Conic_Mirror.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np;\n",
    "import matplotlib.pyplot as plt;\n",
    "\n",
    "def Quasi_Optics(Input,Size=5,F='f1'):\n",
    "    # input parameters:\n",
    "    '''\n",
    "    1.lambda;\n",
    "    2.W_in;\n",
    "    3.d_in;\n",
    "    4.angle(incident angle);\n",
    "    # next parameters just one of them need to be given.\n",
    "    5.f(focal length)\n",
    "    5.dout(distance between output beam waist and mirror center.)\n",
    "    '''\n",
    "    #1. read the data from input file.\n",
    "    #Input=input('Type in the full name of input file');\n",
    "    \n",
    "    Para={};\n",
    "    with open(Input) as File:\n",
    "        for line in File:\n",
    "            (key,val,sep)=line.split(',');\n",
    "            Para[key]=np.asfarray(np.array([val]),float)[0];\n",
    "    \n",
    "    Lambda=Para['lambda'];\n",
    "    angle=Para['angle']/2;\n",
    "    w_in=Para['W_in'];\n",
    "    print('win:',w_in);\n",
    "    d_in=Para['d_in'];\n",
    "    # beam size\n",
    "    Theta_beam=np.arctan(Lambda/(np.pi*w_in)); \n",
    "    zc=np.pi*w_in**2/Lambda;\n",
    "    print('half axis of mirror:',Size/2*w_in*np.sqrt(1+(d_in)**2/zc**2))\n",
    "    \n",
    "    #2. check which parameter we used.\n",
    "    if 'f' in  Para.keys():\n",
    "        f=Para['f'];\n",
    "        fact1=d_in/f-1;\n",
    "        fact2=np.pi*w_in**2/(Lambda*f);\n",
    "        fact2=1/(fact1**2+fact2**2);\n",
    "        w_out=w_in*np.sqrt(fact2);\n",
    "        d_out=f*(1+fact1*fact2);\n",
    "        Rin=d_in+zc**2/d_in;\n",
    "        zc_out=np.pi*w_out**2/Lambda;\n",
    "        Rout=d_out+zc_out**2/d_out;\n",
    "        print('Rin:',Rin,'\\n','dout:',d_out,'\\n','wout:',w_out,'\\n','Rout:',Rout,'\\n','dout:',d_out,'\\n');\n",
    "        \n",
    "    elif 'd_out' in Para.keys():\n",
    "        d_out=Para['d_out'];\n",
    "        a=d_out+d_in;\n",
    "        b=-(d_in**2+zc**2+2*d_in*d_out);\n",
    "        c=d_out*(zc**2+d_in**2);\n",
    "        d=b**2-4*a*c;\n",
    "        \n",
    "        f1=(-b+np.sqrt(d))/(2*a);\n",
    "        f2=(-b-np.sqrt(d))/(2*a);\n",
    "        if F=='f1':\n",
    "            f=f1;\n",
    "            fact1=d_in/f-1;\n",
    "            fact2=np.pi*w_in**2/(Lambda*f);\n",
    "            fact2=1/(fact1**2+fact2**2);\n",
    "            w_out=w_in*np.sqrt(fact2);\n",
    "            zc_out=np.pi*w_out**2/Lambda;\n",
    "            Rin=d_in+zc**2/d_in;\n",
    "            print('w',w_in*np.sqrt(1+50**2/zc**2)*2.5)\n",
    "            Rout=d_out+zc_out**2/d_out;\n",
    "            print('f1:',f1,'\\n','Wout:',w_out,'\\n','W_in:',w_in,'\\n','R_out:',Rout,'\\n','R_in:',Rin,'\\n','Conic center:',Rin,'\\n','Conic center out:',Rout);\n",
    "            print('ratio:',Rout/Rin);\n",
    "        elif F=='f2':\n",
    "            f=f2;\n",
    "            fact1=d_in/f-1;\n",
    "            fact2=np.pi*w_in**2/(Lambda*f);\n",
    "            fact2=1/(fact1**2+fact2**2);\n",
    "            w_out=w_in*np.sqrt(fact2);\n",
    "            zc_out=np.pi*w_out**2/Lambda;\n",
    "            Rin=d_in+zc**2/d_in;\n",
    "            Rout=d_out+zc_out**2/d_out;\n",
    "            print('f2:',f2,'\\n','Wout:',w_out,'\\n','W_in:',w_in,'\\n','R_out:',Rout,'\\n','R_in:',Rin,'\\n','Conic center:',Rin,'\\n','Conic center out:',Rout);\n",
    "            #print(Rout/Rin);\n",
    "            \n",
    "        \n",
    "    return f,Rin,d_in,Rout,d_out,w_out,angle*2,Theta_beam,Lambda;\n",
    "\n",
    "\n",
    "def Mirror(focal_length,Rin,Rout,angle,Theta_beam,Size=5,Mirror_type='concave'):\n",
    "    angle=angle*np.pi/180;\n",
    "    if Mirror_type=='concave':\n",
    "        a=np.abs(Rin+Rout)/2;\n",
    "        b=np.sqrt(Rin*np.abs(Rout)/2*(1+np.cos(angle)));\n",
    "        c=1/2*np.sqrt(Rin**2+Rout**2+2*Rin*np.abs(Rout)*np.cos(angle));\n",
    "        p=b**2/a;\n",
    "        e=c/a;\n",
    "        phi_0=np.arccos((Rin**2+4*c**2-Rout**2)/(4*c*Rin))\n",
    "        phi_max=phi_0+Size/2*Theta_beam;\n",
    "        phi_min=phi_0-Size/2*Theta_beam;\n",
    "        t=np.linspace(phi_min,phi_max,101);\n",
    "        \n",
    "        dx=np.linspace(0,1,101)\n",
    "        rho_0=p/(1+e*np.cos(phi_0))*dx;  \n",
    "        print('phi_0:',phi_0/np.pi*180);\n",
    "        plt.plot(rho_0*np.cos(phi_0),rho_0*np.sin(phi_0));\n",
    "        \n",
    "        \n",
    "        # plot the mirror size;\n",
    "        Curve=p/(1+e*np.cos(t))\n",
    "        plt.plot(Curve*np.cos(t),Curve*np.sin(t),'r-')\n",
    "        #plot the elliptic \n",
    "        t=np.linspace(0,2*np.pi,101);\n",
    "        print('p',p)\n",
    "        Curve=p/(1+e*np.cos(t))\n",
    "        plt.plot(Curve*np.cos(t),Curve*np.sin(t),'k--');\n",
    "        \n",
    "    else:\n",
    "        a=np.abs(Rin+Rout)/2;\n",
    "        b=np.sqrt(Rin*np.abs(Rout)/2*(1-np.cos(angle)));\n",
    "\n",
    "        c=1/2*np.sqrt(Rin**2+Rout**2+2*Rin*np.abs(Rout)*np.cos(angle));\n",
    "        p=b**2/a;\n",
    "        e=c/a;\n",
    "        phi_0=np.pi-np.arccos((Rin**2+4*c**2-Rout**2)/(4*c*Rin))\n",
    "        phi_max=phi_0+Size/2*Theta_beam;\n",
    "        phi_min=phi_0-Size/2*Theta_beam;\n",
    "        t=np.linspace(phi_min,phi_max,101);\n",
    "        \n",
    "        dx=np.linspace(0,1,101)\n",
    "        rho_0=p/(1+e*np.cos(phi_0))*dx;  \n",
    "        print('phi_0:',phi_0/np.pi*180);\n",
    "        plt.plot(rho_0*np.cos(phi_0),rho_0*np.sin(phi_0));\n",
    "        \n",
    "        \n",
    "        # plot the mirror size;\n",
    "        Curve=p/(1+e*np.cos(t))\n",
    "        plt.plot(Curve*np.cos(t),Curve*np.sin(t),'r-')\n",
    "        #plot the elliptic \n",
    "        t=np.linspace(0,2*np.pi,101);\n",
    "        print('p',p)\n",
    "        Curve=p/(1+e*np.cos(t))\n",
    "        plt.plot(Curve*np.cos(t),Curve*np.sin(t),'k--');\n",
    "        \n",
    "    print('e:',e,'\\n','a:',a,'\\n','b:',b,'\\n','c:',c)\n",
    "    return phi_0,Size/2*Theta_beam,e,a,b,c;\n",
    "\n",
    "def Ellips(focal_length,Rin,Rout,angle,Theta_beam,Size=5):\n",
    "    angle=angle*np.pi/180;\n",
    "\n",
    "    a=np.abs(Rin+Rout)/2;\n",
    "    b=np.sqrt(Rin*np.abs(Rout)/2*(1+np.cos(angle)));\n",
    "    c=1/2*np.sqrt(Rin**2+Rout**2-2*Rin*np.abs(Rout)*np.cos(angle));\n",
    "    p=b**2/a;\n",
    "    e=c/a;\n",
    "    phi_0=np.arccos((Rin**2+4*c**2-Rout**2)/(4*c*Rin))\n",
    "    phi_max=phi_0+Size/2*Theta_beam;\n",
    "    phi_min=phi_0-Size/2*Theta_beam;\n",
    "    t=np.linspace(phi_min,phi_max,101);\n",
    "        \n",
    "    dx=np.linspace(0,1,101)\n",
    "    rho_0=p/(1+e*np.cos(phi_0))*dx;  \n",
    "    print('phi_0:',phi_0/np.pi*180);\n",
    "    plt.plot(rho_0*np.cos(phi_0),rho_0*np.sin(phi_0));\n",
    "        \n",
    "        \n",
    "    # plot the mirror size;\n",
    "    Curve=p/(1+e*np.cos(t))\n",
    "    plt.plot(Curve*np.cos(t),Curve*np.sin(t),'r-')\n",
    "    #plot the elliptic \n",
    "    t=np.linspace(0,2*np.pi,101);\n",
    "    print('p',p)\n",
    "    Curve=p/(1+e*np.cos(t))\n",
    "    plt.plot(Curve*np.cos(t),Curve*np.sin(t),'k--');\n",
    "        \n",
    "    print('e:',e,'\\n','a:',a,'\\n','b:',b,'\\n','c:',c)\n",
    "    return phi_0,Size/2*Theta_beam,e,a,b,c;\n",
    "def Ellips2(focal_length,Rin,Rout,angle,Theta_beam,Size=5):\n",
    "    angle=angle*np.pi/180;\n",
    "\n",
    "    a=np.abs(Rin+Rout)/2;\n",
    "    b=np.sqrt(Rin*np.abs(Rout)/2*(1+np.cos(angle)));\n",
    "    c=1/2*np.sqrt(Rin**2+Rout**2-2*Rin*np.abs(Rout)*np.cos(angle));\n",
    "    p=b**2/a;\n",
    "    e=c/a;\n",
    "    phi_0=np.pi-np.arccos((Rin**2+4*c**2-Rout**2)/(4*c*Rin))\n",
    "    phi_max=phi_0+Size/2*Theta_beam;\n",
    "    phi_min=phi_0-Size/2*Theta_beam;\n",
    "    t=np.linspace(phi_min,phi_max,101);\n",
    "        \n",
    "    dx=np.linspace(0,1,101)\n",
    "    rho_0=p/(1+e*np.cos(phi_0))*dx;  \n",
    "    print('phi_0:',phi_0/np.pi*180);\n",
    "    plt.plot(rho_0*np.cos(phi_0),rho_0*np.sin(phi_0));\n",
    "        \n",
    "        \n",
    "    # plot the mirror size;\n",
    "    Curve=p/(1+e*np.cos(t))\n",
    "    plt.plot(Curve*np.cos(t),Curve*np.sin(t),'r-')\n",
    "    #plot the elliptic \n",
    "    t=np.linspace(0,2*np.pi,101);\n",
    "    print('p',p)\n",
    "    Curve=p/(1+e*np.cos(t))\n",
    "    plt.plot(Curve*np.cos(t),Curve*np.sin(t),'k--');\n",
    "        \n",
    "    print('e:',e,'\\n','a:',a,'\\n','b:',b,'\\n','c:',c)\n",
    "    return phi_0,Size/2*Theta_beam,e,a,b,c;\n",
    "    \n",
    "def center_projector(beta,alpha,e,a,c):\n",
    "    y0=(1+e)*(e*np.cos(beta)+np.cos(alpha))*np.sin(beta)*(a-c)\n",
    "    Y=(1-e**2)*np.sin(beta)**2+(np.cos(beta)+e*np.cos(alpha))**2\n",
    "    y0=y0/Y;\n",
    "    \n",
    "    a2=((1+e)*np.sin(alpha)*(a-c))**2/Y\n",
    "    \n",
    "    b2=((1+e)*(np.cos(beta)+e*np.cos(alpha))*np.sin(alpha)*(a-c))**2/Y**2;\n",
    "    \n",
    "    return y0,np.sqrt(a2),np.sqrt(b2);\n",
    "\n",
    "size=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#produce input file\n",
    "#produce M2.txt\n",
    "Lambda=1.0162456203\n",
    "win2=1.4;din2=33.73731665;angle2=90;f2=67.80690232;\n",
    "\n",
    "\n",
    "M2=np.array([['lambda',Lambda,''],\n",
    "             ['W_in',win2,''],\n",
    "             ['d_in',din2,''],\n",
    "             ['angle',angle2,''],\n",
    "             #['d_out',dout2,'']])\n",
    "             ['f',f2,'']])\n",
    "np.savetxt('M2.txt',M2,delimiter=\",\",fmt='%s')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M2\n",
      "win: 1.4\n",
      "half axis of mirror: 3.959996129742437\n",
      "Rin: 34.8255047614632 \n",
      " dout: -63.00810134571082 \n",
      " wout: 2.7433005371299104 \n",
      " Rout: -71.59822731629545 \n",
      " dout: -63.00810134571082 \n",
      "\n",
      "phi_0: 64.06162944529693\n",
      "p 67.80690232\n",
      "e: 2.1651538810504327 \n",
      " a: 18.386361277416125 \n",
      " b: 35.30895358344659 \n",
      " c: 39.809301478192914\n",
      "phi_0: 64.06162944529693\n",
      "p 67.80690232\n",
      "e: 2.1651538810504327 \n",
      " a: 18.386361277416125 \n",
      " b: 35.30895358344659 \n",
      " c: 39.809301478192914\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# mirror 2\n",
    "size=1\n",
    "print('M2');\n",
    "f2,Rin2,din2,Rout2,dout2,w_out2,angle2,Theta_beam,Lambda=Quasi_Optics('M2.txt',size,'f2')\n",
    "beta2,alpha2,e2,a2,b2,c2=Mirror(f2,Rin2,Rout2,angle2,Theta_beam,Size=size,Mirror_type='concave')\n",
    "#Theta_beam*Rin2\n",
    "beta2,alpha2,e2,a2,b2,c2=Ellips(f2,Rin2,Rout2,angle2,Theta_beam,Size=size)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "phi_0: 115.93837055470306\n",
      "p 67.80690232\n",
      "e: 2.1651538810504327 \n",
      " a: 18.386361277416125 \n",
      " b: 35.30895358344659 \n",
      " c: 39.809301478192914\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta2,alpha2,e2,a2,b2,c2=Ellips2(f2,Rin2,Rout2,angle2,Theta_beam,Size=size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#produce M1.txt\n",
    "win1=w_out2;din1=169.438;angle1=90;f1=170\n",
    ";\n",
    "M1=np.array([['lambda',Lambda,''],\n",
    "             ['W_in',win1,''],\n",
    "             ['d_in',din1,''],\n",
    "             ['angle',angle1,''],\n",
    "             #['d_out',dout1,'']])\n",
    "             ['f',f1,'']])\n",
    "np.savetxt('M1.txt',M1,delimiter=\",\",fmt='%s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M1\n",
      "win: 2.7433005371299104\n",
      "half axis of mirror: 10.083515116651487\n",
      "Rin: 172.6323691953813 \n",
      " dout: 140.0094193072804 \n",
      " wout: 20.039997738068436 \n",
      " Rout: 11148.703158625072 \n",
      " dout: 140.0094193072804 \n",
      "\n",
      "phi_0: 89.11287298590774\n",
      "p 170.0\n",
      "e: 0.9848696398237212 \n",
      " a: 5660.667763910227 \n",
      " b: 980.9757998364377 \n",
      " c: 5575.019821804015\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "20.262676952198436"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sjJUrVyIrK0t2RJKIl7TAS1qkLTg4GDNmzMCePXvw22+/oXv37rIjEVEBCSGwZ88eTJ48GREREShbtiyuXbvGmc4NDC9pEb2GS5cuoWfPnnjrrbewZ88eqNVqXLp0SXYsInoNKpUKXbp0wcWLF7Fq1SosXrxYKXaEEPzZLoFY8FCJFxkZiT59+qB+/frYuXMnVCoVPvroI4SHh2P69Omy4xHRGzA2NsawYcMwaNAgZd3u3btRr149fPTRR7hx44a8cFSsWPBQiSaEQN++ffHzzz9DCIH3338fFy9exObNm1GrVi3Z8YioCJw9exYqlQpbt25F7dq1MWnSJDx8+FB2LCpiLHioxImOjkZqaiqAJ93eM2fORJcuXRAcHIxt27ZxAkEiAzdnzhycPXsWbdq0QWZmJvz8/ODs7IxvvvkGmZmZsuNREZFe8FSrVg0qlSrPMnLkSABA69at82wbNmyY1j6io6PRqVMnWFhYwMbGBpMmTUJ2draMwyEddufOHYwaNQo1a9bEihUrlPVdunTB7t274e7uLi8cERWrhg0b4uDBg9i7dy9cXV3x4MEDjBs3Dj179pQdjYqI9Kel//vvv8jJyVFeX7p0Ce+++y569eqlrBsyZAjmzJmjvLawsFD+nJOTg06dOsHOzg4nT55EbGws+vfvDxMTEyxYsKB4DoJ02t27d/HVV1/hu+++Q3p6OgDgzJkzklMRkWwqlQodO3ZEu3btsG7dOsyYMQPDhw9XtgshlCe2k/7TudvSx40bhz179uDKlStQqVRo3bo13N3dsWzZsnzb79+/H507d8adO3dga2sLAFi9ejWmTJmCe/fuwdTU9KWfydvSDVNCQgL8/PywfPly5RJW8+bNMXfuXLRp00ZyOiLSNY8fP4a5ublS5Pj5+eH06dPw9fVFjRo1JKej/OjtbemZmZnYtGkTPv30U62qevPmzahQoQLq1q2LqVOn4vHjx8q2oKAg1KtXTyl2AMDb2xvJyckIDQ0t1vykWyZMmICFCxciNTUVjRs3xv79+3H8+HEWO0SULwsLC+W7Jy0tDb6+vti2bRvq1KmDCRMm4MGDB5IT0pvQqYLn999/R2JiIgYOHKis++ijj7Bp0yYcOXIEU6dOxcaNG/Hxxx8r2+Pi4rSKHQDK67i4uHw/JyMjA8nJyVoL6b+UlBTcu3dPeT1lyhS89dZb2LVrF06fPo327duze5qIXom5uTmOHDkCb29vZGVl4euvv0aNGjWwZMkSZGRkyI5Hr0GnCp4ff/wRHTp0QKVKlZR1Q4cOhbe3N+rVq4e+ffvip59+wm+//YZr16699uf4+vrC2tpaWRwcHAojPkny+PFj+Pn5oXr16pg8ebKy3tXVFWfOnEHXrl1Z6BBRgdWvXx8BAQEICAhAvXr1kJiYiM8//xzu7u64ePGi7HhUQDpT8Ny8eRMHDx7E4MGDX9jOw8MDAHD16lUAgJ2dHeLj47XaPH1tZ2eX7z6ePkzu6RITE/Om8UmC9PR0fPvtt6hRowYmTZqE+/fv49SpU8rAZAAsdIjojXl7eyM4OBg//vgjbG1tce3aNfby6CGdKXj8/f1hY2ODTp06vbBdSEgIAMDe3h4A4OnpiYsXL+Lu3btKm8DAQFhZWcHV1TXffWg0GlhZWWktpD8yMzOxZs0a1KxZE2PHjkVcXByqVauGdevW4eLFizAzM5MdkYgMjJGRET799FNcvHgRv/76Kxo3bqxs40NJ9YNOFDy5ubnw9/fHgAEDYGz8/++Uv3btGubOnYuzZ8/ixo0b2L17N/r3749WrVqhfv36AIB27drB1dUV/fr1w/nz53HgwAFMnz4dI0eOhEajkXVIVISWLVuGYcOG4datW6hcuTJWr16NyMhIfPLJJ1p/f4iIClvFihW1HigcHByMWrVq4eDBg/JC0asROuDAgQMCgIiMjNRaHx0dLVq1aiXKlSsnNBqNcHZ2FpMmTRJJSUla7W7cuCE6dOggzM3NRYUKFcTEiRNFVlbWK39+UlKSAJBnv6QbsrOzRWxsrPL64cOHwsXFRXzzzTciLS1NYjIiKum6d+8uAAiVSiWmTJkiMjMzZUcqUQry/a1z8/DIwHl4dFNubi527tyJmTNnwsrKCidPnlTG5AhOCEZEOuDx48cYP3481q5dCwBo0qQJtm7dynl7ionezsNDBDwpZnbv3o233noLvXr1QlhYGCIiIrSeasxih4h0gYWFBdasWYMdO3agbNmy+Pfff+Hu7o6NGzfKjkb/wYKHdIYQAgcOHICHhwe6deuG8+fPw9LSEjNmzEBUVBSqV68uOyIRUb569OiB8+fPo1WrVkhJSUH//v2xe/du2bHoGRzhSTojICAAHTt2BPDkt6YxY8bg888/R/ny5SUnIyJ6OQcHBxw+fBgLFizAiRMn0LlzZ9mR6BkcwwOO4ZHp/v37qFChAoAnD4Jt1qwZWrVqhSlTpsDGxkZyOiKi15Obmwu1+slFlMePH+Onn37C0KFDlXVUODiGh3Tev//+i/bt26NBgwZIS0sD8GSei1OnTmHJkiUsdohIrz1b2EyYMAHDhw9Hu3btcOfOHYmpSjYWPFSszp8/j27duqFp06Y4cOAA7t69i+PHjyvbjYyMJKYjIip8TZs2hYWFBQ4dOoT69evjjz/+kB2pRGLBQ8UiLCwMvXr1gru7O3bv3g21Wo0BAwYgMjIS7777rux4RERF5tNPP8W5c+fg7u6OhIQEdO3aFaNHj9Z6DA4VPRY8VORu3ryJevXqYfv27VCpVOjTpw/CwsKwfv16ODk5yY5HRFTkateujVOnTmH8+PEAgBUrVsDDw0Nrug0qWix4qEgkJSUpf65atSq6deuGHj164MKFC9iyZQtq164tMR0RUfHTaDRYunQp9u/fDxsbG9y+fRuZmZmyY5UYvEsLvEurMMXExGD+/PnYtGkTwsLC4OjoCODJw/VMTEwkpyMi0g23b99GbGys1kNIqeB4lxYVu9jYWIwZMwbOzs5Ys2YNUlNTsWPHDmU7ix0iov+vcuXKWsXOn3/+iZ9++kliIsPHiQfpjdy7dw+LFi3CypUrldvL3377bcyZMwetWrWSnI6ISPddu3YNPXv2REpKCm7duoWpU6fy8TlFgD089NoyMjJQr149+Pn5IS0tDZ6enjh48CCOHDnCYoeI6BVVr14dI0aMAABMmzYNI0aMQE5OjuRUhocFDxVIamqq8meNRoNPPvkEjRo1wr59+3DixAm0bduWv5kQERWAWq3GV199hW+//RYqlQqrV69Gjx498PjxY9nRDAoHLYODll/VtWvX0Lx5c2zbtk3pwcnIyICpqSmLHCKiQrBjxw707dsXGRkZaNasGf744w/l8TuUFwctU5GYPXs27t69i2XLlinrNBoNix0iokLSs2dPHDx4EGXLlsWpU6e0/r2lN8MeHrCH51Vcv34dtWrVQk5ODk6fPo0mTZrIjkREZLDCw8Px9ddfY+XKlbzL9QXYw0OFbtGiRcjJyUG7du1Y7BARFbE6depg7dq1SrGTnZ2N06dPS06l31jw0Evdvn0b/v7+AJ7cQUBERMVHCIHRo0ejefPmyr/FVHAseOil/Pz8kJmZiRYtWvB2cyKiYpabm4vHjx8jJycHn376KdasWSM7kl5iwUMvlJCQoPxwsXeHiKj4GRkZYf369fj8888BAMOHD8fGjRslp9I/nGmZXqhcuXL47bff8Ntvv8Hb21t2HCKiEkmlUmHRokXIyMjA8uXLMXDgQFhYWKBnz56yo+kN3qUF3qVFRET6ITc3F0OGDMG6detgYmKC33//HR07dpQdSxrepUWFIjc3V3YEIiJ6hlqtxtq1a/Hhhx8CANLT0yUn0h8seChfKSkpqF27NmbOnKk8FJSIiOQzMjLCTz/9hOPHj6NHjx6y4+gNFjyUr7Vr1+Lq1avYvHkzJ70iItIxJiYmaNq0qfL65s2bCAkJkRdID7DgoTzS09Ph5+cHAJg6dSqMjTm2nYhIV0VFRaFly5bw8vJCaGio7Dg6iwUP5bF+/XrExsbCwcEB/fr1kx2HiIheoHz58rC1tUVCQgLeffddXL16VXYkncSCh7RkZWVh4cKFAIBJkybB1NRUciIiInoRKysrHDhwAPXq1UNsbCzatm2L6Oho2bF0Dgse0rJlyxbcvHkTNjY2GDx4sOw4RET0CsqVK4fAwEDUqlUL0dHR6Ny5M1JSUmTH0ikseEghhMDixYsBABMnToS5ubnkRERE9KpsbW1x8OBB2NnZ4eLFi/j44485vcgzWPCQQqVS4ffff8eIESMwfPhw2XGIiKiAHBwc8Pvvv0Oj0eDq1atISEiQHUlnSC94Zs2aBZVKpbW4uLgo29PT0zFy5EiUL18epUuXRs+ePREfH6+1j+joaHTq1AkWFhawsbHBpEmTkJ2dXdyHYhCcnZ2xcuVKWFpayo5CRESvwcPDA/v27cPJkydRsWJF2XF0hk7cb+zm5oaDBw8qr5+9DXr8+PHYu3cvtm3bBmtra4waNQo9evTAiRMnAAA5OTno1KkT7OzscPLkScTGxqJ///4wMTHBggULiv1Y9FVmZiYHKBMRGYg2bdpovU5JSUHp0qUlpdEN0nt4gCcFjp2dnbJUqFABAJCUlIQff/wRS5cuRZs2bdCoUSP4+/vj5MmTOHXqFADgzz//RFhYGDZt2gR3d3d06NABc+fOxcqVK5GZmSnzsPSGEAJt2rRB7969ObKfiMiACCHg5+cHFxcX3Lp1S3YcqXSi4Lly5QoqVaoEJycn9O3bV/nSPXv2LLKysuDl5aW0dXFxgaOjI4KCggAAQUFBqFevHmxtbZU23t7eSE5O5gRMr+jIkSM4ceIEdu/eDY1GIzsOEREVkvT0dPz000+4ffs2unXrhsePH8uOJI30gsfDwwPr169HQEAAVq1apcwY+ejRI8TFxcHU1BRlypTReo+trS3i4uIAAHFxcVrFztPtT7flJyMjA8nJyVpLSTZv3jwAwODBg/OcSyIi0l/m5ubYvXs3KlSogHPnzmHgwIEQQsiOJYX0gqdDhw7o1asX6tevD29vb+zbtw+JiYn49ddfi+wzfX19YW1trSwODg5F9lm6LigoCEeOHIGJiQkmTZokOw4RERWyatWqYefOnTAxMcG2bdvg6+srO5IU0gue/ypTpgxq1aqFq1evws7ODpmZmUhMTNRqEx8fDzs7OwCAnZ1dnru2nr5+2ua/pk6diqSkJGWJiYkp/APRE/PnzwcA9O/fH46OjpLTEBFRUWjZsiW+++47AMCMGTOUG39KEp0reFJSUnDt2jXY29ujUaNGMDExwaFDh5TtkZGRiI6OhqenJwDA09MTFy9exN27d5U2gYGBsLKygqura76fodFoYGVlpbWURMHBwdi7dy/UajV8fHxkxyEioiI0aNAg9O3bFzk5Ofjoo49K3HAO6belf/755+jSpQuqVq2KO3fuYObMmTAyMkKfPn1gbW2NQYMGYcKECShXrhysrKwwevRoeHp6olmzZgCAdu3awdXVFf369cOiRYsQFxeH6dOnY+TIkRyA+xLLli0DAPTu3RvOzs5ywxARUZFSqVRYtWoVQkJCMGzYsBI335r0gufWrVvo06cPEhISULFiRbRo0QKnTp1SJkv6+uuvoVar0bNnT2RkZMDb21vplgMAIyMj7NmzB8OHD4enpydKlSqFAQMGYM6cObIOSW+sWLEC9erVQ4cOHWRHISKiYmBpaYmQkBCt+e5KCpUoqcO1n5GcnAxra2skJSWV2MtbRERU8iQnJ+PevXuoUaOG7CivpSDf3zo3hoeK3uPHj0vsbYlERPREaGgo3nrrLXTp0gWpqamy4xQ5Fjwl0IQJE/DWW2/h2LFjsqMQEZEkFStWRGpqKsLDwzF+/HjZcYocC54S5vbt2/D390dISIjsKEREJJGNjQ02bdoElUqF77//HgcOHJAdqUix4Clh/Pz8kJmZiZYtW6JVq1ay4xARkURt27bF6NGjAQBDhw7Fo0ePJCcqOix4SpB79+5hzZo1AIBp06ZJTkNERLpg/vz5qFatGqKjow16TjYWPCXIsmXLkJaWhkaNGqFdu3ay4xARkQ4oXbo0fvjhBwDAd999h7/++ktyoqJR8m7EL6ESExOxYsUKAE96d1QqleRERESkK9q2bYshQ4bg7t27qFmzpuw4RYIFTwmxZcsWJCcnw83NDd26dZMdh4iIdMyKFStgYmJisL8Qs+ApIYYNGwYHBwdoNBqo1bySSURE2kxNTbVeZ2RkGNQjmljwlBBqtRpdunSRHYOIiHRcfHw8Pv/8c0RHR+Po0aMG0+PDX/UNXEZGRomYQZOIiApHRkYGdu7ciWPHjmHr1q2y4xQaFjwGzt/fH9WqVcPq1atlRyEiIj3g6OiIL774AgAwadIkpKSkSE5UOFjwGLCsrCwsXLgQ9+/fR3Z2tuw4RESkJyZOnAgnJyfcuXMH8+bNkx2nULDgMWBbtmzBzZs3YWtri0GDBsmOQ0REesLMzAzffPMNAGDp0qW4fPmy5ERvjgWPgcrJyYGvry+AJw8LNTc3l5yIiIj0SefOndGxY0dkZWUZxOz8LHgM1M6dOxEZGYmyZcti+PDhsuMQEZEe+uqrr6BWq3Hs2DE8ePBAdpw3woLHAAkhMH/+fADA2LFjYWlpKTkRERHpo7p162LHjh24evUqypUrJzvOG1EJIYTsELIlJyfD2toaSUlJsLKykh3njZ05cwZNmzZFqVKlcPPmTb3/S0pERJSfgnx/s4fHADVu3BihoaH48ccfWewQEVGhEEJg3759yM3NlR3ltbDgMVB16tTBBx98IDsGEREZACEE2rVrh06dOuH333+XHee1sOAxMHfu3JEdgYiIDIxKpUKzZs0AAHPmzIE+joZhwWNATp48CUdHRwwePFgv/zISEZHuGjduHEqXLo3z58/jjz/+kB2nwFjwGJD58+cjJycHAAzmYW9ERKQbypcvj1GjRgEAZs+erXe/WLPgMRDBwcHYt28f1Go1fHx8ZMchIiIDNHHiRFhYWODcuXM4ePCg7DgFwoLHQCxYsAAA0Lt3bzg7O0tOQ0REhqhChQoYPHgwAMDPz09ymoJhwWMAwsPDsWPHDgBQnnBLRERUFMaNGwe1Wo24uDi9epK6sewA9OZ8fX0hhED37t1Rt25d2XGIiMiAVa9eHefOnUP9+vX1arwoCx499+jRI+zbtw8ADOLhbkREpPsaNGggO0KB8ZKWnrO0tMTVq1exceNGNG7cWHYcIiIqQVJTUxESEiI7xithwWMAypQpg48//lh2DCIiKkHOnj2LypUro0uXLsjOzpYd56VY8OixK1eu6N08CEREZBjq1q0LU1NT3Lp1Sy8mImTBo6fu3buHBg0aoFmzZkhISJAdh4iIShiNRoNPP/0UAPDDDz9ITvNy0gseX19fNGnSBJaWlrCxsUH37t0RGRmp1aZ169ZQqVRay7Bhw7TaREdHo1OnTrCwsICNjQ0mTZqkF11sr+vrr79GWloacnJy+ER0IiKSYtCgQQCAgIAA3Lp1S3KaF5Ne8Pz1118YOXIkTp06hcDAQGRlZaFdu3ZITU3VajdkyBDExsYqy6JFi5RtOTk56NSpEzIzM3Hy5Els2LAB69evx4wZM4r7cIpFYmIiVq5cCeDJnVn6dFsgEREZjpo1a6JVq1bIzc3F+vXrZcd5IekFT0BAAAYOHAg3Nzc0aNAA69evR3R0NM6ePavVzsLCAnZ2dspiZWWlbPvzzz8RFhaGTZs2wd3dHR06dMDcuXOxcuVKZGZmFvchFbkVK1YgOTkZbm5u6Natm+w4RERUgj3t5fnpp590elyp9ILnv5KSkgAgz2WazZs3o0KFCqhbty6mTp2Kx48fK9uCgoJQr1492NraKuu8vb2RnJyM0NDQ4gleTFJSUrBs2TIAT2ZVVqt17n8hERGVID169ICFhQWuXLmi09+5OjXxYG5uLsaNG4f//e9/WjMGf/TRR6hatSoqVaqECxcuYMqUKYiMjMTOnTsBAHFxcVrFDgDldVxcXJ7PycjIQEZGhvI6OTm5KA6nSKxZswYJCQmoUaMGPvjgA9lxiIiohCtdujQ2btwId3d3ODk5yY7zXDpV8IwcORKXLl3C8ePHtdYPHTpU+XO9evVgb2+Ptm3b4tq1a6hRo0aBP8fX1xezZ89+47wyPJ1V2cfHB8bGOvW/j4iISqgePXrIjvBSOnM9ZNSoUdizZw+OHDmCKlWqvLCth4cHAODq1asAADs7O8THx2u1efrazs4uz/unTp2KpKQkZYmJiSmMQygWgYGB2LlzJ/r37y87ChERkd6QXvAIITBq1Cj89ttvOHz4MKpXr/7S9zydxtre3h4A4OnpiYsXL+Lu3btKm8DAQFhZWcHV1TXP+zUaDaysrLQWfaFWq/Hee+/B1NRUdhQiIiLFP//8g+7du2PChAmyo+RLesEzcuRIbNq0CVu2bIGlpSXi4uIQFxeHtLQ0AMC1a9cwd+5cnD17Fjdu3MDu3bvRv39/tGrVCvXr1wcAtGvXDq6urujXrx/Onz+PAwcOYPr06Rg5ciQ0Go3Mwys0ERERyjkhIiLSNQ8ePMCuXbvwyy+/IDc3V3acPFRC8j1kz5tDxt/fHwMHDkRMTAw+/vhjXLp0CampqXBwcMB7772H6dOna/XM3Lx5E8OHD8fRo0dRqlQpDBgwAAsXLnylcS7JycmwtrZGUlKSTvb25OTkwNXVFUlJSdi9ezeaNm0qOxIREZGWjIwMVKxYEY8ePcKpU6eU4SdFqSDf39JHvb6s3nJwcMBff/310v1UrVpVGdBraHbs2IHLly+jbNmyqFOnjuw4REREeWg0GnTo0AG//vor9uzZUywFT0FIv6RFLyaEwIIFCwAAY8eOhaWlpeRERERE+evcuTMAYM+ePZKT5MWCR8ft3bsX58+fR+nSpTF69GjZcYiIiJ6rffv2UKlUCAkJwZ07d2TH0cKCR4cJITBv3jwATwZ38yGhRESkyypWrIhGjRoBePLYJ10ifQwPPd/hw4fxzz//wMzMDOPHj5cdh4iI6KW6dOkCc3NznbsJiD08Ouzvv/8G8ORJ8f99dAYREZEumjFjBo799Rd61KsH6NDDRKXflq4LdPm29AsXLqBChQqoVKmS7ChEREQvl5sL1KwJXL8OhIUBRXh3cUG+v9nDo+Pq16/PYoeIiPSHWo20SlXwEECQ/xbZaRQseHRQVFQUoqOjZccgIiJ6LbOzgPIA5qxfJzuKggWPDpo8eTKcnZ3xww8/yI5CRERUYJYNmkIACE+If2nb4sKCR8eEh4djx44dyMrKQrNmzWTHISIiKrCK3t0AADdzc3AvLExymidY8OgYX19fCCHQvXt31K1bV3YcIiKiAjO2qYwKFmUAAKcjIuSG+T8seHTI9evXsWXLkwFe06ZNk5yGiIjo9QgAadUbAgDOXLwoN8z/YcGjQ7766ivk5OTA29sbjRs3lh2HiIjotQghYGrnDAA4e/as5DRPsODREbdv38b69esBsHeHiIj0n6ltDQBASEiI3CD/h4+W0BHnzp2DiYkJPDw80LJlS9lxiIiIXpsQgGnFaqjn1RPD3msDIQRUKpXUTCx4dESXLl1w8+ZNJCQkyI5CRET0RgQE1Gal4TV4Okb0dpcdBwALHp1Svnx5lC9fXnYMIiKiN6I8tEpup44WjuGRLDExEceOHZMdg4iIqNA8rXey09Nx5swZBAcHS80DsOCRbsWKFXj77bcxePBg2VGIiIgKxdMentC/dqFJkyaYNWuW1DwACx6pUlJSsGzZMgBAmzZt5IYhIiIqJOL/+njK2jkCAK5duyYzDgAWPFKtWbMGCQkJcHZ2xgcffCA7DhERUaF42sNTxrYygCcPxRbKwB45WPBIkp6eDj8/PwCAj48PjI05fpyIiAyLVUV7AMDjx49x//59qVlY8Eji7++PuLg4ODg4oF+/frLjEBERFToTEw3s7OwAANHR0VKzsOCRICsrC1999RUAYNKkSTA1NZWciIiIqPA8vXylUgFVqlQB8OSJAjKx4JHgxo0bMDY2ho2NDe/OIiIig/N0uI5KBdjbP7msFRsbKzERJx6UombNmoiIiMDVq1dhbm4uOw4REVGh+v/Dk1UYOHAgWrdujebNm0tMxIJHGmNjY7i4uMiOQUREVOie7eHp8V4PuWH+Dy9pFSMhBLZu3YqMjAzZUYiIiIrM03l4dOjJEix4itOePXvw0UcfoWHDhsjNzZUdh4iIqEg828OTmJiIU6dO4cyZM1IzseApJkIIzJ8/HwDQtWtXqNU89UREZJienWLw6NGj8PT0xOjRo6XlATiGp9gcPnwY//zzD8zMzDB+/HjZcYiIiIrO/3XxqFUqWJa2BAA8evRIZiL28BSXefPmAQCGDBkCW1tbyWmIiIiKzrM9PKVKlQIApKamygnzfwyq4Fm5ciWqVasGMzMzeHh44PTp07IjAQBOnjyJo0ePwsTEBJMmTZIdh4iIqEgpY3gAWFhYAADS0tLkBYIBFTy//PILJkyYgJkzZ+LcuXNo0KABvL29cffuXdnRlLE7AwYMgIODg+Q0RERERUu5S0ulgkajAQDpdygbTMGzdOlSDBkyBJ988glcXV2xevVqWFhYYN26dVJzZWRkIDc3F0ZGRpgyZYrULERERMXNxMQEwJPHKslkEAVPZmYmzp49Cy8vL2WdWq2Gl5cXgoKC8rTPyMhAcnKy1lJUNBoN9u/fj6tXr8LZ2bnIPoeIiEhXPHtbupGREQAgJydHYiIDKXju37+PnJycPIOBbW1tERcXl6e9r68vrK2tlaU4LjNVq1atyD+DiIhIFzwdtKyCCmZmZnjnnXfQunVrmZEMo+ApqKlTpyIpKUlZYmJiivTz4uPjsWnTpiL9DCIiIl3RzKk8Rr5TAy1qlkd6ejqOHDmCo0ePSs1kEPPwVKhQAUZGRoiPj9daHx8fDzs7uzztNRqNMoiqqN29exdOTk5IS0tDo0aNUKdOnWL5XCIiIlnerlURb9eqCAC4fv06gP9/aUsWg+jhMTU1RaNGjXDo0CFlXW5uLg4dOgRPT0+JyQAbGxu8++67EEJg4cKFUrMQEREVt6eDlZ8OXpbFIAoeAJgwYQK+//57bNiwAeHh4Rg+fDhSU1PxySefyI6GadOmAQA2b96sVLpEREQlQXp6OgAU25WV5zGYgqd3797w8/PDjBkz4O7ujpCQEAQEBOjErMZNmjTBu+++i5ycHCxatEh2HCIiomLzdMJBc3NzqTkMpuABgFGjRuHmzZvIyMjAP//8Aw8PD9mRFNOnTwcA+Pv74/bt25LTEBERFY+nj5R4+ogJWQyq4NFlrVq1QosWLZCZmYklS5bIjkNERFQsns51Z2VlJTWHQdylpS+mTZuG7t27w9iYp52IiEqG+vXr49tvv0X58uWl5lAJIcTLmxm25ORkWFtbIykpqUgrUCEE7t27BxsbmyL7DCIiopKiIN/fvKRVjFQqFYsdIiIiCVjwSPLvv/9ix44dsmMQEREVqXPnzuH48eO4f/++1BwseCQIDAxE06ZN8dlnnymj14mIiAzRzJkz0bJlS+zcuVNqDhY8ErzzzjuoUaMGEhISsGbNGtlxiIiIisydO3cAAPb29lJzsOCRwNjYGD4+PgAAPz8/ZRZKIiIiQ/N07rnKlStLzcGCR5L+/fujSpUqiI2Nxfr162XHISIiKnTp6enKg70dHR2lZmHBI4mpqSkmTZoEAPjqq6+Uh6sREREZips3bwJ4Msuy7Hl4WPBINHjwYNjY2ODGjRvYsmWL7DhERESFKioqCgBQvXp1qFQqqVlY8EhkYWGBCRMmoEqVKjA1NZUdh4iIqFBduXIFAODs7Cw5CWdaBlB8My3nJy0tDUZGRix4iIjI4ERERODw4cOoXLkyunXrVuj7L8j3Nx/qJJm5ubnsCEREREXCxcUFLi4usmMA4CUtnZGdnY3Nmzfjr7/+kh2FiIjI4LDg0RGLFi3Cxx9/DB8fH/AqIxER6bvk5GT4+/vj7NmzsqMAYMGjMwYNGgQzMzOcOnUKR44ckR2HiIjojZw7dw6ffvop3n//fdlRALDg0Rm2trYYPHgwAGD+/PmS0xAREb2Z4OBgAIC7u7vcIP+HBY8OmTRpEoyNjXH48GEEBQXJjkNERPTanl7KatSokeQkT7Dg0SGOjo4YMGAAAPbyEBGRfvv3338BsOCh5/Dx8YFarcbevXsREhIiOw4REVGBPXz4EJcvXwYANG3aVHKaJzgPj45xdnZG7969cevWLeTm5sqOQ0REVGCnTp0C8OQ7TfYztJ5iwaODfvzxR05ISEREeuvEiRMAgObNm0tO8v+x4NFBLHaIiEifTZkyBa1atUK5cuVkR1FwDI8OS0hIwIwZM3D9+nXZUYiIiF6ZpaUl2rVrh8aNG8uOomAPjw4bNGgQdu3ahbt372L16tWy4xAREekt9vDosAkTJgAA/P39cfv2bclpiIiIXm7VqlWYPHkyzp8/LzuKFhY8OqxVq1Zo2bIlMjMzsWTJEtlxiIiIXur777/H4sWLceHCBdlRtLDg0XHTpk0DAKxevRr37t2TnIaIiOj54uPjlUdKtGvXTnIabSx4dFy7du3QqFEjpKWlYdmyZbLjEBERPde+ffsAPJld2dbWVnIabSx4dJxKpVJ6eVasWIHExES5gYiIiJ5jz549AIDOnTtLTpIX79LSA926dUPDhg3RqFEjZGZmyo5DRESUR1paGg4cOABANwseaT08N27cwKBBg1C9enWYm5ujRo0amDlzptYX+o0bN6BSqfIsT6esfmrbtm1wcXGBmZkZ6tWrp3SpGQq1Wo3Tp0/j+++/h42Njew4REREeRw8eBCpqalwcHDQmQeGPktaD09ERARyc3OxZs0aODs749KlSxgyZAhSU1Ph5+en1fbgwYNwc3NTXj/7XI6TJ0+iT58+8PX1RefOnbFlyxZ0794d586dQ926dYvteIqasTE744iISHclJyfDzs4O3bt3h0qlkh0nD5UQQsgO8dTixYuxatUqZWbhGzduoHr16ggODoa7u3u+7+nduzdSU1OV64YA0KxZM7i7u7/yZH3JycmwtrZGUlISrKys3vg4itL58+exYsUKLF++HGZmZrLjEBERKXJycpCamlps36UF+f7WqUHLSUlJ+T53o2vXrrCxsUGLFi2we/durW1BQUHw8vLSWuft7Y2goKDnfk5GRgaSk5O1Fn2Qk5ODLl264IcffoC/v7/sOERERFqMjIx0tuNAZwqeq1evYvny5fjss8+UdaVLl8aSJUuwbds27N27Fy1atED37t21ip64uLg8t77Z2toiLi7uuZ/l6+sLa2trZXFwcCj8AyoCRkZGmDRpEgDgq6++QlZWluREREREwMWLF5GTkyM7xgsVesHj4+OT70DjZ5eIiAit99y+fRvt27dHr169MGTIEGV9hQoVMGHCBHh4eKBJkyZYuHAhPv74YyxevPiNMk6dOhVJSUnKEhMT80b7K06DBw+GjY0Nbt68iS1btsiOQ0REJVxSUhKaNGkCR0dHxMbGyo7zXIU+EnbixIkYOHDgC9s4OTkpf75z5w7eeecdNG/eHGvXrn3p/j08PBAYGKi8trOzQ3x8vFab+Ph42NnZPXcfGo0GGo3mpZ+li8zNzTFhwgT4+PjA19cXH3/8MYyMjGTHIiKiEmr79u3IyMiAtbX1C797ZSv0gqdixYqoWLHiK7W9ffs23nnnHTRq1Aj+/v5Qq1/e4RQSEgJ7e3vltaenJw4dOoRx48Yp6wIDA+Hp6Vng7Ppi+PDhWLhwISIjI7Fjxw588MEHsiMREVEJtW7dOgBA//79dfLurKekjeG5ffs2WrduDUdHR/j5+eHevXuIi4vTGnuzYcMGbN26FREREYiIiMCCBQuwbt06jB49WmkzduxYBAQEYMmSJYiIiMCsWbNw5swZjBo1SsZhFQsrKyuMHTsWALBgwQLo0I12RERUgoSHh+PkyZMwMjLCgAEDZMd5IWmTuwQGBuLq1au4evUqqlSporXt2S/wuXPn4ubNmzA2NoaLiwt++eUXvP/++8r25s2bY8uWLZg+fTq++OIL1KxZE7///rtBzcGTnzFjxmDLli3o168fsrOzYWJiIjsSERGVMD/++COAJzMrP3v1RRfp1Dw8sujTPDzPEkLodPchEREZrrS0NFSpUgUPHjzAH3/8IeVxEno7Dw8VDIsdIiKSJSAgAA8ePEDVqlXRoUMH2XFeis8r0HM5OTnYuXMnjh49ipUrV8qOQ0REJcR7772Hf/75B/fv39eLu4V5SQv6e0kLAG7dugUnJydkZWXh5MmTBn13GhER0bN4SasEqVKlCvr37w8AmD9/vuQ0RERUEqSkpMiOUGAseAyAj48P1Go19u7di+DgYNlxiIjIgF25cgV2dnYYOXIkcnNzZcd5ZSx4DICzszN69+4N4Mm8PEREREXl66+/RmpqKqKjo19pwmBdoT9J6YW++OILAMCOHTsQHh4uOQ0RERmiuLg4+Pv7AwA+//xzyWkKhgWPgahbty66d+8OIQQWLlwoOw4RERkgPz8/pKeno1mzZmjVqpXsOAXC29INyLRp0xAbG8tnaxERUaG7e/cuvvvuOwDAzJkz9W4uOBY8BqRx48YICgrSu7+ERESk+5YsWYK0tDQ0adIE3t7esuMUGC9pGRgWO0REVNgyMzPx008/AQBmzJihl9817OExQImJiVixYgVyc3MxY8YM2XGIiEjPmZqaIiQkBP7+/ujUqZPsOK+FMy1Dv2dazs+BAwfQvn17mJub4+bNm6hYsaLsSERERIWOMy2XcO3atUPjxo2RlpaGZcuWyY5DRER6LCwsTHaEQsGCxwCpVCpMmzYNALBixQokJibKDURERHopODgYbm5u6NixI7KysmTHeSMseAxU165d4ebmhuTkZKxYsUJ2HCIi0jNCCEyaNAkAULZsWZiYmEhO9GZY8BgotVqtzL68bNkyvXzQGxERybNz504cOnQIGo0G8+bNkx3njbHgMWAffPABnJ2dkZCQgLVr18qOQ0REeuLx48eYMGECAGDy5MmoXr265ERvjrelGzBjY2NMnz4dhw8fRseOHWXHISIiPbFw4UJER0fD0dERPj4+suMUCt6WDsO7LZ2IiOh1Xb9+Ha6ursjIyMD27dvRs2dP2ZGeqyDf3+zhISIiIsXdu3dRuXJlVK9eHT169JAdp9BwDE8JER4ejn79+mHTpk2yoxARkQ5r1qwZQkNDsXHjRr18hMTzsOApIf744w9s2rQJ8+bNQ05Ojuw4RESkw8zMzGBvby87RqFiwVNCDB8+HGXLlkVkZCR27NghOw4REemYESNGYPny5cjNzZUdpUiw4CkhLC0tMWbMGADAggULwLHqRET01L59+7Bq1SqMGzcOFy9elB2nSLDgKUHGjBmD0qVL4/z589i7d6/sOEREpAOSk5Px2WefAQDGjRuHBg0aSE5UNFjwlCDlypXDiBEjAADz5s1jLw8REWHy5Mm4desWatSogblz58qOU2RY8JQwEyZMgJmZGf755x8cPnxYdhwiIpJo3759WLNmDQDgxx9/hIWFheRERYfz8JQwtra2mDx5MjQaDRo3biw7DhERSXLnzh0MGDAAADB69Gi8/fbbkhMVLRY8JdDs2bNlRyAiIslOnDiBxMRENGjQAIsWLZIdp8ix4CEiIiqBevXqhapVq8La2hpmZmay4xQ5juEpwf744w94eHggODhYdhQiIpKgadOmqF27tuwYxUJqwVOtWjWoVCqtZeHChVptLly4gJYtW8LMzAwODg75drtt27YNLi4uMDMzQ7169bBv377iOgS99vPPP+P06dNYsGCB7ChERFQMHj58iPbt2+P8+fOyoxQ76T08c+bMQWxsrLKMHj1a2ZacnIx27dqhatWqOHv2LBYvXoxZs2Zh7dq1SpuTJ0+iT58+GDRoEIKDg9G9e3d0794dly5dknE4emXq1KkAgB07diA8PFxyGiIiKkpCCAwePBgHDhxA3759DXZG5eeRXvBYWlrCzs5OWUqVKqVs27x5MzIzM7Fu3Tq4ubnhww8/xJgxY7B06VKlzTfffIP27dtj0qRJqFOnDubOnYu33noLK1askHE4eqVu3bro3r07hBB5etaIiMiwLF++HDt37oSJiQnWr18PtVp6CVCspB/twoULUb58eTRs2BCLFy9Gdna2si0oKAitWrWCqampss7b2xuRkZF4+PCh0sbLy0trn97e3ggKCnruZ2ZkZCA5OVlrKammTZsG4ElxGRUVJTkNEREVhcDAQEyYMAEA8NVXX5XIaUmkFjxjxozBzz//jCNHjuCzzz7DggULMHnyZGV7XFwcbG1ttd7z9HVcXNwL2zzdnh9fX19YW1sri4ODQ2Edkt5p3LgxvL29kZOTg6+++kp2HCIiKmSXL1/GBx98gJycHPTv3x/jxo2THUmKQi94fHx88gxE/u8SEREB4Mmsv61bt0b9+vUxbNgwLFmyBMuXL0dGRkZhx9IydepUJCUlKUtMTEyRfp6ue9rL4+/vjzt37khOQ0REheXhw4fo0qULEhMT4enpiTVr1kClUsmOJUWhz8MzceJEDBw48IVtnJyc8l3v4eGB7Oxs3LhxA7Vr14adnR3i4+O12jx9bWdnp/w3vzZPt+dHo9FAo9G87FBKjJYtW2LYsGHw8vJ64XkjIiL9olKpULVqVaSlpWHnzp0lYr6d5yn0gqdixYqoWLHia703JCQEarUaNjY2AABPT09MmzYNWVlZMDExAfDkOmTt2rVRtmxZpc2hQ4e0uugCAwPh6en5ZgdSwqxatUp2BCIiKmRlypTBvn37cOvWrRL/C620MTxBQUFYtmwZzp8/j+vXr2Pz5s0YP348Pv74Y6WY+eijj2BqaopBgwYhNDQUv/zyC7755htl4BUAjB07FgEBAViyZAkiIiIwa9YsnDlzBqNGjZJ1aHqPT1EnItJvYWFhyr/lxsbGqFatmtxAOkBawaPRaPDzzz/j7bffhpubG+bPn4/x48drzbFjbW2NP//8E1FRUWjUqBEmTpyIGTNmYOjQoUqb5s2bY8uWLVi7di0aNGiA7du34/fff0fdunVlHJZey8zMxKJFi1C7dm0kJibKjkNERK/hr7/+QoMGDTBixAitO59LOpXgr/NITk6GtbU1kpKSYGVlJTuONLm5uahfvz5CQ0Mxd+5cTJ8+XXYkIiIqgGvXrsHDwwMJCQn48MMPsWXLFoMepFyQ72/p8/CQ7lCr1fjiiy8AAF9//TVSUlIkJyIiolcVExODtm3bIiEhAY0bN8a6desMutgpKBY8pOWDDz6As7MzHjx4gDVr1siOQ0REryA+Ph5eXl64efMmnJ2dsXv3bpibm8uOpVNY8JAWY2Nj+Pj4AAD8/PyQnp4uOREREb3IgwcP8O677+Ly5ctwdHTEoUOHYG9vLzuWzmHBQ3n069cPDg4OiIuLg7+/v+w4RET0AidOnEBoaCjs7e1x6NAhODo6yo6kk1jwUB6mpqaYNGkSAGDRokXIycmRnIiIiJ6nS5cu2L59Ow4ePAhnZ2fZcXRWoU88SIZh8ODBuHjxIkaPHg0jIyPZcYiI6Bnp6elISkpSniX53nvvSU6k+9jDQ/kyNzfH2rVrUa9ePdlRiIjoGVlZWejduzdatGiB6Oho2XH0BgseeiWcvIqISL6nTzzfvXs3YmJiEBUVJTuS3mDBQy8UFxeHQYMGwdPTk4+cICKSKDc3F0OHDsXPP/8MExMT7Ny5E2+//bbsWHqDBQ+9kKmpKX799VecOXMGe/bskR2HiKhEysnJwahRo7Bu3Tqo1Wps2bIFHTt2lB1Lr7DgoRcqV64cRowYAQCYP38+e3mIiIpZWloaevfujVWrVgEA1q9fj/fff19yKv3DgodeasKECTAzM8M///yDw4cPy45DRFSiZGRkICIiAqampvj555/Rr18/2ZH0EgseeilbW1sMHjwYADBv3jzJaYiISpYyZcpg//79CAwMRO/evWXH0VsseOiVTJo0CSYmJjh69ChOnjwpOw4RkUELCQnBjz/+qLx2cHBAq1atJCbSfyx46JU4Ojqif//+AJ5MY05EREUjMDAQrVq1wpAhQ7B//37ZcQwGCx56ZTNmzECzZs0watQoZV10dDQfPUFEVEg2btyIjh074tGjR3j77bfh6ekpO5LBYMFDr8zR0REnT56Eubk5gCe3SXbo0AH16tXDr7/+itzcXMkJiYj0kxACCxcuRP/+/ZGdnY0PP/wQAQEBKFOmjOxoBoMFDxWISqVS/hwZGYnY2FiEh4ejd+/eaNiwIX7//Xfeuk5EVAA5OTkYOXIkpk6dCgD4/PPPsXnzZmg0GsnJDAsLHnptrq6uiIqKwqxZs2BlZYULFy7gvffeQ5MmTbB//34WPkREr+CPP/7AqlWroFKpsGzZMixevBhqNb+eC5tK8FsJycnJsLa2RlJSEqysrGTH0UsPHjyAn58fvv32W6SmpgIAjh07hpYtW0pORkSk+3x8fNC4cWNOKFhABfn+ZsEDFjyF6e7du1i0aBGCg4Nx8OBB5RJYbGws7O3tJacjItINUVFRKFeuHKytrWVH0WsF+f5mnxkVKhsbG/j5+WkVO4mJiXB1dYW3tzdOnz4tOSERkVzbt2/HW2+9hZ49eyIzM1N2nBKDBQ8ViWcHNx87dgwpKSn4888/4eHhgS5duiA4OFhiOiKi4peamoqhQ4eiV69eSExMxKNHj5CUlCQ7VonBgoeKXNeuXREZGYmBAwdCrVZjz549eOutt/D+++8jNDRUdjwioiJ3/vx5NG7cGN9//z1UKhWmTp2K48ePo2LFirKjlRgseKhYODk5wd/fH2FhYejTpw9UKhV27NiBhg0bIj4+XnY8IqIiIYTAN998g6ZNmyIiIgL29vY4ePAgFixYABMTE9nxShQWPFSsateujS1btuDChQvo2bMn+vXrB1tbW2X7/fv3JaYjIipc6enpWL16NTIzM9GlSxdcuHABbdq0kR2rROJdWuBdWjLl5OTAyMgIABAWFoa33noL/fv3x/Tp0+Ho6Cg5HRHRmwsJCcGJEycwYsQIrfGN9OZ4lxbpjafFDgDs2rULGRkZ+P7771GzZk2MHj0asbGxEtMRERVMZmYmpkyZgqVLlyrr3N3dMXLkSBY7krGHB+zh0SXHjx/HjBkzcOTIEQCAmZkZRowYgSlTpsDGxkZyOiKi57t69Sr69OmDM2fOwMTEBFevXmVPdRFjDw/prRYtWuDw4cM4dOgQmjdvjvT0dCxduhRNmjThU9mJSGdt3LgRDRs2xJkzZ1C2bFn8/PPPLHZ0DAse0klt2rTB8ePHsX//fjRu3BgjR45ULn8JIZCcnCw5IRHRkx6Gjz/+GP3790dKSgpatWqF8+fPo0ePHrKj0X+w4CGdpVKp0L59e5w+fRrjx49X1v/xxx+oVq0aFixYgJSUFIkJiagky8rKQrNmzbB582YYGRlh7ty5OHz4MBwcHGRHo3xIK3iOHj0KlUqV7/Lvv/8CAG7cuJHv9lOnTmnta9u2bXBxcYGZmRnq1auHffv2yTgkKiIqlUprvopNmzbh4cOHmDZtGqpXrw4/Pz88fvxYYkIiKolMTEwwePBgVK1aFceOHcP06dO1bsQg3SJt0HJmZiYePHigte7LL7/EoUOHcO3aNahUKty4cQPVq1fHwYMH4ebmprQrX7688gV48uRJtGrVCr6+vujcuTO2bNmCr776CufOnUPdunVfKQsHLeuXnJwc/Pzzz5g1axauXr0KALCzs8MXX3yBoUOHQqPRSE5IRIbqzp07yvMBASA3NxcpKSn87pBEL5+WnpWVhcqVK2P06NH48ssvAUApeIKDg+Hu7p7v+3r37o3U1FTs2bNHWdesWTO4u7tj9erVr/TZLHj0U3Z2NjZu3Ig5c+bgxo0bAICOHTti7969coMRkcHJzMzE6tWrMXv2bFSoUAFnz55F6dKlZccq8fTyLq3du3cjISEBn3zySZ5tXbt2hY2NDVq0aIHdu3drbQsKCoKXl5fWOm9vbwQFBT33szIyMpCcnKy1kP4xNjbGJ598gsjISKxevRpVqlTB0KFDle0ZGRnIzs6WmJCI9J0QAjt37oSbmxvGjh2LBw8eoFSpUnmuUJDu05mC58cff4S3tzeqVKmirCtdujSWLFmCbdu2Ye/evWjRogW6d++uVfTExcVpPZoAAGxtbREXF/fcz/L19YW1tbWycICZfjM1NcVnn32GK1euoGvXrsr6b775Bm5ubtiyZQtvaSeiAjt16hRatmyJnj174urVq7C1tcWaNWtw+vRp3nKuj0QhmzJligDwwiU8PFzrPTExMUKtVovt27e/dP/9+vUTLVq0UF6bmJiILVu2aLVZuXKlsLGxee4+0tPTRVJSkrLExMQIACIpKamAR0u6KicnR7i4uCh/51xdXcW2bdtETk6O7GhEpAeCg4OVfz/Mzc3Fl19+KZKTk2XHov9ISkp65e9v48IuoCZOnIiBAwe+sI2Tk5PWa39/f5QvX17rt/Pn8fDwQGBgoPLazs4uz9O24+PjYWdn99x9aDQaDmw1cGq1GqdPn8a3334LPz8/hIWFoVevXmjQoAHmzJmDLl26cJp3ItLy7LP93N3d0b59e1SqVAlz5sxB5cqVJaejNyV90LIQAjVq1ECPHj3g5+f30vZDhgzB2bNnce7cOQBPBi0/fvwYf/zxh9KmefPmqF+/PgctEwAgMTERX3/9Nb7++ms8evQIAODj4wNfX1/JyYhIF2RkZGDlypVYvnw5Tp8+jYoVKwJ4cmOEsXGh9wtQIdKrQcuHDx9GVFQUBg8enGfbhg0bsHXrVkRERCAiIgILFizAunXrMHr0aKXN2LFjERAQgCVLliAiIgKzZs3CmTNnMGrUqOI8DNJhZcqUwezZsxEVFQUfHx9YWlqiX79+yvaMjAyJ6YhIFiEEfv31V9SpUwcTJ07EjRs3sGbNGmU7ix0DU8SX116qT58+onnz5vluW79+vahTp46wsLAQVlZWomnTpmLbtm152v3666+iVq1awtTUVLi5uYm9e/cWKENBrgGS/nv06JHW608++US888474vjx45ISEVFxO378uGjWrJkyTsfe3l78+OOPIjs7W3Y0KoCCfH9Lv6SlC3hJq+R68OABHBwclJma27dvjzlz5qBJkyaSkxFRURBCoE+fPvjll18AAKVKlcLkyZMxceJElCpVSnI6Kii9uqRFJFO5cuUQHh6OIUOGwNjYGAEBAWjatCm6deuG8+fPy45HRIVMpVKhQoUKUKvVGDJkCK5cuYIZM2aw2CkB2MMD9vDQE9evX8ecOXOwceNG5ObmAgC2bt2KDz/8UHIyInpd6enpWL58Oby9vVG/fn0AwP379xEfH6/1yCLST+zhIXoNTk5OWL9+PcLCwvDhhx+iXLlyaN++vbKdszYT6Y/c3Fxs2bIFLi4umDx5MiZNmqRsq1ChAoudEogFD9F/1K5dG1u3bsXVq1dRpkwZAE+u+7dt2xaffvopoqKi5AYkohf666+/4OHhgb59++LmzZuoXLkyPvroI/CCRsnGgofoOcqWLav8+cyZMzh27Bj8/f1Rq1YtDBs2DLdu3ZKYjoj+KzIyEt27d0fr1q1x5swZlC5dGvPnz8fly5cxYMAATjZawrHgIXoFTZo0QVBQEN59911kZ2djzZo1cHZ2xtixY1/43DYiKj4BAQHYtWsXjIyMMHz4cFy9ehVffPEFLCwsZEcjHcBBy+CgZSqYv//+G19++SX++usvAIC5uTlOnDiBhg0bSk5GVHLk5OTgyJEjSE1NRbdu3QAAmZmZGDNmDMaOHYs6depITkjFoSDf3yx4wIKHCk4IgcOHD+PLL79EUlISLly4oDyDJzc3F2o1O0+JisLly5exYcMGbNy4ETExMXB2dsbly5d5uaqEKsj3N+fNJnoNKpUKbdu2RZs2bXDv3j2l2ElLS0Pjxo3Ru3dvjBs3jgU0USFITEzEL7/8gg0bNiAoKEhZX6ZMGXh5eeHx48ecR4deij08YA8PFZ5169Zh0KBBAJ5Majhp0iSMHj2a/xgTvYFPP/0U/v7+AAAjIyN4e3tj4MCB6NKlC8zMzCSnI5k4Dw+RJAMHDsQvv/wCFxcXPHjwAFOnTkX16tWxdOlSpKWlyY5HpPNCQ0MxefJkXLhwQVnXr18/1K1bF35+frh16xb27t2LXr16sdihAmEPD9jDQ4UvJycHW7ZswezZs3Ht2jUAQKVKlXDp0iWt292JCEhISMDWrVuxYcMGnDlzBgAwZswYfPPNNwCgzJ/DcTr0X+zhIZLMyMgI/fr1Q3h4OH744Qc4OjqiSZMmWsUOf9egkiwnJwe7d+9Gz549YW9vj9GjR+PMmTMwNjZGt27d0KFDB6WtSqVisUNvjD08YA8PFb3MzEwkJibCxsYGABATE4P27dtj8uTJ6Nu3L4yNef8AlSzZ2dmoUqUK4uPjAQANGzbEwIED0adPH1SsWFFyOtIX7OEh0jGmpqZKsQMAy5YtQ1hYGAYOHIi6deti69atygNLiQxNfHw8li5divbt2yMnJwcAYGxsjHHjxmHixIm4cOECzp07hzFjxrDYoSLDHh6wh4eKX2pqKlauXIlFixYhISEBAFC3bl3Mnj0b7733HrvvSe9lZGTgjz/+wIYNG7B//36l0Dlw4ADatWsnOR0ZCk48WEAseEiWR48e4ZtvvoGfnx+SkpIAAC1atMCxY8dY9JBeunbtGpYuXYqtW7fi4cOHynoPDw8MGDAAH374IQfuU6HhJS0iPWFpaYnp06cjKioK06dPR+nSpfG///2PxQ7plWd/b05ISMB3332Hhw8fonLlyvDx8UF4eDhOnTqF4cOHs9ghadjDA/bwkO64f/8+jI2NUaZMGQBPnts1bdo0zJ07F2+//bbccETPSEtLw65du7B+/XpUq1YNq1evBvCk+Pn888/h7e2Ntm3bKrOQExUFXtIqIBY8pKu8vb3x559/AgDatm2LuXPnwtPTU3IqKqmEEAgKCsL69evx66+/KpdhrayscPfuXWg0GskJqaThJS0iA7Fu3TqMGDECJiYmOHToEJo3b46OHTsqk7MRFZe1a9eidu3a+N///ofvv/8eSUlJqFq1Kr788kucPXuWxQ7pPBY8RDqscuXKWLlyJa5cuYJBgwbByMgI+/fvR5MmTTBmzBjZ8cjAZGdnIzIyEr/99hvmzZuH6OhoZdvt27dx5coVlCpVCgMGDMDhw4dx/fp1zJkzB87OzhJTE70aznZGpAeqVq2KH374AT4+PpgzZw42b96Mhg0byo5Fei4iIgLbt29HWFgYQkNDERkZiYyMDGV7rVq14OjoCODJAzydnJzQs2dPlC5dWlZkotfGMTzgGB7SP5GRkahRo4YyQ/O6deuwfft21KhRA7a2trC1tYWdnZ3yZ0dHR975VQLl5OTg+vXrSkETGhqKIUOGoHXr1gCA3377DT169NB6j7m5OVxdXeHq6oqhQ4eiRYsWEpITvZqCfH+zh4dID9WuXVv5c3Z2NmbPnq11+eFZKpUKmZmZSnE0Z84cXLx4UasgYnFkOMLDwzF//nyEhoYiIiIC6enpWtvd3NyUgqdhw4bo168f3Nzc4OrqCjc3N1SrVg1qNUc7kOFhwUOk54yNjbFr1y4cO3YM8fHxyhIXF4f4+HgIIbSe1XX06FEcOXIk332p1WpkZmYqtxLPmTMHly5dem5x5ODgwOKoGOXm5uLGjRtKb01oaCjCwsLw6aefYuTIkQCeFMCbN29W3mNmZoY6derAzc0Nbm5uePfdd5Vt1apVw08//VTsx0EkAwseIgPg7u4Od3f3fLf996r15MmT0b17d6UgerY4UqlUWvOmHDlyBEePHs13v/kVR6GhofkWRiyOCiY3NxdpaWkoVaoUAODGjRt4//33ER4ejsePH+dp36BBA+XPtWrVwvz585UCp3r16pwLhwgcwwOAY3iInhJCaBUlAQEBiIyMzFMYxcfHQ61W4+bNm0rb1q1b46+//sp3v0ZGRsjMzFQulcyZMwdhYWH5Fkd2dnaoXLlyiSiOcnNzERMTo9VjExoaivDwcPTr1w+rVq0C8OTZa08HCpuamsLFxUUpaNzc3NCwYUNUrVpV5qEQScGJBwuIBQ9Rwf23ONq3bx8uX7783OLo2TFGb7/9No4dO5bvfv9bHM2ePRvh4eF6XRwJIRATE4PHjx/DxcUFwJMixs7ODikpKfm+55133sHhw4eV1/v374eTk5PWYHWiko4FTwGx4CEqWgUpjoyMjLR6jlq1aoW///473/0aGxsjIyNDqziKiIh4bnFUqVKlIi2OnhY2z94V9XScTUpKCt59911l5mzgyTxL9+7dQ+3atbUGDru5ucHZ2ZmFDdFLsOApIBY8RLrjv8XR3r17n1scmZiY4MaNG0rbli1b4vjx4/nu18TEBBkZGcq+Z82ahcjISKUo+m9xZG9v/9ziSAiB27dvIzQ0FGlpaejevbuyvmLFikhISMjzHmNjY7Rq1QqHDh1S1sXExMDOzg4mJiYFPU1EBBY8BcaCh0g//bc42rNnD65cuZKnMIqLi4NGo0FUVJTStkWLFjhx4kS++zU1NUV6erpWcXT58mWYmZkhIiICoaGhSE5OBgBUr14d169fV97r5eWF2NhYpafmaa9NzZo1WdgQFTKdmIdn/vz52Lt3L0JCQmBqaorExMQ8baKjozF8+HAcOXIEpUuXxoABA+Dr65vnFtoJEyYgNDQUDg4OmD59OgYOHKi1n5UrV2Lx4sWIi4tDgwYNsHz5cjRt2rSoDo2IdMR/e2A6d+783Lb//d1uypQpzy2OzMzMtPYdGBiIkydPar3f2NgYNWvWRN26dZGbm6tcVgsMDNT5MUVEJVGRFTyZmZno1asXPD098eOPP+bZnpOTg06dOsHOzg4nT55EbGws+vfvDxMTEyxYsAAAEBUVhU6dOmHYsGHYvHkzDh06hMGDB8Pe3h7e3t4AgF9++QUTJkzA6tWr4eHhgWXLlsHb2xuRkZGwsbEpqsMjIj3z3yKkS5cuz2373+LIx8cHV65cQWpqKmrVqgU3NzfUqlULpqamL/0cItINRX5Ja/369Rg3blyeHp79+/ejc+fOuHPnDmxtbQEAq1evxpQpU3Dv3j2YmppiypQp2Lt3Ly5duqS878MPP0RiYiICAgIAAB4eHmjSpAlWrFgB4Mltng4ODhg9ejR8fHxeKSMvaREREemfgnx/S5s/PCgoCPXq1VOKHQDw9vZGcnIyQkNDlTZeXl5a7/P29kZQUBCAJ71IZ8+e1WqjVqvh5eWltMlPRkYGkpOTtRYiIiIyXNIKnri4OK1iB4DyOi4u7oVtkpOTkZaWhvv37yMnJyffNk/3kR9fX19YW1sri4ODQ2EcEhEREemoAhU8Pj4+UKlUL1wiIiKKKmuhmTp1KpKSkpQlJiZGdiQiIiIqQgUatDxx4sQ8d0j9l5OT0yvty87ODqdPn9ZaFx8fr2x7+t+n655tY2VlBXNzcxgZGcHIyCjfNk/3kR+NRgONRvNKOYmIiEj/FajgqVixIipWrFgoH+zp6Yn58+fj7t27yt1UgYGBsLKygqurq9Jm3759Wu8LDAyEp6cngCdzZTRq1AiHDh1SJv7Kzc3FoUOHMGrUqELJSURERPqvyMbwREdHIyQkBNHR0cjJyUFISAhCQkKU58a0a9cOrq6u6NevH86fP48DBw5g+vTpGDlypNL7MmzYMFy/fh2TJ09GREQEvvvuO/z6668YP3688jkTJkzA999/jw0bNiA8PBzDhw9HamoqPvnkk6I6NCIiItI3oogMGDBAAMizHDlyRGlz48YN0aFDB2Fubi4qVKggJk6cKLKysrT2c+TIEeHu7i5MTU2Fk5OT8Pf3z/NZy5cvF46OjsLU1FQ0bdpUnDp1qkBZk5KSBACRlJT0OodKREREEhTk+5uPlgDn4SEiItJHejEPDxEREVFxYcFDREREBo8FDxERERk8FjxERERk8FjwEBERkcEr0MSDhurpjWp8iCgREZH+ePq9/So3nLPgAfDo0SMA4ENEiYiI9NCjR49gbW39wjachwdPHkdx584dWFpaQqVSyY6jc5KTk+Hg4ICYmBjOU/QaeP7eDM/f6+O5ezM8f2+mOM6fEAKPHj1CpUqVoFa/eJQOe3gAqNVqVKlSRXYMnWdlZcUf+jfA8/dmeP5eH8/dm+H5ezNFff5e1rPzFActExERkcFjwUNEREQGjwUPvZRGo8HMmTOVp9hTwfD8vRmev9fHc/dmeP7ejK6dPw5aJiIiIoPHHh4iIiIyeCx4iIiIyOCx4CEiIiKDx4KHiIiIDB4LnhJk/vz5aN68OSwsLFCmTJl820RHR6NTp06wsLCAjY0NJk2ahOzsbK02R48exVtvvQWNRgNnZ2esX78+z35WrlyJatWqwczMDB4eHjh9+rTW9vT0dIwcORLly5dH6dKl0bNnT8THxxfWoRaLy5cvo1u3bqhQoQKsrKzQokULHDlyRKtNcZ1PfbV37154eHjA3NwcZcuWRffu3bW28/y9WEZGBtzd3aFSqRASEqK17cKFC2jZsiXMzMzg4OCARYsW5Xn/tm3b4OLiAjMzM9SrVw/79u3T2i6EwIwZM2Bvbw9zc3N4eXnhypUrRXlIRe7GjRsYNGgQqlevDnNzc9SoUQMzZ85EZmamVjuevzejkz9zgkqMGTNmiKVLl4oJEyYIa2vrPNuzs7NF3bp1hZeXlwgODhb79u0TFSpUEFOnTlXaXL9+XVhYWIgJEyaIsLAwsXz5cmFkZCQCAgKUNj///LMwNTUV69atE6GhoWLIkCGiTJkyIj4+XmkzbNgw4eDgIA4dOiTOnDkjmjVrJpo3b16kx1/YatasKTp27CjOnz8vLl++LEaMGCEsLCxEbGysEKJ4z6c+2r59uyhbtqxYtWqViIyMFKGhoeKXX35RtvP8vdyYMWNEhw4dBAARHBysrE9KShK2traib9++4tKlS2Lr1q3C3NxcrFmzRmlz4sQJYWRkJBYtWiTCwsLE9OnThYmJibh48aLSZuHChcLa2lr8/vvv4vz586Jr166ievXqIi0trTgPs1Dt379fDBw4UBw4cEBcu3ZN7Nq1S9jY2IiJEycqbXj+3oyu/syx4CmB/P398y149u3bJ9RqtYiLi1PWrVq1SlhZWYmMjAwhhBCTJ08Wbm5uWu/r3bu38Pb2Vl43bdpUjBw5Unmdk5MjKlWqJHx9fYUQQiQmJgoTExOxbds2pU14eLgAIIKCggrlGIvavXv3BABx7NgxZV1ycrIAIAIDA4UQxXc+9VFWVpaoXLmy+OGHH57bhufvxfbt2ydcXFxEaGhonoLnu+++E2XLllXOkxBCTJkyRdSuXVt5/cEHH4hOnTpp7dPDw0N89tlnQgghcnNzhZ2dnVi8eLGyPTExUWg0GrF169YiOio5Fi1aJKpXr6685vl7M7r6M8dLWqQICgpCvXr1YGtrq6zz9vZGcnIyQkNDlTZeXl5a7/P29kZQUBAAIDMzE2fPntVqo1ar4eXlpbQ5e/YssrKytNq4uLjA0dFRaaPrypcvj9q1a+Onn35CamoqsrOzsWbNGtjY2KBRo0YAiu986qNz587h9u3bUKvVaNiwIezt7dGhQwdcunRJacPz93zx8fEYMmQINm7cCAsLizzbg4KC0KpVK5iamirrvL29ERkZiYcPHyptXnTuoqKiEBcXp9XG2toaHh4een3u8pOUlIRy5copr3n+Xp8u/8yx4CFFXFyc1pcLAOV1XFzcC9skJycjLS0N9+/fR05OTr5tnt2HqalpnnFEz7bRdSqVCgcPHkRwcDAsLS1hZmaGpUuXIiAgAGXLlgVQfOdTH12/fh0AMGvWLEyfPh179uxB2bJl0bp1azx48AAAz9/zCCEwcOBADBs2DI0bN863zZucu2e3P/u+/NoYgqtXr2L58uX47LPPlHU8f69Pl3/mWPDoOR8fH6hUqhcuERERsmPqjVc9n0IIjBw5EjY2Nvj7779x+vRpdO/eHV26dEFsbKzsw5DmVc9fbm4uAGDatGno2bMnGjVqBH9/f6hUKmzbtk3yUcjxqudu+fLlePToEaZOnSo7sk55nX8Lb9++jfbt26NXr14YMmSIpORUXIxlB6A3M3HiRAwcOPCFbZycnF5pX3Z2dnlG0j+9c8rOzk7573/vpoqPj4eVlRXMzc1hZGQEIyOjfNs8u4/MzEwkJiZq9fI820aWVz2fhw8fxp49e/Dw4UNYWVkBAL777jsEBgZiw4YN8PHxKbbzqUte9fw9LQpdXV2V9RqNBk5OToiOjgZQfH8fdUVB/u4FBQXleT5R48aN0bdvX2zYsOG55wV4+bl7dvvTdfb29lpt3N3dC3x8Ra2g/xbeuXMH77zzDpo3b461a9dqtSuJ56+wVKhQQXd/5qSOICIpXjZo+dmR9GvWrBFWVlYiPT1dCPFkkGjdunW13tenT588g0RHjRqlvM7JyRGVK1fOM2h5+/btSpuIiAi9GrS8e/duoVarxaNHj7TW16pVS8yfP18IUXznUx8lJSUJjUajNWg5MzNT2NjYKHfC8Pzl7+bNm+LixYvKcuDAAQFAbN++XcTExAgh/v+g28zMTOV9U6dOzTPotnPnzlr79vT0zDPo1s/PT9n+9P+bvg+6vXXrlqhZs6b48MMPRXZ2dp7tPH9vRld/5ljwlCA3b94UwcHBYvbs2aJ06dIiODhYBAcHK1/aT28DbteunQgJCREBAQGiYsWK+d4GPGnSJBEeHi5WrlyZ723AGo1GrF+/XoSFhYmhQ4eKMmXKaN1tM2zYMOHo6CgOHz4szpw5Izw9PYWnp2fxnYw3dO/ePVG+fHnRo0cPERISIiIjI8Xnn38uTExMREhIiBCieM+nPho7dqyoXLmyOHDggIiIiBCDBg0SNjY24sGDB0IInr9XFRUVlecurcTERGFrayv69esnLl26JH7++WdhYWGR57ZqY2Nj4efnJ8LDw8XMmTPzva26TJkyYteuXeLChQuiW7duen9b9a1bt4Szs7No27atuHXrloiNjVWWp3j+3oyu/syx4ClBBgwYIADkWY4cOaK0uXHjhujQoYMwNzcXFSpUEBMnThRZWVla+zly5Ihwd3cXpqamwsnJSfj7++f5rOXLlwtHR0dhamoqmjZtKk6dOqW1PS0tTYwYMUKULVtWWFhYiPfee0/rHxx98O+//4p27dqJcuXKCUtLS9GsWTOxb98+rTbFdT71UWZmppg4caKwsbERlpaWwsvLS1y6dEmrDc/fy+VX8AghxPnz50WLFi2ERqMRlStXFgsXLszz3l9//VXUqlVLmJqaCjc3N7F3716t7bm5ueLLL78Utra2QqPRiLZt24rIyMiiPJwi5+/vn++/g/+94MHz92Z08WdOJYQQEq6kERERERUb3qVFREREBo8FDxERERk8FjxERERk8FjwEBERkcFjwUNEREQGjwUPERERGTwWPERERGTwWPAQERGRwWPBQ0RERAaPBQ8REREZPBY8REREZPBY8BAREZHB+38szM30OQpX8wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('M1');\n",
    "f1,Rin1,din1,Rout1,dout1,w_out1,angle1,Theta_beam,Lambda=Quasi_Optics('M1.txt',size,'f2')\n",
    "beta1,alpha1,e1,a1,b1,c1=Ellips(f1,Rin1,Rout1,angle1,Theta_beam,Size=size)\n",
    "\n",
    "center_projector(beta1,alpha1,e1,a1,c1)\n",
    "Theta_beam*Rin1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "phi_0: 90.88712701409226\n",
      "p 170.0\n",
      "e: 0.9848696398237212 \n",
      " a: 5660.667763910227 \n",
      " b: 980.9757998364377 \n",
      " c: 5575.019821804015\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta1,alpha1,e1,a1,b1,c1=Ellips2(f1,Rin1,Rout1,angle1,Theta_beam,Size=size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rotation of M2 coord z: 0.437404117484204\n",
      "Rotation of M2 coord x: -0.8992650543682128\n",
      "x0: 31.821226377681466\n",
      "y_axis: 3.983679326403789\n",
      "x_axis: 5.347625393602494\n",
      "m1 origin coord system z: 34.82550476146321\n",
      "m1 origin coord system x: -66.20247054109214\n",
      "rotation of m1 coord z: 6.123233995736766e-17\n",
      "rotation of m1 coord x: -1.0\n",
      "roation angul of surface m1: -89.11287298590774\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "produce coordinate frame of concave case;\n",
    "1. A2 coordinate M2 (Z,X);\n",
    "2. rim x0, y_axis, x_axis;\n",
    "3. origin of m1 coordinate and rotation anglu;\n",
    "4. \n",
    "'''\n",
    "\n",
    "A2=0-np.arccos(-(Rout2**2-4*c2**2-Rin2**2)/(4*c2*Rin2));\n",
    "print('Rotation of M2 coord z:',np.cos(A2));\n",
    "print('Rotation of M2 coord x:',np.sin(A2));\n",
    "\n",
    "x0,y_axis,x_axis=center_projector(A2,alpha2,e2,a2,c2)\n",
    "print('x0:',x0);\n",
    "print('y_axis:',y_axis);\n",
    "print('x_axis:',x_axis);\n",
    "\n",
    "print('m1 origin coord system z:',Rin2+(Rin1-(din1+dout2))*np.cos(angle2/180*np.pi));\n",
    "print('m1 origin coord system x:',0-(Rin1-(din1+dout2))*np.sin(angle2/180*np.pi))\n",
    "\n",
    "\n",
    "\n",
    "print('rotation of m1 coord z:',np.cos(-angle2/180*np.pi));\n",
    "print('rotation of m1 coord x:',np.sin(-angle2/180*np.pi));\n",
    "\n",
    "A1=np.arccos(-(Rout1**2-4*c1**2-Rin1**2)/(4*c1*Rin1));\n",
    "print('roation angul of surface m1:',-A1*180/np.pi)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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