diff --git a/LICENSE b/LICENSE deleted file mode 100644 index b47d5b3e..00000000 --- a/LICENSE +++ /dev/null @@ -1,11 +0,0 @@ -CytoPy License -=============== - -Copyright 2020 Ross Burton - -Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/cytopy/cytopy_widgets/README.md b/cytopy/cytopy_widgets/README.md new file mode 100644 index 00000000..af4f5648 --- /dev/null +++ b/cytopy/cytopy_widgets/README.md @@ -0,0 +1,38 @@ +[![License: GPL v3](https://img.shields.io/badge/License-GPLv3-blue.svg)](https://www.gnu.org/licenses/gpl-3.0) +[![Python](https://img.shields.io/pypi/pyversions/cytopy)](https://pypi.org/project/cytopy/) + + +# CytoPy-Widgets + +This package provides a GUI wrapper for CytoPy gating, using the [ipywidgets package](https://ipywidgets.readthedocs.io/en/latest). +CytoPy-Widgets facilitates iterative batch gating of a large number of samples that should be processed in the same way. + +## Prerequisites +* Please make sure you have [ipwdigets installed](https://ipywidgets.readthedocs.io/en/latest/user_install.html) +* Before using CytoPy-Widgets, you must create a new CytoPy experiment and add samples +* When creating your experiment, please make sure that all of your control samples are added first + +## Use instructions +* To start using the package, please simply create a new cell in your notebook and type (replacing `PROJECT_NAME`, `EXPERIMENT_NAME` with your actual projet and experiment names): +``` +from cytopy.cytopy_widgets.cytopy_widgets import Gating_Interface +project = Project.objects(project_id=PROJECT_NAME).get() +experiment = project.get_experiment(EXPERIMENT_NAME) +Gating_Interface(experiment=experiment, source_population='root') +``` + +* You should see the GUI, which should look like this: +![image](https://user-images.githubusercontent.com/83017469/129480204-d16f765c-147d-4176-aadc-f3ab8fc0e538.png) +* Below this, you should see the results of the default gating method (ellipse widget) on the first sample in your experiment: +![image](https://user-images.githubusercontent.com/83017469/129480237-c261deb1-d010-4124-9367-5b6beb98c4b3.png) +* The GUI automatically shows the recommeded ellipse parameters for the first sample in your experiment, based on the automatic +fitting routines in CytoPy. +* Now you can modify the gating parameters using the GUI, and then click on `Create Gates` to preview the resulting gates (don't forget to change the target population name in the `Target pop` widget): +![image](https://user-images.githubusercontent.com/83017469/129480598-d20d1005-2827-4817-9930-c614604556d4.png) +* Keep on tweaking the ellipes parameters until you're happy with then. Once you're happy, change the `#preview` widget to `All` and then click on `Create gates again`. This will show you the results for all of your samples. +* Once you preview the results for all gates, the `Save gates` widget stop being disabled. When you click `Save gates`, the resulting populations will be saved to the CytoPy database. +* Now you can create a new cell, and start a new gating process, this time using a different source population (for example, you can use the `live cells` population that you just defined). + + + +**Happy gating!** diff --git a/cytopy/cytopy_widgets/cytopy_widgets.py b/cytopy/cytopy_widgets/cytopy_widgets.py new file mode 100644 index 00000000..fc145a67 --- /dev/null +++ b/cytopy/cytopy_widgets/cytopy_widgets.py @@ -0,0 +1,1210 @@ +""" +This is a GUI wrapper for CytoPy, allowing to apply batch-gating +to a large number of samples semi-automatically. + +Copyright 2021 Eleven TX + +This program is free software: you can redistribute it and/or modify +it under the terms of the GNU General Public License as published by +the Free Software Foundation, either version 3 of the License, or +(at your option) any later version. + +This program is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU General Public License for more details. + +You should have received a copy of the GNU General Public License +along with this program. If not, see . +""" + +import numpy as np +import pandas as pd +from tqdm.auto import tqdm +import logging +from typing import List + +import matplotlib.pyplot as plt +import seaborn as sns +sns.set_style('whitegrid') +sns.set_context('notebook', font_scale=1.5) + +import ipywidgets as widgets +from ipywidgets import interactive, interact, Box, HBox, Layout, VBox, fixed, Checkbox, Layout, Text, Label +from ipywidgets.widgets.interaction import show_inline_matplotlib_plots +from ipywidgets.widgets.widget_output import clear_output +import string +import random + +from cytopy.data.experiment import Experiment +from cytopy.data.gating_strategy import GatingStrategy, EllipseGate, ThresholdGate, PolygonGate +from cytopy.data.geometry import probablistic_ellipse + + +def generate_random_name(N=20): + ''' + Generate a random string with N letters + ''' + gate_name = ''.join(random.choices(string.ascii_uppercase + string.digits, k=N)) + return gate_name + + + +def get_experiment_channels(experiment: Experiment): + """ + Returns a list of all the channels in a specific experiment + + Parameters + ---------- + experiment: Experiment + An experiment object + """ + + channels = None + for sample_id in experiment.list_samples(): + sample = experiment.get_sample(sample_id) + df_sample = sample.load_population_df('root', transform=None) + sample_channels = df_sample.columns + if channels is not None: + assert len(sample_channels) == len(channels), \ + 'not all samples in the experiment have the same channels' + assert np.all(sample_channels == channels), \ + 'not all samples in the experiment have the same channels' + channels = sample_channels + return list(channels) + + + + +class FACS_Gater: + """ + This class acts as a wrapper to the CytoPy package. + It basically applies a specific gate to a set of samples + (refitting the gate for each sample). + + Parameters + ---------- + experiment: Experiment + A CytoPy experiment object + parent_population: str + The gating parent population + sampling: dict (optional) + Options for downsampling data prior to application of gate. + See cytopy.flow.sampling for details. + plot_bins: int or str (optional) + How many bins to use for 2D histogram. + See cytopy.flow.plotting.flow_plot for details + autoscale: bool (default=True) + Allow matplotlib to calculate optimal view + (https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.autoscale.html) + """ + + def __init__(self, + experiment: Experiment, + parent_population: str, + sampling: dict or None = None, + plot_bins: int or None = None, + autoscale: bool = False + ): + + #save constructor arguments + self.experiment = experiment + self.sampling = sampling + self.plot_bins = plot_bins + self.autoscale = autoscale + self.parent_population = parent_population + + #initialize gate and gate parameters + self.dict_sampleid_to_gates = {} + self.sample_ids = None + self.gate = None + + #initialize gate and plotting parameters + self.gating_params = { + 'transform_x': None, + 'transform_y': None, + 'x': None, + 'y': None + } + + self.plot_params = { + 'xmin':None, + 'xmax':None, + 'ymin':None, + 'ymax':None + } + + #store all sample_ids in this experiment + self.experiment_sampleids = set(experiment.list_samples()) + + def update_params(self, + x: str, + transform_x: str, + y: str or None = None, + transform_y: str or None = None, + xmin: int or None = None, + xmax: int or None = None, + ymin: int or None = None, + ymax: int or None = None + ): + """ + Update the gating and plotting parameters + + Parameters + ---------- + x: str + The x axis channel + transform_x: str + The transformation to apply on the x-axis channel. + Please see cytopy.flow.plotting.gate for details + y: str (optional) + The y axis channel (can be left empty for threshold 1d gates) + transform_y: str (optional) + The transformation to apply on the y-axis channel. + Please see cytopy.flow.plotting.gate for details + xmin: int (optional) + The minimum x axis value to show in the plots + xmax: int (optional) + The maximum x axis value to show in the plots + ymin: int (optional) + The minimum y axis value to show in the plots + ymax: int (optional) + The maximum y axis value to show in the plots + """ + + self.gating_params['transform_x'] = transform_x + self.gating_params['transform_y'] = transform_y + self.gating_params['x'] = x + self.gating_params['y'] = y + + self.plot_params['xmin'] = xmin + self.plot_params['xmax'] = xmax + self.plot_params['ymin'] = ymin + self.plot_params['ymax'] = ymax + + + def ellipse_gate(self, + gate_name: str, + target_pop_name: str, + method: str = 'GaussianMixture', + n_clusters: int = 1, + conf:float = 0.8, + centroid: (float, float) or None = None, + angle: float or None = None, + width: float or None = None, + height: float or None = None + ): + """ + Apply an ellipse gate on all of the samples + + parameters + ---------- + gate_name: str + The name of the gate + target_pop_name: str + The target population name + method (default='GaussianMixture'): + The Ellipse estimation method. + see cytopy.data.gate for details + n_clusters: int (default=1) + The number of clusters (currently it must be 1) + conf: float (default=0.8) + The confidence level (i.e. the size of ellipes), must be between 0 and 1 + centroid: (float, float) (optional) + The centroid of the ellipse (only required if method == 'manual') + angle: float (optional) + The angle of the ellipse (only required if method == 'manual') + width: float (optional) + The width of the ellipse (only required if method == 'manual') + height: float (optional) + The height of the ellipse (only required if method == 'manual') + """ + + self._check_gating_params() + method_kwargs = {'n_components': n_clusters, 'conf': conf} + if method == 'manual': + assert angle is not None + assert width is not None + assert height is not None + assert centroid is not None + assert conf is None + method_kwargs['angle'] = angle + method_kwargs['width'] = width + method_kwargs['height'] = height + method_kwargs['centroid'] = centroid + + #define a population names dictionary + assert n_clusters==1, 'Only n_clusters==1 is currently supported' + dict_popnames = {'A':target_pop_name} + + #define a gate + self.gate = EllipseGate(gate_name=gate_name, + parent=self.parent_population, + x=self.gating_params['x'], + y=self.gating_params['y'], + transform_x=self.gating_params['transform_x'], + transform_y=self.gating_params['transform_y'], + sampling=self.sampling, + method=method, + method_kwargs=method_kwargs) + self._apply_gate(dict_popnames=dict_popnames, legend_delta_y=0) + + + def threshold_gate(self, + gate_name: str, + method: str = 'density', + q: float or None = None, + x_threshold: float or None = None, + y_threshold: float or None = None, + bandwidth: float or None = None + ): + """ + Apply a 1d or 2d threshold gate on all of the samples + + Parameters + ---------- + gate_name: str + The name of the gate + method: str + The gating method. + Please see cytopy.data.gate for details + q: float (optional) + The desired thresholding quantile + (only relevant if method=='quantile') + x_threshold: float (optional) + The threshold to apply on the x-axis channel + (only required if method=='manual') + y_threshold: float (optional) + The threshold to apply on the y-axis channel + (only required if method=='manual') + bandwidth: float (optional) + The density estimation bandwidth. + Please see cytopy.data.gate for details + """ + + self._check_gating_params() + method_kwargs = {} + create_plot_kwargs = {} + + if bandwidth is not None: + method_kwargs['bw'] = bandwidth + create_plot_kwargs['bw'] = bandwidth + + if method == 'density': + pass + elif method == 'quantile': + assert q is not None + method_kwargs['q'] = q + elif method == 'manual': + assert x_threshold is not None + if self.gating_params['y'] is not None: assert y_threshold is not None + method_kwargs['x_threshold'] = x_threshold + method_kwargs['y_threshold'] = y_threshold + else: + raise ValueError('unsupported method: %s'%(method)) + + self.gate = ThresholdGate(gate_name=gate_name, + parent=self.parent_population, + x=self.gating_params['x'], + y=self.gating_params['y'], + transform_x=self.gating_params['transform_x'], + transform_y=self.gating_params['transform_y'], + sampling=self.sampling, + method=method, + method_kwargs=method_kwargs + ) + + self._apply_gate(create_plot_kwargs=create_plot_kwargs, legend_delta_y=0.2) + + + def polygon_gate(self, + gate_name: str, + method: str = 'MiniBatchKMeans', + n_clusters: int = 2, + random_state: int = 111, + batch_size: int = 1000 + ): + + """ + Apply a polygon gate on all of the samples + + Parameters + ---------- + gate_name: str + The name of the gate + method: str + The gating method. + Please see cytopy.data.gate for details + n_clusters: int (default=2) + The number of clusters + random_state: int (default=111) + A random initial state for the random number generator + batch_size: int (default=1000) + The batch size of the gating algorithm + """ + + self._check_gating_params() + method_kwargs = {} + method_kwargs['n_clusters'] = n_clusters + method_kwargs['batch_size'] = batch_size + method_kwargs['random_state'] = random_state + self.gate = PolygonGate(gate_name=gate_name, + parent=self.parent_population, + x=self.gating_params['x'], + y=self.gating_params['y'], + transform_x=self.gating_params['transform_x'], + transform_y=self.gating_params['transform_y'], + sampling=self.sampling, + method=method, + method_kwargs=method_kwargs + ) + self._apply_gate(legend_delta_y=0.07*(n_clusters-1)) + + + def _check_gating_params(self): + """ + Make sure that gating parameters were specified + """ + for c in ['x']: + assert self.gating_params[c] is not None, \ + 'please call update_params(...) first' + + + def _apply_gate(self, + legend_delta_y: float, + dict_popnames: dict or None = None, + create_plot_kwargs: dict or None = None + ): + """ + Apply the object gate (specified in self.gate) to all + sample_ids that were specified for gating + + parameters + ------------ + dict_popnames: dict (optional) + a dictionary mapping automatically-generated + population names to new population names + create_plot_kwargs: dict (optional) + A dictionary of arguments for the constructor + of the CytoPy FlowPlot object + + """ + self._check_gating_params() + assert self.sample_ids is not None, 'no sample ids specified' + + #prepare a figure + nsamples = len(self.sample_ids) + + ####Code for 2-columns view + nrows = nsamples//2 + (1 if nsamples%2 == 1 else 0) + ncols = (1 if nsamples==1 else 2) + figsize = (11, 6) if nsamples==1 else (11, nrows*6) + fig, axs = plt.subplots(figsize=figsize, nrows=nrows, ncols=ncols) + +# ####Code for 1-columns view +# nrows = nsamples +# ncols = 1 +# figsize = (11, nrows*6) +# fig, axs = plt.subplots(figsize=figsize, nrows=nrows, ncols=ncols) + + if ncols==1 and nrows==1: axs = np.array([[axs]]) + elif ncols==1 or nrows==1: axs = np.array([axs]) + if create_plot_kwargs is None: create_plot_kwargs = {} + create_plot_kwargs['bins'] = self.plot_bins + create_plot_kwargs['autoscale'] = self.autoscale + plot_kwargs = {'legend_kwargs': + { + 'loc':'lower left', + 'bbox_to_anchor':(0.99, 0.1), + 'fontsize':'xx-small' + } + } + + #iterate over sample_ids and plot the gate fitted to each sample_id + iter_tqdm = tqdm( + zip(axs.flatten(), self.sample_ids), + total=nsamples, + desc='Creating gates' + ) + for ax, sample_id in iter_tqdm: + + #fit the gate on this sample_id + gates = GatingStrategy(name=generate_random_name()) + gates.load_data(experiment=self.experiment, sample_id=sample_id) + create_plot_kwargs['ax'] = ax + + #Fit the gate + self.gate.reset_gate() + gates.preview_gate(self.gate, + create_plot_kwargs=create_plot_kwargs, + plot_gate_kwargs=plot_kwargs, + plot=False) + #ax.clear() + + #rename gate populations + gate_populations = [c.name for c in self.gate.children] + dict_labels_new = {} + if dict_popnames is None: dict_popnames = {} + for pop in gate_populations: + if self.parent_population == 'root': + new_pop_name = dict_popnames.get(pop, pop) + else: + new_pop_name = '%s->%s'%( + self.parent_population, dict_popnames.get(pop, pop) + ) + dict_labels_new[pop] = new_pop_name + self.gate.label_children(dict_labels_new) + gate_populations = [c.name for c in self.gate.children] + + #save the fitted GatingStrategy object in the dictionary + self.dict_sampleid_to_gates[sample_id] = gates + + #delete existing populations with the same names if there are any + pops_to_delete = [p for p in gate_populations if p in gates.list_populations()] + gates.delete_populations(pops_to_delete) + + #apply the gate (finally!) + gates.apply_gate(self.gate, + plot=True, + add_to_strategy=True, + create_plot_kwargs=create_plot_kwargs, + plot_gate_kwargs=plot_kwargs, + hyperparam_search=False, + fda_norm=False, + verbose=False + ) + + #add title of sample_id + population_size = \ + gates.filegroup.get_population(population_name=self.parent_population).n + title = '%s\n%d cells'%(sample_id, population_size) + ax.set_title(title, fontsize='xx-small') + + #change axis labels + xlabel = str(self.gating_params['x']) + if self.gating_params['transform_x'] is not None: + xlabel += ' (%s)'%(self.gating_params['transform_x']) + ylabel = str(self.gating_params['y']) + if self.gating_params['transform_y'] is not None: + ylabel += ' (%s)'%(self.gating_params['transform_y']) + ax.set_xlabel(xlabel, fontsize='x-small') + ax.set_ylabel(ylabel, fontsize='x-small') + + #change ticks font size + ax.tick_params(axis='both', which='major', labelsize='small') + + #make sure that the tick labels aren't rotated + plt.setp(ax.get_xticklabels(), rotation=0) + + #move the legend to the bottom + leg = ax.get_legend() + #legend_bbox = leg.get_window_extent() + leg.set_bbox_to_anchor((-0.1, -0.1-legend_delta_y), transform=ax.transAxes) + + ax.xaxis.tick_top() + ax.xaxis.set_label_position('top') + + #enforce uniform limits + x_min = min([ax.get_xlim()[0] for ax in axs.flatten()]) + y_min = min([ax.get_ylim()[0] for ax in axs.flatten()]) + x_max = max([ax.get_xlim()[1] for ax in axs.flatten()]) + y_max = max([ax.get_ylim()[1] for ax in axs.flatten()]) + if self.plot_params['xmin'] is not None: x_min = self.plot_params['xmin'] + if self.plot_params['ymin'] is not None: y_min = self.plot_params['ymin'] + if self.plot_params['xmax'] is not None: x_max = self.plot_params['xmax'] + if self.plot_params['ymax'] is not None: y_max = self.plot_params['ymax'] + for ax in axs.flatten(): + ax.set_xlim(x_min, x_max) + ax.set_ylim(y_min, y_max) + + def list_populations(self): + """ + Return a list of all of the populations that were created + """ + if len(self.dict_sampleid_to_gates) == 0: return ['root'] + gates = next(iter(self.dict_sampleid_to_gates.values())) + return gates.list_populations() + + def list_gate_populations(self): + """ + Returns a list of the gate populations for the current gate + """ + return [c.name for c in self.gate.children] + + def save_populations(self): + """ + Save all created populations to the DB + """ + assert len(self.dict_sampleid_to_gates) > 0, 'no gated were fitted yet' + set_sampleids = set(self.sample_ids) + assert len(set_sampleids) == len(self.dict_sampleid_to_gates) + for sample_id, gates in self.dict_sampleid_to_gates.items(): + assert sample_id in set_sampleids + gates.save(save_strategy=False, save_filegroup=True) + + def update_sample_ids(self, + sample_ids: List[str] + ): + """ + Specify the set of sample_ids that the object is gating + + Parameters + ---------- + sample_ids: List[str] + The list of sample ids that the gating will work on + """ + assert all([(s in self.experiment_sampleids) for s in sample_ids]) + self.sample_ids = sample_ids + self.dict_sampleid_to_gates = {} + + +class Gating_Interface: + """ + This class provides a gating GUI. + + Parameters + ---------- + experiment: Experiment + A CytoPy Experiment object + source_population: str + The parent population + """ + + def __init__(self, + experiment: Experiment, + source_population: str + ): + + self.experiment = experiment + + #make sure that the source population is valid + sample_ids = self.experiment.list_samples() + for sample_id in sample_ids: + #sample_pops = get_sample_populations(self.experiment, sample_id) + sample_pops = self.experiment.get_sample(sample_id).list_populations() + err_msg = 'Population %s not found for sample %s.'%( + source_population, sample_id) + err_msg += ' The available populations are: %s'%(sample_pops) + assert source_population in sample_pops, err_msg + + #save gating info + self.source_population = source_population + + #create a FACS_Gater object + self.gater = FACS_Gater(experiment, parent_population=source_population) + + #create layouts and widgets + self._create_widget_layouts() + self._create_widgets() + + #mark that the gates were not yet saved + self.gates_saved = False + + #create a first gate + self._create_gate() + + + + + def plot_gates(self): + assert self.gates_saved, 'No gates were saved yet' + display(self.gater.fig) + + + def _create_widget_layouts(self): + """ + define widget layouts + """ + + self.widget_small_layout = Layout(width='160px', height='auto') + self.widget_xsmall_layout = Layout(width='140px', height='auto') + self.widget_xxsmall_layout = Layout(width='55px', height='auto') + self.widget_xxsmall2_layout = Layout(width='40px', height='auto') + self.label_layout = Layout(margin='0px 0px 0px 10px') + self.label2_layout = Layout(margin='0px 0px 0px 0px') + self.hbox_layout = Layout(flex_flow='row nowrap', + align_items='stretch', + align_content='stretch', + display='flex', + justify_content='flex-start') + self.vbox_layout = Layout(flex_flow='column nowrap', + align_items='flex-start', + align_content='flex-start', + display='flex', + justify_content='flex-start') + + self.hbox_left_layout = Layout(flex_flow='row nowrap', + align_items='flex-start', + align_content='flex-start', + display='flex', + justify_content='flex-start') + + + + def _create_widgets(self): + """ + This function creates all the widgets of the gating GUI + """ + + #num_preview widget + self.widget_numpreview = widgets.Dropdown( + options=[], + description='#preview', + layout=self.widget_xsmall_layout + ) + self.widget_numpreview.observe(self._change_numpreview_callback) + + #x_min widget + self.widget_xmin = Text(value='', layout=self.widget_xxsmall_layout) + self.widget_xmax = Text(value='', layout=self.widget_xxsmall_layout) + self.widget_ymin = Text(value='', layout=self.widget_xxsmall_layout) + self.widget_ymax = Text(value='', layout=self.widget_xxsmall_layout) + self.widget_numpreview.observe(self._change_numpreview_callback) + + + #prepare top-box + self.hbox_top = Box([ + self.widget_numpreview, + Label('X range', layout=self.label_layout), + self.widget_xmin, + Label('-', layout=self.label2_layout), + self.widget_xmax, + Label('Y range', layout=self.label_layout), + self.widget_ymin, + Label('-', layout=self.label2_layout), + self.widget_ymax, + ], + layout=self.hbox_layout) + + #define x-axis and y-axis widgets + experiment_channels = get_experiment_channels(self.experiment) + self.widget_xchannel = widgets.Dropdown( + options=experiment_channels, + value='FSC-A', + description='X channel', + layout=self.widget_small_layout + ) + self.widget_ychannel = widgets.Dropdown( + options=experiment_channels, + value='SSC-A', + description='Y channel', + layout=self.widget_small_layout + ) + self.widget_xtransform = widgets.Dropdown( + options=['Linear', 'Logicle', 'Log'], + description='X transf.', + value='Linear', + layout=self.widget_small_layout + ) + self.widget_ytransform = widgets.Dropdown( + options=['Linear', 'Logicle', 'Log'], + description='Y transf.', + value='Linear', + layout=self.widget_small_layout + ) + self.hbox_axes = Box([self.widget_xchannel, + self.widget_ychannel, + self.widget_xtransform, + self.widget_ytransform, + ], + layout=self.hbox_layout) + + #prepare Gate-type selector widget + self.widget_gatetype = widgets.Dropdown( + options=['Ellipse', 'Threshold', 'Threshold1d', 'Clusters'], + value='Ellipse', + description='Gate Type', + layout=self.widget_small_layout + ) + self.widget_gatetype.observe(self._change_gate_type_callback) + + #prepare create-gate button + self.widget_createegate = widgets.Button(description="Create gates") + self.widget_createegate.on_click(self._create_gate_clicked) + + #prepare save-gate button + self.widget_savegate = widgets.Button(description="Save gates", disabled=True) + self.widget_savegate.on_click(self._save_gate_clicked) + + #prepare boxes that define the layout of all the widgets + self.widget_output = widgets.Output() + self.hbox_gate = Box([ + self.widget_gatetype, + self.widget_createegate, + self.widget_savegate + ], + layout=self.hbox_layout) + self.hbox_gate_params = Box([], layout=self.hbox_left_layout) + self.vbox = Box([], layout=self.vbox_layout) + display(self.vbox) + + #update the num_preview widget + sample_ids = self.experiment.list_samples() + list_numpreview = [c for c in [1,2,4,10] if c <= len(sample_ids)] + ['All'] + self.widget_numpreview.options = list_numpreview + num_preview = 1 + self.widget_numpreview.value = num_preview + self._change_numpreview(num_preview) + + #reset the display (like when we change a gate) + self._change_gate_type(self.widget_gatetype.value) + + + def _change_gate_type(self, + gate_type: str + ): + """ + Change the type of gate shown in the GUI + + Parameters + ---------- + gate_type: str + The gate type + """ + self.widget_output = widgets.Output() + self.widget_savegate.disabled = True + if gate_type == 'Ellipse': + widgets_list = self._prepare_ellipse_widgets() + elif gate_type == 'Threshold': + widgets_list = self._prepare_threshold2d_widgets() + elif gate_type == 'Threshold1d': + widgets_list = self._prepare_threshold1d_widgets() + elif gate_type == 'Clusters': + widgets_list = self._prepare_clusters_widgets() + else: + raise ValueError('unknown gate type: %s'%(gate_type)) + + self.hbox_gate_params = Box(widgets_list, layout=self.hbox_left_layout) + self.vbox.children = [self.hbox_top, + self.hbox_axes, + self.hbox_gate, + self.hbox_gate_params, + self.widget_output + ] + + + + + def _change_numpreview(self, + num_preview: int + ): + """ + Change the number of samples that will be previewed + + Parameters + ---------- + num_preview: int + How many samples will be displayed + """ + sample_ids = self.experiment.list_samples() + if num_preview != 'All': + num_preview = int(num_preview) + assert len(sample_ids) >= num_preview + sample_ids = sample_ids[:num_preview] + self.gater.update_sample_ids(sample_ids) + + + def _change_numpreview_callback(self, widget): + if widget['type'] != 'change' or widget['name'] != 'value': return + self._change_numpreview(widget['new']) + + def _change_gate_type_callback(self, widget): + if widget['type'] != 'change' or widget['name'] != 'value': return + self._change_gate_type(widget['new']) + + + def _prepare_ellipse_widgets(self): + self.widget_popname = Text( + value='A', + description='Target pop', + layout=self.widget_xsmall_layout + ) + self.widget_conf = widgets.Dropdown( + options=np.round(np.arange(0.05, 1.01, 0.05), 2), + value=0.80, + layout=Layout(margin='3px 0px 0px 0px', width='55px'), + indent=True + ) + self.widget_x = Text(value='', layout=self.widget_xxsmall2_layout, disabled=True, ) + self.widget_y = Text(value='', layout=self.widget_xxsmall2_layout, disabled=True, ) + self.widget_width = Text(value='', layout=self.widget_xxsmall2_layout, disabled=True, ) + self.widget_height = Text(value='', layout=self.widget_xxsmall2_layout, disabled=True, ) + self.widget_angle = Text(value='', layout=self.widget_xxsmall_layout, disabled=True, ) + self.widget_auto_ellipse = Checkbox(value=True, + layout=Layout( + width='15px', + height='auto', + margin='3px 0px 0px 0px' + ), + indent=False) + self.widget_auto_ellipse.observe(self._toggle_auto_ellipse, 'value') + return [ + self.widget_popname, + Label('Auto', layout=self.label_layout), + self.widget_auto_ellipse, + Label('Conf.', layout=Layout(margin='0px 0px 0px 5px')), + self.widget_conf, + Label('X', layout=self.label_layout), self.widget_x, + Label('Y', layout=self.label_layout), self.widget_y, + Label('Width', layout=self.label_layout), self.widget_width, + Label('Height', layout=self.label_layout), self.widget_height, + Label('Angle', layout=self.label_layout), self.widget_angle, + ] + + + def _prepare_threshold2d_widgets(self): + self.widget_x = Text( + '200', + description='x threshold', + disabled=True, + layout=self.widget_small_layout + ) + self.widget_y = Text( + '200', + description='y threshold', + disabled=True, + layout=self.widget_small_layout + ) + self.widget_automeans = Checkbox(description='Automatic threshold', + value=True, + indent=False, + layout=self.widget_small_layout) + self.widget_automeans.observe(self._toggle_auto_means, 'value') + self.widget_bandwidth = Text('', + description='Bandwidth', + layout=self.widget_xsmall_layout + ) + return [self.widget_automeans, self.widget_x, self.widget_y, self.widget_bandwidth] + + def _prepare_threshold1d_widgets(self): + self.widget_x = Text('200', + description='x threshold', + disabled=True, + layout=self.widget_small_layout + ) + self.widget_automeans = Checkbox(description='Automatic threshold', + value=True, + indent=False, + layout=self.widget_small_layout) + self.widget_automeans.observe(self._toggle_auto_means, 'value') + self.widget_bandwidth = Text('', + description='Bandwidth', + layout=self.widget_xsmall_layout + ) + return [self.widget_automeans, self.widget_x, self.widget_bandwidth] + + + + def _prepare_clusters_widgets(self): + self.widget_nclusters = widgets.Dropdown( + options=np.arange(1,9), + value=1, + description='#clusters', + layout=self.widget_small_layout + ) + return [self.widget_nclusters] + + + def _create_gate_clusters(self): + """ + Create a clustering gate + """ + self.gater.polygon_gate(gate_name=generate_random_name(), + n_clusters=self.widget_nclusters.value) + + + def _create_gate_ellipse(self): + """ + Create an ellipse gate + """ + if len(self.widget_popname.value)==0: + logging.error('Please provide a target population name') + return + + #determine if it's a manual or automatic ellipse + if self.widget_auto_ellipse.value: + centroid, width, height, angle = None, None, None, None + conf = self.widget_conf.value + method = 'GaussianMixture' + + else: + conf = None + method = 'manual' + + try: + x = float(self.widget_x.value) + except ValueError: + logging.error('X value is not a number') + return + try: + y = float(self.widget_y.value) + except ValueError: + logging.error('Y value is not a number') + return + try: + width = float(self.widget_width.value) + except ValueError: + logging.error('Width value is not a number') + return + try: + height = float(self.widget_height.value) + except ValueError: + logging.error('Height value is not a number') + return + try: + angle = float(self.widget_angle.value) + except ValueError: + logging.error('Angle value is not a number') + return + centroid = (x,y) + + if len(self.widget_popname.value)==0: + logging.error('Please provide a target population name') + return + + + #create the gates + self.gater.ellipse_gate(gate_name=generate_random_name(), + target_pop_name=self.widget_popname.value, + method=method, + conf=conf, + centroid=centroid, + width=width, + height=height, + angle=angle + ) + + #update ellipse parameters if we only have one ellipse + if ( + self.widget_numpreview.value == 1 + and self.widget_xtransform.value=='Linear' + and self.widget_ytransform.value == 'Linear' + and self.widget_auto_ellipse.value + ): + gate = self.gater.gate + ellipse_means = gate.model.means_ + ellipse_params = [probablistic_ellipse(covar, conf=gate.conf) + for covar in gate.model.covariances_] + assert len(ellipse_means) == 1 + assert len(ellipse_params) == 1 + width = ellipse_params[0][0] + height = ellipse_params[0][1] + angle = ellipse_params[0][2] + x, y = ellipse_means[0][0], ellipse_means[0][1] + + self.widget_x.value = str(int(x)) + self.widget_y.value = str(int(y)) + self.widget_height.value = str(int(height)) + self.widget_width.value = str(int(width)) + self.widget_angle.value = str(int(angle)) + + + + + + def _create_gate_threshold2d(self): + """ + Create a threshold2d gate + """ + + #settings for automtic thresholds + if self.widget_automeans.value: + x_threshold = None + y_threshold = None + threshold_method = 'density' + try: + if len(self.widget_bandwidth.value)>0: + bandwidth = float(self.widget_bandwidth.value) + else: bandwidth = None + except ValueError: + logging.error('bandwidth value is not a number') + return + + #settings for manual thresholds + else: + threshold_method = 'manual' + bandwidth = None + try: + x_threshold = float(self.widget_x.value) + except ValueError: + logging.error('x value is not a number') + return + try: + y_threshold = float(self.widget_y.value) + except ValueError: + logging.error('y value is not a number') + return + + #create the gates + try: + self.gater.threshold_gate(gate_name=generate_random_name(), + method=threshold_method, + x_threshold=x_threshold, + y_threshold=y_threshold, + bandwidth=bandwidth) + except ValueError as e: + if str(e) == 'Unable to solve for support numerically. Use a kernel with finite support or scale data to smaller bw.': + logging.error('Threhold gate could not use the provided bandwidth \ + (or find it automatically). \ + Please provide a bandwidth parameter' + ) + else: + raise + + + def _create_gate_threshold1d(self): + """ + Create a threshold1d gate + """ + + #define a manual threshold if needed + if self.widget_automeans.value: + x_threshold = None + threshold_method = 'density' + else: + threshold_method = 'manual' + try: + x_threshold = float(self.widget_x.value) + except ValueError: + logging.error('x value is not a number') + return + + #bandwidth is used for both manual and automatic gating + #(for the purposes of plotting the histogram) + try: + if len(self.widget_bandwidth.value)>0: + bandwidth = float(self.widget_bandwidth.value) + else: + bandwidth = None + except ValueError: + logging.error('bandwidth value is not a number') + return + + #create the gates + try: + self.gater.threshold_gate(gate_name=generate_random_name(), + method=threshold_method, + x_threshold=x_threshold, + bandwidth=bandwidth + ) + except ValueError as e: + if str(e) == 'Unable to solve for support numerically. Use a kernel with finite support or scale data to smaller bw.': + logging.error('Threhold gate could not use the provided bandwidth \ + (or find it automatically). \ + Please provide a bandwidth parameter') + else: + raise + + + + def _create_gate_clicked(self, _): + self._create_gate() + + def _save_gate_clicked(self, _): + + self.gater.save_populations() + self.gates_saved = True + with self.widget_output: + logging.info('Saved populations to DB') + + #disable all the widgets + for hbox in self.vbox.children: + try: hbox.children + except AttributeError: continue + for widget_obj in hbox.children: + widget_obj.disabled = True + + #delete the gating object to save memory + del self.gater + + + + def _create_gate(self): + """ + Create a gate (this is a general function + that calls a gate-specific function depending on the gate type) + """ + + #update gater object + transform_x = None if self.widget_xtransform.value=='Linear' \ + else self.widget_xtransform.value.lower() + transform_y = None if self.widget_ytransform.value=='Linear' \ + else self.widget_ytransform.value.lower() + x = self.widget_xchannel.value + y = self.widget_ychannel.value + if self.widget_gatetype.value == 'Threshold1d': y = None + + + #verify that axis limits are valid + with self.widget_output: + try: + xmin = float(self.widget_xmin.value) if self.widget_xmin.value!='' \ + else None + xmax = float(self.widget_xmax.value) if self.widget_xmax.value!='' \ + else None + except ValueError: + logging.error('X range is not a a number') + return + try: + ymin = float(self.widget_ymin.value) if self.widget_ymin.value!='' \ + else None + ymax = float(self.widget_ymax.value) if self.widget_ymax.value!='' \ + else None + except ValueError: + logging.error('Y range is not a a number') + return + + + self.gater.update_params( + transform_x=transform_x, + transform_y=transform_y, + x=x, + y=y, + xmin=xmin, + xmax=xmax, + ymin=ymin, + ymax=ymax + ) + + with self.widget_output: + clear_output(wait=True) + gate_type = self.widget_gatetype.value + if gate_type == 'Ellipse': + self._create_gate_ellipse() + elif gate_type == 'Threshold': + self._create_gate_threshold2d() + elif gate_type == 'Threshold1d': + self._create_gate_threshold1d() + elif gate_type == 'Clusters': + self._create_gate_clusters() + else: + raise ValueError('unknown gate type: %s'%(gate_type)) + show_inline_matplotlib_plots() + + #enable gate saving if we view all gates + if self.widget_numpreview.value == 'All': + self.widget_savegate.disabled = False + + + def _toggle_auto_means(self, checkbox): + """ + Disable or enable the x and y text boxes, depending on the value in the checkbox + """ + self.widget_x.disabled = checkbox['new'] + self.widget_y.disabled = checkbox['new'] + + + def _toggle_auto_ellipse(self, checkbox): + """ + Disable or enable the manual ellipse widgets + """ + self.widget_x.disabled = checkbox['new'] + self.widget_y.disabled = checkbox['new'] + self.widget_width.disabled = checkbox['new'] + self.widget_height.disabled = checkbox['new'] + self.widget_angle.disabled = checkbox['new'] + self.widget_conf.disabled = not checkbox['new'] + + + + \ No newline at end of file diff --git a/cytopy/data/experiment.py b/cytopy/data/experiment.py index 7a5b0e3c..67484bd1 100644 --- a/cytopy/data/experiment.py +++ b/cytopy/data/experiment.py @@ -49,6 +49,7 @@ import os import re import gc +import io __author__ = "Ross Burton" __copyright__ = "Copyright 2020, cytopy" @@ -659,9 +660,9 @@ def delete_all_populations(self, ------- None """ - for f in self.fcs_files: + for f in self.fcs_files: if sample_id == 'all' or f.primary_id == sample_id: - f.populations = [p for p in f.populations if p.population_name == "root"] + f.delete_populations('all') f.save() def sample_exists(self, sample_id: str) -> bool: @@ -942,7 +943,7 @@ def add_fcs_files(self, if self.sample_exists(sample_id): raise DuplicateSampleError(f'A file group with id {sample_id} already exists') feedback("Creating new FileGroup...") - if isinstance(primary, str): + if isinstance(primary, str) or isinstance(primary, io.IOBase): fcs_file = FCSFile(filepath=primary, comp_matrix=comp_matrix) else: fcs_file = primary @@ -964,7 +965,7 @@ def add_fcs_files(self, data_directory=self.data_directory) for ctrl_id, path in controls.items(): feedback(f"Adding control file {ctrl_id}...") - if isinstance(path, str): + if isinstance(path, str) or isinstance(primary, io.IOBase): fcs_file = FCSFile(filepath=path, comp_matrix=comp_matrix) else: fcs_file = path diff --git a/cytopy/data/gate.py b/cytopy/data/gate.py index 0b858720..d65ed33e 100644 --- a/cytopy/data/gate.py +++ b/cytopy/data/gate.py @@ -1507,10 +1507,11 @@ def _manual(self) -> ShapelyPoly: raise TypeError("Centroid should be a list of two float values") if not all(isinstance(x, float) for x in [width, height, angle]): raise TypeError("Width, height, and angle should be of type float") - return ellipse_to_polygon(centroid=centroid, + polygon_obj = ellipse_to_polygon(centroid=centroid, width=width, height=height, angle=angle) + return [polygon_obj] def _fit(self, data: pd.DataFrame) -> List[ShapelyPoly]: @@ -1527,6 +1528,9 @@ def _fit(self, list List of Shapely polygon's """ + if self.method == "manual": + return self._manual() + params = {k: v for k, v in self.method_kwargs.items() if k != "conf"} self.model = globals()[self.method](**params) if not self.method_kwargs.get("probabilistic_ellipse", True): diff --git a/cytopy/data/gating_strategy.py b/cytopy/data/gating_strategy.py index 40b8cbb9..27554467 100644 --- a/cytopy/data/gating_strategy.py +++ b/cytopy/data/gating_strategy.py @@ -212,7 +212,9 @@ def get_gate(self, def preview_gate(self, gate: str or ThresholdGate or PolygonGate or EllipseGate, create_plot_kwargs: typing.Union[dict, None] = None, - plot_gate_kwargs: typing.Union[dict, None] = None): + plot_gate_kwargs: typing.Union[dict, None] = None, + plot: bool = True + ): """ Preview the results of some given Gate @@ -240,6 +242,9 @@ def preview_gate(self, data, ctrl_parent_data = self._load_gate_dataframes(gate=gate, fda_norm=False) plot_data = data gate.fit(data=data, ctrl_data=ctrl_parent_data) + + if not plot: return + create_plot_kwargs["transform_x"] = create_plot_kwargs.get("transform_x", None) or gate.transform_x create_plot_kwargs["transform_y"] = create_plot_kwargs.get("transform_y", None) or gate.transform_y create_plot_kwargs["transform_x_kwargs"] = create_plot_kwargs.get("transform_x_kwargs", diff --git a/cytopy/data/read_write.py b/cytopy/data/read_write.py index f92211c5..d6ebaa1a 100644 --- a/cytopy/data/read_write.py +++ b/cytopy/data/read_write.py @@ -212,6 +212,7 @@ def _get_spill_matrix(matrix_string: str) -> pd.DataFrame: """ matrix_list = matrix_string.split(',') n = int(matrix_list[0]) + if len(matrix_list) <= n+1: return None #Omer: Added by me header = matrix_list[1:(n+1)] header = [i.strip().replace('\n', '') for i in header] values = [i.strip().replace('\n', '') for i in matrix_list[n+1:]] diff --git a/cytopy/flow/plotting/flow_plot.py b/cytopy/flow/plotting/flow_plot.py index 3141f4c0..c180e2bc 100644 --- a/cytopy/flow/plotting/flow_plot.py +++ b/cytopy/flow/plotting/flow_plot.py @@ -244,11 +244,11 @@ def _hist2d_axis_limits(self, X limit, y limit """ if self.transform_x == "log": - xlim = transform.safe_range(data, "x") + xlim = transform.safe_range(data, x) else: xlim = [data[x].min(), data[x].max()] if self.transform_y == "log": - ylim = transform.safe_range(data, "y") + ylim = transform.safe_range(data, y) else: ylim = [data[y].min(), data[y].max()] xlim = pd.DataFrame({"Min": [xlim[0]], "Max": [xlim[1]]}) @@ -468,13 +468,16 @@ def plot_gate_children(self, if isinstance(gate, ThresholdGate): return self._plot_threshold(definitions={c.definition: c.name for c in gate.children}, geoms=[c.geom for c in gate.children], - lw=lw) + lw=lw, + legend_kwargs=legend_kwargs + ) # Otherwise, we assume polygon shape return self._plot_polygon(geoms=[c.geom for c in gate.children], labels=[c.name for c in gate.children], colours=gate_colours, lw=lw, - legend_kwargs=legend_kwargs) + legend_kwargs=legend_kwargs + ) def plot_population_geoms(self, parent: pd.DataFrame, @@ -484,7 +487,9 @@ def plot_population_geoms(self, transform_x: str or None = None, transform_y: str or None = None, plot_kwargs: dict or None = None, - legend_kwargs: dict or None = None): + legend_kwargs: dict or None = None, + plot_stats:bool = True + ): """ This will plot the geometric shapes from the list of child populations generated from a single Gate, overlaid on the parent population upon which the Gate has been applied. The parent data should be provided @@ -552,20 +557,42 @@ def plot_population_geoms(self, **plot_kwargs) # If threshold, add threshold lines to plot and return axes if isinstance(children[0].geom, ThresholdGeom): - return self._plot_threshold(definitions={c.definition: c.population_name for c in children}, + + #definitions={c.definition: c.population_name for c in children} + definitions = {} + for c in children: + label = c.population_name + if plot_stats: label += '\n%0.0f%% of cells'%(c.n/parent.shape[0]*100) + + definitions[c.definition] = label + + return self._plot_threshold(definitions=definitions, geoms=[c.geom for c in children], - lw=lw) + lw=lw, + legend_kwargs=legend_kwargs, + ) # Otherwise, we assume polygon shape + + #labels = [c.population_name for c in children] + labels = [] + for c in children: + label = c.population_name + if plot_stats: label += ' (%0.0f%% of cells)'%(c.n/parent.shape[0]*100) + labels.append(label) + return self._plot_polygon(geoms=[c.geom for c in children], - labels=[c.population_name for c in children], + labels=labels, colours=gate_colours, lw=lw, - legend_kwargs=legend_kwargs) + legend_kwargs=legend_kwargs, + ) def _plot_threshold(self, definitions: Dict[str, str], geoms: List[ThresholdGeom], - lw: float): + lw: float, + legend_kwargs: dict or None = None, + ): """ Plot Child populations from ThresholdGate @@ -587,7 +614,9 @@ def _plot_threshold(self, self._add_threshold(x=x, y=y, labels=definitions, - lw=lw) + lw=lw, + legend_kwargs=legend_kwargs, + ) return self._ax def _plot_polygon(self, @@ -595,7 +624,8 @@ def _plot_polygon(self, labels: List[str], colours: list or Generator, lw: float, - legend_kwargs: dict): + legend_kwargs: dict, + ): """ Plot the Child populations of a Polygon or Elliptical gate. @@ -656,7 +686,8 @@ def _add_polygon(self, ------- None """ - self._ax.plot(x_values, y_values, '-k', c=colour, label=label, lw=lw) + #self._ax.plot(x_values, y_values, '-k', c=colour, label=label, lw=lw) + self._ax.plot(x_values, y_values, c=colour, label=label, lw=lw) #Omer: I removed '-k' to suppress a warning def _add_ellipse(self, center: (float, float), @@ -700,7 +731,10 @@ def _add_ellipse(self, label=label) self._ax.add_patch(ellipse) - def _2dthreshold_annotations(self, labels: dict or None = None): + def _2dthreshold_annotations(self, + labels: dict or None = None, + legend_kwargs: dict or None = None, + ): """ Annotate a 2D threshold plot @@ -721,30 +755,38 @@ def _2dthreshold_annotations(self, labels: dict or None = None): legend_labels = {} for definition, label in labels.items(): for d in definition.split(","): - if "-+" == d: - legend_labels["A"] = label - elif "++" == d: - legend_labels["B"] = label - elif "--" == d: - legend_labels["C"] = label - elif "+-" == d: - legend_labels["D"] = label - else: - raise KeyError(f"Definition {d} is invalid for a 2D threshold gate.") + if "-+" == d: legend_labels["A"] = label + elif "++" == d: legend_labels["B"] = label + elif "--" == d: legend_labels["C"] = label + elif "+-" == d: legend_labels["D"] = label + else: raise KeyError(f"Definition {d} is invalid for a 2D threshold gate.") self._threshold_annotation(0.05, 0.95, "A") self._threshold_annotation(0.95, 0.95, "B") self._threshold_annotation(0.05, 0.05, "C") self._threshold_annotation(0.95, 0.05, "D") - self._ax.text(1.15, 0.95, f"A: {legend_labels.get('A')}", transform=self._ax.transAxes) - self._ax.text(1.15, 0.85, f"B: {legend_labels.get('B')}", transform=self._ax.transAxes) - self._ax.text(1.15, 0.75, f"C: {legend_labels.get('C')}", transform=self._ax.transAxes) - self._ax.text(1.15, 0.65, f"D: {legend_labels.get('D')}", transform=self._ax.transAxes) + #Omer: Change this to be in a legend + # self._ax.text(1.15, 0.95, f"A: {legend_labels.get('A')}", transform=self._ax.transAxes) + # self._ax.text(1.15, 0.85, f"B: {legend_labels.get('B')}", transform=self._ax.transAxes) + # self._ax.text(1.15, 0.75, f"C: {legend_labels.get('C')}", transform=self._ax.transAxes) + # self._ax.text(1.15, 0.65, f"D: {legend_labels.get('D')}", transform=self._ax.transAxes) + patchmp = patches.Patch(edgecolor=None, facecolor=None, label=f"A: {legend_labels.get('A')}") + patchpp = patches.Patch(edgecolor=None, facecolor=None, label=f"B: {legend_labels.get('B')}") + patchmm = patches.Patch(edgecolor=None, facecolor=None, label=f"C: {legend_labels.get('C')}") + patchpm = patches.Patch(edgecolor=None, facecolor=None, label=f"D: {legend_labels.get('D')}") + + legend_kwargs = dict(legend_kwargs) if legend_kwargs is not None else {} + legend_kwargs['ncol'] = 2 + list_patches = [patchmp, patchmm, patchpp, patchpm] + self._ax.legend(handles=list_patches, handlelength=0, **legend_kwargs) def _threshold_annotation(self, x: float, y: float, text: str): self._ax.text(x, y, text, ha='center', va='center', transform=self._ax.transAxes, backgroundcolor="white", bbox=dict(facecolor='white', edgecolor='black', pad=5.0)) - def _1dthreshold_annotations(self, labels: dict or None = None): + def _1dthreshold_annotations(self, + labels: dict or None = None, + legend_kwargs: dict or None = None, + ): """ Annotate a 1D threshold plot @@ -765,16 +807,28 @@ def _1dthreshold_annotations(self, labels: dict or None = None): legend_labels = {"A": labels["-"], "B": labels["+"]} except KeyError: raise KeyError(f"Definitions for 1D threshold gate must be either '-' or '+', not: {labels.keys()}") + self._threshold_annotation(0.05, 0.95, "A") self._threshold_annotation(0.95, 0.95, "B") - self._ax.text(1.15, 0.95, f"A: {legend_labels.get('A')}", transform=self._ax.transAxes) - self._ax.text(1.15, 0.85, f"B: {legend_labels.get('B')}", transform=self._ax.transAxes) + #self._ax.text(1.15, 0.95, f"A: {legend_labels.get('A')}", transform=self._ax.transAxes) + #self._ax.text(1.15, 0.85, f"B: {legend_labels.get('B')}", transform=self._ax.transAxes) + + patchm = patches.Patch(edgecolor=None, facecolor=None, label=f"A: {legend_labels.get('A')}") + patchp = patches.Patch(edgecolor=None, facecolor=None, label=f"B: {legend_labels.get('B')}") + legend_kwargs = dict(legend_kwargs) if legend_kwargs is not None else {} + list_patches = [patchm, patchp] + self._ax.legend(handles=list_patches, handlelength=0, **legend_kwargs) + + + def _add_threshold(self, x: float, y: float or None, lw: float, - labels: dict or None = None): + labels: dict or None = None, + legend_kwargs: dict or None = None, + ): """ Add a 1D or 2D threshold (red horizontal axis line and optionally a red vertical axis line) @@ -794,13 +848,17 @@ def _add_threshold(self, None """ self._ax.axvline(x, lw=lw, c="#c92c2c") - if y is not None: + if y is not None and not np.isnan(y): self._ax.axhline(y, lw=lw, c="#c92c2c") # Label regions for two axis - self._2dthreshold_annotations(labels=labels) + self._2dthreshold_annotations(labels=labels, + legend_kwargs=legend_kwargs, + ) else: # Label regions for one axis - self._1dthreshold_annotations(labels=labels) + self._1dthreshold_annotations(labels=labels, + legend_kwargs=legend_kwargs, + ) def backgate(self, parent: pd.DataFrame, @@ -1037,13 +1095,25 @@ def _set_legend(self, ------- None """ - anchor = kwargs.get("bbox_to_anchor", (1.1, 0.95)) - loc = kwargs.get("loc", 2) - ncol = kwargs.get("ncol", 3) - fancy = kwargs.get("fancybox", True) - shadow = kwargs.get("shadow", False) - self._ax.legend(loc=loc, - bbox_to_anchor=anchor, - ncol=ncol, - fancybox=fancy, - shadow=shadow) + # anchor = kwargs.get("bbox_to_anchor", (1.1, 0.95)) + # loc = kwargs.get("loc", 2) + # ncol = kwargs.get("ncol", 3) + # fancy = kwargs.get("fancybox", True) + # shadow = kwargs.get("shadow", False) + # self._ax.legend(loc=loc, + # bbox_to_anchor=anchor, + # ncol=ncol, + # fancybox=fancy, + # shadow=shadow) + + #Omer: More general code + legend_kwargs = dict(**kwargs) + for (key, value) in [ + ('bbox_to_anchor', (1.1, 0.95)), + ('loc', 2), + ('ncol', 1), + ('fancybox', True), + ('shadow', False), + ]: + if key not in legend_kwargs: legend_kwargs[key] = value + self._ax.legend(**legend_kwargs) \ No newline at end of file diff --git a/cytopy/flow/plotting/logicle_cache.py b/cytopy/flow/plotting/logicle_cache.py new file mode 100644 index 00000000..51361a44 --- /dev/null +++ b/cytopy/flow/plotting/logicle_cache.py @@ -0,0 +1,6255 @@ +def logicle_cache(): + d = {} + d[0.0] = 0.1111111111111111 + d[0.001] = 0.11111223154317106 + d[0.002] = 0.11111335197523094 + d[0.003] = 0.1111144724072907 + d[0.004] = 0.11111559283935024 + d[0.005] = 0.11111671327140953 + d[0.006] = 0.11111783370346849 + d[0.007] = 0.11111895413552705 + d[0.008] = 0.11112007456758514 + d[0.009] = 0.11112119499964272 + d[0.01] = 0.1111223154316997 + d[0.011] = 0.11112343586375602 + d[0.012] = 0.11112455629581161 + d[0.013] = 0.1111256767278664 + d[0.014] = 0.11112679715992034 + d[0.015] = 0.11112791759197337 + d[0.016] = 0.11112903802402538 + d[0.017] = 0.11113015845607635 + d[0.018] = 0.1111312788881262 + d[0.019] = 0.11113239932017485 + d[0.02] = 0.11113351975222226 + d[0.021] = 0.11113464018426834 + d[0.022] = 0.11113576061631304 + d[0.023] = 0.11113688104835628 + d[0.024] = 0.11113800148039801 + d[0.025] = 0.11113912191243815 + d[0.026] = 0.11114024234447664 + d[0.027] = 0.11114136277651342 + d[0.028] = 0.1111424832085484 + d[0.029] = 0.11114360364058154 + d[0.03] = 0.11114472407261276 + d[0.031] = 0.11114584450464202 + d[0.032] = 0.11114696493666922 + d[0.033] = 0.11114808536869429 + d[0.034] = 0.1111492058007172 + d[0.035] = 0.11115032623273786 + d[0.036] = 0.11115144666475621 + d[0.037] = 0.11115256709677218 + d[0.038] = 0.11115368752878571 + d[0.039] = 0.11115480796079673 + d[0.04] = 0.11115592839280518 + d[0.041] = 0.11115704882481098 + d[0.042] = 0.11115816925681407 + d[0.043] = 0.1111592896888144 + d[0.044] = 0.11116041012081188 + d[0.045] = 0.11116153055280646 + d[0.046] = 0.11116265098479806 + d[0.047] = 0.11116377141678663 + d[0.048] = 0.1111648918487721 + d[0.049] = 0.11116601228075439 + d[0.05] = 0.11116713271273346 + d[0.051] = 0.11116825314470921 + d[0.052] = 0.1111693735766816 + d[0.053] = 0.11117049400865055 + d[0.054] = 0.111171614440616 + d[0.055] = 0.1111727348725779 + d[0.056] = 0.11117385530453616 + d[0.057] = 0.11117497573649071 + d[0.058] = 0.11117609616844151 + d[0.059] = 0.11117721660038848 + d[0.06] = 0.11117833703233154 + d[0.061] = 0.11117945746427066 + d[0.062] = 0.11118057789620574 + d[0.063] = 0.11118169832813672 + d[0.064] = 0.11118281876006354 + d[0.065] = 0.11118393919198613 + d[0.066] = 0.11118505962390444 + d[0.067] = 0.11118618005581839 + d[0.068] = 0.1111873004877279 + d[0.069] = 0.11118842091963294 + d[0.07] = 0.11118954135153342 + d[0.071] = 0.11119066178342926 + d[0.072] = 0.11119178221532043 + d[0.073] = 0.11119290264720684 + d[0.074] = 0.11119402307908842 + d[0.075] = 0.11119514351096511 + d[0.076] = 0.11119626394283687 + d[0.077] = 0.1111973843747036 + d[0.078] = 0.11119850480656523 + d[0.079] = 0.11119962523842172 + d[0.08] = 0.111200745670273 + d[0.081] = 0.11120186610211899 + d[0.082] = 0.11120298653395963 + d[0.083] = 0.11120410696579486 + d[0.084] = 0.1112052273976246 + d[0.085] = 0.1112063478294488 + d[0.086] = 0.11120746826126737 + d[0.087] = 0.11120858869308028 + d[0.088] = 0.11120970912488744 + d[0.089] = 0.11121082955668878 + d[0.09] = 0.11121194998848424 + d[0.091] = 0.11121307042027377 + d[0.092] = 0.11121419085205728 + d[0.093] = 0.11121531128383472 + d[0.094] = 0.11121643171560601 + d[0.095] = 0.1112175521473711 + d[0.096] = 0.11121867257912992 + d[0.097] = 0.11121979301088238 + d[0.098] = 0.11122091344262845 + d[0.099] = 0.11122203387436803 + d[0.1] = 0.1112231543061011 + d[0.101] = 0.11122427473782755 + d[0.102] = 0.11122539516954733 + d[0.103] = 0.11122651560126036 + d[0.104] = 0.11122763603296659 + d[0.105] = 0.11122875646466597 + d[0.106] = 0.11122987689635841 + d[0.107] = 0.11123099732804384 + d[0.108] = 0.11123211775972221 + d[0.109] = 0.11123323819139344 + d[0.11] = 0.11123435862305747 + d[0.111] = 0.11123547905471425 + d[0.112] = 0.11123659948636368 + d[0.113] = 0.11123771991800571 + d[0.114] = 0.1112388403496403 + d[0.115] = 0.11123996078126734 + d[0.116] = 0.1112410812128868 + d[0.117] = 0.11124220164449858 + d[0.118] = 0.11124332207610264 + d[0.119] = 0.11124444250769891 + d[0.12] = 0.11124556293928732 + d[0.121] = 0.1112466833708678 + d[0.122] = 0.11124780380244029 + d[0.123] = 0.11124892423400472 + d[0.124] = 0.11125004466556102 + d[0.125] = 0.11125116509710914 + d[0.126] = 0.11125228552864899 + d[0.127] = 0.11125340596018053 + d[0.128] = 0.11125452639170368 + d[0.129] = 0.11125564682321837 + d[0.13] = 0.11125676725472454 + d[0.131] = 0.11125788768622213 + d[0.132] = 0.11125900811771107 + d[0.133] = 0.11126012854919128 + d[0.134] = 0.11126124898066271 + d[0.135] = 0.11126236941212528 + d[0.136] = 0.11126348984357895 + d[0.137] = 0.11126461027502361 + d[0.138] = 0.11126573070645925 + d[0.139] = 0.11126685113788576 + d[0.14] = 0.11126797156930308 + d[0.141] = 0.11126909200071117 + d[0.142] = 0.11127021243210994 + d[0.143] = 0.11127133286349933 + d[0.144] = 0.11127245329487927 + d[0.145] = 0.1112735737262497 + d[0.146] = 0.11127469415761056 + d[0.147] = 0.11127581458896176 + d[0.148] = 0.11127693502030325 + d[0.149] = 0.11127805545163498 + d[0.15] = 0.11127917588295685 + d[0.151] = 0.11128029631426883 + d[0.152] = 0.11128141674557082 + d[0.153] = 0.11128253717686278 + d[0.154] = 0.11128365760814463 + d[0.155] = 0.1112847780394163 + d[0.156] = 0.11128589847067774 + d[0.157] = 0.11128701890192887 + d[0.158] = 0.11128813933316963 + d[0.159] = 0.11128925976439995 + d[0.16] = 0.11129038019561976 + d[0.161] = 0.11129150062682902 + d[0.162] = 0.11129262105802763 + d[0.163] = 0.11129374148921554 + d[0.164] = 0.11129486192039269 + d[0.165] = 0.11129598235155899 + d[0.166] = 0.1112971027827144 + d[0.167] = 0.11129822321385885 + d[0.168] = 0.11129934364499226 + d[0.169] = 0.11130046407611457 + d[0.17] = 0.11130158450722573 + d[0.171] = 0.11130270493832564 + d[0.172] = 0.11130382536941426 + d[0.173] = 0.11130494580049152 + d[0.174] = 0.11130606623155735 + d[0.175] = 0.11130718666261169 + d[0.176] = 0.11130830709365447 + d[0.177] = 0.11130942752468562 + d[0.178] = 0.11131054795570507 + d[0.179] = 0.11131166838671276 + d[0.18] = 0.11131278881770863 + d[0.181] = 0.11131390924869261 + d[0.182] = 0.11131502967966464 + d[0.183] = 0.11131615011062464 + d[0.184] = 0.11131727054157253 + d[0.185] = 0.11131839097250829 + d[0.186] = 0.11131951140343183 + d[0.187] = 0.11132063183434306 + d[0.188] = 0.11132175226524195 + d[0.189] = 0.11132287269612842 + d[0.19] = 0.11132399312700239 + d[0.191] = 0.11132511355786383 + d[0.192] = 0.11132623398871264 + d[0.193] = 0.11132735441954876 + d[0.194] = 0.11132847485037213 + d[0.195] = 0.11132959528118269 + d[0.196] = 0.11133071571198036 + d[0.197] = 0.11133183614276508 + d[0.198] = 0.1113329565735368 + d[0.199] = 0.11133407700429543 + d[0.2] = 0.1113351974350409 + d[0.201] = 0.11133631786577318 + d[0.202] = 0.11133743829649216 + d[0.203] = 0.1113385587271978 + d[0.204] = 0.11133967915789003 + d[0.205] = 0.11134079958856878 + d[0.206] = 0.11134192001923399 + d[0.207] = 0.11134304044988559 + d[0.208] = 0.11134416088052351 + d[0.209] = 0.11134528131114768 + d[0.21] = 0.11134640174175806 + d[0.211] = 0.11134752217235455 + d[0.212] = 0.1113486426029371 + d[0.213] = 0.11134976303350565 + d[0.214] = 0.11135088346406012 + d[0.215] = 0.11135200389460045 + d[0.216] = 0.11135312432512659 + d[0.217] = 0.11135424475563845 + d[0.218] = 0.11135536518613597 + d[0.219] = 0.11135648561661908 + d[0.22] = 0.11135760604708773 + d[0.221] = 0.11135872647754184 + d[0.222] = 0.11135984690798136 + d[0.223] = 0.1113609673384062 + d[0.224] = 0.1113620877688163 + d[0.225] = 0.11136320819921161 + d[0.226] = 0.11136432862959204 + d[0.227] = 0.11136544905995756 + d[0.228] = 0.11136656949030806 + d[0.229] = 0.1113676899206435 + d[0.23] = 0.11136881035096381 + d[0.231] = 0.11136993078126893 + d[0.232] = 0.11137105121155878 + d[0.233] = 0.1113721716418333 + d[0.234] = 0.11137329207209243 + d[0.235] = 0.1113744125023361 + d[0.236] = 0.11137553293256423 + d[0.237] = 0.11137665336277679 + d[0.238] = 0.11137777379297367 + d[0.239] = 0.11137889422315482 + d[0.24] = 0.11138001465332019 + d[0.241] = 0.1113811350834697 + d[0.242] = 0.11138225551360328 + d[0.243] = 0.11138337594372087 + d[0.244] = 0.1113844963738224 + d[0.245] = 0.11138561680390782 + d[0.246] = 0.11138673723397705 + d[0.247] = 0.11138785766403002 + d[0.248] = 0.11138897809406666 + d[0.249] = 0.11139009852408692 + d[0.25] = 0.11139121895409072 + d[0.251] = 0.11139233938407801 + d[0.252] = 0.11139345981404872 + d[0.253] = 0.11139458024400277 + d[0.254] = 0.1113957006739401 + d[0.255] = 0.11139682110386064 + d[0.256] = 0.11139794153376434 + d[0.257] = 0.11139906196365111 + d[0.258] = 0.11140018239352091 + d[0.259] = 0.11140130282337365 + d[0.26] = 0.1114024232532093 + d[0.261] = 0.11140354368302775 + d[0.262] = 0.11140466411282895 + d[0.263] = 0.11140578454261285 + d[0.264] = 0.11140690497237936 + d[0.265] = 0.11140802540212842 + d[0.266] = 0.11140914583185998 + d[0.267] = 0.11141026626157396 + d[0.268] = 0.11141138669127029 + d[0.269] = 0.11141250712094891 + d[0.27] = 0.11141362755060977 + d[0.271] = 0.11141474798025276 + d[0.272] = 0.11141586840987787 + d[0.273] = 0.11141698883948499 + d[0.274] = 0.11141810926907407 + d[0.275] = 0.11141922969864504 + d[0.276] = 0.11142035012819784 + d[0.277] = 0.1114214705577324 + d[0.278] = 0.11142259098724866 + d[0.279] = 0.11142371141674655 + d[0.28] = 0.111424831846226 + d[0.281] = 0.11142595227568694 + d[0.282] = 0.1114270727051293 + d[0.283] = 0.11142819313455304 + d[0.284] = 0.11142931356395808 + d[0.285] = 0.11143043399334435 + d[0.286] = 0.11143155442271177 + d[0.287] = 0.1114326748520603 + d[0.288] = 0.11143379528138987 + d[0.289] = 0.11143491571070041 + d[0.29] = 0.11143603613999184 + d[0.291] = 0.1114371565692641 + d[0.292] = 0.11143827699851713 + d[0.293] = 0.11143939742775087 + d[0.294] = 0.11144051785696525 + d[0.295] = 0.1114416382861602 + d[0.296] = 0.11144275871533564 + d[0.297] = 0.11144387914449153 + d[0.298] = 0.11144499957362779 + d[0.299] = 0.11144612000274436 + d[0.3] = 0.11144724043184115 + d[0.301] = 0.11144836086091812 + d[0.302] = 0.11144948128997521 + d[0.303] = 0.11145060171901233 + d[0.304] = 0.11145172214802944 + d[0.305] = 0.11145284257702644 + d[0.306] = 0.1114539630060033 + d[0.307] = 0.11145508343495991 + d[0.308] = 0.11145620386389625 + d[0.309] = 0.11145732429281223 + d[0.31] = 0.1114584447217078 + d[0.311] = 0.11145956515058286 + d[0.312] = 0.11146068557943738 + d[0.313] = 0.11146180600827127 + d[0.314] = 0.11146292643708448 + d[0.315] = 0.11146404686587694 + d[0.316] = 0.11146516729464857 + d[0.317] = 0.11146628772339932 + d[0.318] = 0.11146740815212912 + d[0.319] = 0.1114685285808379 + d[0.32] = 0.11146964900952559 + d[0.321] = 0.11147076943819215 + d[0.322] = 0.11147188986683747 + d[0.323] = 0.11147301029546153 + d[0.324] = 0.11147413072406422 + d[0.325] = 0.1114752511526455 + d[0.326] = 0.11147637158120531 + d[0.327] = 0.11147749200974356 + d[0.328] = 0.11147861243826021 + d[0.329] = 0.11147973286675518 + d[0.33] = 0.1114808532952284 + d[0.331] = 0.11148197372367981 + d[0.332] = 0.11148309415210934 + d[0.333] = 0.11148421458051692 + d[0.334] = 0.11148533500890251 + d[0.335] = 0.11148645543726601 + d[0.336] = 0.11148757586560737 + d[0.337] = 0.11148869629392652 + d[0.338] = 0.11148981672222338 + d[0.339] = 0.11149093715049792 + d[0.34] = 0.11149205757875005 + d[0.341] = 0.1114931780069797 + d[0.342] = 0.11149429843518682 + d[0.343] = 0.11149541886337133 + d[0.344] = 0.11149653929153316 + d[0.345] = 0.11149765971967227 + d[0.346] = 0.11149878014778856 + d[0.347] = 0.11149990057588198 + d[0.348] = 0.11150102100395247 + d[0.349] = 0.11150214143199996 + d[0.35] = 0.11150326186002438 + d[0.351] = 0.11150438228802566 + d[0.352] = 0.11150550271600373 + d[0.353] = 0.11150662314395855 + d[0.354] = 0.11150774357189003 + d[0.355] = 0.11150886399979812 + d[0.356] = 0.11150998442768273 + d[0.357] = 0.11151110485554382 + d[0.358] = 0.1115122252833813 + d[0.359] = 0.11151334571119512 + d[0.36] = 0.1115144661389852 + d[0.361] = 0.11151558656675149 + d[0.362] = 0.11151670699449392 + d[0.363] = 0.11151782742221243 + d[0.364] = 0.11151894784990693 + d[0.365] = 0.11152006827757738 + d[0.366] = 0.11152118870522369 + d[0.367] = 0.11152230913284582 + d[0.368] = 0.11152342956044367 + d[0.369] = 0.11152454998801721 + d[0.37] = 0.11152567041556635 + d[0.371] = 0.11152679084309104 + d[0.372] = 0.11152791127059121 + d[0.373] = 0.11152903169806677 + d[0.374] = 0.11153015212551769 + d[0.375] = 0.11153127255294387 + d[0.376] = 0.11153239298034527 + d[0.377] = 0.11153351340772182 + d[0.378] = 0.11153463383507344 + d[0.379] = 0.11153575426240007 + d[0.38] = 0.11153687468970165 + d[0.381] = 0.11153799511697812 + d[0.382] = 0.11153911554422939 + d[0.383] = 0.1115402359714554 + d[0.384] = 0.11154135639865612 + d[0.385] = 0.11154247682583143 + d[0.386] = 0.1115435972529813 + d[0.387] = 0.11154471768010564 + d[0.388] = 0.1115458381072044 + d[0.389] = 0.11154695853427751 + d[0.39] = 0.11154807896132492 + d[0.391] = 0.11154919938834654 + d[0.392] = 0.1115503198153423 + d[0.393] = 0.11155144024231216 + d[0.394] = 0.11155256066925602 + d[0.395] = 0.11155368109617385 + d[0.396] = 0.11155480152306556 + d[0.397] = 0.1115559219499311 + d[0.398] = 0.11155704237677037 + d[0.399] = 0.11155816280358336 + d[0.4] = 0.11155928323036995 + d[0.401] = 0.1115604036571301 + d[0.402] = 0.11156152408386374 + d[0.403] = 0.11156264451057081 + d[0.404] = 0.11156376493725123 + d[0.405] = 0.11156488536390495 + d[0.406] = 0.11156600579053189 + d[0.407] = 0.11156712621713198 + d[0.408] = 0.11156824664370517 + d[0.409] = 0.11156936707025139 + d[0.41] = 0.11157048749677057 + d[0.411] = 0.11157160792326264 + d[0.412] = 0.11157272834972752 + d[0.413] = 0.11157384877616519 + d[0.414] = 0.11157496920257554 + d[0.415] = 0.11157608962895853 + d[0.416] = 0.11157721005531407 + d[0.417] = 0.1115783304816421 + d[0.418] = 0.11157945090794258 + d[0.419] = 0.11158057133421542 + d[0.42] = 0.11158169176046055 + d[0.421] = 0.11158281218667793 + d[0.422] = 0.11158393261286745 + d[0.423] = 0.11158505303902909 + d[0.424] = 0.11158617346516275 + d[0.425] = 0.11158729389126838 + d[0.426] = 0.11158841431734591 + d[0.427] = 0.11158953474339528 + d[0.428] = 0.11159065516941642 + d[0.429] = 0.11159177559540925 + d[0.43] = 0.11159289602137373 + d[0.431] = 0.11159401644730978 + d[0.432] = 0.11159513687321732 + d[0.433] = 0.11159625729909631 + d[0.434] = 0.11159737772494666 + d[0.435] = 0.11159849815076832 + d[0.436] = 0.11159961857656123 + d[0.437] = 0.1116007390023253 + d[0.438] = 0.11160185942806047 + d[0.439] = 0.11160297985376669 + d[0.44] = 0.11160410027944388 + d[0.441] = 0.11160522070509198 + d[0.442] = 0.11160634113071093 + d[0.443] = 0.11160746155630064 + d[0.444] = 0.11160858198186106 + d[0.445] = 0.11160970240739214 + d[0.446] = 0.11161082283289378 + d[0.447] = 0.11161194325836593 + d[0.448] = 0.11161306368380854 + d[0.449] = 0.11161418410922151 + d[0.45] = 0.1116153045346048 + d[0.451] = 0.11161642495995833 + d[0.452] = 0.11161754538528204 + d[0.453] = 0.11161866581057588 + d[0.454] = 0.11161978623583975 + d[0.455] = 0.1116209066610736 + d[0.456] = 0.11162202708627737 + d[0.457] = 0.11162314751145098 + d[0.458] = 0.11162426793659438 + d[0.459] = 0.1116253883617075 + d[0.46] = 0.11162650878679027 + d[0.461] = 0.11162762921184262 + d[0.462] = 0.11162874963686448 + d[0.463] = 0.11162987006185579 + d[0.464] = 0.11163099048681649 + d[0.465] = 0.11163211091174652 + d[0.466] = 0.11163323133664578 + d[0.467] = 0.11163435176151425 + d[0.468] = 0.11163547218635182 + d[0.469] = 0.11163659261115845 + d[0.47] = 0.11163771303593407 + d[0.471] = 0.11163883346067861 + d[0.472] = 0.111639953885392 + d[0.473] = 0.11164107431007418 + d[0.474] = 0.11164219473472509 + d[0.475] = 0.11164331515934466 + d[0.476] = 0.1116444355839328 + d[0.477] = 0.11164555600848948 + d[0.478] = 0.11164667643301461 + d[0.479] = 0.11164779685750813 + d[0.48] = 0.11164891728196999 + d[0.481] = 0.11165003770640008 + d[0.482] = 0.11165115813079839 + d[0.483] = 0.11165227855516482 + d[0.484] = 0.1116533989794993 + d[0.485] = 0.11165451940380179 + d[0.486] = 0.1116556398280722 + d[0.487] = 0.11165676025231046 + d[0.488] = 0.11165788067651652 + d[0.489] = 0.11165900110069032 + d[0.49] = 0.11166012152483178 + d[0.491] = 0.11166124194894084 + d[0.492] = 0.11166236237301742 + d[0.493] = 0.11166348279706147 + d[0.494] = 0.11166460322107291 + d[0.495] = 0.11166572364505169 + d[0.496] = 0.11166684406899774 + d[0.497] = 0.11166796449291097 + d[0.498] = 0.11166908491679135 + d[0.499] = 0.11167020534063879 + d[0.5] = 0.11167132576445324 + d[0.501] = 0.11167244618823462 + d[0.502] = 0.11167356661198286 + d[0.503] = 0.1116746870356979 + d[0.504] = 0.11167580745937969 + d[0.505] = 0.11167692788302813 + d[0.506] = 0.11167804830664319 + d[0.507] = 0.11167916873022478 + d[0.508] = 0.11168028915377284 + d[0.509] = 0.11168140957728731 + d[0.51] = 0.11168253000076811 + d[0.511] = 0.11168365042421519 + d[0.512] = 0.11168477084762847 + d[0.513] = 0.11168589127100789 + d[0.514] = 0.11168701169435338 + d[0.515] = 0.11168813211766489 + d[0.516] = 0.11168925254094232 + d[0.517] = 0.11169037296418563 + d[0.518] = 0.11169149338739476 + d[0.519] = 0.11169261381056962 + d[0.52] = 0.11169373423371017 + d[0.521] = 0.11169485465681632 + d[0.522] = 0.11169597507988802 + d[0.523] = 0.11169709550292518 + d[0.524] = 0.11169821592592775 + d[0.525] = 0.11169933634889569 + d[0.526] = 0.1117004567718289 + d[0.527] = 0.1117015771947273 + d[0.528] = 0.11170269761759087 + d[0.529] = 0.11170381804041951 + d[0.53] = 0.11170493846321317 + d[0.531] = 0.11170605888597177 + d[0.532] = 0.11170717930869524 + d[0.533] = 0.11170829973138353 + d[0.534] = 0.11170942015403658 + d[0.535] = 0.1117105405766543 + d[0.536] = 0.11171166099923664 + d[0.537] = 0.11171278142178354 + d[0.538] = 0.11171390184429492 + d[0.539] = 0.1117150222667707 + d[0.54] = 0.11171614268921085 + d[0.541] = 0.11171726311161527 + d[0.542] = 0.11171838353398392 + d[0.543] = 0.11171950395631672 + d[0.544] = 0.11172062437861359 + d[0.545] = 0.11172174480087449 + d[0.546] = 0.11172286522309935 + d[0.547] = 0.11172398564528808 + d[0.548] = 0.11172510606744065 + d[0.549] = 0.11172622648955696 + d[0.55] = 0.11172734691163697 + d[0.551] = 0.1117284673336806 + d[0.552] = 0.11172958775568778 + d[0.553] = 0.11173070817765846 + d[0.554] = 0.11173182859959255 + d[0.555] = 0.11173294902148999 + d[0.556] = 0.11173406944335074 + d[0.557] = 0.11173518986517471 + d[0.558] = 0.11173631028696182 + d[0.559] = 0.11173743070871205 + d[0.56] = 0.11173855113042529 + d[0.561] = 0.11173967155210149 + d[0.562] = 0.11174079197374058 + d[0.563] = 0.1117419123953425 + d[0.564] = 0.11174303281690717 + d[0.565] = 0.11174415323843455 + d[0.566] = 0.11174527365992455 + d[0.567] = 0.11174639408137711 + d[0.568] = 0.11174751450279218 + d[0.569] = 0.11174863492416967 + d[0.57] = 0.11174975534550952 + d[0.571] = 0.11175087576681167 + d[0.572] = 0.11175199618807605 + d[0.573] = 0.11175311660930258 + d[0.574] = 0.11175423703049123 + d[0.575] = 0.1117553574516419 + d[0.576] = 0.11175647787275454 + d[0.577] = 0.11175759829382907 + d[0.578] = 0.11175871871486544 + d[0.579] = 0.11175983913586358 + d[0.58] = 0.11176095955682341 + d[0.581] = 0.11176207997774489 + d[0.582] = 0.11176320039862792 + d[0.583] = 0.11176432081947246 + d[0.584] = 0.11176544124027843 + d[0.585] = 0.11176656166104577 + d[0.586] = 0.11176768208177443 + d[0.587] = 0.1117688025024643 + d[0.588] = 0.11176992292311536 + d[0.589] = 0.1117710433437275 + d[0.59] = 0.1117721637643007 + d[0.591] = 0.11177328418483487 + d[0.592] = 0.11177440460532993 + d[0.593] = 0.11177552502578585 + d[0.594] = 0.11177664544620253 + d[0.595] = 0.1117777658665799 + d[0.596] = 0.11177888628691794 + d[0.597] = 0.11178000670721654 + d[0.598] = 0.11178112712747565 + d[0.599] = 0.1117822475476952 + d[0.6] = 0.11178336796787512 + d[0.601] = 0.11178448838801534 + d[0.602] = 0.11178560880811582 + d[0.603] = 0.11178672922817647 + d[0.604] = 0.11178784964819723 + d[0.605] = 0.11178897006817803 + d[0.606] = 0.11179009048811882 + d[0.607] = 0.11179121090801951 + d[0.608] = 0.11179233132788004 + d[0.609] = 0.11179345174770035 + d[0.61] = 0.11179457216748037 + d[0.611] = 0.11179569258722005 + d[0.612] = 0.1117968130069193 + d[0.613] = 0.11179793342657805 + d[0.614] = 0.11179905384619628 + d[0.615] = 0.11180017426577386 + d[0.616] = 0.11180129468531076 + d[0.617] = 0.11180241510480692 + d[0.618] = 0.11180353552426225 + d[0.619] = 0.1118046559436767 + d[0.62] = 0.1118057763630502 + d[0.621] = 0.11180689678238268 + d[0.622] = 0.11180801720167408 + d[0.623] = 0.11180913762092433 + d[0.624] = 0.11181025804013336 + d[0.625] = 0.11181137845930111 + d[0.626] = 0.11181249887842751 + d[0.627] = 0.11181361929751249 + d[0.628] = 0.111814739716556 + d[0.629] = 0.11181586013555796 + d[0.63] = 0.1118169805545183 + d[0.631] = 0.11181810097343697 + d[0.632] = 0.11181922139231389 + d[0.633] = 0.11182034181114898 + d[0.634] = 0.11182146222994221 + d[0.635] = 0.11182258264869349 + d[0.636] = 0.11182370306740276 + d[0.637] = 0.11182482348606995 + d[0.638] = 0.11182594390469501 + d[0.639] = 0.11182706432327784 + d[0.64] = 0.1118281847418184 + d[0.641] = 0.11182930516031662 + d[0.642] = 0.11183042557877243 + d[0.643] = 0.11183154599718576 + d[0.644] = 0.11183266641555654 + d[0.645] = 0.11183378683388473 + d[0.646] = 0.11183490725217024 + d[0.647] = 0.11183602767041301 + d[0.648] = 0.11183714808861296 + d[0.649] = 0.11183826850677005 + d[0.65] = 0.1118393889248842 + d[0.651] = 0.11184050934295534 + d[0.652] = 0.11184162976098341 + d[0.653] = 0.11184275017896834 + d[0.654] = 0.11184387059691006 + d[0.655] = 0.11184499101480852 + d[0.656] = 0.11184611143266364 + d[0.657] = 0.11184723185047535 + d[0.658] = 0.11184835226824359 + d[0.659] = 0.1118494726859683 + d[0.66] = 0.1118505931036494 + d[0.661] = 0.11185171352128684 + d[0.662] = 0.11185283393888054 + d[0.663] = 0.11185395435643043 + d[0.664] = 0.11185507477393647 + d[0.665] = 0.11185619519139856 + d[0.666] = 0.11185731560881666 + d[0.667] = 0.11185843602619068 + d[0.668] = 0.11185955644352058 + d[0.669] = 0.11186067686080628 + d[0.67] = 0.11186179727804771 + d[0.671] = 0.11186291769524481 + d[0.672] = 0.11186403811239751 + d[0.673] = 0.11186515852950574 + d[0.674] = 0.11186627894656945 + d[0.675] = 0.11186739936358855 + d[0.676] = 0.111868519780563 + d[0.677] = 0.11186964019749271 + d[0.678] = 0.11187076061437763 + d[0.679] = 0.11187188103121769 + d[0.68] = 0.11187300144801281 + d[0.681] = 0.11187412186476295 + d[0.682] = 0.11187524228146802 + d[0.683] = 0.11187636269812795 + d[0.684] = 0.1118774831147427 + d[0.685] = 0.1118786035313122 + d[0.686] = 0.11187972394783635 + d[0.687] = 0.11188084436431513 + d[0.688] = 0.11188196478074842 + d[0.689] = 0.11188308519713622 + d[0.69] = 0.11188420561347841 + d[0.691] = 0.11188532602977494 + d[0.692] = 0.11188644644602574 + d[0.693] = 0.11188756686223077 + d[0.694] = 0.11188868727838992 + d[0.695] = 0.11188980769450316 + d[0.696] = 0.11189092811057041 + d[0.697] = 0.1118920485265916 + d[0.698] = 0.11189316894256666 + d[0.699] = 0.11189428935849555 + d[0.7] = 0.11189540977437817 + d[0.701] = 0.11189653019021448 + d[0.702] = 0.11189765060600439 + d[0.703] = 0.11189877102174786 + d[0.704] = 0.11189989143744479 + d[0.705] = 0.11190101185309514 + d[0.706] = 0.11190213226869886 + d[0.707] = 0.11190325268425584 + d[0.708] = 0.11190437309976603 + d[0.709] = 0.11190549351522938 + d[0.71] = 0.1119066139306458 + d[0.711] = 0.11190773434601524 + d[0.712] = 0.11190885476133763 + d[0.713] = 0.11190997517661291 + d[0.714] = 0.111911095591841 + d[0.715] = 0.11191221600702184 + d[0.716] = 0.11191333642215537 + d[0.717] = 0.11191445683724151 + d[0.718] = 0.1119155772522802 + d[0.719] = 0.11191669766727137 + d[0.72] = 0.11191781808221497 + d[0.721] = 0.11191893849711092 + d[0.722] = 0.11192005891195915 + d[0.723] = 0.1119211793267596 + d[0.724] = 0.11192229974151222 + d[0.725] = 0.11192342015621691 + d[0.726] = 0.11192454057087362 + d[0.727] = 0.11192566098548229 + d[0.728] = 0.11192678140004284 + d[0.729] = 0.11192790181455521 + d[0.73] = 0.11192902222901935 + d[0.731] = 0.11193014264343518 + d[0.732] = 0.11193126305780261 + d[0.733] = 0.11193238347212162 + d[0.734] = 0.1119335038863921 + d[0.735] = 0.11193462430061402 + d[0.736] = 0.11193574471478729 + d[0.737] = 0.11193686512891185 + d[0.738] = 0.11193798554298763 + d[0.739] = 0.11193910595701458 + d[0.74] = 0.11194022637099262 + d[0.741] = 0.11194134678492168 + d[0.742] = 0.1119424671988017 + d[0.743] = 0.11194358761263261 + d[0.744] = 0.11194470802641435 + d[0.745] = 0.11194582844014685 + d[0.746] = 0.11194694885383004 + d[0.747] = 0.11194806926746387 + d[0.748] = 0.11194918968104825 + d[0.749] = 0.11195031009458312 + d[0.75] = 0.11195143050806843 + d[0.751] = 0.1119525509215041 + d[0.752] = 0.11195367133489006 + d[0.753] = 0.11195479174822626 + d[0.754] = 0.11195591216151261 + d[0.755] = 0.11195703257474907 + d[0.756] = 0.11195815298793554 + d[0.757] = 0.111959273401072 + d[0.758] = 0.11196039381415834 + d[0.759] = 0.11196151422719451 + d[0.76] = 0.11196263464018046 + d[0.761] = 0.11196375505311609 + d[0.762] = 0.11196487546600137 + d[0.763] = 0.11196599587883621 + d[0.764] = 0.11196711629162054 + d[0.765] = 0.11196823670435431 + d[0.766] = 0.11196935711703745 + d[0.767] = 0.11197047752966989 + d[0.768] = 0.11197159794225157 + d[0.769] = 0.11197271835478241 + d[0.77] = 0.11197383876726236 + d[0.771] = 0.11197495917969133 + d[0.772] = 0.11197607959206927 + d[0.773] = 0.11197720000439614 + d[0.774] = 0.11197832041667181 + d[0.775] = 0.11197944082889627 + d[0.776] = 0.11198056124106943 + d[0.777] = 0.11198168165319122 + d[0.778] = 0.1119828020652616 + d[0.779] = 0.11198392247728046 + d[0.78] = 0.11198504288924778 + d[0.781] = 0.11198616330116345 + d[0.782] = 0.11198728371302745 + d[0.783] = 0.11198840412483967 + d[0.784] = 0.11198952453660008 + d[0.785] = 0.11199064494830857 + d[0.786] = 0.11199176535996512 + d[0.787] = 0.11199288577156964 + d[0.788] = 0.11199400618312207 + d[0.789] = 0.11199512659462234 + d[0.79] = 0.11199624700607037 + d[0.791] = 0.11199736741746613 + d[0.792] = 0.11199848782880951 + d[0.793] = 0.11199960824010048 + d[0.794] = 0.11200072865133896 + d[0.795] = 0.11200184906252487 + d[0.796] = 0.11200296947365818 + d[0.797] = 0.11200408988473878 + d[0.798] = 0.11200521029576663 + d[0.799] = 0.11200633070674167 + d[0.8] = 0.1120074511176638 + d[0.801] = 0.11200857152853298 + d[0.802] = 0.11200969193934913 + d[0.803] = 0.11201081235011222 + d[0.804] = 0.11201193276082214 + d[0.805] = 0.11201305317147883 + d[0.806] = 0.11201417358208224 + d[0.807] = 0.1120152939926323 + d[0.808] = 0.11201641440312894 + d[0.809] = 0.11201753481357209 + d[0.81] = 0.11201865522396168 + d[0.811] = 0.11201977563429766 + d[0.812] = 0.11202089604457996 + d[0.813] = 0.1120220164548085 + d[0.814] = 0.11202313686498322 + d[0.815] = 0.11202425727510407 + d[0.816] = 0.11202537768517096 + d[0.817] = 0.11202649809518382 + d[0.818] = 0.11202761850514262 + d[0.819] = 0.11202873891504725 + d[0.82] = 0.11202985932489767 + d[0.821] = 0.11203097973469381 + d[0.822] = 0.1120321001444356 + d[0.823] = 0.11203322055412297 + d[0.824] = 0.11203434096375588 + d[0.825] = 0.11203546137333421 + d[0.826] = 0.11203658178285794 + d[0.827] = 0.11203770219232699 + d[0.828] = 0.1120388226017413 + d[0.829] = 0.11203994301110079 + d[0.83] = 0.1120410634204054 + d[0.831] = 0.11204218382965506 + d[0.832] = 0.11204330423884971 + d[0.833] = 0.11204442464798928 + d[0.834] = 0.1120455450570737 + d[0.835] = 0.11204666546610292 + d[0.836] = 0.11204778587507686 + d[0.837] = 0.11204890628399544 + d[0.838] = 0.11205002669285863 + d[0.839] = 0.11205114710166633 + d[0.84] = 0.1120522675104185 + d[0.841] = 0.11205338791911504 + d[0.842] = 0.11205450832775592 + d[0.843] = 0.11205562873634103 + d[0.844] = 0.11205674914487036 + d[0.845] = 0.1120578695533438 + d[0.846] = 0.11205898996176131 + d[0.847] = 0.1120601103701228 + d[0.848] = 0.11206123077842822 + d[0.849] = 0.1120623511866775 + d[0.85] = 0.11206347159487057 + d[0.851] = 0.11206459200300738 + d[0.852] = 0.11206571241108783 + d[0.853] = 0.11206683281911188 + d[0.854] = 0.11206795322707946 + d[0.855] = 0.1120690736349905 + d[0.856] = 0.11207019404284493 + d[0.857] = 0.1120713144506427 + d[0.858] = 0.11207243485838371 + d[0.859] = 0.11207355526606792 + d[0.86] = 0.11207467567369528 + d[0.861] = 0.11207579608126568 + d[0.862] = 0.11207691648877909 + d[0.863] = 0.11207803689623543 + d[0.864] = 0.11207915730363462 + d[0.865] = 0.1120802777109766 + d[0.866] = 0.11208139811826133 + d[0.867] = 0.11208251852548873 + d[0.868] = 0.11208363893265871 + d[0.869] = 0.11208475933977122 + d[0.87] = 0.11208587974682621 + d[0.871] = 0.11208700015382358 + d[0.872] = 0.1120881205607633 + d[0.873] = 0.11208924096764528 + d[0.874] = 0.11209036137446945 + d[0.875] = 0.11209148178123576 + d[0.876] = 0.11209260218794415 + d[0.877] = 0.11209372259459452 + d[0.878] = 0.11209484300118683 + d[0.879] = 0.112095963407721 + d[0.88] = 0.11209708381419699 + d[0.881] = 0.1120982042206147 + d[0.882] = 0.11209932462697408 + d[0.883] = 0.11210044503327506 + d[0.884] = 0.11210156543951758 + d[0.885] = 0.11210268584570157 + d[0.886] = 0.11210380625182696 + d[0.887] = 0.11210492665789369 + d[0.888] = 0.11210604706390168 + d[0.889] = 0.11210716746985089 + d[0.89] = 0.11210828787574122 + d[0.891] = 0.11210940828157262 + d[0.892] = 0.11211052868734504 + d[0.893] = 0.11211164909305839 + d[0.894] = 0.11211276949871261 + d[0.895] = 0.11211388990430764 + d[0.896] = 0.1121150103098434 + d[0.897] = 0.11211613071531984 + d[0.898] = 0.11211725112073688 + d[0.899] = 0.11211837152609445 + d[0.9] = 0.11211949193139252 + d[0.901] = 0.11212061233663098 + d[0.902] = 0.11212173274180978 + d[0.903] = 0.11212285314692885 + d[0.904] = 0.11212397355198814 + d[0.905] = 0.11212509395698757 + d[0.906] = 0.11212621436192706 + d[0.907] = 0.11212733476680657 + d[0.908] = 0.11212845517162602 + d[0.909] = 0.11212957557638534 + d[0.91] = 0.11213069598108448 + d[0.911] = 0.11213181638572335 + d[0.912] = 0.11213293679030191 + d[0.913] = 0.11213405719482007 + d[0.914] = 0.11213517759927777 + d[0.915] = 0.11213629800367496 + d[0.916] = 0.11213741840801154 + d[0.917] = 0.11213853881228748 + d[0.918] = 0.11213965921650271 + d[0.919] = 0.11214077962065713 + d[0.92] = 0.1121419000247507 + d[0.921] = 0.11214302042878335 + d[0.922] = 0.11214414083275501 + d[0.923] = 0.11214526123666561 + d[0.924] = 0.1121463816405151 + d[0.925] = 0.1121475020443034 + d[0.926] = 0.11214862244803045 + d[0.927] = 0.11214974285169618 + d[0.928] = 0.11215086325530052 + d[0.929] = 0.11215198365884341 + d[0.93] = 0.11215310406232477 + d[0.931] = 0.11215422446574456 + d[0.932] = 0.1121553448691027 + d[0.933] = 0.1121564652723991 + d[0.934] = 0.11215758567563373 + d[0.935] = 0.11215870607880651 + d[0.936] = 0.11215982648191737 + d[0.937] = 0.11216094688496625 + d[0.938] = 0.11216206728795307 + d[0.939] = 0.11216318769087778 + d[0.94] = 0.1121643080937403 + d[0.941] = 0.11216542849654057 + d[0.942] = 0.11216654889927853 + d[0.943] = 0.11216766930195411 + d[0.944] = 0.11216878970456724 + d[0.945] = 0.11216991010711785 + d[0.946] = 0.11217103050960588 + d[0.947] = 0.11217215091203127 + d[0.948] = 0.11217327131439393 + d[0.949] = 0.11217439171669381 + d[0.95] = 0.11217551211893086 + d[0.951] = 0.11217663252110498 + d[0.952] = 0.11217775292321612 + d[0.953] = 0.11217887332526423 + d[0.954] = 0.11217999372724921 + d[0.955] = 0.11218111412917102 + d[0.956] = 0.11218223453102957 + d[0.957] = 0.11218335493282482 + d[0.958] = 0.1121844753345567 + d[0.959] = 0.11218559573622511 + d[0.96] = 0.11218671613783002 + d[0.961] = 0.11218783653937135 + d[0.962] = 0.11218895694084904 + d[0.963] = 0.11219007734226302 + d[0.964] = 0.11219119774361322 + d[0.965] = 0.11219231814489958 + d[0.966] = 0.11219343854612203 + d[0.967] = 0.11219455894728049 + d[0.968] = 0.11219567934837492 + d[0.969] = 0.11219679974940525 + d[0.97] = 0.11219792015037137 + d[0.971] = 0.11219904055127328 + d[0.972] = 0.11220016095211087 + d[0.973] = 0.11220128135288408 + d[0.974] = 0.11220240175359286 + d[0.975] = 0.11220352215423712 + d[0.976] = 0.11220464255481681 + d[0.977] = 0.11220576295533187 + d[0.978] = 0.1122068833557822 + d[0.979] = 0.11220800375616778 + d[0.98] = 0.11220912415648851 + d[0.981] = 0.11221024455674433 + d[0.982] = 0.11221136495693518 + d[0.983] = 0.11221248535706098 + d[0.984] = 0.11221360575712169 + d[0.985] = 0.11221472615711722 + d[0.986] = 0.11221584655704751 + d[0.987] = 0.1122169669569125 + d[0.988] = 0.11221808735671211 + d[0.989] = 0.11221920775644628 + d[0.99] = 0.11222032815611496 + d[0.991] = 0.11222144855571806 + d[0.992] = 0.11222256895525552 + d[0.993] = 0.11222368935472729 + d[0.994] = 0.11222480975413328 + d[0.995] = 0.11222593015347343 + d[0.996] = 0.11222705055274768 + d[0.997] = 0.11222817095195596 + d[0.998] = 0.1122292913510982 + d[0.999] = 0.11223041175017434 + d[1.0] = 0.11223153214918431 + d[0.0] = 0.1111111111111111 + d[0.05] = 0.11116713271273346 + d[0.1] = 0.1112231543061011 + d[0.15] = 0.11127917588295685 + d[0.2] = 0.1113351974350409 + d[0.25] = 0.11139121895409072 + d[0.3] = 0.11144724043184115 + d[0.35] = 0.11150326186002438 + d[0.4] = 0.11155928323036995 + d[0.45] = 0.1116153045346048 + d[0.5] = 0.11167132576445324 + d[0.55] = 0.11172734691163697 + d[0.6] = 0.11178336796787512 + d[0.65] = 0.1118393889248842 + d[0.7] = 0.11189540977437817 + d[0.75] = 0.11195143050806843 + d[0.8] = 0.1120074511176638 + d[0.85] = 0.11206347159487058 + d[0.9] = 0.11211949193139252 + d[0.95] = 0.11217551211893086 + d[1.0] = 0.11223153214918431 + d[1.05] = 0.11228755201384912 + d[1.1] = 0.11234357170461898 + d[1.15] = 0.11239959121318516 + d[1.2] = 0.11245561053123643 + d[1.25] = 0.11251162965045908 + d[1.3] = 0.11256764856253698 + d[1.35] = 0.11262366725915157 + d[1.4] = 0.11267968573198181 + d[1.45] = 0.1127357039727043 + d[1.5] = 0.11279172197299317 + d[1.55] = 0.1128477397245202 + d[1.6] = 0.11290375721895475 + d[1.65] = 0.11295977444796382 + d[1.7] = 0.11301579140321204 + d[1.75] = 0.11307180807636166 + d[1.8] = 0.11312782445907263 + d[1.85] = 0.11318384054300251 + d[1.9] = 0.11323985631980658 + d[1.95] = 0.11329587178113779 + d[2.0] = 0.11335188691864674 + d[2.05] = 0.11340790172398182 + d[2.1] = 0.11346391618878907 + d[2.15] = 0.11351993030471227 + d[2.2] = 0.11357594406339297 + d[2.25] = 0.11363195745647044 + d[2.3] = 0.11368797047558168 + d[2.35] = 0.11374398311236153 + d[2.4] = 0.11379999535844254 + d[2.45] = 0.11385600720545512 + d[2.5] = 0.11391201864502741 + d[2.55] = 0.1139680296687854 + d[2.6] = 0.1140240402683529 + d[2.65] = 0.11408005043535156 + d[2.7] = 0.11413606016140086 + d[2.75] = 0.11419206943811812 + d[2.8] = 0.11424807825711857 + d[2.85] = 0.11430408661001526 + d[2.9] = 0.11436009448841918 + d[2.95] = 0.11441610188393918 + d[3.0] = 0.11447210878818202 + d[3.05] = 0.11452811519275242 + d[3.1] = 0.11458412108925298 + d[3.15] = 0.11464012646928425 + d[3.2] = 0.11469613132444476 + d[3.25] = 0.11475213564633097 + d[3.3] = 0.11480813942653732 + d[3.35] = 0.11486414265665625 + d[3.4] = 0.11492014532827818 + d[3.45] = 0.11497614743299155 + d[3.5] = 0.11503214896238277 + d[3.55] = 0.11508814990803634 + d[3.6] = 0.11514415026153477 + d[3.65] = 0.1152001500144586 + d[3.7] = 0.11525614915838646 + d[3.75] = 0.11531214768489503 + d[3.8] = 0.1153681455855591 + d[3.85] = 0.1154241428519515 + d[3.9] = 0.11548013947564323 + d[3.95] = 0.11553613544820333 + d[4.0] = 0.11559213076119904 + d[4.05] = 0.11564812540619568 + d[4.1] = 0.11570411937475675 + d[4.15] = 0.11576011265844388 + d[4.2] = 0.11581610524881691 + d[4.25] = 0.11587209713743381 + d[4.3] = 0.11592808831585079 + d[4.35] = 0.11598407877562221 + d[4.4] = 0.1160400685083007 + d[4.45] = 0.11609605750543708 + d[4.5] = 0.1161520457585804 + d[4.55] = 0.11620803325927799 + d[4.6] = 0.11626401999907539 + d[4.65] = 0.11632000596951646 + d[4.7] = 0.1163759911621433 + d[4.75] = 0.11643197556849631 + d[4.8] = 0.1164879591801142 + d[4.85] = 0.11654394198853402 + d[4.9] = 0.11659992398529108 + d[4.95] = 0.11665590516191907 + d[5.0] = 0.11671188550995001 + d[5.05] = 0.1167678650209143 + d[5.1] = 0.11682384368634069 + d[5.15] = 0.1168798214977563 + d[5.2] = 0.11693579844668668 + d[5.25] = 0.11699177452465573 + d[5.3] = 0.11704774972318581 + d[5.35] = 0.11710372403379768 + d[5.4] = 0.11715969744801052 + d[5.45] = 0.11721566995734203 + d[5.5] = 0.11727164155330827 + d[5.55] = 0.11732761222742386 + d[5.6] = 0.11738358197120181 + d[5.65] = 0.11743955077615371 + d[5.7] = 0.11749551863378961 + d[5.75] = 0.11755148553561807 + d[5.8] = 0.1176074514731462 + d[5.85] = 0.11766341643787963 + d[5.9] = 0.11771938042132253 + d[5.95] = 0.11777534341497767 + d[6.0] = 0.11783130541034634 + d[6.05] = 0.11788726639892845 + d[6.1] = 0.11794322637222251 + d[6.15] = 0.1179991853217256 + d[6.2] = 0.11805514323893343 + d[6.25] = 0.11811110011534037 + d[6.3] = 0.1181670559424394 + d[6.35] = 0.11822301071172213 + d[6.4] = 0.11827896441467889 + d[6.45] = 0.11833491704279862 + d[6.5] = 0.11839086858756902 + d[6.55] = 0.11844681904047642 + d[6.6] = 0.1185027683930059 + d[6.65] = 0.11855871663664122 + d[6.7] = 0.11861466376286492 + d[6.75] = 0.11867060976315826 + d[6.8] = 0.11872655462900122 + d[6.85] = 0.11878249835187261 + d[6.9] = 0.11883844092325 + d[6.95] = 0.1188943823346097 + d[7.0] = 0.11895032257742685 + d[7.05] = 0.11900626164317546 + d[7.1] = 0.11906219952332826 + d[7.15] = 0.11911813620935689 + d[7.2] = 0.1191740716927318 + d[7.25] = 0.11923000596492232 + d[7.3] = 0.11928593901739665 + d[7.35] = 0.11934187084162183 + d[7.4] = 0.11939780142906385 + d[7.45] = 0.11945373077118757 + d[7.5] = 0.11950965885945677 + d[7.55] = 0.11956558568533418 + d[7.6] = 0.11962151124028142 + d[7.65] = 0.11967743551575911 + d[7.7] = 0.11973335850322683 + d[7.75] = 0.11978928019414309 + d[7.8] = 0.11984520057996542 + d[7.85] = 0.11990111965215035 + d[7.9] = 0.1199570374021534 + d[7.95] = 0.12001295382142911 + d[8.0] = 0.12006886890143109 + d[8.05] = 0.12012478263361195 + d[8.1] = 0.12018069500942337 + d[8.15] = 0.1202366060203161 + d[8.2] = 0.12029251565773998 + d[8.25] = 0.12034842391314392 + d[8.3] = 0.12040433077797592 + d[8.35] = 0.12046023624368314 + d[8.4] = 0.12051614030171184 + d[8.45] = 0.12057204294350742 + d[8.5] = 0.1206279441605144 + d[8.55] = 0.12068384394417651 + d[8.6] = 0.12073974228593665 + d[8.65] = 0.12079563917723683 + d[8.7] = 0.12085153460951836 + d[8.75] = 0.1209074285742217 + d[8.8] = 0.12096332106278652 + d[8.85] = 0.12101921206665177 + d[8.9] = 0.1210751015772556 + d[8.95] = 0.12113098958603541 + d[9.0] = 0.1211868760844279 + d[9.05] = 0.12124276106386904 + d[9.1] = 0.12129864451579409 + d[9.15] = 0.1213545264316376 + d[9.2] = 0.12141040680283344 + d[9.25] = 0.1214662856208148 + d[9.3] = 0.12152216287701423 + d[9.35] = 0.1215780385628636 + d[9.4] = 0.12163391266979418 + d[9.45] = 0.12168978518923657 + d[9.5] = 0.12174565611262078 + d[9.55] = 0.1218015254313762 + d[9.6] = 0.12185739313693167 + d[9.65] = 0.1219132592207154 + d[9.7] = 0.12196912367415505 + d[9.75] = 0.12202498648867774 + d[9.8] = 0.12208084765571003 + d[9.85] = 0.12213670716667797 + d[9.9] = 0.12219256501300706 + d[9.95] = 0.12224842118612231 + d[10.0] = 0.12230427567744821 + d[0.0] = 0.1111111111111111 + d[0.5] = 0.11167132576445324 + d[1.0] = 0.11223153214918431 + d[1.5] = 0.11279172197299317 + d[2.0] = 0.11335188691864674 + d[2.5] = 0.11391201864502741 + d[3.0] = 0.11447210878818202 + d[3.5] = 0.11503214896238277 + d[4.0] = 0.11559213076119904 + d[4.5] = 0.1161520457585804 + d[5.0] = 0.11671188550995001 + d[5.5] = 0.11727164155330827 + d[6.0] = 0.11783130541034634 + d[6.5] = 0.11839086858756902 + d[7.0] = 0.11895032257742685 + d[7.5] = 0.11950965885945677 + d[8.0] = 0.12006886890143109 + d[8.5] = 0.1206279441605144 + d[9.0] = 0.1211868760844279 + d[9.5] = 0.12174565611262078 + d[10.0] = 0.12230427567744821 + d[10.5] = 0.1228627262053556 + d[11.0] = 0.12342099911806849 + d[11.5] = 0.12397908583378783 + d[12.0] = 0.12453697776839014 + d[12.5] = 0.12509466633663197 + d[13.0] = 0.12565214295335841 + d[13.5] = 0.12620939903471512 + d[14.0] = 0.12676642599936316 + d[14.5] = 0.12732321526969664 + d[15.0] = 0.12787975827306233 + d[15.5] = 0.12843604644298073 + d[16.0] = 0.12899207122036854 + d[16.5] = 0.1295478240547616 + d[17.0] = 0.13010329640553783 + d[17.5] = 0.13065847974314027 + d[18.0] = 0.13121336555029892 + d[18.5] = 0.13176794532325134 + d[19.0] = 0.13232221057296167 + d[19.5] = 0.13287615282633716 + d[20.0] = 0.13342976362744205 + d[20.5] = 0.13398303453870805 + d[21.0] = 0.13453595714214145 + d[21.5] = 0.1350885230405255 + d[22.0] = 0.13564072385861853 + d[22.5] = 0.13619255124434676 + d[23.0] = 0.13674399686999134 + d[23.5] = 0.13729505243336942 + d[24.0] = 0.13784570965900864 + d[24.5] = 0.1383959602993143 + d[25.0] = 0.13894579613572952 + d[25.5] = 0.13949520897988688 + d[26.0] = 0.140044190674752 + d[26.5] = 0.1405927330957581 + d[27.0] = 0.14114082815193127 + d[27.5] = 0.14168846778700606 + d[28.0] = 0.14223564398053068 + d[28.5] = 0.14278234874896198 + d[29.0] = 0.14332857414674902 + d[29.5] = 0.14387431226740538 + d[30.0] = 0.1444195552445698 + d[30.5] = 0.1449642952530544 + d[31.0] = 0.14550852450988025 + d[31.5] = 0.14605223527530023 + d[32.0] = 0.14659541985380822 + d[32.5] = 0.14713807059513498 + d[33.0] = 0.14768017989522944 + d[33.5] = 0.14822174019722628 + d[34.0] = 0.14876274399239797 + d[34.5] = 0.1493031838210925 + d[35.0] = 0.14984305227365546 + d[35.5] = 0.15038234199133607 + d[36.0] = 0.15092104566717815 + d[36.5] = 0.15145915604689386 + d[37.0] = 0.15199666592972186 + d[37.5] = 0.15253356816926772 + d[38.0] = 0.1530698556743284 + d[38.5] = 0.15360552140969855 + d[39.0] = 0.1541405583969599 + d[39.5] = 0.15467495971525266 + d[40.0] = 0.15520871850202939 + d[40.5] = 0.15574182795379016 + d[41.0] = 0.15627428132680027 + d[41.5] = 0.15680607193778867 + d[42.0] = 0.1573371931646286 + d[42.5] = 0.15786763844699866 + d[43.0] = 0.15839740128702587 + d[43.5] = 0.15892647524990908 + d[44.0] = 0.15945485396452352 + d[44.5] = 0.15998253112400618 + d[45.0] = 0.1605095004863217 + d[45.5] = 0.16103575587480928 + d[46.0] = 0.16156129117870965 + d[46.5] = 0.16208610035367277 + d[47.0] = 0.16261017742224632 + d[47.5] = 0.16313351647434396 + d[48.0] = 0.16365611166769453 + d[48.5] = 0.1641779572282715 + d[49.0] = 0.16469904745070268 + d[49.5] = 0.16521937669866057 + d[50.0] = 0.16573893940523296 + d[50.5] = 0.1662577300732743 + d[51.0] = 0.16677574327573694 + d[51.5] = 0.16729297365598375 + d[52.0] = 0.1678094159280809 + d[52.5] = 0.1683250648770712 + d[53.0] = 0.1688399153592288 + d[53.5] = 0.16935396230229408 + d[54.0] = 0.16986720070569014 + d[54.5] = 0.17037962564071985 + d[55.0] = 0.17089123225074465 + d[55.5] = 0.1714020157513441 + d[56.0] = 0.17191197143045728 + d[56.5] = 0.17242109464850594 + d[57.0] = 0.17292938083849893 + d[57.5] = 0.17343682550611905 + d[58.0] = 0.17394342422979156 + d[58.5] = 0.1744491726607355 + d[59.0] = 0.17495406652299694 + d[59.5] = 0.17545810161346512 + d[60.0] = 0.17596127380187152 + d[60.5] = 0.17646357903077176 + d[61.0] = 0.17696501331551098 + d[61.5] = 0.17746557274417246 + d[62.0] = 0.17796525347751 + d[62.5] = 0.17846405174886443 + d[63.0] = 0.1789619638640638 + d[63.5] = 0.17945898620130843 + d[64.0] = 0.1799551152110404 + d[64.5] = 0.18045034741579755 + d[65.0] = 0.18094467941005318 + d[65.5] = 0.1814381078600409 + d[66.0] = 0.1819306295035645 + d[66.5] = 0.18242224114979488 + d[67.0] = 0.18291293967905195 + d[67.5] = 0.18340272204257357 + d[68.0] = 0.1838915852622711 + d[68.5] = 0.18437952643047165 + d[69.0] = 0.1848665427096477 + d[69.5] = 0.18535263133213417 + d[70.0] = 0.1858377895998333 + d[70.5] = 0.18632201488390754 + d[71.0] = 0.18680530462446052 + d[71.5] = 0.18728765633020708 + d[72.0] = 0.18776906757813167 + d[72.5] = 0.1882495360131364 + d[73.0] = 0.18872905934767797 + d[73.5] = 0.1892076353613948 + d[74.0] = 0.1896852619007239 + d[74.5] = 0.19016193687850813 + d[75.0] = 0.19063765827359397 + d[75.5] = 0.19111242413042007 + d[76.0] = 0.19158623255859697 + d[76.5] = 0.19205908173247854 + d[77.0] = 0.1925309698907243 + d[77.5] = 0.19300189533585455 + d[78.0] = 0.19347185643379752 + d[78.5] = 0.19394085161342833 + d[79.0] = 0.19440887936610188 + d[79.5] = 0.1948759382451779 + d[80.0] = 0.19534202686553961 + d[80.5] = 0.19580714390310625 + d[81.0] = 0.19627128809433877 + d[81.5] = 0.19673445823574054 + d[82.0] = 0.19719665318335153 + d[82.5] = 0.1976578718522379 + d[83.0] = 0.19811811321597592 + d[83.5] = 0.19857737630613143 + d[84.0] = 0.19903566021173427 + d[84.5] = 0.1994929640787488 + d[85.0] = 0.1999492871095401 + d[85.5] = 0.2004046285623361 + d[86.0] = 0.20085898775068653 + d[86.5] = 0.2013123640429179 + d[87.0] = 0.20176475686158607 + d[87.5] = 0.20221616568292472 + d[88.0] = 0.20266659003629256 + d[88.5] = 0.20311602950361668 + d[89.0] = 0.20356448371883468 + d[89.5] = 0.2040119523673338 + d[90.0] = 0.20445843518538923 + d[90.5] = 0.20490393195959958 + d[91.0] = 0.2053484425263221 + d[91.5] = 0.20579196677110567 + d[92.0] = 0.2062345046281234 + d[92.5] = 0.206676056079604 + d[93.0] = 0.20711662115526255 + d[93.5] = 0.20755619993173113 + d[94.0] = 0.2079947925319883 + d[94.5] = 0.20843239912478953 + d[95.0] = 0.20886901992409684 + d[95.5] = 0.20930465518850905 + d[96.0] = 0.2097393052206922 + d[96.5] = 0.21017297036681068 + d[97.0] = 0.21060565101595896 + d[97.5] = 0.21103734759959422 + d[98.0] = 0.21146806059096993 + d[98.5] = 0.2118977905045704 + d[99.0] = 0.2123265378955472 + d[99.5] = 0.21275430335915615 + d[100.0] = 0.21318108753019682 + d[0.0] = 0.1111111111111111 + d[5.0] = 0.11671188550995001 + d[10.0] = 0.12230427567744821 + d[15.0] = 0.12787975827306233 + d[20.0] = 0.13342976362744205 + d[25.0] = 0.13894579613572952 + d[30.0] = 0.1444195552445698 + d[35.0] = 0.14984305227365546 + d[40.0] = 0.15520871850202939 + d[45.0] = 0.1605095004863217 + d[50.0] = 0.16573893940523296 + d[55.0] = 0.17089123225074465 + d[60.0] = 0.17596127380187152 + d[65.0] = 0.18094467941005318 + d[70.0] = 0.1858377895998333 + d[75.0] = 0.19063765827359397 + d[80.0] = 0.19534202686553961 + d[85.0] = 0.1999492871095401 + d[90.0] = 0.20445843518538923 + d[95.0] = 0.20886901992409684 + d[100.0] = 0.21318108753019682 + d[105.0] = 0.21739512496493815 + d[110.0] = 0.22151200377214766 + d[115.0] = 0.22553292575473766 + d[120.0] = 0.22945937155164767 + d[125.0] = 0.23329305284090643 + d[130.0] = 0.23703586861502243 + d[135.0] = 0.24068986574423434 + d[140.0] = 0.24425720386073854 + d[145.0] = 0.24774012445922144 + d[150.0] = 0.2511409240104117 + d[155.0] = 0.2544619308187165 + d[160.0] = 0.2577054853160472 + d[165.0] = 0.26087392346581834 + d[170.0] = 0.2639695629486443 + d[175.0] = 0.2669946918100686 + d[180.0] = 0.26995155926715125 + d[185.0] = 0.27284236839207493 + d[190.0] = 0.27566927041490735 + d[195.0] = 0.27843436041268127 + d[200.0] = 0.28113967417683144 + d[205.0] = 0.28378718607498005 + d[210.0] = 0.28637880774556973 + d[215.0] = 0.28891638748460086 + d[220.0] = 0.29140171020260164 + d[225.0] = 0.2938364978469128 + d[230.0] = 0.29622241019944745 + d[235.0] = 0.29856104597339445 + d[240.0] = 0.30085394414398847 + d[245.0] = 0.30310258545862373 + d[250.0] = 0.30530839408038085 + d[255.0] = 0.30747273932661723 + d[260.0] = 0.3095969374707808 + d[265.0] = 0.31168225358117074 + d[270.0] = 0.3137299033751107 + d[275.0] = 0.31574105507102534 + d[280.0] = 0.3177168312243166 + d[285.0] = 0.3196583105358078 + d[290.0] = 0.3215665296239374 + d[295.0] = 0.3234424847539042 + d[300.0] = 0.3252871335186523 + d[305.0] = 0.3271013964679821 + d[310.0] = 0.3288861586832347 + d[315.0] = 0.3306422712959446 + d[320.0] = 0.3323705529496393 + d[325.0] = 0.3340717912045914 + d[330.0] = 0.3357467438858426 + d[335.0] = 0.33739614037522075 + d[340.0] = 0.3390206828483918 + d[345.0] = 0.34062104745823624 + d[350.0] = 0.34219788546602387 + d[355.0] = 0.3437518243220012 + d[360.0] = 0.34528346869709853 + d[365.0] = 0.34679340146752796 + d[370.0] = 0.34828218465407806 + d[375.0] = 0.3497503603179227 + d[380.0] = 0.3511984514147555 + d[385.0] = 0.3526269626090431 + d[390.0] = 0.35403638105015733 + d[395.0] = 0.35542717711210553 + d[400.0] = 0.35679980509853465 + d[405.0] = 0.35815470391462895 + d[410.0] = 0.3594922977074693 + d[415.0] = 0.3608129964763616 + d[420.0] = 0.3621171966545856 + d[425.0] = 0.36340528166395386 + d[430.0] = 0.3646776224435125 + d[435.0] = 0.36593457795365575 + d[440.0] = 0.3671764956568695 + d[445.0] = 0.3684037119762611 + d[450.0] = 0.3696165527329798 + d[455.0] = 0.37081533356357654 + d[460.0] = 0.37200036031830236 + d[465.0] = 0.3731719294412941 + d[470.0] = 0.37433032833354907 + d[475.0] = 0.375475835699544 + d[480.0] = 0.3766087218783113 + d[485.0] = 0.3777292491597429 + d[490.0] = 0.3788376720868525 + d[495.0] = 0.3799342377446899 + d[500.0] = 0.3810191860365646 + d[505.0] = 0.38209274994820136 + d[510.0] = 0.3831551558004185 + d[515.0] = 0.3842066234908894 + d[520.0] = 0.3852473667255173 + d[525.0] = 0.38627759323992633 + d[530.0] = 0.3872975050115455 + d[535.0] = 0.3883072984627387 + d[540.0] = 0.3893071646554072 + d[545.0] = 0.3902972894774721 + d[550.0] = 0.3912778538216218 + d[555.0] = 0.3922490337566891 + d[560.0] = 0.3932110006920043 + d[565.0] = 0.39416392153505364 + d[570.0] = 0.3951079588427527 + d[575.0] = 0.396043270966633 + d[580.0] = 0.39697001219222017 + d[585.0] = 0.39788833287287123 + d[590.0] = 0.39879837955832265 + d[595.0] = 0.39970029511819083 + d[600.0] = 0.40059421886065105 + d[605.0] = 0.401480286646513 + d[610.0] = 0.40235863099889707 + d[615.0] = 0.40322938120870855 + d[620.0] = 0.40409266343609385 + d[625.0] = 0.4049486008080566 + d[630.0] = 0.4057973135124008 + d[635.0] = 0.40663891888816106 + d[640.0] = 0.4074735315126723 + d[645.0] = 0.4083012632854224 + d[650.0] = 0.4091222235088266 + d[655.0] = 0.40993651896605376 + d[660.0] = 0.4107442539960303 + d[665.0] = 0.41154553056573895 + d[670.0] = 0.4123404483399274 + d[675.0] = 0.41312910474833353 + d[680.0] = 0.41391159505053016 + d[685.0] = 0.41468801239848757 + d[690.0] = 0.41545844789694764 + d[695.0] = 0.4162229906616972 + d[700.0] = 0.41698172787582805 + d[705.0] = 0.41773474484406237 + d[710.0] = 0.41848212504522225 + d[715.0] = 0.41922395018291797 + d[720.0] = 0.41996030023452346 + d[725.0] = 0.42069125349850844 + d[730.0] = 0.42141688664019084 + d[735.0] = 0.422137274735971 + d[740.0] = 0.4228524913161069 + d[745.0] = 0.4235626084060859 + d[750.0] = 0.42426769656664776 + d[755.0] = 0.4249678249325099 + d[760.0] = 0.42566306124984404 + d[765.0] = 0.4263534719125516 + d[770.0] = 0.4270391219973825 + d[775.0] = 0.42772007529794154 + d[780.0] = 0.42839639435762206 + d[785.0] = 0.429068140501508 + d[790.0] = 0.4297353738672815 + d[795.0] = 0.4303981534351728 + d[800.0] = 0.43105653705698627 + d[805.0] = 0.4317105814842376 + d[810.0] = 0.43236034239543264 + d[815.0] = 0.4330058744225192 + d[820.0] = 0.43364723117654164 + d[825.0] = 0.43428446527252546 + d[830.0] = 0.43491762835362047 + d[835.0] = 0.4355467711145265 + d[840.0] = 0.4361719433242287 + d[845.0] = 0.43679319384806586 + d[850.0] = 0.4374105706691532 + d[855.0] = 0.4380241209091837 + d[860.0] = 0.4386338908486291 + d[865.0] = 0.43923992594635886 + d[870.0] = 0.4398422708587002 + d[875.0] = 0.4404409694579541 + d[880.0] = 0.4410360648503892 + d[885.0] = 0.4416275993937283 + d[890.0] = 0.4422156147141453 + d[895.0] = 0.44280015172278914 + d[900.0] = 0.4433812506318493 + d[905.0] = 0.44395895097017857 + d[910.0] = 0.4445332915984872 + d[915.0] = 0.44510431072412227 + d[920.0] = 0.4456720459154456 + d[925.0] = 0.44623653411582337 + d[930.0] = 0.44679781165723914 + d[935.0] = 0.4473559142735433 + d[940.0] = 0.4479108771133491 + d[945.0] = 0.4484627347525873 + d[950.0] = 0.44901152120673016 + d[955.0] = 0.4495572699426941 + d[960.0] = 0.4501000138904324 + d[965.0] = 0.450639785454226 + d[970.0] = 0.4511766165236827 + d[975.0] = 0.45171053848445325 + d[980.0] = 0.45224158222867344 + d[985.0] = 0.45276977816513914 + d[990.0] = 0.45329515622922445 + d[995.0] = 0.45381774589254825 + d[1000.0] = 0.45433757617239867 + d[0.0] = 0.1111111111111111 + d[50.0] = 0.16573893940523296 + d[100.0] = 0.21318108753019682 + d[150.0] = 0.2511409240104117 + d[200.0] = 0.28113967417683144 + d[250.0] = 0.30530839408038085 + d[300.0] = 0.3252871335186523 + d[350.0] = 0.34219788546602387 + d[400.0] = 0.35679980509853465 + d[450.0] = 0.3696165527329798 + d[500.0] = 0.3810191860365646 + d[550.0] = 0.3912778538216218 + d[600.0] = 0.40059421886065105 + d[650.0] = 0.4091222235088266 + d[700.0] = 0.41698172787582805 + d[750.0] = 0.42426769656664776 + d[800.0] = 0.43105653705698627 + d[850.0] = 0.4374105706691532 + d[900.0] = 0.4433812506318493 + d[950.0] = 0.44901152120673016 + d[1000.0] = 0.45433757617239867 + d[1050.0] = 0.4593901895677716 + d[1100.0] = 0.464195736700962 + d[1150.0] = 0.46877698741886425 + d[1200.0] = 0.473153729560641 + d[1250.0] = 0.477343264142555 + d[1300.0] = 0.48136080249859864 + d[1350.0] = 0.48521978765285556 + d[1400.0] = 0.4889321565409323 + d[1450.0] = 0.4925085556164441 + d[1500.0] = 0.49595851939878344 + d[1550.0] = 0.49929061931810104 + d[1600.0] = 0.5025125885713728 + d[1650.0] = 0.5056314274657838 + d[1700.0] = 0.5086534927841142 + d[1750.0] = 0.5115845739842417 + d[1800.0] = 0.5144299584858012 + d[1850.0] = 0.517194487861094 + d[1900.0] = 0.5198826064049333 + d[1950.0] = 0.5224984032873038 + d[2000.0] = 0.5250456492771423 + d[2050.0] = 0.5275278288528761 + d[2100.0] = 0.5299481683762453 + d[2150.0] = 0.5323096608932256 + d[2200.0] = 0.5346150880340785 + d[2250.0] = 0.536867039409415 + d[2300.0] = 0.5390679298373589 + d[2350.0] = 0.5412200146858311 + d[2400.0] = 0.5433254035715986 + d[2450.0] = 0.5453860726224161 + d[2500.0] = 0.5474038754790412 + d[2550.0] = 0.5493805531890869 + d[2600.0] = 0.5513177431237496 + d[2650.0] = 0.5532169870307634 + d[2700.0] = 0.5550797383218957 + d[2750.0] = 0.5569073686805172 + d[2800.0] = 0.5587011740638474 + d[2850.0] = 0.5604623801651112 + d[2900.0] = 0.5621921473928014 + d[2950.0] = 0.5638915754173054 + d[3000.0] = 0.5655617073291641 + d[3050.0] = 0.5672035334480475 + d[3100.0] = 0.5688179948170153 + d[3150.0] = 0.5704059864127202 + d[3200.0] = 0.5719683600987793 + d[3250.0] = 0.5735059273465483 + d[3300.0] = 0.5750194617449148 + d[3350.0] = 0.5765097013184136 + d[3400.0] = 0.5779773506709466 + d[3450.0] = 0.5794230829705975 + d[3500.0] = 0.5808475417894534 + d[3550.0] = 0.5822513428109444 + d[3600.0] = 0.5836350754159736 + d[3650.0] = 0.5849993041580077 + d[3700.0] = 0.5863445701363166 + d[3750.0] = 0.5876713922756764 + d[3800.0] = 0.5889802685200721 + d[3850.0] = 0.5902716769472341 + d[3900.0] = 0.5915460768102202 + d[3950.0] = 0.5928039095116956 + d[4000.0] = 0.5940455995160553 + d[4050.0] = 0.595271555204084 + d[4100.0] = 0.5964821696744398 + d[4150.0] = 0.5976778214958777 + d[4200.0] = 0.5988588754138018 + d[4250.0] = 0.6000256830144273 + d[4300.0] = 0.601178583349567 + d[4350.0] = 0.6023179035248085 + d[4400.0] = 0.6034439592536236 + d[4450.0] = 0.6045570553797486 + d[4500.0] = 0.6056574863699902 + d[4550.0] = 0.6067455367794402 + d[4600.0] = 0.6078214816909334 + d[4650.0] = 0.608885587130437 + d[4700.0] = 0.6099381104599364 + d[4750.0] = 0.6109793007492648 + d[4800.0] = 0.6120093991282118 + d[4850.0] = 0.6130286391201566 + d[4900.0] = 0.6140372469583716 + d[4950.0] = 0.6150354418860688 + d[5000.0] = 0.6160234364411775 + d[5050.0] = 0.6170014367267774 + d[5100.0] = 0.6179696426680452 + d[5150.0] = 0.6189282482565114 + d[5200.0] = 0.6198774417823738 + d[5250.0] = 0.6208174060555591 + d[5300.0] = 0.6217483186161822 + d[5350.0] = 0.6226703519350038 + d[5400.0] = 0.6235836736044555 + d[5450.0] = 0.6244884465207555 + d[5500.0] = 0.6253848290576106 + d[5550.0] = 0.6262729752319671 + d[5600.0] = 0.6271530348622407 + d[5650.0] = 0.6280251537194343 + d[5700.0] = 0.6288894736715197 + d[5750.0] = 0.6297461328214442 + d[5800.0] = 0.6305952656390936 + d[5850.0] = 0.6314370030875278 + d[5900.0] = 0.6322714727437847 + d[5950.0] = 0.6330987989145286 + d[6000.0] = 0.6339191027468073 + d[6050.0] = 0.6347325023341621 + d[6100.0] = 0.6355391128183223 + d[6150.0] = 0.6363390464867055 + d[6200.0] = 0.637132412865925 + d[6250.0] = 0.6379193188115039 + d[6300.0] = 0.6386998685939743 + d[6350.0] = 0.6394741639815387 + d[6400.0] = 0.6402423043194542 + d[6450.0] = 0.6410043866062954 + d[6500.0] = 0.6417605055672425 + d[6550.0] = 0.6425107537245308 + d[6600.0] = 0.6432552214651954 + d[6650.0] = 0.643993997106231 + d[6700.0] = 0.6447271669572879 + d[6750.0] = 0.6454548153810126 + d[6800.0] = 0.6461770248511389 + d[6850.0] = 0.646893876008431 + d[6900.0] = 0.6476054477145695 + d[6950.0] = 0.6483118171040749 + d[7000.0] = 0.6490130596343501 + d[7050.0] = 0.6497092491339247 + d[7100.0] = 0.6504004578489777 + d[7150.0] = 0.6510867564882125 + d[7200.0] = 0.6517682142661515 + d[7250.0] = 0.6524448989449202 + d[7300.0] = 0.6531168768745792 + d[7350.0] = 0.6537842130320687 + d[7400.0] = 0.654446971058818 + d[7450.0] = 0.655105213297079 + d[7500.0] = 0.6557590008250314 + d[7550.0] = 0.6564083934907099 + d[7600.0] = 0.6570534499448044 + d[7650.0] = 0.6576942276723713 + d[7700.0] = 0.6583307830235036 + d[7750.0] = 0.658963171243 + d[7800.0] = 0.6595914464990704 + d[7850.0] = 0.6602156619111158 + d[7900.0] = 0.6608358695766186 + d[7950.0] = 0.6614521205971768 + d[8000.0] = 0.6620644651037154 + d[8050.0] = 0.6626729522809037 + d[8100.0] = 0.6632776303908121 + d[8150.0] = 0.6638785467958321 + d[8200.0] = 0.6644757479808916 + d[8250.0] = 0.6650692795749871 + d[8300.0] = 0.6656591863720605 + d[8350.0] = 0.666245512351244 + d[8400.0] = 0.666828300696494 + d[8450.0] = 0.6674075938156389 + d[8500.0] = 0.6679834333588589 + d[8550.0] = 0.6685558602366205 + d[8600.0] = 0.669124914637082 + d[8650.0] = 0.669690636042992 + d[8700.0] = 0.6702530632480955 + d[8750.0] = 0.6708122343730671 + d[8800.0] = 0.6713681868809847 + d[8850.0] = 0.6719209575923627 + d[8900.0] = 0.6724705826997583 + d[8950.0] = 0.6730170977819644 + d[9000.0] = 0.6735605378178038 + d[9050.0] = 0.6741009371995391 + d[9100.0] = 0.6746383297459096 + d[9150.0] = 0.6751727487148083 + d[9200.0] = 0.6757042268156099 + d[9250.0] = 0.6762327962211638 + d[9300.0] = 0.6767584885794589 + d[9350.0] = 0.6772813350249753 + d[9400.0] = 0.6778013661897295 + d[9450.0] = 0.6783186122140251 + d[9500.0] = 0.6788331027569169 + d[9550.0] = 0.6793448670063986 + d[9600.0] = 0.6798539336893229 + d[9650.0] = 0.6803603310810606 + d[9700.0] = 0.6808640870149099 + d[9750.0] = 0.6813652288912597 + d[9800.0] = 0.6818637836865197 + d[9850.0] = 0.6823597779618185 + d[9900.0] = 0.6828532378714819 + d[9950.0] = 0.6833441891712954 + d[10000.0] = 0.6838326572265573 + d[0.0] = 0.1111111111111111 + d[500.0] = 0.3810191860365646 + d[1000.0] = 0.45433757617239867 + d[1500.0] = 0.49595851939878344 + d[2000.0] = 0.5250456492771423 + d[2500.0] = 0.5474038754790412 + d[3000.0] = 0.5655617073291641 + d[3500.0] = 0.5808475417894534 + d[4000.0] = 0.5940455995160553 + d[4500.0] = 0.6056574863699902 + d[5000.0] = 0.6160234364411775 + d[5500.0] = 0.6253848290576106 + d[6000.0] = 0.6339191027468073 + d[6500.0] = 0.6417605055672425 + d[7000.0] = 0.6490130596343501 + d[7500.0] = 0.6557590008250314 + d[8000.0] = 0.6620644651037154 + d[8500.0] = 0.6679834333588589 + d[9000.0] = 0.6735605378178038 + d[9500.0] = 0.6788331027569169 + d[10000.0] = 0.6838326572265573 + d[10500.0] = 0.6885860756450265 + d[11000.0] = 0.6931164509595955 + d[11500.0] = 0.6974437722467081 + d[12000.0] = 0.701585457055321 + d[12500.0] = 0.7055567743220574 + d[13000.0] = 0.709371183783936 + d[13500.0] = 0.713040610920793 + d[14000.0] = 0.7165756715840447 + d[14500.0] = 0.719985856969919 + d[15000.0] = 0.7232796870511483 + d[15500.0] = 0.726464838708131 + d[16000.0] = 0.729548253405909 + d[16500.0] = 0.7325362282138048 + d[17000.0] = 0.735434493167005 + d[17500.0] = 0.738248277357696 + d[18000.0] = 0.7409823656702158 + d[18500.0] = 0.7436411477057375 + d[19000.0] = 0.746228660152137 + d[19500.0] = 0.7487486236253403 + d[20000.0] = 0.7512044748257517 + d[20500.0] = 0.7535993947069092 + d[21000.0] = 0.7559363332354201 + d[21500.0] = 0.7582180312254542 + d[22000.0] = 0.760447039652978 + d[22500.0] = 0.7626257367909274 + d[23000.0] = 0.764756343453809 + d[23500.0] = 0.7668409365966299 + d[24000.0] = 0.7688814614768238 + d[24500.0] = 0.7708797425576164 + d[25000.0] = 0.7728374933059419 + d[25500.0] = 0.7747563250167283 + d[26000.0] = 0.7766377547773843 + d[26500.0] = 0.7784832126710939 + d[27000.0] = 0.780294048304578 + d[27500.0] = 0.7820715367349441 + d[28000.0] = 0.7838168838608007 + d[28500.0] = 0.7855312313347159 + d[29000.0] = 0.7872156610471243 + d[29500.0] = 0.7888711992257775 + d[30000.0] = 0.7904988201896223 + d[30500.0] = 0.7920994497914883 + d[31000.0] = 0.7936739685800316 + d[31500.0] = 0.7952232147079672 + d[32000.0] = 0.7967479866106344 + d[32500.0] = 0.7982490454763177 + d[33000.0] = 0.7997271175274556 + d[33500.0] = 0.8011828961298457 + d[34000.0] = 0.8026170437451796 + d[34500.0] = 0.8040301937406652 + d[35000.0] = 0.8054229520681092 + d[35500.0] = 0.806795898823598 + d[36000.0] = 0.8081495896978228 + d[36500.0] = 0.8094845573261226 + d[37000.0] = 0.8108013125464522 + d[37500.0] = 0.8121003455727082 + d[38000.0] = 0.8133821270901592 + d[38500.0] = 0.8146471092790993 + d[39000.0] = 0.8158957267723016 + d[39500.0] = 0.8171283975513374 + d[40000.0] = 0.8183455237863915 + d[40500.0] = 0.8195474926237907 + d[41000.0] = 0.8207346769251058 + d[41500.0] = 0.8219074359613565 + d[42000.0] = 0.8230661160655529 + d[42500.0] = 0.8242110512465376 + d[43000.0] = 0.8253425637668511 + d[43500.0] = 0.8264609646871217 + d[44000.0] = 0.8275665543792792 + d[44500.0] = 0.8286596230107105 + d[45000.0] = 0.8297404510013116 + d[45500.0] = 0.8308093094552325 + d[46000.0] = 0.8318664605689822 + d[46500.0] = 0.8329121580174276 + d[47000.0] = 0.8339466473191092 + d[47500.0] = 0.8349701661821874 + d[48000.0] = 0.8359829448322424 + d[48500.0] = 0.8369852063230531 + d[49000.0] = 0.8379771668314108 + d[49500.0] = 0.838959035936935 + d[50000.0] = 0.8399310168878039 + d[50500.0] = 0.8408933068532376 + d[51000.0] = 0.8418460971635213 + d[51500.0] = 0.8427895735382964 + d[52000.0] = 0.8437239163038049 + d[52500.0] = 0.8446493005997184 + d[53000.0] = 0.8455658965761477 + d[53500.0] = 0.8464738695813859 + d[54000.0] = 0.8473733803409044 + d[54500.0] = 0.8482645851280854 + d[55000.0] = 0.8491476359271434 + d[55500.0] = 0.8500226805886641 + d[56000.0] = 0.8508898629781545 + d[56500.0] = 0.8517493231179798 + d[57000.0] = 0.8526011973230383 + d[57500.0] = 0.8534456183304996 + d[58000.0] = 0.8542827154239188 + d[58500.0] = 0.8551126145520132 + d[59000.0] = 0.855935438442379 + d[59500.0] = 0.8567513067103991 + d[60000.0] = 0.8575603359635887 + d[60500.0] = 0.8583626399016039 + d[61000.0] = 0.8591583294121269 + d[61500.0] = 0.8599475126628329 + d[62000.0] = 0.8607302951896276 + d[62500.0] = 0.8615067799813343 + d[63000.0] = 0.8622770675610028 + d[63500.0] = 0.8630412560639996 + d[64000.0] = 0.8637994413130311 + d[64500.0] = 0.8645517168902421 + d[65000.0] = 0.8652981742065279 + d[65500.0] = 0.866038902568186 + d[66000.0] = 0.8667739892410298 + d[66500.0] = 0.8675035195120795 + d[67000.0] = 0.8682275767489392 + d[67500.0] = 0.8689462424569632 + d[68000.0] = 0.8696595963343099 + d[68500.0] = 0.8703677163249769 + d[69000.0] = 0.8710706786699032 + d[69500.0] = 0.8717685579562257 + d[70000.0] = 0.8724614271647665 + d[70500.0] = 0.8731493577158288 + d[71000.0] = 0.8738324195133719 + d[71500.0] = 0.8745106809876336 + d[72000.0] = 0.875184209136267 + d[72500.0] = 0.8758530695640501 + d[73000.0] = 0.8765173265212302 + d[73500.0] = 0.8771770429405572 + d[74000.0] = 0.8778322804730609 + d[74500.0] = 0.8784830995226207 + d[75000.0] = 0.8791295592793783 + d[75500.0] = 0.879771717752039 + d[76000.0] = 0.8804096317991063 + d[76500.0] = 0.8810433571590881 + d[77000.0] = 0.8816729484797226 + d[77500.0] = 0.882298459346252 + d[78000.0] = 0.8829199423087901 + d[78500.0] = 0.883537448908812 + d[79000.0] = 0.8841510297048024 + d[79500.0] = 0.8847607342970943 + d[80000.0] = 0.8853666113519277 + d[80500.0] = 0.8859687086247579 + d[81000.0] = 0.8865670729828408 + d[81500.0] = 0.8871617504271239 + d[82000.0] = 0.8877527861134652 + d[82500.0] = 0.8883402243732085 + d[83000.0] = 0.8889241087331331 + d[83500.0] = 0.8895044819348081 + d[84000.0] = 0.8900813859533643 + d[84500.0] = 0.8906548620157105 + d[85000.0] = 0.8912249506182115 + d[85500.0] = 0.8917916915438465 + d[86000.0] = 0.8923551238788681 + d[86500.0] = 0.8929152860289755 + d[87000.0] = 0.8934722157350237 + d[87500.0] = 0.8940259500882802 + d[88000.0] = 0.8945765255452472 + d[88500.0] = 0.8951239779420644 + d[89000.0] = 0.8956683425085026 + d[89500.0] = 0.8962096538815694 + d[90000.0] = 0.8967479461187314 + d[90500.0] = 0.8972832527107721 + d[91000.0] = 0.8978156065942943 + d[91500.0] = 0.8983450401638793 + d[92000.0] = 0.8988715852839164 + d[92500.0] = 0.8993952733001083 + d[93000.0] = 0.8999161350506685 + d[93500.0] = 0.9004342008772177 + d[94000.0] = 0.9009495006353888 + d[94500.0] = 0.90146206370515 + d[95000.0] = 0.9019719190008572 + d[95500.0] = 0.9024790949810391 + d[96000.0] = 0.9029836196579295 + d[96500.0] = 0.9034855206067507 + d[97000.0] = 0.9039848249747557 + d[97500.0] = 0.9044815594900398 + d[98000.0] = 0.9049757504701247 + d[98500.0] = 0.9054674238303245 + d[99000.0] = 0.9059566050919012 + d[99500.0] = 0.9064433193900118 + d[100000.0] = 0.9069275914814589 + d[0.00025379627379329417] = 0.11111139547259297 + d[4.713547159428973] = 0.11639115983372282 + d[1.389981369572302] = 0.11266846118278132 + d[1.679568253545624] = 0.1129929009522883 + d[1.8345743410422193] = 0.11316655887523717 + d[1.7744184670497338] = 0.11309916479707334 + d[1.0973675306736648] = 0.11234062230673775 + d[0.11436776472941645] = 0.11123925240487532 + d[0.8697144657747741] = 0.1120855598322717 + d[0.15610418369813628] = 0.11128601520134947 + d[0.643633465726553] = 0.111832255743828 + d[0.3260266792251372] = 0.11147640147337082 + d[0.9559481561869934] = 0.11218217644512668 + d[2.784238038596791] = 0.11423042213016256 + d[1.5729354610935244] = 0.11287343549822376 + d[1.732434289781432] = 0.11305212865606885 + d[0.36422016700222326] = 0.11151919453111041 + d[1.3154762792316592] = 0.11258498780576945 + d[2.0408634559470453] = 0.1133976661144319 + d[1.4929262267780572] = 0.11278379681530022 + d[1.747687533911083] = 0.11306921734956173 + d[2.0325969982782772] = 0.11338840524711741 + d[0.8157229324781325] = 0.11202506725593565 + d[1.975195705723162] = 0.11332409864055071 + d[0.5500404258454007] = 0.111727392205646 + d[0.2193760715565949] = 0.11135690697865118 + d[1.3107660461820108] = 0.11257971057852 + d[0.4014773991833288] = 0.11156093854794104 + d[1.2695745114346573] = 0.11253356053229273 + d[0.3583816906259165] = 0.11151265294017765 + d[0.4349085987453747] = 0.1115983957424437 + d[1.4615739528187714] = 0.1127486709882414 + d[3.544704233181] = 0.11508221857693064 + d[0.32636369146994115] = 0.11147677907150985 + d[0.12792613216730953] = 0.11125444362785568 + d[1.1708768520364945] = 0.11242298137711222 + d[1.8416142598747096] = 0.11317444583775765 + d[0.6382605683890366] = 0.11182623585036425 + d[1.0591312466249143] = 0.11229778261931789 + d[0.5167209742162112] = 0.11169006033721543 + d[0.09147486824491691] = 0.11121360247774911 + d[0.37802495003352343] = 0.1115346617897731 + d[0.01608798118697341] = 0.1111291366009672 + d[0.52277581475982] = 0.11169684432062049 + d[0.7989510573385972] = 0.11200627587084791 + d[1.4136277070133167] = 0.11269495375878105 + d[1.1757756536194648] = 0.11242846992826278 + d[1.5423915637173038] = 0.1128392155910341 + d[0.986842697931896] = 0.11221679071570097 + d[1.860327442160904] = 0.11319541056234529 + d[1.60007875296191] = 0.11290384544961968 + d[1.4739420201981592] = 0.1127625276851044 + d[2.3279021733920837] = 0.11371922800933647 + d[3.699426703038229] = 0.11525550707908791 + d[1.5512166870705295] = 0.1128491028428299 + d[0.3258287512648723] = 0.11147617970923317 + d[1.3732272406946313] = 0.11264969037852474 + d[0.3167655295537861] = 0.11146602501597205 + d[0.35635063159073255] = 0.11151037728508864 + d[0.312154352204836] = 0.1114608585200996 + d[1.5480096157168393] = 0.11284550979233408 + d[1.5236632431476091] = 0.11281823323800869 + d[0.9299226929185243] = 0.11215301744720375 + d[0.47766888955633857] = 0.1116463054487565 + d[1.9476112965334362] = 0.1132931957019038 + d[2.54430545557679] = 0.11396165054477346 + d[0.06932214056004282] = 0.11118878185619335 + d[1.5407538217650338] = 0.11283738074134873 + d[0.9884603550744485] = 0.11221860313842329 + d[0.1673911257144156] = 0.11129866144328768 + d[0.8915288793422533] = 0.11211000084104795 + d[2.1675076527064254] = 0.11353954373446012 + d[0.0687758699419001] = 0.11118816979716536 + d[1.4738151119752771] = 0.11276238550219228 + d[0.9932074563050762] = 0.11222392178865367 + d[1.43203009304618] = 0.1127155711484776 + d[1.766363627715799] = 0.11309014073339352 + d[0.637988615569637] = 0.11182593114936742 + d[3.015802867689485] = 0.11448981007860981 + d[1.157918107308376] = 0.11240846256552875 + d[2.709550001513826] = 0.11414675796992195 + d[0.16543217619972217] = 0.11129646657523913 + d[0.8003225360037904] = 0.11200781249051393 + d[3.7503087783015117] = 0.11531249350555736 + d[0.43347843250263884] = 0.11159679334724348 + d[0.10480304677937469] = 0.11122853579203483 + d[1.526582821421389] = 0.11282150420219864 + d[1.643845847473721] = 0.11295287969114097 + d[0.055616152651607464] = 0.11117342522970036 + d[1.3212601007996754] = 0.11259146785208404 + d[0.7154303027592896] = 0.11191269812475114 + d[2.4425690682807044] = 0.1138476828268168 + d[0.7335615291296645] = 0.11193301261737776 + d[0.45373391621577785] = 0.11161948810884853 + d[0.7317127565334298] = 0.11193094122610067 + d[0.12559752297025484] = 0.1112518345806918 + d[1.7169755764056776] = 0.11303480974155976 + d[1.6937409369093346] = 0.11300877914534631 + d[1.1689841552240714] = 0.1124208608246594 + d[1.603233926749343] = 0.11290738033937903 + d[1.0463310372590262] = 0.11228344132373584 + d[1.1194445551919725] = 0.11236535721524979 + d[0.8642672601983308] = 0.11207945674392865 + d[0.23066570431408095] = 0.11136955622625326 + d[1.830910108247589] = 0.11316245375922174 + d[1.0041255129271818] = 0.11223615436908255 + d[0.2472238679491291] = 0.11138810849240588 + d[0.020183743233433638] = 0.11113372562402936 + d[0.5466285541585991] = 0.11172356946912969 + d[1.3816028090528456] = 0.11265907410770555 + d[1.2385515288223439] = 0.11249880300300687 + d[0.5654258621873276] = 0.11174463038358558 + d[1.59548708519441] = 0.11289870118612755 + d[2.3693960593174967] = 0.11376571149615448 + d[1.7211130205089145] = 0.11303944506148515 + d[0.11313662545332503] = 0.11123787299748615 + d[0.13692441036319347] = 0.11126452558201796 + d[2.9553507514850157] = 0.11442209548808206 + d[1.8353075009768156] = 0.11316738024932527 + d[1.0263025913343906] = 0.11226100152249109 + d[0.9555440842193876] = 0.11218172372214948 + d[2.564947341070919] = 0.11398477390432236 + d[1.3140151236638808] = 0.11258335076383902 + d[0.4830863232455095] = 0.11165237527383098 + d[0.5975775429013144] = 0.1117806537979885 + d[0.032820496015733] = 0.11114788424668184 + d[0.5793308951920413] = 0.11176020987777649 + d[1.9563369511402806] = 0.11330297110302126 + d[0.8404252739542527] = 0.11205274399106205 + d[1.5333017261491602] = 0.1128290317575909 + d[0.6142631820057253] = 0.1117993487204719 + d[0.14753315570977366] = 0.1112764119533301 + d[0.8684317213671588] = 0.11208412263635616 + d[0.4152744517458181] = 0.1115763971319306 + d[0.1046286509055504] = 0.11122834039336982 + d[0.28548208386025886] = 0.1114309741342613 + d[0.8598480154813457] = 0.112074505389085 + d[3.089928630263422] = 0.11457284000869887 + d[1.3016600422994422] = 0.1125695084341598 + d[2.500706173064623] = 0.113912809717468 + d[0.3474445138275568] = 0.11150039862165494 + d[2.046843853612829] = 0.11340436591545368 + d[0.037218405640678354] = 0.11115281180544415 + d[0.5344240708032275] = 0.11170989529256035 + d[0.47228820827400275] = 0.11164027680105901 + d[1.0353986975862295] = 0.1122711927717524 + d[2.3916729910203376] = 0.11379066709639116 + d[0.9458643137576641] = 0.11217087848640604 + d[3.464503995459429] = 0.11499239241116342 + d[2.1694616957801074] = 0.1135417328022551 + d[1.5046177599801696] = 0.11279689551417021 + d[2.5705014381768816] = 0.11399099567745426 + d[0.92648395560018] = 0.1121491646736666 + d[1.022487408596744] = 0.11225672700189548 + d[0.71825785864629] = 0.11191586616097765 + d[0.6303936762717871] = 0.11181742163686602 + d[0.47641577559022663] = 0.11164490142911798 + d[0.6537187978914559] = 0.11184355553302677 + d[1.636405508722714] = 0.11294454396008878 + d[1.5642663723468244] = 0.11286372307976754 + d[1.0276247118213024] = 0.11226248282253874 + d[1.5766516745509502] = 0.11287759895766297 + d[1.2596023360474453] = 0.11252238791516195 + d[2.0552319863379878] = 0.11341376307837003 + d[1.7214669601574326] = 0.11303984159206992 + d[2.2945413346235384] = 0.11368185536746192 + d[2.8885344684238485] = 0.11434725132881762 + d[0.4148130099516175] = 0.11157588012037704 + d[0.5127486123804198] = 0.1116856096104448 + d[1.1820444936115027] = 0.11243549344922019 + d[1.7156702115551399] = 0.1130333472963335 + d[1.3127320930788748] = 0.11258191328850367 + d[0.31676050693774105] = 0.11146601938848866 + d[2.18953030189808] = 0.11356421515051761 + d[1.8282145230671705] = 0.1131594338381811 + d[0.1399232012321242] = 0.11126788552155108 + d[1.4992496353739753] = 0.1127908812962942 + d[0.1362397506400148] = 0.11126375846773572 + d[0.6943287134350987] = 0.11188905557422432 + d[0.4832873620671899] = 0.11165260052262098 + d[1.7367931946716457] = 0.11305701207829752 + d[1.2248122419654748] = 0.11248340975542387 + d[0.6473845131066019] = 0.11183645848590083 + d[0.4157811253897248] = 0.11157696482243451 + d[0.10331486419108815] = 0.11122686838508396 + d[1.321899586501575] = 0.11259218431539084 + d[0.40068165022197155] = 0.11156004696952258 + d[1.975650562554057] = 0.1133246082178872 + d[0.29135014715544527] = 0.11143754888438212 + d[1.1373894363535018] = 0.11238546247925922 + d[0.21987443013511998] = 0.11135746535478597 + d[3.3175190501077725] = 0.11482776195746494 + d[0.2628587091292177] = 0.11140562623611408 + d[2.1696357011298755] = 0.1135419277362667 + d[0.9083421014227878] = 0.11212883846369505 + d[0.8856258180198947] = 0.1121033870160513 + d[2.723113836425034] = 0.11416195200296211 + d[1.6329309757085322] = 0.11294065128946702 + d[3.6475372192995525] = 0.1151973917264345 + d[0.7396736428280175] = 0.11193986071586068 + d[0.29704194954820284] = 0.11144392614598798 + d[0.11695279090614985] = 0.11124214874993764 + d[0.9765814672823355] = 0.1122052940310673 + d[0.08898942266371468] = 0.11121081770550487 + d[1.3330525573355003] = 0.11260467981082599 + d[2.679323444770274] = 0.11411289845152736 + d[1.5148659658625463] = 0.11280837715899311 + d[1.818226527924709] = 0.11314824406847784 + d[0.10014678952335565] = 0.11122331877374059 + d[0.7192286435782722] = 0.11191695384295743 + d[0.6774767028315622] = 0.11187017430339988 + d[0.9028611596702814] = 0.11212269758951628 + d[2.8373784002582227] = 0.11428994835420639 + d[2.0836820205642987] = 0.11344563536903729 + d[3.326890759833196] = 0.11483825888366088 + d[0.6377138361018885] = 0.11182562328133805 + d[0.6164476551853457] = 0.11180179624691303 + d[1.2642909169481606] = 0.1125276409043654 + d[3.2283192508759546] = 0.11472785139930053 + d[0.404000293144935] = 0.11156376526569864 + d[1.0061171946750125] = 0.11223838584659769 + d[0.20315932069383558] = 0.11133873723499398 + d[2.222200099304671] = 0.11360081416679119 + d[0.697221601934133] = 0.11189229681294269 + d[0.4301962792967431] = 0.11159311593779075 + d[0.8738906302305353] = 0.1120902388358362 + d[0.060156101148966856] = 0.11117851193304484 + d[0.14024970002066495] = 0.11126825134104971 + d[0.8918601453324949] = 0.11211037199337182 + d[1.0039102841692917] = 0.11223591322705981 + d[0.5505682653493338] = 0.11172798360866545 + d[0.3191786369936038] = 0.11146872873085176 + d[0.5371977105104719] = 0.11171300294109303 + d[1.524043199210332] = 0.11281865892374164 + d[3.227610946343302] = 0.1147270580374465 + d[3.0439618926705982] = 0.11452135176592033 + d[0.37035467399563626] = 0.11152606780207616 + d[2.371992897550656] = 0.11376862059277994 + d[1.626872125059894] = 0.1129338632921466 + d[2.2080305426667444] = 0.11358494044711578 + d[1.6228824731320168] = 0.11292939350715207 + d[0.9703091401592998] = 0.11219826651129154 + d[0.2745456365506692] = 0.11141872061640269 + d[0.9405319947865125] = 0.1121649041421966 + d[0.36902514877790904] = 0.11152457816540111 + d[1.1266519621048336] = 0.11237343232421226 + d[1.3240306026269537] = 0.11259457185070242 + d[0.7762438606408624] = 0.11198083446549222 + d[0.27886088232153783] = 0.11142355554519702 + d[0.6055640806404745] = 0.11178960207538076 + d[0.1886280573023551] = 0.11132245596004343 + d[0.46978691076350787] = 0.11163747428547668 + d[1.3487047701634258] = 0.11262221612019388 + d[2.702842096214967] = 0.11413924384859181 + d[1.4902192389802775] = 0.11278076401883076 + d[0.9446533535682314] = 0.11216952172357862 + d[1.8702431530696568] = 0.11320651929935742 + d[0.7340128721755843] = 0.111933518308561 + d[2.29020900369881] = 0.1136770020401641 + d[0.7263138375284407] = 0.1119248921990304 + d[0.12869730036445404] = 0.11125530766900812 + d[2.316076459386232] = 0.11370598021529227 + d[0.8329581516709483] = 0.11204437776074004 + d[0.7208184308454951] = 0.1119187350643291 + d[0.7814745668652457] = 0.11198669501151598 + d[0.2650192604457311] = 0.11140804698210463 + d[1.7181542535498242] = 0.11303613025401592 + d[0.6682710302868907] = 0.11185986011054333 + d[2.5763504327400093] = 0.1139975477929186 + d[1.2122888879614853] = 0.11246937880358156 + d[0.5072456015532443] = 0.11167944390799159 + d[0.2678848752918157] = 0.11141125770212935 + d[0.5730888745670015] = 0.11175321618625213 + d[0.9874114673895593] = 0.11221742796490122 + d[0.7392734607546847] = 0.11193941234627143 + d[1.694586993043246] = 0.11300972701331112 + d[1.710362171369363] = 0.11302740051399555 + d[1.3383465677362252] = 0.11261061107711626 + d[1.4828608814001596] = 0.11277252001758055 + d[1.7254176273799828] = 0.11304426765749215 + d[2.4583859899716414] = 0.11386540146153086 + d[0.8506170944062661] = 0.11206416299247118 + d[0.3157140807346005] = 0.11146484694247938 + d[0.8462698597444279] = 0.11205929231488092 + d[0.04188104712959828] = 0.11115803597821136 + d[1.5072200697783407] = 0.11279981103005368 + d[1.2488323082854358] = 0.11251032139156157 + d[3.4405103414386184] = 0.11496551865992012 + d[1.9055212435636957] = 0.11324604183555985 + d[0.6369932606011743] = 0.11182481593512185 + d[0.7451985246931337] = 0.11194605086993341 + d[1.6815396826503022] = 0.11299510962020133 + d[0.16720195931688042] = 0.11129844949536606 + d[1.1812535088120806] = 0.11243460724104434 + d[0.2787115360654193] = 0.11142338821324706 + d[0.3300166306833392] = 0.11148087192871936 + d[2.156015709446364] = 0.11352666957372695 + d[2.735060834704789] = 0.11417533484882748 + d[1.495846046489974] = 0.11278706805897509 + d[0.891263089770838] = 0.11210970304887626 + d[0.689139556228429] = 0.11188324155821794 + d[0.9721280611508881] = 0.11220030443192694 + d[2.364525538614643] = 0.11376025531386369 + d[0.06927420539478324] = 0.11118872814810499 + d[2.193662071907834] = 0.11356884385995981 + d[0.8835606111290131] = 0.11210107314549084 + d[0.35522951900258093] = 0.11150912115929074 + d[0.3136464331651738] = 0.11146253029061771 + d[2.9612912220691934] = 0.11442874965504773 + d[0.21484878872756563] = 0.1113518344728737 + d[0.5642806281926727] = 0.1117433472387792 + d[0.2612409054929239] = 0.11140381360072288 + d[1.8586858020666321] = 0.11319357140427767 + d[3.420671549634663] = 0.11494329840324265 + d[2.4495306230155816] = 0.11385548139389964 + d[0.2912935078527302] = 0.1114374854240503 + d[2.134552845971246] = 0.11350262516892907 + d[2.442865919262161] = 0.11384801536940257 + d[0.31575415529406814] = 0.11146489184316861 + d[1.3998745179718979] = 0.11267954514603722 + d[0.9829867159365996] = 0.1122124704735951 + d[0.13385997321876641] = 0.1112610920902507 + d[2.1113049261022265] = 0.11347658092843528 + d[0.5924366133799406] = 0.11177489379589697 + d[3.1239731250424385] = 0.11461097363379048 + d[2.186870253697202] = 0.11356123516963088 + d[0.5283708781685115] = 0.1117031131579616 + d[0.6793975709178888] = 0.11187232647635673 + d[0.8788644821665823] = 0.11209581157265835 + d[0.23138376750323797] = 0.11137036076600564 + d[0.44718111458952803] = 0.11161214618376226 + d[1.1316353968922834] = 0.11237901571405957 + d[0.16492032343449226] = 0.11129589307945217 + d[1.9119149294511333] = 0.11325320475414911 + d[2.2350271026328556] = 0.11361518383960159 + d[0.14095300083409878] = 0.11126903934136975 + d[0.4115560992358491] = 0.11157223099156695 + d[0.7227675697941918] = 0.11192091890852121 + d[1.6384803490643502] = 0.11294686849343992 + d[0.236176041369077] = 0.11137573017463394 + d[0.5612564549781618] = 0.111739958889812 + d[1.8115530903741877] = 0.11314076766352035 + d[0.5172299522108499] = 0.11169063060798269 + d[1.0136398353037093] = 0.11224681420051373 + d[2.145206600074277] = 0.11351456035888023 + d[1.6972475009134533] = 0.11301270767811003 + d[1.0415797542149192] = 0.1122781180052126 + d[0.9230599747741073] = 0.11214532843263512 + d[0.49508534968153994] = 0.11166581927287995 + d[2.6328704178530513] = 0.11406086186945169 + d[1.1242454741761625] = 0.11237073611885345 + d[0.6935008424691944] = 0.11188812801423217 + d[0.8479350703760967] = 0.11206115803074004 + d[1.500699083771989] = 0.11279250519674804 + d[0.5745556227571511] = 0.11175485956198483 + d[1.1375417405589112] = 0.11238563311925276 + d[0.24725990416614607] = 0.11138814886846599 + d[2.0633629613242013] = 0.11342287214020678 + d[1.1410838976570523] = 0.11238960171347186 + d[1.730490479372456] = 0.11304995094164959 + d[0.9655946574638439] = 0.11219298439985671 + d[2.240888291615181] = 0.11362174993002265 + d[0.28876924856815966] = 0.11143465717003441 + d[1.2036121502109394] = 0.11245965752746549 + d[1.8794658436988834] = 0.11321685162318286 + d[1.3213056254841509] = 0.11259151885676896 + d[0.1417110880206094] = 0.11126988872605771 + d[1.3124031427297562] = 0.11258154474074765 + d[0.864411105937986] = 0.11207961790975281 + d[1.8974886404153128] = 0.11323704281210219 + d[0.37879091784709973] = 0.11153552000104452 + d[0.764061902151518] = 0.11196718564758082 + d[0.2494971016288413] = 0.11139065549166888 + d[1.8925058689171423] = 0.11323146054821961 + d[0.5729614940370418] = 0.11175307346640505 + d[1.1051022584468544] = 0.11234928823332209 + d[3.4392802044350055] = 0.11496414085888079 + d[1.2769792645918927] = 0.1125418566577421 + d[1.2299695036347666] = 0.11248918785958338 + d[0.16910079797445676] = 0.11130057701330161 + d[0.42632490948006874] = 0.11158877835439417 + d[2.867187673694646] = 0.11432333956672558 + d[1.4720819322522933] = 0.11276044371658818 + d[1.835253935707917] = 0.11316732023905984 + d[1.9268208135700828] = 0.11326990396447126 + d[0.384833521044619] = 0.11154229029828747 + d[1.6517953892593775] = 0.11296178589754814 + d[1.8269532135730564] = 0.11315802076619787 + d[0.0672626036753452] = 0.11118647428535623 + d[0.6983676483749348] = 0.11189358086166755 + d[0.4483251195899267] = 0.11161342795606259 + d[1.5489486435605957] = 0.11284656183466135 + d[0.2970756621826085] = 0.11144396391860613 + d[1.29820716476465] = 0.11256563991262333 + d[3.0614469091733523] = 0.11454093712610801 + d[1.9692974600271627] = 0.11331749081750654 + d[1.1634939075994455] = 0.11241470962233309 + d[0.803471206396208] = 0.11201134029481173 + d[1.163403415309531] = 0.11241460823592407 + d[0.7775420455136222] = 0.11198228896753376 + d[0.6155352175261691] = 0.11180077393395174 + d[1.1696128807117605] = 0.11242156524040345 + d[2.3713145391589157] = 0.11376786066487353 + d[1.2385051435567993] = 0.11249875103382337 + d[1.7647080863893039] = 0.11308828598280979 + d[1.040210449022856] = 0.11227658384086153 + d[0.8751233079471509] = 0.11209161993629008 + d[0.30053876304995253] = 0.11144784407763039 + d[2.552439925963843] = 0.11397076291302095 + d[0.10587402879107388] = 0.11122973575422397 + d[1.5349570870641536] = 0.11283088634799732 + d[1.1436430020489166] = 0.11239246890555958 + d[1.6919645005281172] = 0.11300678893773322 + d[0.9571734811488212] = 0.11218354930140895 + d[1.1932864683278794] = 0.11244808879329007 + d[0.33016864195780016] = 0.11148104224647755 + d[0.2836479684453981] = 0.11142891913745494 + d[0.7656695748901304] = 0.11196898690455913 + d[0.6741567720558514] = 0.1118664545966519 + d[1.8541638137408984] = 0.11318850534006403 + d[1.794522945783881] = 0.11312168837819198 + d[1.475200124148958] = 0.1127639372145155 + d[2.0273997064137483] = 0.11338258274473981 + d[1.7407895451136397] = 0.1130614893171187 + d[1.6352424388217073] = 0.11294324092238285 + d[1.4788442277522507] = 0.11276801992175323 + d[0.7875973712678224] = 0.11199355507324546 + d[2.1217328329908187] = 0.11348826314067556 + d[1.0971966838980718] = 0.11234043089133974 + d[1.0446807694838272] = 0.11228159237049658 + d[0.4874783531105308] = 0.11165729621071857 + d[0.5407316620129097] = 0.1117169624597261 + d[0.23937995951411117] = 0.11137931994125791 + d[2.2697568269866473] = 0.11365409029217653 + d[0.5480793002619575] = 0.11172519491720931 + d[0.9716718938626806] = 0.11219979334172689 + d[0.9700460449137343] = 0.11219797173913566 + d[3.0133286971776867] = 0.11448703868550521 + d[0.4621567747418458] = 0.11162892529120527 + d[0.06278538044862536] = 0.11118145786153869 + d[0.35454307650989825] = 0.11150835204997085 + d[1.8216427661080785] = 0.11315207135629161 + d[0.06090728376989207] = 0.11117935358204534 + d[0.9757470812728076] = 0.11220435918453436 + d[2.2157661384880636] = 0.11359360640150348 + d[0.12555000104611347] = 0.11125178133562919 + d[2.934052652508832] = 0.11439823854892726 + d[0.20406678125250333] = 0.11133975398165452 + d[1.2364740220564727] = 0.11249647540312993 + d[0.9001449016208913] = 0.11211965427993131 + d[0.6433913299446861] = 0.1118319844504499 + d[1.4384180502930937] = 0.1127227279848622 + d[1.7486053850959262] = 0.11307024564651541 + d[0.5747126257895278] = 0.11175503547150221 + d[0.8878340395896485] = 0.1121058611208649 + d[1.324792052941568] = 0.1125954249598303 + d[0.2848326269490087] = 0.11143024646366086 + d[0.29136830816310166] = 0.11143756923250642 + d[0.4832356262502273] = 0.1116525425565523 + d[1.5309202018098174] = 0.11282636360651781 + d[1.859891593290162] = 0.11319492227327607 + d[2.2621345481544477] = 0.11364555134470847 + d[2.2726522808539324] = 0.1136573339561136 + d[0.20919667215617688] = 0.11134550166865277 + d[0.8909625313926454] = 0.11210936630152751 + d[0.23394249898123765] = 0.1113732276462115 + d[0.818508097510812] = 0.11202818778263302 + d[0.6210354326131955] = 0.11180693648176675 + d[0.47151387266678557] = 0.1116394092163179 + d[1.8251651641764475] = 0.11315601757591359 + d[0.05556573306032975] = 0.11117336873797899 + d[2.52006932100479] = 0.11393450075976451 + d[2.563536617276643] = 0.11398319359200662 + d[0.5619778981887478] = 0.11174076721039339 + d[1.7090664397831081] = 0.11302594886027356 + d[1.0335776555202505] = 0.1122691524823167 + d[3.035831449065446] = 0.11451224465205864 + d[1.2358772867525203] = 0.11249580683194703 + d[0.6021529770368698] = 0.11178578020665933 + d[2.5563724289939387] = 0.11397516816391964 + d[0.5891446964640654] = 0.11177120546462513 + d[3.7845613530223585] = 0.11535085501645691 + d[1.9041118368665537] = 0.11324446286060519 + d[1.9482357018651177] = 0.11329389522712131 + d[0.08724191268984927] = 0.11120885973975307 + d[1.2480923156683492] = 0.11250949231828689 + d[0.03446386021585801] = 0.11114972552455644 + d[0.5260516612597915] = 0.11170051465428818 + d[0.6225697327399695] = 0.11180865554120849 + d[0.5711241283567233] = 0.11175101484286411 + d[1.2214662922756425] = 0.11247966101180391 + d[0.3114961607601052] = 0.11146012106341753 + d[0.7761732539942222] = 0.11198075535694839 + d[1.5380469407998678] = 0.11283434807758595 + d[0.28068644053654923] = 0.11142560095442833 + d[1.3763458231331729] = 0.11265318434311902 + d[0.8382261001009025] = 0.11205028001740795 + d[1.8077966013350801] = 0.11313655918044165 + d[0.5551212982741496] = 0.11173308492672998 + d[0.7841754111779822] = 0.11198972106934144 + d[0.23833601967085893] = 0.11137815027955612 + d[2.947203221645055] = 0.1144129690914024 + d[1.551237370368613] = 0.11284912601541174 + d[0.029268399225405695] = 0.11114390436367103 + d[0.19390475087124115] = 0.11132836813031292 + d[0.149127341123934] = 0.11127819812861935 + d[0.49741768109929063] = 0.11166843247279301 + d[1.31226387703191] = 0.11258138871093493 + d[2.4306000650634063] = 0.11383427472961526 + d[0.4593503516889701] = 0.11162578090453107 + d[1.9238055630101443] = 0.11326652595154822 + d[0.4953747515968516] = 0.11166614352571846 + d[1.1334498624980496] = 0.11238104862247941 + d[1.1838374960024074] = 0.11243750230354417 + d[1.949216245206462] = 0.11329499373588756 + d[0.09582099311802339] = 0.11121847201413476 + d[1.5721737005653431] = 0.112872582059701 + d[0.5135900636987706] = 0.11168655239215543 + d[2.163177547801184] = 0.11353469281937369 + d[0.4387967946978186] = 0.11160275217732483 + d[1.3756263917444067] = 0.11265237831422464 + d[1.9323049999485802] = 0.11327604794590598 + d[1.4447092832731028] = 0.11272977645106969 + d[0.6558711209379333] = 0.11184596703426378 + d[0.13866757585832334] = 0.11126647867943151 + d[0.2630543095269613] = 0.11140584539262391 + d[2.239089085752755] = 0.11361973434150856 + d[0.04299625744746072] = 0.11115928549553877 + d[0.5823609357529833] = 0.11176360479857354 + d[0.38279013356266844] = 0.11154000083138729 + d[1.6977011569618705] = 0.11301321592558332 + d[0.21186556458120676] = 0.11134849197738332 + d[2.5165707884993127] = 0.11393058162807362 + d[0.17925856455536304] = 0.11131195809045616 + d[0.32132603196495324] = 0.1114711347337473 + d[0.907332952579836] = 0.11212770780848834 + d[0.7487568056219074] = 0.11195003761631486 + d[0.5663796941858004] = 0.11174569907744016 + d[1.2732345967623167] = 0.11253766121339201 + d[1.2843618290659649] = 0.11255012791884958 + d[1.9629360417119766] = 0.11331036409563215 + d[1.8533519708798711] = 0.11318759581775317 + d[0.6325677541389032] = 0.11181985751474996 + d[0.6984969271181519] = 0.11189372570763112 + d[0.539083075851859] = 0.11171511534682071 + d[0.010682798316263398] = 0.11112308046082131 + d[1.3204046258433404] = 0.11259050939992458 + d[2.522974629076764] = 0.11393775534707003 + d[2.294789862167116] = 0.11368213378228212 + d[1.6096813145771418] = 0.11291460364825028 + d[1.3396832494685569] = 0.11261210865883974 + d[2.2676586505533036] = 0.11365173978623455 + d[1.6713590504813236] = 0.11298370386144248 + d[1.669643228390371] = 0.11298178155798791 + d[0.34398596703948003] = 0.11149652356860916 + d[0.17844183782048728] = 0.11131104300450097 + d[0.4225517508480401] = 0.11158455080895575 + d[1.474571077746378] = 0.11276323245607286 + d[1.4094064551464085] = 0.112690224411334 + d[2.6484245070781465] = 0.11407828556960266 + d[0.27976634739511597] = 0.11142457005496119 + d[1.954025242689866] = 0.11330038128368998 + d[0.49399686601235315] = 0.11166459970967796 + d[0.018114959508929718] = 0.11113140769244437 + d[3.0601877489642084] = 0.11453952671452139 + d[0.5636454632977327] = 0.11174263558634474 + d[1.380940924289141] = 0.11265833255260728 + d[2.906279728054332] = 0.11436712873936532 + d[1.7727931574380698] = 0.1130973439174905 + d[2.2643791799923116] = 0.11364806592082141 + d[0.6811178763803679] = 0.11187425393543099 + d[0.11757436272566757] = 0.11124284517864956 + d[0.03982917165951261] = 0.11115573699126473 + d[0.04635066902037854] = 0.11116304388558625 + d[0.42024460269355723] = 0.11158196581973383 + d[0.40277821969780714] = 0.11156239602199942 + d[0.7485773174041144] = 0.11194983651528778 + d[1.045714902576319] = 0.11228275100898928 + d[0.251607890382742] = 0.11139302048268372 + d[2.5678923389798944] = 0.11398807293063754 + d[1.7614983324582782] = 0.11308469000221061 + d[0.28549254671777446] = 0.11143098585715414 + d[2.139893708015708] = 0.11350860843303336 + d[1.2972776028308761] = 0.11256459845345493 + d[1.8235498419045326] = 0.11315420789521748 + d[0.83570132354041] = 0.11204745123529702 + d[0.9548461136388257] = 0.11218094171460033 + d[2.4355205278558367] = 0.11383978680742447 + d[2.980771914816144] = 0.11445057073633991 + d[0.06668853823657606] = 0.11118583108411914 + d[0.03739836687916864] = 0.11115301343977703 + d[0.23301170558040374] = 0.11137218475711988 + d[1.5024264017444184] = 0.1127944404102039 + d[0.3479198527206745] = 0.11150093120469179 + d[2.818362501026451] = 0.11426864738046985 + d[0.9817035742598615] = 0.11221103284148613 + d[1.2676725706761973] = 0.11253142963821458 + d[0.25507225174549863] = 0.11139690205687745 + d[1.1509548005133574] = 0.11240066096046858 + d[1.6658274104336153] = 0.11297750654481213 + d[0.5987423017422844] = 0.1117819588173605 + d[1.0959400555715042] = 0.11233902297467543 + d[1.3118607383831418] = 0.11258093704444301 + d[0.944011281254852] = 0.11216880234411429 + d[0.19340747610347242] = 0.11132781096833642 + d[2.3146028812874073] = 0.11370432943318942 + d[0.7710792539677247] = 0.11197504797681963 + d[0.09364796210991755] = 0.11121603728116997 + d[1.332989911640282] = 0.11260460962426594 + d[0.9585412770930177] = 0.11218508178232267 + d[1.51591486810467] = 0.11280955230292043 + d[0.9191989682330332] = 0.11214100254548476 + d[1.716165638138151] = 0.11303390233983021 + d[0.8174348736425062] = 0.11202698533195035 + d[0.7828021311696202] = 0.11198818243026895 + d[1.4919544016753385] = 0.11278270802298389 + d[1.5322341374887893] = 0.11282783568009845 + d[1.1467582937753567] = 0.11239595924307882 + d[0.8000404811558646] = 0.11200749647319186 + d[0.9490724658736815] = 0.1121744729076229 + d[1.526580406542002] = 0.11282150149667673 + d[0.04876452378762486] = 0.11116574844567527 + d[2.532860213021083] = 0.11394882937583163 + d[0.5280473968309387] = 0.11170275072208305 + d[1.7037473151099405] = 0.11301998965560851 + d[0.8191597907582884] = 0.11202891794619048 + d[1.2556998642765493] = 0.11251801566499134 + d[1.9966608153646583] = 0.113348146031175 + d[1.119387073271509] = 0.1123652928130468 + d[2.299177922038843] = 0.11368704953727916 + d[0.7485676225757738] = 0.11194982565307092 + d[0.17437627714847292] = 0.11130648782416089 + d[1.640370116963327] = 0.11294898568172365 + d[0.20154101258356838] = 0.11133692403289282 + d[0.9697185229449798] = 0.11219760478321349 + d[0.9602424805148385] = 0.11218698781337844 + d[1.6148669373037094] = 0.11292041333969081 + d[0.00985404615727592] = 0.1111221519003355 + d[0.2368782513225236] = 0.11137651695188104 + d[0.6238982083079674] = 0.11181014399076818 + d[2.1404529701918262] = 0.11350923496336182 + d[2.304552897448312] = 0.11369307088735106 + d[1.9715896409475033] = 0.11332005875548011 + d[1.0639026273224448] = 0.11230312844932797 + d[0.5724804608013354] = 0.11175253450656111 + d[0.8828551979753465] = 0.11210028279617787 + d[0.4562084911500478] = 0.11162226068501285 + d[2.447018031401603] = 0.11385266670541873 + d[0.09571200135690638] = 0.11121834989630434 + d[0.8826260261153613] = 0.11210002603058515 + d[1.0994374675391523] = 0.11234294144772673 + d[1.2688277805334576] = 0.11253272391086838 + d[0.28333810126515957] = 0.1114285719531545 + d[1.154508450918916] = 0.11240464242804275 + d[2.5471608787046107] = 0.11396484923825925 + d[0.3992497971329463] = 0.1115584426829848 + d[3.1512704037607215] = 0.11464154945139066 + d[0.5815590658032002] = 0.11176270636675052 + d[0.9903073132918285] = 0.11222067246981214 + d[1.5952605224370648] = 0.11289844735705153 + d[0.7547422651350957] = 0.11195674380519971 + d[0.30291578124284935] = 0.11145050735787213 + d[2.184412816485427] = 0.11355848216750464 + d[1.759458678209111] = 0.11308240491766001 + d[0.32224074598769126] = 0.11147215960553515 + d[1.577738625952644] = 0.1128788167233029 + d[1.3210129863010185] = 0.11259119099135599 + d[0.16827394793975525] = 0.11129965058479097 + d[0.3034572824324464] = 0.11145111407152115 + d[0.14606816836098213] = 0.11127477053557966 + d[2.276618256076194] = 0.11366177688127824 + d[0.47446385504143596] = 0.11164271444933732 + d[1.7710269737013542] = 0.11309536521235301 + d[1.4118672498700982] = 0.1126929814024985 + d[1.1466789204589083] = 0.11239587031412442 + d[1.693562602012732] = 0.11300857935015848 + d[0.29092710608431904] = 0.11143707489678785 + d[0.30180573829261337] = 0.11144926363351514 + d[0.24058064566488846] = 0.11138066522623125 + d[1.4180837324060604] = 0.11269994613671257 + d[0.07459766292122283] = 0.11119469271967747 + d[1.2826637947874115] = 0.11254822547940456 + d[1.437836240461245] = 0.112722076146319 + d[1.8816371421111218] = 0.11321928416103945 + d[1.526369522392705] = 0.11282126523158922 + d[2.256693331728522] = 0.11363945575269427 + d[0.620990284923634] = 0.1118068858974235 + d[0.7734444471476571] = 0.11197769796844258 + d[1.897183740692048] = 0.11323670122905624 + d[1.481166300598486] = 0.11277062147817765 + d[0.311248276470215] = 0.1114598433267059 + d[2.395635309637923] = 0.11379510585200674 + d[1.2428613910027078] = 0.11250363169117118 + d[1.422765204321074] = 0.1127051910951793 + d[1.4379992232086327] = 0.11272225874625579 + d[1.3636956515865089] = 0.11263901147148246 + d[1.4497399327981513] = 0.11273541260317677 + d[0.8649283661222311] = 0.11208019745185592 + d[0.43755532350792403] = 0.1116013612010785 + d[0.5547328451996899] = 0.1117326496954053 + d[1.3829427559924077] = 0.11266057534244849 + d[1.8639091042858191] = 0.11319942315981885 + d[0.6513684127028816] = 0.11184092211919443 + d[1.3872920123278611] = 0.11266544811240867 + d[1.568588658608459] = 0.112868565556591 + d[0.8563292524101733] = 0.11207056293981899 + d[0.3603913266295464] = 0.11151490459220947 + d[1.302954989106468] = 0.11257095926137438 + d[0.5985755645791463] = 0.11178177200167261 + d[0.4515409899826527] = 0.11161703109883848 + d[1.322127006326409] = 0.11259243911069546 + d[1.469437040119806] = 0.11275748048410929 + d[1.5309659721046436] = 0.1128264148854706 + d[1.5173040476671682] = 0.11281110867841722 + d[0.19951284033999217] = 0.11133465160638152 + d[0.11412567648001781] = 0.1112389811615437 + d[0.059657494821344415] = 0.11117795327858916 + d[1.3831668944912179] = 0.11266082646021305 + d[0.8238525102834893] = 0.11203417571486017 + d[0.06772603738139082] = 0.11118699353126844 + d[1.4549182182852096] = 0.1127412141585678 + d[0.4027525822155573] = 0.11156236729707979 + d[1.9208375891498517] = 0.11326320090201188 + d[0.8754078529786271] = 0.11209193874245604 + d[0.9482137431313247] = 0.11217351079269514 + d[2.401484553039159] = 0.11380165841538664 + d[2.15922790100628] = 0.11353026812024442 + d[1.3013990633712256] = 0.11256921603963661 + d[0.7409563014850229] = 0.11194129782449784 + d[0.8677321537126377] = 0.11208333883576352 + d[0.9278290764726551] = 0.11215067175196877 + d[1.382508504966324] = 0.1126600888211661 + d[0.20107990852420166] = 0.11133640739773888 + d[0.39073063661103047] = 0.11154889758632944 + d[1.0530907408225432] = 0.11229101486587936 + d[0.42544043391718833] = 0.1115877873649181 + d[0.6949209586519203] = 0.11188971913530484 + d[1.1226976219717817] = 0.11236900192027005 + d[0.7008201881860292] = 0.11189632872621397 + d[0.6326879645117751] = 0.11181999220071526 + d[0.2938303416790258] = 0.11144032776682734 + d[0.37977749063930655] = 0.11153662538414125 + d[0.1990946649155254] = 0.11133418306977787 + d[2.9271937945115827] = 0.11439055562094858 + d[2.2797408248344526] = 0.11366527496986777 + d[0.797772996203943] = 0.1120049559582148 + d[2.3214568281816916] = 0.11371200759336912 + d[1.5443366347538903] = 0.11284139475753256 + d[0.0479244683407849] = 0.11116480722068531 + d[1.1667544653093604] = 0.11241836270923994 + d[1.8334277858753723] = 0.1131652743658738 + d[3.0686565956278224] = 0.1145490128398976 + d[0.007952628911485737] = 0.11112002149149897 + d[0.1510310449771719] = 0.11128033109803318 + d[1.425303070450006] = 0.11270803443134308 + d[1.0954835632116833] = 0.11233851152413543 + d[2.6958208988595835] = 0.11413137877229328 + d[0.08379555886372303] = 0.11120499833526866 + d[1.0748456337918935] = 0.11231538893054337 + d[1.427063794468432] = 0.11271000708439648 + d[0.4239705735203655] = 0.11158614049496635 + d[1.2149610501402732] = 0.11247237264949002 + d[2.189854985608413] = 0.11356457888492782 + d[1.1124906461044852] = 0.11235756611914541 + d[1.304539229950214] = 0.1125727342064632 + d[2.7428674968087474] = 0.11418407973901391 + d[1.1279387220625718] = 0.11237487399721027 + d[0.41740552161779254] = 0.11157878483873142 + d[2.5248072956824856] = 0.11393980833808005 + d[0.3348031074415515] = 0.11148623483326071 + d[2.221877237851425] = 0.1136004524753378 + d[1.5624725616941308] = 0.11286171338201786 + d[2.2482594626216192] = 0.11363000759461757 + d[2.027599457174643] = 0.11338280652467372 + d[0.8861834791485519] = 0.1121040118229825 + d[1.1302632587742756] = 0.11237747838459909 + d[1.058878760774742] = 0.11229749973544566 + d[0.048099713594783156] = 0.11116500357107291 + d[1.157488482016948] = 0.11240798121863453 + d[1.7747910501384405] = 0.11309958221223104 + d[0.9824553960559259] = 0.1122118751827416 + d[0.5441435627206143] = 0.11172078522948382 + d[1.9855435748766226] = 0.1133356913795908 + d[1.9525397027144114] = 0.11329871702495027 + d[1.429937233024014] = 0.11271322638291872 + d[0.8819157207522268] = 0.11209923019997116 + d[1.326858239297139] = 0.11259773986102681 + d[1.9861654631227006] = 0.11333638808181944 + d[0.05038872516812387] = 0.11116756825284199 + d[1.365195697845592] = 0.11264069207894299 + d[1.6254827115641204] = 0.11293230667043382 + d[0.6877535442737448] = 0.11188168864770688 + d[1.970158691573957] = 0.11331845565817784 + d[1.5835509678541162] = 0.11288532857651018 + d[2.3956838989981253] = 0.11379516028383184 + d[3.3141344235482872] = 0.11482397095016547 + d[2.1777618732701747] = 0.1135510312867553 + d[0.1527491912203992] = 0.11128225616285876 + d[1.0982011383140717] = 0.11234155627422122 + d[1.1372323449043356] = 0.11238528647568743 + d[0.29055862252807174] = 0.1114366620370268 + d[0.9225353640058035] = 0.11214474065668831 + d[1.0404820298136468] = 0.11227688811896122 + d[0.4510062364117349] = 0.11161643194739206 + d[0.5624229010022538] = 0.11174126580116352 + d[0.058033485461494116] = 0.1111761336866224 + d[2.5997043653096843] = 0.11402370909609076 + d[0.09807033465415371] = 0.11122099224780757 + d[0.04472830299659436] = 0.1111612261347913 + d[0.5675960544432507] = 0.1117470619135444 + d[0.6947327092010165] = 0.11188950821758956 + d[1.6487786012424697] = 0.11295840606371368 + d[2.7028650241209853] = 0.11413926953219236 + d[1.2687914580358775] = 0.11253268321591321 + d[0.9943685447717188] = 0.11222522267145998 + d[1.375800923921085] = 0.11265257385473444 + d[0.7602937346264381] = 0.11196296374426078 + d[1.121779898961417] = 0.11236797371223423 + d[0.6298755253336101] = 0.11181684109074427 + d[0.9514407441264338] = 0.11217712633176248 + d[0.4910146955290974] = 0.11166125841416569 + d[1.1205610938821033] = 0.11236660817464683 + d[1.4754699405495326] = 0.11276423950601264 + d[0.19332533769501858] = 0.11132771893793167 + d[0.9126966409697469] = 0.11213371730999833 + d[0.370929647783256] = 0.11152671201853179 + d[1.082673620333119] = 0.11232415935620435 + d[1.7743795993965477] = 0.11309912125256359 + d[0.09966787673013422] = 0.11122278218465098 + d[1.6080299940594216] = 0.11291275359738612 + d[1.6270056370096693] = 0.11293401287150892 + d[1.811510581330624] = 0.1131407200396479 + d[2.22484524300664] = 0.11360377743686588 + d[1.778616199713182] = 0.11310386763233927 + d[1.9241535625489443] = 0.11326691581869021 + d[2.5519785982420293] = 0.11397024612637825 + d[0.3914072244880299] = 0.11154965565365939 + d[0.34934524649414356] = 0.11150252825584994 + d[2.613702804076156] = 0.11403939023862966 + d[1.6565841234384997] = 0.11296715091475489 + d[2.1683403524329457] = 0.11354047658814706 + d[0.11134073016783641] = 0.11123586081957904 + d[2.4188298680457567] = 0.11382108931950337 + d[0.523390927594136] = 0.11169753350719812 + d[0.01850643671618446] = 0.11113184631605379 + d[1.249175825178635] = 0.11251070626116376 + d[2.317201669028403] = 0.11370724073593173 + d[0.3009868075233568] = 0.11144834607968383 + d[0.590050644303199] = 0.11177222050721888 + d[0.479640374058834] = 0.11164851434827204 + d[0.3899928242282521] = 0.11154807092139625 + d[1.7067248039095444] = 0.1130233254426666 + d[2.13720078758742] = 0.11350559160704246 + d[0.5675768769104657] = 0.11174704042662603 + d[1.3161467100916246] = 0.1125857389395723 + d[1.078169859818779] = 0.11231911337249058 + d[2.9775614537333475] = 0.11444697457924179 + d[0.18305131345584758] = 0.1113162076038089 + d[2.1055740886999508] = 0.11347016075923363 + d[2.298786239992132] = 0.11368661075282545 + d[0.6557789881669032] = 0.11184586380706338 + d[1.0242571388896162] = 0.11225870980313314 + d[0.21322975395524602] = 0.11135002045685836 + d[2.831364268494549] = 0.11428321153250141 + d[1.2223060814570972] = 0.11248060189702733 + d[1.2282041597609348] = 0.11248720999997919 + d[0.47065513965358274] = 0.11163844707061658 + d[1.2858286497695963] = 0.1125517713116038 + d[0.4691571615451571] = 0.11163676869884948 + d[0.12924677541435892] = 0.11125592331816836 + d[0.8689086000666612] = 0.11208465693463822 + d[0.2512162766536289] = 0.11139258170692411 + d[1.4447031287927892] = 0.11272976955581798 + d[0.031486900947608754] = 0.11114639004405805 + d[0.5173507007839627] = 0.11169076589748735 + d[0.8011617821376542] = 0.11200875279099347 + d[1.9360994575981354] = 0.11328029890737182 + d[1.0746180035905841] = 0.1123151338950677 + d[0.7771858235402733] = 0.1119818898521326 + d[0.9999563619306253] = 0.11223148325713597 + d[0.5960867148997089] = 0.11177898344405332 + d[1.8699086936802771] = 0.11320614459910018 + d[1.0780147233344728] = 0.11231893955856616 + d[2.419795824952317] = 0.11382217142100459 + d[1.1918863635702672] = 0.11244652013693768 + d[0.49592517419009663] = 0.11166676023236967 + d[0.57995179617143] = 0.11176090554824442 + d[0.45023431095584243] = 0.11161556706254301 + d[0.766549972777651] = 0.11196997331349132 + d[2.0763511270046973] = 0.11343742265247825 + d[0.20738417718023316] = 0.11134347089377034 + d[1.6320305743951238] = 0.11293964253045734 + d[0.9072491626844793] = 0.11212761392988471 + d[0.6366945087833087] = 0.11182448120801258 + d[2.3741759038077603] = 0.11377106609512878 + d[0.5972358530570652] = 0.1117802709617634 + d[1.4961536679763356] = 0.11278741270515091 + d[2.07806747866829] = 0.11343934546236421 + d[1.5562597349350789] = 0.11285475283210758 + d[0.19739183644812064] = 0.1113322751683806 + d[0.6528533433330157] = 0.11184258586220375 + d[1.4961332926181592] = 0.11278738987745682 + d[1.0084752717893228] = 0.11224102783264014 + d[0.5618937177742978] = 0.11174067289283682 + d[1.6794787523361854] = 0.11299280068062788 + d[0.9570111000370333] = 0.11218336736932588 + d[1.9808629443185606] = 0.11333044766131983 + d[0.4799002662592865] = 0.11164880553784864 + d[0.9949671554957303] = 0.11222589335451356 + d[0.7099481273985022] = 0.11190655581178455 + d[1.9902150435345316] = 0.11334092483088834 + d[0.8679771808481503] = 0.112083613365918 + d[0.819984641086281] = 0.11202984211661986 + d[0.7729738000156121] = 0.11197717064961131 + d[0.08130882143153784] = 0.11120221211548453 + d[3.103914461182381] = 0.11458850572571887 + d[1.029517450233049] = 0.11226460344108555 + d[0.4585101447299387] = 0.11162483951556493 + d[0.11573273245137661] = 0.1112407817578752 + d[0.878935779707968] = 0.11209589145488794 + d[0.9023071126988265] = 0.11212207683245604 + d[0.03626598917596102] = 0.11115174468754509 + d[0.23115402204359425] = 0.11137010335223288 + d[0.8380711768440392] = 0.11205010644002343 + d[2.375678960761627] = 0.11377274988707596 + d[0.6722783280386244] = 0.11186434995589815 + d[0.6845569652351289] = 0.11187810714782635 + d[0.638365725317539] = 0.11182635367014189 + d[2.746003761215441] = 0.1141875929259584 + d[1.2011378000057236] = 0.11245688530456217 + d[2.0301860307944697] = 0.1133857042516917 + d[2.4725100911372353] = 0.11388122370857089 + d[0.8935574000130132] = 0.11211227360719193 + d[2.766230139606531] = 0.11421025010772945 + d[1.2221346232248425] = 0.11248040979820441 + d[0.6144017219327133] = 0.1117995039433193 + d[2.342055653477335] = 0.11373508346232783 + d[3.1107507899486335] = 0.11459616317466018 + d[0.21321959083032394] = 0.11135000906978264 + d[1.2995901786883488] = 0.1125671894085209 + d[1.7503106326737456] = 0.1130721560876416 + d[1.0168817378170851] = 0.11225044642147071 + d[1.774035713739692] = 0.11309873598791784 + d[1.5874624514347635] = 0.11288971080242223 + d[1.0007910680890677] = 0.1122324184610412 + d[2.4920468273168512] = 0.11390310929959813 + d[1.7269736017061832] = 0.11304601086739505 + d[0.22611690387239547] = 0.1113644596122413 + d[0.9394938291464948] = 0.11216374097847488 + d[0.3500142507544519] = 0.11150327782696887 + d[0.6084060197752027] = 0.11179278624048847 + d[0.13738005606650883] = 0.11126503610178891 + d[1.0415681375471473] = 0.11227810498994258 + d[0.6583968235414965] = 0.11184879687637828 + d[0.420269640602595] = 0.1115819938728637 + d[0.6178830112347726] = 0.11180340444777574 + d[0.15688430652514795] = 0.11128688927534462 + d[1.571078071710013] = 0.11287135457164137 + d[0.6981243195683833] = 0.11189330823219387 + d[0.5085558991654913] = 0.11168091199627368 + d[1.7403702702863288] = 0.11306101959024793 + d[2.927741674539715] = 0.11439116932735754 + d[2.4550961449044495] = 0.11386171607249067 + d[1.3967252638954182] = 0.11267601682468442 + d[1.707034109694486] = 0.11302367196892833 + d[0.30225519308287363] = 0.11144976721571724 + d[1.124010156678355] = 0.11237047247142484 + d[0.921975475707056] = 0.11214411335564052 + d[0.48154777171011287] = 0.11165065144319275 + d[1.5546906591474592] = 0.11285299491503108 + d[0.547419176674079] = 0.11172445530012397 + d[0.16384658109437822] = 0.11129469002506837 + d[0.04178614495541244] = 0.11115792964677833 + d[1.1331328869544144] = 0.11238069348639021 + d[0.5764319310520779] = 0.11175696181741271 + d[0.6826152874630009] = 0.11187593165979756 + d[0.24573623060264382] = 0.11138644169881448 + d[3.228855223553244] = 0.11472845173461751 + d[0.7648735526468226] = 0.11196809503113246 + d[1.1265815503165975] = 0.11237335343554478 + d[0.7314553758682403] = 0.11193065285310654 + d[0.7490550728100711] = 0.11195037179890349 + d[1.0831632107456275] = 0.11232470789000087 + d[0.0717433025032237] = 0.11119149460325911 + d[0.3819851616531602] = 0.11153909891894141 + d[2.1471498648980383] = 0.11351673735827465 + d[1.2587174166276407] = 0.11252139646951496 + d[3.351203729032968] = 0.11486549090408602 + d[0.14892719768729612] = 0.11127797388164314 + d[2.245666161639911] = 0.11362710241132086 + d[0.7390746208220503] = 0.11193918956322835 + d[0.16891267723799974] = 0.11130036623697478 + d[0.08701500250887939] = 0.11120860550236845 + d[1.7194520131768571] = 0.11303758417848123 + d[0.5394215951385779] = 0.11171549463142898 + d[0.5608879376079421] = 0.11173954599497019 + d[1.0249308690327184] = 0.11225946464858512 + d[0.657883312358579] = 0.11184822152933906 + d[2.4301011240943042] = 0.11383371579793827 + d[1.6429158634832004] = 0.1129518377904649 + d[1.3575783351834136] = 0.11263215780901707 + d[0.8351933566128568] = 0.11204688210459145 + d[0.8586477160865329] = 0.11207316056447074 + d[1.0241573885616233] = 0.1122585980431296 + d[2.6416787733455775] = 0.11407072899982044 + d[1.3680382721209938] = 0.112643876814525 + d[1.9769402339185214] = 0.11332605304005336 + d[0.44239903124710556] = 0.11160678821553478 + d[0.8869914622098988] = 0.1121049170921021 + d[0.16750635674600334] = 0.11129879055172306 + d[2.2512662456722117] = 0.11363337598598186 + d[0.6428242868139584] = 0.11183134912489973 + d[1.8080338004989742] = 0.11313682492029752 + d[0.18876945557692126] = 0.1113226143870372 + d[1.2210595314022978] = 0.11247920528396067 + d[2.3049971007103673] = 0.11369356850865653 + d[1.0231732831196545] = 0.11225749545396017 + d[1.5922623849696032] = 0.11289508839996626 + d[0.7277076673101808] = 0.11192645386624563 + d[1.1063013789800975] = 0.11235063171790023 + d[0.4425848245650379] = 0.11160699638312263 + d[0.8725097627176533] = 0.11208869170242755 + d[1.991740448073561] = 0.1133426337425885 + d[0.5347973811078925] = 0.11171031355786767 + d[0.4815120917779906] = 0.1116506114665263 + d[0.4195802242580672] = 0.1115812214327056 + d[1.385131975518469] = 0.11266302807534455 + d[2.324270301743285] = 0.11371515939577145 + d[2.567550491155625] = 0.11398768998817743 + d[0.03537081000226516] = 0.11115074170013739 + d[0.3096415909518633] = 0.11145804314985618 + d[0.34954313102639767] = 0.11150274997122574 + d[1.8727252741845641] = 0.11320930005930771 + d[0.23385757676192287] = 0.11137313249678783 + d[3.8684261553548898] = 0.1154447789769315 + d[0.6511007330116222] = 0.11184062220603953 + d[0.796625374584367] = 0.1120036701502782 + d[1.8289980592697042] = 0.11316031165043745 + d[0.006389788755267967] = 0.111118270435286 + d[0.4298628453435611] = 0.11159274234973719 + d[1.2066544911904868] = 0.11246306611759503 + d[2.239113749183569] = 0.11361976197110601 + d[1.747917144477239] = 0.11306947458936054 + d[0.2887362796791022] = 0.11143462023072494 + d[1.4886105420682259] = 0.11277896170141787 + d[2.330486142928023] = 0.1137221227066187 + d[1.0623540837803782] = 0.11230139346940782 + d[1.3999574605418568] = 0.11267963807216969 + d[0.5744897685128243] = 0.11175478577749667 + d[1.7726143974323625] = 0.11309714364766306 + d[1.6538407369435073] = 0.11296407738556638 + d[3.2881058016892664] = 0.11479481707472841 + d[1.7499995139085247] = 0.11307180753177852 + d[1.1571274392167745] = 0.11240757671070933 + d[0.6566442833229627] = 0.11184683329917945 + d[0.4997127561015602] = 0.11167100392955226 + d[0.2882581797694904] = 0.11143408455357282 + d[0.4005545008992728] = 0.1115599045080193 + d[2.254371567071006] = 0.1136368547649081 + d[1.066846441098371] = 0.11230642668210548 + d[1.1083420814659124] = 0.11235291810359008 + d[1.9554168465158765] = 0.11330194030497645 + d[3.09777256021036] = 0.11458162610493589 + d[0.04888656412504622] = 0.11116588518357232 + d[0.24487465145429033] = 0.11138547635962694 + d[0.7998822420930631] = 0.11200731918042145 + d[0.752080737844661] = 0.1119537617946498 + d[1.6607784427815846] = 0.11297184998233457 + d[1.5261220744099318] = 0.11282098800202642 + d[0.030244466325566433] = 0.11114499798051419 + d[2.292192313879914] = 0.11367922385912192 + d[1.7743006135764032] = 0.11309903276255831 + d[1.2285190386368883] = 0.11248756278464117 + d[0.28619358917014837] = 0.11143177132570105 + d[0.6251277676565714] = 0.11181152161262957 + d[0.15517647334826679] = 0.11128497576567326 + d[1.0140867259121] = 0.11224731489588094 + d[0.2703008606158923] = 0.1114139646437641 + d[1.017372136944388] = 0.11225099586359011 + d[0.9358336443262084] = 0.11215964009650724 + d[2.2512873493721792] = 0.11363339962769634 + d[2.477751128927676] = 0.11388709486992425 + d[2.2382022725905033] = 0.11361874087501296 + d[0.24017641040400295] = 0.11138021230885668 + d[0.2428624858754368] = 0.11138322186875507 + d[1.957285553597898] = 0.11330403382722316 + d[1.432802021195272] = 0.11271643598907805 + d[1.6967747490548053] = 0.11301217803687702 + d[1.7837201253595236] = 0.11310958569770466 + d[1.3804252614703296] = 0.11265775481999936 + d[1.0711653972039625] = 0.11231126561568343 + d[1.739113507547545] = 0.11305961159901849 + d[1.2558451627963525] = 0.1125181784545268 + d[0.30109492793259496] = 0.11144846722093299 + d[2.592766736255305] = 0.11401593750613413 + d[0.9437591114392931] = 0.11216851981240006 + d[0.8005198902602275] = 0.11200803360836875 + d[0.6467376551798851] = 0.11183573373449479 + d[0.16198779093661808] = 0.11129260737861217 + d[2.0916750332857936] = 0.11345458984167149 + d[1.9943687200877398] = 0.11334557819671812 + d[0.41229375965876014] = 0.11157305748581835 + d[0.7763078082135217] = 0.11198090611312853 + d[0.16085856443768165] = 0.11129134215801154 + d[0.9434356757431205] = 0.11216815743420286 + d[1.0854525739243073] = 0.11232727287683907 + d[0.5912953277698302] = 0.11177361507612502 + d[1.3238695258586768] = 0.11259439138447418 + d[0.0761843397424733] = 0.11119647048295901 + d[1.9782801470037183] = 0.11332755414791786 + d[0.4971241074562782] = 0.1116681035458705 + d[2.887050489576874] = 0.11434558904231402 + d[1.1852602200740496] = 0.11243909630313721 + d[2.2092647864127315] = 0.11358632313370061 + d[1.3061697298758408] = 0.11257456097888081 + d[3.4450359928706966] = 0.1149705875616363 + d[1.6337481067977455] = 0.11294156675712305 + d[0.26467679283797807] = 0.11140766327121089 + d[1.3302500926432836] = 0.11260154000406093 + d[0.1716341637201615] = 0.1113034154750743 + d[0.7402995081146546] = 0.11194056194406128 + d[1.0641908535820033] = 0.1123034513764723 + d[1.8605709429689536] = 0.11319568336052475 + d[1.9400889316508505] = 0.11328476834528797 + d[0.09249330500653974] = 0.11121474356666335 + d[2.9422959397090964] = 0.11440747222870885 + d[0.1437830441026422] = 0.11127221021068462 + d[3.3051947395791053] = 0.11481395789620923 + d[0.10680215353339895] = 0.11123077565459437 + d[1.3787900173159549] = 0.11265592274307153 + d[2.6442144000695382] = 0.1140735694093858 + d[1.6968163340378073] = 0.11301222462605853 + d[3.3834640292544544] = 0.11490162421981388 + d[2.8262285929446582] = 0.11427745872156496 + d[0.34608756290001363] = 0.11149887825572259 + d[0.9122395761683153] = 0.11213320521252883 + d[1.134075772344481] = 0.11238174988531337 + d[1.1528706690722732] = 0.11240280747689509 + d[1.2294501136637386] = 0.11248860594440459 + d[1.8030226954268487] = 0.11313121085885615 + d[0.2720666344037451] = 0.11141594306903724 + d[1.3364256580587597] = 0.11260845894207401 + d[0.8205127085721591] = 0.11203043376861127 + d[2.8845190431563656] = 0.1143427534286676 + d[1.0789783884144013] = 0.11232001924272814 + d[0.8064001913324893] = 0.11201462196067961 + d[0.05030633676120666] = 0.11116747594223642 + d[0.42809578417709027] = 0.11159076248849936 + d[0.06439399625054243] = 0.11118326020604054 + d[1.65047377540116] = 0.11296030523837058 + d[2.758542610271101] = 0.11420163870101974 + d[1.3187343535521192] = 0.11258863806958291 + d[1.0140154675390252] = 0.11224723505813944 + d[0.4265746662370151] = 0.111589058188371 + d[0.7335207309357372] = 0.11193296690649916 + d[1.3967721140003895] = 0.11267606931401775 + d[0.6929124782768246] = 0.11188746880147565 + d[1.1676599740831106] = 0.11241937722947376 + d[1.6718501867564135] = 0.11298425410080594 + d[0.32559490479961495] = 0.11147591770097595 + d[0.7894329855173408] = 0.11199561171655921 + d[0.1931852441537555] = 0.11132756197280944 + d[1.0074554236238296] = 0.11223988519633918 + d[3.1742041628810176] = 0.11466723754807434 + d[1.8643612031983592] = 0.11319992965386741 + d[1.698666882243051] = 0.11301429786288081 + d[1.3390886780879359] = 0.11261144251731539 + d[0.015769907545254647] = 0.11112878022106425 + d[0.12909210231852009] = 0.11125575001755819 + d[0.953553934583041] = 0.11217949395467841 + d[1.5766630792010892] = 0.11287761173485959 + d[2.478625093288978] = 0.11388807390951151 + d[2.454119796143053] = 0.11386062233522629 + d[1.0792375113741355] = 0.11232030956241548 + d[1.6057676772536085] = 0.11291021901860711 + d[1.0682976210013897] = 0.11230805257586894 + d[1.0201759736040334] = 0.11225413727579539 + d[0.8768727002223932] = 0.11209357996708032 + d[1.641890133326469] = 0.11295068862117129 + d[1.060473467257854] = 0.1122992864364657 + d[1.3744501797636266] = 0.11265106052224284 + d[0.5180165542601631] = 0.11169151193517177 + d[3.0904970635556004] = 0.11457347671924908 + d[2.115862358132693] = 0.11348168654631609 + d[1.132385948359032] = 0.11237985662415773 + d[0.3438100732283753] = 0.1114963264922313 + d[0.12374853289320398] = 0.11124976291387996 + d[1.2537258921283063] = 0.1125158040661756 + d[1.6889807388589682] = 0.11300344611799097 + d[1.2149187970582962] = 0.11247232530984662 + d[1.9278409116774728] = 0.11327104678949593 + d[2.397174151325867] = 0.11379682972637721 + d[0.6107727173145092] = 0.11179543793521628 + d[0.2686148144842784] = 0.11141207554766742 + d[0.29414493350593385] = 0.11144068024469783 + d[0.28617319156196597] = 0.11143174847162207 + d[2.271346653670184] = 0.11365587131310441 + d[0.9023757400740209] = 0.11212215372291916 + d[0.31248056937085855] = 0.11146122402321974 + d[1.9530145908334253] = 0.11329924904479609 + d[0.13351265648971034] = 0.11126070294565749 + d[1.7263808985489142] = 0.1130453468423241 + d[0.176667919567421] = 0.11130905545146541 + d[0.5003008223150027] = 0.11167166281293242 + d[0.2936639448797914] = 0.1114401413309931 + d[0.502152624715758] = 0.11167373761633605 + d[0.674277568109726] = 0.11186658993860801 + d[1.271443971280286] = 0.11253565503514851 + d[0.06793176633977549] = 0.11118722403655783 + d[1.9311431925348763] = 0.11327474636333337 + d[0.8417463390438048] = 0.112054224123834 + d[2.1952229564015067] = 0.11357059247571077 + d[1.0387558670552912] = 0.11227495413259264 + d[1.6845372214517613] = 0.1129984678774748 + d[0.6585695410036472] = 0.11184899039208436 + d[1.1353764531067672] = 0.11238320715431736 + d[1.0904732729307893] = 0.1123328980323261 + d[0.34396666582380464] = 0.11149650194298377 + d[0.5914833829203645] = 0.1117738257769707 + d[1.3275602880699215] = 0.11259852641803954 + d[1.6787656703792724] = 0.11299200178734874 + d[1.9423549203009745] = 0.11328730694857603 + d[1.044547848042071] = 0.11228144344585081 + d[1.6612016925040787] = 0.11297232416620924 + d[1.1960631755278404] = 0.11245119977389485 + d[1.674714523023463] = 0.11298746312930219 + d[1.3072468290358281] = 0.11257576773442844 + d[1.1516242451784566] = 0.11240141099836894 + d[1.1581100286617798] = 0.11240867759184883 + d[0.8658909415777055] = 0.11208127592841331 + d[2.57888620645155] = 0.114000388395917 + d[0.8529478918216631] = 0.11206677443669215 + d[1.111523551658814] = 0.1123564825950958 + d[1.522555736320602] = 0.11281699243694432 + d[0.7409172840817939] = 0.11194125410885662 + d[1.538904251260079] = 0.11283530856850474 + d[0.1398944758837778] = 0.11126785333676842 + d[0.17165306103586775] = 0.11130343664821428 + d[2.9289654518574184] = 0.11439254013817127 + d[1.4138470777753485] = 0.11269519953429824 + d[1.3405911078791097] = 0.11261312579852924 + d[1.861333002897432] = 0.11319653710943536 + d[0.18535109667515992] = 0.11131878435208169 + d[0.8419454779395185] = 0.11205444724076967 + d[0.16912427817177766] = 0.11130060332124528 + d[0.5951917811843166] = 0.11177798074212232 + d[2.3086041027320015] = 0.11369760927267275 + d[1.0644319320679843] = 0.11230372147950128 + d[0.5034611302622742] = 0.11167520369696828 + d[1.9703801338018438] = 0.11331870374065356 + d[0.00124742563213176] = 0.11111250876678173 + d[0.9151285325579208] = 0.11213644201211363 + d[0.6839042358184435] = 0.11187737581896455 + d[2.3567115714432254] = 0.11375150173907295 + d[0.27373401544094844] = 0.11141781125210563 + d[0.6145824462930545] = 0.11179970643043084 + d[0.5808102079591724] = 0.11176186733077456 + d[2.485770018076748] = 0.1138960778515406 + d[0.2913984540176038] = 0.11143760300880373 + d[0.25283214405824783] = 0.11139439217317883 + d[0.4403167252967246] = 0.11160445514659288 + d[1.297758111933952] = 0.11256513680447959 + d[0.1778789760067504] = 0.11131041235666955 + d[1.175111239004945] = 0.11242772552720895 + d[2.8550253602631095] = 0.1143097158269338 + d[0.14332576565010813] = 0.11127169786155726 + d[1.934229241460418] = 0.11327820368940095 + d[0.0014702266770847405] = 0.11111275840021548 + d[0.8163625617799724] = 0.11202578390302577 + d[0.8248165139747877] = 0.11203525579383816 + d[0.5538394521979637] = 0.11173164871831615 + d[0.3659538281076349] = 0.11152113697295954 + d[0.36549920680579073] = 0.11152062760268683 + d[2.4246708590515067] = 0.11382763261649549 + d[0.2423234214624369] = 0.11138261788475222 + d[1.8025186170690064] = 0.11313064612759108 + d[1.0267588226096527] = 0.11226151268273273 + d[2.2828863098109062] = 0.11366879872908352 + d[0.33882831069633856] = 0.11149074478494926 + d[0.26932784671170884] = 0.11141287445013089 + d[2.926531031783942] = 0.11438981322890006 + d[0.02264603788837971] = 0.1111364844578645 + d[0.37689990897029424] = 0.11153340126299312 + d[0.12759166404694233] = 0.11125406887923085 + d[0.2263450977520045] = 0.11136471528759415 + d[0.37919977458802534] = 0.11153597809530466 + d[1.9036643674218616] = 0.11324396155525333 + d[1.6408942980281362] = 0.11294957294425438 + d[0.5083639463163601] = 0.11168069692778759 + d[1.0674765230938266] = 0.11230713262243121 + d[0.9902781063763719] = 0.11222063974639525 + d[0.14279437415810137] = 0.11127110247385237 + d[0.3851324652355814] = 0.11154262524347926 + d[0.10443034605562729] = 0.11122811820632987 + d[0.2002534733466831] = 0.1113354814343696 + d[1.046236004216913] = 0.1122833348491108 + d[1.0479266367834832] = 0.11228522902671197 + d[0.9247357944838415] = 0.11214720602744817 + d[1.5532202240024517] = 0.11285134750995772 + d[3.0785257098346968] = 0.11456006741458882 + d[0.1658012782725784] = 0.11129688012870062 + d[0.9269565389206108] = 0.1121496941577448 + d[1.428036685950305] = 0.1127110970775531 + d[2.312126170898501] = 0.11370155488713958 + d[1.9927588601631006] = 0.11334377467014538 + d[2.3505379435860996] = 0.11374458574302611 + d[0.3876949521701011] = 0.11154549632335209 + d[1.4414909069920148] = 0.11272617070104295 + d[2.210045804744393] = 0.1135871980852088 + d[1.6833158790474716] = 0.11299709956102554 + d[0.6641525707025349] = 0.11185524571681862 + d[1.8613174935232144] = 0.11319651973401607 + d[0.7043034720242487] = 0.11190023145225514 + d[2.1618465845538504] = 0.1135332017718855 + d[1.0988369990988307] = 0.11234226868763955 + d[0.14219421428740286] = 0.11127043003589455 + d[0.2513198969395436] = 0.11139269780619843 + d[0.4583257642705659] = 0.11162463293106742 + d[0.5443468391883222] = 0.11172101298496522 + d[1.4950640002785525] = 0.11278619188724773 + d[0.10845454093364704] = 0.11123262704178102 + d[1.2756031220744477] = 0.112540314857749 + d[0.08593350339428263] = 0.11120739375635467 + d[1.6763303482047858] = 0.11298927340135696 + d[1.2970399462956954] = 0.11256433218869129 + d[1.0786796576431477] = 0.11231968454669909 + d[1.029692738882905] = 0.11226479983396068 + d[1.2822695173087375] = 0.11254778373974314 + d[0.47175867611121036] = 0.11163968350014593 + d[2.275114252717167] = 0.11366009200608701 + d[1.6229511684565963] = 0.11292947046960254 + d[0.6267746603216362] = 0.11181336682263987 + d[1.8318220450997447] = 0.11316347542114832 + d[0.9879059186090935] = 0.11221798194794338 + d[1.988504178179833] = 0.1133390081469494 + d[2.3772189028933752] = 0.11377447499908683 + d[1.1889818146247793] = 0.11244326592340796 + d[1.8870904508309263] = 0.11322539358118439 + d[2.2588680036629967] = 0.11364189195716447 + d[0.08049844426549702] = 0.11120130414310218 + d[0.4260101339284408] = 0.11158842567166347 + d[0.7401837238018931] = 0.11194043221770303 + d[0.16736982831546743] = 0.11129863758101881 + d[1.1140533765077618] = 0.11235931698829954 + d[1.5495348589608193] = 0.11284721860258884 + d[2.098567122692259] = 0.11346231095649445 + d[2.0256731232922536] = 0.11338064846073594 + d[0.16314045034487934] = 0.11129389885416144 + d[0.22636052817659558] = 0.11136473257631045 + d[0.5173640189161395] = 0.1116907808194318 + d[0.7483025224340918] = 0.11194952863128323 + d[0.37556046379047126] = 0.11153190051193528 + d[3.4515887388463415] = 0.11497792687798995 + d[0.4877041814539639] = 0.1116575492342603 + d[1.14445007062919] = 0.11239337313611449 + d[1.3404932108957968] = 0.11261301611743486 + d[1.196644619087985] = 0.11245185121435773 + d[0.862861883447001] = 0.11207788214942299 + d[1.5593645012743433] = 0.11285823126229785 + d[2.2620209972342824] = 0.11364542413788913 + d[0.7380035991587159] = 0.11193798957553563 + d[0.5868757694177753] = 0.11176866331195177 + d[0.36247642894481125] = 0.11151724079869257 + d[1.0339163368820614] = 0.1122695319397981 + d[1.3207783772820776] = 0.1125909281414408 + d[1.2063880328859677] = 0.11246276758200585 + d[0.48420121053795406] = 0.11165362442067851 + d[0.21073934676764028] = 0.11134723012849929 + d[1.8413664554474214] = 0.11317416821758143 + d[1.5663839834053495] = 0.11286609554723034 + d[1.8039416344054642] = 0.11313224036850358 + d[0.32391459768000863] = 0.111474035036863 + d[0.2937063613353843] = 0.11144018885562895 + d[1.0127375131076468] = 0.11224580324044191 + d[1.9433271206208054] = 0.11328839611134317 + d[1.2295442844950664] = 0.11248871145171134 + d[2.046313628132495] = 0.1134037719074563 + d[0.29146203819243666] = 0.11143767425037332 + d[0.9250797559714069] = 0.11214759140319328 + d[0.17451338664026306] = 0.11130664144589343 + d[3.4037580482762406] = 0.11492435452034806 + d[0.6122328782869517] = 0.11179707392833371 + d[0.2153435428707462] = 0.11135238881052148 + d[1.7193885187680344] = 0.11303751304352937 + d[1.4065296004091379] = 0.11268700127988722 + d[1.1729530648079207] = 0.11242530753809638 + d[0.24085648886495603] = 0.11138097428926819 + d[2.6677123540364818] = 0.1140998917681647 + d[0.9710201146698731] = 0.11219906308776689 + d[0.37920127087529365] = 0.11153597977178578 + d[2.714269666803755] = 0.11415204488191993 + d[1.227497281772729] = 0.11248641802649216 + d[0.05767059954619158] = 0.11117572709764888 + d[0.6325959021200656] = 0.11181988905227812 + d[0.23701568759500935] = 0.11137667093963206 + d[1.4351514462592627] = 0.1127190682002707 + d[0.8598581580009019] = 0.11207451675284107 + d[0.1665943366095637] = 0.11129776869596338 + d[1.074209085178133] = 0.11231467574538749 + d[2.5353207974023837] = 0.11395158576908891 + d[0.21405803010418434] = 0.1113509484827615 + d[1.5059235388412358] = 0.11279835845268449 + d[0.8948150792666413] = 0.1121136827180878 + d[0.5481568563113477] = 0.11172528181272337 + d[2.064244219951556] = 0.11342385940617707 + d[0.6347352329159957] = 0.11182228599869194 + d[0.9919249698136616] = 0.11222248489147174 + d[0.9482549210333927] = 0.112173556928512 + d[1.9388331511216719] = 0.11328336148509646 + d[0.20094786437125856] = 0.11133625945141282 + d[0.5867856921203232] = 0.11176856238748517 + d[0.5681569505155755] = 0.11174769035350753 + d[0.6185293208612965] = 0.11180412858563682 + d[0.26820697107306457] = 0.11141161858780463 + d[1.509274641603208] = 0.11280211288341055 + d[0.7608954947656579] = 0.11196363796410205 + d[1.6023131336372578] = 0.11290634873160821 + d[0.9224477981764132] = 0.11214464254759059 + d[0.5068161853802875] = 0.11167896277999273 + d[0.3890218173832837] = 0.11154698297906412 + d[1.5421686008427788] = 0.11283896579384647 + d[1.977262042223448] = 0.11332641356269588 + d[0.31998162100922] = 0.11146962841717727 + d[0.1573529297746845] = 0.1112874143354754 + d[0.6576828501383234] = 0.11184799692790809 + d[1.0956933741674855] = 0.11233874659472357 + d[0.05210892170171444] = 0.11116949561603848 + d[1.7520163364222485] = 0.11307406703949174 + d[1.1932719412158557] = 0.11244807251733263 + d[0.31902581392762996] = 0.11146855750350322 + d[1.596106827311045] = 0.1128993955127874 + d[0.28302318701329066] = 0.11142821911396476 + d[2.7634720613006225] = 0.11420716056837546 + d[1.1129275330335515] = 0.11235805560336783 + d[1.7210428228342936] = 0.11303936641664927 + d[0.40162223034685296] = 0.11156110082064832 + d[0.20181334251527383] = 0.11133722915971335 + d[1.1386778881443602] = 0.11238690604673174 + d[0.9017172474276585] = 0.11212141594436946 + d[1.4568505295891852] = 0.11274337904647527 + d[0.7904749134603617] = 0.11199677910452989 + d[2.2749474069588613] = 0.11365990509539366 + d[2.4491209585814855] = 0.11385502247428016 + d[1.055594570754492] = 0.11229382014511535 + d[1.5629885162263841] = 0.1128622914322832 + d[0.7007295257878934] = 0.1118962271466285 + d[2.3542515903029564] = 0.11374874595012342 + d[0.05771932915223832] = 0.1111757816958564 + d[1.3777695577873499] = 0.11265477945168242 + d[1.534733954875422] = 0.11283063636094863 + d[0.48760155078003964] = 0.11165743424436947 + d[1.7363742887190026] = 0.11305654276449553 + d[0.4011119367078101] = 0.11156052907401133 + d[2.3880171269429455] = 0.1137865716417983 + d[0.5803097285263566] = 0.11176130658314842 + d[0.13299298275023674] = 0.11126012068684377 + d[0.2224786685615725] = 0.11136038322280299 + d[1.5644835818595106] = 0.11286396643066278 + d[1.4669337086130163] = 0.11275467584992536 + d[0.08330050861114535] = 0.11120444366520847 + d[1.8913803749602027] = 0.11323019964223136 + d[0.25306971795573774] = 0.11139465835808808 + d[0.3621103413906027] = 0.11151683062404763 + d[0.5814133399170474] = 0.1117625430924244 + d[0.9786022611974949] = 0.11220755812946785 + d[0.3934702241833423] = 0.11155196709416007 + d[0.25870822452801145] = 0.11140097590942631 + d[1.6185215958971901] = 0.11292450781992863 + d[0.4760585396169903] = 0.11164450117315808 + d[0.5463267746606453] = 0.11172323134868382 + d[2.013278261110785] = 0.11336676253561022 + d[0.3260508297526633] = 0.11147642853231131 + d[0.6830954081053149] = 0.11187646959495628 + d[1.1146724563806663] = 0.11236001059979725 + d[1.0450100600476016] = 0.11228196130630722 + d[1.5750225956827513] = 0.11287577381946558 + d[2.3208548141499454] = 0.11371133318514148 + d[0.01120230322842286] = 0.11112366253077816 + d[0.8338478321730382] = 0.11204537456686159 + d[1.6056399498779494] = 0.11291007591966896 + d[0.9338705191043081] = 0.11215744060482286 + d[1.8935358371715947] = 0.11323261443534154 + d[1.2263990851208826] = 0.11248518762647501 + d[0.05512476714481307] = 0.11117287466567449 + d[1.7679847677413107] = 0.11309195694289846 + d[2.7330497457859164] = 0.11417308205940742 + d[0.33903476951328515] = 0.1114909761072433 + d[0.4294285586593114] = 0.11159225576366193 + d[1.695195685687072] = 0.11301040895413306 + d[1.1916104545810045] = 0.11244621101262972 + d[0.707854971423999] = 0.11190421060750295 + d[0.14192141343813947] = 0.11127012438125884 + d[2.0565739838859196] = 0.11341526650738508 + d[1.7134558673762865] = 0.11303086648979765 + d[1.882130948751524] = 0.11321983737986988 + d[2.151193471790883] = 0.11352126732572507 + d[0.6307279128514096] = 0.11181779612185229 + d[1.8587606796797873] = 0.11319365529098262 + d[2.6353679614138565] = 0.1140636596221217 + d[1.0439679944677112] = 0.1122807937802369 + d[2.1825231032755807] = 0.11355636517101518 + d[3.2104460139204276] = 0.11470783180731299 + d[1.1270658010421053] = 0.11237389598523556 + d[0.06211299398670045] = 0.11118070449827665 + d[1.6466812588739175] = 0.11295605632272074 + d[1.4364087777405046] = 0.11272047686894525 + d[1.7903199072828917] = 0.11311697960657 + d[0.267791037972112] = 0.1114111525640103 + d[0.005094145470445843] = 0.11111681875501284 + d[0.8262399894026207] = 0.1120368506692621 + d[0.11411106084022171] = 0.11123896478571858 + d[0.29945006034970223] = 0.11144662426345793 + d[1.175185420756769] = 0.11242780863943158 + d[0.4177043911335885] = 0.11157911969999687 + d[2.4805513870521607] = 0.11389023179780265 + d[0.5698012018653515] = 0.11174953260784014 + d[1.0562858723905544] = 0.1122945946761278 + d[0.25465166530353334] = 0.11139643081924626 + d[3.0125660699790293] = 0.11448618444350254 + d[0.5414621581561267] = 0.11171778092395569 + d[0.7430354763884464] = 0.11194362736086799 + d[0.37533240560360515] = 0.11153164498929329 + d[0.05357124285811299] = 0.11117113404740926 + d[1.5957141434813118] = 0.11289895557036356 + d[0.5436727707193661] = 0.11172025774363534 + d[0.9519936636811853] = 0.11217774582399134 + d[1.1605837198714228] = 0.11241144908475359 + d[1.4109159373932427] = 0.11269191558424767 + d[1.7403164005547909] = 0.11306095923827975 + d[1.7034852255756756] = 0.11301969602729339 + d[0.8604609212623598] = 0.11207519209337406 + d[1.4104176407698423] = 0.1126913573095686 + d[1.1025904084343956] = 0.11234647397731545 + d[0.17184044789202202] = 0.11130364660227299 + d[1.8221685092204736] = 0.11315266035789844 + d[1.577823257951969] = 0.11287891154072989 + d[2.294530184237617] = 0.11368184287615933 + d[0.4558744757688522] = 0.11162188644576676 + d[2.965540572297183] = 0.11443350952384024 + d[1.0580815432552753] = 0.11229660653693108 + d[0.4101207289455896] = 0.111570622764681 + d[3.5483633112102146] = 0.11508631679496559 + d[0.08268691298716035] = 0.11120375617313906 + d[0.3501319316920575] = 0.11150340967998774 + d[2.201964506318206] = 0.11357814484363984 + d[0.36076161338944446] = 0.11151531947177608 + d[0.5212961150937715] = 0.11169518643100285 + d[0.9244026414410454] = 0.11214683276151834 + d[1.8257063239781777] = 0.11315662384894624 + d[1.543193639193614] = 0.11284011419888215 + d[1.0723838798616616] = 0.11231263079640519 + d[0.24983645280779399] = 0.11139103571091066 + d[2.1411432956935634] = 0.11351000832127427 + d[2.052877331651444] = 0.11341112517714654 + d[2.818245374802607] = 0.1142685161793841 + d[0.4589644926347538] = 0.1116253485783643 + d[0.5939997242184323] = 0.11177664513721124 + d[1.8821045493535942] = 0.11321980780423749 + d[1.2731579979932643] = 0.11253757539378563 + d[2.013056563265251] = 0.11336651416802355 + d[1.7532440435733294] = 0.11307544247698882 + d[1.3468427387315653] = 0.11262012995246105 + d[1.120217793776335] = 0.11236622354446239 + d[0.31848867971408745] = 0.1114679556829128 + d[0.8217366849799541] = 0.11203180512372726 + d[0.3423730847314127] = 0.11149471644983776 + d[1.5899883641542885] = 0.11289254070483497 + d[0.5503708957446254] = 0.11172776247140938 + d[0.05632097224760213] = 0.11117421493209931 + d[0.0780514618001773] = 0.11119856246600568 + d[2.0109216091946713] = 0.11336412238355033 + d[2.7179254541102473] = 0.11415614004789705 + d[1.609556335714329] = 0.1129144636286515 + d[1.5290553834272043] = 0.11282427434879144 + d[0.22631987391841446] = 0.111364687026045 + d[1.025842592766555] = 0.1122604861413711 + d[1.5667195833958107] = 0.11286647153694013 + d[0.6385651381973767] = 0.11182657709603841 + d[1.2728082029349008] = 0.11253718349095124 + d[1.4945513047984564] = 0.11278561748473341 + d[2.0502748384249] = 0.11340820962346582 + d[1.1079540603365885] = 0.11235248336804406 + d[1.2871982234216297] = 0.11255330575079442 + d[2.197553218405538] = 0.11357320300315717 + d[1.6209830066281934] = 0.11292726544950842 + d[1.6482958583983032] = 0.11295786522661545 + d[1.1574225017567952] = 0.11240790729516104 + d[1.2886824434453206] = 0.11255496863699331 + d[1.8687162884100212] = 0.11320480872809913 + d[0.12012924273682812] = 0.11124570774693165 + d[0.3375119998565569] = 0.11148926995305658 + d[0.5773204810757109] = 0.11175795736757221 + d[0.11069391704652687] = 0.11123513610968434 + d[2.04397734734105] = 0.11340115458752914 + d[0.3100918540765897] = 0.11145854763766835 + d[1.628059544030926] = 0.11293519361024745 + d[2.588546042722861] = 0.11401120944595575 + d[2.708364973392632] = 0.114145430515116 + d[1.3172693363712522] = 0.11258699670161468 + d[1.2255545217676929] = 0.1124842413926327 + d[2.183782507547537] = 0.11355777604887618 + d[1.810732285101058] = 0.11313984809620017 + d[1.5206430733734684] = 0.11281484957471921 + d[0.6710821399928445] = 0.11186300972630339 + d[0.3361154688708896] = 0.11148770524020142 + d[2.0356994170151945] = 0.11339188087094412 + d[0.21984639605446632] = 0.111357433944548 + d[2.4009140374385183] = 0.11380101930055239 + d[1.4549099567632904] = 0.11274120490267288 + d[0.9578828780547524] = 0.11218434411092967 + d[1.0877449998194206] = 0.11232984129474612 + d[0.5024581856684882] = 0.11167407997407584 + d[0.20067027547434768] = 0.11133594843228291 + d[2.383979384802638] = 0.11378204838867359 + d[1.0373715152684575] = 0.11227340310982387 + d[2.0336805452726123] = 0.11338961913941527 + d[0.5759860714913152] = 0.1117564622669596 + d[1.4054733640782255] = 0.11268581790797522 + d[2.2463590677342964] = 0.11362787864959048 + d[0.6426621679234878] = 0.11183116748391138 + d[1.8584071887446207] = 0.11319325926887423 + d[2.6049467168662304] = 0.11402958161652614 + d[1.6034466006167034] = 0.11290761860788857 + d[0.4860062713112854] = 0.11165564685460147 + d[0.1510849743123317] = 0.11128039152214862 + d[0.6170796935398963] = 0.11180250439500097 + d[1.755707594526239] = 0.11307820246718986 + d[0.5696973057701882] = 0.11174941620043896 + d[1.5560206956872202] = 0.1128544850240429 + d[0.9525515175453904] = 0.11217837084461134 + d[1.7778816058238507] = 0.11310304464676685 + d[1.9926839589552894] = 0.11334369075829069 + d[1.022582854040058] = 0.11225683393872844 + d[0.4563918683227415] = 0.1116224661454145 + d[1.9169964611532637] = 0.11325889764786735 + d[0.14621699605759353] = 0.1112749372867974 + d[1.5311702526027384] = 0.11282664375203004 + d[1.380007363642455] = 0.11265728662023326 + d[0.32842649618547826] = 0.11147909029674208 + d[2.6434554630030087] = 0.11407271924805008 + d[0.9742336429198045] = 0.11220266352727651 + d[2.542617413609344] = 0.11395975957084163 + d[2.0929450628164457] = 0.11345601263912534 + d[1.3959966966842159] = 0.11267520056165892 + d[0.8548148859838439] = 0.11206886623178662 + d[0.17643736335775673] = 0.11130879712913382 + d[2.5154202795420355] = 0.11392929280263747 + d[1.060667165058548] = 0.1122995034544827 + d[1.2490552020503527] = 0.11251057111737335 + d[0.7299499071603579] = 0.11192896610427841 + d[0.5615934171903783] = 0.11174033642956707 + d[0.6659163601285049] = 0.11185722189724948 + d[1.3218900506706583] = 0.1125921736316918 + d[1.8523989381693609] = 0.1131865281177846 + d[1.81439577270567] = 0.11314395238631023 + d[0.11955634522121772] = 0.1112450658544598 + d[0.5187621339715484] = 0.11169234729996194 + d[1.3261731688975995] = 0.1125969723260959 + d[2.078143618600209] = 0.11343943076108286 + d[1.6652532851116852] = 0.11297686332915677 + d[2.6639623984383136] = 0.11409569108231628 + d[2.2536471026821348] = 0.11363604317386035 + d[0.770576509724433] = 0.11197448469592926 + d[0.4004535753349133] = 0.11155979142831621 + d[1.3302255381662451] = 0.1126015124938761 + d[0.1271849527391794] = 0.11125361318706044 + d[0.6324467339072337] = 0.111819721921403 + d[1.368336555393921] = 0.1126442110021803 + d[0.7730232784888782] = 0.11197722608590141 + d[0.12613158049655926] = 0.11125243295558675 + d[0.40715829039772755] = 0.11156730356990167 + d[0.3084058030640917] = 0.11145665853738591 + d[0.9304658728237056] = 0.11215362602783731 + d[0.7813939796359188] = 0.11198660472062788 + d[1.6249250699421791] = 0.11293168191967337 + d[1.2529592079793495] = 0.1125149450885402 + d[0.8580732735227545] = 0.11207251695460359 + d[0.3110929252102187] = 0.11145966926667057 + d[1.2993571593557414] = 0.11256692833921582 + d[2.299759585022426] = 0.11368770114911507 + d[0.03516228893275464] = 0.1111505080664545 + d[2.3213224495792986] = 0.1137118570552963 + d[1.117846017619561] = 0.11236356622869902 + d[1.7266549819249624] = 0.11304565390705619 + d[0.39316629960909666] = 0.11155162656887674 + d[1.9913249929831307] = 0.11334216830801017 + d[1.3780394396449556] = 0.1126550818190029 + d[3.524543545583675] = 0.11505963827109587 + d[1.2201371642177303] = 0.11247817187967965 + d[0.680403175704298] = 0.11187345317283057 + d[0.571815066665678] = 0.11175178898483863 + d[0.7850824004151666] = 0.1119907372706962 + d[0.027675843899170105] = 0.1111421200136689 + d[0.5071134349298484] = 0.11167929582539304 + d[0.7300563033611531] = 0.11192908531211813 + d[0.2021875359152978] = 0.1113376484174911 + d[1.7415859815628556] = 0.11306238159004618 + d[2.2408454551192256] = 0.11362170194177353 + d[1.1188530809987434] = 0.1123646945331157 + d[1.4100878148871394] = 0.11269098778379515 + d[0.27162324685233696] = 0.11141544628449199 + d[2.2675101518387883] = 0.11365157342884054 + d[0.030744896089612173] = 0.11114555867805022 + d[0.41320442433907556] = 0.11157407781859582 + d[2.071475522444647] = 0.11343196056411343 + d[0.8064157647180917] = 0.11201463940926522 + d[0.40634960680039733] = 0.11156639749929367 + d[0.24031479512594522] = 0.11138036735927193 + d[1.2803366524749769] = 0.11254561820105843 + d[2.943232920180553] = 0.11440852178217971 + d[0.1584953524193139] = 0.11128869434149155 + d[0.0774929959570827] = 0.1111979367430822 + d[0.6745191249284492] = 0.1118668605829799 + d[2.7949111303043397] = 0.11424237784664905 + d[2.4906285906474297] = 0.11390152055386582 + d[2.1918515317086085] = 0.1135668155613781 + d[2.682727886190809] = 0.11411671208452055 + d[0.6823029082279181] = 0.11187558166489778 + d[1.0971422081964823] = 0.11234036985718712 + d[1.302159932898534] = 0.11257006849956461 + d[0.012146770767081483] = 0.1111247207424838 + d[1.7628406705552715] = 0.11308619386273354 + d[3.0346562630924203] = 0.11451092829565988 + d[1.8064035299281247] = 0.11313499848932805 + d[1.7395792342941832] = 0.11306013336751233 + d[2.298242883154357] = 0.11368600205362554 + d[0.4161079180368872] = 0.1115773309695252 + d[0.8044866375131198] = 0.11201247799468443 + d[2.4717891517575428] = 0.11388041609117769 + d[0.6797981672228433] = 0.1118727753111831 + d[0.5314396924737523] = 0.11170655152741503 + d[1.2147214293971746] = 0.11247210418243202 + d[1.2354075178567958] = 0.11249528051155594 + d[1.066965243376407] = 0.1123065597875121 + d[0.48168133644593547] = 0.11165080109238103 + d[2.0196755677763796] = 0.1133739294207251 + d[2.298457326532963] = 0.11368624228528702 + d[0.3203525995436981] = 0.11147004407216458 + d[1.059422390008231] = 0.1122981088148896 + d[1.0689585031782758] = 0.11230879302447622 + d[1.2717295826601915] = 0.11253597502800836 + d[1.7080355264945197] = 0.1130247938916793 + d[0.9933230484148364] = 0.11222405129798657 + d[1.9545319921040687] = 0.11330094899782628 + d[1.1395717573140123] = 0.11238790752802295 + d[1.00254191749869] = 0.11223438011073496 + d[0.361744386470792] = 0.11151642059800673 + d[0.15831033464746813] = 0.11128848704180162 + d[1.1646839603409365] = 0.11241604294220818 + d[0.9239399039393298] = 0.11214631430865912 + d[0.3637858127426046] = 0.11151870786857396 + d[1.9373363188125179] = 0.11328168457255217 + d[1.1109676246821638] = 0.11235585973940485 + d[0.2863102299565746] = 0.11143190201346194 + d[0.11444310656094836] = 0.11123933682024627 + d[0.5718708646361645] = 0.11175185150207055 + d[2.0866990244073733] = 0.1134490152819204 + d[0.7301158208856944] = 0.1119291519964118 + d[1.3086175763378167] = 0.11257730348602485 + d[0.13752598733703714] = 0.11126519960777191 + d[1.3605965299648444] = 0.11263553930663872 + d[1.4738188904202323] = 0.11276238973541136 + d[1.2842131958528964] = 0.11254996139354775 + d[1.6071833115849883] = 0.11291180501967933 + d[0.38588768383443994] = 0.1115434714109013 + d[0.05922519524462877] = 0.11117746891633433 + d[0.7724168816890902] = 0.11197654667145879 + d[0.594428783967822] = 0.11177712586450239 + d[0.21323743273149032] = 0.11135002906039392 + d[0.8754912531352913] = 0.1120920321845513 + d[1.3677335846997674] = 0.11264353545184522 + d[1.6267088700214285] = 0.11293368039027947 + d[0.8439325232323586] = 0.11205667354332612 + d[2.171182680408379] = 0.1135436607797829 + d[2.903299688730348] = 0.11436379064282949 + d[1.9561544525715564] = 0.11330276664892465 + d[0.13180395132387013] = 0.11125878845860165 + d[0.08014967768954107] = 0.11120091337392334 + d[2.8651550691978307] = 0.11432106272597065 + d[0.18450874142393703] = 0.11131784055120374 + d[0.37230644676693303] = 0.11152825462197129 + d[1.4976495393610676] = 0.11278908861640523 + d[1.6444564455484394] = 0.1129535637701204 + d[0.9180410926795297] = 0.11213970525691276 + d[0.009703363337131177] = 0.11112198307047341 + d[1.141871574381562] = 0.11239048421776301 + d[0.5503356796308493] = 0.11172772301449903 + d[2.2648940392130106] = 0.1136486426980176 + d[1.4677253325993016] = 0.11275556275437724 + d[0.9833853904123229] = 0.11221291714851006 + d[1.4152142612169112] = 0.1126967312798783 + d[1.2405566527897403] = 0.11250104950620886 + d[1.7156983660058744] = 0.11303337883873693 + d[1.1496496324720278] = 0.11239919866550359 + d[1.4219924578584098] = 0.11270432533703544 + d[1.7645182178887842] = 0.11308807326764496 + d[0.5155990429331736] = 0.11168880329931549 + d[0.47909971956356323] = 0.1116479085857479 + d[0.09683596719942833] = 0.1112196092233246 + d[1.6269730959103903] = 0.11293397641427147 + d[1.911505784350221] = 0.11325274638442188 + d[1.2994040176780428] = 0.1125669808381634 + d[0.7664091518152574] = 0.11196981553590599 + d[0.8874745970775277] = 0.11210545839931806 + d[1.970131496473488] = 0.1133184251914145 + d[1.4097223868037916] = 0.11269057837050726 + d[1.3812185866263826] = 0.11265864363685683 + d[0.47197037271613795] = 0.11163992069025142 + d[1.852468619383501] = 0.11318660618292647 + d[1.9018960470303847] = 0.11324198048459622 + d[1.060628058078739] = 0.11229945963922441 + d[0.6800484292604256] = 0.11187305570896842 + d[0.4505632861278337] = 0.11161593565466738 + d[0.21128358723201346] = 0.11134783991216354 + d[0.6222201573629889] = 0.11180826387022519 + d[0.4114426161340443] = 0.11157210384209636 + d[0.17359146397563396] = 0.11130560849510553 + d[1.2200145053012894] = 0.11247803445474058 + d[1.3083636613514806] = 0.11257701900592541 + d[1.3200757952622955] = 0.11259014098657391 + d[0.9084260003332224] = 0.11212893246443419 + d[0.4202866018599001] = 0.11158201287670118 + d[2.863685080187789] = 0.11431941610367342 + d[0.8494717607937938] = 0.11206287975134305 + d[1.1502012329441462] = 0.11239981667221859 + d[2.7119005603433575] = 0.11414939103800767 + d[1.2222487088251839] = 0.11248053761772812 + d[1.3714723070526273] = 0.11264772420403805 + d[0.3383816642881833] = 0.1114902443496859 + d[1.2479079659955432] = 0.11250928577650712 + d[2.209089149080963] = 0.1135861263724317 + d[0.4443009514439846] = 0.1116089191755456 + d[1.7513491510278874] = 0.11307331957141813 + d[0.024035995083559802] = 0.11113804181044294 + d[0.15264358438739611] = 0.11128213783765863 + d[1.3828481346836854] = 0.11266046933169191 + d[0.4153417521649536] = 0.1115764725370943 + d[0.35127198562555806] = 0.11150468702833247 + d[1.4778439234906555] = 0.11276689922118564 + d[2.3507883221987553] = 0.11374486622935467 + d[0.10894469508648608] = 0.11123317622601694 + d[0.5712278196050526] = 0.11175113102074494 + d[0.6430975627400506] = 0.1118316553082739 + d[2.3348496840025144] = 0.1137270109702929 + d[0.48632693716823594] = 0.11165600613640342 + d[0.26004384167864014] = 0.11140247237473369 + d[0.16827687736438546] = 0.11129965386700949 + d[1.0524713515966353] = 0.11229032090504706 + d[1.1894633755280495] = 0.11244380545714275 + d[0.5449168795571844] = 0.1117216516708814 + d[2.8372312184702664] = 0.1142897834863564 + d[3.039150361460742] = 0.11451596225071584 + d[1.772477910733176] = 0.11309699073779914 + d[0.6322470493378292] = 0.11181949819104908 + d[0.7191585285692639] = 0.11191687528505254 + d[0.5445789641091044] = 0.11172127306289409 + d[1.3694192694836578] = 0.1126454240425872 + d[1.0819910450008203] = 0.11232339460337644 + d[3.5552898658890077] = 0.11509407462338819 + d[2.1660409194110697] = 0.11353790058781192 + d[0.9961391918977659] = 0.11222720650324369 + d[3.0245866973742883] = 0.11449964910154965 + d[2.515081299671686] = 0.11392891306988956 + d[0.6607209823371583] = 0.11185140090498064 + d[0.855758323923662] = 0.11206992326707596 + d[2.1666554544718024] = 0.11353858903695517 + d[1.6583361393452423] = 0.11296911377009823 + d[2.2517266635892694] = 0.11363389177556515 + d[0.03201714453628668] = 0.11114698414595674 + d[1.9950982726955442] = 0.11334639551461781 + d[2.8283024870893074] = 0.11427978182859767 + d[1.1915217355607604] = 0.11244611161316412 + d[0.04044066536858093] = 0.11115642212838832 + d[0.07530657229708537] = 0.1111954870043383 + d[0.1811255495750197] = 0.11131404991832565 + d[1.5995373553986476] = 0.11290323889633087 + d[0.8488855514001372] = 0.11206222295752495 + d[1.7814241744105457] = 0.11310701348240099 + d[2.025244192641506] = 0.11338016793142135 + d[2.4247347593708692] = 0.11382770419999724 + d[1.325183871265709] = 0.11259586394286998 + d[1.3070912236025127] = 0.11257559339791405 + d[1.2107267863342064] = 0.112467628650723 + d[1.8814855219386901] = 0.11321911429872773 + d[1.283185666230717] = 0.11254881017246751 + d[1.2778245820694556] = 0.11254280373288525 + d[0.09948203397959632] = 0.111222573960536 + d[3.626230993608809] = 0.11517352892017901 + d[0.2920099548386226] = 0.11143828815220945 + d[1.9710065319293948] = 0.11331940549655646 + d[0.6729971241631013] = 0.11186515530736894 + d[0.9534052218464407] = 0.11217932733663294 + d[2.1766280584043796] = 0.11354976110246175 + d[0.7830555679016088] = 0.1119884663837715 + d[2.007007693991755] = 0.11335973763114922 + d[1.7964554719180275] = 0.11312385343598277 + d[1.2407440728878067] = 0.11250125948814683 + d[2.5652246461022785] = 0.11398508454521586 + d[0.44522500743917737] = 0.11160995451146762 + d[1.050796133561651] = 0.11228844399835225 + d[0.5848888468615789] = 0.11176643712276305 + d[0.6399231633043057] = 0.11182809865256145 + d[2.2012851700745113] = 0.11357738380273773 + d[1.291475597125359] = 0.11255809802204005 + d[2.6858795669653737] = 0.11412024257484786 + d[0.8948306939904345] = 0.11211370021291141 + d[0.6895302167414594] = 0.11188367926064392 + d[2.1752261893961715] = 0.11354819062359338 + d[1.590613927507321] = 0.11289324155366709 + d[1.4265708610459151] = 0.11270945481921532 + d[0.2608536409977531] = 0.11140337969803851 + d[1.4699318251724858] = 0.11275803482175406 + d[1.103531439271113] = 0.11234752830054626 + d[0.9346295859848487] = 0.1121582910657759 + d[1.5377325687117471] = 0.11283399586964508 + d[1.357171853987592] = 0.11263170239924876 + d[1.3988563812771238] = 0.1126784044590567 + d[2.6009926690117706] = 0.11402515226373182 + d[0.8663727098730766] = 0.11208181570510356 + d[1.588508533238425] = 0.11289088277863633 + d[1.5189911345191318] = 0.11281299881583742 + d[0.20109158354416934] = 0.11133642047878997 + d[0.6295135606873385] = 0.11181643553869454 + d[0.5910822417431172] = 0.11177337633017088 + d[3.0041152874516848] = 0.11447671845624578 + d[0.360343923223421] = 0.11151485148011689 + d[1.3492155813118747] = 0.1126227884186075 + d[1.5713843258051559] = 0.11287169768350537 + d[1.2264044219225776] = 0.11248519360573304 + d[0.5949234129573877] = 0.11177768005689812 + d[0.8598460759150346] = 0.11207450321598016 + d[0.3147068340227921] = 0.11146371839427725 + d[0.899233208064981] = 0.11211863281365134 + d[1.018062423263566] = 0.1122517692588586 + d[1.0921617786995237] = 0.11233478982178113 + d[2.0104176198194983] = 0.11336355776524375 + d[0.2691522953833636] = 0.11141267775721479 + d[0.7037459001728817] = 0.11189960674001431 + d[2.097702200033094] = 0.11346134199566583 + d[0.05078247429328986] = 0.11116800942195215 + d[0.2708200886631559] = 0.11141454640225917 + d[0.4422671003412998] = 0.1116066403967712 + d[1.4594955756712358] = 0.11274634245466701 + d[1.3239236788650903] = 0.11259445205609654 + d[0.7184965671505077] = 0.1119161336135657 + d[2.623616991272418] = 0.11405049615527452 + d[0.47029581252817354] = 0.11163804447161361 + d[0.6904862447227427] = 0.11188475040999557 + d[1.9129749637315372] = 0.11325439232203743 + d[1.577734551551556] = 0.11287881215854922 + d[0.1509749839046013] = 0.11128026828545236 + d[0.43283443975617986] = 0.11159607180111658 + d[0.5044339873259742] = 0.11167629370904693 + d[1.3280753261752345] = 0.1125991034531828 + d[2.6236746633053447] = 0.11405056075969247 + d[2.3991194260199817] = 0.11379900890334096 + d[1.0765938027052133] = 0.11231734756810458 + d[2.2358191005757857] = 0.11361607108822508 + d[0.35297414356765755] = 0.11150659417368924 + d[2.1161064771380316] = 0.11348196002883322 + d[0.49499516526371523] = 0.1116657182280973 + d[2.7220973190936126] = 0.11416081331450359 + d[0.26959834694911056] = 0.11141317752662032 + d[0.37752373110808723] = 0.11153410021038333 + d[2.5510367819381714] = 0.11396919108868063 + d[1.2023234815007766] = 0.11245821372344982 + d[2.701947177490961] = 0.11413824136992193 + d[0.9628891560282895] = 0.11218995315252353 + d[1.6450640511052184] = 0.1129542444964144 + d[0.7142203327921055] = 0.11191134245605017 + d[1.0953096649914102] = 0.11233831668989873 + d[1.9284785946170298] = 0.11327176119132337 + d[0.39112392169339705] = 0.11154933823355857 + d[1.8159728082004332] = 0.11314571917524466 + d[0.15995603403842984] = 0.11129033093478403 + d[0.5773039391827948] = 0.1117579388336873 + d[0.3438300758062969] = 0.11149634890368276 + d[2.218513544478809] = 0.11359668423534515 + d[1.601307345436072] = 0.11290522189974406 + d[0.5765332423949727] = 0.11175707532877645 + d[1.1372937715035443] = 0.11238535529738941 + d[1.9465015022611682] = 0.11329195239228097 + d[0.44968425291024694] = 0.11161495076355395 + d[0.9289599111599172] = 0.11215193874316613 + d[0.5692299818401616] = 0.11174889260073449 + d[1.8505666997588608] = 0.11318447542728319 + d[1.2572984983980031] = 0.1125198067423699 + d[0.29542076911155424] = 0.11144210972815129 + d[0.9527897517198861] = 0.11217863776266582 + d[0.3675261503298932] = 0.11152289864619908 + d[1.7122095087414315] = 0.11302947015077315 + d[0.57590439829028] = 0.1117563707585822 + d[1.1584982300945912] = 0.11240911252794326 + d[2.432244515568926] = 0.11383611690212361 + d[1.190450692316234] = 0.11244491163225583 + d[2.039991433730741] = 0.11339668919314887 + d[2.3714299416720683] = 0.11376798994401971 + d[1.0667635139677634] = 0.11230633377101244 + d[0.6054450366820685] = 0.11178946869615594 + d[0.7535835109701329] = 0.11195544552167598 + d[0.7870336678593709] = 0.11199292349342907 + d[1.0322907454572285] = 0.11226771063245243 + d[0.6426960131711215] = 0.11183120540474976 + d[2.095999250838812] = 0.11345943420505762 + d[0.049952098459348226] = 0.11116707904231553 + d[1.3298236076632892] = 0.11260106218159295 + d[0.7984218760865147] = 0.11200568297037052 + d[2.6351847148370195] = 0.11406345434902264 + d[0.6977789177877627] = 0.11189292123852825 + d[1.0586506321835778] = 0.11229724414131964 + d[0.28849164469451627] = 0.11143434613451836 + d[0.13290724260564035] = 0.11126002462088698 + d[0.27690967485712126] = 0.11142136935477535 + d[0.8684511410187258] = 0.11208414439427196 + d[0.41554770334107616] = 0.11157670329022029 + d[0.48515692110970443] = 0.11165469522202376 + d[1.6964636944940916] = 0.11301182955103917 + d[3.401513000795899] = 0.11492183996121842 + d[0.033085617507391474] = 0.11114818129729138 + d[0.22003570785141546] = 0.11135764605525215 + d[0.2833579629973876] = 0.11142859420682338 + d[0.4521969141315251] = 0.11161776601285808 + d[1.8024708829420661] = 0.11313059264988416 + d[0.787334372643519] = 0.11199326040654806 + d[0.041509273374669364] = 0.11115761943099862 + d[1.0883185062584546] = 0.11233048384728195 + d[1.51114078794386] = 0.11280420363264314 + d[0.8328980476070376] = 0.11204431041959893 + d[1.308240664358963] = 0.1125768812031211 + d[0.6301610136998297] = 0.11181716095731657 + d[1.9312018491122176] = 0.1132748120767922 + d[0.5796883975299613] = 0.11176061043088896 + d[1.8031874812479594] = 0.1131313954724196 + d[0.23830442641598903] = 0.11137811488151975 + d[0.22195672116416332] = 0.1113597984170566 + d[1.988285265322952] = 0.11333876289865828 + d[1.070363131885223] = 0.11231036676233491 + d[1.1308833152305557] = 0.11237817308950443 + d[2.332764095419385] = 0.11372467458680795 + d[0.5315193489101284] = 0.11170664077629647 + d[0.4210087693807365] = 0.11158282201212189 + d[0.6686076892588846] = 0.11186023730907584 + d[2.9382045803371755] = 0.11440288931321764 + d[1.3650438290397298] = 0.11264052192963413 + d[0.7272425093248525] = 0.11192593269646534 + d[1.501283348469753] = 0.11279315978205334 + d[2.355549811044474] = 0.11375020027942927 + d[1.6155841311797245] = 0.11292121684472141 + d[0.8514301513265832] = 0.1120650739480364 + d[1.3662675651308565] = 0.11264189296722112 + d[1.5595440776231078] = 0.11285843245093173 + d[1.3874271331244303] = 0.11266559949747007 + d[0.38257505070428266] = 0.1115397598466979 + d[1.6962472767296328] = 0.11301158709027023 + d[0.531334687281817] = 0.11170643387721148 + d[0.09192399877212287] = 0.11121410569786619 + d[0.6257485462988328] = 0.11181221714489521 + d[1.7305504171748152] = 0.11305001809193774 + d[1.3230886953298129] = 0.11259351656219442 + d[1.1198302456583735] = 0.112365789339214 + d[1.0830951431973088] = 0.1123246316275798 + d[0.779133744295956] = 0.11198407232599321 + d[0.716160852141233] = 0.11191351664332423 + d[1.8105802739147678] = 0.11313967779450855 + d[0.3357523261374691] = 0.11148729836479444 + d[1.2785821518378708] = 0.11254365249737013 + d[0.513651578261221] = 0.11168662131450703 + d[2.718158754725607] = 0.11415640138816727 + d[0.9558908215494047] = 0.1121821122072937 + d[0.7390441205953402] = 0.11193915539034735 + d[0.6642264064634078] = 0.11185532844369545 + d[1.9400338209144334] = 0.11328470660432764 + d[0.07354672362800474] = 0.11119351521379067 + d[0.6524403763410318] = 0.11184212316656136 + d[1.1672357185633588] = 0.11241890189912421 + d[0.7305106579104282] = 0.11192959437750978 + d[1.4729941264351942] = 0.11276146570269407 + d[0.6326554817086439] = 0.11181995580637104 + d[1.455584570516829] = 0.11274196071424135 + d[0.17462189666468353] = 0.1113067630238944 + d[0.6255465951083541] = 0.11181199087492004 + d[0.24471665341023396] = 0.11138529933386569 + d[0.9188556514570577] = 0.11214061789195369 + d[1.020230550582788] = 0.11225419842371277 + d[0.89376737856005] = 0.11211250886834127 + d[0.18665959755663453] = 0.11132025043692463 + d[1.3426068590751865] = 0.11261538419067939 + d[1.2103811089812386] = 0.11246724135950058 + d[1.469101319880066] = 0.11275710435638936 + d[0.556459085377622] = 0.11173458381263146 + d[0.5264297602131341] = 0.11170093828501677 + d[0.3962527885502314] = 0.11155508475415102 + d[2.9098235923182973] = 0.11437109840320794 + d[1.0162935215299136] = 0.11224978738519603 + d[1.5025587323655074] = 0.11279458866778094 + d[0.8084330077700199] = 0.112016899549563 + d[1.2023617620290035] = 0.11245825661234934 + d[0.48489912169270044] = 0.11165440637729615 + d[1.5322019763916859] = 0.11282779964827484 + d[0.08996977724056232] = 0.11121191612594371 + d[2.8474439902465245] = 0.11430122346352646 + d[2.16406109852708] = 0.11353568264077256 + d[1.7082995678733737] = 0.1130250897065799 + d[1.9889215132770697] = 0.11333947568785603 + d[1.5304788515870416] = 0.1128258691378274 + d[0.37156364206759906] = 0.11152742236316684 + d[1.6619932285697518] = 0.11297321095619674 + d[0.4377264869079506] = 0.1116015529769561 + d[0.30432203977347494] = 0.11145208297073202 + d[1.2570374571896044] = 0.11251951427708737 + d[0.055150683783452226] = 0.1111729037035047 + d[0.0444657858078068] = 0.11116093200213394 + d[1.396420900010972] = 0.11267567582528588 + d[1.6669015312050757] = 0.11297870992535182 + d[2.3269883259390847] = 0.11371820426956662 + d[1.2335397975289633] = 0.11249318795203087 + d[0.7728211510276732] = 0.11197699961980664 + d[1.1165250809840495] = 0.11236208626349972 + d[2.9219461950046086] = 0.11438467753285032 + d[0.32945616977884884] = 0.11148024397236672 + d[0.8451929144132557] = 0.11205808569628063 + d[1.904706704325254] = 0.11324512929766961 + d[0.013807201504817734] = 0.11112658114230646 + d[0.38861830165760713] = 0.11154653086912397 + d[1.4333964109692554] = 0.11271710192201474 + d[0.8063204444050742] = 0.11201453261138021 + d[1.4986602876148387] = 0.11279022101602382 + d[1.9044651770132073] = 0.1132448587117647 + d[1.0962420164035633] = 0.11233936128926822 + d[0.8572669457693068] = 0.11207161353875461 + d[0.9761128723875165] = 0.11220476901710116 + d[2.006814630850355] = 0.11335952134279446 + d[2.14535565132467] = 0.11351472733793266 + d[2.1139465972006435] = 0.11347954035047933 + d[2.732610368943769] = 0.11417258987644667 + d[2.3487262541039136] = 0.1137425561998512 + d[0.9487467665945774] = 0.11217410799340992 + d[2.3485921497947846] = 0.11374240596962416 + d[1.2087902593667876] = 0.11246545899762676 + d[1.071227637038279] = 0.11231133534882613 + d[0.05966711031602934] = 0.11117796405209654 + d[1.3384525934528548] = 0.11261072986544061 + d[1.7825435095059008] = 0.1131082675035474 + d[0.44552936576203195] = 0.11161029552229527 + d[0.9101975437119046] = 0.11213091730998045 + d[0.928456088211443] = 0.11215137425815612 + d[1.9628164739458929] = 0.11331023014334454 + d[0.316885516980405] = 0.11146615945333375 + d[1.5708307132291717] = 0.11287107744348873 + d[2.472143583801417] = 0.11388081313633724 + d[0.110439235281371] = 0.11123485075617238 + d[1.983994764832813] = 0.1133339562454185 + d[0.9259084026609552] = 0.11214851982203294 + d[1.936759842175689] = 0.1132810387413438 + d[0.3615315954226963] = 0.1115161821810138 + d[0.081010312884094] = 0.11120187765700272 + d[1.0600121337704427] = 0.11229876956079485 + d[0.2854319425464984] = 0.1114309179544608 + d[2.151871236276106] = 0.11352202661074311 + d[1.2166168134854216] = 0.11247422773881986 + d[2.2569882679255144] = 0.11363978615883996 + d[0.006021184129894053] = 0.11111785743884675 + d[0.4932348041567849] = 0.11166374587727965 + d[0.9604962832823744] = 0.11218727217439249 + d[0.8989162467516378] = 0.11211827768850856 + d[0.6911288990221769] = 0.11188547045033667 + d[0.6253910971036541] = 0.11181181665198126 + d[0.7764601842810926] = 0.1119810768371226 + d[2.049293192091644] = 0.11340710989218708 + d[1.0122544111823153] = 0.1122452619739414 + d[1.0381937593175663] = 0.11227432434911852 + d[2.152686384192651] = 0.11352293980338603 + d[1.2046172281953422] = 0.11246078360083098 + d[0.337692592607442] = 0.11148947229428448 + d[1.816268811069413] = 0.11314605079399548 + d[0.4151833334270858] = 0.11157629504056414 + d[1.6296104490671026] = 0.11293693115766773 + d[2.13149507402093] = 0.11349919960452962 + d[0.17133821912025538] = 0.111303083889544 + d[0.166506812766407] = 0.11129767063152367 + d[0.46591193007660503] = 0.11163313266091197 + d[1.6648678574829172] = 0.11297643151908483 + d[2.746533252551661] = 0.11418818605244652 + d[1.3570358085697318] = 0.11263154997789639 + d[1.24367672135722] = 0.11250454517172506 + d[0.6773036657012969] = 0.11186998042967655 + d[4.385344736291335] = 0.11602365769817592 + d[1.2994556746610109] = 0.1125670387134158 + d[0.49593340304266376] = 0.11166676945217302 + d[0.5133348726136484] = 0.11168626647010577 + d[2.211238388443974] = 0.11358853410093246 + d[1.293941670600074] = 0.1125608609534034 + d[1.7176467230368417] = 0.11303556165018347 + d[0.7757582636556123] = 0.11198029039673119 + d[0.6593796201571989] = 0.11184989801910966 + d[0.4562289280216678] = 0.11162228358299846 + d[1.8197229476985974] = 0.113149920541092 + d[0.8544352547483833] = 0.11206844088994981 + d[2.3804677877947915] = 0.11377811454394722 + d[1.4541993141105065] = 0.11274040872564974 + d[0.4176480687775299] = 0.11157905659494811 + d[1.4674021994043822] = 0.11275520072863238 + d[0.12926979463968025] = 0.11125594910963371 + d[1.62306153560221] = 0.11292959411886044 + d[1.7164664405784427] = 0.11303423933917026 + d[0.23543507459914137] = 0.11137489997307039 + d[1.1725863122663558] = 0.11242489663348476 + d[0.18062108227174245] = 0.1113134846975309 + d[1.198817128574564] = 0.112454285260488 + d[0.7347003632372395] = 0.11193428858332871 + d[1.8722504764717902] = 0.11320876813590187 + d[1.618743834455322] = 0.11292475680384659 + d[0.6507192176270066] = 0.11184019474931493 + d[2.017625726851149] = 0.11337163299015467 + d[1.087614153655545] = 0.1123296946956313 + d[0.3185975680356805] = 0.11146807768451428 + d[0.6059692144706856] = 0.11179005599539849 + d[0.30068197396897767] = 0.11144800453530788 + d[0.3260352065667498] = 0.1114764110276478 + d[2.5470042003088462] = 0.11396467372449504 + d[2.3885716611451615] = 0.11378719285475832 + d[2.1278265109211834] = 0.11349508978054677 + d[1.7271987793944001] = 0.11304626314144202 + d[0.20875027267675228] = 0.11134500150900832 + d[1.0545592603069116] = 0.11229266018823035 + d[1.928810326077949] = 0.11327213283298738 + d[1.6436264091542807] = 0.11295263384505351 + d[0.04396175738028418] = 0.11116036727255714 + d[0.8603892923219144] = 0.11207511183976662 + d[0.09181461444513328] = 0.11121398314018986 + d[0.36084428713739003] = 0.11151541210173822 + d[0.06485771846118715] = 0.11118377977520831 + d[0.0025958298166129934] = 0.11111401956205964 + d[1.444637487200235] = 0.11272969601340975 + d[1.0155280030187308] = 0.11224892969985252 + d[1.3657298438221215] = 0.11264129052024704 + d[1.2442811712450477] = 0.11250522238579716 + d[0.18425248109334513] = 0.11131755342920137 + d[0.05803426063548245] = 0.1111761345551521 + d[1.5403905000700122] = 0.11283697369263282 + d[3.4460417721393686] = 0.11497171407202839 + d[1.719165547751389] = 0.11303726324149072 + d[0.7117700417580131] = 0.11190859711260397 + d[0.1064833512742912] = 0.1112304184584422 + d[0.46454434291194835] = 0.11163160038218933 + d[2.4449745519233383] = 0.11385037753115719 + d[0.5230930992176395] = 0.11169719981343161 + d[0.023524121867464] = 0.11113746829129055 + d[0.6715347754230276] = 0.11186351686680714 + d[1.3567039857436183] = 0.11263117821318981 + d[0.8450360889984614] = 0.11205790998776244 + d[0.13778448992373304] = 0.11126548924219587 + d[1.3688330629914867] = 0.11264476727442077 + d[2.530849091649766] = 0.11394657647879859 + d[1.3889677876919007] = 0.11266732559793849 + d[1.9166171733073758] = 0.11325847272779493 + d[1.9120020948829728] = 0.11325330240653211 + d[0.03572228641328823] = 0.11115113550556197 + d[1.4499529934435653] = 0.11273565130832403 + d[1.3901135847239385] = 0.11266860931241744 + d[0.13632759003670913] = 0.11126385688575803 + d[1.212746399259954] = 0.11246989139164554 + d[2.4703174392770384] = 0.11387876743551845 + d[1.0277473677015398] = 0.11226262024583342 + d[0.9455993920421497] = 0.1121705816674607 + d[1.8361692716941858] = 0.11316834570862318 + d[0.35288986195826744] = 0.11150649974221885 + d[1.3105225942975047] = 0.11257943782106779 + d[4.046542262089142] = 0.11564425313173458 + d[1.2582752664113406] = 0.11252090109341731 + d[0.8809007523208143] = 0.1120980930228806 + d[1.9989368978195783] = 0.11335069592577698 + d[0.8921974343359993] = 0.11211074989390779 + d[1.7324991675207664] = 0.1130522013407161 + d[0.5377938050533075] = 0.11171367081883782 + d[2.5179552049723495] = 0.11393213248155924 + d[0.7402376168405526] = 0.11194049260021499 + d[1.4014931826769126] = 0.11268135864471826 + d[0.29517041167415947] = 0.11144182922037314 + d[0.08827108784052906] = 0.1112100128603255 + d[1.1591158862972715] = 0.11240980454230626 + d[1.1784411324465531] = 0.11243145629396666 + d[1.1733453463096821] = 0.11242574704499984 + d[0.10509300049318337] = 0.11122886066536623 + d[0.9169905278598967] = 0.1121385281996615 + d[0.4006355030631348] = 0.1115599952650111 + d[1.7958433339360091] = 0.11312316764240385 + d[0.4948209208166112] = 0.11166552300044293 + d[1.0531350349544248] = 0.11229106449281942 + d[0.553987500225883] = 0.11173181459457168 + d[2.709329891491096] = 0.11414651140523745 + d[0.9092304162830394] = 0.11212983373587695 + d[0.6263416519675415] = 0.11181288167181702 + d[0.7811109598724386] = 0.11198628762192352 + d[2.3543827045726227] = 0.11374889283064554 + d[3.123196243605913] = 0.11461010344275425 + d[0.22961070802997152] = 0.11136837417643894 + d[1.1552904523857277] = 0.11240551857303938 + d[2.0064607242647243] = 0.11335912486175166 + d[0.2145379505242656] = 0.11135148620025846 + d[0.6631905613604823] = 0.11185416786471808 + d[2.813116104284348] = 0.1142627705305055 + d[0.8685699560820628] = 0.11208427751551392 + d[0.6318676434152812] = 0.11181907309750028 + d[0.029303688517864135] = 0.11114394390292467 + d[0.9465656669311142] = 0.11217166428421516 + d[1.2549526959689619] = 0.11251717855263875 + d[0.9427316480902574] = 0.11216736863976257 + d[1.7588987898945534] = 0.11308177765825485 + d[0.42244928787033] = 0.11158443600675493 + d[0.3873387365255553] = 0.11154509720969108 + d[0.12385371532783618] = 0.11124988076359864 + d[2.1440418299910364] = 0.11351325549078588 + d[0.0377275630547822] = 0.11115338228171087 + d[0.7287487525600903] = 0.11192762031328188 + d[0.4027506035473579] = 0.11156236508012711 + d[1.4094137108117082] = 0.11269023254033679 + d[1.9664149164884863] = 0.11331426149333587 + d[1.5024203040608177] = 0.11279443357861954 + d[0.02737280658437724] = 0.11114178048095362 + d[0.5899438059070998] = 0.11177210080328397 + d[1.4931798108711138] = 0.11278408092032728 + d[1.2143156098079801] = 0.11247164950896632 + d[0.9616990331873997] = 0.11218861973719417 + d[1.4541476220705358] = 0.11274035081185059 + d[1.737183555564204] = 0.11305744941213307 + d[1.3011957778823113] = 0.11256898828345313 + d[1.3199736183569868] = 0.11259002651018744 + d[0.4664922072705827] = 0.11163378281791604 + d[0.7682120001278169] = 0.11197183546985556 + d[1.5035273139846126] = 0.11279567382521316 + d[1.0313551236236262] = 0.11226666236471092 + d[0.9819924427943926] = 0.11221135648984082 + d[0.05390146561024656] = 0.11117150403953618 + d[0.8048278181394932] = 0.11201286025709123 + d[1.7572745705015378] = 0.11307995799711928 + d[0.4900562405098824] = 0.11166018453805582 + d[0.8859146206745101] = 0.11210371059230999 + d[1.0229069231992918] = 0.1122571970249891 + d[1.4298045141380658] = 0.11271307768940897 + d[1.3680882164670676] = 0.11264393277067673 + d[0.3223375351177572] = 0.11147226805084741 + d[0.2942435184292913] = 0.11144079070212473 + d[0.0018338394672718916] = 0.11111316580364299 + d[0.15901167688264217] = 0.11128927284754388 + d[0.7012272690279535] = 0.11189678482602602 + d[0.9933750463635397] = 0.11222410955645792 + d[2.1946795234335035] = 0.11356998368281909 + d[0.20307561566085108] = 0.1113386434493055 + d[1.5770813353966209] = 0.11287808032806272 + d[0.17009962397296485] = 0.11130169612902384 + d[1.5604733951791583] = 0.11285947361320761 + d[0.4394482273131345] = 0.11160348205916114 + d[1.0316274619572732] = 0.11226696749172427 + d[2.096736805161546] = 0.11346026047709155 + d[0.5475313467752717] = 0.1117245809779903 + d[1.588235147705276] = 0.11289057649156646 + d[3.834250451924594] = 0.11540650428810839 + d[1.7928920681101603] = 0.11311986126443656 + d[1.1101104649951723] = 0.11235489938519232 + d[2.491562962650667] = 0.11390256726180793 + d[1.359354407949832] = 0.11263414766937085 + d[1.6082911126782973] = 0.11291304614068907 + d[0.45287351913587126] = 0.11161852409821817 + d[1.3630281796290893] = 0.11263826365557833 + d[0.347036251768414] = 0.11149994119338132 + d[1.4352937486174002] = 0.11271922763068877 + d[0.429762870402985] = 0.11159263033521886 + d[0.35887700126978817] = 0.111513207899998 + d[0.8540956343505501] = 0.11206806037656483 + d[0.7601006233160172] = 0.11196274737984763 + d[0.1900679865435354] = 0.11132406930122433 + d[0.8072118640159586] = 0.1120155313673041 + d[0.7911955596216556] = 0.11199758652468866 + d[2.1069417346419423] = 0.11347169291241378 + d[1.1928216691393052] = 0.11244756803927383 + d[1.3273368157674863] = 0.11259827604554386 + d[4.159921006701821] = 0.11577122277113457 + d[0.9169185336609689] = 0.11213844753705517 + d[1.8002074416850635] = 0.11312805686111245 + d[1.712568274041374] = 0.11302987208806271 + d[0.15938258290844898] = 0.111289688422236 + d[0.9295958166772337] = 0.11215265121393025 + d[0.9815257944994833] = 0.11221083365701 + d[1.2780218432253898] = 0.11254302473994485 + d[1.2557180518430786] = 0.1125180360419747 + d[0.6342398674622347] = 0.11182173098194856 + d[1.3215009204897452] = 0.11259173766026531 + d[0.7637767710748339] = 0.11196686618308334 + d[2.1658071512594974] = 0.11353763870284762 + d[2.8864670694737335] = 0.11434493552118233 + d[0.636661578697834] = 0.11182444431253034 + d[2.3416690155664908] = 0.11373465033115948 + d[1.4081562874880258] = 0.11268882376556343 + d[1.3556637886356415] = 0.11263001280634165 + d[0.4987093781661105] = 0.11166987972100892 + d[0.347643396393692] = 0.11150062145526457 + d[0.4613672589907678] = 0.11162804069800893 + d[0.7309906381146692] = 0.1119301321542441 + d[1.9722520388891773] = 0.11332080084198788 + d[0.9018644155482982] = 0.11212158083229143 + d[0.022952071954640774] = 0.11113682734823853 + d[0.13485831817660832] = 0.11126221066735321 + d[0.6859195370407878] = 0.11187963379580895 + d[1.2360941150946372] = 0.1124960497624092 + d[1.3196645489695484] = 0.11258968023675994 + d[2.313472692253506] = 0.11370306333391365 + d[0.20755835653490995] = 0.11134366604965587 + d[1.774691201824971] = 0.1130994703494005 + d[2.1394244269801854] = 0.1135080827067585 + d[2.567793550212997] = 0.11398796226615457 + d[2.043718483144436] = 0.11340086458363521 + d[2.4912393365928764] = 0.11390220472745492 + d[0.6374867164131617] = 0.11182536881220964 + d[2.5767397833086734] = 0.11399798394799406 + d[1.2608002959695357] = 0.1125237300848909 + d[2.2034236227350887] = 0.11357977944966796 + d[1.9089744382125795] = 0.11324991048921185 + d[1.270362976256267] = 0.11253444391146318 + d[0.4418341946933513] = 0.11160615535819962 + d[1.931636130430332] = 0.11327529860580583 + d[2.173115376098867] = 0.1135458259315926 + d[0.7773163154371189] = 0.11198203605683059 + d[1.110613548380529] = 0.11235546303542147 + d[0.27257813940600095] = 0.11141651617438758 + d[1.4227667893255898] = 0.11270519287096294 + d[1.3860868880014028] = 0.11266409792920347 + d[1.312450031414165] = 0.11258159727365924 + d[0.5715357269087623] = 0.11175147600663685 + d[4.071798168591206] = 0.11567253680919545 + d[0.7841255311627532] = 0.11198966518318745 + d[0.3896020991110005] = 0.11154763314240979 + d[0.9523327439019825] = 0.1121781257301724 + d[0.6037295655446084] = 0.11178754664802304 + d[1.0494842962021003] = 0.11228697422158307 + d[0.23161440763655783] = 0.11137061918219707 + d[0.23484576835983906] = 0.11137423969654295 + d[1.878522795675592] = 0.11321579511229408 + d[0.4950201264714005] = 0.11166574619523252 + d[0.7404533654956114] = 0.11194073432801492 + d[1.3986188867050404] = 0.11267813837790885 + d[1.8503695445051882] = 0.11318425455058981 + d[0.7293398352158272] = 0.11192828257085187 + d[0.6276044579754616] = 0.11181429654374417 + d[0.45824514916050907] = 0.11162454260787308 + d[1.98544226999911] = 0.11333557788759704 + d[0.8207618417955949] = 0.1120307128999135 + d[0.8757108880825546] = 0.11209227826501832 + d[1.0959603525709654] = 0.11233904571527766 + d[0.2818178679133021] = 0.11142686863897835 + d[2.0889681602014596] = 0.11345155736645 + d[0.9024312140819815] = 0.11212221587628197 + d[0.7295514799032377] = 0.11192851970062145 + d[1.2705507971378798] = 0.11253465434196555 + d[2.1353264071676485] = 0.11350349177477662 + d[0.3461845038608372] = 0.11149898687109931 + d[2.810508583914733] = 0.11425984966561273 + d[0.7670126345866646] = 0.11197049168562008 + d[0.6793070667945651] = 0.11187222507401633 + d[0.14159695841943243] = 0.11126976085166919 + d[0.3354783043623293] = 0.11148699134303212 + d[0.7904488813201764] = 0.11199674993782331 + d[0.0008531389444907944] = 0.1111120669953361 + d[1.0220000625547272] = 0.11225618098061466 + d[1.0921461812393813] = 0.11233477234650235 + d[0.576972599566925] = 0.11175756759380691 + d[1.5751211031905372] = 0.1128758841823409 + d[0.6099593758516539] = 0.1117945266513818 + d[1.8228371595149793] = 0.11315340946152562 + d[0.3141349712992173] = 0.11146307766281549 + d[1.855810009570987] = 0.11319034960291968 + d[0.6387729423239008] = 0.11182680992364187 + d[0.3873560663187865] = 0.1115451166264611 + d[0.9415490621825955] = 0.11216604366732098 + d[0.05484747848431115] = 0.11117256398259708 + d[1.3008469720335984] = 0.1125685974897423 + d[0.14797172624618715] = 0.11127690334150347 + d[1.3559081097440506] = 0.11263028653667584 + d[1.0325101295041315] = 0.11226795642963566 + d[0.96341144534864] = 0.1121905383261949 + d[1.4880320885253144] = 0.11277831362595653 + d[0.31289444773197295] = 0.11146168774446766 + d[1.5060759062920368] = 0.1127985291586166 + d[1.3301689736873015] = 0.11260144912053387 + d[0.4874913122878214] = 0.11165731073049451 + d[0.24701943283857397] = 0.1113878794371662 + d[0.8870767907987906] = 0.1121050126947681 + d[1.1079097028159324] = 0.11235243367025757 + d[0.3980553526447451] = 0.1115571043953584 + d[1.6819815041751696] = 0.11299560460980339 + d[2.2752257811438117] = 0.1136602169469628 + d[1.2124693583476165] = 0.11246958099960833 + d[0.7555151737450239] = 0.11195760978221256 + d[1.7073915371751383] = 0.1130240724076222 + d[1.086998322431332] = 0.11232900472267493 + d[0.17595114548722657] = 0.11130825235554205 + d[0.9722497814475586] = 0.11220044080744389 + d[2.037517736494139] = 0.11339391792434168 + d[0.5897228269239874] = 0.11177185321388791 + d[0.4607321823838001] = 0.11162732914227895 + d[2.1333906120208486] = 0.11350132314025214 + d[1.0054435563635296] = 0.11223763110318138 + d[2.130914929608161] = 0.11349854967950693 + d[0.4018083050729798] = 0.11156130930374486 + d[0.9505362089027561] = 0.11217611288855911 + d[0.9424936815044842] = 0.11216710202136485 + d[2.9020795703348687] = 0.11436242392446663 + d[1.438067215192652] = 0.1127223349219987 + d[0.8584405954031173] = 0.112072928504866 + d[0.8072664587084681] = 0.11201559253577141 + d[0.3046118804277096] = 0.11145240771660574 + d[0.276929992125712] = 0.111421392118843 + d[0.19586431876282573] = 0.11133056369054432 + d[1.887401116687174] = 0.11322574162449657 + d[1.9104634260587683] = 0.11325157861894222 + d[1.8281325898707192] = 0.11315934204667588 + d[0.060754989080802124] = 0.11117918294621172 + d[1.0155205755296703] = 0.11224892137810907 + d[2.1421082199808135] = 0.11351108930662411 + d[1.5116229262228442] = 0.11280474379935404 + d[0.2841459704328737] = 0.11142947711352177 + d[1.4581391385248605] = 0.11274482275459266 + d[1.190633006341161] = 0.11244511589418194 + d[0.9813406458886321] = 0.11221062621647027 + d[0.28586022377712517] = 0.11143139781332793 + d[1.3399389455889745] = 0.11261239513377486 + d[0.9266927702164185] = 0.11214939863032697 + d[2.1027069275644052] = 0.11346694872088478 + d[2.5224032169599626] = 0.11393711523929129 + d[0.9626500601396084] = 0.11218968526915589 + d[1.6014496712333286] = 0.11290538135404052 + d[1.0091645374634686] = 0.1122418000847918 + d[0.8189770301336873] = 0.11202871317938214 + d[1.5278451422289197] = 0.11282291844939131 + d[1.9841023136536895] = 0.11333407673253108 + d[0.9763834581362332] = 0.11220507218151779 + d[0.07587047294433813] = 0.11119611881659573 + d[0.21813153785676298] = 0.1113555125651612 + d[1.3845070552744165] = 0.11266232793434748 + d[2.06264922317021] = 0.11342207254581074 + d[0.6084931711930321] = 0.11179288388666454 + d[0.6834544132202114] = 0.11187687183025545 + d[1.4773617691903675] = 0.11276635903491053 + d[0.19673226837997526] = 0.11133153616801725 + d[0.39405291735988257] = 0.11155261995929111 + d[0.6983644248456962] = 0.11189357724997402 + d[0.49620107614869] = 0.11166706935952575 + d[1.1776327845952825] = 0.11243055063224494 + d[0.7707688031847402] = 0.1119747001439105 + d[0.03876510877213257] = 0.11115454478114616 + d[0.8259400493340973] = 0.11203651461356245 + d[0.7362079149019738] = 0.11193597766558418 + d[2.536078832010867] = 0.11395243493361798 + d[0.46938759790914064] = 0.11163702688546251 + d[2.1212192542420674] = 0.11348768778722523 + d[0.5566121521688134] = 0.11173475531200464 + d[1.575891391374805] = 0.112876747174587 + d[1.6506057553317681] = 0.1129604531010051 + d[0.7927922059395989] = 0.11199937542529334 + d[0.7047199882981845] = 0.11190069812360685 + d[1.8269847499766172] = 0.11315805609710713 + d[1.1133809351930928] = 0.11235856359109242 + d[2.7532536480184926] = 0.11419571411179126 + d[1.9259513788093643] = 0.11326892992883497 + d[2.821908675550662] = 0.11427261969162048 + d[0.6824529001909293] = 0.11187574971839281 + d[0.0642996330700234] = 0.1111831544785207 + d[0.04887671678673844] = 0.11116587415029955 + d[0.02084477489052272] = 0.11113446626508142 + d[0.410373105934821] = 0.11157090553454746 + d[2.6181616566507957] = 0.1140443850672584 + d[0.7273739978027818] = 0.11192608001807178 + d[1.1239388939691437] = 0.11237039262937992 + d[1.7197747052582142] = 0.11303794570141919 + d[1.850214028390191] = 0.1131840803229937 + d[0.526880087823117] = 0.11170144284238036 + d[0.3534772908323862] = 0.11150715791394152 + d[1.3237990084242572] = 0.11259431237857118 + d[0.8916679412867339] = 0.11211015664685246 + d[1.3002173798487306] = 0.11256789210972527 + d[2.411295623683286] = 0.1138126491685486 + d[2.1041501198396118] = 0.11346856550805702 + d[1.06944405920715] = 0.11230933703865134 + d[0.48404311714144976] = 0.1116534472889931 + d[0.06296747748269105] = 0.11118166188886991 + d[0.4383191988625863] = 0.11160221706667466 + d[0.19625559221468014] = 0.11133100208536727 + d[1.557007337550136] = 0.11285559041004585 + d[1.7726931094960978] = 0.11309723183098708 + d[2.717006803151204] = 0.11415511098712142 + d[3.442734917624296] = 0.11496801027043732 + d[0.37459973038177485] = 0.11153082407988872 + d[0.4042197390529064] = 0.11156401113874526 + d[0.7619883353201353] = 0.11196486239674404 + d[0.8120783177585429] = 0.11202098379259964 + d[1.6643411901877645] = 0.11297584147250835 + d[1.480798503194848] = 0.11277020941288955 + d[0.8727431430764723] = 0.11208895318338599 + d[1.6002716370498298] = 0.11290406154677592 + d[0.940420084864026] = 0.1121647787580059 + d[2.5283034081267446] = 0.11394372475393404 + d[1.1445077528281395] = 0.11239343776259916 + d[2.291668866242381] = 0.1136786374628133 + d[0.6173892348288358] = 0.1118028512110867 + d[1.1017546805359508] = 0.11234553763457872 + d[1.1688729818769956] = 0.11242073626750443 + d[0.48639585275455743] = 0.11165608335109703 + d[0.11690102799653479] = 0.11124209075313755 + d[1.2831827527030226] = 0.11254880690821648 + d[2.7314300887039655] = 0.11417126774509241 + d[1.0209656247793812] = 0.11225502199907732 + d[1.1155329979789677] = 0.11236097474278404 + d[1.7866760421053605] = 0.11311289728943644 + d[0.5611687253591762] = 0.11173986059564757 + d[0.5887234358823012] = 0.11177073347559335 + d[1.9174114771748383] = 0.11325936259456125 + d[0.31526572688077237] = 0.11146434459392159 + d[1.1931201332961447] = 0.11244790243402561 + d[0.06737930849196982] = 0.11118660504515687 + d[1.1352912009878549] = 0.11238311163874663 + d[0.6252677997651974] = 0.11181167850728414 + d[1.294610718030098] = 0.1125616105384929 + d[3.322435620496445] = 0.11483326883942747 + d[0.4177097053578873] = 0.11157912565419352 + d[3.2492584532980406] = 0.11475130505386362 + d[2.013538003995744] = 0.11336705352495871 + d[1.503546093099036] = 0.1127956948645291 + d[0.6184925781552997] = 0.11180408741839569 + d[1.5126717091432533] = 0.11280591880994012 + d[0.8858379484119584] = 0.11210362468823908 + d[1.8158514645996466] = 0.11314558323124399 + d[0.7116865667426183] = 0.11190850358591858 + d[0.4563720627857669] = 0.11162244395479223 + d[2.0519945237055452] = 0.1134101361741165 + d[0.08009347898995667] = 0.1112008504071105 + d[0.4747336894845038] = 0.1116430167784897 + d[1.562443528690975] = 0.11286168085485791 + d[0.927183755588367] = 0.1121499487321243 + d[1.401125225853685] = 0.11268094639802076 + d[1.0034950936469709] = 0.11223544804812541 + d[0.026337652924307342] = 0.11114062066163054 + d[1.8106021370196153] = 0.11313970228825704 + d[1.712165669171608] = 0.1130294210357717 + d[1.969644211616603] = 0.11331787928451942 + d[1.136801323595205] = 0.11238480356403424 + d[0.14426112765566124] = 0.11127274587049728 + d[1.0731403058827211] = 0.11231347829156667 + d[1.5857006722530325] = 0.11288773699544004 + d[2.2175230860360333] = 0.11359557465555539 + d[1.2040792273086585] = 0.1124601808332165 + d[0.12202466340596763] = 0.11124783143609891 + d[2.10506568648582] = 0.1134695912038125 + d[2.3945375467910774] = 0.11379387609224248 + d[0.5012344303430059] = 0.1116727088495612 + d[0.5119568472974643] = 0.1116847224983309 + d[1.8366250700601285] = 0.11316885634878529 + d[1.0520177763458116] = 0.11228981272141081 + d[0.28227522578120945] = 0.11142738107619461 + d[0.4603392948909232] = 0.11162688894128961 + d[2.7285394812861883] = 0.11416802973107376 + d[0.5520762866809241] = 0.11172967322896245 + d[0.948606512808776] = 0.11217395085274728 + d[0.0025497000968632832] = 0.11111396787684273 + d[0.38679649481619405] = 0.11154448966737983 + d[0.5073456379570559] = 0.11167955599113477 + d[1.2593343025664216] = 0.11252208761593023 + d[1.2212090302951937] = 0.11247937277993465 + d[0.3359521012264196] = 0.11148752219846443 + d[1.582254007678491] = 0.11288387552838657 + d[0.47970943111751363] = 0.11164859172148946 + d[1.2552610080304465] = 0.11251752397928051 + d[0.07239056544349454] = 0.11119221981729761 + d[1.2313662364505058] = 0.11249075273379133 + d[0.7455775278331158] = 0.11194647551023952 + d[0.3171101249669277] = 0.11146641111057716 + d[0.26916789920783835] = 0.11141269524020266 + d[2.16447435248306] = 0.11353614559956231 + d[1.0593299032158785] = 0.11229800519315664 + d[0.9688229446415438] = 0.11219660137640387 + d[0.2998596784060097] = 0.11144708321144553 + d[0.9766599036652129] = 0.11220538191123046 + d[0.8525629590933254] = 0.11206634315498015 + d[0.15174859822698916] = 0.11128113506715591 + d[2.6212138728522443] = 0.11404780417289259 + d[1.390260336869764] = 0.11266877372883599 + d[1.2629053666498669] = 0.11252608856261974 + d[0.4968457713387675] = 0.11166779169143297 + d[0.30603014739365264] = 0.11145399678401641 + d[2.5658473510628923] = 0.1139857821077921 + d[0.3868146900972864] = 0.11154451005386616 + d[2.802546153631044] = 0.11425093038587489 + d[0.6623862253998503] = 0.11185326667260194 + d[2.7408332432219504] = 0.11418180100379632 + d[0.8800483645788362] = 0.11209713800218285 + d[1.42022336712645] = 0.11270234330936367 + d[1.1357963961952122] = 0.11238367765409611 + d[1.1070246977087066] = 0.11235144211808012 + d[0.22710329334827084] = 0.11136556479296066 + d[2.5567738277635517] = 0.11397561781690031 + d[0.293084731431145] = 0.11143949236332246 + d[1.0950013211819367] = 0.11233797122384623 + d[1.6006896514729916] = 0.11290452986806915 + d[1.3194789028784546] = 0.11258947224362922 + d[0.5398470402807802] = 0.11171597130971131 + d[1.2862914573876907] = 0.11255228983075782 + d[0.6549811211018094] = 0.11184496986255349 + d[0.14228040609805315] = 0.11127052660790493 + d[3.4735871753157532] = 0.11500256586302553 + d[0.2322959308493634] = 0.11137138278144318 + d[1.3146577944260955] = 0.11258407079601211 + d[0.7519250496945381] = 0.11195358735956626 + d[1.4090728047299639] = 0.11268985060065057 + d[1.0438534232670276] = 0.11228066541512144 + d[1.6131659757906651] = 0.11291850767465895 + d[0.31639534225261834] = 0.11146561024747728 + d[0.8173249078697962] = 0.11202686212520277 + d[0.8018484819475857] = 0.11200952217688778 + d[0.24949331111783812] = 0.11139065124466661 + d[2.6108161333791866] = 0.11403615657404394 + d[0.4826219026640979] = 0.11165185492570054 + d[0.550383493696823] = 0.11172777658643279 + d[1.5098739100431038] = 0.11280278427775649 + d[0.8728953375315154] = 0.11208912370309801 + d[0.3902762902983683] = 0.1115483885244436 + d[0.9099015438309557] = 0.1121305856703327 + d[0.4949669787332325] = 0.11166568664723311 + d[0.4649691631331929] = 0.11163207636135264 + d[1.0997635441054059] = 0.1123433067813193 + d[1.4574007194903902] = 0.1127439954581963 + d[0.8629599493830656] = 0.11207799202322667 + d[1.7978793839146503] = 0.11312544868023663 + d[0.9390704034441107] = 0.11216326657110012 + d[0.3233892743465927] = 0.11147344644957628 + d[2.777225465196442] = 0.11422256681846256 + d[0.38755861619598453] = 0.11154534356883258 + d[1.0886462482627177] = 0.11233085104708217 + d[1.9679268348281913] = 0.1133159553011703 + d[0.2735588412621828] = 0.11141761498177297 + d[0.37636635237351657] = 0.11153280345157691 + d[2.311763636957502] = 0.11370114875676823 + d[2.323444694023368] = 0.11371423450631313 + d[1.2442374941580714] = 0.11250517345082685 + d[0.9491583839376673] = 0.11217456917041609 + d[1.5344407732851573] = 0.11283030789376235 + d[2.7235302063532] = 0.1141624184146622 + d[0.7262094467228992] = 0.11192477523804567 + d[1.0033211356218792] = 0.11223525314577142 + d[0.3776860019282533] = 0.11153428202304819 + d[0.450372448282916] = 0.11161572183510733 + d[0.5295575938032594] = 0.1117044427812306 + d[1.176583875221374] = 0.11242937544865356 + d[2.4995909617423795] = 0.11391156043026993 + d[1.317841535700853] = 0.11258763777920476 + d[0.994956911861141] = 0.11222588187755245 + d[0.3267073295292735] = 0.1114771640933981 + d[0.07366974643830204] = 0.11119365305246942 + d[0.8236989762107818] = 0.11203400369380843 + d[0.37425822640156725] = 0.11153044144946254 + d[0.46224690673393587] = 0.11162902627734254 + d[1.1891760176856885] = 0.11244348350565583 + d[2.682691987647881] = 0.11411667187121854 + d[0.32618253242385165] = 0.11147657609574377 + d[1.4690590892749047] = 0.11275705704288361 + d[0.5793815509183282] = 0.11176026663351424 + d[0.04203766082280991] = 0.11115821145320516 + d[2.779375942025662] = 0.11422497573051515 + d[0.6542069530373363] = 0.11184410247080079 + d[1.1921750888009397] = 0.11244684362036453 + d[1.8399739763693037] = 0.11317260819572919 + d[2.008346757775012] = 0.11336123778220894 + d[2.533054490202356] = 0.11394904700884918 + d[1.9395243909189115] = 0.11328413588616616 + d[1.254094109673788] = 0.1125162166097552 + d[0.3975432987254741] = 0.11155653067640812 + d[0.22227439626153622] = 0.1113601543499027 + d[1.2268307747203875] = 0.1124856712838442 + d[1.0398497749295053] = 0.11227617974295186 + d[0.42358628067064275] = 0.11158570992321754 + d[0.27936661669047025] = 0.11142412218489635 + d[0.2670261576461712] = 0.11141029556937775 + d[1.1096232060928666] = 0.11235435346455795 + d[1.3028489937579684] = 0.1125708405067442 + d[1.9000951696914001] = 0.11323996293959226 + d[2.321620267440374] = 0.1137121906867343 + d[1.9335556352364427] = 0.11327744904289609 + d[0.6998305122411408] = 0.1118952198776045 + d[1.4622566847271943] = 0.11274943589464113 + d[2.28406396248825] = 0.11367011800521766 + d[2.051307893632214] = 0.11340936694759213 + d[2.539810466962307] = 0.11395661517938613 + d[0.37963961925188094] = 0.11153647090927539 + d[2.606432042864489] = 0.11403124548867308 + d[2.5418932488093464] = 0.11395894834870673 + d[2.075737186228002] = 0.1134367348612818 + d[0.860277471402654] = 0.11207498655476109 + d[0.257867463541515] = 0.11140003389571497 + d[2.1676557863360375] = 0.11353970968504738 + d[0.02411580427592641] = 0.11113813123121923 + d[2.34352320737575] = 0.11373672748955556 + d[0.20461306426418746] = 0.11134036605390128 + d[0.07932546705026844] = 0.11119998990207196 + d[0.9055178394740238] = 0.11212567414689961 + d[2.4615920103175717] = 0.11386899294575033 + d[0.7560380201531736] = 0.11195819558621553 + d[0.32349264765615326] = 0.11147356227198921 + d[1.2832028713535462] = 0.11254882944870093 + d[0.17173763113747675] = 0.11130353140318511 + d[2.3431274068790824] = 0.1137362840940895 + d[1.9465599337871209] = 0.11329201785349727 + d[1.8945019100278095] = 0.11323369673947851 + d[0.05592821505827028] = 0.11117377487439345 + d[0.9277266701253002] = 0.11215055701552984 + d[1.4354247912599585] = 0.11271937444612683 + d[0.5107394757427506] = 0.11168335852673208 + d[0.43591320261879085] = 0.1115995213265377 + d[0.2700969740851169] = 0.11141373620325011 + d[1.930519679832902] = 0.11327404783676169 + d[0.8845972620425727] = 0.11210223461561059 + d[0.495493584017738] = 0.11166627666840864 + d[1.1821824365351021] = 0.1124356479985147 + d[0.44658890007218477] = 0.11161148265153878 + d[0.8703575997155051] = 0.11208628040405634 + d[0.45698182713766733] = 0.11162312715011882 + d[1.3747847197176308] = 0.11265143533060332 + d[0.4228947017512178] = 0.1115849350601177 + d[0.763413504363798] = 0.11196645917441791 + d[0.46585063778782354] = 0.1116330639875062 + d[3.3987732950058356] = 0.11491877135988818 + d[0.740460565684876] = 0.11194074239520728 + d[0.16826079983435815] = 0.11129963585324444 + d[1.181897308188834] = 0.1124353285447592 + d[1.4335638051556745] = 0.11271728946443794 + d[0.9725019223510493] = 0.11220072330630913 + d[2.209462204534223] = 0.11358654429533376 + d[1.8206181707309943] = 0.11315092347939182 + d[2.020425671184555] = 0.113374769759157 + d[0.7264301850746415] = 0.11192502255652156 + d[0.7878022019028181] = 0.11199378456785307 + d[0.24661508456042358] = 0.11138742639320559 + d[0.04184118367306078] = 0.11115799131391894 + d[0.06527114241872511] = 0.11118424298860691 + d[0.3572527790783515] = 0.11151138807626217 + d[2.529073530994186] = 0.11394458746086635 + d[0.3732602245419905] = 0.11152932326078939 + d[1.3345112674861828] = 0.11260631411053457 + d[0.41391040916515387] = 0.11157486882263917 + d[2.7898292036152847] = 0.11423668520873316 + d[0.10159001255742595] = 0.11122493580661276 + d[0.056608343026978813] = 0.11117453691150336 + d[0.5591979789811272] = 0.1117376525286642 + d[0.5592984050399403] = 0.111737765048202 + d[0.7826507046076804] = 0.11198801277016204 + d[1.4328200400707973] = 0.11271645617677896 + d[1.5804015062468595] = 0.11288180007982847 + d[1.2387358665259833] = 0.11249900953151874 + d[0.34389201204090203] = 0.11149641829878375 + d[0.855204459573303] = 0.11206930271310694 + d[0.10051962632988332] = 0.11122373651192782 + d[1.6105180287755947] = 0.11291554105781172 + d[0.6516761179384709] = 0.11184126687768742 + d[0.9637271934916961] = 0.11219089209083931 + d[2.010934578431744] = 0.11336413691296068 + d[0.7412771851347991] = 0.11194165734699896 + d[1.2970413710011415] = 0.11256433378489761 + d[0.5350994524719059] = 0.11171065200545129 + d[0.8667157048918527] = 0.11208219999920067 + d[0.4483724548544632] = 0.11161348099169613 + d[1.7511640971682811] = 0.11307311224994611 + d[1.1310604995649935] = 0.11237837160501339 + d[2.522816047104907] = 0.113937577700241 + d[3.981253379159884] = 0.11557113638099044 + d[0.2357447169836332] = 0.11137524690575745 + d[0.22771111271238997] = 0.11136624581222469 + d[1.1890308375241267] = 0.11244332084794231 + d[1.9337227734772215] = 0.11327763628922548 + d[0.4748679910824062] = 0.11164316725330517 + d[0.40128953354162966] = 0.11156072805825316 + d[1.3533430206111619] = 0.1126274126844104 + d[0.10348833112865541] = 0.1112270627429409 + d[1.3877997493377328] = 0.11266601696486657 + d[0.7814630394970468] = 0.11198668209611587 + d[1.3692010466913649] = 0.11264517955232149 + d[0.9589256335636845] = 0.11218551241594797 + d[1.2055985320404068] = 0.1124618830379516 + d[1.253303157812016] = 0.11251533044308157 + d[1.9496407662571786] = 0.11329546932940611 + d[1.5000914628167419] = 0.11279182444404966 + d[0.28334638873348017] = 0.11142858123867773 + d[3.033630417130691] = 0.11450977921866685 + d[2.033954290523509] = 0.11338992581483053 + d[1.808015910201904] = 0.11313680487737313 + d[0.5708185495709135] = 0.11175067246588843 + d[0.5535126231571483] = 0.11173128253189221 + d[0.9665781238324795] = 0.11219408627674148 + d[1.3350093241088152] = 0.1126068721197662 + d[0.17660913667792266] = 0.11130898958929202 + d[0.8114020496232044] = 0.11202022609483595 + d[2.1230730606621417] = 0.11348976457453903 + d[1.129171576818682] = 0.11237625527524299 + d[0.22289785923268735] = 0.11136085289678355 + d[0.2978473414257343] = 0.11144482853051456 + d[1.558044566599128] = 0.11285675247138616 + d[2.9753467583215816] = 0.11444449381518766 + d[1.6683238669426657] = 0.11298030342487442 + d[0.32497933032900217] = 0.11147522799375557 + d[0.6240931308710272] = 0.11181036238574811 + d[1.1554039386532904] = 0.11240564572167872 + d[0.08636170561082057] = 0.11120787352774131 + d[0.07964646585680601] = 0.11120034955935905 + d[1.717814356445558] = 0.11303574945564117 + d[1.8830073796960445] = 0.1132208192582517 + d[0.6724624604170539] = 0.11186455626096618 + d[2.286332065776209] = 0.11367265886798318 + d[0.35622992460001723] = 0.11151024204161263 + d[1.5494031367449295] = 0.11284707102726943 + d[1.729902917050898] = 0.11304929267626523 + d[1.9464635188576085] = 0.11329190983922816 + d[2.9937152775323534] = 0.11446506905847599 + d[1.955435168440077] = 0.11330196083112547 + d[0.5079195923597251] = 0.11168019906316047 + d[1.4926487637001067] = 0.11278348595724848 + d[2.177612731258345] = 0.11355086420671905 + d[2.5514237169602687] = 0.11396962453950361 + d[1.4465859165276913] = 0.1127318789612621 + d[1.0190933808561624] = 0.1122529243414101 + d[2.0900397194445004] = 0.11345275782065715 + d[1.3359323373889544] = 0.1126079062389384 + d[2.8977562293016623] = 0.11435758112197636 + d[1.0111739975385563] = 0.11224405148044356 + d[0.3239332158659507] = 0.11147405589721089 + d[1.4148210396548717] = 0.1126962907279035 + d[0.14913651135034423] = 0.11127820840322827 + d[1.2745496352859007] = 0.11253913455407284 + d[0.9579042373467628] = 0.1121843680419169 + d[0.8076613270857308] = 0.11201603495044685 + d[2.0028174655451925] = 0.11335504332323751 + d[0.6248268369627741] = 0.11181118444411801 + d[1.5011903664992166] = 0.11279305560901247 + d[1.6986069907760704] = 0.11301423076428638 + d[0.061928400885765456] = 0.11118049767427175 + d[0.10638689221730302] = 0.11123031038265835 + d[0.35170370196784506] = 0.11150517073540109 + d[0.8886148481227398] = 0.11210673594340322 + d[0.41252611545532103] = 0.11157331782339633 + d[0.5355774373905071] = 0.11171118755055084 + d[3.1611467580951045] = 0.11465261196649647 + d[0.9403590261783228] = 0.11216471034768304 + d[1.8213269667022003] = 0.11315171755923453 + d[0.7108034913405985] = 0.11190751417469673 + d[1.894552893933274] = 0.11323375385741564 + d[0.366839004478702] = 0.11152212874901835 + d[0.5658024266260737] = 0.11174505229447351 + d[1.3095056603387798] = 0.11257829847343133 + d[0.4227436048569271] = 0.11158476576720573 + d[2.331901908688812] = 0.11372370872073745 + d[0.3214629255645929] = 0.111471288113258 + d[1.9864473065753407] = 0.11333670383139723 + d[1.3498460743409462] = 0.11262349480519479 + d[1.9133013997519592] = 0.11325475803181884 + d[0.8161300138799373] = 0.1120255233540269 + d[2.5740777216406503] = 0.11399500187475975 + d[0.4454292122991572] = 0.11161018330780134 + d[1.0858096812990696] = 0.11232767297746393 + d[2.635123442564735] = 0.11406338571172706 + d[0.45403350999956804] = 0.11161982378128933 + d[0.4326829084815704] = 0.11159590202155614 + d[0.7333123084564045] = 0.11193273338697818 + d[0.7155721473650798] = 0.11191285704959407 + d[0.08227380012206109] = 0.11120329330833342 + d[0.01169184181629701] = 0.11112421102550447 + d[0.43563223016578356] = 0.11159920651775647 + d[0.38878266028249076] = 0.11154671502097614 + d[2.7987225810213947] = 0.11424664732831764 + d[2.4473879232053477] = 0.11385308107055293 + d[0.8253680816153424] = 0.1120358737754879 + d[0.6061977060902293] = 0.11179031200195998 + d[0.5641886768994577] = 0.11174324421456991 + d[0.883355367427605] = 0.11210084318916604 + d[1.1741554689376443] = 0.11242665469542737 + d[1.9157262434886664] = 0.11325747460988923 + d[0.9215337536832324] = 0.11214361844853753 + d[2.359097308485401] = 0.11375417435531424 + d[2.6461723630494283] = 0.1140757627191349 + d[0.9425937480865658] = 0.11216721413623087 + d[1.2498812205919247] = 0.1125114965723448 + d[0.3763588176106163] = 0.11153279500942226 + d[1.3609060582163917] = 0.1126358860930399 + d[2.2246649301695496] = 0.11360357543818167 + d[0.29399255409781655] = 0.11144050951435899 + d[0.5914639099562726] = 0.11177380395906261 + d[2.998236352150084] = 0.11447013326750938 + d[1.081645809056435] = 0.1123230078033253 + d[1.383885127989016] = 0.1126616311465316 + d[1.8096817789051982] = 0.11313867118945266 + d[2.4896582414434625] = 0.11390043354316992 + d[1.518756533480452] = 0.11281273597923683 + d[0.6902820760510884] = 0.11188452165608753 + d[1.9333200322654194] = 0.11327718509496693 + d[0.9744697107672393] = 0.11220292801784713 + d[2.2880042703821544] = 0.11367453216947979 + d[-0.30000000000000004] = 0.11077498179038106 + d[-3.0] = 0.10775011343404019 + d[-1000.0] = -0.23211535395017646 + d[-995.0] = -0.23159552367032604 + d[-990.0] = -0.23107293400700224 + d[-985.0] = -0.23054755594291693 + d[-980.0] = -0.23001936000645123 + d[-975.0] = -0.22948831626223104 + d[-970.0] = -0.22895439430146047 + d[-965.0] = -0.2284175632320038 + d[-960.0] = -0.2278777916682102 + d[-955.0] = -0.22733504772047192 + d[-950.0] = -0.22678929898450795 + d[-945.0] = -0.2262405125303651 + d[-940.0] = -0.22568865489112688 + d[-935.0] = -0.2251336920513211 + d[-930.0] = -0.22457558943501693 + d[-925.0] = -0.22401431189360116 + d[-920.0] = -0.22344982369322341 + d[-915.0] = -0.22288208850190006 + d[-910.0] = -0.222311069376265 + d[-905.0] = -0.22173672874795636 + d[-900.0] = -0.2211590284096271 + d[-895.0] = -0.22057792950056693 + d[-890.0] = -0.21999339249192307 + d[-885.0] = -0.2194053771715061 + d[-880.0] = -0.218813842628167 + d[-875.0] = -0.21821874723573187 + d[-870.0] = -0.217620048636478 + d[-865.0] = -0.21701770372413665 + d[-860.0] = -0.21641166862640687 + d[-855.0] = -0.21580189868696148 + d[-850.0] = -0.21518834844693097 + d[-845.0] = -0.21457097162584365 + d[-840.0] = -0.2139497211020065 + d[-835.0] = -0.2133245488923043 + d[-830.0] = -0.21269540613139826 + d[-825.0] = -0.21206224305030325 + d[-820.0] = -0.21142500895431943 + d[-815.0] = -0.210783652200297 + d[-810.0] = -0.21013812017321043 + d[-805.0] = -0.20948835926201537 + d[-800.0] = -0.20883431483476406 + d[-795.0] = -0.20817593121295058 + d[-790.0] = -0.2075131516450593 + d[-785.0] = -0.20684591827928578 + d[-780.0] = -0.20617417213539985 + d[-775.0] = -0.20549785307571933 + d[-770.0] = -0.20481689977516027 + d[-765.0] = -0.20413124969032936 + d[-760.0] = -0.20344083902762183 + d[-755.0] = -0.2027456027102877 + d[-750.0] = -0.20204547434442555 + d[-745.0] = -0.20134038618386368 + d[-740.0] = -0.2006302690938847 + d[-735.0] = -0.1999150525137488 + d[-730.0] = -0.19919466441796863 + d[-725.0] = -0.19846903127628623 + d[-720.0] = -0.19773807801230125 + d[-715.0] = -0.19700172796069576 + d[-710.0] = -0.19625990282300004 + d[-705.0] = -0.19551252262184016 + d[-700.0] = -0.19475950565360584 + d[-695.0] = -0.194000768439475 + d[-690.0] = -0.19323622567472543 + d[-685.0] = -0.19246579017626536 + d[-680.0] = -0.19168937282830795 + d[-675.0] = -0.19090688252611132 + d[-670.0] = -0.19011822611770518 + d[-665.0] = -0.18932330834351674 + d[-660.0] = -0.1885220317738081 + d[-655.0] = -0.18771429674383155 + d[-650.0] = -0.1869000012866044 + d[-645.0] = -0.18607904106320017 + d[-640.0] = -0.18525130929045008 + d[-635.0] = -0.18441669666593885 + d[-630.0] = -0.18357509129017857 + d[-625.0] = -0.1827263785858344 + d[-620.0] = -0.18187044121387164 + d[-615.0] = -0.18100715898648634 + d[-610.0] = -0.18013640877667486 + d[-605.0] = -0.17925806442429076 + d[-600.0] = -0.17837199663842884 + d[-595.0] = -0.17747807289596862 + d[-590.0] = -0.17657615733610044 + d[-585.0] = -0.17566611065064902 + d[-580.0] = -0.17474778996999796 + d[-575.0] = -0.1738210487444108 + d[-570.0] = -0.17288573662053047 + d[-565.0] = -0.17194169931283143 + d[-560.0] = -0.1709887784697821 + d[-555.0] = -0.17002681153446692 + d[-550.0] = -0.16905563159939957 + d[-545.0] = -0.1680750672552499 + d[-540.0] = -0.167084942433185 + d[-535.0] = -0.1660850762405165 + d[-530.0] = -0.16507528278932326 + d[-525.0] = -0.16405537101770412 + d[-520.0] = -0.16302514450329508 + d[-515.0] = -0.1619844012686672 + d[-510.0] = -0.16093293357819627 + d[-505.0] = -0.15987052772597915 + d[-500.0] = -0.15879696381434238 + d[-495.0] = -0.15771201552246766 + d[-490.0] = -0.15661544986463027 + d[-485.0] = -0.15550702693752066 + d[-480.0] = -0.15438649965608908 + d[-475.0] = -0.1532536134773218 + d[-470.0] = -0.15210810611132686 + d[-465.0] = -0.15094970721907192 + d[-460.0] = -0.14977813809608015 + d[-455.0] = -0.14859311134135433 + d[-450.0] = -0.14739433051075757 + d[-445.0] = -0.14618148975403888 + d[-440.0] = -0.14495427343464728 + d[-435.0] = -0.14371235573143354 + d[-430.0] = -0.14245540022129027 + d[-425.0] = -0.14118305944173165 + d[-420.0] = -0.13989497443236337 + d[-415.0] = -0.1385907742541394 + d[-410.0] = -0.1372700754852471 + d[-405.0] = -0.13593248169240674 + d[-400.0] = -0.13457758287631244 + d[-395.0] = -0.13320495488988332 + d[-390.0] = -0.13181415882793512 + d[-385.0] = -0.13040474038682087 + d[-380.0] = -0.12897622919253326 + d[-375.0] = -0.12752813809570052 + d[-370.0] = -0.12605996243185585 + d[-365.0] = -0.12457117924530575 + d[-360.0] = -0.12306124647487632 + d[-355.0] = -0.12152960209977898 + d[-350.0] = -0.11997566324380166 + d[-345.0] = -0.11839882523601403 + d[-340.0] = -0.11679846062616961 + d[-335.0] = -0.11517391815299854 + d[-330.0] = -0.11352452166362037 + d[-325.0] = -0.1118495689823692 + d[-320.0] = -0.11014833072741709 + d[-315.0] = -0.10842004907372238 + d[-310.0] = -0.10666393646101247 + d[-305.0] = -0.10487917424575988 + d[-300.0] = -0.10306491129643008 + d[-295.0] = -0.10122026253168198 + d[-290.0] = -0.09934430740171518 + d[-285.0] = -0.09743608831358558 + d[-280.0] = -0.09549460900209439 + d[-275.0] = -0.09351883284880314 + d[-270.0] = -0.09150768115288849 + d[-265.0] = -0.08946003135894853 + d[-260.0] = -0.08737471524855861 + d[-255.0] = -0.08525051710439502 + d[-250.0] = -0.08308617185815864 + d[-245.0] = -0.08088036323640152 + d[-240.0] = -0.07863172192176626 + d[-235.0] = -0.07633882375117224 + d[-230.0] = -0.07400018797722524 + d[-225.0] = -0.07161427562469058 + d[-220.0] = -0.06917948798037943 + d[-215.0] = -0.06669416526237865 + d[-210.0] = -0.06415658552334752 + d[-205.0] = -0.06156496385275784 + d[-200.0] = -0.058917451954609235 + d[-195.0] = -0.05621213819045906 + d[-190.0] = -0.05344704819268514 + d[-185.0] = -0.05062014616985272 + d[-180.0] = -0.04772933704492904 + d[-175.0] = -0.044772469587846364 + d[-170.0] = -0.04174734072642211 + d[-165.0] = -0.038651701243596126 + d[-160.0] = -0.03548326309382499 + d[-155.0] = -0.032239708596494276 + d[-150.0] = -0.028918701788189505 + d[-145.0] = -0.025517902236999235 + d[-140.0] = -0.022034981638516332 + d[-135.0] = -0.018467643522012134 + d[-130.0] = -0.014813646392800223 + d[-125.0] = -0.011070830618684219 + d[-120.0] = -0.007237149329425457 + d[-115.0] = -0.0033107035325154466 + d[-110.0] = 0.0007102184500745456 + d[-105.0] = 0.004827097257284058 + d[-100.0] = 0.009041134692025388 + d[-95.0] = 0.013353202298125366 + d[-90.0] = 0.017763787036832984 + d[-85.0] = 0.022272935112682107 + d[-80.0] = 0.026880195356682596 + d[-75.0] = 0.03158456394862824 + d[-70.0] = 0.03638443262238891 + d[-65.0] = 0.04127754281216903 + d[-60.0] = 0.046260948420350695 + d[-55.0] = 0.05133098997147756 + d[-50.0] = 0.05648328281698925 + d[-45.0] = 0.061712721735900505 + d[-40.0] = 0.06701350372019282 + d[-35.0] = 0.07237916994856675 + d[-30.0] = 0.0778026669776524 + d[-25.0] = 0.08327642608649269 + d[-20.0] = 0.08879245859478016 + d[-15.0] = 0.09434246394915988 + d[-10.0] = 0.099917946544774 + d[-5.0] = 0.1055103367122722 + d[0.0] = 0.1111111111111111 + d[-100.0] = 0.009041134692025388 + d[-99.5] = 0.009467918863066055 + d[-99.0] = 0.009895684326675008 + d[-98.5] = 0.010324431717651822 + d[-98.0] = 0.010754161631252285 + d[-97.5] = 0.011184874622627988 + d[-97.0] = 0.011616571206263249 + d[-96.5] = 0.01204925185541153 + d[-96.0] = 0.012482917001530008 + d[-95.5] = 0.012917567033713162 + d[-95.0] = 0.013353202298125366 + d[-94.5] = 0.01378982309743268 + d[-94.0] = 0.014227429690233911 + d[-93.5] = 0.014666022290491076 + d[-93.0] = 0.015105601066959656 + d[-92.5] = 0.015546166142618223 + d[-92.0] = 0.01598771759409881 + d[-91.5] = 0.016430255451116538 + d[-91.0] = 0.01687377969590012 + d[-90.5] = 0.017318290262622632 + d[-90.0] = 0.017763787036832984 + d[-89.5] = 0.01821026985488841 + d[-89.0] = 0.018657738503387533 + d[-88.5] = 0.01910619271860553 + d[-88.0] = 0.01955563218592965 + d[-87.5] = 0.02000605653929749 + d[-87.0] = 0.02045746536063614 + d[-86.5] = 0.020909858179304297 + d[-86.0] = 0.02136323447153568 + d[-85.5] = 0.021817593659886114 + d[-85.0] = 0.022272935112682107 + d[-84.5] = 0.022729258143473402 + d[-84.0] = 0.023186562010487938 + d[-83.5] = 0.023644845916090784 + d[-83.0] = 0.024104109006246294 + d[-82.5] = 0.024564350369984306 + d[-82.0] = 0.025025569038870682 + d[-81.5] = 0.02548776398648167 + d[-81.0] = 0.025950934127883435 + d[-80.5] = 0.026415078319115964 + d[-80.0] = 0.026880195356682596 + d[-79.5] = 0.027346283977044306 + d[-79.0] = 0.027813342856120332 + d[-78.5] = 0.028281370608793877 + d[-78.0] = 0.028750365788424687 + d[-77.5] = 0.029220326886367665 + d[-77.0] = 0.029691252331497914 + d[-76.5] = 0.030163140489743667 + d[-76.0] = 0.03063598966362524 + d[-75.5] = 0.031109798091802143 + d[-75.0] = 0.03158456394862824 + d[-74.5] = 0.03206028534371408 + d[-74.0] = 0.032536960321498304 + d[-73.5] = 0.03301458686082742 + d[-73.0] = 0.033493162874544236 + d[-72.5] = 0.033972686209085806 + d[-72.0] = 0.034453154644090545 + d[-71.5] = 0.03493456589201513 + d[-71.0] = 0.03541691759776169 + d[-70.5] = 0.03590020733831467 + d[-70.0] = 0.03638443262238891 + d[-69.5] = 0.03686959089008804 + d[-69.0] = 0.03735567951257451 + d[-68.5] = 0.037842695791750564 + d[-68.0] = 0.03833063695995112 + d[-67.5] = 0.038819500179648636 + d[-67.0] = 0.03930928254317026 + d[-66.5] = 0.039799981072427326 + d[-66.0] = 0.040291592718657704 + d[-65.5] = 0.04078411436218132 + d[-65.0] = 0.04127754281216903 + d[-64.5] = 0.041771874806424664 + d[-64.0] = 0.042267107011181804 + d[-63.5] = 0.04276323602091378 + d[-63.0] = 0.043260258358158415 + d[-62.5] = 0.04375817047335778 + d[-62.0] = 0.044256968744712216 + d[-61.5] = 0.04475664947804975 + d[-61.0] = 0.04525720890671123 + d[-60.5] = 0.045758643191450454 + d[-60.0] = 0.046260948420350695 + d[-59.5] = 0.04676412060875709 + d[-59.0] = 0.04726815569922527 + d[-58.5] = 0.0477730495614867 + d[-58.0] = 0.04827879799243065 + d[-57.5] = 0.04878539671610316 + d[-57.0] = 0.04929284138372328 + d[-56.5] = 0.04980112757371627 + d[-56.0] = 0.05031025079176493 + d[-55.5] = 0.05082020647087812 + d[-55.0] = 0.05133098997147756 + d[-54.5] = 0.051842596581502365 + d[-54.0] = 0.05235502151653207 + d[-53.5] = 0.052868259919928134 + d[-53.0] = 0.05338230686299342 + d[-52.5] = 0.05389715734515102 + d[-52.0] = 0.0544128062941413 + d[-51.5] = 0.05492924856623846 + d[-51.0] = 0.05544647894648527 + d[-50.5] = 0.055964492148947914 + d[-50.0] = 0.05648328281698925 + d[-49.5] = 0.057002845523561635 + d[-49.0] = 0.057523174771519525 + d[-48.5] = 0.05804426499395071 + d[-48.0] = 0.05856611055452768 + d[-47.5] = 0.05908870574787825 + d[-47.0] = 0.059612044799975894 + d[-46.5] = 0.06013612186854944 + d[-46.0] = 0.060660931043512556 + d[-45.5] = 0.06118646634741293 + d[-45.0] = 0.061712721735900505 + d[-44.5] = 0.06223969109821603 + d[-44.0] = 0.06276736825769869 + d[-43.5] = 0.06329574697231313 + d[-43.0] = 0.06382482093519634 + d[-42.5] = 0.06435458377522355 + d[-42.0] = 0.06488502905759361 + d[-41.5] = 0.06541615028443354 + d[-41.0] = 0.06594794089542194 + d[-40.5] = 0.06648039426843205 + d[-40.0] = 0.06701350372019282 + d[-39.5] = 0.06754726250696955 + d[-39.0] = 0.06808166382526232 + d[-38.5] = 0.06861670081252366 + d[-38.0] = 0.0691523665478938 + d[-37.5] = 0.06968865405295449 + d[-37.0] = 0.07022555629250035 + d[-36.5] = 0.07076306617532835 + d[-36.0] = 0.07130117655504406 + d[-35.5] = 0.07183988023088614 + d[-35.0] = 0.07237916994856675 + d[-34.5] = 0.0729190384011297 + d[-34.0] = 0.07345947822982424 + d[-33.5] = 0.07400048202499593 + d[-33.0] = 0.07454204232699277 + d[-32.5] = 0.07508415162708723 + d[-32.0] = 0.07562680236841399 + d[-31.5] = 0.07616998694692198 + d[-31.0] = 0.07671369771234196 + d[-30.5] = 0.0772579269691678 + d[-30.0] = 0.0778026669776524 + d[-29.5] = 0.07834790995481683 + d[-29.0] = 0.0788936480754732 + d[-28.5] = 0.07943987347326023 + d[-28.0] = 0.07998657824169153 + d[-27.5] = 0.08053375443521615 + d[-27.0] = 0.08108139407029094 + d[-26.5] = 0.08162948912646412 + d[-26.0] = 0.08217803154747022 + d[-25.5] = 0.08272701324233533 + d[-25.0] = 0.08327642608649269 + d[-24.5] = 0.0838262619229079 + d[-24.0] = 0.08437651256321357 + d[-23.5] = 0.08492716978885279 + d[-23.0] = 0.08547822535223087 + d[-22.5] = 0.08602967097787545 + d[-22.0] = 0.08658149836360368 + d[-21.5] = 0.08713369918169672 + d[-21.0] = 0.08768626508008076 + d[-20.5] = 0.08823918768351416 + d[-20.0] = 0.08879245859478016 + d[-19.5] = 0.08934606939588505 + d[-19.0] = 0.08990001164926054 + d[-18.5] = 0.09045427689897087 + d[-18.0] = 0.0910088566719233 + d[-17.5] = 0.09156374247908194 + d[-17.0] = 0.09211892581668438 + d[-16.5] = 0.09267439816746062 + d[-16.0] = 0.09323015100185367 + d[-15.5] = 0.09378617577924148 + d[-15.0] = 0.09434246394915988 + d[-14.5] = 0.09489900695252557 + d[-14.0] = 0.09545579622285905 + d[-13.5] = 0.09601282318750709 + d[-13.0] = 0.0965700792688638 + d[-12.5] = 0.09712755588559024 + d[-12.0] = 0.09768524445383207 + d[-11.5] = 0.09824313638843438 + d[-11.0] = 0.09880122310415372 + d[-10.5] = 0.09935949601686661 + d[-10.0] = 0.099917946544774 + d[-9.5] = 0.10047656610960143 + d[-9.0] = 0.10103534613779432 + d[-8.5] = 0.10159427806170782 + d[-8.0] = 0.10215335332079112 + d[-7.5] = 0.10271256336276544 + d[-7.0] = 0.10327189964479536 + d[-6.5] = 0.10383135363465319 + d[-6.0] = 0.10439091681187587 + d[-5.5] = 0.10495058066891394 + d[-5.0] = 0.1055103367122722 + d[-4.5] = 0.10607017646364181 + d[-4.0] = 0.10663009146102317 + d[-3.5] = 0.10719007325983944 + d[-3.0] = 0.10775011343404019 + d[-2.5] = 0.1083102035771948 + d[-2.0] = 0.10887033530357547 + d[-1.5] = 0.10943050024922904 + d[-1.0] = 0.1099906900730379 + d[-0.5] = 0.11055089645776897 + d[0.0] = 0.1111111111111111 + d[-10.0] = 0.099917946544774 + d[-9.95] = 0.0999738010360999 + d[-9.9] = 0.10002965720921515 + d[-9.85] = 0.10008551505554424 + d[-9.8] = 0.10014137456651218 + d[-9.75] = 0.10019723573354447 + d[-9.7] = 0.10025309854806716 + d[-9.65] = 0.10030896300150681 + d[-9.6] = 0.10036482908529054 + d[-9.55] = 0.100420696790846 + d[-9.5] = 0.10047656610960143 + d[-9.45] = 0.10053243703298564 + d[-9.4] = 0.10058830955242803 + d[-9.35] = 0.10064418365935861 + d[-9.3] = 0.10070005934520798 + d[-9.25] = 0.10075593660140741 + d[-9.2] = 0.10081181541938877 + d[-9.15] = 0.1008676957905846 + d[-9.1] = 0.10092357770642812 + d[-9.05] = 0.10097946115835317 + d[-9.0] = 0.10103534613779432 + d[-8.95] = 0.10109123263618681 + d[-8.9] = 0.10114712064496661 + d[-8.85] = 0.10120301015557044 + d[-8.8] = 0.10125890115943569 + d[-8.75] = 0.10131479364800051 + d[-8.7] = 0.10137068761270385 + d[-8.65] = 0.10142658304498538 + d[-8.6] = 0.10148247993628556 + d[-8.55] = 0.1015383782780457 + d[-8.5] = 0.10159427806170782 + d[-8.45] = 0.1016501792787148 + d[-8.4] = 0.10170608192051037 + d[-8.35] = 0.10176198597853907 + d[-8.3] = 0.10181789144424629 + d[-8.25] = 0.10187379830907829 + d[-8.2] = 0.10192970656448223 + d[-8.15] = 0.1019856162019061 + d[-8.1] = 0.10204152721279884 + d[-8.05] = 0.10209743958861026 + d[-8.0] = 0.10215335332079112 + d[-7.95] = 0.1022092684007931 + d[-7.9] = 0.10226518482006881 + d[-7.85] = 0.10232110257007188 + d[-7.8] = 0.10237702164225679 + d[-7.75] = 0.10243294202807912 + d[-7.7] = 0.10248886371899539 + d[-7.65] = 0.1025447867064631 + d[-7.6] = 0.10260071098194079 + d[-7.55] = 0.10265663653688803 + d[-7.5] = 0.10271256336276544 + d[-7.45] = 0.10276849145103464 + d[-7.4] = 0.10282442079315836 + d[-7.35] = 0.10288035138060038 + d[-7.3] = 0.10293628320482556 + d[-7.25] = 0.10299221625729989 + d[-7.2] = 0.10304815052949041 + d[-7.15] = 0.10310408601286532 + d[-7.1] = 0.10316002269889395 + d[-7.05] = 0.10321596057904675 + d[-7.0] = 0.10327189964479536 + d[-6.95] = 0.10332783988761252 + d[-6.9] = 0.10338378129897222 + d[-6.85] = 0.1034397238703496 + d[-6.8] = 0.10349566759322099 + d[-6.75] = 0.10355161245906395 + d[-6.7] = 0.10360755845935729 + d[-6.65] = 0.10366350558558099 + d[-6.6] = 0.10371945382921631 + d[-6.55] = 0.10377540318174579 + d[-6.5] = 0.10383135363465319 + d[-6.45] = 0.10388730517942359 + d[-6.4] = 0.10394325780754332 + d[-6.35] = 0.10399921151050008 + d[-6.3] = 0.10405516627978281 + d[-6.25] = 0.10411112210688184 + d[-6.2] = 0.10416707898328878 + d[-6.15] = 0.10422303690049661 + d[-6.1] = 0.10427899584999971 + d[-6.05] = 0.10433495582329376 + d[-6.0] = 0.10439091681187587 + d[-5.95] = 0.10444687880724454 + d[-5.9] = 0.10450284180089968 + d[-5.85] = 0.10455880578434258 + d[-5.8] = 0.104614770749076 + d[-5.75] = 0.10467073668660413 + d[-5.7] = 0.1047267035884326 + d[-5.65] = 0.1047826714460685 + d[-5.6] = 0.1048386402510204 + d[-5.55] = 0.10489460999479835 + d[-5.5] = 0.10495058066891394 + d[-5.45] = 0.10500655226488018 + d[-5.4] = 0.10506252477421169 + d[-5.35] = 0.10511849818842454 + d[-5.3] = 0.1051744724990364 + d[-5.25] = 0.10523044769756648 + d[-5.2] = 0.10528642377553553 + d[-5.15] = 0.1053424007244659 + d[-5.1] = 0.10539837853588152 + d[-5.05] = 0.10545435720130791 + d[-5.0] = 0.1055103367122722 + d[-4.95] = 0.10556631706030314 + d[-4.9] = 0.10562229823693113 + d[-4.85] = 0.1056782802336882 + d[-4.8] = 0.105734263042108 + d[-4.75] = 0.1057902466537259 + d[-4.7] = 0.10584623106007891 + d[-4.65] = 0.10590221625270575 + d[-4.6] = 0.10595820222314682 + d[-4.55] = 0.10601418896294422 + d[-4.5] = 0.10607017646364181 + d[-4.45] = 0.10612616471678513 + d[-4.4] = 0.1061821537139215 + d[-4.35] = 0.1062381434466 + d[-4.3] = 0.10629413390637142 + d[-4.25] = 0.1063501250847884 + d[-4.2] = 0.10640611697340531 + d[-4.15] = 0.10646210956377833 + d[-4.1] = 0.10651810284746546 + d[-4.05] = 0.10657409681602653 + d[-4.0] = 0.10663009146102317 + d[-3.95] = 0.10668608677401888 + d[-3.9] = 0.10674208274657898 + d[-3.85] = 0.10679807937027071 + d[-3.8] = 0.1068540766366631 + d[-3.75] = 0.10691007453732718 + d[-3.7] = 0.10696607306383575 + d[-3.65] = 0.10702207220776361 + d[-3.6] = 0.10707807196068744 + d[-3.55] = 0.10713407231418587 + d[-3.5] = 0.10719007325983944 + d[-3.45] = 0.10724607478923068 + d[-3.4] = 0.10730207689394403 + d[-3.35] = 0.10735807956556596 + d[-3.3] = 0.10741408279568489 + d[-3.25] = 0.10747008657589124 + d[-3.2] = 0.10752609089777745 + d[-3.15] = 0.10758209575293796 + d[-3.1] = 0.10763810113296923 + d[-3.05] = 0.10769410702946978 + d[-3.0] = 0.10775011343404019 + d[-2.95] = 0.10780612033828303 + d[-2.9] = 0.10786212773380303 + d[-2.85] = 0.10791813561220695 + d[-2.8] = 0.10797414396510364 + d[-2.75] = 0.10803015278410409 + d[-2.7] = 0.10808616206082135 + d[-2.65] = 0.10814217178687065 + d[-2.6] = 0.10819818195386931 + d[-2.55] = 0.10825419255343681 + d[-2.5] = 0.1083102035771948 + d[-2.45] = 0.10836621501676709 + d[-2.4] = 0.10842222686377967 + d[-2.35] = 0.10847823910986068 + d[-2.3] = 0.10853425174664053 + d[-2.25] = 0.10859026476575177 + d[-2.2] = 0.10864627815882924 + d[-2.15] = 0.10870229191750994 + d[-2.1] = 0.10875830603343314 + d[-2.05] = 0.10881432049824039 + d[-2.0] = 0.10887033530357547 + d[-1.95] = 0.10892635044108442 + d[-1.9] = 0.10898236590241563 + d[-1.85] = 0.1090383816792197 + d[-1.8] = 0.10909439776314958 + d[-1.75] = 0.10915041414586055 + d[-1.7] = 0.10920643081901019 + d[-1.65] = 0.10926244777425839 + d[-1.6] = 0.10931846500326747 + d[-1.55] = 0.10937448249770201 + d[-1.5] = 0.10943050024922904 + d[-1.45] = 0.10948651824951791 + d[-1.4] = 0.1095425364902404 + d[-1.35] = 0.10959855496307064 + d[-1.3] = 0.10965457365968523 + d[-1.25] = 0.10971059257176313 + d[-1.2] = 0.1097666116909858 + d[-1.15] = 0.10982263100903705 + d[-1.1] = 0.10987865051760323 + d[-1.05] = 0.1099346702083731 + d[-1.0] = 0.1099906900730379 + d[-0.95] = 0.11004671010329135 + d[-0.9] = 0.11010273029082969 + d[-0.85] = 0.11015875062735164 + d[-0.8] = 0.1102147711045584 + d[-0.75] = 0.11027079171415378 + d[-0.7] = 0.11032681244784404 + d[-0.65] = 0.11038283329733801 + d[-0.6] = 0.11043885425434709 + d[-0.55] = 0.11049487531058524 + d[-0.5] = 0.11055089645776897 + d[-0.45] = 0.1106069176876174 + d[-0.4] = 0.11066293899185227 + d[-0.35] = 0.11071896036219783 + d[-0.3] = 0.11077498179038106 + d[-0.25] = 0.11083100326813149 + d[-0.2] = 0.11088702478718131 + d[-0.15] = 0.11094304633926536 + d[-0.1] = 0.11099906791612112 + d[-0.05] = 0.11105508950948877 + d[0.0] = 0.1111111111111111 + d[-1.0] = 0.1099906900730379 + d[-0.995] = 0.10999629206874878 + d[-0.99] = 0.11000189406610725 + d[-0.985] = 0.11000749606510499 + d[-0.98] = 0.1100130980657337 + d[-0.975] = 0.11001870006798509 + d[-0.97] = 0.11002430207185084 + d[-0.965] = 0.11002990407732263 + d[-0.96] = 0.11003550608439219 + d[-0.955] = 0.11004110809305119 + d[-0.95] = 0.11004671010329135 + d[-0.945] = 0.11005231211510436 + d[-0.94] = 0.11005791412848191 + d[-0.935] = 0.1100635161434157 + d[-0.93] = 0.11006911815989744 + d[-0.925] = 0.1100747201779188 + d[-0.92] = 0.1100803221974715 + d[-0.915] = 0.11008592421854725 + d[-0.91] = 0.11009152624113773 + d[-0.905] = 0.11009712826523464 + d[-0.9] = 0.11010273029082969 + d[-0.895] = 0.11010833231791457 + d[-0.89] = 0.110113934346481 + d[-0.885] = 0.11011953637652064 + d[-0.88] = 0.11012513840802522 + d[-0.875] = 0.11013074044098645 + d[-0.87] = 0.110136342475396 + d[-0.865] = 0.1101419445112456 + d[-0.86] = 0.11014754654852693 + d[-0.855] = 0.11015314858723171 + d[-0.85] = 0.11015875062735164 + d[-0.845] = 0.1101643526688784 + d[-0.84] = 0.11016995471180371 + d[-0.835] = 0.11017555675611929 + d[-0.83] = 0.11018115880181681 + d[-0.825] = 0.110186760848888 + d[-0.82] = 0.11019236289732454 + d[-0.815] = 0.11019796494711814 + d[-0.81] = 0.11020356699826053 + d[-0.805] = 0.11020916905074338 + d[-0.8] = 0.1102147711045584 + d[-0.795] = 0.11022037315969734 + d[-0.79] = 0.11022597521615184 + d[-0.785] = 0.11023157727391364 + d[-0.78] = 0.11023717933297443 + d[-0.775] = 0.11024278139332594 + d[-0.77] = 0.11024838345495985 + d[-0.765] = 0.1102539855178679 + d[-0.76] = 0.11025958758204175 + d[-0.755] = 0.11026518964747314 + d[-0.75] = 0.11027079171415378 + d[-0.745] = 0.11027639378207536 + d[-0.74] = 0.1102819958512296 + d[-0.735] = 0.1102875979216082 + d[-0.73] = 0.11029319999320286 + d[-0.725] = 0.1102988020660053 + d[-0.72] = 0.11030440414000724 + d[-0.715] = 0.11031000621520037 + d[-0.71] = 0.11031560829157641 + d[-0.705] = 0.11032121036912707 + d[-0.7] = 0.11032681244784404 + d[-0.695] = 0.11033241452771905 + d[-0.69] = 0.1103380166087438 + d[-0.685] = 0.11034361869091001 + d[-0.68] = 0.1103492207742094 + d[-0.675] = 0.11035482285863366 + d[-0.67] = 0.1103604249441745 + d[-0.665] = 0.11036602703082365 + d[-0.66] = 0.1103716291185728 + d[-0.655] = 0.11037723120741369 + d[-0.65] = 0.11038283329733801 + d[-0.645] = 0.11038843538833748 + d[-0.64] = 0.11039403748040381 + d[-0.635] = 0.11039963957352872 + d[-0.63] = 0.11040524166770391 + d[-0.625] = 0.1104108437629211 + d[-0.62] = 0.11041644585917201 + d[-0.615] = 0.11042204795644835 + d[-0.61] = 0.11042765005474184 + d[-0.605] = 0.11043325215404418 + d[-0.6] = 0.11043885425434709 + d[-0.595] = 0.1104444563556423 + d[-0.59] = 0.11045005845792151 + d[-0.585] = 0.11045566056117644 + d[-0.58] = 0.1104612626653988 + d[-0.575] = 0.1104668647705803 + d[-0.57] = 0.1104724668767127 + d[-0.565] = 0.11047806898378766 + d[-0.56] = 0.11048367109179692 + d[-0.555] = 0.11048927320073222 + d[-0.55] = 0.11049487531058524 + d[-0.545] = 0.11050047742134772 + d[-0.54] = 0.11050607953301136 + d[-0.535] = 0.1105116816455679 + d[-0.53] = 0.11051728375900904 + d[-0.525] = 0.11052288587332652 + d[-0.52] = 0.11052848798851204 + d[-0.515] = 0.11053409010455732 + d[-0.51] = 0.1105396922214541 + d[-0.505] = 0.11054529433919408 + d[-0.5] = 0.11055089645776897 + d[-0.495] = 0.11055649857717052 + d[-0.49] = 0.11056210069739043 + d[-0.485] = 0.11056770281842042 + d[-0.48] = 0.11057330494025222 + d[-0.475] = 0.11057890706287755 + d[-0.47] = 0.11058450918628814 + d[-0.465] = 0.11059011131047569 + d[-0.46] = 0.11059571343543194 + d[-0.455] = 0.1106013155611486 + d[-0.45] = 0.1106069176876174 + d[-0.445] = 0.11061251981483008 + d[-0.44] = 0.11061812194277833 + d[-0.435] = 0.11062372407145389 + d[-0.43] = 0.11062932620084848 + d[-0.425] = 0.11063492833095383 + d[-0.42] = 0.11064053046176166 + d[-0.415] = 0.11064613259326368 + d[-0.41] = 0.11065173472545164 + d[-0.405] = 0.11065733685831726 + d[-0.4] = 0.11066293899185226 + d[-0.395] = 0.11066854112604836 + d[-0.39] = 0.11067414326089729 + d[-0.385] = 0.11067974539639078 + d[-0.38] = 0.11068534753252056 + d[-0.375] = 0.11069094966927834 + d[-0.37] = 0.11069655180665586 + d[-0.365] = 0.11070215394464483 + d[-0.36] = 0.110707756083237 + d[-0.355] = 0.11071335822242409 + d[-0.35] = 0.11071896036219783 + d[-0.345] = 0.11072456250254994 + d[-0.34] = 0.11073016464347216 + d[-0.335] = 0.1107357667849562 + d[-0.33] = 0.11074136892699381 + d[-0.325] = 0.1107469710695767 + d[-0.32] = 0.11075257321269662 + d[-0.315] = 0.11075817535634527 + d[-0.31] = 0.11076377750051442 + d[-0.305] = 0.11076937964519577 + d[-0.3] = 0.11077498179038106 + d[-0.295] = 0.11078058393606201 + d[-0.29] = 0.11078618608223037 + d[-0.285] = 0.11079178822887786 + d[-0.28] = 0.11079739037599622 + d[-0.275] = 0.11080299252357717 + d[-0.27] = 0.11080859467161244 + d[-0.265] = 0.11081419682009379 + d[-0.26] = 0.11081979896901291 + d[-0.255] = 0.11082540111836157 + d[-0.25] = 0.11083100326813149 + d[-0.245] = 0.11083660541831439 + d[-0.24] = 0.11084220756890202 + d[-0.235] = 0.11084780971988611 + d[-0.23] = 0.1108534118712584 + d[-0.225] = 0.1108590140230106 + d[-0.22] = 0.11086461617513448 + d[-0.215] = 0.11087021832762176 + d[-0.21] = 0.11087582048046415 + d[-0.205] = 0.11088142263365343 + d[-0.2] = 0.11088702478718131 + d[-0.195] = 0.11089262694103952 + d[-0.19] = 0.11089822909521982 + d[-0.185] = 0.11090383124971392 + d[-0.18] = 0.11090943340451358 + d[-0.175] = 0.11091503555961052 + d[-0.17] = 0.11092063771499648 + d[-0.165] = 0.11092623987066322 + d[-0.16] = 0.11093184202660245 + d[-0.155] = 0.1109374441828059 + d[-0.15] = 0.11094304633926536 + d[-0.145] = 0.11094864849597251 + d[-0.14] = 0.11095425065291913 + d[-0.135] = 0.11095985281009693 + d[-0.13] = 0.11096545496749767 + d[-0.125] = 0.11097105712511307 + d[-0.12] = 0.11097665928293489 + d[-0.115] = 0.11098226144095487 + d[-0.11] = 0.11098786359916474 + d[-0.105] = 0.11099346575755624 + d[-0.1] = 0.11099906791612112 + d[-0.095] = 0.11100467007485111 + d[-0.09] = 0.11101027223373797 + d[-0.085] = 0.11101587439277341 + d[-0.08] = 0.11102147655194922 + d[-0.075] = 0.1110270787112571 + d[-0.07] = 0.1110326808706888 + d[-0.065] = 0.11103828303023608 + d[-0.06] = 0.11104388518989067 + d[-0.055] = 0.11104948734964432 + d[-0.05] = 0.11105508950948875 + d[-0.045] = 0.11106069166941575 + d[-0.04] = 0.11106629382941703 + d[-0.035] = 0.11107189598948435 + d[-0.03] = 0.11107749814960945 + d[-0.025] = 0.11108310030978406 + d[-0.02] = 0.11108870246999995 + d[-0.015] = 0.11109430463024884 + d[-0.01] = 0.1110999067905225 + d[-0.005] = 0.11110550895081268 + d[0.0] = 0.1111111111111111 + d[5000.0] = 0.6160234364411775 + d[10000.0] = 0.6838326572265573 + d[15000.0] = 0.7232796870511483 + d[20000.0] = 0.7512044748257517 + d[25000.0] = 0.7728374933059419 + d[30000.0] = 0.7904988201896223 + d[35000.0] = 0.8054229520681092 + d[40000.0] = 0.8183455237863915 + d[45000.0] = 0.8297404510013116 + d[50000.0] = 0.8399310168878039 + d[55000.0] = 0.8491476359271434 + d[60000.0] = 0.8575603359635887 + d[65000.0] = 0.8652981742065279 + d[70000.0] = 0.8724614271647665 + d[75000.0] = 0.8791295592793783 + d[80000.0] = 0.8853666113519277 + d[85000.0] = 0.8912249506182115 + d[90000.0] = 0.8967479461187314 + d[95000.0] = 0.9019719190008572 + d[100000.0] = 0.9069275914814589 + d[105000.0] = 0.9116411815836145 + d[110000.0] = 0.9161352427369731 + d[115000.0] = 0.9204293164283553 + d[120000.0] = 0.9245404457324075 + d[125000.0] = 0.9284835838577515 + d[130000.0] = 0.9322719224551675 + d[135000.0] = 0.9359171578855062 + d[140000.0] = 0.9394297090048819 + d[145000.0] = 0.9428188966893398 + d[150000.0] = 0.946093092891858 + d[155000.0] = 0.9492598452334021 + d[160000.0] = 0.9523259817941958 + d[165000.0] = 0.9552976997650153 + d[170000.0] = 0.9581806408526314 + d[175000.0] = 0.9609799557455935 + d[180000.0] = 0.9637003594912915 + d[185000.0] = 0.9663461792798675 + d[190000.0] = 0.9689213958510767 + d[195000.0] = 0.9714296795188672 + d[200000.0] = 0.9738744216319898 + d[205000.0] = 0.9762587621473756 + d[210000.0] = 0.9785856138787673 + d[215000.0] = 0.9808576838903705 + d[220000.0] = 0.9830774924296242 + d[225000.0] = 0.9852473897311522 + d[230000.0] = 0.9873695709728305 + d[235000.0] = 0.9894460896225733 + d[240000.0] = 0.9914788693792662 + d[245000.0] = 0.9934697148818794 + d[250000.0] = 0.9954203213361739 + d[255000.0] = 0.9973322831876855 + d[260000.0] = 0.999207101952172 + d[265000.0] = 1.001046193299868 + d[270000.0] = 1.0028508934772877 + d[275000.0] = 1.004622465139544 + d[280000.0] = 1.0063621026569507 + d[285000.0] = 1.0080709369517669 + d[290000.0] = 1.009750039914137 + d[295000.0] = 1.0114004284404103 + d[300000.0] = 1.0130230681319403 + d[305000.0] = 1.0146188766880468 + d[310000.0] = 1.0161887270230014 + d[315000.0] = 1.0177334501335364 + d[320000.0] = 1.0192538377404623 + d[325000.0] = 1.0207506447254209 + d[330000.0] = 1.022224591381542 + d[335000.0] = 1.0236763654948084 + d[340000.0] = 1.0251066242711788 + d[345000.0] = 1.0265159961229884 + d[350000.0] = 1.0279050823267777 + d[355000.0] = 1.0292744585635 + d[360000.0] = 1.0306246763509792 + d[365000.0] = 1.0319562643775384 + d[370000.0] = 1.0332697297448734 + d[375000.0] = 1.034565559127479 + d[380000.0] = 1.0358442198552646 + d[385000.0] = 1.0371061609253862 + d[390000.0] = 1.0383518139487744 + d[395000.0] = 1.039581594036353 + d[400000.0] = 1.0407959006295044 + d[405000.0] = 1.0419951182789304 + d[410000.0] = 1.04317961737572 + d[415000.0] = 1.0443497548380913 + d[420000.0] = 1.0455058747570007 + d[425000.0] = 1.0466483090035366 + d[430000.0] = 1.0477773778007822 + d[435000.0] = 1.0488933902626123 + d[440000.0] = 1.0499966449016935 + d[445000.0] = 1.051087430108773 + d[450000.0] = 1.0521660246051854 + d[455000.0] = 1.0532326978703515 + d[460000.0] = 1.0542877105459088 + d[465000.0] = 1.0553313148179917 + d[470000.0] = 1.0563637547790634 + d[475000.0] = 1.057385266770597 + d[480000.0] = 1.0583960797078102 + d[485000.0] = 1.0593964153875717 + d[490000.0] = 1.0603864887805114 + d[495000.0] = 1.0613665083082982 + d[500000.0] = 1.0623366761069832 + d[505000.0] = 1.0632971882772357 + d[510000.0] = 1.064248235122249 + d[515000.0] = 1.0651900013740412 + d[520000.0] = 1.0661226664088153 + d[525000.0] = 1.0670464044520187 + d[530000.0] = 1.0679613847736766 + d[535000.0] = 1.0688677718745567 + d[540000.0] = 1.06976572566367 + d[545000.0] = 1.0706554016275909 + d[550000.0] = 1.0715369509920454 + d[555000.0] = 1.0724105208761834 + d[560000.0] = 1.0732762544399335 + d[565000.0] = 1.074134291024806 + d[570000.0] = 1.0749847662884922 + d[575000.0] = 1.0758278123335843 + d[580000.0] = 1.0766635578307224 + d[585000.0] = 1.0774921281364553 + d[590000.0] = 1.078313645406083 + d[595000.0] = 1.0791282287017399 + d[600000.0] = 1.0799359940959505 + d[605000.0] = 1.080737054770893 + d[610000.0] = 1.081531521113572 + d[615000.0] = 1.0823195008071078 + d[620000.0] = 1.0831010989183296 + d[625000.0] = 1.0838764179818494 + d[630000.0] = 1.084645558080786 + d[635000.0] = 1.0854086169242974 + d[640000.0] = 1.0861656899220713 + d[645000.0] = 1.0869168702559202 + d[650000.0] = 1.0876622489486059 + d[655000.0] = 1.088401914930032 + d[660000.0] = 1.0891359551009152 + d[665000.0] = 1.0898644543940563 + d[670000.0] = 1.0905874958333133 + d[675000.0] = 1.091305160590385 + d[680000.0] = 1.0920175280394953 + d[685000.0] = 1.0927246758100766 + d[690000.0] = 1.0934266798375365 + d[695000.0] = 1.0941236144121913 + d[700000.0] = 1.0948155522264447 + d[705000.0] = 1.0955025644202876 + d[710000.0] = 1.0961847206251911 + d[715000.0] = 1.0968620890064578 + d[720000.0] = 1.0975347363040961 + d[725000.0] = 1.0982027278722837 + d[730000.0] = 1.0988661277174703 + d[735000.0] = 1.0995249985351825 + d[740000.0] = 1.1001794017455795 + d[745000.0] = 1.1008293975278134 + d[750000.0] = 1.1014750448532373 + d[755000.0] = 1.1021164015175118 + d[760000.0] = 1.1027535241716508 + d[765000.0] = 1.103386468352052 + d[770000.0] = 1.1040152885095431 + d[775000.0] = 1.104640038037495 + d[780000.0] = 1.1052607692990253 + d[785000.0] = 1.1058775336533353 + d[790000.0] = 1.1064903814812106 + d[795000.0] = 1.1070993622097158 + d[800000.0] = 1.1077045243361172 + d[805000.0] = 1.1083059154510573 + d[810000.0] = 1.1089035822610134 + d[815000.0] = 1.109497570610066 + d[820000.0] = 1.1100879255009994 + d[825000.0] = 1.110674691115762 + d[830000.0] = 1.1112579108353073 + d[835000.0] = 1.1118376272588413 + d[840000.0] = 1.112413882222492 + d[845000.0] = 1.1129867168174281 + d[850000.0] = 1.1135561714074407 + d[855000.0] = 1.11412228564601 + d[860000.0] = 1.1146850984928762 + d[865000.0] = 1.115244648230126 + d[870000.0] = 1.1158009724778202 + d[875000.0] = 1.1163541082091695 + d[880000.0] = 1.1169040917652808 + d[885000.0] = 1.1174509588694832 + d[890000.0] = 1.1179947446412524 + d[895000.0] = 1.1185354836097439 + d[900000.0] = 1.1190732097269493 + d[905000.0] = 1.1196079563804897 + d[910000.0] = 1.1201397564060525 + d[915000.0] = 1.1206686420994931 + d[920000.0] = 1.1211946452286021 + d[925000.0] = 1.121717797044555 + d[930000.0] = 1.1222381282930558 + d[935000.0] = 1.122755669225177 + d[940000.0] = 1.123270449607914 + d[945000.0] = 1.12378249873446 + d[950000.0] = 1.1242918454342055 + d[955000.0] = 1.1247985180824809 + d[960000.0] = 1.1253025446100402 + d[965000.0] = 1.1258039525123007 + d[970000.0] = 1.1263027688583431 + d[975000.0] = 1.1267990202996814 + d[980000.0] = 1.1272927330788054 + d[985000.0] = 1.1277839330375097 + d[990000.0] = 1.1282726456250098 + d[995000.0] = 1.1287588959058528 + d[1000000.0] = 1.1292427085676322 + d[0.0] = 0.1111111111111111 + d[50000.0] = 0.8399310168878039 + d[100000.0] = 0.9069275914814589 + d[150000.0] = 0.946093092891858 + d[200000.0] = 0.9738744216319898 + d[250000.0] = 0.9954203213361739 + d[300000.0] = 1.0130230681319403 + d[350000.0] = 1.0279050823267777 + d[400000.0] = 1.0407959006295044 + d[450000.0] = 1.0521660246051854 + d[500000.0] = 1.0623366761069832 + d[550000.0] = 1.0715369509920454 + d[600000.0] = 1.0799359940959505 + d[650000.0] = 1.0876622489486059 + d[700000.0] = 1.0948155522264447 + d[750000.0] = 1.1014750448532373 + d[800000.0] = 1.1077045243361172 + d[850000.0] = 1.1135561714074407 + d[900000.0] = 1.1190732097269493 + d[950000.0] = 1.1242918454342055 + d[1000000.0] = 1.1292427085676322 + d[1050000.0] = 1.1339519424005882 + d[1100000.0] = 1.1384420391056893 + d[1150000.0] = 1.1427324894904565 + d[1200000.0] = 1.1468402943377674 + d[1250000.0] = 1.1507803712846143 + d[1300000.0] = 1.1545658818456337 + d[1350000.0] = 1.1582084966803439 + d[1400000.0] = 1.1617186125909829 + d[1450000.0] = 1.16510553142189 + d[1500000.0] = 1.168377608615648 + d[1550000.0] = 1.1715423773997347 + d[1600000.0] = 1.1746066532488404 + d[1650000.0] = 1.1775766222667323 + d[1700000.0] = 1.1804579163695803 + d[1750000.0] = 1.1832556775675207 + d[1800000.0] = 1.1859746131880575 + d[1850000.0] = 1.1886190435311168 + d[1900000.0] = 1.1911929431672972 + d[1950000.0] = 1.1936999768704795 + d[2000000.0] = 1.1961435310001933 + d[2050000.0] = 1.1985267410081526 + d[2100000.0] = 1.2008525156295526 + d[2150000.0] = 1.20312355822735 + d[2200000.0] = 1.2053423856823657 + d[2250000.0] = 1.2075113451602348 + d[2300000.0] = 1.2096326290352746 + d[2350000.0] = 1.2117082882091679 + d[2400000.0] = 1.2137402440272895 + d[2450000.0] = 1.2157302989662142 + d[2500000.0] = 1.2176801462413982 + d[2550000.0] = 1.21959137846337 + d[2600000.0] = 1.221465495453311 + d[2650000.0] = 1.2233039113141229 + d[2700000.0] = 1.2251079608404998 + d[2750000.0] = 1.226878905340794 + d[2800000.0] = 1.2286179379342776 + d[2850000.0] = 1.230326188379528 + d[2900000.0] = 1.2320047274828694 + d[2950000.0] = 1.2336545711299531 + d[3000000.0] = 1.235276683978489 + d[3050000.0] = 1.236871982845736 + d[3100000.0] = 1.2384413398205405 + d[3150000.0] = 1.2399855851263697 + d[3200000.0] = 1.241505509758872 + d[3250000.0] = 1.2430018679189436 + d[3300000.0] = 1.2444753792600354 + d[3350000.0] = 1.2459267309664643 + d[3400000.0] = 1.247356579677754 + d[3450000.0] = 1.2487655532724913 + d[3500000.0] = 1.2501542525238314 + d[3550000.0] = 1.251523252637574 + d[3600000.0] = 1.2528731046826682 + d[3650000.0] = 1.2542043369230507 + d[3700000.0] = 1.2555174560588676 + d[3750000.0] = 1.2568129483843864 + d[3800000.0] = 1.2580912808692146 + d[3850000.0] = 1.259352902168841 + d[3900000.0] = 1.260598243569975 + d[3950000.0] = 1.2618277198756656 + d[4000000.0] = 1.263041730234747 + d[4050000.0] = 1.264240658919759 + d[4100000.0] = 1.2654248760571405 + d[4150000.0] = 1.2665947383131597 + d[4200000.0] = 1.2677505895387702 + d[4250000.0] = 1.2688927613763048 + d[4300000.0] = 1.2700215738306873 + d[4350000.0] = 1.271137335807622 + d[4400000.0] = 1.2722403456210274 + d[4450000.0] = 1.2733308914718 + d[4500000.0] = 1.274409251899827 + d[4550000.0] = 1.2754756962110243 + d[4600000.0] = 1.2765304848810386 + d[4650000.0] = 1.2775738699371244 + d[4700000.0] = 1.278606095319598 + d[4750000.0] = 1.279627397224167 + d[4800000.0] = 1.280638004426333 + d[4850000.0] = 1.2816381385889881 + d[4900000.0] = 1.2826280145542308 + d[4950000.0] = 1.2836078406203735 + d[5000000.0] = 1.2845778188050245 + d[5050000.0] = 1.2855381450950834 + d[5100000.0] = 1.286489009684419 + d[5150000.0] = 1.2874305971999525 + d[5200000.0] = 1.2883630869168181 + d[5250000.0] = 1.2892866529632292 + d[5300000.0] = 1.2902014645156334 + d[5350000.0] = 1.2911076859847046 + d[5400000.0] = 1.2920054771926845 + d[5450000.0] = 1.2928949935425509 + d[5500000.0] = 1.2937763861794618 + d[5550000.0] = 1.294649802144891 + d[5600000.0] = 1.2955153845238554 + d[5650000.0] = 1.2963732725855956 + d[5700000.0] = 1.2972236019180587 + d[5750000.0] = 1.2980665045565116 + d[5800000.0] = 1.2989021091065807 + d[5850000.0] = 1.2997305408620157 + d[5900000.0] = 1.3005519219174393 + d[5950000.0] = 1.30136637127634 + d[6000000.0] = 1.3021740049545454 + d[6050000.0] = 1.302974936079403 + d[6100000.0] = 1.3037692749848793 + d[6150000.0] = 1.304557129302774 + d[6200000.0] = 1.3053386040502464 + d[6250000.0] = 1.3061138017138214 + d[6300000.0] = 1.306882822330053 + d[6350000.0] = 1.3076457635629948 + d[6400000.0] = 1.3084027207786353 + d[6450000.0] = 1.3091537871164383 + d[6500000.0] = 1.3098990535581145 + d[6550000.0] = 1.3106386089937663 + d[6600000.0] = 1.311372540285511 + d[6650000.0] = 1.3121009323287065 + d[6700000.0] = 1.312823868110883 + d[6750000.0] = 1.3135414287684821 + d[6800000.0] = 1.314253693641506 + d[6850000.0] = 1.3149607403261596 + d[6900000.0] = 1.3156626447255846 + d[6950000.0] = 1.3163594810987544 + d[7000000.0] = 1.3170513221076243 + d[7050000.0] = 1.3177382388625973 + d[7100000.0] = 1.3184203009663868 + d[7150000.0] = 1.3190975765563393 + d[7200000.0] = 1.3197701323452822 + d[7250000.0] = 1.320438033660958 + d[7300000.0] = 1.3211013444841038 + d[7350000.0] = 1.321760127485231 + d[7400000.0] = 1.3224144440601582 + d[7450000.0] = 1.3230643543643466 + d[7500000.0] = 1.3237099173460887 + d[7550000.0] = 1.3243511907785943 + d[7600000.0] = 1.3249882312910146 + d[7650000.0] = 1.3256210943984539 + d[7700000.0] = 1.326249834530999 + d[7750000.0] = 1.3268745050618123 + d[7800000.0] = 1.3274951583343195 + d[7850000.0] = 1.3281118456885312 + d[7900000.0] = 1.3287246174865253 + d[7950000.0] = 1.3293335231371288 + d[8000000.0] = 1.329938611119824 + d[8050000.0] = 1.33053992900791 + d[8100000.0] = 1.3311375234909486 + d[8150000.0] = 1.3317314403965177 + d[8200000.0] = 1.3323217247113002 + d[8250000.0] = 1.3329084206015323 + d[8300000.0] = 1.333491571432833 + d[8350000.0] = 1.3340712197894398 + d[8400000.0] = 1.3346474074928676 + d[8450000.0] = 1.3352201756200164 + d[8500000.0] = 1.3357895645207432 + d[8550000.0] = 1.3363556138349204 + d[8600000.0] = 1.3369183625089938 + d[8650000.0] = 1.3374778488120642 + d[8700000.0] = 1.3380341103515023 + d[8750000.0] = 1.3385871840881194 + d[8800000.0] = 1.3391371063509028 + d[8850000.0] = 1.3396839128513356 + d[8900000.0] = 1.3402276386973129 + d[8950000.0] = 1.3407683184066674 + d[9000000.0] = 1.3413059859203191 + d[9050000.0] = 1.3418406746150606 + d[9100000.0] = 1.3423724173159894 + d[9150000.0] = 1.3429012463086007 + d[9200000.0] = 1.3434271933505495 + d[9250000.0] = 1.3439502896830953 + d[9300000.0] = 1.3444705660422374 + d[9350000.0] = 1.3449880526695506 + d[9400000.0] = 1.3455027793227357 + d[9450000.0] = 1.3460147752858853 + d[9500000.0] = 1.3465240693794818 + d[9550000.0] = 1.3470306899701328 + d[9600000.0] = 1.347534664980051 + d[9650000.0] = 1.348036021896289 + d[9700000.0] = 1.3485347877797347 + d[9750000.0] = 1.3490309892738759 + d[9800000.0] = 1.3495246526133409 + d[9850000.0] = 1.3500158036322218 + d[9900000.0] = 1.3505044677721858 + d[9950000.0] = 1.350990670090384 + d[10000000.0] = 1.3514744352671608 + d[30000000000.0] = 2.12416911232663 + d[20000000.0] = 1.4183705218613656 + d[30000000.0] = 1.4575020903223461 + d[40000000.0] = 1.4852663428490493 + d[50000000.0] = 1.5068019546183335 + d[60000000.0] = 1.5243978226322783 + d[70000000.0] = 1.5392749123994307 + d[80000000.0] = 1.5521620307847297 + d[90000000.0] = 1.563529272819441 + d[100000000.0] = 1.5736976159159275 + d[200000000.0] = 1.6405932238998318 + d[300000000.0] = 1.6797246326066593 + d[400000000.0] = 1.707488805202229 + d[500000000.0] = 1.729024368992151 + d[600000000.0] = 1.7466202050100108 + d[700000000.0] = 1.7614972719174529 + d[800000000.0] = 1.7743843731547622 + d[900000000.0] = 1.785751601850096 + d[1000000000.0] = 1.795919934273698 + d[2000000000.0] = 1.8628154942118993 + d[3000000000.0] = 1.9019468868955325 + d[4000000000.0] = 1.9297110514775262 + d[5000000000.0] = 1.951246610458546 + d[6000000000.0] = 1.9688424432701106 + d[7000000000.0] = 1.983719507887146 + d[8000000000.0] = 1.996606607406533 + d[9000000000.0] = 2.0079738347656297 + d[10000000000.0] = 2.018142166120191 + d[20000000000.0] = 2.085037721247064 + d[40000000000.0] = 2.1519332761065177 + d[50000000000.0] = 2.173468834606246 + d[60000000000.0] = 2.1910646670969367 + d[70000000000.0] = 2.2059417314847694 + d[80000000000.0] = 2.2188288308322495 + d[90000000000.0] = 2.2301960580576385 + + + + + return d diff --git a/cytopy/flow/plotting/logicle_transform.py b/cytopy/flow/plotting/logicle_transform.py index 0c4b1f89..dafe1d10 100644 --- a/cytopy/flow/plotting/logicle_transform.py +++ b/cytopy/flow/plotting/logicle_transform.py @@ -31,6 +31,10 @@ from matplotlib import scale as mscale import pandas as pd import numpy as np +from .logicle_cache import logicle_cache + +from ipdb import set_trace as bp +import time __author__ = "Ross Burton" @@ -43,8 +47,11 @@ __status__ = "Production" + + class LogicleScale(mscale.ScaleBase): name = "logicle" + dict_cache = logicle_cache() def __init__(self, axis, w: float = 0.5, m: float = 4.5, a: float = 0.0, t: int = 262144): super().__init__(axis=axis) @@ -64,15 +71,41 @@ class LogicleTransform(mtransforms.Transform): output_dims = 1 is_separable = True has_inverse = True + #t = 0 def __init__(self, scaler: LogicleTransformer): mtransforms.Transform.__init__(self) self._scaler = scaler def transform_non_affine(self, data): - data = pd.DataFrame(data, columns=["x"]) - data = self._scaler.scale(data=data, features=["x"]) - return data.values + # data2 = pd.DataFrame(data.copy(), columns=["x"]) + # data2 = self._scaler.scale(data=data2, features=["x"]) + # return data.values + + # t0 = time.time() + if data.ndim==1: fx = np.array([LogicleScale.dict_cache.get(x, np.nan) for x in data]) + else: fx = np.array([LogicleScale.dict_cache.get(x, np.nan) for x in data[:,0]]) + if np.all(~np.isnan(fx)): + fx = fx.reshape((len(fx), 1)) + else: + data = pd.DataFrame(data, columns=['x']) + data['y'] = fx + no_y = data['y'].isnull() + data_no_y = data.loc[no_y, ['x']].copy() + data_no_y = self._scaler.scale(data=data_no_y, features=['x']) + data.loc[no_y, 'y'] = data_no_y['x'] + #for r in data.loc[no_y].drop_duplicates().itertuples(): print('d[%s] = %s'%(r.x, r.y)) + for r in data.loc[no_y].itertuples(): LogicleScale.dict_cache[r.x] = r.y + fx = data[['y']].values + + # t1 = time.time() + # LogicleScale.LogicleTransform.t += (t1-t0) + # print(LogicleScale.LogicleTransform.t) + # assert np.allclose(data2[['x']].values, fx) + + return fx + + def inverted(self): return LogicleScale.InvertedLogicalTransform(scaler=self._scaler) diff --git a/cytopy/flow/transform.py b/cytopy/flow/transform.py index e16c5fde..9e424501 100644 --- a/cytopy/flow/transform.py +++ b/cytopy/flow/transform.py @@ -363,7 +363,7 @@ def inverse_scale(self, ------- Pandas.DataFrame """ - if data.shape[0] == 1 and data[features].iloc[0] == 0: + if data.shape[0] == 1 and np.all(data[features].iloc[0] == 0): return data data = remove_negative_values(data, features) data[features] = self.inverse(data[features].values) @@ -688,9 +688,10 @@ def remove_negative_values(data: pd.DataFrame, f">=0, all values <=0 will be forced to the minimum valid values in {f}") valid_range = data[data[f] > 0][f].values if len(valid_range) == 0: - raise TransformError(f"All values for {f} <= 0") - min_ = np.min(valid_range) - data[f] = np.where(data[f].values <= 0, min_, data[f].values) + data[f] = 1e-6 + else: + min_ = np.min(valid_range) + data[f] = np.where(data[f].values <= 0, min_, data[f].values) return data