thermohub/module_7/N2_phases.ipynb
Eric e5bf977ca5 Replace spaces with underscores in module directory names
Rename module directories (module 6 → module_6, module 7 → module_7) to
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Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-03-16 07:53:35 -06:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "7af16f2a",
"metadata": {},
"source": [
"# Phase diagram calculations for nitrogen"
]
},
{
"cell_type": "markdown",
"id": "32d5dd49",
"metadata": {},
"source": [
"In this example, we will construct a PT phase diagram for nitrogen using empirical relations like the Antoine equation and approximations such as the Clausius-Clapeyron equation."
]
},
{
"cell_type": "markdown",
"id": "bb1887c3",
"metadata": {},
"source": [
"## Antoine equation\n",
"\n",
"The Antoine equation is an emprical equation of the form\n",
"\n",
"$$ \\log P^\\mathrm{sub}(T) = A - \\frac{B}{T + C} $$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "83c296bf",
"metadata": {},
"outputs": [],
"source": [
"# Antoine equation given parameters A, B, and C\n",
"# Pressure is returned in Pa\n",
"def P_antoine(A, B, C, T):\n",
" return 10**(A - B/(T + C))*100000"
]
},
{
"cell_type": "markdown",
"id": "ed693003",
"metadata": {},
"source": [
"## Clausius-Clapeyron equation\n",
"\n",
"Given $\\Delta^\\mathrm{sat}\\underline{H}$, $T_1$, $P_1$, and $T_2$, return $P_2$ by the equation\n",
"\n",
"$$ \\ln \\frac{P^\\mathrm{sat}(T_2)}{P^\\mathrm{sat}(T_1)} = \\frac{-\\Delta^\\mathrm{sat}\\underline{H}}{R} \\left ( \\frac{1}{T_2} - \\frac{1}{T_1} \\right ) $$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "4a95c76a",
"metadata": {},
"outputs": [],
"source": [
"# Clausius-Clapeyron equation\n",
"# Pressures in Pa, Temperatues in K\n",
"# Enthalpy in J / mol\n",
"\n",
"import numpy as np\n",
"from scipy import constants\n",
"R = constants.R\n",
"\n",
"def P_CC(delta_sat_H, T1, P1, T2):\n",
" return P1*np.exp(-delta_sat_H/R*(1/T2-1/T1))"
]
},
{
"cell_type": "markdown",
"id": "93580680",
"metadata": {},
"source": [
"## $P-T$ plot for nitrogen"
]
},
{
"cell_type": "markdown",
"id": "87fec321",
"metadata": {},
"source": [
"### Data for nitrogen -- sublimation, VLE, critical point, and triple point\n",
"\n",
"NIST Webbook data is included below:\n",
"\n",
"https://webbook.nist.gov/cgi/cbook.cgi?ID=C7727379&Units=SI&Mask=4#Thermo-Phase\n",
"\n",
"We can find other thermodynamic data in:\n",
"\n",
"The solid phase of nitrogen, including estimates of the melting (fusion) line are available on wikipedia with references:\n",
"\n",
"https://en.wikipedia.org/wiki/Solid_nitrogen\n",
"\n",
"Streng (Miscibility and Compatibility of Some Liquid and Solidified Gases at Low Temperature, J. Chem. Eng. Data, 1971, 16, 357) gives the melting temperature at 1 atm as $ T^\\text{fus} = 63.3 $ K.\n",
"\n",
"The enthalpy of sublimation is measured by NIST and reported in:\n",
"\n",
"H. Shakeel, H. Wei, and J. Pomeroy, Measurements of enthalpy of sublimation of Ne, N2, O2, Ar, CO2, Kr, Xe, and H2O using a double paddle oscillator, The Journal of Chemical Thermodynamics 118, 127 (2018).\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "2b4bdcfe",
"metadata": {},
"outputs": [],
"source": [
"# Data for nitrogen\n",
"# Molecular weight\n",
"MW = 28.0134 # g/mol\n",
"\n",
"# Critical parameters and acentricity\n",
"Pc = 33.978*100000 # Critical pressure in Pa\n",
"Tc = 126.19 # Critical temp in K\n",
"Vc = 1/(11.18*1000) # Critical volume in m^3/mol (original is 11.18 mol/l)\n",
"omega = 0.040 # acentric factor\n",
"\n",
"# Triple point\n",
"T_triple = 63.14 # temp in K\n",
"P_triple = 0.1252*100000 # pressure in Pa\n",
"\n",
"# Normal melting point\n",
"T_melt = 63.3 # in K\n",
"P_melt = 101325 # in Pa\n",
"\n",
"# Antoine equation parameters\n",
"# Valid temperature range in K\n",
"T_Antoine_min = 63.14\n",
"T_Antoine_max = 126\n",
"\n",
"A = 3.7362\n",
"B = 264.651\n",
"C = -6.788\n",
"\n",
"# Enthalpy of sublimation is given by \n",
"H_sub_1 = 7.34*1000 # J / mol, 23 to 27.5 K\n",
"\n",
"# Enthalpy of vaporization\n",
"H_vap_1 = 6.1*1000 # J / mol, data from 63. to 126. K. (NIST)\n",
"H_vap_2 = 5.57*1000 # J / mol (data wikipedia)\n"
]
},
{
"cell_type": "markdown",
"id": "72d6aac4",
"metadata": {},
"source": [
"### Solid-liquid equilibrium\n",
"\n",
"Data for N2 lists the heat of fusion as\n",
"\n",
"$$\\Delta^\\mathrm{fus}\\underline{H} = 720 \\text{ J/mol}$$\n",
"\n",
"By the Clapeyron equation, we can then find\n",
"\n",
"$$ \\left ( \\frac{\\partial P^\\mathrm{sat}}{\\partial T} \\right )_{\\underline{G}^I = \\underline{G}^{II}} = \\frac{\\Delta \\underline{H}}{T \\Delta \\underline{V} }$$\n",
"\n",
"As expected, this line should be quite steep. We can integrate the function to give\n",
"\n",
"$$ P^\\mathrm{sat}(T_2) = P^\\mathrm{sat}(T_1) + \\frac{\\Delta \\underline{H}}{\\Delta \\underline{V} } \\ln \\left ( \\frac{T_2}{T_1} \\right )$$\n",
"\n",
"In the case for nitrogen, we have data for the triple point and normal melting point. Therefore, we can estimate the entire melting (fusion) line.\n",
"\n",
"Rearranging,\n",
"\n",
"$$ \\Delta \\underline{V} = \\frac{\\Delta \\underline{H} \\ln (T_2/T_1)}{P^\\mathrm{sat}(T_2) - P^\\mathrm{sat}(T_1)}$$\n",
"\n",
"Using the triple and normal meltint point temperature and pressures, we can find the change in molar volume and use the Clapeyron equation to plot the melting line."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "cd670958",
"metadata": {},
"outputs": [],
"source": [
"# Integrated Clapeyron equation\n",
"def P_clapeyron(T1, P1, T2, delta_H, delta_V):\n",
" return P1 + delta_H/delta_V*np.log(T2/T1)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "1f0615ef",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Calculated molar volume: 2.05e-05 m^3/mol\n"
]
}
],
"source": [
"# Data for nitrogen\n",
"\n",
"# Other data\n",
"delta_fus_H = 0.72*1000 # Heat of fusion, J/mol (Wikipedia, 0.72 kJ/mol)\n",
"\n",
"# Calculate Delta V\n",
"delta_fus_V = delta_fus_H*np.log(T_melt/T_triple)/(P_melt-P_triple)\n",
"\n",
"print(f\"Calculated molar volume: {delta_fus_V:.2e} m^3/mol\")\n",
"#print(delta_fus_H/delta_fus_V)"
]
},
{
"cell_type": "markdown",
"id": "3289cdae",
"metadata": {},
"source": [
"### Building the PT diagram plot"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "69d95f54",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'P-T diagram for nitrogen')"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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QEBmJOyPeSyw6trdX9Th5e/XSullERJRODHSIUhEfFoZbg95B5JEjsHNxQeFvZsDzhRe0bhYREWWAzQY6nEeHnjV8/Gb/txB15gzsPT1R5Id5cK9RQ+tmEVFWkH/3d+8G/P0Bb2+gcWPAwUHrVpGJcB4dzqNDKQQ5N958E9Fnz8EhTx4UXTCfI6uIrMXq1cDw4YDMZK7n6wvMmgV06aJly8hE12/7jO6YyNq7qySTo4KcfPlQ7JfFDHKIrCnI6dYtaZAj7txJ3C6vk9VhoENkVHgsNTnSXSWZnGKLFsKlTBmtm0VEWdVdJZmclDox9NtGjEh8H1kVBjpE8u9cXBzuvPe+KjyWmhzprmKQQ2RFpCYneSYnebBz61bi+8iqMNAhmydlavcmTET4zp1qdFWReXPZXUVkReIS4nDxbOK6dM8kBcpkVWx21BWRXtCCBQj5/Xc1T07h6V/DvWZNrZtERFnwBeZU4Cmsv7oe669uRJmbN7EwPT8oo7DIqjDQIZsWtmMHAr6erh57jR4Nz5YttW4SEWXC1dCrWH9lA9Ze+hsBUXcM2w+XKgD/XA/gFfo45a4MWZRXRl/JUHOyKgx0yGZFX72Gu6M+VH3zuV/tgTy9X9e6SUT0HO4/vo8N1/7Bqgt/4Ub4RcN2XYIT4sL8YP+4BpoWaYjbn59EoZFvP3lRlzTIEbKWHefTsTo2G+hwwkDblhARgdvDhiIhPBxutWqi0CefwE7/jx0Rmb2I2AhsubEFS86sxrmQYxK5qO06nT3iw8vCIaIGmhVpjg61i6Np2QJwc5YApg5QPG/K8+hIkMN5dKwSJwzkhIE26e7oMQhduxaOBQqgxOpV6p6IzFuCLgEH/Q9i8alV2H9vB+IQbXgtLqI4HB7XQJPCLfBylbJoUrYAXJ1Syc5wZmSbun7bbEaHbFfoX3+pIEeKj32mf80gh8jM3Xh0AwtO/IFN19fjcUKgYXtCTD4gvCYaFWqNrrWqpB3cGJOgplkz0zaazAYDHbIpsXfu4N74Cepx/sGDkaNOHa2bREQpeBTzCEtPr8PKC2txP+aCYbsu3hW68KqokbcVetVrgublC6YvuCGbxUCHbIYuIQF3P/4ksS6nenXkHzRQ6yYRUbL5bjZc3onFJ1fhUvh+6Ozi1Hadzg4JEWVRPkdzvF69Hdr4FYG7My9flD78SyGbEbJiBSIOHICdmxt8pkyGnSP//InMwdkHV/DtwaU48GAT4uxCEzfaAQlRXvB1aoJXKnRCt2oVkcvNSeumkgXiv/RkE2Lv3TPMl1PwvffgXKyY1k0ismlh0RH4/uAa/HVtLUJ15/8f3MTlQB5dXXQs0RH9ajdCwZyuWjeVLBwDHbIJ97+chITHj+FWtSryvNZL6+YQ2SQZ5PvnuUNYeGI5rkbtBuyjnmy3g0tsBTT17oB3676EUgVyad1UsiIMdMjqhe/ejbAtW9RIi0ITxsOOw0iJstWFBwGY+d9y7A/ciDjHW4kbZXriuDzw82yFQTV6oGmpMpzLikyCgQ5ZNV1sLO5Pmqwe5339dbiWK6d1k4hsQnhULH44uAVrL69BsN1h2NnHqSuOTucAL4da6F62C96s+SKcWStHJsa/MLJqwcuWI+baNTjkzYv8Q97VujlEVt81tf3iNcw9sgLnH2+BnfMDwEGV3sAlwQdNfTrg/fo9UThnfq2bSjaEgQ5ZrfiwMAR+/716XGDYUDh4emrdJCKrdDs4AnP3bcfGm2sQ7XJUZW/snGVGPxeU92yMt6v3RMuStdk1RZpgoENWK2jhQsSHhMC5ZEnk7tZN6+YQWZXouHj8dfI65h9fhRuxW+Hg6g+4JWZvctoXQ+dS3TCoVjd4OHto3VSycQx0yCrFBQcjaNFi9bjA8OGcM4coi5zzf4Qf9+/FtjtrkeB+BHYO0WpFBTudE6rmaYqhtfugtnc1Zm/IbNjsv/5cvdy6SZAjK5S7VKwAzxdbad0cIosWHh2HNceuY+GJdfBP2A5H9xuA55PsjYMPXin3Ct6o0g25XDgsnMwPVy/n6uVWJ/7RI1xu/oKaN8d39nfwbNlS6yYRWRy5NJy4HYoF+45h2921gOcB2Ds+Vq/ZwQFV8zbEOzVeR32feszekCa4ejnZ9EgrCXJcypSGxwsvaN0cIovyKCoWa4/exqKjO3FXtwWOnmdgnydBvebhkA/dy3VHb79XUMC9gNZNJUoXBjpkVRJiYhD026/qcb633oKdvcxKRkTPcvJ2CH7Zdxkbrv0D5NoNB09/6FeWKp+rGgZW74tmRZrB0Z6XDbIs/Islq/JowwbEPwiEY8GCyNmundbNITJrETFxWHf8LhYfPI4r0VvglPsQHLwSu6cc7ZzRtnh7vFH5dZTNU1brphI9NwY6ZFWCf1ui7vO89hrsnLjSMVFKLgeE49d917H67G7EeuxW3VMunondU/lcvNDHrxe6lu3K4mKyCgx0yGpEnjqFqNOnVYCTuzvnzSEyFhefgK3n7mPRvis4HLgdznn3wsHnrqF7qnqBWujr9zqaFmnK7imyKvxrJqsR8vvv6t6zbRs45s2rdXOIzEJgeDRWHLqFXw+cQ5DDLjjl+Q9uPo/Ua072LnipZAf0qtiL3VNktRjokFWQUVaP1m9Qj/N07651c4jMorh40d7r+Pvcadjl2g0nr8NwsY9Rr+VzLYDXK/ZCtzLdkNs1t9ZNJTIpBjpkFR5t3qImCHQuVgxutWpp3RwiTcTEJeCf0/5Y/N91HH9wAs55d8O5+BnY2SVOl1Ymd1m8Uakv2hZvCycH1rCRbWCgQ1YhdN2f6j7Xy504eRnZnKDHMVh64AYW77uGYBxVAU6O4jcNrzcs3BB9K/ZFPW9O7ke2h4EOWbzY+wGI2H9APc7Z8SWtm0OUbS7cC8PCvdew5vh1JHgchHPB3XBzDlKvOdk7oUPJDuhTsQ9K5ymtdVOJNMNAhyxe2KaNMl893KpXh7NvYa2bQ2TypRn+vfgA8/dcw+4rt+CcZz+ciu+FvWO4ej2Xcy619lSvCr2Q3y2/1s0l0hwDHbJ4j/7ZqO5ztm2jdVOITCYqNh5/Hr+Dn3dfw+WH/nDKuwcepfer1cOFTw4f9PXri5dLvwx3J3etm0tkNhjokEWLDQhA5LFj6rFn69ZaN4coywU/jsGv+2/gl33X8TDaH875diFH6SOws49Tr5fOXRpvVnoTbUq0Ud1VRJQUAx2yaOHbd6h71ypV4OTlpXVziLLMzYcRmL/nKn4/fBvR9rfhnG8nPHKeBJ6MoKpaoCreqvwWmvg2gb0d13QjSg0DHbJoYdu3qXvPFi20bgpRljh1OxTz/r2ihonbuV6Hc6EdyOFxIckIqrcqvYWaXjU5gorIVgKda9eu4c0338T9+/fh4OCA/fv3I0eOHFo3i0wsISoKEQcOqscezZtp3RyiTBUY7738UAU4ey4HwsH9KlyKbIVjjqvqdcnYvFjsRfSv3B/l85bXurlEFsUqAp033ngDX3zxBRo3boygoCC4uLho3STKBhEHD0IXHQ3HQoXgUqaM1s0hyrD4BB02nbmHuTuv4NSdEDi4X4F7sW1wcL+mXpc1pzqV6qRqcIrmLKp1c4ksksUHOmfOnIGTk5MKckRernFkM8L37FH3Ho0bM4VPFjeD8drjd1QG5+qDcDjkuASP4tth53ZdvS5FxV3KdEH/Sv3h7eGtdXOJLJrmFWy7du1Cx44d4ePjoy5Wa9eufeo9c+bMQfHixeHq6oq6devi4MHE7gpx6dIleHh4qH3UqFEDkyZNyuYjIK1E7Nun7nM0bKB1U4jSPUR80d5raDZtBz5ceQI3Io7As+RcuBddoIIcZ3tn9CrfCxu6bMCn9T5lkENkDRmdx48fo2rVqqrGpkuXLk+9vmLFCrz//vuYN2+eCnJmzpyJ1q1b48KFCyhYsCDi4uKwe/duHD9+XD1v06YNateujVatWmlyPJQ94h48QPSly4CdHdzr1tW6OURpCo+Ow5L9N/DT7msIDI+Cg8c55Cy1AzrnW+p1FwcXdC/bXXVRFXAvoHVziayK5oFO27Zt1S01M2bMwIABA9CvXz/1XAKe9evXY8GCBRg9ejQKFy6MWrVqoUiRIur1du3aqaAntUAnOjpa3fQePXqU5cdEpvf4SVbPpXx5OObJo3VziFIUGhmrFthcsPcaQiJi4OBxAblKb0WC023IIHE3Rzf0KNdDTfTHWYyJrDTQSUtMTAyOHDmCMWPGGLbZ29ujZcuW2Pek20KyNwEBAQgODkauXLlUV9jAgQNT3efkyZMxfvz4bGk/mU7kkSPq3r02Vyon8xMaEauCG7mFRcXBwf0y8pTeijin60h4EuD0LN9TrUOVzy2f1s0lsmpmHegEBgYiPj4eXskmgpPn58+fV48dHR1VXU6TJk3UEM0XX3wRHTp0SHWfEjRJV5hxRkefDSLLEXH4SaBTk4EOmQ/J2sgaVIv2XkdYdBzs3W4gX+ltiHG6CJnH2NXBFT0r9EQ/v37I48pMJBFsPdDJqu4vYzL0nMPPLVv8o0eIvnRJPXavWUPr5hCpDI7MYrxg73VVj2Pvegf5S21HtPMZxDwZRSU1ODKTMWtwiLKXWQc6+fPnVxMAykSAxuR5oUKFMrVvGcklN8kYkWWJPHlKrVbuVLQoHPOzroG08ygqFgv2XFNZHOmisne+jwKldiDK+TikEtDBzkEtsjmwykCOoCLSiFkHOs7OzqhZsya2bduGl19+WW1LSEhQz4cMGZKpfb/77rvqJl1XUttDliPq1El171alitZNIRv1ODoOi/67jh/+vYJHUXGwc3qIgiV3IsrlMKKggx3s0K5kOwyuOpgT/RHZeqATHh6Oy5cvJ1nOQUZNycR/RYsWVfU0ffv2VSOr6tSpo4aXy5B0/SgsstGMjgp0KmvdFLLBeXB+238D3++8gqDHMbBzCIdX8d2Idt+LSF3iauKtirVSAU7pPKW1bi4RmUOgc/jwYTRv3tzwXF8oLMHNokWL0KNHDzx48ACff/457t27h2rVqmHjxo1PFSiT7Yg8lRjouFZioEPZIzY+AcsP3cJ32y4hICwasItBwSL7kZBzJyISIiBjxRv6NMTQGkPhl89P6+YSkRE7nQxVskHGNToXL15EaGgocubMqXWz6BliAwJwuUlTmWcA5Y4chr2bm9ZNIiuWkKDDuhN3MWPLRdwMipBSeBTwOQ7HfFsRHhes3lMxX0W8V/M91POup3VziWzKoyelJ8+6fmue0dEKa3QsU/STaQWcS5RgkEMmI9//tp8PwLRNF3D+XphsQZ4CF+DpvQXBsXcgY8V9PXwxvMZwvFj8RbW6OBGZJ5sNdMgyRZ1LDHRcy5fXuilkpY7cCMKUf87j0PXEjI1nrpvwKr4V92MuIjgWyOOSBwOrDsQrZV+Bk4OT1s0lomdgoEMWJer8OXXvWoGBDmWtywFhmLrxAjafTZzOwsXtIUqW3YHbMYdxPyZxNmOZyfgNvzfg4eyhdXOJKJ0Y6JBF0U8U6FK2rNZNISsREBaFb7ZcwopDN5GgA+wdIuDndxC34rbgdky8mguna5muGFR1ECf7I7JANhvocMJAy6OLjUXM9RvqsUtpDt2lzM+F8+Ouq/hp91VExMi/A/GoXOEsAp3+wvXYxMV+m/g2wQe1PkDJXCW1bi4RPSebHXWV0apt0l701au42q497Nzd1YgrOzs7rZtEFig+QYffD99SI6keyFBx6FC2xG0g71/wj7ip3lM6d2mMqj0KDXwaaN1cIkoFR12R1Yl+MrGkS8mSDHLouey+9ABfrj/3ZCQVULhACLxKbMalsKNARGKh8ZDqQ9ClTBc42vOfRyJrwP+TyWLEXL2q7l1KldK6KWSBhcYS4Oy48EA9z5kjGpUq7cOZsM14FJaggpreFXpjQJUB8HT21Lq5RJSFGOiQxYi5dt0whw5ReoRExOCbLRfx24GbqsvK0T4B9atfwKWYlTj16LF6T8uiLfF+zfdRJGcRrZtLRCZgs4EOi5EtT8ytW+reuSgvSJS2uPgELDlwU9XhhEbGqm11KgQjwuMPHA9PzAxWyFtB1eHULlRb49YSkSmxGJnFyBbjYuPGiH8QiOIrV8KtEtcTopTtuRSICX+fwcX74ep56UJxKFJmOw4HblfPc7vkxrAaw9CldBc42Dto3Foiel4sRiarkvD4sQpyBDM6lJJbQRH4Yv1ZbDqTOOFfbnc7NKp5DgdDVuBwYKRapqF72e4YWn0ocrlw2RciW8FAhyxCzO3b6t4hVy44MPNGRqJi4zF35xXM+/cKouMS4GBvh1Y1Q3ATS/FvYOK8S9UKVMPHdT9GhXwVtG4uEWUzBjpkEWJuJs5v4lS0qNZNITMhve5bzt7H+L/O4k5IpNpWo2QC8hTZiL0Bu9TzfK751IR/HUp24JQERDaKgQ5ZhLi7d9W9U+HCWjeFzMCNh48xbt0Zw3Bx71xOaFTrLHbeX4JLAVFwtHNErwq98E7Vd7guFZGNs9lAh6OuLEus/z1171SokNZNIY27qb5/0k0VE5cAJwc7vFwvFpfif8bGu4kTSsooqk/qfoJSuTnfEhHZcKDz7rvvqpu+apvMW+y9J4GONwMdW7XzQgA+//MMbgZFqOf1y7jCp8QObLz1p3ousxqPrD0SHUt2ZDcVERnYbKBDliXO31/dOxby1roplM3uhUZh4t9nsf5U4t9AoVwu6FjfH5vu/4TTt4LVts6lO6tJ/3K75ta4tURkbhjokEWIvZ84ZJgZHdshMxn/su86pm++iPDoODWaqls9ZwQ4L8PyGwfVe0rlKoXP6n+Gml41tW4uEZkpBjpk9nRxcYgLCFCPHVmjYxNO3wnFx2tO4eTtUPW8WlEP1Kh8DGuv/4LYhFi4OLhgUNVB6FuxL5wcnLRuLhGZMQY6ZPbiHjwAEhIAR0c45sundXPIhCJi4jBr6yX8vOeayuh4ujqiTzM77A35Bn9cvaLe07BwQ1VsXMSTE0cS0bMx0CGzZ8jmFCgAOwdO2W+t/r34AJ+sOYXbwYlz4rSpnBfexXfityvLkaBLQF7XvBhdZzTaFG/DYmMiSjebDXQ4vNxyxD0MUvfM5lin4McxmLj+LFYfvaOeF87tht7NY/Dn7QnYezlxRmyZ8O+j2h+x2JiIMsxmAx0OL7cccQ8T17hyyJdX66ZQFs9svOHUPYxddxqB4TGQJE2vegWAvH9jzvk16j1e7l74vP7naOLbROvmEpGFstlAhyxHvCGjk1/rplAWCXgUhU/Xnsbms4mj6coU9ECPZo+w7PIYBFxN7KrsUa4HRtQYwZmNiShTGOiQ2Yt7+FDds+vKOrI40kU1/q8zeBQVp2Y27te4AAJdV2DWqU3qPcVyFsO4+uNQq1AtrZtLRFaAgQ6ZvXh2XVnNxH8yZHz7+cSMTeXCudC9SQjmnx+JoPtBcLBzQF+/vmp9KldHV62bS0RWgoEOWVAxMruuLDWLs/LIbUz4+yzCouLg7GCPQS94I8BpBaYd/1u9p3Tu0vii0Rfwy+endXOJyMow0CGLKUZ2zM+uK0sTEBaFj1efwtZziVmcqkVyo1fTCPx49gMERAbA3s4e/fz6YXC1wXB2cNa6uURkhRjokMUUIzvkZaBjSf46cRef/XkaIRGxKoszuIUvQlxW4Ysjqwy1OF80/ALVClbTuqlEZMUY6JBZ0yUkID4kRD12zJtH6+ZQOoRExOCTtaex/mTiIpx+PjnxZst4/HRuFO6EJ86V81qF1zC8xnC4Obpp3FoisnYMdMisJYSHS5GHemyfM6fWzaF0zG486o8TCAiLVotwDmxWFPG51mPcod/U6z45fDCx4UTU8a6jdVOJyEbYbKDDmZEtQ/yjMHVv5+ICexcXrZtDqYiMiceUf85h8b4b6nnJAjnwfntPLLj4OS75X1LbupbpipG1RnJeHCLKVjYb6HBmZMuQEPZI3dvn9NS6KZSKU7dDMXzFMVx98Fg971u/KIqXPIaxh2YhJiFGrVE1ocEENC3SVOumEpENstlAhywro+OQk8GouZHVxX/cdRXTN19AXIIOXjld8OlLvvjb/xusPvqfek/jwo0xoeEE5Hfj1ABEpA0GOmQRGR0HT2Z0zIl/aCTeW3Ec+68mjohrW6kQ2tZ9iKlHBiAkOgQuDi6qm0qWceBK40SkJQY6ZBEZHXZdmY9/Tvlj9OpTCI2MhbuzAz5uXwpX4pfik/9WqtfL5y2PKY2noFTuUlo3lYiIgQ6Zt/hHoerewZMjrrQWFRuvZjdeeuCmel7FNxeGtXXHrJPv4/qj67CDnVrCYWj1oZz8j4jMBgMdMmsJ+hqdXAx0tHTxfhiGLD2Ki/fDIT1RA5uUROFiR/Hhf9MRmxCLgu4FManRJNT1rqt1U4mIkmCgQ2YtPuxJ1xUzOpqtU7X04E1M+OssouMSUMDTBV90KYV/7s3CkkPb1HuaFWmGiQ0mIrdrbq2bS0T0FAY6ZNYSHj0pRmaNTrYLi4rFmNWn8PeTGY6bli2AN1vY4ctDA+H/2B+O9o74oOYHapZjFhwTkblioEMWktFhoJOdTt8JVV1V1x9GwNHeDqNal4FDnl0Y/u93iNfFo4hnEUxrMg1++bnaOBGZNwY6ZBnFyJxHJ9u6qn47cBMT/zqLmPgEFM7thkndimPZtanYe2yvek/b4m3xef3POcMxEVkEBjpk1hIiItS9fQ53rZti9cKj4zB61UlDV1XLCl54rWkMxh3sj8DIQDU3zpg6Y9ClTBd2VRGRxWCgQ2ZNFxml7u3duMq1qUdVDfrtiFrGQbqqPmpTDvZ5dmLErm+RoEtAqVylMK3pNJTJU0brphIRZYjNBjpc1NMyJEQlBjp2rgx0TOXP43cwetUpRMbGo1BOV0x9pQxW3vwaO47uUK+/VOolfFL3E7g7MatGRJbHZgMdLuppGXSRkere3pUrl2e16Lh4fPH3Ofy6P3HF8Ual82NoG3eMPzgIt8JuwcneCWPqjkG3Mt3YVUVEFstmAx2yDMzomMa90Ci8s+QIjt0MUc+HvlAaJUucw7s7v0B0fDR8cvhgRrMZHFVFRBaPgQ6Z9Qgg3ZNAx97NVevmWI2D14IweMlRBIZHI6erI6a9UhH7Qxfg8ydrVTUs3BBTGk3hBIBEZBUY6JDZ0kVHGx7buzLQyYrAcdF/1/Hl+nOIS9ChfCFPTOjqjeknRuLsw7Nqrap3qr2DgVUGwt7OXuvmEhFlCQY6ZLYSntTnCDsGOplekPPj1aew+tgd9fylqj7o0vAx3t/bD6HRocjlkgtfNf5KZXOIiKwJAx0yW/puKztnZ9g5OGjdHIvlHxqJgb8ewcnboXCwt8OYtuXhnHcPhu+croaOV8pXCdObTYePh4/WTSUiynIMdMhsJTyZQ4fZnOd35EYQBv6aWI+Tx90JM3tWwub7c7Du8Dr1eqdSnfBZ/c/UZIBERNaIgQ6ZLV2Ufmg5A53nsfzgTXz252nExifW40zuXhRTj32A0w9Pw8HOAaNqj0Kv8r04dJyIrBoDHTJbCVGJxch2HHGVIXHxCfhi/TlVeCzaViqEPs11qh5HlnKQepzpTaejrnddrZtKRGRyDHTIAjI6nEMnvUIjYzF02THsuvhAPX+/VVn4FDmBwdu/RFxCHMrmKYtZzWfB19NX66YSEWULBjpk9pMFsusqfa4HPkb/xYdw5cFjuDk5YFp3P5yI+AXj9y1Xr7cq1gpfNPyCSzkQkU1hoENmP7zcjgt6PtO+Kw/VTMchEbFqvaqZvcripwvjcPDeQTU/zpDqQzCg8gDW4xCRzWGgQ2bLMCuyC0cEpWXlkdsYs/qkKjquWiQ3xnYugLEHBuP6o+vI4ZQDUxpPQbMizbRuJhGRJhjokPkPL2dGJ0UJCTrM2HIRs3dcVs/bV/FGryaxGLbrTTUJoHcOb8xuMVvV5RAR2SoGOmS2OLw87ZmOR/5xAn+f9FfP321eCqVKnMOQHRNU0XGV/FUw64VZyO+WX+umEhFpioEOmS0OL09Z0OMYDPjlMI7cCIajvR2+7OyHO/arMHbfQvV6m+JtMLHhRLg68rwREVlFoFO8eHHkzJkT9vb2yJMnD3bs2KF1kygLcHj50248fIw3Fh7CtcDHauXxWT0r4s+707Ht5jb1uizIObjaYC7KSURkTYGO+O+//+Dh4aF1MyiLxOt02OPsgqu1aqFUvrx4SaeDg42MGNLF6xCyOwQx/jFw9nZG7sa5YedghxO3QvDmokN4+DgGhXO7YUbPEphxKnHlcSd7J4xvMB4dS3XUuvlERGbFagIdsh6rHzzA8MuXcbtKZUBuAHz378es0qXRpUABWLMHqx/g8vDLiL6d2G0nXHxdEDEqP4Y8uILI2Hj4+eTEuC758en+Qbj7+C7yuORR9TjVC1bXtO1EROZI8/z2rl270LFjR/j4+Kg5PtauXfvUe+bMmaO6p1xdXVG3bl0cPHgwyevyc02bNkXt2rWxZMmSbGw9mSLI6XbmDG5H//9CL+5ER6vt8ro1Bzlnup1JEuSIqNvRsB9+GxVPA03LFsDHXVwxYvdbKsgp6lkUS9otYZBDRGSugc7jx49RtWpVFcykZMWKFXj//fcxduxYHD16VL23devWCAgIMLxnz549OHLkCNatW4dJkybh5MmT2XgElJXdVZLJ0aXwmn7biMuX1fussbtKMjkpHbx02Mnmt3a74dXGwRi2YxAexTxClQJV8Gu7X1EkZxEtmkxEZBE0D3Tatm2LL774Ap07d07x9RkzZmDAgAHo168fKlasiHnz5sHd3R0LFiwwvKdw4cLq3tvbG+3atVMBUWqio6Px6NGjJDcyD7tDQp7K5BiTi/2t6Gj1PmsjNTnJMznG7GEHt4c6/DT/B8QkxKB5keb4+cWfkdc1b7a2k4jI0mge6KQlJiZGZWpatmxp2CYjq+T5vn37DBmhsLAw9Tg8PBzbt2+Hn59fqvucPHkycuXKZbgVKcJvw+bCPyYmS99nSaTwOD1yhuZEj3I98E2zb+DmyNFoREQWHegEBgYiPj4eXl5eSbbL83v37qnH9+/fR6NGjVSXVr169dCnTx9Vq5OaMWPGIDQ01HC7deuWyY+D0sfb2TlL32dJZHRVerSq3Qqf1P0EDvYOJm8TEZE1sPhRVyVLlsSJEyfS/X4XFxd1I/PTOHdu+Lq4qMLjlKpwpFZFXpf3WRsZQu5U2Bkxd2LUcSank/+8dejVtxcX5iQispaMTv78+eHg4KCyNsbkeaFChTRrF5mGzJMjQ8hF8ku5/vnM0qWtcj6de+FRWNoyRh/SJHlNnktwU3l2ZTWfDhERWUmg4+zsjJo1a2LbtsRZX0VCQoJ6Xr9+/UztW0Z5SXFzWt1clP1knpyVfn4onCzrJpkc2W6N8+jILMfd5u7D+kKPsaRXAuwKJe2WcijsAL+VfijQxfqOnYjI6ruupID48uXE1ZfFtWvXcPz4ceTNmxdFixZVQ8v79u2LWrVqoU6dOpg5c6YqQJZRWJnx7rvvqpuMupKiZDIfEsx0yp8fqz4fi5vXrqF8925o+9JLVpnJOXv3EfosOIDA8BiUyJ8D/d7Jj7H7R8DzmCeKRxXH2y3fRvm25ZnJISKy1EDn8OHDaN68ueG5BDZCgptFixahR48eePDgAT7//HNVgFytWjVs3LjxqQJlsi4S1NS7fw+VDx+Gd5cuVhnkHL8Vgj7zD+BRVBwqeufE6Jfd8OF/A9UcOR71PDC61Wh45eDfORGRRQc6zZo1g+4ZE8ANGTJE3cjGxCeoOzsHs+5hfS4HrwWpdavCo+NQo2huvNM2HiP3DEZkXCSq5K+C71t+j1wuzDQSEWWW9V1B0ok1OuZPlxCf+MDKhlLvuRSouqskyKlXMi/6tgrFh3uGqyCngU8D/PTiTwxyiIiyiM0GOlKfc/bsWRw6dEjrppANZXS2nbuPNxcfQlRsglq3qkuTu/jsv9GIS4hDm+JtMPuF2XB3cte6mUREVkPzrisiW8nobDpzD0OWHkVsvA6t/bzQqMYFTDwwRb3WvWx3TgRIRGQCDHTI7DM6sIKMzj+n/DF02THEJejQsaoPqlU6jqmHZ6jXelfsjVG1RnEiQCIiE7D8K8hzYo2OBUh40nVlb9l/putP+mPIkyCnU1VvVCi/HzOPJgY5AyoPYJBDRGRCln0FyQTW6Jg/3ZNABxYc6Kw7cRfDlh9DfIIOnav7oHjZXZh78nv12tDqQzGsxjAGOUREJsSuKzJf8Yk1OnYODhYb5IxYfgwJOqBrjcIoUGwTFpz+Tb02stZI9PXrq3UTiYisHgMdsoCMjoNFdle9t+K4CnJeqVkYOQqvw5Lzf6jXpOj41fKvat1EIiKbwECHLCCjY1ldVxtP+xu6q7rW8IGz9yqsvLQWdrDD+Abj0blMZ62bSERkMyzrCpKFWIxs/iwxo7Pl7H0MWfqkJqeaN9x91uDPK2thb2ePyY0nM8ghIspmNhvosBjZkkZdWUax7o7zARi85EjiEPIqheBZ5E+svbJGBTlTGk9B+5LttW4iEZHNsdlAhyxowkALKEbeezkQA387oiYDbFfJC/mK/YU1l1erIGdSo0loW6Kt1k0kIrJJDHTI/JeAMPPh5YevB+GtxYcRE5eAlhUKwqvkBqy6vEoFOV82+pKZHCIiDZn3FYRsmiVkdE7fCUW/hYcQGRuPRmXyoWiZjVh56Q9VePxFwy/QoWQHrZtIRGTTGOiQ+S8BYaYZnYv3w9B7/gGERcehdvE8KFthG/649LsKciY2nIiOpTpq3UQiIptnnleQbMBRV5aT0THHCQNvPHyM134+gOCIWFTxzYkqVXbij0vLDUPIO5XupHUTiYjIlgMdjrqyADLbnrAzrz/T+4+i8Pr8A3gQFo1yhTzQoNYB/H5pmXptXINxHEJORGRGzOsKQmTmEwaGRMSgz/yDuBUUiWL53NGm4RksubBYvfZZvc/QpUwXrZtIRERGzOcKQmTmEwZGxMThzUWHcOF+GAp6uqBb82tYcHauYe2qV8q9onUTiYgos0tAhISEYM2aNdi9ezdu3LiBiIgIFChQANWrV0fr1q3RoEGDjO6SyOwzOjJ0fNBvR3H0ZghyuTnhjdYPMPfMN+q1wVUHc4FOIiIzle4ryN27d/HWW2/B29sbX3zxBSIjI1GtWjW0aNECvr6+2LFjB1q1aqUKfFesWGHaVpNtZXQ0LkZOSNDhgz9OYNfFB3BzcsDAdo8w78xk9Vrfin0xqOogTdtHRERZkNGRjE3fvn1x5MgRFcykRIKftWvXYubMmbh16xZGjhyZ3t0TpbEEhHYZHZ1Ohy/Wn8NfJ+7CycEO77aPxk/nvoQOOnQv2x0f1PoAdnaWsUQFEZEtSnegIyOU8uXLl+Z73Nzc0LNnT3V7+PBhVrSPbNj/a3S0C3R+2n0VC/ZeU4/faaPDwksTEKeLU7Mdf1rvUwY5RERmLt1XkGcFOZl9f3bjPDqWU6OjVaCz5thtTNpwXj1+q4UjVtycgJiEGLxQ5AU167Es8UBERObNTie5+eckWZ6bN28iJiYmyfaXXnoJluLRo0fIlSsXQkNDkTNnTq2bQ0/In+X5ColdpGX27oFjNgfOUo8jI6xkJfIe9V2wP2oigqKCUNe7Lr5v8T2cHZyztT1ERPR81+8Mj7oSV69eRefOnXHq1CmVutfHSvo0frz+mzjR89J3W2mQ0ZH1q9757YgKclpXccPx2K9UkFMxX0XMaj6LQQ4RkQV5rivI8OHDUaJECQQEBMDd3R1nzpzBrl27UKtWLezcuTPrW0m2xyhYzs4lIO6GRKpMzuOYeNQt5YaAHLNx9/FdFMtZTGVycjjlyLa2EBFR5j1XRmffvn3Yvn078ufPD3t7e3Vr1KgRJk+ejGHDhuHYsWNZ0DSyZUl6VLNpwsBHUbFqJfKAsGiU8XKGo89CnA28hPxu+TGv5TzkczPvujMiIsqijI50TXl6eqrHEuzIHDuiWLFiuHDhwvPskij1jI696Uc2xcYn4N0lR9Wsx/k9HVGs4hqcDDwOTydPFeT4evqavA1ERGQmGZ1KlSrhxIkTqvuqbt26mDp1KpydnfHjjz+iZMmSWd9Kst2h5cLEXVeSPfpkzSnsvhQId2d71K+zAzvv7oaLgwu+a/EdyuUtZ9LPJyIiMwt0Pv30Uzx+/Fg9njBhAjp06IDGjRurIeWcFZmyPqNj2mLkOTsu4/fDtyGJo7aNT2Dz3fVq6Pi0JtNQ06umST+biIhM67muIM2aNVPrWonSpUvj/PnzCAwMVMXJL7zwQla3kWxQdmV01p/0x9ebL6rHXZvewea7S9Tjz+t9juZFm5vsc4m08tFHH2HBggWG52+++aZav1DIl9aaNWuqrP2SJUtw/fp1VKlSBa+88goqVKigZsePi4tLc/8yWWzBggXVz5oLuWaNGDEiS/f56quvYvr06Vm6TzKDQOfBgwdo27YtPDw81Jj1evXq4fLly+q1vHnzWtQssZww0MxlQ0bn5O0QfPDHcfW4be1QbAn4Xj1+u8rb6Fq2q0k+kyg7NG3aVP17LDcnJyeUK1cOS5cuVa91794df/zxh3osQcu2bdvUv+vil19+Ucv8HDhwAF9++SWio6Nx+vRpfPjhhzh37hxiY2Px22+/pfnZ8nOdOnVC8eLFUxzI4uDggPbt22drwLJ69WpMnDgRWUl6NuRYZQ4XMm/2Gf0mcPz4cdVd9fXXX6uVzAcMGABL9O6776oJDw8dOqR1U0iDBT39QyPx1uLDiIpNQN1ykTgaNQvxunh0LNkRQ6oNMclnEmUHqTmTka8yCtbf318NEKlfv77Kxly7dk1NAyJzoQUHB6sgp2HDhnB1dVU/+80336Bq1apo0KCBmgxWRtRK1l5+Rp/F2LNnT6qfHRERgfnz56N///4pvi6vDR06VE1Hoh/Ekh3ki7h+AE1WkaxXqVKlnhn4kYUFOlu2bMGiRYswZswYvPfee/jrr7+we/duFfUTZSkTrnMVEROnghwZRl7aOw4BOb5HRFwE6hSqg/ENxltUZpIouUuXLiEsLExN+VGoUCE1QET+zZbszcmTJ9V7Xn75ZbUA88qVK1WGR+zYsQN79+5V2RwZbFK+fHn1b7vx/w/6LFFqNmzYABcXF5XtTy48PFzVcL7zzjsqoyPXkuTZGpmeRLJHEphI28eNG2d4/Y033sC///6LWbNmGdqh7x6TdsrPSpeZBG1y7MZfYpNngp71WSIhIUEFizLoRtZxlABQzpexjh07Yvny5en4rZCWMnQVkQhcftl6ZcqUUX/U8q2ByBRdV1ndbZWQoMN7K47jzN1HyOsRD7ciixAY+QClcpXCN82/gZODU5Z+HllPlkQCZC1uGV2lR7qeJAiQ2hq927dvq3svLy91L8HNsmXLsHXrVkO3lUynLwNKJFCQzL0EO/rA6ejRo+qxBCoSRKRGvvhKjU9Kfv/9dxU8STfa66+/ruqEkh/b4sWLkSNHDhVsyWhe6T2QL9hCAhzJTEkvglxz5FakSBH1mgQsq1atUj8vbZUslNSRBgUFpdrWtD5LSJAjXXnz5s1Tk+LKl3tptwRbenXq1MHBgwf5Zd/aRl1J/2ry55lYLosoW7uuZm69iE1n7sPZQYcylVfjbMhlNSHg9y2/R05nrnVGKYuMjUfFzzdp8tlnJ7SGu3P6/6mWC71kIfRr/8hgEQkEqlWrpi7MQrqipL5SAgd9t1WbNm0wd+5cVbvo5+dnCFiki+arr75S2SCpaezVq1eqn33jxg34+Pik2m0lgYL+s6S2RYIGya7oSXA2duxYwxfp2bNnq+61Vq1aqTWNZBoTmY1fMjB6MgJY2i0ZIn3Q9tNPP6mgRT5z1KhRKbYnrc+SwGXSpEkqEJRzJCQzJt12P/zwg6qBEnKsstbjvXv31DxyZAWBjgQ0ZcuWTZK6lHRk9erVVV+uXlpRNJFWGZ0Np/zx7XYpntehbp3tOB5yBG6ObpjTYg58PFL+x5nI0kigI106MmhEuqvk3+sePXqoYMX432mp0zEm2fmNGzcm2Sb7keAivdOGREZGGgInY1InJJkP/eguR0dH1SYJRJIHOsa8vb3VaN60XLlyRRVJS62RnhRgS1AnBdSpSeuzJAiUeiMJeoxJUCPXOz3p0hLyXrKSQGfhwoWmawmRCTM65/wf4YPfE1PxDWuewvGQLWqunK+bfq0W6yRKi5uTg8qsaPXZGQ10JIvx1ltvqeyHXMCzq+5MZsqXIufkJKCRoMs42yNfnCW4kkyKZGv0AYoxabfUyphCWp8lX+DF+vXrUbhw4STvkzYn/1JfoEABk7SRNAh0pGqfKFs8+QcnK/6BDnocgwG/HFbdD1XK3sKpiGVq++g6o9HEt0mm90/WT/4OM9J9pBXJ0shoWMlESJ1KZskQ8cOHD6f7/ZLtSD4KSQIcqXWROWdefPHFJK9JUbTUCg0aNChd+5fskixBZExGPsl2KaTWdx9JhkeKkZ937hzpvpOARkae6bupUiJD7319fVWAR+Yr3f/nSvTN0SiUXXTxWZPRkTWsBi85gtvBkSjsFYx7zgugi9ehR7ke6Fm+Z9Y0lshM6AuR9cPBs5sUAMsIL8nq5MmTR237+++/1XMZcq7P3Oh17dpVZXvSG+hI4CXFw/quORkxJQXFMpJLsljyvGjRoqq4WLqTUhvm/iwyFH3kyJGqAFmyPFKALTVFEkxJ7ZP+S78UXycP3sj8pLsAQorTZBid9FGmRSr05Y9uypQpWdE+slUJWVOj8+X6c9h/NQg53B7D2WcRIuMjUc+7Hj6q81EWNZTIfOhHHCUPKLJL5cqVUaNGDTXCSk8CmZYtW6bYJgl0JGOkH/b+LBJ8yAAYybhId5FkXIRcb2RfvXv3Vp8vNTabNm0yBFvPQyYY/Oyzz9ToK5kVWgqopStLCr1FVFSUGqJvqXPJ2RI7XTqHTEk1ukwYKKlRSYvKNwbpb5XCM4nWZfI9qUiXYXhDhgzBxx9/rNn/bBkhQyqlnRKt60cpkPYiT5/B9W7d4FioEMrs3PFc+1hz7DbeW3ECsIuFX80luPn4PIrnLI7f2v2GXC7m/7dJZIkkGJDsinTrGBc/WxsZ6SXF1Zs3b9a6KTbrUTqv3+nuumrRooWKvCWYkQp8WQdFhhJKlb30T0rfbJ8+ffDaa69lKoomyoqMzpm7oRiz+pQaYVW12iZcfXxeDR+f3WI2gxwiE5LJACWzf+fOHcM8N9ZIipm/++47rZtBWZnRsVbM6JiniGPHcKNnLzgVKYLSWzL2jSkkIgYdZ+/BraBIlCt3AHft18DRzhHzWs1DXe+6JmszERGZ3/XbevOKZNn08bd9xgrg4xN0GLb8uApyCnlfUkGOGFN3DIMcIiIbZLOBDlcvt5QJAx0yPPPxrosP4JojAHH5Eldrfq3Ca3il3CsmaSYREZk3mw10uHq5pQwvT/+f6Pbz9/GdzHxsHwGv0ssRHR+JuoXqYmStkaZrKBERmTWbDXTIUoqR05fRuR0ckTjCCgko7bcOQTF34ZPDB9OaToOjvflP9EZERKbBQIcsfsLAmLgEvLv0GEIjY1Gk5C7cjzsOFwcXtRp5HleOACQismUZCnRkhkhZGE4WT5PaltGjR6vh5URaDi+ftOEcTtwKQc585xDikrgo4bgG47iGFRERZSzQ+fLLL9VEgDL1tix0NmvWLFXrQmSyRT2fEeisP+mPRf9dh73zfTgVSlxhuXfF3uhQskN2NJOIiKwp0JGF2b7//ns1tbZMff3XX3+piQNNtbos2TD9op5pBDpXH4Tjo1UnAftIFCq7DDEJUar4+P2a72djQ4mIyGoCHVlXpF27dobnsn6JLCB39+5dU7SNbJhOv0JxKjU60XHxGLL0GMKjY1Co9CqExd9j8TEREWUu0ImLi1NrWyWfBjs2NjYjuyHKdEZn8obzOOv/CLm8d+Oxw2lVfDyz+UwWHxMRURIZ+uorq0W88cYbcHFxMWyTFVwHDRqEHDlyGLatXr06I7slylBGZ/OZe6oux8H9EnS5E4uPP6v3GSrkq5DdzSSyatevX0e3bt3UOodENhHo9O3b96ltr7/+ela2h0iJj9XhYERtPLpRH5V3Ao0bJ8Y8d0MiMWrlSdg5hiJP8T8QrdOha5mu6FS6k9ZNJiIiSw90Fi5caLqWED0hCcGhb7fA3YcdgFsAmgO+vsCMbxKw4oHMlxOF/GV+R7TuEcrnLY/RdUZr3WQiixEeHq6yNLK6uPj6669Rrly5JJmbkSNHolKlSmjWrBliYmLwyiuv4NSpU6hTpw7mz58PR8fULx0PHz5EhQoVcPDgQRQvXjzd7ZLPqlatGmbOnJkFR2l+n2cpbckur776qpqm5oMPPjD5Z3HCQDK7IKdbN+Duw6S1YPJv8ivd7bBrsws8vTcj2vEKPJw8MKPpDLg6Jn0vka1r2rSpGigiN6mjlEBm6dLEtd9k1Gy+fPlU4HLy5EnUr18/zX2dPn0aH374Ic6dO6fqMX/77bdnTkPSqVOnJEHOvXv3MHToUJQsWVKVPhQpUgQdO3bEtm3boBUpsZg4caLJP8ccj90cfPrpp+pvRVYeNzUGOmQ2pCxn+HD9wuV2KS5mHrSjDHQ5d6vHXzT8AkVyFtGgpUTmS2opjx07hsmTJ8Pf3x8XLlxQwYyUHly7dg2VK1fGrl27VPCyf/9+5MyZM839lS5dGrVq1TJ8C9+zZ0+q742IiFAZn/79+yep86lZsya2b9+OadOmqQBr48aNaN68uabzsOXNmxeenp4m/QxzPfbnJdm9rCIZw1KlSj0zcM4KDHTIbOzeDdy+ndY77BAfmhOPL9RA34p90aJYi+xrHJGFuHTpEsLCwtCoUSMUKlRIZRLGjBmjRs1KBqds2bI4fvw4/Pz88P7772P27NmqK8p4PrTo6GjDY8kKGT82fp7chg0bVNaiXr16hm2DBw9WPyNdWV27dlWfr/9sCbRSIwGBHEPu3LlVBqpDhw64cuWK4XXJGCXv6pHun3Hjxhmer1y5UgV2bm5uah8yJcrjx48N3UUjRozIsv2lxFTHLm0fMmSIuuXKlQv58+fHZ599poJcPfl9SrBbokQJ1d6qVauq9hvPiyf7Nv5di5dffhm9e/dO8jlynuQzWrdurbbLzwwbNgwFCxZUI7GlrcYLZMvPyesSTEtAKX+HxudRTzJby5cvh6kx0CGz4e+fvvf56mpjeM3hpm4O0f/JBSTmsTY3o4tXehw5ckRdXKtUqWLYdvvJNwgvLy8175mMkpUMj1zAJOiRC5ZslwBJani2bNmSJHA6evSoerxixQp1UUvN7t27VQZDLygoSF20JXthPDJXTy7kqZEAQgICqRuSbh57e3t07tw53RPUSjarZ8+eePPNN1W3286dO9GlS5ckwUBGZHR/pj72xYsXqwBVgihZpWDGjBn4+eefDa9LkCPBzLx583DmzBm89957avDQv//+q17v3r074uPjsW7dOsPPBAQEYP369eoYjT/H2dkZe/fuVfsSEsCsWrVKvSZ/G5L1kyBIjtn45+S4Dxw4gKlTp2LChAlJ/q6E1HxJ+5MHW1mNM6uR2fD2Tt/73mv2KpzsnUzdHKL/i40AJvlo89kf3wWcn75QpkYuPPItXt8ldf78eXVhkuyEXFjkYiPFxg4ODuqbvnQ1yYVM3lO9enUULVpUZS2MuxhkjUPJBknxaK9evVL97Bs3bsDH5//n6fLlyyoQKF++fIYPWzIgxhYsWIACBQrg7Nmzqk3pCUwkiyXBSLFixdQ24+PKqIzuz9THLrU+33zzjQpqpQZLusXk+YABA1TgMGnSJGzdutVQgyWZPel2/OGHH1QNl/zu5Xcpg4wk6BHSjSS/f8nI6JUpU0YFKsZB2Ny5c7Fo0SK0bdtWbfvpp5/U35X8LY0aNUptk0B77Nixhn1I5lCCtlatWhn2JX8r0h0mdUz6c2oKVhPoSN+wVPrLL0xGEZDlkSHkvoUTVOGxLsVkYwIK+sSi04t5NWgdkWWQQEdqQ2RNQrkwy4WwR48eKliRzIB889Z3QRiTDILckpMAJ71kkWfjSWWfN3uizyR9/vnnKiMQGBhoyGbIDP3pCXSkq6ZFixYqGJHjffHFF9XIsjx5nm9S0bT2J0shDRw40PDef/75RwWPpjx26R407kaUgGb69OkqSyNBllwTjYMKIUGFBLN6EhRJ8Coj8GT9SgleZK484/0aZ+iEdKFJUbos7q0nBe8SREumS884oyi8vb1VxsiYBFtC2mpKVhPoSPW2cb8wWR6ZJ2fW22vRbezLsENCsmAnQQoEMPc7l9RWhSAyHSf3xMyKVp+dwUBHvlW/9dZbcHd3VxeYtOpqspLUcQQHBxueyzd5+WzJKmWU1G/It3zJFsg3f7nYy0VeXxArQVvyQMp4ln7JWEmW4b///sPmzZvx3Xff4ZNPPlHBg2S8ksvM/l566SXUrVvX8F4JGiToM9WxP4t0PwrphipcuHCS14wn/JWgRwI46eKSwE26uORnjKXU7ZYeEvwYk3ORvNtR39Ul2SpTsooaHYl+5Y9Jn0YjCxV8HV3s38HKV/ogX96kEb57/mD8/nsCunTRrHVkyyRQkO4jLW4ZCFKuXr2KkJAQ9U1e6ibkIpldQY7+windK3pSiCrZjzlz5qRYtCttTW0uHhktJkOQJYsi2XrjAEp/cZTuJL1Hjx6pUWXG5Ngl8zB+/Hg1Ek2yLGvWrEnxMzOzPxm9Jedbf5NMhSmPXUiAZUyKmyWwlICsYsWKKqCRDFBpo3bJTbq8jElALJkc6cKS4urkrycnI6X0NTvGAaEUI8vnZoRMXeDr66sCZKsOdGSYo0Sv+v8hZVX05OQPRSriJSUqUbMULxmT/mYpvCILt/FjIC4KXdqFYsuROJQb8S18B32ISp8NxcUrsejejakcovQUIuuHg2c3ubBLVsD4wiz/fkt3inRtSAGrfDGVLo5vv/021Tl8pDtIRgT9+OOPqhtGhmcn71Z74YUX8Ouvv6oCaKlPkeJqucgbBwJSpyIFvXLBl3lzHjx4oAKHlGT1/kx57ELaINslKFq2bJnKMA2X+TkAFXjJdVEKkBcvXqy6myTTJ++R58akTkeK1SV7ZFyEnBrJ8LzzzjsqayjF1hLYSheYdD8ZTyuQHnKuJZNkapp3XUmkK6kzOcFS5JWcVPnLL1OqvSXIkeF/8j+T/HJlpMCff/6phuzJTVKKZKEubQEurAdk5fG20/Ao5iScqv0EGZfwbfNvUThnIa1bSGT29CNgZMixFqR+pUaNGvj9998NNStSBCvtkvICmQVXsiaSPZHaDylqTYl0I8mwYxmiLF02UmwrwYFxkawMmZeMiwy9luOVyf+MMzBSjC1fpOWaIdkZ6QqSGpbUMv9ZvT9THrvo06eP6h6TIEoCMgly3n77bcPr0n75rMmTJ6tMn4zykt/Nxx9/nGQ/cqxS/CxdVjK0PD2mTJmiuqFkGLqM1JPAWiaizEj9k6yTKYkNCZZMTmdGpDlr1qxJsq1OnTq6d9991/A8Pj5e5+Pjo5s8ebJ6Pnr0aJ2vr6+uWLFiunz58uly5sypGz9+fKqfERUVpQsNDTXcbt26pT5XHpNG4mJ0um9r6nRjc+p0Gz9Wm5afW66rtriabsqBKVq3jogy4O+//9ZVqFBB/VtNptG0aVPd8OHDs2x/L7zwgm7o0KG67PT999/rWrVqlal9yHU7PddvzTM6aZHCK0nFSqRtHO1KP+K+ffvUc4lW9d1W0s8ofX5SrZ4aea/0r5IZOfgT8PCSFOIATT9Um3qU74EqBaqgVO5SWreOiDKgffv2qotGRvI8q96DtBUcHKzmA5Lb999/n62fLcXK0pWWHcw60JFhddK/KZNcGZPnz1PJLiRoMu7vlBQk/2fU0ONAYOeUxMctPgdc/59yr5Av9b5vIjJfxjMOk/mqXr26CnZk6gHpIstOUgSdXcw60MkoGf//LFKJbjy8jjS240sgOhQoVBmo/rrWrSEiMnuSgckK169fhy3QfNRVWmTImRRZ3b9/P8l2eS5rZ2SGVMPLUDiZLIk0cu80cGRR4uM2XwH2HFVFREQ2FOjIWH2pTjdezl4qveV5akPz0kvWH5FhccYLkVE2ktrzjaMBXQJQsRNQ/P+zbBIREVlN15XM4ChzBejJcD5ZZE4mW5I1N6SeRuYzkOFrMoxOhvbJkPR+/fpp2m7KpPN/A9d3Aw4uQKuJWreGiIislOaBjky+1Lx5c8NzfaGwBDcyikrWaJFJmWQklSz8JQvTybj75AXKZEHiooHNnyY+bjAUyGO6xdyIiMi22ckYc9ggqdHRz1p58eJFhIaGGlb7JRPb8w2wdRzgUQgYegRw8dC6RUREZGFk1LRMePis67fNBjoZPVGURcLuA9/VAGLCgZfnAdV6at0iIiKy4uu3WRcjkxXaOSkxyPGpAVTpoXVriIjIyjHQoewTcA44+kvi49aTZJprrVtERERWjlcayj5bxiYOJy/fASiWuekBiIiI0sNmAx1OGJjNru0CLm0C7ByAluO0bg0REdkImw10OGFgNkpI+P9w8lr9gPxltG4Rkc366KOPsGDBAsPzN998E2vWrFGPO3TooCZprVSpEpYsWaKWCKhSpQpeeeUVVKhQQU37ERcXl+b+Hz58iIIFCz7X8gLNmjXL1nWysvvzLKUt2eHVV1/F9OnTs+WzbDbQoWx0eiXgfwJw9gSajta6NURWr2nTprCzs1M3WSVaFmxcunSpeq179+74448/1GMJWmSm+bZt26rnv/zyC44cOYIDBw7gyy+/RHR0NE6fPo0PP/wQ586dQ2xsLH777bc0P1t+rlOnTihevHiS7TIP2tChQ1GyZEm13qAsptyxY8ckM99nt9WrV2PiRNNPWGqOx661Tz/9VP2tyIgpU2OgQ6YVGwVsm5D4uNEIwKOA1i0ismoyY8ixY8cwefJk+Pv748KFC2rJHMnGyMzzMsv81atX1arVcqFt2LAhXF1d1c9+8803qFq1Kho0aICbN2/C3t4epUuXVj+j/xa+Z8+eVD87IiIC8+fPR//+/ZNsl+yOZIq2b9+OadOm4dSpU2riV5ksVrLrWpEZ+D09PU36GeZ67M8jJiYGWUWyhqVKlXpm4JwVGOiQaR38AQi9BXj6APUGa90aIqt36dIlhIWFoVGjRmrxY8kijBkzRmVvTp48qd7z8ssvY+3atVi5cqXK8IgdO3Zg7969Kptz4sQJlC9fXmV0JCukp88SpWbDhg0qY1GvXr0k2wcPHqx+7uDBg+jatSvKli0LPz8/NRP+/v37U9yXBANyDLlz50a+fPlUt9qVK1eSvEeyRrIskDGZPX/cuP/XAcoxVq5cGW5ubmo/LVu2VMsIpdRdlNn9pcRUxy5tHzJkiLrJXDKyCPZnn32mAl3jtSEnT56MEiVKqPZKECvt12fvZN/yOzYmfxu9e/dO8hlyjmT/rVu3VtvlZ4YNG6a6KCVIlrYmLwORn5X3SDZQAkr5WzQ+j0KyWsuXL4ep2Wygw2LkbBARBOx60gf7wqeAs7vWLSKyetL1JBdWqa3Ru337trrXL50jwc2yZcuwdetWQ7eVTL4mFz65cMl6gxLs6AOno0ePqscrVqxQF7XU7N69W2UvjAUFBakLt2QvcuTI8dTPyMU8JRI8SDAgywRJ5kmyS507d1YX7/SSjFbPnj1VHZJ0ve3cuRNdunRJEgxkREb3Z+pjX7x4MRwdHVUQNWvWLMyYMQM///yz4XUJcn755RfMmzcPZ86cwXvvvYfXX38d//77r/obkJUB1q1bZ3h/QEAA1q9fr47P+DNkgW0JgmU/QoKXVatWqdfkb0OyfhIEyfEmb58ctwTPU6dOxYQJE7BlyxbD67J+pbQ9ebBldWtdaUX+8OSmn1mRTGDXNCA6FPCqBFR9VevWED03uZBFxkVq8tlujm5pZlGSkwuPfIPXzxR7/vx5dWGSzIRcWIR0RcliytKlpe+2atOmDebOnau+AErGQR+wSBfDV199pbJB8sWwV69eqX72jRs34OPjk2SbfI6cP8kQZYRkP4xJAXWBAgXUIBJpU3oDE8lkSTBSrFjimnqSjXleGd2fqY9dan2ku1H+PqQOS7rF5PmAAQNU8DBp0iQVzMrvWUh2T7oef/jhB1XHJb/LhQsXGrJ60o0ki2lLNkavTJkyKkgxDsLk70TWotQHyT/99JMKYKTbctSoUYb3SrA9duxYw35mz56tArdWrVqpbfK3It1hUsOkP5+mYLOBDplY8HXg4E+Jj1tNAOwdtG4R0XOTIKfu0rqafPaBXgfg7uSeoUBH6kI8PDzURVkugrI4sgQrkhnQkzodY9LlJNkHY7If+TYvmZz0iIyMNAROes+bPZFMkizmLNmAwMBAQzZDaofSG+hIV02LFi1UMCIZhxdffBHdunVDnjx5nqtNae1PRqkNHDjQ8N5//vlHnTtTHrt0ERoHwRLQyEgmydRIkCU1U62eBBV6ElhUr15dPZaASILXO3fuoHDhwip4eeONN5LsM3mGTrrQpChdarv0pOBdgmjJchkzzioKb29vlTXSk+40Ie00JQY6ZBo7JgMJsUDJZkDpFlq3hshmSKAj36rfeustuLu7q4tLRjJCmSF1HFLkbEy+ycvnS2YpI6R+Q77lS7ZAvvnLxV4u8sYFsRK4JQ+k5CKs5+DgoDIN//33HzZv3ozvvvsOn3zyiQogJOuVXGb299JLL6Fu3f8HwxI4SOBnqmN/lvDwcHW/fv161ZbkQa2QgEeCN+nekqBNurfk/cZS6nJLLwmAjMm5MO5+03d1SbbKlBjoUNa7fxY4+eQbYIvEtCWRJZPuI8msaPXZ6SVZmpCQEPUtXuomMkuKc6VOJL3kwpl8FI0Uokr2Q+oipTg1+YVT2pu8VkXm4pHRYnKhb9y4sdqW0mgvuUBKd5KelCLIyLLkF1fJPshNsiQSQMi8QVIDk9X7Sz6CSzIWpjp2IQGWMSlulsBSAjLpgpSA5ubNm6qbKjUSEEsBtmR1pLBausPSIiOl9DU7+u4mCQalGDmj8wDJ1AW+vr4qQDYlBjqU9bZ/IQlroMJLQOEaWreGKNPk4paR7iOtC5H1w8Gzm1zUZYSXZHWMu4fkQi+BgXRvSEGqdGlIt5pkR6TeI3mXh/ysFEb/+OOPKiMlF+vRo5+eg+uFF15Q3S2SAZGAQQIPucgbBwJSEyLZChkhJM8fPHigJj9MSVbvz5THLuQ1CbCky0wyeZJh0k/CJ0HXyJEjVQGyZFGkiFzmrJEAReq3ZLoBIXU68j4JrCSz8ywSrL3zzjsqayhBrNT0SA2PdD8ln1bgWaR4Xc6lqdlsoCN/fHKTvkzKQrcOARfWA3b2iSOtiCjb6EfAaDXAQmpXatSogd9//z1JvYoUwUrbZIK4Dz74QGVNJHsi9R9ysU+pC0mGHUsWRLpspND222+/TVIkKySokoyLDL+WY5bJ/4wzMHJB37Vrl8pYSHZGMhASCOiLaJPL6v2Z8thFnz59VPeYBFESkA0fPhxvv/224XVpf4ECBdToK8n2SfAmv5+PP/7Y8B45Til+li4rGVqeHlOmTFHBkwxDl6kMJLDetGlThmqfoqKi1BQHyevCTMFO97yVYlZCP+pKIl39KAV6TvKntLgjcH03UO114OU5WreIiLKZXDDl2750SxgXP1PWksBHRtIln/fnebRo0UKNtJOAKrtIkCddflLrZOrrt81mdMgEru5IDHIcnIFmXOqByBa1b99ejRqSmo9n1XuQtoKDg9VcQHL7/vvvs/WzpVBZutqyAwMdyrpsjn6ph1r9gdz8B47IVtnS4pSWrHr16irYkakHpIssO0kRdHZhoENZ49w64O4xwCkH0PgDrVtDRGTVJAuTWdefY4V5S8QOVMq8+LgnI61kxqp3uXAnERGZDQY6lHknlwOBFwG3PECDIVq3hoiIyMBmAx0u6plF4qKBnVMSH0uXlSvXDSMiIvPB4eUcXp45h34G1n8AeHoDw6RGJ/2zuBIREZn6+m2zGR3KomzO7hmJjxu9zyCHiIjMDgMden5HfwEe3QE8fYAafbRuDRER0VMY6NDziY0CdieuqYLGks1x1bpFRERET2GgQ8/n6GIgzB/I6ctsDhERmS0GOpRxsZH/r82RbI6ji9YtIiIiShEDHcq4I4uA8HtAriJA9d5at4aIiChVDHQoY2IijLI5HwCOzlq3iIiIKFUMdChjDi8AHgcAuYoC1V7TujVERERpstlAhzMjP4eYx8DemYmPm4xkNofIQo0aNQp+fn748ssvtW4KkclxZmTOjJx+e78FtnwG5C4GDD0CODhp3SIieg4FChTA/fv3YW9vs991yQpwZmTK+pFW/32b+LjJKAY5RBaqc+fOCA4ORo0aNfD999+jVq1ahtdGjhyJRYsWITw8HG3atEHlypXVbdOmTWnu8+HDhyhYsCCuX7+eobY0a9YMI0aMQHbK6s989dVXMX36kznFyCwx0KH0z4L8+EFibU7VV7VuDRGloWnTprCzs1M3JycnlCtXDkuXLlWvrVmzBrlz58bx48fRrl27FH9eApt8+fLh1KlTOHnyJOrXr5/m50kXWKdOnVC8ePEk2+/du4ehQ4eiZMmScHFxQZEiRdCxY0ds27YNWlm9ejUmTpyYZfv79NNP1fFLVoHMEwMdera4GGDvrMTHjYYzm0NkxqQa4dixY5g8eTL8/f1x4cIFFaj07dsX165dS9c+JIuza9cufPjhh9i/f3+a3QIRERGYP38++vfvn2S7ZHdq1qyJ7du3Y9q0aSpo2rhxI5o3b453330XWsmbNy88PT2zbH+VKlVCqVKl8Ntvv2XZPilrMdChZzuxLHFNK49CQLXXtW4NEaXh0qVLCAsLQ6NGjVCoUCGVTRkzZgzi4uJUdsaYo6MjEhISDM+jo6PVfdmyZVXGRwqW33//fcyePTvVz9uwYYPK1tSrVy/J9sGDB6uM0sGDB9G1a1e1T/3+JHhKiQRC0m7JOElGqUOHDrhy5UqS90jWaObMJ4MinqhWrRrGjRunHq9cuVIFam5ubmofLVu2xOPHj1Ptusrs/oRkqZYvX57qOSJtOWr8+WTu4uOAPd8kPm4wlGtakc1mSXSRkZp8tp2bmwoY0uvIkSPq/VWqVDFsu337trr38vJK8l6pq7l7964KjORntmzZorIwsk0yH5IFcnV1VdtTs3v3bvUzxoKCglTQIl06OXLkeOpnJJBJiQQQEghJ26VO6PPPP1c1RRJ0padwWjJYPXv2xNSpU9XPyXFJ+553zE1691enTh11rBIoStBH5oWBDqXtzBog+Brglheo1U/r1hBpQoKcCzWSXsyzS7mjR2Dn7p7u9x89ehQlSpQwdDedP39edUFJlkIuyMacnZ3Va9WrV0fRokVV5kJIN5MUJjs4OKhMhnRNpebGjRvw8fFJsu3y5csqGChfvnyGjlUyP8YWLFigRoidPXtWdRGlJzCRzFWXLl1QrFgxtU1/TM8jvfuT44+JiVE1Sfr3kflgoEOpk5S2foXyeoMB56e/mRGReZFAR+pjPDw81EVaMjU9evTAV199ZciKBAYGGt4vGRS5Jde6det0fV5kZKTK+hh73gyKdLtJFufAgQOqjfputZs3b6Yr0KlatSpatGihghFp/4svvohu3bohT548z9We9O5PgkF9vRKZHwY6lLoL64EH5wCXnECdAVq3hkgz0n0kmRWtPjujgY5MCPjWW2/B3d0d3t7eGer6yqj8+fOr4erGypQpoz5TskkZIbUukhH56aefVJZEAh0JcCRboifBWvJAKjY2Vt1LBkq62f777z9s3rwZ3333HT755BMVOEmWKyVZsT/pqhOSfSLzw2JkSpn8j7/r68THEuS4pdynTmQL5KJt7+6uyS0jQcrVq1cREhKCVq1aoXTp0ipYMGWQI6TbS7qWjEl9j2RAZAb65IW7QtqY0lw8MkJMhmtLFqVChQpPBVD6YEK6lIwnjTMeTSbH27BhQ4wfP16NPpPuORlSn5qs2N/p06fh6+urgj4yPwx0KGVXtgH+xwEn98RuKyIye/pCZONJAE1NApozZ848FZRIkBMfH6/qglatWqW6pc6dO4dvv/02xXl5pDtIRjX9+OOPqsZHhqWn1KX2wgsv4Ndff1VFwVJLJAXTknkRkmmZNGkSDh8+rLq7ZM6cBw8eqKApNVmxP/lZ6dYi88SuK0rZrie1OTX7ATn4LYXIEki3lWRyZFr87CL1KzLL8u+//46BAwcatsuwdmmPjEb64IMPVNZEsicyQmvu3LkpdiHJEO1hw4ap7iqZ5FCCIhkObkyGykvGRYaey3HK5H/6DIwUYMv8PzJcXDIz0g0msxa3bds21fZndn9RUVFYu3atGmVG5slm17qSbxv6bxwXL17kWlfGru8FFrUDHJyB4SeBnN5at4iIzNj69etVXZB04dja+lkStElXltTwUPbiWlfPIDNzSr/yoUOHtG6K+dHPm1PtNQY5RPRM7du3x9tvv407d+7A1sgSG1KkTObLZjM6ely9PJl7p4F5DQE7+8QVyvOW1LpFRERET2FGh57Pf0++mVTsxCCHiIgsHgMd+r+QW8DplYmPGwzTujVERESZxkCH/m//XCAhDijRBChcQ+vWEBERZRoDHUoUGQwcWZT4uOFwrVtDRESUJRjoUKJD84HYx4BXJaBUC61bQ0RElCUY6BAQGwUcmPf/2hwTTxlPRESUXRjoEHBiGfD4AZDTF6jURevWEBERZRkGOrYuIf7/Q8rrvws4OGndIiIioizDQMfWnV8PBF0BXHMDNfpo3Roiyibjxo1DtWrVMvQzsu7UiBEjoLU33ngDL7/8stbNIAvBQMfW/fdt4n3ttwAXD61bQ2RV4uOBnTuBZcsS7+W5KWUkEBk5ciS2bdsGSzRr1iwsWvRklGg6yarusvgm2R6uXm7Lbh0Ebh9KXLyzzttat4bIqqxeDQwfDty+/f9tvr5ykQa6aFgKJ6v+yGLGHh4e6maJsnN1drJ8zOjYsn1zEu8rvwJ4emndGiKrCnK6dUsa5AhZ81K2y+um6M75999/VbZDshdyu379Onbu3Kke//PPP6hZsyZcXFywZ8+ep7qu9N1B48ePR4ECBdTaQYMGDUJMTEyqnxkdHa0yQ4ULF0aOHDlQt25d9XlpkbbIit9t27aFm5sbSpYsiZUrn8zI/sSpU6fwwgsvqNfz5cunFgwNDw9/qq3Gmaxhw4bhww8/RN68eVGoUCF1fHrFixdX9507d1afr39OtoGBjq0KuQmcW5f4uN4grVtDZDWke0oyOSktl6zfJr1LWd2NJQFO/fr1MWDAAPj7+6tbkSJFDK+PHj0aU6ZMwblz51ClSpUU9yFdWfK6BCvLli3D6tWrVeCTmiFDhmDfvn1Yvnw5Tp48ie7du6NNmza4dOlSmm397LPP0LVrV5w4cQKvvfYaXn31VfW54vHjx2jdujXy5MmDQ4cO4Y8//sDWrVvVZ6Vl8eLFKtg6cOAApk6digkTJmDLli3qNdmPWLhwoTov+udkGxjo2KoDPwC6hMTlHgpV1ro1RFZj9+6nMznJg51btxLfl9XdOc7OznB3d1cZDbk5ODgYXpcLf6tWrVCqVCmV9UiJ/PyCBQvg5+eH9u3bq5/59ttvkZCQ8NR7b968qQIHCUQaN26s9ivZnUaNGqntaZGA6K233kLZsmUxceJE1KpVC999lzj6c+nSpYiKisIvv/yCSpUqqczO7Nmz8euvv+L+/fup7lOCt7Fjx6JMmTLo06eP2qe+BkkyVCJ37tzqvOifk22w+BqdkJAQtGzZEnFxceo2fPhw9Y2G0hAdBhz9JfFxvXe1bg2RVfH3z9r3ZRW58D9L1apVVaCkJxki6TK6desWihUr9lT3ktT6SLCSvDtLupvSIvtN/vz48ePqsWR2pB2SndFr2LChCrYuXLgAL6+Uu9mTZ6m8vb0REBDwzGMm62fxgY6npyd27dql/ueUlKd8A+jSpcsz/0ezaceWANGPgHylgTIvat0aIqvi7Z2178sqxoFDVpAASDJGR44cSZI5EloUOTs5JZ0DTGpxUspEke2x+K4r+R9M/w1EvknIiAK5URoTBB6Ym/i47iDA3uL/BIjMSuPGiaOrUltJRbZL6Yy8L6tJ15NkWZ6X1MxERkYanu/fv18FLca1PnrVq1dXnyVZk9KlSye5SfdQWmS/yZ9XqFBBPZZ7aYd8cdXbu3cv7O3tUa5cuUwFQpk5N2S5NL/KSTamY8eO8PHxSXWegzlz5qgqeVdXV1XVf/Dgwae6ryTV6evri1GjRiF//vzZeAQW5sI/QPD1xAkCq/XSujVEVkeSGzKEXCQPdvTPZ85MfF9Wk38npRhXRlsFBgZmOKMhI6z69++Ps2fPYsOGDarmRYqAJchITrqspJBY6mGkaPnatWvq3+bJkydj/fr1aX6O1PVILdDFixfVZ8jP6YuNZZ/yb33fvn1x+vRp7NixA0OHDkXv3r1T7bZK77mRmp179+4hODj4ufdDlkfzQEeidglSJJhJyYoVK/D++++r/xmOHj2q3isV+cZ9r1JgJt8A5H80KWRLq2DN5u1/ks2p+QbgnLWpbCJKJPPkyIjpwoWTbpdMj2w31Tw6UgwsWe6KFSuqglspGM6IFi1aqGLeJk2aoEePHnjppZeSDNNOToqOJdD54IMPVLZFhnzLiKaiRYum+TkykktGakldjRQdywgvabOQDP2mTZsQFBSE2rVro1u3bqpdUpCcGdOnT1ejsCQ7Jdkosh12OjPq55GMzpo1a5LMjyAZHPlj1/+RyzcU+UOVCF+GSyY3ePBgVaUv/3OkRLq35Kb36NEjtb/Q0FA1b4RV8z8B/NAEsHcEhp8EciX7V5iIspT0lMjoKik8lpoc6a4yRSYnK8jcNJIdN/XswSn9O0/0POT6LaMNn3X91jyj86w0qhS6yagqPUmhynOZu0FI9iYsLEw9loOVrrC0+nElrSonRn9Lqe/Zau37PvG+4ssMcoiygQQ1zZoBPXsm3ptrkENkzcw60JE+ZikeS94vK8+ln1XcuHFDzeEgXVpyL5meypVTnxdmzJgxKiDS32TYpE0Iuw+cXpX4uP5grVtDRESULSx+eHmdOnUM8y+kh0x/Ljebc2QRkBAL+NYBCtfUujVEZGYyukjm8zKjagmyEWad0ZHRU1JYl7y4WJ4/a/giGYmPBQ4vSHxcd6DWrSEiIso2Zh3oyJwQsgidfhpvfTGyPE8+s2ZGySgvqfKXQmerd+4vIPwekKMgUOElrVtDRERkO11XMrvm5cuXDc9liLh0RclaLDJEUYaWy3wKMn25dFPNnDlTDUnv169fpj733XffVTd91bZVO/hT4n2tfoCjs9atISIisp1A5/Dhw2jevLnhuQQ2QoIb6TOWuRwePHiAzz//XBUgV6tWDRs3bszUxFE25d4p4OZ/iUPKa2YuOCQiIrI0ZjWPjjmPw7dY64YBRxcDfp2B7tlTbEhERGRqVjGPjinZRI1OZDBw8vfEx3Xe1ro1RERE2c5mAx2pz5H1XGS6cqtepTwuEvCqDBTNXPE2ET3n1Mg7dwLLliXem+GiklIiIMvoPEtqaxFmZu0pqbk0pZ07d6p2y4zPZLtsNtCxerKY36EnRch1BqS+lDIRmcbq1XI1B6QGsVevxHt5LtvNiNRByuKaerK2ldRCJufv74+2bdvCkjRo0EC1OyMDTmQpDC5PYV0Y6Firy1ufrFKeC6jcXevWENkWCWZkvb3bt5Nuv3MncbuZBDuxsbFwc3NDwYIFn/lembvM0iZblSlKpN2S1SHbZbOBjtXX6Bz8MfG+em/A2V3r1hDZDumeGj5cpgB++jX9thEjTNKNJfOMTZ06FaVLl1ZBiUzR8eWXX6rXrl+/ri74K1asQNOmTeHq6oolS5Yk6bqSx7Ky+IkTJ9R75aafMTl519Xt27fRs2dPNRVIjhw51BQgBw4cUK9duXIFnTp1UqNjPTw81L+zW7duzdCx6DMr0h5ZiV2KTQcNGqTWQNSTBZqHDRumAjU5nkaNGiUpR0jedaU/VlkdvUKFCqptbdq0UVkffTZr8eLF+PPPPw3HL/sgy6b58HKtWPU8Og+vAJe3yD9NQO3+WreGyLbIcuXJMznJgx1ZY0/eJyt9ZiFZy++nn37CN998oy76cgE/f/58kveMHj0a06dPR/Xq1VVwIBd9426s06dPqyk89IFJSv8+yvxnEiwVLlwY69atU1mTo0ePqkBL/3q7du1UkCUB1y+//IKOHTviwoULKvhKL5kcVtoowYYEajJ/Wr58+QzB24cffohVq1ap4KRYsWIqyGvdurWam00CsJRERETg66+/xq+//qoWiX799dcxcuRIFfTJ/blz59R1YeHCher9qe2HLIfNBjpWTb/cQ5lWQN6SWreGyLY8yQ5k2fvSKSwsDLNmzcLs2bPVPGSiVKlSKuAxNmLECHTp0iXFfUg3lmQ5HB0d01xmZ+nSpWp+M8me6AMBySLpySLLctObOHEi1qxZo4KiIUOGZKjracGCBXB3d4efnx8mTJiAUaNGqf1FRkZi7ty5Kkujrx2SIG/Lli2YP3++el9q3XXz5s1T50ZIe2S/Qo5dzoFkirjMkPVgoGNtYqOA40sTH9d6U+vWENkeb++sfV86SSZCLtAtWrRI833SxZRZMnu9ZIRSy3ZIRke6gdavX6+ySnFxcSowuXnzZoY+R4IlCXL0ZOkf2fetW7fU3CkStDRs2NDwupOTk5pBX85FamR/+iBHeHt7IyAgIEPtIsvCQMca17WKDAJy+gJlXtS6NUS2p3FjwNc3sfA4pTodKYyV1+V9WUgyEekh9TSm/izpApLMinQRSaZH3t+tW7ck9TVakWDImNTh2Pi8uVaPxcjWVox8JLFfGTX6APYOWreGyPY4OACzZiU+Tj7aR/9c5o+R92WhMmXKqIDCeBHk5yHdRfHPKJSuUqWKyuoEBQWl+PrevXtVMXHnzp1RuXJl1Q0kNTYZJUXRkgnS279/v+peKlKkiMrKSFvls/QkwyPdafJvuymPnyyLzQY6VjlhYMB54MZewM4BqNFb69YQ2S6pgVm5EihcOOl2yeTI9lRqZDJDinY/+ugjVaArxb8y8kkCA6lXyehEfvrFlQMDA1V3WHIy2kqCFxkVJYHG1atXVVHwvn37DEHX6tWr1T4kWOnVq5ehUDkjJAPUv39/9W/1hg0bMHbsWFVTI0XEkpl65513VC2OFE/LewYMGKCKjeVnnpcc/8mTJ1XhtBy/BE9k2dh1ZU2OPFnLqmwbIKeP1q0hsm0SzHTqlDi6SgqPpSZHuquyOJNj7LPPPlOFxLII8t27d1X9iQzJzoiuXbuqIEUWW5Zh2TL6SLIzybMemzdvxgcffKBGV0kNjmRRJFMuZsyYgTfffFNN2Jc/f34VgMlIpoySeiMJmpo0aaICLgmwpPZHb8qUKSqA6t27tyrGlvojGUWWJ08ePC8JlmSUl+xL6oF27NiBZlk8Oo6yFxf1tJZFPWMjgenlgKhQ4LVVQJmWWreIiOi5SXAlgVZWLjtB1oWLetqaM2sTg5zcRYFSL2jdGiIiIrPAQMfa5s6p0Rew56+ViIjIpmt0pC9ZblZRXX//DHD7IGDvmLjkAxGRhdMvPUGUWTb71d+qRl0dfjKkvHx7wNNL69YQERGZDZsNdKxGzGPg5IrExzX7ad0aIiIis8JAx9KdXgVEPwLylABKNNW6NURERGaFgY6lO/pL4n3NN1iETERElAyvjJY+E/LtQ4kzIVfrpXVriIiIzA4DHUt27Nf/z4TsUVDr1hARPdeSCzNl7S8NJiSUJSzSIjMky6KfMnGhJZC2coLFpzHQsVRxMcCJ5YmPua4VkVmK1+mwMzgYy+7fV/fynMyTLPMwYsSIJNtkCQt/f381+64lkLa2bds2Q0P4c+fODWvHeXQsdR6dS5uAiEDAwwso3Urr1hBRMqsfPMDwy5dx22hRTF8XF8wqXRpdChSApZCFNWVtK1skxy2Ll1oKS2prdrLZjI7Fz6Nz9Em3VdWegIPNxqtEZhvkdDtzJkmQI+5ER6vt8rqpshLDhg1TK5jnzZtXXfiMF8EUN2/eRKdOneDh4aHWB3rllVdw//59w+vy/mrVquHnn39GiRIl1Kro+m6RH374AR06dIC7uzsqVKigViu/fPmy+lxZTVwyILJqup48ls/y8vJSn1e7dm1s3br1ubqYJk2apPYjGYgJEyaohURl5XI5Tl9fX7X4qLFbt26pY5P3y3ukHdevX0/1M/7991/MmjVLHafc5L3Ju670GRBZOFSOX46pTZs2KpOiJ+2S34G8L1++fGpB0759+6bZTabfr3Q7ySKmcs5bt26tjsHY3LlzUapUKRWAlStXDr/++uQ6kELXlbRfnq9+skCr/M6qVq1qWGFejq1fv35qnSj9MSf/W7EWNhvoWLRHd4HLWxIfcyZkIrMi3VOSyUmpk0q/bcTlyybrxlq8eLEKOg4cOICpU6eqoGDLlsR/L2Slb7ngBwUFqQu7bL969Sp69OiRZB8SvKxatUpdJI8fP27YPnHiRPTp00dtK1++PHr16oWBAwdizJgxOHz4MGSN6CFDhhjeL6t/y+rm27Ztw7Fjx1RQ0LFjRxVsZcT27dvVauy7du1SK6OPHTtWBVyySrkcp6zQLu24ffu2en9sbKwKFDw9PbF7927s3bvXEJRIhio5CXDq16+vVi6XoEVuRYoUSbEtERER+Prrr1WQIe2RYxk5cqTh9a+++gpLlixRgZd8riw8mZ66Gdnvl19+iV9++UX9nARXr776quH1NWvWYPjw4WrF+NOnT6vjlUBFVldPyyeffKLaJ7+zsmXLqhXgJRiToFRqoyTY1R+z8XFYFZ2NCw0NlX9t1L3F2PW1Tjc2p043v7XWLSGiZHYEBemwY8czb/K+rNa0aVNdo0aNkmyrXbu27qOPPlKPN2/erHNwcNDdvHnT8PqZM2fUv4EHDx5Uz8eOHatzcnLSBQQEJNmPvOfTTz81PN+3b5/aNn/+fMO2ZcuW6VxdXdNso5+fn+67774zPC9WrJjum2++SfX9ffv2Ve+Jj483bCtXrpyucePGhudxcXG6HDlyqM8Xv/76q3pPQkKC4T3R0dE6Nzc33aZNmwz77dSpU5JzN3z48CSfvUN+V4AuODhYPV+4cKF6fvnyZcN75syZo/Py8jI8l8fTpk1L0raiRYsm+azk9Pvdv3+/Ydu5c+fUtgMHDqjnDRo00A0YMCDJz3Xv3l3Xrl07w3N5/5o1a9Tja9euqec///zzU79r2bf+c3PlyqWz9us3MzqWRv6Wj/2W+JjZHCKz459CxiAz78uoKlWqJHnu7e2NgIAA9fjcuXMqU2GcrahYsaLqNpHX9IoVK4YCKdQRGe9bupFE5cqVk2yLiopSWQx9RkeyBNLNI58hWRX5nIxmdPz8/GBvNE+YfI7x5zo4OKhuIv1xnjhxQmWlJKMjnyk36b6Sthl3rT0P6QKS7qOUzq90A0k3YJ06dZK0rWbNms/cr6Ojo+ra05OMmfHvRe4bNmyY5GfkufHvLSVVjH5n0lahb6+tYHGHpbnxHxB0FXD2APzSHhpJRNnPO52Fu+l9X0Y5OTkleS61F9JllRHS9fWsfct+U9um/zwJcqR7TLp6SpcuDTc3N3Tr1i3F7qOMHlNaxykBlgQX0oWUXEoBXGbbkphMMU9Oafx+bAUzOpY6d06lLoBzyv8YEZF2GufOrUZXJV5Snibbi7i4qPdlN8msSIGrcZGrDMqQehDJ7GQ1qTWRQt/OnTurDIwUR6dWEJyVatSogUuXLqFgwYIqwDK+pTZUXAp8MzsKV/Yt2SbjQS6yz6NHjz7zZ6VuRuqc9C5cuKB+L/I7E3Iv59OYPM/M7805C47ZEjDQsSRRocCZJ0Vt1fto3RoiSoGDnZ0aQi6SBzv65zNLl1bvy24tW7ZUAcdrr72mLr4HDx5UxcVNmzZFrVq1svzzZASRvqBZupOkeDk7sglyfPnz51eF11KMfO3aNTXKSEZD6QuWU5q4UAqbJRALDAx87nYOHToUkydPxp9//qmCFSkgDg4ONmRT0sq8yM9KG44cOaICxHr16hm6wWSEmYzOkpFXEsRJUbac28wUEBcvXlxlv6RYXI5ZCqKtEQMdS3J6NRAXCeQvB/hm/T9KRJQ1ZJ6clX5+KOzikmS7ZHpku1bz6MjFVi7AMlqpSZMmKvApWbIkVqxYYZLPk4uxfJaM8JHRVjISSrItpiZ1NDIiqmjRoujSpYvKhvTv31/V6Mgoo5RIwCD1NJIhke6tjNYR6clwchnZJAGkjOSS+iA5bv0w/bTaLD8rwaDU3sjPGf9eZHi6jA6TbkCpWZKh/jKyS4b2P68GDRqoEWsy6k6OWUbpWSM7qUiGjU8YePHiRVVEltr/AGbjpxbAncPAi18ADYZq3RoiegYZQr47JEQVHktNjnRXaZHJIe1IZkgCLZnTR4bnp0QyNTIrs6UsNWEupOhdugufdf12tOUJA+WmP1FmL/BSYpAjC3hWSTrnBRGZJwlqmuXJo3UzKBvduHEDmzdvVt2B0dHRmD17tuo6k0wNaYNdV5bixLLE+9ItuYAnEZGZkmHwkqGRoeLSBXXq1Ck1G7S+qJiyn812XWU09aUpKYqbWRl4dBvotjBxxBUREZENe5TO6zczOpbgxp7EIMclF1CundatISIishgMdCzBieWJ95U6A05pV+4TERHR/zHQMXcxj4Gzf/5/pXIiIiJKNwY65u78eiAmHMhTHChSV+vWEBERWRQGOpYy2kqyOZx/g4iIKEMY6JizR3eBqzsTH3PuHCIiogxjoGPOTv0B6BKAovWBvCW0bg0RUZaT9ZZmzpyZ6uuy5pMsf5AZss6VLH+hn3lY5rnJbbSo6rhx41CtWjVYguTHQs/GQMdcyfRGx/XdVq9q3Roieg66eB2Cdwbj/rL76l6eU/aTNZ38/f1TnQVf1rmShS2t4VhMFSxaMptdAsLs3TsJPDgHOLgAFW33D5TIUj1Y/QCXh19G9O1owzYXXxeUnlUaBbpos6jn84iJiYGzszMsmbS/UKFCqb4uC2jKzRqOhZ7GjI65z51Tvh3g9v8UKxFZRpBzptuZJEGOiL4TrbbL66YgK1kPGzYMH374IfLmzasuiNItY0xW5e7UqZO6sMtssrLY5P3795/qxvn5559RokQJw6rb0l0iK2Z36NBBrbQtSxrs27cPly9fVp+bI0cOlW24cuWKYV/yWD7Ly8tLfZ4siyDLITyP8ePHqxW2pc2y4rYEYHqyppQcd8GCBVV7GzVqhEOHDqW7uyd515U+AyIrhXt7eyNfvnxqbcTY2FjDeySr0r59e7i5uanztHTp0nR3w2Xlsei74TZt2qR+J3Ke27Rpo9qnP7bFixerVevl5+Qm+7AlNhvoyMrlFStWVP/jmZ342MT6HMG5c4gsinRPSSYHKfVSPdl2ecRlk3VjyUVNgo4DBw5g6tSpmDBhArZs2WJYSVsCj6CgIPz7779q+9WrV9GjR9LBDhK8rFq1CqtXr8bx48cN22X17T59+qht5cuXVwtVDhw4EGPGjMHhw4chKwoNGTLE8P7w8HC0a9dOdQsdO3ZMXYA7duyogq2MkJ8/d+6cukAvW7ZMtUuCBT0J7KS9cuxHjx5F6dKl0bp1a3Wcz2vHjh0qUJN72a8EFHLTk/Nw9+5d1Sb57B9//BEBAQGaHEtERIQKyn799Vfs2rVLnV/pjhMjR45Uwaw++JGbBKQ2RWfjQkND5V8bdW82Lm7R6cbm1Om+KqnTxcVo3RoiyoCgHUG6HdjxzJu8L6s1bdpU16hRoyTbateurfvoo4/U482bN+scHBx0N2/eNLx+5swZ9W/gwYMH1fOxY8fqnJycdAEBAUn2I+/59NNPDc/37dunts2fP9+wbdmyZTpXV9c02+jn56f77rvvDM+LFSum++abb1J9f9++fXV58+bVPX782LBt7ty5Og8PD118fLwuPDxctXfJkiWG12NiYnQ+Pj66qVOnquc7duxQbQ0ODlbPFy5cqMuVK5fh/XLMVatWTfKZ0q64uDjDtu7du+t69OihHp87d07t79ChQ4bXL126pLZpcSzy/PLly4afmTNnjs7LyyvJ53bq1Elnq9dvm83omDV9NsevM+DgpHVriCgDYvxjsvR9GVWlSpUkz6XrRZ9pkExCkSJF1E1PMtvS9SGv6RUrVkx1raS1b+mOEpUrV06yLSoqSi22qM/oSEZBulTkM6RbRT4noxmdqlWrqu4yvfr166t937p1S2VdpEtJVgrXc3JyQp06dZIcU0b5+fnBwcEhxfN44cIFODo6okaNGobXJfOSJ08eTY5F9leqVKkU20osRjY/sZHA+b8TH1furnVriCiDnL2ds/R9GSUXRmNSkyFdVhkhXV/P2rfsN7Vt+s+TIEe6x6RbRQIBqWfp1q1bkpoUc5UV51HLtiYm4Ugwo2NuLm5MXPIhV1GgSB2tW0NEGZS7cW41ugqpTWRuB7gUcVHvy26SWZHMgdz0zp49qwpbJbOT1fbu3asKcDt37qwyP1Icff369Qzv58SJE4iMjDQ8379/v8oOSWZKMhkyEkk+S0+yIlLAa4pjEuXKlUNcXJyqOzKuawoODjbLY3F2dkZ8fDxsFQMdc3NqZeJ95a5c8oHIAtk52Kkh5IlPkr+YeFd6Zmn1vuzWsmVLFXC89tprqtD14MGDqqi2adOmqFWrVpZ/XpkyZQwFzXKBl+Ll58mKSAaof//+KijbsGEDxo4dq4qe7e3tVfbpnXfewahRo7Bx40b1ngEDBqgCXfkZU5BCbDmXb7/9tjqHEvDIY8lY6bNa5nQsxYsXx8mTJ1WXW2BgYJLRY7aAgY45iQwBLm1OfFypm9atIaLnJPPk+K30g0thlyTbJdMj27WaR0cuwjLMWGpJmjRpoi7WJUuWxIoVK0zyeTNmzFCfJaN8ZLSVjB4yrmtJrxYtWqigSdosI8ReeumlJMPmp0yZgq5du6J3795q/5JdkeHW6amZeV6//PKLqkmSNknGSgIST09Pw3B8czqWAQMGqCyUBLNSe2WcMbIFdlKRDBsmRXMyw2RoaKia00BTR38F1g0BClQABu9jRofIwskQ8pDdIarwWGpypLtKi0wOmd7t27dV95PMEyTBTEqkG0+6CdeuXZvt7bPl6zeLkc3JaX23VTcGOURWQIKaPM1Ml1Ug7Wzfvl2NlpKuQJmbRua/kS4iydSQeWGgYy7C7gHXdiU+rtRV69YQEVEapM7l448/VhMuSpeVdM8tWbLkqRFQpD12XZlL19X+ucDG0YBvbeCt55sinYiIyFY8Suf1m8XI5jbaikXIREREWYaBjjkIugrcOQzY2SfOhkxERERZgoGOOTi9KvG+RBPAM3FadSIiIso8BjpakxKpk0/WtuKSD0RERFmKgY7W7p8GAi8ADi5AhY5at4aIiMiqMNDR2pk1ifdlWgGuubRuDRERkVWx+EBHFqdr1qyZWvCsSpUq+OOPJ91AltJtdebJDJksQiYiIspyFj9hoKOjI2bOnIlq1arh3r17qFmzJtq1a6cWRzN7904BQVcSu63Ktta6NURERFbH4gMdb29vdROFChVC/vz5ERQUZBmBztm1/++2cvHUujVERERWR/Ouq127dqlVbX18fNTKuiktdjZnzhy1hoisClu3bl0cPHgwxX0dOXIE8fHxamE1s8duKyIiIusPdB4/foyqVauqYCYlK1aswPvvv4+xY8fi6NGj6r2tW7dGQEBAkvdJFqdPnz748ccfYTGjrdhtRUREZN1dV23btlW31MyYMQMDBgxAv3791PN58+Zh/fr1WLBgAUaPHq22RUdH4+WXX1bPZWG1tMh75aYna2To18zIVgeXA9E6oEyzxPvobP58IiIiC6a/bj9ryU7NA520xMTEqO6oMWPGGLbZ29ujZcuW2Ldvn+EA33jjDbzwwgvo3bv3M/c5efJkjB8//qnt2nV3/QH0t6CRYkRERGYkLCxMLe5pkYFOYGCgqrnx8kq6LII8P3/+vHq8d+9e1b0lQ8v19T2//vorKleunOI+JWiSrjC9kJAQFCtWDDdv3kzzRFHmom4JJGUqAE1XiLdiPMemx3NsejzHpvfIis6xJDokyJEa37SYdaCTHo0aNUJCQkK63+/i4qJuyUmQY+m/dHMn55fn2LR4jk2P59j0eI5NL6eVnOP0JCg0L0ZOiwwVd3BwwP3795Nsl+cylJyIiIjIYgMdZ2dnNQHgtm3bDNskeyPP69evr2nbiIiIyPxp3nUVHh6Oy5cvG55fu3YNx48fR968eVG0aFFVT9O3b1/UqlULderUUbMgy5B0/SiszJJuLBm6nlJ3FmUNnmPT4zk2PZ5j0+M5Nj0XGzzHdrpnjcsysZ07d6J58+ZPbZfgZtGiRerx7NmzMW3aNLXEgyz18O2336qJA4mIiIjMOtAhIiIisskaHSIiIqLMYKBDREREVouBDhEREVktmwx0pkyZolZKHzFihGFbVFQU3n33XeTLlw8eHh7o2rXrU/P3UNru3LmD119/XZ1DNzc3NTv14cOHDa9LOdjnn38Ob29v9bos5XHp0iVN22xJZJbwzz77DCVKlFDnr1SpUpg4cWKSdV54jjNm165d6Nixo5pZVf5N0M+unpHzKQsKv/baa2rytdy5c6N///5qNCk9+xzHxsbio48+Uv9W5MiRQ71HFme+e/dukn3wHGfu79jYoEGD1HtkBLOtnGObC3QOHTqEH374QS0ZYey9997DX3/9hT/++AP//vuv+h+tS5cumrXT0gQHB6Nhw4ZwcnLCP//8g7Nnz2L69OnIkyeP4T1Tp05VI+ZkYdYDBw6of9hkJXoJMunZvvrqK8ydO1eNQjx37px6Luf0u+++M7yH5zhjZKqKqlWrYs6cOSm+np7zKReHM2fOYMuWLfj777/VReftt9/OxqOw3HMcERGBo0ePqgBe7levXo0LFy7gpZdeSvI+nuPM/R3rrVmzBvv3709xyQSrPsc6GxIWFqYrU6aMbsuWLbqmTZvqhg8frraHhITonJycdH/88YfhvefOnZOvybp9+/Zp2GLL8dFHH+kaNWqU6usJCQm6QoUK6aZNm2bYJufdxcVFt2zZsmxqpWVr37697s0330yyrUuXLrrXXntNPeY5zhz5/33NmjWG5+k5n2fPnlU/d+jQIcN7/vnnH52dnZ3uzp072XwElneOU3Lw4EH1vhs3bqjnPMdZc45v376tK1y4sO706dO6YsWK6b755hvDa9Z+jm0qoyNdU+3bt1fpZ2OyQrqkUI23ly9fXk1YqF8lndK2bt06Nalj9+7dUbBgQVSvXh0//fRTkokgZR4k43Msa5TIfEg8x+nToEEDNSv4xYsX1fMTJ05gz549aNu2rXrOc5y10nM+5V7S/PK3ryfvt7e3VxkgyrjQ0FDVtSLnVfAcZ15CQgJ69+6NUaNGwc/P76nXrf0caz4zcnZZvny5So1K11Vy8o+ZLDeh/x/LeJV0eY2e7erVq6pbRWay/vjjj9V5HjZsmDqvMvmj/jymtBI9z3H6jB49Wq08LEG4rAEnNTtffvmlSjkLnuOslZ7zKfcS2BtzdHRUM7vznGecdAlKzU7Pnj0NC07yHGfeV199pc6Z/JucEms/xzYR6Mhy9MOHD1d9j66urlo3x2q/Mci3gUmTJqnnktE5ffq0qm2QQIcy7/fff8eSJUuwdOlS9a1MlkqRgnrpb+c5JksnWfVXXnlFFYDLlybKGkeOHMGsWbPUF33JlNkie1v5RQcEBKBGjRoqSpWbFBxLkaE8lm9oMTExCAkJSfJzXCU9/WRUSsWKFZNsq1ChAm7evKke688jV6J/fpJ2lqzOq6++qkapSCpaiugnT56sXuc5zlrpOZ9yL/+2GIuLi1MjWHjOMx7k3LhxQ30h1WdzBM9x5uzevVudPynF0F//5Dx/8MEHKF68uE2cY5sIdFq0aIFTp06pb8D6m2QfJOWvfyyjhYxXSZfKf7lIc5X09JERV3LOjEktSbFixdRjGRIt/8MYn2PphpH+X57j9JERKtJnbky6sCSbJniOs1Z6zqfcyxck+TKlt337dvU74Xp8GQtyZNj+1q1b1fQUxniOM6d37944efJkkuufZIHli9OmTZts4xzrbJTxqCsxaNAgXdGiRXXbt2/XHT58WFe/fn11o/SRkRKOjo66L7/8Unfp0iXdkiVLdO7u7rrffvvN8J4pU6bocufOrfvzzz91J0+e1HXq1ElXokQJXWRkpKZttxR9+/ZVoyb+/vtv3bVr13SrV6/W5c+fX/fhhx8a3sNznPGRmMeOHVM3+edwxowZ6rF+xE96zmebNm101atX1x04cEC3Z88eNbKzZ8+eGh6V5ZzjmJgY3UsvvaTz9fXVHT9+XOfv72+4RUdHG/bBc5y5v+Pkko+6svZzzEDnCfmHa/Dgwbo8efKoC3Tnzp3V/2yUfn/99ZeuUqVKavht+fLldT/++GOS12W47meffabz8vJS72nRooXuwoULmrXX0jx69Ej9zUpA7urqqitZsqTuk08+SXJB4DnOmB07dqgLQ/KbBJXpPZ8PHz5UFwQPDw9dzpw5df369VMXHnr2OZaAPaXX5CY/p8dznLm/4/QEOtZ8jrl6OREREVktm6jRISIiItvEQIeIiIisFgMdIiIisloMdIiIiMhqMdAhIiIiq8VAh4iIiKwWAx0iIiKyWgx0iIiIyGox0CEiqyRrr8laVWFhYen+mY0bN6JatWqG9cOIyPIx0CEis2VnZ5fmbdy4can+7JgxYzB06FB4enqq5zt37lQ/I4sX6t29e1etBN+kSROEhoaiTZs2aoHfJUuWZMvxEZHpMdAhIrPl7+9vuM2cORM5c+ZMsm3kyJEp/tzNmzfx999/44033kh131euXEGjRo1QrFgxtYpzrly51Hb5mW+//dZkx0RE2YuBDhGZLel60t8kEJGMjPE2Dw+PFH/u999/R9WqVVG4cOEUXz958qQKcurXr4+1a9fCzc3N8FrHjh1x+PBhFQgRkeVjoENEVmf37t2oVatWiq/9999/aNq0Kbp27YrffvsNjo6OSV4vWrQovLy81D6IyPIx0CEiq3Pjxg34+Pik+Frnzp1V1mb27NkqQ5QS+VnZBxFZPgY6RGR1IiMj4erqmuJrnTp1wpo1a9LM2EhXVkREhAlbSETZhYEOEVmd/PnzIzg4OMXXfvjhB7z66qto27Ytdu3aleJ7goKCUKBAARO3koiyQ9LOaSIiK1C9enWcPXs2xdeku+rHH3+Evb092rVrh/Xr16uaHb2oqChViCz7ICLLx4wOEVmd1q1bY9++fYiPj0812Jk3bx769Omjgh2ZY0dv//79cHFxUSOyiMjyMdAhIqsj3VIymmrr1q2pvkeCnTlz5qBfv35o3749duzYobYvW7YMr732Gtzd3bOxxURkKnY6nU5nsr0TEWlEgph169apyQDTKzAwEOXKlVPz6JQoUcKk7SOi7MEaHSKySgMHDlTLPchaV/plIJ7l+vXr+P777xnkEFkRZnSIiIjIarFGh4iIiKwWAx0iIiKyWgx0iIiIyGox0CEiIiKrxUCHiIiIrBYDHSIiIrJaDHSIiIjIajHQISIiIqvFQIeIiIhgrf4HAAmcQqKCR9QAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"# Make a blank plot\n",
"fig, ax = plt.subplots()\n",
"\n",
"# Plot the Antoine equation\n",
"T = np.arange(T_Antoine_min, T_Antoine_max+1, 1)\n",
"ax.plot(T, P_antoine(A, B, C, T), label=r\"$P^\\mathrm{vap}$ (Antoine)\")\n",
"\n",
"# Use Clausius-Clapeyron to plot the sublimation curve\n",
"T = np.linspace(24, T_triple, 300)\n",
"P = P_CC(H_sub_1,T_triple, P_triple, T)\n",
"ax.plot(T, P, label=r\"$P^\\mathrm{sub}$ (Clausius-Clapeyron)\")\n",
"\n",
"# Use Clausius-Clapeyron to plot the vaporization curve \n",
"# starting from the critical point down\n",
"T = np.linspace(Tc, T_Antoine_min, 300)\n",
"P = P_CC(H_vap_1,Tc, Pc, T)\n",
"ax.plot(T, P, label=r\"$P^\\mathrm{vap}$ (Clausius-Clapeyron)\")\n",
"\n",
"# Use the integrated Clapeyron equation to plot the melting line\n",
"T = np.linspace(T_triple, T_triple+18, 100)\n",
"P = P_clapeyron(T_triple, P_triple, T, delta_fus_H, delta_fus_V)\n",
"ax.plot(T, P, label=r\"$P^\\mathrm{fus}$ (Clausius)\")\n",
"\n",
"# Plot the triple point\n",
"plt.plot(T_triple, P_triple, \"bo\", label=\"triple point\")\n",
"\n",
"# Plot the critical point\n",
"plt.plot(Tc, Pc, \"ro\", label=\"critical point\")\n",
"\n",
"# Plot the normal melting point (from Streng)\n",
"plt.plot(T_melt, P_melt, \"co\", label=\"normal melting point\")\n",
"\n",
"# Plot the normal boiling point (from Streng)\n",
"plt.plot(77.4, 101325, \"mo\", label=\"normal boiling point\")\n",
"\n",
"# Label and axes\n",
"plt.ylim([100,Pc*2])\n",
"plt.xlim([40,Tc*1.2])\n",
"ax.set_yscale(\"log\")\n",
"ax.legend(frameon=True, fancybox=True, edgecolor='none')\n",
"plt.xlabel('T (K)')\n",
"plt.ylabel('P (Pa)')\n",
"plt.title('P-T diagram for nitrogen')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f15f416f",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": ".venv",
"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": "3.12.11"
}
},
"nbformat": 4,
"nbformat_minor": 5
}