{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f970d28d",
   "metadata": {},
   "source": [
    "# Local Field Potential Analysis\n",
    "\n",
    "This tutorial covers the LFP tools of `braintools.analysis`: generating an LFP from spikes, and the spectral, coupling, and laminar analyses. `unitary_LFP` and `current_source_density` are in `braintools.analysis.field`; the spectral and coupling measures are in `braintools.analysis.spectral`. Each analysis is first checked on a synthetic signal whose answer is known.\n",
    "\n",
    "| Function | Purpose |\n",
    "|---|---|\n",
    "| `unitary_LFP(times, spikes, spike_type, location=...)` | kernel-based LFP contribution of an excitatory or inhibitory population |\n",
    "| `power_spectral_density(lfp, dt, nperseg=None, ...)` | Welch power spectrum |\n",
    "| `coherence_analysis(x, y, dt, nperseg=None, ...)` | magnitude-squared coherence (Welch) |\n",
    "| `spectral_entropy(lfp, dt, freq_range=(1, 100))` | normalized entropy of the spectrum, 0 (one peak) to 1 (flat) |\n",
    "| `phase_amplitude_coupling(lfp, dt, phase_freq_range, amplitude_freq_range, n_bins=18)` | Tort modulation index |\n",
    "| `theta_gamma_coupling(lfp, dt)` | the same with 4-8 Hz phase and 30-80 Hz amplitude |\n",
    "| `lfp_phase_coherence(signals, dt, freq_band)` | pairwise phase-locking value between channels in a band |\n",
    "| `current_source_density(lfp_laminar, electrode_spacing)` | second spatial difference of a laminar recording |\n",
    "\n",
    "For the spectral functions, `dt` is the sampling interval: a plain number is in **seconds**, and a quantity is converted. `unitary_LFP` takes `times` in milliseconds."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9da5096e",
   "metadata": {},
   "source": [
    "## 1. Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ba2ec3f2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:09:55.170108Z",
     "iopub.status.busy": "2026-10-15T08:09:55.170108Z",
     "iopub.status.idle": "2026-10-15T08:09:56.676562Z",
     "shell.execute_reply": "2026-10-15T08:09:56.676562Z"
    }
   },
   "outputs": [],
   "source": [
    "import brainunit as u\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import braintools.analysis as ba\n",
    "\n",
    "rng = np.random.default_rng(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beb2fdf3",
   "metadata": {},
   "source": [
    "## 2. An LFP from Spiking Activity\n",
    "\n",
    "`unitary_LFP` places the neurons of a population at random in a 0.2 mm x 0.2 mm area around the electrode. Each spike adds a Gaussian waveform whose amplitude decays with distance and whose delay grows with distance (axonal conduction). The amplitude and sign of the excitatory and inhibitory contributions depend on the recording `location` (`'soma layer'`, `'deep layer'`, `'superficial layer'`, `'surface layer'`).\n",
    "\n",
    "Below, 200 excitatory and 50 inhibitory neurons fire with a rate modulated at 8 Hz (theta) for 10 s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b7dc10d1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:09:56.678565Z",
     "iopub.status.busy": "2026-10-15T08:09:56.677565Z",
     "iopub.status.idle": "2026-10-15T08:09:59.062437Z",
     "shell.execute_reply": "2026-10-15T08:09:59.062437Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "superficial layer: correlation of E and I contributions -0.79\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "soma layer       : correlation of E and I contributions +0.79\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x280 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt_ms = 0.5\n",
    "T = int(10_000 / dt_ms)\n",
    "t_ms = np.arange(T) * dt_ms\n",
    "rate = 10 * (1 + 0.8 * np.sin(2 * np.pi * 8 * t_ms / 1000))  # Hz\n",
    "exc = (rng.random((T, 200)) < (rate * dt_ms * 1e-3)[:, None]).astype(float)\n",
    "inh = (rng.random((T, 50)) < (2 * rate * dt_ms * 1e-3)[:, None]).astype(float)\n",
    "\n",
    "lfps = {}\n",
    "for location in [\"superficial layer\", \"soma layer\"]:\n",
    "    e = np.asarray(ba.field.unitary_LFP(t_ms, exc, \"exc\", location=location, seed=0))\n",
    "    i = np.asarray(ba.field.unitary_LFP(t_ms, inh, \"inh\", location=location, seed=0))\n",
    "    lfps[location] = e + i\n",
    "    print(f\"{location:17s}: correlation of E and I contributions {np.corrcoef(e, i)[0, 1]:+.2f}\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 2.8))\n",
    "for location, x in lfps.items():\n",
    "    ax.plot(t_ms[:2000], x[:2000], lw=0.8, label=location)\n",
    "ax.set_xlabel(\"time (ms)\")\n",
    "ax.legend(fontsize=8)\n",
    "plt.show()\n",
    "\n",
    "lfp = lfps[\"soma layer\"]\n",
    "dt = dt_ms * u.ms"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "419ea29d",
   "metadata": {},
   "source": [
    "## 3. Power Spectrum and Frequency Resolution\n",
    "\n",
    "`power_spectral_density` uses Welch's method: the signal is cut into Hann-windowed segments of `nperseg` samples with 50 % overlap, and their periodograms are averaged. The frequency resolution is $1 / (\\texttt{nperseg} \\cdot dt)$. The default `nperseg = n_time // 8` is fine for long recordings but too coarse for short ones, so set it from the resolution you need: 2 s segments give 0.5 Hz bins.\n",
    "\n",
    "The result equals `scipy.signal.welch` with the same (symmetric) Hann window and `detrend=False`; scipy's defaults differ slightly (a periodic window and mean detrending)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b767baab",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:09:59.063946Z",
     "iopub.status.busy": "2026-10-15T08:09:59.063946Z",
     "iopub.status.idle": "2026-10-15T08:09:59.615051Z",
     "shell.execute_reply": "2026-10-15T08:09:59.615051Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "resolution 0.50 Hz; max relative difference from scipy 9.1e-08\n",
      "spectral peak at 8.0 Hz (rate modulation 8 Hz)\n",
      "  delta    0.9 % of 1-100 Hz power\n",
      "  theta   86.6 % of 1-100 Hz power\n",
      "  beta     4.4 % of 1-100 Hz power\n",
      "  gamma    8.1 % of 1-100 Hz power\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import signal as sps\n",
    "\n",
    "freqs, psd = ba.spectral.power_spectral_density(lfp, dt, nperseg=4000)\n",
    "f_ref, p_ref = sps.welch(lfp, fs=1000 / dt_ms, window=np.hanning(4000), nperseg=4000, detrend=False)\n",
    "print(f\"resolution {float(freqs[1]):.2f} Hz; max relative difference from scipy {np.max(np.abs(np.asarray(psd) - p_ref)) / p_ref.max():.1e}\")\n",
    "print(f\"spectral peak at {float(freqs[np.argmax(np.asarray(psd)[2:]) + 2]):.1f} Hz (rate modulation 8 Hz)\")\n",
    "\n",
    "\n",
    "def band_power(freqs, psd, lo, hi):\n",
    "    f, p = np.asarray(freqs), np.asarray(psd)\n",
    "    m = (f >= lo) & (f < hi)\n",
    "    return p[m].sum() * (f[1] - f[0])\n",
    "\n",
    "\n",
    "total = band_power(freqs, psd, 1, 100)\n",
    "for name, (lo, hi) in {\"delta\": (1, 4), \"theta\": (4, 12), \"beta\": (12, 30), \"gamma\": (30, 100)}.items():\n",
    "    print(f\"  {name:6s} {100 * band_power(freqs, psd, lo, hi) / total:5.1f} % of 1-100 Hz power\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 3))\n",
    "ax.semilogy(freqs, psd)\n",
    "ax.set_xlim(0, 100)\n",
    "ax.set_xlabel(\"frequency (Hz)\")\n",
    "ax.set_ylabel(\"PSD\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e56ef7cc",
   "metadata": {},
   "source": [
    "## 4. Coherence\n",
    "\n",
    "`coherence_analysis` estimates $C_{xy}(f) = \\lvert\\langle P_{xy}\\rangle\\rvert^2 / (\\langle P_{xx}\\rangle\\langle P_{yy}\\rangle)$ by averaging over Welch segments; with a single segment it would be 1 everywhere, so make sure many segments fit. For two signals that share a component $s$ plus independent noise of equal power, $x = s + n_1$, $y = s + n_2$, the true coherence is $\\left(S / (S + N)\\right)^2$ , where $S$ and $N$ are the signal and noise spectra. The Welch estimate is biased upward by roughly $(1 - C)/K$ for $K$ averaged segments, which matters where the true coherence is small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "392e8cd3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:09:59.616055Z",
     "iopub.status.busy": "2026-10-15T08:09:59.616055Z",
     "iopub.status.idle": "2026-10-15T08:10:00.047787Z",
     "shell.execute_reply": "2026-10-15T08:10:00.047787Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coherence at 10 Hz (shared sinusoid): 0.994\n",
      "coherence elsewhere (shared noise only): mean 0.061; true value 0.040, plus estimator bias (1 - C)/K = 0.016 -> 0.056\n"
     ]
    }
   ],
   "source": [
    "fs = 1000.0\n",
    "n = 60_000\n",
    "shared = np.sin(2 * np.pi * 10 * np.arange(n) / fs) + rng.normal(size=n) * 0.5\n",
    "x = shared + rng.normal(size=n)\n",
    "y = shared + rng.normal(size=n)\n",
    "f, coh = ba.spectral.coherence_analysis(x, y, 1 / fs, nperseg=2000)\n",
    "f, coh = np.asarray(f), np.asarray(coh)\n",
    "\n",
    "S_noise = 0.25 / (fs / 2)  # one-sided PSD of the shared white noise (variance 0.25)\n",
    "N = 1.0 / (fs / 2)  # one-sided PSD of each private noise (variance 1)\n",
    "print(f\"coherence at 10 Hz (shared sinusoid): {coh[np.argmin(np.abs(f - 10))]:.3f}\")\n",
    "K = 2 * n // 2000 - 1  # number of 50 %-overlapping segments\n",
    "C = (S_noise / (S_noise + N)) ** 2\n",
    "print(f\"coherence elsewhere (shared noise only): mean {coh[(f > 20) & (f < 400)].mean():.3f}; \"\n",
    "      f\"true value {C:.3f}, plus estimator bias (1 - C)/K = {(1 - C) / K:.3f} -> {C + (1 - C) / K:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7b1713c",
   "metadata": {},
   "source": [
    "## 5. Spectral Entropy\n",
    "\n",
    "`spectral_entropy` normalizes the power spectrum in `freq_range` to a probability distribution and returns its Shannon entropy divided by the maximum (log of the number of bins): close to 1 for white noise and close to 0 for a single sharp peak."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e034ba06",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:10:00.048982Z",
     "iopub.status.busy": "2026-10-15T08:10:00.048982Z",
     "iopub.status.idle": "2026-10-15T08:10:01.072300Z",
     "shell.execute_reply": "2026-10-15T08:10:01.072300Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "white noise            spectral entropy 0.994\n",
      "10 Hz sine + 1% noise  spectral entropy 0.158\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "simulated LFP          spectral entropy 0.380\n"
     ]
    }
   ],
   "source": [
    "t = np.arange(20_000) / fs\n",
    "signals = {\n",
    "    \"white noise\": rng.normal(size=t.size),\n",
    "    \"10 Hz sine + 1% noise\": np.sin(2 * np.pi * 10 * t) + 0.01 * rng.normal(size=t.size),\n",
    "    \"simulated LFP\": None,\n",
    "}\n",
    "for name, sig in signals.items():\n",
    "    h = ba.spectral.spectral_entropy(lfp, dt) if sig is None else ba.spectral.spectral_entropy(sig, 1 / fs)\n",
    "    print(f\"{name:22s} spectral entropy {float(h):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6aa146b",
   "metadata": {},
   "source": [
    "## 6. Phase-Amplitude Coupling\n",
    "\n",
    "`phase_amplitude_coupling` extracts the phase of a slow band and the amplitude envelope of a fast band (analytic signals via an FFT band-pass), averages the amplitude in `n_bins` phase bins, and returns Tort's modulation index: the Kullback-Leibler divergence of that amplitude distribution from uniform, divided by $\\log(\\texttt{n\\_bins})$. It also returns the bin centres and mean amplitudes.\n",
    "\n",
    "The index is small in practice: even strong coupling gives values of a few hundredths. Calibrate it with synthetic signals before interpreting a measurement. Here theta (6 Hz) modulates the amplitude of a 60 Hz oscillation with depth $k$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "43f3fdad",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:10:01.073302Z",
     "iopub.status.busy": "2026-10-15T08:10:01.073302Z",
     "iopub.status.idle": "2026-10-15T08:10:01.792153Z",
     "shell.execute_reply": "2026-10-15T08:10:01.792153Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " depth k        MI  theta_gamma_coupling\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     0.0   0.00003               0.00006\n",
      "     0.2   0.00339               0.00320\n",
      "     0.5   0.02195               0.02066\n",
      "     0.9   0.07078               0.06335\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "simulated LFP: MI 0.01374\n"
     ]
    }
   ],
   "source": [
    "t = np.arange(20_000) / fs\n",
    "theta = np.sin(2 * np.pi * 6 * t)\n",
    "print(f\"{'depth k':>8s} {'MI':>9s} {'theta_gamma_coupling':>21s}\")\n",
    "results = {}\n",
    "for k in [0.0, 0.2, 0.5, 0.9]:\n",
    "    sig = theta + (1 + k * theta) * 0.5 * np.sin(2 * np.pi * 60 * t) + 0.3 * rng.normal(size=t.size)\n",
    "    mi, bins, amps = ba.spectral.phase_amplitude_coupling(sig, 1 / fs, phase_freq_range=(4, 8), amplitude_freq_range=(50, 70))\n",
    "    results[k] = (bins, amps)\n",
    "    print(f\"{k:8.1f} {float(mi):9.5f} {float(ba.spectral.theta_gamma_coupling(sig, 1 / fs)):21.5f}\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 3))\n",
    "for k, (bins, amps) in results.items():\n",
    "    ax.plot(np.degrees(bins), np.asarray(amps) / np.mean(amps), \"o-\", ms=3, label=f\"k = {k}\")\n",
    "ax.set_xlabel(\"theta phase (deg)\")\n",
    "ax.set_ylabel(\"normalized gamma amplitude\")\n",
    "ax.legend(fontsize=8)\n",
    "plt.show()\n",
    "\n",
    "mi_lfp, _, _ = ba.spectral.phase_amplitude_coupling(lfp, dt)\n",
    "print(f\"simulated LFP: MI {float(mi_lfp):.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ce6b7f6",
   "metadata": {},
   "source": [
    "For no coupling the index is close to 0 but not exactly 0 (finite data); compare with surrogates, for example by shifting the amplitude series relative to the phase series, to judge significance. The simulated LFP has no gamma *rhythm*, yet its index is clearly non-zero: the spike waveforms contribute broadband high-frequency power, and that power rises and falls with the theta-modulated firing rate. This is genuine phase-amplitude coupling, which is why a non-zero index alone does not prove a nested oscillation.\n",
    "\n",
    "## 7. Phase Coherence Across Channels\n",
    "\n",
    "`lfp_phase_coherence(signals, dt, freq_band)` band-passes every channel, takes its instantaneous phase, and returns the matrix of pairwise phase-locking values $\\lvert\\langle e^{i(\\phi_i - \\phi_j)}\\rangle_t\\rvert$, which is 1 for a constant phase difference regardless of its value. Channels that carry no power in the band are reported as 0 rather than an arbitrary phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f9b5ccfb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:10:01.793157Z",
     "iopub.status.busy": "2026-10-15T08:10:01.793157Z",
     "iopub.status.idle": "2026-10-15T08:10:02.346411Z",
     "shell.execute_reply": "2026-10-15T08:10:02.346411Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.    0.998 0.998 0.076]\n",
      " [0.998 1.    0.998 0.076]\n",
      " [0.998 0.998 1.    0.081]\n",
      " [0.076 0.076 0.081 1.   ]]\n"
     ]
    }
   ],
   "source": [
    "alpha = np.sin(2 * np.pi * 10 * t)\n",
    "channels = np.stack([\n",
    "    alpha + 0.5 * rng.normal(size=t.size),\n",
    "    np.roll(alpha, 25) + 0.5 * rng.normal(size=t.size),  # 90 degree lag at 10 Hz\n",
    "    -alpha + 0.5 * rng.normal(size=t.size),  # anti-phase\n",
    "    rng.normal(size=t.size),  # unrelated\n",
    "], axis=1)\n",
    "plv = np.asarray(ba.spectral.lfp_phase_coherence(channels, 1 / fs, freq_band=(8, 12)))\n",
    "print(np.round(plv, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17e3b0f0",
   "metadata": {},
   "source": [
    "Channels 0-2 lock to each other at different but constant phase differences (0, 90 and 180 degrees) and all give a PLV near 1. The unrelated channel is low but not 0: for independent signals the PLV has a finite-data floor of roughly $1/\\sqrt{\\text{duration} \\times \\text{bandwidth}}$ (here $1/\\sqrt{20\\,\\text{s} \\times 4\\,\\text{Hz}} \\approx 0.1$).\n",
    "\n",
    "## 8. Current Source Density\n",
    "\n",
    "For a laminar recording with electrode spacing $h$, `current_source_density` returns\n",
    "\n",
    "$$\\text{CSD}_k = -\\sigma\\,\\frac{V_{k+1} - 2V_k + V_{k-1}}{h^2},$$\n",
    "\n",
    "the negative second spatial difference along the electrode axis (the last axis by default), scaled by the conductivity `conductivity` (default 1). The two boundary electrodes are dropped. **Negative CSD is a current sink** and positive a source. A potential trough at a depth therefore appears as a sink flanked by sources:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "83af461e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-15T08:10:02.347414Z",
     "iopub.status.busy": "2026-10-15T08:10:02.347414Z",
     "iopub.status.idle": "2026-10-15T08:10:02.557938Z",
     "shell.execute_reply": "2026-10-15T08:10:02.557938Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CSD shape (200, 18) (two boundary electrodes dropped)\n",
      "at the trough depth: CSD -141.9, analytic -V'' -156.2\n"
     ]
    },
    {
     "data": {
      "image/png": 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HQHpg5CTwUI7kVfFA/C0RER0uKY4lPcGLFi1SF2SbQnq6JXiV9lbSfCWz7FA8xcbqCx49PPOCy+9///79G71vckFXUukl0DzU76+cF0ihUQnafdsHOb/wJbNYSPsmxVt907ElPftw2xnpRZb3nTt3rioEK/viSTMXnswyOeZNbU9kxpWGZP1JgVR/84/7kp5t6emWReZml4sEkg0hwXhztXdSGE/S0uVvVTLb5MKEv4s78jciQXd9mWVEDcUx3kS1eKbo8PCkGEvVaXHSSSep29rVoqVhEL7VMOVKtb9gVsZQycmIjGmrTbavb6qqg5HP8rz+UOSKcO3ecvmeDblSfTjv15h99CXVyT3kc+SxnBx4UubkeMpnybRgtcmx9Hye50q4777KGC/pAaiP9N7Lv5P0qEtPhGfam4OR73m4KfYNFYi/JSKiwyVZOPJbKOnCcmG6NvktlVRyIYG1pFj7+w2T3zdJFW5I0CNDiKQdkIvnMhvEwUgNEJk6SrKZmkLaE+mRl3He/nr2pffXQy4CSK+177RccnH6tddeq/Oetdsoue85TofTnkqwKlOESc+xLCNGjKjRySBtnPT6Si0TSfU/2PcJ9Bhv6fGvTdLihe+0rc1BjsvMmTNVz7dUxPeXVSAV8Jt68YjIF3u8ifxc2ZQCKNLDKQ2+jCs777zzMHDgQPW83ErvrlzJ96Quy3QfciVZUrlkjmrfhl2m1ZKCMZKiJQ2b9J7efvvtqgGWq6ySPibbSREVudotvccydrmxKU3yHkKm0pJGXhpwSdXzRz5XegUkqOzTp4/6ntJj3NC5Upv6ftJwyn7JHNMSmEr6mxyPg43Fk15naRDlmMv0IDIWS1LPZLoYz4mY/BtI8TMZr7Vy5UpVIEUCczmZk+JjctIiY8OkQI2cwMl7yXGSHgPZ70Ol7Mu/hWdOUWmkZZqZg41zk38LObGRAnzSAyApdVKAJxAC8bdERNQc2TgyZZb0qkp2mARbMm2VXOyUKQ/lt1l+s8SqVatUOysXuKUQlgSIEqhKuyrTZsmF7topxNIWSEFMubgogb0E3fI7Lb3L8ptYX9qwhzwvbYW0Vb5TUzbG448/rnpgpW2SQmnS/knQKMOX5H09AaS0T3LBeOrUqWo6MUmllyDVs4+e3mvphZfjJune8v0lZV8Ce3/jkxvT5gtpE2WctASZ0kbIVFv+Oh6knZMMAPk+0gsux1badEnhl3+ng2muMd7y7yGp5tKRIf+eMrZcLpDLkADZv+Ym524yXE7+RuWYy8UHD/lsqaNSu/AuUZMctOY5URhOJ7Zu3Trt7LPP1mJiYrSEhATtuuuuU9N++JLpJx566CGtc+fOapqp9PR0bfr06TWm4BD79u1TU0vJe8l7+04tVlxcrF7TrVs3NW1JUlKSmrLjySef1CorK+tMeVFb7Sk5ZJoQmXYrOTlZTTvi+7937W1luqpp06apz4yOjtYmTZqkpqqSqUBkOo7GTifW0PcTr732mtalSxc11dWh3lteK1Nlbd26VTv++OPVlF8y1Yx8F3/Ter366qtqyhCZFkSOuUyLcscdd2h79+71bvPHH39oo0aNUtu0a9dOPS9TiNTeF9/pxDxkahmZOqZ3794HneakpKREO++887T4+Hj1vp6pxeqb/kS+Y23+Pl/Ie8nflK+G/C0REQWDTHUoUzFmZGSo3yf5bR47dqyalsvTZso0TY8//rj63ZPfWKPRqNrfY489Vvv000/9TifmWeQ909LStOOOO0577rnntKKiogbv2+zZs1V7WXvaRXlfma6rNn9tmuy7bCvnAXI+IPsi03JJe+Rr27Zt6rdb2h5pp2+99VY1VaV81uLFi73byTnIxIkTVVsqv+Vy7DxTmfm2HY1p8z1++ukn9Zxsv2vXLr/HRNrbCy+8UH0P+T7t27fXTjnllDr/DoE0d+5cNRWdtNHy7yu3MiWa77SZjWlPPed3tV9b+9zqxRdfVOtleliPl156SZ17NObviqg+OvlP00J2otZFxhs99NBDKp2KPYShQXpDpNdWxjATERE1JxmiJL3UMmTH31ClQJOe/Jtvvln1Jh8si4qCZ/DgwSoF/5lnngn2rlArwDHeRERERBR2JD1b0polxTrQF3hl2k1fMsZbUpplClMG3aFJhrnJkLXp06cHe1eoleAYbyIiIiIKSzIG3be6d6DI+GqZG1xqnUiNE6kfI2PU65sGk4JPav0w446aEwNvIiIiIqIAkgJor7/+ugq0PSnuUujsSAT9RBQaOMabiIiIiIiIKIA4xpuIiIiIiIgogMIu1dzlcqk5IWNiYrzzJhIREYULSXQrLi5Gu3btoNcf/vV3tqtERBSutEa0qWEXeMvJQXp6erB3g4iIKKh27dqFDh06HPb7sF0lIqJwt6sBbWrYBd5yRd5zcGJjY4O9O0REREdUUVGRCpQ97eHhYrtKRC1ZZWWlKnp3/vnnw2w2B3t3qBW3qWEXeHvS4OTkgCcIREQUrporLZztKhG19MA7IiJC/X4x8KZAtqksrkZEREREREQUQAy8iYiIiIiIiAIo7FLNiYiI6MhwOp2w2+3B3g0iv0wmEwwGQ7B3g4jCBANvIiIianYlJSXYvXu3mmqFKFTHZEoV4ujo6GDvChGFAQbeRERE1Ow93RJ0R0ZGIjk5mfN7U8iRC0LZ2dnq77R79+7s+Sai8Ai8X3jhBTzxxBPYt28fBg4ciOeffx4jRoyod/tPPvkE9913HzIzM9WP5X/+8x+cdNJJR3SfiYiIyD9JL5fARoJuqRZMFIrk71POJeXvlYE3EbX64mqzZs3CLbfcggceeAArVqxQgfekSZNw4MABv9svXLgQU6dOxaWXXoq//voLZ5xxhlrWrl17xPediIiI6seebgpl/PskorAKvJ9++mlcfvnlmDZtGvr06YOXX35Zpaa9+eabfrd/7rnncMIJJ+D2229H79698cgjj2DIkCH43//+53f7iooKNbG570JERNQSvPDrFtz2ySqs2V2IUMF2lYiIqIUF3jJh/fLlyzFx4sTqHdLr1eNFixb5fY2s991eSA95fds/9thjiIuL8y7p6enN/C2IiIgCY97GA/h0+W7sKShDqDgS7WpWoQ0Lt+aoWyKigKksBX64133f5Qr23lArF9TAOycnRxVgSU1NrbFeHst4b39kfWO2nz59OgoLC73Lrl27mvEbEBERhZemtKsy3rus0tGg5b1FmRj7+C8477Ul6lYeN+R1La16+oMPPojy8nK0Vt988w3+8Y9/BOS9JTtSagOJlStXYubMmQH5HAoDjgpgxdvB3gsKEyFRXC2QLBaLWoiIiCg47arN7kSf+39o9Ge5NOC+L/9Wy6Gse3gSIs2BO61xOBwwGmu+v3QeNLUo10MPPYSbbroJVqsVwXI4+x9MV111lfe+BN5ffPEFzj333KDuExFRSPd4JyUlqR/8/fv311gvj9PS0vy+RtY3ZnsiIiIiIcPSxo0bpwq5DhgwAF9++SUyMjJU8OYxbNgwzJs3T92XHtsbbrgBo0ePxvHHH4+3334bxxxzDM466yz0798ff/75J5YuXYpjjz1WvW7w4MFq5hUh1bLj4+NV8dihQ4eiW7du+O6772oEjuPHj8egQYPqLShrs9kwZcoUVQNH9ln2wUN6fPv27av24/zzz1fZB56edAnoPaQGzsUXX6zu+9t/f8dEbN68GSeffDKGDx+u1tdXS8dDKoNfc801arYZmZnm119/rfH8e++9h5EjR6q6PEcddRRWrVrl3ScZQiiFc2Wf5Dhu27bNuw9jx45V+ybP3XvvvTW+oxy3+++/X32WHEc5rk8++SSuuOIK7+cWFBSo8828vLxD/n0QEbXaHm+z2awao7lz56rK5MLlcqnH1113nd/XSOMnz/s2Kj/99JNaT0RERKEnwmRQPdKHsq+wHBOf/k31dHvodcDPtxyNtDjrIT/jYCTwknONTz/9VAW8cr4hQdmhbNq0Cb///jtMJpMKEpcsWaJmVenZs6d6vQSyElC3bdtWDaGTwHLMmDHqtRIMS9Aqvdtz5szBjTfeqKY/lVTpV155BfPnz1fBeX3kNfIZ69at834H8f3336sitBI0y+sl0Lzrrrvw0ksvHfL7+O6/vJ8Uqq19TKQnXALh999/H7169UJZWRlGjRqlAmcJxP159dVXsXHjRvz999/e+jsef/zxBz766CN1HCVbQr73eeed591WLl7IxY/OnTur7yHTxMrxkWD/lFNOUcMbfL+/R0pKCh5++GHV4y2LkP3v0aMH/vvf/6pj89Zbb+H0009HmzZtDnlsiIhadaq5TCV20UUXqSuccoX02WefRWlpqapyLi688EK0b99eFXMR0mgdffTReOqpp9SVWBnXs2zZMvWDT0RERKE5bVND0sC7JEfjscn9cffstXBqGgw6HWZM7qfWHy4JUiXYlADTU8y1IcHYv/71LxV0e0hQLe/jmeJUemdPPPHEGq+RALRLly4qjXzy5MlqnXQQbN26tVH7LD2969evVz3Jcu4jQbv4+eefVU+4J2i/+uqrcc455zToPX33v75jIoG+BMW+6dvFxcVqfX2Bt3SKyDmbdKqISy65BG+88Ya6L73o0sMtgbuHBNHSo+85NhJ0e+4///zz6r70jMssNiUlJer71y6u648ck7PPPltdmLj55pvVxQiZupaICOEeeEvDkZ2drVKFpECapArJFV5PAbWdO3eqhsC3wfjwww9VutHdd9+tUprkKme/fv2C+C2IiIioOUwZ3hFH9UhGZk4ZMpIi0TYuIqCfJ+O2pYfXo3bBs+jo6HofS0E3SfeWALw2STWX3l3PXNEytM73cxpCgncJdn/55RcVbN9xxx010uL9zUfd2O/jj3wvCcD9fVZD+e6TvJ90ssyYMcPvtr7j3OU4yXh6ISnxct4nmY3S+y2dM550/YOR4QGnnXaa6s1PTk5WQwCIiBDu83gLSSvfsWOHmhtUUqB8r4jKOCtJ7fIlV3XlarJsv3btWu8VYCIiImr5JNge3TWxWYNuCeBkzLCkOQtJq5ZeVxl7LeceQsY8y/lFY95z+/btKij2kGBVpks9lJiYGO+47Prs3r1bBbASRMrYZQlgpYq89Px+/PHH3jnUJS3bM/5bvo9kAkrwLSnin332WaOPifSCx8bGqjRtjy1bthx0nLTsk6Smy1hv+f6+r5X9l+ekM8XzObKPhyL7Jh0x0pMuqeOLFy+us43sZ+3jKOnxctFCUvDrG7pIRBSWgTcRERFRICUkJODzzz9XY4hl3LWMxZaxx//+97/xwgsvqLRuSU+WHuzGvOe3336renLl9VIETd5fAstDufXWW3HccccdtLjamjVrvMXFpNf2ggsuUPsuqe0yJE/SsqXomATgniF5ktrerl071dsr46MP1ttb3zGRXnOZDmz27NlqvRyTSy+91Jsa7s/ll1+ushDlGEixNvleHpLKLoHzmWeeqb6LvF9DpgCTsefy/eQ7SIakjI2vbcKECaojRvbTt9q57I/0nEvaOVG9rHHA1VUZKz5ZGkSBoNNa2sSXh0kap7i4OHV1VK6SEhERhapzXl6IpZn5ePlfQ3BCv7Yh2Q76ez9Jb5aeYBm3G8zpsih8SU+39Jbfd9999W7Dv1MSO3MKMWf2LJwweQo6JsUFe3eohWlMm8oebyIiIiJqFfbu3atSzVesWFFjBhwif2Yt3Ynjn/5d3ZdbeUzUaourEREREYUzSZH2N35Zqo5HRAS2uFxjSEq871ziHpIyL/OKhwJJs9+wYUOwd4NagKxCGx6evRQ3Gb8CMBaa5lIzKkhxx0AXdaTwxMCbiIiIKIj8jV0ORTJv9uFUOicKJdtzSmHS7LjE+D3exli1TqYxlBkVGHhTIDDVnIiIiIiIwkrnpCjofeqpyV2DTqemMSQKBAbeREREREQUVqRX+9ZJvbyPJQifMbkfe7spYJhqTkREREREYefU/u2A39z3v7luLLq0Swr2LlErxh5vIiIiIiIKO5pPrnlyrCWo+0KtHwNvIiIiokbKzMxEfHz8IbeTYmQzZ86ssW7QoEEoLi4O4N4RUUPofMZ4ay4tmLtCYYCBNxERER0ZlaX1L/byRmxrQ0vhL/CWdTExMUHbJyJy06mSakRHBsd4ExER0ZExo139z3U/Hjj/k+rHT3QD7GX+t+00Dpj2baM//vzzz8fGjRtRWVmJ9PR0vPHGGygvL1c90DfeeCO++eYbFBYW4v/+7/9w0kkn1fuatLS0Gu/75JNPYtOmTXj11VfV44KCAnTr1g3r1q3D/fffr95TPmPUqFFq6jCdTof8/HzVY75+/XrcdNNNyMrKUq+95ppr1LzeRBR4OksMzqh4GGdIj7eOYREFFnu8iYiIKCw8++yzWLZsGVavXo3x48fjwQcfVOslMB4wYACWL1+O//3vf7j55psP+Rpfl112Gb744gsVcIu33noLp59+upr3+uGHH8Yxxxyjerlrz9ftcDjUdhdffLF6f1nOPvvsgB8HInLT6Q3YorVX9zV2flOA8dIOERERHRl3763/OZ2h5uPbtxxk26b1G3z44Yd47733VC+3LElJ7grGVqsVkydPVvdHjx6NrVu3HvI1vqTnWgLmN998UwXtL730EmbNmnXI/ZGedHnPqVOnetf5e38iCvwY7/2FFYiP5hzeFDjs8SYiIqIjwxxV/2KyNmLbxs+zu2DBApVC/t1332Ht2rV4+umnVdArLBaLSv8WBoMBTqfzkK+p7YYbblA92nPmzEFycjIGDx7c+ONDREfU50u342rDV+r+5Bd+w6ylO4O9S9SKMfAmIiIKURqL7DYbGVMtBc0SExPVeO1XXnmlWV/Tq1cvdOnSBVdccQWuu+467/rY2FiVyu5Pz549ERkZiY8++si7Licnp9HfjYgaL6vQhse/WYVrTV+qx3rNibtnr1XriQKBgTcREVHI4+DDw3XCCSeoQFcWGastxc6a+zWXX365GrftO057woQJqKioUGPIaxdNMxqN+PLLL9WY8P79+2PgwIH47LPPDuNbElFDbc8pRaVWPcTFBCecmobMnHqKOhIdJo7xJiIiClHs8G4+JpOpzrjrRx99VN16iqKJ6OhoaFWpBgd7TUZGRo3XiV9//VVVJZfXecTFxWHhwoU1tvO8v5Cg/scff2yGb0hEjdE5KQoOn0rmZthh0OmQkcRx3hQYDLyJiIhaUAEgCj179+7FscceizZt2uCHH34I9u4QUQO0jYvAjMkDUfmtu9fbqnNgxpn91HqiQGDgTUREFKJ8e0YpdLVr1w4bNmwI9m4QUSNNGd4RBd+Z1f2HTumOo4d3DPYuUSvGMd5EREQhyhN2t9QOb144oFDGv08S9qp082iDI9i7Qq0ce7yJiIhCnGeqq5ZCxjjLPmdnZ6uptVra/lN4BN3y9yl/m75j8in8OHTuHu+K8opg7wq1cgy8iYiIQlRL7ZCTubA7dOiA3bt3IzMzM9i7Q+SXBN3ydyp/rxS+nk+4CxmoQG4E08wpsBh4ExERhbiW2F8s1cG7d+8Ou90e7F0h8kt6uhl0U3ZUT2TYV6PUxcwHCiwG3kRERCGqhXZ4e0lQw8CGiEKZ1WwA7MD6rCJkFdpY1ZwChsXViIiIQjzXnEOkiYgCI+PAXHW7eOmfGPv4L5i1dGewd4laKQbeREREIY6BNxFR85Me7pH536n7PXW74NKAu2evVeuJmhsDbyIiohAlJ4FC1yJHeRMRhbbtOaUohUXdT9QVqVunpiEzpyzIe0atEQNvIiKiEFXpcKlbs5HNNRFRc+ucFIW1Wmd1f4h+k7o16HTISIoM8p5Ra8SWnIiIKERVOhl4ExEFihRS6zf6RHV/uH4j9DoNMyb3Y4E1Cgi25ERERKHe421gc01EFAjH/OM4ddtGV4Ire1VgynDO502BwZaciIgoRFU4nOrWYmJzTUQUEEaz965uxx9weYprEDUztuREREQhqoI93kRER0x65Tb8tSs/2LtBrRRbciIiolAPvDnGm4gooP6b8QamOy7DnLX7gr0r1EqxJSciIgpBmqaxqjkR0REyZOBANXnj92v3qd9foubGlpyIiCgE2Z3VJ34WoyGo+0JE1NqN6ZYEq0mP3fk2/L3XPac3UasLvF944QVkZGTAarVi5MiR+PPPP+vd9rXXXsP48eORkJCglokTJx50eyIiopZcWE1Y2ONNRBRQkTl/46PY/+Ex42t4Y8E2ZBXagr1L1MoEvSWfNWsWbrnlFjzwwANYsWIFBg4ciEmTJuHAgQN+t583bx6mTp2KX3/9FYsWLUJ6ejqOP/547Nmz54jvOxERUaB40swFi6sREQWYy4HBpQswybAUX/y1G2Mf/wWzlu4M9l5RKxL0lvzpp5/G5ZdfjmnTpqFPnz54+eWXERkZiTfffNPv9h988AGuueYaDBo0CL169cLrr78Ol8uFuXPn+t2+oqICRUVFNRYiIqJQV+l0B95GvQ56vQ6hgu0qEbVG+6J6oEyzqPm8j9cvh8wqdvfstez5ptYReFdWVmL58uUqXdy7Q3q9eiy92Q1RVlYGu92ONm3a+H3+scceQ1xcnHeRHnIiIqJQtyO3TN0mRVsQStiuElFrtKOgEnNcw9X9l0zP4lbjx4DmwNo9hcHeNWolghp45+TkwOl0IjU1tcZ6ebxvX8NK+d95551o165djeDd1/Tp01FYWOhddu3a1Sz7TkREFEjLMvPU7dCMBIQStqtE1Bp1SozEPY7L8IFjAvQ6Ddcbv8CH5kfx1KfzMHf9/mDvHrUCRrRgjz/+OGbOnKnGfUthNn8sFotaiIiIWpKlmfnqdnin0Aq82a4SUWuUFhuBBycPxd2zLVjs6o0ZpjcwUr8BR1fMw6XvxODsoR1w3yl9EBdhCvauUgsV1MA7KSkJBoMB+/fXvIokj9PS0g762ieffFIF3j///DMGDBgQ4D0lIiI6cpwuDSt2uAPvYRn+h1IREVHzmjK8I47qkYzMnJGwGc5DxN9vQ9MuhO6Pnfh0+W78sSUHj581AEf3SA72rlILFNRUc7PZjKFDh9YojOYplDZ69Oh6X/ff//4XjzzyCObMmYNhw4Ydob0lIiI6MjbuK0ZxhQPRFiN6pcUEe3eIiMJG27gIjO6aiJSMvjCe/ATuPqU/PrlyNHq0MeCG0udx15vfY/rs1Sgutwd7V6mFCXpVc5lKTObmfuedd7B+/XpcffXVKC0tVVXOxYUXXqjGk3n85z//wX333aeqnsvc3zIWXJaSkpIgfgsiIqLms2yHe3z34I7xMHIqMSKioJLMo+/6/oKpxl/xnWU69i/7Eic8O1/1gBO1mDHeU6ZMQXZ2Nu6//34VQMs0YdKT7Sm4tnPnTlXp3OOll15S1dDPPvvsGu8j84A/+OCDR3z/iYiIAjW+e1gnppkTEYUC4+irgN1LkJC1Em+an8QrJetx0etTcO6oLph+Ym9EWYIeVlGIC4m/kOuuu04t/kjhNF+ZmZlHaK+IiIiCY3lVRfPhIVbRnIgobLXpAlz6I/DT/cCSl3Gl8VsM12/E9Yuvx2+bsvHfswaqFHWi+jB/jYiIKITsKbBhb2E5DHodBnWMD/buEBGRh9ECnPgfYMr7gDUOQ/Rb8L31HrQvWI6pry3Gg1/9jbJKR7D3kkIUA28iIqIQnL+7X7tYRJpDIjGNiIh89T4VuHI+0H4oYqwmDBowSK1+e2EmTnpuPpZm5iGr0IaFW3PULZFgi05ERBRC5IRNcBoxIqIQltAJmDYHutzNuCu1L8YMycadn61GRe4unPNyKXTQQZNeTh3w2OT+aqoyCm8MvImIiELEkm25+GZ1lrrP8d1ERCHOaAZS+6q7Mv/33FPKEPnZ9dinJWCxqzcWu/qo27s+01QgfkL/NMRaTcHeawoSBt5ERERBpmka3vwjEzO+Ww+nS0OftrH4R8+UYO8WERE1QuTmb+DSm5DmyscZhoVqERKIL/mqN06Z/U8ktO+O0V2TMKZrIoZlJHBIURjhvzQREVEQSSGeOz9bg69X7VWPTx/UTqUlWk2GYO8aERE1xuRXsP+oGbjt6TcwQr8eo/TrMEi3BWm6fJxuWIiH7Rdg5+5CrNpdiG3zZ+JHfTGK0kYio/sAjO6WjMEd4/nb34ox8CYiIgqS7TmluOq95di4vxhGvQ73nNwbF4/JgE6nC/auERFRE7RNSsRpZ56Lu2evxTMODZE6O144yoFjErLxTe8zsWhrLhZuzcWU9Y9juGs1kPM69mfHY8mC3piBvihtOwqdew7E6G5JGNAhHiYDa2G3Fgy8iYiIguDndftx86yVKK5wIDnGghfPH4LhLKhGRNTiSSE1GfOdmVOGjKRItI2LUOvbSqf4kA5q0eZPRvmGKJiyliPVVYDTDItwGhYBB17H1n1tMeGnJ1Ua+ojObTC6SyLGdE1Cn3axaqpJapkYeBMRER1BMob72Z834flftqjHwzolqKA7JdYa7F0jIqJmIsG2J+D2Rzf+ZljH3wzYy4E9y6Btnw/b5t9g2bcc5ZHpSCg3I7/Mjnkbs3H19uuR+XM8vjD0Q2WHsejSa5DqEe+REgM9A/EWg4E3ERHREVJQVokbZ67Eb5uy1WNJK7/7pN4wG5lKSEQUlkxWIGMcdBnjEHnMdBWI9y3LxfKYdtiwrxir1q3DyAUb1KanYjGw+3Vk74rDkh9643Njf1R0PArdeg9Uxdo6J0VxqFIIY+BNRER0BKzdU4irP1iOXXk2WE16VUDtzMEdgr1bREQUaoF4XHvI5VhJLe+TMgTo9h2c2+ejbNM8ROxfgWRXIU4xLMYp2mJ8sHUb7tl4qXppuxgDTk0vR9deQ1SPeHqbyGB/G/LBwJuIiCjAPlu+G3d/vgYVDhc6tonEy/8aqk6oiIiIDjlXeMZYGDLGIuaYuwBHBbBnORzb3IF4fPwkjCpsgxU7C5BWsh7Ttz2I7K2xWOLqjY+tA6F1GodufYaqQDyVQ5qCioE3ERFRgFQ6XHjkm3V4b/EO9fiYnsl4dspgxEWagr1rRETUEhktQKcxMHYag9hj7sTJgFrK7U7snLcX9kUWJLuKcIphCU6xLwG2vIqczRKI98JXMVOQ3GMkRndJwqgubZAYbanx1lmFNjXbhqSsH2x8OjUNA28iIqIA2FdYjms+WK56IcSNE7qrhYVwiIioucn83z2OuxQ45l/AnhWo3PobSjf+hujs5UhyFeFkw594I/8k/LB4J95fvBNDdRtxbPw+6DpLj/gw7CmsUBeKXRogzZQMh5Lq7NR8GHgTERE1Yw/3uqwiLN+Rj5fmbUVOSQVirUY8e+4gHNsrNdi7R0REYdEjPhpmWY6V1PRKYO8KlG/+HVennI2FmUVqLvEzcxbgX7a5wLpXkPt3DByu3rhE3x1rXF3wt9YJ02evUVOisee7+TDwJiIiaqIDReVYsTNf9Wqv2JGPNXsK1Thuj15pMXjlgqHolBgV1P0kIqIwHiPecRSsHUfhOADH9XevLlm4GdkrbYjLWYFEVzFOMvypFuHSdBhU8QqmvrYYE3ul4ujUcgzoloG4hDbB/S4tHANvIiKiRvRmS4AtwfZfOwuwp8BWZ7uESBMGd0zAyM5tcMHoTog0s6klIqLQEj3mUrVIj3jO5sV484MP0F+3Ff3126FpOhQhGkU5ZXh9wXYcbZqBGP3f2Gloj/z4vjCnD0X7PqMR23koYOaF5Ybi2QAREVETerOFjIPrmRaLwR3jMaRjAoZ0jOc8qkRE1HIYzUjqfRQ6nZ6B62avhVPTEK2rwN0n9UZqrAWLt+Wh3dpi6F0aOrp2o2PebiDvB2AV4IQeu6P6Ye2kjzGySxskSbE2pwMwMMT0p9FHZfv27Zg/fz527NiBsrIyJCcnY/DgwRg9ejSsVpaoJyKiltub/ZdPoO2vNzs+0uQNsOV2QHo8oi08wSAiopZNCqnJmO7MnDJkJEV6x3afPqg9MHk1svftxPbVf6B421JE5KxBF/tmpOnysavIiWs/XKG27ZYSjZnl18BsjYQpfQgiOg0D2g0GUvsCJo4Vb/DZwgcffIDnnnsOy5YtQ2pqKtq1a4eIiAjk5eVh69atKug+//zzceedd6JTp06B3WsiIqIj0JvdIzUGQzpJoM3ebCIiat0k2K6vmFpyWke1AFPV49ySCvyybgPWZe5Gr70x2LCvGNkH9iHJuhuoBPD3JuDvmWpbl84AZ1IvmPpPBo66DeGqQYG39GibzWZcfPHF+Oyzz5Cenl7j+YqKCixatAgzZ87EsGHD8OKLL+Kcc84J1D4TERE1qjd7vYzNbmBv9uD0eBVsD2RvNhERkV8yB/ixIwaq5ToA+aWV+HN7Lp7Z+CVKti9FXMHf6K/bpsaMJ6EI+uy/8eXvHbBg/yqM6pKIkR0j0eHzs4C0/u5e8XaDgJS+7mJwrZRO0zTtUBv98MMPmDRpUoPeMDc3F5mZmRg6dChCUVFREeLi4lBYWIjY2Nhg7w4RETUz9mYf2XaQ7SoRtWSVlZV4++23VQejdDRS8ygss2NpZh6WbMvB1q2bYD6wCntdbbBa66qeH6jbgi8t99d4jWYwQ5fSxx2I9z0T6HI0Ql1j2sAGXcpvaNAtEhMT1UJERBRKvdmqJ1uCbPZmExERBVRcpAkT+6SqBeiL4vJTsGxHPhZvy8WSbXnI3NMOV1XehAH6bein265u452lQNZKteRaOqBN56PcF8TzdwAL/w9oO8gdlCf3apEF3Jq8xwcOHFCLy1WzF2HAgAHNsV9ERET19GYXVBVBy8fq3ezNJiIiCnUxVhOO6ZmiFlFa4cDyHf/Aku25eG5bHlbvzkeaaz/6qyB8O77+NQLZS+diZJdETLEswrjVr1e/mdFanaIuwXjXY4HYtmh1gffy5ctx0UUXYf369fBkqcvJjNyXW6fTGYj9JCKiMGN3urBuL3uziYiIWpsoi1FVUZdF2Cqdqr1fsi0Xv2zPw+adBagsrsDXq/Zim07DaYaTMdSUib66TEQ4SoHdS92LmPIBsrQJ2J5Tiu7YheSSje6APKk7oDcgVDT6zOSSSy5Bjx498MYbb6jq5uxBICKi5nCguBwrdhy8N1uanJ6pMRjsmdKrUwK6sDebiIioRYswGzC2W5JaRLndib92Fqge8SXbEvH0zi6osLmggwsZOukZ34bh5h0Yad2J9/404f0Nv0D6hG8wzsYtxk/db2qKAtoOdBdu8/SOJ3YD9PqWEXhv27ZNVTbv1q1bYPaIiIhaFZdLQ25pJfYXlavg+kBRBfbLUnVf1u0rlOcq6ryWvdlEREThx2oyYHTXRLWICocTq3YVqh7xJdtT8NOODviq3AmUAyhweF+XpbXBUldPDDXvhN5eCuxc6F48rvoDSOvXMgLvCRMmYNWqVQy8iYjCnG9AnV0swXS5CqglkPbcSmCdXVIBp+uQE2iwN5uIiIjqrZJeZLOrYWgGvQ4Wkx42e90hzj85hyJfi8HD/QrRbtsnQHmh+4n0kUDOZndhtiBpdOD9+uuvqzHea9euRb9+/WAymWo8f9pppzXn/hERUZAC6ureaXdvtCewzq4KrHNKKuBoQEAtJHZOirYgJcaC1FgrUmMtSI5x36bEWNX6LslRqvgKERERha+Csko1FagMOVu1q0Dd7iuSru2aTAYduiZHY8O+Ytxl/AgT9CvQXb/H/eQ6nw3jOgLT5rjvBynNvEmB96JFi/DHH3/g+++/r/Mci6sREYV2QJ1XVpXy7dMz7QmspWJ4UwLqxCgJpt0BtQTQKbHVAbXnNinaDKMheI0dERERhZ7SCgf+3luE1bsLsGq3BNsF2JFbVmc7mbGkZ7IVJyQewFjzFnTWdiH6nBdhMRkxa+lOtPnqKW/QXRjdBXE9xgMdR7mXhM7uE5Yga3Tgff311+Nf//oX7rvvPlVcjYiIQiig9gmgvSnfVeslHbwpAbWnl1oCat8eawbURERE1FAVDifWZxVjjU+QveVACfydmmQkRmJ4WyMmRGeiv2sD0gpWwrB3OVDkM7tJ6b1AfEdMGd4RuZH3YEN2LuJ7jUVaWnuEokYH3rm5ubj55psZdBMRHaGAWqV7q7TvqtRv7xhqd1DdlIDaHUDX7qWuDqwZUBMREVFTOZwubD5QooJrSRVfvbsQG/YVwe6se77SNs6KAR3iMCbJhq6dO6N/x1TERZqA7+8ClrxUc+OIBCBderJHuufzrpLYdwLcZdhCV6MD78mTJ+PXX39F165dA7NHRERhFlBnV6V7e6p872+GgNqb5l2jl9qKxGgzTAyoiYiIqBnPazJzS91jsncXYM3uQpU+7q/4WZsoswqyB7aLxujo/ejrXIeYA8uBnYuBrXuAXt8AkR3cG0ua+KY5QMfR7kBbbhNlbu6WeR7T6MBb5vCePn06FixYgP79+9cprnbDDTc05/4REbWohidfpXxX+C9MJuneVY8bF1Cba4yXVoXJJJD2poBbVOEyBtREREQUSJqmYW9hOVbvcqeLr9nj7tEuLq+e0stDpv/s3z5OBdoDOsSr2w5l66D79VFg+VKgsrjmC/RGIG8b0Hm8+3Gf04G+Z6C1aFJV8+joaPz2229qqV1cjYE3EYVDQO2vMFljAmoh6dyqorekfNcKqD0FyhhQExERUbBIwVVV+GyXBNnucdk5JZV1trMY9ejbLtYbYA9OqECn0jXQ7/oV6HoM0KO3e8NyA7D1l6oXxQIdhlf1aI8C2g8FzJHVbxoCBdGCGnhv37692XfihRdewBNPPIF9+/Zh4MCBeP755zFixIhDvm7mzJmYOnUqTj/9dHzxxRfNvl9E1Lp5AmpPj3R9hclkHmp/Y5IOFlB7pspKrQqsVSDNgJqIiIhCVKHNjrV73Oniq6sC7T0FPsXMqhj1OvRMi/EG2QPax6CHfi9Me/50p4zPXwzkZ1a/oLIE6DHJfT+1P3DSk+5AO6UPoDcgXDQ68G5us2bNwi233IKXX34ZI0eOxLPPPotJkyZh48aNSElJqfd1mZmZuO222zB+fFUqAhGRTxpUfpm9at7pmj3S1XNRu4PrxgTUKuXbW9G7bqVvuU2OYUBNREREoSWr0IbtOaXonBSFtnERsFU68fdeCbLdvdiSLi7P1yadzjJXtjvAjsOA9Hj0STbDWpkPxFWNxS7NBZ4YU+uFeiC1r7sQmifoFgYjMOJyhCNjU05oP/30U1Vg7cCBA3C5XDWenz17dqPe7+mnn8bll1+OadOmqccSgH/77bd48803cdddd/l9jcwVfv755+Ohhx7C/PnzUVBQ0NivQUQtULndibzSSrXklrqnz5IAumaA3fSA+mCVvqWH2mxkQE1EREShT2K20konisvt+HjZLjz782ZoVadGabEWdc7kb3RcepsI1ZM9UNLFE53oneBEtGYDinYDuz4FflwCZK1091hf9LX7RVGJQNtBgDW2quL4KHcKuTympgfeN910E1555RUcc8wxakoxGdfdVJWVlVi+fLkq1uah1+sxceJELFq0qN7XPfzww6o3/NJLL1WB98FUVFSoxaOoqKjJ+0tEzcfudKk07/xSuwqk5b4nqPZ97LuNv+qYhwqok2vNO1270jcDaqLGYbtKRHRkOhukYJkEzkVVt/K4yGavsb7IZ32prQLO8iJo5cXQ2YsR6SqDBh1WaD2873uxYQ46lGUjylCOJFMF0qx2JJoqEKsrhyU2CaZLv6/eiZfGAfvX+N/Bgl0S3VePw75iXqsbkx30wPu9995TvdonnXTSYX94Tk6O6r2uPSe4PN6wYYPf10g19TfeeAMrV65s0Gc89thjqmeciALH6dLUuKAaAbME0Cpolsf2GoG03PqrftkQJoMOCZFmNR2F77zTqjCZZ1w1A2qigGG7SkR06DmsSyokOHao86ODB9CVqCgrQXm5DVmVESqQlu3GuJajDYoRrbMhGjZE68qrbm3QtDj8n+N87+d9Yb4XPXW7EaHzKXpWNfHUdlcajql82rt6imEeeut3uh9Ij7cM4fYM43bUyiK2xgEWWWKAyASg3ZDqQmgJGTUDbQbdzR94x8XFoUuXLgiG4uJiXHDBBXjttdeQlJTUoNdIb7qMIfe9Mp+enh7AvSRq+alJxRWOqoDZEyjbawXSVUvV4wKb3Zu+1Bh6HVQQnRBlRht1a1IBtSew9t76PC9TUxxOpg0RHR62q0QULinavgGyJyBWAbStOoA2leyGZiuCVlEEVJRAX1kMk7NUBcl5Wgxmu47yvvcLpmfRWZePKJSrADoGZWo7g07DSlcXnFH5b++2/7a8hQ66HL/7uN+cjt1970aM1YgYqwmdlhkRUVwddLsMFnewbIlF25h06DfDm1b+mXM8klzFOP+oPoiJa1O1XQxgjnYH2r4u/oYBdTAD7wcffFBd6ZYx2BEREYf14RI8GwwG7N+/v8Z6eZyWllZn+61bt6qiaqeeeqp3nWeMudFoVAXZunbtWuM1FotFLUThSopn5JZWuNO1fQLn2j3Qvs83ZkosX7FWY61A2TeANtUIpCUNPNZqgl6ibyJqMdiuElGLTdG22VFeVoSKsiLYywrhtBUB5UVIsRox6ZnfkVfuUtvfapiJWAmKPb3NKEeSzh0kr9U643p79fTJqy1XIFZXVr0DkmxXlXC3SuuKBebjvAHyyLxMJDkP+N3vbvE6fHzm6KptjUj5+RhotlzorFWBsUy9JcGxJQapMWl4eEC/6hf3m+muDl61jd5o9j5llUylpTtx9+y1cGoa3nKdghmT+yFmeMdDH0wG3cENvP/5z3/io48+UmOsMzIyYDJV5TFUWbFiRYPfy2w2Y+jQoZg7dy7OOOMMbyAtj6+77ro62/fq1Qtr1tQcZ3DvvfeqnvDnnnuOV9yp1atwOFFQZm9QKrfn+XJ7zQKIDRVpNngD5Ta1A2g/gXV8pInVvImIiKjZU7SLy8pQUVKonjvgiFLrS8rL0TvvF+gqi2GoLIHeXgqTswSRLknHLsM6VwZecLrjC8mpXmW53Nu77KtSZ8Hbbf+tps2q1NznMRcYfkKsru40WkIXkYRL+nT2Bsi6xcmocJTAJUGxOUYVFDNExMJgjcXA5O748+iJ1S/e8Kx7XLTFHUCrQLmqxznaFIkRvoHuOa83/MAl1ux4rG3K8I44qkcyMnPKkJEUqaqaUwsIvC+66CJVEO1f//rXYRdXE5KuJu85bNgwNXe3TCdWWlrqrXJ+4YUXon379mpMmdVqRb9+Pld3AMTHx6vb2uuJWsK46IKy6lTuOkXFfAPrqgJj0uA0hdmgr+6J9u159pPK7VlvNYXPvIpEREQUoBRtWzmQuw32sgLYy4rgUmnZxUBFsUrL3qK1w3eOEep1zsoyvG3+b1Uvsw1pKh3bBovOrj7jG+cozKjqbdbBhResj9XcCZ/e5jh9Bb6IiVDBsWTYmfcDhqpxcS7oYTdGwWGMRrk5Qa374PKRSIiW7U2IWHoDNJ0GnVTl9qZiu28zopJwf1L36s8cv7rhB6nXyQgWCbYZcLewwFum+vrhhx8wbty4ZtmBKVOmIDs7G/fffz/27duHQYMGYc6cOd6Cazt37lSVzolCmculqcYlr96gubpX2rOusInjog16KS7mDp5r9jy71yVG1x0jLb3XHBdNREREh0zRLi1FaXEhbCX5qpe5stQdMGfr2mCroYsa62wvLcCJ2W/B6CiByVEKi6sMVpd7XLOkZ893jsQjjgvU+8aiFKut9c/b/LVzFN60D1D39TBhlH59vdt2STDiyl5d3MF0hAn7/hoPg9Gs0rH11lgYI2NhjoqHOTIO49p0wR/dj61+cd4fgClKBc96UwQsOh1k0IypshJ4+20M7BCvsnGVCXc323ElanLgLencsbHNOyebpJX7Sy0X8+bNO+hr33777WbdFyK5YltW6Z4vumb6ds0CYzKPtNyqYLrMrnqwm0JStD3Bs99Ubp+UbrkvjQ3HRRMREZGHw+FASXERyorzUWg3oAAxqgdZHifu+gEuWzFcMsVUZTH0dndqtgTMC/RD8aFzghoLneQ4gF8ttyK5qne5tg8cE/C241J1PxYleN76Rc0NfPrJ2puK0CkuUp2zxFniUbovBhWGKNXL7JTFHA3NHKN6lHunDMLX/cd5g2n7trdhsnpSsX0Wcwz6GIzo4/uZo79p+EFqE5zi0ERNDryfeuop3HHHHXj55ZfVGG+ilnAF118BsYMF1pWOpo2LlorbKl07smEFxuIjTDByXDQREVF4p2iXlsCWtQHlJQUol17mskJ38S81J3MRtkQMxBrLENUjbSnegcuzZ8DiLEOEqxSRmg2RKEe8ToMMwPzKcSoed0xV791BdwALLA/U+9mbHDHIcYxX90th9aZ0i3JYYNNHokIfhUpjJNISuuDajK4qFTvOrMPm7VfAYI2BMTIOlqhYWKLiERGdAHNUHE6ITsEJce19Pmk3ohp6QPqf2bQDSdTaAm8Z211WVqaqh0dGRtYprpaXl9ec+0dUg93pUsXFGjpXtCzSe90UMgd0Yp1x0DIG2uK3wJj0XFuMHBdNREQUKrIKbdieU4rOSVHNN75VZtSpLFFjlGWpKCuErbgAFaUFyIvqihxrJxUgO3O3odumN1Qvs66y1JuWbXaWqoD5fcOZeNV5iuqZ7o1MfGupP735T8dp+MDhnko3XZeHJywbq5/0SYJzaHrEmjV0TYhSAXKaJQJ/542EwxQFl4xRNkerXmZ9RAyM1jgMTumN79OHV42DNsBVPlqlbMt2VoNRVcT2kBrYE3x3avQTzXM8icJEowNvKX5G1FzjomWckCdQzi3x6Xn2G1hXqlSopjDKuOhGzBUtjyNMHBdNRETUUs1auhPTZ69R8xfLCK3/nN4T5/SPB2S+5YgEtUgV7dKcnXBu+B6VpYVw2IrhtBXWKP71Z+IZWBoxHsUVdrQtWIH7sm+r8TkyTtgzwd7b9nPxkvM0db+vbju+tXxW7/7pyvNR6HD3MBfqIrFfi0eZTnqY3UulMRoOowTM0WiTMAo3pnVXAXKCuQeWF74IS2QsLNHSyxyPyJh4RMe2gdkaifN0OpxX45N8xjkfSkQDppgioiNX1ZyoIT3TO3LLsOVACbZml2B3flmdVG8JrpsyLFpiYUnR9j8Ouu5c0XIbYzEyiCYiImrp7DagNAcoywFKc6tu3Y8rup2E7Lh+OFBcgfx189B/4QOYZ3LPxRwlidNzHMAc99v8x3Al3rUfq6pwj9b/jY/Mj9b7kR9md8Esp3t4ZV9dhTfKtmsGlCACJVoESmCFTRcJR0QyekXHqAC5ncmM720Xq7HM0ousj4iFKSIOJikAFh2PsfFt8XN8suqZlqrbVtPFjThX8amqTUStJ/CW6b2ioho8MqPR21PLZat0qsBaFgmyPUtmbinszoZF1RIUJzRwrmi5jYswqcreRERE1MLZy4HiLKAs1yegrg6stSEXojB5qAqmXX9/iV6/X1vvWz30a5EqFCbG6DfhQ/MOv9uVaFaUlpej1OkeirZfS8CP2nBU6t3FvxymaNXLrIp/WWLQJr4PbkuQ3mYT4iy98bvuGFij4xETHY2YCJM6L2lvdhc+HVLn045rtkNFRGEQeHfr1g033nij6u1u27ZtvYUhfv75Zzz99NM46qijMH369ObeVwoimfpK9V4fKMHmA8XuAFv1ZNvqnRJLprDqmhyNbinR6JQYicRoS41UbrkfH2lWY6mJiIiolbAVANkbq4Ln7KpA2iewHnMDKjsdjeySClSuno3Ov1xT71s9sCIC79rd9YNG6bMw0wxUagbkIRZ5WixytZiq+zHY4EqH2aBHcowFDkt/XJh9p+qNLkakui3VReDu04ciPSkW51hNuMRqVD3TElCbjfVPd0VEdMQCb5nS6+6778aDDz6IgQMHYtiwYWjXrh2sVivy8/Oxbt06LFq0CEajUQXcV155ZbPsHB1ZcvEku7jCG1TL7eb97vuyvj5SVKx7ijvA9gTa3VNj0DbWymmviIiIWoOiLGD3n3WDaM/jCfdD6348imwOlK2ag7Y/1H8u+Oi2LnjNVqbuj9Rl4W2zGblVwbMKpuG+lWW5q6vaTnqVC6MH49Lo2YiJTUByrFUF2Ckx7ts+MRacGWNR23nStWct7Ye7Z6+FU9Ng0OkwY3I/TBnOMcxEFMKBd8+ePfHZZ59h586d+OSTTzB//nwsXLgQNpsNSUlJGDx4MF577TWceOKJMBhY1bklFDXbU2Cr7rn2WQ5WvCwt1oruqdXBtWeRcdQcP01ERBTinNLGa4ChakaavG3A5p/rpHd7H5/8FND3DFW3pWTTH0j4xj2Hsz9PfvwzXi13qek4h+iy8IwpRfVEqx5pCaJ97i/X3OOTTQYddkUNwrmxnyO5KoBOibGo244xFgyLseD8qsdNmTVEguyjeiQjM6cMGUmRzVfVnIgo0MXVOnbsiFtvvVUtFPqk8duRW+oNqjdX3W7LKUG53f881dJB3bFNpLv3WnquU2KqerLd01IQERFRiHBUuHubLbGAJdq9bv86YO2n/numywuAs98E+p2lstxsu1Yj8vvb6337/329CG/OjlLFUfvrsvCAqYfqlc5VgXRV77TqoY7FxvJ0VMJ9brHF0geXxLzm7Y32BNN9Yi1Ijrbiiqp10jsd6Mw4CbYZcBNRi6xqTqGnrNKBrQdKsSW7uEaQvTO3DI56yobLGKguyVEquO7mTQ+PRkZiFKwmZi0QEREdcZVl1UFyfCcgKtG9fvdyYNmbdXumK4vdz5/1BtD/bHXXmbMFhvlP1fsRr81Zine/S1BDyDIcWbjBOMIdTFeNmfa9v6c8CcWoVK9br+uK66yPI0UFzxbvbYakfEdbagTYPI8gIqqLgXcLUlBWWaPn2rNI2nh9osyGqpRwd8+1Z0lPiIDRwKJmREREASGVR2UuaE+QLEXG2g0CYtu5n89cACx4tmZ6t9097rl2MK0V74Vu5ft+P8YJA976ZS0+nZuigul42z5coD++Kr27qnfaZ9x0QXk0XHCfN2xAR9ypvw3J3mDaHUT39Q2uJZiOtqiZRVi3hYio6Rh4hxhJ/dpfVFXgTMZgZ7sLnMl0XTkl7qvO/sg4a9V7XdWDLb3Xcl/GZXP8NRER0WFyudyp2rXTt7v8A2jT2b2NjJee+2B1IO2s1W5Pfh0YcI77fnkhsOWnOh/j1JlQYozHZwu24bsFC9U0WpbiPBzv+qc3vTvHZ8x0EaKALGnn3b3fuWiPRzANSdFmb/GxjGgLRsTW7JWWlG+5jTCzd5qI6Ehg4B0kTpeGXXllNSqIe6brKq6ov8BZ+/iIGunhnkWm5yIiIqIGcjkBW747eJbeaN8K3X3PBJJ7urdb/zXwzS3u9Zp73uc6wbQn8JZAe9+aGk87DBGwmeJRYojHnKX7MW/ZnyqY1hWVoL/9CuR4K3m707xLIOORdVVxdH7VuyRhM85AtMXoDpqrqnh7gujaY6mld9rA3mkiopDCwDvAKhxOVU3TnSJePQZ7W06pKn7mjzSWndpEVhU3qw6upZp4lIX/ZERERH4rdtcYA12ruNjQaUDbAe5tV38MbfYV0EmFb3/adKkOvPVGoPRA9ceYYlBpSUCpMQHFhjjMX12CJWtW4EBxOexFFUh13YW99mjvWOlyWKrfN1f+k131IBrr8A9V1DRR0rpjLOhykGBalkgzzwGIiFqqJv2CFxQU4M8//8SBAwfgktQrHxdeeCHCUUmFFDgrqdODvTOvTPVu+2MxSoGzuunhnRIjmzRtBhERUasi6dh52+tOc+V5PP4WoMMw97arZwJfXlv/e6WP8gbe83eWY3xV0J2vRQORiTDGJKPUGI8iXRyWbgJWbVqleqbLCgGT8UlsK7Wq1O7KcpMnq9ttj/wnq+qBZJ+5PyPSbEBarSDas/gG15Kxxt5pIqLWr9GB99dff43zzz8fJSUliI2NrTF+WO6HW+C9v6gcF77xJzbu922Fa4qxGNEttW56eIeESDa2REREtW2fD/z8ALBn+cG363NadeAdmQTo9EBEGyAqyf1YqoKr2yQgpbfaLKvQhiv/iEak9hLyEa2Kk6HCJ6vba7fPfXdBNDnlSYqqHTz776FmhhoREflqdKsgc3hfcsklmDFjBiIjIxHupIKo9HAfrOjZqC6JNQLuzkmcsouIiKheBTsPHnQndgNGXQN0GA5smQt8fSMQEe8udBaVUhV4J7pvM8a5U8eFy4Xt2SUo0ywo800BbwBpz3umxSAtzuo30JZbGYPNgqZERNQsgfeePXtwww03MOiu0q99HObd9g+s3VNYY5ovqUJe4XAht7QS367xpKC5SSd3eptINX67dqG0GKspaN+FiIgoJEgAfe6HNdPKfdPMJ81wB9Ri52KgcJd78efMV6sD780/YvTHF2CxJcpd0EwKm1UVNeuU3hGrosZgjSNdjdcuLCpGWWkx8lyR0KBX7fnCrWqQdr2sJn11WrnPXNeeabk8z0kQzyk9iYjCS6MD70mTJmHZsmXo0qWqESMVRMtyos86Gde9J9+GLdnVBdU8c3AXlzuwI7dMLT+vry7YImT6L28xNZ/iatJI8yo6ERGFhbj27qUhep0EJP9SqzK5T7DuCbpFWQ50zkqk6WSplVueBRw7eQQwYLj78cbvgY+ugKYzwGlNQIVZCqrFo0gfh3zEYp51ApY6uqrMN1txPmIqDyDPHoPdeTGqvsvBSHMu7XpyfUG6Z07tql50IiJq+Rr0a/7VV19575988sm4/fbbsW7dOvTv3x8mU80e2tNOO63597IFkrHbHRMj1XJsr9Qa83Sr9PSqImwyR7fnvqzfV1SulgVbcmq8X3ykyVuATaqbe4LzdnER0HOcOBERhauIBKDD0IZt2/8coPPRKgDPy96L3ANZSDUUI9ZV6A7YPZXMha1A3eg0J4y2HLVEAUipenr45BOBAaPdDzZ8B8y8Q93VoIPdHAtbVdXzfF0svrOeit8dfVSxNq0kGz11O5BXGovcklhsyYqB/SCnY1Kkreb821VBebQFyT7BemKUhXVjiIhCmE6TSPAQ9PqGpUNJj6zT6WeOyxBSVFSEuLg4FBYWquJwoaSwzF5VEd2nlzy7BLvzbajvXynCZKgxftwTlEtldBPT2IiIKMDtYCi3q4fNUemekszf9GT9zgZSerm3+/tz91zfMi+4vynKZK7vAeeou87138Aw6/waT1cYolFijEehLg6zrOfgB/sgdTE+ujIbY/R/q3T4XJ/5vitU9fSaPNOSqYC8TvE3a40edU5LRlStsrISb7/9Ni6++GKYzXX/3yJqrjawQb+8tacMo8CIizRhaKcEtfiyVTrVmHFZfNPWt+eUwmZ3Ys2eQrX4Mhl0yEiMqhGUewJzFnYjIiJqAKMZiG3rXg6m75nuReYSl+C7Rtp7bo0eeYPBBCT3dj8vz2kuWJwlaknEbkw/+RZM73+M2rZ8zZewfvZSnY+r0Eeoac/esF6ITytGIre0Au1wACeXLUFeWQxy98disxaLxXAH66WwSveI9/VR3l70+qc5k1tOdUZE1Hwafcnz3XffxZQpU2CxWOpcLZo5c2bYTSd2JESYDaqImyy+7E6XGifuKebmHkNejK0H3AG5jCeXpfa4sg4JEVVp6zHqVhV4S4lGXAQLuxERETWZwQhEJ7uX+vSY5F6EdGyUF/iMS88B2lcH6dboBHehOd/ici47LC4bkmHDXSf0xF39J8LhdKFk1ReI/+ojvx9ZCROeNl+Fd2zj1PlBqn0Xzi+ci9wCd3G5PVosVmuxyKsK1IsgBXR1Kuh2j0Wvf9o0z2M5VyEiosNMNfdlMBiQlZWFlBTPKCe33NxctY6p5sHncmnYW2ir0TvuSVsvKLPX+zppRGv0kEvaemq0Sk1jYTciotaBqeYtmJyyVRRV96RL4TiZMk3sWgosfb1uWrzD5n7+7Deh9Z2M0konSlZ+jrTvL6v3Y/6rvxQv2Saoj+ul24lrjV8gVwLzquA8R4tTleAl7T1LS0QZrKoInJxHJB00SLcgIdLM2jQUUphqTiGVau5L4nR/Qdju3bvVh1LwSYPWISFSLf/omVLj306mQ/FUV9/qE5RLQTcp+iJL7elSYq3GGgF595QYdds+noXdiIiIjhg5/7LGuZfErjWfSx/uXmqrLHUH4BEJ6vxNAuToTr2AMTfUHLPuCdYrS3DH5HG4ufeJyCutRPmqz9Fp7uJ6d+kh5zS8ZT8OJRUOZFRuwi1FH3jHo0tv+mqfselbXO2Rp09AUrTZb1DuTnm3eu9zaBwRtSYNDrwHDx6sfrBlmTBhAozG6pdKL/f27dtxwgknBGo/qRnIv11StEUto7ok1niuqNxeHYjLePKq4HxXXhmKyh1YsbNALbXnK+2S5K607jsXeafEKJiNLOxGREQUdOYo9+Irrb978cdeDuj0qkBraqwV6DMCMM6od071+085Gjd3O14Vg3OuzUeP39bXuyv32qfhfedx2F9UgfbFa3CP6RVversE61sQiz+1WORosVipdUO+pX3NAnH1jEWPjzDV2xGQVWhTNXE6J0WhbVzEYR1KIqIjEnifccYZ6nblypVqLu/o6Gjvc5KWkZGRgbPOOuuwdoaCJ9ZqwuCOCWrxVW53qgardtq6rCu3u7Auq0gtvox6naqq7ttLLoXeZKqThCiTutrO1HUiIqIQZJJCbD6kZ330tfVuLq15bNV5BIYcAyS94b8nvTQHD044Dte1m4ADxeXQrctB14VZ6CoTqNcXpJenorjcgeScZXjU/KQ31V3S3vdqsVhbdX8x+iM3uocKwttF6dApshzRsW2wrcCFL1btU3XmJS6ffmJvnD+qo5oRhuchRBSygfcDDzygbiXAluJqVmutH2ZqlSTNq3fbWLX4kkIuu/Jt3oJuqsBbVVAu48e2Zpeq5Ye/99d5T6m4LmO8pFqquo02o02kGQlRcmty33qeq7rPdDMiIqIQF9ce6H/2QU8602SJswJtTgV6dPXbk66V5eCuEafg4sRRKkg3bdiH2KU2xOpsyEDd84p77Jfgg8KOyCosR7R+LaabZ6j1Lk2HhyxWlCICJVoESn6OwO1zTsIPGI0YqxFdzQU4Cz/DZY6BZo4GrLHQW2NgsMbBFBkLfVw6LLGJiI0wqe1jrCY1/E5umdlHRI3V6DHeF110kbpdtmwZ1q93pxP16dMHQ4dWV+Gk1s9o0Ku0LVmO65NaYxy5NHy+Bd3kdndeGfLL7Kqaqt2peceTN5RcnVbBeJSpZtCu1nkCd5O3V12e4zzmREREISqyDZAxzu9T0hcteZXdZEmJBjqeB4w8uiowz64RrDtLsnFzn9Pwz9jB6rzCvCUXrhUG6OGEXqchFja1eGZTi9OVwuHU1DmJqTwTU82zgHL/u/iYfSpecZ6q7vfVbcc75v+gRLNiHyJQqotEhT4SFYYoOIxRWB09DjsSxiA2wogkYwV625bDGCkBfBwsUXGIkCUmAdGxcYiJsCDGYmSdHKIw0+jAe8+ePTj33HPxxx9/ID4+Xq0rKCjAmDFj1HRiHTp0CMR+UgshqVvt4iPUclSPutOpyJzk+WWVqmCL97bUfZtXJvftNZ8rq1SBugTsewpsamkouTpdI0BXt1U96p4edp/nZTo1zldKREQUYkwRQJIKw+s8JflwUte9qrY70OdC4NQLkJWbh9OfmoMo2NQSo3P3mN897RzckNxF1bax70vC7rU7oJUXQasogb6yGAZ7CYyOEpgdZUht0xbDTAlq285lDiTZi5Ck8xleJznsDveysjgO3+7u7A3Sb7XcU+/XedYxGc86zlbBd1dLAe53vYhKCeBN0XCaot2975YY6KyxKEvqD3vqIHdPuxlo4ziAqJh4RMcmICIikinzRK058L700ktht9tVb3fPnj3Vuo0bN2LatGm47LLLMGfOnEDsJ7USMs9nhNkdmDeE9KBLpVQVkKvAvFbQ7g3eq5+XdS4NalyYLDLXeUNI2yUFWjyBuSfNvWag7tPjHmVWjSYbPSIiohCi06FtUiJunTwed89eC6emwQAdZpzZD526dVSbqHT31JHAwJH1vs0lVYtSOQzIPx7O8mKUlxTAVlKAitIC2MsK4SgrwqiEEUiL7KMK0kbkOZG5vT9MjlKYnaWwuMoQpZXCAJd6q3LNPWVVcYUD9spsDLGsdAfwfhIBX1x3Gv7rcM/821G3H79bbvY+V6kZUaqLQFlV7/sfUcdhftIUlRqfaKrAcQfeAVTqfCwMEbEwR8XDHBkHa3Q8IhLTEZXckSnzRKEceP/2229YuHChN+gWcv/555/H+PHjm3v/KMxJUCtjqWTpmBjZoNc4XRqKbP4CdXvNXnaf56WhlPlKJfVMlm0obdBnSSE531T32j3sidF1U+Ll4gMREREF1pThHVX2XWZOGTKSIg+vqrlUhk/to3rYpUZ8rTrxtfriuwM4reYGcpLhKAcqinEzTLgMkepcpaygDzZut6oA3ik97+XFqgdeV1kCvb0Epoj+GGVsgyKbA8m2AygttyKqKjferHPAjGIkaMWAE/ghLws/HnCPgU/X7cd0y/v1fp33HBNxn+MSNUNNB0s5vnRcDZukzusjYTdEwV7V+y7j33OTRyK7y5mqgJ70urffOwfWKHcAHxkdD31ELGCOUb30MFrcPRlEdPiBd3p6uurxrk2mFGvXrl1j346o2Um6uAS5sqButrtfdqcLBWV1A/O8Ep8AXZ73CeTLKp1wuDQ1hYosDSWNnL9U94OlwvOKNBERUeNJsB0S04hJMCop86YIWAC1yPSuSI4Gul9W78sGALjc+0g6uKZBczpQVlKE0uJ8lBXnqx74itJC9DAk49+mTio13lkUjwW7zlUBvFGlz7t7362uUkS4ynBAcw8XlRlqyh0FiLLYEOWyAa7cOr3vH+wpwz3Luqj7cSjBKusN9e7v79Zj8HbaPSo1Ps6iw2XbboDLFAPNIunzVcXrIuJgjoyFMa0PLD0nVFeZz94IqDT7aPetnh0VFOaB9xNPPIHrr78eL7zwAoYNG+YttHbjjTfiySefDMQ+EgWcFGKTaUhkaSiZas1fqnvdVHgZt16htql0ulQjt7ewXC0NJSntnosJ3srvfoJ3Typ8fKSZ49WJiIhaIZ3BiKi4Nmqpn/TBj6332ZtcGi4rd6ggvaisDH/lDEB5SSEqSwthtxXCaSuCS419L0a+PgPjDUkqO1Bf5sCSsgEqgI/SbIjW2RANuXWf0+wq0eOXDQfU/ViU4CHrqnr34SvnaNxgd6jsQQnSl2vn1ni+XB/hHvtujMLepLFYN+BuVb9HUul7rHwMJkukqj5viY6HMSKuKmiPAWLSgCTJOiAKLTpNBtE2QkJCAsrKyuBwOGA0uuN2z/2oqJqJN3l5eQg1RUVFiIuLQ2FhIWJja06RRRRI8r+aTLVWs5hcrVR4n/We4F3GqzeWXDiWYnGe4Ny3Nz3Rb0V4s7o6zfHqRK1fc7eDbFeJwlOFw6lq6UjKfHFZheqFL66wI99pVetLS0vQdv9v7vT5ymJVvE5fWQqTU4rXlWKxvRvecU5S7xWNMvxuuUkF8Wads85nfe0chevt7p52PVzYZv1Xvfu13DQUz6Y9plLjpcr8fX+fDL1OB7sxCk6zFK9zp8XrrbHQ0gbAMeIazJ71AS6++GKYN34F6I3uXndLrDuQl8UT1LMXng6jDWx0j/ezzz7b2JcQUdV49WiLUS3pbRo2Xt3l0lTjlee3Anzt3nV3RfhCm10NJZPUeVmQ0/Dx6tJTXruAnN/CclXj173pYURERBRWLEYDLNEGd8q8mgAusZ5kef9O0DTcUVkVvJfbsb18jepVLykpRXmpp3hdEZy2QuTYI3AMktW2ZbYyvFV6NsyOElW4Ltqncr3cX2+Lx/zNOeozdHDhMau7Er3VUVhn6rjfNmXi8l964bbOwKgZczEf16n38mdfbH/MHfuBdz73QfOvhFmrUAG8MTJWFbHTeQL1+I4157Q/sB4wmKsDeaOVY+HDUJPn8W4ukrIu6ev79u3DwIEDVZG2ESNG1Lu9TF12zz33YPbs2apHvVOnTupiwEknndSs+0UUCmSOz7hIk1pkzvSGcMh4dZu9QYXlcqsel1aNV88pqVBLQ1mMej9zqpvqGb/uLkAnDTURERGFN7lwH2UxqkVVmW+Uid6CuiWelPlyO3LKHUix2fGUmtnGrnrj/6/4Szik+nxV4TpJn9fLYi9BptM91l2UVNix0NgbsTp3MO9OobchBmWqF35TPnDP52u926+2LEKkzn+QvsHYEw8t6uBNjb9v0zmIs7sL3wmXzuidOs6e0g/lk99VAb2q6fPrY0BlSXWQ7u11jwEi2wDth1R/kMslJ4sNOmJZhTZszylV55MhUfcgDDU68BZbt27FW2+9pW6fe+45pKSk4Pvvv0fHjh3Rt2/fBr/PrFmzcMstt+Dll1/GyJEjVQA9adIkNT2ZvGdtlZWVOO6449Rzn376Kdq3b48dO3Z45xMnIsBo0Kurz+4r0A0fry694/6naqtbWE4C9kqHCxUOF7IKy9XSUFFmg5+x6bUKzPkE8jLFm3wnIiIiIl8Gnw6K+vU46HsUl9nw0fvv4Zvrx8PmPMo9FW25XQXunlT60rIy2Gw2HGc3VwX0Dvy77BYYZO73yhL3fPEqSHcH7LvsKVi0Ldf7GVeajdDrIlRFer1Og15zQF9ZAFQW4O8iK87898/eAry/Gl5HW7h77GvLi8jA1+O/dAf0VhPG/HgqrCU73enz1hjoZf53FajHAvHpwIn/Ua+btXQn5n3xBqxahZqCbuq4vjhmYNea6fRS/I9CbzqxE088EWPHjsXvv/+ORx99VAXCq1atwhtvvKEC4oZ6+umncfnll6s5wIUE4N9++y3efPNN3HXXXXW2l/XSyy3TmZlM7v/BMjIyDvoZFRUVavHNwyeimqwmA9LiDA2+4izj1W12Z53Ccp4e9PqmcpMr09K7Xlppw+58/1eJ/VHj1VVg7jNlW7QZqTFWpMRakBpr9d6X70JEgcN2lYhaE08mXkZSFMxm9xzrDTPee05U5pMyL4F5UrkDz8nY96p1s8tnuwP5skpU2opV8TqZPk6mlyuqrH5HKcD7umsSknVFaty7p3idJ41+V0kyHvjqb+/2Cyy56CC97g4bUOYuauexS98et+w4XRUQXrg1F9+bZ6O3fqf7ySVVi0d0KnDbpurHX1wD5G6p2eMemQi0GwJ0HAVE1+0gpQAE3hIQ//vf/1Y91TExMd71xx57LP73v/81+H2k93r58uWYPn26d51er8fEiROxaNEiv6/56quvMHr0aFx77bX48ssvkZycjPPOOw933nknDAb/J9uPPfYYHnrooUZ9RyI6dHpYpNmolg4JDXuNNEwydqvewLzWernvGa8ut7Jsb8DnyLgrCcRVQB5jRXLVre86BuhETcd2lYiouVLm4Sdlflx10bpyB3arde7UeXl8kqcnvtyB68qeUenzEsCbne5AXfW662wo10xYmpnv/Yxlrh7I1uK8wXycoRyxunJYXWWoMERB53BWDwfMWg3sX+N/Z01RwF07AUNVGFmSDUQlccx6IALvNWvW4MMPP6yzXnq9c3L8p0X4I9vK3N+pqak11svjDRs2+H3Ntm3b8Msvv+D888/Hd999hy1btuCaa65R84o/8MADfl8jgb1cJPC9Mi9zkRPRkW+YpOdalgw0fLy6BNzV07JVp8DLWPQDMod6UQX2F5djf1G5ulIsDVFReQk2HyhpVICeIvdj3L3nDNCJ6sd2lYgoGCnzjagyrwJ1ByaW27ErrwyPf78B9zku8fs6KUBnkbnfH/gBvdJiMaBDHI7tcgd6DrKhrcUBg70EqCgCCvcAu/5093Z7gm7x1olAWa67Jzx9JNBxNNBuEGBs+JDHcNHowFvGU2dlZaFz58411v/1119qzHUguVwuFeC/+uqrqod76NCh2LNnjyrOVl/gbbFY1EJELY+M7U6MtqilIT3qxRUOHCiSIFyCcvetBOQSoB+oum1qgK4C8hhLjQA9NdaCFAboFGbYrhIRhXqV+ZriI024e/ZaODUNBp0Od53YSxVZW727AKt2F6pbmR1nzZ5CtXwAOaeJVrPX9G3XGQM6xGNgehz6j4pDRoIF3so7FcVA4W53qvvG79yLMFiAdoOBvmcAo64+osehVQXe5557rkrt/uSTT1QPlgTDf/zxB2677TZceOGFDX6fpKQkFTzv319d4U/I47S0NL+vadu2rRrb7ZtW3rt3b1URXVLXGzcug4haE/k9UnN2Wk3ollI9DKa+lPfs4voDdM/6xgTo0pPv7TGvCtA9gTkDdCIiIgqWKcM74qgeycjMKUNGUqS3qvnEPqnecyOpvbO6KghftbsAa/cUoaTCgWU78tXiIYXdpFdcBeMd4tD/6o1oV7YJul2LgZ1VS1kOII+TulfvhNMOfH8H0GG4u3c8oXPYpac3OvCeMWOGGmMtaWWSKt6nTx91K2Ot77333ga/jwTJ0mM9d+5cnHHGGWqdBPHy+LrrrvP7GinoJmnusp2MBxebNm1SATmDbiJqbMp7YwJ0T2CubmsF7FLd3TMOvVEBeq3AXG5lfXIMA3QiIiJqPhJs1zeNmJwbpbeJVMvJA9qqdS6Xhm05JVXBeKEKxv/eW6RS2P/YkqsWj6RoMwZ0GIUBHSZh4MA4DIzOQ5uc5UCbrtUfsm8NsOxN9yKiUtwBuGdJGwAYmp5q3xLoNDm7bIKdO3di7dq1KCkpweDBg9G9u88VjUZMJybzgr/yyitq7m6ZTuzjjz9WY7xlrLf0oEv6uhRyEbt27VLTlclrrr/+emzevBmXXHIJbrjhBjW3d0PIWLS4uDgUFhYiNja20ftMROQvQPdNZT9YgN5QEqD79pT7BuaewJ0BOjVFc7eDbFeJqCWTrNm3334bF198MTvyDsHudGHjvmKVjq56xncVYuP+YlUcrrb28RHennF1G5WHmDXvuXvE9/4FuOw1X3DsfcBRt1V9kA1wVgLWOIS6xrSBTZrHW8ic3bIcjilTpiA7Oxv333+/ShcfNGgQ5syZ4y24JsG9p2dbSC/7Dz/8gJtvvhkDBgxQQfmNN96oUt+JiILdg949NaZRAbonpV0CdN+A3bcHfdP+kkYF6L6BOQN0IiIiai4yNVm/9nFqmTrCHQeW252qJ3zN7gJvz/i2nFLsKbCp5fu1+7yv75I0AQM6TMbgo60Yad2Brra/YdqzBNi1xN3r7bFpDvDJNCC1H9CxqmCbFG6Tuclbe4+3b/XShszNHcp4ZZ6IQpkK0G0Ob0+5b495dq0e9ab0oHsCcd/A3BO4M0APD+zxJiKqxh7v5idTn8kY8dU+wfjufJvfau7dU6IxqH0s+neIxYD0RPRMi4F5/uPAb/+p+8axHdyB+DH3AIk+aeytqcdbKpb7WrFiBRwOB3r27OkdZ+2pMk5ERIfZg141pcghe9B9AnTfgNwToO+v6k1vTA+6VD717SlXgXmtYnEM0ImIiKg+MVYTRndNVItHbkkFVkvVdG8Bt0J1vrJhX7FaZi7fo7YzG/Xo3fZojO03BuPMW9Hb/jfic1dAJ3OLF+0G1u4GJj5U/WF/fwHkbHL3iHcYBpgbNmVtMDQo8P71119r9GjHxMTgnXfeQUJCglqXn5+PadOmYfz48YHbUyIianKA7gnCa4xB96zzCdALyuxqaUyA7k1zrxWgyzqZ3oSIiIjCW2K0Bcf0TFGL5/xkX1G5t5K6p4ibdBKs2iXjx4EXITNdpSHKfDyGtDVjUtxuDDbvRLSzDTpqmjoXwqqZwKbv3e+pM8Ce0g/mzmOr5hQfBcT4ny2rRRRXk3HVP/74oypy5ksKrR1//PHYu3cvQhlT4oiIGhage+7XTnuvbESKuwToqT4F4jwBum9VdwboRxZTzYmIqjHVPLTORXbklqme8dW73MH42r2FKKt0+j2/6C9jzc3z0SF3EZLyV6CdLq/mRkYrcNcuwFj171qSDUQmAj41xEK6uJq8uRREq03WFRcXN/btiIgoxHrQezSwB91Tuf1gAbqnB12qnh6MNKDdkqMxpFMChnSMx5COCar3nIiIiMLnXCQjKUotpw1sp9ZJxfQtB0p8esULsD6rWJ1bzN+cg/noDajlErRDDobpN2K4YRPOTd0DU3QiUF7orqKetRL49VH3B130NdD5qCP+/RodeJ955pkqrfypp55SU4CJJUuW4Pbbb8fkyZMDsY9ERNQCA3RJF/OdWq12gO5Je/cE6Mt25KvFdyoS30C8d9tYNfaLiIiIwoNBr1MF12Q5c3B7rMsqUgH3h0t2qqrpvvYiCV+5ZBmLo9L/QqfN7wFPdqv7pjImvCUE3i+//DJuu+02nHfeebDb3fOvGY1GXHrppXjiiScCsY9ERNQCA/T4SLNaGhKgyzgvqYC6Ymc+VuzIx6b9xd6pSL5e5R7CZDHq1VygEoQPZq84ERFRq583fO2eQizZnocl23KxNDMfJRUO9VwcSjBOvx1DjdvRU9uGAfptOKfiAWQhEQadDm2sOqBEpjLTAUndgXaDgdS+QNoAoMs/gvJ9Gh14R0ZG4sUXX1RB9tatW9W6rl27IioqdCvIERFR6AfovdJicfbQDmq9NKxSXEWCcAnG/9pVoHrFpdGVpb5e8T7tYtU8o0RERNSyVDpcWLOnAIu35WHxtlws35FfY3z3aP3fuNg6F0OMmUh2VM8P7tFfvw0HtCTMmNwPMV17Az3/AbQdAFjq7wAI6cDbQwLtAQMGNO/eEBERAYi2GDG2W5JaPD3j23JKqwLxAvy1syG94gkY0ileFXAjIiKi0FLhcGLVrkIVZC/Z7g60TfYS9NNvR3/dNkzRb8dM62mI7DISI7sk4nhnDtJ/XQy4O72BNl3cPdntBiM3tjcuNfbAQ22T0TYuour5zgglTQ68iYiIjmTPeNfkaLWcMyxdrWOvOBERUctRbneq9nrJtjwVaP+1swDxjhycYliEf+q34xHdNnSx1uzJPmniydCPG+Z+UGgCDA+5g+22A4GIeO92MmN49azhoYmBNxERtdpecammzl5xIiKiI6+s0oEVOwpUkL1yyx44965Eb20r1mmdsNjlnpq6V1QJ7nN+UPOF8R2rgutB0Hc7tnp9XAdg3E1oqRh4ExFRq+0VLy63qzQ2CcIP1iveISFCBeKqV7yTu4I6e8WJiIgarrTCoWYnWbplH/I2L0ZE9mr00W3DabrtuFm3F3qjprZbEHcqThkzBaO6JKJLvAGYvdDdg12VNo7INmiNGHgTEVGrFWM1YVz3JLUcrFd8d75NLV+xV5yIiKhB5OL2ii17sWPdEvy9txCfHmiv5t2ORzFWWm+rE2k6otvC0H4wxvU6AeMGd6p+Ysp7CAcMvImIKGwcrFd8hadXfGeBmuKMveJERETVCouLsXHlIuRuXgLj/lVIt23AWN0eHK1zYYGzL2a57lFt5cjOHZCTNRBR8amwdhoKXVXauDEmFeGMgTcREYW1pvaKW016DGgfr+YUZ684ERG1dFmFNmzPKUXnpCi0jdKjcP8OLMqPVWO0l2zNxbv552OErqj6BVXXnouNbdCxfWf8cc6xqqCp2+9B+Q6hjIE3ERFRE3vF/8zMU4u/XvFRXRPV3OREREQhzeXED7/8jN9+/QH9dNsRo9+GJP1uFLkScFXlc97N1ps6op9xFw5E91Y92Cm9RiGh6wjExLZDjE4X1K/QEjDwJiIiamSvuMvl7hV3F22rv1f8wtGdcO/JfWA2MiWdiIhCi1xALvjsZqRs+xyTXCWYZKr5fJTOhv7JBgzs2h4jOyeiV/svkZCYiAQG2U3CwJuIiKiR9HoduqVEq8Vfr/jyHfn4bVM23l20A3/vLcKL5w9BaizT0ImIKAicDmDfalRs/R1FmxbgrbT7sCCzGGv3FOJBwz5caCxBsRaBla6uWKN1wRpXZ3V773nH4+v+7YK9960GA28iIqIA9IrPXb8fN81aqYLwU55fgBfOG4IRnVvnFClERBR6gbZ92+8o3jAPUfv+hMVZCguAZAB/bh2N1VovtencuDOQnXw2XtwQBadn0DYAg06HgR0TgvglWh8G3kRERAEwoXcqvr5uHK56fzk27CvGea8txt0n9ca0sRlqHDkREVGzBdqaC5UwYtXuAlT89gzGbf8/SOa453JvkRaJP109scE6EIN7DsC/evXB6K6J3mysDkt34u7Za+HUNBV0z5jcD23jPIXSqDkw8CYiIgqQjKQozL5mDKbPXoMvV+7Fw9+sUydFj03uj0gzm2AiImpioJ21Cs7tv6N04zxYs5bi9bjr8Xz2YNjsTgzSJWGAORJLXL3wt7k/nOnj0LHPCIzqloKJbSL9vuWU4R1xVI9kZOaUISMpkkF3ALDVJyIiCiAJsJ+dMggDO8RjxnfrVQC+cV8xXv7XUBWYExERHVJpLlwr3kXZpnkw7/0TZmcZDAA8c2dEHVgOm2MAEqPM6NBlLL7u8gdGS6CdFNXgLCsJthlwBw4DbyIiogCTk55LxnVGv/ZxuOaDFSr1/NT/LVABuaSkExEReTntqkdb01zYaumNhVtzsW7jRjye+SCiqzYp1KRHuzdWGvqivP0YdOw9HHO6paBHSowqAEqhh4E3ERHRESLF1b69YZwKvqXo2qXvLMMNE7rjpgndeaJERBTOgfbeldAy56N8828w7vkTJmcZFusGYartDu9m/YwTsFvfHmXtRyO91zCM6pqKCe1iYWD70SIw8CYiIjqCpJDNR5ePwqPfrsM7i3bg/+ZuxurdBar3Oz7SHOzdIyKiI8j2/nkwbf8FRqcNEj57Er3ztWhkOaNhMeoxLCMBo7skonfXNzClQxxMhurq49RyMPAmIiI6wsxGPR46vR8GdYxXhdfmbcxWqecy7rtvu7hg7x4RETV7j/ZfQOZ82PZvxU/d78WirblYtDUHDxftxFEGmwq0JXV8KfqgIGUk2vccijHdkrEqPR5Wk4zmppaOgTcREVGQnDm4A3qmxuLK95dhV54Nk19cqCqeTx7SIdi7RkRETeWoRM7mxarieFLOUliylsHoLFNPSY/2I8vGIhvx6vHT+n/i06Sr0L7HEIzumoxbMxI460UrxX9VIiKiIOrTLlbN933TrJWq5/uWj1dh9e5CPHBqH873TUTUAq1/8yr03vsZknzW5VX1aC929UHn1DY4rXsnjOmaiOGdj0esVWbcptaOgTcREVGQydjuNy8ajmfnblZjvt9emIkT+6VhZJfEYO8aEREdSlEWEBEPmCLw7qJMrMhMxf2maBVkL64KtgcMGoGJfdvips6JSIhiPY9wxMCbiIgoBEhV81uO64Ft2SX4ZnUWlmzPY+BNRBTqtvwMzL4C5d1Owq22S/DtmiwYMQpfVoyBhuoiaA8N64TRXfmbHs5YEo+IiCjEphwTSzPzgr0rRERUH6cD+PlB4P2zgLJcZK6ej1/XbIdBBzhhrBF0G3Q6ZCRFBnV3KfgYeBMREYWQYZ3cgfdfOwvgdGnB3h0iIqqtcA/wzinAgmfUw/ccE3F6+YNIT03Gl9eNw+Nn9VfBtpDbGZP7oW2cZ6IwCldMNSciIgohPdNiEGMxorjCgQ37iji9GBFRKNn0I/D5lYAtDyWIwJ2Vl+N7bRSuPqYrbpjQHRajAf3ax+GoHsnIzClTPd0Mukkw8CYiIgohBr0Ogzsl4PdN2ViWmc/Am4goVFQUw/X5ldDb8rDGlYFr7TfCnNwVn58zEAPT3dODeUiwzYCbfDHVnIiIKMQM75SgbjnOm4godPy63Ybb7FfiLccknGN/CCceNRrfXD+uTtBN5A97vImIiELMsIzqAmuapnE+byKiYNn4PcrsLjy4oQM+XrYbQH+sTBqFD84ZiKFVF0mJGoKBNxERUYgZlB4Po16H/UUV2J1vQ3obVsMlIjqiHJXA3IeARf+DA9GYX/4YdLpEXDK2M26f1BNWkyHYe0gtTNBTzV944QVkZGTAarVi5MiR+PPPPw+6/bPPPouePXsiIiIC6enpuPnmm1FeXn7E9peIiCjQIszu4jxi2Q6mmxMRHSlZhTYsX7US5a8er4Ju8YljPCLbpGHWFaNx3yl9GHRTy+vxnjVrFm655Ra8/PLLKuiWoHrSpEnYuHEjUlJS6mz/4Ycf4q677sKbb76JMWPGYNOmTbj44otVCt7TTz8dlO9AREQUCMMzErByVwGWZubjzMEdgr07RESt3qylO/HLF2/iv8ZXYNWVoVCLxG32q9B+1Nn4+oSeiDQzWZhaaI+3BMuXX345pk2bhj59+qgAPDIyUgXW/ixcuBBjx47Feeedp3rJjz/+eEydOvWgveQVFRUoKiqqsRAREbWYcd7bQ6vHm+0qEbVG+4ps2Pzlf/CK6RnE6cqwwtUNJ1U8htOnXI4HT+vLoJtabuBdWVmJ5cuXY+LEidU7o9erx4sWLfL7Gunlltd4Au1t27bhu+++w0knnVTv5zz22GOIi4vzLpKeTkREFOr6tI1VtztyyxBK2K4SUWskv7Wn6N0xyIeOY/DPyvuxB8lIjLYEe9eolQjapZucnBw4nU6kpqbWWC+PN2zY4Pc10tMtrxs3bpyq8upwOHDVVVfh7rvvrvdzpk+frtLZPeTKPE8SiIgo1HnGEFY6XSFV2ZztKhG1Rp0SI3G0/WGk4wD2aW3ggBEGnQ4ZSSxuSa2kuFpjzJs3DzNmzMCLL76IFStWYPbs2fj222/xyCOP1Psai8WC2NjYGgsREVGoMxurm2gJvkMF21Uiao3SYiMwIiMRO7VUVMKkgu4Zk/uhbVxEsHeNWomg9XgnJSXBYDBg//79NdbL47S0NL+vue+++3DBBRfgsssuU4/79++P0tJSXHHFFbjnnntUqjoREVFrYPENvB0uWIysoktEFChOl4at2aXq/p0n9MQZg9sz6KZmFbRI1Ww2Y+jQoZg7d653ncvlUo9Hjx7t9zVlZWV1gmsJ3oWk4REREbUWZkN1e1fhCJ0ebyKi1qjy5WPw74rH0dlSjEvHdWHQTc0uqOX5ZIzYRRddhGHDhmHEiBFqOjHpwZYq5+LCCy9E+/btVSEXceqpp6pK6IMHD1bTj23ZskX1gst6TwBORETUGuj1OpgMOtidmurxJiKiwIko3IJ/6F34uWdGjaE+RK0i8J4yZQqys7Nx//33Y9++fRg0aBDmzJnjLbi2c+fOGj3c9957ryouI7d79uxBcnKyCrofffTRIH4LIiKiwJD0crvTwcCbiOgIWOHqjokDOgV7N6iVCvqEdNddd51a6ium5stoNOKBBx5QCxERUWunel0qQqu4GhFRa7VM1xeX9UgO9m5QK8U8CiIiohAf511hZ+BNRBQQPnWiKjuMRaQ56P2S1Eox8CYiIgpRFpO7ma50OoO9K0RErVPuFnVTrpmQ0ntMsPeGWjEG3kRERKHe480x3kREAfH7z1+r25Wubnjwuy2YtXRnsHeJWikG3kRERCHKU1mXgTcRUfPLKrThq41l6v4iVx+4NODu2WvVeqLmxsCbiIgoRBn1OnWr+YxBJCKi5rE9pxRzXMPV/TecJ6lbp6YhM8cdjBM1JwbeREREIY5xNxFR8+ucFFVnnUGnQ0ZSZFD2h1o3Bt5EREShSufu8SYioubXNi4C/dvH1gi6Z0zup9YTNTcG3kRERCGOPd5ERIHxePHd6vae/oVYcNcxmDK8Y7B3iVopBt5EREQhytPfzbibiCgwLK5SddsxKZo93RRQDLyJiIhCFDPNiYgCy+CqVLcmszXYu0KtHANvIiKiEMeq5kREgWHU7OrWbGHgTYHFwJuIiChEscObiCiwTN7Am2nmFFgMvImIiEIc+7uJiALDCIe6tTDwpgBj4E1ERBSidFWDvJlpTkQUAJoGK9xjvEucDIsosPgXRkREFKKYak5EFDizlmzHUldPdf+qmeswa+nOYO8StWIMvImIiEIeu7yJiJpTVqEN079cj2mVd6jHxVoE7p69Vq0nCgQG3kRERCGK04kREQXG9pxSuGpd03RqGjJzyoK1S9TKMfAmIiIiIqKw0jkpCvpaFzcNOh0ykiKDtUvUyjHwJiIiIiKisNI2LgJPnNoZ8yw3q8dWnRMzJvdT64kCwRiQdyUiIiIiIgphZw1pj8qfitT9b24ch46pScHeJWrF2ONNREREREThx2euxrQYa1B3hVo/Bt5ERERERBSGfKqrsZolBRgDbyIiIiIiCnMMvCmwGHgTEREREVFYp5oTBRoDbyIiIiIiCm9MNacAY+BNREREREThR28A0voHey8oTDDwJiIiIiKi8GONA6Z9Xx2EEwUQA28iIiIiIiKiADIG8s2JiIio6R45ox9Kyh3omhwd7F0hIiKiw8DAm4iIKET1SosN9i4QERFRM2CqOREREREREVEAMfAmIiIiIiIiCiAG3kREREREREQBxMCbiIiIiIiIKIAYeBMREREREREFEANvIiIiIiIiogBi4E1EREREREQUQGE3j7emaeq2qKgo2LtCRER0xHnaP097eLjYrhJRS1ZZWQmbzaZ+w8xmc7B3h1pxm6rTmqvlbSF2796N9PT0YO8GERFRUO3atQsdOnQ47Pdhu0pEROFuVwPa1LALvF0uF/bu3YuYmBjodLpmu9IhJx1ywGNjY5vlPcMNj2Hz4HFsHjyOzYPHMTSPoTT7xcXFaNeuHfR6fUi2qw3Fv7Eji8f7yOGxPnJ4rI+colZ4rBvTpoZdqrkckOa4wu+P/AG1lj+iYOExbB48js2Dx7F58DiG3jGMi4trEe1qQ/Fv7Mji8T5yeKyPHB7rIye2lR3rhrapLK5GREREREREFEAMvImIiIiIiIgCiIF3M7BYLHjggQfULTUNj2Hz4HFsHjyOzYPH8fDxGB4cj8+RxeN95PBYHzk81keOJcyPddgVVyMiIiIiIiI6ktjjTURERERERBRADLyJiIiIiIiIAoiBNxEREREREVEAMfAmIiIiIiIiCiAG3kREREREREQBxMC7CR599FGMGTMGkZGRiI+Pb9BrpHj8/fffj7Zt2yIiIgITJ07E5s2bEc7y8vJw/vnnIzY2Vh3HSy+9FCUlJQd9zb59+3DBBRcgLS0NUVFRGDJkCD777DOEs6YcR7Fo0SIce+yx6jjKa4866ijYbDaEq6YeR8//3yeeeCJ0Oh2++OILhKvGHkPZ/vrrr0fPnj3V72LHjh1xww03oLCwEOHkhRdeQEZGBqxWK0aOHIk///zzoNt/8skn6NWrl9q+f//++O677xAOGtL2yv+DtZeZM2fW2GbevHmq7ZDpbLp164a33377CH2D1nWsd+7ciZNPPlltk5KSgttvvx0Oh6PGNjzWTSO/B7X/jh9//PEa26xevRrjx49XvwPp6en473//G7T9DaffXzq0Bx98sM7fr7RZHuXl5bj22muRmJiI6OhonHXWWdi/fz/CAQPvJqisrMQ555yDq6++usGvkR/E//u//8PLL7+MJUuWqGBn0qRJ6o8vXMkJ+t9//42ffvoJ33zzDX7//XdcccUVB33NhRdeiI0bN+Krr77CmjVrMHnyZPzzn//EX3/9hXDVlOMoQfcJJ5yA448/XjUyS5cuxXXXXQe9Pnx/EppyHD2effZZ1bCEu8Yew71796rlySefxNq1a9VJ+Zw5c1TAHi5mzZqFW265Rc1rumLFCgwcOFC1DQcOHPC7/cKFCzF16lR1jOR374wzzlCLHL/WrqFt71tvvYWsrCzvIsfHY/v27SpYPOaYY7By5UrcdNNNuOyyy/DDDz8cgW/Qeo610+lUx1G2k7/Jd955R/3/Kx0MHjzWh+fhhx+u8XcsFyk9ioqKVPvdqVMnLF++HE888YQKdl599dWg7nNr//2lhuvbt2+Nv98FCxZ4n7v55pvx9ddfq4vIv/32mzoPkPP5sCDzeFPTvPXWW1pcXNwht3O5XFpaWpr2xBNPeNcVFBRoFotF++ijj7RwtG7dOpk/Xlu6dKl33ffff6/pdDptz5499b4uKipKe/fdd2usa9Omjfbaa69p4aipx3HkyJHavffee4T2svUeR/HXX39p7du317KystR7fP7551o4Opxj6Ovjjz/WzGazZrfbtXAwYsQI7dprr/U+djqdWrt27bTHHnvM7/b//Oc/tZNPPrnO/89XXnmlFi4O1vYe6v/BO+64Q+vbt2+NdVOmTNEmTZrU7PvZmo/1d999p+n1em3fvn3edS+99JIWGxurVVRUqMc81k3XqVMn7Zlnnqn3+RdffFFLSEjwHmtx5513aj179jxCexiev7/UMA888IA2cOBAv88VFBRoJpNJ++STT7zr1q9fr367Fy1apLV24du9dQTJVV9JkZb0co+4uDiV0iI9j+FIvrekrw0bNsy7To6P9LhKRkB9JPVNrlBKiqrL5VIphJI18I9//APhqCnHUa7kynOSGijHMzU1FUcffXSNq5Hhpql/j2VlZTjvvPNUqpoMfwhnTT2GtUmauaSqG41GtHbSWyi9Vb5tgxwveVxf2yDrfbcX0kMTrm2JP5LCmJSUhBEjRuDNN99UQ0E8ePyahxwvGeYg7YfvcZSeWMl68WzDY910klouqbiDBw9WPdq+afxyDGV4mNlsrnFsJSMwPz8/SHvc+n9/qeFkOG27du3QpUsXlQ0nQ1OEHHO73V7juEsaugw1C4fj3vrPbEKABN3Ct4HyPPY8F27ke0vg50tOtNu0aXPQY/Lxxx9jypQpqjGS7WVs2eeff67GjoWjphzHbdu2qVtJS5MU30GDBuHdd9/FhAkTVLpq9+7dEW6a+vco6VJy8eL0009HuGvqMfSVk5ODRx55pMEp/i2dfF9J2fXXNmzYsMHva+RYsi05eHqu1K6QtuHHH3/ENddco+oMSO2Agx0/CRilxoXUGqBDq+84ep472DY81ocmf68yNl5+PyWVf/r06Spd9+mnn/Ye286dO9d7/BMSEoKy363995caRjoWZeiJ1G+Rv9uHHnpI1SNYu3at+vuUC0a1a0eESzvGHu8qd911l9+iLL4L/0cM/nG87777UFBQgJ9//hnLli1TY3NkjLeM925NAnkcJVNAXHnllZg2bZq6mv7MM8+oH0jpHWpNAnkcpc7AL7/8osZ3t2ZH6rdRTsZlPGifPn3URSEKD8399yVtxNixY9Xv2p133ok77rhD9RYSz3Na0vGXcxvJ5BswYACuuuoqPPXUU3j++edRUVER7K9BdEhSbFZqRMjfr2RiSAFQOXf/+OOPEe7Y413l1ltvxcUXX3zQbSRdoik8KahSsU+qmnvIY+ltDMfjKMekdvEKSaOSFPL6Una3bt2K//3vf+qKmRRtEFIIY/78+SrVVwrXtRaBPI6ev0EJcHz17t3bmwrUWgTyOErQLX+Tta/aSnVOubIr1Xxbg0AeQ4/i4mJV7C8mJkZlsJhMJoQDSYc2GAx1qrnK4/qOmaxvzPbh3PZ6el4ki0ICFqmsXd/xk+ENrb0HtjmPtRzH2tWfPcfV87cYzse6uY+//B3L72lmZqa6SF7fsRUt9begJfz+UtPIeVKPHj2wZcsWHHfccSrNXwJx3/OncDnuDLyrJCcnqyUQJB1I/pjmzp3rDbSld0fGPTamMnprOo6jR49W/9PJWI+hQ4d6AxnpjZUGpr7xtKJ25W354fT04rYWgTyOMm2GjLuRsWC+Nm3apK5StiaBPI7SeyEVen3JmEfJHjj11FPRWgTyGHp+C+WKuARFkkUgU7qEC0m3k2MlbYOn8rYcL3ksswzUd5zleakQ7SFV5GV9SxTItldINW1Ju5W/LyHHqfb0ay35+AXrWMvxkinH5GKbZ4iJHEcJqj0XdcP5WDf38Ze/Yzn38RxrOYb33HOPGivruVApx1aCcqaZB+73l5pGhvtIR8UFF1ygjrn8zcpxlo4KIeej0vETFr8Nwa7u1hLt2LFDVTJ+6KGHtOjoaHVfluLiYu82Ully9uzZ3sePP/64Fh8fr3355Zfa6tWrtdNPP13r3LmzZrPZtHB1wgknaIMHD9aWLFmiLViwQOvevbs2depU7/O7d+9Wx1GeF5WVlVq3bt208ePHq3VbtmzRnnzySVU1+dtvv9XCVWOPo5BqqVJ9VqpKbt68WVU4t1qt6piGq6Ycx9rCuap5U45hYWGhqsjdv39/9bcnleE9i8Ph0MLBzJkz1QwXb7/9tqoMf8UVV6i2wlMt+oILLtDuuusu7/Z//PGHZjQa1W+fVIKV6rFSIXbNmjVauLe9X331lZrhQo6F/K5J5efIyEjt/vvv977Htm3b1Lrbb79dHb8XXnhBMxgM2pw5c4L4zVresZb/P/v166cdf/zx2sqVK9XxS05O1qZPn+59Dx7rplm4cKFqo+W4bt26VXv//ffVsb3wwgtrVIZOTU1Vvw9r165VvyNyrF955ZWg7ntr+/2lprn11lu1efPmadu3b1dt1sSJE7WkpCTtwIED6vmrrrpK69ixo/bLL79oy5Yt00aPHq2WcMDAuwkuuugidYJde/n111+928hjmYbDd0qx++67T/1Qyv/kEyZM0DZu3KiFs9zcXHVSLo26BIHTpk2rcfFC/oetfVw3bdqkTZ48WUtJSVGNzIABA+pMLxZumnIchUyX0aFDB3Uc5Qdv/vz5Wjhr6nH0Fe6Bd2OPodz6+y2VRbYNF88//7w6CZFp1GR6m8WLF3ufO/roo1WbU3vKtR49eqjtZbqmcLnweKi2V6avGzRokPr7k6knZTqbl19+WU0R5Eu2l+3k+HXp0qVGW00NP8/JzMzUTjzxRC0iIkKdVMvJdu1pAHmsG2/58uXqgqRM4yYXxHv37q3NmDFDKy8vr7HdqlWrtHHjxqlzSpnSUjp4qHl/f6lpZNrAtm3bqmMqf5vy2Ldjx2azaddcc42aEk/OQc8880x1wT0c6OQ/we51JyIiIiIiImqtWNWciIiIiIiIKIAYeBMREREREREFEANvIiIiIiIiogBi4E1EREREREQUQAy8iYiIiIiIiAKIgTcRERERERFRADHwJiIiIiIiIgogBt5EREREREREAcTAm4iIiIiIiCiAGHgTERERERERBRADbyIiIiIiIiIEzv8Dcva/R1f3YSIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x320 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = 0.05  # mm\n",
    "depth = np.arange(20) * h\n",
    "z0, s = 0.5, 0.08\n",
    "profile = -np.exp(-(depth - z0) ** 2 / (2 * s ** 2))  # a potential trough at 0.5 mm\n",
    "V = profile[None, :] * np.sin(2 * np.pi * 8 * t[:200])[:, None]  # (time, electrodes), oscillating amplitude\n",
    "\n",
    "csd = np.asarray(ba.field.current_source_density(V, h))\n",
    "exact = -(np.exp(-(depth - z0) ** 2 / (2 * s ** 2)) * ((depth - z0) ** 2 / s ** 4 - 1 / s ** 2)) * -1  # -d2V/dz2\n",
    "print(f\"CSD shape {csd.shape} (two boundary electrodes dropped)\")\n",
    "peak = np.argmax(np.abs(V).max(axis=1))\n",
    "print(f\"at the trough depth: CSD {csd[peak, 9]:.1f}, analytic -V'' {exact[10] * np.sin(2 * np.pi * 8 * t[peak]):.1f}\")\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 3.2), sharey=True)\n",
    "axes[0].plot(V[peak], depth)\n",
    "axes[0].set_title(\"potential at peak time\")\n",
    "axes[0].set_ylabel(\"depth (mm)\")\n",
    "axes[1].plot(csd[peak], depth[1:-1], \"o-\", ms=3, label=\"current_source_density\")\n",
    "axes[1].plot(exact * np.sin(2 * np.pi * 8 * t[peak]), depth, \"--\", label=\"analytic\")\n",
    "axes[1].axvline(0, color=\"0.6\", lw=0.8)\n",
    "axes[1].set_title(\"CSD (negative = sink)\")\n",
    "axes[1].legend(fontsize=8)\n",
    "axes[0].invert_yaxis()\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18b87247",
   "metadata": {},
   "source": [
    "The 3-point difference slightly underestimates the analytic second derivative when the spacing is not small compared with the width of the profile (here $h = 0.05$ mm against $\\sigma = 0.08$ mm).\n",
    "\n",
    "## Summary\n",
    "\n",
    "- `unitary_LFP` turns population spikes into an LFP whose shape depends on the recording location.\n",
    "- Choose `nperseg` from the frequency resolution you need ($1/(\\texttt{nperseg}\\cdot dt)$); the default is too coarse for short recordings. Results equal `scipy.signal.welch` / `coherence` with the same window and no detrending.\n",
    "- Coherence needs many segments; spectral entropy runs from 0 (peaked) to 1 (flat).\n",
    "- Tort's modulation index is small even for strong coupling: calibrate with synthetic signals and test against surrogates.\n",
    "- `lfp_phase_coherence` is a phase-locking value in a band; `current_source_density` is $-\\sigma\\,\\partial^2 V/\\partial z^2$ with sinks negative."
   ]
  }
 ],
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   "language": "python",
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