msc_thesis/Electrochemical/HIPed_Stellite1_Sample1/EIS.ipynb

{
 "cells": [
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   "cell_type": "markdown",
   "id": "a3a2e70b-c76f-4092-81e1-7a1cc873e02b",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9e37c18c-4cd1-493c-b518-017e548ea236",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from impedance.models.circuits import CustomCircuit\n",
    "# from impedance.visualization import plot_nyquist # Kept if you want to switch plotting methods"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7f0aa03-7702-49c3-9e7e-985a2e46acfe",
   "metadata": {},
   "source": [
    "## Data Loading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "4a0dbc36-458e-42c7-abf3-e1ae9ab6882b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Freq</th>\n",
       "      <th>Ampl</th>\n",
       "      <th>Bias</th>\n",
       "      <th>Time</th>\n",
       "      <th>Z'</th>\n",
       "      <th>Z''</th>\n",
       "      <th>GD</th>\n",
       "      <th>Err</th>\n",
       "      <th>Range</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100000.000000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>3.49460</td>\n",
       "      <td>15.55570</td>\n",
       "      <td>5.27726</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>89051.300000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>5.78299</td>\n",
       "      <td>13.80450</td>\n",
       "      <td>16.94240</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>79301.400000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>8.05283</td>\n",
       "      <td>13.90250</td>\n",
       "      <td>14.04590</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70618.900000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>13.68890</td>\n",
       "      <td>4.37749</td>\n",
       "      <td>1.17738</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>62887.000000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>15.97240</td>\n",
       "      <td>4.40899</td>\n",
       "      <td>1.03117</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <th>...</th>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>0.014616</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>1041.78000</td>\n",
       "      <td>33173.20000</td>\n",
       "      <td>-7535.82000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>0.013016</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>1120.51000</td>\n",
       "      <td>59320.90000</td>\n",
       "      <td>-4182.78000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>137</th>\n",
       "      <td>0.011591</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>1208.77000</td>\n",
       "      <td>47652.70000</td>\n",
       "      <td>-9034.40000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>138</th>\n",
       "      <td>0.010322</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>1307.67000</td>\n",
       "      <td>38840.50000</td>\n",
       "      <td>-11131.10000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>139</th>\n",
       "      <td>0.010000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-0.246816</td>\n",
       "      <td>1409.71000</td>\n",
       "      <td>38631.00000</td>\n",
       "      <td>2761.22000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "<p>140 rows × 9 columns</p>\n",
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      "text/plain": [
       "              Freq  Ampl      Bias        Time           Z'          Z''   GD  \\\n",
       "0    100000.000000  10.0 -0.246816     3.49460     15.55570      5.27726  0.0   \n",
       "1     89051.300000  10.0 -0.246816     5.78299     13.80450     16.94240  0.0   \n",
       "2     79301.400000  10.0 -0.246816     8.05283     13.90250     14.04590  0.0   \n",
       "3     70618.900000  10.0 -0.246816    13.68890      4.37749      1.17738  0.0   \n",
       "4     62887.000000  10.0 -0.246816    15.97240      4.40899      1.03117  0.0   \n",
       "..             ...   ...       ...         ...          ...          ...  ...   \n",
       "135       0.014616  10.0 -0.246816  1041.78000  33173.20000  -7535.82000  0.0   \n",
       "136       0.013016  10.0 -0.246816  1120.51000  59320.90000  -4182.78000  0.0   \n",
       "137       0.011591  10.0 -0.246816  1208.77000  47652.70000  -9034.40000  0.0   \n",
       "138       0.010322  10.0 -0.246816  1307.67000  38840.50000 -11131.10000  0.0   \n",
       "139       0.010000  10.0 -0.246816  1409.71000  38631.00000   2761.22000  0.0   \n",
       "\n",
       "     Err  Range  \n",
       "0      0      0  \n",
       "1      0      0  \n",
       "2      0      0  \n",
       "3      0      0  \n",
       "4      0      0  \n",
       "..   ...    ...  \n",
       "135    0      0  \n",
       "136    0      0  \n",
       "137    0      0  \n",
       "138    0      0  \n",
       "139    0      0  \n",
       "\n",
       "[140 rows x 9 columns]"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Data Loading ---\n",
    "FILENAME = \"EIS_10mV_Timing task2025_04_29_11_50_C001.z60\"\n",
    "\n",
    "try:\n",
    "    data_df = pd.read_csv(\n",
    "        FILENAME,\n",
    "        skiprows=11,\n",
    "        sep='\\s+',\n",
    "        names=[\"Freq\", \"Ampl\", \"Bias\", \"Time\", \"Z'\", \"Z''\", \"GD\", \"Err\", \"Range\"],\n",
    "        header=None\n",
    "    )\n",
    "    # Extract frequencies and impedance components\n",
    "    frequencies = data_df[\"Freq\"].to_numpy()\n",
    "    # Z' is the real part, Z'' is the imaginary part\n",
    "    Z_real = data_df[\"Z'\"].to_numpy()\n",
    "    Z_imag = data_df[\"Z''\"].to_numpy()\n",
    "    Z = Z_real + 1j * Z_imag\n",
    "\n",
    "\n",
    "except FileNotFoundError:\n",
    "    print(f\"Error: The file '{FILENAME}' was not found.\")\n",
    "    exit()\n",
    "except Exception as e:\n",
    "    print(f\"Error reading the CSV file: {e}\")\n",
    "    exit()\n",
    "\n",
    "data_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b481dbed-deac-4250-887b-673df223ea33",
   "metadata": {},
   "source": [
    "## Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "21b2f1d3-ace5-4134-8901-2f8a913f44e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# --- Preprocessing ---\n",
    "# Keep only the impedance data in the \"first quadrant\" of a Nyquist plot\n",
    "# (Re(Z) > 0 and -Im(Z) > 0  => Im(Z) < 0)\n",
    "mask = (Z.real > 0) & (Z.imag < 0) & (frequencies > 100)\n",
    "frequencies_filtered = frequencies[mask]\n",
    "Z_filtered = Z[mask]\n",
    "\n",
    "if len(Z_filtered) == 0:\n",
    "    print(\"Warning: After filtering for the first quadrant, no data points remain.\")\n",
    "    # Decide how to proceed: exit, or try to fit with unfiltered data, etc.\n",
    "    # For now, we'll try to fit with unfiltered if filtered is empty.\n",
    "    if len(Z) > 0:\n",
    "        print(\"Attempting to fit with unfiltered data.\")\n",
    "        frequencies_to_fit = frequencies\n",
    "        Z_to_fit = Z\n",
    "    else:\n",
    "        print(\"Error: No data to fit.\")\n",
    "        exit()\n",
    "else:\n",
    "    freq_data = frequencies_filtered\n",
    "    Z_exp = Z_filtered"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63ce4e78-ab23-46e3-add7-e800de8d0b61",
   "metadata": {},
   "source": [
    "# Circuit Elements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "771a8570-2eb8-471d-a3ea-2202c46e7043",
   "metadata": {},
   "source": [
    "\n",
    "| Circuit Element | Impedence                                    |\n",
    "| --------------- | -------------------------------------------- | \n",
    "| Resistor        | $$ Z = R $$                                  |\n",
    "| Capacitor       | $$ Z = \\frac{1}{C \\cdot j 2 \\pi f} $$        |\n",
    "| Inductor        | $$Z = L \\cdot j 2 \\pi f $$                   |\n",
    "| CPE             | $$Z = \\frac{1}{Q \\cdot (j 2 \\pi f)^\\alpha}$$ |\n",
    "\n",
    "| Impedences in parallel | Impedences in series |\n",
    "| --------------- | -------------------------------------------- | \n",
    "| $$ Z_{parallel} = \\frac{1}{\\frac{1}{Z_1} + \\frac{1}{Z_2} + ... + \\frac{1}{Z_n}}$$ | $$ Z_{series} = Z_1 + Z_2 + ... + Z_n $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "736a0854-c83b-4717-b0a2-060f9c706f2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import functools\n",
    "import numpy as np\n",
    "\n",
    "def R(f, R): return np.zeros(len(f)) + (R + 0 * 1j)\n",
    "def C(f, C): return 1.0 / (C * 1j * (2 * np.pi * np.array(f)) )\n",
    "def L(f, L): return L * 1j * (2 * np.pi * np.array(f))\n",
    "def CPE(f, Q, alpha): return 1.0 / (Q * (1j * (2 * np.pi * np.array(f))) ** alpha)\n",
    "\n",
    "def s(*args): return functools.reduce(np.add, [*args])\n",
    "def p(*args): return np.reciprocal(functools.reduce(np.add, np.reciprocal([*args])))\n",
    "\n",
    "f = np.linspace(1e5,1e-2,70)\n",
    "\n",
    "# Some common-sense tests to make sure the code is correct\n",
    "assert (s(R(f, 10),R(f, 10)) == R(f, 20)).all()\n",
    "assert (p(R(f, 10),R(f, 10)) == R(f, 5)).all()\n",
    "assert (s(C(f, 10),C(f, 10)) == C(f, 5)).all()\n",
    "assert (p(C(f, 10),C(f, 10)) == C(f, 20)).all()\n"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "7fbe1978-0c3c-4d09-bf56-baad9f28458b",
   "metadata": {},
   "source": [
    "# Simplified Randles Cell\n",
    "\n",
    "![image.png](attachment:b1431edd-37ac-4f71-a624-649177863415.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "cb098c7e-b8cf-4c8c-9978-f53442ef77a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def randles_circuit(f, Rs, Rp, Q, alpha): \n",
    "    return s(R(f, Rs), p(R(f, Rp), CPE(f, Q, alpha)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "22b91a0d-960e-4843-b9c0-d33db2030698",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fake data\n",
    "\n",
    "# Parameters for the simplified Randles circuit (R_s + (R_ct || C_dl))\n",
    "#freq_data = np.logspace(5, -1, 60) # 10 kHz down to 0.01 Hz\n",
    "R_s_true = 20.0      # Ohms\n",
    "R_ct_true = 100.0    # Ohms\n",
    "Q_dl_true = 1e-5     # Farads\n",
    "alpha_dl_true = 0.98 # -\n",
    "Z_fake = randles_circuit(freq_data, R_s_true, R_ct_true, Q_dl_true, alpha_dl_true) + \\\n",
    "        (0.5 + 0.5 * 1j) * np.random.normal(size=freq_data.size)\n",
    "Z_fake_concat = np.concatenate([Z_exp.real,Z_exp.imag])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "672eb5f0-bd38-4d42-a77f-583db50ae9c2",
   "metadata": {},
   "source": [
    "## Curve Fitting\n",
    "\n",
    "Fitting is performed by non-linear least squares regression of circuit model to impedence data via the scipy.optimize.curve_fit function.\n",
    "\n",
    "The objective function is:\n",
    "$$ \\chi^2 = \\sum_{n=0}^{N} [Z^\\prime_{exp}(\\omega_n) - Z^\\prime_{fit}(\\omega_n)]^2 +\n",
    "               [Z^{\\prime\\prime}_{exp}(\\omega_n) - Z^{\\prime\\prime}_{fit}(\\omega_n)]^2 $$\n",
    "               "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "a62ea723-f23f-43de-9622-fd4c0157b871",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_func(f, Rs, Rp, Q, alpha):\n",
    "    Z_fit = randles_circuit(f, Rs, Rp, Q, alpha)\n",
    "    return np.concatenate([Z_fit.real,Z_fit.imag])\n",
    "\n",
    "# Initial guesses for the parameters (R_s, R_ct, C_dl)\n",
    "# Good initial guesses are VERY important for convergence and finding the global minimum.\n",
    "initial_params_simple = [10.0, 50.0, 1e-6]\n",
    "\n",
    "# Parameter bounds (optional, but highly recommended)\n",
    "# Helps to keep parameters within physically realistic ranges.\n",
    "# Format: ([lower_bounds], [upper_bounds])\n",
    "bounds_simple = ([0, 0, 1e-9], [1000, 1e4, 1e-2]) # (R_s, R_ct, C_dl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "a7567100-ca22-440b-ab44-f3cf0142571a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting curve_fit for real data...\n",
      "curve_fit finished successfully!\n"
     ]
    }
   ],
   "source": [
    "print(\"Starting curve_fit for real data...\")\n",
    "try:\n",
    "    popt, pcov = curve_fit( \n",
    "        model_func,\n",
    "        freq_data,\n",
    "        np.concatenate([Z_exp.real,Z_exp.imag]),\n",
    "        # Initial guesses for the parameters (R_s, R_ct, C_dl)        \n",
    "        p0=[10.0, 50.0, 1e-6, 0.87], \n",
    "        # Helps to keep parameters within physically realistic ranges.        \n",
    "        bounds=([0, 0, 1e-9, 0], [1000, 1e4, 1e-2, 1]), \n",
    "        maxfev=50000) # Max number of function evaluations\n",
    "\n",
    "except RuntimeError:\n",
    "    print(\"Curve fitting failed. Could not find optimal parameters.\")\n",
    "    print(\"Try adjusting initial guesses, bounds, or the model itself.\")\n",
    "except ValueError as e:\n",
    "    print(f\"An error occurred: {e}\") \n",
    "else:\n",
    "    print(\"curve_fit finished successfully!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "1937913c-acbe-44e2-83bd-8c5817724160",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimized Parameters:\n",
      "Rs: 4.6838e+00\n",
      "Rp: 1.0000e+04\n",
      "Q: 3.6437e-05\n",
      "alpha: 9.6664e-01\n",
      "\n",
      "Standard Deviation Errors:\n",
      "R_s_err: 6.84e-02\n",
      "R_ct_err: 2.04e+04\n",
      "C_dl_err: 1.34e-06\n"
     ]
    }
   ],
   "source": [
    "# Results\n",
    "\n",
    "print(\"\\nOptimized Parameters:\")\n",
    "for name, val in zip([\"Rs\", \"Rp\", \"Q\", \"alpha\"], popt):\n",
    "    print(f\"{name}: {val:.4e}\")\n",
    "\n",
    "# Standard deviation errors on the parameters\n",
    "perr = np.sqrt(np.diag(pcov))\n",
    "print(\"\\nStandard Deviation Errors:\")\n",
    "for name, err in zip(param_names, perr):\n",
    "    print(f\"{name}_err: {err:.2e}\")\n",
    "\n",
    "# Calculate the fitted impedance values using the optimized parameters\n",
    "\n",
    "Z_fit = randles_circuit(freq_data, *popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "c5985667-18a5-4bf9-8c7c-e310d18af276",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DZrMZO3bs8Pm6c845x5gwYYJhGIaRkZFhSDI2btxYob6LLrrI573OOOMM7+clJSVGbGysMXToUO+5Xbt2GZKMNWvWGIZhGA8++KCRlpbmc98//vjDkGT88ssvld7XMAzj1FNPNcaPH+/9XJKxYMGCSn6Kvjp37mw8++yz3s/btGljzJgxo9JrS0tLjfHjxxvdunWr9PXx48cbDoejyvf66quvDEnGvn37DMMwjOXLlxuSjJycnGprzM7ONiQZ33//faWvV/fv2Z+8Rs8rAAAWlxgbJXtEmJwlbtkjwpQYe2R7y9fE2Wefreeff97nXJMmTbzHUVFRev3119W1a1e1adOm0ifne/Xq5bNBQ+/evfXUU0+ptLRUGzZskGEY6tChg8/XOJ1ONW3a1Od9unbteth6y18THh6upk2b6sQTT/SeS0pKkiTvn9PXr1+v5cuXq1GjRhXutXnzZm9dh753ixYtvPeoSn5+viZPnqyPPvpIO3fuVElJiQoLC+tk5lUq2661/M/1m2++UXp6ujZu3Kg9e/Z4Z063b9+uzp07V3mfzZs368EHH9TatWu1e/dun6/r0qVLndRaGcIrAAAW1yrBoWXjUpWT71JibJRaJdT/VrOxsbFq3759tdesXr1akrRnzx7t2bNHsbGxNb6/2+1WeHi41q9fr/DwcJ/XygdKh8NRox3KIiMjfT632Ww+5zz38AQ0t9utwYMH+/SOepRvfajsvof7s/o999yjjz/+WE8++aTat28vh8Ohyy67TC6X67DfR0389NNPateunaSyoJyWlqa0tDS9/vrrat68ubZv364BAwYc9v0GDx6s1q1b6+WXX1bLli3ldrvVpUuXOquzKoRXAABCQKsER4OE1pravHmzxowZo5dffllvv/22rrvuOm/fpMfatWt9vmbt2rVKSUlReHi4unfvrtLSUmVnZ+vMM89s6PJ18skn691331Xbtm0VEVH7OBUZGanS0lKfc5999pmGDx+uiy++WFJZD+zWrVuPpFyvn3/+WUuWLNGECRO8n+/evVuPP/64WrduLUn6+uuvfb4mKqpspr58nX///bd++uknvfjii96f/+eff14nNR4OD2wBAIA653Q6lZWV5fPheRK/tLRUQ4cOVVpamkaMGKGMjAz98MMPeuqpp3zu8ccff2js2LH65Zdf9Oabb+rZZ5/VXXfdJUnq0KGDrrnmGl133XWaP3++tmzZonXr1umJJ57QokWL6v37u/3227Vnzx5dddVV+uqrr/T7779r6dKluv766yuE0eq0bdtWn376qbKyspSTkyNJat++vebPn6+NGzfq22+/1dVXX12rh6BKSkqUlZWlnTt36vvvv9ezzz7rfcjsnnvukSQdc8wxioqK0rPPPqvff/9dH3zwgR555BGf+7Rp00Y2m00fffSR/vrrL+3fv1+JiYlq2rSpXnrpJf32229atmyZxo4d63eNtUF4BQAAdW7JkiVq0aKFz8cZZ5whSXrssce0detWvfTSS5Kk5ORkvfLKK5o4caI2btzovcd1112nwsJCnXbaabr99tt1xx136Oabb/a+npGRoeuuu0533323OnbsqAsvvFBffvmldwaxPrVs2VJffPGFSktLNWDAAHXp0kV33XWXGjdu7DN7fDhPPfWUMjMz1bp1a3Xv3l2SNGPGDCUmJqpPnz4aPHiwBgwYoJNPPtnvGjdt2qQWLVromGOOUWpqqt5++21NmDBBn332mbe1onnz5po9e7beeecdde7cWY8//riefPJJn/u0atVKkydP1n333aekpCSNGjVKYWFhmjdvntavX68uXbpozJgx+uc//+l3jbVhM4xyC6ZZUF5enho3bqy9e/cqPj6+Tu9dXFysRYsWadCgQRV6WhDcGDtzYtzMi7GrnaKiIm3ZskXt2rVTdHR0g7+/2+1WXl6e4uPj/QpkdSE1NVUnnXRSyG6BeiQCOW7Vqe7fsz95LXi+IwAAAOAwCK8AEIq2fyk9e4r0cj9pw2uBrgYAaozVBgAgFOVnS3//VnZ8/AWBrQWoRPltXoHyCK8AYEI7cguPbM3Oor0Hj6Mb111hAFDPCK8AYDKefeo9uyUtG5fqf4Atyjt4THgFYCL0vAKAyeTku+QsKVvz0VniVk5+LXazYeYVgEkRXgHAZDz71Euq/T71hFcAJhXQ8Jqeni6bzebzkZyc7H3dMAylp6erZcuWcjgcSk1N1aZNmwJYMQAEnmef+o/uOKN2LQMS4RWAaQV85vWEE07Qrl27vB/ff/+997Vp06Zp+vTpmjVrltatW6fk5GT1799f+/btC2DFABB4rRIc6tKqce33qie8AjCpgD+wFRER4TPb6mEYhmbOnKkHHnhAl1xyiSRpzpw5SkpK0ty5c3XLLbdUej+n0ymn0+n9PC+v7KGE4uJiFRcX12ntnvvV9X1R/xg7c2Lc6k54YY539qI4PEaq558pY1c7xcXFMgxDbre7VnvbHynPJpyeGupCv3791K1bN82YMaNO7nc4s2fP1tixY7Vnz54Geb+qjBgxQrm5uVqwYEGNrl+xYoXOOecc/f3330pISPDrvepj3OqC2+2WYRgqLi5WeHi4z2v+/G4IeHj99ddf1bJlS9ntdvXs2VNTpkzRscceqy1btigrK0tpaWnea+12u/r27avVq1dXGV6nTp2qyZMnVzi/dOlSxcTE1Mv3kJmZWS/3Rf1j7MyJcTtyqX/9qcaSSm0RWrR0mWSzNcj7Mnb+8Uzw7N+/Xy5XLR7MqyP+/sVz5MiRevPNNyucX79+vTIyMhQREeGdXOratatuu+023Xbbbd7r5s6dqwkTJmjbtm1HVrjKtiQ1DMP7fpVJTEyUVJYVTj31VO95p9OpTp06KScnRx9++KHOOOOMWtdRXFyskpKSausor6CgQFLZz762W7wG21+qXS6XCgsLtWrVKpWUlPi85vl+ayKg4bVnz5567bXX1KFDB/3vf//To48+qj59+mjTpk3KysqSJCUlJfl8TVJSUrX/mCdMmKCxY8d6P8/Ly1Pr1q2VlpZ22L1y/VVcXKzMzEz179+fvbpNhrEzJ8at7kT8/oBUKIXFJGrQ+efX+/sxdrVTVFSkP/74Q40aNaqwF3xDMAxD+/btU1xcnGx+/B+cyMhIDRgwQK+++qrP+ebNm1eYcQsLC1N0dLTPf6Ojo6Nls9nq5L/bNb1X69at9c477+icc87xnps3b57i4uKUk5OjmJiYI6onMjJSERERNb6HZ8ItLi7O7/et7bjVt6KiIjkcDp111lkV/j3XNNRLAQ6vAwcO9B6feOKJ6t27t4477jjNmTNHvXr1kqQKP3TDMKodCLvdLrvdXuF8ZGRkvf3CrM97o34xdubEuNWBA+u82qIbN+jPkrHzT2lpqWw2m8LCwmo9+3YkPH9y9tRQUzabTdHR0WrZsmWF11JTU3XSSSdp5syZSk1N1bZt2zR27FjvxNPy5ct1ww03SJI36E6aNEnp6elyuVyaOHGi3njjDeXm5qpLly564oknlJqa6r3/7Nmz9dBDD2n37t0aMGCAd7b0cPUPGzZMzzzzjJ5++mk5HA7vvYYNG6ZHHnnEZwy+//573XXXXVqzZo1iYmJ06aWXavr06WrUqJGksnG755579Oqrryo8PNz7/ZT/ORqGoX/+85964YUXtGvXLnXo0EEPPvigLrvsMp96azP2tR23+hYWFiabzVbp7wF/fi8EvG2gvNjYWJ144on69ddfNWTIEElSVlaWWrRo4b0mOzu7wmwsAMAPbrfkPDDLwcNa5vNiX2l/doO8lU1SvOGWzRYmNTpKumVlnd5//vz56tatm26++WbddNNNkqQmTZpo5syZeuihh/TLL79IkjcUjhgxQlu3btW8efPUsmVLLViwQOedd56+//57paSk6Msvv9T111+vKVOm6JJLLtGSJUs0adKkGtVyyimnqF27dnr33Xd17bXX6o8//tCqVav03HPP6ZFHHvFeV1BQoPPOO0+9evXSunXrlJ2drRtvvFGjRo3S7NmzJUlPPfWUXn31Vf373/9W586d9dRTT2nBggXq16+f9z4TJ07U/Pnz9fzzzyslJUWrVq3Stddeq+bNm6tv37518eO1rKAKr06nUz/99JPOPPNMtWvXTsnJycrMzFT37t0llfVKrFy5Uk888USAKwUAE3Ptk1T2QIfsddtOhQawP1vat7NB3sp24KM2PvroI2/olMr+2vrOO+/4XNOkSROFh4crLi7O5+Htxo0bV1g+c/PmzXrzzTf1559/emd0x40bpyVLligjI0NTpkzR008/rQEDBui+++6TJHXo0EGrV6/WkiVLalTziBEj9Oqrr+raa69VRkaGBg0apObNm/tc88Ybb6iwsFCvvfaaYmNjJUmzZs3S4MGD9cQTTygpKUkzZ87UhAkTdOmll0qSXnjhBX388cfee+Tn52v69OlatmyZevfuLUk69thj9fnnn+vFF18kvB5GQMPruHHjNHjwYB1zzDHKzs7Wo48+qry8PA0bNkw2m02jR4/WlClTlJKSopSUFE2ZMkUxMTG6+uqrA1k2AJgby2SZW6OjGuytDEnGgZlXm5/ve/bZZ+v555/3fu4JerW1YcMGGYahDh06+Jx3Op1q2rSpJOmnn37SxRdf7PN67969axxer732Wt133336/fffNXv2bD3zzDMVrvnpp5/UrVs3n+/n9NNPl9vt1i+//KLo6Gjt2rXLG0qlsgfvevTo4V0F4Mcff1RRUZH69+/vc2+Xy+WdsEPVAhpe//zzT1111VXavXu3mjdvrl69emnt2rVq06aNJOnee+9VYWGhRo4cqZycHPXs2VNLly5VXFxcIMsGAHMjvJpbHf/pvjqG2628vDzFx8fL5mfvZGxsrNq3b19ntbjdboWHh2v9+vUVHvryzPB6wmFtNW3aVBdccIFuuOEGFRUVaeDAgRWe2K/u2ZuaPhzl6UlduHChWrVq5fNaZc/twFdAw+u8efOqfd1msyk9PV3p6ekNUxAAhALCK4JIVFSUSktLD3uue/fuKi0tVXZ2ts4888xK79W5c2etXbvW59yhnx/O9ddfr0GDBmn8+PEVQrLnPebMmaP8/Hzv7OsXX3yhsLAwdejQQY0bN1aLFi20du1anXXWWZKkkpISrV+/XieffLL3Hna7Xdu3b6dFoBaCqucVANAACK8IIm3bttWqVat05ZVXym63q1mzZmrbtq3279+vTz/9VN26dVNMTIw6dOiga665Rtddd52eeuopde/eXbt379ayZct04oknatCgQbrzzjvVp08fTZs2TUOGDNHSpUtr3DLgcd555+mvv/6qcnmqa665RpMmTdKwYcOUnp6uv/76S3fccYeGDh3qfaD8rrvu0uOPP66UlBR16tRJ06dPV25urvcecXFxGjdunMaMGSO3260zzjhDeXl5Wr16tRo1aqRhw4bV+ucZCoJn/QQAQMMgvCKIPPzww9q6dauOO+4478NRffr00a233qorrrhCzZs317Rp0yRJGRkZuu6663T33XerY8eOuvDCC/Xll1+qdevWkqRevXrplVde0bPPPquTTjpJS5cu1cSJE/2qx2azqVmzZoqKiqr09ZiYGH388cfas2ePTj31VF122WU655xzNGvWLO81d999t6677joNHz5cvXv3VlxcXIVe3EceeUQPPfSQpk6dqk6dOmnAgAH68MMP1a5dO7/qDUU240gbRIJcXl6eGjdurL1799bLJgWLFi3SoEGDWLfQZBg7c2Lc6sja56UlZU9j65JXpK6X1/tbMna1U1RUpC1btqhdu3YB2aTAXa7nNZjWC0X1gnXcqvv37E9eC57vCADQMJh5BWBihFcACDVF5bZhJLwCMBnCKwCEGp+ZVzYpAGAuhFcACDVFuQePmXkFYDKEVwAINfS8mo7Fn61GiKirf8eEVwAINZ7wGhYhRcYEthZUy7NIvsvlCnAlwJErKCiQpCNecYRNCgAg1HjCa3RjqYbbWSIwIiIiFBMTo7/++kuRkZENvuyR2+2Wy+VSUVFRUC25hOoF27gZhqGCggJlZ2crISGh0p3L/EF4BYBQUz68IqjZbDa1aNFCW7Zs0bZt2xr8/Q3DUGFhoRwOh2z8Hx3TCNZxS0hIUHJy8hHfh/AKAKHE7ZacB5bKIryaQlRUlFJSUgLSOlBcXKxVq1bprLPOYnMJEwnGcYuMjDziGVcPwisAhBLXfslwlx0TXk0jLCwsIDtshYeHq6SkRNHR0UETgnB4Vh+3wDdCAAAajpMNCgCYG+EVAEJJ+WWy7GxQAMB8CK8AEEpY4xWAyRFeASCU+ITXhICVAQC1RXgFgFDCzCsAkyO8AkAoIbwCMDnCKwCEEsIrAJMjvAJAKCG8AjA5wisAhJKi3IPHhFcAJkR4BYBQUsQmBQDMjfAKAKHEp22ATQoAmA/hFQBCiSe82sKkqEaBrQUAaoHwCgChxBNeoxtLNltgawGAWiC8AkAoKR9eAcCECK8AECoMg/AKwPQIrwAQKlz5klFadkx4BWBShFcACBVsUADAAgivABAqCK8ALIDwCgChwll+g4KEgJUBAEeC8AoAoaL8zKudDQoAmBPhFQBCBW0DACyA8AoAoYLwCsACCK8AECqKcg8eE14BmBThFQBCBTOvACyA8AoAoYLwCsACCK8AECoIrwAsgPAKAKGC8ArAAgivABAqig5sUmALk6IaBbYWAKglwisAhArPzKs9Tgrj1z8Ac+K3FwCECk94pWUAgIkRXgEgFBgG4RWAJRBeASAUFBdK7uKyYzvhFYB5EV4BIBSUX2nAkRCwMgDgSEUEugAAQO3tyC1UTr5LibFRapXgqPpCZ97BY3t8/RcGAPWE8AoAJrUjt1D9nlwhZ4lb9ogwLRuXWnWAZY1XABZB2wAAmFROvkvOErckyVniVk6+q+qLfcIrM68AzIvwCgAmlRgbJXtE2a9xe0SYEmOjqr6YmVcAFkHbAACYVKsEh5aNS61ZzyvhFYBFEF4BwMRaJTiqD60ePLAFwCJoGwCAUMDMKwCLILwCQCggvAKwCMIrAISConJtA6w2AMDECK8AEAp8Zl4TAlYGABwpwisAhILy4ZUHtgCYGOEVAEKBZ7WByFgpnIVmAJgX4RUAQoFn5pWHtQCYHOEVAEIB4RWARRBeAcDqSoul4oKyY1YaAGByhFcAsDqfZbKYeQVgboRXALA6JysNALAOwisAWB27awGwEMIrAFgd4RWAhRBeAcDq2BoWgIUQXgHA6ph5BWAhhFcAsDrCKwALIbwCgNU5y7UN2AmvAMyN8AoAVsfMKwALIbwCgNURXgFYCOEVAKyO1QYAWAjhFQCsjplXABZCeAUAq/OE1/AoKSI6sLUAwBEivAKA1TkPhFd7vGSzBbYWADhChFcAsDrPzCstAwAsgPAKAFbmdkvOfWXHPKwFwAIIrwBgZa79kuEuO2bmFYAFEF4BwMpYaQCAxRBeAcDKfLaGpW0AgPkRXgHAyph5BWAxhFcAsDKf8JoQsDIAoK4QXgHAytgaFoDFEF4BwMpoGwBgMYRXALAywisAiyG8AoCVOcuFV1YbAGABhFcAsDJmXgFYDOEVAKyM8ArAYgivAGBlrDYAwGIIrwBgZd6ZV5sUFRfQUgCgLhBeAcDKPNvD2uOlMH7lAzA/fpMBgJV5Zl7pdwVgEYRXALAywisAiyG8AoBVFRdJpa6yYx7WAmARhFcAsCqWyQJgQYRXALAqwisACyK8AoBVOcut8crWsAAsgvAKAFZVlHvwmJ5XABYREegCAABHZkduoXLyXUqMjVKrBMfBF3x216JtAIA1BM3M69SpU2Wz2TR69GjvOcMwlJ6erpYtW8rhcCg1NVWbNm0KXJEAEGR25Baq35MrdMGzn6vfkyu0I7fw4Iv0vAKwoKAIr+vWrdNLL72krl27+pyfNm2apk+frlmzZmndunVKTk5W//79tW/fvgBVCgDBJSffJWeJW5LkLHErJ9918EV6XgFYUMDD6/79+3XNNdfo5ZdfVmJiove8YRiaOXOmHnjgAV1yySXq0qWL5syZo4KCAs2dOzeAFQNA8EiMjZI9ouxXuT0iTImxUQdf9GkbILwCsIaA97zefvvtOv/883Xuuefq0Ucf9Z7fsmWLsrKylJaW5j1nt9vVt29frV69Wrfcckul93M6nXI6nd7P8/LKfnkXFxeruLi4Tmv33K+u74v6x9iZE+NW0VGxEVp61+nKKShWYkykjoqN8P58wgpyFH7gupKIWBkB/LkxdubEuJmTGcfNn1oDGl7nzZunDRs2aN26dRVey8rKkiQlJSX5nE9KStK2bduqvOfUqVM1efLkCueXLl2qmJiYI6y4cpmZmfVyX9Q/xs6cGLfKbZO0sdznJ2/9Sa0PHK9Y+43yo7MavqhDMHbmxLiZk5nGraCgoMbXBiy8/vHHH7rrrru0dOlSRUdHV3mdzWbz+dwwjArnypswYYLGjh3r/TwvL0+tW7dWWlqa4uPr9s9mxcXFyszMVP/+/RUZGVmn90b9YuzMiXHzT/hbr0s5Zcd90wZLjY4KWC2MnTkxbuZkxnHz/KW8JgIWXtevX6/s7Gydcsop3nOlpaVatWqVZs2apV9++UVS2QxsixYtvNdkZ2dXmI0tz263y263VzgfGRlZbwNYn/dG/WLszIlxqyHXfu9hZKOmUhD8zBg7c2LczMlM4+ZPnQF7YOucc87R999/r40bN3o/evTooWuuuUYbN27Uscceq+TkZJ8pb5fLpZUrV6pPnz6BKhsAzMOz2kC4XYqs+i9cAGAmAZt5jYuLU5cuXXzOxcbGqmnTpt7zo0eP1pQpU5SSkqKUlBRNmTJFMTExuvrqqwNRMgCYi2edV9Z4BWAhAV9toDr33nuvCgsLNXLkSOXk5Khnz55aunSp4uLiAl0aAAQ/z1JZLJMFwEKCKryuWLHC53Obzab09HSlp6cHpB4AMC23+2DbABsUALCQgG9SAACoB659koyyY9oGAFgI4RUArIjdtQBYFOEVAKzI87CWxMwrAEshvAKAFTnLzbzS8wrAQgivAGBFzLwCsCjCKwBYkU/PK+EVgHUQXgHAimgbAGBRhFcAsKKi3IPHrDYAwEIIrwBgRbQNALAowisAWBFtAwAsivAKAFbEagMALIrwCgBWxA5bACyK8AoAVlR+5pW2AQAWQngFACvy9LxGxUlh4YGtBQDqEOEVAKzI0zZAywAAiyG8AoAVedoGeFgLgMUQXgHAakpcUklh2TH9rgAshvAKAFbjZKUBANZFeAUAq2GNVwAWRngFAKthdy0AFkZ4BQCrYeYVgIURXgHAathdC4CFEV4BwGrYXQuAhRFeAcBqfFYboG0AgLUQXgHAaooIrwCsi/AKAFZD2wAACyO8AoDV0DYAwMIIrwBgNT5LZTHzCsBaCK8AYDWs8wrAwgivAGA1nrYBW7gUGRPYWgCgjhFeAcBqDsy8lkTFacfeogAXAwB1i/AKABZTWlg287qjMEr9nlyhHbmFAa4IAOoO4RUArMQwFHagbWCfYuQscSsn3xXgogCg7hBeAcBKigtkM0okSXlGjOwRYUqMjQpwUQBQdyICXQAAoA6V212ry7GtteziVLVKcASuHgCoY4RXALCSchsUxCc0VTzBFYDF0DYAAFbCBgUALI7wCgBWUq5tQHbCKwDrIbwCgJU42V0LgLURXgHASsrPvNI2AMCCCK8AYCVO2gYAWBvhFQCshAe2AFgc4RUArMSnbYCeVwDWQ3gFACvxaRsgvAKwHsIrAFgJD2wBsDjCKwBYCQ9sAbA4wisAWInnga3wKCkyOrC1AEA9ILwCgJV42gZ4WAuARRFeAcBKPDts0TIAwKIIrwBgFW635NxXdszDWgAsivAKAFbh2i8Z7rJjZl4BWBThFQCswskyWQCsj/AKAFbB7loAQgDhFQCsgt21AIQAwisAWAW7awEIAYRXALAKzwYFEg9sAbAswisAWIWzXHhl5hWARRFeAcAqeGALQAggvAKAVfg8sMXMKwBrIrwCgFXwwBaAEEB4BQCr4IEtACGA8AoAVuGk5xWA9RFeAcAqiuh5BWB9hFcAsArPzGuEQ4qICmwtAFBPCK8AYBWemVce1gJgYYRXALAKzwNbtAwAsDDCKwBYgbtUcu0rO2bmFYCFEV4BwAqc+w4es9IAAAsjvAKAFbC7FoAQQXgFACtgdy0AIYLwCgBWwO5aAEIE4RUArMBnd62EgJUBAPWN8AoAVkDbAIAQQXgFACvggS0AIYLwCgBWUL7nlZlXABZGeAUAK+CBLQAhgvAKAFbgpOcVQGggvAKAFfg8sMUOWwCsi/AKAFbAA1sAQgThFQAswJmfe/ATwisACyO8AoDJ7cgt1PadWZKkfMOuHfuKA1wRANQfwisAmFxOvkuNVCBJ2qcY5eS7AlwRANQfwisAmFxibJTiD4TX/YpRYmxUgCsCgPoTEegCAABHplV8lGQrkiQd0yJZUQmOAFcEAPWHmVcAMLtyKw1ExSYErg4AaACEVwAwuyI2KAAQOgivAGB2rPEKIIT41fNqGIZWrlypzz77TFu3blVBQYGaN2+u7t2769xzz1Xr1q3rq04AQFWYeQUQQmo081pYWKgpU6aodevWGjhwoBYuXKjc3FyFh4frt99+06RJk9SuXTsNGjRIa9eure+aAQDl+cy8sjUsAGur0cxrhw4d1LNnT73wwgsaMGCAIiMjK1yzbds2zZ07V1dccYUmTpyom266qc6LBQBUgplXACGkRuF18eLF6tKlS7XXtGnTRhMmTNDdd9+tbdu21UlxAIAaoOcVQAipUdvA4YJreVFRUUpJSal1QQAAPxXtPXjMzCsAi6vVJgVFRUX67rvvlJ2dLbfb7fPahRdeWCeFAQBqiJlXACHE7/C6ZMkSXXfdddq9e3eF12w2m0pLS+ukMABADdHzCiCE+L3O66hRo3T55Zdr165dcrvdPh8EVwAIAGZeAYQQv8Nrdna2xo4dq6SkpPqoBwDgL5+ZV5bKAmBtfofXyy67TCtWrKiHUgAAteIz8xoXuDoAoAH43fM6a9YsXX755frss8904oknVljz9c4776yz4gAANeCZeY2MkcIrrsMNAFbid3idO3euPv74YzkcDq1YsUI2m837ms1mI7wCQEPzzLzS7wogBPjdNjBx4kQ9/PDD2rt3r7Zu3aotW7Z4P37//Xe/7vX888+ra9euio+PV3x8vHr37q3Fixd7XzcMQ+np6WrZsqUcDodSU1O1adMmf0sGAGvzzLyy0gCAEOB3eHW5XLriiisUFub3l1Zw9NFH6/HHH9fXX3+tr7/+Wv369dNFF13kDajTpk3T9OnTNWvWLK1bt07Jycnq37+/9u3bd8TvDQCW4C6VXAd+JzLzCiAE+J1Ahw0bprfeeqtO3nzw4MEaNGiQOnTooA4dOuixxx5To0aNtHbtWhmGoZkzZ+qBBx7QJZdcoi5dumjOnDkqKCjQ3Llz6+T9AcD0nOX+zzwzrwBCgN89r6WlpZo2bZo+/vhjde3atcIDW9OnT69VIaWlpXrnnXeUn5+v3r17a8uWLcrKylJaWpr3Grvdrr59+2r16tW65ZZbKr2P0+mU0+n0fp6XV/bntOLiYhUXF9eqtqp47lfX90X9Y+zMiXGrRP4eeX4Lu6PiVBqkPxvGzpwYN3My47j5U6vf4fX7779X9+7dJUk//PCDz2vlH97y5369e/dWUVGRGjVqpAULFqhz585avXq1JFVYTzYpKUnbtm2r8n5Tp07V5MmTK5xfunSpYmJi/K6vJjIzM+vlvqh/jJ05MW4HxRdu19kHjrdn5+rbRYsCWs/hMHbmxLiZk5nGraCgoMbX+h1ely9f7u+XVKtjx47auHGjcnNz9e6772rYsGFauXKl9/VDA7FhGNWG5AkTJmjs2LHez/Py8tS6dWulpaUpPr5u/6RWXFyszMxM9e/fv8IMNIIbY2dOjFtFtu1rpJ/Ljlu3P0Gtzh0U2IKqwNiZE+NmTmYcN89fymvC7/Ba16KiotS+fXtJUo8ePbRu3To9/fTTGj9+vCQpKytLLVq08F6fnZ1d7e5edrtddru9wvnIyMh6G8D6vDfqF2NnToxbOSUHZyvCYxIVHuQ/F8bOnBg3czLTuPlTp98PbOXn5+vBBx9Unz591L59ex177LE+H0fKMAw5nU61a9dOycnJPlPeLpdLK1euVJ8+fY74fQDAEnx21+KBLQDW5/fM64033qiVK1dq6NChatGiRa36XD3uv/9+DRw4UK1bt9a+ffs0b948rVixQkuWLJHNZtPo0aM1ZcoUpaSkKCUlRVOmTFFMTIyuvvrqWr8nAFhK0d6Dx6w2ACAE+B1eFy9erIULF+r0008/4jf/3//+p6FDh2rXrl1q3LixunbtqiVLlqh///6SpHvvvVeFhYUaOXKkcnJy1LNnTy1dulRxcezdDQCSmHkFEHL8Dq+JiYlq0qRJnbz5v//972pft9lsSk9PV3p6ep28HwBYTlG58MrMK4AQ4HfP6yOPPKKHHnrIryUNAAD1hJlXACGmRjOv3bt39+lt/e2335SUlKS2bdtWeDpsw4YNdVshAKBqzLwCCDE1Cq9Dhgyp5zIAALXiM/PaOHB1AEADqVF4nTRpUn3XAQCoDWZeAYQYvx/YKiwsVGZmpv773//KZrOpQ4cOOvfcc+VwOOqjPgBAdQ7MvLojHPoxq0CJsVFqlcDvYwDW5Vd4/eCDD3TjjTdq9+7dPuebNWumf//73xo8eHCdFgcAOIwDM6+7i+264NnPZY8I07JxqQRYAJZV49UGVq9ercsuu0xnnXWWvvjiC+3Zs0d79uzR559/rjPPPFOXXXaZ1qxZU5+1AgAOdWDmdZ9RFladJW7l5LsCWREA1Ksaz7w++uijGjFihF588UWf83369FGfPn10yy236JFHHtGiRYvqvEgAQCXcbsm5T5KUb4uRJNkjwpQYGxXIqgCgXtU4vK5Zs0ZPPPFEla/ffvvt6tu3b50UBQCoAdd+SYYkqUObVvpowBn0vAKwvBqH16KiIsXHV/0ka+PGjeV0OuukKABADZRbJis6NkFdWrFUFgDrq3HPa4cOHbRs2bIqX//000/Vvn37OikKAFADLJMFIATVOLwOHz5c48aNq7SndeHChbr33ns1YsSIOi0OAFANNigAEIJq3DZw1113afXq1brgggvUsWNHderUSZL0448/6tdff9WQIUN011131VuhAIBDMPMKIATVeOY1LCxM77zzjt5880117NhRP//8s37++Wcdf/zxeuONN/Tuu+8qLKzGtwMAHCmfmde4wNUBAA3I7x22rrjiCl1xxRX1UQsAwB9Few8e25l5BRAaajRVmp+f79dN/b0eAFALB9Z4lUTbAICQUaPw2r59e02ZMkU7d+6s8hrDMJSZmamBAwfqmWeeqbMCAQBV8GkbILwCCA01ahtYsWKFJk6cqMmTJ+ukk05Sjx491LJlS0VHRysnJ0c//vij1qxZo8jISE2YMEE333xzfdcNAOCBLQAhqEbhtWPHjnrnnXf0559/6p133tGqVau0evVqFRYWqlmzZurevbtefvllDRo0iIe2AKChsFQWgBDk1wNbRx99tMaMGaMxY8bUVz0AgJoqYrUBAKGHaVIAMCsnbQMAQg/hFQDMyhNewyKliOjA1gIADYTwCgBm5WkbiI6XbLbA1gIADYTwCgBm5Zl5ZZksACGE8AoAZmQYvjOvABAi/A6vbdu21cMPP6zt27fXRz0AgJooLpCM0rJjZl4BhBC/w+vdd9+t999/X8cee6z69++vefPmyel01kdtAICqFLG7FoDQ5Hd4veOOO7R+/XqtX79enTt31p133qkWLVpo1KhR2rBhQ33UCAA4lHPfwWPaBgCEkFr3vHbr1k1PP/20duzYoUmTJumVV17Rqaeeqm7duunVV1+VYRh1WScAoDwnM68AQpNfO2yVV1xcrAULFigjI0OZmZnq1auXbrjhBu3cuVMPPPCAPvnkE82dO7cuawUAeBTtPXjMzCuAEOJ3eN2wYYMyMjL05ptvKjw8XEOHDtWMGTN0/PHHe69JS0vTWWedVaeFAgDKYeYVQIjyO7yeeuqp6t+/v55//nkNGTJEkZGRFa7p3LmzrrzyyjopEABQiSK2hgUQmvwKr6Wlpfr3v/+tCy+8UE2aNKnyutjYWGVkZBxxcQCAKvjMvMYFrg4AaGB+PbAVHh6uW2+9VXv37j38xQCA+lN+tQF748DVAQANzO/VBk488UT9/vvv9VELAKCmaBsAEKL8Dq+PPfaYxo0bp48++ki7du1SXl6ezwcAoAHwwBaAEOX3A1vnnXeeJOnCCy+UzWbznjcMQzabTaWlpXVXHQCgcocslbUjt1A5+S4lxkapVYIjcHUBQD3zO7wuX768PuoAAPij3MzrzqIo9XtmhZwlbtkjwrRsXCoBFoBl+R1e+/btWx91AAD84el5tYVpjytCzhK3JMlZ4lZOvovwCsCyar3DVkFBgbZv3y6Xy+VzvmvXrkdcFADgMDyrDdjjlNjILntEmHfmNTE2KrC1AUA98ju8/vXXXxoxYoQWL15c6ev0vAJAA/C0Ddgbq1WCQ8vGpdLzCiAk+L3awOjRo5WTk6O1a9fK4XBoyZIlmjNnjlJSUvTBBx/UR40AgEN52gYOLJPVKsGhLq0aE1wBWJ7fM6/Lli3T+++/r1NPPVVhYWFq06aN+vfvr/j4eE2dOlXnn39+fdQJAPAocUqlzrJjdtcCEGL8nnnNz8/XUUcdJUlq0qSJ/vrrL0llmxds2LChbqsDAFTks7sWa7wCCC1+h9eOHTvql19+kSSddNJJevHFF7Vjxw698MILatGiRZ0XCAA4xCFrvAJAKPG7bWD06NHatWuXJGnSpEkaMGCA3njjDUVFRWn27Nl1XR8A4FA+M6+0DQAILX6H12uuucZ73L17d23dulU///yzjjnmGDVr1qxOiwMAVIKtYQGEsFqv8+oRExOjk08+uS5qAQDURFG58ErbAIAQ43d4LS0t1ezZs/Xpp58qOztbbrfb5/Vly5bVWXEAgErwwBaAEOZ3eL3rrrs0e/ZsnX/++erSpYtsNlt91AUAqAptAwBCmN/hdd68eXr77bc1aNCg+qgHAHA4tA0ACGF+L5UVFRWl9u3b10ctAICa8Jl5ZbUBAKHF7/B699136+mnn5ZhGPVRDwDgcGgbABDC/G4b+Pzzz7V8+XItXrxYJ5xwgiIjI31enz9/fp0VBwCoBG0DAEKY3+E1ISFBF198cX3UAgCoCVYbABDC/A6vGRkZ9VEHAKCm6HkFEML87nkFAASYp20gMkYKj6z+WgCwmBrNvJ588sn69NNPlZiYqO7du1e7tuuGDRvqrDgAQCU8bQPMugIIQTUKrxdddJHsdrskaciQIfVZDwDgcDxtA/S7AghBNQqvkyZNqvQYANDA3O6DM6+sNAAgBNHzCgBm4ton6cA627QNAAhBfq82kJiYWGnPq81mU3R0tNq3b6/hw4drxIgRdVIgAKAclskCEOL8Dq8PPfSQHnvsMQ0cOFCnnXaaDMPQunXrtGTJEt1+++3asmWLbrvtNpWUlOimm26qj5oBIHSxQQGAEFerHbYeffRR3XrrrT7nX3zxRS1dulTvvvuuunbtqmeeeYbwCgB1zWeN18aBqwMAAsTvntePP/5Y5557boXz55xzjj7++GNJ0qBBg/T7778feXUAAF8+bQP0vAIIPX6H1yZNmujDDz+scP7DDz9UkyZNJEn5+fmKi+OXKgDUuaK9B49pGwAQgvxuG3jwwQd12223afny5TrttNNks9n01VdfadGiRXrhhRckSZmZmerbt2+dFwsAIc+nbYDwCiD0+B1eb7rpJnXu3FmzZs3S/PnzZRiGjj/+eK1cuVJ9+vSRJN199911XigAQLQNAAh5fodXSTr99NN1+umn13UtAIDDqWS1gR25hcrJdykxNkqtEhwBKgwAGkatwqtHYWGhiouLfc7Fx/NnLACoN4e0DezILVS/J1fIWeKWPSJMy8alEmABWJrfD2wVFBRo1KhROuqoo9SoUSMlJib6fAAA6tEhmxTk5LvkLHGXvVTiVk6+K0CFAUDD8Du83nPPPVq2bJn+9a9/yW6365VXXtHkyZPVsmVLvfbaa/VRIwDA45C2gcTYKNkjyn6V2yPClBgbFaDCAKBh+N028OGHH+q1115Tamqqrr/+ep155plq37692rRpozfeeEPXXHNNfdQJAJAOaRuIU6soh5aNS6XnFUDI8Hvmdc+ePWrXrp2ksv7WPXv2SJLOOOMMrVq1qm6rAwD48oRXW7gUGSNJapXgUJdWjQmuAEKC3+H12GOP1datWyVJnTt31ttvvy2pbEY2ISGhLmsDABzK0/Nqj5NstsDWAgAB4Hd4HTFihL799ltJ0oQJE7y9r2PGjNE999xT5wUCAMrx9LyyuxaAEOV3z+uYMWO8x2effbZ+/vlnff311zruuOPUrVu3Oi0OAHAI78wr4RVAaDqidV4l6ZhjjtExxxxTF7UAAKpT4pRKnWXHhFcAIapW4fWrr77SihUrlJ2dLbfb7fPa9OnT66QwAMAhyq/xStsAgBDld3idMmWKJk6cqI4dOyopKUm2cg8M2Hh4AADqT9Heg8f2uMDVAQAB5Hd4ffrpp/Xqq69q+PDh9VAOAKBKh+yuBQChyO/VBsLCwnT66afXRy0AgOocskEBAIQiv8PrmDFj9Nxzz9VHLQCA6hyyNSwAhCK/2wbGjRun888/X8cdd5w6d+6syMhIn9fnz59fZ8UBAMqhbQAA/A+vd9xxh5YvX66zzz5bTZs25SEtAGgoPm0DhFcAocnv8Praa6/p3Xff1fnnn18f9QAAqkLPKwD43/PapEkTHXfccfVRCwCgOvS8AoD/4TU9PV2TJk1SQUFBfdQDAKiKT88rM68AQpPfbQPPPPOMNm/erKSkJLVt27bCA1sbNmyos+IAAOXQ8woA/ofXIUOG1EMZAIDDYrUBAPA/vE6aNKk+6gAAHA49rwDgf88rACBAPDOvEQ4pPLL6awHAomo089qkSRP997//VbNmzZSYmFjt2q579uyps+IAAOV4el55WAtACKtReJ0xY4bi4sp+Wc6cObM+6wEAVMUTXmkZABDCahRehw0bVulxdR5//HHdeuutSkhIqFVhAIByDONg20C5mdcduYXKyXcpMTZKrRIcASoOABpOvfW8TpkyhRYCAKgrrv2S4S47PrDSwI7cQvV7coUuePZz9XtyhXbkFgawQABoGPUWXg3DqK9bA0DoqWSDgpx8l5wlZYHWWeJWTr4rEJUBQINitQEAMIPy4TW6sSQpMTZK9oiyX+P2iDAlxkYFojIAaFB+r/MKAAiA8mu8Hph5bZXg0LJxqfS8AggphFcAMIMqtoZtleAgtAIIKQFtG5g6dapOPfVUxcXF6aijjtKQIUP0yy+/+FxjGIbS09PVsmVLORwOpaamatOmTQGqGAACxFlx5hUAQlG9hdczzzxTDkf1swErV67U7bffrrVr1yozM1MlJSVKS0tTfn6+95pp06Zp+vTpmjVrltatW6fk5GT1799f+/btq+bOAGAxPj2vrPMKIHTVOLzecMMN+vLLL6t8PScnR/369fN+vmjRIrVo0aLaey5ZskTDhw/XCSecoG7duikjI0Pbt2/X+vXrJZXNus6cOVMPPPCALrnkEnXp0kVz5sxRQUGB5s6dW9PSAcD8Kul5BYBQVOOe14yMDM2dO1f/+te/NGLEiAqvu1wurVy58oiK2bt3r6Sy7WglacuWLcrKylJaWpr3Grvdrr59+2r16tW65ZZbKtzD6XTK6XR6P8/LK/uFX1xcrOLi4iOq71Ce+9X1fVH/GDtzCuVxCyvMVfiB45LwGBkm+xmE8tiZGeNmTmYcN39q9euBrXvvvVe33HKLNm7cqBkzZigsrO66DgzD0NixY3XGGWeoS5cukqSsrCxJUlJSks+1SUlJ2rZtW6X3mTp1qiZPnlzh/NKlSxUTE1Nn9ZaXmZlZL/dF/WPszCkUx63Ln9/puAPHqzdsUs5/zbmmayiOnRUwbuZkpnErKCio8bV+hdfbb79d/fr10z/+8Q9t2rRJb7/9tneW9EiNGjVK3333nT7//PMKr9lsNp/PDcOocM5jwoQJGjt2rPfzvLw8tW7dWmlpaYqPr9s+seLiYmVmZqp///6KjIys03ujfjF25hTK4xb+0cfSX2XHvVPTpKM6BbYgP4Xy2JkZ42ZOZhw3z1/Ka8LvpbL69u2rr776ShdffLFOPfVUvf/++96Z0tq644479MEHH2jVqlU6+uijveeTk5Mllc3Alu+fzc7OrjAb62G322W32yucj4yMrLcBrM97o34xduYUkuNWvN97GNmoiWTS7z8kx84CGDdzMtO4+VNnrf7u36ZNG33xxRc67bTT1Lt3b82fP782t5FhGBo1apTmz5+vZcuWqV27dj6vt2vXTsnJyT7T3p7e2j59+tTqPQHAlHhgCwAk+THzeuif6R0Oh95880098cQTuvLKK3XjjTf6/ea333675s6dq/fff19xcXHeHtfGjRvL4XDIZrNp9OjRmjJlilJSUpSSkqIpU6YoJiZGV199td/vBwCmVX6prCjCK4DQVePwahhGpefHjx+vbt261SpMPv/885Kk1NRUn/MZGRkaPny4pLKHxAoLCzVy5Ejl5OSoZ8+eWrp0qeLi+OUNIIR4NimIipPq8GFZADAbv5bKaty4caWvnXfeefryyy/15ptv+vXmVQXi8mw2m9LT05Wenu7XvQHAUjwzr2xQACDE1fj/vg8bNqzCg1BffPGFd03VlJQUPfTQQ3VbHQCgjKfnlX5XACHuiP72NHDgQO3YsaOuagEAVMZdKhUf2Dab8AogxB1ReK3Jn/0BAEfIWX6lAdoGAIQ2uv4BINiVX2mAmVcAIe6IwuuLL75Y5WYBAIA6Uj688sAWgBDn9w5b5bHWKgA0gCLaBgDAg7YBAAh2Pm0DhFcAoe2IZl4BAA3AWfXWsDtyC5WT71JibJRaJTgauDAAaHiEVwAIduXDa7me1x25her35Ao5S9yyR4Rp2bhUAiwAy6NtAACCXfme16hG3sOcfJecJW5JkrPErZx8V0NXBgANjvAKAMGuitUGEmOjZI8o+zVujwhTYmxUQ1cGAA2OtgEACHY+D2w19h62SnBo2bhUel4BhBTCKwAEu2oe2GqV4CC0AggptA0AQLBjhy0A8CK8AkCwq2K1AQAIRYRXAAh2ntUGbGFSZExgawGAACO8AkCw87QN2OMkmy2wtQBAgBFeASDYecNr4+qvA4AQQHgFgGBXfuYVAEIc4RUAgllpsVRSWHZMeAUAwisABLUqdtcCgFBFeAWAYFbNBgUAEIoIrwAQzIoIrwBQHuEVAIIZu2sBgA/CKwAEM5/wylJZAEB4BYBgRs8rAPggvAJAMCO8AoAPwisABDOWygIAH4RXAAhmrDYAAD4iAl0AAKAa1aw2sCO3UDn5LiXGRqlVgqOBCwOAwCC8AkAwq2K1gR25her35Ao5S9yyR4Rp2bhUAiyAkEDbAAAEM5/w2sh7mJPvkrPEXXZJiVs5+a6GrgwAAoLwCgDBzGe1gYMPbCXGRskeUfYr3B4RpsTYqIauDAACgrYBAAhmnvAaFiFFHmwLaJXg0LJxqfS8Agg5hFcACGaetgF7nGSz+bzUKsFBaAUQcmgbAIBgVj68AgAIrwAQ1DzrvNrZoAAAJMIrAASvEqdU6iw7JrwCgCTCKwAEL+f+g8e0DQCAJMIrAAQv596Dx4RXAJBEeAWA4FXN1rAAEKoIrwAQrMqH12h6XgFAIrwCQPBi5hUAKiC8AkCwKqp8a1gACGWEVwAIVs7y4ZWZVwCQ2B4WAIKXT9uA78zrjtxC5eS7lBgbxRaxAEIK4RUAglUVPa87cgvV78kVcpa4ZY8I07JxqQRYACGDtgEACFZVtA3k5LvkLHGXXVLiVk6+q6ErA4CAIbwCQLCqom0gMTZK9oiyX9/2iDAlxkY1dGUAEDC0DQBAsKpinddWCQ4tG5dKzyuAkER4BYBgVT68RjXyealVgoPQCiAk0TYAAMHK0/MaFiFFElQBQCK8AkDw8sy82uMkmy2wtQBAkCC8AkCwKh9eAQCSCK8AELw828OyNSwAeBFeASAYlTilUmfZMTOvAOBFeAWAYOTcf/CYmVcA8CK8AkAwqmJ3LQAIdYRXAAhGPrtrEV4BwIPwCgDBiPAKAJUivAJAMPIJr/S8AoAH4RUAghEzrwBQqYhAFwAAqEQ1D2ztyC1UTr5LibFRapXAtrEAQgvhFQCCURUzrztyC9XvyRVylrhljwjTsnGpBFgAIYW2AQAIRlXMvObku+QscZddUuJWTr6roSsDgIAivAJAMKriga3E2CjZI8p+ddsjwpQYG9XQlQFAQNE2AADBqIq2gVYJDi0bl0rPK4CQRXgFgGBUzWoDrRIchFYAIYu2AQAIRuV7XqNZ5xUAPAivABCMPDOvtjApMiawtQBAECG8AkAw8oRXe5xkswW2FgAIIoRXAAhG3vBKywAAlEd4BYBgVH7mFQDgRXgFgGBTWiIVF5QdE14BwAfhFQCCjavqZbIAINQRXgEg2BRVvjUsAIDwCgDBp5oNCgAg1LHDFgAEG5/w6rvawI7cQraGBRDSCK8AEGyqCK87cgvV78kVcpa4ZY8I07JxqQRYACGHtgEACDbOyntec/Jdcpa4yy4pcSsn39XQlQFAwBFeASDYVNHzmhgbJXtE2a9te0SYEmOjGroyAAg42gYAINhUEV5bJTi0bFwqPa8AQhrhFQCCTTWrDbRKcBBaAYQ02gYAINiwVBYAVInwCgDBppqlsgAg1BFeASDYVLHaAACA8AoAwYe2AQCoEuEVAIJN+fAa1ShwdQBAECK8AkCw8YTXqDgpjF/TAFAevxUBINh4wistAwBQAeEVAIIN4RUAqsQmBQAQTNxuyVUxvO7ILWRnLQAQ4RUAgotr/8HjA+F1R26h+j25Qs4St+wRYVo2LpUACyBk0TYAAMGkkmWycvJdcpa4y14ucSsn3xWIygAgKBBeASCYVLK7VmJslOwRZb+u7RFhSoyNCkRlABAUaBsAgGBSycxrqwSHlo1LpecVAER4BYDgUsXWsK0SHIRWABBtAwAQXHxmXtldCwAORXgFgGBSSc8rAOCggIbXVatWafDgwWrZsqVsNpvee+89n9cNw1B6erpatmwph8Oh1NRUbdq0KTDFAkBDqKTnFQBwUEDDa35+vrp166ZZs2ZV+vq0adM0ffp0zZo1S+vWrVNycrL69++vffv2VXo9AJgeM68AUK2APrA1cOBADRw4sNLXDMPQzJkz9cADD+iSSy6RJM2ZM0dJSUmaO3eubrnlloYsFQAaRhUPbAEAygTtagNbtmxRVlaW0tLSvOfsdrv69u2r1atXVxlenU6nnE6n9/O8vLL/EBQXF6u4uLhOa/Tcr67vi/rH2JlTKIxbeOFe75/EisMdUnGxduYWKqegWIkxkWpp0hUHQmHsrIhxMyczjps/tQZteM3KypIkJSUl+ZxPSkrStm3bqvy6qVOnavLkyRXOL126VDExMXVb5AGZmZn1cl/UP8bOnKw8bqds/a+OPnC8fPXX2qFteuybcJUYNkXYDD3QvVRN7AEt8YhYeeysjHEzJzONW0FBQY2vDdrw6mGz2Xw+NwyjwrnyJkyYoLFjx3o/z8vLU+vWrZWWlqb4+LrtHysuLlZmZqb69++vyMjIOr036hdjZ06hMG7h816TcsuOzz7vQm3KCVfJhrWSpBLDpu49z9AJLc3XCxsKY2dFjJs5mXHcPH8pr4mgDa/JycmSymZgW7Ro4T2fnZ1dYTa2PLvdLru94rREZGRkvQ1gfd4b9YuxMydLj5trv/cwMjZRzd0lskeEyVnilj0iTM0bx5j6e7f02FkY42ZOZho3f+oM2vDarl07JScnKzMzU927d5ckuVwurVy5Uk888USAqwOAeuJZbSAiWgqPVKuESLaGBYByAhpe9+/fr99++837+ZYtW7Rx40Y1adJExxxzjEaPHq0pU6YoJSVFKSkpmjJlimJiYnT11VcHsGoAqEee8MrWsABQqYCG16+//lpnn32293NPr+qwYcM0e/Zs3XvvvSosLNTIkSOVk5Ojnj17aunSpYqLY/kYABblqhheAQAHBTS8pqamyjCMKl+32WxKT09Xenp6wxUFAIFiGAdnXqMaBbYWAAhSAd1hCwBQTkmR5C4pO45uHNhaACBIEV4BIFj4bA1L2wAAVIbwCgDBgvAKAIdFeAWAYOEst0g34RUAKhW067wCQMipZOZ1R24ha7wCQDmEVwAIFoeE1x25her35Arv7lrLxqUSYAGEPNoGACBY+ITXeOXku+QscZe9VOJWTr4rQIUBQPAgvAJAsDhk5jUxNkr2iLJf0/aIMCXGRgWoMAAIHrQNAECwOOSBrVYJDi0bl0rPKwCUQ3gFgGBRfub1wA5brRIchFYAKIe2AQAIFj5tA2wPCwCVIbwCQLBw7j94bGd7WACoDOEVAIIFO2wBwGHR8woAweKQB7bYoAAAKiK8AkCw8My82sK1I1/q9xQbFADAoWgbAIBg4Qmv9jjlFBSzQQEAVILwCgDBwhte49mgAACqQNsAAAQLb3htxAYFAFAFwisABIPSEqmksOz4wEoDbFAAABXRNgAAwcDFMlkAUBOEVwAIBpVsDQsAqIjwCgDBoHx4jY4PXB0AEOToeQWAYOCzu1Y8GxQAQBUIrwAQDMqF1zy3Xf2eZIMCAKgMbQMAEAzKhdd8xbBBAQBUgfAKAMGgXHiNjktggwIAqAJtAwAQDMqF18SEJmxQAABVILwCQDA45IEtNigAgMrRNgAAwcAnvLLOKwBUhfAKAMHAxSYFAFATtA0AQDA4ZJMC1nkFgMoRXgEgGJQLrzuLItRvFuu8AkBlaBsAgGDg3O893FMcxTqvAFAFwisABAPPzGuEQ4lxsazzCgBVoG0AAIKBJ7zaG6lVgoN1XgGgCoRXAAgGntUG7HGSxDqvAFAF2gYAINAMo9zMa1xgawGAIMfMKwAEWkmR5C4pO46KY5ksAKgG4RUAAq3cMlmF4THq9yTLZAFAVWgbAIBAKxdenWGxLJMFANUgvAJAoJULrxEx8SyTBQDVoG0AAAKtXHhtFJfAMlkAUA3CKwAEmuvg7lqyx7FMFgBUg7YBAAi0cjOvue5o/bBjr3bkFgawIAAIXsy8AkCgOfO8h49/+qfmLfmclQYAoArMvAJAoJWbec0pjS47xUoDAFApwisABFr5pbLCYyWx0gAAVIW2AQAINOfBB7amXXO6suO6sNIAAFSB8AoAgVZu5vWops11VPPGASwGAIIbbQMAEGjlHtj6OcdgpQEAqAbhFQACrdzM66Wvfq9+T64gwAJAFQivABBoBzYpcBs2FcjOSgMAUA3CKwAE2oGZ13xFy1AYKw0AQDV4YAsAAu1AeI2JS9BHN5/BSgMAUA3CKwAE2oGlssKj49WlFSsNAEB1aBsAgEByuyVX2cxrQVgMD2oBwGEQXgEgkFwHNyhYv6uYlQYA4DAIrwAQSOXCa74crDQAAIdBeAWAQCq3xut+OVhpAAAOgwe2ACCQyoXXk9sfrbmpvVhpAACqwcwrAARSufC66Nd8Xf3yWnpeAaAahFcACKRy4TXfoOcVAA6H8AoAgVTuga199LwCwGHR8woAgVRu5vWqM0/Qbb1S6XkFgGow8woAAbR3b473eNYXWQGsBADMgfAKAAHkys/1HueW2ul3BYDDILwCQAA5jALvsTMsln5XADgMwisABFAjFXmPH/5Hb/pdAeAwCK8AEECF+3O9x7e8/QtrvALAYRBeASCASgvzvMd7SqLoeQWAwyC8AkAARZXmS5JKjDC5Ixz0vALAYbDOKwAEUNiBTQqMqEZadvvZ9LwCwGEw8woAAbIjt1B7cvZIkrJdzLgCQE0QXgEgQHLyXWqksge09hvR9LsCQA0QXgEgQBId4YqxOSVJ+aLfFQBqgvAKAAFiO9DvKpWFVwDA4RFeASBAtuz4n/d4H20DAFAjhFcACIAduYV6dP6X3s8LbDG0DQBADRBeASAAcvJdinYXeD/veXwblskCgBogvAJAACTGRikhvMj7eeOEJgGsBgDMg/AKAAESe2CZLKlskwIAwOERXgEgAH7J2ieHcbBtYL8RHcBqAMA8CK8A0MB25Bbq1v98rVgdbBtwxCUGsCIAMA/CKwA0sJx8l1ylhnd3LUlqkkjPKwDUBOEVABpYYmyUosLD1Mh2cOZV9LwCQI0QXgEgAAzDUCMd7HmVPS5wxQCAiRBeAaCB/ZK1T8VuQ7HlZ14JrwBQI4RXAGhgf+93SpJPz6vs8QGqBgDMhfAKAA1oR26hHljwvSQpzlY+vNLzCgA1QXgFgAbkWWlAKrdJgS1cimCdVwCoCcIrADQgZ4nbe+xd59UeJ9lsAaoIAMyF8AoADWhvYbH32Ns2wMNaAFBjhFcAaFCG98j7wBbhFQBqjPAKAA2osSNKkhSuUjlsrrKTbFAAADVGeAWABuRpG4j1WSaLmVcAqCnCKwA0oINrvJbfoICZVwCoKcIrADSgnIKyVgGf3bWimHkFgJoivAJAA9mRW6hpS36WJMWp4OALtA0AQI0RXgGggeTku+RZ5tVn5pXwCgA1RngFgAaSGBulyPCyzQgaia1hAaA2TBFe//Wvf6ldu3aKjo7WKaecos8++yzQJQGA31olOHTPgI6SpEa2cuGVpbIAoMaCPry+9dZbGj16tB544AF98803OvPMMzVw4EBt37490KUBgN8SY8rWef3LSNDy0m7andhdatw6wFUBgHkEfXidPn26brjhBt14443q1KmTZs6cqdatW+v5558PdGkA4JcduYXaX1QiSVrhPkkjisfruwFvSR3SAlwZAJhHRKALqI7L5dL69et13333+ZxPS0vT6tWrK/0ap9Mpp9Pp/TwvL0+SVFxcrOLi4kq/prY896vr+6L+MXbmZOZx25lbqLSnv5DT88SWpKhwm45r6jDl9+MvM49dKGPczMmM4+ZPrUEdXnfv3q3S0lIlJSX5nE9KSlJWVlalXzN16lRNnjy5wvmlS5cqJiamXurMzMysl/ui/jF25mTGcftjv+QsOfgrd2j7Eh0bL21cvVwbA1dWgzPj2IFxMyszjVtBQcHhLzogqMOrh81m8/ncMIwK5zwmTJigsWPHej/Py8tT69atlZaWpvj4+Dqtq7i4WJmZmerfv78iIyPr9N6oX4ydOZl53HbmFurZn8pmXu0RYbrxorPVMsER6LIajJnHLpQxbuZkxnHz/KW8JoI6vDZr1kzh4eEVZlmzs7MrzMZ62O122e32CucjIyPrbQDr896oX4ydOZlx3No0j9SycanKyXcpMTZKrUIouJZnxrED42ZWZho3f+oM6ge2oqKidMopp1SY9s7MzFSfPn0CVBUA1E6rBIe6tGocssEVAOpCUM+8StLYsWM1dOhQ9ejRQ71799ZLL72k7du369Zbbw10aQAAAGhgQR9er7jiCv399996+OGHtWvXLnXp0kWLFi1SmzZtAl0aAAAAGljQh1dJGjlypEaOHBnoMgAAABBgQd3zCgAAAJRHeAUAAIBpEF4BAABgGoRXAAAAmAbhFQAAAKZBeAUAAIBpEF4BAABgGoRXAAAAmAbhFQAAAKZBeAUAAIBpEF4BAABgGoRXAAAAmAbhFQAAAKZBeAUAAIBpEF4BAABgGoRXAAAAmAbhFQAAAKZBeAUAAIBpEF4BAABgGoRXAAAAmEZEoAuob4ZhSJLy8vLq/N7FxcUqKChQXl6eIiMj6/z+qD+MnTkxbubF2JkT42ZOZhw3T07z5LbqWD687tu3T5LUunXrAFcCAACA6uzbt0+NGzeu9hqbUZOIa2Jut1s7d+5UXFycbDZbnd47Ly9PrVu31h9//KH4+Pg6vTfqF2NnToybeTF25sS4mZMZx80wDO3bt08tW7ZUWFj1Xa2Wn3kNCwvT0UcfXa/vER8fb5p/HPDF2JkT42ZejJ05MW7mZLZxO9yMqwcPbAEAAMA0CK8AAAAwDcLrEbDb7Zo0aZLsdnugS4GfGDtzYtzMi7EzJ8bNnKw+bpZ/YAsAAADWwcwrAAAATIPwCgAAANMgvAIAAMA0CK8AAAAwDcJrLWzdulU33HCD2rVrJ4fDoeOOO06TJk2Sy+XyuW779u0aPHiwYmNj1axZM915550VrkHDeuyxx9SnTx/FxMQoISGh0msYt+D1r3/9S+3atVN0dLROOeUUffbZZ4EuCeWsWrVKgwcPVsuWLWWz2fTee+/5vG4YhtLT09WyZUs5HA6lpqZq06ZNgSkWXlOnTtWpp56quLg4HXXUURoyZIh++eUXn2sYu+D0/PPPq2vXrt7NCHr37q3Fixd7X7fquBFea+Hnn3+W2+3Wiy++qE2bNmnGjBl64YUXdP/993uvKS0t1fnnn6/8/Hx9/vnnmjdvnt59913dfffdAawcLpdLl19+uW677bZKX2fcgtdbb72l0aNH64EHHtA333yjM888UwMHDtT27dsDXRoOyM/PV7du3TRr1qxKX582bZqmT5+uWbNmad26dUpOTlb//v21b9++Bq4U5a1cuVK333671q5dq8zMTJWUlCgtLU35+fneaxi74HT00Ufr8ccf19dff62vv/5a/fr100UXXeQNqJYdNwN1Ytq0aUa7du28ny9atMgICwszduzY4T335ptvGna73di7d28gSkQ5GRkZRuPGjSucZ9yC12mnnWbceuutPueOP/5447777gtQRaiOJGPBggXez91ut5GcnGw8/vjj3nNFRUVG48aNjRdeeCEAFaIq2dnZhiRj5cqVhmEwdmaTmJhovPLKK5YeN2Ze68jevXvVpEkT7+dr1qxRly5d1LJlS++5AQMGyOl0av369YEoETXAuAUnl8ul9evXKy0tzed8WlqaVq9eHaCq4I8tW7YoKyvLZwztdrv69u3LGAaZvXv3SpL3v2mMnTmUlpZq3rx5ys/PV+/evS09boTXOrB582Y9++yzuvXWW73nsrKylJSU5HNdYmKioqKilJWV1dAlooYYt+C0e/dulZaWVhibpKQkxsUkPOPEGAY3wzA0duxYnXHGGerSpYskxi7Yff/992rUqJHsdrtuvfVWLViwQJ07d7b0uBFey0lPT5fNZqv24+uvv/b5mp07d+q8887T5ZdfrhtvvNHnNZvNVuE9DMOo9DxqrzbjVh3GLXgdOgaMi/kwhsFt1KhR+u677/Tmm29WeI2xC04dO3bUxo0btXbtWt12220aNmyYfvzxR+/rVhy3iEAXEExGjRqlK6+8stpr2rZt6z3euXOnzj77bPXu3VsvvfSSz3XJycn68ssvfc7l5OSouLi4wv8LwpHxd9yqw7gFp2bNmik8PLzCbEF2djbjYhLJycmSymbxWrRo4T3PGAaPO+64Qx988IFWrVqlo48+2nuesQtuUVFRat++vSSpR48eWrdunZ5++mmNHz9ekjXHjZnXcpo1a6bjjz++2o/o6GhJ0o4dO5SamqqTTz5ZGRkZCgvz/VH27t1bP/zwg3bt2uU9t3TpUtntdp1yyikN+n1ZnT/jdjiMW3CKiorSKaecoszMTJ/zmZmZ6tOnT4Cqgj/atWun5ORknzF0uVxauXIlYxhghmFo1KhRmj9/vpYtW6Z27dr5vM7YmYthGHI6nZYeN2Zea2Hnzp1KTU3VMcccoyeffFJ//fWX9zXP/0NNS0tT586dNXToUP3zn//Unj17NG7cON10002Kj48PVOkhb/v27dqzZ4+2b9+u0tJSbdy4UZLUvn17NWrUiHELYmPHjtXQoUPVo0cP7187tm/f7tNrjsDav3+/fvvtN+/nW7Zs0caNG9WkSRMdc8wxGj16tKZMmaKUlBSlpKRoypQpiomJ0dVXXx3AqnH77bdr7ty5ev/99xUXF+f9C0fjxo3lcDhks9kYuyB1//33a+DAgWrdurX27dunefPmacWKFVqyZIm1xy1g6xyYWEZGhiGp0o/ytm3bZpx//vmGw+EwmjRpYowaNcooKioKUNUwDMMYNmxYpeO2fPly7zWMW/B67rnnjDZt2hhRUVHGySef7F3KB8Fh+fLllf7va9iwYYZhlC25NGnSJCM5Odmw2+3GWWedZXz//feBLRpV/vcsIyPDew1jF5yuv/567+/E5s2bG+ecc46xdOlS7+tWHTebYRhGQ4ZlAAAAoLboeQUAAIBpEF4BAABgGoRXAAAAmAbhFQAAAKZBeAUAAIBpEF4BAABgGoRXAAAAmAbhFQAAAKZBeAWAIDZ8+HANGTLksNcNHTpUU6ZMqdV72Gw2vffee7X62upcdtllmj59ep3fF0BoI7wCCGkrVqyQzWar8uPss88OdImH9d1332nhwoW64447fM5v2rRJ//jHP9S8eXPZ7XalpKTowQcfVEFBQYPU9dBDD+mxxx5TXl5eg7wfgNBAeAUQ0vr06aNdu3ZV+HjxxRdls9k0cuRIv+9pGIZKSkrqodrKzZo1S5dffrni4uK859auXauePXvK5XJp4cKF+u9//6spU6Zozpw56t+/v1wuV73X1bVrV7Vt21ZvvPFGvb8XgNBBeAUQ0qKiopScnOzzkZOTo3vuuUf333+/Lr/88sPewzN7+/HHH6tHjx6y2+367LPPZBiGpk2bpmOPPVYOh0PdunXT//3f/3m/rrS0VDfccIPatWsnh8Ohjh076umnn/arfrfbrXfeeUcXXnih95xhGLrhhhvUqVMnzZ8/X6eddpratGmjyy+/XB9++KHWrFmjGTNm+Nxn9+7duvjiixUTE6OUlBR98MEHlX5/3bt3l8PhUL9+/ZSdna3FixerU6dOio+P11VXXVVhVvfCCy/Um2++6df3BADVMgAAXjk5OUaHDh2MwYMHG263u0Zfs3z5ckOS0bVrV2Pp0qXGb7/9Zuzevdu4//77jeOPP95YsmSJsXnzZiMjI8Ow2+3GihUrDMMwDJfLZTz00EPGV199Zfz+++/G66+/bsTExBhvvfWW997Dhg0zLrrooirf+5tvvjEkGVlZWd5zGzZsMCQZc+fOrfRr+vfvb3Tr1s37uSTj6KOPNubOnWv8+uuvxp133mk0atTI+Pvvv32+v169ehmff/65sWHDBqN9+/ZG3759jbS0NGPDhg3GqlWrjKZNmxqPP/64z3stWrTIsNvtRlFRUY1+lgBwOIRXADigtLTUGDhwoNGpUydj7969Nf46T7h77733vOf2799vREdHG6tXr/a59oYbbjCuuuqqKu81cuRI49JLL/V+frjwumDBAiM8PNwnaM+bN8+QZHzzzTeVfs2dd95pOBwO7+eSjIkTJ/rUbrPZjMWLF/t8f5988on3mqlTpxqSjM2bN3vP3XLLLcaAAQN83uvbb781JBlbt26t8nsAAH9EBGjCFwCCzv333681a9boq6++Unx8vN9f36NHD+/xjz/+qKKiIvXv39/nGpfLpe7du3s/f+GFF/TKK69o27ZtKiwslMvl0kknnVTj9ywsLJTdbpfNZqvx1xiGUeH6rl27eo9jY2MVFxen7OzsKq9JSkpSTEyMjj32WJ9zX331lc/XOBwOSWqwh8QAWB/hFQAkvfXWW3ryySe1cOFCpaSk1OoesbGx3mO32y1JWrhwoVq1auVznd1ulyS9/fbbGjNmjJ566in17t1bcXFx+uc//6kvv/yyxu/ZrFkzFRQUyOVyKSoqSpLUoUMHSWUBurIg/PPPP1f4HiMjI30+t9ls3u+hsmtsNluNvmbPnj2SpObNm9f4ewKA6hBeAYS8jRs36vrrr9fjjz+uAQMG1Mk9O3fuLLvdru3bt6tv376VXvPZZ5+pT58+PisabN682a/38YTT8kH1pJNO0vHHH68ZM2boyiuvVFjYwWdzv/32W33yySeaOnWqf99QLf3www86+uij1axZswZ5PwDWR3gFENJ2796tIUOGKDU1Vddee62ysrJ8Xg8PD6/VrGFcXJzGjRunMWPGyO1264wzzlBeXp5Wr16tRo0aadiwYWrfvr1ee+01ffzxx2rXrp3+85//aN26dWrXrl2N36d58+Y6+eST9fnnn3vDq81m0yuvvKK0tDRdeumlmjBhgpKTk/Xll1/q7rvvVu/evTV69Gi/v6fa+Oyzz5SWltYg7wUgNBBeAYS0hQsXatu2bdq2bZtatGhR4fU2bdpo69attbr3I488oqOOOkpTp07V77//roSEBJ188sm6//77JUm33nqrNm7cqCuuuEI2m01XXXWVRo4cqcWLF/v1PjfffLNmz56tUaNGec+dfvrpWrt2rSZPnqxBgwYpLy9PxxxzjIYNG6YJEyZ4WxfqU1FRkRYsWKCPP/643t8LQOiwGYZhBLoIAEDtFRUVqWPHjpo3b5569+4d6HK8nnvuOb3//vtaunRpoEsBYCFsUgAAJhcdHa3XXntNu3fvDnQpPiIjI/Xss88GugwAFsPMKwAcxq233qrXX3+90teuvfZavfDCCw1cEQCELsIrABxGdna28vLyKn0tPj5eRx11VANXBAChi/AKAAAA06DnFQAAAKZBeAUAAIBpEF4BAABgGoRXAAAAmAbhFQAAAKZBeAUAAIBpEF4BAABgGv8PHWSao7lBl4QAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Nyquist Plot\n",
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "ax.plot(Z_exp.real, -Z_exp.imag, 's', markersize=2, label='Experimental Data')\n",
    "ax.plot(Z_fit.real, -Z_fit.imag, '-', linewidth=2, label='Fitted Model')\n",
    "ax.set_xlabel('Z_real (Ohm)')\n",
    "ax.set_ylabel('-Z_imaginary (Ohm)')\n",
    "ax.set_title('Nyquist Plot')\n",
    "ax.legend()\n",
    "ax.axis('equal') # Important for Nyquist plots\n",
    "#ax.set_xlim(left=0,   right=popt[0]+popt[1])\n",
    "#ax.set_ylim(bottom=0, top=popt[0]+popt[1])\n",
    "ax.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "d03517e4-53a4-4196-9382-31e0f9b9898f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bode Plots\n",
    "plt.figure(figsize=(10, 6))\n",
    "    \n",
    "# Magnitude\n",
    "ax1 = plt.subplot(2, 1, 1)\n",
    "plt.loglog(freq_data, np.sqrt(Z_exp.real**2 + Z_exp.imag**2), \n",
    "           'o', markersize=5, label='Experimental |Z|')\n",
    "plt.loglog(freq_data, np.sqrt(Z_fit.real**2 + Z_fit.imag**2), \n",
    "           '-', linewidth=2, label='Fitted |Z|')\n",
    "plt.ylabel('|Z| (Ohm)')\n",
    "plt.legend()\n",
    "plt.grid(True, which=\"both\", ls=\"-\")\n",
    "plt.title('Bode Plot')\n",
    "\n",
    "# Phase\n",
    "ax2 = plt.subplot(2, 1, 2, sharex=ax1)\n",
    "phase_exp = np.arctan2(-Z_exp.imag, Z_exp.real) * 180 / np.pi\n",
    "phase_fit = np.arctan2(-Z_fit.imag, Z_fit.real) * 180 / np.pi\n",
    "plt.semilogx(freq_data, phase_exp, \n",
    "             'o', markersize=5, label='Experimental Phase')\n",
    "plt.semilogx(freq_data, phase_fit, \n",
    "             '-', linewidth=2, label='Fitted Phase')\n",
    "plt.xlabel('Frequency (Hz)')\n",
    "plt.ylabel('Phase (deg)')\n",
    "plt.legend()\n",
    "plt.grid(True, which=\"both\", ls=\"-\")\n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "882538cf-b7c6-4956-bf25-cf047ceabc86",
   "metadata": {},
   "source": [
    "--- Optimization and Best Practices ---\n",
    "1.  Model Selection: Choose an equivalent circuit that accurately represents your electrochemical system.\n",
    "    Start simple and add complexity (e.g., CPE instead of C, Warburg, inductors) if justified by the data and system knowledge.\n",
    "2.  Initial Guesses (p0): Crucial for convergence and finding the correct solution.\n",
    "    - Estimate from Nyquist plot features (e.g., R_s from high-freq intercept, R_ct from semicircle diameter).\n",
    "    - Use values from literature for similar systems.\n",
    "    - Perform a rough manual fit or a grid search for initial estimates.\n",
    "3.  Parameter Bounds: Constrain parameters to physically meaningful ranges.\n",
    "    This prevents the optimizer from exploring unrealistic solutions and can speed up convergence.\n",
    "4.  Data Quality & Weighting:\n",
    "    - Ensure your EIS data is clean and free of significant artifacts.\n",
    "    - If some data points are more reliable than others, use the 'sigma' argument in curve_fit to provide weights (inverse of variance).\n",
    "    - Logarithmic spacing of frequencies is common and often appropriate.\n",
    "5.  Function to Fit (model_func):\n",
    "    - Ensure it correctly calculates the complex impedance for the chosen model.\n",
    "    - The output format (concatenated real and imaginary parts) is required by curve_fit when fitting complex numbers this way.\n",
    "6.  Solver Options (curve_fit arguments):\n",
    "    - `maxfev`: Increase if the fit terminates prematurely (max function evaluations reached).\n",
    "    - `ftol`, `xtol`, `gtol`: Tolerance parameters for convergence. Adjust if needed, but default values are often fine.\n",
    "    - `method`: `curve_fit` uses 'lm' (Levenberg-Marquardt) by default, which is usually good for these problems. 'trf' (Trust Region Reflective) and 'dogbox' are alternatives, especially if bounds are used.\n",
    "7.  Complex Numbers: `curve_fit` doesn't directly handle complex numbers. The common workaround is to fit real and imaginary parts simultaneously by concatenating them into a single array, as done here.\n",
    "    Alternatively, you could fit the magnitude and phase, or fit real and imaginary parts separately (less ideal as it uncouples them).\n",
    "8.  Global vs. Local Minima: `curve_fit` (and 'lm') can get stuck in local minima.\n",
    "    - Try different initial guesses.\n",
    "    - Consider global optimization algorithms (e.g., `scipy.optimize.basinhopping`, `scipy.optimize.differential_evolution`) if local minima are a persistent issue, though they are computationally more expensive.\n",
    "9.  Alternative Libraries: For more advanced EIS analysis, specialized libraries like `impedance.py` exist. They offer more built-in models and fitting routines tailored for EIS.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "93325d10-ab5b-48d4-8b36-515657c8fae4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:.conda-EIS]",
   "language": "python",
   "name": "conda-env-.conda-EIS-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}