diff --git a/week8/nmap8.ipynb b/week8/nmap8.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..644864d5c69f54f237a8a24ea0a7578a5d31df58 --- /dev/null +++ b/week8/nmap8.ipynb @@ -0,0 +1,2522 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "incomplete-medline", + "metadata": {}, + "source": [ + "<h1 style=\"text-align: center; vertical-align: middle;\">Numerical Methods in Accelerator Physics</h1>\n", + "<h2 style=\"text-align: center; vertical-align: middle;\">Python examples -- Week 8</h2>" + ] + }, + { + "cell_type": "markdown", + "id": "executive-television", + "metadata": {}, + "source": [ + "<h2>Run this first!</h2>\n", + "\n", + "Imports and modules:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "biological-product", + "metadata": {}, + "outputs": [], + "source": [ + "from config8 import (np, plt, sys, Madx, interp1d, PyNAFF, pysixtrack, elements, M_drift, M_dip_x, M_dip_y, M_quad_x, M_quad_y, track, track_sext_4D)\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "id": "58404467-c2fd-491c-87f5-42848bd0e7d9", + "metadata": {}, + "source": [ + "<h2>Twiss parameters</h2>\n", + "<h3>Compute Twiss parameters</h3>\n", + "\n", + "Use the Methodical Accelerator Design (`MAD-X`) code to compute the optical Twiss function (install `cpymad` via pip):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "734808ec-8325-4524-bb69-f80ffdcdeb88", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " ++++++++++++++++++++++++++++++++++++++++++++\n", + " + MAD-X 5.09.03 (64 bit, Darwin) +\n", + " + Support: mad@cern.ch, http://cern.ch/mad +\n", + " + Release date: 2024.04.25 +\n", + " + Execution date: 2024.12.11 12:41:32 +\n", + " ++++++++++++++++++++++++++++++++++++++++++++\n" + ] + } + ], + "source": [ + "madx = Madx(stdout=sys.stdout)" + ] + }, + { + "cell_type": "markdown", + "id": "e3835284-fe11-44e9-a7c3-b6b0909cdd8d", + "metadata": {}, + "source": [ + "Define the following periodic beam line of $10$m length:\n", + "- focusing quadrupole centred at $3$m (strength $k=0.1$m$^{-2}$ and length $L=0.6$m)\n", + "- dipole sector bend centred at $5$m (bending angle $\\theta=\\pi/8$ and length $L=0.6$m)\n", + "- defocusing quadrupole centred at $7$m (strength $k=-0.5$m$^{-2}$ and length $L=0.4$m)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "cdd4c0b3-4476-4570-a8fe-403f8899f457", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input('''\n", + "k1l_f := 0.1 * 0.6; // inverse focal length qf\n", + "k1l_d := -0.5 * 0.4; // inverse focal length qd\n", + "\n", + "qf: quadrupole, l = 0.6, k1 := k1l_f / 0.6;\n", + "qd: quadrupole, l = 0.4, k1 := k1l_d / 0.4;\n", + "dip: sbend, l = 0.6, angle := pi / 8;\n", + "\n", + "seq1: sequence, l = 10;\n", + "qf, at = 3;\n", + "dip, at = 5;\n", + "qd, at = 7;\n", + "endsequence;\n", + "''')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "e5487b92-0634-4a6a-98d1-51a7edbfaf83", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.command.beam(particle='proton', energy=1) # energy is in GeV!\n", + "madx.use(sequence='seq1')\n", + "\n", + "# output the Twiss parameters every 0.1m\n", + "madx.command.select(flag=\"interpolate\", sequence=\"seq1\", step=0.1)" + ] + }, + { + "cell_type": "markdown", + "id": "df47119a-fa79-4414-9c68-72bf9ba82712", + "metadata": {}, + "source": [ + "Now we compute the periodic solution to the Hill equation (in terms of the Twiss paremters):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "695d7753-4b13-43e3-a7ee-e05e8ddf7646", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "enter Twiss module\n", + " \n", + "iteration: 1 error: 0.000000E+00 deltap: 0.000000E+00\n", + "orbit: 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00\n", + "\n", + "++++++ table: summ\n", + "\n", + " length orbit5 alfa gammatr \n", + " 10 -0 0.09572878063 3.232054955 \n", + "\n", + " q1 dq1 betxmax dxmax \n", + " 0.2393933525 -0.4979445041 11.70243519 7.345182369 \n", + "\n", + " dxrms xcomax xcorms q2 \n", + " 6.588466214 0 0 0.2224798695 \n", + "\n", + " dq2 betymax dymax dyrms \n", + " -0.1070464578 11.39223223 0 0 \n", + "\n", + " ycomax ycorms deltap synch_1 \n", + " 0 0 0 0 \n", + "\n", + " synch_2 synch_3 synch_4 synch_5 \n", + " 0 0 0 0 \n", + "\n", + " synch_6 synch_8 nflips dqmin \n", + " 0 0 0 0 \n", + "\n", + " dqmin_phase \n", + " 0 \n" + ] + } + ], + "source": [ + "twiss = madx.twiss();" + ] + }, + { + "cell_type": "markdown", + "id": "7bd4cca0-a4e5-40a9-b1b4-3f63c5402374", + "metadata": {}, + "source": [ + "Let us investigate the optical functions along this periodic beam line: (red areas mark quadrupoles, gray areas mark dipoles)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "76bd8d6d-d385-41da-8c6f-b2b09743e611", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(twiss['s'], twiss['betx'], label=r'$\\beta_x$ [m]')\n", + "plt.plot(twiss['s'], twiss['bety'], label=r'$\\beta_y$ [m]')\n", + "plt.plot(twiss['s'], twiss['alfx'], label=r'$\\alpha_x$ [1]', c='C0', ls='--')\n", + "plt.plot(twiss['s'], twiss['alfy'], label=r'$\\alpha_y$ [1]', c='C1', ls='--')\n", + "\n", + "ylim = plt.ylim()\n", + "plt.fill_betweenx(ylim, 3-0.3, 3+0.3, color='red', alpha=0.2)\n", + "plt.fill_betweenx(ylim, 7-0.2, 7+0.2, color='red', alpha=0.2)\n", + "plt.fill_betweenx(ylim, 5-0.3, 5+0.3, color='black', alpha=0.2)\n", + "plt.ylim(ylim)\n", + "\n", + "plt.xlabel('$s$ [m]')\n", + "plt.ylabel(r'$\\beta_{x,y}$ and $\\alpha_{x,y}$')\n", + "plt.legend(loc='upper left', bbox_to_anchor=(1.05, 1));" + ] + }, + { + "cell_type": "markdown", + "id": "a3d66a59-524e-412a-8c76-314d4ee68220", + "metadata": {}, + "source": [ + "$\\implies$ periodic functions, right values at $s=10$m are equal to left values at $s=0$m!<br />\n", + "$\\implies$ $\\beta_{x,y}$ functions change sign of gradient at locations of the quadrupoles!<br />\n", + "$\\implies$ Dipole affects horizontal plane due to dispersion!" + ] + }, + { + "cell_type": "markdown", + "id": "67a77045-9dcf-4cbe-8fcc-0d0e337e9f6c", + "metadata": {}, + "source": [ + "<h3>Compare tracking with Twiss and betatron matrices</h3>\n", + "\n", + "We provide interpolation functions for any position $s$ given the `MAD-X` computed Twiss table $s-\\beta_{x,y}-\\alpha_{x,y}-\\psi_{x,y}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "817df1db-389c-4903-a160-e72c91ffbab6", + "metadata": {}, + "outputs": [], + "source": [ + "beta_x = interp1d(twiss['s'], twiss['betx'], kind='linear')\n", + "alpha_x = interp1d(twiss['s'], twiss['alfx'], kind='linear')\n", + "psi_x = interp1d(twiss['s'], 2 * np.pi * twiss['mux'], kind='linear')" + ] + }, + { + "cell_type": "markdown", + "id": "8d9e1d88-ac6a-4531-84d5-fd96b4ebf190", + "metadata": {}, + "source": [ + "Define the Floquet transformation matrix and the rotation matrix for the Twiss transport matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "190cc457-9e47-4f9f-a5ed-5f1278e78baa", + "metadata": {}, + "outputs": [], + "source": [ + "def F(beta, alpha):\n", + " '''Floquet transformation matrix to normalized phase space.'''\n", + " return np.array([\n", + " [1 / np.sqrt(beta), 0],\n", + " [alpha / np.sqrt(beta), np.sqrt(beta)]\n", + " ])\n", + "\n", + "def R(angle):\n", + " '''Rotation matrix.'''\n", + " return np.array([\n", + " [np.cos(angle), np.sin(angle)],\n", + " [-np.sin(angle), np.cos(angle)]\n", + " ])\n", + "\n", + "def M_tw(beta0, alpha0, beta1, alpha1, delta_psi):\n", + " '''Transport matrix with Twiss parameters from index 0 to 1.'''\n", + " F0 = F(beta0, alpha0)\n", + " F1 = F(beta1, alpha1),\n", + " F1inv = np.linalg.inv(F1)\n", + " Rot = R(delta_psi)\n", + " return F1inv.dot(Rot.dot(F0))" + ] + }, + { + "cell_type": "markdown", + "id": "65978195-c651-4a23-ab3d-ec267e2f0e5c", + "metadata": {}, + "source": [ + "Prepare the tracking of a particle along this periodic beam line: once with betatron matrices from each element, once with the Twiss matrix!" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "fa4fb2e2-2f47-43a6-a6a4-4216642f4a6b", + "metadata": {}, + "outputs": [], + "source": [ + "# path length positions at edges of elements\n", + "s = [0, 3 - 0.6/2, 3 + 0.6/2, 5 - 0.6/2, 5 + 0.6/2, 7 - 0.4/2, 7 + 0.4/2, 10]\n", + "ds = np.diff(s)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "4c001052-5624-4962-a745-2759a55edc16", + "metadata": {}, + "outputs": [], + "source": [ + "# betatron matrices\n", + "d1 = M_drift(ds[0])\n", + "qf = M_quad_x(ds[1], 0.1)\n", + "d2 = M_drift(ds[2])\n", + "dip = M_dip_x(ds[3], 0.6 / (np.pi / 8)) # rho0 = L / angle\n", + "d3 = M_drift(ds[4])\n", + "qd = M_quad_x(ds[5], -0.5)\n", + "d4 = M_drift(ds[6])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "face3784-b9b0-49ec-846d-5266a18c1e11", + "metadata": {}, + "outputs": [], + "source": [ + "# Twiss transport matrix\n", + "def M_tw_s0to1_x(s0, s1):\n", + " '''Twiss matrix from s0 to s1 (evaluating Twiss parameters at these points!).'''\n", + " return M_tw(\n", + " beta_x(s0), alpha_x(s0),\n", + " beta_x(s1), alpha_x(s1),\n", + " psi_x(s1) - psi_x(s0)\n", + " )[0]" + ] + }, + { + "cell_type": "markdown", + "id": "8990868f-7ad5-49e0-8856-b66863b002a4", + "metadata": {}, + "source": [ + "The initial horizontal coordinates of the particles at $s=0$m:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e86209bd-deb3-4187-b010-a9703580c992", + "metadata": {}, + "outputs": [], + "source": [ + "x_ini = 0.02\n", + "xp_ini = 0.01" + ] + }, + { + "cell_type": "markdown", + "id": "3545573f-710b-4647-a385-804fe2f73684", + "metadata": {}, + "source": [ + "Some plotting helper functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "46dad3e9-fa2e-40f8-8bfc-f070e9e8c394", + "metadata": {}, + "outputs": [], + "source": [ + "def scatter(s, x, label=None):\n", + " plt.scatter([s], [x], c='red', s=30, marker='D', label=label)\n", + "\n", + "def scatter_tw(s, x, label=None):\n", + " plt.scatter([s], [x], c='cyan', s=40, marker='.', label=label)" + ] + }, + { + "cell_type": "markdown", + "id": "931f809f-4575-49a5-91ab-51ae0500f675", + "metadata": {}, + "source": [ + "Go for the tracking!" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "fb425668-5e79-4d41-85e1-9861d60d1f88", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# track with betatron matrices from one element to the next:\n", + "scatter(0, x_ini, label='betatron matrix')\n", + "\n", + "x, xp = track(d1, x_ini, xp_ini)\n", + "scatter(s[1], x)\n", + "\n", + "x, xp = track(qf, x, xp)\n", + "scatter(s[2], x)\n", + "\n", + "x, xp = track(d2, x, xp)\n", + "scatter(s[3], x)\n", + "\n", + "x, xp = track(dip, x, xp)\n", + "scatter(s[4], x)\n", + "\n", + "x, xp = track(d3, x, xp)\n", + "scatter(s[5], x)\n", + "\n", + "x, xp = track(qd, x, xp)\n", + "scatter(s[6], x)\n", + "\n", + "x, xp = track(d4, x, xp)\n", + "scatter(s[7], x)\n", + "\n", + "# track with the Twiss transport matrix\n", + "scatter_tw(0, x_ini, label='Twiss matrix')\n", + "xt, xpt = x_ini, xp_ini\n", + "for i in range(len(s) - 1):\n", + " M_tw_x = M_tw_s0to1_x(s[i], s[i + 1])\n", + " xt, xpt = track(M_tw_x, xt, xpt)\n", + " scatter_tw(s[i + 1], xt)\n", + "\n", + "plt.xlabel('$s$ [m]')\n", + "plt.ylabel('$x$ [m]')\n", + "plt.legend(loc='lower right');" + ] + }, + { + "cell_type": "markdown", + "id": "75551d47-4e4d-4b78-afb9-70c1686ae8bb", + "metadata": {}, + "source": [ + "$\\implies$ the transfer maps via the Twiss parameters $\\beta_x(s)$, $\\alpha_x(s)$, $\\gamma_x(s)$ are identical to the element-by-element betatron matrices from the previous lecture! Both correctly describe the solution to the equation of motion (Hill differential equation!).<br />\n", + "$\\implies$ the advantage with $\\mathcal{M}_\\mathrm{tw}$: only require one single matrix to describe solution at any location $s$! (Need to determine the optics functions / Twiss parameters before!)<br />\n", + "$\\implies$ matrices are not identical in case of an unstable lattice." + ] + }, + { + "cell_type": "markdown", + "id": "ca54647e-b245-4069-95b3-848daad2a8c2", + "metadata": {}, + "source": [ + "<h3>Determine the Tune from tracking and compare to computed phase advance</h3>\n", + "\n", + "Let us track a particle with the compiled betatron matrix for a number of periods. We can determine the tune via Discrete Frequency Analysis (using NAFF) and then compare to the phase advance computed via the Twiss matrix approach:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "b1900574-4686-4834-b179-4c83469835c9", + "metadata": {}, + "outputs": [], + "source": [ + "M_period = qf.dot(d1)\n", + "M_period = d2.dot(M_period)\n", + "M_period = dip.dot(M_period)\n", + "M_period = d3.dot(M_period)\n", + "M_period = qd.dot(M_period)\n", + "M_period = d4.dot(M_period)" + ] + }, + { + "cell_type": "markdown", + "id": "dfd6e1ef-f2f5-44d8-bec6-1ad7ef7bcfee", + "metadata": {}, + "source": [ + "We need to record the oscillation for a useful number of turns:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "535f5877-c1f4-4c01-99ea-a95ed84ecb64", + "metadata": {}, + "outputs": [], + "source": [ + "nperiods = 128" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "983ffd8c-8507-4606-9531-6d3819409ea0", + "metadata": {}, + "outputs": [], + "source": [ + "rec_x = np.zeros(nperiods, dtype=float)\n", + "rec_x[0] = x_ini" + ] + }, + { + "cell_type": "markdown", + "id": "6a95a346-81ea-4539-ac13-a1b598e82c62", + "metadata": {}, + "source": [ + "Tracking:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "d9685288-d349-4ddf-bec1-9a38e9d6a8fc", + "metadata": {}, + "outputs": [], + "source": [ + "x, xp = x_ini, xp_ini\n", + "for i in range(1, nperiods):\n", + " x, xp = track(M_period, x, xp)\n", + " rec_x[i] = x" + ] + }, + { + "cell_type": "markdown", + "id": "59c8d757-2e23-4c87-ae78-18348f0e0777", + "metadata": {}, + "source": [ + "The horizontal motion at this location looks as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "c457d9dc-40fc-4704-a3af-401c4d80f0b4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(rec_x)\n", + "plt.xlabel('Periods')\n", + "plt.ylabel('$x$ [m]');" + ] + }, + { + "cell_type": "markdown", + "id": "de69eacf-b890-4f85-a288-0ac8eecea8e1", + "metadata": {}, + "source": [ + "We determine the tune via the `PyNAFF` library which implements the Numerical Analysis of Fundamental Frequencies algorithm:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "6ef79bf6-0217-4954-a3cc-9349fd071bcf", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.239334575934871" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tune = PyNAFF.naff(rec_x, turns = nperiods, nterms = 1)[0, 1]\n", + "tune" + ] + }, + { + "cell_type": "markdown", + "id": "d348ac71-7ae6-4899-8bce-b0d6ca536eb8", + "metadata": {}, + "source": [ + "$\\implies$ this is the tune of the particle (number of oscillations per period) measured via tracking data!\n", + "\n", + "Now what about the phase advance from the full-period transfer matrix, $2 \\cos(\\Phi_x)=\\mathrm{Tr}(\\mathcal{M})$?" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "39c75299-76c2-4309-961b-849e20009828", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.5041527952010787" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trace = np.matrix.trace(M_period)\n", + "\n", + "np.arccos(trace / 2)" + ] + }, + { + "cell_type": "markdown", + "id": "31237ac0-169b-4851-8d3c-393ebd51b611", + "metadata": {}, + "source": [ + "Convert from phase advance to tune units by dividing by $2\\pi$:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "f2937733-ebba-497e-a4e9-da843687dc3e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.23939335252174299" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.arccos(trace / 2) / (2 * np.pi)" + ] + }, + { + "cell_type": "markdown", + "id": "021566ed-3ca7-46dc-a3f5-194919cb093a", + "metadata": {}, + "source": [ + "$\\implies$ the particle follows the same frequency as determined via the Twiss matrix approach!\n", + "\n", + "This was also computed by `MAD-X`:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "9ba0c026-fbef-469a-bbb7-a7463aa9114f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.2393933525" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "twiss.summary['q1']" + ] + }, + { + "cell_type": "markdown", + "id": "2fe54f2f-f6cc-4d0b-aee0-f8ec9c7f6e4b", + "metadata": {}, + "source": [ + "<h3>Exercise: Periodic transport matrices</h3>\n", + "\n", + "Consider the following numerical (horizontal) transport matrices, each for a full period of a lattice.\n", + "\n", + "<p style=\"color:#e6541a;\">Can you determine:</p>\n", + "\n", + "<p style=\"color:#e6541a;\">\n", + "a) whether they are valid transport matrices (symplecticity)?<br />\n", + "b) whether they provide stable transport?<br />\n", + "c) the covered phase advance $\\Phi_x$ per lattice period (and the tune $Q_x=\\Phi_x\\,/\\,2\\pi$)?<br />\n", + "d) the local Twiss parameters $\\beta_x, \\alpha_x$?\n", + "</p>\n", + "\n", + "<p style=\"color:#e6541a;\">\n", + "How do the eigenvalues represent stability and phase advance? (check absolute values and complex phases, picture on the unit circle)</p>\n", + "\n", + "<i>Hint: you might need the following functions for a given matrix `M`:</i>\n", + "\n", + "- determinant: `np.linalg.det(M)`\n", + "- trace: `np.matrix.trace(M)`\n", + "- eigenvalues: `np.linalg.eigvals(M)`\n", + "- arccos: `np.arccos(...)`\n", + "- sin: `np.sin(...)`\n", + "- absolute value: `np.abs(...)`\n", + "- phase $\\phi$ (radiant units) from complex number $e^{i\\phi}$: `np.angle(...)`\n", + "- matrix multiplication $M_1\\cdot M_2$: `np.dot(M1, M2)` or `M1.dot(M2)`" + ] + }, + { + "cell_type": "markdown", + "id": "368e96c1-d417-483d-8339-7e5194d777d4", + "metadata": {}, + "source": [ + "$$\\mathcal{M}_1 = \\begin{pmatrix}\n", + " -0.03701215 & 0.19960535 \\\\\n", + " -5.04003498 & 0.16259319\n", + "\\end{pmatrix}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "b4da55f4-3620-412f-a782-2d23276ed74b", + "metadata": {}, + "outputs": [], + "source": [ + "M1 = np.array([\n", + " [-0.03701215, 0.19960535],\n", + " [-5.04003498, 0.16259319]\n", + "])" + ] + }, + { + "cell_type": "markdown", + "id": "0c13a25e-c04f-4741-b3ef-61735a1e7778", + "metadata": {}, + "source": [ + "$$\\mathcal{M}_2 = \\begin{pmatrix}\n", + " 0.5 & 13 \\\\\n", + " -0.0961538 & -0.5\n", + "\\end{pmatrix}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "19ad28dd-c484-406e-881e-efc790935de3", + "metadata": {}, + "outputs": [], + "source": [ + "M2 = np.array([\n", + " [0.5, 13],\n", + " [-0.09615385, -0.5]\n", + "])" + ] + }, + { + "cell_type": "markdown", + "id": "985f835a-738e-4f89-aec5-42d7dae93ad8", + "metadata": {}, + "source": [ + "<p style=\"color:#e6541a;\">$\\implies$ what happens to particles in this lattice after a short number of lattice periods? (Investigate by applying the transport matrix repetetively.)</p>" + ] + }, + { + "cell_type": "markdown", + "id": "745b84be-31d1-445a-b4ab-5c8a2563aefe", + "metadata": {}, + "source": [ + "$$\\mathcal{M}_3 = \\begin{pmatrix}\n", + " 0.31803855 & 22.193583 \\\\\n", + " -0.1533821 & 0.93858321\n", + "\\end{pmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "id": "0989ec4c-8395-4cca-8573-fb707943a78a", + "metadata": {}, + "source": [ + "$$\\mathcal{M}_3 = \\begin{pmatrix}\n", + " 0.31803855 & 22.193583 \\\\\n", + " -0.1533821 & 0.93858321\n", + "\\end{pmatrix}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "bb0bd07b-34a2-478e-9bb1-4ac053b0ebc9", + "metadata": {}, + "outputs": [], + "source": [ + "M3 = np.array([\n", + " [0.31803855, 22.193583],\n", + " [-0.1533821, 0.93858321]\n", + "])" + ] + }, + { + "cell_type": "markdown", + "id": "f1bb9fba-5478-454a-9c62-13e96ab8a085", + "metadata": {}, + "source": [ + "$$\\mathcal{M}_4 = \\begin{pmatrix}\n", + " -0.75105652 & 0.69069571 \\\\\n", + " -0.02118063 & -1.31197933\n", + "\\end{pmatrix}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "e31d4535-decf-4747-9408-5e3fc5aae1cf", + "metadata": {}, + "outputs": [], + "source": [ + "M4 = np.array([\n", + " [-0.75105652, 0.69069571],\n", + " [-0.02118063, -1.31197933]\n", + "])" + ] + }, + { + "cell_type": "markdown", + "id": "d0a60ba6-7386-49ad-a3f8-a8e29b00f01e", + "metadata": {}, + "source": [ + "<h3>Solution</h3>" + ] + }, + { + "cell_type": "markdown", + "id": "91be4f43-606d-4833-b0f2-7cc02fd8edf8", + "metadata": {}, + "source": [ + "a) Symplecticity? $\\det(\\mathcal{M})=1$" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "19bc0c20-97cf-45fa-b9ec-0503b043c92d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "det(M1)=1.0000000226578842\n", + "det(M2)=1.00000005\n", + "det(M3)=3.702604010227046\n", + "det(M4)=1.0000000001778289\n" + ] + } + ], + "source": [ + "print(\"det(M1)=\"+str(np.linalg.det(M1)))\n", + "print(\"det(M2)=\"+str(np.linalg.det(M2)))\n", + "print(\"det(M3)=\"+str(np.linalg.det(M3)))\n", + "print(\"det(M4)=\"+str(np.linalg.det(M4)))" + ] + }, + { + "cell_type": "markdown", + "id": "3faf8e40-94b3-436b-bd91-0be1b04dd72c", + "metadata": {}, + "source": [ + "$\\implies$ Only $\\mathcal{M}_3$ is not symplectic.\n", + "\n", + "b) Stable transport? $1/2\\cdot|\\mathrm{Tr}(\\mathcal{M})|\\leq1$" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "1f18c7c9-6cee-4b15-8276-02f26f6f15dc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "M1: 0.06279052\n", + "M2: 0.0\n", + "M3: 0.62831088\n", + "M4: 1.031517925\n" + ] + } + ], + "source": [ + "print(\"M1: \"+str(0.5*np.abs(np.matrix.trace(M1))))\n", + "print(\"M2: \"+str(0.5*np.abs(np.matrix.trace(M2))))\n", + "print(\"M3: \"+str(0.5*np.abs(np.matrix.trace(M3))))\n", + "print(\"M4: \"+str(0.5*np.abs(np.matrix.trace(M4))))" + ] + }, + { + "cell_type": "markdown", + "id": "1afd95af-dab7-466e-b2ca-2914102eb390", + "metadata": {}, + "source": [ + "Eigenvalues? $|\\lambda|\\leq1$" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "59c6b991-352e-4ec6-ad3a-3c8ac1d15d53", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "M1: [1.00000001 1.00000001]\n", + "M2: [1.00000002 1.00000002]\n", + "M3: [1.92421517 1.92421517]\n", + "M4: [0.77847795 1.2845579 ]\n" + ] + } + ], + "source": [ + "print(\"M1: \"+str(np.abs(np.linalg.eigvals(M1))))\n", + "print(\"M2: \"+str(np.abs(np.linalg.eigvals(M2))))\n", + "print(\"M3: \"+str(np.abs(np.linalg.eigvals(M3))))\n", + "print(\"M4: \"+str(np.abs(np.linalg.eigvals(M4))))" + ] + }, + { + "cell_type": "markdown", + "id": "596cbd93-12db-4dc8-8e6f-76e89355f802", + "metadata": {}, + "source": [ + "$\\implies$ $\\mathcal{M_3}$ and $\\mathcal{M_4}$ unstable\n", + "\n", + "c) Phase advance per lattice period? $\\Phi=\\arccos(1/2\\cdot\\mathrm{Tr}(\\mathcal{M}))$" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "e68642fd-4246-4860-85c0-1fc03271b191", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Phi1=1.5079644732514834\n", + "Phi2=1.5707963267948966\n", + "Phi3=0.8914162343864628\n", + "Phi4=nan\n" + ] + } + ], + "source": [ + "print(\"Phi1=\"+str(np.arccos(0.5*np.matrix.trace(M1))))\n", + "print(\"Phi2=\"+str(np.arccos(0.5*np.matrix.trace(M2))))\n", + "print(\"Phi3=\"+str(np.arccos(0.5*np.matrix.trace(M3))))\n", + "print(\"Phi4=\"+str(np.arccos(0.5*np.matrix.trace(M4))))" + ] + }, + { + "cell_type": "markdown", + "id": "faa306f1-7109-4085-860b-8d3945eb6328", + "metadata": {}, + "source": [ + "Tune?" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "33172b0c-a809-4174-8982-ce887aad51ad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Q1=0.23999999992493978\n", + "Q1=0.25\n", + "Q1=0.14187330005496912\n", + "Q1=nan\n" + ] + } + ], + "source": [ + "print(\"Q1=\"+str(np.arccos(0.5*np.matrix.trace(M1))/(2*np.pi)))\n", + "print(\"Q1=\"+str(np.arccos(0.5*np.matrix.trace(M2))/(2*np.pi)))\n", + "print(\"Q1=\"+str(np.arccos(0.5*np.matrix.trace(M3))/(2*np.pi)))\n", + "print(\"Q1=\"+str(np.arccos(0.5*np.matrix.trace(M4))/(2*np.pi)))" + ] + }, + { + "cell_type": "markdown", + "id": "7c98db05-7bb8-4cb6-8e19-c7f67762ef11", + "metadata": {}, + "source": [ + "d) local Twiss parameters? $\\beta_x=M_{1,2}/\\sin(\\Phi_x)$, $\\alpha_x=(M_{1,1}-\\cos(\\Phi_x))/\\sin(\\Phi_x)$" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "b0b69245-2fdd-490e-930c-933762f04d6b", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta1=0.2000000043288102\n", + "alpha1=-0.09999999715451934\n", + "beta2=13.0\n", + "alpha2=0.49999999999999994\n", + "beta3=28.52783638214871\n", + "alpha3=-0.39882691605713466\n", + "beta4=nan\n", + "alpha4=nan\n" + ] + } + ], + "source": [ + "print(\"beta1=\"+str(M1[0,1]/np.sin(np.arccos(0.5*np.matrix.trace(M1)))))\n", + "print(\"alpha1=\"+str((M1[0,0]-np.cos(np.arccos(0.5*np.matrix.trace(M1))))/np.sin(np.arccos(0.5*np.matrix.trace(M1)))))\n", + "print(\"beta2=\"+str(M2[0,1]/np.sin(np.arccos(0.5*np.matrix.trace(M2)))))\n", + "print(\"alpha2=\"+str((M2[0,0]-np.cos(np.arccos(0.5*np.matrix.trace(M2))))/np.sin(np.arccos(0.5*np.matrix.trace(M2)))))\n", + "print(\"beta3=\"+str(M3[0,1]/np.sin(np.arccos(0.5*np.matrix.trace(M3)))))\n", + "print(\"alpha3=\"+str((M3[0,0]-np.cos(np.arccos(0.5*np.matrix.trace(M3))))/np.sin(np.arccos(0.5*np.matrix.trace(M3)))))\n", + "print(\"beta4=\"+str(M4[0,1]/np.sin(np.arccos(0.5*np.matrix.trace(M4)))))\n", + "print(\"alpha4=\"+str((M4[0,0]-np.cos(np.arccos(0.5*np.matrix.trace(M4))))/np.sin(np.arccos(0.5*np.matrix.trace(M4)))))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8ead81b8-81aa-4f93-83e9-2fbb2b2b4bd7", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "dac2e2f5-857d-4003-b35f-7d4f25454572", + "metadata": {}, + "source": [ + "Phase of Eigenvalues?" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "33568edf-5462-473b-b275-95bd07b6f2d6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "M1: [ 1.50796447 -1.50796447]\n", + "M2: [ 1.57079633 -1.57079633]\n", + "M3: [ 1.23816803 -1.23816803]\n", + "M4: [3.14159265 3.14159265]\n" + ] + } + ], + "source": [ + "print(\"M1: \"+str(np.angle(np.linalg.eigvals(M1))))\n", + "print(\"M2: \"+str(np.angle(np.linalg.eigvals(M2))))\n", + "print(\"M3: \"+str(np.angle(np.linalg.eigvals(M3))))\n", + "print(\"M4: \"+str(np.angle(np.linalg.eigvals(M4))))" + ] + }, + { + "cell_type": "markdown", + "id": "1a2d32f0-2f63-44f6-b219-9f3e9fd09441", + "metadata": {}, + "source": [ + "$\\implies$ Phase of eigenvalues is equal to phase advance if motion is bounded." + ] + }, + { + "cell_type": "markdown", + "id": "7b20aa58-c8ec-4acd-a2e5-fbea7623981e", + "metadata": {}, + "source": [ + "<h2>FODO cell</h2>\n", + "<h3>Computing optics of a FODO cell</h3>\n", + "\n", + "Consider a $110$m long FODO cell with $3.3$m long quadrupole magnets (LHC scheme). We start with a non-bending FODO cell, i.e. the dipoles switched off. Let us determine the optical functions, again via `MAD-X`:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "7e5d6ade-62cc-4792-9e53-a44435c9edf2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " ++++++++++++++++++++++++++++++++++++++++++++\n", + " + MAD-X 5.09.03 (64 bit, Darwin) +\n", + " + Support: mad@cern.ch, http://cern.ch/mad +\n", + " + Release date: 2024.04.25 +\n", + " + Execution date: 2024.12.11 12:42:59 +\n", + " ++++++++++++++++++++++++++++++++++++++++++++\n" + ] + } + ], + "source": [ + "madx = Madx(stdout = sys.stdout)" + ] + }, + { + "cell_type": "markdown", + "id": "71a68737-5245-4142-8e90-025031e3d863", + "metadata": {}, + "source": [ + "We define the FODO cell with two quadrupoles of opposite strength, $k\\cdot L=0.008\\cdot3.3$m$^{-1}$, and with three dipoles in between each quadrupole. For the moment the dipoles are switched off (their bending angle $\\theta=0$):" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "e12eb1de-f11b-4f5d-9422-b8e094ed1c9e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input('''\n", + "k1l_f := 0.008 * 3.3; // inverse focal length qf\n", + "k1l_d := -0.008 * 3.3; // inverse focal length qd\n", + "theta := 0; // in LHC: 2 * pi / 1232;\n", + "\n", + "qf2: quadrupole, l = 3.3 / 2, k1 := k1l_f / 3.3; // half a focusing quad\n", + "qd: quadrupole, l = 3.3, k1:= k1l_d / 3.3;\n", + "dip: sbend, l = 14.3, angle := theta;\n", + "\n", + "fodo: sequence, l = 110;\n", + "qf2, at = 3.3 / 4;\n", + "dip, at = 12;\n", + "dip, at = 2 * 110 / 8;\n", + "dip, at = 110 / 2 - 12;\n", + "qd, at = 110 / 2;\n", + "dip, at = 110 / 2 + 12;\n", + "dip, at = 6 * 110 / 8;\n", + "dip, at = 110 - 12;\n", + "qf2, at = 110 - 3.3 / 4;\n", + "endsequence;\n", + "''')" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "78e5606d-7840-4cdf-9c9d-34d8eb108478", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.command.beam(particle='proton', energy=7e3) # energy is in GeV!\n", + "madx.use(sequence='fodo')\n", + "\n", + "# output the Twiss parameters every 1m\n", + "madx.command.select(flag=\"interpolate\", sequence=\"fodo\", step=1)" + ] + }, + { + "cell_type": "markdown", + "id": "9dade201-1d7e-4b80-b9e1-04811eacd112", + "metadata": {}, + "source": [ + "We call the TWiss routine to compute the optics:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "d917fc9a-6cd0-4402-bdd5-4a673ad046ba", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "enter Twiss module\n", + " \n", + "iteration: 1 error: 0.000000E+00 deltap: 0.000000E+00\n", + "orbit: 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00\n", + "\n", + "++++++ table: summ\n", + "\n", + " length orbit5 alfa gammatr \n", + " 110 -0 0 0 \n", + "\n", + " q1 dq1 betxmax dxmax \n", + " 0.2518947018 -0.3220961047 186.9084848 0 \n", + "\n", + " dxrms xcomax xcorms q2 \n", + " 0 0 0 0.2518947018 \n", + "\n", + " dq2 betymax dymax dyrms \n", + " -0.3220961047 186.4581481 0 0 \n", + "\n", + " ycomax ycorms deltap synch_1 \n", + " 0 0 0 0 \n", + "\n", + " synch_2 synch_3 synch_4 synch_5 \n", + " 0 0 0 0 \n", + "\n", + " synch_6 synch_8 nflips dqmin \n", + " 0 0 0 0 \n", + "\n", + " dqmin_phase \n", + " 0 \n" + ] + } + ], + "source": [ + "twiss = madx.twiss()" + ] + }, + { + "cell_type": "markdown", + "id": "91c4faf3-63b3-481e-a3c0-273112b8e913", + "metadata": {}, + "source": [ + "Save some values for this FODO cell for later:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "a276f989-81bb-4ff9-b40c-4949005bd4ad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beam->beta = 0.999999991 ;\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input('value, beam->beta;')" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "5430ab05-4f02-46e9-8463-040927f11c70", + "metadata": {}, + "outputs": [], + "source": [ + "qx_fodo = twiss.summary['q1']\n", + "qpx_fodo = twiss.summary['dq1'] * 0.999999991" + ] + }, + { + "cell_type": "markdown", + "id": "7957fec1-a691-4a25-b2e9-06f39369c26a", + "metadata": {}, + "source": [ + "The optics of this FODO cell looks as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "56b3184c-bb9c-4ff9-a3aa-0f84c571886a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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6HdeuXQMSCqGU9gny9fVl9OjRTJs2jfz582dZPq+jU6dO8UVQnIoVK2Jvb09YWBjFihVTFEFxatSowe7du3n8+LGpUk1GpsYJo3q/UWnsrS3iP47V6Vlw6KaKGQlhBpJ2irPPB7UHZs29nApB7feUsXMr4cWjrLmfENnA2dtB/Ov3VBEb2qws1pbyNiizxm29mKOLIIAnL6MYt/Vilt7jzp07hIWFAQmF0Pz58zl79iw7d+7ku+++i48fP36cwYMHm2wfobTENUxIKq44Sq3xg6OjocFPdHR01iSWDvITQBhVHgdr+jVQLt7bcs4f/+AwlTISQmWPLoPvLmXsjRFgbZ/y8cbw5kjQJmpeEhsJx3/JuvsJYeZ+SdK8p6CzDd1ry2iQMB8pNUqwsLDAyckJd3d3evXqxebNm2nevDkAV69excvLK8VrmZqbm1uK8biW9HEFT1JZuSdReqmfgchxPmhcBlurhH9aMTo9vx6WUSGRSx2dofzYzi15dzdjcykGHp7K2Nml8DIga+8rhBn6794zjl4LVMSGNCmLrZVFKmeI1zG1S3XyOVqnfWA2ls/RmqldqmfpPXx8fABwdXWlSJGUG3hYWloycGDCbIKHDx9maU7pZWubBdO8TUTWCAmjy+9kQ+96JVh2/HZ8bOPZe3zUvBxFXO3US0wIUwvwhqs7lLEGww0boGa1Rp/CuVWGznEAMeFw4hdoPTnr7y2EGZlz4Jri43yO1vSuV0KlbHKeDtUL07ZqIWmWkElxhVDFihVfeVziUZTEa4T0ej1dunTBx8eHnTt3Ur58+fjXHj9+TM+ePQkLC2Pt2rWUK1fOyNlnX1IIiSwxtGlZ1py6S1SMYf5qdKxhVGhSp6oqZyaECR2ZDugTPrZxgXqDTXNvt1JQozf8tzohduZ3eGOkobucELnAhXvPOOSrHA36sHEZ7KxlNMiYLLQa8joacSuAXChualxq62ninD9/HgArKyuqV08YpdJoNHz66ad8+OGHzJ07l19+MUyHfvnyJYMHDyYoKIilS5dKEZSETI0TWaKgsy296yrb9W44c4+HIeEqZSSEiQX4wJVtyliDYWDnarocmnwOmkRv+KLD4N+5qR8vRA7zS5J9g/I6WNOvoXlsQilEnKCgIAICDFOXnZ2dUz0uOjqazZs3A9CoUSMcHJQdeZs0aUK9evXYt28fPj4+REdH8/HHH3Pt2jVmzpxJnTp1su6TyKakEBJZZmizslhbJPwTi4rVyVohkXscTToa5AwNhpo2hzxloHpPZez0Egh9mvLxQuQgF/2f8bePcl3ch03KYG8tk2GEeYmbFgewYsUK7ty5k+wYvV7PtGnT4l97//33U7zW559/jl6vZ86cOUyYMIETJ07w9ddfp9i+WkghJLJQYRc7eiYZFVp/+h6PQiJUykgIEwn0hctblbEGwwyNEkytyRdJRoVCZVRI5ApJR4NS6moqhDlI3DHu2bNn9OzZk8WLF3P27FkuX77Mjh078PT0ZNWqVQD069ePevXqpXitmjVr0rJlSw4ePMj27dsZNmwYffr0McnnkR3JYxGRpYY1K8v6M3eJjjU8GY+K1bHwyE0mvltF5cyEyEJHZ5B8NGiYOrnkLQvVe8CFdQmxU4uh4cfgkDf184TIxi7fD+GAd5LRoMZlcLCRtz3C/MSNCNnZ2REeHk5wcDAzZ85MdpxWq2XgwIGMHj36ldfLkycPAEWKFGHkyJHGTzgHkREhkaWKuCYfFVp7+i6Pn8uokMihAq/Bpc3KWP0h6owGxWkyGjSJftxHh8K/89TLR4gsNvuAcjTIzd6K/rI2SJipuEKoffv2zJo1i3r16uHi4oKFhQWOjo5UrFiRfv36sWPHDsaMGRO/P09KFi1axKZNm8iXLx8PHjzg4MGDpvo0siV5NCKy3LBm5dhw5l7CqFCMYa2QjAqJHCnpaJC1k6FltpryloVq3eHihoTY6cXwxsdgn0e9vITIAobRoMeK2AcyGiTMVFRUFH5+fgC4u7vTvn172rdvn6Frbdu2jZ9//pmWLVsyfvx42rVrx+zZs2nevLnRNy+tX78+vr6+rzxm//79r3y9S5cudOnSxZhpvTYZERJZrqirHd3ryKiQyAWeXIfLKYwGmUOxkXRUKOqljAqJHGlOkrVBrvZWvPdGKXWSESIN169fJyYmBjAUQhl19OhRJkyYQM2aNfn5558pXrw4PXr04Nq1a+zcudNY6eY4UggJkxjerCxWFglDuXGjQkLkKEemgV6X8LG1IzT8SL18EstXHqp2U8ZOLZIOciJHuXw/hP1XlaNBHzYug6OMBgkzlbhRQoUKFTJ0jUuXLjFy5EiKFSvGwoULsbW1BWDIkCHY2Ngwd+5coqOjjZJvTiOFkDCJYm72dKudfFRI9hUSOUagb8prg8xhNChO0zHJR4VO/KJePkIY2ewD1xQfu8raIGHm4tYH5c+fP77Jweu4e/cuQ4YMwd7eniVLluDmlrAetWDBgvTu3Rt/f382bNjwiqu8WlRUFKGhoYSGhqLT6dI+IYOio6Pj72Oqwk0KIWEyI1qUSzYqtOCQjAqJHOLwVJKtDWo4QrV0UpSvPFTroYyd/g1eBqqTjxBGdOHes2Sd4gY3KYOTrZVKGQmRtrhCKKPT4kqUKMGJEyc4fvw4xYsXT/b6+PHj8fX1pW/fvhnOccKECdSqVYtatWqluS4oM9asWRN/n0WLFmXZfRKTQkiYTNEUOshtOHOP+89kVEhkc4+vwpVtyliDYeY1GhSn6Zjk+wqdmKNePkIYSdLRoDwO1rzXsJQ6yQiRTnGFRWbWB4mMk0mzwqQ+al6OjWf8iYo1DK1GxeqYf+gGP3SupnJmQmTCkSSjQTYu0FDlTnGpyVsWavSC/9YkxE4vgTc+AccC6uUlRCacuxvMIV/lyOaQJtIpTpi/M2fOqJ1CiooVK5aloz8pGTBgAAMGDDDpPWVESJhUYRc7+tQvoYhtOnuPe0FhKmUkRCY9ugxXdyhjDYeru29QWpp8oRwVigmHf2arlo4QmZV036B8jtb0k7VBQog0SCEkTG5Ys7LYWCb804uO1TP/0A0VMxIiEw7/qPzY1sUwLc6c5SkDNXsrY2d/hxeP1MlHiEzwuhPE0WvK0aChTctiby2jQUKIV5NCSJhcQWdbPOsrn9Rt9vLn7lMZFRLZzMML4POnMtbwY0MxZO6ajAZtojeKMRFw7Gf18hEig2btV44G5XeySfY7RgghUiKFkFDF0GZlsLVK+OcXo9Pzy8HrrzhDCDN06Aflx3ZuhpbZ2YFbKajpqYx5LYMQf1XSESIjTvo95Z8bTxSxYU3LYmdtkcoZQgiRQAohoYoCTrb0a6B8Yrf1nD83A1+qlJEQr8n/LFz7Sxl742OwdVYnn4xo8gVoE7UWjo2Coz+pl48Qr0Gv1/PzPmWnuILONsnWoQohRGqkEBKqMczhTnhqp9MnX/AqhNk6OFn5sX0+qJdNRoPiuJaA2gOUsfOrIOiWKukI8TqOXX/C6dtBitiI5uWwtZLRICFE+kghJFST19GGgW+WUsT+uPAAn0fP1UlIiPS6/Q/4HVLGGn0KNo7q5JMZjT8HS9uEj3UxcGS6evkIkQ56vZ6Z+5StfYu62tGjbvINJYUQIjVSCAlVDW5cFidbZWefWfuvpXK0EGZAr4eDU5Qxx0JQd5A6+WSWc2Go+4EydnE9PJHRWWG+/vYO4IJ/iCI2smV5bCxlNEgIkX5SCAlVudhb8WHjMorY3iuPuZTkF5wQZuPmQbh7Qhlr8gVY2amTjzG8OQqsHBI+1uuStwUXwkzodHpmJnlgViqvPV1qFVUpIyFEdiWFkFDdwDdL4WZvpYjN3G/a3YyFSBe9Hg4lGQ1yKQG1+quTj7E45ocGQ5Wxy1vg8RV18hHiFfZcfoT3Q+UU6lFvVcDSQt7SCCFej/zUEKpzsrViSNOyithh30C87gSlcoYQKrn2F9z3UsaajgZLG3XyMaaGI8AmSce7pO3BhVBZrE7PrAPK0aDyBRx5p0YRlTISQmRnUggJs9C/YUnyOSrfTE7/yxe9Xq9SRkIkodPB35OUsTxloEZvdfIxNvs8hmIoMZ8/kxd+Qqho+/n73AhQbrPwaasKWGg1KmUkhMjOpBASZsHe2pKPmitHhU7dCkq2UZ4QqrmyFQKSTBVrOg4srFI+PjtqMAzs8ihjSYs/IVQSFaNLNhpUubAzbasUUikjIUR2J4WQMBt96pegiIutIjZjr4wKCTMQG518bVD+SlCtmzr5ZBVbZ0Mb8MT8DsGtY+rkI0QiG87cxT84XBEb3cYdrYwGCSEySAohYTZsLC0Y+VZ5Reyifwj7rj5WKSMh/u+/tRDkp4y1mADaHNiqt96H4FRYGTs4ydAoQgiVhEfFMvfgDUWsTkk3mrnnVykjIUROIIWQMCtdaxWjdD4HRWzmPl9idfImTKgkOgKOTFPGitSCih3UySerWdlBk9HK2L1TcH2fOvkIAaz89zYBLyIVsdFt3NFoZDRICJFxUggJs2JpoeWzVhUUsWuPX7Lzwn2VMhK53tml8DzJv7+W30BOfgPm0Q/cSiljf08yNIwQwsSeR0Tz65GbiliTCvmpXyavShkJIXKKXFcIDR8+HHd3d86ePZvqMVu2bMHd3T3NP9OmTUvxfJ1Ox6ZNm+jVqxe1atWiRo0atGvXjpkzZxIcHJxVn1qO0aFaYSoVVrbxnbX/OlEx8iZMmFjkCzg2Uxkr1RjKNFMlHZOxtIZmXypjjy/B1W3q5CNytSXHbvEsLFoRG93aXaVshDCdixcvMm7cOFq2bEn16tWpUaMGbdq04bvvvuPBgwdqp5cj5KpCaM2aNfz9999pHnf16tUM30On0zFy5EgmTJjA+fPnCQ0NJSIiAj8/PxYvXsw777yDr69sFvoqWq2G0W2Uo0J3g8LYcPaeShmJXOvkrxCWpHNhTh8NilOtm6EhRGIHpxgaRwhhIk9fRvL7MeX6vHZVC1GtmItKGQlhGrNmzaJHjx5s27YNf39/IiMjiYiI4Pbt26xdu5bOnTtz7568L8osS7UTMJVNmzYxaVL62sBeuWJokdu3b18+++yzVI+zskreNnfGjBns27cPrVbL4MGD6dq1K/b29hw9epRp06YRGBjIsGHD2LVrF3Z2dhn7ZHKB5u4FqF3SDa87CSNov/x9nW61imFnnQMXqAvzE/oUTsxVxiq0g+L11MnH1LQWhoYQGzwTYkE34b81UHuAammJ3GX+oZuERsXGf6zVkGz6tBA5zfLly1m4cCEAlStX5r333qNcuXIEBweze/dutm7dyrNnz1i0aBGTJ0/Okhz8/f1p2bJlsvj27dupVKlSCmdk3vLly/nxxx8VMQsLi0wNUKQlxxdCUVFRTJ06lTVr1qTreJ1OFz9iU7NmTRwcHNI4I8GjR49YtWoVAB9//DHDhw+Pf61Lly5UrlyZ7t27c//+fVatWsXgwYNf4zPJXTQaDaPbuNNr8cn4WOCLSJYev8VHzcupmJnINf75GSKfK2MtvlInF7VU7GBoDPHgXELs8FSo1gOs7dXLS+QK/sFhrD55RxHr5FGU8gWdVMpIiKwXEBDA7NmzAWjcuDELFizA2to6/vXGjRtz69Ytzp8/z+XLl1XKMufI0VPj9u/fz9tvvx1fBFWpUiXNc27dukVYWBgA1apVe637rVmzhujoaJydnXn//feTvV6xYkU6d+4MGEaoxKs1KJOXJhWUrVEXHrnJs7AolTISucaze3D6N2WsWnco9Ho/E7I9jQbe+lYZe/EQTi9WJx+Rq8zaf52o2IS1odYWWj59S0aDRM62adMmwsPDsbKyYvLkyYoiKE6pUqUAw8N7U5g8eTLnzp3j3LlzuLtn3fo8T0/P+PsMGTIky+6TWI4thJ4/f86IESO4c+cO9vb2fPPNN4wdOzbN8+KmxTk7O1OyZMnXuueRI0cAaNiwIba2tike06JFCwDu3r3L9evXX+v6udGYNspvuBcRMfx6+GYqRwthJEemQmyiVr1aS2iey0aD4pRpBmWaK2P//Azh0vhFZB3fRy/Yet5fEfNsUILieWQkUuRsBw8eBKBRo0YUKlQoxWMCAgIAKFasmElysra2xsHBAQcHB7TarCsdrKys4u+T0vKTrJBjCyEwzCvs2LEju3btwtPTM+0TSGiUULVqVf7++2+GDBlC/fr1qVq1Ki1atODbb7/F398/2XnR0dHcvGl4g165cuVUr594XmVc0SVSV7WoC+/UKKKILT9xm4ch4amcIUQmBfgYNlBNrPZAyFNanXzMQctvlB9HhMDxOerkInKFGXt9FXv4OlhbyLRokeOFhYXh7e0NQP369VM85sWLF5w7Z5iuXKdOHZPlllPl2ELIzs6Offv2MX36dIoUKZL2Cf8XV5ycOXOGjz76iMOHD/Ps2TOio6O5f/8+69evp0OHDuzbp9xc8NGjR8TExABQtGjRVK+fP3/++Co3pYJKJPd5qwpYahO6dEXG6JhzQEbTRBY5OAn0iaYbWDlA0zHq5WMOitaCyp2UsZML4flDVdIROZvXnSAOeD9WxD5sUoZ8jjYqZSSEaVy7do3YWENzkNQaEixfvpzw8HC0Wm2KzQxM5dSpU7i7u8cvI7l48SKffPIJb7zxRvy2MQsXLox/bxweHs4vv/xC27ZtqVatGg0bNmTUqFHcunVLtc8BcnAhZGVllaEhQx8fH8AwwtOsWTNWrVrFv//+y759+/jiiy+wt7cnIiKCzz77jP/++y/+vMT7Azk7Oye9bDytVhvfgCEkJOS188uNSuVzoFe94orYxrP3uBHwUqWMRI7lfxZ8/lTGGg4HxwLq5GNOWnwNmkQdG2PC4eh09fIROZJer2faHuUWE3kcrPmgcRmVMhLCdOJGgyDlQmjHjh3x3eTatWv32ks4ssr27dvp3bs3e/fu5enTp/HbxsyaNYsvvviCoKAgunfvzvz587l16xZRUVEEBQWxZ88eevbsqWob8BzfNe51PH36FFdXV8LCwvD09OTLLxM2FMyTJw8ffvgh9erVw9PTk+joaL7//nu2bt0KGLrTxUltfVAcGxvDU63IyMhXHrd+/Xo2btyYrtz9/PzSPigb+6RFebZ43Sc82vCkRKeHmft8+bVvbZUzEzmGXg8HJipjdnngjY9VScfs5CsHtfqB1/KEmNcKaDgC8pZVLS2Rsxz2DeT07SBFbETzcjja5Py3K35+fnTp0iXdx/fo0YNevXplYUavQRebs9cN2rkZthTIYnGFUNGiRXFxcSEkJISbN29y8+ZNdu3axb///gtA8eLF+eabb151KZOJiYlhwoQJFCtWjDFjxlCjRg0ePHjAxIkTuXLlCnv27MHb25tHjx4xfvx4WrdujYWFBVu2bGHu3LmEhIRkaRvwtOT8nyyvIW/evOzfv5+YmJhUF4PVqFGDnj17snr1aq5cuYKPjw8VK1bMksVjgYGB6V5HFB6es9fMFHC25f1GpZh/KKFRwp7Ljzh3N5haJdxUzEzkGNf3w+1jyljjz8FWNm6M13QsXFgPMRGGj/Wx8Pd30GOlunmJHCFWp2fqHh9FrKirHZ4NSqiUkWmFh4e/1trhwMDALMzmNVzZBrtHQ6iZ5JMVHPJD+xlQpXOW3iZu+5a40aBVq1Yxd65yPzt3d3eWLVuGq6trluaSXjqdDicnJ9auXUvevHkByJcvHz/88AMdO3YE4Pbt28ybN49WrVrFnzd8+HCuX7/O7t274ws8NUghlAJLy1f/b2nZsiWrV68GDHMiK1asiL19QiebtEZ64l5Pa+Qof/786Wr5DYYOImndN7sb3KQsa07d5VlYws72U/f4sGFwAzQazSvOFCINutjko0HOxaDuB6qkY7aci0D9IcpGCVd3GKYUFpNFuyJztp2/j+/jF4rYZ60qYGOZOzbRtrOzS/fvfDC8RzALO0dCZA6f6h8aaPg8s7AQ0ul0XLt2DUgohFLaJ8jX15fRo0czbdo0s/k30KlTp/giKE7ce+OwsDCKFSumKILi1KhRg927d/P48eNkr5mKFEIZULhw4fi/BwUZhvCdnBI2eHv5MvW1KzqdjtDQUADc3F49ktGrV690D3vXrl07votITuViZ8WI5uWYvCthDu3pW0Ec9AmgZaWCKmYmsr2LGyAgyZPYFl+B1asfVuRKjT41TImLeJYQ2/8tDPjTsO+QEBkQER3Lz/uUa4MqFnKik0fqzYdymjJlysRPtxe5z507d+L3sYwrhObPn09YWBgPHjzg/PnzrF+/Hm9vb44fP87gwYPZsmVLlrazTq/U9t3MmzcvYWFhqTZ+cHR0BAzr8tWi/v89M6RP3LMzBYm/YHGjOoULF47/+4MHD1I9NzAwMP78xAWVSJ++DUpS1NVOEZv2lw+xuld/zYRIVXQEHJyijBWoAtV7qpOPubNzM0wZTOzOP3B9X8rHC5EOK07c5kFIhCI2tl1FLLRSXJu9d+cYpo7lZA75DZ9nFkqpUYKFhQVOTk64u7vTq1cvNm/eTPPmhn3drl69ipeXV5bmlF6pPdiPm60TV/AkZQ5FnIwIJfL777+zdOlSQkJC+Oeff1Kdf3njxo34v5cubdhbRKvVUrZsWa5cuaL4x5xU3D5F8Or9hkTKbK0s+Lx1BT7beCE+du3xS7ac86dHneKvOFOIVJxeBM+TtLJ/a6JJFsZmW/UGw+nFEJKo08+BiVDuLfn/Jl7bs7Ao5h+6oYg1LJOXZhVy+JvrnKJKZ6j0rjRLyKS4rsWurq6pbvtiaWnJwIEDOXToEAAPH5rHFgZpLfUwZ+qXYmYkb968PHnyhOjoaI4dO5bqcX/88QcA9vb21K6d0LWsSZMmAJw4cSLV9Tpx/3gLFSpE+fLljZV6rtKpZlEqFVa2KJ+1/xoR/+8oJ0S6hQXBsZnKWKnGUD75XGaRiJUtNP9KGQu4ChfWqZOPyNYWHL7J84gYRWx8+4qy9jM70VqAQ76c+8cED3jiCqGKFSu++n91olGUxGuEZs+ejbu7e7J9LuPMmzfvla/nVlIIJdKyZcv4pgezZs1Kca3Prl27OHjwIADdu3dXDPe98847aLVagoKC4vu8J+bj48O2bdsA6N+/v/yQzyCtVsO4dsofFA9DIlh2/LY6CYns65+fISLJIt9W38lal/So3gMKVlXGDv0A0Tm7g6UwrvvPwll+4rYi9nb1wlQv5qpKPkKoJW42UWrraeKcP38eMOyXWb169fi4h4cHYGjildTDhw9ZsmQJ9evXp3Xr1sZKOUeQQigRJycnRo4cCcD9+/fp0aMHf//9NwEBAdy6dYuff/6ZMWMMO8yXLl2aTz75RHF+2bJl45sbLFiwgMmTJ3Pr1i2ePn3K9u3bGTBgAFFRURQrVoyePWX9QWY0KZ+PN8spO5QsOHyD4NCoVM4QIolnd+HUYmWsSmcoKntTpYvWAt76Thl7fh9OJX8IJERqZu7zJSpGF/+xlYWG0W3cVcxICNMLCgoiICAAAGdn51SPi46OZvPmzQA0atQIBweH+Ndq1KiBRqNJsRCaMWMGUVFRiv0xhYGsEUpiwIABPHnyhN9++42bN28yfPjwZMdUqFCB3377LcXFX2PHjuXOnTscP36cVatWsWrVKsXrefLkYcmSJakuHBPpo9FoGNe2Eu/M+yc+9iIihrkHb/DNO7L2SqTDwckQm2gKq9YSWnytXj7ZUbmWULoJ3DqaEDv2M3j0B4e8qZ8nBHD5fgjbzt9XxDzrl6RkXodUzhAiZ4qbFgewYsUKOnToQMmSJRXH6PV6pk2bxp07dwB4//33Fa+7urpSqlQprly5gl6vj5915OXlxa5du+jZs2ea0+5yIxkRSsEXX3zB2rVr6dChA4UKFcLKygpXV1dq167NN998w9atWylUqFCK59ra2rJkyRImT55MrVq1cHJywsrKihIlStC/f3927twZ32BBZE61Yi68W0O5oHDVydvceRqqUkYi23hw3tAyO7E670Pesurkk11pNNDqe2Us8jkcmaZOPiLb0Ov1/LjHm8RNWh1tLBnRopx6SQmhksRNtp49e0bPnj1ZvHgxZ8+e5fLly+zYsQNPT8/4h+v9+vWjXr16ya7j4eHBy5cv8fPzAwxbtkyZMgUnJydGjRplks8lu8lVI0L169eP37U3LbVr11Y0QngdWq2W7t2707179wydL9JvdBt3/rr8iKhYw9SK6Fg90//yZb5nLZUzE2ZLr4d9SUZ+bJyh6Vh18snuinhAtR5waWNC7Ozvho1XpbAUqTh8LZDjN54qYsOalSWfo41KGQmhnrgRITs7O8LDwwkODmbmzJnJjtNqtQwcOJDRo0eneB0PDw+2bt3KxYsXKVu2LFu2bOHKlSuMGzeOPHnyZOnnkF3JiJDI1ornsWfAm6UUsV2XHuJ1Jwe38RSZc30f3E7SFbLRp4bOQCJjWn4NFonewOpiDO20hUhBTKyOH3crt5ko7GLL+2/KbAmRO8UVQu3bt2fWrFnUq1cPFxcXLCwscHR0pGLFivTr148dO3YwZsyYVJtt1axZE4BLly7x8uVLZs+eTalSpejbt6+pPpVsJ1eNCImc6aNm5dhw5h4h4Qkb3f6w25vNQxtKZz6hFBuTfDTIuRg0GKZOPjmFawnDCNCJXxJi3jvh7kko0UC9vIRZ2uzlz7XHyq6sn7d2x85a9qASuU9UVFT8VDZ3d3fat29P+/btM3StcuXK4ejoyMWLF5k/fz5Pnjxh8uTJWFlZGTNlIH2zrPbv3//K17t06UKXLl2MmdZrkxEhke252FvxSUvlnkxed4LZe+WRShkJs3V+FTxJ8oO75ddgZadOPjlJ488Nmw4mtu9rFItARK4XFhXDz/uvKWKVCjvT2aOoShkJoa7r168TE2PYR8vdPXMdE7VaLTVq1MDHx4dVq1bRqFEjmjdvbow0cyyTFkLbt2835e1ELtKvQUlK5LFXxKbu8VG0ZRW5XORLwz43iRWqbljfIjLPzjX5Oiv/03B1uxrZCDP129FbBLxQbjj+ZfuKWGhl9F7kTokbJVSoUCHT1/Pw8CA6Ohq9Xs/48eMzfb2czqSF0Lhx4+jVqxdXr1415W1FLmBtqWVMW+WTlNtPw1hz6o5KGQmzc3wOhAYoY60ngVYGxo2mziBwS7LO48BEiIlM8XCRuzx+HsHCIzcVsaYV8tO4fH6VMhJCfXHrg/Lnz2+UhgZFixpGV3v16kW5csbpwhgVFUVoaCihoaHodFn3gDk6Ojr+PtHR0WmfYAQmfQfQtWtXLly4QPfu3fnmm28IDpYF7cJ4OlQrjEcJV0Vs9oHrPAuTTVZzvRB/ODFXGSvXCso0UyWdHMvSGt6aqIwF34bTi1M6WuQyM/f5Eh4dG/+xRgPj28u+JiJ3iyuEMjstDgztsleuXImLiwsff/xxpq8XZ8KECdSqVYtatWqlu/tyRqxZsyb+PosWLcqy+yRm0kJoypQpbNiwgUqVKrFx40batm3LmjVr0MsccmEEGo2GCR0qKWIh4dHMPXhDpYyE2fh7EsSEJ3yssYDWk9XLJyer3BGK11fGjsyA0KcpHy9yhSsPQtjk5a+I9axTnIqFnFXKSAjzEFdYGKMQWr58Od7e3nz66ae4urpm+nq5gcm7xlWvXp3NmzezadMmfv75ZyZPnsymTZuYMGECderUMXU6IoepXTIPHaoXZtfFh/Gxlf/epm+DkpTOJ7uV50r3z8HF9cpY7QFQQJ5EZwmNBtr8AEtaJsQiQ+Dwj9DhJ/XyEqrR6/VM/lO5eaq9tQWftc78egghsrszZ85k6vxHjx6xc+dO/Pz82LFjB40aNaJXr16ZzqtYsWJZOvqTkgEDBjBgwACT3lO1yfHdu3dn79699O7dm+vXr9OvXz8+//xzHj9+rFZKIocY17Yi1hYJ/7SjY/XJ9qwQuYReD3u/UsZsnKGZLCDNUsXqQLUkG0qfXQqBpv2lKszDAe8A/vVTjggOb1aWAk62KmUkRM7xzz//MHPmTA4dOkSnTp2YM2eObB3yGlRdJezs7Mw333zDli1bqFWrFrt27aJt27YsXrzYZIukRM5TPI89AxuVUsT2XX3Mvzdlak6u4/0H3D2hjDX+HBxlcXaWa/ktWCZ6o6uPTb6Hk8jxomJ0/JDkQVQRF1s+aFxGpYyEyFm6deuGr68vp06d4scff8TR0VHtlLIVs2iXVLFiRaZPn07Lli0JDw9n1qxZvP322xw5ckTt1EQ29VHzcuRxsFbEJu+6ik4n69FyjZhI2P+NMuZaAuoPVSef3Ma1ODT8SBm7vhduHlQnH6GKNafucOtJqCI2pm1FbK1k81QhhPpUKYRCQ0M5efIkixcv5qOPPqJRo0a89dZbHDxo+AWp1+u5e/cuQ4cO5ZNPPiEoKEiNNEU25mxrxaetlPPPrzx4zpZz/qmcIXKc04sh+JYy9tZ3YCXTcUym0afgkGT0be8EiI1RJx9hUs/Copjz93VFrEYxF96tUUSljIQQQsmkzRK+/PJLLl26hJ+fHzqdLr5bnKWlJdWqVcPDwyP+T3h4ONOnT2ffvn1cunSJFStWUKJECVOmK7K53nWLs+LEbW4EvIyPTd/rS7tqhXG0MXmfEGFKLwPhyHRlrFg9qNJZnXxyKxsnaDEB/hiZEAu4AudXQp331ctLmIRh+wLlNPcJb1dGK5unCiHMhEnfDW7duhWAPHnyULNmzfiip3r16lhbWyc7fsGCBWzfvp3x48czdepUFixYYMp0RTZnaaFlQodKDFiW0JEl8EUkvx6+weg20jEsRzs0BSKfK2NtfzR0NBOm5dEPTv8Gjy8nxA5OhipdwM5VtbRE1roR8IJVJ5UbWrevVoi6pTK/YaQQQhiLSQuhqVOn4uHhQcmSJdN9TqdOnfjjjz84e/ZsFmYmcqpm7gVo5p6fw76B8bHfjt2iV90SFM9jr2JmIss8ugznVihj1XsaOpkJ09NaGNppr3w3IRb2FI7OgDZT1MtLZKlJf3oTm2hNprWllvHtKr3iDCGEMD2TrhHq1KnTaxVBcQoVKsSLFy+yICORG0zoUBnLRFMxomJ0/LhH2mnnSHo9/DUO9LqEmJU9vDVRtZQEUKYpVHxbGTu1CJ7eVCcfkaUO+QRw5FqgIvZh49Ly8EkIYXbMomtcWt5//32+/PJLtdMQ2VS5Ao70a6gswHdfesQpP2mnneP47ILbx5SxRp+CsyzOVl3rSaC1SvhYF518jyeR7UXH6pi066oiVsDJhuHNyqmUkRBCpC5bFEJly5alX79+aqchsrGRLcvjam+liH3/51XF1A2RzcVEwr4JyphzMWg4Qp18hFKeMtBgmDJ2bY+0085hVv17B7/A5O2yHaRBjRDCDGWLQkiIzHK1t+azFNppb/a6p1JGwuhO/pq8XXar78BapuOYjSajk7fT/utLaaedQwSFRjH7wDVFrEYxF7p4FFUpIyGEeDUphESu0adeCSoUVO64PP0vX0LCo1M5Q2QbLx4ZFt8nVrwBVO2qTj4iZbbO0OJrZSzQG84uVScfYVQz9/nyPEJZ1H7zjrTLFkKYLymERK5haaHl67crK2JPQ6P4JcmGfyIbOjARol4qY9Iu2zx59IVC1ZSxQ5MhVNbsZWdXHoSw9vRdReydGkWoXVLaZQshzJcUQiJXaVw+P60qF1TEDJuuSlfCbOveGbiwThnz6AtFa6mTj3g1rQW0S7LZbUQIHJykTj4i0/R6Pd/tvIo+0ZJLOysLxreT/dqEEObN7Aqh8ePH880333Du3Dm1UxE51IQOlbC2SPinH6PT890fV9HrpXFCtqPTwZ7RypiNM7T8Vp18RPqUfCP5tEWv5fDwgirpiMz54+JDTt8OUsSGNytLEVc7lTISQoj0MbtCaNu2bWzatAlPT08GDRrExYsX1U5J5DAl8zrwYZPSitix60844B2gUkYiw/5bAw/OK2NNx4JjAXXyEenX6nvDHk/x9LBnLMgDiWwlLCqGH3cr92UrnseOD5uUUSkjIYRIP7MrhEaMGMGwYcNo1qwZFy5coGfPnmqnJHKg4c3KUcjZVhGb9OdVIqJjVcpIvLaIEPj7O2UsXwWoN1idfMTrcSkGjT9Txu7+C5e3qJOPyJBfD9/kYUiEIjahQ2VsrSxUykgIIdLP7Br7jxiRsOeHTqfj8uXLKmYjcioHG0vGt6/IyPX/xcfuBoXx+z+3+Ki5bPyXLRyZDqHK3etp+yNYWquTj3h9DT+Gc6vg2Z2E2L6voUJbsHFM/TxhFu4FhbHoqJ8i1qhcPlonWYcphBDmyqQjQleuXHmt47VaLdWrV8+ibERu926NItQp6aaIzTt4gwfPwlXKSKRbgLdh36DE3NtDubfUyUdkjJUttPlBGXvxAI7NVCcf8Vq+//MqUTG6+I8ttBq+facyGunWKITIJkxaCPXv358TJ06Y8pZCpEqj0TDx3SqKDsvh0bFM2eWd+klCfXo97B4N+kTTGC2soc0U9XISGVexA5RproydmAtPbqiTj0iXQ74B7L/6WBHr37Ak5Qs6qZSREMKY/P39cXd3T/bH2zvt90jDhw/H3d2ds2fPJntt+fLlya5ZuXLlFK5iGiZfIzRkyBD++OOPNI87cuSICbIRuV3Voi70qVdCEdt16SH/XH+iUkYiTVe2we1jytgbn0AeWZydLWk00G4aaBPN1NZFw54x0jjBTEXGxPLdTuUMj3yO1ox6q4JKGQkhzMWaNWv4+++/1U4j3UxaCK1ZswZXV1fGjh3L0qUp7yTu5eWFp6cnQ4cONWVqIhf7orU7rvZWiti3Oy8rpnwIMxH5EvZ+pYw5p7DoXmQv+d2hwTBl7Obf4LNLnXzEKy05dovbT8MUsbFtK+JiZ5XKGUKI7Gzy5MmcO3eOc+fO4e7unupxmzZtYtKkV+8J5+npGX+tIUOGGDvV12bSQqhixYps2LCB0qVLM2PGDKZOnRr/mo+PD0OGDKFv3754eXlRunTpV1xJCONxc7BmTBvlxn83A0NZfuKWShmJVB37ybCGJLG2P4C1gzr5CONpOhYcCyljf42HaFmzZ07uPwtn7sHrilitEq50rVVMpYyEEFnN2toaBwcHHBwc0GqTlw5RUVF8//33TJgwIc09Ga2srOKvZWWl/sMTk0+NK1KkCOvWraN27dqsWLGCUaNG8fnnn9OlSxeOHDlC8eLFmTZtGn/++aepUxO5WM+6xalW1EURm3PgOo+fR6RyhjC5J9fhxDxlrEwzqPSuKukII7NxgtaTlbGQu/DPLHXyESmasusqEdEJo+UaDXzfsSparTRIEMJYdDodf/75Jx988AENGjSgatWqtGzZkunTpxMRkfC+ZMiQIbi7uzN//nzVct2/fz9vv/02a9asAaBKlSqq5ZIRquwj5OzszE8//YSrqyt79+5l9+7dFCpUiEmTJrFnzx46duyYYsUpRFax0Gr4vqPymzc0KpYfdkvjBLOg//9mm7rohJjWEtrNAOlQlXNU6wYl31TG/pkNQTI6aw7+uf6E3ZceKWKe9UtQNclDJCFExvn7+9OjRw8+//xzjh07RnBwMNHR0fj7+/P7778zcuRIwDCT6vDhwzg7O9O/f39Vcn3+/DkjRozgzp072Nvb88033zB27FhVcskok1cbISEh/Pzzz7Rv357g4GAsLCzQ6/WULl2aDh06YGEhm7AJdXiUcKNHHeX0jh3/PeDETWmcoDrvnYY1I4k1GA75ZXF2jqLRQPsZoEn0eyA2UhonmIHImFi+2aHc18/N3oovWqe+XkAI8Xru3btHz549uXTpEg4ODnz22Wds3LiRRYsWUalSJQAOHz6Mr68vv/32GwD9+vXDyUm9bo0WFhZ07NiRXbt24enpqVoeGWXSQmjOnDm0bNky/os3bNgw/vnnHzp16sTx48fp168fT58+NWVKQiiMbVsRZ1vlPsPf7LgijRPUFPkS9oxTxpwKQ9Mx6uQjslbBKlBvsDJ2fZ80TlDZkmO38HsSqoiNblMRV3vZwFgIY9DpdIwcOZInT55ga2vLqlWrGDJkCDVq1KBZs2YsWLAgfrBgz5497NmzBwcHB9577z3Vcrazs2Pfvn1Mnz6dIkWKqJZHZlimfYjx/Prrr1hZWeHp6cnw4cPJkycPAFOnTqVAgQIsXryYXr16sWTJEkqWLGnK1IQAIK+jDaPbuPP1joTWsDcCXvL7P7cY1qysipnlYkemJW+Q0OYHw5oSkTM1Hw9XtsLLRPvU/DUOyjaXxhgquBcUxi9/Kxsk1CjuSq+6xVXKSJijpy8jM3yug40ltlYpzwgKCo1KcwF+auysLbC3Tvmt7rOwKGJ16btuXkebDN3/dezYsYMrVwzvPQYNGpRsrU2RIkUoXbo0N27cYMWKFcTGxtK3b19cXNSbmmplZUWxYtm7UYpJC6HOnTszYsQIihYtmuy1zz77jIIFCzJlyhR69erFwoULqVGjhinTEwKAPvVLsvGsP5fuh8THfvn7Ou/WLEJRVzsVM8uFHl+FkwuUsTLNoEpnVdIRJmLrAq2nwNYPEmIh9+DoDHhrompp5Vbf/XGFyESj4loNTJYGCSKJ2pMPZPjc7ztWoX/DUim+9tbPRwgKjcrQdUe2LM+nrVKeQt194b9cD3iZruvcntohQ/d/HevWrQMgf/78fPjhhykeEzeAEBYWhr29PQMGDMjyvHI6k06N+/HHH1MsguJ4enoye/ZsQkND5YsrVGOh1TC5U1XFGvzw6Fi+/+NK6icJ49PrYdfnoItJiFlYQ/uZ0iAhN6jWDUo1VsZOzIUAH3XyyaX2X33MAe8ARaxfg5JUKyYNEoQwlocPH3LhwgUA2rRpg51dyg9dEzcS69WrV3xhJDLO7FqztW7dmqVLl2JtLfOOhXpqFHelT70SitjeK4855BOQyhnC6C6sh7snlLE3R0K+curkI0xLo4EOM0GbaJ8JXQzs/kIaJ5hIeFQsE3cqHwDlc7ThM2mQIIRRnT59Ov7vzZs3T/U4nc4wMmtra8ugQYOyPK/cwCiF0IMHD9I+6DXUqVOHtWvXGvWaQryuMW0qktdBWZB/u/MKEdGxKmWUi4QHw/6vlTHXktD4c3XyEerI7w5vfKyM3T4Glzapk08uM+/Qde4/U25o+1WHirjYqb8JohA5ibd3wlYdNWvWTPW46GjDFhLdu3cnX758WZ1WrmCUNUJt2rSha9euDB06lEKFCqV9QjqULSsL04W6XOytGNeuIqM3X4yP3Q0KY97BG3zRRp6IZqkD30FooDLWbjpYyRqtXKfJF4bCJ+ReQmzvl1C+Fdi5qZdXDncj4AWLj/opYvVL56FTzdSnt4vczWvCWxk+18Em9bejBz5rmqlmCanZNLRhupslZLV79ww/39zc3HB0dEzxGG9v7/jpcxUqpLzuSa/X06VLF3x8fNi5cyfly5ePf+3x48f07NmTsLAw1q5dS7lyMrsCjDQiFB0dzYYNG2jdujXff/89jx8/TvskDIu9wsLCjJGCEFmia61i1C2lfLO16OhNbgS8UCmjXODeafBapoy5twf3turkI9Rl7QDtpiljoYGGYllkCb1ez5fbLhMdm/Am0VKrYVKnqmhkfZ5IRV5Hmwz/Sa1jHEAeB+sMXze1jnEArvbpv25Wi3svbGtrm+oxM2bMiJ8al9qemxqNhk8//RSdTsfcuXPj4y9fvmTw4MEEBQWxYMECKYISMUohtGjRImrUqEFUVBTr1q2jVatWTJ48Oc2C6MSJE9SpU4c2bdoYIw0hjE6r1TClczUsE3VHio41vEnI6BMq8Qqx0fDHKGXMyt4wGiRyr4odDMVwYl7LDEWzMLpNXv6cvhWkiH3YpAwVCkrLeiGygo2Nodh6+vQpUVHJO+QdOHCA48ePx3+cWiEE0KRJE+rVq8e+ffvw8fEhOjqajz/+mGvXrjFz5kzq1Klj/E8gGzNKIdS0aVPWr1/PihUrqF+/PlFRUaxZs4bWrVszZcoUAgMDUzzvwoUL6HQ67t69a4w0hMgSFQo68WGTMorY6VtBbPLyVymjHOzkAghI0p2v2Xhwlf1Kcr120wxFcWJ/jDIUz8JogkKj+HG3tyJWPI8dn7Qon8oZQojMilsOEhUVxa5dys2j7927x8SJExWxgIBXN276/PPP0ev1zJkzhwkTJnDixAm+/vprWrVqZdS8cwKj7SOk1+t58eIF5cqV48GDB9y9e5fIyEhWr17Npk2baNmyJQ4ODmi1WrRaLdeuXcPLywuNRkOBAgWMlYYQWeKTFuX548ID/IMTFg7/uNubtyoVJI+DdDg0imd34fBUZaxgVWgwTJ18hHlxLWEoihM30Qi4Aid/hTc/US+vHObH3d4EhymLy+/frfrKtRZCiMxp27YtS5YsAeC7777j+fPneHh4cO3aNebMmUNgYCDu7u64ublx8uRJVq5ciYeHB4ULF05xQ9OaNWvSsmVL/v77bwCGDRtGnz59TPo5ZRdGKYTCw8MZNGgQ58+fT/aaXq8nIiKC3bt3p/gawODBg42RhhBZxs7agkkdqzJw+Zn4WHBYND/s9uan7rLxb6bp9bB7DEQnXjOogbdng4V0qBL/12AYXNwAjy8nxA7/CFU6GQolkSmn/J4mG+luX60QzSvKw0ohslK1atXo3bs369atIzw8nB9++EHxesmSJfn11185cOAAJ0+eJDAwkL59+/Luu+8yY8aMFK8Zt8dQkSJFGDlyZJZ/DtmVUabGLViwgHPnzqHX69Hr9ZQoUYIGDRrQtGlTmjRpQuPGjSlRokR84aPX67GwsKBDhw7Mnj0bT09PY6QhRJZqXrEA7aspuyJu9vLn35tPVcooB/H+A67tUcbqDITiddXJR5gnCytDcUyiBfvRYbB7tOwtlEmRMbF8tf2yIuZoY8m371RRKSMhcpeJEycyZcoUatWqhbOzM1qtFjc3Nzp06MD69espWrQo/fr14/3338fBwQGASpUqpXitRYsWsWnTJvLly8eDBw84ePCgKT+VbMUoI0L79u0DwMXFhUWLFqXYA12n07Fu3Trmz59PUFAQsbGxvHz5ksaNGyc7Vghz9e07VTh67QkvI2PiY19tu8TukY1f2fVGvEJECOwZo4w55IeW36iTjzBvxetC7QHKzoLX/oKrOwwjQyJDfj18kxsBLxWxL1pXoKBz6l2shBDG1a1bN7p165bq61qtlrFjxzJ27NhUj9m2bRs///wzLVu2ZPz48bRr147Zs2fTvHlztFqjjH+8Uv369fH19c3y+xiLUf6PPHz4EI1Gw6BBg1LdCEqr1eLp6cm+ffvo0qULer2eo0eP8sknn8S3AxTC3BV0tmV0kj2E/J6EMv/QDZUyygEOfAcvHipjbX6UPWJE6t76FhySTNfaM8awEa94bTcCXrDg0E1FrHoxF/o1LKVOQkKIDDl69CgTJkygZs2a/PzzzxQvXpwePXpw7do1du7cqXZ6ZskohVBc3/OUFmwl5ejoyA8//MDXX3+NXq/nxIkTzJ8/3xhpCGESfRuUpGZxV0Xs18M38X0kewu9trsn4ezvyli5t6Ba6k/EhMDOLfneQi8fw4GJqqSTnel0er7cepmo2IQHkhZaDT92qYaFVvYMEiK7uHTpEiNHjqRYsWIsXLgw/r35kCFDsLGxYe7cuURHS5fNpIxSCJUuXRqA69evp/scT09PWrdujV6v588//zRGGkKYRNybhMR7C8Xo9IzfehGdmexSnS3ERMEfSRZwWtlDh5kgmzaKtFTpDOWT7EHntRzunFAlnexq/Zl7nL6t3DPog8alqVLERaWMhBCv6+7duwwZMgR7e3uWLFmCm1vCjIqCBQvSu3dv/P392bBhQ4auHxUVRWhoKKGhoZmexRUdHR1/LXMozIxSCDVv3hy9Xs/GjRsJCgpK+4T/a9GiBWCYWidEdlKpsDODk+wtdO7uM9aclj2x0u34HAj0UcaafwlupVRJR2QzGg10+AmsHJTxP0ZCTKQ6OWUzAc8j+HFP8j2DRrWsoFJGQoiMKFGiBCdOnOD48eMUL558373x48fj6+tL3759M3T9CRMmUKtWLWrVqpXp9T9r1qyJv9aiRYsydS1jMEoh1KdPH5ycnAgKCuK9995L9/+k0NBQADTy9FdkQ5+0LE/JvMoNHqfv8eFRSIRKGWUjT27A0enKWOEaUF/2DBKvwbUEtJigjD25Bsd+ViefbOa7P67yIiJGEZvSqZrsGSSEyDWMUgg5Ozvz1VdfodfruXHjBl27dmXy5MmvHOkJCwtjzZo1AOTNm9cYaQhhUrZWFvzQuZoi9iIyhq93XI5vFS9SoNPBH59AbFRCTKOFd34BC6Pt8Sxyi/pDoIiHMnZsJgT4pHy8AGDflUfsuqT8Hd3ZoyhNKuRXKSMhhDkpVqwYvr6+yf6k1rI7vQYMGJDsmlevXjVS1q/PaH30OnXqxNChQ9Hr9cTGxrJmzRpatGhBly5d+OWXX9izZw9nzpzh5MmTrFq1is6dO+Pn54dGo6FevXrGSkMIk3qzXD661lI2Cdl/9TG7Lz1SKaNswGsZ3DmujDUYDkVqqpKOyOa0FoYiWpNoFEMXDTtHgC5WvbzMWEh4NF/vUO4Z5GpvxYQOmXuDI4QQ2Y1RH7+OGjWKUqVKMW3aNIKDDW1Mvb298fb2TvUcS0tLBg4caMw0hDCpCR0qcdg3gKehCSMc3+68zBtl8+LmYK1iZmYo5D7s/1YZcy1hWBskREYVrg5vfAzHZyfE/M/A6cXQQKZbJjV1jzePnyvXUX3doTJ5HW1UykgIIdRh9J2VOnXqxL59+xg3bhwVKlRAr9en+sfZ2ZlZs2bh7u6e9oWFMFNuDtZMfFe5+/qTl1FM3pX6A4BcSa+HPz+FqCRtxt/5BawdUj5HiPRqNg7ylFXG/v4egu+ok4+ZOnHzCetO31PEmlTIT5daRVXKSAgh1JMlE/KdnJwYMGAAAwYM4MmTJ3h5eXHz5k0ePXpETEwMLi4uVKpUiVatWmFnZ5cVKQhhUm9XL8yO/x5wwPtxfGzLOX/erVmEpjLn3uDyFri+Vxnz6Atlm6uTj8hZrOzg3bmwvH1CLDrM0EWu3zZpyQ6ER8UyfuslRcze2oIfOleVpkVCiFwpy1cm58uXjzZt2qR9oBDZmEajYXKnqpzye8qLyIQuTF9uvcS+T5vgYJPLmwCEPoU9Y5Qxx4LQerI6+YicqdSbUOd9OLs0IeZ3CP5bCx6e6uVlJmYduMadp2GK2Jg27hRzs0/lDCGEyNmMPjVOiNyqkIst49srFxvffxbO9L+kexV/jYWwp8pY+5/Azi3l44XIqLe+A+ck07z2fgkvcncDkwv3nrHkmJ8iVrukG/0allInISGEMANSCAlhRL3qFqdBmTyK2Ip/73DK72kqZ+QCPrvg0iZlrNK7UPlddfIROZutM7w9SxmLeAZ/fmZYp5YLRcbE8sWmC+gSffrWFlqmda2GhVamxAkhci8phIQwIq1Ww9Qu1bGxVH5rjdlykfCoXNjKNyzI0CAhMVsXw2iQEFmlQhuo1l0Z891lWKeWC839+wbXA14qYh+3KEe5Ak4qZSSEEOZBCiEhjKxUPgdGt1F2QrzzNIwZe31VykhFf42Hl4+VsbbTwKmgOvmI3KPtNHBI0qhk9xfwMkCdfFRyyT+EX4/cVMSqFHFmaLOyqZwhhBC5hxRCQmSBgW+WplYJV0Vs2YlbnL0dpE5CavD9Cy6uV8bKt4EavdTJR+QuDnmhw0xlLDwYduWeKXJRMTpGb75AbKI5cZZaDTO61cDKQn79CyGE/CQUIgtYaDXM6F4D60RT5PR6GL35IhHRuWCKXHgw/DlKGbNxgXdmSxtjYTqVO0KVzsqY9x9wZZs6+ZjYvEM38Hmk3LdrRItyVC7irFJGQghhXqQQEiKLlM3vyBetKyhit56EMnNfLpgit/crePFQGWv7AzgXUScfkXu1/wns8ypju7+Al4Hq5GMil++HsODQDUWsUmFnhjcrp1JGQghhfqQQEiILDWpUhprFXRWxJf/cwutOsDoJmcL1/fDfGmWs3FtQU/ZxESpwyJe8OUfYU0MxlEMZpsRdJCbZlLjqilFqIYTI7eQnohBZyEKr4afu1ZNPkdt0IWd2kQsPhp0fK2PWTvDOHJkSJ9RTpTNUekcZu7o9x3aRm3foBt4Pnytiw5uVpWpRF5UyEkII85QrC6Hhw4fj7u7O2bNnX3lcYGAgU6ZMoXXr1lStWpX69evTr18/du7cmeY9oqKiWLp0KV26dKFmzZp4eHjw7rvvsnDhQsLDw431qYhsoFwBJz59SzlFzu9JKNP35sCNVveMTT4lrs0UcCmmTj5CgKEI7/Bz8g18d30OLx6nfE42ddH/GfOTTImrWMiJES3Kq5SREEKYL8vXPWHevHlZkQcjRozIkusmtWbNGv7+++80j7t16xZ9+vQhKCihy9ezZ884ffo0p0+fZt++fcyePRtLy+T/C8PDwxk4cCDnz59XxH19ffH19WX79u2sWLGCggWlhXBu8WHj0vx15REX7j2Ljy07fpvWlQvRsGze1E/MTq7uhIsblLGyLaBWf3XyESIxxwKGKXJbBiXEwoPhj0+g9/ocMWIZER3LZxuTd4n7KUnjFiGEEAYZKoQ0WfALwxSF0KZNm5g0aVKax718+ZIPPviAoKAgChcuzPjx46lbty7BwcGsXr2atWvXsn//fn7++WfGjBmT7PyxY8dy/vx5bGxsGDVqFO3atUOj0fDXX38xe/Zsbt26xYgRI9i4cWOW/L8U5sfSQsvM7jXo8MsxImN08fHRmy/w16gmONq89reieXkZmHzjVBsXeHdejniDKXKIql0NXeOubk+IXfsL/lsLHtl/Ddus/de4kWTj1BEtysmUOCGESEWGHhHp9fpX/kl8DIC9vT3Ozs5YWFgo4lqtFltbW2xtbY306aQsKiqK77//ngkTJsTf+1XWrVuHv78/1tbWrFixgjZt2pAnTx7Kli3Lt99+y+DBgwFYuXIlDx48UJx78eJF9u7dC8CkSZN4//33KVy4MIUKFWLAgAHMnTs3/rjdu3cb+TMV5qxcAUfGtK2oiPkHhzNll7dKGRmJXg+7PoWwJ8p4++ngUlSdnIRISdwUuaQbrf41Dp7dUycnIzl7O4jFx/wUsapFnfmouXSJE0K8Pn9/f9zd3ZP98fZO+z3Lq5agLF++PNk1K1eunBWfQrq8diH0999/p/rnq6++Qqs1XLJTp06sWrWKc+fO4eXlxalTp7h48SLbt29nwIABWFhYYGlpyXfffZdsCpkx7d+/n7fffps1awxdrKpUqfLK4/V6PStXrgSgc+fOlCxZMtkxw4cPx8XFhejoaLZv3654bfny5QCUKVOGd999N9m5jRs3plGjRoBhhErkLgPfKEX90nkUsXWn73LYNxvvdn9pk+Epe2IV34bqPdXJR4hXccgL7/yijEU+h50jQKdL+RwzFxYVw+ebLij2ibW20PJzj5qycaoQwqTSuwTFXLz2T8iiRYum+CcqKoqffvoJjUbDnDlzmDp1KnXr1sXOzi7hZlotFStWZNy4cSxduhS9Xs+XX37JxYsXjfpJxXn+/DkjRozgzp072Nvb88033zB27NhXnuPt7U1AgOFNaYsWLVI8xs7OjgYNGgAovth6vZ5jx44B0KxZs1SnvcVd9/Tp07x48SLFY0TOpP3/ru721haK+JjNFwkOjVIpq0wIuZ+8DbFdHnh7lkyJE+arYnuo0VsZ8zsMZ5aokk5m/bDbmztPwxSxz1pXoEJBJ5UyEkLkJJMnT+bcuXOcO3cOd3f3VI9LzxIUT0/P+GsNGTLE2Km+NqM9Klq8eDGRkZF0796d1q1bp3l8vXr18PT0JCYmht9++81YaSRjYWFBx44d2bVrF56eac8BTzzkV6lSpVSPixvG8/X1JSYmBjAMIz5//lzxekrirhsbG4uPTw7sHCZeqURee77qoPy3FfAikgk7Lqdr6qbZ0Olg+zCICFHG355lWJguhDlrOxWckmzwu/8bCLymTj4ZdMg3gNUn7ypitUq48mHjMiplJITIaaytrXFwcMDBwSF+5ldir7MExcrKKv5aVlZWWZVyuhmtEDpx4gQajYY2bdqk+5y4kZFz584ZKw0FOzs79u3bx/Tp0ylSJH072t+/fx8wfNELFEj9zVzhwoUBiI6O5vHjx4pzwTBylprEufj7+6crL5Gz9KlXgqYVlOsUdl18yM4LD1I5wwydXgy3jihjVbtBlU6qpCPEa7FzhU7zlbGYcNg2GGKjVUnpdQWHRjFms3JGhZ2VBTN71MRCKyOyQmRXOp2OP//8kw8++IAGDRpQtWpVWrZsyfTp04mIiIg/bsiQIbi7uzN//vxXXC1rve4SFHNjtELo2bNngKExQrpv/v+qMiwsLI0jM8bKyopixV5v/5Lg4GAAnJycXtnRzckpYcpB3ChQ3LkALi6pd+lxdHSM/3tISEiqx4mcS6PRML1bdVztlU9DJmy/zINn2WCfqUBfOPCtMuZUBDr8pE4+QmRE2RZQL8nUjAfn4egMdfJ5DXq9ni+3XSLwRaQi/lWHSpTO56BSVkKIzPL396dHjx58/vnnHDt2jODgYKKjo/H39+f3339n5MiRAPj4+HD48GGcnZ3p31+dbSoysgTF3BitZ2/hwoW5c+cO58+fp0aNGuk65/jx4wCvXaxkpchIwy+VtDrZJX497py4/wLY2Nik69yoqNTXhaxfv56NGze+OuH/8/PzS/sgYVYKOtsypVM1PlqbMCL6IiKGLzZdYPWg+mjN9YluTBRs/RBiIpTxTguSb1gphLl7ayL4HYIniabEHf0JyreGYnVUSyst287fZ8/lR4pYM/f8eNYvoVJGIrP8/Pzo0qVLuo/v0aMHvXr1ysKMhKndu3ePXr168eTJExwcHBgyZAgNGjQgODiY2bNn4+3tzeHDh/H19Y1fVtKvXz/Fw3lTs7Cw4O2332bUqFEUKVKEU6dOqZZLRhitEPLw8OD27dssXryYtm3bUqhQoVce7+Pjw7Jly9BoNLz55pvGSiPTLCws0j4oC85NSWBgIFeuXEnXseHh2WAUQSTToXphDngXZdv5hGmVJ24+ZenxW3xgrnP8j06HhxeUsfrDoGxzdfIRIjOs7aHzIvi9FegM6z3Rx8LWwTD0GFib3+iKf3AY3+5Q/m5ws7dietfqsjddNhYeHp7u3/lgeI9gVkKfpH1MaqwdwMou5ddCnwIZXD9rZZf693BYEOjT2SnSIV/G7v8adDodI0eO5MmTJ9ja2rJq1SrFNLMKFSrw1ltvERsby549e9izZw8ODg689957WZ5bauKWoJjTgMbrMloh9N5777F9+3aCg4Pp2bMnY8aMoVWrVlhbWyuOCwsLY9u2bcyZM4fw8HBsbW0ZMGCAsdLItLgud4lHd1KSeI5m3AhP4g55rzo/8bmvGjnKnz9/uudaBgQEpJmzME8T363CKb+nPAhJ+Hcxfa8vjcrno2IhZxUzS8Hdk3BspjKWzx3e+jbl44XIDorWgqbj4NDkhFjQTdj7FbwzW7W0UhKr0/PZxgu8iIxRxH/sUo0Czlm7J5/IWnZ2dq+1viJ//vxpH2RKM8pm/Nz2P0G9D1N+bX5dCHuases2HQfNx6f82rJ2EJjOhlUTs34Zw44dO+IL4UGDBiX7t1CkSBFKly7NjRs3WLFiBbGxsfTt2/eVSzGyWkaWoJgboxVCFStW5NNPP+Xnn38mICCAL774Amtra0qXLo2rqyt6vZ6goCBu3bpFbGwser0erVbLjBkz0hw9MiVnZ8Mbz5cvX77yuLh1QQBubm6Kc9M6P3HL7LhzU9KrV690D3vXrl07y5pOiKzlYmfFTz1q0Oe3hOHkqBgdI9f9x44Rb2JrZdyRxgyLCDFMiUv8BE1rCV0Wp/4kT4jsotGncH0v+J9JiHktg/KtoGIH9fJKYuGRm5y+FaSIda1VjLZVC6uUkTCWMmXKsHXrVrXTECpZt24dYChwP/ww5aIwTx7DPoRhYWHY29ub1UBCdmXUndYGDx7MhAkTcHR0RK/XExkZia+vL6dOneL06dNcv36dmJgY9Ho9RYoUYeHChbRq1cqYKWRaqVKlAMOoTVBQUKrHPXpkmJttZWVF3rx5FecCPHiQevevhw8fxv89vd3sRM72Rtl8fNCotCLm+/gF0/4yo/bqu76AZ8o2vTQbD0VqqpKOEEZlYWmYImeVZBrNjhHw/GHK55jYhXvPmLVf2d67qKsd376r3q7sQojMe/jwIRcuGKact2nTRjHDKLHErat79eoVXxiJjDP6ltN9+/Zl7969fP311zRp0oSiRYtia2uLra0tJUuWpGXLlkybNo1du3bRpEkTY98+08qXLx//98R7CiV19epVwDBn09LSMLBWoEABXF1dAV65P1DcuVqt9pUbU4ncZXRbdyoWUi54XHb8Nod9A1TKKJGLG+FSksYdJd80PEUXIqfIWxbaTVPGwoMM+2Xp0rmWIIuERsYwasN/xOgS1kpoNTC7V02cbdXfi0MIkXGnT5+O/3vz5qmvt9X9/+eQra0tgwYNyvK8cgOjTY1LLE+ePHh6eqZrA1NzU6FCBQoXLszDhw85ePBgio0cwsPDOXnyJACNGzdWvNakSRN27tzJwYMH+fTTlN8kHjp0CICaNWuq2ulDmBcbSwt+6e3BO3P/ITIm4U3XF5susndUY/I6pr6eLEsF34FdnytjNi6Gp+daM5m2J4SxePSF6/vAe2dCzO8QnPoVGn6kWlqT/rzKrSehitiI5uWoW0qeCAszMfpmxs99VVOSj86QqWYJqRm4J/3NErJY4gfvNWvWTPW46GjDHmfdu3cnX76sb+CQGxh9RCi702g0dOzYEYDNmzdz/fr1ZMcsWLCAkJAQrKys6NOnj+K1Tp06AXDt2jU2b96c7Nxjx47xzz//AKja6UOYpwoFnfiqQyVF7MnLSMZuuZjmbs1ZIjYGtg2ByOfK+DuzwLW46fMRIqtpNPDOHMO+WIkdmAiPLqmS0l+XH7L+zD1FrGZxVz5uWT6VM4RQgUO+jP95VcHikDfj131VgWWfJ/3XyWL37hm+v93c3BR7TSbm7e0dP32uQoUKKR4ze/Zs3N3d2bdvX4qvz5s375Wv50ZSCKXgww8/JH/+/ERERPDee++xY8cOnj59yq1bt/j+++9ZvHgxYOjdXrBgQcW5b775Jk2bNgVg4sSJzJs3j/v37/P48WNWrlzJJ598AkD16tVp3bq1aT8xkS30a1CS5u7KbkAHvANY+e8d0ydz7Ce4+68yVqM3VO1q+lyEMBX7PNB5IZCoFXVsFGx+H6JCUz0tKzx4Fs7YLcoCzMHagjm9amJlIb/ChcgJwsLCgFfvYTljxoz4qXGpbdfi4eEBwMWLF5O99vDhQ5YsWUL9+vXl/WciRp8a9+jRI/788098fHwIDQ2N7xD3KhqNJr64MAeOjo4sWLCADz74gKdPnzJmzJhkx7Ru3ZrRo0eneP60adMYOHAg3t7ezJ07l7lz5ypeL1WqFAsXLlQsehMijkajYXq3GrSbc5QnLxM23J2y25u6pfJQuYiJWmrfPg5HkqyXcC0J7aab5v5CqKlMU3jjYzjxS0LsyTX4axy8Ozf184woJlbHqPX/ERIerYhPfLcKJfOa3/5GQoiMidtK5enTp0RFRSXbeubAgQMcP348/uPUCqEaNWqg0WhSLIRmzJhBVFQUX375pREzz/6MWght2rSJyZMnExUVlfbBZq569ers3r2bxYsXc/jwYR4+fIilpSXu7u507dqVrl27plrIuLm5sXHjRlatWsWuXbu4desWMTExFC9enNatW/PBBx+kOvQpBEB+JxtmdK/BwGUJrXyjYnR8vO4cf3zcCHvrLFnelyAsKHmrbI0FdF0Ctma2t5EQWaXF13DrKDz8LyF2biWUaQ5Vu2T57ecdusHp28rupR2qF6Zb7ey9b4cQQqls2bIcOnSIqKgodu3aRefOneNfu3fvHhMnTlQcHxCQchMlV1dXSpUqxZUrV9Dr9fEbLHt5ebFr1y569uxJxYoVs+zzyI6M9m7K29ubb7/9Fr1e/9prGUy5E3b9+vXx9fVN17H58uXjyy+/zFD1bG1tzaBBg6Srh8iw5u4F+KBRaZb8cys+djMwlO//uMrUrtWz7sZ6Pez8GJ7fV8ZbfAXF62XdfYUwN5bW0G0pLGwM0YmmxP0xCorWBreSWXbrU35P+eVv5RrVYm52/NC5mkl/Zwohsl7btm1ZsmQJAN999x3Pnz/Hw8ODa9euMWfOHAIDA3F3d8fNzY2TJ0+ycuVKPDw8KFy4cLINTT08PNi6dSt+fn6ULVsWnU7HlClTcHJyYtSoUSp8dubNaIXQihUr0Ol0aDSa+I1AixcvjoODDN8LkVGj27pz8tZTLt9PaFaw/sw93iyXj3dqZNEeVGd/B58/lbHSTeDNUVlzPyHMWd6y0GEmbB+aEIsMgS2DDF2nLIzfuvpZWBSjNvxHok7ZWGg1zOnlgYudtMoWIqepVq0avXv3Zt26dYSHh/PDDz8oXi9ZsiS//vorBw4c4OTJkwQGBtK3b1/effddZsyYoTg2rhC6ePEiZcuWZcuWLVy5coVx48bJvkMpMNoilVOnTqHRaGjfvj0TJ06kYsWKUgQJkUk2lhbM7V0Le2vlfOAvt17iXlCY8W/4+Ars/UoZs88LnRdLq2yRe9XoBdV6KGP+Z+Dwj0a/lV6vZ8zmizwMiVDEP2tVgdol3Yx+PyGEeZg4cSJTpkyhVq1aODs7o9VqcXNzo0OHDqxfv56iRYvSr18/3n///fj315UqVUp2nbj225cuXeLly5fMnj2bUqVK0bdvX1N+OtmG0UaEnjx5AqCY1yiEyLzS+RyY1LEqn2+6EB97ERnDiLXn2DT0DawtjfQ8I/IlbBoAMco3YHT6FZwLG+ceQmRHGo1hVMj/DAQnTFXl2M9QqhGUbWG0Wy0/cZt9Vx8rYm+UzcvQpmWNdg8hhHnq1q0b3bp1S/V1rVbL2LFjGTt2bKrHlCtXDkdHRy5evMj8+fN58uQJkydPxsrKNKPJr7MExRwYbUTIxcUFAGdnWUgthLF1rV2Mzh5FFbEL/iFM+8vHeDfZ/YWhK1Zi9YdChTbGu4cQ2ZWtM3T7HbSJnx/qYcuH8OKRUW5x0f8ZP+z2VsTyOFgzq2dNLLSyLkgIkTatVkuNGjXw8fFh1apVNGrUiObNm6udltkyWiEUNzx37dq1NI4UQmTEpE5VKZ1POd30939usT/J0+MMOb8GLqxTxgrXgFbfZ/7aQuQURWvDWxOVsbAnsOUD0MVm6tLPI6IZsfY80bHKZkMze9SgoHPqe4sIIURSHh4eREdHo9frGT9+vNrpmDWjFULdu3dHr9ezYsWKHNE+Wwhz42hjybw+Hsmmwn2x6QL+wZlYLxTgYxgNSszaCbotA0ubjF9XiJyo4Qio0FYZu30MjmR8fy29Xs+4LRe5m2Td35CmZWjuXiDD1xVC5E5FixpmkPTq1Yty5cpl+npRUVGEhoYSGhoav6lrRkVHR8dfKzo6Ou0TspjRCqHWrVvToUMHrl+/zrBhw/Dz8zPWpYUQ/1eliAtfv11ZEQsJj+bjdeeJjs3AD6eoMMO6oOgkhdS7vxi6ZQkhlDSa/6+bS7KXz5Fp4HckQ5dcffIOuy8pp9fVLunGF63dM5qlECKX0ul0rFy5EhcXFz7++GOjXHPChAnUqlWLWrVqZXr9z5o1a+KvtWjRIqPklxlGa5awcuVKqlWrxqlTpzhx4gQdOnSgYMGCFC1aFHt7+1eeq9FoWLx4sbFSESJH61u/BCdvPmXXpYfxsfN3nzFtjw8TkhRJr6TXG0aCApVrEqjzvkk2ixQi27LPY9hfaFk70MdNidMbpsgNPQZOhdJ9qUv+IUz6U/k96GJnxS+9PbCyMNqzSiFELrF8+XK8vb2ZOHEirq6uaqdj9oxWCP3www+KTd70ej2PHz/m8WMjrF8QQsTTaDT82LUal+6HKKbSLPnnFnVKudG2ajo7vJ1fBf+tUcYKVoM2xm8JLESOU6I+tPwaDkxMiIUGwOb3of9OsEj712tIWDTD13oRlWQ0d2b3GhR1tTNywkKInOrRo0fs3LkTPz8/duzYQaNGjejVq1emrlmsWLEs6f42YMAABgwYYPTrZpRRHzfp9fr4P0k/ftUfIcTrcba1Yn6fWlgneWI8etNFbj8JTfsCDy/CrqTrghyh+3KwkoXZQqTLGyOhXCtl7M5xODgpzVN1Oj2fb/qPe0HhivigRqV5q3JBY2YphMjh/vnnH2bOnMmhQ4fo1KkTc+bMUQxOiNQZbUTIx8eIbXyFEGmqVsyFb96pzITtl+NjLyJjGLbmHNuGv4GtVSoboEaEwMb+EBupjL87F/JlflGlELmGVgtdFsPCxvDcPyF+fDYUrw8V26d66uJjfhzwDlDEapd0Y1y7ilmUrBAip0pr/yGROpmALEQ25lm/BJ1qFlHEvB8+Z+LOKymfoNfD9uHKTSHBsF+QrAsS4vXZ54EeK0CbZLPC7UMh+HaKp5z0e8qMvcopJ3kcrJnXR9YFCSGEKclPXCGyMY1Gw5TO1ShXwFERX3/mHhvP3kt+wr/zwOdPZaxoHWiV9lQeIUQqitWBNj8oY3Ejr9ERinDAiwg+XneeWF3CtHCNBub0qklhF1kXJIQQpmQWhdD58+fVTkGIbMvBxpKFfWthb62cCjdh+2Uu3w9JCNw6Bvu/VZ5sl8ewLsjSOusTFSInq/chVEkyqvrwAuz+3DASC0TH6hix5jyBL5TTUke1rEDj8vlNlakQQoj/M9oaoTg3b95k//79PH78mKioqBQ3XoqNjSUqKooXL15w8+ZNAgICuHr1qrFTESLXKFfAiR+7VGPk+v/iY1ExOoau9uKPEY1wiwmEzQMTtfoF0ECX38C1uMnzFSLH0WgM+289ugRPryfEz682jLrWGcgPu705fTtIcVqTCvn5uIWszRNCCDUYtRBasmQJs2bNeq1dZ/V6vXS2EMIIOtYsitedYFb+eyc+5h8czufrT/O7biKa0EDlCU3HQvm3TJylEDmYjRP0XAW/tYToRN0b94zhyItCLDuu/N1Y1NWO2T1rotXK70AhhFCD0abGXbp0iZ9++gmdTvdaLbOrV6/O0KFDjZWGELnahA6VqV3STRFrfmsWmvtnlAeWb20ohIQQxlWgEnScp4zFRlHh8EfkJWGqqrWlll/71iKPg0xLFUIItRitENqwYUP83wcOHMj27ds5duwYTk5OWFhYsHv3bv7++29Wr15N9+7d44+tX78+I0eONFYaQuRq1pZaFnjWIr+TDQBdtUfpZ3lAeZBbKUPLX61ZLBEUIuep2gUajlCECmueMtdqLhYYpqdO6liF6sVcVUhOCCFEHKO9E/Ly8kKj0dC0aVPGjh1LxYoVyZ8/P7Vr10an0+Hj40PRokWpU6cOkyZN4vvvv0ev17N06VKuX7+e9g2EEOlS0NmW+X1qUdPCjx+sfle8prO0hZ6rwc4tlbOFEEbx1nfoS76pCL1hcZVxluvoXa84PeuWUCkxIdKWeMnC6yx3EEJtiWedpWfpjdEKoSdPngDwzjvvKOKVK1dGr9cn6wzXvXt3GjRogE6nY926dcZKQwgB1Msfw2rHudhoohXxqZbDeO4qGzYKkeUsLJmf9yse6vMowh9a7ub70qns8yWEmdBoNFhYGDqRRkVFqZyNEOkXHW1436PVak1bCIWHhwNQtGhRRbxcOUM3nGvXriU7p2PHjuj1es6dO2esNIQQMVGwsT+OkY8V4WUxbVj8rC6j1v+HLtEeJkII4/vz4gN+OvGM4VEjidQr+xJZ7RoFD2TbCGHeHBwcAHjx4oXKmQiRfi9fvgTA3t4+XccbrRBycnICIDJSuT9C8eKG1rw3b95Mdk7JkiUBuH//vrHSEEL8NRbu/qsI/RtbmSkxngAc9Ang5/3JH0wIIYzj6oPnjN50EYDz+vJ8HTNQeUBMBKzvCy8DUzhbCPPg7OwMwLNnz+IfdgthzmJjY3n27BmQUMinxWjtswsXLsyzZ8+4efMm9evXj4/HFUJPnz7lyZMn5MuXL/61uKJJvsGEMJKzy+DsUkUoxqkoE0I/JyY64dt93qEbVC7iTPtqhU2doRA5WnBoFINXnSU8OmHPro2xzXm/zHMq3ktoKsRzf9jYH97bCRZWKmQqxKs5ODhgb29PWFgYd+/exdXVFScnJ6ytrdFKsx1hRnQ6HaGhoTx9+pTo6GisrKziC/m0GK0Qqlu3LlevXmX16tW888478SNErq6u5MmTh+DgYI4cOULXrl3jz/Hy8gLSP3wlhHiFOydg92hlzNIOyz7rmBJeDM8lp4hNNCXu840XKJnXnipFXEycqBA5U3SsjuFrzuEfrHy417NOcdw7zYNV/nDneMILd///Pfv2LMOGrEKYEa1WS/Hixbl37x5hYWEEBQURFBSU9olCqCju362lZfpKHKOV9F26dEGj0XDr1i26dOnCmjVr4l9r2LAher2e2bNn4+XlRUREBPv27WPZsmVoNBrc3d2NlYYQuVPwHdjQF3TK5gh0nAeFa9CgTF6+ebuy4qXw6Fg+XHGWwBfK6axCiIz57o8r/Ov3VBGrVcKV7ztVQWNpDd1XgHMx5Uley+DMEhNmKUT6xb2pLFasGM7OzvENFIQwN1ZWVuTLl48yZcpgY2OT7vOMNiLk7u5Onz59WLNmDffu3WPmzJl4ehrWJLz33nvs2rWLJ0+e0Ldv3/hz9Ho9Go2Gd99911hpCJH7RL6Adb0hTPkGjDc+gWrd4j/s37AkVx6EsPGsf3zsQUgEQ1d7sfbD+thYyi84ITJq1b+3WX3yriJWwMmGhX1rJ3xvOeaHXqthaVvDOqE4e8ZCvvJQppnpEhYinbRaLU5OTvEzffR6vaJFsRBq02g06eoQlxKjFUIAX331FS4uLvz++++K7nHVq1dnxIgRzJs3L9k5TZs2VWywKoR4DTodbB0CAUna8ZZvDW9NVIQ0Gg2TOlXFLzCUs3eC4+Ned4KZsO0y07tVz/APEiFysxM3njDxj6uKmI2llt/616GAs63y4CIe0GkBbH4/IaaPhY3vwYcHIW9ZE2QsRMZl5k2nEObGqKvdtFotn3zyCSdOnGDy5MmK10aMGMGiRYto1qwZpUuXplatWnz11VfMnz/fmCkIkbscmgy+u5SxfO7Q9XfQJh/hsbG0YGG/2hR1tVPEN3n58/s/t7IyUyFypNtPQhm25pxi/R3A9G7VqVHcNeWTqnaFJmOUsYhnsLYnhD/LijSFEEKkwKgjQnEcHByoUaNGsnjTpk1p2rRpVtxSiNznwno4NlMZs3OD3uvANvVuKfkcbfitfx26/npC0dlqym5vSuV14K3KBbMqYyFylJCwaN5fcYaQcOXavBHNy9GxZtFUzvq/ZuMh0Bu8/0iIPb0OmwaA5ybpJCeEECYg/Q+FyI5uH4cdI5QxrSX0WJmuqTWVizgzq2dNRUyvh0/Wn+fKgxAjJipEzhQVo2Poai/8AkMV8daVC/JZqwppX0Crhc6LoGA1ZdzvkKGTnKzBEEKILCeFkBDZzdObsMEzeYe4dtOhdJN0X6Zt1UJ80Vr5hi0sKpZBy8/y+HlEKmcJIfR6PV9vv5ysQ1zFQk7M6lkTrTad6yesHQwjuA4FlHGvZXBygZGyFUIIkRophITITsKCYG0PCA9WxhsMh7qDXvtyHzUvRxcP5RSeR88jGLTiDGFRMZnJVIgca9FRPzacvaeI5XeyYemAujjYvOaMc9fihmLIMklThb1fgc/uTGYqhBDiVaQQEiK7iIky7ET/9IYyXqEttJ6c8jlp0Gg0/Ni1GvVK5VHEL99/zsj1/yVbAC5Ebrfn0kOm7vFRxGyttPz+Xh2KJGlCkm7F6kDnhUmCetgyCB78l7FrCiGESJMUQkJkB3o97PwYbh9TxgtVS7VDXHrZWFqwqF9tSuW1V8T3X33MlF3eGb6uEDnNubvBjNrwnyKm0cDsnh5UL+aauYtX6QwtvlbGosMMneSe3Uv5HCGEEJkihZAQ2cGhKXBxvTLmWAh6bwAbx0xf3s3Bmt8H1MXFTtmpaunxW9JWWwgMbbI/WHGWyBidIj6ubUXaVi1knJs0/hxq9FHGXj6CNd2lrbYQQmQBKYSEMHdeK+DoDGXMyh76rAeXNFr0voay+R1Z2Lc2VhbKhd6Td11lz6WHRruPENnN05eRDFh2mqDQKEW8V93iDG5Sxng30mjgnTlQspEyHugNG/pCTKTx7iWEEEIKISHM2vX98OenyphGC92WGXaoN7KGZfMyvVt1RUyvh1Eb/sPrTpDR7yeEuQuPiuWDlWe5/TRMEW9SIT+TOlVFo0lnh7j0srSGXqsNGyMndvuYoWW+tNUWQgijMWkhtH37dlPeTojs7eEF2Pge6GOV8Q4zwb1tlt22s0cxRrdRvgmLjNHxwYqz+AW+zLL7CmFuYnV6Rm04z/m7zxTxyoWdWeBZCyuLLPoVaucGfTeDY5LNjS9thL+/z5p7CiFELmTSQmjcuHH06tWLq1evmvK2QmQ/QbdgdTeIVm7WSKNPoc77WX774c3K0rtecUUsOCya/ktPEyB7DIlcQK/X8+3Oy+y98lgRL+pqx7KBdXF83TbZr8u1BPTZCFYOyvg/P8OpxVl7byGEyCVMWgh17dqVCxcu0L17d7755huCg4PTPkmI3OZlIKzuAqEByni17tDiG5OkoNFomNSxKs3d8yvi/sHhvLfsDM8jolM5U4icYe7BG6w+eVcRc7K1ZNnAuhR0tk3lLCMrUhN6rABNkq6Qe8bAlW2myUEIIXIwkxZCU6ZMYcOGDVSqVImNGzfStm1b1qxZg17mPAthEPkC1nSDID9lvFRj6DgftKb7lrW00DKvTy2qFXVRxL0fPmfwyrNExsSmcqYQ2du603f5ef81RczaQsuifrWpUNDJtMmUbwVvz0oS1MPWwXDrqGlzEUKIHMbkzRKqV6/O5s2bmTRpElqtlsmTJ9O5c2fOnj1r6lSEMC8xUYbOUA//U8YLVoNea8DSxuQpOdgYnoCXTLLH0Em/ID7bcEE2XBU5zr4rj/hq2yVFTKOBWT1r8kbZfOokVfs9aPalMhYbBev6wMOL6uQkhBA5gGpd47p3787evXvp3bs3169fp1+/fnz++ec8fvw47ZOFyGl0sbB9KPgdVsZdSxgWTdu6pHiaKeRztGHl+/XI52itiO+69JCJO6/IiK7IMU7fCuLjdedJWt9PfKcKHaoXViepOE3HJF8fGJXKCLIQQoh0UbV9trOzM9988w1btmyhVq1a7Nq1i7Zt27J48WKio2UNgsgl9HrYPRoub1HG7fNC323gZKTNGjOhZF4Hlg+sh4O1cq3CqpN3mJVkCpEQ2dHl+yEMWn4m2YapHzUvy3tvlFInqcQ0Gmj/E1R6Rxl/+RhWdoLnsteXEEK8LrPYR6hixYpMnz6dli1bEh4ezqxZs3j77bc5cuSI2qkJkfUOToazvytjVvbQZxPkK6dOTimoWtSFRf3qJNtw9ZeDN1hyTJ5Ii+zrZuBL3lt6mheRMYp4jzrF+KK1eypnqUBrAV2WQMk3lfFnd2BVZwiTvb6EEOJ1qFIIhYaGcvLkSRYvXsxHH31Eo0aNeOuttzh48CBgaFt69+5dhg4dyieffEJQkPxwFznUiblw7CdlTGsFPVdBsdrq5PQKjcrnY3ZPD5LuITl5lzcbz95TJykhMuHBs3D6LTnF09AoRfytSgX5oXM142+YmllWttBrLRSqpowHesOa7hApe30JIUR6ZfFGCEpffvklly5dws/PD51OF7+2wNLSkmrVquHh4RH/Jzw8nOnTp7Nv3z4uXbrEihUrKFGihCnTFSJrnVsF+yYoYxotdF0C5d5SJ6d06FC9MM8jqjF+q3JB+bgtF3G2taRtVZXXUgiRTk9fRtL391M8CFHujdWwTF7m9fHAMqs2TM0sO1fouxWWtoWgmwnx+2dhg6dh/yEVmqsIIUR2Y9JCaOvWrQDkyZOHmjVrxhc91atXx9raOtnxCxYsYPv27YwfP56pU6eyYMECU6YrRNa5tBn++CR5/O3ZUKWTqbN5bb3rlSAkPJqpe3ziYzo9fLzuPL/1t6CZewEVsxMibSFh0fT9/TR+gcpNi2sUc+G39+pga2WRyplmwrEA9N8Ov7eBFw8S4n6HYdMA6LESLKxUSk4IIbIHkxZCU6dOxcPDg5IlS6b7nE6dOvHHH39Ie22Rc3j/adgDRK9clE2r7w1tcrOJoU3L8iwsmoVHEp5IR8fqGbLKi+UD69GwbF4VsxMidS8ioum/7DTeD58r4uUKOLJsYD0cbUz6qzHjXEsYiqFl7SDsaULcdzds/RC6/m5YVySEECJFJh3379Sp02sVQXEKFSrEixcvsiAjIUzs+gHYPBD0STYjbfQpvDlSnZwyYWxbd/rUV05ZjYzRMWjFGbzuBKuUlRCpC4+KZdDys1y490wRL+pqx6pB9cjjkHx2glnL7w59t4B1ko1er2yDHSNAp0v5PCGEEObRNS4t77//Pl9++WXaBwphzm4dM8zfj1UuyqbeEGj5rTo5ZZJGo2FSx6p09iiqiIdFxTJg6Wku+YeolJkQyUVExzJ41VlO31Y24CnobMPaD+tT2MVOpcwyqYgHeG4ydJtM7MJa2P25oUW/EEKIZLJFIVS2bFn69eundhpCZNydf2FtT4hRLsqmVn9oO5VkbdiyEQuthhndqtOuqnK/oxeRMfRbeoqrD56ncqYQphMZE8vwNec4dv2JIp7P0Zo1HzSgZF4HlTIzkpINDd3kLJI0STi7FP4aJ8WQEEKkIFsUQkJka3dPGnZ/j1YuyqZaD0NzBG32/za0tNAyp5cHLSoqmyQ8C4vGc8lJKYaEqiJjYhm++hwHfQIUcVd7K1YNqk+5Ao4qZWZkZZsbWu9rkzRJOLUQ9n4pxZAQQiSR/d+BCWHO7p6C1V0hKsneHpXehU6/5qiFzNaWWhZ41qJRuXyKePD/i6GkC9OFMIXImFg+WnOOv5MUQU42lqx8vx6VCjurlFkWqdAGuv1uaMWf2MkFsPcrKYaEECIRKYSEyCr3TqdcBLm3N3Rzssgmnaleg62VBYv716ZBmTyKuKEYOoXPIymGhOlExej4aM05DngriyBHG0uWv1+P6sVc1Uksq1XuCF1+S6EYmm/Yu0yKISGEAKQQEiJr3DsNq7pAVJJuhxXaQfcVYJnNOlO9BntrS5YOqEv90spiKCg0ij6/STEkTCMqRsfwFIogB2sLVrxfl9ol3VTKzESqdYPOi5MXQ//Og/1fSzEkhBCYYSE0fvx4vvnmG86dO6d2KkJkzN2TqRRBbaFHzi6C4thbW7JsYF3qpVIMyZohkZUMjRG8OOD9WBF3sLZg5aB61C6ZJ5Uzc5jq3aHzouTF0Im5MjIkhBCYYSG0bds2Nm3ahKenJ4MGDeLixYtqpyRE+t06mnIRVL6NYad3S5uUz8uB7K0tWTagLvVKJS+Gev92kov+z9RJTORoEdGxfLjSK5WRoFxUBMWp3gM6LUx5ZGj3F7LPkBAiVzO7QmjEiBEMGzaMZs2aceHCBXr27Kl2SkKkz40DsKZ78u5w5dsYOjnloiIojoPN/0eGkhRDIeHReP52SjZdFUYVFhXDwGVnOHotUBG3t7Zg+fv1qFMqlxVBcWr0NBRDJGnTf2YJ/DkSdLEpniaEEDmd2a3WHjFiRPzfdTodly9fVjEbIdLJdw9s7J98s1T39tB9ea4sguLEFUODVpzhpF/CRpYvImPo9/splg6oS4MyeVXMUOQELyKiGbjsDGeTFNeONpYsH1g39xZBcWr0NIwKbRsC+kSFz7mVEBMJHRfkyAYuQgjxKiYdEbpy5cprHa/VaqlevXoWZSOEkVzeAhv6Ji+CKnfKddPhUuNgY8myAfVoXF7ZWjssKpYBy05z2DcglTOFSFtwaBR9l5xKVgQ521qy+oP6UgTFqd4dui0FbZKC5+IG2DzQUBAJIUQuYtJCqH///pw4ccKUtxQia3kth82DQBejjFfr8f8W2VYpnpYb2Vlb8Fv/Osk2XY2I1vHhyrP8efGBSpmJ7OxRSAQ9Fv3LBf8QRdzN3oq1HzagZnFXdRIzV1U6Qc/VYJGkaYv3TljXC6JCUzxNCCFyIpOvERoyZAh//PFHmscdOXLEBNkIkQn/zIY/RgJJOi959IPOC2WaSQpsrSxY2Lc2basUUsSjY/V8vO48607fVSkzkR3deRpK90UnuB6g3Ksrn6MN6wc3pGpRF5UyM3Pu7aD3OrC0VcZvHoRVnSFc1u4JIXIHkxZCa9aswdXVlbFjx7J06dIUj/Hy8sLT05OhQ4eaMjUh0k+vhwPfwYFvk79Wbwi88wtoLUyfVzZhballXh8POnsUVcT1ehi/9RKLjtxUKTORnfg+ekG3hf9yLyhcES/iYsuGIQ1wL+SkUmbZRLm3wHMzWDsq4/dOwfK34aVMVxVC5HwmLYQqVqzIhg0bKF26NDNmzGDq1Knxr/n4+DBkyBD69u2Ll5cXpUuXNmVqQqRPbIxhFOifn5O/1nQstJsGWrNrxmh2LC20zOxeg/4NSyZ77cc9Pvy4xxu97HEiUnH2dhDdF54g8IVyTUuZfA5sGvYGZfM7pnKmUCjdGN7bCXZJNpd9fBl+bw1BfurkJYQQJmLyuTtFihRh3bp1DB8+nBUrVvDo0SMsLCzYs2cPOp2OEiVK8NFHH/HOO++YOjUhXi063LAeyHdX8tdaT4E3RiSPi1RptRq+e7cKzrZWzDt0Q/HaoiN+BL6IZFrX6lhZSGEpEuy/+pgRa88RGaPc/6ZyYWdWDqpHPkdpTvJaitaGgXsMU+JePEyIB98yFEOem6FITdXSE0KIrKTKOwxnZ2d++uknXF1d2bt3L7t376ZQoUJMmjSJPXv20LFjR7TyVF2Yk7AgWNkpeRGk0cK7c6UIyiCNRsMXbdz5sn3FZK9tPXefD1acJTQyJoUzRW60/vRdhqw6m6wIqlPSjXWDG0gRlFEFKsH7f4FbKWU8NBCWd4Cbh1RJSwghsprJR4RCQkL4/fffWb16NWFhYVhaWhITE0Pp0qXp0KEDFhbmsbZi7NixbN++Pc3jFi5cSPPmzRWxly9f8vvvv7Nv3z7u3buHtbU1pUuXplOnTvTs2RNLS1lEn62E3IfVXSHQWxm3sIGuS6Dyu+rklYMMblIWV3trxm+9RKwuYUrckWuB9PntJEsH1CWvvMnNtfR6PfMO3mDm/mvJXmtRsQDz+nhgby0/VzPFrRS8v8/ws+7xpYR41EvDRtGdF0K1bqqlJ4QQWcGkwy5z5syhZcuW/PbbbwAMGzaMf/75h06dOnH8+HH69evH06dPTZlSqq5evZqh854+fUrXrl1ZsGABN27cIDIykhcvXnDx4kW+//57+vbty8uXL9O+kDAPDy/CkpbJiyAbF+i3TYogI+pRpziL+9XG1kr5Y+mCfwhdfj2BX6B83+RG0bE6xm+9lGIR1L12MRb1qy1FkLE4FYSBu6BUY2VcFw1bBsE/swxdTYQQIocw6W+PX3/9FSsrKzw9PRk+fDh58hg2uZs6dSoFChRg8eLF9OrViyVLllCyZPJF1KYSGRmJn59hkeisWbNo2rRpqsfa2ia0H9XpdAwdOpTbt2/j4uLC6NGjadasGREREWzdupXFixdz/vx5vvrqK+bMmZPln4fIpOsHYNN7hieiiTkVhr5boGAVdfLKwVpWKsiaDxowaMUZnoVFx8fvPA2jy68nWNK/jmyOmYu8iIhm+JpzHLv+JNlrHzUvyxet3dFoNCpkloPZuhh+vm0bAle2KV87MBGC70D7n2R7ACFEjmDSEaHOnTvz119/MWHChPgiKM5nn33G119/zf379+nVqxcXLlwwZWoKPj4+xMQY1iXUrl0bBweHVP8knsr3119/cfHiRQAWLFhA9+7dyZ8/P8WLF2fkyJF8/fXX8cf9999/Jv+8xGs4uwzW9kheBOUtD4P2SRGUhWqXdGPz0IYUdbVTxJ+FRdNnySn+uCAbr+YGD0PC6b7w32RFkEYDE9+pzOg2FaUIyiqWNtB1qWE7gKS8lhk2Xo18Yfq8hBDCyExaCP34448ULVo01dc9PT2ZPXs2oaGhDBgwwHSJJXHlyhUAChQoQMGCBdN93ooVKwBo1KgRderUSfZ6z549KVOmDACbNm0yQqbC6HQ62P8t/DkK9LHK10q+aSiCXEuoklpuUq6AE1uHv0GVIs6KeFSMjo/XnWf+oRvSXjsHu3w/hE7zj+PzSPlm28ZSy6+etRjwpmyvkOW0WsN2AK0mJX/txn5Y1g5C/E2flxBCGJHZtWZr3bo1S5cuxdraWrUc4tYHVatWLd3nPHv2LH4Uq0WLFikeo9FoaNasGQAHDx7MXJLC+CJfwoa+cHx28teqdjOsCbKXaVmmUtDZlo1DGtLcPX+y12bs9eXzjReIjIlN4UyRne259JBuC0/w+Llyj6C8DtasG9yAtlULq5RZLqTRwJufQPflhuYwiT26BL+1AH8vVVITQghjMLtCCKBOnTqsXbtWtfvHFUIVKlRg1apV9OrVCw8PD2rWrMk777zD/PnzkzU88PHxiX9CXalSpVSvXblyZQCCgoJ48ECm+JiNZ/dgaduU9whq/Dl0+c0wXUSYlIONJb/1r4Nn/eSjcFvP36fPb6d48jIyhTNFdmPoDHedYWvOERGtbI9dJp8DW4e/Qa0SbqmcLbJUlc7w3h9gl+RB0MvHsLw9XNqsTl5CCJFJGVrt+PLlS65evYper6dkyZIUKlTI2HlRtmxZo18zPaKjo7l2zdCdaMmSJURHRytev3btGteuXWPLli389ttv8Xnev38//phXTf8rXDjhaaa/vz9FihQxZvoiI+6dgfW9DXtmJKa1hA4/Q+331MlLAGBpoWVyp6qUzGvPj3t8FE2rvO4E03HecZa8V4dKhZ1Tv4gwaxHRsYzdcpEd/yV/OFSvdB4W96uNq716swQEUKI+fHDA0Eo76GZCPCbC0FEu0BeajTdMqRNCiGzitQuhVatW8dNPPxEVFRUfK1myJB07dqR///44ODjEx+/cucOqVau4fv06tra2VKpUiTfeeIN69eoZJ/sscP369fjiJzY2lvfee48uXbpQsGBBHjx4wMaNG1m/fj3379/nww8/ZOvWrbi6uhIcHBx/DRcXl1Sv7+TkFP/358+fZ90nItLn3ErY9TnERinjdm7QYyWUbqJOXkJBo9EwuElZSudzZNT684RGJUyJu/8snK6/nuCn7jVoX02mTWU3D56FM3S1Fxf9Q5K91rNOcSZ1qoq1pby5Ngt5y8KHf8PG9+DWEeVrR6dDwFXo9CvYykMJIUT28FqF0JkzZ5gyZUqy+O3bt/nll19Yt24dixYtolKlSpw7d45BgwYRERERf9zRo0dZtGgRJUqUYNSoUbRr1y7zn4GRBQYGUqBAAZ48ecKcOXNo3bp1/Gtubm589913lC5dmh9//JH79++zcOFCxo0bR2RkwvQcG5vUp1Albred+JyUrF+/no0bN6Yr77h23yKdYqJg73g4syT5a/kqQO/1hl/6wqy0qlyQzcPe4IMVZ7n/LDw+HhYVy/A15/ioeVk+a+WOhVa6iWUHp28FMXyNF09eKh9EaDTwVftKDGpUWjrDmRs7N0N77T1j4ezvytd8/oQl16HXWshXTp38sjE/Pz+6dOmS7uN79OhBr169sjAjIXK+1yqE1q1bBxieznbt2pVq1arx+PFj9u3bx40bNwgICOC9995jy5YtjBkzhvDw8BSvc+fOHT777DP+/fdfvv/++8x/FkbUtGlTjh07RlRUVKoNGwYMGMCWLVu4du0a27ZtY+zYsYo22sYSGBgY38EuLan9vxYpeBlgeKJ590Ty18q2gG7LwM7V5GmJ9KlU2JntH73J0NVeeN0JVrw2/9BNrjx4zpxeHrjYWamUoUiLXq9n9ck7fPfHVWJ0yu5/jjaW/NK7Ji0qpr9jpzAxCyt4+2coUMlQECXusPnE19BEoesSqNA69WuIZMLDw9P9Ox8M7xGEEJnzWoXQhQsX0Gg0tG7dmsmTJ8fHP/nkEzZu3Mj333/Pixcv6Nu3L48fP0aj0dCkSRPGjh1LoUKFuH37NgcOHGDdunUEBwezadMm8ufPz8cff2z0Tyyz0upa16JFC65du8azZ8+4c+cOdnYJe55ERUWlOiqUeITsVSNHAPnz56dKlfTtVxMQEJDmCJMA7p2GTQPg+f3krzUcAW99JxsFZgP5nWxY+2F9vt5+mY1nlS18D/sG0nHeP/zat7asGzJD4VGxfL3jMpu9krdeLpXXnsX961ChoFMKZwqzU+9DyFfe8DM1PNFDicgQwz5szcZDk9Gybiid7Ozs0v07HwzvEYQQmfNa7/iePn0KwBtvvJHstR49ehAdHc2kSZMICAgAoESJEsyfPx9LS8NtKleuTOXKlenfvz8jRozg7NmzLFq0iC5duryywYA5StzkICgoCGfnhDdcL168SLXIefEiYV8MN7dXd0Dq1atXuoe9a9euzblz59J1bK6k18OpRbDvK9DFKF+ztIV3foEaPdXJTWSIjaUF07pWp1pRl2QjC7efhtF5wXEmd6pGt9rFVMxSJHb7SShDV3sl2x8IoJl7fhnJy47KNIPBh2G9Jzy+nOgFPRz+Ae6dMnTddMirUoLZR5kyZdi6davaaQiRq7zWYxqdztDSNPGb/sT69OlDiRIl0Ov1aDQaevToEV8EJebq6sr8+fNxc3MjNjaWzZvNr/VmWps1Ju4mZ2dnR6lSpeI/flVb7IcPH8b/XTrGmUjkC9g8EP4am7wIci4G7++VIiib0mg09GtYijUf1Cefo3IUNyJaxxebLjBuy0UiomW/IbX9dfkR78z9J8UiaHizsvz+Xl0pgrIrt1KGzaarpLC+5ebfsKiJ7DckhDBLr1UI5c1reKJz7969FF/XaDS0bNky/uO6deumei0XFxfeffdd9Ho9p06dep00stTHH39MvXr16Ny58yuPu3HjBgAWFhYUL16c8uXLxy/q9fHxSfW8uD2KXF1dFa20RRZ5fMUwX/3KtuSvlWpseJJZpKapsxJGVr9MXnaOaESNYsk7Nq4/c4+uv57g1pNQFTITUTE6puy6ytDVXryIVD6IcLC2YH6fWoxpW1EaXGR31g7QbSm0+h40Sd5aPPeHpW3g5P/au+/wqMrE7ePfmUkvlNBL6AQwoSQgylJtoAsqigtYEFFYy4quBbtrfe2KvSDYFStL/S2CKIhSVSAQIPQWSoAklNQp5/1jmCHJFNITMvfnunKRmfOcZ56Z4WTOPU8578MZvmQUEalKpQpCCQkJGIbBrFmz3L1DxXXocHqlmNjYWL/1uS4uumvXrtI0o1JFR0dz7NgxNm/ezKFDh7yWyc/PZ+HChQAkJiYSFRVFVFQUSUlJAPz8889e9zMMg8WLFwPQv3//im+8nGYYsHoaTLkAjmzx3N7vXhgzE6I0xrq2aF4vnG9v68ONfVp7bEvZf5xhby5l1lovc8Ok0uw5msM/3l/Gh0t3emyLaxLFrDv7MbSbvhCqNUwm6Hu38+KrkY2LbnNYnb3yX18PORnV0z4RkWJKFYSGDRsGOJd4fPzxx7HbPYebtG/fng4dOmA2m4mKivJbn2vYXE26ns7ll18OOENL4QUhCnvuuec4cuQIAOPGjXPfP3z4cAAWL17M8uXLPfb75ptv3Mtcjx2ri3RWmtws+PZGmHcv2IstIBFWF679Bi5+Qosi1EKhQRaevjKBN0b3IDy46EqO2QV27v56LZO+W0dOgc1HDVJR5qzbz9A3l7LOy/WBhvdozsx/9aVDY/+fEXKWatMPblsKrft6bkudB+/3h92en5EiIlWtVEFo8ODBJCUlYRgGM2bM4IorruC7777j4MGD7jI9evRg7ty5rF69muBg/+O9d+/eDXDGclWpT58+XHjhhQAsWLCAW2+9lb/++ouMjAySk5O56667+PrrrwFnMLz44ovd+44YMYJOnTphGAZ33HEHX3zxBYcOHSItLY233nqLZ555BoAhQ4bQtWvXqn9ygWDPCueH7KbZntua9YBbf4VOl1Z5s6RqXdmjBbPv9H6i/d2f+7j8rd/YkOZ5gi7ll51v46Efkpk4fY3HULgQi5lnhicweVQPIkL0RUStFt0Ubpzt7CEq7vg++GQoLHkJ7PpSQkSqj8k406oAxRw5coRx48axdevWIhe6a9iwIfHx8SQkJBAfH098fDyNGzf2WU9BQQFDhw5l7969tG3blv/9739lfxYVLDs7mzvvvJNly7xcZ+aUyy67jJdfftkjxO3du5exY8eSluZ9CE5iYiIff/xxkeW2K4Jr1bikpCT+/LOCJqU6HLBmDWzaBJ06FV0C1eGA1FTo0gUSE6t/eVS7FZa8CEtfBcPLsM3z74CLn4Qg/0uWS+2SU2DjydkpHktsAwRbTNw3uBMT+rer9vkp/g41f/vUpEMQYM2eTO75Zi27juZ4bGvXMJK3rkskvrnnPC6p5bYuhP/eCjlHPbfFngdXfQAxbau+XYVV4+ddpXx+i0iJlPoruYYNG/Ltt9/y9ttvM336dHJynB94hw8fZsmSJSxZssRdtkGDBu5Q5Ppp2rQpJ0+e5JFHHmHv3r2YTCb69OlTcc+oAkRGRjJt2jTmzp3LrFmz2LBhA9nZ2dSrV49u3bpxzTXXuHuNiouNjWX27NlMmzaNhQsXsm/fPgzDoF27dgwbNowxY8ac8RpFUkpHtsGM8bB/jee28Pow/D3odFnVt0uqXURIEC9d052+HRryyIz1ZBecHs5rtRu88L/N/LI5nddG9aBFvYr9ciKQ2OwO3vllO2/+vBW7w/O7tauTWvDMlQlEhqoXKCB1vARu+x1mTIBdS4tu27vS2Yv/95eg+7XOeUYiIlWk1D1ChZ08eZIlS5awcuVKkpOT2bZtGzZb0W5uU7E/aq5r52RmZmIYBnXr1mXmzJlaQa2cArJHyOGAP6bBwv+A1fMbaFr9zXl187pn1zWqpHLsOpLNxOlrWO9lSFx0WBBPXh7P1UktPP5mVYWzuUdox+GT3PfdOtbsyfLYFhFi4ZkrExihazkJgMPu7LVf/Lz3nvsul8PQydWziI16hEQCUrm+nouKimLo0KEMHToUcA53S01NZePGjaSkpJCSksLWrVspKChw75OR4VwtxmQyYTKZOH78OMOHD6dLly506dKF+Ph4unTpQrt27arlhETOEpm7YNadnt8uApiD4IJHnWPTzRbP7RKQ2jSM5Ifb/8brP23hvSXbi6zieyLPxn3freP/1h/guau70qROWPU19Cxhdxh8/PtOXv4xlXyb50ltYqt6vD6qB60bRFZD66RGMltg4APOi7DO+CdkFltNcNMc2L0Mhr4K8f4vYSEiUhEqdJxCSEgIXbt2LbIQgM1mY9u2baSkpLgDUmpqKrm5ue4yx44dY+XKlUWuJxQWFkanTp3cCxOIAM5v5v78CBb8B6xergvTMM55FXNdG0i8CAky88ClnRnUqTH3fLOWtKzcItsXbU5n8ORfefKKcxjeo3p6h84GO49kM+m7dfyxO9Njm8Vs4q4LO/KvC9oTZKkBE5ek5ont7VxVbv7DsObzottyjsJ3N0HKTGcgimxYHS0UkQBR6QO2g4KC6Ny5M507d2bEiBEAOBwOduzY4e412rhxI5s2bSI7+/SJbW5uLuvWravs5snZ5Oh2mHO3914ggHPHwyXPQEhE1bZLzjq928bwv3/358lZKcxYU3Rhk2O5Vu75Zh1z1x3gmeEJNNfcITeb3cG033Yy+act5Fk9e4HaNIhg8qgeJLaqXw2tk7NKaDRc+TbEXQpz7vJcSGHjTNj1G1z6AnS9RnOHRKRSVMvMVbPZTIcOHejQoQNXXnml+/5du3Z5hCMR7FZY9iYsftHzukAAdWOdH6jtBlV50+TsVScsmNdG9eDShKY88t8NHDlZ9P/Wos3prHhtCZOGdGJMnzbVvrJcdVu/7xgPzUgmZb/ndd9MJrjpb214YEhnwkM0HFVKocsw58px8+71vOxBzhHnQjjJX8PQ16C+58WSRUTKo0Yt4dOmTRvatGnjnnMkwr4/nd8WHtrgfXvPm5y9QGF1qrRZUnsMjm/KuW1ieGJ2CrPX7S+yLbvAzpNzNjJz7X5eGNGVzk0D7/9ZToGNyQu3MO23nXhZEI5WMRG8fE03zmvXoOobJ7VDVCMY+Rls+AH+737ILTbkcttP8O75cOFj0PtWXQxbRCqMBnBLzZST4RwGN/Ui7yGobizcMAMuf0MhSMqtfmQIb16byPs3JNEwyvNaU2v3ZjH0zd94du5GTuRZq6GFVc8wDP63/gAXv7qED5d6hiBXL9D8f/dXCJLyM5mcQ+DuWAmdh3lut+bAj4/AlEGwZ6XndhGRMlAQkprF4YA/P4W3esKfnwDFz77Mzouj3rECOlxUHS2UWuzShGYsuncgo8+N9dhmdxhM/W0nF726hFlr0yjHlQdqvJ1Hshn78Wpu//Iv9h/L89ge1ySK72/7G09eEU9EiL6dlwoU3QRGfwmjvoCopp7bD62HjwbDzH/BycNV3z4RqVUUhKTm2Lsapl3sHAqXm+G5vUkCjP8JLn0eQqOqvn0SEOpGBPPCiG5Mn3A+7Rp6Lv2cfiKfu79ey7UfrmCjl/kyZ7MTeVZenL+ZIZN/5dctnieZIRYz910Sx9yJ/enZWgsiSCXqcjncuQp63ex9+9ov4O2esOI95zxSEZEyUBCS6ndsH/ww3hmC0rxcTC44Ei5+Cv65GFr0rPLmSWDq074B/3d3f+66qCMhQZ5/KlfsyGDoW0t5eEYyh094WcTjLGJ3GHyzeg8XvLKE9xZvp8DuuSJc3w4N+N+/+zPRx+shUuHC6sKwyXDzj9A43nN73jGY/xC82we2/Ai1uJdWRCqHxjRI9ck/Ab+/CcveAluu9zLnXAlDnoO6ujK9VL2wYAv3XhLH1YkteGJ2CkuK9ZIYBkxftZc56w5wxwXtublvW8KCz65V05ZtO8Kz8zax8YD33q0mdUJ5fNg5DO3aTNdVkurR6ny49VdYNQV+eQ4KThTdfnQrfDUS2l8Ig5+FJl5Ck4iIFwpCUvVsBfDnx7DkJefyqN406ACXvaR5QFIjtGkYySfjzmXBxkM8PWejx4VYT+bbeGl+Kp8t2809l3RkRFLLGn8x0ZT9x3hxfqrXIXAAQWYT4/q24e6L44gK1UeFVDNLEPS5A+KvggWPwYbvPcts/xne6wvdR8MFj0C9VlXfThE5q+jTTaqOw+FcHvXnZyBrt/cyoXVh0INw7gQICqna9on4YTKZGBLflIFxjfjw1x28u3g7uVZ7kTIHj+fx4A/r+XDpTu4f3Ikh8U1qXC/KnqM5vLowlVlr9/ssc1HnxjwytAvtG2kuntQwdZrBNdOg9wSY/zDs/6tYAQPWTXd+1pw7HvrfD5Fa1VBEvFMQksrncDivEr7kRTi82XsZk8U5KXbQw/rQkhotLNjCxIs6MvLcWF6an8oPf+3zKLMt/SS3ffEnXVvU5d8Xd+TCzo2rPRDtzcjh7Z+38cNf+7B5uyAQztXgHht6DgPiGlVx60RKqdX5MH4RrP8WfnoSThwout1eACveda5Cet4/4W93QURMtTRVRGouBSGpPA4HbJoFi1+Ew5t8l+v0d7joP9C4S9W1TaScmtQJ49WR3bnpb214/n+bWLb9qEeZ9WnHuOXTP+jW0hmILuhU9YFob0YO7/yyje//9B2AGkeHcvfFHRnVK7bGD+kTcTObncPgulwOy96GZW9CwcmiZazZ8NtkWPUhnHcr9LlTgUhE3BSEpOLZrbD+O/j9Dd89QACx5zlXg2vdp+raJlLBurasy5fjz2Pp1iO8OH8zKV6W1E7ed4ybP/mD+OZ1uH1Qey5LaIbFXLmBaOuhE7y/ZAez1qb5DEDRoUHcNqg94/q20fWA5OwVEnlqSPUt8OsrsHoqOIotqV1wEpa+Cis/gJ43QZ9/QZ3m1dJcEak59MknFacgG/76zPnN3HHP4UJujePhwkedPUE1bP6ESFmYTCYGxDWiX4eGzEnez+s/bWXnkWyPcin7j3PnV2to0yCVWwe25+qkFoQGVewqc3/tyeS9xdtZuPGQzzKhQWbGnN+af13QgfqRmosntURkQ7jsBTj/NvjleeewOaPYUvAFJ2H5285A1H009L0bGnasnvaKSLVTEJLyO7YX/vgI/voUcjN9l2t8Dgx8ELpc4RzSIFLLmM0mruzRgqFdmzF73X7eXLSVXUdzPMrtOprDwzPW8+qCLVx/Xiuu690KCCvz49rsDhZsOMjHv+/iz92+j8HQIDM3nN+aWwe2o3F02R9PpEar3wau/gAG3A+/vuwcoVA8EDmssOZzWPMFxA2B3reCUadamisi1UdBSMrGYYXcrfDHNzD3dzDsvss2PgcGPgBdrlQAkoAQZDFzdVJLrujenFlr9/PWz94D0ZGT+byxaCvvLt7G31o2p4ulDXFGXaBkPaUnbfnM2LyXOxfs5sCxPJ/lwoLNXNu7FbcPbE/jOgpAEiAadoSrpzhXjvv1JedKcsUDEQZsme/8iW4DYX2goCmE1a+OFotIFVMQkjMzHHBiFxzfAlmpkLUZju/wHINdXOx50O9e6DhYAUgCUpDFzIieLRme2IL5Gw7y3pJtbEjznENktRss2Z3GEtL4en8oPZo0pEfTRnRr3JCo0NND1+wOB1szslh78DBrDh5mZ5b3i6C61AkL4qa/tWHs39rQICq0wp+fyFmhURyMmOq8ttCyt529QPZ8z3Indjl/Fk6HiGZQr5Pzp04cFM9PIlIrKAiJbyfTYc3zkPYrbPfyoeFLx8HOAKRFEEQAsJhNDO3WjL93bcpv247w3uLtXleZA8jKy2fx7jQW704r8+M1rRPG+P5tGd27lS6GKuIS0w6GveYcor3yfVg9DfKPeS+bc8D5s3/xqTtMcLQj1H0ROlxYVS0WkUqmT0jx7ednYN/CkpUNjoQe1zrHWTeKq9x2iZylTCYT/Ts2on/HRmzcf5xPlu1k5tr9FNgq5uvmxFb1GNe3LZclNCVYy2CLeBfdBC5+Avrf57z46sr34ei2M+xkwLEt8N2NcM9GCNN8IpHaQEFIfDvmZ+U3l6jW0GcCJI2B8HqV3iSR2uKc5nV46ZruPHhpZ75auYfPl+0lPTu31PWEWSwMTmjCzf3a0iO2XsU3VKS2Co2C3hOg1y2w7Sf46VU4/CcYfoZ955+A/OMKQiK1hIKQ+NZ7Auz6DQyb83ZY49Njput2hHQzJPSExETNARIpowZRofzrgo70qduB39blcDziMMnph9mQfpQ8u/dFSNrVq0O3Jo2IyW/E4J716d3TrENQpKzMZuhwMZxoABs3QPNQZ++Pa07siZ2nFwQ65yqo06J62ysiFUZBSHzr9He46EvYtBI6nw8RDU9vczjgaGr1tU2kljGZTDQMjaRvh0iGxrXB6nBwJCcXh1H0Yqh1QkOIDgnB4YDUVAhWABKpOCYL1GkP9TpC66HO+6y5sGEJtO8I/a/S9e9EahEFIfEvvBGEt4ewmOpuiUhACTabaRYVWd3NEBFLKIS1dgYkc8VeAFlEqpe+SxQRERERkYCjICQiIiIiIgFHQUhERERERAKOgpCIiIiIiAQcBSEREREREQk4CkIiIiIiIhJwFIRERERERCTgKAiJiIiIiEjAURASEREREZGAoyAkIiIiIiIBR0FIREREREQCjoKQiIiIiIgEHAUhEREREREJOApCIiIiIiIScBSEREREREQk4CgIiYiIiIhIwFEQEhERERGRgKMgJCIiIiIiAUdBSEREREREAo6CkIiIiIiIBBwFIRERERERCTgKQiIiIiIiEnAUhEREREREJOAoCImIiIiISMBREBIRERERkYCjICQiIiIiIgFHQUhERERERAKOgpCIiIiIiAQcBSEREREREQk4CkIiIiIiIhJwFIRERERERCTgKAiJiIiIiEjAURASEREREZGAoyAkIiIiIiIBR0FIREREREQCjoKQiIiIiIgEHAUhEREREREJOApCIiIiIiIScBSEREREREQk4CgIiYiIiIhIwFEQEhERERGRgKMgJCIiIiIiAUdBSEREREREAk5QdTegtkpJSWHatGmsWrWKrKws6tevT1JSEmPHjiUpKam6myciIiIiEtDUI1QJ5s+fz8iRI5k3bx6HDx/GarWSnp7O/Pnzuf7665k6dWp1N1FEREREJKApCFWwDRs2MGnSJGw2G7169eKrr75i+fLlTJ8+nfPOOw+Hw8Err7zC4sWLq7upIiIiIiIBS0PjKtgbb7xBQUEBHTt25KOPPiI0NBSAmJgYpk2bxrhx41i9ejUvvfQSAwYMwGw+O7OozWGw+mQQu3bkYHHsI8hidv6YTVjMJoLMJuKaRBMbE+F1/+2HTwIQbDZjsZiK7Gcxmwi2mN23TSZTVT41kbNGpHUPMXt/B4sZeozyXuhYGhzdBpZgMAeB2XLqXz8/lsK/h4COQRERqYUUhCrQ9u3b+fXXXwG4/fbb3SHIJTg4mPvvv59Ro0axfft2/vrrL3r16lUdTS2XtRkFPPTHcTYfi4Zdx+HP9V7LPXVFPGP/1sbrtlEfLOfIyYISPZ7ZRJGQddvA9vzrgg5ey97x5Z/sy8x1h6ggs5kgS9GQ5Xmfs+7ebWO4vHtzr/XOSz7AoeN5BFlO7e+qy0s9rvuDzM4wFxMZQtuGkV7rPZ5nxW43ioVBM2YTCoDik9l2khabn6fn7ncx73ZgpMb4DkKp/wf/d3/ZH+w/md6DUOp8mPtvH+HKAubgYreLBa3L34Twep71ZuyEP6Z57m8pXp+P+tsOgLA6nvVa8+Do1kL7eWlzkccIUgAUEanlFIQq0NKlSwGwWCwMGDDAa5nu3bvToEEDjh49yqJFi86qIJRtc/DKhpN8sjUHowTlLWbfJxE2R0lqcHIYUGBz4IpNNrvvfVMPnmD74ewS112YyYTPIPTp8l2s2plRpnqHdm3GO9d7XyDjoR+S+b/1B71uK9xLVry3LchiJqlVPV4fneh1349/38kvqYd91hFsOR26ioZEE43qhDHm/NZe603Zf4wth04UDX1e2lek7lMhL9hi9tlD6HAYmBT+SqTOoQW0Wn8fobl7Tt9p9vOn3GEv+4OZzOCr19qaDScOlL3uoZO9339sLyx7q+z13rHSexDK3Anv9ytdXaZCYemG76H13zzL5GTAJ0MLBatiQctnT9yp2z3HQfMenvUaBvz++hl677wETNfvMe0guqn353X8wKn3ttg+5iDn/ToORSRAKAhVoE2bNgEQGxtLdHS01zImk4nOnTvz+++/k5KSUpXNK5dfDuTz2NoTpOU4SrxPkJ8gZPcTZs5Yr6ViAlZxfoObveTPuzT1Wv28DjaHgc1hkA+A58lsbEy4z323HDrBr1sOl6KVp3VuGu0zCM3fcJC3ft5WpnobRoXyx2MXe9326fJdPDVno7P3z0ePndcAZ3EGrB9u93KCCvy5O4PPlu/2qCvI4qUXz2zCYjE5h2ueKjOyVyxhwRaPejOyC1i3L8sz9BXrDSzeQ+h6jKiQIMx+/l94E5SfTuyGB4nZP8Nzo98gZCvV45S83nIELHCexHtjt5azXh9tLsvrYNjBbgd7PuDj/bIXQPrG0tft0v4i70HIYYefnix7vUNfg3Nv8b7tvT6Qm+l7X2+9ba5A1+dOOP827/vNuNUZjt3BLNh3QCxef+x50OlS7/WmzoecoyUMmMFF7wurC3Waea/XVuAMff7+n4tIraajvwKlpaUB0KJFC7/lmjVz/lHet29fpbepvA7n2fl/e0KYeTwLbycCLSMsNIiJwuYwsDsMrHYH9lMn8NFhwT7rrbzAUvZ6gy2+52vZy9Fev4GwXK+D7/aW53WorKBZktfBYUCB3UFBKc6xg/20d29GLrPW7i95ZcVc2aOF1yCUsv8Y4z5eXeZ6f75vIO0aRXncbzccPLZ4BY0jw2kUEU6TyAgaRYSTdGI28dufJsia5b3CBu19P1hQKEQ0cJ5YO+zOQOCwliwYVFbA8lf32RawalJwK0m9cObX2GF1/nhTcNL3fntXOnveyuK8230Hod9ec9ZdFgnXwDXTvG/7fhxsnuv83WRx9oZhgYNNIKLp6Z+wJpCXD7Y2ZWuDiNRYCkIVKDPT+Q1bnTpehmUU4uotOn78eKW3qbyeXnuCXjnf8lzor+wzGrLPaMQ+oxEHaUi3OnW5uFscQV3OcU6o9hhjn+8cNhIR41HvxqeHuAOTzWFgtxvYHA5sp8KUwwE2h+NUuDJwGKfK2h20qO+7J+TxYV04nmfDZjewGwZ2u+P0Y5z6cdVjL3S/1e4gqVU9n/V2j61HVFiQs153ux3u23aHgdXhOPU8TtfpMCAsxMeJGZUfLMrCX8AqX73V0JNXjnrB92tc/nq9v8bHrXmkHs0k9ajzb0ms6RDPBU2jh2WD1/LbgnqxtstzxCZ2JGRPJuc0r0NoULH/b70nYO15C8dyrZ6Lk5gMTA6b82TeOBWU7KdOgh12532+tLsAxvzXcx+H3fl74TqLPIbNeV9QqPd6o5tC92tP7+Mq7w5wxQOd6/dT5YPCvNdrOJwnu/6ekz++AlZ5A4vFxxdGlVVveeuurF5CX68vVGJ7C9VruP6/W+HkbudPcU1CAe+9zyJydlIQqkD5+c5BTGFhPj6IT3EtouAq78vXX3/Nt99+W6LH3rFjR4nKldaDXaPZfugwEaZ84kxpxJF2emMOsOLUjy89rofh73rcbTKZCJr+D4J2/OJjvHux4Q2WYrdbnQ+XPO1R76UJzeCPj2D/au+Tn11j4oODPOvPtcCmptBlmEe9T1+ZAEe2wrF9hfYJ9THMw8skb2seBHv+v3j7ukTyra5Q5gxWnr1rDuyFgqGrTExkiM+X/YoezenSrM7p0GcYhep2FAmXdvupEHcq4LX2MY8HoHF0KOc0q+NuS9Ew6azbddt2Kty6MoO/nqby9bj5C25lH9IIvkNWeXrcACw+XovMglwAzDgYZ5nPfUHfEWHy/DuRZUTy/2zX813eQFh9xPkD/PbgBbSs7/n+pew/zvB3fvf6mK7hiIWHBxZdEGQ3H4zpSeemxb7gqdOMdFN97vt2nd+5YT6HI/68k+GJLTwXEmnWDesV7zJr7f5iQyI956V5Dj80YSkw0yjfRlRosY+3lr3giQzsdgdmw4bJKBygbKd/d/8UClt2GzSM8/r6EdkQRkwrGshc+xj2QmHOVqzMqdv1Wnmv12SCjkOK7VusLo+6CwVDX0ETqiZYnA31lrI3zxbWpFJPmnbs2MHVV19d4vIjR45k9OjRldgikdpPQagCWSx+vtEqg8OHD5d4HlFubm6FPrZLy0gLkUHpUNbzSb/f8hX6EC+tiAa+t+1eDutLFiA9tDzXaxAC4I+PYcU7Zau3fhu4e53H3XXCgmHte7D0VR+TrL0tdVxozP0fUTDC8wK9gzo1ZlDEbtg483T5kOCi4czXhGuzBTamQudhHu/f+P7tGN8rBrJ2l3gSt8MUhB0T/rLDdb1bMficJu6A5gqBxXsDiwS4U8HR3wILnZvW4fZB7XE4ivfUuYLb6dveevt89QiFBJlpUS+8UDudga9wL6Y/wT7qzbTmEG/axfPBH9LN7H2I0Wx7H5623sgR6nps8xUK/QVC13BEL9PQ3HwFv+x8O0u3HvG94xkkta7vdUXFPKud+7/zPF5K6rWR3bk6qaXXbV2e+JECm8PrUv2+w6AJi3kdN/dtw5U9ig19Do2Grtfw+MwNnMizel3YpOhCImaCggs93hYTXXMy6dm6ftF6QyLh+m9ZtTODnAKbe+6ct8BpMZs8evuCzWZCrXavQzu5f6uPXrViYapwT5thPxUIO/p+4S98FPJP+OnJK35fodvNuvmut1FnwOS9h9EdYq3gcBSt23BUaE/Tp/vr4mPWVYXIzc0t1dzhw4fLNg9URE5TEKpA4eHOIVtn6ukpac9Ro0aNiI+PL9Fjp6enn/Fxy8QwqGeU/USn1g6jqMh6809Cdhk/0MI8T4bdDm2A5W+XrV6Ax48AXl7nXb/BN9eXuBrzqZ9gV0i6aw3UKbo6X/3IEOof3wQzJpzutfMV/oqHN0swpFlg4INQt+jJb/fYenRv4HD2EvrqXfT3GHt+h6YJEF70JHVgXCN+f2AQHE/z3P9UyLRjwWYUHo5puINSgyjv39b3tuzk1dDHMXtJJfuNGB6z3szPDu8rEELl9WD56s0rb4+br6BZnh5C8D9c0lW3ezESW8mfw1E/S/7/mHKQ9BNl+xv8rwvaewahU56YncKmA2UbRj363FheGOElYITX45+f/cGqXRleLwcQXCxkBZmDCTKHnrp9mJ6tbEy8yEsgSryB7/7YS0r6cY9evGCLCUuw70sPBNtMNNx2hL4dGnrWe/UU9mbkkJFd4Ln4SJG6ioVFE5gxfC1zAVd9AAXZp4JVAWxMYf2GLczJyiW8IJ2WpsPEmg/T0nSYOuTw8hYTV2UXEBPt/7O7rMLDw0v8mQ/OcwQRKR8FoQrkmvtz4sQJv+Vcc4Pq1/f+wecyevToEnd79+zZk7/++qtEZUvL1Oo/0CwC8tIh9yDkHITsA3B8H5isYDaKfktXeHHt2jSMwtfk4XLXWwNfB3DOp6jIel3fLvtqc/5JOJJatroBzrvNIwgBkH0Efn6m7PXeOAvaDfK8Py8LXk/wuZsFsLiWKPY23HPoK9B5aJF97NH9yLb2JjpzeZH798eOY3XLSZybb6F1Ti6Hs3M5dDKHvZm55Bh5YHIGLF8LR5Q3WFTWXCmfwa2S5mAZp4JpmeutpOGd/uflVc6KlSfybGTllO1vWmiQ7/Yu2XKYucllW1b93Db1vQchYNpvO/lk2a4y1duhcRQ/3TvQc0OdZny2fBef/L7P+VrlxbD1eC+vdXQMtfL5gAZ+hySXV7t27Zgxw8uqkCJSaRSEKlDbtm1ZtWoVBw74/xA4eNB53RjX6nE1mskEwfWhQSeKXE/E4YDUVOjSBRITPbe5TnpNvj8wGf6u8+S3+JAGu9U5pKHIsAxHoeEWVudQM186/d057r74mP3C7fI2ydphhyZ+vo0LiYKoJt7nFZxpAra5OiYul6Nef9ePqbTVws62ekvQo2k4nN802730JHi7z2RmV9c3iF/aF7NhJTeqE7u7vUF2gz60BArHPH+HYHHnto3hz8cuLtI7ZTdOzxfzd9tmN2ha1/sCJY2iQnl82DnY7IXmhp0axlh0gRJHsaGHzrobRnk/qTQBXVvULTJssfB8N2+9bIWHI1ZWwKqshTn8LXxSrhUgK2lBlaBKWmHT/+tb9kDob6H6oycL2HHE97Xngk3wr86R3G7aR2jD2DK3QURqJgWhCtSxo3OowO7du8nJySEiwnPSsmEY7usNnXPOOVXavipjNoM5BDjDN2cx7Srn8XtcWzn1Dn7G+eONYXhOtnZNlj5TIEy8Adr299zHFc68juE/9RhBvlfQo2Gcc7GK4qt1FV8lzNvqXP4YhjMclDVgVNbqWz4Dy9m1vHFedCcOdHoIDAeH2t+NYfEz6b2Egi1mn8PxyqNBVCi39GtbKfXOmdiv1Pu5QpevHiGLycRP9w70WOyjcKByB8VCIc5qN3A4DJJ8DF8DGN+vLTlWuzsEusJk8duulSULL37i75pgDaNDybXaPQKm67a/3OGvp8lajmDhN7hV2sInlROw/NXbq0EwL/SqS4coM5Sjs1pEai4FoQo0cOBAnn32WaxWK0uXLmXIkCEeZdauXUtGRgYA/fv3r+omSmUxmZxzQ/wtWetLTFvnT0XrcJHzp6J1+4fzB0rQy1Z8pSyrs2fNmyYJcM3Hnr1//pZkLhwYw+p5rzckytlL6HP1ruK9hcUmiVt8BPrKCm7AwY73l6/uAGUxm7D4mT9oNpvo0NjH/79y8jpnpgJ8e2sfv9sNo1hPW6FQF+ptoYRT/t/wrhzPs3r0/hXuyXMvBuJwBkHX7fZeroHlMqBjQxpEhhRpk+tyBa667IXCZeHFSWL9rFhpMZsICzaXaDGS4kp7bbToIBMPdovmunbhmE0m598HEamVFIQqUKtWrUhMTGTNmjW8+eab9OvXj8jI0ysiWa1WXn31VQDi4uLo08f/B5xIjVfS3r+SiG4CCSVfOrbEGrSHa6dXfL11WsDDaRRZKtnncszFlz62QdPuFd8mCTgm06nFA0q5aOk5zf1f766sxvRpUyn1Pju8K88O7+q+XWTYZbFevOKXHvB30eWrk1rQI7YuNpsD+86dhB9I4/webahTfPl1EamVdKRXsIcffphRo0axbds2xowZwwMPPECnTp3YvXs3kydPZvXq1ZhMJu655x6/y/6KSA1nNkNo5fQuiIh/llMrw4XgZ9hxCcQ1iSauSbSz18d+ELKtEFy+OkXk7KEgVMG6d+/OU089xZNPPklKSgpjx471KPPQQw9x4YUXVkPrREREREQEFIQqxahRo0hISOCjjz5i1apVZGZmEhkZSWJiImPHjtWQOBERERGRaqYgVEni4+Pd84FERERERKRm0UBYEREREREJOApCIiIiIiIScBSEREREREQk4CgIiYiIiIhIwFEQEhERERGRgKMgJCIiIiIiAUdBSEREREREAo6CkIiIiIiIBBxdUFVKxuHwf1tEKkRJDy0dgiKVRJ93IgHDZBiGUd2NkPKLiYkhMzOT8PBwunTpUnEV5+RAXp7v7WFhEBFRcY8nEqDOdKj5okNQpIJU0+fdpk2byM3NpX79+mRkZFR4/SLim4JQLREREUFubm51N0NERETKIDw8nJycnOpuhkhA0dC4WqJx48akp6cTFhZG27ZtK6zeHTt2kJubS3h4OO3atauweqX89N7UTHpfai69NzVToL8vO3fuJC8vj8aNG1d3U0QCjnqExK+rr76alJQU4uPjmTFjRnU3RwrRe1Mz6X2pufTe1Ex6X0SkumjVOBERERERCTgKQiIiIiIiEnAUhEREREREJOAoCImIiIiISMBREBIRERERkYCjICQiIiIiIgFHQUhERERERAKOgpCIiIiIiAQcBSEREREREQk4CkIiIiIiIhJwgqq7AVKzjRw5ksOHD9OoUaPqbooUo/emZtL7UnPpvamZ9L6ISHUxGYZhVHcjREREREREqpKGxomIiIiISMBREBIRERERkYCjOULiVUpKCtOmTWPVqlVkZWVRv359kpKSGDt2LElJSdXdvFrtl19+4fvvvyc5OZnMzEzCwsJo06YNl1xyCddffz1RUVEe+6xYsYKxY8eese4hQ4bw5ptvVkaza7UHH3yQmTNnnrHc+++/zwUXXFDkvpMnTzJt2jQWLFjA3r17CQkJoW3btgwfPpxRo0YRFKQ/w2UxZswYVq1aVap9UlNT3b//8MMPPPLII2fc5+abb+bBBx8sdfsC1R133MGiRYv48ssv6dWrl89yhw8fZsqUKSxZsoT9+/cTGRlJXFwc//jHP7jiiiv8PkZBQQFffPEFc+fOZceOHZhMJmJjY/n73//O2LFjCQ8Pr+inJSK1lD6BxcP8+fO57777sNls7vvS09OZP38+CxYs4L777mP8+PHV2MLayWaz8cADDzBv3rwi91utVtavX8/69ev59ttvmTJlCu3bty9SZuPGjVXZ1IBT1tf36NGjXHfddezatct9X35+PsnJySQnJzNnzhymTp3qNdxKxYqIiChyW8dMxfvyyy9ZtGjRGcvt3LmT6667joyMDPd9WVlZrFq1ilWrVrFgwQJef/11r18S5ObmMm7cONasWVPk/tTUVFJTU5k5cyaffvopTZo0Kf8TEpFaT4slSBEbNmzg2muvpaCggF69enHvvffStm1bdu3axeuvv87KlSsxmUy8//77DBo0qLqbW6s8//zzfPLJJwAMHTqUm266idjYWA4dOsSPP/7Ihx9+iNVqpWXLlsyZM6fIid19993H3LlzueCCC3j11Vd9PkZQUBChoaGV/VRqlfz8fJKSkrDZbEyePJmBAwf6LBsWFobFYgHA4XAwatQokpOTqVu3LpMmTWLQoEHk5eUxY8YMpkyZgs1m49JLL+WNN96oqqdTa+Tl5WG32/2W+eyzz3j99dcxmUy8++67XHjhhe5to0ePZs2aNdxwww3ce++9PusIDg4mJCSkwtpdW3333Xc8/vjjuE4pfPUInTx5kiuvvJJ9+/bRrFkzHn74Yc4991wyMzP54osv+OqrrwC45ZZbeOCBBzz2v+uuu/jxxx8JDQ3l3//+N5dddhkmk4n58+fz+uuvk5ubS7du3fj2228xmUyV+6RF5OxniBQyfvx4Iy4uzhg6dKiRl5dXZFtBQYFx/fXXG3FxccZll11m2O32ampl7XPw4EHjnHPOMeLi4ozHH3/ca5nFixcbcXFxRlxcnDF16tQi2y699FIjLi7OeO+996qiuQFl7dq17tf94MGDJd5v3rx57v1Wr17tsX369Onu7WvWrKnAFothGMa6devcx9SLL75YZJvdbjd69OhhxMXFGbNnz66mFtYO+fn5xlNPPeX+v+zv/7xhGMaUKVOMuLg4IyEhwdi1a5fH9ldeecWIi4sz4uPjjbS0tCLb1q1b565/5syZHvv++uuv7u1z586tmCcoIrWaFksQt+3bt/Prr78CcPvtt3v0HAQHB3P//fe7y/71119V3sba6qeffsJms2Eymbjrrru8lhk4cCCJiYkALF682H1/Tk6Oe+hV165dK7upASclJQWAxo0bl2q4zaeffgpAv379vH4zPmrUKNq1awc4v02XipOfn8+kSZOw2Wx07NiRf//730W279y5k5ycHEDHTHksXLiQYcOG8eWXXwIQHx/vt7xhGHz22WcAXHXVVbRu3dqjzB133EHdunWxWq0e8/JcPebt2rXzOo+of//+9OvXD9AxJSIloyAkbkuXLgXAYrEwYMAAr2W6d+9OgwYNAEo0FlxKJj09ndDQUJo3b07Dhg19lmvVqpW7vMumTZtwOBwAJCQkVG5DA5BrLklpTpizsrJYt24dQJHhWIWZTCb38NKff/65fI2UIqZMmcKuXbswmUw8/fTTHkPbXOG2Tp06Xk/G5cyOHz/OnXfeye7du4mIiOA///nPGReV2LRpk/tvl6/jIjw8nPPPPx8o+hljGIb7M2rQoEE+h7256l21ahUnTpwo3ZMSkYCjICRumzZtAiA2Npbo6GivZUwmE507dwZOn0xI+d1zzz0kJycze/Zsv+X27NkDQN26dd33uU7UW7duTWpqKnfffTf9+vUjISGBAQMGMGnSJDZv3lx5ja/lXK9vXFwcn3/+OaNHjyYxMZEePXpw+eWX884773Dy5Mki+2zevNk9V6JLly4+6z7nnHMAyMjIYP/+/ZX0DALLwYMHmTp1KgDDhg3zusql6z1NSEhg0aJF3HrrrZx33nkkJCRw4YUX8sQTT7Bv374qbffZyGKxcOWVVzJv3jyuv/76M5Z3fcZAyY6L1NRU96I9+/bt4/jx40W2e+Oq12636++eiJyRVo0Tt7S0NABatGjht1yzZs0AdKJQCfytHpaamsratWsB6Nmzp/t+10nd/v37GTNmTJF9Dh06xOzZs5k3bx6PPvpoiU5W5DSr1cqWLVsAmDp1Klartcj2LVu2sGXLFn744Qc+/PBD92p+rmMJ/B9PrmMJnMdT8+bNK7L5Aemdd94hLy+PoKAg7rnnHq9lXF/irF69mmXLlhXZlpaWxtdff83MmTN5+eWXGTx4cKW3+WwUHh7OggULaNmyZYn3cR0XISEhNG7c2Gc513FhtVo5dOgQLVq0KPExVfgY2rdvH+eee26J2ycigUc9QuKWmZkJOIeL+OPqLXJ9OyeVr6CggP/85z8YhkFQUBAjR450b3Od1FmtVhITE5kyZQq///47P//8M0899RQNGjTAbrfz9NNP8+OPP1bXUzgrbd261R1+7HY7Y8eOZdasWaxYsYIZM2YwevRowHmCN2HCBLKysoDTxxIU7b0rrnDPq46n8jty5Ih7XsnQoUN9njC7egqsViuDBg3i888/Z/ny5SxYsID777+fiIgI8vLyuPfee91fPkhRwcHBpQpBcPq4iI6O9ruim7fjoqTHVOEvk44dO1aq9olI4FEQErf8/HzAuQSwP65FFFzlpXI5HA4effRR9wnZzTffTNu2bd3bDMMgJCSEIUOG8OWXXzJw4EAaNmxIixYtGD16NF9//bX7xOHZZ5+loKCgup7KWefw4cM0btwYs9nMG2+8wSOPPELnzp2pX78+8fHxPPXUUzz88MOAMwy9//77QNFjw99y5YWPNR1P5ffll19SUFCAyWRiwoQJXsscPXqUevXqERQUxNixY/nggw/o3bs3MTExtG7dmgkTJvDJJ58QHByM1Wrl6aefruJnUXuV9DPG23FRlmNKf+tE5EwUhMTNdf0TqTnsdjuPPvqoe+7Qeeedx9133+3ebjabmTNnDuvWreO1117z+h62atWK2267DXAusuCacCxnNnDgQJYuXcq6det8DpG66aabiIuLA+C///0vhmHoWKoGBQUFfP3114BzMn3Hjh29lmvQoAELFy5k3bp1PPTQQ17LdO/enVGjRgHOHlfNNakY5TkudEyJSGVQEBK38PBw4MzfTJf0Wz0pn9zcXCZOnMiMGTMA58nZu+++6/Vq62az2ev9LhdddJH79+Tk5IpvbC13pgtqulaqysrKYvfu3e5jCfx/K52Xl+f+XRe6LZ/ff/+djIwMAK6++uozlg8KCsJs9v0RqGOm4pX0M6bwceH6nCl8TPnbX8eUiJSGgpC4ucZln2nJUdeY7fr161d6mwLVkSNHGDNmjHv52N69e/PRRx/5XUzBn8KT8l0ni1JxCk/QzsjIKDLPzt/xVHibjqfyWbhwIQCRkZEMHDiw3PXpmKl4ruOi+CqLxRWeL+c6LgofU/721zElIqWhICRurnknBw4c8Fvu4MGDQNETBak427dvZ9SoUaxfvx6AIUOGMG3atDKHIKDIamfqySs911LYvhR+fcPDw2nTpo37tr9lsQsfa1oxruzsdrv7WkwXXnhhiXoCSvOe6pipGK7jIi8vz2+4dH3GBAcHu69bp2NKRCqDgpC4ucbU7969233V9eIMw3BfC8LftRykbDZv3sx1113nXpp83LhxvP766z6HZs2dO5f+/fuTkJBQ5BodxW3fvt39e+ETCvFv4sSJ9O7dm6uuuspvuW3btgHOeQyxsbF07NjRvSqWv/klrqXP69Wrpy8WymHDhg3uVcUKD2nzZtq0afTt25euXbu6V/nzxvWewukviaR8Cs/b8vf3qvC1u1xDfhs3bky9evWAkh1TZrOZTp06lbfJIlLLKQiJm2s4idVq9Tmhfu3ate5v8vr3719lbQsEu3btYty4cWRlZWEymXjkkUd46KGH/M5jaNq0Kenp6VitVpYsWeKznGuxBZPJpPetFKKjozl27BibN2/m0KFDXsvk5+e7h2UlJiYSFRVFVFSU+0Kerp6K4gzDYPHixYCOpfJas2aN+/du3br5LdugQQOOHDni9+8cwJw5cwCIiIgoct0uKbu4uDh34Pd1XOTm5rJixQrA87gYMGCA330BfvnlFwB69Ojh88LgIiIuCkLi1qpVKxITEwF48803yc7OLrLdarXy6quvAs4PtD59+lR5G2urgoIC7r33XnfIfOaZZxg7duwZ90tKSnJfK2Xq1KnuISWF/fHHH0yfPh1wflveqlWrCmx57Xb55ZcDztDy7LPPei3z3HPPceTIEcDZg+cyfPhwABYvXszy5cs99vvmm2/YsWMHQInea/HNdS2tmJiYM14Q+qKLLiIiIgKAyZMne51vMm/ePPfJ9j/+8Y9yDUuV00wmE1deeSUA33//PVu3bvUo8+6773Ls2DGCg4O57rrrimxzHVNbtmzh+++/99h36dKl/Pbbb4COKREpGQUhKeLhhx/GZDKxbds2xowZw4oVK8jMzGTt2rWMHz+e1atXYzKZuOeee/xeEE9K59tvv3WfzF111VX8/e9/Jzs72+dPbm4u4Bz+4bqOzYkTJxg5ciRz5szhwIED7Nu3j6lTpzJhwgRsNhsNGzbkscceq7bneDbq06ePe0W4BQsWcOutt/LXX3+RkZFBcnIyd911l3vJ5mHDhnHxxRe79x0xYgSdOnXCMAzuuOMOvvjiCw4dOkRaWhpvvfUWzzzzDOCcA9a1a9eqf3K1iGvoZ0lCfnR0tHsJ+rS0NEaOHMmiRYtIT09n586dvPbaazzwwAOAc0jcXXfdVXkND0ATJkygUaNG5OXluS9QfPToUXbu3MnTTz/NlClTABgzZgxNmjQpsm/fvn3dIxeefPJJ3n77bdLS0jh06BCfffaZ+73q1q2bz+XuRUQKMxlnmjEqAeebb77hySefxOFweN3+8MMPc9NNN1Vto2q5Sy65hD179pS4fIsWLYoMD/niiy94/vnnsdlsXss3b96c999/X2PmyyA7O5s777yTZcuW+Sxz2WWX8fLLLxMcHFzk/r179zJ27FjS0tK87peYmMjHH39cZGlgKb3zzz+fzMxM+vfvz9SpU0u0zyuvvMKHH37oc3tcXBwffvghTZs2rahm1norV67kxhtvBJwXt+3Vq5fXcsnJyYwfP55jx4553T548GDeeOMNr8OCMzMzGTdunM85Rm3atOGrr75yL7IgIuKPgpB4lZKSwkcffcSqVavIzMwkMjKSxMRExo4dqyFxFSwjI6PUr2nxIATO4SKffvopK1asID09ndDQUFq3bs3gwYO54YYbiIyMrMhmBxSHw8HcuXOZNWsWGzZsIDs7m3r16tGtWzeuueYad6+RNydPnmTatGksXLiQffv2YRgG7dq1Y9iwYYwZM+aM1yiSM4uPj8dmszF06FBee+21Eu/3559/8uWXX/Lnn39y9OhRIiMjad++PUOHDmXkyJEewVb8K2kQAuclAqZMmcLixYs5cOAAQUFBdOrUiREjRjBixAi/cyMLCgr4/PPPmTdvHjt37sRmsxEbG8vgwYMZP368hjKKSIkpCImIiIiISMDRHCEREREREQk4CkIiIiIiIhJwFIRERERERCTgKAiJiIiIiEjAURASEREREZGAoyAkIiIiIiIBR0FIREREREQCjoKQiIiIiIgEHAUhEREREREJOApCIiIiIiIScBSEREREREQk4CgIiYiIiIhIwFEQEhERERGRgBNU3Q0QERGnTp06edzXuXNnZs2aVSWP/8knn/D888973H/ffffxz3/+s0raICIiUlXUIyQiIiIiIgFHPUIiIjVMYmIiTzzxBAChoaFV9rhXXHEF5513HgAbNmzgscceq7LHFhERqWoKQiIiNUxkZCRdunSp8seNiYkhJiYGgOPHj1f544uIiFQlDY0TEREREZGAox4hEZEySk9PZ8aMGSxbtozt27dz7NgxQkJCiImJoWnTppx77rn07duXXr16VXdTRUREpBgFIRGRMpg+fTovvfQSOTk5Re63Wq1kZ2ezd+9eVq9ezaxZs/j5558r7HFdK8s9/vjjXH/99cyePZvvvvuOLVu2YLVaadmyJVdccQVjx44lJCQEgFWrVvHpp5+ybt06srKyaNy4MQMGDOCOO+6gcePGFdY2ERGRs4mCkIhIKX3zzTc8+eSTAISHh3PJJZeQkJBAo0aNsNlsHDhwgLVr17J8+XISEhIqpQ1Wq5Xbb7+dX375pcj9W7Zs4ZVXXmHZsmVMmzaNd955h3feeQfDMNxl0tLSmD59OosWLeL777+nSZMmldJGERGRmkxBSESkFHJycnjxxRcBiI+PZ+rUqe4FBoo7ceIE+/btq5R2fPDBB2RmZtK1a1duvPFGWrZsydatW3nttdfIyspi2bJl3HbbbSxZsoR27dpxyy230LFjR9LT05kyZQrJycmkp6czefJkXnjhhUppo4iISE2mICQiUgorV64kOzsbgIkTJ/oMQQDR0dGVtvpbZmYmffv25f3333cPgUtKSqJp06bui58uWbKErl278tlnnxEREeHet3///gwZMoSDBw/yyy+/YBgGJpOpUtopIiJSU2nVOBGRUjhy5Ij794MHD1ZjS+DBBx90hyCXAQMGEB4e7r49adKkIiEIICwsjL59+wKQlZVFVlZWpbdVRESkplEQEhEphbZt27p/f+GFF5gyZUq1BIkGDRq4F04ozGQyuRdACAkJoWfPnj73dym+4IOIiEggUBASESmFXr16cckllwCQl5fHq6++Sr9+/bjxxhv56KOP2LNnT5W0o0WLFj63uXqJ6tevT1CQ9xHQhXuSCi+kICIiEigUhERESmny5MlMmjSJpk2bAs4V3FauXMmLL77IJZdcwo033khycnKltiEyMvKMZXyFIBEREVEQEhEpteDgYMaPH8/ixYv5/vvvmTRpEklJSe4FB1auXMl1113Hpk2bKq0NFoul0uoWEREJBApCIiJlZDKZ6Nq1K+PHj2f69OnMmTOH7t27A85eoq+++qqaWygiIiK+KAiJiFSQjh078uabb7pvHz58uBpbIyIiIv4oCImIVKDjx4+7f2/dunU1tkRERET8URASESmB1NRUXnrpJdLS0nyWycjI4PHHHwecw+Yuv/zyqmqeiIiIlJKWFBIRKYHk5GSmTZvGRx99RLdu3ejVqxft2rUjMjKSo0ePsmnTJubNm0dubi4At9xyCwkJCdXcahEREfFFQUhEpARSU1MB5zV31q1bx7p167yWCwkJYeLEifzzn/+syuaJiIhIKSkIiYiUwKRJkxg4cCArV65k/fr17N69m6NHj+JwOIiKiqJ9+/b06dOHESNG0Lx58+puroiIiJyBgpCISAmEhobSv39/+vfvX63tcPVM+TN37twzlpk4cSITJ06siCaJiIiclbRYgoiIiIiIBBwFIRERERERCTgaGiciUsNkZ2ezadMmwDkkr127dlXyuBkZGRw6dAiAPXv2VMljioiIVBcFIRGRGmbNmjUMHz4cgM6dOzNr1qwqedzZs2fz/PPPV8ljiYiIVDcNjRMRERERkYBjMgzDqO5GiIiIiIiIVCX1CImIiIiISMBREBIRERERkYCjICQiIiIiIgFHQUhERERERAKOgpCIiIiIiAQcBSEREREREQk4CkIiIiIiIhJwFIRERERERCTgKAiJiIiIiEjAURASEREREZGAoyAkIiIiIiIB5/8DI32Ggw+s9MIAAAAASUVORK5CYII=", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(twiss['s'], twiss['betx'], label=r'$\\beta_x$ [m]')\n", + "plt.plot(twiss['s'], twiss['bety'], label=r'$\\beta_y$ [m]')\n", + "plt.plot(twiss['s'], twiss['alfx'], label=r'$\\alpha_x$ [1]', c='C0', ls='--')\n", + "plt.plot(twiss['s'], twiss['alfy'], label=r'$\\alpha_y$ [1]', c='C1', ls='--')\n", + "\n", + "ylim = plt.ylim()\n", + "plt.fill_betweenx(ylim, 0, 3.3/2, color='red', alpha=0.2)\n", + "plt.fill_betweenx(ylim, 110/2 - 3.3/2, 110/2 + 3.3/2, color='blue', alpha=0.2)\n", + "plt.fill_betweenx(ylim, 110 - 3.3/2, 110, color='red', alpha=0.2)\n", + "plt.ylim(ylim)\n", + "\n", + "plt.xlabel('$s$ [m]')\n", + "plt.ylabel(r'$\\beta_{x,y}$ and $\\alpha_{x,y}$')\n", + "plt.legend(loc='upper left', bbox_to_anchor=(1.05, 1));" + ] + }, + { + "cell_type": "markdown", + "id": "852db466-b195-4778-b2ab-b4faa57c6386", + "metadata": {}, + "source": [ + "<h2>Off-momentum particles, dispersion & chromaticity</h2>\n", + "<h3>Computing the Dispersion function of a FODO cell</h3>\n", + "\n", + "For illustration, we use again the LHC FODO cell, but now we switch on the dipole magnets:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "04597b2b-6efb-4482-b937-66875223a622", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "++++++ info: theta redefined\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input('theta := 2 * pi / 1232;')" + ] + }, + { + "cell_type": "markdown", + "id": "70db6a47-d754-461e-a60f-743ebe61cec9", + "metadata": {}, + "source": [ + "Let us recompute the optics function, as this time also the dispersion function will assume finite values:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "2a938109-9837-47a0-bc15-ec244ee3cc3a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "enter Twiss module\n", + " \n", + "iteration: 1 error: 0.000000E+00 deltap: 0.000000E+00\n", + "orbit: 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00\n", + "\n", + "++++++ table: summ\n", + "\n", + " length orbit5 alfa gammatr \n", + " 110 -0 0.0004388874913 47.73351305 \n", + "\n", + " q1 dq1 betxmax dxmax \n", + " 0.2519723158 -0.3218296078 186.8781443 2.249453549 \n", + "\n", + " dxrms xcomax xcorms q2 \n", + " 1.634089545 0 0 0.2518947018 \n", + "\n", + " dq2 betymax dymax dyrms \n", + " -0.3218849941 186.4581481 0 0 \n", + "\n", + " ycomax ycorms deltap synch_1 \n", + " 0 0 0 0 \n", + "\n", + " synch_2 synch_3 synch_4 synch_5 \n", + " 0 0 0 0 \n", + "\n", + " synch_6 synch_8 nflips dqmin \n", + " 0 0 0 0 \n", + "\n", + " dqmin_phase \n", + " 0 \n" + ] + } + ], + "source": [ + "twiss = madx.twiss();" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "a03853ba-04d3-4f16-bf56-43a54ed12dd8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beam->beta = 0.999999991 ;\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input('value, beam->beta;')" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "9762e470-7f6e-44c5-bcfe-4a0a19a6c6b5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(twiss['s'], twiss['dx'] * 0.999999991)\n", + "plt.xlabel('$s$ [m]')\n", + "plt.ylabel('$D_x(s)$ [m]');" + ] + }, + { + "cell_type": "markdown", + "id": "d27e7ce4-67f3-42b7-bc70-8877009b7e1c", + "metadata": {}, + "source": [ + "$\\implies$ Dispersion function $D(s)$ is focused by the quadrupoles in a similar way as the horizontal $\\beta_x(s)$-function!" + ] + }, + { + "cell_type": "markdown", + "id": "bf03c154-729f-48d8-959f-fd3a09a262b5", + "metadata": {}, + "source": [ + "<h3>Dispersion effect in tracking</h3>\n", + "\n", + "To illustrate the dispersion effect, we use the thin-lens tracking code `PySixTrack` (like our thin-lens betatron matrices but for 6D, i.e. including the momentum deviation $\\delta$)!\n", + "\n", + "We define a drift of $5$m length and a dipole with a bending angle of $0.1$ rad:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "fb6e1be3-f155-461a-9a35-d96c9f3c6058", + "metadata": {}, + "outputs": [], + "source": [ + "drift = elements.DriftExact(5)\n", + "dipole = elements.Multipole(knl=[0.1], hxl=0.1)" + ] + }, + { + "cell_type": "markdown", + "id": "854c5490-054c-4096-8abc-d7a59fd84359", + "metadata": {}, + "source": [ + "Initialize two particles, both at $x=0.04$m but only one at a momentum deviation of $\\delta=10^{-3}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "834537d2-3a38-4363-9369-0aa3ab95ecba", + "metadata": {}, + "outputs": [], + "source": [ + "part0 = pysixtrack.Particles(x=0, delta=0)\n", + "part1 = pysixtrack.Particles(x=0, delta=0.001)" + ] + }, + { + "cell_type": "markdown", + "id": "f18e0bc4-dafc-4bd8-8e47-484ce4dfd4c3", + "metadata": {}, + "source": [ + "Track through the drift, then the dipole and again the drift:" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "8561af3b-17d6-4fab-8ed5-a46aed483a4f", + "metadata": {}, + "outputs": [], + "source": [ + "rec_x0 = [part0.x]\n", + "rec_x1 = [part1.x]\n", + "\n", + "drift.track(part0)\n", + "drift.track(part1)\n", + "\n", + "rec_x0 += [part0.x]\n", + "rec_x1 += [part1.x]\n", + "\n", + "dipole.track(part0)\n", + "dipole.track(part1)\n", + "\n", + "rec_x0 += [part0.x]\n", + "rec_x1 += [part1.x]\n", + "\n", + "drift.track(part0)\n", + "drift.track(part1)\n", + "\n", + "rec_x0 += [part0.x]\n", + "rec_x1 += [part1.x]" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "f666ad3f-c9e6-4dc8-9379-9d245d6448a6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot([0, 5, 5, 10], rec_x0, label='$\\delta=0$')\n", + "plt.plot([0, 5, 5, 10], rec_x1, label='$\\delta=10^{-3}$')\n", + "\n", + "plt.xlabel('$s$ [m]')\n", + "plt.ylabel('$x$ [m]')\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "id": "093cd882-b50a-4b90-baf6-efe74d929bdf", + "metadata": {}, + "source": [ + "$\\implies$ Bending at dipole position due to dispersion!" + ] + }, + { + "cell_type": "markdown", + "id": "33132070-cdd2-4f99-a101-8624c8ca41cc", + "metadata": {}, + "source": [ + "<h3>Chromaticity effect in tracking</h3>\n", + "\n", + "Let us illustrate by tracking particles in `PySixTrack` again. We define a quadrupole with an integrated focusing strength of $k\\cdot L=0.3$m$^{-1}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "efcdd2ab-4deb-444f-b7bf-58326adb19bc", + "metadata": {}, + "outputs": [], + "source": [ + "quad = elements.Multipole(knl = [0, 0.3])" + ] + }, + { + "cell_type": "markdown", + "id": "f79a3523-2745-493c-b472-c04407d8f44d", + "metadata": {}, + "source": [ + "Initialize two sets of particles with the same distribution in $x$, one of which features a momentum deviation of $\\delta=0.1$:" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "1f96ebd7-85ab-4101-a770-270ac9086581", + "metadata": {}, + "outputs": [], + "source": [ + "npart = 11\n", + "x_dist = np.linspace(-0.05, 0.05, npart)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "facfdce4-cae6-41de-8ca5-5085311cf698", + "metadata": {}, + "outputs": [], + "source": [ + "part0 = pysixtrack.Particles(x=x_dist.copy(), delta=0)\n", + "part1 = pysixtrack.Particles(x=x_dist.copy(), delta=0.1)" + ] + }, + { + "cell_type": "markdown", + "id": "ab860330-ef76-42c0-9c69-13ba24213fd2", + "metadata": {}, + "source": [ + "Track through the $5$m drift, then through the quadrupole and again through the same drift:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "115c9205-d3a8-4416-8711-16b6db4e4118", + "metadata": {}, + "outputs": [], + "source": [ + "rec_x0 = [part0.x.copy()]\n", + "rec_x1 = [part1.x.copy()]\n", + "\n", + "drift.track(part0)\n", + "drift.track(part1)\n", + "\n", + "rec_x0 += [part0.x.copy()]\n", + "rec_x1 += [part1.x.copy()]\n", + "\n", + "quad.track(part0)\n", + "quad.track(part1)\n", + "\n", + "rec_x0 += [part0.x.copy()]\n", + "rec_x1 += [part1.x.copy()]\n", + "\n", + "drift.track(part0)\n", + "drift.track(part1)\n", + "\n", + "rec_x0 += [part0.x.copy()]\n", + "rec_x1 += [part1.x.copy()]" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "8aee3ecf-8d18-43de-9be5-712f0a375513", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(npart):\n", + " l0, = plt.plot([0, 5, 5, 10], np.array(rec_x0)[:, i], c='C0', lw=1)\n", + " l1, = plt.plot([0, 5, 5, 10], np.array(rec_x1)[:, i], c='C1', lw=1)\n", + "\n", + "plt.xlabel('$s$ [m]')\n", + "plt.ylabel('$x$ [m]')\n", + "plt.legend([l0, l1], ['$\\delta=0$', '$\\delta=0.1$']);" + ] + }, + { + "cell_type": "markdown", + "id": "28a083dd-ab66-4775-bb41-2e620a0dead4", + "metadata": {}, + "source": [ + "$\\implies$ we observe less focusing for $/delta>0$ particles $\\implies$ less phase advance in quasi-harmonic oscillation $\\implies$ negative tune shift!" + ] + }, + { + "cell_type": "markdown", + "id": "6422374a-d30d-4294-8979-da7853bed8ab", + "metadata": {}, + "source": [ + "<h3>Natural chromaticity of a FODO cell</h3>" + ] + }, + { + "cell_type": "markdown", + "id": "50d7028f-52fd-4e14-97d7-41eaef85d89c", + "metadata": {}, + "source": [ + "<h3>Chromatic detuning in a FODO cell from tracking</h3>\n", + "\n", + "Let us track with `PySixTrack`through the LHC FODO cell for a distribution of particles with momentum spread and observe the chromatic tune shift.\n", + "\n", + "We first define the same FODO cell as in `MAD-X` before (just in thin-lens approximation and without dipoles):" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "a0637557-fc81-49bc-8382-30414e339f78", + "metadata": {}, + "outputs": [], + "source": [ + "kL = 0.008 * 3.3\n", + "\n", + "qf2_fodo = elements.Multipole(knl=[0, kL / 2.])\n", + "qd_fodo = elements.Multipole(knl=[0, -kL])\n", + "drift_fodo = elements.DriftExact(110 / 2.)\n", + "\n", + "fodo = [qf2_fodo, drift_fodo, qd_fodo, drift_fodo, qf2_fodo]" + ] + }, + { + "cell_type": "markdown", + "id": "e0bc21a8-5129-4359-b627-a7831ab5dbc0", + "metadata": {}, + "source": [ + "We initialize a distribution of `npart` macro-particles, with a momentum spread between $\\delta\\in[-10^{-3},10^{-3}]$ at a fixed initial horizontal position of $x=0.04$m:" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "6812f00b-00df-4d9c-89bb-02f84ffd3f98", + "metadata": {}, + "outputs": [], + "source": [ + "npart = 21\n", + "x_ini = 0.04\n", + "delta = np.linspace(-0.001, 0.001, npart)\n", + "\n", + "particles = pysixtrack.Particles(x=x_ini, delta=delta)" + ] + }, + { + "cell_type": "markdown", + "id": "5d304ecf-2b3a-4c15-b04c-8fe12e7f8a0b", + "metadata": {}, + "source": [ + "We will record the $x$ position after each FODO cell for each particle:" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "d694591a-ac02-484c-97c1-d35bde1d47e6", + "metadata": {}, + "outputs": [], + "source": [ + "ncells = 1024\n", + "\n", + "rec_x = np.zeros((ncells, npart), dtype=float)\n", + "rec_x[0] = particles.x" + ] + }, + { + "cell_type": "markdown", + "id": "f6bd84c7-9702-416f-9604-4a537e0d2db3", + "metadata": {}, + "source": [ + "Let's go for the tracking:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "daba67ac-640e-412d-b969-e8420e5e18bb", + "metadata": {}, + "outputs": [], + "source": [ + "for i in range(1, ncells):\n", + " for el in fodo:\n", + " el.track(particles)\n", + " rec_x[i] = particles.x" + ] + }, + { + "cell_type": "markdown", + "id": "8833b9e9-05da-4f5a-8d28-2ddcd15ea4e4", + "metadata": {}, + "source": [ + "Comparing two particles with same initial $x$ but different $\\delta$, we already see the different phase advance in the recorded horizontal motion:" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "2d41497f-a2a6-43ef-9d52-e8eafcba5e7b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(rec_x[:, npart//2 + 1], lw=2, label='$\\delta=0$')\n", + "plt.plot(rec_x[:, 0], lw=2, label='$\\delta=-0.001$')\n", + "\n", + "plt.xlabel('number of FODO cells')\n", + "plt.ylabel('$x$ [m]')\n", + "plt.legend(bbox_to_anchor=(1.05, 1));" + ] + }, + { + "cell_type": "markdown", + "id": "4920a86f-afd0-4d4a-8ad9-e678a49183f3", + "metadata": {}, + "source": [ + "Let's evaluate the tune of each particle using the NAFF algorithm:" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "6497daaa-383a-45b5-be98-4b27d01c5f16", + "metadata": {}, + "outputs": [], + "source": [ + "Qx_delta = np.zeros(npart, dtype=float)\n", + "\n", + "for i in range(npart):\n", + " Qx_delta[i] = PyNAFF.naff(rec_x[:, i], turns=ncells, nterms=1)[0, 1]" + ] + }, + { + "cell_type": "markdown", + "id": "64f0501a-e387-41db-85ab-a75af6de81e4", + "metadata": {}, + "source": [ + "The tune of the $\\delta=0$ particle should be the tune of the reference particle in this linear lattice:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "522400fe-208e-4124-863b-2f535f465df1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.2585892190147644" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Qx_delta[npart//2 + 1]" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "ea818b1f-63fe-431f-bda6-e1d26dc2d27b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.2518947018" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qx_fodo" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "a4842a92-6e55-46b0-8cd3-1fd320699c9d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(1e3 * delta, Qx_delta)\n", + "\n", + "plt.xlabel('$\\delta$ [$10^{-3}$]')\n", + "plt.ylabel('$Q_x$');" + ] + }, + { + "cell_type": "markdown", + "id": "c86b4a98-4e67-41c3-9b45-0753718a4088", + "metadata": {}, + "source": [ + "$\\implies$ the tune changes with the momentum, as anticipated! The slope of this line is the first-order chromaticity $Q'_x$!\n", + "\n", + "The `numpy` function `polyfit`is useful for a quick linear regression, the output is $(a,b)$ for $y=a\\cdot x+b$:" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "226c3fb7-8a6c-4e86-8be1-6f474a564675", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.3360318 , 0.25862306])" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.polyfit(delta, Qx_delta, 1)" + ] + }, + { + "cell_type": "markdown", + "id": "dd77e3d2-00ce-4f8a-8cbb-a634c791fbe5", + "metadata": {}, + "source": [ + "The slope and thus the chromaticity of the LHC FODO cell is approximately $Q'_x=-0.3$, measured via particle tracking.\n", + "\n", + "The analytical formula $Q'_{\\mathrm{FODO}}=-\\frac{1}{\\pi}\\tan\\left(\\frac{\\Phi_{\\mathrm{FODO}}}{2}\\right)$ gives:" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "144a702f-be28-4eda-84ac-c1ffc8c386ff", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.32212202611662033" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "-1 / np.pi * np.tan(2 * np.pi * qx_fodo / 2)" + ] + }, + { + "cell_type": "markdown", + "id": "7717044d-c33c-4aff-bdf6-24d3bf98862e", + "metadata": {}, + "source": [ + "`MAD-X`would have given us this value, too, we evaluated it as `twiss.summary['dq1'] * beta` (where `beta` is the speed of the particles):" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "b944cb03-e6a8-4775-b278-466993bfb8ed", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.32209610180113507" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qpx_fodo" + ] + }, + { + "cell_type": "markdown", + "id": "dc1a1c71-4743-4777-999e-f93b6196826e", + "metadata": {}, + "source": [ + "<h3>Chromaticity correction in a FODO cell</h3>\n", + "\n", + "For demonstration, we add sextupoles to the FODO lattice in `MAD-X`and compute their necessary strength.\n", + "\n", + "Make sure that dipoles are switched on, the dipole angle `theta` should be non-zero:" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "b0699b3b-195d-476a-ac92-932204594ab7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = 0.005099988074 ;\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input('value, theta;')" + ] + }, + { + "cell_type": "markdown", + "id": "a8a5f616-fb48-4283-99be-5662317c39fb", + "metadata": {}, + "source": [ + "We add two sextupole magnets, one next to each quadrupole:" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "048379f8-1a2f-4528-a43b-812302f080ab", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "++++++ info: seqedit - number of elements installed: 2\n", + "++++++ info: seqedit - number of elements moved: 0\n", + "++++++ info: seqedit - number of elements removed: 0\n", + "++++++ info: seqedit - number of elements replaced: 0\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input('sext1: sextupole, l = 1, k2 := k2sext1;')\n", + "madx.input('sext2: sextupole, l = 1, k2 := k2sext2;')\n", + "madx.command.seqedit(sequence='fodo')\n", + "madx.command.install(element='sext1', at=3.3/2 + 1)\n", + "madx.command.install(element='sext2', at=110/2 + 3.3/2 + 1)\n", + "madx.command.endedit()" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "059c46ec-6472-4401-bc2d-6c10436e9627", + "metadata": {}, + "outputs": [], + "source": [ + "madx.use('fodo')" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "a45d55d7-80e6-47c8-b790-2561353f2a20", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "START MATCHING\n", + "\n", + "number of sequences: 1\n", + "sequence name: fodo\n", + "number of variables: 2\n", + "user given constraints: 2\n", + "total constraints: 2\n", + "\n", + "START LMDIF:\n", + "\n", + "Initial Penalty Function = 0.20718425E+00\n", + "\n", + "\n", + "call: 4 Penalty function = 0.11711009E-26\n", + " ++++++++++ LMDIF ended: converged successfully\n", + "call: 4 Penalty function = 0.11711009E-26\n", + "\n", + "MATCH SUMMARY\n", + "\n", + "Node_Name Constraint Type Target Value Final Value Penalty\n", + "--------------------------------------------------------------------------------------------------\n", + "Global constraint: dq1 4 0.00000000E+00 2.20777692E-14 4.87427893E-28\n", + "Global constraint: dq2 4 0.00000000E+00 -2.61471410E-14 6.83672981E-28\n", + "\n", + "\n", + "Final Penalty Function = 1.17110087e-27\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Variable Final Value Initial Value Lower Limit Upper Limit \n", + "--------------------------------------------------------------------------------\n", + "k2sext1 1.27667e-02 0.00000e+00 -1.00000e+20 1.00000e+20\n", + "k2sext2 -2.53671e-02 0.00000e+00 -1.00000e+20 1.00000e+20\n", + "\n", + "END MATCH SUMMARY\n", + "\n", + "VARIABLE \"TAR\" SET TO 1.17110087e-27\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "madx.input(\n", + "'''match, sequence = fodo;\n", + "global, sequence = fodo, dq1 = {Qpx}, dq2 = {Qpy};\n", + "vary, name = k2sext1, step = 0.0001;\n", + "vary, name = k2sext2, step = 0.0001;\n", + "lmdif, tolerance = 1e-12;\n", + "endmatch;\n", + "'''.format(Qpx=0, Qpy=0))" + ] + }, + { + "cell_type": "markdown", + "id": "68d106f0-7d8e-4aad-b5d9-69b6a4c7c6f7", + "metadata": {}, + "source": [ + "$\\implies$ the iterative algorithm in `MAD-X` has found suitable values of the sextupole strengths `k2sext1` and `k2sext2` such that the target chromaticity has been corrected to 0." + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "e7a59560-f9a8-46a0-a521-c1b223420f89", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "enter Twiss module\n", + " \n", + "iteration: 1 error: 0.000000E+00 deltap: 0.000000E+00\n", + "orbit: 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00\n", + "\n", + "++++++ table: summ\n", + "\n", + " length orbit5 alfa gammatr \n", + " 110 -0 0.0004388874913 47.73351305 \n", + "\n", + " q1 dq1 betxmax dxmax \n", + " 0.2519723158 2.20777692e-14 186.8781443 2.249453549 \n", + "\n", + " dxrms xcomax xcorms q2 \n", + " 1.634424445 0 0 0.2518947018 \n", + "\n", + " dq2 betymax dymax dyrms \n", + " -2.614714098e-14 186.4581481 0 0 \n", + "\n", + " ycomax ycorms deltap synch_1 \n", + " 0 0 0 0 \n", + "\n", + " synch_2 synch_3 synch_4 synch_5 \n", + " 0 0 0 0 \n", + "\n", + " synch_6 synch_8 nflips dqmin \n", + " 0 0 0 0 \n", + "\n", + " dqmin_phase \n", + " 0 \n" + ] + }, + { + "data": { + "text/plain": [ + "2.20777692e-14" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "twiss = madx.twiss();\n", + "\n", + "twiss.summary.dq1" + ] + }, + { + "cell_type": "markdown", + "id": "99af4d31-cfb8-4161-936c-205e98d8855b", + "metadata": {}, + "source": [ + "$\\implies$ the chromaticity from the `MAD-X` optics computation has really become (numerically) zero!\n", + "\n", + "We return to the `PySixTrack` tracking: after adding sextupoles of these strengths and the dipole magnets, we should be able to see the change via evaluating the chromaticity via NAFF from tracking data again!\n", + "\n", + "As a short cut, we make the `MAD-X` lattice \"thin\" (apply thin-lens approximation) and transfer the lattice with dipoles and sextupoles to `PySixTrack`:" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "id": "16912973-cf3f-4dc5-8e4a-f4262307fa5b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "makethin: style chosen : simple\n", + "makethin: slicing sequence : fodo\n" + ] + } + ], + "source": [ + "assert madx.command.select(\n", + " flag='MAKETHIN',\n", + " class_='quadrupole',\n", + " slice_=1,\n", + ")\n", + "\n", + "assert madx.command.select(\n", + " flag='MAKETHIN',\n", + " class_='sextupole',\n", + " slice_=1,\n", + ")\n", + "\n", + "assert madx.command.select(\n", + " flag='MAKETHIN',\n", + " class_='sbend',\n", + " slice_=1,\n", + ")\n", + "\n", + "madx.command.makethin(\n", + " makedipedge=False,\n", + " style='simple',\n", + " sequence='fodo',\n", + ")\n", + "\n", + "fodo_sext = pysixtrack.Line.from_madx_sequence(madx.sequence.fodo)" + ] + }, + { + "cell_type": "markdown", + "id": "03d735e6-74bc-4e5b-933e-dfc68f3bfac3", + "metadata": {}, + "source": [ + "Go about with the tracking again:" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "53fd9c3d-fe91-47f7-a070-c3f00adc3850", + "metadata": {}, + "outputs": [], + "source": [ + "# define initial particle distribution & prepare recording array\n", + "particles = pysixtrack.Particles(x=x_ini, delta=delta)\n", + "\n", + "rec_x = np.zeros((ncells, npart), dtype=float)\n", + "rec_x[0] = particles.x" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "6fbd3e59-ede7-4837-b7cf-5882e49ec410", + "metadata": {}, + "outputs": [], + "source": [ + "# tracking!\n", + "for i in range(1, ncells):\n", + " fodo_sext.track(particles)\n", + " rec_x[i] = particles.x" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "5f892269-ac90-4239-8b2b-d4dda6f833f1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(rec_x[:, npart//2 + 1], lw=2, label='$\\delta=0$')\n", + "plt.plot(rec_x[:, 0], lw=2, label='$\\delta=-0.001$')\n", + "\n", + "plt.xlabel('number of FODO cells')\n", + "plt.ylabel('$x$ [m]')\n", + "plt.legend(bbox_to_anchor=(1.05, 1));" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "id": "90637ca2-35d5-4a54-a6aa-5dac1de8dae2", + "metadata": {}, + "outputs": [], + "source": [ + "# evaluate tunes via NAFF\n", + "Qx_delta = np.zeros(npart, dtype=float)\n", + "\n", + "for i in range(npart):\n", + " Qx_delta[i] = PyNAFF.naff(rec_x[:, i], turns=ncells, nterms=1)[0, 1]" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "id": "6f8fd381-3b63-4878-9622-e0975c38aed5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(1e3 * delta, Qx_delta)\n", + "\n", + "plt.xlabel('$\\delta$ [$10^{-3}$]')\n", + "plt.ylabel('$Q_x$');" + ] + }, + { + "cell_type": "markdown", + "id": "c7753141-5775-4f2f-bd6a-5d57854de678", + "metadata": {}, + "source": [ + "The fit for the now much flatter slope of the tune change with $\\delta$ gives:" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "id": "06f0c77d-c228-4170-9867-6d1680d6ee7e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.01098794, 0.25440583])" + ] + }, + "execution_count": 81, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.polyfit(delta, Qx_delta, 1)" + ] + }, + { + "cell_type": "markdown", + "id": "f3447a58-7614-4e99-8f5b-2b8a08c53795", + "metadata": {}, + "source": [ + "$\\implies$ $Q'_x=-0.01$ is nearly zero, i.e. the chromaticity correction scheme works! (The remainders are due to the thin-lens approximation!)\n", + "\n", + "<i>Hint: we have used 2 sextupoles as 2 degrees of freedom to correct both the horizontal and the vertical chromaticity to zero. One could use only one sextupole degree of freedom, but then only one of the transverse planes can be corrected to $Q'=0$, the other one likely increases!</i>" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.20" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}