diff --git a/Project.ipynb b/Project.ipynb index ea9396b..2d69072 100644 --- a/Project.ipynb +++ b/Project.ipynb @@ -19,14 +19,1733 @@ "1. Compute the process leading-order cross section, $\\sigma(\\theta; \\sqrt{s})$, as a function of the scattering angle $\\theta$ and with the center of mass energy $\\sqrt{s}$ as a parameter. Start by computing it in the center of mass system. N.B.: textbooks reports such cross section in the relativistic limit, i.e. for $\\sqrt{s}\\gg m_\\mu$, which is clearly not the case here ($\\sqrt{s}\\sim 2m_\\mu$);\n", "2. compute and display the angle and momentum components distributions of the emerging muon pairs;\n", "3. boost muons four-momenta in the laboratory frame, i.e. in the frame where the electron is at rest and the positron has enough energy to give rise to the process;\n", - "4. write a Monte Carlo simulation that generates scattering events following the distrubtions that you found analytically; \n", + "4. write a Monte Carlo simulation that generates scattering events following the distributions that you found analytically; \n", "5. produce a synthetic dataset of about $N=10^5$ (or more) events. Events should be listed as rows in a file with columns representing the muons coordinates (keep in mind that in the lab frame muons are relativistic and thus the number of coordinates can be only 3 per muon);\n", "6. assume a $3$ cm thick Beryllium block is used as target and a rate of positron on target of $10^6$ Hz. Compute the rescaling factor (weight) you need to apply to the $N$ simulated events such that they represent the statistics that would be gathered in a week of countinuous operations;\n", "7. repeat what done so far simulating now the actual transverse shape and energy spread of the beam: for the former assume a flat distribution in a circle of radius $r=1$ cm and for the latter a gaussian distribution centered at the nominal beam energy and a width of $0.5$ GeV;\n", "8. given that the electrons traversing the target lose energy as $E(z)=E_0 \\exp{-z/X_0}$ (with z the longitudinal coordinate of the target, the one parallel to the beam direction and $X_0$ is the Beryllium radiation length), compute the nominal beam energy $E_0$ such that muon pairs can be generated along the whole length of the target;\n", - "9. (optional) take the former point into account when generating the events (i.e. the proccess $\\sqrt{s}$ depend on the position along the target where the $e^+ - e^-$ scattering occurrs.\n", + "9. (optional) take the former point into account when generating the events (i.e. the process $\\sqrt{s}$ depend on the position along the target where the $e^+ - e^-$ scattering occurrs." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Compute the process leading-order cross section, $\\sigma(\\theta; \\sqrt{s})$, as a function of the scattering angle $\\theta$ and with the center of mass energy $\\sqrt{s}$ as a parameter. Start by computing it in the center of mass system. N.B.: textbooks reports such cross section in the relativistic limit, i.e. for $\\sqrt{s}\\gg m_\\mu$, which is clearly not the case here ($\\sqrt{s}\\sim 2m_\\mu$);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The main goal of this project is the simulation of a muon source induced by an electron-positron pair annihilation.\n", + "\n", + "The calculation of the cross section comes from the derivation of the unpolarised scattering amplitude - we are not interested in the polarisation of both incoming and outgoing particles. \n", + "Moreover, we are not interested in considering the annihilation in the usual Ultra Relativistic limit ($m \\sim 0$), but we are interested in the range of energy close to the threshold for the muon pair production: $\\sqrt s \\sim 2m_\\mu$. \n", + "\n", + "1. The differential cross section for the considered process, in the CoM frame (\\*-quantities), has the following expression: $$\\left(\\frac{d\\sigma}{d\\Omega}\\right)^* \\Big\\rvert_{CoM} \\left(\\sqrt s, \\theta^*, \\phi^*\\right)= \\frac{\\alpha^2}{4s}\\left(1-\\frac{4m_\\mu^2}{s}\\right)^{1/2}\\left(1-\\frac{4m_e^2}{s}\\right)^{-1/2}\\left[1+\\frac{4}{s}\\left(m_e^2+m_\\mu^2\\right)+\\left(1-\\frac{4m_\\mu^2}{s}\\right)\\left(1-\\frac{4m_e^2}{s}\\right)\\cos^2\\theta^*\\right]$$\n", + "\n", + "where the differential cross section in the center of mass is expressed as a function of the (CoM) energy $\\sqrt s$ (the first Mandelstam variable, equal for both $e$ and $\\mu$ pairs in che CoM frame), the masses of $e^+$ and $e^-$ $m_e$ and of the muons $m_\\mu$, and the emission angle in the center of mass $\\theta^*$. ($\\alpha$ is the EM constant, $\\alpha=\\frac{e^2}{4\\pi}$). One can also notice that the differential cross section depends only on the $\\theta^*$ angle, and not on the other angle $\\phi^*$.\n", + "\n", + "The total cross section can be found by integrating over the solid angle. \n", + "$$ \\sigma (\\sqrt s) = \\int_{4\\pi} d \\Omega^* \\frac{d\\sigma^*}{d\\Omega^*} = \\int_0^{\\pi} d\\theta^* sin\\theta^* \\int_0^{2\\pi} d\\phi^* \\frac{d\\sigma^*}{d\\Omega^*} = 4\\pi\\frac{\\alpha^2}{3s^3}\\left(1-\\frac{4m_\\mu^2}{s}\\right)^{1/2}\\left(1-\\frac{4m_e^2}{s}\\right)^{-1/2}(2m_e^2+s)(2m_\\mu^2+s) $$ \n", + " \n", + "2. The angular distribution can be simply computed normalizing the differential cross section with respect to the total one: \n", + "$$ f(\\theta^*, \\phi^*) = \\frac{1}{\\sigma} \\frac{d\\sigma^*}{d\\Omega^*}$$ \n", + "\n", + "In order to get the distribution of just the $\\theta^*$ angle we integrate over $\\phi^*$, and we consider the module of the determinant of the jacobian of the trasformation from cartesian coordinates to spherical coordinates $$\\begin{vmatrix} \\frac{\\partial(x,y,z)}{\\partial(\\theta^*,\\phi^*)}\\end{vmatrix}=sin(\\theta^*) $$ getting \n", + "$$ pf(\\theta^*) = \\frac{1}{\\sigma} \\frac{d\\sigma^*}{d\\Omega^*}\\times 2\\pi\\times sin(\\theta^*)$$ \n", + "\n", + "As we are considering a case in which we have a stationary target, we need to pass from the CoM coordinates to the LAB ones. Of course a Lorentz boost is going to be involved for both angles and spatial coordinates. \n", + "\n", + "In the CoM frame, the 4-momentum for the incoming and outgoing particles can be written as: \n", + "$$p_{e^\\pm}^* = (E^*, \\pm \\vec p_e^{\\,*}) \\,\\,\\,\\,\\,\\,\\, p_{\\mu ^\\pm}^{\\prime\\,*} = (E^*, \\pm \\vec p_\\mu^{\\,\\prime\\,*})$$\n", + "\n", + "The speed of the center of mass $\\beta^*$, in the case in which we consider the electron at rest, is given by: \n", + " $$ \\beta^* = \\frac{p_{e^+}}{E_{e^+}+m_{e^-}}$$\n", + "Moreover, as we consider a process in which two muons are produced ($m_\\mu \\sim 207 m_e$), we can well approximate the parameter $ \\beta^* \\sim \\frac{p_{e^+}}{E_{e^+}} = \\beta_{e^+} $ (The energy of the incoming positron needs to be over a certain threshold to produce the muon pair ( $\\sim 45 \\, GeV$ )\n", + "\n", + "The energy of the CoM $E^*$ can be written in terms of the Mandelstam variable *s*: $ s = (p_{e^-}+p_{e^+})^2 = 4E^{*2}$ ( $\\sim 4m_\\mu^2$ in the considered case).\n", + "\n", + "And so, it follows:\n", + "\n", + "$$\\beta^*_{e^\\pm} = \\frac{\\lvert\\vec p^{\\,*}\\rvert}{E^*} = \\frac{ \\sqrt{(E^*)^2-m_e^2}}{E^*} = \\sqrt{1-\\frac{4m_e^2}{s} } $$\n", + "\n", + "And analogously, $$\\beta^*_{\\mu^\\pm} = \\sqrt{1-\\frac{4m_\\mu^2}{s}}$$\n", + "(These two factors also appear in the cross section formula)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Angle and momentum components distributions of the emerging muon pairs;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. compute and display the angle and momentum components distributions of the emerging muon pairs;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At first, we define physical constants and import libraries." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "#import cell\n", + "import numpy as np \n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "import matplotlib.colors as clr\n", + "from scipy.interpolate import UnivariateSpline\n", + "from scipy.interpolate import InterpolatedUnivariateSpline\n", + "from scipy.interpolate import interp1d" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "alpha = 1/(137.035999084) #dimensionless CODATA 2018 Fine-Structure constant\n", + "m_muon = 105.6583755 #[MeV] CODATA 2018 Muon mass\n", + "m_e = 0.51099895 #[MeV] CODATA 2018 Electron mass\n", + "s = 220**2 #[MeV] For the sake of simplicity we take as a reference pow(sqrt(s),2). \n", + " #We have choosen a s-value close to 2 m_muon, as required by the considered process\n", + "N = 10**6 #number of generated muon pairs\n", + "\n", + "def dsigmadtheta(s,theta, phi = 0):\n", + " '''\n", + " differential cross section\n", + " '''\n", + " return (alpha**2/(4*s))*(1-(4*m_muon**2)/s)**0.5*((1-(4*m_e**2)/s))**-0.5*(1+(4/s)*(m_e**2+m_muon**2)+(1-(4*m_e**2)/s)*(1-(4*m_muon**2)/s)*np.cos(theta)**2)\n", + "\n", + "def sigma(s):\n", + " '''\n", + " total cross section\n", + " '''\n", + " return 4*np.pi*(alpha**2/(3*s**3))*(1-(4*m_muon**2)/s)**0.5*((1-(4*m_e**2)/s))**-0.5*(2*m_e**2+s)*(2*m_muon**2+s)\n", + "\n", + "def pf(s,theta, phi = 0):\n", + " '''\n", + " theta probability distribution\n", + " '''\n", + " return dsigmadtheta(s,theta)/sigma(s)*2*np.pi*np.sin(theta)\n", + "\n", + "#plotting pf\n", + "x = np.linspace(0,np.pi,100)\n", + "plt.title(\"Angular Distribution\")\n", + "plt.xlabel(r'Center of mass emission angle $\\theta^*[rad]$' )\n", + "plt.ylabel(r'Angular distribution $f(\\sqrt{s} = 220 MeV, \\theta^*)$' )\n", + "\n", + "plt.plot(x, pf(s,x))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computing the cumulative function $g(\\theta^*)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to write the actual components of the momentum of the emitted muons, we need to generate some random numbers distributed accordingly to the angle distribution just shown.\n", + "\n", + "In order to achieve such a result, we need to calculate the cumulative density funcion (CDF) of the angle distribution $CDF(f(\\theta^*, \\phi^*)) := g(\\theta^*)$. \n", + "\\begin{aligned}\n", + "g(\\theta^*) = \\int _{0}^{\\theta^*}dx\\sin x\\frac{3}{4}\\frac{2\\pi}{4\\pi} \\dfrac{s^2}{\\left( 2m_e^{2}+s\\right) \\left( 2m_{\\mu }^{2}+s\\right) }\\left( 1+\\dfrac{4}{s}\\left( m_{e}^{2}+m_{\\mu}^{2}\\right) +\\left( 1-\\dfrac{4m_{e}^{2}}{s}\\right)\\left( 1-\\dfrac{4m_{\\mu}^{2}}{s}\\right) \\cos^2x \\right)\\\\\n", + "\\end{aligned}\n", + "\n", + "\n", + "\\begin{aligned}\n", + "= \\frac{3}{8} \\dfrac{s^2}{\\left( 2m_e^{2}+s\\right) \\left( 2m_{\\mu }^{2}+s\\right) }\\left( - \\left( 1+\\dfrac{4}{s}\\left( m_{e}^{2}+m_{\\mu}^{2}\\right)\\right)\\cos x+\\left( - \\frac{1}{3}\\left( 1-\\dfrac{4m_{e}^{2}}{s}\\right)\\left( 1-\\dfrac{4m_{\\mu}^{2}}{s}\\right) \\right)\\cos^3 x \\right) \\Big\\rvert_0^{\\theta^*}\\\\\n", + "\\end{aligned}\n", + "\n", + "\\begin{aligned}\n", + "= \\frac{3}{8} \\dfrac{s^2}{\\left( 2m_e^{2}+s\\right) \\left( 2m_{\\mu }^{2}+s\\right) }\\left( \\left( 1+\\dfrac{4}{s}\\left( m_{e}^{2}+m_{\\mu}^{2}\\right)\\right)(1-\\cos \\theta^*)+\\left(\\frac{1}{3}\\left( 1-\\dfrac{4m_{e}^{2}}{s}\\right)\\left( 1-\\dfrac{4m_{\\mu}^{2}}{s}\\right) \\right)(1-\\cos^3 \\theta^*) \\right)\\\\\n", + "\\end{aligned}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def g(s, x): #x stands for theta star\n", + " '''\n", + " function computing the cumulative density function of the angle distribution\n", + " '''\n", + " return s**2*3./8.*((1+4*(m_e**2+m_muon**2)/s)*(1-np.cos(x))+(1-4*m_e**2/s)*(1-4*m_muon**2/s)*(1-np.cos(x)**3)/3)/((2*m_e**2+s)*(2*m_muon**2+s))\n", + "\n", + "#plotting g(x)\n", + "\n", + "plt.plot(x,g(s,x))\n", + "plt.title(\"Cumulative function for the angular distribution\")\n", + "plt.xlabel(r'Center of mass emission angle $\\theta^*[rad]$' )\n", + "plt.ylabel(r'Cumulative function, $g(\\sqrt{s} = 220 MeV, \\theta^*)$' )\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Boosting muons four-momenta in the laboratory frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3. boost muons four-momenta in the laboratory frame, i.e. in the frame where the electron is at rest and the positron has enough energy to give rise to the process;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now observe that the norm of the momentum of the outgoing muon can be written as follows:\n", + "$$ \\lvert \\vec p^{\\,*}_\\mu \\rvert = \\sqrt {\\frac{s}{4}-m_\\mu^2} $$\n", + "The momentum components' distributions can be simply derived knowing the center of mass energy - $\\sqrt s$ - and the emission angles in the CoM - $ \\theta^* $ and $ \\phi^* $. \n", + "\n", + "$$ p^*_\\mu = \\lvert \\vec p^{\\,*}_\\mu \\rvert ( \\frac {\\sqrt s}{ 2 \\lvert\\vec p^{\\,*}_\\mu \\rvert}, cos\\theta^*, sin\\theta^* cos\\phi^*, sin\\theta^* sin\\phi^*) $$\n", + "\n", + "3. Finally, the relation between the Lab angles and the COM ones has the usual formula: \n", + "$$tan \\theta_\\mu = \\frac {sin\\theta^*_\\mu}{\\gamma(cos\\theta^*_\\mu+\\frac{\\beta}{\\beta^*_\\mu})} $$\n", + "\n", + "\n", + "If we are considering, without loss of generality, a boost along the x axis, the relations between the energy and momentum components are the following: \n", + "$$ E_1 = \\gamma ( E^*+\\beta p^*_x) \\,\\,\\,\\,\\,\\, p_{1,x} = \\gamma(\\beta E^*+p^*_x ) $$\n", + "\n", + "$$ E_2 = \\gamma ( E^*-\\beta p^{\\,*}_x) \\,\\,\\,\\,\\,\\, p_{2,x} = \\gamma(\\beta E^*-p^{\\,\\,\\,\\,*}_x ) $$\n", + "The relation $$\\vec p^*=\\vec p_1^*=-\\vec p_2^*$$ turns out, setting $$\\theta_1^*=\\theta^*, \\,\\,\\,\\,\\,\\, \\phi_1^*=\\phi^* $$ in the following relation between the angles of the two emerging muons: $$\\theta_2^*=\\pi+\\theta^*, \\,\\,\\,\\,\\,\\, \\phi_2^*=\\phi^*$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4. In order to sample the angles accordingly to the angle distribution, we use the inverse CDF method. \n", + "So we define a uniform distribution for $\\theta ^* \\in [0,\\pi]$ and we interpolate with three different methods available in the scipy library the $g(s, \\theta^*)$ function - the ordinate is represented by $g(s, \\theta^*)$, the abscissa by $\\theta^*$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(2,3, figsize = (15,10))\n", + "\n", + "#angles on which we sample the inverse CDF\n", + "theta_star = np.linspace(0, np.pi, N)\n", + "\n", + "#three version of inverse CDF sampling\n", + "inv_cdf1 = UnivariateSpline(g(s,theta_star),theta_star, ext=0)\n", + "inv_cdf2 = InterpolatedUnivariateSpline(g(s,theta_star),theta_star, ext=0)\n", + "inv_cdf3 = interp1d(g(s, theta_star), theta_star)\n", + "\n", + "#same plot on each ax of the points\n", + "for i in range(3):\n", + " ax[0][i].plot(theta_star,\n", + " g(s,theta_star),\n", + " '*',\n", + " alpha = 0.005,\n", + " color = '#B0A084',\n", + " label = 'Samples'\n", + " )\n", + " ax[1][i].set_title('Angular distribution in the CoM')\n", + " ax[1][i].set_ylim(0,15000)\n", + " \n", + "random_num = np.random.rand(N)\n", + "num_sorted = np.sort(random_num)\n", + "\n", + "\n", + "#------UnivariateSpline plots------\n", + "\n", + "ax[0][0].set_title('CDF sampled with UnivariateSpline')\n", + "ax[0][0].plot(inv_cdf1(num_sorted),\n", + " num_sorted,\n", + " color = '#73683B',\n", + " label = 'inv_CDF',\n", + " linewidth = 3\n", + "\n", + " )\n", + "\n", + "sns.histplot(inv_cdf1(num_sorted),\n", + " ax = ax[1][0],\n", + " color = '#73683B',\n", + " kde = True\n", + " )\n", + "\n", + "#------InterpolatedUnivariateSpline plots------\n", + "\n", + "ax[0][1].set_title('CDF sampled with InterpolatedUnivariateSpline')\n", + "ax[0][1].plot(inv_cdf2(num_sorted),\n", + " num_sorted,\n", + " color = '#4F5D75',\n", + " label = 'inv_CDF', \n", + " linewidth = 3\n", + " )\n", + "\n", + "sns.histplot(inv_cdf2(num_sorted),\n", + " ax = ax[1][1],\n", + " color = '#4F5D75',\n", + " kde = True \n", + " )\n", + "\n", + "#------interp1d plots------\n", + "\n", + "ax[0][2].set_title('CDF sampled with interp1d')\n", + "ax[0][2].plot(inv_cdf3(num_sorted),\n", + " num_sorted,\n", + " color = '#D64045',\n", + " label = 'inv_CDF', \n", + " linewidth = 3\n", + " )\n", + "\n", + "sns.histplot(inv_cdf3(num_sorted),\n", + " ax = ax[1][2],\n", + " color = '#D64045',\n", + " kde = True \n", + " )\n", + "\n", + "for i in ax[0]:\n", + " i.set_ylabel(r\"$g(s, \\theta^*)$\")\n", + " i.set_xlabel(r\"$\\theta^*$\")\n", + " \n", + "for j in ax[1]:\n", + " j.set_ylabel(r\"Count\")\n", + " j.set_xlabel(r\"$\\theta^*$\")\n", + "\n", + "\n", + "plt.subplots_adjust(left = None,\n", + " bottom = None,\n", + " right = None,\n", + " top = None,\n", + " wspace = 0.3,\n", + " hspace = 0.3\n", + " )\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It can be noticed how different interpolating function lead to different distribution: in particular the 'Interpolate Spline' method is not able to fit the extremes providing a wrong angular distribution.\n", + "\n", + "From now on, we will use **interp1d** as fitting method." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4. write a Monte Carlo simulation that generates scattering events following the distributions that you found analytically; " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def mom_mu_cm(m_muon, s, t, p):\n", + " ''' \n", + " CoM momentum using cartesian components \n", + " ''' \n", + " p_norm = np.sqrt(s/4-m_muon**2)\n", + " p_x_cm = p_norm * np.cos(t)\n", + " p_y_cm = p_norm * np.sin(t)*np.cos(p)\n", + " p_z_cm = p_norm * np.sin(t)*np.sin(p)\n", + " return p_x_cm, p_y_cm, p_z_cm\n", + "\n", + "def e_pos_lab(s, m_e):\n", + " ''' \n", + " positron energy in the laboratory frame\n", + " ''' \n", + " return s/(2*m_e)-m_e\n", + "\n", + "\n", + "def p_pos_lab(s, m_e):\n", + " ''' \n", + " positron momentum in the laboratory frame\n", + " ''' \n", + " e_pos = e_pos_lab(s, m_e)\n", + " return np.sqrt(e_pos**2-m_e**2)\n", + "\n", + "def beta(s, m_e = 0.51099895):\n", + " ''' \n", + " lorentz beta function\n", + " ''' \n", + " e_pos = e_pos_lab(s, m_e)\n", + " p_pos = p_pos_lab(s, m_e)\n", + " return p_pos / (e_pos + m_e)\n", + " \n", + "def gamma(s, m_e):\n", + " ''' \n", + " lorentz gamma function \n", + " ''' \n", + " return 1./np.sqrt(1-beta(s, m_e)**2)\n", + "\n", + "def Ecm(s):\n", + " ''' \n", + " CoM energy\n", + " ''' \n", + " return np.sqrt(s)/2.\n", + "\n", + "def boost(s, t, p, m_e, m_muon):\n", + " '''\n", + " boosting the muon-four momentum to the laboratory frame\n", + " '''\n", + " e_cm = Ecm(s)\n", + " b = beta(s, m_e)\n", + " g = gamma(s, m_e)\n", + " px_cm, py_cm, pz_cm = mom_mu_cm(m_muon, s, t, p) #py pz does not change \n", + " px = g * (b * e_cm + px_cm) #boost px\n", + " e = g * (e_cm + b * px_cm) #boost energy\n", + " return px, py_cm, pz_cm\n", + "\n", + "\n", + "def mc_sampling(s, m_e, m_mu, N):\n", + " '''\n", + " montecarlo sampling to get theta^* distribution with inverse cdf method\n", + " '''\n", + " prob = np.random.rand(N)\n", + " theta = inv_cdf3(prob)\n", + " phi = np.random.uniform(0, 2*np.pi, N)\n", + " muon_1 = boost(s, theta, phi, m_e, m_muon) \n", + " muon_2 = boost(s, np.pi+theta, phi, m_e, m_muon)\n", + " return np.asarray(muon_1 + muon_2)\n", + "\n", + "\n", + "def mc_df_sampling(df, m_e, m_muon):\n", + " ''' \n", + " sampling function using dataframe and multiple energy values\n", + " ''' \n", + " phi = np.random.uniform(0, 2*np.pi, df.shape[0])\n", + " muon_1 = boost(np.asarray(df.energies), np.asarray(df.angles), phi, m_e, m_muon)\n", + " muon_2 = boost(np.asarray(df.energies), np.asarray(df.angles+np.pi), phi, m_e, m_muon)\n", + " return np.asarray(muon_1 + muon_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "5. produce a synthetic dataset of about $N=10^5$ (we chose $10^6$) events. Events should be listed as rows in a file with columns representing the muons coordinates (keep in mind that in the lab frame muons are relativistic and thus the number of coordinates can be only 3 per muon);" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "events = mc_sampling(220**2, m_e, m_muon, N)\n", + "df_monochromatic = pd.DataFrame(events.T, columns = [ \n", + " '$px_{\\mu_1}$',\n", + " '$py_{\\mu_1}$',\n", + " '$pz_{\\mu_1}$',\n", + " '$px_{\\mu_2}$',\n", + " '$py_{\\mu_2}$',\n", + " '$pz_{\\mu_2}$'\n", + " ]\n", + " )\n", + "df_monochromatic.to_csv('Events.csv')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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$px_{\\mu_1}$$py_{\\mu_1}$$pz_{\\mu_1}$$px_{\\mu_2}$$py_{\\mu_2}$$pz_{\\mu_2}$
020355.30659313.98320122.41437227002.401048-13.983201-22.414372
122779.260047-30.155888-3.07668124578.44759330.1558883.076681
229894.5246892.792474-9.73497417463.182952-2.7924749.734974
324168.412929-26.404425-15.29516123189.29471226.40442515.295161
424826.452397-25.20126216.51615622531.25524325.201262-16.516156
.....................
99999528077.489040-7.598814-21.47167819280.2186007.59881421.471678
99999626089.24865928.4659390.78563621268.458981-28.465939-0.785636
99999717876.34109612.721890-6.91921329481.366545-12.7218906.919213
99999826285.3161710.993608-28.08402521072.391470-0.99360828.084025
99999929997.811668-5.743206-6.45322917359.8959735.7432066.453229
\n", + "

1000000 rows × 6 columns

\n", + "
" + ], + "text/plain": [ + " $px_{\\mu_1}$ $py_{\\mu_1}$ $pz_{\\mu_1}$ $px_{\\mu_2}$ $py_{\\mu_2}$ \\\n", + "0 20355.306593 13.983201 22.414372 27002.401048 -13.983201 \n", + "1 22779.260047 -30.155888 -3.076681 24578.447593 30.155888 \n", + "2 29894.524689 2.792474 -9.734974 17463.182952 -2.792474 \n", + "3 24168.412929 -26.404425 -15.295161 23189.294712 26.404425 \n", + "4 24826.452397 -25.201262 16.516156 22531.255243 25.201262 \n", + "... ... ... ... ... ... \n", + "999995 28077.489040 -7.598814 -21.471678 19280.218600 7.598814 \n", + "999996 26089.248659 28.465939 0.785636 21268.458981 -28.465939 \n", + "999997 17876.341096 12.721890 -6.919213 29481.366545 -12.721890 \n", + "999998 26285.316171 0.993608 -28.084025 21072.391470 -0.993608 \n", + "999999 29997.811668 -5.743206 -6.453229 17359.895973 5.743206 \n", + "\n", + " $pz_{\\mu_2}$ \n", + "0 -22.414372 \n", + "1 3.076681 \n", + "2 9.734974 \n", + "3 15.295161 \n", + "4 -16.516156 \n", + "... ... \n", + "999995 21.471678 \n", + "999996 -0.785636 \n", + "999997 6.919213 \n", + "999998 28.084025 \n", + "999999 6.453229 \n", + "\n", + "[1000000 rows x 6 columns]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_monochromatic" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#plotting momentum components distribution in the LAB frame\n", + "fig, ax = plt.subplots(1,3, figsize = (18,6))\n", + "\n", + "#px\n", + "sns.histplot(df_monochromatic['$px_{\\mu_1}$']/1000,\n", + " ax = ax[0],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#73683B'\n", + " )\n", + "#py\n", + "sns.histplot(df_monochromatic['$py_{\\mu_1}$']/1000,\n", + " ax = ax[1],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#4F5D75'\n", + " )\n", + "#pz\n", + "sns.histplot(df_monochromatic['$pz_{\\mu_1}$']/1000,\n", + " ax = ax[2],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#D64045'\n", + " )\n", + "\n", + "\n", + "plt.suptitle('Momenta histogram for $\\mu_1 (monochromatic)$')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$p_y$ and $p_z$ components distributions are as expected uniform, equal and centered in zero. On the other hand, the $p_x$ distribution displays a negative concavity and peaks at the interval extremes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Berillium target statistics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "6. assume a $3$ cm thick Beryllium block is used as target and a rate of positron on target of $10^6$ Hz. Compute the rescaling factor (weight) you need to apply to the $N$ simulated events such that they represent the statistics that would be gathered in a week of countinuous operations;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to compute the rescaling factor that retrieves the statistics for a one week data gathering, we compute the number of pairs produced per positron bunch on target $n(\\mu^+ \\mu^-)$:\n", + "\n", + "$$n(\\mu^+ \\mu^-)=n^+ \\rho^- l\\, \\sigma(\\mu^+ \\mu^-)$$\n", + "\n", + "where $n^+$ is the number of positrons in the bunch, $\\rho^-$ is the electron density in the medium, $l$ is the target thickness and $\\sigma(\\mu^+ \\mu^-)$ is the muon pairs production cross-section.\n", + "Then, expressing it as a function of the impinging positrons rate $f^+$ it holds:\n", + "\n", + "$$f(\\mu^+ \\mu^-)=f^+ \\rho^- l\\, \\sigma(\\mu^+ \\mu^-)$$\n", + "\n", + "It is possible to express $\\rho^-$ as:\n", + "\n", + "$$\\rho^-=N_A \\frac{\\rho_{Be}Z}{M_t}$$\n", + "\n", + "in which $N_A$ is the Avogadro number, $\\rho_{Be}$ is the Beryllium density, Z is its atomic number and $M_t$ its molar mass.\n", + "\n", + "Then the rescaling factor is given by $W=f(\\mu^+ \\mu^-) \\Delta T$, where $\\Delta T$ is the number of seconds in a week." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "freq = 10**6 #[Hz] frequency of positrons on target\n", + "rhoBe = 1.848 #[g/cm^3] Beryllium density\n", + "N_a = 6.022*10**23 #Avogadro's number\n", + "Z = 4 #Beryllium charge\n", + "M = 9.012 #[amu] Be mass\n", + "l = 3 #[cm] Beryllium target thickness\n", + "rho_elec = N_a * (rhoBe*Z) / (M) #Be Electron density\n", + "fmu = freq * rho_elec * l * sigma(230**2) * 1e-24 *38937 #[Hz] muon pair production frequency\n", + "deltaT = 60 * 60 * 24 * 7 #Seconds in a week\n", + "fweek = fmu * deltaT #rescaling factor(number of mu produced in a week)\n", + "\n", + "weights = np.full(int((N)), fweek/N) #array of rescaling factors\n", + "df_monochromatic['weights']=weights \n", + "\n", + "sns.histplot(x=df_monochromatic['$px_{\\mu_1}$']/1000, \n", + " weights= df_monochromatic['weights'], \n", + " bins = int(np.sqrt(N)), \n", + " kde=True\n", + " \n", + " )\n", + "plt.suptitle('One week activity histogram')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Montecarlo with real beam" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "7. Repeat what done so far simulating now the actual transverse shape and energy spread of the beam: for the former assume a flat distribution in a circle of radius $r=1$ cm and for the latter a gaussian distribution centered at the nominal beam energy and a width of $0.5$ GeV; \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get a simulation for the real beam we must add the information on how colliding particle energy and position distributes within the chosen set. For $s$ we assume a Gaussian with mean in 48.4 GeV and variance 0.5 GeV, where the beam energy is obtained as $\\frac{s}{2 m_e}$. \n", + "\n", + "As the InvCDF method is not feasible due to too large computation time, we decide to exploit the accept-reject method in order to get a computationally reasonable task.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Showing the accept-reject method main idea\n", + "fig, ax = plt.subplots(1, 1, figsize=(8,5))\n", + "\n", + "thetas = np.linspace(0,np.pi,100)\n", + "ax.plot(thetas, pf(220**2,thetas), label=r'$pf(\\theta^*)$')\n", + "ax.axhline(pf(220**2, np.pi/2), color='red', label='Max value')\n", + "ax.set_xlabel(r'$\\theta^*$')\n", + "ax.set_ylabel(r'PDF')\n", + "ax.set_ylim([0,0.55])\n", + "\n", + "\n", + "plt.arrow(np.pi/4,0,0,pf(220**2,np.pi/4)-0.01, linewidth=1,\n", + " head_width=0.05, head_length=0.01, fc='g', ec='g')\n", + "\n", + "plt.text(np.pi/4-.65, 0.45, 'Reject', fontsize=16)\n", + "plt.text(np.pi/4-.65, 0.04, 'Accept', fontsize=16)\n", + "ax.legend(loc = 'best')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "#generating energies in CoM (s=220**2 )\n", + "\n", + "#48400: s=220**2=48400 middle energy\n", + "#500: std_dev of the gaussian distribution\n", + "#2*N: Number of generated events \n", + "energies_gauss = np.random.normal(48400, 500, 2*N) \n", + "energies_gauss = energies_gauss[energies_gauss > 4 * m_muon**2] #check on threshold production\n", + "\n", + "\n", + "\n", + "#we are sufficiently (>3 sigma) far from threshold. Pair production threshold is ok\n", + "\n", + "#accept and reject method for angular distribution generation\n", + "pts = np.random.uniform( 0, np.pi, len(energies_gauss))\n", + "check = np.random.uniform( 0, pf(energies_gauss,np.pi/2), len(energies_gauss) )\n", + "\n", + "df_energies_real_beam = pd.DataFrame(pd.Series(energies_gauss), columns = ['energies'])\n", + "df_energies_real_beam[\"angles\"] = pts\n", + "df_energies_real_beam[\"check\"] = check\n", + "df_energies_real_beam[\"label\"] = df_energies_real_beam.angles[df_energies_real_beam.check < pf(df_energies_real_beam.energies, df_energies_real_beam.angles)]\n", + "df_energies_real_beam = df_energies_real_beam.dropna()\n", + "df_energies_real_beam = df_energies_real_beam.iloc[:N] #Taking only the first N values\n", + "\n", + "df_events_real_beam = pd.DataFrame(mc_df_sampling(df_energies_real_beam, m_e, m_muon).T, columns = [\n", + " '$px_{\\mu_1}$',\n", + " '$py_{\\mu_1}$',\n", + " '$pz_{\\mu_1}$',\n", + " '$px_{\\mu_2}$',\n", + " '$py_{\\mu_2}$',\n", + " '$pz_{\\mu_2}$'\n", + " ]\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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BqdrAkUce2cSoiYh6R9Fc64+2YvtKqR8C+CEAnH322WqJmxMR9Tyl1JeXuH5j0c8KwO9XuN01AK5panBERF2kbQ07W92ciPP7iIhq0tK51kRERERErdDO1Ua4w0xE5DPOtSYiIiKibtS25AV3mImI2o9zrYmIiIioF7Ss54W7w3wugFVCiH0AvqOUurrCzbcAuBjODnMawDcAZ4dZCOHtMAPcYSYiqgvnWhMRERFRL2hZ8oI7zERERERERETUDO3seUFEREREREREVDcmL4iIiIiIiIioozF5QURERERE1OGUUrBtG86Me6L+w+RFm1UbdGzbhm3bPkRF/Yh/b0REteF4SUSdQEqJ/VdfCyml36EQ+YLJizaTUuKBu3/IQYeIiIiIiOqiazx8o/7Fv34faBx0iIiIiIiIiGrGo2ifsRSViIiIiIioe7D/iD+YvOhgjSQ2mAwhIiIiInLwIJNagf1H/MHkhU84kBIRERERLc9S+9S9fpDJE5f+Yf+R9uMr3mKVBhSvcadpmhxwiIiIiIgaUEtyggeZRL2Bn+Q28jLDcBPDtTTu7MdsKqtSiIi6F8dwImo3Jica04/HGdTd+ElvI9M0cf9dzjKpxUkMz3IHkF7ZYeRyspU18h4v9Xe13OuJiIpJKXHjbVs4hhORr6rtv7Rj32apfTbuX7VOrxwT0WJMXrSZJjRIqbD13qthWfUNWksNcs5B/4+W3GFs5mBZ6+BQ72NyOdnylpPYyefzyOfzLYiKiLpNq3fsOIYTUT8q3t+tt9fGcvbPW5UI6dYES72vPZMd3YN7Fz7RxPxLX+kD08gHSdO0qvdr1iDkbYdVEu1R/J62+6CAAzpR7+m36ohmjmPdujNPRI527Nd448RS01k6bTzx4in9143qmUrU601dewmTF21k2zakWvihUErBNE08cNfiBICUElvvvbruD1K7Ewq1Hkx38wDYDMv5svQzSSSlxNZ7ruKATtRjuqE6olkHGf2WrCGiyqSU2H/Npr4bD2rdD2/27RrV7pNn7JvSHfgutZFt27BKEhhSSmy7/xoIIcrep7hCo1SlD7Vt2xAov71K28nn87Asq+b7NKpXzuI3MmA3koAofpzSA41W9qoofZ/qfWwi6k6Vzrb5Vc7czKRDNyRrltIr36FEfit3oNopn69a4mj1flizK7Ub0QnVEJ3yN0Hzuv+bvAeUS1DU8mFv1tl4KSXuvfNfYZrmknEsdzBrVQVBsweXZj9vTzt2nr3XwmsM20hzz3LvExMWRK3VaZ+xTomnkXGzU2L3NCseVpAQtU4nHCw3Iw4/D7ib/djFSabicbTWx1luPLW8F532fdPrmLzwgS3loukjNd3PtpHP5xd8QBafEZfuh0jW1yCzSoVH8eN36gF8rUmRThxgmh2T91pYlrVoukc9j9ULZymJqLNYloV8Pl/TjmQnjtdLaUXMpdvk2ExUu/mD19puX23qQDMOzGvdRrU4bFl9H3+pA24vBsuyFm2n0b55xSe/mpUAcrZX/nWq9XHqiceWsvCaeK9DLX1Llqsbv+v8xG/ALtToH3kvfzjqnSrTCtWm8TRSxVEuWVUrb+eW/UiI2qMbP0NStj9mKSVuvmOb72c2gfrfs1YsVb0c3fg3R9RsS30OvP4WSqnapmNUSQxIKbHnR1eXrVSu1XIO7us6ASVExedaLQYpJQ5ce/2yxmh9icUDgMrPpdzllW5bNcFTlPiodLtyMTby/hTHV8vz4lSU5WHyosN4/SdM03T+sFH/2SnbXtwYtFa1DIyd1rW9U3bgSqs/vLhaOUgtlQU3y2TVa92ukvNf9FLVPwWFiGrXKeOYp5Vjc7dWDrRqykatr7U3HjcLd6CpX3gHr82oCljuWfh8Po+ay0AaUKiAUAoHrrmu8FxLP+/VnsdSSYFq45CXNDBNE7v+9arC8cxS96m4L1slmbRUBcpSKv09NPoe15qg6JTpSd2qO/cgephzAPwjp+T/vmtgNWkHsrgMCmjGyhc/Kvuhq6ckuNuVG2zL7ZQ3e7WOeqcEOfep7+/IS1hIKfHAPVfBthtb+YaIyvMzWdHpSeNmNJFuVXzlxvh6Hmu537033b6lad+v7J9B/ajcgelyxotG71tpLKg2zaX0sbx97nLTP4CFz7WRFVbqTayWPpdam6I2e7wuTPmoUF1Y/HjlYrTcyuf5HnKq7hiXSlBUSpB02omMTsTkRRsopWBZFizLqqmSolDyX0MfilqVJhy8KoFGPySVVp/wDtRN06w45aGRg+92accOr21Xnw6Sz+eRy+WW3MFtpDFnIzvO3t+h9z8HVqLa+HVmu9UNjFvNO0jvloPqel4fKSWu33xfw2Xnza5a6dYqGKJ6NXKWvpVjuJQSe666pjAWFO9He9NclhpbpJQLqiuWUm9FQa1j21KJkeLXsdYGmPVMmy6O07ZtmKaJ/dde1/AJYKkUxjdVnzqzVC8V27YBhYp/P6x8axy/tdpASon77vxXbL3vmkWlYrlcGqm5GOKxCex660Xs2fUKstkUpKzeI6H0g1rLh9PbSfFur2laIalROkguZ2e1lp2hpUvI5pvmVMool26jUlKknufSzJ30xfE5UzFqeZxq1S3e85TSqYawLKtss9JylTa2bS9ZBeJl8mvIsxFRFVJK3HDrAzBNs+El7ypdt1RJavEZ9UZ2khrt75DP58tW39U7tlb6HimNa6nvx+LL2rmTWO35ln4XL2f7yz3rS9SNyu1fVWrsWKvSg9HCQbB7oO2Nb7U8TvFn07Qqf0YrJRNq6RnhXa9ry+/31ox93wWrgpQkikqTLJVWEGlE8XFC8ck8XdMWxFHphF+1pJa3XVvaCypcCkkYN8lUGo+3vdKpO8WqXUfVMXnRIsWDTumgats2Jg/txvNPb8f/+q+X4vmntuG5px7E1f/3j/Cj7/0HPPnLu/G337kUr770M8xOH4BtWxUHsFp3MIsPnEsV7yT6kQkstxNm2xKmaS44KPd2iovvs+D+RQNQuS+25SY2WqFadrm0WsMyy0xT8aoilkgYSSmx9b5rIKUse9vSrPi2+69lNpioCYRASxpUliv5XziezR+cNjI9QEqJzXdtb8uOVS3jsHcb77l4v9c7TrVjzK/1MWqZZtmMHfty92/2FBSidiqXxFRqef3GKh2MNtL/oBn70qZtY/81mxZUMhcnWKSUOLDphgWNSCud7AMWJniqVTUUv5bVLNrPLpMEKI6rOMdSXJEupSxUHC9+ntXHRu/5eMkRy7LKVoAo5fTg2HfVtWVvU22c9F5j7/fiqpFa/jYa7S1ClfFVa5FKS3cqJfHWa7/Gm68+Btu28MGPfAknnPIBnHrGuTjhtA/hS1//Do476X045YzfQioxgzde/gX+6W+vxI++90dIp5LuNooPNFXhoLRZcZeemV9q2aTSpEhxBUQjZxSLNVLSWhxvrQNgLTuH9exENuOLq55t1DIVx0t0VOquXPy+izqnLPmdBCLqZEslDJu53WLFCd9GxtLi+5Q70K71c+/tqJqm6e5cW4XYKiWVq0+Zk8hms4WEzFLJ6fnKs8YaGNej2vtaelLDtm3ccmflBFGjB2G14pQR6lblpkuUO9tffJBay7SRaqtSeAfYlQ7sS08CHbj2erfqrvxBcrkTm6XxlcYjpcT4dTcUpkMUNyI9uOn6ilV+xd8F1ZSLodL4Wu4kbeltpVIYv+6GRWOcVAr7rrkOB67ZBMuycOC6GxfcxjTNRQmGpcZB77Uo9x5KpXDg2uuLqlVqW6Wk3PYq3bf4O3K+sq16tXXp0qxUG35ztVBxaai3+sfed17E7PR+HHn06TjrvRfh3Au+ilWHHYmxlYdjdGwtjj/pfVi3/nh84rN/iDPeezGOPfH9GBpZhXfeeg5//1dfwdZ7foDxA+9gyz1eB9/6sqOl1Q3ez8WDQukOjZeI8ToGL0cjS3/W29uheMpFpekXy20YtNQZM6/R5XKSSqZlY1tRYmqpMt9aqkts24Zll586sqiPiXdQICUsu/wKNkxaENVm0U6dbHzJ0PkxsfJUv1qWQV3qNsXXSylxy53bYdt23c00nee6BTfe/gBuvmNLTb2fFj72wjiVcqpChKitXNp7/Foetxbea13ue0BKiVt+XP599aodLCuPm93bVOoftTj+be53Wm1jcS1jc6VtefdvdKluonaodgDqjZH19I4rPWgtJqXE/murl/hL6SyjmkqlkM/nF8W3YF+sjv4bpfurlZ63EKJsoqB4rGp0n7TSSS9vSdVq1RpevKXPWdc0Z2qHbaPczJfS+5X2CCmVtyxkMpmy03RsKRc8xnJXKfHGx+K/l+LXw/t7qWX6ZCONVPtdwO8Aelnp2fBE7BAOHdiJw9Ydh/VHnrLo7LaX2fX+gDVNw9iqIyAArFq9Abadx69/fhd+9eiPYYSieOWFRxEIBCGEhjtviUEIgb2734BlpjExvgfPP/0IVqxah8GhMQQCYZhmDsnEDGzbhJISycQsZqbHYZkWbGnjwQc24aJPXVkU//xUDmk7Z86EEGV2tpznqev6gkSN95xs217yDI83KJbbvpQSD95/Lc676HLs2LIJn/rcvyvEpet62e0Vb6PSCiAP3P1DXPjJKxddVxwTgLKP4UzDuBqf+PS3oOt6YfD27mfbNgRE4ffS18R7n4PBYNUEiijuFK0Utt1/DUSZnKPXI6TwXJfYRy9OrBWbL/HLI2ebyGbTZV+T0t8rvQ9E/Wx+XCt/faWVK4DqnynvILj04N0bW+o5o+7thOm6vuTnWAgB0zSx+c7t+NJnP7bk7YvHC03TnHFQLL6NN5YvtT3vjKa3vXpomrZoWKzltfYes1JvkZvv2IYvfuaCBdsrjc3bhmVZUEpCKolgmemamjvPvTip4V1Xa6LGi6P4+7HWcZrjOXWDpRJz3vXj191Q2A8DFh+w2u50heK/d1tKCMx/5pwx3LlOE6JiAqDw2S/cR0Ep76C7/mbqtpRQSkLBGXOnbroFG/7NN5fcjl60b2daNoL6fGXG+A03IRQILrkNmU7D3n8AiVvvgD2XhAhHEFy/DhOvvIp1f/B7EIH5Q8fix7PTGaR/8SvkX3kV2ccex4FHfgo7mQQMA9N79sJMpZF89nkMnHJS2cctfl+tTAYqnYY1MQlVtG8tSr9AKqj0uhdXidT7XVlpu8V/V8WJJV3Tal4Sl9NH6sPkRZtIKXFw3+sIGmEcsfE0APNL8XiUUnhwyyboegCZTKYwiAlNQzg6gvMu/BrOv/hKvPHKY/jVz+9FNp1ALpuCkhI730hBEwKZTArPPLEVlpnHrreeXRTH47/48YLfn3tyCzRNR3RwFEPDK/Hay48hm8uWTQxIKbFj63X4+CW/s2i7lb5MvMTDRZf8m5peo0q3nd+RW3wA3ShvW95zNQyjUL4VDodr2ILAtvuuxqc+9+8q3qLSa7J9yyZ87OKvY/sDm/DRi69AIFDbR1ET2oLXoHjQ9KpMbClhmzk8/ot78PrLv8Q7bz4FyzKRz2eRzyYQi01hdHQVLMuErgeQz+eRiE1iYvwd3H3bd/Hicz9DNp0AALz41DYMDK7AuiNPwsqVh9cUIxHNk9JGxezFMngHusVM08Tmu7bjss9fvOT9y1WelSrdoVbKqSrwduqLD7C9A3xvTC0+IK/nwLuaBX0ahChUZJR+V9WaNC+9j5c0KI7X67Hx5c99rNI9qybSi+P+wiXnV7z+1rt24Gtf/DhM08Qtd27HFV/6ZOG6zXduQyBo1PxclsJmndTLCvt1mlaYylAtgbBg/JISUM5KE2u/fjkOXHt9oTrAtG2M33gzIoZR8fMjlcL4DTdh5Wcugb3/AOY23w7r6WdwKBaDsG3Y2SzsXA75vfsw/vwLsCamMP7ccxBCg5lMInrWmTAOXwf74EGogUHY0QjGr78RRoV9RKUUVDaL7Esvw9q7D9KWSDywFSochnVwHPrQAMxkErZ7/0rVETKXQ/rpZ5H8yU8x96tfA5aF+C8fgwiFoHK5wu3e3vEIjCM3IHzsMdBXr0bu2eew/y/eQv6d3ZDT05jesg0iHAYGBhA89WTI3XugcjlY7+yCPDSBiT/7C0DXoY0MQw0PQ4ZCmE0kIV94EbNvvYOZWBz2zAxk0pkmf/D+rQCA/T95FIF1a2HlskiuXQN17DGwQyHI6RmkH3sc5qFDsJ59DtO7diH/+psY3/EwpG0DQ4OYW7ESKpOFCIfmp7EoYPy6G7H+m1cU8gvFfye2lIu+t+eT5/Uvm1qO97dWa4KL5jF50SZziWnMJaZwxMbToWnOTo5UCg9tvR6GYRTORlXa2ZJKYev910CDwIWf/CYmJicAqMJO1oWf+AaEEHjg3qthmyZ0TeCs956HTDqOueQM5pJxvPXGszjxlPcDQiAcjuLlF36F4088C08/8SCSiSmM79+JzZv+EkJomBzfiRNOfh8OW7sRI2NrIaUNJSUEROEDnMmkYObzSGdTSMSnMTg4BKEFinZ03Q+lWnrnztOsObgLpsQs6smxeNqMR0qJh7Zch4s//TtVY/F2zqvdptoOdPHyo8WDYLX72LaFfC4FM5/DOzufRygcRTqdQDIxAzOfxcF9b2J8/5uYmtiLRHwCABAKRbHymNMQCBjYu/tVvPjcT5DPZQAAzz21A+HIADLpOUjplIAboSiiAyNYuXoDgsEwDj/iGDz5q/vxxks/x+EbToKUkmfliFqk9Kx7JaWJh2KVqjnKla9WmzLglQHfevcOfO3SjwNwEjGaphembXhJknIH+LZt4uYfb8HXLv3kgjFDSrtsT53icTCfz0Oq8r0sNE2DaZoQmg6p5pMXxYloZ+rGVlz66Y/CMIzCgYkqei1KqxO85/DVSy8ubG+p19R7PsVVd8DCpI/3Hb24otCu+Bilt13q76HWvxsvRtu2C0mg5qfViPznHRAWPuvSXlAJUXzA6JXtr/7qVwr31zXNaSaZSgHZDNJPPg01MQndMKCCi6sXCuPKxATEm29h5v6tgGXBFAIIhZDNZJyKhWAQCAQApaCFI0DIgDY0DAEFHJpA+qePIpXOzG84EIAYGoI5MoypvAklBMyXXoZMZzD5zLMw9+yFaZpI332fEweAmaeeLtw9A2DP1gchohFAD8CKRjCRSkOsWIHcq69j5robkd+9G+mnn4XKZqGNDGPwwo8il0xi5e/9W+jhMMxMFmJyErGbNyO4bh2sXbuRevpZ2DMzgKbBPnID7GgY2rpTsPobV8A45mgcuOEmZKWCGhuFLgRWffUrmL72eoyceQasN3ci+dOfQR0ch2WaSB84CEgJGQ4juG4twqedAjk8jOzrr2PwN85B/JGfwp6bg2bbkLv3Yvqf/gXTRa/9xEMPF14rO28CA1FIw4AwTah4HImrrgEAaIethtiwAYEjDocMBAvTbAK6m9ixLMjpGSTuugfy8Scg0xmMP/scrEQS2sgwkitWIPHqa4isXlX5704WVaJLCaEA6LWN0dWOBcol1vsZkxdtMnHwLeh6EKvWbFxwuajjYF0Tlf9wi1eI0HQdgUAAa9YdjWDQ+YBaloV0KoUz3nMBdmy9Dhd+4ps4eGAP3nX2RzE9M+l8SARw3Aln4pHtN2AuGcO2e3+44DF+9eitAIDH3P9/+ZNbCtc989g9xc8KTz92DwLBECwrD10L4K03nkAwGMLI6GFIp5I4dHAX1h5+9PwcPncHstIZodJEQ7kPeT3zmavt/EMIbLnnKnzsE9+o6UDd62Jcuj2pFB58YBM++vGvI5WcxX13fA8vv/ALPP3EFuRzGYzvexWWZeG1lzfiuBPOhGGsg2ma2HrfNbjwE99ALpvGXHIKW+7+Pna//SIO7NsJbz7Iy88/Unic55/cAgB48ld3AQDCkSGsP+pUXPSp38ULz/0MH/v416HrOrbfvwnnnv8lbLvvR8im41i95ghkMnPYt/sNvOs9H8HB/e/gU1/4Qzy09QZYtjNF6NwLvoZMJoe9u17Agb2v4d7bv4vPfOmPl0zcEPWjctOqpJI1N5fy+iV81U0WFCutbii+3NkRX94cXs/iPgdqwYG6EBoEajvA1twzlo1aToWAEMBt9+zAFV/6VNH2nKTL5V/85IIpFcXTPSo9Xj1xKCVxy53b8NUvfBzBMgc6ztm76j1K6nk8r7Ljsi8srLjxXr98Pg/DMBYkeZznKhdUr3DaCPWK3Du7kH/+ecjpGRzYsg2AAkIhxGdmYU3PIPmzX0DG41D5PGAY0GwbudffgNy1G4jHkUkkkXlgW6ECYOKRRwE4B00qGMDBN3cicuKJMA5fB6UUsrv3IP3U07DHDwHBIEIfORdmJov88CAMw8DabzgVtkopZLNZTN20GSsvv8z5/7IvwTAMjF93A0Yu/Tz0bA6HfnQ1ZCwOlUxAJZKwxw8h8eBDgG070ygiEWiHHQPtyA3QhoYwfMknMPuLX0IEglj9xS/ASiQwffudCNo2Bk85CflDE5h75lkgk0Xqscch43EAwOyLLyGw5jAMfPi3Ef2tD8A49RRIAJM33oyJW2/H6su+jPFbNmPd5V8FNmzAwBc/j8mbbsH6v/z/oGkaDlx7PVZ/9cs4eP1NkLaFwLHHQLgH7roQsIt2i0U4hNDZ70Hy9TcROve3kcnnEdQEVn/tMoxffyNWXvZlRCIRAEAmk0HqhpsR338A6sTjAaWQU0DwlJOx5uILgckpTNx3PyAExj5zCYx16zB+593IWVZhCoamabCkDcQTEAcOQu7bDzz9DOxnngVWrYQYHgZCBvJ5C+Ovvobc629A5XLIAUA0CjEwAH1sDNZsDPau3Yj/4EcAgLQA9j/+JLTRUZgzMxCBAKanpiA0Deau3UiOjiB62qnu+CrdCiCJvVdvwuFf/9qCSuv5CvzF08cnb7gJ66/8BgBgz4+uxvpvft052U1MXrSSd8AtpY3Y7DhGxtZC1xe+5FI68191zO8sFB+Me/O7vJ3W0nJWYH6nUQgNSi3O2m1/YBMuuOhy52B663XQ3G1IpbD9/muhe+VkEDjqmDNw5DHvwkWf/CYy6QQmxvdgemo/nn7iQWw85nTsfvtFHHvCmXj7zRcAAZx0yvvxxmtP48RT3gdNAKaZw+svP4ENG0/CW28+71Zs2BgZXQ0zn8Out57HXHIW//x3v4PRFWtx4snvx8ln/CaOPuZ0aHoAUipsvffqRdPElFKwTBOmmcPE+G4k4tPIZjMIhyOIDo7i17/aCl2b3xldUA5dZafetm3ksmkc3P8mZqb2I5VKYuLg2xgYWlHoaVGu+dHCnU6nOeeFn/jGouvz+Qzu2vx3eOm5nyJohDE4NIajjzsTu99+GdK2ML7/Tdx5898AAEZGV2NoeCVisxN4+dkdmEvOAgB2vWlgw8aTcfiGkxGJDkEPGm41iYK0LZxw8nvw8gu/wnve/zHs3fUagkYEUkmsXH3E4r8nTUMkOoTh4TGcd9HlME0TO7Zej/d+4JP4yfabyu60anoAR2w8A4YRwdOPb8PI2Bpkszl84jPfKvuaEtHicaLSNIpylQWVtnXLj7cvmr7gVQxc+unzcetd26AHgmWnhEglFzSYLI1NSgkFYCaWwMTkDKZm4nhr1zhMy8Z1t25FNBLCgfEZrFwxirChQ3O/y7ypj6UH35ZlI5XJ4K1d+xGJhGFZNjS9fPK9+LXxxqBMNo+nn38ND//8KUAI/OQXT2PtmlVIZ7II6IBtmUsmUIuvl9KGAhZVVXgH98VjX3FC2tvR9Jb0qzRVpfg2tm0BQuCWO7fjy58tP91EKYnb7nkQoVCk7Ovhzccud8KiXAyVejvdeNv9sKWNr136ybJx1NLYlUkN6hb56WlM/d9/ReaXvwI0AYyMQoyMQMGZXpF//gXI2RimX3wJALBvx8OArgOWhfQdzgkgaBowOoLIOe9DdnIKaiAKEQhC2hbseBz6XArKshG75z7A/WwIwwBWjEF/79mQh69F9EuXInH7ndDl/LTeA9dejzWXX1Y2btu2C40mjeEhaKtXAStWFI4DggEdq792mXNQe+PNAICVX/0Kpm7aDE0A4bPOhHjxJQgI6CvGgJFhYPUqBAwDI5//LPL5POY2XQ8AWPv1yyFzOcRuuR2H/5uvw3SnUoydcboTi9uIUi8cWwhM3ngzAm6/jOLLpVI4dP1NZU8G2lJCKkAvGffr6e+gewkI92epFOSKMUTWH47g88874+AxR8M98im7bX10BBgbhX7aqbBjMWD/AcjxQ1C7djtjWyAA7agjMXjBechOz2D17/4bHLj7PgQ0gdVfvxyHrr8JUtoYveB8TF57HQLJJIIjI7DiCai5OSjLQi6VhpI2VCyO5Js7kQSASBhYdzjsjUdCuUkMoPhEhLMc7vj1NyISCpV97o28Zv2AyYsWKN1p3bf7NdhWHiMr1i24nXQb8gDzzXkA5w/7kQdvdHaaGigRklLCFsD2LZtw8SevLExNkEq60xXmB5lylR/ejuTA4CiOOmYYRxx1Mg4e3Ivf+vAXoRTw4Y9+Dfn8Jkgl8d4PfAqxeAxnvffCQsY0OZfChz/2NVjqBggAAV3HRZ+60kkU5HJ44O4fYC4xCU0AT/zqPjz+y3ug6wGsWLUe+VwWQtMgNGfqyviBd/DCM48gGZ/GLx/dDCiFJ39516KYNS2A4dHDsP6Io3HK6b9Zw2tkY3bmIO646a/xxiu/dnY2SwQCBhIzB3Dcie/G0cediZWrjygkkEoH6tKO1qm5GHa/9axbcRPA4RtOwpr1JyAajuIjF34N2+6/FhdcdDke3nYDjj/pPfjZQ7cgnYrBCEWhBwxsPOY0xGIziAyMYGR4BS665HfwwL1XQ7jvj1f5IITA2ed8HNPTUzj5tN/E5Phe929pPmEhpcSObdcviNG2JUzTxLYHroUmNOdsq6y8AyuEwBEbT8Vha47AI9uuwylnnMsdWqI6FPc1UEohk8lUnLZRPO3A66yu63pRAzlVcnun8dxSJaVzqTSu3/wA3nPmyZiaieO1N/fi+5vuwvRsAnv2jiNXZgUrXddw8NAsMtn5ec8hI4jRkUFEIwM48og1CIcM7B+fwt1bf4Zde8exa89BHJqcAQA8+thLhftFwgYGByIYGR7A40+/jA3r12BwMAIzb+KWO7chlc5jZGQYr7z+DianY3j4588V7vvK67sXxDQ8GMHw0AB+8stncNzRG7Bm9QoEAzoyuTymZ2IYn5xFOmviqhvvRTKVxju79kEP6BiIhPHEs6/g9JOPRSQ8v8PofG/PL6V68x1b8PlPnV94TaWUuO2eHTBNiV8/9TJ27T2IyekYXt+5G48/+zqUgntWNYdAQEcwqCNkhGBZCgMDEby16wC2PPwY3nh7v9NvKKAjGg5hZEQiV7KEoTfl5iufu7jm8bV02UIvueE0Kq1vPnW56Toc76nTyVgcB37/27CTSQxc+jlYuRysQBBQCgoKpmUDAghrGkY/9EFMbb4dA8dshCYlUq+9jsGLL0LsqaehIhEEDQOjX/0yxq+/EUo6+1tK2lBjoxC6jrGvXYa523+MtV/4PJSUyBtBTN10C6QCVMn+5PzynIubhxZ/biv1o2jqa+QmG1Zd9iXIgA6paYBtFxqNet8xgIIt55Pc5Q6evamFAU1fNF6Uu21xP4lyq4t4SpcZbRYhBMToKPSxMdinngIohWBAh2lLSKUwdPllMG/eDIyMOFOMpHCnHElAAfrqVcC6tQgeuQGHfeMK5PN5zNy8GUJoWHnZl5ymqNffiBUXnAf5xpuY2XwHsGsX8m+/jX3Pvwg1NorMaadAO/547L/zrsKUvaUSE8WvHTmYvGghb/3e115+DEIIDI8cVvN9F54xckqPnH0orTBgLHisMpcJiKoDynzyRHPnUzkfJeVOd7jg4itqnkfrxeDdf8eW65zEixCw3KSFJxIdwuCg04B0671X4fgT34X9e17DxKE92LfndUhLQkkb6cgAND2Aw9ZuRCAYgq4bCIUieP9vXoxIdBhSAlJa+OWjdyE1N4vY9AHcefPf4r5gCEMjq3HYmvVOj49CfBb2730TLz73KJ57cgcS8SlEosN49/svwomnnIPXXn4SHzj38/jZwzdjLjGD+Ow4Dux/E6++9EsAQCgcxerDjkQ+n8MpZ3wQ05N7MTy0Avm889wsy0IqGceOB67Gr39xL/K5DFav3YjPX/af8dxTD8G0bFjSLkzvcd5nHes3nIj1R54EXdNx/sWXY/v9m/CxT3wdW++7FrZtQQkND9x7lTOOl1TeVHpvlFJ4eNsN0HRvGaqixIWUgDbfubm03NxLfgDzc88BZ+D/+Gf/PQ7sexNvvPoYYrMTGB2r/W+aqNfUe0CnufOonRU7tsEIhRdsB3ASq6Zp4uY7tuJLJWftvYaZl376ggWNQJ3pENswM5vE9GwSf/8vN2P3vnE89cJOZHN55PMmMpkc7t76CwDAo79+AYDzmY4nM1g5NoIVY8M4+6yTsWJ0GGMjg1i9chSP/PzXCIXC+MrnLkI2m8NVN96J2XgKsXgK8WQat97z8IL4nnj2NRy2agxHHbEGo0MRRKMhfPA33o2f/eoZZLJ5JFNpJJJpTM3E8Q8/vK3sazQ0GMUJx2zA6pVD+MzF5+KJZ14ChEI+byGTzSOTzSORTCGRzGD/wSlcfdP9VV/zN3buw+pVo0ilczAtG/tz03jjB7dCCIGNG9bi5BM24tSTjsHxR69fkEzSNA3pTBa79h7Cznf24V+uvQvPv+y8ng8++hSCgQBWrRxBIKDjqCPWIhDQoQkNb+3ah1zeiTM5l8Ejv3ga2ZyTnHjh1bfLxvjor57HQDSMyZkk1h62Arv3TsAwAnjptbcxEI0gMZdGIBBY0OC7lDNVZb7RZ+XblZ925DWrLtWMqUhErVDcXyD7zi7kf/oo9KEhrPk//wv22jWY3Xw7lJILVqjQNQ0iGIRx3LHQj9yAka84UzbMTdcj8v73Iv7661BSVa3YlUrh0A03YyAcgj4y7BxcZjJlbwtUP7sulcKB627Emq9+uepzLbdUaWG/v2j/zqvaKtvjSCpoovzBsmnbOLDpBqz52lcwfuPN0IUo25vIewxvqewaF9NwYqhxaqNpmjhw/U0I6ppTveHGXSmWwjQ4twFmpbhtKZ1ErtAXXR4sOv7xVpQpXYWm7PgoJXQNhcSFUgpYuRLRD69HfM8+2Nks9MkpGEIg8+RTmPrOf8MUABgGMDQENTQINToCddRRS74uNI/JixaTUuLZJx/E4PAq6DUsUdSo8mfjFLY/cG2h1Kue7Whu07MdW67DBRdfUfU+5ZqTiaIl3wBg+/3XQkLh/I99zXkc70snEMQJJ78fJ55yDpRS2HrftfAakX704iuw/YHrcP6FX8VD226ElDaCgQBOO/PcBaW+b7z+PFZKG0cdexZOO/0cvPLCz/Dskztwz23/GwAQCITw4jMPIpNOuBUWAseddDbWrj8Rn/vKf4IQGnZsuQ5CD+Dnj9yOUHgAkcgwVh52JD7y0csQj01g+30/wooVh2Fqci8mxnfjpw9eX3j+zz21FYGAgaceuxv5XAZCaDjp1N9AIDTkTNEYWVWorJFSwOvO6lXDeK9HtbOmmnCWGVxqHWjbnYbkvQceWbL9Wr5EvARIcUe3YNDA57/65/j+//k9bLn7+/jKN75TdRtEvajctIJy42C5cTmZTOGam+9GOptDLi+x+a4dyJsWlFIYjEawe98Enn7+NSTmUshmcwiHF+7wlia2X3z1LTz/yts4cGga+bwFIYCBaBghI4jD16zEwEAUwYCOd/YcwHvPOgWvvfkWouEwPn3xb+Mnv3gSX/rMhQgGg9h85zZ88ZLzAMxPBQkE5nfegsEARoYHMDw0gKOOAAKBID7x0Q9i34FJ7Hj01wgFg/jK5y/CQDQM27Zx+z0PwpYSp590NN7etceN11l2UAgdH3jfmTgwPomfPfYszjr9RLzy+lsYGhrAlV/5lHP/e3fg2I3r8fzLr8OyTEQjIQwNRku2I3Deh87B/oNTmJyeRd60MDo8hHAoiMefeQHRSAiDA4O49JLzcfOPH4AQzuoD8WQaa1avwitv7MKDP30CWx56DIBTUfLsi29B0zUcmpjGPdsfKzz/FWPDGBsZwIqxdfjCp87DsRvXIxAI4Kbb78clF51b6Cmx+c6tzk40AMMI44ufvgBzcyn8+IGf4HOf+Aju3fpTmFYetgSy2RzSWRMbDl+Lx59+Ga/t3I1fPvFC4TGffmHngvf+0V85z2l4KIo1hz2NU088BuvWrKzYFLT479WyrMK0oZt/vAVBd/USrynrV79w8YK/19KEHCsvlkcIcQ2ATwCYUEqd5l72dwA+CSAP4C0A31BKxdzr/hzAlXB6MP6hUmq7e/mFAP4RgA7gKqXU37T5qXSMwn5MJouZv/k7QGiw330WsP7wwnSOivctc8KvXt40j8K/Kvtnuntwvbin0MJkwvz3SMljFSUXqnFWO7kZK774+UKT0qV4iQ0vjqWW+JRK4eB1N8KSttPXQggoJQsH/qV9fkorKUpX8vAev/g7tNZpElIpHLrxliWTPwuer5vEEBBFVe/zCymM33hzfVkZl65pyFuW0xPkG+5xUzAI/cgNWHXFVzF+9SaMvvc9UPsPYHb7DtixGMT+A1C7diP34suYjUSw+vLLnGlMqD3Z04+YvGixbDaFTDqBwzec4mSAK2QE6+Ut11PL9rydkfm16mtvcFk6raTch0kphYe334CLPnnlgs7tpdvRygwG3kHAQ9tvwMcu/npNz6XcAQHgTm046mQcdcxpEHoEp5z+fux55yU8/8xPcfj6YzE8shIHD+7C2Ip1+Pin/y223+8sS2uaJiQUhFr4fL3YnnhsK9asOwYf/fjXkc/n8ZMHb8IHPvQZbLnnX2Hm08imkzDNHI7ceDJisxO45NJvY3BoBbbcew287tbOl4gCaujtXsj8lnzpVHrPq30JN9rwzqv0cZJQsnCZbds4bM1R2HDUqXj1xV/g1Rd/hZNP/wC7IFNf8RokFldGeM02v/y5Cxf1T5iJxXHzjx/EL554AXdv+/mCEtDX3tyDQECHAJA3nbNZz7/inKH/6a+ex4qxEaxZPYY1q1dgYmIauq7jzgcexZPPvYHJmTju3/E4dE3DYatHsXb1KFatGIZhOI2aP/vxjyASibjJgIfxiQs+gERiFkJoGBsZAuA0tbz0kgsqTmGpZiAawXFHr8fzL48BSmEgWssS0860j2M3rsfGDWux78A4zv/Q2ZiNOT1+br37QXz24x+uaewSQmDN6hU44vA1zgokQiAYDCKXy+GNt5zX0BuDgflqtVUrRvC5T5yLT9s28nkTu/Ydwmtv7MLjz7yM1atGAQCWaeL97z4VRx6xBq+9uRtf/uwF2HzXNmiahieeeQHHHX1ETc9VSok7H3gYwUAQIfd9EUIgGNBgDEUxNhrEZz/+21DKxmWfvxiZbBbX33ov8qbEuR84G3nTwsM/ewKmaeKIw9fiyedexaHJWfzohnsBACPDgzjpuCORSqUwNDSAN97ag5ARhGlZsCwb07MJmJaJf/zhZggh8L6zTsX4xCwUBAKahkBQw0A0glwuj9vu3o4vXHLBgkSF18eDDZqXbROAfwZwfdFlOwD8uVLKEkL8LYA/B/CnQohTAHwJwKkADgfwkBDiBPc+/xfABQD2AXhSCHGvUuqVNj2HjjTxj//sNMr8wG9AHxqq677lpkgBSx842lLCshdWK9lyYZVH6e2FWJykKJ0aIaXEoetvAoQoJEN0TRQaYNZCCIHJW26tmABo1kFx6XOVSmHypluw9vKvLrr80E2bEdBEoaoBbsLDm5rh7W/P3HIbVn7lixUfszgRa9leVYYoJHy8iIqnpnivfem0Hef1XJyM9ZbGrUXxe+5ViQT18q+7CAYROv00BM46E8mpaSjLhGlaCKTmIHa+jfjm25B54kms/cv/D2p0FJY9X1lECzF50WIH9r4JAIgOjla8jWVZaMffZnGPjQe3bHK6xjdwvGnbdmE1Co83T65S0zAhnESmk2GdrwLwpphoJS/A/DKrckGixbJtbL33alxw8RWFxyue/lJs7eHHYcNRJyORnMP5F34VhmFg+/2bFjxn0zTx4AOboOlOIyDlVTdoolB5EAgu/piEwlEMDK2Apq1CQNehFHD+RV/Dzx66BSOjqxdMofGmb1QjpYTylkQqnnZT4bbOjJzaElcPb78Buh5Y8H41skJLsXVHnIRsJoEtd/8Ldu58AZ/8zO+yCzL1lUqrawDzO1hPPfcafvnkK4gn0tA1DSMjg/j4BR/AgYOHEI0YiEbC+Nqlnyiq5ABuuXM7zjn7DNz/4M+QSuewauUKvPrGO9i7fwLJuTQA4MXX3kYkHMLha1biC5ech9feeAtCzFckeDF4421pwre0SsT72WsSWTqNpZYduQXlu3blZVgr3a/ca3jHfQ85c81V5fZP3sHHrXdvxxc//THcfs/D+MzHf7umxwacipITjjkCTz3zAk4/+Sh86TMX4vZ7dmDt6iFcdN77YRgGdu05UDbG4vgrrl4FQNOEW+GwveKSqd50odvv3o6QYSAS1nDS8UdB13W89sZbkEriC586DwHdOdz57d88G2+8tRevvrELr76xC1MzzuoBjz1V/Tj2yefeKHv5r59+DSPDAzjlpONw2knHFJ6naZq47Z4d+PJnL6y6XapOKfUzIcTGksseLPr11wA+7/58CYDNSqkcgHeEEDsBvM+9bqdS6m0AEEJsdm/b88kLr5K39POTefY5JH/yUwx88fNIFU1PLlZcEeEdYDYrpuI+EdXGqVLegX6lA1PnwN47AK/cm84bdkr7IhQ3h1xqfKqVVzliWnbFaRyVEiZOs02JyZs3I6AHYCvlVHvo8wsITN68GaGgUX26u1I4dOPNCOgBaNp85cSk23ui2utfnAxajnqSP6VJLq9xa+HvUAjIoSGId5+FFV+7DLHvfg/7v/3HEGe/G9rwSEOP2Q9alkoXQlwjhJgQQrxUdNnfCSFeE0K8IIS4SwgxWnTdnwshdgohXhdCfKzo8gvdy3YKIf6sVfG2yviBtwAA0YHRBZcXN+isR71n0mWFxym3413pgLZ4B7h4u8U7tUopPLTt+qrTGrwDaW8QLew8L9qZk4UpK0pKPLTt+gUlXF7C4qGtlR/PSwAsNc0CqL5crSgkR8oP/KXXlS7putT2i5WuClKvSgcMld7rh7fdsOB19b6Yqv1degcKmqbhY5/8FmKzh3Bg75vIZDJN+XKk5uNY3DyWZSGTySCXyxU+r+XG44OHpvAf/uK7+Kerf4x83sJpJx2Ff/rrb+Pc3zgTn//EuVi1YgjRSAiBgNPozDRN3H7vDgQCOqKREI4/5ggcsW4VTjr+SPzuFZfgt95/Kv75r/8jLvrw2Tjvg2fgB//rj3H+B8/CGadsxFmnHY+Ari9IXHhj6B33PQTLspypDEU7UEop/Pj+h+E1ibvtngedhqJ3P1iYDlO8Yzw/D1gt2D4wP44729lRuLz4NsVKL/cev9z44Y31S06Xcw8gvPsspfi7yzRNbL5rGxbmgtXCgwK1+Dl5773zWj6yKMZycdcSW7nEiG1bKE5CCSGwfu1qnP+h9+Lfff0z+N9/+Qc4/4Nn4kPnnIE//fdfxe9/87P49rcuxX/83S/ivWceh7PfdRzOefeJ+NA5p+Mv/+Sb+OD7T8VHfutMnPsbZ+C9Zx6HM045Gu9510mYnI7jf/3zzfg/P7gVmzbft2hFM2qpbwLY6v68HsDeouv2uZdVunwRIcS3hBBPCSGempycbEG47SWlxP6rr104dkiJ6X/5VwTWrUV8bs5JGrtTimvZHynu99JIQkMqhUPX3QjLsnDoxluqPmalff5yj1spweLto0mpCtMlLLt6M0fTtrH/2sr7wsUVIOXGfe93e8E+f22vVbnn7E2fsWyr7HW10DVt0W2XbHq5xDFXxZ4WbmVz6WvjTcGz7PqP5SrFGnz3mVj7d38NZVqwf/EYrHRmYWVPhf2NftTKb6RNAEpT9TsAnKaUOgPAG3BK5FBSInchgH8RQuhCCB1OidxFAE4B8GX3tl3j0MG3YISiCAQXN+opVu0AuZjXTFMWLb+03Hl73mMXH9CWfpBLEw/eZQ9tvb5wWb07ZsXmmwzNPxfvAL70PoV1kZfInpZOAam10sB7PYpf24UdoZfeViPzKaVS2HLf1VBldoKbkRgoPhNbLmm08PGWWAUBCsee8G4ce8K7cXDfq9h631XI5/M17zRQW20Cx+KmkFLi5ju2Fg7wy/n5r5/Hn/237yOWSOHk44/Ah845DRs3rMFAdPGSmMXKV60t3BEPBgMIGUEE3Wow23aSKZV2TLXCGCoWJL5LEwxes2YhUEhklD7v2+7evuA5FycApHRXs6rjINcb8y3LqeIrVyFSTnGSpnR73oF+1TN3ZcbTeg/OS6tRhCjf3wTAgh3ecorfl9JtZLNZ3HTHA84yj0rh9nt3FH72busknbYjEBAYGgzjtJOOxvvOOhnve/cpeM8ZJ2L1yhGsHBvC2OggRkcGseHwwzA4EMZANIzhoShWrxzBUUeswbe+9imc/1vvwonHrscrr7+Dx556FZPTsxzP20AI8RcALAA3NWubSqkfKqXOVkqdvXr16mZttu3K9UHwDuLknj2w9h/Ait/5JnS3z4JUChM33eKu0rTEWKKcZpmmaRb2ees9seiNY7omGj4pWfpcK8Vden0tB/vlprIUb0dKiQPuUqdeQqQw1dythljw+y23+jImFL+2y3mdq923tHqlOGGx6LWQsmLCqlpzz6WSD8bRG7Hqv/xnqGwW8oknIe36Ekb9omXJC6XUzwDMlFz2oFLKW0Po1wC8SaOFEjml1DsAvBK598EtkVNK5QF4JXIdrXhnZPzAW2WnjNRzQFp6MNnIWflaLbXtRSuaLHH7cgfC5S4rTYRU256U9qKqAW8bxTt/xQfaUkpse+Ba90vKXrKsufT9kUph2wNO1l8qhQe3Xrfo8Uu3Wfm5qwV/I8VKl1xdSvFzLk5M1PMa15vY2bHlusI2PnLh12FbJqYO7YKUElvvuaqmahdqn34ei1tBKRub79o2P6WtaGfm5dd34V+uvRMbj1yHD3/gDBx1xOpCYsDrfVN2jFLldpiqX+Zdfts9O8pWBiyO26twWHxd8f20Mklh27ZraddT5jEXjnPFj1MuIeJcXt/ZpeIKiFvv3l7xNS59/Ipz3d1pkfWMY05i4aFFSa3S903K8u/hHfc9VPW7r/gqZ5vO0rLlKiOklLjlzq3IZrN1n6XTdQ3HHLUWZ552NHK5PP7if/7rgmVceeav+YQQX4fTyPMyNf9HsB/AhqKbHeFeVunyniWlxJ4fXV1YMtqjbBv2q6/DOOZoRN7/vgXXeT0fKn2mig9Kvf4GXm+c4oPX4t/LVUPYUsKWNsZvvBlWmRNW9U5R8ZIDpdvyttOs5IHXg8JyP89eNYRScsmKhtLfl5uw8UPx+1L6HhX/XprMKZ2KUzr9pNbXYqnbhU48Afq7TgcmJxG7937svfraZb/nvcbPWsCmlsh1Eikl7r/7R8jns5idPoiBwTHf46llh6MZVRy1bqvcAbPCwuTIwgPxhR/cckkTpRZOFVFKYfv91xYqGbzEgFfuVS/v/rIkk128wkfhsiXOIHqVLIWzjQ1mVb2EhJQSO7ZeV6jIKeW9H5Vet0cevNFZq7xMo9BSxdtYv+EEDI2sxvj+N5BJpxo6wCHfsVy5TprbyPbWu7fDNE2kM1l8919vxZvv7Me5v3kW/tPvfxmh0OJVnkwzi1vu3LrgwPr2e3csOFD2tivdMdJrcOZcVjw+Ojvf5ZINzvWyqJrBi7u5H9DSg9nSxINSzpSKSgmK5UxHqJSosW3LqVAovMbOMrK2vXSCpx7e94j3OEIAt9+7A7a0i76DyidoSp+HJ5/PV1yxoDTxAyx+/b3v1aXe56Wm9KwcG8ZZpx+L5FwGD+x4rHB22VsekZrDXTnkTwB8SimVLrrqXgBfEkKEhBBHAzgewBMAngRwvBDiaCGEAadK7t52x91u5SoMUr98DJibw8iXLi3bLNw7IC+XPHBW5LipkCQoTVoAS1dBVIuvnvsWT8fwkin1PFa9j1dtO0vHWX77pcmA5SQ4m3H/5U3JX/gcy71O3ook1ZJjhcakNTzGgvi9qqKjjoQ6bDXmrrsRMpNpaFpTL/MledGKErlO22HWhIZ0KgZgcb+LcpqZOGiGes7GF6ul7NfbfrnqiXqVTs8oPTj3lmwtt4NX6Tm2+r3wtq+5sRW/Ds7BxuK5gNViK55e02js5WJZivf6rV1/Asx8Fi+/8LO6H5f8xXLl2hV2KhZUKWgwTQt/+70b8MQzL+Pk4zfg61+8CIEqHZhLD9iLf/eqt4qbVt75wE8WVA6UfjybdTBebTtLTX3wlK8QUU1LFpTu1FaqSPEO3kunxRTfz+tYX65SohZSysI0joXbXni7WhM0FSsHK7zw5SpUlqquKZdEUqr8Yx22ahRHHL4KD+x4DMm5dCFRxzOAjRFC3ALgMQAnCiH2CSGuhLP6yBCAHUKI54QQPwAApdTLAG6D04hzG4DfV0rZbrXcHwDYDuBVALe5t+07qQd3ANEooh84p6H7L25oKRccWJZWOdRzUFytQqLcAWzplIRaeTEtdTBd6X61XNfINJpavy+q3b8Z0yTqqXzxqlFqfQ2rLW9b+n4WKqOVxORN1XujeIQQkKedBiEl1Ovlmyz3s7YnL1pVItdpO8y2lMimkwCASHS4oW3UeiBaa2VFPY9R7UC2eK5t+QZEladLFF9Xrgqg2nOu9fUoTWh4VQ7FA4lX9bCcBEqlREO9iZ9WTgOqVz2xSCmx7f5rMTi8GuHIEJ576sEld7ipc7BcefmUUvjRjffi+ZffxNe/dDGO3biu7FnAeg+Kiw/2a62WWCqJUS7xsVze8/J23GzbXtC0s9m85+A9V69ypd6Dau9+t9/7UEnVizeFY+Htbdsq28+ndLpGPa9/6e9OlcrDC76nin8vfQyvKsf5Xm2sukZKCcuykMtlcfOPtxa+s7zHOeWEoyA0gXf2jAPAoteLaqeU+rJSap1SKqiUOkIpdbVS6jil1Aal1Jnuv98tuv3/UEodq5Q6USm1tejyLUqpE9zr/oc/z6a9is/G27aN7P4DyD//IrSNRxUq1BrlJRpsKRcdvNZbnVCs0n1lmcdZzmNVmu5Reptyr1GlCoHlaDQRs+D+NU6NafaUlWpLy1Z7HK+Sp9Lfjtdbxbbn36dyTUsXTcsbHACOOhJ4ZzdUurgwi9p61NRvJXK57Bx0PQAjFC1c1q6z+s3YDsTiA/FGKzKqPY6TAGjO9iodJFQ629nMxEFxUqdcT4x6Nfpe1t9PpfE4naWpBFat2Yh9u1/FXDLGvhddoN/G4laQ0sae/ZP41ZMv4aTjNuDcD5xV8ba2beG2e3aUHRLqSfgVTwWpZSnS4m3XUqFRb4JDSrnoAHs5U1O851a94mDh8xBC4M4HflK4fa3PQdO0srFqi87IOiuplD7PengxL/UelCZDqlHK6XdS2gug+PrSSqFqSqtVACAcMvAbZ5+KfQenkDctAMs7UCRaLtu2kdz+ICAEtI1HNmWb3gHlcpIVjTye30p7OjTLcp9fp7w+tSrXFLVUrc+ptIpDnHgCoBTU2+8sN8ye0sqlUvuyRK44c5bNzmFkbE3LH7PZCYXSbRdXJ1SryGhFYsM7eF/qQN67XqmFq7Esvk39sS2VYCne4fbU23iz9PmVxrrcJEPxYzSaFCl+f72MvbedVYcdCU3TMX7wbfa96DD9OhY3Q7XEQjqTwyuv78GpJx6NE4/dsOD2pdMRgMoH9d4Z9kZ78SwV/x33PVz3mFxPQqU0MVxLlUm17ZerOFg6hsYGnaXiuOO+hwvJgXJLmPpdYVbteZumiVvv3r7sapuP/vZ7IaXCvgNTy9sQURNIKZF69Ocw3nUGRDRa1BeoSh+BZZzUq/e+9TbpbKbG+z1038kmP1/n5bClhGlVXt5WSrmgikOGQ8DaNVC7d0NVSFT3o1auNtKXJXLFB3i5TAojY2taklQofcxHHrxx2Wf6KynXR6JSHM3oY9Goak0pK922m7X7OXjvr3TP5j34wCZYlgmlJIJGGMee8B5MT+yGtLv7de01/ToWN4OUEjfetqXsmevX33JmzXzzyxcXLlNKFhpw1lPF4PWccZpbNiX0om3Xd2CvlIJpmk7So0owlQ7ga3keSqlF/SJKe4k0i9Mro/LSz8VVG6WEwKLnIt2d5mr3m6+yqK1Cplm8vznvvSk3hWn+trWtuLV+3WqMDg9gfDLWMUkb6l+5Xbtgjx9C8L3vgZTFK7fxb5KqK9fPo7jRaK37061KnHh/y6UnP+2jjgRyeWQee7zpj9mtuqs2pwtIKbH1vmugpEQuO4dkYrapB/OVDlhLd/aKz9TXciasWTqpfwPgT5Ki0Z27ZlRXtJooagoqSs5EHn/yOTDzWSQT0z5GSNRc5Q6k44kUDh6axcYjD8NDP/s1bOlUTZQ7SK4vibH8sqXSaQL1TgXxDui9497SA9bifhNehUQtfTqK+zI4t+mM74riWMtNsaj0njR75ZZqMVRS6bu9XFKmkcau3vbXrB5Fci6DVDqLW+7cVnGqClErKaWQdg/gjPe8G4B7prqOZpWAf2ftmWhZrBtfk0aqcbzbV7qvd9LgULm/5dWrgWgUyR0PF1Z9cvY3+ncKX2fsPfQYpYB8PgMpbYQjg36H45wxL2pYSdRsSins27PTWV99Yk9fD6rU+97aPY5gQMfRR64tVE2UJi1rPVhs1mohzVR8YF5tGsdylzrt9a+kVjzH4m16VS62XVvSpd7KCadXy4NYs2oEAHBoMtYxSSfqP1IpJLdsA8bGgJFh2O6KO/X0SGh2k8d61LuiBVA5Xj+fRzM18prUyu/XqJEVarRy1XJCAOsPR/7Fl3Dwh+wpBzB50TK5bAoAEAoP+ByJoxd3ONpZUVKrSl2d61mZpZHbdIKAEcLQyGGYntwLy7L8DoeoKYqXpLRtG+lsDhNTMRxx+CoEA86SqI00dKyWtFgqobGcpejq1Y4dpXLPtxOTOp2oNElR7XXzkhH19RPREImEMDwYwaHJ2HJCJVoWK5UGZmPA2jU1H/C2+gC23ioOP5pRdnp1Q7c16GwVXdMq/72uWwvYNuRBZ+Wnfp/Cx7+YFsll5gB0TvKiky2ngWQ7K0oKS9N16BdAJxhbeTjyuTTGD7ztdyhELbH/4DSUAo5cvwrA/JnwcqtUFOPBeHs08jovVSHRzPeu+LH8+Jto9ETG6lUjiCfTME0mpqn98vk8rEOHnF8OW80D3iJLJVDqWX6UOkNpEkONjkCFQrD3Ob22pJQ4cM11fbtPwU9/k5TusDqVFwKGEa1+R1qWdlaUtLoxaiM6rSpj2F1dZ+frT/kcCVHzeHNMTdPEvoPTWDk2hIFouOxtG1ktox8wedPdVow6U2CnZ5OLVtciagc1OQUEAsDIyLK24/d0Aj90a7KnH9+rsoSAWrcWcvwQpLsqWbe+p83Qv8+8yaSUeODuH8I0ndUXctkUjFCk4xpYdovlHpS36qC+UrLES15JJVu2XGw3MIwIItERvPHqk8hms+5yqjyIo+4mpcQtP96GvfsPIZPNY92aFVVv34vT9JqNyYyF/H49ylWfFMc0MjQATQhMzcR9iI76WWH/anIKWLkCNpypevMnDf2OkKj11GGrAdvG3Isv9f1+NfewmsjbYZVSIp/PIGhEfI6I2sWrylBS+rpcrN+klBgeXY3db7+IdHoOW+9hcyHqDZqm4bmXdwIAVq9c3pm/ftMPzTl7na5rGBmOYno2waoLaivTtjF+1TVAMgmxalXhcqkUJm9uTbNHolqrPtpWHbJyJQBg+oabC/vV/dr7gsmLJipuIGnmMzCM8mXF1Ju85FW/V9sMj66BUhJvv/kcz0BTT3nupZ0YHooiHAr6HUpD/D67T/W/B530no2NDiKRTCORTPXdzjL5S5+dBQColQur3vq5dJ76TDAIjI5ATU0VLpJSYv/V13bMd0S78FPfRFIqbLn3ati2BTOfRbBK8qLbpgMQ1WpweCWEpuGdN5+FbZdffYWo22Rzebyz5wAOc6suOumgkpUN1A5jI07fi2tvua9j/vapP6jpWShNgxoZ9jsU39W7wgmV15X9NFatgpqegczlChf1YwKv/55xiwmhQdoWpLQ5baSDMFm0UCtfD03TMTC4Arvfebkl2yfyw9R0HEoBq1Yu3HnupCRGI5j46E+NvO/Dg84+TSKZbkFERFXE48DwENCHB2pEHrF6FSAl8q+97ncovuIo0AL5fAYAqlZeEPWyoeFVOHTwbViW6XcoRE0xPZtAKBTE4IC/43q/znHtRP2W+AkEdAxEQ4glUn6HQn1EKQURT0Atc5URoq7nTpvKvvyqz4H4i8mLFjDNLAAgGGTlBfWnwZFVUEoiGZ/0OxSippiOJTAYDUMUXeZH1YVSCnc+8BMmL8gXw0NRxBNzfodB/SSVgrAsJi+ob3lTXEQwCAwOIvfGm0CTVjXsRkxeNJFtO39cZt5NXrDygvrU4JDT9yIWm2DPC+p66UwWiWQaYyMDfocCANA0sfSNiFpgZCiKbM7ETCzhdyjUL2ZjAAA1yn4X1N9sKSFHR5B76WXYdvdOV10uJi9agMkL6ne6HsDadcciEZvwOxSiZXvz7X0AgFG3YSFRvxoeigIA3t51wOdIqF+oWAxK04ChIb9DIfLf6ChELgeVzvgdiW+YvGgBM5+Frgeh6wG/QyHyzfojT8Lc3Cxs2wIA2LbNKgzqSm+8vRdCOGedifrZkNu0c+c7ewv9VziuU0vNxoGhQTbrJAKgRkcBAHJ2xt9AfMSRoAVMs/oyqUT9YO3hx0JJG4cO7vI7FKJl2bXnIAYHIggEdL9DIfJVQNcxOBDGr558satX2aEukkhADXPKCBEAYHgYSgjY09Nu826/A2o/Ji+ayGmoomDmmbwgWrv+eADAvj393RWZut/uveOFZSKJ+t3gQATJOS6XSq1l2zbyszEgl4Ma4pQ9IgBAQAeGBiFnYjhw7fV92bybyYsWYPKC+p1SCoNDKxEIGNi/p7/Xo6bulsnmEEvMYWgwUjjT3G9LZBIVGxqMIJXOIt3Hc66p9WzbRnbXbueXQSYviDxqeBgqkYCuabCl7Lupe0xeNJlSitNGqO8ppfCTHTdhYGgF9u5+re8GVuoN+Xwes3FnVYXBAVZeEAHAkPtZ2LP/EMd2ailz714AYOUFURE1NAhks1D5vN+h+ILJiyazbRNQCsFgyO9QiHylaRqig2OYnNiDVCrRl6Vt1P0SSac8fojTRogAzH8W9h7galLUOrZtI7d7D6DrQITjL1GBu/KOjMf8jcMnTF40mWU6WbBAgMkLoujAKKAU7tz8XTZ3o66ilEI+n0c8kUI4bMAIcvUoIgCIRsLQNIF9buUFE9PUKvnde6AGBwAh/A6FqGMoN3lhx+I+R+IPJi+azLJyAIBA0PA5EiL/RaJOh/DUXIw7udRVTNPELT/egsRcms06iVxOElphMBrBnv2HcMuPtzExTS1j7dtfOMtMRK5IGErXoRLJwpLV/bR/zeRFk7Hygmhe0AgjGAxjLjGD++/+EUzT9Dskorqk0llOGSEqIqXE4EAY+w5MQtO4G0mtITMZyKkpgP0uiBYSAhgegoonIJXC+Kbr+yqJzG+dJrMtN3nBygsiAEB0cASpuRg0weGGuks6k4NSwGCUDZiJig0MhDETSyDPhDS1SH7ffgCA4kojRIsNDUElnIbiep8lkfvr2baBaXrTRlh5QQQ4fS8y6TikZFd66g5eGeZcKgsAiDJ5QbTAgPuZSKWzPkdCvco8cBAAoKJRnyMh6kBDQ0AuB5XL+R1J2zF50STefCPLykMIDZqm+x0SUUeIDoxCKYVUKuZ3KEQ1kVLi5ju2YC6dATB/oEZEjoGIc4ImmUpzuVRqCevguPPDwIC/gRB1okHnc6Hm5nwOpP2YvGgy28whEDQg2BmZCAAQjjrNtlJzsz5HQlQb27YhhEAqnYNhBKBrHM+JikWjTvKClRfUKtahQ4BhAAGu9ES0yICXvEj5HEj7MXnRRFJKmFaezTqJioTCg9A0HalkjGfoqKuk0jkMRFh1QVQqoOsYHRlEKsXkBTWfbdvOtBFWXRCVF3UaibPygpbNcisviMghhEBkYASZdH+uR03dSSmFVDqLgSiT0USllFJYs2qMlRfUEpZlwRofBwbY74KoLF0HolGoZNLvSNqOyYsms6089ACTF0TFItFhZNIJv8MgqlnetGBaNqIRJi+ISimlMJdOY47JC2oir1mylc3Cnpxis06iKlQ0ysoLWj7LzCPIyguiBSLRYVhmDqkUqy+oO8ylvGadTF4QlTMYDcM0LSTn0n6HQj1CSon9V1+L/PghCICVF0RVqIEBgD0vaDmklLBtEzp7XhAtEBkYAQBMHNxVWJmHqJN55fCsvCAqLxIOAgDGJ6Z9joR6ia5pzpQRgD0viKoZHABME1Ym21c95Zi8aCLbygMAApw2QrRANDoMAJgY34UH7v4hpJQ+R0RUXTrjrJ0eDnE8Jyon4ib2Dk1yJSlqHltKp1knwMoLoiqU+/lQqf6aOsLkRRNZprOzy4adRAvpgRB0PYhDB3dBExx2qPOlMjmEwwY0LpNKVFbETexNTDF5Qc1lTUxAaRoQYuUbUUV9ulwqjyKayLTc5AUrL4gWEEIgHB3Cm6896U6v4tQR6kxew7h0OoNomGM5USW6riFkBDE5zeTFUoQQ1wghJoQQLxVdtkIIsUMI8ab7/5h7uRBCfE8IsVMI8YIQ4t1F97nCvf2bQogr/Hgu7WBPTgGRCCCYPCaqyG1oK5OsvKAGWSanjRCVI6VEODKETDoBKRXuv+uHME3T77CIFpFS4uY7tiCdySHC5AVRVZGIgYnJ2ULSj0npijYBuLDksj8D8LBS6ngAD7u/A8BFAI53/30LwPcBJ9kB4DsA3g/gfQC+4yU8eo09NQVEI36HQdTZdB0qZECmUux5QfUpLO3k9rzgUqlEi4XCg7CsPEwzx6kj1NGkUsjlrcKcfiIqLxoOYWI6BtM0ccOtD7CfUQVKqZ8BmCm5+BIA17k/Xwfg00WXX68cvwYwKoRYB+BjAHYopWaUUrMAdmBxQqQnFCoviKi6SAQqnfE7irZq2RFEP5XISSnxwD1XFRp26oGgzxERdZ5wZBAAkEknfI6kv/TTWNwsXrNOThshqi4SMTA9E0cun4emMSldpzVKKbczJcYBrHF/Xg9gb9Ht9rmXVbp8ESHEt4QQTwkhnpqcnGxu1C2mbBtyNsbkBVENVCQCpNN9VfnWym+aTeijEjlNaE7yQghomu53OEQdh8kL32xCH43FzZBOO8mLSJiVF0TVRMIGlFI4OD7ZNzvOraCcF69pL6BS6odKqbOVUmevXr26WZttC5XJAEpx2ghRLSIRqEwa45tu6JvKt5YlL/qxRM62TAT0IAQbDBEtYoSiEEIgnWLyop36cSxerrl0GoBzVpmIKvNWHLn93oegmnfs3S8OueMr3P8n3Mv3A9hQdLsj3MsqXd4zbNuGnXRWTlBhJi+IlqIiEQhbQnP7LvaDdtf49XSJnGWbnDJCVIEQGkLhQWQyTF50gJ4ei5crnclB1zUYwYDfoRB1NK8vTDbHBswNuBeANwXvCgD3FF1+uTuN7xwAcXe83g7go0KIMbfy7aPuZT3FTrvJi0jY50iIuoD7OVHuSZd+4NsExV4skbMtE7rO5AVRJc6KI0m/w6AivTgWL4dt24WVRlhFR1RdOBSEEPN9Yqg8IcQtAB4DcKIQYp8Q4koAfwPgAiHEmwDOd38HgC0A3gawE8CPAPweACilZgD8NwBPuv/+yr2st3jNB1l5QbQk5U6vUimn70U/rDrS7tNKh4QQ65RSB+sokTu35PKftiHOhtgWKy+IqglHBxGfHYfqk3l5Haynx+JGeStHZTI5hEOcMkK0FCEEwiEDGSYvqlJKfbnCVeeVua0C8PsVtnMNgGuaGFrHUek0YBhAgP3jiJbkNrbtpxVH2l150bMlcraUsKw8Ky+IqghHhqCURDrD6guf9exYvBxSStx8xxZkcybCIY7lRLWIhA1ksv0z35paS6XTbNZJVKtgEErX+2raSMsqL9wSuXMBrBJC7IPTqf5vANzmlsvtBnCpe/MtAC6GUyKXBvANwCmRE0J4JXJAh5fI2ex5QVSVt+JIOp3oi9K2TtCPY/FyKKWQNy2EuUwqUU3CYQMzs3NcbYSaI52BikaglAQEl98lqkoIZ8URJi+Wrx9L5Njzgqi6cNhJXmQzcz5H0j/6cSxeDu8MMisviGoTCRnI5fNMXtCyePP1VSYDrFzhdzhEXUP1WfKCKc0mkbYFpSQrL4iqCARD0DQduWzK71CIyppPXrDygqgW4bABpYB0Jut3KNTFlFLIJpOAaUKFudIIUc0iIahMtm8qmpm8aBLLcpYJCzB5QVSRUgqh8ACymTnnDAvP1FGHyWSdxoMRThshqomX6GPfC1oOKSXGr9rk/BIK+RoLUVcJhYFsForJC6qHZTlf2rrOHV6iakLhQeSyc3jw/mshueoIdRjv7DGnjRDVxkv0eYk/okZpOedviJUXRLXzPi/2bMzfQNqEyYsmsd3KC04bIaouFBlALpuCEMLvUIgWyWTzMIIBaBq/HolqYRhO+7QsKy9omWTGnbfP5AVR7cJOpZI905N91Bfh3lkT2LZdVHnRsh6oRD0hHB6ElDbMPOdHU+fJZPNcaYSoDsGAjoCusfKCls/rmxJh8oKoVl7lRX5isi/6XjB50SSF5EWAO71ElUgpYYSc9duzWa44Qp0nk81xyghRnUIhg8kLWhbbtqGyGShdAwI8EUhUM2/aCCsvqB52IXnBnV6iakJcLpU6lFLKqbzgSiNEdQmHgshkOG2ElimTdQ7EOK2UqHYhAxAC9jSTF1SHQs8LnckLomqChpMhZvKCOk06k4NtS1ZeENUpHAoik831RckytVA2y34XRPUSAgiHYE5N9cUqfkxeNIll5aFpOpu8ES1B03QEjQinjVDHmZqeBQCEmLwgqks4ZCBvWsibpt+hUDfL5pi8IGqACoeRfemVvljFj0faTWJbJqsuiGoUCg8gm0n5HQZRgW3bmJ6JA+AyqUT1CoWcHgXTM3FWX1BDlFKsvCBqVDgM5PqjET6TF01iWSb7XRDVyElesPKCOstMLAEACBkcy4nq4X1mZmNJnyOhbiVTKQjbZvKCqBHh8PxqPT2OyYsmsW1WXhDVyghFkc9nkOdyqdRBpmedygtOGyGqj/eZmY0zeUGNKayUEA75GwhRNwqHAdOE7INVn5i8aBInecGlnYhqEQoNAABmp8d9joTImTJi2zZi8TkEAjoCuu53SERdxau8mJlN+BwJdSt7Jub8wOQFUf3cz01+crLnp+4xedEktmVC47QRopqEwk7yYnJir8+REM2bjSUQMoJ90fCKqJmCAR2aJlh5QQ2xbRvm9LTzS4jTRojq5iYvcn2w4giTF03gnLVj5QVRrQw3eTEzddDnSIjmzcSSbNZJ1AAhBEKGgZnZeM/vOFNrWLPOak+svCBqgJv0i91zX8+fgGHyokls22LygqhGgYABTQ9gZprJC+ocsXiSzTqJGhQOBfD6zt09v+NMrSFnY1CaBgS4L01Ut5ABABD5vM+BtB6TF00gpQ1pW9DYsJOoJkIIhMMDmJ0+4HcoRAAAKSVi8Tk26yRqkBEMIJsz/Q6DupQdiwGhECCE36EQdR/DgAIANuykWuTddXVZeUFUOyM8gOkpJi+oMyTn0rClZOUFUYNCoSCyuTynjVDdlFKwZ2OFs8dEVCdNAwwDyDF5QUtQSiGddhpUcalUotqFwgOYnR7nji51BG+VhJDBJDRRI0JGELYtkemDM3/UXFJK5N55ByrEfhdEDQuFoLJZv6NoOSYvlklKiR1bbwDAyguiehhGBJaVRyI+7XcoRJiajQMADCYviBriTbnicqnUCJHNOdNGiKgx4RArL6g2Ujrr6bLnBVHtjFAEABCbOeRzJERA3F3ikdNGiBrjfXa4XCrVS9k2kM8zeUG0DIqVF1Qr23IaVOnskExUMyMUBQDMMnlBHSCWmAPAyguiRhWSFzFWXlB97GQSUAqKPS+IGhcKAdlcz0/HZvKiCWzbAsCeF0T1MAwneRGbZfKC/BdPpBDQNegavxaJGuH1i4klUj5HQt3Gno05P7DygqhxoRAgJWQ67XckLcW9tGWybRu25aypy54XRLXT9AAMI4LZmXG/Q6E+p5RCLJ6EwSkjRA3TdQ2apiHGaSNUJ3tmFgDYsJNoOdzPTyEZ2KOYvGgC03SSFxqTF0R10fQAZrjiCPlMSok3397LlUaIlkEIgVAoiFh8zu9QqMvYsZjzA5MXRA1TheTFrM+RtBaTF00gOW2EqCGhcBR7dr0CKaXfoVCfy+dNGEGO4UTLETICiMWTTEhTXcxpd9Ux9rwgalyYlRdUI9s2oWk6hBB+h0LUVYxQFLlsb8/No+6Qy5ts1km0TCEjiN37DjIhTXWxYzEoTQPY+J6ocay8oFrZtsWqC6IGGKEoLDOHubkEbNv2OxzqU5ZlwbRsJi+IlilkBJHLmRzPqS7WbMw58OJJQKLGGU7lksXKC1qKbZnQmC0mqlvIXS41PjvhcyTUz2bcpR1DbNhJtCzBoI68acGyLL9DoS4i4wlOGSFaLiGAkAEZj/sdSUsxedEEtm2y8oKoAYaXvIgxeUH+ibtLOxpBJqGJlsNLAMa5XCrVwLZt5188Dhhs1km0XCpowGTlBS3FmTbCnV6iennJixgrL8hHs6y8IGoK7zMUS3DFEaqdjMWhWHlBtHwhAzKR8DuKlmLyogmkbTJ5QdQAIxQGIJi8IF/Fk27lBXteEC2L9xmKM3lBNVJKOQdbBpMXRMtmGLDj8Z7uO8TkRROwYSdRY5QCjFCEPS/IV96BFpMXRMtTqLyIJ32OhLqFTKeh8nn2vCBqhlCIlRe0NNsyobHygqghoVAUsdlDfodBfSyRTEHXNQR03e9QiLpayE0AxuKsvKDaePPzFSsviJbPMCCTc1CsvKBKlFJOw84AKy+IGhEKR1l5Qb6KJ1Js1knUBJqmIRjQMT0bh1LK73C6ghDiPwohXhZCvCSEuEUIERZCHC2EeFwIsVMIcasQwnBvG3J/3+lev9Hn8JctPzPj/MDkBdGyKSMIKAUr0bvVb0xeLJOZzwIAdI07vkSNCIaiiMcmIWXvZomps8WTc2zWSdQkhhHAi6++BSml36F0PCHEegB/COBspdRpAHQAXwLwtwC+q5Q6DsAsgCvdu1wJYNa9/Lvu7bqajMUAgA07iZrAq2CyZmd9jqR1mLxYplwuAwCcNkLUoFAoCiltJBMzfofSd/r9jJ8nkUgxeUHUJEYwiLxp+h1GNwkAiAghAgCiAA4C+AiAO9zrrwPwaffnS9zf4V5/nhBCtC/U5rPj7vx8LpVKtHxu8sLu4b4XviQvemmHOe8mL7jaCFFjgkYEADA7w74X7cQzfvPiyRSbdRI1iWEEkM9bfofRFZRS+wH8PYA9cJIWcQBPA4gppbwXcR+A9e7P6wHsde9rubdf2c6Ym82OxZ0fWHlBtGxe5UXhc9WD2p686LUd5kzGaUrFyguixhihKABgZvqgz5H0pb4+4wcAtm1jLpVm5QVRkxjBAHJ5s6eX6msWIcQYnLH1aACHAxgAcGETtvstIcRTQoinJicnl7u5lpLxGBDQATZMJlo+L3kRZ/Ki2XpmhznHyguiZTHcygs27WwvnvFzxJMpZ8leJi+ImsIIBmCaFpMXtTkfwDtKqUmllAngTgC/CWDU3UcGgCMA7Hd/3g9gAwC4148AmC7dqFLqh0qps5VSZ69evbrVz2FZ7HiCU0aImsXdl2HyoolatcPsV5Y5z54XRMuiB4LQAwZmpg9yZ7eNeMbPEYs5HbkNg2f9iJrBm4KVnMv4HElX2APgHCFE1D0xdx6AVwD8BMDn3dtcAeAe9+d73d/hXv+I6vJlXexYHAgxeUHUFLoOBAKQ7HnRPK3aYfYry1zoecHVRogaFgpFEZ/t/APdHtP3Z/wAYCbmfMFzqVSi5vA+S4m5lM+RdD6l1ONwqoqfAfAinP3yHwL4UwB/JITYCeeE3dXuXa4GsNK9/I8A/Fnbg24yGY+z3wVRM4VCsGO9m7zwY2+tsMMMAEKIBTvMbnVFuR3mfdV2mP2SyThfzqy8IGqcEYogEZ/yO4x+UzjjByAD54zfU5g/47cZ5c/4PYYeOeMHALOF5AWnjRA1g5e8mJmJAUdv8DeYLqCU+g6A75Rc/DaA95W5bRbAF9oRVzvk83lYsRjU4KDfoRD1DBEyOG2kyXqqRC6f93pesOSYqBFSSgSNMOKxCXTQR7vn8YyfI55wmi6HuNoIUVN400Zi8TmO6VSVUgoyOcfKC6ImksEgrFjM7zBapu17a0qpx4UQ3g6zBeBZODvMDwDYLIT47+5lxTvMN7g7zDNwVibpGOx5QbR8QSOCdCqBXC6LQIBnYNqln8/4Ac5KI7PxJDRNQNf96l9N1Fu8yotHH3sG5/32+3hyhypS2SxgmoUVEoioCQwDdiIBpRQ6aI2LpvHliLuXdpjzuQyEENA0HTzBQNQYwwgDABLxSQwMMHlB7RNPzCFkBHvyC57ID0E3eZE3rSVuSf3O9poKMnlB1DTKMCD3H0A+n0eoB5vh8lTTMuVyGWhs1km0LMHCcqls2kntFU+kEOIyqURNI4RAMBhAPs/kBVUnE85qT0xeEDWPChmAlFDp3lzxqabkhRDiN2u5rB/lcxnonDJCtCxGyE1exJi8qITjcPMppRBPzBXm6BNRcxhBHfm86XcYLcGxuHkkKy+Ims/9PPVq085aKy/+qcbL+k4+n2W/C6Jl8iovEkxeVMNxuMmklBifmEYwwDn5RM1kBAPI9WjyAhyLm8YuVF6w+o2oaXo8eVH1qFsI8RsAPgBgtRDij4quGgbAvT0A+VyayQuiZdL1APSAgRiTF4twHG4dKSXypsXKC6ImM4IBpDJ5v8NoKo7FzcfKC6LmU4XkRcLnSFpjqT02A8Cge7uhossTmF/WtK/lc1lOGyFqglAogvjsBGzbZnf6hTgOt8hcypkP6q2OQETNEQwGkIvP9dp4zrG4yexkEhDCSV5I6Xc4RL0h1MeVF0qpRwE8KoTYpJTa3aaYukoul2bDTqImCBoR9rwog+Nw6ySSKQDzqyMQUXMYRgCmacO2bb9DaRqOxc0n4wmIgQEorvZE1Dz9PG2kSEgI8UMAG4vvo5T6SCuC6ib5fBa6zrl6RMshpYQRYvJiCRyHmyw5lwbAyguiZvM+U8m5DCKRiM/RNB3H4iaxk0mIoUEo5XckRD1E1wFN69tpI57bAfwAwFUAeieN3gT5XAbRwZ77YiZqO8OIYDIVh2nmoOtRv8PpRByHm4zJC6LW8D5Ts/EEVq8ag+itM+sci5vEjidgZ3NQzF4QNY8QQCgE2efJC0sp9f2WRtKl8rkMBke440u0XN5yqYn4NMJhJi/K4DjcZIk5b9pIz8zJJ+oI3lSsu7c8ij/+/a/2Ut8LgGNx08hkEoLNOomaL2T07LSRWpdKvU8I8XtCiHVCiBXev5ZG1gVs24Jl5aGz5wXRsgXd5EV8dsLnSDoWx+EmK/S8CHAMJ2omr/LCNHtyuVSOxU0iE4lCc0Eiah5hhHo2eVHrHtsV7v//qegyBeCY5obTXfI5p1M9l0olWj4j6CQvYkxeVMJxuMmSc2nougZdrzWPT0S18JYfzuV7MnnBsbhJZCIJjI76HQZR7+nhyouajrqVUke3OpBulHOTFz1WDknki4ARBsDkRSUch5svkUxxpRGiFggGnP2iXkxecCxuDpnNQuXzhZURiKh5RMiAPTXtdxgtUdNemxDi8nKXK6Wub2443SWXdZq9sfKCaPl0PQA9EERs5hBs22ZSsATH4eZLzqXZrJOoBYQQMIIB5HswecGxuDks76ywwRX7iJouFILKZCDzeWg9liCsda/tvUU/hwGcB+AZAH09UGcycwCcgy4iWh4pJQwjgnh8yu9QOhXH4SaybRuJZAoGm3UStYQRDCCXt/wOoxU4FjeBORsDAKggkxdEzSaMEADAjsehrV7tczTNVeu0kX9f/LsQYhTA5lYE1E1yWWfaiNC480vUDEYoikRs0u8wOhLH4eaaT14w+UzUCkGjNysvOBY3h51IOj+wYSdR87mfKzsWR7DHkheNdilLAej7OX+plLN+LlcbIWoOIxRBPDbJNd9rw3F4meZSGfa8IGqRUDDQkz0vyuBY3AAzNuv8EGTygqjp3ORF3q1w6iW19ry4D04nZQDQAZwM4LZWBdUt8rksAEDj3HyipggaEaTm3kE+n0UgMOh3OB2F43DzKKWQyWaRzeVZeUHUIsFgALn8nN9hNB3H4uaQcecEICsviJpPuH0u7ETvrThS617b3xf9bAHYrZTa14J4uko+5zTsZM8LouYwQs5yqYn4NKJRJi9KcBxuEiklrt98P4D5JR2JqLkMIwDTtGBZPdeAmWNxE9hJd9oIe14QNV+h50XC50Car6ZpI0qpRwG8BmAIwBiAfCuD6hb5vNPzQuO0EaKmCAad5VJnp8dh27bP0XQWjsPNZVpOI8FggOM3USt4VU3JVNrnSJqLY3Fz2PGEk7jQGp3BTkQVuav4SK+3TA+pacQQQlwK4AkAXwBwKYDHhRCfb2Vg3SBXmDbCnV+iZggaTvIiHuOKI6U4DjeX10iQPS+IWsNLXiQSKZ8jaS6Oxc1hxxNQXCaVqCVspSAGBmDGYn6H0nS17rX9BYD3KqUmAEAIsRrAQwDuaFVg3SCfS0PTdAgh/A6FqCd400ZisxM+R9KROA43Ud50Ki+4VCpRaxjugWk82XN9LzgWN4GdSAAG+10QtYJUCgLOUqm9ptZaLc0bpF3Tddy3Z+VzGVZdEDWRrgeh60Ek4lwutQyOw02Uz7vTRlh5QdQSXuVFPNFzyQuOxU0gk0kmL4hayTBg9WDPi1r32rYJIbYDuMX9/YsAtrQmpO6glEI2m2azTqImM0IRJDhtpByOw02UN91pI4EA5hcOIKJmCQSc4/nZWAJKqV6qUuVY3AR2PAGEQ36HQdS7DAMy0WfJCyHEcQDWKKX+kxDiswB+y73qMQA3tTq4TialxN7dr7NZJ1GTGaEoKy+KcBxujVzeRDCgQ9MEpGTygqjZggFnStZjT72IT134oa5fcYRjcXPJZBIYHvI7DKLeZRh92bDzHwAkAEApdadS6o+UUn8E4C73ur4mbYvTRoiazAhF2LBzoX8Ax+Gmy+ctThkhaiEhBILBAEyzZ1aO+gdwLG4KO5eDymahOG2EqHVCTuVFr63et1TyYo1S6sXSC93LNrYkoi5iS4vTRoiazDAiSM3NwrJMv0PpFByHWyBvWoU5+UTUGkYwgFy+Z8ZyjsVNUlgBIcjVRohaxjCg8nnIbNbvSJpqqeTFaJXrIk2MoyvZtgVN6+4ySKJOY4SiAIBEnNUXrtEq1/X9ONyovMnKC6JWM4KBwrLEPWC0ynUci+sg3SaCrLwgaiH382X32NSRpZIXTwkhfqf0QiHEvwHwdGtC6h7SMll5QdRk3nKpM9PjPkfSMTgOtwArL4hazwgGCs1xewDH4iax3SaCimMwUet4yYseWy51qVHj2wDuEkJchvmB+WwABoDPtDCurmBL9rwgajbDcCsvYmza6fo2OA43lVIKZt6CEWTlHFErGUYA8WTa7zCa5dvgWNwUtrd8IysviFqnRysvqh55K6UOAfiAEOLDAE5zL35AKfVIyyPrcEop2BaTF0TNFjTCAIA4kxcAOA63Qiabg1SK00aIWiwQ0JHLm1Cq+1f04VjcPF7lBZMXRC1USF70V+UFAEAp9RMAP2lxLF3FsvIAFKeNEDWZpgeg6wHEZib8DqWjcBxunoR7JpjTRohaywgGoJRCOpPD8FBvfN44Fi/ffPKCDTuJWibkTRtJ+BxIcy3V84IqyOcyAABN640vY6JOEjQiiM0yeUGtEY87JZSsvCBqraA7NSs5l/I5EuokdiIBBAKAxsMQopZxV/ORPTZthKNGg3JZJ3nBygui5pJSImhEkIhP9USpMXWehHsgZRgcv4layatuisV7a+eZlseOJzhlhKjVNA1icKDnGnYyedGgXM4pO2bPC6LmCxphTE7sgZTS71CoByXnOG2EqB28z5j3mSMCACsWL5S0E1FrKKWgDQ7B4rQRAoBcjpUXRK1iGBGY+Sxs2/I7FOpBiaRTecFpI0St5X3GvM8cEQDIZJKVF0QtJpWCncux8oIc7HlB1DreiiOJ+LTPkVAvSs6lIQQQ0PkVSNRKXuVFPDHncySdSwgxKoS4QwjxmhDiVSHEbwghVgghdggh3nT/H3NvK4QQ3xNC7BRCvCCEeLff8TeC00aI2kOEDNjJ3pq258ueWy8M1Lksp40QtUrQiADgcqmt1gtjcSMScykYwQCEEH6HQtTTdF2DJgSnjVT3jwC2KaVOAvAuAK8C+DMADyuljgfwsPs7AFwE4Hj337cAfL/94S6PZVlOw04mL4haL2RActpIU3T9QJ3NOiWQnDZC1HxGyEleJJi8aLWuH4sbkZxLwwhyiT6iVhNCwDACTF5UIIQYAfAhAFcDgFIqr5SKAbgEwHXuza4D8Gn350sAXK8cvwYwKoRY19agl8nO5aAyGSguk0rUeoYBOxHvqQb4bU9e9MpA7fW8YOUFUfN500ZYedE6vTIWNyKRTBWWcCSi1jKCgcIKP7TI0QAmAVwrhHhWCHGVEGIAwBql1EH3NuMA1rg/rwewt+j++9zLFhBCfEsI8ZQQ4qnJyc76HrW9ZRtZeUHUekEDKpeHle6dBLIflRctGajbLe9OG9HZ84Ko6XQ9CE3TmbxorZ4YixvhJC84dhO1QzAYQCKZ6qkzf00UAPBuAN9XSp0FIIX5ajcAgHJeuLpePKXUD5VSZyulzl69enXTgm0GO+GWsDN5QdR67ueskDTsAX4kL1oyULc7y5zLZwAICI0N34iaTQgBIxRBbHbC71B6WU+MxY1wpo0weUHUDkYwgAPjU1z6urx9APYppR53f78Dzrh8yKtsc//3vgz3A9hQdP8j3Mu6hnSTFzLAaSNErSbdfZ1eWnHEjyPvlgzU7c4y57IZ6DobvhG1ihGKsvKitXpiLK6XZdtIpTMIBjhthKgdDCOAvMllr8tRSo0D2CuEONG96DwArwC4F8AV7mVXALjH/fleAJe7DZTPARAvqpTrCqy8IGqjkFd50TtNO9uevOiVgTqfy7DfBVELGUaEDTtbqFfG4nolkykoBfa8IGqTYDAA07Rg27bfoXSqfw/gJiHECwDOBPA/AfwNgAuEEG8CON/9HQC2AHgbwE4APwLwe22Pdpnme16w8oKo1Wy3wqmXkhd+HX17A7UBZxD+BpxEym1CiCsB7AZwqXvbLQAuhjNQp93b+i6fz3ClEaIWMkIRzEztg5Q2NI0Hmi3S9WNxvbzGgex5QdQe3hStuVQGK3i2fRGl1HMAzi5z1XllbqsA/H6rY2qlwrKN/Fsgaj03SWj30HKpvuy99cJAncummbwgaqGgEYaUNuaSsxgeWeV3OD2pF8bieiWSTvKCPS+I2sP7rCWSKawYG/E5GvKbFY8DAR3QdUCxDwpRS7nLwudnZn0OpHnYbbJB+XwGms6SN6JWCRoRAEBsllNHqHmSSWelKE4bIWqPQvJirneW6qPG2YkEqy6I2kXTgGAQMsnVRvqe17CTiFojGAwDAOIxrjhCzeNNGzECHL+J2iFoOJ+1pFv1RP1NJpNMXhC1k2EUVvnpBUxeNIgNO4lay6u8iLPygppovvKC4zdROxRPGyGy46y8IGorw+ipnhdMXjQol2PPC6JWCgQN6HoQMVZeUBPFE3PQdQ26zq8/onYIctoIFZHJJBAK+R0GUf8IGZw2Qk7lBZMXRK0jhMDQyEpWXlBTxZNzrLogaiNd0xDQdcQTc36HQh3ATiS5TCpROxlGTy2VyuRFA6SUyOeznDZC1GLDI6sQjzF5Qc2TnEvDYLNOorYyjACSc5w20u+UZUGlUhAGKy+I2oY9LyifzwIAKy+IWmx4ZBXis5w2Qs3jJC84dhO1kxEMIJHktJF+Zyec0nUVZOUFUbsIw4DK5SGzWb9DaQomLxqQzzlfwDqXSiVqqaHhlYjHpqCU8jsU6hFMXhC1l5QSwSArLwiw43HnBzbsJGqfkPN565WpI0xeNCCXdZIXnDZC1FpDwythWXmk5mJ+h0I9IjmXZs8LojZzpo2w8qLfFQ6emLwgah/389YrK44wedGAXC4DANA0zpsmaqXB4RUAgKnJgz5HQr3ANC1ksjlWXhC1mREMcrURghVn8oKo7dzPW3521udAmoPJiwZ4yQv2vCBqHaUUBgbHAAAJNu2kJvBWO2DlBVF7GUYAuVweubzpdyjko/lpI5x2TdQ2BqeN9D1OGyFqPaUUnnvmJwDAFUeoKZi8IPKHV+2USLLvRT+zYk7ygg07idooxGkjfS/PyguitggGwwAE4nEmL2j5Em7DQE4bIWovwz1YTTJ50dfsZALQdSDAaddEbeOOv72SvOAeXAMKlRfseUHUUkIIGKEwErEpv0OhHpB0l2o0ghy7idopGHDOlSW44khfs2Jx9rsgajOhaRCDg5CcNtK/Cg07WXlB1HJBI4LY7ITfYVAPiCc5bYTIDwE3eRFPMHnRz6x4Aor9LojaThseYs+LfpbLeZUX3AEmajUjFEUizsoLWj5vqcZggGM3UTt5CcMkKy/6mkwkWHlB5ANtaKhnpo0wedGAXC4NPRCEpvHlI2o1w4ggEZuEUsrvUKjLJZIpBAM6NE34HQpRXwkGdAgh2LCzz9mJJJMXRD4QQ0OwvNV+uhyPvhuQz2YQCkX9DoOoLxhGBPl8Fpl00u9QqMsl59IwWLJM1HZCCAwNRJBw+85Qf2LlBZE/tOEhyERv7EczedGAXC4Nwwj7HQZRXwi6n7XZmUM+R0LdLjGX4kojRD4ZHIwW+s5Q/1G2DZlKMXlB5ANtiD0v+loul4ERivgdBlFfCLqftXiMy6XS8iSSKRhBHVJKv0Mh6juDAxFOG+ljdjIJKMXkBZEPtOEhqFwOMpv1O5RlY/KiAbmsU3mhwDn4RK1mGE7ygpUXtFzJZJorjRD5ZGggiiSTF32rcNY3xOQFUdsNDgJAT1RfMHnRgGw2jURixskgE1FLBd3kRWyGy6VS45RSnDZC5KPBwQgSc+x50a8KKx2w7xBRWymlgAGnV2MvrDjC5EUD8rkMNJ2DL1E7aJqGYDCMRJzTRqhx2WwOlmXDMJi8IPLD8GAUybkUV47qU7a30gGnjRC1lVQKscceB4CeWHGEyYsG5HJp6Bp3gInaxQhFEI9N+R0GdTHvjG8goPscCVH/UUphIBqGbUuk0t0/55rqZ8WcgyYZYPKCqN30sNP8npUXfcqpvGDygqhdjFCUDTtpWeIJZ5UDThshaj+lFF5+/W0AQIIrjvSlQuUFe14QtZ9b8cSeF30ql81AZ/KCqG2c5MUEy42pYYk5p1EgkxdE/ggGnF1OL5FI/cWOxSHCYUBn9RtR2wWddgc2p430H8syYdsmKy+I2sgIRZHPZZBJJ/0OhbpUMulMG+FqI0T+MNydZy6X2p/MWAza8JDfYRD1J02DNjjIaSP9KJ/LAAArL4jayAhxuVRannjSmzbCs35EfvA+e0xe9Cc7Foc2POx3GER9Sxse4rSRfpTNOmfvmLwgag8pJYLBEABgZuqgz9FQt0okUtB1nQ07iXziVT1xudT+ZCcSTF4Q+UgbGuK0kX6Uc5MXXCqVqH2MkLM+dWyWlRfUmFg8ieGhKIQQfodC1Jd0XYOmCSRZedGX7FgMYngIAHtXEflBGx6GxWkj/SeXdb50WXlB1D6aHoQQGpMX1LB4MoXhwQG/wyDqW0IIGEaQlRd9yo4nkN67j423iXzCaSN9KpfzKi9YekzULkIIGKEoZqaZvKDGxBNzGBqM+h0GUV8LBYPsedGHZCYDlctBC4X8DoWoLymlINiwsz9lM27lhcbKC6J2CoWjiLPyghqUSKYwMxsDT/oR+ccwApw20ocKB0xMXhD5QiqFzFtvQeVykNms3+EsC5MXdSo07Ayw5wVROxmhKGKzE36HQV0qnkwhFOK4TeQnIxhEYo7Ji35juU0CbS5VTeQbYRgA0PXVF0xe1Gm+YScHYKJ2CoWiSCamYduW36FQl8nl8sjl8ggZTF4Q+ckwgkiy50XfsWMx5weDlRdEfpFBZx+o2/teMHlRpywbdhL5wghFoZRCPDbpdyjUZeJumbrBs35EvjKCOuZSGdi27Xco1EZWzF2ekQlkIv+4lRdWly+XyuRFnXLZNILBEITgS0fUTqGw02xxdoZ9L6g+8cQcALDygshngYDT7JzVFwsJIXQhxLNCiPvd348WQjwuhNgphLhVCGG4l4fc33e612/0NfAa2d7BEnteEPlGuidwOG2kQd06UOeyqcIZYCJqn6ARAQDMTB3wOZLe0q1jcT285EUwyFWiiPxkGM7OM1ccWeQ/AHi16Pe/BfBdpdRxAGYBXOlefiWAWffy77q363h2PA4EAs4/IvKH1/OC00Ya1pUDdS6bRigc8TMEor5kuMmLWS6X2mxdORbXYzaeBADoOivmiPzkTd1i0855QogjAHwcwFXu7wLARwDc4d7kOgCfdn++xP0d7vXnubfvaFYsDm14COj8UIl6l9fzgtNG6tfNA3U2m0YoFPXr4Yn6lqbrCARDmOVyqU3TzWNxPRJu5QV7XhD5a77ygtNGivwDgD8BIN3fVwKIKaW87tT7AKx3f14PYC8AuNfH3dsvIIT4lhDiKSHEU5OT/veJsmNx6MPDfodB1N80DdrgIOwYkxeN+Ad06UCdy6VhhFh5QeSHUCiKOJdLbaZ/QJeOxfWIJ1PQNMHKCyKfBXRn6lYiOedzJJ1BCPEJABNKqaebuV2l1A+VUmcrpc5evXp1MzfdEDseh8bkBZHvtJGR+Qa6Xarte3LdPlBnM6lC40Aiaq9QeAAxVl40RbePxfVIJOYQMoLokkIRop5lBL3kBSsvXL8J4FNCiF0ANsOpfPtHAKNCCK9U7AgA+92f9wPYAADu9SMAptsZcCOsWBxieMjvMIj6mlIKYngIlrd0cZfy4zRUVw/UuRynjRD5xQhFEJudYMPc5ujqsbge8WSKU0aIOoAQApFwiJUXLqXUnyuljlBKbQTwJQCPKKUuA/ATAJ93b3YFgHvcn+91f4d7/SOqC74Q7TinjRD5TSoFMx6HNRvzO5RlaXvyotsH6mwmxeQFkU+MUBT5XAaZdNLvULpet4/F9UgkU4W59kTkH6UUhAASCTbsXMKfAvgjIcROONPzrnYvvxrASvfyPwLwZz7FVzNlWZBzc5w2QtQBRCgEOxbr6pOAnbQ396cANgsh/juAZ7FwoL7BHahn4Oxk+8breZHN236GQdSXDDdxGJs9hOgAd4RapCvG4nrEkymEWHlB1BEMI4g4l0pdRCn1UwA/dX9+G8D7ytwmC+ALbQ1smSx3ZQNteBhIc7oQkZ9UyIBKJGCbJgLu0qndxte9uW4bqG3bgmXmEQpFkM2z5JGo3byqp9mZQzj8iON9jqZ3dNtYXA+lFBKJORyxblFvUSLygREMIMHkRd+w4wnnh6FBYLx7z/YS9QIRCkEBsBNJBFZ1534RW6/XIZd1Msah8IDPkRD1JyM8n7wgqkU2m0PetDhthKhDhEJBxNnzom/YbnPAmV8/3tWl6kQ9IRQCMP+57EZMXtQhm3XOFHCpVCJ/BINhBAIGZqcP+h0KdQmvPJ0NO4k6Q8gIIpFI8UC2T9jusox6OOxzJEQEd6oIkxd9Yr7ygg07idpNSgkpJcZWrsX01AG/w6EuEU84Z3hDRtDnSIgIAEKGAcu2MZfK+B0KtYHX80IFOQYT+c6tvOjm5VKZvKiDV3kRYuUFkW/GVqzDDJMXVKNC5QWnjRB1BC+R6CUWqbdZMSYviDpGyKu8iPscSOOYvKhDofKCS6US+carvGDJMdXCO0AyAkxeEHUCXXf+jyW45HU/sGIxwAhCCeF3KERkGIBg8qJvFHpecNoIkW9GRtcgl00jneregZfax0teBIK6z5EQETDffyYWY/KiH9ixOGCE/A6DiABIpYBQiD0v+kUu68zPZOUFkX/GVqwFAPa9oJokEimEQkFoGr/uiDpB0E0kzsaZvOgHVixWKFUnIn/ZUkIYIfa86BfZjHsGL2BAgSXrRH4YXekmLyaZvKClxZNzGB7k8tZEncKrvGDPi/4gE4lCk0Ai8p8IhzhtpF9kM860kUceug3gfHsiX4yNrQEANu2kmsQTKQwPsVqOqFMIIRAygogxedEX7HgcgtNGiDqGMgxOG+kXmUwSofAAdI1zp4n8oJSCVAKDQyswPbXf73CoC8QTcxhi5QVRRwkZQcTjTF70OiUl7HgCiktVE3UMEQrBno35HUbDmLyoQzaTQiQywFUOiHyilMKOrdcBEJicYPKClpZIpjA8xOQFUScJhYKIJ5m86HV2MglICRFm5QVRxwiHIdNpyFzO70gawuRFHTKZOYTDg36HQdTXNE1DKDKA2emDfodCHU4phXhijtNGiDoMp430B2tmxvkhHPY3ECIq8JKJ1uysz5E0hsmLOmQzcwhHeQaPyE9SSoRCA4jHJmFZpt/hUAdLpbOwbJsNO4k6iJQSBqeN9AV7Jub8wIadRJ3D/TzaM0xe9LxMeg7hMHeCifwWCg9AKYnYzCG/Q6EO5q1mMDTIyguiThIygsjlTWRzeb9DoRbyKi8UG3YSdQzhVkJZTF70vkxmDuEIp40Q+S3kJhGnueIIVRGLJwEAw0NR9ioi6iCG28BxNpb0ORJqpUJZOisviDqHN23Em9bVZZi8qEOWyQuijsDkBdViNpYAAPzq8WeZvCDqIOGQk7zwEozUm6yZWSAYBIIBv0MhIpcdDAJCsOdFr1NKIZtJIRzhtBEivwWNMAKBIGaYvKAqZtyzupEIz/oRdZJQyAAwn2Ck3mTPzEIfHQGE8DsUInIJTYM2NMRpI70ul8tAKYkIKy+IfCeEwOiKtay8oKpi8SR0XUcwoPsdChEV8T6SM5w20tOs2VnoY2N+h0FEJfSxMU4b6XXZtPMFy2kjRP6TUmJ0bA2mJ/f7HQp1sNlYEqPDA5CcMkLUUQK6Bl3TMBtn5UUvs2ZmoY2N+h0GEZXQx0Zhz8b8DqMhTF7UKJNxutZztRGizuBVXrCXAVUyE09gdIQJZ6JOI4TA8PAAG3b2OGt2FvroqN9hEFEJVl70gayXvGDlBVFHGFuxFrlsCpk0d36pvFg8idHhIb/DIKIyRoeH2POihynbhh2PM3lB1GGUUtBGhmHNzHblCUAmL2rkVV4YoSiUkj5HQ9TflFIYGl4FAJgY3+NzNNSpZmNJjAwz4UzUiUZHBll50cPseByQktNGiDqMVArpt96GyuUg02m/w6kbkxc1ymZSADhthKgTKKXw+qtPAQAmJ/b6HA11ItOykEimOG2EqAMppTAyPIAZVl70LG8lA1ZeEHUeLRoBgK5ccYTJixp5penBUKQrS2yIek04OgQhNEwxeUFlxBNOtRyTF0SdRymF/QcmkEimYFm23+FQCxQOikaG/Q2EiBYR4TAAwO7CvhdMXtRovmFn1OdIiAjwlktdg8lDTF7QYl45OqeNEHWmcDgEAIglOHWkF3nNAPXREZ8jIaJSXvLCnJ72OZL6MXlRo2wmhUDQgBA6FFh5QeQ3pRSUVJw2QmV5jQBHmbwg6kjhUBAA2PeiR1lTzkGRvmKFz5EQUSkRcaeNTDF50bMymSQikUFsue8agNNGiDpCODqEqcl9kJJNdGmh2bhzQDQ6wtVGiDqREdQBgCuO9Chragra0CBEKOR3KERUIi8ERCgEa3LK71DqxuRFjbKZFMKRQWiCLxlRpwiFh2Dms4jNTvgdCnWY2VgSQggMRsPsU0TUgcIhAwArL3qVOTWFwMpVfodBRGUIIaCvXAGL00Z6VyY9h3CE5cdEnSTkrv7DvhdUanomjpHhAdx+z3YmL4g6kGEEIYTA9Gzc71CoBazpGegrV8C22ZCVqBPpK1fC5LSR3uVNGyGizuElFLniCJWano1jxegwIPyOhIjK0TSB0ZFBTM9y2kgvsqamoK0YQz6fB9grjqijKKWgrxiDNcVpIz0rnUogOsDlnog6SdCIQNMDmDi02+9QqMNMzcQxNsp+F0SdbOXYCKZmYn6HQU2mbBvWzCz0FWM4dNNmVr8RdRipFLIHx2FNTXfd55PJixql5uJMXhB1GKUUItEhTIwzeUELTc/EMDU9y/7KRB1s5YoRTM9w2kivsWZjgJTQV66ErvFQg6jT2FJCi0agTBN2oruq3zii1MC2LWQzc4gOcK1qok4TjY7gEJMXVCSTzSGVziIaNvwOhYgqkNLG2MgQpmZiXXfmj6rzStH1lVwmlahTFZZL7bIVR5i8qEE65XTCHmDygqjjRAaGkYhNIpOZ8zsU6hAzbgPAMJMXRB1t5YphZLN5pDNZv0OhJiokL1YweUHUqUQ4DACwuqxpJ5MXNUinnB1hThsh6jzhiNPXYOLgLn8DoY4x5Zahh0NBnyMhomrGhp3xe4pTR3qKt4IBKy+IOpdXeWF2WdNOJi9qkJpj8oKoU0Wizufy0PgufwOh/7+9Ow+To77vPP7+ds99aO4ZjS4kQIDEKW5igwm2YyA4ONhxvJu1HceOrzhrO85u7HifBCferHNsnA3eNQEbW8jYgLmMzWXMYcwhGQECJARIGmmkGUlzSZrRnN1d9ds/ugYaWWrNaKa7uno+r+eZR93VNV0fdVd/p/vbv/pVwRh4o3mhkRcihayxIV2/Ne9FcUn1D0A8jqupQWcaESlQlcHIiwGNvCg6kyMvqmt02IhIoSmvqKaktIwejbyQwMB+NS9EomCyedE/cCDcICExs8Vm9piZvWJmm8zs88HyRjN72My2BP82BMvNzP7dzLaa2Utmdna4/4PDS/X3U9LYyO41t2g+E5ECZbEY8fp6zXlxNFEs1CMj6VlYKypqVIRFCoyZ0dK6RM2LaYpiLZ6q/oFBamuqiMUs7CgikkV9XQ0xszcajnNQCviSc24lcCHwZ2a2Evgy8IhzbjnwSHAd4ApgefDzSeDb+Y98dMm+fkqadaYRkULm+T4lLc0ke3rDjjItYVSVyBXqyZEX5RXVOOfne/MichSt849j7+6OsGNETeRq8VT17zuAGTgNVxYpaCXxOPV1tXN25IVzbo9z7vng8kFgM7AQuBpYHay2GnhfcPlq4GaXthaoN7P2/KY+uuTeHuKtLXieF3YUEcmipK2VZE9P2DGmJe/NiygW6pHhQUpKyigtq8jnZkVkClKpFC1tx3Fgfy+jI9E6V3WYoliLp2pg3yCVOtOISMHzPI+mxnn0z92RF28ws6XAKmAd0Oac2xPctBdoCy4vBHZl/FpXsKxgON8n1ddHvLUl7CgikkXK87DmJpK9fZE6siDU8VyzWajN7JNmtt7M1vf19c1qztGRQapr6jDTEGSRQtTWfjwAezT64phEpRZPVd/AfqoqykPZtohMT1ND3ZwdeTHJzGqAO4EvOOfe0oV36U8V0/pkEWYdTu3bj0smKWltzet2RWR6kp7H6PYduIkJvAMHwo4zZaE1L2a7UDvnbnDOneucO7elZXa7vSMjQzrTiEiBcs7R0rYEgD1dW0NOEz1RqsVTMTwyxsjoOJUVZUToiwSROcnzPJob6+jt34/vz83Dcs2slHQNvsU5d1ewuGdyZFvw7+RB6d3A4oxfXxQse4sw6/DkEPQSjbwQKXjx6mqASM17EUrzIheFOpdGhwepqtaZRkQKkXOOJx67i6rqOvZ0bws7TqRErRZPRW/fPgAqKzXyQiQKWpobSCZTHBg8GHaUvLP0kN7vApudc/+acdO9wEeDyx8FfpKx/CPBBMoXAoMZI+UKwpvNC428ECl0Vl0FEKl5L8I420jkCvXIyCDVNRp5IVKoYrEYbe3L2K2RF1MWxVo8Fb39+wGoUvNCpKA550ilUjQHp0vt6dsfcqJQvA34MHCZmW0Ifq4EvgG828y2AO8KrgPcD3QAW4Ebgc+GkDmryW9wrakR39fwN5FCZlWTzYvojLwoCWGbk4X6ZTPbECz7a9KF+XYz+zjQCXwwuO1+4ErShXoU+Fhe05KesLO6uj7fmxWRKXLOMTo6zL6+Xfi+RywWDztSFESuFk9FTzDyQs0LkcLmnOPH9z5MIpn+gLu3b4AVJy0NN1SeOeeeBI40odo7D7O+A/4sp6FmKLm3h9i8WlxZGdM86lBE8q20lFhVJcm90Rl5kffmRdQKtXOOsdGDmvNCpMBV1TTQs3sr/b1dtM4/Luw4BS9qtXiqevr2UVVZTmlJHG+OHkMvEhWxWIzKinSzefKQL4m2ZE8PpW1tdK9eE6kzGIjMRWZGSWtbpEZehHq2kSgYHxvG9z2qazTnhUghm5yXpmvnayEnkTD19u2jpakB36lxIRIF8XiMxoZ5c/WwkaKT3NtLaVsr8Zg+YogUOs/3KWlt0ZwXxWR4+ACAmhciBa6svBqLxdi5Y3PYUSREvf37aWmux/f9OXv2ApGoaW1uoKd3IOwYMkPOOZI9PZqsUyRCStpaI3XYiJoXRzE0mP5jWjuvKeQkIpKNWYyamga6NfJiznLO0dO3j9amhrCjiMg0tDY3aORFEfAGB3Hj48RbWzRZp0hElM5vwx8ZITU4FHaUKVHz4igOBs2LeXVNeJ4XchoRyaa6tpHuXVvwfb1W56LBgyNMJJK0NNeHHUVEpqG1uYGB/YMkU6mwo8gMJLrSZ88uXbgg5CQiMhXOOeIL2gFIdneHnGZq1Lw4iqHBfiD9oei+e7+ryYdEClhNbQOJxBi9ezvDjiIh2NuTbja3NmvkhUhU+L5Hc1M9zjl6Nfoi0iabF2ULF4acRESmwneOfc+sA958/RY6NS+OYmhwgJKSMiora4iZHi6RQlZT2wjArk4dOjIXde/tA6C9rTnkJCIyVb7v09pUD8Cenv5ww8iMJLq6IR7Hb2zQnEMiERGvrYVYTM2LYjE02E9tXRO+72vUhUiBq6yqpay8kp3bN4UdRUKwe08fJfE4TQ06tbVIlLS3pecV69oTndP1yW9KdHVROr+NrtU/0HtmkQjwfB9nRklrCwkdNlIchgYHqKvTt3giUZDyfBYuPpkdHRvDjiIh6NrTS2tLAz+84z48T9/6iURFbU0VdbXVdO/uCzuKzECiq5uSBQuIWdhJRGSqPN+nZEG7Rl4Ui6HBAWrrdKYRkSjwPI+Fi09h7+4OxsdGwo4jeda9pw/P89ARfiLRs3BBq0ZeRJhzjkR3N6UL28OOIiLTVLpgAYnu7kiMmNJbvKMYGuxnnpoXIpHgnKO3twvnfDp16Mic4nkee3sGqK2uDDuKiEyDc45EIsGCtma692jkRVSl+gdw4xOUaLJOkcgpXbAAf2QU78CBsKMclZoXWSQTE4yPDTOvrhnP83BOw5BFCl1NbSNmMXZseznsKJJHvf37SXkeNTVqXohEiXOOH9/7CxbMb2bo4AhDBzVqLoomj5cvXaCRFyJRUxKMmEp07Q45ydGpeZHF5GlSNfJCJDriJaW0LVjGjm0vhR1F8mjyG9vqyjIiMOpRRDKYGfNb02eL0uiLaErs3AVAbH5byElEZLpKF6VHTE3s3BlykqNT8yILNS9Eosf3fZYsPZUd2zeRSiXDjiN5MnmsfE1VRchJRGS6PC/F+g2vADrjSFRNdGwnVlUFjY34vjrIIlHh+T7W3IxVVDDRsT3sOEel5kUWQ4MDAMzT2UZEImXZiWeRTIxr3os5ZFdXD/NqqykrKw07iogcg5rqSspKS9jV1RN2FDkG4x3bKV22lGRSXxqIRI3FYpQvW6rmRdS92bxoCua8UCdZJAqWnnAGZjG2vLo+7CiSJx2du1m2pF11WiSizIwli+azfWfhH3Mtb+WcY6Kjg7Klx4UdRUSOUcXxy5jo2F7w76PUvMhi/769lJaWU1VdF3YUEZmGsrJKFh13ipoXc0QylWJXdw9LF2uiOJGocs6xdEk7HZ27C/7Ns7xVqqcXf2SU0mVL8TwP0PMnEjXlJxyPNzREamBf2FGyUvMii4G+bppa0hOYeJ6HUzEWKXjOOTzP48STz2bXjs2MjQ2HHUlybFd3LynPY8miNnydFUokkpLJCXp6BxgZHaO3f3/YcWQaxjs6ACg5bgk9t9yq5pNIhEy+by5fthSAieD1XKjUvMiiv6+L5paF+L7P/T+9CU1hL1L4nHM8dN/3WLL0dHzfY8tmjb4odpPDzBcvaFWZFoko3/epn1cNQMeO7pDTyHRMHicfW7SQeEwfLUSixHeOvavXYMEZR8a3qXkRSb7vM9C/m6aWRQDETA+VSFTEYjEWLjmFkpIyNr74q7DjSI5t7+ymvKz0jVMtikg01dZUEYvF6OhU8yJKxrdtp7R9PrHKyrCjiMgx8HyfZGkpVlXJ+NZtYcfJSp/Ij2BosJ9UMkFTy0JN1ikSMc45Eokk9Y3tbN74DJ6XCjuS5ND2zt0sXdxOTN/4iURaPB5j0YJWOjo1aWeUjL/6KuXLTww7hogco8lDR+KNjYy/+lrYcbLSO70j6O/rAqA5mPNCRKLDOccjD66hvmkBY6ND7Nj2ctiRJEc8z2NbZzcnLFsUdhQRmSHnHMuWtLOlY5e+NIqIZP8Ayb09VJ66MuwoInKMfOfo+8EPiTU3k9y9h9T+wp13SM2LIxjoS3f9m1sXBSMvNAmcSJRYLEZdfSvxeCkvb3gi7DiSI9s7dzM+nuCU5cdplJxIxCWTE+w/MMjQwRG69/SFHUemYGzTJgAqVq7QmUZEIi7WlD78dmzT5pCTHJmaF0cw0NdFPF5CfUNr2FFE5BjF4iXUNbSxYf0jOnSkSG16LT1R3CnLj+PWux5Q80Ik4lqa6gHY9GphTxonaWMbN2Hl5ZQev4zdN9+iGiwSUZ7vQ309lJQwtumVsOMckZoXR9Df101jUzuxWDzsKCJyjHzfp23+MoYP7uP1zc+GHUdy4JXXt9PW2kj9vBrMLOw4IjJD1VUVNNTXslHNi0gY3fgKFSefhG9GPKYaLBJVnu9DzKhYfiKjal5ET3/vLpqC+S40FFkkuuY1tFFZNY/n1j0YdhSZZb7v88pr2zn15OPDjiIis8TMWHnSMja91qH3XgXOHx9nfMtWylecwo4bb8LzdIi1SNRVnrqS8Vdfw08kwo5yWGpeHEYyOcHe3dtZsGh52FFEZAZ83yfleZx21jvYuOFXDB8s3AmIZPp27e7l4PAoK05aytjYGCnPCzuSiMyQ73usWH4c+/YPsaenP+w4ksXICxvA8yg//TQ06EKkOFSuOhOXTDK64cWwoxyWmheHsXvXFnzfY/HSU944dYzTBEQikXX+b72XVCrB2ifvDTuKzKL1L6QnlFpx4hJuueM+fUsrUiTOODV92s31Gwp30jiB4WfWEauspOL0U8OOIiKzIOV5lKxcgZWXM7z212HHOSw1Lw5jV+erACxZuhLf97n/pzeB3hSLRJJzjrqG+Zy04nye/uVdpFLJsCPJLFn3/CZOXLaIpsY6YvraT6RozG9tYunidp5ZvzHsKHIEzjmGn1lH9XnnYKWlYccRkVngO0fvj26j6uyzGH5mbUF+KaTmxWHs3LGZeXVN1NW3ABAzPUwiUeWc4+EHVvNbl1zD0OAA65+5P+xIMgsG9g3y+radnLdqJYlEQv1lkSLg+z7JZIJEIsGF55zKq1s62X/gYNix5DAmtm4j1d9P9YUXkEgk8H3NdyESdZ7vYxjVF5xPcm8Pic6dYUf6DfpUfhi7Ojez+LgVYccQkVliZixaehq185r5+f3fJ5mYCDuSzNC65zcBcP6qFZpUWaSIOOf44Z0PsOqMk3DOse55jb4oREOPPwGxGOVnn8Wu792sGixSJDzfp/K8c8CMoUcfDzvOb1Dz4hBjowfp69nJ4qXp5oXeFItEn+d5PPSz77Hk+DMYOtDHE4/eHnYkmQHnHI/+aj2LF7TS3DiPW+9+UHVapEj4vo9zPk+ufYGF7S088sR6vb4LjEulOPDgz6m58HxKGhqIx/RxQqRYeL6PNTRQfd45HHjgIVyBTYauanOI1zc/C8CyE84IOYmIzCaLxaiZ18yK097Gw/d/j77eXWFHkmP0+radbN3exbvecR4/vON+zDTfhUixicfjXPHOi9jSsYvXtxXe0OW57ODTa/H27aP+qiuDL/l0yIhIsam/6kpS/f0MryusiTvVvDjEi88/Su28RpadmG5eqCiLFAff90mlUrzrdz9BSUkZt63+BzwvFXYsOQb3PfwUVZXl7N3bg6YkEik+6dEXjkvfdjZVlRX87OdPhh1JAs459t/zE0pamik98wxGR0c134VIEUl5HmNjY1Sedy7xxkb233VP2JHeQm/7MkyMj7L55Wc4fdWlxGJxQIeNiBQL3/fxfY+1T/2Mq675HDs6Xuand3wr7FgyTTt27eHJdS9x2cXnUlamGe5FitXExBheKsm7Lz2fp9a9REfn7rAjCTDy7HpGX3iRhg9cQ+dN36fr+2v0PlmkiPjOsffmH5ByjqY//AAjz73A8Prnwo71BjUvMrzy8lMkkxOcec5lQLq77HkeDhVlkWKyfMVFXHTJNTz5+B08+tCasOPIFDnnuHHNT6iurOD3r3wHnpfSWUZEipRzjlvvfoirL7+Y2poqbrj5bn3DHzKXStH77RsoXbCA2t+9At936CzVIsUnZsbExATVV1xO6fw2eq+/EZcqjNHKal4EPC/FIw+uobGpnWUnnA5AMpnk/nu/i94dixQP5xzJZJKkB6eddSn33/Mf/PTOb+kQkgj46UNPsunVDv7oD95DVWU5nufpw4xIUXNUVpTxkT+8kle3dHLnzx4PO9Cc1nP9jUzs6KTtM3+KH4vpsGqRIpX0PHZ//2b2/OAWmj/1p0xs66D3P24MOxag5sUb1v7qJ+zd3cF73/85YrE4zjkSiUTYsURkljnneOTBNXieR0n5PNoWnMAvf3Er3/7XP6d715aw48kRPLnuRb73o59x4Tmn8c6Lz+UHt/8UX41lkaLmeR4TExNcctFZXHLRKm6540EeeeLZsGPNSfvuuJv9d95Nw/t/n7LzzmVsbEzf7YkUOcOovfhtNFzzPvbdcTcDt98R+mFiJaFufRrM7HLg/wBx4DvOuW/M1n2nkgkevv/7nHjyOZx21iVA+vj4++79buhPkIjMPgu+MYrH4yw5fhUXvv193HfXdfzb//o4p6+6hAvffjUnnLSKeDwyJTIvclmHj2R0bJzb7/kF9zzwBKcsP44vfvpDpFIpPD896iKmU/SJFC3nHGtu/xnl5RV88sO/x4HBg1z3nR+zpaOL//z+32FebXXYEUORz1qc2r+f3htuYvDBh6i66ELqP/YRkskke9fcovfIIkXM833GExMcOHCA2o/+F5J9ffR++wbGt26j9VOfoLSpKZRckXhnbmZx4P8C7wa6gGfN7F7n3Cuzcf8lpWV85ovXEYvFMLM35rqIWYzCOrOtiMymyUMOdnZu5azzr6CqspJnn7mPl55/nPKKKhYsWs6CRctpa19KQ2MbdfXNVFXNo7yymvLyyjcm9p0Lcl2HJw2PjLJ7bz+79/az6bUOnnn2ZYZHxnj3O87jwx+8nLGxURKJBL6vN80ic0EsZjjncfNtP2Hh/AaWLHob9z38NI8//RwXnH0aF190JueeuSLsmHmT61rsnCOxo5Ox115n5NnnOPj007hEksb/9IcMJ5OMjI+TSCTQVBcixc93jq7vr6GqrJT5f/lFShYv4sDtd3Lw8SeouegCqs89h4oTT6C0fT7xurq8nLo+Es0L4Hxgq3OuA8DMbgWuBmbtTXNb+1I8zyORSDA8PMx999xILB4DB37mMX3Zrh/rbWHcj7IX/jaVPX/bBJIpnwODB1m+8mIODvZTV9fA66/+mh3bXj7icb1f+Mp3WbTk5MPeVoRyXocfemwt3/7eXW9cr6woZ9XpJ2EuhZHi4NAQ9zzwy0PmuXCAy2hmZF7Pdtt01i20+5kr24xydj1es3k/qZQXXPf40Hsv5eILzuCBR9eyfsNmPM+bU80L8lCLO7/0V3j79xObN4/q376UqquuwObPZ2LNLey8aTXO+ZSWlOA73vL3MfN6ttums26h3Y+yF/42o5y9EB8vgJGJCTq/cxOLP/4xyi5+O/3/8k1GX97IwSfePI310uu/ReXJJ5FrFoUhX2b2AeBy59wngusfBi5wzn0uY51PAp8Mrp4MvJblLpuB/hzFnSplUIZCyhD29udShuOccy053sasm0odDpZnq8WF8BwfqtAyKU92ypOd8hxdM1AdxToMM35PXGjPh/JkpzxHV2iZlCe7Q/NM+z1xVEZeHJVz7gbghqmsa2brnXPn5jiSMihDZDKEvX1lKB7ZanEhPr6Flkl5slOe7JTn6IJMS8POkUtHqsOF9nwoT3bKc3SFlkl5spuNPFGZ6awbWJxxfVGwTERE8kN1WEQkfKrFIjJnRaV58Syw3MyWmVkZ8CHg3pAziYjMJarDIiLhUy0WkTkrEoeNOOdSZvY54CHSp4W6yTm3aQZ3OaXDS3JMGdKUIS3sDGFvH5ShoM1SHS7Ex7fQMilPdsqTnfIcXSFmmrIZ1uJC+78rT3bKc3SFlkl5sptxnkhM2CkiIiIiIiIic1dUDhsRERERERERkTlKzQsRERERERERKWhF37wws5vMrNfMNh6y/M/N7FUz22Rm/5TvDGZ2lpmtNbMNZrbezM7PcYbFZvaYmb0S/J8/HyxvNLOHzWxL8G9Dnrf/z8Hz8JKZ3W1m9bnYfrYMGbd/ycycmTWHkSFf+2SW5yJv+6SZVZjZr83sxSDD14Lly8xsnZltNbPbgsnI8p3hFjN7zcw2Bq/d0lxlKEZTrSlm9tFgnS1m9tHD3H7voXU7jDxm9mDGPnK9mcXDzGRmVWZ2X0at+EaYeYLl/9PMdpnZ8AxzXB689raa2ZcPc3t5UBe2BnViacZtXwmWv2Zm75lJjpnmMbOmoMYOm9m3ZiPLDPO828yeM7OXg38vCznP+cHfmQ3Ba+v3w8yTcfuS4Dn7y9nIExbV4NzlUf1V/VX9nd08GbdPvf4654r6B7gEOBvYmLHst4FfAOXB9dYQMvwcuCK4fCXweI4ztANnB5drgdeBlcA/AV8Oln8Z+Mc8b/93gJJg+T/mavvZMgTXF5Oe/KoTaA7hecjbPpklQ972ScCAmuByKbAOuBC4HfhQsPx64DMhZLgyuM2AH+UyQzH+TKWmAI1AR/BvQ3C5IeP2a4AfZtbMsPIA8zL2lzsn98+wMgFVwG8H65QBv5p83Yb4GF0Y1JXhGWSIA9uA44P/14sE9Tljnc8C1weXPwTcFlxeGaxfDiwL7ic+w8dkJnmqgbcDnwa+NdP9ZRbyrAIWBJdPA7pDzlPFm3/324Heyeth5Mm4/Q7gx8BfzsZzFtbPTF/Pwe1FW4NnkgfVX9Vf1d9ZzZNx+5Trb9GPvHDOPQHsO2TxZ4BvOOcmgnV6Q8jggHnB5Tpgd44z7HHOPR9cPghsBhYCVwOrg9VWA+/L5/adcz93zqWC1daSPl95TmR5DAC+Cfx30s9LzmTJkLd9MkuGvO2TLm3yW4LS4McBl5EuYJDD/TFbBufc/cFtDvg1Odwni9RUasp7gIedc/ucc/uBh4HLAcysBvgL4OuFkMc5NxSsU0L6j/Js1IhjzuScG3XOPRZkSwDPM/N9dKaP0Vrn3J4ZZjgf2Oqc6wj+X7cGuY6U8w7gnWZmwfJbnXMTzrntwNbg/kLJ45wbcc49CYzPMMNs5XnBOTdZzzcBlWZWHmKe0Yy/+xXMzmtqJvsPZvY+YDvpxyfqVINzlEf1V/VX9Xd288D062/RNy+O4CTg4mDYyi/N7LwQMnwB+Gcz2wX8C/CVfG04GKqzivQ3zW0ZRW8v0Jbn7Wf6E+CBXG//0AxmdjXpTuiL+dj24TIQ0j55SIYvkMd90sziZraBdNf3YdJd2wMZRbWLN5tLecngnFuXcVsp8GHgwVxmKEJTqSkLgV0Z1zOf678H/jcwWiB5MLOHSO8jB3mzuRZqpiBXPfBe4JFCyDNDU7n/N9YJ6sQg0JSjbDPJkwuzlef9wPOTjfKw8pjZBWa2CXgZ+HRG3c97nuDD+l8BX5thhkKhGpzjPEGmelR/VX+nl0f1l5nX35IZRY2uEtJDry4EzgNuN7Pjg29a8+UzwBedc3ea2QeB7wLvyvVGg53kTuALzrmhoOkFpL9yNrOcPgaHbj9j+VeBFHBLLrd/aIZgm39N+vCVvDnM85D3ffIwGb5OHvdJ55wHnBW8AbgbOCVX25pqBjM7zTk3eYzv/wOecM79Kt+5Cp2Z/QKYf5ibvpp5Zbo1xczOAk5wzn3x0OMhw8iT8XvvMbMK0vXpMtLNtlAzBTXjR8C/O+c6ws4jhc/MTiV9eGZe/94dTtAoPtXMVgCrzewB59xsflM6HdcC33TODWe+JypkqsHZa7DqrxQa1d8jupZp1t+52rzoAu4KPhj+2sx8oBnoy2OGjwKfDy7/GPhOrjcYfJN8J3CLc+6uYHGPmbU75/aY2eSxT/ncPmb2x8BVwDtz3UA6NIOZnU76GL0XgxfNIuB5MzvfObc3HxmCxXndJ4+QIe/7JIBz7oCZPQZcBNSbWUnQlV0EdOc5w+XARjP7W6AF+FQ+th81zrkjNrXMbCo1pRu4NOP6IuBx0vvAuWa2g/Tfp1Yze9w5dylZ5DBP5jbGzewnpIc+HrV5kYdMNwBbnHP/drQsecozU92k5x7KvP9DX/+T63QFHx7qgIEp/m4+8+TCjPKY2SLSTeKPOOe2hZ1nknNus6UnGjwNWB9SnguAD1h6oux6wDezcefcrE32N9tUg7PXYNXfaVP9zWEe1d+seaZff90sTGRS6D/AUt46Weangb8LLp9EehiL5TnDZuDS4PI7gedyvH0Dbgb+7ZDl/8xbJwr6pzxv/3LgFaAlD/vBYTMcss4Ocjth55Eeh7ztk1ky5G2fJN0YqA8uV5Ke9Ooq0k2TzAk7PxtChk8ATwOVud4ni/FnKjWF9Cij7aQnHmsILjcess5bamYYeYAaoD1YpwS4Dfhc2I8R6WPR7wRiBfaczWTCuBLSk9At480Jv049ZJ0/460Tft0eXD6Vt04Y18HMJ4w75jwZt/8xszdh3Ewen/pg/WtmI8ss5FnGmxPGHUd6fqUZ/d2djecrWH4t0Z+wUzU4h48Pqr+Hvp5Vf7M/PvWo/h71+QqWX8sU6u+sPIiF/EN6WNceIEn62+2PBw/sD4CNpCfbuSyEDG8Hngue4HXAOTnO8HbSk7K8BGwIfq4kffzTI8AW0me7aMzz9reS/qA+uez6fD8Gh6yzY6Yv4mN8HPK2T2bJkLd9EjgDeCHIsBH4m2D58aQnydxKupFRHkKGFOn5NyYfm7/JVYZi/DlSTQHOBb6Tsd6fBM/zVuBjh7mfpczOG+djzkP62ONnM/aR65jhrNyzkGlR8PrdnLGPfiLM54z0bPldgB/8e+0x5riS9NmPtgFfDZb9HfB7weWKoC5sDerE8Rm/+9Xg915jhrP/z1KeHaQn6h4OHpOVYeUB/gcwkrG/bGAWzmg1gzwfJj0x2wbSf+/eF/bzlXEf1xL95oVqcO7yqP6q/qr+zvLzlXEf1zKF+mvByiIiIiIiIiIiBWmunm1ERERERERERCJCzQsRERERERERKWhqXoiIiIiIiIhIQVPzQkREREREREQKmpoXIiIiIiIiIlLQ1LwQERERERERkYKm5oXMaWb2IzO7zcx+bWadZva7wfLHzOzdweWvm9l14SYVESleh6vFZnaamT2dsc7ZZvZImDlFRIpZlvfFj5rZhuBn3Mw+GHZWmZvUvJC57kygwzl3PvBHwN8Gy/8W+KqZ/RGwCvhCOPFEROaEw9XiV4DjzSwerPOvwH8LKZ+IyFxw2PfFzrnLnHNnAf8B3AvcGVpCmdNKwg4gEhYzqwBagK8Fi14BGgCcc0+YmQF/AVzqnPPCSSkiUtyOVIudc76ZbQJONbPlQKdz7vmwcoqIFLNs74uD2z8CXAG8X++LJSwaeSFz2WnAFufceHD9bOBFADM7HWgHEs65g8GylWb25eDydWZWG0JmEZFic8RaDKwF3gZcC/w1qBaLiORItvfFf0B6JMYHnXNJ1WEJi5oXMpedCSwxswozqybdaf6mmbUDtwBXA8Nmdnmw/nnAhuBy3WRTQ0REZuSwtTi4bS3wdeBu51x3sEy1WERk9h3pffFVwGeBazIaG6rDEgo1L2QuOxO4C1gHPAt8G3ghWPYl59xm4O95cx6M84BXgoKOmV1iZrfmPbWISHH5jVrsnHsquO1VYAL4x4z1VYtFRGbfkWrxamAR8FQwYefHOaQOg2qx5IfmvJC57Ezgk865/3rI8osmLzjnnsi4vgz4KjAEtAbzYvxWXpKKiBSvI9VigM8DX3HOjWQsUy0WEZl9h63FzrmmQ1c0s/vIqMPBeqrFknNqXshcdgKwZSormlkpMOCc+1RuI4mIzDm/UYvN7ATgPuAp59zqjOWqxSIiuTGl98WqwxImc86FnUEkkoJJPf8BuM459/Ow84iIzEWqxSIi4VMtlnxQ80JERERERERECpom7BQRERERERGRgqbmhYiIiIiIiIgUNDUvRERERERERKSgqXkhIiIiIiIiIgVNzQsRERERERERKWhqXoiIiIiIiIhIQVPzQkREREREREQKmpoXIiIiIiIiIlLQ/j/20pgvYnfGFQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1,3, figsize = (18,6))\n", + "\n", + "#px\n", + "sns.histplot(df_events_real_beam['$px_{\\mu_1}$']/1000,\n", + " ax = ax[0],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#73683B'\n", + " )\n", + "#py\n", + "sns.histplot(df_events_real_beam['$py_{\\mu_1}$']/1000,\n", + " ax = ax[1],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#4F5D75'\n", + " )\n", + "#pz\n", + "sns.histplot(df_events_real_beam['$pz_{\\mu_1}$']/1000,\n", + " ax = ax[2],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#D64045'\n", + " )\n", + "\n", + "plt.suptitle('Momenta histogram for $\\mu_1 (non-monochromatic) $')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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8k+9973s89thjdb7viPz8fFatWsVll13GhAkTeOCBB1i7di2zZs1i+/btvPfee8ydO5eXX36ZNWvWkJOTw5w5c+p8D8OGDWP8+PHccccdrFmzhiOPPJIzzjiDlStX8tZbb3H00Uczc+bMBv5l40dBgIgQCoWiw/ziQUMHm+aAAw5g9erVzJgxg86dO3P22Wc3agGak08+mby8PPr27UtlZSVjx44FwsvTbtq0qdq+paWlfPnllxx//PEATJo0ib///e8NvkZ+fn618x5//PHR16z5GjWtXLmSkSNH0rlzZ3Jzczn33HOjr1lz2eHIuYYPH87kyZN5+OGHo1fc9Yks0du5c+f9lujdtGlTg+97/Pjx0f179+7NYYcdRtu2benRowebN2+utnTygAEDeP7556MTF9X1Hmpau3YtI0aMoG/fvsyZM4d33323wfcVL8oJEBEgvDxwJC+gtUUmEpr37+PrvRcuX8vJyWHkyJGMHDmSvn37Mnv2bCZPnkxubi5VVVUA+y2VG7scbewyvpHlaVtDzfPWXAIXqFbH2urZ0Hljlx1+6KGHeP3111m0aBHHHnssq1evplOnTnWep6ElehsSu3/Nc1VUVDRr6eSa6lu+ONHUEyAiURXlu1s4KqBuuW3jcashM61fv54PP/ww+nzNmjXRpXm7devG6tWrAXjyySeb/RoHHnggHTt25KWXXgLgD3/4Q/TquKW6devGmjVrqKqqYvPmzaxYsQKAwYMH8+KLL7Jt2zYqKyt5/PHHG3zNjRs3MmTIEG6++WY6d+7M5s2bW1S3lr7vMWPGMH/+fD7//HMAduzYwSeffFLvMTWXcq65fHEyqSdAJMtF8gEiWjoqoKHXSceRAvv2fJXQc+3cuZOf//znfPnll+Tm5vLtb3+bGTNmAOHldadMmcL1118fTQpsrtmzZ3PZZZexa9cuevTowaOPPtqi80UMHz6c7t2706tXL44++miOOeYYAA477DBuv/12Ro0ahbtz6qmnMmHChHrPNW3aND788EPcnTFjxtC/f/8W168l7zt26eSqqiry8vJ44IEHokFabc455xx+8pOfcO+99zJ//vzo8sWdO3dmyJAhSc2XsWy7Rzdo0CBftWpVsqshkjLKysr40a/nRWf9q0u7gzpTVbGHPTvDf7DueOw2AKZdcG2j9gcwIy1uCbz33nscffTRAHG5RZKOgZCkh9jPboSZrXb3QbXtH7eeADN7BBgHfO7ufYKybwBzgW7AJuAsd//Cwv8b7gFOAXYBk939jeCYSUBkbMat7j47KD8WmAUUAs8C/+bZFtGItJLcgnZxSwqs9jppeEvAzFI+aBFprnjmBMwCxtYouxp43t17As8HzwFOBnoGP5cA0yEaNNwIDAEGAzeaWcfgmOnAT2KOq/laIpJiIrcEFK+LpIa4BQHu/ndgR43iCcDs4PFs4LSY8sc87DXgIDM7DDgJWOLuO9z9C2AJMDbY1sHdXwuu/h+LOZeIpCgtNyySWhI9OuBQd/80ePxP4NDgcRcgNuVzS1BWX/mWWsprZWaXmNkqM1u1devWlr0DEWmRyJwBVVVVKd0rkKr1EqlLcz6zSRsiGFzBJ+R/mbvPcPdB7j6oc+fOiXhJkZTm7pSWllJaWlptZEAiRHoDSkpKWn2a4tZSUFDA9u3bFQhI2nB3tm/fTkFBQZOOS/QQwc/M7DB3/zTo0v88KC8GDo/Zr2tQVgyMrFG+LCjvWsv+ItIIoVCIibfPJ/+AjlRVlCckKTBWTn4hoVAoTtMUt1zXrl3ZsmUL6jmUdFJQUEDXrl0b3jFGooOAhcAk4Pbg959jyqea2ROEkwBLg0BhMfCfMcmAJwLXuPsOMyszs6HA68AFwH2JfCMi6Sh2pcDcgnbkFbSnqiKHyp2JvRqPTEpU0KHumd+SKS8vj+7duye7GiJxF7fbAWb2OPAq8F0z22JmUwh/+Z9gZh8CPwieQ3iI30fABuBh4GcA7r4DuAVYGfzcHJQR7PP74JiNwF/i9V5EMkU8VgpsrnhNSiQijRe3ngB3/3Edm8bUsq8Dl9dxnkeAR2opXwX0aUkdRbJRqnbBi0jiae0AkSwTr0WCmkPzBogkl4IAkSwTz0WCmlMXzRsgkjwKAkSyROxCQal0Pz4dpxIWyRQKAkSygLtTXFzMhQ8sTokeABFJDQoCRLJAKBTiwgcWN7hSoIhkFwUBIlkiVUcFRG5TKEFQJPESPVmQiEg1FeW7uXT2CtrktGH6eYPo0qUL4dXFRSTe1BMgIkmXV9AeM+Oi3y2luLhYPQIiCaIgQERSiAIBkURSECAiKcY0d4BIgigIEMlwsfMDpAvNHSCSGAoCRDKY5gcQkfooCBDJYJofQETqoyBAJENFbgOk6vwAIpJ8CgJEMlSkFyAdbwNodUGRxFAQIJLB0rUXQKsLiiSGggARSUkaISASfwoCREREspSCABFJScoLEIk/BQEiGSgdJwiqSXkBIvGnIEAkA6XzyIBYygsQiS8FASIZKl1HBohI4igIEBERyVIKAkQySCQXIN3zASKUHCgSXwoCRDJIKBTivOlL+cnMl9I+HwCUHCgSbwoCRDJMXkF78jIoHyAnv1C9ASJxoiBARFKaegNE4kdBgEiGyIS5Aeqi3gCR+FAQIJLmYpMBM2FugNqoN0AkPhQEiKS5UCjEOXctIhQKZfTcAJo4SKT1KQgQyQA5bQt1lSwiTaYgQCQDVJTvZuqs5Rl5KyBCcwaItD4FASIZIie/MNlViCvlBYi0PgUBIpI2lBcg0roUBIiIiGQpBQEiIiJZKjfZFRARaazYCZGKioowsyTXSCS9qSdARNJGRfluLp29gvOmL1WCoEgrSEoQYGZXmNm7ZrbWzB43swIz625mr5vZBjOba2b5wb5tg+cbgu3dYs5zTVC+3sxOSsZ7EUmmTJ4quC7hBZLaJ7saIhkh4UGAmXUBfgEMcvc+QA5wDvAb4C53/zbwBTAlOGQK8EVQflewH2bWKziuNzAWeNDMchL5XkSSLRQKZexUwSISf8m6HZALFJpZLtAO+BQYDcwPts8GTgseTwieE2wfY+EbgROAJ9y93N0/BjYAgxNTfZHki/QCZPJUwSISXwkPAty9GPgt8A/CX/6lwGrgS3evCHbbAnQJHncBNgfHVgT7d4otr+UYkYynXgARaalk3A7oSPgqvjvwTaA94e78eL7mJWa2ysxWbd26NZ4vJZJQ2doLoCmERVpHMm4H/AD42N23uvs+4ClgOHBQcHsAoCtQHDwuBg4HCLYfCGyPLa/lmGrcfYa7D3L3QZ07d27t9yMiCVZRvktTCIu0gmQEAf8AhppZu+De/hhgHbAUmBjsMwn4c/B4YfCcYPsLHg7/FwLnBKMHugM9gRUJeg8iSZWNowJq0hTCIi2X8MmC3P11M5sPvAFUAG8CM4BFwBNmdmtQNjM4ZCbwBzPbAOwgPCIAd3/XzP5EOICoAC53d90clawQyQew3LbJroqIpLGkzBjo7jcCN9Yo/ohasvvdfQ9wZh3nuQ24rdUrKJIGcgvaKSlQRFpEMwaKSFpyd0pLSyktLVWCoEgzKQgQkbRUUb6byff/lbP++3+VICjSTAoCRCRt5eQXKkFQpAUUBIikGY0MEJHWoiBAJM1opkARaS0KAkTSULbOFCgirUtBgIikNU0hLNJ8CgJE0oS+7GpXUb6bi363lOLiYrWNSBMpCBBJE6FQiLPvfIaSkpJkVyUFmdYSEGkGBQEi6cSMqbOWKymwFhoqKNJ0CgJE0kxOfmGyqyAiGUJBgIhkBOVMiDSdggARyQgV5buVFyDSRAoCRCRjKC9ApGkUBIiIiGQpBQEiIiJZKjfZFRCRurl79B63Et5EpLUpCBBJYaFQiPOmLwXgwXOPTXJtRCTTKAgQSXF5Be2r9QiIiLQW5QSIpIGK8l2aKbCRNF+ASOMpCBBJUZEvswjNFNgwd6ekpIRz7lqknhORRlAQIJKiQqEQFz6wWFf/TVBRvpups5ZjuW2TXRWRtKAgQCSF5RZo8pumUo+JSOMpCBAREclSCgJERESylIIAERGRLKUgQEREJEspCBBJQTWHB0rTaK4AkcZRECCSgjQ8sGUqynczZcYyzRUg0gAFASIpSsMDWyYnv1C9ASINUBAgIhlJvQEiDVMQIJJilA/QenLbqjdFpD4KAkRSiLtTXFysfAARSQgFASIpJJIQqLnvRSQRGhUEmNnwxpSJSMspIVBEEqWxPQH3NbJMRCTlaN4Akdrl1rfRzL4HDAM6m9mvYjZ1AHLiWTERkZaKfPmXlZVxycyXeOKKU+nQoUOyqyWSMuoNAoB84IBgv6KY8jJgYrwqJSLSGirKd3Pp7BVUVZTTRnkWIvupNwhw9xeBF81slrt/0lovamYHAb8H+gAOXASsB+YC3YBNwFnu/oWZGXAPcAqwC5js7m8E55kEXBec9lZ3n91adRRJNA0NjI+8gvZUVeRotIVILRqbE9DWzGaY2XNm9kLkpwWvew/wV3c/CugPvAdcDTzv7j2B54PnACcDPYOfS4DpAGb2DeBGYAgwGLjRzDq2oE4iSaWpgkUk0Rq6HRAxD3iI8NV7i/5CmdmBwPeByQDuvhfYa2YTgJHBbrOBZcBVwATgMQ9n9LxmZgeZ2WHBvkvcfUdw3iXAWODxltRPJJlyC9opCBCRhGlsEFDh7tNb6TW7A1uBR82sP7Aa+DfgUHf/NNjnn8ChweMuwOaY47cEZXWVi6Qd3QoQkWRo7O2A/zWzn5nZYWb2jchPM18zFzgGmO7uA4Gv+LrrH4Dgqr/VxvKY2SVmtsrMVm3durW1TivSanQrQESSobFBwCRgGvAK4Sv31cCqZr7mFmCLu78ePJ9POCj4LOjmJ/j9ebC9GDg85viuQVld5ftx9xnuPsjdB3Xu3LmZ1RaJL00SJCKJ1qggwN271/LTozkv6O7/BDab2XeDojHAOmAh4WCD4Pefg8cLgQssbChQGtw2WAycaGYdg4TAE4MyEZH9aMIgkf01KifAzC6ordzdH2vm6/4cmGNm+cBHwIWEA5I/mdkU4BPgrGDfZwkPD9xAeIjghcFr7zCzW4CVwX43R5IERdKJ8gESI7K08Lx/H68Jg0QCjU0MPC7mcQHhq/c3gGYFAe6+BhhUy6YxtezrwOV1nOcR4JHm1EEkVWjRoMTR0sIi1TUqCHD3n8c+Dyb7eSIeFRLJRhoaKCLJ0NylhL8iPNRPRCRtKC9ApLrGLiX8v2a2MPhZRHiK36fjWzURkdYVyQsIhULJropISmhsTsBvYx5XAJ+4+5Y41EdEJK6UFyDytcYOEXwReJ/wSoIdgb3xrJSIiIjEX2NvB5wFrADOJDx073Uz01LCIi2k4YEikkyNvR1wLXCcu38OYGadgb8Rnu1PRJpJwwMTLxJ4FRUVEV6pXCR7NXZ0QJtIABDY3oRjRSRG5EsokqWu6YITK5IcGPtvIJKtGvtF/lczW2xmk81sMrCI8Ex+ItJEoVCI86Yv5dwHX6CkpCTZ1clKOfmFlJSUcM5dizRSQLJavbcDzOzbhJf4nWZmZwD/Gmx6FZgT78qJZKq8gvbs2/MVU2ctJye/MNnVyToV5buZOms5BR06JbsqIknVUE7A3cA1AO7+FPAUgJn1Dbb9MI51E8l4CgCSR20v0vDtgEPd/Z2ahUFZt7jUSERERBKioSDgoHq2KYwWERFJYw0FAavM7Cc1C83sYmB1fKokIiIiidBQTsAvgafN7Fy+/tIfBOQDp8exXiIiIhJn9QYB7v4ZMMzMRgF9guJF7v5C3GsmIhJnmjhIsl1j1w5Y6u73BT8KAEQkI2hVQcl2mvVPRLKaVhWUbKYgQCSBtGCQiKQSBQEiCRRZMKiyojLZVZFAJDDTGgKSjRQEiCSYFgxKLcoLkGymIEAkQXQrIHUpL0CyVUPzBIhIC8UuHXzRg89huW2TXSUREUBBgEjchUIhJt4+n6qqKi1aIyIpRUGASALkFrRTMqCIpBzlBIhI1tMIAclWCgJEJOtphIBkKwUBIiJohIBkJ+UEiIhQfQinFhSSbKGeABERwrcELp29gvOmL9VtAcka6gkQiSNNEJRe8grak5Obk+xqiCSMegJE4khrBaQfjRSQbKIgQCTOtFZAeqko38VFv1tKcXGxAgHJeAoCRET2YxoyKFlBQYCISC00ZFCygYIAkThRUqCIpDoFASJx4O4UFxcrKVBEUpqCAJE4iIwK0LLBIpLKkhYEmFmOmb1pZs8Ez7ub2etmtsHM5ppZflDeNni+IdjeLeYc1wTl683spCS9FZFaaVSAiKS6ZPYE/BvwXszz3wB3ufu3gS+AKUH5FOCLoPyuYD/MrBdwDtAbGAs8aGaa5UNEWoXmC5BskJQgwMy6AqcCvw+eGzAamB/sMhs4LXg8IXhOsH1MsP8E4Al3L3f3j4ENwOCEvAERyXhaWVCyQbJ6Au4GrgSqguedgC/dvSJ4vgXoEjzuAmwGCLaXBvtHy2s5RkSkxTRMUDJdwoMAMxsHfO7uqxP4mpeY2SozW7V169ZEvayIiEhKS0ZPwHBgvJltAp4gfBvgHuAgM4ssaNQVKA4eFwOHAwTbDwS2x5bXckw17j7D3Qe5+6DOnTu37rsRERFJUwkPAtz9Gnfv6u7dCCf2veDu5wJLgYnBbpOAPwePFwbPCba/4OFMnYXAOcHoge5AT2BFgt6GSJ00SVDmUHKgZLpUmifgKuBXZraB8D3/mUH5TKBTUP4r4GoAd38X+BOwDvgrcLm7a1YWSTqtHJg5Ksp3azEhyWi5De8SP+6+DFgWPP6IWrL73X0PcGYdx98G3Ba/Goo0T25BOwUBGSO8mNC8fx9Phw4dkl0ZkVaVSj0BImlPtwIyk0YJSKZSECDSinQrIDMpN0AylYIAkRaq+QWh6YIzjyYOkkylIECkhUKhEOfctUhfEBlOtwQkEyU1MVAkU+S0LVQugIikHQUBIq2gonw3l85eQVVFufIBRCRt6HaASCvJK2hPnvIBMpaSAyUTKQgQEWkETRwkmUhBgIhIo5lGCUhGURAg0gKaHCj7aJSAZBIFASItoMmBRCSdKQgQaSFNDpRdlCAomURBgIhIE2j2QMkkCgJEmkn5ANlLeQGSKTRZkEgzuDvFxcVc+MBiLLdtsqsjCRYbABYVFWFmSa6RSPOoJ0CkGSIJgQoAslNkhsjzpi/VbQFJa+oJEGmm3IJ2GhWQxfIK2pOTm5Psaoi0iHoCREREspSCAJEmUkKgiGQKBQEiTRCbEKhbAaI5AyTdKQgQaQIlBEqsivJdmjNA0pqCAJEm0gyBEisnv1C9AZK2FASIiLSAlhiWdKYgQESkxbTEsKQnBQEiIq1AUwlLOlIQINJIGhooIplGQYBII0VGBmhooNRGwwUlHSkIEGlA7B93jQyQumiJYUlHCgJEGhAKhTj7zmcoKSlJdlUkxSkvQNKNggCRxjBj6qzluhUgIhlFQYBII+XkFya7CpIGlBsg6URBgEg9NCJAmsLdKSkp4Zy7Fik3QNKCggCRemhEgDRFRflups5arrUlJG0oCBBpgEYESFPk5BfqloCkDQUBIrWI/BHXrQBpDg0XlHSRm+wKiKSiUCjEedOXsm/PLt0KkGbRcEFJB+oJEKlDXkF78nQrQEQymIIAERGRLJXwIMDMDjezpWa2zszeNbN/C8q/YWZLzOzD4HfHoNzM7F4z22Bmb5vZMTHnmhTs/6GZTUr0exERqYuSAyUdJKMnoAL4v+7eCxgKXG5mvYCrgefdvSfwfPAc4GSgZ/BzCTAdwkEDcCMwBBgM3BgJHESay90pLS2ltLQ02VWRNKfkQEkHCU8MdPdPgU+DxyEzew/oAkwARga7zQaWAVcF5Y95OJx+zcwOMrPDgn2XuPsOADNbAowFHk/Ym5GMEwqFmHj7fKqqqig65FvJro6kuZz8QsrKyigqKsLMkl0dkf0kNSfAzLoBA4HXgUODAAHgn8ChweMuwOaYw7YEZXWVi7RIbkE7TREsrUK9AZLqkjZE0MwOAJ4EfunuZbFRsru7mbXajTQzu4TwrQS+9S1d3UntNEWwxENOfiGlpaW4O2amXgFJKUkJAswsj3AAMMfdnwqKPzOzw9z906C7//OgvBg4PObwrkFZMV/fPoiUL6vt9dx9BjADYNCgQcrSkVpFpgjWlK/SmirKdzP5/r9S0KETObk5/PGno+jQoUOyqyUCJGd0gAEzgffc/c6YTQuBSIb/JODPMeUXBKMEhgKlwW2DxcCJZtYxSAg8MSgTabJIL4CmCJZ4yMkvDOadaJ/sqohUk4yegOHA+cA7ZrYmKPt/wO3An8xsCvAJcFaw7VngFGADsAu4EMDdd5jZLcDKYL+bI0mCIk3h7hQXF6sXQOIuEmzqloCkimSMDlgO1PXpH1PL/g5cXse5HgEeab3aSTbSbQBJlIryXUyZsYx5/z5etwQkJWjGQBG0UqAkjtYUkFSiIECymkYEiEg2UxAgWS1yK0ArBUqiaDphSSUKAiTr6VaAJFJF+W4u+t1SiouLFQhI0ikIkKylWwGSPKaZBCUlKAiQrBQ7LFC3AiQZlCAoqUBBgGQlDQuUZFNugKQCBQGSdTQ7oKQCLS4kqUBBgGQdjQiQVBFZXCiywJBIoikIkKykXgBJBZHFhc767/9Vj4AkhYIAEZEkyskvVJKgJE1SlhIWSbTY4YC64pJUo4WFJFkUBEhWCIVCTLx9PvkHdKSqolz5AJJSIkmCWlhIEk23AyTjxY4GCK/prq5XST05+YUaMigJpyBAMpomBZJ0oemEJRkUBEjGig0ANCmQpAeLBgLqFZBEUBAgGUkBgKQv49LZKzhv+lIlsUrcKTFQMpKmBZZ0llfQnpzcnGRXQ7KAegIk42haYMkUWl9A4k1BgGQUJQJKpnB3SkpKOOeuRbotIHGjIEAyim4DSKaoKN/F1FnLISdfvQESNwoCJCO4e3QhFt0GkEyRk1+ooYMSV0oMlIwQmRGwqqqKnPzCZFdHpJWFhw7OvGQkHTp0oEOHDppeWFqFegIkY+QWtFMAIBnMtOKgtDoFAZLWItnTkcWBRDJZTn6hpheWVqUgQNJWZCTAedOX8pOZL2k0gGSFyGJD6g2Q1qAgQNJS7FDANrkFWhRIsop6A6S1KAiQtBHp+q+qqtKUwJLVNGJAWouCAEkboVCIs+98hvXr1ysAEIlZbCgyPFYBgTSVhghKyquW/GfG1FnLNQpABIgsNlRVUU5lRQWPXDqKLl26aPigNJp6AiSlRe79T7x9PpPv/yuVFZUKAERi5BW0D3JiTLcIpMkUBEjKqrkcsL78RRqiQECaRkGApJRI139paSlbtmzRvX+RJgsHAlu2bFGegDRIOQGSMiJX/j+bs5p9e3axd9dOXf2LNEt4dsGc/AJmXjKSoqIizEzTDct+FARIUsWulx4Khbjowedof3BX8grQ5D8iLRAJoCff/9fgeUF07YEIBQWiIECSIjbj/6IHn6OqqgpAV/4irSz2/9Tk+/9KQYdOGk0gUQoCJGFqu+qPrPqXk+zKiWSBnPxC8graU1WRQ+XOkFYmFAUBEh+xX/gAZkYoFOLCBxZXu+rXl79IMtWeO1BUVMTOnTujzyVzpX0QYGZjgXuAHOD37n57kquUdSJX9gcccAChUGi/K30g2gVpuW31xS+SQmrLHbjn/wziV3Pf5OGLv09RUVG1YF49BpklrYMAM8sBHgBOALYAK81sobuvS27NMlNtV/cAZWVlXDLzJe48eyC/eOyVWq/0Y7sgRST1xOYORGbljMxGuHfXzmCfr3sMYik4SF9pHQQAg4EN7v4RgJk9AUwAsjoIiFyJ1+zKq/klXlNk37q213V1HxnKF/nDoSt9kfQWCQiiwXvMSJ1Ij0H1/Qt45NJR1XoNGlLz740CieRI9yCgC7A55vkWYEgiK1BWVpbIl2uUsrIyLnxwMY/+7KRqw4HKyso4/64FVFVW1XpcQYdvULWvnL27v6rz3Llta8/er9y7u9rvmvbt+SqckVzH9ubuG89zqx717+se/hwl+t88Vdsjm+tRuXcPU2Ysa/DvR6yaf29y2xYy++cnV/ubla0S2QbpHgQ0ipldAlwSPN1pZutbcLqDgW0tr1X8Hf7rZNegQWnTlmkg4W05MPLgvy6pb7d0pM9l62lSWx7+X3GsSfpryefyiLo2pHsQUAwcHvO8a1BWjbvPAGa0xgua2Sp3H9Qa58p2asvWo7ZsPWrL1qO2bD3xast0XztgJdDTzLqbWT5wDrAwyXUSERFJC2ndE+DuFWY2FVhMeIjgI+7+bpKrJSIikhbSOggAcPdngWcT+JKtcltBALVla1Jbth61ZetRW7aeuLSlaZlJERGR7JTuOQEiIiLSTFkdBJhZjpm9aWbPBM9nmdnHZrYm+BkQlJuZ3WtmG8zsbTM7JuYck8zsw+BnUkz5sWb2TnDMvZbhM2DU0pZmZreZ2Qdm9p6Z/SKmXG1Zj1ra8qWYz2SJmS0IytWWDailLceY2RtBWy43s28H5W3NbG7QLq+bWbeYc1wTlK83s5NiyscGZRvM7OqEv7kEq6UtRwdtudbMZptZblCuz2U9zGxT8F7XmNmqoOwbZrYkaJclZtYxKI9/W7p71v4AvwL+B3gmeD4LmFjLfqcAfwEMGAq8HpR/A/go+N0xeNwx2LYi2NeCY09O9vtNcFteCDwGtAmeH6K2bF5b1tj2JHCB2rLZn8sPgKODxz8DZsU8fih4fA4wN3jcC3gLaAt0BzYSTkLOCR73APKDfXol+/0mqi0JX0BuBr4TbLsZmKLPZaPacRNwcI2y/wKuDh5fDfwmUW2ZtT0BZtYVOBX4fSN2nwA85mGvAQeZ2WHAScASd9/h7l8AS4CxwbYO7v6ah/9VHgNOi8sbSQF1tOVPgZs9mFbO3T8PytWW9ajvc2lmHYDRwIKgSG1Zjzra0oHIdGwHAiXB4wnA7ODxfGBMcAU1AXjC3cvd/WNgA+HpyqNTlrv7XiAyZXlGqqUtOwF73f2D4PkS4EfBY30umy728zebr99/3Nsya4MA4G7gSqDmHLq3Bd0ud5lZ26CstumJuzRQvqWW8kx1N/u35ZHA2Wa2ysz+YmY9g3K1Zf3upvbPJYT/Mz/v7pG5qtWW9bub/dvyYuBZM9sCnA9EVh2Ntpm7VwClhL/omtrGmepuqrflNiDXzCKT10zk64nb9LmsnwPPmdlqC89mC3Cou38aPP4ncGjwOO5tmZVBgJmNAz5399U1Nl0DHAUcR7ib5apE1y3d1NOWbYE9Hp7h6mHgkYRXLs3U05YRPwYeT2CV0lY9bXkFcIq7dwUeBe5MeOXSTG1tGVxlngPcZWYrgBBQWccppLp/dfdjgJOBy83s+7Ebg7ZN2LC9rAwCgOHAeDPbRLgbb7SZ/dHdPw26XcoJ/4EYHOxf1/TE9ZV3raU8E9XaloQj0KeCfZ4G+gWP1ZZ1q6stMbODCX8eF8Xsr7asW21tuQjo7+6vB/vMBYYFj6NtFiS4HQhsp+ltnInq+nv5qruPcPfBwN8J51uAPpf1cvfi4PfnhP82DgY+C7ryCX5Hbp/Gvy2TkRiRSj/ASL5OGjos+G2Eu79uD56fSvXkjBX+dXLGx4QTMzoGj7/htSdnnJLs95rgtrwduCimfKXasnltGTy/DJhdYx+1ZRPakvDkaNv4OpltCvBk8PhyqicG/il43JvqiYEfEU4KzA0ed+frxMDeyX6vifxc8nWyb1vgeWC0PpcNtl97oCjm8SvAWOAOqicG/lei2jLpjZLsnxof6heAd4C1wB+BA4JyAx4gnA38DjAo5viLCCcLbQAujCkfFJxnI3A/wcRMmfxToy0PInzV+g7wKuErMLVlM9oyeL4MGFtjH7Vl0z+Xpwdt9VbQpj2C8gJgXtBeKyLlwbZrg/ZaT0ymNeHM7Q+Cbdcm+30moS3vAN4L2uWX+lw2qv16BJ+9t4B3I58bwvknzwMfAn/j6y/0uLelZgwUERHJUtmaEyAiIpL1FASIiIhkKQUBIiIiWUpBgIiISJZSECAiIpKlFASIiIhkKQUBIiIiWUpBgIiISJb6/yZdizKNl8e1AAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#check on the momentum distribution: useful for an experimental check\n", + "\n", + "fig, ax = plt.subplots(1, 1, figsize=(8,5))\n", + "\n", + "ax.axvline((48400)/(2*m_e), color='red', label='Positron energy (Lab frame)')\n", + "\n", + "df_events_real_beam[\"pmu1\"] = np.sqrt(df_events_real_beam['$px_{\\mu_1}$']**2+df_events_real_beam['$py_{\\mu_1}$']**2+df_events_real_beam['$pz_{\\mu_1}$']**2)\n", + "df_events_real_beam[\"pmu2\"] = np.sqrt(df_events_real_beam['$px_{\\mu_2}$']**2+df_events_real_beam['$py_{\\mu_2}$']**2+df_events_real_beam['$pz_{\\mu_2}$']**2)\n", + "\n", + "sns.histplot(df_events_real_beam[\"$px_{\\mu_1}$\"]+df_events_real_beam[\"$px_{\\mu_2}$\"], ax = ax, label = 'Sum of muons\\' momenta')\n", + "ax.legend(loc = 'best')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Real beam spatial distribution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since the total and differential cross sections do not depend on the position, the only difference in the simulation regards the collision point. We proceed defining the new distribution and showing the new collision points. These can be simply generated using a uniform distribution over the axes y and z by selecting the points satisfying r < 1.\n", + "\n", + "\n", + "Simulating the real spatial distribution is useful in applications, because from the position of the muons we can retrieve also the position of the incoming positron from a scintillator before the target. \n", + "\n", + "The beam distribution has been chosen to avoid to have more than one positron fitting the reconstucted vertex. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "pts = np.random.uniform(-1, 1, size = (2*N, 2)) #point generation\n", + "acc = pts[np.sum(np.square(pts), axis=1) < 1] #accepted points\n", + "acc = acc[:N] #array of 10**6 valid points" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#plotting yz plane distribution\n", + "fig,ax = plt.subplots(1,1,figsize=(8.5,7))\n", + "\n", + "h = ax.hist2d(acc[:,0],\n", + " acc[:,1],\n", + " bins=1000,\n", + " cmap='autumn',\n", + " norm = clr.LogNorm()\n", + " )\n", + "\n", + "fig.colorbar(h[3], ax=ax)\n", + "\n", + "ax.set_xlabel('Y coordinate')\n", + "ax.set_ylabel('Z coordinate')\n", + "ax.set_title(\"Points distributions\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Longitudinal energy loss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "8. given that the electrons (positron) traversing the target lose energy as $E(x)=E_0 \\exp{-x/X_0}$ (with x the longitudinal coordinate of the target, the one parallel to the beam direction and $X_0$ (35.28 cm) is the Beryllium radiation length), compute the nominal beam energy $E_0$ such that muon pairs can be generated along the whole length of the target; " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to have threshold production of a muon pair along the entire length of the target, $\\sqrt {s}$ should be slightly grater than the sum of the mass of two muons:\n", + "$$\\sqrt {s} \\sim 2m_\\mu \\implies s \\sim 4m_\\mu^2 $$ \n", + "\n", + "So, we can compute $s$ taking into account the electron at rest:\n", + "$$ s = (p_{e^+}+p_{e^-})^2 = E_{e_+}^2 + E_{e_-}^2+2E_{e_+}E_{e_-}-\\vec p_{e_+}^2 = E_{e_+}^2 + m_{e_-}^2+2E_{e_+}m_{e_-}-\\vec p_{e_+}^2=$$\n", + "$$=\\vec p_{e_+}^2+m_{e_-}^2+m_{e_-}^2+2E_{e_+}m_{e_-}-\\vec p_{e_+}^2$$\n", + "By joining the two conditions we obtain:\n", + "$$2E_{e_+}m_{e_-}+2m_{e_-}^2>4m_{\\mu}^2\\Rightarrow 2E_{e_+}m_{e_-}>4m_{\\mu}^2-2m_{e_-}^2$$\n", + "And finally the condition on the energy of the positron:\n", + "$$E_{e_+}>\\frac{4m_{\\mu}^2-2m_{e_-}^2}{2m_{e_{-}}} \\sim 43.7\\,\\mathrm{GeV} $$\n", + "\n", + "The energy trend along the target:\n", + "$$E_{e_{+}}=E_0e^{-\\frac{x}{\\chi_0}}$$\n", + "\n", + "where $\\chi_0$ is the radiation length of the Berylium: $\\chi_0=35.28 \\, cm$ (PDG). In order to have the condition satisfied along the whole length of the target we impose the energy threshold at $x_{max} =3\\, cm$. Finally, to find $E_0$ satisfying the condition we explicit for $E_0$ and we obtain:\n", + "\n", + "$$E_0>\\left(\\frac{4m_{\\mu}^2-2m_{e_-}^2}{2m_{e_{-}}}\\right)e^{\\frac{x_{max}}{\\chi_0}}\\approx47.6 \\, \\mathrm{ GeV}$$ " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Threshold energy: 47571.03 MeV\n" + ] + } + ], + "source": [ + "rad_length = 35.28 #cm radiation length of Beryllium\n", + "x_max = 3 #cm target thickness\n", + "\n", + "E_0_thres = ((4*m_muon**2-2*m_e**2)/(2*m_e))*np.exp(x_max/rad_length)\n", + "print ( \"Threshold energy: {:.2f} MeV\".format(E_0_thres)) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Last Point" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "9. (optional) Take the former point into account when generating the events (i.e. the process $\\sqrt{s}$ depend on the position along the target where the $e^+ - e^-$ scattering occurrs." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Monochromatic analysis\n", + "\n", + "We now take into account the energy loss along the target lenght. \n", + "This leads to a variable pair-production probability depending on the cross-section along the target.\n", + "We then generate the x-coordinates spread and retrieve the $\\theta^*$ distribution, **both through an accept-reject method**. \n", + "\n", + "We have observed that with an $s = 220^2 \\, MeV^2$ the energy is not sufficient to reach a non-zero cross section through all the target. \n", + "We then choose a new value for the invariant mass $s = 225^2 \\, MeV^2$, corresponding to a positron energy $E_0 = 48658.5 \\,MeV$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "def s_bremss(x, E0):\n", + " '''\n", + " This function computes the s variable depending on the initial energy E_0 and the position z\n", + " \n", + " Parameters:\n", + " x: Position inside the medium\n", + " E0: Incoming energy\n", + "\n", + " '''\n", + " \n", + " return 2 * m_e**2 + 2* E0 * np.exp(-x/rad_length) * m_e\n", + "\n", + "def sigma_bremss(x, E0):\n", + " '''\n", + " Cross-section computation directly from the initial energy and position of interaction\n", + " \n", + " Parameters:\n", + " x: Position inside the medium\n", + " E0: Incoming energy\n", + "\n", + " '''\n", + " \n", + " return sigma(s_bremss(x, E0))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "E_0 = 48658.5 #impinging beam energy\n", + "n_slice = 20 #slices for the beryllium target\n", + "\n", + "scal = x_max/n_slice* 1e-24 *38937 *rho_elec #scaling factor for the conversion from MeV to cm^2\n", + "\n", + "slices = np.linspace(0,x_max,n_slice)\n", + "slices = (slices[1:] + slices[:-1])/2 #taking the middle points for each slice\n", + " \n", + "tot_par1w = 60*60*24*7*10**6 #number of particles for 1 week @10**6 Hz\n", + "\n", + "part_per_slice = np.zeros(n_slice) #slices vector initialization\n", + "part_per_slice[0] = tot_par1w\n", + "\n", + "#computation of interacting particles in each slice\n", + "for i in range(n_slice-1):\n", + " part_per_slice[i+1] = part_per_slice[i]*(1-(scal * sigma_bremss(slices[i], E_0)))\n", + "\n", + "part_per_slice = part_per_slice[:-1] - part_per_slice[1:]\n", + "part_per_slice = np.asarray(part_per_slice)\n", + "\n", + "#plot\n", + "plt.scatter(slices,part_per_slice/part_per_slice.sum())\n", + "\n", + "#intep1d to find the normalised distribution for the interaction points\n", + "func_pts_dbt = interp1d(slices,\n", + " part_per_slice/part_per_slice.sum(),\n", + " fill_value = \"extrapolate\"\n", + " ) \n", + "\n", + "plt.plot(slices, func_pts_dbt(slices))\n", + "\n", + "plt.title(\"Distribution of interaction points\")\n", + "plt.xlabel(\"x [cm]\")\n", + "plt.ylabel(\"Number of interactions\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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wPIVg05V57AbOr23RzKwWPB3YqmnMlkhE3A/cL2l1RDxTpzKZWR2UW8xx2Oty2RGqdIrvFEkrgXnZayLiXbUolJnVR+lijvl8nmXX3wPgdbmsIpUGke8A36Cwr8eB2hXHzOqpdIwECi0U1OCCWcuoNIjsj4gbaloSM2uIXFc3B/a+yBVr+hneu4fjeuZ4zxKrWKVB5PuSLgHuIO2FDpDZfdDMWlyuq5sDkxw87MhUGkSKe5l/MpMWwOurWxwzayYeaLfDqeg3IiJOKvM4bACRtErSDkmPZtK6JW2U9GT6OSOlS9K1kgYlDUg6LXPN0pT/SUlLM+mnS3okXXOtJPfkmlVBccB9YGCAZdfdw9LrfuBlU6ysiloiki4qlx4RNx/m0tXA14FsvquAH0XECklXpedXAu8B5qfHmcANwJmSuoHPAH0UWj+bJa2LiN+lPB8BHgTWA4uAuyupk5mNLruI43E9c0bGTLybopWqtDvrLZnjHHAO8BAHB4dDRMRPJM0rSV4MnJ2ObwLuoxBEFgM3R0QAD0iaLmlmyruxOP4iaSOwSNJ9wLSIeCCl3wy8HwcRs6ooHSPJLjMP7t6ygoqCSET8dfa5pOnAmnG+Z29EDKXj3wC96XgW8Gwm37aUNlb6tjLph5C0HFgOMHfu3HEW28y8v7uVGu+fEXuAk472zVOrI472dSp4n5UR0RcRfT09PbV+O7O2luvqJjetGygMvA8NDXmsZAKrdEzk+7z6Zd8J/GvgtnG+Z17SzIgYSt1VO1L6dmBOJt/slLadV7u/iun3pfTZZfKbWY0VB97z+TxXrn0Y5DvcJ6pKx0S+lDneDzwTEdtGy3wY6yhMGV6Rft6ZSb9M0hoKA+svpECzAfjb4iwu4Fzg6ojYJWm3pLMoDKxfhJenN6uL0oF3j5VMXJWOidwvqZdXB9ifrOQ6SbdSaEWcKGkbhVlWK4DbJF0MPANckLKvB84DBoHfAx9K771L0ueBTSnf5zI3OV5CYQbYsRQG1D2oblYn2YF3j5VMXJV2Z10A/D2FbiQBX5P0yYhYO9Z1EXHhKKfOKZM3gEtHeZ1VwKoy6f3AqWMW3szqwrO3JqZKu7P+BnhLROwAkNQD/BAYM4iY2cTiTa8mnko/2Y5iAEmeO4JrzWwC8aZXE0ulLZEfpAHuW9Pzv6IwhmFmVla5Ta+s/Rxuj/U/pnBz4Ccl/QXwp+nUT4Fbal04M2ttke4jGR4epqOjw11bbehwLZH/BVwNEBHfBb4LIOnfpHP/roZlM7MWt++l5/notf10/dHrPHOrTR0uiPRGxCOliRHxSJk1sczMDjF56jR3bbWxwwWR6WOcO7aK5TCzNle6n7u7tdrD4T7FfkkfKU2U9GFgc22KZGbtqDD91zO22s3hWiKXA3dI+g+8GjT6gMnAB2pYLjNrQ74hsf2MGUQiIg+8TdI7efXO8P8TET+uecnMrC2V3pBYXFnbs7daU6VrZ90L3FvjspjZBJHr6h7ZLXF47x46clM9e6tFVXqzoZlZ1RUXcezMdbmbq0U5iJhZU/C6W63Jn46ZNQ2vu9V63BIxs6bjmxNbh1siZmY2bm6JmFlTKt7hPjw8DHgKcLNyEDGzppTdx91TgJtX3UO6pDdJ2pJ57JZ0uaTPStqeST8vc83VkgYlPSHpzzPpi1LaoKSr6l0XM6utXFc3U7qmk+vqJjetu9HFsTLq3hKJiCeAhQCSOoHtwB3Ah4CvRsSXsvklnQwsAU4BXgv8UNIb0+nrgHcD24BNktZFxGP1qIeZ1ZcXcGxOje7OOgd4KiKekTRansXAmojYB/xK0iBwRjo3GBFPA0hak/I6iJi1oWL3VrFbq7e310GlCTT6X30Jr265C3CZpAFJqyTNSGmzgGczebaltNHSDyFpuaR+Sf07d+6sXunNrK5yXd1MOX46+XyegYEBll13j+8nabCGBRFJk4H3Ad9JSTcAb6DQ1TUEfLla7xURKyOiLyL6iou9mVlrKi4pf/nq++k8tstjJQ3WyO6s9wAPpZWCiysGAyDpRuCu9HQ7MCdz3eyUxhjpZtbGimtugcdKGq2R/9oXkunKkpSdt/cB4NF0vA5YImmKpJOA+cDPgE3AfEknpVbNkpTXzCYQb3bVWA1piUiaSmFW1UczyV+UtBAI4NfFcxGxVdJtFAbM9wOXRsSB9DqXARuATmBVRGytVx3MrHl4s6vGaUgQiYg9wAklaR8cI/81wDVl0tcD66teQDNrOaWzt3xTYn00eoqvmVnVeOHG+nMQMbO24oH2+nIQMbO2Urq51YIFCxxIasj/smbWdoqbW12ycgMDAwMMDQ2NrAZs1eUgYmZty7sk1p67s8ysrXn6b205iJhZ2ysdJ+nt7XUwqRL/C5rZhFAcJ3H3VnW5JWJmE4rvJakuBxEzm3B8L0n1OIiY2YTjMZLq8b+YmU1IHiOpDrdEzGxC8xjJ0XEQMTNLhj1WcsQcRMxswisOtOfzea5c+zAILydfIQcRM5vwigPtw3v3cFzPHHdvHQEHETMzvG/7eDmImJmV8C6JlWtYeJX0a0mPSNoiqT+ldUvaKOnJ9HNGSpekayUNShqQdFrmdZam/E9KWtqo+phZe8l1dZOb1t3oYjS9RrdE3hkRv808vwr4UUSskHRVen4l8B5gfnqcCdwAnCmpG/gM0AcEsFnSuoj4XT0rYWbtqditVdyLpKOjw91bJRodREotBs5OxzcB91EIIouBmyMigAckTZc0M+XdGBG7ACRtBBYBt9a32GbWjrID7h25qe7eKqOR4TSAeyRtlrQ8pfVGxFA6/g3Qm45nAc9mrt2W0kZLP4ik5ZL6JfXv3LmzmnUwszaX6+pmStd0d2+NopEtkT+NiO2S/hWwUdIvsicjIiRFNd4oIlYCKwH6+vqq8ppmZtbAlkhEbE8/dwB3AGcA+dRNRfq5I2XfDszJXD47pY2WbmZmddCQICJpqqSu4jFwLvAosA4ozrBaCtyZjtcBF6VZWmcBL6Rurw3AuZJmpJlc56Y0M7OqKw60Dw0NjQy2T3SN6s7qBe6QVCzDP0fEDyRtAm6TdDHwDHBByr8eOA8YBH4PfAggInZJ+jywKeX7XHGQ3cys2nz/yKEaEkQi4mngT8qkPwecUyY9gEtHea1VwKpql9HMrJxcVzfHHNPpqb9Js03xNTNreqVTfyfy5lYTp6ZmZlWUnfo7kTe3ckvEzKwKJurmVm6JmJnZuLklYmZWJRNxCXkHETOzKikOuE+kgfb2rZmZWQNMtIF2BxEzsxrIdXUz5fjpB91P0o4cRMzMamTfS89z6Y0b27o14jERM7Mamjx1WlsPtrdXbczMmszLe3a39fiIWyJmZjWWXW8L2qtF4iBiZlYH7boCsIOImVmdtGOLxEHEzKyO2q1F4iBiZlZn7bRYo4OImVkDtMs6Ww4iZmYN0C7rbNW9tJLmSLpX0mOStkr6REr/rKTtkrakx3mZa66WNCjpCUl/nklflNIGJV1V77qYmR2NdlhnqxEtkf3Af46IhyR1AZslbUznvhoRX8pmlnQysAQ4BXgt8ENJb0ynrwPeDWwDNklaFxGP1aUWZmZV0spjJHUPIhExBAyl4xclPQ7MGuOSxcCaiNgH/ErSIHBGOjcYEU8DSFqT8jqImFnLadUxkoaWUtI84M3AgynpMkkDklZJmpHSZgHPZi7bltJGSy/3Pssl9Uvq37lzZzWrYGZWFYUxktbr1mpYEJF0PHA7cHlE7AZuAN4ALKTQUvlytd4rIlZGRF9E9PX09FTrZc3MqirX1U1uWneji3FEGjI7S9IkCgHkloj4LkBE5DPnbwTuSk+3A3Myl89OaYyRbmbWklqtW6sRs7MEfAt4PCK+kknP3rb5AeDRdLwOWCJpiqSTgPnAz4BNwHxJJ0maTGHwfV096mBmViut1q3ViJbI24EPAo9I2pLSPgVcKGkhEMCvgY8CRMRWSbdRGDDfD1waEQcAJF0GbAA6gVURsbV+1TAzq41WWmOrEbOz/i+gMqfWj3HNNcA1ZdLXj3WdmVmrapWbEZurNGZmNqIVbkb0sidmZk2umW9GdEvEzMzGzS0RM7MW0KxTfx1EzMxaQLNuZuUgYmbWIppx6q+DiJlZC2m2qb/N0almZmYVa6apv26JmJm1qGaY+usgYmbWwho9a8tBxMyshTV61paDiJlZi2vkrC0HETOzNtCoFomDiJlZm2jEQLuDiJlZG6n3QLuDiJlZG6l3t5ZvNjQzazO5rm6mHD+dfD7P8PBwTd/LQcTMrA3te+l5Lr1xY83vZm/5ICJpkaQnJA1KuqrR5TEzaxaTp04jn88zNDRUsxZJSwcRSZ3AdcB7gJOBCyWd3NhSmZk1h5f37K75+lqtPrB+BjAYEU8DSFoDLAYeq8Wb7d29i30vPk/HK68wvHfPEf98ec9u9r64a1zXVutnI8swUd+7Gcrg9564n/uUrhm1+Doc0epBZBbwbOb5NuDM0kySlgPL09OXJD0xzvc7EfjtOK9tNq5L82mXeoDr0nRe+wXg6OryunKJrR5EKhIRK4GVR/s6kvojoq8KRWo416X5tEs9wHVpVrWoS0uPiQDbgTmZ57NTmpmZ1UGrB5FNwHxJJ0maDCwB1jW4TGZmE0ZLd2dFxH5JlwEbgE5gVURsreFbHnWXWBNxXZpPu9QDXJdmVfW6KCKq/ZpmZjZBtHp3lpmZNZCDiJmZjZuDSBmHW0pF0hRJ307nH5Q0rwHFPKwK6rFM0k5JW9Ljw40oZyUkrZK0Q9Kjo5yXpGtTXQcknVbvMlaignqcLemFzGfy3+tdxkpJmiPpXkmPSdoq6RNl8rTK51JJXZr+s5GUk/QzSQ+nevyPMnmq+/0VEX5kHhQG6J8CXg9MBh4GTi7JcwnwjXS8BPh2o8s9znosA77e6LJWWJ93AKcBj45y/jzgbkDAWcCDjS7zOOtxNnBXo8tZYV1mAqel4y7gl2V+x1rlc6mkLk3/2aR/5+PT8STgQeCskjxV/f5yS+RQI0upRMTLQHEplazFwE3peC1wjiTVsYyVqKQeLSMifgLsGiPLYuDmKHgAmC6pPvuDHoEK6tEyImIoIh5Kxy8Cj1NYRSKrVT6XSurS9NK/80vp6aT0KJ09VdXvLweRQ5VbSqX0l2kkT0TsB14ATqhL6SpXST0A/jJ1M6yVNKfM+VZRaX1bwVtTd8Tdkk5pdGEqkbpE3kzhL9+slvtcxqgLtMBnI6lT0hZgB7AxIkb9TKrx/eUgMrF9H5gXEQuAjbz614k1zkPA6yLiT4CvAd9rbHEOT9LxwO3A5RGxu9HlORqHqUtLfDYRcSAiFlJYweMMSafW8v0cRA5VyVIqI3kkHQO8BniuLqWr3GHrERHPRcS+9PSbwOl1KlsttMUSOBGxu9gdERHrgUmSTmxwsUYlaRKFL91bIuK7ZbK0zOdyuLq02mcTEc8D9wKLSk5V9fvLQeRQlSylsg5Ymo7PB34caZSqiRy2HiV90++j0A/cqtYBF6XZQGcBL0TEUKMLdaQk/VGxf1rSGRT+jzbbHyhAYeYV8C3g8Yj4yijZWuJzqaQurfDZSOqRND0dHwu8G/hFSbaqfn+19LIntRCjLKUi6XNAf0Sso/DL9o+SBikMki5pXInLq7AeH5f0PmA/hXosa1iBD0PSrRRmx5woaRvwGQqDhkTEN4D1FGYCDQK/Bz7UmJKOrYJ6nA/8J0n7gT8AS5rwD5SitwMfBB5JffAAnwLmQmt9LlRWl1b4bGYCN6mwYV8HcFtE3FXL7y8ve2JmZuPm7iwzMxs3BxEzMxs3BxEzMxs3BxEzMxs3BxEzMxs3BxEzMxs3BxGzOpI0T9IfMvciHO3r3SvpJUl91Xg9syPlIGJWf0+ltY2OWkS8E+ivxmuZjYeDiFmVSHpLWhE5J2lq2hTosIvfSbooXfewpH9Maasl3SDpAUlPpw2RVkl6XNLqmlfGrEJe9sSsSiJik6R1wBeAY4F/ioiyOxgWpeXEPw28LSJ+K6k7c3oG8FYK65qto7A0x4eBTZIWRsSWGlTD7Ig4iJhV1+coLH65F/h4BfnfBXwnIn4LEBHZDau+HxEh6REgHxGPAEjaCswDtlSx3Gbj4u4ss+o6ATiewharuaN8reIy/cOZ4+Jz/wFoTcFBxKy6/jfw34BbgL+rIP+PgX8v6QSAku4ss6bnv2bMqkTSRcArEfHPaSnu/yfpXRHx49GuScvzXwPcL+kA8HOaeEl+s1JeCt6sjtL+3XdFRNW2LJV0H/BfIsJTfa3u3J1lVl8HgNdU82ZD4PXAK9V4PbMj5ZaImZmNm1siZmY2bg4iZmY2bg4iZmY2bg4iZmY2bv8ftSJVgCuc4o0AAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#accept-reject according to the distribution found just above\n", + "pts_dbt = np.random.uniform( 0, x_max, 3*N)\n", + "check = np.random.uniform( func_pts_dbt(3), func_pts_dbt(0.16), 3*N) \n", + "accepted_mono = pts_dbt[check < func_pts_dbt(pts_dbt)]\n", + "\n", + "sns.histplot(accepted_mono) #hist of accepted points\n", + "plt.xlabel(\"x [cm]\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "#accept-reject on previously accepted points according to cross section in each slice \n", + "angles = np.random.uniform( 0, np.pi, len(accepted_mono))\n", + "ang_check = np.random.uniform(0, pf(s_bremss(accepted_mono, E_0),np.pi/2), len(accepted_mono))\n", + "\n", + "df_energies_bremss_mono = pd.DataFrame(pd.Series(s_bremss(accepted_mono, E_0)), columns = ['energies'])\n", + "df_energies_bremss_mono[\"angles\"] = angles\n", + "df_energies_bremss_mono[\"emission_pt\"] = accepted_mono\n", + "df_energies_bremss_mono[\"check\"] = ang_check\n", + "df_energies_bremss_mono[r\"$\\theta^*$\"] = df_energies_bremss_mono.angles[df_energies_bremss_mono.check < pf(df_energies_bremss_mono.energies, df_energies_bremss_mono.angles)]\n", "\n", + "df_energies_bremss_mono = df_energies_bremss_mono.dropna()\n", + "df_energies_bremss_mono = df_energies_bremss_mono.iloc[:N]\n", "\n", + "#montecarlo simulation for the two muons momentum with respect to the previously accepted angles\n", + "df_events_bremss_mono = pd.DataFrame(mc_df_sampling(df_energies_bremss_mono, m_e, m_muon).T,\n", + " columns = [\n", + " '$px_{\\mu_1}$',\n", + " '$py_{\\mu_1}$',\n", + " '$pz_{\\mu_1}$',\n", + " '$px_{\\mu_2}$',\n", + " '$py_{\\mu_2}$',\n", + " '$pz_{\\mu_2}$'\n", + " ]\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#plots for muon_1\n", + "\n", + "fig, ax = plt.subplots(1,3, figsize = (18,6))\n", + "\n", + "#px\n", + "sns.histplot(df_events_bremss_mono['$px_{\\mu_1}$']/1000,\n", + " ax = ax[0],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#73683B'\n", + " )\n", + "#py\n", + "sns.histplot(df_events_bremss_mono['$py_{\\mu_1}$']/1000,\n", + " ax = ax[1],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#4F5D75'\n", + " )\n", + "#pz\n", + "sns.histplot(df_events_bremss_mono['$pz_{\\mu_1}$']/1000,\n", + " ax = ax[2],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#D64045'\n", + " )\n", + "\n", + "plt.suptitle('Momenta histogram for $\\mu_1$ (Beryllium target - monochromatic)')\n", + "plt.show()" + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "def theta_lab(theta_star, s):\n", + " betas = beta(s)\n", + " beta_star = np.sqrt(1-4*m_muon/s)\n", + " return np.arctan(np.sin(theta_star)*np.sqrt(1-betas**2)/(np.cos(theta_star)+betas/beta_star))\n", + "\n", + "pd_df[r\"$\\theta_{lab}$\"] = theta_lab(pd_df.angles, pd_df.energies)\n", + "pd_df[\"random_number\"]=np.random.randint(1,3, len(pd_df))\n", + "pd_df[r\"$\\theta_{lab}$\"] = pd_df[r\"$\\theta_{lab}$\"]*(-1)**pd_df[\"random_number\"]\n", + "\n", + "sns.histplot(pd_df[r\"$\\theta_{lab}$\"], bins = 2000)\n", + "plt.title('Angular distribution in the LAB')\n", + "plt.xlabel(r'$\\theta$ [rad]')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Non monochromatic analysis\n", + "Now, we have to take into account that the impinging beam energy follows a Gaussian distribution. Then for each starting energy, the beam will have a different cross-section value and maximum pair-production distance. \n", + "In our analysis this leads to different pair-production energy distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "def max_d(E0, m_e, m_muon, rad_length):\n", + " '''\n", + " The function returns the maximum distance for producing a muon pair from e+e- annihilation\n", + " \n", + " Parameters: \n", + " E0: incoming energy\n", + " m_e: e mass\n", + " m_muon: muon mass\n", + " rad_length: radiation length of the considered medium\n", + " \n", + " '''\n", + " return np.log(E0/((4*m_muon**2-2*m_e**2)/(2*m_e)))*rad_length" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "n_slice = 20 #slices\n", + "\n", + "scal = x_max/n_slice* 1e-24 *38937 *rho_elec #scaling factor for the conversion from MeV to cm^2\n", + "\n", + "tot_par1w = 60*60*24*7*10**6 #number of particles for 1 week\n", + "func_pts_dbt_real = []\n", + "\n", + "#from CoM to LAB\n", + "energies_gauss = energies_gauss[energies_gauss > 4 * m_muon**2] #check on threshold production\n", + "energies_gauss_lab = energies_gauss / (2 * m_e) #passing from s to E_e+\n", + "\n", + "size = len(energies_gauss_lab) \n", + "\n", + "#empty list that will contain either the size of the target or the maximum distance that allows muon generation,\n", + "#depending on the outcome of the if statement below\n", + "x_max_arr = []\n", + "\n", + "#cycle over all the generated energies\n", + "for E in energies_gauss_lab:\n", + " \n", + " #if the max distance to have p.production is greater then the target lenght assign automatically 3 cm,\n", + " #otherwise we will have p.production also after the target (x_max > 3 cm)\n", + " if max_d(E, m_e, m_muon, rad_length) < x_max:\n", + " d_max = max_d(E, m_e, m_muon, rad_length) #cm\n", + " else:\n", + " d_max = 3 #cm\n", + " \n", + " x_max_arr.append(d_max)\n", + " \n", + " slices = np.linspace(0,d_max,n_slice)\n", + " slices = (slices[1:] + slices[:-1])/2 #middle points for each slice\n", + "\n", + " part_per_slice = np.zeros(n_slice)\n", + " part_per_slice[0] = tot_par1w\n", + "\n", + " #computation of interacting particles in each slice\n", + " for i in range(n_slice-1):\n", + " part_per_slice[i+1] = part_per_slice[i]*(1-(scal * sigma_bremss(slices[i], E)))\n", + " \n", + "\n", + " part_per_slice = part_per_slice[:-1] - part_per_slice[1:]\n", + " part_per_slice = np.asarray(part_per_slice)\n", + "\n", + " #array of interp1d functions, one for each energy in the beam\n", + " func_pts_dbt_real.append(interp1d(slices,part_per_slice/part_per_slice.sum(), fill_value = \"extrapolate\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "#accept-reject according to the distribution for each energy in the beam\n", + "pts_dbt = np.random.uniform(0, x_max_arr, size)\n", + "\n", + "#random uniform that generates one point between the minimum and the maximum of the\n", + "#distibution (interp1d) for each different energy in the beam. \n", + "check_uniform_real = np.random.uniform([func(i) for i,func in zip(x_max_arr,func_pts_dbt_real)],\n", + " [func(0.16) for func in func_pts_dbt_real], size) \n", + "\n", + "df_pts_bremss_real = pd.DataFrame(pd.Series(energies_gauss_lab), columns = ['energies_lab'])\n", + "df_pts_bremss_real[\"pts\"] = pts_dbt\n", + "df_pts_bremss_real[\"check\"] = check_uniform_real\n", + "df_pts_bremss_real[\"accepted\"] = df_pts_bremss_real.pts[df_pts_bremss_real.check < [func(i) for i,func in zip(df_pts_bremss_real.pts,func_pts_dbt_real)]]\n", + "df_pts_bremss_real = df_pts_bremss_real.dropna()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1,2, figsize = (18,6))\n", + "\n", + "\n", + "sns.histplot(df_pts_bremss_real.accepted, ax = ax[0]) #hist of accepted points\n", + "ax[0].set_title(\"Distribution with real beam\")\n", + "ax[0].set_xlabel(\"x [cm]\")\n", + "\n", + "sns.histplot(accepted_mono, ax = ax[1]) #hist of accepted points\n", + "ax[1].set_title(\"Distribution with monochromatic beam\")\n", + "ax[1].set_xlabel(\"x [cm]\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "#accept-reject on previously accepted points according to cross section in each slice \n", + "angles = np.random.uniform( 0, np.pi, len(df_pts_bremss_real.accepted))\n", + "ang_check = np.random.uniform(0, pf(s_bremss(df_pts_bremss_real.accepted, df_pts_bremss_real.energies_lab),np.pi/2), len(df_pts_bremss_real.accepted))\n", + "\n", + "df_energies_bremss_real = pd.DataFrame(pd.Series(s_bremss(df_pts_bremss_real.accepted, df_pts_bremss_real.energies_lab)), columns = ['energies'])\n", + "df_energies_bremss_real[\"angles\"] = angles\n", + "df_energies_bremss_real[\"emission_pt\"] = df_pts_bremss_real.accepted\n", + "df_energies_bremss_real[\"check\"] = ang_check\n", + "df_energies_bremss_real[r\"$\\theta^*$\"] = df_energies_bremss_real.angles[df_energies_bremss_real.check < pf(df_energies_bremss_real.energies, df_energies_bremss_real.angles)]\n", + "df_energies_bremss_real = df_energies_bremss_real.dropna()\n", + "df_energies_bremss_real = df_energies_bremss_real.iloc[:N]\n", + "\n", + "#montecarlo simulation for the two muons momentum with respect to the previously accepted angles\n", + "df_events_bremss_real = pd.DataFrame(mc_df_sampling(df_energies_bremss_real, m_e, m_muon).T,\n", + " columns = [\n", + " '$px_{\\mu_1}$',\n", + " '$py_{\\mu_1}$',\n", + " '$pz_{\\mu_1}$',\n", + " '$px_{\\mu_2}$',\n", + " '$py_{\\mu_2}$',\n", + " '$pz_{\\mu_2}$'\n", + " ]\n", + " )\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#plots for muon_1\n", + "\n", + "fig, ax = plt.subplots(1,3, figsize = (18,6))\n", + "\n", + "#px\n", + "sns.histplot(df_events_bremss_real['$px_{\\mu_1}$']/1000,\n", + " ax = ax[0],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#73683B'\n", + " )\n", + "#py\n", + "sns.histplot(df_events_bremss_real['$py_{\\mu_1}$']/1000,\n", + " ax = ax[1],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#4F5D75'\n", + " )\n", + "#pz\n", + "sns.histplot(df_events_bremss_real['$pz_{\\mu_1}$']/1000,\n", + " ax = ax[2],\n", + " bins = int(np.sqrt(N)),\n", + " kde = True,\n", + " color = '#D64045'\n", + " )\n", + "\n", + "plt.suptitle('Momenta histogram for $\\mu_1$ (Beryllium target - non-monochromatic)')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#plot energies distribution\n", + "fig, ax = plt.subplots(1, 1, figsize=(8,5))\n", + "df_events_bremss_real[\"pmu1\"] = np.sqrt(df_events_bremss_real['$px_{\\mu_1}$']**2+df_events_bremss_real['$py_{\\mu_1}$']**2+df_events_bremss_real['$pz_{\\mu_1}$']**2)\n", + "df_events_bremss_real[\"pmu2\"] = np.sqrt(df_events_bremss_real['$px_{\\mu_2}$']**2+df_events_bremss_real['$py_{\\mu_2}$']**2+df_events_bremss_real['$pz_{\\mu_2}$']**2)\n", + "\n", + "sns.histplot(df_events_bremss_real[\"pmu1\"]+df_events_bremss_real[\"pmu2\"], label = 'Sum of muons\\' momenta')\n", + "plt.axvline((48400)/(2*m_e), color='red', label='Positron energy (Lab frame)')\n", + "\n", + "ax.legend(loc = 'best')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Babayaga comparison" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Babayaga](https://www2.pv.infn.it/~hepcomplex/babayaga.html) is an event generator based on QCD considerations. For this simulation, we have considered the BabayagaNLO package.\n", + "\n", + "We made a comparison between our results and the output of the generator for the angle distribution (in the CoM) of the $\\mu_-$ emission. The generation parameters (*input.txt*) are:\n", + "- ecms = 0.2200 GeV\n", + "- thmin = 0.0000 deg\n", + "- thmax = 180.0000 deg\n", + "- acoll. = 10.0000 deg\n", + "- emin = 0.0000 GeV\n", + "- ord = exp \n", + "- model = matched \n", + "- nphot mode = -1\n", + "- seed =700253512\n", + "- iarun = 1\n", + "- eps = .000500000\n", + "- darkmod = 0\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1,1, figsize=(8,5))\n", + "\n", + "sns.histplot(inv_cdf3(num_sorted),\n", + " ax = ax,\n", + " color = '#D64045',\n", + " stat = \"density\",\n", + " label='QED calculations'\n", + " )\n", + "\n", + "#importing babayaga results and comparison with our simulation\n", + "file_data = np.loadtxt(\"matched_el_th_exp_200.txt\", usecols=(0,1,2))\n", + "x,y = file_data[:,0],file_data[:,1]\n", + "x = x * np.pi/180\n", + "x_cen = x + (x[0] + x[1])/2\n", + "y = y / ((x[1] - x[0])*y).sum()\n", + "\n", + "plt.plot(x_cen, y, label='Babayaga results')\n", + "plt.xlabel(r'Center of mass emission angle $\\theta^*[rad]$')\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SUMMARY\n", + "\n", + "For this project, we: \n", + "- Studied the angular distribution of the emitted muons\n", + "- Generated random number using the ICDF method accordingly to the angulad distribution\n", + "- Studied the muon momenta in the lab frame\n", + "- Considered a real beam with an energy and position spread\n", + "- Considered the effects related to the presence of a thick target\n", + "- Compared the QED calculations with the Babayaga-generated events\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "#### Part 2: use the synthetic dataset to design an experiment\n", "\n", "Assume a $2$ meter long, $1.7$ Tesla dipole magnet is placed after the target. Assume a number of tracking detectors can be placed before the target, after the target before the magnet (one line) and after the magnet (two lines, one for positive the other for negative muons); those could be made of silicon pixels, with a single-hit resolution varying from 50 to 200 ${\\rm \\mu m}$. \n", @@ -50,7 +1769,7 @@ "\n", "### Contact\n", "\n", - "* Marco Zanetti \n", + "* Marco Zanetti \n", "* Camilla Curatolo \n", "* Jacopo Pazzini \n", "* Alberto Zucchetta " @@ -80,7 +1799,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.4" + "version": "3.9.1" } }, "nbformat": 4, diff --git a/matched_el_th_exp_200.txt b/matched_el_th_exp_200.txt new file mode 100644 index 0000000..0d88aac --- /dev/null +++ b/matched_el_th_exp_200.txt @@ -0,0 +1,200 @@ + -9.9999999999999978E-002 2.3838156663279226E-002 8.9408323697924336E-004 + 0.80100000000000005 9.4331973849387282E-002 1.8545703188645360E-003 + 1.7020000000000000 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