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"source": [
"# Fractional Differencing\n",
"\n",
"**Docker image**: `ml4t`\n",
"\n",
"This notebook demonstrates **fractional differentiation** (FFD), a technique that\n",
"achieves stationarity while preserving as much memory as possible.\n",
"\n",
"**Learning Objectives**:\n",
"- Understand the memory-stationarity tradeoff controlled by $d \\in (0, 1)$\n",
"- Compute FFD weights and apply fractional differencing via ml4t-engineer\n",
"- Select $d$ by asset class using bounded grids (no in-sample search)\n",
"- Validate stationarity with ADF and quantify sample loss\n",
"\n",
"**Book Reference**: Chapter 9, Section 9.1 (Diagnostics and Stationarity Features)\n",
"\n",
"**Prerequisites**: `01_visual_diagnostics` for stationarity testing concepts."
]
},
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"\"\"\"Fractional Differencing — achieve stationarity while preserving memory.\"\"\"\n",
"\n",
"import warnings\n",
"from typing import Any, cast\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import plotly.graph_objects as go\n",
"import polars as pl\n",
"from IPython.display import display\n",
"from plotly.subplots import make_subplots\n",
"from statsmodels.tsa.stattools import adfuller\n",
"\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n",
"from ml4t.engineer.features.fdiff import (\n",
" fdiff_diagnostics,\n",
" ffdiff,\n",
" find_optimal_d,\n",
" get_ffd_weights,\n",
")\n",
"\n",
"from data import load_etfs"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "08d7f8ab",
"metadata": {
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"tags": [
"parameters"
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"outputs": [],
"source": [
"# Production defaults — Papermill injects overrides for CI\n",
"START_DATE = \"2015-01-01\"\n",
"END_DATE = \"2024-01-01\""
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0a8dc7be",
"metadata": {
"execution": {
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"source": [
"# Load data\n",
"all_etfs = load_etfs()"
]
},
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"source": [
"## 1. Load Data"
]
},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SPY: 2264 days\n"
]
}
],
"source": [
"def load_etf_data(symbol: str, start: str = START_DATE, end: str = END_DATE) -> pl.DataFrame:\n",
" \"\"\"Load ETF data from cached parquet.\"\"\"\n",
" df = (\n",
" all_etfs.filter(pl.col(\"symbol\") == symbol)\n",
" .filter(pl.col(\"timestamp\") >= pl.lit(start).str.to_date())\n",
" .filter(pl.col(\"timestamp\") <= pl.lit(end).str.to_date())\n",
" .sort(\"timestamp\")\n",
" )\n",
" return df\n",
"\n",
"\n",
"# Load SPY for demonstration\n",
"spy = load_etf_data(\"SPY\")\n",
"print(f\"SPY: {len(spy)} days\")"
]
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"source": [
"## 2. Bounded d Grid (Default Workflow)\n",
"\n",
"Rather than searching for \"optimal d\", use **fixed grids by asset class**.\n",
"This is simpler, more robust, and avoids overfitting to in-sample data.\n",
"\n",
"### Recommended d Values by Asset Class\n",
"\n",
"| Asset Class | Recommended d | Rationale |\n",
"|-------------|---------------|-----------|\n",
"| **US Equities** | 0.4 | Moderate persistence |\n",
"| **Fixed Income** | 0.5 | High persistence (rates) |\n",
"| **Crypto** | 0.5-0.6 | Strong trending |\n",
"| **Commodities** | 0.4 | Similar to equities |\n",
"| **FX** | 0.3-0.4 | Mean-reverting tendency |\n",
"\n",
"These are starting points. The exact value matters less than being consistent\n",
"and avoiding lookahead from searching on the full sample."
]
},
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"name": "stdout",
"output_type": "stream",
"text": [
"Asset Class d Recommendations:\n",
" equities : d = 0.4\n",
" fixed_income : d = 0.5\n",
" crypto : d = 0.5\n",
" commodities : d = 0.4\n",
" fx : d = 0.35\n"
]
}
],
"source": [
"# Asset class d recommendations\n",
"ASSET_CLASS_D = {\n",
" \"equities\": 0.4,\n",
" \"fixed_income\": 0.5,\n",
" \"crypto\": 0.5,\n",
" \"commodities\": 0.4,\n",
" \"fx\": 0.35,\n",
"}\n",
"\n",
"# For teaching: small fixed grid (not search)\n",
"TEACHING_D_GRID = [0.3, 0.4, 0.5, 0.6]\n",
"\n",
"print(\"Asset Class d Recommendations:\")\n",
"for asset, d in ASSET_CLASS_D.items():\n",
" print(f\" {asset:15s}: d = {d}\")"
]
},
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"source": [
"## 3. FFD with Validity Mask and Sample Loss\n",
"\n",
"The standard output format includes:\n",
"- **transformed**: The FFD series\n",
"- **valid**: Boolean mask (True where FFD is computable)\n",
"- **sample_loss**: Number of observations lost to warmup"
]
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"source": [
"def ffd_with_diagnostics(\n",
" series: pl.Series, d: float, threshold: float = 1e-5\n",
") -> dict[str, pl.Series | int | float]:\n",
" \"\"\"\n",
" Apply FFD and return transformed series with validity mask and diagnostics.\n",
"\n",
" Parameters\n",
" ----------\n",
" series : pl.Series\n",
" Input series (typically log prices)\n",
" d : float\n",
" Differentiation order\n",
" threshold : float\n",
" Weight cutoff threshold\n",
"\n",
" Returns\n",
" -------\n",
" dict with:\n",
" - transformed: FFD series\n",
" - valid: Boolean mask\n",
" - sample_loss: Number of NaN observations\n",
" - d: The d value used\n",
" - n_weights: Number of FFD weights\n",
" \"\"\"\n",
" # Get weights to determine warmup period\n",
" weights = get_ffd_weights(d, threshold=threshold)\n",
" n_weights = len(weights)\n",
"\n",
" # Apply FFD\n",
" ffd_series = ffdiff(series, d=d, threshold=threshold)\n",
"\n",
" # Create validity mask\n",
" arr = ffd_series.to_numpy()\n",
" valid = ~np.isnan(arr)\n",
"\n",
" # Count sample loss\n",
" sample_loss = np.sum(~valid)\n",
"\n",
" return {\n",
" \"transformed\": ffd_series,\n",
" \"valid\": pl.Series(\"valid\", valid),\n",
" \"sample_loss\": sample_loss,\n",
" \"d\": d,\n",
" \"n_weights\": n_weights,\n",
" }"
]
},
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"name": "stdout",
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"text": [
"FFD Results (d=0.4):\n",
" Total observations: 2264\n",
" Valid observations: 2264\n",
" Sample loss: 0 (0.0%)\n",
" FFD weights used: 1458\n"
]
}
],
"source": [
"# Apply FFD to SPY log prices with recommended d for equities\n",
"log_prices = spy[\"close\"].log()\n",
"d_equity = ASSET_CLASS_D[\"equities\"]\n",
"\n",
"ffd_result = ffd_with_diagnostics(log_prices, d=d_equity)\n",
"ffd_valid = cast(pl.Series, ffd_result[\"valid\"])\n",
"ffd_transformed = cast(pl.Series, ffd_result[\"transformed\"])\n",
"\n",
"print(f\"FFD Results (d={d_equity}):\")\n",
"print(f\" Total observations: {len(log_prices)}\")\n",
"print(f\" Valid observations: {ffd_valid.sum()}\")\n",
"print(\n",
" f\" Sample loss: {ffd_result['sample_loss']} ({100 * ffd_result['sample_loss'] / len(log_prices):.1f}%)\"\n",
")\n",
"print(f\" FFD weights used: {ffd_result['n_weights']}\")"
]
},
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"source": [
"## 4. Compare d Values from Grid\n",
"\n",
"Show how different d values affect stationarity and memory preservation."
]
},
{
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" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>d</th>\n",
" <th>sample_loss</th>\n",
" <th>adf_pval</th>\n",
" <th>stationary</th>\n",
" <th>corr_with_orig</th>\n",
" <th>n_weights</th>\n",
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" <th>0</th>\n",
" <td>0.3</td>\n",
" <td>0</td>\n",
" <td>1.177846e-19</td>\n",
" <td>True</td>\n",
" <td>-0.524725</td>\n",
" <td>2275</td>\n",
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" <tr>\n",
" <th>1</th>\n",
" <td>0.4</td>\n",
" <td>0</td>\n",
" <td>8.328753e-19</td>\n",
" <td>True</td>\n",
" <td>-0.418547</td>\n",
" <td>1458</td>\n",
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" <td>True</td>\n",
" <td>-0.282273</td>\n",
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" <th>3</th>\n",
" <td>0.6</td>\n",
" <td>0</td>\n",
" <td>2.528302e-18</td>\n",
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" <td>-0.174915</td>\n",
" <td>590</td>\n",
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" d sample_loss adf_pval stationary corr_with_orig n_weights\n",
"0 0.3 0 1.177846e-19 True -0.524725 2275\n",
"1 0.4 0 8.328753e-19 True -0.418547 1458\n",
"2 0.5 0 2.804332e-21 True -0.282273 927\n",
"3 0.6 0 2.528302e-18 True -0.174915 590"
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"source": [
"# Apply grid of d values\n",
"grid_results = {}\n",
"\n",
"for d in TEACHING_D_GRID:\n",
" result = ffd_with_diagnostics(log_prices, d=d)\n",
" transformed = cast(pl.Series, result[\"transformed\"])\n",
" valid = cast(pl.Series, result[\"valid\"])\n",
"\n",
" # Quick stationarity check (for display only)\n",
" clean = transformed.drop_nulls().to_numpy()\n",
" if len(clean) > 50:\n",
" adf_stat, adf_pval, _, _, _, _ = adfuller(clean, autolag=\"AIC\")\n",
"\n",
" # Correlation with original (memory preserved)\n",
" valid_mask = valid.to_numpy()\n",
" orig = log_prices.to_numpy()[valid_mask]\n",
" ffd = transformed.to_numpy()[valid_mask]\n",
" corr = np.corrcoef(orig, ffd)[0, 1]\n",
"\n",
" grid_results[d] = {\n",
" \"sample_loss\": result[\"sample_loss\"],\n",
" \"adf_pval\": adf_pval,\n",
" \"correlation\": corr,\n",
" \"n_weights\": result[\"n_weights\"],\n",
" }\n",
"\n",
"grid_df = pd.DataFrame(\n",
" [\n",
" {\n",
" \"d\": d,\n",
" \"sample_loss\": res[\"sample_loss\"],\n",
" \"adf_pval\": res[\"adf_pval\"],\n",
" \"stationary\": res[\"adf_pval\"] < 0.05,\n",
" \"corr_with_orig\": res[\"correlation\"],\n",
" \"n_weights\": res[\"n_weights\"],\n",
" }\n",
" for d, res in grid_results.items()\n",
" ]\n",
")\n",
"display(grid_df)"
]
},
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"source": [
"## 5. Visualize FFD Weights\n",
"\n",
"FFD weights determine how much memory is preserved. Lower d = longer memory."
]
},
{
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",
"dtype": "f8"
}
},
{
"marker": {
"size": 4
},
"mode": "lines+markers",
"name": "d=0.5",
"type": "scatter",
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}
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"
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Weight Counts (threshold=1e-5):\n",
" d=0.3: 2275 weights\n",
" d=0.4: 1458 weights\n",
" d=0.5: 927 weights\n",
" d=0.6: 590 weights\n"
]
}
],
"source": [
"# Visualize weights for different d values\n",
"fig = go.Figure()\n",
"\n",
"for d in TEACHING_D_GRID:\n",
" weights = get_ffd_weights(d, threshold=1e-5)\n",
" fig.add_trace(\n",
" go.Scatter(\n",
" x=list(range(len(weights))),\n",
" y=weights,\n",
" mode=\"lines+markers\",\n",
" name=f\"d={d}\",\n",
" marker=dict(size=4),\n",
" )\n",
" )\n",
"\n",
"fig.update_layout(\n",
" height=400,\n",
" title=\"FFD Weights by d Value\",\n",
" xaxis_title=\"Lag (k)\",\n",
" yaxis_title=\"Weight (w_k)\",\n",
" # Cap x-axis at the first 100 lags — beyond that, weights decay below the\n",
" # 1e-5 threshold and the curves crawl along zero, compressing the visible\n",
" # decay structure near k=0 where the differences across d live.\n",
" xaxis=dict(range=[0, 100]),\n",
")\n",
"fig.show()\n",
"\n",
"# Weight counts\n",
"print(\"\\nWeight Counts (threshold=1e-5):\")\n",
"for d in TEACHING_D_GRID:\n",
" weights = get_ffd_weights(d, threshold=1e-5)\n",
" print(f\" d={d}: {len(weights)} weights\")"
]
},
{
"cell_type": "markdown",
"id": "30134307",
"metadata": {
"papermill": {
"duration": 0.002693,
"end_time": "2026-06-13T03:34:08.692925+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:08.690232+00:00",
"status": "completed"
}
},
"source": [
"## 6. Feature Engineering Output Format\n",
"\n",
"Standard format for downstream ML: transformed series + validity mask."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "e8aa11c2",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-13T03:34:08.698918Z",
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"start_time": "2026-06-13T03:34:08.695547+00:00",
"status": "completed"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Feature Engineering Output (d=0.4):\n",
" Total rows: 2264\n",
" Valid rows: 2264\n",
" Sample loss: 0 observations\n",
"\n"
]
}
],
"source": [
"# Create feature table with FFD at recommended d\n",
"spy_features = spy.select([\"timestamp\", \"close\"]).with_columns(\n",
" [\n",
" pl.col(\"close\").log().alias(\"log_close\"),\n",
" pl.col(\"close\").pct_change().alias(\"return_1d\"),\n",
" ]\n",
")\n",
"\n",
"# Add FFD with recommended d\n",
"d_use = ASSET_CLASS_D[\"equities\"]\n",
"ffd_result = ffd_with_diagnostics(spy_features[\"log_close\"], d=d_use)\n",
"ffd_transformed = cast(pl.Series, ffd_result[\"transformed\"])\n",
"ffd_valid = cast(pl.Series, ffd_result[\"valid\"])\n",
"\n",
"spy_features = spy_features.with_columns(\n",
" [\n",
" ffd_transformed.alias(f\"ffd_{d_use}\"),\n",
" ffd_valid.alias(\"ffd_valid\"),\n",
" ]\n",
")\n",
"\n",
"# Show sample loss prominently\n",
"print(f\"Feature Engineering Output (d={d_use}):\")\n",
"print(f\" Total rows: {spy_features.height}\")\n",
"print(f\" Valid rows: {ffd_valid.sum()}\")\n",
"print(f\" Sample loss: {ffd_result['sample_loss']} observations\")\n",
"print()"
]
},
{
"cell_type": "markdown",
"id": "6a833525",
"metadata": {
"papermill": {
"duration": 0.002663,
"end_time": "2026-06-13T03:34:08.712289+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:08.709626+00:00",
"status": "completed"
}
},
"source": [
"The feature table below shows the last 10 valid rows. Note the `ffd_valid`\n",
"column — downstream ML pipelines should filter on this mask to exclude the\n",
"warmup period where FFD weights require more history than is available."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "aaeaed48",
"metadata": {
"execution": {
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"exception": false,
"start_time": "2026-06-13T03:34:08.714960+00:00",
"status": "completed"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Feature Table (valid rows):\n"
]
},
{
"data": {
"text/html": [
"<div><style>\n",
".dataframe > thead > tr,\n",
".dataframe > tbody > tr {\n",
" text-align: right;\n",
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"</style>\n",
"<small>shape: (10, 6)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>timestamp</th><th>close</th><th>log_close</th><th>return_1d</th><th>ffd_0.4</th><th>ffd_valid</th></tr><tr><td>date</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>bool</td></tr></thead><tbody><tr><td>2023-12-15</td><td>456.760101</td><td>6.124158</td><td>-0.001647</td><td>0.251733</td><td>true</td></tr><tr><td>2023-12-18</td><td>459.329468</td><td>6.129768</td><td>0.005625</td><td>0.256018</td><td>true</td></tr><tr><td>2023-12-19</td><td>462.122559</td><td>6.13583</td><td>0.006081</td><td>0.258665</td><td>true</td></tr><tr><td>2023-12-20</td><td>455.718842</td><td>6.121876</td><td>-0.013857</td><td>0.240667</td><td>true</td></tr><tr><td>2023-12-21</td><td>460.039886</td><td>6.131313</td><td>0.009482</td><td>0.253813</td><td>true</td></tr><tr><td>2023-12-22</td><td>460.964417</td><td>6.133321</td><td>0.00201</td><td>0.252426</td><td>true</td></tr><tr><td>2023-12-26</td><td>462.910828</td><td>6.137534</td><td>0.004222</td><td>0.254589</td><td>true</td></tr><tr><td>2023-12-27</td><td>463.747833</td><td>6.139341</td><td>0.001808</td><td>0.253614</td><td>true</td></tr><tr><td>2023-12-28</td><td>463.923004</td><td>6.139719</td><td>0.000378</td><td>0.251948</td><td>true</td></tr><tr><td>2023-12-29</td><td>462.579987</td><td>6.136819</td><td>-0.002895</td><td>0.247742</td><td>true</td></tr></tbody></table></div>"
],
"text/plain": [
"shape: (10, 6)\n",
"┌────────────┬────────────┬───────────┬───────────┬──────────┬───────────┐\n",
"│ timestamp ┆ close ┆ log_close ┆ return_1d ┆ ffd_0.4 ┆ ffd_valid │\n",
"│ --- ┆ --- ┆ --- ┆ --- ┆ --- ┆ --- │\n",
"│ date ┆ f64 ┆ f64 ┆ f64 ┆ f64 ┆ bool │\n",
"╞════════════╪════════════╪═══════════╪═══════════╪══════════╪═══════════╡\n",
"│ 2023-12-15 ┆ 456.760101 ┆ 6.124158 ┆ -0.001647 ┆ 0.251733 ┆ true │\n",
"│ 2023-12-18 ┆ 459.329468 ┆ 6.129768 ┆ 0.005625 ┆ 0.256018 ┆ true │\n",
"│ 2023-12-19 ┆ 462.122559 ┆ 6.13583 ┆ 0.006081 ┆ 0.258665 ┆ true │\n",
"│ 2023-12-20 ┆ 455.718842 ┆ 6.121876 ┆ -0.013857 ┆ 0.240667 ┆ true │\n",
"│ 2023-12-21 ┆ 460.039886 ┆ 6.131313 ┆ 0.009482 ┆ 0.253813 ┆ true │\n",
"│ 2023-12-22 ┆ 460.964417 ┆ 6.133321 ┆ 0.00201 ┆ 0.252426 ┆ true │\n",
"│ 2023-12-26 ┆ 462.910828 ┆ 6.137534 ┆ 0.004222 ┆ 0.254589 ┆ true │\n",
"│ 2023-12-27 ┆ 463.747833 ┆ 6.139341 ┆ 0.001808 ┆ 0.253614 ┆ true │\n",
"│ 2023-12-28 ┆ 463.923004 ┆ 6.139719 ┆ 0.000378 ┆ 0.251948 ┆ true │\n",
"│ 2023-12-29 ┆ 462.579987 ┆ 6.136819 ┆ -0.002895 ┆ 0.247742 ┆ true │\n",
"└────────────┴────────────┴───────────┴───────────┴──────────┴───────────┘"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"print(\"Feature Table (valid rows):\")\n",
"spy_features.filter(pl.col(\"ffd_valid\")).tail(10)"
]
},
{
"cell_type": "markdown",
"id": "15827d16",
"metadata": {
"papermill": {
"duration": 0.0051,
"end_time": "2026-06-13T03:34:08.732804+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:08.727704+00:00",
"status": "completed"
}
},
"source": [
"## 7. Multi-Asset Application\n",
"\n",
"Apply fixed d values by asset class (no search)."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "eab0612b",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-13T03:34:08.739986Z",
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"status": "completed"
}
},
"outputs": [],
"source": [
"# ETF symbols with asset class mapping\n",
"ETF_ASSETS = {\n",
" \"SPY\": \"equities\",\n",
" \"QQQ\": \"equities\",\n",
" \"IWM\": \"equities\",\n",
" \"TLT\": \"fixed_income\",\n",
" \"GLD\": \"commodities\",\n",
" \"EFA\": \"equities\",\n",
" \"EEM\": \"equities\",\n",
"}\n",
"\n",
"etf_ffd_results = {}\n",
"\n",
"for symbol, asset_class in ETF_ASSETS.items():\n",
" data = load_etf_data(symbol)\n",
" if data.height < 100:\n",
" continue\n",
"\n",
" d = ASSET_CLASS_D[asset_class]\n",
" log_prices = data[\"close\"].log()\n",
" result = ffd_with_diagnostics(log_prices, d=d)\n",
"\n",
" # Quick stationarity verification\n",
" clean = cast(pl.Series, result[\"transformed\"]).drop_nulls().to_numpy()\n",
" if len(clean) > 50:\n",
" _, adf_pval, _, _, _, _ = adfuller(clean, autolag=\"AIC\")\n",
"\n",
" etf_ffd_results[symbol] = {\n",
" \"asset_class\": asset_class,\n",
" \"d\": d,\n",
" \"sample_loss\": result[\"sample_loss\"],\n",
" \"sample_loss_pct\": 100 * result[\"sample_loss\"] / data.height,\n",
" \"adf_pval\": adf_pval,\n",
" \"stationary\": adf_pval < 0.05,\n",
" }"
]
},
{
"cell_type": "markdown",
"id": "84c15fe8",
"metadata": {
"papermill": {
"duration": 0.005308,
"end_time": "2026-06-13T03:34:08.993288+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:08.987980+00:00",
"status": "completed"
}
},
"source": [
"When building a mixed-portfolio feature set, different asset classes will have\n",
"different optimal d values. This is acceptable — each security's FFD features\n",
"use its own d, and the ML model learns from the resulting feature distributions.\n",
"Consistency within each security over time matters more than uniformity across\n",
"securities."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "990aa232",
"metadata": {
"execution": {
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"status": "completed"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>symbol</th>\n",
" <th>asset_class</th>\n",
" <th>d</th>\n",
" <th>sample_loss</th>\n",
" <th>sample_loss_pct</th>\n",
" <th>adf_pval</th>\n",
" <th>stationary</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>SPY</td>\n",
" <td>equities</td>\n",
" <td>0.4</td>\n",
" <td>0</td>\n",
" <td>0.0</td>\n",
" <td>8.328753e-19</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>QQQ</td>\n",
" <td>equities</td>\n",
" <td>0.4</td>\n",
" <td>0</td>\n",
" <td>0.0</td>\n",
" <td>8.064936e-19</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>IWM</td>\n",
" <td>equities</td>\n",
" <td>0.4</td>\n",
" <td>0</td>\n",
" <td>0.0</td>\n",
" <td>2.070530e-16</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>TLT</td>\n",
" <td>fixed_income</td>\n",
" <td>0.5</td>\n",
" <td>0</td>\n",
" <td>0.0</td>\n",
" <td>2.849230e-10</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>GLD</td>\n",
" <td>commodities</td>\n",
" <td>0.4</td>\n",
" <td>0</td>\n",
" <td>0.0</td>\n",
" <td>2.851341e-11</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>EFA</td>\n",
" <td>equities</td>\n",
" <td>0.4</td>\n",
" <td>0</td>\n",
" <td>0.0</td>\n",
" <td>8.457089e-15</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>EEM</td>\n",
" <td>equities</td>\n",
" <td>0.4</td>\n",
" <td>0</td>\n",
" <td>0.0</td>\n",
" <td>1.543391e-16</td>\n",
" <td>True</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" symbol asset_class d sample_loss sample_loss_pct adf_pval \\\n",
"0 SPY equities 0.4 0 0.0 8.328753e-19 \n",
"1 QQQ equities 0.4 0 0.0 8.064936e-19 \n",
"2 IWM equities 0.4 0 0.0 2.070530e-16 \n",
"3 TLT fixed_income 0.5 0 0.0 2.849230e-10 \n",
"4 GLD commodities 0.4 0 0.0 2.851341e-11 \n",
"5 EFA equities 0.4 0 0.0 8.457089e-15 \n",
"6 EEM equities 0.4 0 0.0 1.543391e-16 \n",
"\n",
" stationary \n",
"0 True \n",
"1 True \n",
"2 True \n",
"3 True \n",
"4 True \n",
"5 True \n",
"6 True "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"multi_df = pd.DataFrame([{\"symbol\": sym, **res} for sym, res in etf_ffd_results.items()])\n",
"display(multi_df)"
]
},
{
"cell_type": "markdown",
"id": "89aed446",
"metadata": {
"papermill": {
"duration": 0.005305,
"end_time": "2026-06-13T03:34:09.020701+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.015396+00:00",
"status": "completed"
}
},
"source": [
"## 8. Visualize FFD Transformation"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "94fd52b7",
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"status": "completed"
}
},
"outputs": [
{
"data": {
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"config": {
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"data": [
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"name": "Log Price",
"type": "scatter",
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Kw9bviP+n2FRlMRp4KR1X8cL5XKCtF3iHTFgo0nR5K+QpXjpzoE/g3fzZXvQcPM3nN5O8lvQi5A0MKUykXa+xbi88gQDvolWfipANil2lGO189+cWnmXyHJPXcM74t0T/AgHeQOZ7IOPSArx0zbT5azDzg/UiSwrZgGyhBl4C+ycb+s4qIkNKtHh41cCrtotWTSj0p3K9LuLFmF6QlUUNvDQG+j79/uc5ZM1ypwhtoRjyejUqc/yutX/vuPesACuQjhUwHfDWf7Ufzpy7iC/Xvec3hlf+2FHYAqUvUxb6YaZMAuSNpY1n3oBXbhxSA68nMPQGvLKNAW+8gqb1nxYp1b75/qhInfZA3pyubo2csggfrf40JMBL3k8CEQm8z73SB3dmjsOSGU44lMVI4P3l+CmQvZQQoRd45UY5CmmRmwCV/ad4zkL5naEc3jy8cl7Q5riSJQp6/Ho/XLSA8Nx5A8Pd+34UMcBKD79W4CU7kDcxX95cmDext1uGi0Zt+oPiUvUAr5b5Hsi4tAIv5cYmLy/FYMuVBDXw0ma1pxp1F5sw1Zso5X3oBZTgPxjgVdtF6zOAYrQJxFs1reUWg0198nTwxLWkFBGWQYBNG9corpfa+GBKX9f8S8e/Gzx0VoAVYAUsp4DpgJc2Bs1Z/LHYtEUbebwVip09/NMJ4VklsFEfBtBnxPvYuG2335AGI4B3+YYdoLhFWiqtULoYard4S3iCZFyrHEM4gZfidI+dPI0dKye6ZYUwEnhJ43WffCnSVdFhFFT0Ai/ldaUMGMo2vc0Bb8ArPe60uYwAx1cJBAy795+C/x057haDLdtWxvDSkj+l7KLYaXVeXjXwUhYK8sZ7mu/qGF45Li3zPZBxaQVeuo4OgqEYVhk/rgZeiqmt8GxHlC9dDNNGvuFTe19j19p/rZpkzBiDsrU6iE2p6lhyLSet7TtwFC27jxSHa1D4BhdWgBVgBVgBaylgOuClDVi04YgyIdAPpnojF53uNHLKh2jz4rMifRed9EQ5Yle8P8R1AAJtcCIPJ8VekoeOSqg8vBSb26zjYPx99ZqIO6VsAJRqipZDP1k8xuWlPPbbaXR/Z7JIUxWKkAa1h1f+iL83orvISEGFNs7N+GCd8GjpydJAabtosx8BGb2UyFRcRgAvpWEj+1coUwwzRvUQespCMbCUaowyHFDxBrzkYa3V/E2Rioy87Mo0UhRjuvvbH1G5rDObhVawomuHTlgoNm/R6sOdd8S7fdOVwEsZGR6t1V7oTrHhshAsvjl0hvCQSg8veU2faNDVlb1A2agaeGlcWud7IOMKBHjV16qBlz6neHaKa1dvDqPPCFDJw0veUl9j19r/QDSh1HL7//eziDeXGxEpcwPZhDzHMksDpVIrXijRbcNdUvJ1AfIUojSwR0trPeW5t6wAK8AKsAIwHfCSTeg0NdrcQjBJG3woVpAAmDxClAuVgIJiU8nLRGm3aHNRgQfyoHa1CiItGZ1QRT9Qi6f1d2VYMAp4KbXUo48UFtBF/aA0X7TcSSERNf7bIEVp0d55d44AcvL4nvsvHViM3SZyvIYDeCkOsW7LPkIH6hcto3+170ec/P2MCH0IBHgp92jGDBnEpit6mSBgJFihDXoj+7ZH7H/5h40AXmpDwvr99+YU6aOyJ2TBsd/+FFo//VgZF2D72vBHdurSZ4JI8fZs9UqgzBa03E4wQ+AvcxtrBSvq16dffAvy8pL9KTXV73+eF2nmKBuEOktD35HvY+2WL0WoDaXMo+X7vfsPI0OGDCjzUCEX8FK75PU9/vsZtGxSU7wgURovysXrKS2Z1vkeyLiMBl7KktK80xCR/ovmCH0PaNPbnu8Oi/y7yrzC3sYeSP+1akJx+QS9tOGOPL30PaCXEPoe0/dSAi+F1ZDt6lSrKOLvb9y4hc079uLwTydFSMMjETjmmX+rWAFWgBVgBfQpYErgpSGdPnsB85ZuEpkGKB2Q3WYTeUCfKP8wGj37pCu/Ll1LKbhmLHQ/eOL1dk1cy650jVHASwcKEMRQ7s4r//yLIgXuF8vW6hji+cs248MVn+DSlasomJhXHDhBOVjDFcNLY6a+0sYpGnvmuFgBaZQ7lTxwythUX8CzbP0O18cEY/ck3C02qTWo+bg4Wlhd9IY0yPa2fr4PtPGLPLqUL5k2epUrXUzkdS3y4P3iMl/AS5/TQSQETt98fwT/XL2GnNkTROhFg1pPuA5/CASsqE3auEWHlhDwU58oT68n4KU8yZRtYuvOfUh1OERe3c4t62PQuPluMbzUJsVCD524ED8ePY5MGTOidfM64oAKbwdPaJnvgY7L0xxQZmnwNkc8eXjpWnq5oI2jBJTn/qKsDneK72yNKuWEl1QeGuNt7IH2X4sm1C+aV5NnrxT5d+/NfQ9ealwDFy//LVITSuCl7w2lpNv97SGcO39JbFyjeUMhKg8XK6Dvicu1WQFWgBVgBSKigGmBNyJq+Lmpt01rZuyrtz7JDAar5gx1gaOV+s99ZQVYAVaAFWAFWAFWIFAFGHgDUMxqwEvLyMpMB7SU36XvRPxw+FdQuictJ9kFIA9fygqwAqwAK8AKsAKsgCkVYOANwCxWA966r/QRO+ppKZkOh9j1DaVY+tXtGNgAhs+XsgKsACvACrACrAArYEkFGHgDMJvVgJeOcqUYaIqnpBho2jxFOXPr1XgsgFHzpawAK8AKsAKsACvAClhbAQZea9uPe88KsAKsACvACrACrAAr4EcBBl6eIqwAK8AKsAKsACvACrACUa0AA29Um5cHxwqwAqwAK8AKsAKsACvAwMtzgBVgBVgBVoAVYAVYAVYgqhVg4I1q8/LgWAFWgBVgBVgBVoAVYAUYeHkOsAKsACvACrACrAArwApEtQIMvFFtXh4cK8AKsAKsACvACrACrAADL88BVoAVYAVYAVaAFWAFWIGoVoCBN6rNy4NjBVgBVoAVYAVYAVaAFWDg5TnACrACrAArwAqwAqwAKxDVCjDwRrV5eXCsACvACrACrAArwAqwAgy8PAdYAVaAFWAFWAFWgBVgBaJaAQbeqDYvD44VYAVYAVaAFWAFWAFWgIGX5wArwAqwAqwAK8AKsAKsQFQrwMAb1eblwbECrAArwAqwAqwAK8AKMPDyHGAFWAFWgBVgBVgBVoAViGoFGHij2rw8OFaAFWAFWAFWgBVgBVgBBl6eA6wAK8AKsAKsACvACrACUa0AA29Um5cHxwqwAqwAK8AKsAKsACvAwMtzgBVgBVgBVoAVYAVYAVYgqhVg4I1q8/LgWAFWgBVgBVgBVoAVYAUYeHkOsAKsACvACrACrAArwApEtQIMvFFtXh4cK8AKsAKsACvACrACrAADL88BVoAVYAVYAVaAFWAFWIGoVoCBN6rNy4NjBVgBVoAVYAVYAVaAFWDg5TnACrACrAArwAqwAqwAKxDVCjDwRrV5eXCsACvACrACrAArwAqwAgy8PAdYAVaAFWAFWAFWgBVgBaJaAQbeqDYvD44VYAVYAVaAFWAFWAFWgIGX5wAroEGBhcu34N2pi7Ft+XjkzpFNQ43QXHLkl9/QuO0AV+MZM8QgT657ULfGY2jZpCbuyBzn98bVm/ZE9mxZsGR6Wjt+Kxlwweipi/HRmm2YObonKpQu5rVFOcYZ7/bEExUe1nXnP06fx+hpi/H1d4dx8+YtFC+ciJ4dX0CpEgV1tWu1ynu+O4QfDv2K9i/VDarr3uqv3vQF3nl3DoywVVAdM6jS31evoWW3EciUMSM+fK8fMmbMYFDL3AwrwAqYRQEGXrNYgvthagXMBrwtGj2DRx8pjH+vJeHg4WNYsXEnihXKh0VT+4Mg2FeZ/dFGAcbNG1QLm+af7zmATm9PwOj+HfFstYo+72sU8F5LSka9ln2RMWNGtH3xWcTFZcKSNdtx6KcTWPH+YOR/IE/Yxh/pG02avRIfrNiCfZtnBdUVb/V/PHoCW3bsRaM6TyLx/txBtW2WSucvXEb9Vv1Qt0Zl9Onawizd4n6wAqyAQQow8BokJDcT3QqYDXhH9W0vfphlmb5wLd6bu9qUnrZbt1JR/9V+yHdfLkwd8brfiWIU8C5atRUjJi/CugUj8GC+e8V9CYKrNemBak88imG92/jtS7RcECrgjRZ95DhWffw5Bo2bj3XzR1ge4KPNNjweVkCvAgy8ehXk+ulCAa3A+9W+/wnwPPzLb4jNlBGVy5ZAjw4v4L48Odx0+vSLbzF5ziqc/P0McmTPisfKPYQVG3b6BVYJg2rg/e7gT3i56wgM6tUKTZ6rgibtByFv7uxoUOtxTFuwBkd/+R31aj6GoW+1RrNOQ5AjWxZMGd7d1SfyEk+Zuwrf//gLbDYbCibmRb0aldG0/tPimhs3b+H9D9dj3Sdf4cz5i8iVPQFPP14GXVo1wJ13xPucA+QB7DFoGlbOHoKiBR+47dqVGz/HvKWbQOEHeXLeg4eL5sfGbXv8auFv4nXpOxEn/ziLDQtHul3arf9k4RX/bMVEf03c9jkBc7naHdGuxXNITrkuvJt//3MNJYokYmCPlngwMa9bnQ9XbsXiNdtw6vR5JGS9C7WrVkDXNo0RH5dJXLfjq+9B/RzZt53476/2/Qi7zYYnKjyCd15/GXfdmVlTH385fsplP+pj3tw5UL50MRG+MWPhOsz6cL1bO3a7DQe3zxN/e2voDGH3vy5eQYYMMbj/3px4sWF1NH72SfE5wbK3+l98fRAde4+7zbb+xh2Ijv76p9RxwaQ+2LT9a2zesRdXryYJDQlgPYVc0Pflxo0bWDJjoEsbh8OBZ5r2RMVHS6SrFyJNk4wvYgUsrgADr8UNyN0PjwJagJd+/Dv3GY8nK5ZE3Wcq499ryaDwAfpxXzVnKO5JuFt0dvmGHRg0dj5qPFVWXHstKQWffrEPe/cf8Qt53oD3o9XbMHzSB5g99k1UKltCAO+J388gQ4wdzz1TCTmzJ4jYY/IKq4H3m++PoF2vMXioaAE0qVtFhDtQCMKuvQexffkE0eeu/SaJ9lo3ryNg6o/T5zB13hoUL5KIKcO6+TQCAcvPx//A6rnDbrtu/tLNGDN9CZ6qVBJVKpdGSsp1AX4UM6qElNRUB27cvOnzPjYAmTJldF3z7Mtv495c2fH+2F5u9Sa+vwLvL9oglvcleGqdRRLU6KWAtKpf8zEkJ1/HyPcWwZHqwJp5w0EwSYXuQ/Z/qfEzKFeyKI7/fhozP1iPR4oXEHaiNiTwkuYUX0svSMd+O42hExaiztMVMLBnK79du3zlKp57pQ8KF7gPzRtWEy9aBw79imXrPhOa37hxU7xcEZzPHvfmf+3ZUObhQuK/ew6ehsIF7hega7NBaE8vX2MHdELtpyvg9NkLXut7Al4t4w5ER3/9UwJv5vg4FC+cD5UeLYHrN26geYPqaN5pMIoWzIf3RqS94NF8bPDqO1C/OEq70fg/Xz3ZZUu/RuALWAFWwPQKMPCa3kTcQTMooAV46QdUxIkqNoORN7TWi28J6OnVsSn+uXoNNZr1wlOVS4kfW1m0LuPL6wiEalUtj3//TRJwOn7WchR58H6Qh0vAWPtB4gefwCrHPVndJFQDL22CIyhaNXcoMsSkxf/+eeYv3Js7OwhquvefLDbsJWS5y9XWZ1/tx2t9J2HnqkliE5y3UvX519Gg1hPo3rax2yWkxdNN3sBj5R7GxCGv+dRiy45v0GPQVJ9TgTzNX2+c7rrmqUbdxea0SUO7utUjbyV5LcnDmzO7uzb+5poEtdfbPS+8vLKs/+QrvD1iFjYtehcP5M0lvKUUOvFKk5rCyyqLHMf0UW+Ilx0JvB9N64+SxR90Xdd/9Fzs2vuDywtN3uQLl/52696dmeOR5e47hP0pPpo8leQdlyUp+ToyZowRNg00pIHmRN482TF5qPNlxlt9NfBqHbdWHb3ZQ90/qWPfbi+hRaPqt9mbVi8+WTIOeXI6N5wOmbAQW3d+I17o1BvUvjv4M+J5hLsAACAASURBVF7uOhxr5g1Dofz3+ZsS/DkrwApYRAEGXosYirsZWQX8Ae/Fy//giQZdBdy0blbHrbOvvjFKeHuXzRzkApz5E99GuVJFfUKepxGrszTIa6o9UQaDer6KbFmdQCpDGpQgKa9VAu+lK//g8fpdoQY45b0pDpbiYW/bue4gr+stfDCln8tbqO4zLRE/Uq01Rrzdzi3mmK6TkDJn3Fuo+Ghxn1pc+ftfnPjjjM9JEBNjx0NF0oCPgPfRR4pg/KDObvXIyzp5zkrsWDnxtpcBf7NMgpoarPYdOIqW3UeKF46yJYsIbyqFcaghlOKZS9doi5efr4E3OzVzaaCGq2kL1mLqvNX4ccd80SWplbJ/tOmQluwpbIO82Y8UK4AWjZ8R4KwOofEFvL+dOosPV36K73/8GbRxi+Yq/Y9sQrYJBHi1jlurjnRvLf2T+niCVHpRqNbkDbE60a1NYzG2Ko27CxvQv9VFfidoZaBy2Yf8TQn+nBVgBSyiAAOvRQzF3YysAv6Al5ah677SB8PfbiviZpWFlmR/OHwMW5eMBW2KIe/dpkWj8UDenEEDL3kXKe43LjaT8CiSp09ZtALv8d9Oi+VwT/2W7fUaMh0U9jBv4tsejUBxt95CA67+m4QKz3YSYQ8U86ssgWgRbEgDbZSbNvINt/vKkIZvNs1E5vjYgCaWN1CjEIIXOw/FvAlvo3zpoli6drvTi7hkrPCSK8uTDbuJGF3S3BuoUcgF9VMCL0EbxR0rC0FtwfzOmOFtX3wnYrXphYgKea5fbVpbeJh9AevRX39Hiy5DcUfmeLEKQaENWbPciZFTFuGO+DjMGR8Y8Godt1YdtfbPF/DS+Cms5uv9h/HpsvFYvn4HRr23CFuXjEOuHAm32T/l+g2UqdEO4wZ2FqsoXFgBViA6FGDgjQ478ihCrIA/4JUeXtqg1qa5u4e31etOD+/yWYMgwwDovyknrCyBhjR4ij0MBnhlv315eCmedOm6z7D34+mgGMlAivTwjuzbHs9Vr+RWdefuA+jcZ8JtG548aRFMSANtBjt28k/xcqEsXd9xblojD2+gRSuouTyd0wfg4WIFXLdxeXgb18Cbnb17eNXAq7Wf5Ak/eOSYiMHd+vk+yJUE8mjTHFanJRs8fgE2bP1KwB+Brixtejg1k8Drrb46pEHruLXqqLV//oBXhilQXPL0BWtRMP99t3n+5djld4I9vFpnHV/HClhDAQZea9iJexlhBfwBL3WPUm9R4vplMweKOFoqFAdb56XeeOn5GiKGlzIR1Gz+pohnVR4CQBuFCDL8JfD3tmlNLY9WDy/Vq9eqn6i+es5QUFiALBR/TBvdKKNE9/5TRH/VcbjkIaaDL8jT7K1QDC9ljujcqoHbJafPXUSNZj3x9msvgvIKy3LwyHE06zjYTYtgQhooUwB5KtfOG+7yhBJoPU1pyR4vIzysgRatoEaxrBSfTOPq3aW56zaUfYK8jeoYXvVSfCDASzomZLnTzQb0t+ov9HB57mlz4NgZS297aek78n3s/f4IPl06zk2KFl2GifYk8Hqr7ymGV8u4teqotX/+gJcG16hNfxDMUtjGwsl9RR5rT0WGp3AMb6DfDr6eFTC3Agy85rYP984kCkjgfatLc9ytShUVmykT6lSrAPJYkleRQg0oGwJtKJu9+GOReYCyNMiNXRTi8Onn3+Kl558RO+Mpef/6rV+JjWN0Ctnj5b2fLhYK4JX9pg1elIoqPi5WLP9+8fUPAoQonIBST335zf/EuGg5nsrufT8K7+BnKye6bWZTm4wA77c/z3k82a338Jn4fPcBUEwsLc/v/98vmLFwrdig5Q/+/U0NCqeo16qvADc6eCI21nnwxI9Hj2P5+4NduXmpnX6jZmPN5l1+9dcKatTm+JnLMGfxx+KAD4rXppcDAlnK0jB3fG+3LA16gJe8ue/NWy3uQxkKxAbEj7/Atz8cFVkjaNl+//9+xkuvDRde9meeKotTZ/4SJ/Nt/myvyNJAseeUJePcX5dEZgmybcUyxV3A662+pywNWsatVUet/dMCvMvW78DgcfPF5k76PnordCIgpd/jLA3+vmH8OStgLQUYeK1lL+5thBSQwOvp9hQ/+9U6ZwYBSuU1df4aHP75pEgPRemRCCYIbGWh7AS0EWzbrm/FcbelHy6EOk9XxIAxc7Fo6js+j70NBfBSv/Z8ewh0eAWdQkbeaYrlbFj7CVcuVoKo+cs2Y/3W3WITEUEknaxFntJWTWv7PN1NLnNTPlz16WYU6jFi8odi+Z1ywD5ctIDIXkB/0wu8NC7q6+ipS7D3e+fRwiWK5EePDk1Q+iFnSi5ZyAt91x2ZsXb+cJd33pOttYIa1aVwjg9WfIIla7fj1Om/RB5eigmljVIydlhrDK+vaf/bqXOY+cE6AbVnzl0UaeXo5eW11o0E3MlCsP3R6k9x6fI/Yj6u/y8/MXlvqZ8Xr/wj4srr1XgM23d95+bhpTY81fcEvFrGHYiOWvqnBXh/PXFKrGYMebO1a16rdaWQE/JQ00tdejqYJEKPVb4tKxBWBRh4wyo334wV8KwAHb4wZPwC7Fo7RfNhA1bRkiCCPK0lCieKo4XNViQIyUM7zNY/7o8xClB4C6WP275igtcQHAL/0dMWY/2CkXzSmjGycyusgGkUYOA1jSm4I+lFAYrjJE/qA/fmxF133oFfTvwBijd9tnolcVpXNBa5QU3GrpppjOS9n/nhemxbNt5nLLKZ+sx9CUwBCm+p+vwbaFq/qoil91R+//OciPNtVOdJ9OnaIrAb8NWsACtgegUYeE1vIu5gtClAGQfem7sKp89dwI0bt0TaqrrPVEK7l+r6DA2wug4UG7l8w07MndDb7YCESI+rY+/xKFYo320b8iLdL76/cQrITXdbFo8RR26rC20ypMMm6CjnRe+9c3vOaeO6wi2xAqxAhBRg4I2Q8HxbVoAVYAVYAVaAFWAFWIHwKMDAGx6d+S6sACvACrACrAArwAqwAhFSgIFXp/B/XkjS2QJXN7sClFI3d0I8Tl9kW5vdVkb37674DIDNhn+u3TC6aW7PpArce088+LluUuOEqFtkcy7RrwADr04b84NRp4AWqM7AawEjhaiLDLwhEtbEzTLwmtg4IeoaA2+IhDVZswy8Og3CwKtTQAtUZ+C1gJFC1EUG3hAJa+JmGXhNbJwQdY2BN0TCmqxZBl6dBmHg1SmgBaoz8FrASCHqIgNviIQ1cbMMvCY2Toi6xsAbImFN1iwDr06DMPDqFNAC1Rl4LWCkEHWRgTdEwpq4WQZeExsnBF07ccKOyo/GhqBlbtJsCjDw6rQIA69OAS1QnYHXAkYKURcZeEMkrImbZeA1sXEM7BqB7sdbbDhz1obZkzIa2DI3ZVYFGHh1WoaBV6eAFqjOwGsBI4Woiwy8IRLWxM0y8JrYOAZ0jUB3+04bTpy0uVpj4DVAWAs0wcCr00gMvDoFtEB1Bl4LGClEXWTgDZGwJm6WgdfExgmia8nJNowYHSNqJuZzuEA3NtaBShVSUawY8GjxuCBa5ipWU4CBV6fFGHh1CmiB6gy8FjBSiLrIwBsiYU3cLAOviY0TRNf2H7Bj9Vq7q6YE3coVgbg4h/g7b1oLQlgLVmHg1Wk0Bl6dAlqgOgOvBYwUoi4y8IZIWBM3y8BrYuME0LWPN9uRLRtA/68sDeunonTJVLe/MfAGIKyFL2Xg1Wk8Bl6dAlqgOgOvBYwUoi4y8IZIWBM3y8BrYuNo7Nrur+3YtCUNdLNmceDyFWfM7hvdbyEhi9OzK0s0AW+9Vv3QpVUD1KxSTqNagV+2Zcc36DFoqqiYOT4WhQvcjzc7N0OpEgW9NlbqmbaYPvINVCpbIvAbGlSDgVenkAy8OgW0QHUGXgsYKURdZOANkbAmbpaB18TG0di14aNjkJLsBNwqT95CgUQb5i60g8IZ+vW+dVsrDLwahf3vMgLeqfNWY/n7g3H13yQsWbMNi1Z9ig0fjEK2rHd5bOzor7/j/ntzIHN85OKlGXgDs/NtVzPw6hTQAtUZeC1gpBB1kYE3RMKauFkGXhMbR0PXLl2xYcKkGJBXt1F9BxITneELp886AThPLnfvLv0tvQDvzt0HMH7WMvx55gKKF86HAT1a4sF89wpd/jzzFwaPX4BvfziKbFnvxvUbN/Haqw3x/HNP3aa6AN75a7Bu/nDXZ0827IZ+3V9GgXx58NJrw9GzwwuYt3QTriWlYOeqSaDPp416Aw8VyY+k5OuYMGs5Ptn5DVJSrqNsySIY8lZrJGS5Cys3fo45izfi8pWrKFmiIAb3ehU5s2fVYHn/lzDw+tfI5xUMvDoFtEB1Bl4LGClEXWTgDZGwJm6WgdfExtHQNUo7Rt7cfA840KbV7d5cT03oAd51m93jgTV0UfclMXbg2RruscmyUW8hDb+dOovn2w3E5KHdUOqhgli5cScWLv8EGxaORExMDJq0H4jKZR9Cm+Z1cOWff0XIQvMG1TQBr8PhwBMNumFUv/bIlSMBDV59Bw1rP4Gm9aoiPi4WBfPndQPeQWPn448z5zGsdxvE2O1Ys3kXalYpj5+P/YFxM5di5uieyJPrHkyYuRy/nz4n+mxEYeDVqSIDr04BLVCdgdcCRgpRFxl4QySsiZtl4DWxcTR0TcbvViyfijq1tMFosMB7/TrQ+c0bGnpl7CWZMgHTxng+LMMb8M5YuA6/njyFMf07uTpTu8VbGNijFbLcfQfa9RorPLExRNMAOr09AdUeL+MXeG/dShUe2Q9XbsWmRaPx59m/hIf3643T3QYtPbzFCubDozXbiXCIQvnvc7umw1vjUKdaRdSv+Zj4+4VLf6NGs174dsssQwRMl8Cbcv0GZn24Hhu27saZcxfRpG4VvPP6yz4FXbvlS8xZ/LGbC58qfHso2eMSiSHW4UZMoQADrynMEJFOMPBGRPaI3pSBN6Ly6745ZWXYs9cuYnefrnJ7+IKnGwQLvNSWVTy8FK5wR+Y49OrY1CVBq9dHCU8seWHnfLQRS2cOdH3mD3h7DZmGu+7MLEIW8t2XCyPebocSRRLx8/E/fAJvznsSUPX51/HNppliw5uy1H2lD/6+eg0ZM2Zw/fmfq9ewffkE0Xe9JV0C72t9J+HmrZt4rXUj3Jc7B5KvX0fuHNk8annur8to2X0ELl25ipzZE24D3rbdb3jc9anXMFzfPAow8JrHFuHuCQNvuBWP/P0YeCNvAz09GD85Bpcv29D6lVRX/K6/9vQAr7+2w/25Lw/vLydOYeyANA9vrRffwqCerWC329F31Pv4dOk4zcA7ec5KzBn/FuJjY4WHWBZ/wCs9vCtnD8GDiXnd5GnTczQa1XkSz1arGBLZ0h3w7vn2EAaNmy/ANVMm7edn7/jqe4yftdwj8DZ/IRXFimpbOgmJFbnRkCrAwBtSeU3dOAOvqc0Tks4x8IZE1rA0+tnnMfhsh01sWOvRXVv8LnUs2oD31aa1UKVyKZfmmTJmxIVLV9C47UBMGvoayjxc2C2G9+atVFRv2gPdWjfC04+Xwbc//IQRkz9EtzaN/YY0qA3rD3hp01qfEe/j4uW/MeTN1oiLy4R1W77EU5VK4eCRY3hv7mq82689Cj94P06d+Qu79h5EyyY1DZk/6Q543526GPsOHIXdZhOud/LavtG+id+cdb6At+pTqaimcenEEKtxI2FVgIA3Z9Y4nL2UHNb78s0ir8Cd8TGAzYar125GvjPcg7AokDtbHM5c5O96WMQO8ibHT9iQPzEtXOHSZRvmLLAJzy6VOjUdqFxRuxOKbB4thTy8v5445Tacpx8rjSnDu4OyNIybuQynz/6F4oUT3bI0kDNwyIQFIm62ctkSOH32Apo3rO6Kp1U26ClLg/xcC/BSKjPqx/Zd34FCTMspsjSs2LATC1d8gj/+PIdsCXfjmSfLoneX5oaYJ90Bb/f+U3Dz1i28/dqLyJU9AVu/+BbvvDsHi6f1R9GCD3gV1RfwFnrQhje7Os/q5hKdCtALUqpDWzxYdCqQPkdlg/MH1AG2fXqZAfxdN7el/7oI9B1yE5XK2fBqC+fv7tJVt7Dtcwfy3mtD80YxKOz9/AOPgyObc3FXoFmnIXi93fOoWKZ41EiT7oD39QHvoWBiXrzWuqHLiM07DxUe3lYv1AoKeGPjHOj3lnP5ZPFSO+hts+pTDg5ziJKvCYc0RIkhgxgGhzQEIZrFq3BIg7kNqDxFrVTJVOHNnTbLLry7nTrcCmoTeTSFNARrPfL+UiowcgR+sfcHjJm2RGRdUG8sC7Z9M9RLd8A7bsYyUD66SUO7uvR/ocMgvNiwOhrUejxg4O3y1nWkpNjExrUrl5ynuVChL2Kj+tqXVMwwGbgPnhVg4E2/M4OBN/3Z3kjgPXzUjuPHgStXgOZN+ffAiNk0bWYMzvx3iISyvUDjdpV1GXgBYqMVG3aIAycK5c+Lt7u28HlUsBG2DHcb6Q54fzl+Cs+3H4hRfduD4lo+/eI7DJu0EOsXjMQ9CXdj9aYv8OU3/3PbyUhG8RbSMHTcdZz8zYaG9VORnAzX+d2BJL0Ot9H5foEpwMAbmF7RdDUDbzRZU9tYjABeOtWLVvtkTCndOZA0Wdp6Gr1XkX7799tw5CdnXC6tohYr4kBcLETKMToiuHWrVCxeYsflK85whEDy7qqVY+CN3rmkHFm6A14a/BdfH8SY6Uvw55nzKFzgfvTt/pI47o7KpNkrsWbzF/hsxUTx79PnLqJx2/64efMWkpJTRN65ejUeEzHAVDZuT8HqtXbxhcyTCzhx0vnlU4Y5pI+pFL2jZOCNXtv6GxkDrz+Fou/zQIGXnvmJ+dJivAnItu2wISXZ+VtAq33fH7Aja1YHenTTnjkg+pTVNqLkZJsrRMFbDeXLw0dL7UhKsqFO7dSgwhnoHgy82mxj9avSJfAaaTQ6aW38pBjXW6aybT1vnEb2kdvSpwADrz79rFybgdfK1guu74EA7/4DduHwoEJhbZs320BhDLLIlb4BQ5yJ9IcM4Gwf/qwyd0FMmuMo1oGe3VORlAIcOWJDUpLzxaJyRSAuzriNpAy8/qwSHZ8z8Oq0IwHvpSs2nDltw+kzDhw/4XzYUZiDfAgmZDHui6mzu1w9CAUYeIMQLUqqMPBGiSEDGEYgwOsGZ3EO4dWl5fb4OAgniHR6SKdIsJuqAui+pS9dtdYuvOGkIaUdy58IVKoQ+thnBl5LTxvNnWfg1SyV5wsJeNWF3vq/228T0Gt1Ly/FUm3abEd8nCPdbrpg4NX5JbFwdQZeCxsvyK5rBV56Nk6f6Z6OMldOB15snooTJ2y4dMmBYsUgltnnzI8Rvwfy9K/tO5wOEa1H36qHQhu3ErI6kJRsQ+1awS/lBymR4dXIaTRvQVrMcyCnpBnRGQZeI1Q0fxsMvDpt5Al4qUn5MKRY3p7dUg1dftHZ5YCqK1PA0JJdevRWM/AGNGWi6mIG3qgyp6bB+ANeijHdvdeOr/ZAeHQpbCF/Yiri421evZEfb7aLzVYUe0oQTKAc7G+DMoxCDojihKtWcbg9n+k3KOW/8zOUMcaaRAjzRXJMlGmhUX2H5iOBjeomA69RSpq7HQZenfbxBrzUrHyrt/LuXPmgpvHUrpkaluUlnSYxvDoDr+GSWqZBBl7LmMqwjvoDXuUzUeaB9RdP6gK6rM7wNpm9QZm+kkDaXztUd/zkGGfmglgHSpd0CJCmotwUR6EBZ87YXOm7wu0xDdQY5PHe8XlMxDJZMPAGajFrXs/Aq9NuvoD3xAm7yMtr5d25EtpJJgrPoCU48m7kz5fqtjNZp4ymrs7Aa2rzhLRzDLwhldeUjfsD3uGjY4Rnt/kLqQEdLqTc3EyhD2fPOcMaKK539x6biF3VEgKn3gAnwgHmO9NzUZ+On3Cm7lIWSptZumToY2GDNag65CPYdoKtF03AqzxamA6NKF+6GAb2aIWc2bP6laf3sJnixNlXm9X2e60VL2Dg1Wk1X8Ar3sb/y+Dg74Ejl8moTtUnnalraElqxw4bihZFRB5WdP+5C+yu9Dq0dJc53uHahZxedhwz8Or8kli4OgOvhY0XZNd9Ae/hI3YsXmYHAWuXjoGlGJMOEAm5lGdW5JT9b7Mb/d1fOksZKqe+vww9I+eKMvevlIBWGQvkB3LnMja7QZAS31ZNvkREKmwu2oC3w8t1Uf2JR3Hh4hUMnfgBUlKuY+6E3n7NxcDrV6L0fYE/4JVLWUWLpOJFHyftyAcpqSlBUvkQC3f+RgJwgl060UZ6I5QPZvnQpg0Z0V4YeKPdwt7Hx8Cb/mxP8HPsVLLH8ALK+XrkqD3o8C7yZBYv5hChYfSMHTfJLk7qpPAEKvLUTm97JSQ0qw82orZGjE7bQEeeYnlAA7UpS+5cDrRuaa49JeShnjApRmjQr3dgLxFGzc5oA94urRqgZpVyQh46TGv2Rxux8YNR4t/n/rqMoRMXYv/BnxEfH4v2Lz2HJs9VwZrNuzBgzFzYbTZkyBAjPMPTRr6BUs+0xbr5w/FA3lyi/uBx85E1y13o3rYxFq36VBzK9WDivdiwdTcqlS2OUiUKYevn+5D/gTzYunMf4mIzYkCPlniyYklRf893h8SxxSd+PyMO+2pa/2m0aV7HKFP6bIc9vDpl9ge83h5Q6tsq48L6vnVLPGxlihYlBOvsrubq8vhGgt02rVLdHqb0YKKHqNnjwjQP1s+FDLxGKWm9dhh4rWezYHtM0Lh6rQ3nzttx4aLT20qne9Wp6RDPYyVUBuuJJLhTwiz9m/LLJiY68PEmu1smB0/j8BXrSr8Xh4/YUKcWxfamghwm1K7MJEEbwpSp0oLVyeh6Wn8jjb6vsj09wJu8fG4ou+a57ZgMiGv0isfPKKSBgPeZJ8vi1Jnz6DPifZQvXRTd2jRGaqoDL3QYJGCYwhb++PM8Xuk2ArPG9BKhDJ48vP6Ad+yMpejcsj6qVC6FuNhM+HzPD5g8ZyW6t30eT1R4GBs+3Y0V63di2/LxuHUrFU806Irhfdri8XIP4/jvZ7DvwFG82LBaWDRk4NUpsz/gpea1JB1Xng8uQVIZPyshWGd3NVVXPtjlfYe/GyMglzzV5CWI5AYDTYMw8CIGXgPFtFhTDLwWM5iO7ipDDpTNyFhdueLmb7Uu2C5Ip4cyjpeexeRVpkIrhHLVzdNGaAp3oOJt1c0MYKnURm6sS05xbuKL5ObuoIE3JRmXX64erMmDrxcbh6wffOoVeH89ccr1WbsWzwlvrM1mww+HfkWvIdPxyZKxrs+HTFiIvLmzCy9rMMC759sfMWV4d1d75PVV/u38hcuo0vh17Ns8S3iOKz7bCV1bN8Lzzz2FO++ID16DIGoy8AYhmrKKFuCVsOgLWiUUU9sSeD39TWd3NVX39GAkTwTlliSPx/4DNmzaYhdHZjaqb96NEJoGq+EiBl4NIkXpJQy81jesOBjojA3xsfCZ7koCbeXydtSqdR1qAJVOCX/7MYJVzNMmZ2WoGzkaZIgZrbppyeig7IvSkWGG/RdKhw71M1S6arFH0MALwKweXvLi9hg0FZeu/IM543rDbrdh82d70Wfk+yKUQJbr12+gUZ0n8Xq750MCvNeSklGudkfs3jANd9+ZGdu/3I8ZC9fi6C+/i1AI8gQ/VckZ7hDqwsCrU2EtwOtvB6ras0Aehdx5HCKuSZZwhA9Ib8LlK843bm87hpUP5tKl0jbZ6ZTStNUZeE1rmpB3jIE35BKH/AYy7pY2dL3aMtVrLnEJuE0bxqDEwymQzzkCTcqd+9kOZ6xtKONMlZucc+d2uG0aJqHo/q1bBX/QxNQZMSI7RKRPfFNuiCbQpUM6SpdGxPK86wHekE/gAG8gQxoIeP++eg2N2vRHg5qP47XWDfHdwZ/xzruz8fGH73pslcIfCubP6xZTS7C6aOo7KFzgPlFHHcPrz8OrBl5542tJKVi8ZhtmL9ogYDgchYFXp8pagFfG4np7g1XG71J36MFctHBafkX6WziWe9Tg7euNW+l9DkffdJpJV3UGXl3yWboyA6+lzSc6r3xWUVxu5YqeX9KlY+LN1zLgrmzOExvk6pxUQUvaMD2KyU3OdFBEcjJceXSNcnzI3yK9OdXJa37lMsU5ew+h8KaD+uAMM3iboxV4yQbf//gLWnUfiemjeqBsqaJo3HYAqj9RBi8/XwM22HDwyDFkzJgBFcsUx6TZK3H455MY078jkpKvi1RmzToORskSBdGiUXXs3X8EE99fgSZ1q7g2rQUCvORNXrh8C16oV1WEUWz8dA/em7camz8aredro7kuA69mqTxfqAV4/SXVlonEKTaMdgB7KuGASuWpatQHXxszpKdAArqnLBIE0OSlCHTpTadJDK/OwGu4pJZpkIHXMqby2FFlGrE8eRwi1y0VAsrWLdMyAihf9iePyojL15xHxss0YBS+Vaak75AII5RSZm4Qz9Ys/x1UccUm/rtHd31ZDOQzPtBwNPkbRr9RdBLauMnOdJXqbBG+NCDtDx+BK62lHJ/eMRmhezQDL+kz68P1+GDFJ1g1Zyhu3LiJMdOXiM1iySk3xGa1Xp2aomTxB3Hm/EW83n8KjvzyG2o8VQ6j+3fEgUO/os+IWbh0+R88WakkkpOvo0A+CkVwZmkIBHgzxNjxzrtzxL2TklNQKP996Nf9ZZQokmiEGf22wcDrVyLfF2gBXvnQ9fRwcIUHZHGgUkWHiI1VPuSoDp3BLh9QdP2Zc0CRIu7HSOoZBnmYKTZMhjJQW1qW7ujhPG2mM+G5p5AL6TEJ9OGqZyyhqMvAGwpVrdEmA6817OStl9KjKR0G9PxctNQmNuBSqAJlYKBCBwRRoWfVa61joeW5HiplZJ9lhpxLV4DDh4GEBJvufOwS4GnsnTtog2cB4f8BrtRIvjj4yxssNZLALP8tM0YEAsyh0pvajSbgDaVOVm+bgVenBbU8oJw6ugAAIABJREFUGJWxYOqHjHy4qXfmUrforHY6n50gWD4Y5PVG7hRWZoiQcmh9EMlwDE9QKz3X1KYZlq2CNTUDb7DKWb8eA6+1bSifQcqYVfXRwHlyw/WMbdQwFSUKxEUUeOXJaZ07BL4xTYu1ZIgHbaL+/gcbHA74PDJ+8VK7m1dWfQ8tz3bp/JCndR4/YRMnwuVPRECn1WkZXzDXMPAGo5r16jDw6rSZFuClW3hLTSZPmPG2iUCdMUE+wLUCqZbhyb5RXFdSUmCbB6THQHkohRyLMnYunGnVtIw5kGsYeANRK7quZeC1rj3ls0kdCkAey8NHKeeu89h3Cm8gj6WMa/V3tHA4FFHn6zXynhI+5alsvlbgZAgErfjRsfLkfJFe3kuXbH7zBst+R/okNX/6MfD6Uyg6Pmfg1WlHrcArNz8o42JlqIO/2CzlG7k8Tcco4DUiVY0ynpfkpPCGLAnhzzKh05ReqzPwhkpZ87fLwGt+G3nroa/VJ6qj3pAmw7LMALyhVF29SdrbbwlBN4WsUayuzEVMGS+Skmxo0SwVq9baxJ4Tf+nEvL14hHKMgbbNwBuoYta8noFXp920Aq8yNRnB4JVLNhw74TzAwd/OXwm89NChc9xl0bKU5G94RiQjV292E+e2J9pccXHUB38PRX/9jOTnDLyRVD+y92bgjaz+wd5dQpZ8AU9MvD1fOL3sS2ij6+QqVLQDr/K4ewJWb3G4Mp2bt/A5f5uxpe2M+I0Jdh5orcfAq1Upa1/HwKvTflqBV75VFyuSimMnbcifz6H5xDKZm1HdVSOAV/nwo5N8ginCEzDDeSY8FVoipOUyubGB/haOLBPB9F1LHQZeLSpF5zUMvNa0q9yX4M+ZQKOjlTaCty4dnZu4oh145XHGlSqkukLtaBMbFco3TKVS+VTXRjVv2Xp8bcZWzppgM0OEc+Yx8IZT7cjdi4FXp/ZagVe9S5XeqnPnhKYYKHpDJk8EZUNQFuWDiB5ilBi9apXAsjdofUv3JxM9/A4fhRvkUh2K/SIQ1vLD4+8ekfqcgTdSykf+vgy8kbdBoD2QzzQKFQtm41e0A69ST3U4mvyMntd79jpXE705Vug3hw5H8pepwajfmEDnQSDXM/AGopZ1r2Xg1Wk7rcArl3UIAKkQBMqNXlpPUSNvLEFtliy3g7Iyj6T0sNJpabVr+T6Vx6hE5DQmWiKkzBKyUIaJuDiIzSFGxRzrNFdQ1Rl4g5ItKiox8JrbjBS6cPKkDfnyOZ+rq9fYQWm8KO5U63NVPcL0BLzK431pFY7SU1KYg9zQ5u+57WlvilpPubqp97CLUM5EBt5Qqmuethl4ddpCK/DSg3nVajtebJ4qoFW53B/og1nGVikfIOpT0pRv6nVqeQ9V8HfssU55XMdz+ntw6r1PKOsz8IZSXXO3zcBrbvuoV85kb/U8b9IT8FK4waHDNhQv5hCpydS/I/5W5rT8fmi5JtKzjIE30hYIz/0ZeHXqrBV4lbeRsU/yb4HG4nqKu5UPfkoxo4RpelP3dAqavHeo08VYYcOCvylgBuAl77nVT6zzp7MZP2fgNaNV0vqkzjggPwnUiaAcZXoCXrV1ZZiC/Ls/r6wyXIEOxtj/vQ2VKjjccusy8Jr7O5SeesfAq9PawQCvMhUY3T5Q4FXWl+lilA8eemuXG8iofV9HBHvLD6xTFld12Vd/cV5G3S8U7UQaeOkFZ/cem+aTkUKhQXptk4HX3JZXwlRsvAMpSTbQ/+f5bxNWML1Pz8BLesnfBC2ZdaTzhcLoqJyg8JIHHGjTKu0Ut1D/xgRjY3WdaPLw1mvVD7+eOOU2xLIli2DikNfweP2ut8nVuWV9vNiouuuzmBg7st59J8qXLoY2zeugWKF8RkhsijYYeDWY4ez5S5g0ewW++PoHXPnnX4x+pyNqVS0vagYDvFRPGTsVKPBSfVdC8Djnxozdu21ikwHFYR0/YReb4fy9pYcrP6IVHni+pkGkgJdeFj7ekhb+4uvFRcM05kuCUICBNwjRwljF00lqem+f3oGXVuUoZWbp0kBCFifIeivK9G/yGuWqYrh+Y4ywud42zFKfgJdAtepjpV1dyhBjR8r1GwJqN380GlnuvtP1WWymjLiWlCw+2758AuLjY3H67AWs3/oVlqzZhinDuqNS2RJmGZ6ufjDw+pGPALdx2wGoWaUcmjxXBXffdQcIgBKy3KULeI1IByZjeSmlTGxs2ka2r76G2HggMyR4y6MYrnADBt7Av6P0Q0EbcGgTiSyU0q5WrcCycAR+Z66hVICB19zzIRTPlvQOvIFaXMYBK50s0oljhZRkNN5o8/B2adVAMIuyXLryj4DaXWunuPhFfu7ts4XLt+DDlVuxZfEY2Ah8LF4YeP0YcPKclTh15i+826+DxyuD9fAaMW/IAzhuknv4AsWu0S7l7/bbkD8xVRxs4S2OV4ZB+NuYoLevcicvxRfHxUIcUamMRyX4p9iv0qUcKF0yuFzAevvoq34kPLxyBSBXTgfyJzpcKYKsnM84lDYKVdsMvKFSVl+7tHROWWgoy4y/kyoDvRMDb6CKOa+n3yM6mY3SZ8rj5aVTRkt4RHB3NaaWHuAdfHqfMZ0IoJWMNjv65i7jsQZ5eI0C3n+vJaN8nY5YNWcoijx4fwA9NOelDLx+7ELe3Rz3ZMHJP87izPlLKFbwAQzq9SoKF7hP1Iwk8NL91Rvg1MvevtLGhCs/ojJ8g/pMHmlKVyYBV/bDmyc60l+dSAIvvcDkzu3A/gM2cY69nt3nkdbRivdn4I2M1WgzWrZsEPm7ZfGWicbo5wYDb/A2l896ubck1Juig++pe81ggfda6k3csf99o7qhuZ077BlwtXQ7r8B76vR5ZMgQ4/p8zdxhiIvLJDy8d2SOc3lr8+S8B2vmDYMv72+52h0xeWjXqAhrYOD1M8Uq1+2CFxtWR4vG1ZEpY0a8N281PtnxDTYteheZMmVEaqrvGCfNMzjIC3//04GhY9I2CMyakMGtpTFTbuHnYw50bp0BSckO/HURqPakDZnjAeVnpR4OsgMaqsn7qC99rqYN9WrFYOnqW9j2uQOFCtjwZte0L6mGpsNziQ2w22xhtXX7N26KsU0ckUHYStr5vnttGPCmCTUKjyXCfhe5jOdwRPZ7HvaBR/iG6mdGfDzQtEEM5i92Puvy5rHh1GmnTV5oEIPqTxm33Gq3h/e7HmGpDb39us23sGGLQ/zGVK5gF79N9yQAIwe4/y4ZelMDGiObB1vM6OF9sWE1PFHhEdeQcuVIwD9XrwngXfH+YBGaSYU2qOXOkc0r8EoP79p5w1Ewf95gJTJNPQZef8BbrwsmDH4NFUo7z1xMSr6OcrU7YNnMgSheOBFnLiVH3JjvDHICEC3t9XrDPSRg22c2fLbTjqpPpYr/p1KnlgOVK6Zi9jy72FXbplWqWDYPZfnuexsOHXbGFstCfapW1eHqB+30bfuqCUMaAOTMGoezl8Nna2nTYYPSXmY8/S2UNuO2gTvjYkBB+1eTnC8gXMKjgJzryrtRnliKCZXPjWEj7UhOMf75lTshzhTP9fAobexdjp+wYc58u1iVypMLYmWqdEkHGjc033NdOXKyebQUI0MaKH53ydrt2LBwZFTIw8Drx4zNOg5G3RqV0aLRM+LKa0kpAni3LhmLe3Nnj3hIA/VJbtzwtNwtQx4IhuXRxPK6UGz48CWnOkm8jEfVm7Ei1N/EcIc0yJ3NFL/bpWMa8I6fFOMWHxfqcXP7AIc06JsF9PzZ/bVNhDFRiEKRIv43Xap39svngzyZUi6X6+uZ99oc0qBPWfm7IluxQnaZYEMa9CkVmtp6gJeyNGSOj8W5vy5h7ZYvsXjNNkwf1QOU1iwaCgOvHysuW78DU+etxszRPfFA3lwiPdmhn07igyl9Rc1Ix/BSH+QPAm0Ka1Tf/U1anUicrpc5ccMNvOoYPNlfBl73Segte4ZMsh/qTYbR8GAzagyhAl5aWaEi85ca1d9ItUMblo4ctYG+08oijy6Xf9Myd9U7+9WHS+g5VEKLPgy8WlTyfo3yee7pN0lf66GpzcDrzOBAhcI7KA9vxUeLo03zZ1G04AOhET0CrTLwahB97pKPRWoOimd5rNxD6NvtJWTPlsV0wOttB7/cuKYcKr11T5gUI1KX9eud5kXUIEfQl6iBV3qaZS5NatiM3oBwe3jlD74aDlyer/9Oz6PsFuS1px8Vf/kygzZaOq8YCuBVHhxjxvmu1eQ0H6nQoSiHj9qQkmyD0vtK45y7wJlajzaWUTiTp1Wozz6PQaXyqSJzC72gUzo+eiGQzzP5fZD9CiZvudYx0XUMvIGodfu1ypU8q8zvaAJefdaL7toMvDrtawYPL/3w0AlDWRI8LxeqsyTQkOnHhFKWhXPXvzfgVS6Bhdp7E4y5ww280ivm6VhPZVjD4qV2kZrJjJoFo7MZ64QCeJXfAwLEw0chjgNXv7AS9GXJ6j/5fyR0U76kKu+vPnFL5mbt+9YtjBjt3Gsg4VdZj0IeihUDPtuRtnlIzmvl4QbqMJ9QjJ2BV5+q9NKyfz9ARw2bMc2kp9Ex8OqzuVVqM/DqtJQZgNffENSxs3Q9/cCQ5yWcwKsOr1DHElO/zAhv4QbeaTNjhG08aaEMa6CT9aiYPcelv/lp5s9DAbxKj6XyZETld1F5DcGiMm91uPSi+NtNn9jQub3T+6os8iWVVohoU1LxosDchWkbUpXXynFNnRGDs+e074ZXegfli56WkAi9+jDw6lXQevUZeK1ns2B6zMAbjGqKOlYAXmWuXvrxUZ6IE+4YK6U31xPwGnGwAoH1lcswzDsWSuClsATnjuY0oPAVWy29XXIDD01FIzTT+TWI2uqhAF7lCyjZkQqFA8jYerIxhQLQ36iEepOW2ngUirB6LYUppL1QJWR19vP4STsuXXIIj7Ta2yoPgciT24bFy9LgV+bJVcfi0uEEH29yXhcf70BSUtphOfQ3ZegCfU/ovuQFVn5XQjHxGHhDoaq522TgNbd9jOodA69OJa0AvMqYQYIjWmpavdb5QxNuWFLv4KUfc+WPY7D9oTFSIU+U/GENti31lAgl8EpvLnncy5R2HhFNtvG1dCu9XbKfRo1T51chKquHAnhliJEyc4oUj7yai5c4417l0eDh8GoqjecpBMqTcX0d+KD8nsv5qT4kx1MsLn2Pz5yxITbe/SUwnJOLgTecapvjXgy85rBDqHvBwKtTYSsALw1RLidKbxFBIZXSpcP7w0I/aLTBRQK39FQS4NFyZzA/7tJjRtDYsEGq8BqRF5s8yHVqp2L6TGfsYLCbXYwEXvI+nzyRtptd/QIgp6Mvz7vaU8bAq/NL7KN6KIBXxr9SyMrGzTa3ZX4ZakQwXLumQ7wM0t86dwjPxlKSQp6ORf1btNSGlBTnyyR9n/LkdoByrdJ31de8U4YvyOuUL97h3Cwb6Oxg4A1UMetfz8BrfRtqGQEDrxaVfFxjFeDVOUzDqytBjzxFlSs4YwCDiSlWe6QkRFNb5DWVcC3Pdw90MEYCr9ywlDUrHf7h9EbTj3+j+g7X5iXqn6cNa7LfBM3z5jszNFAJ5iUhUA3S6/WhAF5lyApB4KUrwOHDEJtIZZFzVV4bzjheZf8olIC+P8oXMJp/VHxlBlF+J5UhGXJ1IpjvebjmIANvuJQ2z30YeM1ji1D2hIFXp7oMvMEJKH9UyZPVuUOqWMbUC7zq+GTqGf1QU7whlWA3dxkJvOoUS9Jz1qaV04NHcZBUqlbxn6DfW75ebxYheDlyBChaFJbZPa11dpGN1Tlgtdb1dZ1RwCszqdBSPa040Lzv0T3Na6vM3KB82ZHgGK44Xk9ziuaklvmo1FG5CqHcfCkzkDDwGjE7uQ2jFGDgNUpJc7fDwKvTPgy8wQlI4Hf8hBPsaBOKzOAgN+4E0qpcgqX4x02bKQG+593iwS79Gwm8EgSUqZl8xUL60iEQ4CVP4rjJzo1QZoaNQOyuvJZeoMhr/vRTDkPB1wjglflo4+Ig+uftxY5iXC9fAegIXVnkC1KwcyRQPWWcrd77KQFeubJCfz92woECiTYkJprzuFn28AY6a6x/PQOv9W2oZQQMvFpU8nENA69OARXVg12+VS7Bqj2o5EkrWsQBSuEVLOgZCbzSY6eM3wwWxAMBXmVmgGB1MM7SxrekDJEJ1pPvqVdGAO9HS+2ulzC54qDV5loPqaAXKdroRoXy9wYbr27khk+an95ygxs/A4xrkYHXOC2t0hIDr1Uspa+fDLz69DPF0cI6h2Ca6koYDMT7owRemfT8+Am7iN+lxOeBgKEnMYwEXrlhibxe5PG7csn7gSH+DKN1XN7yH/tr3yqfK6GQ+qzXO6kctxHAK1cglO36itFW6y7DAHxBsnrzY7DAq5yfoU7/Zdb5xcBrVsuErl8MvKHT1kwtM/DqtAZ7eHUKqKju64Qxij/d/70NpUs5IVYW13G7qphIZa+0gqG3kRgJvL5y7AajpJb2pHdXpsGKNg+vtK/M9EE6GrXJSy/wukJ1Yh2ubAfUv0AOWFFudOzR7fZsDcrxU9uUQSGQ9gP5LgUzR61Wh4HXahbT318GXv0aWqEFBl6dVmLg1SmgoroMR/CUkksuC992/OoJu9/Nbnrig6l7RgGvhHMjj0eVwOtrGV++SMjldIp19QROxlkytC3RPEn+L1UWjYm85DIulg4woBhuo8Ia9AAvvWicOGkXIQb0kpGQ4DywIRggl9kNPG1eU77QUduUki+YTW56XwxDa/Xwtc7AGz6tzXInBl6zWCK0/WDg1akvA69OARXV5Q+up7yjMtxB7Z3U+iOtxRMaag+v3BBkpIdVpo2ivnuDPGWoiDz+Ndglb+OsHXxLctmdWiDgLVMyLaWdTEOnDmugsIfd/x3FXPVJ7TltgwVe5SZB6ie9qJUuDaxabRfg26h+YBu21LHpSltLDz7dgwqlN/MXI0zzhtLakU4ydEHZztNV3I8SDt5a1qvJwGs9m+ntMQOvXgWtUZ+BV6edGHh1Cqiq7g1MvQGvBAF/uWjNALyhAgol9HoCWWUWiwmT9B3CYay1A29NGcIi8xAT3BHkEfzWqenAiNHOMSrDGpSnfAWSj9kf8EovLr2k5c8P5M/nEKf9Sa86hZEkJjoElAcSl65WxlucMo3r9BmHC3Lj423YtMWOxHwO1K6VBrPq9uQJfxKMaRVk82bnccKBxBcHbkHz12DgNb+NjO4hA6/RipqzPQZenXZh4NUpoKq6XLolKElJsuH4bzaQR04Cq9o7qhUih78bI2Iog4ntNCqkwVeMsl4V5clWnmBOCft6wF9vH42oL+1NLzjJKXCFCEgvKnkmZfiL0guqzAvrz/up7Kcv4FV7cWU9So8nXyzov30d0BCIJkovL4WlULl82SbSsdH/U9wuZUWQh5Jo2eRGoE5FZnig/w4m/jeQcZj9WgZes1vI+P4x8BqvqRlbZODVaRUGXp0CqqorYSUhi3OpWh63Ki9VejElyPjzSgWbAYLuaRTw6umDP5U9QR7VUYd8WAF4KYXcocM2kbOWXnjISyo3KspxUoxq1gTnIQ6ySMDzFAuuDIMIJKTEF/DK+1B7+RNTQf+mlyqZY9nX8dD+7Ontc+nh9vS5hGt/qx7qrB3UFp32RyV/InmG/R96Emz/rVCPgdcKVjK2jwy8xupp1tYYeHVahoFXp4Cq6kqPLSWnlzGnysuUwKsVIrVe52k0wQKvOF0rGcidC2KZW08f/Kms9HzWqZUWHyrDHWRMq9mB1xPQkQezdk0HihVJhVyKl15I5RG2EnhdYQ//bc5ThnyQjkYBr/olQ33EtZHeXaX96T5nzgJ1atHR1DYB2cqT2zzFtRPkTpvpPHiEXhYWL3M/nCWYlQ9/c9KqnzPwWtVywfebgTd47axUk4FXp7UYeHUKqKqu3LhGcYjk7ZPptOSlyh9nrRCp9TojgVfCpdwxr4ylNWqZW/bX2+Y9dciHr9AHYy0ZXGvKE7rULSg9/fKlR3m9MoRBhrDQSX6HDzuX7GWsbyCn+fny8KrtqTxggvoeqo2BFLdLnlh6iSL7Us7p4sUcrhPaJPArN38qdVKvmBiZNSQ4q5urFgOvuewRjt4w8IZD5cjfg4FXpw0YeHUKqKruabmVQIW8vYuWOr1ZyhhDCR3+PFRaY32NAl7lOEQmgVIOzF0Qug1jyk1NlAGA7klFGQJQrGhqSL3MRswECWa0xE629lTos3690zItUNx3lixAndppm7TU8El1enZPdW1o0wqj3oDXU/5n5Wl2kYZItSdf7eWWm+kOH7GhdSvvm9uMsKnV2mDgtZrF9PeXgVe/hlZogYFXp5UYeHUK6KG6+sdZLlUrvbS0OefKZWiGyHADrzIrgHqIWmErUGWVS+rypcBbCIBZNyYpPdUEsHQa3bQZdsTH0Qlq2o+IVqfxkvG00vOrNdzAG/B6ihNW3jOQsIlA7azlevUx3XLDpKxrVvtrGVuor2HgDbXC5mufgdd8NglFjxh4darKwKtTQC/VlUelquM1KUTg8NG0HfpavGnhBl6lt4+GKD2WylhLo5Ujr/KmzTa3gxfUnj4JxZ5yHRvdn2Da07Lh6sQJm9tpe57uI4+Yps/I+12pknMjVqChLd6A19MmQWXYQCg2rAWip3Kcx04405ZRoe8KefrTc55dfzoy8PpTKPo+Z+CNPpt6GhEDr047M/DqFNBLdemJo48l8CqhlQ4RoA04VPzl4KVr1Ju3Aul1MJvWJBDJ7BHe8ggH0g8t1yo3rxHkUXosJWQrl/rN6OXT82KiRR+jgFe+SKg9xfLvgaQ+09LvQK+R46SXw6/22MTpa8rvUqDtpafrGXjTk7WdY2XgTR82Z+DVaWcGXp0CeqnuaXlewhB5qc6eswmvKWVAqFaFkvv7PrlK64ls5A2kzUDKEgzwqsFKpk8L9VK30sso87Oq7ymXt406ftfIGRBq4A20faWHl16a9n9vQ3KycxOcp5UFaXd/afKM1MxTW8px0qY2Al7qU+mSzs1uXLwrwMCb/mYHA2/6sDkDr047M/DqFNBLdaUnUsa8quMytXh2ZfNagZeu+3iLDQ0bpG3kCQZ4Zd5XZW7U7/bbxO56Zdowo9UjYP9qD1w5Yal9tU5KGKLjbo3OGOFtTLTR6+RJG/Llc7iOs1VfGyiQBqpfoO0rgVd5eIUnXQPtSyiv97Qa4m9jZyj7Y6W2GXitZC1j+srAa4yOZm+FgVenhRh4dQropTrB0cebnJ4pTymoqFogR8R6StXk6dZKqCZQpFjH+HgHcifE4/TFJFGFNqR9fwAoVQoiN6ynEul8t0rwpTFUqpDWT2XqN+o7eSvD4e3VEj+sziph9OySmwllXmKK9aXNj1myegZ/JfDK/lO4ApVwviwEqoO0sfTyU/1QbZYMtG9mv56B1+wWMr5/DLzGa2rGFtMd8KZcv4EyNdrdZouPpvVHyeIP3vb3a0nJGDN9Kbbu3IeYGDueq14J3ds2RqZMGcW1DLyhnda0jCxP2XJbrs/iQI/uaamptPRCC4SqN5sRGLVoluoGvMprPMXBypRkodygpmW88hp1mIYyhZm8JhybrGTGCLqnN+98oDG2gehA16o9/RKwvcXcegJeM8Y+q3VQ5zM2y1wM1F6RuJ6BNxKqR/aeDLyR1T9cd0+3wLtu/nDkyJ7g0vmO+DgBtOrSd+T7uPLPvxjxdjtcvZaEHgOn4tFHCuOtLs0ZeMM1S/+7j/IUrkDCGWQ3AwFeinsl7zJlM+jS8ZYb8CqXtulwjNYt3cFba/hEmOVzu508gEL+MdSxxXQfZeYN+rcncAw18LpeRv47hU3ej+z4YlNKg5YW30rXPpA7RpwtffDwTZDdyRseyMpCJG1M/aeMFqdPO3sRylCaSI7T6Hsz8BqtqPnbY+A1v42M6GG6Bd5ty8cjd45sPjW8dSsVj9Zqj4+mvoPihRPFtbv2HsRbw2bgq3VTGXiNmIEBtkHQkT8RrpOmAqmuBaaUsY8yldPQgTfdgFd9hKw6HEBmhAiH1zSQ8SuvlWm7EhJsWL3WjkBOHwv0nqTHkSPA4aPOF0p54hktt/fo5v6yoMVGgd5ffb0EbwLX6TOd6bqokAaVK0Ic2iGP4W1Y14ZyjwJ9B6WBMIcG6LWAuesz8JrbPqHoHQNvKFQ1X5vpFnjvSbgbmePjUPjB+9C9TWM8mJj3Nutc/TcJFZ7thNVzh6FwgfvE56fPXkD1pj2xZ8M03HVnZg5pMN+c9tojT7lT1RcrY0gJfikbRJuWqahYOtYVwys3pJGXWRx9/B+40X8fP07g5MwRHOnUVFpNoz6kQGs9rdfJ0/AEVP53Spo3b7sWL7zW+3q7Tr7UKONbfbVJh19QZgZZGHj1WsDc9Rl4zW2fUPSOgTcUqpqvzXQHvKmpDvxw+Ffkyp4gQhQ+WPEJvvrmf9jwwSjExWa6zUItugxDrhzZMOCNV5AhQww2f7YXA8fOcwHv9Zu+02GZz+Tpt0cbtqTi408cqFPDhudq3h6+QsqMn3oLvxwD3ugUg6++ScXX+xx4vr4dtZ6OgbR1555Or+S0cTF4Z+gtXLwMdHg1BjPnuXsrqd7TT3o+HtdMVlCOuVBB43sm9aKWCxYAenSJcdNZ3vP3P4GR49K0Nb4naS0OH3sLp/5b6pd/pXnx0y8OYX8q2bKKaAZcuJRWj/42rH+aVziUfeS2I6NApgx213c9Mj3gu4ZbAbI5l+hXIN0Br9qkFLZQtnYHzB77pojNVZez5y+h/+g52HfgqPDolipREF/vP4zd66fCZrPhrysp0T9LomSEhw7bsXAxULyoA6+86DkX6cw5Nhw/aUP7Vx3484wNGzYBj1V0oFWzTLjwdwq+3GPD+o9t4jCHt3s6sGu3XVyTP59D1FMWaqNAfvPnPF34kQ2HjtjQpKEDj5Y2tr+k4eRpabqQTh3aOKDBCT6QAAAgAElEQVTUmTTauh3YtiPtR2fUkNC+SF66bMOkqTYkpzjtW7eOc9zHjtswa56zv/T3pg3t+PpbGzZuuYXLV2zCztR/LtGrQPYssfxcj17zehwZ2ZxL9CuQ7oE3Kfk6KjzbEavnDPUY1qCeAjM/WI+fj/+BsQM6iY84S4N1viTKdFydO3jO8KCMIaWRzV3ojG9NvM+Oo7+kgY48WEC5kY6uJxAmMKKl+9at0nL5mlmlQHPTBjIWdbYAmQ5MqXPu3A6Mm5x2ch61H46wAYotjouFOGpXFmUGCwpJqV/buWnt/MWbSEoJX87iQDTma41VgEMajNXTCq1xSIMVrKS/j+kOeLfv+g5/nr2Ax8s/jNhMGTFpzkr8fOwPLJ81GHa7Das3fYEvv/mfC2j/vZYMSk1248ZNbP9yP2Z+sA4LJ/dF/gfyMPDqn39hb8FfjKjyc0/pu+h0LfXhEeMnxQjIpULZDho1TA3bYQ5GCKjOTWtEm7INmdeYNoKVKQkQ3FImBJnpgl4ckpIckBsEpYZtWgWWcs7IPstjrelY3vKl7QJ4/7l2w8hbcFsmVoCB18TGCVHXGHhDJKzJmk13wHvg0K8YM20JfjlxSpii7CNF0LdbC9ybO7v496TZK7Fm8xf4bMVE8e+DR47j5deGIS4uVlz7ervnUTB/2gY39vCabEb76Y6EU2+ppdRArIRZb/lX5VG9dGurbFRTyqTF803w//0PNrEpr2F97cfTyg1+6kwW0qtMIHz4qA0pyU6veEqKTbw0RBJ4yfN76ZJDHCwh05Ix8Frre66ntwy8etSzZl0GXmvaLdBepzvgDVQgf9cz8PpTyFyf+0t7pQZeJcx6W2aXHlKrAi/125/nWxmaIMM5/FlWpmfzdOiB+oAPAt9Ll2wi93GkgVc5LuXBE/7Gy59HhwIMvNFhx0BGwcAbiFrWvZaBV6ftGHh1Chjm6hK06KCB/PmB/A84kJjojOGU8bhKQJPQdt+9NrRv631Zm9KZUfqqShUdyJPLepua5DL+G91veQzHUAKvjMP1Zzpv3l2qJ3WVbdB9N2224chROwOvP2H585AqwMAbUnlN2TgDrynNYninGHh1SsrAq1PAMFeXMaXytjIEgZbs5y5wnqSlBjpKTZU7Id6VhzfMXQ7L7fx5vpUeWU8HRqg76cu7S9eqN7OR9zyUm+eCFZE9vMEqZ916DLzWtV2wPWfgDVY5a9Vj4NVpLwZenQKGuboatCTwKj2O6jjc9AC8MnTDW7iCOgTBXxYFf/Aqj/gl88sQBrLN6bNA0aIO02z6Y+AN8xfUBLdj4DWBEcLcBQbeMAseodsx8OoUnoFXp4Bhrq7OvECnpdWplQp5whqFMzRv5p5OLD0Arz9AVQOvtw180pzKE+uUab+U5pZhFFpDJMI8VcTtGHgjoXpk78nAG1n9I3F3Bt5IqB7+ezLw6tScgVengBGoLkFLehdbNEvFiNHO07P6vnVLpM1SlvQAvNLz7W3DmEwjJnXxBrzkub1yGSLtGIWH+AJjGUZh5swWDLwR+IJG+JYMvBE2QARuz8AbAdEjcEsGXp2iM/DqFDAC1SmOd/cem8idS4BXprQDq9fab4vdlV1LD8Dr2rCX1YEe3W6JDXy0gYw83qVLpkLCqT/glZ5df9fR5wKOL9mQJcE8IQzq6cjAG4EvaIRvycAbYQNE4PYMvBEQPQK3ZODVKToDr04BI1Rd6dGMj3cIuPMWv5oegJfMoExNJkMYpMdXAi8dvHH2nM2rVjIzgzSrJ495hEwe1G0ZeIOSzdKVGHgtbb6gOs/AG5RslqvEwKvTZAy8OgWMUHUJvBLgqBveUnKlF+BVHspx+DDE6We5czlAxzBL4CUAply53sIQJDRLs/rb3BYh82u+LQOvZqmi5kIG3qgxpeaBMPBqlsrSFzLw6jQfA69OASNYXQlnBL5dOno+zja9AK/M1FCsSCooipm83lQIWqXnljaY0d89Aa86A4asG0ET6741A69uCS3XAAOv5Uymu8MMvLoltEQDDLw6zcTAq1PACFZXAq+v08PSC/BSBotxk+zieN/YOIc47ldCq9SKdNq0xQ6Z3YI+P3HSed3pMzbxmTwi2NdLRATNHtCtGXgDkisqLmbgjQozBjQIBt6A5LLsxQy8Ok3HwKtTwAhWVwKvt3AG6l56AV4aq/pgDvobeXMpvIEA9tlaDsxd6H4amtRR6f2legkJNrHhzcqFgdfK1guu7wy8welm5VoMvFa2nva+M/Bq18rjlQy8OgWMYHUJav48kekJeMkcU2fEiI1pssi4XfLqFi8KN+BVhjHQCWyXL9vQqcMtSx6v7GkqMvBG8AsaoVsz8EZI+AjeloE3guKH8dYMvDrFZuDVKWAEqxOsfXcAqFTR4RPQ0hvwUkqyjzc543dpg5oMb2hYPxUJWZzAS3DbuX0qzpyxiX/LQuEM/Xp7joWOoKmDvjUDb9DSWbYiA69lTRd0xxl4g5bOUhUZeHWai4FXp4AWqJ7egFeaRH26GoV9xMcCc+bbhQe4VMlUlCnpBGBZzHxqWjBTjYE3GNWsXYeB19r2C6b3DLzBqGa9Ogy8Om3GwKtTQAtUT6/Au/+AXRzIQYUOoOjR3em5JQ/w3PnOzW2UtoxOVJPF1+Y/C5j6ti4y8FrRavr6zMCrTz8r1mbgtaLVAu8zA2/gmrnVYODVKaAFqqdX4FXG56o9t4eP2LF4WZpnV5oxmuJ3aUwMvBb4ghrcRQZegwW1QHMMvBYwkgFdZODVKSIDr04BLVA9vQKvPG6YTOTJc6s+bpius/pBE+rpyMBrgS+owV1k4DVYUAs0x8BrASMZ0EUGXp0iMvDqFNAC1dMr8JJpZCYLT55bpZeXMl3ExQFtWkXPhjX28FrgyxmCLjLwhkBUkzfJwGtyAxnUPQZenUIy8OoU0ALV0zPwUlgDlcREz/l06TjipGSgdavUqElFppyS7OG1wBfU4C4y8BosqAWaY+C1gJEM6CIDr04RGXh1CmiB6ukZeC1gnpB2kYE3pPKasnEGXlOaJaSdYuANqbymaZyBV6cpGHh1CmiB6gy8FjBSiLrIwBsiYU3cLAOviY0Toq4x8IZIWJM1y8Cr0yAMvDoFtEB1Bl4LGClEXWTgDZGwJm6WgdfExglR1xh4QySsyZpl4NVpEAZenQJaoDoDrwWMFKIuMvCGSFgTN8vAa2LjhKhrDLwhEvb/7J0HnBVF8sdrIywskgUV1BMz/glmMcOJigFFwAACpgPMBLOSMSCCGTGDGVTMih4mBNRTAQMmPD1BBRUUCQsb/5/qfTXW6+1Jb2bezntb8/nc5/DtTE/3r3p6vlNdXR2zYgV4AxpEgDeggBlwuQBvBhgpoioK8EYkbIyLFeCNsXEiqpoAb0TCxqxYAd6ABvlzQ2nAEuTyTFCgqF4elGzJrpRbmaB7bdcxPy8XcB+5sgpzlorarp/cP3wFGtTLh01bysMvWEqMrQJNigtjWzepWHgKCPCGp6WUJAqIAqKAKCAKiAKigCgQQwUEeGNoFKmSKCAKiAKigCggCogCokB4CgjwhqellCQKiAKigCggCogCooAoEEMFBHhjaBSpkiggCogCooAoIAqIAqJAeAoI8IanpZQkCogCooAoIAqIAqKAKBBDBQR4Y2gUqZIoIAqIAqKAKCAKiAKiQHgKCPCGp6WUJAqIAqKAKCAKiAKigCgQQwUEeGNoFKmSKCAKiAKigCggCogCokB4CgjwhqellCQKiAKigCggCogCooAoEEMFBHhjaBSpkiggCogCooAoIAqIAqJAeAoI8IanpZQkCogCooAoIAqIAqKAKBBDBQR4Y2gUqZIoIAqIAqKAKCAKiAKiQHgKCPCGp6WUJAqIAqKAKCAKiAKigCgQQwUEeGNoFKmSKCAKiAKigCggCogCokB4CgjwhqellCQKiAKigCggCogCooAoEEMFBHhjaBSpkiggCogCooAoIAqIAqJAeAoI8IanpZQkCtRJBWbOngs33fWE1faCgnzYrnULOP6og+Cc03pAYWGBL11W/PwrvDB3AfQ54UjYukUTX9fG6eRJdz0Bjz83D6ZPGgEHdN7DsWoHHDcUTj3xSBg+uG8oTfjks2/gzIuuh3eevQ1aNGucVOazr7wL1016EG4ddyEcddi+odxPChEFRAFRIO4KCPDG3UJSP1Eg5goQ8I4eMQgaN2oIGzaWwIeLv4SX/r0Iuh++L0wde6GvFiz66As4d+TN8NT00bDXbv/wdW1cTn73/aUw9MqpMOm6IXBctwNdqxUm8P606ne4+ob74KOlXxuBFytz631PwxPPzYM5D4yHbVu3cK2fnCAKiAKiQKYrIMCb6RaU+osCtawAAe+82VOgdctmVm2Gj7kL5r79H3h3zu3QvOlWnmuZ6cBbUVEJPc+6BnZo0wruuv5ST+0OC3hPOXcUfLX8R+ueJg8v/nFLaRmcdNa10LF9O7jx6n95qqOcJAqIAqJAJisgwJvJ1pO6iwIxUMAOeO9//GWYeu9seOXRmxT80fHKvA/gwSdfge/+9zNsVdwAOu+1Cwwf3Ae2364VEOzqzXrkjquVJ7Jbn+EK0E7o3sU6Zf4Hn8GQK26BZ+4fB7vvvL36vc+/xqiwipOOOQTunvEcfL18BZx49MFw1UVnwH7HDoHz+h0Pm7eUwty3P4S/1m+C9rvtCKOHD4R2O25nlbv8+5/gjgefhSVfLIdNJZthu9YtYf/Oe8CIIX2hnkOYBpY5fMzdSfXh7cFwg6n3Pg2ff/298ogfvN9e8OqbH0D/U44KHNLw6+9/Qll5Obz0xiK4/YFnbD28WJ+nX3oHxtzyMLz+xM3i5Y3BcyRVEAVEgWgVEOCNVl8pXRTIegXsgPey8dPg7YVLYcHzd1hxvDNmz4V7ZjwP5/U/HvbcdUcV/jBj1mvw86o18PzDE6GqqgrmvDpfxQSPu+xs+Mf2rZV+u+7UFjZsKvEFvD+sWAX5ebkqlnjrFk2V97nboXsr4M3JyYE+JxwBPY8+GDZvLoUb7nwMqiqr4LmHJkJubg78uW4DHD/gKth1pzZw+sndFOAuXfYdzHrhLZjz4IQacbHcyJePvwe+/X6lOk8/EJ4HXnwD/GP7baBXj0Ohfr1CVe4Lry+As0491gLeysoqBa5ORw6AbXz0U8+/CeOmznQE3vUbNsFhvS6BkUNOhX69/pn1/VQaKAqIAnVbAQHeum1/ab0oEFgBAt6XH7kRWjZvAn/+tQFe/vciuO3+ZxTAnXN6D3WPdX9thCN7X6oWSx12YEfrvn9t2AQHn3gB3HTNEOjR7QDLy6vH8K76ba0v4C0tK4P7J1+m6kQHemoReC89r7fy8tLx4usL4crr74VXH7tJeZopBvfJe0bD/+3+dxxxyeZSKCjIg/y8PFvdsI0nHXMoXHLuKTXOOfOiifDL6jXw4swboah+ofV3PaQBQ0EwJMTpKG5YBB+8PM14ihfgxQvPGTEJGjVsoGwihyggCogC2ayAAG82W1faJgqkQQE9SwPeEjM1XHvJmdD7+MOtGvx7/sdwyXV3qL/pR1lZOVx8zikw+MwTQgNeDGnQQY6A9+qL+yd5NXGB18BLboAZt10F+3bcDf63cjUcd+aV0GGPnaDfKUdBxz3bQZttWrqqiR7qDt3OhuuvPC8p7AIvRG82gi22EdvKDx148ePgh5WrHO+Xl5dru6jPK/BOuPUR+PLb/8Fjd13r2jY5QRQQBUSBTFZAgDeTrSd1FwVioAAB723jL4JmTRrB2wuXwANPvALXDRsAp/XsatUQwwHGTpkB900eCa23bl6j5k0bF0PTxo1qBXgxrOCM88fDQ1OvhP07767qNm/+Jyr+lxaBYYo0DDsY0OdoW9UJau+YcDF0PWTvpPMw3doxZ1yuQjVOOe4wR+BNR0gDVmDK9Fnw1oLF8OLMG2LQk6QKooAoIApEp4AAb3TaSsmiQJ1QwBTDi9Px6NGdftMIOGjf9koHWsx1z03D4dADOthq8/7Hy9RUux7SgAuyMFxgwhXnwMnHHmpd77RozauH1wS8dAP0tn721X/VIq833v0IHr71StivUzUU6wd5eG+4+l9w/D8PSvrzppItsN+xg+GKC06vAc21FdIwfupMBfTi4a0Tj6o0UhSo0woI8NZp80vjRYHgCpiAF2Nd+10wHn5evQaeuPs6tUjr97Xr4J99h0OHPdvBw7depRaH0YGe0T/WrYe2224NX3z9A/QdPAam3TgsKda3vKIC9u5+Hgwd2BOGDuhpXUvxrqYsDakC7y+/rgX0OOOiMjrwN6z/xCvPVdkf7A6E8j7HHwHnDzqpxinH9rtCLYRDbzgd6M1F4D39pK7WorV0hTScNexGaNyoWGJ4gz8GUoIoIArEXAEB3pgbSKonCsRdAbssDT+v+h36Dh4LjYqL4Mlpo6HxVg3h3kdfVIvZMBUZQiP+9vlX38MzL7+rQiCOPmI/QE9otz7DoO12W8M5px8HmE3gwH32VDG0uJnDV8v/Bzdc9S9oVNwA5r33MTz01GtQWlpmTEuWKvCiN/fOh+bA6Sd1gz133QEwxvjZV+bDx59+rTI5tGrZ1NYsmKXhx59/hSenjapxDrZz9OSH4IKzToLDDugIuEnE9EdeUF5WXNwXdKe173/8ReXYxY8A1PqBWy6HJo2L1cI9PRcyQvXhvS6Gy84/XbI0xP0hk/qJAqJAYAUEeANLKAWIAnVbATvgRVVwMdg5wydB5//bBe6bfBkU5Oep0IZHn3lDQR56N3FxWZf99lLxsQSS8z/4FHBrXox7bdK4kdqed7d2bQHDGsZNmQEfLvlSZRfAvLgIpDfe+XiowPvjT78qEF38+bew6te10LBBfejUfme48Oxeqh5OB4VuvDSzOv2Yftz32Euq/Rs3lUC7HbZTac+uv/1RFe8cFHhPHHQNfPfDTzXuqWelwBMenzNP3Vfy8Nbt51daLwrUFQUEeOuKpaWdooAokBYFcKe1EwddDe133VFtLRzHA7NVnDDgativ8+6y01ocDSR1EgVEgdAVEOANXVIpUBQQBeq6Au8sWgrnXzW1RhxyXHTBxWov/XsRzHlgvOyyFhejSD1EAVEgUgUEeCOVVwoXBUSBuqoAhmTMfukdeHDqFUmbV9S2Hg/Peg1uvvtJtVDtqMP2re3qyP1FAVFAFEiLAgK8aZFZbiIKiAKigCggCogCooAoUFsKCPDWlvJyX1FAFBAFRAFRQBQQBUSBtCggwBtQ5t/+3BywBLk87gpgttjGxYXw54bSuFdV6heyAvUL81SJm0srQi5ZiourAk0b1YM/1m+Ja/WkXhEo0LJJ/QhKlSLjpoAAb0CL/LymJGAJcnncFcjJAWjdtAh+WSu2jrutwq5fo6J8gJwcWL+pLOyipbyYKrBt8yKQcT2mxomoWmhzObJfAQHegDaWgTGggBlwuQBvBhgpoioK8EYkbIyLFeCNsXEiqpoAb0TCxqxYAd6ABhHgDShgBlwuwJsBRoqoigK8EQkb42IFeGNsnIiqJsAbkbAxK1aAN6BBBHgDCpgBlwvwZoCRIqqiAG9Ewsa4WAHeGBsnoqoJ8EYkbMyKFeANaBAB3oACZsDlArwZYKSIqijAG5GwMS5WgDfGxomoagK8EQkbs2IFeAMaRIA3oIAZcLkAb/qMVG/KCMj79lPYMmwyVOzaMX03trmTAG+tmyDtFRDgTbvktX5DAd5aN0FaKpCVwPv519/DmMkPw/LvV6ptM6+6qB8cekAHW0Gdzp//wWcw5Ipbkq4tKMiHJW/cr34T4E1LP63Vmwjwpk9+Ad70aS13MisgwFv3eoYAb92wedYBb1lZORx9xmVw+knd4NSeXeGdhUtg3NSZMPeJm6FZk0Y1rOp2PgLv+Kkz4On7x1nXYl7WRsUNBHjrxjOCWakkLVmabC3Amyah5Ta2Cgjw1r3OIcBbN2yedcD74eKv4JLrbocFL9wFubmIpgB9B4+B03p2hV49DqthVbfzEXgn3vYIvPb4JGOPEA9v9j8oArzps7EAb/q0ljuJh1f6QLUCArx1oydkHfDOeuEteObld+Gp6aMtC14+/h5o1bIZjBjSt4ZV3c5H4L3g6qnQtHEj2Kq4AezfeQ+45Lze6t94rPpDdlrL9kcFgXfrxvVhteyqF7mpC28ZDrnffAqlIyZD5a6dIr+f2w2K6+PGEwAbSsrdTpW/Z4kCrZvWl3E9S2zptRloczmyX4GsA94Zs+fCvPkfw8zbr7asN+rmB6EgPx+uGzaghkXdzv9j3XpY/dsf0HirYlj16xq45Z5Z0LJ5Y5g69kJVVmVlVfb3Emmhmi0QW0ffETaOvQgqvlwCDUfdDnl7do7+hi53wI8dJN6qKnnOa90YaaqAPOtpEjpGt6HZ4BhVSaoSgQJZB7zosZ3z2nvwxN3XWXKhh3frlk1h5JBTa0jo9/zFn38LAy+5AZb++wHIycmRRWsRdMq4FSkhDemziIQ0pE9ruZNZAYnhrXs9Q0Ia6obNsw54P1j8JQwbdScseOFOBaR49D5vNJza80joc/wRNazq9/wF//kcrpgwHd57/g5VlsTwZv+DIsCbPhsL8KZPa7mTAK/0gWoFBHjrRk/IOuAtLS2Do04bCQP6HA19TzgC3v3gUxg16UG16Kxl8yZqWvq8kTfDoFOPUanK3M5/4IlXoM02LaBj+53hz3Ub4NqbHoB9OuyqUp0J8NaRh0SyNKTN0AK8aZNabmSjgHh4617XEOCtGzbPOuBFsy1d9h2MmzIDln//E2zbujlcdv7p0PXg6njA8ooK6NjtHBg78izoffzh6jen8+e8Oh8envUarPz5N5WKrPvh+8Gwf/WBovqFArx14xmRtGRptLMAbxrFllsZFRDgrXsdQ4C3btg8K4E3naaTkIZ0ql0795KQhvTpTsBbOvAyKD+we/pubHMn2Wmt1k2Q9goI8KZd8lq/oQBvrZsgLRUQ4A0oswBvQAEz4HIB3vQZqf7EwZC78r9Q1qM/lJ0wMH03FuCtda3jUgEB3rhYIn31EOBNn9a1eScB3oDqC/AGFDADLhfgTZ+RGgw9St1MgDd9msudkhUQ4K17PUKAt27YXIA3oJ0FeAMKmAGXC/Cmz0gCvOnTWu5kVkCAt+71DAHeumFzAd6AdhbgDShgBlwuwJs+Iwnwpk9ruZMAr/SBagUEeOtGTxDgDWhnAd6AAmbA5QK86TOSAG/6tJY7CfBKHxDgrUt9QIA3oLUFeAMKmAGXC/Cmz0gCvOnTWu4kwCt9QIC3LvUBAd6A1hbgDShgBlwuwJs+Iwnwpk9ruZMAr/QBAd661AcEeANaW4A3oIAZcLkAb/qMJMCbPq3lTgK80gcEeOtSHxDgDWhtAd6AAmbA5QK86TOSAG/6tJY7CfBKHxDgrUt9QIA3oLUFeAMKmAGXC/Cmz0gCvOnTWu4kwCt9QIC3LvUBAd6A1hbgDShgBlwuwJs+Iwnwpk9ruZMAr/QBAd661AcEeANaW4A3oIAZcLkAb/qMJMCbPq3lTgK80gcEeOtSHxDgDWhtAd6AAmbA5QK86TOSAG/6tJY7CfBKHxDgrUt9QIA3oLUFeAMKmAGXC/Cmz0gCvOnTWu4kwCt9QIC3LvUBAd6A1hbgDShgzC4veHEGFLzyKFTs0gG2DL9F1U6AFyBn0wbI/ek7qCoqhso27SKzWqrAW2/KSFWnLcMnh1q3RkX5qgOs31QWarlSWHwVwG1mZVyPr32iqJlsLRyFqvErU4A3oE1kYAwoIADkLVkAuT/9Fyp36QAVu3YMXmCAEgR4zeLlfbMU6k0dmfQhEEBm20tTBV66btO0N0KtlgBvqHJmRGECvBlhplArKcAbqpyxLUyAN6BpBHgDCggABJllPfpD2QkDgxcYoAQBXgFeroAAb4CHKUMvFeDNUMMFqLYAbwDxMuhSAd6AxhLgDSigAG9wAdNQQv77r0PhjJvT5uGt6HAQbBk6znPLyMNbcsscqGpQ7Pk6txMFeN0Uyr6/C/Bmn03dWiTA66ZQdvxdgDegHQV4AwqIwDvrbih4aw7EycNb2WYn2HzNdNU4ieH92wvPY5uDW75mCQSufu9D120ZNjnUsBgB3iisHO8yBXjjbZ8oaifAG4Wq8StTgDegTTIJeKNa2BNQQqg3ZQTkfftprIAX20TxoH6BN13xrkF193O9KdSDrs/7dqn6Z8UuweOvBXj9WEXOjUIBAd4oVI13mQK88bZPWLUT4A2oZCYBb1QLewJKWGeAFz3ZuSv/C2V9h0aa6SCoPUzXE/DyDwE6zwonmPAI5L//BlQ1bwXlB3ZPqRqpAC99YOANxcObkuxyEVNAgLfudQcB3rphcwHegHYOArz4os5/6RGo7NQFyrr2ClgT98vjArz6IrWgHt7cld9BTskGqNyuXcrxmxzoSMmgHl4dDqmdpQMvSxkI3a0czRlegBdhM2gmBwHeaOwnpXpXQIDXu1bZcqYAb7ZY0rkdArwB7RwEeAkieLxowOo4Xh4X4NUB1w54c9as8uQxDArMKBrFEXMBowLeOMQq++1npLGTh3fL4DFQb/oYtbANU8xhPmPeVlz4lrNmNZQfeBRUNW9trIIAr1/LyPlhKyDAG7ai8S9PgDf+NgqjhgK8AVUMA3ixCiUTHrGFgIBVtC7PNOD1GgsbBvByoCPBNl9zjwo9SDWG187Dm63Ai+2iTTsIePniM9LYKewgzsCL/TH3209jkS86rDFByqmpgABv3esVArx1w+YCvAHtHBbwBp3mJm8obFwPZX3Pd/SeEVxjKEDBrGmAHma7awLKY7xcB1SCHPT8lQ683LqGgBdjQksmPGpblaJr+yvPYdmRJ6fcDhPwEpgJ8IIVZ61DPI+fJeDFc+jf3HZePkyCAm9Zn6GhhgfxLA1xyhcdxXMpZVYrIMBb93qCAG/dsLkAb0A7hwW8fvOO6tUm8LALj0AgLrr2TH+pb3EAACAASURBVHUZgRyHlbB3qHKS1Q549VRUuAMbTpHrkKWXnQok2ZXBf68t4C14+RFVjbLjqu0Vh8MupMENeLnt0gK8IW9eYgTeAB9WcbCl1MFZAQHeutdDBHjrhs0FeAPaOSzgrSpqCCVTnku5Nm7walrJ7nZNypVxudAr8PKFUuQxNIUDZBzwugBTXEJPuBnrTxysMkzoHx9egJc+HDIeeBP5ov3mCI7qOYp7uTmbNkDuT99BVVFxRmUlEeCNe88Kv34CvOFrGscSBXgDWiUI8BbOmKQWZdERJKWSG7xmK/DiS7VoxMlKQvJuozc7d+1qqGzWylNcNIZ21J84pEZP8OvhJc8sxq9itgIdDgn43IApDsBL3nWqK9XJK/DidZhbGQ9czFbR6WBP6edS+XjRoTvM7am5h9er/QIOKVlzudcY/Lg1WIA3XIt4WXxc2zniBXjDtXlcSxPgDWiZIMBLL9DK7XaC3J/+G2jjBX36X8/56ga8YW/J6iRrKh5eDPnI+3SRpZGV4SKhHd0PQzP8xlpybXi9yZvsNYaXYA3jsXEb3lSAl8N3GGEmqaZs0zeaCAK8pKMXYIwL8NJmGg067KO22lu/qcwCdresKtQGWvQYcIjJ2MutGHxt9iru+agFeMPtcl4+fGr7I1+AN1ybx7U0Ad6AlgkDeC2YCxAbyKf/0TOZ/9JM5WEzxevSbwVvPgsFs6dVe+FC3pLVK/BWdD7E8q7qnk/eJvIYEjyZ8uYSYPoFXkyXRYAaBvDi4jvy3HNdvQAfh28Epir0UjcoTrmXesmMYCo8FeClfozlVTXbGnLW/qqKpvh0L+2PC/BSPfIefqsG8OofMrp+dG3csnGk24tmN+vkJbQl5Q4fwoUCvCGIyIpwyuFNp/HNa+xSFoZbq+TSBHijVDc+ZQvwBrRFGMDL0zltGX6LY43stnFNCXhfnKHSSEUFvHbeRf7Cq9ytkzX97wS8JIrlLZw2Snl89QM91fnznqmRA9ZJVDt4TtXDmzSdzz4kvACf7m0OmnUgrcDLwhi43uQRdYNZ7t12C/vg5SeFNAT4aORlhgG8bp7ggENP0uVO2zvjBx0+E6YY7DDroJclwBuluplTth/gTafjhSsowJs5/SlITQV4g6gHAOkEXqc4XVvgTcRPmkIa9Gsqdu0YUI3ky+1gi3vAUgbeKSOsGFF+Vxwwc79e4g94E4uR9MaHDbyUPo2DUOHMSZDz+6/WdsM1gDcgwPF7Yk5hnvbNy0cAgiemrOMxzjzUgteXg75T2XYwq5fl9vFH90j1Ors68rjwIB5eLD9doUJOU8L6B10YoTJeBgo34A2amcZLHVI5Rzy8qahmfw3f1If3PR7aQuOLAG+42ktpyQoI8AbsEVECL+XJrejSXW1F6xV40SuY/+az1blpE2ma3ICX5wEOawvcKIGXQE43nwrnmPdMUryvycR8YRuGM9ACK34u5QXWY3jtQiZ4nCuVwwdw/nfKGUy/mUJPsAw/nk5TO/U6ed3ghIc0lB8/wPLC4z3sgNfPo0RlFLz1LMBvq6G828mQu2a1rbffqWwvwGu3y5vJlrw8O+D1snkG1lnPr41l43bi0KAhVLbdOZTUc3oYDH7Y8MMr8PLFRVhG0HAaXi8O/l5mOrz2JbxH2JuBxB1445i20MlePKWhqR/gWFjw1hxVhACv154v56WigABvKqqxa6IEXn2lvGfgTex4hdX0Crw83jCsGDsd5kg2rx5ePYsFb48JLtWAOXiMgn0EWKcYSg46+MI0AS/Bpi3wat5XP8CrZz+wA14dMHl39RKuoNfJa1ypE/Dyl5Ldgj+3x4qA12tfoPLUhwqmRytqCDQjocd6mzzDdlrVS4TGcF3CBF59MxWv8OmmH/+76WPWDXjRi63Hhuu2pOwaprp4WQxpN4NEtnDbUMaLBuQ9DNNbHHfgre14Vy92MY1TOtDyDx8ro0tIa0n8xqtLSINfq2bm+QK8Ae0WBvDiiwU3WNBz8eoLhyIFXgZvHHjLu52Sci5NC2a03a845FS13MZaMKZ7M027nxGY6CDHF7URwHoFXopj1ruCG/Dy+tqBn52Hl0CWZ3bQvfhUHzuvLOXG9eptxPK8QkZYwGsX5qADL9ardMBllofXLv7V5JH1Arx2C8lMH3degBc9tziDoj7CtA1CeN+0e6bJtqlkFdH7aVIMs2GnOYJ6fk/TB0CNcBqHTTy89D074LXL6ew2FFP9eN/w4i32m6YwU4C3tryhbnbS/140/CTIKdmofjYt4q0sagC5JZtq/N3vffj5frM+CPAGUTtzrhXgDWirUIB32GRj3tZUgZdnCXDy8HKgJBDC6bL8RXOtcAiKsfUyta4vnLGDDP47yk/A6RV4edwvmc8EvLp3zeR14NvhegVeAogwgddkJ6qP3YvNzoNuGvj5b06eOzovCXi79rJ2vNNfWnYZLqgcBMP8fz+j0u7xQwdeBY5sapM+CHSbWPXqcBBsGTpO/TlS4L1yKsAenZPSkuE9OcjzEA+K/8WXeE5RscpUwdOTmTy8OsRT+AXmc/YSV8+zrZg+8vQPR6yvqe/owOv0zHvpe3bAyz8ITDHOJhvrdibNCZ6dNu7xmrUFwbhw9jQoatoY/jx1eMA3QzSX84WdUQMves9xTC87boDKo+33oJA8ei/YAW/S2BSCh9culMap/gK8fq2bmecL8Aa0W5TAq4NV0oM84ZGkTRX49D9/GVsgxbbp1TcC4GBFGybgbwiMGMeHQOoFePWv6rQCL+XpPfJkwIEWp8ic6mx5hhLXUS5k3h3o+tw1q6DZz1/BH/WaKgAxeZX8eHjJPvjCIr2dgNfOU+0FOjhc0H29TP9Sf8JrELy4F5y/aO0yXPA+lbdobtIGK/g3gkDdG0qeIDvg5fWi0AU34OWL0Ch2murn6uH1CbzUD1A3PLAfokeyqqiRWpiYt/i9JC0R3PSwCmqj0wcb76dJ7WcfAnob6b9xxoC2GbcL5cBznWYDvPQ9L8Brgja6TodYPsbRdbz/2C3Go7AHu+eIwCynZH3aM1l4ef3w6Xm38BUv5Xk9h54NUz90ygpC5ZvGBv6xbZzBM8xQeK0vnZeKRgK8flXOzPMFeAPaLWzg3TJkLFR07KJqpYOV04PMBw8OvARtfPDRNwKgnKk8jyreX4cdt9Xd+kswKuCFho2s/ME6rHPQoLabBmc9fsw09U4v3IKXZkDBy4865pO1A16EBrQpLgIiPfwCrx34eIEODgR+0t9xfYICL2XNMHly7GKx7YDX9LHhFhfrtKgtVeDlbTEt4uP9kPdRXQsE/2pP2t8x5+S19PKRiWW7Ab8OFqYPLQXn3yxNWpyIv9llmfDS95LGHAYy3OZOwMs/jPh4iP/GhbkYAkS7LKq6ak4Ap48abj9Tu8PYNIQWl5UfeXKgXNrckcDrqi+IDPgqq3G5kyee/uakkwl4+UeHaeGx1zUGTm0V4A27J2RPeQK8AW3JgZc8BejRwVRObgePoyu4Z5QVx2Q3Xcd3U9NfFPylhvennJtegJcATPdy6i9tqhcCpGnb3rQBLwuDcANenlKLg4m1cCaxQQIPA+GbJuA15FkiAPbj4cX66d4omrrn4RQmO1HbTODjdVDX4QI9yl5AKt3Aa/rgMH1g8X5uZXpg+aRNoOwEvPTStV20ZuPhNcE7h0Yj8A4eA7krltfwltMmMVgHjJkniPNiJwWCLCe1aWpfB17e73i7jR45mylm38DL4oH1jzB9K2g7zzCPBcXnteKgo5MAXR8TsZzcbz+D3JXLVQyp3cyGCXjDgElLo0RqyCTI/nap+s+KXZxTQerrNngIkRc49OKJtXtPcTtxPTD0g2YInMIq9Nhx9aHC1oqYPna9tMntvco1Ms1Gme4hHl43VbPj7wK8Ae3IgddpUZnpNvTAoxel8J7RVqYAU3wjX9zCIUr3Yuj38QK8dnGsJuDVtzDm9+MvQVwBTrkV+QCTNL3coz9AyUYrJY3+grdbtMavofujpwHvhx5VhHEKaeAptUzAS9fr8EmrhvGa+lNGqNRHSneWBYIvnnHKVlADeBNZNLwCrxvEeV20Rp49rrPdgp50AG9l81bqxYkfGOUdD7b6gfURk1jMyevrB3ipbbkrvrNmBPRpetMsRNKitQTwblr6kfLE0odkKsCL9sZDDw/hwOuUl9puqDLF6PJzawAvi5V2A167jU8s3RymoJM8vDagY4IPL6EQyqnQ5/wk4NUhVfcg2n1A8BhoPh7oIK5shxlgFs1VsF3WtZfj28PSSMvm4mf78CSP7oDLIWfFt9Zz4gUO9TAzP6+7pHAoFirj9WM7yQmT2AKej5lOwIv3gByAyu3aefKOo6Z44ExaUv9hHxv0u2nGTIDXT8/I3HMFeAPaLgzgVXF8bCOFdAEvX2nNY3dJEoQDWolO0MW/2k2LdQjG8f+pTP6iSVpR3qO/AkmCSy/Ai14aBF49jRhfiGPFqu7SAcrZgitH4O0z1IIi7m3UgdduYZUf4KWsHHx1sp2Hl7zN+nStl5eOXicT8JL3Wn95cuDFFGB8Vzs/Mbz6h5oFFH2GqpcTeZz1sAk8j9uR4nX5c0LT7XYhDXbxxbwfeAXeioFH2I4UpjRtWHd8fmiLabzYFXiPPFmlW7NbxOkVePVpZh14+UyO8ip3OVoVnb9wrnVv6ptu4TRO0GUXamEHUtQ+Xl8O3Dog8dAM0pcglXshqVxb4NVmCKjv6entTDMFBNWmj06qr55xxKtjBJ0DCHKmsVlvr9430LOL3mMvoQf6tabFZngOPW9ePaj8gwP7Sd5bz6pZTBrL7ICXz3J4WZin62kK30MtaQdOUz8Q4A0IQhlyuQBvQENx4OWeAi8J/vWvb7v/Jti083wouLTZeczJw8vvV394Tyukwk4SHPB4zJzdBgQ4SJmAVx/AcRB0Al4+hclfWvhvDrwIhSUTH6sRI+sUg+wU14jX5axcXj043zIH6t0z2vLwmj4CVH0M8Y9UZ93Dq7+o8TwrXpi9fBE6qtrsrNqqZ1ZwW5nP64SAQyE2ekiDKYaV9yfuMdfbg//ttmjNFnh79AeeAUTf3MIL8JKudsBryuNMzxK1hUMJ7kKHEG7y8DoBL/cs8kVrOsS7Aa+aUWEfF06ZB/gzaurLPLuD3SYtvAy+QJVrb0oPx2HSK/By3ZOAd5cOoINlEvAaQiEI2PWZKfwYLe/WS31kYOhI3tKFSUOZH+A1hoYYQkecQjvsYmB5f3VaF8F3KDONyXYfI9yDbHpm9bLUuPzTd1BVVFyj/6u+QAuCE7awew9Z2TUSNuUfk/is04ZA9LzYAS9PVWkCXux/ed98BpVtd6pRX/zY4wtDsY/gBi+U9lOFthj6nABvQBDKkMsFeAMaKgl4Gax4+TJ1Al4+9W8CXn2q0Q54TSBFLyl+f1tg7nCQ8jJgeiX9BbNleDXYoidB9ziagFe/h+6t1QciC0ZYnkY8pzrpfXVeR3o540uToJ2gNAjwKmBE0Bw2GQpemmkBr95d6IXllJ5LB179w4HK1OGQ118HC5MXQ68bhy/UR/9vPN8Uw6psxz6g9PjaUDy8HoBXt69eL3oG7IDXrk+bPLzcBn6Bl8clOgEv9nc15frKo5apUEsKaVB9e+3qGrMq3K5Yvr6zGH0YUhy6PjaYwMI07PHYcvSU2k2H67M0pql/ZSsGiPjfpswKpkwQbsBL7TQtsq3ocrSV11tvox/gxWv1BXs8fzC1x8qyooV26B7mpGeGbWVOjhEaPzjEmj5UVP7nH5ersAa79pg+9JzeR3bjBI2tfB0E1jd/3rPGsAoOvFhPDFfCj/bNU55XpqA2Uiy1HfDmrF1tzYwYFzW++ayajaO+k9Qfjx+gtpYnh4hyqmDWnk8XWd2B3olYHzwXP3QFeAOCUIZcLsDrYqjKyiqYPO1JmPPqfCgrL4duh+4DY0eeBfXrFaor/QIv374Tt7TFwxTCoA/mOgzZTUGbmmN3LX+hmbwJtBKa4ov5FDy/D5afEvCy1E0cXKlsqh8HLh2++HU1gFqbVnYKaeAhEfjip9RmHHj5YjYOSPhvk6eTe6J0gDAN9ibgpRe4vuAmLOA1TekHAV7dPl49vAjkdmCGLyh8ueGBITb0sUNwoGtPEJEK8KK98YVLz2buGRdCzh6doOK6cx1HCrqnI/BqHlyCpoLZ1bHBptR4ugeQ2sqff25DhGl9bPAKvKgzakvX158wWOVPpk02sH6Yj9Uz8CY+mui5IRA31ccuTpvqkqRrp4Mt4MH+YGWZMaTQ4+OoZ+Bt0BBg08Ya29zq9UZdqJ9QPQlS9fGb24T3SwI6PQWlyUtL/UU9nw6LT00zYyZwpI8n8oaTPqbQDZ4qDzXnQEkfPLwNNGOjrxdQMftFDaF0yFhjqAbqhh901jN+0FEqD3BV89bW88eBXn/36A8pjuUqrzVzkOA5mCKwYNY0a2ZNgDdDiDVgNQV4XQR88vk3Ycas1+CuG4ZBg6J6cNm4adCx/c4wcsipjsBrN9XHB26+MAoL4wMqvXw4WDlBDg1ydi9N07VJwJv4atZBVocfk1z4ss9ds9oawOxCGkxAiuXZxfCagJdebqb4V7fyeWyjaaEPBwcKteDAq8fv8o8VE/AS/Jk86gQTXE/0KFGcGYE8vTj0qWU+6PO+xldlO3lusHy7fKy6zSnrB2nu5OH1Crz4YsNYPf7i9gpmpJld3LMFETZhPgSRpjAUPewgp+cAyN2zM1TcMMwylekZIy+vK/Bq4Tim8BauIb6Yy478e3EUD0HB9HxqAedLM1XdKDZc/zjyqytNOevPCI5J+GGCs09WfH5iups/CySUFQeeOAc/UHChGYZFYV/Cg3bYIm8delH5R41JV+5xVPCibaVOHnS1GPLA7pZHnXuTaQGiKTdyvR59YMsrs5M+HAhAscyqkg2q3hxq1dT5bp1s4205+HHPre71tvo08wLzMQLPpwXBJu+43UyTCXhNnmAdIHUIVuFe2H7c3pttXc/HDDyH1k7ofdE07rkxjD72cU87tkvFHM+epj4YURuV+zqxSM6tbPw7vhdad9zLy6lyToYrIMDrYsCBl9wA3Q7ZGwb0qV7Y8c6ipTBuygyYN3uK+m/u4eVTeHbAS7GX/KVm8vDq1XLz8Fqwpu1WRS8iN+A1vfypXqbVtvogrAa8qSOrX7yal4wGLH1KUIcjGlwppowSrtt5dXVQ1qdQVUwkAww+6HMvCA6Om6+dbk3j89hiDrwmOCGN/AKvyfuoBu+vl9RYtMSBhfqV27QvwjMteDF5bshOpoWF+De7+Gk9nlhvtxF4DR9T6qV4/IBAwGv1bQ0OTFPneC59LNHfTX1eD4MxAS+1UQFVt1OqvY1FDWHzhEeTNNen1+3iofVFSU47znHg1bfEpv6pezL9Ai/pYwIibCcCJ3k2+Thgt1iOgJRnVtCfTSyHe0ypXBNw6bMBHHjLDzoK8he9oS5HwEYI5XXVxzS8Z97CudZHN44FxT1Pg013X6+ux+luPPh0vGnRrGqPtrgTr+PgZRrnlXMAPyCmj1H3oel2u7hrvW/X0FwLIyEdTcBresa9AC9fP2HyXPNnqEYolg3Iu3EUbyfvz2r24bdf1JiZ9OHvsKZC2QU/uJq1VjMYOPPQsk8/tyrI37NAAQFeFyMe3usSGH/52XDYgdX5Ev+3cjX06H8FfPTavVBUvzAZeJlHyRZ4E3G+PFeuV+B1Amp9WpM3ywTLFZ0PUWm8CPb0mGGCCQWyWjxnNZD+vVUs/8rG83EAgY3ra+wopb947YBXBxGeI5e/CHXgdYMvPuibFs5wmKA4Mv4SRh3V9Nhvv1T//9pfrWlPN+CtarEtFM6cZOltF2dnAl6+oNAr8HIvux3wclDwAkl0Pu/bJs1pwR/1ITuwDAK8BBJ84wb95W7X35yAV/Vf9tHoBLykWZLXNZF2zM7jp/d500cU/+DizyF/Fk3PBMWGIzRVttkZKrp0Vx5OL8DLyyN97J4nffaJdFehQGtXq3AAfTtZ/jFMXn28jsOTWguQyE/rBrz6Bx9f/Eqwix8j3BvNtaSPb11r9Eg2Pvl02DD2YrVD3uZrpquq0Pk6INNHFF/Mym2sPKKJ8VKf+cJy8Td9J0JKsWgKITN9zPFFk9a6B83DqQOv3SLbGsCbSEdG5/P3FulMHwV8wxQVq/7WnBrhNTytJYEnefn5O0t/Tmh2IG/pIjWOWn2Opfrj45Lpfcb7FH60oUMAP4bQdk2nPZMFOCdNcFNAgNdFof17DIE7Jl4CB3TeQ525+rc/oGufYTD/uTugWZNGsKWs0iphy4SLoPLL6oTieYcdA7k77gL5R/dJukPZ0w9C+ZyHk34reuxd9d/8er1aeA7/e/7Jg6Cg99nWaSX9DlP/xt/18uvf+hSUvzobyuc+bZ2T174zbJlwCeTu0RHqXXuH+r3kvGPVy4oOU73wfDVQJdqJ/y4cfBVU/vqLdV+sgxoMWTuxLKojlY9l8XKoLpUfzYctU6+x6mFqE/+NrtO11cuvd+1tkLtH5+q2JvTCf9P1pG/hmRdB5Yb1qv78PqQHtxWVabIr3Z/Xw66uWCaWVfGf+Zad9HqRfdHuW64+Cyr/V517kvcFaheWVV3Pv21c+eVi9d8m/Xk/0PWh80kLfj+9z+r9AzXT70ua5+97GJQ+cgfkH90bCgZcbNlEt5v+LOB/5+19MFR8skD1vfJ3X0nqR2QTu/5GfzfVS9Vt+3ZQ+WO1toW9BkH+XnvDpnEX/90fj+6tbJR36DFQOORqq305LVqr36jf0DPG65/TvBVUrVmt+hz2fbu+XfnVYqtNpn6na0L2420mO+k6mPSsN2yi9czZ9emie1+GLRMutrTRy8lpUAxVmzbUKB7LK5t5u7qO2ov1zd29c42xqkaZLVpDTsOGkNNiG6j4+D3rWcXy+HjG9aJniZ513p9JSz5e0rVo9/xj+0KDbsfBn4OOVmMh1h3tuvnSUwEaNISi+15NGoe5bqpfHnoM5O24i+rX1M/x/9HWeK56JtnYhu+Jyo/eS9INxx+8HsuqmP9akiSmMRmfhcIRN1j9ENuBdcbngw58Tio+ml/dp4dfr+xB+vEbYHurflsFpdNvUD9bz/rG9VDyr+Nq2Dbp/ZEYU/kYwMdcupg/d+rcjRuq+8bRvZUOFR/Ph3rDr08aq5S2hx0DFe9W68GfI+pHdu9E/Znmddp8cR/1PDaZ9Z7psZDfskwBAV4Xg6KHd+KV58Ih+/+fOlP38G6e/SDU71MNnhvGXAjly5Yklag/SBsnXQllHyU/XHSO6XoqDM/hf8c4s6JBf8PLn30PUac2HHk9bJx8dVIdikffDlhPqlv93mdBfvvOyouRv2cnKB5zpzp/86wHoPTtV6Dy99Xqv6le+Pvmpx+qHgD37KT+n7cTy1PXJ87B/67EQfOdV616YFlUR/oRy+LlUF34/fBcLI/Kpmv5b/jv+n3PUXXHqUg6clu2VvWgA3XIb7+3+k9eF7ov6YvnlX+xWN2T34fbkp+LZep1Jq2wfbwedC+9rnh+4RHHqvtinYsGXqxshC9PbndqK68//Vbxw7ew/vJqW2AbsBzUo/DwY6HBBddA+RefKJtb+rRoZdma9wNdH11zuh/+rvdZ7JdYD7Irasbvm7fDzlDxv+WAcITnksZoP2qT3i+SOnPiP8gu+P/lyxYn9SNsO+q27qxjrUvxvjkNi9V51A9MNtDvpfdt/HuD869Wfa3wiB7qf3j8df4pSsvchKb8GVMnJBZC6X3f1LexfmX/ma/iSPEw9Tu9nmQ/vV9g/f66MPmj26Qn3pP6BumT1KcbNIQmD89VtqU+RuUU7HuI+p3GDbIxf+5K335VjQd4Lo5/WN/8PTvXeK5NdeO/mcYI1BBBifSi/k/POu/PpCXpxPsPHx+o7VjHvB13VmXTc/T336rHTq45lqGei8Rzxttp6kumZ5H3bX3cs3tXbHXnbGUDHPtN2vJnCs/dMPaipLGR6oHPJR6oJ/ZlfMcU7F/tTEkavxP9mY8b/PnF8/mzptvVdC6OefWO66vaUbVxvaUhxVTzMtAW2J+wvvhc41jHxyU8d/1lg9RYw599vW+UPHybsq0Ar9uTlx1/F+B1seOAi6+How7bF87s3V2d+dbCxTD2lhnw9jO3Jg0CVQd1h5wlCwFKkj0clTc+DlUt/l5hmjvpUsj5pnrXLjoq7n9T/dP0N34O/3vVrh2g8vLqOuCRd25X9f+Vl02B3JuHJ5WPv+U8/7B1X7y2qucgdZ5eDr8H1QuvzX2xemEMno8Hb0PlCQOq6584B/87Z8kCyFlR7SXDA8uiOtJvWBYvh+qi369qt05W2XStusfiBZCz8jvAf2N7cr5eUqPtXAjUAcvielGbUEtqO54HXy2pcU/SQ7X1jmshZ+lCqLxgHFR1PkTpS+23ax+/l5+6Jtn9oO5Qec6VSVqa2s/b4EUfu/5ktaVNO6jqfLBqI5WndND6s7LL10ssu6JmvK3c5nguL4/6h+pjmzYq29od1M+T+mOzrQHW/gpVZ1+hpin5c8DPo36g20zvj6qfnDRQ7fhUMWdGUl/W65W7cC7kPHiT9bN6Jg4+BmDBa5Dze/VHV86i162/071IA1M/zbv8NNWeytH3QlXbnWv0W34N2Y8/Y6oOu3cyPhNVbdol6cufT0ufxe9B7l2j1G14/9CfY3wG1PMy71nr3KTxgT1P1G41Bh3V2yrf6mcdu6jnSt0zkTUiSZtuvaDq9AuT+xTa+7dfkp4/rhl/3ukZtsbLbr0gZ8Vy1V+p3c23KoQ1q9ZA7hVnVK/uLypW4zovk2yKY3uS5jc+DrBmlaW5eh4aNoKcJ++CSrzXpg2qH/C2oS2qLhwPuVeeUd1ufJfgOWdfAfDeq0ljpPWu0Ppb1WkXKEik50k9m4nxWO+reC7Wx+3gzznXkPoDambsF5hRZU2106Ti9ucBGjSqcSv+rKM9Pu8U2gAAIABJREFUMY65qm0761w+ZmCb+TijxtzdOkLexT2TyuXju2p/YmxSNvhxudWv+Hn03ArwuvWG7Pi7AK+LHR979g149Jl/w7QbMUtDfRgx9m7Yc9cd4KqLqoPcda+lnrpKj52qsesRy1Nol0YJ74OxVXosLU/YTrFbpphA/I1yfapByLBgiGTg9zAtyDItNtGT1vPYUCrXVC+KUbPi4IoaQsmU55JSfPG6clPx2Ds9dZGdSd1ieFV+300bVK5Uni2ByuMpovT0UJTWja/ctos9Vivd2X70VD5f4MLrylPGUdyoaSGbnhqO4oG96OMWw2u3EEXvs8ouLO+laREMT2nEF5vwrBzqBZvYzpn0obg+vf/SufR3U/ws77d2MaqmfpuDH0g7tIOq1/+O8bPbLMBkE6q7XTys3bOCG0dYscF9h0L5Ad3VCnS7eFyyH18F75Q5gMdIUq5UXCOAC7IwJhTTQJnSU2F7+D3o2qRFsdrCWR7jz1OI6ZuN6Bky1MLLb5ZW58FOrBkw9WUsH7epzl+60NotUbdR0TX9VMy9nlHG1C8wRRUuRuZ9mza3MY0tVDaN0/j/fE0F32BF76s0HvOFeGQbfdzm5VM9KCYWP/DKO3Spjps1rKHg9SbY1uNk9bbp61CS1j0kMm/YrQ8wjZm8fOpD+rhD56j0nQvnqv/EtGdqpzTMRtKitbWls9uGK3gtjkVVzVoljed8bKXsGwK82QG0bq0Q4HVRqKKiEm666wl44fUFUF5eDkce3Fnl4UX4xYMDLw6Kpbi/e2LFrXpYtYTkTvu7JwFtYgtdWgBkgtYogFfPcYht0F9mlKOWgwjfVYoGUgQ4TGGjNq1gW/fqkvOB15SL1rQLlwl4TRDJ7+UGvPxcp6wV6qW1ZIGys2nhEq2eN8EMH+DpBcJXg/MPF9otS9+i1QQK+FJIyo/KXnrpBl7VZxKbK6QMvIYV77SAEDXEPJ60658FwrQj1JEnQ2Wng5NSROGCKlWvBBCUde1VI3eyDut2Q0MqwKuni9LrbOqnpkwcdsBLfUi/htuC30NfWKXvdqb6OFvpzjfX4Iv0KAcrX4ykf9ziIix98ZiyYWJzAryX9RHCMnqYssRQX+bPuum51m1k1fnIXlDZqUvStud6ekgCXi+5rrHuJieBCXi5/vxjWP+I5cCLHzmFD0+ygN/U96wNdxIecfWBwbK92PVjfXzSF9DpwMs/dCgFHt/EQc/cQQuiTfe3UtYZdj1zgxb6u77w15SJgs7lttR3QcVnc+vjkr3FXusg52WWAgK8Ae3Fgde0CtfpKxlvzQHINHDSb1g2bgBBCbT5dXq+Vf2liINT/pvPJuW7JUCtkTYmkUWCl68P/PqKaD3dEnkQcFCnJOUm+OPAzF86OuDhixG9PLhlKB0m4MW/Oa1I5x8fpiwNfoCXXriUC9PkYXcDXnpR6VkPsB7lXY62kq17BV4OVVgmZZqgdpsgnq8yL5lQvQOYbbquRML/pN2ghp+UlNSde+nI+8fLw2tzV3ynXuC0Kp/azz28+ra8WNaWCY9Ve2waVG+BqudpJr1NswK8XnQ/PY2d7mHEuhb88StUfV29EJUOO+A1ZdOga3RNubda92TTDl9J8HrkySodmF3/ttqkZYpReXrfmlNjlON9087Lxjc/4FtbYz/D7VsxCwJ9lPH28fzOeGPT5gA65JlyIzsBL3/WnUDHBDw8o4IpW06qwMsBjz/bqBPfkh3rxB0AJtvhOdYGKizVmKnv6ZsGYf/J+3Sh7Y5zfAzlqe10O+nvBt4fKZME2de0cZFdv8JrwgBe/b3Ex0y9w7tt5ywbTwQEoQy5XIA3oKEIeO1SHblNFfOUMm7Ay/N1+gFeDocE2X6AVwcpHXipTP3FjYN67pIFCrSDAC/fFpfMxT3efGA2AQGFTtidZxqYdUDBxRl/XVS9Mx4dOuTiC2/L0LFqS031UmMJ8eka0weO/mKpMVgzr5cdzKGnzW5aWd8FjJeve9fxb17TiJk86hwaTdOdel8knbD+NDWM1+nAa7KRnsSeIALP1XPgGoFX25gCz6lsu7M1Q4P/jYvpqj5ZABWP3q5mKpymtu1yI2Mbda2cgNcEejogkg1p2h8aFCv45HXgH5x6n/ICvBwqda+YXh5PA4X158+hE/Dq5fC+5wa8BJVegJf6dcE9o6zNLpKeg0T6LfyNgJePe47ew0RuWadnm+uBZdHmEbz/61P0ppAyE/DyDxPTR6bdK04fn/wAL7exHm5H9+MfxnodyDvrBMVur2YrVVoij7rT+QK8bmrWjb8L8Aa0sxvw8lyO+kuP7zOO1XACXj0pu0ri3vf8ai9ZYurR7qUYFHj1rUT5Xuckn2nbXQ6lpnhWDoFWXOfxAwAqK2tsvqBDGC+bfzTweDq9/LCBl+xFbaMB3iknctJLMeG5cQNePZbSLqSBD+rkxeI7HZlAltvF8rIlwjX4o6FgMLGTlAWyhvNUIvhNG1QspRF42UcQla97uExQb3p5mgDBTns+zWvnUeNtJBBB4IWcHNj81P2qT3rxWnGI4RrqMb5YntN2wkkxpM1bQemAy5LCNExTxnqcP+bF5dvvWpqzECOnNmGfwYM8uU7DJT9XB159q1x9By4q1w/w8ph7BEgvR3XfvNuaeaJrONAT8Oox8XYa0HPH26SHfeh64H0tL3Ai7C1V4FVlJbaB1h0hPMevPkb7BV6+vTDm3qU24bhh2sTCaVyzNAsQ0uDF3nSOAK8ftbL3XAHegLbVgReL072Mpuk69RLRHnYn4LXzkOJUI3p3nLZo1YEXQw7KcWGJtjsN1sk0EOnAq85LxGg6yce//LknUb/GtO88lW+CJryeA6/dAi874K3hbWPeHdOLF38zeXjpBUAhHBQ6YIIu8jJzm2M9cEtmXHDD94rX9VEJ0hNxfHYe3txvP4PctavUi5wf/GNAhw4CMx5vy/sALwf7kLVZSSIhv2mzDR7Ww9tKmjhtFMGnOe2gntdJn0blXif9efECvGqxVrNWf+8YOHgMNDjo8NCAl3+MOc14mDyb1OftZnlIFx147UKFeJytkycu1eHRBHhOi/roPrRYqarlNmrTDL0/8v6cat3oOus5TYSL0O8m4LULY8FrcHzEmFn8ILRCPJYsUOMyPdsmPWgTG5qK57bjzhB6zpxiYlWYycK5akvfik4HW9LwZ1R3OlAcLp5MZfOx3qQ1fjDgwRdQUgiLvlGGAG/QHirXh62AAG9ARQl4Ke4Oi9OB125K2Q/w0mClDyroySvtPTRpARWPJSSo0cMQKHZNH9T8Aq9pNyA+gHKI0UMeSHr95Z803art9EPX4AsbPc246xmP3dJ38lHtT6wapwFY93SaBmYvIQ20TTSvE77wTMBLUB9kCs8UJ6xDK+/O+gyCqW/qO8k5AS+GHXCvjiluzw546eVOi5z4y50+WHhf4QuaCLYxbjcJeBPx5vQbQgn3dGF/w+em4qCjkzJvkL11r5Q+1Yz/3aDjPtXA+9JTSV5r07BhahM/LynkwWYRpwl0rOdEu4YvJKNzTDv4Ecxw+OHA6zbDkMoQSf2Et8cL8Jrupdfbi7fZS52xXPwIRG8l9xAT8GIZaDM8TIv6vNyDzqGPHdMzSefoHyt0zyDeUD4emj4C9a3Fk+K2h0129OxzLzbNfvAx3unjxPSR4EdPv+eKh9evYtl5vgBvQLsS8HIPQI1FY4mBw7RSmw+kTh5e8pCaU11Vb8lJMKVPjdnF8tFCID7Y+wVeO88teY1MXkBdcn0g5m20g1S3uD3T9LEf4OUxiRhP2nTC3fDL2pKkqutQrHuBdM+425S4W1e0A17dQ07lmDx3pr5JLz2V2uiAo6zFbrw+pB0HXtPHDNoFwZQvLvMKh/pCFuw7GFPLPVa8LP3jxjSjwGGOnj+CYGw3/2CjPsV1JuDdtOSjpFkUr21KAvRErKcCqGGTLU+yacW+6cPD9GFIHxB0H9PzRuMC/U1lkxl4uXX/KICXPrpNXn6/HmWnFfZuz0wqf+fAm8r1Tn0jlZCYQMDLMm2gR5eneMM+SDHNJju5jbH0vFL4FN+Sm/p4WB8nQe3A370mb70sWguqcGZcL8Ab0E5OwGstluozFMo7doH8ec8mrZjWB34n4KVYP766V4/J0oGXT6NjerDclf9NesGbXjymwVVfrZ27YrkV0mAXm0vT+6kAL4fooMCLGlQc2SspfMOLhxe7heWlsgHeJCi2WThBcY2UJigMD6+e4s3uowPDB3SvqCnchv9m93FE3ho6F2c0MGsIenT4/d1ekiZvlsnD68WjZvrgIK8zhZlwLxOPdafngUNkUODlHm+TDnYe1iRvK5te158d3c5u9yCt6RnizzYPGYkCeE2r8E1ZSbwMv27eOS9l+Dmn1oA3EdOvjxGhAa+Wj52HhQUBXtIWnzUMqyAvr9exwI9tUj3XFBvOyxLgTVXZzLpOgDegvZyAl15Qph2D8Lb6i8YJeKma/OWI5SPQUNohWjShe974izIJTgaPqeE9sxtcudeL53i0y69Lg11tA6/SaJcOkQAv2oSmKk3Ty0nePUO6N79dTw+VoA8avvAJP4IIcrcMHVfjFhxuKeMA/w31UouBSjaqjASYmYB7a6hv6VPiFAfs9SXnGNJgiKk2acU/OKgten/j9dEBGa/ZfM10K2VUYOBlIRY8xInqzj3SFMuMbdh87XSrH/H0X3bPjrJx89Zq0apbmIcaZxKLovizrYeM6J5iv31TP98EvFbfMYw7Tvcj71yQj0U/7akt4CX76I6IsIBXz6bAgZePX3ysd/LQ6jOJvDzU2/QM+LFDmOcK8IapZuaWJcAb0HZOwKtP8dCtTGmy8G8mT4ZpUOFxVyZPjRVblYhd5cBNwGsXS+YHeCkkQs8xiW0xpdSxk1qfquW5MYN6ePkiL7sFcHYeLjcPr7LZrLsVIKIdnF4OQV5apJsOvLrHD8G3dNDlNSCI605lIDQh5ODCIL2P4flYFoa66N4aN+A1eZVNdncCXj8eR2oP2VYPG3ICXt1rrXuaeQzvhhUr1M5PfDGV3i43T6TbSxcXbPHFi3bA62UxEK8btYsWNuEHII/H9vqR4meoNAGv+pD6fRVUtm3nuEhTvw9+FOC1eKRjiry2gJfsgyn1aMEefy+kAvzU50wfhHwBKe9TXoFXjxfXgdppoZ+fvhTGuVYKM7azKS9XPLxhqBz/MgR4A9rIBLyW18+QhxVvR6vB9dX5XoCXr0THARC9PPUnDlGtoEGLEuqbVoJTCIKdR1LfQUyHLXw54mIxFV/Zph2gFzHJQ9jhIAVKGCOoQ7yd1NxbqJ9jB7xugylfgU27bkUBvAG7j6/L3YDXCyjqgIgVMAEv9g++o54Og9S3uAedf+i4NSws4OW5e+3yNZs2R+B11V/wfPV8cZs2atHa+k1lbk0yfrDyixDcMAwEDy8hGzzmljzt/Dk3VcgEyXaeNq9g49pwwwn8oxvHqEw6ogBesouXZ1TXKsjHMn0s0GYt+juGLzwjL7/XfsHrhWMs7l5oxfU22xpKJj4WG7PrqTv1ignwxsZUkVZEgDegvCbgNXnB+G3sPCo0gHDvqw4jScCbmPrlIMQ3IDABL4EiDoRec1di3Z0GQb4BgA6ieiYDk9yRAq8pfyxbyOEEENTm8q4nQ/PBI2osWgvYdXxfbmUgYPvY81XRXl6mRuBlOzlRpfTd+aIEXvIKm16+biLpnkQ99ZqTh5f6qlPfblSU7xt4nVbiu7WH/52eHd2T7+jhZZuUUFl2H4dewcZPnencVGyZyn2iuCZ2wJuwaSoeXjt4xt+5R1Zf3KlnvzHpbMq0QHb3uzAxCjvyMgV4o1Y4M8oX4A1oJwRep92X9BRheDu7aV/TlzwHXhrwdMB1Al49HZmbZ9RODqeXo2n6ksoxbXag38ML8Oog49YO64WbWDCIu5/RNsBeF61Zi2yO6w8tBgypdeAlz721qcQuHayQAydw53qbgNfkFbSbntTjw9ETDEUNrUWMbnaxgMiwXSqfmfAaU2rasYnPOPANBZJ2pGKLDLH9eOAWsPpHoC/gDRFM9GeEf1Q6Aa/et50gSYDXPNpFAbxec24HfB25Xq6H1aQaV213IyvES8sH7FqxWj5BPLy1bIA03V6AN6DQCLxeU824eVxMwMthxA54eQgFggL/8s5/aWYSFHkFEl0WBAvc1MBpoYxJh8DAm1hwg/XhIOPWDu5l57lx8TqvwGtBc0yA15TWzmveS7KnF+DVFz+SNwj/vwbw9uivitY3r3B7rEzhO6lM+5qeGad+Ymq/U139AK+bF8lNE6e/m0JATOcj1CN0UL+w29GMP09e46791J8yVniZdfBTbjrOjQJ401FvL/dwiyP3UkY2niPAm41WrdkmAd6AdnYDXlMieDtYcwNeirvVPbpO04fkNXOD7SAyOMWYBQFeXF2OizfI6+YHePGFm790gYolrgG82pa4di/luAGvvkNcjZ2TXBLFc8jhHyc1PgAMW51aixATuWRpISSGPvA0dW4fItTPwgJe+rjDXeAoY4HTjEOUwKvHSwZ5pvRruV5eFpnpY4SpLnSOV5v5aU9cPJp+6kznZjPw8lmOKOyeit5xuEaANw5WiL4OArwBNXYDXrvpYtNtXYG3R3+1upqmN61FalNGKI+OCdz0+0cxyCmv0osz1NazfHUxttEL8OKiGlOmB/3F7gd4dX35y13XJFOAF9vktD2tHxAyAS9lbsC/YbYAEzjq2uE9eZo6r/0rLOA1PUdOcYRRAm/AocTxch4L78fOPM2ZCaLxN6/hI1G2L05lZzPwxknnONVFgDdO1oiuLgK8AbV1A17ydOQtmgv577/hGP7gBryURkn36Kp0P5s2WPu28yalA3idJPQCvHwhHi8rTOCljwQd0NQLP/Ehobcjbh5erB+fMdAXJfoBIS8LYLwAL8bIYrouDGmgLWy9PFJRAq9deiesV6YCL3+O/Ng5inAFL/bN5HMEeDPZeqnVXYA3Nd0y7SoB3oAWW3NNdfJ3t9Q7XpKnm4DX9KIjEHHaq5yapcd9evXABZTFupxvDmBXZjqAl8f0co9kpgEvt6cOvF5s6wf4TKmlTB9QqaRNihJ4nfouT1fn9sxiOX5ieMN6Zkzl8HAWrxDrNxNLlPXPpLIFeDPJWuHUVYA3HB3jXooAb0AL/bymxFMJXuL77MAB43ARqsu7HJ001ezF08OBOax0SZ4azE7ioQima/0CrxfvpJ231uThtftw4JkeWvTuV+tZGrBNHHzSBrzMA85BVU9m78cutQ68Nl59vd/EBXixXjhLgfHsXnL4+n1G5fy/FRDgrXu9QYC3bthcgDegnb0Cr5fbePWU6RkInMrmwOsHSLzU1+s5BLy0w5x+XVqAN5EGC+EWc0xSVgGsi92HA4WKVLVtB622axkL4MX64gcQlGwE3JGpcMbNlpxhe3hNu8iZsobYbVbi1D+oHJ7SLx0Lnfzmh40T8Hp93uS8YAoI8AbTLxOvFuDNRKv5r7MAr3/Nkq6oDeC1YnbbtHPdPIKHFNQ28GKKpLxPFyXpR8Bj8gLbxfCm0g6e8gor4AV4qaI5OQCtmxbFBnipXvxjxikXNBfcT0iD6dFIAt7ExieppOPy+nEX8PGscbkAb9iKZl95ArzZZ1O3FgnwuimUHX8X4A1ox9oAXr9VDgo5fu+nn89TJHHQxPP03ML8WgFeZ+VT8d4H7QvkzcWa0WI/yv3qJZZdh/VUPl6C9EcB3iDq1Y1rBXjrhp15KwV464bNBXgD2jlM4MUpXVzxXtVymxrpvYJUMyjkBLk3XivAG1RB8/VBgDfVrT/5PTFPclnXXik1LhWvcEo30i7yu7OUhDSEoXpmlSHAm1n2CqO2ArxhqBj/MgR4A9ooTOANWBXby50S8Ud1T14u96r58fDqq9GDgLsVZ9rhILUAMNtCGrx6Sr1sSODUJ/ymx7Irq7aAF7NcYAw3LQB16/8CvG4KZd/fBXizz6ZuLRLgdVMoO/4uwBvQjgK87gKmCrz6IqxAwPvNUqg3daQKoajcpUPWAa/XLVzDBF6v6bFMPcRL1hL3nhX9GQK80WsctzsI8MbNItHXR4A3eo3jcAcB3oBWEOB1F5BnlUDo5AcuZNsydJy1exz/W1TAi/fAnenocEvvlgmL1rwCb/3hPSG3ZJPtZhtu1uQeXi9ZIdzKi/vfBXjjbqHw6yfAG76mcS9RgDfuFgqnfgK8AXXMBOCtrRXxJC2lt8JE//UnDklSXN8emacuswNer3DHb0R7yFe22QmqiorrLPD6XbSlPx4CvAEHDLk89goI8MbeRKFXUIA3dEljWaAAb0CzCPD6E1BPP6YDL4YckPc1TODFWvKQiGzw8CZtQuFxAVlQ4M2UUAR/vdL+bPHwhqVk5pQjwJs5tgqrpgK8YSkZ73IEeAPaJyOA981noWD2NCsFWMAmB7ocPYR4UGiDDryYPSD//TfUOQK87lITxLuFZVBJQYHXvUbZdYYAb3bZ00trBHi9qJRd5wjwZpc97VojwBvQzpkAvAGbGMnl+uIp08K2sIGX7qE3yA0W4xrDy73Wbm0Q4E2tGwvwpqZbJl8lwJvJ1kut7gK8qemWaVcJ8Aa0mABvagLaAe+WwWOg3vQxkXh4MZa44K05NSrsBosCvKnZOBuuEuDNBiv6a4MArz+9suFsAd5ssKJ7GwR43TVyPEOANzUB9al4nskh/6WZKlcuLnLjR9CUWpiDtXDGzVkJvCW3zHHdZhobLiEN/vqrAK8/vbLhbAHebLCivzYI8PrTK1PPFuANaDkB3tQEdALeil07GgsNCrx8kRfeoHK7nRQklg4Z6wiLmeDh9ZoiTIDXX38V4PWnVzacLcCbDVb01wYBXn96ZerZArwBLSfAm5qAgYDXY0YCU80oDy3+zS2Uga6PM/Biyjko2VjDG25nFQFef/1VgNefXtlwtgBvNljRXxsEeP3plalnC/AGtJwAb2oCBgFer6BqqhlfuOa1nDgDr1/1BXj9KSbA60+vbDhbgDcbrOivDQK8/vTK1LMFeANaToA3NQF14MX42pzffoHyLkdDVfPWxkL9puAyFUKbcODfvMa9CvCmZuNsuEqANxus6K8NArz+9MqGswV4s8GK7m0Q4HXXyPEMAd7UBCR49QqdeJeia/pBztpfPYcimGqWyk5hAryp2TgbrhLgzQYr+muDAK8/vbLhbAHebLCiexsEeN01EuANqFFYl/NMDnYL29zuhTuFFY04WZ3mdaGXAK+bqtn7dwHe7LWtXcsEeOumzeteq+teiwV4A9pcPLwBBfRxeRjAi7fLXfmdSnvm9RDg9apU9p0nwJt9NnVrkQCvm0LZ93fx8GafTU0tEuANaGcB3oAC+rg8LOD1cUt1qgCvX8Wy53wB3uyxpdeWCPB6VSp7zhPgzR5bOrVEgDegnQV4Awro43IvC9t8FOf5VAFez1Jl3YkCvFlnUtcGCfC6SpR1JwjwZp1JjQ0S4A1oZwHegAJmwOXZCLxeU7JlgHkiraIAb6TyxrJwAd5YmiXSSgnwRipvbAoX4A1oCgHegAJmwOUCvBlgpIiqKMAbkbAxLlaAN8bGiahqArwRCRuzYgV4AxpEgDeggBlwuQBvBhgpoioK8EYkbIyLFeCNsXEiqpoAb0TCxqxYAd6ABhHgDShgBlyeTcCbAXLHqooCvLEyR1oqI8CbFpljdRMB3liZI7LKCPAGlFaAN6CAGXC5AG8GGCmiKgrwRiRsjIsV4I2xcSKqmgBvRMLGrFgB3oAGEeANKGAGXC7AmwFGiqiKArwRCRvjYgV4Y2yciKomwBuRsDErVoA3oEEEeAMKmAGXC/BmgJEiqqIAb0TCxrhYAd4YGyeiqgnwRiRszIoV4A1oEAHegAJmwOUCvBlgpIiqKMAbkbAxLlaAN8bGiahqArwRCRuzYgV4Axrktz83ByxBLs8EBZoUF8KfG0ozoapSxxAVqF+Yp0rbXFoRYqlSVJwVaNqoHvyxfkucqyh1C1mBlk3qh1yiFBdHBQR442gVqZMoIAqIAqKAKCAKiAKiQGgKCPCGJqUUJAqIAqKAKCAKiAKigCgQRwUEeONoFamTKCAKiAKigCggCogCokBoCgjwhialFCQKiAKigCggCogCooAoEEcFBHjjaBWpkyggCogCooAoIAqIAqJAaAoI8IYmpRQkCogCooAoIAqIAqKAKBBHBQR442gVqZMoIAqIAqKAKCAKiAKiQGgKCPCGJqUUJAqIAqKAKCAKiAKigCgQRwUEeONoFamTKCAKiAKigCggCogCokBoCgjwhialFCQKiAKigCggCogCooAoEEcFBHjjaBWpkyggCogCooAoIAqIAqJAaAoI8IYmpRQkCogCooAoIAqIAqKAKBBHBQR442gVqZMoIAqIAqKAKCAKiAKiQGgKCPCGJqUUJAqIAqKAKCAKiAKigCgQRwUEeONoFamTKCAKiAKigCggCogCokBoCgjwhialFCQKiAKigCggCogCooAoEEcFBHjjaBWpkyiQJQrMnD0XbrrrCdvWfPH2w/DV8h/hlHNH2Z7z0NQrYf/Ou8MBxw2FDRtL1HkF+XlQ3LAB7LTDNnBkl87Q98QjoWGD+p5VKyuvgAEXXw+/r10Hj915LWzdoonttdSGT16/D+oVFni+h+nE9z9ZBrfd/wx8vfxHVVaX/faCy88/HVq1bOq73IeefBUm3/MUXH1xf+jX65/q+qqqKrjmxvvhzQWL4en7xkKbbVr6LlcuEAVEAVEgGxUQ4M1Gq0qbRIGYKECwePkFp8NWxQ1q1OrkYw+1gLfP8UdAx/btapxz6AEdoEWzxgp499rtHwpuyysqYM3adfDO+0vhg0++VGA37cZh8I/tt/HUcgTFJ5+bB88+MB62366V4zVhAe/nX38P/S+YAPt12gN69TgU1m/YBPc++iIU1a+n6lFQkO+p7ngu+nloAAAgAElEQVTS3Lc/hMvHT1c6cODFv1VUVMKgS2+EzVtK4clpoyAvL9dzuXKiKCAKiALZqoAAb7ZaVtolCsRAAYLFebOnQOuWzYw1Ig/vjVf/C07o3sW21gi83Q/fD8ZffnbSOV98/QOcf9VUKG5YBM/cPw7q1yt0bPlPq36HHv2ugGGD+8Cgvse4qhQW8F5y3R3wxdffwyuP3gSFCU/x4s+/hf4XToQbrj4PTux+sGtd8IRPPvsWzh0xCS47/zSYcOsjNYAXz/nufz/DKedcB6OGD4RePQ7zVK6cJAqIAqJANisgwJvN1pW2iQK1rEA6gBeb+M6ipQp6Rw8fqDzATsf4qTNh7tv/gbefvRXy8/KSTt1SWgZ3PPgsvPj6QhU+0W7HbaFxo2JY+NHnEDSkYf8eQ+C4fx6k6kgHhiAc3PNCOHT/DnDTtYNdrfXDilVwxgXj4dwzjgP0jh/S8yIj8GJBV0yYDkuXfQevPT7JtVw5QRQQBUSBbFdAgDfbLSztEwVqUQECXownbdk8OU62SeNiBZzk4b3mkjOh++H7JtW2YYMiKKpf7bG18/Di3xAcjzjlUth95+1h+qQRji0+svelcNRh+8HVF/ercR5C8/wPPoVTT+wK7XfbEX79/U948Y2F8P2PvyQBL4YSYOiA05Gbm6tijfHAWOHDe10Cl57XG87rd3zSZWecP16V9dT00Y7lrf1zPeC5B++3F1w3bAD8sW69I/Au+M/n8K/LJsNzD02AXf7RphZ7gdxaFBAFRIHaV0CAt/ZtIDUQBbJWAadFawRiTovWeHyqE/CigGdeNBH+XLcBXpx5g62eP/60Go7tdwXcP/kyOGjf9knnvf/xMjhnxKQaHlNTSAOGEjzx3DxHu3U9uDPcMfESdQ4C8/EDrlKQ3a/XUUnXnTvyZvjpl9/h1cdusi0P43ExLrd5063g9vEXq7hcN+BFKN/v2CEwcsip1qK2rO1o0jBRQBQQBVwUEOCVLiIKiAKRKUCwiPG5TRo3SrrPPh12gQZF9S0P71mnHQsHdN4z6Zydd9wWtmnVXP0WBvB+tPRrGHjJDWCKKb757idh5tNz4ePX7rVibPG+JuDFOGD02jodjRs1hB3btk4CXvTMntaza9JlCNm/rF6jYnvtDsx08eHiL+HBKVdA/YTHG+G+a59hcMUFp8OpPbtCYUE+5OTkJBVx4qBrAMEbPctyiAKigChQlxUQ4K3L1pe2iwIRK5CuGF4KacAwhLtvGGbbKkzXddE1t8H7L90NjbSsEVdef6+CyjdnT0263gS8qYY0XDb0NBh0avJCOS8hDRiP+9K/FzlaCz3bO2lZKk4bOg723HVHGDVsQMSWluJFAVFAFIi3AgK88baP1E4UyGgF0gW8FK864Ypz1GIuu4M8vG89fWuN3Ls3T3sSnn7pHfjg5WmuwOs3pAELxPCCY7vuD+Mu+zvLRGVlFRzS80I4ZP//g0nXDbGt948//apCGPiBac0GX36LyjTR/Yj9VPyynif4xIFXQ9dD9hYPb0Y/RVJ5UUAUCEMBAd4wVJQyRAFRwKhAOoD32+9XKvDbqrghzL53jGM+W4rhffjWK2G/Trsn1Rk9qOhJnfPgBNh1p78XeT345Ctwyz2zkhat+Q1pwBtdfN3t8NmX/4XXn5hs1fGTz76BMy+6HiZeeS6cdMwhqj4IstimFs2awPbbbW3bs9xieHFzjf2OHQzoVaaNKaSbigKigChQVxUQ4K2rlpd2iwJpUCBs4KWNJzCrwR/r/oLFny+HN975CNpsixtPDHcERGouZmk44aguMHxw3yQFEBCP63+F2rFt5NDT1EYZr7/zETzyzOtQVlYeOC3Zp8u+g/4XTVRxynzjCczJ+9yDE6y44UUffQG4kK3vCUfA6BGDUgbetxYuhguvvk2yNKShn8stRAFRIP4KCPDG30ZSQ1EgYxUIG3hpa2HMUlDcoEgtCvvnYfvAaT27QYOiep50wjy8by74BObNmgq5ucmLvDCbwripM2DJF99Bs8aNVCYHBOBHn3kjMPBi5TD04o4HnoGv/7uyemvhffeCyy84LWlTjrCAd9joO+HLb3+UPLyeeoWcJAqIAtmugABvtltY2icKiAJJCqz85Tc4rv+VcO2wMwG3M87GY9k3P8CpQ8bC2JFnyU5r2WhgaZMoIAr4VkCA17dkcoEoIApkugKT73lKLVB7/qGJ0Kpl00xvTlL9S0vL4IwLJqgUZU9OG6Vy9sohCogCokBdV0CAt673AGm/KFAHFcB43QEXXw8bN22GmbddBbjrWzYcGNt86ag74D9Lv1YL+Npua7/oLRvaK20QBUQBUcCrAgK8XpWS80QBUUAUEAVEAVFAFBAFMlIBAd6MNJtUWhQQBUQBUUAUEAVEAVHAqwICvF6Vsjnvzw2lAUuQyzNBgaJ6eVCypSITqip1DFGBgkT8a1lFZYilSlFxVqBBvXzYtKU8zlWUuoWsQJPiwpBLlOLiqIAAb0Cr/LymJGAJcnncFcjJAWjdtAh+WSu2jrutwq5fo6J8gJwcWL+pLOyipbyYKrBt8yKQcT2mxomoWmhzObJfAQHegDaWgTGggBlwuQBvBhgpoioK8EYkbIyLFeCNsXEiqpoAb0TCxqxYAd6ABhHgDShgBlwuwJsBRoqoigK8EQkb42IFeGNsnIiqJsAbkbAxK1aAN6BBBHgDCpgBlwvwZoCRIqqiAG9Ewsa4WAHeGBsnoqoJ8EYkbMyKFeANaBAB3oACZsDlArwZYKSIqijAG5GwMS5WgDfGxomoagK8EQkbs2IFeAMaJNuB94uytTB6zYewZ0FTGNf8gIBqZeblAryZabcwai3AG4aKmVWGAG9m2SuM2grwhqFi/MsQ4A1oo2wH3tc2/Qjn/PomHFivNTyzzTEB1crMywV4M9NuYdRagDcMFTOrDAHezLJXGLUV4A1DxfiXIcAb0EbZDry3/LEYpqxbqlT6acdBAdXKzMsFeDPTbmHUWoA3DBUzqwwB3syyl6m2Kyo2wE/lG5SjxsshwOtFpcw/R4A3oA0FeAMKmAGXC/Cmz0izNi6HleUboU9xO2ibV5y+G9vcSYC31k2Q9goI8KZd8tBvuN0PD6syv9z+DNgq131TCQHe0E0QywIFeAOaJduB99Lf58PsDd+Jh1c2ngj4pHi7/JRfXoP3t6yCp1sfCwfVb+XtogjPEuCNUNyYFi3AG1PDeKzWX5WlsMePj6uzvY4jArwexc3w0wR4Axow24GXAARlkpAG2Wkt4OPiejn1t6ktD4G+DXd2PT/qEwR4o1Y4fuUL8MbPJn5qtGjzaui96lV1CY0j5PF9fbsToX1BsxrFCfD6UThzzxXgDWi7ugS8XqeHAkoau8trI6QBs2Ms2/IH7FmvqXGAjp1IIVWIgHd4444womnnkEpNvRgB3tS1i8uVtA7Ba58S4E2/5XBWBw+vMbdONeTAizZvX6+5Wnjt5PEV4E2/zWvjjgK8AVV/9ufvQ3lIA1YjtMt7r3otMTAcAxj43/2n5+GvyjLHwSK0m8e0oNoAXgI/jGW9tcWhMVUm/GoJ8IavaV0vcdSaD+CB9V9CVMCLH6cYb+4lVrSu28Ku/W4eWD+6ceBFgG5b0NAKy9NDHDD8Ae0mwOtH4cw9V4A3oO1yPp6W8VP9+PW7omw99N1qF5VzFw/05vb+5VX4ouwPSyGv8VABJY3d5bUJvGSLuvIyFeCNXffP+ApRn/KaWtGPh/fAlU/DivIN1tR5xotVSw0g4A3jHYMLX4f99p5qSdv8YmUfOqh8dOacs2oebJVXD55ufYwAby3ZPd23zUrg/fzr72HM5Idh+fcrYdvWLeCqi/rBoQd0MGpbsrkUrrnxPljyxXL4c90G2GmHbWHkkFPhwH32VOfP/+AzGHLFLUnXFhTkw5I37le/hQm8lP4LPRF44EOJC8ba5DeMLJ4R73HgiqfV/XBziWUMcPE3vPdWOYXq9zAGo3R38DDuV9vAO7b5/nBuo+r+mO2HXziJWo+oQhroBV9X4+Kjthsv30+fwqn13AYA+1eY01mh93D0mvfhwPqt1UY8ZMejG7SFB7fuls5mZdW9SEevXninxvNUmvp5fTH7S8FWcN+6z62ZSxxfR+24T1bpKY0xK5B1wFtWVg5Hn3EZnH5SNzi1Z1d4Z+ESGDd1Jsx94mZo1qRRDRUQcu955AU46ZhDoGXzJjDn1fkw/ZEX4K2nb4XihkUKeMdPnQFP3z/OujYHABoVNzACL05vmYLi3Togn4ahlyD95tUz4XYP09/517Dp7wi5k/9YHKuV86m0M8g1tQG8GEpC3nX0UrzfpneQJmTMtX7ghDcqKoCMAnj5R6YAb/Rd02uf4mPw+217G9PiEUxtlVsAT29zLHT/6QWrAWLL1G1Jz28YIVwm4EXHDaY75Ae+V/EDB8fXHzuemXrl5cqMUSDrgPfDxV/BJdfdDgteuAtycxFNAfoOHgOn9ewKvXoc5mqY8ooK6NjtHHj6vrGwxy47KOCdeNsj8Nrjk4zXooeXBkcaMA+q3xpGNOnsOa0SeXLxQcWDBs507HLG047pDaSvbTonLivnXY0Y8gm1Abz0AqCBuq54173CiW7iTAJe08dtyF1WimMK7PHjY8qb5/bhyO1iB14UD4zF4zNJ2QD4uE23Hvb7fMAxfGzzAyKbocsGQ+sxt7ij5wPrl8G6yrKU8nHrwIu2xFjduZtWWHLRrNkBK2crEK7aZ2g2SCltcFEg64B31gtvwTMvvwtPTR9tNf3y8fdAq5bNYMSQvq4d4tNl38FZw26Cd569zfLwXnD1VGjauBFsVdwA9u+8B1xyXm/1bzwQeAlG9NWhXleZ6w8oAS/9HqWHl14GpnAGahdf5Xxe4/awrGytansYK2pdDRKDE8IEXi8fMbhwcNHm6lXL+NGBoS5heD5iIKVrFQhc3eDEDnjtPHOuN7Y5IQoPLx8n7NIkpVrfunYdarloyyrbsC/+LJmglOt1//pl1hoG/N3Ul3iaRj0+VPfwUl/GsnAqfWodWnzqpx/y50H3nKfyoX/2r/MU3D6wdVdonFsP2hc2hfvWfWHtGIq/H9Nge1VF+oAR4PVjscw9N+uAd8bsuTBv/scw8/arLauMuvlBKMjPh+uGDXC01MZNm6HfBROgR7cD4F/9T1Dn/rFuPaz+7Q9ovFUxrPp1Ddxyzyxo2bwxTB17oQW8b+3aEw4v3hbe2fAzHPnN89UPUut9Ycy2+3nqGXgNXktH5d7VX5tjfv4PjFv1EXQqag6f7OEO655uxk5aUvI77P3lbNihsBgubdURhq1YkFQEtYvqgW3q3LAFnPxddSYHqqff+2bi+Qi9VVXBa05aOumX+8k060b/3as/7PT5o3VGb952P/2LrqM+G9xSrAScKArB9lTijLVfwVk/vKX+M5L6htr4eBfmNEby8VgfW02t4s8m/n1As93g4R27Jp2Kz+IPpeut3xrnFUKTvEL4X+kG+GSPPtAkr556XnHMXlKyRp2H56yrKFV/71TUIrCgXb99Hv4s3wLPtjsWdiysGaYX+AZpLkC308Ut/w9u/+0zVYuHdjwSBjbb3VeNyEb82eK25b/f9tun6r0nwOtL4ow9OeuAFz28c157D564+zrLKOjh3bplU7UYze5A2B1yxRTYoU0rGH/52ZCDhGM4Fn/+LQy85AZY+u8H1Dno4X1mm+pdodB7d/bq6nx/w5t0hJEe84hu+331Noh0/PyPQeqfGDs75c+l6t/0W5g9Db+sT/nlVTioXmu4detD4IDE4jW6xwcYx5ZfbNUD24RTQ/f/9WVkdUqlfRg3jfXC2OkoshlgV2jVpAhW/RF84wluU9KXtxlXFHM7oN33X1E97fZGG3PS9FQ0i+s1/Fn4agdv24JiW+g6ehbDap/y8EIOrC+pTs0XxsH7QNj1DaN+mVSG0xiJ3jsaq6hNTn2KyhrYfDeYseZrQG/jVzv0S5KD908MN3qodTcY9duHysuMtsTZsIWJ2Rm8sFFuAexV0Nz6exi7B1IdcFr+vK0yfzErvYdM/e7crfYAnFXE9xAdeP5Zq/+tYqzfaNMz6bL7/1oGo9Z8qDz+H7btY/3N7pmjewvwZtJTn3pdsw54P1j8JQwbdScseOFOC1p7nzcaTu15JPQ5/gijUr+vXadgd+//20VldLCDXbx4wX8+hysmTIf3nr9DlcVDGnhogtcwBIQ1XPjAg+ppaozHi0WxIEJfFEfxTCSSHlqB0+tzN/1oLaaKok6pdOWoU1mFGdJA023YTj61xgdzigvEl+VX2/eDuG23m4qNvF7Dp4G9TmfSM4T38HqN1/pEEdLAx4mw6+u1XdlyHg8x0LWklGE4Fn9RtgbWV5YZnznSgsbbqW0PhvtWLVOZafi6BRovMfwL4RYP/MCmOpzTaA+V75cfeG+cUveTB9jNNtmWGYKHNJja3r6gqVogSM4M/vzQZkg4Bpyz+k0rBZme7cHpmTsKFwh3OM1Ndvl7FiiQdcBbWloGR502Egb0ORr6nnAEvPvBpzBq0oNq0RlmYaisrILzRt4Mg049RqUq+3nV7zDo0htVlgb8jY78vDwoLCyAB554Bdps0wI6tt9ZpS279qYHYJ8OuyowDgN4KUsCprWhoHoCyai39TVlgTDdk2LbMI4U06TpQFzbz0HUmzSECbxcXxyU8aW6rrIU0FuDHmrTAg4BXucexjULGyCjAF6+UDTs+obxLNIufwcWtTJmKgjjHmGVoT9PtG6COxI+aNNHeV7dYuGpLJzyfnfNLyqel6cbs4u/5x+x2C4+TiLwdqnfSt0bgRhTmQU5eIYPv3HuQe4bxrWYEWFPbRYOZ+bQI047odF9+PsQf+PamZwGZF90HI1tdoAVo0vlceA1xc3LxhNhWDj+ZWQd8KLkS5d9B+OmzIDl3/8E27ZuDpedfzp0Pbh6m1LKwjB25FnQ+/jDYd78T+Di626vYSmE5dEjBqk0ZQ/Peg1W/vybSkXW/fD9YNi/+kBR/cJQgJfvArRw8+qk9F9xAV67L/C4eXi9etX9PpZhAi95nbAOfFA3LXyk9tRV4PWakzPVxaJe+kEUwKt7JdsUNISfyjfAdvnFsQBMqh9mm8Gk/HE+uJb8+dcBl4Oi3cJGDrxFJQVWfnLyItptUazP7GF4GOU2xzphaBvO2oQxPuljcVzGYKc+wmdg+DNNetPsJkItHo1zC5O2A8aZLvTO0xjJx1ACYbdMQtxGJs0EeOP8lIdXt6wE3vDkcS8JQxpoapp7brwObhxm9Hy3cQfesLxTfve6160StU5hAi+fsuervKkPmTy8QfVx78XxOYPrUxeAF+3+xZY1ygPotb1RW4syt+B9TGE3Ud/fT/k8XzVeRzBDv/P60/ise1oRhnFnri9K16j0Zejh3bW0aY1QIrpe3wjG5D2kfhw18GZCqkg9CwN63HkoCNmb93/0/H5RWr3L58KSn9XzgePluY33TMqkgeEOr2/X0zXsyy0VoACvn6cuc88V4A1oOwReelDtvA1Ot6CBEb0IZ61+M60eXpqi4ymvTF/Cdh5eN+Al77XbeUGBjr/0wk5LhbaLCnh5v6A+JMD79wJOrx+NmezhRbujBwzDmeICvPpH2evbnhjJYtCAQ6+6nOpKaRUx/Vff4l2VR5Vi4Ok+5OXFxWgEXfg3fXzDBUw/rymxIIqg2W6mBe332ob/qdtQSAXfOQwXXe3x4+NqEdyX2ycvgvOrgV5XvS16eRhGgEdtppDU62x6X2Idnfo/xtnyXUBp0wi8Dt+duP4EP1bsxn8BXr89LTvPF+ANaFc74PUSX8UXQbxh+ErlLx63qSscdDHmDKeDcID2cphAk37jLws+WODv7Quae9p5jV4Qbl6IoMCbykInL/rQOVEAr573WAdenObDl2ffhjtb8YduLwU/bYrrudyW2Qq8fEoW7U6hTHED3trc9ATXNmBmEvwYx9X4eKDXb/bG5WpDAtp+ne/QxdcX4Pmm3NU0JuFW3ccWb69iSl8r+VF5ePHA5xIXMCHw6uMSeb4pxMHpGSJAI5vyjVGwHWf/Wp3Nx2/ICDkp+L2dxlfuUIkig42XcYTeHxSaQJBODh4qw6n/87AIPB+99OgBRqCnXOX4u917UoDXi6Wy/xwB3oA2RuBFuB3etBNM+WOJtUrU6eGjW/LFYLe2OLTGtIwf4HV7oE3NdAJeDhu61xHLwoHGzXNLL3a3F3mYwFu9+Ks6DRCmWwsjDVBYwIsvOvT04MCPic/5C5pezqaFhDwhvpuWAbtzpJfjS2t9ZWmNhSv8przPO3nE+BbevH/yRUZhNCaKGF49bCNOwEteUOyjXeq3thL4U6J+0pRmVdzGAAQ0TBV1TMPtASHT60FwyUMSTIsTSUuEPoJWvAfC+q0tDqvx/OveRrxuRel6a1MCfL5u2blLDeAlL62XcR3P0TPHcOBNZawm3WisRODbvrCRcnI4OVfovm528mqXVM6j8YtDKnrisW+gV9YL8OI5OGNIYQ7nNd7TCgWi6/FjBR1HpkN3LunnSEhDKpbNvGsEeAPaDIHX7nBb9KGDnj5lxl+MtLLUbooqlZXqXoGXL/igqTEvwEv1d1udHCbw4r3Qyx1mTGRYwMthllZuU9+hDwz+cqAV3WFN2SMkvr95FXRvsH2tLI7y4vHnfR61wW1GG+EiloJm1mOG3r/Raz6wpodNYSABH2vr8iDAiyn8cNOB637/QE3HErzZAS/1AWzfrPXLfUNiGG029VHTR5ZXkKJn28uMl+nDh9+bMtrgeTi2Iqzi4jCEW0xbdfaqeda0t9OHoa4/lsfHC4Qf7uHFMeXYhjv6WnjmBLx+09LxMV8fKymVJPfykgcZnxkcT/CoTeDldT6meAeV+x0XoemH3495/ePFaUYIx75Rv3+oUsSZMmUI8IYxesS/DAHegDbiwIveJdw3nVboYtFO019OwIsrt3k5OGBtlVegcvbioU/d8IcfvZw/lq5Xgz+luzI10yvw4rUcXldWbLD1/JheWm5T02ECL08D5HcAtesKUQAvrdyme9LiC5MWOFifvXqemuLlbfLiMeVt4nlJESTTfXjJl0z9jOel5v2HT+maFvr5BSs3DVIFXv6RSPegDz834KXFUW7PjVvdU/m7X+B1C1fiKaS8QpfdBx4HRWwbpf/iHwrk5XW6l57KzA54uRZtCxqqGZlUt/jmHl5TWjqenvLBrbslmY5fq48PdB3v9/zDgAryqn0qfcbtGr3OPL88XkvhXW59yXSfVBa5msoR4HWzYnb8XYA3oB0JePmA4jWm1Al4sVq0AQH+G8vnv+kDGJ/2xkF5RdlG17CDVICXYue8eFD5SmUnwKIBMNUXvD4N3qfhzqEmek8H8NJHjB38m0Id/KQr01MnpRN4sZ7rK7cAQiBOYTpBA+8z3LNF9eXtIIDUPT1u8e5+Hnk74EUv2rKytfBF6Vo4xzBVr8MZ3hP7N09Zhb/h8zR743cqFIr6P4ULhA3vXtrtF3ix/m0T29tivLl+cLgku7vl+bULUSFN+ccQ6Yr9w+ssFwdO04wQeXipPJ5NJdVFsRTTizN1w36db23eQxkf6MNAtzmPXcV+bcoUoXt5efviCLx6PG6qmmLbeFl69gwv/Z3OEeD1o1bmnivAG9B2BLz8JcsBzOkhDAK8TjvJoLewUW49BbxOX80muCJw1uGTrzomjwhJR15sPdzCawwyvRRTAV7+gqb7k8egtj28w36frwBvTPP9VQiBDq369D1+xFAKHr3uQYAX4YxWMXNACNj1PV/O01y53d9uEZK+6x+WQ3CgA2+Y3iw74OX3NM3i8IVpXCisG/+Q1TcpQHDj/QJjZ70sQiUAD7Ian6bCF+FGAI32gC5F26gNAUxx0VRHrN/Czb9AYxxv2vR2BF6KyXbbKMbu44yPV7Sojfcn7lV3+ujRy2+cV5A0Y6UDLzUqyHjCP065/bFMHh9MH750T97PEAxp1o9DInl0aZZIf97IYRJkPQPOrOCMIfYFHl7kZRAwvWe8vhu8lO81vMapLAFeL0pn/jkCvAFtiMCrgxpPoeIUv2oHvPgS2S6vYdI2lbqH1wl4eZOcBmnTQET5DzF8gg9sfFAhKNO9B3QODcZeB7WwgBfrQ9CL/05lARO+YHDBG3qRyGPl18NrB2BuwMsX0HgBXq8Dve4ZS+XDIshjooO902I0/mGFswh0EMDou1qhx2xF2YaknZrCzB3rBXhxAc7UFodaddU9WFw7rBvfVYqnV8J/j2uxvxW2pLfdyQakm2kXKa+200MJuhRtq+CcQIrKocWXermmj2vu4cXzsf33rVumnlO7fsCBFM/p23AXOLcJ5l/9wAJTyl2MZfIxFq/Fg9KD2bWdP4s0btCHEgEv/k664iK+DxP5Y73qyc/j4Ty8X+MYhR8WuPjMZG9uE/o4Ms2QUD31xXtUZhDvJ35I4KwDfrzT2OGnv9Ezy59Lr+8GL1rj8/ZXRZmKz001E4UArxelM/8cAd6ANhyxfGGNARa/uJ/6a7ka1J3gQh8ITFNRHCrx3+Qd0EHaNIWK5zsBr58pcSfg1VPv4ItDj0F28riEBbwUZ0eapQJ2pCO/Nizg1eP0TCDYvrA5oIctCuAluEpFlyCPid5OLMuuP9i9uOkjSt+diYfYUB3t+nwqOUm9AC/elwOF03PMUyjhdXy6HMHy3CbtVbYBnrbOLUSDA6jbAlHSyBT/TXBFGQ74eIP1RKhHL6H+QUfppkwhGOTppl0FeRo2LN8EyfQMUrn8eabFsisq1ltZGVLxvFIb+GyYCXjRlvg8ohfWT5YJ/XnhXm2MBaawDHwWMdzni7LqTRYUfLftbS0q5Voj/NvlmqXyqT/p2qWiEdYF+1bvX1616qeH5XiJuzW9ZygMA3XAnMi1fQjw1rYF0nN/Ad6AOuNqXtPBk5zbJRvXBwI7aMXydQ+vDi121/IXoP7C9295FA0AACAASURBVAO8lBIGPVCYZF33UuBCCw7F/GWpAw55USltWFjAa5f5wI+JSUf+8g4LeHWPOs/Vif2FpynLFuA1Ld5Ce9h5Inkf0mPYEbZ0cKA8rbw/ml7uHBzcAJL3FzvgJVsSmPINAGhKWYdbLJfAD/8f439xISI/8Hl9YP2XnnKL0nW8bV7jfk3Pvj4DYfJUY3aEg+q1sp5/BKtnMENCYlGlHk5C9iTPNrZ7XUWZNRNjmoXhzwmu6qeFuvTB5jbb5fV51+PFTcDrtSy380hvBGyEW+oHBLF2+c31BWh2H6v6QjAeKoN1SxV4MSxrFgN0rP/wpp2tWQovH1imvhZkzHfTOpW/C/CmolrmXSPAG9BmdsCLxdKAapepIQrgNXlFaMEP1Yde+H6Al8tklw7GK/DS4EyD8P+3d95xVxRXHz90kN47dqMiGjXWqCFqbCHxtSeS1zciGLsSu1EUrFixIQpi72AhomJv2GIXUCNqpARFilSFh/J+zpJzc555ZvveuXfv/e0/ynN3Z2a/Z3b3N2fOnEnz8tMfac7NaE4X870f+u0zXvOjJHnXAwfhlFbwihfEL4RFOGjPoDkFKV48mQbWXr2wKXzttQ6bdUj5ONS53OwrcoJfnK2eKhWhIwM+LXhFTOqsHEEebJ3dIUvBqz2WtpkOLdo1HD63dcMmtaay+Xct6k6b96oniMMW9SSJYbZlzLDFiWvvvO3dckfnPb1pZL9td80BjMQY69Aj8/780jMWS/CKXWQQpkMasnoeTEFqi+W2LTQ2HRl+z7ru37Jpjc5LnETwynoOGdTI86gHclFmiyB4s+pFKCctAQjelASDBG+YoAwSvDJVK4sF+AU5tWZ+4QPp5+HVMYHyATUFrwjwsPb5obGJGL2gwvTAcDlaZJgf2zSC188bJPeu039FETr6AyMf4rSCVz42YYI3bJW5HrCY8ZZBMYtm/GCUj1TKx6JwuZ/g9fsA63tkXuamDHIvPCCQpPuHNd/Y8zgGCV5t1yg7ZckNaA+vlGGu7JdYVx6MPNv9wFoLi2SRkZlZwLZYievU09anzX09NNMKX2MyjpI6SzJBaDvYBK9MPXM9zG30oqkF767uR7pvH95qU2+2YsqKeV7MrQxYWPzr95N4ITkGepdmXQsx8+Z7ydxWVp5j7T02N8aI0n/53cpCXXLCSrnFELymcGWWO856xKtbNkyQQYMeILPo1Jsz+A0U9UwKc+X3wcOLv/A2d+DFZvw3HjzF2YlT7CDtEd7inTa/L37MIXij9Eac44IABG9KykGCV0b1fgsGggSvvHy1N5SbKlO3pmjxWxShF5yYi5ySCl7bohW9GMcmePUUdrEEL7/ktUeKGaURvPJxKZbgNT3dmqvtw1ZKwWsTQ1EeHVtOUL4uiuDl80QosCga2Lp3YXqbBQPvWidl8XMh4QC2xVC23KdR2m8TvLa4TylfTyXzMyyhQGa4jc2rXxDZ9RvRZ73619l5MWwAKqI6aFGglKEXB8pgybaI1ZYTWAsfyRkr3kAdk6zFrbaXtMEM+eBzBs973cv6wCJPngF5X8h1puBNk5WDwzb4vvdrvn5BcBdD8PJzMPqHqbR47Urq0aClt6GK3JeEBfgNiLXdg+5VBif6e6PTVUo5UXlJ++TdLXaXsAwuL0oIjW1LZttaiSjPY7HOQUhDsciWV7kQvCntESR4bbtm6eqiCF79EowieM2pMr7G7wORVPBymeZCJP3x4v8Xr5ftJVtMwau9QWkFr3g2iiV42Sszq2aZt8CP05bxsfmM+zyvT6UIXr8FXH5eZjPsRn+wxfspfVpYicjUfdD05mvRFPWDz/VowavvRWJ3pSxbrLJugzlIFMHL1/GObHqVvrCJ+nzKoMIU2/pdIynH+G8c2hNV8LIg5Jh9zrUrWUtEWNm8w7bXqbmyX84RL738m+ODeYGY+c7wE7xBz0qa13oxBK+tPTIY4lAs9lDrd72ZqkyuDwpvsWUrsM2wRA1v8AuBM+8lbObMLIevh+BN00NxbVICELxJyf3nuiDBG+YVy7Pg1VOdjEK8a/z//ELt3aR9rXhaLTKSCF5mOa1mfp1tcYO8Ijq+k9sVFgupX8RyH+z9ykrwSlaOoJXNLF5mrlxCPC0sIli6qP5waCEY9gHLIqQhyaIvv3AGvh8z1RX/TUSjXrntVwZ/ZHUoDMeEMgfJz2raWucmTSp4TeG1Tjzu72Uu4MMcBJpCQP9utsGWyjCq4NXPgMwABe3EyL9FFby216Mt/lcvcDMXTPkJXtvgXNcX5uHNIh2V7f5cCV6zbj1w2W+99Wu9P+XcMHFplqmfH5kBiJquMUjw6hCdoDbJM81xwDxrIYf02SjhNyk/0ZEuh4c3EqbcnwTBm9KEQYLXXGhkVuUneCWmSwswiekNC2mI4uGVhQ+2qaaoOMQ7IUnb9fSl2VZTGCQRvLbpVpMPi1MtSlhU7bter0IYSBSho2Pt5GUcV/Ca8Xrm4rwo7bDZQQYZLOY4Pk/6QpjgFTtL2EmSGN4kglfiRE0B5Pfxtg0QgwSvDCD0RiMS8+uXLYDrjpJKSdqoPbw2wWuLTedrzQ88/y3Iy6x/i9tf9LPhJ/g1R56i1guQgkIabP3QDMWRc/geeJ3BiA67WxePmvzCBK8t93KSvhv1nSbnlUrw6v7POWU5WwcLSz4km0cawSs5eqMyNAWvzoGt3/dBbfJz+sjsVprcuXHtGnQ+BG+WNMu3LAjelLYJErxctEy72RbK+Alev8UgXJ6IHNNDpssyV4bzh0XnxTVXk8d9iWpk4mnUcV1xBa8IsqAXsZ/gNXMZmxsT6GnuKEJTi1VpT1LBK0Is7hS1X5fUNtabf4QJXttK+bhbC8cVvOKt4g/2c90OLMTb6nsznwnbx9FvkwPus7aBhQhevZrdFM1hvHQbgwSvKWq1oLP15SDBq/ut9FO/Pm/2D32en+A3F0TKO4Kf2yNaberNnMggKg4fv75qxtLrmFU94JHzZDt0nUtb3ku2ZzLlazvw8nIQvJKbl/uCftaTvKtFXPJNy8LBKM+/KXi1HYLChzRcM/d4Me2WpmwI3jT08nMtBG9KW4UJ3qBpyTSCl5tt8y7ZvCbmIrIsBa9fjNgjy76kmauWFugGhTTofJh+L+Igr5Iko+epZVME6RXFUQSvFiWyIMMUvHq1/rD2O9XpQTo+TacBizpF7dcltbjXO02FCZQsBK/mGuWja4o1aQMPAlr9Z9tr0x5+3iDdPzRPm+CVQaFmolM28e9hvKIKXr+Fo3y9TfDq9pr3bvvNheC19bWwNHdRXpla8MpMiTkY5X7ENudDwkJs/axaBK9M/+uFf3pgl3aThrAZR21XCVHRs436OeI+IhkugrKeRO3DUfpUMc+B4C0m3fIpG4I3pS3CBG9QpgbxbEq8oS2QX14yLNz4kDQ/QYL36LnPF1Lt8HnFFLy25PSyuMhP3JghDVEEry1ukO8tKA5ahIfk/IwreIWxn+D180jbBO+Z7X5OVy34MFKaKb8uafPkRRFw5SR4mZmEwZjCyk/wiijie7164QfEGQ94Gt7mubUJXr8QkyiPfpCH14w/1LlWbX1Dx12bgwbbb1HFgo4Nlx0e/QYTfM9+288KjyjPSRg7LXjNtHx8rS3kg/9um0moFsHL96+5Sayt7bsQxt/vd9sCMtu5tmdRL8zksJgh894JfZ/55WdO2v5iXQfBWyyy5VUuBG9Ke4QJXvmQBe1/Lh8/fqHwtKJeEa1fPNxUnbBdfzT1i8yMlTOzJmTp4TVf0hqnno7TXjWXglev7I/iuTLZ8WCkV8MW1KVtM5qzYN2uemEfIFPwml0sqaDQWT+mrlxY6AtBHku9EGxEhz1iTWnqdmvREWfxn7RN4o/1QkLdbvY+PbJsOg2Z/07gdty6TabgZfvywZuPmAsW9eAn6qIdT5g1a0i8anHJ8prC4EpCdjgTiXgmdb+QuszZiqCwkCChxynZhrbbydvgwXboQR8PCPSMh5yvyzdzdXvM/rPDG/9/0v6p2xYmeP0Gi2GC18Uip1KFNJjvUnOgEDX2NuiT5id4+fnjd0XvRu28y/0Gn/we4EOvlwjqL2lntVJ+niNfDsEbGVWuT4TgTWm+MMEblKkhymi7GILXXDUdZYo6CJOZsUF/8G1eqmIKXnP6Wrc7ylS2bWHNrs061xK84rUw851KfPXaNWtqbYRgsouz8YFN4LH9+JDBT9B96f7Du2Jx7tooeVrNNgdNx9v6hjmzoTMq7N+il5eGS4sXna83zofdzHzAbZE4RVn4I+2TuMM45dsEr98HPswTqT1k5jPHMyXsMeMYVl70ZQpov1zefF4UweuXD1nY6IVsxRK82ovtZ4OgQT+3NcoznPKVTqUUvPpdKgP0sAF2nPvVfUU2MpIQCr0uJOi7JfVFEbM7zxrnhbb5bSUep+3FPBeCt5h0y6dsCN6UtggTvFy8n7CtFMFrW71uhmnoD5WZEkn+bUtVZb5czQ+evFClvqBUWFE+lnIvknaHhcagVlvWErz6fm1edvGgsSdx6soFhRXWci9JBxgSPsIfqFb1GtHUmoVekVEFL3sco/Q52yMRV/CaH0MteGUzEC16ePtnycEaR5CaglcWZzKj7g1a1JoRsa1SZyH48JLpdHjLTQp5Zvn+JcPE4i0G1vHw+gnCKIKObShetLBXjy5PNiewXaNZj148xQt70rMZfI/XLvywVky9WQ73SV5gy8f4rvtHbqPfPchiXf5dxLrpZY6ycIqv12FTUZ7hMK5hv5dS8NoWL9oGAWH34Pe7bXCkz+X36JgfptGbP83x3i9BHnW/cDLdV5O+b5LeX9LrIHiTksvXdRC8Ke0VRfBKjk1zlBvlZZCFh5eF16BWW3meLz5YUIi3zy+WLg4WnZCfRUXvxu0KH0ybh9dP8HKdfmLQL4bXZCieMh36IQI0ysdSCzPJ7XpGu219Ba/21uqFWbydp9THHyzuA+YWpnEYy7la4Mnf8iZ4R3Tazdt+VxYFmps2xBG8On+tCFFzkZtwkgWdunzpuyZDKUMLXhHBft6qpIIuqB+Ynjbb86QHfbZMC2YMs1lf2sVQQSKcfxO7pOFjvjOSPDtRryml4I27ODTqPcl5Qdl8bGUFvVvMDDmmJ9qWVztue12dD8HrinRp64HgTck/iuA190g3xUuUxN0sDvjQmQ+ixvDyB15vsav/HUdc+KEKekkHCV7xHmgRl1bwmmxZ0A9quaUXYhBH8EruWB4s3NF5L1/Bq719phi1xS0HifooXVF7zqIIXp3MnqfKowyybO2I6uE1d1YTPhLiYAunMQVZnD6pve0iRIWRpIXj++H/H9Z+Z2/Qp2cSbAMp7VGcvNFB1KdpBxo6510vdjvIflrQxYkTDrK7Xrn/Vo9Da8URS/5cbVNhye+Lv7b9uee1DhO8cXhH6aN8ji0Fmx7YxK1TygsK7YjatrDzSil4pQ9l4YgIGojomG0/HjwQGtt5L19vv/luNwVvlLCIMFu4+h2C1xXp0tYDwZuSfxTBKy8CfskMatObHln6pZdQfPD3rwd+QE3xxv/m6xatWel5C23eRRaMIjrEs2kKXo7hHNtp78QLmExkIqp0Chs5J0jwmuLHFBO8kIKnZ9fWW0uy+tzPE2cKZfH8sfDgKeS4glfHez7abT9fwaunjk3Bqz/OfmEQcbufLXwkaLrb5J+F4A1a/GeLgdbp4myCVzyUwiKOGNKZEaQP2Bj5xa3bBK8Wrk+t3492a96VWk0bXTCV36BMXxdlcBXV9rYFqX7Txlrc2rIjSJ16p6w4vKO22SZ4+dooGVlsdRRrVzVbXaUUvPzO4wWprRo0Sh1WEjZwNX+XxZh+mxuZ55vvFvH4Sn8yB9tR+04pzoPgLQV193VC8KZkHkXw6pHuEa028YSuXikdFtOphRSLqKeXzqizEtvm5REvJXt7ruuweyGkgW/ZNr2bFEXQS1qLfU5wv2TNSs/7w0eY4BVuLND5WLymps4Kfj8BJx9cDrHo2aBlZHGvBRC/+LmNpuDV29TaYpOFoy33sCnq4zI3PaiaY9AHLm1mDl1vkJgLE7zi+RS7ST9MKsBsC3psgtfv/rMUvFrQZSl4ZfDGrC6c/5YXW8n9cvbqpXVmfGyC16/PRFn0GLd/yvl+gleHDEWN4U3ahqTXlVLwJm1z1OuCvP3cv2auXlJwxIQNhEzBa9rW5uyI2k7X50HwuiZemvogeFNyjyJ49W5R4jnU6bLiCF5eVHDa3NcjCV6pSwtcLcbi7LqTFFNQDLKOJZbyNQvbAjR5CesXt236T0Q4r9Rnj0nUe5U4TR5YcCYBm+DVAxBpjy0fsU3whn1EwjjbPlhBZWbl4dUCJkjMCT9T9LO3h730PODjaXYJO5CNQfQUaxxGsouU9ojZGIm33RwgyX1pj6nud+d02Jb2aNGdDvjXkwXTBD2vxYg11Xl2ZVZIb06gBz02wWsbAOhcvFmKc5vg1TNR4pF3kV4s7Fny+71aBC+/N2VdAbNgO8m7kv8dNHPEv5shC6bg9QvlS2qXYl4HwVtMuuVTNgRvSltEEbza86N3/rKJPFtz5CMq3jF5sXAs4riuPCpfSvvMnuDFKT7X/UDvRcTbUXKeUFmoZu7AlqWHNwihfinKdplyvhlqwX9PInjDBFKcWDLT8xgmeCXFl02ca8FrxrAm7Xa29FJB929+dJKGNEQVvGZYh19GA1OE8UCOF7Jp8ZaUkU3wmgvazPAHzbDcBK8etMh0s8nGNhAUUWkTvJo3i18ehGR5iEg3F8Tpd5POYZxl3WnLqhbBa36LZOc7+WaEDYT8BK+8E80sDmntUszrIXiLSbd8yobgTWmLuIJXL6ThqqOskBZvmHyYTPEhwtYmfCSvo7lIwZaiKSUK6+X6pagzJ4iw0YvpTMEbJO70NG2pBK94SEzPiIDQYs829Z6Et20DgaD7Nz86xRC8IsL4A5lU8PLHNml8p8lRp/OSxWrs6eeNG+R5kDR24pHm80Z02t2Lm9SM+7Vcn05o3yeyh1fCD8LEQhzbS25pHQblJ3htmRBsglfzziLvrtkebvPoRdOIcy4PbLllnNst+bmVLHj1O1XPAMosWZw4dD1zqfuTvMfNlJElN2xAAyB4y9k62bUNgjcly6iC1/bRiePN0vk7+WPyxo9z6PYln3qbCHB8ruwuZcbF6WkmLTiTJOFPgiqN4A2avtc8SyV4RYCYWzcXU/CaK93ZpqUWvFpEpxG8IhbD7BnWD4PSX/kNAKRMzvSweHVNrXj3Pk3a0ScrFhSqDQppsMUEh7U37Peg3NIS+yyzP1EErxk7XwzBG3ZP5fx7JQte3T90WIstNCvKoM3v2dcCOCxkrxz6AgRvOVih+G2A4E3J2JXgtTXTFLM2oeAneEWsRXmppUEU9LHmNuzatLOXQUEO/XIspeDVL2xOxN9gvbX0s5p29MZP33qDC/YI7tK0izfoYIY6fKSYgpfLlo+MeO3LRfCaYTPcVr9d5cwBIPPOakFTUHqwMMHLNj29zbae4DVjHG191Hw2iiF4tc11fSx2OTXZlJ/m0/7NNyhsc+w31czXcr/db71e3nXSj5Lu/JfmvVDO11aL4OXnVbai1u8Q6RdRUsDpBZUSCsG2lZCZKDOY5dAXIHjLwQrFbwMEb0rGaQRv2peBKSZtwkdi6cxQirwLXtvCMT9TJonh1YL3r222oWt/WCfKZbEhi9yejVt6K5rNjT1sglcWbfHU+rD2O6XqdTItH8VLb04rZhHSYPYzM+5Z31xYXmUtIrMSvEE7c4UJXm6PPBscA7u8Xg1NXDKjlr2CPFZs55krl3gDoCxjVG3bd/stKpL7l3zDfhkT+LngI8t2purYZXJxtQhevQBaLyLUz3NY39ADPO24cLVGJKsuA8GbFcnyLgeCN6V90gjetFO33PSwqX2/NDT8MeT0RsX28NqyFwhyvv/WDRp5uXZt3rMgD68WvGH3ILFmspgiyOS2KToteOVanvrmgxcLMsuh/9nUQJddrKliCW+JIuRNgWv+mxfTPbJsOg1tv1PgwiW/fqbta/PwlkLwsg38vFRBglenRuMyuF8N7rI17frVozSzZplnWluu6ZSvkEiX20KigvIhazvnKZYyEowin1QtglfPqtjSK0Z5f8liXJ11iM0jWW7KORuH7kYQvEV+qMqkeAjelIaIKnhtuTDDhFqUpsmCFj7XJqBN0WhO02bRhrB2mnGdWvDy/+vY4ighDbItspQT5R6iejZtgneXJl3ozRXfermL+eAMGOYuVyw+JNSBtxXmI8oHI4xd0O9ZCN6oU/A63ZhfRgP5yOk2l1rwmjbwS9MmAveNn74r9EfuVxd124FmrFpGY+dO80JvshikJrG53mCDRcQRLTYjWYhnK8/Wj/MQS5mETdbXVLLgZVayYyC/w2zPfxwPr/l9kZlEVzOIWdkegjcrkuVdDgRvSvtEFbxmfkye8uzRqDn1bLBuy+CkR9ACHXm56akm/ojzwife7U0+8iLekrYh7LogwWtLni/lCTNzUwIzs4NLwWtO8emFVizc9cpn2eo2jE/S322C14zL9PPwju20J+27Xi+STTTCGPqFkJirus20WVEEr3hNswppYJ5cFh8jOvHGI/99xrTgHdS6N20x4/4CfmbQumETL/+yPBsseKlePbruu48KeZlLsWGCzjwR5NmVm4HgTfpUEVW64NVkJATn8FabFp4THZcbFtKgHS48EOOZEH4Pyju7GCnvklvW/0oI3mJQLb8yIXhT2iSJ4M3S8xcmeM04XxE2/AHlNE37Nevl/beYR5DgNVOV2Ty8HKvYq3HLguAohuDlQcBbP37nbcssAkzarT285gdAPPfiOQ8TjllyDhK83Md4QMW5bXWsuLYFL1YSwRfmuYwieOPkmLallRPBKxkHsmRlDqJsCw3ZQ927UftChgbx8LLgfXbBrMiblxSj3fo5jvL+gOBNboVqErzJKa27UvdLHuAPmfdOrRm7KH01bRuyuB6CNwuK5V8GBG9KGyURvFmvipaPm01s+QnelLcd6/K0gleLExZmnNtTvHDiiQvzUoeFNGgPvJm2KUjwmlN6pRS8Oi+mTpVmW4Et3MQjawpeLmtazQJqWb+xl5s2iuA1Y2C5Dj8Pr4131PCKWJ3POFl7eM3MGmZ6uXISvDodXRQRIV46FiEcZx5kizQ8K/FaCN7oVpUdLXlLYt68xLahTNpZzOitSX4mBG9ydnm6EoI3pbWSCN6sY+nyKngFvU6ob/PwmoLXTGUWd4rXZnIdIxlH8JZyQCF186K5Vg2a0OLVK7yFiHxEEbzaI2sKXklQb7LgsmX1v+nhsXGNI3glo0gxBw0SGiBxsDqVUpDgnb10mbftqt7COOWrI/blEqbBMexhszJ6cZ7cY9bvndg3kJMLIHiTG0q/R/M0yILgTW7zPF1ZlYL3iUmT6caxj9K8BYuoz+Yb0aXnHEO9une22m3Sy+/Q6Psm0jezvqWmTRrT3rtvT+ec3J+aNG7knR9V8EZZYJS04wQJXi4zTkaDpG0Ius7Pw6sF76zVS2jWqmVe/kbxCOhtcXs2aFmYUubFOpz/lj2KPRq0pGEdeCq6XWDTwzy82jMhU+riJZOCbZ557VXl84op1swbDMqAYQ4SJO5U35NOVWcKXr0zHMfBSmgE20h/yILyLAd98GweXnNBWTH6on4OzdAYHQYitpQY3iXLa4rRnKKVCcGbHC0Eb3J2+rlOm3YzeSviXwnBG59ZHq+oOsE7/evZdMRxQ2nEsJNo6y02ppF3PU4fTplOD916odV+Dzz+ArVr05J+3ntT+mHxUjpj6Ejap+8OdPKAg2MJXpn6KYaHqNwFry2HqIbNMbrsPeN43sNbbOztHMeH/mjzv9lTxcKMDz43ytSu1CNt8FtIpgWviFbb5gi2TqLvz6XgNQczum1mnuCxnfaqxdS8j54NW9BbPQ4t/FkLXhGGNk+8TfBqz3EcD69rwSszBTJwkgVuOqXZ4E5be4vW8ip4JXtInsRHqT+kELzJLaC3Lg5bF5C8luyvhODNnmk5llh1gvfmOx6jz6bPoBsvPdWzx5Kly2nX359IT907nHp26xRqI/YMfz59Jt102brro3p4QwtOcUJY7KP2sEaZ/k/RFOulthyipjjT6aBEJGUpeM38q2ZDJVsB/z2u4LWJ5awZ+pXn5z3ne+CDY3S1CA+yhS2chD9acQVvlA0xysHDK4LXHKTotEz7tO2eS8Er4SEcusEZWfIkPlw9O371QPAmt4AeAOclBy/fLQRvcpvn6cqqE7xnDLuFunRqR2ccd0TBTn0POY0uPmsA7b7T1qG2+8tZ19CWm21Apw48JDeCV09jx/GKhsKIeIJON2VmZeAiOHXNQ4unF1b3hgleSWWmwx/CmhImeG1hH1E9vFq8uU7DI+028yuzx3bmqqUeFteCV/LxBokszUxCSFx7eCU0xtxCtRIEr7CUfpEn8RH2LBf7dwje5IT14spSOFeSthyCNym5fF1XdYL3pPOup8036UUnDTioYKn9+59Fpw06lPbtu2Og9R57+jW6fsx4evT2i70wBz4WLSt9bN9vv5lIk3+cQ2e335bO7bh9nXuQ3/mHJ3v1o93WWxcW4OqQ+n/ZrKvXTvPgNl3+/XuF317b8CDq06Q9yXX8e5+mbWn9f95Dres3pkVrVnpF/LD5wMi3oMuy3X+bz8YUyhrZbQ86stVmhfrlB7/6Xl/+LZ3z3Rveaa9vuC7UxdUh7T6u7ZY0auG0OtXy37lPtK7fxPtN9wX+t7aJvj+2x/D5H3i/n9B+K+o/6zk6oEUvemrpum125dyJS7/xftMH26vfjCe9ayeu/1srCimff5R+K3/z68dZMF20ZoXXj/S9m8/Ebl8/SlNWLPCelb3bdPfO/Wnl6iyqd1aG5suVSp921oAcV9S6eaOyeK/nFSH3vU9WzKf7+uBGfAAAIABJREFUe+yTm1tgm+OofAJVJ3jZw9u9SwcafOxhBeuyh3fYmUfTHjuvmwa2HZNe/gddfN3dNOaaMz3BLMeyn1aVvJfs9/WT9PryOXRux+3ob53qCl75nRv69Ab9aPfmXZ22+aw5b9DHPy3w6r38+/fr1M1tunTue9496DZKu6XNLaaOrnXt0t6DIt+HWZa+8LVlc2j/fz1Z+JPUp7lt06w9Td7IrZiNcnPc9leX/duzOzNctHoFjVwwlfo0aUe39uxLWzdpX6sYfU/8Q/82m9LfF39DHGM+e4ujCsKYy2Jb7bZe14LduH+J/YS9nCeV8Pm39ehL9yz8nDZo3JL6t9nMehv6Oum3ci97NO9W1D4q/WjrJu3o4xUL6jwTuq/s2aqbF9JQs2pNFHOUzTmmXbRty6aRZdqQ5k0bUjm818sUT0U2i22Oo/IJVJ3gvWnsY/T5VzPpxktO8azLMby7/O5EmnjPFbR+D3umhocnvESj7plAo4afTptt1KNWryiHGF5erb94dY3vzm06VUzWOYDjPCJ+K/r1nu5cnoRdmGEIOuxANoeIWn9QSIO0i8sc1n7nwpatOqThVy260f0dyt9jwVOKk5bPoIEtt7SiMcM0ONxB4qd1uItetKZjXUcvmUZL1tQUsmmYeYijxoqaO7SF5VGOauco55lxz2ZojDxPHPLQvfl6uYzhtYWMRGGDc6prpzXYex0BhDRUR0+oOsHLC9aOPOFib9HaVptvSKPunkBvvz/NC1Pgg8MWJv9jCl095Hjv3yPvfJyefP5NTyB37fxfb1mzpk2oXr16ZbFoLayr6o9fKXNxBglevgedhkwnMRch5rf5Qdj98+9BgldWFps7fOVR8IaxkHuSPLQs6o7+7sU6WS/MrbBl8ZspjvMoeHlQMPqHqcR2Z/Ee9Ey0bNYwl4JXP2tmjHJYH6n23xHDW309AIK3OmxedYKXzTp+4quekJ2/cBFttflG3oK1DXutm+bnGN3Hn3mNXho3wvv3wcdcQJ9/ObNOb3jl0eupQ7vWuRK8Ub1vxer6ekGD1KE9teaipSAPb9ztZ00xre8xaLEUt7keEe3QsSPNWfBjsdA4K9eW0cM2GNBin9PGcd5jmzfYFLx87rD2O4XeTyk9vNI4DuMYvWgqBXmXK0HwxlncGWq4KjgBgrcKjGzcIgRvddi8KgVvlqYth5CGsPt5ZvkMGr1oGvVs1JxG/CfHbdg1xfrdnE7WIjyO4I2b79Ysm4Xs7FVLqXvDFvTw4i/qpO/S91+vHlGXts2qVvBK/l32tF+98INa3uCkWyuXg+CN0sfzKni5f3O/5v+W+pmPwrmczoHgLSdruGkLBK8bzqWuBYI3pQXyIHhT3mKml5uCV6dLkm1f2Xt7bOvedPR3L9BiFS+aZsc4U/Dqf3PM5qTlM8kvjU6lC16J8dZT39rDWwzBy97VIQve9nLExh28ZNohQwrLq+B1yajS6oLgrTSLht8PBG84o0o4A4I3pRUheOMBNAWvFjthMb5pNtAwBa8k5vdbtFVNHl5bSEdSwRs3DzEPNvgI2xo6Xi/L7mwI3uxY5qUkCN68WCq7dkLwZseynEuC4E1pHQjeeABNwau9inEEb9wNNPzCJVjwclaDqTULyW/b4Ur38GYpeOPaJV7vcX82BK975qWuEYK31BZwXz8Er3vmpagRgjcldQjeeABNwasFUqkEL2cg4MNvtX61C16xMPORxX8yUDFjeCF44z0POLv8CEDwlp9Nit0iCN5iEy6P8iF4U9oBgjceQJ4q50O2GDYFkimItRDVv8VNrxbk4a1GwavjlSUtm46nNvP1ih38YqGlF/h5yeP1kvI5Gx7e8rGFq5ZA8LoiXT71QPCWjy2K2RII3pR0IXiTAeQFaotWraBBrXtTq/qNC4WYgrdl/Ub0Wa/+3u9pBK8siBNRp/PR8sKpHg2b09s9/rv7nr6rSvLw6k0VhLt41nXGjKiCV2KhtRc4WY8oz6sgeMvTLsVsFQRvMemWZ9kQvOVpl6xbBcGbkigEb0qAxuVBacvktyBx6tcaU9SJoJMMBEE5iitJ8Nr42ATvPrOf8OKa9cFedT9POQRvts8BSisdAQje0rEvVc0QvKUi77ZeCN6UvCF4UwI0Ljc9i1qIiuBNsoEGBK+/nYRNq/qNaGynvWmXpp1redP5StkgBII32/6O0sqPAARv+dmk2C2C4C024fIoH4I3pR0geFMCDBG8eke1LAXvzrPG0cxVSwu1B+WCrXQPL+fE5cVonItYOPh52oMEb5KBSLa9J/vSENKQPdNyLxGCt9wtlH37IHizZ1qOJULwprQKBG9KgCGCVwtREWFRt6/VRZse3qB8wOYdVbrg5fsN4yNi1hS8OvQBgjfbZwGllYYABG9puJeyVgjeUtJ3VzcEb0rWELwpARqXy65f8meb4E2yM1eYoNP5gCF496sT0iBilrepPmbui8T/vqPznrTFjPs9XPzv3o3b0rD2O2XbIUpcGjy8JTZACaqH4C0B9BJXCcFbYgM4qh6CNyVoCN6UAI3LzbyuWoj+ZvYTNK1mIQWJU7/WhAneoPyx8PASiVddOHJM75K1NV5YiA47ybY3lL40CN7S28B1CyB4XRMvfX0QvKW3gYsWQPCmpAzBmxJggOA1RagsaEuyuQGn49pn9gTq3agtPdv9wDoezGoXvMKnZ8MW9FaPQ+vwEa+6uTkIZ8wY23mvst0aOG3vhOBNSzB/10Pw5s9maVsMwZuWYD6uh+BNaScI3pQAjctlEwT+c5aCl8uTuF1Or2XG8H7a68ha+YB1s6rBw6v5MPdDv326lmX8BG+SwUe2Paa4pUHwFpdvOZYOwVuOVilumyB4i8u3XEqH4E1pCQjelACNy7UHMUiEJqk1SPAG7dxWbYKXd2HjOF192ARvJS5SM/sVBG+SJy3f10Dw5tt+SVoPwZuEWv6ugeBNaTMI3pQAAwRv3O2Dw1oigvetnofSzjPH1Todgve/HnAWt7LdskC6ruNudHjzTQrZHGwe+DD+efwdgjePVkvXZgjedPzyeDUEbx6tFr/NELzxmdW6AoI3JUDjcokl5T8XS/CaU/Zhnspq8fDKokCOczZ3WZPQBc7ZO3XlQppaM58GttwyW+OXYWkQvGVolCI3CYK3yIDLsHgI3jI0ShGaBMGbEioEb0qAlst16EGWpe806xGatWoZsbdy8PevF4qG4F2HwtzlTnt6Kz1W16+fQfBm+QTmoywI3nzYKctWQvBmSbN8y4LgTWkbCN6UAB1eLoLOnLKH4F1nBF4wOHPlkoJFWjdsQhfOf8f7NwRvjcOeiqpKSQCCt5T0S1M3BG9puLuuFYI3JXEI3pQAHV4OwRsPtg4vebb77ys29VgQFXh44/WZSjgbgrcSrBjvHiB44/HK69kQvCktB8GbEqDDy2UXN94oYdLymYWa4eH1N0Kxwkscmj1VVRC8qfDl8mII3lyaLVWjIXhT4cvNxRC8KU0FwZsSoMPLZRc3Frhvrfi2UHPYVsXVsmjNZgpOE8fHLk07O7RU+VQFwVs+tnDVEgheV6TLpx4I3vKxRTFbAsGbki4Eb0qADi8Xwcvb4vIWxXJA8Do0Qs6qguDNmcEyaC4EbwYQc1YEBG/ODJawuRC8CcHJZRC8KQE6vPyZ5TPqbKjA1UPwOjRCzqqC4M2ZwTJoLgRvBhBzVgQEb84MlrC5ELwJwUHwpgRXgsv1Lm66egjeEhgjJ1VC8ObEUBk2E4I3Q5g5KQqCNyeGStlMCN6UAOHhTQnQ4eUQvA5hV0hVELwVYsgYtwHBGwNWhZwKwVshhgy5DQjelHaG4E0J0PHlknUAHl7H4HNaHQRvTg2XotkQvCng5fRSCN6cGi5msyF4YwIzT4fgTQnQ8eU2wRu2qUI1Z2lwbJ6yqw6Ct+xMUvQGQfAWHXHZVQDBW3YmKUqDIHhTYoXgTQnQ8eWbz7iPlqypvWsWBK9jI+SoOgjeHBkro6ZC8GYEMkfFQPDmyFgpmgrBmwIeXwrBmxKg48tltzVdLQSvYyPkqDoI3hwZK6OmQvBmBDJHxUDw5shYKZoKwZsCHgRvSngluByCtwTQc1wlBG+OjZew6RC8CcHl+DII3hwbL0bTIXhjwLKdCg9vSoCOLz9t3mv0yNIva9UKD69jI+SoOgjeHBkro6ZC8GYEMkfFQPDmyFgpmgrBmwIePLwp4ZXgctltTVcNwVsCQ+SkSgjenBgqw2ZC8GYIMydFQfDmxFApmwnBmxIgPLwpATq+XAveoe13pN6N2tMuTTsHtgJZGhwbqYyqg+AtI2M4agoEryPQZVQNBG8ZGaOITYHgTQkXgjclQMeX6+2Fwzy70jQIXsdGKqPqIHjLyBiOmgLB6wh0GVUDwVtGxihiUyB4U8KF4E0J0PHlerc1CF7H8HNYHQRvDo2WsskQvCkB5vByCN4cGi1BkyF4E0DTl0DwpgTo+HIIXsfAc14dBG/ODZig+RC8CaDl/BII3pwbMGLzIXgjgvI7DYI3JcASXC67rX3a60hqVb9xaAsQ0hCKqGJPgOCtWNP63hgEb3XavPruuvruGII3pc0heFMCLMHlInhnb/DnSLVD8EbCVJEnQfBWpFkDbwqCtzptXn13XX13XJGCd8rnX9NFV99J07+eRd26dKBzT+5Pu++0daB1Fy9dTgMGD6dB/fvRvn13KJz72tuf0HFnX1Pr2kaNGtKHz43x/gbBm7+HhsMa+AjLziB3BsGbPxtn1WII3qxI5qccCN782CqrliKkISuS5V1OxQnemppVtO+RZ9If/2cvOuLAPemVNz6kYdfdTZMeuIratWlptcb1Y8bT48+8RvMXLqarLji+juC9+Lq7aNyYYYVr6xFRyxbrQfCWd9/OrHUQvJmhzF1BELy5M1nqBkPwpkaYuwIgeHNnskQNrjjB+84Hn9GpF9xAkyfcTPXrszQlOvwvF9EfDtyTDj5gj0BIhx17EQ088rd1BO+l199Dz9x/pfVaeHgT9btcXQTBmytzZdpYCN5MceaiMAjeXJgp00ZC8GaKs2wLqzjB+/CEl2j8xFfpoVsvLEA/6+JR1LljOzr9uMMTCd4Tz7uO2rZuSa1arEc7brsFnTroUO//+YDgLdu+nVnDIHgzQ5m7giB4c2ey1A2G4E2NMHcFQPDmzmSJGlxxgveuRybRC6+9R3ffcF4ByJCrxlKjhg3pgsFHxRa8Cxctoe++X0itW7Wgb+fOp2tGPUwd27em64ae5JW1es3aROBxUb4INKhfD7bOl8kyaS0PdvhYi8c8E555KATPeh6slG0b2eY4Kp9AxQle9vA+9szr9MDICwrWYw9vp45t6YzjjogteM0LPpjyBf3fqZfTR8/fTvXq1aPvFv5U+b2kyu+QRU/H1k1p7g+wdbV1hRZNGxLVq0dLf6yptluv2vvt3LYp3utVZn22OY7KJ1BxgvftDz6lwUNuoskTbvIEKR+HDrqQjjjw13RYv76pBe/kf0yhsy+5lV5/4sbK7x24QxAAARAAARAAARCoAAIVJ3hXrqyh3/zhDDrqsH3p8N/1pVff/piGXDnWW3TWsX0bWrNmLQ064yr68xH71UlVZlu0dvsDT1GPrh1om96b0A+LltL5w2+n7bfezEt1hgMEQAAEQAAEQAAEQKD8CVSc4GXkH037koZdexdN/3o2devSns484Y+05y+39ayxavVq2mavY2joGUfTof1+5f2NszBMfOEtWrrsR2rSuDE1atSAnrjjUk8gP/b0a3Tnw8/QrH9/76Ui2+dXO9DgYw+jZk3Dd+gqf/OjhSAAAiAAAiAAAiBQ+QQqUvBWvtlwhyAAAiAAAiAAAiAAAlEJQPBGJYXzyprABVeOpadffIt+WlFDF581gA7af/fQ9u5x0Ck08orBtNXPNqxz7hdfz6LLbriX/vnVLOLNTLbrsymdf9pR1KNrR+9czt5xwfCx9Ma7U6hF82b0v4fu4+3Sx8ePP62kv10xmj6cOt0Lg9lo/W7egsmdt9/S+33Sy+/Q6Psm0jezvqWmTRrT3rtvT+ec3J+aNG4U2macsI7AzH/PpYMGnO9lzmjfthU9/1Dt3RCz4HTj2EfpqRfepm+/X0Ad27X2wqT+dMhvCkU/MWky8TnzFiyiPptvRJeecwz16t451MZr166l8y4fQ+99/DnNnf8DtW/Tig7//a/p2D/1K6w7yKL9lVqG62edw+CuvuVBb7avZtUq2mv37b0ZQn52w571WXO+p0tG3E2ffjGDFi1ZRuv36EynDDiE9tp9u0o1D+4LBMqWAARv2ZoGDUtC4A/HD6Mjfv/r1IL3rfen0T+/nEl9d/05NW7ciIbfdD/NW7CY7rlxXbq7v140klavXu2lupszdwEdf/a1dNm5A2mPnbfxRO6oeybQ/+y3WyEs5tZ7JtBL40Z44viBx1/wdv37ee9N6YfFS+mMoSNpn7470MkDDk5yy1V9DW/9PfTaO4sieK8e9RDtsdM2tPEG3WjaP/9Fp15wozdA2nm7Lb1wqSOOG0ojhp1EW2+xMY2863H6cMr0Qv7vIBuzgLp73CRvDUGHtq3p0y++ob+cdQ3de/P51GfzuoOvqjZwwM27etYffOJFuuvhZ+jmywfTes2a0JnDbvHWdPAgNuxZ/3rGHJr6+b9o2z6beteyaL7lrifo7YmjChsjwb4gAAJuCEDwuuGMWhwR0B/BY8+82ou5llht9tbd/9jzdO9Nf/NaE+ThNZvLAviU82+gd54aRbwwcsffHk8P3jKENt+kl3fqVbc86G1NfcV5x9a5U4kbHzd6KG2x6fp1fmcv4efTZ9JNl53qiFLlVGMK3nMuu41efesjWv7jCurZtSOdMvAQ+s0ev/Bu+LQhN1HbNi1pznfz6L2Pv6ANe3Whq4ecQL26d4oE5H9Pvoz23mN7+r/D9qWb73iMPps+g268dJ3NlixdTrv+/kR66t7h1LNb3fL8bMx9iTPLXHj1HTRu9DDf7c8jNbDKTtLP+uj7nvQGIcPP/4tHgb3uvzr4VProhdupYYMGiZ91LovTUO6123aeh5+PV978yFsj8sIj18Z61nmNyN3jnqX3Pvqcbr/2rCqzFm4XBEpPAIK39DZACzIkUCzBO+b+ifTyGx96Ypm9Nv2OOpfefea2wuLFR558mcY/+Qo9OOq/O/zJbX087Us6evBweuXR6z0Pr3mwd2/LzTagUwcekiGJ6ijKFLy8YLVrp/bUulVzz3PKGVkmP3GT56VnwcuhKqf/5XDabOOedPmN93kLUW2DFJMeT13vdfhgumbICbTLL3rTGcNuoS6d2tXK7d33kNO8cBr23EaxMW+DfvTgK6hDu9Z006WnUp8tNqoOo2V0l8USvPpZ56aycGa78uwNH9/M+o4O+NPZtZ7/sGedB0gj73rC8+CPGn46tWndIiMKKAYEQCAqAQjeqKRwXi4IFEPwskhi7x6Lkl9s8zNPSHFu5ykv3VGIuXzyuTfptnv/ThPuuqwWp2XLf6L+J15CB+y1Ex37p9/VYchTnNePGU+P3n4xvHsJepgpeDlu+qEnXqKPpk0nZs+evr/ffTlt1KurJ3g5Fls8dZyZ5e6HJ9XahtyvCX+7YgzNnfcD3XbV6Z7NTzrves+7f9KAgwqX7N//LDpt0KG0b98daxUTZGP28E5+dwqdd9loGj9mGHXr0iEBheq8pBiC13zWmeyOBxznefJ32nYLDzTvvLnnYYPptcdvrPXMhj3r/PvYB5/yBs4P33oRNWhQvzoNh7sGgRIRgOAtEXhUWxwCWQver2bMoQGDh3veV1kIJx7eD54d7XkO+WAP77i/v1JLPPEH7rizr/UWqrCHSDZCkTuf9PI/6OLr7qYx15xZCI0oDpXKLVULXlnIxmkD++29q+fl5TCDu64/lzbdsEcdwcvC44bb1w02go7hNz9A73zwKd054hzPI8wHe3i7d+ngpSiUgz28w848uuAJ5L9HtTH3W475/sOBe1ausTK+s6wFr+1Z5yazh/fScwbSbjv28e7A5uENe9bl1n9asZK23/dYb2C88frdMiaC4kAABIIIQPCif1QUgUMGDqGjj9if+v1mFzrxvBG06y96U/+D162sjxvDy9PjHLd79olHeh5aObwY3gOO88IXJIb3ypsf8LyJV15wnHca/z+LXfYo8iYlptjlLbB5YRtPb262UY+KsoHLm3lx8gd01cgH6On7riT2st87/tlaYSVpBC/HXl941R00Y/Z3NPLywQWxy/d309jH6POvZtKNl5zi3S7H8O7yuxNp4j1XeAMcPuLY+HdHnUsD/nhApMWWLvmWc136Wedc6R988gVdf/HJhecvTgyv37POhR11ymVeHDhnYuHjpTc+oKHX3EUvjx8R6VnXDDnOn9cOPPvg1d6ACQcIgIA7AhC87lijpiIR+NfMb6ld21Y0/etZNOCvV9JDoy6kn23ck64Z9TB9OPULuuTsgV4KsBGjx9F6zZpGWrTGnsPzLr+Nhp45gHbebt1UJh/s0eVFMLxiv379el6qsrnzFhIvkLvo9KO9dEP//nYe/fm0KzyPHe/oJwdfx9ePvPNxevL5Nz2x1LVz+8LvzZo2QVqqCH1k8dLlnsDktFBX3HQfrVy5yhM6HM7A8dC8IKhd65Z07/jn6K5HJtHjd1wS28PLYpcHLJwq7pKzjymkjKtXr74Xt80L1o484WJvqnsrjsu8ewK9/f60grc4yMYfTPmCnn/1PW9QxpvbPPL3l712sljmeF4c/gT8nvXX3v6Yzr70Vrr1yjOI1q4l3iHzuVffjbRoLexZv+/R5+je8c/TLVdwloamdPrQkbTlZut7A9mwZ/2+R58nTkPH3uH69et7g7N5CxfT/Tefj2cdHR0EHBOA4HUMHNVlT4Cnl5975V1q17YlHfPH3xZypbI3hT9OUz//mnr/bEPaeouN6P1PvogkeHlBEwsm87jqguM9by97cDkfKGdvaN6sKfU/ZG86/qgDvdNfeO19OuWCG+pcy1tdX3j6n+ngYy6gz7+cWed3XtQGwRPePzhFGA9s2NPO6Z4uPnNAIfb12lsfpgcef5FaNG9Kh/Xr662K51RycUMaWFTv0u+EOo3ZoGcXT5jyMX7iq97gZf7CRbTV5ht5YSsb9urq/RZk4xUra+jyG+6jTz77ipYt/9HL3HHWCX/EorVw03uhJLZnnUXlRdfc6c3idO3UzstrzM9wlCwNYc/66tVriMNaJjw7mVatWkW//uW2Xh5eFr9hzzrn6R555xM0/V+zqX69erTz9r3p3JOP9AY6OEAABNwSgOB1yxu1gQAIgAAIgAAIgAAIOCYAwesYOKoDARAAARAAARAAARBwSwCC1y1v1AYCIAACIAACIAACIOCYAASvY+CoDgRAAARAAARAAARAwC0BCF63vFEbCIAACIAACIAACICAYwIQvI6BozoQAAEQAAEQAAEQAAG3BCB43fJGbSAAAiAAAiAAAiAAAo4JQPA6Bo7qQAAEQAAEQAAEQAAE3BKA4HXLG7WBAAiAAAiAAAiAAAg4JgDB6xg4qgMBEAABEAABEAABEHBLAILXLW/UBgIgAAIgAAIgAAIg4JgABK9j4KgOBEAABEAABEAABEDALQEIXre8URsIgAAIgAAIgAAIgIBjAhC8joGjOhAAARAAARAAARAAAbcEIHjd8kZtIAACIAACIAACIAACjglA8DoGjupAAARAAARAAARAAATcEoDgdcsbtYEACIAACIAACIAACDgmAMHrGDiqAwEQAAEQAAEQAAEQcEsAgtctb9QGAiAAAiAAAiAAAiDgmAAEr2PgqA4EQAAEQAAEQAAEQMAtAQhet7xRGwiAAAiAAAiAAAiAgGMCELyOgaM6EAABEAABEAABEAABtwQgeN3yRm0gAAIgAAIgAAIgAAKOCUDwOgaO6kAABEAABEAABEAABNwSgOB1yxu1gQAIgAAIgAAIgAAIOCYAwesYOKoDARAAARAAARAAARBwSwCC1y1v1AYCIAACIAACIAACIOCYAASvY+CoDgRAAARAAARAAARAwC0BCF63vFEbCIAACIAACIAACICAYwIQvI6BozoQAAEQAAEQAAEQAAG3BCB43fJGbSAAAiAAAiAAAiAAAo4JQPA6Bo7qQAAEQAAEQAAEQAAE3BKA4HXLG7WBAAiAAAiAAAiAAAg4JgDB6xg4qgMBEAABEAABEAABEHBLAILXLW/UBgIgAAIgAAIgAAIg4JgABK9j4KgOBEAABEAABEAABEDALQEIXre8URsIgAAIgAAIgAAIgIBjAhC8joGjOhAAARAAARAAARAAAbcEIHjd8kZtIAACIAACIAACIAACjglA8DoGjupAAARAAARAAARAAATcEoDgdcsbtYEACIAACIAACIAACDgmAMHrGDiqAwEQAAEQAAEQAAEQcEsAgtctb9QGAiAAAiAAAiAAAiDgmAAEr2PgqA4EQAAEQAAEQAAEQMAtAQhet7xRGwiAAAiAAAiAAAiAgGMCELyOgaM6EAABEAABEAABEAABtwQgeN3yRm0gAAIgAAIgAAIgAAKOCUDwOgaO6kAABEAABEAABEAABNwSgOB1yxu1gQAIgAAIgAAIgAAIOCYAwesYOKoDARAAARAAARAAARBwSwCC1y1v1AYCIAACIAACIAACIOCYAASvY+CoDgRAAARAAARAAARAwC0BCF63vFEbCIAACIAACIAACICAYwIQvI6BozoQAAEQAAEQAAEQAAG3BCB43fJGbSAAAiAAAiAAAiAAAo4JQPA6Bo7qQAAEQAAEQAAEQAAE3BKA4HXLG7WBAAiAAAiAAAiAAAg4JgDB6xg4qgMBEAABEAABEAABEHBLAILXLW/UBgIgAAIgAAIgAAIg4JgABK9j4KgOBEAABEAABEAABEDALQEIXre8URsIgAAIgAAIgAAIgIBjAhC8joGjOhAAARABsy8GAAAAdUlEQVQAARAAARAAAbcEIHjd8kZtIAACIAACIAACIAACjglA8DoGjupAAARAAARAAARAAATcEoDgdcsbtYEACIAACIAACIAACDgmAMHrGDiqAwEQAAEQAAEQAAEQcEsAgtctb9QGAiAAAiAAAiAAAiDgmMD/A/7HJd6TNYPDAAAAAElFTkSuQmCC"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Compare original, returns, and FFD\n",
"d_plot = ASSET_CLASS_D[\"equities\"]\n",
"ffd_series = ffdiff(spy[\"close\"].log(), d=d_plot)\n",
"\n",
"fig = make_subplots(\n",
" rows=3,\n",
" cols=1,\n",
" shared_xaxes=True,\n",
" subplot_titles=[\"Log Price (d=0, non-stationary)\", \"Returns (d=1)\", f\"FFD (d={d_plot})\"],\n",
" vertical_spacing=0.08,\n",
")\n",
"\n",
"dates = spy[\"timestamp\"].to_list()\n",
"log_prices_arr = spy[\"close\"].log().to_numpy()\n",
"returns_arr = spy[\"close\"].pct_change().to_numpy()\n",
"ffd_arr = ffd_series.to_numpy()\n",
"\n",
"# Use last 500 points for visibility\n",
"n = 500\n",
"\n",
"fig.add_trace(go.Scatter(x=dates[-n:], y=log_prices_arr[-n:], name=\"Log Price\"), row=1, col=1)\n",
"fig.add_trace(go.Scatter(x=dates[-n:], y=returns_arr[-n:], name=\"Returns\"), row=2, col=1)\n",
"fig.add_trace(go.Scatter(x=dates[-n:], y=ffd_arr[-n:], name=\"FFD\"), row=3, col=1)\n",
"\n",
"fig.update_layout(height=600, title=\"Comparing Differentiation Methods\")\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"id": "e970f6bc",
"metadata": {
"lines_to_next_cell": 2,
"papermill": {
"duration": 0.003785,
"end_time": "2026-06-13T03:34:09.120328+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.116543+00:00",
"status": "completed"
}
},
"source": [
"---\n",
"\n",
"## 9. [OPTIONAL] Walk-Forward d Search\n",
"\n",
"> **WARNING: Research Helper Only**\n",
">\n",
"> If you need to search for d, do it with **walk-forward validation**:\n",
"> estimate d on training data only, then apply to test data.\n",
"> This avoids lookahead bias from using the full sample."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "27bef20b",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-13T03:34:09.128413Z",
"iopub.status.busy": "2026-06-13T03:34:09.128330Z",
"iopub.status.idle": "2026-06-13T03:34:09.131158Z",
"shell.execute_reply": "2026-06-13T03:34:09.130818Z"
},
"papermill": {
"duration": 0.007428,
"end_time": "2026-06-13T03:34:09.131514+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.124086+00:00",
"status": "completed"
}
},
"outputs": [],
"source": [
"def find_d_walk_forward(\n",
" series: pl.Series,\n",
" train_end_idx: int,\n",
" d_grid: list[float] | None = None,\n",
" adf_threshold: float = 0.05,\n",
") -> dict[str, Any]:\n",
" \"\"\"Find the smallest $d$ on the grid that makes the series stationary.\n",
"\n",
" Estimated on training data only — no leakage from the held-out tail. The\n",
" smallest stationary $d$ is the López de Prado convention: keep as much\n",
" long-run dependence as the stationarity diagnostic allows.\n",
" \"\"\"\n",
" if d_grid is None:\n",
" d_grid = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]\n",
"\n",
" train_series = series.head(train_end_idx)\n",
" d_grid = sorted(d_grid)\n",
"\n",
" for d in d_grid:\n",
" ffd_train = ffdiff(train_series, d=d)\n",
" clean = ffd_train.drop_nulls().to_numpy()\n",
"\n",
" if len(clean) < 50:\n",
" continue\n",
"\n",
" _, adf_pval, _, _, _, _ = adfuller(clean, autolag=\"AIC\")\n",
" if adf_pval < adf_threshold:\n",
" valid = ~np.isnan(ffd_train.to_numpy())\n",
" orig = train_series.to_numpy()[valid]\n",
" ffd = ffd_train.to_numpy()[valid]\n",
" corr = np.corrcoef(orig, ffd)[0, 1]\n",
" return {\n",
" \"optimal_d\": d,\n",
" \"train_adf_pval\": adf_pval,\n",
" \"train_correlation\": corr,\n",
" }\n",
"\n",
" # No d on the grid produced a stationary series — fall back to first differences.\n",
" return {\"optimal_d\": 1.0, \"train_adf_pval\": float(\"nan\"), \"train_correlation\": 0.0}"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "21578266",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-13T03:34:09.139691Z",
"iopub.status.busy": "2026-06-13T03:34:09.139627Z",
"iopub.status.idle": "2026-06-13T03:34:09.168531Z",
"shell.execute_reply": "2026-06-13T03:34:09.168099Z"
},
"papermill": {
"duration": 0.033531,
"end_time": "2026-06-13T03:34:09.168876+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.135345+00:00",
"status": "completed"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Walk-forward d search:\n",
" Training period: 2015-01-02 to 2022-03-11\n",
" Test period: 2022-03-14 to 2023-12-29\n",
"\n",
"Results (estimated on training data ONLY):\n",
" Selected d: 0.1\n",
" Train ADF p-value: 0.0000\n",
" Train correlation with original: -0.2828\n",
"\n",
"Out-of-sample verification:\n",
" Test ADF p-value: 0.0000\n",
" Stationary in test: Yes\n"
]
}
],
"source": [
"# [OPTIONAL] Walk-forward example\n",
"# Split: 80% train, 20% test\n",
"train_pct = 0.8\n",
"train_end = int(len(spy) * train_pct)\n",
"\n",
"print(\"Walk-forward d search:\")\n",
"print(f\" Training period: {spy['timestamp'][0]} to {spy['timestamp'][train_end - 1]}\")\n",
"print(f\" Test period: {spy['timestamp'][train_end]} to {spy['timestamp'][-1]}\")\n",
"print()\n",
"\n",
"wf_result = find_d_walk_forward(spy[\"close\"].log(), train_end_idx=train_end)\n",
"\n",
"print(\"Results (estimated on training data ONLY):\")\n",
"print(f\" Selected d: {wf_result['optimal_d']}\")\n",
"print(f\" Train ADF p-value: {wf_result['train_adf_pval']:.4f}\")\n",
"print(f\" Train correlation with original: {wf_result['train_correlation']:.4f}\")\n",
"print()\n",
"\n",
"# Apply to test data (out-of-sample)\n",
"test_series = spy[\"close\"].log().tail(len(spy) - train_end)\n",
"ffd_test = ffdiff(test_series, d=wf_result[\"optimal_d\"])\n",
"clean_test = ffd_test.drop_nulls().to_numpy()\n",
"\n",
"if len(clean_test) > 50:\n",
" _, test_pval, _, _, _, _ = adfuller(clean_test, autolag=\"AIC\")\n",
" print(\"Out-of-sample verification:\")\n",
" print(f\" Test ADF p-value: {test_pval:.4f}\")\n",
" print(f\" Stationary in test: {'Yes' if test_pval < 0.05 else 'No'}\")"
]
},
{
"cell_type": "markdown",
"id": "db5bdd86",
"metadata": {
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"status": "completed"
}
},
"source": [
"### ml4t-engineer: Automated d Selection and Diagnostics\n",
"\n",
"The manual walk-forward search above builds intuition for the\n",
"memory-stationarity tradeoff. For production use, `find_optimal_d()`\n",
"automates the grid search and `fdiff_diagnostics()` provides a\n",
"comprehensive diagnostic summary."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "50ce2de2",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-13T03:34:09.185601Z",
"iopub.status.busy": "2026-06-13T03:34:09.185513Z",
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"shell.execute_reply": "2026-06-13T03:34:09.238883Z"
},
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"duration": 0.058632,
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"exception": false,
"start_time": "2026-06-13T03:34:09.181060+00:00",
"status": "completed"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"=== ml4t-engineer: find_optimal_d ===\n",
"Optimal d: 0.05\n",
"ADF p-value: 0.0088\n",
"Correlation with original: 0.5642\n"
]
}
],
"source": [
"# find_optimal_d: automated grid search\n",
"log_prices_series = spy[\"close\"].log()\n",
"optimal = find_optimal_d(log_prices_series, d_range=(0.0, 1.0), step=0.05)\n",
"print(\"=== ml4t-engineer: find_optimal_d ===\")\n",
"print(f\"Optimal d: {optimal['optimal_d']:.2f}\")\n",
"print(f\"ADF p-value: {optimal['adf_pvalue']:.4f}\")\n",
"print(f\"Correlation with original: {optimal['correlation']:.4f}\")"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "06c83a81",
"metadata": {
"execution": {
"iopub.execute_input": "2026-06-13T03:34:09.251191Z",
"iopub.status.busy": "2026-06-13T03:34:09.251041Z",
"iopub.status.idle": "2026-06-13T03:34:09.288451Z",
"shell.execute_reply": "2026-06-13T03:34:09.287865Z"
},
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"end_time": "2026-06-13T03:34:09.288817+00:00",
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"start_time": "2026-06-13T03:34:09.245699+00:00",
"status": "completed"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"=== ml4t-engineer: fdiff_diagnostics ===\n",
"d: 0.05\n",
"ADF statistic: -3.4682\n",
"ADF p-value: 0.0088\n",
"Correlation: 0.5642\n",
"Number of weights: 3237\n",
"Weight sum: 1.3528\n"
]
}
],
"source": [
"# fdiff_diagnostics: detailed analysis at a specific d\n",
"diag = fdiff_diagnostics(log_prices_series, d=optimal[\"optimal_d\"])\n",
"print(\"=== ml4t-engineer: fdiff_diagnostics ===\")\n",
"print(f\"d: {diag['d']:.2f}\")\n",
"print(f\"ADF statistic: {diag['adf_statistic']:.4f}\")\n",
"print(f\"ADF p-value: {diag['adf_pvalue']:.4f}\")\n",
"print(f\"Correlation: {diag['correlation']:.4f}\")\n",
"print(f\"Number of weights: {diag['n_weights']}\")\n",
"print(f\"Weight sum: {diag['weight_sum']:.4f}\")"
]
},
{
"cell_type": "markdown",
"id": "2159b46f",
"metadata": {
"papermill": {
"duration": 0.003807,
"end_time": "2026-06-13T03:34:09.297715+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.293908+00:00",
"status": "completed"
}
},
"source": [
"**Note**: For the recommended workflow, use **fixed d by asset class** (Section 2).\n",
"`find_optimal_d()` is a convenience for exploratory analysis — it searches the\n",
"full sample, so wrap it in a walk-forward scheme to avoid lookahead bias."
]
},
{
"cell_type": "markdown",
"id": "2b440677",
"metadata": {
"papermill": {
"duration": 0.00371,
"end_time": "2026-06-13T03:34:09.305214+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.301504+00:00",
"status": "completed"
}
},
"source": [
"## 10. Distribution Comparison"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "c4b41672",
"metadata": {
"execution": {
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},
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"end_time": "2026-06-13T03:34:09.381310+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.308991+00:00",
"status": "completed"
}
},
"outputs": [
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",
"dtype": "f8"
},
"xaxis": "x",
"yaxis": "y"
},
{
"name": "Returns",
"nbinsx": 50,
"type": "histogram",
"x": {
"bdata": 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"dtype": "f8"
},
"xaxis": "x2",
"yaxis": "y2"
},
{
"name": "FFD",
"nbinsx": 50,
"type": "histogram",
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N1D87QujuIhbUP4w8CH5mutM/QMHfGi260z/vbPRTViXUP/vYUQBPxdM/YRut85kK1D+H3wnzq7XTP3jRjU0kKdQ/EnCFDAsM1D/6G+6ale7TP05PnYtFEtQ/xEwAVaSb0z8s0sOTMcXTP1J1lOpzitM/OgehRsZR0z9jy+rYd2zTP2pZobayy9M/aK9w0gzU0z8pIOx8coPUP+FQPWh3RNQ/3KJQHJ1w1D9CyM2rNhnUP7h3qnETbdQ/fTZRCwyl0z/V9GPMsADUP2B1Ew2HwNM/xXO1HE3g0z+ui9NUhgfUP42xi+2astM/5RyKMEyV0z8fsCiAmK/TP2vV/DGvyNM/v8d63Wom0z/1gAllVUvTP3ND+2ImFtM/O6wkwX+q0z+VWsJR/N3TPwgZllbkmtM/v/1wjNjE0z8n/M5ISGrTP7Om3QREbtM/OF2qlPGV0z8Q4xmY21LTP34ekyf/e9M/e8fN9f8t0z9tMh8zoF7TP0am7VGMEdM/NXQpEHVd0z8NWKRNzhrTP6El6fGNitM/CKd8E0Tr0z8AR4YE8ZDTP9PuSy3DYdM/EhU/x+/10j+Ao1QtfRPTPykVBL+EHdM/8hgEEdgj0z/xuY7zoYvTP7MPYBQsO9M/87DcMGE00z//MXuVSEDTP2/a2TY+kNM/EAIiXtSf0z+baHpe38rTP7iTTagf09M/W7lvVHL00z+afvDKnKrTP/X1V5FkrdM/7Mab1tHx0z8ajPDKCarTPzkGGuuNoNM/0p2nvL6f0z+EEww6TaHTP7y0P1QDW9M/IXfE2lJA1D+uL6P54HXTP/o9EC+ShdM/Mq0hO9dF0z+E1jYw/xvTPxi/GA3aC9M/F8N5+ZAr0z8MuZuo3VvTP0DMYOo5R9M/Nmvv60f40j+q7CVY6ZPTP0mpkdDKOdM//newPe4U0z9aBwzpawTTPzo9ZTJPMtI/+XGXlECp0j9S8tuNbZzSP1pKJvLHmtI/xz70A2yR0j+VdTB5fxDTPyQziMvV8dI/9nuDFwcR0z+QuoNv/srSP96n6tNVr9I/dpZkU46/0j+MIz42H4jSP8S39pl4xNI/IWZ3Ujai0j+ebTL7UavSPyu/JZ4lkNI/OQeHZKdK0j9YxSQ7FPrRP6a0DHZxutI/z9dQ6T1d0j9EaPuTKkfSP4qL9ogw19I/PnslTT1v0j+fOpIMtSbTP/12X2wrOtM/uuv4ae3v0j+XR6oIiubSP+7P0MSyrNI/D5NUErbV0j84K1vMHMTSP3ancxs3odI/VzjPc86x0j/kVGcf8+PSP7NtT5N5vtI/zO8vqxih0j8ml6xjtrnSP3dvEFs2hdI/uYkj+KJs0j8R2DWjTM3SP0Asn1wKmNI/pQAewRJq0T9HHMb56RjSP/22FpaZhNI/LdR1hTWx0j/M9HrmKqnSP11tlOgrsNI/TEbOOvzf0j+RO6hOLa7SP+s28LHwjNI/OaRREQGB0j8u0g1rS/vSPzjh1CsD9tI/9KRQIES90j96z3jM9XfSPxE7BchcndI/Cq0pYR6U0j/C07IIyG3SP9GB91vBatI/gT0J47K20j9gbTgoYXzSPytRBVjDVdI/IyPWnZpd0j8CRf8XKuDSPyWTkb2FNdI/OJygDgVI0j+9aRqDYkHSP17zGBt+VNI/pUJp8uVT0j9fLYDTbcTRP0Cff8pXhNI/9iMZ8BLD0T9BTf2wuQzSPwx8+11kJNI/G8RTymo90j9IgYjSH5LRP3dbzWomL9I/aPf7Wsoh0j+gSgwC1AXSP1Xh6n+QfdI/YC5xEJNj0j/5XUCJwpHSP9ZDFNDoYdI/hovZ+EFX0j9atQ6Qw57SP6yPieD3dtI/K1Ynh0VR0j9W7OxsSETSP07uBpbNY9I/AyVbJStM0j86WLpkITDSP0oor18pGdI/MD/qO/MQ0j8GkgnK2TTSP6slOOgzKtI/i9WMWyj+0T9gjhU7jSDSPyNuSjr1L9I/kStfIpnz0T+MiM/6+/jRPzgKml9hDdE/hTupyZ1+0T/Nk2XvEi7SPxgMA9fr8tE/slp5538A0j+uC8KGAuvQPzcehNKJLtE/JDpG3Edd0T9/rsAPEhDSP7W0CmFxltE/9s27eT120T/3iRGnUqnRP0n7ze9anNE/jd63Krqp0T8YLYDGwevRPzi1QuZVKdI/yoR0uGQL0j8Doeh1TXfRP6L0eitaztE/oVAqbLu40T9oYyuo9p3RP9SOI0BHTdI/GvbwC6g70j9daIbauRTSPyJulACW9tE/KbwO9wH/0T+3LFdXqQ3SP3x+Pa3wA9I/MH8Qr1310T9gfNQyd7rRP2jervikxNE/8hilaiKe0T/k8j+B86/RP55Vdnss6tE/Yy9IUODf0T8t1Y+sWQXSP8PnyipVKtI/YiK+4q8h0j/+kViAwBPSP+udsTQ5W9I/cHOsJawS0j8XCxO6v+fRP1P5erD6D9I/NYZCOj4Q0j9rVYiOMODRP92xQ9Bg8NE/M9lgvYz20T+uRL1pa+/RPzrtxb7J79E/wG0v/4Xj0T/hkXW9gSvSP4pI0PeywNE/wGrSpOTk0T/PX7M6H4PRP+XYihs+r9E/FsHyIvMt0j/qcr+b6bbRP5aPok1A1NE/AB/l68zZ0T/EKHt9Hs7RPw3vEX3W99E/yHzcb0ny0T+D0kRCjM7RP9Zh+sCL4dE/0bojnwCS0T/psRWpfZnRPxEumL7tqNE/3K3dCl150T97JQw9SzDRP0RkNrLu2tE/q0FytUh60T+zqsgupJrRP6r+EA3f9tE/8C9fBia20T82XFge6c7RPwTVWa4grdE/JeSV6LZI0j+ojsuuyPPRP0b6ATAYa9I/d4Jvvqz/0T+TI//FxNvRP8c7gsUxmdE/BJrXvnup0T9PKaD+M9nRP+AnVAQ9GNI/dNH3XdgZ0j8MijkQJw/SPyQPc7k57tE/aIeR/GKa0T9zA9GoGjDSP5aDOCiHXtI/S+AMoI/g0T+vD/GwVNbRPw11Qljy8NE/GuPeICLW0T+nyQewi7fRP0hznN+jvdE/0s4yycrV0T9bD8FdyYLRP6DFKS9HBdI/31Z7o2480j98ZuzsM0bSP7WrBrISf9I/o9qyfvdY0j8Wzw+T8FPSP2C/k7UCFNI/wE39tuR+0j9okaKZ4KvSP5FxS6yXLtI/nb/NChXB0j+AWJmtXVjSP0t29PiVjdI/RfmNmNHh0j/1Km9t+rbSPxfk8LSUgNI/uAQfBF9u0j8d92huLRTTP9hI1SJGStI/eV/hGXmn0T/itoxdGOfRP0uG05bV2NE/pzWZeJR10D/EG95LDY/MPyyjHKsMxtA/I/aqa+NS0D+p/G1B/CfMP13+TN41G9A/56/cSlkD0T/E6jPdWOLQP96Hcz5po9E/Frrg7nwV0j/K5zq0iqvRP/2nMkzCG9E/UbFmoZPc0D8mlScEnA/RP0TaBa1HD9I/zd9bqb1i0j/5xoQHrSfRPznCem9GqdA/8rurgjH2zz9/WWKpGr7QP9p4TT1MetE/bPdFLuVe0T+Zy7LlyDXRP/ICNXuGeNE/fICLztlq0j++hJ6W9tTRP8+ANRRNRtE/eOwOU44E0T8hqArNvg/RPzmQ+4XWK9E/iP1E2xRG0D8Q2z16EbfQP6FaAQQbo9A/+7sQ9Gsvzj9OJ/09fMfMP+zB2Ixd4NA/5B8M5pu5zj9dk9fW6x/PP8uYM2+Xk9A/k9s0Gg/nzT+NksZxS0rQP8/qIL5YztA/7XhJwlQH0T9F4aGfbJ/OPwEcPlP4G9A/2drtt3Ed0T+rblI8Y2XQP8iEm0AP89A/ux6BSeGJ0D/beYLq+Q/RP+DiuF8cg9E/KdAtTYM00T9FW+l+2LLQP33jOt7uNdA/cdA1feFm0D9n8LZi7CjPPx8dtg0eGdA/AUREsMnJ0D/F+gjYc5/QP3uFF+whDNA/ngz1NodS0D+0B+UzRcPPP6fNklJY088/Y3TFEKzX0D/u03daQMXQP0gTpmOYm9A/YZXnH4wo0T8Ptnrm0nfRPzEdsnN/UtE/WhFS4B0k0T+SzijFipTQPwS++n0O89A/DbZ4Zp7I0D+qa0jdTZjQP17fD79wG9E/AnOF9Wq60D9Z7FazA+fQP8R08ha4rNA/sYiy4CGH0D9lTdn1rqjPP84qSsGz+NA/LV7zZjNR0D/L8h56RAjRP5zsGSBnGNE/7kcuoH/x0D/B9toi/l/RP4ApIeuCGNE/rTs+PRcu0T8EUc6RAh/RP+RuK4RuGNE/J2OMSx3L0D/BXPCYHvrQP8wrVzw1z9A/zF7GWlWq0D9f5nCvSnLQP3zrHsnapNA/qqtIER020D93NJhOWHnQP9WgAl3jKs8/f4NJzrES0D/j/7vwwirPP2kZxDpTMdA/8xbWAZQ40D9tHL4CUVLQP3ma4z6ZCNA/ncAnJuaf0D/uV5YxnPjQP0fN/12pRdE/F8QyrPgs0T97gm9m1nzQPzZgraHrJdE/aU9HVA300D+/dmcviMjQP6//mHt8/9A/2PsbKIH80D/5aTUvfZ/QP/qgDhXxlNA/U2obtQS20D+YKo9IPPjQP6szurTUWdE/uRIWuaLq0D8rDvbng27QPxtw//7UN9A/2AKW1++s0D+TM/wLNnnQPwkMxNxC1dA/oR8JmzX10D+JSazxHwfRP0yq0JhmE9E/iwPwMs3j0D+UXnDagLzQPw8zwnNQStA/36fqChMx0D+ZNKxih7fQP4l0GQx5GtA/zTFTySfF0D9jni0xytHQP4Urjrsk0NA/c1AGWy7Z0D8XB+L4r7HQPx8moH3ykNA/yMtMZm7y0D/aurNIgkbRPximdhFxCdE/DeBszABD0T9csDCA6srQP6BQaf3FzdA/rDstuH+o0D+wiNAxp37QP9IZVqwFWtA/tj4l8mVN0D+KJmj2gXnQP/tpccwqp9A/AZZLJxOS0D8RYj0lV+fQP9uzdoU4vNA/gv6HUZRS0D/L52oLP8LQP6Y7k7adsdA/KPDSgjUi0T9GAM1lg9PQP2wEOQXkitA/jQq/LtqD0D+hqiEnqFTQP14UiXFWktA/b8z65QWD0D+397QmDLTQP6CR9uHxjdA/gP8OAsWO0D/5hC8bUQPQP3iuZxO/ps8/w712kVIB0D/ACoTCFe7PP/hckPP57ss/lQr5zTfGyj/y7WNn2DHOP1mFeGKdYc0/NjaUTl9K0D9yhO7jKLXPP3fqApBFps0/cK3x8MtAzj8rAvZNWuXNP32kMcJclc0/cT6ggCEMyj//Clc2xBDOP03O63AFdss/A4lFUkK2yz/KyiGx9jnOPwa1QRWoIc8/06IUqAvqzz8rjThPf3nOP2jwR0QRRc8/BaKIbb/Hzz8hYqgI8QjRP2yTWev7TNA/N1F8vowGzz/t7PMp3ujMPzm/0zM2pc0/xZBCSMUgzT9NiuKF+/XOP1RAG9jg884/UTr9qC6WzD8UmJUPVATLP7JZkrtNpcw/h4T3XWYGzD8K19AqJZnOP4f7rjc7cM4//CUs8cCK0D+EV8sCoJDPP729GozRCdA/RGw/pnGk0D/leZIonzHMP2II2D5zW80/g114RKO7yj/etKnVG1XMP4DhqN3gtMw/ytRND8OMzT+Ao6wB/WLNP/qpwlJOCss/kOHXxkN/yT9GlnR0GrHKP35fHTuCTck/iwqHOwxHyD/ZrDeC9ufGP9Lf3m5fEcU/EZVPt79mzT/89M1LPq7MP0m1jwGP4ss/xwsfdqzrzD/tOs19p5fMPxeKLRNyVMk/wgET9pm5zj/Ku4Zgn2TOP/psbkwl4M4/bxesmXm8zj8RrwcNrKrOPzTlrlVXTc4/hBJY4rJMzT99WL3Mge/OP7B35auSqM4/q9MpyLRNzz8x3fWv8jnQP4mM/5Vf0M0/+hiSmkNvzj/7BKc8ymTOPxhb6x2kX88/5XtVsHjlzT9VenzTDu7NP5pG/djbANA/+Ugctm8o0D84V++dKqvPPzufYPKSINA/ai091TMf0D9SZbfWO57PP88rSP53O84/CBGnupy9zj/DUpxtscjOP20eOdWmLdA/nGuKmNMI0D99Y9AHkGDPP1SAt7QnV9A/SDcWz4of0D8uePby2xTQP79Wac8Tas8/WwafmSMc0D+CRyW42wDQP+k+5epzrc8/oYYiIxCFzz+GD/GwNzXPPzD5eqEbA9A/OY4tcOMyzz8LLclWbRHPP6bp1VJLUc4/F39hqWOGzT969V0XQMHNP3GK9iEL188/zHmfQ42tzz+YK1/g3xPQP7pr0oiGlc8/JTaw0nEG0D9Da8VsmRLQP9XW5OTb088/gmS+er9Czz+mulsJmF3QPwxFef7Jns0/uxJzVNpKzj9gK5MDl2/PP7+ruQpVcs4/wxQOhCMbzz+0voBCLb3PP0DH4ZinbtA/LrhpjW4X0D/kR309bQvQPwo9cFuPFtA/oCTxeX5B0D8yblJNGRvQP+DyB0ONVM8/TNEuh2njzz/FsLSnKqbPPwUmlnSXNtA/DRcAZ37szz+zqYMdgN/PP0e/BssqbM8/n7Q2fa+0zz90I8c9/6zPP016FOCgWdA/lHf8uJThzz8eKJ+RNrfPPyC3X52hH9A/0TG8PNAR0D9tfdbbF/3PPwJMEIFU4M4/YUv+lgzjzj8M+eIw2yPQPyi1kOOYR88/M9uBe6AuzT/+dZyIrtXNPxz1IVfPvM0/WoWA4nanzj/8VLk5zT/LP7Y8pXYFsM0/yvtzlwVczj9yCfdhCU7PP3dWmV6K980/U6xfH+tMzT9ezbqNnc/OP8NA01DjD84/DK0s7xiPzD/5RHG5NHvNP9qewtlYWsw/2sKN0xUHzD+8wyDMHefMP3AIock/O8s/6Sg9iQGuyz+VI1/LxtPOP6aotS77Bs8/iQggSJM2zz9xJLrBl/DPP1xBAVNKzc8/O2IDlP9Bzz/ZZd/OX87OP5PJ9nTXRc8/R7nRIRnWzj9CoedXI87OP2saiJ8YBdA/k8GsIt64zz+uujW1LU3QP2UWb8/Qwc8/GUm9nGhozz8MpKiSIg/OPztnoLCNVs4/O1WjhXLozj+LyFNAr2fPPyJxgK+WHtA/EE5N7yD8zz+pAbpFLlPQP+h336vy6s8/JSGHIzIGzz9566BxMFLPPyNV946i1s8/y11pYn3Tzz/CIJnKWhLQP26kqCRr088/vfYzQeE6zz/7q25KfmbOP5GpR9IhLM8//q4qBuZSzj+wk2vT1d7OP3eGm2Llss8/l0OzOcjmzz9fgZ8N+OjOP2LI1dfJ2c8/tOPChHI+zz+9cZfc5eDOP2ckXQcgh80/os8Vet3yzD8O6bHCZZDMP6Lfu90pO8k/e5nTY5PJzD8pVlTmGbzMP6qbhanVTM8/EHyqOYOEzT8qsT/8YRLMP+UUcSbZrM4/uuVQYio6yj+2mmXj9vXLP9SfhciaGM4/0bvH/WYLzz+u0PcD41TNPwvyh2B7ic4/X0vGoW8Vzj9xbXpg/aHKP3IAK1uXTM0/aFLtiaOUzD800M/nKq/NP30zpsCABs8/w8cvnI9Bzj+YpE8iVE7NP7lc5pIJ8M4/n4akDiwB0D+yQwhXv0XPP/1f0e/N/s4/61Y2wYu/zj89nf/464bPP8rnIqRbgc8/XpPz2lgNzz/Gwd+CiILOP7VrPcJb4M4/I+x/oDvHzj+4gyp716XOPypM2f3h9s0/lvPiIKkczj+wMi7/tyHNPxBYC3YbSM4/pVXqapDQzT9yKQGsSi7NP/qI2iXqDM4/sZwzTfhazD9SXNwObKXKPxqZC/UGw8w/0JxNP09qzj/oZ48//TzNPxMJZhMiTss/PBZAD0hQzT+sv3xeXO3NPxR7K0sb4c4/Uu0PKNMazj9vadswRDbPP5TfeL2fZs4/+DFo+1yjzj/EZ27I3tDNP2erd0zvxs4/b3JrJkr9zT9jYUfj3WPOP0qmCJHmaM4/DCZZVf7Czj9rlm3pyC7PP52ojq1yus4/drCd4h72zj/SLHykY1rOP3t9ZC+9ic8/gNmsGmmGzz+hBpClY/vOP6Fxl4Rc4c4/pe8uwuk0zz+LZUunkD/PPzAmEhDSvs4/rUVTp4L6zj+nPsV3t9fOPzSXe/E06s4/+vW4Dpmuzz8aRb5aKlHPP8hvWVltD88/UNDJV2Z3zj9vpq5QRVvOP6Dxlt+ds84/jomAXByQzz+edVLwO2XPP+bcOBcIrs8/obXDAE3Vzj9JHHAU78LNP3samiC/Rs0/FyU0jix6zj/6bEP99oHOP6AYbh1FiM8/I0z40tKazj88XVS62nDOPwwlIXxOzM4/kNaQvF22zz/5YuyM/UPPP8ChncTU6s8/EdpefJl2zz8Fkh7hIELPP6YOjCgwpM8/aXd5yujizz+WNHQ4bLXPP3W0H6DFdc8/21sBFuz9zz+wDWI875PPP6GxWNH2tc4/vBOE2dQvzz9CwZatNx/QPxoDbSuiuM4/KHEbEY9kzz/K11F8Y9LOP3NzE4RyjM8/k2NP4w0O0D/ef6VBqEXPP0iqTX21DdA/Si0XF8p6zz9mWi/OAqvPP75h/HnjQdA/S8/WjW0v0D/oBPZWCr7PP4zh5315qs8/obnrjBKzzz/E+c/CCWfOP8yHMQv2sMw/soy80ULozj8GGxgVOoTOP72ldqqH7c4/hUJmaHJnzD8cOWUKRTnOP/wRJ+IkAtA/VILDqd9a0D8A5ar4LynQPyh+NGbRKc8/WU7+7g4U0D8K/YrSeuzPP4cNyyYAPNA/GeSaMkTZzz80zLvrQOXPPxidU0a/Ws8/ZXwUhtz3zz8Wbq93nyLPP//OzBQZ4s0/YiqAcxQPyj+a13Y7B/XHP4JSjHMenck/Pq/XyhCtxD9m6XHOlvjGP0gPod7IoM0/Vk32wv5lyD8WL5dMafLOP6TbYcNs78g/+wUwP+opyD9pPHtgSfi9P/1Dc71wEso//jgBYMifwj/FotPsOs6wP4wiqtpj/sg/DCJXoCEqsD8Ud6s9trnEP3XO89EIsro/FuEkuZmhwD+h2LXQnyK4P+v4G0Aqfrc/Wqsfh5BpyT+8e+sr0hXIP70zSZ7JFM4/HBKjZDz/xj9mH9CSDLHLP5Qynr5LJsg/tl0gtwyJwj9spjUGzczHP4+RtTTAdcU/MJ7ozP+Mzj9EFBxs26TLPy2PVX3aAs8/qCFX35Dazj+Xnw8cESvMPz3rnl5Utc8/PTWldG82yz99h+gaxEfMP9nGqpXNYc8/UPuTGhSRyz8NU1UhY/zHP0XQkNn/Ucw/pA8ioheTyz+IZvVOvy7NP9CyWkmoN84/fMHRu0mezD9jaClyJcfPP79Zlb08GM0/7HBOQzSdyT9ovLywRivLP/DJYYOFeMw/tb5HSVYvyz9N52293fHMPxEmMXTcdc4/n6PSrdR1zT/+Ayy/s4LKP/O5z8A8Csk/3Yxf6guiyz8UeE1lwu7LP1ltCwGWg88/0jbGfpaUzD/w1EFBE8POP/K/eFEA5cw/uKoIM+ghzT9BQCXwAX3OP4dhybvLns8/VbR2CTVWzj+KRvleg5bOP00W4eZPpc4/HED67oBAzz9DEQ37WCTQP2F7X3J8+M4/CNC67sL30D8m91SIofnQPw0UFSzbzs8/sDPR+C/vzj8V3gnwJGDHP/hEcaO90Ms/oBzfOLwszT8LbkSzk1HPPyps8Yejxc0/4C0mBNy5zT9Ds3tNaN3MP7aAfIeW4s0/EN/djZoozj/K2sRj83/KP62A1k6ECc0/3gnXsl61yT+Z9lmT/8XMP1PfCNaQAc4/FtvYxcczzj8xXuVxR1fOPwjrHOh4zc8/E4ZBMJd5zT8wp2uZKpvOP3NBSXpVas0/m7yQ1rrPzj+PlrihTyHNP3krl5D8Ac8/k+KOYtyCzz+R7QHdpWLOP+7cezydos4/utl3Tlthzz/1TAll8RTPP+U5fBifdM8/gE3WazNuzT9SBecdI/zMP66AST0DRM4/aoTn6oQlzT9/YJRr1u7OPzXzi5ec380/p+Bi2Zvdzj/QlvgZGEjPP8r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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Compare distributions of different transformations\n",
"d_compare = ASSET_CLASS_D[\"equities\"]\n",
"ffd_compare = ffdiff(spy[\"close\"].log(), d=d_compare)\n",
"\n",
"fig = make_subplots(\n",
" rows=1,\n",
" cols=3,\n",
" subplot_titles=[\"Log Price (d=0)\", \"Returns (d=1)\", f\"FFD (d={d_compare})\"],\n",
")\n",
"\n",
"log_vals = spy[\"close\"].log().drop_nulls().to_numpy()\n",
"ret_vals = spy[\"close\"].pct_change().drop_nulls().to_numpy()\n",
"ffd_vals = ffd_compare.drop_nulls().to_numpy()\n",
"\n",
"fig.add_trace(go.Histogram(x=log_vals, nbinsx=50, name=\"Log Price\"), row=1, col=1)\n",
"fig.add_trace(go.Histogram(x=ret_vals, nbinsx=50, name=\"Returns\"), row=1, col=2)\n",
"fig.add_trace(go.Histogram(x=ffd_vals, nbinsx=50, name=\"FFD\"), row=1, col=3)\n",
"\n",
"fig.update_layout(height=350, title=\"Distribution Comparison\", showlegend=False)\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"id": "0207984e",
"metadata": {
"papermill": {
"duration": 0.004975,
"end_time": "2026-06-13T03:34:09.391507+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.386532+00:00",
"status": "completed"
}
},
"source": [
"**Finding**: The log price distribution (left) is multimodal and non-stationary.\n",
"Returns (center) are approximately symmetric with fat tails. The FFD series (right)\n",
"preserves more of the original series' shape than returns while achieving\n",
"stationarity — the key benefit of fractional differencing."
]
},
{
"cell_type": "markdown",
"id": "e5fb4416",
"metadata": {
"papermill": {
"duration": 0.00485,
"end_time": "2026-06-13T03:34:09.401195+00:00",
"exception": false,
"start_time": "2026-06-13T03:34:09.396345+00:00",
"status": "completed"
}
},
"source": [
"---\n",
"\n",
"## Summary\n",
"\n",
"### Default Workflow (Recommended)\n",
"\n",
"1. **Use fixed d by asset class** - no search, no lookahead\n",
"2. **Output format**: transformed series + validity mask + sample loss count\n",
"3. **Verify stationarity** with quick ADF check (but don't optimize on it)\n",
"\n",
"### Asset Class d Recommendations\n",
"\n",
"| Asset Class | d |\n",
"|-------------|---|\n",
"| US Equities | 0.4 |\n",
"| Fixed Income | 0.5 |\n",
"| Crypto | 0.5 |\n",
"| Commodities | 0.4 |\n",
"| FX | 0.35 |\n",
"\n",
"### Note on Sample Loss\n",
"\n",
"`ml4t.engineer.features.fdiff.ffdiff` applies truncated weights at the start\n",
"of the series rather than NaN-padding a warmup region. The feature is\n",
"therefore non-null from observation 0 — the diagnostic tables above show\n",
"`Sample Loss = 0` for every ETF. Classical FFD as described in López de Prado\n",
"(2018) drops the warmup explicitly. Choose the convention deliberately when\n",
"building features: the truncated form keeps every observation but the\n",
"earliest values use only a partial weight set, while the warmup-dropping\n",
"form discards them.\n",
"\n",
"### ml4t-engineer Functions\n",
"\n",
"- **`ffdiff(series, d)`**: Apply fractional differentiation\n",
"- **`get_ffd_weights(d, threshold)`**: Get FFD weight vector\n",
"- **`find_optimal_d(series)`**: Automated grid search for minimum stationary d\n",
"- **`fdiff_diagnostics(series, d)`**: ADF, correlation, weight analysis at given d\n",
"\n",
"### Key Points\n",
"\n",
"1. **Always report sample loss** - FFD loses early observations\n",
"2. **Use validity mask** for downstream ML pipelines\n",
"3. **For walk-forward search** (optional): estimate d on training data only\n",
"4. **For stationarity testing details**: see `01_visual_diagnostics`\n",
"\n",
"**Next**: See `04_kalman_filter` for signal transform features and\n",
"`05_spectral_features` for frequency-domain features."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.14.3"
},
"papermill": {
"default_parameters": {},
"duration": 7.333385,
"end_time": "2026-06-13T03:34:12.021541+00:00",
"environment_variables": {},
"exception": null,
"input_path": "09_model_based_features/03_fractional_differencing.ipynb",
"output_path": "09_model_based_features/03_fractional_differencing.ipynb",
"parameters": {},
"start_time": "2026-06-13T03:34:04.688156+00:00",
"version": "2.7.0"
},
"jupytext": {
"cell_metadata_filter": "tags,-all"
},
"ml4t_provenance": {
"source_py_blob": "43d5a1aefef1c0d1e2b96cc5cbb79bd79350d775",
"executed_at": "2026-06-13T03:34:12.244930+00:00",
"executor": "cpu-local",
"production": true,
"parameters": {},
"notes": "executed-state finalization batch (2026-06-13 run)"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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