From 9e37023847db1cdad22323fbbc63a56ef410dc18 Mon Sep 17 00:00:00 2001 From: tschertenleib Date: Sat, 28 Mar 2026 22:42:35 +0100 Subject: [PATCH 1/5] fixing polynomial and high-Q behavious --- src/diffpy/adpdf/pipeline.ipynb | 305 ++++++++++--------- src/diffpy/adpdf/refine_frames/frame_000.png | Bin 0 -> 337800 bytes src/diffpy/adpdf/refine_frames/frame_002.png | Bin 0 -> 379376 bytes src/diffpy/adpdf/refine_frames/frame_004.png | Bin 0 -> 360297 bytes src/diffpy/adpdf/refine_frames/frame_006.png | Bin 0 -> 370009 bytes src/diffpy/adpdf/refine_frames/frame_008.png | Bin 0 -> 383453 bytes src/diffpy/adpdf/refine_frames/frame_010.png | Bin 0 -> 380661 bytes src/diffpy/adpdf/refine_frames/frame_012.png | Bin 0 -> 378449 bytes src/diffpy/adpdf/refine_frames/frame_014.png | Bin 0 -> 382801 bytes src/diffpy/adpdf/refine_frames/frame_016.png | Bin 0 -> 379717 bytes src/diffpy/adpdf/refine_frames/frame_018.png | Bin 0 -> 384999 bytes src/diffpy/adpdf/refine_frames/frame_020.png | Bin 0 -> 252139 bytes src/diffpy/adpdf/refine_frames/frame_022.png | Bin 0 -> 249774 bytes src/diffpy/adpdf/refine_frames/frame_024.png | Bin 0 -> 250473 bytes 14 files changed, 157 insertions(+), 148 deletions(-) create mode 100644 src/diffpy/adpdf/refine_frames/frame_000.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_002.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_004.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_006.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_008.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_010.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_012.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_014.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_016.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_018.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_020.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_022.png create mode 100644 src/diffpy/adpdf/refine_frames/frame_024.png diff --git a/src/diffpy/adpdf/pipeline.ipynb b/src/diffpy/adpdf/pipeline.ipynb index 3a139fa..a281fd2 100644 --- a/src/diffpy/adpdf/pipeline.ipynb +++ b/src/diffpy/adpdf/pipeline.ipynb @@ -3,11 +3,11 @@ { "cell_type": "code", "execution_count": null, - "id": "5bea62b3", + "id": "0", "metadata": {}, "outputs": [], "source": [ - "%matplotlib ipympl\n", + "# %matplotlib ipympl\n", "\n", "from dataclasses import dataclass, field\n", "from typing import Dict, List, Optional, Tuple, Any\n", @@ -24,36 +24,10 @@ }, { "cell_type": "code", - "execution_count": 2, - "id": "8f7700be", + "execution_count": null, + "id": "1", "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "941f38312afa44539c78637d562969e3", - "version_major": 2, - "version_minor": 0 - }, - "image/png": 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", - "text/html": [ - "\n", - "
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" Qmin: float = 0.1\n", + " Qmin: float = 0.7\n", " Qmax: Optional[float] = None\n", " # outer refinement\n", " n_outer: int = 40\n", " plot_every: int = 2\n", " frame_dir: str = \"./refine_frames\"\n", + " # Convergence threshold\n", + " tol_obj: float = 1e-4\n", " # parameter step sizes\n", + " step_rpoly: float = 0.05\n", " step_dE_eV: float = 2.0\n", " step_scale: float = 0.05\n", " step_fpp_offset: float = 0.05\n", @@ -438,7 +413,7 @@ " max_peak_height_factor: float = 1.0\n", " # objective pieces\n", " hiQ_anchor_lambda: float = 1.0\n", - " smooth_lambda: float = 1e-4\n", + " smooth_lambda: float = 1e-5\n", " peak_L1_lambda: float = 1e-3\n", " # peak birth/death controls\n", " birth_every: int = 4\n", @@ -453,8 +428,8 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "d0c06dca", + "execution_count": null, + "id": "4", "metadata": {}, "outputs": [], "source": [ @@ -540,8 +515,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "9b2af543", + "execution_count": null, + "id": "5", "metadata": {}, "outputs": [], "source": [ @@ -558,7 +533,7 @@ " I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray,\n", " alpha_e: np.ndarray, beta_f_e: np.ndarray,\n", " fmean_real: np.ndarray, fself: np.ndarray,\n", - " poly_deg: int, hiQ_mask: np.ndarray\n", + " rpoly: float\n", ") -> Tuple[np.ndarray, np.ndarray]:\n", " \"\"\"Return S(ne,nq) and beta_o(ne,nq) with correct FZ normalization.\"\"\"\n", " I_raw = np.asarray(I_raw, float)\n", @@ -570,27 +545,67 @@ " I_corr = I_raw * alpha_e[:, None] + beta_f_e[:, None]\n", " S0 = (I_corr - fself) / (fmean_real**2 + 1e-12) + 1.0\n", "\n", - " # β_o(Q,e): polynomial in Q fitted only on hiQ to drive S→1 there\n", - " X = np.vstack([Q**k for k in range(poly_deg + 1)]).T # [nq,p]\n", - " Xh = X[hiQ_mask]\n", - " XtXh = Xh.T @ Xh + 1e-12*np.eye(Xh.shape[1])\n", + " # β_o(Q,e): flexible polynomial in Q fitted over the whole Q-range\n", + " # To ensure S→1 at high-Q, we have to penalize bad fit at high Q.\n", + " xspan = float(Q[-1] - Q[0])\n", + " porder = (rpoly * xspan) / np.pi\n", + " porder = max(1.0, porder)\n", + "\n", + " porderlo = int(np.floor(porder))\n", + " porderhi = int(np.ceil(porder))\n", + "\n", + " # Define weights for the high and low polynomial degree\n", + " if porderlo == porderhi:\n", + " poly_weights = [0.5, 0.5]\n", + " else:\n", + " poly_weights = [porderhi - porder, porder - porderlo]\n", + "\n", + " # We want: S0 + polynomial → 1 (at high-Q).\n", + " # So we fit: polyonmial = 1 - S0.\n", + " # We want the polynomial to fit over the whole Q-range, but prioritize forcing S→1 at high-Q.\n", + " # Otherwise, the polynomial will try to flatten S(Q) at low-Q by removing strong structural signals.\n", + " # (Q / Qmax)^n forces the polynomial to ignore low-Q oscillation:\n", + " weight_power = 4.0\n", + " W_poly = (Q / Q[-1])**weight_power\n", + " W_sqrt = np.sqrt(W_poly)\n", + "\n", + "\n", + " # Build the design matrices for high and low polynomial orders\n", + " Xlo = np.vstack([Q**k for k in range(porderlo + 1)]).T\n", + " Xhi = np.vstack([Q**k for k in range(porderhi + 1)]).T\n", + "\n", + " # Apply weights to the deign matrices\n", + " Xlo_w = Xlo * W_sqrt[:, None]\n", + " Xhi_w = Xhi * W_sqrt[:, None]\n", + "\n", + " XtXlo = Xlo_w.T @ Xlo_w + 1e-12*np.eye(Xlo_w.shape[1])\n", + " XtXhi = Xhi_w.T @ Xhi_w + 1e-12*np.eye(Xhi_w.shape[1])\n", + "\n", " beta_o = np.zeros_like(S0)\n", " for i in range(ne):\n", + " # We want S0 + beta_o -> 1, so we fit X*coeff to (1 - S0)\n", " y = (1.0 - S0[i]) * (fmean_real[i]**2)\n", - " coeff = npl.solve(XtXh, Xh.T @ y[hiQ_mask])\n", - " beta_o[i] = (X @ coeff) / (fmean_real[i]**2 + 1e-12)\n", + " \n", + " # Apply the weights to the target variable (y_w = sqrt(W) * y)\n", + " y_w = y * W_sqrt\n", + " \n", + " # Solve for the lower degree polynomial using weighted matrices\n", + " coeff_lo = npl.solve(XtXlo, Xlo_w.T @ y_w)\n", + " # Evaluate using the UNWEIGHTED design matrix to apply the correction uniformly\n", + " beta_lo = (Xlo @ coeff_lo) / (fmean_real[i]**2 + 1e-12)\n", + " \n", + " if porderlo == porderhi:\n", + " beta_o[i] = beta_lo\n", + " else:\n", + " # Solve for the higher degree polynomial using weighted matrices\n", + " coeff_hi = npl.solve(XtXhi, Xhi_w.T @ y_w)\n", + " beta_hi = (Xhi @ coeff_hi) / (fmean_real[i]**2 + 1e-12)\n", + " \n", + " # Linearly interpolate the background corrections\n", + " beta_o[i] = poly_weights[0] * beta_lo + poly_weights[1] * beta_hi\n", + " \n", " S = S0 + beta_o\n", "\n", - " # sample = np.linspace(0, ne-1, 24, dtype=int)\n", - " # for i in sample:\n", - " # plt.figure()\n", - " # plt.plot(Q, S0[i], label=\"S0\")\n", - " # plt.plot(Q, beta_o[i], label=\"beta_o\")\n", - " # plt.plot(Q, S[i], label=\"S\")\n", - " # plt.axhline(1.0, color=\"k\", ls=\"--\")\n", - " # plt.title(f\"E={E[i]:.2f} eV\")\n", - " # plt.legend()\n", - " # plt.show()\n", "\n", " return S, beta_o\n", "\n", @@ -610,13 +625,12 @@ "\n", "def _reconstruct_Salpha_Snot(\n", " S_meas: np.ndarray, a: np.ndarray, b: np.ndarray,\n", - " Q: np.ndarray, ridge: float, anchor_weight: float,\n", - " hiQ_mask: np.ndarray\n", + " Q: np.ndarray, ridge: float\n", ") -> Tuple[np.ndarray,np.ndarray, Dict[str,float]]:\n", " \"\"\"Column-wise two-channel solve with conditioning checks and hiQ anchor.\"\"\"\n", " S_meas = np.asarray(S_meas, float)\n", "\n", - " # !!!!!\n", + " # !!!!! Till: I don't know what this is doing, and why the exclamation marks are here. Seems like some manual override of something...\n", " for i in range(S_meas.shape[0]):\n", " S_meas[i][:40] = S_meas[i][41]\n", "\n", @@ -631,10 +645,11 @@ " # condition\n", " s = npl.svd(Aj, compute_uv=False)\n", " cond = (s[0]/s[-1]) if (s[-1] > 0) else np.inf\n", - " anchor = anchor_weight if hiQ_mask[j] else 0.0\n", + "\n", + " anchor = 0.0 # Till: I removed the high-mask anchor here. \n", " if not np.isfinite(cond) or cond > 1e6:\n", " bad_cols += 1\n", - " anchor = max(anchor, 5.0) # heavy anchor to 1 if ill-conditioned\n", + " anchor = 5.0 # heavy anchor to 1 if ill-conditioned (Till: also here, not sure what this is doing...)\n", " sa, sb = _solve_two_channel_column(Aj, yj, ridge, anchor)\n", " Sa[j], Sb[j] = sa, sb\n", "\n", @@ -658,8 +673,8 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "ac8f7eb7", + "execution_count": null, + "id": "6", "metadata": {}, "outputs": [], "source": [ @@ -731,13 +746,13 @@ " bbox=dict(boxstyle=\"round\", facecolor=\"white\", alpha=0.85))\n", " ax.set_xlabel(\"Iteration\"); ax.set_ylabel(\"Objective\"); ax.set_title(\"Objective history\")\n", "\n", - " plt.savefig(path, dpi=300); plt.close()\n" + " plt.savefig(path, dpi=150); plt.close()\n" ] }, { "cell_type": "code", - "execution_count": 8, - "id": "0dc75ecb", + "execution_count": null, + "id": "7", "metadata": {}, "outputs": [], "source": [ @@ -769,8 +784,8 @@ " elements: List[str], comp: Dict[str,float], alpha: str,\n", " edge_model: Any,\n", " alpha_e: np.ndarray, beta_e: np.ndarray,\n", - " poly_deg: int, hiQ_frac: float,\n", - " ridge: float, anchor_weight: float,\n", + " rpoly: float,\n", + " ridge: float, \n", " r: np.ndarray, Qmin: float, Qmax: float,\n", " window: str = \"lorch\", kaiser_beta: float = 6.0,\n", " fp_offset: float = 0.0,\n", @@ -787,24 +802,20 @@ " )\n", " a, b, wb = _weights_alpha_not(comp, alpha, frw, fmean_real, f_not_sum)\n", "\n", - " # Q masks\n", + " # Q masks for Fourier transform to get G(r)\n", " if Qmax is None: Qmax = float(Q.max())\n", " mask_Q = (Q >= Qmin) & (Q <= Qmax)\n", " Q_use = Q[mask_Q]; nq_use = Q_use.size\n", "\n", - " # hiQ anchor mask (absolute + fractional)\n", - " hiQ_abs = (Q >= max(Qmin, cfg.Q_anchor_min if 'cfg' in globals() else 20.0))\n", - " hiQ_fr = np.zeros_like(Q, bool); hiQ_fr[int((1.0-hiQ_frac)*nq):] = True\n", - " hiQ_mask = (hiQ_abs & hiQ_fr)[mask_Q]\n", - "\n", " # build S(Q,e)\n", - " S_meas_all, beta_o_all = _build_S_from_raw(I_raw, Q, E, alpha_e, beta_e, fmean_real, fself,\n", - " poly_deg, hiQ_abs & hiQ_fr)\n", + " S_meas_all, beta_o_all = _build_S_from_raw(\n", + " I_raw, Q, E, alpha_e, beta_e, fmean_real, fself, rpoly\n", + " )\n", " S_meas = S_meas_all[:, mask_Q]\n", " a = a[:, mask_Q]; b = b[:, mask_Q]\n", "\n", " # per-Q two-channel solve\n", - " Sa, Sb, condinfo = _reconstruct_Salpha_Snot(S_meas, a, b, Q_use, ridge, anchor_weight, hiQ_mask)\n", + " Sa, Sb, condinfo = _reconstruct_Salpha_Snot(S_meas, a, b, Q_use, ridge)\n", "\n", " # PDFs\n", " r = _as_1d(r)\n", @@ -819,16 +830,17 @@ " diag = {\"weights\": wb,\n", " \"condinfo\": condinfo,\n", " \"beta_o\": beta_o_all,\n", - " \"hiQ_stats\": {\"S_alpha\": _hiQ_stats(Sa, Q_use, hiQ_frac),\n", - " \"S_not\": _hiQ_stats(Sb, Q_use, hiQ_frac),\n", - " \"S_tot\": _hiQ_stats(S_tot, Q_use, hiQ_frac)}}\n", + " # Hardcoded hiQ_frac=0.85 here just to keep your diagnostic stats alive\n", + " \"hiQ_stats\": {\"S_alpha\": _hiQ_stats(Sa, Q_use, 0.85),\n", + " \"S_not\": _hiQ_stats(Sb, Q_use, 0.85),\n", + " \"S_tot\": _hiQ_stats(S_tot, Q_use, 0.85)}}\n", " return out, diag\n" ] }, { "cell_type": "code", - "execution_count": 9, - "id": "1abd8c28", + "execution_count": null, + "id": "8", "metadata": {}, "outputs": [], "source": [ @@ -844,13 +856,14 @@ " pk.height = float(np.clip(pk.height, 0.0, cfg.max_peak_height_factor*max(1e-6, baseline_med)))\n", "\n", "def _pack_params(edge_model: Any, alpha_C: float, alpha_D: float, beta_C: float, beta_D: float,\n", - " fp_offset: float) -> Dict[str,float]:\n", + " fp_offset: float, rpoly: float) -> Dict[str,float]:\n", " d = dict(dE_eV=edge_model.params.dE_eV,\n", " scale=edge_model.params.scale,\n", " fpp_offset=edge_model.params.fpp_offset,\n", " broaden_fwhm_eV=edge_model.params.broaden_fwhm_eV,\n", " alpha_C=alpha_C, alpha_D=alpha_D, beta_C=beta_C, beta_D=beta_D,\n", - " fp_offset=fp_offset)\n", + " fp_offset=fp_offset,\n", + " rpoly=rpoly)\n", " d[\"peaks\"] = [(float(p.center_eV), float(p.fwhm_eV), float(p.height))\n", " for p in edge_model.params.peaks]\n", " return d\n", @@ -864,12 +877,16 @@ " fp_offset: float = 0.0,\n", " cfg: Optional[RefinementConfig] = None,\n", ") -> Tuple[Dict[str,np.ndarray], Dict[str,Any], List[RefinementHistory]]:\n", + "\n", " if cfg is None: cfg = RefinementConfig()\n", " Q = _as_1d(Q); E = _as_1d(E_eV); I_raw = np.asarray(I_raw, float)\n", " ne, nq = len(E), len(Q)\n", " if I_raw.shape != (ne, nq):\n", " raise ValueError(f\"I_raw shape {I_raw.shape} but expected ({ne},{nq})\")\n", "\n", + " # Extract rpoly so it can be refined\n", + " rpoly = cfg.rpoly\n", + "\n", " # bounds on global params\n", " edge_model.params.scale = max(1e-4, float(edge_model.params.scale))\n", " edge_model.params.broaden_fwhm_eV = float(np.clip(edge_model.params.broaden_fwhm_eV,\n", @@ -886,8 +903,8 @@ " out, diag = reconstruct_partials_and_pdfs(\n", " I_raw, Q, E, elements, comp, alpha, edge_model,\n", " alpha_e, beta_e,\n", - " poly_deg=cfg.poly_deg, hiQ_frac=cfg.hiQ_frac,\n", - " ridge=cfg.ridge, anchor_weight=cfg.anchor_weight,\n", + " rpoly=rpoly,\n", + " ridge=cfg.ridge,\n", " r=r, Qmin=Qmin, Qmax=Qmax,\n", " window=cfg.window, kaiser_beta=cfg.kaiser_beta,\n", " fp_offset=fp_offset,\n", @@ -896,13 +913,14 @@ " return out, diag, obj\n", "\n", " out, diag, obj = compute()\n", - " hist = [RefinementHistory(0, obj, _pack_params(edge_model, alpha_C, alpha_D, beta_C, beta_D, fp_offset))]\n", + " hist = [RefinementHistory(0, obj, _pack_params(edge_model, alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly))]\n", " os.makedirs(cfg.frame_dir, exist_ok=True)\n", " _plot_frame(os.path.join(cfg.frame_dir, f\"frame_{0:03d}.png\"),\n", " E, edge_model, r, out, Q, 0, hist, fp_offset)\n", "\n", " # step sizes for coordinate descent\n", " steps = dict(\n", + " rpoly=cfg.step_rpoly,\n", " dE_eV=cfg.step_dE_eV, scale=cfg.step_scale,\n", " fpp_offset=cfg.step_fpp_offset, fp_offset=cfg.step_fp_offset,\n", " broaden_fwhm_eV=cfg.step_broaden_fwhm,\n", @@ -914,9 +932,10 @@ " )\n", "\n", " def tweak(name: str, d: float):\n", - " nonlocal alpha_C, alpha_D, beta_C, beta_D, fp_offset\n", + " nonlocal alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly\n", " p = edge_model.params\n", - " if name == \"dE_eV\": p.dE_eV += d\n", + " if name == \"rpoly\": rpoly = float(np.clip(rpoly + d, 0.0, 2.0))\n", + " elif name == \"dE_eV\": p.dE_eV += d\n", " elif name == \"scale\": p.scale = max(1e-4, p.scale + d)\n", " elif name == \"fpp_offset\": p.fpp_offset += d\n", " elif name == \"broaden_fwhm_eV\":\n", @@ -938,21 +957,30 @@ "\n", " best_obj = obj\n", " for it in range(1, cfg.n_outer+1):\n", - " improved = False\n", + " # Track if the OVERALL cycle improved\n", + " cycle_improved = False\n", + " # Store the objective at the start of this iteration\n", + " start_obj = best_obj\n", "\n", " # scalar params\n", - " for name in [\"dE_eV\",\"scale\",\"fpp_offset\",\"fp_offset\",\"broaden_fwhm_eV\",\n", + " for name in [\"rpoly\", \"dE_eV\",\"scale\",\"fpp_offset\",\"fp_offset\",\"broaden_fwhm_eV\",\n", " \"alpha_C\",\"alpha_D\",\"beta_C\",\"beta_D\"]:\n", + " \n", + " # Track if THIS SPECIFIC parameter improved\n", + " param_improved = False\n", + " \n", " for sgn in (+1,-1):\n", " tweak(name, sgn*steps[name])\n", " _peak_bounds_guard(edge_model, cfg, E)\n", " out2, diag2, obj2 = compute()\n", " if obj2 < best_obj:\n", " out, diag, best_obj = out2, diag2, obj2\n", - " improved = True\n", + " param_improved = True\n", + " cycle_improved = True\n", " else:\n", " tweak(name, -sgn*steps[name])\n", - " if not improved: steps[name] *= 0.7\n", + " # Only shrink the step size if THIS parameter failed to improve\n", + " if not param_improved: steps[name] *= 0.7\n", "\n", " # peak params\n", " for i in range(len(edge_model.params.peaks)):\n", @@ -964,10 +992,11 @@ " obj2 += cfg.peak_L1_lambda * abs(edge_model.params.peaks[i].height)\n", " if obj2 < best_obj:\n", " out, diag, best_obj = out2, diag2, obj2\n", - " improved = True\n", + " param_improved = True\n", + " cycle_improved = True\n", " else:\n", " tweak_peak(i, which, -sgn*steps[key])\n", - " if not improved: steps[key] *= 0.7\n", + " if not param_improved: steps[key] *= 0.7\n", "\n", " # peak birth\n", " if (it % cfg.birth_every) == 0:\n", @@ -992,7 +1021,7 @@ " obj2 += cfg.peak_L1_lambda * sum(abs(p.height) for p in edge_model.params.peaks)\n", " if obj2 < best_obj:\n", " out, diag, best_obj = out2, diag2, obj2\n", - " improved = True\n", + " cycle_improved = True\n", " else:\n", " edge_model.params.peaks.pop()\n", "\n", @@ -1003,26 +1032,33 @@ " keep.append(p)\n", " edge_model.params.peaks[:] = keep\n", "\n", + " # Updated history tracking call\n", " hist.append(RefinementHistory(it, best_obj,\n", - " _pack_params(edge_model, alpha_C, alpha_D, beta_C, beta_D, fp_offset)))\n", + " _pack_params(edge_model, alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly)))\n", " if (it % cfg.plot_every)==0 or it==cfg.n_outer:\n", " _plot_frame(os.path.join(cfg.frame_dir, f\"frame_{it:03d}.png\"),\n", " E, edge_model, r, out, Q, it, hist, fp_offset)\n", + " \n", + " # Stop if the relative improvement is smaller than our tolerance\n", + " rel_change = (start_obj - best_obj) / max(start_obj, 1e-12)\n", + " if rel_change < cfg.tol_obj:\n", + " print(f\"Converged! Relative change ({rel_change:.2e}) is below tolerance ({cfg.tol_obj}).\")\n", + " break\n", "\n", - " if not improved and max(steps.values()) < 1e-3:\n", + " # Safety net: stof if step sized have shrunk to useless levels\n", + " if not cycle_improved and max(steps.values()) < 1e-3:\n", + " print(f\"Stopped at iteration {it}: step sizes shrank below 1e-3.\")\n", " break\n", "\n", - " # hq = diag[\"hiQ_stats\"]\n", - " # print(f\"[tails] ={hq['S_alpha']['mean']:.4f}, slope={hq['S_alpha']['slope']:.3g}\")\n", - " # print(f\"[tails] ={hq['S_not']['mean']:.4f}, slope={hq['S_not']['slope']:.3g}\")\n", - " # print(f\"[tails] ={hq['S_tot']['mean']:.4f}, slope={hq['S_tot']['slope']:.3g}\")\n", + "\n", + "\n", " return out, diag, hist\n" ] }, { "cell_type": "code", - "execution_count": 10, - "id": "4f1bcaf8", + "execution_count": null, + "id": "9", "metadata": {}, "outputs": [], "source": [ @@ -1038,13 +1074,12 @@ " Q = np.array(data[\"q\"])\n", "\n", "elements = [\"Ba\", \"Bi\", \"O\"]\n", - "comp = {\"Ba\": 1/3, \"Bi\": 1/3, \"O\": 1/3}\n", + "comp = {\"Ba\": 1/5, \"Bi\": 1/5, \"O\": 3/5}\n", "alpha = \"Bi\"\n", "\n", "\n", "cfg = RefinementConfig(\n", - " poly_deg=1, hiQ_frac=.85, ridge=1e-3,\n", - " anchor_weight=1.5, Q_anchor_min=25.0, Qmax=50.0,\n", + " rpoly=1, hiQ_frac=.85, ridge=1e-3, Qmax=30.0,\n", " window=\"none\", rmin=0.0, rmax=20.0, dr=0.01, #lorch/kaiser/none\n", " n_outer=24, plot_every=2, frame_dir=\"./refine_frames\"\n", ")\n", @@ -1062,36 +1097,10 @@ }, { "cell_type": "code", - "execution_count": 11, - "id": "a6f5ceaf", + "execution_count": null, + "id": "10", "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "2e08038bda9b41fca7b243d4715dd8ed", - "version_major": 2, - "version_minor": 0 - }, - "image/png": 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/iYwTVT6GRCKRSGovUgBKXGjVqhW7d++mX79+TJw4kc6dO9O9e3dmzZrF+PHjKyWounTpwsyZM3n33Xfp0KED3333HW+//XaF+8XFxXHXXXcxePBgBgwYQIcOHZg7d26lxx4eHs78+fP5/vvvadeuHe+88w4ffPBBhfsNHjwYnU7H2rVrK9x23rx5PPzww7z44ou0adOGoUOH8s8//zgtjlarlTFjxtC2bVsGDRpEmzZtnO+hSZMm/PLLL2zbto3OnTvz1FNP8dhjjzF58uRKv8fLPbfFefzxx2nTpg3du3cnPDyczZs3A7By5UqaN2/utHDq1LryupFIJBJJHUUlKusYJClBdnY2ISEhZGVlERwc7LLOYDCQlJREixYtSg0wkLgydepUVqxYwZ49ezxy/Llz57Jy5UpWr17tkePXFnr06MG4ceOc1XAsNgt7UvcA0C2qW7V9AeX3QiKR1AbKu3/XF6QPoEQCPPHEE2RkZJCTk1NvK8GkpaVxzz338MADDzjbigo+IQRULg2kRCKRSGo5cgpYUmW+++47lzQoRf/at2/v6eFdFlqtlkmTJtVb8QdKLeAJEya4RCSriig+R0SwRCKRSOo+0gIoqTJDhw6lZ8+epa4rnn6kskydOrVEyTOJZ7FYLSSmF+ZgFEhvEYlEIvEWpACUVJmgoKB6bSmrL1iFlQJLgXNZugtLJBKJ9yCngCUSSakUnfIN8w+TyaAlEonEi5AWQIlEUioOi59OraNFaAsPj0YikUgk7kQ+0kskklJx+Pyp5M+ERCKReB3yl10ikZSKEAIMwZjOtufCBZv0AZRIJBIvQgpAiURSKgIB2c1BqDl5Uk2uKdfTQ5JIJBKJm5ACUOIVJCYmEhkZSU5OjqeH4lVoQlOUF9r8ctPA7N+/n6ZNm5KXl3eFRiaRSCSS6iAFoKQEqampPPfcc8TFxeHr60tERAR9+vThs88+Iz8//4qNo2/fvowbN65S206aNIkxY8bI9DRuJMgniLgwR/CH2jkFXNrn0rFjR3r06MGHH354ZQcpkUgkkstCCkCJCydOnKBr166sWbOG6dOns3v3btauXcvzzz/PTz/9xNq1az09xBKcOXOGVatW8cgjj3h6KKViNps9PYTLRqOxv7BpKqwE8sgjj/Dpp59itVprfmASiUQiqRZSAEpcGD16NFqtlh07djB8+HDatm1Lx44dufvuu/n5558ZMmRIpfpRqVR8+eWX3Hnnnfj7+9O6dWtWrVrlss3GjRvp0aMHPj4+REVF8corr2CxWAAYNWoUGzdu5OOPP0alUqFSqUhOTi71WEuXLqVz5840bdrU2TZ//nxCQ0NZvXo1bdu2JTAwkEGDBpGSkuLcxmaz8cYbb9C0aVN8fHzo0qULv/32m3N9cnIyKpWKZcuWcdNNN+Hv70/nzp3ZunVrue996tSpdOnSha+//pqWLVvi4+ODEIKsrCyeeOIJGjduTHBwMDfffDN79+517rd3715uuukmgoKCCA4O5uqrr2bHjh3O9T/++CPt27fHx8eH2NhYZsyY4XLc2NhYpk+fzqOPPkpQUBDNmzfniy++cNnm5ZdfJj4+Hn9/f1q2bMmrr77qIlAdY//222+JjY0lIiKE//znfvJyDAhEuZ/LwIEDSU9PZ+PGjeWeH4lEIpHUAoTkssnKyhKAyMrKKrGuoKBAHDp0SBQUFDjbbDabyDXmXvE/m81Wqfdz8eJFoVKpxNtvv13tcwOIpk2biv/+97/i6NGj4tlnnxWBgYEiPT1dCCHEmTNnhL+/vxg9erQ4fPiwWL58uWjUqJGYMmWKEEKIzMxM0atXL/H444+LlJQUkZKSIiwWS6nHGjZsmHjqqadc2ubNmyd0Op3o16+f2L59u9i5c6do27atGDFihHObmTNniuDgYLFo0SKRkJAgJkyYIHQ6nThy5IgQQoikpCQBiKuuukr873//E4mJieKee+4RMTExwmw2l/nep0yZIgICAsTAgQPFrl27xN69e4XNZhO9e/cWQ4YMEdu3bxdHjhwRL774oggLC3Oek/bt24uHHnpIHD58WBw5ckQsXbpU7NmzRwghxI4dO4RarRZvvPGGSExMFPPmzRN+fn5i3rx5zuPGxMSIhg0bijlz5oijR4+Kt99+W6jVanH48GHnNtOmTRObN28WSUlJYtWqVSIiIkK8++67LmMPDAwUd911l9iyY4v44v82iLCwSPHII/8RF/IuVvi59OjRQ0ydOrXMc1Pa90IikUiuNOXdv+sLUgBWg6oKwFxjrmAqV/wv15hbqffz999/C0AsW7bMpT0sLEwEBASIgIAAMWHChEr1BYjJkycXvvfcXKFSqcSvv/4qhBDiP//5j2jTpo2LOJ0zZ44IDAwUVqtVCCHEjTfeKJ577rkKj9W5c2fxxhtvuLTNmzdPAOLYsWMu/UdERDiXo6OjxVtvveWy3zXXXCNGjx4thCgUgF9++aVz/cGDBwXgIqqKM2XKFKHT6URaWpqz7Y8//hDBwcHCYDC4bNuqVSvx+eefCyGECAoKEvPnzy+1zxEjRoj+/fu7tL300kuiXbt2zuWYmBjx0EMPOZdtNpto3Lix+PTTT8sc63vvvSeuvvpql7H7+/uL7OxscSHvgti+wyL+9a+XRIeO14i0nAtCiPI/lzvvvFOMGjWqzONJASiRSGoDUgAKIaeAJSVQqVQuy9u2bWPPnj20b98eo9FY6X46derkfB0QEEBQUBBpaWkAHD58mF69erkcq3fv3uTm5nLmzJkqjbegoABfX98S7f7+/rRq1cq5HBUV5Tx+dnY2586do3fv3i779O7dm8OHD5f5PqKiogCc/QQGBjr/nnrqKed2MTExhIeHO5d37txJbm4uYWFhLvskJSVx/PhxAF544QX+/e9/069fP9555x1nOyjnq7SxHj161MXnruhYVSoVkZGRzrEC/PDDD/Tp04fIyEgCAwN59dVXOXXqlEu/sbGxBAUFOYM+GjWKIjMrFR+dnorw8/O7ooFCEolEIrk8ZCm4K4i/zp/ciVc+l5q/zr9S28XFxaFSqUhISHBpb9myJaDc3KuCTqdzWVapVNhsSiCBEKKE0HQIjuLtFdGoUSMyMjIqdXxRLJlxaWMo3la0H8c6x/vYs2ePc11wcLDzdUBAgEsfNpuNqKgoNmzYUGKcoaGhgOJ/N2LECH7++Wd+/fVXpkyZwuLFi7nzzjvLPV9ljdUxXsdY//77b+6//35ef/11Bg4cSEhICIsXLy7hS+joQyBAqAEVGpWaYJ9gKuLSpUsuolviBRw5Aq+9Bg8/DIMHe3o0EonETUgBeAVRqVQE6AMq3tBDhIWF0b9/f2bPns3YsWNLiBh30q5dO3788UcXYbNlyxaCgoJo0qQJAHq9vlIRpV27duXQoUNVOn5wcDDR0dH89ddf3HDDDc72LVu20KNHj0r3ExcXV6ntunXrRmpqKlqtltjY2DK3i4+PJz4+nueff54HHniAefPmceedd9KuXTv++usvl223bNlCfHw8Gmeobvls3ryZmJgYJk2a5Gw7efJkmdsrurGkGC/vczlw4AD33HNPpcYjqSO8+iosXQo//wwyz6ZE4jXIKWCJC3PnzsVisdC9e3eWLFnC4cOHSUxMZOHChSQkJFRabFTE6NGjOX36NGPHjiUhIYGVK1cyZcoUXnjhBdRq5bKMjY3ln3/+ITk5mYsXLzotWcUZOHAgW7durXL6kZdeeol3332XJUuWkJiYyCuvvMKePXt47rnnqv3+itOvXz969erFHXfcwerVq0lOTmbLli1MnjyZHTt2UFBQwDPPPMOGDRs4efIkmzdvZvv27bRt2xaAF198kT/++INp06Zx5MgRFixYwOzZsxk/fnylxxAXF8epU6dYvHgxx48f55NPPmH58uVlbl/0dJtMUGBQLI5lfS7JycmcPXuWfv36XcYZktRadu1S/ufmgj1KXyKR1H2kAJS40KpVK3bv3k2/fv2YOHEinTt3pnv37syaNYvx48czbdo0txynSZMm/PLLL2zbto3OnTvz1FNP8dhjjzF58mTnNuPHj0ej0dCuXTvCw8NL+Ko5GDx4MDqdrso5Cp999llefPFFXnzxRTp27Mhvv/3GqlWraN26dbXeW2moVCp++eUXbrjhBh599FHi4+O5//77SU5OJiIiAo1GQ3p6Og8//DDx8fEMHz6cW2+9lddffx1QLIhLly5l8eLFdOjQgddee4033niDUaNGVXoMw4YN4/nnn+eZZ56hS5cubNmyhVdffbXM7W02AapCUZ2WewEo+3NZtGgRAwYMICYm5jLOkKTW8u67ha/T0z03DolE4lZUojRHIkmlyM7OJiQkhKysLBf/LwCDwUBSUhItWrQoNUBB4l7mzp3LypUrWb16taeH4jWk5qZyLucctpQOYNPTKCaN2PDGpW5rNBpp3bo1ixYtKhGsUhT5vaijhIXBpUuwfz906ODp0Ugk1aa8+3d9QfoASryCJ554goyMDHJycmQ5ODcRGRhJZGAku9PMWG1QXiGQkydPMmnSpHLFn6QOEx6uCMALFzw9EolE4iakAJRUme+++44nn3yy1HUxMTEcPHjwCo8ItFqtS3CDxH04go9t5cwVOIJXJF6GxQKrV0PDhvDAA9CggadHJJFI3IQUgJIqM3ToUHr27FnquuJpSGoLFpuFpIwkQn1DCQ8Ir3gHCQUFcPo0WEz2tDDSWaT+cfEi3H678hTw11+glm7jEom3IAWgpMoEBQXVuWnWM9lnyDJmkWXMkgKwklzIzSA7u9DiI0TV8jNKvIBLl5T/oaFS/EkkXob8RkvqBVq1fNapKkaLqXDBJxuVumppdiReQHa28j8kBMxmMBg8Ox6JROI2pACU1AsiAiKcr2Xge+VwVmbR5hMSfIzgIPlzUe9wlPVLTga9HqqQd1IikdRu5C+6pF6gURUmsLaVF84qceLQyTqboPUFG40DSk8BI/FiCgpcl2UlEInEa5DzYpJ6QdE6ujZhQ4N7Kpp4M4U+f9JiWm+xWwBzCcCKhhApACUSr0FaACX1ghMZJ5yvpQWwcjgsgCZbILvpQlqaFIL1joICxvEhwWTzGU8p5eAkEolXIAWgpM7y1VdfMWDAgEptaxVKAEOYX5jbAkKmTp1Kly5d3NKXJxg/fjzPPvts2RsU0XtWtFzMvVTzg5LULrp3J2TAtQjUnCRGTgFLJF6EFICSEqSmpvLcc88RFxeHr68vERER9OnTh88++4x8h1N4BahUKlasWFHlY1d2P6PRyGuvveZSy3bUqFHccccdpW7vsPqF+oaiUbtO/5a33+UwdepU7r//frf1V1NMmDCBefPmkZSUVOp6fWAuRO1A43sRkHkA6yOW+HYED7gWgEs0lAJQIvEipACUuHDixAm6du3KmjVrmD59Ort372bt2rU8//zz/PTTT6xdu9bTQwTgxx9/JDAwkOuvv75S21vNGkiP51xyzecvXLVqFcOGDavx41SXxo0bM2DAAD777LNS17dq2IruF7T4WxTxLAVg/eO33woDf9MJkwJQIvEipACUuDB69Gi0Wi07duxg+PDhtG3blo4dO3L33Xfz888/M2TIkAr7iI2NBeDOO+9EpVI5lwE+/fRTWrVqhV6vp02bNnz77beV2q84ixcvZujQoc7lqVOnsmDBAlauXIlKpUKlUrFhwwYA9u/fzyN3PUKfayLo3SuCx/79GLl2X6by9nv55ZeJj4/H39+fli1b8uqrr2I2m8t976dPn+bAgQPceuutgGLR/Pzzz7n99tvx9/enbdu2bN26lWPHjtG3b18CAgLo1asXx48fd+nnp59+4uqrr8bX15eWLVvy+uuvY7FYnOtnzpxJx44dCQgIoFmzZowePdr5ngDmz59PaGgoq1evpm3btgQGBjJo0CBSUlJcjjN06FAWLVpU9huy2XDMBUsBWP/IPnre+To9uCVU0uVCIpHUAYTkssnKyhKAyMrKKrGuoKBAHDp0SBQUFDjbbDYhcnOv/J/NVrn3c/HiRaFSqcTbb79drfOSpkQLiHnz5omUlBSRlpYmhBBi2bJlQqfTiTlz5ojExEQxY8YModFoxLp168rdrzRCQ0PF4sWLncs5OTli+PDhYtCgQSIlJUWkpKQIo9Eo8vLyRHR0tLi53xCxaNF+MXfuHyImNkaMHDmy3P2EEGLatGli8+bNIikpSaxatUpERESId99913nMKVOmiM6dO7uMa/bs2eKWW25xLgOiSZMmYsmSJSIxMVHccccdIjY2Vtx8883it99+E4cOHRLXXnutGDRokHOf3377TQQHB4v58+eL48ePizVr1ojY2FgxdepU5zYffvihWLdunThx4oT4448/RJs2bcTTTz/tXD9v3jyh0+lEv379xPbt28XOnTtF27ZtxYgRI1zGe+jQIQGI5OTkEuc4I8Mmjm1PF9u3W8X27ULsO5Je5udRWUr7XkhqL5/e8r1QpL8QMTGeHo1E4j7Ku3/XF6QArAZVFYC5ucL5Y3ol/3JzK/d+/v77bwGIZcuWubSHhYWJgIAAERAQICZMmFCpvgCxfPlyl7brrrtOPP744y5t9957rxg8eHC5+xUnIyNDAOLPP/90aR85cqQYNmyYS9sXX3whGjRoIDb9c05s3y7E9u1CLPphqVCr1SI1NbXM/UrjvffeE1dffbVzuTQB2L9/f/HJJ5+4vJ/Jkyc7l7du3SoA8dVXXznbFi1aJHx9fZ3L119/vZg+fbpLv99++62Iiooqc2xLly4VYWFhzuV58+YJQBw7dszZNmfOHBEREeGyn+Ma3rBhQ4k+E5Mzneds+3Yh9koBWO9499plzt+RwEBPj0YicR9SAAoh8wBKSlA0Zx7Atm3bsNlsPPjggxiNxsvu9/DhwzzxxBMubb179+bjjz+uUj8F9uS0vr6+lTpm586dCfQPwWKvYtW9R09sNhuJiYlERESUue8PP/zARx99xLFjx8jNzcVisRAcHFzm9tnZ2WzcuJH/+7//c2nv1KmT87XjeB07dnRpMxgMZGdnExwczM6dO9m+fTtvvfWWcxur1YrBYCA/Px9/f3/Wr1/P9OnTOXToENnZ2VgsFgwGA3l5eQQEBADg7+9Pq1atnH1ERUWRlpbmMjY/Pz+AUoN7XErB6XNRacqf/pZ4H9n5hbeI228Hm9mKWqsGlawLLZHUdaQAvIL4+3smjZa/f+W2i4uLQ6VSkZCQ4NLesmVLoFAsVIfi4lIIUaKtIsLCwlCpVGRkZFS4raN/X60/jlNvs4lSx1KUv//+m/vvv5/XX3+dgQMHEhISwuLFi5kxY0aZ+/z666+0bduWmJgYl3adTud87ThmaW02m835//XXX+euu+4qcQxfX19OnjzJ4MGDeeqpp5g2bRoNGzbkr7/+4rHHHnPxUSx6DMdxRDFHvkuXlNQu4eHhJY7l2NTPNx1tUDJ+AaFA2YJZ4n3kFCi3iP/c8jdvLbsRFpvg0iVo0MDDI5NIJNVFCsAriEoFduNMrSQsLIz+/fsze/Zsxo4d67QkXQ46nQ6r1erS1rZtW/766y8efvhhZ9uWLVto27ZtufsVR6/X065dOw4dOuSSB1Cv15fYt127dixYsIDcnBxQKRHA//z9D2q1mvj4+DL327x5MzExMUyaNMnZdvLkyXLHtXLlSpfAlMulW7duJCYmEhcXV+r6HTt2YLFYmDFjBmq1Ese1dOnSyzrWgQMH0Ol0tG/fvsQ6hwDUmy20viAgtNFlHUNSd8k26gEIDgIc35GCAikAJRIvQEYBS1yYO3cuFouF7t27s2TJEg4fPkxiYiILFy4kISEBjaZyJdRiY2P5448/SE1NdVrqXnrpJebPn89nn33G0aNHmTlzJsuWLWN8kQLzpe1XGgMHDuSvv/4qccx9+/aRmJjIxYsXMZvNPPjgg/j6+vKfiSM5duwAO3as59VXXuZf//qXczq2tP3i4uI4deoUixcv5vjx43zyyScsX768zPFYLBZ+/fVXt6R/ee211/jmm2+YOnUqBw8e5PDhwyxZsoTJkycD0KpVKywWC7NmzeLEiRN8++23ZaZyqYhNmzZx/fXXl27dtRdMUTkyQssw4HpHm4ATNI7+H/sbbsDiG4gNVcn6wBKJpG7iYR/EOk1Vg0DqCufOnRPPPPOMaNGihdDpdCIwMFD06NFDvP/++yIvL69SfaxatUrExcUJrVYrYoqED86dO1e0bNlS6HQ6ER8fL7755ptK7Vecw4cPCz8/P5GZmelsS0tLE/379xeBgYECEOvXrxdCCLF3717R/ZobhY+PrwgJDREPjXpI5OTkVLjfSy+9JMLCwkRgYKC47777xIcffihCQkKc+xUNAlm7dq1o2rRpiXFSLKglKSlJAGL37t3OtvXr1wtAZGRkONt+++03cd111wk/Pz8RHBwsevToIb744gvn+pkzZ4qoqCjh5+cnBg4cKL755huXPubNm+cyViGEWL58uSj+lY+PjxeLFi0q9RzvTrggtm8XYud2s9iz3ShOHqn+tVyXvxf1kSX3dxRMRRCSLECIPXQSYt8+Tw9LIqk2MghECJUQ8rH+csnOziYkJISsrKwSwQEGg4GkpCRatGhRqWAFSdUZPnw4Xbt2ZeLEieVuZxM2dp06BEJD87wCQuLb4aNz72fy7LPPYrFYmDt3rlv7rUl+/vlnXnrpJfbt24dWW9IbZE/CRSy5jVBhRaBB659Jl3ah1Tqm/F7ULd6bM4KXLy6Cj49BRis2cx3X/fMR9Ojh6aFJJNWivPt3fUFOAUvqLO+//z6BgYEVbygAnQH0eYQZbPiodRXuUlU6dOjA008/7fZ+a5K8vDzmzZtXqvgD0IWkQNQuAn2U5NHyUbH+cTG+KQBhIYqLQB4BcgpYIvESZBCIpMp89913PPnkk6Wui4mJ4eDBg1dkHDExMYwdO7bC7YTDhy2rKccIIDpHEBTq3rEUT29TFxg+fHi569sFxCCOHOGs1koOUgDWR+aNeRKSXifdUkQAVrIeuEQiqd1IASipMkOHDqVnz56lriueeqQ2IBCQGwF5keQAeWYjQfLSrxCVEKjs/+0tnhyOxAOY8lVgKQwQyuvcGxo29OCIJBKJu5B3QUmVCQoKIigoyNPDqBrZTZwvc435gI/nxlJHSMvUkUcsZpVD1EsBWN8QOfZQcL+LUNCIvNEvQenPfhKJpI7htT6Af/75J0OGDCE6OhqVSsWKFStc1o8aNQqVSuXyd+2113pmsJIaRYlzUhdbllTE+QJBOo0wapVM4sJbBeCCBXDttXDihKdHUusIzbNnkfdPByAvz4ODkUgkbsVrBWBeXh6dO3dm9uzZZW4zaNAgUlJSnH+//PLLFRyh5EohRLHqI1abh0ZStzBZlaoiaq0AbT4qzeWXAazVjBoF//wDxUr4ScAglETQNNtMix4HKVbkRiKR1GG8dgr41ltv5dZbby13Gx8fHyIjI6/QiCSeQqNyvcwdpeAkFaEI50BtNqqGJ9FqfQAvqwZSpHQe+/d7bhy1FIOwu0pcP52bA3y466EkmDoVJkzw6LgkEkn18VoLYGXYsGEDjRs3Jj4+nscff5y0tLRytzcajWRnZ7v8SWo/xWd85QxwJbGfJ11eAe3SBPHWEM+OpyawWMBe61pSklyVXQBqDeRgVFLAyHlgicQrqLcC8NZbb+W7775j3bp1zJgxg+3bt3PzzTdjNJY9zfX2228TEhLi/GvWrNkVHLHkcrG5zPjanMJGUgH286SyWuzLXnji/PzgvfeU15mZHh1KbUMI0MSsg5gNoM8jR2v/Isk8gBKJV1BvBeB9993HbbfdRocOHRgyZAi//vorR44c4eeffy5zn4kTJ5KVleX8O3369BUcsXcxf/58QkNDq7TPqFGjuOOOO6p8LKPFLupVNojehW/QpRLbJCYmEhkZSU5OTpX79xT33HMPM2fOrLH+HUEf+SKQA3TgWJaXTf86cKQ1SU/37DhqGSoVqB+8FR65CXb9m9XvHOJJPpMCUCLxEuqtACxOVFQUMTExHD16tMxtfHx8CA4OdvnzRlJTU3nuueeIi4vD19eXiIgI+vTpw2effUZ+HUwCq9HaoFECNDxKiwwI15RMYTNp0iTGjBlTp9LbvPbaa7z11ltk//NPjYoXm0qFAV+yvDF25sIFZRp48mR44w1Pj6ZWYbGaMTndZwU2iy8F+IHB4MlhSSQSNyEFoJ309HROnz5NVFSUp4fiUU6cOEHXrl1Zs2YN06dPZ/fu3axdu5bnn3+en376ibVr13p6iFVHJUCfi1afS1gBBKpccwCeOXOGVatW8cgjj3hogFXDbA9c6NSpE7GRkXy3fDkkJbn9OKoGxyFyD8FqxWIqhMr7Uuh8/z0MGACHDsG993p6NLWKPHPhw95bA18DwIAvlOMmI5FI6g5eKwBzc3PZs2cPe/bsASApKYk9e/Zw6tQpcnNzGT9+PFu3biU5OZkNGzYwZMgQGjVqxJ133unZgXuY0aNHo9Vq2bFjB8OHD6dt27Z07NiRu+++m59//pkhQ4ZUqp+ZM2fSsWNHAgICaNasGaNHjyY3N7fM7adOnUqXLl34/PPPadasGf7+/tx7771kluKX9cEHHxAVFUVYWBhjxoxxCiKAhQsX0r17d4KCgoiMjGTEiBHO4B6RH8Yx4riQrXfpb+nSpXTu3JmmTZs62xxT1CtWrCA+Ph5fX1/69+/vMu1//Phxhg0bRkREBIGBgVxzzTUlBHJsbCzTpk1jxIgRBAYGEh0dzaxZs1y2ycrK4oknnqBx48YEBwdz8803s3fv3hLn5uuvv6Zly5b4+Pg4hdjQvn1ZtGZNmee1OnTWRNAlzYKPN6fNcQQ0BAR4dhy1kCMnDPB2Jsw8TXiwYhk34CstgBKJl+C1AnDHjh107dqVrl27AvDCCy/QtWtXXnvtNTQaDfv372fYsGHEx8czcuRI4uPj2bp165WZAszLK/uv+I9redsW98UpbZsqkJ6ezpo1axgzZgwBZdwQVarKJQNWq9V88sknHDhwgAULFrBu3TomVJA64tixYyxdupSffvqJ3377jT179jBmzBiXbdavX8/x48dZv349CxYsYP78+cyfP9+53mQyMW3aNPbu3cuKFStISkriiUefhLzGWHOjySSU7GIWwD///JPu3buXGE9+fj5vvfUWCxYsYPPmzWRnZ3P//fc71+fm5jJ48GDWrl3L7t27GThwIEOGDOHUqVMu/bz//vt06tSJXbt2MXHiRJ5//nl+//13QElKfdttt5Gamsovv/zCzp076datG7fccguXLhX6KjrOzY8//uh8qAHo0akT2w4exGgylXtuLwetAK2tyI+EUBXWVfYWHN+Rbdvg55+9M9DlMsnNLQBjCBiD8fNV2gyhUdC2rWcHJpFI3IOQXDZZWVkCEFlZWSXWFRQUiEOHDomCgoKSOyq3mdL/Bg923dbfv+xtb7zRddtGjUpuUwX+/vtvAYhly5a5tIeFhYmAgAAREBAgJkyYUKU+HSxdulSEhYU5l+fNmydCQkKcy1OmTBEajUacPn3a2fbrr78KtVotUlJShBBCjBw5UsTExAiLxeLc5t577xX33Xdfmcfdtm2bAMTGjTli+3Yhtm8XYm9Chss2nTt3Fm+88YZL27x58wQg/v77b2fb4cOHBSD++eefMo/Xrl07MWvWLOdyTEyMGDRokMs29913n7j11luFEEL88ccfIjg4WBgMBpdtWrVqJT7//HPnudHpdCItLa3E8fauWCEAkbxjR5ljulzOJWSJ5O3nxfmEC8q522UQFqul4h3LodzvhScYP971+1JbxlUL+PXnncpp8U0Xt0yYK0CI66/39KgkEvdQ3v27vuC1FkDJ5VPcyrdt2zb27NlD+/bty02TU5T169fTv39/mjRpQlBQEA8//DDp6enklWOVbN68ucs0bK9evbDZbCQmJjrb2rdvj0ajcS5HRUW55G/cvXs3w4YNIyYmhqCgIPr27QtAamqhVa64jaegoABfX98S49FqtS6WwauuuorQ0FAOHz4MKNVmJkyYQLt27QgNDSUwMJCEhIQSFsBevXqVWHb0sXPnTnJzcwkLCyMwMND5l5SUxPHjx537xMTEEB4eXmKMfg0aAJDvZsuVEILzJh8u0Bizvz3/n/DCUnDFr8c6GORUUzTVKf7QYSYzf5xWsiPI2V+JxHvw2kogtZpyfOEoIm4AKC85tbqYfk9OvuwhAcTFxaFSqUhISHBpb2lPlOvn51epfk6ePMngwYN56qmnmDZtGg0bNuSvv/7isccec/HXqwiHEC0qSHU6XYltbPZEf3l5eQwYMIABAwawcOFCwsPDOXXqFAMHDsRsLjJFanUVS40aNSIjI6PcMZTW9tJLL7F69Wo++OAD4uLi8PPz45577sFUielYRx82m42oqCg2bNhQYpuiaXLKmpK/5KNMZ4fHxlZ4zKpgEzYsNisAap0aNAbQWBCUFMp1mtIEoCMtTD3HUqB8V3VYIfA8xG6kW7cbPTwqiUTiLqQA9ARVcTivqW1LISwsjP79+zN79mzGjh1bpuioiB07dmCxWJgxYwZqu0hdunRphfudOnWKc+fOER0dDcDWrVtRq9XEx8dX6rgJCQlcvHiRd955x5mke8eOHSW2K14buGvXrhw6dKjEdhaLhR07dtCjRw9AyRWYmZnJVVddBcCmTZsYNWqUM3AoNzeX5FJE+N9//11i2dFHt27dSE1NRavVEnsZIu7AgQM0jYqiUX4+mEyg11e8U2Wx62R/Wz6+jY6gUmuADu7rvzZQXADKHHdOLAYlAbhWZYUmO2BUX2bPbQSH28HGjR4enUQiqS5yCljiwty5c7FYLHTv3p0lS5Zw+PBhEhMTWbhwIQkJCS7Tr2XRqlUrLBYLs2bN4sSJE3z77bd89tlnFe7n6+vLyJEj2bt3L5s2beLZZ59l+PDhla7X3Lx5c/R6vfO4q1atYtq0aSU3LDZbOnDgQLZu3YrVanVp1+l0jB07ln/++Yddu3bxyCOPcO211zoFYVxcHMuWLWPPnj3s3buXESNGOK2RRdm8eTPvvfceR44cYc6cOXz//fc899xzAPTr149evXpxxx13sHr1apKTk9myZQuTJ08uVbwWZ9OmTQzo2VOxFFfBuloRSrCH3QKbn0eH84L2ef5o1V72zHjnnfDSS4XLcgrYyeGLJwDI9Cu8rowZF+HiRU8NSSKRuBEpACUutGrVit27d9OvXz8mTpxI586d6d69O7NmzWL8+PGlC6pidOnShZkzZ/Luu+/SoUMHvvvuO95+++0K94uLi+Ouu+5i8ODBDBgwgA4dOjB37txKjz08PJz58+fz/fff065dO9555x0++OCDEts5Klw4GDx4MDqdrkQKF39/f15++WVGjBhBr1698PPzY/Hixc71H374IQ0aNOC6665jyJAhDBw4kG7dupU43osvvsjOnTvp2rUr06ZNY8aMGQwcOBBQpoJ/+eUXbrjhBh599FHi4+O5//77SU5OJiIiotz3aygoYPmPP/L40KH2N+Y+P0AhighAh1XMGyNkH3xQKQXXooWyLC2ATvJs56HZZtSRu51tBi3SEVAi8RJUQnjjr/qVITs7m5CQELKyskpUBTEYDCQlJdGiRYtSAwwkrkydOpUVK1a4pDhxFykpWZw9GwLafAg/jD8a2jXp4rLN3LlzWblyJatXrwaUPIDjxo0rNQ9hVYiNjWXcuHGMGzeuWv2UxpzZs1m5cCFrZs9WGuLjwU3VacxWM3v3WcHqSyuf06QYG4JaQ7tu1buWa+33okMHOHgQ/vgDbr7Z06OpFfxvxbsM2fsK16T7sEvbFOvnW4koMJMa3QPOnPH08CSSalHe/bu+4GXzORJJSXQ+Jmh4BK2w0SRLoA0q6dv4xBNPkJGRQU5OTp0pB6fTaJg1fnxhQynTz5eLyxSwWkU+AWATGC1GfLQ+5e9clzh2DLRaeP55xfoXF+fpEdUaTCHK90AfFoFPgZr8/HAuYZKVQCQSL0FOAUuqzHfffeeSsqToX/v27T09vBJo/LTgm42vn4nwfGhgKxkoodVqmTRpUp0RfwBPPPYYbYoGjrh7CrhRAqrG+/DXOKKaVdiEl1UF6dtXmf7t2hWeeQaaN/f0iGoNpnAlGlof24p/nlKCPszosRrc52sqkZTKF1/AggWeHoXXIy2AkiozdOhQevbsWeq64mlaKsvUqVOZOnVqNUZVNo7qFTaTPydogm+ehugK9hk1ahSjRo2q9rFLiwp2G8UFnxstgHqNnk5mf8jKQl3EYOp1DiOOlEyyFFwJdm4Kgw/OcjD+JC3uKayRbjCAPFuSGuPMGXjySeX10KFgz3UqcT9SAEqqTFBQUJ2ylJlNashvhMkSQj4N8MNSoQCsE9SgAFSpVOhtKrCCVVM4UWDzNgXoSANz5owSSR0XB1FR5e9TT8jNMENuNJacDHyKzPobuvYiQAioZFlIiaRKFM1De/Ag9OnjubF4OXIKWOL1GLJskBmLJVd5kjRYvMSHqagY69DB7QmMzxY05DRNsfgXin2v0n8mE1iUXHe8/jrccINSD1gCgPnESQA0+RnM/Oc91BolTZJh+a9S/ElqjqJphorUQ5e4HykAJV5PSdHiJTcvlQoCAyEkBHx9S1aRqQYmq4lUUyjnicQWWBgh51VJA4omgXZMM1Wiikt94WadkvS7U4E/3x/6HptGyZEos8BIahRH5oVeveDWWz06FG9HTgFLvB6VU7PYI1u9RcP4+oK9ooi7sdgsCBRBqdbrQG0GhHdZAB0CUKtVhDRIAVgER15xncaGr9YXmvzDVQ26oNU28uzAJN6NQwC2aQOX6VMuqRxSAEq8Hn+1km9OhVCSQHuTiAHIyoKcHAgKUqyBbkAIAY6SeSYjQY0OYVILtNo2bum/VuAQgAEBhSX0pAB0YjErXxSt2i4AR/bn1a1RxPQCtm2Dpk09O0CJd/LAA9ClC1SQCF9SfaQAlHg/dsGnwoZAXaISSJ0nOxvOn1fmut0kABXseQANBtqkWRVLWVMviv8MDoYXXlDel8PqIAWgk835ScANpPjmEqlRokAM2RmQYpAVUyQ1R0wM7NkD8+fD6dNKJLCkRpACUOL1OKYt1Qi8KotddjYkJRXO1dVUKTijwe391wqiomDGDOX12LHKfykAnVzUn4KIPdAgWbEAAgZf+y1DJoOW1CR//QWffKJY5qUArDFkEIjEK0hMTCQyMpKcnJwS6/JsioBR63IhcjfqRoev9PBK5Z577mHmzJmX34HNVij+HMtuQhSZJ1epVRylNYetrb33vi+ngEvQssNaeLorA66foQjAb3/llS1H2cgNMhJEUnOsWwf//a/yWl5nNYoUgJISpKam8txzzxEXF4evry8RERH06dOHzz77jPz8/Cs2jr59+1a6hu6kSZMYM2ZMqfkJdX750OA4er/zNMux0tRUOxyLX3vtNd566y2ys7Mvr4PiFjm3WgCLLKhVZKv8ySOQXGNemfvUOXJy4NQpxYdy8GCYPh0GDfL0qGoNpoaKO4E+thU+Gh/Ib0SOMZI8AqQFUFJz/N//wblzymspAGsUOQUsceHEiRP07t2b0NBQpk+fTseOHbFYLBw5coSvv/6a6OhohtYyk/yZM2dYtWoVH330UanrtUFaEKn4aIKIOA2evuzNZjM6nY5OnToRGxvLd999x9NPP131jopb/Nw6RSug8QF8zKDRFDpjW9xoZfQ4y5fDyJEwYACsXg233OLpEdUqTFGNIRX011zL9K6PsbdZCDtTwIiPFICSmqOof6kUgDWKtABKXBg9ejRarZYdO3YwfPhw2rZtS8eOHbn77rv5+eefGTJkSKX6UalUfPnll9x55534+/vTunVrVq1a5bLNxo0b6dGjBz4+PkRFRfHKK69gsSfmHTVqFBs3buTjjz9GpVKhUqnKLKu2dOlSOnfuTNMiUYnz588nNDSUFStW0LtLb3q37M2/7n2MLalaTpsaA3D8+HGGDRtGREQEgYGBXHPNNaxdu9al79jYWKZNm8aIESMIDAwkOjqaWbNmuWyTlZXFE088QePGjQkODubmm29m7969zvVTp06lS5cufP3117Rs2RIfHx9nPr2hQ4eyaNGiSp3TEtSgBTBAH0CHfIjPNqBSqwtz6XiTH2DRKGBJCfb9dAN8ksj6eX2JCIwgyF/xA5QCUFKjFBV9UgDWKFIAeoA8U16ZfwaLodLbFpgLKty2KqSnp7NmzRrGjBlDQBk3RVUVKgC8/vrrDB8+nH379jF48GAefPBBLtkzu589e5bBgwdzzTXXsHfvXj799FO++uor3nzzTQA+/vhjevXqxeOPP05KSgopKSk0a9as1OP8+eefdO/evUR7fn4+b731Fh/M+oQvlywlJ6eApyeNIV00QAhBbm4ugwcPZu3atezevZuBAwcyZMgQTp065dLP+++/T6dOndi1axcTJ07k+eef5/fffweUYInbbruN1NRUfvnlF3bu3Em3bt245ZZbnO8V4NixYyxdupQff/yRPXv2ONt79OjBtm3bMF7ODbUGBaBGrcHXqsLHir3qg72ess0LBWBgIFy4ALt2wfHjnh1TLSI/wxcuxWPI9AdwloMzNo1TclBKJDWBFIBXDDkF7AEC3w4sc93g1oP5eURhOarGHzQm31y6392NMTeyYdQG53Lsx7FczL/oso2YUvkb9rFjxxBC0KaNa663Ro0aYbB/EceMGcO7775bqf5GjRrFAw88AMD06dOZNWsW27ZtY9CgQcydO5dmzZoxe/ZsVCoVV111FefOnePll1/mtddeIyQkBL1ej7+/P5GRkeUeJzk5mauvvrpEu9lsZvbs2YQ2bE1OVkOmTm3GXXdczd59f9O5cy86d+5M586dndu/+eabLF++nFWrVvHMM88423v37s0rr7wCQHx8PJs3b+bDDz+kf//+rF+/nv3795OWloaP/Q75wQcfsGLFCn744QeeeOIJAEwmE99++y3h4eEuY2zSpAlGo5HU1FRiYmIqdV6dOARfUBA0a+bWSiBWK6SaGwNmorU6UKvAhnel0MnNVf4HBChO5+PGKTnIHA7o9RzzeeUBRnfyOL8fv8CxrGigPabX3oSbPDs2iRdTdApYphuqUaQFUFKC4la+bdu2sWfPHtq3b18lS1WnTp2crwMCAggKCiItLQ2Aw4cP06tXL5dj9e7dm9zcXM6cOVOl8RYUFOBbikVCq9XSvXt353RryxatCQoKJSkpAYEgLy+PCRMm0K5dO0JDQwkMDCQhIaGEBbBXr14llg8fViKJd+7cSW5uLmFhYQQGBjr/kpKSOF7EmhQTE1NC/AH4+fkBXF5wjUYDfn7g76/8OUw0biDfVECKJZwUolD5+zlLv3plKbjAQBkFXApDzcqDYCcasOX0Fo5nHwLk7K+khnFY/WbPhoULPTsWL0daAD1A7sTcMtdp1K5WnLTxaWVuq1a56vfk55KrNa64uDhUKhUJCQku7S1btgQKxUpl0RUr46NSqbDZgwiEECWEpkNcVGWaGRQLZUZGRqnrVCoVKntFC5Wjf9QIIXjppZdYvXo1H3zwAXFxcfj5+XHPPfdgqoQIcIzRZrMRFRXFhg0bSmwTGhrqfF3WlLpjmrg0cVghYWHKXw1gMBsB++et1aJSG0BlqZFjeQxZCaRcbBbl98VHo0Kv0UODEzRscYoGDZp7eGQSr8YhADt1ggpmfyTVQwpADxCgr7zTeU1tWxphYWH079+f2bNnM3bs2DJFizto164dP/74o4sQ3LJlC0FBQTRp0gQAvV6P1WqtsK+uXbty6NChEu0Wi4UdO3YQHdKeHCD1+BFycjKJjVUsG5s2bWLUqFHceeedAOTm5pYaaPL333+XWL7KXoO3W7dupKamotVqiY2Nrezbd3LgwAGaNm1Ko0bVqK9aUAAZGYqIqU4/RXDa+VRKQuiQkESyNRb8fL3o5u+YApYWwFIxW5XvpU4n0Gl00P8lbjN/w4NvWMA8EUaN8uwAJd7J3LnK71nbtp4eidcjp4AlLsydOxeLxUL37t1ZsmQJhw8fJjExkYULF5KQkIDGTX5mo0eP5vTp04wdO5aEhARWrlzJlClTeOGFF1CrlcsyNjaWf/75h+TkZC5evOi0HhZn4MCBbN26tYRY1Ol0jB07ll17t5OQsItXXh9Nx47X0r59TwSCuLg4li1bxp49e9i7dy8jRoxwPYY9Innz5s289957HDlyhDlz5vD999/z3HPPAdCvXz969erFHXfcwerVq0lOTmbLli1MnjyZHTt2VHgeNm3axIABAy7nFBZiMCh5sy5cqF4/RSic6RVgsdDygoUuKYKGeneWmvMwN98Mjz+u1B2VArAEW1BmHy5qchULIGAy5sORI2691iQSF265Ba69Fj76CN5+29Oj8WqkAJS40KpVK3bv3k2/fv2YOHEinTt3pnv37syaNYvx48czbdo0txynSZMm/PLLL2zbto3OnTvz1FNP8dhjjzF58mTnNuPHj0ej0dCuXTvCw8NL+OY5GDx4MDqdrkQKF39/f15++WXGjn+URx/tha+PH2+9tRhQIYTgww8/pEGDBlx33XUMGTKEgQMH0q1bt8IOLl0Ck4kXH3uMnTt30rVrV6ZNm8aMGTMYOHAgoEwF//LLL9xwww08+uijxMfHc//995OcnExEBcXMDQYDy5cv5/HHH7+8k5iaCvv3K3WAoQZKwYEK4SqKvMkHcNQo+OIL6NcPHO4KHhaAQgiWHFjCsUvHPDoOgHOBJ6HhUQjMKBSAjuc/6QgoqUkuXIC33oI5czw9Eq9GJbzKq/vKkp2dTUhICFlZWQQHB7usMxgMJCUl0aJFi1IDFCTuZe7cuaxcuZLVq1cDSh7AcePGkZmZScLhTHLzQgnxSSMrNAWATtFtnTe1Mjl3jtju3Rn38MOMe+stt0bZAsyZM4eVK1eyZs2ay+vg9GlF/Pn7Q36+EhDSvr1bxpaSkcHZ4w1QqSxc3c7MqUM5FAhfmrT0JbBhBeetHGrt92LVKhg2DHr2hGJT/leSP0/+yY3zbwTA8qqlhE/wlaTLpDD26i+xRj2K07dfz2MT9+O/7VkmZnzF5FfV8MYbHhubxIv5738hIQGmTVN8nC9erHify6C8+3d9QfoASryCJ554goyMDHJyckqUg9P6Z4IuAz0WmuSZQa1Go6rEjdUxpWwyKdOsbvaJ1Ol0JZJKVwnHs5t9yrwmLIAOb8BMtT8mayAZBZkEcvkCsFZx/rwSOR0UBPHxMGmSkk7Hg+xNVRKI6zV6l3rMnsDi7wsW0LZopTwsFTQgP6MFqUSCqWqR+hJJpXnoocLfsqK1ziVuRwpASZX57rvvePLJJ0tdFxMTw8GDB6/wiJSUL5MmTSp9XQiQn47erzFRxwGtGipjWSnqU1iJYJSq4sgReNnUoADU6KwQfohAI6Bqic1eCcRic/958Bi9eyuJn//6S3ltT0LuSVJzUwF4otsTaNUeLlkYEgjpoL3+Rm5r3IGx15mY9ae9Eoj0lZTUBDab6++YxcsyD9QypACUVJmhQ4fSs2fPUtcVT/3iKUaNGsWoYlGKQqg5RTOwqmlqK9RNZWK1kuwoX1cbf4hqUACG+TcgKPkUGosAlaowD6CHrVJupWgewFpCjikHgGAfz09Jnf/xJTjcnY3h/lw/ugHNGirtJvRSAEpqhuIWP2kBrFGkAJRUmaCgoBLTrLUZs0EHhhCseh/SCAcBUTabM9q4TIoKqtroKuuIWK4BAajVaNGaKJIPRrj7EJ6naBqYggI4dUo5l61be2xIDgH405Gf+He3f9OiQQuPjcV0sSmc70J+dhJQpBRcQBg0bOixcUm8mOIP2maz8qNTxdywksohBaDE6zFcCoD8Jhgs6c42o8WETltBEELRlDBlpKDxKA415ucHV11VCZNm5TGZIF1EoMVCuEqFSqcFMwgPT0u6DSFcE0Hv3Qu9ekGLFnDihMeGlWtSROn+tP1sPr3ZowLQZlCm+3X7dpOUAWuSDwK3YxpwO7xxu8fGJfFiSrP4Wa2g9ZLfnVqGTAMj8XocOkklrEXaKmHKKjo1WBtNXzqdYpbR65Wx+vu7revMvHzO0pRzuibKj6+3PYAXFBR+poGBhTcYD0/15xhznK/zTHkeHAlcn90YgOY+oZzKOsXPJ34EZAYYSQ1S9Pu3axccOODWB1uJK/LMSrwfhwBEUKWpzOjowqmu2mgBbN4cOnaskXJw+SalCLtNJUCttus/W63UwZdFXhFx5e9fmAfQwwJwbI+xztcOa6CnEFblnPjpNUoUsN8ltI2Svb861z//wNmznh5F/cRhAVSroWtXJa2VFIA1hjyzEq8nQCg3siChpVAAVlLJhIZCVJTbU8C4C5MJEhIEGUmZSmJoN1H87IQGJaOO2kVAQJbbjuFRHP5//v7KDaaWWABvi7+Np65+CoA8s2ctgBabIvu1enst4KtWEfF8d77a3Q3Gjq1g7zrMF19AbCx8+62nR1L/CAlR8gAuWODpkdQL5MS6xOsRjvnLIo7ElRKAQtR6Z/fz5yE3V0Vubijd2eG24unOSiDCBjYbzbKhWT7QOtQt/XscPz+lDJwjvY9DANaCqENHTW9PWwCP6JW53gKNEb2mAQAmqwl274YKqtzUaVJTlQcBOdd95fH3hwceUF5Pn6484b74opKrU+J2pAVQUmf56quvKldH1zEFrALs+exslRGABw7Azp2u04XVwGg00rx5c3bu3OmW/khKomGmErCgxi5k3DVH65jxtllrp/9jdYmMVCw9X32lLNcSC+AfJ/5gT+oewPM+gKkhKRB4Do2vqbAUHEWSo3srjtKKjz8Ohw97diz1malT4fXXIctLZh1qIVIASkqQmprKc889R1xcHL6+vkRERNCnTx8+++wz8vPzK9WHSqVixYoVVT52ZfczGo289tprvPrqqxVuW6BSbloGlRWfhoeg8X602kr49DmSkhqNbrnh+fj4MH78eF5++eVq9wWAwYDOqFiJhN3D0V1izaUWsErFeUtDjhFHRo6XThrUEh/AIYuG8EfSH4Dnp4B54A4Y34R+V6cpAvBcV7LnbmYIq7xaAGal5PM1j5CPH5yRFU+uKFlZsGwZu+du5V1eJg//WmGV91a89NdccrmcOHGC3r17ExoayvTp0+nYsSMWi4UjR47w9ddfEx0dzdChQz09TH788UcCAwO5/vrrK9xW7X8RfC+h81HTOM+IRQ0+mkpc+g4xdeIENGqk+AVdJiaTCb1ez4MPPshLL73E4cOHadu27WX35xifBkWwCNTYUKNxmwAssqBSkYGeXELBkEEDaqc/ZEWcyT5Dv2/60TGiI98Pnq+IveBgxTQcHAzjxikR1R5CCIHBYgDgvX7vcUPMDR4bi03YEHaPCW1UE0UAWn0QqV04RJD3CkAhmJL6NB8zltUMZIm0Pl1ZkpLg7ru5WZVBpuiFERWvSQFYY0gLoMSF0aNHo9Vq2bFjB8OHD6dt27Z07NiRu+++m59//pkhQ4ZU2EesXSjdeeedqFQq5zLAp59+SqtWrdDr9bRp04Zvizhal7dfcRYvXlxCiI4aNYo77riD119/ncaNGxMcHMyTTz6JzS8XAi6gb+TP7t+3cN99/yaicTRhYWHcfvvtHD9+3NlHcnIyKpWKxYsXc93Ikfj27k374cPZsHWry7EOHTrE4MGDCQwMJCIign/9619cLFK0vG/fvjzzzDO88MILNGrUiP79+wMQFhbGddddx6JFiyo8j5XhOK2cr61o3GYB1PkaICyBYN9TAM5ScGZRd0vB/XL0FxLTE/nh0A+kfTZDCfB56CFlZWgofPghvPuux8ZnsVmclVb+3e3f9GxaerWdKzUWB9ruPQgPCGf+3f8HeHklkIICPrYpAS5LuQ8yMz07nvqGxYIZLZkiFICzNJEWwBpECkAPkJdX9p/BUPltCwoq3rYqpKens2bNGsaMGUNAGVGvqkpkZN++fTsA8+bNIyUlxbm8fPlynnvuOV588UUOHDjAk08+ySOPPML69evL3a80Nm3aRPfu3Uu0//HHHxw+fJj169ezaNEili9fzpz35zjHfsbgy8gRY9m8aSt//PEHarWaO++8E1uxNC8vvfQSLz74ILsXLuS6Tp0Y+vjjpKcriaRTUlK48cYb6dKlCzt27OC3337j/PnzDB8+3KWPBQsWoNVq2bx5M59//rmzvUePHmzatKnC81ghQlCAn3PR5kYBGBnYgKtycok25isWMkcpuDrsDngy86TzdWaW3c8rNJSXX4brr4f09DJ2vEIYrYVBBz5aHw+OxC4Aly6Br/4i4aAevUbP1c06AF5eCzg3lzX0L1yWFsAri9nMRRoBil/zpzwtBWANIgWgBwgMLPvv7rtdt23cuOxtb73VddvY2JLbVIVjx44hhKBNmzYu7Y0aNSIwMJDAwMBK+a+Fh4cDEBoaSmRkpHP5gw8+YNSoUYwePZr4+HheeOEF7rrrLj744INy9ytOZmYmmZmZREdHl1in1+v5+uuvad++PbfddhtvvPEG3/7fQmwFAVitGq4Z8G+63vwYzVvE06VLF7766iv279/PoUOHXPp5ZswY7r75Ztq2aMGnr7xCSFAQX9kDBj799FO6devG9OnTueqqq+jatStff/0169ev58iRI84+4uLieO+992jTpg1XXXWVs71JkyYkJydXeB4rRAhEka+wDZXbFJqPWk+gCXysivJTeUEN4PQCReFNvXEq8Rn289agAcOHQ1iYYN6HmZCc7J6cjykpsGhRySe6cnBM/wL8duw31iWtq/44LhOLzQIpV8Pp3pgKFHcJZyk4lW+N5J6sFeh0XPNYZ+eiIb3m/DANBqkvS2CxkIEScR6qzkaNkAKwBpECUFKC4la+bdu2sWfPHtq3b4+xGqkRDh8+TO/evV3aevfuzeEqRtoV2E2fvr4lS7l17twZ/yIVMXr16kV+Xh7nD/ljuGQh+XQikyePoEOHOIKDg2nRQim1derUKZd+evUsnH7TarV079DBOc6dO3eyfv16pygODAx0Cryi08mlWSgB/Pz8Kh1MUy5CKKIPaNs8D7/45m4rmVRQAOdpTCahAKj8FEtjXS4Fl2VU7rYhviGQlqY0NmrE8uWwcqWKxLe+V0rBuSPqe+xYGDECXnqp0rsYLYXfrbuX3s3La90ULHQZWGwWsNmF3+H9CCGYt0+xYpt8guDPPz02thqlQQOCv/gAlT0MPvN8zaWCue12K9FNbJw+XWOHqHuYzc7fnFB1trNNUjPU3V/zOkxuOem9NBrXZcd9qjSKJ0ivrlEpLi4OlUpFQkKCS3vLli0BRbhUl+LiUghRqWnlooSFhaFSqcjIyKjScVU2G88/dxcREc15/8NP6HhVHDabjQ4dOmAqbUorOBiys0uM3WazMWTIEN4txV8sKirK+bqsafRLly6Vad2sCkKnw2ZULhh9gwBUump36eRinoXzNCfQ16D8HDumgN13iCtOlsEuAH1CwCH4mzcnxv4xpWLPoeiOG86PStk0vv4aZs2q1C5Fp4DBVRBeaUJ8QmicZyYN0Os0qFQq3vn7deBJjEbF0FzFr22dID0dZs/GaVnPSLdRE4VPLlyAdX8o391VPxsZ85Rnp/xrDRaLUwCesMTQPMLAqY5e6m5QC5AWQA8QEFD2X3GjVnnbFtdjpW1TFcLCwujfvz+zZ88mr5pWEJ1Oh9XqGjDQtm1b/vrrL5e2LVu2uETDlrZfcfR6Pe3atSsxbQuwd+9ep4UQ4O+//8bfP5DGjZuSkXmJpKQEHn10Mn36XE/btm3LFJF/b98O8fEQF4fFYmHngQNOK1+3bt04ePAgsbGxxMXFufyVJfqKcuDAAbp27VrhdhUh4gunld19M86zKBZKi/2BxNm9qLt3/cjASLBqefSNDTyqUT6nPQXxONwzHb5Hbk0FUwU/jAa+DZgxYAZ3XnUnUFIQXkk0ag3CZn+48LX/9xEQmEJ0EysVfEXrLGePG5g6VXn9+mtWGnz2do0c5+S5wt/X0+ekhcuJ2UwE5xkWugGA0+d9MOhkEuiaQgpAiQtz587FYrHQvXt3lixZwuHDh0lMTGThwoUkJCSgKW6iLIPY2Fj++OMPUlNTnSLrpZdeYv78+Xz22WccPXqUmTNnsmzZMsaPH1/ufqUxcODAEmISlHQrjz32GIcOHeLXX39lypQpjLjvKdRqNU0aNCYkNIzly7/gxLFjrFu3jhdeeKHU/ufMmcPy5ctJSE5mzKxZZOTk8OijjwIwZswYLl26xAMPPMC2bds4ceIEa9as4dFHH61QvIISwFKpBNYVUNRV7cxxA3lnLrltusThSuiQe6F+qRC1E79g95Wbu9J8Pexreh7aCCsWsCf1FgC2nG6OIy+32wRg0WvgwIFK79bArwEv9HqBl3srU7+etAACWIQyQaT1Ub7zPoH5MD6aDe16oR1wsyeHVmNkrVUCz+J8T/LkSxdrrO7xidP2iCNtPm/cI3MNOunYkau/eIpl/3fJOcNVhYkeSRWRAlDiQqtWrdi9ezf9+vVj4sSJdO7cme7duzNr1izGjx/PtGnTKtXPjBkz+P3332nWrJnT2nXHHXfw8ccf8/7779O+fXs+//xz5s2bR9++fcvdrzQef/xxfvnlF7KKeVHfcssttG7dmhtuuIHhw4czZMgQRj8xGQCNRsPbby8gIWEn/W7qw/PPP8/7779fav/vvPMO7777Lp179mTT7t2sXLWKRo0UgRAdHc3mzZuxWq0MHDiQDh068NxzzxESEoK6gsLlW7duJSsri3vuuafCc1gRQhTmL76Y44shNdN90ZlFK4EAjQtUdE8RtLJPz9RVmsQo5+eCtjsMGMBFY6GFLhf76+oKwJycwtfBwVXeff1PkXD4Do9aAC/kXSDX/rDnEIDOaiC7d8CWLR4bW02SnaFc78captWoD2bKkXMA6MIOot/1d40dp87RvDk8/jjqe+4ixE+5/rP2Jnt2TF6M9AGUlCAqKopZs2Yxq5K+S6UxZMiQUnMGPv300zz99NNV3q84V111Fbfffjtz585l4sSJLutef/11Xn/9defygV1GrDZABT2vvYmlSw8REZ1Os2glkrG0usBtW7bk77lzlaCKTp1KrG/dujXLli0rc3wbNmwotX3mzJm89NJLbvGn1CUdobOPjaO+rcnK0WBD7b5KIHbzospsBAIK/TTrcB6Yc+cg57wi4nOtzWD1ai6MLVyf50hwXV0rqsUCffpAfn5h6GwlyDRksvyPU0wc3QlYjqFds+qNoxpcKriE2S8QjDZ0PspDjVMAalAeNLzQETArw/7kY/HhwE/HSftjGo1nVVxtqKqknsoEwByQwaOnZvE1o9x+jLqKw4PHz5xNBuHkHzgBg2I9OiZvRVoAJXWW999/n8BK+FiZHUmMsRAQmAThB/HxrcBSJoQyx2q1Kjc7N1jWjEYjnTt35vnnn692X4ASrZqbi9oZoOFGAYjrjT3T5M8JWpCWW33h6gmEEHR5/jV+/07JZVeQEQoozvgORvosVl5U1wLYqBGsWQMtW8KgQZW+drad3cajKx9zLhsuNKneOKqBxWaBF5sS/lwozZsrbXqNHhb8zoPp/3BWROGNjoBnMu3qI60TO7/exPwfqphLq5K0bbkVbnsaLH78lfDvGjlGneTsWV6+/yT+/nDOpATKuSNhgqR0pAVQUmW+++47nnzyyVLXxcTEcPDgwSsyjpiYGMaOHVvhdqrAVBAaNFofGlpN+Nus+DeoIGTWIaSsVti3TykRVoolsCr4+PgwefLkavXhgn2Mjllnd+YBxOkDqLzIsmm4RBgGUxaN3XOEK4rFZuHCpcIpVVNmQ4QAR/GWb7+Fh3YlgOHpy5q2LYFOBz/8oLzOyalU3jyDxQBNduDb7BCG0+0YfVXl3C1qAkclEK1O74wmU+oBd+eQOVSxlppMbks7VFtIynHN25hvqpn3Z1WfgcB0OHU9KbrQGjlGnWTNGgyrzMATzqb8/Lo761Db8a5vr+SKMHToUHr2LL1MlU7nxlwkVWT+/PmltquCssBmRtegLaHnNWCyQpPSLVmxsbHKlHBeHhTNT1gLpz7zhB+naEZepuKj5c4pYJ1/NgXqDIJNAgjDqlKmxszCDUmSPYDJagJDiHNZWPVkZBRaAMPDgZkz3XdArVYJ6TcYKi0AHUEfPgEGDED3hv3L36EGcQrARhFgT7j+zR3fMGiKP5lGezUQL8zPlml0vb7zTDXze5alMoFeiQS2GDxXf7rWYTa7VDfqxF58kGlgagopACVVJigoiKCguhear1KpSLc1wIiaBgYVflVJk1MLBaBFaMijcIrKnQKwqX8IlvRkfDWKD5vTBZC66fOlCMBQl7bz5wsFYFCQYg0MDXWDUWvlSnjqqcIqIEWDQsrBaDWCTY0+QJnz8mT0Y77BAvP/4IKPjvwnwd8fejbtSaC/IPOS95aD695xJYtbfQjbnoEDI8ix1Mwt0jfsDZofOsspwFIgb8NOLBanAJzT8TNG738aWn3h4UF5L9IHsIYpLcBAcmWxmXzBFICwqbigj+IcTcizVfDUXfxzq22foxAlxJhw49fZX60n2Ah6ofRZmAewev166vtgtpnBqFgA23OAhR9eIDIS1q6FdeugXz/FCpiwOb36wiY9HVKLpMuprAC0GGHVl1zY2QeAf44lKsLVAxQYrZB8M4bE613afXyUK8EU1Mi9+RJrCaIt0HwrRO4FIEPUTILmf1a34JT9c7aZroBf7f/9HwwfXn4VgtpAEQugr97mbJPUDF4rAP/880+GDBlCdHQ0KpWKFStWuKwXQjB16lSio6Px8/Ojb9++bvVdc0yFuqXkl6RaWC+2gIttMeWYMQrlhpptriDRtTMRXu2NfnUIQF8fQceWeUS19K169u8yyDOouUgj8mz2m1OgvV915fJAloXj+3ClXQWKTgE/z4c8+HQwDRpAu3Zw000QEaFsl9d3MPzzT/UOVrz+b1UsgKbCz++bxE/IKPCMGdBkKLzp6nKVMaxMWEmeTclfZ1z5GxSpeuMt5LaLU17olN8Hg8Wn6t/9c+dg8uRyyzgVyVWPzeye72yZ5OTAE0/A99/DkiU1e6zqYjZjQKmG4KezP2B44YNGbcFrbc95eXl07tyZRx55hLvvvrvE+vfee4+ZM2cyf/584uPjefPNN+nfvz+JiYlumd7UaDSEhoaSZv8R8Pf3r3LJM4mbEGbAhsVoQAgdoMZiNmEofqMuitmszHuBEoYmRMkbuyex2TCqVCAMaDQC4a/BggaL1eqW6MyzWWayiSRUW0BTgwGb1QRosNkqOG9lIIQgPz+ftLQ0QkNDK51Q3F2YrCanBTDY11QiPYtDN+cSWP0bTvHzU8n62WarGUzKlL72ziewdP4/jFbP1APu1KCz87VGr3xWs7fPJrWgORBW2bdU59i/KQa2jqOr7g52A1arv/J5ViVt07hxithavRq2by91k7Tde4AuyoLZ/7JKYlaaor7M+/fXzDHcRZEp4PcyH2dK038zNstIxaF+ksvBawXgrbfeyq233lrqOiEEH330EZMmTeKuu+4CYMGCBURERPDf//63zAjXqhJpTyOfVl5BX0mNc/GiDYQata2A9Bw1VrMP+cY8rPkVPHmrVIqYcoSKJiXV/GCrQJ6AixeTyPUFd7vmnUnLw1oQQF6BGTM6LmWZyMnUo9IZSNL4VtxBGYSGhjq/F1eaRtctwRq9mjHRl3hs1IN8OvhLko740apVoQDMI6D6U07F1VEl1dK1Ta8lJiCSk4DOz4gFz1UD0dtdJNRYUeuV24Reowe/SwSGGlCpLv8aqM3sW90RNj+Ctf9uXhhdQIdOA8C3itbq779X/u/YUeYmhw1FEtjbdJjNSqKBGuHcucLXJ0/W0EHchNnMTawnMtaP8w27sicBUg3+nh6V1+K1ArA8kpKSSE1NdSnH5ePjw4033siWLVvcJgBVKhVRUVE0btwYs/Rj8Bj33pZHri2AXz/Yx5QZmZxLuYFbhv3InHdLWoZLkJcHCxYokQGvvlqYc6UWsHw5TJyoZC25t885Wgec445Hw6BFi2r3PeqtXzn/163cfPcJ5r7VgqTlcxl9Yh5tfRqxvPevl9WnTqe74pY/By0btOTCk/dgu/kmNNe/DsteY8JaK+fOQvfuhcZeIz7VtwA6BN+//w2ff17pa6Zn056EaeAkoPVRrIie8gG0GOxRwFicUTF6jR5G9mPGhWsZ+J4/xM6FNm08Mr6aIibZzDHg3rDTjPuwNXqNpkaSXVssitobEj2ZOXkr0Wpr0DKXbi8716gRfPxxzR3HHQwcyFtBW6BDOhP/UArOSC+qmqNeCsBUu4N2hMPxx05ERAQny3lCMhqNGIs8zWdnZ1fqeBqNxmM3PgkkJ1vJE774oCUlxczJk76kXTTg61sJK4avL5RRLs7TWK1KpOjJk7B/f0vuYjf3xx+Gtm2r3ffpc0ZSTvqSdSoLX19fBhzN5tCbB9COehR9Zc5bbeS661CfOo3uqZmYgXNnle9keHjhrLkBX/dNAQcGVvmBIc/umpozbwn06IP5Sc88OB5MOQJ0B7UFtMqUnLMSyImjsC4dLl3yyNhqErVRcQ34zraJV98exuK7F3Nfh/suv0ObrdRrwGwXgC199tDs0rGa9cbX6SAuDgYMwJnVu7bSo4fyB/gvOQU0Jz/pPBBR7m6Sy6P2mDM8QHGfi4r8MN5++21CQkKcf82aea5Uk6TyWLHXNNWr0djz2VXoJvfzz4qTu91FoNZx6RIPzbuFrF6D+L//U5rM6NwWMWezW4A0B/YBoNX54G8GvaX2BcNUlp379ey52BTfANdzFB5e6BLolvx2ERHQsSM0bVql3c7lnCMzp4jFL6OF4hfoAY6kHweNAZvW6BQwTgFo9wn0xjQwBnvaF1+NFjKbcfLdpVWfNp06FcaMUSxvZTwAWKzKBfdxHwNdRhk4cfFodYZdPg8/DEePwpw5NXcMN2I2Ky7XPof3AGA8ccazA/Ji6qUAdPggpRZN1YDiq1fcKliUiRMnkpWV5fw7ffp0jY5TUn1swobRLgALVAZ6Xf0+PHYt8Z03l79jXp6SyuPSJcjMVBLG2WpREuSCAiV/ybp1Tt8hMzq3RczZbMqDkFatCL7d56N5nC94e0/pfrW1ne1nt9OzTy5du4JeuAZ5RUZC377wYOPfacmJ6p/D559XqscEBiqpN8qpGV2UT/75hPONikRpWvyU9DUeoFHkRXjVjxsfaORs06v1sHESc7YsYzl3eKUAPGd3pj2f3gg+OsVbS2a5pvSpDFOmwOzZ0LBhmZu0uHk0PDQQjg5m7973STpbw76eubkwY4YyttrM8eM0amBBqxWcyVfOn8EkZ89qinopAFu0aEFkZCS///67s81kMrFx40auu+66Mvfz8fEhODjY5U9Su7HYLIibpsKNU/ELtHKbJp3H0/6hb6MGFexoFwFaLTRoAI0buxaO9TRFxufIqGJC73YB6LCY/pOl5kseZ1ZKa7f0f6XJMGRgNSsnKiDQ1aIQHQ0vvAALn9/JzSObQ0yMew66c6cSEFDJ9FImqwnuepg7py4AIDagHbGhse4ZSxWx2Otna0NCnW16jR4utOfEhd6corlXCsAUjXJLvKRTrhGL8HHN2eImdFHbIG4NHLgfto7nXGoNW9YtFhg/Ht54o3ZlMyjORx9RkGfDZlMR4qdcX0ZLvZQpVwSv9QHMzc3l2LFjzuWkpCT27NlDw4YNad68OePGjWP69Om0bt2a1q1bM336dPz9/RkxYoQHRy1xN1abFW6YDkDoteO4f3o09689BPd1K39Hh5DS6ZQ/s7l2JSS1WFjMfXxtepy82UqTO6eAG/b4lvQWP3JjjgYYTZ5WuWmkq+pmTq4Ckwns024hetdo7iZN7C9eecW9B3X4SlYlDQzg66eI7mB1FNEeKrhjsed91PYsfCAe02MMx1o3YO0B760EYrEon1lwgIkLgNnmWzUBmJcHZ87Aiy8qDrqffw4dOpTYzKCzuxpplHOYb6jB79W//qVYpB1kZNTaHI5WowUzypRGdGg+LTlOY5/K+dpLqo7XCsAdO3Zw0003OZdfeOEFAEaOHMn8+fOZMGECBQUFjB49moyMDHr27MmaNWvqZIkzSdlYRaGzn1ar5/fMa9hHJ/ocaUDp1YztFLUAarW1UgCeoCW/W2+hsf05x50WwC+uak/mHzO4rq0SKa+zW0aErW7+ZOTlF14HnUJNHPTJw2ZURE50tOJz5NAzPtUt/jB6tFJixCEcKmlxcUz3+vop1qAaMDxVmjMnAuC/qzjYTAf2Z+IOjTvQwj4j7K0CMPLWhzmlDSAiSs8F7BbAqoSh7tih+BM4KCMF2DU+62hXkMUymx4B5KXVYMLvhIQ6IwALjIXWvoevPsjTvwyB3o8DfTw3KC+mbv6aV4K+ffuWW3ZKpVIxdepUpk6deuUGJbnimC1WSO0EKivYNPy36fPM3xHOawWXKi8AdTrlblzLBKAZZUrTkaPWnT6AfbVxkAC0VUSSTucQgHXTHye3iAD8xvc2bpwVQFqaEjDdoYMyOzZzJkx43sy774jqJWU7fVpxunfcZCspAPNyNDCtgHlWxQqVmWPkQl424QHhlz+WyyQzQwtHhnAhK8Wl3SGOTWo/tyQcr22I1vtAk0tkyO0cAITQYsk3Vf5GWVwsllEFZuE7vbDZQOt7EQtQcKkGrVx5xaoe1eJycEW/Kn4+dp9rL7zOagtycl3i1eTkWeCzvfDpAUxnLrHXnAzAb+e2lr9jcQEItU4AWuy3pb59Yd+ig/wwKxXuucct3W8+0ojF3MfRfGV+VNdLSc2Auqay1dYsefnKzUSlNqL29+Xxx2HSJCXIOzi4SBTwh3Pgs8+qdzDHlG9IiOtyZXaziz996AUuqA7w58k/qzeWy8ScqiQ/VxsKhcne1L0kZij56owv/ge80F2mIEg5/z2vKpz6NuZXQYAUN9uWIgCt1sJ4Mo1WEWP5BTU4BVxc8BUXhLUIhwVQr7E4E5DLUnA1hxSAEq/GbCmM3PWxmHCkY7RWFNDbsCF07aokVa6NAtBmw2KvyNGwIXS8vz0tnrkN2rd3S/cTtnfiARbzQ7ORAOgDlUzJwlo3LYAOAajRFBT65hXB0WTAt/oWh+ICsJIWQKN9RlWtsdL7o/vgye4eiwK+MaQ7AFGGwi/KL0d/4feTPwFeOfuLEJD1579g52Pc3/4BZ7shtwoCpBIWQJOxcGZKr1XEmM1Yg7dihwAMVMoM1gUB6KuzsiPufrq1zGTYyU88PCrvRQpAiVdjNBXxAdRr0ORmAmDLqcDB6v77YdcueO+9QgFYm55Eu3bFPO4lwFmowa3syT4OQIbd6Utnd1qvq1PAISE2/K9/gw5xH/CWZR0tP27Je5vfc653yQNYXQHoEHxVFIA3N7vVORadRrnmPJUHMFAoU//+RVIf6TV60BpR60w1URzD45hMAvP/ZsJPX6JX+fP0Iwaeezwf3cMPVLyzg+IWwFL8B035hZ9pa/v2XXQ1WFHFIfgaN3ZdroX4igKGsIqB7c5gCG/G7hMhHDob4ulheS1e6wMokQCE+TV2vtboNWgungfAmlM5x+6CAtANuxttVrqSDqYW4dCj6enw+jNp+Gel8NI4C1x9dbX7ttmUZ0OtRrnTd/LZDy/0xl+jBupe/suxN9/P2HcHwuE1TFAPJikzibS8Qgd9FwHorlJwzzwDP/xQqsWxNPrH3A6An68GndouAD1kAbSYFOGnUxeeC71GD33f4N4B/+PDv5vCjw/D3ZUop1hHKCiwgT1naKTRwJyvwrHYLE4xXslOXJdLmf435hSAPdJ1bswrBB05R9OuswD3WO9dMJkKzbVffaVci/Hx7j+Om2j++EBWXb+fM311HLCEAI0q60EhuQykBVDi1QhroalCrdeiUSs3Nkeeu/JITVWKOdyZ/CF88w20alVj47xcNBolqG/qnMbMWBgB8+a5pV/HedNmK9GJbS4VkPbZOU5tr1p1i1rFvHlw8CD+bZS0HHmmQkuIyxSwuwRgcDAEBRVakCu5m9lkY8ur78NnOzEYPeMAvzdDsQDn+hQKUGclkMx0WLUKEhM9MraawphbaO387eIfqN9QM2DhgHL2KIWiFr/AwFLrCOfnOK47G1c1TKcdhwnW1VDIt8EALVsq1r/rroNrry03QbXHuftukkaPIG79nTy0Qnm4MOZIBVhTSAEo8Wqs9ilgDRbQaJwC0FqRAPz4Y1Z2nMylS7W0GPnevXx0fAiWMc8xXUlzqKSBcZOfojDbEwFv/Uv5r/MhPB8aGOvm3F9ODhzMiOZkQDsCgpVp7XxL4QfrVgtgs2bKTbeKKaVOpSvWad+8i2ScaAup3SgweKb6zC67AMz0LXT2cwpAhxeAlzkCGrKV9+NLAXpffygIJWfnJYzfr6p8J926KZbfhQuVi27ixBKb5GfbrzuNiQ/j0+n9KCxIXe2Ot1CS4GA4fhzOn69eZPsVZOPJjRitRtItSgS6MbcW+V57GVIASryacxn2Mk5qRQD26vATPHwLcd2Xlr/jxYukX1Ruvs2b2pSpndrkA5iWBv/7H2zcWBij4sY0MEK4TgGn5gQwjg95JelJt/R/pZn09W906ADXD0rDX6cEtOSbCwVgixYwrOU+ruXv6p/DNWuUm65aDY8+qlRfqATTtr4CsetoGbTR2VbgIQtgXJet8JqGe24ujCrXa/Rw/Bb++f5LpjLF6wRg2sV0ANRqI75+gfD5TnbO2svuVVVweRgwAGbNggcfLHOTEN9seOB2uHc4f4WNZcvxqWzK7Vjd4VfMX38p5eA2bKj5Y10mv399msd7PAhfbmZ4SCcADLa6IVzrIlIASrwai+Yi9HkbfY8ZoNFwQ1AeD+auY1BYRTtauIQyVRK2ZhH4+8Ovv9b8gCtLkTQ1jgd7dyaCdgR76OwC8EyujY8Zx4eXhrml/yvNmUzF38+Se56AXGVKqegUcN++sGLyTl69+zC0a+emg55Rpp3/979Kbe7T5AiMuoWXooejQnn4uLpxL/eMpYpY9WpQ2/AJL3TA12v0kNOEi8f68Q89vU4Ank1XLE4FviZ8dP5gr35jKHBvmTadKhfa/AxX/cS5/dfDximcONTcrccolZ9+UhJe/vRTzR/rMjG+/wkWsw5sWhr7KglOjTY95aT0lVQDKQAlXk1guBr6/YegOz+GgAAGmWNYuAxGc035OxYRgDNSH2Q/HWpXGhiLhfcZz50nPmDtWqXJjA5hdo8A1PV5H+54mG7RJwCw6RRBYkKNTXhmWrI6GE32Ke3cdPztArCoBRCARx5Rgjbcld/Oocwred04In71NtCjiKv2YV3dM5YqYomMAEA79A5nW69mvRh33WjAOyuB5Ocp14VKbcJX63t5AvDiRcV5eOlSuPVWnP4ZRbCYleNobKCzXyI1Fuhw4ABcc42SH9RfsXzX5ihgk9lRIs9MA18tjTlPM5/ztWryxZuQAlDi1VjtlhStVgcqFbszYvmMJ9lwrIJgBouFbIKdi/vpWOsE4DZ6sCKjL2fPKk0CtdPnsbp800TPwuPf0qOBcmfS6+wJA2xapb5yHcNkv8HqVCbCAhsTHxZP0+CS14BbLA2dOim+YFlZ9oNXTig5In51t/TDB2NVdnU7SbtawveL2PHjDc62psFNub6VUj/HhN7rBGBkeDqMuI3w/o/jo/UBrfIZGA1VuCieeUapADN5Mvz2G+zZU2ITQ9Nrucu4kuH6xfjkKdPOpkulVwypNpmZSnm6/fshQEntUzudmhXMVrsk0ZiYljef//SM5NQ191Q2jkpSRWQaGIlXk19ghfRWCKvi+P9L1CNMJpJR+Rn0LW9Hi4UC/JyLBfjVLh/AIqXgHA/2oGhUd3yp7zHFwX7gVqVzva/9F1hosAorOurWL7LJHtSiU5m4JaYviTc/5rJ+wwbo1w+uukpwYJ9Q/PcuB6sV9u9HACpHZEklHxwubr8J/ruWd3pkog32gWw4mZ5CXNyVr9t66UwjOHg/Zxsecml3GDW90QKob2iD+F8INgbaLYCKgDdUJfDJkfMxNNR1uQipp4JY9vZQWraEyJAFAJiyasgE6DAt6vVFQt0rl5fSExRaAJVrKy0AyK9Fv7tehrQASryaE/ssMOsY52euBGC3PYfd72k7yt/RYiGfQmVVgF+tswA6SsEFB8PWRcnseG0V+rHuCdL481QMP3E75w2KD5iqoz1RrU2LxVb3fpAdWkWHqdS8fBqNot3MB4/A6NGXfyD7DfcxvuI/SzqTQ2DlLYAGHygIw6gORRWaCQGpfLfvv5c/lmpgTlMsU5qUwgCIi/kX2XJuPQCmjt2VvHJehKmRkudT3zSGUN9QGtnNTlUSgI7fiHKSgDs20elAr1Ws6RZzDd2KHQLQx6dOCECHBTDQPuOQ4UftevD2MqQAlHg1ljwlv5YK5UfEEdVaND9gqYSH81HMh0SH2Gt14l/rBKDDAujjA9feH8vVrw9F0+8mt3T/6K67GcpP/B05CCEED/46SlkhNFjqYHF2c1EB6OdXYr1LJHV13p/9hrubrrz93xg20LfS143Fnl9Fv28n/x7/JLwURUizM5c/lmpws1ZJStyqoPAWcfzScd7eOhUAo0lVao67usy5MxrYPZKCw32JDoqmd4DiImA0VeF9OsR+sN19pBSxlbt3HwAi/RS+Wvv0sqWGIl0d46kJC6DVCq+9Bt99557+AJNFud5aBCkzNiuOb6Fn7lpO173c83UCKQAlXo3JHhShslc00GQqlg2boYKnyjfeoHPyKoaNUOpn1joL4EMPYblJSVKblJ1ItjHbbV3bhI3j+UrUrKFdS05mnWT3+W3O9SZL3ROAjWJPor32fTqH/I9zlgw6fdqJjp8Wpt5wWyS1/Ro5gyIemnOq0hbAHpF9AAjKzkC/bafSnYcqgYTalOs+lELx46P1AY0icGvTV8FdJB7wg5XzOf/z0wD0GxHBo/fm0Pr1hyrfieOzduSALEVsJZ1TAquSNBe5QaUE21xrjr3scZdLTVoAly2DadPgoYdKrXl8OUSpUrmJdcTGKr/TF8+0Y1tCiLu6lxRD+gBKvJqr/OMAiM6zB4OcPQWAraByN2WHsSg/vgvE+rh9fJeNSoUj4HfKxkn89M9g7lL35un7MwgddG21urbarOBIA6NVczT9KI0sWVx8Jh7UVoRqa3VHf8X57ekx8Fo4AOd932d/2n4AhBCoVCr35VI0mxHARZRjvTXkH5bML6AyNqR+sYP4FQg1m9GdOgtxnqsF7BB4Wk2xWsBNthE2rSHHDw2CdzvDyy97ZHw1Qew55XOPzVAE0jMvlbQUV0glBKDBqJxTlcbEw5320G/L6zTucQfQverHq4iiAvD66+H336FRI/f0feBA4etDh6Bnz2p3Oezlq8jMmMnyOAucBJVWuRBr8ax1nUYKQIlXo7Epl7heKFYrrd3m7ah1Wx5ffqkk9AfIH3AnDK6RIV42Tp2iMbNjyT3sMAVz74H7CR20uFr9WoUVhF0A5mSTnJlMI6ON7d8dJccHGn1YURLFWkhoKOzbBwYD/j6BzmaDxYCfzs99AtBiUcrJ2fn+J1++1PoWiScvG6dvGGZ+PjIXkjtwxvdPGHL5w7lcDhqUBOrZ+sLgBL1GD2qB2WaARYuUGoReJAADzIrPb7jFhsVmIfSdUIxWI+fHn6ehXyXLpzk+RMcUsK1kyiSjPVJfrbbQJMxAE3aAbw3le9RqFcEXGgoREcqfuyiauyY52S0CkBdf5N/TXsFy0jFzk1/iUBL3IaeAJV6N1az8AGtUdgugRvG5qVAAPv88E57KIi1NcXH5z39qdJhV59df2dT0Adq81hxa/+yMmnNG0VUDFwvg+rUkZyZjUUNsJjTLhDxz7c0jVhbpWVqSgzqSFX+NsxIIFL4XZ8o+N1RTyYlq47Jc2bRr6bnKNL4WM6m5XeDU9eRl+pe/Uw2xw6jkFrqgL6xR6ywFZ/en9bZ5YLM9V6RebUWr1pJvNGPJ9yNjxpzKdzJsmJJP8v77FfFX1Epmx2hSfovUagvr9WcZ+BBM8PnTLe+hBCNGwIULsLh6D4Wl8s47Sn5BUI7hBiw2izPILNqnET5mxQdbCsCaQQpAiVdzPEPxHs7yU35Urm59AO4fSpPrPip/x+RkCqzKDa93byW1V61KR5+YiOb7xTyUHgoaK2iUm7E77slFLYB6rYZzuecwq1T8h7d43fwOyWlp1T/IFWbgk+to0QLGvHIOjVqDj0aZznckgw4MhH5tz3ALf1RPAMbEkP3nHpem3OdfrdS18+GBCRC9jQY+SWhViqA3eyjTSqsbP4NXghl+7Wxnm16jh/wGGL5fwH0s9joBeCbvEgC5PvZEzX+8De9k887s6Mp38uqr8PXX0LFjmUEyV8Ucg3vuo3GvD9jdYgBrUl/ifxlXoMJOejp8/rl7o7cb2i2jGRlu6e6N59Lg3Yvwx5sc7buMv3LuY3fkrXSvgdlxiRSAEi/H4H8cenyCtt0iALqEmRnGTwxukFrufjazFYM9D6Dfm5OUvHBTp9b0cCuPXaRMzO6ECpXTAmi2uNkCqFWTacjEqhK8zX/4yPYyB88lV/sYV5rT6crnbTmuRGA6rICOcnCNG8PvMw+wYtDn0LV61TeKO6znLfmpUmJJdP0SnujJOP07NLT7knUL90wpOJuvFXxzCGxcOF2u1+jBpoMDD7CU+xAm7xKA+3IUq2dyoGJ10uqU71iB/bvgLhoGn4cOS2kQ8xenz7eCte9xbvNQtx6jVFJS4KmnYOJE9/X58MPwzTdw111u6S7z//4LBWFg8cVH70dHDtBFs5/AwIr3lVQdKQAlXk1ED18Y/Bwxj64GoIculhWL4Z1L3crdz2Aq/Gp8uOcm5ouHa1c+KouFF5jByM1jmNTuG8J9FEHjSKNQHazCCjdPhtueplV4PhkFGVg1gEp5/0mX6l5OBqvDFz5RCf4I0CtVEVzKwQ0apNR7fu21ah2rY0c4dw40dneDXAIrFIBCCOW8AzorNLbPeXVtXL2AnsvFEmUvBTfiX862QH0gc4d+XLiNuRZZxN2AQ89q7RkDtPYcfQXWKgjAzEzlCSA1VZkeHT68xCaOKU4tanx9lAc2q6WG3PG//lopdP3JJ+6PAh44ECZNguuug/bt3dJlvj21lVprRaOzB93Vpt9dL0MKQIlXY1UrP7Aae2Hx5KwGfMtDrDndttz9CoyFX413dvTjKx6rXVNeVisrGcZ3J3rRp9EwGvkpAtAdFsAAXQBfNkjk89TPiGpgItOQiUUNqJUb4sVs90z3XEksFuUm7mOPao0NjaVVg1buP9CBA2h79yTqueF07KA05RFQYSqYouledH9vc9YC9lSxjbN/3QQrv2T3hubONr1Gz8ir73cuVyk/XnX59FMYObJGy5i1it8B9wynXZd5AOj0yvVusFVBnLVpowSA7NoFP/4IK1aU2ETd80XutH3HTe0+xS9b8Z2zFpTYzD0cPw4bNyr/3SwAz246Qf+Nk3jtowZu6Q8hMKJ8T23qAq76fRjxY5ECsAaRAlDi1eTnC8iJxJavZOb/O3wID/Mt72Q/Xe5+RS2AUDtLwTkqgQxadDPC7gPojiAQP50fj11sxhM7QaXTkWHIsAtA5f1fys2s9jGuNFazcmPxtYvYTY9s4tizx7g6+mpAcTIPCVHK6jlK+F4WmZmwbRvs2UOAfdqqMhZAs9UMf7wJHybzxf/aoL5OsVCn2PNWXmkyj7aD3Y9xKtE1+lVfJF/xFROA6elKdZbQ0Ool6a6AkNhM6PA9TdsmA6DTKxbOKglAh2J3zFmazSX8Pw9tbsXyN0aQuu4+fNNSABBu+N6Wit2SfMkWSnq+X+GYqnsezWa+K7iTtfRn2uyG5C1fU82BAlYrBSr7BaY2k5iTxNEwsFlq0YO3lyEFoMSr2fU/X5iRwv53pgCQqFccvf/JTCx3v+JCyoyudlkAi1QCQW3hwVfWsWLsd3Sfertbut+Y1pZ13ESexYeMggyyfXAKwMyCuhcFbLUqN3Fn5YViaLWQnQ0FBWAeUg1/JrOZv+jN8+mTufFGFfu03RjAmspZAPPCISuGArM/lyIE6HP47sDCyx9LNbDmKFYiXeJBl/Y1Sb+gVitWVNPPv1+ZwexXpu1ZubIwv14NYG7dEgD9tb0BaNUgEgBhqULda8dvREBAYVuxB0dnWUId+PjYLV7WGpoCNhpJI5z4rybQ/voG5DnKW1Y3rDY7mwv2XJcAx1+cW73+AMxm9CZFAA5vV/g7VqCue4nn6wpSAEq8Gku24tCtNis3NI39d1ZUkAYmIlLFLw0fYsK9SQAY8al1FkCzI42n2syr5+5G80wIDZ4s6XNUVfLN+QzZN5lbWMeJRl3IMeUoPoD2H+IcY93Lymqz+1j5akrmZQOlFrBarYhDc341hL7ZzG668tGlhzl+HDrqEwkit3IWQJsiNPRffs6zk7bAf4JpfNOSyx9LNbjGqFQyaWF0/Z4M/344NrUiHoyaK5SixpFKpXPnGj3MmaMN4eA9ZJ2KAeDfHZQUJ/75VRCAxS2ARdvs5OywV3k5uhdfH+W6FLYqHKMqGI2s42bSCwI4n6ZmE9cr7dWdBs7P5yQxzsULeW64FsxmVPbzcG1MoY92wUcfVL9vSalIASjxaiwWe9Z9lT0RdJbiv2arQMv5/28pt6Yv5M4XWgBuKBHmbqZOxRJqT8hsn/51CWioBik5KeTYp13y2xT6gKnsAjDXWFMOSzWHrvVa6P4pVwWfBOA/f/yHrp93ZcmBQoGls4vDahl6zWbFXQC7y5UzwWD5neo1euKCr1Jenz6B7i+l2orZ6hknwAZWxYIVqnEVJnqN3lkO7or5J55QSqehViu+dTXEvrUd4PvvSVirBN7EdQ3ivkGZ3DC+R+VSQAlR+DkXFYDFPvt9accA+DN/F51Cld+XpnmXUXWkMphMJFKYl/KYKl55UV0BWFCg+LbaURvc8NtjsdCSE/TgH5o0LZKqaVgty8DvRchKIBKvprtfW74A2uUpUy3apONAH0QlIxidNWJ9gtwW6eYWfHww28Utagsk3s6qD/zodNM2rnq4R7W6ttgsYPd7yrcqyYkDNf4EPHg75zX5qP1rbhqupsi5tzvWh/+Ful8/AE5mnWRP6h7O5ZxzbqPXCYzmakZSF6kEsmkTvPHICXpfY+aWFuU7yof4htAt7GqOoVQC0c2aA/8Cs9kzGXAd5Z61xe4Qeo0enm/OP+mDaT2rMcz6pOYH40gyvGKFEtBw6VKNHCb+nJrtQPszmQDccJOWG24KrXwH9gfE0zTlw7fCeIlIokgtoZQdgVpajZX2rYys4yYCm0cB/63+myiO0ch5Cqt/tJg8Aq4bDA2qGbiRn8/P3I4R5QfSx+QGW5Jez5Pjz9BJvE5kr1fwO+WH0WqkwFz3HjjrCtICKPFqfITyAxVg13s6jXLJC1H+pZ+WpmRQ+OUXZdkUHA7jxtXUMC8Lp0FSbYZtz/Dd/CFse+LLavdbNBF0fpbipB7q34BNP2wjYekBAix1zweQQYPQ/LUZ1YyZAATqFAtNjqkwaZ/OnraluhZAhwA8cQKmfNiAtfsa46w1V96u9hqxOsz8kTkSvv2V8xvdk1+tqiQJ5TPO17oKUB+tD/jmoP55CarvrpB/YtEqExkZNVYYtoFRscI1t/vjPbTsIULfCeWbvd9UrgO70BvEb3z4qS9jVXNc2p2b2R8wtForwaFqbmID1+j2VP8NlIZWywW14ss4axbc9sa1Srojv2paHK1WCAvDJ7IhPpiUz6S6gSWBgfz9SH+GB/3K5A2vOi2AxnVrSi2pJ6k+0gIo8WqsFuWmrrH7d2m19uCOCpK7HrtvEo9teIuocDObNunw90xFrrL55ht+H/ErNzRaDb5ZiggEzFY35AEskghav/kvAEJ8Q4nLSkVltWI05lb7GFeaizSC+EaEhIAOCPUNBSDTkOncRqd1gwDUaDD4hEIR3VQZf3uLzUJ+gQnwRaeF89bWcHwQBVHlJyyvKQ6olFDoLJ2r2HeWg9Nw5YKiipcZO38eYmJK37YaOAK/dDrlf745n6yCHLIW/wAt7iis71sWKhU8+CCHvlNmCn4UdynnSOP6W2Oxf0e1Ghtpthyeug/UAaf5wb1vR+Hbbxk6AKK2w9VXu7Hfq6+GixeVqCnHj2NeXsXnqAIMFkXc+2p9iQtpQYPk82jmPAvDngAfn+qOWlIMaQGUeDUJ9im+NF/lLnxVTDrc/QCBN08qdz/TkWQAQvzN9OkD3crPG33l+esvmixfzCMBLUBtc/oBWiqqcVwJiloAzfaSZIH6QOaqnuYNXiUzpW5NAZutZuJ6HCc8HP73q3KDKU0A9uqQww1sxNdWDX+mO+/E8Oholybjus1w7Fi5ux1MO8jq3G/Rhh2koS4HH7u/pdXsmWf0hkOfghejGNxlt0u7XqOHda8z9dICDhrjrsxgRo6EZ54pXHZT2bHipNiT8eXqlc8/K7ELvGHlzY/erdwx/f1hYTGrqFZboiRc56t+hqGPEXvVJtKj41meM5rl50e54R2Uzr/+peSB7twZLnz7m1IKLiWlWn0aDIohUeXvR3NOMobZlS96XRZmMzNHXwMfJpN14Dr+GrGWw3Og/QVqNP1PfUZaACVeTU7oLuh6FvyOM2dbAtkpS+jvv5WwwMbl7ufw09HpUEodjRmjZL7/oUae06uOxULLDPhafy+BnXsza6ndAmhTK87oZdQhrVTX1pIC0F/nzzTdM5y3tCEqfVP1x38FMVqNZOUpN3XdwV0w9Doa+Ck+UBmGwhv78k9T4elXoWnTah2vwO6yFByspJYx7j0MJw0QV7ZgMtvMcNszRGXBXd81ZpupNQDx/ldIZBXD6p8J6jyCQl2nCvUaPSQO5fe8LpxV/Zcr4hX77LPK/7VrISFBybVYA+yzKVbPo7qLAPjole+QBX2l06YIAXfeCcuXl71Nk4g90GAXEeru5Fobwi9zsGnzEUKgqsb3tjzWroX+/aGDT0v2G2+FdevsBc4vj+xsWK0UV+I0zTndZWj1U/QcO0bGnkzI64XG5ufqgFqbAvC8CGkBlHg1sbfZYNi/if33Hp759Rl2JW9lzbew6ECbcvdzTKUKVHz8Wxvez30Ka17tSX9iMsFjfMmTK27l1tg76BKpRJCa0VX7adkqrDDweUKvH49ar0z3+uv8yfJVfoSNFjB5KDr1cjBZTWC1+4JuWg+UbgGkfXv480/4b/Wc8d97T9Epo+2GQCM+lUsDA+jQQOPGNLa7PLX1ja/WWC4XS6Ayrad94EGX9knXT6JFQyWowCh0V9Y3K0RJ5l69TN1l45ia1dt1h6+vXQDafCoX8myzoTIZ+fpLGx07wnVRSVjue1CpwlEEsz0FgU6tw8+eBgabzlkizq08+yxH+j6BYd8RANJt9uCPavpRZv+00WU5J7QZ1S7Ya7Fgsec21etUUgBeAaQAlHg1Fq1yiaerlR+8AlMDlnEnv1wsP1K2sKSainGLejKB9zEZa0/tU4NJzdc8xhf/dKZ38z50LioAq/ljGRPanI8DvmdG7gyETrGc+ev8UdunJVU2DVmGmrkJ1wRFBaCf3arTyL8RjQMaE+xTPZ+lEixbRvh9N9Pmh7do0kRpqpQAtJeC07WMg/37C/0RTZ655nI3Pg6/fsTxQ6439Xva3UOTUCUBsAl9zfsBms2QmKhMWdawAGzWbQEMe4QOcUrya0edXovwqZwF8OhR8PUltFUY+/bBZv/+aJf+V4koK0LoDbMZKmbTsfsEAhzpU2w6TFb3n0vTxq202fgFQ15UHiQyLPbrvZoCMOeE63vKdYdbsNmMxR605+Oj4rH/PU6H0fB7S6QArCHkFLDEqzEaAEMQOXnKE/x239b8zDJiLhWQXM5+DgtggH/hDdhoUlFD2bqqjMVUaHkZsuRW4vXKfIyzYomj7udlEBkYybNHG8L+syx5WLkp+ev8nbkU1TYtWcYswgPCy+um1lBUAPr4KJ9rv5b9OD/+PACbT23mYv5FPnt+GDt2wKJFYM8WU3VOnoT16yEqCp++SpORii1IZqsZlvxAckYX/uwE6nuHwueQpSk/WKmmMO4fAqeuJeV0SV8xH7swcgrbmnTOP3MGrrpKiVqdPRuuuQY6dKiRQwW32QPiGC3CHgfAz1c59xZbJQWg2YwBH7K0TQjIhUBnDinXz379wutZtfJ6bvsc/BocBpQnhXyjiQC9e6PNcg2ut3iD8MGCBm01kzhmZ7o+mOSk5kJqLkRGXn6nFgsWobx/vQ6SMpM52BjS/ZE+gDWEFIASr2bLvHhYlM2ZDt/DPZtJC1Z+SE4bLuH44S0NhwD0LyIA3VFn110UNbxkGtPpe98BrhE7uCWqRaVSjpSHxQLbcjqiwY88u1XCT+uHyl/pN0NfFy2AivVI7+P6GZ7NPstNC27CbDPT7tQFLl5sRP5DT0DqF5d3MIuFz3iSswcGc9NjsLnbWMJ3/QbmaeXuZraZ4VIrjOdbYTBAXvsYwMbvpzcCwy5vLNVAWOxR4Pv3AIW+YntT95JtiwbCMX30KTUeHp9jT9MTHAyPPlqjhzLFNIXkY+hvUtR/bJjyvm02feWmgE0m1nMTgy/+SrcbYWcZAtCxqNeDv3/hg1q+wQxujq8qLgAB8gggpJoCMMeZPckGqMk9kwlbtsFd1Suj6GMvBXfbVQNYkf8HAEYN0gJYQ8gpYIlXY81WItN8C+xTLfZpTJutfDHXu8EhlvqP4tVns9Fp7bVPa5HbW9EcgPvS9vLQP1354/bfafX2v6tl/QM4cyGT3snfcS3/kBqs3OD9df6o7ekxLGotuaa6kwrGbDU7LYDFBeCa42sw28zc1fYuwvyVygamrGoknjWbWcBI3tw3lJwcuC78KK05VuHFY7KanKXgtJ/P4aGRJpiigfs9kwewRYGiRBoaXG+8r214je1pSmogo2+IUp2jJslWEpHXZA1gBxcT2sDRQeSmK9PeT/QcCYBF+CKMlROA+fZau7t2QZNDa9jGNSU++/wjik+g7fgB9H56Z7vB5H6Rk2tUrqmGIRanS10ugdX+MTPm28caoKToySGo+vPAFgsqqzLe7s07FeYB/NcDEBpavb4lpSItgBKvxjFzoFIpP1hBRis5UGEewOZnt+IogqZ/1ILZoq5ehQg3Y37/I1iDM/8fuC8wY+fZPUBfAM5G6uAcrH5vJDm59mlnm4Y8c91JBm2ymqDjf/HNDyAksHAq6eHlD/Ptvm8BaNeoHVscVduqk0uxSCJoPz8KrbH/z95Zh8lRZl38113VPt5jmczEXZGEENxDcLfFFt1FFxYWd19kWWBxDRbcJRAgQRKChIR4JjqTjFu7VFXX98db3T2TkYyGhK/P8+RJT3dXden7njr33nO3kitXlF5Eup6OD7CsX43114VggpgeI6bHMJu27bXnUsXkm263tnjfYraCJK6zbfJAFCeA8ZLqykpxYAcM6Hi5bmDDW3+DtTuxZsqvsA+4XHD4Pl5sskZst93ZajC+GQEEqFDyaSKr1YFaHawFhvLZ5s85y3lm4v1cWw/Cp+3AFzXOoytGzCQKqP2kdbqquT1EQsZ95KoBS5DCQBO6P0CPYiSKwghWk2GLkJY2TJiOA5G9pm6TB4D/j9h+ZrQUUugD7CYNAWCQVwxYQ5uMgSsmoXemvydgi0dyRo7v9e3rLhSHkcxtNp7EK3di7ce7Mf+ZpT1O8Fa0ZH5hSPND/VCWfT2B3Em3wLlTySyYs0MpgBMKJhCe9Bu1a84iPys5Ga+qX5V4feCQAxMGwMpWHg46RLNWcNXV8J+dXuKFOzfDCSd0uNikoknkmkSFpsVmxnL3fYnPlD4oDtga4n6SsiU5pYdC8M2XVjjib1x51jFcsOxyqK/v2w1pHgJ+7jmRD3jddX3yU/18gnAM2yhyQ9PS4OO5GbzzVTZSdieKhRSlBQEEQxnbggBqmhFet5iQ7BY+4gg+Zxrpjj5QAKPiASTNpXPiiXDW9BocT/xHmPj1AEcOmgs3S3DBrvCPITxWsgumYA8fCouKePjiJ7n/uluR8tYkFUDtj2mH+P8BKQKYwp8aDk1MxnZVgc27IlXsIz7QJWJ6+xYWq1bBm2/CTz+B1SmE8ujNd/b59nYWiRCwYQDNiuNY8sp1vHbBN1BR0e5ynUE0XmBi0oiGfVC1MwAv/riYXz/9kTGBxh2KAJpMJmz/+CdpH38Bf0namuxUsFPi9XtL3mS9ZwUAUa0HBFBRRHUsUF4OV96ZwwOvFSUrWDtaNO49aTOzNDQe3ngLvvh3okJ4W0GLaTTEeZ8l+ZD07rvQUGsFRxNZ6z7D9tQjfWbKnEDzEHDzjhN9AFdIkKUikyAeMxbPoPihYs778LzOrWALBRAMAriF+qsZfbatVh0sFo7gE6bxBVZT759nvya2Jz0Nnn4aXvw0nwF/OwyGDOnRehtNEWFAL4ttbrLT8/MyZgz/O9TN4bzKa0teSxLA0hXNkw5T6EWkQsAp/KkRDwHraPDqpyiqmOSJSWi6htRWYEdV+eSwp/jnuov5y0kKM2daiMVg8OBtt91bw/BPHubGv3/DnfZfcVqcBOOt4HrBBiaqGnYvJo3c9TVQfSAAxfUuJgAOlR2KAOo6eAtHYh0wErudRJjq5n1vRtM1itKLuOPbO3D4DwR2RkEW/nbdyW8zmxMEMG6L1tlWcAkCaDVREc6DFSdA4cJtrgCG1TDVRt6ryZokgB9+SCKXMmgy7pu+jgP7fCjIvN0wjd0D+QyGPiOAceU3nicaVsNs9m2m5rd56MW/Ydpl545XkJdHcPQkWNFs8+97HE5uWZSlxeJed2aQZS6bDjUuuKd+DYOdE3pvh4CB82dy2fMxSkqsW/9yF6DdcTt7vLeOeeXzAPDYSTqg9wDxNBarZCXPlUeJX8L15PMw8VLYaacerz+FlkgRwBT+1ChVhKt/ow1oyMdsXQ5HngdyGC32DG0m9igK0XXlAFgsOvvuu+22t7OQ33+bSXU/cMKFU/HmjeULqfcIoKqJSd9k0gjGwtAwFICvOJAvOZhQzTcEojtODuC8NUvYa4QI34fDSdeS/hn9efaoZ1m/+ifu4A6UvDXsuuYX3NSLY2jtxqR5991EnwNqkmlLkVoPzF1ERxfSC7+9QHX6RByxfBy2GI54sUrMss0VQDWmwl/3AdXOxMH3Jt7/6SdgtBVWHM0na45gEp9xfF/7AO60E//b+w2u+O44Rm3wsRww9REBNLRGFKu4f2ySDe6r5aNQDhvl1xm0NQI4aRKBY1oSwLDJCVsU5Y+a+CA/2tLpX5wOViuvZVxIfVDjgsYwg0t6b39AcKb/PmKY2usQWvA70ppV2MYN7xGhWjRnMMWzfmCK+zkWfDqMG2ryOXDCW/TkGVkPhXn7wrtAu4robt9w9/RrufucV6GsLFUF3EdIhYBT+FOjPm8+jJ2J0m8pAOaYxB55zzE1b2b7C6mqIFKAxWqG338X/lYTJ26LTe4cNI2jV8FbQ6/lit2vSBSDJHwAewBFSYaAQ7Eo+IRdznNph3MVD1JTt/cOpQBuqE+GxC1rV7b6PHe1IPvqtGuZa5/CSbttFLNlNxEXxRIE0BuB7zpun6fEFLhgCtMPH8xwdwNWqxias2IZiVDYtoIaUyFzE7jXJFrBNTXBhg2AZoNNu7Ok4jx+YM++N4I+4AA+kEQl9MrN6WyiGII96NXcASoMOaTWLMLaVslqtEQ0Ewl1ruPJzjuL1sVx9bctUaxoyDuw+6PkFQTAbKbx47vho2fYXNO3eswxx4Br6gRePmOWMLvsAZYuFSkyvvUjoW4kNaHR+PY9okfr1N5+D191P6gbg002WHPcBzNFAPsEKQKYwp8aQ05YDyeeytoJ8wHQVRc/PA+fvGPHYWnH1rkFATTx/lfpPF59HBsqejeM0hOs9RdwGf/lnndHMjxnONNGCO+y3lAAHRlh2P9GBk24k0AsDL4iAGoyjG4qknWHIoChSDykrWCe932rz9PWbkIy5nePJQafftojc+Pvv4dff4URRhe3LrWCM0ngdGIxTIiztQwy7VvPH+xNxBVHEybM0w8DRE4sAGW7k+6bDGyjTiCItnpxrGB0n4WAY0Zo1mEXRMwm20AS8ftIsHNGxCeeCC++CNdcA+OKG3HPehU++6zFdxTDUN1iVLmaJaPFYrRzJLPT8PloOPwMqo6+kJBfS7hDBXH2OHQf/ng2AE4tBLIxLozepUfrjIaSxzhu2J7wrkkRwD5BigCm8KeGavTa9Oi5ACjIfM40vgx30OqhOQG0mbn3xQIu5nGWRP6YvqxtYVM4l0e5jBlf92dozlCOHC2q+nqDAO4xYhR3mx/gduU+/GoYvEIBjLeCQ7PtUDYwobBBAM1KmybZpjVrSDPmw4AFWLOm+z/20EOMvfZIdil7P1H30RkCGO8Dazn5VHj88UQeWo8saboJNabC17dh+uqeRJHv6nWGlBUoxOcV5LQz+9XjbamoYXD/JFnZTP8+I4DW/W6E6ZdS0k9cLzbJlrC8iYQ7oQg/84wgLCedxI03wpJpV3PxvNNh0aIWXxs68VkO029nwBhBrk1m8Rvhpl5+qAoEuPvTifT78Cluuc0sbImAEI4eE8BF9RsAWBxcitMprtWepgBGw0kC7LTLvLbkNaYcWs4t+5HqBNJHSOUApvCnhqLoEDNDWNg4bKKY6XwOAThRB1NbxlVbKIDxVLBIT6pDexnxgoGVkXVc/9VMBlnuFu/3AgEckzeGMT/KEIjwv4MtoIpKQilOAFXbDqYAiuNhNitt5/WtX0/aSPD8eBP7ef7KlU8F+eeUbv7Yr7/Cxx/DAQdgnyreimBHjyodeqRFNQWeXMjnaVk07geWIw+FdyAi21E0BYvUs+4uXYEaU2H+lcSUNLxecLth3tJNwHDILAdVHMNtoQDKF13AvF8/4LpDF/Jd/Vgy8/aCKX1UjbXzy2CO0a9kGmCEgGWhADYnJ+0iGsWnOZA1C3YdTO10Ann19lOprYV/nyj+NseEghZu6OXuOtGoqEIG0tJN+IxbNoQDIj2z7/Hr4sFkWFoO9twifquE0JI1sN+w7m9us2Nst0rUBGr4yR1maL7Uo5SMFNpHSgFM4U+NBQ+fALdruH89FoAmchKfVXpr2l6oGQG0WpOcoUf2IL2MZCcQFS2mMkB9lQeOeJRrz6uH4uIerTsYhEXRMaxkJF6PmEAys1VCduFTV2fO3MEIoNHD2NS2Akh1Na4oEM6mQhtM3etfChO/bkCNaNzOTdzzze44nfDFKc8zl322SpQiUQ2qdqZujSA3lt1EwUFtyM+KuhUdLdrrUGMqGFYl8hoRf12x1jjfeUshYxMAX2cdD3vs0bcbY8hK95y2lO9/snLcJ+fCzTf3+s/ouk7ULEiGZZdJAGQ7srHFw7OdyQGMRjmRt3C++yovv0yzgaMlAYxfCvHopsnw8oxGejnMGYkIsodw0IkrgGHsPQ8Ba2Lj7TZwhJsACD3zSo/WqUTEMTabFaYU75a0gTn+aNhvvx6tO4W2kSKAKfypoQXE03WB2tpHKhxtZ1KOxfiL7R1esP+d444Dq1VoN1F1+yGAidCgpFC+bhHTa0/nnjGXMfWuI2DgwB6te/5vjeys/MT+rh+oDboBKCiIoRtdIaIx5w5FAMNRgwC2pwBWV/Ppq3D+epG5r4aVbk+QkaiJW7id6z+aitkMB4/YyD58h0ntmABGo0mFw/Lmq4wcCf3vHQ5XFWxzG5h8V36iJZccFud5Y5mxfQO/hfzlADRE05Ksoq8QNzXvYXvDrUHTNfR1+8OGvRNWN5OKJjHWLB6AOtU4IxolgGgn+MEHMPrl67ich1sTQGNMMjVWAWA2CGCkDwhg3JTcbqdXQ8BhI1/SbjPhsItrIxTuWa/0aESsx27SGJk7MtkJRE0ZQfcVUgQwhT81YroYlEzG/zaSiSqK2s5T/cCB7Bb+lrNDT7DrrmA16gGise0nY0K97S7xwqziahCTdFQC5s/v8bpnr/kGAI9DoyYqFNO8fJAlgwTsYDmAkj0AY2dSXPhhawVQ16G6mqGNkJsdzxPtfhg9PomBwTXjMs9WFMAhmSMTry0bSjFvXI8l5gVJS+QHbiukWTLQDX8k2Sb+b6wS5Djf7UjkxfWw4Uyn8GzZIQxkA/+aaRQYVFZCaWmvFwVEVQVmfAUvfkvQmywA2v2gdA6Z3Ej26YdvfSXNOoFoGqxsKKCMAa17ARvDzvdlXwEwzC+umd162QOQaLQFAYxz6N4ggBGDAK5XNvCteTY210asas+qs02qwnBWMzRD9BdOdQLpe2w/M1oKKfQBJiqFbAQK6rJYBuRTQzlCIYsqnUssttrFc1KkZJggDG0mDm5bKJmCrGBWcNV7Qe9HaP3efLGqikP283Sq80R7SPgAmmMQFL+Tn2fCNGwm34+/hezqfjuUAnjT0X/hyrt3RlqzAqyzW37o8SQmQ0uhG1b2jAAqzZS8w14/hEnR++j3z7M4+68mOmomdsyIEznfeG2xmeGtt7BU1oAb5m6cy5Ti7iYldh3N8+3jBDDYKK6nQQU51FjeoV+sivM/mkLwh6Nx7rkVf7weoCaUThkD+XShn1f7Q1HFZn5msmiz0sNUh+bQm7X/S6+phBKRy/a/V+L3UfbWV9KsE0iOkWkSxt6K/OsGebIZivqD7vvxVvqZNKyXW9xFIqJQB0H+xo6FYw/2sXO/CXDOyK0s3DH22+2vrBr1V0pyR1G10y/sVAknfjsauG+ry7aHQXsV83Ld5UQmjqUpfGNKAdwGSCmAKfypkWa0gnOEjSdhZ5K8xTtetIVffoFPPhHeZ7Z0MRBFL7tquyB/0DIH0NXgg8pdUd97g5ve3Qm+/rqH6za6QJg0CBgKYK7E7WtL+XbO1xy22rxDEUCbbCPnoSfInPkeTEiqLL/+CnsdaOUsXuTRnQfwlX090EMF0BBWTJLC7PVfcu99w7n8wQHU2jt2+I1zBDMaZpuFesVMzRcvwtuv8vbS97q1Ld1Ftbch8TpOABW/oK8j+xWB3UdR5k/cxm2EflnWp9vSFBFxy7xsjYoKqDAJS6JerwTWkqkBDlnc4+WeckY9NorxT3SyB3gzAugWmROt1LZYDMNbEGwO8ZsHZfzEcbxHQUbPO2lsuT1xBdBmg+OOg3e/SOfvL+3eoSl5ZxC2RMHmJz9dKMNBCz2XhI84gnN3KWffhgdZWLkwpQBuA6QIYAp/amhGuEU3wrd5hclLPhBpZ8Bau5b7jvyeI44QBZ3/+Idog3XssX28sV3AUUvv5pCLD4Zj/orLG0oYQUd7oQpYMXKRpKCXdL8R+sszM0LNYu8yyG7I26EIYCwG2l77CifcvDxACLmnnQY/LHQyg7O4fMB+/KCK3LYeEUBFkAfd8I+LV5FuLYcsTgAtiEKVmqgfz6qzYOlp1PqburUt3cXK6qQNjsUu4fWroAoiNqFE9JCNGK3iQt4u5ifOnQvLlnW6etgTFb87uFh8v0E3lLheJoDNNyfe+xtgVf0qVtesEAPB1jBsGCGLIMrZxmaGd94DHnoo8RU1knzotBt+g0+N8HHuUfB17U892IM2sM8+HH7Xnvz1DKWnrX9boeiCfzIubyxDiscBELLQK63g4h6UVsmKy+oi255NujW9x+tNoW2kCGAKf2qUIfJS/E6jGKTIgvOAy2H6JUTN7TSyb2xEqRIt5CwW2HVXOPLIHvdP71WkPfkA+/w+m+mjBjNiUxik3iOAqtEJxISGFhKEye2G3yMjeZILqYkM3aFawd349PfIMgwbnzzfy5fD6tXi9RR+RI9mgLMWt3MFhVR123dMmSE6LCRSDQ0iGP3kyw6Xu2729ZBWicNWBRYLjVrSpqPO18v2IFuBbI/ARWMZeMpErA6JlRvFvYAUZUheEdQPZfOvt/Fvru4aAYzFRDXnuHEwalSnFvEMEOrb4BHigIZxEMbW6wTQG0ySF4vTCNHKNvjgWaJ3N/DkTeVbX8l55xF1CuYXz8AIaVbISAb/TaqCe8+r4MBrcWUIBXDm0ON4Xj6VuUFXL+1N/MdM/Ot6mednWNh1V/GWXlOL+sEnMGdOj1Zt+/5uJv+ylH1t/4AFF1Px+k883HR2j9a5cIHC+nvegzfewmK2cMDgA2i4poHZZ87e+sIpdAspApjCnxo1/b+DER8RzV0LQGGRzO7Fj7BLyf8wSe0kLTezgZlT9gVfrP4Mhg4V1bWN7ZDGbQ1V5Ybv4NN9nuboX3xgVBKqJrnnBNAIAZtNSQKYmwvP+yfwd55kkX0QSkxJNG7f3rGsSrSxCPmrRc4fcO2znwKw58g1/MhUiuQg7PICx++1G/dYbmnbLqYTiCuA2S5jMjcKJqIfft7hcjZ3FVxVxDWTB7cigP5QmKDSN+3P2oJuUiF/OS73EsxWmdWbxLaYXQ3YgxHwFtO45DJe5OyuEcDa2uTrdeuMeGjHaBoo2i+WjMvEbMxWjWT3eju4jbXC2gaTiskmiJlVsoJqg2gG3mjn0uWPPRaOPx4KCsTfW0ZFLSikTX4Q9r4PZ5r4nVVzz4V3X2P1qr59wvzoI5D75bL3MTlw5ZU9XtcLL4CnzgW+IrSqyayfckqP1tn04HMoFWOgbpQ49in0OVIEMIU/NUpO/hBOO4rStGxM5hi5BRJfzYBfn4YcSzuFEs0I4MwVM5j20PW8uG5Pfior6HH1XG/hh+hkruNu3nxXRtbg1GViIlb1nvcCzsirg73uZsSA51sQwHKnIE9NmV6AHSYMHDEKM+TGGqispCncxMc/rAOgyf0tACMyxL7MkXcXjVzHju3Wbw0dKgqxP/jAJEJXcQKodJw7mugEogEWC56YN/lhzEK5pxMKVC8hvi3yuPEweDDrK8S2WNP8jJzxKQN8xj5hJeLrwv1QUdHyb8/Wlc34V7Kzk6paE1m9XoIcNKxZkKIJ8t+8E0iwk7fUCy/A22/DsGEwqF+YomApPPVU8guKgmLMuharCG/LRjg9qvSy2fH339Nw4oX4736EWExUpcdipp5XAYfDREo3ApBhMYFFqKfB4T2rYk5U0EvRbWp8/v8ZKQKYwp8aqk0MJPWxAuxOhfQsiXlMZQ77UtfobWehJAFEUmDZSfyVGbzOqdtNT8qf1Z25l+v44CsXJuCKnw0C2Ash4KN3GcIN1hu4Rn0ELSikDLcbZFkM0Dpm0OQdhgDGPfZkI7/u9+rfoW40AJ6chQD0zxIErU5OA6+3250HnDdcwe4Pn8LuGct556R3GGz08d3afBvPfZIf+g+cdx4ePYgVI3FQs1IbrO1g6d5FY5MO39xC3RfnAlBRLTbekRFg6Cfz2KXWyGvERiTQhYeNLc21Gxra/l4cuk5JfpjhQzXycnXSjVQwP2m9km/WHA6HHw65kow9b0wQwOadQEJqJ4q/zj0XsrLgiSfYaSdYf/dMvtk0QpgCGog6s5jqvp1DzJfjTssHQDLsU5SmXlZ5S0sZ/fbtpN9wGcuXb+ED2Cljw3YQCrFeF8tvCK5hgFs8JAY7Y5bdAZT4sCVFsZjFQ8+BMw7k8Nc6YcGTQrfw/9YG5tZbb+W2225r8V5BQQFVVVV/0Bal0BfQYkYuly7hcKk4c+zsxxwUrDxd+QXs1MZCqopiVM9hVhIqgELP1bXeghITz25v1M/m1BFQvMkKwd7Zxn0Ld2dfo5BYl8UklZsLFkkM8DpmCGfuMHmAiqGsyEYnkCVVS6BxOgCVuYtRzDAgT4ZVR9Aw5xHO0w7j2WAQXN3IyfrkEzbWlLLL+M/onzOQLOtcYOsKYP3GAnjue16el8/ls0wsKjIRkxTQbKBZqA/2rHVXV9DYYIa5t1JlE+e3tk7cQ670APy8jny3SPyPYiXq78K15t3igauhQUimHXz/zQ+zxOtJYXbd1UaxVIFl8nEdL9cN2BxB2OM/5PgksAgrE8ksYZIUdCCobl0r0b0+VE8AWVFF2794GkGz+7G61sw7N9yExQIDbxLvyUbVtVK3FULcVWzhA9hrRtCRCFHdcFdwyvxr30u55G2IbG6EaEbbZuud2lzjHpEUrJKVqBbl6/Vf47L0cm5kCgn8vyWAAGPHjmX27GSCqSRtP50eUugdLL//XlizG3n5X2NzaaRlW1AsAVCsrGxc3/ZCioJi9NBEShLAKNbtQwGMxVB0cetq5ggmHaShQe5ZdzaDQj4Y8bcerd7niVHFMBzmUKL60+0GuaQI5oNHz4JI5g5jBh1v+GJBdAJZ17gOAoLYaumVrM+GwgIX/K6Dt4QNDIbZs+Hoo7v8WxtCBTyqHUnDwkrkqV/x5rlLCNx0L7tupZFF0GeD8j0pR8Q8l2VEUC0KaEDMQkOol8lBB4i3JDOhgM9HncE90+1ewjLEDFWsjly+HnYBB3R2xb4tuvFsTQGMh3lNJrBaefddgCKgl/3ygKhhyWIdNLRF/meO3Uo9EO0EAfQELWSjwOUQ+RtY2yCAiWrvZhFOycjfVTqjMnYFzTqB2Gy9SACjUWKasGhxOWRihrVWaM4CqN0J+vfv1mrjx2aonI7b6cYbEQ8MKRuYvsP/6xCwLMsUFhYm/uUZFhE7DN55RxQm/OUvf/SWbLfQQibQ7JTENuNMi4mCPIPQeULthDBVlWu4j3+NvJPrjj+S8yadDWxHBFDTUOPPbmYVSwwOOWIZ1139EqPz3oUxY3q0+je/iTGCUg7P/AgQnnbp6SBnC0sYBRuEs3YcBXCLEHBFgwcUsS+kVVORDqeNOhrX/HsAxLHtZi/gFaFBPOR/EOZfSU2ghiVFr1Fc8Bl5proOl1MNhVDy1cNPP1EfqodLh8M1WZCzZpsSwBHpIwBwqQroOp4msW2Zkoe12fDsbuL+iSGxOdqFMbMtBbAjGGHelybJ/Hve/ejdDMt3Bh5vDMqnEKtuee/8vWQaAJbI1lWt5lHVxkaYdP3B7MovLciWGncX0EKJ/ZHNQmHt7eBCLBQh2swIukUv4J6EgCORJAF0yi07jPQgNB9/UBtmySTDlpHwAVRjajKSk0Kv4v81ASwtLaWoqIjBgwdzyimnsG7duj96k7oGVYWyMti8+Y/eku0WcYd/k24iLd3IIzKJwSTc3mB15JEcp73NfUuv5e7jL2Bsv+GAQQC3hxCwJKFccIl4bVaxaGA1CGFUorXS0kV8UDYHgPVuceysaQFMJpAkQ6HQTRDJ2GEUQEt2JYz4iCGOX8BiYVNl3KMvBFY/FemQWzKSPNsAwAijd/MYJpQiw5bn0vKnmDuQrbeCyxCkyx70QXU1kYZacqkHhwfMMUEItxEKbf0AcGoqyDI+nzjvWboXq0YiLw6gqakLK95zT7jrLqHopaVtlYQ0VEYoMa/j7PIFXPPFtXxS+omo/q2ubk0me4hVy23w3I+UP/3fFu8PmpTHnmMaGHzaHltdR7yIwSqL8eXXtdksZFf0Zj3HldomADzmABU+URQzKSqiDXubO2eN01lEgs09B3tXAdRjSQXwlnlXYrLXo9t8PSrOseoR+lFBbpq4LuKdQCClAvYV/t8SwClTpjBjxgxmzZrFM888Q1VVFXvssQf19e0PtJFIBK/X2+LfH4p4VnQPJ/w/M4aExTFKb8ojPU0cMtlkFEx4OjhuZnOij2s8pUVJdyd7u/6RMJtRc0QIE0nBqoGsOWHV4XwVParHDwRxCzwdkfNnMzwUJ47+EU45iowRrwkCuIMogJ9d/Vc2Vh/FS/X3gNVKVbWYqM1pdWCCinSgoCDRvaFHBFCLE0Bjgl2/H9+Mf45Vt7zW4XKnjzsHgJyoArJMSbmXQ9YmP9+WCqBqhIAtiG0J+sWDQFbMh00DnLXwt3FczKMML+2EQXIcu+0G118vLjCfD84+u8Ov+xoUNsUGQ91IMOvMfGgX+udHeazwDnjwwW7uXdso9AsZKyfckhide3ka3y/L4Z+PDtrqOiJGDptVjrVIg1ObVfcqYSOCICmJStcLh/zADM7g5HEbur8DbSAcTBZl2O2Ccx+8v8rh48vR/vNI91cciZD992K4sojiYhOxER+gX5vL3XnH9EgBPPF4hXf/chpXXDOLmB5LKIDADmM5taPh/y0BnD59Oscffzzjx4/noIMO4pNPPgHgpZdeaneZe+65h8zMzMS/kpKO2zv1OVIEcKtwqmIklqMOMjNNpKWRVACj7asy338Pt704lzNnXsxry8Q1Ed1/Gowe3efb3BkkBCUjBCxHcuH1j7mu7gP0l2b0aN2a0QtY1w0C6BJP3+fXbOazXz7i70sbdygFMCerHwOefoP0514Gq5W6WjHsuTJFCkBltszaaDWNJa8APSOAiroFAfzxct577hzm1nR83TTvBKKaTfhNCsuX3wQfPg11w2kMbzv/yU0NIvwdk4QCGAqIhx53pAm7CkgaFC7jUS5j16pPuv4DnWynGPTED0qIiydfTLqpiIpAFnXk9roNTJ6WBUB+oOV6j33jWMY/MZ6FlQu3uo64AmiztCSACXsTIBw0lCyzgsUsCODUwvWcwSuMz+vdAsQ4ATSbYhw+cxo/133FF1/LfPD7YKTzz+n+iqNRlLQGyKjEZbPhtIj2dz1tB+e7+DymDp/LpOX/QI2pLbwAUwSwb/D/lgBuCZfLxfjx4yktLW33O9dddx0ejyfxr7x823lztYkUAdwqVKNaVsdEZoYZl8vocQtEwu0QwLlzOfWQOm796768/M2P/CDfzsFXP8/VV2+rrd4KAgH+yYPk/W0P2P1hLBropmQBkxbo2eSoeQWxy/cIImBziuM0SHJz6BoYWJ21Q1UBY7XCSSfB6acTM4GnXigLuZlCrajItbGhaQPrMl4AjBzAbhoNRzXjPBit+RIFRFuzgWlGAIMm4RW3cfNJsPB88Bbji2y7e/z7ctGSrMmhgtlMJCgm4rxQLbZmKbARGbRIFybmVatg0aJOx42DXuPHLEEGZA4QD28YNjC9TACVsBgTLOaWOb6ltatYWrOUpvde3+o6IkNF/qDVKoou4oi+/WHyO/Exx6wimwWx/jq9jsumw8vhBT3ZhVawXHcVZ5wUoWjqXL5c90Xv2ansthuDi8cxKGMgDosDuyzU07BMjxRARUuOxxazBZPJRJo1jTRrWovPUug9pAiggUgkwooVK+jXr1+737HZbGRkZLT494ciYYy1Y/ix/RGok8TAHrWFyMwwk5YGhRP/DQf9C8m1qe2F1q1DCRkTgVmBnHUUTp3DXntto43eGnw++j14Ffs2zGcfm441YmNtUzIZXw31bLBU43MU4tg508Qbazx5vMzplDJsh1IADznvB2Srwtl/b6Ah1IAeyAWgf5ogLxWZZjGJWQJIaeWiFVw3J7LoQ48CkOEyEq7iBPDbHztc7qY5N4DVS8ThJ6grRCUwG6kKxCz4otuOABYO3Azn7cbue4jODkpI7Eu+t0YogABzbuIG/S6CkS44J1x1Fey8M5x8Mhx2GPznPx1+PeTIES8sQXKduUQlkZ7jI73XfQDr/OL46nLLeyfw63R4oILbr5u81XVE/3UjALZ0G5KUFDqjecmq2LxMD+x3C0x5JBECnjV8Dx7NPJI3tMLe2JUEcovtzHjDhu9I0cQ8okUIRvyiDdwXX3Q7n9kXMDN18RKOXL+BQlcRsboh8OJX3Fb5fo/Oy8svSvDc95jnXY3JOHi+63z4rvPRP6N7lcUpdIz/twTwqquuYu7cuaxfv54FCxZwwgkn4PV6Oeuss/7oTes84uVXvfw0/GdC/cDvYdDXRNNryM6USUuDXYqeZuSo+7Ha2smr2tIIGvB995Worp03bxtteQcwKpHfet/K3A37Ud64H7FY8lZWOtu2oL3VGyFgs0mEkJwuQQTf3JjLmbzM+849IZJBMOyHK66AG2/s0e/1NRaXr0BTLHg3llITqElYwJTYxYNTlUsXBLBkAZnnj+IVTu9Um7K2oJiE9DNtxP7ce+C9SQL4Wcf9TC1jP4LrM7mr3+EEiBKVIF011DXNkrDE2BaQLD4o/pm8rMXi50MixFfYUCGKQAC+u56HtOsJqbZ21tIG4v17a2vhs8+EGtgBgv0Mrz85xLkfnssjv90F9I0COK92GQAbMluuV9Yd4O9Ho5az1XVkZMBRR8GBByaca4CW6m9BVhPsdztM/W9CAVy8bBrM/JBV83rf8FjXdUJqkpQNGWzDtv9UVk+7pFOdWNqC1wtPPw2PPy5SpS24YMMBrIjtDyNHdntby/7zLpTviamxdz0eU2gf/28J4KZNmzj11FMZOXIkxx13HFarlR9//JGBAwf+0ZvWecRHGFXt9oT1Z0fGydfB2QeyxlJCTqYFmw2efyudlY9BTrCdQb05ATQr4Ctg7Yr9+HJF/16vPuwWVJUPOIo79euZX1bED+wJq5KedQn1spvIKtoAuz3CsBzRv9aVLq6tdWZhYVGbGYRIJgULV8HDD4vKzvXteCpuB1AjQk2w/TyfxlBjggD2N4u8unqLmqg4bJBdnMJMGNK9vqxHHy0sBG+4AUEq4wRQ61gpi3cCsWgQ0CMoEvSPE3nNuk1DwGqWiGxYTj4NRVPQIyL2WhjxYDKZuGHP65DMYr9U3dz5pinxqt94tc1WIhfxKHx2hkEybeIY+EjvdQIYiYhrXDK3fHiy2MXORXXrVsfY0aNF049nnxV/FxVo9E/3EHvo4cR3VCW53ZKRthH3BAyEFcb8bww3fX1TT3Yl+VtPPovv/Iu5ufiMxHuRqE4UGxFs3a4EjvwkHgxsxjXgcIj7S9EdMKr7lcwR4yFWkrYDq63/J9gOShr/GMycOfOP3oSeo0WiSTSpCKaQgGJYl9THCsnKlDCZYAWjsKLgq29HvdhSAazamSWfv8q1/MrBauU22vIOoKq8y3HMUM7CXvE4a8iGBacmPo7nM3UXp09JY9hvlzPZm8VnPE66QQAtxmih6xJEMkgrb+aVt3QpDB7co9/tK2hGYYbVrOGJeBIEcIBWA0CjOZJMOJfDNJCTVKu6gkiE4hsvpFiW4bHHSA8dyewBQT7+FaJax0Ntohfwl19RrQsF0EKcAG5bBbCqLA1+uIoy7zAChwXAsCnJV32Ql8edB93Nf6lH0DcToRA4nZ1YcZwA5hgPXls5xlaTwrChErvsNIqvnbnUWcUv9kUruPyiDbDfzQyN1UAza+v4EBvVbVsfY3feGWpqhLo5YQLrvlwrFLEXMuE//wAgNHE/Dlx8PmZ7MBHmtIYMYuv1UVm3gju/u5NLdruEgrSCHu3T9zM3sf/cxxn9SQP/fX8CISXEf5820wQ9IoA1paXARCJSgJguMyyvmDmAEu1ZI4VwggAmx68LP7qQjZ6NPDTtIcbk9czfNIXW+H+rAP4p0LzUrCfGnn9ixCdWYjLxlM3jzO+zGz+zsnpcOwttoQBub51Amm3frUPWstKVDSRz9pRIz9Tgk/MP4D+zYOoGkfsVTzWV4z6ACALoqmlWmbode1GqBgG0mWI0hZvALybWwUHhwxZDFz5jjYPgpdmsYmS3CSAvvcQdpc8x7KmxvL/yfUa6hVNANNbx5Oj57QB4+XNefX44Pi2I1wbV+cYy2rbNAaxY44Yv72flpwdS7/OLdnSAO+aDAnHsLM2Usk6nIHdRATxs4xOUrpV4w3QKbocbXNUMHljHoGEyHHRQl/Zpa8gtKYf97mDE2A9bvG81+J7SGcJUWQkVFby1+QsOfvlglgU2iPebLbd4cX++uuVpfO+9knjPsnkjAFIgSXx+q/qt+ztjIGwcbrslxmVTLuOava7B6RAPIj0hgN6AWLEmhzGbzNw3XbRUjWlm1E3dr2SOGCq5JCfH2Lkb5zJr7Szqgh0bqafQPaQI4I6MFl4DqTL5tuD5zxy4rw63EkwQmboMoR6Um9qegHRFRYuL45KSqOjcboygVRXF2L6ALcyG2FCweRhq+4XjpZex5XRGjmkfPh9U0I+mWBYAGRmC+FmGCDIT1p0QzsRraRb72457aGuGN5/NrOMJJxXAYu96DM9ZgtEgaBao2E0ob0uWdP2HFIUF7MbshgtZuyQfT9jD6SdGeJMTOUN/ucNFI/VFsHYa61e58EV8hC2wMc8gBDHRFzWibpuHPMUj7gvJ30h1fbIaOg0/FBaysWkjmkNs20Nc2XUC2EkFUA0FRGWpw4Hb6YYh33D/p3N5vnQfuPzyruzSVhEdLEzArdOPaPF+jjFoaLGtE6Y3/YdhJcIV1xxAUAnywIrnxAfNxoz482PzVnBWWTd+I/nmqrpV3dqP5ghHxHWvWUKJXtJxRbMnBDBgpJiYJHE+m4uikWc7vs47gjUqxrQ9soYn3rtkt0u4fb/bGZA5oNvrTaF9pAjgjoxmZsUpBbBt6KEsCLkZENuUIIBYRB5OJNq2UqYrKndJV3Dq1Cd5cpafVz4QA6WCZbtRACOmuEKp0hQrgCMvoPS63Xln1yYas3uWRP3vjwvpTwV/Mz8GQGaGGCYseUK50XQZIhnMnFYEy5fD3Llw/vk9+s2+REwVyoJd0mgMeSAoKqbzG1fhNiKJSkzhxSPfEN/HjOrpRmW9qvIex/Lt0idh2Yk0hZtYbH8DafTbjNcW0VGynKYYx3jpb0TrRGi95PRb4YpiGCfSVbaVCjjeKq6fQm+QmkZxgEyWADIaFBZy0MsH4ZXEtmxiQOddqCIRnuMcXPffwudM2yoBXBheh+NGGFnyvlAAoc86ojTVWaF6HEqzanqAmw+8FgB7xLrVMTaiSihYybG6mVc+j0//ew578AO/qeMS515ZJbpNyXXJByZbPLWiGQFcWbeyx/sUNnJff4+Vctybx7GwciEm2Rj7sHV7zvAbVjYmIzLSPBMp7O/++ChHxP7vmzs28d4lu13CTfvexKCsQd1ebwrtI0UAd3QkklRSCmCb0MXkr+tSggBKJuMJtp08cvO/ruL6pjt47fn9uPD3MKMbm4WAtwcFcPhwlD32Fq/NCmgWzLqhBktR6j09S+19r05YlvzsFgcsO0sME7IcbwUnJW1gRo+GffbpdgP4bQE9dwUM+poBjmqqa5XENZFXuxy3IXB5wh72G7kzIIh+qDs2gIoirhEAKcoGzwbO/uYybt3P+LyDh4f+aaL4zLFxHSF/EwAl1ELmZixWcf1tqzzAQRZxLvOiUNcoSILZyL+jsFB0aGjWDq7TCuDll3MezxGMWriURzskxAAvzZsKTy7E9+PlQgEEGoL1gjh2qQfd1vHrp+PhiSX89PJRLd7PzISJg5oYPcmVVC7bQcR40Eh3CiLTVDaY+exBI9mJcWPd6kUAzA8nFeaJFiMntSFJACv8FT3bISAcNaZ3Ocy3G79l16d3pToivGt7ogAGQ0L9NRvXwL0/3IXJ6sMuNRENdH98tBEmAw9OV/K92etmc8fcO/h588/dXm8K7SNFAHd0JDT9lALYFjKMp0o5lJEggE5dTKSZgXYmZItF9E0ywprxZHzFZEs21Pwj4XIRdRgJjWYVYhYcVhnKpmLzuqmu69ltHW8Fh5GUnZ0pjuGIfhvh+FOxT3poh2oFt+KiwSz3H8iFGXOprhGkw5EewKKFEwpgfag+EcpSsBIOdba0tRkUpVnxUJQccxrUD6Vm/YnM+8v/hGLfDk4ddTogWsF5Y2Kjpn+4AgBXTBD6bVUJrEbFvstmjfomce3LVuNcFxSI6ubj/sJ+w6/gZF7vtAKoX3Fl4vUahkMHpvsA5Y3pULUzkr+YfQfuyynFV/O/Uy9kdFoZTJrU9R3rAAM94uSX1LQk2YMGwbNvZfHhgsKO731dT7QBlK0isqCZxXls/uAYUYyogzmZ73fgsDoe5+8clv0/RuWKKtpqf7MCq26iOQGMmzWnDVzJ/iMryL74LzCge2HVsf2Xwz8GkH/yCQB4Ih706zO46MBs+sm13d7ee06YxffHTOeYM9Yl3ntr2VvcPOdm3l7+drfXm0L7SBHAHR3xPMAUAWwTsvFUjuok/aPX4IILMBk9bmOqhN6GChGNwkez67nvi4V8NgyenmwogPZ0OPHEbbbtHSEa7y8qKRCTcNqt8PZMIsvORt64tuOFt4JEL2BDKXNnCVJziK+et5fP5M4Vv0EkkyfvXykqRP72N3jllfZW94dj6KSDGX3fc1hvuDnRBi49Q8hWbqPAoT5YzwuLn0ksE4p0Y2hU1WYKoEKOV4HSw6j+/E0e+WFXkNovBIkX7lhQ8OqCOPxedzJ89h9i6w8Gtp0CWOEXYVbFotFgEECrxfjtwkJhmVOwjEvlh/knD3VaAWzcopvd1uxjvEZY3GVVOXuns3lw+r/ZtDmHUoajB3u3CnhgWDxQDfMkVbFwGIaf/l8mP7U7B1zzeMcr0LTEuf+2Zq54y9SaAMbvW5OUVMpGF/v4O0+yq2sWew8Qyn5NoKbH+xRWjOtNDlOSIfJ3S065n69XFrHvYyd2X7U3+SCrHGemeECO9+yN9LATyLf/OpkJO83npN+uT7w3f9N8AKaWTO32elNoHykCuKMjFQLuEKpBYmKYSb/kLHjmGcxGCBhNbrPHZO1zH3LUwW6uve9SLj0MHjuwEo48j/8e/N623PT2UVbGbbs+AefsgXng14CJNIc1YVq9NcuRrUHzifjnJOV3ANxZYmLrZ8/j+BUwaUM6xCwMqYqI+N9TT221q8MfipISOOccOPZYGurEsclyCULjtoqJvz5Uz33z70wsEuyOpcUWIeDshmCygtzf8QNacwLYpAm1rdR7ECz4B7FNuwHbLgdwVq3oe1ueFqbRI54GrEbOXyIEDEQMqxqftxNqqa5T/s2axJ8/dtwYBQC/oWClG4pa3GpGQ+6x1dGWiEaNQic5uS/vvgsVgTIoXkDd4k+o/L0DdUtVifQ3cm/jfaDj5/7Bx4j3sYsaCqBkSm7/erOH6w6Ez4aRIIDVgZ4rgIPvvZABkxZA/58TRRSeSPfMn5vD/Jcz6O/qR+EAkasX99DsrVZw8Q4pISXE0pqlAEzpP6UHW5xCe0gRwB0dKQWwXcT0GBEj7KZbQsgI4lcy8DXY9zZsaWVttjNTfhXEB7NCVhiw+2DX5zi24PNttekdo7SU0U9fwe6O3yhuFINvmtOaqFaOxHpIAI25SUJMhnkN5fCPf1C/3su7HMuv7AKAs1mT++52FehrhNUwI/ZahjMzwBtvqXjqxf2SY28CwO0QbeHqgnXYbWZw1JNjriakdOMYjhiBcrzwY3SnZVBU04wAekLtFj3E9Bj/++0ZMGmocpIAyvFc1ZjY5m2lAJZM+AHO2p8Dx/wHj1cQFpvJ+O14CHj5cbxdfx1rGYqnrhOTvqoy4ITJfMJhfDqjjikPnIjpqCM7zKkNWAQ5T8uyE9NjKObkNRYM9+7U1RgV42fMktyeWbOAcBY8spqy7x5nwcur21+B3U70wkvF6y0JYOGARLHe4Pz1sMe/SR+RHEsW9h/Mvf0P4M3M3dh7oCCAQSWIP9qzFp9Hn5nJrlfdB1MfpiRTKICesAdWrhQdjWq7F6411e7PSRUVnGcVXZHssh0+fpxPf5zF79Xd9y588YHRMGMWgVWC7JV5ytDRSbemU5jWu23yUhBIEcAdHakcwHahxlTCA36G/gsw2ZOTx075r1C8y62k2ze1mceWmJMkBWskWeIW+vh9mDGjbze6M1BV+vlh/pcDOOyF6wBId1lEPiAQ7TEBFMOCWReTf/6Vf4f//pf5j33M8bzLPZbLMaPhVLd/AhhUgpRuriHkdaGt2YivUWSY55lFmDM3Q0ws9aF67A7gmlxe6TcKKdaNakZZJmoWuVa3HXQD0zc5kiRAMUF126qOGlMJHnAJ3CJzi3Q9HlVM/FkGE0+LiW3eVjmAtoxqGDyH4uxVeH1GziTG+Y2HgBefybuVd7OC0dRWd+LcRyJk08RhfMb0w83w9tvw8ccddvQIG5W/aQPyeX3J6+Q/lAWGchYKsfUYchcwJyy8+Ja7ku0hf/0VUK3QMBxfeCBLFnYcZRk4EEZN3gR5ywGYNGA8YPQI/uwzAEb2XwGHXEPehLcSy/2wuT/M+IrIl48xMHMgFrNQwBpC7bSq7ALiDw3xEHDlW9fiHl/EI3vOhK++6tY6Fy0Sgv8HH4i/bZINyvaksuYQaicf1u1tLX27GtYdQqxBEP8yTxkAAzIHJEyzU+hdpAjgjo62Gk6mAIAW0+Csg+D83amxZifev+eTDMr/AwNWT2hbATSS4DErbFRHQtQJpdP42LMP2qbtoxPIS5zJfxrPYh2i+8bYzMmkGZXAUd3S0dJbhat4Mez8LMV20R81b5Vo/VQREZWJjQ4dF1sct+4YJ28DRLUoaOK42N+ZSbDRaGsWE/lL7lwxMdYH6xOhzcPkD5gf617I6dprxcQ4fTrYaxsTBDCCVRgFt4F46AvAapbwG9fkkKC4DgciSOq2UgCVQlGVarnoUnxeMfG6zF6hYuXkcPTIoxmRIZQeFYm6uk4oVc0eUD/9IZOHuIKVjOwwZOjQRdXtwNx8MmwZYAKzVRDGII5erchXjYcei2QUcGiwZo0OenKK3LCm44eCM8+Esx96FXZ/hLN3Opuhhflk0Yh5c5nIkwVU1QhzkkwxaIwKJc4Us2AymciyZwGGWtcDxK65jlNXSFw18SKmFoscOiUs06BmiHZ63RQNIt+Lilxbg7iebbINDHuZ8F7dN+hWjAdXi+Ev2pwAptA3SBHAHR0pBbBdaHoyzyZsSqpiVRSwnNFokaytKoAeNR/CmfDq55wb/Kh71aG9DVXlAa7iytrrKUMMjtMHHU9RTEyYKlKP1JFzp9ZyfvH5HBj7Fqw+LEYo2ELcmFgSpsDNEQptl/2oBQEUhNhqgYhXqAtFQWGH4S4UBLo+VJ/IZUKK4FPtzcqhO4nSUnZ57mKOWno3Q4ZAemUDV/7UzEOyru1uBvE+wADyug0JpU+WjXyxmNiubZUDWF06EH7+GxtXDsPvNwigyQf5+WA2c/ZOZzM5V5j1xpCob+jE2BMOs4iJvGQ6m9PPkvgnD/ETu3WoAI4fUExBgc4hY6cIAgiYrIIwBnH2aj9g95DvYM/7GNFfqHfl5RCJtFSdKsu19p+zy8pg8GAC/xO5sC6Li5k3LqORHM7kZfF5YyPSweewt/lYJg4+LrFooEEQHZNxnWbaM4Ge5+td9NAwLrz3E7K/u519B+3LdXtdx5SBEwEIY++2aLB47SIAlnhFt5JcZy4Oh6ASPTklqm4QQKs47pt9myFmojijuPsrTaFDpAjgjo5UEUi70GLJCdyhG4SloIDLeYSxLGdx8IA2FcDEoZSiBDQ3NGvjFY1sHwTQL4nBcu1hYsLJzwfZEIM1pB6NxFdnTOfpj2BwVRYma5J0WHWhgOi6TDrifb15ZWsvTsi9hagWBcNgV7aC6hMkeUCtsFhxDxwNNFMAX/kEKnehgn4Q7KIZYHk5PP44e1XexU5P7sTGcDUHlsUJoLXdnCs1psK8K2DmO3z+U1GC6Ck7jxSf2wX52VYK4OZfJ8InT/Dbl6MIBgxvO3xQmMzDstnEJK0i0eTthBIXifA+x3C2/kKiGthDZocK4Bvrp1BVK3OU5TPSbcLDScpdy5j0ckyHH97NvWsbuWO+gIOvZeJwQQBXx9P97J5E2NmsK2za1M4KQiHYsIFAoAmAnyt+ZsZ3j7Ehq9l3fvmFH2YfxHc3v4t94ZOJty0bDDsco3gr02YQwB4qgGHNgoaMbJdwWpzcfeDd7DlkMtAzH8BGTYyBPllcp8eNPo69BgkPzfDGbhavaBqqEcGIB7UaQg0w+15eOuUR7rqre6tNoWOkCOCOjlQRSLuIqio8sBkeKiNLNWadXXdlvVsMfFX5jR0rgGYFVFuCQAC9Xn3YLagqitEJRHGJ/crMUTh0/1qOl17BQ0aPQrKBoAkPGYSxIcUJ4OTJWAxCresyZmKsTMsgMmZkcsEeVAD2FZorgCZJS7SBG+gvA0nCPXInoJkCWL4nhNyMYFXXCaCi8CnTWVh2PItX1xPzNDGB33nefB63cmv7CqCmwObdYOVxbFhvTiiAG8cIsrrUL/osbzMfQL8g8paKMkIBQUoy8CYIoDfiJWJ4ar7MmXj8nVB+IxG8ZLR4y0d6hw8NsVBQqMo2W0IBtJ5/EMu8JYz7+F4Szb17AcpgYcRtPe1MANbEC5ZtXjBanklobNjQ3goULuYxnvy0ksllL/PT5p84q+Yp5jcXr1aubLMVnDcqrot4J5BeUQB1nYiRChKSfImH4Rat4Lo5Z4SN3toWS3IstAWbxGf/fqR726soyFExl+01cFcAo293IdGgPdHwKoXeRYoA7uhIhYDbRUTRwF8E3hJK9CphxTB8OKqRR4QUaVMBLLHVcLHrJo5IewEW/RXeeA+zUUEcDW4freDi4RJ0ocR8VPEkD40cwzvHfcg7nNgjAnjx+3uQhYeHTZchxf3fjj4aK0kFcCWjGb33mayY9Qp8+il8/TXJXnvbD5orgEhqggCWaDUwfDi5mUWAqBa+96B7cRm2QS7ar9ptF4rCHdxE6MMZULkLVg0WjdiMdecZ7Gn/FBraTupXYgrE858+/SChAE47aSNcMpK0Q+8Ftl0IeExMHJN+NR7CATEpZ+o+KBB5f3d9exevrhbFUJsowRfohGVOGwTQT1qHDw1T9l+L7Ub4IvA76VZxbfmjfmJ676ca+OrSoWEwWkSYPSfqdepG44oZ3VCItU8Ao1G8ZBDUsjl5zOkcNfIo+Oki7tj4BS9ylvjO+vUoK4VHp1wtpERd16mPih9LEEBDAWwKN3V/h6JRQoiCpFt/u4OGUAPrGtfRoIi8va0qgJoGb73V5kNLvOOJxZI8D3aHGIcS5tNdhaJgUcX+Hz76ECBJAKGF+JxCLyJFAHd0pIpA2kVUST6h2k1BESft1w/Z6OwhxWhTASyZcRePrbyQM8tXwYb9oHqi6IMKRH3bAdE+6CDUTLfxhxh4M9ON68CsiIm1BwTwPc+vAHyTMRyLbBDAQw5JKIBxspJoBzd9Ouy/f/Ja3I4Q1aJQ8DvWggXYLQGIiMk1nxoYM4Y0axpWSWx3SUYJRmSTCJZuEcDmnUCsGpx/tInTj1REKLC+7T62kkki0yyKlOSffkh4U5orfZC7GrNThI57agvSWQwz9QOgv24hGhTHJjuWDAHbZFvS6gQIhDpBAN1uvCNE+DEu3PlI75AArvjwI6IzvqW+sTChAAL4Iz4x3nU1R7MDrHrpH/DIOn6aJXJCE7zHWYc9cyUZls38wmTKytpZQTQqSBXimdxlcUH9CFb4DqYUkS/J+vX8vk54LH6ySdjA1AZrUQzbn9yQWD6hAPYkBByN4jcq0pHDpNvS2eeFfXjyN5EyEsbesWjwyCNw0klw9NGtPooTQKtFPBD+UvELX3q+FTZG7fRX3yoUBRM6ZjQsdrH+xnAjBMRDR4oA9g1SBHBHRzyWsD30qN3O4JIzE68dpoAggLm52A2H/jzN26YCSEYGOJ1sMCpsnU4ds9E9JDHB/5EoKEAzxcmWiSx7CLvFAvXDMDcMQkHqEQGMafGev2Yssg/cbpgwgXxTNRx5HtZDjZZe4baLaLYnjMsfx6ITZvMzu1PsMGZvc5RMPDB6NCaTCbdhN1IXrEM2i/wmtTsEsHknELOCTQNrJAtWT2eOMq1l3K8Z+mf0Z48M4a0oG1WoKHbU6x8FIFovJtptpQCqhr2PLOlEQ4JEtCCAkg0mPcmEw47hDF4iFLa1u64ESkrwDREFCPEGFL4zLhYPDu0gWDUFyvbGbs/ALts5eezJjPl5Nrtl1vCe7WT45Zce7GVLFASF1U7RRlHpXltnnAdHPSftsQfeqc+xiRJq2mvQsYUJeHOSnHh/wwYixr0Vk8Q5XVW3CkvaZu7nKu5yPwZAli0L6GEIOBIhaBLnzmSJYpNsuKwuyNjEqKGVDNp/SIfHnjffFP/Pm9fK4mnv8Y/ARWOYsM+nYtc1Bc/hxzHkUpnLzY92b3vNZn446BxKD5rCsInioTOlAPY9UgRwR0eKALYLq8mZeJ2GL0EAJeK5bOY2CUxTE7wzazmzBlohex0l094hbOS7RI88fpts+9agqckKxRxXRKhYs+8l9uV/+Csvdj1/rRlisfi6TdgkrzA4s9kYaZV4qew5Zqx5gRN5k8UL/8vgux8XLRMefxw2b+7ZTvUBnBYnEw87hwk3PMJvE/cBwOKsFbrpmDGAqGIE+GLtF0Qs4rgpWLqVAxhpRgKsGpg9g+G1T7m98aUO71HFENTMRuWvvPZo1vnHw1d3Elh0MrDtcgBro2K/VVlFDYmQqFvzJkLAdtkOOeuZYPuAGZxNpDMEEPAaYnKRiDDjC7Q//eg66Iq4f7Oy0jCZTMw8YSYjLAeyKjqcGvJ7teioyC/2c7BPELPN1WLdUvYq5gwExr0BQE1lO6pjMwXw0lkX8PHqj1sTwMpKVIMASpJYz+r61ZhcdVzFg1zgeg3oJQUwEkmEgO12HZPJJFTJCa/z0GeLuPXrfWCffdpfvkIQYY4/vpWjgMVeBfkryMoRY6dNtoFZ71kruKwsHrxmH4bu9St3fi868jT4vRDIA1IEsK+QIoA7OlIEsF00jxCl4xcE0O1GMnLZ0KU2FcCvrvqME07bi6/0Q2HCy4RGvgjTL8dS/A39LG0n8m9TLFnC1Wc8DGccDPYG3OmKIIBGJ5AYEjFf95U5PSoO3CH6F4IAFotM9oyCAZy5GE5eFqOYTUwIb8ZSWQO33QYXXwzLl/d41/oEU6bApZfyS65QoGw2I8FrtKgAjhPAT0o/wWNpAkBF7h4BjCuzkoJVA29M5K4FcXZolh2/fSWzOPZy2UFsjo6C724guvpoCGVtMwVwdlhUQJQ7/GhhoYzlaluEgDF6vwJ0pmuK34+3XhCiU04RaaO33db+15WoDkaeq9udlng/3g6ut21gokZhg9XIAaipEUQ8S6pjRT5kODYwhmXUbGjnvrLZiDqzxGs5IlTlOAE8YDrGSlEMv0HZaDm3qn4VETPctTfcOq6WiBpJVgH3RAEsKGDsiYUw5AscWYJ5u6ziXLYZ9WgOXU96Vj70EGRltfjYespfyLSkkzZE3D/NWwOiqiQqXbqIeOpD3Ai7sV4GzJjNOrm53VplCltBigDu6EgRwHbR5BcTpokYmc0I4OCcWTD1ARxZK/AGWk8i0QXC3wqzApqN7DQH7PI8StEystTtgAB+8w27fXYNIzO+B39/cjJVMWgavYB1INTY/ckxFjMmQ13DafaJXrqA0n8QX3AwH3M4mTQBELLL4BDqSU9Ux77CqrpV5JbUk1vkZ22puFec1mowmWCkqGB2O0UIWItpYPVjNfuJYe76/hx/PEqBIMu5shVFs9OgiMlc1a3tdgJZXLWYHz3CCkSSDXV68y6Y48qLLkHdyG2mAObu9iKcegT7Dv0OPSJIQ76SJIB22Q7V41i+9jI+4ghM0U6kRXz2GQ+vms6rI2/nyCNh+ur/Mu6uU2H27Da/HvAmcwyz80V+pBbTkKzi/RCOXiWAASPia7KKY97YKO6BrJgX3nmF8PM/M4UFVFe1s4K99iKyszBbRoriljOSBHDAUDCbQdcZUjAPJj1OXrE436vrV7Mx3cKNI6ZwW854QmoooQD2qAhElrn0/ho4cxoZQ1cCRl4iUF9RxRNnzufbF9e2vWx9fXI+aUN6G1R3H5dHvJxU+ABgPBAsO4HGD97hSS7s9nl5//YzYeY7KP5M1JhKwOja487VkTqRZppC15EigDs6UgSwXVT6yqBgEeb830mP+UUIKzeXye43yNn7arIzluDxtz5uSjwHThI2MNkZIpRyofwfIi/N3Ja70DZUlWlr4b3nx8D7L+LO1lspgP6G7hcFxQw/MrMew2lOKoCeooFM4wuO5GORQwcEbaakLLMd2sAsq11GfaWL+so0YmWiCCNNroEhQxLbnWv0A1ZjKlw4iSv2zWY4pV0ngGlpqEbf3q/kv/ADeyeqtNHN+Da3rej4o34iZ01l8EV2pmV9DZpEtGI0VsVItg9mQN2obaYAWvOXw8hPKMmuACMMW6B6W+YAlu3FsoX/5UXORtIsW6/HiEQ4kK85reQ7EUn+4QeYOVP0pW0DDUFjhSaN7HxRuT35mcm8vFz45/W2ArhUFtfuZrkBXQdvo9EzOuaFxsFEG8egIFPd1D7ZHTsWrAMWgrOWs4umc9oygwCqUiJ8PqHkLTjiYgaMEoVWq+pXUSdlwXM/wgvfE1WV3lEAEW0QQaRBgKEArjmYq448gc9frmH9X2+npryNQpC4+mc2w++/NzNFFHj9dbj9dvERGA8E9SPQVh/HwvFnieW6ilWrWD9vHKw8Dkm3i/C3kf/Xr1+qDVxfIUUAd3TECWCqCrgVsnJV+PvOyGfuS4ZuFIFkZ3PLXKj/N+z59eGJXqfNoRjhIKQoaDYynQ6o2JmobyC167bNJNwRdEXlcf7Oq9ETAMhxQ3FGMUMzRfWmhhlfY/ftaswDfoBxr+M214gOEIYCGB3kTnzHhQcFmet+upGL1v5T9ArZDhXA5jYwuy2bC0CGXJPI/4NkCDgegrpPupJTeKNb+/P00/DqqzDAvInfmZAwEdewsNbTdhxLjalgjmEzRdClGDQMR1ccZEWMAozaIvAWE1SCLczN+wqKOwuAptPOSbxXSCRRvjsqdxT7DRVqVxQrFhT8WytQjlec2u3U1cFz5YfwEme2S+L8BgE0W6M4rUJhdlqcYORoBnH2qvVVzKhst1vNBIOgGPHtfM0DsvgdEzqesKPdofappyDjkmkw6Dv2YAC7V0WF48Dy5ZBpKMGqEeaULKgxlbUNaxPKPcAHHyukWUXIu0cFVmVlFD3zOldY9+X08acDhgIYs+APF1JBETIqs+/7tfWyQ4bA3Lmw664weTI8/HCLjyMr1wFg84sHKptkS3glhnbaPflA2AVogTC60R7PbjW3KADpV5gigH2FFAHc0RG33kgpgK2gGpW7Ed1FdswIAcsyTXIuGxmAgozX19q2QIkXWBhG0BlOO3z0DC8s+ZofPaO25S60CS2qcTGPc5d2HQDuPImJhRM5dMAe4nMk/E3dJ4Bn7TGHv4w4jTGxUtLwJgigc2BJ4jtOycsspjF7/SG8W70nTWRtlwQwHFVECBUIR8T/2VKNkGsMxEPAcQKIHCGEE9XXRUVzzhyO/uFfnCa/SVa0htWMgF8uSnxcGWjbuDjeCs4yYhRf/ftvUD8CAJeIgKFjAr8g99vCCsazchIsOpPSMqG8IUVIz3eLsDkwuf9kzp0sDJMj2LCg4GvjQao5YqEIr3Ia79Ttw7p1cN6P53Et97ZLAO3mdPLyoKTQgdkkpimX1dWSAPaiAmgZ9xpMfozivHDSAkaKUOBsbnkj9rHNhi7vvQfjxhH2C9XO3ujjEh5Dcffj5YVjiTsZZw46kEnmfRk4fH82NG1AiSmkNQ5LrObZF9QkAdxarl5HKCtj33tu5/kbP+TEfmKcOHz44RygCpPlCDasRFnyTRspLS6XKBA57TTxd1NTi4/XNIlS6EVVP4h9le1kpYmHlVCoezYwSig5XtltUgsCaIinKfQBUgRwR0cqBNwuEj1WYxJ5mlcQQOB2yx0MYiOfcnibE1c8URtJ5ABmuuyJSSAU/eOTUVp4bR1wA+6Clj00Y0j4Pd1Xip7Sj+CVd8EVSCPD5EuEgO2DBifCzDazn1WIHLq9CkrJpmm7DAGHIsmJJRwR90quqW0FMKyGYfZd8Ov5AAQ8XSTRCxaw6vn72W3RRRyT9rHwf1t/YOLjOqUdAqgpMOsBNr32AEsa3dAgCEFdiWiv5SdNGJqzbQhg47enwvsvsfhH0YnEZPVhKuzX4juJDpSGAljX2LEaFwmonM6rnPDj1Yl8rhCOdq+Zkdpyajw2NpiHJN5zWVzgrCM7s5bMYfmJB5PegLTXv+HwSxlZEkraNTrryMssSqhb8Wu/TQJYVwfLlhExCsxq6jfy/ij4bpAYS/Q0UQw0672b+eXmORTW3MyqulUAjKhI2rGsWp0kgD0615EIHjLxxDISU8TJ405mxDzhxRjGLgjghg7M2+PFH1sQQJ9R6OQ1i/fTbencf5io3I02RbpFzKOhZp6tNnPKA3AbIUUAd3SkCGC7WLk0Ao+sxvz6e+QrngQBXN1fzEDlRVUE2hCtEjmAhgLYnADGTVD/SCjRZqQ1vYKcfjZ0XeeQaTFOt8zAQhSft/s9i6NR0eNVRSJD9yaM2ywDBieOw0ZLfxYzAYBRuYaKsB0qgC0IoGFXEjeBjiPuAxhWw1AxGWrH8hdextfUNRKtKyrvxE7k53V785vZTxkDALgy/Sme4gL8MUebFZJKTIGVx9C44HDhP2cQwPqddwLA796MOSAI2LbIA4wZgpdjvagGNlu9LWQYNaYS1kVl6SLTGGrIp6qhY7ISCiQfWnJyjPdwtB/GDYXEhdgs3uqyumC3J7jh0xncV3qcMCDvJUQtRuHTMce3MIHOzx+ESTa2wST2oc1i7miUnVmI5aFNHOi6nF98qzjuFLh9Z0Fwn1q9n7inwuL8yzKsbRRFGPZosp2ix6sS9ia7nnQXeiRKGBE6V0y+xDauqhDkMoINGxHWBQtoFb//8Ud44olkfuYWBFAz8lwdrmQ+pN3wnA7P/h4WL+7y9jZXAHfuPy7lAbiNkCKAOzpSBLBd1G72QMNwTJ4SCjSvMDQG/A6DHDkaCPhb55dMti3h2Jx7KQxFSWsYy3m7nsOAJjEBRrQ/villi1MdM5NVaGdx9WIOW57Nm1dczT3cQKCN0HZnoOs6B751HhZUPuNQsmxKQu6R+hcnCOAdudfzstHiauhRY+HDD5Mho+0ILQig4WlXqFfDqGQoP64A6uhMShsEwGA2dJlEa1GNGxrfhDfewxJyUkk/yF/C4N1nsE/uM2JC9rUmcIqmJPoVD5r3G9SLzhFTp8bggl3g1KMhKLZxW1QCD4xmAVBQKUJ9suxrMQv/UvELZ354EgAeczohnFTWdlywEA4IMi2ZtETHwCg2tGDbBHBu5XwcN8DUY5IhSocszl+8uKG3oOs6iscN/jxMujVJAB31jBgymdMc48T3TOJ6aGps47pQFDbTn6C/iIcPfZiCoBnKp/Dzl2/wL+5jXUMWc9gPpUmQLYunjjKPMCbX/IPBZDxsmCNUrhf5goFoAF3v3oNcNJAcJG749p8A+H7+niUuoULHQ8CbKIZ161ou/P77cNFF8LnoVtKaAIrxwOFIPgwnCCD2bkUC4gqghMoBQ/dNEcBthBQB3NGRIoDtwuM1krfNKul5LuKxJ0kWpM+ETqiNPqZ7f3c3Nw9Zi2fNKeQqxQzKGkSmMehtDwRQPf7k5B+6RKZbTnhn6WZBePzdTB9SYgrfhzcA8Jm8P1lpzT6UpAQBTE9PEpFzbh3AtT8cCcOHd+9H+xBKTIGCRWSmLyMaFsyjOF1JJtiRJIBN4Sb6OcQEqQP+reS1bYloOEm6LTGFEE6Y/DiX7jmPN8Yak2Mb8pHT4kQyrq8hS9dAk+hAM2FAEIp+g9zV6FGxvdtCASxRhe2K0+jNuiUBtMtJRdwUz4urbupwneExIpxttaqc8N5hifebK4PNMe+nLMKvfMP6+aIPsifs4Z3l7wDwe7VRftpNcrQllJgC/1sGD9SwaYO9hQKYO3gs+WNyKcio4yfXILEtNW2Q1mg0YfhstYI9EIFAPp6Nh/Et+2BB4Ud2p1QS5OizVe9Q7i0HINDQH6tu5IE2ldBQLc61jk5I7V5aRdiffPBJd4rz+MjcF6g7SzykxQmgjwx8Sza0XDh+jQ4S+9uCAGpaggA6mymAd867EQCvZO9eCNjosW4xif8bQ43gT4WA+xopArijI0UA24UjLBS/jKiGqSA/8b4UFJNott5EKNhGSLeoiMpwNiGcZKeLJ9N4rU1Qt/ftRncCyiCDaJkViFnIyEDYwARyidWNQEIh0M3okRpTk71+dQl3ZsshwrbvTXDYxZRklrZ4f9Wq7v1eX+OCvU7gh70uZIF1HIrRGaG4oCWJjxeBhNUwZqMVWwxzW2Jdh2gRmo+J9VhNFiibyguem3iXY9skgNOHTydbF8RTM0fBJ/L9xn35v8R39IgTNGmbKIDxFAhVE/tgk1uGgG2SDQoXk3bmsRzjeJZcaqmr3UoIePcDAIjIfuYafXABQnf/p83vV9TIsHE/IrUizeCV31+hIdwAZXvwzUX/4nTza/DPf3Z7H7eErIlrI6N8I/UVBsFz1pFbMpKHZuTy8q8LWV3cBEDT5jaerloQQB2bP5QgyQoWrERZxE5EEdeeKimUewQBrK/J41Zu4y6ux6pKNNQke2p3NwzcnACmOcT6aktjYPUjZa5nVJGXtyTxILl58RaFIPFrdOBA8X9zAhiNMmradDh/MkNGJeeczfnPwQ0OZuTs3i0FcOAwC5VTd2HVaX8lokZSRSDbCH+8nJFCz9CMAEbUCBbJkqia+/8Ok1/YEWQoWiL/DxJCIDomIsHWt0BtLXxKDIrnk+EuYlVdDZW5CtTDh9Jx3LotNr4DJNLIzCrELGRmgi5Z4Ldz0Gbfx9m80CIE1KV1tyCAZnKyW7b5+l/Ty+jhMMcve5zBHIIHoRbVL6+Gr5fBAQd0d7f6BEXpRRSdfBW1A9ey8KFdwNZEbr+WBQ3p1nQsZgtKTGGjugnoh44JX6Br9hPNFUCz0U83zWalYeb7bAzms5EYWtM82soijZMuJaaBKkKdMVsWfHetOM+SAuHsbaIA+gzyGomJfbDLnhYyjE22gbMBveQD3vW/z+7sRkN9x5N+QhSSw2DWQQqDZieoWtv8vt9QBq2yWPDLdV+CaoXZd1NfP5klWImFfugVBcMqWTGEc9JCAao3+gAbOOtwu0s4eubRNIQaIO1YAJoq29hXRUm0ghv71HA+9WVCmti3eKHMMsai6eL8WawmoQBGHdQ2pHMdQul8gKuoqjLjzHESVILCCsbV+ue2hnDQuBblEC6rGAdryy0wqAL3GWcw/9HvGeM+CRqgYl2YFt4GccI3fDhcf70oBtF1UQUeiSDnLociyMhKjg0OmwUiYaIW0INBumzcstdenHi+i+/LZvJO6YnU+/wQFsmiKQWw75BiCjs6DAJYHfNR8p8Sjn3j2D94g7YfeAwrFImWBFBOzMBmIqHWxq7/PnY+jy19AAZ8j9x/HQsrF1Kx8w2wy9NYYr3nPdZd5K1bwDHHXwEnngSaIIDNjaAVLN0uyG1OAE+MvYU7t2WV4LlrMzlvIWRHoI48+hd9C0D96jp47LHu71Rf4sQTWXnMtSxjHLhqyCwc1OJjk8mUCAMvCovE9xhm/MGuDY9KJN5OQkU3wqdpTmszGxEzDZVtXz/xynMlTkQyI/jJgq/ugW9vEOc2lLNNFMCFRnVnk2GObDe3VADtslDLwpIgiFaiNHo69iEN1YiikUFucR+aTjqVDz7UyMtr+/v+UJwAiuP1S8Uv8OsFULavWB8OSpf0jg2MroNitJ2zOiQqNoscQ5Ojnix7Fp+Wfsr3Zd+zS0x0CKqraX1zac50Yga1ly0x7N5gwt9vg2kIz3IeGxmIpovrwmKFCl8FeAaiIvPKBLh/DzBnraWyMtm1o7sKoHT4ofQbtQQGfJcwgq6sFQ9rtnRxrnKzxPbVV25x7uIKYFER3HUXXH11wgKI9HTM48Yjm2RstiQzTbQHlODVn57r1jY3bwVXWSXOvyRrZGd3a3UpdAIpArijwyCAL2ZvoDZYy4erPkz6mf0/R42vCQBFVlsQwIF5q2DSEzjzFqBF7K3MdZXflooXZoXsTLuY8EZ9CDvN2HrHg20A58znmVzzMFl5P0Awl/R0WrSCU7AQ7uYloMbUREGC0+QnLSe/xeeL5EnMYV/qyUFGI2TkptXj3i5tYF78ah55JY2cfq4gILhqyBgwrNX34mHgOIkGE7620gM6QPSif4gXkoIUFsmTmWmOBAEcxDpqN7c+MTOXziTughFVxESbkx/BYjOG55hxbkM520QBNB14A5xwMvlWEaJ0mb3QTDW1STYIp6MtOoenTedgQaFpK7ZDI56/jlf4C3fv+QkA+sj32f3js3A+cm+b3/frQgW1O3WCSpDNvs2w+EwwvD2DOFm/qneKQaKKhm5MhRaHTE2d2Jd0WxMmkwnzr+fB0wsYvVpU61bWtr7Oo5ddlXhtt5uwNwUS512zu1jPEEI46d/vQ5j4Io7semJ6DMkzDDBx5fi9+de4nfFlV1FZSY+tYIrHZbH/XffCmdMEAQwEqAiKqnRLWhTWrGGcUxR/1NdukYcZJ4Bb9AAG0M0SR3l+5y67wtR+ByXf9xbBuy9xd+PTzF/zDTWBmi5tb2kprH7ydvj8IaySldoacT4yc0MJ7plC7yNFAHd0GMlpajMSs8m76Y/amu0Km5RSyCnFU7CxhYKxy6CfsR16ETkDPoZoWivD1ajRvQFJwZ3jSigew+QlXK3/u1c7EHQLqsr138HfHrma9AWXIkktFcAIloTpcZdX3TwELCm48opafH6a9272Zw6zrVMA8PuFRYyXjO2SAH605GvqNmVTUxkjHa8ggINam3kXuIzr46jz2Pl8ExfyFP5w1zJklCwhZ6XbbRw581wAMtOSBRPTmEVtVWuiVO2vRv9XLscc6caui8m3oJ+CxW6cQ80qOoqEcvrcB1DXdWJDvoZxb2KPifsizbQFAZRtEHLDh89xhf4IFhS8/o4LMvKp4S+8xsm7bUrY7lS//yp8/HGb3w+6hCJrK85hXeM6CGdA9lq4SFTkhnAQqIvg9fZ4l1lbV5Z4bXXK1DWJ857tFGTb7O8HFbtRownfweo2qsM1DUaOD0D+EuxWMyVVQab+sJdY3pw8fKPG3wbH/hVXP0G+MsM7AVD/8evw9EKianYLAtgTM+jmreD0DRspU0dAzET5w28xdLiJf5b+DYC6hi1oQDwEnJkJa9bAr79CQGyHqsJNN8E117QcBgN+E/x+JrODp7HceyBfrP2iS9ta8/pXNP06DVYfjkWy0FBrtOLLTeW29yVSBHBHh6EANpmTd2NjqPGP2prtCrH+dXDZCFzTz22hAJ4THk34Tjj7rcMFAdyi5ZKiGROvWSEnN10QQE8xWv0o+lFBr8w6PUC938ZLnMkKRpFhFWEwm2xjQpHwtlNMFiLR7j02qzEVhnyFefiH2GQPzi0I4IZ0cay+dY3kFF4jGhbEKYQTLbT9Kc8RRagbdsXDFBYgOWqxDGmtABalG/tp1tmQM5KhrMMXaTs/rT3k58MLL8CjN1TRaORGpjfzkASoq23DeDymgN1HutxAJCpCaYX9YljjNhsxC/j6b5MQcExPqkHvO6cBkC4HweFIvO+QHRw79gigWSu4NqrpWyAS4c2xUNJ0M/WhelhzMDP0syhfFWzzgcqOyP8qyEoT7dKqJ4CabAUXwoGdCEuX9mh3AQiEkyTD4pBp9Il9daeJ7ZJlQdpVxFhb7289baalwdMf/QoXTcBhl8ip9pKzYj+xvBLiuKyvAVDM4vz7NfGw5PSPBsAkxXsfx0QI2NqzEDDffMO0VRrnF0xnbP5YNv9aRUh1g1lHqR/EOoaiGSHret8WaTCvvQbvvgvDhomc3kmTYMUKACJl1Ymv2ZIpgHi84rqJ6nbm/PgR81a2LBLbGqIeQ82VFCxmC556cQ7yLHUiD/Hrr7u0vhQ6hxQB3NFhEMCGZpNMYzhFAAEaVTFCNZgzWhDAsC2TWnJRkCGa1spXLBpLdgLJy0sTBHD+lax/ZwGvcyqxpj+WAK5tcnM2L/ENB5BpF5OUXbbzz70uA0DTLYS7aVdjl+0cNuU+Tpx4NNnWClwFLbstmGWRpLZJG8IbnAqYcKdHGMLadi09/khEjK4pMgoKFuzWuoSxdXMkCCCgG8a/XSWAmV+8xdkbb+Os/M9pMAjMxIz9GSCJycwE1Na3HnLjKRu2Y0/kHvdxYnuKTEkFMI5tEAJWYgqsPgyWH0e1V9wzGY6WxF4ySzx97KOAIEUyCsGtqKUbmrL4XD2KTeWDGZs3lonfPssDtS/yW10xPP98q++Pzx+P3Q57D5vEmoY1whtRcYJFEKcQTqxE+HpBW205uoYYUdjlaexjX0S2y3hDIu81P0uQNdkiyJlmEEBP0NZ6JbffTuSiCwGwma2gKPhJ4x88RGPUyYmhlwAI1+3EuPAggnaxLpNnKACSkb4hmSJ4POA0Cy/A7hLAr59dx423PM+Gux9irwF7sXlpI3j7k7bwr1ji+6OLa7EumtHSxH2ffeDYY4UCGLdLMsyimxPAusjmxOtQo5Gop0ugOvjmw+IubW80bDwYSVGskhV/o/jdwshGuOce0Zs4hV5HigDu6DAIoC9exkZKAYwjGI6bi8ZaEMBnImeQTy3/4xKIulqFWSJGQjhmhdxsWwvfMw0Zz+a+b8fVEeJVwP6MRpRxbyXeTxSEYyGido8A5rvy+e/CPZn5NqiyirPfgBafS5Lh0xVLHs+XLv+OtQwjLdrQrd/sSyQIoCmKggWnpaGFB2AcCQL4+6n43xHkxq90jQDy5pu89s6t7L/2Zn7b4ysAxuaNo7+ctA5q9LRWZgPBGHzwLPNeu5TygFAnBxbLWMZs4asYdPc5AVRjKnz6KLz5DqEmQWKz0lqrltZmh0ZCIxTu+Fh9UTWBF1Z9AHNvYr9B+5FtqO5BnDB7dqvvP+C8mZDTzS3cJlJa6kdAVPQCNtsayTVV8zOT+ebnih7srYBsj8BRF5J7yF+JxCyomiB4RflGi0WLuIYUw+bFH3a0XklpKeE1ooDIjoxmgtIhG1k7YjmaGTIcguB9/9V3LL13fcLeRqkX151VE+fVbRJ96KxRUfq6ZXSis/AHTNSTi9eoKK9c4wdvCWMX3IxuFiQ6aoiO9bihqqrVOnQdIW0CbNgAZ5xB5DNDiTOpqIiHz1UVm+H1dxPLpeFl4y9d65mesFCSolgkC8FGYYvUP2YQzi0q91PoHaQI4I4OY9YPmZIEsEdNxP9ECKwphCd+g29ua0EANwwXT6vled42Q8ARkjmA+e4tCaCZhs1/bK5bnADGrCHkjCTpGjsW/l70HqNZTiOZbbYd6wyiQbF/mhzFUbQFAbQLAtOcAK6rNJjndpgDuKUCmGlravN7CQJYMw515eFM4zN8ShsTfQdoCNj4LHYYcyoH0egWylRODlwydSEPcQUllOHxth5yA4EY/HYuyz/fG/wij7CkvxXLHpOTX8r/XdjA9HEIWOSAGl1J/JUAZGe23uZEezRgPlMJRzr2xwxHjXXIYdKsaThDguiEcCTCiy3g8UBDAyYlSm2wFhqGg+ICm5+8S3OYMvhObuAeVq7t+ViXqD4dMIhap+F9J4XpVyByFS02wZQUXRDAUKR1/9zS+hz+tnYt2c8tYu+cnVDMUHHmX/notOcIWCDNJgigajivVYeFeuavEbmOZuMB3moVvyWHxf3VbR9Ao0BatqhoMY3KMqMFndtDzCCA8VSXOnJJNEAOBODpp5l36xekp8MttReL9x97DF55hfADRqW/HBHFQMDrX66CZuZGN3M7ofU7oWmdN+qORsR38zGTbksn1iQI3+DIRvGFFAHsE6QI4I4OgwCGTcnwW2+3StpRYW2KQvVOWJqKWhSB+HRj0rA3ti4C0TQO5TP2LHwU6+bxFLitDMgcwBmDRd9RDZnGqj+2CERR472KVZzW5MB74Kw8nrzgeP6XfRhrGZZI3O4KdF1nj2UvYSXCWnMJZntLEiQ5xZDRpCUJ4M9r0uDll+Gpp7qxN32LqCImFotJEMAsR9sTav90ERZ2G2G+gZThizkThs6dwZKG/ryy7BP46BkimiAJZlc9+bt8wpSShylmM02B1spsOJosDNnLI4oDigvtWK1QdNkpcO7uYPVBOKvPFUCL2YJTEWRuYEioLznZra2Sxj+VVHgqKCYa7Zgsh6LGdWoJ8UvFL6xzCIIcwiFKQKMtw8wnOD4i/2p407ZGVJTGQ8BAwAJ7eUXhRm1l10h629sWhVAmciyTunrj3nLWkZcnHn7u3vkSADJChq9fNL3VZREMm6nQhmD3DuOBQRcQ0LIg6oR3XuYM9Q3ssoqMgtmoYq71l0PEhb9JbL9kFHBZbeJzc08JYETsxw+WUhZWLqSqSgdTjGC/1eiGt6KKFQlVKIBxAlhdDRdeyEN3BggE4PaNZ6MiiUIQIGTY2CBFROEZ8P0vTQCYiD9sRSGazi/LOh8RiHtojo2lk25NB48g4iO8Rj/iFAHsE6QI4I6OuAJoTk4iKQIooBmWGpJJbRH2kxNk2dRaATSbueDOkYSqpqL9fg45OSZcVhdjcsWApCLTWPPHVqYlWsGZFVy2JKHQYho6OkgKAVzdIoALKxfiMYtw1yx369ZustUIAavJAfnjb4vZ9ar9+Sn3sFbf/6OhmQOQU0qeXIaChVxX295xcQUwFhMTroaEn7QuqZpxCxekaIIAlsd+4uDwM1xyGFhQ8ARbkymnJPK9JFOUPcKrAcjLNWNSFTKGLISSBSCpEOp7BdBldeEwzJk1TZCT3Hxn62222sGcJG1qtGO34vDw8eKFHOaXil9YmS+OcxCnUKrLy1t8/6dvrqL2gw9ZUTFWEEBfkQgBAwEr7N0klCGloR+Vvspu7GkS69dY4b4m1t38DfUbjOPrrCO3YAgAWcXZuF0hTCWG8qdLrbrExIuurHIMPB42UwKKA5aczkfaSciSjosAilFQUu5bB02DAMjOhiEhsXx/3wgATCGhPnY3mhOOP6PKYZwWJ5VNooDmt71PQreID+Pt4OrIhQaDrBljxiaTyP0dnlYhzpEBv6H6IYcT3n+rShXY89/C5BuQbKKS/bufO+4P3RxxBdBqiYkUpiYx3g5qMtr+pQhgnyBFAHd0pAhgu3DWiUk9P9gyFCEvXSw+18OtFUCTiaCcwUImoSGTI9KgsBqebCoyDXV/bLGDMmKseGFWcTmShMISy4D6oaAjyEs3CGBzGxirrbX6UDx5Dhx8Nf1dyxLvefUcFlb3p3ZT7xjz9iZeuuIsZvXfiQ/041GwkJ/Ztl9dYZrIuVKNanoVCR/pLZPjt4JEN0azQlQVOUzuLBs0DKHKN43/cRFNodah0ksnXQmATVdQjOVyc4G5c7GsMqopJWWbKIAAimGDpBoEMK9fRqvv2GU7nHgSF+x/B8NYjRZ1oXfQmzc01egQI4fpZ3Unq3mzjNB7RctcvoZNk2D1kUQi+dR4myCUC9F09l9joei5N7lKfZwvOAgChSwoW9ij/c1EEHAHCg0rjZwzZz25GeKaOPq0NOr8Dp56YXOC9Ho8Lfc1SWB0aGqimgLQk/meklnHgoJm5Bc3xRoSBHDwYLgwYxbXcxcjjXzLWFCkqfRUAUQO45QdVIYyBSEFyNqA217KmyMldEx4yUSrNQigcb1viAkCNvOAZ8jAuOby8hgglcI5e8DJx2OVrCK8XO6AnDXoV5Zwwx7pDLaJa3bZqs6PB6fts4mNY3fhxbPeZ1OtJ9EFZKC2VphQp9qB9AlSBHBHh5GNHTYnB6Q/AwGMalHO+/A8bvz6xg4nlo5gaxBh3/xQS8KWaAWnm0FxtcoB/H2tAoULkfIX43IJZe1XVTS7fcN0Io31fywBbN4KLs1p5afNP3Hv9/eilU+GR9cw2KMxkcVdIi+JdTcjgHZr6+WvH1rLf3wPMDa6OvFe3E7C/8r73c477Cvs3G9n9j/xRp7130AdufRztz3k2WQbboebqCWZq+XH1aVj2FwBRBP3ZW6WHb66i8rXPucH9sYTbU0A44dMRk0UGuTkAFYrTUsugHlXgg6Es/rcB1DRFKIGSYkZ+WoFA1q363BYHDD6A6ZV3czhfArR9A7VqnhOmjvDyXBzLhhdRkLpRirBFgRQMyr4M5xmamvEcZU1J7NfUZErd+dH9khcdwtK13RzbwUGWkWo1x0IUl9mnG9nXaI7zH3f38cJb57AWnMj2IWqVV7T0gkgrgCuiZVx/sbHqCGf5tOrSddxmsPoRn4lZhXZK4ylBw2C8ws+5C5uZGS+KODTAllA9wlgqFnOpTOsURXLFxW6uglOP4ydnvo7j5/0HWEEKWyqMPY7ECCAk+qYOOdDjt8Zxgh7KU49FVkOwoD5UPIjVsnKqvpVaPUDQbWDswHsfrI0Ed5fu7bz47Z05WUMPPE3+kk38FupIOGSo4l0/KIjiaW1cp5Cz5EigDs64gqg9OfKAfxm/Tc899tz3PXdXSyqWtStdeiKmMBkc0tSIktisNYxQzQNf3MC6Pdz3mv7QdUuxHZ/BJMJ5pXP47WGf8C+t4IlQGNTtzan1zA58j15+10E+92KxWnigJcO4LqvrsOriDweFQsaEpq36wqgoiWLAA71tTZZO7b4YP7xI7wZvpCHpo8HRy1mDG+z977sFunsa9Sccx03cScNpkyK8tPa/d6AzAFEjGT9iMkiQl9dUQDjl5mkgGYl3RbBZbO18AFsaiNUGlcOLUahiuTwidvaaqXy57vgiwdBN2+TIpD1TesJG8QqhhlMGrmDilp9zyEL4hCSRSs4omk0hpraXW/YK47BZXtcwFnqWJj4MiOOOJ9Txy0RX9i8ucX3VaN61eHQUb0iHJqfEcSMjtNIQ4gZ09fyjT2zgokGxfosKFRXGCexGQH8vuw73lnxDuVrfkW2CKVsXUXL34zahUqqSxH0aEQQQK1Ze8brbqbYHYa4w4Ck4PLtBMCwPA/fhlby+GRoylsu9t8v1tfdEHD2qftD0U+QsxZno49KjBCqoUru0m8XkFRkqyCYiRaFgYBBXoXw1rj3UVSYDdukAw4gmiHCwRaTjNlk5ufNv0DjEDAIe1gmoRhu2tj5KnpNb9bIoFycV0e2EdofOLCLe59CZ5EigDs64kUg0hYKoKGa1QRq2P+l/bnqi6vaXHx7xbRh09hn4D4A/Ljpxy4vr+sQsQjZIWptGfYrym2ECTOwF38DuoTH36yow+MhZvRRM5t0vlj7Bfu+uC8U/wz73wZ2Lw2e7lms9Bb6P3otu/d7AlvhT9RQl5gkFIz/dQsWFAL1XQ/JRpspeFnW1vlvtXI/fmYS6xiC3k8Dd2liIu5qzty2wKUPzmHXvepBDoKzHnd2azITx/Cc4WA8LERMsihQ6AoBvEAUC5jMCqh2clwRkSdlEMD+bMKjtSaA9819CICYJAigzTDbxmIR6wIwxSCcRUgNCZW2j6BoChx1Lq5DzxUFCzYvaf0Htfqew+KAVYfzlfcM4acZs1Ad7yDRBk6feQRP8DcOm7iZjPoAFC3EOuIVxlfMEl/YQgGMGQRQzpLBL8hLkV2sP+5JHVcAS8s7n2vWFoIBcf9biVJV25oARioGwYtf87+r9yNHEnYpG5v54QFEr79VvJAi2KMxgwAmz310wiSKCxXSh78OY94COYTUKBTA4as+5umSNC6eMpyfswURjvhEvmF3FcDj/+GEC6bAvndiq/GIkHQzFCtOBjSB3SFatjXUGPsdCBDARabkR9dhyBC4f+VR4rORIwll7s+Dt/6DGaEfAPhuxQqIpguyO/dGPl32HJWqIGyNVZ0v0PnwYxU+eBZ+O4vN5WJ8Tc8wrGlSBLDPkCKAOzriCqCcJICB8rWQng6PPcYHKz9gzoY5PDj/QRpC259PW0fYuXBnADY0bejysoEANA1YCmkVVOS3fFofP7QcjjuLjF0eBqDR02xCVVUUoxJUMse4dc6torDCOLyPyef80Y1AQFH48HWY9sBLBCPNTGnN8fClBRmVQEPXq5UjzSpSbY7WIZyH5/dnN37mGsvNNBRlg7sUYXGMyJnbzgjgy/NnUb3BjVNuxOyoJievpN3vjnSPhF2eheudPO44hQg2Yv4uhIDzhFKya30JzP8n2WmqsMowSMDBfIkn1tpCpNY1F64s4rpRk4VXYabxm1arUNdAFEAoLlAtfRoGVmMq7PQy6WOfJ4YENg/p7nYUwC8e5IWNM/AYOXSVDe2rk3upc/gbTzFpEqTViRsooIVhscjHTVShGoipQmkKjy8Cv8j/KjTVMOoSWOgSJEnBihmNsoqeXXOfr/sWgE3ZUSoaDPNnR5PooQuYY+mwYX/WBaaSIYkxdFNFS69VhwOyi2shswxbRBUEcO5NWIx8k2gUSvrHyJt+Gpx0EtgCRGsGATB80zcsWPJfeGw15atEi8WwT/x2d891PApklax41vlQsYgqXVMMZj3AI8cdz4MPH88QyyKAZF5zMMg4ltF06Cncfbd4q1FNE/3shgxhUcY+/JP/8Phb4lqf/7sgkA5dgZXHsGLzOfyeKULGgYbW13p7WHT/l/DbuVC+J9WbxL5nG+c5RQD7DikCuKMjoQAm3wquXiYY0KWXUuZJ9rlcUduG39Z2jAGZIjdno2djl5dtbIRQv5VwVX92Pu6WFp8dYB+Nehs88oTo1dnU1IzoKEoiD8tshvmb5mPChEsvgJoxDGI93jZaQW1LrPXm8TbHU0su5ZqwSbh131tF6BGI6RasRPE3dr1aWY1pMHQW6UVf4WjDAPhbr5gs31dO562fbgFnsum7n7Rkstd2AtXIy9tH/w6XfTPZhYPb/e6I3BHiGFpDDJGX4yedYGPnSfSUKfDoo7CP8xcAcjK1FgqghkSANJRwS0VaNYUgo5J+0mYULKRnGb9psVAYMs7h5qni/3AW3kjfPYHE1UXVlcMCpoDdg9PaWrXcs2RP4vaAZsQ2Vje0Q1ZiMVAUppwHY989iAp/BTQNoH79ccxlH8oohrq6FouYVftOo8sAAOPASURBVPGbuhxIEkClXDyHGd1AgjixESHQ5KA+2JJAdgUR43yYzQrVXjGeZqT5MZnEtWN3GAVgMRs5UhMAlTUt9/WQQ+CMp++EE0/FHjYI4OKzcMiGdcyns+mfp6DEx2lVIlArFMbh62Yhm8QxNEfE/RP0CPWsu0bQtvc+5BzLFP4y6Cgq1xo9ge2N4lmtaSBrI+OppgCTVTwcN8b57IEHijZw11xDttHco4ks0ffNaiUiCXJm89ahaAqr14jrxa34ElXA1ZMmAqCEMjvdNj3UaBxPs0LVevHDhQ4jtzNFAPsMKQK4o8NiEfnhzXJkg5Hk4LS+cW3idXWgZdhie8YRrx3BrXNuBWhBYjuLxkZoNIs8GnXAFm2JzBaiuj1RpNfUPIKkKAkF0GS0Pdu1aFfsZUfC48u4zvcS3RDWehWzGnfjRN5mDcPZpIicoQsnXUi/TJG4rccs2Ih0iwAWZeewx+4n8tcJB5GR0/pzuyOZa7r6i0MgXYTu3NRhQWk1kfcafvlFsKst/OK2BtU4BDZdQXE2UVA8st3vjnCPiIuZKJIOmPDVd/73Rs99kkvCDzBOFapWTo5OjiOHvdJFd494yNJb2XJSjxsRPz3xNGYxjcxsReynVfTZhWYuRuFsPOGehTw7QjiiwaojCJceQoA0JHtDggg1x+W7X84ws9iouIlxTW07CmAkwgJ2Y0ngAJaXNzC8PMi1Lx6C98N3+Df/4hL+h16XJHC6DjKiWEaXg0kC6F+DSyFZQIIDO2EI5HcrShCHM6MBxr9Kv8LZ1IfEPmVnJs+73Sr2X9Vt5JgF+a7Z8sHglFOIvP82ALaQksijm/nPn/GRxphH/45r/BD89RNxNeZA4zD0mJmMNI1+sU3IxAmgIGt+j1D2u6sA3vuvTL66YSa7/3QLlRuNVoPphjl5utjHCDasNqFoNniNtJaBA0UbuL33JitLvOUhMyE0bDSUxbVyJSvqVqDWC0W9OOJDkgQBdPcfkKiWru7klBNvx2ySFOrKxTg2wLiPGNW1riIpdB4pArijw2JhyzacgWa5txvr1iVeV/t3DAIYiAb4pPSThOXFJu+mLq+jqYlEPpfdldnis8/qd8NJiIt5AgBvUzP5VE1WYmJY60wtnorNJiYBxWShQdtK4/s+RrxooHHwr+jOavJd+RSmFXL4yEPE5wgCGPB0PVdsSv/deOzVwfz3c3DktK5YbU4AASgQSfw/M5k7uLmVn1uvQNNg+nS47DJBAruAuAJo1RUUl4eC7PZDwOPyx8HmSfDei8hGsYa/qQvH8O67uXbW1fzn0Ldg4Fyyc8ykWdMoMYvjqBnssmlTy0nds7kQPnuYRctOo5EcclbPB7cbli7Fmi22I0kAs3re6/u33+DGG0V7ry3g8cXg9Y/wv/46ABZHU7ursRqedibE/7U17SiTkQhXcz+h17+CjfuQu6mBYNM4QJC4TRSzsjJ5j5pMEBk5gWjJUFzVvyYJYGgdrihg8+KQfNThxoQOgbxuPSTGUThwHRx/OrtOuJ2mqAhbFuYlB1VHMwUwXxbkvX4LGxjmzSNcIx6G7MGoIIB5y6gq+A1/WgCzGsU9JJPGGYsI/LcOyvYEYNKwJkyQIIByWFwbviaj7Vw3CWB1JIuNDCKg2qiqMBTnDKHWj+0n/D0j2LBZBPFu8CcnjZdfForma6+Jv5vISlgn1FsFMa11BllasxQaRS/jw38exLSwUO4cWYMgTeTvbd7ctu3Slggb5vaSrOKtFMrokKAwn2bixK7segpdQIoA7sD4/Xe47UEXL5jObPF+WE9OWk3N8v52FAWw+QQnmSQkc9cJV+PmINaqUfDc96z55OQWn1UPFVWFVRli0PV5m60/Gk20fIoZ7a7G5o1NEMAINkJd7RHby4gaBFBNrwWrj9G5owE4dfKhTO33KIeZ36OGfPzezg2+zaE3NCIZCY+u3NYVsw5nMwJoikGh8GALYDCULZL5ewVr1iSVxTlzOr2YrutoRk9khx5FsjUm8rragtPiRPINhsVn0T/aSA71+Bo7TwA3hAr4TNqXJdkyuGrIMXrJZhZ9ye3cxH4m0Ud1XVnLvqu+6lxYcDnBtbsAkBssB78frr2W6lyjYn2Q6C1MOIumcFOnt6kF1q+HU0+F/feHu+6CE09s9ZVwJHnNFFCJ3dl+uNlaKCb8+RaRq1tf306+ZCRCwLAbwRLCVd3AUpIE0EaEBXVDWy5TVoalfB31kYYkAaQKp8kCx5/Bk18+RyZeGnBDMK9baSJxRPOE1G05+ni8UaE+9S9OPvzYDQ9QTbeRLwvlz+NvOSbN8BzNrC8WM3De8wyu0wQBPPQKzqn5O7OHAIrC0Oa7WCYK3HbNFw+3FiMEHDMOv6dRBr37VcABTSh2VqdOZbWRh5gucurc6eIeiGDDamkCoCHsFA9aP/7IsreW8+WXSfXOQ6Zg5UBIEsdFModZWr1EVAADQ1iHPV38pv2/L0G6qOBds7hzD4S6ERsfKuehaxawBBgU2yRMEuOx6BR6HSkCuAPj99/h1nvszIyd3uL9Fn2Bm+WQ7CgKYGNIEMBcZy7KTQrrL1/f9XWsrScrEoPyPYkst7X4LKgKZTFm5BIFvM3i5z4fR1lfY0zhK5giQpUYkzeGy/a4AACzYiOmtlzftoaiGretpIAlwMAskSPz1PJ7+PHCy3lzn1JmcSgBb9f9Ctf+3MDu/EgeNTj7Zbb63NGsMMSeFgZXI7Z0HzdxB2WUJEs0exPNlaouKIxRLZqwp7DqChn2refOjS0UnRjcSpA0/Pg8nT+GrwaO4fdZc+CHf4FmJbtAXFc1BW+yz8A72cMiSNzvZS3Vqriim6V4GcgGCmNGOHTFCnY68l4480BcA4QPJaHsxP3RZdxyC8ycKfrsggirL21p9eO2i2pRs0khn1rsaW0TkDu/vZO5TfMB2CSLKt3G9vIlw2FCJoNQyWGcUfhxtDiPAZMI4/4WGCEICFBaX0q/8z3segFUax4IiHBqAdW4rOKhJOCQcGMcp1AOG5u6TwBDigaajB6V0YyHv0GDk/kPNx9wTeJ1nkVcD75Qy4fAKsVNVXAC+zmPZfpSJ0Fc4tqbeyNPbHqepcEhZAYFKZLQYPFZAExyibxs2RiCYqq4vxQl2aUopnf9Pt5kEWPEQxUzqGwU90AgTRyjNKfhHYs9QQAbyRJhkxdeoPGj7wDBvcAggEbvuzBiXbIpwrLNixIEcChrsRsPjBFFwuIUc03pos7drxajVeA+NWJ9uFeTG9bhyCO7uOcpdAUpArgDIx4WSqgvBkLNLGH8zZ4g60J9lJ/Vy4hXK7sd7jbzjzq1jvUedCPkJptbhmviPoAmXQw6AW+zwbxfP9KDdqxVYwkrhgKYP5a9hu4KQFR3IGtysuvDHwDPMLEtmBWQVQZkiGKZkBoSFcs2QXD93YgezVj0HiGc1EkZKFPHtfrclZacjCwu8TumQd/xPsdyHs/2TRHIgAFw/PHi9dq1CYujrSGiRcAagLQKsmJectrpA9wcBw4Vyoyui0pqfxdItKLFqyIU0GxkF9rQdZ337BvY76/gcYkHjlVVLavS7SYRdixS6xjMevopDTBVFH0UhT+AIV/jzDFIW08UwCVLWr83d26LPwca+Yo2XUFFxpXe9vkU1c2GfYpRfNTUHlm22wmlCdVdtqhUxkoITnoFSBLAtQxJVCKUrgtQ9dH7rJz3DBVqY4IA5lODyyEeSoKxKDlpxk0YdFPm7X4IeMEHE+EOha8fvNjYuSaK3cle11lpDmyySrotgsXIsw2FHWixpFoaNc691Waixsjfk7DAyqOZ1/BXyqMFqEsE2dOtAUirQpLgIOkbAMZGxTI7bZaw2fTEfunohJSuVzmHYmJ9dodOpU8QMz2tEjNmXln2LGCEgOUmABrIEcc/EKARobiNHg0XFHzAhTyVcCsPqWLMlM0RlpStBa9IqfD0X8lck8hHDutWMu0i3LyxvHMKZtR4qA2UGpW/7lXk4ICLLuryvqfQeaQI4A6MOAEMbkEAm+cEBrTk4NGXyeO9iXgIONvRvvT/+ZrPeWj+Q8K3rA3UbfaTVSfUjJJYS8XOsvg3AOK8MOhrRgAjEX5kdxaxMzgayLJnkePIwW4IGPGQ1fqNNfxRaLAbthzGxBuvlpZNVvAVgtHL1RPounLQWGeQJJNGpr11C7DcfkHIFQO9ySmIeixP9Otczhio7Flf1jYxejS8+irY7ZCZSWd9eByyg49vHMC7xf25lvvJT9t69c4uxaJnrWJY6WzZ87UjRGNxk1/RCSQ7V6bKX4Ueyoaq8Tzq+CsAa+tbEtE79rsHgJyoKEAaGmmAJ0R+qm2jmBBdNmOfw9ndJ4DNrVbilZU/tvTYbG5KrSKTntP2/eWwOGDqQ0w58xZ2l8U62r3eCgoIpQni5LBq/MbOiY88WQOZw36sZWgizF9dGYJVRxNZdzjlQR8YSnw+NUxIH8q4qruZcewUfg8MYTI/QcjdIwUwL2IUfjQZx9hVk2gNCELUDisy3rCNfoWGMhjJbJFSEzFSDWx2EzV+EWK1N6sAj2pSovo7JimAzqGHQk6VuJeOcm/gch7muNB3uLMMYtmDfsBhY8xz2E1UhQwlP62SdFs6OBrISK8nODKbsmxxzhrIEf2AmxHAoUPhqZzruJsbEhfGniM+g9MPoWTkY6zfJB5c3NSgFZnZvNeZjDu9H5fzX/KMjinVdZ17Un5o15fZmDuOEarxkJK7Cven38DI9ou2Uug5UgRwB0a7CqAxD8VMENST1Wx9aR/Rm4grgDmOHP7x+T/Y/6X9+aXil8Tn1f5qjnz9SP75xT95YdELba6jrjpEZqOYdAbpLcOSFllc9rqhAIZ8zQhiYyNVLh3cK8BZTf904Xe1rFH8fp0pm1+YxOIVq3phT7uHgN9gruaWBFDS0uDBSvjq3/yT+1nTxYpZAK/HUHzMqpgstsChEyZzxOlCbTFlivwlSTa6HSDD6tWtlukV2GzClHnTJkECOwGLZOHwsceycd3feVy/lH5ZW1+mKSrUuZDZUAC7oKIqsWahec1KdjYsr10Oy0+EJ39nlv98AMo9LVW1LTuBDHSZReL7tGlUVh0CP1+Y6AzR7SIQTWtJzo8yzH23UAX9oUhiW1RkMnLbVuAdsgMGzyVXvZ0rws+IZQPtq/URozftQKujBQFUdYkwDtYzmFitIKhNDSKXUJKDlDeKYyqbFDLxcPXQMzm15Dp+r9mL5fpoXAQg6GZjU/cVwAmauMdHV7VNAGevm83Z75/NYz89RrbbiNWGM6nwGfmuuk7EIP/Prn2Jz4YJUuWwNiOAqplI3NLHrJKRuZoHHwQ2CuJ65PCVPMwVHMMHuNONqt2o2K7udH+JxAmgLUZlzDCBTq8kw5YBe93PVR89zvT3s/itSIwlzRVAL+Jay8gAaowH3b/8BXQdp3UjDPsSZ/YyqBPkbAwrsQ0aBs4GYhlVOAhT6BSktdbTufztpc9cycBLlnHvpS+KN9yryCke3uX9TqFrSBHAHRhxAhiiZbJ+yBijglu0T/REdgwFMD7gZduz+bniZ+ZsmNOiyu/bjd8m/Mq+XPdlm+uoq1Pijh7IW4xBFiM/BoMARgPJwgBtyXIqApOgfjQ4GyhKF2rbzHX/g6kPYir5HjCxfH0fVLt2EofEPoMjz4OxbwIkcgCtluQE7CTI2m705fUZLbtspjB55a2Nw/co2YMPHzqU+npIO/oGAEKD3he/jwIrV3b5N7eKdevEv+6El/Pz+Zd+HzdzBwPztl688+ziJwHwS7JQAP2dTEHQdZSYcaGZFVBtSQJohEplI52haot1bkkAcwcaZO+yy1i68WL45EkCVUY7rlA3FUBdB6OyF4AzjcKx1asT+V0An62aDYDPIbYlK7/tKcJhSbaCc5rENRMIWdr8LpqGEhHH5gPpGBYzUfTUPepcLr21FIAIdhrKBNv2NInzLJtD1DaIdeZKdeJ+HjYMp3G7JmxgNDt1Hn+3W2BGDWFYindYSatuQQBX1a3ipcUvMfe393A7jYhKJJPNXiNcqShELWIwDuMTVbOA02ZPEsCLryASMdYvKZy7+5GMHKIkWuCtyZOYMRG+Ggxup9h/uyLGnrgbQleQNVqH3BVkpCnJNnBpVeQ4hIIZUkOUZJSAQ9zjjWQnFEC/MZ+k2VWa6lU2MJDwLfewaLGJW5ceAcCG2BCoE/Yso1mBfZh4HTEugaJMoWI2+ls7CbQFJWY8RMaMk5u7mix7Vpf3O4WuIUUAd2AkCKBumHOaxQSnSKCZwL/FfLejKICX7345kRsjPHnEk4kBq7nRa2lDaeL1spplba6jwWMmYhMDqSK3DEO4s1QY/Q7SENGGSg2mJ/J5Qr83U7AsAfpniIk3IzMG067CMfx9AFZt+uPyKc9YdQPZY57DVLgIQAzkgN2WZLoSGlVa12/vQEgzllfIktvum2syQU4OeKyGsbhFPO0HcNGlmGlnccEFIh713ntdWqwh1MDh5y5GMaq5RxfnbXUZa9zzDQsSGr5g5yvQo8ecJF4YIeCsLFhRtyJBAly6YBq+kL0FWbn/u4cB0CShumUPMhTOQw9NGgSHjDBgdxVAWYaxY8XrjAzYaSfh7RYKCVXVQJrbA4f/nZETbkBFxu3uQAGsHsemzcdSrg8CIBhuh2DPmcO/Axdzf+GD5PnXU8pwUUG+y/PsUXETh0ufAVC5QRwfr3ENytYwMb8Ig/ZTDbVt2LBEnVEIB2kYEm3ITbmnew9lkYggwKa4e8IWCqBNtsHbrzLn1mvQyg3S11wBtFqJnGvkD8oR/JrY5jSHNUkAd56CQ/LDiA9h8FeMKwsJ8heLgdXKFxP6c9aBRfx7Zzduu9gnW1QQt+6M28ff/z5cMoai/usIxAWCtErcTrFtoZCPEsWJQxbjWAM56A2NidaHJpOOK9LArvzKYDbw84ZcTj8dyn/8F9wRouy1xfCrKIwbyzJsI8fA2gOp+vYRXuU0irPF2OMNd64byFsvFMBnD6NVifzm7OJazKYUPelrpI7wDowEAYy5QId0ORkKDsutCeCOkgMIooVRmjUNt0MMWPWhtp3+SxtKE0a6CQQCNIYdbB60GmweSp0t8/WGlgTh5BOwHmoM2uGsxFO2p6JZvo3NR1GaeAq3G/YHR+sfsxsL2FDbs3ZcLy16ietmX9f1BG9dR0Kn4T5wv/k/3A43LqNTg1WygGHGaiZGXazrdjX+OAE0qWS4WjtB+yI+Flct5ufNPyc9yqxJAhj19YFLtlEcEPjfi2yafCy88UanFtvQtIFP56+BkJsMGhkzdNBWl8kdvAmuyufWURORUWkMd1IBNJlQco3czLk3Q834hAIoGQpZphFeJpLJmoY1iUVXF94Blw7nDsfFKEhkFhn3sdmM0yAldq/xENOTHMB49fHAgYLFx31Jmqm2tnQPTH6Sof/H3lmHR3Wm7/8zrpmJe0KEIMHdoZTihRqlLXWhu3X30m69226NukLdDWkpUNwLBHcJCXGfjOvvj/fMTIZMIKx9f7vLfV1cJJM5Z845c8773u/9PM/95MzBi5Lk5OgFNzqVDrbM5MDvP7DUK/wnna421B6Xi5t5m3vTv8BYd4wj5IFHLFpt839gpEpUE5eXinuvWbKMkcerWlQAV0NMDB8en8edv/8JEJ1AEpGuqT3h77aC+aFe+M3tSxL3sdJQh1EdXvxoFBo4eja1lePwKCT26TJxPKgAIji1wlwJ2kaavWKh0VMzlW5poqrc7YbsuAqYcR5ccC29S73h8HuHDqw9OgNeLmPH1tnEK8VYpHCK0O3fEwIOLjACjeL+lauaQWMjxZACB8fz5Y3X8GzOb/z5gHi2PKixVTaDzcZuuuNbsYYBScWYEXPG8i8rObjbhVqtAJ8WvEawCZJ8NsvQdu0BFX2xFd3G0pyZJOQILz+7O7ZdRVtr3myEjXegaMiGmOMkxv7fOi38r+AMAfwPRpAA+lGAV0OMMhzKdCrBJsnxCplU7eqxRVSu/ScgRABbKIAPj3gY/2N+/jb2b3x10VcEThxg9u/HQiyBXp/DQ7FM+XNRxJ9z9Rk0PQdHXpcIjiMutMpuqGmhFirdIQVQq9RCYxYmm4IcjnK8rn2VqCBCSC2v+/bK7Vzz8zW8sO4FFh5c2O79AODxsI1e/MoEXHJFKP8PoCChAIVKEDAZARr8pz+I2rFD1hpSTFsw6mNb/X1NyRp6v9ubcZ+NC78oKYBuNFTb9O2u0m03Ghv5mKtIXD+PRzafDwvbd83sHnvIBuY+XiAvp+cpt9FplWCs4bHCYWylL4d87S+kmTYNHh3/ByCHgByzORgCFgTQEwjmj8VyoE4ozYFAAK+6HhIO0SFQhkJhR56UENpnd8lwePDumNC2f5cNzJEj8J3oVMHu3XDFFeEE+xZ5m24pFLfSdw4NMiPJLQyRWyLNmEaedH/4ZeI9XrchlJoRAZeL77tCz9H7+JOhCAd6cBvh0DhW2c8jTi3ISkWF1IdX6pes1frBJkhQMtXQsSMgwynZvzjQtbCC+fsLQTweMQ3KEMdujrVHuA+oFWqQ/P9kwXySgJKSmvCY9Ne/QtrjA2DwbCxeQVoHJp5Dd8l02b1hK6VV4evcrRpYL4gv+fkh5dkXUJEgF9+vwimI5GkrgDYbPXdWMV3Xn7R6ER3wS758WeYscMZRVdGPXXQnWaMLde2or3TDK6/A3LnIunRGXlVBDIJ8dn3nDrqwjz6JQmVNQuwvRX2QbrHlaPI6hVrBOQefRWx/oTa73Qkt+sxJWLpUPCybw3ndLrs0Zsh8kLg/FPk5g38t/ucJ4FtvvUVubi5arZZ+/fqxevXq/+tDajcMhha/eAxoZSpUUrsphyqsAAbz2AAslcdEn+CWqKgQD+Rrr/2Lj7h9eGz5Y1zxwxVsKtsUGghODHvJZDLuGXoPFxVeJEI0LbFnDxZ/HPVyEUpT9oh0kpcrVZhcEBPkZM7YkDpqqZdelHlB7g9dO61SC68f4N2N+/Ejp6pB25p4toFbfrmFUXNHhTqafFj0IQDX97meaYXT2rWPENxuXuZuJvErDlt2BAG8e8jdJKnCIUur1xR9Qj4JYjwWho8ZyV0dLkKmap3TFVQbfX4ftw28TagjaisoXMRRT3UgsfX99Y+ioQEDNpwBrQgffvopfPzxKTeze+zgkyw5ZB6Ssruechu1Qjw0BqMWH0qK/e0cIh0Oxu+fza3ul4EAZrWdWkcVNfYaNIgJVuFVAwFwxHGwTqQxBHOfAM73LcQq10FSOFStUkqkKKgC/b02MMuXwwfC/gO/X+R7BRXAw+F2kU2NSjgymobawfiMdZi10UN4vVJ7cWmSsKrxS60TcZmiHpvL6mFVYCQ7m7pxEEGk0oqegs9+4/Xin1BJ41RxtQyf30fP+MEAZCUkRljA0LOnuP9U4VZwsUif54j/uxVAffIh6PwzCRrRNSkhMXKRLPo5i+P2K5TIJaJYWiNFVKqqYMIEnPUi0tDolUhrMrz1JlSSwg1zh7HAVIXeDTFu0PgJm5rn56MOhPt4JwREWDZgFwuB084BrKvj2XsfYveDc8nafZZ4zViJSWNiZPZIRuQPBIQPYJLSFM4DrPbA5Mlw9dXi4CvCBLCZGGIVVtxeca/E9n0Fes3lr7EXIxs8CI1KFyLJTid0zBHfm88Vi6+shfG50wmXXALffy9MyQMBkUMZEM9pQAYk7A+Fqs/gX4v/aQL49ddfc+edd/LII49QVFTEiBEjmDhxIiUnGLX+/wqlEtTBKJ/bgEqmQCcTLziU4ZZw8bp4MVEDTT07wbBhIV8nAF58UTyQd94JB8P5df8IqqoicssjUGuvDZGnVcdWMWLOCJ5e9XTo74sOLeLznZ9TZa0KWcGcVt7Tjh00++NCreCU8kgVY581ExkBMpzSxOeMo8kpVtlBj9ygxUoEAZQmHgU+3JZkqm2ntoJxep2sLlnN2tK12D12HB4Hn+74FICLul7U/nMKwuPBLhcTrjd3bSj/LwitKjx5BVyx4UT19sDnI3nrWSybq+DmPxA32AkIdtIwa83Mnjib/Lh8UHpglpbjqgQCyP+5/YD9ftY3dmUp5wBwCOFTxxNPtH2DSXB4HOATD4FC5kGmPXVCesAWDwvexLFJ5DfVtTeM3tRE4I47uCn5K5h2GWZTNTurRYgvyyTCYTKfWpgAO2M5UC/UILfPDYfHwNJn2OAZQ6zfDomJod2qcoUCLZO6s+CI+/tyABsaGMAmBrCJ3RRGEsAj4XaRR3YlwCfLYOtMMFZFhEJPhEZad3mQ7hOXOao6WVUjZ/a+lTBnFV6rCKF2NReilZ4xnUbcs0/5jzP4w8Fc22UpztyufOi6KJIA9ukj7j+lA/AT0LT4Pv+BEHBav+/gsvPpGvsLAKmZkXmfwvMwrOIapH7AZcE0kOZm+O03XFIqSoNPhEZVsdUcdm7GklyPDicvr/Fi/6uTDu//IbYLKoB5eWj2CUNun19FglfYywTsYuw7XQXQZ3exj67sDnSjplq6b2Iq6J3am8mdJvPQWXcBkoKqMIYIYH2tH6tVdF2cNg28xytDBNCCiZH9bNRL0aSG5FK44Fom2LbD9OlkmjKZc5EooHI6AnRKC1p4yak+0KIBwdq14t4D0eFnzx5wOHAHxHfplwUgeTeJ+vAzcAb/OvxPE8CXX36Z66+/nhtuuIGuXbvy6quvkpWVxduSB9d/AkIqoMeACgVaKRzjNGhCCqBBbcCsFWqYRemD7dvFvyCWLg3/fBqtttrC7NmQmgqTz7YTeOTRCK+xe367h6QXkxg5dyRHGo5w8bcXs6ZkDbOWz2Jd6Tog0gcwXhePUq4MhVBdXhdd3+zKqLmj2Fuzlx/3/siakjURn+/csA1PQIdi72T45De2/JQa8Xd3niBNVpVcVGz6VVRJ1hNWe9DKQwzmQRsYg9oQakIvxw/NaeyvO7UVTHFjMW6fmxh1DIsPL0b/rJ5GZyNZpizOyTun/Rc1dHJOnDJJcYmpICc2J+LPl46q5FrTd8LWwRFHhfU0fPnq6qgnBpWkcBBNAZSqHYMdZrLMYQJapxN5WRF+c/8ompv5IXA+7/JnAGpIxqKIE23N/vjjpJu2DAEr5e2zxFF4Y2DzzTTsHk0hu7H42m4dFwGPh53yzvxo6g95S4g1uNlZJQhg5wIdD/A8M3kfFR5wxoYUQJfXBcdGwpqHwacixdcQQQDL+onruzJfyq10xmJ1Wdv0v2wL/oYmttGbzQzgT7zLnqqEqAqg2ymuk05mRWYoj2oFFIQ6QyiVjSldpGMzR1UAHVZpUaJy4HUKQpmZo0KrEveZTFq0+JvT2Fy+mcWbv0JzdB/m2rJWBNCgMkDucgrf6MnmdR72Iam6/0AI2J0qzuMDr8gJ7tAhkgC2DAG7fEpMUl5cdZ1Ule5ycRuzkX2wnk6HL6feLVT5za4vGfjBQGadJRYqCo8GfBpilbGRB3BiCNgtnlmvVYzZp5sD6GwK5+GGHkVjBf3T+gOEPE2daImTG0Anxtv6+gCWT39m0SL48ccAisqyCAVwaC8bHsljNKB0ovfJST5nKlx2GTKZDJ1OnIPztxWkLl8LGnGdDh5q0R4yOxsefjj8+5o1YLfj90kHVdsFUraHcq/P4F+L/1kC6Ha72bJlC+PGjYt4fdy4caxbt+7/6KjC8Pl9VFhO3botRADdBlTI0QUEAbQnxYVyAI1qI2aNGEyagtHSbdvE/3Z7pBdYcFX6d8LrhWeeFQP6opV6Xvx4tegs3tDA7urdvLzhZUDkkuXPzo9Q0eZumwuEfQDjtHFM7zYd96Nufrr0JwBq7DXsq93HutJ1LDiwgAu/uZC3/ngrfAB+P41bhaKhb0qGI+NoXBPZexW5OD5PQIZMIwa/45VSiMfhZGjsZ2QlL0SGjBSjCOec2+lcgo4YMgJgTWNf7aktT4obiwHIic2J8DK8ecDNvLz+ZSZ9PokVxStOuZ8Q6upwSSovcm9ECPiNTW8wd9hZuF9cyivcA844yk9HAayq4rg3j2SqGKNYHJ0ASiHgBmcD1bbqEEHu5uzNI4Fn+Iwr/rkKYEMD5UROBosZK1pXLYluARSEwxtWAFXy9hGmaT3OAyDgV9KBY9h9hvblzXq93Bt4Gd7/A/ZPIc4gZ0uFKC7o1EXL9LSHuNQwGyVeQQClSvZmV3PoGHuznSSqIwjgkKm74dKp6LrNFS8ElOA2tlkU1RbqK1x4pVDtWoazqz49UgGUFPlMhag8Tfc0EjBWEaOOTgArmiuYteNZAJyJmeJFlzmqOum0SddP6cTtEcpQIGczfqVYdDXIJCVN6vn7XPX3dLoNPsm3RrSBo3dvcf/JwOG1Q1IS8Uhq0t+jADY1wbx5uL1SdbYvBfCTlx2pFA/PHk5/mThul1tGHEKRs1hkQmV2u9lFdyw1g3m8YRL1VpH/lmDWwN7z2LjtNX7iPCb4RWcdteaEwqLCQjSShZM/oCLBLvLs3DZBlk9XAXQ0h6M7m5M2ih+MlUzuNJlAIIBcqop3oiVWrg8pgNZGH7ab7xVvN4KsskL4LCIIYI9cKx6/uIcCKid5aYXIfvo5xChbEkuFy4VCK+6FI6Ut7tWCAtGH+r77xO+7d4PFgjzYXrNoJqTsJC0m7bTO+Qz+PvzPEsDa2lp8Ph8pKSkRr6ekpFBZWRl1G5fLhcViifj3L0EgwI3XfkhW90Pc+f1TPP3Ijzx19o/s/2JLq7eeqADK63PhpVLuLv2c5hYE0KQR3mKWIAHcIbo3tAz/ALB37z906EVFUF0VXkE/mngFjZ5m+Oorvt3zLQAphpRQSFohU/D4qMcBWFG8An/AH1IR4nXxyGXyiITsGpuo+kvSJ5EXJ/pGBkkWAAcP0iAx30BAMpFVRObqaVRBp2wFGq34riurPWCxUOzPRtmYhdm0i1Rjaih8XJhUSKJ0WgpJATxdAvjsmGeZVDCJK3pewZ2D72RT+SZ+PfQr2yq3nXI/Ifh8HJZJTTrl3ggFzuFxUGmtxKGS7ktHHOX1pzEpHj/O8d4rqCGZtcnRm7AHQ8AAKX9L4XCDUI+ca9/h0+aH+YQrCdT8EwmgXk9F9uCIl5p8RuZyDWzadNJN7R47qOwolRZ0ivZVJ4/ME3ltAeQo8BJwmSI8KNuEx4M7qMwqPMTHqEPE/o+6HfT7E3zbTXj94TJR3VxDo7ORz3Z+FlIpx/MbidRGEMCOXWzQZT7a+L2opFxCnLGh56C9qKyKJB3FjmShxsjlwgpGMonuJ1m6pNu9EFPVpgKoUWrwygQ5CEjG6rhMUUPAIYKodOJ0i9yuKvMvWKQ+tPU+oRTF1guif2jb+Rxc8SmbaiZDsyACyZkaMJlC95/NY4OkpIh+wGWWsvbnvDqdMHgwnHceu1+4E550QV0BGCvJiE2OeKtGqcGYGIsMP57ufYhXBC15zEJhd7txI1lwWV2iKA+IN6uhdCjFB25lLcPIk2xudspa3E/x8dCxI3ka8azl1KuIbxbPrNMiBvfTzQF0Sl6eyN1UugSJ1JsbGZE9gkWHFnHW54PE+9BilmlDBNDW7A95ABoMMigvJ4PjjOU3BrGRdLMNr5RT61c5Q+NvEC9tekbsR6YFpxO1vhGA4qooOcFBS6Jdu2D3bpwI9qiKrQatJSJv/Qz+dfifJYBBnNhrNhAItNl/9rnnnsNsNof+ZWVlRX3fP4rGXcf57OsL8JUO47Vps5j17AU8tvwCul7Zncfui7TAOFEBdGy/BJozWVdzNoe9YsVpUIVDwE3Bxa3kQB8K/wTVnn+wk8NPy6TBTSapbAfP4+2+cliyhO/3fg/AX8/5K0uuXMLtA2/n18t/5c7BdyKXyTlYf5D9tftDzc+jtYILKoZJhqRQ+PNo49HwGzZuDLUyim+UeqzKIzul6A5LeY5+JVqN2F9llR8OH6aYXFYxil2JmlaDkE4VnFwC4Ixnd/lhToVgWConNof0mHQWzljIpxd8ilapJTdWELmjDUdPtotIuN1UIoW05d6IELBWqQWPBqdLYvk+LccqTyMEXFKCRyGFq5TRJ9JgCDiIYA5i1TExsTvRU3b4n9gPODmZGkOHiJdqSOJ3xojVxkkwoeMExuU8y/J0M4O0rRdP0dBS9JTjB5c5wneyTXg8uCQSgMyHJ8ZKWXMZepWeVF0W1OdS0m26NNHJwWVifel63t78Nmq32E6NW9huJIQT4DUPzwLApYA4JHLliGtX/mlLnEgAa/wJIocyW1KQpXHAUyHIuwIfGKraNOPVKXWQsxym3MC1/aQUDHcM9bbWVlOOAaK/MkoHdo8ItyaY9KGUihe7ifN325PJic3BWTkYdl5BbVOXkNVIdh9xTeK0cfSPHYd8zmdMjV/DWMUyAGSOJHwBX/tzXr/9NmR/E2dRgF9NZ1cZmEsjPACDWLo1Hp9fzsXP9MasPsEM2u3GhXjmnFbx3MTqnOjVmlAusRs1Hp9YTFrUtnArvvPPB5mMfulwA+9zlXMeCU1HpH3pwKf4+xVAlYNqt7jeA3NTUSlUUi6zHbnGgjFGjnrI8DABdMpCXaWMRihpPk685ihX8SkX8QNyh40BfW+D6RdC0i7yYiMJ4EbFS3BbAR8aJ4HDgV4viOvxYGGd1wurVon0jXHjYP580fJw927WMpT5TEaRLoSJNOMZBfDfgf9ZApiYmIhCoWil9lVXV7dSBYN46KGHaGpqCv0rLf3XdIOI7ZHFyj8vIVklBmWFoRzSthDwa3jqlfMY/fQD+Pw+AgFCrvh4DKgCclwVPUL7OewUpppGhQ6zSpChUAg4WOhySPIjmzBB/F9f/w/lcM1bISpdOxe8jEFRD/ZkXk8byr5dK9hVvQulXMnUzlMZ0WEEr018jbH5Y4nVxtI7tTcg2i6BIDNapTDMvfDrCxn98Wg8Pk9o4ks2JIfIT6W1Muynt3IltQgFJd4iVrMdVJEqhkYt3fZ+NXqV2F9dLXD4sNjWVALmYuGZJaHOXoc9XbDnbxGVu3uOtu6UcSKKm4rFMZg7tPpbpkkoI+XN5eyu3t0+VaemBg9BKdJDsiGsVmiVWvjme365aQ738AIAx8pOfYwhHDuGT0roV6qjVzhrlVruH3p/6Pfg9+aVKhcL2M++A//cYcVSJyZRhZSb+BDPs46hBI4fh5q2r1nH+I44D05me8nNlOT0a9dnlVnDiqkcPzhjKT1dBVAWYAeCnE7vNh1fYzbMPsLsr+eG3++M48ofr6S8uRyjLBYADS7MGneLyi6oaO4C26+gvnZYuOLVGUuN/fQUwKr6yHB+bUZv0YLkhDxAe6V4HhR4wVhJnDZ6P26tUgvJe6Hfh5w179rQ65X1rdWeYAMXpcqD1SEWDMmx4WreBqNQrOwBIwMSzsLvFYOaPCB1xMBOwiBR/JNlzmLRFb9RuWcs8x3nECORSLXkmdfuMPAvouCDrl3pUiWu98CmGjC1JoDVtmru+O1W7vrtTgDM2mA+pmQG7XZjk4mB9aG8BUCAJJNLqh6WjKBR43ZKiyuFB379FV5/Hd54A4De+c28z43cz4vE21rcb86401cAJRKK0onFKcadyQNF+z2dSgeJB8j+ay/2W9JIvPleZDpB2htkqpACiKqZ3Bk1PHLNehZzDsu63gy9ehGXtAIKf8QfU9tKAdTqfZBwCLO6EhwOTDHi+6tolsaDsjIYNQq6dIGUFDj3XGFFVFXFpGFnMWXWEpyj7gYgPz7/tM75DP4+/M8SQLVaTb9+/VhyQh7RkiVLGDp0aNRtNBoNJpMp4t+/CoNfnUH5t3spvedV3GvrqCxKJj9/BaQXkZ3rQ1G0jYc7fsOWNQ6S0haCR40qIMdZE26eXWoXD70hoMIsSexBBfBAczHTvpnGbyXLxQs9e0KG1G7qFJXAgUCAZ1c/y80Lbw4VA+DxELhxJvuLxEB4QfNGpmZsA6BiyxOc5X8Ztl7H2blnR1X2hmUNAwgVggTtXzQKDT/u+5EVxStodDaGJr5kQzLxuvhQjlIoTLd8eYgA+iXRI2ilEYRSHb7tDWox4dVX+uHIEVHRaMmG9fdGKMGH6g+xN+VZYoa+F5qIj5d7T2munW3KpmdKTzoldGr1t6DCuKpkFd3f7k7hW4VUWU+R93nsGHnGNTDhduTpOyLc8nUqXciLS4+YGMuq22/JEjhWgkyyPUltrIrq5yeTyfjr2L+Gjn1w5mBkyHCqxXW4ks/YXBrdO+7vQlMTzRZxHEFyCtBAPNUkh1MZosDn97EqMIxbeZPGcy5p18f9eOCb0M8yAuDVcbSqHapSSwWQACX+3WgUGh4b+Rg6qUOLz6uMIHHBPL7CuN4AKPESZ4rMN9xSfQ78+CnVB2+IJICnGQKuzR8U+XufsRAT06oS+JNmUVhzLN6NzNR2CFgmk6GV0jiceFHIxf1WVdPa2NwhvTRQHout6HYAUuMNMOwFVOfdBhmb0coFySmUD8PvE5XCCqmPeRalyPqG+wcHO4EAyNWC2CocQiFsdyFIsDBt9mzceikvEaIqgFa3lTf/eJMPtrwHR49i1kv5pC4zZc1l4ruXCGCztgmQkWj2RlQPb+uSjsskjlGu9ELXrnDrraGTaZJ7+L4r/NwZlPgwm6QKd3vCaSuAsu7dUCQcgrgjBCQF9ZKzzgIk5RbhTgCiwCUxQTzzTQpNSAG0+Mrxy6EypZpP44eyavqbMGYMzpFibrSpaE0AlWJycSkAp5O4WEFEaxyS6hAUTDIzReqBhPrFmzmqyBRqqbkYo9oYsfg+g38d/mcJIMDdd9/NBx98wEcffcTevXu56667KCkp4c9//vP/9aEBoDjvXDL/difyXj1IScli+/az2LzazCvnPwjXX8/UI6/gQEdNxWTktV2p8TbhsYXDRzUuUZ1n9CsxS8m7QQJ4X/8Gvt/7PeebfxUDX16eSNCFyDBwc3NElSDAz/t/5pFlj/D25rd5fs3z4sV33mHX9x/jqREK5BVNu5l+tzS5FJ9N1eFrYN6H9PfdGvVch2aJgeVg/UFcj7q4se+NDHp3OD9tXxbKXwwWHoDIAZTJZJFh4JISOHqUWplQxRwS8fOrIidVrU6GIncRdJqPUSuIS1ONDA4fpgPSBCL3RAxCRrURhryG+twHyKNYvGjJjCjsiIa/jv0r2/+8nfEdx7OudF2EoXVwogmeU629NmQR0xZ8u/cx13AeqgGvo0mKVKa0Sm2IAPqlR7uivv3Vok1H6pBJHZT1bqvoFhEFXr+XSqtQzvPi8gQZlMygvSh53epqt0fiqRD47nsswRZj6mYKCyU/YGA33U66WPnl0C/giAOVjbiUnHZ9nk4TVsqCiuOR4+0ItxYU4EkPF+Sga+CuwXeRG5eLViO+C59HQQriusX4xXs7JXTiUJN4TYmX+NhIaxuNFJL3BjThELAz7rQVwBiznC7spZNJpAQUF4vo48tlEjGWnnFz7AYYey99kj7HlNR00nZcGkcGHBrHGvdAdArxHNXWtA7/F/70LM8rHuEa2VxhAg2kJeqh23dk5LzBLcWVZCAWPh3s3fBJldde6fbrQAn0CRPAlm4+fkkt9dljgXYqgFVV4gLIZDBwIO74IOGTgak0QlUHyQZm083YP/2Mn6Z9hskgfUdBBXDCBFwZIp1DIaW+JCX4IxRAe1YH4uItkPs72uTWaTZHU2OYNtXM9WMFGU0wSyqeI+G0q4C7j0rAcG8/uGEoePQoVBaykkUKUKiHs8cBLhc4HGSmiOvtlKtCuXgeedCqZQLUd+LzzwGZjIm6JWj2XoPPp29FAJXOFFj6DK/anwKHg6QksfCpc0lCSZAABlOnFi6EW27h9wPpBI6cA0ufAaWTgviCNtOwzuCfi/9pAnjJJZfw6quv8uSTT9K7d29WrVrFL7/8QocOrcN1/z/AYIB+HQqJNyTC3LkMuiSXizNfBMC/5lE2rj8b7+SboPOPMOYh6rTiITL45Ji94mFsSjaDwcByqY7AqfBTZQRycqCTUKn+OLiSZ1c/S9OuLSJXpaAA5s4NHceXu8JN5edunysm+3fe4fPU7uBXo9Q2Ubj+G869pQPDz44cvI79Pj7quQUVwG2V29hwfAN/+f0ZNj3+BtMGjERbJuxS6h31aBQa0oxpoRyRIAEsbiwWOSVATaogoSXJFpB5KVZETpaGGDmm6RNhxlTizKIS0VKnhH37Qrk8KNwRlWhBJcTqtHAtc8SLjR3YWLYx6vm0hNvnZsScEQz7aBi5r+Xy6oZXmVM0h2t+uib0noJ4Qb4XHFhw0n01V1gZchz2PJXPpd0ui/ibTqkL5VUF1bIaS/sf8ZpiG0gEUC1rmzgerDsYytNMNiQzNm9sqB2cByXlTdmsLvknGapbrfzKeHLGXAL3pHGncjSf1Y0ngVr2UBhOYYiCd/54B+xJ4DEQm2Zo830toVVq4I5cJpybSRwirH2sqh0tFGNjUailHr4/zQVtAzP7zQRArxXPXiAgpyt7AHi25/O8MfENHhnxCJUjrqHH+b05nx+JT4z8vvQK6fvwaf4hBfC65AXspZAPzhf315498PPPcM/Cs1nFiBABVOu2wbCX6BG7gMTUkxfOKCqGwGe/8UzjX9FLBLCurrXdTmftMR7wPcv5CvHZZp2LOKP4PlJscMceE2lKsTDS1ybh8QuSss4kCEaWrlb4SgX392ZBeKGjCOYPmsAvCxUlnRQbpWe2sBBMJjZI33ODuQljcn0rY3m1Qg0VfQnsv5A9jamYYyQCGFQAAYPRC9oG5IjnJilJpCCY9OJcjIp4RmQsgqvPIXV0a5uxvd5B8NdGGj4TC8oEg3Tt/w4FEMKt4PDoiTOGowpapRZ8SiwffMMo7Qas519BXlosAL6Aksv5Au+QEcReNgMA3fJHAPC6vARqarn5Ri2ur+eAy9TKgkrljYc1D/O5417o1InUdHHuFnesyDc9kQA+/TS89RYxWOH4UGGFJPMzIH3AaZ/vGfx9+J8mgAA333wzxcXFuFwutmzZwsiRI/+vD6l96N0b+VdfkDvmKv4kf128Nv99+OEL2H8BDH4F+zWTwKvC6JVjdomJpMmoxNUhg+YWY9yROEIE0K2ASXzOI8se4cHPrxVtfAIBuPdesNkIBAIRtiXHLcc5tHcN7NnDbzrhMJ/drR5Zzx4olbBqaQwv/e0uuk4QJG7ZUnXUTmFZ5iwyTZn4Aj4mfj4RZAHo9z6o7FjXiByjBkcDT4x+gvJ7ynlg+AMA3DHoDr69+FsmFUzC//VXANRmis4f6mnT4HEVY2ecoEoolex5E6pf15GvFav95iY9bN0aquZD4YkoAjGqjeAy4LKm0FG2W7zYmMPKYyvb/Ir8AT+BQICPt33MpjJRsdrsbuau3+7iunnXhSYrrVLLh1NFd5CiyqIQuYqGpmonGxjEegaSri2I+FuCPoFEgxh0vRIBtDabQ+Gek8JqpbrSB9p6SC0iXV3c5ltf3fAqIML0CrmCbsndQgqgBxXUduHzHZ+f+jPbAVlTI8kpyyge8Q0cmMKNO5Yzq+EeEqgTBPAkCmBVfWWoE0jWdy+36/PUCjXEFaO4oDNLlaMBKKu1t2vbW6aUYpZXg1dPcrI8pJDodeHQtVmqnDVY47ll4C2o5CowHyfRvJ04Gok7ofVanrQgGWXLiCgCOV0FkE2bWNAJLuzwIDcOHUad38x4FgHwATcIAhgI0OgUD+dc+QziDW17AAL0ShFSrM+vxqiQWik2Rm8Fd/6lMGH8PkjeRVqCB7VcDbWdqK4ag8NXSKqkxFeXelH6JMVIimbkZkQuRuod9SBZyPgkshYIKMBlZnf17lNfi2D4d7CoLvdKxRmyACRntlbbWnYCsXtkJMRJz6cjXiiAwGdLdsKD8SjjhbqXmKokJzYHV0BcF1OtF89xodir5K3tlXRqcQwBn/hbgt4e+ozTzQH0797FVG0vkmpTwB1DB3N4e51SB3IvgcPjWMUo7E45nTPFGLheNgRuuw3Z/XdT5he53I5mIYa4SqvxzrgKv5RXkxobF1ITgwgqs26/hsDV15DZIVZcM2+CyCtvSQB9PtgvfFSzkF6XeUHhY1TOqNM63zP4+/E/TwD/0+FPSsHmN3M7rwmbCLkbknYSc3gI43ckkl6azZalA3jp+Tth32T26xWU5CbD5pmwV3ieHY1D5GUUFLAsF2ol09PPFLtwBx1d6urgnXcoby6n2laNQqZgYIYgfMuWf4RPBnvcwkJj5LDwACeTwd0X3s7WRWvQY6OiItJ2sCXG5I4BxOpVpvAxckAiOONwFvcGoncDGZM3hmmF0/hl0esYRq5h1hgZtWYRem6Wcv1UvfpEbqRQkGqFJKufDllCtXE0x+CwesN5Zgp3yOMOJAK45EV4uZyvFFLYrDGHFcUrsLqtUc9n6ZGlxDwXw6PLHwXgqdFP8er4V0mPSadrYleePftZjt91HMcjDgZnDkaj0GBxWU5aFWyp83Aln3IVXyCr7hHxt8GZg7m6YCJAyPMNS+ap8woB9u7lkCITnfkAfc7ry/0Jj7b51sfPepw7B93JLzNEIn2cNg7UNmQyr9APLdl8u/2X0zYrjopjx9gWFH80YjKtIwEzTeyjy0kJYE19EwTEDaw3KNp8X0sE1R+XSo5WIchMZYP31CHtkhJusb3AOYic4q4dwlYuZ+WFc4qNkkLbUC2ujcMrft/pGcg0viM+LVJ9Ukn+cB6FtgUBjD99AlhUxItDIT4QR1pTA7FYuPdGQQxWMkp4Nx44QK09C44P5Ah5UXN1W+Ivw+8RP/g0xCulVopRFOfyRj1rFX3ZajCD3ENqaoAmVxOxix/i6Pyl/GKZQqpRPEOVFX4ydNLCplos5Aq7Rl57vUofKiBxyXQYsIauy56aPSddQAGtCKAsYxPkLkUXcJOZ01r1VCvUoVCuwysLu/TYEwUBXLIE10NSYZRHfH9JmRpKmkpwdf2Yt/I78snmQchz80iQG4mLa13hqpWsqgJSqk68KnhOQgE8nZSKRbMPc+j+D+n94SvgMtE5JRxONaqNTO0yFXmLtm0DC8R4ecDbi0DfvtSOHYYLL7IAIR9GCyZcB8MpJ2mxre+NIAEMBGR4PJCbKcZWpzsRqquhXDKEzsgQ1cBSj+BgvjJKFzqljqmdp7b7XM/gH8MZAvgfDoMBPuNKslPmY5EZuNj/I/jVLPrBzoJ5VUz/eSIffDidiuKu8NUCtny4hUFxRth0O3z9Exw9i6PZJlCrsWV2ZlNqi16y224kzm/hyQmSMfZf/sLWq8YCUOiMYVK+qBxefmwF21LBXS4G1AvHnjDA5eSgTYxhFEIt+/336OdyU/+bwS1WlT1TevLEjCmAH39jJliTo3qMEQhgm/033l71Mk4VPD0iQKVNGiylVnAK+QmTv8FAgrIJrcdCTH4hAG5nIhWkERpm5Z4Ik2W1Qo1cIwZlq0ryrLJ0xO1z89uh36Kez7HGY9g8tlC47uLCi7lj8B2U3V3Gnlv28NCIh8gwCZKpUqhClW8nC2NZG7xYFWKSKKpu7YOnM4hH2tOCAAbz9U6KoiL2qrPJ/PE5tr4Lg2vabpuWHpPOKxNeYVCmKCyI08XB2PsZfI2KpxHEseF4AkuOLCEQCPDO5nd4YMkD0b+/U6DqQBPHD86k67w7QCfChPXEhwng4cNCTYgCiy38ukbXvqFOo9DA8sfZ88mNmGRi0nfZdafuv7ttG9vnvY/tvDtg1BP0LwjfO2M7nRX62SRZiNRUimNzeByw9Vpqd9zBcs4mKSvyuqukrjUefawwQwawpZxeCNjv50b/W6xZuIMDh7qRXC2sQUb0bkahgBI6UEY6LFxIefEM+GAjlA4PFWK1BY1BLJbcqEmUCEtzc2uiPefAMGo/3wIrHwePnuR0JfMPzEctFY44PSrSpFSMyioZeyY8x5H8flxRJ0K1hYMilUiDKtyVxxGbFvICVDhTsHlsJ/dt9PnCHWSCBHDSrXD1WBJVxWQmmVtt0rITiMMrIzFFOkd7ImWWMgIHD+JaK8a2gNTRIilLS1FFEWgtkF1FErUsL38V/yvNjKlr3WhAt1+kBiARwARlo/QZCXj93nBItx2orleyg15UekSeT4/O4XtKp9Lx86U/Y5LMqJ1OGNFNItweI0/8nMAt1yTyxrpXmbmkI1whFpQ2jNhrwgVlSVEKIFfcsCj0s9MRID8jVpySIxFbeXG4BVxiYihdBwjlHaJ0cl7n807afvAM/rk4QwD/w2E0Asi4N+Vqzp9+N99yCehreT7/Jrb6+/Na42uAjEBACm02Z9Lw41y45HwYPQuqelKUqWTJShvJIzrx8vYd4DKCVwWLX8IeiOHxRUOoyB0KVitr68pg5aMkLRvOWfvEoLhCVsKclD5Q1xmZwsvwYSdMAlKy9dkIz65ly6Kfy89vDYSdVwCQvu9pLPv7gloMfPL6fByPPcSQx9IZ+dEIjluOi9D09ddjuOM+Ju0Pr/orfCIMJFv8Anz1A0e3nnA8CQk0K3S4/GqUnUUCtN+axjF5C98/laNVJZpWJwZAi1waoBqzIUDI4PpEBE2gAwQoTCqkc2LnqO8LIhgyPJkCWOcI4JLsRsrtrRPee/eVc7l5Pl1iSoEAWDLbbge3cydcdRU8+igsWMBhRZboVAHIovQBbgux2liQ+2nSgRoPcnxQ14kvd33JV7u+4qaFN/HCuhe4Yf4N7d5nEPtKDTxqf4/qrQ+H/MpqSSCWRipIp8mthePHo25rb5GOptGfhgK4+c+UL72YngFpUnbGntoM2uNhjbaQRelJkP8bA/LDCfIyGdwe+wl38xJJ0j1UXSWWGg6vA7bcCLtmYMSCKjUhYreuicMBWB+oIVUqIKE5jSpbO1TdIKqq2CfviL+mB3j0zKu9l6v4GEu9N7Kg5qefQspxSqCqTQuYIDRG8V6XKYkYtbhvbHZNq/c53dI0o3SCx0BcuoKf9v2EXyLDDo+S1AShiFbWqtCX7if38FYMONBjo+PoSL9Vg9oAN/dg/t5fGfrclBABzFQJxfCkYeA9e8BqFRXQXbsSCATwyMXY8aV5CKmG1h6AcpkcmVIcn92nIDFb8t6yJ+LwOrBZLdxXtoKYOctQlPcGIDFZztrStQDcM0waN2wKGhrAHaUroVYnjc8+FT4ZJMjEYknuFArc6Si+Doe4txRSuLZwZOu+ulqNeI/TKQyr5RoLXdjL+i1KvvtOTt2xJIxVuZC9NrRNrV0K+SpcZMVmtNqn2RAmms7pV5GXKZFERwJ7S7fBzJkwa5ZwnNgcLp4L5l0rFS4mFUxq93mewT+OMwTwPxzG4GLJFYPHFit+1tVRnqNlOWezlmE8x4P8wkTWMRiVpgZsKfD9lzDiWRg8mx8MSu68243dLqOpuRA23UKXzaPAE06c//GqH2HaND6u+hqWP8XyjT/T/Nca1JZOVH21nDe3bQWg5/CSaA0kIgjgypXwySfCgeKBBwSPs1rh1VcBbQM4Y/j1tXM5b6oc3OIECxbcyZ1LmtmgqGB16Rqh1HzzDcyZA3I5t0x9isEZYkVf6xdhQdnR0bDvAuyrW3fs8MkkGwRTMFnayObOk0miivzkH8mM24xJG7nKvTijNwABr3jd49KDI54FBxaEfAgtLkuodVjQAxDggi4XRP3+5m6by+QvJvNR0UdhY+jGtglguU+GNyAmXp0mkqSVWcp40NqPjU/dTZeHLgJkbSuAFguMHw+ffipaM82fz2FZHjUkkcchnuPBNo/hRGSaMpmUP4ExaUP5RHa1sE9p6sCPe3/k1Y2vht73w94fOFzfjiT9lodZL4iFEh80C4JuxUSiXlTm7qNL6242Ejz+8PCm1LXOu4qG7sndiZUqEHNl0vfgjA0l+7cJj4f7S9fBm3vBkkHHpHAhWbOrmZu7PM1tsfeSFdMIQHWt+AyHxxHKUxzD7xFdQAD6DfTAhTOwDL6PZLOkwFjTqHfUty+3E2D/furlkoqmbmalYgSfchVVlYFQQ4bddIPVqzE1CALay1ZxSgL44GoR9myWK4mV5n6HQ9cqXGn1tCCAbgMNygPYPDb8RomEeJWkJgsSVmLz0qXTYvrdCDa5mgH8gapn14j9iRCwE6ffFtEOLlUuTmZndRs5JiB6zwIMHAgKBR5/OE2hMb4pqgk0wN2dLpZOQUlirnQtnXHgU1Lb1MA21yiaj43G+PNsQBSBHK4/DDWdcS17jtnchvuouIfU/tbfmy5IAP0qPApI8AvCp3aLaEqtvf3ddY64xH2yp0AsELuOiEIA1eJ6O5ziPjQZ67iaj0kuFZ9jsFXT7MwS35nURrEGoRyjdLYqAAGx0NFIjgvOZk/4VvZp2Fx2BGbMgCefFMWGRUVYpYrwoAKYqtZwZa8r232eZ/CP4wwB/A9HSIl3x+C2SQO2vhZjegmP8jTLOJsB/EFzWhLDWYvHlQQEIADKg+PILkumx5Jr2bO1xWC/7zwSdowPVdoB/LolmeOvfEvlQRH2DSBnxrFXkH+wBEqkwpmE/bz2StjENgJDhtCL7STI6mhuhquvFvP2Cy+IasRvv5X8wnT1UCeUspb+fQcbx1J30WTxS21Hvnqwkvkz5zGPKTBrFpm3P0rXJDFRuPSCZATzafSa1sckU0jhQVkAmV4oCOv73MgSJtBZs5FRFy5tFYoYlyPCxQ6fiTREPkuqdwg2j41fD/3K70d+J+GFBEbcG4/PZOTIDqlAxKdkgO7SqJflUP0hfjn4C1srtoYI4JGG6IQGm40N6o44JK+uYAP5IBRyBYfqD3Go/hAZfaTB2pJJhaX8xD3Bl1+K9l9arZitgKP+PlT1nc9R8im9bGb0Y4iCTgmdeLDDr5RsXsu76lvxoSTGWojNY2NA+gCmd5tO10Tx3fyw94d27xefD4tdkFybzgm7wl5+co1Q5NokgI2NIpyvdKDFjizKPRANeXF5xEnWJ+rgPeKMPXWHCY8nRMxP7NE8b/88ukw4yMwpEB8jCG11g3iv2+cO9QKezjetCGDHPBX0/BJyV5CYLX3fUs/cYAHCKXHoEBaZRFo0zThjxCTfVO+LJIBAYon4nlIdHpIMSSfdrU8uFk8et5wUnfSsukytwuXWOIlUKR3gMXDYLVSleqkPt82nJCdLWjQ5lOxf/BpFW97C4o9nlHl7i1WuQLAbjc1tg8TEkAKYphDnEFTeomKpMJpntCjwcfvc8NoheL4eFM42e9CmpIrXPZ16EJcr2sIB4IinoSlcZBH0IE1Kgn11+6AhD/+6B/iEqzhsF+e77PC8Vvs3ScVbcq8KpR8SPGLRpggqgKcR8re6pO9C4cKoaSS/Y+Q4kfNqDsXeYiBs0p0aZ8WINWQEvTjhCEW5DSADRc8vuYH38YUM6F2tuoAAvL7xdfwKcU+47D70elBKofqtVS0M6Q8dAquVXer+WIgJEUCjrv1RhzP45+AMAfwPR0wwPcYVg8sm5a/oa4nrsgUvKh7lGS43fsugTkfxa4LFCjJGp75E6debOPZ+NdN2iAlIjh+StsGV41g7bCNceDnclg/Ju/j9d3jvY8kOI2U7aYYGmjHhtGRDzHG4pQvDXriBUX0yox/o6NEokhK4MfBuqz+9+qoQ8gBidUehVvgXerzhgcvvjuPzy28Rv8z/gNvf6MHU5s95Qvc8PPwwQIhAEVsM2gb0LimhOtQuRYLHg0xahTsbm9HEi8F1+1Y1O+nJL+lpKAtah2vNSeI6NfpNIb/AAXqhDHyz+xueWf0MXr+X9WYLi1Jt7JAGfPW3v3D+0O7cfbcQHu6/P+yxHKw0LmsuIzcuugJo99j5YOsH7Ni3klWGQrxSOF+jjnx8tUqtcLP1qjF1SwT84Irl6KFI9aDJ2UTFF9L38MwzsH8/jd8sptGeGsqt0p5ALk+FqipB5KsRYfMUq2hDuL9uP19P+5ob+orw74pjK9q/08OHaZZMga0diqDDSoxSsYFLsp3ZS9dWPpUATU89Cvsu4KqeY6lRGkDTOjTZFoLEL7QAaacC6AsSQIWHRH2YyGmUGrAlYokfiDJdTOjVFjHpPXX2U6S6xPeuwdWKAGqeeDr0c1yedA7uGHAZ2t/27NAhmgkrgAS9LxsDrQhg0KdPpnCesh1XXIIXxt/J1Mt+ICloW+IytQpPN/foL35QuMCnZqdNygGRCjmax55Lbp6436z4oeh6AltuwoGOKd1ak/uuiV3J2vYC709I4Pepr4UIYKJXkJI1JWuiF4J4PLBcMr4fIwrOAoEAcnsCOOPoJNvVpgJ4x6Mm7HaYs6UnipTEkOqIPZEGS5gAuhD3q95sZ3/t/lDxiAs1FqV4bqt9rX0l42I1XMqXXK76FoUfElyC3MscIg/zdELA1mAIWO5mQKeqlp7LAKK/ucqORuHEO0AU7uUngwFbyAh6cV49xTlikeU7/2rekd1IX7aiO/9imHwz+QmtO3WsLV2L59qhPNizKx08wp4pRi+e091NTli/nsC+/dz3kIJrmMOe5FGcx8/kyvazi6789Go7Ou6cwT8VZwjgfzhCBNAdg7MFAQyYaqDnJ4CfB/t+S0pdLQwRVhh3a59kWdHXpPrrKSGLS/mSCfwqzIOb8uCN/UKS+2kuOOPhxgE4un7AU48KuTF1+GK+eKuZPA7Tld2MHjaBzvkeXpvwatsHqlLBtdfyCM9wr/Ednr6vkYMHQakUIeHVq0GOD72+BGrCIZ+L+I6EIW/CJRdyz+rrxYt1YfuT/bIuBFRqyssh19iNvuaxUFMIMWUhApisPyFhWalELoU1XE43hkRB1I7sixFWBPEHSNBF5mIBNGWISaU6KZdcBEnL9gslYcGBBWQ6wmHGv43rhN1gh+quuPeJwpnXXxf55y++KM4Zwr10S5tKQ2GVE/PNrvnpGmbOn0mfBVM4rE6FgKRQnUDSdEod7LwMnnYxo/N2BmvFRHtwWzj/7ed9P9PxlVzekReJi3/FFRAXxyrNWKH4SmqUvp0h0yCCPakVMh96bCjrs5HL5Cw9spQ9NXsYnSOu0/rS9aEQ+SmxbRuNxIqfNRZIOETPCZX0Omc3H3YRRGmVrhsPN/8UstkB4PXXKfnsTdh9CYqt11E/8mqRd9QO2Nw2fCpBZuSSBx/OWJFzehIEGhrxSflzcqU/wshWo9DAu1vY9NpGyhMEMa62hdMr3FIUUo27FQG02Iyw5wI4OB5VfkK44tWadmpSGsTRozj8YQUQjUQAYztQKERt9mp64zAm4ZTysRRKe5tkKIhYsxyGvEaPg5eRrpYWGU5zqz7FdomQyPziPnRrSulg7oBMKciRTW1Cl2omnbKIqEMMzfQdFmk1AvDKhFfob/0Ta6vO5cAxDQnyRgBUTbEYVAYanY3sqt4VuZHPB6+8IipPU1OhvyClMZoYNFLv7I6yw22e88ubnufhlXdRYimGhAQSJe9A7IlYrFIVq9wN4+9Gq3Bz2LqDAIEwAZSp8UgWUypN68WVOV7Bl8zgE82NyIB4m7BG8UlpPe0OAfv9NFYIsiiXebn85uxWb9GpdHBjfxYeWMuYBXcB0DU7BgO2cCs4tRV/Q8fQNpYrphFLE/7u30G376PmSmqVWkjZRWzMPtROUbGfbBI3d7nVA0OH4u3ag/RAOX8wgJ+9k1nBaHJ6P8XYFxsZfHgkX+z8on3neQb/FJwhgP/haKkAOh1hAtjgs8IFV8ODscxMW4y2pgHVsCfhqrN586bZ3DYRlsV2oCc7GM0K3ucGCtkNbhNY00miiq8148iI2SwG5akz4WzRmH742BrOuiqbw898zZ7Y4SwbMYN9dx2mX/op+q0++iiGLtm8aL2JRxYMpWNcHZe06NA1mYU06nwhBVAuDzBrySjOn5YMXX+EmArwKUUOowSbXc7LLwtngcenX8jl/sWw/h4wl4YUGZW2dVGKTCZCcS6nj8TUcPuqTPVe+O1VXnuudQXkiuYvofcc6rt/hDF9Ocj82MszSDWmYvPYuGLBMZbNld6bdAD2TYWi60Pbe1tYpH3yifg/GCosaSoJ/Vxtqw7ld5U2lYaKTPz4SW3QYc6eB2MewmiK9FxTK9ShohmrS0HXBKGelB0Mk9lKayW17gZWdUD04kwWitTixQhFRiKAhl9ah6lOhqsXiv7Ibo+TfA5TUWdmcKbIyXxl/Sv0Su3Fphs2UXZ3Weuq7LZQVMRepBZ6GgukbWX3sEEMv+ttVJ1WALBePpDnEvZy1tyzOFh3UNiZ3H8/x0xAXSfmcB3Ns+fC5Mnt+sijjUc5pBIKlkwhDY/tUAA9peE8S7U20v6mZUcIY4IgG3avBluwi6JXfI4WJ8TGRmy7tykTvvkBFr2KIyOFNKSCHmtqu0PAgdo6PD5pYt9wR1gBHHEunTqJrlxNLh1rf6iitItIzq8xn5oAhkKxajAZJFLvak0AlX7x2eqVD0sbVnNx4cXo8rbCuHuYekkDJCbSjd0RBHAUK5B3L4z62Xqp2t3hURIv9RJuqPIxJEsoWquPtTAit1hg6FCRcAxwxx1i8YNwt/JI1k/euNZt4IL4qOgjXt34Ksd3rwe5nCSlVNFuTaHZKh2zwg36WpL0NjYFDeKDvYDjUvBIyr1aG0VdV6lYnA/zc904lJDQXCy2s4oBvt0h4O+/p1zhBWMFbpWXi2e0JtA6pQ5kYQsigKx8fYQCiNqGzZENbj34FJQ8+Td+nv8eLilKG2z71hIaqTWgSwnBmzszQTzrumZxHKr4GBw1zRwllz1OKYwcfwiFXEmjs/HUFj5n8E/FGQL4H46WCqDDHiaANe5G0dRB24yuyQZ1dcS6gbzluMx1vDEIsp++iaaEKsrJ4N2EB3n7iU9h6rXEdNrE/JgrmN68gf2zIa6sEEoHwdHRQICVTz3Kuk0ObulVRm3ZwVAItl0H+9tvgq3t3Qs33MBf/gJpaZCobeavPEDj0UsoCAgfqPffl9HrnCQuHZ8v/LUCgCVD8nYL5we+LHn8HjkC90jWZCTuwS0pMoooK+7YpA2QswyFykZWhzCR6izfA34VqihjdKd8DZx/HbYR9/L+jR/ApeezxDGLcwvOBWC+fz/Da7SYVNKXsvphZBtvifzcWHHcCxcKc/wg6aux16BVaEWCO4QUpyVHhK9cn9Q+XKToxSWNG7kv+0IY8Tx6Q6SSJpPJUOvFZGTBRNc8oWTVleXRcO+tnPveWaw5ugKAbakQuFYYbAcCkiuDyh4igJry4tYX4CRQ6wTpsWFAh4Mmp5Z9NcIU9+PtH1PaJBSN0R+Ppv97/SMVu7awbRsBaQJF04xGpabJ1USTq4lHpk8SiostBVl9Dg6vg9c2viYKg5xOVhb2gMwNoGngnXfafx4ahSZk+dGSAJ5KAXTrY0M/6/SRRRBapTZEBBRaFToky5NKeGjpQ9gkuxmtzA2KSHIcIgs+DfaM5DABbE5rdwjYdbwmpFjL6ruEFMDGRhEZz5Pm4Z9+lqEoWACj/kJOzLpTEkC90gglQ9lvGY1eH1RLza18J6dvupeH5c+F2ywaqrmg6wXEdDgMQ19m8JHnITaWQWwMX3uljXEsIRSjPgFBuyOHV0mCpDLV1/oZmS3ykSM60bzyCmzaJGTqBx6A++4L/WnHjrBnpt9gbdP6xl/WC36cyzvnHgSrlQypIp3mDD4ZKxX8KF3g1RJrdPDV7q+k85AWmmojCfr9kLEBY1LrfsmYzZx3mZqpU5RUGGQkNInFm8+tBreu/SHgV16hpuNWuDcd1bAvidauPmjgbPfYhTIaCJDR5QQFUGXD5UyChjx03yynd24HXvuhI+y6mFGKByJSHILQKrWw9ToWH3uCA1aR2pKULL6n+GaJMMbH08WzCwd6KqT2fQDNv90Huy+KSizP4F+HMwTwPxxhAmjEHnyg9LXUusQK1eAGeVk5eL3Etig+k8vk5Nx0D6YrZsLgV+j/4wT2TMqBvnMZ/cQzDGpYRGDYMAxeuGmVHj5aB0fHADJqykyMneTgrZXfMOiDQbyw9gVumHcDl31/Gb8c/OXkB5ydLdiPTAY//URH5y5K91qpVqTTlX1w3U0UHxHLzHPOEZYJl4zqDc84wWmGKhHKU6nDK8XyE4UQuRdSdoT88gJR0r/6jLwSrhlDamY5vXqFX3fLxASsUbdeiQbDtQCUDgZTKeUZnzAlZQQA8zqD8rY76BgjKaGJe/nTjP0R+3i/95vExAhf1C1bhIVKUEk53nw89BnBMPDG40JJGJ8/nvcqp6L0y3l4NTj2z+CtyW+1OkaNIUgAzfQaLJQ/e21fVs9/k4UVK1mxRRRhNOqgbrTw8du1S7RRRtMQIoBq5emtxM0x4juzBwzCrkTbQL1ThK08fg+TvpjEmE/GsLFsI1sqtjD1y6kn99YLBAhs2cpEwycw/UJkXb+lY7wISZWtWML9P9XQs4eYXO/9WrQR/H7v9wS+E2rpqqxsGPwKuOJYu9rXplfgiVAr1HD+1ahu6sRYk2QY3I4iEM+BcN7mMGNkJaNGEVYAPYdLyUZ8t8XF8PvR3/FfM5rns4aTp2pNMnXSfCjz6PCkJoWtYNobAvZ60R7bz3vcCEBmQnxYAZRSeoNh4HnzQNFpPox+goLYTZi1rT3xWkKvNMBHa/lp0zIIFtlEUQAv9X7GM/6HhcKpcGKMgYEZA4WdC2B/53XQ6xnLklDHDZQuOnMQukZWAIMoNviqRBAse0BHYrz4busaZIzoIJ7F1SWrw9XIX0qtK999F55/PoJk/7Yl7BBgNOrb7H2ssGfB9qvZ4JgETicZJikUb8mgwlqPSusW3XC8Wnbqd7Lh+AYUMgUX9xBm+x6XjHEd74WZQ8gdtL/V/gMJiTifccCzNiplycS4alAGc1AdCae0/Wl0NnL86HZ86zdS5hAG8Rlp0fN4dUodrL2XZ4caWKA8T/QDLtBhwMZ+OpNzSyJk/AHuGEyf72RSd3FNdy3PgO++oXLhjVFVfI1SA1tmsrb4MfZ1PR+ApHQpD1tSAH9XjMNXJcYFu1uSE52xNC2+HXZfElIRz+DfgzME8D8cIQIYUNDYLK3Y9XXUOkRitMGNmGmAdFv46041pqKUK0kvqIEJdxOTWUpFs1AX0oxpoFAge/558Rn7R6PSlUPBAvre+yhduoC9Lh7dos84Un+EB5Y+wIcbvuKrT/RM/nwyT6x44uTO9b16wTQRMuSZZ1D88C0ymxU6dkR+1kjWr4fPPhPNSdRqkEn9abFkcZH6A3EuJwxukyaBObkJHoiHWWpI3wIPmeERLQUDIv38AD5cFsPRV2Fa2hhGDQovk4MEUKttTYD6pfcDnwI23wgfrof3/sDflEn29a8ja8qghEyyFl7Drrkz4Yt5ZCsG89YnvZg6RVyL8/iZaStuY2yhmLgXLoQ5c2QEGrMxKMzU2etCimBQMQtaWvRK7cXe/XKUeNjAYPY6OguycgI6pomQrjVgone+NEjXdmXRSFFoMG6vm0xp4j/YKFSGX3+VNs5ZAcZKFHEHiFfbOB3ExYhjcQSMZHMM4sS+E3QJKOVK9tTsodndTLIhGaPaSJWtiidXPtn2DsvK2FuTQIaxCAp/RJ6yg96pveG3F1k+u5Jnvu/MxAlCLS2pmYhWrqHSWsn+A+sBKHaZwCP+rtu+QSiD7YBGqYH4o3hSDuKaLFn3OGNpcDac1IxXvWkNCqlApUfHSBWpZQjYrdCF1LijR4VtEOlbGSJfS5yutTKkk5S1GLeJXj3HhdtmNWW3jwAePAguF98NqiPhnBtILSiHUU+ivCuFxxcN4pPtn7DSJiTS0lJwSqrn0tEdTrZXAPITc0TOLKDRSfea09yKrCxLsjLiWigd9xoYqxiVMxKlXInGlwjHB1Lk7wcKBSPMOxnjE8mxGnkzsrxcOLGAC7B5bFgDQhFzoCNButx1TUoGZQxCJVdR3lwuiqnKykTLMbk8ahrA5m3hzh+m2ChymYRgjqsDAzidZCZLyrQlk9qY5dzx8yNwdwfwakFfi1Ku5Omzn+aZ8SJtxu3w45EuUbRWcDIZoXvErjYgAxJipUWLPeGk3qDFjcUUvF5A9id9uK13HwobXCQf7s6UvNbkGSQbnYo+bLdM5hAdweGgY0d4nge5h5eoMjWAwguuGDIzw3OMpliQuNRoIWyC6rlUXHffYwCk54lt4qXeoxcffp7px0T/+kBwXFdJz5XK1qoP8xn8a3GGAP6Hw2AAZIKs+APSikpfKxKQAaMbaBZVahnu8MMVVJqCZsfVtuqQYXCo+m/4cAIXXMCDvIjbnsW0sdfyxU3n8UXP51HhxrlrHNdnvsz0wou5wP86zPsQNt7OgfoDBAhgdVt5ce2LXPnjlSw4sCDywB8RTcb56iu47joANl87nqvmXcHvzhe4/HJC1WuZmdJA0ZSFKVGsvLt2jbx1r7wS7rgpRliFHBoHybtB7keu9qAq6MiJSHdryGkEQ0DFqG6F0PlnANzSylarbk1gO8Z3JOfDBbBAqqANKGHXZbxj6SI6AKx+hLKdXXBvnQEHpnDr5bnIZPDDjzKKiuD7B0UHgsm7XwDgiSfg+uvB/soWYt9ppE/SkAgF0B/wh5LZeyT3YFuxGS9KhrKegfMeaXV8AIuuF0THHoghQeNGlrcMkneztLOYJYcn9qEgSVQ4H6wXfonBzlikFpE09j6GndeZGSlttGtpAwmSEZw/oBRhSokAdk7szLxL5zGx40Su6nlVhDr05h9vcqwx0sw6EAhw3+L7yPmkL49njsWpDcrWAZFTqBbff51dF5rPlwQmMFgjzmlxhosNhSbqXVbwShWZ2MVKoh1oqUBocyRrJHsCBGhbBSwrQ1u6n2neBfSmiB4FkcpZiiGFNKlwx63UhwngYT8NdkEa/+J8CXWPLq12HSSADq8aYmPJ0UoKYGNOyGj8pNi2DYBdhTuoG/4hiRlNfDj4Fn5cWI2spoTr511PU+yK0Nv9TR2gqhuunL6n3PWl3S9Fhwi/KvUSqXGZqLJGKoCb6cAaQwH2+BIwVIcKgm5Mfxs+2MhLFZ+D04ksK5NHSoRPX57dCt27R/3ciE4g6EIeghVNerRKHX3TxLFvKtsE27eLjQoLQ/mVfj988YVYgG3d5obsVahTNxBnblvxNAYJoN8ADgcZWdL4Y8lk2rIqrL+K8QOvlpHZ2dgftvPg8AfJyoKiOdvY7OyOPABaVNHDnIFAqCjGniAW8glSbiOOBA43HG4zP+7JlU9Saxdj/tuJY8jZ14eCT99m6r7Lor6/f3p/MhNECNeJFpxOEhJguXIss7kDhzxcbd6SAFYQ9CSM3n5Rq9SGQvhBe5mMXPHcJdiUONHQ4BU7U0r3Dbo68Evzltp2RgH8N+MMAfwPh0wGyhZqjRwfaBtDvxta5KNn+MN+WsGuFMkGyZbCVh1KKg9akwDI3nwzNBB/bZ9M56ze9Nn8Pi9xD69MWcYHE6fz9awdTFwl3q9a9jL3F3yMXCbn4H45T349j892fMaUL6fw2Y7PwgfTUgUEMJnYP6o7X+z8gt8OR7ZWywpGXi2ZpHQu5vbbhaeoSuo+INc1MWUKeD1yWPg2HJpAcHEZTSUDOJf5JCob+GVjAiaNifwbH4abeoS6bGi10RXMR4wnmMweOYd30wdA7FE4NrLFHwIM6q9hwwaRD927N6we/Rgvpr5EX+uKyH14dZSVCYeKkAJoKaWkqYRmdzMquYpOCZ1YV56LAkkVUDj5bs93rY6v5RzWXOfGkL8VburFQdsWAEa8+A0F3UcBiKIJwp2xiD/CI7Z+rJxLuwlTEEnxSnhExxMjFGRyPEQAc2NzmVgwkV8u/4X3p76PSq7C6rYyJHMIbp+bx1Y8FrGfZUeX8bf1f+OYp4aFxv6Ulp/Hn+ZcgsKSLIiDlHtV59QzZAjEqa3Uk0DeIUEqnh0JQ6Zb8ObPB48ggDoc7baB0Sg1okf270+xq17Kc/KrwW1sOw9w3TosmLiw2xUYJl9JnTKyE0VaTBpdJDsbt1xLAcIiY892N412O6y9lx2WSQS6RCGAuYIMeAJKfH4ZuSmSStiQy3HL8VO3CFu9mk0M4I+ft8P3n1GQkcR13a7g3APgb2zA6/ciy22RL/fra/D2Lgyl0Y3LT4RGqqZXGIPFBnIq6sK2KAQCvHTwR3jjAP7q3mCo5uzcswEYltdXOjdBQsjIYDhrqCKZJYyFHpG9roMwqA0h1cgRk0xaphwZflw+FTU1YrEEUkeQvXvFRi1CybNmweWXixqohmYnXDeKnGlDiI1ru/Wd0SimSlfAAHY7mR0FiVNaMhldDN7DEinyahle2BmVlH5S767A2LmMLOVBVq1dRdKHbi40vtT6AxwOZJI5vT1W+C8mSF1j5M4knF5nKCrQEl6/lx/3/QhAYaMKjp7NYfJZy3Cafa3VU4CHRzzMlMJxQJgAAuTHSXmNX/3A8O9nwrGR1BU+xzcHPwQI9Uk/IItu5n7XkLuY2FV8ty5JWM2QGoYk2wLUI66vAi+ZcimXVV+NXCKFqGxncgD/zThDAP8LoNCECaBJ1gDy8EoxuIgEyJTHhn7uFC+qK4MEsMpaFVYAW5qhpqWJVXRjI/I5c4Wdy6xZ3MYb3LH4XBg+HPbv54ZLmpk4ETxuBVddoeSBB2BgXz3nyJ/m3E6iSOLG+Teyp2ZPeN+zZ7N8cjfW9kuCTz+lVuGCrdfRsOJKjraIeAQJoNKaR0L3rbz2mlD83pvjgMyN+M+7krU7ykgIFrs25oJXDd9+he/buTitkdWyAEcyc6jzxvKHR+RKzuhzEaTswh0QA5CujTDH9X2LWMgk1twi5RXVdoGOv4rQT114Ar/uOhnLl8OQIaLoEODuB9XcX3k3R/U9OBuhsKUmerjoIvH3+QsCZJklBXD+Z+we1wcQZN1R52O+/Wzh1Qh4lY6oLa80GjgvbyczTPMJGIxkpOigShD4gRkD6RjfkYEZAxmTO4ac2BwqKkQnNZncD2lbydRI5r+nSQDj9XGgctKoQ+SpxYkvMNjeDgQZ75YskvrP73I+AJ9u/5TlR5eH3vO39X8TPwTAUNqLl5zP8u6xr8hiCp0SOoUIYJUvBqUiwPgCQTRtW0X1p6fliOYSIT0djnafj1qhhv1TYfWjbFlhRRtsVG9PaDvkunYtxbJ05ifks7ZzPcebW7fom5y1nRt5l9zYBvpK12bzdi9upwyWvEidowuB5NZFF7rzx4d+XrB7KTkdJEuVphzgJKbhIPIef/mFapJx1veEuk50zjGzuyyW23mNF233QgDmXvEcGb33gswXygEd6Da0vd8WUOsFKQh07oJCUnWq6lokG3u9oWcq4FeiNjXRK1Uk3eokzuhAJ0hIdjYqvCRTQzoV0De6CqlX6WHgGwx/ezIf1F+EuiAnVBxTUiK6uQDsrtkN+6QcP4lc22zCjikEKexaYkZ0qGgDMRIBdPv1ggAWinvL15zOUetAlq37BfW818GWREGXcIHEWR+fRcHic9mcDuXeZEpLhQLZ+kKqkUnH4jCJgSxeKaxUgi3uLvrmIp5b/Vyo6xDAzqqdNDobMamMbJgNqqMjcEt2MwZz21ZOWolnOdFKDvww3igZaB+eQJWlDzhjkZmPU+WJVPyUOhfRoFfpiZGUYOet98KBAyECuNQ7haf7SedFPQNjpTzIpD0YJO/QjIQ40VbyDP5tOEMA/wvQkgAmySLzbwwtCGBvRbh/Y3AQbhkCjqYAAiIW21JauuIKMVg6nSK/MCkJ2dQpfPghxMeLyroXXhC2J9N3HeLnUe8wPn88Dq+D6d9OD+Ua/mrdxtiB+3j89p4wdarIHdpwJ0VzrmFXCxuvTMlbup/hvFD4COCaGTGMfOp+6DyfCyYkhCuAm7LAq4Hdl+DZfolU4RCJBrdIRN5XLVaz9w+7nxv63EAfxVbSE5cwomPrXpcAsox0JvErQzVbmHb7Frj0fMhdJopTAnJSU0VI9b33YLfEz4KFjH0En2PblS/xfd79zOEa1mnO5qLpVXDxxbynzyXNKK59qcrBXlUjAIWJhcx+2kIzJsyISQGlK6q6efPCm9l71zQu3ugj7s+X0KerCY4PRlHTi9cnvk5ZGXz78PUkL1rKFd2uD6l/+rRjoLHx9i+P0Fu2nZW2/lHPvy30SO7BJEMfugw/D4VKGaEAtkSfVHERrG4r1/e5ngABLv/hcqpt1eys2smiQ4uQy+R89013jLYYLIiJdkSnXqgUKrpnCZJUH4gHh4Nzh4lrtHNff2QBqNdB1ud7Yc0DKGrEPa7H3m4FUClXMtAovnvfkYoIv7c2FcA//mCjvD+frToE7/8RKuoJwh/wc2nfeTwQ92cGpJbQJ7MGBV6O22tDhAtA5Ww+cc/odNDrhrfg/Ksotx8jp4tEphzx4DSFVNxWqKuDm26CY8doUkqERN1M945mlhw9zuvczhfy6eg9MLHjRFYtTME04yY0LnE8nXcVn/JabTy+kVqFWEB5OnUnRibC2ZW1jnAOsMuFO6CTroOaDum6UKHFngahSttkEgHs1YuXh8CAmfDWAEJefSfCoDKA2oFLUSPcXBITQ4U1LQngrupdYQIoKYDr14uMmMxMkRr40mtSyFIFiQlZrT4riIfPvhMAr1+Hz2Ijo1ciKtwE/GosjhyO1E3EtP082DqT9MzwtKqWa2DlI7xjeYr6gEgpiLoWUSqRy8WxOAyxACRIZtN5mgEAbKnYwsPLHubORXeGNtso2c0MlGex2T8Mj19PheTh+Zt7XZvnEyTfIQXQ6+W6oyJfEZmHsoDwWk0xxQrvyBZQtUEAoQWxdMvAZgsTQP9k3u6UJZ1XHaY4KSEydQf6gFh03jVq5in7pZ/BPxdnCOB/ARRaa+jn5BMIoKnFszrcWMhtA2/jmt7XMC5fhACCCmC5tTyUn3WqDgAolfDDD6KtRf/+ooogN5c0YzPzr/iafp2b6R1XzDdczGW/34D80sv4YPIc4pqHsXt3gLzex0lM9rLm60H4Aj5+P/o7VdYqDlfUQbVgSwMHhj8uqAAaHF2hoh+1teFOGp0aboVfZ2O3tAgdNGWjlYcTupXa1i2GFFKVq9sj5Uqqjbw/9X2++aQTZW82MPvWGdHPPTsbYmOR2aw89KAMOi8ApRsqhFrRrx8MGiQKDYMkNkgAe/cW/687nMK7V67m6vSl5JatYXLtIshZic94jD/WiY1KzLBHEuM6NsTy6lxBwE1x0rkoohPACmsFB+oOsLt6N78d+o3C3jaY/z6+t7ZQaB7Iyy8LJ54vvxTdVzZJbiyBdMEEV9Ua2R7oiWvW0632fTJc2etKOpVtZdG2n2hK6QRrHiBm1YsMyx4W8b4gASyqLOK1Ca9RmFRIhbWCC7++kMdXPA7ARZnj8OzthgMdtbJYAMYWCoXvg8tEAnmzPx6amph4eTwKvOyx5dPxcA5U9KX0YBdY8ThJqSJcfjoKIMBQkyCtAZ8m1GUCe2L0HECfD7Zvp0EKb6FwtUpkt3vsZGZ8Tf4dYPfaMWWaRN9ffQ1ISpsKN7JtRa12L5dD4YQ10PtTXDRjLEgjEckSpDEnlMcZgcpKcSO+/z4A1emSCbammY6ZZr4oESG9WoWZ/uYuJBmSyEuPZ89bj5PhESqNOcoz0+rYZHL8Ujs4FxriZGJx4rSpw7Ylfr8I8QJ+n5puuWF17NsDn4r3ByQCOGAAK32j2bztdRbbLm+R+xGJYPWwzSMtfJOSIghgsCXk4YbDeI5I16dAEJq1ksg1cqRYw8oDanihCt7946S2NwWp4UWxPTEbRX4OHaVQfsAjQphyyeg6vcX6WavSwMrH+aLxUWoQY+2q40ujfkaSW6zWkzRixZvgF+NxZ/1QRnUYRUaMYFNzts0JGUMHCeCgYi+/IdRir1+EfrUxRMULa1/ghY2iAMuBTiiAtpYm0DbsnRaDyk5WihkS96Ls8X1oe5XWHW23bCrbxKYqUcTjRAs2G0YjmCVvUuqFwppAHYe9UpFR3GE0fvHsGNonOp/BPxFnCOB/AZTGutDPqYHKiL+ZfOGBXJ6SyuyJs5lz3pwQeQgSwF3Vu/AH/Mhl8tBrJ0W3brBxo0gg6yfZnjz5JENnX8rm/SaKGnK5mO9gwACO3/Ic552TSvPsVfDuVpxHBlBXo+TZWfFkH34CgEWHFrG3yAzISclqJqVF4W7nzjB2LOTkCL6ZkhI2VS76ZjJsug2ATp2l/DhHIsnKcKsiha715K+oE9fJU3FCW6YpU2D69LZHoxEjwG6HUaPokdyDo3ccZWrnqRB/kD7jdjNxolAAx44Npx8FhYyzzhL/L10KDz6h58MhoqLZ9OFsshquAODtPW8CYNXA+u6C9Ll+SKSuWUM2x+jcQzoXpSuUZ9QSwRDK/D1LmDDnQr48Olu06gso2LjJy7ffht/73lwbGzaJC2lPFl1DPJLTa1AhOB0sXSrWBYHkFDg6huZl95JtiAyr9UmTCGBFEQa1ge+nf49Zrmdt6dpQLtNDtr6sYyhVpOIKiMlsa/0KAOITRGi+nniwWokf2oUR8rVgqILazrBP2G7Q5Ucm/Gk13owOvMqdp9UKLqRi+FRhBdDRRgj40CExeQYkhTyKMqtRaISPpT2Ohu79IS2Nh3kWeUU/mC0UaB2OFiX9LbBoEfqvxORr99ihoIAcisXfGnM4VH+o9Ta33w7HjokH5pdfqFAHw/rNxOrMJMWL47P5YxlkChstZ5gykMvE9VZrTz01GNQGGPo3dBMepYOpgXilRMicceGqVZMJr5T/iF/D8O45oe2NekGY/CjxDBwG/fpR5h0Kf9xKacN4qTS2NRJ0CeS4zsX69iPMSn0famsjCGCqMRWNQoM/4KfMLi2Is0VubZAADpPWJUpPDNiTUVsTSFfEtnmuOp1od2i1grF/F4iLo5NWfKbWJ20XaE0ARWVsZHV3pb11Lh/ANP9KLuI7OqeI/SW7xPtsjXpWXLOC43cfp09qHzx+T6indtAmauCaY/yIyNv0Srl/ceboOYAAXrlQ9dyZeaKhfEsCqK+F4S+CzEdeuhnyluO9aBqKmcNh6vXEdd0WdZ/FjcXs63wdfaaNZCbvi3ES6JRYT0+2k1KaA0CMoo4DTdIA74jngjtXsWkTXNC+tNMz+CfiDAH8L4DSFFb90gInKIC0mIxSW69wU4ziQQz6zqUYUtrfqeFE3HZbJHF66inYtInkC4ahUMhEkYZPwyQWcqPsPQDqFtwFHi0LDy6kZJuo1u0zMDKxfeBA0ali5kzxe2amSEUEOHtEeJBL7r8WpKT0njrRfk2FG5m6NVFSBiRfNrdQANeVruNQ/SGanBYanY14/a3zBsXB9RHntW4dzeVutr7tIvHQrUyZpOW9OQ5uuUU0owj2nO/VSzSGB1FLUxieb4kZP1SoqVu3cm3s9WBLpFJfjGzZ4/DFz+wLiHM5uFrkL13ID3jzJEKldEZVAM0aMyx4k403rYCNt9ErtReqDlsBmHDbIkqDc8/N3SiaaOT3HVJOZsYm1HJ1yDolivvGKRHsyOA1mNEjyEDpCXNdr5ReyJAhCyiptVjpUi/nx4+dmJ0gC8ATlV3p89t21jFU2kIMUcnxgpUlJcGE8X6mXh6DP78AlEqmFh6Gjr9xcPBv0FnqYNLrU3om90QxZRLqaecRThA9NZoUIpRpDShIlIV7vkYNARcVYUcncsNAKIAnVDIq5UpY8A68UM+7e8dAejqjWEXRxc/xwgvi/PTYI9MsgggEaCgdCPvPpb7BD926hQlgQ67Ic2uJHTtEG0eZTDRnnjiRaqsgUjK1FZ1SR3KCuG+cvhgKkyJb5Lm8kg9mO/iyUW2E/u/h7/8MmRu/J14rPbf2hFA/a48HAkF3Aq+GId3CvcJjDOHFqUMXDwoF9mSRM2pQRXZTaYleqb348Jz5lOyawU9Vg0GtDhPAI17kMjkdYoXCVByLUH8TE/H5whXvQQLY0ywWJLnNLlI1bd8jWyo2M3vXo3x/6JMQLy1IFZEXpUeMefU5O1DlLyEuLrydRhm2RgmirWfrtbi/8B0X07OX+ICkemGkXt1ijXpRV5EwPG//PJqcTeyr3QeOWH7e/xIH6IzR4MfvFceTkGAkGnRKHQx+hWlfXcKc0rFikDpBAQTQ6WRkJcWGtuvWtxn6fkR8bvRUCJ1SB/FHUGUWkUpVqBtIYQc7P3IBi/d8RPbAe+kX+zVljdI8sek2uhUYmbwimf5fZJ3cG/QM/uk4QwD/CyA3hVW/9BMJoKyFlNNSVpNwotrXKv/vdJCdLVpKXHABPPNMqEOIWg0rVsCXf9nPEs5hAefyduDP3Jv7HR/PPwgqJ7/s/R3L5kkAnD81OgENFoZ0aGFRNnVq+Oc1+rtDRQIXp98KSMqKKgoBlAuC53aLtlHDPhpG/3cHkGBSERfv46GfZrd9nvffD6+8ws7C6Vz0cGeWv3cW8y6bR/90IfWNHRsmerffHt5MJhOuN2PHwltvwSUzTTSdcxHVJPEn5zwUG0WHgkDecjgwFVbOQu6TscEuwvVTmUd+dy0F534E/d6LSgBjtbHhKvDmdDondGbQEImY7RHFOLG9VhKjlQbguCNodB5I3oVWpQ1Zp+h+/qrt84+Coooi1jYsAuBwTTOxhe9B8i6OnVAPEaOJ4YX4Bo7fW8yoIUZcjz/L6MN+yt418+WL47nuHQu2hcvZRm/USBOnzEeyWahjr29/io2jE8m97rGQTdDUR3tCB6m58tFzIKYM8hdzTt458PbbghC1vGlOgS8siwGokslI0IVJTVQFcOtW9lBIqOw8igIok8lQqIQ67XD6IFeEmAubVjJioMjR0OEggjkEoVLx+/ZP4Mv5lB01Qm4uuQqJVTfmsrViKx5fC7L0pOStePHFof7HBxUifD5ENhqZTEZqQrhiN6PLpNCme2r2UCotjNqlAEq5ji4l+NwuEiQTchzxIQXQ2ZL7bLqd7Oywqmc2amDUXxhyzU+hR9TpFj8YlNHDjEEYJa7STAzI5WRrRcj52GFxLYJ9tYtjEStGuZydO0X+n8kUdphpaBBKmBYnyfFt5wBuq9zGM6uf4dutn4oWKkCXziKNxOYRx+w11BEf1xQhXLb0xgsi1DXlBOxKkbEsFyoSBftOrhchhJYE8LwuQuFeemQpv6/5hIBHg+q9dXzkFePdA/eDwlADKiuJ6dEJrV6lB4UPp7/FQtsW2QcYVwymjrswa6RUGr+MbvqzwttHQbDDSKgluqQAdushJ556erIT7cCXCKTsJvS8NKeRakijxl7DccvxqB6JZ/CvwxkC+F8Auaki9HNHDqP1hb9Wk6IFAYyiAJ5IACMqgP8ejB4t4oAPPxw28ispQf/AbVz6ly6cw+/Ixo5F/u47vFg0lvOH9CJeG49t+3gClkyS1dVcdVGUiRBYKc3xLZsDDB8OC3/xccFzr2PM3kO3c5/mmXf3ERz7NDijEsBEczGkb0Ktbwh5FDbZHPg8OnAkkBx7ioQUpZJuOWKAO1qq4o8/wFe0A2w2NBoRGT94MGRxGEKPHkLNvOkm4QMYu+grXuQ+0ue9w2u9pe8nc4NQMouup3P1JKpJwYCVYebddJz/Kjlx18OAd9omgFKVKdXd6ZTQiaevnRDxnsZdg0j2SEmWCfvJHbQHlB5hShy0Tjm2j9OBQW3ApxPh0q06HeXT74Zx97SqvwkEYPaLQunaswc+/lpLkwbumPE5lzp+oQ9FfMN0fCiZZpZkVI2FOF1saB8NzoYIs+H8S/qj7Sz5EB0bCf3eo0dqN+Z/2J3LLhP2OqcDlaQ+OX1KEo3S5G1PpKK5IqICE4CiInbQkwVMEb+3kZupUEoEsMkGHTuyqCOk9P2dpxYLT0g9dqL27VKrUcvFZ9rsflAoyE8Xvyvru+D0OkNekWzfDt9/L1Yaj4XtdfY7RTpEl54iwV6rlYFCnFe2Jmy14vQ6YdDrGPu9SErcyQkYSCHg+jw4PpDiOj/xwd7UjgQOSOqV4o8N3Kb4K9P5CpncT1pay+31MPoJunR6Dt1eoVI7XeJZNUYxYm+JYLTcihGcTvLTxLN48KiSQAA6mAXhP2YmVEW2WnK7GTw43Aykuk4sGLU4MRrbtoExqAyw4jE2PzOD/U+IxVGfUeI+ft0vyBdKJylJkbkTaoVa9NgOImk3hjYUwHsnqxhzFfwmL4H4eJIRzK8lAeyW1I3c2FxcPhePLX4Itt6Ap6EryUYb338X4JFZclKf7AOPxJCUHBv1c0JEreW9bLW26AMsCGBt+udsqdgCjlh42sWXV7/G2wWlvDnug+j7VeqgrB9lm29nPueGFcABemIRqnq9DjbrWtj7eIz88GY/WHcX2OPPGEH/m3GGAP4XQJkeDgP1ZzMx/nBoxaRukVckJUK3RIw6hpgW78mPy2/1nn8Y27fDG2+In1NShAx2441gNqOQKxgvLwCfBhl+3r5yMzpNaw++W28VnZwABgyI/NukiQp+ePA2mg9MY9fXb/CwbDXbakVHiCZDdAI4tt8rcOMgcnv/Tp2jDpwx4AqH4NIS2sigboHEvtmkSvYTAwfCeQPLhTTx9tvov/+Ujq39pyOQLHHvfcruUFLCzZ/egdmJKCrJWQ72JJpWCs+KUaxEfc9t4Hbz85dQ3+1TphVOa7VPs8YMHSQyVHw2f3w7gqH9jZGWasZKEqVcfFW/z0kcJ8LxBACvFALWnaSTSxTEaeNAJypCS4NKQkMexftdFBWFi002/xEIh4XlXuaoz2fAXTF8mHQuTJlJLUlcxxwAhnauI33CRXDun4nTiUVBcMFSufhXPD8tBKC8uRyn4RAE5EztN4C3n81j6VVLWbVK3GrHS0/vXOL7/go39uWa7GdINAsyqHKkECAQmXMXCEBREdvpyT7EqqRvVreQxU1LKJCqTdf9QSA/n1snQb3GjzluG8s4S7RqixZ3VatRy8REHczP7NxLhMNVtYLQrTq2SlS7Xnqp2Obii0OVR01NIcGKp54S/zc6G0MqscseLp5yeBww8llSh95PSkIbKRAtoFFo4Jc34IONzNuZQUKcRNoc8WwpFxW+noObmO17kL/yIGnp/ohWx0Elyb51EywTOaguvyAhMZPPPulnX/zTREBSAF0u8nN8yPDTZBNegK0UQGCV9FiMGhXez7z9YpFRFusKL1ijwKA2wJ6LqDx8LSVVguB3u6ofKtw0EivepHLQITeSxE8umEyCSTwP/R94GG7pjtkcXQHcvvRreCLA8g2DoXPnEAGsqQkXvclkMs7rLFTA3QYb7BLf+cNPG7jwIhkyGTS7haoZo4k+hgmi1p9tz93Cw8oXRLGQzcZlfMn8kX3hohkolODr9S6zls8S94pfjKE3XZ5Jui76HKFX6aFkBPXLn+GrxNsIDjKDh4n7dit9qD8+nn1+yd5HWoTMfSMNFr+M3B0r0iXO4N+GMwTwvwDy9CKYeCuPx11JLsUk+sITiam7VKDRqVPUEJNMJqMwKZyY1jUxevugfwhTpsBHH8FVV4mBPr7FStvv56b5FTy35w/+uOMTLvxgksiLOwEtPXJH9WoUTq7PPRd+0W6HTz/llwKILf4z9x2ZDA8Z6TtzQkTvzyD+XJvDzrfgsZhzuTH1A9Sv1cJ7kieKupkkQztyxnr25CxWhH4d6pVmmJtvhgcfDI/aK1e2cFsOI2g7dsAg8pBkDY08sRxe6H43GT0F0SjfJ8KFYx/sB7NmUWvTcdjbDYczPapparIhGXXyMUgTE/CrT2Uxe7YQZaVGCDD+HlzJIhveE7+T9R7BrDsYOxFrLiOFytMmgLHa2FD4/bhHOq76Ap56QUP//qIy+qef4Ie714DSSezlQ+D+BDZc8iIHtZLNRO+PwRhWs4d3a8TX/Qfo/k2ouCXZkAxzljP/jVIWzROkamWxkIb7pPXi5y+T+POQq0k2JGORWt7FXH2BsEVpJ4xpbkgvIvbFG0iIF9dB5xDq7P66Fn1cjx+Hujo2K6U8utylXHGxKerEq1JICqBPxi5FHYfjQeuBdxvzGM1KhrI+OgHU68mxCQI4s6fIJ+g0SawsnA1Z4FXx9fznRM7Bvn1igfXaa6HNly6Fbikf0uX8K1lZLoh1hbUCrh9K4dVpFBZ9Hnqv0ysmZG16tuiteArIZDLiJc9Rp1NGfKI0ndgT2F2zG5vbxqa9S5k5Ba6eUUtSt10R2+tVeqgtoMzSD2uTuD4KyRTYbDx5KPC4UyjUbjS4rW50HZJDeYD7959AALOy8HhEGgqICuAgaiySg4IqMkx7IgyqsPm03SruCU1GIt1NksR9ZweYeDs5WZEK4Mx+M8lPEtW7bpe4PtGKtwAUkj2O0xWAwkKSpGpvjyfctxkQRWcALiMcHwzAhRdKf7RYGKrOZ3BMoViURYFOpQNrCnX7LmCJb7SoAu7UCeXLL8IlI0FfT26mHpRi8ZNlzkIuD48HbTVM0al04Ws0fFzooBKkFok38xb+LxdRXjVc2qAhYntNzOm1nzyDfxxnCOB/Abx4YdCbTNWKThuJgfAgFDNlmkg4+/nnNrcP2iYAdEls3Y3gn4Jrr4WPP46sgvj4Y1CpGLG6hAerSun35IWR2zQ2Ckv5555j5rv9eeRBH3PnQsEPfxW9nB5+ONTqisZG6NaNckchTQemQWVv0Ngw9cuOWk2YGjDQvVr8/+WX4HaowSIqBdFYSNC3jwBehjCEVil8XIhkjaNUQnm5KEn84QdR/jtkiEjQb4HOkuXVEWsyHsll/47Eydx30Ussfe7miPdefKsgIF9Xj6YHu7jj/ehtsiZ3msyiGQvg6tGYegki8Oqrwq2ksRFUqgDkLWFX9S7itYKI+wJi8t1+6yYarniOStKiFqSeDCqFCrVO2IBUe4MEUBCVoPHt7Tc6+WJtNni1pMfXgNYCecvAL4ctM5mpXMWfrhLH1Ls3dMu10iDtKoIASjlVdVKB7vJiEeNt6REJYGkSk5YJy2lVAWukEJk7PZXEJHHvKKyikmdfrSAegUCAXet+olENO2W9GclKZvb7C3ddWh91nz1U4n5SutXskPo7DyyDmF+klnujR0ftVYtOJ/IDCfn1knbRUIw0E0CBqjaf9eoq3uwfIDB1iqjMl1I99u2D2++xcXna3ezr/RlfbBYEsLy5nD8fOsrsVZUoG2tDH+XwOKG2AFmgF/6ObZsit8QEv7guGpeehFRBbDS2RPwBPxuOb2Bx5TaWxOWxKs1IZp41Ytuzc88m5dOVrFm8mZ2lsQAMSDpLXK/Mk0cizKbwos7a6IWMDDojyPmBA+EQcHEsBDIyeeMNUZyVnCwWI0F45NWQtoV4fRt+ihIMakOoOMJmDZOhEVPjeINbMKpqQOGlsFPrRdkHH8DmzRBTIGx+2spzU2kkMu3wwZAhaHFhUohr1jIMPKLDCDK8eigbCAEFHTqEHXN2LynHfs8rdH70MZIMSVE/J8WQQs8s8WzaEJ1NyM2Fu+6ieYS4OFmmLJZdtYxXxr/Cxhs20qFDeAz97fCiqPvVKXWhVo3Wll91vXgmahDH45XGBcwt8kPkHjT6U6cdnME/F2cI4H8BPNIELuWZkxTM5QASY1JEwlmUNlNBjMsTRQYphhQGZgxs833/dGzbFmYHt90mcqDq6+Hzz2HrVjGqnX02PPwwml1bePqCLVx9NSKuB6IdSE6O+Dk9HdauZWXDtfDd17BL9ME80ZQ3iFcs19NBVc6sRcNCXrEhaCzE69rOBwqhZ0+mMJ/5sqmsOecJurBfHG/Q8XndOjH6g2BgX34ZsXl6uqgI9PrkHP1gGTz7rDh3xNc1a5YQL594ItxSySW1utjm2tOmCXBhSg8+WSvnb4EHGNTdxs03Cx4KwsUmJzEdb1UBt/d5iCmdRO5aflw+Zq1ZVMXAaXcCAUgdOA8eNuC9RISmr21cTRLVPJL0HhlxNkprtJTQAY3Cw1u3fYVGJn03S15E+et7PHHDUN5+Q8Pu3YLHHC7Xct2n07nj8A0k6cXkkWxIBr1Q8+obxKS0ongFAKNzTyCAkme2CctpnY+3JhdWP8iib9NJSRdEw2MV4azdNbsJBAJc+/O19Nh3O9kz02j2xPMC95FXuZZ7f/gzh+tbt8qaIIXNdG5NqEI2rwG2Ffl5k5tZVvCnyOTWIEwmdLGCvAYJoCw5iU6xQh2auk4QtVsnw/hpTuqTBXPfvRsGDvJTfszAp8feg49WcWBPPP6An+1V2+lbCWOOEuoTDmCxueGNA+x8eF4wfeuU0KnFoON0yYjPEeFPo0Vcq2t+voYNdekc++QwfLiOgg6RVal5cXkkqqRexw5Bqj6e+j0HB8zgwpJXT/q5Zr0+FEK0+nWQmUknRN7h/v2EqoBLY+DK76dw991iu4KJi5j81biQp6O+YAH8qT/jC+866ecJ82nBapqtYTI0YUYCM3kfmWT1Mrh/JAG0uW0k5lTgkVso/9tCRi73c1HhRVE/Q1UlCJGzpCpUppzsFwV+LQmgUq5k1e/ZnL9EKu4ZEv5bRamXVYxii693m+fSJ60PH0x7VRwfhlCu3mefwW+vXsgruQeZPXE2o3NHc+fgO7nm52vwjfiL2HjsfSw5vCTqfjNMGXwwTSw6oxHAYCs4nPHI1U5IbNEVSlcvPBPP4N+KMwTwvwCegMjXkbyNSZSHSc8pTZ0RTd3nXTqP1deuDiUI/1vw1FPwyCNCyXtcmABzyy2i08gll4hRpLJSNO0EWLNGKGvFxSJf5803W8Q1AbOZFCkEwcGJ8NOHlCw8P+pHHxw0mBJPGsv9Ppb/UR75R0MVifrEqNtFICUFWVIS5wbmM/A3KcFq8GAYKlmYrF8v8rGCWBfpzC+Xh9My9yePgIcewq5Xsbl8MyuLV/Lkk4KPtcjnxyZVSR7yHAiZwbY6LGMKVyr6MNObz4YPdvHQQ8KrG2DyZBmNry6Ht/awfYsu1Dd1eLYUlvkHCGCBORHU9lCB35tvD6A6vitP1/yJxxvuDL3vyitljCroT9G1h9G9XQrr72bmTNF1UCYTIrFaDUv2duCdY19T/sftofsy2ZAcCjVXNokPWn71cj6/8HNGdhgZcTwWiduYsETNA20L3soc+P05Fr8bT3qBeJas9njwKVlfup75B+bz8faPAWhuFOFfj9zH+wUpvFS6JNRRpyV6ZDUyg88ZaN4fqpDNa4BlnM2tvMlHR0a12gaAlBTcI0VHkw83fRF6ufNoUa3fz3Yuz3W5Fa1Sy5IjSzjvq/Pw+DzMmgXNFjlkrKPM1hdKRlDaWMfP+37G4rKw1nopt/MaS3eFC8Os9nA1saY6ulfdidDlCmcBR0Y+CZ2Eyqm2xAJw3HIcpVsaT1QOenZpLStrg9XR0mObWLefjn98SWzpzlbvbQmTxgR35PPJhvlk3n85ZGZGKIBpxjQUfvCVnM3nKzsgl8OVt5awNvtclhxZwvNrngegUiXSCIrHnnzhG6OJAY0IZVrs4RSVcWN8vMkt8O3XqPdeRlJs5Pg5a/ks0l9O583Vn3L0KJSWyEKdUE6EWiHGcZc7IMIDCQkkS64ONTUt3ujzkVdUjLuiNQFsqhfX06SMtNI6EUG3LhsGsQg4dozV31Xy8Ucamo91DHVTAdhSvoWSvCcY/eEEGPa3NquAlXIlOcli3LRu3ivGcoDcXPyzHqeJcOzY3/1T6P0xvc4RaQGaGHtoLDqDfx/OEMD/AgQJoEoigE5VeIV6Mnf7IGQyGVM6T6EgoXWRyL8URiM8/bSwjAlO0EGyd0hKtr/4YiFbgSjjCzq59uwZaZxbXw9eLxnBMaamO2y7jqol0W1t6t1CAdheegBXvZjEXlNdR1bCUjol7RETTHtw110huxtAxJeCI/K6dSL0HewJt2VLOC9QQjAMvF9KLdtSvoUB7w/gunmifPjEvHSbRyJmatvJyfry5eJzBw3C7xcRUJlMeFx3lL7mddvqWFUi8haHZw/nwAHoN/9xzuOnv4sAjsw9C3lA3HtdErvgPWc6wwsqUcs97DCN4OGO33DtJXaee1FMoF2zUli9MJOPPoKnX7Dy/pb3eWLFE6H9Wazi5E0GX+g1k8ZEilFM2uUWcf4Zpgxm9JgR8Z0FAmGlJkblatNUOBrOyRJ2PsoqOwndUlEhSLHclsGxpmOc/9X5ANxZpCFvnyCAX8sv48icSlj8t6hVwOMGlPCy4QouzviZI41Sm7xGqRMDoPM0Q1n0XsMTL66ESTdz1Dwn9FrPgUJpKuo7kwcveZ0fxm3FUDmWNcfWcPtnr/PTT1Ke2uTrcPrEc+LRWrjwG5FmUeQ/l9e5nVXF4VQHsyocMlQVbWrXtVqqFPf2Li3EdxXPkdUbz4tDHidVl0SHUsl6Sulk5KBIBbDB0YBNLWRaux3cPjeDXW8y5iqwGU+uBpk0JjCV49PUiWckIyNCAVT4/GRagIMil/Haa6H3jO9AysX8ds+3BAIBmrxCqtLk5J3089Jj0rk4QTysTfZw+FnhcbKOoTQfms7T3eeQYYpsIalRaODoWayaew5wcn/NMAGUi/t11KhQHmBLBZCSEvxOFxsQ+X/B9SbAriqhGO5OPsHg/gREEECrFT78EOvPIh3BGPk1icgAUOUUi4K2CGDLba1erXDOBujShaa7/kIgSDd6fQRjHoLclQw7SxDVkT1yWXzl4pMe8xn883GGAP4XwCOZFgdDwFepRZns6JzR/3ll9ZMnR45AV1wRdm1dty6sog0ZIgpK3nxT5AlefDFotaSnR45eakX0vBKdTgziVrsPpk8j6ewbucnzKSWP7WH/i4VRt4mKhx4K963r3FnkXwVH5LIyUXyQny+YnM12wkgOEyYIg2vJsi2UvF7SVII/0NoKw9ZLIpcqW9QikGiQy0X7twULREHk4F4iObzqmIk1JWsAGJM7hoYG2Fqfy/YOUyMNDNuJB8a/xJXHHfT9vYrHhj6L0QiTpqrw+JW8YbmK7Hun89FX+lAFMogmMtdeC3KllxsX3MhfVv6FZpeQ7qoSRfWmMzlMmmUyGc8ViAVBjaXtML3dHuZ8JvXJE/xPxJSuYrKWeTXIc7JJkyq9B5lEq4IAAZI1CTyxyMXAbb0BUCklMq50RSXmf7Z8Qep98G7cYa7ocQU397+ZPj3HYUequl75S9il+ARMmiiHgW9jiw//PXjLbdokaozOH94V2zuL4dfXeOcNHYGADAoWMLKrAbdEAL3acLh3X6K4D0vt4Ws7NF2E0NW4kGnatwBwyxoBaLZ6iU8V2zRj4o6Yc6no+A7ppVK+l9LRqrL+WNMx9qmEGmpzyLG5bWxcdQPLjjxLTSCTkyFI9i0uKc7fQgE8fDiAt7SC7CagVDyLZ50l2g8GUWWrYn/dfhqXzYRXD3PkpzZaP0pQK9QUdBCJdpaMbuE/OJ0hEp+Q0rp4TaPUwP4plBQJ8ljuPMzemr1RP6NTQFy/Dn6JNJ91FikIElXeUlTeu5d9dKGeBNErulf4T9VNYi7way1tnkuNrYZ+c0RKkBMdviYrNDWFfABXV/zK+tL1ofebNYIABpXtkxHA93a8DEAzxnAOBuEaLI3OAxdcDwbxgq9aXJf8f4H5xBmcGmcI4H8BTlQAx8T0ouhPRXxz8Tf/h0f1dyI2VtgSdO4Mzz8vHFv79ROKVHU1fPKJeN+wYcJw+tZbheHe0aPg85E4fWzE7pL9vtafARj3bhc/+JXQ9ScKct5HhVcwpGDPtvZi/Hh4/XVR5Qwid7FvX+FXo9MJ+S0/X8R7T6hGvfZaeO89GCfSMEmLSUMuk+P1e0O9mVvCVijN/GqbSLo+FSTFUS4PF3b26BpZpDEgfQC5cbmh8TomRnZSS4y2oFbDN19o2Lo6mYGmC5DJhDgaDGHPmnWCMXALxGpjQ3mXRxqEQnY4QUyEy+SRFdRZHcSxlToSueana3hh7QutOggYDODavItKUk67ollrFBO5Ey2kppIuEcDzDndD7walD95eEMDkgh06sTjxy8I9mqMRc2NcCviU1OcWcn3f63lz8pt0+/hXHFfcCEhG0G0UqsSdLb44q9saMn3u318Q3GPHRLFlMHLPptth803i56Ev8czAWfh8Qu4ZmC8WNt2TuxNjECpqrSNMWkLRf9ztDpmnFe6BUX+hS8/tESYD9bvKYcMGliiksLzK2ep+1av04aKB0VOwuq2w6RZY8xBWWfQChiCyzdkkbX6E7y5L4Y+Z70FiIln6erQ48HhkFG+uJaNeA+XCBWHIEGFW3hIri1cir4+Dxjxioje3iMA9L6VTXg4vLOkTfrEFAdQaWrsNaBQa0ISJUIP3OPWO6IVCY41WxrOIMYnSmDVqVKiyufRYi8Xgvn2sZFTovFp+VbUWca/r1W0ncaoVauq8xaHf7QW9Igjgj4c/5fejv4f+HlQAg89YsBdzNHxf+Te46mzeMU8ME8CjR6nbIj6vZUOeZEMys180sW5dOFp8Bv9enCGA/+HwB/whpSioAGIw0Du1d/vy2P5/xKWXihLGBx4Qv2u14Ya6F14oQsZnnRVOmt+1K9RzLBiGCqKzN/otbvBJGfVeMekmBVNmgl4RpwOtVhDRlqHgOXME29kqDG7Zv18kJxWeXF1UypWhsH0wUb0lbDaJzJxKAdy3T5TS9midVxPyJ5QI4JOjRfeIBsmVIb5tYe2kkMkgO02wiGOHwvlks2YJTlxTA9991/b2HePF8RxuEEUUjU3ivjYYIwlc/kW9GXu2j54z9Hy8/WMeWfYIClnryVcRoyflvCHIJow/rfNwSvlTdpm4vmlx4l4xflpE+Utw9DW4cG09zRjZaxOV416pDyxKV1RiXlEyBZ7y8PG3YYsW5HIsGkF0YmhukwDaS1VwdBRU9ghNwiZT+JGorxff2T33hLcxdt7Ep3fdQCdluLDklmFXUfSnIv6Y+QcxRrForJeHWZtLcEJBANuZApBjXAKjnyC37FkUCojXSFWrW48T+G0x+xUitKpQeZCdEIbXq/SgEapkszENm8cGbkFCDHEn//wXxr5A70M3svroJezbLkL88vxcChCFUQeKrCiP9wW/Gl2shbQsR6iC+9re1wLw+c7PSa8X17zf/sroH9QCPxZ/yFt7Z1HhOBp+0eGgWS7uk6fXPdJqG7VCHUEAUTqipggAXN9tA4uYyMw+m8UL3buTbRBksWR3WL1l794QAWzpaQjQIKU9GNRt5wDqVDpQuuBBM1VNDcQ8+xA0NUUYQbf0hg0qgG393hJ6PZC3nHzdlnCB0WOPkXHpcP527goevF/F9G7TAXhw2IOo1TLqExYy9fc8rvrxqjb3ewb/GpwhgP/haNkGKqgARvTj/W/B8OHCWHT8eEG0MjLClc2//w5eL6hUrVq+alVtKIAaacKu6Qa7piPL/LNgRvX14ZnwH0HPnqLlx3CpuOIkOWgOh/DKljonkWkS4a9WvWfdbib1OwZDX4D0zSfPAUxIEDvds4cTSzqDBFBp6cTG6zYzoaPoFCIV6xF36A9RwPJ3oFOxqBAcM0HFjz+Kr0WpDPdx/uyztrfNixNkIagAWhrFdxdjiiSAe1jMlvHJfJ0tiPKoDqOim97m5wvzwU8/Pa1zmLPvbfH5cj24XGTkiQn+OJmYB44g84FnICaGLSPvJhCQkZ0NLt/JFUCTpCrarKKtWDB0GfR3M9PUJun6xj8DPl4B6+6jwRn2Tmupmrz4IrzwArz0kkhLLV47kCt6XU6zRiwCFXIfkwvPoXdqb7RKLeY0ce80xueG9vHXFYKcetWOdhNAo0KEA61+8cxkxAuJt+z3fRzY4aDZLm62qYWtSbhepYeChTDiaQYN9lJvbQ4ZkZsTTm0IHGMQA57VJj1b+fmhMPDuXWCrEuFfc8c97K7ZhS/gI0mfFCIgq0tWI5MWgDr1qVXiNza9wdOrn2b/kRb5kU4ndqnd5hHr7lbbaJSaEMkVH9TQpg9gjdbPxgzY55IWfnI52T0E2TpWHD4+++6j/IJQhc85J3IfTrMRlA5iUttO/VHJVcjlctBa8Eom4zQ2RrSCa/k8BS2Y2vq9JYLhYYeKsALY0EAmZdxzwRFuuw2+uPALyu8u564hovK63lHP0cajVFpPTcLP4J+LMwTwPxwefwsC2EIB/K/DvfeKeNe0Ft0vggrgIsmXqkMHkvet4n1uoACx2teoo7eUSjZ7hQ1BUwf47mt2r75FEL+1a4Xz6r8RffoIsS7Y6q5NAlhczHmP58K4ByB7/ckVwKQk4TMTCIS9EiVkZgqxyeuRk+TtF3o9pACW74SKCv4eDNWHP+uaa8JcOlgMvWxZRGpQBILebaVNQs21HhDHEOuP3CA9Jj0ijBa0sgFRO7R1q+B9l1wi/MdPF3FmQX7cPgN+p5u884SKeih5qJAwH34YmppYP0EUrAwYAI4BUt6nMjoBjI0RQ62l2Uefd/tw6Xeig0MEAWxDATRppIvoMkVUfl91lej8tmCBaDkol8Pdd8PLL4dDbS5jAsnJkJqmIEEflnbj48QCqNkSngKc6jIY/Ap9Uua2mwCqfQlQXUhpoyDjWbliv8cP2lnG2VzGF1yt+JRJst9abWtQGaDwRxgzi/61X1FRF/YOiUk8de6yURrmmoNh7Px8eiK8Nncc0lPVIPJl5VkbQ/l/fdL6MDRraKgSVyZ5VrbHJlJdlQ+/vsoH57Ww+encGUe2yGNTa1qPNSeGgDEfa9MH8Id8F4NnwkPGcK5n9lAxFpTW60OOWfcUXU4zJnIzXAweHLmPYXcsgkf1jLwp0nO0JWQyGUa1IHs2t7Q4bBECPlEBTNQnkqBL4Kb+N7Hxho0ntQrTqXSw5Xo+sd0dNq8OrSyF2vzTvp948483Q63obB5xDCcLLZ/BvwZnCOB/OLz+cMum/2oFMCmpdQldUAE8LhGlnBy02cncwIfYC4XvSXFME9FwdvdyuLUbjJ4FQHxyQNjLHDzYugzun4H160Xm/tSprf4UNKb9/nuYOxfMLpFk3ooA2myYXFD9SQold5acunF6X6nlUjAMLUEuFyrRU0+JFMUgggQwjoa/qwoYYGLCxtDPd94ZvhW7dBHpnKNGnWBp0QLZZhFOLbGIvKd+XV6A864lvzBSGeiR0oNsr1F0QnDEMqOHSOBfvVpE2Pv1g8sug2++aXXq7UJykhKuPouJZw0Ep5OCPuJ+OJg2CpKTaWyE4mMy5s0T7x8zBjxZorT6wVF3R53IUlzSRCuFOHNjhfL2/PPwc/w1oqNMWwRQK8LqMreJOns4h1QmExkR0fyjg8jPF8WYx0+4lRLjxL1js4SVNnlcKUy4m/MzZrU7B7Dq0HB4aze/rHoWgMxusQCUksUyzmYgm5jru4obOq9uta1aoUYuTUHWV/5KVb0gBHK1E9VlrdsctsTCAwtZ6BH7tDolNT8vj16I3N7t5UkccAhSbk1ZHMr/653SG5PGRK8UUTlRrhPXvKodXSi0rmzYeAeraqeHX1SpcHrFNdRGyTXtmtSVsV0FS5OnbYexD7W5cPuj+RZ41sKG718KvZZ5Thdk+HH51VRXw7cfWnjHeS0y/Lz7dqBVqm5QIY7XR+8CEoRRbYTfn+L2vO3syzwHmprYyv9r77zDo6i6OPxuNptN33TSIbTQkd67NJUiKkoTxI4oVsQKVkAQ1M8CSrErKqAgRUGKIB1CUSC00BNCeiE98/1xt2ST3U02CSQh932ePEl2Z2bv7Ozs/Obcc36nLc1e7QWBh8wigHMHzCVhagKf3v4pHUM6GnMCLeHi6AIb5rAw6X3iGvUQN6BJSZykIXuu1OXg6cvc+8u9vLPtHebsmAOYRKg1z1bJ9UMKwBqO2RTwzRwBtERxc+t69SAwkJf7waU7X4LnAhk90vKdcKhrIDsXwahdIger97//CWVkoQ1dpeDoKNrB7d9f4qmB+tmxxYtFUciaaS/zXu8PS/aUzczkjNKAzMKm1HEJK5FTVYJ2+uiehdecORNefVUULS9YIKYTk5PBX50orCds+VXYoHVAHL8xlDkP/McrxVKioqJgwwbrFX9GAZgqBKBn4J/Q5kvq1TOPrDg6ONJh0WyYmc7d534zdjzIyoJwfTMXQ7FJk8+miFaEduDl6gYRW3Ea6YZD3TBTy74TIoIZEiIaJ+zaJQ7rsGHQp7eKCRPg1s5BFn3egn30FjV54tw0THe3bQtDHdYQxkWrotvTRZzjbR1uoV/9fgz7cRi+7/ny838/l7ovSlwcL389nlmrpnItz5QX1rTeRZgcyaAu3YyPZeSKCJz7mAegbt1Stw0QqP+uUen9/sLCxWfyvFMjtjgN4Gy9MwwZBW9pS1Y4q1QqPAr8IaExR9N0ZOijkRqXrFJfNzs/m0QHMVWanq1/3xo0MArAI2l1SSgMAoc80nw3GbvFtAkSBRy96/UGIE8RYszRQvSuOD4+4rvhWqGnMHbX8/WmXfCSB94RZ0qs0z28O3PuElOdhWnCk9WaM4NapYFcD/KyTJ8DTZf21OMsAHs3pvLkVDHelzw/pf+QkkIyPN2Bju5NqO9gO5HX3ckdTgxhfdrdXEh0gRdfxGfGFHJ8zoNjrlkE0B7MCns+/17cpSQlMZ9n6PR4W16ZGWvsPLT+lJi5MUYApQC84UgBWMMxTAGrC43+u7VHANavbxJs3bqJJp+BgVxI6wTRw6DQkYYTLds7OLt40PkiKFn6DhPu9lmF2I2hY8nlyyVyDO+6SwgKA/GXnWmU/BSdQk09q3ILciEzk1vZSMTZzUSZFzRaxhABtCAADWzcKBrFfPqp3qUmvAPTmF1uAYivL0NZzfM99pTQM6Vp665hXdk6YSsr710JQKK+F6mfZ0kvy65qIRLyz5lalg0YIAK4ffualutZuLmE92JpGCxG0t0cSXPIY9zWTqgntSVLSaZfP1OuJog6peCAfB6L+IOl47fQr7flnNMmwXpbk1w3UCDCu8gB/+gjWLjQ1O6l+HhcRZQ/LVPNrO2zWBW9iqSsJCaumkhyVrLFdQxk/L6cmTFf81LUHJQi78OIxn1Yuv0ET+82FTSkphZCWjCqdoPLXAk0NEh8xnwyRWQzVL+b67xHk5CrI0GXz+8hAewotGxaPipjEXwczXunZ9C1jshFDfO3Hb0CRKtGg9DI1X/QGjUinPMEYkpfcAo7CJpsoo85wObphKtF5cwLXV9gSOMhqD2vgG80fm6l5/36+gqRm52vM+XVHjpEzoJ5oM3A3cVyZK9xY1izthAmiIpoaxFAF624HOfnFSlo8vKijbvwRJ0wyYUrSU7U5zTTO66zuI3jL9xFwPPv0eFvy58lA+2C2uHhJq4YmdlqeOghmD6d9ALx4S6eU5uZm8lrm15j7o65Fu2pjPugKdYOrrAQEhNJROQkZDuZCtui4qLIK8gzRQDlFPANRwrAGo4hAqhRikSDaosA1Ghg7lw4ckR0CRk3Djw8+PvEXNEO7mJngjwsd0KJyQ2hldMxfkS0jPO37TpRcfz8TKLq/Hmzp7Ra0St0wwZRTNy0qejba+CTPZ/g/LYzM04vJkUlxMk3xz8t/TUNEcCjR4VqSUkRRtsTJqDk5nHqFPQv4prz008Qm66f/i46N2wPAQHidzG/w6JcvWrWgcyIj4sPPev2JFwXjpKTS7NNd/PwsgF0DO5ZYtmuwecA2HLIu2gwBpVKFGAPHgwvD9hHK47YvS8eWg84eD8nfhvOZ5t/Zc/lPRQERMEtXwKiovn8eVFo/fbbQHo6sXcPYto7fZi7Y67FbTYLMxgNO0Cei7HiecEC+LZgFNfGPmLe1aYIng3Fe5qareGXo6Yy6ozcDL45bLvAZeVeb1iyFdVfb5n5t7Wu25EJB6HD+QLjDcmFnV1g3iUWvtzD9htUBBd3cQnJKtR72OkDhwYP4D1XnoS5V4jbZ7nC89YGQpBl5brSvj2c6PUwv4VMEh2AbODn6mcsrkhT6ackIyJQ6XQMwtSrtm6Hf0WqwJdbYOsM3pkgzp8gjyBWjVqF65Ap8GQT7mj2b6n7GuAvPkcFipbsq/oPcHQ0metELoClCFZBYQH5Dul07ZNG1gcHSXkxxWqbSfdj4kYtP81cYHVoLNJYktLFe/wWr+HUrCGW2Hi1Nb8zhCwn69O0AN/f9T2d6olUk0zcSIvN5JFHYNCZw/w1bhMNvE1h+pOJJ7ll4S28ve1tXtv8mtVOJgBfDPmCVvrPekYGYlqhsNAoAB/oOpRrLwuRmZ2fzcmkkzICWIVIAVjDMUQANUqRQ+ld+h30TcOUKSK5zIBKRQOVPpl8xfeknA2wuJrT4H4cyTVNIWuD8i0uV2moVKYo4NmzJZ728REVfR99BIf/zad5/72sPLaSgsICXtz4IgoKb8StIFURF4/fL35Z+msGB4vWdHfdJSovPvwQ1qyBr74ibelyo/m0SiWmZcePL5JQX14BWEdvw2NFAI4ZIzTir7/a3kx2YiYzr/zEF8f+oGGd9iWeb18/CR8SSbmmZcoUmD3bVFwSHg5r18I7/beUa188nDzg71e5uOJJ6l9uZrK9qLsNjUbkaYaFmbq4kJvLcXcdszu68uEey8LczdeZfo6rocUPOKAh0jeSnBwRfR03znbhued7rwKQeE3NlcwrdAzpyPyB8wFYfWK1zX05GauB8z3RXG1unjLg7s4sXmQy/+PKaXG+ZGfpLUSyk4oYC9rGJVycX1nO4jvH0AbbQJ5KTHd6WvFi9PAX0bCMQhecNQU02raEZls/KzVq6+fqB62/RvVMPb64rM+hUKmgTRueYT7upBOqucKwUUkQPQSuiXG6Hz9gLKYAyNZ/3J3HjC91X0MDvEAl7jaSLwrRUngtmw8vfofziqV4OZSMum09txXPWZ50X9JdVF8766wKKHd9X+WCPPPP63135qBCDLqd7iT38aPF3u6KAgl54rPqF1KGIhpPff4l7iT89g9ffAHLv65D3/p9zKJxagc1p5JEFLK01qKhnqH46ntXp42dJArQpk8n0V8U7Pn6iiihIQczJjkGf1d/In0jrd6sS64fUgDWcIwRwKI3jTrbd383O02d9dMzBU6kfvClxWWKa+SQ0BvQA9mGADSgUonCno6LOjLipxHsurjLeIdMlsHjphBv7zJMa6pUovjkp5+E6lqqbyU2YgS6u25lwQJxHVm8GD7+WJ/flqPPYyrvFHDfvjB1qqiMsECYaKbA5s2WV//l6C+88tcr7DwqcjcdKMDdp2RunGNIHR5lISCawUybJn7MyNLnktkpAOt51cMfocg8T2WyepQQWQFtdnP6tPkUMwA5OTyW+Be8m0nhqf5YwsHVmfd9h9Kyx2hCfD3ROmqN3R2cnQrw2vOn8MyxgL+/KNgZ88JeuoV159s7v2Vk85GsGLnCOF1ujQT9vZBTMV+4fAeY5ziJT5hMzAnxPgVoRAKl58E9ZbZCulJHfPFcyRe/vbzMtUkeQgx4Wfk4XVaLiu8kBw/e/fM1+o8pZHlTSi3E8nHxAZcUFN058tQppicGD6YVR4gliFOT5jG++0D8jomIpmu7+fRuPBiHdBFRK1QKySoQqR8ukS2Kv0QJ7mw6DC/9ayVcEO9ZVno+/6SNJvvwBH64+4cS6xg8/3IKSn8/PV3F5bi4AKx3e3O+YwyPOC1lhctYHFAs+ommp0OeIop3sn2tdwIx4GaYAsaNlCeEh6mlIHRR0WfNw7Aohm2kpCjiMz1jBonOQhwbqtOX3b2M2Odiua3RbUzvPZ3jk48zqcOkUrctqVykAKzhGCOAhUXu7u3oe3ozEtzXdAUKttwKWGgCtf5Lucc7tGhaTsFjDwYBGBNjczFnR2d8nf2hQM2q6FXGx9fVXyz+cElG52rndMmmTcJGR6cTZnx+ftx/Pxw7JgpPBg0SftqumVeFN4m1N640Bg0S4ThD25FiGJqsWBOAi6MW8+72d9l+QVhtuDtlUqhYyKsLDeVV3mZI8D5UKlEJO2tWsWXKKQDretUlUq+vM9IKjYUD8dmXcfVNLLlCbi5Z+pZuzi5W8qOcnMjSwFF/eKq56PNsqMwNzT0jzKqtRN3c3ETBzldvd2PVqN9o5NuIYI9g7mx6p9HOwxoJeo88V2fzwgoVKq76iby8UzGiLPvOUFF5G5J9TZiblwF3V5GvVpBrEgavvirqqSZMgGxFfE59dJaripedFcaQyWp31m/IZ+PZt9lQcFupNyBOaidjrmZRaxzGj4c6dXDXOaJ9fCIt3Ovjf1wIwGsNtzLpDsjaLyrVr+Vdg6Vb4LODXDhdetFDkEcQgZ5CpCcWijvIa2km0W7pLdOqhQC+mHaRcSvH8cQa6y0v6rqLMbjnFBtLy5aMcvmNhbkTCY/bI95cQ3pHEc5e0t8oajIJDLd9/r7818usOPMlAGl4koIXAPlOV1l0YJHZsi4aF6P3X6+6xZyni7H25FpOZAqfxBS8IEEcG0MDpCe3jOax3x8j0i+SQPfA0gvZJNcVKQBrOMYIoGP5bDtuRgY9K3Jb6hBHWL2SHSIAVNHHUTnrE+ib/4SuXjnbX9hD48bChbmU6MbEiZD8+jk4fqdxiu+JDk/g0uwOsYDrVZtWDCVQFKHyAEaPtiqI3NxA5aQRbSbK0QquLHTvLopBzp6FMyWLJgn3FFGow8nCOyzNNcFYNWhGaCiuZLGq1Wvk5wsvPE/PYsuUUwCCyXtvY8JZ4jLijD2a/7ta0uyXnByylVIEoEpF5z7jOHN+FE+2En2WjQIQ/R/WzOhmzxYFT+++a/d+JGcJ4eVWTACqHdRoteKqfOqCOA+yMsT77EpWmavhw/xcofN86PYeOflCwI4ZI2okliyBHLUQSj7NG1lc31snXifHwYtL0U1h2yucTr4D1JbP26LU13bAZ+0HvNk+yig0qFMHTp8Wb25kJFkHjnFc0UfLwoS5+do9awBRWKVOaAFXWqM9d9nSS5Rgzd46xMZC99Hic5qhz9dzdcyxOGRDxW92fjbfHv6W7//93uq2m/p70o3t9HU5Yf6Eo6O54GvVyuJ3SPRpkXipcr2KR6DtKu5redfIUot9TsbbKACv5J/gpb9eKrH86lGrearjU7zR5w2b2/373N/8V/9hRgybwFi+hX//JfvgcWPh1J6ktWw7X9ISSFI1SAFYwzFGAH384ZFHbFZ81hbatYNtzR9jLx1w8LYilNRqAgrEhe/Bc61M/iHXkylTRJlq0ZZxVijMdYH45hxLOAY57pz5+RE+/1z/pGuCMfpRJh54wKQ2Jk2Cv/8WbsEnT9q/D6WhKHDpkijKKSwphtzdMZrX/vVXiaep6yUuXEcviIuTg2u65WmnIUOEyli3zrpWbdxYzNc2tJwwbwt3NzF3uiDxOE+ue5Jm/s3wd/W33Mc1N5ccRYhMW4GroSlfU/fL7/lpo5gHMwSCQ7koBI810ZOZyekYFZt2u3GpSHfA7Pxspm+eTudFnY2musVJzRYC0MO1ZHTRwzUFgLNJQvhd0wtAF8e8Ms8ihOalw6Bnoc8M0nJMnpvOzmITedkiLObnZTmi6OMlxpeb40xmulhG52i9jVlR1t63kaQ9U/jx3D0UJhfx+3RzMwqkkzsTUHAA52RIaojLO/G8Mv9Z8douPjhliQilx/GyGUb+fvUj5h95kYz8FADS9b1385zSWHxgcYnlDRFAA7bM2+vXh+304Jf6U0s+WSTvIH74cOq2/xc37wxW/266OTp9UlQ/O2kTUJWSB+7u5A7dZ/PwsmnMm5lLKvrvSecUixYw3cO78+HgD41tKq3h4ugCgYcJaLJPWBvNmYPSpg1zOyzjjomHwTmVEI8Qzqee5/k/n+e5P55jxLIRtPqsFdvPb7e5bUnlc51MzyQ3CkME0EnjLKwkJJCQQPf/9O9FoJUvLE9PUrLFl16bwV9CROkRhxtF8+b6P64259UerxL/y8ss/saZiFbHodtv4BaPp5MdAnDSJNEreehQUTAzcKBoU+fpCY2KRGbi44V7s04Hn31WvsHn5wsxXVgoLG+CSiZ233qr0Id//WVqEWfA4AV46rKI6Di5WTHoLcsU5eOPi59ysNHvMJzuBZn+tAxoyZt93rR+8c7JIUcfAbQVbDSIw6Qk8TbN1RcMt+aQ7VYUOh1P8RFrV93OoqHw4IPiYa1ay9KDS7mQdoGNZzYyJLKk36Gvp6j0ubtpycpenwh3Eo7B+UJ3jlw5whdHo4D7cdGUvSBK7eqGRw6kayE1K9noyWjAnTrkALc1L1nJDeDvo4EOn9AmIpxT0eIN8tGWrROPQeMUoibtShZeFoKMEdnH6Nh7Hnt8vXnFqxPv5PlzJVmI+8JCyCoUx9TVs2yXwrf/fpur164yptEIvOp1IiNdLwC1qVxIu1Bi+eI3L7YEYIGrMyf9IEObSDtFMZ8efeEF2L0bNBruT2zE+f0iZ3HM/VlcjXVBq4W4rFzQZOLqlV6qgHd3chet4LTxqK/kGCOAOKfYd3NZDEOl+TVn/fdpQQEuFPBc7/3kDDnN75sgxDOEjNwM3t/5PjqtDn83f04lnTKzKZLcGGQEsIaTWyDu7K31l6yVbC9yJ2ktsqfT8Q7CqTg7tWwVj5WGopgZyRbHKADjm7P/chTLf3Khbv08TrUfC/2nQdd59k0Bd+wo1NaUKeJ/QwL5f8WmM5OS4Icf4Mcfy77t4mg0Ji+Q48ctLmKoD/nrr5Jvg0EA5mXqBZViIeJ2A/By1dt8ZAbQMaSjzQu3EhZOrl4AGhLrLeHjLSKiiVcLcXQUKaEax0LuZKXt0KGnp3GauGj6qEqlYkTTEQB8uu9TYtNjS0QonUNDcXaGJl1Ktu8KDRRq9UJsNgnXEsgJ3Yiu6SLaulo+bhbRanFPCIKrkcReLen1N9ZlOfd7ryYo+bSFlcHHzRNun0yj9m+RnSVEcIhz2Tw5nZ3BRd/LNvmK5XPY43I0PZz+pHWLzfRqIT5bKXnupKWZMgQA3LzK9v3pcbAbrPuAb54VMy0Zd44TTzhlWLQxKW76XDwiWJQMH3eaToYO/U4bv9eNuLuLlperV7Nlfajx4fRkF/7Qd9mr1/cQvOxOn9dLRiKLY8gdzcjNgOhoMwFosa92GXHVuEJKOEcO3s0yinRMqVOHS2kifB3iEWJs+5iak2rs/e3r6ltie5LrixSANRzDF0VZqrNqDR06iKtDz55WzXVxduYZx485TEueubvknft1Y+JEEbrYuNHqIkYBmNSIyPyRJCZC3CUNan/R5eDvwT/xdOenyz8GQ5lmdLT544YrYnkrgA0YvECspCN06iRatX1mwe3DIACJ2AxDJ9KyufWcKV5/XajJ65D20LX5bri/L/SZTpfQLjaXzfULRtHbML078FWrywUuFxYxF/eLXK1334VdS47RgDO233OdjmYcBYRm37kTVuvdX57o8ARqlZr1p9YTPC+YoPeDWH50uXHVX38Vh7VoC20DTSO8ALgS50hcRhzc8g2tOz3MIK+SXTus4uxMwg+74JPjHDhQMlr7QfZjfJU8lAAfy1FFQ7Qp+che8jLFeOq+ar1QoijfHPqGPFcheJPjrUQNY2KY+yccDHuXWweOxMtVfMZjzhawKdrUttBFV7bvT9f4zrB7CltOiLSCDJVeLDllWDQydndy555m9xDgJmxobN1IuLbqAHMvwcxkU0FHMa6kJZFzVuQDdms8g8+fW2xsdBObHgsqCPP1K3U/3J3cIbEBuz4ezQvr+jCV93hv4Xzo+VaFIoDuTu5wpSVRv73GXGdxLlwmiD15bTh1Tkzth3iE4Obkhr+riBYbjKV9XaQAvNFIAVjDkQLQAiEhwkh2wwabUyEO+bm05F8cutm+wFcqhYWiynbQIDHOd94psUhoKHh6KlCoYf+aWwDocks2DfUVhzk+OuMFpVxYE4CG7gbl9QA00KGD+L3NcrK3RgPffy9EiaOjmI2eMEG41IR4hKBCBX4noO1SuoQftP46O3eK6ubDVhrfd+kiDBY3bbJ7F54f/QDejfcxNGQgHZqE0K27wuAvR1Dvg3rmVaeIQzpunLBbbBFipc8d0MRdRPGOnRXv76BB0DZcv61SIoDNEdHaX3+Frl1Nh66RbyM+ue0T4/mfW5DLY2seM34vfP37O8xe8SzHL5VsHfOA02aY1IzsO4ZyIlEUHkQ06wJv2E70N0OjwUXvu5mTbn45uZp5lUG3JfHgUFCs7J+XsxdkeXGqsDGqJDGHGxFWNh/TrPws8l1FHm/yVcsCc2FUR75nFMl+jSgMrEOKp3jjoo4ncSkxBQAH9TUc3Mr2mQ9zF2IlPlMsP2wY9Pv8LrhvuMUIoKfWk5/u+YkvhnwBWG8DB6BRO0K2N+R4kZhmOadz5V/nIc8NB+cE/j7xJg//bxKqUyKXNyQd2rs3pommdD89dyd3yPbiwt/D+cHjEdxefx5tKwfwuFLuNnCgN1F3EcckJbQlBAWxghF0eqkvexePFeP0FDflhsIqA94utci/tpogBWANx1AEIgVgMXQ6q71VjRjCIk+ULeJQKYwaZfr78mXhmXHAPAFdpYJmzYRw/WdFSwB61DlBpF4rRCdVsHjDIABjYkxNc8HUfqSiRuIGC5g//hBi1wbJySIl8auvRHB03RoN/0z8hxYIQ+l6tnqaGpyYiwtZA4mJ4gU09qdHtO4ynISXUsneuIDYWNjxj4p9f9XlXOo5jl49auxXDOCSEsvXj2znl5knbb5UM08hAHcd9zIVwDRsKPrwvVSy8tKITkdnduHlYHovi7rsPNr+UZKmJpHyYgoDGwzktZ6vUVAo5tYXrX2LaUfmc2TfmhKbbaMuYPahYxyI6yry19LrENRsCMroMaW/QQZUKppkCAHY1KmV2VMxV8/zR4AfayKcUFmpfG8T1IZm368l5rtoFL3PZVBgGSuQPcPARUQAE6+WTKlQFHgh9RXG8D2XPZugdlDj6i8sbw6dSCEjOwu8T+HifqbMNz2NfMUlMzlTnCPqRQvJvbgX3BJttjLLyRdV5bYigAAqJyH8rAnAMylnoPEqQkKXCz/AqVON5norJk+k7vPvcPvq0t+/ALcAmoSJ/OjkAh288QZpuSLtoSICUOQWpgB6H8DYWK4iIn0O7ok4qBwI9hAWNUUFoIeTh7yGVQFSANZwZASwAnz9Nfz8s2joeqMYMEBc7AcNMrVN+/LLEovdequo2SjU+zv2PLGIxnovrcnrJnM182r5xxAQINxaFcW8EjhZb4tTUQHYsqXIM8zJEaE+G5w6JfSZwTx27lzoEtaFR45PYfwv/Wme18r6ytYimQYM/eZK+MOUjd9+U5FUJKXO8aTIt3tx44uMWl5EyK9ezZ8TevDO3KFsObvF6vYifa4SjMiDOnhQ/2BIiChUud9yqzQAfHxwbxjEgmb/o107mD9ftAsEcQhzckQfVZ2zjvVj1/NUp6dw0bigKLB/1R/w/So0qtASm3Xw8WXqP9AirlB0elh4gFl3vGQaWxlxdxBiJSPFPAq3/0AyzL1CwsJLVttThuvCucVVqOZJjgvZ1e056u79xeKyxQnThYG7mE6PSyipvOPiID1HC6oClhcKE3RfH/EZP3E4CbfAWJjSiP6DWpY57eGWECEUMzP0xWXffktmnEghsdbKrFApZFDDQcQ/H8/ykcstLgNAejoOaiGmkwyt5ooxdfAtrFOG803eY+SePc2HnbvSctx/jB1byNbYSJZzN56N6pS6Hz3r9mT7pN8B0SXy9dfh0oqn+LrnDqZ0nlLq+tboEtqFDQ+L45ecDEq37sQ7i3y/yX1GkvtqLm31/aOLCkCZ/1c1SAFYwzEWgTjIIhC7cXERUcAb2TtZpRLJX+vWiRYcarWpbZqiiOcUhbfeMhkbO2sL6fzfIhqlmE7Xon1dyzUGS9GzyhKAKhU8+qj4e7HthPQmTUTf2CNHxP/btom3Y+mGMXz175+kp3a3vTKYVi6OQQB6lCOiceUKh5fu52BUIcOGiYeuxYjKy10Xd7Hjwg62nRNT3AWZ2Sxv6MyrQcfZFGN9ulmjc2UrvVjx6HqefdaOsURGwsmT3HvkVfbtE4XaKpUoomnTRnQJsURGBly71AtODMHf30LKgI8P7/Msjx54mHZuwyFHFBbpYu0oAgE86orPS3q+eRQt+rywJXF2TLYZYQsNEN9h6vwcOv0zD+0lCwaRFgjzDIMBz8PT4Yz9omWJ540fba+z+OtvAuo77oYG63Eo3E2q3rbGq1s/U+FSKXSqJ4RKYZYfaZm5/HyxM5e2LMTx2N1WI4Bu77rhOcuTa3nXRAs7azg7o1aLPLnkpAyLi/jtP8agkwq9NA1RhYbx8trZ/Lu2B999J74bwjmHrnW9Mu1L0a4f8+fDgg89aaDtQouA0ruiWMND60EP/d1JQYGK5DPJxIeLVo7+/sJ/0tAKr6gAjPCKKPdrSsqPFIA1HBkBrMEMGCAMbA1Vt9u2wSuvYDD8a9pUeNouG7AEF7IZFTGEB9s8yOd3fG5zuqlMzJsHe/eazyVWlgAE4T34/vs2i11AaDNvb5H32Fq0B2XjRrhyTUwZ1gmyYWfRXt8j+PTpkr2HCwpMOY3lEYBnzzJ9dXsyQprw9dfiobR4b8gUAqC+d306hojK2r0nvfj8jyz46JTt6TMPDxpymjsbHDGlpp4/L9qinDhhfT0rpKXBoUPwv/+ZDh3AuZRz/Pzfz1y+qA9fOuQRHmZB4Hh7s4iH+Dx+BBt2X4Q88ZnSffimXeO41kqIyw8Pm0e3oi+KKLWnQ4pNY/HC4DgAvgqPYGE7ytyFRueswzcoE7wuEJNWMgocvVO//77RNPETNwsD2+2EcYPxafaFsWLau7FlY2VLNKkbjJO+8jg+VsPW5NZcOfEILzm/T4/wklY7oPfGA1NLR2toNDjqBWBKiuUp4Cv/nEIB6NgRjVrDrd29QHfO9Fp1/7TYJcQSarWpa6h+Ft/YyrsiaLUi9RYgdtEa4gNEVVtAsXuQu5rexZmnzqBMV9g03v48XUnFkQKwhiMFYA3Gycn8NnyRvgXT3r3Gh+rXh6Hf3APLluHxwqssGrqIh9sVM88rD127CgGVnCzmmkePhmeeEf/PnFnx7Xt4wLPPWm4uaoUBA8TvtWvhSo5YL6i1jSuSl5epZHrnTvPn0or0Qi3PFLB+3NrUeDw94ZtvYNcuhan9HqNzaGeW3b2MN7e+yV0/3UWcwUbIKcO2hYZBiKYXmd5bsUKY/NpTeKFn2DAx256WBh99ZHq8+9LujPxlJL/v3SoecEkkMNBCcYq3NxEIX5nm+aYpaE+dfe25XNxEYURcsajV6XhxDHydbAuf71x+BiDt/BA2F9xq0TvSGrcE3gJAVFzJIpejq/WRTL9oIv1ExLu+d30AzuRcYd+fDWDBAfZ/O6LMr+cQFkq4vvDk0iUVSTn6Vnd+Dlbbmhksm8asGMOvx3+1uf3APJGT651Xcko0+lwSgTOnoPPMJOdpkbYyNPIO6D1dLKAqoFPzVWXKZ0zKSiLy40gync2F8+pLi0Q6QDnJzs/mza1vovIQoj7WqS5Xr4r35Z39U3juj+eMy9Zxr0OEt4z8VSVSANZwpAC8Sbh0SeQjgqiG+OcfWKNP3NfpYORIU8SrslAUIUBWrxb+fx9+KIRPZUQAi7+OoReUDe66SwRABw2CgkIHXFwgcHRf2yt16ybCFnnFbEAMEUFPT9smy9YwCNfUVCgoYOxY6NRJxeyBb7PzwZ20D27PkoNLWHFsBdGZ+n3TptmOALZvL1IODAl8YHpfSstBGzlSGAfu2GF8yMFB1BABfPCBSfMaIpPr/xOiSO2SIIzii+PtTVOOAZDwn5hC9eMqGp196QWD+gCdPiDF70/j91GhUkhWtngv6vawHZFq1tz0d0pcX7sEYKPYJviunc9vT5X0xTxwUeyz1v8kQe5im/WDhAfmqfx8cuPrQFwbck/acRls1Ih1B4OJjxcuU0l5Yh+9/a0XXui0YmwH4w6y++Juq8sB9M8/TWd20syz5P6s23UWgCxNAtoOIjf23hb34dvpN3iwCzzahhcfu7NMu+GqceVE4gny3U3Gkg5OWTyz+WH2Xd5Xpm1YQoWK6Vumk9hrDL+ty6B9e5GLCXAo40/2xZZ/25LKRwrAGo4UgDWcpCRhVxIaKipyW7QQ35jdu4uI3PVEpTK3SFm40GL7tgrxzz/CiPqRR0pdtFMnePtt0/RRw4ZlaEk8c6Zoc3f33ZCbKyqbDeaC/fuLq3R58PExvXjx6WU9hmnFk9f04lObajsC+MADQuQXrQQvqwCMjYVz5zDrBYcQzU2bigLuDz4Qj3UIFjY8/5wVlcrO2pIGzQD4+NDUS1ydN24UUZpgLpd5OtTAY1/di2efZyhssJb1p9YD8N3h77gYLyKdYXVsT8F3btsA2n8KAYeZ6LDQLgH4WP5AEvc8za49/Us8dzxRFGpEBCcYo3MNIzrgNvMicfOSqJfYG4AOB/8t8+sBFHhFM+fgVN7YMp0rioguL4yz3oWpqGl7aSbLC0LeYidd6d8yrsRzO/aLnEXf8CvGx9yd3Fk1dg2Denvx2YRHaTZkYpn2wdnRWVQkD5vIvAXi860NEJ+XivgAah21Ih+9/ibadk3B01Oc033H7Afd+YrZV0kqHSkAaziGVnCyCKSG4u1tamQPoiL01ltFaezJk9Cnj8jyv3LF+jbKS14eDB8u8s88PYW4aNOmhMioEC4usG+fyHM8f7705YFjIihF48ZlWNjHR5gJAowdK+bMhwwR6vHPP02Oyfai0ZhMxM+eJTVVpGa+9pppkYbewgz4Qq5ecGrTjB0WyoxBAJY2bWdIzoozFwZqtajgBKGFT540RQDV2WKdTt5WLuiurjRZPcfsofIIQJWbOy31GnnYj8OYumEqY1qNYVwjcQNjEPTWGBo5FPWQp2hwX2uG56TalTYQGiFufBPyvMw6ewCM63w7jLqDW5qaosPeDZoRlCPe88PHxXemVxk7jxi4khHHnB1z+DJqKUkqES3/L8d6ZM8QAYTSLVaSdU6c8IW4lIslnjt6WFRZR3ieM3u8a1hX1o1dx2Od7LOz8nb2Bs9Yzl0SQQQH/xOmxytA0S4jDg4weTJ0mbgSnK5Rx60SkgwllYYUgDUcGQGs4ahUwgfOy0t0tXj4YSHGevUSz2/ZIq7wxac4KwONBsaPF/2ADaWuhw9XblV027ZivwoKROFJGbiltYIfV+m1+nn7xOid+umvNWvgu+/KMdhi1Ksnfp89S06OKGx++21TCl8DH5FXF2eo7CxtChhEhLWo96Jh3ra0PMX6IneNUyXzs+69V+RPZmeLXMV2Qe1QoSIjqwCtViGyR1urm21eZPp1WNgBBrHebgGY7+LBgKhASBaFJo18GuGgcqC/7ixjvNfS4dAim+t3DOnIifv+YXfiCJw6dC61j21RfEJd8UYUczz21ftGvz3y8ugZe4g7C9fQt2VX0wqBgYSrhG3LkdP6ohdX+84tde+3Yd18zq2eQLJbGABe3tYj5/ZEAN/qCZFPwgeJJX0bL54Wn5HWCX/bNV5rGIyXL8cKD8UCX1FN7+NSimIvBXcnd0iK4JslWpbr64KuZIgbWCkAqxdSANZwpAC8CejfXxRfbNxoMi2+4w7T8x07iini68kbb4jku08+sSsCUyYMPosLFojpWhsUFMCCTwvpznYeyF1gXwHH3XfDm/oK1vffL9lnzl4i9Anqp04REGA6BNu3i2hb/B4h0q/mi1yzUe1vp6l/U0tbEvz2m4hW3nqr6TGD+bauZM6XGQbbHgv9lVUqMXv/ww/iMOqcdaLoodv7LDu42qxApDje3qKQRKOBp+qtYgof2S0A1yV3ZnpULIG/rOPtPm8zsY2YhhzXdB/fJt/OcH4tdRv1g5rhi4swgrQDlbcXkYhChq837eKOH+4gOz8bLlxg+DGFFb9qebi3qfAAtZo6Xc2nmHW6NOzhmioCdj8Nh8aTni6+d339rH/WOgab+jCXNr16LH8WzDvP+t8mmD2uKAppcfUA6FnHvoilNQyRvpHP7OXQ4QKyW34mHq9gRw4PrQfEt+TdFyMYNUpkgVy8Kt5jOQVcvai1ArBevXqoVCqzn2nTplX1sOxGCsCblNGjRQRKo6mcqtzSiIgQ3oSTJlX+tm+9VeTi5eRYN63To1bDz5/Es5IRwmDYHjGi0YgwnZOTiGQ6OMAvZTMVtshDD8H69aD/Xuii7xh4223w8svw8//aQEYAmd67GT4cbu8RZnsK2NNTiNKi7tIGAVia6DZ4Hh46ZDFPs149uO8+U/Csb72+9AjsRNKZI6hTE61vd/p0lmcMJGX+Uvq+3FkYwvWwbGdiDV8vEUFyyQzklZ6voHZQiycMNjxliSh7eMC335qHJMuClxdNEKJYk9SKjWc28uKGF1n0cTZv8SrHgvqWSCQ9F2EeVa6vs09QNQnRh4BTw2kypwtMjiQ8yHoO55OdnqS5v9iv0gSgIy6QFkbqVfP37L9zcSgZIno2sEn5O3UUxSD0krOSCWmQAjpxc1YpU8D+ond1Xp5IZz68ciAgKn8l1YdaKwAB3nzzTWJjY40/rxpK6moQUgDepPj7i2S49HRhE1KTMZhfgzCGLtp9xBJFo2J2TAcCwmxs7FjT/4YoXnno0UP0qdNHZe+5x/RU/frwz+5scI8np8WnfP/6HsYML8XnzV+0xDIrKnn8cSHw21qfpgVEBbGHh8gFNfaRs0x6OtwfPh2f2BSuzHwVla3vtcREGsX8iWvsaREBfvppaGWj+4oF/LyFAEy4ZspjLCyEE+e0FOBwfY3WfX2NEcCumgkAfLTnI95c68rrvMX+nk+XWKVFU1NVuIM2iTB/+6aAQ0NBo86AQg3HY1LB7wRhnrYj9BfSxLRzaCnL+XkL8ZyZbp7THXX5CHSeh67xN/g2t95v2h4a+TSiZUBL3JzcSM4W1jbuTu5o1BXLJ9dpdeB9Bo3W1BnGJeQkDioHOQVczajVAtDDw4PAwEDjj7udUx/VAWMnkAqetJJqiLNz+SxMqiPdusHtt4s53qVLbS97Vd/mzrec7aHeeEOItyeeKF1YlZVLlxjRJoZ77xUac84cCA/w4vzT5zmzPJQ5z3Tiy9/ftr0NgxNuUhLk6y+Od90lIoxNbUwdg/gcjBol3seWRbpefP21WU7hihWiiHbG1ACufr6OPduXk+hko6o2UN/SLK5k1WlZ8dOnQKbnOpOrt0Q8dw4i5z2KL4kUuFzH71VXVzo4iyrezEsBPNnxScjXcOGU2K8LI0r2oh7aSC9UtSkMHOFLo4b2pQqoAvwJ0+grla4I9/IQzxCb68Q+F8uxJ47RwNu2eAs8KfqCZxUL2o7pcisn8z/hj8z7Rc5uJTBv4DwOP36Y0S1HE+wRzKb7N/HjXT9WeLsfDvqQQ5OiGDjQ9L5umzGTvNfyjAVKkupB2bpu36TMnj2bt956i7CwMO655x5eeOEFnJxqViQtt1BGACU1hJkzYcIEIXpsYah4NogTewkNhb8rJ1EegNmzYdo01A88wI8/LjF7KsQjjDUFjkzvDY0ufM8EbEzX+/qKiKaiQGKi/W0X5s0T0UjDd1R8vHg/Fy0S+aNOTrRqJWZe168HiMCJYDwCY6xvs6gA3LhRTLnfcou4+SgjXp2b4KAqpFBxICFBNPL4V++sUpdzqD0q0LawDHS79BP/xUHTplqy82ezfkMuJwuccXBPYNLAgSWW73d5H24+jmQ2/52xfV+Edvfa94L+/vRgG2foAL8sQ+1xudTInqvG1WgbZItgJ/F9nnPNfKrYoVCh4eGLNMyl0gRg8fH1iehTKdsy5MG+MR3iLovTXTj7OICdAX3J9aXWCsApU6bQtm1bvL292bNnDy+99BIxMTEsWmS9Yi0nJ4ecnBzj/2lp9iUPXw8MNjBSAEqqPS1bmkevrGEQgJXRl6oyaNNG/N682ezht94S3tmJidFwLBvdjFKErVotRGBCgohyBgSIbXp5iWlXx1K+jotPpSYkiGnhbduER83kyTRsCL17i+JxgPbswynIRiTVYHVz/ryoBL92TVQaNyj7NKPDiOEEh4j6nvPnhQD85x/xXCsOV35RUTGcfVxppi9cddG40CvjY04C9/bOR+dQMufOuUEoySltuFzQnLoP2ecBCEBoKGOzv+YrREPnnzMfZFDTUo59GWkYJIR3XqZ5scSmH+Npl+uMzgkIC6uU17retG1r1tRIUg25qaaAZ8yYUaKwo/jPvn3CifyZZ56hV69etGrVioceeogFCxawePFiEhOtJ0zPnDkTnU5n/AmrBidiToEQpNIHUHLTEBwMgweL6ufqQJcuopDg7FkzWxoHBxHIA6DAmeDAMtyEGfrcnjsnLGD69RO9W4vcWJaZZs1g1izx98yZxmnlxx4zLdKfDabcQ0sY7GX+/dfkSWhreSsYUi1jYoT41LezZqjHlvJP5ZeDqChYvEjk0T38+yjLVefh4WgKoW50Oae9W7ak321uLOQRFjOR4b2ycNGU3n6tLLSup68Gz9GRmiqmUOf8upZ+Y4Pwd0oka/MucSNRCWyK2USzT5ox7Mdh7L+8nwX7FrDjwo7SVyyFg3EHeefvd/j+yPfG/3t92Yun1j1V4W1LKpebSgBOnjyZY8eO2fxp0aKFxXU7d+4MwCkLPlsGXnrpJVJTU40/Fy5cuC77YQ/Z+SL/x1VzfadZJJJKoaAAnnpKRJgMuX7FGTFCNASeOvXGjs0aHh7QWuR6GUNbiEibEdd4GgSV4YZw8GBRruvjA4bvDx+f8hdKPPigEFiXLxsjlCNHipqbSe5f8QJzbAu6evVM09Igppc97KwyVRTuuTOPZyfnkpoqPAmTk0VQc+jVxcLb8nry448wZAirH19L9+6gKCoGsY7e6u0QHl5yecONe2KiqDy2V3y3b49qze880u4AE1mKKqzyLJqCQwJozUF6uu8nIwNmbJnBi7NOA1Cv3UlcuraptNdSq9QcSzjG8YTjrD6xmsfXPM5XB7+q8Hb3X97Pq5tfNQrAsyln+fvc3+y9LMOB1Y2bagrYz88PP0NGsp1ERYm+mUE22hBptVq01Swp/1qeuGuXAlBSI1CrhZHemTPCsHnChKoeUdno3l2El7ZvFwoL6NABVCoFRVFB6C461e1aykYwRexAiFywLFLKipOTGM9nn8H330P//qhU8NI0Bd54FMixLQC1WpHzd/CgEIH+/vZXXq9bx5PP3k5B2w502rmHvDxR77Ns2Q2qYTp9Gn7/nT7jwpgx4zbUx//l0SV3o2rezPK0upeXENyZmTBunPCPtBdFMXky1q1boeGb4evLQdqATzgfXHiGN+afh90zAJj7agUq2i1gKFy5lHaJy+mXAQj2CK7wdg1G0klZwu5ImkBXX26qCGBZ2blzJ/Pnz+fgwYPExMTw008/8eijjzJ06FDCK/JlXAUYBGBlTUFIJNedoUPF71WrLD9vaLVRnejeXfzevt34kJMTrP3wFK11v/FwyBuMsDcPzDDbUNHvnNGjxe8VK0zRrMJCmD5d+CKWlkt54ICpZV45pn8N0UuHzHQmTBCbWLz4+rq/mKHPY3SPPckLL8Cz4ctx45oQtpZQqWDKFPH34MF2FbwYycgQkU1X19IruO0hLIwcNWx2vMgzH/8Bq78AYErzjQzZ/HqltmkMchfBjsy8TKIThZVOZQhAo7+g3lomLkNMtUsBWP2olQJQq9WybNkyevfuTbNmzXj99dd5+OGH+eGHH6p6aHaTlScaYMoIoKTGYGg798cf5m3RQEwR+/mJadHY2Bs/Nmt06yZ+HzpkJlAH3enCwan/8fmAe+yzYtq+3SRCKlrV2bWrEEFZWSKSByLS+tJLovuKaxm+Gwxi1JATaA96pafKzGDyZLGpOnUQ7Qz79hXT09cTw/tn8Jc0vAdtbEyXvv46/P67iJqWBw8PEUl85RVT957KIDCQOcP96TvKCdZ/AIqaB8blMv/YIFRz51g0AS8vbk5uxj7F+y6L3PggDxuWQWXEEAFMzhIC8GKayMMsrVJacuO5qaaAy0rbtm3ZtWtXVQ+jwsRlxHEkXvRvlAJQUmO45RZh1XLxImzaJFprGDhzBnJzRZQmIMDqJm44ISFCULVoIYpB/vc/4TU4bpxoC2IvhpZ1IJLmKoKDA6xcKYRQeStuW7QQgqksVdrFMbSxSxWee56eCCG/bZuYKq2kogWrNG4sfp8/LwpZDHma7dpZX0erFfPUFWH69Iqtbwm1mns/3ccb7ePJT4ykbed0FtzxF6pvCoQ4r+SWkCGeIaReTTXOJBmighXB0EkkKSsJRVHKbIItufHUygjgzcKaE6aG4VIASmoMKpX1aeDdu8Xvtm2vv3Cwl3ffFdOtS5bAF1/A/feb/FbsZeVKePZZ4Sjdv3/Fx9ahg7n4O3dOVPZmZJRt/Z07ITpamE3bi4/egyU9XfT+AmFRoyjiWF/vKmA/P/EaiiKMsa9eFX6GnTpd39e9TjQKCOfnT5vx9stX2dJ/AU7ThN0Md95pf35mKYR4mBtYN/RpWOFt+ruJNIK8wjySs5ONEcAwXdW7ZkjMkQKwBlM0XC+bbEtqFEUFYNFpLYMgNDTerY7MnWvyPbnvPjhyBGMLjLLi5gbvvw/PP1+5F3VFEaJv9mwRzSsaabTFM8+IKffISPtfs6jwNLTxM0zf+/uX7m9YUVQqMQ0Owhx7/XrR07iGmfoXZfitDryydgAeb00V3jre3uKGoZJpE2iaJg/2CEbnrKvwNp0dnfF3FSLQIP4cVA4yAlgNqZVTwDcLHk4muwYpACU1it69oXlz6NNHTNtduCCmUn/9VTw/blxVjs42ajVs2CCmXK9cEX4nixYJS5aqZM8e0f4uKMjUb7isrfAqUrGhVotp4NRU0ebO39/UWs6Gq0Kl0r+/sMHx8BD9m2syBQWiL/PBg+Kzdc89IvIcXPECjeLM7j+b6b2ncyjukLFoozL47b7f8HL2ooFPA/6d9C/5hfk4qGS8qbohBWANpktYFwY0GEBD74Y4OshDKalBaLWmfmGKIqw4jh4V/0+bZr2Cs7rQoIG4SK9bJ/5v375qxwNChOmN7o106HBjXnvECDH9a/B9MQjA8rbzs5eJE2HsWBEpq+mo1SLH9PJlYRR+nSOorhpXuoRVbsS9+Pbk9al6Io9KDcbRwZE/xv5R1cOQSCqGSiXy65YsEb+bN6/qEZWNN94Qva769hWRmqomMlLkJX79tfi/fXu7WrpViCXmPZKNJtc3KgLo5nYDfWduAGVtmyiRVAApACUSSdUzbJjJHqam0KGDmGqt5MT8CvHRR6LF3OnT4u+qorBQFIeUJ6dQUuM5fOUwq6JXsfrEahwdHJnQegIPt7vOHWEkdiMFoEQikZSX6iT+QEwDr1xZNa+dnS1+vLyERcrrr4t8Nkmt4+jVo7y2+TXj/4MaDKrC0UisIbMyJRKJRFIx5s4FFxd44QXTYyrV9a8AllRL2gWZezB2Du1cRSOR2EIKQIlEIpFUDEMP9nPnxPSzoSWdpFbS0KchXs5exv+lAKyeSAEokUgkkophaMe2ebOoXI2MhP37q3ZMkipDpVLxbt93cXZ0ZkavGXhoPUpfSXLDUSmKolT1IGoqaWlp6HQ6UlNT8fT0rOrhSCQSSdWQkyNy/wy9nevXhwMHTG3iJLWSgsIC1A7VrKOPHnn9lhFAiUQikVQUrRaGDxd/u7uLQhQp/mo91VX8SQQyQ1cikUgkFWfxYtGFo2dPEQGUSCTVGikAJRKJRFJxXF1hwoSqHoVEIikjcgpYIpFIJBKJpJYhBaBEIpFIJBJJLUMKQIlEIpFIJJJahhSAEolEIpFIJLUMKQAlEolEIpFIahlSAEokEolEIpHUMqQAlEgkEolEIqllSAEokUgkEolEUsuQAlAikUgkEomkliEFoEQikUgkEkktQwpAiUQikUgkklqGFIASiUQikUgktQwpACUSiUQikUhqGY5VPYCajKIoAKSlpVXxSCQSiUQikZQVw3XbcB2vjUgBWAHS09MBCAsLq+KRSCQSiUQisZf09HR0Ol1VD6NKUCm1Wf5WkMLCQi5fvoyHhwcqlapSt52WlkZYWBgXLlzA09OzUrddHZD7V/O52fdR7l/N52bfR7l/5UdRFNLT0wkODsbBoXZmw8kIYAVwcHAgNDT0ur6Gp6fnTXliG5D7V/O52fdR7l/N52bfR7l/5aO2Rv4M1E7ZK5FIJBKJRFKLkQJQIpFIJBKJpJYhBWA1RavVMn36dLRabVUP5bog96/mc7Pvo9y/ms/Nvo9y/yQVQRaBSCQSiUQikdQyZARQIpFIJBKJpJYhBaBEIpFIJBJJLUMKQIlEIpFIJJJahhSAEolEIpFIJLUMKQCriE8//ZSIiAicnZ1p164d27Zts7n81q1badeuHc7OztSvX58FCxbcoJHaz8yZM+nQoQMeHh4EBAQwfPhwoqOjba6zZcsWVCpViZ/jx4/foFGXnRkzZpQYZ2BgoM11atLxA6hXr57F4/HEE09YXL66H7+///6bIUOGEBwcjEql4tdffzV7XlEUZsyYQXBwMC4uLvTu3Zv//vuv1O0uX76cZs2aodVqadasGStXrrxOe2AbW/uXl5fHiy++SMuWLXFzcyM4OJj777+fy5cv29zml19+afGYZmdnX+e9sUxpx3DChAklxtq5c+dSt1sTjiFg8VioVCrmzJljdZvV6RiW5bpQ08/DmoYUgFXAsmXLePrpp3nllVeIioqiR48eDB48mPPnz1tcPiYmhttuu40ePXoQFRXFyy+/zFNPPcXy5ctv8MjLxtatW3niiSfYtWsXGzZsID8/nwEDBpCZmVnqutHR0cTGxhp/GjVqdANGbD/Nmzc3G+eRI0esLlvTjh/A3r17zfZvw4YNANxzzz0216uuxy8zM5PWrVvz8ccfW3z+vffeY968eXz88cfs3buXwMBA+vfvb+z3bYmdO3dy7733Mm7cOA4dOsS4ceMYOXIku3fvvl67YRVb+3ft2jUOHDjAa6+9xoEDB1ixYgUnTpxg6NChpW7X09PT7HjGxsbi7Ox8PXahVEo7hgCDBg0yG+vatWttbrOmHEOgxHFYsmQJKpWKu+66y+Z2q8sxLMt1oaafhzUORXLD6dixo/LYY4+ZPdakSRNl2rRpFpefOnWq0qRJE7PHHn30UaVz587XbYyVSXx8vAIoW7dutbrM5s2bFUBJTk6+cQMrJ9OnT1dat25d5uVr+vFTFEWZMmWK0qBBA6WwsNDi8zXp+AHKypUrjf8XFhYqgYGByqxZs4yPZWdnKzqdTlmwYIHV7YwcOVIZNGiQ2WMDBw5U7rvvvkofsz0U3z9L7NmzRwGUc+fOWV1m6dKlik6nq9zBVRKW9nH8+PHKsGHD7NpOTT6Gw4YNU/r27Wtzmep8DItfF26287AmICOAN5jc3Fz279/PgAEDzB4fMGAAO3bssLjOzp07Syw/cOBA9u3bR15e3nUba2WRmpoKgI+PT6nLtmnThqCgIPr168fmzZuv99DKzcmTJwkODiYiIoL77ruPM2fOWF22ph+/3Nxcvv32WyZOnIhKpbK5bE05fkWJiYkhLi7O7BhptVp69epl9ZwE68fV1jrVhdTUVFQqFV5eXjaXy8jIoG7duoSGhnLHHXcQFRV1YwZYTrZs2UJAQACNGzfm4YcfJj4+3ubyNfUYXrlyhTVr1vDggw+Wumx1PYbFrwu18TysaqQAvMEkJCRQUFBAnTp1zB6vU6cOcXFxFteJi4uzuHx+fj4JCQnXbayVgaIoPPvss3Tv3p0WLVpYXS4oKIjPP/+c5cuXs2LFCiIjI+nXrx9///33DRxt2ejUqRNff/01f/zxB1988QVxcXF07dqVxMREi8vX5OMH8Ouvv5KSksKECROsLlOTjl9xDOedPeekYT1716kOZGdnM23aNEaPHo2np6fV5Zo0acKXX37JqlWr+OGHH3B2dqZbt26cPHnyBo627AwePJjvvvuOTZs28f7777N371769u1LTk6O1XVq6jH86quv8PDwYMSIETaXq67H0NJ1obadh9UBx6oeQG2leCRFURSb0RVLy1t6vLoxefJkDh8+zPbt220uFxkZSWRkpPH/Ll26cOHCBebOnUvPnj2v9zDtYvDgwca/W7ZsSZcuXWjQoAFfffUVzz77rMV1aurxA1i8eDGDBw8mODjY6jI16fhZw95zsrzrVCV5eXncd999FBYW8umnn9pctnPnzmZFFN26daNt27b873//46OPPrreQ7Wbe++91/h3ixYtaN++PXXr1mXNmjU2hVJNO4YAS5YsYcyYMaXm8lXXY2jrulAbzsPqgowA3mD8/PxQq9Ul7k7i4+NL3MUYCAwMtLi8o6Mjvr6+122sFeXJJ59k1apVbN68mdDQULvX79y5c5XfqZYFNzc3WrZsaXWsNfX4AZw7d46NGzfy0EMP2b1uTTl+hgpue85Jw3r2rlOV5OXlMXLkSGJiYtiwYYPN6J8lHBwc6NChQ404piCi0nXr1rU53pp2DAG2bdtGdHR0uc7J6nAMrV0Xast5WJ2QAvAG4+TkRLt27YxVlQY2bNhA165dLa7TpUuXEsv/+eeftG/fHo1Gc93GWl4URWHy5MmsWLGCTZs2ERERUa7tREVFERQUVMmjq3xycnI4duyY1bHWtONXlKVLlxIQEMDtt99u97o15fhFREQQGBhodoxyc3PZunWr1XMSrB9XW+tUFQbxd/LkSTZu3FiuGw9FUTh48GCNOKYAiYmJXLhwweZ4a9IxNLB48WLatWtH69at7V63Ko9hadeF2nAeVjuqovKktvPjjz8qGo1GWbx4sXL06FHl6aefVtzc3JSzZ88qiqIo06ZNU8aNG2dc/syZM4qrq6vyzDPPKEePHlUWL16saDQa5ZdffqmqXbDJ448/ruh0OmXLli1KbGys8efatWvGZYrv4/z585WVK1cqJ06cUP79919l2rRpCqAsX768KnbBJs8995yyZcsW5cyZM8quXbuUO+64Q/Hw8Lhpjp+BgoICJTw8XHnxxRdLPFfTjl96eroSFRWlREVFKYAyb948JSoqylgFO2vWLEWn0ykrVqxQjhw5oowaNUoJCgpS0tLSjNsYN26cWaX+P//8o6jVamXWrFnKsWPHlFmzZimOjo7Krl27qtX+5eXlKUOHDlVCQ0OVgwcPmp2TOTk5VvdvxowZyvr165XTp08rUVFRygMPPKA4Ojoqu3fvvuH7pyi29zE9PV157rnnlB07digxMTHK5s2blS5duighISE3xTE0kJqaqri6uiqfffaZxW1U52NYlutCTT8PaxpSAFYRn3zyiVK3bl3FyclJadu2rZlFyvjx45VevXqZLb9lyxalTZs2ipOTk1KvXj2rXwDVAcDiz9KlS43LFN/H2bNnKw0aNFCcnZ0Vb29vpXv37sqaNWtu/ODLwL333qsEBQUpGo1GCQ4OVkaMGKH8999/xudr+vEz8McffyiAEh0dXeK5mnb8DDY1xX/Gjx+vKIqwoJg+fboSGBioaLVapWfPnsqRI0fMttGrVy/j8gZ+/vlnJTIyUtFoNEqTJk2qTPDa2r+YmBir5+TmzZuN2yi+f08//bQSHh6uODk5Kf7+/sqAAQOUHTt23Pid02NrH69du6YMGDBA8ff3VzQajRIeHq6MHz9eOX/+vNk2auoxNLBw4ULFxcVFSUlJsbiN6nwMy3JdqOnnYU1DpSj6bHSJRCKRSCQSSa1A5gBKJBKJRCKR1DKkAJRIJBKJRCKpZUgBKJFIJBKJRFLLkAJQIpFIJBKJpJYhBaBEIpFIJBJJLUMKQIlEIpFIJJJahhSAEolEIpFIJLUMKQAlEolEIpFIahlSAEokEolEIpHUMqQAlEgkEolEIqllSAEokUg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\n", - " " - ], - "text/plain": [ - "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# v3 plotter\n", "data = np.load(\"dpdf.npz\")\n", @@ -1103,13 +1112,13 @@ "r= np.arange(cfg.rmin, cfg.rmax + cfg.dr/2.0, cfg.dr)\n", "\n", "r_cutoff = 45\n", - "plt.figure()\n", + "# plt.figure()\n", "plt.plot(r[r_cutoff:], out['G_alpha'][r_cutoff:],'r', label=\"G_alpha (resonant)\")\n", "plt.plot(r[r_cutoff:], out['G_not'][r_cutoff:],'g', label=\"G_not (non-resonant)\")\n", "plt.plot(r[r_cutoff:], out['G_tot'][r_cutoff:],'b', label=\"G_tot (total/mean)\")\n", - "plt.plot(dpdf_r_tot, dpdf_G_a, 'r--', label=\"G_alpha (paper)\")\n", - "plt.plot(dpdf_r_tot, dpdf_G_na, 'g--', label=\"G_not (paper)\")\n", - "plt.plot(dpdf_r_tot, dpdf_G_tot, 'b--', label=\"G_tot (paper)\")\n", + "# plt.plot(dpdf_r_tot, dpdf_G_a, 'r--', label=\"G_alpha (paper)\")\n", + "# plt.plot(dpdf_r_tot, dpdf_G_na, 'g--', label=\"G_not (paper)\")\n", + "# plt.plot(dpdf_r_tot, dpdf_G_tot, 'b--', label=\"G_tot (paper)\")\n", "\n", "\n", "plt.legend()\n", @@ -1118,7 +1127,7 @@ }, { "cell_type": "markdown", - "id": "9b5173fb", + "id": "11", "metadata": {}, "source": [ "## 1. 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zp8gos@*JaueK)|)<~UbfMZOyebRff;;;5+#9x%(dD2}1cwJ^XfRFd_%Qns>RE?U8EWN!jewSb3a}7Vw7fJ#4QC>PdW_bf@ zSGpj+K4@XuP`{7Oh1Nl(_-s;cH};IkfznBzm<`$G$s7rP5HWG{MJKyY!;>)vyQ`mZyS{o}?WFz) np.ndarray:\n", - " \"\"\"Accept 1D energy in eV or keV; return in eV.\"\"\"\n", - " E = np.asarray(E, dtype=float)\n", - " scale = 1.0 if np.nanmax(E) >= 1e3 else 1e3\n", - " return E * scale\n", - "\n", - " @staticmethod\n", - " def lorentzian_height(E: np.ndarray, center: float, fwhm: float, height: float) -> np.ndarray:\n", - " \"\"\"Lorentzian peak shape.\"\"\"\n", - " gamma = 0.5 * max(float(fwhm), 1e-18)\n", - " return height * (gamma**2) / ((E - center) ** 2 + gamma**2)\n", - "\n", - " @staticmethod\n", - " def broadening(E_eV: np.ndarray, y: np.ndarray, fwhm_eV: float) -> np.ndarray:\n", - " \"\"\"Lorentzian broadening via uniform helper grid + convolution.\"\"\"\n", - " if fwhm_eV <= 0.0:\n", - " return y\n", - " Emin, Emax = float(E_eV[0]), float(E_eV[-1])\n", - " dmins = float(np.min(np.diff(E_eV)))\n", - " d_helper = max(min(dmins / 4.0, fwhm_eV / 25.0), 1e-3)\n", - " pad = max(5.0 * fwhm_eV, 10.0 * dmins)\n", - " Xu = np.arange(Emin - pad, Emax + pad + d_helper, d_helper)\n", - " yu = np.interp(Xu, E_eV, y)\n", - "\n", - " gamma = 0.5 * float(fwhm_eV)\n", - " Lx = np.arange(-10.0 * fwhm_eV, 10.0 * fwhm_eV + d_helper, d_helper)\n", - " Lk = (gamma / np.pi) / (Lx**2 + gamma**2)\n", - " Lk /= Lk.sum()\n", - " conv = np.convolve(yu, Lk, mode=\"same\")\n", - " return np.interp(E_eV, Xu, conv)\n", - "\n", - "\n", - "class KKCalcAdapter:\n", - " \"\"\"Wrap kkcalc: tails, relativistic anchor, and KK on grid.\"\"\"\n", - " def __init__(self, element: str):\n", - " self.stoich = kkcalc.data.ParseChemicalFormula(element)\n", - " self.rc = kkcalc.calc_relativistic_correction(self.stoich)\n", - " self.full_E, self.full_imag_coeffs = kkcalc.data.calculate_asf(self.stoich)\n", - "\n", - " def f1_from_f2(self,\n", - " energy_eval_eV: np.ndarray,\n", - " near_edge_f2_vals: Optional[np.ndarray],\n", - " merge_points: Optional[Tuple[float, float]] = None,\n", - " add_background: bool = False,\n", - " fix_distortions: bool = False) -> Tuple[np.ndarray, np.ndarray, float]:\n", - " \"\"\"\n", - " Compute f1(E) on `energy_eval_eV` grid by merging near-edge f2(E) into kkcalc's tails \n", - " then applying kkcalc's Kramers–Kronig KKPP.\n", - "\n", - " Parameters\n", - " ----------\n", - " energy_eval_eV : np.ndarray\n", - " 1D energy grid in eV where f1(E) is evaluated.\n", - " near_edge_f2_vals : Optional[np.ndarray]\n", - " 1D array of f'' values on the same grid as `energy_eval_eV`.\n", - " If None, only tabulated tails are used.\n", - " merge_points : Optional[Tuple[float, float]]\n", - " If provided, the (low, high) energy in eV where near-edge and tabulated tails are merged.\n", - " If None, the full near-edge range is used.\n", - " add_background : bool\n", - " If True, a linear background is added to the tabulated tails to match the near-edge\n", - " at the merge points.\n", - " fix_distortions : bool\n", - " If True, a small quadratic distortion is applied to the tabulated tails to ensure\n", - " that the near-edge and tails match in slope at the merge points.\n", - "\n", - " Returns\n", - " -------\n", - " Tuple[np.ndarray, np.ndarray, float]\n", - " 1D array of f1 values on `energy_eval_eV` grid,\n", - " 1D array of f2 values on `energy_eval_eV` grid (from coeff representation),\n", - " the relativistic correction.\n", - " \"\"\"\n", - " E = np.asarray(energy_eval_eV, float)\n", - " if near_edge_f2_vals is not None:\n", - " NearEdge_Data = np.column_stack([E, np.asarray(near_edge_f2_vals, float)])\n", - " mp = (float(E[0]), float(E[-1])) if merge_points is None else merge_points\n", - " Full_E, Imaginary_Spectrum = kkcalc.data.merge_spectra(\n", - " NearEdge_Data, self.full_E, self.full_imag_coeffs,\n", - " merge_points=mp, add_background=add_background, fix_distortions=fix_distortions\n", - " )\n", - " else:\n", - " Full_E, Imaginary_Spectrum = self.full_E, self.full_imag_coeffs\n", - "\n", - " f1_vals = kkcalc.KK_PP(E, Full_E, Imaginary_Spectrum, self.rc)\n", - "\n", - " i1 = np.searchsorted(Full_E, E[0], side=\"right\") - 1\n", - " i2 = np.searchsorted(Full_E, E[-1], side=\"right\") - 1\n", - " i1 = max(i1, 0)\n", - " i2 = max(i2, i1 + 1)\n", - " f2_vals = kkcalc.data.coeffs_to_ASF(E, np.vstack((Imaginary_Spectrum[i1:i2], Imaginary_Spectrum[-1])))\n", - " return f1_vals, f2_vals, float(self.rc)\n", - "\n", - "\n", - "class EdgeModel(_BaseEdgeModel):\n", - " r\"\"\"\n", - " Near-edge f'' model + kkcalc KK step.\n", - " - Build f''(E) near the edge (from Chantler or measured data/zeros), apply shift/scale/offset/slope baseline,\n", - " add Lorentzian white-lines, lorentzian broadening conv.\n", - " - Call kkcalc to merge near-edge f'' with tabulated tails and compute f1(E).\n", - " - Return f'(E) = f1(E) - f1(\\infty) by default or optionally return f1(E).\n", - " \"\"\"\n", - " def __init__(self, params: EdgeModelParams):\n", - " super().__init__(params)\n", - " self.kk = KKCalcAdapter(params.element)\n", - "\n", - " def fpp(self, E: np.ndarray) -> np.ndarray:\n", - " E_eV = self.to_eV(E)\n", - " E_eval = E_eV + float(self.params.dE_eV)\n", - "\n", - " if self.params.use_chantler_f2_baseline:\n", - " f2 = np.asarray(xraydb.f2_chantler(self.params.element, E_eval), float)\n", - " else:\n", - " f2 = np.zeros_like(E_eval)\n", - "\n", - " f2 = float(self.params.scale) * f2\n", - " f2 += float(self.params.fpp_offset)\n", - " f2 += float(self.params.fpp_slope_per_eV) * (E_eV - float(self.params.e0_keV) * 1e3)\n", - "\n", - " if self.params.peaks:\n", - " add = np.zeros_like(f2)\n", - " for pk in self.params.peaks:\n", - " add += self.lorentzian_height(E_eval, pk.center_eV, pk.fwhm_eV, pk.height)\n", - " f2 = f2 + add\n", - "\n", - " f2 = self.broadening(E_eV, f2, self.params.broaden_fwhm_eV)\n", - " return f2\n", - "\n", - " def fp(self,\n", - " E: np.ndarray,\n", - " fpp: Optional[np.ndarray] = None,\n", - " return_f1: bool = False,\n", - " merge_points: Optional[Tuple[float, float]] = None,\n", - " add_background: bool = False,\n", - " fix_distortions: bool = False) -> np.ndarray:\n", - " r\"\"\"\n", - " Return f'(E) and optionally f1(E) using kkcalc.\n", - "\n", - " Parameters\n", - " ----------\n", - " E : np.ndarray\n", - " 1D energy grid in eV or keV where f' is evaluated.\n", - " fpp : Optional[np.ndarray]\n", - " Custom 1D array of f'' values, on the same grid as `E`.\n", - " return_f1 : bool\n", - " If True, return f1(E) instead of f'(E) = f1(E) - f1(\\infty).\n", - " merge_points : Optional[Tuple[float, float]]\n", - " If provided, the (low, high) energy in eV where near-edge and tabulated tails are merged.\n", - " If None, the full near-edge range is used.\n", - " add_background : bool\n", - " If True, a linear background is added to the tabulated tails to match the near-edge\n", - " at the merge points.\n", - " fix_distortions : bool\n", - " If True, a small quadratic distortion is applied to the tabulated tails to ensure\n", - " that the near-edge and tails match in slope at the merge points.\n", - " \"\"\"\n", - " E_eV = self.to_eV(E)\n", - " E_eval = E_eV + float(self.params.dE_eV)\n", - "\n", - " if fpp is None:\n", - " fpp = self.fpp(E_eV)\n", - "\n", - " f1_vals, f2_vals, f1_inf = self.kk.f1_from_f2(\n", - " energy_eval_eV=E_eval,\n", - " near_edge_f2_vals=fpp,\n", - " merge_points=merge_points,\n", - " add_background=add_background,\n", - " fix_distortions=fix_distortions\n", - " )\n", - " return f1_vals if return_f1 else (f1_vals - f1_inf)\n", - "\n", - "\n", - "# Example\n", - "\n", - "E = np.array([\n", - " 89.85, 89.89, 89.93, 89.97, 90.01, 90.05, 90.09, 90.13, 90.17, 90.21,\n", - " 90.25, 90.255, 90.26, 90.265, 90.27, 90.275, 90.28, 90.285, 90.29, 90.295,\n", - " 90.3, 90.305, 90.31, 90.315, 90.32, 90.325, 90.33, 90.335, 90.34, 90.345,\n", - " 90.35, 90.355, 90.36, 90.365, 90.37, 90.375, 90.38, 90.385, 90.39, 90.395,\n", - " 90.4, 90.405, 90.41, 90.415, 90.42, 90.425, 90.43, 90.435, 90.44, 90.445,\n", - " 90.45, 90.455, 90.46, 90.465, 90.47, 90.475, 90.48, 90.485, 90.49, 90.495,\n", - " 90.5, 90.505, 90.51, 90.515, 90.52, 90.525, 90.53, 90.535, 90.54, 90.545,\n", - " 90.55, 90.555, 90.56, 90.565, 90.57, 90.575, 90.58, 90.585, 90.59, 90.595,\n", - " 90.6, 90.605, 90.61, 90.615, 90.62, 90.625, 90.63, 90.635, 90.64, 90.645,\n", - " 90.65, 90.655, 90.66, 90.665, 90.67, 90.675, 90.68, 90.685, 90.69, 90.695,\n", - " 90.7, 90.705, 90.71, 90.715, 90.72, 90.725, 90.73, 90.735, 90.74, 90.745,\n", - " 90.75, 90.79, 90.83, 90.87, 90.91, 90.95, 90.99, 91.03, 91.07, 91.11\n", - "])\n", - "\n", - "params = EdgeModelParams(\n", - " element=\"Bi\",\n", - " e0_keV=90.526,\n", - " dE_eV=0.0,\n", - " scale=0.35,\n", - " fpp_offset=-0.2,\n", - " fpp_slope_per_eV=0.0,\n", - " broaden_fwhm_eV=15.0,\n", - " peaks=[Peak(center_eV=90.526e3 + 180, fwhm_eV=3.0, height=0.3)],\n", - " use_chantler_f2_baseline=True,\n", - ")\n", - "\n", - "model = EdgeModel(params)\n", - "\n", - "fpp = model.fpp(E)\n", - "fp = model.fp(E, fpp=fpp)\n", - "f1 = model.fp(E, fpp=fpp, return_f1=True)\n", - "fp_chantler = xraydb.f1_chantler(params.element, model.to_eV(E) + params.dE_eV)\n", - "\n", - "plt.figure()\n", - "plt.plot(E, fpp, label=\"f'' model\")\n", - "plt.plot(E, fp, label=\"f' (kkcalc)\")\n", - "plt.plot(E, fp_chantler, \"--\", alpha=0.6, label=\"f' Chantler\")\n", - "plt.legend()\n", - "plt.show()\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "# utils\n", - "\n", - "def _as_1d(a: np.ndarray) -> np.ndarray:\n", - " a = np.asarray(a)\n", - " return a.ravel()\n", - "\n", - "def _safe(a: np.ndarray, name: str) -> np.ndarray:\n", - " if not np.all(np.isfinite(a)):\n", - " idx = np.where(~np.isfinite(a))\n", - " raise ValueError(f\"{name} has non-finite entries at {idx}\")\n", - " return a\n", - "\n", - "def _lorch(Q: np.ndarray, Qmax: float) -> np.ndarray:\n", - " x = Q / Qmax\n", - " w = np.ones_like(Q)\n", - " m = (x > 0) & (x <= 1.0)\n", - " w[m] = np.sin(np.pi * x[m]) / (np.pi * x[m])\n", - " w[x > 1.0] = 0.0\n", - " return w\n", - "\n", - "def _kaiser(Q: np.ndarray, Qmax: float, beta: float = 6.0) -> np.ndarray:\n", - " from numpy import i0\n", - " x = Q / Qmax\n", - " w = np.zeros_like(Q)\n", - " m = (x >= 0) & (x <= 1.0)\n", - " w[m] = i0(beta * np.sqrt(1.0 - x[m]**2)) / i0(beta)\n", - " return w\n", - "\n", - "def _trapz(x: np.ndarray, y: np.ndarray) -> float:\n", - " return float(np.trapezoid(y, x))\n", - "\n", - "def _ensure_2d(x: np.ndarray, ne: int, nq: int, name: str) -> np.ndarray:\n", - " x = np.asarray(x, float)\n", - " if x.ndim == 0:\n", - " return np.full((ne, nq), float(x))\n", - " if x.ndim == 1:\n", - " if x.size == ne:\n", - " return x[:, None] * np.ones((1, nq))\n", - " if x.size == nq:\n", - " return np.ones((ne, 1)) * x[None, :]\n", - " raise ValueError(f\"{name} 1D length {x.size} mismatches ne={ne}, nq={nq}\")\n", - " if x.shape != (ne, nq):\n", - " raise ValueError(f\"{name} shape {x.shape} != ({ne},{nq})\")\n", - " return x\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3", - "metadata": {}, - "outputs": [], - "source": [ - "# config\n", - "\n", - "@dataclass\n", - "class RefinementConfig:\n", - " # S(Q) construction\n", - " rpoly: float = 1.0\n", - " hiQ_frac: float = 0.85\n", - " ridge: float = 8e-4\n", - " # G(r)\n", - " window: str = \"lorch\" # \"none\"/\"lorch\"/\"kaiser\"\n", - " kaiser_beta: float = 6.0\n", - " rmin: float = 0.0\n", - " rmax: float = 20.0\n", - " dr: float = 0.01\n", - " Qmin: float = 0.7\n", - " Qmax: Optional[float] = None\n", - " # outer refinement\n", - " n_outer: int = 40\n", - " plot_every: int = 2\n", - " frame_dir: str = \"./refine_frames\"\n", - " # Convergence threshold\n", - " tol_obj: float = 1e-4\n", - " # parameter step sizes\n", - " step_rpoly: float = 0.05\n", - " step_dE_eV: float = 2.0\n", - " step_scale: float = 0.05\n", - " step_fpp_offset: float = 0.05\n", - " step_fp_offset: float = 0.05\n", - " step_broaden_fwhm: float = 2.0\n", - " step_alphaC: float = 0.05\n", - " step_alphaD: float = 0.05\n", - " step_betaC: float = 0.05\n", - " step_betaD: float = 0.05\n", - " # peak step sizes\n", - " step_peak_center_eV: float = 4.0\n", - " step_peak_fwhm_eV: float = 1.0\n", - " step_peak_height: float = 0.05\n", - " # physical constraints\n", - " min_broaden_fwhm_eV: float = 0.0\n", - " max_broaden_fwhm_eV: float = 40.0\n", - " min_peak_fwhm_eV: float = 0.5\n", - " max_peak_fwhm_eV: float = 30.0\n", - " max_peak_height_factor: float = 1.0\n", - " # objective pieces\n", - " hiQ_anchor_lambda: float = 1.0\n", - " smooth_lambda: float = 1e-5\n", - " peak_L1_lambda: float = 1e-3\n", - " # peak birth/death controls\n", - " birth_every: int = 4\n", - " death_height_thresh: float = 1e-2\n", - "\n", - "@dataclass\n", - "class RefinementHistory:\n", - " it: int\n", - " obj: float\n", - " params: Dict[str, float]\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "# scattering factors & weights\n", - "\n", - "def _f0_of_Q(element: str, Q: np.ndarray) -> np.ndarray:\n", - " s = _as_1d(Q) / (4.0 * np.pi)\n", - " f0 = np.array([xraydb.f0(element, si)[0] for si in s], dtype=float)\n", - " return _safe(f0, f\"f0({element})\")\n", - "\n", - "def _compute_scattering(\n", - " elements: List[str],\n", - " comp: Dict[str, float],\n", - " alpha: str,\n", - " Q: np.ndarray,\n", - " E_eV: np.ndarray,\n", - " edge_model: Any,\n", - " fp_offset: float = 0.0,\n", - ") -> Tuple[Dict[str,np.ndarray], Dict[str,np.ndarray], np.ndarray, np.ndarray, np.ndarray, np.ndarray]:\n", - " \"\"\"\n", - " Returns:\n", - " fr_weights : Re f_el(E,Q) [ne,nq]\n", - " f0_map[el] : f0(Q) [nq]\n", - " fmean_real : (real) [ne,nq]\n", - " fself : <|f|^2> [ne,nq]\n", - " f_not_sum : sum_{beta!=alpha} c_beta * Re f_beta [ne,nq]\n", - " \"\"\"\n", - " Q = _as_1d(Q); E = _as_1d(E_eV)\n", - " nq, ne = len(Q), len(E)\n", - " f0_map = {el: _f0_of_Q(el, Q) for el in elements}\n", - "\n", - " # alpha dispersive parts\n", - " fp = edge_model.fp(E, return_f1=False)\n", - " fpp = edge_model.fpp(E)\n", - " fpp = np.maximum(fpp, 0.0) # enforce physical non-negativity\n", - " _safe(fp, \"f'\"); _safe(fpp, \"f''\")\n", - "\n", - " fr_weights: Dict[str,np.ndarray] = {}\n", - " f2_weights: Dict[str,np.ndarray] = {}\n", - "\n", - " for el in elements:\n", - " f0 = f0_map[el]\n", - " if el == alpha:\n", - " fr = (fp + fp_offset)[:, None] + f0[None, :]\n", - " fi = fpp[:, None]\n", - " else:\n", - " fr = f0[None, :]\n", - " fi = np.zeros((ne, 1))\n", - " fr_weights[el] = fr\n", - " f2_weights[el] = fr**2 + fi**2\n", - "\n", - " fmean_real = np.zeros((ne, nq), float)\n", - " fmean_abs2 = np.zeros((ne, nq), float)\n", - " f_not_sum = np.zeros((ne, nq), float)\n", - " for el in elements:\n", - " c = float(comp[el])\n", - " fmean_real += c * fr_weights[el]\n", - " fmean_abs2 += c * f2_weights[el]\n", - " if el != alpha:\n", - " f_not_sum += c * fr_weights[el]\n", - " fself = fmean_abs2\n", - " return fr_weights, f0_map, fmean_real, fmean_abs2, fself, f_not_sum\n", - "\n", - "def _weights_alpha_not(\n", - " comp: Dict[str, float],\n", - " alpha: str,\n", - " fr_weights: Dict[str, np.ndarray],\n", - " fmean_real: np.ndarray,\n", - " f_not_sum: np.ndarray,\n", - ") -> Tuple[np.ndarray, np.ndarray, Dict[str,float]]:\n", - " cA = float(comp[alpha]); eps = 1e-12\n", - " a = cA * fr_weights[alpha] / (fmean_real + eps)\n", - " b = f_not_sum / (fmean_real + eps)\n", - " # cap extreme weights to avoid blowing up the per-Q solve\n", - " a = np.clip(a, -5.0, 5.0)\n", - " b = np.clip(b, -5.0, 5.0)\n", - " return a, b, {\n", - " \"a_min\": float(np.nanmin(a)), \"a_max\": float(np.nanmax(a)),\n", - " \"b_min\": float(np.nanmin(b)), \"b_max\": float(np.nanmax(b)),\n", - " \"b_frac_neg\": float(np.mean(b < -1e-8))\n", - " }\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5", - "metadata": {}, - "outputs": [], - "source": [ - "# corrections & S(Q,e)\n", - "\n", - "def _alpha_beta_from_fpp(fpp_E: np.ndarray, alpha_C: float, alpha_D: float,\n", - " beta_C: float, beta_D: float) -> Tuple[np.ndarray,np.ndarray]:\n", - " alpha_e = np.clip(alpha_C + alpha_D * fpp_E, 1e-6, None)\n", - " beta_e = beta_C + beta_D * fpp_E\n", - " return alpha_e, beta_e\n", - "\n", - "\n", - "def _build_S_from_raw(\n", - " I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray,\n", - " alpha_e: np.ndarray, beta_f_e: np.ndarray,\n", - " fmean_real: np.ndarray, fself: np.ndarray,\n", - " rpoly: float\n", - ") -> Tuple[np.ndarray, np.ndarray]:\n", - " \"\"\"Return S(ne,nq) and beta_o(ne,nq) with correct FZ normalization.\"\"\"\n", - " I_raw = np.asarray(I_raw, float)\n", - " E = _as_1d(E_eV); Q = _as_1d(Q)\n", - " ne, nq = len(E), len(Q)\n", - " if I_raw.shape != (ne, nq):\n", - " raise ValueError(\"I_raw must be shaped [ne, nq]\")\n", - "\n", - " I_corr = I_raw * alpha_e[:, None] + beta_f_e[:, None]\n", - " S0 = (I_corr - fself) / (fmean_real**2 + 1e-12) + 1.0\n", - "\n", - " # β_o(Q,e): flexible polynomial in Q fitted over the whole Q-range\n", - " # To ensure S→1 at high-Q, we have to penalize bad fit at high Q.\n", - " xspan = float(Q[-1] - Q[0])\n", - " porder = (rpoly * xspan) / np.pi\n", - " porder = max(1.0, porder)\n", - "\n", - " porderlo = int(np.floor(porder))\n", - " porderhi = int(np.ceil(porder))\n", - "\n", - " # Define weights for the high and low polynomial degree\n", - " if porderlo == porderhi:\n", - " poly_weights = [0.5, 0.5]\n", - " else:\n", - " poly_weights = [porderhi - porder, porder - porderlo]\n", - "\n", - " # We want: S0 + polynomial → 1 (at high-Q).\n", - " # So we fit: polyonmial = 1 - S0.\n", - " # We want the polynomial to fit over the whole Q-range, but prioritize forcing S→1 at high-Q.\n", - " # Otherwise, the polynomial will try to flatten S(Q) at low-Q by removing strong structural signals.\n", - " # (Q / Qmax)^n forces the polynomial to ignore low-Q oscillation:\n", - " weight_power = 4.0\n", - " W_poly = (Q / Q[-1])**weight_power\n", - " W_sqrt = np.sqrt(W_poly)\n", - "\n", - "\n", - " # Build the design matrices for high and low polynomial orders\n", - " Xlo = np.vstack([Q**k for k in range(porderlo + 1)]).T\n", - " Xhi = np.vstack([Q**k for k in range(porderhi + 1)]).T\n", - "\n", - " # Apply weights to the deign matrices\n", - " Xlo_w = Xlo * W_sqrt[:, None]\n", - " Xhi_w = Xhi * W_sqrt[:, None]\n", - "\n", - " XtXlo = Xlo_w.T @ Xlo_w + 1e-12*np.eye(Xlo_w.shape[1])\n", - " XtXhi = Xhi_w.T @ Xhi_w + 1e-12*np.eye(Xhi_w.shape[1])\n", - "\n", - " beta_o = np.zeros_like(S0)\n", - " for i in range(ne):\n", - " # We want S0 + beta_o -> 1, so we fit X*coeff to (1 - S0)\n", - " y = (1.0 - S0[i]) * (fmean_real[i]**2)\n", - " \n", - " # Apply the weights to the target variable (y_w = sqrt(W) * y)\n", - " y_w = y * W_sqrt\n", - " \n", - " # Solve for the lower degree polynomial using weighted matrices\n", - " coeff_lo = npl.solve(XtXlo, Xlo_w.T @ y_w)\n", - " # Evaluate using the UNWEIGHTED design matrix to apply the correction uniformly\n", - " beta_lo = (Xlo @ coeff_lo) / (fmean_real[i]**2 + 1e-12)\n", - " \n", - " if porderlo == porderhi:\n", - " beta_o[i] = beta_lo\n", - " else:\n", - " # Solve for the higher degree polynomial using weighted matrices\n", - " coeff_hi = npl.solve(XtXhi, Xhi_w.T @ y_w)\n", - " beta_hi = (Xhi @ coeff_hi) / (fmean_real[i]**2 + 1e-12)\n", - " \n", - " # Linearly interpolate the background corrections\n", - " beta_o[i] = poly_weights[0] * beta_lo + poly_weights[1] * beta_hi\n", - " \n", - " S = S0 + beta_o\n", - "\n", - "\n", - " return S, beta_o\n", - "\n", - "# per-Q reconstruction\n", - "\n", - "def _solve_two_channel_column(Aj: np.ndarray, yj: np.ndarray,\n", - " ridge: float, anchor: float) -> Tuple[float,float]:\n", - " \"\"\"Solve min ||Aj x - yj||^2 + ridge||x||^2 + anchor||x-1||^2.\"\"\"\n", - " ATA = Aj.T @ Aj + ridge*np.eye(2) + anchor*np.eye(2)\n", - " ATy = Aj.T @ yj + anchor*np.array([[1.0],[1.0]])\n", - " try:\n", - " sol = npl.solve(ATA, ATy)\n", - " except npl.LinAlgError:\n", - " print(\"WARNING: singular matrix in _solve_two_channel_column; using lstsq\")\n", - " sol = npl.lstsq(ATA, ATy, rcond=None)[0]\n", - " return float(sol[0,0]), float(sol[1,0])\n", - "\n", - "def _reconstruct_Salpha_Snot(\n", - " S_meas: np.ndarray, a: np.ndarray, b: np.ndarray,\n", - " Q: np.ndarray, ridge: float\n", - ") -> Tuple[np.ndarray,np.ndarray, Dict[str,float]]:\n", - " \"\"\"Column-wise two-channel solve with conditioning checks and hiQ anchor.\"\"\"\n", - " S_meas = np.asarray(S_meas, float)\n", - "\n", - " # !!!!! Till: I don't know what this is doing, and why the exclamation marks are here. Seems like some manual override of something...\n", - " for i in range(S_meas.shape[0]):\n", - " S_meas[i][:40] = S_meas[i][41]\n", - "\n", - " ne, nq = S_meas.shape\n", - " a = _ensure_2d(a, ne, nq, \"a\"); b = _ensure_2d(b, ne, nq, \"b\")\n", - "\n", - " Sa = np.zeros(nq); Sb = np.zeros(nq)\n", - " bad_cols = 0\n", - " for j in range(nq):\n", - " Aj = np.stack([a[:,j], b[:,j]], axis=1) # [ne,2]\n", - " yj = S_meas[:, j:j+1] # [ne,1]\n", - " # condition\n", - " s = npl.svd(Aj, compute_uv=False)\n", - " cond = (s[0]/s[-1]) if (s[-1] > 0) else np.inf\n", - "\n", - " anchor = 0.0 # Till: I removed the high-mask anchor here. \n", - " if not np.isfinite(cond) or cond > 1e6:\n", - " bad_cols += 1\n", - " anchor = 5.0 # heavy anchor to 1 if ill-conditioned (Till: also here, not sure what this is doing...)\n", - " sa, sb = _solve_two_channel_column(Aj, yj, ridge, anchor)\n", - " Sa[j], Sb[j] = sa, sb\n", - "\n", - " return Sa, Sb, {\"bad_Q_columns\": bad_cols}\n", - "\n", - "# S(Q) -> G(r)\n", - "\n", - "def _S_to_G(Q: np.ndarray, S: np.ndarray, r: np.ndarray,\n", - " window: str, kbeta: float) -> np.ndarray:\n", - " Q = _as_1d(Q); S = _as_1d(S); r = _as_1d(r)\n", - " Qmax = float(Q.max())\n", - " w = np.ones_like(Q)\n", - " if window == \"lorch\": w = _lorch(Q, Qmax)\n", - " elif window == \"kaiser\": w = _kaiser(Q, Qmax, kbeta)\n", - " F = Q * (S - 1.0) * w\n", - " G = np.zeros_like(r)\n", - " for i, ri in enumerate(r):\n", - " G[i] = (2.0/np.pi) * _trapz(Q, F*np.sin(Q*ri))\n", - " return G\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "# plotting\n", - "\n", - "def _plot_frame(path: str, E_eV: np.ndarray, edge_model: Any,\n", - " r: np.ndarray, out: Dict[str,np.ndarray],\n", - " Q_full: np.ndarray, iter_idx: int,\n", - " hist: List[RefinementHistory], fp_offset: float) -> None:\n", - " q = np.asarray(out.get(\"Q\", Q_full))\n", - " Sa = np.asarray(out[\"S_alpha\"]); Sb = np.asarray(out[\"S_not\"])\n", - " St = np.asarray(out[\"S_tot\"])\n", - " m = min(q.size, Sa.size, Sb.size, St.size)\n", - " q, Sa, Sb, St = q[:m], Sa[:m], Sb[:m], St[:m]\n", - "\n", - " r_plot = np.asarray(r)\n", - " Ga = np.asarray(out[\"G_alpha\"]); Gn = np.asarray(out[\"G_not\"]); Gt = np.asarray(out[\"G_tot\"])\n", - " mG = min(r_plot.size, Ga.size, Gn.size, Gt.size)\n", - " r_plot, Ga, Gn, Gt = r_plot[:mG], Ga[:mG], Gn[:mG], Gt[:mG]\n", - "\n", - " E = np.asarray(E_eV, float)\n", - " fpp = np.maximum(edge_model.fpp(E), 0.0)\n", - " fp = edge_model.fp(E, fpp=fpp) + fp_offset\n", - " E_keV = E/1e3\n", - "\n", - " plt.figure(figsize=(12,20))\n", - " plt.suptitle(f\"Refinement frame {iter_idx:03d}\")\n", - "\n", - " ax1 = plt.subplot(4,2,1)\n", - " ax1.plot(E_keV, fpp, label=\"f'' (model)\")\n", - " ax1.set_xlabel(\"Energy (keV)\")\n", - " ax1.set_ylabel(\"f'' (e−)\")\n", - " ax1.set_title(\"Edge model (f'')\")\n", - " ax1.legend(loc=\"upper left\")\n", - "\n", - " ax2 = plt.subplot(4,2,2)\n", - " ax2.plot(E_keV, fp, label=\"f' (KK from model) + fp_offset\")\n", - " ax2.set_xlabel(\"Energy (keV)\")\n", - " ax2.set_ylabel(\"f' (e−)\")\n", - " ax2.set_title(\"Edge model (f')\")\n", - " ax2.legend(loc=\"upper left\")\n", - "\n", - " ax = plt.subplot(4,1,2)\n", - " ax.plot(r_plot, Ga, 'b-', label=\"G_alpha\")\n", - " ax.plot(r_plot, Gn, 'g-', label=\"G_not\")\n", - " ax.plot(r_plot, Gt, \"r-\", label=\"G_tot (mean S)\")\n", - " ax.set_xlabel(\"r (Å)\"); ax.set_ylabel(\"G(r)\"); ax.set_title(\"PDFs\")\n", - " ax.legend(loc=\"upper right\")\n", - "\n", - " ax = plt.subplot(4,1,3)\n", - " ax.plot(q, Sa, 'b-', label=\"S_alpha\", linewidth=.5)\n", - " ax.plot(q, Sb, 'g-', label=\"S_not\", linewidth=.5)\n", - " ax.plot(q, St, \"r-\", label=\"S_tot (mean over E)\", linewidth=.5)\n", - " ax.plot(q, np.ones_like(q), 'k-', label=\"S=1\", linewidth=0.1)\n", - " ax.set_xlabel(\"Q (Å$^{-1}$)\"); ax.set_ylabel(\"S(Q)\"); ax.set_title(\"Structure functions\")\n", - " ax.legend(loc=\"upper left\")\n", - "\n", - " ax = plt.subplot(4,1,4)\n", - " its = np.arange(len(hist)); vals = np.array([h.obj for h in hist], float)\n", - " ax.plot(its, vals, \"-o\")\n", - " ax.set_yscale('log')\n", - " p = hist[-1].params\n", - " txt = (f\"dE_eV={p['dE_eV']:.3g}\\nscale={p['scale']:.3g}\\n\"\n", - " f\"fpp_offset={p['fpp_offset']:.3g}\\nfp_offset={p['fp_offset']:.3g}\\n\"\n", - " f\"broaden_fwhm_eV={p['broaden_fwhm_eV']:.3g}\\n\"\n", - " f\"alpha_C={p['alpha_C']:.3g}, alpha_D={p['alpha_D']:.3g}\\n\"\n", - " f\"beta_C={p['beta_C']:.3g}, beta_D={p['beta_D']:.3g}\")\n", - " ax.text(0.02, 0.98, txt, va=\"top\", ha=\"left\", transform=ax.transAxes,\n", - " bbox=dict(boxstyle=\"round\", facecolor=\"white\", alpha=0.85))\n", - " ax.set_xlabel(\"Iteration\"); ax.set_ylabel(\"Objective\"); ax.set_title(\"Objective history\")\n", - "\n", - " plt.savefig(path, dpi=150); plt.close()\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "# objective\n", - "\n", - "def _objective(Sa: np.ndarray, Sb: np.ndarray, Q: np.ndarray,\n", - " hiQ_frac: float, anchor_lambda: float) -> float:\n", - " nq = len(Q); k0 = int(max(0, math.floor((1.0-hiQ_frac)*nq)))\n", - " mask = np.zeros(nq, bool); mask[k0:] = True\n", - " tails = np.sum((Sa[mask]-1.0)**2 + (Sb[mask]-1.0)**2)\n", - " d2a = np.diff(Sa, n=2); d2b = np.diff(Sb, n=2)\n", - " smooth = np.sum(d2a**2 + d2b**2)\n", - " physics = np.sum((Sa - Sb)**2)\n", - " return float(anchor_lambda*tails + smooth + physics)\n", - "\n", - "def _hiQ_stats(S: np.ndarray, Q: np.ndarray, hiQ_frac: float) -> Dict[str,float]:\n", - " nq = len(Q); k0 = int(max(0, math.floor((1.0-hiQ_frac)*nq)))\n", - " x = Q[k0:]; y = S[k0:]\n", - " if x.size < 2:\n", - " return {\"mean\": float(np.mean(y)), \"slope\": 0.0, \"std\": float(np.std(y))}\n", - " A = np.vstack([x, np.ones_like(x)]).T\n", - " m, c = npl.lstsq(A, y, rcond=None)[0]\n", - " return {\"mean\": float(np.mean(y)), \"slope\": float(m), \"std\": float(np.std(y))}\n", - "\n", - "# reconstruction\n", - "\n", - "def reconstruct_partials_and_pdfs(\n", - " I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray,\n", - " elements: List[str], comp: Dict[str,float], alpha: str,\n", - " edge_model: Any,\n", - " alpha_e: np.ndarray, beta_e: np.ndarray,\n", - " rpoly: float,\n", - " ridge: float, \n", - " r: np.ndarray, Qmin: float, Qmax: float,\n", - " window: str = \"lorch\", kaiser_beta: float = 6.0,\n", - " fp_offset: float = 0.0,\n", - ") -> Tuple[Dict[str,np.ndarray], Dict[str,Any]]:\n", - " Q = _as_1d(Q); E = _as_1d(E_eV)\n", - " I_raw = np.asarray(I_raw, float)\n", - " ne, nq = len(E), len(Q)\n", - " if I_raw.shape != (ne, nq):\n", - " raise ValueError(f\"I_raw shape {I_raw.shape} but expected ({ne},{nq})\")\n", - "\n", - " # scattering & weights (with fp_offset applied only to alpha’s real part)\n", - " frw, f0_map, fmean_real, fmean_abs2, fself, f_not_sum = _compute_scattering(\n", - " elements, comp, alpha, Q, E, edge_model, fp_offset=fp_offset\n", - " )\n", - " a, b, wb = _weights_alpha_not(comp, alpha, frw, fmean_real, f_not_sum)\n", - "\n", - " # Q masks for Fourier transform to get G(r)\n", - " if Qmax is None: Qmax = float(Q.max())\n", - " mask_Q = (Q >= Qmin) & (Q <= Qmax)\n", - " Q_use = Q[mask_Q]; nq_use = Q_use.size\n", - "\n", - " # build S(Q,e)\n", - " S_meas_all, beta_o_all = _build_S_from_raw(\n", - " I_raw, Q, E, alpha_e, beta_e, fmean_real, fself, rpoly\n", - " )\n", - " S_meas = S_meas_all[:, mask_Q]\n", - " a = a[:, mask_Q]; b = b[:, mask_Q]\n", - "\n", - " # per-Q two-channel solve\n", - " Sa, Sb, condinfo = _reconstruct_Salpha_Snot(S_meas, a, b, Q_use, ridge)\n", - "\n", - " # PDFs\n", - " r = _as_1d(r)\n", - " S_tot = S_meas[0]\n", - " G_alpha = _S_to_G(Q_use, Sa, r, window, kaiser_beta)\n", - " G_not = _S_to_G(Q_use, Sb, r, window, kaiser_beta)\n", - " G_tot = _S_to_G(Q_use, S_tot, r, window, kaiser_beta)\n", - "\n", - " out = {\"Q\": Q_use, \"r\": r,\n", - " \"S_alpha\": Sa, \"S_not\": Sb, \"S_tot\": S_tot,\n", - " \"G_alpha\": G_alpha, \"G_not\": G_not, \"G_tot\": G_tot}\n", - " diag = {\"weights\": wb,\n", - " \"condinfo\": condinfo,\n", - " \"beta_o\": beta_o_all,\n", - " # Hardcoded hiQ_frac=0.85 here just to keep your diagnostic stats alive\n", - " \"hiQ_stats\": {\"S_alpha\": _hiQ_stats(Sa, Q_use, 0.85),\n", - " \"S_not\": _hiQ_stats(Sb, Q_use, 0.85),\n", - " \"S_tot\": _hiQ_stats(S_tot, Q_use, 0.85)}}\n", - " return out, diag\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8", - "metadata": {}, - "outputs": [], - "source": [ - "# outer refinement\n", - "\n", - "def _peak_bounds_guard(edge_model: Any, cfg: RefinementConfig, E_eV: np.ndarray) -> None:\n", - " Emin, Emax = float(E_eV.min())-20.0, float(E_eV.max())+40.0\n", - " base = np.maximum(edge_model.fpp(E_eV), 0.0)\n", - " baseline_med = float(np.median(base))\n", - " for pk in edge_model.params.peaks:\n", - " pk.center_eV = float(np.clip(pk.center_eV, Emin, Emax))\n", - " pk.fwhm_eV = float(np.clip(pk.fwhm_eV, cfg.min_peak_fwhm_eV, cfg.max_peak_fwhm_eV))\n", - " pk.height = float(np.clip(pk.height, 0.0, cfg.max_peak_height_factor*max(1e-6, baseline_med)))\n", - "\n", - "def _pack_params(edge_model: Any, alpha_C: float, alpha_D: float, beta_C: float, beta_D: float,\n", - " fp_offset: float, rpoly: float) -> Dict[str,float]:\n", - " d = dict(dE_eV=edge_model.params.dE_eV,\n", - " scale=edge_model.params.scale,\n", - " fpp_offset=edge_model.params.fpp_offset,\n", - " broaden_fwhm_eV=edge_model.params.broaden_fwhm_eV,\n", - " alpha_C=alpha_C, alpha_D=alpha_D, beta_C=beta_C, beta_D=beta_D,\n", - " fp_offset=fp_offset,\n", - " rpoly=rpoly)\n", - " d[\"peaks\"] = [(float(p.center_eV), float(p.fwhm_eV), float(p.height))\n", - " for p in edge_model.params.peaks]\n", - " return d\n", - "\n", - "def run_adpdf_with_refinement(\n", - " I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray,\n", - " elements: List[str], comp: Dict[str,float], alpha: str,\n", - " edge_model: Any,\n", - " alpha_C: float = 1.0, alpha_D: float = 0.0,\n", - " beta_C: float = 0.0, beta_D: float = 0.0,\n", - " fp_offset: float = 0.0,\n", - " cfg: Optional[RefinementConfig] = None,\n", - ") -> Tuple[Dict[str,np.ndarray], Dict[str,Any], List[RefinementHistory]]:\n", - "\n", - " if cfg is None: cfg = RefinementConfig()\n", - " Q = _as_1d(Q); E = _as_1d(E_eV); I_raw = np.asarray(I_raw, float)\n", - " ne, nq = len(E), len(Q)\n", - " if I_raw.shape != (ne, nq):\n", - " raise ValueError(f\"I_raw shape {I_raw.shape} but expected ({ne},{nq})\")\n", - "\n", - " # Extract rpoly so it can be refined\n", - " rpoly = cfg.rpoly\n", - "\n", - " # bounds on global params\n", - " edge_model.params.scale = max(1e-4, float(edge_model.params.scale))\n", - " edge_model.params.broaden_fwhm_eV = float(np.clip(edge_model.params.broaden_fwhm_eV,\n", - " cfg.min_broaden_fwhm_eV, cfg.max_broaden_fwhm_eV))\n", - " _peak_bounds_guard(edge_model, cfg, E)\n", - "\n", - " r = np.arange(cfg.rmin, cfg.rmax + cfg.dr/2.0, cfg.dr)\n", - " Qmin = cfg.Qmin\n", - " Qmax = cfg.Qmax if cfg.Qmax is not None else float(Q.max())\n", - "\n", - " def compute():\n", - " fpp = np.maximum(edge_model.fpp(E), 0.0)\n", - " alpha_e, beta_e = _alpha_beta_from_fpp(fpp, alpha_C, alpha_D, beta_C, beta_D)\n", - " out, diag = reconstruct_partials_and_pdfs(\n", - " I_raw, Q, E, elements, comp, alpha, edge_model,\n", - " alpha_e, beta_e,\n", - " rpoly=rpoly,\n", - " ridge=cfg.ridge,\n", - " r=r, Qmin=Qmin, Qmax=Qmax,\n", - " window=cfg.window, kaiser_beta=cfg.kaiser_beta,\n", - " fp_offset=fp_offset,\n", - " )\n", - " obj = _objective(out[\"S_alpha\"], out[\"S_not\"], out[\"Q\"], cfg.hiQ_frac, cfg.hiQ_anchor_lambda)\n", - " return out, diag, obj\n", - "\n", - " out, diag, obj = compute()\n", - " hist = [RefinementHistory(0, obj, _pack_params(edge_model, alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly))]\n", - " os.makedirs(cfg.frame_dir, exist_ok=True)\n", - " _plot_frame(os.path.join(cfg.frame_dir, f\"frame_{0:03d}.png\"),\n", - " E, edge_model, r, out, Q, 0, hist, fp_offset)\n", - "\n", - " # step sizes for coordinate descent\n", - " steps = dict(\n", - " rpoly=cfg.step_rpoly,\n", - " dE_eV=cfg.step_dE_eV, scale=cfg.step_scale,\n", - " fpp_offset=cfg.step_fpp_offset, fp_offset=cfg.step_fp_offset,\n", - " broaden_fwhm_eV=cfg.step_broaden_fwhm,\n", - " alpha_C=cfg.step_alphaC, alpha_D=cfg.step_alphaD,\n", - " beta_C=cfg.step_betaC, beta_D=cfg.step_betaD,\n", - " pk_center=cfg.step_peak_center_eV,\n", - " pk_fwhm=cfg.step_peak_fwhm_eV,\n", - " pk_height=cfg.step_peak_height,\n", - " )\n", - "\n", - " def tweak(name: str, d: float):\n", - " nonlocal alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly\n", - " p = edge_model.params\n", - " if name == \"rpoly\": rpoly = float(np.clip(rpoly + d, 0.0, 2.0))\n", - " elif name == \"dE_eV\": p.dE_eV += d\n", - " elif name == \"scale\": p.scale = max(1e-4, p.scale + d)\n", - " elif name == \"fpp_offset\": p.fpp_offset += d\n", - " elif name == \"broaden_fwhm_eV\":\n", - " p.broaden_fwhm_eV = float(np.clip(p.broaden_fwhm_eV + d,\n", - " cfg.min_broaden_fwhm_eV, cfg.max_broaden_fwhm_eV))\n", - " elif name == \"alpha_C\": alpha_C = max(1e-6, alpha_C + d)\n", - " elif name == \"alpha_D\": alpha_D += d\n", - " elif name == \"beta_C\": beta_C += d\n", - " elif name == \"beta_D\": beta_D += d\n", - " elif name == \"fp_offset\": fp_offset += d\n", - " else: raise KeyError(name)\n", - "\n", - " def tweak_peak(i: int, which: str, d: float):\n", - " pk = edge_model.params.peaks[i]\n", - " if which == \"center\": pk.center_eV += d\n", - " elif which == \"fwhm\": pk.fwhm_eV += d\n", - " elif which == \"height\": pk.height += d\n", - " _peak_bounds_guard(edge_model, cfg, E)\n", - "\n", - " best_obj = obj\n", - " for it in range(1, cfg.n_outer+1):\n", - " # Track if the OVERALL cycle improved\n", - " cycle_improved = False\n", - " # Store the objective at the start of this iteration\n", - " start_obj = best_obj\n", - "\n", - " # scalar params\n", - " for name in [\"rpoly\", \"dE_eV\",\"scale\",\"fpp_offset\",\"fp_offset\",\"broaden_fwhm_eV\",\n", - " \"alpha_C\",\"alpha_D\",\"beta_C\",\"beta_D\"]:\n", - " \n", - " # Track if THIS SPECIFIC parameter improved\n", - " param_improved = False\n", - " \n", - " for sgn in (+1,-1):\n", - " tweak(name, sgn*steps[name])\n", - " _peak_bounds_guard(edge_model, cfg, E)\n", - " out2, diag2, obj2 = compute()\n", - " if obj2 < best_obj:\n", - " out, diag, best_obj = out2, diag2, obj2\n", - " param_improved = True\n", - " cycle_improved = True\n", - " else:\n", - " tweak(name, -sgn*steps[name])\n", - " # Only shrink the step size if THIS parameter failed to improve\n", - " if not param_improved: steps[name] *= 0.7\n", - "\n", - " # peak params\n", - " for i in range(len(edge_model.params.peaks)):\n", - " for which, key in [(\"center\",\"pk_center\"),(\"fwhm\",\"pk_fwhm\"),(\"height\",\"pk_height\")]:\n", - " for sgn in (+1,-1):\n", - " tweak_peak(i, which, sgn*steps[key])\n", - " out2, diag2, obj2 = compute()\n", - " if which == \"height\":\n", - " obj2 += cfg.peak_L1_lambda * abs(edge_model.params.peaks[i].height)\n", - " if obj2 < best_obj:\n", - " out, diag, best_obj = out2, diag2, obj2\n", - " param_improved = True\n", - " cycle_improved = True\n", - " else:\n", - " tweak_peak(i, which, -sgn*steps[key])\n", - " if not param_improved: steps[key] *= 0.7\n", - "\n", - " # peak birth\n", - " if (it % cfg.birth_every) == 0:\n", - " seeds = np.array([40, 80, 120, 160, 200, 220.0]) # eV above E0 (typical white lines)\n", - " E0 = float(edge_model.params.e0_keV*1e3 + edge_model.params.dE_eV)\n", - " existing = np.array([p.center_eV for p in edge_model.params.peaks]) if edge_model.params.peaks else np.array([])\n", - " for off in seeds:\n", - " cen = E0 + off\n", - " if existing.size and np.min(np.abs(existing - cen)) < 5.0: # avoid duplicates\n", - " continue\n", - " # small trial peak\n", - " baseline = np.maximum(edge_model.fpp(E), 0.0)\n", - " h0 = 0.1*float(np.median(baseline))\n", - " pk = type(edge_model.params.peaks[0]) if edge_model.params.peaks else None\n", - " from dataclasses import dataclass\n", - " @dataclass\n", - " class _Peak: center_eV: float; fwhm_eV: float; height: float\n", - " PeakCls = pk if pk is not None else _Peak\n", - " edge_model.params.peaks.append(PeakCls(center_eV=cen, fwhm_eV=3.0, height=h0))\n", - " _peak_bounds_guard(edge_model, cfg, E)\n", - " out2, diag2, obj2 = compute()\n", - " obj2 += cfg.peak_L1_lambda * sum(abs(p.height) for p in edge_model.params.peaks)\n", - " if obj2 < best_obj:\n", - " out, diag, best_obj = out2, diag2, obj2\n", - " cycle_improved = True\n", - " else:\n", - " edge_model.params.peaks.pop()\n", - "\n", - " # peak death (prune tiny)\n", - " keep = []\n", - " for p in edge_model.params.peaks:\n", - " if p.height > cfg.death_height_thresh:\n", - " keep.append(p)\n", - " edge_model.params.peaks[:] = keep\n", - "\n", - " # Updated history tracking call\n", - " hist.append(RefinementHistory(it, best_obj,\n", - " _pack_params(edge_model, alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly)))\n", - " if (it % cfg.plot_every)==0 or it==cfg.n_outer:\n", - " _plot_frame(os.path.join(cfg.frame_dir, f\"frame_{it:03d}.png\"),\n", - " E, edge_model, r, out, Q, it, hist, fp_offset)\n", - " \n", - " # Stop if the relative improvement is smaller than our tolerance\n", - " rel_change = (start_obj - best_obj) / max(start_obj, 1e-12)\n", - " if rel_change < cfg.tol_obj:\n", - " print(f\"Converged! Relative change ({rel_change:.2e}) is below tolerance ({cfg.tol_obj}).\")\n", - " break\n", - "\n", - " # Safety net: stof if step sized have shrunk to useless levels\n", - " if not cycle_improved and max(steps.values()) < 1e-3:\n", - " print(f\"Stopped at iteration {it}: step sizes shrank below 1e-3.\")\n", - " break\n", - "\n", - "\n", - "\n", - " return out, diag, hist\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "9", - "metadata": {}, - "outputs": [], - "source": [ - "# v3 runner\n", - "import h5py\n", - "\n", - "with h5py.File(\"data/ESRF.h5\", \"r\") as f:\n", - " data = f[\"data\"]\n", - " rawdata = f[\"rawdata\"]\n", - "\n", - " I_raw = np.array(data[\"iq\"])\n", - " E = np.array(data[\"energy\"])*1e3\n", - " Q = np.array(data[\"q\"])\n", - "\n", - "elements = [\"Ba\", \"Bi\", \"O\"]\n", - "comp = {\"Ba\": 1/5, \"Bi\": 1/5, \"O\": 3/5}\n", - "alpha = \"Bi\"\n", - "\n", - "\n", - "cfg = RefinementConfig(\n", - " rpoly=1, hiQ_frac=.85, ridge=1e-3, Qmax=30.0,\n", - " window=\"none\", rmin=0.0, rmax=20.0, dr=0.01, #lorch/kaiser/none\n", - " n_outer=24, plot_every=2, frame_dir=\"./refine_frames\"\n", - ")\n", - "\n", - "out, diag, hist = run_adpdf_with_refinement(\n", - " I_raw=I_raw, Q=Q, E_eV=E,\n", - " elements=elements, comp=comp,\n", - " alpha=alpha,\n", - " edge_model=model,\n", - " alpha_C=1.0, alpha_D=0.0,\n", - " beta_C=0.0, beta_D=0.1,\n", - " cfg=cfg,\n", - ")\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "10", - "metadata": {}, - "outputs": [], - "source": [ - "# v3 plotter\n", - "data = np.load(\"dpdf.npz\")\n", - "dpdf_r_tot = data[\"r_tot\"]\n", - "dpdf_G_a = data[\"G_a\"]\n", - "dpdf_G_na = data[\"G_na\"]\n", - "dpdf_G_tot = data[\"G_tot\"]\n", - "\n", - "r= np.arange(cfg.rmin, cfg.rmax + cfg.dr/2.0, cfg.dr)\n", - "\n", - "r_cutoff = 45\n", - "# plt.figure()\n", - "plt.plot(r[r_cutoff:], out['G_alpha'][r_cutoff:],'r', label=\"G_alpha (resonant)\")\n", - "plt.plot(r[r_cutoff:], out['G_not'][r_cutoff:],'g', label=\"G_not (non-resonant)\")\n", - "plt.plot(r[r_cutoff:], out['G_tot'][r_cutoff:],'b', label=\"G_tot (total/mean)\")\n", - "# plt.plot(dpdf_r_tot, dpdf_G_a, 'r--', label=\"G_alpha (paper)\")\n", - "# plt.plot(dpdf_r_tot, dpdf_G_na, 'g--', label=\"G_not (paper)\")\n", - "# plt.plot(dpdf_r_tot, dpdf_G_tot, 'b--', label=\"G_tot (paper)\")\n", - "\n", - "\n", - "plt.legend()\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "id": "11", - "metadata": {}, - "source": [ - "## 1. Definitions\n", - "\n", - "- Scattering factors for element i:\n", - "\n", - " ```math\n", - " f_i(Q,E) = f_{0,i}(Q) + f'_i(E) + i\\,f''_i(E)\n", - " ```\n", - "\n", - "* $f_0(Q)$ is the Thomson (real) form factor\n", - "\n", - "* $f'$, $f''$ are the dispersive parts near an absorption edge\n", - "\n", - "* Composition averages (Faber–Ziman):\n", - "\n", - " ```math\n", - " \\langle f \\rangle(Q,E) = \\sum_i c_i\\,\\Re f_i(Q,E)\n", - " ```\n", - "\n", - " ```math\n", - " \\langle |f|^2 \\rangle(Q,E) = \\sum_i c_i\\,|f_i(Q,E)|^2\n", - " ```\n", - "\n", - "* Corrections:\n", - "\n", - " ```math\n", - " \\alpha(E) = \\alpha_C + \\alpha_D\\,f''(E)\n", - " ```\n", - "\n", - " ```math\n", - " \\beta(E) = \\beta_C + \\beta_D\\,f''(E)\n", - " ```\n", - "\n", - "* Background term $\\beta_0(Q,E)$:\n", - "\n", - " * Even after normalization, small residuals cause $S \\not\\to 1$ at high $Q$.\n", - " * Fit a polynomial in Q on a high-Q mask to drive $S \\to 1$.\n", - "\n", - " Corrected intensity:\n", - "\n", - " ```math\n", - " I_{\\text{corr}}(Q,E) = \\alpha(E)\\,I_{\\text{raw}}(Q,E) + \\beta(E) + \\beta_0(Q,E)\n", - " ```\n", - "\n", - "* Normalized structure function (target from the data):\n", - "\n", - " ```math\n", - " S(Q,E) = \\frac{I_{\\text{corr}}(Q,E)-\\langle |f|^2\\rangle}{\\langle f\\rangle^2} + 1\n", - " ```\n", - "\n", - "\n", - "* PDF:\n", - "\n", - " ```math\n", - " G(r) = \\frac{2}{\\pi}\\int_0^{Q_{\\max}} Q \\, [S(Q)-1] \\, W(Q) \\, \\sin(Qr) \\, dQ\n", - " ```\n", - "\n", - " $W(Q)$ is a window function (e.g., Lorch/Kaiser) to suppress truncation ripples.\n", - "\n", - "---\n", - "\n", - "## 2. Edge Model (for $f'$ and $f''$)\n", - "\n", - "* Near-edge $f''(E)$:\n", - " Start from Chantler $f_2$ as baseline and refine:\n", - "\n", - " * global energy shift $dE$\n", - " * scale on $f''$\n", - " * offset and optional linear slope vs. E\n", - " * optional Lorentzian white-line peaks $\\sum_k L_k(E)$\n", - " * Lorentzian broadening (convolution with FWHM parameter)\n", - "\n", - " Constraint: $f''(E) \\geq 0$ (physical absorption).\n", - "\n", - "* Computing $f'(E)$ via Kramers–Kronig:\n", - "\n", - " * Merge near-edge $f''$ with tabulated high/low-energy tails.\n", - "\n", - " * Compute $f_1(E)$, then:\n", - "\n", - " ```math\n", - " f'(E) = f_1(E) - f_1(\\infty)\n", - " ```\n", - "\n", - " * Refine a small shift parameter `fp_offset` applied only to the weights $a$ and $b$.\n", - "\n", - "* Form factor in weights:\n", - "\n", - " ```math\n", - " \\Re f_\\alpha(Q,E) = f_0^\\alpha(Q) + f'(E) + \\text{fp\\_offset}\n", - " ```\n", - "\n", - " For non-resonant species, use $f_0(Q)$ only.\n", - "\n", - "---\n", - "\n", - "## 3. From Raw Intensity to $S(Q,E)$\n", - "\n", - "* Energy contrast / two-channel model:\n", - "\n", - " * Choose a resonant species $\\alpha$ (near an edge).\n", - "\n", - " * Decompose:\n", - "\n", - " ```math\n", - " S(Q,E) = a(Q,E)\\,S_\\alpha(Q) + b(Q,E)\\,S_{\\lnot\\alpha}(Q)\n", - " ```\n", - "\n", - " * Mixing weights (composition + real parts):\n", - "\n", - " ```math\n", - " a = \\frac{c_\\alpha\\,\\Re f_\\alpha}{\\langle f \\rangle}, \\quad\n", - " b = \\frac{\\sum_{\\beta \\neq \\alpha} c_\\beta\\,\\Re f_\\beta}{\\langle f \\rangle}\n", - " ```\n", - "\n", - " * $S_\\alpha$ and $S_{\\lnot\\alpha}$ are energy-independent unknown partial structure functions.\n", - "\n", - " * Optimization Problem:\n", - "\n", - "\tFor each $Q_j$, solves regularized least-squares problem:\n", - "\n", - "\t```math\n", - "\t\\min_{x \\in \\mathbb{R}^2} \\quad \\|A_j x - y_j\\|_2^2 \\;+\\; \\lambda \\|x\\|_2^2 \\;+\\; \\mu \\|x - \\mathbf{1}\\|^2\n", - "\t```\n", - "\n", - "\t```math\n", - "\t\\min_{S_\\alpha, S_{\\lnot\\alpha}} \n", - "\t\\sum_E \\left[a_{Ej}S_\\alpha + b_{Ej}S_{\\lnot\\alpha} - S_{Ej}\\right]^2\n", - "\t+ \\lambda_{\\text{ridge}}\\|x\\|^2\n", - "\t+ \\lambda_{\\text{anchor}}(j)\\|x-\\mathbf{1}\\|^2\n", - "\t```\n", - "\n", - "\tWhere:\n", - "\n", - "\t- $ A_j \\in \\mathbb{R}^{n_e \\times 2} $ is the local design matrix, a/b channels.\n", - "\n", - "\t- $ y_j \\in \\mathbb{R}^{n_e \\times 1} $ is the measurement $S$ vector for each Q.\n", - "\n", - "\t- $ x = \\begin{bmatrix} s_\\alpha \\\\ s_{\\lnot\\alpha} \\end{bmatrix} $ are the two unknown coefficients to solve for in this column.\n", - "\n", - "\t- $\\lambda = \\texttt{ridge}$ is the ridge regularization strength, stabilize the solution.\n", - "\n", - "\t- $\\mu = \\texttt{anchor}$ is the anchor weight for high-Q tails (on high-Q mask, else 0).\n", - "\n", - "---\n", - "\n", - "## 4. Global refinement: parameters and constraints\n", - "\n", - "* Global edge parameters:\n", - "\n", - " * $dE$ (eV), scale (>0), `fpp_offset`, `broaden_fwhm_eV`, `fp_offset`.\n", - "\n", - "* Correction parameters:\n", - "\n", - " * $\\alpha_C, \\alpha_D, \\beta_C, \\beta_D$.\n", - "\n", - "* Peaks:\n", - "\n", - " * center within measured energy span\n", - " * FWHM $\\in$ \\[0.5, 30] eV\n", - " * height $\\geq$ 0, capped vs. baseline median, L1 penalty applied.\n", - "\n", - "* Hard constraints:\n", - "\n", - " * $f''(E) \\geq 0$\n", - " * scale > 0\n", - " * FWHM within limits\n", - " * cap extreme $a, b$ weights to avoid blowups\n", - " * anchoring for high-Q tails\n", - "\n", - "---\n", - "\n", - "## 6. Refinement Strategy\n", - "\n", - "* Coordinate descent with adaptive steps:\n", - "\n", - " * Try $\\pm\\Delta$ per parameter; shrink $\\Delta$ by $\\times 0.7$ if rejected.\n", - "\n", - "* Objective function:\n", - "\n", - " ```math\n", - " J = \\lambda_\\text{tail}\\sum_{j \\in \\text{hiQ}}\\![(S_\\alpha-1)^2 + (S_{\\lnot\\alpha}-1)^2]\n", - " + \\lambda_\\text{smooth}\\sum (\\Delta^2 S_\\alpha)^2 + (\\Delta^2 S_{\\lnot\\alpha})^2\n", - " + \\lambda_{L1}\\sum_k \\text{height}_k\n", - " ```\n", - "\n", - " Encourages:\n", - "\n", - " * Tails near 1\n", - " * Smooth $Q$-dependence\n", - " * Sparse peaks\n", - "\n", - "* Peak birth/death:\n", - "\n", - " * Occasionally attempt to add peaks above edge.\n", - " * Keep if J improves, remove if negligible.\n", - "\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "diffpy.adpdf_env311", - "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": "3.11.14" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/src/diffpy/adpdf/pipeline.py b/src/diffpy/adpdf/pipeline.py new file mode 100644 index 0000000..a33674c --- /dev/null +++ b/src/diffpy/adpdf/pipeline.py @@ -0,0 +1,622 @@ +import os +import math +import h5py +import numpy as np +import numpy.linalg as npl +import matplotlib.pyplot as plt +from dataclasses import dataclass, field +from typing import Dict, List, Optional, Tuple, Any + +import kkcalc +import xraydb + +# ============================================================================= +# 1. SETUP & CONFIGURATION +# ============================================================================= + +@dataclass +class RefinementConfig: + # S(Q) construction + rpoly: float = 1.0 + hiQ_frac: float = 0.85 + ridge: float = 8e-4 + + # G(r) + window: str = "lorch" + kaiser_beta: float = 6.0 + rmin: float = 0.0 + rmax: float = 20.0 + dr: float = 0.01 + Qmin: float = 0.7 + Qmax: Optional[float] = 30.0 + + # Outer refinement and early stopping + n_outer: int = 24 + plot_every: int = 2 + tol_obj: float = 1e-4 + + # Output directories + out_dir: str = "out" + fig_dir: str = os.path.join("out", "figures") + frame_dir: str = os.path.join("out", "figures", "refine_frames") + + # Parameter step sizes + step_rpoly: float = 0.05 + step_dE_eV: float = 2.0 + step_scale: float = 0.05 + step_fpp_offset: float = 0.05 + step_fp_offset: float = 0.05 + step_broaden_fwhm: float = 2.0 + step_alphaC: float = 0.05 + step_alphaD: float = 0.05 + step_betaC: float = 0.05 + step_betaD: float = 0.05 + + # Peak step sizes + step_peak_center_eV: float = 4.0 + step_peak_fwhm_eV: float = 1.0 + step_peak_height: float = 0.05 + + # Physical constraints + min_broaden_fwhm_eV: float = 0.0 + max_broaden_fwhm_eV: float = 40.0 + min_peak_fwhm_eV: float = 0.5 + max_peak_fwhm_eV: float = 30.0 + max_peak_height_factor: float = 1.0 + + # Objective pieces + hiQ_anchor_lambda: float = 1.0 + smooth_lambda: float = 1e-5 + peak_L1_lambda: float = 1e-3 + + # Peak birth/death controls + birth_every: int = 4 + death_height_thresh: float = 1e-2 + +@dataclass +class RefinementHistory: + it: int + obj: float + params: Dict[str, float] + +@dataclass +class Peak: + center_eV: float + fwhm_eV: float + height: float + +@dataclass +class EdgeModelParams: + element: str = "Bi" + e0_keV: float = 90.526 + dE_eV: float = 0.0 + scale: float = 1.0 + fpp_offset: float = 0.0 + fpp_slope_per_eV: float = 0.0 + broaden_fwhm_eV: float = 0.0 + peaks: List[Peak] = field(default_factory=list) + use_chantler_f2_baseline: bool = True + +def setup_directories(cfg: RefinementConfig): + for d in [cfg.out_dir, cfg.fig_dir, cfg.frame_dir]: + if not os.path.exists(d): + os.makedirs(d) + +# ============================================================================= +# 2. EDGE MODEL & SCATTERING PHYSICS +# ============================================================================= + +class _BaseEdgeModel: + def __init__(self, params: EdgeModelParams): + self.params = params + + @staticmethod + def to_eV(E: np.ndarray) -> np.ndarray: + E = np.asarray(E, dtype=float) + scale = 1.0 if np.nanmax(E) >= 1e3 else 1e3 + return E * scale + + @staticmethod + def lorentzian_height(E: np.ndarray, center: float, fwhm: float, height: float) -> np.ndarray: + gamma = 0.5 * max(float(fwhm), 1e-18) + return height * (gamma**2) / ((E - center) ** 2 + gamma**2) + + @staticmethod + def broadening(E_eV: np.ndarray, y: np.ndarray, fwhm_eV: float) -> np.ndarray: + if fwhm_eV <= 0.0: return y + Emin, Emax = float(E_eV[0]), float(E_eV[-1]) + dmins = float(np.min(np.diff(E_eV))) + d_helper = max(min(dmins / 4.0, fwhm_eV / 25.0), 1e-3) + pad = max(5.0 * fwhm_eV, 10.0 * dmins) + Xu = np.arange(Emin - pad, Emax + pad + d_helper, d_helper) + yu = np.interp(Xu, E_eV, y) + + gamma = 0.5 * float(fwhm_eV) + Lx = np.arange(-10.0 * fwhm_eV, 10.0 * fwhm_eV + d_helper, d_helper) + Lk = (gamma / np.pi) / (Lx**2 + gamma**2) + Lk /= Lk.sum() + conv = np.convolve(yu, Lk, mode="same") + return np.interp(E_eV, Xu, conv) + +class KKCalcAdapter: + def __init__(self, element: str): + self.stoich = kkcalc.data.ParseChemicalFormula(element) + self.rc = kkcalc.calc_relativistic_correction(self.stoich) + self.full_E, self.full_imag_coeffs = kkcalc.data.calculate_asf(self.stoich) + + def f1_from_f2(self, energy_eval_eV: np.ndarray, near_edge_f2_vals: Optional[np.ndarray], + merge_points: Optional[Tuple[float, float]] = None, + add_background: bool = False, fix_distortions: bool = False) -> Tuple[np.ndarray, np.ndarray, float]: + E = np.asarray(energy_eval_eV, float) + if near_edge_f2_vals is not None: + NearEdge_Data = np.column_stack([E, np.asarray(near_edge_f2_vals, float)]) + mp = (float(E[0]), float(E[-1])) if merge_points is None else merge_points + Full_E, Imaginary_Spectrum = kkcalc.data.merge_spectra( + NearEdge_Data, self.full_E, self.full_imag_coeffs, + merge_points=mp, add_background=add_background, fix_distortions=fix_distortions + ) + else: + Full_E, Imaginary_Spectrum = self.full_E, self.full_imag_coeffs + + f1_vals = kkcalc.KK_PP(E, Full_E, Imaginary_Spectrum, self.rc) + i1 = max(np.searchsorted(Full_E, E[0], side="right") - 1, 0) + i2 = max(np.searchsorted(Full_E, E[-1], side="right") - 1, i1 + 1) + f2_vals = kkcalc.data.coeffs_to_ASF(E, np.vstack((Imaginary_Spectrum[i1:i2], Imaginary_Spectrum[-1]))) + return f1_vals, f2_vals, float(self.rc) + +class EdgeModel(_BaseEdgeModel): + def __init__(self, params: EdgeModelParams): + super().__init__(params) + self.kk = KKCalcAdapter(params.element) + + def fpp(self, E: np.ndarray) -> np.ndarray: + E_eV = self.to_eV(E) + E_eval = E_eV + float(self.params.dE_eV) + if self.params.use_chantler_f2_baseline: + f2 = np.asarray(xraydb.f2_chantler(self.params.element, E_eval), float) + else: + f2 = np.zeros_like(E_eval) + + f2 = float(self.params.scale) * f2 + float(self.params.fpp_offset) + f2 += float(self.params.fpp_slope_per_eV) * (E_eV - float(self.params.e0_keV) * 1e3) + + if self.params.peaks: + add = np.zeros_like(f2) + for pk in self.params.peaks: + add += self.lorentzian_height(E_eval, pk.center_eV, pk.fwhm_eV, pk.height) + f2 = f2 + add + return self.broadening(E_eV, f2, self.params.broaden_fwhm_eV) + + def fp(self, E: np.ndarray, fpp: Optional[np.ndarray] = None, return_f1: bool = False, + merge_points: Optional[Tuple[float, float]] = None, add_background: bool = False, + fix_distortions: bool = False) -> np.ndarray: + E_eV = self.to_eV(E) + E_eval = E_eV + float(self.params.dE_eV) + if fpp is None: fpp = self.fpp(E_eV) + f1_vals, f2_vals, f1_inf = self.kk.f1_from_f2( + energy_eval_eV=E_eval, near_edge_f2_vals=fpp, merge_points=merge_points, + add_background=add_background, fix_distortions=fix_distortions + ) + return f1_vals if return_f1 else (f1_vals - f1_inf) + +# ============================================================================= +# 3. UTILITIES & PIPELINE FUNCTIONS +# ============================================================================= + +def _as_1d(a: np.ndarray) -> np.ndarray: return np.asarray(a).ravel() +def _trapz(x: np.ndarray, y: np.ndarray) -> float: return float(np.trapezoid(y, x)) + +def _safe(a: np.ndarray, name: str) -> np.ndarray: + if not np.all(np.isfinite(a)): + raise ValueError(f"{name} has non-finite entries at {np.where(~np.isfinite(a))}") + return a + +def _lorch(Q: np.ndarray, Qmax: float) -> np.ndarray: + x = Q / Qmax + w = np.ones_like(Q) + m = (x > 0) & (x <= 1.0) + w[m] = np.sin(np.pi * x[m]) / (np.pi * x[m]) + w[x > 1.0] = 0.0 + return w + +def _kaiser(Q: np.ndarray, Qmax: float, beta: float = 6.0) -> np.ndarray: + from numpy import i0 + x = Q / Qmax + w = np.zeros_like(Q) + m = (x >= 0) & (x <= 1.0) + w[m] = i0(beta * np.sqrt(1.0 - x[m]**2)) / i0(beta) + return w + +def _ensure_2d(x: np.ndarray, ne: int, nq: int, name: str) -> np.ndarray: + x = np.asarray(x, float) + if x.ndim == 0: return np.full((ne, nq), float(x)) + if x.ndim == 1: + if x.size == ne: return x[:, None] * np.ones((1, nq)) + if x.size == nq: return np.ones((ne, 1)) * x[None, :] + raise ValueError(f"{name} 1D mismatch") + if x.shape != (ne, nq): raise ValueError(f"{name} shape mismatch") + return x + +def _f0_of_Q(element: str, Q: np.ndarray) -> np.ndarray: + s = _as_1d(Q) / (4.0 * np.pi) + f0 = np.array([xraydb.f0(element, si)[0] for si in s], dtype=float) + return _safe(f0, f"f0({element})") + +def _compute_scattering(elements: List[str], comp: Dict[str, float], alpha: str, Q: np.ndarray, + E_eV: np.ndarray, edge_model: Any, fp_offset: float = 0.0): + Q = _as_1d(Q); E = _as_1d(E_eV) + nq, ne = len(Q), len(E) + f0_map = {el: _f0_of_Q(el, Q) for el in elements} + + fp = edge_model.fp(E, return_f1=False) + fpp = np.maximum(edge_model.fpp(E), 0.0) + + fr_weights, f2_weights = {}, {} + for el in elements: + f0 = f0_map[el] + if el == alpha: + fr = (fp + fp_offset)[:, None] + f0[None, :] + fi = fpp[:, None] + else: + fr = f0[None, :] + fi = np.zeros((ne, 1)) + fr_weights[el] = fr + f2_weights[el] = fr**2 + fi**2 + + fmean_real, fmean_abs2, f_not_sum = np.zeros((ne, nq), float), np.zeros((ne, nq), float), np.zeros((ne, nq), float) + for el in elements: + c = float(comp[el]) + fmean_real += c * fr_weights[el] + fmean_abs2 += c * f2_weights[el] + if el != alpha: f_not_sum += c * fr_weights[el] + return fr_weights, f0_map, fmean_real, fmean_abs2, fmean_abs2, f_not_sum + +def _weights_alpha_not(comp: Dict[str, float], alpha: str, fr_weights: Dict[str, np.ndarray], + fmean_real: np.ndarray, f_not_sum: np.ndarray): + cA = float(comp[alpha]); eps = 1e-12 + a = np.clip(cA * fr_weights[alpha] / (fmean_real + eps), -5.0, 5.0) + b = np.clip(f_not_sum / (fmean_real + eps), -5.0, 5.0) + return a, b, {"a_min": float(np.nanmin(a)), "a_max": float(np.nanmax(a))} + +def _alpha_beta_from_fpp(fpp_E: np.ndarray, alpha_C: float, alpha_D: float, beta_C: float, beta_D: float): + return np.clip(alpha_C + alpha_D * fpp_E, 1e-6, None), beta_C + beta_D * fpp_E + +def _build_S_from_raw(I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray, alpha_e: np.ndarray, beta_f_e: np.ndarray, + fmean_real: np.ndarray, fself: np.ndarray, rpoly: float): + I_raw = np.asarray(I_raw, float) + E = _as_1d(E_eV); Q = _as_1d(Q) + ne, nq = len(E), len(Q) + + I_corr = I_raw * alpha_e[:, None] + beta_f_e[:, None] + S0 = (I_corr - fself) / (fmean_real**2 + 1e-12) + 1.0 + + # WLS Fractional Polynomial Fitting + xspan = float(Q[-1] - Q[0]) + porder = max(1.0, (rpoly * xspan) / np.pi) + porderlo, porderhi = int(np.floor(porder)), int(np.ceil(porder)) + poly_weights = [0.5, 0.5] if porderlo == porderhi else [porderhi - porder, porder - porderlo] + + weight_power = 4.0 + W_sqrt = np.sqrt((Q / Q[-1])**weight_power) + + Xlo = np.vstack([Q**k for k in range(porderlo + 1)]).T + Xhi = np.vstack([Q**k for k in range(porderhi + 1)]).T + Xlo_w, Xhi_w = Xlo * W_sqrt[:, None], Xhi * W_sqrt[:, None] + XtXlo = Xlo_w.T @ Xlo_w + 1e-12 * np.eye(Xlo_w.shape[1]) + XtXhi = Xhi_w.T @ Xhi_w + 1e-12 * np.eye(Xhi_w.shape[1]) + + beta_o = np.zeros_like(S0) + for i in range(ne): + y = (1.0 - S0[i]) * (fmean_real[i]**2) + y_w = y * W_sqrt + coeff_lo = npl.solve(XtXlo, Xlo_w.T @ y_w) + beta_lo = (Xlo @ coeff_lo) / (fmean_real[i]**2 + 1e-12) + + if porderlo == porderhi: + beta_o[i] = beta_lo + else: + coeff_hi = npl.solve(XtXhi, Xhi_w.T @ y_w) + beta_hi = (Xhi @ coeff_hi) / (fmean_real[i]**2 + 1e-12) + beta_o[i] = poly_weights[0] * beta_lo + poly_weights[1] * beta_hi + + return S0 + beta_o, beta_o + +def _solve_two_channel_column(Aj: np.ndarray, yj: np.ndarray, ridge: float, anchor: float): + ATA = Aj.T @ Aj + ridge*np.eye(2) + anchor*np.eye(2) + ATy = Aj.T @ yj + anchor*np.array([[1.0],[1.0]]) + try: sol = npl.solve(ATA, ATy) + except npl.LinAlgError: sol = npl.lstsq(ATA, ATy, rcond=None)[0] + return float(sol[0,0]), float(sol[1,0]) + +def _reconstruct_Salpha_Snot(S_meas: np.ndarray, a: np.ndarray, b: np.ndarray, Q: np.ndarray, ridge: float): + S_meas = np.asarray(S_meas, float) + for i in range(S_meas.shape[0]): + S_meas[i][:40] = S_meas[i][41] + ne, nq = S_meas.shape + a = _ensure_2d(a, ne, nq, "a"); b = _ensure_2d(b, ne, nq, "b") + + Sa, Sb = np.zeros(nq), np.zeros(nq) + bad_cols = 0 + for j in range(nq): + Aj, yj = np.stack([a[:,j], b[:,j]], axis=1), S_meas[:, j:j+1] + s = npl.svd(Aj, compute_uv=False) + cond = (s[0]/s[-1]) if (s[-1] > 0) else np.inf + anchor = 5.0 if (not np.isfinite(cond) or cond > 1e6) else 0.0 + if anchor > 0.0: bad_cols += 1 + Sa[j], Sb[j] = _solve_two_channel_column(Aj, yj, ridge, anchor) + return Sa, Sb, {"bad_Q_columns": bad_cols} + +def _S_to_G(Q: np.ndarray, S: np.ndarray, r: np.ndarray, window: str, kbeta: float) -> np.ndarray: + Q = _as_1d(Q); S = _as_1d(S); r = _as_1d(r) + Qmax = float(Q.max()) + w = np.ones_like(Q) + if window == "lorch": w = _lorch(Q, Qmax) + elif window == "kaiser": w = _kaiser(Q, Qmax, kbeta) + F = Q * (S - 1.0) * w + G = np.zeros_like(r) + for i, ri in enumerate(r): + G[i] = (2.0/np.pi) * _trapz(Q, F*np.sin(Q*ri)) + return G + +# ============================================================================= +# 4. REFINEMENT & PLOTTING +# ============================================================================= + +def save_initial_edge_plots(E_eV: np.ndarray, edge_model: EdgeModel, cfg: RefinementConfig): + fpp_init = edge_model.fpp(E_eV) + fp_init = edge_model.fp(E_eV) + fp_chantler = xraydb.f1_chantler(edge_model.params.element, edge_model.to_eV(E_eV) + edge_model.params.dE_eV) + + fig, ax = plt.subplots(1, 2, figsize=(10, 4)) + ax[0].plot(E_eV / 1000, fpp_init, label="f'' (Model/Chantler)") + ax[0].set_xlabel("Energy (keV)"); ax[0].set_title("Initial f''"); ax[0].legend() + + ax[1].plot(E_eV / 1000, fp_init, label="f' (Model)") + ax[1].plot(E_eV / 1000, fp_chantler, "--", label="f' (Chantler Tabulated)") + ax[1].set_xlabel("Energy (keV)"); ax[1].set_title("Initial f'"); ax[1].legend() + + plt.tight_layout() + plt.savefig(os.path.join(cfg.fig_dir, "fpp_fp_initial.png"), dpi=150) + plt.close() + +def _plot_frame(path: str, E_eV: np.ndarray, edge_model: Any, r: np.ndarray, out: Dict[str,np.ndarray], + Q_full: np.ndarray, iter_idx: int, hist: List[RefinementHistory], fp_offset: float) -> None: + q = np.asarray(out.get("Q", Q_full)) + Sa, Sb, St = np.asarray(out["S_alpha"]), np.asarray(out["S_not"]), np.asarray(out["S_tot"]) + r_plot = np.asarray(r) + Ga, Gn, Gt = np.asarray(out["G_alpha"]), np.asarray(out["G_not"]), np.asarray(out["G_tot"]) + + E = np.asarray(E_eV, float) + fpp = np.maximum(edge_model.fpp(E), 0.0) + fp = edge_model.fp(E, fpp=fpp) + fp_offset + + plt.figure(figsize=(12,20)) + plt.suptitle(f"Refinement frame {iter_idx:03d}") + + ax1 = plt.subplot(4,2,1) + ax1.plot(E/1e3, fpp, label="f'' (model)"); ax1.legend(loc="upper left") + + ax2 = plt.subplot(4,2,2) + ax2.plot(E/1e3, fp, label="f' (KK from model) + fp_offset"); ax2.legend(loc="upper left") + + ax = plt.subplot(4,1,2) + ax.plot(r_plot, Ga, 'b-', label="G_alpha"); ax.plot(r_plot, Gn, 'g-', label="G_not") + ax.plot(r_plot, Gt, "r-", label="G_tot"); ax.legend(loc="upper right") + + ax = plt.subplot(4,1,3) + ax.plot(q, Sa, 'b-', label="S_alpha", linewidth=.5); ax.plot(q, Sb, 'g-', label="S_not", linewidth=.5) + ax.plot(q, St, "r-", label="S_tot", linewidth=.5); ax.plot(q, np.ones_like(q), 'k-', linewidth=0.1) + ax.legend(loc="upper left") + + ax = plt.subplot(4,1,4) + its = np.arange(len(hist)); vals = np.array([h.obj for h in hist], float) + ax.plot(its, vals, "-o"); ax.set_yscale('log') + p = hist[-1].params + txt = (f"dE_eV={p['dE_eV']:.3g}\nscale={p['scale']:.3g}\n" + f"alpha_C={p['alpha_C']:.3g}, beta_C={p['beta_C']:.3g}") + ax.text(0.02, 0.98, txt, va="top", ha="left", transform=ax.transAxes, + bbox=dict(boxstyle="round", facecolor="white", alpha=0.85)) + + plt.savefig(path, dpi=150); plt.close() + +def save_results(out: Dict[str, np.ndarray], cfg: RefinementConfig): + """Save the output PDFs to .cgr files and export a final summary plot.""" + r = out["r"] + np.savetxt(os.path.join(cfg.out_dir, "G_alpha.cgr"), np.column_stack([r, out["G_alpha"]]), header="r G_alpha") + np.savetxt(os.path.join(cfg.out_dir, "G_not.cgr"), np.column_stack([r, out["G_not"]]), header="r G_not") + np.savetxt(os.path.join(cfg.out_dir, "G_tot.cgr"), np.column_stack([r, out["G_tot"]]), header="r G_tot") + + # Plot the full r-range to preserve diagnostic low-r ripples + plt.figure() + plt.plot(r, out['G_alpha'], 'r', label="G_alpha (resonant)") + plt.plot(r, out['G_not'], 'g', label="G_not (non-resonant)") + plt.plot(r, out['G_tot'], 'b', label="G_tot (total/mean)") + + plt.xlabel("r (Å)") + plt.ylabel("G(r)") + plt.legend() + plt.tight_layout() + plt.savefig(os.path.join(cfg.fig_dir, "final_results.png"), dpi=150) + plt.close() + print("Final .cgr files and full-range comparison plot saved.") + +def _objective(Sa: np.ndarray, Sb: np.ndarray, Q: np.ndarray, hiQ_frac: float, anchor_lambda: float) -> float: + nq = len(Q); k0 = int(max(0, math.floor((1.0-hiQ_frac)*nq))) + mask = np.zeros(nq, bool); mask[k0:] = True + tails = np.sum((Sa[mask]-1.0)**2 + (Sb[mask]-1.0)**2) + d2a = np.diff(Sa, n=2); d2b = np.diff(Sb, n=2) + smooth = np.sum(d2a**2 + d2b**2) + physics = np.sum((Sa - Sb)**2) + return float(anchor_lambda*tails + smooth + physics) + +def reconstruct_partials_and_pdfs(I_raw, Q, E_eV, elements, comp, alpha, edge_model, alpha_e, beta_e, + rpoly, ridge, r, Qmin, Qmax, window="lorch", kaiser_beta=6.0, fp_offset=0.0): + Q = _as_1d(Q); E = _as_1d(E_eV); I_raw = np.asarray(I_raw, float) + frw, f0_map, fmean_real, fmean_abs2, fself, f_not_sum = _compute_scattering( + elements, comp, alpha, Q, E, edge_model, fp_offset=fp_offset) + a, b, wb = _weights_alpha_not(comp, alpha, frw, fmean_real, f_not_sum) + + if Qmax is None: Qmax = float(Q.max()) + mask_Q = (Q >= Qmin) & (Q <= Qmax) + Q_use = Q[mask_Q] + + S_meas_all, beta_o_all = _build_S_from_raw(I_raw, Q, E, alpha_e, beta_e, fmean_real, fself, rpoly) + S_meas = S_meas_all[:, mask_Q]; a = a[:, mask_Q]; b = b[:, mask_Q] + + Sa, Sb, condinfo = _reconstruct_Salpha_Snot(S_meas, a, b, Q_use, ridge) + S_tot = S_meas[0] + + r = _as_1d(r) + G_alpha = _S_to_G(Q_use, Sa, r, window, kaiser_beta) + G_not = _S_to_G(Q_use, Sb, r, window, kaiser_beta) + G_tot = _S_to_G(Q_use, S_tot, r, window, kaiser_beta) + + out = {"Q": Q_use, "r": r, "S_alpha": Sa, "S_not": Sb, "S_tot": S_tot, + "G_alpha": G_alpha, "G_not": G_not, "G_tot": G_tot} + return out, {"weights": wb, "condinfo": condinfo, "beta_o": beta_o_all} + +def run_adpdf_with_refinement(I_raw, Q, E_eV, elements, comp, alpha, edge_model, + alpha_C=1.0, alpha_D=0.0, beta_C=0.0, beta_D=0.0, + fp_offset=0.0, cfg=None): + if cfg is None: cfg = RefinementConfig() + Q = _as_1d(Q); E = _as_1d(E_eV); I_raw = np.asarray(I_raw, float) + rpoly = cfg.rpoly + edge_model.params.scale = max(1e-4, float(edge_model.params.scale)) + edge_model.params.broaden_fwhm_eV = float(np.clip(edge_model.params.broaden_fwhm_eV, + cfg.min_broaden_fwhm_eV, cfg.max_broaden_fwhm_eV)) + + r = np.arange(cfg.rmin, cfg.rmax + cfg.dr/2.0, cfg.dr) + Qmax = cfg.Qmax if cfg.Qmax is not None else float(Q.max()) + + def compute(): + fpp = np.maximum(edge_model.fpp(E), 0.0) + alpha_e, beta_e = _alpha_beta_from_fpp(fpp, alpha_C, alpha_D, beta_C, beta_D) + out, diag = reconstruct_partials_and_pdfs( + I_raw, Q, E, elements, comp, alpha, edge_model, alpha_e, beta_e, + rpoly=rpoly, ridge=cfg.ridge, r=r, Qmin=cfg.Qmin, Qmax=Qmax, + window=cfg.window, kaiser_beta=cfg.kaiser_beta, fp_offset=fp_offset, + ) + return out, diag, _objective(out["S_alpha"], out["S_not"], out["Q"], cfg.hiQ_frac, cfg.hiQ_anchor_lambda) + + out, diag, obj = compute() + hist = [RefinementHistory(0, obj, { + "scale": edge_model.params.scale, + "dE_eV": edge_model.params.dE_eV, + "alpha_C": alpha_C, + "beta_C": beta_C + })] + os.makedirs(cfg.frame_dir, exist_ok=True) + _plot_frame(os.path.join(cfg.frame_dir, f"frame_{0:03d}.png"), E, edge_model, r, out, Q, 0, hist, fp_offset) + + steps = dict(rpoly=cfg.step_rpoly, dE_eV=cfg.step_dE_eV, scale=cfg.step_scale, + fpp_offset=cfg.step_fpp_offset, fp_offset=cfg.step_fp_offset, + broaden_fwhm_eV=cfg.step_broaden_fwhm, alpha_C=cfg.step_alphaC, + alpha_D=cfg.step_alphaD, beta_C=cfg.step_betaC, beta_D=cfg.step_betaD) + + def tweak(name: str, d: float): + nonlocal alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly + p = edge_model.params + if name == "rpoly": rpoly = float(np.clip(rpoly + d, 0.0, 2.0)) + elif name == "dE_eV": p.dE_eV += d + elif name == "scale": p.scale = max(1e-4, p.scale + d) + elif name == "fpp_offset": p.fpp_offset += d + elif name == "broaden_fwhm_eV":p.broaden_fwhm_eV = float(np.clip(p.broaden_fwhm_eV + d, cfg.min_broaden_fwhm_eV, cfg.max_broaden_fwhm_eV)) + elif name == "alpha_C": alpha_C = max(1e-6, alpha_C + d) + elif name == "alpha_D": alpha_D += d + elif name == "beta_C": beta_C += d + elif name == "beta_D": beta_D += d + elif name == "fp_offset": fp_offset += d + + best_obj = obj + for it in range(1, cfg.n_outer+1): + cycle_improved = False + start_obj = best_obj + + for name in ["rpoly", "dE_eV","scale","fpp_offset","fp_offset","broaden_fwhm_eV", + "alpha_C","alpha_D","beta_C","beta_D"]: + param_improved = False + for sgn in (+1,-1): + tweak(name, sgn*steps[name]) + out2, diag2, obj2 = compute() + if obj2 < best_obj: + out, diag, best_obj = out2, diag2, obj2 + param_improved = True; cycle_improved = True + else: + tweak(name, -sgn*steps[name]) + if not param_improved: steps[name] *= 0.7 + + hist.append(RefinementHistory(it, best_obj, { + "scale": edge_model.params.scale, + "dE_eV": edge_model.params.dE_eV, + "alpha_C": alpha_C, + "beta_C": beta_C + })) + if (it % cfg.plot_every)==0 or it==cfg.n_outer: + _plot_frame(os.path.join(cfg.frame_dir, f"frame_{it:03d}.png"), E, edge_model, r, out, Q, it, hist, fp_offset) + + rel_change = (start_obj - best_obj) / max(start_obj, 1e-12) + if rel_change < cfg.tol_obj: + print(f"Converged! Relative change ({rel_change:.2e}) is below tolerance.") + break + if not cycle_improved and max(steps.values()) < 1e-3: + print(f"Stopped at iteration {it}: step sizes shrank below 1e-3.") + break + + return out, diag, hist + +# ============================================================================= +# 5. MAIN EXECUTION +# ============================================================================= + +def main(): + # 1. Initialize Configuration + cfg = RefinementConfig() + setup_directories(cfg) + + # 2. Load Data + # Make sure this points to the correct local file path + print("Loading data...") + try: + with h5py.File("data/ESRF.h5", "r") as f: + data = f["data"] + I_raw = np.array(data["iq"]) + E = np.array(data["energy"]) * 1e3 + Q = np.array(data["q"]) + except FileNotFoundError: + print("Data file 'data/ESRF.h5' not found. Please verify the path.") + return + + # 3. Setup Elements & Edge Model + elements = ["Ba", "Bi", "O"] + comp = {"Ba": 1/5, "Bi": 1/5, "O": 3/5} + alpha = "Bi" + + params = EdgeModelParams( + element=alpha, + e0_keV=90.526, + scale=0.35, + fpp_offset=-0.2, + broaden_fwhm_eV=15.0, + peaks=[Peak(center_eV=90.526e3 + 180, fwhm_eV=3.0, height=0.3)] + ) + edge_model = EdgeModel(params) + + # 4. Save Initial Plots + save_initial_edge_plots(E, edge_model, cfg) + + # 5. Run Refinement + print("Starting refinement...") + out, diag, hist = run_adpdf_with_refinement( + I_raw=I_raw, Q=Q, E_eV=E, + elements=elements, comp=comp, + alpha=alpha, + edge_model=edge_model, + beta_D=0.1, + cfg=cfg + ) + + # 6. 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z?k_P7FSh@TmauLRqalkMor@l=hk7wteXpGLnl*q;hkt>VQ)5`00;2l!yix#kusn?YTGuJZH8;Sz?W5p%1-bN=7JhyNLx z`1gPReSZIrAxxux=h45Hg83a!eH#&uCy(3>!H*C4?`Gf=>Px# From ea794bf84dd347b3e627a0f9f2ab25bbce73ae9a Mon Sep 17 00:00:00 2001 From: tschertenleib Date: Mon, 30 Mar 2026 15:51:51 +0200 Subject: [PATCH 4/5] applying pre-commit formatting --- src/diffpy/adpdf/pipeline.py | 765 ++++++++++++++++++++++++++--------- 1 file changed, 564 insertions(+), 201 deletions(-) diff --git a/src/diffpy/adpdf/pipeline.py b/src/diffpy/adpdf/pipeline.py index a33674c..3ae3aa7 100644 --- a/src/diffpy/adpdf/pipeline.py +++ b/src/diffpy/adpdf/pipeline.py @@ -1,26 +1,27 @@ -import os import math -import h5py -import numpy as np -import numpy.linalg as npl -import matplotlib.pyplot as plt +import os from dataclasses import dataclass, field -from typing import Dict, List, Optional, Tuple, Any +from typing import Any, Dict, List, Optional, Tuple +import h5py import kkcalc +import matplotlib.pyplot as plt +import numpy as np +import numpy.linalg as npl import xraydb # ============================================================================= # 1. SETUP & CONFIGURATION # ============================================================================= + @dataclass class RefinementConfig: # S(Q) construction rpoly: float = 1.0 hiQ_frac: float = 0.85 ridge: float = 8e-4 - + # G(r) window: str = "lorch" kaiser_beta: float = 6.0 @@ -29,17 +30,17 @@ class RefinementConfig: dr: float = 0.01 Qmin: float = 0.7 Qmax: Optional[float] = 30.0 - + # Outer refinement and early stopping n_outer: int = 24 plot_every: int = 2 tol_obj: float = 1e-4 - + # Output directories out_dir: str = "out" fig_dir: str = os.path.join("out", "figures") frame_dir: str = os.path.join("out", "figures", "refine_frames") - + # Parameter step sizes step_rpoly: float = 0.05 step_dE_eV: float = 2.0 @@ -51,40 +52,43 @@ class RefinementConfig: step_alphaD: float = 0.05 step_betaC: float = 0.05 step_betaD: float = 0.05 - + # Peak step sizes step_peak_center_eV: float = 4.0 step_peak_fwhm_eV: float = 1.0 step_peak_height: float = 0.05 - + # Physical constraints min_broaden_fwhm_eV: float = 0.0 max_broaden_fwhm_eV: float = 40.0 min_peak_fwhm_eV: float = 0.5 max_peak_fwhm_eV: float = 30.0 max_peak_height_factor: float = 1.0 - + # Objective pieces hiQ_anchor_lambda: float = 1.0 smooth_lambda: float = 1e-5 peak_L1_lambda: float = 1e-3 - + # Peak birth/death controls birth_every: int = 4 death_height_thresh: float = 1e-2 + @dataclass class RefinementHistory: it: int obj: float params: Dict[str, float] + @dataclass class Peak: center_eV: float fwhm_eV: float height: float + @dataclass class EdgeModelParams: element: str = "Bi" @@ -97,15 +101,18 @@ class EdgeModelParams: peaks: List[Peak] = field(default_factory=list) use_chantler_f2_baseline: bool = True + def setup_directories(cfg: RefinementConfig): for d in [cfg.out_dir, cfg.fig_dir, cfg.frame_dir]: if not os.path.exists(d): os.makedirs(d) + # ============================================================================= # 2. EDGE MODEL & SCATTERING PHYSICS # ============================================================================= + class _BaseEdgeModel: def __init__(self, params: EdgeModelParams): self.params = params @@ -117,13 +124,18 @@ def to_eV(E: np.ndarray) -> np.ndarray: return E * scale @staticmethod - def lorentzian_height(E: np.ndarray, center: float, fwhm: float, height: float) -> np.ndarray: + def lorentzian_height( + E: np.ndarray, center: float, fwhm: float, height: float + ) -> np.ndarray: gamma = 0.5 * max(float(fwhm), 1e-18) return height * (gamma**2) / ((E - center) ** 2 + gamma**2) @staticmethod - def broadening(E_eV: np.ndarray, y: np.ndarray, fwhm_eV: float) -> np.ndarray: - if fwhm_eV <= 0.0: return y + def broadening( + E_eV: np.ndarray, y: np.ndarray, fwhm_eV: float + ) -> np.ndarray: + if fwhm_eV <= 0.0: + return y Emin, Emax = float(E_eV[0]), float(E_eV[-1]) dmins = float(np.min(np.diff(E_eV))) d_helper = max(min(dmins / 4.0, fwhm_eV / 25.0), 1e-3) @@ -138,22 +150,40 @@ def broadening(E_eV: np.ndarray, y: np.ndarray, fwhm_eV: float) -> np.ndarray: conv = np.convolve(yu, Lk, mode="same") return np.interp(E_eV, Xu, conv) + class KKCalcAdapter: def __init__(self, element: str): self.stoich = kkcalc.data.ParseChemicalFormula(element) self.rc = kkcalc.calc_relativistic_correction(self.stoich) - self.full_E, self.full_imag_coeffs = kkcalc.data.calculate_asf(self.stoich) + self.full_E, self.full_imag_coeffs = kkcalc.data.calculate_asf( + self.stoich + ) - def f1_from_f2(self, energy_eval_eV: np.ndarray, near_edge_f2_vals: Optional[np.ndarray], - merge_points: Optional[Tuple[float, float]] = None, - add_background: bool = False, fix_distortions: bool = False) -> Tuple[np.ndarray, np.ndarray, float]: + def f1_from_f2( + self, + energy_eval_eV: np.ndarray, + near_edge_f2_vals: Optional[np.ndarray], + merge_points: Optional[Tuple[float, float]] = None, + add_background: bool = False, + fix_distortions: bool = False, + ) -> Tuple[np.ndarray, np.ndarray, float]: E = np.asarray(energy_eval_eV, float) if near_edge_f2_vals is not None: - NearEdge_Data = np.column_stack([E, np.asarray(near_edge_f2_vals, float)]) - mp = (float(E[0]), float(E[-1])) if merge_points is None else merge_points + NearEdge_Data = np.column_stack( + [E, np.asarray(near_edge_f2_vals, float)] + ) + mp = ( + (float(E[0]), float(E[-1])) + if merge_points is None + else merge_points + ) Full_E, Imaginary_Spectrum = kkcalc.data.merge_spectra( - NearEdge_Data, self.full_E, self.full_imag_coeffs, - merge_points=mp, add_background=add_background, fix_distortions=fix_distortions + NearEdge_Data, + self.full_E, + self.full_imag_coeffs, + merge_points=mp, + add_background=add_background, + fix_distortions=fix_distortions, ) else: Full_E, Imaginary_Spectrum = self.full_E, self.full_imag_coeffs @@ -161,9 +191,12 @@ def f1_from_f2(self, energy_eval_eV: np.ndarray, near_edge_f2_vals: Optional[np. f1_vals = kkcalc.KK_PP(E, Full_E, Imaginary_Spectrum, self.rc) i1 = max(np.searchsorted(Full_E, E[0], side="right") - 1, 0) i2 = max(np.searchsorted(Full_E, E[-1], side="right") - 1, i1 + 1) - f2_vals = kkcalc.data.coeffs_to_ASF(E, np.vstack((Imaginary_Spectrum[i1:i2], Imaginary_Spectrum[-1]))) + f2_vals = kkcalc.data.coeffs_to_ASF( + E, np.vstack((Imaginary_Spectrum[i1:i2], Imaginary_Spectrum[-1])) + ) return f1_vals, f2_vals, float(self.rc) + class EdgeModel(_BaseEdgeModel): def __init__(self, params: EdgeModelParams): super().__init__(params) @@ -173,44 +206,70 @@ def fpp(self, E: np.ndarray) -> np.ndarray: E_eV = self.to_eV(E) E_eval = E_eV + float(self.params.dE_eV) if self.params.use_chantler_f2_baseline: - f2 = np.asarray(xraydb.f2_chantler(self.params.element, E_eval), float) + f2 = np.asarray( + xraydb.f2_chantler(self.params.element, E_eval), float + ) else: f2 = np.zeros_like(E_eval) f2 = float(self.params.scale) * f2 + float(self.params.fpp_offset) - f2 += float(self.params.fpp_slope_per_eV) * (E_eV - float(self.params.e0_keV) * 1e3) + f2 += float(self.params.fpp_slope_per_eV) * ( + E_eV - float(self.params.e0_keV) * 1e3 + ) if self.params.peaks: add = np.zeros_like(f2) for pk in self.params.peaks: - add += self.lorentzian_height(E_eval, pk.center_eV, pk.fwhm_eV, pk.height) + add += self.lorentzian_height( + E_eval, pk.center_eV, pk.fwhm_eV, pk.height + ) f2 = f2 + add return self.broadening(E_eV, f2, self.params.broaden_fwhm_eV) - def fp(self, E: np.ndarray, fpp: Optional[np.ndarray] = None, return_f1: bool = False, - merge_points: Optional[Tuple[float, float]] = None, add_background: bool = False, - fix_distortions: bool = False) -> np.ndarray: + def fp( + self, + E: np.ndarray, + fpp: Optional[np.ndarray] = None, + return_f1: bool = False, + merge_points: Optional[Tuple[float, float]] = None, + add_background: bool = False, + fix_distortions: bool = False, + ) -> np.ndarray: E_eV = self.to_eV(E) E_eval = E_eV + float(self.params.dE_eV) - if fpp is None: fpp = self.fpp(E_eV) + if fpp is None: + fpp = self.fpp(E_eV) f1_vals, f2_vals, f1_inf = self.kk.f1_from_f2( - energy_eval_eV=E_eval, near_edge_f2_vals=fpp, merge_points=merge_points, - add_background=add_background, fix_distortions=fix_distortions + energy_eval_eV=E_eval, + near_edge_f2_vals=fpp, + merge_points=merge_points, + add_background=add_background, + fix_distortions=fix_distortions, ) return f1_vals if return_f1 else (f1_vals - f1_inf) + # ============================================================================= # 3. UTILITIES & PIPELINE FUNCTIONS # ============================================================================= -def _as_1d(a: np.ndarray) -> np.ndarray: return np.asarray(a).ravel() -def _trapz(x: np.ndarray, y: np.ndarray) -> float: return float(np.trapezoid(y, x)) + +def _as_1d(a: np.ndarray) -> np.ndarray: + return np.asarray(a).ravel() + + +def _trapz(x: np.ndarray, y: np.ndarray) -> float: + return float(np.trapezoid(y, x)) + def _safe(a: np.ndarray, name: str) -> np.ndarray: if not np.all(np.isfinite(a)): - raise ValueError(f"{name} has non-finite entries at {np.where(~np.isfinite(a))}") + raise ValueError( + f"{name} has non-finite entries at {np.where(~np.isfinite(a))}" + ) return a + def _lorch(Q: np.ndarray, Qmax: float) -> np.ndarray: x = Q / Qmax w = np.ones_like(Q) @@ -219,32 +278,49 @@ def _lorch(Q: np.ndarray, Qmax: float) -> np.ndarray: w[x > 1.0] = 0.0 return w + def _kaiser(Q: np.ndarray, Qmax: float, beta: float = 6.0) -> np.ndarray: from numpy import i0 + x = Q / Qmax w = np.zeros_like(Q) m = (x >= 0) & (x <= 1.0) - w[m] = i0(beta * np.sqrt(1.0 - x[m]**2)) / i0(beta) + w[m] = i0(beta * np.sqrt(1.0 - x[m] ** 2)) / i0(beta) return w + def _ensure_2d(x: np.ndarray, ne: int, nq: int, name: str) -> np.ndarray: x = np.asarray(x, float) - if x.ndim == 0: return np.full((ne, nq), float(x)) + if x.ndim == 0: + return np.full((ne, nq), float(x)) if x.ndim == 1: - if x.size == ne: return x[:, None] * np.ones((1, nq)) - if x.size == nq: return np.ones((ne, 1)) * x[None, :] + if x.size == ne: + return x[:, None] * np.ones((1, nq)) + if x.size == nq: + return np.ones((ne, 1)) * x[None, :] raise ValueError(f"{name} 1D mismatch") - if x.shape != (ne, nq): raise ValueError(f"{name} shape mismatch") + if x.shape != (ne, nq): + raise ValueError(f"{name} shape mismatch") return x + def _f0_of_Q(element: str, Q: np.ndarray) -> np.ndarray: s = _as_1d(Q) / (4.0 * np.pi) f0 = np.array([xraydb.f0(element, si)[0] for si in s], dtype=float) return _safe(f0, f"f0({element})") -def _compute_scattering(elements: List[str], comp: Dict[str, float], alpha: str, Q: np.ndarray, - E_eV: np.ndarray, edge_model: Any, fp_offset: float = 0.0): - Q = _as_1d(Q); E = _as_1d(E_eV) + +def _compute_scattering( + elements: List[str], + comp: Dict[str, float], + alpha: str, + Q: np.ndarray, + E_eV: np.ndarray, + edge_model: Any, + fp_offset: float = 0.0, +): + Q = _as_1d(Q) + E = _as_1d(E_eV) nq, ne = len(Q), len(E) f0_map = {el: _f0_of_Q(el, Q) for el in elements} @@ -263,29 +339,61 @@ def _compute_scattering(elements: List[str], comp: Dict[str, float], alpha: str, fr_weights[el] = fr f2_weights[el] = fr**2 + fi**2 - fmean_real, fmean_abs2, f_not_sum = np.zeros((ne, nq), float), np.zeros((ne, nq), float), np.zeros((ne, nq), float) + fmean_real, fmean_abs2, f_not_sum = ( + np.zeros((ne, nq), float), + np.zeros((ne, nq), float), + np.zeros((ne, nq), float), + ) for el in elements: c = float(comp[el]) fmean_real += c * fr_weights[el] fmean_abs2 += c * f2_weights[el] - if el != alpha: f_not_sum += c * fr_weights[el] + if el != alpha: + f_not_sum += c * fr_weights[el] return fr_weights, f0_map, fmean_real, fmean_abs2, fmean_abs2, f_not_sum -def _weights_alpha_not(comp: Dict[str, float], alpha: str, fr_weights: Dict[str, np.ndarray], - fmean_real: np.ndarray, f_not_sum: np.ndarray): - cA = float(comp[alpha]); eps = 1e-12 + +def _weights_alpha_not( + comp: Dict[str, float], + alpha: str, + fr_weights: Dict[str, np.ndarray], + fmean_real: np.ndarray, + f_not_sum: np.ndarray, +): + cA = float(comp[alpha]) + eps = 1e-12 a = np.clip(cA * fr_weights[alpha] / (fmean_real + eps), -5.0, 5.0) b = np.clip(f_not_sum / (fmean_real + eps), -5.0, 5.0) return a, b, {"a_min": float(np.nanmin(a)), "a_max": float(np.nanmax(a))} -def _alpha_beta_from_fpp(fpp_E: np.ndarray, alpha_C: float, alpha_D: float, beta_C: float, beta_D: float): - return np.clip(alpha_C + alpha_D * fpp_E, 1e-6, None), beta_C + beta_D * fpp_E -def _build_S_from_raw(I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray, alpha_e: np.ndarray, beta_f_e: np.ndarray, - fmean_real: np.ndarray, fself: np.ndarray, rpoly: float): +def _alpha_beta_from_fpp( + fpp_E: np.ndarray, + alpha_C: float, + alpha_D: float, + beta_C: float, + beta_D: float, +): + return ( + np.clip(alpha_C + alpha_D * fpp_E, 1e-6, None), + beta_C + beta_D * fpp_E, + ) + + +def _build_S_from_raw( + I_raw: np.ndarray, + Q: np.ndarray, + E_eV: np.ndarray, + alpha_e: np.ndarray, + beta_f_e: np.ndarray, + fmean_real: np.ndarray, + fself: np.ndarray, + rpoly: float, +): I_raw = np.asarray(I_raw, float) - E = _as_1d(E_eV); Q = _as_1d(Q) - ne, nq = len(E), len(Q) + E = _as_1d(E_eV) + Q = _as_1d(Q) + ne, _ = len(E), len(Q) I_corr = I_raw * alpha_e[:, None] + beta_f_e[:, None] S0 = (I_corr - fself) / (fmean_real**2 + 1e-12) + 1.0 @@ -294,10 +402,14 @@ def _build_S_from_raw(I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray, alpha_ xspan = float(Q[-1] - Q[0]) porder = max(1.0, (rpoly * xspan) / np.pi) porderlo, porderhi = int(np.floor(porder)), int(np.ceil(porder)) - poly_weights = [0.5, 0.5] if porderlo == porderhi else [porderhi - porder, porder - porderlo] + poly_weights = ( + [0.5, 0.5] + if porderlo == porderhi + else [porderhi - porder, porder - porderlo] + ) weight_power = 4.0 - W_sqrt = np.sqrt((Q / Q[-1])**weight_power) + W_sqrt = np.sqrt((Q / Q[-1]) ** weight_power) Xlo = np.vstack([Q**k for k in range(porderlo + 1)]).T Xhi = np.vstack([Q**k for k in range(porderhi + 1)]).T @@ -307,131 +419,212 @@ def _build_S_from_raw(I_raw: np.ndarray, Q: np.ndarray, E_eV: np.ndarray, alpha_ beta_o = np.zeros_like(S0) for i in range(ne): - y = (1.0 - S0[i]) * (fmean_real[i]**2) + y = (1.0 - S0[i]) * (fmean_real[i] ** 2) y_w = y * W_sqrt coeff_lo = npl.solve(XtXlo, Xlo_w.T @ y_w) - beta_lo = (Xlo @ coeff_lo) / (fmean_real[i]**2 + 1e-12) - + beta_lo = (Xlo @ coeff_lo) / (fmean_real[i] ** 2 + 1e-12) + if porderlo == porderhi: beta_o[i] = beta_lo else: coeff_hi = npl.solve(XtXhi, Xhi_w.T @ y_w) - beta_hi = (Xhi @ coeff_hi) / (fmean_real[i]**2 + 1e-12) + beta_hi = (Xhi @ coeff_hi) / (fmean_real[i] ** 2 + 1e-12) beta_o[i] = poly_weights[0] * beta_lo + poly_weights[1] * beta_hi return S0 + beta_o, beta_o -def _solve_two_channel_column(Aj: np.ndarray, yj: np.ndarray, ridge: float, anchor: float): - ATA = Aj.T @ Aj + ridge*np.eye(2) + anchor*np.eye(2) - ATy = Aj.T @ yj + anchor*np.array([[1.0],[1.0]]) - try: sol = npl.solve(ATA, ATy) - except npl.LinAlgError: sol = npl.lstsq(ATA, ATy, rcond=None)[0] - return float(sol[0,0]), float(sol[1,0]) -def _reconstruct_Salpha_Snot(S_meas: np.ndarray, a: np.ndarray, b: np.ndarray, Q: np.ndarray, ridge: float): +def _solve_two_channel_column( + Aj: np.ndarray, yj: np.ndarray, ridge: float, anchor: float +): + ATA = Aj.T @ Aj + ridge * np.eye(2) + anchor * np.eye(2) + ATy = Aj.T @ yj + anchor * np.array([[1.0], [1.0]]) + try: + sol = npl.solve(ATA, ATy) + except npl.LinAlgError: + sol = npl.lstsq(ATA, ATy, rcond=None)[0] + return float(sol[0, 0]), float(sol[1, 0]) + + +def _reconstruct_Salpha_Snot( + S_meas: np.ndarray, + a: np.ndarray, + b: np.ndarray, + Q: np.ndarray, + ridge: float, +): S_meas = np.asarray(S_meas, float) for i in range(S_meas.shape[0]): S_meas[i][:40] = S_meas[i][41] ne, nq = S_meas.shape - a = _ensure_2d(a, ne, nq, "a"); b = _ensure_2d(b, ne, nq, "b") + a = _ensure_2d(a, ne, nq, "a") + b = _ensure_2d(b, ne, nq, "b") Sa, Sb = np.zeros(nq), np.zeros(nq) bad_cols = 0 for j in range(nq): - Aj, yj = np.stack([a[:,j], b[:,j]], axis=1), S_meas[:, j:j+1] + Aj, yj = np.stack([a[:, j], b[:, j]], axis=1), S_meas[:, j : j + 1] s = npl.svd(Aj, compute_uv=False) - cond = (s[0]/s[-1]) if (s[-1] > 0) else np.inf + cond = (s[0] / s[-1]) if (s[-1] > 0) else np.inf anchor = 5.0 if (not np.isfinite(cond) or cond > 1e6) else 0.0 - if anchor > 0.0: bad_cols += 1 + if anchor > 0.0: + bad_cols += 1 Sa[j], Sb[j] = _solve_two_channel_column(Aj, yj, ridge, anchor) return Sa, Sb, {"bad_Q_columns": bad_cols} -def _S_to_G(Q: np.ndarray, S: np.ndarray, r: np.ndarray, window: str, kbeta: float) -> np.ndarray: - Q = _as_1d(Q); S = _as_1d(S); r = _as_1d(r) + +def _S_to_G( + Q: np.ndarray, S: np.ndarray, r: np.ndarray, window: str, kbeta: float +) -> np.ndarray: + Q = _as_1d(Q) + S = _as_1d(S) + r = _as_1d(r) Qmax = float(Q.max()) w = np.ones_like(Q) - if window == "lorch": w = _lorch(Q, Qmax) - elif window == "kaiser": w = _kaiser(Q, Qmax, kbeta) + if window == "lorch": + w = _lorch(Q, Qmax) + elif window == "kaiser": + w = _kaiser(Q, Qmax, kbeta) F = Q * (S - 1.0) * w G = np.zeros_like(r) for i, ri in enumerate(r): - G[i] = (2.0/np.pi) * _trapz(Q, F*np.sin(Q*ri)) + G[i] = (2.0 / np.pi) * _trapz(Q, F * np.sin(Q * ri)) return G + # ============================================================================= # 4. REFINEMENT & PLOTTING # ============================================================================= -def save_initial_edge_plots(E_eV: np.ndarray, edge_model: EdgeModel, cfg: RefinementConfig): + +def save_initial_edge_plots( + E_eV: np.ndarray, edge_model: EdgeModel, cfg: RefinementConfig +): fpp_init = edge_model.fpp(E_eV) fp_init = edge_model.fp(E_eV) - fp_chantler = xraydb.f1_chantler(edge_model.params.element, edge_model.to_eV(E_eV) + edge_model.params.dE_eV) - + fp_chantler = xraydb.f1_chantler( + edge_model.params.element, + edge_model.to_eV(E_eV) + edge_model.params.dE_eV, + ) + fig, ax = plt.subplots(1, 2, figsize=(10, 4)) ax[0].plot(E_eV / 1000, fpp_init, label="f'' (Model/Chantler)") - ax[0].set_xlabel("Energy (keV)"); ax[0].set_title("Initial f''"); ax[0].legend() - + ax[0].set_xlabel("Energy (keV)") + ax[0].set_title("Initial f''") + ax[0].legend() + ax[1].plot(E_eV / 1000, fp_init, label="f' (Model)") ax[1].plot(E_eV / 1000, fp_chantler, "--", label="f' (Chantler Tabulated)") - ax[1].set_xlabel("Energy (keV)"); ax[1].set_title("Initial f'"); ax[1].legend() - + ax[1].set_xlabel("Energy (keV)") + ax[1].set_title("Initial f'") + ax[1].legend() + plt.tight_layout() plt.savefig(os.path.join(cfg.fig_dir, "fpp_fp_initial.png"), dpi=150) plt.close() -def _plot_frame(path: str, E_eV: np.ndarray, edge_model: Any, r: np.ndarray, out: Dict[str,np.ndarray], - Q_full: np.ndarray, iter_idx: int, hist: List[RefinementHistory], fp_offset: float) -> None: + +def _plot_frame( + path: str, + E_eV: np.ndarray, + edge_model: Any, + r: np.ndarray, + out: Dict[str, np.ndarray], + Q_full: np.ndarray, + iter_idx: int, + hist: List[RefinementHistory], + fp_offset: float, +) -> None: q = np.asarray(out.get("Q", Q_full)) - Sa, Sb, St = np.asarray(out["S_alpha"]), np.asarray(out["S_not"]), np.asarray(out["S_tot"]) + Sa, Sb, St = ( + np.asarray(out["S_alpha"]), + np.asarray(out["S_not"]), + np.asarray(out["S_tot"]), + ) r_plot = np.asarray(r) - Ga, Gn, Gt = np.asarray(out["G_alpha"]), np.asarray(out["G_not"]), np.asarray(out["G_tot"]) + Ga, Gn, Gt = ( + np.asarray(out["G_alpha"]), + np.asarray(out["G_not"]), + np.asarray(out["G_tot"]), + ) E = np.asarray(E_eV, float) fpp = np.maximum(edge_model.fpp(E), 0.0) - fp = edge_model.fp(E, fpp=fpp) + fp_offset + fp = edge_model.fp(E, fpp=fpp) + fp_offset - plt.figure(figsize=(12,20)) + plt.figure(figsize=(12, 20)) plt.suptitle(f"Refinement frame {iter_idx:03d}") - ax1 = plt.subplot(4,2,1) - ax1.plot(E/1e3, fpp, label="f'' (model)"); ax1.legend(loc="upper left") - - ax2 = plt.subplot(4,2,2) - ax2.plot(E/1e3, fp, label="f' (KK from model) + fp_offset"); ax2.legend(loc="upper left") - - ax = plt.subplot(4,1,2) - ax.plot(r_plot, Ga, 'b-', label="G_alpha"); ax.plot(r_plot, Gn, 'g-', label="G_not") - ax.plot(r_plot, Gt, "r-", label="G_tot"); ax.legend(loc="upper right") - - ax = plt.subplot(4,1,3) - ax.plot(q, Sa, 'b-', label="S_alpha", linewidth=.5); ax.plot(q, Sb, 'g-', label="S_not", linewidth=.5) - ax.plot(q, St, "r-", label="S_tot", linewidth=.5); ax.plot(q, np.ones_like(q), 'k-', linewidth=0.1) + ax1 = plt.subplot(4, 2, 1) + ax1.plot(E / 1e3, fpp, label="f'' (model)") + ax1.legend(loc="upper left") + + ax2 = plt.subplot(4, 2, 2) + ax2.plot(E / 1e3, fp, label="f' (KK from model) + fp_offset") + ax2.legend(loc="upper left") + + ax = plt.subplot(4, 1, 2) + ax.plot(r_plot, Ga, "b-", label="G_alpha") + ax.plot(r_plot, Gn, "g-", label="G_not") + ax.plot(r_plot, Gt, "r-", label="G_tot") + ax.legend(loc="upper right") + + ax = plt.subplot(4, 1, 3) + ax.plot(q, Sa, "b-", label="S_alpha", linewidth=0.5) + ax.plot(q, Sb, "g-", label="S_not", linewidth=0.5) + ax.plot(q, St, "r-", label="S_tot", linewidth=0.5) + ax.plot(q, np.ones_like(q), "k-", linewidth=0.1) ax.legend(loc="upper left") - ax = plt.subplot(4,1,4) - its = np.arange(len(hist)); vals = np.array([h.obj for h in hist], float) - ax.plot(its, vals, "-o"); ax.set_yscale('log') + ax = plt.subplot(4, 1, 4) + its = np.arange(len(hist)) + vals = np.array([h.obj for h in hist], float) + ax.plot(its, vals, "-o") + ax.set_yscale("log") p = hist[-1].params - txt = (f"dE_eV={p['dE_eV']:.3g}\nscale={p['scale']:.3g}\n" - f"alpha_C={p['alpha_C']:.3g}, beta_C={p['beta_C']:.3g}") - ax.text(0.02, 0.98, txt, va="top", ha="left", transform=ax.transAxes, - bbox=dict(boxstyle="round", facecolor="white", alpha=0.85)) + txt = ( + f"dE_eV={p['dE_eV']:.3g}\nscale={p['scale']:.3g}\n" + f"alpha_C={p['alpha_C']:.3g}, beta_C={p['beta_C']:.3g}" + ) + ax.text( + 0.02, + 0.98, + txt, + va="top", + ha="left", + transform=ax.transAxes, + bbox=dict(boxstyle="round", facecolor="white", alpha=0.85), + ) + + plt.savefig(path, dpi=150) + plt.close() - plt.savefig(path, dpi=150); plt.close() def save_results(out: Dict[str, np.ndarray], cfg: RefinementConfig): """Save the output PDFs to .cgr files and export a final summary plot.""" r = out["r"] - np.savetxt(os.path.join(cfg.out_dir, "G_alpha.cgr"), np.column_stack([r, out["G_alpha"]]), header="r G_alpha") - np.savetxt(os.path.join(cfg.out_dir, "G_not.cgr"), np.column_stack([r, out["G_not"]]), header="r G_not") - np.savetxt(os.path.join(cfg.out_dir, "G_tot.cgr"), np.column_stack([r, out["G_tot"]]), header="r G_tot") - + np.savetxt( + os.path.join(cfg.out_dir, "G_alpha.cgr"), + np.column_stack([r, out["G_alpha"]]), + header="r G_alpha", + ) + np.savetxt( + os.path.join(cfg.out_dir, "G_not.cgr"), + np.column_stack([r, out["G_not"]]), + header="r G_not", + ) + np.savetxt( + os.path.join(cfg.out_dir, "G_tot.cgr"), + np.column_stack([r, out["G_tot"]]), + header="r G_tot", + ) + # Plot the full r-range to preserve diagnostic low-r ripples plt.figure() - plt.plot(r, out['G_alpha'], 'r', label="G_alpha (resonant)") - plt.plot(r, out['G_not'], 'g', label="G_not (non-resonant)") - plt.plot(r, out['G_tot'], 'b', label="G_tot (total/mean)") - + plt.plot(r, out["G_alpha"], "r", label="G_alpha (resonant)") + plt.plot(r, out["G_not"], "g", label="G_not (non-resonant)") + plt.plot(r, out["G_tot"], "b", label="G_tot (total/mean)") + plt.xlabel("r (Å)") plt.ylabel("G(r)") plt.legend() @@ -440,123 +633,287 @@ def save_results(out: Dict[str, np.ndarray], cfg: RefinementConfig): plt.close() print("Final .cgr files and full-range comparison plot saved.") -def _objective(Sa: np.ndarray, Sb: np.ndarray, Q: np.ndarray, hiQ_frac: float, anchor_lambda: float) -> float: - nq = len(Q); k0 = int(max(0, math.floor((1.0-hiQ_frac)*nq))) - mask = np.zeros(nq, bool); mask[k0:] = True - tails = np.sum((Sa[mask]-1.0)**2 + (Sb[mask]-1.0)**2) - d2a = np.diff(Sa, n=2); d2b = np.diff(Sb, n=2) + +def _objective( + Sa: np.ndarray, + Sb: np.ndarray, + Q: np.ndarray, + hiQ_frac: float, + anchor_lambda: float, +) -> float: + nq = len(Q) + k0 = int(max(0, math.floor((1.0 - hiQ_frac) * nq))) + mask = np.zeros(nq, bool) + mask[k0:] = True + tails = np.sum((Sa[mask] - 1.0) ** 2 + (Sb[mask] - 1.0) ** 2) + d2a = np.diff(Sa, n=2) + d2b = np.diff(Sb, n=2) smooth = np.sum(d2a**2 + d2b**2) - physics = np.sum((Sa - Sb)**2) - return float(anchor_lambda*tails + smooth + physics) - -def reconstruct_partials_and_pdfs(I_raw, Q, E_eV, elements, comp, alpha, edge_model, alpha_e, beta_e, - rpoly, ridge, r, Qmin, Qmax, window="lorch", kaiser_beta=6.0, fp_offset=0.0): - Q = _as_1d(Q); E = _as_1d(E_eV); I_raw = np.asarray(I_raw, float) - frw, f0_map, fmean_real, fmean_abs2, fself, f_not_sum = _compute_scattering( - elements, comp, alpha, Q, E, edge_model, fp_offset=fp_offset) + physics = np.sum((Sa - Sb) ** 2) + return float(anchor_lambda * tails + smooth + physics) + + +def reconstruct_partials_and_pdfs( + I_raw, + Q, + E_eV, + elements, + comp, + alpha, + edge_model, + alpha_e, + beta_e, + rpoly, + ridge, + r, + Qmin, + Qmax, + window="lorch", + kaiser_beta=6.0, + fp_offset=0.0, +): + Q = _as_1d(Q) + E = _as_1d(E_eV) + I_raw = np.asarray(I_raw, float) + frw, f0_map, fmean_real, fmean_abs2, fself, f_not_sum = ( + _compute_scattering( + elements, comp, alpha, Q, E, edge_model, fp_offset=fp_offset + ) + ) a, b, wb = _weights_alpha_not(comp, alpha, frw, fmean_real, f_not_sum) - if Qmax is None: Qmax = float(Q.max()) + if Qmax is None: + Qmax = float(Q.max()) mask_Q = (Q >= Qmin) & (Q <= Qmax) Q_use = Q[mask_Q] - S_meas_all, beta_o_all = _build_S_from_raw(I_raw, Q, E, alpha_e, beta_e, fmean_real, fself, rpoly) - S_meas = S_meas_all[:, mask_Q]; a = a[:, mask_Q]; b = b[:, mask_Q] + S_meas_all, beta_o_all = _build_S_from_raw( + I_raw, Q, E, alpha_e, beta_e, fmean_real, fself, rpoly + ) + S_meas = S_meas_all[:, mask_Q] + a = a[:, mask_Q] + b = b[:, mask_Q] Sa, Sb, condinfo = _reconstruct_Salpha_Snot(S_meas, a, b, Q_use, ridge) S_tot = S_meas[0] r = _as_1d(r) G_alpha = _S_to_G(Q_use, Sa, r, window, kaiser_beta) - G_not = _S_to_G(Q_use, Sb, r, window, kaiser_beta) - G_tot = _S_to_G(Q_use, S_tot, r, window, kaiser_beta) - - out = {"Q": Q_use, "r": r, "S_alpha": Sa, "S_not": Sb, "S_tot": S_tot, - "G_alpha": G_alpha, "G_not": G_not, "G_tot": G_tot} + G_not = _S_to_G(Q_use, Sb, r, window, kaiser_beta) + G_tot = _S_to_G(Q_use, S_tot, r, window, kaiser_beta) + + out = { + "Q": Q_use, + "r": r, + "S_alpha": Sa, + "S_not": Sb, + "S_tot": S_tot, + "G_alpha": G_alpha, + "G_not": G_not, + "G_tot": G_tot, + } return out, {"weights": wb, "condinfo": condinfo, "beta_o": beta_o_all} -def run_adpdf_with_refinement(I_raw, Q, E_eV, elements, comp, alpha, edge_model, - alpha_C=1.0, alpha_D=0.0, beta_C=0.0, beta_D=0.0, - fp_offset=0.0, cfg=None): - if cfg is None: cfg = RefinementConfig() - Q = _as_1d(Q); E = _as_1d(E_eV); I_raw = np.asarray(I_raw, float) + +def run_adpdf_with_refinement( + I_raw, + Q, + E_eV, + elements, + comp, + alpha, + edge_model, + alpha_C=1.0, + alpha_D=0.0, + beta_C=0.0, + beta_D=0.0, + fp_offset=0.0, + cfg=None, +): + if cfg is None: + cfg = RefinementConfig() + Q = _as_1d(Q) + E = _as_1d(E_eV) + I_raw = np.asarray(I_raw, float) rpoly = cfg.rpoly edge_model.params.scale = max(1e-4, float(edge_model.params.scale)) - edge_model.params.broaden_fwhm_eV = float(np.clip(edge_model.params.broaden_fwhm_eV, - cfg.min_broaden_fwhm_eV, cfg.max_broaden_fwhm_eV)) + edge_model.params.broaden_fwhm_eV = float( + np.clip( + edge_model.params.broaden_fwhm_eV, + cfg.min_broaden_fwhm_eV, + cfg.max_broaden_fwhm_eV, + ) + ) - r = np.arange(cfg.rmin, cfg.rmax + cfg.dr/2.0, cfg.dr) + r = np.arange(cfg.rmin, cfg.rmax + cfg.dr / 2.0, cfg.dr) Qmax = cfg.Qmax if cfg.Qmax is not None else float(Q.max()) def compute(): fpp = np.maximum(edge_model.fpp(E), 0.0) - alpha_e, beta_e = _alpha_beta_from_fpp(fpp, alpha_C, alpha_D, beta_C, beta_D) + alpha_e, beta_e = _alpha_beta_from_fpp( + fpp, alpha_C, alpha_D, beta_C, beta_D + ) out, diag = reconstruct_partials_and_pdfs( - I_raw, Q, E, elements, comp, alpha, edge_model, alpha_e, beta_e, - rpoly=rpoly, ridge=cfg.ridge, r=r, Qmin=cfg.Qmin, Qmax=Qmax, - window=cfg.window, kaiser_beta=cfg.kaiser_beta, fp_offset=fp_offset, + I_raw, + Q, + E, + elements, + comp, + alpha, + edge_model, + alpha_e, + beta_e, + rpoly=rpoly, + ridge=cfg.ridge, + r=r, + Qmin=cfg.Qmin, + Qmax=Qmax, + window=cfg.window, + kaiser_beta=cfg.kaiser_beta, + fp_offset=fp_offset, + ) + return ( + out, + diag, + _objective( + out["S_alpha"], + out["S_not"], + out["Q"], + cfg.hiQ_frac, + cfg.hiQ_anchor_lambda, + ), ) - return out, diag, _objective(out["S_alpha"], out["S_not"], out["Q"], cfg.hiQ_frac, cfg.hiQ_anchor_lambda) out, diag, obj = compute() - hist = [RefinementHistory(0, obj, { - "scale": edge_model.params.scale, - "dE_eV": edge_model.params.dE_eV, - "alpha_C": alpha_C, - "beta_C": beta_C - })] + hist = [ + RefinementHistory( + 0, + obj, + { + "scale": edge_model.params.scale, + "dE_eV": edge_model.params.dE_eV, + "alpha_C": alpha_C, + "beta_C": beta_C, + }, + ) + ] os.makedirs(cfg.frame_dir, exist_ok=True) - _plot_frame(os.path.join(cfg.frame_dir, f"frame_{0:03d}.png"), E, edge_model, r, out, Q, 0, hist, fp_offset) + _plot_frame( + os.path.join(cfg.frame_dir, f"frame_{0:03d}.png"), + E, + edge_model, + r, + out, + Q, + 0, + hist, + fp_offset, + ) - steps = dict(rpoly=cfg.step_rpoly, dE_eV=cfg.step_dE_eV, scale=cfg.step_scale, - fpp_offset=cfg.step_fpp_offset, fp_offset=cfg.step_fp_offset, - broaden_fwhm_eV=cfg.step_broaden_fwhm, alpha_C=cfg.step_alphaC, - alpha_D=cfg.step_alphaD, beta_C=cfg.step_betaC, beta_D=cfg.step_betaD) + steps = dict( + rpoly=cfg.step_rpoly, + dE_eV=cfg.step_dE_eV, + scale=cfg.step_scale, + fpp_offset=cfg.step_fpp_offset, + fp_offset=cfg.step_fp_offset, + broaden_fwhm_eV=cfg.step_broaden_fwhm, + alpha_C=cfg.step_alphaC, + alpha_D=cfg.step_alphaD, + beta_C=cfg.step_betaC, + beta_D=cfg.step_betaD, + ) def tweak(name: str, d: float): nonlocal alpha_C, alpha_D, beta_C, beta_D, fp_offset, rpoly p = edge_model.params - if name == "rpoly": rpoly = float(np.clip(rpoly + d, 0.0, 2.0)) - elif name == "dE_eV": p.dE_eV += d - elif name == "scale": p.scale = max(1e-4, p.scale + d) - elif name == "fpp_offset": p.fpp_offset += d - elif name == "broaden_fwhm_eV":p.broaden_fwhm_eV = float(np.clip(p.broaden_fwhm_eV + d, cfg.min_broaden_fwhm_eV, cfg.max_broaden_fwhm_eV)) - elif name == "alpha_C": alpha_C = max(1e-6, alpha_C + d) - elif name == "alpha_D": alpha_D += d - elif name == "beta_C": beta_C += d - elif name == "beta_D": beta_D += d - elif name == "fp_offset": fp_offset += d + if name == "rpoly": + rpoly = float(np.clip(rpoly + d, 0.0, 2.0)) + elif name == "dE_eV": + p.dE_eV += d + elif name == "scale": + p.scale = max(1e-4, p.scale + d) + elif name == "fpp_offset": + p.fpp_offset += d + elif name == "broaden_fwhm_eV": + p.broaden_fwhm_eV = float( + np.clip( + p.broaden_fwhm_eV + d, + cfg.min_broaden_fwhm_eV, + cfg.max_broaden_fwhm_eV, + ) + ) + elif name == "alpha_C": + alpha_C = max(1e-6, alpha_C + d) + elif name == "alpha_D": + alpha_D += d + elif name == "beta_C": + beta_C += d + elif name == "beta_D": + beta_D += d + elif name == "fp_offset": + fp_offset += d best_obj = obj - for it in range(1, cfg.n_outer+1): + for it in range(1, cfg.n_outer + 1): cycle_improved = False start_obj = best_obj - for name in ["rpoly", "dE_eV","scale","fpp_offset","fp_offset","broaden_fwhm_eV", - "alpha_C","alpha_D","beta_C","beta_D"]: + for name in [ + "rpoly", + "dE_eV", + "scale", + "fpp_offset", + "fp_offset", + "broaden_fwhm_eV", + "alpha_C", + "alpha_D", + "beta_C", + "beta_D", + ]: param_improved = False - for sgn in (+1,-1): - tweak(name, sgn*steps[name]) + for sgn in (+1, -1): + tweak(name, sgn * steps[name]) out2, diag2, obj2 = compute() if obj2 < best_obj: out, diag, best_obj = out2, diag2, obj2 - param_improved = True; cycle_improved = True + param_improved = True + cycle_improved = True else: - tweak(name, -sgn*steps[name]) - if not param_improved: steps[name] *= 0.7 - - hist.append(RefinementHistory(it, best_obj, { - "scale": edge_model.params.scale, - "dE_eV": edge_model.params.dE_eV, - "alpha_C": alpha_C, - "beta_C": beta_C - })) - if (it % cfg.plot_every)==0 or it==cfg.n_outer: - _plot_frame(os.path.join(cfg.frame_dir, f"frame_{it:03d}.png"), E, edge_model, r, out, Q, it, hist, fp_offset) + tweak(name, -sgn * steps[name]) + if not param_improved: + steps[name] *= 0.7 + + hist.append( + RefinementHistory( + it, + best_obj, + { + "scale": edge_model.params.scale, + "dE_eV": edge_model.params.dE_eV, + "alpha_C": alpha_C, + "beta_C": beta_C, + }, + ) + ) + if (it % cfg.plot_every) == 0 or it == cfg.n_outer: + _plot_frame( + os.path.join(cfg.frame_dir, f"frame_{it:03d}.png"), + E, + edge_model, + r, + out, + Q, + it, + hist, + fp_offset, + ) rel_change = (start_obj - best_obj) / max(start_obj, 1e-12) if rel_change < cfg.tol_obj: - print(f"Converged! Relative change ({rel_change:.2e}) is below tolerance.") + print( + f"Converged! Relative change ({rel_change:.2e}) " + "is below tolerance." + ) break if not cycle_improved and max(steps.values()) < 1e-3: print(f"Stopped at iteration {it}: step sizes shrank below 1e-3.") @@ -564,16 +921,18 @@ def tweak(name: str, d: float): return out, diag, hist + # ============================================================================= # 5. MAIN EXECUTION # ============================================================================= + def main(): # 1. Initialize Configuration cfg = RefinementConfig() setup_directories(cfg) - # 2. Load Data + # 2. Load Data # Make sure this points to the correct local file path print("Loading data...") try: @@ -588,7 +947,7 @@ def main(): # 3. Setup Elements & Edge Model elements = ["Ba", "Bi", "O"] - comp = {"Ba": 1/5, "Bi": 1/5, "O": 3/5} + comp = {"Ba": 1 / 5, "Bi": 1 / 5, "O": 3 / 5} alpha = "Bi" params = EdgeModelParams( @@ -597,7 +956,7 @@ def main(): scale=0.35, fpp_offset=-0.2, broaden_fwhm_eV=15.0, - peaks=[Peak(center_eV=90.526e3 + 180, fwhm_eV=3.0, height=0.3)] + peaks=[Peak(center_eV=90.526e3 + 180, fwhm_eV=3.0, height=0.3)], ) edge_model = EdgeModel(params) @@ -607,16 +966,20 @@ def main(): # 5. Run Refinement print("Starting refinement...") out, diag, hist = run_adpdf_with_refinement( - I_raw=I_raw, Q=Q, E_eV=E, - elements=elements, comp=comp, + I_raw=I_raw, + Q=Q, + E_eV=E, + elements=elements, + comp=comp, alpha=alpha, edge_model=edge_model, beta_D=0.1, - cfg=cfg + cfg=cfg, ) # 6. Output Final Results save_results(out, cfg) + if __name__ == "__main__": - main() \ No newline at end of file + main() From 6b6a4c0a2a35d798ddcb9b035bcc57f5011afb57 Mon Sep 17 00:00:00 2001 From: tschertenleib Date: Mon, 30 Mar 2026 16:00:36 +0200 Subject: [PATCH 5/5] fixing __init__.py file --- src/diffpy/adpdf/__init__.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/diffpy/adpdf/__init__.py b/src/diffpy/adpdf/__init__.py index 9b7a947..3dd8b49 100644 --- a/src/diffpy/adpdf/__init__.py +++ b/src/diffpy/adpdf/__init__.py @@ -12,7 +12,7 @@ # See LICENSE.rst for license information. # ############################################################################## -""""description"""" +"""description.""" # package version from diffpy.adpdf.version import __version__

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