docs/tutorials/eos/python/core_user_defined_eos.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing an equation of state in python\n",
    "\n",
    "> In `FeOs`, you can implement your equation of state in python, register it to the Rust backend, and compute properties and phase equilbria as if you implemented it in Rust.\n",
    "> In this tutorial, we will implement the Peng-Robinson equation of state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of contents <a id=\"toc\"/>\n",
    "\n",
    "- [Implementation](#Implementation)\n",
    "- [Computing properties](#Computing-properties)\n",
    "- [Critical point](#Critical-point)\n",
    "- [Phase equilibria and phase diagrams](#Phase-equilibria-and-phase-diagrams)\n",
    "- [Mixtures](#Mixtures)\n",
    "- [Comparison to Rust implementation](#Comparison-to-Rust-implementation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from feos.eos import *\n",
    "from feos.si import *\n",
    "import numpy as np\n",
    "\n",
    "optional = True\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "if optional:\n",
    "    import matplotlib.pyplot as plt\n",
    "    import pandas as pd\n",
    "    import seaborn as sns\n",
    "\n",
    "    sns.set_style(\"ticks\")\n",
    "    sns.set_palette(\"Dark2\")\n",
    "    sns.set_context(\"talk\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation <a id=\"Implementation\"/>\n",
    "[↑ Back to top](#toc)\n",
    "\n",
    "To implement an equation of state in python, we have to define a `class` which has to have the following methods:\n",
    "\n",
    "```python\n",
    "class MyEquationOfState:\n",
    "    def helmholtz_energy(self, state: StateHD) -> D\n",
    "    \n",
    "    def components(self) -> int\n",
    "    \n",
    "    def subset(self, indices: List[int]) -> Self\n",
    "    \n",
    "    def molar_weight(self) -> SIArray1\n",
    "    \n",
    "    def max_density(self, moles: SIArray1) -> f64\n",
    "```    \n",
    "\n",
    "- `components(self) -> int`: Returns the number of components (usually inferred from the shape of the input parameters).\n",
    "- `molar_weight(self) -> SIArray1`: Returns an `SIArray1` with size equal to the number of components containing the molar mass of each component.\n",
    "- `max_density(self, moles: np.ndarray[float]) -> float`: Returns the maximum allowed number density in units of `molecules/Angstrom³`.\n",
    "- `subset(self, indices: List[int]) -> self`: Returns a new equation of state with parameters defined in `indices`.\n",
    "- `helmholtz_energy(self, state: StateHD) -> Dual`: Returns the helmholtz energy as (hyper)-dual number given a `StateHD`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "SQRT2 = np.sqrt(2)\n",
    "\n",
    "class PyPengRobinson: \n",
    "    def __init__(\n",
    "        self, critical_temperature, critical_pressure, \n",
    "        acentric_factor, molar_weight, delta_ij=None\n",
    "    ):\n",
    "        \"\"\"Peng-Robinson Equation of State\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        critical_temperature : SIArray1\n",
    "            critical temperature of each component.\n",
    "        critical_pressure : SIArray1\n",
    "            critical pressure of each component.\n",
    "        acentric_factor : np.array[float] \n",
    "            acentric factor of each component (dimensionless).\n",
    "        molar_weight: SIArray1\n",
    "            molar weight of each component.\n",
    "        delta_ij : np.array[[float]], optional\n",
    "            binary parameters. Shape=[n, n], n = number of components.\n",
    "            defaults to zero for all binary interactions.\n",
    "            \n",
    "        Raises\n",
    "        ------\n",
    "        ValueError: if the input values have incompatible sizes.\n",
    "        \"\"\"\n",
    "        self.n = len(critical_temperature)\n",
    "        if len(set((\n",
    "            len(critical_temperature), \n",
    "            len(critical_pressure), \n",
    "            len(acentric_factor)\n",
    "        ))) != 1:\n",
    "            raise ValueError(\"Input parameters must all have the same lenght.\")\n",
    "        \n",
    "        self.tc = critical_temperature / KELVIN\n",
    "        self.pc = critical_pressure / PASCAL\n",
    "        self.omega = acentric_factor\n",
    "        self.mw = molar_weight / GRAM * MOL\n",
    "\n",
    "        self.a_r = (0.45724 * critical_temperature**2 * RGAS \n",
    "                    / critical_pressure / ANGSTROM**3 / NAV / KELVIN)\n",
    "        self.b = (0.07780 * critical_temperature * RGAS \n",
    "                  / critical_pressure / ANGSTROM**3 / NAV)\n",
    "        self.kappa = (0.37464 \n",
    "                      + (1.54226 - 0.26992 * acentric_factor) * acentric_factor)\n",
    "        self.delta_ij = (np.zeros((self.n, self.n)) \n",
    "                         if delta_ij is None else delta_ij)\n",
    "        \n",
    "    def helmholtz_energy(self, state):\n",
    "        \"\"\"Return helmholtz energy.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        state : StateHD\n",
    "            The thermodynamic state.\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        helmholtz_energy: float | any dual number\n",
    "            The return type depends on the input types.\n",
    "        \"\"\"      \n",
    "        n = np.sum(state.moles)\n",
    "        x = state.molefracs\n",
    "        tr = 1.0 / self.tc * state.temperature\n",
    "        ak = ((1.0 - np.sqrt(tr)) * self.kappa + 1.0)**2 * self.a_r\n",
    "        ak_mix = 0.0\n",
    "        if self.n > 1:\n",
    "            for i in range(self.n):\n",
    "                for j in range(self.n):\n",
    "                    ak_mix += (np.sqrt(ak[i] * ak[j]) \n",
    "                               * (x[i] * x[j] * (1.0 - self.delta_ij[i, j])))\n",
    "        else:\n",
    "            ak_mix = ak[0]\n",
    "        b = np.sum(x * self.b)\n",
    "        v = state.volume\n",
    "        rho = np.sum(state.partial_density)\n",
    "        a = n * (-np.log(1.0 - b * rho) \n",
    "                 - ak_mix / (b * SQRT2 * 2.0 * state.temperature) \n",
    "                 * np.log((1.0 + (1.0 + SQRT2) * b * rho) / (1.0 + (1.0 - SQRT2) * b * rho)))\n",
    "        return a\n",
    "    \n",
    "    def components(self) -> int: \n",
    "        \"\"\"Number of components.\"\"\"\n",
    "        return self.n\n",
    "    \n",
    "    def subset(self, i: [int]):\n",
    "        \"\"\"Return new equation of state containing a subset of all components.\"\"\"\n",
    "        if self.n > 1:\n",
    "            tc = self.tc[i] \n",
    "            pc = self.pc[i]\n",
    "            mw = self.mw[i]\n",
    "            omega = self.omega[i]\n",
    "            return PyPengRobinson(\n",
    "                SIArray1(tc * KELVIN), \n",
    "                SIArray1(pc * PASCAL), \n",
    "                omega, \n",
    "                SIArray1(mw * GRAM / MOL)\n",
    "            )\n",
    "        else:\n",
    "            return self\n",
    "        \n",
    "    def molar_weight(self) -> SIArray1:\n",
    "        return SIArray1(self.mw * GRAM / MOL)\n",
    "    \n",
    "    def max_density(self, moles:[float]) -> float:\n",
    "        b = np.sum(moles * self.b) / np.sum(moles);\n",
    "        return 0.9 / b "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing properties <a id=\"Computing-properties\"/>\n",
    "[↑ Back to top](#toc)\n",
    "\n",
    "Let's compute some properties. First, we have to instanciate the class and register it to Rust.\n",
    "This is done using the `EquationOfState.python` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "tc = SIArray1(369.96 * KELVIN)\n",
    "pc = SIArray1(4250000.0 * PASCAL)\n",
    "omega = np.array([0.153])\n",
    "molar_weight = SIArray1(44.0962 * GRAM / MOL)\n",
    "\n",
    "# create an instance of our python class and hand it over to rust\n",
    "pr = PyPengRobinson(tc, pc, omega, molar_weight)\n",
    "eos = EquationOfState.python(pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thermodynamic state: the `State` object\n",
    "\n",
    "Before we can compute a property, we create a `State` object. This can be done in several ways depending on what control variables we need.\n",
    "If no total amount of substance is defined, it is set to $n = \\frac{1}{N_{AV}}$.\n",
    "For possible input combinations, you can inspect the signature of the constructor using `State?`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mInit signature:\u001b[0m \u001b[0mState\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m/\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m     \n",
       "A thermodynamic state at given conditions.\n",
       "\n",
       "Parameters\n",
       "----------\n",
       "eos : Eos\n",
       "    The equation of state to use.\n",
       "temperature : SINumber, optional\n",
       "    Temperature.\n",
       "volume : SINumber, optional\n",
       "    Volume.\n",
       "density : SINumber, optional\n",
       "    Molar density.\n",
       "partial_density : SIArray1, optional\n",
       "    Partial molar densities.\n",
       "total_moles : SINumber, optional\n",
       "    Total amount of substance (of a mixture).\n",
       "moles : SIArray1, optional\n",
       "    Amount of substance for each component.\n",
       "molefracs : numpy.ndarray[float]\n",
       "    Molar fraction of each component.\n",
       "pressure : SINumber, optional\n",
       "    Pressure.\n",
       "molar_enthalpy : SINumber, optional\n",
       "    Molar enthalpy.\n",
       "molar_entropy : SINumber, optional\n",
       "    Molar entropy.\n",
       "molar_internal_energy: SINumber, optional\n",
       "    Molar internal energy\n",
       "density_initialization : {'vapor', 'liquid', SINumber, None}, optional\n",
       "    Method used to initialize density for density iteration.\n",
       "    'vapor' and 'liquid' are inferred from the maximum density of the equation of state.\n",
       "    If no density or keyword is provided, the vapor and liquid phase is tested and, if\n",
       "    different, the result with the lower free energy is returned.\n",
       "initial_temperature : SINumber, optional\n",
       "    Initial temperature for temperature iteration. Can improve convergence\n",
       "    when the state is specified with pressure and molar entropy or enthalpy.\n",
       "\n",
       "Returns\n",
       "-------\n",
       "State : state at given conditions\n",
       "\n",
       "Raises\n",
       "------\n",
       "Error\n",
       "    When the state cannot be created using the combination of input.\n",
       "\u001b[0;31mType:\u001b[0m           type\n",
       "\u001b[0;31mSubclasses:\u001b[0m     \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use input variables other than $\\mathbf{N}, V, T$ (the natural variables of the Helmholtz energy), creating a state is an iterative procedure.\n",
    "For example, we can create a state for a give $T, p$, which will result in a iteration of the volume (density)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.6605\\times10^{-24}\\,\\mathrm{ mol}$"
      ],
      "text/plain": [
       "1.6605390671738466e-24  mol"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# If no amount of substance is given, it is set to 1/NAV.\n",
    "s = State(eos, temperature=300*KELVIN, pressure=1*BAR)\n",
    "s.total_moles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1\\,\\mathrm{ mol}$"
      ],
      "text/plain": [
       "1  mol"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_pt = State(\n",
    "    eos, \n",
    "    temperature=300*KELVIN, \n",
    "    pressure=1*BAR, \n",
    "    total_moles=1*MOL\n",
    ")\n",
    "s_pt.total_moles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use other variables as well. For example, we can create a state at given $h, p$ (using the enthalpy from the prior computation as input):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_ph = State(\n",
    "    eos, \n",
    "    pressure=1*BAR, \n",
    "    molar_enthalpy=s_pt.molar_enthalpy()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rel. dev.\n",
      "entropy    :  1.2028878239185388e-16\n",
      "density    :  -1.8532974044002563e-15\n",
      "temperature:  1.5158245029548805e-15\n"
     ]
    }
   ],
   "source": [
    "# check if states are equal\n",
    "print(\"rel. dev.\")\n",
    "print(\n",
    "    \"entropy    : \", \n",
    "    (s_ph.molar_entropy() - s_pt.molar_entropy()) / s_pt.molar_entropy()\n",
    ")\n",
    "print(\n",
    "    \"density    : \", \n",
    "    (s_ph.mass_density() - s_pt.mass_density()) / s_pt.mass_density()\n",
    ")\n",
    "print(\n",
    "    \"temperature: \",\n",
    "    (s_ph.temperature - s_pt.temperature) / s_pt.temperature\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Critical point <a id=\"Critical-point\"/>\n",
    "[↑ Back to top](#toc)\n",
    "\n",
    "To generate a state at critical conditions, we can use the `critical_point` constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Critical point\n",
      "temperature:  369.9506174234607 K\n",
      "density    :  198.1862458057177 kg/m³\n",
      "pressure   :  4.249677749116942 MPa\n"
     ]
    }
   ],
   "source": [
    "s_cp = State.critical_point(eos)\n",
    "print(\"Critical point\")\n",
    "print(\"temperature: \", s_cp.temperature)\n",
    "print(\"density    : \", s_cp.mass_density())\n",
    "print(\"pressure   : \", s_cp.pressure())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phase equilibria and phase diagrams<a id=\"Phase-equilibria-and-phase-diagrams\"/>\n",
    "[↑ Back to top](#toc)\n",
    "\n",
    "We can also create an object, `PhaseEquilibrium`, that contains states that are in equilibrium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "||temperature|density|\n",
       "|-|-|-|\n",
       "|phase 1|300.00000 K|488.99014  mol/m³|\n",
       "|phase 2|300.00000 K|11.53399 kmol/m³|\n"
      ],
      "text/plain": [
       "phase 0: T = 300.00000 K, ρ = 488.99014  mol/m³\n",
       "phase 1: T = 300.00000 K, ρ = 11.53399 kmol/m³"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vle = PhaseEquilibrium.pure(eos, 300.0*KELVIN)\n",
    "vle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each phase is a `State` object. We can simply access these states and compute properties, just like before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "|temperature|density|\n",
       "|-|-|\n",
       "|300.00000 K|11.53399 kmol/m³|"
      ],
      "text/plain": [
       "T = 300.00000 K, ρ = 11.53399 kmol/m³"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vle.liquid # the high density phase `State`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "|temperature|density|\n",
       "|-|-|\n",
       "|300.00000 K|488.99014  mol/m³|"
      ],
      "text/plain": [
       "T = 300.00000 K, ρ = 488.99014  mol/m³"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vle.vapor # the low density phase `State`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Heat of vaporization:  14.782343503305114 kJ/mol\n",
      "for T = 300 K\n",
      "and p = 9.95 bar\n"
     ]
    }
   ],
   "source": [
    "# we can now easily compute any property:\n",
    "print(\"Heat of vaporization: \", vle.vapor.molar_enthalpy() - vle.liquid.molar_enthalpy())\n",
    "print(\"for T = {}\".format(vle.liquid.temperature))\n",
    "print(\"and p = {:.2f} bar\".format(vle.liquid.pressure() / BAR))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also easily compute **vapor pressures** and **boiling temperatures**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vapor pressure      (T = 300 K): 994.7761635610093 kPa\n",
      "boiling temperature (p = 3 bar): 247.84035574956746 K\n"
     ]
    }
   ],
   "source": [
    "# This also works for mixtures, in which case the pure component properties are computed.\n",
    "# Hence, the result is a list - that is why we use an index [0] here.\n",
    "print(\"vapor pressure      (T = 300 K):\", PhaseEquilibrium.vapor_pressure(eos, 300*KELVIN)[0])\n",
    "print(\"boiling temperature (p = 3 bar):\", PhaseEquilibrium.boiling_temperature(eos, 2*BAR)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Phase Diagram\n",
    "\n",
    "We could repeatedly compute `PhaseEquilibrium` states for different temperatures / pressures to generate a phase diagram.\n",
    "Because this a common task, there is a object for that as well.\n",
    "\n",
    "The `PhaseDiagram` object creates multiple `PhaseEquilibrium` objects (`npoints` of those) between a given lower temperature and the critical point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "dia = PhaseDiagram.pure(eos, 230.0 * KELVIN, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access each `PhaseEquilbrium` and then conveniently comput any property we like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "enthalpy_of_vaporization = [\n",
    "    (vle.vapor.molar_enthalpy() - vle.liquid.molar_enthalpy()) / (KILO * JOULE) * MOL \n",
    "    for vle in dia.states\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 4))\n",
    "sns.lineplot(x=dia.vapor.temperature / KELVIN, y=enthalpy_of_vaporization, ax=ax);\n",
    "ax.set_ylabel(r\"$\\Delta^{LV}h$ / kJ / mol\")\n",
    "ax.set_xlabel(r\"$T$ / K\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A more convenient way is to create a dictionary. The dictionary can be used to build pandas `DataFrame` objects.\n",
    "This is a bit less flexible, because the units of the properties are rigid. You can inspect the method signature to check what units are used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0mdia\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_dict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Returns the phase diagram as dictionary.\n",
       "\n",
       "Units\n",
       "-----\n",
       "temperature : K\n",
       "pressure : Pa\n",
       "densities : mol / m³\n",
       "molar enthalpies : kJ / mol\n",
       "molar entropies : kJ / mol / K\n",
       "\n",
       "Returns\n",
       "-------\n",
       "dict[str, list[float]]\n",
       "    Keys: property names. Values: property for each state.\n",
       "\n",
       "Notes\n",
       "-----\n",
       "xi: liquid molefraction of component i\n",
       "yi: vapor molefraction of component i\n",
       "i: component index according to order in parameters.\n",
       "\u001b[0;31mType:\u001b[0m      builtin_function_or_method\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dia.to_dict?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>density liquid</th>\n",
       "      <th>density vapor</th>\n",
       "      <th>molar enthalpy vapor</th>\n",
       "      <th>temperature</th>\n",
       "      <th>molar enthalpy liquid</th>\n",
       "      <th>pressure</th>\n",
       "      <th>molar entropy liquid</th>\n",
       "      <th>molar entropy vapor</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14125.988947</td>\n",
       "      <td>52.208491</td>\n",
       "      <td>22.140400</td>\n",
       "      <td>230.000000</td>\n",
       "      <td>3.376293</td>\n",
       "      <td>96625.278174</td>\n",
       "      <td>0.039106</td>\n",
       "      <td>0.120689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14118.006852</td>\n",
       "      <td>52.811929</td>\n",
       "      <td>22.135738</td>\n",
       "      <td>230.280462</td>\n",
       "      <td>3.383021</td>\n",
       "      <td>97830.133956</td>\n",
       "      <td>0.039135</td>\n",
       "      <td>0.120569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14110.010220</td>\n",
       "      <td>53.420767</td>\n",
       "      <td>22.131064</td>\n",
       "      <td>230.560924</td>\n",
       "      <td>3.389761</td>\n",
       "      <td>99046.729400</td>\n",
       "      <td>0.039164</td>\n",
       "      <td>0.120449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14101.999011</td>\n",
       "      <td>54.035036</td>\n",
       "      <td>22.126380</td>\n",
       "      <td>230.841386</td>\n",
       "      <td>3.396514</td>\n",
       "      <td>100275.143120</td>\n",
       "      <td>0.039193</td>\n",
       "      <td>0.120330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>14093.973182</td>\n",
       "      <td>54.654773</td>\n",
       "      <td>22.121683</td>\n",
       "      <td>231.121849</td>\n",
       "      <td>3.403278</td>\n",
       "      <td>101515.453964</td>\n",
       "      <td>0.039221</td>\n",
       "      <td>0.120211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   density liquid  density vapor  molar enthalpy vapor  temperature  \\\n",
       "0    14125.988947      52.208491             22.140400   230.000000   \n",
       "1    14118.006852      52.811929             22.135738   230.280462   \n",
       "2    14110.010220      53.420767             22.131064   230.560924   \n",
       "3    14101.999011      54.035036             22.126380   230.841386   \n",
       "4    14093.973182      54.654773             22.121683   231.121849   \n",
       "\n",
       "   molar enthalpy liquid       pressure  molar entropy liquid  \\\n",
       "0               3.376293   96625.278174              0.039106   \n",
       "1               3.383021   97830.133956              0.039135   \n",
       "2               3.389761   99046.729400              0.039164   \n",
       "3               3.396514  100275.143120              0.039193   \n",
       "4               3.403278  101515.453964              0.039221   \n",
       "\n",
       "   molar entropy vapor  \n",
       "0             0.120689  \n",
       "1             0.120569  \n",
       "2             0.120449  \n",
       "3             0.120330  \n",
       "4             0.120211  "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_dia = pd.DataFrame(dia.to_dict())\n",
    "data_dia.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have a dataframe, we can store our results or create a nicely looking plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def phase_plot(data, x, y):\n",
    "    fig, ax = plt.subplots(figsize=(12, 6))\n",
    "    if x != \"pressure\" and x != \"temperature\":\n",
    "        xl = f\"{x} liquid\"\n",
    "        xv = f\"{x} vapor\"\n",
    "    else:\n",
    "        xl = x\n",
    "        xv = x\n",
    "    if y != \"pressure\" and y != \"temperature\":\n",
    "        yl = f\"{y} liquid\"\n",
    "        yv = f\"{y} vapor\"\n",
    "    else:\n",
    "        yv = y\n",
    "        yl = y\n",
    "    sns.lineplot(data=data, x=xv, y=yv, ax=ax, label=\"vapor\")\n",
    "    sns.lineplot(data=data, x=xl, y=yl, ax=ax, label=\"liquid\")\n",
    "    ax.set_xlabel(x)\n",
    "    ax.set_ylabel(y)\n",
    "    ax.legend(frameon=False)\n",
    "    sns.despine();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phase_plot(data_dia, \"density\", \"temperature\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phase_plot(data_dia, \"molar entropy\", \"temperature\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixtures <a id=\"Mixtures\"/>\n",
    "[↑ Back to top](#toc)\n",
    "\n",
    "Fox mixtures, we have to add information about the composition, either as molar fraction, amount of substance per component, or as partial densities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# propane, butane mixture\n",
    "tc = np.array([369.96, 425.2]) * KELVIN\n",
    "pc = np.array([4250000.0, 3800000.0]) * PASCAL\n",
    "omega = np.array([0.153, 0.199])\n",
    "molar_weight = np.array([44.0962, 58.123]) * GRAM / MOL\n",
    "\n",
    "pr = PyPengRobinson(tc, pc, omega, molar_weight)\n",
    "eos = EquationOfState.python(pr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "|temperature|density|molefracs\n",
       "|-|-|-|\n",
       "|300.00000 K|40.96869  mol/m³|[0.50000, 0.50000]|"
      ],
      "text/plain": [
       "T = 300.00000 K, ρ = 40.96869  mol/m³, x = [0.50000, 0.50000]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = State(\n",
    "    eos, \n",
    "    temperature=300*KELVIN, \n",
    "    pressure=1*BAR, \n",
    "    molefracs=np.array([0.5, 0.5]), \n",
    "    total_moles=MOL\n",
    ")\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we can compute properties by calling methods on the `State` object. Some return vectors or matrices - for example the chemical potential and its derivative w.r.t amount of substance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-15625.3474516824, -12435.866602695127] J/mol"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.chemical_potential()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.90827975, -0.10593968],\n",
       "       [-0.10593968,  4.85467746]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.dmu_dni() / (KILO * JOULE / MOL**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Phase equilibria can be built from different constructors. E.g. at critical conditions given composition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "|temperature|density|molefracs\n",
       "|-|-|-|\n",
       "|401.65486 K|3.99952 kmol/m³|[0.50000, 0.50000]|"
      ],
      "text/plain": [
       "T = 401.65486 K, ρ = 3.99952 kmol/m³, x = [0.50000, 0.50000]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_cp = State.critical_point(\n",
    "    eos, \n",
    "    moles=np.array([0.5, 0.5])*MOL\n",
    ")\n",
    "s_cp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or at given temperature (or pressure) and composition for bubble and dew points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "||temperature|density|molefracs|\n",
       "|-|-|-|-|\n",
       "|phase 1|350.00000 K|879.47505  mol/m³|[0.67625, 0.32375]|\n",
       "|phase 2|350.00000 K|8.96382 kmol/m³|[0.50000, 0.50000]|\n"
      ],
      "text/plain": [
       "phase 0: T = 350.00000 K, ρ = 879.47505  mol/m³, x = [0.67625, 0.32375]\n",
       "phase 1: T = 350.00000 K, ρ = 8.96382 kmol/m³, x = [0.50000, 0.50000]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vle = PhaseEquilibrium.bubble_point(\n",
    "    eos, \n",
    "    350*KELVIN, \n",
    "    liquid_molefracs=np.array([0.5, 0.5])\n",
    ")\n",
    "vle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to pure substance phase diagrams, there is a constructor for binary systems."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "vle = PhaseDiagram.binary_vle(eos, 350*KELVIN, npoints=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7V3448PvWuO7OLtzaJILx4d0Jq1bb5AovTCGp5UvNEBEREREREalUSqxWlh6K4/3dv7L55EHbeC1PX8Y0j2Jk80hqePiYWOGlKSS1/KkZIiIiIiIiIpVCTlEBC5Ni+CBuHQezztjGw6vXZULL7twc3BY3O9ga92KsViuJiYkkJSUBCkktT3bzX8HWrVuZMWMGiYmJpKen4+3tTbNmzRg3bhw9e/Y859x169bx9ttvEx8fj7e3N/3792fSpEn4+fmZVL2IiIiIiIiY5VhOBh/vWc+nCZvOyQPpW785E1p2p2vdJnazNe7FKCS1YtlNMyQzM5Pg4GBuvfVWatasSWZmJgsXLmTChAm8+eabDB48GIBNmzYxYcIE+vbty2OPPcbJkyd5/fXXSUxMZP78+QqRERERERERqSJ2nz7Gu7t/5dt9Oyj+Qx7I7aEdGB/ejdCAWiZXeHkUklrx7KYZ0qtXL3r16nXOWO/evenbty8LFy60NUNee+01mjZtyltvvWX7DyMwMJB77rmHJUuWMGjQoIouXURERERERCqIYRisOZbEu7t+4ddjybbxmh4+3N2iC6ObR1HdwzFmUygk1Tx20wy5EBcXF3x9fW0hMSkpKcTGxvLMM8+c0yHr1q0btWvXZunSpWqGiIiIiIiIVEKFJcV8s28H7+7+lfi0E7bxZgG1mNDyOoaEtMPDxXECRi8UktqmTRvc3NxMrqxqsLtmiNVqxWq1cvr0aRYuXMiBAwf4+9//DkBiYiIATZs2Pe+6Zs2a2UJmREREREREpHLIKMjjk4RNfLhnPSm5mbbxbnWbcF+rHvQOamb3eSB/pJBU+2B3zZDHHnuMpUuXAuDj48Nbb71Fjx49AM4Jkvkzf39/4uLiLvq6HTt2vOT7ZmVl4evre5VVi4iIiIiISFk6mp3O+7t/ZUHiZnKKCwFwtjhxU3Ab7mt5Ha1rBplc4ZVTSKr9sLtmyFNPPcX48eNJTU3l+++/57HHHuPll1/mxhtvtJ1zsa6fI3UDRURERERE5HxxZ44za9cvfLNvByVnQ1G9XdwYHtaZ8eHdCfIJMLfAq6SQVPtid82QBg0a0KBBAwD69OnD/fffz/PPP8+gQYMICAgAfp8h8kcZGRkXnDHym5iYmEu+71/NHBEREREREZHyYRgGG07sY2bsGn4+mmgbr+3pyz3h3RgZFom/u6eJFV69oqIidu7cybFjxwCFpNoLu2uG/Fnr1q1ZvXo1Z86csWWFJCUl0b1793POS0xMJCIiwowSRUREKiXDMCguLsTFRUFuIiJSPkqsVn46tJt3YtewI/WIbTzUP5AHWvdkSEg73J3t/mvrRSkk1X7Z9X9VhmEQHR2Nn58fAQEBuLi40KpVK7777jvGjBljm060YcMGUlJSGDBggMkVi4iIVA7HstOZ/eX/sBTmgpohIiJSxvKKi/gyeQuzdv3KwazTtvFOtRrxQOue9GvQHCeL4y4fUUiq/bObZsiTTz5JUFAQLVu2pFq1apw6dYpFixaxceNGnn32WVxcSkudNGkS48aN44knnmDYsGGkpKTw+uuv07ZtW66//nqTfwoRERHHZjWsfJIQzZcrZ/O/LZ+wmPpml1SucnJymDJlCkuWLCEzM5PQ0FAeeugh+vbt+5fXLl26lI8++oi9e/cCEBISwpgxYxg0aFB5ly0i4rAyC/OZG7+RD+LWciov2zY+sGE497fqQafajc0rrowoJNUx2E0zJCIigu+++46FCxfadnZp1aoV77zzDn369LGd16VLF2bNmsW0adOYMGEC3t7e9OvXj6eeegpnZ2cTfwIRERHHti/jFE+t+4pj+7cwddtneFqLMBz4qdzlmDhxInFxcUyaNIn69euzaNEiJk6cyKxZs+jZs+dFr1u0aBHPPPMMAwcO5IEHHgDgq6++4vHHHyc3N5fbbruton4EERGHcDI3i9lxa5kXv5GsogIAXJ2cubVJBPe36kHTgFomV1g2FJLqOCyGYRhmF2EPfgtQ/augVRERkcqmyFrCu7t+Zcr2FfjmpjFt23xqF2Ri8a3JXeuDwOJUKT8f16xZw4QJE5g+fTr9+/cHSpfoDh8+nPT0dH766aeLXjtq1CiOHj3KihUrbDe4VquVfv36ERQUxLx5866qJt2PiEhlcyDzNO/u+oXPk7dQUFIMgJeLG6PCIhnfsjt1vS++CYYjUUhq+SqPz0e7mRkiIiIiFS829SiT1n3J7jPH8SnK543di0obIe7eNHjiB9hwv9kllpvly5fj6+t7zpIYi8XC0KFDefbZZ0lOTiY0NPSC17q4uODl5XXOkz4nJye8vLwUiiciAuw+fYyZsWv47sBOrGefv1dz92JceDfGtOhCNXcvkyssOwpJdUxqhoiIiFRBecVFTNm+gnd3/UqJYcW9pJjZ+1dSKysFnF2p9/BXeARX7m3nk5KSCA0NPW/qclhYGFC6U93FmiEjRozg4Ycf5p133mHYsGEALFy4kP379/P3v/+9fAsXEbFj0SkHmLZjNauPJtjGgrwDuK/VddzZtBNerpWnQaCQVMemZoiIiEgV88vRJP6xYREHs84A0NyvBlOTl+NyPA6AOvd+hHer/maWWCHS09Np3LjxeeP+/v624xfTr18/3nnnHZ566ineeustALy8vHj77bfp0aPHRa/7bZrvxfyWmyYi4kgMw2DNsSSm7VjFppQDtvFmAbV4sHVPbglph6tT5cp3VEiq41MzREREpIo4nZ/Nf6N/4Ou924DS4LqJrXtwZ8wCcvasBCBw+BT8ou4ys8wKZbFYrurYunXrePLJJxk8eDADBw6kpKSE7777jieeeIKpU6fSq1evcqhWRMS+WA0rSw/FMX3nz+xIPWIbb1uzPo+06U3/hi0cenvcizl8+DCxsbEKSXVwaoaIiIhUcoZh8GXyVv67+QfSC3IBiKzdmJe6DKXaktdIW18a9ln9pslUG/CImaVWqICAgAvO/sjIyAB+nyHyZ4Zh8PTTTxMVFcXzzz9vG+/RowcnTpzgf//730WbIX8V/PZXM0dEROxBsbWEb/fvZMbOn0lIT7GNd60TwsNte9O9buglG8qOSiGplYuaISIiIpXYvoxU/rFhEeuO7wXAz82DyR0HcVezjqT/8BqpS6cA4N/7Pmrc+l8zS61woaGhLFu2DKvVes7TvMTERACaNWt2wetSU1M5deoUrVq1Ou9Yq1atiI6OpqCgAHd39/IpXETEJAUlxXyRvIV3YtfYlloC9K3fnEfa9qZDrUYmVle+Tp8+zbZt28jLywMUkloZqBkiIiJSCRWWFDNr1y+8vWOVbSvDm4Pb8J/ON1HLy5f0n98n9ct/AuDT+XZqjZpWKZ/iXUr//v358ssvWbVqFf369bONL168mODg4IuGp/r7++Pu7s7OnTvPO7Zjxw4CAgLUCBGRSiWvuIjPEjczM3YNx3NLZ89ZsHBj49ZMbNOLljXqmVxh+VFIauWlZoiIiEglsznlAM+sX2SbuhzkHcCLXYbQt0FzALI2f8XJOQ8C4NWyH3UnzMVSyYLtLkfPnj2JjIxk8uTJpKenU79+fRYvXsyWLVuYOXOm7bxRo0YRHR1NQkLpzghubm7ceeedzJkzh8mTJzNw4ECsVqvt2scee8ykn0hEpGzlFhXyScImZu36hZN5WQC4WJy4tUkED7XpRRP/QJMrLF8XCklt3749Pj4+5hYmZULNEBERkUoiLT+HF7csYUHiZgCcLBbGh3fjyYj+eLuWzlTIiV3K8VkjwLDiEdKZeg9/hcWlak7xtVgszJw5kzfffJMpU6aQmZlJaGgo06dPp0+fPpe89umnnyYkJITPP/+cpUuX4uTkROPGjXn11Ve5+eabK+gnEBEpH9lFBczZs4H3dv/K6fwcoDR0e1jTjjzUuicNfKubXGH5U0hq5WcxDMMwuwh78Ftg2V8Fm4mIiNib3wJS/7f5R84UlN60tqkRxMtdh9KmZn3beXlJ6zny2kCMwlzc6oXT4J8/4+xT45Kvrc/HiqXfbxExU0ZBHh/tWc/suHW2wG13ZxfuataJB1v1pJ5PgLkFVgCFpNqn8vh81MwQERERB5aUfpJ/bFjExhP7AfBxdefp9gMZ3TwK5z88vSo4tIOjb96IUZiLa2Aw9Z9a+peNEBERqRoyCvKYHbeWD+LWkVmYD4CniyujwiK5r1UPanv5mVxhxfhzSGqdOnVo27atQlIrKTVDREREHFBecSFTd6xm1q5fKLKWTuG9ObgNz3W+kTp/umktPJHIkdevx5qXgXNAXYKeWoZLtcobdiciIpfnQk0Qbxc37m7RlQmtulPDo2pkYygktWpSM0RERMTBrD6SwOQN33Aou3Rbw0a+1XmhyxB6BZ2/FWzR6UMceXUAJZkncfKuTv2nluJWK6SiSxYRETtyoSaIj6s797Toyr0tu1PNw9vkCiuOQlKrLjVDREREHMSxnAz+G/09PxyIBUrD7B5s3ZOJbXrj6eJ63vnFGSkceW0gxWcOY/Hwof6TP+Ie1LKiyxYRETtxsSbIuPBujG/ZnWruXiZXWLEUklq1qRkiIiJi54qsJczevZYp21eSW1wIQJc6IbzUZQihAbUueE1J9hmOvDaQohOJWFzcCXr0GzxCOlVk2SIiYifUBDmXQlIF1AwRERGxa+uP7+VfG78hMf0kADU9fPhXp0H8rUkEFovlgteU5GVy5I1BFB6JBWcX6k78Aq8WvSqwahERsQdZhfnMjlvL+7vXqglylkJS5TdqhoiIiNihk7lZ/G/zDyzatx0AJ4uFMc27MCmiP/7unhe9zlqQw7EpN1GwfzNYnKh73yf4tBtcQVWLiIg9yCkq4KM9G5i16xfbFrlVvQmikFT5MzVDRERE7EixtYQ58Rt5fesysooKAGgf2JAXu9xCqxpBl7zWWpjPsam3kpe4FoA64z/At/Pt5V6ziIjYh7ziIubFb2RG7M+czs8BSrfIvadFN+5vdV2VCkb9I4WkyoWoGSIiImIntpw8yD83LGb3meMAVHP34p8db2BY0w44WS4d5mYUF3F85jByd68AoNbo6fh1G13uNYuIiPkKSoqZnxDNtJ2rOZmXBYC7swtjmkfxYOte1PSsul/6Dx8+zK5duyguLgYUkiq/UzNERETEZKfysngpZgmfJ28BwIKF4c068UyHgZf1FM8oKeb4uyPJ2f49ADWHvUZAnwfKtWYRETFfkbWEhUkxTN2ximM5GQC4OTkzPKwzE9v0po6Xn8kVmkchqfJX1AwRERExSbG1hI/3bOCNbcttS2Ja1wjixS5DiAhscFmvYVhLODF7LNmbvwSgxpB/U/2GJ8qtZhERMV+J1co3+3fwxrYVHMw6DYCLxYlhTTvySNs+BPkEmFugyRSSKpdDzRARERETrD++l2c3fktCegoAAe5ePNN+IHc164TzZU7dNaxWUj68l6wN8wGofuM/qH7Ls+VWs4iImMswDJYdiuPVrctsnx9OFgt/axLBY+360si3hskVmkshqXIl1AwRERGpQMdyMnhh8498s38HULokZmRYZ/7efsAVBdsZhsHJuQ+SuXYOANWuf4Iaf/vfRbfbFRERx7buWDIvb13KtlOHbWM3Nm7NpIj+hAbUMrEy+6CQVLlSaoaIiIhUgIKSYmbvXsvbO1aRW1wIlO4S80LULbSueeldYv7MMAxOffIoGT+/D0BAv4nUHPaqGiEiIpXQ1lOHeHXLMtYeT7aN9Q4K4+/tB1zx50dlpZBUuRpqhoiIiJSzVUcS+M+m79iXmQpATQ8fJne8gb+FRvzlLjF/ZhgGqZ89RfrKGQD4976PwBFvqREiIlLJJKSl8OrWpSw9FGcb61y7MU+3H0hknWATK7MfCkmVa6FmiIiISDnZl5HKf6O/Z+WReACcLU6MbdGFJyL64+fmccWvZxgGqQv/TtrSKQD4XTeWWqOmqxEiIlKJHM1O541ty/kieSsGBgCtqtfj6Q4D6RXUTH/mn6WQVLlWaoaIiIiUseyiAt7evorZcWspspYA0LVOCP+NvJkW1etc1WuWNkKeJm3JmwD4dRtF7bHvYtEUYBGRSiEtP4fpO3/m4/gNFJSULvcI8avJ39sPYFDjVlc8k7CyUkiqlBU1Q0RERMqI1bDy9d5tvBizhJN5WQDU9wng2U6DGdSo1VU/zTMMg9TPnyFtyRsA+HYdSe1xH2Bxci6z2kVExBx5xYV8ELeOmbFryCzMB6C2py+PR/TjzqYdcdGf9TYKSZWypGaIiIhIGdh+6jDPbvrWlvLv4ezKxDa9uK9VDzxdXK/6dQ3DIPWLf5D20+sA+HYZQZ3xH6oRIiLi4IqtJXyWFMOUbStIOdtA93Pz4MHWPRkX3g1PFy33+COFpEpZUzNERETkGpzKy+LlLUtYmLTFNnZzcBsmdxxEkE/ANb12aSPkn6T9+BoAvl2GU+fej9QIERFxYIZh8NPB3byydSl7M04B4O7swt3NuzCxTa8r2ma9KlBIqpQXNUNERESuwm9b5U7buZrsogIAwqvX5fnIm4iqE3LNr2+bEfJbIyTqLurc+7EaISIiDmzLyYP8b/OPxJw8CIAFC7eHtufJiP7X3ECvjBSSKuVJzRAREZErYBgGSw7t5v82/8jBrDMAVHP34u/tBzC8WWecy2C6rmEYnPpsEulL3wLUCBERcXT7M1N5ectSfjgQaxvr16A5z3S4nubVri5YuzL7LSQ1OTkZwzAUkirlQs0QERGRyxR35jj/2fQd60/sA8DF4sTdLbrwWLu+BLh7lcl7GIbBqU8fI33FdKA0LFUZISIijulMfg5vbV/JvIRNtt3F2tQI4l+dBtG1bhOTq7NPCkmViqJmiIiIyF84nZ/Nq1uWsSBpM1bDAKBP/TCe6zSY0IBaZfY+htXKyU8eJmPVLAD8rrub2mPfUyNERMTB5BcX8eGe9Uzfudq2Q0x9nwCebn89t4S00Ta5F6GQVKlIaoaIiIhcRGFJMR/tWc9b21eSdTYXJNQ/kH93vpHe9cPK9L0Mq5WUj+8n85cPAPDvdS+1Rs/EohtAERGHYTWsLN63g1e2LOVoTjpQukPMI236cHeLLnhcw+5ilZlCUsUMaoaIiIj8iWEYLDsUx//F/MT+zFQA/N08eCKiP6ObR+FaxjM1DGsJKR/eS+baOaXv1ecBao2cqkaIiIgDiU45wH+jv2dH6hEAXJ2cGdM8ikfb9tEOMZegkFQxi5ohIiIif7Dr9FGej/7BlgvibHFiZFgkkyL6lcvNrFFcxIn3RpMV/TkAAf0fIXD4m1gsljJ/LxERKXuHss7wYsxPfP+HcNSbGrfh6Q4DaexXw8TK7JtCUsVsaoaIiIgAKbmZvLp1KZ8nbcWgNBekV1Aznu00mLBqtcvlPa2F+RyfOYyc7d8DUG3Q36l5+4tqhIiIOICswnym7VzN7N1rKTwbjtquZgP+0/lGOtZuZHJ19i0nJ4dt27aRlpYGKCRVzKFmiIiIVGl5xYW8u+tXZsauIbe4EIBmAbV4ttPgMs8F+SNrQS7Hpg4ld/cKAGoM/S/Vb56sRoiIiJ0rsVpZkLSZ17cuJzU/G4C6Xv78o+P1DAlpq3DUv/DnkNQmTZrQvHlzhaRKhVMzREREqiSrYWXRvh28HLOE47kZANTw8GZSRH/uatYJl3LcwaUkL5NjU24mL/FXAALvfJ1q1z9ebu8nIiJl49djSfw3+gfi004A4OniyoOte3J/qx54uijj4lIUkir2Rs0QERGpcjad2M/zm3+whdy5OTkzLrw7D7ftjZ+bR7m+d0n2GY6+OZj8fdEA1Bo9nYA+D5Tre4qIyLXZn5nK/6J/YNnhPbax20Pb8/f2A6nr7W9iZY5BIalij+ymGbJhwwa++eYbtm3bxokTJ/D396dNmzY8/PDDhIX9Pk151KhRREdHn3f9oEGDmDJlSkWWLCIiDmZfxilejFnCkkO7bWM3Nm7NPzpeTyPf8g+5K04/zpHXr6fwyC6wOFF73Gz8u48p9/cVEZGrk11UwNQdq87JBYms3Zh/d76RNjXrm1yd/btQSGrLli1p1EiZKmI+u2mGLFiwgPT0dO6++26aNGlCamoqs2fP5rbbbmPevHm0a9fOdm7jxo155ZVXzrm+WrVqFVyxiIg4ijP5Oby1fSVz4zdSbFiB0pC75zoPpnPtxhVSQ9Gp/Rx5dQBFp/aBsyt175uHb+fbK+S9RUTkylgNK1/v3c5LMT+RkpcFQJB3AM92GsTgxq2V73QZFJIq9s5umiH//ve/qVHj3Kdy3bt3p2/fvnzwwQdMmzbNNu7h4XFOc0RERORC8ouL+GjPeqbtXE1mYT4ADXyq8Y8O13NTcJsKu5ktOBrHkdcGUpJ+DIubJ/Ue/grv1gMr5L1FROTKbD91mOc2fcfWU4cAcHd24aHWvXigtXJBLpdCUsUR2E0z5M+NEAA/Pz8aNWrEiRMnTKhIREQclWEYfLt/Jy9vWcLh7NInUn5uHjzSpg9jw7vi7lxxH3/5+zZz5M3BWLNP4+TpT9Dj3+LZrHuFvb+IiFyeU3lZvLxlCQuTttjGbmrchn91GkSQT4B5hTkQhaSKI7GbZsiFnDlzhqSkJAYPHnzO+P79++nUqRM5OTnUr1+fIUOGcO+99+Lq6mpSpSIiYi+iUw7wfPQPbE89DICLxYkxLbrwWNs+VPPwrtBacvf8zNG3b8HIz8bZN5CgSUvwaNSuQmsQEZFLK7KW8GHcOqZsX0l2UQEALarV4fmom+lSJ8Tk6hzHmTNn2Lp1q0JSxWHYbTPEMAyeffZZrFYr48aNs4136NCBQYMGERISQm5uLitWrGDq1Kns3r2bGTNmXPT1OnbseMn3y8rKwtfXt8zqFxGRipWcfpKXtixh6aE429gNjVryjw43EOJf8U+ksrYs4sQ7IzCKC3Cp3oD6Ty3FrW7YX18oIiIVZt3xvTy78RsS008CEODuxd/bD2B4OW+xXpkoJFUcld02Q1599VVWrFjBSy+9RJMmTWzjjz322Dnn9e7dm5o1azJr1ixiYmL+sukhIiKVy8ncLKZsX8H8xM2UnA1HjQhswLOdKi4c9c8y1swm5eMHwLDiWieM+k8twbVGQ1NqERGR8x3PyeD/Nv/IN/t3AOBksTAqLIpJ7ftTzd3L5Ooch0JSxZHZZTNkypQpfPjhh0yePJlbb731L88fMmQIs2bNYvv27RdthsTExFzyNdREERFxLDlFBby761dm7fqF3OJCABr51uAfHa9ncKNWpiT9G4bBme9f5vRX/wLAPbgT9Z/4HmdfrZUWEbEHRdYSPti9jinbV5Bz9rOjQ2BDXuhyC61qBJlcnWNRSKo4Ortrhrz99tvMmjWLp556itGjR1/WNVZr6ZNA/Y8nIlL5FVtL+Cwxhje2L+dUXjYA1d29eaxdH0aGReJWgeGof2RYrZxa8CTpy6cC4NWyH/Ue/gonDz0dExGxB39eElPDw5vJHW/gttD2OFn0PeJyKSRVKgu7aoZMnz6dmTNn8uijjzJ+/PjLvu6bb74BoG3btuVVmoiImMwwDJYdiuOlLUtIzjgFlG53OKHldTzQuid+bh7m1VZcyInZ95C1cQEAvpHDqHPvx1i0BaOIiOkutCRmdPMoJkX0J0BLYq6IQlKlMrGbZsiHH37ItGnT6N27N127dmX79u22Y25uboSHhxMTE8N7773HgAEDCAoKIjc3l5UrV/L1119z/fXX06FDB/N+ABERKTebUw7wYsxPbD55EAALFu5o2oEnI/pTz9vf1NpK8jI5Pv02cnevBCCg70MEjngLi2YrioiYqthawsd7NvDa1mW2JTEdazXihahbaFmjnsnVORaFpEplZDfNkNWrV9v+/tuvfxMUFMSqVasIDAwEYOrUqaSlpeHk5ERwcDDPPPMMo0aNqvCaRUSkfCWmp/DKlqXn7BDTOyiMf3a8gRbV65hYWani9OMcffNGCg5tB6DGrc9T/aZ/mpJXIiIiv9t66hD/WL+I3WeOA1oScy0UkiqVld00Q+bNm/eX5zRq1Ij33nuvAqoREREzHcvJ4M1ty/k8eQtWwwCgbc36/LPjDXSr2+Qvrq4YhcfiOfLGIIpPHwQnZ2qPfRf/68aaXZaISJWWUZDHK1uXMi9+EwYGFiyMDOvM0x0GaknMVVBIqlRmdtMMERERySjIY0bsz3wQt46CktIbr2C/mjzdYaBpO8RcSF7SOo6+NQRrzhks7t7Ue2gh3m1uMLssEZEqyzAMFu/bwfObv7eFa4dXr8tLXYbSoZa2Nr9SFwpJbdeunW2mvkhloGaIiIiYLr+4iDnxG5i6YzUZhaWhbIGePjzerh93NeuEq5OzyRX+LmvLIk7MGolRlI+zXy2CHv8Oj2Btzy4iYpZ9GalM3riYX48lA+Dl4sZT7fsztkVXXOzo88NRKCRVqgo1Q0RExDTF1hK+TN7KG9tWcDw3AwBvFzceaN2Te1t2x9vV3eQKf2cYBunLpnLqsyfBMHCt3ZSgJ3/ErVaI2aWJiFRJBSXFzNj5MzNif7bNJryhUUv+2/km6vkEmFqbI1JIqlQ1aoaIiEiFMwyDJYd28+qWZSRlnATA1cmZEWGdeaxtX2p62lcom2Et4dSnj5O+cgYAHk2iqPfoYlz8NF1YRMQMm07s5+/rv2bv2a3W6/sE8H9Rt9CvQQuTK3NMCkmVqkjNEBERqVDrj+/lpS1L2HbqMFC6Te7QJu14MqIfjXxrmFzd+az52Rx/Zzg5O34AwKfjrdSZMBcnN0+TKxMRqXoyCvJ4MeYnPk2MBsDZ4sSEltfxeLu+eLlqGcfVUEiqVFVqhoiISIXYdfooL21ZypqjibaxvvWb83SHgYRXr2tiZRdXnH6co1NupuDgVgCq3TCJmre/hEU3iCIiFe7HA7t4duM3pORlAaW7jL3W7VbCq9czuTLHpJBUqerUDBERkXK1PzOV17cu55v9O2xjHWs14h8drieyTrCJlV1awZFdHJ1yE8WnD4HFiVqjphLQ5wGzyxIRqXKO52Twr43fsPRQHFAakPr39gMY26IrzmpOXxWFpIqoGSIiIuXkeE4Gb21fyWdJMZQYVgDCAmrzTIeB9GvQwm62yb2QnJ0/cXzmXVjzs7C4e1P3wc/waTvI7LJERKoUq2Hlk4RoXor5iayiAgB6B4XxUtch1PepZnJ1jkkhqSK/UzNERETK1Jn8HGbs/JmP4zfY0v3r+wQwKaI/Q0Mi7PopnmEYpK+Yzqn5T4BhxaVaEPUe+waPRhFmlyYiUqUkpZ/k7+u+YvPJgwDU8PDmP51vYkhIW7tuptszhaSKnEvNEBERKRPZRQW8v/tX3t31K9lnn+AFevrwSJs+DA/rjLuzfX/kGMVFnPz0UTJWvwuAe+MOBD26GJdqWotemeXk5DBlyhSWLFlCZmYmoaGhPPTQQ/Tt2/cvrzUMg88//5yFCxeyd+9eXF1dCQkJ4ZlnnqF9+/YVUL1I5VNkLWFW7C9M2b6CQmsJALeHtue5ToOp5uFtcnWOSyGpIuez7ztTERGxe/nFRcxL2Mi0HT9zpiAHAH83Dx5o3ZN7WnRziHT/kpx0js+8g9zdKwHw6fg36tz7MU7uXiZXJuVt4sSJxMXFMWnSJOrXr8+iRYuYOHEis2bNomfPnpe8dvLkySxbtozx48cTERFBXl4eu3btsq3BF5ErE3fmGE+u/YrY00cBaOhTnVe6DeW6ek1NrsxxKSRV5OLUDBERkatSZC3hi+QtTNm2kuO5GQB4urgyLrwb97fqQYCDNBIKU5I59tYtFB6PB6D6TZOpMfQ/2jGmClizZg3r169n+vTp9O/fH4CoqCgOHz7Myy+/fMlmyNKlS1m0aBHz588nIuL3ZVS9evUq77JFKp3CkmKm7VzNtB2rKTasWLBwT3hXnm4/0CEa6vZKIakil6ZmiIiIXJESq5Vv9u/gzW0rOJB1GgBXJ2dGhHXmkTZ9qOXla3KFly9n9wqOz7wTa04aFhc3at/zPn5dR5pdllSQ5cuX4+vre86SGIvFwtChQ3n22WdJTk4mNDT0gtd+8skndOzY8ZxGiIhcuZ2pR3hi7ZfEp50AIMSvJm90v41OtRubW5gDU0iqyOVRM0RERC6LYRgsObSb17cuJyE9BQAni4VbQyJ4IqIfDX2rm1zh5TMMg/Tl0zi14EkwrDj71aLew1/i2bSb2aVJBUpKSiI0NPS8NfNhYWEAJCYmXrAZUlRUxPbt2xk2bBhvvvkmX375Jenp6QQHBzN+/HiGDh1aIfWLOLL84iKmbF/JrF2/UGJYcbJYuK9lD56I6Ieni6vZ5TkshaSKXD41Q0RE5JIMw2DNsSRe27qMHalHbOM3Nm7NkxH9aRpQy8Tqrpy1qICTcx8k89ePAXBvFEG9R77GtUZDcwuTCpeenk7jxo3PG/f397cdv9h1hYWFLFq0iDp16vDss8/i5+fHl19+yTPPPENRURF33HHHBa/t2LHjJWvKysrC19dxZleJXI0tJw/y5NovSc44BZRuu/5699uICGxgcmWO7ciRI8TGxiokVeQyqRkiIiIXtenEfl7dupRNKQdsY33rN+ep9v1pVSPIvMKuUnH6CY5Nv4385A0A+Ha+g9rjPlBQahV2qS06L3bMarUCUFBQwHvvvUdQUOn/C127duXw4cPMmDHjos0Qkaosv7iIN7atYNauXzAwcLY4MbFNLx5p28fudxyzZwpJFbk6+lNHRETOs/3UYV7btpw1RxNtY13rhPD39gPpWNsx1xzn74/h2LS/UXymdHZLjb/9H9VvfOaSX4alcgsICLjg7I+MjNJA4N9miPyZv78/FouFkJAQWyMESpsn1113HTNnzuT06dPUqFHjvGtjYmIuWdNfzRwRcVSxqUd57NfPbcssw6vX5c3utzlkY92eKCRV5OqpGSIiIjZxZ47x+tblLDu8xzYWEdiAp9sPpHu9CwdJOoKMXz/i5JyHMIoLsHj4UPe+efhE3Gx2WWKy0NBQli1bhtVqPWcaeWJiaROwWbNmF7zOw8PjokGEhmEAl55xIlKVFFlLmLZjNVN3rKLYsNpmgzzatg9umg1y1RSSKnLt9CeQiIiQmJ7Cm9tW8P2BWNtYy+p1mRTRn34NWjjsFzujuJCT858gY9U7ALjWDqXeI1/jHtTS5MrEHvTv358vv/ySVatW0a9fP9v44sWLCQ4OvuhOMr9d+/HHH3PkyBHq168PlDZCfvnlFxo0aED16o4TKCxSXhLSUnjs18+JPX0UgKb+tZhy3e20UzbINVFIqkjZuKJmSH5+PkuWLCE4OJi2bduWV00iIlJB9memMmX7Shbt3Y5B6RPtZgG1eDKiPzc0aomTxXFD14rTj3NsxjDyk9YB4N12EHUmzMPZO8DcwsRu9OzZk8jISCZPnkx6ejr169dn8eLFbNmyhZkzZ9rOGzVqFNHR0SQkJNjGxo0bx3fffcf48eOZOHEivr6+fPXVV+zevZspU6aY8eOI2I0Sq5X3d6/ltW3LKCgpxoKFCS27M6n9AO0Uc40UkipSdq6oGeLm5sa//vUvJk+erGaIiIgDO5KdxlvbV/JF8lZKjNIwyMa+NXgioh+3BLfF2cFvqvKSN3Bs+u2UpB8HoPotz1HjlmexOPjPJWXLYrEwc+ZM3nzzTaZMmUJmZiahoaFMnz6dPn36XPLaatWq8emnn/Lqq6/y3//+l/z8fJo1a8aMGTPOmWUiUtXsz0zliV+/YPPJgwA08q3Om91vJ7JOsMmVOTaFpIqUvStqhjg5OVG3bl2ys7PLqx4RESlHx3IymL5zNQsSN1NkLQGgvk8Aj7frx9+aRODi5GxyhdfGMAwyVs3i5PzHoaQIJ08/6kyYo3wQuSgfHx+ee+45nnvuuYueM2/evAuO169fn6lTp5ZXaSIOxTAMPk2I5r+bvyevuAiAUWGR/KvTILxd3U2uzrEpJFWkfFxxZsiQIUP49ttvGTNmjP4HFBFxECdyM5mx82c+TdhE4dkmSB0vPx5t24dhTTtWihA7a0EOKR/dR9bGBQC41WtBvYe/wq1umMmViYhUbql52Uxa9yUrDscDpZ8vr3e/jV5BFw4hlsujkFSR8nXFd7/t27dn+fLl3HLLLQwfPpxGjRrh6el53nmdOnUqkwJFROTqnczNYmbsz8xL2ERBSen64lqevjzYuicjwyLxqCRrtwuPxXNs+u0UHosDwKfz7dQZ+z5Onr4mVyYiUrmtOLyHSWu/IjW/dOb4LSFteSHqFgLcvUyuzLH9OSTVz8+PDh06KCRVpAxdcTNk7Nixtl+/8MIL5+0wYBgGFouFPXv2/PlSERGpIKfzs5kZ+wtz9mwgv6R0unJNDx8eatOTkWFRlSrALiv6C058OB4jPxucXQi883UC+k102B1wREQcQW5RIf/b/APzEjYB4OfmwQtRQxjapJ25hVUCCkkVqRhX3Ax56aWXyqMOEREpA2n5Ocza9Ssf7VlPbnEhANXcvXiwdU/GNO+Cl2vlWd5oFBdx6vOnSV/2NgAu1YKo++BneDbtanJlIiKV247UIzy85jP2ZaYCEFk7mLd73EF9n2omV+bYFJIqUrGuuBkydOjQ8qhDRESuQVp+Du/tXsuHcevIOdsE8Xfz5IHWPbi7RVd8Kll4XVHqQY6/M5z8vRsB8ArvS537P8HFr5bJlYmIVF4lViszY9fwxrblFBtWXJ2cear9AO5reZ3D70JmNoWkilQ8x0/MExGpwi7cBPFgQsvruCe8G75uHiZXWPayt33Lidn3YM0pXUdd/aZ/UmPof7A4+E44IiL27FDWGR79ZaFty9ym/rWY1nMYrWoEmVyZY1NIqoh5rroZEhsby86dO8nIyMBqtZ5zzGKx8NBDD11zcSIicmFpBbm8v+tXPtyznuyiAqB0vfa9LbtzT4tu+LufH2zt6IziQlK/+CdpS6cA4OxbkzoT5uLdeqDJlYmIVG7f7tvB0+u/Juvs583dLbowueMNeLpo1sK1UEiqiLmuuBmSn5/PxIkTWbdunS0s1TAMANuv1QwRESkfF2uCjA/vzrjwytkEASg6dYDj79xF/r5oADzDelDn/k9wraYnkiIi5SW3qJDnNn3LZ0kxAAR6+vBG99vpU19bll8rhaSKmO+KmyEzZsxg3bp13H///XTp0oXRo0fz8ssvU6NGDd577z3y8/N55ZVXyqNWEZEqK60gl9m71/JB3DpbE8TX1Z3xLbszPrx7pW2CAGRtWUTKB+Ox5qaDxUL1G/9JjSHPYXHWSk8RkfISd+YYD/68gOSMUwD0DGrGW9fdTqC2LL8mRUVFxMbGcvToUUAhqSJmuuI7yaVLl3L99dfz6KOP2qZ01a5dmy5dutClSxduu+02Fi1axJNPPlnmxYqIVDW/ZYJ89IeZIL6u7oxr2Z3x4d0IcPcyucLyYy3M49Rnk8hYNQsAZ99A6tw3D+9W/U2uTESk8jIMg4/3bOD/Yn6koKQYVydnnukwkHtbdsfJolkL10IhqSL25YqbIcePH+fuu+8GwNm5NKyuqKio9MVcXBg8eDALFixQM0RE5Bqcyc/h3V2/8vGe9bZgVF9Xd+4J78b4lt2pVombIAAFR3Zx/J3hFB7dDYBni97UnTAXl2r1TK5MRKTySsvP4cm1X7Ls8B4AGvnWYGavu2hbs77JlTk2wzBITEwkKSlJIakiduSKmyHe3t6UlJTYfu3k5MTJkydtx319fUlNTS27CkVEqpDT+dnMiv2VOfEbyD3bBPFz82BceDfGVfKZIFB6w5ixahanPpuEUZQPTs7UvPV5qg16SrvFiIiUo/XH9/LILws5kZsJwNCQdrzYZUil3JWsIikkVcR+XXEzpGHDhhw4cAAonRkSGhrK0qVLue222zAMg+XLl1O3bt2yrlNEpFI7lZfFrF2/Mjd+A3nFpbPt/N08GF+Jd4f5s5Ls05z4YDw5274FwDUwmDr3fYJnaJTJlYmIVF4lVitTdqzk7e2rMDDwcnHjxS5DuC20vdmlOTyFpIrYtytuhnTp0oWvvvqKf/7znzg7OzNs2DD+97//0a9fPywWC0eOHOHxxx8vj1pFRCqdlNxM3t31C3PjN5Ff8lsTxJMJLbszNrwbflXkiVxu3EpOvD+W4rTSQDnfqDupNXomzl7+JlcmIlJ5peRmMnHNZ2w4sQ+A1jWCmNHzLkL8a5pcmWNTSKqIY7jiZsiECRO45ZZbbNvpjhgxgsLCQr799lucnJx4/PHHuffee8u8UBGRyuRYTgbvxK5hfmI0BSWlT4yquXtxX6vrGNO8S5WZlmwtzCf1q8mkL30LAIu7N7VGTcOv22gsFou5xYmIVGLrjiUz8ZfPOJWXDcD48G78o+MNuGunrmuikFQRx3FVmSEhISHnjI0dO5axY8eWWVEiIpXVkew0Zuz8mYVJMRRaS/OXanh4c1+rHoxuHoWPq7vJFVacgsM7Of7uKAqP7ALAIySSOhPm4FanqcmViYhUXiVWK9N2rubN7SuwGgZ+bh680f02bmjUyuzSHJpCUkUcj1q/IiIV4EDmaabvXM2XyVspNqwA1PL05f5WPRgZFomXa9V5YmRYraQtfYvTX03GKC4EJ2dq3Pwvqt/0Tyx6IikiUm5S87J55JeF/HIsCYA2NYJ4p/dwGvnWMLkyx5abm8vWrVsVkiriYK76rrOwsJBNmzZx+PBhABo0aEDnzp1xd686TzVFRP7KvoxTTNu5mq/3bqfkbBOktpcfD7XuyV3NOuPp4mpyhRWr6PRhTsweS96e1QC41g6lzoS5eDaJNLkyqSyKiooYN24cc+fONbsUEbuy6cR+HlyzgJSzu8WMad6F5zoP1rKYa6SQVBHHdVV/+i1evJiXXnqJzMxMW3aIxWLBz8+Pp59+mltvvbVMixQRcTTxaSeYtmM13x3YifXsn5P1vP2Z2KY3d4R2wKOKNUEMwyBz7RxOzX8ca17pjbh/r3sJvPN1nDz05EzKjmEYbN682ewyROyG1bDyTuwvvLp1GSWGFR9Xd17teis3h7Q1uzSHppBUEcd3xc2QH3/8kWeeeYZ69eoxbtw4mjRpgmEY7N27l88++4zJkyfj4eHBoEGDruh1N2zYwDfffMO2bds4ceIE/v7+tGnThocffpiwsLBzzl23bh1vv/028fHxeHt7079/fyZNmoSfn9+V/jgiImUqNvUob+9YxZJDu21jDX2qM7FtL25r0h63KvgErjj9BCkf30fO9u8BcPYNpPY97+ETcbPJlYmjGj169EWP/faQRkQgrSCXx375nJVH4gFoUa0O7/YeQYi/vrBfC4WkilQOV3xXPmvWLEJCQvj888/PWQfXr18/hg8fzu23384777xzxc2QBQsWkJ6ezt13302TJk1ITU1l9uzZ3HbbbcybN4927doBsGnTJiZMmEDfvn157LHHOHnyJK+//jqJiYnMnz9fU9JExBRbTh7k7R2rWHUkwTbWxD+Qh9v04paQdrg6OZtYnXmyNi0kZe5ErDlnAPDpeCu1Rs/ExU834nL1tm/fztixY6levfp5x4qLi4mJiTGhKhH7suv0Ue5d9QmHs0tzLIY368x/I2+qcsszy5JCUkUqlytuhuzfv59HH330goFAvr6+3HrrrUyfPv2KC/n3v/9NjRrnhjd1796dvn378sEHHzBt2jQAXnvtNZo2bcpbb71la3wEBgZyzz33sGTJkituwoiIXC3DMNhwYh9Td6xm7fFk23hYQG0ebduHwY1b41xFG7QlWamkzJtIdvQXADh5V6PWqGn4Rt6pLXPlmoWFhdG6dWv69et33rGCggJee+01E6oSsR9fJG3hmQ2LKCgpxsPZlZe7DuW20PZml+XQFJIqUvlccTMkMDDwklNQnZycqFmz5hUX8udGCJT+IdOoUSNOnDgBQEpKCrGxsTzzzDPnzADp1q0btWvXZunSpWqGiEi5MwyDn48mMm3naqJTDtjG29QI4tG2fejfsAVOlqrZBAHI2rKIk3MeoiQzBQDvtoOoffe7uFSrZ3JlUlkMGTLkosdcXFyYOHFixRUjYkcKS4r5T/T3zI3fCEAj3xq832ck4dXrmlyZY1NIqkjldMXNkKFDh7Jo0SKGDx+Ot7f3Oceys7P56quvyixA9cyZMyQlJTF48GAAEhMTAWjatOl55zZr1oykpKQyeV8RkQuxGlaWHIxj+s7V7Dx91DbesVYjHm3bh15Bzar0rIfizJOc/OSR32eDePgSOPxN/K4bW6V/X6TsjRgx4qLHnJ2d1QyRKul4Tgb3rf6UracOAdC3fnPe7nEHAe5eJlfmuBSSKlK5/WUz5M+J7B07dmT16tXcdNNNDB8+nJCQECwWC8nJySxYsIBq1arRoUOHay7MMAyeffZZrFYr48aNAyA9PR0Af3//88739/cnLi7uoq/XsWPHS75fVlYWvr6+V1+wiFRaxdYSvtm/kxk7V5OYftI23q1uEx5p24eudUKq9Jd9wzDI2rSQU58+SklWKgBerfpT++53ca2pddRy7V588UUeeeQRTUcXuYgNJ/bxwOr5pOZnY8HCExF9ebRtnyo9S/FaKSRVpPL7y2bIqFGjzrvJ/22ZzOuvv2479tvYsWPHuOeee9izZ881Ffbqq6+yYsUKXnrpJZo0aXLOsYt96ajKX0ZEpOwVlBTzRfIW3oldw8GsM7bxfg2a83CbPnSo1dDE6uxDcdoxUuY+SM627wBw8vQncPgb+HW/W38mS5mZP38+3333HY8++ijDhg3Tf1siZxmGwfu71/JCzE+UGFb83TyY1vMu+tQP++uL5YIUkipSdfxlM+Sll16qiDrOMWXKFD788EMmT558zpKbgIAA4PcZIn+UkZFxwRkjv/mrZPm/mjkiIlVHblEh8xOjmbXrF07kZgJgwcKNjVvzcNtehFdX9oVhGGSu/ZhT85/EmpcBgHfETdQePVPZIFLmvv32W1566SX+85//sGDBAv75z38SGRlpdlkipsopKuCpdV/x7f6dAIRXr8v7fUbSyPf8HD65PApJFala/rIZMnTo0Iqow+btt99m1qxZPPXUU4wePfqcY79lhSQlJdG9e/dzjiUmJhIREVFhdYpI5ZNRkMec+A3M3r2OMwU5ALhYnLi1SQQPtelFE3+tEQYoTEkm5eMHyNuzCgAnnxrUGjkV30g9sZfyERISwvvvv8/PP//MSy+9xN13303//v15+umnCQoKMrs8kQp3MOs096yYS0J6aVD135pE8HLXoXi6aAnH1VJIqkjVc8UBquVp+vTpzJw5k0cffZTx48efd7xOnTq0atWK7777jjFjxtj+cNqwYQMpKSkMGDCgoksWkUrgVF4Ws3evY078BrKLCgBwd3ZhWNOOPNCqBw18q5tcoX0wiotIW/Imp795HqMoHwDfzncQOPJtXPxqmVydVAW9evWie/fuzJkzh3feeYdBgwZx9913c9999+HlpZBIqRrWHUvmvp/nk16Qi4vFif9E3sSY5lFqRl8lhaSKVF120wz58MMPmTZtGr1796Zr165s377ddszNzY3w8HAAJk2axLhx43jiiScYNmwYKSkpvP7667Rt25brr7/epOpFxBEdyU5j1q5fWJC4mYKS0idB3i5ujGoexb0tu1Pby8/kCu1H3t5NpHx0H4VHYgFwqd6AWqNn4NNusMmVSVXj4uLCuHHjGDp0KG+88Qbvv/8+X3/9NU8++eQlt9wVcXSGYfDRnvX8N/oHSgwrNTy8ea/3SCLrBJtdmsNSSKpI1WY3zZDVq1fb/v7br38TFBTEqlWl07G7dOnCrFmzmDZtGhMmTMDb25t+/frx1FNP4ezsXOF1i4jjSU4/yczYNXy9dxvFhhWAAHcvxoV35e4WXammbQhtrHlZpH71L9JXzgDDAIsTAf0fpuatz+PkoTXUYp6MjAw6d+7MoUOH2Lx5M//4xz+YP38+//rXv2jTpo3Z5YmUqYKSYiZvWMxnSaUZeC2r1+WDvqOp71PN5Mock0JSRQTsqBkyb968yz63R48e9OjRoxyrEZHKaGfqEWbEruHHA7swKN0Bq7aXH/e3uo7hzTrj7epucoX2wzAMsrcu5tSnj1F85ggA7g3aUnvsu3iEdDK5OqlqTp06xc6dO9m5cyexsbHs2rWLrKwsoHQnuaZNm9KmTRuio6O58847GTt2LJMmTdKyAakUTuVlce+qT4g5eRCAGxu35s3ut+PlqtkLV0MhqSLyG7tphoiIlAfDMFh/Yh8zdv7ML8eSbOONfKvzYOte3BbaHndn/VH4R4Un93Hqk0fI2fkTABZXD2oM/Q/VBjyGxcXV5OqkKrruuuuwWCwYhoG/vz8RERG0bduWiIgI2rRpg7e3NwDFxcV88MEHTJ06FYvFwqRJk0yuXOTa7Ew9wriV8zieW7pr19/bD+DhNr3V6LtKCkkVkT+6rG8APXv2pF+/fvTr14/OnTtrOYqI2D2rYWX5oT1Mj/2ZbacO28ZbVKvDg617cVNwa1yc9GfZH1mLCkj76XXOfPeiLSDVq8311Bo5FbdaTUyuTqqyO+64g/bt29O2bVuCgy+ej+Di4sJ9991HdnY2ixYtUjNEHNrifdt5cu2XFJQU4+3ixrSedzKgYbjZZTkkhaSKyIVcVjOkT58+rFixgk8//RQ/Pz969uzJgAED6N69O56enuVdo4jIZSuylvDNvu3MjF1DYvpJ23inWo2Y2KY3feqH6YnaBeTGrSRl7kSKTiQC4FK9PoHDp+DTYah+v8R0zz///BWd37x5c1JTU8upGpHyZTWsvLJlGTNifwagkW8NPuw7mrBqtU2ty1EpJFVELuaymiH//ve/+fe//83OnTtZvnw5K1as4LvvvsPd3Z2uXbvSv39/evfuTbVqCnESEXPkFRfyWWIM7+7+hSPZ6bbxPvXDeKh1L6XtX0Rx2jFOLXyKrI2flQ44OVNtwGPUGPKcAlLFYXXv3p033njD7DJErlhuUSGP/LKQJYd2A3BdvVBm9hquYO+roJBUEfkrV7RQvk2bNrRp04Ynn3ySvXv3smLFClasWMHkyZNxcnKiffv29O/fn759+xIUFFReNYuI2KQV5DJ3zwY+iFvPmYIcAJwsFm5q3IaH2vQkvHo9kyu0T0ZxIWnL3ub0t/+HkZ8NgEfTbtQePQP3Bq1Nrk7k2vj7+zN4sLZ9FsdyIjeTsSvmEHu6dCnH2BZd+XfnwVrSeRUUkioil+OqUwObNGlCkyZNuO+++0hJSbHNGHn11Vd56aWXaN68OY8//rh2fRGRcnEsJ4PZu3/lk4RocosLAXBzcub20A7c37oHwX41Ta7QfuXsXMLJ+Y/blsQ4+wZS846X8Os2BotC5EREKtyu00e5e8UcTuRm4mSx8HzkzdzdoovZZTmkP4ekhoSE0KJFC4Wkish5ymQLhdq1azNy5EhGjhxJZmYmq1atYsWKFSQlJakZIiJlKjn9JO/sWsPXe7dTZC0BwNfVnVHNoxgX3o3aXn4mV2i/Ck/u49SCJ8jZ9l3pgJMzAX0fpMaQ/+DsHWBqbSIiVdWyQ3FMXPMZucWF+Li6806v4fSuH2Z2WQ7nzyGp7u7uREREKCRVRC6qzPeT9PPzY8iQIQwZMqSsX1pEqrCtpw4xc+calh6Kw8AAINDTh/Hh3RnVPAo/Nw+TK7Rf1oJcznz/Mmk/vY5RXACAZ/Ne1BrxlpbEiIiYxDAM3tv9K/+3+ScMDOr7BPBxv7tpXq2O2aU5nDNnzrBt2zZyc3MBhaSKyOUp82aIiEhZMQyDVUcSeGfXGjae2G8bb+RbnQda9eS20PZ4uLiaWKF9M6xWsjYuIPXLf1J85ghwdpeYO1/Dp9Pt2iVGRMQkRdYS/rXhGz5NjAagfWBDPug7ikBPX5MrcywKSRWRa6FmiIjYnSJrCd/u38k7sWuITzthG29VvR4Ptu7JoMatFCj3F/KSN3Bq/pPk79sEgMXFjWo3TKL6jc/g5O5tcnUiIlVXRkEe9//8Kb8eSwbg5uA2vNH9djzV3L8iCkkVkWulZoiI2I3cokLmJ0bz/u61HM1Jt413rxvKg617cl29UM1m+AtFqQdJ/eIfZG1aaBvz6fg3at7xMm61QkysTEREDmWdYfTyj0jOOAXAo2378GREP5wsCve8EkePHmXnzp0KSRWRa6JmiIiY7nR+Nh/t2cDHezaQXlC63tfJYmFwo9Y80LoHbWrWN7lC+2fNz+bMD6+QtuRNjKJ8ANwbtSdw+Bt4hSnIWkTEbDtTjzB6+cek5mfj5uTMa91v429NIswuy6EoJFVEypKaISJimoNZp3lv11oWJsWQX1IEgLuzC8OaduTelt21Pe5lMKwlZP76MamL/k1J+nEAnAPqUvO2F/DrOkpb5YqI2IFVRxK4f/Wn5BYX4u/myYd9RxNZJ9jsshyKQlJFpKxdVTMkNTWVn376iaNHj+Ll5UV4eDjdunXD09OzrOsTkUpoR+oRZsX+wg8HY7EapTvD+Lt5cneLLoxt0ZWanlrv+1cMwyBnx4+kfvEPCo/uBsDi6lGaCzLoKZw89HsoImIPFiRu5pn1iygxrNT3CeCT/vcQGlDL7LIchkJSRaS8XHEzJCYmhnvvvZf8/HyMs19iAAICAnjwwQcZPXp0mRYoIpWDYRj8fDSRd2LXsP7EPtt4PW9/7m3ZneHNOuPt6m5ihY4jf38MpxY+TV78z6UDFgt+XUdS49bnca3R0NTaRESklGEYvLl9BVO2rwRKQ8Dn9L+b2l5+JlfmOBSSKiLl6YqbIa+88goAL774Il26dMFqtbJ9+3Y+/vhjXnzxRXbs2MEbb7xR5oWKiGMqspbwzb4dzNr1yzk7w7SoVof7W/fk5uA2uGpnmMtSdGo/qV/9i6yNn9nGvFr2o+Ydr+DRqJ15hYmIyDmKrCU8s34RC5NiAOhZrynv9hmJj5r+l+3IkSPExsYqJFVEys0VN0OSkpIYO3YsQ4cOtY3Vq1ePQYMG8cUXX/Dcc88RERHByJEjy7RQEXEs2UUFzE+IZnbcWo7lZNjGu9VtwgOte9KzXlPtDHOZSrJSOf39S2SsnIlRXAiAe4O21Bz2Mt6tBphcnYiI/FFOUQH3rf6Un48mAnBHaAde6XarGv+XSSGpIlJRrrgZ4u3tTb169S547Pbbb2fjxo189tlnaoaIVFEncjP5YPc6Pk3cRGZh6a4mThYLNzZuzf2ttDPMlbDmZZG2dAppS97Emp8FgEv1BtT82/P4dhmBRTfWIiJ25WRuFmNWfEzs6dIv8o+27cOkiP5q/l+mP4ek1q5dm3bt2ikkVUTKxRU3QyIjI1mzZg233377BY9HRUWxfPnyay5MRBxLfNoJ3tv1K4v2bafIWgKAh7Mrw5p2ZEKr7jTyrWFyhY7DWphPxqp3OPPDy5RkpQLg5BVA9cFPE9D/YZzcFFYtImJv9macYuSyDzmcnYaTxcKLXYYwMizS7LIcwp9DUp2cnGjZsiWNGzc2uzQRqcSuuBlyxx138OSTTzJnzhzGjBlz3vEjR45Qq5YSskWqAsMwWH9iH7Nif2H10QTbeA0Pb8a26MqY5lFU8/A2sULHYpQUk7n2Y05/8z+KzxwBwOLmRbUBj1Lthkk4eweYW6CIiFzQjtQjjFr2EWcKcvB0ceWdXsPp16CF2WU5hNzcXLZt28aZM2cAhaSKSMW54mbI3XffjYuLCy+//DIrVqzgtttuo1WrVjg7O7N582bmzp3LpEmTyqNWEbETxdYSfjiwi1m7frFNBQYI8avJhFbX8bcm7fF0cTWxQsdiWK1kx3xJ6tf/puhE6RpznF0J6DWB6jf9E5eAOuYWKFKJ5eTkMGXKFJYsWUJmZiahoaE89NBD9O3b97JfwzAMxowZw6ZNmxg9ejSTJ08ux4rF3qw7lsw9K+eSU1xIdXdv5vS/m4jABmaX5RCOHj3Kzp07FZIqIqa44mbIgw8+SHx8PPHx8WzevJnNmzefsw6yRYsW+Pn5kZiYSEhICC4uV/wWImKnsosKWJAYzQdx6ziSnW4b71y7Mfe1vI7+DVvgZNENzOUyrFayty7m9OLnKTwSWzr42za5Q/6Na2CwuQWKVAETJ04kLi6OSZMmUb9+fRYtWsTEiROZNWsWPXv2vKzX+Pzzz9m3b99fnyiVzo8HdjFxzQIKrSXU8/Zn/oBxhAZohvRfUUiqiNiDK+5UPPLII7ZfZ2ZmEhcXR3x8PHv27CEuLo7ExESeeuopLBYLLi4uBAcHExYWxmuvvVamhYtIxTmek8GHcevPCUW1YOH6RuHc36onHWo1NLlCx2IYBjnbv+P0ov9ScGi7bdy7/S3U/Nv/cA9qaV5xIlXImjVrWL9+PdOnT6d///5AafbZ4cOHefnlly+rGZKSksJrr73GCy+8cM49klR+CxI38/T6r7EaBqH+gcwfMI56PgFml2X3FJIqIvbimqZt+Pn5ERUVRVRUlG2ssLCQpKQk9uzZY2uQrF69+poLFZGKF3fmGO/u+pVv9u2g2LAC4Oniyh2hHRnfshvBfjVNrtCxGIZBzo4fOb34vxQc2GIb9247mBpD/41H4w4mVidS9SxfvhxfX99zlsRYLBaGDh3Ks88+S3JyMqGhoZd8jX//+9907NiRgQMHlne5Ykdmxq7hxZifAGhbsz7z+o+lujKyLkkhqSJib8p8DYubmxstW7akZUs92RRxRIZhsOZYEu/u+oVfjyXbxgM9fRjboiujwiIVinqFDMMgN3Yppxf/l/x90bZxr9YDqTH0P3iGdDaxOpGqKykpidDQ0PPyCcLCwgBITEy8ZDPk+++/Z9OmTfz444/lWqfYD8MweCHmJ2bt+gWA7nVDmd13FD6u7iZXZt8uFJLavn17fH19Ta5MRKoyBXqICAAFJcUs3red93b9SkJ6im28qX8t7mt1HUNC2uGhUNQr8ttMkDPfvkD+vk22ca+W/UqbIKFdTKxORNLT0y/4VNrf3992/GLOnDnDCy+8wOOPP07dunUv+z07dux4yeNZWVn6gminiq0lPL1+EQuTYgAY1KgV03reibuzbqcvRSGpImKv9Ke3SBWXlp/D3PiNfBy/gVN52bbxbnWbMKHldfSu30yhqFfIsFrJ3rKIM9+9eE4miGeLPtQc+m88m3U3rzgROccfQ+Cv5NgLL7xA/fr1GTlyZHmUJXYmv7iIiWs+Y8mh3QAMb9aZl7oMwVlf6C9KIakiYu/UDBGpovZlnOL93Wv5Inkr+SVFALhYnLgpuA0TWl5H65pBJlfoeAxrCVmbFnLmu5coPBZnG/dq1Z/qN/0Tr7AeJlYnIn8WEBBwwdkfGRkZwO8zRP5s3bp1/Pjjj8yZM4fs7OxzjhUWFpKZmYmXl9cFd9SLiYm5ZE1/NXNEKl5OUQFjV8xh/YnSHYMmtunF0+0HXrJZVtUpJFVEHIGaISJViGEYbEzZz3u7fmXF4XgMDAD83DwY0SySseFdqed94Zt/uTijuIjMDZ9w5vtXKEpJso17t7uR6jf9E88mkSZWJyIXExoayrJly7BaredM2U9MTASgWbNmF7wuKSkJq9XKqFGjzjv22Wef8dlnn/H+++/To4caoI4uszCfUcs+ZMupQwA822kQ97XSv9eLUUiqiDgSNUNEqoAiawnf74/l/d2/svP0Udt4Q5/qjGvZjWFNOyr87SpYC3LJ+PUj0n56g+LTB0sHLRZ8OtxK9Zv+iUejdqbWJyKX1r9/f7788ktWrVpFv379bOOLFy8mODj4ouGp119/PS1atDhvfPTo0QwcOJARI0bYQljFcaXl5zBi2YfsPH0UCxZe6TaU4c0UeH0xCkkVEUejZohIJZZekMv8xM18GLeOE7mZtvH2gQ2Z0Oo6bmjYUuudr0JJ9hnSV84kfcU0SrJSSwctTvhG3Un1G/+Be1C4uQWKyGXp2bMnkZGRTJ48mfT0dOrXr8/ixYvZsmULM2fOtJ03atQooqOjSUhIAKBOnTrUqVPngq9Zu3ZtIiM1G8zRncrL4q6lHxCfdgJnixNTrrudW5tEmF2W3VJIqog4IjVDRCqh/ZmpfBC3js+TtpBbXAiAk8XCDY1acW94dzrWbmRyhY6p6PRh0pa9RcbP72MU5ABgcXHDr/sYqt0wCbfaF9+CU0Tsj8ViYebMmbz55ptMmTKFzMxMQkNDmT59On369DG7PDHJ8ZwM7lo6m+SMU7hYnJjR6y4GN25tdll2SSGpIuLI1AwRqSQMwyA65QDv7f6VZYf22PJAfFzduatZJ8a26EpD3+omV+mYCo7tIe3H18jc8CmUlD71cvL0w7/3/VQb8AguAZe/raaI2BcfHx+ee+45nnvuuYueM2/evMt6rd9mjojjOpKdxrAl73Mw6wzuzi6813skfRs0N7ssu6SQVBFxdGqGiDi4wpJivj8Qywdx69iResQ2HuQdwLjwbtzZrBN+bh4mVuiYDMMgL3EtaUveJGfbt7ZxZ/86VBv4GP69JuDspbBZEZHKYn9mKsOWvM+xnAw8nF35qN9orqvX1Oyy7I5CUkWkslAzRMRBpeXn8GliNB/t2UDKH/JAIgIbMKHlddzQqCUuTs4mVuiYjOIismK+JG3pWxTs/30LTNfaoVS74Un8uo7GSc0lEZFKJTE9hbuWzCYlLwtvFzfm9L+bqDohZpdldxSSKiKViZohIg4mOf0ks+PW8WXyVvJLigDlgZSFktwMMtZ8QPryqRSfOWwb9wiJpNr1j+PT8VYsai6JiFQ6cWeOcdfSDzidn4O/mwfzBtxD+8CGZpdldxSSKiKVjZohIg7AMAx+PZbM+7vXsvro72vSfV3dGd6sM3e36EID5YFclaJTB0hbMY3MNR9gzc8qHbRY8Gk/hGrXP4Fn067mFigiIuVmZ+oR7lr6ARmFeVRz92LBwHG0qhFkdll2RSGpIlJZqRkiYsfyiotYvG87s3evJSE9xTbeyLc694R3Y1jTjvi4uptYoWMyDIP85A2kLZ9K9uavwLACYHH3xv+6sQQMeAS3Wk1MrlJERMpTbOpRWyMk0NOHBQPH07zahbdMrqoUkioilZmaISJ26ERuJvPiNzIvfhNnzm7hChBZO5h7W3anf4MWOGta6hWzFuaTFb2Q9BUzKDiwxTbuHFCPav0fxr/XvTh7VzOxQhERqQi7Th/lzqWzySjMo5anL59ffy+hAbXMLstuKCRVRKoCNUNE7MjO1CPMjlvHd/t3UmQtAcDVyZmbgttwb3h3WtfU1N2rUZR2lIxV75Lx83uUZJ2yjbs37kC1/g/jGzkMi4uecomIVAW7Tx/jzj/MCFmoRsg5FJIqIlWFmiEiJiu2lrD0UBwfxK0jOuWAbby6uzejmkcyunkUtb38zCvQQf22FCZ9xXSyYr6CktLAN5xd8O34NwL6P4xHkygsFou5hYqISIWJO3OMYUtnk16QS02P0kZIUzVCbBSSKiJViZohIibJKMjjs6TNfLRnPUey023jzavVYXx4N4aEtMPDxdW8Ah2UtTCPrE0LSV8589ylML6B+Pe+j4De9+FSrZ6JFYqIiBnizhxn2JLSRkgND28WXn8vzQJqm12WXVBIqohURXbVDDlx4gSzZ89m9+7dxMfHk5uby9y5c4mMjDznvFGjRhEdHX3e9YMGDWLKlCkVVa7IVdmbcYoP49bxRfJWcosLAbBgoV+D5owP70bXuk00W+EqFJ5IJH31u2SunYM1J802XroUZiI+nYfhpLBZEZEqKT7tBHcumU1aQS7V3UsbIWHV1AgBhaSKSNVlV82QgwcP8sMPPxAeHk5UVBSrVq266LmNGzfmlVdeOWesWjUFH4p9shpW1hxN4oO4dfx8NNE27u3ixu1NO3BPi26E+Nc0sULHZBQXkb3tWzJWv0tu3MrfDzi74tvpbwT0m6ilMCIiVVxCWgrDlrzPmYIcqrl7sfD6e7VrDKXLSZOSkkhMTFRIqohUSXbVDOnUqRMbNmwAYMWKFZdshnh4eNCuXbsKqkzk6uQUFfBl8lY+2rOe5Izfgzsb+lRnbHgXhjXthJ+bh4kVOqaiM0fIWDObjDWzKUk/bht3qdmYgF4T8OsxFhc/rQEXEanqEtNLGyGn839rhIynRXU1QhSSKiJiZ80QhTNJZXE46wwfx2/ks8RoMgrzbeNd64QwLrwb/bQ17hUzrCXk7lpO+s/vkbP9ezi72w4WC95tbsC/9/14t7kei5OzuYWKiIhdSE4/ybAl75Oan02AuxefDRxPeHVlRikkVUSklF01Q67E/v376dSpEzk5OdSvX58hQ4Zw77334uqqwEkxh2EYbDixjw/j1rPscBxWwwDA3dmFISHtGBfejfDqdU2u0vEUnT5M5q8fkfHrRxSfPmQbd/arhX+Pe/DveS+ugY3NK1BEROzOwazTDFs6m1N52fi7efLZwHG0rFG1GyFFRUXs2rWLI0eOAKUhqe3ataNWLc2kFJGqySGbIR06dGDQoEGEhISQm5vLihUrmDp1Krt372bGjBkXvKZjx46XfM2srCxNDZSrkldcxOJ92/kwbh170k7Yxmt7+TGmeRQjwjpTw8PHxAodj1FcRPaO78lYM5vc2KVwtrEE4BnWE//eE/DteCsWF4W7iYjIuY7lZHDnktmk5Gbi5+bBgoHjaFUjyOyyTHWhkNS2bdvi7q5gcRGpuhyyGfLYY4+d88+9e/emZs2azJo1i5iYmL9sfIiUhWPZ6cxN2MinCdGkFeTaxjsENuSe8G4MatwKVy3ZuCKFJ5LI+OVDMtfOoSQzxTbu7Fcbv+5j8O9xD251mppYoYiI2LPUvGyGL53N4ew0PF1cmdtvLG1q1je7LNMoJFVE5OIcshlyIUOGDGHWrFls3779gs2QmJiYS16vBopcDsMwiDl5kA/j1vPjwV2UGFYAXJ2cuTm4DWNbdKVdYAOTq3Qs1oJcsrd8TcaaD8lLWPP7AYsFr9YD8e85Hp+2N2Jx0RI4ERG5uIyCPEYs+4DkjFO4OTnzYd/RdKzdyOyyTKOQVBGRS6s0zRCrtfRLqcKfpDzkFxfx7f4dfBi3nl1njtnGAz19GBUWxciwSGp56ebichmGQX7SOjLWziE7+gus+Vm2Yy7VG+Df4x78rrsb1xoNTaxSREQcRU5RAaOXf8TuM8dxtjgxq/cIrqtXdWcSKiRVROSvVZpmyDfffANA27ZtTa5EKpNjORnMiy9dCnOmIMc23rZmfe4J78ZNjVvj5lxp/jcqd0WnD5G5bh6Za+dQdHLv7wecXfGJuAn/HuPwatVfO8KIiMhlyy8u4p6Vc9ly6hAWLLzd4w4GNAw3uyxTFBcXExsbq5BUEZHLYHff4pYsWQJAbGwsAJs3byYtLQ1PT0969uxJTEwM7733HgMGDCAoKIjc3FxWrlzJ119/zfXXX0+HDh3MLF8qAcMw2HzyIB/GreOng7vPWQozuHFr7gnvSvtAzVi4XNaCHLK3LCJz7Vxy96w6JwzVPbgj/t3G4Bs1DGefGiZWKSIijqjIWsIDP89n3fHSBvvLXYcyJKSduUWZRCGpIiJXxu6aIY8++ug5/zxt2jQAgoKCWLVqFYGBgQBMnTqVtLQ0nJycCA4O5plnnmHUqFEVXq9UHnlnl8J8dIGlMCPDIhkZFkltLz8TK3QchtVKXsIvZK7/hOzNX56zDMbZrzZ+XUfi13007vVbmViliIg4shKrlcd++Zzlh/cA8O/OgxkR1tnkqiqeQlJFRK6O3TVDEhISLnm8UaNGvPfeexVUjVQFR7LTmBu/kQWJm8/ZFSYisAFjW3TlRi2FuWwFh2PJ3PApWRs/o/jMYdu4xcUN73Y34dd9DN6tB2LR76eIiFwDwzB4ZsMivtm/A4An2vXj3pbXmVxVxVNIqojI1dM3EqmSDMNg/fG9fLRnA8sOx2E9u3TD1cmZGxu3ZqyWwly2otOHydr0GZnrP6XwSOw5x9yDO+HfbbSWwYiISJkxDIPnN//AgsTNANzX8joeb9fX5KoqnkJSRUSujZohUqXkFBXw9d5tfLxnAwnpKbbx2l5+jAqLZERYZwI99TTlr5TkpJMd8xWZG+aXbof7hxwQ11pN8O0yAr8uw3GrU3WT/EVEpHzMiF3D+7vXAjCiWWf+1WkQFovF5KoqjkJSRUTKhpohUiXsz0xlbvxGFibFkFmYbxvvVKsRY1t05YbGrXDVDiaXZC3MI2fHj2Rt+oyc7T9gFBfYjjn7BuLb+Q58u47AI6RzlbopFRGRirMwKYaXt5SG7d8c3IYXuwypUp85aWlpbN26VSGpIiJlQM0QqbSshpXVRxL5eM8GVh/9PYvG3dmFISHtGNuiC61qBJlYof2zFhWQu2spWZs+J3v7dxj52bZjFjdPfNoPwbfLcLxb9sfi4mpipSIiUtmtOLyHv6/7GoDudUOZct0dOFeRJSEKSRURKXtqhkilk16Qy+dJW5gTv5GDWadt40HeAYxuHsXwZp2o5uFtYoX2zSguIjduJVnRn5O9ZTHWvIzfDzq74BXeF7+ou/BpPwQnLSkSEZEKsOXkQe5fPZ8Sw0qr6vV4v89I3KtIGLdCUkVEykfV+BSRKiHuzDE+3rORr/duI7+kyDZ+Xb1Q7m7ehX4NWlSZJ0hXyrCWkBe/hqzoz8mK+Rpr9u9NJCxOeDbvhW/kHfh2vFVBqCIiUqGS0k8yZsUc8kuKaORbnXkDxuLr5mF2WRVCIakiIuVHzRBxaEXWEn46sIs58RvYlHLANu7t4sbtTTswpnkXmgYoUOxCjJJi8hJ/JSvma7I3f0VJZso5xz2bdce38zB8Ot6KS0Adk6oUEZGq7FhOBiOWfUB6QS41PXz4ZMA9VSLoXCGpIiLlT80QcUgncjP5NGETnyZEczIvyzYe6h/I3S268rcmEVXmqdGVMIoLyY1bRVbM1+Rs+4aSrNRzjnuEROIbeQc+nW7DtXp9k6oUEREpXfY6atmHHMvJwNvFjbn97ybYr6bZZZU7haSKiFQMNUPEYRiGwaaU/Xy8ZwNLDu6m2LAC4GSx0L9BC8a26Eq3uk2qVKr85bAW5pG7a1lpA2T791hz08857h7cEd+Of8O38+24BgabU6SIiMgf5BUXcc/KuSSkp+Dq5MzsvqNoU7NyN+kVkioiUrHUDBG7l1NUwNd7t/Hxng0kpP++lKO6uzfDwzoxKiyKIJ8A8wq0Q9b8bHJ2/kR2zNdk7/zxnF1gsFjwCO2Kb8db8ekwFNeajcwrVERE5E+KrSU89PN8os8uf33ruju4rl5Tc4sqZwpJFRGpeGqGiN1KTj/J3PiNfJG8hayiAtt4RGAD7m7RlRsbt64ySfKXoyQrlezt35O97VtyY5diFOX/ftDJGc+wnmcbIENwCahrXqEiIiIXYRgG/9iwmGWH9wDwn843cktIW5OrKl8KSRURMYe+SYpdKbaWsOzQHubEb2Dd8b22cXdnF4aEtGVM8y6VfprslShMSSZ767fkbPuWvKR1cHbpEADOrni17Itvh1vxaX8Lzr6Vf521iIg4tqk7VrEgcTMAD7buyfiW3U2uqPwoJFVExFxqhohdSMnNZEHiZj5J2MSJ3EzbeEOf6oxqHsmdTTtSzcPbxArtg2G1kr9/MznbviV767cUHos757jF3Rvv1gPxaX8L3m1vxNk7wJxCRURErtCivdt5bdtyAG5r0p5/dLje5IrKj0JSRUTMp2aImOa3QNS58Rv58cAuWyCqBQt96ocxunkUves3w8lStaeJWgvzyd2zqrQBsv17StKPn3Pc2b8OPhE34R1xM14t+uCkXXRERMTBbDqxnyfXfgFAlzohvNrt1koZiK6QVBER+6FmiFS47LOBqHP+FIhazd2LO5t2YlTzSBr6VjexQvMVpx8nZ8eP5Oz8kZzdK84NQAXc6oXj0/5mvCNuxiO4ExatKxYREQe1LyOVcavmUWgtoYl/IO/3GYlbJcwEU0iqiIh9qXyfNGK34tNOMC9+I18mbyWnuNA2HhHYgDHNo7ixcRs8XFxNrNA8tuUvO34kZ8ePFBzceu4JFic8m3bDO+JmfNrfjFvtUHMKFRERKUNp+TmMXv4R6QW51PDwZm7/uwlw9zK7rDKnkFQREfujZoiUq8KSYn46uJu58RvYdHaLPPgtELUdo5tH0baKBqKW5KSTu3vZ2RkgSyjJOnXOcSdPP7xa9se77SC82w7GxS/QpEpFRETKXkFJMeNWzeNA1mncnV34sO8YGvnWMLusMqWQVBER+6VmiJSLo9npfJqwifmJm0n9wxKPYL+ajGkexW2h7Svlk59LMQyDwmN7bLM/8pLWgrXknHPc6jY/2/wYhGfT7liq6EwZERGp3AzD4Mm1XxJ99kHJ29fdQYdaDc0tqoz9OSS1Vq1atGvXTiGpIiJ2Qs0QKTNWw8qao0nMi9/IiiPxWA0DACeLhQENwhnTIopudZtUqUDUktwMcuNWkhu7lJxdyyg+feic4xYXdzyb98S77WC82w7CrVaISZWKiIhUnDe2r2Dxvu0A/KPD9dwY3MbcgsqQQlJFRByDmiFyzc7k5/BZUgyfJmziYNYZ23gtT1/uataJEc06U88nwLwCK5BhLaHgwFZyzjY/8vduPG/2h0u1INvsD6/wvji5a8tgERGpOr5I2sJb21cCMLxZZx5s3dPkisqOQlJFRByHmiFyVQzDIObkQebGb+SHA7EU/uELf5c6IYxuHsXAhuGVMg3+z4rTj5MTu5TcXcvI2b0Ca/bpc45bXNzwaNod79YD8G41ALcGbSrldoEiIiJ/Zd3xvfx9/dcA9KjXlBe63FJpPhMVkioi4lgq/zdVKVPZRQUs2ruNOfEbiU87YRv3c/PgtibtGdU8iqYBlTsUzFqYT37yOnJil5GzaxmFh3eed45r7aZ4txqAV+sBeDXvhZOHjwmVioiI2I/k9JNMWDWPImsJYQG1mdV7BK5OzmaXdc0Ukioi4pjUDJHLEnfmOPPiN/L13m3nbIvbpkYQo5pHcUtwW7xc3UyssPwY1hIKDm4jN24VuXEryEtch1GUf845Th6+eLbojXfrAXi1GqjsDxERkT9IL8jl7hVzyCjMp5anL3P7j8XPzcPssq6ZQlJFRByXmiFyUfnFRXx/IJZ58RvZcur34M/SbXHbMiosinaBDUyssHwYhkFRShK5u1eWhp/G/4w1J+2889wbtce79UC8Wg/As0kX7fwiIiJyAcXWEh78ecEfttAdTZCDZ4kpJFVExPGpGSLn2ZeRyqcJm1iYvIX0glzbeKh/ICPDIivltrjF6cdLGx9xq8iNW0nxmSPnneMaGIJXeB+8WvbFs3lvXPwCTahURETEsbwQ8xO/HEsC4PVutzn8g5S8vDy2bt2qkFQREQenZogAUGQtYdmhOObFb2Lt8WTbuIvFiRsatWJU80i61AmpNCFnJdlnyEv8ldw9q8ndvZLCY3HnnePsG1ja/Ajvg1d4X1wDg02oVERExHF9nhTD+7vXAvBAq54MbdLO3IKu0dGjR4mNjaWoqAhQSKqIiCNTM6SKO5KdxvyEaD5LiuFkXpZtvL5PACOaRTKsaUdqeTn+k46S7DPkJfxCbsIv5MWvoeDwDjCMc86xuHvjFdYDr/C+eLXsi1tQKyy6uREREbkqW04e5Jn1iwDoUz+MZzoMNLmiq6eQVBGRykfNkCqoxGpl9dEE5sVvYtWRBAxKmwIWLPSpH8bo5lH0CmqGswM3AkqyT59tfJxtfhzZeV7zA2dXPJtEljY/wvvgEdIZi0vlDIEVERGpSMdyMrh31ScUWksI9Q9kes+7HPa+QiGpIiKVk5ohVUhKbiafJW7m08RojuVk2MZre/pyZ7NO3NWsE/V9qplY4dX7vfmxhtz4NRfc7va35odnWE+8WvTEo0kXnCpZ9omIiIjZ8oqLGL9yLifzsvB38+DDvqMdcueYC4WkhoeHExysZbMiIpWBmiGVnNWwsvbYXuYlbGTZoT2UGFbbsR71mjIyLJL+DVvg6uRsYpVXrjjtGHlJa8lLWEtuwi8UHok97xyLixseIZF4Nu+JV/OeeDSJUvNDRESkHBmGwVPrvmLn6aM4WSzM7DWcEH/HCxxXSKqISOWnZkgllZqXzcKkGOYnRnMw64xtvLq7N8OadmR4WCeC/WqaWOHlMwyDwuPx5CWuJT9pHXmJayk6tf+88ywubng0iTq3+eHmaULFIiLiKHJycpgyZQpLliwhMzOT0NBQHnroIfr27XvJ67744gtWrlxJQkICp0+fpk6dOvTo0YMHH3yQ6tWrV1D19mdm7BoW79sOwL86DqJnUDNzC7oKCkkVEaka1AypRAzDYP3xvXySEM2SQ7spspbYjkXWDmZkWCSDGrfC3dm+/7UbxYXkH9hK3tnGR17SOqzZp887z+LmWdr8aNYdr+a98GgSqeaHiIhckYkTJxIXF8ekSZOoX78+ixYtYuLEicyaNYuePXte9LqpU6cSGRnJE088Qe3atUlOTmbGjBmsWrWKxYsX4+fnV4E/hX1YeTiel7csBeD20Pbc27K7yRVdGYWkiohULfb9rVguy5n8HL5I3sInCdHsz0y1jfu7eXJ7aHtGhEXSNMB+P8hL8jLJT95AXuI68pLWkb9vE0Zh3nnnOfvWxKNpNzybdsczrDseDSOwuLiaULGIiFQGa9asYf369UyfPp3+/fsDEBUVxeHDh3n55Zcv2QxZvHgxNWrUsP1z586dCQ0NZdSoUXzzzTeMGjWq3Ou3J0npJ5m4ZgEGBhGBDXipy1AsFovZZV02haSKiFQ9aoY4KMMw2Jiyn08TovnxQCyFf5gF0qlWI0aERTK4cWs87axZYBgGRSnJ5O/dSN7ejeQnb6Tg8E74Q5bJb1xrNcGzaTc8m3XDs9l1uNZp5lA3ViIiYt+WL1+Or6/vOUtiLBYLQ4cO5dlnnyU5OZnQ0NALXvvHRshvWrduDcCJEyfKp2A7lVmYzz0r55JVVEBtLz9m9xmFh53df1yMQlJFRKouNUMcTFp+Dl8kb+XTxGj2Zpyyjfu5eXBrkwhGhkXSvFodEys8lzU/m/z9m8lL3kh+8gby922iJCv1/BMtTrg3bFfa+Gha+pdLtXoVX7CIiFQZSUlJhIaGnpcFERYWBkBiYuJFmyEXsnHjRgCaNm1adkXaOcMwePzXz9mfmYq7swsf9BlFbS/HWCL055BUX19fOnTooJBUEZEqQs0QB3CpWSDtAxsyIqwzNwe3wdPFzcQq/zjrY8PZ5sdGCo7EXnDWh5OnPx5NOuPRpAueoVF4hHbB2dMxbp5ERKRySE9Pp3HjxueN+/v7245fyWv93//9H40bN2bQoEEXPa9jx46XfJ2srCyH+jL+zq5fWHooDoD/i7qFdoENTK7o8vw5JDU4OJjw8HCFpIqIVCFqhtixi80C8XV159Ym7RkR1onw6ubNnrDmZf0+62PvxovP+gDc6oXjERqFZ5MoPEKjcKvbAotuOERExGSXWn55uUsz8/LyeOihh8jIyOCTTz7Bzc3chxMVZd3xvby8ZQkAw5p25K5mnUyu6K8pJFVERH6jZoidMQyDDSf28WliND8d2HXOLJCIwAaMDIvkpsZt8HKt2Bsto7iQgsM7yd+3mfz9m8nft5nC43vAMM47t3TWRySeoV3waBKJR0gkzt4BFVqviIjIXwkICLjg7I+MjAzg9xkil5Kfn88DDzxAXFwcH3zwAc2bN7/k+TExMZc8/lczR+zF8ZwMHvp5AVbDoFX1evxf1C1ml/SXFJIqIiJ/pGaInTidn80XSVuZnxjNvj/sCFM6CySCEWGdK2wWiGG1UnQikfz90eTviyF//2YKDm3HKC48/2SLpXTWR5MoPJtE4hHaBbe6zTXrQ0RE7F5oaCjLli3DarWeszwiMTERgGbNml3y+oKCAh588EG2b9/Oe++9R/v27cu1XntRWFLM/as/JTU/G383D97rM9LuAtv/SCGpIiJyIWqGmMhqWNlw/OwskIO7KbpAFkh5zwIxDIPitKPk74smf38M+fs2U3AgBmte5gXPd6kWhEdIJzyCO+MR0hH3xh1x9vrrJ2ciIiL2pn///nz55ZesWrWKfv362cYXL15McHDwJcNTCwsLefDBB4mJiWHWrFl07ty5Ikq2C/+3+Ue2nDoEwNQed9LQt7rJFV2cQlJFRORi1Awxwam8LL5I3sr8hGgOZJ22jfu5efC3Ju0Z3qwzLaqXz44wxZknKTiwlfwDW2zLXUoyLrwFoJNXAB7BHfEI6Vz69+BO2uFFREQqjZ49exIZGcnkyZNJT0+nfv36LF68mC1btjBz5kzbeaNGjSI6OpqEhATb2COPPMLatWt56KGH8PLyYvv27bZj1atXp2HDhhX5o1SYxfu28+Ge9QA82rYPfRtcelmQmRSSKiIil2JXzZATJ04we/Zsdu/eTXx8PLm5ucydO5fIyMjzzl23bh1vv/028fHxeHt7079/fyZNmoSfn33uSGI1rPxyLJn5CdEsOxRH8R92WOlUqxEjwjozuHHrMtsRxjAMStKPk39gCwUHt5F/cCsFB7ZSnHb0gudbXD1wb9T+bPOjEx7BnXCtHXrZ4XEiIiKOxmKxMHPmTN58802mTJlCZmYmoaGhTJ8+nT59+lzy2tWrVwMwY8YMZsyYcc6xoUOH8vLLL5db3WZJSEvhqXVfAdCzXlOeaNfvL64wh0JSRUTkcthVM+TgwYP88MMPhIeHExUVxapVqy543qZNm5gwYQJ9+/blscce4+TJk7z++uskJiYyf/58u+r4H8/JYGFSDJ8lbeZIdrpt3N/Nk781iWBEWCRh1Wpf03sYhkHx6UO2hkfp37dRkply4QucnHELaolHcCc8QjriEdwZ96CWWOx4va+IiEh58PHx4bnnnuO555676Dnz5s07b+yPs0SqgqzCfO5dNY+84iKCvAOY1vNOnO3ofus3CkkVEZHLZVfNkE6dOrFhwwYAVqxYcdFmyGuvvUbTpk156623bI2PwMBA7rnnHpYsWcKgQYMqrOYLKbaWsPpIAvMTN7PySDzWP+y4ElUnmOHNOnNDo1ZXFTZmGAZFJ/dScHAr+Qe2UXBwC/kHtmHNOXPB8y0ubrjVb41HowjcG7fHo1F73Oq3xsnN46p/PhEREak6DMPgybVfsi8zFTcnZ97tPYLqHt5ml3UOwzBITk4mISFBIakiInJZ7KoZcjkzOlJSUoiNjeWZZ5455/xu3bpRu3Ztli5daloz5HDWGT5LimFhUgwncn8PIK3u7s3tTTswvFknmvgHXvbrWYsKKDy6m4LDOyg4tJOCwzspOLgNa17GBc+3uHrg3qDt2aZHafOjdMZHxW7DKyIiIpXHe7t/5ceDuwB4PvJm2gU2MLmic10oJLV9+/Z2u3RaRETsg101Qy7Hb9vdNW3a9LxjzZo1IykpqULrKSwpZtmhOBYkbuaXY8kY/D4LpEe9pgxv1okBDcNxc770b3Vx5kkKDm0/2/TYQcHhnRQej4eS4gueb3H3Lm14nP3Lo3GH0i1t/+J9RERERC5XdMoBXoxZAsDtoe0ZEWZfu+ZcKCS1RYsWODs7m1yZiIjYO4f75pyeng6Av//527n6+/sTFxd3wes6dux4ydfNysq6om3W9macYn7iZr5M3sLp/BzbeG1PX+5o2pE7m3WkkW+N864zSoopPJF4drbH2b8O77zoji4Azr6BuDdsUzrro1EEHo3a41qnKRYnfdCLiIhI+UgryOWhnxdQYlhpUa0OL3YZYjfB6gpJFRGRa+VwzZDfXOzDuDw/pPOKi/jhQCwLEqPZlHLANu5ksdC3fnPuataJPvXDcDnbpCjJSafgyM7S2R6HtpfO9ji6G6Mo/8JvYHHCrW4Y7g3ONj4alv7l7F/Hbm4+REREpPIzDINJa7/keG4GXi5uzOo9osx2vLtWCkkVEZGy4HDNkICAAOD3GSJ/lJGRccEZIwAxMTGXfN1LzRzZffoY8xM3s2jfNjILf29kNPCpxp1NO3J7o5ZUzzhG4eEY0jbMoeDoLgqP7KL4zJGLvqaTp19pw6NBG1vTwy2oJU5unpesU0RERKS8fbRnPUsPlc62fSHqlivKPCsvCkkVEZGy5HDNkN+yQpKSkujevfs5xxITE4mIiCiT98kszOebfdtZkLiZnaePAuBkWAnJz+QWT3d6O1mpfSKZwi0fk52STLZhvehruQaG/L7MpUEb3Bu2w6VmI832EBEREbuz6/RR/m/zjwDc2iSC20Lbm1yRQlJFRKTsOVwzpE6dOrRq1YrvvvuOMWPG2HaU2bBhAykpKQwYMOCaXj865QALEjaxac866mYdJzwnlcE5qTTPTyMoJxWnkiLbuTl/utbZtyZu9VvjHtQSt/otz/69Nc6e+qAWERER+5ddVMADPy+g0FpCsF9Nu8gJUUiqiIiUB7trhixZUppYHhsbC8DmzZtJS0vD09OTnj17AjBp0iTGjRvHE088wbBhw0hJSeH111+nbdu2XH/99Vf93oX52Rx94TpG56TyQEnhRc+zuHvjHtSqtOFRvzXu9VviFtQKZ79apt8wiIiIiFytyRsWsz8zFTcnZ2b2vAsfV/NyOBSSKiIi5cnumiGPPvroOf88bdo0AIKCgli1ahUAXbp0YdasWUybNo0JEybg7e1Nv379eOqpp67pKYGLtZiWmcd+H3B2xa1eC9yDWuJevxVuQaXND5caDbGcnZEiIiIiUhl8mbyFr/ZuA2Byp0G0rhlkWi0KSRURkfJmd82QhISEyzqvR48e9OjRo0zf2+rkgrX/owQ1jcItqBVutZticXEt0/cQERERsTd7M07xzw3fADCgQQvuadHVlDoUkioiIhXF7pohZnLx8KH5iDfNLkNERESkwuQX/397dx9VVZ32f/xzgJBQgqTUFArtCD7jA4jxMw0F7c7u+uk0ZYkPMzmMCjqlTjaD2ZrCSdN0xnFgtHGWmbUqdeSX6VhapqMomuZTlhpM+RTdCgFKIgj790cLbg00OYezD/uc92ut/nDv/d374los9tW197lOpSZ+/Ka+v1yhOwKD9Ur/R9zysV+GpAIAzEQzBAAAwItlfLJBR4q+kY/NpsUDR+rWgOamx8CQVACA2WiGAAAAeKmNX3+m5Z/vlCRN7ZmouDbmfhzl8uXLOnz4sE6ePCmJIakAAPPQDAEAAPBCpy8Ua9r21ZKk+DYdNLlHgqnXZ0gqAMCdaIYAAAB4marqak3Z9rZKKi6qZbPmWjRwpHxN+qY8hqQCAJoCmiEAAABeZuln/1but/+RJC289+dqE2jOkFKGpAIAmgqaIQAAAF7kSNEZvbzvA0nS6Kg4DQ7vZMp1z5w5o4MHDzIkFQDQJNAMAQAA8BLllys1Zds7qqyuUkRQqJ6LHebyazIkFQDQFNEMAQAA8BLzPt2kL74rkK/NR4sGPqbAm/xder3vvvtOn376qcrKyiQxJBUA0HTQDAEAAPACOd/kaenhf0uSJkcnqPftd7rsWgxJBQA0dTRDAAAAPFxpRbme/vcqGTIUfVuYfhM9yGXXYkgqAMAKaIYAAAB4uFm73tXpsmIF+N6kRQMe000+rhlaypBUAIBV0AwBAADwYO99dUir8/ZJkmbGPqC7g29v9Gv8eEiqv7+/evbsqdatWzf6tQAAaAw0QwAAADzUt9+X6tmctZKkge0iNbZTv0a/BkNSAQBWRDMEAADAAxmGoWnbV6v40vcK9r9Zr/R/RDabrVHPz5BUAIBV0QwBAADwQK8fzdXHp49JkubGD1ebwMYbYMqQVACA1dEMAQAA8DD5JWf1wu71kqQRd/fSg+17NNq5GZIKAPAENEMAAAA8yOXqKk3Z9o7KqyrVtnmwXox7qHHOy5BUAIAHoRkCAADgQf7+2Q7tP/dDw2Jh/58ruNnNTp+TIakAAE9DMwQAAMBD5Jec1bxPP5Akje3UT/+nrd2p811rSGpERESjDmMFAMBsNEMAAAA8QLVRrWnbV+tS1WWFtQjR72L+y6nzMSQVAODJaIYAAAB4gOWf79Se//lakvRy/M/U4ibHP8LCkFQAgKejGQIAAGBxJ84X6aW9GyVJIzvGaEC7jg6dhyGpAABvQTMEAADAwgzD0G93rNHFy5VqHXiLnosd5tB5GJIKAPAmNEMAAAAs7M1je7TjmzxJ0tz44Q3+9hiGpAIAvBHNEAAAAIs6c6FYL+5ZL0ka3qGnEsM7N2j9xYsX9emnn6qwsFASQ1IBAN6DZggAAIAFGYahGTlrdaHykm4LaKEX4v67QesZkgoA8GY0QwAAACxoTd4+bTl9VJKUcc/DujWg+Q2tY0gqAAA0QwAAACzn2+9L9XzuOknSA3d104MR3W9oHUNSAQD4Ac0QAAAACzEMQ7/fma2SinKFNAtURr+Hb2jNj4ekdu7cWe3bt2dIKgDAK9EMAQAAsJD3vjqk908ckST9Ie6/1Sow6LrHMyQVAIC6aIYAAABYRFF5mWbu+n+SpMTwThrRoed1j2dIKgAA9aMZAgAAYBGzP9mgwvIyBd3UTC/dM/yaH3FhSCoAANdHMwQAAMACdhXk6+3jeyVJz/a5X3c0D673uOLiYu3bt48hqQAAXAfNEAAAgCauouqyfpeTLUnqeVu4kqPi6hzDkFQAAG4czRAAAIAmbuln/9bxkv+Rj82mOfH/V74+PlftZ0gqAAANQzMEAACgCfv6fKEW7v9QkvTLzvHqFtruqv0MSQUAoOFohgAAADRRhmFo5s53danqstoE3qLpvYfU7mNIKgAAjqMZAgAA0ESt//qwtpw+Kkl6Ie4htbjphyGoDEkFAMA5NEMAAACaoPMV5Xo+d50kaXBYJ/3XXV0ZkgoAQCOhGQIAANAEzdv3gb79vlQBvjcpo99DKi8vZ0gqAACNxJLNkNzcXI0ZM6befRs2bNDdd99tckQAAMCKysrKtHDhQm3cuFGlpaWy2+1KTU3V4MGDf3LtiRMnNGfOHOXm5qq6uloxMTGaMWOG7Ha703EdPHdKy7/YKUl6uudg+Z4v19aDuxmSCgBAI7FkM6TG9OnTFRsbe9W2sLAwN0UDAACsJi0tTUeOHNH06dMVFhamtWvXKi0tTX/72980cODAa64rLCzUE088odDQUM2dO1e+vr7KyspScnKysrOz1aZNG6fi+t3ObFUbhjoG3aa+l4O0d+9eSQxJBQCgsVi6GdK+fXv17NnT3WEAAAAL2rp1q3JycrR48WIlJSVJkvr166eTJ09qzpw5122GLFu2TKWlpVqzZk1tY6Jnz54aPHiwsrKy9Ic//MHhuCqqLuvAuVOq/r5cP7+lrQpOn5HEkFQAABqTj7sDAAAAcIdNmzYpKCjoqo/E2Gw2DR8+XPn5+fryyy+vuXbz5s2Kj4+/6g2NW2+9VQkJCdq0aZNTcV2quqzL3xYp7sLNCvcPko+Pj7p27aq+ffvSCAEAoJFYuhkya9YsdenSRX369NGvf/1rHT582N0hAQAAizh+/Ljsdrt8fK4uh6KioiRJx44dq3ddeXm5Tpw4ocjIyDr7oqKiVFhYWDvk1BHV1dUKOFemR+29FRQUpHvvvVcdOnTg22IAAGhElvyYTFBQkMaOHau+ffsqJCREeXl5Wrp0qR5//HGtXLlS0dHRddbExMRc95znz5+/oeMAAPAm58+f99j/CS8uLlZERESd7cHBwbX761NSUiLDMGqPu1JISEjt2tDQ0Dr7b6QesUlq/sFBvfzhEQakAgAg19QjlmyGdOnSRV26dKn9d0xMjAYNGqQHH3xQCxcu1PLly90XHH5STeMpKCjIzZF4PnJtLvJtHnJtLsMw3B2Cy1yvsPqpostVTSKbpJv9+TiMq/F3xDzk2jzk2lzk21yNXY9YshlSn9tvv139+/fXRx99VO/+Tz755Lrra57U/NRxcB65Ng+5Nhf5Ng+5No8nvzEZEhJS79sfJSUlklTvmx812202W71ra7bVvCHyY9QjTQe5Ng+5Ng+5Nhf5No8r6hFLzwz5serqaneHAAAALMJutysvL69O/VAzK6S+mSCSFBAQoPDw8Hpnihw7dkwtW7as9yMyAACg6fCYZsjZs2eVk5PDV+0CAIAbkpSUpNLS0jpvlWZnZ6t9+/ay2+3XXJuYmKicnBydPXu2dltxcbG2bNlS+zW9AACg6bLkx2SmTZum8PBwde3aVbfccovy8/P16quvqry8XFOnTnV3eAAAwAIGDhyouLg4paenq7i4WGFhYcrOztbevXuVmZlZe9zo0aO1e/duHT16tHbbk08+qXfffVcpKSlKTU2Vn5+fsrKy5OfnpwkTJrjjxwEAAA1gyWZIVFSU1q9fr5UrV+rixYsKCQlR3759NXHixGu+0goAAHAlm82mzMxMLViwQAsXLlRpaansdrsWL16sQYMGXXftbbfdpjfeeENz587VM888I8Mw1KdPH61cuVJt27Y16ScAAACOsmQzJCUlRSkpKe4OAwAAWFyLFi00a9YszZo165rHvP766/Vuj4iIUFZWlqtCAwAALuQxM0MAAAAAAABuBM0QAAAAAADgVWyGYRjuDgIAAAAAAMAsvBkCAAAAAAC8Cs0QAAAAAADgVWiGAAAAAAAAr+LxzZCysjJlZGSof//+6tGjh0aMGKEPP/zwhtaeOHFCkyZNUp8+fdSrVy/96le/0pdffuniiK3L0VyvWrVKEyZMUEJCgnr06KEhQ4YoIyNDRUVFJkRtTc78XtcwDENjxoxRVFSUZs+e7aJIPYMz+TYMQ2+//bZGjBih6OhoxcTE6NFHH9W+fftcHLU1OZPr999/XyNHjlRsbKxiY2P12GOPacOGDS6O2LoKCgqUkZGhxx9/XL169VJUVJRyc3NveD33yIahHjEP9Yh5qEfMQy1iLuoR87izHvH4ZkhaWprWrVun3/zmN1qyZInsdrvS0tK0devW664rLCzUE088odOnT2vu3LlasGCBSkpKlJycrIKCApOitxZHc71o0SK1aNFCU6dO1d///neNGzdO//rXv/TII4+otLTUpOitxdFcX+mdd95Rfn6+C6P0HM7kOz09XfPmzdOQIUO0dOlSzZ8/XwMGDNDFixdNiNx6HM312rVrNWXKFLVq1Urz58/X/Pnz1bp1az399NNavXq1SdFby9dff63169crMDBQ/fr1a9Ba7pENRz1iHuoR81CPmIdaxFzUI+Zxaz1ieLCPP/7YiIyMND744IPabdXV1cbIkSON+++//7pr586da3Tv3t0oKCio3VZUVGT06tXLmDVrlstitipncn3u3Lk623Jzc43IyEhjxYoVjR6r1TmT6xoFBQVGnz59jI0bNxqRkZFGRkaGq8K1PGfyvXHjRqNTp07Gvn37XB2mR3Am18nJyUZCQoJRVVVVu62qqspISEgwkpOTXRazlV2Zq02bNhmRkZHGrl27bmgt98iGoR4xD/WIeahHzEMtYi7qEXO5sx7x6DdDNm3apKCgIA0ePLh2m81m0/Dhw5Wfn3/d12c2b96s+Ph4tW7dunbbrbfeqoSEBG3atMmlcVuRM7kODQ2ts6179+6SxFOvejiT6xrPP/+8YmJiNHToUFeG6hGcyffKlSsVExOjXr16mRGq5TmTaz8/PwUGBsrH539vaz4+PgoMDJS/v79L47aqK3PVUNwjG4Z6xDzUI+ahHjEPtYi5qEfM5c56xKObIcePH5fdbq+T4KioKEnSsWPH6l1XXl6uEydOKDIyss6+qKgoFRYWqrCwsPEDtjBHc30tu3btkiR17NixcQL0IM7m+r333lNubq6ef/55l8XoSRzNd2Vlpfbv36+oqCgtWLBA8fHx6tKli4YNG6a1a9e6PG4rcuZ3e9SoUcrLy1NWVpaKiopUVFSkrKws/ec//9HYsWNdGre34R7ZcNQj5qEeMQ/1iHmoRcxFPWINjXGP9HNVcE1BcXGxIiIi6mwPDg6u3V+fkpISGYZRe9yVQkJCatfW9wTBWzma62udKyMjQxEREXrggQcaKULP4Uyui4qKNHv2bD399NO64447XBShZ3E038XFxaqoqNDatWvVpk0bPffcc7rlllu0evVqPfvss6qsrNSjjz7qwsitx5nf7cTERGVlZem3v/2t/vSnP0mSAgMD9ec//1kDBgxwQbTei3tkw1GPmId6xDzUI+ahFjEX9Yg1NMY90qObIdIPrzQ5su9G9uNqzuS6xsWLF5WamqqSkhKtXLmS18muwdFcz549W2FhYUpOTnZFWB7LkXxXV1dLki5duqSlS5eqXbt2kqT4+HidPHlSf/3rXylA6uHo7/aOHTs0bdo0DRs2TEOHDlVVVZXWrVunqVOnatGiRbrvvvtcEK134x7ZMNQj5qEeMQ/1iHmoRcxFPWIdztwjPboZEhISUm/nrqSkRJLq7SLVbLfZbPWurdlW023CDxzN9ZXKy8s1ceJEHTlyRMuWLVOnTp0aO0yP4Giud+zYoQ0bNui1117ThQsXrtpXUVGh0tJSBQYGys/Po/8sNJizf0c6dOhQW3xIP/zBvvfee5WZmanCwkKe6F7B0VwbhqEZM2aoX79+euGFF2q3DxgwQAUFBXrxxRcpPhoR98iGox4xD/WIeahHzEMtYi7qEWtojHukR88MsdvtysvLq+2K1qj5nFd9ny+SpICAAIWHh9f7ebBjx46pZcuW/NH4EUdzXePSpUuaNGmS9u/fryVLlqh3794ui9XqHM318ePHVV1drdGjR9d+73lsbKwk6a233lJsbKxycnJcG7wFOfN35K677qp3n2EYknja+2OO5vrcuXM6e/asunXrVmdft27ddOrUKV26dKnxA/ZS3CMbjnrEPNQj5qEeMQ+1iLmoR6yhMe6RHt0MSUpKUmlpqT766KOrtmdnZ6t9+/ay2+3XXJuYmKicnBydPXu2dltxcbG2bNmipKQkl8VsVc7kuqKiQpMmTdInn3yizMxM9e3b19XhWpqjub7//vu1YsWKOv9J0tChQ7VixQr16NHD5fFbjTO/20lJScrPz9epU6dqtxmGoW3btik8PFwtW7Z0WdxW5Giug4OD1axZMx08eLDOvgMHDigkJETNmjVzSczeintkw1CPmId6xDzUI+ahFjEX9Yh1OHuP9Oj3zwYOHKi4uDilp6eruLhYYWFhys7O1t69e5WZmVl73OjRo7V7924dPXq0dtuTTz6pd999VykpKUpNTZWfn5+ysrLk5+enCRMmuOPHadKcyfWUKVO0fft2paamKjAwUPv376/d17JlS915551m/ihNnqO5btOmjdq0aVPvOVu3bq24uDhT4rcaZ/+OrFu3TuPHj1daWpqCgoK0Zs0affbZZ1q4cKE7fpwmzdFc+/v7a+TIkXrttdeUnp6uoUOHqrq6unbtU0895aafqOnbuHGjJOnQoUOSpD179ui7777TzTffrIEDB0riHtkYqEfMQz1iHuoR81CLmIt6xHzuqkdsRs07Uh7qwoULWrBggd5//32VlpbKbrcrNTVViYmJtcfUl1hJ+uqrrzR37lzl5ubKMAz16dNHM2bM4OvVrsHRXNd8TVV9hg8frjlz5rg0bity5vf6x6KiojRmzBilp6e7OmzLcibfp06d0ssvv6ydO3eqvLxckZGRmjhx4lVr8b8czXVVVZVWrVqld955RydOnJCPj48iIiI0atQoPfTQQ7wGfA3X+vvbrl272idi3CMbB/WIeahHzEM9Yh5qEXNRj5jLXfWIxzdDAAAAAAAAruTRM0MAAAAAAAB+jGYIAAAAAADwKjRDAAAAAACAV6EZAgAAAAAAvArNEAAAAAAA4FVohgAAAAAAAK9CMwQAAAAAAHgVmiEAAAAAAMCr0AwB4LDy8nINGDBA9913nyoqKq7al56ers6dO2v9+vUuufasWbMUFRWlb7/9ts6+/Px8devWTRkZGS65NgAAAABroxkCwGEBAQGaPHmyvvnmG7355pu121955RWtXr1aM2fO1LBhw1xy7V69ekmSDh06VGffSy+9pObNm2vy5MkuuTYAAPAM7nywA8C9aIYAcMqIESPUsWNHLVmyRGVlZVq+fLmWLl2qyZMna9SoUS67bnR0tCTp4MGDV23/+OOPtW3bNk2ZMkXBwcEuuz4AALA+dz7YAeBeNsMwDHcHAcDatmzZogkTJuiee+7Rrl27lJycrJkzZ7r8unFxcercubOWL18uSaqsrNSDDz4of39/ZWdny9fX1+UxAAAAa6uqqtLDDz+swsJCbd68WatWrdJLL72kyZMnKy0tzd3hAXAR3gwB4LSEhAR17dpVO3fu1AMPPKD09PQ6x7zxxht65JFH1L17d40ePbpRrhsdHa3Dhw+rpqe7YsUKffXVV/r9739f2whxxXUBAIDn8PX11bRp01RUVKTU1FTNmTNHo0ePphECeDiaIQCctmHDBn3++eeSpObNm8tms9U55vbbb1dKSorGjRvXaNeNjo7W+fPnlZ+fr8LCQmVmZioxMVH33HOPS68LAAA8i7se7ABwHz93BwDA2rZv365nnnlGSUlJ8vPz05o1azRu3DjdfffdVx03ZMgQSdKZM2ca7dpXDlHds2ePKioq9Oyzz7r8ugAAwLM05MHOoUOHtH//fpMjBNDYeDMEgMMOHDigyZMnq3fv3po/f76eeuop+fj46JVXXjHl+j169JCPj49Wr16tf/7znxo7dqzCw8NNuTYAAPAMVz7YGTZsmNasWaO8vLw6xw0ZMkRDhgxRaGioG6IE0NhohgBwSF5enlJSUhQREaHMzEz5+/vrzjvv1M9+9jN9+OGH2rt3b4PPOWjQIEVFRd3w8S1atJDdbteePXsUGhqqCRMmNPiaAADAe7n7wQ4A96EZAqDBzpw5o1/+8pcKCgrSq6++qhYtWtTuS01NVUBAgObNm9fg85aVlalVq1YNWtO9e3dJ0tSpU6+KAwAA4Hpc8WAHgHUwMwRAg7Vt21Zbt26td1+rVq104MCBBp/ziy++UHFxsf74xz/e8JrKykrt3r1b3bp10/Dhwxt8TQAA4J1+6sFOdna25s2bp7feesuNUQJwJZohAExx+fJlVVVVqaqqStXV1bp06ZJsNpv8/f0l/fB53U6dOjWoqfGPf/xDp06d0vz58+sddHYj1wUAAN7HFQ92AFgLzRAApsjKytLixYtr/92jRw/17dtXr7/+uiRp/PjxGj9+/E+ep7i4WNu3b9fRo0e1bNky/eIXv1DPnj0dvi4AAMCN4AEL4FlshmEY7g4CAG7Ue++9p2nTpik0NFQPP/ywpk+fLl9fX3eHBQAAPNxf/vKXqx6wSOIBC2BhNEMAAAAAAIBX4dtkAAAAAACAV6EZAgAAAAAAvArNEAAAAAAA4FVohgAAAAAAAK9CMwQAAAAAAHgVmiEAAAAAAMCr0AwBAAAAAABehWYIAAAAAADwKv8f8jXiOou6rOwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1296x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(18, 6))\n",
    "# fig.title(\"T = 350 K, Propane (1), Butane (2)\")\n",
    "sns.lineplot(x=vle.liquid.molefracs[:,0], y=vle.liquid.pressure / BAR, ax=ax[0])\n",
    "sns.lineplot(x=vle.vapor.molefracs[:,0], y=vle.vapor.pressure / BAR, ax=ax[0])\n",
    "ax[0].set_xlabel(r\"$x_1$, $y_1$\")\n",
    "ax[0].set_ylabel(r\"$p$ / bar\")\n",
    "ax[0].set_xlim(0, 1)\n",
    "ax[0].set_ylim(5, 35)\n",
    "# ax[0].legend(frameon=False);\n",
    "\n",
    "sns.lineplot(x=vle.liquid.molefracs[:,0], y=vle.vapor.molefracs[:,0], ax=ax[1])\n",
    "sns.lineplot(x=np.linspace(0, 1, 10), y=np.linspace(0, 1, 10), color=\"black\", alpha=0.3, ax=ax[1])\n",
    "ax[1].set_xlabel(r\"$x_1$\")\n",
    "ax[1].set_ylabel(r\"$y_1$\")\n",
    "ax[1].set_xlim(0, 1)\n",
    "ax[1].set_ylim(0, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison to Rust implementation <a id=\"Comparison-to-Rust-implementation\"/>\n",
    "[↑ Back to top](#toc)\n",
    "\n",
    "Implementing an equation of state in Python is nice for quick prototyping and development but when it comes to performance, implementing the equation of state in Rust is the way to go.\n",
    "For each non-cached call to the Helmholtz energy, we have to transition between Rust and Python with our Python implementation which generates quite some overhead.\n",
    "\n",
    "Here are some comparisons between the Rust and our Pyhton implemenation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# rust\n",
    "from feos.cubic import PengRobinsonParameters\n",
    "eos_rust = EquationOfState.peng_robinson(PengRobinsonParameters.from_json([\"propane\"], \"peng-robinson.json\"))\n",
    "\n",
    "# python\n",
    "tc = SIArray1(369.96 * KELVIN)\n",
    "pc = SIArray1(4250000.0 * PASCAL)\n",
    "omega = np.array([0.153])\n",
    "molar_weight = SIArray1(44.0962 * GRAM / MOL)\n",
    "eos_python = EquationOfState.python(PyPengRobinson(tc, pc, omega, molar_weight))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's first test if both actually yield the same results ;)\n",
    "assert abs(State.critical_point(eos_python).pressure() / BAR - State.critical_point(eos_rust).pressure() / BAR) < 1e-13\n",
    "assert abs(State.critical_point(eos_python).temperature / KELVIN - State.critical_point(eos_rust).temperature / KELVIN) < 1e-13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "import timeit\n",
    "\n",
    "time_python = timeit.timeit(lambda: State.critical_point(eos_python), number=2_500)\n",
    "time_rust = timeit.timeit(lambda: State.critical_point(eos_rust), number=2_500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Critical point for pure substance\n",
      "Python implementation is slower by a factor of 48.\n"
     ]
    }
   ],
   "source": [
    "rel_dev = (time_rust - time_python) / time_rust\n",
    "print(f\"Critical point for pure substance\")\n",
    "print(f\"Python implementation is {'slower' if rel_dev < 0 else 'faster'} by a factor of {abs(time_python / time_rust):.0f}.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_python = timeit.timeit(lambda: PhaseDiagram.pure(eos_python, 300*KELVIN, 100), number=100)\n",
    "time_rust = timeit.timeit(lambda: PhaseDiagram.pure(eos_rust, 300*KELVIN, 100), number=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Phase diagram for pure substance\n",
      "Python implementation is slower by a factor of 31.\n"
     ]
    }
   ],
   "source": [
    "rel_dev = (time_rust - time_python) / time_rust\n",
    "print(f\"Phase diagram for pure substance\")\n",
    "print(f\"Python implementation is {'slower' if rel_dev < 0 else 'faster'} by a factor of {abs(time_python / time_rust):.0f}.\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
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 },
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