEzJxowXxTulBB7IAOiLXyzvdF2t2obZRgMgLZ/wIuSVkzNrIySwxl+oOZk4qnDKwCj7Kp0/Fck4Og+J4xsCTel5ZliggSD5imNQ4zBwU2MLIMESGP3/a3wum/XX5yEtYrC7fNs5ufKY+qBsZVsyL1+sFX26W23fazaz1XUMvo3pxYYZIL0nDrM8uq20rw0/6y2mJQZoCJyMAR1DAGgZBmgVCSzFs29fBgpe3hHHcuqpuRouepbbTj5ZgpBSH46VAdAUBsmLd4qlc8u2t8dtTFmt2obYRgMgT1qJqpX03ji8TJbBjGQkwgNUyV+8eSLLOL4/9/ypAbkouRMgp79tmZRkehfr4llgEZjR2wvQm4hyjTwQBj2nBDDmltXydgAHgzCW4QoVXcwIdu9DxQAJlmUMjj9Asib6L3UGKyUAtCwD9I1vKMoTqzFAQ7JT28r5jjlaYqclsPQcg5QIZDCgGANIGFzx9gFDIKbEAJWO3ijFO8VOOgk488zu5yqDVbsX2WYDIHXtFqhgwQMtXi2UBKbyZdhfwJboc7j83ajlwiqAiZZ+VE6Rl7tk8pDURoju3kGt7Cs2IVSxNAE4k4nTuo8EJoJZMyXtDGbKuTSWwfNAmAdu5RYHerdnIeshvRsVn2bWyJdNss9zAiDBy0knQRiDBS1dMYugwdFYAORVWZU2D9SLr24fYoC0RHYsJLCU+xIBIGZphlidqTk9yc++fcDevd2/oT6AD1yOJQME1DygavdK22wA5OTfhPKTWvh9iSkxC7wQSskjAxaOowxywAu/klBM4m0BhOl5cxUY78Gj5T7hT8Qn31+UtCyqykxOEYMMyYRFeyW5VWUmt0r3cebE/pr0HvQ5bxAmmSvfn95h2z1GRPXpATEvthpA8O8a5JSYlCk5QKWS8lUlsKkAacyYY59J7/X+9++uR474uTfLMkBTJLD07FgQsy4AxDlIU60CoGr3QjsmAOgd73gHLrroIpxyyim49NJL8dGPfjR89kMf+hCe9rSn4eyzz8bpp5+Oyy+/HH+azhuaaHO1us+8v9AJYAhgQit1lH8j/BlwJGUSlpHCii4FPnih1ouxmBPHrebUP06T8kAOy0UznevTv4fuag54hQQ53Ee+I8msxfsK2eNC0mdpy9Yd8GFAGNfeSRBWPJDV+MtzAj0uQJiprlOsEYOCUtVVCWyU8l00wNELaEnmWlUCG2pflQE6+WQ/Th7rfvfL9zywwgAoAZV1SWDMLgHjQYwGTmlMjmGMrYMBuv326X2rVTtBbccB0Ac/+EG85jWvwZvf/GbcdNNNeNKTnoRnPvOZuO2229zn/+qv/gpPe9rTcO211+KTn/wknvKUp+B7v/d7cdNNN00e2z3fKZCS0HACq9wI0eTfuIuuvOpEWS/Hxua+5FVXs1D6zCpfftKykJ+r4p2OLuQi6EVc+vMYFjunPGGW6FxmzQOCGlhSojHPv5Q3JFgtavNkuJzgnvtodig8ZNYBsN6RIAAkyLnrLhlMKWGY++m2EoujQUhJAhsCI1OrwMYwQGMAULr3Ld/SXUvA5vTT4/H53pgk6DSfsQwQ+wZWA0DHWgJ70IO6K+8pVa3ahtuOA6Bf+qVfwktf+lK87GUvw8UXX4xrrrkG559/Pn7t137Nff6aa67BT//0T+Nxj3scHvawh+Hnfu7n8LCHPQx//Md/PHnsHuQsim18loDagjyRSFqBl/uyuO6hNztvJShJ4+gN9gSYUXJRVP3ECEPn84QyHAq5UB74UAu/ZmXcM7BydEoCY0ZEg1Gak4pLsy8+Gxcxa7KqzD2QtR8vM3jaX+6Tf9YSmKmuYxQGSNAwn8tFmtv0QlsCRww8dD8NUkrsUQkceb+vgwGakuCc2B0PhKR797lPftel58YwQF5Z+9gcIGA8iEntnBS/CgCaWgYPAOef312DP0yrVdtE21EAdM899+CTn/wkrrjiCnH/iiuuwA033DDKx3w+x9e//nWcccYZbvvhw4dx6NAh8a83wwRYsCBYgr6bnydSWvjRSrAg2ZdWVSv5cpHYJBGRBOYwHzoPiRd+AjMCfBgpkBZ+OSVitVQf8meTtG0MgGTCooThWRMDnT3qG6vL2vmeTPougxm9MziDZc02SXaPfTnbAdCcAJTzZtbBAJWAk9fOgGMI0AwBnKGxS+xOAg3eM2nu972vPw6PxRVYQxLYEAPEgGYnAdBukMAuuKC7VgBU7V5kOwqAvvzlL2N7exvnnnuuuH/uuefiwMhku1/8xV/EN7/5TTzvec9z26+++mpsbW31/85Pf8nA+6s+Zj60LMTrpGV5SC4ybE53NcdQLH72GZY0DoZjaGXfmecvjQUp0Y1NGE4O3b12gj4WLFB8TgyzgRjyey0AS5YWG2f36D5u6c+TwGwMUo7srpIJS20lGc7sA1SSjY41A7S9Xc4tmloFNgSASjlAW1u+D/aTGCBP2hpb3TUlCdrLFxq7DxBwYklgCQB97nPT+1ardoLaMUmC1qeIt21r7nn2gQ98AFdddRU++MEP4py0WZeyN77xjTh48GD/73P0H7CXh2HzTjJLoHM7kvW7ynt5Jz2bo//i13NOffJGiF6iLLNDfsJwmluak2Vs0g/dOWHWn2Q3Sv4k+DBVYKA+ak7JNDskd7CWY/tMmLzqz8gr7dfJ7+JzpxiEv/492O+Deef00XK+mOhDMYo+JUCyLAPE/UqVZXo8DXCGNhMc8j30u7eYj5G3pjyzb18GIGOZoiEANJYBWjYHyJPAjhcDdMcd08asVu0Etr076fyss87Cnj17DNtzxx13GFZI2wc/+EG89KUvxe/+7u/iqU99avjcvn37sI//ciIzIMeVKLBo08m6FpTM9eLO+TdqTLsLM4MPzShlf0KyEvKKPzkGGMlcMMPyk2AqJHCTDJX0pxOx3dPW+z5pvo3LvpTlQwLNrXhElfZnKDObwflsExCUVWX8OSZ/9mBax18CgkoCE3Jff19+uqEEto4coBKLUwJcJT9j2ofyi6bsFJ3krVLi8hgJbIit0SxN9Jx+tpRXpJ8/XknQq5TBf8u3dPlTd90FfP7zwMMeNt1HtWonmO0oA3TyySfj0ksvxfXXXy/uX3/99XjiE58Y9vvABz6Al7zkJfid3/kdPPvZz156fE9iKh5+6SQgz4QU0t1N+TyzWSEpdxYs1I0EBDKGQq6Krn5a3C+BGTjz7W43UJhJ5uaoe3oDQAv24u0FRLIzs1oO0BL+0j2Vz8NnPLbU2WOhRPJ7k3uJ/K7geA931/DFMwzC0OrPT/bpY/CSoIGYvZnCAHHb9rY8Y2ws46TbvPZ1/87xleStMSDJk8BKvsYkQU+RyziGE7EKrGlqHlC1e53tKAMEAK973euwf/9+PPaxj8Xll1+OX//1X8dtt92GV77ylQA6CesLX/gC3ve+9wHowM+LXvQivO1tb8MTnvCEnj069dRTsZXyBEZaSaoxuzBzPwwBgmSOVOOxBNCAIIivkf50gq3o4yzUdvNEyVCJXCOViM3j6OM4hD8Rd8ySRUCiFANLU6V9hZIJCYz99dHnl86fIU85nBOsvAmaUx8DRV2MIdkUBqht8xdmLDhKfdOxCiWQM8TglMDaOn7neyV2R4OkdSVB79kTP8f39+3LSHYn9gFK7cczCRroAND/+T81D6javcZ2HAA9//nPx1e+8hW89a1vxe23345LLrkE1157LR7ykIcAAG6//XaxJ9C73vUuHD16FD/+4z+OH//xH+/vv/jFL8Z73/veSWPrv+pJsbLyk2Ix3L2DzOLusS+d6U0I3cV98bt3mvi8leXa+SBSyYg09L82P4hkvTmVa/NctT+HxeiZD71nDp3lafswkJD3uvveJpLZVxHUkT8faMXM37yFOpC16X3xeHDeQ7S9AMt6trpOvp8iqOC2tu1+T4vpWAYIkACoBHLWDXAiBumkk7qxlmF32nZaDtDYJOh9+zIAGsMApQ9yyj5AY050n8/z53A8y+CBygBVu9fZjgMgAHjVq16FV73qVW6bBjV/8Rd/sbZxzaaBQL8SGQkMMoGV82j4GAXtz7BDLksg80RM6bUDPqCYiuIeNwZIOP7g++tPQRegSbEY/cKv2Q30961klcaRLIsEWjKGKHeJY+AyeGZzGp6TAYISmDAQy6X98ir2FVLz3aPlTQJGpXcEYLwEBnSLrQeA7rmne2lJvysBkWXbhmKd8vt97wvceedyAIiPsyixRMzWjGWA0llsYwBQ+vzWLYHxfD0G6FhJYEDdC6javc42/CywxXXxu7dQJ+sqplI/Pwm690v+7C7Mi4WaAdAcYpGMWChxBITKVbFHQKQ+dp+iZHwERMdU8Jzke+Az0VKjPXleDl7KfYEAErnNz/ORsejtAPQ7ShbPCeIn3VaUFpm50jEE4FawiIufzSaXqcMUSYoXvxIwGMsqDY0XAaCoqiqNEyUIT0lwjnKA+PcxfqYkQU/ZB2inzgLjNi8H6FhLYECVwKrda2yzAVC6lpJU+wVK5Yk4ckxe3LM/GH/dVR+YmRdJZnMsY8NgRlQrRRVYsLkqUvqxMXhHYUw7kb4V95k94znn+Jz3ACsfQsRQZqGSP08+9Hf5JiBIcc7MZ+G8BwMSaZ6tHieeE4DpDFCynQA5Y6u4IuChNygsMUBee5L5+JlSIvZYCWxMGfxOJkFPyQHiGLky7VgnQQNVAqt2r7PNBkDuoqYXVmojloXzOuxCmNrK/sD32F/ELFBH7sP+yhJYZ7LSKmKAgrgR+7OHwmbWqFHPuu+VYkCBWesOFZWBRQxQavEZpdyHgeCoozDoPfRsjlNVJvw18nMXc0rRTQEyWvaK2pat9Epte/eWxzjtNL99KDdHA6BShdoQyOI41iWBDTFAU57l56cwQBw3f3mWSYJepQweABZ5mfjsZ2WCX7VqG2obDYDyBnt5kdRykQASyPfEEQYRa9TwIimXXb1bsKxW8mOAAhLehn1aLhIMi2JsGLzJPXisnCXloohRasRchTSmpKT8PvR7sDH0feY2hrlq02XwDLT0SexzB2wxY5P6cQz9nGYEWpS2KCrlWvl+TGUbs4VAWeIZWyE21DaVAWIAw3NdleHR7Toej92JfCxT3l56joFSBDI8ULXuHCCvAmxsX23rYID27OnGrKfCV7sX2EYDoGT+gtfd9HYSjo5YcNkNNYYGC54/c66Xl/ui4o6lGscf5RuB/YH7wJ3TrJEgg83smdO3xCwZ+2uJ1ppRMpTdsTu32eo69V6pT8hCQQIdf9NHOQ7ArJGMhT/3OfuD9cfJ7wB2hgFaNtFZMzxtK3OLUt8hBmgKAIoAX8TucCXZWGZnbA5Qek6/d88nM0AKEBvfGgCVWJzUR1duHQ8AdNJJwIUXdj//3/+7nI9q1U4g23gAFIIPzZaQVCNOb4dNruVF1+7CTOCjv6f8aWmF5CevYgrgMnjVp0HIYhhWi/qkWWV/xGo5idPdnDS7kf0V9ykiNkeAkpIcme5B/iArsCTLYyr8kGPIblo3BpO0rKQ74U/IhPnDFd+hue6zsCk5QCWZa6wEltpSxZM3XgRQpjJAEXhJ4CYav2nyoj2GAVqXBJZybjymqG19tih6nuW95HeZxOlkq+wDtGwZPAB867d213/4h+V9VKt2gti9AAA5lTjIf6GL3Bxq8/Jo4Cz8JvEWThtaJYHFQEIu1dnywipZI28R5xhmpHVFbBfHAOi48/0I7HmgrnXawEnLIhHbsnHRwaYz+SEK5sqwUARGZR5Snk8ogdE47l5J9BnO2V8QwygJbAoD5PUrgRxvXyAtgQE+ezQEcIYA0qmn5j13vNhKstUqyc2rACB+T8wAAeUzzYA8fsm/9rUbJDAA+LZv664VAFW7F9jmAyDIxdMseI78ZPI6AinE9dcDBkrxDfxpTslINQxKdA8PhOlFl/sJBmj8YaOSAQK1qaqy3CL9zVQM/L7V2HkcK9FlZk2xOYufi8nlDYSc5UlgOm4vCVowaI6/vo1joDkBmJawPBYcaSlratspp2SdsiSRRQzVUBJ0BDamAqCpOUBjD00t+dPxR8/zWGn8KQyQZm2Oxz5AQGaAqgRW7V5gGw+A5i1LFLzPTmpPbVqSyYuk2bgQ2R80++KxDuwPEhDwlZNo5xosaBQG7gPRxvFJWS/7452R+/eU3oMjBQJWfoLo489JyHp0H2h6dspLGJZck3xHfE9uIaAktf6dS0DFsZkjQUpMHXI//k54cp8Gy2tngDwgU2J5vLYhgDK2CmyIARoDgCJ2h/ciGiuBjWWKSgBIA5qmyQxbaXwgP7eKBLbMPkCrVoEBlQGqdq+yjQdAIukV3kJNy5rDvjT0vyV5xx7nICvO3HyZxcgyjyX7c32lPlwxpdscICFzX/jgULm6S4Dml4yntgy0vHwZ63A+VyfSky+Ov0Hsr3TGmvHngFu08n2b90phz8LPVktgrelj5NIU9LpygMbKXGMksJNOyou213fVKrApACjysRNJ0GMYoNksy3djABPvGr0uCSxKumbb3s6f3boYoDHjVqt2AtvmAyCdd0L3u2tnzLJ053BRH7UQ8nlRpqw+NxGbwxv25ZXaVj/BB03KF/eBSJxWCzX83BcPNEkwk+/x/wfOFPjIIMx5R7xnDvdxwaN8H3A+J2bqQM/zFgca3EZnn4m8IfNZ2D4ZzPiMV/8dmjn+6HsEYPkqMJ3nk35v21y5tawEFgGgqQzQGAnM8z81B2gdZfBT/CUbW16vn19FAuOzwkrGTNEqAOihD+2uBw8CX/nK8n6qVTsBbPMBUMS+9ItkapN5MW6uivqrXh5dkdryguzliTQT/Lnl2qYPCFDJNnMSu4BN+j3kuGcamYDGoth9sCe7ijO1GEyRfOjNyfTRQALysxVzovYcn7yXn/djEKyWDMEmOzO4NRJr/gwBTNsHyGNjNBjhsvUxDFDEwIwBQBHAGbOHz7ISWARsNDsxtQpsKAfIk6amPr8OCQwYJ4PxM6tUgZ16KvDgB3c/Vxms2obbvQMAuRKYXPF0m0hmDuQY7pMa/SMl2uLC6p/ELiWwfj49I8KAygIMwFZGCaAVyDtpXroPoM43UxJdJC2GMlzjSEz9+E4CsvcZKnYP6rOVrNYAE2bYONpXKFXeie8K+XOBqvUHYBwDpKu5SiwP+yvJXMswQFMlsFWSoIckMAZAOs7ouVVygDwGaJ2AKVkkgfHvJQCVLAGgk0+ON/Iaa494RHf93/97NT/Vqu1y23wApBbdfF9etfTDAMOe3k59Fv31Qs3jSbakEcCITTM9ftm6ihuO/NT3a3x/BAjMfjWN3wdQEpiOL93X+TKQjNLcARHmRPom9qeTvhmU6NwqcB+SppjtUiqXZGwUEeZ9V+ZtG8p9ek4AbJ6GVwU2BeTw4jo1CXqsBLbqWWCrVIGxTFaqxJqa3LwKABrKLUq2igTWNON2n062jgqwZI98ZHf9279d3Ve1arvYNh8A0SLpyTG8sPrHG3jSCgOM1GbBkU4a7u/3OyPLq6hKMmyJXtwdhsWTcYgdEgt46qPi6zAOy3DZ7Dlc9I6UQ48VERtCMpBxYojzeWQFW5alLBj1AZqU7ozcR5+7kUsp+cv11zSmT2rtsWMEcvhnDVa887CSnyEGqDTeVAlsiAE6ckR+MdadBF0CQJ4ENjYHSMet/SUbA5i855eRwIBpewHtBAD6u79b3Ve1arvYNh8Aobzwy/Oi1D1YFoX7+vsKpTb/HC6Z59OKq5frY2OQ0sqscZKgyZ+QmdqCv/waBLsR7gOkJDB7qGhq030KchH50/CIQUvjzamJ35GVwOgzp7nKPuMS5tmfNyeR/A6UQUUEVviZiB3as6ecaLwOCWw+Lx+V0bbysNN15wDt2ePvVzTWV/QcUJbUki2bA7SMBAZMA0DrKIFPdskl3bUCoGobbpsPgDiXZmDhh1jUFvfVAs59IMCM9GsW3QLI6SUUxVC5LJRiNzjGDOp4vjYG9qfnpo/P4J2gTQIy5eUk8871kjHkmM27I74prXM5/6Z3KN6FJxPmGHOnDN64Is/G0Fe2wX5OHtjiqCU4UzFoCWxMxdYYlmcsiFlFAuOjLEoAie/xz8wwDQGg+TwGUXyNGKASm7S9nf9j4yToIX/JSoBm1SRoL3H5eDFA3/Ed3fULXwC+9rXV/VWrtktt4wGQPi/KSD+Lq64CKx/LEC+SUs4if3Mbm+vPi0EkLatxBiSwfiyOoZF7FPFVH8jKGpjeg4e3A9DSor8XEQFEh1mTpe6N6dPFlx1q+SnauJAB35wmNZvF7J4EWonN8b8TQmINYujf3Jg9eyIGiGUgDY7GgphlJLAUK/fx4o3ap+QAlZ7haySVlSQwBiJjc4qmVoGNzRnS/XaTBLa1lSvBaiJ0tQ22jQdAMp8n7z7c56q4eSetXFh7mUReRRKtI7vA8SckKy/Bl+Wn5AuIxyEdp1WwTifrisVYST+8B8+MUAGzMlwFZmU9Hjn/0L1zeg8O0LIn0vubUqaw/V2YlTQGdRK7448Jo9JnYcGyzDcSgFPFwP4AlCWwoRwgD+QMgZhVGCAP4Ay1LwuAGDh4x3HoA0bHJEFHMll6bs+e/KUp+eM+nl9+3mOAjh71/wIC1ieBreMgVLaUB/Q3f7Mef9Wq7ULbeAAkz4uyeT7M2MgjGyyIgFrU5KK7uDrJupE/74wpHsqV0yD7dMm68l4MJJiV8f1pGUeAD2aUWslcxceFSMnKZWz6KXtMmD0UVgxbONgAACAASURBVPpjNm7B8qS1xk2CluDWHMfh+Cu+V/H9sknQ4T5AmpFh6SdigDwgscpmhmP78llhXv99+8oAaggA8fiRj9Tu+WnbaQnVyV/TjJPUki2bAxT14X67SQIDgMc8prt+6lPr8Vet2i60zQdAauGHXtSYLen7tOECnnoBWgpRrIPKN5IgTLFQnj9EJ6dnnzo+r/opV26pw0tHAhbONdojs6AVENRggYFEjmBcjo0vMXWxy37uvks6aXmm+xDrh3yfr74/AcXsO1LMEFv/MYzJ84naPKAyFsQMnQVW6hvt5LxqlRe3N81wnhBfPSAGlCUwPV7kj39fZSPEiNUa6pfseAKgxz2uu/7P/7kef9Wq7ULbfAAE9Zd7f7/A5jBogpVCctIyhLTCpnNzMmCJNyG0CdIWnHVtvkQHtfCHMYAXdxm/yLFpvSU/xy63F5Bz8jeEJInMYdb8/YtaASZkblVGYcWjMAy7R97MZ1HyR3MS3xUs+kgZlfuGVWBjKr1KQGXdSdARQ6MX/+3tzFgN9R8DgPi67DN6rFKlGD+vfUTPji2v176jPhzjbgVAn/70tANZq1U7gWzjARCfF+WxDmLRhV0kpcQkmQAt4zBTISQU5c+wDqkPISruw75SP3enZcNiNG4MTYMwF0qDIwZ29iT27M/OKb8jZt1EPpZh4xx/5CsFOLqqrOU+eZ4y7iAGWGYN9F55e4Hcxyvfz58TgBiQjK300gu2JyNNPSfM68sVUx7AYT/LlrmvAoDYT5TcvIqstQ4JbDYrnyAPZHCzqgS2zjJ4ADj/fODcc7vvwc03r8dntWq7zDYeAIkkWm+RTE2KzfFAiZuzs+jDScGATpAm5gMSlKS+i/DcpGWx+/Giny+1Of7SGHPFGqmxBZBo8nxF6TwFwfExwjAgDPLEdS/Pxzs41NsOIMdH76GX1BoLVBlABnlD+jT4ll6EZdboXbA/J7+r/yxoiwMAsQSWrk2TF74xLA/LVFEbMF0CiwCOx1hNAUDR+Gl+JR989Z7Zs6f7N0YC49hLz47d2DBicoYqwXYrA9Q0VQartvG2sQAoSlIN804gNw30c1UUWIAEOXpvHt4l2jvvy134HX+cE5Pi8PJv+vHJH6cblU5iFxKdO04GJamfYJRGzGlu4lYxpHeHbFKEczaYRO5k8qS4D38fiIWCilvmTyl/AegUEiuNw9d+TpEE5uXbaHA0VQLz8orGMkD8XKn8XrcP5QhFOUZ8jRK1o2fGsETec5E/7rsKA8S/n2gSGABcdll3veGG9fmsVm0X2eYCoPQDAQmWs/Jf9Z3NZhnO8BELnNiqGRs+LoHbu25U0j7XbMTieUd2iXJVGBUwM+OCGc+fkqx6qa1njbhPHovjZrPJxFp+4vh8CczGYN+r2MdprD8dQ+P3KUlg3rEp/t5GJLGSP80W9t8TLYGNkbJKEti6AJAGKBrgaHZGsy5DwGRVdqdUBq/ByjoSm6cmQXvgivvvtAS27jJ4AHjyk7vrRz4iadhq1TbENhYAifOinAXPPS+KmB4vV0UjDCl5SAkMZpHM/rQE1ifyUrUSArak98esg17EOZHXiUEmditWS8tPyL5SLEV/HpCQkedXpJg1Zq48hsW+i2AXZiOBMWvkg8feowCJchQ5lgVU3pyMvzEM0JS9fsbsEQRMl8BYkvOO2ZgqX42RwKY8442TwEa6HjkiP5wprM7UJOhNk8AA4AlP6PzdcUc9FqPaRtrGAiC9wAML8FNYoLxFjxdJ95iH/nk5ljknTMhZoIYgnwcMPpQs1AZ5J1D+eE7UZzZzdrd28oa4FD/dFGDQYUR6Zs0FiXJzQnN+GKw/vQ+Qya1yZELXH33uYnsB8t2BWO9zz+P1/eg74fkzMaRBhqrAxpa6T5HH9u71AcrY8vqmiccdK02tiwGa8szQc5E/oEpgQDffJz2p+/nDH16f32rVdoltLABieaXP53HkLLeiK5JJUh9adNNKqJOg9YGeHijpF1ZKROoZqrk+w0xSFYxLZmpSBvRBMWEqd4ltNgOBRAmM+DpvtWzmy0XpXaTwXKClAQYkcJurID2ZkP2VNpgUMRBoyvPlPvx9kMyVxIEZqNrqutwHQF4Io71+hnKAIqlq7C7RbZvL18cCoOQjislrj+JeF7jxqsDWCYDWlQR9rCWwdQIgAPju7+6uf/Zn6/VbrdousM0FQIJJWdzy8jrm+fEoUVbLO+5f/FoKgUyiFfsK9YBKsiXmnCtaPHVeTpsnRSCnwL7oXBXFhA1tB5Ce9/3luDVLFiUty80JVQxNtG+PBpA5Bv6c4M2JEEvr+NL+TKm7+mzd3a0BMVd+D2EV2LIM0LJt3phDshtfx7bzPkFDEliJRZqSBJ3AxhAAmpIDNJYBinKAjpUEtu4y+GTPelZ3vf564NCh9fquVu0428YCoL4qiZkUhwFKxuBoPpcsCvo+alGDYiOEBEb+aOGnXN0gAZkXVmZLmE3ihV+yEexXJ/LKRVyzWjk+LfklX6KfYUv8GLQElsmuphgD6PODiduZk/ceUhMBSFGJJrgwC/iEfJhDEBIYN3qH1nKOGYBxDNC6c4C439i+GnhE+wBF7I0uox8jga1LJkuJ2UB536HIH/e7N0tgAHDJJcC3f3sX/5/8yXp9V6t2nG1jAZDI7XDyeXIOkCPJQOZ7JFkjSysekyKPP5D5RCp/BLmP8Rf1Uf44b6i/n/y5uTQaGOkY/PjMAu4xa5BAKz9hJURvOwCdOG1YqEJulcifgoqBgCXYH0lW/EUJ/VGf1M+rUuu+JjIGfq9Cfppy4OlOMUDrlMCiHKH0zLpL3EtVYKs+x797Z3stA4BOVAmsaYDnPrf7+b/9t/X6rlbtONvmAiBnkZwpIAEoqYbAkbeZoMnr4Da0YpGUMUh/Olm3fx5BDDrmVrJaJvmXF/HAH0tZQHR+mFrAIXfFds/UWlzDM9FctkSB0SKw1JVtHhMm5zSbqaoy9iWApS8Tyk0fQdBI+gOcOfUtKJelj5WjlmWH9u7NY++kBOYBoDH7BHk+vGc8EDIWrCyTA7QqA3Ssq8DWWQaf7PnP765//MfAF7+4fv/Vqh0n21wAtLjyeVECLPTyU8CWLH4WuSr9omYX1k42o/EdSQYonxelj8lgCUczQHAWfpt/A3/hR2ZlciK2E7eW7qifkLOafFi4ZtaivZI6Nk4za857UMBSAMj80S7iXvibO2MJf9aXnpPOuRKJ2OQwBKMKjc5mkAtnAkDpFPhSpdeyDBAv4k2TQdA6JLCh/J10TXLUUBUa+1gVJPHPngQ2JgdoqgQ2tA+Q12c+z3PdrRIYADz60V1J/JEjwHves37/1aodJ9tcACRyaRb3qF0nDAO8eOVOnrQiGKCefbFHYfgLtfUnThN3/Im9iBb9+IgFzVDJ08mzPzdXxchFsk1LYCGTot8RPS+YFAdwQveBenfI5klnfdzSXZiH5J3ebuaEgURsGss73sPmdzX+0RRAd39MErSXS7MMiJkCgJZNgh4DXMZIYGOeGQtWdlsVGN/brRJYsle9qrv+6q/Ww1GrbYxtMADqrvL4BZur4ktg+hgK+WxLq7sABIqpyIuhktRCmcT3J6W2xMzQWASaOL5uESd/DmuURnfzWNhXnwSdY/f2zOnlJ72BEKSc5b4HAQRprgJ8SAlMbHGgmbVezmoEuPVyoXp/rgzHEMyCW09i1TGgQQyA7rnHL4P3KsSWLYPn65g9hMYyPGN883VVdmcVZudYH4Yaxav7eP2A3QWAnvc84IILgNtv70BQtWobYJsLgBbXFvERBoDMO3EXfnKmz4vSR0CYhZoZBArMJiAH/hxfqV/Eboh3QChD5tKMY2y6Nn4/klnj7QA4NuuPx0pz9ZgwUFv2Iz+jgN1rmANa+HO3ONCMTfRedQzZr/BHnRr1+fHcGiAvnHv3yoV1LANUAjk7xQCNrQIrbdDotXtjrGuvIMBnXkoMEAOzIZ/rqgLj2DhJPdluKINPtm8f8Na3dj//5/8M3HbbzoxTrdoxtA0GQJ4EVqp+WkLe0YyNGF/KIYJ16PNvFGNjGCXrK40vmSuW2nIUFkjkuVpWi2eFPj6OO/X1/JkqsBDMFGLoI8gDRRJm0Z8BguozdD7z3h+NlefUihwgDXRi8Cg/dwEa9uzJDx85snoZ/FAbsHz+EF+XYZe8/np8vu5UFdi6JLBlcoA8BogrwBr97cbuYoAA4Id/uMsFOnQIeNGL4tL+atVOEDsmAOgd73gHLrroIpxyyim49NJL8dGPfrT4/F/+5V/i0ksvxSmnnIKHPvSheOc73zl5TJZ4xEKt/0JPz0NvfGelkN6j8JfuqWRdQi0sWWk2QsRA/ky+DC/UWlKjPqJiisaK9g4qJk5DSlZ8nas5mdPg6XlZOZbu58lmIJjn621CmEAYJ1yLHKXIH7VxDEYCU+9cyofZTJ5UkuH4vpIWG5bAvOMllmWAxrJDfJ1aQZae4T5TJbJjcRTGEFjZySToVSQwT/4CxgOgo0e7f8DOAqA9e4D3va9L4P/LvwRe/OIKgqqd0LbjAOiDH/wgXvOa1+DNb34zbrrpJjzpSU/CM5/5TNwWUKj/+I//iGc961l40pOehJtuuglvetOb8OpXvxq/93u/N2lceRiqBR994q0jP+ljHgT7QhRCQ+MwWABU3gl80KRjYH8pjuRLyEzUV7AO5EuPJfNv8qxMsi5LSQxyPPmpACxlLg2zOY5cZBgb/VmoGKitdfpoYMk5O3wYKvvq2xjwBcyazhvyYpjrOaGJQcM6GKCpEljbrqcKbKeToPU7G3MaPD+37EaIYyvLdAzLSGCrAiBOSt6JMni2hz2s2w9o717gv/wX4ClPAW65ZWfHrFZth2zHAdAv/dIv4aUvfSle9rKX4eKLL8Y111yD888/H7/2a7/mPv/Od74TF1xwAa655hpcfPHFeNnLXoYf/dEfxS/8wi9MGlfIT4ufZzPJ8gDRwaEEcprGgJIo6dWAhb4PJwzL3CC+NpG/vp389fOU8o5gKkTseXV3E3wFCMtxmSRowawl8EhMiiP95CbFxilmbe740xKmjgFuH8u+cHie5Ni7SyzZTO83lK1jhxhgW39WAkM5b2YnGSBPAksbMo7tu6wEpo+nKElgpWeWLYNfNgl6qgTm+eb+JQnsRAJAAPCMZwB/+IfA6acDN9wAPOpR3WaJ//W/dknS1aqdILZ3+JHl7Z577sEnP/lJvOENbxD3r7jiCtxwww1un4997GO44oorxL2nP/3peM973oMjR47gJC9Z0DGWIuSBnvIvdJH74iz8M7VQC6lLMAHoV2oNWGidXpzEjkUMzkLNC2gr/TQ0jifVAE6uigckFCDga7fvUQZUpgy+fw8qX6b304orx2/ysZDNVHvlFvO+h2PI7TaG1u2TYhZ5Vxz3nGPTQNX2SVFwyX1RkiqVunsM0JhKrhIDFB1Vse6doHejBLYTVWBeDEN9pjBAbWv/YkiWANC+fVkf3ml71rOAm24CXvta4I/+CPjQh7p/ALC1BVx0EXD22cD97tcBpVNO6WJL+0Klf7zR2olqJ3r8u8miDUN3yHYUAH35y1/G9vY2zj33XHH/3HPPxYEDB9w+Bw4ccJ8/evQovvzlL+OBD3ygaDt8+DAO00s71B/YZ6UaOMxHlkmkJOMxLOl5ueDZPubcLOojgJZiCRigcZ+cgNwsZCktj3U/MxvRx8f+qM+M0R7kwaF5rpKx4VjYH0ii805iF3MSwI3GKjApgkUBvXOOu2nsSew5PAF08g7R2Vcaa06BS6ktAJY0J/0dEjGgKTMeYxmgdZTB83hjxuRrVAU2tUzeG0M/07bjyuCnSmBTDkPdyaMwxgKgJFdqdinZTleARfbQh3ZM0N/+LfDe9wJ//ufA//pfwMGDwM03H9tYqlVbwnYUACVrFEJu29bcG3reuw8AV199Nd7ylrc4PlLfuLw6tSffDI7EX+6CAfJPg5+39ugKGQO3pQW8DWNgf/2cKAbJYqRFVz1PK7+Ij2IzG0JqFqq/LeUn9lfa3Vqcqi7AjJSfbHxNfz9/FDIGAW7p/egkaF0pB/IndnzmuCGZNR6HK/mY3ZMnyMv30QxJYGP2ARqbA3T0aF40eRxvPN33eFaBaR8psbc0Dv98vBig7e0sKS4DgCLZiu/ffXcMgI5FBVjJLrkESCkK3/wm8NnPdv/uvBP4+tc7QHT4cN71nP/N5yXPu990AmO11ezwYWCJoqdlbUcB0FlnnYU9e/YYtueOO+4wLE+yBzzgAe7ze/fuxZlnnmmef+Mb34jXve51/e+HDh3C+eefL0//hl1YM/viLbqSdZiphVoe87DwAzgLtV3E9fEUbMKfWli79gYpI8U70FOwMgP+SvvVeKxRfgcRS5ZjADK40xVnXhJ0P1Yft84BUsAS7M/po+dUikHkdwX+aK5p/Pj7le9zLLOmKSdBryMHiBfIo0fHSWBJhljXURhD+UclQBKN4Y1zrHKAxiRB8+8apKwigfH9u+/upCTPjjcAYjvtNOCRj+z+Vas21Q4dOqYAaEcF45NPPhmXXnoprr/+enH/+uuvxxOf+ES3z+WXX26e/7M/+zM89rGPdfN/9u3bh9NPP13860xKG0A598UkyvZeZAUWm1hAeZFUC7X2F55HBglMmOXhH0ziLc1T5AAV/BkZbtHGC79ktWL2hd+DlfVkDOIPPsWsQXxOHgiTwFLHwOCM5xTFoD9VMyfuw++VXqCWWE0MHN8YRoZZnu1tyeSMZYCSzxJLE+UjaYlrLMDZCQlM5ylFftZdBcbSm8cqHT0qv8jcd50SWNPktlIi9G4CQNWqnUC24xlzr3vd6/Abv/Eb+M3f/E3ccssteO1rX4vbbrsNr3zlKwF0DM6LXvSi/vlXvvKV+Kd/+ie87nWvwy233ILf/M3fxHve8x68/vWvnzRuJOM0jBYgF1eR2ErSBS+UYpHkfB7NyogYfH9WLoKIr/c3S+ORP2IxRF6OegdeDFL2kXKRmK9iPkQMNFoj7nfmJXan/KXuvtqDBz6TIuRDJ4bScRwiN8dhcwyoU/4g3h29AyWlFo/CYH+l87U8BqjUVpLHUvsYBmjMHkF8XTYJmsFD22Y5ZMwY7H/safCrSGUpRh6XnwUkOCvt6LwKAALGVYLt5Enw1aptsO14DtDzn/98fOUrX8Fb3/pW3H777bjkkktw7bXX4iEPeQgA4Pbbbxd7Al100UW49tpr8drXvhZvf/vbcd555+GXf/mX8dznPnfSuLxIurkqi3bJmGRzQYnyJ8GMJ4HlsYTEpKUaOP5Q8NcG/gjkuLETa5QShj3Gpm+DBEaAPO08/RE8mzX2NPgUg3kP+bMwB7xyfDwnkDPyxwBNAMGeWaP30HdpzZyaFK/yl/pwErTN71LALYcm30ODMuvisTzA8B5BEQPEwMkrg5+yS7SOldunAqTUlxHlEMuUNo70xvHGWtdzgJ8EnZ7R4GbfPvkfXOQ/2VgAdPBgZYCqVdsBOyZJ0K961avwqnSasLL3vve95t6Tn/xkfOpTn1ppTC+fh6uVjEyiFtCcw6KqwJT8hH6cuGIKYgG1R2vwBoUib0gtuhow9P4EW0LvgKQfk6ui/Iicnb5N5sRwLPyO0ljCn4iP32t63mPWGAhaCSw9LyvR+HNScyJtyjtdnv2l/B9OuOdxoGJwgWojP3P9HoqsS8QARXsEtW3HoOjdpffu7RgMBlWexFQqyefrupOgk48SAIp8eM8A4yWwUg6QJ5WxH45zzPilOHS/dTFAFQBVqzbJNvcssIG/0OcKAc3oT34GM+yrbyN//mnrTd+u/QlZqpdqnLbWLvzsb+6CBalZRf7gxCAObxd9LFuS+gnA58hIOT5+DwQEFbPmskaUHDRj7Q7qc2p0H8XmOCyZBnVyg0nZRx/8Kk+XJxBGvvjaAOXKqDEMkE509kDOWJZnrAQ2FpyMTYLWcXs+okRrfmaZ8vZlGKC99Ddi2rtmzPjJjgUAOl5l8NWqneC2+QAIerdnzb74rIO3z05qE4DF66OCEPIOeJFkrwXmo1+oPRbDr5hKcUT7FFnGps3+CuxLGEOaCQMtL4YecAJFZo3ejDmPLHqvFDf/YCq6FFPH7yL+3AnIUF/tL6yuKzFAmpFpmrzQailrisxVYnmGkpyXrQKLABIDCZ4vkOcaJUGvW9qawiiNkbRKQKYkgQ3tBA1UBqhatR20zQVA8BZdr1w7Py8XNWaN/IXaLqxypRYyiQdylEyi/dkzsMifA+o0c6Xn6+0DZN6DZo3IFxv743wePp/Li4HhmQWW2Z9f6SWZNX6v3vYCMnmaQF2OANQkJTDE3yHuG82JP4d+iJKsNJatGUp05gV3jAQ2lAM0leGJAFDT+PPl/J4hH3oOyVbZCLGUVO1JWlMBUJXAqlXbtba5AMiRUKy0ovNOFm3g3Bf1RyCxLKT8gLkXyxJkVCD9WZnEiyEzSnZOMmfHlmtL6ce/T6EIwDJv2/6k83RTJDsH/qJEbHF6u3qv4kiJJt5nJ7UX55SkRScGLZuxX46bd+hnaUzrkR6jJGJgua2UBD1mj6CTT+7YkjTQkJQ1Jgl63RJYCbx48y2BG++ZdVSBjc0BKgGaY50DVDoioFaBVau2lG0sAIpPYrdMRmoTVUTEOsjDUP1FV2yeuFi9vfJ098BMisGTVpIf7+R5WYov2Re9RxC/Gz7mIc1LxyBi66+W6WH5iX2mNjd5GzB9Wp4Tja8ZIC8JWiZ867HkbtTMXAl/OgaW2uYShDFAE0yYqq5j+XVH8nXW3Tafd//WXQWmn9H+p/rg3ZdXYYrGAqUxz0+VwCoDVK3acbWNBUAeK1I6rVtKYK3LygBKSmp4kdSHrkpmgRdQUV0EBidcreSUa3ssC4O6VgIdiLEoBs1qQQIdGUMauxExAD6bo/OQQAxVtNNyHzuVWvEGk/ERI20IHtOc+7aCBBbJjszGJStJYDoXSvcdvQ8QX6cyOSWZqwRAhnKLxlaBRe36mRIAilgo7S89V5LAhoDNVEZnJySwEnNTAVC1ajtmGwuAIMDC4paSSWKpxmdsen80hGAqqE/y6fpb/KwrhcSxFq2zUMO2zRo+fyrLRXYzRpWrkqdkgI6ck/LHMbh9dB6SnBMcgJH69fsKMVAlfxZYqhgInAE6+T13GlfZNpA4Td8vMSeKu58zRkhgyzJAy8pcEXDS8ew2CUzHyVdPAhtbLTa0Y3Tp+ZoDVK3aCWnHZB+g42EuMFEyCS/UDDGMbMYSDvSi68kneTzfH/o+/QPJn9Onz1VxJTBfhssxj5iTZlkCSUjHIIBgI+WnZHpOXkVeP5bnj04cmCn0wWxTQzH67zXfMgnNQ/4g71MIYs5edV1RAhvDAC3L5AzJakP79EzNEZqawJySyUoSmFcFxs8nALGuKrC27T6oqZLWWMYo+df9ahl8tWrHxTaWAcpVSXHyLycMhxVYyq/ZK0bcz9IYd7b+ssQE6IU/9ymzL8xiOJJV8hn4K52C7jMijj9XApPv1cyJ5EMbgy8/larhGGCYk9g5UZy/DxjnT84p3U+foPUn3o+YmQJAXuXUunJ5PAlsTIUYJ1cPgS6+LpMDNCSBlXzMZrmkPrWPkcA4Z8h7rm3LOUWRX/65xAC1rTzdnuOuDFC1asfFNhYANbSqifLqfFslDENJSdLPzPNHlUIAHbKp+ugF0izUfXyqAitkX6Q/XnRLmzF6e+aktuzP31dIl6DLE+59hsXOV280KGMQ/jz5Cak9tTHg8zYhtG3sj2NM/kB9xCaXYR5SxO5JCaxBEwOSVY6tWBdwYv/HSwIbwyKVxipJWwxYIkktPbsTOUD83Jh+ySoAqlZtx2xzAVCUpEpoQUpgqoqoVUCCpR+xSPryCccwbxXIoT79eEhggWUhf9Gdz6WMI87nYoRB8bc0YMM0D+QCzxsUCkYkufXmy3IWSVn9fGHjY/Bj/CH4/NRn0flilky+18GjNRx/reePY3DfQ2pzKtH694DlwMo992TmYF0yVwSAxuYW8VX7TkzKKlVg6agMLwkasCzMlHyi6Lkhf5FfYDwA0iCmHoZardpxtc0FQENSDRSTwmxOaxkgIT9lmsBP1jUsQZA43UtgjoTS2nueLCRjcyrRvDnx/d5fapPVcKMShqH27VEUi+tPt3HydBN/ftwX6p0b9sWZL8uROlG85I+lO/kepD+F66R8F4GKkuR0113Zme7HbWNkrilJyBEDdPRoh8BLOURDDM8QA5WeGcMApXj0cxFI0s/t3SulP76WcoCGzhhLtmdPluwqA1St2q6yjQVAyVj6ATRYkPfFotaXrSeWILXZPJvOX/5ZnzGV4kg3dZ6IWHQpBpusm59nFkOAugiEQfVRsTObI8838/0JBk3FIN63AjPJdF4TM0dSfmoFQ6bfg9iSILsS48n9kJwNK+n5DCyjvYh0DDlw/vz6sfo5N+Uk6AiseCDHa1tVOhsbT2qPwBwwDmANVXiNBUAMbMZIYLzzNND9HD07lgEqASa+rwFQPQqjWrXjahsLgLxqpVkAFtLznqyhK7DmJOOwnCUOKO27kj8CTeYoDIoPFAOzPOyv60NykQswGtFHggXnaAvBfFB8CoTJzRgD+UnF4cqHA/7kmVoKjDpyFvviPK1+vjPyF0hgQupq5GcuPiOOW4BEklhTGzNAUxiZ1PbNb+YJ6n6lNq+ybEiCGsNIRb6nAKAxDFDkg38/fFiCipIENiWvZ2oS9BCTEwGgygBVq3ZcbYMBUHfVMo5XDQQoIEEsj04mNv76+15uCflD9sf3k0/tT1avpUXXjiUBhgVh6QdZvSb3NvISrkN/HJ/jr4XzXsU4vgQ2F0xKfhHMopT2NtInsYfsHn3uTd+X/NF7ndGHq1m/zA5JWc9UtlF8k3JyPJCTpJTUzwNAU0vkxzJAQ+BEV2cNJTl740eVaBogRAwQH7g6Jk9IP6uToNchvrd6DQAAIABJREFUgbGfnc4BqgCoWrVJtrkAaHEVf9XDByyAPR7CyCQOyyKSoGmcvj2BrTmDI170pc/IX46BwJsju8hxHKZC9JFMRc+yKMmKZS72a/3lGKQEpqvKZHyCJaOh+PMzJegO0OE56c9CAiovEZtBcb4jZT1iciDfkThBnt7rXAOnZTY0TCCHpRstgXEey9hE5rFVWlwmn2wMw7OMBMZy1BgGSIMkRvWRrDVmb58xEtjYjRCB+DyvuhN0tWrH1TYYAFk5ZDZT5zspmUQu/GrBUwsboJJexTipT98kWAKumKKLOdGcK7PYugXe+tMSjokBTtx9fCmGxgUSZi8i+t8GfvVaH59bgUUPIH5HXEGXuzRBnzS+jEFLanE+j2bjLNjTHJDxx+91igQ2lAPkARUGR7ptaI+gsWXw6R6Dk7vv9hOPx+b4RAwU/z4WAEXsyyqy1hS2iH+OgEyVwKpV25W2sQBIViV1P6v1yTI2/f14Q0F9mjj3sfv2LNoCxiYBkjkNRjAiltSUPMbyTiQxeed6weunQFjJn8yFonHIN/uDmydl/fEmicKfASy2Wg+Qn0XXrZHfBwQxqCqwDM7iI0a0Px1H/qo0sQR2990ZRZUYoGQlcDRGVltGAuN2lt6W3efH2+WZfy8BIAYsY54BMtjQgIv7jkmCLgGg45ED1LYVAFWrtqRt7FEYnEzMMo4HCAB1OGfLbIkjJSV34LyTRcc8tMu+8OnyaXyWwHp/c9iFOpBkxKKrQRO4LWBswHOSoCSU1MgfAobFzBd8H9Jfy+/In5P+LHhOs6YRJ7ELGGZAnfQnJbr8OaVRtITZ9aU+gj2TcYt+Y/J81sUAeTk0QwCoJIFF8S7DAN1zT34xGpCsIoF5z8znXan8FAmsBEw8Oet4AqAjRzIbVwFQtWqTbGMBkAs+4MsnAERlVAcwpCPhT4CPtOjaxGmuSvKOWDBVXuzPYYB8EAYFqBQIc/OG1AGvaoGXgKXAKFEMJfkwGe8RVCzth5af/BjiLQ4kCGMJrH8AMCAMoN28ocFeut+Iq/4+6Oo6kTsUbR7oAQoNgEoM0NjNDJeRqLz2b3zDjjfVv9dfP7MOCUw/V9qscFUJbAgA7UQSdGJ/gAqAqlWbaJsLgAalGsVU9P/T7QGkFzy/KknuFWN3TV74a6U/D0x58Zn9b1K/QALTx0nI96BAGL0rUckUsGS2Gs4yKX0Maf7qPRhGhP1BvVchMck+fdwMBDluSHbPzEn5E+8v7KOBZQ7CA4Kev7B0vFTNldpKDNDYSquxDNDhwz4DpGPasycnvHH7mCRr3Uf/PrYMfkgCS76mVHatGwB5rFFipkr9uO8QAGqasp9q1aoZ21wAtLjO1aIrFkl+vtHJvyrnA6A29meZiowuAn8OKElPl08g5zZYf3BAWODP7lejQlf+NJrRTI/Hlpi9iNhfnyfl+3OrzQp9RKKzksDoFcnvw0h/qU3Mid65kFh1n74f4qRkD1CMkbm8tuRz7CaJXl9ebMcCL/59jASmfY71ET2jF38uiS8BJS+uY5EDxD+vAwCdcor9C6FatWpF2+AkaAtZGGBwdVH3fJmpyPklct8XFxhB9uWFsDELq5ThRrElGiyAYguYCu1PAx3JfFggkQFV7hPGXYqhmCeV7jFL5szJ7ROAkj6+BMLs6fL8Hvo+UGyhfDRLi/Psz6uuy0nfjV2sx4CcJDd5QGJMfhC3j60C8xgpbvdi4mcjwDEEwHSMq0hgTeM/N0YCG/PsqgCIAc06AFCVv6pVm2wbC4C8hT+SmLrn1aLLCxcU+KAxRslFvOhSRRKgGSD/yIaZWvn1Kegzd+G3MSQTCd+9P2Y+rD+b/Ktkvd6frYYTp8G30o/3/jSg0vv2yBjavs2TufR8JRBc+JvlfiK5fNF/3lrQFAE3NiO3jdnrJ9kYmWtMP288byfnqG8JAEXg5V/+Jb/kKUnS7HMqAzRU3j5lb59jzQB5lWnJKgCqVm3HbIMlMJZdsr7DC3Wr/q6PNg3srtafrujSyb/+cQlSfhJ7Ec38KivjDwRolFykD/qcOW0NdAwQoEXmT7XCjzwSxLJQc+c9uDIXxvkT7wGeP5g+7Kt/t0IK7F+daJPymPzMw++DisFU13HspZ2gAbmAjgFApTL4BFKaJm9iWDonjH+OAJBmpaLKK06SjpKg03tahgHygM1Qbs+YHKBjmQTNfUrSFQOgtrXPVgBUrdrStrEMUJ/QrJNUKU9E5GdAsRGpj5P8K/JlmN3ox0mLO/kj1oH/L0yf6u72UWyOTnaOWJQoBjQqPiUz8Vwhu7B4J+bkMkOaLdGMCPj/z4OjNZgJMxtMFirbjATG8UmQ6Mag3mv6slh2D8KfiGEupcWQAUo2NdF5bH5QCmpIAtMAZzaTO0APSWBjAVQ0vo5xFQkseu54VIEtUzqv+3LSNFsFQNWqLW0bC4C8fVr0yenmiAXktghImHLy1Mdljcjf4jkGOYCV4ZLxwgq9UAvGRsbd+zIgLM7nQSsBQz441AFhgT8v/8ZW0Ek5kmOwTArf16xREAPNn1+GkAkdCUzG4ABBMaccY9cnBrdmY8WIAUq2LAM0VTobSoL2/HJ7xACl57/+dXuP+48BN1NPg1+nBDY1B2joVPdldo9Oxu2eDFYBULVqS9vGAiBPAhP5La3dETitalou6pqsjNP9xU/3exYlLayOP+oDANuEgKy/dF/5g1qoXYCR30Tuo/wJSW3RNlOgziQgR7KQ9x6cPkp25Bgg+kXjyDa5vxK917b0XoPPlsei+wJw9nlI1h+3pzYR8TIMUFrgxrJDpfL59DNvDFhKgo7yc4YYoASAovO51pUEPVba2i0S2DIMELdXAFSt2lptcwGQkC/yvWJex+I5IWeV2ijtVZ6oDvFDS2jGMEAEgIb8MdBJFp4Gr2Qu4a9JfbM/kavCQDBtDKhlM8XmeIxI3hAy9ynFEB6tod6Dy+ao5HIGlpJZYylQxiJztfTp8j57plkeEUOrYlgGAJXalk2eBqbvMM3Pjs0BGpPgvC4JbAjYTAE1xzoHqGRNE2+kCFQAVK3aCrbxAAiQi2S/qM1tnk9asOeEjoo7Fjf+sQx5cbfMBzMs3VgSoMmKLsWkeEAHeTGeU85JMgYL0MxHn/yrKrDSfATYy+19H0d+EiDC66PlMRGDMycFSrS/nJvDPhXwhfz8zFEY/VgyP0h8FmouCPyJ5HJm9+bbwPZ290skgXlsTanNS2QeC4BKewgN7fMzxAANAaQScFknAGIJbBkGaF1l8KvkAHH/EgC6z32G/VSrVk3Y5gIgXli9BF/kBcpjWMINBY3kAbov7/Eizkcs6AosETcn0yD30f6YxWgKIGz0SeyLW7ZkfJw/eYyIfHkCmBBgYb/6/Xn+BucUsi/8fShIYOYzpPtKAiv5Sybyu45QAuu6GCDv91KpOvso5Q9FZe5jq8BYAvPajxyJAUDpLDPtZ8oOz8ucBVZigKawOatIYMA4AFQZoGrVJtvGlsGLv9BJxnEBhgIszH2YvWegjtagHqD77JfzjdDEDJAAH7BSkvSXYi7vHZQTp1tnEc/9JKPEzNWIGAYkKz9hWD7Tos2AlPyh4A+t3F9JSIvi823g7UXkxkDIUn4WEuSwP2h/TQLRFMQR5/iHEsuzLADiROdSvzEM0JAENjVHiMFNYsOWYYCWYXbGgJplJLAxR1pUAFSt2q60zWWABLPgSDVAAWA4+UHMEjisg5s4TfFwcjLLZjJXRUpJhklhxkZINY25bxd3h0lx5tsxSnzfZ8kAhKCpl6VmCmiJ+Jx3nkMQc+2lO90HuQ8a+b4zmFJxC2ZNg0T52fJnYdg9J25PUks2YwCkz+ZKtiwAGtvWNLmsfWr+ELdPSYL22seyO8dbAhsDgMYcabFM5RhbBUDVqu2IbS4AWly1TMJsRLHSq/cjhQ25ICupTa2S/untmqkgAER95f5FUnaRC7VO1pXzbwr+9Mnlqa20p8+ssfMdG4MHLEUM7M+Rn7Js5rU1wpcFoxmgJXCU9hWKzjHzNsbUFXk8VrL+Hc3pXmJk9uzJIGRMGfyYtkjmKv3uLcBjy+CHAE7UzuzUUA7Q1NPgx0pgQ+XyfB2TAzQFAC2TBA1UAFSt2g7Z5gIgXpAX92a8sKKcXBuzJa1aJGH9Qf4gEnwV5hCLZBPtV5Pa01i2Sq3vQ75k3A6QWDxrSvEL78gbSzA2rbO/kvNZuJs7kj+IzyLuI3e3zvGlOen3wONIzshJxObPXKWX+7KeHEvkIZXOxkq2E21Dv3sAaOioi7FJ0MsAl50og596GvxYuaxtJQDyngdWT4KuVWDVqu2IbWwOUM8GKBmnKO+wjBPknYgjG0DAgPxlgGGZBb1Q6yqw0on0IGbBnROo8siNQYO6zObkGLL2M8iSpfnO6L4Tt7cnkyct8rEb7j47Th/v3XVzEq+syEJFSdDeKfYW1Fng2/Vr5Xs94izme9V/fuvMAfL6ee2lzRf1Jn16A8ahMvgSu5OQ/7GSwNZ9Gnzbdrk/DJYcRlX0qTlA1artKttcBmhx1UmvIrEV+T5fBZMy03KR7CfAR7BIamZG5AAp8OHmISnmQzMzskJNzt/PsdFMSh9CmCfl5RRxfP2MWgYmMQullwo9ljeOZq5MH8GGJeBm350+L80fK6iGSzNzgZuYtiyD95KSmyaWr0pApgRqhgCQ/p1BTqltjC+9E3SpwmuIASrJVsswO8ucBl8CQGP86j5eDtDQTtD8TAVA1aqt1TYXADkLP5CrwOShnXqRLGx8pxb4fD/DEtOH/OlkXd6vhvsAVjZz85eanMsCOHKMNye9UHOybtOglAsl8oOImWFgGZ2czp9EsVIumqsBVLmPzmea58CdPnJOJakrzSkDYjknWQUWA0t4DBAQA6ApFWIlELMMA+S1eb6i9qF9hErAhXfATt/LdWyEOBYotW0GQh6oWAUAMYBJP48BLhUAVau2I7axACgtQ/ovfo+pMAm5rbeABv5YCgn8ibwY8gUA23P0vriv9CdZKCOp9YnYjvzkMUDK37aigJgRSQP1C78nJekYFMvTny0mQKd8R/r9iUNrAbcPYHOokuUcIBkLz8l8TpDSmdwYM/nx2D3fn6jwG2Iz9M9TJDAGQKtIYEMAZyq7tMw+QFpGK/ndCQmMWRqPndm7N//HMBYAeTlAU4BLCQAlObICoGrVJtuOAqA777wT+/fvx9bWFra2trB//3587WtfC58/cuQI/sN/+A941KMehdNOOw3nnXceXvSiF+Gf//mfJ48tkl4JSHgSmJsoG8hPc0r64H2FeH8gK4GpPXMoTnt0RdP3MXksIH/enJy4Z54/5x3xe5Psi/8e9H5IzAwls6xMHAOzVzK5PN63R25y6VfXZcCS30MsE8r3xyAn3IxR9JH+ZA6QI4EBy0lgUwDQEGhZRQKbyhBNkcAYAJWOy1i3BMYgI5KnGNBUCaxatRPWdhQAvfCFL8TNN9+M6667Dtdddx1uvvlm7N+/P3z+rrvuwqc+9Sn87M/+LD71qU/hQx/6EP7+7/8e3/d93zd5bFFNtbjHTIVY1FTf7g/+gEmB9sfj6DwRanNYIyDeO4hjGPTHfRRYgNPHAAnFonjjWClJ+eP3owGLw5akm+77Y3+C1ZKBMwsl2D1YwCLPHFOgk2JIn26X2J28Fc4jQ+xPSIsRA8GLe0mOWlYCGwIpJb9T+k75fQwASnlEOk9qrB/93NjT4BPImM1sknoyBjTLAqB1MUAVAFWrtrTtWBXYLbfcguuuuw433ngjHv/4xwMA3v3ud+Pyyy/Hrbfeioc//OGmz9bWFq6//npx71d+5Vdw2WWX4bbbbsMFF1wwenxZ0ZUXw6a4UDvyjtvG/uI+LMPJZF0r4YyKgf3RPEedSC/6yLH0XkRZErIsGc8p95GJ2KU9eExCsyvrye0KGKCNeQ+ALYNH6XNyZb3sy5MPx3xXZA5QwABFEthYoARIAKQXQv27Zotms3HP6hi8OMYCqMOH492T0zMHD+aYFJO4FLMzFiglQHHKKXZc7bcyQNWqndC2YwzQxz72MWxtbfXgBwCe8IQnYGtrCzfccMNoPwcPHkTTNLj//e/vth8+fBiHDh0S/wD6/642OLqCpIu0VEsmRUkofZvvL/VL9zkGyQ7Jtu2APeDFvcR8MKgbPEE+xd1XtskY+PnUR/vz9inSrJYFC54/7x1Zf2J/IO+9MhjNIThnuaXY4r2IJJujwbJklPJcy3sbJWuihSqq4NKHW3I/3VYCQHqB5b560dZ9V2WAShshDo2x+O/YBQjHQgIrAZNlARADmMoAVat23G3HANCBAwdwzjnnmPvnnHMODhw4MMrH3XffjTe84Q144QtfiNNPP9195uqrr+5zjLa2tnD++ecD4EWIZRfFOCiZS1Y4LbqUZByohTqSXQbyWPh3mY8i2+RGiM7CX5K5WrunT8/mCAZIMUranwBb+b16CcjeewCG40MwJ/M5KWnKkxa1dMfJ1sXPne6XgOXcia9v4yTof1kkq2rwwqCB25YFQKV++ne9yA+Bp1XkNe/3kg9mgLQdCwlsnQAo+Tp6NNOZzDQNWQVA1artiE0GQFdddVWf/Bv9+8QnPgFASj3J2rZ172s7cuQIXvCCF2A+n+Md73hH+Nwb3/hGHDx4sP/3uc99Toytk1Qle7C4r+UY0aakJNXPOy5BH13hVXRxfByD66+x/phJkaAOrr/kkxt7FookJgZU3p7JofyUXTggzM6pdKxFgyZXjgFoNfhgf8h+pLSowWMJ1EWfU+6TgVv5+8DPiCqwqOw5Yn00kOHfh2StdNSG9+wqDNCqVWC6v3dPnze2CgPkMTtDx1tMBUBjzvTSpfNALYOvVm0X2OQcoCuvvBIveMELis9ceOGF+PSnP40vfvGLpu1LX/oSzj333GL/I0eO4HnPex7+8R//ER/+8IdD9gcA9u3bh33O//kIKSmSrCI5Bt4OyLnNSFP9fZ8tgcO+zBpgG1wGb2MYd/wCzZUQQWmfHS0LxVVg8t3pOclcqBxnzwAZmau8T5GIgeZk8po8lozeedtmWU8fyMoj6RgA/8gSefyJvLoSGLFD/e93HSMGKD2bAESJAdL/3Qz51QBH+16mSizK74liYL9TJLASUEj3/uVfdlYCS31OPbVKYNWq7QKbDIDOOussnHXWWYPPXX755Th48CD++q//GpdddhkA4OMf/zgOHjyIJz7xiWG/BH4+85nP4CMf+QjOPPPMqSECkMyCzOsgqSaQiySzYP15C7/P2Cza4PhDA6AlsCCtCD56r5KF0sd0mBgCfzIJWiUgB1ISz4nPWEtx2HiVP8hn+LaoRKM2A0ZbP9dnqE90wr1koWTcEchhia5/R6mJx0kLlQYZEQOUmJzt7e53XuCGpKplAdDUHKDSXKL+CaF67d4YJQmsbfOmi0MAqMS4MAAaI00xAIo+VzZ+LymOdSRBb2/nfKoKgKpVm2w7lgN08cUX4xnPeAZe/vKX48Ybb8SNN96Il7/85XjOc54jKsAe8YhH4Pd///cBAEePHsUP/uAP4hOf+ATe//73Y3t7GwcOHMCBAwdwT9LwR5rLbiiphs+e6h7wpBoHzLD8JMCCHFucWaX85YRmzW4wcBNhBVKS2tvIIrfQn3tqeaMW9+QONj4h/dCL1e81OmuLnxFyEf2vlwQNeue6Tfuz8qGzX1Pgj895s0DQfu56viLBPdqwLgJATRPLXnrRLAGZVZKgh6rASmwWAJx2mvy9aeS9Uj5OFIN+Jjp3jO+lhGqgDIC2t3P5/VQAVAIgTWMrwdbBACUfY/1Uq1ZN2I7uA/T+978fj3rUo3DFFVfgiiuuwHd+53fit37rt8Qzt956Kw4uEh4///nP44/+6I/w+c9/Ho95zGPwwAc+sP83pXIMgFiQhVykpA02N1kXuS+gF+RhOSb5i+UnBPedPuTP28NIAAzHn5nT4qrPI+PkX5Ozw/FRDDMKxJP7AJ+F0n3SPP19e5Q/cmh30lbvx2OU9OdEbM6MYpAbY6r3MLcbK/bVdbwb9VQJDJBgoQSOSsnMJQZIA5RVGaChdn3Pa5/CAI19LiVUR89xHHfe2V3HAqDoc9Wmd4NeBwNUAVC1aivZjp4Gf8YZZ+C3f/u3i88wCLnwwgsNKFnW5DEUJFkVpBqRZKz255k5bADLTz74IH/BoqtlOD6WAaZPZmxcEAa5gGt/UbKu3geIGZbS6e0yBvtetSSkQVMcg65Eg+qT/fmfIZ9HJpmhLu4Y3Ooy/fQeUnSG1QIM8O3fH/uKpJKxeT8ekEmL7/3uN61fsvveV7bNZt3inhZpDZCmMkDrAEDRcRQlv9pX2n1+zx4/EZulua9+NR432VQGiPskELNOBujkk+V+TtWqVRtlG/tfTVZxVJIqEQ96szzBBESJt6L0WuaqxAnIDPTkgjzXUk0O3C66uYlyZhoFzuDHLYCbZF9EGbxitfIoNgb2xx7n5r3m+IxC1/fJ/ZuZYrZMHwIfPZiRDs0Gk+TLypuOv8b//DzWKFmYW9UgL8IarJxxRv5ZL4b8OekFnkHAFADEfjQA0s/r9pIvYFgC0/e8dg08PCDSNOOYogQ6SiX1yV+ayxQG6O67xwOZ5D89v44y+JT/5L3HatWqDdrGAiAEi5eQatR+Nfw3v2FLUgsteE3D9+NT0GXlmGwr9ZkrfYyBiX8gayxzAVaq6VkoUQbfKLAQLfzxHjw6sVuCRx90ahZK3A/6oOWcJzm3UfsrFebEVtrHSciRqi29h8d+7u+AD3ygu6mT+nmDz2/5FtnGOwdrMJJ2UgYsAGJgUgJHQwBI99XVmKV8Jh2Hd89buIdAVzK9a7bHCuljNUogJbWNAUAMZsYeRpr6pOfXUQZfAVC1aivZxgIgeUJ6uudLNXaRtDsWp0adrCvkJ9Ei2RzLzEh/PgslY2BgAvLnHzXhsVAyBpswLNtLfVK7jgEogLqW35GMU+YA6aM10n3lz5mv9ufm+UD6YfDWA9WZOhNNMU3ee83xp/fQXe+4H1VN6h3NeeHW1ZUabUdtevFn4KLHW4UBKgEt3ddr1/e8dr2YR0CE85Oi/JsxLJFuGyOBMZgZUwWm+7TteiSwBKYqAKpWbSnbWADk7RY8m408iR1SCgGYWeAxcq7KfG5ZApnP4zMzUeWYl4DMUpcEdYvblMOiq5U4edsc8BrE1iIGHxFjI+ek3mtBotsOKtGYNfL9+UyP3l9JnG+mNDV3k0RzX7+H1Gb3NtIg7MD9z87sziMfCWHMqgwlIbOVFmgGUltbso0XSw8AlQDSEADSDNE6GKBonqXk8WRDVW5eXGMYoBT3N785XQK7666udD19aaoEVq3acbONBUBu/gbkQh3tAzQnmiDd4+MSeAzBRqAVz+Z8lPhojVgCi1kMTiY2e+ZElWNeHot6D67EpPyxtDh3YnDn5MRtgSADKs2+SD+ubBYANMWbqLhlm6j2UiBMAzfvNPhI3mxne4D/8T+AD38Y+LZvk4P+8A8DD3oQcOWVMPbc53bXxz7WtqX9gTxjEKEZoLPP9p/zntftQ/LUfe8r/wMbYniixOXSmWj83JRnvHi9tikSGDNAUwDQ1OqtIQA0xD5Vq1bNtR2tAjuepqt4gARYWMLRYIH+4l/ci/Z2SWPIvWLk2GVpSks/lt2wc8n+mJkpHsvgxKCZlHB/oLH+1HuN9uBhmTCDRP0e1JzgsEaj5hSwe4I9i9tmTdP71iCa4y75E/Lmv/7XcO0hDwE+/3m/7d//+y6B96UvtW1XXgn87M8CP/RDtq0kYz3gAflnb0d2fl4zOrrSyPv9vvfNOTfLMEAphgRENOuUrLQzdrJlANCXvlSOjcf75jfHl8F7AKhp/JJ+bZUBqlZtR2xzARCzL7SACqZinu8DA+zLok3kAM1kH+g+DluiE5rFXjEqhlLlkXcgKyBZmaiPzc2RElPP8hSSlsfEUGah5DuPd4j2SudtDGOTyzXLI94DFNARzJrfR7CFilHSCdqT7cEPBn791/22N7wBeOhDgac/3bZ9//cDP//zwNOeZoNiAOQcVizK8SLwUTLOR+IKt2RDOUDAOADE4GydEtgYAJTalmWAeA8g/fl4xgCobXOfCoCqVVvJNh4ACTCjnsnSj+rjVAPxotvf033Us3lhjTfSM4sxNWR/GqD5Z4G5/tw+Esxs62oz8qXXcDe3qqFS/EIMQIu2lWPnTQPzHNiflwfMc7I5T9KfAY/0vxZQSX9Nm++HWxzAAWEJfAffu7XY3r3AC1/otz3+8cDf/z3wwAfatq0t4N/+W+DWW4F/829sOwOLMYuzNpbmhiQwnZ+UrMRCefdLQIptDAOUjpbw5EE93rI5QFNK4Pm5+byr/ksSYQVA1aqtZBucA+TJQnKhzieGd/fk4aYQ99wN+8hft3miZDe8TRJ1Uq4+OLR0rlfkT1a2+f78hGEt1ZTfHfuVCc1ykdeVbcUT7iMJjAGGAh8zSsCJEqSj94A2kxzJj0hWTzGQvDn0WWRSMPhslwESq9q3fqsPDJoG+PM/72Q370y/n/mZrlT/Z37G9/ugB8mrNi7P9+bNY0bn/DH4WIUB0uCpcKhycRdubR4DNEUCm1q9xUCJZbAKgKpVW8k2FwAtrkKmgZZqFvedv9zDhGFzZlUeR7MlrowTsQSKGnL3ngn8cTKvLWnnPspfil3n0fRzcmQz8gdq4/eqk8vB7zXYp0huuijvRwe8jqps85gwVYzf+6PPdqbmFLF7wPBnq5Otj7vt3evvmwMAj3408OUvA//pP/nt//E/dterrvLbzz+/PDbLbp5EBkwHQDrRO9m+fTLHpgSAvITuyDwwM4UBSueXjQUuLOUxAKpl8NWqrWSbC4D6RUhVK9EzOu8kmWAqjD9eJFW1kmFLFm2wICO1mpwdjgGyj8eK8IGs7M/s9ozYX7xnjj0awp0vJAs1qax+cTWbMdLnpwgsh1DiAAAgAElEQVSWDBJpUvqd6zJ44S8EviqG/CtJcc578MMzydsbYa94RXe46Mte5rf/xE9015e8xG9nABQxQAxUIplsDADSz00BQGOToJeRwBJzUwJZbLNZBnIeA1SrwKpVW8o2NweIVkmRL+PIRf6p5RJI8MaK/RjkjwGGrnByE5CdRdfE0Es/ck5i0WW6hPzlEHIfBP5MGTzzGwosJM8dmPEZjmjTRw2a+CqBJY3Tylwj8R7ggTfpL4dG/vpxfDDa36Hvis0Xy31MfGEMG2Kl5OhXvKLb6+jyy/32iy7KP3/7t/vPsLzGSdtsDGb0DtpsW1sdo6X7aFtWAlumCmwqAwR0Mtg991QJrFq1NdrGAiBxArmSwZIVj67QYMFhgIQ/kY8S+9NjlfYBModsEjPDbVLWi/2F+/Oooyv4tHUtWck26WfWdODHyHAUQ/rf0nvlE+lF3Gq8UpK2rrob549jAOhrY45NSda29nNqBvpstJ10EvBd3xW3f8d3AG95SyfBXXih/wwDLK9UH1g/A6TbxkhgX/1qTpou+eY+yzBAQAeADh2qAKhatTXaxgIgP5FXgYXgxHfukxr14aXp3sxhArwk6CgpVx8cmvsU/EHuOeQldmd/yPHltyP86koqztnpWaOZlH54vsKfk7OTtovpJDXpR4Ow3iPrfZDPepVomdmT77XEhGl/Ir8rkEtNcjksEGyUv42SwFa1psl5RJF9z/d0ZfyXXRbvhs3AKJLSgPEASIOoMQxQ2u8IGAYz62CAgAqAqlVbo20sAErGpdK6YiraAdmvmFr0EYsk9YFlS7w8lniRlPeZfenHQ/YnYqBn7EGkOcChxO6ixNTHQAv/IPOh/AmWTLZtG3muDzvsIz4n/V6NbEb+1Fx0DMkPv/0od8mV9RSwrPBnoj3tacAnPhEzREC3gWSy0nNj8okAK6OVZD4td93nPsCePfHz3GcVBgioAKhatTXa5gIgAh9crZSubeuwBIurqOhSq5cAH9zHYWxy14yA9FgmZ4djMLkleaxk9hgKGXfGPxIIclspCTozYbKNc6u0PwNmmLHpHdmxut9jpikxSV585v0VE7vjtmQNO4Nl1nic0qaLfL/aBLv00nL7Yx7TVZG1LfCd3xk/x+zQeefFz2kGqMQqDZ2BVuqzKgPEx2jUKrBq1VayjQVA7vEQyIsXy0gwAAPO4p7+qpcySZ+XgwGWYNEnS0nSX6NWz47dUP4WPsxBpLRSmyMgYGPQDFUIIsCJ3SUmJfnr3qzZWZpjGAJhvU9meXi2Moa+JfQXf7ZRn76Nfo928m4x7G9WEdD6bWsL+Nu/7XTsUhI0s0NjAdBpp5UPotUAaMyO2asyQNw/Wa0Cq1ZtJdtYACTyRNS9KFcl/SRlF9lXVyvJyqw47ySS1Cx7QDEE/mwlWv7dzEnkvsix+g37DPuSV/do88Ri8q9JQI7fQ940UL4XyRppxsbGMNNzMv4a8ifj7SUwdSL9nL4Z20HcYgdw5a9KYDts3k7X2i6+uLueemr5eQZA0f5Eyfbs6Z7/2te636cCoMQATQFAaYzUF6gSWLVqK9rGAqAs1ZTPhQJ48Vx0aa0ElvvwGLlaqeun+vAiHrT1CzVkDN4ZU24eEqQEphd+Lwlaszl2J+gUdzwn118wJwn25LPJ7OGlixgEg2f92QNoA39gf/589Yn0syb/bpOtF/fB/vR7aN0+1Y6hff/3d0nXj3tcvPkjICWvUq5QsjPOyABoigT2jW8sB1wSWKoAqFq1tdkGA6D0V7hXrdT9ZpJ1iWGJjlhg8MH32Z9OJp4zO2TaYvbFApZGjANgcSArxRAlDMMyM5kdkhwGA8F+nJI/9Yzd3JGZNTWnRs7JZZqC9yBYMsX0RP7kRoh+DL2/lhigUceF6Db5fqodB9u3ryu7HzJmh8Z8bmeeCfy//9f9PAYAJVB16NByDFB6livPKgCqVm0l29ydoBdXX6rxJQoijWIGKNjjRvjTTEqJxSiwL9EJ6SYRm4Lo/ZmE4TjXR8cNMFgI4nMXfhmDvl9m4+De5xPpS+9VW+ivdSQ11Se1laRFZpqi4z363ag39r+yDbLZDHj4w7ufn/a04edZJjv77OHnk8R29Chwxx3dz1OAi5bAtrdzRVgFQNWqLWUb+3/N/g7NcsWzO0EvHmRpxSS2wu8DBixKdnH2qzELv+5TqCrTybouCFP+4MWgpBqvasskivOcKIauvwKWLpiBsD4GxVy5B6hCXoGCDKc+W/e0+iAGjiNZ9H1gVksnSGs2rtout7e/HfihHwLe9KbhZxkA8fEekZ12Wi6V/6d/6q5jpLZkWgJjKWxMDlK1atWMba4EtriWmQ/ZIBe1SELRf+3nxS0qr/Z2ibYJyE4M/bOqTVWB8eK+Hc2ptf5mZk4ahNlEbD6Jvd8kUQEdu78SgRklBdoNIb33oPrMGBzJ96f9Fdm4IIb0vACWZrfsHKAG0ua9VvxzYtj3fE/3b4xNZYCappPK7rwTOHCgu1eqXtOmAdChQ931pJPKFWvVqlULbXMZoMXVk1BMpVDqoxYugKSkxe8G5NAb1EyKt1uwZqF0ngjHEFZMiUo0mQRdAm52Q8FgTg77ohOnZXyKWTN5UrlP9ie6hEnLItFZAQm5+7YdS7yHxbVjtSIJbBhYWgbIqQILYqi2Qcan3pfK69n0XkOlIzy0JZYn5QAlAHT66RVhV6u2pG0uAHKYj8FT0EF9tJSUZBKzy3E2LT/l+/Gia3dhzjHkKjAdg5yn2N068gcUwIKMyZ2TahTvdSSYETGYz0KN7TE2qo+fIC396eDmzvchXQywRLYQNM1hP6dFmz6RvtoG2SWX5J8f8YhxfbTktQ4GaEwCdrVq1VzbYAkssRiFv/g1WCDmI9qfJzptPY0l+jhMClQ/mzjtyUV5VjyOZ6P89d60XKQBRkZhuo8nEyZpqnQifTSn6H13Y/ltY6TKme7jsUbI8fVRNSoGA9BSDHafqb7NdKq2Mfbd3w085SkdiHnUo8b10YxPBUDVqh1X21gAJFJVAlAQJ+tawMIHenp9AOccLvaX7jUyvgicQcTts1Cdn9wmcmK8GJQ/BDFwMnPEGnUgUcUH6c8/10vOv2eAFAjz9lfyKtHC3bKjE+4RV7bJHKAGDX0JdE7RTMRQltQq/tlAO/VU4MMfntaHGaBTT52Wu1OSwKpVq7aUbawElv8KZ/ChJIqw8ij/Xa/3nskgR4IS4U8t4sw6RHv6WHnHywGS4/DzOa9Js1qOP7WI680Tk3nVa7zDto5B75WUk5aTw5bybKQ/mwyegzH+KAa9h1Fj/El2j/dXaoIY9Ly4rbS3kZlT/14rBKoG4Kyz8s9Du01r0wxQAkIVAFWrtrRtLAASf4WHDIJedNP9OPdlW7EHbnm1WsS9aiW9UNvKLMefJ9Woq64CE+Xkpo+WizRoKhzVUYghqpQT+TeBP+2r5E/mACW/Elh6uz1raUqDUe2L2+x3JT6qQzNh1e7l9uAH558f9KBpfasEVq3a2m1zARBJHvZgTJ+pyFJNXlm90nDuwxYewCkqhWS/ViMCxH108raInUBLFEOUVB1VmwnpTjMsgQwnYlBoRjBKatoRcwWQNOWBj1CGU3EjxeAkTjeqDw2u2+B8H0qVchxDtXu5ceVYBUDVqh1321gA5DIfhg1Y/J460QI+9Fe9XsABZ0NBkD+Td1L2JxdW6U+Cj9Sm/Kk112dLoPpoIDNcts7PDwLLtgQ+YglMbz7ZzwleErSKz2HjbJK2ioHGMGBGgzA47FUwp2r3cmMA9JCHTOvLOUBtWwFQtWprsI0FQNlas0hGG9X5Z1bJ67ZmI2AX6kathJ6kpv2ZaiXEVWX6QFZ+pnRm1ejKNpaY9CLuxaBYEX1yevkEee3PMkBFfzKseE6ChdLARPWhscOqMs4XC+ZUc4CqCftX/8r/eYwlBmh7Gzh8uAKgatXWYBtbBdb/FT4vJEEr2YWTlqNjLcLjMxBXMpWSdYunoPc9VB+10aDrz0g/Yw6FhYo7ThieSwSkYi/4UyAjioEhwxh/hlEK9kOaqz2UvDkxYJk1wDac5PcUGwqslqpEq3Yvt7PPBt72NuBv/gZ43vOm9eXzvg4dqgCoWrU12MYDIFnJJK9WfiowC31yrbzPsswyyb9ztRu1qESLknUdacX4U/HxifSaxTCSFb2fkN0gCUyzV3YzRppT/x4acdXJ4GM2d5wLoKrmVJDUItCkmaYcu92Nmtm4+NDaKoFVU/bqVy/Xb8+ebh+hr30N+OpXuysw7TyxatWqCdt4CcytVurBzIS8jsU1OmIBKByXQDTBcO4LxQC/jy7J9tp0DGgZHGkgoefiAUE/br9NxuTlNcXvVcbmxeeWtCvmKN7l2wFNpfypCCyTv6haLzrCo1q1pSyVzn/1q8BXvtL9fOaZxy+eatVOcNtYABSdmwXYhV/LXMxU6F2i7UGfeUy7EPYtIdtkAAvFEB1RoUEExxNJSWLfnj6G7moP8xwfA98zMTgyXHiqusmRsswadJ9CZZuuhhOVbUEfLZtx7EbepP9yQqnSAarVqi1tCewwAJq6n1C1atV621gA5OXLaEbCyi7dtVskfWbGskZ2odYAw0/WVf50n1IMrgQ2IoaAFSkfhlqOQcch2hRqEv5U3GPK4D0QZmU96c9loXSfPm75u5yv/F0minf3+oNzA9aoWrWVrDJA1aqt1TYXAC2uXrVSyJY0dlGzYEGPUFp0HdbBsATw+3DcihXROTscTugPVlLT/vTMuI9hrgr7AG0ruY/ZF93HY+q0aX9+SbvvT1dgidPlIf15fYw/h+VpVZt5r5UBqrYOSwDoi1/MSdAVAFWrtrTtKAC68847sX//fmxtbWFrawv79+/H11Ly3gj7sR/7MTRNg2uuuWby2B5TkZOJZZuWauYt7+7ryxol9sVL1rUHenZmj1jIfYyEUmAWpvjr+wRSDSdi97lLM/89lPxpxoZjaFRjxDQJfw4LFbFa0f5Abf8/HjsUv1dbOp/uW3aP27S/atWWtgSAPvOZ7to00w5UrVatmrAdBUAvfOELcfPNN+O6667Dddddh5tvvhn79+8f1fcP/uAP8PGPfxznnXfeUmPrvX66e901sxiL+zN5v21tdZY9NiKPZSrE1H3BVBimJ5DUWskCiRics7uMPycGzWoh8MfsVFjZ5paTj59T5M/LAbKymWW18pQk+6KPGGEJTPvTDB7HHu6v5OwzFfWpVm0l0wDo/vfvqsOqVau2lO1YGfwtt9yC6667DjfeeCMe//jHAwDe/e534/LLL8ett96Khz/84WHfL3zhC7jyyivxp3/6p3j2s5+9UhzbIgcoYHOcyqNW9UkgSe8Hw/1Msi776psSy+L74z5hsm5rYzD+nBgyWBhmtbo+tHeQkbkcCQx6TqKriKFn45Q/7Yv9aRZKgjrNeKn7vUPn+IzG71PyJ0+Dj2LwZbhq1ZayJHfdemt35cNVq1WrNtl2jAH62Mc+hq2trR78AMATnvAEbG1t4YYbbgj7zedz7N+/Hz/1Uz+FRz7ykYPjHD58GIcOHRL/AGJlrAJmZRxHCrFyiPQnWQLINnVfni6fnvH9lfvIuF0WSrNGWcOxybq9PxlTAhqlhOGWAJBlPhbjaBBG79Vr83yxPz0eZxUNyVn8vksl8nyfG0MWqi0liut4q1Vbwc4+u7vefnt35cNVq1WrNtl2DAAdOHAA55xzjrl/zjnn4MCBA2G/n//5n8fevXvx6pEbhl199dV9jtHW1hbOX5y34y7UCnxopqKUrNsval6ptJLbdC5N1ybHhvLXqD6t06eUBN2DGbO7NclFQbKuOeZh4auYZOwxa30/DSw5BjlGNCfBximA4cYQ+oO4is0YU5+Z/31wx9L+4PgLvg/Vqq1kF1wgf68AqFq1lWwyALrqqqvQNE3x3yc+8QkAPvXftm0oCXzyk5/E2972Nrz3ve8dLRu88Y1vxMGDB/t/n/vc5xZjd+1etVJ/9EGwQHnJupp9YTPSj2EC4mTdqFR6Ttm1Y5iFUM7iGNSz5h0psFfeRZvGVj8YadGNQbdJX/yRGMkvxU0xGBlOaW09OEMsm+lqM45ju49Pgz3kRPFACqwUULW1WAVA1aqt1SbnAF155ZV4wQteUHzmwgsvxKc//Wl88YtfNG1f+tKXcO6557r9PvrRj+KOO+7ABfQf+vb2Nn7yJ38S11xzDT772c+aPvv27cO+ffvMfT4CQlt0rIWbWxL48yUwH8yISiHlbzsAGH6yrhpHxKD8qT7uHjxB3JwwDPhz8vYB0nPyGKUsgfkxaNao7G9YAvMOhdVtRubi96rGsknQ5So19lGt2kp23nld0vP2dvf71BPlq1WrJmwyADrrrLNw1ojku8svvxwHDx7EX//1X+Oyyy4DAHz84x/HwYMH8cQnPtHts3//fjz1qU8V957+9Kdj//79+JEf+ZFJcZqFle7lv/iDvA7EybrFc7iC6ic3WVcvulB9YPug0eMQU7G49hJYnzBMMagxoso2Blp93lAj/blHYagYvPdgAaSOQbIvXUWe70/EAH9ORQmsgduHIYut6LKfX+4lEZWtuqtWbQXbuxf4tm/LSdCPetTxjadatRPcdqwK7OKLL8YznvEMvPzlL8e73vUuAMArXvEKPOc5zxEVYI94xCNw9dVX4wd+4Adw5pln4ky1sddJJ52EBzzgAcWqMc+MDIHhfB5mX6I9ffRCKP2l37XsEjMV0UGfaJ1FHHocmm/AOuQYLJBAFLfDbmCpGNScAJMxo98DP9uoGMx+TXP1MF2j9yrZPf19cOaUxgolTGfTTDOnioCqrcme/OQOAO3dCzz60cc7mmrVTmjb0dPg3//+9+PVr341rrjiCgDA933f9+FXf/VXxTO33norDh48uP7BXZYgNSWpRi7uGdRQ/o3q48kadvdheV/smdNffaYiJy3HybXuYaiaxdD+vORfHXc/18VbcKU7jI7BzKlt0baNauuuc1U51j3TUUDGX9qSwJXhpD/DQoGkRdXHPQ1ey6Xq/hh/s43db73aMbc3vQk4cAD4d/8OOO204x1NtWontO0oADrjjDPw27/928VnOI/DMy/vZ4y5ybpaqomYAFr4Z2oXu9JeMbrKqlELIeCwUEprEzEY+WnR5rElyp+OoZSsGyVosz8jgZViMIxS9tWYHCUfNHVjAtueP8gY5Jw0GG16X2muQ/78JOhW9UFy6OwDlAEf/16t2sr2kIcAf/iHxzuKatU2wjb2b1NvkdTMR+kYhSgx2Fv4rewi/bl5SI1edG0MUXylM6tCf3Aq27RU04OF7Nfm38g5SQnMZ8KS8a7J9vwwL6+pzFD57J6KT/ni/C7dRx+Oy89ELFTb/4/jz9lZulq1atWq7Q7bYADUmSeT2Pwbeb9FIa+jUCkUbWooT6SXDILxxzEEcZfO2Az9MasVMmHWb5T7kqvXLBNWPJF+ZAz8S7RTtVsGb96Rvl/aksCZk2HdFGvUOue8BTFUq1atWrXdYxsPgDwJLJlNUk3MEOd1BAu1zlWBV8nUiD7ds/JqJCuOwSziWlqxfkN/kIyJ66+RfQEn6XtKDMqfDywVs+YBS3O0hozBG0szYcn4FeR9haw//UyWAmVwXNmmZThvx+5q1apVq7Y7bEdzgI6nZdbByy1RC9Qs3c99bNKr8kdj6XO4SvfV+kll67IPxxdJK34lmlx0eU5DrFa/gBMs1qDJnjmW2yK2pJeLWmAODcJGzCkBjMXg7nsN2D3z+cECE+2Pk5aj+Sa/vK9Q9DlV/FOtWrVqu882lwFK+SiFZN28gGqGJT+rj5TwF2rJEmjGRp5I7/trVAzeWKVTy+2RDXZOVn5KfeR74XcVJfh678G+I4g+XIkWsSWlOWXwqOYK+/70XkkzQkCGWdPvld7AkL/We0fB96FatWrVqu0e21wAtLiOYhb0X/VwFuQS87G4RgnIfhK0anPAR8TYuJsGQrfJPp385Oeq2Oo1D4TpPjZeHYPZ9LEQg7e9wKA/T1o0few48SaJEHNlK22sGMYQyHDVqlWrVu342+YCIMXmlCQwb1Ezm+UppkKOBenP3KdnlQhmNlykOMMNAG0IlqlQffw5daZBnS/DqT4OCEP0Xp0YwiToQm6V9jdmewEvF0ryftafmwQ94vtgP3c9UrVq1apV2y22uQBocfXLqxdtQWVPt0hGDEJ3lQeoNmKsfAzFok8hV8VUYHECcsDm+MdxKH8eA4QUe+RPvgcgZoA0c+XGAPkeBPjQ/grMWnQMhQs+Ugwhc0UgTH9OpcTu8D3kZ+2BrJUBqlatWrXdahubBJ0SWd0DKVWOhifv2EqmhT83/0a19cNIYDTGn0hAVujI7vVj0YJdqDMTFu0SHb0HbmuUP28/pP49GOBGMUC2RbtR85gaa+kY+NloV25Xhgv8uXlIUel8IQbPX7Vq1apV2x22wQxQaVGDarNMgJaLisdQaDZAMwHOjsWRP14rNZOSzNuLyC7U0p9/sKmMT0s4AC/wAbsx4/fgv3Mvhv6uAU3WXwQ+JLCM2BzJarngNr2HKWyhC271nCD6VKtWrVq13WMbywDpRc1LGLYswWKRpP9NTFJZfloshgX2RY8dg4/sOPLnnpul+pg5OTGkn4oSWMDm6G0CRAwmrynTL0ZahPLH71W/I+UvvwcKQvnTn18Xhj9fz1+US6Zj8+bkldVXq1atWrXdYRsLgJK5C/VAwjBa+9d7ljw8f4tuYdJyzFToPFn22xbYnDgGP+52RAy+BObHoGPjfv3hr2pObf8/cT6PKEHvx5K/j4pBvVjBrA3u8WRjiN8DzLMlf9WqVatWbXfYxv5tGu/O7ElgEFd5ZhVEo14IAY/5kP6kBJb6+PEx+BhKgpYJyDo+FUPrxaDja0QsQJz865+bFQBLAgQK74XMVfezZtakPzdvSPnTzBXHFyUtN47DkI3zKtFK/qpVq1at2q6wjWWAzG7BzkKtF/F8SKrNEynvgJwWat3HLpKafdESGIOPyN+2J4EFC7Xuw/O3eUipPZtexK2/8TFwArLOhYpOgx8Tg7cZozm8lIGlKfvXn1/Bn46tlIjt+KtWrVq1arvDNpcBMmyEaOza1ALFckeWjFJb7G9YAnPiKyz8yUwMigGSMfjsi/WVO5q41X2A5SLL5uhnc3zWT4otyqXxE4YTIFVjqRhQikF9fimO4pxMBN5uz9LXWH/VqlWrVm132OYCIM1GEAWgy7XNwop4z5zSztLRSeyaEaGmUN5hf5FkNS4JWvoa48+TizSY+f/t3WtsU/UbB/DvKdsYg3EUZ+lQuQxhvEDM3IQVuUXGAOMyNDEKZBReGCFuhoshBBMZL5SLgi8AJSSEERA1EVAcBJi6bhoGm9oFdGEYBmwvdmFjrF3Lum7n93/BqPS6dv+uXdvvJ2lg5/x+p8959qR9ODd8OQXmvE/C7UXQTjE8VpGecm6f4y4GTzn3cgTIZZ+8xvDf3j6+3GGfnHLO5wAREQ09kdsA9f3p5gyYy106Pv1P7M7bc/fF73y3kst1Oa5Nk+vzhh5rPpy253od0mMxuGzPKQaHL2rHRsftPjl98bvegeXmgmEPR6gev7vO5YnPXo5ceTqC5jUGDzl3OKrlchTK9+3BaXsOT/l2ao5cfn9ERDRkRNw1QI9OO1gsZihWC2wYBsXaC2VYLIxGIwCg19q3LsYGxWqD1dIJo9EIc6cVitUCAOgRKijdCjpNRhjjemF90OmwvZ4Hw+3bU6xmKNYH9nUPOk0wGo140Gl6OKdvWyqVZJ9je+AYn9VihtFoRE+vYo/h0TqzyQijUYUui+P2erpU/+1Tl8Vhe13mhzFYzEaH5QBgMhqhDI9x2SdbXwwAgO4HUBRhz5Gl0wSjcTi6zCaHOb3WXpcYuqW+GPq2ZzY9gGK1oLfnYb+t9CroNBphVNnQbel02Cdbl/mxvFqgWK3/5dX88Pf0wCkGRagey6vj9h79bjutPW7yaoLRKMFqcdxeT1eMa630bc+e106Tm7yaYI1R/RdD37ruvhiIiMizR5+TDpdsDCJJBOudgqSurg6TJ08OdRhEREQ0ADdv3kRKSsqgv0/EHQEaM2YMAKC+vh6yLIc4mvBmNBrx3HPPoaGhAaNHjw51OGGNuQwM5jFwmMvAYS4Do6OjA+PHj7d/jw+2iGuAVH1XsMqyzEIMkNGjRzOXAcJcBgbzGDjMZeAwl4GhCtLj8yP2ImgiIiIiT9gAERERUdQZVlhYWBjqIAJt2LBhWLBgAWJiIu4MX9Axl4HDXAYG8xg4zGXgMJeBEcw8RtxdYERERET94SkwIiIiijpsgIiIiCjqsAEiIiKiqMMGiIiIiKJOWDVAO3bswMsvv4zExESo1WosW7YMtbW1/c4rKytDeno64uPjkZKSgoMHDwYh2qGvvLwcOTk5GDduHCRJwg8//OB1vF6vhyRJLq/r168HKeKhyd88AqxJb7788ktMmjQJ8fHxSE9Px2+//eZxLGvSO39yCbAufdXe3o68vDzIsgxZlpGXl4f79+97nbN69WqXOs3MzAxSxEPXJ598gtmzZyMhIQFPPPGET3OEECgsLMS4ceMwYsQILFiwAP/884/f7x1WDVBZWRnef/99XL58GSUlJejp6UF2djbMZrPHObdu3cJrr72GuXPnwmAwYOvWrfjggw9w8uTJIEY+NJnNZrz44ovYv3+/X/Nqa2vR2Nhof02ZMmWQIgwP/uaRNenZd999h/Xr1+Ojjz6CwWDA3LlzsXTpUtTX13udx5p05W8uWZe+W7FiBaqrq3H+/HmcP38e1dXVyMvL63fekiVLHOr03LlzQYh2aOvu7sZbb72FdevW+Txn9+7d2Lt3L/bv34+qqipoNBosWrQIJpPJvzcXYaylpUUAEGVlZR7HbN68WUybNs1h2XvvvScyMzMHO7ywAkCcPn3a65jS0lIBQLS3twcpqvDjS70sypMAAAlTSURBVB5Zk57NnDlTrF271mHZtGnTxJYtW9yOZ0165m8uWZe+qampEQDE5cuX7csqKioEAHH9+nWP83Q6ncjNzQ1GiGHpyJEjQpblfscpiiI0Go3YuXOnfVlXV5eQZVkcPHjQr/cMqyNAzjo6OgDA63+cVlFRgezsbIdlixcvxh9//AGbzTao8UWqtLQ0JCcnY+HChSgtLQ11OGGHNeled3c3/vzzT5fcZGdn49KlS17nsiYdDSSXrEvfVFRUQJZlzJo1y74sMzMTsiz3W6d6vR5qtRpTp07Fu+++i5aWlsEON+LcunULTU1NDrU6fPhwzJ8/v9/8OwvbBkgIgY0bN2LOnDmYPn26x3FNTU0YO3asw7KxY8eip6cHra2tgx1mRElOTsahQ4dw8uRJnDp1CqmpqVi4cCHKy8tDHVpYYU2619rait7eXre5aWpqcjuHNeneQHLJuvRNU1MT1Gq1y3K1Wu0xtwCwdOlSfP311/j111+xZ88eVFVV4dVXX4XVah3McCPOoxz7U9uehO0zu/Pz83H16lX8/vvv/Y6VJMnhZ9H38Gvn5eRdamoqUlNT7T9rtVo0NDTg888/x7x580IYWfhhTXrmLjee8sKa9M6fXHoa7255JCosLMT27du9jqmqqgLgPh/95fbtt9+2/3369OnIyMjAhAkTcPbsWbz55psDjHpo8jWXGRkZA34Pf2vbnbBsgAoKCnDmzBmUl5fj2Wef9TpWo9G4dIUtLS2IiYnBU089NZhhRoXMzEwcP3481GGEFdake0lJSRg2bJjb3Dj/a88b1uTAchntdZmfn4933nnH65iJEyfi6tWraG5udll39+5dv+o0OTkZEyZMwL///ut3rEOdr7kcCI1GA+DhkaDk5GT7cn8/J4Awa4CEECgoKMDp06eh1+sxadKkfudotVr89NNPDssuXryIjIwMxMbGDlaoUcNgMDgUIfWPNeleXFwc0tPTUVJSgjfeeMO+vKSkBLm5uT5vhzU5sFxGe10mJSUhKSmp33FarRYdHR2orKzEzJkzAQBXrlxBR0cHZs+e7fP7tbW1oaGhISJr1ddcDsSkSZOg0WhQUlKCtLQ0AA+veSsrK8OuXbv825hfl0yH2Lp164Qsy0Kv14vGxkb7y2Kx2Mds2bJF5OXl2X+uq6sTCQkJYsOGDaKmpkYcPnxYxMbGiu+//z4UuzCkmEwmYTAYhMFgEADE3r17hcFgEHfu3BFCuObyiy++EKdPnxY3btwQf//9t9iyZYsAIE6ePBmqXRgS/M0ja9Kzb7/9VsTGxorDhw+LmpoasX79ejFy5Ehx+/ZtIQRr0h/+5pJ16bslS5aIGTNmiIqKClFRUSFeeOEF8frrrzuMSU1NFadOnRJCPPyM2LRpk7h06ZK4deuWKC0tFVqtVjzzzDPCaDSGYheGjDt37giDwSC2b98uRo0aZf8sNZlM9jGP51IIIXbu3ClkWRanTp0S165dE8uXLxfJycl+5zKsGiAAbl9Hjhyxj9HpdGL+/PkO8/R6vUhLSxNxcXFi4sSJ4quvvgpu4EPUo1uInV86nU4I4ZrLXbt2icmTJ4v4+Hjx5JNPijlz5oizZ8+GJvghxN88CsGa9ObAgQNiwoQJIi4uTrz00ksOj7lgTfrHn1wKwbr0VVtbm1i5cqVITEwUiYmJYuXKlS6PYnj8u8lisYjs7Gzx9NNPi9jYWDF+/Hih0+lEfX19CKIfWnQ6ndvPz9LSUvsY5+95RVHEtm3bhEajEcOHDxfz5s0T165d8/u9pb6NExEREUWNsL0NnoiIiGig2AARERFR1GEDRERERFGHDRARERFFHTZAREREFHXYABEREVHUYQNEREREUYcNEBEREUUdNkBEREQUddgAEVFYamtrQ0xMDOLj49HZ2QkAKCoqgiRJkCQJt2/fDm2ARDSksQEiorBUXFyM3t5eZGVlYdSoUaEOh4jCDBsgIgpLP/74IwAgNzc3xJEQUThiA0REYaerqwsXL16EJEnIyckJdThEFIbYABFRUO3atQuSJCEuLg6VlZVux5w7dw4qlQqSJOHEiRMu60tKSmA2mzFr1ixoNJrBDpmIIhAbICIKqs2bNyMrKws2mw3Lly+HyWRyWN/Y2IjVq1dDCIFVq1ZhxYoVLtt4dPpr2bJlQYmZiCIPGyAiCipJknDs2DGo1WrU1dVh7dq19nWPmp67d+/i+eefx4EDB1zmK4qC4uJiALz+h4gGjg0QEQWdRqOx37J+4sQJHD16FMDD02M///wzYmNj8c0337i9u+vy5ctobm7G1KlTMW3atGCHTkQRgg0QEYXE0qVLsWHDBgBAfn4+jh8/jo8//hgA8OmnnyIjI8PtPN79RUSBwAaIiEJmx44dSE9PR2dnJ/Ly8mCz2ZCdnY1NmzZ5nMMGiIgCgQ0QEYVMXFwcioqK7D/LsoyjR49CkiS3469fv47a2lqo1WpotdogRUlEkYgNEBGF1KFDh+x/NxqNqK6u9jj20dGfnJwcqFT8+CKigeMnCBGFTHFxMfbt2wcAmDFjBoQQ0Ol0aG5udjuep7+IKFDYABFRSDQ2NmLNmjUAgDVr1qC8vBwTJ05ES0sLdDodhBAO45ubm3HlyhUkJCQgKysrFCETUQRhA0REQacoCvLy8tDa2oopU6Zg3759kGUZJ06cQExMDC5cuIC9e/c6zDlz5gwURcHixYsxYsSIEEVORJGCDRARBd3u3bvxyy+/2J/3M3LkSACAVqvFtm3bAABbt27FX3/9ZZ/j7+mv9vZ2tLa2enzdu3cvwHtFROFEEs7HmYmIBlFlZSXmzJkDm82Gzz77DB9++KHDekVRsHDhQuj1ekydOtXeBCUlJcFms6GpqQlJSUlut11UVGQ/rdYfWZZx//79/29niChs8QgQEQWNyWTC8uXLYbPZsGjRIrfP+1GpVDh27BjGjBmDGzduID8/HxcuXEBXVxdeeeUVj80PEZE/eASIiIa8VatW4dixY9izZw82btwY6nCIKAKwASKiIa23txdqtRr37t3DzZs3kZKSEuqQiCgCxIQ6ACIib9ra2lBQUIDExEQ2P0QUMDwCRERERFGHF0ETERFR1GEDRERERFGHDRARERFFHTZAREREFHXYABEREVHUYQNEREREUYcNEBEREUUdNkBEREQUddgAERERUdRhA0RERERR538laBN53NTvygAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "xmax = 2*L\n",
+ "xmin = -5\n",
+ "N = int(20*(xmax-xmin)*k0) #number of points (this formula gives you enough points per period)\n",
+ "x = np.linspace(xmax, xmin, N)\n",
+ "\n",
+ "x_under_L = np.array([xj for xj in x if xj < L])\n",
+ "x_over_L = np.array([xj for xj in x if xj >= L])\n",
+ "\n",
+ "xi = -k0**(2/3)*L**(-1/3)*x_under_L\n",
+ "Ai, _, Bi, _ = ssp.airy(xi)\n",
+ "\n",
+ "#Free wave\n",
+ "E0_FS = 1\n",
+ "phi = 0\n",
+ "E0 = E0_FS*np.cos(k0*x_over_L + phi)\n",
+ "\n",
+ "fig, ax = plt.subplots()\n",
+ "\n",
+ "ax.plot(x_over_L/L, E0, label='Wave in free space')\n",
+ "ax.plot(x_under_L/L, Ai, 'r', label='Ai(x)')\n",
+ "ax.set_ylim([-0.5, 1.0])\n",
+ "ax.set_xlim([xmax/L, xmin/L])\n",
+ "\n",
+ "plt.xlabel(\"x/L\", fontsize=18)\n",
+ "plt.legend(loc='upper left')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In order to match these two, we would need to match both phase and amplitude.\n",
+ "For the sake of this lecture, we will declar ourselves satisfy with just amplitude."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/javascript": [
+ "/* Put everything inside the global mpl namespace */\n",
+ "window.mpl = {};\n",
+ "\n",
+ "\n",
+ "mpl.get_websocket_type = function() {\n",
+ " if (typeof(WebSocket) !== 'undefined') {\n",
+ " return WebSocket;\n",
+ " } else if (typeof(MozWebSocket) !== 'undefined') {\n",
+ " return MozWebSocket;\n",
+ " } else {\n",
+ " alert('Your browser does not have WebSocket support. ' +\n",
+ " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
+ " 'Firefox 4 and 5 are also supported but you ' +\n",
+ " 'have to enable WebSockets in about:config.');\n",
+ " };\n",
+ "}\n",
+ "\n",
+ "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
+ " this.id = figure_id;\n",
+ "\n",
+ " this.ws = websocket;\n",
+ "\n",
+ " this.supports_binary = (this.ws.binaryType != undefined);\n",
+ "\n",
+ " if (!this.supports_binary) {\n",
+ " var warnings = document.getElementById(\"mpl-warnings\");\n",
+ " if (warnings) {\n",
+ " warnings.style.display = 'block';\n",
+ " warnings.textContent = (\n",
+ " \"This browser does not support binary websocket messages. \" +\n",
+ " \"Performance may be slow.\");\n",
+ " }\n",
+ " }\n",
+ "\n",
+ " this.imageObj = new Image();\n",
+ "\n",
+ " this.context = undefined;\n",
+ " this.message = undefined;\n",
+ " this.canvas = undefined;\n",
+ " this.rubberband_canvas = undefined;\n",
+ " this.rubberband_context = undefined;\n",
+ " this.format_dropdown = undefined;\n",
+ "\n",
+ " this.image_mode = 'full';\n",
+ "\n",
+ " this.root = $('');\n",
+ " this._root_extra_style(this.root)\n",
+ " this.root.attr('style', 'display: inline-block');\n",
+ "\n",
+ " $(parent_element).append(this.root);\n",
+ "\n",
+ " this._init_header(this);\n",
+ " this._init_canvas(this);\n",
+ " this._init_toolbar(this);\n",
+ "\n",
+ " var fig = this;\n",
+ "\n",
+ " this.waiting = false;\n",
+ "\n",
+ " this.ws.onopen = function () {\n",
+ " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
+ " fig.send_message(\"send_image_mode\", {});\n",
+ " if (mpl.ratio != 1) {\n",
+ " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
+ " }\n",
+ " fig.send_message(\"refresh\", {});\n",
+ " }\n",
+ "\n",
+ " this.imageObj.onload = function() {\n",
+ " if (fig.image_mode == 'full') {\n",
+ " // Full images could contain transparency (where diff images\n",
+ " // almost always do), so we need to clear the canvas so that\n",
+ " // there is no ghosting.\n",
+ " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
+ " }\n",
+ " fig.context.drawImage(fig.imageObj, 0, 0);\n",
+ " };\n",
+ "\n",
+ " this.imageObj.onunload = function() {\n",
+ " fig.ws.close();\n",
+ " }\n",
+ "\n",
+ " this.ws.onmessage = this._make_on_message_function(this);\n",
+ "\n",
+ " this.ondownload = ondownload;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_header = function() {\n",
+ " var titlebar = $(\n",
+ " '');\n",
+ " var titletext = $(\n",
+ " '');\n",
+ " titlebar.append(titletext)\n",
+ " this.root.append(titlebar);\n",
+ " this.header = titletext[0];\n",
+ "}\n",
+ "\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
+ "\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
+ "\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_canvas = function() {\n",
+ " var fig = this;\n",
+ "\n",
+ " var canvas_div = $('');\n",
+ "\n",
+ " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
+ "\n",
+ " function canvas_keyboard_event(event) {\n",
+ " return fig.key_event(event, event['data']);\n",
+ " }\n",
+ "\n",
+ " canvas_div.keydown('key_press', canvas_keyboard_event);\n",
+ " canvas_div.keyup('key_release', canvas_keyboard_event);\n",
+ " this.canvas_div = canvas_div\n",
+ " this._canvas_extra_style(canvas_div)\n",
+ " this.root.append(canvas_div);\n",
+ "\n",
+ " var canvas = $('');\n",
+ " canvas.addClass('mpl-canvas');\n",
+ " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
+ "\n",
+ " this.canvas = canvas[0];\n",
+ " this.context = canvas[0].getContext(\"2d\");\n",
+ "\n",
+ " var backingStore = this.context.backingStorePixelRatio ||\n",
+ "\tthis.context.webkitBackingStorePixelRatio ||\n",
+ "\tthis.context.mozBackingStorePixelRatio ||\n",
+ "\tthis.context.msBackingStorePixelRatio ||\n",
+ "\tthis.context.oBackingStorePixelRatio ||\n",
+ "\tthis.context.backingStorePixelRatio || 1;\n",
+ "\n",
+ " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
+ "\n",
+ " var rubberband = $('');\n",
+ " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
+ "\n",
+ " var pass_mouse_events = true;\n",
+ "\n",
+ " canvas_div.resizable({\n",
+ " start: function(event, ui) {\n",
+ " pass_mouse_events = false;\n",
+ " },\n",
+ " resize: function(event, ui) {\n",
+ " fig.request_resize(ui.size.width, ui.size.height);\n",
+ " },\n",
+ " stop: function(event, ui) {\n",
+ " pass_mouse_events = true;\n",
+ " fig.request_resize(ui.size.width, ui.size.height);\n",
+ " },\n",
+ " });\n",
+ "\n",
+ " function mouse_event_fn(event) {\n",
+ " if (pass_mouse_events)\n",
+ " return fig.mouse_event(event, event['data']);\n",
+ " }\n",
+ "\n",
+ " rubberband.mousedown('button_press', mouse_event_fn);\n",
+ " rubberband.mouseup('button_release', mouse_event_fn);\n",
+ " // Throttle sequential mouse events to 1 every 20ms.\n",
+ " rubberband.mousemove('motion_notify', mouse_event_fn);\n",
+ "\n",
+ " rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
+ " rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
+ "\n",
+ " canvas_div.on(\"wheel\", function (event) {\n",
+ " event = event.originalEvent;\n",
+ " event['data'] = 'scroll'\n",
+ " if (event.deltaY < 0) {\n",
+ " event.step = 1;\n",
+ " } else {\n",
+ " event.step = -1;\n",
+ " }\n",
+ " mouse_event_fn(event);\n",
+ " });\n",
+ "\n",
+ " canvas_div.append(canvas);\n",
+ " canvas_div.append(rubberband);\n",
+ "\n",
+ " this.rubberband = rubberband;\n",
+ " this.rubberband_canvas = rubberband[0];\n",
+ " this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
+ " this.rubberband_context.strokeStyle = \"#000000\";\n",
+ "\n",
+ " this._resize_canvas = function(width, height) {\n",
+ " // Keep the size of the canvas, canvas container, and rubber band\n",
+ " // canvas in synch.\n",
+ " canvas_div.css('width', width)\n",
+ " canvas_div.css('height', height)\n",
+ "\n",
+ " canvas.attr('width', width * mpl.ratio);\n",
+ " canvas.attr('height', height * mpl.ratio);\n",
+ " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
+ "\n",
+ " rubberband.attr('width', width);\n",
+ " rubberband.attr('height', height);\n",
+ " }\n",
+ "\n",
+ " // Set the figure to an initial 600x600px, this will subsequently be updated\n",
+ " // upon first draw.\n",
+ " this._resize_canvas(600, 600);\n",
+ "\n",
+ " // Disable right mouse context menu.\n",
+ " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
+ " return false;\n",
+ " });\n",
+ "\n",
+ " function set_focus () {\n",
+ " canvas.focus();\n",
+ " canvas_div.focus();\n",
+ " }\n",
+ "\n",
+ " window.setTimeout(set_focus, 100);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_toolbar = function() {\n",
+ " var fig = this;\n",
+ "\n",
+ " var nav_element = $('');\n",
+ " nav_element.attr('style', 'width: 100%');\n",
+ " this.root.append(nav_element);\n",
+ "\n",
+ " // Define a callback function for later on.\n",
+ " function toolbar_event(event) {\n",
+ " return fig.toolbar_button_onclick(event['data']);\n",
+ " }\n",
+ " function toolbar_mouse_event(event) {\n",
+ " return fig.toolbar_button_onmouseover(event['data']);\n",
+ " }\n",
+ "\n",
+ " for(var toolbar_ind in mpl.toolbar_items) {\n",
+ " var name = mpl.toolbar_items[toolbar_ind][0];\n",
+ " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
+ " var image = mpl.toolbar_items[toolbar_ind][2];\n",
+ " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
+ "\n",
+ " if (!name) {\n",
+ " // put a spacer in here.\n",
+ " continue;\n",
+ " }\n",
+ " var button = $('');\n",
+ " button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
+ " 'ui-button-icon-only');\n",
+ " button.attr('role', 'button');\n",
+ " button.attr('aria-disabled', 'false');\n",
+ " button.click(method_name, toolbar_event);\n",
+ " button.mouseover(tooltip, toolbar_mouse_event);\n",
+ "\n",
+ " var icon_img = $('');\n",
+ " icon_img.addClass('ui-button-icon-primary ui-icon');\n",
+ " icon_img.addClass(image);\n",
+ " icon_img.addClass('ui-corner-all');\n",
+ "\n",
+ " var tooltip_span = $('');\n",
+ " tooltip_span.addClass('ui-button-text');\n",
+ " tooltip_span.html(tooltip);\n",
+ "\n",
+ " button.append(icon_img);\n",
+ " button.append(tooltip_span);\n",
+ "\n",
+ " nav_element.append(button);\n",
+ " }\n",
+ "\n",
+ " var fmt_picker_span = $('');\n",
+ "\n",
+ " var fmt_picker = $('');\n",
+ " fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
+ " fmt_picker_span.append(fmt_picker);\n",
+ " nav_element.append(fmt_picker_span);\n",
+ " this.format_dropdown = fmt_picker[0];\n",
+ "\n",
+ " for (var ind in mpl.extensions) {\n",
+ " var fmt = mpl.extensions[ind];\n",
+ " var option = $(\n",
+ " '', {selected: fmt === mpl.default_extension}).html(fmt);\n",
+ " fmt_picker.append(option);\n",
+ " }\n",
+ "\n",
+ " // Add hover states to the ui-buttons\n",
+ " $( \".ui-button\" ).hover(\n",
+ " function() { $(this).addClass(\"ui-state-hover\");},\n",
+ " function() { $(this).removeClass(\"ui-state-hover\");}\n",
+ " );\n",
+ "\n",
+ " var status_bar = $('');\n",
+ " nav_element.append(status_bar);\n",
+ " this.message = status_bar[0];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
+ " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
+ " // which will in turn request a refresh of the image.\n",
+ " this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.send_message = function(type, properties) {\n",
+ " properties['type'] = type;\n",
+ " properties['figure_id'] = this.id;\n",
+ " this.ws.send(JSON.stringify(properties));\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.send_draw_message = function() {\n",
+ " if (!this.waiting) {\n",
+ " this.waiting = true;\n",
+ " this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
+ " }\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
+ " var format_dropdown = fig.format_dropdown;\n",
+ " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
+ " fig.ondownload(fig, format);\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
+ " var size = msg['size'];\n",
+ " if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
+ " fig._resize_canvas(size[0], size[1]);\n",
+ " fig.send_message(\"refresh\", {});\n",
+ " };\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
+ " var x0 = msg['x0'] / mpl.ratio;\n",
+ " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
+ " var x1 = msg['x1'] / mpl.ratio;\n",
+ " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
+ " x0 = Math.floor(x0) + 0.5;\n",
+ " y0 = Math.floor(y0) + 0.5;\n",
+ " x1 = Math.floor(x1) + 0.5;\n",
+ " y1 = Math.floor(y1) + 0.5;\n",
+ " var min_x = Math.min(x0, x1);\n",
+ " var min_y = Math.min(y0, y1);\n",
+ " var width = Math.abs(x1 - x0);\n",
+ " var height = Math.abs(y1 - y0);\n",
+ "\n",
+ " fig.rubberband_context.clearRect(\n",
+ " 0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
+ "\n",
+ " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
+ " // Updates the figure title.\n",
+ " fig.header.textContent = msg['label'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
+ " var cursor = msg['cursor'];\n",
+ " switch(cursor)\n",
+ " {\n",
+ " case 0:\n",
+ " cursor = 'pointer';\n",
+ " break;\n",
+ " case 1:\n",
+ " cursor = 'default';\n",
+ " break;\n",
+ " case 2:\n",
+ " cursor = 'crosshair';\n",
+ " break;\n",
+ " case 3:\n",
+ " cursor = 'move';\n",
+ " break;\n",
+ " }\n",
+ " fig.rubberband_canvas.style.cursor = cursor;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
+ " fig.message.textContent = msg['message'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
+ " // Request the server to send over a new figure.\n",
+ " fig.send_draw_message();\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
+ " fig.image_mode = msg['mode'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.updated_canvas_event = function() {\n",
+ " // Called whenever the canvas gets updated.\n",
+ " this.send_message(\"ack\", {});\n",
+ "}\n",
+ "\n",
+ "// A function to construct a web socket function for onmessage handling.\n",
+ "// Called in the figure constructor.\n",
+ "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
+ " return function socket_on_message(evt) {\n",
+ " if (evt.data instanceof Blob) {\n",
+ " /* FIXME: We get \"Resource interpreted as Image but\n",
+ " * transferred with MIME type text/plain:\" errors on\n",
+ " * Chrome. But how to set the MIME type? It doesn't seem\n",
+ " * to be part of the websocket stream */\n",
+ " evt.data.type = \"image/png\";\n",
+ "\n",
+ " /* Free the memory for the previous frames */\n",
+ " if (fig.imageObj.src) {\n",
+ " (window.URL || window.webkitURL).revokeObjectURL(\n",
+ " fig.imageObj.src);\n",
+ " }\n",
+ "\n",
+ " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
+ " evt.data);\n",
+ " fig.updated_canvas_event();\n",
+ " fig.waiting = false;\n",
+ " return;\n",
+ " }\n",
+ " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
+ " fig.imageObj.src = evt.data;\n",
+ " fig.updated_canvas_event();\n",
+ " fig.waiting = false;\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " var msg = JSON.parse(evt.data);\n",
+ " var msg_type = msg['type'];\n",
+ "\n",
+ " // Call the \"handle_{type}\" callback, which takes\n",
+ " // the figure and JSON message as its only arguments.\n",
+ " try {\n",
+ " var callback = fig[\"handle_\" + msg_type];\n",
+ " } catch (e) {\n",
+ " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " if (callback) {\n",
+ " try {\n",
+ " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
+ " callback(fig, msg);\n",
+ " } catch (e) {\n",
+ " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
+ " }\n",
+ " }\n",
+ " };\n",
+ "}\n",
+ "\n",
+ "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
+ "mpl.findpos = function(e) {\n",
+ " //this section is from http://www.quirksmode.org/js/events_properties.html\n",
+ " var targ;\n",
+ " if (!e)\n",
+ " e = window.event;\n",
+ " if (e.target)\n",
+ " targ = e.target;\n",
+ " else if (e.srcElement)\n",
+ " targ = e.srcElement;\n",
+ " if (targ.nodeType == 3) // defeat Safari bug\n",
+ " targ = targ.parentNode;\n",
+ "\n",
+ " // jQuery normalizes the pageX and pageY\n",
+ " // pageX,Y are the mouse positions relative to the document\n",
+ " // offset() returns the position of the element relative to the document\n",
+ " var x = e.pageX - $(targ).offset().left;\n",
+ " var y = e.pageY - $(targ).offset().top;\n",
+ "\n",
+ " return {\"x\": x, \"y\": y};\n",
+ "};\n",
+ "\n",
+ "/*\n",
+ " * return a copy of an object with only non-object keys\n",
+ " * we need this to avoid circular references\n",
+ " * http://stackoverflow.com/a/24161582/3208463\n",
+ " */\n",
+ "function simpleKeys (original) {\n",
+ " return Object.keys(original).reduce(function (obj, key) {\n",
+ " if (typeof original[key] !== 'object')\n",
+ " obj[key] = original[key]\n",
+ " return obj;\n",
+ " }, {});\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.mouse_event = function(event, name) {\n",
+ " var canvas_pos = mpl.findpos(event)\n",
+ "\n",
+ " if (name === 'button_press')\n",
+ " {\n",
+ " this.canvas.focus();\n",
+ " this.canvas_div.focus();\n",
+ " }\n",
+ "\n",
+ " var x = canvas_pos.x * mpl.ratio;\n",
+ " var y = canvas_pos.y * mpl.ratio;\n",
+ "\n",
+ " this.send_message(name, {x: x, y: y, button: event.button,\n",
+ " step: event.step,\n",
+ " guiEvent: simpleKeys(event)});\n",
+ "\n",
+ " /* This prevents the web browser from automatically changing to\n",
+ " * the text insertion cursor when the button is pressed. We want\n",
+ " * to control all of the cursor setting manually through the\n",
+ " * 'cursor' event from matplotlib */\n",
+ " event.preventDefault();\n",
+ " return false;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
+ " // Handle any extra behaviour associated with a key event\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.key_event = function(event, name) {\n",
+ "\n",
+ " // Prevent repeat events\n",
+ " if (name == 'key_press')\n",
+ " {\n",
+ " if (event.which === this._key)\n",
+ " return;\n",
+ " else\n",
+ " this._key = event.which;\n",
+ " }\n",
+ " if (name == 'key_release')\n",
+ " this._key = null;\n",
+ "\n",
+ " var value = '';\n",
+ " if (event.ctrlKey && event.which != 17)\n",
+ " value += \"ctrl+\";\n",
+ " if (event.altKey && event.which != 18)\n",
+ " value += \"alt+\";\n",
+ " if (event.shiftKey && event.which != 16)\n",
+ " value += \"shift+\";\n",
+ "\n",
+ " value += 'k';\n",
+ " value += event.which.toString();\n",
+ "\n",
+ " this._key_event_extra(event, name);\n",
+ "\n",
+ " this.send_message(name, {key: value,\n",
+ " guiEvent: simpleKeys(event)});\n",
+ " return false;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
+ " if (name == 'download') {\n",
+ " this.handle_save(this, null);\n",
+ " } else {\n",
+ " this.send_message(\"toolbar_button\", {name: name});\n",
+ " }\n",
+ "};\n",
+ "\n",
+ "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
+ " this.message.textContent = tooltip;\n",
+ "};\n",
+ "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
+ "\n",
+ "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
+ "\n",
+ "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
+ " // Create a \"websocket\"-like object which calls the given IPython comm\n",
+ " // object with the appropriate methods. Currently this is a non binary\n",
+ " // socket, so there is still some room for performance tuning.\n",
+ " var ws = {};\n",
+ "\n",
+ " ws.close = function() {\n",
+ " comm.close()\n",
+ " };\n",
+ " ws.send = function(m) {\n",
+ " //console.log('sending', m);\n",
+ " comm.send(m);\n",
+ " };\n",
+ " // Register the callback with on_msg.\n",
+ " comm.on_msg(function(msg) {\n",
+ " //console.log('receiving', msg['content']['data'], msg);\n",
+ " // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
+ " ws.onmessage(msg['content']['data'])\n",
+ " });\n",
+ " return ws;\n",
+ "}\n",
+ "\n",
+ "mpl.mpl_figure_comm = function(comm, msg) {\n",
+ " // This is the function which gets called when the mpl process\n",
+ " // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
+ "\n",
+ " var id = msg.content.data.id;\n",
+ " // Get hold of the div created by the display call when the Comm\n",
+ " // socket was opened in Python.\n",
+ " var element = $(\"#\" + id);\n",
+ " var ws_proxy = comm_websocket_adapter(comm)\n",
+ "\n",
+ " function ondownload(figure, format) {\n",
+ " window.open(figure.imageObj.src);\n",
+ " }\n",
+ "\n",
+ " var fig = new mpl.figure(id, ws_proxy,\n",
+ " ondownload,\n",
+ " element.get(0));\n",
+ "\n",
+ " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
+ " // web socket which is closed, not our websocket->open comm proxy.\n",
+ " ws_proxy.onopen();\n",
+ "\n",
+ " fig.parent_element = element.get(0);\n",
+ " fig.cell_info = mpl.find_output_cell(\"\");\n",
+ " if (!fig.cell_info) {\n",
+ " console.error(\"Failed to find cell for figure\", id, fig);\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " var output_index = fig.cell_info[2]\n",
+ " var cell = fig.cell_info[0];\n",
+ "\n",
+ "};\n",
+ "\n",
+ "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
+ " var width = fig.canvas.width/mpl.ratio\n",
+ " fig.root.unbind('remove')\n",
+ "\n",
+ " // Update the output cell to use the data from the current canvas.\n",
+ " fig.push_to_output();\n",
+ " var dataURL = fig.canvas.toDataURL();\n",
+ " // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
+ " // the notebook keyboard shortcuts fail.\n",
+ " IPython.keyboard_manager.enable()\n",
+ " $(fig.parent_element).html('
');\n",
+ " fig.close_ws(fig, msg);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.close_ws = function(fig, msg){\n",
+ " fig.send_message('closing', msg);\n",
+ " // fig.ws.close()\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
+ " // Turn the data on the canvas into data in the output cell.\n",
+ " var width = this.canvas.width/mpl.ratio\n",
+ " var dataURL = this.canvas.toDataURL();\n",
+ " this.cell_info[1]['text/html'] = '
';\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.updated_canvas_event = function() {\n",
+ " // Tell IPython that the notebook contents must change.\n",
+ " IPython.notebook.set_dirty(true);\n",
+ " this.send_message(\"ack\", {});\n",
+ " var fig = this;\n",
+ " // Wait a second, then push the new image to the DOM so\n",
+ " // that it is saved nicely (might be nice to debounce this).\n",
+ " setTimeout(function () { fig.push_to_output() }, 1000);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_toolbar = function() {\n",
+ " var fig = this;\n",
+ "\n",
+ " var nav_element = $('');\n",
+ " nav_element.attr('style', 'width: 100%');\n",
+ " this.root.append(nav_element);\n",
+ "\n",
+ " // Define a callback function for later on.\n",
+ " function toolbar_event(event) {\n",
+ " return fig.toolbar_button_onclick(event['data']);\n",
+ " }\n",
+ " function toolbar_mouse_event(event) {\n",
+ " return fig.toolbar_button_onmouseover(event['data']);\n",
+ " }\n",
+ "\n",
+ " for(var toolbar_ind in mpl.toolbar_items){\n",
+ " var name = mpl.toolbar_items[toolbar_ind][0];\n",
+ " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
+ " var image = mpl.toolbar_items[toolbar_ind][2];\n",
+ " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
+ "\n",
+ " if (!name) { continue; };\n",
+ "\n",
+ " var button = $('');\n",
+ " button.click(method_name, toolbar_event);\n",
+ " button.mouseover(tooltip, toolbar_mouse_event);\n",
+ " nav_element.append(button);\n",
+ " }\n",
+ "\n",
+ " // Add the status bar.\n",
+ " var status_bar = $('');\n",
+ " nav_element.append(status_bar);\n",
+ " this.message = status_bar[0];\n",
+ "\n",
+ " // Add the close button to the window.\n",
+ " var buttongrp = $('');\n",
+ " var button = $('');\n",
+ " button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
+ " button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
+ " buttongrp.append(button);\n",
+ " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
+ " titlebar.prepend(buttongrp);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._root_extra_style = function(el){\n",
+ " var fig = this\n",
+ " el.on(\"remove\", function(){\n",
+ "\tfig.close_ws(fig, {});\n",
+ " });\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._canvas_extra_style = function(el){\n",
+ " // this is important to make the div 'focusable\n",
+ " el.attr('tabindex', 0)\n",
+ " // reach out to IPython and tell the keyboard manager to turn it's self\n",
+ " // off when our div gets focus\n",
+ "\n",
+ " // location in version 3\n",
+ " if (IPython.notebook.keyboard_manager) {\n",
+ " IPython.notebook.keyboard_manager.register_events(el);\n",
+ " }\n",
+ " else {\n",
+ " // location in version 2\n",
+ " IPython.keyboard_manager.register_events(el);\n",
+ " }\n",
+ "\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
+ " var manager = IPython.notebook.keyboard_manager;\n",
+ " if (!manager)\n",
+ " manager = IPython.keyboard_manager;\n",
+ "\n",
+ " // Check for shift+enter\n",
+ " if (event.shiftKey && event.which == 13) {\n",
+ " this.canvas_div.blur();\n",
+ " // select the cell after this one\n",
+ " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
+ " IPython.notebook.select(index + 1);\n",
+ " }\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
+ " fig.ondownload(fig, null);\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.find_output_cell = function(html_output) {\n",
+ " // Return the cell and output element which can be found *uniquely* in the notebook.\n",
+ " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
+ " // IPython event is triggered only after the cells have been serialised, which for\n",
+ " // our purposes (turning an active figure into a static one), is too late.\n",
+ " var cells = IPython.notebook.get_cells();\n",
+ " var ncells = cells.length;\n",
+ " for (var i=0; i= 3 moved mimebundle to data attribute of output\n",
+ " data = data.data;\n",
+ " }\n",
+ " if (data['text/html'] == html_output) {\n",
+ " return [cell, data, j];\n",
+ " }\n",
+ " }\n",
+ " }\n",
+ " }\n",
+ "}\n",
+ "\n",
+ "// Register the function which deals with the matplotlib target/channel.\n",
+ "// The kernel may be null if the page has been refreshed.\n",
+ "if (IPython.notebook.kernel != null) {\n",
+ " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
+ "}\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "
"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "By clicking on the figure, try and estimate the amplitude of the Airy functions at the maximum x value (on the left handside)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#necessary to interact with figure\n",
+ "%matplotlib notebook \n",
+ "\n",
+ "fig, ax = plt.subplots()\n",
+ "\n",
+ "ax.plot(x_under_L/L, Ai, 'r', label='Ai(x)')\n",
+ "ax.set_ylim([-0.5, 1.0])\n",
+ "ax.set_xlim([max(x_under_L)/L, xmin/L])\n",
+ "\n",
+ "plt.xlabel(\"x/L\", fontsize=18)\n",
+ "plt.legend(loc='upper left')\n",
+ "plt.show()\n",
+ "\n",
+ "coords = []\n",
+ "\n",
+ "def onclick(event):\n",
+ " global ix, iy\n",
+ " ix, iy = event.xdata, event.ydata\n",
+ " print('x = %d, y = %d', ix, iy)\n",
+ "\n",
+ " global coords\n",
+ " coords.append((ix, iy))\n",
+ "\n",
+ " if len(coords) == 2:\n",
+ " fig.canvas.mpl_disconnect(cid)\n",
+ " \n",
+ " return coords\n",
+ "\n",
+ "#necessary to interact with figure\n",
+ "print(\"By clicking on the figure, try and estimate the amplitude of the Airy functions at the maximum x value (on the left handside)\")\n",
+ "cid = fig.canvas.mpl_connect('button_press_event', onclick)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.247238827990247\n"
+ ]
+ }
+ ],
+ "source": [
+ "amplitude_at_FS = coords[0][1]\n",
+ "print(amplitude_at_FS)\n",
+ "alpha = 1/amplitude_at_FS\n",
+ "\n",
+ "Ai, _, Bi, _ = ssp.airy(xi)\n",
+ "E = alpha*Ai"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "matplotlib.rcParams['figure.figsize'] = (15, 8)\n",
+ "\n",
+ "fig, ax = plt.subplots()\n",
+ "\n",
+ "ax.plot(x_over_L/L, E0, label='Wave in free space')\n",
+ "ax.plot(x_under_L/L, E, 'r', label='Ai(x)')\n",
+ "ax.set_xlim([xmax/L, xmin/L])\n",
+ "\n",
+ "plt.xlabel(\"x/L\", fontsize=18)\n",
+ "plt.legend(loc='upper left')\n",
+ "plt.show()"
+ ]
+ }
+ ],
+ "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": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/hack/LIHEDP_notebooks/Assignment_answers.ipynb b/hack/LIHEDP_notebooks/Assignment_answers.ipynb
new file mode 100644
index 0000000..23a88b4
--- /dev/null
+++ b/hack/LIHEDP_notebooks/Assignment_answers.ipynb
@@ -0,0 +1,658 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true
+ },
+ "source": [
+ "#### Import modules "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from sympy.solvers import solve\n",
+ "from sympy import Symbol\n",
+ "from scipy import constants as sc\n",
+ "from matplotlib import pyplot as plt\n",
+ "from scipy.optimize import fsolve"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "def sciprint(a):\n",
+ " print(f\"{a:0.2g}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Given Information"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "n = 1.2 \\times 10^6 \\sqrt{ \\frac{Y}{<\\sigma v> V_{hs} \\tau} }\n",
+ "$$\n",
+ "\n",
+ "This formula gives the density in $m^{-3}$.\n",
+ "\n",
+ "Where $Y$ is the fusion yield in J. \n",
+ "\n",
+ "$<\\sigma v>$ is the fusion reaction rate in m$^3$.s$^{-1}$\n",
+ "\n",
+ "$V_{hs}$ is the volume of the hot-spot m$^3$.\n",
+ "\n",
+ "$\\tau$ is the burn duration."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We give, based on: https://scitechdaily.com/national-ignition-facility-breakthrough-experiment-puts-researchers-at-threshold-of-fusion-ignition/\n",
+ "\n",
+ "$Y = 1.3 \\text{ MJ}$\n",
+ "\n",
+ "$V_{hs}$ : \"a hot-spot the diameter of a human hair\"\n",
+ "\n",
+ "$\\tau$: \"for 100 trillionths of a second\", where we understand a trillion as $10^{12}$\n",
+ "\n",
+ "We give, based on: https://www.nature.com/articles/s41586-021-04281-w\n",
+ "\n",
+ "$<\\sigma v> = 4.2 \\times 10^{20} T_i^{3.6}$ with $T_i$ in keV, and $<\\sigma v>$ in cm$^3$.s$^{-1}$.\n",
+ "\n",
+ "Finally, based on: https://aip.scitation.org/doi/10.1063/5.0003298\n",
+ "\n",
+ "It would seem that $T_i = 4.4 \\text{ keV}$ is a good bet."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Question 1 - Evaluate the number density $n$ (be careful about units)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Y = 1.3e6\n",
+ "Ti = 4.4 #[keV]\n",
+ "tau = 100*1e-12\n",
+ "R_hair = (75/2)*1e-6\n",
+ "V_hs = (4/3)*sc.pi*R_hair**3\n",
+ "sigma_v = (4.2e-20*Ti**3.6) * 1e-6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "9.9e+31\n"
+ ]
+ }
+ ],
+ "source": [
+ "n = 1.2e6*np.sqrt(Y/(sigma_v*V_hs*tau))\n",
+ "\n",
+ "sciprint(n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$n = 9.9 \\times 10^{31} \\text{ m}^{-3}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Question 2 - In order to find the ionisation fraction, should we use the Thomas-Fermi model, or the Saha ionization equation?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Thomas-Fermi, because we are outside of the density range where Saha's equation is valid."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Question 3 - Use both models to estimate the ionisation fraction."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##### a) For the Saha ionisation equation model, use the \"simple\" equation given in lecture 2 for x (in Saha_first_impressions.ipynb or Saha_first_impressions.html). We give the ionisation energies of Deuterium (Ui_De = 15.4667) and Tritium (Ui_Te = 13.603). For the sake of simplicity, you can consider the ionisation fraction for a single virtual specie which would have the ionisation energy: Ui = (Ui_De+Ui_Te)/2."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$ \\frac{x^2}{1-x} = 2.4 \\cdot 10^{21} \\frac{T^{3/2}}{n} e^{-U_i / k_B T}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "code_folding": [
+ 0,
+ 14
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "def rhs_Saha_Chen(n,T,Ui):\n",
+ " \"\"\"\n",
+ " Computes the right hand side of Saha's equation for a given temperature T\n",
+ " \n",
+ " n = density (nb.m^-3)\n",
+ " T = temperature (K)\n",
+ " Ui = Ionisation energy (J)\n",
+ " \"\"\"\n",
+ " rhs = 2.4*1e21*(T**(3/2)/n)*np.exp(-(Ui/(sc.k*T)))\n",
+ " return rhs\n",
+ "\n",
+ "#Assuming x > 0 forces the solver to return only positive solutions\n",
+ "x = Symbol('x', positive=True) \n",
+ "\n",
+ "def solve_Saha(n,T,Ui):\n",
+ " \"\"\"\n",
+ " Computes the ionisation fraction x for a given temperature T\n",
+ " \n",
+ " n = density (nb.m^-3)\n",
+ " T = temperature (K)\n",
+ " Ui = Ionisation energy (J)\n",
+ " \"\"\"\n",
+ " #Note: sympy.solvers.solve struggles when rhs is large. So let's use two cases:\n",
+ " if (rhs_Saha_Chen(n,T,Ui) <= 1e2):\n",
+ " sol = solve((x**2/(1-x)) - rhs_Saha_Chen(n,T,Ui),x) \n",
+ " else:\n",
+ " sol = [1 - 1/rhs_Saha_Chen(n,T,Ui)] #for x->1, x²/(1-x)-> 1/(1-x)\n",
+ " if len(sol)==0:\n",
+ " sol = [np.nan] #If there is no solution, returns a NaN rather than an empty array.\n",
+ " return sol"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Ui_De = 15.4667\n",
+ "Ui_Te = 13.603\n",
+ "\n",
+ "Ui_DT = (Ui_De + Ui_Te)/2 * sc.eV\n",
+ "\n",
+ "T = Ti*1e3*sc.eV/sc.k"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[0.906989765277499]"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "solve_Saha(n, T, Ui_DT)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$x_{saha} = 0.907$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##### b) For the Thomas-Fermi model, assume A = 2.5 and Z = 1 (equimolar mixture of deuterium and tritium)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "code_folding": [
+ 0
+ ]
+ },
+ "outputs": [],
+ "source": [
+ "def Zav_TF(Z, A, rho, T):\n",
+ " \"\"\"\n",
+ " Finite Temperature Thomas Fermi Charge State using \n",
+ " R.M. More (1985), \"Pressure Ionization, Resonances, and the\n",
+ " Continuity of Bound and Free States\", Adv. in Atomic \n",
+ " Mol. Phys., Vol. 21, p. 332 (Table IV).\n",
+ " \n",
+ " Z = atomic number\n",
+ " rho = mass density (g/cc)\n",
+ " T = temperature (eV)\n",
+ " \"\"\"\n",
+ "\n",
+ " alpha = 14.3139\n",
+ " beta = 0.6624\n",
+ " a1 = 0.003323\n",
+ " a2 = 0.9718\n",
+ " a3 = 9.26148e-5\n",
+ " a4 = 3.10165\n",
+ " b0 = -1.7630\n",
+ " b1 = 1.43175\n",
+ " b2 = 0.31546\n",
+ " c1 = -0.366667\n",
+ " c2 = 0.983333\n",
+ " \n",
+ " rho1 = rho/ A*Z\n",
+ " T1 = T/Z**(4./3.)\n",
+ " Tf = T1/(1 + T1)\n",
+ " Ac = a1*T1**a2 + a3*T1**a4\n",
+ " B = -np.exp(b0 + b1*Tf + b2*Tf**7)\n",
+ " C = c1*Tf + c2\n",
+ " Q1 = Ac*rho1**B\n",
+ " Q = (rho1**C + Q1**C)**(1/C)\n",
+ " x = alpha*Q**beta\n",
+ "\n",
+ " return Z*x/(1 + x + np.sqrt(1 + 2.*x))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "A = 2.5\n",
+ "Z = 1\n",
+ "\n",
+ "n = 9.867843498781554e33\n",
+ "rho = A*sc.m_p*n *1e3*1e-6 #[g/cc]\n",
+ "T = 4400 #Ti*1e3 #[eV]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "41262.92843900966"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "rho"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0.9865621266583642"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Zav_TF(Z, A, rho, T)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$x_{TF} = 0.992$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##### c) Briefly comment your results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We see that the Thomas-Fermi model ends up giving a stronger ionisation ratio than the Saha equation. This is because it takes the pressure ionisation into account."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 4) What would the wavelength $\\lambda$ of a laser need to be in order for it to be able to go through the plasma. Comment your result. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "n_C \\text{ [cm$^{-3}$]} = 1.1 \\times 10^{21} \\left( \\frac{1}{\\lambda \\text{ [µm]}} \\right)^2\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In order for the laser to go through a plasma with density $n_e \\sim 9.9 \\times 10^{31} \\text{ m}^{-3}$, it needs:\n",
+ "\n",
+ "$$\n",
+ "\\lambda \\text{ [µm]} < \\sqrt{\\frac{1.1 \\times 10^{21}}{n_e \\text{ [cm$^{-3}$]}}}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 1.2e6*np.sqrt(Y/(sigma_v*V_hs*tau))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0.0033387601094728683"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.sqrt(1.1e21/(n*1e-6))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This would be $\\lambda = 3.3 \\text{ nm}$. To my knowledge, lasers cannot go that low in wavelength. This suggests that such a dense plasma cannot be created simply by hitting a target with a laser and letting it expand. It has to be heavily compressed."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Question 5 - Estimate the coupling constant $\\Gamma_{ee}$: Is the plasma strongly or weekly coupled?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 1.2e6*np.sqrt(Y/(sigma_v*V_hs*tau))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.015\n"
+ ]
+ }
+ ],
+ "source": [
+ "T = Ti*1e3*sc.eV/sc.k\n",
+ "gamma_ee = sc.e**2 * n**(1/3) / (4*sc.pi*sc.epsilon_0 * sc.k*T) \n",
+ "sciprint(gamma_ee)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The plasma is rather weakly coupled."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Question 6: Estimate the Fermi energy and compare it to $k_B T$. Are the electrons degenerate? (a nuanced answer is allowed)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "E_F \\text{ [eV]} = 7.9 \\left ( \\frac{n_e \\text{ [cm$^{-3}$]}}{10^{23}} \\right )^{2/3}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 1.2e6*np.sqrt(Y/(sigma_v*V_hs*tau))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "7.8e+02\n",
+ "4.4e+03\n"
+ ]
+ }
+ ],
+ "source": [
+ "E_F = 7.9*(n*1e-6 / 1e23)**(2/3)\n",
+ "sciprint(E_F)\n",
+ "\n",
+ "sciprint(Ti*1e3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$E_F \\sim 780$ eV \n",
+ "\n",
+ "$k_B T \\sim 4.4$ keV\n",
+ "\n",
+ "$k_B T > E_F$ but not so much that the electrons can be treated classicaly."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Question 7: Estimate the Fermi pressure and compare it to the thermal pressure "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "P_F \\text{ [Mbar]} = 0.5 \\left ( \\frac{n_e \\text{ [cm$^{-3}$]}}{10^{23}} \\right )^{5/3} \n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.9e+10\n",
+ "7e+11\n"
+ ]
+ }
+ ],
+ "source": [
+ "P_F = 0.5*((n*1e-6)/1e23)**(5/3) * 1e6 #[Mbar = 10^6 Bar]\n",
+ "sciprint(P_F)\n",
+ "\n",
+ "P_th = n*sc.k*T / 1e5 #1 bar = 10^5 Pa]\n",
+ "sciprint(P_th)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The thermal pressure ($7 \\times 10^{11}$ bars) dominates over the Fermi Pressure, which is itself not small ($5 \\times 10^{10}$ bars). \n",
+ "\n",
+ "This makes a very similar point to the comparison of $E_F$ and $k_B T$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Question 8: Place the NIF experiment in the Temperature-Density diagram. Does this match your previous results?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.6\n",
+ "7.7\n"
+ ]
+ }
+ ],
+ "source": [
+ "sciprint(np.log10(Ti*1e3))\n",
+ "sciprint(np.log10(T))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This corresponds to all of our estimations:\n",
+ "\n",
+ "- The plasma is pressured ionised (actually if we plotted the rest of the Saha's equation line in the domain where it is not valid, we would see that our NIF experiment is just above it. This means more than half ionised, but not necessarily completely ionised).\n",
+ "- The NIF experiment is quite safely away from E(coulomb)=kT, which suggests a weak coupling\n",
+ "- The plasma is just above the E(fermi)=kT line, which suggests that quantum effects may still play a role but shouldn't dominate. This fits with our estimations.\n",
+ "- We are quite above the 1Gbar line, which again fits our estimations."
+ ]
+ }
+ ],
+ "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": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/hack/LIHEDP_notebooks/E_Fermi.ipynb b/hack/LIHEDP_notebooks/E_Fermi.ipynb
new file mode 100644
index 0000000..3151422
--- /dev/null
+++ b/hack/LIHEDP_notebooks/E_Fermi.ipynb
@@ -0,0 +1,252 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true
+ },
+ "source": [
+ "#### Import modules "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from sympy.solvers import solve\n",
+ "from sympy import Symbol\n",
+ "from scipy import constants as sc\n",
+ "from matplotlib import pyplot as plt\n",
+ "from decimal import *"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Fermi Energy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "\\boxed{\n",
+ "E_F = \\left (\\frac{3}{8 \\pi} \\right )^{2/3} \\frac{h^2}{2m_0} n_e^{2/3} \n",
+ "}\n",
+ "$$ "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "7.8560385133597475"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "(3/(8*sc.pi))**(2/3) * sc.h**2 / (2*sc.m_e) / (sc.eV) * (1e23 * 1e6)**(2/3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "\\boxed{\n",
+ "E_F \\text{ [eV]} = 7.9 \\left ( \\frac{n_e \\text{ [cm$^{-3}$]}}{10^{23}} \\right )^{2/3}\n",
+ "}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ns = np.logspace(27,34.7,100)\n",
+ "E_Fs = (3/(8*sc.pi))**(2/3)*sc.h**2/(2*sc.m_e)*ns**(2/3)\n",
+ "Ts = (1/sc.k)*E_Fs"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(np.log10(ns*sc.m_p*1e-3), np.log10(Ts), color='red', linewidth=3)\n",
+ "plt.xlim([-12, 11])\n",
+ "plt.ylim([1.8, 11.2])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Fermi Pressure"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "\\boxed{\n",
+ "P_F = (2/5) n_e E_F = \\frac{2}{5} \\left (\\frac{3}{8 \\pi} \\right )^{2/3} \\frac{h^2}{2m_0} n_e^{5/3}\n",
+ "}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.5034704536763671\n"
+ ]
+ }
+ ],
+ "source": [
+ "a = (2/5)*(3/(8*sc.pi))**(2/3)*sc.h**2/(2*sc.m_e) / (1e11) * (1e23 * 1e6)**(5/3) \n",
+ "print(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "\\boxed{\n",
+ "P_F \\text{ [Mbar]} = 0.5 \\left ( \\frac{n_e \\text{ [cm$^{-3}$]}}{10^{23}} \\right )^{5/3} \n",
+ "}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "ne = (1/a)**(3/5) * 1e23 * 1e6 #Corresponds to P_F = 1 Mbar\n",
+ "plt.vlines(x=np.log10(ne*sc.m_p*1e-3), ymin=0, ymax=3.3, color='red', linewidth=3)\n",
+ "plt.xlim([-12, 11])\n",
+ "plt.ylim([1.8, 11.2])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Pressure ionisation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "a0 = sc.physical_constants['Bohr radius'][0]\n",
+ "n = 3/(4*sc.pi) * (a0)**(-3)\n",
+ "plt.vlines(x=np.log10(n*sc.m_p*1e-3), ymin=2.5, ymax=4.3, color='red', linewidth=3)\n",
+ "plt.xlim([-12, 11])\n",
+ "plt.ylim([1.8, 11.2])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/hack/LIHEDP_notebooks/Inverse_Bremsstrahlung.ipynb b/hack/LIHEDP_notebooks/Inverse_Bremsstrahlung.ipynb
new file mode 100644
index 0000000..232adc0
--- /dev/null
+++ b/hack/LIHEDP_notebooks/Inverse_Bremsstrahlung.ipynb
@@ -0,0 +1,100 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from scipy import constants as sc"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "equation (5.15), page 104\n",
+ "\n",
+ "\\begin{equation} \n",
+ "K_{ff} = 8 \\sqrt{\\pi} \\left( \\frac{e^2}{4 \\pi \\epsilon_0} \\right)^3 \\frac{4}{3 c^3} \\frac{Z_i^2}{m_0^2} n_e n_{Z_i} \\left( \\frac{m_0}{2 k_B T} \\right)^{1/2} \\frac{\\pi^2 c^2}{\\hbar \\omega^3} \\left( 1 - \\exp \\left( - \\frac{\\hbar \\omega}{k_B T} \\right) \\right) \n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "exercise 5.8, page 112\n",
+ "\n",
+ "\\begin{equation}\n",
+ "K_{ff} = 2.7 \\times 10^{-50} \\frac{\\lambda^2 n_e n_{Z_i} Z_i^2}{(k_B T)^{3/2}} \\text{ m}^{-1}\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "equation (5.15), with $h \\nu \\ll k_B T$, becomes:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "k_{ff} = \\frac{8 \\sqrt{\\pi}}{3 \\sqrt{2}} \\left( \\frac{e^2}{4 \\pi \\epsilon_0} \\right)^3 \\frac{1}{m_0^{3/2} c^{3}} \\frac{\\lambda^2 n_e n_{Z_i} Z_i^2}{(k_B T)^{3/2}}\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2.731832444805521e-47"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "8*np.sqrt(np.pi)/(3*np.sqrt(2)) * (sc.e**2/(4*np.pi*sc.epsilon_0))**3 * (1/((sc.m_e**(3/2)*sc.c**3))) * (1e-12 / (sc.e**(3/2)))\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/hack/LIHEDP_notebooks/Res_absorption.ipynb b/hack/LIHEDP_notebooks/Res_absorption.ipynb
new file mode 100644
index 0000000..620bef9
--- /dev/null
+++ b/hack/LIHEDP_notebooks/Res_absorption.ipynb
@@ -0,0 +1,148 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Import useful modules"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from scipy import constants as sc\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def sciprint(a):\n",
+ " print(f\"{a:0.2g}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Resonant Absorption Ratio"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "tau = np.linspace(0,2.5,1000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def phi(x):\n",
+ " return 2.3*x*np.exp(-(2/3)*tau**3)\n",
+ "def A(x):\n",
+ " return (1/2)*phi(x)**2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(tau, phi(tau))\n",
+ "plt.xlabel(r'$(k_0 L)^{1/3} \\sin \\theta$', fontsize=18)\n",
+ "plt.ylabel(r'$\\Phi$', fontsize=18)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(tau, A(tau))\n",
+ "plt.xlabel(r'$(k_0 L)^{1/3} \\sin \\theta$', fontsize=18)\n",
+ "plt.ylabel(r'$A$', fontsize=18)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/hack/LIHEDP_notebooks/Saha_first_impressions.ipynb b/hack/LIHEDP_notebooks/Saha_first_impressions.ipynb
new file mode 100644
index 0000000..02c4ae7
--- /dev/null
+++ b/hack/LIHEDP_notebooks/Saha_first_impressions.ipynb
@@ -0,0 +1,516 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this notebook, we explore the Saha equation using F. Chen's expression."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true
+ },
+ "source": [
+ "#### Import modules "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from sympy.solvers import solve\n",
+ "from sympy import Symbol\n",
+ "from scipy import constants as sc\n",
+ "from matplotlib import pyplot as plt\n",
+ "from decimal import *"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "def sciprint(x):\n",
+ " print(f\"x = {x:0.1g}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# The Saha-Boltzmann equation: first impressions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\\frac{n_i}{n_n} \\sim 2.4 \\cdot 10^{21} \\frac{T^{3/2}}{n_i} e^{-U_i / k_B T}$$\n",
+ "\n",
+ "Where $n_i$ and $n_n$ are the density of ionized atoms and of neutral atoms (in [nb.m$^{-3}$]), $T$ is the temperature (in [K]), $k_B$ is Boltzmann's constant and $U_i$ is the ionisation energy of the specie considered (in [J])."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It is generally more convenient to define: $$x = \\frac{n_i}{n}$$ where where $n = n_i + n_n$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "We can show that this expression can be rewritten as:\n",
+ "$$ \\frac{x^2}{1-x} = 2.4 \\cdot 10^{21} \\frac{T^{3/2}}{n} e^{-U_i / k_B T}$$ \n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 1. Numerical computation "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 1.1. First, we compute the right hand-side term. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def rhs_Saha_Chen(n,T,Ui):\n",
+ " \"\"\"Computes the right hand side of Saha's equation for a given temperature T\"\"\"\n",
+ " rhs = 2.4*1e21*(T**(3/2)/n)*np.exp(-(Ui/(sc.k*T)))\n",
+ " return rhs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 1.2. Then, we solve for the ionisation fraction $x$. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#Assuming x > 0 forces the solver to return only positive solutions\n",
+ "x = Symbol('x', positive=True) "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def solve_Saha(n,T,Ui):\n",
+ " \"\"\"Computes the ionisation fraction x for a given temperature T\"\"\"\n",
+ " #Note: sympy.solvers.solve struggles when rhs is large. So let's use two cases:\n",
+ " if (rhs_Saha_Chen(n,T,Ui) <= 1e2):\n",
+ " sol = solve((x**2/(1-x)) - rhs_Saha_Chen(n,T,Ui),x) \n",
+ " else:\n",
+ " sol = [1 - 1/rhs_Saha_Chen(n,T,Ui)] #for x->1, x²/(1-x)-> 1/(1-x)\n",
+ " if len(sol)==0:\n",
+ " sol = [np.nan] #If there is no solution, returns a NaN rather than an empty array.\n",
+ " return sol"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2. Examples"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.1. ITER Plasma:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$n \\sim 1 \\cdot 10^{19} \\text{ m}^{-3}$ and $T \\sim 8 \\text{ keV}$, $U_i \\sim 15.6 \\text{ eV (for Deuterium)}$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x = 1\n"
+ ]
+ }
+ ],
+ "source": [
+ "n = 1e19 #[nb.m^-3]\n",
+ "T = 8e3 * sc.electron_volt / sc.k #[K]\n",
+ "Ui = 15.5*sc.electron_volt #13.6 eV -> [J], ionisation energy of hydrogen\n",
+ "\n",
+ "x_i = solve_Saha(n,T,Ui)[0]\n",
+ "sciprint(x_i)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.2. This room:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$n \\sim 3 \\cdot 10^{25} \\text{ m}^{-3}$, $T \\sim 300 \\text{ K}$ and $U_i \\sim 14.5 \\text{ eV}$ (for $N_2$)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x = 1e-122\n"
+ ]
+ }
+ ],
+ "source": [
+ "n = 3e25 #[nb.m^-3]\n",
+ "T = 300 #[K]\n",
+ "Ui = 14.5*sc.electron_volt #14.5 eV -> [J], ionisation energy of N2\n",
+ "\n",
+ "x_i = solve_Saha(n,T,Ui)[0]\n",
+ "sciprint(x_i)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "Note: This extremely low value of ionisation is unrealistically low, because Saha's equation does not take into account ionisation by cosmic rays which takes the real $n_i / n_n$ ratio closer to $10^{-22}$. That's still not much.\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.3. A wood burning stove:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$n \\sim 3 \\cdot 10^{25} \\text{ m}^{-3}$, $T \\sim 460 \\ ^\\circ\\text{C}$ and $U_i \\sim 14.5 \\text{ eV}$ (for $N_2$)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x = 2e-50\n"
+ ]
+ }
+ ],
+ "source": [
+ "n = 3e25 #[nb.m^-3]\n",
+ "T = 460 + 273.15 #[K]\n",
+ "Ui = 14.5*sc.electron_volt #14.5 eV -> [J], ionisation energy of N2\n",
+ "\n",
+ "x_i = solve_Saha(n,T,Ui)[0]\n",
+ "sciprint(x_i)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 2.4. Lightning"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$n \\sim 3 \\cdot 10^{25} \\text{ m}^{-3}$ and $T \\sim 20,000 \\ ^\\circ\\text{C}$, $U_i \\sim 14.5 \\text{ eV}$ (for $N_2$)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x = 0.2\n"
+ ]
+ }
+ ],
+ "source": [
+ "n = 3e25 #[nb.m^-3]\n",
+ "T = 20000 #[K]\n",
+ "Ui = 14.5*sc.electron_volt #14.5 eV -> [J], ionisation energy of N2\n",
+ "\n",
+ "x_i = solve_Saha(n,T,Ui)[0]\n",
+ "sciprint(x_i)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3. Plotting x in terms of _T_ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.1. At atmospheric density"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "code_folding": []
+ },
+ "outputs": [],
+ "source": [
+ "n = 3e25 #[nb.m^-3]\n",
+ "Ui = 14.5*sc.electron_volt #14.5 eV -> [J], ionisation energy of N2\n",
+ "\n",
+ "Ts = np.logspace(0,7,100)\n",
+ "xs = []\n",
+ "for j in range(0, len(Ts)):\n",
+ " xs = xs + solve_Saha(n,Ts[j],Ui)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAG3CAYAAABIcHTrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAgAElEQVR4nO3de3yT9d3/8XeaHoG2SEtbCqWUkwM5t4KA6MRRBxvIdD+45yYqqKubMlvcBH3IUKd1Thk6BPVW5q1TbxSPmyj2x2/jIKACRUVQQQ4t0FJaoCktpG1y/f4oidS2kJSkV5K+no9H1uTKdSWfeI303e/pshiGYQgAACBEhJldAAAAgC8RbgAAQEgh3AAAgJBCuAEAACGFcAMAAEIK4QYAAIQUwg0AAAgphBsAABBSws0uoK05nU4dOnRIsbGxslgsZpcDAAA8YBiGqqqqlJqaqrCws7fNtLtwc+jQIaWlpZldBgAAaIXi4mL16NHjrPu0u3ATGxsrqeE/TlxcnMnVAAAAT9hsNqWlpbl/j59Nuws3rq6ouLg4wg0AAEHGkyElDCgGAAAhhXADAABCCuEGAACEFMINAAAIKYQbAAAQUgg3AAAgpBBuAABASCHcAACAkEK4AQAAIcXUcLN27VpNnjxZqampslgsevvtt895zJo1a5SZmano6Gj17t1bTz/9dBtUCgAAgoWp4aa6ulpDhw7V4sWLPdp/7969mjRpksaNG6fCwkLdc889mj17tt544w0/VwoAAIKFqdeWmjhxoiZOnOjx/k8//bR69uypRYsWSZIGDBigzZs367HHHtO1117rrzIBAEAQCaoLZ27cuFHZ2dmNtl111VV6/vnnVVdXp4iIiCbH2O122e1292Obzeb3OgG0L4Zh6FSdU1Wn6nSyzqFTdU6dqnPIXt/w03W/zuFUvcNQnfP0T4dT9U5D9Q6nHE7JYRhyOo3vfp6+bxiS0zBO3xrez+ls2GZIMk5vM3TmTzV63PA/kiHj9P7fPZbOfHzm52rySVt8rsmuZ/y3afG/W4vPNPfe/tXGbxfyOsdE6MlfDDft/YMq3JSWlio5ObnRtuTkZNXX16u8vFzdunVrckx+fr7uv//+tioRQIgwDEO2k/U6cLxGh46f0qHjJ3Xw+EkdOn5SlSfrZDtZJ9up+tM/61Tn4Ncj4JIUG2Xq+wdVuJGaXurc9VdBS5dAnzdvnvLy8tyPbTab0tLS/FcggKBjGIb2V9Ro8/5j2rL/mAqLjqn4aI2qax1evY7FIsVEWBUdYVV0eJiiI6yKirAqOiJMUeFhirA23MLDLA0/rRaFhzU8tlotslossoZZFGaxyBomhYU1bAuzWBRmafiec90PC2v4zguzWGSxSJYz7jfUYpHldE2STt+3NHrsemA5o/6Gx5bvPW78Gd339b3v3ea/hlva7K6zNVp3lH+08iOEtOgIq6nvH1ThJiUlRaWlpY22lZWVKTw8XAkJCc0eExUVpagocxMkgMCz/WClNn5boc37j2rL/uMqP2Fvdr/ETpFK7Ryj7p1jlNo5Rt3io5XQKVJx0RGKjY5QXEy44qIjFBcToY6R1lb/sgbgO0EVbkaPHq1//vOfjbZ9+OGHysrKana8DQB836Y9FXpy9S5t+Lai0fZIa5gG94hXZvoFyky/QP2TY9UtPtr0v0ABeM/UcHPixAnt3r3b/Xjv3r3atm2bunTpop49e2revHk6ePCgXnzxRUlSTk6OFi9erLy8PN1yyy3auHGjnn/+eb366qtmfQQAQcAwDG34tkJPrN6lT/YelSRFWC26vH9XZfXqoqz0CzSoezxBBggRpoabzZs364orrnA/do2NueGGG/TCCy+opKRERUVF7uczMjK0cuVK5ebm6qmnnlJqaqqefPJJpoEDaJZhGFrzzRE9uXqXthYdl9TQQjP94jTl/LCPuneOMblCAP5gMc42Ty8E2Ww2xcfHq7KyUnFxcWaXA8BPjlXX6taXNuvTfcckSVHhYfrFyJ7KubyPUuKjTa4OgLe8+f0dVGNuAMAT1fZ63fTCp9pWfFzREWH61ah03XpZbyXFEWqA9oBwAyCk1NY7lfOPLdpWfFydO0To9V+PVr/kWLPLAtCGuCo4gJDhdBqa8/pnWrerXDERVi278WKCDdAOEW4AhATDMHT/P7/UPz87pAirRU9fn6kRPS8wuywAJiDcAAgJT67erf/ZuF8Wi/TY/xmqy/t3NbskACYh3AAIei9t2q+//t9vJEkLJl+kq4d1N7kiAGYi3AAIav/6/JDmv7NdkjT7yn66YUwvcwsCYDrCDYCgVVp5SnmvfSbDkH51SU/l/qif2SUBCACEGwBB69VPilRb79Twnp11/5RBXLQSgCTCDYAgVedw6n8/bbg8y41jeskaRrAB0IBwAyAord5ZpsM2uxI6RurHg1LMLgdAACHcAAhKL3+8X5L0f7LSFBXO1bwBfIdwAyDo7C2v1rpd5bJYpF+O6ml2OQACDOEGQNB59ZOGsTaX9++qtC4dTK4GQKAh3AAIKqfqHHp9c7Ek6Zej0k2uBkAgItwACCorvyjRsZo6pcZHa/wPkswuB0AAItwACCr/2NQwkPgXI3sy/RtAswg3AILGjkM2bS06rvAwi6ZfnGZ2OQACFOEGQNBwTf/OvihZSXHRJlcDIFARbgAEhRP2er1deFCS9CsGEgM4C8INgKDwduFBVdc61LtrR43uk2B2OQACGOEGQMAzDMM9kPiXo9K5QCaAsyLcAAh4W4uO6avSKkWFh+naEd3NLgdAgCPcAAh4/9jUsCLx5KGp6twh0uRqAAQ6wg2AgHay1qH3viiRJP3qEgYSAzg3wg2AgLaz1KbaeqcSO0VpaI94s8sBEAQINwAC2vaDlZKkwd3jGEgMwCOEGwABzRVuBnWn1QaAZwg3AALa9oM2SYQbAJ4j3AAIWKfqHPrmcJUkwg0AzxFuAASsbw5Xqd5p6IIOEUqN51pSADxDuAEQsL44Y7wNg4kBeIpwAyBgMd4GQGsQbgAErC8PuaaBE24AeI5wAyAg1dY79VXJ6cHEqYQbAJ4j3AAISLvKqlTrcCouOlxpXWLMLgdAECHcAAhI2xlMDKCVCDcAAhKDiQG0FuEGQEDafojLLgBoHcINgIBT73BqZ8nplpvUOJOrARBsCDcAAs63R6p1qs6pTlHh6pXQ0exyAAQZwg2AgONamXhgapzCwhhMDMA7hBsAAcc9U4r1bQC0AuEGQMBxr0zcg/E2ALxHuAEQUBxOQ18ecg0mpuUGgPcINwACyt7yatXUOhQTYVXvrp3MLgdAECLcAAgo288YTGxlMDGAViDcAAgo3w0mZrwNgNYh3AAIKKxMDOB8EW4ABAyn09CXXFMKwHki3AAIGEVHa1Rlr1dkeJj6JjGYGEDrEG4ABAzXysQDusUpwsrXE4DW4dsDQMBwj7dhMDGA80C4ARAwXONtBjPeBsB5INwACAiGYbi7pRhMDOB8EG4ABIQDx06q8mSdIqwW9UtmMDGA1jM93CxZskQZGRmKjo5WZmam1q1bd9b9X375ZQ0dOlQdOnRQt27ddNNNN6mioqKNqgXgL67F+y5MiVVUuNXkagAEM1PDzfLly3XnnXfq3nvvVWFhocaNG6eJEyeqqKio2f3Xr1+vGTNmaNasWfryyy/1+uuv69NPP9XNN9/cxpUD8LXvBhPTJQXg/JgabhYuXKhZs2bp5ptv1oABA7Ro0SKlpaVp6dKlze6/adMm9erVS7Nnz1ZGRoYuvfRS/frXv9bmzZvbuHIAvradxfsA+Ihp4aa2tlZbtmxRdnZ2o+3Z2dnasGFDs8eMGTNGBw4c0MqVK2UYhg4fPqwVK1boJz/5SVuUDMCPvuSyCwB8xLRwU15eLofDoeTk5Ebbk5OTVVpa2uwxY8aM0csvv6zp06crMjJSKSkp6ty5s/72t7+1+D52u102m63RDUBgsZ2qU/mJWklSP1YmBnCeTB9QbLFYGj02DKPJNpcdO3Zo9uzZmj9/vrZs2aIPPvhAe/fuVU5OTouvn5+fr/j4ePctLS3Np/UDOH8lx09Jkjp3iFDHqHCTqwEQ7EwLN4mJibJarU1aacrKypq05rjk5+dr7Nix+v3vf68hQ4boqquu0pIlS7Rs2TKVlJQ0e8y8efNUWVnpvhUXF/v8swA4P4eOn5QkpcbHmFwJgFBgWriJjIxUZmamCgoKGm0vKCjQmDFjmj2mpqZGYWGNS7ZaG6aMGobR7DFRUVGKi4trdAMQWA66wk1nwg2A82dqt1ReXp6ee+45LVu2TDt37lRubq6Kiorc3Uzz5s3TjBkz3PtPnjxZb775ppYuXao9e/boo48+0uzZszVy5Eilpqaa9TEAnCdXy033ztEmVwIgFJjauT19+nRVVFTogQceUElJiQYNGqSVK1cqPT1dklRSUtJozZsbb7xRVVVVWrx4sebMmaPOnTtr/Pjx+vOf/2zWRwDgA4douQHgQxajpf6cEGWz2RQfH6/Kykq6qIAAMe3pjfpk31H97RfDNXkorbAAmvLm97fps6UAgDE3AHyJcAPAVA6noVJbw1Tw7oQbAD5AuAFgqrKqU3I4DYWHWdQ1NsrscgCEAMINAFO5BhOnxEfLGtb8Ap4A4A3CDQBTHTy9OjHjbQD4CuEGgKm+W+OGcAPANwg3AEz13Ro3LOAHwDcINwBMxQJ+AHyNcAPAVIy5AeBrhBsApmLMDQBfI9wAMM0Je70qT9ZJkrrFM+YGgG8QbgCYpuR0q01cdLhioyNMrgZAqCDcADAN15QC4A+EGwCmOXSca0oB8D3CDQDTMA0cgD8QbgCYhnADwB8INwBMc5DViQH4AeEGgGkOVbLGDQDfI9wAMIXDaai0ktWJAfge4QaAKcpP2FXnMGQNsygpNsrscgCEEMINAFO4xtukxEUr3MpXEQDf4RsFgCkOMZgYgJ8QbgCYgmngAPyFcAPAFK7ViQk3AHyNcAPAFFxXCoC/EG4AmMLVLdWdMTcAfIxwA8AUjLkB4C9eh5vDhw+3+Nznn39+XsUAaB9qaut1rKZOEuEGgO95HW4GDx6sd999t8n2xx57TKNGjfJJUQBCm2swcWxUuOKiI0yuBkCo8Trc3H333Zo+fbpycnJ08uRJHTx4UOPHj9df/vIXLV++3B81AggxdEkB8Cevw82cOXO0adMmffTRRxoyZIiGDBmimJgYff7555oyZYo/agQQYljAD4A/tWpAce/evXXRRRdp3759stlsmjZtmpKTk31dG4AQRcsNAH/yOty4Wmx2796tzz//XEuXLtUdd9yhadOm6dixY/6oEUCIOcgCfgD8yOtwM378eE2fPl0bN27UgAEDdPPNN6uwsFAHDhzQ4MGD/VEjgBDz3Ro3hBsAvhfu7QEffvihLr/88kbb+vTpo/Xr1+uhhx7yWWEAQtehSrqlAPiP1y033w827hcKC9N999133gUBCG1Op6ESd7cUA4oB+B4rFANoU+XVdtU6nAqzSMlxhBsAvke4AdCmXAv4JcdFK8LKVxAA3+ObBUCbYho4AH8j3ABoU4QbAP7m9WwpSXI6ndq9e7fKysrkdDobPXfZZZf5pDAAoekgqxMD8DOvw82mTZt03XXXaf/+/TIMo9FzFotFDofDZ8UBCD2scQPA37wONzk5OcrKytJ7772nbt26yWKx+KMuACHKNaA4NZ5wA8A/vA43u3bt0ooVK9S3b19/1AMgxDHmBoC/eT2geNSoUdq9e7c/agEQ4k7VOVRRXSuJbikA/uN1y80dd9yhOXPmqLS0VIMHD1ZERESj54cMGeKz4gCEFlerTcdIq+JiWjWfAQDOyetvl2uvvVaSNHPmTPc2i8UiwzAYUAzgrA6dcTVwxusB8Bevw83evXv9UQeAdoDxNgDagtfhJj093R91AGgHDhJuALSBVnV6f/vtt1q0aJF27twpi8WiAQMG6He/+5369Onj6/oAhJDv1rhhAT8A/uP1bKlVq1Zp4MCB+uSTTzRkyBANGjRIH3/8sS666CIVFBT4o0YAIeJQJS03APzP65abuXPnKjc3V4888kiT7XfffbcmTJjgs+IAhJYzBxQDgL943XKzc+dOzZo1q8n2mTNnaseOHT4pCkDoMQxDJadbbrrF0y0FwH+8Djddu3bVtm3bmmzftm2bkpKSfFIUgNBTZa/XqbqGC+0mxRJuAPiP191St9xyi2699Vbt2bNHY8aMkcVi0fr16/XnP/9Zc+bM8UeNAEJAmc0uSYqNCldMpNXkagCEMq/DzX333afY2Fg9/vjjmjdvniQpNTVVCxYs0OzZs31eIIDQcKSqIdx0jY0yuRIAoc7rcGOxWJSbm6vc3FxVVVVJkmJjY31eGIDQUlbVMJiYcAPA37wec3Om2NjY8w42S5YsUUZGhqKjo5WZmal169addX+73a57771X6enpioqKUp8+fbRs2bLzqgGA/7labpLiGG8DwL88arkZMWKEVq9erQsuuEDDhw8/6zVhtm7d6vGbL1++XHfeeaeWLFmisWPH6plnntHEiRO1Y8cO9ezZs9ljpk2bpsOHD+v5559X3759VVZWpvr6eo/fE4A5ylzdUp1ouQHgXx6Fm6uvvlpRUVHu+7664N3ChQs1a9Ys3XzzzZKkRYsWadWqVVq6dKny8/Ob7P/BBx9ozZo12rNnj7p06SJJ6tWrl09qAeBf37XcEG4A+JdH4eaPf/yj+/6CBQt88sa1tbXasmWL5s6d22h7dna2NmzY0Owx7777rrKysvToo4/qpZdeUseOHTVlyhQ9+OCDiolpflEwu90uu93ufmyz2XxSPwDvuMbcJDHmBoCfeT3mpnfv3qqoqGiy/fjx4+rdu7fHr1NeXi6Hw6Hk5ORG25OTk1VaWtrsMXv27NH69eu1fft2vfXWW1q0aJFWrFih3/72ty2+T35+vuLj4923tLQ0j2sE4DuuqeCscQPA37wON/v27ZPD4Wiy3W6368CBA14X8P0uLsMwWuz2cjqdslgsevnllzVy5EhNmjRJCxcu1AsvvKCTJ082e8y8efNUWVnpvhUXF3tdI4Dzd+QEU8EBtA2Pp4K/++677vurVq1SfHy8+7HD4dDq1auVkZHh8RsnJibKarU2aaUpKytr0prj0q1bN3Xv3r3Rew8YMECGYejAgQPq169fk2OioqLc44UAmMNe79DxmjpJdEsB8D+Pw83UqVMlNbS03HDDDY2ei4iIUK9evfT44497/MaRkZHKzMxUQUGBfvazn7m3FxQU6Oqrr272mLFjx+r111/XiRMn1KlTJ0nSN998o7CwMPXo0cPj9wbQtlyDiSOsFnXuEGFyNQBCncfdUk6nU06nUz179lRZWZn7sdPplN1u19dff62f/vSnXr15Xl6ennvuOS1btkw7d+5Ubm6uioqKlJOTI6mhS2nGjBnu/a+77jolJCTopptu0o4dO7R27Vr9/ve/18yZM1scUAzAfEfOmAbuq9mWANASr1co3rt3r8/efPr06aqoqNADDzygkpISDRo0SCtXrlR6erokqaSkREVFRe79O3XqpIKCAt1xxx3KyspSQkKCpk2bpj/96U8+qwmA77nXuGEBPwBtwGIYhuHNAbNnz1bfvn2bXEdq8eLF2r17txYtWuTTAn3NZrMpPj5elZWViouLM7scoF14adN+3ff2dk0YmKz/npFldjkAgpA3v7+9ni31xhtvaOzYsU22jxkzRitWrPD25QC0A0dsrHEDoO14HW4qKioazVZyiYuLU3l5uU+KAhBamAYOoC15HW769u2rDz74oMn2999/36tF/AC0HyzgB6AteT2gOC8vT7fffruOHDmi8ePHS5JWr16txx9/PODH2wAwh2tAMd1SANqC1+Fm5syZstvteuihh/Tggw9Karh45dKlSxtN2wYAF/dUcMINgDbgdbiRpNtuu0233Xabjhw5opiYGPeCegDwfU6nofITXBEcQNtpVbhx6dq1q6/qABCijtbUqt7ZsOJEYifCDQD/a1W4WbFihV577TUVFRWptra20XNbt271SWEAQoNrMHGXjpGKsHo9hwEAvOb1N82TTz6pm266SUlJSSosLNTIkSOVkJCgPXv2aOLEif6oEUAQc00DZzAxgLbidbhZsmSJnn32WS1evFiRkZH6wx/+oIKCAs2ePVuVlZX+qBFAECs7vYAfg4kBtBWvw01RUZHGjBkjSYqJiVFVVZUk6frrr9err77q2+oABL3vpoGzxg2AtuF1uElJSVFFRYUkKT09XZs2bZLUcEFNLy9TBaAdYBo4gLbmdbgZP368/vnPf0qSZs2apdzcXE2YMEHTp0/Xz372M58XCCC4HWEBPwBtzOvZUs8++6ycTqckKScnR126dNH69es1efJk5eTk+LxAAMGtrOr0RTNZ4wZAG/Eq3NTX1+uhhx7SzJkzlZaWJkmaNm2apk2b5pfiAAQ/15ibrqxxA6CNeNUtFR4err/85S9yOBz+qgdAiHF3S8UxoBhA2/B6zM2PfvQj/ec///FDKQBCzQl7vWpqG/4YYswNgLbi9ZibiRMnat68edq+fbsyMzPVsWPHRs9PmTLFZ8UBCG6uNW46RlrVMeq8rvYCAB7z+tvmtttukyQtXLiwyXMWi4UuKwBuTAMHYAavw41rphQAnAsL+AEwg0djbrp06aLy8nJJ0syZM92rEgPA2bhnSjENHEAb8ijc1NbWymazSZL+53/+R6dOnfJrUQBCwxGmgQMwgUfdUqNHj9bUqVOVmZkpwzA0e/ZsxcTENLvvsmXLfFoggODFAn4AzOBRuPnHP/6hv/71r/r2229lsVhUWVlJ6w2AczrCmBsAJvAo3CQnJ+uRRx6RJGVkZOill15SQkKCXwsDEPzKbFxXCkDb83q21N69e/1RB4AQdOQEU8EBtD2vVygGAE/U1jt1tLpWEi03ANoW4QaAX5SfbrUJD7Pogg6RJlcDoD0h3ADwC9dg4sROUQoLs5hcDYD2hHADwC/cqxMzDRxAG2vVleycTqd2796tsrKyJpdjuOyyy3xSGIDg5l7jhvE2ANqY1+Fm06ZNuu6667R//34ZhtHoOS6cCcDFNQ28K2vcAGhjXoebnJwcZWVl6b333lO3bt1ksdCXDqAppoEDMIvX4WbXrl1asWKF+vbt6496AIQIFvADYBavBxSPGjVKu3fv9kctAELIEcbcADCJ1y03d9xxh+bMmaPS0lINHjxYERERjZ4fMmSIz4oDELzcVwQn3ABoY16Hm2uvvVaSNHPmTPc2i8UiwzAYUAxAkmQYhnvMTVIcA4oBtC2uLQXA547V1KnO0TCbsmsnWm4AtC2vw016ero/6gAQQlxr3FzQIUKR4awVCqBttWoRv2+//VaLFi3Szp07ZbFYNGDAAP3ud79Tnz59fF0fgCDEeBsAZvL6T6pVq1Zp4MCB+uSTTzRkyBANGjRIH3/8sS666CIVFBT4o0YAQea7aeCMtwHQ9rxuuZk7d65yc3P1yCOPNNl+9913a8KECT4rDkBwcl9XipYbACbwuuVm586dmjVrVpPtM2fO1I4dO3xSFIDgRrcUADN5HW66du2qbdu2Ndm+bds2JSUl+aQoAMHNNaCYcAPADF53S91yyy269dZbtWfPHo0ZM0YWi0Xr16/Xn//8Z82ZM8cfNQIIMu5uKda4AWACr8PNfffdp9jYWD3++OOaN2+eJCk1NVULFizQ7NmzfV4ggODj7pZijRsAJvA63FgsFuXm5io3N1dVVVWSpNjYWJ8XBiB4HXG33BBuALS9Vq1z40KoAfB9NbX1OmGvl8RsKQDm8CjcjBgxQqtXr9YFF1yg4cOHy2KxtLjv1q1bfVYcgODjWuMmJsKqTlHn9fcTALSKR988V199taKiotz3zxZuALRvrgtmdo2N4rsCgCk8Cjd//OMf3fcXLFjgr1oAhIDvViemSwqAObxe56Z3796qqKhosv348ePq3bu3T4oCELxca9wwmBiAWbwON/v27ZPD4Wiy3W6368CBAz4pCkDwYho4ALN5PNrv3Xffdd9ftWqV4uPj3Y8dDodWr16tjIwM31YHIOiwgB8As3kcbqZOnSqpYZ2bG264odFzERER6tWrlx5//HHfVgcg6JRxXSkAJvM43DidTklSRkaGPv30UyUmJvqtKADBq8x2eswN4QaASbwec7N3716fBpslS5YoIyND0dHRyszM1Lp16zw67qOPPlJ4eLiGDRvms1oAnD93t1Qs3VIAzNGqFbaqq6u1Zs0aFRUVqba2ttFz3lxfavny5brzzju1ZMkSjR07Vs8884wmTpyoHTt2qGfPni0eV1lZqRkzZujKK6/U4cOHW/MRAPjBqTqHjlY3fCekdibcADCHxTAMw5sDCgsLNWnSJNXU1Ki6ulpdunRReXm5OnTooKSkJO3Zs8fj1xo1apRGjBihpUuXurcNGDBAU6dOVX5+fovH/dd//Zf69esnq9Wqt99+W9u2bfP4PW02m+Lj41VZWam4uDiPjwNwbvvKq/XDx/6jmAirdjxwFYv4AfAZb35/e90tlZubq8mTJ+vo0aOKiYnRpk2btH//fmVmZuqxxx7z+HVqa2u1ZcsWZWdnN9qenZ2tDRs2tHjc3//+d3377beNFhY8G7vdLpvN1ugGwD8OVZ6UJHWLjybYADCN1+Fm27ZtmjNnjqxWq6xWq+x2u9LS0vToo4/qnnvu8fh1ysvL5XA4lJyc3Gh7cnKySktLmz1m165dmjt3rl5++WWFh3vWo5afn6/4+Hj3LS0tzeMaAXintLJhMHE3uqQAmMjrcBMREeH+iyw5OVlFRUWSpPj4ePd9b3z/rzvDMJr9i8/hcOi6667T/fffr/79+3v8+vPmzVNlZaX7Vlxc7HWNADxTcjrcpMTFmFwJgPbM6wHFw4cP1+bNm9W/f39dccUVmj9/vsrLy/XSSy9p8ODBHr9OYmKirFZrk1aasrKyJq05klRVVaXNmzersLBQt99+u6SG6emGYSg8PFwffvihxo8f3+S4qKgo90U/AfhXyeluKQYTAzCT1y03Dz/8sLp16yZJevDBB5WQkKDbbrtNZWVlevbZZz1+ncjISGVmZqqgoKDR9oKCAuChCBsAABq9SURBVI0ZM6bJ/nFxcfriiy+0bds29y0nJ0cXXnihtm3bplGjRnn7UQD4WMnx0y038YQbAObxuuUmKyvLfb9r165auXJlq988Ly9P119/vbKysjR69Gg9++yzKioqUk5OjqSGLqWDBw/qxRdfVFhYmAYNGtTo+KSkJEVHRzfZDsAcrm6p1Hi6pQCYx+twc/LkSRmGoQ4dOkiS9u/fr7feeksDBw5sMvPpXKZPn66Kigo98MADKikp0aBBg7Ry5Uqlp6dLkkpKSlo1jgeAOVzdUrTcADCT1+vcZGdn65prrlFOTo6OHz+uCy+8UJGRkSovL9fChQt12223+atWn2CdG8A/TtU59IP7PpAkfTY/W/EdIkyuCEAo8es6N1u3btW4ceMkSStWrFBKSor279+vF198UU8++WTrKgYQ9FzTwGMirIqLadXi5wDgE16Hm5qaGsXGxkqSPvzwQ11zzTUKCwvTJZdcov379/u8QADBwb2AX2cW8ANgLq/DTd++ffX222+ruLhYq1atco+zKSsro5sHaMfcC/gx3gaAybwON/Pnz9ddd92lXr16adSoURo9erSkhlac4cOH+7xAAMGBBfwABAqvO8Z//vOf69JLL1VJSYmGDh3q3n7llVfqZz/7mU+LAxA8WMAPQKBo1ai/lJQUpaSkNNo2cuRInxQEIDixgB+AQOFRuLnmmmv0wgsvKC4uTtdcc81Z933zzTd9UhiA4MICfgAChUfhJj4+3j37IT4+3q8FAQhOLOAHIFB4FG7+/ve/N3sfAKSGBfyO1dRJouUGgPm8ni0FAN9XwgJ+AAKI1+Hm8OHDuv7665Wamqrw8HBZrdZGNwDtTwkL+AEIIF7/iXXjjTeqqKhI9913n7p168YXGQAW8AMQULwON+vXr9e6des0bNgwf9QDIAiVuMMN420AmM/rbqm0tDR5eSFxACHO3S1Fyw2AAOB1uFm0aJHmzp2rffv2+aEcAMHItYAfLTcAAoHX3VLTp09XTU2N+vTpow4dOigiIqLR80ePHvVZcQCCQwljbgAEEK/DzaJFi/xRB4AgduZsKQAwm9fh5oYbbvBHHQCC1JkL+HXjiuAAAkCrVttyOBx6++23tXPnTlksFg0cOFBTpkxhnRugHXJ1SXWIZAE/AIHB62+i3bt3a9KkSTp48KAuvPBCGYahb775RmlpaXrvvffUp08ff9QJIECdeU0p1r0CEAi8ni01e/Zs9enTR8XFxdq6dasKCwtVVFSkjIwMzZ492x81Aghg382UYrwNgMDgdcvNmjVrtGnTJnXp0sW9LSEhQY888ojGjh3r0+IABL5SG9PAAQQWr1tuoqKiVFVV1WT7iRMnFBkZ6ZOiAASPQ8dZwA9AYPE63Pz0pz/Vrbfeqo8//liGYcgwDG3atEk5OTmaMmWKP2oEEMBKufQCgADjdbh58skn1adPH40ePVrR0dGKjo7W2LFj1bdvXz3xxBP+qBFAAGMBPwCBxusxN507d9Y777yjXbt26auvvpJhGBo4cKD69u3rj/oABDgW8AMQaFq9KEW/fv3Ur18/X9YCIMiwgB+AQORRuMnLy9ODDz6ojh07Ki8v76z7Lly40CeFAQh8LOAHIBB59G1UWFiouro69/2WsIAX0L6wgB+AQORRuPn3v//d7H0A7ZtrAb9UZkoBCCBez5YCABfXAn4pzJQCEEAINwBazbWAXyrhBkAAIdwAaDXXAn4pdEsBCCCEGwCtdsi1gB9r3AAIIIQbAK1WWsl1pQAEHsINgFY5WXvGAn50SwEIIIQbAK3iminVIdKquGgW8AMQOAg3AFql5IwuKRbwAxBICDcAWsW1gB9dUgACDeEGQKuwgB+AQEW4AdAqLOAHIFARbgC0Cgv4AQhUhBsArcICfgACFeEGQKuwgB+AQEW4AeA1FvADEMgINwC8xgJ+AAIZ4QaA10qOs4AfgMBFuAHgtZJKFvADELgINwC85uqWYjAxgEBEuAHgtUPHmSkFIHARbgB4rdS9xg3dUgACD+EGgNeKj9VIouUGQGAi3ADwSm29U3uOVEuS+iXHmlwNADRFuAHglX0V1ap3GuoUFc5FMwEEJMINAK98c7hKktQvuRNr3AAISIQbAF75prQh3PRPoksKQGAyPdwsWbJEGRkZio6OVmZmptatW9fivm+++aYmTJigrl27Ki4uTqNHj9aqVavasFoA3xw+IUnqn0K4ARCYTA03y5cv15133ql7771XhYWFGjdunCZOnKiioqJm91+7dq0mTJiglStXasuWLbriiis0efJkFRYWtnHlQPvl6pbqn9zJ5EoAoHkWwzAMs9581KhRGjFihJYuXereNmDAAE2dOlX5+fkevcZFF12k6dOna/78+R7tb7PZFB8fr8rKSsXFxbWqbqC9OlXn0MD5H8hpSJ/cc6WS4hhQDKBtePP727SWm9raWm3ZskXZ2dmNtmdnZ2vDhg0evYbT6VRVVZW6dOnS4j52u102m63RDUDr7DlSLachxcdEqGtslNnlAECzTAs35eXlcjgcSk5ObrQ9OTlZpaWlHr3G448/rurqak2bNq3FffLz8xUfH+++paWlnVfdQHvm6pK6MDmWmVIAApbpA4q//wVpGIZHX5qvvvqqFixYoOXLlyspKanF/ebNm6fKykr3rbi4+LxrBtqrM6eBA0CgCjfrjRMTE2W1Wpu00pSVlTVpzfm+5cuXa9asWXr99df1ox/96Kz7RkVFKSqK5nPAF9wtN8yUAhDATGu5iYyMVGZmpgoKChptLygo0JgxY1o87tVXX9WNN96oV155RT/5yU/8XSaAM7imgfdjjRsAAcy0lhtJysvL0/XXX6+srCyNHj1azz77rIqKipSTkyOpoUvp4MGDevHFFyU1BJsZM2boiSee0CWXXOJu9YmJiVF8fLxpnwNoD2pq61V0tOGCmUwDBxDITA0306dPV0VFhR544AGVlJRo0KBBWrlypdLT0yVJJSUljda8eeaZZ1RfX6/f/va3+u1vf+vefsMNN+iFF15o6/KBdmV3WUOrTWKnSCV0oqsXQOAydZ0bM7DODdA6r28u1u9XfK7RvRP06q2XmF0OgHYmKNa5ARBcdp1uuWEwMYBAR7gB4JGvS5kGDiA4EG4AeGTXGQv4AUAgI9wAOCfbqTodqjwlSepHuAEQ4Ag3AM5p1+n1bVLiohUfE2FyNQBwdoQbAOfEZRcABBPCDYBz+obxNgCCCOEGwDm5wk1/wg2AIEC4AXBOrmtK9WeNGwBBgHAD4KyOVdfqSJVdktQviTE3AAIf4QbAWbm6pLp3jlHHKFMvRwcAHiHcADgr92BiuqQABAnCDYCzco23YRo4gGBBuAFwVl8zDRxAkCHcAGiRYRjua0oxDRxAsCDcAGjRkRN2Haupk8Ui9WWmFIAgQbgB0CLXNaXSu3RQdITV5GoAwDOEGwAtYmViAMGIcAOgRYQbAMGIcAOgRVx2AUAwItwAaJZhGPqm1NVyw2BiAMGDcAOgWaW2U6qy18saZlFGYkezywEAjxFuADTr69OtNhmJHRUVzkwpAMGDcAOgWa5p4HRJAQg2hBsAzfqamVIAghThBkAThmHo470VkqSB3eJMrgYAvEO4AdDEl4dsKj56UtERYbq0X6LZ5QCAVwg3AJr4YHupJOmH/ZPUITLc5GoAwDuEGwCNGIahldtLJEkTB6eYXA0AeI9wA6CRXWUntOdItSKtYRr/gySzywEArxFuADTy/hcNXVKX9ktUbHSEydUAgPcINwAaef90l9SPB9ElBSA4EW4AuO0rr9ZXpVWyhlk0YUCy2eUAQKsQbgC4vX96ltTo3gm6oGOkydUAQOsQbgC4vc8sKQAhgHADQJJ04FiNPj9QKYtFyh5IuAEQvAg3ACR9t3Dfxb26qGtslMnVAEDrEW4ASPou3ExklhSAIEe4AaAy2yltKTomiSngAIIf4QaAVn1ZKsOQhqV1Vrf4GLPLAYDzQrgBoJVf0CUFIHQQboB2ruKEXR/vrZAkTRzUzeRqAOD8EW6Adq5gx2E5Demi1Dj1TOhgdjkAcN4IN0A79z6zpACEGMIN0I5VnqzThm/LJUk/pksKQIgg3ADt2Oqdh1XnMNQvqZP6JnUyuxwA8AnCDdBOnapz6Nm1eyTRJQUgtBBugHZqwbtf6qvSKiV2itSvRqebXQ4A+AzhBmiH3tx6QP/7abEsFumJ/xqupNhos0sCAJ8h3ADtzK7DVbr3re2SpNnj+2ls30STKwIA3yLcAO1ITW29fvPyVp2sc2hs3wTNvrKf2SUBgM8RboB25L63v9SushPqGhulRdOHyxpmMbskAPA5wg3QTry2uVhvbD2gMIv0t18MV9fYKLNLAgC/INwA7cDXpVWa/07DOJu8Cf11Se8EkysCAP8h3AAhrtper9+8vEWn6py6rH9X/eaHfc0uCQD8KtzsAgD4R01tvV79pFjPrdujkspTSomL1l+nDVUY42wAhDjTW26WLFmijIwMRUdHKzMzU+vWrTvr/mvWrFFmZqaio6PVu3dvPf30021UKRAcjtfU6on/u0tjH/l/evBfO1RSeUpJsVFa8qsRSujEOBsAoc/Ulpvly5frzjvv1JIlSzR27Fg988wzmjhxonbs2KGePXs22X/v3r2aNGmSbrnlFv3jH//QRx99pN/85jfq2rWrrr32WhM+ARA4DttO6bl1e/TKx0WqrnVIktITOujXl/XRNSO6KzrCanKFANA2LIZhGGa9+ahRozRixAgtXbrUvW3AgAGaOnWq8vPzm+x/9913691339XOnTvd23JycvTZZ59p48aNHr2nzWZTfHy8KisrFRcXd/4fAmhD9Q6nDh4/qX0VNSqqqNa+ihrtr6jR/opq7S2vVr2z4Z/zD1Ji9Zsr+mrSoBSFW01voAWA8+bN72/TWm5qa2u1ZcsWzZ07t9H27OxsbdiwodljNm7cqOzs7EbbrrrqKj3//POqq6tTREREk2Psdrvsdrv7sc1m80H1TR2vqdXs/93ml9dGcDrb3w2GIRkyZBiS02j46drmNKTaeqdO1TlkP+Onvd6hU3XOs75nVvoF+s0VfXTFhUmyWBhbA6B9Mi3clJeXy+FwKDk5udH25ORklZaWNntMaWlps/vX19ervLxc3bp1a3JMfn6+7r//ft8V3oJah1Nrvzni9/cBosLD1LNLB6UndFR6Qgf1Smi4n5HYUWldOphdHgCYzvTZUt//69IwjLP+xdnc/s1td5k3b57y8vLcj202m9LS0lpbbovioiO0cNpQn78ugtvZGk/CTj8ZZrHIYjn9Uw3/X44KD1NURJiiwq2KCg9TdETDz5hIq7p0iGTGEwCchWnhJjExUVartUkrTVlZWZPWGZeUlJRm9w8PD1dCQvOLkkVFRSkqyv8zRKIjrLpmRA+/vw8AADg700YaRkZGKjMzUwUFBY22FxQUaMyYMc0eM3r06Cb7f/jhh8rKymp2vA0AAGh/TJ1GkZeXp+eee07Lli3Tzp07lZubq6KiIuXk5Ehq6FKaMWOGe/+cnBzt379feXl52rlzp5YtW6bnn39ed911l1kfAQAABBhTx9xMnz5dFRUVeuCBB1RSUqJBgwZp5cqVSk9PlySVlJSoqKjIvX9GRoZWrlyp3NxcPfXUU0pNTdWTTz7JGjcAAMDN1HVuzMA6NwAABB9vfn+zuhcAAAgphBsAABBSCDcAACCkEG4AAEBIIdwAAICQQrgBAAAhhXADAABCCuEGAACEFMINAAAIKaZefsEMrgWZbTabyZUAAABPuX5ve3JhhXYXbqqqqiRJaWlpJlcCAAC8VVVVpfj4+LPu0+6uLeV0OnXo0CHFxsbKYrF4fNzFF1+sTz/99Lze29vX8HT/c+3X0vPebD9zm81mU1pamoqLi9v8+lych8bbzDoXZpwHT4/hPPj/Nfx5Hlp6LtTPQ2tep72dB8MwVFVVpdTUVIWFnX1UTbtruQkLC1OPHj28Ps5qtZ73SfL2NTzd/1z7tfS8N9ub2xYXF9fm4Ybz0Py+bX0uzDgPnh7DefD/a/jzPLT0XKifh9a8Tns8D+dqsXHXtGDBggU+fecQNnLkyDZ/DU/3P9d+LT3vzXbXNrvdrkceeUTz5s1TVFSUR/X5Eufhu21mngszzoOnx3Ae/P8a/jwPLT0X6uehNa/DeWheu+uWwvnz5rLz8C/ORWDgPAQGzkNgCITzQMsNWsVqteqHP/yhwsPbXc9mwOFcBAbOQ2DgPAQGs88DLTcAACCksIgfAAAIKYQbAAAQUgg3AAAgpBBuAABASCHcAACAkEK4gU9VVVXp4osv1rBhwzR48GD993//t9kltWs1NTVKT0/XXXfdZXYp7VZ4eLiGDRumYcOG6eabbza7nHZr7969uuKKKzRw4EANHjxY1dXVZpfU7nz99dfufwvDhg1TTEyM3n77bb+8F1PB4VMOh0N2u10dOnRQTU2NBg0apE8//VQJCQlml9Yu3Xvvvdq1a5d69uypxx57zOxy2qXExESVl5ebXUa7d/nll+tPf/qTxo0bp6NHjyouLo61cEx04sQJ9erVS/v371fHjh19/vq03MCnrFarOnToIEk6deqUHA6HR5enh+/t2rVLX331lSZNmmR2KYCpvvzyS0VERGjcuHGSpC5duhBsTPbuu+/qyiuv9EuwkQg3+J61a9dq8uTJSk1NlcViabbJcMmSJcrIyFB0dLQyMzO1bt26Rs8fP35cQ4cOVY8ePfSHP/xBiYmJbVV+yPDFebjrrruUn5/fViWHJF+cB5vNpszMTF166aVas2ZNW5UeUs73POzatUudOnXSlClTNGLECD388MNtWX7I8MW/B5fXXntN06dP91uthBs0Ul1draFDh2rx4sXNPr98+XLdeeeduvfee1VYWKhx48Zp4sSJKioqcu/TuXNnffbZZ9q7d69eeeUVHT58uK3KDxnnex7eeecd9e/fX/3792/LskOOL/497Nu3T1u2bNHTTz+tGTNmyGaztVX5IeN8z0NdXZ3WrVunp556Shs3blRBQYEKCgra8iOEBF/8e5AaAv9HH33k31ZlA2iBJOOtt95qtG3kyJFGTk5Oo20/+MEPjLlz5zb7Gjk5OcZrr73mtxrbg9ach7lz5xo9evQw0tPTjYSEBCMuLs64//7726zmUOSLfw8//vGPjU8//dRvNbYHrTkPGzZsMK666ir3c48++qjx6KOP+r/YEHY+/x5efPFF45e//KVf66PlBh6rra3Vli1blJ2d3Wh7dna2NmzYIEk6fPiw+y9Tm82mtWvX6sILL2zzWkOZJ+chPz9fxcXF2rdvnx577DHdcsstmj9/vhnlhixPzsOxY8dkt9slSQcOHNCOHTvUu3fvNq81lHlyHi6++GIdPnxYx44dk9Pp1Nq1azVgwAAzyg1ZnpwHF393SUkSI6rgsfLycjkcDiUnJzfanpycrNLSUkkNX+CzZs2SYRgyDEO33367hgwZYka5IcuT8wD/8+Q87Ny5U7/+9a8VFhYmi8WiJ554Ql26dDGj3JDlyXkIDw/Xww8/rMsuu0yGYSg7O1s//elPzSg3ZHn6vVRZWalPPvlEb7zxhl/rIdzAaxaLpdFjwzDc2zIzM7Vt2zYzymp3znYeznTjjTe2UUXt09nOw5gxY/TFF1+YUVa7c65/DxMnTtTEiRPbuqx251znIT4+vk3GYdItBY8lJibKarU2aR0oKytrktbhP5yHwMB5CAych8AQaOeBcAOPRUZGKjMzs8ksg4KCAo0ZM8akqtofzkNg4DwEBs5DYAi080C3FBo5ceKEdu/e7X68d+9ebdu2TV26dFHPnj2Vl5en66+/XllZWRo9erSeffZZFRUVKScnx8SqQw/nITBwHgID5yEwBNV58OtcLASdf//734akJrcbbrjBvc9TTz1lpKenG5GRkcaIESOMNWvWmFdwiOI8BAbOQ2DgPASGYDoPXFsKAACEFMbcAACAkEK4AQAAIYVwAwAAQgrhBgAAhBTCDQAACCmEGwAAEFIINwAAIKQQbgAAQEgh3AAAgJBCuAEAACGFcAMgZFRUVCgpKUn79u3z6rif//znWrhwoX+KAtDmCDcAAs4HH3wgi8Vy1tv777/f5Lj8/HxNnjxZvXr1cm+78cYbNXXq1Eb7rVixQtHR0Xr00UclSfPnz9dDDz0km83m188FoG0QbgAEnMsvv1wlJSXuW0JCgu65555G2yZMmNDomJMnT+r555/XzTfffNbXfu655/TLX/5Sixcv1h/+8AdJ0pAhQ9SrVy+9/PLLfvtMANoO4QZAwImJiVFKSopSUlLkcDhUUVGhSy+91L0tJSVF4eHhjY55//33FR4ertGjR7f4uo8++qhuv/12vfLKK01C0JQpU/Tqq6/65fMAaFuEGwABrbCwUJKUmZl51v3Wrl2rrKysFp+fO3euHnzwQf3rX//Stdde2+T5kSNH6pNPPpHdbj+/ggGYLvzcuwCAebZu3aru3bsrKSnprPvt27dPqampzT73/vvv65133tHq1as1fvz4Zvfp3r277Ha7SktLlZ6eft51AzAPLTcAAtrWrVs1YsSIc+538uRJRUdHN/uca0zN/PnzVVVV1ew+MTExkqSamprWFwsgIBBuAAS0rVu3nrNLSpISExN17NixZp/r3r271qxZo5KSEv34xz9uNuAcPXpUktS1a9fzKxiA6Qg3AAJWRUWFiouLPWq5GT58uHbs2NHi8z179tSaNWtUVlam7OzsJtO+t2/frh49eigxMfG86wZgLsINgIC1ZcsWSfIo3Fx11VX68ssvW2y9kaQePXroP//5jyoqKpSdna3Kykr3c+vWrVN2dvb5Fw3AdIQbAAGrsLBQSUlJ6t69+zn3HTx4sLKysvTaa6+ddT9XF9Xx48c1YcIEHT9+XKdOndJbb72lW265xVelAzCRxTAMw+wiAMAXVq5cqbvuukvbt29XWJjnf7s99dRTeuedd/Thhx/6sToAbYWp4ABCxqRJk7Rr1y4dPHhQaWlpHh8XERGhv/3tb36sDEBbouUGAACEFMbcAACAkEK4AQAAIYVwAwAAQgrhBgAAhBTCDQAACCmEGwAAEFIINwAAIKQQbgAAQEgh3AAAgJBCuAEAACHl/wP1Up3xigEZPQAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.cla()\n",
+ "plt.plot(Ts, xs)\n",
+ "\n",
+ "plt.xlabel(r'$T$ (K)')\n",
+ "plt.semilogx()\n",
+ "plt.ylabel('ionisation fraction x')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### 3.2. At other densities"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Ts = np.logspace(0,7,100)\n",
+ "Ui = 13.6*sc.electron_volt #Hydrogen. Remember, the usual T-rho diagram is for hydrogen\n",
+ "\n",
+ "plt.cla()\n",
+ "\n",
+ "for n in [1e23, 1e24, 1e25, 1e26, 1e27]:\n",
+ " xs = []\n",
+ " for j in range(0, len(Ts)):\n",
+ " xs = xs + solve_Saha(n,Ts[j],Ui)\n",
+ " label = f\"n = {n:0.1g} [m^-3]\"\n",
+ "\n",
+ " plt.plot(Ts, xs, label=label)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.xlabel(r'$T$ (K)')\n",
+ "plt.semilogx()\n",
+ "plt.ylabel('ionisation fraction x')\n",
+ "plt.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 4. Plotting the Saha equation in the Temperature-Density diagram"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us now assume that $x=1/2$.\n",
+ "\n",
+ "We can show that the Saha equation becomes:\n",
+ "\n",
+ "$$ \\frac{n}{2} = 2.4 \\cdot 10^{21} T^{3/2} e^{-U_i/k_B T} $$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Ts = np.logspace(2,10,100)\n",
+ "ns = []\n",
+ "for T in Ts:\n",
+ " n = 2*2.4e21*T**(3/2)*np.exp(-Ui/(sc.k*T))\n",
+ " ns = ns+[n]\n",
+ " \n",
+ "# ns = np.array([n if 1e12\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog10\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mns\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0msc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mm_p\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m1e-3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog10\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mTs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'red'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m11\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mylim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1.8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m11.2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+ "\u001b[0;31mTypeError\u001b[0m: can't multiply sequence by non-int of type 'float'"
+ ]
+ }
+ ],
+ "source": [
+ "plt.plot(np.log10(ns*sc.m_p*1e-3), np.log10(Ts), color='red', linewidth=3)\n",
+ "plt.xlim([-12, 11])\n",
+ "plt.ylim([1.8, 11.2])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.plot(ns*sc.m_p*1e-3, Ts, color='red', linewidth=3)\n",
+ "plt.xlim([0, 0.15])\n",
+ "plt.ylim([1e2, 2e5])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/hack/LIHEDP_notebooks/Temperature-Density_answer.png b/hack/LIHEDP_notebooks/Temperature-Density_answer.png
new file mode 100644
index 0000000..24d95a0
Binary files /dev/null and b/hack/LIHEDP_notebooks/Temperature-Density_answer.png differ
diff --git a/hack/LIHEDP_notebooks/Thomas_Fermi.ipynb b/hack/LIHEDP_notebooks/Thomas_Fermi.ipynb
new file mode 100644
index 0000000..4ce39cb
--- /dev/null
+++ b/hack/LIHEDP_notebooks/Thomas_Fermi.ipynb
@@ -0,0 +1,430 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true
+ },
+ "source": [
+ "#### Import modules "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from sympy.solvers import solve\n",
+ "from sympy import Symbol\n",
+ "from scipy import constants as sc\n",
+ "from matplotlib import pyplot as plt\n",
+ "from scipy.optimize import fsolve"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true
+ },
+ "source": [
+ "### Re: The Saha-Boltzmann equation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true,
+ "hidden": true
+ },
+ "source": [
+ "#### Original Saha equation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 211,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "Ui = 13.6*sc.electron_volt #Hydrogen. Remember, the usual T-rho diagram is for hydrogen\n",
+ "Ts = np.logspace(2,10,100)\n",
+ "ns = []\n",
+ "for T in Ts:\n",
+ " n = 2*2.4e21*T**(3/2)*np.exp(-Ui/(sc.k*T))\n",
+ " ns = ns+[n]\n",
+ " \n",
+ "ns = np.array(ns)\n",
+ " \n",
+ "# ns = np.array([n if 1e12:1: RuntimeWarning: divide by zero encountered in log10\n",
+ " plt.plot(np.log10(ns*sc.m_p*1e-3), np.log10(Ts), color='red', linewidth=3)\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(np.log10(ns*sc.m_p*1e-3), np.log10(Ts), color='red', linewidth=3)\n",
+ "plt.xlim([-12, 11])\n",
+ "plt.ylim([1.8, 11.2])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Calculating the average charge thanks to the Thomas-Fermi model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note:** This is not actually the Thomas-Fermi model, which requires serious computations to solve.\n",
+ "This is a fit of the result of the Thomas-Fermi model, which is used here for pedagocial purposes.\n",
+ "The fit is given in the classic textbook by _Atzeni & Meyer-ter-vehn: The Physics of Inertial Fusion_. The authors took it, in turn, from [_Pressure Ionization, Resonances, and the Continuity of Bound and Free States - More (1985)_](https://doi.org/10.1016/S0065-2199(08)60145-1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 205,
+ "metadata": {
+ "code_folding": []
+ },
+ "outputs": [],
+ "source": [
+ "def Zav_TF(Z, A, rho, T):\n",
+ " \"\"\"\n",
+ " Finite Temperature Thomas Fermi Charge State using \n",
+ " R.M. More (1985), \"Pressure Ionization, Resonances, and the\n",
+ " Continuity of Bound and Free States\", Adv. in Atomic \n",
+ " Mol. Phys., Vol. 21, p. 332 (Table IV).\n",
+ " \n",
+ " Z = atomic number\n",
+ " rho = mass density (g/cc)\n",
+ " T = temperature (eV)\n",
+ " \"\"\"\n",
+ "\n",
+ " alpha = 14.3139\n",
+ " beta = 0.6624\n",
+ " a1 = 0.003323\n",
+ " a2 = 0.9718\n",
+ " a3 = 9.26148e-5\n",
+ " a4 = 3.10165\n",
+ " b0 = -1.7630\n",
+ " b1 = 1.43175\n",
+ " b2 = 0.31546\n",
+ " c1 = -0.366667\n",
+ " c2 = 0.983333\n",
+ " \n",
+ " rho1 = rho/ A*Z\n",
+ " T1 = T/Z**(4./3.)\n",
+ " Tf = T1/(1 + T1)\n",
+ " Ac = a1*T1**a2 + a3*T1**a4\n",
+ " B = -np.exp(b0 + b1*Tf + b2*Tf**7)\n",
+ " C = c1*Tf + c2\n",
+ " Q1 = Ac*rho1**B\n",
+ " Q = (rho1**C + Q1**C)**(1/C)\n",
+ " x = alpha*Q**beta\n",
+ "\n",
+ " return Z*x/(1 + x + np.sqrt(1 + 2.*x))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Evidence of pressure ionisation at T=0"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 115,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Aluminium\n",
+ "A = 27\n",
+ "Z = 13\n",
+ "\n",
+ "rho_list = np.logspace(-10,10,101)\n",
+ "T = 0\n",
+ "\n",
+ "Zav_list = []\n",
+ "for rho in rho_list:\n",
+ " Zav = Zav_TF(Z, A, rho, T)\n",
+ " Zav_list.append([Zav])\n",
+ " \n",
+ "plt.plot(rho_list, Zav_list, label=f\"T={T:0.1g} eV\")\n",
+ "plt.semilogx()\n",
+ "plt.xlabel(r'$\\rho$ (g/cc)')\n",
+ "plt.ylabel(r'$Z_{av}$')\n",
+ "plt.legend()\n",
+ "\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Temperature ionisation, recombination, and pressure ionisation - at any Temperature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 116,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Aluminium\n",
+ "A = 27\n",
+ "Z = 13\n",
+ "\n",
+ "rho_list = np.logspace(-10,10,101)\n",
+ "T_list = np.logspace(-3,5,9)\n",
+ "\n",
+ "Zav_metalist = []\n",
+ "for T in T_list:\n",
+ " Zav_list = []\n",
+ " for rho in rho_list:\n",
+ " Zav = Zav_TF(Z, A, rho, T)\n",
+ " Zav_list.append([Zav])\n",
+ " Zav_metalist.append([Zav_list])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 117,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "for j in range(0, len(T_list)):\n",
+ " plt.plot(rho_list, Zav_metalist[j][0], label=f\"T={T_list[j]:0.1g} eV\")\n",
+ " plt.semilogx()\n",
+ " plt.xlabel(r'$\\rho$ (g/cc)')\n",
+ " plt.ylabel(r'$Z_{av}$')\n",
+ " plt.legend()\n",
+ " \n",
+ " \n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true
+ },
+ "source": [
+ "#### Failed attempt at plotting the 50% ionisation line in the T-n diagram"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true,
+ "hidden": true
+ },
+ "source": [
+ "##### Test:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 182,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": [
+ "Z = 13\n",
+ "A = 27\n",
+ "rho = 1e-2 #[g/cc]\n",
+ "\n",
+ "def func(Tx):\n",
+ " return Zion_TF(Z, A, rho, Tx) - Z/2 #When this is 0, it means 50% ionisation: Zav = Z/2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 186,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "50% ionisation for T=8e+01 eV\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "array([-8.8817842e-16])"
+ ]
+ },
+ "execution_count": 186,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "root = fsolve(func, x0=1e-2)\n",
+ "print(f\"50% ionisation for T={root[0]:0.1g} eV\")\n",
+ "func(root) #This should be 0, if the root is correct"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "heading_collapsed": true,
+ "hidden": true
+ },
+ "source": [
+ "##### 50% ionisation line in T-n space"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 202,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ ":28: RuntimeWarning: invalid value encountered in power\n",
+ " Ac = a1*T1**a2 + a3*T1**a4\n"
+ ]
+ }
+ ],
+ "source": [
+ "Z = 1\n",
+ "A = 1\n",
+ "rho_list = np.logspace(-10,2,101)\n",
+ "\n",
+ "rho_50percent_list = []\n",
+ "T_50percent_list = []\n",
+ "for rho in rho_list:\n",
+ " def func(Tx):\n",
+ " return Zion_TF(Z, A, rho, Tx) - Z/2 #When this is 0, it means 50% ionisation: Zav = Z/2\n",
+ " root = fsolve(func, x0=1e-2) \n",
+ "# print (f\"For rho={rho:0.1g} [g/cc], the estimation is {func(root)}, which should be close to 0\")\n",
+ " root_list.append([root])\n",
+ " if abs(func(root)[0])<0.1:\n",
+ " rho_50percent_list.append(rho)\n",
+ " T_50percent_list.append(root[0])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 203,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAh8AAAGdCAYAAACyzRGfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAVJElEQVR4nO3df6yVBf3A8c8F4wp271FgcLnzIrQoUxR/YORPdCmNGJk2lz9yZKtFoYDkEqYFGnDDmvkHlcMa4RjqHw1zs5asKebEAtTmWKkkEybeqHT3AOUl4fn+odyvV678yHM+5x57vbbnj/Oc557n4549O2+f85xDQ1EURQAAJOlX6wEAgP8t4gMASCU+AIBU4gMASCU+AIBU4gMASCU+AIBU4gMASHVUrQd4t3379sX27dujqakpGhoaaj0OAHAYiqKInTt3Rmtra/Trd/BrG30uPrZv3x5tbW21HgMA+C9s27Ytjj/++INu0+fio6mpKSLeGr65ubnG0wAAh6NcLkdbW1v3+/jB9Ln42P9RS3Nzs/gAgDpzOLdMuOEUAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVEccH48//nhMnTo1Wltbo6GhIR588MEezxdFEQsWLIjW1tYYOHBgXHjhhbFp06aKDQwA1Lcjjo/du3fHuHHjYunSpb0+f8cdd8Sdd94ZS5cujfXr10dLS0tccsklsXPnzvc9LABQ/4460j+YPHlyTJ48udfniqKIu+66K2655Za4/PLLIyJixYoVMXz48Fi1alV8/etff3/TAgB1r6L3fGzZsiU6Ojpi0qRJ3esaGxtj4sSJ8eSTT/b6N11dXVEul3ssAMAHV0Xjo6OjIyIihg8f3mP98OHDu597t/b29iiVSt1LW1tbJUcCAPqYqnzbpaGhocfjoigOWLffvHnzorOzs3vZtm1bNUYCAPqII77n42BaWloi4q0rICNGjOhev2PHjgOuhuzX2NgYjY2NlRwDAOjDKnrlY/To0dHS0hJr1qzpXrdnz55Yu3ZtnHPOOZXcFQBQp474yseuXbti8+bN3Y+3bNkSzz77bAwePDhGjhwZs2fPjsWLF8eYMWNizJgxsXjx4hg0aFBcffXVFR0cAKhPRxwfGzZsiIsuuqj78Zw5cyIiYtq0afGLX/wivv3tb8e///3v+OY3vxmvv/56TJgwIR555JFoamqq3NQAQN1qKIqiqPUQ71Qul6NUKkVnZ2c0NzfXehwA4DAcyfu3f9sFAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEglPgCAVOIDAEhV8fh4880349Zbb43Ro0fHwIED4yMf+UjcfvvtsW/fvkrvCgCoQ0dV+gWXLFkSd999d6xYsSJOPvnk2LBhQ1x33XVRKpVi1qxZld4dAFBnKh4f69ati0svvTSmTJkSERGjRo2K++67LzZs2FDpXQEAdajiH7ucd9558bvf/S5eeOGFiIj405/+FE888UR89rOf7XX7rq6uKJfLPRYA4IOr4lc+br755ujs7IwTTzwx+vfvH3v37o1FixbFVVdd1ev27e3tcdttt1V6DACgj6r4lY8HHnggVq5cGatWrYqnn346VqxYET/84Q9jxYoVvW4/b9686Ozs7F62bdtW6ZEAgD6koSiKopIv2NbWFnPnzo0ZM2Z0r1u4cGGsXLky/vKXvxzy78vlcpRKpejs7Izm5uZKjgYAVMmRvH9X/MrHv/71r+jXr+fL9u/f31dtAYCIqMI9H1OnTo1FixbFyJEj4+STT45nnnkm7rzzzvjKV75S6V0BAHWo4h+77Ny5M77zne/E6tWrY8eOHdHa2hpXXXVVfPe7340BAwYc8u997AIA9edI3r8rHh/vl/gAgPpT03s+AAAORnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKnEBwCQSnwAAKmqEh+vvPJKfOlLX4ohQ4bEoEGD4rTTTouNGzdWY1cAQJ05qtIv+Prrr8e5554bF110UfzmN7+JYcOGxV//+tc49thjK70rAKAOVTw+lixZEm1tbbF8+fLudaNGjar0bgCAOlXxj10eeuihGD9+fFxxxRUxbNiwOP300+Oee+55z+27urqiXC73WACAD66Kx8dLL70UP/3pT2PMmDHx29/+NqZPnx4zZ86Me++9t9ft29vbo1QqdS9tbW2VHgkA6EMaiqIoKvmCAwYMiPHjx8eTTz7ZvW7mzJmxfv36WLdu3QHbd3V1RVdXV/fjcrkcbW1t0dnZGc3NzZUcDQCoknK5HKVS6bDevyt+5WPEiBFx0kkn9Vj3iU98IrZu3drr9o2NjdHc3NxjAQA+uCoeH+eee248//zzPda98MILccIJJ1R6VwBAHap4fNx4443x1FNPxeLFi2Pz5s2xatWqWLZsWcyYMaPSuwIA6lDF4+Oss86K1atXx3333Rdjx46N733ve3HXXXfFNddcU+ldAQB1qOI3nL5fR3LDCgDQN9T0hlMAgIMRHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAqqrHR3t7ezQ0NMTs2bOrvSsAoA5UNT7Wr18fy5Yti1NPPbWauwEA6kjV4mPXrl1xzTXXxD333BPHHXdctXYDANSZqsXHjBkzYsqUKXHxxRcfdLuurq4ol8s9FgDgg+uoarzo/fffH08//XSsX7/+kNu2t7fHbbfdVo0xAIA+qOJXPrZt2xazZs2KlStXxtFHH33I7efNmxednZ3dy7Zt2yo9EgDQhzQURVFU8gUffPDBuOyyy6J///7d6/bu3RsNDQ3Rr1+/6Orq6vHcu5XL5SiVStHZ2RnNzc2VHA0AqJIjef+u+Mcun/70p+O5557rse66666LE088MW6++eaDhgcA8MFX8fhoamqKsWPH9lh3zDHHxJAhQw5YDwD87/ELpwBAqqp82+XdHnvssYzdAAB1wJUPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACCV+AAAUokPACBVxeOjvb09zjrrrGhqaophw4bF5z//+Xj++ecrvRsAoE5VPD7Wrl0bM2bMiKeeeirWrFkTb775ZkyaNCl2795d6V0BAHWooSiKopo7+Pvf/x7Dhg2LtWvXxgUXXHDI7cvlcpRKpejs7Izm5uZqjgYAVMiRvH8fVe1hOjs7IyJi8ODBvT7f1dUVXV1d3Y/L5XK1RwIAaqiqN5wWRRFz5syJ8847L8aOHdvrNu3t7VEqlbqXtra2ao4EANRYVT92mTFjRjz88MPxxBNPxPHHH9/rNr1d+Whra/OxCwDUkT7xscsNN9wQDz30UDz++OPvGR4REY2NjdHY2FitMQCAPqbi8VEURdxwww2xevXqeOyxx2L06NGV3gUAUMcqHh8zZsyIVatWxa9+9atoamqKjo6OiIgolUoxcODASu8OAKgzFb/no6Ghodf1y5cvjy9/+cuH/HtftQWA+lPTez6q/LMhAECdq/rvfByp/fHi9z4AoH7sf98+nIsQfS4+du7cGRHh9z4AoA7t3LkzSqXSQbep+s+rH6l9+/bF9u3bo6mp6T3vH+lL9v8uybZt29yj0sc5VvXF8aovjld9qcbxKooidu7cGa2trdGv38F/w7TPXfno16/fQX8XpK9qbm52wtUJx6q+OF71xfGqL5U+Xoe64rFfVX9eHQDg3cQHAJCq/4IFCxbUeoh6179//7jwwgvjqKP63KdYvItjVV8cr/rieNWXWh6vPnfDKQDwweZjFwAglfgAAFKJDwAglfgAAFKJj//SokWL4pxzzolBgwbFscce2+s2W7dujalTp8YxxxwTQ4cOjZkzZ8aePXuSJ+W9jBo1KhoaGnosc+fOrfVYvO0nP/lJjB49Oo4++ug488wz4/e//32tR6IXCxYsOOA8amlpqfVYvO3xxx+PqVOnRmtrazQ0NMSDDz7Y4/miKGLBggXR2toaAwcOjAsvvDA2bdpU9bnEx39pz549ccUVV8Q3vvGNXp/fu3dvTJkyJXbv3h1PPPFE3H///fHLX/4yvvWtbyVPysHcfvvt8eqrr3Yvt956a61HIiIeeOCBmD17dtxyyy3xzDPPxPnnnx+TJ0+OrVu31no0enHyySf3OI+ee+65Wo/E23bv3h3jxo2LpUuX9vr8HXfcEXfeeWcsXbo01q9fHy0tLXHJJZd0/ztrVVPwvixfvrwolUoHrP/1r39d9OvXr3jllVe61913331FY2Nj0dnZmTki7+GEE04ofvSjH9V6DHrxyU9+spg+fXqPdSeeeGIxd+7cGk3Ee5k/f34xbty4Wo/BYYiIYvXq1d2P9+3bV7S0tBTf//73u9e98cYbRalUKu6+++6qzuLKR5WsW7cuxo4dG62trd3rPvOZz0RXV1ds3LixhpPxTkuWLIkhQ4bEaaedFosWLfKxWB+wZ8+e2LhxY0yaNKnH+kmTJsWTTz5Zo6k4mBdffDFaW1tj9OjRceWVV8ZLL71U65E4DFu2bImOjo4e51pjY2NMnDix6uean6Grko6Ojhg+fHiPdccdd1wMGDAgOjo6ajQV7zRr1qw444wz4rjjjos//vGPMW/evNiyZUv87Gc/q/Vo/9P+8Y9/xN69ew84f4YPH+7c6YMmTJgQ9957b3zsYx+Lv/3tb7Fw4cI455xzYtOmTTFkyJBaj8dB7D+fejvXXn755aru25WPd+jtxql3Lxs2bDjs12toaDhgXVEUva6nMo7kGN54440xceLEOPXUU+OrX/1q3H333fHzn/88/vnPf9b4v4KIA88f507fNHny5PjCF74Qp5xySlx88cXx8MMPR0TEihUrajwZh6sW55orH+9w/fXXx5VXXnnQbUaNGnVYr9XS0hJ/+MMfeqx7/fXX4z//+c8BlUnlvJ9j+KlPfSoiIjZv3uz/2Gpo6NCh0b9//wOucuzYscO5UweOOeaYOOWUU+LFF1+s9Sgcwv5vJXV0dMSIESO612eca+LjHYYOHRpDhw6tyGudffbZsWjRonj11Ve7D+ojjzwSjY2NceaZZ1ZkHxzo/RzDZ555JiKix0lIvgEDBsSZZ54Za9asicsuu6x7/Zo1a+LSSy+t4WQcjq6urvjzn/8c559/fq1H4RBGjx4dLS0tsWbNmjj99NMj4q17rtauXRtLliyp6r7Fx39p69at8dprr8XWrVtj79698eyzz0ZExEc/+tH48Ic/HJMmTYqTTjoprr322vjBD34Qr732Wtx0003xta99LZqbm2s8PevWrYunnnoqLrrooiiVSrF+/fq48cYb43Of+1yMHDmy1uP9z5szZ05ce+21MX78+Dj77LNj2bJlsXXr1pg+fXqtR+Ndbrrpppg6dWqMHDkyduzYEQsXLoxyuRzTpk2r9WhExK5du2Lz5s3dj7ds2RLPPvtsDB48OEaOHBmzZ8+OxYsXx5gxY2LMmDGxePHiGDRoUFx99dXVHayq36X5AJs2bVoREQcsjz76aPc2L7/8cjFlypRi4MCBxeDBg4vrr7++eOONN2o3NN02btxYTJgwoSiVSsXRRx9dfPzjHy/mz59f7N69u9aj8bYf//jHxQknnFAMGDCgOOOMM4q1a9fWeiR68cUvfrEYMWJE8aEPfahobW0tLr/88mLTpk21Hou3Pfroo72+V02bNq0oire+bjt//vyipaWlaGxsLC644ILiueeeq/pcDUVRFNXNGwCA/+fbLgBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKQSHwBAKvEBAKT6P5PW/H5pmw9WAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(np.log10(rho_50percent_list), np.log10(T_50percent_list), color='red', linewidth=3)\n",
+ "plt.xlim([-12, 11])\n",
+ "plt.ylim([1.8, 11.2])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hidden": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/hack/LIHEDP_notebooks/critical density.ipynb b/hack/LIHEDP_notebooks/critical density.ipynb
new file mode 100644
index 0000000..7e5e8f9
--- /dev/null
+++ b/hack/LIHEDP_notebooks/critical density.ipynb
@@ -0,0 +1,140 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Import useful modules"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from scipy import constants as sc"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def sciprint(a):\n",
+ " print(f\"{a:0.2g}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Critical density"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "\\boxed{\n",
+ "n_C = \\frac{m_0 \\epsilon_0 \\omega^2}{e^2}\n",
+ "}\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Radiowaves refraction on the ionisphere"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.1e+11\n"
+ ]
+ }
+ ],
+ "source": [
+ "f = 5*1e6\n",
+ "w = 2*sc.pi*f\n",
+ "\n",
+ "n_c = sc.m_e * sc.epsilon_0 * w**2 / sc.e**2\n",
+ "sciprint(n_c)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Laser-Plasma"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1.1e+21\n"
+ ]
+ }
+ ],
+ "source": [
+ "sciprint(sc.m_e * sc.epsilon_0 * (2*sc.pi * sc.c)**2 / sc.e**2 *1e6)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "\\boxed{\n",
+ "n_C \\text{ [cm$^{-3}$]} = 1.1 \\times 10^{21} \\left( \\frac{1}{\\lambda \\text{ [µm]}} \\right)^2\n",
+ "}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}