Pore_Fluid_Factor_diffP.ipynb

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    "from IPython.display import HTML\n",
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   "execution_count": 2,
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "from numpy import linalg as LA\n",
    "# Set default font size for plots:\n",
    "font = {'size'   : 20}\n",
    "plt.rc('font',**font)\n",
    "\n",
    "def extension_failure(sigma3,T,sigmav):\n",
    "    return (sigma3+T)/sigmav\n",
    "\n",
    "def hybrid_shear_failure(diffP,sigma1,sigma3,T,sigmav):\n",
    "    return (8*T*(sigma1+sigma3)-(diffP)**2)/(16*T*sigmav)\n",
    "\n",
    "def brittle_shear_failure(diffP,sigma1,sigma3,T,C,mu,sigmav):\n",
    "    theta2=(90+np.arctan(mu)*180/np.pi)*np.pi/180\n",
    "    c1=(1+np.cos(theta2))/np.cos(theta2)\n",
    "    c3=(1-np.cos(theta2))/np.cos(theta2)\n",
    "    return (1/(2*sigmav))*(-2*C*np.tan(theta2)+c1*sigma1-sigma3*c3)\n",
    "\n",
    "def lambdav_diffP(C,T,mu,h):\n",
    "    '''Input: lambdav_diffP(C=10e6,T=5e6,mu=0.75,h=10000)\n",
    "    Funcion for the interactive plot'''\n",
    "    #Input parameters\n",
    "    rho=2670\n",
    "    rhow=1000\n",
    "    g=9.8\n",
    "    sig_v=rho*g*h\n",
    "    sig_h=rhow*g*h\n",
    "    C=C*1e6\n",
    "    T=T*1e6\n",
    "    bl=2*C/np.sin(theta2)\n",
    "    ######################### TECTONIC REGIMES ####################################\n",
    "    ####################### 1. REVERSE FAULTING ###################################\n",
    "    diffP=np.linspace(0,300,3000)*1e6\n",
    "    sigma3=sig_v\n",
    "    sigma1=diffP+sigma3\n",
    "    #Extension failure\n",
    "    lv=extension_failure(sigma3,T,sig_v)\n",
    "    ef=np.where(diffP<4*T)[0]\n",
    "    lv=lv*np.ones(len(ef))\n",
    "    fig=plt.figure('Pore fluid factor vs. diff. stress',figsize=(8,12.9))\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.plot(diffP[ef]*1e-6,lv,c='r',lw=2,ls='-')\n",
    "    #Hybrid extensional-shear failure\n",
    "    lamv=hybrid_shear_failure(diffP,sigma1,sigma3,T,sig_v)\n",
    "    hesf=np.where((diffP>=4*T)&(diffP<bl))[0]\n",
    "    plt.plot(diffP[hesf]*1e-6,lamv[hesf],c='g',lw=2,ls='-')\n",
    "    #Brittle Shear Failure\n",
    "    lam=brittle_shear_failure(diffP,sigma1,sigma3,T,C,mu,sig_v)\n",
    "    bsf=np.where(diffP>=bl)[0]\n",
    "    plt.plot(diffP[bsf]*1e-6,lam[bsf],c='b',lw=2,ls='-',label='reverse')\n",
    "    ###############################################################################\n",
    "    ####################### 2. NORMAL FAULTING ####################################\n",
    "    sigma1=sig_v\n",
    "    sigma3=sigma1-diffP\n",
    "    #Extension failure \n",
    "    lv=extension_failure(sigma3,T,sig_v)#(sigma3+T)/sig_v\n",
    "    ef=np.where(diffP<4*T)[0]\n",
    "    ax.plot(diffP[ef]*1e-6,lv[ef],c='r',lw=2,ls='--')\n",
    "    #Hybrid extensional-shear failure\n",
    "    lamv=hybrid_shear_failure(diffP,sigma1,sigma3,T,sig_v)\n",
    "    hesf=np.where((diffP>=4*T)&(diffP<bl))[0]\n",
    "    ax.plot(diffP[hesf]*1e-6,lamv[hesf],c='g',lw=2,ls='--')\n",
    "    #Brittle Shear Failure\n",
    "    lam=brittle_shear_failure(diffP,sigma1,sigma3,T,C,mu,sig_v)\n",
    "    bsf=np.where(diffP>=bl)[0]\n",
    "    ax.plot(diffP[bsf]*1e-6,lam[bsf],c='b',lw=2,ls='--',label='normal')\n",
    "    ###############################################################################\n",
    "    ######################## 3. STRIKE-SLIP FAULTING ##############################\n",
    "    sigma3=sig_v-diffP/2\n",
    "    sigma1=sig_v+diffP/2\n",
    "    #Extension failure \n",
    "    lv=extension_failure(sigma3,T,sig_v)#(sigma3+T)/sig_v\n",
    "    ef=np.where(diffP<4*T)[0]\n",
    "    ax.plot(diffP[ef]*1e-6,lv[ef],c='r',lw=2,ls=':')\n",
    "    #Hybrid extensional-shear failure\n",
    "    lamv=hybrid_shear_failure(diffP,sigma1,sigma3,T,sig_v)\n",
    "    hesf=np.where((diffP>=4*T)&(diffP<bl))[0]\n",
    "    ax.plot(diffP[hesf]*1e-6,lamv[hesf],c='g',lw=2,ls=':')\n",
    "    #Brittle Shear Failure\n",
    "    lam=brittle_shear_failure(diffP,sigma1,sigma3,T,C,mu,sig_v)\n",
    "    bsf=np.where(diffP>=bl)[0]\n",
    "    ax.plot(diffP[bsf]*1e-6,lam[bsf],c='b',lw=2,ls=':',label='strike-slip')\n",
    "    ##############################################################################\n",
    "    plt.axis([0,300,0,1.1])\n",
    "    plt.ylabel('$\\lambda_V$')\n",
    "    plt.xlabel('$\\sigma_1-\\sigma_3$, MPa')\n",
    "    ax.axvline(4*T*1e-6,0,1.1,ls='--',lw=1)\n",
    "    ax.axvline(bl*1e-6,0,1.1,ls='--',lw=1)\n",
    "    ax.axhline(sig_h/sig_h,0,300,ls='--',lw=1) #Lythostatic\n",
    "    ax.axhline(sig_h/sig_v,0,300,ls='--',lw=1) #Hydrostatic\n",
    "    ax.text(120,sig_h/sig_h,'lythostatic $P_f$',fontsize=12)\n",
    "    ax.text(200,sig_h/sig_v,'hydrostatic $P_f$',fontsize=12)\n",
    "    ax.text(4*T*1e-6,0.1,'$4T$',horizontalalignment='center',rotation=90,fontsize=12)\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    return"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Influence of fluid pressure and stress states on brittle failure modes in intact rock\n",
    "\n",
    "There will be three main types of failure under compressive stress states driven by fluid pressure ($P_f$), namely: extensional failure, hybrid extensional-shear failure, and brittle shear failure.\n",
    "\n",
    "## Extensional failure\n",
    "\n",
    "Extension fractures occur only when the fluid pressure ($P_f$) is as large as the minimal stress and the rock's tensile stress ($T$) combined:\n",
    "\n",
    "$$P_f = \\sigma_3 + T$$\n",
    "\n",
    "which in terms of pore fluid factor ($\\lambda_V$) becomes:\n",
    "\n",
    "$$\\lambda_V = \\frac{\\sigma_3 + T}{\\sigma_v}$$\n",
    "\n",
    "where $\\sigma_v$ is the overburden's stress to a desired depth of estimation.\n",
    "\n",
    "## Hybrid extensional-shear failure\n",
    "\n",
    "Under effective normal stresses $-T < \\sigma_n' < 0$, the hybrid extensional-shear failure condition is approximated by the Griffith failure criterion:\n",
    "\n",
    "$$(\\sigma_1+\\sigma_3)^2 = 8T(\\sigma_1'+\\sigma_3')$$\n",
    "\n",
    "$$P_f = \\frac{8T(\\sigma_1'+\\sigma_3')-(\\sigma_1+\\sigma_3)^2}{16T} $$\n",
    "\n",
    "$$\\lambda_V = \\frac{8T(\\sigma_1'+\\sigma_3')-(\\sigma_1+\\sigma_3)^2}{16T\\sigma_v} $$\n",
    "\n",
    "## Brittle shear failure\n",
    "\n",
    "This kind of failure happens at differential pressures $\\ge5.7T$ and when shear stress ($\\tau$) becomes equal to shear strength ($\\tau_f$).\n",
    "\n",
    "$$\\tau_f = C + \\mu_i(\\sigma_n -P_f)$$\n",
    "\n",
    "with $C$ being the cohesive strength and $\\mu_i$ being the coefficient of internal friction.\n",
    "\n",
    "Cox (2010) has some typos in the equation (Eq. 4 in the paper).  The typo on Equation 2 of Cox (2010) leads to the following expression for the pore fluid factor:\n",
    "\n",
    "$$\\lambda_V = \\frac{1}{2\\sigma_v}\\left[2 C tan(2\\theta_{opt}) - \\left( \\frac{1-cos(2\\theta_{opt})}{cos(2\\theta_{opt})} \\right) \\sigma_1  + \\left( \\frac{1+cos(2\\theta_{opt})}{cos(2\\theta_{opt})} \\right) \\sigma_3 \\right]$$\n",
    "\n",
    "The correct expression to use is:\n",
    "\n",
    "$$\\lambda_V = \\frac{1}{2\\sigma_v}\\left[\\left( \\frac{1+cos(2\\theta_{opt})}{cos(2\\theta_{opt})} \\right) \\sigma_1  - \\left( \\frac{1-cos(2\\theta_{opt})}{cos(2\\theta_{opt})} \\right) \\sigma_3 - 2 C tan(2\\theta_{opt})\\right]$$\n",
    "\n",
    "where $\\theta_{opt}$ is the angle of optimally oriented faults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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SpUvD19cXlSpVwpo1awDgseNTzwKcO3cOL7zwAvz9/ZEvXz707ds33a//wIEDadqX1qpVCwBw9+5d3d9TIvpPVu4T2MOfkJAQuelx545SSUlpb4T8/LPc/8+TR6nLl3XcSXm8EkPWZXn8oUNKtWyZvH+VUoUKKfXFF0rdu2etKMnRJN+nP3/+vPLx8VFXr15VSil179495e/vryIiItKMe/i1NWrUUHFxcery5cuqQoUKas6cOeru3buqdOnSavz48erOnTsqPDxc5cyZU0VHRyullIqOjlYBAQEqLi5OKaXU6dOn1cmTJx97nlWrVqm4uDiVlJSkvvrqK+Xj46POnz//xLg2bdqkEhMTVZUqVdSAAQNUfHy8un37ttq5c2e634fOnTurMWPGKKWUunr1qurevbsKCQlR9+/f1/29JXIWcPl7/Mm8vAC3VF/OnTspN9OHDJG1AHamcmXZonLbNqBGDeDvv4E33gCCg+VuhXLs3kqUBYULF8bTTz+N1atXA5A9xvPnz4+QkJAnvq5fv34oUqQI8ubNi1atWuHAgQPYtWsX4uPjMXToUHh5eeGZZ55By5YtsXLlSgDSl/zOnTs4cuQI7t27h8DAQJQuXfqx52jXrh2KFCkCNzc3tG/fHmXLls3UdqJ79uzB+fPnMWXKFOTIkQPe3t6oV69eumMPHDiAKVOmIG/evAgJCYGmaVi7du2DErELFy6gXr16aN68eYbnJaK0bJb4NU1bqGnaRU3TDj3m85qmaTM1TTupaVqkpmnVdZ0oNhZo3VpK+3LmBFatAt57L+XzMTHAf9OfWbG2b/q/sPSMb9AA2L0b+PproFQpIDoaeP554OmngV27shopOaquXbti+fLlAIDly5ejc+fOGb6mUKFCDx77+PggPj4e58+fR7FixeCW6o1xiRIlEBcXBwAoU6YMpk+fjjFjxqBAgQJ45ZVXcP4Jm6AvXboUVatWRe7cuZE7d24cOnQIly5dyjC2c+fOoUSJEhnuUX7nzh0cPXoU0dHRuHLlCk6dOoX58+ejcOHCD8asXLkSAwYMwI8//pjheYkoLVte8S8G8NwTPt8MQNn//rwOYI6usyQmAps3A199JX+7uaU09rl6FWjcWDKtna2o0zTg5ZeBo0eBmTOB/PllrWKdOkC7drIugFzL888/j8jISBw6dAjr1q1Dp06dHnzOkuYoRYoUwblz53D//v0Hz8XExKBo0aIPPu7YsSN++eUXnD17FpqmYciQIeme5+zZs+jVqxdmzZqFy5cv49q1awgKCoL6b3rqSXEVK1YMMTExSExMfGK8hw4dQo4cOR5bv7xz505MmDAB06ZNw7p16578xRPRI2yW+JVSOwBcecKQNgCW/ncLYxeA3JqmFX7C+PQFBgIjR8rjPn3SlvVdvCgfJyQAOXJYfOjUWs36xZDxXl7A228DJ08Cw4dLBcA330gFQN++8iWQa/D29sZLL72Ejh07ombNmihevPiDzxUsWBB//vlnpo5Tq1Yt5MiRA5MnT8a9e/ewbds2rF27Fq+88goA4NixY9iyZQvu3LkDb29vZM+eHe7/NcF6+Dw3b96Epmnw9/cHACxatAiHDqVM4j0prpo1a6Jw4cIYOnQobt68iYSEBPz666+PjPvjjz9QuXLlx3499evXR3BwMHbu3ImWLVtm6ntARCns6R5/UQDnUn0c+99zlhs0CKhQQQrlp05Neb58eWDvXrmxnjOnPGenN9L9/IDx41MqAO7fB2bPBkqXBj78ELh50+wIyRa6du2KqKioR6b5hw0bhnHjxiF37tyYmvpnPB1eXl744YcfsGHDBuTPnx+9e/fG0qVLUaFCBQAytT506FDkz58fhQoVwsWLFzFhwoR0z1OpUiUMGjQIderUQcGCBREVFYW6detmKi53d3esXbsWJ0+eRPHixREQEICvv/76kXgPHDiAoKCgx349yTMXqW9dEFHm2XR3Pk3TAgGsU0o98r9a07T1AD5SSv3y38fhAN5TSu1LZ+zrkNsByFu0ZIjvq58++FzyvfTUV9j9q+fHwJdroeb4zbh4Q2YAgormwrq362PYsIVYqVL65+8eHoao2OvouTRlz78JbYPRsVZxBA5dnyaOMxNboMfivQiPvpjmuRW7YzB8TdSD5+Z3CU1zPEC26f3ohSpo+elOHIr7FwBQwDcb9ox4FtM2HU9TLri2bz2cOgUM2JDyNSUdLItRL5TDvIvpfE3fRWLlnpT3UJn9msIqFMCCbjUy/TUFB/ih1oRw3V8T8NC/U1hZDGxcLv1/Jxf9mt6pkxdDO4Qh/xtL4JbNxym+pqz+O41pkBfhX8/HzkIvOM3X5Iz/TvyajPuaGlculKXd+WxaegcgEMChx3zuCwAdUn18DEDhjI75oJwvPZ06SZ1c8+ZKpVcGdOqUUh4eSrm7K7Vnz+OPk45PNh4zdPzjbN2qVGhoSglgxYpKff99+l8eObakpCTVv39/9dprr5kdil1ZvXq1mjVrltlhEJkGWSzns6cr/hYA+gJoDqAWgJlKqZoZHTM0NFRFRESk/8m//5bauO7dZd48vdXE27bJfHqvXpn/Qkx2/z6werU0KTx9Wp6rXx+YMgX4r88JObibN2+iYMGCKFGiBH766ScUK1bM7JCIyE5ompalK36bJX5N01YCaAggP4ALAEYD8AQApdTnmiwHngVZ+X8LwGtKqcdk9BRPTPwAcOMG4Oub+UCjooDz54GmTZ84rOb4zZnu169nfGbcvQt8/rl0/bt8WZ5r1w6YMEG6ARIRkfPJauK35ar+DkqpwkopT6VUgFJqgVLqc6XU5/99Ximl+iilSiulgjOT9DMlddLPoIwI165JD4DmzYEM6oOT78VklqXjM8PLC+jXDzh1Sq7+vb1lJqBiRakMYAUAERE9zHWWxX77rfTwP3z48WNy5QK6dgVCQoBGjWwXWxb5+clV/okTclcjKQmYNUuu+seNYwUAERGlcJ3Ev3kzcOYM0Lv340v43NyAMWOAnTulgB6QLJrOpXNQ0VwWnd7S8XoEBAALFgAHD8qkxY0b0tKgbFlg3ryMJzyIiMj5uU7inzAB8PcHduwAli178tjUW/oOGQJUqyb1/6mse7u+Rae3dHxWBAcD69cDW7bI5MVffwGvvw5UqSItDOy0dQEREdmA6yT+PHlSmvkMHgxceVITwf/cuSMJ/+LFR/r7D/su0qLTWzreGho1AvbsAVauBEqWlHbArVsDDRvK3gBEROR6XCfxA0DnzrLzzT//ACNGZDw+WzZg0yYgPFzq5VJJ3VQhMywdby1ubsArr0jSnzZNNincsQOoXVv2Bjh50pSwiIjIJK6V+DUN+Owzqef/4gu5HM6Il5e8WUi2fz/w0kvGxWiQbNmAAQOkAmDo0LQVAP36yXshIiJyfq6V+AGgcmXgnXeAEiWA27cte61SQM+e+K2kNAI6deWUAQEaK3du4KOPZBuD116TtYuffip7AIwfD9y6ZXaERERkJNdL/AAwerSU9TVoYNnrNA34/nuMDr6EWO8u+GLfF5l+6e7hYRYGaaxixYCFC4EDB4BmzaQC4P33pQJgwQJWABAROSvXTPw+PvInmSXL3IsVw7ftv0O3SqMwIWxCpl8WFXvdggBtp0oV6VUUHi4VAOfPAz17Ak89BaxbxwoAIiJn45qJP9n163KDu2tXi16WK1subN5fBh5uMuV/N+kuNpzY8MTXPLw7n7155hlZ8rBihVQAHDkCtGqVUhlARETOwbUT/5Ur0tlm2TIpetdBKYWu/9cVzVc0x5y9c6wcoG25uQEdOqStANi+XTb+ad9eFgYSEZFjc+3EX7Kk3NgGpKPf3bsWH0LTNNQJqAO/bH6oUbSGlQM0R+oKgCFDpAJg1SqpAOjfnxUARESOzLUTPyDNfMqXB44dS2nwkwkT2gY/eNyvVj+c7HcSoUUev1lS6vGOInduYOJEqQDo1k0W/M2cKRUAEyawAoCIyBHZbFteo2S4LW9mhIcDzz4rl7ZHjshMQBb8EvMLIi9EoneN3lmLy85ERkoPgA3/LWcoUgT48ENZIuHubm5sRESuwmG25bVrYWFyczshQeayMyFw6Pp0n/87/m88t/w59PmxDzb/uTnD8Y4kuQJg82agenWpAOjRQyoA1q9nBQARkSNg4k/28ceyLW/27I/05bdEoZyFMCFsArpX7Y6GgQ2tF58dCQuTLQy+/BIIDJSWCC1bSmXAQ3sZERGRnWHiT1a4sEzzf/21TPlnQb9a/TC/9fwH5X7OyM0N6NgRiI4GPvlE9kDatg2oWVP2BmAFABGRfWLiT61o0ZTHGcxbh1Uo8MTPa5oGQGr831r3FmqWyp7l8OxRtmzAwIGS6N97Tz7++mupABgwALh0yewIiYgoNSb+9OzZA9SpIzMAj7GgW+ZK9yb9Mgmf7/scXvkXWis6u5QnDzBpklQAdO0qFQAzZkgFwEcfsQKAiMheMPGnZ+FC2bC+d+/HXvn3WJy5m9mD/jcIYxuOxfU/38aOHdYM0j4VLw4sXgz88QfQtCnw77/A8OFAuXLybU1KMjtCIiLXxsSfngkTAH9/aVv35ZfpDgmPvpipQ/l4+qBu4ihEXbqEDh2Ay5etGaj9euop4KefgE2bgGrVgLg4qQCoWlUqA1gBQERkDib+9OTNC0yZIo8HDQKuXcvS4ZI3AezVC/Dzy2JsDubZZ4GICGD5ctkJ+dAhoEULqQDIavsFIiKyHBP/43TpAtSvD1y8CIwYkaVDefy3uH/MmJTHrsTNDejUSSoAPv44pQKgRg1pn/Dnn2ZHSETkOti570kOHZJ56qQkWfAXqrtRUho3bwJ//QWUKWOVwzmcq1dlwd/MmcCdO4CnpyyneP99IH9+s6MjIrJv7NxnpKAgqVXLlQs4ezbNp1bsjrHoUMnjz56VK91mzYAbN6wWqUPJkweYPFkqALp0SVsBMHEicPu22RESETkvJv6MjB4tG/i8+GKap4evibLoMMnjCxYEvLzkKtfVd7krXhxYsiRtBcCwYVIBsGgRKwCIiIzAxJ+RHDkkW1uJtzfwww+ysK1UKasd1qElVwBs3Cir/mNjge7d5fGGDawAICKyJib+zLp3T1am9c76jnvFiwM+PmkPTUDjxsC+fWkrAJo3l8qAffvMjo6IyDkw8WdWXJysPpszB9i2DfO7WLauIr3xiYlyJ6FOHVnkRmkrAKZOlfUAW7bIusqOHYHTp82OkIjIsTHxZ1ZgYEpZX+/eCC5gWe/94IBHC/hv35b+QPv3A+HhVojRiXh7SwuFU6eAd9+VPQBWrgTKl5f1lq7SCImIyNqY+C3x7rtAuXK45+2FWlN3WvTSWhMezey+vrKhTXi4TGnTo5IrAI4dAzp3llmS6dOlAmDSJFYAEBFZionfEtmy4cb671CtZyIA4Oy1sxm8IGMhIUCjRlk+jNMrUQJYulRmR5o0Aa5fB4YOlQqAxYtZAUBElFlM/BbyLVMZQQWCAAADfx5o1WMfPixtfRMTrXpYp1K1KvDzz/LnqaekAuC116TP0k8/sQKAiCgjTPw6fNzkYyR4bsaa6DX4+eTPmXpNh5rFnvj5xESgTRtg/nxg1ixrROncmjSRq/9ly6RKIipKmiI1bizPExFR+pj4dSiaqyjeea4wAKDfT/1wN+luhq/56IUqT/y8hwcwd67Ur/fqZZUwnZ6bG/Dqq3L/f8oUIHduWS8REiKVAawAICJ6FBO/Ttv31Ua5fOVw/PJxzNw9M8PxLT/NeDHgM88ACxZIzyDKPG9vYPBgqQAYPFg6I65YAVSoIJUBrAAgIkrBxK/T4fM3ML3pdADAB9s/wMWbF584/lDcvxYdPylJSv14zzrzkndTPnZMZgLu3gU++UQqACZPZgUAERHAxJ8lzco2w2tVX8O0ptOQL3s+qx67XTtJXjMznkyghwQGyr3//ful69/168CQIdIDYMkSVgAQkWtj4tepgG82AMDCNgvRo3oPuLu5Z2p8ZnXuDBQqBFSurDtEl1etGrBpU0oFwLlzQLduQPXqrAAgItelKQf/7RcaGqoiIiLMDgMAcPHmRfj7+EPTNKscLz4eyJnTKodyecm3Tt5/X94AAEBYmNwCqF7d3NiIiCyhadp9NoqGAAAgAElEQVQ+pZRlfeNT4RW/TtM2HU/z8dTfpiJweiDWn1ifqfGZkTrpx8VZ/HJKxd0d6NIFOH5ckr2fX0oFwKuvAmfOmB0hEZFtMPHrNCP8RJqPPdw8cDvxNt7b9B4S7z/agefh8ZZYsgQoW1buW1PWeHtL5+U//5QV/15eMhNQvrx8fOWK2RESERmLid9KetfojVJ5SuHopaNYsH+BVY+dlCQr0nftsuphXVrevLL7X3oVAFOmAAkJZkdIRGQMJn4r8XL3wkdhHwEAxmwfg/i78VY79muvAdu3A7NnW+2Q9J/kCoB9++Se/7VrwHvvyR4AS5eyAoCInA8Tv05r+9Z75Ll2ldqhRpEa+Dv+b0z7fVqG4zNL04Cnn0752MHXY9ql6tWlAuCnn4AqVWQBYNeusgZg40azoyMish4mfivSNA2TG08GAEz5bQou3bpk9XOcPy/96H/4weqHdnmaBjRtKvX/S5YAxYoBBw/Kc40bA3/8YXaERERZx8SvU6tZv6T7fMPAhniuzHOoFVAL/975N8PxlvrmG1mNPnQocP++VQ5JD0muADh2DJg0SSoANm+WWYHOnYGzWd+NmYjINEz8Bvim3TfY1HkTSuUpZfVj9+0LjBoFbNkim9SQcbJnl/v9p04B77wjFQDLl8v9/8GDWQFARI6JqcMAObyM22XHzQ0YO1a6+pFt5MsHfPyxzAB06iQVAB9/LBUAU6eyAoCIHAsTv079w8pmOOaPv/5A65WtceLyiUyNt5RSwKJFwI4dVj80pSMwUK74IyJkJ8Vr16QnQPnyUhnAWy9E5AiY+HUa2LhchmNm752NtcfXYsz2MZkab6nVq4Hu3YGOHYEbN6x+eHqMkBC5579hAxAcDMTEyJqAkBCpDCAismdM/DrVHL85wzEjnx4JTzdPrIxaieof/mT1GNq2ldXm48ezp7+taRrw3HOy0n/xYiAgADhwAGjSRP4cOGB2hERE6WPi1+nijTsZjimRuwR6Ve8FBYUrN63fCcbTU3ae69pVEhHZnru7fP+PHwcmTpQKgE2bpAKgSxdWABCR/WHiN9jw+sPh7+MPADBiJ8TUCf/vv4GjR61+CsqE7NmBIUOkAmDgQMDDQ+77ly8v6wCuXjU7QiIiwcSvU1DRXJkaVzRXUUS9dg753XNh/XrjLssjI2XP+eefl+18yRz58knP/2PHgA4dgDt3ZOV/6dJSCcAKACIyGxO/Tuverp/psWu+yYZ9E+pjzBjj2u2WLQsUKCD3mm/dMuYclHklSwIrVkgFQKNGcsU/eLDMACxfzgoAIjIPE79Ow76LzPTYrl2BIm0isW8fsG2bMfFkzy4rzTdulDcAZB9CQqTT4o8/AkFBUgHQuTMQGir/XkREtsbEr9PKPecyPTZ7dsCzgoyfMsWoiICCBWWxWTKW+NkHTQOaNZOV/osWAUWLSjVA48ayDwArAIjIlpj4bSh7dqn9PnTI2PPEx8ssQ8OGco+Z7IO7O9CtG3DiBPDRR0CuXDJDwwoAIrIlJn4b6t5d/p461djzJCVJN7+jR2WnObIv2bPLJkunTgEDBqStAHjvPVYAEJGxNCNKzGwpNDRURURE2Py8F/5NQMFc3haNv3nJG2XLSr/9M2dkytco+/cD3t5ApUrGnYOs488/gfffB1aulI/z5AFGjAD69JF/QyKi1DRN26eUCtX7el7x6xQVe93i8aVKAWPGAN9+CxQubExcyapXZ9J3FKVKSQXA3r1pKwAqVAC+/JIVAERkXUz8OvVcatksQ/L4kSOB1q1tu6Xupk3AK6/ILQCyX6GhaSsAzp4FXn2VFQBEZF1M/CayRTOX27dlod/XXwNLlxp/Psqa1BUACxemrQB47jng4EGzIyQiR8fEb4IbN6SWu0IF2dvdSNmzS8IfO1ZWjpNjcHcHXntN9gBIrgD4+WegWjV5IxcTY3aEROSomPh1mtA2WPf4nDnlKu7sWbm3a7RnnwVGjUpb40+OwccnpQKgf3+pAFi6FChXTvYGuHbN7AiJyNEw8evUsVZx3eM1TTZuAaS0z5aLt27eBGbNMq51MBkjf35g+nQgOlrWa9y5A0yeLHsAfPIJ+zUQUeYx8esUOHR9lsZ36CD3bw8flqY+tqCUXP2//Tbw2We2OSdZV6lSUva3Z480aLpyBRg0SG4brVjBCgAiyhgTv0m8vGTqFjC2jW9qmga88w5QuTLQoIFtzknGqFED2LIFWL9e/j3PnAE6dZLnw8PNjo6I7BkTv4lef10WbW3fLjXcttCunawvCAqyzfnIOJoGNG8uK/0XLACKFJHGTc8+K5UBkZnfR4qIXAgTv05hFSzbAi+98X5+wBtvyC/wnTutFVnGPD1THh85YrvzkjHc3aUd9IkTwIQJgK8v8NNPQNWqUhlwLvP7SRGRC2DLXpNdvAhcvw6ULWv7c48bJ6v9ly2TaWJyDv/8I/+2c+YA9+5J29/+/aU6IHdus6Mjoqxiy16T9Fhs2dz848YXKGBO0k8+t6YBsbHmnJ+M4e8PzJghmzS1by+NoiZNkgqAadNYAUDk6pj4dQqPvmjV8UpJW9ZLl7ISlWV69ZIOcUOG2O6cZDulSwNffQXs3i2LOa9ckcWdFSpIZQArAIhcExO/nRgwQNqyzp5tu3NqGhCcqg9RYqLtzk22U7MmsHUrsHatbNx05gzQsaM8v2WL2dERka0x8duJtm3l71mzgFu3bH/+qCjgqadkgxhyPpoGtGwpFQDz50sFwL59QFiYVAZERZkdIRHZChO/TmcmtrDq+AYNZBe2S5eAxYuzEJhOGzbICv9Jk9jVz5l5eAA9ekgFwPjxUgGwYYO86WMFAJFrYOLXacVuy3ZJyWi8pgHvvSePP/nE9lvoDh4sC79+/FFiIefm4wMMHy57APTrJyWBixfLHgDDhnEPACJnxsSv0/A1ls2NZmb8Cy9IS9ZTp4A1a/RGpo+bm6wzyJHDtuclc6WuAHj5ZakAmDhRFgZOn84KACJnxMRvR9zdZdU1IBuwmDXlnpgIjBkD/PqrOecn2ytTBvj6a6kAePppqQAYOBCoWJEVAETOhonfzrz2mpRbNW9u3ir7uXOBsWOBV18F7t41JwYyR82awLZtKRUAp0+nVABs3Wp2dERkDUz8Os3vYlnTpMyO9/GRRXZjxqRtrWtLvXoBzz8v/d+9vMyJgcyTugJg3jygcGGpAHjmGaBFC1YAEDk6Jn6dggP8DBtv9uI6T09ZY/DMM+bGQeby8AB69pQKgHHjpALgxx+lAqB7d3Z8JHJUTPw61Zpg2d6nlo6Pj5dV9iNGWPQyQxw+DBw6ZHYUZJYcOeTn8NQp4O23ZS3KokXSanr4cNlrgogcBxO/nbpwQUrspkwB4uLMi2P7dukv0K4dcPOmeXGQ+fz9gZkzpQKgXTupAPjoI6kAmDGD60GIHAUTv50qXVrK++7dk1+2ZqlRAyhZEqhTx7wYyL6UKQOsWgXs2gXUrw9cviyloBUrSmUAKwCI7BsTv04dahYzdDyQ0tDn88+Bf/+1+OVW4eMD/P47sHAha/wprVq1ZEbohx8k6f/5J/DKK/L8tm1mR0dEj8PEr9NHL1QxdDwgV9sNGkjSnzvX4pdbjV+qdYlJSbLfOxEgC1FbtQIiI+VntHBhICICaNRIKgO4NoTI/jDx69Ty052Gjk/27rvy9/Tp5t9D/ftv2dSlRQvzYyH74uEhZaAnTgAffgjkzAmsXy8VAD16mLtOhYjSYuLX6VCcZXPvlo5P1qyZNFKJi7N9G9+HZcsmW7rGxMgKb6KH5cgBvP++/Hz06SOtoBculAqAESNYAUBkD5j47Zybm6zsX70aeOklc2PJk0fu5x48KPd0iR6nQAHZYvrIEfm5vX0bmDBBFq3OnMkZIyIzMfHrVMA3m6HjU2veXH55urvrPoTVVKkCFCyY8jG38KUnKVtW3rT+/jtQr55UAPTvL28cV63izw+RGZj4ddoz4llDxz/O5ctWOUyWKSVTuM8/z/Ityljt2sCOHcD338teFH/+CbRvn1IZQES2w8Sv07RNxw0dn56BA4EiRaRvutmuXQOGDpWp/3XrzI6GHIGmAa1bS6//uXOBQoWAvXuBhg2lMuDwYbMjJHINTPw6zQg/Yej49Hh4yL3RKVOyfKgsy5MHWLYMWLJEfpkTZVZyBcDJk8AHH0gFwLp1chupZ09WABAZjYnfgfTvL780V6+WqVKzNW0KdOlidhTkqHLkAEaOTFsBsGABKwCIjMbE70ACAoBOneSe+rRpZkeT1l9/AePHc7EWWS65AuDwYeDFF1MqAMqUAT79lBUARNbGxK/T2r71DB3/OIMHy98LF9rPQr/ERODpp6V+e8ECs6MhR1WuHPDNN8Bvv0kFwKVLQL9+0seCFQBE1sPE72CCgqSpz61bwGefmR2N8PCQbm3PPittWomyok4dqQD4v/8DypeXWwHt20tlACsAiLKOiV+nVrN+MXT8kyS38T1zxmqHzLJXXgE2bpSV2kRZpWlAmzbS6/+LL+Tnas8eVgAQWQMTvwNq2FB6otvbtLqmyd9KAb/+am4s5Bw8PIDXX5ef97Fj01YA9OoFnD9vdoREjoeJ3wFpmix8slevvy73aL/+2uxIyFnkzAmMGiUlgL17y/+B+fPl/8H775u3bTWRI2Li16l/WFlDx2eGUnLP096urqtXB3x8ZNEfkTUVLAjMni1T/S+8IBUA48fLHgCzZrECgCgzNOXgS2VDQ0NVRESE2WGYYuVKoGNHaXv6++8pU+1mUwqIjQWKFTM7EnJ2v/0GvPdeypvfMmWkFPCll+zn/wORtWmatk8pFar39bzi16nm+M2Gjs+M1q2BfPmA3buBX6y3djDLNC1t0r91y7xYyLn973/Azp2yZXX58nIr4OWXUyoDiOhRTPw6Xbxxx9DxmZEjh3Q8A+yjjW96Nm6UadiffzY7EnJWmiabRR06BHz+udwO2L0baNBAKgOOHjU7QiL7wsTv4Pr2Bby9gbVr7fMX3N69wN9/A4sXmx0JOTsPD+CNN+Sqf8wYeWP8ww/S++L111kBQJSMiV+noKK5DB2fWf7+QLdu8njqVENOkSVDh8pGPsuXmx0JuYqcOYHRo+UNwFtvyYzAvHmyB8DIkawAIOLiPidw8qS0O/X0lKY+hQubHRGR/Th2DBg2TNYBAPJmefRomQXw9DQ3NiI9uLjPJMO+izR0vCXKlAF69AAGDQK8vAw7TZbFxwPdu0sFApGtlC8PfPedLID93/+Af/6RW2SVK8veAA5+7UNkMSZ+nVbuOWfoeEvNmydlTPnyGXqaLPn0U2DRItlz/f59s6MhV1O3riT/NWtkhuzECaBdu5TKACJXwcRPNjNoENCli1xlufEnj0yQugJgzhypANi1S3aXfP55+1wgS2Rt/PXrRO7dk65mDRvKY3vj5SUL/SpWNDsScnWensCbb6atAPj+e6kAeOMN4K+/zI6QyDhM/DrtHh5m6Hg93N0l8W/f7hh98jdvlisvIrOkrgB4802ZEZg7V9bNjBoF3LhhdoRE1sfEr1NU7HVDx+vh5gYMHiyPJ0+270VLa9YATZrIdr7s7EdmK1RIpv4PHwbatpWfyQ8/lOZTs2fb5wwakV5M/Dr1XGpZCaGl4/Xq1EnK+aKipGuevWrSBKhUSdqrZstmdjREInUFQJ06aSsAvv3Wvt9ME2UWE7+TyZYN6N9fHttrG19A7qnu2yfTqe7uZkdDlFbdurLxz7ffplQAvPSSVADY074YRHow8TuhN96Qe5fh4cD+/WZH83ipr/Rv3mRLVbIvmiZb/x46BHz2GVCggFQA1K8vFQDR0WZHSKQPE79OE9oGGzo+K3Lnlq5kALBggc1Oq9vx40BIiPyS5b1UsjeentL69+RJWQjo45NSAfDmm6wAIMdj08SvadpzmqYd0zTtpKZpQ9P5fHFN07ZqmvaHpmmRmqY1t2V8luhYq7ih47Nq4EBgxQpgxgybnlaX/PllMVV8PHDxotnREKXP11dK/06elFk1APjiC6kAGD2aFQDkOGyW+DVNcwcwG0AzAJUAdNA0rdJDw94HsEopVQ3AKwA+s1V8lgocut7Q8VkVEAB06CA7ltm7vHll2949e4CiRc2OhujJCheW7X8PHZIp/1u3gA8+kDcAc+Zw1orsny2v+GsCOKmU+lMpdRfAVwDaPDRGAUjexs4PAO/6WsHFi8B146sJs6RiRZlCTZaUZF4sRJlRoYKUpe7cCdSuLf/PeveWWwDffccKALJftkz8RQGkblgf+99zqY0B8KqmabEAfgTwdnoH0jTtdU3TIjRNi/jnn3+MiNVpfPYZUKKE9Ml3BImJsnVqixbs50+OoV494LffpBV12bKyZuXFF1MqA4jsjS0Tv5bOcw+/J+4AYLFSKgBAcwDLNE17JEal1FylVKhSKtTf39+AUDMWVqGAoeOtpXx5ICFBEn9CgikhWOTSJZlG3biRvzTJcWiaJPvDh6Xhj7+/7EJZr540BGIFANkTWyb+WADFUn0cgEen8nsAWAUASqnfAXgDyG+T6Cy0oFsNQ8dbyzPPANWryzTk0qWmhGCRQoWAL78EtmyRsikiR+LpKdP9p07JzJWPD/B//yfT/2+9Bfz9t9kREtk28e8FUFbTtJKapnlBFu/98NCYGABhAKBpWkVI4rfLufwei/caOt5aNA149115/PHHjnHvvEkT2WiIyFH5+sqCv5MnpbRWKZnJKlNGKgPi482OkFyZzRK/UioRQF8APwM4Clm9f1jTtA80TWv937BBAHppmnYQwEoA3ZSyzyUy4dGW1Z1ZOt6aXnoJCAyUe48/PPxWy85FRQFDh3KhFDmmwoWl5O/QIaBNG2lUNXasvAH4/HNWAJA5bFrHr5T6USlVTilVWik1/r/nRimlfvjv8RGlVF2l1FNKqapKKTvuNu84PDykrh+w7za+D7t1CwgLAyZNAlauNDsaIv0qVpQp/+QKgAsXZOo/KEgqA/jGlmyJnftcRI8eUi+fK5fjTDP6+ADTp0vsbR4u/CRyQKkrAMqUkVm4F15IeZ7IFjQ7nUnPtNDQUBURYZud7xzdpUvSJY+IzHfvHjB3rkz9J1clt20LfPSRVOMQPY6mafuUUqF6X88rfp1W7I4xdLwRHD3pJyYCa9eaHQWRdXh6An36yALA5AqANWtkC+DeveV2AJERmPh1Gr4mytDxRvrtN1lY5EiUkqY+rVvLNCmRs8iVSyoATpwAevWSn/U5c4DSpWU2wFFuzZHjYOJ3MTExcj+xf3/HqinWNKBVK6nzz5fP7GiIrK9IEZn6j4qSN7g3b0rpHysAyNqY+F1M8eKyscjdu47TxjdZnz7AkSNAo0ZmR0JknEqVZNvf7duBmjVTKgCCg6UywMGXZZEdYOLXaX4Xy9ZVWDreSMkNfT77zLG2EtU0IE+elI8vXzYvFiKjPf00sGsXsHq1XPUfOyaL/1gBQFnFxK9TcICfoeONVKeObCBy7RqwYIHZ0eizYIFsPrR5s9mREBlH06QB1+HDMkPn7y9Jv25d2Rvg+HGzIyRHxMSvU60J4YaON9p778nf06Y55r3DuDi5B/rzz2ZHQmQ8Ly+gb1+pAHj/fSB7dtn6t1IlVgCQ5Zj4XVTLlrKfeEwMsGqV2dFYbsQI4McfHasTIVFW5coFfPihvAHo2TOlAqBMGakMYAUAZQYTv4tyc5Mrh8GDHXNDHHd3oFkzs6MgMkeRIsC8eVIB0KqVJPzRo4GyZWVvgMREsyMke8bEr1OHmsUyHpSF8bbQqZNcMRctanYkWRMXBzRtCuzZY3YkRLZVqZJsvLVtG1CjhpTovvmmVAB8/z0rACh9TPw6ffRCFUPH25oj/4KYPRvYuBEYMMCxvw4ivRo0AHbvltt2pUsD0dFStptcGUCUGhO/Ti0/3WnoeFtatkx2D/vjD7Mj0Wf0aKBfP2l3qmlmR0NkDk0D2rWTXhczZ0qL7l9+kSqel15iBQClYOLX6VDcv4aOt6X9+6VG2FEXymXLBsyYARQsaHYkRObz8gLefhs4dUoWwWbPDnz7rewB0KcPKwCIiZ8ADBwoi+VWrQLOnjU7mqxRCli4UK56iFxZrlzAuHGyB0CPHsD9+9K0q0wZqQy4edPsCMksTPw6FfDNZuh4WypeHHjlFSApSer6HdncufJLrn17aUtM5OqKFgXmzwciI6WMNz4eGDVK3gDMncsKAFekKQdfDRUaGqoiIiLMDsPhHTwIVK0K5MgBnDuXtjWuI4mPl4VO/fsDXbqYHQ2R/dm+Xdp2790rH1eoAEyaJGWBXCPjGDRN26eU0t0Hnlf8Ok3bZNlKGUvH29pTTwGNG8v035w5ZkejX86c8guNSZ8ofckVAF9/DZQqJRUAbdqkPE/Oj4lfpxnhJwwdb4bkNr7ffefYZXFuqX6q//oLiI01LxYie6RpwMsvA0ePplQA7NwJ1K4tlQEn7P/XFWUBEz89EBYmq39/+805pvz27JGZjPbteR+TKD3JFQAnTwLDh0sFwDffSGOgt98GLl40O0IyAhM/PaBpwAsvyC8DZ1C6tHwt2bM71vbDRLbm5weMH5+2AmDWLPk/NG4cKwCcDRO/Tmv71jN0vNmuXJF7f44sXz5pYLJxo+MuViSypeQKgIMHgRYtZLHsyJGyB8C8eZw5cxZM/PSIbduAYsXknb+jCwxMueevFJCQYGo4RA4hKAhYtw7YuhUIDZW1Mq+/DlSpInsDOPIaIGLi163VrF8MHW+m0FDphvfbb/LHGdy4ISv9X3hBpjGJKGMNG8pK/6++AkqWlMWArABwfEz89IicOYG33pLHjtrG92HXrwM//ig1zOzqR5R5bm6yQDY6Wlpj58uXUgHw8suyMJAcCxM/pevtt2Vh3PffSx9/RxcQIC2J9+2TaUwisoyXl2yGdeoUMGwY4O0NrF4tG3yxAsCxMPHr1D+srKHjzVaokEyNKwV8/LHZ0VhHWJh0KSMi/fz8gAkTpAKge3dp9T1rlrQAHj+eFQCOgC176bGOHZN3815esnmPM+1+t3GjLF6aMcM5ehYQmSUqChg6VG6lAUDhwsAHHwDdugEeHqaG5rTYstckNcdvNnS8PShfHmjdGvjf/4CrV82OxnquXJH9yT/9VJI/EekXHAysXw9s2QKEhEgFQK9e0jxr7VpWANgjJn6dLt64Y+h4e/HVV/If2pmmyPPmBWbPlsYkzZubHQ2Rc2jUSLplrlwpFQBHjsiFQ8OG8jzZDyZ+eiJvb7MjMEbnzsCIEYC7u9mREDkPNzfZ4vvoUdniO29eYMcOoFYtqQw4dcrsCAlg4tctqGguQ8fbm4gIoHdv4N49syOxvvh44MsvzY6CyHlkywYMGCCJfuhQuYBYtUpmDvv1A/75x+wIXRsX91GG7t+XRX7Hj0uC7NjR7IisJzERqFYNOHRIdiVs29bsiIicT2wsMGoUsHix3PP39ZU3BAMGAD4+ZkfneLi4zyTDvos0dLw9cXMDBg2Sx1OmONdiHQ8PaU0cFCSLGYnI+gICgIULZQ+A5s2lk+aIEbIHwIIFUhJItsPEr9PKPecMHW9vunQBChQADhwAwsPNjsa6+vcH9u6VrUiJyDjJFQDh4VIBcP480LOnVACsX+9cFxX2jImfMsXbW+7NAc7TxjeZpqVdxHjmjGmhELmEZ56Rlf4rVkgFwOHDQMuWUhmwd6/Z0Tk/Jn7KtLfeAnLkkOY3Bw6YHY0xRo6UDmRbt5odCZFzc3MDOnRIWwGwfTtQs6ZUBrACwDhM/DrtHh5m6Hh7lDdvyla9ztLG92GaJtONUVFmR0LkGlJXAAwZIrNvX38tC4r79wcuXTI7QufDxK9TVOx1Q8fbq4EDZcr/ww/NjsQYo0bJdqPJtzWIyDZy5wYmTpTqoW7dpOJm5kygdGngo4+AW7fMjtB5MPHr1HOpZSWElo63V4GB0t8+MNDsSIzh4QGEpiqSuX/fvFiIXFGxYsCiRXI7sVkz4N9/geHDgXLlpDKAFQBZx8RPut2/D9y9a3YUxjl4EKhaVZoXEZFtVakiG/9s3gxUrw7ExcmtxqpV5XlWAOjHxE+6bNok/zGd9V4/IFcdUVHOe1uDyBGEhclK/y+/lJnGQ4eAFi2kMoAVAPow8es0oW2woePtnVJSgjNzJnDHMfcfytDEibK96MqVZkdC5Nrc3KRjaHQ08MknQJ48wLZtrADQiy17SRelpNXtwYPA/Pkpq/2JiIx29aq8MZ8xQy48PD1lL5H33wfy5zc7OuOxZa9JAoeuN3S8vdM0YPBgeTxlivMvgktMBMaOlSsOIjJXnjzApElSAdC1q/z/nDGDFQCZxcRPurVvLytwjx0D1q0zOxpjTZoEjBkDdOrk/G9yiBxF8eKy8c8ffwBNm6atAFi0iBUAj8PET7p5ekpdP+B8bXwf1q8f0KABMHWq3G8kIvvx1FPATz/JouNq1aQCoHt3VgA8Dn+F6RRWoYCh4x1Fz56An59MuV24YHY0xvH1lcVEjRqZHQkRPc6zz0r57fLlQIkSKRUAYWEsy02Ni/soy/bulV23Um904+wOHZI3PMWKmR0JEaUnIQH47DNg3DhZDAhIBcD48UCpUubGllVc3GeSHostKyC1dLwjqVHDtZL+hg3yNXfsKIuKiMj+eHsD77wjpX7vvSd7Anz1FVChgtyivHzZ7AjNw8SvU3j0RUPHO6Lr14GffzY7CuOFhsqq4vLlgXv3zI6GiJ4kdQVAly7yZn36dKkAmDgRuH3b7Ahtj4mfrOLKFbmn1qYNcNHJ3+P4+6f0L8ie3exoiCgzihcHlixJqQC4fh0YNkwqABYvdq0KACZ+soq8eYGnn5ZmGrNmmR2N8fz9Ux4nJUkZERHZv+QKgI0bZdV/bCzw2mtSDbBhg2tUAHBxH1nNzp2S/PPmBWJigBw5zI7IeHFxcq/f1xdYu1YaGxGRY7h/X0DCR6kAACAASURBVFpyjxgBnD0rzz3zDDB5MhASYm5sT8LFfSZZsTvG0PGOqF49oHZtmfZfuNDsaGwjKUk28tm3Dzh3zuxoiMgSbm7SlCs6Wnp05MkDbNki63g6dQJOnzY7QmMw8es0fE2UoeMdkaYB774rjz/5xDVWvBcvDnz/vdzzL17c7GiISA9vb2DQIKkAePddqQBYsUIqAN55x/kqAJj4yaratAHKlAHOnAG++cbsaGyjfn2ggHP2ZyJyKXnyyDT/sWNA585StTNtmlQATJrkPBUATPxkVe7usnlPvXpA4cJmR2NbSgHz5gFvvGF2JESUFSVKAEuXAvv3A02aSAXA0KFSAbBkieNXAHBxn06bj1zAs5UKGjbekd2/75r97GNjpbb/1i1Z6FivntkREZE1bNwoTYAOHpSPq1SRGYCmTc1Z0MvFfSYJDvAzdLwjc8WkDwABAcAXX0ifcCZ9IufRpIlc/S9bJmt5IiOBZs2Axo3leUfjor+is67WhHBDxzuDyEi5TxYZaXYktvPqq7IamIici5ub/P8+dkx2I82dGwgPl7I/R6sAYOInw8ybJ1e/U6eaHYk5zp8H5swxOwoisiZvb1nHdOqU/O3llVIBMGiQY1QAMPGTYd55R94lr1zpejXut27JRj69ewPr1pkdDRFZW968cuV/7JjMBNy9K2XMpUtLZYA9VwAw8evUoaZl+7FaOt4ZlCwJtGsn9fwzZpgdjW35+MgOYE2ayBsAInJOgYFy73//fuDZZ6UCYMgQWehrrxUAXNVPhtq3T7pg5cwpV/25c5sdke3cvy9/u+piRyJXlF4FwOTJchFgrQoAruo3SctPdxo63lmEhEjv6/h4WfHuStzcUpK+UsCBA+bGQ0TGS64AWLoUKFZMFjc/95w8/8cfZkcnmPh1OhRn2XZslo53JsltfGfNss9pL6MpJfuAh4QA27ebHQ0RGc3NTSqajh9PqQDYvBmoXl3WA5w5Y3J85p6eXEHTpsCYMbL5hbu72dHYnqZJ7W/27MA//5gdDRHZSuoKgEGDpALgyy/l/v/gwbKhmRmY+HUq4JvN0PHORNOA0aOBsmXNjsQ8Y8fKlN9LL5kdCRHZWt68UtacugLg44+lAmDKFCAhwbbxcHEf2ZRSwNWr8h/Bld29K+/+icj17N8vCwDD/+vrVrw4MG6cNALKzGJgLu4zybRNxw0d74yOHpV7XG3bmh2JuX76Sd7p28tCHyKyrerVgU2b5HdBlSpATIysA6peXaoCjMbEr9OM8BOGjndGAQHS1nLHDmD3brOjMc8PP8iGPuzqR+S6NE3WP+3fL/X+xYpJCWDTpsZXADDxk834+gJvvimPp0wxNxYzffyxJH0mfiJyd5er/WPHZMc/Pz+ZDQgJkcqAs2etf04mfrKpfv0AT0/gu++AkyfNjsYc2bPLGyBXrHAgovRlzy73/U+dknbnnp6y10m5clISffWq9c7FxK/T2r6W7btq6XhnVaSIrGpVSvpau7obN4BevaTel4goXz6ZFTx2TBb73b0rFQGlSsnf1qgAYOInmxs8WP5etAi4eNHcWMw2Zgwwfz7Qo4e8GSIiAmQPgOXLgYgI6X567Zpc+Zcvn/VjM/Hr1GrWL4aOd2aVKgEtWwI5cgCHD5sdjblGjQLatAHmzrVeH28ich4hIdL1b8MGIDhYKgCyiomfTDFnjvwAN2pkdiTm8vMD/u//gIoVzY6EiOyVpkm//z/+ABYvzvrxmPjJFAEBsnUtpbV5MxAXZ3YURGSP3N2Brl2zfhwmfp36h1nWf9bS8a7ixg3ZtS8x0exIzLd0KdC4sSzoccXNjIjINjzMDsBRDWxcztDxriIsDNi7F8iTB3j5ZbOjMddzz8lMSFiY2ZEQkTPjFb9ONcdvNnS8q+jeXf6eMoWr2gsUAKKjgZEjWeNPRMZh4tfp4o07ho53FV27Av7+UrLCveql0iFZfLx1m3YQEQFM/GSy7NmBvn3l8eTJ5sZiTw4fljKebt04E0JE1sXEr1NQ0VyGjnclffrICv8NG4BDh8yOxj7kyAFcuCDtOy9fNjsaInImTPw6rXu7vqHjXUm+fCn3+qdONTcWexEYKBt17N0L5M9vdjRE5EyY+HUa9l2koeNdzTvvAHXqSBc7EjVqyK2QZJzyJyJrYOLXaeWec4aOdzUlSwK//Qa0bWt2JPbn3j1gxAigZ0+zIyEiZ8DET2TnTp8Gpk2TVp1cA0FEWcXET3bl5EnZqW7GDLMjsR/lygELFgBbtgBBQWZHQ0SOTlMOfuMwNDRURURE2Py8F/5NQMFc3oaNd1UbNgDNmwNFisiVrpeX2REREdkXTdP2KaVC9b6eV/w6RcVeN3S8q3ruObmqPX8eWLHC7GjsU2Qk8MknZkdBRI6KiV+nnkstm2WwdLyr0jTg3Xfl8dSpXMn+sCtXgLp1gUGDZCc/IiJLMfGT3XnlFaBoUelet2GD2dHYl7x5pZd/r17A//5ndjRE5IiY+MnueHkBAwbI4ylTzI3FHr37LjB3rnQ7JCKyFBO/ThPaBhs63tW9/jqQKxewbRtw/LjZ0dgXTUt5nJjIzY2IyDJM/Dp1rFXc0PGuLlcuKWE7ckTK2ehR9+4BYWHAM88Av/xidjRE5CiY+HUKHLre0PEEvPQSULGi2VHYL09PaXNcqBAXQRJR5jHxk91TSnapo0d9+CFw8CBQn3tAEVEmMfGTXUtIkKva4GDg0iWzo7E/np5pd+/791/zYiEix8DEr1NYhQKGjifh7S2J7fZtYPZss6Oxb198AZQoITMARESPw8Sv04JuNQwdTymSG/rMmgXcumVuLPZs/37g2jXg//7P7EiIyJ4x8evUY/FeQ8dTiqeflr3pL12SHeoofdOmAWvWAKNHmx0JEdkzJn6dwqMvGjqeUqRu4/vJJ0BSkrnx2CsfH+D5582OgojsHRM/OYQXXgBKlZLV/WvWmB2N/YuNBVq1YjUEET2KiZ8cgru7bEyTOzdw9arZ0di/MWOAdetSWh8TESXTlIN3/ggNDVUREdz5zhUkJEi3Ol9fsyOxf9euAYMHAxMmAAVYUELkVDRN26eUCtX7el7x67Rid4yh4+lR3t5M+pmVOzcwfz6TPhE9iolfp+FrogwdT49365bU9B89anYkjkEpYNEi4Px5syMhInvAxE8OZ+RIoG9fbtmbWZMnA927A507A/fvmx0NEZmNiZ8cTu/egJsbsHw5EBdndjT2r2tXoHRp4LXX5PtGRK6NvwZ0mt/FsnUVlo6nxytdWsr77t0DZs40Oxr7V6iQ3BZ59VWzIyEie8DEr1NwgJ+h4+nJ3ntP/v78c25MkxmenimP4+JYEknkypj4dao1IdzQ8fRkNWoADRpI0p83z+xoHMeOHUDVqkDPnrLoj4hcDxM/OazkNr7TpgF375obi6MICJDv1Y0b3PCIyFV5mB0AkV7NmgHt2wNt2nDRWmaVKgXs2gWUL8/vGZGrYuLXqUPNYoaOp4y5uQFffWV2FI6nYsWUx0rJpkce/E1A5DJs+p5f07TnNE07pmnaSU3Thj5mzMuaph3RNO2wpmkrbBmfJT56oYqh48lyvGdtmX//BTp1At56y+xIiMiWbJb4NU1zBzAbQDMAlQB00DSt0kNjygIYBqCuUqoyALvdYqTlpzsNHU+Zd/Ei8OabQMuWZkfiWGJiZKfDlSuBs2fNjoaIbMWWV/w1AZxUSv2plLoL4CsAbR4a0wvAbKXUVQBQStntJvaH4iyrIbN0PGVetmzAihXAjz8C+/aZHY3jCAoCli2T71mJEmZHQ0S2YsvEXxTAuVQfx/73XGrlAJTTNO1XTdN2aZr2nM2iI4fl5we88YY8Zhtfy7z0kiz0IyLXYcvEr6Xz3MN3ZT0AlAXQEEAHAPM1Tcv9yIE07XVN0yI0TYv4559/rB5oZhTwzWboeLJM//6yQG31auD0abOjcUw//STb+BKRc7Nl4o/F/7d33+FVVenbx78rhBqadOlIEZEmBrCgMiLvjAjYUAEVdUDHQlEBB9uMzoyMAoIoDBZURH+iYhvAithlpI0IKCCI9EEU6S0JrPePFSBAAjk72Wedcn+uK1d2Tp6c3Nkc8mTvvfZakHNoe03gyPXC1gL/ttZmWmt/Apbi/hA4jLX2aWtturU2vXLlyqEFPpbZ914Qar1EpmZN6NnTLUIzapTvNPFnzRro2hXuvRf+8x/faUQkTNFs/HOAhsaYesaYYkB3YMoRNW8DvwMwxlTCnfpfEcWM+TZq+g+h1kvkBg1y7599FjZt8psl3tSqBf/4hzvib9PGdxoRCVPUGr+1NgvoC3wALAZes9Z+Z4z5mzGma3bZB8AmY8z3wCfAYGttTP4KHz1jWaj1ErlmzdykPrt2uYF+Epm77oK774YiRXwnEZEwRXXaDmvtu8C7Rzz2lxzbFrgz+00kYo88Av/8J7Ro4TtJfNu+HT77TLdIiiQizdclCaVZM98J4t+uXZCeDj/+6Bb1Oess34lEpDBptu6ApvZtF2q9FNzs2W46WolMqVJuoN+pp0KFCr7TiEhhU+OXhHTNNdC2Lbz9tu8k8emhh2DWLGjc2HcSESlsavwBdRnzZaj1UjBnnOHeDx+uOfyDKFYMSpQ49PGGDf6yiEjhUuOXhHTDDe409axZ8KX+5grMWjfSv359WLTIdxoRKQxq/JKQ0tLgttvctqbxDc4YtwjSnj2a2EckUajxBzSgw1ETChZqvRRc377udPXUqbB4se808evxx+Grr+DGG30nEZHCoMYf0B0dG4VaLwVXpQpcf73bfvRRr1HiWlraoTEToDETIvFOjT+gNg99FGq9FI4773Sr91Wt6jtJYpg/3/0RoIWQROKXJvAJaOP2vaHWS+Fo2BD+9z8oWdJ3ksTwyCNufoQHH4QJE3ynEZEg1Pgl4anpF56xY6FuXfjLX45bKiIxSo0/oKY1yoZaL4Vrzx548UU32O/aa32niV8VKri1EEQkfhkb5yN10tPT7dy5c33HkBj3zjtuwZmaNWHFCiha1Hei+JeV5U799+4N1ar5TiOSPIwx86y16UG/XoP7Arr7zQWh1kvhuvBCN/3s2rXwyiu+0ySGP/8Z7rvPTZYkIvFDjT+gSbPXhFovhSslBQYPdtuaxrdwDBwIp50GQ4b4TiIikVDjl6Rx9dVw4omwcCF8+KHvNPGvenWYNw/OO893EhGJhBq/JI3ixaF/f7c9bJjfLInCmEPbCxfCli3+sohI/qjxBzTrng6h1ks4br4ZSpeGjz+G//7Xd5rE8cYb0Lo13HSTLqOIxDrdzhfQwrVbqdqkxPELA9ZLOMqXh7//3b1v2tR3msTRooVbyrd8eTfaX3dNiMQuHfEH1GdiZLcQRlov4bn9djeHf7FivpMkjgYN4Lvv4Omn1fRFYp0avyS1jAzfCRJHrVqHtrOy3KRJIhJ71PglKe3bBwMGuGa1aZPvNIllzRr43e/c/hWR2BNx4zfG6AQpMPTSZqHWS7iKFIGlS2HjRhg3zneaxLJpE8yZA9Om6Y8qkVgU8ZS9xphpwNPW2inhRIqMpuyVoGbMgAsugMqVYdUqLeZTmKZNg7Zt3b4VkcLlY8rei4Haxpj/M8Y0CvqN413dIe+EWi/hO/98N/PcL7/AxIm+0ySWzp3V9EViVcSN31q7z1o7BugL3GiMeajwY4mEzxi46y63/eij7rq/FC5r4amn4MEHfScRkQOCXOPvbIwZAowCagE1Cj2VSJR06+bWl1+2DKbExMWrxLJ4Mdx6KzzwACxa5DuNiECwU/0nAO8BN1pru1trry/cSPGhQ+MqodZLdKSmwh13uO3PPvObJRE1aeKmR/6//9OESSKxIuLBfbFGg/ukoHbudEem6YGHyoiIRE9UB/cZY2oZY/5gjBlkjHnBGJO0Hbf3hDmh1kv0pKWp6UfL2rXw6qu+U4gkt+M2fmPMn4wxM40xW4AfgD5AaWAK0DPkfDFrxpKNodaLH/PmwcqVvlMkpk2b3F0U11wDs2b5TiOSvPJzxH83cAdwOjANKAE8Z619w1r7Q5jhRKJp5Eh35P+Q7lMJRcWKcO210KED1KvnO41I8spP4+9srZ1lrf3RWnsFMAaYaoy5wxijKX8lYXTu7G7xmzgR/vc/32kS0yOPwLvvQhWNdRXx5riN21q76IiP3wfaABWAr0LKFfNWPnxRqPUSfY0awSWXuIV7nnjCd5rEVLQopGT/1rEWftA5Q5GoC3TEbq3da629H7iukPPEjZdnrQ61XvwYPNi9HzcOtm/3myWRZWZCjx7QsqVbzldEoqdAp+qT+Rr/PW8tDLVe/DjzTDj7bNiyBZ591neaxFW0KJQo4Y7+f/zRdxqR5KJr9CJHOHDUP3KkOzKVcIwZA998A127+k4iklxSfQcQiTVdusDpp8NZZ8Hu3e7oVApf6dLQsOGhj/ftc8sli0i4dMQf0Phekc34Emm9+JOSArNnw+OPQ9myvtMkh3fegVNO0RwKItGgxh9Qs5rlQq0Xv1L0PyOqxo93CyWNHes7iUji06+3gNoOnRFqvfiXkQEvvAC33eY7SeIbPx5Gj3b3+YtIuNT4RfKwc6dr+v/6lxuEJuGpWBH699eZFpFo0H8zkTyccALceKPbHjHCb5Zksm0b9O0LG7W8hUgo1PgD6tGmVqj1Ehtuv92NNH/1VVi1ynea5NCvn7vWf8stvpOIJCY1/oD+eVnzUOslNtSpA1dd5W41GzXKd5rk8NBDbiGfoUN9JxFJTGr8AXV+4otQ6yV2HJjQZ/x42LzZb5ZkULMmfPQRnHyy7yQiiUmNP6BF67aFWi+xo2VL6NjRDfYbP953muTz0UewdavvFCKJQ41fJB/++ld4+ml3/VmiZ+xY90fXn/7kVvMTkYLTlL0BVSlTPNR6iS1nn+3eJLo6doTy5aF5c9f4jfGdSCT+GRvnf0anp6fbuXPn+o4hSWTrVihTRvecR8vmze7WShFxjDHzrLWB54HXr66ARk2PbEXiSOslNg0fDrVqwdSpvpMkj5xNf/t2t3CSiASnxh/Q6BnLQq2X2FS0qGs+w4f7TpJ85s93qyYOGuQ7iUh8U+MXiUCfPu6a81dfwcyZvtMkl/373SRKX37p7rAQkWDU+EUiULo03Hqr29ZRf3S1agXvvw9ffw1pab7TiMQvDe4LaOHarREttRtpvcSuDRvcjH6ZmbB4sSaaEZHo0uA+kSirVg169XK3lz36qO80ySkzE+6+G/7yF99JROKPGn9AXcZ8GWq9xLZBg9w95StWuGvPEl3ffAPDhsHDD8Pq1b7TiMQXTeAjEsDJJ8P330Pjxr6TJKc2bdyiSaedBrVr+04jEl/U+EUCUtP3q39/3wlE4pNO9Qc0oEPDUOslfixYAB9+6DtFcps/HyZO9J1CJD5oVL9IAXz1FbRr50b5L18OqTqHFnWrV0OjRm6sxaxZ7vS/SCLTqH5P2jz0Uaj1Eh/OPNM1nVWrYPJk32mSU+3acNNN0Lu3Lr+I5Icaf0Abt+8NtV7iQ0rKoSlkhw/X0rG+PPYYjBsHJUv6TiIS+9T4RQro2muhalV3i9mMGb7TJKecKyVmZcG8ef6yiMQ6Nf6AmtYoG2q9xI8SJaBfP7etaXz92rkT2reHc8+FJUt8pxGJTWr8AU3rd06o9RJfbrnFzR//4Yfw7be+0ySvUqWgXj23lO+WLb7TiMQmNf6A7n5zQaj1El8qVIC+feHmmw9fP16iyxj417/c7X1nnOE7jUhsUuMPaNLsNaHWS/x5+GE3wEwzyflVpgxUqnTo4927/WURiUVq/CKSkKx1R/8NGmg+f5Gc1PhFCpG1MGmSG1y2ebPvNPLuu7B+Pbz+uu8kIrFDjT+gWfd0CLVe4pMx8Nxz8MUX8NRTvtMkN2Pg+efdxEp33uk7jUjsUOMPaOHaraHWS/waPNi9Hz0a9mreJq8qV4Zu3XynEIktavwB9ZkY2foAkdZL/OrYEVq0gA0b4KWXfKeRA9asgauugl9/9Z1ExC81fpFCZsyho/4RI9ziMeLfbbfBa68d+rcRSVZq/CIhuPJKqFXLzR43bZrvNAIwZgz06AHDhvlOIuKXGn9AQy9tFmq9xLeiRQ8NKHvmGb9ZxKldG15+2V33F0lmWj08oJ5tI5ulJdJ6iX99+kDx4nDddb6TyJGsdeMvLrnETfgjkkx0xB9Q3SHvhFov8a90aTeHf6lSvpPIke6/H3r1cv8+IslGjV8kCrZvh19+8Z1CDrjmGqhWDTp18p1EJPrU+EVC9tZb7vry/ff7TiIHNG4MP/0EPXv6TiISfWr8AXVoXCXUekkcp5ziloidMAE2bvSdRg4oUeLQ9vr1sGePvywi0aTGH9Cz17cOtV4SR+PG0LWrm8VvzBjfaeRIH30EzZvDXXf5TiISHWr8AfWeMCfUekksByaNGTsWdu70m0UOV748bNsGy5ZBZqbvNCLhU+MPaMaSyM7ZRlovieXss+GMM+C339wiPhI70tNh5kx45x03/4JIolPjF4kCYw6dSh45ErKy/OaRw6WnQ0r2b0NrNc2yJDY1fpEo6doVGjZ0M8dt2OA7jeRm61Y30v9vf/OdRCQ8xlrrO0OBpKen27lztfKdxIeNG13jN8Z3EsnN559D+/ZQtiz8+CNUrOg7kcjRjDHzrLXpQb9eR/wBvTxrdaj1kpiqVFHTj2XnngtPPgmzZ6vpS+JS4w/onrcWhloviW3xYhg1yncKyc1NN0GjRr5TiIRHi/SIRNnOndCmDezYAR06uHvIJTa99x6sW+cWXBJJFDriF4mytDS44Qa3PWKE3yySt0WL3Fz+t90GS5b4TiNSeNT4AxrfK7JxFZHWS2K74w53+9ikSbBmje80kpumTaF/fzfCX6f+JZGo8QfUrGa5UOslsdWrB1de6e7nHz3adxrJy+jR8Oc/H7rHXyQR6OUcUNuhM0Ktl8R3YBrfp592i/hIbNu2zd3uJxLv1PhFPGnVCs4/H7Zvh6ee8p1GjuXXX92/V6dO8MMPvtOIFIxG9Yt4NGQI1K3rZvWT2FWxIrRu7W7D1DwMEu/U+APq0aZWqPWSHDp2dG8S24xxl2SKFoUSJXynESkYTdkrEiMO/FfUEWV82LwZTjjBdwpJRpqy15POT3wRar0kl/ffd8v2vvOO7yRyPFlZbqR/o0Zuch+ReKPGH9CiddtCrZfk8v33bn744cN9J5HjSUmBBQvcEf9nn/lOIxI5NX6RGHDjjVCunLtdbPZs32nkWFJS4IUX3L9Vz56+04hETo0/oCpliodaL8mlTBm4+Wa3raP+2FelCpx1lu8UIsGo8Qc0+94LQq2X5NO/vxs1/sYbsHy57zSSX9984xZb2rTJdxKR/FHjD2jU9Mhm8Yi0XpJP9epwzTVudP/Ikb7TSH4NHAgffwwPPeQ7iUj+qPEHNHrGslDrJTkNGuTev/02ZGT4zSL58/zzbtElNX6JF2r8IjGkSRN4801YuhSKFfOdRvKjTh13hqZkSd9JRPJHjV8kxlx6qRvsJ/EnM9MNzty+3XcSkbyp8Qc0tW+7UOtFdu2ChQt9p5BI3Hwz3HWXG6gpEqvU+EVi0JIlULs2XHIJ7NvnO43k18CBbka/P/7RdxKRvKnxB9RlzJeh1ktya9gQypeHFSvcNX+JD02auFkYzznHdxKRvKnxi8SgIkXc0SPAsGGHFvCR2FekyKHt776DvXv9ZRHJjRq/SIy6/nqoVAnmztWc8PHopZfg9NPh7rt9JxE5nBp/QAM6NAy1XqRkSejXz21rGt/406iRG5+xaxfs3+87jcghxsb5OcT09HQ7d+5c3zFEQvHrr26Q3+7dboR/06a+E0kkli1z4zVECpMxZp61Nj3o1+uIP6A2D30Uar0IuFP9f/wjtGgB27Syc9zJ2fSzsnSHhsQGNf6ANm6PbMROpPUiBwwf7haC0Wpw8Wv1amjfHoYO9Z1ERI1fJOaVLAnG+E4hBbF0KXz1FYwfDzt3+k4jyU6NP6CmNcqGWi9ypOXL3YxwW7f6TiKR6tgRXnwR5s2DtDTfaSTZaXCfSJzo0MEt//rII25aWBFJTnE1uM8Y8wdjzFJjzHJjzJBj1HUzxlhjTOAfLGx3v7kg1HqRIx2Y0Gf0aC3ZG8+shXHj4MknfSeRZBW1xm+MKQKMBS4EmgA9jDFNcqkrA/QHZkUrWxCTZq8JtV7kSBde6G7nW78eXn7ZdxoJauZMuPVWGDAA1ujXgngQzSP+NsBya+0Ka20G8ApwcS51fweGAXuimE0k5hkDgwa57REjNI1vvDr7bPfv+MILUKuW7zSSjKLZ+GsAOf++XZv92EHGmNOAWtbaacd6ImPMTcaYucaYub/88kvhJxWJUT16QI0abg74997znUaCGj4cunf3nUKSVTQbf243JB08ZjHGpACjgIHHeyJr7dPW2nRrbXrlypULMWL+zbqnQ6j1IrkpVgxuv91taxrfxLB2LXz4oe8UkkxSo/i91gI5T2zVBNbn+LgM0BT41LiblqsBU4wxXa21MTdsf+HarVRtUiK0epG83HQTLFlyaB5/iV+rVkGrVpCZCf/9LzRo4DuRJINoHvHPARoaY+oZY4oB3YEpBz5prd1qra1kra1rra0LfA3EZNMH6DMxsliR1ovkpWxZNxFMixa+k0hB1a7tbtNs1879u4pEQ9SO+K21WcaYvsAHQBHgOWvtd8aYvwFzrbVTjv0MIpKbzEwoWtR3CgnCGDfIr3hxSNF0ahIl0TzVj7X2XeDdIx77Sx617aORSSRezZvnrvc3bw5jx/pOI0GVLHlo21p3zV+j/SVM+hszoKGXNgu1XuR4iheHL7+E5593y/dKfNu1C666yl3zX7/++PUiQanxB9Szbe1Q60WOp2lT6NQJdu/WEX88qFu3Lh99lPfy3CVKwJYtsGePu10zL9dffz333XdfCAkL7tRTT+XTTz/15DjAaAAAIABJREFUHUOOQ40/oLpD3gm1XiQ/Bg927594wh0xSvxKSYGJE90SzB07Rv/7H+8Pk/zUf/fdd7Rv3z7i771582aMMZQuXZpSpUpRvXp1HnvssYifR/JHjV8kjp13HrRuDZs2wYQJvtNIQVWrdvgtfZHOzpiVlVW4gaJk/vz5VK5cmR07drBr1y7GjRvHHXfcwdq1a31HS0hq/CJxzJhDR/0jR8K+fX7zyLHNnz+f5s2bU65cOa666ir27NnD8OHDufzyyw+r69evHxdffDvp6fDpp9/QqlUrypQpc/Brcqpbty6PPPIIzZs3Jy0tjaysLBYvXkz79u0pX748p556KlOmHLpp6pFHHqFGjRqUKVOGk08+mRkzZnDttdeyevVqunTpQunSpRk2bBgADz/8MPXr16dMmTI0adKEt956CyDP+pxnAdasWcNll11G5cqVqVixIn379j3mfmnduvXBj9u2bQtAhlajCoe1Nq7fTj/9dOvDH5+fHWq9SH5lZVl70knWli5t7bff+k4jealTp45t3bq1Xbdund20aZNt3LixHTdunF2/fr0tVaqU3bx5s7XW2szMTFu5cmXbtOlcC3ttuXK17ciRI21GRoadPHmyTU1Ntffee+9hz9uiRQu7evVqu2vXLpuRkWHr169vH3roIbt37147Y8YMW7p0abtkyRK7ZMkSW7NmTbtu3TprrbU//fSTXb58+cHnmT59+mGZX3vtNbtu3Tq7b98++8orr9hSpUrZ9evX51l/4LGsrCzbvHlze/vtt9sdO3bY3bt32y+++CLPfXPttdfaBx54wFpr7ebNm+0f//hHe/rpp9v9+/cXcK8nJtwt8IH7po74A3r2+tbHLypAvUh+FSkCkye7ld6aN/edRo6lf//+VK9enQoVKtClSxfmz5/PiSeeyLnnnsvkyZMBeP/996lUqRJTppzOrbd+TalSmdx+++0ULVqUbt26HXZknPN5a9WqRcmSJfn666/ZsWMHQ4YMoVixYpx//vl07tyZSZMmUaRIEfbu3cv3339PZmYmdevWpX79+nnmveKKK6hevTopKSlcddVVNGzYkNmzZx/355w9ezbr169n+PDhpKWlUaJECdq1a5dn/fz58xk+fDgVKlTg9NNPxxjD1KlTMcbw888/065dOzp16pSPPSz5ocYfUO8Jc0KtF4lEq1ZQvrzvFHI81apVO7hdqlQpduzYAcB1113HSy+9BMBLL73EtddeS716cM4566lRowbZ05gDUKdOnaOet1aOG//Xr19PrVq1SMkxI1CdOnVYt24dDRo04LHHHuOBBx6gSpUqdO/enfXHuHdw4sSJtGzZkvLly1O+fHkWLVrEr/m4d3TNmjXUqVOH1NTjTxWzd+9eFi9ezJIlS/jtt9/48ccfGT9+PCeeeCIAkyZN4vbbb+fdd989zjNJfqnxBzRjycZQ60WC2LNHq/bFo0suuYQFCxawaNEipk2bxtVXXw3AiSeeyLp169iyxTJ4MOzcCatXrz7q63P+YVC9enXWrFnD/v37Dz62evVqatRwi6H27NmTL7/8klWrVmGM4c9//vNRzwGwatUqbrzxRsaMGcOmTZvYsmULTZs2xWaPODyyPqdatWqxevXqfA02XLRoEWlpadSsWfOoz33xxRcMHTqUUaNGMW3aMRdtlQio8YskiMxMaNLE3dt/rPvAJfaUKFGCbt260bNnT9q0aUPt2m7ejzPPPJPU1FTOPvtxRozI4vLL3zzuqfa2bduSlpbGsGHDyMzM5NNPP2Xq1Kl0796dpUuX8vHHH7N3715KlChByZIlKVKkCABVq1ZlxYoVB59n586dGGM4sALq888/z6JFiw5+/sj6nNq0acOJJ57IkCFD2LlzJ3v27OGrr77Ktfabb77h1FNPzfVz55xzDs2aNeOLL76gc+fOx/y5Jf+iOmVvGH7etuewe+Sn9nXXkbqM+fLgYwM6NOSOjo1o89BHbNy+F4CmNcoyrd853P3mAibNXnOwdtY9HVi4duthi+oMvbQZPdvWzvVe/N4T5hx2NL/y4Yt4edZq7nlr4cHHxvdKBw6/l79Hm1r887LmdH7iCxat2wZAlTLFmX3vBYya/gOjZyyL+s/UoXEVnr2+db5/pmY1y9F26Az9TDH0MzXpspr9JRdy0YuJ8zMlyr/T2s27uXr8LH6+4AJenrWaxz76gazN/6PukHcY3yudLt26M378eCpeOIC6Q945+DPVvup+Zk98GFPsbmatbcNll13GrBWbDn6vtZt389MvO1m4duvBnymj/UCeeXkC//znP8koXp4yHfvzhwk/Uptf2PPxv/h24XdkkULxGqdQ4fd9+XnbHjpdcwu3DhrMzf3vpNyZVzH24b8ycOBAmrRMB5NC2qm/o3IDN4ik94Q5rKjRkVsH3cfN/e9k2D8eoPo5Vx78GUt+tJehjz7Hi489QNlKJ4IxpDU5j9vu+cdR/067P53KJS2a5vrvtH//fmb++Csn3fOeXns5fqaCMgdO28Sr9PR0O3euVr4TAVi+HE4+2Q34++knyD67K3Fg9erVNG7cmA0bNlA2l6X6rHW3byaTZcuWMXz4cJ5++mnfUWKKMWaetTY96NfrVH9AL886+jpbYdaLBNGgAVx2mTvt//jjvtNIfu3fv5+RI0fSvXv3XJs+HN70P/sMkuEW92+//ZYWWn+60KnxB5Tz9E8Y9SJBHZjQ58knYds2v1nk+Hbu3EnZsmWZPn06Dz744HHrhw2D9u3h3nvDz+Zbt27duO2223zHSDhq/CIJpk0bOPdc1/R1hjT2paWlsWPHDr777rvDbsvLyznnuAV9KlWKQjhJSHE/uE9EjnbXXW7+/nr1fCeRwnbmmW78Ro4pAUQiosYf0IGR+mHVixREp07uLdkGgyWLnE1/xw4oWdIN6BTJD53qD6hZzXKh1osUhDFq+slg3jxo2dJd9xfJLzX+gHLexxlGvUhhWLkSBgyA6dN9J5Ew/PIL/PgjvPGGu5NDJD/U+EUS2Guvudv6/vlP30kkDH/4A7z9Nnz5JRQt6juNxAs1fpEE9qc/QZky8MknoHmuEtPFF7tR/iL5pcYfUI82x7/tpiD1IoWhXDm46Sa3PXy43ywSrsxM+POf4amnfCeRWKcpe0US3Nq17ra+/fth2TI46STfiSQM774LF10EaWmwejVUqOA7kYRFU/Z60vmJL0KtFyksNWtCz56u8Y8a5TuNhKVTJzeb3/vvq+nLsanxB3RgFaaw6kUK06BB7v1zz8HWgi/uJTHqH/+Adu18p5BYp8YvkgSaNXMj+z/7zF33l8T3zTcwbZrvFBKLNHNfQFXKFA+1XqSwDRniO4FEy6JFcMYZbrT//PmaulkOp8Yf0Ox7Lwi1XiRMW7ZA+fK+U0hYTj0VunSBqlU1p78cTaf6Axo1/YdQ60XCsGEDdOgArVvDvn2+00hYjIFXXoGxY908/iI5qfEHNHrGslDrRcJQqRKsWAHLl7sZ3yRxpeY4n5uZCUuW+MsisUWNXySJpKbCwIFue/hwiPNpPCQffvsNzjvPvW3Y4DuNxAI1fpEkc8MN7j7vWbPcHO+S2MqVc6f7ixWD9et9p5FYoMYf0NS+kd0sG2m9SFjS0uC229y2pvFNfEWKwMsvu9H9rVr5TiOxQI1fJAn17etu9Zo6Fb7/3ncaCVvVqlCx4qGPtYRvclPjD6jLmMjOkUZaLxKmKlXg+uuhVCn49lvfaSRarIV//ctN6LRli+804osav0iSeuABt5hLjx6+k0i0ZGXB88/D0qXw+uu+04gvmsBHJElVreo7gURb0aIwaZKbzveKK3ynEV90xB/QgA4NQ60XiZaMDJg4EbZv951EoqFBAzX9ZKfGH9AdHRuFWi8SLT17wnXXwTPP+E4i0bZ6Nfzxj7Brl+8kEk1q/AG1eeijUOtFouW669z7xx7TaO9kYq0b3/H88268hyQPNf6ANm7fG2q9SLRcdBE0bgxr1sCrr/pOI9FijBvhf/nlcNddvtNINKnxiyS5lBQYNMhtDxumaXyTSYsWbnR/pUq+k0g0qfEH1LRG2VDrRaLpmmvc8q0LF8KHH/pOIz5YC6+9pss9yUCNP6Bp/c4JtV4kmooXhwED3Lam8U1OAwbAVVfB/ff7TiJhU+MP6O43F4RaLxJtN98M6elw5ZU63Z+MrrwSTjgBWrb0nUTCpsYf0KTZa0KtF4m28uVhzhy46SY38EuSS7t2sGoVdO/uO4mETY1fREQAKFPm0PaGDbB/v78sEh41fhE5zIYNMHgw3Hef7yTiy3vvwamnarxHolLjD2jWPR1CrRfxZeNGGDECRo2CTZt8pxEf9u+H336DmTM13iMRqfEHtHDt1lDrRXxp3hx+/3s3jeu4cb7TiA8XXQSffAJvvaXxHolIjT+gPhPnhlov4tPgwe79E0/Anj1+s4gf7du7yZ3AHfXryD9xqPGLyFHOPx9OO82d9p840Xca8WnrVjfSf/x430mksKjxi8hRjDk0f/uIEbBvn9884s/06W5Gv/vu0yp+iUKNP6ChlzYLtV7Et27doG5dWLYMPvvMdxrxpVs3GDoUvvoKSpXynUYKg7FxfuEmPT3dzp2r6+ciYXj3XTeb25ln+k4iIgcYY+ZZa9ODfr2O+AOqO+SdUOtFYkGnTmr6crh33oF//9t3CimIVN8BRCQ+rFoFder4TiE+ffkldO4M5crBd99BjRq+E0kQOuIXkWOyFi69FOrVgyVLfKcRn84+213zv+ceOPFE32kkKB3xB9ShcZVQ60VihTFQtar7A+DRR+GZZ3wnEl+McSP8NalPfNPgPhE5rmXL4OSToWhRd8q/WjXfiSQWbNsGP/7o5nyQ6NHgPk96T5gTar1ILGnYEC65BDIy4PHHfaeRWLBmjWv4F14IP//sO41EQo0/oBlLNoZaLxJrDkzjO24cbN/uN4v4V7061KrlrvXv3Ok7jURCjV9E8uXMM6FdO9iyBZ591nca8a1IEXj9dfj6azjpJN9pJBJq/CKSb4MHQ/HirvmLVKrkXg8H7NjhL4vknwb3iUi+7d8Pv/4KVXSTiuSQkQH33uuW8Z03z93nL+HR4D5PXp61OtR6kViUkqKmL0ezFj7+GFauhE8/9Z1GjkeNP6B73loYar1ILMvKgpdfhv/8x3cSiQXFi8Mrr8Dnn8PFF/tOI8ejxi8iERs7Fq6+Gv76V99JJFY0bAhnneU7heSHGr+IRKxXL0hLc2u1f/ON7zQSa+bNg8sug927fSeR3KjxBzS+V2TjKiKtF4llJ5wAN97otkeM8JtFYsv+/XD99W6g36OP+k4juVHjD6hZzciGrUZaLxLr7rjD3cv96qtuGl8RcANAJ06Efv1g0CDfaSQ3avwBtR06I9R6kVhXuzZ07w779sGoUb7TSCw57TQ3tXOJEr6TSG7U+EUksAPT+I4fD5s3+80isSkz0w0Gzcz0nUQO0LK8IhJYixbQpw+0bKmjO8ldjx7wxhuwfj089JDvNAJq/IH1aFMr1HqRePHMM74TSCzr18+N8r/wQt9J5ABN2SsihcZaMMZ3Cok1GRlQrJjvFIlDU/Z60vmJL0KtF4knO3fCPfe4CVz27/edRmJNzqb/ww96jfimxh/QonXbQq0XiSfFirkpfL/+GqZO9Z1GYtX48dCsme4C8U2NX0QKrGhRd18/wPDhfrNI7Kpa1Z32X601y7xS4w+oSpnixy8qQL1IvOnd283o99VXMHOm7zQSi7p0gW+/hdGjfSdJbmr8Ac2+94JQ60XiTenScMstbltH/ZKX5s0Pbe/b5waESnSp8Qc0avoPodaLxKN+/dwSrf/+txvEJZKXVavgnHNgwgTfSZKPGn9Ao2csC7VeJB5Vq+ZW7rMWXnvNdxqJZZ9/Dv/5Dzz8MGRl+U6TXDSBj4gUqiFDoGdPOO8830kkll17rZvm+eqrIVWdKKq0u0WkUJ10knsTOZ7+/X0nSE461R/Q1L7tQq0XSQSLF8OOHb5TSKyz1i3k8/bbvpMkBzV+EQnFffdBkybw3HO+k0ismzIF+vaFG26A337znSbxqfEH1GXMl6HWi8S79OyZxEeO1OAtObauXd21/qeeggoVfKdJfGr8IhKKrl2hUSN329bkyb7TSCwzBl56Ca680neS5KDGLyKhSEmBgQPd9vDhmqhF8m/1apg923eKxKXGH9CADg1DrRdJBL16QZUq8M038PHHvtNIPPjuO2jZEi65BH75xXeaxKTGH9AdHRuFWi+SCEqUOHTLlqbxlfw4+WRo2hRatXKXAKTwqfEH1Oahj0KtF0kUt9ziFu+pUUOD/OT4UlPd0s5Tp0KlSr7TJCZN4BPQxu17Q60XSRQVKsCaNZCW5juJxIty5Q5tW+tO+Vep4i9PotERv4iETk1fgti2Da64As46y21L4VDjD6hpjbKh1oskmn374I033AxtIvlRrBgsXw4bN8LChb7TJA5j4/wem/T0dDt37lzfMUTkOL791o3WLl3anfovX953IokHy5a5W0Pr1/edJHYYY+ZZa9ODfr2O+AO6+80FodaLJJoWLaBDBzd3/5NP+k4j8aJhw8Obfpwfq8YENf6AJs1eE2q9SCK66y73fvRo2KvxrhKhKVPgggtgzx7fSeKbGr+IRE3Hju7If8MGN0WrSH5lZLiZID/+WAs/FZQav4hEjTEwaJDbHjEC9u/3m0fiR7FiMGmSe93cfLPvNPFNg/sC+nnbHqqWLRFavUiiysx012zXrHGnbrt08Z1IJL5ocJ8nC9duDbVeJFEVLQp//7tbrrd9e99pJF5t3Qp/+5tmgwxCjT+gPhMjO8sQab1IIrvuOrjjDihTxncSiUfWwkUXwV//CkOH+k4Tf9T4RcSrzEzfCSTeGOPOGrVuDT16+E4Tf9T4RcSbhx+GmjXhhx98J5F487vfwddfu/v8JTJq/AENvbRZqPUiyeDAdKwjR/pOIvEoJUcH+/prTe6TX2r8AfVsWzvUepFkMHCgez9hgvsDQCSIBx+EM890E0PJ8anxB1R3yDuh1oskg1NOcbfz7d0LY8b4TiPxqkULSE3VvBD5pcYvIl4dmMZ37FjYudNvFolPl1ziLhvdeafvJPFBjV9EvDr7bDjjDPjtN03FKsHVqXNoe9cuXe8/FjX+gDo0rhJqvUiyMAYGD3bbH3/sN4vEv7lzoVkzmDjRd5LYpcYf0LPXtw61XiSZXHyxa/pvvuk7icS7hQthxQp49lkd9edFjT+g3hPmhFovkkyKFHH3ZRvjO4nEu+uvhxdegOnT9XrKS6rvAPFqxpLI7j2KtF4kWS1f7pZgbdLEdxKJR8ZAr16+U8Q2HfGLSMyYPBkaNTp0f79IQWRkuPEjU6b4ThJb1PhFJGacfz6ULAnvvw8LFvhOI/HulVdgxAi46SbYvdt3mtihxh/QyocvCrVeJBlVrAi9e7vtESP8ZpH4d801rum/+ab7g1KcqDZ+Y8wfjDFLjTHLjTFDcvn8ncaY740xC4wxM4wxdXJ7nljw8qzVodaLJKs77nBzsE+aBGvW+E4j8SwlBZ56Cs46y3eS2BK1xm+MKQKMBS4EmgA9jDFHDt/5Bki31jYHXgeGRStfpO55a2Go9SLJql49uOIKyMqCxx7znUYSyX//CzNn+k7hXzSP+NsAy621K6y1GcArwMU5C6y1n1hrd2V/+DVQM4r5RCRGHJjQ5+mnYcsWv1kkMcyc6WaIvPJK+PVX32n8iubtfDWAnCfu1gJtj1HfG3gv1EQiEpNOPx1+/3uoXNlNv1q+vO9EEu/atIHWreG006B0ad9p/Ipm489tKoVc51UyxlwDpAPn5fH5m4CbAGrX9rPc7fhe6aHWiyS7d95xE/uIFIbUVJgxA0qU8J3Ev2ie6l8L1MrxcU1g/ZFFxpgLgHuBrtbavbk9kbX2aWtturU2vXLlyqGEPZ5mNcuFWi+S7NT0pbDlbPqZmbA6ScdcR7PxzwEaGmPqGWOKAd2Bw6ZVMMacBjyFa/oxPdVd26EzQq0XEbe++tSpbhpWrbUuhWXDBjj3XLjgAti+3Xea6Ita47fWZgF9gQ+AxcBr1trvjDF/M8Z0zS4bDpQGJhtj5htjNN+SSBLLyoJbb3Vzr7/7ru80kijKlYOdO2HPnuS8ZTSqc/Vba98F3j3isb/k2L4gmnlEJLYVKwa33w6DBsHw4dC5s+9EkghKloS333aDRitU8J0m+jRzX0A92tQ6flEB6kXEufFGKFsWPv8cZs3ynUYSxUknHd70k+lSkhp/QP+8rHmo9SLilC0Lt9zitocP95tFEo+1MGYMtGsHe3MdTp541PgD6vzEF6HWi8gh/ftD0aJuzvXly32nkUSycyeMHAn/+U/yrOKnxh/QonXbQq0XkUOqV3cLrlgLjz/uO40kktKl3Sp+kye7qaKTQVQH94mIBDV4MJx8MvzpT76TSKJp08a9JQsd8QdUpUzxUOtF5HCnnAJ//rOm75VwrVrlVojct893kvDoiD+g2fdGdudhpPUikrc9e8AYKK6/p6UQ7d8PF14IixdDjRruNtJEpCP+gEZN/yHUehHJ3UsvQd26MH687ySSaFJS3BiSiy+GG27wnSY8avwBjZ6xLNR6EcldiRLw88/w6KNuZj+RwnTBBW5yn4oVfScJjxq/iMSVSy+F+vXhp5/c7X0iYbHWrRJpc11HNn6p8YtIXClSBAYOdNvDhiXeL2WJHX36uGmix471naRwqfEHNLVvu1DrRSRv118PlSrBvHnw6ae+00ii6tTJzRxZtarvJIVLjV9E4k7JktCvn9vWNL4SlssvhxUrEm9iHzX+gLqM+TLUehE5tltvdX8ArF7tpl0VCUPOQX6//eYvR2FS4xeRuFSpEsydCwsWQFqa7zSS6KZMgQYN3O2k8U6NX0TiVpMm7t5rkbD9/DNs3gzTpvlOUnCauS+gAR0ahlovIvm3cqU78u/a1XcSSVR9+kC1anDRRb6TFJyxcX4vTHp6up07d67vGCLiyU8/QcOGUKoUrFkD5cr5TiQSLmPMPGttetCv10mygNo89FGo9SKSP/XqwTnnwPbt8PTTvtNIMtiyBa680k3uE4/U+APauH1vqPUikn+DB7v3jz0GGRl+s0jie+klmDwZ+vePz2mj1fhFJO5deCE0bQrr18PLL/tOI4nu1lvhzjvhww8hNQ5HyqnxB9S0RtlQ60Uk/4w5tITqiBGaxlfClZLiFomqX993kmA0uE9EEkJGBpx0Eqxb5669durkO5Eki6lToUIFOPvs6Hw/De7z5O43F4RaLyKRKVbMLd5z5ZVQu7bvNJIspk1zt5H26OEG/cUDNf6AJs1eE2q9iETujjvg1Vfd9X6RaPj9791dJf37uwV94kEcDksQERGJDUWLwiefuOWi44WO+EUk4UyfDh07wo8/+k4iySBn09+6FZYv95clP9T4A5p1T4dQ60UkuP/7P/joIxg50ncSSSbLlsFpp0HnzrG9YqQaf0AL124NtV5Egjtwa9/zz8Ovv/rNIsmjRg23VHRaWmwv4avGH1CfiZHdQhhpvYgE17Spu51v924YO9Z3GkkWpUrB++/DzJlQq5bvNHlT4xeRhHRgGt8xY2DXLr9ZJHnUqgXFix/6eG8Mztauxi8iCem88yA93Z3qnzDBdxpJNhkZbl6Jc86JvfUj1PgDGnpps1DrRaRgjIG77nLbTz2laXwlunbtgjfegG++gS+/9J3mcJqyV0QS1r598Pjj0KsXVKzoO40km9mzYf9+OOOMwn1eTdnrSd0hkS3EHGm9iBRckSJuNj81ffGhTZvCb/qFQY1fRJJCRgZs2OA7hSSrOXOgTx93Fso3NX4RSXgzZ7qV+/r08Z1EklFGBlx2GTz7LIwf7zuNGn9gHRpXCbVeRApPw4ZuQpV33oHvv/edRpJNsWKu6ffrB9dd5zuNBveJSJK47Tb417/ghhvgued8pxEJToP7POk9YU6o9SJSuO68E1JS4KWXYN0632kkmWVkwAsv+LvFVI0/oBlLNoZaLyKFq359d501M9Pd4ifig7VuEZ/rr4cnn/STQY1fRJLGgWl8n3wStm3zm0WSkzHQuzfUrg0tWvjJoMYvIkmjTRs491yoVg1++sl3GklWV10FixfDWWf5+f4a3CciSeXnn6FSJTe5j0gsWLUK6tTJf70G93ny8qzVodaLSDiqVlXTl9gxdqy73fSVV6L3PdX4A7rnrYWh1otIuNauhWHDtHiP+FWkiBtwOn9+9L5navS+lYhIbNi/3y2XunIlNG8Of/iD70SSrP70JzfI78wzo/c9dcQvIkknJQVuucVtDxvmN4skN2MOb/rROAOlxh/Q+F6RjauItF5EwvWnP0GZMvDJJzBvnu80Iu5Ok7PPhvffD/f7qPEH1KxmuVDrRSRc5cq55g8wfLjfLCIAr78O//kP3HdfuEf+avwBtR06I9fHMzMzI6oXEX8GDIDUVJg8GVas8J1Gkt3AgfC3v8GHH7pLAGFR4z+GvJr4sVStWjWEJCIShpo1oWdPN9hv1CjfaSTZpaTA/fdDhQohf59wnz6+BWniQf5YEBF/Bg2Ciy+Gq6/2nUTkEGthzBiYObPwn1u38x3DsZp4jza1cn3c5HF+Jq96EfGrWTN4+23fKUQON2EC9OvnZvRbvBhKliy859aUvcdQtmxZtkW4kkdqaipdunShRYsWtGzZkpYtW1K3bt1Q8olI4bM23OurIvmRkeFW8bvpJujW7fDPacreEO3atYtLL72UBx54gLfffpuVK1ce/FznJ77I9WuKFi1Kq1atWLhwIQMHDqR+/fqccMIJVGzQkgEDBvD8889HKb2IRGLWLDeRz9NP+04iAsWKwQcfHN30C4NO9R/DgSY+f/58XnzxRVauXEnZsmVp3rw53+wsx/Oll3PDDTcc9TX333//wY+3b9/Ot99+S9cHX2Lnzp2tiRUVAAAP/0lEQVSMGzfuqK8REf9WrXK/aH/8Efr00Xz+4l/OM0+rVsHu3dC4cSE8r0715+3IU/0Hmvj8+fO5+5mpnFJ8M7Nnzz7sa8qUKcP27duPeq66Q95h5cMXhZJTRAouKwsaNXKTqLzxBlx2me9EIs6cOfD//h9Ur+6209J0qj80R/5RVKZMGdq1a0ffvn055crBRzV9gLFjx+b6XFXKFA8lo4gUjtRUuPNOt63FeySWNGkC1apB/fqwd2/Bn09H/McwceJEevXqFcpzi0js2bkTateG336Dzz93C/mIxIKNG6FyZXf6X4P7QpRX009PT+cfbxx9tA8wYMAAvvrqq6MeHzX9h0LNJiKFLy0N+vZ125rGV2JJlSqFd7eJjviPIa/G//rrr2Nqn87lbeoxceLEwz6XmppKqVKlqFKlCr169eK6666jTp06usYvEid++cUd9RvjBlRVruw7kcjhdMQfosmTJ7Nq1SoaNGhA/fr1D74VKVKE1HJVqF+//lFfU7JkSTZs2MD999/PZ599RoMGDfjd737HjoUz2Llzp4efQkQiUbkyvPqqG+Snpi+JSEf8x7Bs2TL69u3LCSecwKOPPkqNGjUAOPHEE0ntNoI1Txw9x+eRdwKsXr2aiRMn8uCoJymRsZXLL7+cCRMmhJJXREQSn474Q9SwYUM++OADLrnkEs4//3xGjBhBVlYWxhhe7N02X89Ru3Zt7rvvPv777Xd88MEHlChRIuTUIlJYsrJgwQLfKUQKlxp/PnTv3p05c+awdu1aWrZsmet9+gcc6wzKWWedxZNPPhlGRBEpZJs2QcOGcO65cIz/8iJxR40/n8qWLctjjz3GSy+9xD/+8Q+ue2lhrnV5/VHQZcyXYcYTkUJWsSLUqgVbt8Izz/hOI1J41Pgj1LKlm3PfpBbzHUVEQjZ4sHv/2GOgFbclUajxR9nDDz/sO4KI5NNFF8Epp8CaNW6kv0giUOMPaECHhoHqP//88zDiiEgIUlJg0CC3PXy4pvGVxKDb+UREjmHvXqhXD/73P3j/ffj9730nkmSn2/k8afPQR/mq++mnnxg7dix1uvRl2bJlIacSkcJWvDj07++af2EskCLimxp/QBu35/4b4JRTTjm4/dlnn9GiRQumTZvGxu+/plWrVnz88cfRiigiheT22+GHH6BrV99JRApOjb+QrV279uD2fffdx5gxY3jvvfeoesWDPPnkk9x3330e04lIECVKuGV7RRKBGn9ATWuUzfVxk2P5pKVLl9KjR4+D9d27d2fJkiVRyScihW/DBrj3Xli50ncSkeD0N2xA0/rlvlB3ZmYmzz//PNZajDFkZGRQtGhRpvU7h71797Jv374oJxWRwjJkCLzwAuzYAaNH+04jEoyO+AO6+83cJ/Bu27YtEydO5MUXX6RJkyZ8//33B+s/++wzTj755GjGFJFCdOed7v348fDbb36ziASlxh/QpNlrcn38008/5ZNPPjn41rp164P1bdu25d13341mTBEpRM2bu9v5du2CceN8pxEJRo0/isqVK0elSpV8xxCRAjgwje/jj8OePX6ziAShxi8iEoHzz4fTToONG2HiRN9pRCKnxh/QrHs6hFovIrHJGLjrLrf96KOwf7/fPCKRUuMPaOHaraHWi0js6tYNbrgBnnrK/SEgEk/U+APqMzGy9QEirReR2JWaCs89B+3bq/FL/FHjFxEpoKws3wlE8k+NX0QkoBUr4OKL4corfScRyT/N3BfQ0EubhVovIrEvLQ0++AAyMmDpUtD8XBIPdMQfUM+2tUOtF5HYV7UqXHcdWOtG+IvEAzX+gOoOeSfUehGJDwMHugF+L7zgFvERiXVq/CIiBdCoEVxyiTvd/8QTvtOIHJ8av4hIAR2Yxvdf/3Ir94nEMjX+gDo0rhJqvYjEjzPPhLPPhp07YeZM32lEjs1Ya31nKJD09HQ7d64mxxERvxYtggoVoHp130kk0Rlj5llr04N+vY74A+o9YU6o9SISX5o2VdOX+KDGH9CMJRtDrReR+LRvH7z/vrvFTyQWqfGLiBSi3/0OLrwQPvrIdxKR3Knxi4gUoj/8wb0fNsxvDpG8aHCfiEgh2rwZatVyI/z/+1847TTfiSTRaHCfJy/PWh1qvYjEpxNOgBtvdNsjRvjNIpIbNf6A7nlrYaj1IhK/br8dihSBV1+FVat8pxE5nBq/iEghq1MHund3I/wfe8x3GpHDqfGLiIRg8GB3rV9L9UqsSfUdIF6N7xXZuIpI60UkvrVoAT/95E75i8QSHfEH1KxmuVDrRST+qelLLFLjD6jt0Bmh1otIYvj1V3jwQZg0yXcSEUen+kVEQvThh/DAA+5a/1VXQYoOt8QzvQRFREJ0xRVQuzYsXQpTp/pOI6LGH1iPNrVCrReRxFC0KNxxh9vWNL4SCzRlr4hIyHbscEf9mzfDV1/BWWf5TiTxTFP2etL5iS9CrReRxFG6NNxyi9sePtxvFhE1/oAWrdsWar2IJJZ+/aBYMfj3v2H5ct9pJJlpVL+ISBRUq+YW7WncGOrX951Gkpkaf0BVyhQPtV5EEk+/fr4TiGhwn4iIF9u3Q5kyvlNIPNLgPk9GTf8h1HoRSUy7dkG3bnDSSW60v0i0qfEHNHrGslDrRSQxlSoF69e7qXyffdZ3GklGavwiIlF2113u/ahRkJXlN4skHzV+EZEo69oVGjWCVatg8mTfaSTZqPEHNLVvu1DrRSRxpaTAwIFue9gwiPMx1hJn1PhFRDzo1QuqVIH582GGVu2WKIpq4zfG/MEYs9QYs9wYMySXzxc3xrya/flZxpi60cwXiS5jvgy1XkQSW4kS0L8/FCnimr9ItESt8RtjigBjgQuBJkAPY0yTI8p6A5uttQ2AUcAj0conIhJtt90GK1bAoEG+k0gyieYRfxtgubV2hbU2A3gFuPiImouBF7K3Xwc6GGNMFDOKiERN+fJu1T6RaIrmlL01gDU5Pl4LtM2rxlqbZYzZClQEfs1ZZIy5Cbgp+8O9xphFoSQ+DhPh+YhI6wtZJY7Yj5In7av80X7KH+2n/NO+yp+TC/LF0Wz8uR25HzmWNT81WGufBp4GMMbMLcjUhclC+yn/tK/yR/spf7Sf8k/7Kn+MMQWapz6ap/rXArVyfFwTWJ9XjTEmFSgH/BaVdCIiIkkgmo1/DtDQGFPPGFMM6A5MOaJmCnBd9nY34GMb76sIiYiIxJConerPvmbfF/gAKAI8Z639zhjzN2CutXYK8CzwojFmOe5Iv3s+nvrp0EInFu2n/NO+yh/tp/zRfso/7av8KdB+ivtleUVERCT/NHOfiIhIElHjFxERSSJx2/iPN/1vsjPGrDTGLDTGzD9w64cxpoIxZroxZln2+xN854w2Y8xzxpiNOed+yGu/GOfx7NfYAmNMK3/Joy+PffWAMWZd9utqvjGmU47P3Z29r5YaY37vJ3X0GWNqGWM+McYsNsZ8Z4wZkP24Xlc5HGM/6TV1BGNMCWPMbGPMt9n76sHsx+tlT2e/LHt6+2LZj0c23b21Nu7ecIMDfwROAooB3wJNfOeKpTdgJVDpiMeGAUOyt4cAj/jO6WG/nAu0AhYdb78AnYD3cPNLnAHM8p0/BvbVA8CgXGqbZP8/LA7Uy/7/WcT3zxCl/XQi0Cp7uwzwQ/b+0Osqf/tJr6mjf3YDlM7eLgrMyn6tvAZ0z378SeCW7O1bgSezt7sDrx7r+eP1iD8/0//K0XJOifwCcInHLF5Yaz/n6Lkh8tovFwMTrfM1UN4Yc2J0kvqXx77Ky8XAK9bavdban4DluP+nCc9a+z9r7X+zt7cDi3GzkOp1lcMx9lNekvk1Za21O7I/LJr9ZoHzcdPZw9GvqXxPdx+vjT+36X+P9QJKRhb40BgzL3uKY4Cq1tr/gftPCFTxli625LVf9DrLXd/sU9TP5bhcpH0FZJ9iPQ13hKbXVR6O2E+g19RRjDFFjDHzgY3AdNwZjy3W2qzskpz747Dp7oED093nKl4bf76m9k1yZ1trW+FWQ7zNGHOu70BxSK+zo40D6gMtgf8Bj2Y/nvT7yhhTGngDuN1au+1Ypbk8ljT7Kpf9pNdULqy1+6y1LXGz3LYBTsmtLPt9RPsqXht/fqb/TWrW2vXZ7zcCb+FeOD8fOKWY/X6jv4QxJa/9otfZEay1P2f/QtoPPMOhU69Jva+MMUVxzez/rLVvZj+s19URcttPek0dm7V2C/Ap7hp/+ezp7OHw/RHRdPfx2vjzM/1v0jLGpBljyhzYBv4fsIjDp0S+Dvi3n4QxJ6/9MgXolT0K+wxg64FTt8nqiGvRl+JeV+D2Vffs0cX1gIbA7Gjn8yH7WuqzwGJr7cgcn9LrKoe89pNeU0czxlQ2xpTP3i4JXIAbE/EJbjp7OPo1lf/p7n2PXizAqMdOuFGhPwL3+s4TS2+4ux2+zX777sD+wV3zmQEsy35fwXdWD/tmEu50Yibur+Teee0X3OmzsdmvsYVAuu/8MbCvXszeFwuyf9mcmKP+3ux9tRS40Hf+KO6ndrjTqguA+dlvnfS6yvd+0mvq6H3VHPgme58sAv6S/fhJuD9+lgOTgeLZj5fI/nh59udPOtbza8peERGRJBKvp/pFREQkADV+ERGRJKLGLyIikkTU+EVERJKIGr+IiEgSUeMXERFJImr8IiIiSUSNX0RCZ4yxxpgXc3ycaoz5xRgzLcdj+7LXY19kjJlsjCnlJ61IYlPjF5Fo2Ak0zZ5+FKAjsO6Imt3W2pbW2qZABnBzNAOKJAs1fpEEYIxpYYz53BjzvTFmf/YR9oMx9tzvARdlb/fATQmcly+ABtnf/+3s5aW/y7HEtIgElHr8EhGJZcaYEsCrQC9r7WxjzN9xc3c/EGPP/Qrwl+zT+82B54BzcvmeqbjlpN/PfuiP1trfss8WzDHGvGGt3RTg+4sIOuIXSQQXAP+11h5YuWwBUAGoZ4x51hjzem5fZIz5KPt6+pFvF+fjuRsbY540xrxujLklPyGttQuAurij/XdzKSlpjJkPzAVW41ZyA+hvjPkW+Bq39GjD/Hw/EcmdjvhF4l9T3OpmB7TCNesVQO+8Gr+19oICPPdi4GZjTApuDfX8mgKMANrjVq/Labe1tmXOB4wx7XF/fJxprd1ljPkUd8ZBRALSEb9I/NuEO3WOMaYRcBnutHqoz22M6Qp8iVtyluzHZhhjahzj+Z4D/matXXiMmpzKAZuzm35j4IzIfwQRyUmNXyT+TQJKG2MWAU8DPQrxGniez22tnWKtPQu4GiD76L8B8FteT2atXWutHR3B938fSDXGLAD+jjvdLyIFYKy1vjOISAiMMRWBh3C3zo231v6zEJ+7Pe7ovziwwFo71hjTFDcQ787C+j4iUvjU+EVERJKITvWLiIgkETV+ERGRJKLGLyIikkTU+EVERJKIGr+IiEgSUeMXERFJImr8IiIiSUSNX0REJIn8f6p5LNCCrvSrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x928.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Input parameters\n",
    "rho=2670\n",
    "rhow=1000\n",
    "g=9.8\n",
    "h=10000\n",
    "sig_v=rho*g*h\n",
    "sig_h=rhow*g*h\n",
    "mu=0.75\n",
    "C=10e6\n",
    "T=5e6\n",
    "theta2=(90+np.arctan(mu)*180/np.pi)*np.pi/180\n",
    "\n",
    "######################### TECTONIC REGIMES ####################################\n",
    "####################### 1. REVERSE FAULTING ###################################\n",
    "diffP=np.linspace(0,300,3000)*1e6\n",
    "sigma3=sig_v\n",
    "sigma1=diffP+sigma3\n",
    "\n",
    "#Extension failure\n",
    "lv=extension_failure(sigma3,T,sig_v)\n",
    "ef=np.where(diffP<4*T)[0]\n",
    "lv=lv*np.ones(len(ef))\n",
    "\n",
    "fig=plt.figure('Pore fluid factor vs. diff. stress',figsize=(8,12.9))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(diffP[ef]*1e-6,lv,c='r',lw=2,ls='-')\n",
    "#\n",
    "#Hybrid extensional-shear failure\n",
    "lamv=hybrid_shear_failure(diffP,sigma1,sigma3,T,sig_v)\n",
    "hesf=np.where((diffP>=4*T)&(diffP<5.7*T))[0]\n",
    "plt.plot(diffP[hesf]*1e-6,lamv[hesf],c='g',lw=2,ls='-')\n",
    "\n",
    "#Brittle Shear Failure\n",
    "lam=brittle_shear_failure(diffP,sigma1,sigma3,T,C,mu,sig_v)\n",
    "\n",
    "bsf=np.where(diffP>=5.7*T)[0]\n",
    "plt.plot(diffP[bsf]*1e-6,lam[bsf],c='b',lw=2,ls='-',label='reverse')\n",
    "\n",
    "####################### 2. NORMAL FAULTING ####################################\n",
    "sigma1=sig_v\n",
    "sigma3=sigma1-diffP\n",
    "#Extension failure \n",
    "lv=extension_failure(sigma3,T,sig_v)\n",
    "ef=np.where(diffP<4*T)[0]\n",
    "#lv=lv*np.ones(len(ef))\n",
    "ax.plot(diffP[ef]*1e-6,lv[ef],c='r',lw=2,ls='--')\n",
    "#\n",
    "#Hybrid extensional-shear failure\n",
    "lamv=hybrid_shear_failure(diffP,sigma1,sigma3,T,sig_v)\n",
    "hesf=np.where((diffP>=4*T)&(diffP<5.7*T))[0]\n",
    "ax.plot(diffP[hesf]*1e-6,lamv[hesf],c='g',lw=2,ls='--')\n",
    "\n",
    "#Brittle Shear Failure\n",
    "lam=brittle_shear_failure(diffP,sigma1,sigma3,T,C,mu,sig_v)\n",
    "\n",
    "bsf=np.where(diffP>=5.7*T)[0]\n",
    "ax.plot(diffP[bsf]*1e-6,lam[bsf],c='b',lw=2,ls='--',label='normal')\n",
    "\n",
    "######################## 3. STRIKE-SLIP FAULTING ##############################\n",
    "sigma3=sig_v-diffP/2\n",
    "sigma1=sig_v+diffP/2\n",
    "#\n",
    "#Extension failure \n",
    "lv=extension_failure(sigma3,T,sig_v)\n",
    "ef=np.where(diffP<4*T)[0]\n",
    "ax.plot(diffP[ef]*1e-6,lv[ef],c='r',lw=2,ls=':')\n",
    "#\n",
    "#Hybrid extensional-shear failure\n",
    "lamv=hybrid_shear_failure(diffP,sigma1,sigma3,T,sig_v)\n",
    "hesf=np.where((diffP>=4*T)&(diffP<5.7*T))[0]\n",
    "ax.plot(diffP[hesf]*1e-6,lamv[hesf],c='g',lw=2,ls=':')\n",
    "\n",
    "#Brittle Shear Failure\n",
    "lam=brittle_shear_failure(diffP,sigma1,sigma3,T,C,mu,sig_v)\n",
    "\n",
    "bsf=np.where(diffP>=5.7*T)[0]\n",
    "ax.plot(diffP[bsf]*1e-6,lam[bsf],c='b',lw=2,ls=':',label='strike-slip')\n",
    "\n",
    "plt.axis([0,300,0,1.1])\n",
    "plt.ylabel('$\\lambda_V$')\n",
    "plt.xlabel('$\\sigma_1-\\sigma_3$, MPa')\n",
    "\n",
    "ax.axvline(4*T*1e-6,0,1.1,ls='--',lw=1)\n",
    "ax.axvline(5.7*T*1e-6,0,1.1,ls='--',lw=1)\n",
    "ax.axhline(sig_h/sig_h,0,300,ls='--',lw=1) #Lythostatic\n",
    "ax.axhline(sig_h/sig_v,0,300,ls='--',lw=1) #Hydrostatic\n",
    "ax.text(120,sig_h/sig_h,'lythostatic $P_f$',fontsize=12)\n",
    "ax.text(200,sig_h/sig_v,'hydrostatic $P_f$',fontsize=12)\n",
    "ax.text(4*T*1e-6,0.1,'$4T$',horizontalalignment='center',rotation=90,fontsize=12)\n",
    "ax.text(5.7*T*1e-6,0.1,'$5.7T$',horizontalalignment='center',rotation=90,fontsize=12)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interactive plot\n",
    "\n",
    "The sliders help vary the constants of the medium with the differential pressure ($diffP$) going from $0$ to $300~MPa$. The material properties $C$ and $T$ are in units of $MPa$, while the depth ($h$) is in meters.  The following conditions are shown: \n",
    "\n",
    "### Normal failure conditions\n",
    "\n",
    "The maximum stress ($\\sigma_1$) is equal to the vertical stress ($\\sigma_v$).\n",
    "\n",
    "$$\\sigma_1=\\sigma_v$$\n",
    "$$\\sigma_3=\\sigma_1-diffP $$\n",
    "\n",
    "### Reverse failure conditions\n",
    "\n",
    "The minimum stress ($\\sigma_3$) is equal to the vertical stress. \n",
    "\n",
    "$$\\sigma_3=\\sigma_v$$\n",
    "$$\\sigma_1=\\sigma_3+diffP $$\n",
    "\n",
    "### Strike-slip failure conditions\n",
    "\n",
    "The strike slip regime in the plots shown assumes that $\\sigma_2 \\approx (\\sigma_1+\\sigma_3)/2$.\n",
    "\n",
    "$$\\sigma_1=\\sigma_v+diffP/2 $$\n",
    "$$\\sigma_3=\\sigma_v-diffP/2 $$\n",
    "\n",
    "  In the interactive plot below, the start of the brittle shear failure is given by:\n",
    "\n",
    "$$\\frac{2C}{sin(2\\theta_{opt})}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "260f7bf14d4744b3a83a0dedb5aad6b4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=10.0, description='C', max=18.0, min=2.0, step=0.5), FloatSlider(value…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interactive(lambdav_diffP,C=(2,18,0.5),T=(1,15,0.5),mu=(0,0.9,0.15),h=(1000,40000,500),continuous_update=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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