{ "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 \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", "import si_units as si\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 \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": 2, "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 / si.KELVIN\n", " self.pc = critical_pressure / si.PASCAL\n", " self.omega = acentric_factor\n", " self.mw = molar_weight / si.GRAM * si.MOL\n", "\n", " self.a_r = (0.45724 * critical_temperature**2 * si.RGAS \n", " / critical_pressure / si.ANGSTROM**3 / si.NAV / si.KELVIN)\n", " self.b = (0.07780 * critical_temperature * si.RGAS \n", " / critical_pressure / si.ANGSTROM**3 / si.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: list[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", " si.array(tc * si.KELVIN), \n", " si.array(pc * si.PASCAL), \n", " omega, \n", " si.array(mw * si.GRAM / si.MOL)\n", " )\n", " else:\n", " return self\n", " \n", " def molar_weight(self) -> si.SIObject:\n", " return si.array(self.mw * si.GRAM / si.MOL)\n", " \n", " def max_density(self, moles: list[float]) -> float:\n", " b = np.sum(moles * self.b) / np.sum(moles)\n", " return 0.9 / b " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 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": 3, "metadata": {}, "outputs": [], "source": [ "tc = si.array(369.96 * si.KELVIN)\n", "pc = si.array(4250000.0 * si.PASCAL)\n", "omega = np.array([0.153])\n", "molar_weight = si.array(44.0962 * si.GRAM / si.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_residual(pr)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "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": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\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" ] } ], "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": 5, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$1.6605\\times10^{-24}\\,\\mathrm{ mol}$" ], "text/plain": [ "1.6605390671738466e-24 mol" ] }, "execution_count": 5, "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*si.KELVIN, pressure=1*si.BAR)\n", "s.total_moles" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$1\\,\\mathrm{ mol}$" ], "text/plain": [ "1 mol" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s_pt = State(\n", " eos, \n", " temperature=300*si.KELVIN, \n", " pressure=1*si.BAR, \n", " total_moles=1*si.MOL\n", ")\n", "s_pt.total_moles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 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": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Critical point\n", "temperature: 369.95061742346076 K\n", "density : 198.1862458057177 kg/m³\n", "pressure : 4.249677749116944 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\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": 8, "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": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vle = PhaseEquilibrium.pure(eos, 300.0*si.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": 9, "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": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vle.liquid # the high density phase `State`" ] }, { "cell_type": "code", "execution_count": 10, "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": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vle.vapor # the low density phase `State`" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Heat of vaporization: 14.782343503305125 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(Contributions.Residual) - vle.liquid.molar_enthalpy(Contributions.Residual))\n", "print(\"for T = {}\".format(vle.liquid.temperature))\n", "print(\"and p = {:.2f} bar\".format(vle.liquid.pressure() / si.BAR))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also easily compute **vapor pressures** and **boiling temperatures**:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "vapor pressure (T = 300 K): 994.776163561008 kPa\n", "boiling temperature (p = 3 bar): 247.84035574956764 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*si.KELVIN)[0])\n", "print(\"boiling temperature (p = 3 bar):\", PhaseEquilibrium.boiling_temperature(eos, 2*si.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": 13, "metadata": {}, "outputs": [], "source": [ "dia = PhaseDiagram.pure(eos, 230.0 * si.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": 14, "metadata": {}, "outputs": [], "source": [ "enthalpy_of_vaporization = [\n", " (vle.vapor.molar_enthalpy(Contributions.Residual) - vle.liquid.molar_enthalpy(Contributions.Residual)) / (si.KILO * si.JOULE) * si.MOL \n", " for vle in dia.states\n", "]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(7, 4))\n", "sns.lineplot(x=dia.vapor.temperature / si.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": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\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[0mcontributions\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", "Parameters\n", "----------\n", "contributions : Contributions, optional\n", " The contributions to consider when calculating properties.\n", " Defaults to Contributions.Total.\n", "\n", "Returns\n", "-------\n", "Dict[str, List[float]]\n", " Keys: property names. Values: property for each state.\n", "\n", "Notes\n", "-----\n", "- temperature : K\n", "- pressure : Pa\n", "- densities : mol / m³\n", "- mass densities : kg / m³\n", "- molar enthalpies : kJ / mol\n", "- molar entropies : kJ / mol / K\n", "- specific enthalpies : kJ / kg\n", "- specific entropies : kJ / kg / K\n", "- xi: liquid molefraction of component i\n", "- yi: vapor molefraction of component i\n", "- component index `i` matches to order of components in parameters.\n", "\u001b[0;31mType:\u001b[0m builtin_function_or_method\n" ] } ], "source": [ "dia.to_dict?" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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4-428.221030101515.453964-18.88292014093.973182231.121849-0.034978621.490660-3.73081454.654773-0.164515-0.003510-0.0001552.410068-0.793228
\n", "
" ], "text/plain": [ " specific enthalpy liquid pressure molar enthalpy liquid \\\n", "0 -429.097170 96625.278174 -18.921555 \n", "1 -428.878435 97830.133956 -18.911909 \n", "2 -428.659501 99046.729400 -18.902255 \n", "3 -428.440366 100275.143120 -18.892592 \n", "4 -428.221030 101515.453964 -18.882920 \n", "\n", " density liquid temperature molar entropy liquid mass density liquid \\\n", "0 14125.988947 230.000000 -0.035166 622.902434 \n", "1 14118.006852 230.280462 -0.035119 622.550454 \n", "2 14110.010220 230.560924 -0.035072 622.197833 \n", "3 14101.999011 230.841386 -0.035025 621.844569 \n", "4 14093.973182 231.121849 -0.034978 621.490660 \n", "\n", " specific enthalpy vapor density vapor molar enthalpy vapor \\\n", "0 -3.570554 52.208491 -0.157448 \n", "1 -3.610123 52.811929 -0.159193 \n", "2 -3.650021 53.420767 -0.160952 \n", "3 -3.690251 54.035036 -0.162726 \n", "4 -3.730814 54.654773 -0.164515 \n", "\n", " specific entropy vapor molar entropy vapor mass density vapor \\\n", "0 -0.003363 -0.000148 2.302196 \n", "1 -0.003399 -0.000150 2.328805 \n", "2 -0.003436 -0.000152 2.355653 \n", "3 -0.003473 -0.000153 2.382740 \n", "4 -0.003510 -0.000155 2.410068 \n", "\n", " specific entropy liquid \n", "0 -0.797483 \n", "1 -0.796418 \n", "2 -0.795354 \n", "3 -0.794290 \n", "4 -0.793228 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_dia = pd.DataFrame(dia.to_dict(Contributions.Residual))\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": 18, "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": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "phase_plot(data_dia, \"molar entropy\", \"temperature\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 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": 21, "metadata": {}, "outputs": [], "source": [ "# propane, butane mixture\n", "tc = np.array([369.96, 425.2]) * si.KELVIN\n", "pc = np.array([4250000.0, 3800000.0]) * si.PASCAL\n", "omega = np.array([0.153, 0.199])\n", "molar_weight = np.array([44.0962, 58.123]) * si.GRAM / si.MOL\n", "\n", "pr = PyPengRobinson(tc, pc, omega, molar_weight)\n", "eos = EquationOfState.python_residual(pr)" ] }, { "cell_type": "code", "execution_count": 22, "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": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = State(\n", " eos, \n", " temperature=300*si.KELVIN, \n", " pressure=1*si.BAR, \n", " molefracs=np.array([0.5, 0.5]), \n", " total_moles=si.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": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ -93.60749754, -120.5269973 ]) J/mol" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.chemical_potential(Contributions.Residual)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 4.90721995, -0.10487987],\n", " [-0.10487987, 4.85361765]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.dmu_dni() / (si.KILO * si.JOULE / si.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": 25, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "|temperature|density|molefracs\n", "|-|-|-|\n", "|401.65562 K|3.99954 kmol/m³|[0.50000, 0.50000]|" ], "text/plain": [ "T = 401.65562 K, ρ = 3.99954 kmol/m³, x = [0.50000, 0.50000]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s_cp = State.critical_point(\n", " eos, \n", " moles=np.array([0.5, 0.5])*si.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": 26, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "||temperature|density|molefracs|\n", "|-|-|-|-|\n", "|phase 1|350.00000 K|879.50373 mol/m³|[0.67631, 0.32369]|\n", "|phase 2|350.00000 K|8.96383 kmol/m³|[0.50000, 0.50000]|\n" ], "text/plain": [ "phase 0: T = 350.00000 K, ρ = 879.50373 mol/m³, x = [0.67631, 0.32369]\n", "phase 1: T = 350.00000 K, ρ = 8.96383 kmol/m³, x = [0.50000, 0.50000]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vle = PhaseEquilibrium.bubble_point(\n", " eos, \n", " 350*si.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": 27, "metadata": {}, "outputs": [], "source": [ "vle = PhaseDiagram.binary_vle(eos, 350*si.KELVIN, npoints=50)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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IiLgvPS+bV1fN4u3D8kDObNaBWzqfRv8GrYIyD+RQCkmtWkHTDAHaEKjnZWAnkAyMAqYbY8611n4LYIzpDnwHrAR+CzQFfge0Bi6s8qpFRERERETEFSv27eDFlTP4YtNyvIfkgVzVrhc3dRxE66T6Lld4fBSSWvWCphlirX2XwAyPMsaYF4CNwN3At6XDjwD7gWHW2tzS8zYDLxtjTrfWfl9lRYuIiIiIiEiVchyHH3as5cW06czauaFsPCU2gbEdBnCd6UedIM4DOZRCUt0TNM2Q8lhr840xewnMEsEYkwicCfznYCOk1ETgSeAqQM0QERERERGRaqbI5+WTjUt5KW0GNmt32bhJbsCtnU/j4tbdiQ7iPJDDlReS2rVrV6KiolyurGYIuv9SjDEJQDRQF7ge6Az8vfRwFwI1Lzz0GmttsTFmKdCj6ioVERERERGRypZVlM+bdh6vrprNnoKcsvHBjdpyW5chDG3cLujzQA6lkNTgEHTNEOA14PLSPxcD/yOwNAagUenrznKu2wkMONKbGmOyjnHfpOMvUURERERERCrTtpwMxq+axaS1C8j3FgMQ7gnjolZdubXzaXSu28TlCk+cQlKDRzA2Q/4GvEggGHU0gVkikUAREFt6TlE51xUeclxERERERERC0Mr96byQNp3PNy3HVxqKGh8Zzaj2fbmx4yAaxye7W+BJUkhqcAm6Zoi1dgWwAsAY8yaBJTGvA1cABaWnRZdzacwhx8t73+Sj3bd05ohmh4iIiIiIiFQxx3GYtXMDL6yYxrT0dWXjDeMSubHjIEaZfiRGxbhY4ckrKSlh+fLlpKenAwpJDRZB1ww5lLW2xBjzKfAnY0wsPy2PaVTO6Y2A9CorTkREpJpzHAdv6bRkERGRyuD1+/hqcxovpE1nxf4dZePtk1O4vfNQLm7djagQCkU9nEJSg1co/FcVC3iABCAN8AK9gY8OnmCMiQK6A2+7UJ+IiEi1k56bxfgPHsJTnA+Eu12OiIhUMwXeYt5bt4iXVs5gS05G2Xi/Bq34VZehDG/anjBP6C4fUUhq8AuaZogxpr61du9hY4nAlcA2a+2e0rGpwGhjzCOHbK87GogH3q/KmkVERKobv+PnTTufD74bz0OL3uQTmrpdUqUyxkQT2LVuNFAbWAY8aK397jiuPQP4E4Hd7sKANcCT1tr3Kq9iEZHQllWUz8Q1c3ll1Sz2F+YB4MHDOS06clvnofRKCf1mgUJSQ0PQNEOAd40xhcBsYBfQDBhHIEh15CHnPVh6zo/GmPGlx+8FvrbWTq3akkVERKqPjdl7uW/Wh6RvWsQzS94h1l+CE8Kfyh2n1wnsYvcUsB4YC3xtjBlqrZ1zpIuMMRcAnxF4Jvm/0uGRBJ5nEqy1r1RizSIiIWdX/gFeXjmTN9fMJa90CWZUWDhXtO3FrZ1Po01SfZcrrBgKSQ0dwdQMeRMYA/yawCczWcBcYLS1dtrBk6y1i0s/ifk38CRwAHgZuL+qCxYREakOSvw+XkybwZNLp5KQn8mzyz8gyVuAJ6Ee4THxkJvndomVwhjTl0AD4zfW2qdKxyYSWJb7b2DIUS6/g0CW2QhrbVHptS8DGwk8z6gZIiICbMzex//SpvPB+kUU+wMNgvjIaEab/tzUaRAN4hJdrrBiKCQ19ARNM8Ra+yrw6nGeOxMYVLkViYiIVH8r9u3gd7M+YGXGTuJLCnl85cc0KDqAJ7oWzX77Jcy5ze0SK9MVQAkw/uCAtbbQGPMK8LAxppG1ducRrk0EMg82QkqvLTLGZHKU3e1ERGqKFft28PyKaXy5ZQV+xwGgXkw8N3UaxGjTn6ToWJcrrDgKSQ1NQdMMERERkapT4C3hyaVTeTFtBj7HT7TPy/hN35GSsxvCI2l814fEtOrtdpmVrQew5pAMsoPmEwhv785PO9kdbhpwvzHmIQJLbSCwxKY98JuKLlREJFTM3bWRZ5f/yLQda8vGmsXX5rbOQ7iqXW9iIyJdrK5iKSQ1tKkZIiIiUsNM37GO++d8XJben5pYl2fWf0vEzlUANLz5NWp1PtPNEqtKI2BHOeMHGyCNj3Ltw0AbAllmfyodywUustZ+e6SLjDFZx6gp6RjHRUSCjuM4/LBjLc8t/4H5uzeXjZvkBtzRdRgXtepKRFj12plMIamhT80QERGRGmJ/YS5/m/8lH21YAkBkWDh3dhnCyIWTyFsd2Dyl/rVPktj/GjfLrEqxQFE544WHHD+SImAtgZ3sPiaw//AtwHvGmBHW2gUVWaiISDDyO36+2rKS55b9QFpGetl4z/rN+XW34YxomorH43Gxwsqxbds2VqxYoZDUEKdmiIiISDXnOA4frF/M3xZ8SVZRPgD9GrTknwMupfbk/5A5+w0A6lz4ILXP+rWbpVa1AiC6nPGYQ44fybNAX6CPtdYPYIx5D1hJYGeacrPNrLXJRyuodOaIZoeISFAr8fv4dONSnlv+I+uz95aNn9a4LXd2Hc7Ahq2rZRNEIanVi5ohIiIi1djG7H3cP+djZu3cAEBSVAwP9D6Pa9r3JuvL/7BvypOB8eG3Uveyv7lZqht2Elgqc7iDY+nlHMMYEwXcBDxysBECYK0tMcZ8DfzKGBNhrfVWdMEiIm4q9Jbw3vpFvLBiGttyM8vGz2rWgTu7Dadn/eqblbF//36WLFlCQUGgT66Q1NCnZoiIiEg1VOzz8r+06Ty97HuKfIHfyS9q1ZW/9r2QlLgEsn58mX0fPABAfN8rSRn9bLX8FO8YlgJ3G2PiDwtR7Vf6uuwI19Ul8AxV3gL4yNJjNe5fpohUXwXeYt6y83khbTq78w8AEObxcGGrrtzZZTgd6jR0ucLKo5DU6kvNEBERkWpmwe7N/HH2x9is3QA0jU/m4f6XMKJZKgA5Cz5kz4RfARDX6Qwa3TIRTzULtjtOHwC/IzDL4ykAY0w0MA6YZa1NLx1rDsRZa9eUXrcHyAIuM8b8zVpbUnpePHAhkHZwTEQklOWVFDFxzVxeTJvBvsJAzzgyLJzL2/Tgjq7DaJVYvZeHlBeS2rNnT+Lj490tTCqEmiEiIiLVRGZhHo8smsyktYHszjCPh5s7DubeHmcSFxmYxpu3Ygo7/zcKHD8xrfvS+K4P8UTUzCm+1tp5xpj3gUeNMY2ADcD1QAsC2+QeNBEYSulsD2utzxjzGPAPYI4x5k0Cs0RuBJoSaLCIiISsnOJCXl89h5dWziCzNGsqKiyca9r34VddhtEkPtndAquAQlKrPzVDREREQtzBgNSHFnxFRlEeAN3qNeVfAy6lS70mZecVrJtN+rNXgK+EqMYdafLbLwiLqfGfbo0BHip9rQ0sB86z1s462kXW2oeNMZuAu4H/IxDEuhy4zFr7ceWWLCJSObKK8nll1SxeXTWL7OLAxlrR4RFcZ/pxW+chNKpV/fOdFZJac6gZIiIiEsLWZe3h/jkfM3fXJgASIqP5Q69zGG36EX7Ip1dFW5ex44kLcIrziazfiqb3TSE8vq5bZQcNa20hcF/p15HOGXaE8beBtyunMhGRqpNZlM/LaTN4dfVscksCO47HRUQxJrU/t3Y+jfqxCS5XWDUOD0lt2LAh3bp1U0hqNaVmiIiISAgq8BbzzLIf+F/adEr8gSm8F7fqxl/6nk+DuMSfnVu8ay3bHzsHf0E24cmNaHLfN0TUbuxG2SIiEkTKa4LER0ZzQ4eB3NRpMHViarlcYdVQSGrNpGaIiIhIiPlhu+XBOZ+yNTcDgBYJdXl4wMUMa9L+F+eW7N/K9kfPwndgD2G16tD0vilEpbSu6pJFRCSIlNcESYyK4YaOg7ip4yCSo+NcrrDqKCS15lIzREREJESk52Xzt/lf8OXmFUAg0f9XXYZyZ9fhxEZE/uJ8b/Zutv/nbLwZ2/DExNPk3i+JbtKpqssWEZEgcaQmyI0dB3FTx8EkRce6XGHVUkhqzaZmiIiISJAr8fsYv3ImTy79jnxvMQADG7bmkQGX0DY5pdxrfLkZbP/P2ZTsWosnIpomd39CbOu+VVm2iIgECTVBfk4hqQJqhoiIiAS12Ts38Ke5n7I2aw8A9WPj+VOf87msdXc8Hk+51/gKDrD98fMo3r4CwiNodOf7xHUYXpVli4hIEMguKuDlVTMZv3KmmiClFJIqB6kZIiIiEoT25Ofw0IIv+XjjUgDCPB7Gpg7gdz3PIjEq5ojX+YvySH/yIoo2LQBPGI1ufZP47udXUdUiIhIMckuKeHXVLF5Mm162RW5Nb4IoJFUOp2aIiIhIEPH6fUxYM5fHFn9DTumneD3rN+eRARfTuW6To17rLyki/ZnLKFg7A4AGN44noe+VlV6ziIgEh/ySYiasmcPzK6aRWZQPQK2IKG7qNJibOw2uUcGoh1JIqpRHzRAREZEgsWjPFh6Y8wkrM3YCUDs6jgd6n8vV7XoR5jl6mJvjLWHn81eTv3IqACljniNp8PWVXrOIiLiv0FvCm3Ye/13xI3sLcgGIjYhkbOpAbu8ypMZskVuebdu2kZaWhtfrBRSSKj9RM0RERMRlewty+OfCyby3fhEAHjxc274Pf+x1NrWP4wHW8XnZ9dIY8pZ8DkC9q/9D8um3V2rNIiLivmKfl3fWLeSZZd+zK/8AANHhEYw2/bij6zDqxya4XKF7FJIqx6JmiIiIiEu8fh+vr57D40u+LVsS06VuEx4ZcAk96jc7rvdw/D52jb+BnPnvAVD3kv+jzrm/rbSaRUTEfT6/n483LuHxJVPZlpsJBLZbv7Z9H+7sOpxGtZJcrtBdCkmV46FmiIiIiAtm79zAn+d+hs3aDUBydBx/7Hk217TvQ/hxTt11/H52v3YLOXPeAqDOBX+kzsV/rrSaRUTEXY7jMHnrSv6z+JuyXcbCPWFc2bYn93QfQdP42i5X6C6FpMqJUDNERESkCqXnZfPwgq/4dNMyILAk5jrTl9/3POu4lsQc5DgOeybewYEZrwNQ+5zfUvfyfxxxu10REQldjuMwI309/148hWX7tpeNX9y6G/d2P5PWSVr6oZBUOVFqhoiIiFSBIp+X8Stn8vSy78n3FgOBXWIe7n8xXeodfZeYwzmOw9637iH7x5cASD7jTupd/agaISIi1dDC3Vv49+IpzNm1sWzszGYduK/nmXSs09jFyoKHQlLlZKgZIiIiUsm+327567zP2XhgHwD1YuJ5sPe5XN62xzF3iTmc4zjse/f3ZE19DoCkYbdQf9RTaoSIiFQzqzJ28ujiKUzdtqZsbEDD1vyx19n0SmnhYmXBQyGpcirUDBEREakkG7P38bf5X/Dd9sCDbLgnjHEdBvDbHmeSGBVzwu8XaIT8gczJTwCQeNpYUsb8V40QEZFqZFtOBo8t+ZaPNizFwQGgW72m/LHX2Qxu1Fbf80spJFVOlZohIiIiFSy3pIinl37P+FUzKfH7ABjYsDV/63cRHeo0PKn3dByHfe/9kczJjwOQMPA6Gox7CY+mAIuIVAv7C3N5ZtkPvLFmLsWlPzvaJaXw+15ncU7zTmqClFJIqlQUNUNEREQqiN/x89GGJTyycDJ7CnIAaBqfzJ/7nM95LTqf9IOs4zjse/9+Mr9+DAg0Qhre9CqesPAKq11ERNyRX1LMyytn8ELadHJLt1lvFJfEvT3O4Iq2PYnQ9/oyCkmViqRmiIiISAVYuncbf573GUv2bgMgJjySO7sO49bOQ4iNiDzp9w00Qh4g86v/AJAwYJQaISIi1UCJ38ektQt4culU9hbkApAUFcOdXYcztsPAU/rZUR0pJFUqmpohIiIip2BvQQ7/WjSZd9ctKhu7qFVXHux9Hk3ik0/pvR3HYd8HD5L51aMAJAy4loY3v6ZGiIhICHMchy82r+Dfi6awOWc/ANHhEdzYcRC/6jKU5Og4lysMLgpJlcqiZoiIiMhJOLhV7rPLfyib1tyxTiP+3u9C+jdsfcrvX7Y05uCMkP7X0PDm19UIEREJYfN3b+ahBV+WzSIM83i4ul1vftP9DBrXSnK5uuCjkFSpTGqGiIiInADHcZi8dSX/WPAVW3IyAKgdHcfve57Fte37El4B03Udx2HvO78ja8pTACT0H6lGiIhICNuQvZdHFn7NlK2rysbObt6RP/Y6h3bJKS5WFpwOhqSuX78ex3EUkiqVQs0QERGR47QqI52/zvuC2bs2AhDhCWNshwHc031EhU1rdhyHvW/dQ9bU5wCFpYqIhLJ9Bbk8uXQqb9r5+Bw/AD3qN+NPvc+jX8NWLlcXnBSSKlVFzRAREZFj2FeQy38Wf8OkdQvwOw4Apzc1/KXP+bStwE/0HL+fPW/eRfb3/wMg8bSxpdvnqhEiIhJKCrzFjF85i/+u+LFsKWWLhDr8sdc5XNCyi7bJPQKFpEpVUjNERETkCIp9Xl5bPZunln5HTunDbNuk+vxf3wsY3tRU6L0cv5/dr9/GgemvAJA09CZSrn8Bjx4ARURCht/x8+H6Jfx78RR25R8AIDk6jnu6nc7o1P5Eh+vXr/IoJFXcoP83ioiIHMZxHKZsXcU/FnxVlvSfFBXLvT3OYHRqfyIreKaG4/ex+9WbOTBzQuBep99GynXPqhEiIhJC5uzayN/mfUFaRuAX+qiwcG7oOIg7uw7TDjFHoZBUcYuaISIiIodI27+Dv83/kjmluSDhnjBGp/bj3u5nUDumVoXfz/GWsOulMeTMfw+A5DPvov61T2oKtYhIiNh0YB8PL/iayVtXlo1d0ro7f+h5Fs0S6rhYWXBTSKq4Tc0QERERYFf+AR5dNIX31y/GIZALMryJ4c99z6N9coNKuae/uJCdL4wkb8nnANQ+7z7qXflPNUJEREJAdlEBzyz7nldXz6bE7wOgV/3m/F+/C+hZX7/QH01eXh5LliwhMzMTUEiquEPNEBERqdEKvMW8mDaD51dMI99bDIBJbsCf+57PsCbtK+2+/qJ80p+5lPyVUwGoe+lfqXPRn9QIEREJcl6/j7fsfB5fMpWMojwAmsYn80Cvc7mwVVd9Hz+Gw0NS27RpQ2pqqkJSpcqpGSIiIjWS3/Hz8cZl/GvhZHbmZwNQN6YW9/U4i5HtexNRiTu4+Aty2PHURRTY6QDUu/pR6px7b6XdT0REKsYP2y0PLfiStVl7AKgVEcVd3YZzY8fBxEZEulxdcFNIqgQbNUNERKTGmbdrE39f8CXL9m0HAiF3N3UazJ1dh5MYFVOp9/blZrDjiQso3DgPgJTRz5E84vZKvaeIiJyajdl7+ev8L/h+uwXAg4eR7XtzX4+zSIlLcLm64KeQVAlGQdMMMcb0AcYCw4EWwH5gNvAna+36Q877ERhazlu8a60dWfmViohIqNqYvZdHFk7+WcjdhS27cn/vc2heBSF33qxdbH/sHIq3rwBPGA1ueImk08ZV+n1FROTk5BQX8tSy73l11ayyXJBBjdrwf33Pp2Odxi5XF/zKC0nt1KkTLVq0cLs0keBphgB/AAYB7wPLgYbAncASY0xfa+3qQ87dCjx42PWbq6JIEREJPRmFeTy59DveWDMXr+MHoEf9Zvylz/n0adCySmoo2buZ7f85i5I9GyA8kka3TiSh71VVcm8RETkxfsfP++sX869Fk9lbkAtA8/g6/KXv+ZzdvKNyQY6DQlIl2AVTM+QJ4FprbfHBAWPMu8AKAo2SsYecm2mtfbNqyxMRkVBT6C3htdWzeXb5DxwoLgQCD7P39z6HC1p2qbKH2aL01ez4z9l4M3fgiYql8Z3vU6vruVVybxEROTGL9mzlL/M+K1tKGRsRya+7ns7NnQYTo1yQ46KQVAkFQdMMsdbOLmdsnTFmJdDh8GPGmAggxlqbWxX1iYhI6PA7fj7btJx/LZrM9twsAJKiYvh1t9MZ22Eg0eFV9+OvcNNCtj9+Hv7c/YTFJtL4ns+IM6dV2f1FROT47Mo/wD8Xfs2HG5aUjV3SujsP9D6XxrWSXKwsdCgkVUJJ0DRDymOM8QANgGWHHeoA5AFRxpidwHPAv6y1/iouUUREgszh4aiRYeFcn9qfu7udTu2YWlVaS/6aaaQ/dTH+whzCE+rR5N6viWnZs0prEBGRoyv2eXl55UyeWfY9eaVbrHep24S/97uwypZSVgcZGRksXrxYIakSMoK6GQKMAprw83yQDcD3BJbPJALXAA8DzYHbjvRGxpisY9xL7V4RkRC2LmsP/1z4Nd9s+yli6rwWnbm/9zm0Sqz6T6RyF33CzheuxfEWEVGnKU1/N4WoxqlVXoeIiBzZjPR1/GnuZ2zI3gsEtlj/Q6+zubptb8K1pOO4KCRVQlXQNkOMManAf4GZwBsHx621Nx526gRjzHvALcaYJ621tgrLFBERl+3OP8ATS6Yyad0C/I4DQM/6zflzn/Nc+0Qve9p4dr9+Ozh+Ihu2p+nvJhNZTw+FIiLBIj03i78t+JIvN68AINwTxtgOA/ht9zNIio51ubrQoZBUCWVB2QwxxjQEvgQygSuPY/nL48CVBLblLbcZYq1NPsY9s9DsEBGRkJFbUsT/0qbzYtp0CrwlALRMqMv9vc/hvBadXUn6dxyHzC//zb4PAhMao1v1pslvviAisX6V1yIiIr9U7PPy0sqZPL3su7KfHX0btOQf/S+mY51GLlcXWhSSKqEu6Johxpgk4GsCjYlB1tpdx3HZttLXOpVWmIiIBIUSv4931i7giaVTy7Y7rBNdi990H8F1qf2IDAt3pS7H72fvpHvJ+vYZAOI6jaDxnR8SFpvgSj0iIvJz03as5c9zP2PjgX0A1I+N5099zuey1t21Ve4JUEiqVBdB1QwxxsQAnwPtgREnsOSldenr3kopTEREXOc4DlO2ruKfiyaXre2OCY/klk6Dub3LUBKiYtyrzVvMrvE3kDN3EgAJfa+i4S0T8EQoNE5ExG07crP42/wv+GpLGhBYEjOuwwB+2+NMEl382RGKFJIq1UnQNEOMMeHAu8AA4GJr7dxyzkkEiqy1RYdd9wDgB6ZWUbkiIlKF5u/ezCMLv2bhni0AhHk8XNW2F/f2OJNGLm936Cs4wM7nriB/5XcAJI+4g/qjnsKjacIiIq4q8fsYv3ImTyydWrYkpl+Dlvyj/yV0qNPQ5epCi0JSpToKmmYIgdyPiwjMDKljjLnukGO51tpPgJ7A28aYScB6IB64CugN/Ntau6lqSxYRkcpkM3fz70WTf7ZDzOlNDff3OjcoHmS9WTvZ8cQFFG1dCkDdS/9GnYse1HRrERGXLdi9mT/O/hibtRuAlNgEHuxznpbEnASFpEp1FUzNkO6lrxeWfh1qC/BJ6ess4HKgAYHZIGnAWGvthCqpUkREKl16XjaPL/mW99cvKtshpnu9ZjzQ+xwGNmrjcnUBxelr2P74eXj3b4GwcBqM/R9JQ25wuywRkRotsyifRxZ+zaS1CwDw4GFshwHc1/MsLYk5CQpJleosaJoh1tphx3HOJgK7xoiISDWUVZTPf5dP49XVsyjyBR68WiXW44+9znZth5jyFKybzY6nLsafl4EnKo7Gd75Hra7nul2WiEiN5TgOH25YzN/nf0VGUR4AXeo24V8DL6VbvaYuVxd6ygtJ7d69O/Xra3c0qT6CphkiIiI1V4G3hAmr5/Ds8h/ILg6EstWPjee33c9gZPs+ru0QU57cRZ+w83+jcEoKCU9MoclvPiemVW+3yxIRqbHWZe3h/jkfM3dXYMV8fGQ0v+95FtenDiBcMxhOmEJSpaZQM0RERFzj9ft4f/1inlgylZ352UDgIfb2zkO4qdNgakVGu1zhz2V+8wx7J/0WHIfIBm1pcu9XRKUEx7IdEZGapsBbwrPLvueFtOmU+H0AXNiyK//X7wIaxiW6XF3oUUiq1DRqhoiISJVzHIevt6zk0cVTWF+6TW5kWDjXmX7c0/106sYEVyib4/exd9K9ZH37LAAxrfvS+J7PiEjUdGERETfMSl/PH2Z/zOac/QC0SKjDP/pfzPCmxuXKQpNCUqUmUjNERESq1KydG/jnwsks3bcNCITbXdamO/f2OJPmCXVcru6X/EV57PzfKPKWfA5AfK9LaXjLRMKi41yuTESk5sksyucfC77k3XWLgEAj/fbOQ7ir2+nERkS6XF1oUkiq1FRqhoiISJVYsW8H/1o0mWnp68rGzmiWyu97nk3HOo1crOzIvFm72PHURRRtDjx01z7nt9S76t949IAoIlKlHMfhs03L+b95n7OvMBeAXvWb8+igyzG1G7hcXWhSSKrUdGqGiIhIpdqYvY/HlnzDZ5uWl431SWnB/b3PpW+Dlu4VdgxFO1ay44kL8O7fCp4wUkY9TfIZv3K7LBGRGmdHbhYPzPmE77avAaBWRBT39z6XMan9CPOoOX0yFJIqomaIiIhUkvS8bJ5a+h3vrluIz/EDYJIbcH/vcxjRNDVotsktT97yyex84Rr8BQfwRNei0e1vE9/9ArfLEhGpUXx+P6+tns2ji78h31sMwJnNOvBw/4tpHJ/sbnEhSiGpIj9RM0RERCpURmEezy3/gQlr5lLkC6w/bhZfm3t7nMmlrbsH/TaHmVP/y9637gHHT3hyY5rc8ykxLXu6XZaISI2yOmMX9836sCxfqn5sPA/1u4jzW3YJ6mZ6MFNIqsjPqRkiIiIVIqe4kJdXzuSllTPILSkCICU2gbu7nc417fsQFR7cP3Icn5c9b91D9vcvABDdoieN7/mEyNpNXK5MKpMxJhr4OzAaqA0sAx601n53nNdfC9wDdAKKgBXAfdba+ZVSsEg1V+zz8tzyH3l2+Q9l2+Ve074PD/Y+l2QFV580haSK/FJwP5mKiEjQK/CW8MaauTy7/Acyi/IBSIqK4fYuw7ihw0DiIoN//bEvL4udL4wkP+1b4OCOMRMIi67lcmVSBV4HLgeeAtYDY4GvjTFDrbVzjnahMeYfwB+AN4CXgFpAN6Bh5ZUrUn0t37ede2d+wOrMXQC0TKjLfwZfzoCGrV2uLHQpJFXkyNQMERGRk1Li9/HeukU8uXQqu/IPABAbEclNHQdza+fTQuYTvOI9G0h/8iKKdwaC+epccD91L/u7doypAYwxfYGRwG+stU+Vjk0E0oB/A0OOcu1A4AHgcmvtx5VfrUj1Vegt4all3/HCiun4HD9hHg83dzqN3/U4g9iI4G+oByuFpIocnZohIiJyQnx+P59sWsYTS6ayJWc/AJFh4Vxn+nFX1+GkxCW4XOHxy1/1Hen/vRp/XiaeiCgajHuJxEGj3S5Lqs4VQAkw/uCAtbbQGPMK8LAxppG1ducRrr0bWGCt/dgYEwbEWWtzK79kkepl0Z6t/G7mB6zL3gNAu6QUHj/tCnrWb+5yZaFLIakix0fNEBEROS6O4/D1lpU8vuRbbNZuAMI8Hi5v04Pfdj+DZgl1XK7w+DmOQ9bU59g76V7w+whPqE/juz4gtv1gt0uTqtUDWFNOE2M+4AG6A0dqhowA3jHGPALcBcQbY7YQyBt5q5LqFak2CrzFPLb4W15eNRO/4xDuCeOOLkO5u/sIooM8YyqYKSRV5PjpO42IiByV4zj8uGMt/1n8Dcv37ygbv7BlV+7tcQZtk1NcrO7E+UuK2PPGnRyY/ioA0S160PjXHxFZV59C1kCNgB3ljB9sgDQu7yJjTG2gLoElNj4CuSEZwB3Am8aY/CMtnTHGZB2jpqRjly0S2ubt2sS9Mz9gc+nswo51GvHE4CvoXFeB1adi+/btrFixQiGpIsdJzRARETmiubs28ujib5i/e3PZ2BnNUrmvx1l0qlvu74lBzZu9m/Rnr6Bw/WwA4vteScMbXyUsRPJNpMLFEtgB5nCFhxwvz8GPWOsC/a218wCMMR8TCGH9C6AcEZHDFHhLeHTxFMavnIWDQ2RYOHd3O51fdRka9DuOBTOFpIqcHH3XERGRX1iydxuPLf6GaenrysYGNWrD73ueRa+U0FxzXLh5EenPXIY3YzsAdS97iDoX3o/H43G5MnFRARBdznjMIcePdB3ApoONEABrbZEx5gPgbmNMfHkZItba5KMVVDpzRLNDpNpZsncb98x4jw3ZewHoWrcJjw++kg51tPnSqVBIqsjJUzNERETKrNyfzmNLvuXbbavLxnrWb84fep7FoMZtXazs1GTPeJ09E36F4y3CExNPo1smEt/zYrfLEvftJLBU5nAHx9KPcF0GgRklu8s5tptA3kgSoEBVqfGKfV6eWvodz634Eb/jEOEJ457uI7ij6zAiw8LdLi9kKSRV5NSpGSIiItjM3Ty+5Fu+2pJWNtapTiPu63kWI5qmhuzsCcdbzJ5J95L93fMARDZoS+O7PiS6aWeXK5MgsZTyZ3H0K31dVt5F1lq/MWYpUF7AQVMCOSIZFVinSEhalbGTe2a8x6qMQAyPSW7A00OuUjbIKVJIqkjFOKFmiDEmFrgSsIdOCxURkdC0MXsvTyz9jk83LsPBAQIPq7/tcQbntuhEmCd0Q9e8WbvY+fzVFKydCUCtrufS8NY3Ca+V7G5hEkw+AH4H3AQ8BWCMiQbGAbOstemlY80JbJ275pBr3wceM8acaa39tvS8ROAqYLa19khLbESqPa/fx//SpvP4kqmU+H2EeTzc3nkov+1xhnaKOUUKSRWpOCf63agIeBm4G1AzREQkRG3NyeDpZd/xwfol+Bw/AK0S6/Hb7mdwUauuhIf4Q1XB+jmkP3cVvqzAKoc6F/+Zuhf/BU+I/3NJxbLWzjPGvA88aoxpBGwArgdaAGMPOXUiMJTA8peDXiDQRPnQGPMkkAncCCQD91d68SJBakP2Xu6Z8R5L9m4DAj9bnjrtypDNmwoWCkkVqXgn1AwpnRa6DUispHpERKQS7cjN4tnlP/DO2gV4S5sgzeJr85vuI7isTQ8iQnz9tuM4ZP/wP/a89RvwlRAWk0DDWyYoH0SOZgzwUOlrbWA5cJ61dtbRLrLW5htjhgP/Ae4isPPMIuCMY10rUh05jsPrq+fwj4VfUeQLzFoY12Eg9/c6h7hIhXmeCoWkilSOk5mnNgEYbYx52lpb3nZ0IiISZHbmZfPc8h+ZtHY+xX4fAI3ikri72+lc1a5XtdjS0F+Ux+7XbydnzlsARDVKpfFdHxLVONXlyiSYWWsLgftKv450zrAjjO8CRldOZSKhY3f+Ae6d+QE/7lgLQJNayTwx+IqQDt4OBgpJFalcJ/P0Oxu4DFhqjHkeWAfkH36StXb6KdYmIiKnaHf+Af67/EfeWju/7JO6lNgE7ug6jFHt+xITEelyhRWjeKcl/bkrKd6xEoD4PlfQ8IbxhMUmuFyZiEj1NnnLSu6b9SGZRYFfB65o05O/97+IxKiYY1wpR3N4SGpiYiK9evVSSKpIBTqZZsi3h/z5aShN3PuJp3QstOdai4iEsL0FObywYhoT1swta4LUi4nnzq7DGGX6EVtNmiAAOQs+YPcrN+EvzIHwCOpf9SjJZ/06ZHfAEREJBXklRfx1/hdMWrsAgKSoWP418FIubNXV5cpCn0JSRarGyTRDxlV4FSIiUiEyCvN4YcV0Xl8zmwJvCQB1omvxqy5DGZPav1qt23a8Jex7/34ypzwJQHhyYxrf8Q6x7Qa5XJmISPW2aM9Wfj39Xbbk7AdgcKO2PHHalTSuleRyZaFNIakiVeuEmyHW2gmVUYiIiJy8jMI8XkybwWurZ5PvLQYgOTqO2zoPYVyHAdSKjHa5wopVsn8rO18YReH62QDEdjidRre/RURiisuViYhUX16/j2eW/cDTy77H5/iJCgvn/t7ncGPHQSG9FXswUEiqSNUL/cQ8EZEarLwmSFJUDLd2HsK4DgNJqIZrtnOXfsGul8fhz8sAoM4Ff6TuZX/HE+I74YiIBLPNB/bz6+nvsnjvVgBMcgOeHTqSjnUauVxZaFNIqoh7TroZYozpDfQjsA3d4a1gx1r70KkUJiIiR5ZZmMeLK2fw2qrZ5B3SBLm502nc0HFQtQyuc7wl7PvgATInPwFAeEI9Gt78OrW6nutyZSIi1dtHG5Zw/+yPy37e3NxpMH/oeXa1CeF2i0JSRdx1ws0QY0ws8BFwFj+FpR5MqXMOGVMzRESkgmUW5fNS2gxeXTWr7KE0MSqGmzsN5oYOg0iKjnW5wspRsm8LO1+4lsINcwGIbX8aDW9/i8jaTVyuTESk+sorKeLBOZ/ywYbFADSITeCpIVdxWuN2LlcW+hSSKuK+k5kZ8hcCjZCHge+AH4DrgT3A/UAsMKaiChQRkcBMkJdXzuTV1bPJLSkCakYTBCB38afseuVG/HmBT87qXHA/dS/9K55wrfQUEaksK/bt4FfTJrHpwD4AzmiWyhODr6ROTC2XKwttJSUlrFixgh07dgAKSRVx08k8SV4BvG+t/Ysxpm7p2A5r7ffGmO+ABcBYAo0RERE5BRmFebx02HKYxKgYbuo4mBs7Vu8miL+4gL3v/p7s754HSpfF3DKRWl3OdrkyEZHqy3Ecxq+aySMLJ1Pi9xEVFs6Dfc7jhg4DtWX5KVJIqkhwOZlmSDPgidI/+0pfowCstV5jzCTgdtQMERE5afsLc3kxbQavr55TFoyaGBXDDR0HcXPHwdW6CQJQtGMlO1+4luLtaQDEpg6j4a0TtSxGRKQS7SvI5bcz3+f77RaA1on1eH7YNXSuq++9p8JxHNauXcu6desUkioSRE6mGZJzyHU5gB9ofMjxbKDhKdYlIlIj7SvI5X9p05mwZg4F3hIgEIx6Yw2YCQKBB8bsH15k76R7cUoKISycupf+jTrn/167xYiIVKKZ6ev59fR32VOQA8DV7Xrx934XVbut2auaQlJFgtfJNEM2AO0BrLU+Y8xKAktnXjXGeIDLgG0VV6KISPW3tyCH/62YzkQ795AmSGwgE6Sa7g5zOF9uBrtfu5ncRZ8AEFGvJY1ue5PYtgPcLUxEpBrz+n08tuRb/rt8Gg4O8ZHR/GvgpVzSurvbpYU8haSKBLeTaYZMBW4wxtxjrfUBLwLPGWM2ENhFphXwQAXWKCJSbe3OP8D/0qbzxpp5FPoCTZDk6Dhu7XQaYzsMIKEGNEEA8ld9z67x4/BmbAcgof9IUsY8T3hcksuViYhUXzvzsrlj2iTm794MQPd6zfjvsJG0SKh79AvlqBSSKhIaTqYZ8i/gDUq307XWPm+MiQGuI5Ah8jLwaIVVKCJSDaXnZvF82jQmrV1AkS/wiVHt6Dhu7TyEsR0GEF9DpiX7S4rY/+GfyJwciKLyRNciZfSzJA4ao6A+EZFKNG3HWu6a9i4ZRXkA3NZ5CH/odTaRWpJ4ShSSKhI6TrgZYq3NBexhY0/wU6iqiIgcwbacDP67YhrvrltIiT+QQV03pha3dR7CmNT+NWptdtG2Fex8cTTF21cAENO6Lw1vmUhUw3YuVyYiUn35/H6eXPYdTy/9HgeHpKhYnh5yFWc06+B2aSFNIakioedkZoaIiMgJ2nxgP88u/4EP1y/G6/gBSIlN4PYuQ7jO9CM2ouZ8YuT4/WR98zT7PngAx1sMYeHUufBB6l74AJ6ISLfLExGptvbk53DX9HeYtXMDEFgW87/h19I0vrbLlYW2/Px8Fi9erJBUkRBz0s0QY0w0MAxoXTq0EZhmrS2sgLpERKqFDdl7eXbZD3y8cSm+0iZIo7gkftVlKCPb9yG2hv3yX5KxnV0vj6Ng9fcARKa0oeEtExSSKhXGGBMFrLHWtj7mySI1yOydG7hz2jtlu8Xc1HEQD/Q+l6hwfTZ6KhSSKhK6Tuq7nzFmDIFlMbUpzQ4hEJ6aZYy511r7esWUJyISmlZn7OLZ5d/z+aYVODgANI1P5s4uw7myXS+ia9jDp+M45Mx+gz1v3oO/IBuAxCE3knLtE4TF6JMzqVAeoKXbRYgEC7/j57nlP/LYkm/xOw6JUTE8NugKzmvZ2e3SQppCUkVC3wk/jRtjrgZeB7YCjwGrSg91Am4DXjHGFFhr3z3B9+0DjAWGAy2A/cBs4E/W2vWHnTuQQEhrT+AA8C5wv7U2/0T/eUREKtLyfdt5etn3TNm6qmysRUId7uo6nMvb9qyRwXTe7N3sfv028pZ8BkB4Qj0ajH2R+F6XuFuYhCxjzMajHA6D0g6kSA2XUZjHXdPfZdqOtQB0qduEF4ZdS8tE7RZzKhSSKlI9nMxHkw8Aa4D+1toDh4x/Zox5HphXes4JNUOAPwCDgPeB5UBD4E5giTGmr7V2NYAxpjvwHbAS+C3QFPgdgeU6F57EP4+IyClbuHsLTy/7nh92/JQv3TapPnd1O52LW3UlogY2QQByFnzA7gm/wp+7H4D4XpeQcv0LRCSmuFyZhLj6BJ41tpZzLAp4p2rLEQk+y/Zt55bv32RHXhYA16f25899ziemhi3PrEgKSRWpXk6mGWKAPx/WCAHAWpttjHkN+OtJvO8TwLXW2uKyGxnzLrCCQKNkbOnwIwRmjQwr3dkGY8xm4GVjzOnW2u9P4t4iIifMcRxm79rI00u/Y/aunz6o7lC7IXd3O51zW3QmvIauGfblZrDnzbvImRv4nTQsLpmU654hYcC12jJXKsJSYLe19tPDD5Rmmuk/MqnRJq1dwJ/mfkqRz0tcRBT/GXQ5F7fu5nZZIU0hqSLVz8k0Q3Yd47gD7D7RN7XWzi5nbJ0xZiXQAcAYkwicCfznYCOk1ETgSeAqQM0QEalUjuPw/XbLs8t/YOGeLWXj3eo15e5up3NGs1TCPDWzCQKQu+Qzdr9+O77swI+LuK7n0GDcS0TWbuJyZVKNPANkHOFYCTCuCmsRCRqF3hL+Mu9z3l47H4BWifUYf/poTO0GLlcW2hSSKlI9nUwz5HVgnDHmhcMaEgebFeOA1yqgNowxHqABsKx0qAuBmhceep61ttgYsxToURH3FREpj9/x89WWlTy37AfSMtLLxvuktODu7iMY2rhdjZ714MvZx5637i6bDeKJiSflmsdJHHJjjf73IhXPWvv+UY75gQlVWI5IUNiRm8UtP7zJsn3bATi7eUeePO0qEqNiXK4sdCkkVaR6O2YzxBgz5LCh6cAFwIrSjJA1peMdgNuBfcCMCqpvFNAEeLD0741KX3eWc+5O4Ih7Mxpjso5xr6QTLU5Eagav38cnG5fx3+U/si57T9n4aY3bclfX4Qxo2LpG/7LvOA65C95nzxu/xpezF4C4TiNoMPYlIuu3dLc4qRaMMU8Bfylvia6IwMz09fzqx0lkFOXhwcPve57FHV2H1uhZiqdKIaki1d/xzAz5kV+msh986v/3IccOjrUAvgVOKS3QGJMK/BeYCbxROhxb+lpUziWFhxwXETllRT4v769bxPMrprE196cZ+Wc168Cd3YbTs35zF6sLDt6snex5405yF30CQFhsIvVHPkbikBtqdINIKtztwLXGmD8DL1lrtVuMCIFm9PMrpvHvxVPwOw7J0XH8d+hIhjZp73ZpIUshqSI1x/E0Q6p83a0xpiHwJZAJXFk65RWgoPQ1upzLYg45/gvW2uRj3DMLzQ4RESC/pJi3187nhbTp7M4PfBDtwcOFrbpwZ9fhdKzT6BjvUP05jsOBWRPZO+le/HmBMLla3c4nZewLygaRytCVQDbYC8Dtxph7rLU/uluSiLtyigv5zYz3mbx1JQBd6zbhxeGjaJZQx+XKQpdCUkVqlmM2Q6y1Vbru1hiTBHxNoDExyFp7aGDrweUx5f0m0ghIL2dcROS4ZBXlM2H1HMavmkVmUT4AEZ4wLm/bgzu6DKN1ktYIAxTv2cCeCbeTv/I7AMJq1SFl1FPaKUYqjbXWAucZY84nsPvcd8aYj4F7rbVbjn61SPWzMXsfN343sWzp5tXtevNw/4u1be4pUEiqSM1zMgGqlcYYEwN8DrQHRpQ+/BwqDfACvYGPDrkuCugOvF01lYpIdbK3IIeXV85k4pq55JYEVuFFh0cwsl0fbu8yhKbxtV2uMDg43hIyv3mK/Z/8Dac4MBEvvvflpIx+logk7VQglc9a+6UxZgpwD/AnYLUx5kngEWttnqvFiVSRaTvW8qsf3ya7uJDIsHAe6ncRo0xfNaNPkkJSRWquoGmGGGPCgXcJhKBebK2de/g51tpsY8xUYLQx5pFDdrMZDcQDR0yXFxE53PbcTF5YMZ131i2gyBf4JCg+Mpoxqf25qeNgUuISXK4weBRuXMDu126laFtgc6+IOk1JGf0s8T0ucrkyqWmstV7gMWPMBOCfwB+AscaYP1pr3zj61SKhy3EcXl45k38s/Aq/41A/Np6Xh4+mdwNlWZwshaSK1GxB0wwBHgcuIjAzpI4x5rpDjuVaaz8p/fODwGzgR2PMeKApcC/wtbV2ahXWKyIhal3WHp5f8SMfb1iK1wlEEtWOjuOmjoO4vsMAkqPj3C0wiPgLctj30V/ImvosOA54PCSfcSf1LnuIsFg1i8RVtQmEvLcDTgNeN8bcAdxlrV3gZmEiFa3QW8IfZ3/MBxsWA4F8kPGnj6ZxfLK7hYUohaSKCARXM6R76euFpV+H2gJ8AmCtXWyMOYPATjZPAgeAl4H7q6RKEQlZy/Zt57/Lf+TrLStxSjfCahiXyG2dh3Bt+77EReqToIMcxyFv8afseesevBnbAIhq1pUGY/9HbJt+LlcnNU1psHrfQ75681PouUNgGe18YBgwxxjzOPBH7Toj1cGu/APc/P0bLNkb+F58Sevu/GfQ5cQqH+SkKCRVRA4KmmaItXbYCZw7ExhUedWISHXhOA6zd27guRU/MiN9fdl4y4S6/KrrUC5v05Po8KD5VhgUSvZuYs+bd5O37EsAPJEx1L3k/6h99m/w6OFb3JFOoOnhATIIzBCdC8wB5ltrcwCMMRHAfcDfS8//oyvVilSQxXu3cvN3b7C7IAcPHu7vfQ63dx6ifJCTpJBUETnUcf0GYIzZRmBmxifAj9ZaXyXWJCJyyvyOnylbV/Hf5dNYum9b2XjHOo24o8swLmjZhXA9/PyM4y0m4+vHyfj84bKA1LguZ5My+lmiUtq4XJ3UcC9R2gCx1q490kmleSL/NMYkAmNRM0RC2AfrF/GH2R9T5POSEBnNc0OvYUSzVLfLCkkKSRWR8hzvx6GfApcAdwCZxpivCOzmMsVam19JtYmInLASv49PNizl+RXTyrYcBOjXoCV3dB3O8Cbt9YlaOfJX/8CeiXdSvHMNABG1m1D/2ieJ732Z/n2J66y1t53gJcsAbXEkIcnn9/PIwq95ceUMAFon1uPVEWNom5zicmWhSSGpInIkx9UMsdbeCdxpjOkLXEqgMTIKKCjd3eVj4HNr7f7KKlRE5GjyS4qZtG4BL6ZNJz0vu2z8jGap3NFlGH0atHSvuCDmzdrF3nfvI2dO6c7kYeHUPvPX1L3k/xSQKqFsCnCt20WInKjckiLunDaJqdsCjelhTdrz36HXkBQd63JloUchqSJyLCe0UN5aO59AQNn9xphUfmqMvAL4jTEzCTRGPrHWbq3gWkVEfiGzMI/X18zh1VWzySwKTFQL83i4qFU3ftVlKB3rNHK5wuDkeIvJ/PY5Mj79O/7CHABi2g6kwfX/JbpZV5erEzk11tpM4B236xA5Eem5WYz9bgKrMnYCcEunwTzY+zwt6TwJCkkVkeNx0qmB1to1wD8JrM1twk+NkceAJ40xy4AHrLWTK6JQEZFDpedm8dLKGby9dgH53mIAosMjuKptL27rMoQWCXVdrjB45aV9y9637ilbEhOeUI96VzxC4mnj8OihW0Skyi3bt50bpk5gd0EO4Z4wHh5wMdcZ7dx1Mg4PSW3dujUdOnRQSKqI/EKFbKFgrd0BPAc8Z4ypTWBr3EuAzoCaISJSYdZl7eGFFdP4aMMSvI4fgITIaK7vMIAbOw6ivpZ2HFHJ3s3sfedechd9EhjwhJE84lfUvfSvhNeq7WptIiI11Veb0/j19Hcp9JWQGBXDi8NHcVrjdm6XFXIOD0mNjo6mR48eCkkVkSOq8P0kS6emTiz9EhGpEIv2bOX5FT8yZeuqsrGU2ARu6jSY60w/EqNi3CsuyPmLC8j48lEyv3oUp6QQgFgzlJTrnia6WReXqxMRqZkcx+H5FdP456LA54YtEurw+hljaaeg1BOWkZHBkiVLyM8PLJdVSKqIHI8Kb4aIiFQUx3H4frvl+RXTmLd7U9l4y4S63N5lKJe36UFMRKSLFQY3x3HImfcO+95/AO/+QIxTRJ2m1L/6UeL7XqVdYkREXFLs83L/nE94d91CAPqktGD8iNHUjVGmxYlQSKqInAo1Q0Qk6JT4fXy6cRkvrJiGzdpdNt6lbhPu6DqMc5t3UqDcMRRsmMfeSfdSuH4OAJ6IKGqfcy91LryfsOhaLlcnIlJzZRblc+v3bzJ710YALm3dnccGX0F0uB7LT4RCUkXkVOm7rogEjbySIiatXcBLK2f8bHvcIY3bcXuXIQxu1FazGY6hZP829n3wwE9b5QLxvS+j3lX/JiqltYuViYjI5gP7GfPta2w8sA+A3/U4k7u7na6fbSdox44dLF++XCGpInJK1AwREdftK8jltdWzeX31HLKLC4DA9rgXtuzKbZ2H0KVeE5crDH7+ojwyvvoPmV8/hlP67zC6RQ/qX/M4calDXa5ORESW7N3G2Kmvs78wj+jwCJ4YfCUXt+7mdlkhRSGpIlKR1AwREddsPrCfl1fO4J11CynyBT7diQ6PYGS73tzS+TRtj3scHL+PA7Mmsu/Dv+DLSgcgPKkh9a74B4mDxuAJC3e5QhERmbptNbf98DaFvhJqR8fx2ojr6d1AuRYnQiGpIlLRTqoZYoxpAFwFtARygSXAN9ba/IorTUSqq6V7t/FC2nS+3pKG33EASIqKZWyHAdzQcaAC5I6D4zjkr5jM3vf+SPH2NAA8EdHUPvde6pz3e8K0xbCISFB4087jgTmf4HccmsfX4c2zxtE6STMZjpdCUkWkspxwM8QYcxrwFRAHHLrAcb8x5iFr7TMVVZyIVB8Hd4b5X9p05pSGxgE0qZXMzZ0Gc037PtSKjHaxwtBRuHkRe9/9IwWrvy8bSxhwLfUu/weR9fRwKCISDBzH4bEl3/L0ssD36q51mzDhzLHUV7P6uCkkVUQq08nMDHms9PUG4DsgDOgP/BZ4yhjTz1o7qoLqE5EQV+zz8unGZfwvbfrPdobpWKcRt3ceygWtuhCppRzHpWTvZvZ9+Cdy5k4qG4vtcDr1r/43MS17uliZiIgcqsTv4/ezPuT99YsBOL2p4YVh16rpfwK2b9/OihUrFJIqIpXmZJohnYHHrbUTDhnbCrxnjLkReMkYM8da+1yFVCgiISmnuJC37HzGr5rJrvwDZeOnNW7LbZ2HMKRxO6XnHydf7n4yPv8nWd/9F8dbDEBU0y7Uv+pfxHU5W/8eRUSCSE5xIbf+8BbT09cBMLJdb/418FIi1Pg/LgpJFZGqcjLNkBwCzY9fsNa+Yow5HbgNUDNEpAZKz8vmlVWzeNvOI6ekCIBwTxgXtOrC7Z2H0LmudoY5Xv6CHDK/eYrMrx/HX5gDQETtJtS97O8kDhqtcFQRkSCzK/8A13/7GiszdgJwb48zuKfbCDWtj9PhIakNGjSge/fuCkkVkUpxMs2QH4DzgPFHOX7ZSVckIiFpVcZOXkybzqcbl+F1/ADERkQysl0fbuk0mGYJdVyuMHT4iwvJ/uFFMr74J76cvQCExSZR5/zfk3zmrwmLjnO5QhEROdy6rD1c982r7MjLItwTxqODLuPqdr3dLiskHB6SGhYWRqdOnWjZsqXbpYlINXYyzZCXgbeNMXdba58u53hLIP2UqhKRkOA4DrN2buCFtOlM27G2bLx+bDzjOgxkdGp/ausX9+Pm+LwcmDWR/Z/8HW/GNgA8UbEkn/lr6px3H+G1artcoYiIlGfx3q2M+fZ1soryiYuI4sXhoxje1LhdVkjIz89nyZIlZGRkAApJFZGqczLNkKmAF3jCGHMpgRkii0rHhgJ3A3+osApFJOiU+H18sWkFL6ZNJy3jp95nm6T63Nr5NC5r3YOYiEgXKwwtjt9P7qKP2PfhXyjZZQOD4REkDb2Zuhc9SERyI3cLFKnGjDHRwN+B0UBtYBnwoLX2uxN8n6+Ac4GnrbX3VHSdErym71jHTd+/Qb63mLoxtXjjzHF0rdfU7bJCwo4dO1i+fLlCUkXEFSfTDPk70L30a0jpl3PI8SVAljGmM7DGWus9xRpFJEjkFBcyae0Cxq+aSXpedtl4vwYtua3zEEY0SyXMoweY4+U4DnmLP2X/J3+naNuywKDHQ0L/a6l76V+JSmntboEiNcPrwOXAU8B6YCzwtTFmqLV2zvG8gTHmfALPQ1LDfLF5BXdNe4cSv4+m8cm8fdZNtE6q53ZZQU8hqSISDE64GWKt/evBPxtjkoEe/NQc6Q50Bd4k0CApMcZYYLm1dvSpFisi7kjPzeKV1bN/Fooa5vFwTvNO3NZlCD3rN3e5wtDiOA55y75k/8d/o2jL4rLxWj0upN5lDxHdrIuL1YnUHMaYvsBI4DfW2qdKxyYCacC/OY4GhzEmCngSeBT4W6UVK0HnTTuP+2d/goND++QU3jrrRhrVSnK7rKCnkFQRCRYnMzOkjLU2i0Bg6g8Hx0ofCjoTaIz0KP268FTuIyLuSNu/gxfTZvD5puU/C0W9ul1vbuo4mJaJdV2uMLQ4jkP+isns+/hvFG1aUDZeq9t51L3k/4hppaA9kSp2BVDCIaHw1tpCY8wrwMPGmEbW2p3HeI+7gVjgMdQMqREcx+G/K37kX4umANCjfjMmnjlOGVnHoJBUEQk2p9QMKY+1thhYXPolIiHGcRx+2LGWl9JmMHPn+rLx+rHx3NBhENel9tMD3wlyHIf8ld+y/6O/UrhxXtl4XOezqHvpX4lt08/F6kRqtB4ElvTmHjY+H/AQ+GDniM0QY0xD4M/AHdbafGMUmFnd+R0//1jwFS+tnAnA0MbteOn066gVGe1yZcGtvJDUnj17kpCQ4HJlIlKTVXgzRERCU6G3hI83LuXllTNYm7WnbLx9cgq3dh7CJa27Ex2ubxknwnEc8pZ/Tcbnj1C4/qfogbhOI6h7yV+JbTfQxepEBGgE7Chn/GADpPExrv8nYAksDz4uxpisY5yidRZByuv3cd+sD3l/feDzvgtbduXpIVcRpZ+NR6WQVBEJVvruLVLDZRTmMWHNHCasnsu+wp8+HB3cqC23dj6NYU3a4/F4XKww9Dh+P7lLPiXjs0d+lgkS22E4dS/5P+LMaS5WJyKHiAWKyhkvPOR4uUrzRsYAQ621zpHOk+qhwFvCHT++zTfbVgMw2vTjH/0vJly/0B+RQlJFJNipGSJSQ23I3svLK2fy/vpFFPkCn9ZEeMK4qHU3buk0mM51m7hcYehx/D5y5r9Pxhf/pHh7Wtl4XKcR1LnwQeJSh7pYnYiUowAob31DzCHHf8EY4wGeBj601s48kRtaa5OPdrx05ohmhwSR3JIixk59nbm7NgFwd7fT+V2PM/VBwVEoJFVEQoGaISI1iOM4zNm1kZdWzmDqtjVl40lRMYwy/RjXYaCS8E+C4y3hwNy3yfjiX5TsWls2XqvbedS58EFi2/Z3sToROYqdBJbKHO7gWPoRrrsU6As8YIxpedixxNKx3dbacpspEjqyiwq47ttXWbJ3GwB/7XsBN3Ua7HJVwUshqSISStQMEakBin1evti8gpdXzmTF/p+WxzePr8NNnQZxdbveCn87Cf7iAg7MeJ3MyY9TsndT2Xh8r0upc9GDxLTo4WJ1InIclgJ3G2PiDwtRPZhqvOwI1zUHwoDvyzk2rvTrXGByBdUpLsgozOPaKa+QlpFOmMfDfwZdztXttOvXkSgkVURCjZohItVYZlE+b9n5vLZ6NrvzD5SN905pwc2dBnNO805a73wSfHmZZH33AlnfPoMvZ29g0BNGQr+rqHPB/UQ37exugSJyvD4AfgfcBDwFYIyJJtDMmGWtTS8daw7EWWsPTqn7HNhczvt9DHwBvIJ21Qtpe/JzuGbKeGzWbsI9YTwz5Goubt3N7bKClkJSRSQUqRkiUg1tzN7HK6tm8t76RRR4SwAI83g4r0Vnbu40mF4pLVyuMDSVZO4ga8pTZP34Ek5p2KwnIoqEgaOpc97viGrY3uUKReREWGvnGWPeBx41xjQCNgDXAy2AsYecOhEYSmC7Xay1G0rP/ZnSrXU3WGs/qdTCpVKl52UzcvLLbDywj8iwcJ4fdg3ntlCTuzwKSRWRUKZmiEg14TgOc3dv4uW0GXy7bQ0Ogc0N4iOjubZ9H8Z1GEizhDouVxmaitPXkPH1YxyY/Sb4SptLMQkkDb+V2mfdTUTtY+2+KSJBbAzwUOlrbWA5cJ61dparVYkrtuZkMHLyeLbmZhAdHsHLp4/m9KbG7bKCkkJSRSTUqRkiEuKKfV4+27ScV1bN+lkeSNP4ZG7sOIiR7fqQEBVzlHeQ8jiOQ+H62WROfoLcxZ+CE2guhSemUPusu0kafhvhtZLdLVJETpm1thC4r/TrSOcMO8730vYiIWxj9l6unjyenfnZxEZE8vqI6xnUuK3bZQUdhaSKSHWhZohIiMoozONNO48Jq+ewuyCnbLxX/ebc3Pk0zmnekYiwcBcrDE2Oz0vuoo/InPwkhRvnl41H1m9N7XPvJXHw9YRFxbpYoYiIVLQ1mbu4Zsp49hbkEh8ZzRtnjqNPg5ZulxV0FJIqItWJmiEiIWZd1h7Gr5zJBxsWU+QLBJWFe8I4r0Vnbuo0mF4pzV2uMDT5Cg5wYPqrZH7zDN79W8rGo1v1oc45vyG+9+V4wvUtU0Skuknbv4NrprxCZlE+SVGxvHXWDXSv38ztsoKOQlJFpLrRk71ICHAch+np63h55Ux+3LG2bDwxKoZr2vflhg4DaRKf7F6BIaxk/1ayvn2W7Gnj8ReU7rjj8RDf82Jqn/0bYtoNwuPRzHcRkepo6d5tjPrmFbKLC6kbU4tJZ99IxzrKgTqUQlJFpLpSM0QkiBV4S/howxJeXTULm7W7bLxlQl1u7DiIq9r1olZktIsVhibHcSjcMI+sb58hZ8EH4PcB4ImKI+m0cSSf9WuiGmiduIhIdbZs33au/eYVDhQX0iA2gUnn3ET75AZulxVUFJIqItWZmiEiQWhnXjYT18zlTTuPzKL8svEBDVtzc6fBjGiaSrimpZ4wf0kRufPfI3PqcxRtWlg2Hp7ciNpn3EnSsFsIj9eOOyIi1d3yfdu5dsr4skbI++feQuskzXQ4SCGpIlITqBkiEkSW7t3G+FWz+GLTcryOH4CosHAuatWNmzoNonPdJi5XGJq8WTvJ+uFFsn94Ed+BPWXj0S16Uvusu0joNxJPhD7lEhGpCVbsC2SEZBcXkhKbwHtqhPyMQlJFpKZQM0TEZV6/j8lbVjJ+1SwW7vkpuLNuTC3GpPZntOlPSpweQE5U2VKYqc8GlsKUhs0SFk5C78tJPvMuYtoOUB6IiEgNkrZ/ByOnjCe7uID6sfG8d87NtFEjpIxCUkWkJlEzRMQlWUX5TFq7gNdXz2FHXlbZeIfaDbm502AuatWNmIhI9woMUf7iAnIXvE/m1Ocp2rSgbDw8oT5Jw24mafitRNZp6mKFIiLihlUZ6Yyc8grZxQXUi4nnvXNuoW1yittlBQWFpIpITRRUzRBjTCPgbqAf0BuIB4Zba3887LzNQIty3uLf1to/VnKZIqdkXdYeXl01iw82LKbAWwKABw9nNe/AjR0HMaBha81WOAnFu9aR/eNLZM94HX9eRtl4dIseJJ95Fwl9ryYsKsbFCkVExC2rMnZy9eTxZBXlUzemFu+dezPt1AgBFJIqIjVXUDVDAAP8AVgPLAcGHuXcRcBTh42lVU5ZIqfG7/j5ccc6Xlk1i2mHbI0bHxnNVW17cUPHQbRMrOtihaHJ8XnJXfo52d//j/yVU386EB5JQq9LST7zTmLaDlRzSUSkBludsYuRk8eTWdoIefecm7VrDIHlpOvWrWPt2rUKSRWRGinYmiGLgHrW2v3GmEuAj49y7nZr7ZtVU5bIyckrKeKD9Yt5dfVsNmTvLRtvkVCXcR0GcHW73iRotsIJ82amkz1tPNnTxuPN3FE2HlG3OUnDbiFpyA1EJOlBV0SkpluTuYurJ79MRlEedaJr8c7ZN5Nau6HbZblOIakiIkHWDLHW5pzI+caYaCDcWpt/zJNFqtC2nAxeXz2HSesWcKC4sGx8UKM23NhxkLbGPQmO30/+qqlk//ASuUs+A78vcMDjoVaXc0g6/TZqdT0XT1i4u4WKiEhQWJu1u6wRUjs6jnfOuYkOddQIUUiqiEhAUDVDTtBZQB4QbozZSCAv5CWXa5IazHEcZu/ayKurZvHtttX4HQeA6PAILmvTgxs6DNJD2EkoydjOgRmvkz39Vbz7f9ptJzyhHomn3UDy8FuIrN/KxQpFRCTYbDqwj5GTx7O/MI/k6DjePecmOtZp5HZZriopKSEtLY3t27cDgZDU7t27k5Ki7BQRqZlCtRmyHJgBrAXqAzcDLxpj6lhr/1XeBcaYrGO8Z1KFVig1RoG3hI83LuHVVbNZk7mrbLxhXCLXpw5glOlLnZhaLlYYehxvCXnLviR7+ivkLZ8Mjr/sWKwZQtKwm4nvfTlhkdEuVikiIsEoPTeLa6aMZ09BDklRMbxz9o10rNPY7bJcVV5Iardu3YiO1s9REam5QrIZYq296NC/G2NeA2YCfzbGvGCtzXanMqlJ0nOzmLBmLm+tnU9W0U8rtXqntODGjoM4p0UnIrVk44QU79lA9rRXODBzAr7snxpL4Qn1SRx8PUlDbiCqkXGxQhERCWZ7C3IYOWU823OziIuIYuKZN9C5bhO3y3KNQlJFRI4sJJshh7PW+owxTwHvAAOAyeWck3y09yidOaLZIXJUjuOwYM8WXl01i6+3rMRXOmMhKiyci1p1Y1zHgXSr19TlKkOLvyif3MWfkD39VQpW//DTAY+HuM5nkTTkRuJ7XIgnQlv8iYjIkWUW5XPtlFfYeGAf0eERvDZiDL1SmrtdlmsUkioicnTVohlSalvpax1Xq5BqqdBbwqeblvHqqlmszNhZNp4Sm8Do1H5cZ/pRP1YPF8fLcRwK188me8YEcue/h7/wp+zkiDrNSDxtHEmnjSWyXgsXqxQRkVCRW1LEmG9fY3XmLiI8Ybw4fBSDGrd1uyzXKCRVROTYqlMzpHXp696jniVyAtJzs5ho5/K2XUBGUV7ZePd6zbih40AuaNmFqPDq9H+jylWyfysHZr3JgVkTKdm97qcD4ZHEd7+ApKE3Etf5LO0IIyIix63AW8K4qRNYsncbYR4Pzwy5mjOadXC7LFd4vV5WrFihkFQRkeMQcr/FGWPqAFnWWv8hYzHAfUAOMMet2qR6cByH+bs38+rq2Uw+ZClMZFg4F7TswriOA+lZv+ZOuz1R/qJ8chd9zIFZE8hf9T2U7rIDEN2iJ4mDryex/0jCE+q5WKWIiISiYp+X2354izm7NgLw6MDLuKh1N5ercodCUkVETkzQNUOMMX8q/ePBlv5oY8xgAg2Q54CLgAeNMR8Am4G6wPVAe+B2a21uFZcs1USBt4RPNy7ltdWzf7EU5joTWAqTEqelMMfD8fspWDuDA7Pf+sUymPDEFBIHXkfioDFEN+viYpUiIhLKfH4/d09/j++2rwHgr30vYGT7Pi5XVfUUkioicnKCrhkCPHTY328ofd0CPAesANYAowlsq1sELAbutdZ+UVVFSvWxPTeTCavnMmndgp/tCtOzfnPGdRjI+S07aynMcSransaB2W+RM3cS3oxtPx0IjyS+x4UkDr6eWp3PxhMR6V6RIiIS8vyOn9/P/pDPNy8H4L4eZ3JTp8EuV1X1FJIqInLygu43PGut5xjHFwEXVlE5Uk05jsPsnRt4dfVsvt22Gn/p0o2osHAuaNWVcR0G0qN+M5erDA0lGdvJmfsOOXPepmjbsp8di27Vm8RBYwLLYOLrulShiIhUJ47j8Nd5X/DuukUA3N55KL/udrrLVVU9haSKiJyaoGuGiFSmvJIiPtywhNdXz2Zt1p6y8QZxiYwx/bjW9NWuMMfBl59N7sIPOTDnbQrW/PizHJDI+q1JGDiKxAHXEtWwvXtFiohItfTs8h94dfVsAMak9ueB3ufg8Rz1s7RqRSGpIiIVQ80QqRE2Zu9j4po5vLd+EQeKC8vG+zZoybgOAzmnRScitYPJUfmLC8hb/jU5c98hb+kXON6ismPhCfWI73sViQNGEdOmX416KBURkaozae0CHl38DQAXt+7GP/pfVKN+5mRmZrJ48WKFpIqIVAA1Q6Ta8vn9/LhjLa+tns2PO9aWjUeHR3Bp6+6M6zCQTnUbu1hh8POXFJGf9g05898jd8lnOIU/5RN7omKJ73ERCQNGUavzWcoBERGRSvXN1lX8YfZHAAxp3I4nB19JmKdmLAlRSKqISMVTM0SqncyifN5bt5CJa+ayJSejbLxpfDJjUgdwTbve1I6p5WKFwc3xlpC/+vtAA2TRJ/jzs346GBZOXMcRJA64hvielxKmJUUiIlIFFuzezO0/vo3fcehatwkvnX5djQk3V0iqiEjlqBk/RaRGWJWRzmur5/DxhqUU+krKxoc0bsfYDgMY0TSVcIWKlcvx+yiw08mZ9x65iz7Cl7Pvp4OeMGJTh5HQ70oSel1GeEI99woVEZEax2buZuzUCRT5vLRMqMvEM8cRH1kzloUoJFVEpPKoGSIhrdjn5estK5mwZg7zd28uG4+PjObKtr24PrU/bZMVKFaeQANkBrkLPyJn4Yf4snf97Hhs+8HE972KhN6XE5Hc0KUqRUSkJkvPzeK6b14lu7iA+rHxvHX2DdSLjXe7rEqnkFQRkcqnZoiEpJ152by1dj5v2/nsKcgpG2+XlMLYDgO4vG3PGvOp0Yk4uAQmd+FH5C7+FF/O3p8dj2ndl4S+VxHf5woi62prYRERcU9mUT6jvnmVnfnZxEdG88aZ42iRUP23aVdIqohI1VAzREKG4zjM2bWRCWvmMnnLSnyOH4Awj4ezmnVkXIcBDGzUpkalyh8Pf3Eh+Su/CTRAlnz+8wwQILplLxJ6X0583yuJSmntTpEiIiKHKPAWM27qBNZl7yEyLJxXTh9N57pN3C6rUikkVUSkaqkZIkEvr6SIDzcsYcLqOdis3WXjdWNqcW37vlxn+tEkPtm9AoOQvyiPvOVfBxogy7782S4wADFtB5LQ+zLie11KZP2W7hQpIiJSDq/fx69+nMTCPVvw4OHp065iUOO2bpdVqRSSKiJS9dQMkaC1LmsPE9fM5YP1i8gpKSob71m/OWM7DOD8ll2IriFJ8sfDl7OP3KVfkLvkM/LTvsEpLvjpoCeM2NShJPS6jPhelxBRW1sKi4hI8HEchz/O/phvt60G4G/9LuCi1t1crqpyKSRVRMQd+k1SgorX72PK1lVMXDOXWTs3lI1Hh0dwSevujE0dQJd61Xua7Iko3r2e3MWfkbfkMwrWzYLSpUMAhEcQ13EECb0vo1aPi4lIrO9eoSIiIsfhqWXf8c66hQDc2XUYN3Qc5HJFlUchqSIi7lIzRILC7vwDvL12Pm/Z+ezKP1A23iKhDqNNf65u14vaMbVcrDA4OH4/hZsXkrf4M3IXf0px+qqfHfdExVGry1nE97yYWt0vJLxWbZcqFREROTEfbljC40umAnBl2578oefZLldUeRSSKiLiPjVDxDWO4zBv9yYmrJ7L11vS8JbOavDg4fSmhus7DGBYk3aEeWr2NFF/SREFq78nd/Fn5C79HF/Wzp8dD09sQK3uFxDf8yLiOo4gLCrWpUpFREROztxdG7lv5gcADGrUhn8PvKxaBqIrJFVEJHioGSJVLrekiI/KCUStHR3HyHZ9GJ3aj+YJdVys0H3erJ3kLf+avGVfkbfy218EoEY1SqVWj4uI73kRMa374dG6YhERCVEbs/dy0/dvUuz30S4phZeGX0dUNcwEU0iqiEhwqX4/aSRorcncxRtr5vLB+sXkeYvLxnvUb8b1qf25oGVXYiIiXazQPWXLX5Z9Rd6yryjavOjnJ3g8xLQdSHxpAySqYXt3ChUREalAGYV5jP72dbKK8qkXE8+EM8eSFF39ZjgqJFVEJPioGSKVqtjn5estK5m4Zg7zdm8uG48Jj+Ti1t0Yk9qfbvWaulegi3z52eSnfRNogKyYjO/Anp8dD4tJIK7zmdTqdh61up1PRKIC1UREpPoo9JZw43cT2ZKzn+jwCF49Y0y1mxmqkFQRkeClZohUih25Wbxl5/H22gXsO2SJR6vEelyf2p8r2vYkOTrOxQqrnuM4FO9cUzb7o2DdTPB5f3ZOZENDfLfzqNXtPGLbD8YTEeVStSIiIpXH7/i5d+YHLNizBYBnhlxNz/rNXa6qYh0ekpqSkkL37t0VkioiEiTUDJEK43f8TNuxjjfWzGXq9jX4HQeAcE8YZzXvwJjU/gxq1KZGBaL68rPJX/09+SumkLfiG7z7t/zsuCciitjUodTqdj61up1HVEoblyoVERGpOo8vmcqnm5YB8GDvczm/ZReXK6o4CkkVEQkNaobIKcsozOOddQt5y85jS05G2XhKbALXmr5c274vjWsluVhh1XH8foo2LyIv7Rvy076hYP0c8Pt+dk54cuOy2R9xHUcQFhPvUrUiIiJV7711C3l62fcAjGrfl9s6D3G5ooqjkFQRkdChZoicFMdxWLhnCxPXzOXLzSsoPuQX/oENWzMmtT9nt+hEZFi4i1VWDW/WzkDzY8UU8lZOxZ+7/+cnhEcS234wtTqfRVzns4hu3q1abhcoIiJyLLPS1/P7WR8BMLRJex4ecHG1+ZmokFQRkdCiZoickNySIj7esIQJa+ayJnNX2XhiVAxXtu3FaNOPtsnVOxTMX1xI4fpZ5K34hry0byjetvwX50Q2aEtc57MCDZAOwzX7Q0REarx1WXu45Yc38Tp+Ums35H/DriWiGnxoopBUEZHQpGaIHJdVGTt5Y81cPtqw5Gfb4nar15TRph8Xt+5GbDUN+3T8Poq2LCF/1ffkr5pKwdpZOCWFPzvHExNPXIfTqdXlLOI6n01USmuXqhUREQk+mUX5jJ06geziQlJiE5hwxlgSomLcLuuUKSRVRCR0qRkiR1ToLeGLzSt4Y81cFu3dWjYeHR7BJa27Mdr0p3v9Zi5WWDkcx6Fk9zryV31H/srvyF/zI/68zF+cF92iZ6D50eVsYtsMwBMR6UK1IiIiwc3r9/GrH98u20L3tTOup0l8sttlnRKFpIqIhD41Q+QXNmbv4y07j3fXLyKrKL9svG1Sfa4z/arltrjerF2B5seq78hf9T3ejG2/OCeyfmviOp5OXKcRxKYOJyKxvguVioiIhJaHFnzFjPT1ADw++Aq61WvqckWnpqCggMWLFyskVUQkxKkZIgCU+H18s3UVb6yZx8yd68vGIzxhnNuiM6NT+zGgYetqE3Lmy8ukYO2M0qUv31O8Y+UvzglPqE9ch+HEdRpBXMcRRNZv5UKlIiIioeudtQt4ZdUsAO7oMoxLWnd3t6BTtGPHDlasWEFJSQmgkFQRkVCmZkgNtz03k7ftfN5Zt5A9BTll403jkxnVvh9Xt+tNSlzof9Lhy80IND/WTKPATqdo61JwnJ+d44muRaw5jVodzyCu4+lENe2CRw83IiIiJ2Xh7i3cP+cTAEY0TeX3Pc9yt6BToJBUEZHqR82QGsjn9/PDDssba+bx/XaLQ6Ap4MHD6U0NY1L7M6xJe8JDuBHgy82gwE7/qfmxbdkvmh+ERxLTui9xHUcQ1/F0Ytv0w1NNQ2BFRESqUnpuFjf/8AYlfh/tklJ4bujIkH2uUEiqiEj1pGZIDbI7/wDvrF3AW2vnk56XXTbeIDaBke37cE37PjSNr+1ihSfPl7uffDudgjXTKVgzjaLty8ttfsS26UesGUps6hBi2w4gLLqWOwWLiIhUUwXeYm76/g32FuSSFBXDKyPGhOTOMeWFpHbs2JFWrbRsVkSkOlAzpJrzO35mpK/nTTuPb7auxuf4y44NadyO60w/zmzegciwcBerPHHerJ0UrJ1JwdqZ5NvpFG9b/suTwiOJbdOf2NShxKUOIabNAMKqWfCriIhIMHEch9/N/JDl+3cQ5vHwwrBRtE6q53ZZJ0whqSIi1Z+aIdXU3oIc3l23iElr57MlJ6NsvE50La5u15trTR9aJYbGw4njOJTstBSsm1naAJlFyd6NvzjPExFFTOt+pc2PocS06a/mh4iIHJUxJhr4OzAaqA0sAx601n53jOsuA64G+gINgK3A58A/rLXZR7u2Ovvviml8umkZAH/pcz5DmrRzuaITp5BUEZGaQc2QasTv+Jm9cyNv2nlM2bqKEr+v7Fi/Bq24zvTjvJadiQ4P7v/ZHW8xhVuWULB2FgVrZ1C4fja+nH2/OM8TFUtMm/7EthtEXIdhgeZHVKwLFYuISAh7HbgceApYD4wFvjbGDLXWzjnKdS8B6cAbBBohXYBfA+caY3pbawsrseag9O3WVfx70RQArmrbixs7DnK5ohOjkFQRkZoluH8rluOSUZjHe+sW8aadx+ac/WXjSVGxXNm2J6NMP9olB+8Pcl/BAQo3zC1tfsykcOM8nOKCX5wXnlCPmHaDiG03mNj2g4hp0UOBpyIictKMMX2BkcBvrLVPlY5NBNKAfwNDjnL5FdbaHw97v0XAhNL3fL3iKw5ea7N2c9f0d3Fw6FW/Of8ceCkej8ftso6bQlJFRGoeNUNClOM4zNm1kbfWzufrzWkUHzILpE9KC0aZfpzfsguxEZEuVvlLjuNQsmcDhevnULBhLoXr51K0bTkckmVyUGT91sS2DzQ+YtsNJrKRCakHKxERCXpXACXA+IMD1tpCY8wrwMPGmEbW2p3lXXh4I6TUxwSaIR0qodagdaC4kBumTiS3pIiGcYm8fProoJ+FepBCUkVEaq7Q+EklZTIK83h//SLesvPZeOCnpSOJUTFc1qYH15l+pNZu6GKFP+cvzKVw0wIK1s+lcP0cCjfOK3fJC54wopt3I7bdoEADpN0gImo3rvqCRUSkJukBrLHW5h42Ph/wAN2BcpshR3DwB3A5P+iqJ7/j5zcz3mNzzn6iwyN4ZcQYUuJCI2T08JDUhIQEevXqpZBUEZEaQs2QEOA4DnN3b+JNO+8Xs0B61m/OKNOXi1p1JdblJSOO41Cyez2FG+ZQsGHeUWd9hMUmEtOmXyDzo+0AYtoOIDw20YWqRUSkBmsE7Chn/GAD5ES78n8AfMBHRzrBGJN1jPdIOsF7uur5FdOZsnUVAA/3v5hu9Zq6XNHxOTwktVWrVnTs2FEhqSIiNYiaIUEsozCPD9Yv5q2189mQvbdsPCEymsva9GSU6UPHOu7NnjjuWR9AVOOOxLTpR2zb/sS0HUBUow549MAhIiLuigWKyhkvPOT4cTHGXAvcCPzTWruhAmoLerPS1/Po4kBg6jXt+zCyfR+XKzo2haSKiMhBaoYEmaNlgfSo34zrTD8ubNmVuMiqnQXieIsp2racwk0LKNy4gMJNCylOXwWO84tzw2KTDpn10Z+Y1v0Ir5VcpfWKiIgchwKgvITMmEOOH5Mx5jTgFeBL4M9HO9dam3yM98oiBGaHpOdl86tpk/A7Dl3qNuGhfhe5XdIxKSRVREQOpWZIkNhfmMv76xbz9tqfZ4EEZoH0YJTpW2WzQBy/n5Jda3/W+CjaugTHW/zLkz2en2Z9tDk46yNVsz5ERCQU7CSwVOZwB8fSj/UGxphuwGfAcuBqa63vGJeEvGKfl9t+eIv9hXkkRcXy4vBRxARZYPuhFJIqIiLlUTPERX7Hz5ydpbNAtqykpJwskMqeBeI4Dt7MHRRunE/hpoUUblxA0eaF+AsOlHt+RO0mxLTuQ0yrPsS07kN0i16a9SEiIqFqKXC3MSb+sBDVfqWvy452sTGmDTAZ2AOcb63Nq5Qqg8xDC75i8d6tePDw7NCRNE+o43ZJR6SQVBERORI1Q1ywtyCH99cv5m07n805+8vGE6NiuLxNT65t35cOdSpnRxjvgT0UbV5M4ebFFG6aT+HGBfiyd5V7blhcMjGtehPTum/gtVUf7fAiIiLVyQfA74CbgKcAjDHRwDhglrU2vXSsORBnrV1z8EJjTEPgG8APnG2trRE7yHyycSmvrZ4NwN3dT+f0psblio5MIakiInI0QdUMMcY0Au4m8IlMbyAeGG6t/bGccy8C/gp0JPCJzCvAw9Zab1XVeyL8jp/p6et5287nm62r8B6yw0qflBaMMn05v2WXCtsRxnEcfFk7Kdy8iKItSyjcspiiLUvwZmwv93xPZAzRLXqWNj8CMz8iG7TF4/FUSD0iIiLBxlo7zxjzPvBo6TPIBuB6oAUw9pBTJwJDCWy3e9BkoDXwKDDYGDP4kGMbrLVzKrN2N6zJ3MV9sz4EYGiT9vym2wiXKyqfQlJFROR4BFUzBDAEtqVbT2Dt7cByTzLmXOAT4HvgLqAL8BegXunfg8bOvGzeXbeQd9YtYHtuVtl4UlQsl7fpwSjTD1O7wSndw3EcvPu3Bhoem5dQuGURRZuX4Duwu/wLwsKJatLpkMZHX6KbdMITxOt9RUREKskY4KHS19oEnj/Os9bOOsZ13Upff1/OsQlAtWqG5BQXcsv3b1LgLaFJrWSeG3I14UE4w0IhqSIicryCrRmyCKhnrd1vjLkE+PgI5z0GLCEwLdUHYIw5ANxvjHnGWruuSqo9Aq/fxw/bLW+vXcB329fgP2THlf4NW3Ft+76c26IzsSfRfHAch5I9GyjaspjCzUsCr1uW4M/dX+75nogoopp2IaZFD6Jb9CCmZS+imnYhLCqm3PNFRERqEmttIXBf6deRzhlWzliNmTrpOA6/nfk+Gw/sIyosnBeHj6J2TC23y/oZx3FYv3491lqFpIqIyHEJqmaItTbnWOcYYzoSWBpz62GJ7c8DDwKXA/+qnAqPbltOBu+sW8i76xayK/+nANI60bW4sl0vrm3fhzZJ9Y/7/fwlRRTvWEnRtmUUbV1O0bblFG1Zgr8gu9zzPZExRDfrRnTLnoHmR8uepTM+qnYbXhEREak+XkybwddbVgLw9/4X0b1+M5cr+rnyQlJ79uxJYmKiy5WJiEgwC6pmyHHqUfq68NBBa226MWb7IcerRLHPyzdbVzFp7QKmp6/H4adZIEMat+Pa9n04q3lHosKP/q/ae2APRVuXljY9llG0bTnFO9eAr/wIFE90rbLZHmUzPhql4jnGfURERESO1/zdm/nnoskAXNW2F6Pa93W5op8rLyS1Q4cOhIeHu1yZiIgEu1D8zblR6evOco7tBMrd7sQYk3WM9006kSI2ZO/l7bUL+GD9IvYX/rSTXoPYBK5q15uR7XvTIqHuL65zfF6Kd60tne1R+rVt+RF3dAEIT6hPdPOugVkfLXoQ06InkQ3b4QnTD3oRERGpHJmFedzx4yR8jp8OtRvy8ICLgyZYXSGpIiJyqkKxGRJb+lpUzrFCIK6yblzgLeHLzSuYtHY+83ZvLhsP83gY0TSVa9r34fSmhojSJoUvL4ui7csDsz22Lg3M9tixEqeksPwbeMKIamSIblba+Gge+ApPahg0Dx8iIiJS/TmOw70zP2BnfjZxEVH8b/ioCtvx7lQpJFVERCpCKDZDCkpfy/uJF3PI8Z+x1iYf7U1LZ46UOztk5f503l67gI83LuFA8U+NjGbxtRnZrjdXtuhEnex0irctJHPOBIp2pFG8Pe2I29gChMUmBhoezbqWNT2imnQiLCr2iNeIiIiIVIXXVs/mm22rAXhkwMUnlHlWWRSSKiIiFSkUmyEHl8c04pdLZRoBsyviJgeKC/l041ImrV3A8v07AAhz/LQuPMDFsdEMD/PTYNd6ihe9Tu7u9eQ6/iO+V2T91j8tc2nWlejm3Ymo10KzPURERCTopO3fwT8WfAXA5W16cEXbXi5XpJBUERGpeKHYDFla+tobWHxw0BjTGGh6yPGTMn/3ZibZecxbPYtGOTvpmLeP8/P2kVqYSZO8fYT5SsrOzTvs2vCEekQ17UJ0k05ENe1U+tqF8Fj9oBYREZHgl1tSxO0/TqLY76NVYj0eHnCJ2yUpJFVERCpFyDVDrLUrjTFrgFuMMa8csr3u7YAf+PBk37u4MJcdD5/GmLx93O4rPuJ5nuhaRDfpHGh4NO1CdNNORDXpTHhiimZ7iIiISMh6cM4nbDqwj6iwcF4Ydg3xke7lcCgkVUREKlPQNUOMMX8q/WOH0tfRxpjBQJa19rnSsfuAz4Apxph3gc7AncCL1tq1J3vvCL+XTgfSfxoIjySqcQeim3QiumlnopoEmh8RdZvjCQs72duIiIiIBJ0P1i/iww1LAPhTn/PoXLeJa7UoJFVERCpb0DVDgIcO+/sNpa9bgOcArLVfGGMuA/4PeBbYC/yjnGtPiD8sAv+Zd9OkXX+imnQmqkE7PBGRp/KWIiIiIkFvQ/ZeHpjzKQBnNevAuA4DXalDIakiIlJVgq4ZYq09rnUm1tpPgE8q8t4RMfGkjnqiIt9SREREJKgVeku4/ce3yfcW0yguiccHX+HKsl+FpIqISFUKumaIiIiIiFSdfyz8ilUZOwnzeHhu6Ehqx9Sq8hoUkioiIlVNzRARERGRGmrylpW8vnoOAPd2P4N+Dat2OYrX6yUtLY1t27YBCkkVEZGqo2aIiIiISA20IzeLe2d+AMDAhq25s+vwKr2/QlJFRMRNaoaIiIiI1DA+v59fT3+X7OIC6kTX4pmhIwmvop3yFJIqIiLBQM0QERERkRrmpZUzmLd7EwBPnnYlDeOqJqRUIakiIhIs1AwRERERqUFWZaTz6OJvABht+jGiWWqV3Dc9PZ3ly5crJFVERIKCmiEiIiIiNUSht4RfT3+PEr+Plgl1+XOf8yv9ngpJFRGRYKRmiIiIiEgN8Z8l37ImcxfhnjCeGXo1cZFRlXq/zMxMlixZQl5eHqCQVBERCR5qhoiIiIjUALN3buCltBkA3NVtOD3rN6+0eykkVUREgp2aISIiIiLV3IHiQn4z430cHLrVa8rd3U6vtHspJFVEREKBmiEiIiIi1dxf5n7GjrwsYsIjeWbI1USGVU5oqUJSRUQkVKgZIiIiIlKNfbF5BR9sWAzAn/qcR5uk+hV+j8NDUqOioujevTsNGjSo8HuJiIhUBDVDRERERKqp3fkH+OPsjwEY2qQ916f2r/B7KCRVRERCkZohIiIi8v/t3XmUHXWVwPFvB2MAEyKiKJsEXC4ZFIJiggiCwuDggrKIKC4IOHOOcxQQGEXBzLCIghpURj0OzkR0PMoijAgoiqhDCIQtLDpcMGxCEEjYGslCkjd/VLV2Ot0heUt16r3v55x3XnfV+1Vdfv1Sdbn1q1+pCzUaDY69+gKeWPIME5+/AV/Z7SD6+vraun0nSZUk1ZXFEEmSpC70/byO3zx4JwBf2nV/XrZh+yYwdZJUSVLdWQyRJEnqMnc/+Sgnz7kUgANesRPv3GaHtm3bSVIlSd3AYogkSVIXWbZiOZ/83XksXv4sm79gIqdM268923WSVElSF7EYIkmS1EXO+f0s5i4oChYzdnsvE8dt0PI2nSRVktRtLIZIkiR1ibuffJQzb74CgI9stwtv2vyVLW1vpElSJ02a1NbJWCVJqprFEEmSpC6worGCY6++gCXLl7Hl+Bdyws77trQ9J0mVJHUziyGSJEldYOb/zeb6R+4D4IxdD2T82OZvYXGSVElSt7MYIkmSVHP39z/G6Tf+HIBDXrUzb97iVU1tx0lSJUm9wmKIJElSjTUaDY6fdSGLlj3LSzfciJPe8I6mtuMkqZKkXmIxRJIkqcZ+eOf1zHpoHgBf2nX/tX56jJOkSpJ6kcUQSZKkmpr/9BOccv2lAOy/7RT23mryWrVftGgRN998MwsXLgScJFWS1DsshkiSJNVQo9Hg09dcxNPPLuHF64/n5GnvWqv2TpIqSeplFkMkSZJq6MJ5N3HVgwnAqW98Nxuv/4I1auckqZIkWQyRJEmqnYefeYrp110CwNu3fg3vnPTaNWrnJKmSJBUshkiSJNVIo9Hgs7Mv5smli3nhuA05dZd3r1GboZOkTp48mW222cZJUiVJPcliiCRJUo387N7b+MX9fwDg36a9i003nLDazztJqiRJq7IYIkmSVBOPLf4LJ177PwDsvdV2HLDtlNV+3klSJUkansUQSZKkmjjthstYuPgvTBg7jtPfuP+It7g4SaokSatnMUSSJKkGrv3z3fz4rhsB+Mzr/4HNXjBx2M898cQT3HTTTU6SKknSalgMkSRJWsctXb6ME665GIApL96KD8a0VT7jJKmSJK05iyGSJEnruO/8/n+568lHGNPXxxd3fQ/rjRmz0nonSZUkae1YDJEkSVqH3de/kBlzrwTg8Mm78ppNtlhpvZOkSpK09iyGSJIkraMajQYnzv4pS5Yv42UbbsRxr9vnr+ucJFWSpOZZDJEkSVpHXXrf7Vz1YAJw8rT9GD+2mATVSVIlSWqNxRBJkqR1UP/SxUy/7hIA9tpyO/bdensnSZUkqU0shkiSJK2DzrzpCh5+5inWX28sp+6yH4sXL3aSVEmS2qSWxZCI2BO4aoTVkzPzjgrDkSRJNRUR44CTgQ8BGwO3AJ/LzCvXoO0WwAxgH2AM8GvgmMy8p9W4bl3wADPvmA3AMVP2Yr3+xfz21jlOkipJUpvUshgyyFnAjUOWzR+FOCRJUj3NBA6kyCn+CBwGXB4Re2Tm7JEaRcR4igszE4DTgGXAMcBvImJKZj7eSlAnzL6YFY0Gr5rwYqYum8CNNxbpjpOkSpLUHnUvhvw2My8e7SAkSVL9RMRU4BCK0RxnlcvOBW4HvgS8eTXNPw68Enh9Zt5ctr28bHsM8Plm41q6fBm3LHiAFc8s5r0bbc6fHyyu8zhJqiRJ7TNmtANoVURMiIi6F3UkSVL1DgKeBc4ZWJCZi4HvArtFxGbP0fbagUJI2fYO4Erg4FaCWrJ8GcsefoxpT2/AVs+fwJgxY9h+++2ZOnWqhRBJktqk7sWQ7wNPAYsi4oqIeO1oByRJkmpjJ+COzHx6yPI5QB8wZbhGETEG2AG4YZjVc4BXR8SGzQa1YsUK1l/wFw5+5euYMGECu+++O9tuu61Pi5EkqY3qOqJiKXABcDmwgCIhOQ64OiLekJl3Dm0QEU88xzYn9vf3s/POO7c7VkmSaqu/vx+gWx9Xshnw4DDLHyrfNx+h3YuAcYM+N7RtX7nteUNXrkk+0vfscl5wxa2cceUfnCBVkiQ6k4/UshiSmdcA1wxa9NOIuITiCs104NBmt93f3/9ki+HpuU0s3+3rzrOvq2V/V8e+rs5Eiv+570YbAEuGWb540PqR2tFk2+fUByxbsvTJZSxtdhNaMx5HqmNfV8e+rpb9XZ225yO1LIYMJzNviYhfAXuNsP6Fq2s/cKXmuT6n1tnX1bGvq2V/V8e+rs4ajGSos0UUIzyGWn/Q+pHa0Uxb85F1h31dHfu6OvZ1tezv6nQiH6n7nCFD/Yli6KokSdJzeYjidpahBpbNH6HdYxSjQkZq22D4W2gkSdI6otuKIdsCj452EJIkqRbmAttFxPghy6eV77cM1ygzVwC3AcNNNDYNuCszn2lXkJIkqf1qWQyJiJcMs2w34C3AL6qPSJIk1dAFwFjgyIEFETEO+CgwKzPnl8teHhHbDdN2l4jYaVDbAN4KnN/pwCVJUmvqOmfIjyPiGYpJVBcArwH+sfz5X0cxLkmSVBOZeV1EnA+cEREDT3/5CLA1cNigj54L7MHKE7d9E/gYcFlEfAVYBnyK4vaYGZ2PXpIktaKWI0OAi4GXAMcC/w4cCPwQeENm3j+KcUmSpHr5MPC18v3rFCNF3p6Zs1bXKDP7gT2Bq4GTgFMobrvZIzMXdjBeSZLUBrUcGZKZX6dIWCRJkpqWmYuB48vXSJ/Zc4TlDwDv7UxkkiSpk+o6MkSSJEmSJKkpfY1GY7RjkCRJkiRJqowjQyRJkiRJUk+xGCJJkiRJknqKxRBJkiRJktRTLIZIkiRJkqSeUstH666NiBgHnAx8CNgYuAX4XGZeuQZttwBmAPtQFI5+DRyTmfd0LuL6aravI+IA4H3AVOClwP3AJcCpmflkR4OuqVa+10O2cxmwL/C1zDy63XF2i1b7OyI+ABwNbA8sAW4Djs/MOR0JuMZaPGbvDZwIvJbimH0HMCMzz+tcxPUVEZsBRwHTgJ2B8cBbMvM3a9h+MsU5cjdgKcVx+9jMXNCRgGvOfKQ65iPVMR+plvlIdcxHqjOa+UgvjAyZCRwD/ICik1cAl0fEG1fXKCLGA1cBuwOnAdOB1wG/iYiNOxlwjc2kib4GvgNMBr4PfBL4Rfk+KyLW71i09TaT5vr6ryLiHcCbOxJd95lJk/0dEacC3wNuL9v+GzAPeFmngq25mTR3zH4ncAVFkX86cBKwHPhxRBzRyYBrLIBPA1sCt65Vw4gtgd8BrwA+C3wZeBdwRUSMbXOc3WIm5iNVmYn5SFVmYj5SpZmYj1RlJuYjVRm1fKSrR4ZExFTgEIqrJ2eVy86lOAh8idUfeD8OvBJ4fWbeXLa9vGx7DPD5zkVePy329UFDK38RcSPFAfsQioORSi329cA2nk9RQT2D4mSoEbTS3xGxK8WB+cDMvKjz0dZbi9/tfwYeAvbKzCVl2/8A7gY+DHy3c5HX1o3AizNzYUS8B1ib7+hngQ2AKZn5IEBEzAF+SXEV7T/bHGutmY9Ux3ykOuYj1TIfqY75SOVGLR/p9pEhBwHPAucMLMjMxRRfwt3KITmra3vtQOJRtr0DuBI4uDPh1lrTfT3CEKiBfwST2xhjt2jlez3gKIoDx5c7EmF3aaW/jwKuz8yLImJMeYVXI2ulrzcCHh9IPMq2S4DHgUWdCbfeMrM/Mxc22fxA4KcDiUe5vV8Bd+I5cjjmI9UxH6mO+Ui1zEeqYz5SodHMR7q9GLITcEdmPj1k+RygD5gyXKOIGAPsANwwzOo5wKsjYsM2xtkNmurr1RgYsue956tqqa8j4mUUQ/Y+m5nPdCTC7tJKf+8FXB8RXwCeBPoj4t6IOLQjkdZfK339W2D7iDglIl5Rvk4BXg18pSPR9qhy/opNGfkcuVO1EdWC+Uh1zEeqYz5SLfOR6piP1EA78pFuL4ZsRjFMaaiBZZuP0O5FwLjVtO0rt62/abavR/JpivvrftJKUF2q1b4+HUiKeyD13Jrq7/Je/k0ohlkeQfGdfj/wJ+AHEbF/+0OtvVa+26cB5wGfA/5Yvo4G9svMX7YxRv3t/DfS32rTiFivwnjqwHykOuYj1TEfqZb5SHXMR+qh5Xyk24shG1DMlDzU4kHrR2pHk217VbN9vYpypusjgDMyc14bYus2Tfd1eQ/khynugWx0ILZu1Gx/DwxB3YTiBPjNzPwRsDfwAN7nP5xWjiNLKIZEnk+R5H0QuAk4LyLe0M4g5TmyCeYj1TEfqY75SLXMR6pjPlIPLZ8ju70YsojiispQ6w9aP1I7mmzbq5rt65VExO4U9+NdSjF0Uqtqqq8jog/4GnBhZl7dodi6UavHkXsy87qBheV9oxcAO3rP7ipaOY58A3g78P7M/FFm/jdFovdn4Kx2BinPkU0wH6mO+Uh1zEeqZT5SHfORemj5HNntxZCHGH746MCy+SO0e4yiwjRS2wbDD8fpZc329V9FxI7ATykeqfS+zFzevvC6SrN9vT8wFfhWREwaeJXrNip/9wrjqlo9jjw8zLqHKYa3T2w5uu7SVF+XTyM4EvhZZq4YWJ6ZzwKXA1MjoqufnlaxgfPfSH+rRzx+r8J8pDrmI9UxH6mW+Uh1zEfqoeV8pNuLIXOB7Yapdk4r328ZrlH55b0N2HmY1dOAu5zoaRVzaaKvB0TEK4CfA48A78jMv7Q9wu4xl+b6+uUU/+Z/Ddwz6AXw0fLnPdoaaXeYS/PHkbnAFsOs3pLiHvTH2hNi15hLc9/tTSgeFT/cfaFjy3V97QhQUM7Y/ijDnyOnUvwdtbK5mI9UZS7mI1WZi/lIleZiPlKVuZiPrPPakY90ezHkAoov3pEDCyJiHMWBdlZmzi+XvTwithum7S4RsdOgtgG8leIeMK2s6b4uZxO/AlgBvC0znbF99Zrt60sorsYMfQH8rPz5po5HXz+tHEfOB7aKiL8f1HYjikd9XZOZDm9fWbN9/QjwBHBARIwd1HY88C7g9vKqjJowMBv+kMUXAvuVM7kPfG4vitnyPUeuynykOuYj1TEfqZb5SHXMR9ZBnchHunqYTmZeFxHnA2eUz4OeB3wE2Bo4bNBHz6WoQA+u1H0T+BhwWUR8BVgGfIpiOM6MzkdfLy329c+BbYEzKJ7dvdugdfMyc3YnY6+bZvu6nPxtlQngipyaeZl5cUcDr6kWv9vfojiRXhgRMyieMX8E8ELghI4HXzMtfLeXR8SXgVOB2RHxA4qrMkdQXPU6rrL/iJqJiBPLHyeX7x8qj8FPZObZ5bIry/dJg5p+AXgvcFVEfINigr7jKa6WndvRoGvIfKQ65iPVMR+plvlIdcxHqjda+UhXF0NKHwZOKd83prj/8+2ZOWt1jTKzPyL2pEg0TqIYRXMVcHRmLuxoxPXVVF8DO5bv/zLMuu8BJh+rarav1ZxmjyPPRMRbgDOBT1DMaH0jsLd/qxE129enRcQ9wFHAdIrJtG4FDsjMizobcq2dMuT3w8v3+4CzGUFm/iki9gC+CnwRWEpxRfdTmbm0E4F2AfOR6piPVMd8pFrmI9UxH6nWqOQjfY2GT7OSJEmSJEm9o9vnDJEkSZIkSVqJxRBJkiRJktRTLIZIkiRJkqSeYjFEkiRJkiT1FIshkiRJkiSpp1gMkSRJkiRJPcViiCRJkiRJ6ikWQyRJkiRJUk+xGCJJkiRJknrK80Y7AEn1FREbAHcBK4BXZeaSQevOAT4KHJqZP+rAvr8N/BOwRWbOH7IugNuAb2fmJ9u9b0mSJEn15sgQSU3LzEXAdGAr4OMDyyPidOAI4BOdKISUZpfvU4dZNwN4qoxNkiRpWBGxQUQ8EBH3R8S4IevOiYjlEXHIaMUnqXMshkhq1Uzg98AJETE+Io4GPgNMz8xvdnC/15bvKxVDIuIdwL7A5zPz8Q7uX5Ik1dwoX9iRNIr6Go3GaMcgqeYi4p3AJcCvgbcAZ3f69pSI6AMWADdn5t7lsrHA7cBSYEpmLu9kDJIkqf4iYj3gFmBTYFvgSIpRptMz8+TRjE1S51gMkdQWEXETsBPwI+ADmdkYsv5g4JPAFGBBZk5qwz4vBd4EbJyZjYg4DjgT2Dszr+zUfiVJUncZjQs7kkaXt8lIallEvA/Ysfy1f2ghpPQ4cDbwuTbu+lpgYhFCbAqcBFw8UAjp4H4lSVIXycyfATcDbwV+DBw19DMRcXBEXB0RT0fEvRWHKKnNLIZIaklE7AOcC1xEMSrk8IiYPPRzmfnL8p7b+9q4+8GTqH4BGAccW8F+JUlSFxnFCzuSRonFEElNi4hpwE+AWcChwIkUj9k9vaIQ5pT7O5LiMb5nZebdFe1bkiR1gVG+sCNplFgMkdSUiPg74DLgTuA9mbkkM+cB3wXeHRFvamKb90bEGk9klJlPAX8AdgceAU5b231KkqTetQ5c2JE0SiyGSFprEfFy4BcUw0X3LYsSA04BFgFnNLHp8cD8tWwzp3w/ITP7m9inJEnqQZ24sCOpPp432gFIqp/MvB/YaoR184EN13abEbEDsAlw+Fq0GQvsCdwAfG9t9ylJknrTGlzY+QjFhR0LIlKXshgiqRIRsR4wtnz1RcT6QCMzl5QfeRtwC2tX1DgO2AY4dISJztZkv5Ikqcd04sKOpHqxGCKpKh8C/mvQ74soJiCbBJCZZwJnPtdGIuJFFIWTHYDjga9m5rXN7leSJGlNeIFF6i59jcYaz1UoSaMuIt4P/JBiwtRzgc9k5vLRjUqSJHW7iDiMlS+wANyXmZOqj0ZSqyyGSJIkSZKknuLTZCRJkiRJUk+xGCJJkiRJknqKxRBJkiRJktRTLIZIkiRJkqSeYjFEkiRJkiT1FIshkiRJkiSpp1gMkSRJkiRJPcViiCRJkiRJ6in/D0ITF3tPvFMEAAAAAElFTkSuQmCC", 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" ] }, "metadata": { "needs_background": "light" }, "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 / si.BAR, ax=ax[0])\n", "sns.lineplot(x=vle.vapor.molefracs[:,0], y=vle.vapor.pressure / si.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 \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": 29, "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 = si.array(369.96 * si.KELVIN)\n", "pc = si.array(4250000.0 * si.PASCAL)\n", "omega = np.array([0.153])\n", "molar_weight = si.array(44.0962 * si.GRAM / si.MOL)\n", "eos_python = EquationOfState.python_residual(PyPengRobinson(tc, pc, omega, molar_weight))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# let's first test if both actually yield the same results ;)\n", "assert abs(State.critical_point(eos_python).pressure() / si.BAR - State.critical_point(eos_rust).pressure() / si.BAR) < 1e-13\n", "assert abs(State.critical_point(eos_python).temperature / si.KELVIN - State.critical_point(eos_rust).temperature / si.KELVIN) < 1e-13" ] }, { "cell_type": "code", "execution_count": 31, "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": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Critical point for pure substance\n", "Python implementation is slower by a factor of 42.\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": 33, "metadata": {}, "outputs": [], "source": [ "time_python = timeit.timeit(lambda: PhaseDiagram.pure(eos_python, 300*si.KELVIN, 100), number=100)\n", "time_rust = timeit.timeit(lambda: PhaseDiagram.pure(eos_rust, 300*si.KELVIN, 100), number=100)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Phase diagram for pure substance\n", "Python implementation is slower by a factor of 57.\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": "feos", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.10" } }, "nbformat": 4, "nbformat_minor": 4 }