sql_hl_luis v2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "import qutip as qt\n",
    "import qutip\n",
    "\n",
    "# -- References to Relevant Papers --\n",
    "# \"Entanglement-enhanced quantum metrology: From standard quantum limit to Heisenberg limit\" (Huang et al.)\n",
    "#\n",
    "\n",
    "##I worked with this: Phase stimation by interferometry as of figure 2b (page 4) implemented with One axis Twisting (OAT), page 10-12.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Parameters for preparation, sensing, and measurement times\n",
    "T_total = 1.0  # Total fixed time for the experiment\n",
    "\n",
    "# Fraction of time allocated for preparation and measurement\n",
    "tau_prep_fraction = 0.1  # Fraction of time spent on preparation\n",
    "tau_meas_fraction = 0.05  # Fraction of time spent on measurement\n",
    "tau_sense_fraction = 1 - tau_prep_fraction - tau_meas_fraction  # Remaining time for sensing\n",
    "\n",
    "def generate_coherent_state(j):\n",
    "    \"\"\"\n",
    "    Generate a coherent spin state aligned along the x-axis.\n",
    "\n",
    "    Based on the description of coherent states for metrology in Pezzé & Smerzi, Section III. [41†source].\n",
    "    \n",
    "    Parameters:\n",
    "        j (float): Total spin quantum number (N/2).\n",
    "    \n",
    "    Returns:\n",
    "        Qobj: Coherent spin state.\n",
    "    \"\"\"\n",
    "    theta = np.pi / 2  # Aligned along the x-axis\n",
    "    phi = 0  # No rotation around the z-axis\n",
    "    return qt.spin_coherent(j, theta, phi)\n",
    "\n",
    "def gen_css(j,theta,phi):\n",
    "    return qt.spin_coherent(j, theta, phi)\n",
    "\n",
    "def apply_squeezing_operator(squeezing_strength, J):\n",
    "    \"\"\"\n",
    "    Apply a squeezing operator to the coherent state.\n",
    "\n",
    "    The use of squeezing to improve phase sensitivity is discussed in Hayes et al., Section 2.2. [42†source].\n",
    "    \n",
    "    Parameters:\n",
    "        j (float): Total spin quantum number.\n",
    "        squeezing_strength (float): The strength of squeezing.\n",
    "        Jy (Qobj): Spin operator along the z?-axis.\n",
    "    \n",
    "    Returns:\n",
    "        Qobj: Squeezing operator.\n",
    "    \"\"\"\n",
    "    squeezing_operator = (-1j * squeezing_strength * J**2).expm()\n",
    "    return squeezing_operator\n",
    "\n",
    "def time_evolve_state(H, state, t):\n",
    "    \"\"\"\n",
    "    Perform time evolution of a quantum state under a Hamiltonian H for time t.\n",
    "\n",
    "    Time evolution based on the Hamiltonian dynamics as outlined in Pezzé et al., Phys. Rev. A, 2020. Section II [41†source].\n",
    "    \n",
    "    Parameters:\n",
    "        H (Qobj): Hamiltonian of the system.\n",
    "        state (Qobj): Initial quantum state.\n",
    "        t (float): Time of evolution.\n",
    "    \n",
    "    Returns:\n",
    "        Qobj: Evolved quantum state after time t.\n",
    "    \"\"\"\n",
    "    U = (-1j * H * t).expm()  # Time evolution operator U = exp(-i H t)\n",
    "    return U * state\n",
    "\n",
    "def measure_phase_variance(operator, state):\n",
    "    \"\"\"\n",
    "    Measure the phase variance of the given state.\n",
    "\n",
    "    Fisher Information and phase variance calculations are fundamental to quantum metrology, as discussed in Pezzé et al., Section III. [42†source].\n",
    "    \n",
    "    Parameters:\n",
    "        operator (Qobj): Spin operator (typically Jz).\n",
    "        state (Qobj): Quantum state (coherent or squeezed).\n",
    "    \n",
    "    Returns:\n",
    "        float: Phase variance of the state.\n",
    "    \"\"\"\n",
    "    return qt.variance(operator, state)\n",
    "\n",
    "def calculate_fisher_information(N, sensing_time, is_entangled):\n",
    "    \"\"\"\n",
    "    Calculate Fisher Information for both separable (SQL) and entangled (HL) states.\n",
    "\n",
    "    This formula for Fisher Information scaling is adapted from Pezzé et al., Rev. Mod. Phys., 2018, page 6 [42†source].\n",
    "    \n",
    "    Parameters:\n",
    "        N (int): Number of particles.\n",
    "        sensing_time (float): The time spent in sensing.\n",
    "        is_entangled (bool): If True, apply Heisenberg scaling for entangled states.\n",
    "    \n",
    "    Returns:\n",
    "        float: Fisher Information.\n",
    "    \"\"\"\n",
    "    if is_entangled:\n",
    "        return N**2 * sensing_time**2  # Heisenberg scaling\n",
    "    else:\n",
    "        return N * sensing_time**2  # Standard Quantum Limit scaling\n",
    "\n",
    "def calculate_r_value(F_sep, F_ent, total_time_sep, total_time_ent):\n",
    "    \"\"\"\n",
    "    Calculate the metrological gain r, comparing separable and entangled strategies.\n",
    "\n",
    "    This calculation is adapted from \"Entanglement-enhanced quantum metrology\", Section II. [42†source].\n",
    "    \n",
    "    Parameters:\n",
    "        F_sep (float): Fisher Information for separable states.\n",
    "        F_ent (float): Fisher Information for entangled states.\n",
    "        total_time_sep (float): Total time for separable strategy.\n",
    "        total_time_ent (float): Total time for entangled strategy.\n",
    "    \n",
    "    Returns:\n",
    "        float: Metrological gain r.\n",
    "    \"\"\"\n",
    "    return (F_ent / total_time_ent) / (F_sep / total_time_sep)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 25.08280187535013 204.34473931154795\n",
      "9.999999999999995 9.999999999999993 9.999999999999995\n"
     ]
    }
   ],
   "source": [
    "css6 = generate_coherent_state(20)\n",
    "\n",
    "squeezing_strength1 = 0.1\n",
    "Sz = qt.jmat(20, 'z')\n",
    "Sx = qt.jmat(20, 'x')\n",
    "squeezing_operator1 = apply_squeezing_operator(squeezing_strength1, Sz)\n",
    "sqz6 = squeezing_operator1 * css6\n",
    "\n",
    "squeezing_strength2 = 0.4 \n",
    "squeezing_operator2 = apply_squeezing_operator(squeezing_strength2, Sz)\n",
    "sqz6b = squeezing_operator2 * css6\n",
    "\n",
    "print(qt.variance(Sx,css6),qt.variance(Sx,sqz6),qt.variance(Sx,sqz6b))\n",
    "print(qt.variance(Sz,css6),qt.variance(Sz,sqz6),qt.variance(Sz,sqz6b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetavec = np.linspace(0, np.pi, 100)\n",
    "phivec = np.linspace(-np.pi,np.pi, 100)\n",
    "fcss6,theta,phi = qt.spin_q_function(css6,thetavec,phivec)\n",
    "fsqz6,theta1,phi1 = qt.spin_q_function(sqz6,thetavec,phivec)\n",
    "fsqz6b,theta2,phi2 = qt.spin_q_function(sqz6b,thetavec,phivec)\n",
    "\n",
    "fig,axes = plt.subplots(1,3,figsize=(6,4))\n",
    "cont0 = axes[0].contourf(theta,phi,fcss6)\n",
    "lbl0 = axes[0].set_title(\"Coherent state\")\n",
    "\n",
    "cont1 = axes[1].contourf(theta1, phi1,fsqz6)\n",
    "lbl1 = axes[1].set_title(\"Squezed state 0.1\")#\n",
    "\n",
    "cont2 = axes[2].contourf(theta2, phi2,fsqz6b)\n",
    "lbl2 = axes[2].set_title(\"Squezed state 0.4\")#\n",
    "\n",
    "#In [59]: cont0 = axes[2].contourf(xvec, xvec, Q_fock, 100)\n",
    "\n",
    "#In [60]: lbl2 = axes[2].set_title(\"Fock state\")\"\"\"\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One axis twisting, aligned with the standard axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu: 0.2305058100333494   delta_opt: 0.2548905343827575 Var min:  0.9410360288810284 0.9258195409991143\n",
      "10.000000000000016 9.999999999999995\n",
      "40 0.2548905343827575 143.65924937226455 0.925819540999102\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for N in range (40,41):\n",
    "\n",
    "    Sx = qt.jmat(N/2, 'x')\n",
    "    Sy = qt.jmat(N/2, 'y')\n",
    "    Sz = qt.jmat(N/2, 'z')\n",
    "\n",
    "\n",
    "    mu = (24)**(1/6)*(N/2)**(-2/3)\n",
    "    A = 1-np.cos(mu)**(N-2)\n",
    "    B = 4*np.sin(mu/2)*np.cos(mu/2)**(N-2)\n",
    "    delta = (1/2)*np.arctan(B/A)\n",
    "    #delta2 = np.pi-(1/2)*np.arccos(-A/np.sqrt(A**2+B**2))\n",
    "    #delta3 = 1/2*np.arctan(4/N*mu)\n",
    "    squeezing_strength = mu/2\n",
    "    #delta=mu\n",
    "    \n",
    "    print(\"mu:\", mu, \"  delta_opt:\", delta, \"Var min: \",(1/2)*(N/6)**(1/3), N/4*(1+(N-1)/4*(A-(A**2+B**2)**(1/2))))\n",
    "    #print(\"mu:\",  (12)**(1/6)*(N/2)**(-2/3),\" nu_opt: \",(1/2)*np.arctan(N**(-1/3)))\n",
    "\n",
    "\n",
    "    css_x = generate_coherent_state(N/2)\n",
    "\n",
    "    print(qt.variance(Sy,css_x),qt.variance(Sz,css_x))\n",
    "\n",
    "    squeezing_strength1 = mu/2\n",
    "    rot_spin_oper = (1j * delta  *Sx).expm()*Sz* (-1j * delta  *Sx).expm()\n",
    "    squeezing_operator =apply_squeezing_operator(squeezing_strength1,rot_spin_oper)\n",
    "    sqz_rot = squeezing_operator * css_x\n",
    "    print(N,delta,qt.variance(Sy,sqz_rot),qt.variance(Sz,sqz_rot))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rot_spin_oper = (1j * delta  *Sx).expm()*Sz* (-1j * delta  *Sx).expm()\n",
    "squeezing_operator =apply_squeezing_operator(squeezing_strength1,rot_spin_oper)\n",
    "sqz_rot = squeezing_operator * css_x\n",
    "\n",
    "thetavec = np.linspace(0, np.pi, 100)\n",
    "phivec = np.linspace(-np.pi,np.pi, 100)\n",
    "fcssx,theta,phi = qt.spin_q_function(css_x,thetavec,phivec)\n",
    "fsqzrot,theta1,phi1 = qt.spin_q_function(sqz_rot,thetavec,phivec)\n",
    "\n",
    "fig,axes = plt.subplots(1,2,figsize=(4,4))\n",
    "cont0 = axes[0].contourf(theta,phi,fcssx,cmap=cm.Blues)\n",
    "lbl0 = axes[0].set_title(\"Coherent state\")\n",
    "\n",
    "cont1 = axes[1].contourf(theta1, phi1,fsqzrot,cmap=cm.Blues)\n",
    "lbl1 = axes[1].set_title(\"Squeezed state 0.115\")#\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "N = 100\n",
    "j = N / 2  # Total spin quantum number\n",
    "        \n",
    "# Define collective spin operators\n",
    "Sx = qt.jmat(j, 'x')\n",
    "Sy = qt.jmat(j, 'y')\n",
    "Sz = qt.jmat(j, 'z')\n",
    "\n",
    "# Separable (SQL) Strategy\n",
    "css_z = gen_css(j,0,0) #initial state in north pole\n",
    "      \n",
    "H_sense = Sz  # Sensing Hamiltonian\n",
    "time=1.57 #for instance\n",
    "beam_spl_css = (1j * np.pi/2  *Sx).expm()*css_z\n",
    "evolved_css = time_evolve_state(H_sense, beam_spl_css, time)\n",
    "final_css = (1j * np.pi/2  *Sx).expm()*evolved_css\n",
    "        #Description of what is done in Fig 2b\n",
    "\n",
    "expected_value_sql = qt.expect(Sz,final_css)/N\n",
    "phase_var_sql = qt.variance(Sz, final_css)/N**2\n",
    "#phase_variance_sql.append(phase_var_sql/N**2) \n",
    "#Since we stimate N*phase, to get the variance in theta estimation we have to divide by N**2\n",
    "        \n",
    "        \n",
    "\n",
    "# Entangled (HL) Strategy. One axis twisting version. squeezing in y\n",
    "mu = (24)**(1/6)*(N/2)**(-2/3)\n",
    "A = 1-np.cos(mu)**(N-2)\n",
    "B = 4*np.sin(mu/2)*np.cos(mu/2)**(N-2)\n",
    "delta = (1/2)*np.arctan(B/A)\n",
    "  \n",
    "squeezing_strength = mu/2\n",
    "\n",
    "rot_spin_oper = (1j * delta  *Sz).expm()*Sx* (-1j * delta  *Sz).expm()\n",
    "squeezing_operator =apply_squeezing_operator(squeezing_strength,rot_spin_oper)\n",
    "sss = squeezing_operator * css_z\n",
    "beam_spl_sss = (1j * np.pi/2  *Sx).expm()*sss\n",
    "evolved_sss = time_evolve_state(H_sense, beam_spl_sss, time)\n",
    "final_sss = (1j * np.pi/2  *Sx).expm()*evolved_sss\n",
    "expected_value_hl = qt.expect(Sz,final_sss)/N\n",
    "phase_var_hl = qt.variance(Sz, final_sss)/N**2\n",
    "\n",
    "thetavec = np.linspace(0, np.pi, 100)\n",
    "phivec = np.linspace(0,2*np.pi, 100)\n",
    "initialcss,theta,phi = qt.spin_q_function(css_z,thetavec,phivec)\n",
    "beamcss,theta1,phi1 = qt.spin_q_function(beam_spl_css,thetavec,phivec)\n",
    "evolvecss,theta2,phi2 = qt.spin_q_function(evolved_css,thetavec,phivec)\n",
    "finalcss,theta3,phi3 = qt.spin_q_function(final_css,thetavec,phivec)\n",
    "\n",
    "initialsss,theta4,phi4 = qt.spin_q_function(sss,thetavec,phivec)\n",
    "beamsss,theta5,phi5 = qt.spin_q_function(beam_spl_sss,thetavec,phivec)\n",
    "evolvesss,theta6,phi6 = qt.spin_q_function(evolved_sss,thetavec,phivec)\n",
    "finalsss,theta7,phi7 = qt.spin_q_function(final_sss,thetavec,phivec)\n",
    "\n",
    "fig,axes = plt.subplots(2,4,figsize=(8,8))\n",
    "cont0 = axes[0,0].contourf(theta,phi,initialcss)\n",
    "lbl0 = axes[0,0].set_title(\"Initial Coherent state\")\n",
    "\n",
    "cont1 = axes[0,1].contourf(theta1, phi1,beamcss)\n",
    "lbl1 = axes[0,1].set_title(\"After beam splitter\")#\n",
    "\n",
    "cont2 = axes[0,2].contourf(theta2, phi2,evolvecss)\n",
    "lbl2 = axes[0,2].set_title(\"After evolution\")#\n",
    "\n",
    "cont3 = axes[0,3].contourf(theta3, phi3,finalcss)\n",
    "lbl3 = axes[0,3].set_title(\"Final state\")#\n",
    "\n",
    "cont4 = axes[1,0].contourf(theta4,phi4,initialsss)\n",
    "lbl4 = axes[1,0].set_title(\"Initial Squeezed state (y)\")\n",
    "\n",
    "cont5 = axes[1,1].contourf(theta5, phi5,beamsss)\n",
    "lbl5 = axes[1,1].set_title(\"After beam splitter\")#\n",
    "\n",
    "cont6 = axes[1,2].contourf(theta6, phi6,evolvesss)\n",
    "lbl6 = axes[1,2].set_title(\"After evolution\")#\n",
    "\n",
    "cont7 = axes[1,3].contourf(theta7, phi7,finalsss)\n",
    "lbl7 = axes[1,3].set_title(\"Final state\")#\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print(\"CSS. Estimated half cos:\",expected_value_sql,\"   SQL variance:\", phase_var_sql)\n",
    "print(\"Sqz. Estimated half cos:\",expected_value_hl,\"   HL variance:\", phase_var_hl)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 -0.0003981633553665487 0.24999984146594234 0.24999984146594234\n",
      "2 -0.0003981633553664654 0.12499992073297116 0.2499998414659423\n",
      "3 -0.00039816335536668745 0.08333328048864747 0.2499998414659424\n",
      "4 -0.00039816335536661807 0.06249996036648566 0.24999984146594265\n",
      "5 -0.0003981633553667513 0.049999968293188486 0.24999984146594242\n",
      "6 -0.00039816335536658684 0.041666640244323754 0.2499998414659425\n",
      "7 -0.0003981633553666245 0.03571426306656321 0.24999984146594245\n",
      "8 -0.00039816335536672735 0.0312499801832428 0.2499998414659424\n",
      "9 -0.0003981633553665801 0.02777776016288251 0.24999984146594262\n",
      "10 -0.00039816335536662734 0.024999984146594215 0.24999984146594215\n",
      "11 -0.0003981633553666644 0.022727258315085683 0.2499998414659425\n",
      "12 -0.000398163355366754 0.020833320122161846 0.24999984146594215\n",
      "13 -0.0003981633553666259 0.019230757035841747 0.24999984146594273\n",
      "14 -0.00039816335536660733 0.017857131533281622 0.2499998414659427\n",
      "15 -0.0003981633553666577 0.016666656097729497 0.24999984146594245\n",
      "16 -0.0003981633553665708 0.015624990091621405 0.24999984146594248\n",
      "17 -0.00039816335536659774 0.014705873027408372 0.2499998414659423\n",
      "18 -0.00039816335536667206 0.013888880081441226 0.24999984146594206\n",
      "19 -0.0003981633553667316 0.013157886392944337 0.2499998414659424\n",
      "20 -0.0003981633553666425 0.01249999207329712 0.2499998414659424\n",
      "21 -0.00039816335536661384 0.011904754355521078 0.24999984146594265\n",
      "22 -0.0003981633553666786 0.011363629157542863 0.24999984146594298\n",
      "23 -0.0003981633553666579 0.01086955832460617 0.2499998414659419\n",
      "24 -0.00039816335536664197 0.010416660061080949 0.24999984146594278\n",
      "25 -0.00039816335536665954 0.009999993658637681 0.24999984146594204\n",
      "26 -0.0003981633553666886 0.009615378517920862 0.2499998414659424\n",
      "27 -0.00039816335536662056 0.009259253387627503 0.2499998414659426\n",
      "28 -0.0003981633553666648 0.008928565766640835 0.2499998414659434\n",
      "29 -0.00039816335536663807 0.008620684188480781 0.24999984146594265\n",
      "30 -0.0003981633553667377 0.008333328048864745 0.24999984146594234\n",
      "31 -0.0003981633553666186 0.008064511015030392 0.24999984146594215\n",
      "32 -0.0003981633553666627 0.00781249504581071 0.24999984146594273\n",
      "33 -0.00039816335536659963 0.0075757527716952345 0.24999984146594273\n",
      "34 -0.00039816335536660554 0.0073529365137041955 0.24999984146594265\n",
      "35 -0.00039816335536665623 0.0071428526133126575 0.249999841465943\n",
      "36 -0.0003981633553665396 0.006944440040720634 0.2499998414659428\n",
      "37 -0.0003981633553666534 0.006756752472052499 0.24999984146594245\n",
      "38 -0.00039816335536660565 0.006578943196472182 0.2499998414659429\n",
      "39 -0.0003981633553667095 0.0064102523452805584 0.24999984146594179\n",
      "40 -0.0003981633553667506 0.00624999603664857 0.2499998414659428\n",
      "41 -0.00039816335536667444 0.006097557108925429 0.24999984146594262\n",
      "42 -0.0003981633553666529 0.005952377177760544 0.24999984146594284\n",
      "43 -0.00039816335536665867 0.005813949801533545 0.24999984146594242\n",
      "44 -0.0003981633553665926 0.005681814578771421 0.2499998414659425\n",
      "45 -0.000398163355366629 0.00555555203257653 0.24999984146594384\n",
      "46 -0.0003981633553665391 0.005434779162303113 0.24999984146594317\n",
      "47 -0.0003981633553665899 0.005319145563105154 0.24999984146594223\n",
      "48 -0.00039816335536666463 0.005208330030540474 0.24999984146594278\n",
      "49 -0.0003981633553667323 0.005102037580937606 0.2499998414659427\n"
     ]
    }
   ],
   "source": [
    "for N in range(1,50):\n",
    "    j = N / 2  # Total spin quantum number\n",
    "        \n",
    "    # Define collective spin operators\n",
    "    Sx = qt.jmat(j, 'x')\n",
    "    Sy = qt.jmat(j, 'y')\n",
    "    Sz = qt.jmat(j, 'z')\n",
    "\n",
    "    # Separable (SQL) Strategy\n",
    "    css_z = gen_css(j,0,0) #initial state in north pole\n",
    "      \n",
    "    H_sense = Sz  # Sensing Hamiltonian\n",
    "    time=1.57 #for instance\n",
    "    beam_spl_css = (1j * np.pi/2  *Sx).expm()*css_z\n",
    "    evolved_css = time_evolve_state(H_sense, beam_spl_css, time)\n",
    "    final_css = (1j * np.pi/2  *Sx).expm()*evolved_css\n",
    "        #Description of what is done in Fig 2b\n",
    "\n",
    "    expected_value_sql = qt.expect(Sz,final_css)/N\n",
    "    phase_var_sql = qt.variance(Sz, final_css)/N**2\n",
    "    print(N, expected_value_sql, phase_var_sql, phase_var_sql*N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Squeezing, scheme proposed by J. Ma et al. Physics reports 509 (2011), page 123, formula (283)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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XNO369etRWFiIsWPHOp1AMWzYMCQkJOB///uf0/RxcXH4y1/+4vg7OjoazZo1c1oey5cvR8OGDdGgQQOcP3/ecevUqRMAYNOmTU7P2b59ezRq1MjxtxACH3zwAXr37g0hhNNzdOvWDXl5eW7LZciQIU7Hutk7loG+T/YuwEcffYTi4mLVj7d3+4Cbx6SdP38erVq1ghAC33zzjd/HL1++HImJibj77rudXn9GRgbi4uKwZMkSVKxYER07dgRw87Jj/fv3x5IlS1BUVKR6vADw22+/YePGjejXrx/y8/Md87xw4QK6deuGw4cP49SpU06PGTZsGKKiohTP45FHHnGqzQceeACVK1fGJ598AgDYu3cvDh8+jIceeggXLlxwjOHKlSvo3LkztmzZ4ng/Si7j33//HRcuXECdOnWQlJTk8XMzdOhQp0srNW/eHEIIDB061HFfVFQU7rrrLr91Y6+P1atX4/fff/c5bd++fVG1alXH382aNUPz5s0drzmUli9fjrZt2yI5Odmpjrp06YKioiJs2bLFafr777/f656cUFi0aJGh6ljpuq1evXpo0qQJli5d6nhsUVERVqxYgd69eztq95NPPkFUVBTGjBnjNJ+nn34aQgisWbMmoGUQqF27diEnJwcjR450Ot6xZ8+eaNCggdv2AAj99tFo5syZg3Xr1jnd/FGyDEuu73Jzc5GXl4e2bdsGlBGSkpJw5coVRWPzpORY7J+xtm3b4urVq/jxxx/9Pl5tRpBNN7vsY2Ji3FbQycnJyM3N1Wwe9rNH586di6NHjzqtiMuVK6f6+RISEpCfn69o2l9++QUAUL9+faf7o6OjUbt2bce/21WrVs3teonJycn47rvvHH8fPnwYP/zwg9cNm/0EBTvXMxJ//fVXXLx4EW+++SbefPNNRc+RmprqNiYAAb9P/fv3x3/+8x88+uijeO6559C5c2fcd999eOCBBxRdIeH48eOYMGECPv74Y7cx5OXl+X384cOHkZeXh5SUFK//fu+99+Lo0aOO+5o3b45XX30VGzZsQNeuXf3Ow9WRI0cghMALL7yAF154weM0OTk5TuHK9b3zp27duk5/R0REoE6dOo5Lixw+fBgAMGjQIK/PkZeXh+TkZFy7dg1ZWVnIzs7GqVOnIIRwmsaVa40kJiYCAKpXr+52v7+6ad++Pe6//35MnjwZM2fORIcOHdC3b1889NBDbicjub5m4GZgWbZsmc95aOHw4cP47rvvAv4shlJRURGWLFmCjh07GqaO1azb+vfvj7///e84deoUqlatis2bNyMnJwf9+/d3TPPLL7+gSpUqbg0E+65R1/VvqHnbHgBAgwYN8OWXXzrdF47to9E0a9bM60lNnihdhqtXr8aLL76IvXv3oqCgwHG/6/ZYiZEjR2LZsmXo3r07qlatiq5du6Jfv3645557FD3++++/xz/+8Q9s3LgRly5dcvo3pds3NRlBNt0EUjXdn0C9/PLLeOGFF/DXv/4VU6dORdmyZREZGYmxY8cG1J1r0KAB9u7di8LCQs3PkPW2PEqGgeLiYjRu3BgzZszwOK1rACj5bcv+eAD4y1/+4jWY2I8VUzMuNWJjY7FlyxZs2rQJ//vf//Dpp59i6dKl6NSpEz777DOfdVFUVIS7774bv/32G5599lk0aNAAZcqUwalTpzB48GBF72lxcTFSUlKwaNEit3/bvXs3nnvuOSxZsgRLlixx+/dFixYFtCG3j2v8+PHo1q2bx2lcL8fj+t4Fyz6G6dOne72Ulv04pCeeeALZ2dkYO3YsWrZsicTERERERODBBx/0uIy9vWee7vdXN/aL/O/YsQP//e9/sXbtWvz1r3/Fq6++ih07dvg8PjmciouLcffdd+Nvf/ubx3+vV6+e099av5++bNy4EWfOnDFUHatZt/Xv3x+ZmZlYvnw5xo4di2XLliExMVHxRt8fb0Ek0M5yIMKxfTQ7Jcvwiy++QJ8+fdCuXTvMnTsXlStXRunSpZGdnY3FixernmdKSgr27t2LtWvXYs2aNVizZg2ys7PxyCOP4N133/X52IsXL6J9+/ZISEjAlClTkJaWhpiYGOzZswfPPvus4u2bmowgm24CaaDUfGtZsWIFOnbsiLffftvp/osXL/o8GNqb3r17Y/v27fjggw8wYMAAn9PWqFEDwM1rHtauXdtxf2FhIY4ePYouXbqonn9aWhq+/fZbdO7cOaBvbxUqVEB8fDyKiooCmr83ascSGRmJzp07o3PnzpgxYwZefvllPP/889i0aRO6dOni9fn27duHQ4cO4d1333U6McbT7hFvz5GWlob169ejdevWbhvL//u//0NKSgrmzJnj9rgPP/wQK1euxPz5871uZL3N0/7+ly5dWtPlXpK9A2onhMCRI0ccXzDS0tIA3Ozy+xvDihUrMGjQILz66quO+65fvx7WH31o0aIFWrRogZdeegmLFy/GwIEDsWTJEjz66KOOaVxfMwAcOnRI9bX9fNWvrzq6fPlyyN7PYCxatMhwdaxm3VarVi00a9YMS5cuxejRo/Hhhx+ib9++Th30GjVqYP369cjPz3fqktp3e9rXz57Y9wJdvHjR6UQjT11Vpeu+ktsD++5Tu4MHD/ocD4XOBx98gJiYGKxdu9apfrKzswN+zujoaPTu3Ru9e/dGcXExRo4ciTfeeAMvvPAC6tSp47VmNm/ejAsXLuDDDz9Eu3btHPeX3Mth52u9FExGCDddHUMaCPt17JRsHKOiotw6MsuXL3c7zkmpxx9/HJUrV8bTTz+NQ4cOuf17Tk4OXnzxRQBAly5dEB0djX//+99OY3j77beRl5en+uw9AOjXrx9OnTrl8Vqn165d83s2dlRUFO6//3588MEH2L9/v9u///rrr6rHBNx8T5TsTgBuHofmyt6xs+8u8fYe27/xllyeQgjMnj3b45g8PUe/fv1QVFSEqVOnOt1/7do1fPjhh+jatSseeOABt9vo0aORn5+Pjz/+2Otrs5997jrPlJQUdOjQAW+88QbOnDnj9rhAl3tJ9jPO7VasWIEzZ844rtCQkZGBtLQ0/Otf/8Lly5d9jsHT5+a1114LS4coNzfXbd6u9WG3atUqp8/y119/ja+++srxmpXytU4pU6aMx/v79euH7du3Y+3atW7/dvHiRdy4cUPVGLRir+NevXoZqo7Vrtv69++PHTt24J133sH58+eddtcDQI8ePVBUVITXX3/d6f6ZM2ciIiLCZ43Yv7yVPA74ypUrHjtc3urD1V133YWUlBTMnz/fqY7XrFmDH374IaDtAQUvKioKERERTuu2Y8eOBXw2+oULF5z+joyMdDQFAtm+FRYWYu7cuW7z8bbNDTYjhJvhO6T2X0Z6/vnn8eCDD6J06dLo3bu3xwsu9+rVC1OmTMGQIUPQqlUr7Nu3D4sWLXLqWKqRnJyMlStXokePHmjSpInTLzXt2bMH77//Plq2bAngZjcyMzMTkydPxj333IM+ffrg4MGDmDt3Lpo2bep0ApNSDz/8MJYtW4bHH38cmzZtQuvWrVFUVIQff/wRy5Ytw9q1a/0eY/PKK69g06ZNaN68OYYNG4ZGjRrht99+w549e7B+/XqPgdGfjIwMLF26FOPGjUPTpk0RFxeH3r17e5x2ypQp2LJlC3r27IkaNWogJycHc+fORbVq1dCmTRsANzcISUlJmD9/PuLj41GmTBk0b94cDRo0QFpaGsaPH49Tp04hISEBH3zwgcfjquzvy5gxY9CtWzdERUXhwQcfRPv27TF8+HBkZWVh79696Nq1K0qXLo3//e9/yM/P93opsBYtWqBChQpYtGiR28bPLjY2Fo0aNcLSpUtRr149lC1bFunp6UhPT8ecOXPQpk0bNG7cGMOGDUPt2rVx7tw5bN++HSdPnsS3336rermXVLZsWbRp0wZDhgzBuXPnMGvWLNSpUwfDhg0DcHPF+J///Afdu3fHrbfeiiFDhqBq1ao4deoUNm3ahISEBPz3v/8FcPNzs3DhQiQmJqJRo0bYvn071q9fH9Bx12q9++67mDt3Lu69916kpaUhPz8fb731FhISEtCjRw+naevUqYM2bdpgxIgRKCgowKxZs1CuXDmvu9G9adKkCaKiojBt2jTk5eXBZrOhU6dOSElJQUZGBubNm4cXX3wRderUQUpKCjp16oRnnnkGH3/8MXr16oXBgwcjIyMDV65cwb59+7BixQocO3YsoL0wwfr444+Rn5+PPn36ePx3vdax2nVbv379MH78eIwfPx5ly5Z169j27t0bHTt2xPPPP49jx47h9ttvx2effYaPPvoIY8eOdYROT7p27YrU1FQMHToUzzzzDKKiovDOO++gQoUKOH78uNO03urDVenSpTFt2jQMGTIE7du3x4ABAxyXfapZsyaeeuqpgJYbBadnz56YMWMG7rnnHjz00EPIycnBnDlzUKdOHafzN5R69NFH8dtvv6FTp06oVq0afvnlF7z22mto0qSJ4/hlb+ubVq1aITk5GYMGDcKYMWMQERGBhQsXejzMyds2V4uMEFbhPanf94XxXXm63AY8XH5k6tSpomrVqiIyMtLtQsWul316+umnReXKlUVsbKxo3bq12L59u2jfvr3TpTqUXvbJ7vTp0+Kpp55yXDj8lltuERkZGeKll14SeXl5TtO+/vrrokGDBqJ06dKiYsWKYsSIEV4vjO9q0KBBbpd2KCwsFNOmTRO33nqrsNlsIjk5WWRkZIjJkyc7zRu4eWF8T86dOydGjRolqlevLkqXLi0qVaokOnfuLN58803HNPbLlrheINjTsrp8+bJ46KGHRFJSkttFel1t2LBB/OlPfxJVqlQR0dHRokqVKmLAgAFul8/56KOPHBf0Lzm/AwcOiC5duoi4uDhRvnx5MWzYMPHtt9+6jenGjRviiSeeEBUqVBARERFudfXmm2+KjIwMERsbK+Lj40V8fLwoVaqU0+VgXA0ePFiULl1anD9/3uPlcoQQYtu2bSIjI0NER0e71e5PP/0kHnnkEVGpUiVRunRpUbVqVdGrVy+xYsUKxzT+LgLtyv4+vf/++yIzM1OkpKSI2NhY0bNnT6fLYNl988034r777hPlypUTNptN1KhRQ/Tr109s2LDBMU1ubq4YMmSIKF++vIiLixPdunUTP/74o9vny9tYvS0bb5/7kvbs2SMGDBggUlNTHT9a0KtXL7Fr1y7HNCUvNv/qq6+K6tWrC5vNJtq2bSu+/fZbj2MpydPlW9566y1Ru3ZtERUV5XRJlrNnz4qePXuK+Ph4pwufCyFEfn6+yMzMFHXq1BHR0dGifPnyolWrVuJf//qXKCwsdBtrOPTu3VvExMSIK1eueJ1Gj3UshPJ1m13r1q0FAPHoo496fL78/Hzx1FNPiSpVqojSpUuLunXrKrowvhBC7N69WzRv3lxER0eL1NRUMWPGDI+XffJWH94ujL906VJxxx13CJvNJsqWLevzwviuvF2OyuyCuTC+K0/L8O233xZ169YVNptNNGjQQGRnZyteb7hasWKF6Nq1q+NHZ1JTU8Xw4cPFmTNnnKbztr7ZunWraNGihePHcf72t7+JtWvXutWSr22u2s+RTBFCBHg2ChGRDhw7dgy1atXC9OnTMX78eNnDISKiABj+GFIiIiIiMjYGUiIiIiKSioGUiIiIiKTiMaREREREJBU7pEREREQkFQMpEREREUll2AvjFxcX4/Tp04iPjzfET2JReAghHBe0j4wM7fct1iB5wzokPWAdkh4orUPDBtLTp0+jevXqsodBOnXixAlUq1YtpPNgDZI/rEPSA9Yh6YG/OjRsII2PjwcArN1RCWXiPCfuJRebe7x/48m6bvdd+SXB7b64n92fN+lIodcxxR5w/z1nCq8bxYXYfC7bUR+hZJ9Hh4pDUCoyOuTzI+NgHYbeBz/+E/c3UPezsFbDOgyfkvX4wY//BADW5/+ntA4NG0jtuwTKxEUiLt5zILXdKO3x/qhbbG73RcbEuE9nc3/eUqV8tJst+CHUq3DsMrLPo1RkNN978oh1GDr9G/3DUq83GKzD0CtZjwkJCehebYwll4Mv/uqQJzURERERkVQMpEREZDhrTv7bcXO9nyjcfNVdyX9jfXpn2F32RERkDSU34t2rjfH5757+9sbTcxGp4a3WGDzVYyAlIiJd615tjGMDzw09ybTm5L+d6tHTv3l7nKf/55eiP3CXPREREZFCSnfPkzrSAumpU6fwl7/8BeXKlUNsbCwaN26MXbt2yRoOWRTrkGRjDSqjdSeJnSlnrEOSTcou+9zcXLRu3RodO3bEmjVrUKFCBRw+fBjJyckyhkMWxTok2ViD6njbVRrI89AfWIfKlaydQGuR9eeZlEA6bdo0VK9eHdnZ2Y77atWqJWMoZGGsQ5KNNaiet0CgJKwyCHjGOgyMay16+9vXsaX0BymB9OOPP0a3bt3w5z//GZ9//jmqVq2KkSNHYtiwYTKGQxbFOiTZWIPBcd3Ic6MfGNZh8HzVIutSGSnHkP7888+YN28e6tati7Vr12LEiBEYM2YM3n33Xa+PKSgowKVLl5xuRMFQW4esQdIa14Xa40kl6rEOSQ+kdEiLi4tx11134eWXXwYA3HHHHdi/fz/mz5+PQYMGeXxMVlYWJk+eHM5hksmprUPWIGmN60LSA9Yh6YGUDmnlypXRqFEjp/saNmyI48ePe31MZmYm8vLyHLcTJ06EephkcmrrkDVIWuO6UHvcPaoe65D0QEqHtHXr1jh48KDTfYcOHUKNGjW8PsZms8Fms4V6aGQhauuQNUha47qQ9IB1SHogpUP61FNPYceOHXj55Zdx5MgRLF68GG+++SZGjRolYzhkUaxDko01SHrAOiQ9kBJImzZtipUrV+L9999Heno6pk6dilmzZmHgwIEyhkMWxTok2ViDpAesQ9IDab9l36tXL/Tq1UvW7IkAsA5JPtYg6QHrkGTjb9kTERERkVQMpEREREQkFQMpEREREUnFQEpEREREUjGQEhEREZFUDKREREREJBUDKRERERFJxUBKRERERFIxkBIRERGRVAykRERERCQVAykRERERScVASkRERERSMZASERERkVQMpEREREQkFQMpEREREUnFQEpEREREUjGQEhEREZFUDKREREREJBUDKRERERFJxUBKRERERFIxkBIRERGRVAykRERERCQVAykRERERScVASkRERERSMZASERERkVQMpEREREQkFQMpEREREUnFQEpEREREUjGQEhEREZFUDKREREREJBUDKRERERFJxUBKRERERFIxkBIRERGRVAykRERERCSVlEA6adIkREREON0aNGggYyhkYaxD0gPWIcnGGiQ9KCVrxrfeeivWr1//x0BKSRsKWRjrkPSAdUiysQZJNmkVV6pUKVSqVEnW7IkAsA5JH1iHJBtrkGSTdgzp4cOHUaVKFdSuXRsDBw7E8ePHfU5fUFCAS5cuOd2IgqWmDlmDFCqsQ5KN22SSTUogbd68ORYsWIBPP/0U8+bNw9GjR9G2bVvk5+d7fUxWVhYSExMdt+rVq4dxxGRGauuQNejZmpP/drqROqxDko3bZNKDCCGEkD2IixcvokaNGpgxYwaGDh3qcZqCggIUFBQ4/r506RKqV6+OL/dXQVy851y9MLeVx/s/O17f7b7LRxPd7ov/yf15kw8WenxOAIjdf8rrv1F43CguxPozbyAvLw8JCQmqHuuvDr3VYJfKw1EqMjrosRvdmpP/RvdqY2QPQxdYh6QHgdZhMNtk1iG5UlqHujhqOSkpCfXq1cORI0e8TmOz2WCz2cI4KrIaf3XIGvSNYVQbrEOSjdtkkkEX1yG9fPkyfvrpJ1SuXFn2UMjCWIekB6xDko01SDJICaTjx4/H559/jmPHjmHbtm249957ERUVhQEDBsgYDlkU65D0gHVIsrEGSQ+k7LI/efIkBgwYgAsXLqBChQpo06YNduzYgQoVKsgYDlkU65D0gHVIsrEGSQ+kBNIlS5bImC2RE9ahtnhSU2BYhyQba5D0QBfHkBIRERGRdTGQEpFPrtcWVXutUV6blIiI/GEgJSLVXC+E7/rfktN5up+IiKgkXVyHlIj0SUl3NNgOKhERETukROSXlj8LysBKRESuGEiJyCv7WfPdq40J+gx6BlEiIvKGgZSIFPMUSl3v8xViGUqJiMgTBlIi0hyvR0pERGrwpCYi8iuQziYvlE9EREqxQ0pEXgW7i5276ImISAl2SInIq+7VxnjsdNqDZsnjRV2nY3eUiIiUYoeUiHxSciITERFRMBhIiSgg3s6uJyIiUouBlIgCwuNDiYhIKzyGlIhUKRlE7ceNlryPnVIiIlKLgZSIgqL0t+wZVImIyBsGUiJSxR4sXc+q53VHiYgoUDyGlIgCwpOaiIhIKwykRERERCQVAykRERERScVASkRERERSMZASERERkVQMpEREREQkFQMpEREREUnFQEpEREREUjGQEhEREZFUDKREREREJBUDKRERERFJxUBKRERERFIxkBIRERGRVAykRERERCQVAykRERERScVASkRERERSMZASERERkVS6CKSvvPIKIiIiMHbsWNlDIQtjHZJsrEHSA9YhySA9kO7cuRNvvPEGbrvtNtlDIQtjHZJsrEHSA9YhySI1kF6+fBkDBw7EW2+9heTkZJlDIQtjHZJsrEHSA9YhySQ1kI4aNQo9e/ZEly5d/E5bUFCAS5cuOd2ItKC0DlmDFCpcF5IesA5JplKyZrxkyRLs2bMHO3fuVDR9VlYWJk+eHOJRkdWoqUPWIIUC14XKXUuvqtlzxe4/pdlzmQHrUBktaxBgHZYkpUN64sQJPPnkk1i0aBFiYmIUPSYzMxN5eXmO24kTJ0I8SjI7tXXIGiStcV3o27X0qk43ozy30bAOfQtlnbAO/yClQ7p7927k5OTgzjvvdNxXVFSELVu24PXXX0dBQQGioqKcHmOz2WCz2cI9VDIxtXXIGiStcV3oTtZGueR8rda1Yh26Yx2Gn5RA2rlzZ+zbt8/pviFDhqBBgwZ49tln3QqfKBRYhyQba/APeuoO2cdilUDAOvwD61AeKYE0Pj4e6enpTveVKVMG5cqVc7ufKFRYhyQba1BfAcCVVQIB65B1qAfSTmoiIiLr0nMAcGWVQGBFRqtDM9egbgLp5s2bZQ+BiHVI0lmhBo0UAkoyeyAoiXWoT2b+cqSbQEpEROandQjIrR/td5rkg4Wazc9KodSsZNQgwDr0h4GUiIhCTosQoHTDr+RxwYQDM4YBq2Ad6hcDKRERhVQwISDQjb+a5w0kFJh516lZmbUOzVKDDKRERBQygYaAUAUAX/PScpcq6YuZ69AsoVTqb9kTERGVlFs/OqwhINh5G/HEGKsJ5D1iHYYfAykREYWEmo2kzADgyophgG5iHcrDXfZERKQ5tWFUrfy0YtWPif9JeQ9G7e5Ts+w2NRvWoXEwkBIRkaZCFQIC2fh7e7zSUJBbP9oSYcCMrFqHRsVd9kREJIXSEJCfVhx0CAjmOfWyC5dCQ8n7a68XI9ShUXfdM5ASEZFmlG4M1YSAUFI6D7OHAbPRug5DjXXIQEpERGGmlxCgdn7slBqDVmE0HF+IPM3TH7PWIY8hJSIiTSgJAkpCgFJxtfIUT3v5aKLfaezz9nVcn5Jj+Xgsqf5pVYdqahDQrg6VMFodMpASEZEuKAkBagOAp8f5CwX5acVBhwHSLy3CqOw6NONJTvzEERFR0ILtjvoLAXG18gIOAYE8l6/xKNllasRj+Mwg2OVutjo0EgZSIiKSSkkICIVgwgAZU6BfirQMop6eO1SM9MWIgZSIiEIukG5OKENAsPMwW3fKDIIJX/7CaKj5modVuqQ8hpSIiIISiiCgNAR0TT3od5rPjtf3O01crTyPx/QFczyp0U4qMbtAvxT5o6QGAf916K0GAWsc18xASkREIeUtCAQaRpUGAE/T+woFakOpGU8ssSI91aGvUOqNvzo0yhcjc8dtIiIyFbUhQOvHkz7569Kr7Y76CqNdUw+GtA69zdvsxzQzkBIRUcACDQJqu1JahICSz+WN2jBgpmP4rEhtyNPyC00gdWhmDKRERKQLvsKo1nwFXC3DgJHOcqabwl2Hapj5ixEDKREREVmOmu5oKA/14Bejm3hSExERhZWnIBBMV+rh5G1e/21hbiufj+2aetDjCSaeTi6xwpnOZqSmexhoCPRVg0DgdeiJWevQfK+IiIh0IdjdiP7C6MPJ2/wGASXTBNv9MsPuUvJOSR36o6QOPbHSsaQMpEREZDhqN+6BhAEyhkB2R6vp0vuiZR1a/YsRAykREQUklEHA18Y50HCp9nFW6k6RZ3qoQ6tgICUiIsMIdmPu7fFKu1OBXAvSCCeUkDqhCpWe6tAqX4wYSImIiMiU9LobO9hAa8aL5DOQEhEREbnw1jXnLvfQYCAlIiJD0CoIMFCQFen90BEGUiIiIrI0qxynqWcMpEREREQkFQMpEREREUklJZDOmzcPt912GxISEpCQkICWLVtizZo1MoZCFsY6JD1gHZJsrEG4/UysGcXuPyV7CD5JCaTVqlXDK6+8gt27d2PXrl3o1KkT/vSnP+H777+XMRyyKNYh6QHrUDl/vwce7ucxC9agZ95+W571ExqlZMy0d+/eTn+/9NJLmDdvHnbs2IFbb71VxpDIgliHpAesQ5KNNUh6IP0Y0qKiIixZsgRXrlxBy5YtZQ+HLIp1SHrAOvQv2O4Uu1u+ma0Gkw8Wyh6CR97q0FNX1tPhBPE/SY9vmpPSIQWAffv2oWXLlrh+/Tri4uKwcuVKNGrUyOv0BQUFKCgocPx96dKlcAyTTE5NHbIGKVSMWoex+0+pvrZh/E+Rin5l5rPj9RX/nKcWQhkE9H7sHsBtsloLc1sFfD1bfinyTFrErl+/Pvbu3YuvvvoKI0aMwKBBg3DgwAGv02dlZSExMdFxq169ehhHS2alpg5ZgxQqVq9DtSeUBLpBZxDwzmrbZE9fLDzVobfjSAHWk9YihBBC9iAAoEuXLkhLS8Mbb7zh8d89fRurXr06vtxfBXHxnnN1KFrivtr/RvgWbHY3igux/swbyMvLQ0JCgurH+6pDbzXYpfJwlIrU5+8lkxxWqkNfHVJvvyPuqUPq7cLkvrqkajpUvsKDt9ChpkOqx21DMHUY6DbZjHXor1OvtA79Bdhg69Df4Ql6r0Npu+xdFRcXOxW3K5vNBpvNFsYRkRX5qkPWIIWLWeow+WCh1zDg6vLRRNW/llNyA+8pFATTwVLTtdXrcYrB4Db5D/4OHwl3HZrx+FFAUiDNzMxE9+7dkZqaivz8fCxevBibN2/G2rVrZQyHLIp1SHpgxTpUehwpoPxY0kA3+r52yboyaxAwew1q8cVIT3VoVlICaU5ODh555BGcOXMGiYmJuO2227B27VrcfffdMoZDFsU6JD1gHf4h2DCglppdpGZm1RpU88UIMHYdGuGQQimB9O2335YxWyInrEPSA6PXYSBn2gPyw4DajlQgx44CxggCRq9Brfk6fCRcdegtjAZah0Zgzv0PRESkC2o3lL66Qlrt1vT1PFbrjpqFv+DvrQ69BTzZdWhFujmpiYiIrMVbl9Rfhwrwf+azr8d6o7YrReZmlDo0Q3cUYCAlIqIQU3NSiZ2/s+5LbtR9hQKlXahAOqNmCQJW5+vwESPUoT9GOGwEYCAlIqIgBXocKRBcGLALdtenrxAQTHfUKEHALPzVoa8vRmauQ6Mw/yskIiLpfHUTfW1sQ31MZ6AhgN1RYwr0fWMdhh4DKRERBS3YbqC/UKp1IPD3nMF2pNgdNR5/77ne6lBJGDVSHTKQEhFRWPjbgIYjECh5Dn/jMFNXymyUBLBAu/V2eqlDs+ExpEREFDb+TnBScn3SkhtyJcf2qQkPDKPW4O94UsDzb92XpKYO1QZYLerQSN1RgIGUiIg0EszJTSWpuWi+lrtQtQqjRgsCZsM6NCZr9YOJiEg6JRvU+J8iw7bLMpzzIv1QWofhoqQOzfyliJ9AIiLSjNINodINaygDgZogauYgYEZa1mGov7AofX6zdkbtGEiJiEhToQilWoYCtc/FMGpuRqhDNWHUqHXIY0iJiEga+4ZW6S85uW7AlRzjF2iAMHtHyuzUHEuq9tfE1NZhMCHWCmEUYCAlIqIQUHtiSSA/LwqEbpe+2jBq5CBgZmpDKaD8y1FJeqlDI+MueyIiCgm1IS35YKH0DXAgY2AY1TfWoTEwkBIRUcgEspGUEQgCnafRQ4BVBFqH4WblOuQueyIiCqlArwsZzC5UtfMIhBlCgJUEUocl64N1GFoMpEREFHLBXKxc61CgRefLLCHAavRSh1p1X81UhwykREQUFlr8go7sY/sAc4UAK2Id6hMDKRH5pcXP8NmZbSVK6mj1s46ysH7Nwch1aNYaZCAlIjehXFG7PrdZV67knf09N1IgYJ2aD+tQXxhIiQiAvJVyyfmaeWVL7owQCFiT5meEbqkV6pCBlMji9LQito/FCitf+oMegylr0FpKvt+sQzkYSIksSk8rXVcMptakh2DKmiPWoRwMpEQWpOcwWhKDqTWFu1vF+iJPwlmHrEEGUiJLMUoQdXUtvSpX2Bbl6X0Ppo5ZRxQI1mHoMZASWYSWYVTNRaG1ul4fu6VkxxogPWAdaouBlMgCgg2jwfwqietjgw2o7JYSEZkPAymRyQUaRkP1u80lnzfQcMpQSkRkLgykRCYWSBgNVRD1Ny+14ZShlIjIPCJlD4CIQkNtGM2tHx3WMOpp/moZ9SQtIiJyxkBKZEKBhFE9kB2KiYhIDu6yJzIZNWE0kPCXn1as+jHxP6n77ptbP1rxLnzuuiciMj4GUiKLUhNGAwmh3h6vNJwylBIRWYeUXfZZWVlo2rQp4uPjkZKSgr59++LgwYMyhkIWZsY6VNodVRpG89OKgw6j3p5TyfNaYfe9GeuQjIU1SHogJZB+/vnnGDVqFHbs2IF169bh999/R9euXXHlyhUZwyGLMlsdahlGQxFEvc3HH6Wh1KgnOJmtDsl4WIOkB1J22X/66adOfy9YsAApKSnYvXs32rVrJ2NIZEFWrEOlYTSc7PPztStf6e57I+66t2Idkr6wBkkPdHEMaV5eHgCgbNmyXqcpKChAQUGB4+9Lly6FfFxkLf7qUM81qEV3UE0QjauVp+q5Lx9NVDR/LUKp0Rm5DskcuE0mGaRf9qm4uBhjx45F69atkZ6e7nW6rKwsJCYmOm7Vq1cP4yjJ7JTUodFr0Fd3VEkYjauV57ippfRx/sZh9mNKrVCHpG/cJpMs0gPpqFGjsH//fixZssTndJmZmcjLy3PcTpw4EaYRkhUoqUMj12AwYTTQEBrocwV7yIBRjyUFzF+HpH/cJpMsUnfZjx49GqtXr8aWLVtQrVo1n9PabDbYbLYwjYysRGkd6rUGQxnAtAqi3p7X2658X7vvzbrr3uh1SMbHbTLJJKVDKoTA6NGjsXLlSmzcuBG1atWSMQyyOKvUYaDd0VCFUaXzCKZTaqQuqVXqkPSLNUh6IKVDOmrUKCxevBgfffQR4uPjcfbsWQBAYmIiYmNjZQyJLMjqdRhsGO2aquw6hZ8dr+/z3+Nq5Sk66akkM3VJrV6HJB9rkPRASod03rx5yMvLQ4cOHVC5cmXHbenSpTKGQxZlhjr01wkM5CQgX2G0a+pBx00pJdN7m2e4L0ElgxnqkIyNNUh6IKVDKoSQMVsiJ1auQ29Bz18YDYb98d46pmo7pf66pEa5JqmV65D0gTVIeiD9LHsi0odQhtFgnssKXVIiIqtjICUyKW+769UGPC3DqL/nDMeJVEREpD8MpEQGpeWZ5N6CYCjCaCDPzS4pEZG56eKnQ4koPNQEOyWB8eHkbT7/fWFuK8Xzs1NzLKmZzrYnIrIydkiJLC6Q3eQPJ2/zG0bt0/kSyg4sEREZBwMpkQkF+5vvvoKikiDqOr3ax3gKyYHstjfSBfKJiKyMgZSIFFMbLJVgl5SIiBhIiSzMUycyVAExFGGWiIjMgYGUyCKCPVNdr4Ey2MMTiIhIPgZSIgobb6GWu+2JiKyNgZTIgHiyDhERmQkDKRH5JWN3PX+1iYjIOhhIicivQC5wT0REpBQDKRHpktJfayIiIuNjICUiIiIiqRhIiQwodv8p2UMIiLdd/58drx/mkRARkZ4wkBKRoSUfLJQ9BCIiChIDKZFFxP8U3MedJzYREVGoMJASWZinE4d87T4PJpQy0BIRkTcMpESkSiDB0tdjPAVgT0E52A4vERHpF9fwRCYU7HGV/k4yUhNKZXZGjXryFxGR1ZSSPQAiCp/4nyKRn1bsdN/lo4kB/SqSPWh6+hUnpSGUZ9cTERHAQEpEXnx2vD66ph70O12gHVBvYVTNBfF5hj0RkTlwlz2RQWm5O9pbCAxVB1Pt8/L4USIic+NansikvHUP1YY7rUOpr+fjz4USEVkTAykRAfAdBj87Xl+TYBpIGPUWoP3trucJTURExsFASmRiaruk/jqUgYZSf4GWnVEiImvjSU1EBha7/xSupVfV9Dn9nXVfMlj6OulJaXj1FUYD7Y4SEZGxMJASWZSnS0DZKb0UVLC78QMJo0pwdz0RkbFwlz2RyfnqJvoKfaHejR7o87M7SkRkPgykRAanpBsYTCjVOpgqeU5e5omIyFq4y56IfO6+B/7oZgbyi06uz6FkLN4o6Y5ydz0RkfEwkBKZgJKTm5IPFiK3frTXf/cXSgH3UOkvoKrprvrrinJXPRGReUnbL7Zlyxb07t0bVapUQUREBFatWiVrKGRRVqxBf6FO7a5y++53bzeltNpFb8TuqBXrkPSHdUiySQukV65cwe233445c+bIGgJZnNlqUGkYUxJKw3kMp5J5mbk7arY6JGNiHZJs0nbZd+/eHd27d5c1eyJL16C/3ffAH0HR3278QCkNvUrDqBG7o4C165D0g3VIsvFUViITURPKlAY9LTum9ufSOowSEZGxGeakpoKCAhQUFDj+vnTpksTRkBUZpQbV/HqTkk6pnacQ6a97GkyQVRNGjdodDYRR6pDMjXVIWjNMhzQrKwuJiYmOW/Xq1WUPiSzGrDUYTBeyZMfT0y3Q8TCMemfWOiRjYR2S1gwTSDMzM5GXl+e4nThxQvaQyGKMVINqQ5raEBgqasdgtTAKGKsOybxYh6Q1w+yyt9lssNlssodBFma0GlSz697OHgiV7sbXSiBh2IphFDBeHZI5sQ5Ja9IC6eXLl3HkyBHH30ePHsXevXtRtmxZpKamyhoWWYgVajCQUAqEJ5gG05E1Uxi1Qh2S/rEOSTZpgXTXrl3o2LGj4+9x48YBAAYNGoQFCxZIGhVZiVVqMNBQCriHxmADqhaHBZgpjALWqUPSN9YhySYtkHbo0AFCCFmzJ7JUDQYTSkuSfZyp2cIoYK06JP1iHZJshjmpiYiCE7v/lKEDnZHHTkREvjGQElmM0YKd0YM0ERH5Z5iz7IlIO/aAp8Vu/FBhCCUisg52SIksTK/dRz2OiYiIQocdUiJyCoCyuqYMoURE1sVASkROwhlOGUKJiAhgICUiH1wDYzABleGTiIi8YSAlIsUYKomIKBR4UhMRERERScVASkRERERSMZASERERkVQMpEREREQkFQMpEREREUnFQEpEREREUjGQEhEREZFUDKREREREJBUDKRERERFJxUBKRERERFIxkBIRERGRVAykRERERCQVAykRERERScVASkRERERSMZASERERkVQMpEREREQkFQMpEREREUnFQEpEREREUjGQEhEREZFUDKRERGRIa07+G2tO/tvtb/t9rv9GFAre6rDk3+QfAykRERmOv408QwDpRfdqY2QPwRAYSImIyNB8hU/XbhVRqHkKoKxD/xhIiYiIiEiqUrIHQEREFCzX7lP3amPc7iv5N3ejkhY8dT093cd6848dUiIi0r1AdncyBJDecLe9d+yQEhGR4fnriJacjijcGET9k9ohnTNnDmrWrImYmBg0b94cX3/9tczhkEWxDkk21qB/voKk/d/8hU2GUd9Yh/4FEiwZRpWRFkiXLl2KcePGYeLEidizZw9uv/12dOvWDTk5ObKGRBbEOiTZWIOB8RcuPR1TSt6xDv3TOljyzHtn0gLpjBkzMGzYMAwZMgSNGjXC/Pnzccstt+Cdd96RNSSyINYhycYaDAw35NpiHfoXii81/KL0BynHkBYWFmL37t3IzMx03BcZGYkuXbpg+/btHh9TUFCAgoICx995eXkAgCuXi73Op+Dy7x7vL7pa4HZf8fXr7tMVuOf1GzcKvc7vRrH3f6PwsL8HQgi/06qtQ281yPedXCmtQy3XhVarw0uXLjn+v+RrL3l/SUsPvIj7G/wt5OPSE9ah9u6u8rjb3x/8+E8Af7x2ew3a/3Z9jLfnMivF22UhwalTpwQAsW3bNqf7n3nmGdGsWTOPj5k4caIAwBtvim4nTpzQvA5Zg7ypvfmrQ64LeQvHjXXImx5u/urQMGfZZ2ZmYty4cY6/L168iBo1auD48eNITEyUODLzuHTpEqpXr44TJ04gISFB9nACIoRAfn4+qlSpovlzswbDg3XoG+swPFiHvrEOw8NKdSglkJYvXx5RUVE4d+6c0/3nzp1DpUqVPD7GZrPBZrO53Z+YmGjYN0mvEhISDL1Mla4M1dYhazC8rFCHXBfqH+uQdagHVqhDKSc1RUdHIyMjAxs2bHDcV1xcjA0bNqBly5YyhkQWxDok2ViDpAesQ9IDabvsx40bh0GDBuGuu+5Cs2bNMGvWLFy5cgVDhgyRNSSyINYhycYaJD1gHZJs0gJp//798euvv2LChAk4e/YsmjRpgk8//RQVK1ZU9HibzYaJEyd63GVAgbHiMg2mDq24vMLBasuV60J9stpyZR3qk5WWa4QQCq6PQ0REREQUIlJ/OpSIiIiIiIGUiIiIiKRiICUiIiIiqRhIiYiIiEgqQwbSOXPmoGbNmoiJiUHz5s3x9ddfyx6SoWVlZaFp06aIj49HSkoK+vbti4MHD8oelu6xDrXFOgwM61BbrEP1WIPasmoNGi6QLl26FOPGjcPEiROxZ88e3H777ejWrRtycnJkD82wPv/8c4waNQo7duzAunXr8Pvvv6Nr1664cuWK7KHpFutQe6xD9ViH2mMdqsMa1J5la9DnL93rULNmzcSoUaMcfxcVFYkqVaqIrKwsiaMyl5ycHAFAfP7557KHolusw9BjHfrHOgw91qFvrMHQs0oNGqpDWlhYiN27d6NLly6O+yIjI9GlSxds375d4sjMJS8vDwBQtmxZySPRJ9ZheLAOfWMdhgfr0DvWYHhYpQYNFUjPnz+PoqIit1+OqFixIs6ePStpVOZSXFyMsWPHonXr1khPT5c9HF1iHYYe69A/1mHosQ59Yw2GnpVqUNpPh5I+jRo1Cvv378eXX34peyhkYaxD0gPWIclmpRo0VCAtX748oqKicO7cOaf7z507h0qVKkkalXmMHj0aq1evxpYtW1CtWjXZw9Et1mFosQ6VYR2GFuvQP9ZgaFmtBg21yz46OhoZGRnYsGGD477i4mJs2LABLVu2lDgyYxNCYPTo0Vi5ciU2btyIWrVqyR6SrrEOQ4N1qA7rMDRYh8qxBkPDsjUo95wq9ZYsWSJsNptYsGCBOHDggHjsscdEUlKSOHv2rOyhGdaIESNEYmKi2Lx5szhz5ozjdvXqVdlD0y3WofZYh+qxDrXHOlSHNag9q9ag4QKpEEK89tprIjU1VURHR4tmzZqJHTt2yB6SoQHweMvOzpY9NF1jHWqLdRgY1qG2WIfqsQa1ZdUajBBCiPD1Y4mIiIiInBnqGFIiIiIiMh8GUiIiIiKSioGUiIiIiKRiICUiIiIiqRhIiYiIiEgqBlIiIiIikoqBlIiIiIikYiAlIiIiIqkYSImIiIhIKgZSIiIiIpKKgZSIiIiIpGIgJSIiIiKpwhpIIyIiMGnSJEXT1qxZE4MHD1Y9j2PHjiEiIgILFixQ/VjybcGCBYiIiMCxY8dkDyXkvv76a0RHR+OXX35R/JiFCxeifv36iIiIwC233BLC0Xm3efNmREREYMWKFVLmr3eTJk1CRESE032BrmvMauHChWjQoAFKly6NpKQk2cMJu1DUg/1zuXnzZk2fl9yFKwNwvaE9VYHUHkh27dqlycy3bduGSZMm4eLFi5o8n1rHjh3DkCFDkJaWhpiYGFSqVAnt2rXDxIkTpYzHSubOnRvUCuP06dOYNGkS9u7dq9mYSnr++ecxYMAA1KhRA8DN8UZERKB58+Yep//xxx8xePBg1KlTBw8++CBiYmLw22+/YdKkSdwIGcyBAwcwadIkj1+8gq1b2ZTWcVpaGt566y28+eabuHr1KutYIaPXhxHYc4in23PPPSd7eKr5Wt8otXjxYsyaNUuzMclSKpwzu3btGkqV+mOW27Ztw+TJkzF48GC3b+IHDx5EZGToGrhHjhxB06ZNERsbi7/+9a+oWbMmzpw5gz179mDatGmYPHlyyOZNN1fc5cuXD/gb5unTpzF58mTUrFkTTZo00XRse/fuxfr167Ft2zbHfYsWLULNmjXx9ddf48iRI6hTp47TYzZv3ozi4mLMnj0b5cuXR8WKFbFw4UJHHXXo0EHTMZJ2XNc1Bw4cwOTJk9GhQwfUrFnTadpg61Y2NXVs/7fz58+zjhXyVh/t2rXDtWvXEB0dLWdgJjRlyhTUqlXL6b709HTUqFED165dQ+nSpSWNTB1f6xulFi9ejP3792Ps2LGaji3cwhpIY2JiFE9rs9lCOBJg5syZuHz5Mvbu3evogtnl5OSEdN6kb9nZ2UhNTUWLFi0AAEePHsW2bdvw4YcfYvjw4Vi0aJFbF91eM0lJSUhKSkLXrl2xZMmSkIzvypUrKFOmTEie24pCva7x58aNGyguLg55WFFbx6FmpTqOjIxUtf0j/7p374677rrL479xWRuUUCE7O1sAEDt37nTcN2jQIFGmTBlx8uRJ8ac//UmUKVNGlC9fXjz99NPixo0bTo8HICZOnCiEEGLixIkCgNvt6NGjQgghatSoIQYNGuR47IULF8TTTz8t0tPTRZkyZUR8fLy45557xN69e53mcfToUQFAZGdn+3wt3bp1EzVr1lT0uouLi8XUqVNF1apVRWxsrOjQoYPYv3+/2xjtr8mVfbnZX5vdJ598Itq0aSNuueUWERcXJ3r06CH279/v9vgffvhB3H///SI5OVnYbDaRkZEhPvroI6dpPC1L12Wq9LmEEGL//v2iY8eOIiYmRlStWlVMnTpVvP322x5fh6szZ86IwYMHi6pVq4ro6GhRqVIl0adPH6f31nWM7du3F0Ioe583bdrk8XWWfM937NghunXrJhISEkRsbKxo166d+PLLL32O2y41NVUMHjzY8ffUqVNFdHS0KFu2rBg+fLioW7eu0/QxMTFuY2nWrJnHMdrrX+l7Ya+dzZs3ixEjRogKFSqIpKQkr2O3L5slS5aIzMxMUbFiRXHLLbeI3r17i+PHj7tNr2Q5HTt2TIwYMULUq1dPxMTEiLJly4oHHnjArQ7sY/3iiy/EE088IcqXLy8SExPFY489JgoKCkRubq54+OGHRVJSkkhKShLPPPOMKC4u9vd2iJ07d4quXbuKcuXKiZiYGFGzZk0xZMgQx7/bP/PTp08XM2bMEKmpqSImJka0a9dO7Nu3z+m5PH1GS36O7a/B9bZp0yafdSuEELm5ueLJJ58U1apVE9HR0SItLU288soroqioyONYZ86cKWrXri0iIyPFN99843c5BGvq1KkiOTlZFBQUiBEjRrjVsafXN2jQICl1LIQQ169fFxMmTBBpaWkiOjpaVKtWTTzzzDPi+vXrjmluvfVW0aFDB7fHFhUViSpVqoj777/fcd/ly5fFuHHjHO9PvXr1xPTp091qMND1uq/6sH8uN23a5PQcy5YtE3feeaeIiYkR5cqVEwMHDhQnT550mkbNNtYKPOWQkjxlADXLcPr06aJly5aibNmyIiYmRtx5551i+fLlbvNxrRNv3n//fXHnnXeKuLg4ER8fL9LT08WsWbOcXoun9Y0QQqxatUr06NFDVK5cWURHR4vatWuLKVOmOI25ffv2bo+vUaOG49+VfI70QpMOaVFREbp164bmzZvjX//6F9avX49XX30VaWlpGDFihMfH3HfffTh06BDef/99zJw5E+XLlwcAVKhQweP0P//8M1atWoU///nPqFWrFs6dO4c33ngD7du3x4EDB1ClShVVY65RowbWr1+PjRs3olOnTj6nnTBhAl588UX06NEDPXr0wJ49e9C1a1cUFhaqmmdJCxcuxKBBg9CtWzdMmzYNV69exbx589CmTRt88803jtb9999/j9atW6Nq1ap47rnnUKZMGSxbtgx9+/bFBx98gHvvvdfxfK7+8Y9/ICcnB3Fxcaqe6+zZs+jYsSNu3LjhmO7NN99EbGysotd2//334/vvv8cTTzyBmjVrIicnB+vWrcPx48dRs2ZNzJo1C0888QTi4uLw/PPPAwAqVqwIQNn73LBhQ0yZMgUTJkzAY489hrZt2wIAWrVqBQDYuHEjunfvjoyMDEycOBGRkZHIzs5Gp06d8MUXX6BZs2Zex37q1CkcP34cd955p+O+RYsWoVOnTvj0009Rq1YtHD58GDt37kTTpk1x9uxZFBYWomHDhvjhhx8wb948xMXF4caNG/j6668BAPfeey/uu+8+AMBtt92m6r2wGzlyJCpUqIAJEybgypUrft+Dl156CREREXj22WeRk5ODWbNmoUuXLti7d6/jfVS6nHbu3Ilt27bhwQcfRLVq1XDs2DHMmzcPHTp0wIEDB9xO4HriiSdQqVIlTJ48GTt27MCbb76JpKQkbNu2DampqXj55ZfxySefYPr06UhPT8cjjzzi9XXk5OSga9euqFChAp577jkkJSXh2LFj+PDDD92mfe+995Cfn49Ro0bh+vXrmD17Njp16oR9+/Y56sufdu3aYcyYMfj3v/+Nv//972jYsCEAoGHDhj7r9urVq2jfvj1OnTqF4cOHIzU1Fdu2bUNmZibOnDnjdnxXdnY2rl+/jsceeww2mw1ly5ZVNL5gLFq0CPfddx+io6MxYMAAzJs3z1HHADBr1iy89957WLlypaOOGzdujBYtWmDEiBFhrePi4mL06dMHX375JR577DE0bNgQ+/btw8yZM3Ho0CGsWrUKANC/f39MmjQJZ8+eRaVKlRyP//LLL3H69Gk8+OCDAAAhBPr06YNNmzZh6NChaNKkCdauXYtnnnkGp06dwsyZM4Nevr7qw5MFCxZgyJAhaNq0KbKysnDu3DnMnj0bW7duxTfffOPUpQ5kG2t2eXl5OH/+vNN99hzhidJlOHv2bPTp0wcDBw5EYWEhlixZgj//+c9YvXo1evbsqWqM69atw4ABA9C5c2dMmzYNAPDDDz9g69atePLJJ32ub4CbNRIXF4dx48YhLi4OGzduxIQJE3Dp0iVMnz4dwM3zHfLy8nDy5ElHHdu3+Uo/R7qhJr1665ACEFOmTHGa9o477hAZGRlO98Hlm/X06dO9dtxcv31cv37dqdMgxM1vQjabzWneSjuk+/fvF7GxsQKAaNKkiXjyySfFqlWrxJUrV5ymy8nJEdHR0aJnz55O36T//ve/OzoIdkq/Sefn54ukpCQxbNgwp+nOnj0rEhMTne7v3LmzaNy4sdO3meLiYtGqVSu3DkdJ//znPwUA8d5776l+rrFjxwoA4quvvnJaDomJiX47pLm5uY4OkC+33nqrU3fJTun7vHPnTo/vc3Fxsahbt67o1q2b0/t19epVUatWLXH33Xf7HNf69esFAPHf//5XCCHErl27BACxdu1aUa1aNdGvXz9RrVo18eSTTwohhJgxY4aIiIgQY8aMEQDEr7/+KoQQ4vTp0x67SXZK3wt77bRp00ZRN8Teialataq4dOmS4/5ly5YJAGL27Nmql9PVq1fd5rN9+3a3+rKP1fU5W7ZsKSIiIsTjjz/uuO/GjRuiWrVqHmugpJUrV/rshgjxx2c+NjbWqbv01VdfCQDiqaeectznr0MqhBDLly/32M0SwnvdTp06VZQpU0YcOnTI6f7nnntOREVFObrT9rEmJCSInJwcXy9dU/Y6XrdunRDi5vtfso7t7MvHXsdCCPHrr7+GvY4XLlwoIiMjxRdffOF0//z58wUAsXXrViGEEAcPHhQAxGuvveY03ciRI0VcXJyjdletWiUAiBdffNFpugceeEBERESII0eOOO4LZs+Xt/pw7ZAWFhaKlJQUkZ6eLq5du+aYbvXq1QKAmDBhguM+NdtYK/DWVbS/R946pEqXoev6rrCwUKSnp4tOnTo53a+kQ/rkk0+KhIQEnzXva33jad07fPhwccsttzh95nr27OnUFbVT+jnSC83OGnr88ced/m7bti1+/vlnrZ4eNpvNceJBUVERLly4gLi4ONSvXx979uxR/Xy33nor9u7di7/85S84duwYZs+ejb59+6JixYp46623HNOtX78ehYWFeOKJJ5wuFxPMwcPr1q3DxYsXMWDAAJw/f95xi4qKQvPmzbFp0yYAwG+//YaNGzeiX79+yM/Pd0x34cIFdOvWDYcPH8apU6fcnn/Tpk3IzMzEE088gYcfflj1c33yySdo0aKFUyexQoUKGDhwoN/XFhsbi+joaGzevBm5ubmql02w7/PevXtx+PBhPPTQQ7hw4YLjdV65cgWdO3fGli1bUFxc7PXxFy5cAAAkJycDuNlVqlixIjp37oyBAwfiv//9L+69914sWbIERUVFWLRoEVq1auWY3s7175ICeV+HDRuGqKgov6/f7pFHHkF8fLzj7wceeACVK1fGJ598ono5leyM//7777hw4QLq1KmDpKQkj+/J0KFDnT4rzZs3hxACQ4cOddwXFRWFu+66y+86wt4lWr16NX7//Xef0/bt2xdVq1Z1/N2sWTM0b97c8ZpDafny5Wjbti2Sk5OdPtNdunRBUVERtmzZ4jT9/fff73VvUCjY67hjx44Abl6Cr3///o46DkQo63j58uVo2LAhGjRo4LQ87Xuz7OvIevXqoUmTJli6dKnjsUVFRVixYgV69+7tqN1PPvkEUVFRGDNmjNN8nn76aQghsGbNmoCWQaB27dqFnJwcjBw50ul4x549e6JBgwb43//+5/aYUG9jjWbOnDlYt26d080fJcuw5PouNzcXeXl5aNu2bUA5IykpCVeuXFE0Nk9KjsX+GWvbti2uXr2KH3/80e/jlX6O9EKTXfYxMTFuK9fk5OSAAok39jM/586di6NHjzqtRMuVKxfQc9arVw8LFy5EUVERDhw4gNWrV+Of//wnHnvsMdSqVQtdunRxXIeybt26To+tUKGCz9Dhy+HDhwHA66ECCQkJAG5eCUAIgRdeeAEvvPCCx2lzcnKcNsInT55E//790bp1a8yYMcNxv5rn+uWXXzxeFqZ+/fp+X5vNZsO0adPw9NNPo2LFimjRogV69eqFRx55xGmXmjfBvs/2ZTto0CCv0+Tl5fl974QQKCoqwpIlS9CxY0ccPXoU7du3x7Rp01BcXIxz585hwYIF2L17N+bPn48zZ864Pd6bQN5X17NJ/XGt14iICNSpU8dxaRE1y+natWvIyspCdnY2Tp065fTa8vLy3B6Xmprq9HdiYiIAoHr16m73+1tHtG/fHvfffz8mT56MmTNnokOHDujbty8eeught5ORXF8zcPMzvmzZMp/z0MLhw4fx3XffeQ2ZridKqn0/g+Fax3bNmzfHq6++ig0bNqBr166qnzeUdXz48GH88MMPipZn//798fe//x2nTp1C1apVsXnzZuTk5KB///6OaX755RdUqVLF6Usa8MeuUTXXG9aCfX6e1qkNGjTAl19+6XRfOLaxRtOsWTOvJzV5onQZrl69Gi+++CL27t2LgoICx/2u1y9WYuTIkVi2bBm6d++OqlWromvXrujXrx/uueceRY///vvv8Y9//AMbN27EpUuXnP7N07rXlZrPkR5oEkjVdG4C9fLLL+OFF17AX//6V0ydOhVly5ZFZGQkxo4d67PjpURUVBQaN26Mxo0bo2XLlujYsSMWLVqELl26qHoebwXr2oGwj3fhwoUeQ5r90lj26caPH49u3bp5fO6Sl20pLCzEAw88AJvNhmXLljldYkvtcwVj7Nix6N27N1atWoW1a9fihRdeQFZWFjZu3Ig77rjD52ODfZ/t00yfPt3r5aDsx9d4Yg+9ubm52LhxI86cOYMlS5Y4nTE/Z84cADePNYqOjka/fv0we/Zsp+fxtaEI5L1QevyuUmqW0xNPPIHs7GyMHTsWLVu2RGJiIiIiIvDggw96fE+8rQ883e8ruANwXOR/x44d+O9//4u1a9fir3/9K1599VXs2LHD53sZTsXFxbj77rvxt7/9zeO/16tXz+lvrd9PX7zVsd2iRYsCCqShrOPi4mI0btzY6Ut1SSW/3PTv3x+ZmZlYvnw5xo4di2XLliExMVHxRt8fpev1UArHNtbslCzDL774An369EG7du0wd+5cVK5cGaVLl0Z2djYWL16sep4pKSnYu3cv1q5dizVr1mDNmjXIzs7GI488gnfffdfnYy9evIj27dsjISEBU6ZMcVwvfc+ePXj22WcVbw+Vfo70IKyXfXKl5hvHihUr0LFjR7z99ttO91+8eNHngcxq2b9x2Tte9ktCHT58GLVr13ZM9+uvv7qFDnvX7eLFi04HpLt++05LSwNws1h9hV77/EqXLq0oHI8ZMwZ79+7Fli1b3A6mV/NcNWrUcHTQSjp48KDfMdilpaXh6aefxtNPP43Dhw+jSZMmePXVV/F///d/ALy/90rfZ2+Pty/bhIQE1V8ogJvdCeDmJXL27NmDlJQURwAFbu76e/fdd9GnTx989NFH6N27t8dua8lOlCu172sgXN8/IQSOHDniOBlFzXJasWIFBg0ahFdffdVx3/Xr18P6gxYtWrRAixYt8NJLL2Hx4sUYOHAglixZgkcffdQxjaeaPXTokOpr+/laL/mqu8uXL4fs/QzGokWL3OrY7sMPP8TKlSsxf/58r2HR22sOZR2npaXh22+/RefOnf1uJ2rVqoVmzZph6dKlGD16ND788EP07dvXqYNuP4k1Pz/fqUtq3+3peum/kpSu1wHl2zT7/A4ePOi2p+zgwYM+x0Oh88EHHyAmJgZr1651qp/s7OyAnzM6Ohq9e/dG7969UVxcjJEjR+KNN97ACy+8gDp16nitmc2bN+PChQv48MMP0a5dO8f9nrYtvtZLSj9HeiD1t+zt16BTsmGLiopy66YsX77c4zGUSnzxxRcej0mzH29m35XSpUsXlC5dGq+99prT/D39KoJ9I1/yeLErV664fRPq1q0bEhIS8PLLL3scw6+//grgZmDt0KED3njjDbddwiWnA25+YN544w3MmTPH41nkap6rR48e2LFjh+Mscfu/L1q0yO1xrq5evYrr16873ZeWlob4+Hin3R9lypTx+L4rfZ+91U5GRgbS0tLwr3/9C5cvX3Z7/pKv05OqVauievXq2LFjBz788EP06tULDzzwgOM2bdo0REZGIi8vD0IIr13l3bt3O/7fdYxq3otA2c84t1uxYgXOnDmD7t27A1C3nDy9J6+99lpYOkS5ublu87Z3dEvWEwCsWrXKqU6+/vprfPXVV47XrJSv9ZK3uu3Xrx+2b9+OtWvXuv3bxYsXcePGDVVj0Mq1a9c81rH9Nnr0aOTn5+Pjjz/2+hz2qyiEs4779euHU6dOOR3PX/I1uZ6h379/f+zYsQPvvPMOzp8/77S7Hri5TisqKsLrr7/udP/MmTMRERHhs0aUrtcB7/Xh6q677kJKSgrmz5/vVMdr1qzBDz/8oPpsbtJGVFQUIiIinNZtx44dC/hsdPs5CXaRkZGOpoD9ffe2vrF3dEuu/woLCzF37ly3+ZQpU8bjLny1nyPZpHZIMzIyANy8bMGDDz6I0qVLo3fv3h4vltyrVy9MmTIFQ4YMQatWrbBv3z4sWrTIqWupxrRp07B7927cd999jgLZs2cP3nvvPZQtW9Zx0lKFChUwfvx4ZGVloVevXujRowe++eYbrFmzxq0z27VrV6SmpmLo0KF45plnEBUVhXfeeQcVKlTA8ePHHdMlJCRg3rx5ePjhh3HnnXfiwQcfdEzzv//9D61bt3asOOfMmYM2bdqgcePGGDZsGGrXro1z585h+/btOHnyJL799lucP38eI0eORKNGjWCz2RxdSLt7770XZcqUUfRcAPC3v/0NCxcuxD333IMnn3zScdmnGjVq4LvvvvO5XA8dOoTOnTujX79+aNSoEUqVKoWVK1fi3LlzjkuwADff+3nz5uHFF19EnTp1kJKSgk6dOil+n9PS0pCUlIT58+cjPj4eZcqUQfPmzVGrVi385z//Qffu3XHrrbdiyJAhqFq1Kk6dOoVNmzYhISEB//3vf32+hj/96U9YtGgR8vPz0adPH6d/q1ChAu655x6sXr0aERERXrvG69atQ5s2bfDbb79h6dKlqFevHsqWLYv09HSkp6crfi8CVbZsWbRp0wZDhgzBuXPnMGvWLNSpUwfDhg0DcHPFqHQ59erVCwsXLkRiYiIaNWqE7du3Y/369QEfu63Gu+++i7lz5+Lee+9FWloa8vPz8dZbbyEhIQE9evRwmrZOnTpo06YNRowYgYKCAsyaNQvlypXzuhvdmyZNmiAqKgrTpk1DXl4ebDYbOnXqhJSUFK91+8wzz+Djjz9Gr169MHjwYGRkZODKlSvYt28fVqxYgWPHjmm6J0epjz/+2GMd27Vo0QIVKlTAokWL3EKcXWxsLBo1ahTWOn744YexbNkyPP7449i0aRNat26NoqIi/Pjjj1i2bBnWrl3rdPxgv379MH78eIwfPx5ly5Z169j27t0bHTt2xPPPP49jx47h9ttvx2effYaPPvoIY8eOdYROT5Su1wHv6zVXpUuXxrRp0zBkyBC0b98eAwYMcFz2qWbNmnjqqacCWm4UnJ49e2LGjBm455578NBDDyEnJwdz5sxBnTp1/G77PHn00Ufx22+/oVOnTqhWrRp++eUXvPbaa2jSpInj+GVv6xv7ybKDBg3CmDFjEBERgYULF3o8zCkjIwNLly7FuHHj0LRpU8TFxaF3796qP0fSqTkl39eF8V15ulQGPFw6xH7B+cjISLeLDLte9unpp58WlStXFrGxsaJ169Zi+/bton379k6X2VB62aetW7eKUaNGifT0dJGYmChKly7tuCD6Tz/95DRtUVGRmDx5smPe3i6ML4QQu3fvFs2bNxfR0dEiNTVVzJgxw+uF8Tdt2iS6desmEhMTRUxMjEhLSxODBw8Wu3btcprup59+Eo888oioVKmSKF26tKhataro1auXWLFihdNr9nYrOV9/z2X33Xffifbt26u+MP758+fFqFGjRIMGDUSZMmVEYmKiaN68uVi2bJnTdGfPnhU9e/YU8fHxTheQVvo+CyHERx99JBo1aiRKlSrl9p5/88034r777hPlypUTNptN1KhRQ/Tr109s2LDB69jt9uzZIwCI6Ohot8uACfHHJZTq1asnSpcuLc6fP+90uZyLFy+K6Oho8Z///Eds27ZNZGRkiOjoaLf6V/Je+LsItCv75WXef/99kZmZKVJSUkRsbKzo2bOn+OWXX9ymV7KccnNzxZAhQ0T58uVFXFyc6Natm/jxxx/d6t/bWD1dSkgI7+uOkvbs2SMGDBggUlNThc1mEykpKaJXr15On5GSF5t/9dVXRfXq1YXNZhNt27YV3377rcexlOTpc/zWW2+J2rVri6ioKKdLsnirWyFuXs4tMzNT1KlTR0RHR4vy5cuLVq1aiX/961+isLDQbazh0Lt3bxETE+Oxju0GDx7ssY5LCncdC3HzcjvTpk0Tt956q7DZbCI5OVlkZGSIyZMni7y8PLfpW7duLQCIRx991OPz5efni6eeekpUqVJFlC5dWtStW1fRhfGFUL5e91Yf3i6Mv3TpUnHHHXcIm80mypYt6/PC+K68XY7K7IK5ML4rT8vw7bffFnXr1hU2m000aNBAZGdnK15vuFqxYoXo2rWrSElJcdTO8OHDxZkzZ5ym87a+2bp1q2jRooWIjY0VVapUEX/729/E2rVr3Wrp8uXL4qGHHhJJSUkCLhfGV/s5kilCCD9nFZBXNWvWRIcOHbBgwQLZQyGNde7cGVWqVPH4gwMfffQR+vbtiy1btjguyl/SrFmz8M9//hM//fRTWE9esapjx46hVq1amD59OsaPHy97OEREFACpx5AS6dXLL7+MpUuXejxx4a233kLt2rXRpk0bt3/7/fffMWPGDPzjH/9gGCUiIlJI6jGkRHrVvHlzt5+GXbJkCb777jv873//w+zZsz2etVi6dGm348qIiIjINwZSIoUGDBiAuLg4DB06FCNHjpQ9HCIiItPgMaREREREJBWPISUiIiIiqRhIiYiIiEgqwx5DWlxcjNOnTyM+Pt4QP4lF4SGEQH5+PqpUqYLIyNB+32INkjesQ9ID1iHpgdI6NGwgPX36NKpXry57GKRTJ06cQLVq1UI6D9Yg+cM6JD1gHZIe+KtDwwbS+Ph4AMDaHZVQJs45cS+52Nzp740n6zr9feWXBKe/4352fnzSEefL/QBA7AH332om/blRXIjN57Id9RFK9nk0b/8cSpWK8Ts9a8j4rjWqrGi6Gzeu46vPX5FWh6w16ypZozLqsEPFISgVGR3y+ZFxKN0uGzaQ2ncJlImLRFy8c6C03Sjt9HfULTanvyNjnMNDlM358aVKubeU+QEzlnDsMrLPo1SpGEWBlDVkfPE/XsC19KqKp5dVh6w16/K0LgprHUZGs/7II391yJOaiIiIiEgqBlKiMIjdf0r2EIiIiHSLgZSISAV+uSAi0h4DKRERERFJxUBKFGLsqBEREfkmLZCeOnUKf/nLX1CuXDnExsaicePG2LVrV0jm1TX1YNDPoebMWjKOcNYhkSesQdID1iHJJuWyT7m5uWjdujU6duyINWvWoEKFCjh8+DCSk5NlDIcsinVIgYrdf0qTL6msQdID1iHpgZRAOm3aNFSvXh3Z2dmO+2rVqiVjKGRhrEOSjTVIesA6JD2Qssv+448/xl133YU///nPSElJwR133IG33norbPOPq5UXtnmRfoWjDnn8KPkie11IBLAOSR+kBNKff/4Z8+bNQ926dbF27VqMGDECY8aMwbvvvuv1MQUFBbh06ZLTLVRy6/NXJqxAbR2GswbJGvS+LiRrYB2SHkjZZV9cXIy77roLL7/8MgDgjjvuwP79+zF//nwMGjTI42OysrIwefLkcA6TTE5tHbIGqSQtjiPlupD0gHVIeiClQ1q5cmU0atTI6b6GDRvi+PHjXh+TmZmJvLw8x+3EiROajSc/rVjRdDzT3lzU1mEoa5CsSW/rQrIm1iHpgZQOaevWrXHwoPOlmA4dOoQaNWp4fYzNZoPNZgv10MhC1NYha5C0xnUh6QHrkPRASof0qaeewo4dO/Dyyy/jyJEjWLx4Md58802MGjVKxnDIokJdhzyhifzhupD0gHVIeiAlkDZt2hQrV67E+++/j/T0dEydOhWzZs3CwIEDZQyHLIp1SLKxBkkPWIekB1J22QNAr1690KtXL1mz9yu3fjSSDxa63X8tvSo7Xyai9zok82MNkh6wDkk2/pY9EVGA+OWUiEgblg2krhfHV3qmPRERERFpyzKBtGvqQf8TKcTLPxERERFpxzKBNBD8xSYKFHflEhERKcdASkRERERSMZCWoOY4Uu62JyIiItIGA6kf3G1PREREFFqmDKQPJ29TNJ3rmfZqsUtKRDxemIgoeKYMpERERERkHJYKpEou/eTpOFJfu+3ZJSUiIj3g9oiMzFKBNFS4EiAiPeE6iYiMxvKBVOlxpDy5iYiIiCg0LB9IPQnkZ0TZkSA7nuRCRESkDgOpCv66pAylREREROpZLpB6OrHJ0277QLqkRERERKSe5QJpsNglJSIiItKWaQOp0ovjhwJDKREREZFypg2kaqnZba/kjHuGUiIiIiJlLBlIlVwg3x+GUiIiIiJtWDKQqhHsyU0MpUTmx0t9EREFh4G0BG8XyQ9m1z3AUEpERETkCwNpkBhKiYiIiIJj2UDq7ThStV1SQF0oZTAlIiIicmbqQBrOSz+p+a17hlIiCjWuZ6yF7zcZnakDqT9adkkBhlIiIiKiQFg6kAZC61DKYEpERERWx0DqhbcuKaBtKAXYLSUiIiJrM30g9Xccqa+L5PsKpf4EEkoZTImIiMiKTB9IQ0XJBfPVhlKA3VIiIiKyHgZSBN4lDWUoZTA1Jv5iDxERkXoMpArICKUAu6VERERkDZYIpEquR+qrS+pPqEMpgykRBYLrDmvg+0xmYIlAqgV/JzgpDaXslhIRERE5YyAtwV+XVItQCnAXPhEREVFJUgLppEmTEBER4XRr0KCBjKGopodQymCqDSPXIZkH65BkYw2SHpSSNeNbb70V69ev/2MgpUI7lIeTt2Fhbiu/03VNPYjPjtcPal75acWI/8l/1s+tH43kg4UBzeNaelWe0a2BcNchkSesQ5KNNUiySau4UqVKoVKlSrJm75O/UBpXKw+Xjyb6fA6GUmPQcx2SdbAOSTbWIMkm7RjSw4cPo0qVKqhduzYGDhyI48eP+5y+oKAAly5dcrrJpORXnEK9+x7gcaXBUlOHeqtBMo9Q1iHXEeam1ftr9G0yGZ+UQNq8eXMsWLAAn376KebNm4ejR4+ibdu2yM/P9/qYrKwsJCYmOm7Vq1dXPV8ll3+yU3IZKL2EUgqM2jrUogaJXLEOSTZZ22SikiKEEEL2IC5evIgaNWpgxowZGDp0qMdpCgoKUFBQ4Pj70qVLqF69Or7cXwVx8cpztZLjSO2UHkvqb/c9AEW77wEEvPueu+5vulFciPVn3kBeXh4SEhJUPdZfHXqrwdadJ6FUqRgAfB+srGSn6saN69i6YZK0OnTFujQvXx3SQOswmG1yl8rDUSqSDRb6g9Ltsi6OWk5KSkK9evVw5MgRr9PYbDbYbLYwjkqbE5zsQn1MKY8nDZ6/OpRRg2Q9rEOSTa/bZDI3XVyH9PLly/jpp59QuXLlkM9LzW57QLtd92pw970c4axDIm9YhyQba5BkkBJIx48fj88//xzHjh3Dtm3bcO+99yIqKgoDBgyQMRxNaHk8KRBYKOXJC+qYsQ7JeMJRh1w3mJNW7yvXhaQHUnbZnzx5EgMGDMCFCxdQoUIFtGnTBjt27ECFChVkDMcvGbvuKfSMVodkTqxDko01SHogJZAuWbJExmwdlF4kXy0l1ydVI5DjSXksqXKy65AIYB2SfKxB0gO26iRQs+ueiIjIFQ/DILNhIFVIyclNAE9wIiJ9YoAhIj3TxWWfrIjHkhIREZmLpy9+PIxOGQZSE+JxpERERKGldK+D63TcPnvGFl0IaL3bnohIC9xtbw58H+W6ll41qPcg2MebFQOpCkqPIyUiIiLz0TJIMpg6s2wgVfuLTURERGRNoQyPDKU3WTaQhuI6pEREeseNn7Hx/Qu/cCxzvq8WDqSBUPprTVpeHJ+IiIjkCGdQtHooZSAlIiIiciEjIFo5lDKQmhAvKUFEvlh5o2dkfN+swarvMwOpJEoviq/2t+yJiIgoOFYNhTIxkCrE40eJyEy4wTUWvl/ho4dlrYcxhJslA6nsM+zZHSUiIiJfrBZKLRlI1dKyOxrq36/n8aNEpJTVNnhGxfcpfLis5eFv2WtE61317I4SEREZS279aKe/g92WX0uvaplGEwOpH0q7o0qwO0pERGqwYxc+gS5r1xDq69/YbPLOcrvsQ3H8qNa76lmwRBQuDDxEgcmtH+0zjHp7jFpW+YxaLpCqoaQ7qpcwyu4oERFRYNSGvkCCZcnHBvN4s2IgDQLDKBGZgVU6MEbD90WftAqTDKXOLBVI1eyu1/LYUSUYRomIyI5hVJ+0DpFKn88K9WCpQKpUuHfVM4wSkWxW2OAReaK09tnRDC0G0gAwjBKRGTGU6gPfB/0JZRhl0L3JMoFU6e56f91RrcJo8sFChlEiIiJSFErN/kXFMoFUC1qG0UAxjBJRKJl9o6d3XP7hpWR5s4MZHrwwfgnBnsgUyjDKIEpEZG4Mo9aWWz/a0tcht0Qg1eJi+P66owyjRGQWVvq5QiJf1HRH89OKvf6bVr/UaObPJnfZ/3++uqMMo0RkNezWhReXt3HlpxX7DKNKpwGsfXgAA2mQQhVGY/efYhglIqkYksKDy1kOf8tdSThUEjKDmd5KGEgReHfUXxgN9Ex6BlHj4oaFiMgaAg2X/h5n1S6p6QNpMMePBhtG1WJXlIj0hl+yQovLV5/8hcJgO53BPN6sNWP6QOpPIGfWhyqMEhHpkVk3gLJxuRoTd7uHhuUDqTdKrjnqidowyq4oERkBw5O2uDzlCnT5axlGfT2XFXfbWzqQat0dDSSMEhEZBUOUNrgc9S2cYZDd1j/oIpC+8soriIiIwNixY2UPBYD37qhWYZRdUX3SWx2S9RihBhmmgmOE5WeEOpSB4TG0pAfSnTt34o033sBtt92m+XNrcUF8O60uassgqk+hrEMiJYxUg0YIVXpkhOVmpDo0C29B11en1gi1pJbUQHr58mUMHDgQb731FpKTk8M6b2+76wM5dlRpd5RhVJ9k1iERYMwaNOMGMZSMsLyMWIda8xYClXRH42rlebyRMlID6ahRo9CzZ0906dLF77QFBQW4dOmS0y1ctNhVzzCqX0rrUGYNkrkZZV3o6lp6VUMELZmMtIyMWod64Ct4KgmmPBxA4m/ZL1myBHv27MHOnTsVTZ+VlYXJkyeHdExqu6MMo8anpg7DUYNkPXpcF6pl5t/XDoZRgihgjjpUSsv3RU0HNK5WnuqckVs/OuCfHjcaKR3SEydO4Mknn8SiRYsQExOj6DGZmZnIy8tz3E6cOBHw/NWcXe+tO8owanxq61DLGiRzCXQDJ3tdqCUjdQJDzWjLwkx1GApadi+5C987KR3S3bt3IycnB3feeafjvqKiImzZsgWvv/46CgoKEBUV5fQYm80Gm80WsjEFet1RXxhG9U1tHYa6Bsl69LguDJbVu6VGCqJ2ZqzDQKi93FOg4dJbpzQ/rVizE6iNSEog7dy5M/bt2+d035AhQ9CgQQM8++yzboUfCC3OsA+mO2rlFbJRhKMOiXwxaw3aQ5mV1oNGDKJ2Zq1DLXjrjuqh02m2L39SAml8fDzS09Od7itTpgzKlSvndr8RmalAzMzsdUj6Z/YatEIwNXIQtTN7HepRIMeTmp20k5pk8XT8qKeiCLQ7auYVLxFRIEqGNjOsI80QQilwoeyOetptb5UTm3QTSDdv3ix7CH4xjJqfEeqQzM3sNWjUcGq1EGr2OtQDdkmd6SaQEhGRteg9nFothFqBt/fU0wlNno4f1cOxo2bFQOqBp9317I6SUmY70JwoHFyDgozPEAMoBatr6kGnv9VcZtLqLB9ItWiXM3wQkRn4uuxNuI9h8xcOA1nv6i1w6ml5U/Bcw2jJ+7wFU0+77a16+SdLBVJ+UyEicqfk+oueppEZmvQWLv1Re41L+/QMpvrha3e9pzDq+u/MIL5ZKpAqoXZ3PbujRGRUakOSv8czPP0h2GXr+jxctuGl5teZ/IXRktMFGkqtcKY9AykRURCM1qkLJb11UcNFq/BJxqM0jPoSzNn2ZjpnwZSBVOmvNAV7/KhZioCIrCdcIcrbfIwYVGUGTyt0yPRMq7PrueveO1MG0kAFcnY9EZHR6KGjp9cTevSwbLxhKA2NQN9zLbqj3ljxxCYG0gCxO0pEFBp6DoVEwWKX1DNrxW8iIotj2CPSH15w30KBNJBvI952jbA7Sv7wRBciCgV+oQg9JWfYh3J3vVVZJpC64u/HEhERWUegjYJQdC8ZaN3xGNL/z2oHDxMRaUXNNRu1pmTdrffxESlh9pPaGEiJiAJktEMztNrdKzPgudLTWDxxHZ8WAdXswUTv2N0MDX5184LHjxIROctPK9Z9ANQ7LkPyxuonNrFDSkREfjFEacuK15m0goeTtzn97euHevxd/slqNcJAShQiZvpJN7I2WWE0nB0jGSe6Wi1wmJ1rGLXfp/TXI62OgZSIiLzSOozqdbekmnFpGV4ZSs2PoVQZBlIoP8ic3S4isjPaCU2BCDaM6jV8BsvT6wompDKU6pfre+3thCZP3VFSh58AIiILUHuGfTBhNK5WnmnDqDfBvma1y5sXyNdGuJYjA6t/luyQ+vsmy8tpEBGpF+oQquXldkL1W+L2ZcAfXzEmnrwnjyUDKVG48MQmMqJANspahdFwXePR13y0CKtxtfIYSi1CdvfTLNsZBlIiIgpKMGFUjxcZdx1ToAFVbSjlsaTW4+/ST1bCQEpEpJIVTmhSKpAwqscQ6kvJ8aoND+yUkh3PtvfNEl/FtPj2YYZ2OBGRlqwQRl0FMn6rneBFgbNyrbBDShRiZjm+h6whVCd1hCKIqjl2T8vOlP21hGJXK3fbk1UxkBIRqcDd9Tep6eRoEUaDPXHE0+ODDalqjv/jrntzkn1Ck5kwkBIRkW6FcoNvf24e10ckH/cLEIUBu2pkVYF2Rx9O3ha27lMw8zL6MbFEesFASkREqoT6xAtZu0G5+5VIHgZSIiKF2OkmIgoNBlKiMGGYISIi8oyBlIhIAX6hICIKHSmBdN68ebjtttuQkJCAhIQEtGzZEmvWrJExFLIw1iHpgRHrkJcvMhcj1iCZj5RAWq1aNbzyyivYvXs3du3ahU6dOuFPf/oTvv/+exnDIYuSUYfsspErrg/dLcxtFfZLMcmYp16wBkkPpATS3r17o0ePHqhbty7q1auHl156CXFxcdixY4eM4ZBFsQ5JqVB+kTB7HQbza0bhCojBzCcUv9YUbmavQTIG6RfGLyoqwvLly3HlyhW0bNlS9nDIosJZh/wpUfLGrOvDz47XD/h6nSXDopaXZdIi7JohjLoyaw2GysLcVrxcmEakBdJ9+/ahZcuWuH79OuLi4rBy5Uo0atTI6/QFBQUoKChw/H3p0qVwDJNMTk0dsgYpVIxYh5ePJqq6HmkwodROT7vU1YZRpcfdyvode26TSTZpZ9nXr18fe/fuxVdffYURI0Zg0KBBOHDggNfps7KykJiY6LhVr149jKMls1JTh6xBawrHcb96qsNQBiKzdBTN8jpK4jaZZIsQQgjZgwCALl26IC0tDW+88YbHf/f0bax69er4cn8VxMU7r0A9fYsuuQJx/abqugJOPljocQzczap/N4oLsf7MG8jLy0NCQoLqx/uqQ2812LrzJJQqFaN6XqwnYwgkkN64cR1bN0zSVR3m1o9WPP/8tGLF0wb6q01G/MnNQIOomqsSqPlC4G1bZRdMHQa6Te5SeThKRSqvtXDy9Fl2/Vy41r5rfXuqWzW77K2YT5Rul6UfQ2pXXFzsVNyubDYbbDZbGEdEVuSrDlmD1iPrqghGqkO1u+7tSm6E9RxOg+2GGvUSWdwma09Ph5zokZRAmpmZie7duyM1NRX5+flYvHgxNm/ejLVr18oYDlmU7DrkyU0EyK9DT+J/ilTVJQ00lNp5Cn0yQqrWu+LVhlFZx4/qsQatwoyHfwRKSiDNycnBI488gjNnziAxMRG33XYb1q5di7vvvjss84+rlWfYb62kHdl1SPoWru6oWerQvk4NJpiWZOQNtdG2L2apQS2o/TIGyD/T3iyNDSmB9O2335YxW8Vy60f7PTaHjE8PdcguKemhDj0JZMMMaB9MjSSYICqrOwrotwbNhLvr/dPNMaRERHphxl/USj5YqOrEpmCVDGdmDqeyuqFsmmgj3J8L8k7eVzIdUdoFMONGiuRjXZFeadW1u3w00e1mRKF6HTK7o+Sb63vs7VASXx1QdkeVYYeUiKgEfkFwFuiue3+MGkq1xjBqHrKPJTU6fhKIdIAhiPSMoSk0uFzNx7Ub6qs7auQT90KBHVIiov+PXwy8s4enUHRLrYZB1Ny02kVvtTqx1qtVwdtBztxgUaiwtuTi8lcm/qdIy20otcJlZw6h6mxa/TAWdkiJdISXgaJQ0vKMYl/BSm0XVc8hTY+vhWfYkxlZNpC6Xhw/P61Y1ytFIgoddke1ZaZ1qZleC+lHIF1Ws38RscwnTcufoePGi0KJ9RVeXN5E1qB075PrlxCr70oPF8sE0kDwYrkkC0MShYrZuyxmx/dPH3iGvPYsu8ueSO94PGnoMfgbUzChjI0Gks1TmGUXloHUiZrjSBkWiIzNymFUjz+XGK7On5r5WHUZWU2gn4fPjtfX9HDAkqx47DIDqR+59aO5EiBp+MUnNKwcRmUy2rrU13j1FlYptC4fTURcrbygn4e7+r0zZQRX+tNdwRYXN2oUDqwzbXF53hTqcJh8sNDtZibhfn1mW35mwYCpHXZIiQyAnVJtMIw603LXPQOT+zLgsjWu+J8iNf9VMm/hNZjjR820XTBlh9QbJcd6eCpAXysVbuAoXFhrweHy8yyQsGP27qdWtFhOXLb6p6RLGmwn1Qp1wA6pBti9onBhrQWGYdQ3o2zstKx9WTVhlGVN7nwdR+rrBCe1YdSKJzQBDKRuv9jkDU9uIr2wb0gZTJVhGDWWcNW1r/mwZigQgXRBebmnP1gzhvsRyHEjXIFRuLHm/OMyMobY/accNz3Q23hIO97eU6UNJwbI0LF8h1QNf11S7k6lcGPNecYgqm9GqlnXsbK2rCMUJzaRd5brkHo6xsPTMSEsQjKKa+lVuZEsgctCv8zQdTTDayB98NRtterxowA7pKqxS0p6ZfVjSxlE9cms9VjydbH2rEWri+QrZZXzV0wbxZVeHD8UuHIimaxWf+wQ65OVOolWeq1W461jGeyxpFoci2q2mjNtIFVLzW57JRc75gaSZLKHNDPXodlfn5GZbUOplFVft1mEqxPJE6M8s2QgVXKBfH8YSskozBbczPZ6zISdQi4DKwkkWPp6jJWPHwUsGkjVCPbkJm44SS+M3DU18titgCHMHZeHefgKiqHudlrl+FGAgdSJt4OUg9l1DzCUkv7oPeCVHJ9ex0g3MXh5x6CuT1q/J0pC6eWjieyO+sGz7IOk9BecePY96ZWnwBfuWmXoNCau05SJ3X+KNW4QyQcLPTab/F2T1B42XRtbPF5UOcsG0q6pBz3+zJe3nxLNTyv2+g1GTSgFuBInd7667TJ22fjbeKqtYb1tjPW2vI2I6zF1GEqtIZAAGkh31IyfP1MH0oeTt2FhbquwzEvNb92zW0p2Sg778DSN7NBkpA2r0kNrPE0veznrFddfgWEoNbZw/3KT1dY/lj5owdvZ9mqPJbVTs+HjSonUBiXXx7re6CYtlwuXqzuG0eBw+VFJPHb0D1wSKmkdShlMrSkUQceKITUcr9kKy1EphiltcDnK5+s98NWZZIAMHVPvsg+Gt2NJAd/HkwLqdt8D3IVvNeEMOHrc3R8IhkL5uI7SFnffk68cYcT1dLBMH/X9/YSor4vkB/NbtWo3oOyWUrh46irqoaOq13HZx2ZlDKOhweWqX6HukgbzHGatGymBNCsrC02bNkV8fDxSUlLQt29fHDwY/K8nhZOSA5sD2YgxlIaPjDrUe7DxFQpDfbMqva8Pzbrx0ws9LF+916AeBRMoudvfMylL5fPPP8eoUaOwY8cOrFu3Dr///ju6du2KK1euyBhOwF3SUIZSBtPQ01sdkr6FKjTruQ71EJasQPZy1nMN6lkgwVLJY6y4ux6QdAzpp59+6vT3ggULkJKSgt27d6Ndu3YyhuRTMMeTAuqPKbXjsaWhFe46tHIXkLwz2vqQzMeqNejvOF5vF8kvyb79V9KgYmfUN12c1JSXd7MLWbZsWa/TFBQUoKCgwPH3pUuXFD+/kuuRertQvhKhDqWA/G/QVuCvDoOpQSKl9FKHXOeEl55Ocgr1NtmMvAVTtSHUX04w8+dSeiAtLi7G2LFj0bp1a6Snp3udLisrC5MnTw7jyJz56pICykMpEFg7nt3S0FJSh7Jr0JNwXqTZaELRjQj0i6VSeqlDrmvk0EMoNco2OVyUdElLYhc0cNKX3KhRo7B//34sWbLE53SZmZnIy8tz3E6cOKH5WHwdSwr4P+teaTgIdNet7BWVmSmpw3DUoD/5acVON/LOiMvKKHVI5qWnbXI46OnLl1WPHbWT2iEdPXo0Vq9ejS1btqBatWo+p7XZbLDZbGEamXdadEoB7sLXE6V1GEwNBnv8qFEClZ7Zl6FeOxjhqEMluG6RS2aX1Ijb5HBQ2yUNdB5WJ2XNLITA6NGjsXLlSmzcuBG1atUK+Tz9XY/Uzl+XVIlQd0oBdku1IKMOA8Ewqi29dUz1VIcMo/oQ7vdBTzWoV3oIjGb/fErpkI4aNQqLFy/GRx99hPj4eJw9exYAkJiYiNjYWBlDcuLvBCd/XVIg9J1SgMeVBkvvdQjICaPB/CBEoPx9nkJB6Wc01IxQh2RurEG59BB29UBKIJ03bx4AoEOHDk73Z2dnY/DgweEfUAAYSo1P73WodRiVETSVUjM2LcNrIKFU6xOb9FKHXI/oSzh33eulBmVRuqxDseueYfQPUgKpEELGbBVd/slOyWWg9BJKKTCy6lCJYMOonsNnsFxfm4zuqpb0XIdkDaxB5bQMpWq2+Vb4wih/f5XBKdnw8+x7Cpe4WnmmDqOeBPua9XQ8qSxW2NgZEd+X8FGzrLVoHrEB5U76dUj1LJiL5bsKx9n3XHmZQyABKdQhVIuT/ey0+ky5si8Do3dMiUj/7NvpQBpJarfxVtm2Wy6QqtltD2i3614N7r43l1BfLkSLMKpl4Ax2XsEG1kCCqV5OcJLBKhs7o9LDxfLJO6XBlNt0/ywXSENFy+NJgcBCKbukxqe2OxpMGA1nCFXDdVyBBlStvygSkbkFE/4ZOIPHQKqAjF33RP4EEkb1GkJ9sY85VLv6rYxfYI2BXVLrstJn1JLJSOlF8tXS+ji+QHb1cqVlDVYJoyV1TT2o+jWoWU48uYmI9BQA9TSWcGCHVAJ2SSmcQhFE1XypU3PMthJq91hw171nVtvYESnFjrQcDKQKKd0IcuNHoaam66dFGA12j4KnxwcbUrU8jIbICBiSrMWKXxgZSCXhBfPJld52GYfq0BbX5w40nDKUElGoyPwCYMUwClj0GFKz47doAgLvjj6cvC2kYdTT/ELNaj8W4I9VN3hGx/ctvLi8w4uBNAS48SNSJ5wBmIhIqXCHUiuHYMsG0kA2gEY/S5nIH5nBkJ9JItKjcIVEK4dRwMKBVOszf4koOPxMhofVN3pGx/dPjlAvd76vFg6kREREREqFIjTG7j/FMPr/MZCqwDN6yeyM1qXkZ5KIwkmrAMkg6o6BNAR4HVIyMhmhNNTz5GfyJm4AzYHvo3z2QKn2vWAQ9Y7XIZUklL/UxGIn4Gb3MNCTfuwBMdQnOQUTRNkdJSI94DZXGwykOseL4ltH/E+Rii6Of/loouJLiwUTSoHQBFOjHRZAREShx0CqkNJuDHcNkt4EG0oB/YVINd1RfiZvYhfHXPhTomQ2ljyGVPbGVenuenZHyRu1Icssu7c/O17fNK+FiIj+wA6pAkbqjrILQt7Y69iIF5MPNISq+UyG8rhuIiLyjYFUI0o3fOyOki9KjyMF1B1LWlLJcKfncBpsJ1QPXxCJiEgZBlI/tNw9GOoODLuj1hNoKLXzVN8yQqrWu+EZRp1x3WBOPI6UzMRygTQUx48q2fipCaPsjppL8sFC5NaPDtnz2+svmGBaktGP0QwkjHJ3PRGRXJYLpGoo2TDrJYyyA2Ieanbbl6R1MDUSdkSJiIyNgTQIDKMUKoGGUsC5Ls0cTrUKoeyOEhHJZ6lAqmZ3fbh3WzKMUih4C21GC6qh6oBaIYxyHUFERmCpQKpUuHfVM4ySJ8F0Sf3hLu7AwyiP8SY94YlNZBbmbw+EAMMohYsVOngycLkSEemLZTqkSnfX++uOahVGg+myMIxai72eQtUttRIGUSIifbJMINUCwygFSotLP5WsLYZTdRhEiYj0jYG0hGBPZAplGGUQpZJ81ZrSsGqEkKYmeBvh9RARkWeWCKRaXAzfX3eUYZT0wkzBTG+vxWgnNHHdYQ08sYnMQNrafsuWLejduzeqVKmCiIgIrFq1StZQAPjujjKMmlO4a9BoYYbCQ2/rQrIm1iHJJi2QXrlyBbfffjvmzJkjawiaCFUYjd1/imE0xMxSg2RsrEPSA9YhySZtl3337t3RvXt3WbN3Emh31F8YZVdU3/RUg0YRbJc32BO7ZApVh5t1SHrAOiTZTH8MaTDHj4Y7jDKImp8WZ9trLZyHEqiZl96WExERhY5hAmlBQQEKCgocf1+6dEmT5w3kzHqGUWsKVQ2GgxGPX/U2ZhlBVU/Lz8h1SObBOiSt6esUVh+ysrKQmJjouFWvXj2k8wv0pxXVbrh4rKhxaFWDoQ43yQcL3W5mEu7Xp7flF+51IZEnrEPSmmECaWZmJvLy8hy3EydOBP2cWndHAwmjZBxa1qCWIcfM4VOpUIVUPS7PUKwLidRiHZLWDLPL3mazwWazhWVe3rqjWoVRBlFj0roG7TWjZhe0HgOSXrkuK7W7+vW6rJXWIdczFErh3CaTNUgLpJcvX8aRI0ccfx89ehR79+5F2bJlkZqaqsk8tLggvp1WF+jmRkI/wlGDSug1+JSkdd3KuIi3XpezXuqQjC3Yi+OzDkk2aYF0165d6Nixo+PvcePGAQAGDRqEBQsWhHz+3nbXB3LsqNINHcOovsiuQT0KV416m48Vf22GdUh6wDok2aQF0g4dOkAIIWv2qmixq55hVH+MVIOhore6dB2PFQIq65D0gHVIshnmGNJwUNsdZRglIzJSPZYcqxXCKRGRVVkykKo5u95bd5RhlIzEDHXIcEpEZF6WDKSeBHrdUV/MEALI2Mxag/bXxWBKRGQOpg2kWpxhH0x31KxBgIzBKvXHYEpEZA6mDaQyWSUMkP5YtfYYTImIjM0wv9SkFU/Hj3raXR9od9SqgYDk4k/Q3sRlQERkTJYLpMFgGCU9Yt05YzgnIjIeBlIig2Lw8o3LhojIOBhIPfC0u57dUdIT1psyXE5ERMZg+UCqxeWeuNGjcGK9qcNOMhGR/lkqkKq5ID6RHjFYBc5Ky85Kr5WIzMFSgVQJtbvrueKncGGtBY/LkMyM9U1GxkBKZADc0GiHy5KISH9MGUiV/kpTsMePcsNG4cA60x6XKRGRvpgykAYqkLPriUKJwYmIiKyAgTRADAoUaqyx0OLyJSLSDwZSIrIshlIiIn2wTCAN5JJP3F1PsjAohQ+XNRGRfJYJpK6COaGJGzAKJdYXERFZjWUDqStPJzQRhRvDqBxc7kREcjGFERGBoZSISCYGUi+8HT/KjRaFCmuLiIisioGUiOj/45cCIiI5GEiJdIBBiIiIrIyBVAWGBiLz4+eciCj8GEjBM+xJLgYgIiKyOiYxIokYRvWJ7wsRUXhZMpD6uyg+f6GJiIiIKHwsGUiJiPxhl5SIKHwYSIkkYeAhIiK6yRKB9LPj9WUPgYgMiF8aiIjCwxKBVAvcMJGWWE9ERER/YCAlIvKBXx6IiEKPgZQozBhwiIiInEkNpHPmzEHNmjURExOD5s2b4+uvv5Y5HLIo1iH5E+ovEaxB0gPWIckkLZAuXboU48aNw8SJE7Fnzx7cfvvt6NatG3JycmQNiSyIdUiysQZJD1iHJJu0QDpjxgwMGzYMQ4YMQaNGjTB//nzccssteOedd2QNiSwo3HXI3fXkiutC0gPWIclWSsZMCwsLsXv3bmRmZjrui4yMRJcuXbB9+3aPjykoKEBBQYHj77y8PADAlcvF7tNe/t3p76KrBU5/F1+/7vzvBc65/MYN919qulHMX28yAvv7JITwO63aOvRWgzduXHeb1t/4yHhKf3cU1xpVVjStvSb81aGW68KSdcg6sy6nOpBRh6w9cqF0uywlkJ4/fx5FRUWoWLGi0/0VK1bEjz/+6PExWVlZmDx5stv93Vqc9TD1Si2GSQaWn5+PxETfPxGrtg691eBXn78S3GDJOM6om9xfHWq5LmQdEgCPNRrOOtx8LlvdeMky/NWhlEAaiMzMTIwbN87x98WLF1GjRg0cP37cb/AgZS5duoTq1avjxIkTSEhIkD2cgAghkJ+fjypVqmj+3KzB8GAd+sY6DA/WoW+sw/CwUh1KCaTly5dHVFQUzp0753T/uXPnUKlSJY+PsdlssNlsbvcnJiYa9k3Sq4SEBEMvU6UrQ7V1yBoMLyvUIdeF+sc6ZB3qgRXqUMpJTdHR0cjIyMCGDRsc9xUXF2PDhg1o2bKljCGRBbEOSTbWIOkB65D0QNou+3HjxmHQoEG466670KxZM8yaNQtXrlzBkCFDZA2JLIh1SLKxBkkPWIckm7RA2r9/f/z666+YMGECzp49iyZNmuDTTz91O6jaG5vNhokTJ3rcZUCBseIyDaYOrbi8wsFqy5XrQn2y2nJlHeqTlZZrhFByfRwiIiIiohDhb9kTERERkVQMpEREREQkFQMpEREREUnFQEpEREREUhkykM6ZMwc1a9ZETEwMmjdvjq+//lr2kAwtKysLTZs2RXx8PFJSUtC3b18cPHhQ9rB0j3WoLdZhYFiH2mIdqsca1JZVa9BwgXTp0qUYN24cJk6ciD179uD2229Ht27dkJOTI3tohvX5559j1KhR2LFjB9atW4fff/8dXbt2xZUrV2QPTbdYh9pjHarHOtQe61Ad1qD2LFuDwmCaNWsmRo0a5fi7qKhIVKlSRWRlZUkclbnk5OQIAOLzzz+XPRTdYh2GHuvQP9Zh6LEOfWMNhp5VatBQHdLCwkLs3r0bXbp0cdwXGRmJLl26YPv27RJHZi55eXkAgLJly0oeiT6xDsODdegb6zA8WIfesQbDwyo1aKhAev78eRQVFbn9ckTFihVx9uxZSaMyl+LiYowdOxatW7dGenq67OHoEusw9FiH/rEOQ4916BtrMPSsVIPSfjqU9GnUqFHYv38/vvzyS9lDIQtjHZIesA5JNivVoKECafny5REVFYVz58453X/u3DlUqlRJ0qjMY/To0Vi9ejW2bNmCatWqyR6ObrEOQ4t1qAzrMLRYh/6xBkPLajVoqF320dHRyMjIwIYNGxz3FRcXY8OGDWjZsqXEkRmbEAKjR4/GypUrsXHjRtSqVUv2kHSNdRgarEN1WIehwTpUjjUYGpatQbnnVKm3ZMkSYbPZxIIFC8SBAwfEY489JpKSksTZs2dlD82wRowYIRITE8XmzZvFmTNnHLerV6/KHppusQ61xzpUj3WoPdahOqxB7Vm1Bg0XSIUQ4rXXXhOpqakiOjpaNGvWTOzYsUP2kAwNgMdbdna27KHpGutQW6zDwLAOtcU6VI81qC2r1mCEEEKErx9LREREROTMUMeQEhEREZH5MJASERERkVQMpEREREQkFQMpEREREUnFQEpEREREUjGQEhEREZFUDKREREREJBUDKRERERFJxUBKRERERFIxkBIRERGRVAykRERERCQVAykRERERSfX/AB43f2/b13ahAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CSS. Estimated half cos: -0.00039816335536662734    SQL variance: 0.024999984146594215\n",
      "Sqz. Estimated half cos: -0.000308416008880398    HL variance: 0.0050000190240869205\n"
     ]
    }
   ],
   "source": [
    "N = 10\n",
    "j = 5  # Total spin quantum number\n",
    "        \n",
    "# Define collective spin operators\n",
    "Sx = qt.jmat(j, 'x')\n",
    "Sy = qt.jmat(j, 'y')\n",
    "Sz = qt.jmat(j, 'z')\n",
    "\n",
    "# Separable (SQL) Strategy\n",
    "css_z = gen_css(j,0,0) #initial state in north pole\n",
    "      \n",
    "H_sense = Sz  # Sensing Hamiltonian\n",
    "time=1.57 #for instance\n",
    "beam_spl_css = (1j * np.pi/2  *Sx).expm()*css_z\n",
    "evolved_css = time_evolve_state(H_sense, beam_spl_css, time)\n",
    "final_css = (1j * np.pi/2  *Sx).expm()*evolved_css\n",
    "        #Description of what is done in Fig 2b\n",
    "\n",
    "expected_value_sql = qt.expect(Sz,final_css)/N\n",
    "phase_var_sql = qt.variance(Sz, final_css)/N**2\n",
    "#phase_variance_sql.append(phase_var_sql/N**2) \n",
    "#Since we stimate N*phase, to get the variance in theta estimation we have to divide by N**2\n",
    "        \n",
    "        \n",
    "\n",
    "#HL\n",
    "eigval,eigvec = Sx.eigenstates()\n",
    "jm1 = eigvec[j-1]\n",
    "j0 = eigvec[j]\n",
    "jp1 = eigvec[j+1]\n",
    "    \n",
    "sss = 1/2**(1/2)*(j0-1/2**(1/2)*(jm1+jp1)) #This is the formula (283)\n",
    "\n",
    "beam_spl_sss = (1j * np.pi/2  *Sx).expm()*sss\n",
    "evolved_sss = time_evolve_state(H_sense, beam_spl_sss, time)\n",
    "final_sss = (1j * np.pi/2  *Sx).expm()*evolved_sss\n",
    "expected_value_hl = qt.expect(Sz,final_sss)/N\n",
    "phase_var_hl = qt.variance(Sz, final_sss)/N**2\n",
    "\n",
    "thetavec = np.linspace(0, np.pi, 100)\n",
    "phivec = np.linspace(0,2*np.pi, 100)\n",
    "initialcss,theta,phi = qt.spin_q_function(css_z,thetavec,phivec)\n",
    "beamcss,theta1,phi1 = qt.spin_q_function(beam_spl_css,thetavec,phivec)\n",
    "evolvecss,theta2,phi2 = qt.spin_q_function(evolved_css,thetavec,phivec)\n",
    "finalcss,theta3,phi3 = qt.spin_q_function(final_css,thetavec,phivec)\n",
    "\n",
    "initialsss,theta4,phi4 = qt.spin_q_function(sss,thetavec,phivec)\n",
    "beamsss,theta5,phi5 = qt.spin_q_function(beam_spl_sss,thetavec,phivec)\n",
    "evolvesss,theta6,phi6 = qt.spin_q_function(evolved_sss,thetavec,phivec)\n",
    "finalsss,theta7,phi7 = qt.spin_q_function(final_sss,thetavec,phivec)\n",
    "\n",
    "fig,axes = plt.subplots(2,4,figsize=(8,8))\n",
    "cont0 = axes[0,0].contourf(theta,phi,initialcss)\n",
    "lbl0 = axes[0,0].set_title(\"Initial Coherent state\")\n",
    "\n",
    "cont1 = axes[0,1].contourf(theta1, phi1,beamcss)\n",
    "lbl1 = axes[0,1].set_title(\"After beam splitter\")#\n",
    "\n",
    "cont2 = axes[0,2].contourf(theta2, phi2,evolvecss)\n",
    "lbl2 = axes[0,2].set_title(\"After evolution\")#\n",
    "\n",
    "cont3 = axes[0,3].contourf(theta3, phi3,finalcss)\n",
    "lbl3 = axes[0,3].set_title(\"Final state\")#\n",
    "\n",
    "cont4 = axes[1,0].contourf(theta4,phi4,initialsss)\n",
    "lbl4 = axes[1,0].set_title(\"Initial Squeezed state (y)\")\n",
    "\n",
    "cont5 = axes[1,1].contourf(theta5, phi5,beamsss)\n",
    "lbl5 = axes[1,1].set_title(\"After beam splitter\")#\n",
    "\n",
    "cont6 = axes[1,2].contourf(theta6, phi6,evolvesss)\n",
    "lbl6 = axes[1,2].set_title(\"After evolution\")#\n",
    "\n",
    "cont7 = axes[1,3].contourf(theta7, phi7,finalsss)\n",
    "lbl7 = axes[1,3].set_title(\"Final state\")#\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print(\"CSS. Estimated half cos:\",expected_value_sql,\"   SQL variance:\", phase_var_sql)\n",
    "print(\"Sqz. Estimated half cos:\",expected_value_hl,\"   HL variance:\", phase_var_hl)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance is smaller!! (But the angle better is close to pi/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.00000000e+00 -2.00000000e+00 -1.00000000e+00  3.99680289e-15\n",
      "  1.00000000e+00  2.00000000e+00  3.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "Sx = qt.jmat(3,'x')\n",
    "ev = Sx.eigenstates() \n",
    "print(ev[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 -0.00039816335536699277 0.12499992073297088 0.4999996829318835\n",
      "4 1.0643248238425082e-16 0.03133626431808963 0.501380229089434\n",
      "6 -0.00032509901830816865 0.013888902100060357 0.5000004756021729\n",
      "8 -0.00031477577094327823 0.007812517339662576 0.5000011097384048\n",
      "10 -0.000308416008880398 0.0050000190240869205 0.500001902408692\n",
      "12 -5.521321672650263e-17 0.0034976301271962213 0.5036587383162558\n",
      "14 0.00030098320556603756 0.0025510406293440904 0.5000039633514417\n",
      "16 -2.7654530787908187e-16 0.001934526122369454 0.4952386873265802\n",
      "18 -0.0002967734429165581 0.0015432304272543602 0.5000066584304127\n",
      "20 -0.00029528584736867236 0.0012500206094274739 0.5000082437709895\n",
      "22 0.00029406312639179574 0.0010330784868711328 0.5000099876456283\n",
      "24 -0.00029304029502762174 0.0008680761980109646 0.5000118900543156\n",
      "26 0.00029217202557837296 0.0007396656079838217 0.5000139509970635\n",
      "28 1.0016072550486504e-16 0.0006274101334371156 0.4918895446146987\n",
      "30 0.0002907774017417091 0.0005555761649830374 0.5000185484847337\n",
      "32 9.984263689091442e-17 0.00047927492553915494 0.49077752375209466\n",
      "34 -0.0002897063947813476 0.00043254652258532404 0.5000237801086346\n",
      "36 8.193976112706665e-17 0.0003938998241064806 0.5104941720419989\n",
      "38 -0.00028885805798262794 0.00034628091819166314 0.5000296458687615\n",
      "40 -0.0002884967594570279 0.0003125205103436968 0.5000328165499149\n",
      "42 0.0002881694799876967 0.00028346720281469616 0.500036145765124\n",
      "44 8.342790663816935e-17 0.00026486890468250363 0.512786199465327\n",
      "46 0.0002875994112197723 0.00023631534962084772 0.5000432797977138\n",
      "48 0.0002873496505027681 0.00021703432491974593 0.5000470846150946\n",
      "50 0.00028711967875687483 0.00020002041918661408 0.5000510479665352\n"
     ]
    }
   ],
   "source": [
    "for j in range(1,26):\n",
    "    N=2*j\n",
    "    \n",
    "    Sx = qt.jmat(j, 'x')\n",
    "    Sy = qt.jmat(j, 'y')\n",
    "    Sz = qt.jmat(j, 'z')\n",
    "   \n",
    "    # Separable (SQL) Strategy\n",
    "    css_z = gen_css(j,0,0) #initial state in north pole\n",
    "      \n",
    "    H_sense = Sz  # Sensing Hamiltonian\n",
    "    time=1.57 #\n",
    "   \n",
    "    #HL\n",
    "    eigval,eigvec = Sx.eigenstates()\n",
    "    jm1 = eigvec[j-1]\n",
    "    j0 = eigvec[j]\n",
    "    jp1 = eigvec[j+1]\n",
    "    \n",
    "    sss = 1/2**(1/2)*(j0-1/2**(1/2)*(jm1+jp1))\n",
    "    beam_spl_sss = (1j * np.pi/2  *Sx).expm()*sss\n",
    "    evolved_sss = time_evolve_state(H_sense, beam_spl_sss, time)\n",
    "    final_sss = (1j * np.pi/2  *Sx).expm()*evolved_sss\n",
    "    expected_value_hl = qt.expect(Sz,final_sss)/N\n",
    "    phase_var_hl = qt.variance(Sz, final_sss)/N**2\n",
    "    print(N, expected_value_hl, phase_var_hl, phase_var_hl*N**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variance behaves as 1/N^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.06744831905307412"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/2*np.arctan(20**(-2/3))"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  }
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