From 210fae56b7f07cf00c8be79b63113110049f743b Mon Sep 17 00:00:00 2001 From: toni Date: Wed, 10 May 2017 23:33:01 +0200 Subject: [PATCH] tex v2 - without experiments --- code/filter/Logic.h | 4 + tex/bare_conf.tex | 2 + tex/chapters/abstract.tex | 4 +- tex/chapters/conclusion.tex | 27 +- tex/chapters/experiments.tex | 132 +- tex/chapters/introduction.tex | 45 +- tex/chapters/method.tex | 78 +- tex/chapters/relatedwork.tex | 34 +- tex/chapters/system.tex | 242 +- tex/egbib.bib | 37 +- tex/gfx/eval/paths.eps | 15091 ++++++++++---------------------- 11 files changed, 4856 insertions(+), 10840 deletions(-) diff --git a/code/filter/Logic.h b/code/filter/Logic.h index cceb9fc..4308086 100644 --- a/code/filter/Logic.h +++ b/code/filter/Logic.h @@ -153,6 +153,10 @@ struct PFTransSimple : public K::ParticleFilterTransition{ for (int i = 0; i < Settings::numParticles; ++i) { K::Particle& p = particles[i]; + // update the baromter + float deltaZ_cm = p.state.positionOld.inMeter().z - p.state.position.inMeter().z; + p.state.relativePressure += deltaZ_cm * 0.105f; + double diffHeight = p.state.position.inMeter().z + height_m.draw(); double newHeight_cm = p.state.position.z_cm; if(diffHeight > 9.1){ diff --git a/tex/bare_conf.tex b/tex/bare_conf.tex index c1afec7..9307c6d 100644 --- a/tex/bare_conf.tex +++ b/tex/bare_conf.tex @@ -201,6 +201,8 @@ \input{chapters/system} +\input{chapters/kld} + \input{chapters/method} \input{chapters/experiments} diff --git a/tex/chapters/abstract.tex b/tex/chapters/abstract.tex index 98f1db5..d562a9b 100644 --- a/tex/chapters/abstract.tex +++ b/tex/chapters/abstract.tex @@ -6,9 +6,9 @@ The sample impoverishment problem can therefore be described as a too small part Restrictive transition models, as they are used in indoor localisation, also enhance this effect significantly. However, an accurate position estimation requires a certain degree of focus and thus behaves contrary to the need of diversity. -The proposed method is able to deal with the trade-off between the need of diversity and focus by deploying an interacting multiple model particle filter (IMMPF) for jump Markov non-linear systems. +Therefore we propose a new method that is able to deal with the trade-off between the need of diversity and focus by deploying an interacting multiple model particle filter (IMMPF) for jump Markov non-linear systems. We combine two similar particle filters using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence and a Wi-Fi quality factor. The main benefit of this -approach is the easy adaptation to other localization approaches based on particle filters. +approach is an easy adaptation to other localisation approaches based on particle filters. %One with a very restrictive transition scheme, providing very accurate results. The other with more flexible and simple dynamics, resulting in a higher sample diversity. diff --git a/tex/chapters/conclusion.tex b/tex/chapters/conclusion.tex index be78a46..61c509c 100644 --- a/tex/chapters/conclusion.tex +++ b/tex/chapters/conclusion.tex @@ -1,20 +1,13 @@ \section{Conclusion} +In this work we presented an approach for mixing two different localisation schemes using an IMMPF and a non-trivial Markov switching process, which is easy to adapt to many existing systems. +By mixing two particle sets based upon the Kullback-Leibler divergence and a Wi-Fi quality factor, we were able to satisfy the need of diversity and focus to recover from sample impoverishment in context of indoor localisation. +It was shown, that the here presented approach is able to improve the robustness, while keeping the error low. +However, in some rare situations given bad Wi-Fi readings we were not able to increase the results as usual. +This requires further investigations regarding the Wi-Fi quality factor. -In this work we presented .. which is easy to adapt to many existing localisation systems. -combining different filter shemes using an IMMPF - -enables us to combine beliebie transition models. - -Looking at the results / experiments -we were able to satisfy the need of diversity and focues to reduce the recover from sample impoverishment in context of indoor localization. - - -The benefits of our approach demonstrated - -This further - -future work completely different localisation approaches, not only transitions. -more then 2 filters -a more advanced wi-fi quality factor -incorporating a smoothing filter as mode, so we are able to draw new particles from a smoothed particle set. .. +Finally, the possibility of combining different localisation models enables many new approaches and techniques. +By incorporating completely different modes, not only transitions, the robustness and accuracy can be further increased. +This would additionally allow an on-the-fly switching between sensor models, e.g. different signal strength methods. +Such a modular solution could be able to fit any environment and thus form a highly flexible and adjustable localisation system. +However, adjusting the Markov switching process to any number of modes is no easy task and therefore requires intensive future work. diff --git a/tex/chapters/experiments.tex b/tex/chapters/experiments.tex index 40e7afe..7a2ffea 100644 --- a/tex/chapters/experiments.tex +++ b/tex/chapters/experiments.tex @@ -5,51 +5,41 @@ \begin{figure} \centering \input{gfx/eval/paths.tex} - \caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy } + \caption{The three paths that were part of the experiments. Starting positions are marked with black circles. The red squares illustrate the \docWIFI{} quality in this sector. The intensity of red indicates a low coverage and thus a bad quality for localisation.} \label{fig:paths} \end{figure} % +%Gebäude All upcoming experiments were carried out on four floors (0 to 3) of a \SI{77}{m} x \SI{55}{m} sized faculty building. It includes several staircases and elevators and has a ceiling height of about \SI{3}{m}. -Nevertheless, the grid was generated for the complete campus and thus outdoor areas like the courtyard are also walkable. -As Wi-Fi is attenuated by obstacles and walls, it does not provide a consistent quality over the complete building. -In fig. \ref{fig:paths} we illustrate the quality obtained by the wall attenuation factor model presented earlier. -Here, the intensity of red indicates a low coverage and thus a bad quality for localisation. -To obtain this information we interpolated the Wi-Fi quality factor given by all test walks using $l_{\text{max}} = \SI{-75}{\dBm}$ and $l_{\text{min}} = \SI{-90}{\dBm}$. -As mentioned before, we omit any time-consuming calibration processes and use the same values for all access-points. That would be $P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}, \mWAF_{\text{wifi}} = \SI{8}{\dB}$. -The position of the access-points (about five per floor) is known beforehand. -Due to legal terms, we are not allowed to depict their positions and therefore omit this information within the figures. +The gridded graph was generated for the complete campus and thus outdoor areas like the courtyard are also walkable. +As \docWIFI{} is attenuated by obstacles and walls, it does not provide a consistent quality over the complete building. +To get an idea about the \docWIFI{} quality, we interpolated the \docWIFI{} quality factor $q(\mObsVec_t^{\mRssiVec_\text{wifi}})$, with $l_{\text{max}} = \SI{-75}{\dBm}$ and $l_{\text{min}} = \SI{-90}{\dBm}$, between some measurements using a nearest-neighbour procedure. +In fig. \ref{fig:paths} the resulting colourized floorplan is illustrated. +Here, the intensity of red indicates a low signal strength and thus a bad quality for localising a pedestrian within this area using \docWIFI{}. -% gewählte parameter (auch mal die optimieren wifi parameter testen) +%Pfade We arranged three distinct walks (see also fig. \ref{fig:paths}). The measurements for the walks were recorded using a Motorola Nexus 6 at 2.4 GHz band only. The computation was done offline as described in algorithm \ref{fig:paths}. -For each walk we deployed $50$ MC runs using 5000 Particles for each mode. -Instead of an initial position and heading, all walks start with a uniform distribution (random position and heading) as prior. -For the filtering we used $\sigma_\text{wifi} = 8.0$ as uncertainties, both growing with each measurement's age. -While the pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters are determined automatically. -The step size $\mStepSize$ for the transition was configured to be \SI{70}{\centimeter} with an allowed derivation of \SI{10}{\percent}. -The heading deviation was set to \SI{25}{\degree}. -The pedestrian's position (state) was estimated using the weighted arithmetic mean of -the particle set. +For each walk we deployed $50$ runs using 5000 particles for each mode. +Instead of an initial position and heading, all walks start with a uniform distribution (random position and heading) as prior $q_1$. +In the graph-based transition of the dominant filter, the to-be-walked distance is given by the number of steps using a step size of \SI{70}{\centimeter} with an allowed deviation of \SI{10}{\percent}. +The deviation for the walking direction was set to \SI{25}{\degree}. +Since the simple transition randomly scatters particles within a specific range, we choose a covariance matrix that allows a variance of \SI{200}{\centimeter} in $x$- and $y$-direction for the multivariate normal distribution. +Here, floors were changed by deploying a discrete distribution for every floor level, providing a chance of \SI{27}{\percent} for changing one floor and \SI{5}{\percent} for two floors in a particular $z$-direction. -% wie für die kld gezogen? begründen warum wir nun keine parzenschätzung machen (weil ähnliche ergebnisse) -To calculate \eqref{equ:KLD} and thus the Kullback-Leibler divergence, we need to sample densities from both modes likewise. -The grid is suitable for this purpose. -However, sampling at any vertex $\mVertexA$ of the grid, given just a set of random variables (particles), is not the easiest task. -We need to estimate the posterior distribution given by the respective particle sets. -A common way is to deploy a kernel density estimation using a Gaussian distribution as kernel. -The density of a specific point $\hat\mStateVec_{t} = \fPos{\mVertexA}$ is then given by - % - \begin{equation} - p(\hat\mStateVec_{t} \mid m_t, \mObsVec_{1:t}) = \sum_{i=1}^{N_{m_t}} \mathcal{N}(d^i_{\text{KL}} \mid 0, \sigma_{\text{KL}}) - \enspace , - \end{equation} - % -while $d^i_{\text{KL}}$ is the euclidean distance between the considered point's $\hat\mStateVec_{t}$ and all particles $\fPos{\vec{X}_t^{i,m_t}}$ of the mode. The variance $\sigma_{\text{KL}}$ is set to \SI{1}{m}. -It is well known, that the computation of the kernel density estimation is rather slow, thus we also used a much simpler estimation by assuming a multivariate Gaussian distribution for both modes. -Here, the mean is given by weighted arithmetic mean of the particles and the variance is defined by the sample covariance matrix. -Calculating a meaningful $D_{\text{KL}}$, both estimation methods performed almost identical and therefore we used the multivariate Gaussian distribution for both modes with $\lambda = 0.03$ for the upcoming experimental discussion. +We omit any time-consuming calibration processes and therefore use the same parameters for all \docWIFI{} access-points, similar to \cite{Ebner-15}. +The position of the access-points (about five per floor) is known beforehand. +Due to legal terms, we are not allowed to depict their positions and therefore omit this information within the figures. +To model the uncertainty of the \docWIFI{}, a white Gaussian noise with $\sigma_\text{wifi} = \SI{8}{\dBm}$, growing with each measurement's age, was chosen. +The pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters are determined automatically as described in \cite{Fetzer2016OMC}. + + +As expected before, the kernel density estimation in \eqref{eq:KDE} and the much simpler multivariate normal distribution estimation are both producing similar results in context of the divergence measure given in \eqref{equ:KLD}. +For this reason and because of the faster processing time, especially in context of calculating on a smartphone, we estimated the posteriors of the modes by approximating a multivariate normal distribution (cf. section \ref{sec:divergence}). +For calculating \eqref{equ:KLD} we set $\lambda = 0.03$ based on best practices. +Finally, the pedestrian's most likely position (state) was then estimated using the weighted arithmetic mean of the particle set. % ground truth The ground truth is measured by recording a timestamp at marked spots on the walking route. When passing a marker, the pedestrian clicked a button on the smartphone application. @@ -65,24 +55,24 @@ The approximation error is then calculated by comparing the interpolated ground \centering \input{gfx/eval/path3.tex} \input{gfx/eval/path3-kld.tex} - \caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy } + \caption{Exemplary results on path 3 for the common particle filter using the graph-based (red) or simple transition model (blue) and our IMMPF approach (green). The Kullback-Leibler divergence $D_{\text{KL}}$ between the standalone filters (purple) proves itself as a good indicator, if one filter gets stuck or loses track.} \label{fig:path3} \end{figure} % - At first, we discuss the results of path 3, starting at the left-hand side of the building. Exemplary estimation results, using the modes standalone and combined within the IMMPF, can be seen in fig. \ref{fig:path3}. As mentioned above, every run of a walk starts with a uniform distribution as prior. Due to a low Wi-Fi coverage at the starting point, the pedestrian's position is falsely estimated into a room instead of the corridor. All three filters are able to overcome this false detection. However, the common particle filter (red) gets then indissoluble captured within a room, because of its restrictive behaviour and the aftereffects of the initial Wi-Fi readings. -It provides an \SI{75}{\percent}-quantil of $\tilde{x}_{0.75} = \SI{3884}{\centimeter}$ and got captured in \SI{100}{\percent} of all runs. -As expected and discussed earlier, the simple transition (blue) is less prone to bad observations and provides not so accurate, but very robust results of $\tilde{x}_{0.75}= \SI{809}{\centimeter}$ and a standard deviation over all results of $\bar{\sigma} = \SI{529}{\centimeter}$. +It provides an \SI{75}{\percent}-quantil of $\tilde{x}_{75} = \SI{3884}{\centimeter}$ and got captured in \SI{100}{\percent} of all runs. +As expected and discussed earlier, the simple transition (blue) is less prone to bad observations and provides not so accurate, but very robust results of $\tilde{x}_{75}= \SI{809}{\centimeter}$ and a standard deviation over all results of $\bar{\sigma} = \SI{529}{\centimeter}$. Looking at $D_{\text{KL}}$ over time confirms our assumption made in section \ref{sec:immpf}. -It is clearly visible, that the Kullback-Leibler divergence between both modes (purple) is a very good indicator to observe, if the dominant filter gets stuck or loses track. +The graph-based filter (red) gets stuck and is not able to recover, starting on from this point, the Kullback-Leibler divergence $D_{\text{KL}}$ (purple) further increases due to the growing distance between both filters (blue and red). +It is clearly visible, that this divergence between both filters is a very good indicator to observe, if a filter gets stuck or loses track. Following, the IMMPF (green) results in a very natural and straight path estimation and a low $D_{\text{KL}}$ between modes and no sticking. The benefits of mixing both filtering schemes within the scenario of path 3 are thus obvious. -The IMMPF filters with an error of $\tilde{x}_{0.75} = \SI{667}{\centimeter}$ and $\bar{\sigma} = \SI{558}{\centimeter}$. +The IMMPF filters with an error of $\tilde{x}_{75} = \SI{667}{\centimeter}$ and $\bar{\sigma} = \SI{558}{\centimeter}$. % zeigen das schlechtes wi-fi (zu hohe diversity) behoben wird. % bild: lauf auf der rechten seite des gebäudes zeige mit und ohne wifi faktor (schlechtes wifi einzeichnen) @@ -90,7 +80,7 @@ The IMMPF filters with an error of $\tilde{x}_{0.75} = \SI{667}{\centimeter}$ an \centering \input{gfx/eval/path2.tex} \input{gfx/eval/path2-wifi-quality.tex} - \caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy } + \caption{Comparison of the estimation results on path 2 with (green) and without (red) the Wi-Fi quality factor in the Markov transition matrix. The low Wi-Fi quality and thus high errors between the \SI{80}{th} and \SI{130}{th} second are caused by the high attenuation and low signal coverage inside the zig-zag stairwell on the building's backside.} \label{fig:path2} \end{figure} % @@ -99,11 +89,11 @@ Here, the overall Wi-Fi quality is rather low, especially in the zig-zag stairwe Path 2 starts in the second floor, walking town the centred stairs into the first floor, then making a right turn and walking the stairs down to zero floor, from there we walk back to second floor using the zig-zag stairwell and after finally crossing a room we are back at the start. This is a very challenging scenario, at first the estimation got stuck on the first floor in a room's corner and after that the Wi-Fi is highly attenuated. Looking at fig. \ref{fig:path2}, one can observe the impact of the Wi-Fi quality factor within the Markov transition matrix. -Without it, the position estimation (red) is drifting in the courtyard, missing the stairwell and producing high errors between \SI{80}{th} and \SI{130}{th} second. +Without it, the position estimation (red) is drifting in the courtyard, missing the stairwell and producing high errors between the \SI{80}{th} and \SI{130}{th} second. As described before, the bad Wi-Fi readings are causing $D_{\text{KL}}$ to grow. It follows that the accurate dominant filter draws new particles from the uncertain support and therefore worsen the position estimation. In this scenario it is cold comfort that the system is able to recover thanks to its high diversity during situations with uncertain measurements. -Only by adding the Wi-Fi quality factor the system is able to improve the approximated path (green) and the overall estimation results from $\tilde{x}_{0.75} = \SI{1278}{\centimeter}$ with $\bar{\sigma} = \SI{948}{\centimeter}$ to $\tilde{x}_{0.75} = \SI{811}{\centimeter}$ with $\bar{\sigma} = \SI{340}{\centimeter}$. +Only by adding the Wi-Fi quality factor the system is able to improve the approximated path (green) and the overall estimation results from $\tilde{x}_{75} = \SI{1278}{\centimeter}$ with $\bar{\sigma} = \SI{948}{\centimeter}$ to $\tilde{x}_{75} = \SI{953}{\centimeter}$ with $\bar{\sigma} = \SI{543}{\centimeter}$. However, this is far from perfect and in some cases ($\sim \SI{9}{\percent}$) the quality factor was not able to prevent the estimation to drift in the courtyard. This solely happened when particles were sampled directly onto the courtyard while changing from first to zero floor. Those particles then received a high weight due to the attenuated measurements, causing a weight degeneracy. @@ -115,43 +105,49 @@ Adapting the bounds $l_{\text{max}}$ and $l_{\text{min}}$ of the quality factor \centering \input{gfx/eval/path1.tex} \input{gfx/eval/path1-time.tex} - \caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy } + \caption{Estimation results and error development while walking alongside path 1. In \SI{20}{\percent} of cases, the the graph-based particle filter failed to detect the first floor change. Therefore, a good (blue) and a bad (red) result are shown. The here presented approach (green) never lost track.} \label{fig:path1} \end{figure} % An exemplary result for path 1 is illustrated in fig. \ref{fig:path1}. The path starts on the first floor and finishes on the third after walking two straight stairs. -Using the grid-based particle filter for localisation, we were able to provide an very accurate path (blue) in \SI{80}{\percent} of the MC runs providing $\tilde{x}_{0.75} = \SI{526}{\centimeter}$ with $\bar{\sigma} = \SI{316}{\centimeter}$. +Using the graph-based particle filter for localisation, we were able to obtain a very accurate path (blue) in \SI{80}{\percent} of the runs providing $\tilde{x}_{75} = \SI{526}{\centimeter}$ with $\bar{\sigma} = \SI{316}{\centimeter}$. Due to a lack of particles near the stairs, the other \SI{20}{\percent} failed to detect the first floor change (red). Using our approach (green), we were able detect all floor changes and thus never lost track. -It performs with $\tilde{x}_{0.75} = \SI{544}{\centimeter}$ and $\bar{\sigma} = \SI{281}{\centimeter}$. +It performs with $\tilde{x}_{75} = \SI{544}{\centimeter}$ and $\bar{\sigma} = \SI{281}{\centimeter}$. Those very similar estimation results confirm the efficiency of the mixing and how it is able to keep the accuracy while providing a higher robustness against failures. +\todo{mehr die ergebnisse von bild 5 diskutieren. an manchen stellen verlieren wir genauigkeit, an anderen wird es besser.} % gegenüberstellung aller pfade und werte in tabelle - \definecolor{header}{rgb}{.8, .8, .8} - \begin{table} - \caption{Median error for all conducted walks.} - \label{tbl:err} - \centering - \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|} - \hline - & \multicolumn{3}{c}{Path 1} & \multicolumn{3}{|c|}{Path 2} & \multicolumn{3}{|c|}{Path 3}\\ - \hline - & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{0.75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{0.75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{0.75}$ \\ - \hline - PF_{\text{grid}}& $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ \\ - \hline - PF_{\text{simple}}& $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ \\ - \hline - IMMPF & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ \\ - \hline - \end{tabular} - \end{table} +% \begin{table} +% \caption{Resulting Errors for all conducted walks in meter.} +% \label{tbl:err} +% \centering +% \scalebox{0.93}{ +% \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|} +% \hline +% & \multicolumn{3}{c|}{Path 1} & \multicolumn{3}{c|}{Path 2} & \multicolumn{3}{c|}{Path 3}\\ +% \hline +% & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{75}$ \\ +% \hline +% $\text{PF}_{\text{graph}}$ & $4.0$ & $3.2$ & $5.3$ & $8.2$ & $4.0$ & $10.7$ & $30.3$ & $12.8$ & $38.8$ \\ +% \hline +% $\text{PF}_{\text{simple}}$ & $4.9$ & $2.8$ & $6.2$ & $7.3$ & $2.9$ & $9.4$ & $6.8$ & $5.4$ & $8.1$ \\ +% \hline +% IMMPF & $4.2$ & $2.8$ & $5.4$ & $7.7$ & $5.4$ & $9.5$ & $6.3$ & $5.6$ & $6.7$ \\ +% \hline +% \end{tabular} +% } +% \end{table} -An overview of all localisation results can be seen in table \ref{tbl:err}. -Again, it should be noted that the localisation system used for the experiments is very basic and can be seen as a slimmed version of our previous works \cite{}. +%An overview of all localisation results can be seen in table \ref{tbl:err}. +The here presented walks were selected because they fail in some way using a restrictive transition model and thus are well suited to represent the benefits and drawbacks of the IMMPF approach. +%So the results of table \ref{tbl:err} should not be seen as best case localization results, but more as proofing robustness while providing room for further improvements. +In this context, it should be noted that the localisation system used for the experiments is very basic and can be seen as a slimmed version of our previous works \cite{Fetzer2016OMC, Ebner-16}. Optimizing the Wi-Fi parameters and adding additional methods will improve the localisation results significantly. + +Especially, the graph-based transition model allows many optimizations and performance boosts. More importantly, the here presented approach was able to recover in all situations and thus never got completely stuck within a demarcated area. All results were similar or more accurate then the ones provided by the standalone filters, even when the localisation did not suffer from any problems. diff --git a/tex/chapters/introduction.tex b/tex/chapters/introduction.tex index 215af33..32dc9ab 100644 --- a/tex/chapters/introduction.tex +++ b/tex/chapters/introduction.tex @@ -1,30 +1,30 @@ \section{Introduction} Localising pedestrians inside buildings can be considered as a time-sequential, non-linear and non-Gaussian state estimation problem. -Such problems are often solved by using Bayesian filter, which update the state estimation recursively with every new incoming measurement. +Such problems are often solved by using Bayesian filters, which update the state estimation recursively with every new incoming measurement. A powerful method to obtain numerical results for this approach are particle filters. %einführen von partikel filter ganz allgemein -Especially in indoor localisation, particle filter can lately be considered as the standard method for solving complex non-linear problems \cite{Doucet11:ATO}. +Especially in indoor localisation, particle filters can lately be considered as the standard method for solving complex non-linear problems \cite{Doucet11:ATO}. By using a set of weighted random samples (particles), they approximate a probability distribution describing the pedestrian's possible whereabouts and therefore the uncertainty of the system. -In its most basic form, the particle filter operates three main steps: -At first, new particles are drawn according to some importance distribution, those particles are then weighted by an incremental importance weight distribution and finally a resampling step is deployed to prevent that only a small number of particles have a signifcant weight and all the other will have negligible small weights instead \cite{orhan2012particle}. +In its most basic form, the particle filter is based on three main steps: +At first, new particles are drawn according to some importance distribution, those particles are then weighted by an incremental importance weight distribution and finally a resampling step is deployed to prevent that only a small number of particles have a signifcant weight and all the other will have negligible small weights instead \cite{chen2003bayesian}. %transition und evaluation einführen -In practice the importance distribution is often represented by the state transition, modelling the dynamics of the system. +In practice, the importance distribution is often represented by the state transition, modelling the dynamics of the system. A new weight is then obtained by the state evaluation given different sensor measurements. -Most localisation approaches differ mainly in how the transition and evaluation steps are implemented and the available sensors are incorporated \cite{Nurminen13-PSI, Ebner2016OPN, Hilsenbeck2014}. -However, as \cite{Li2014} already mentioned, particle filter (and nearly all of its modifications) continue to suffer from two notorious problems: sample degeneracy and impoverishment. +Most localisation approaches differ mainly in how the transition and evaluation steps are implemented and the available sensors are incorporated \cite{Nurminen13-PSI, Ebner-16, Hilsenbeck2014}. +However, as \cite{Li2014} already mentioned, particle filters (and nearly all of its modifications) continue to suffer from two notorious problems: sample degeneracy and impoverishment. As one can imagine, after a few iterations with continuously reweighting particles, the weight will concentrate on a few particles only. This is why the resampling step was presented in the first place. -Here, a new set of equally weighted particles is drawn by multiplying high weighted particles while abandoning low weighted ones. -However, this leads to an decreasing diversity of particles after a resampling step, also known as sample impoverishment. +Here, a new set of equally weighted particles is drawn by duplicating highly weighted particles while abandoning low weighted ones. +However, this leads to a decreasing diversity of particles after a resampling step, also known as sample impoverishment. This high concentration of particles follows a bad approximation of the underlying probability distribution and therefore worse estimation results. -The effect of impoverishment is not solely caused by resampling only. +The effect of impoverishment is not solely caused by resampling. Restrictive transition models, as they are used in indoor localisation applications, also enhance this effect significantly. -An example is illustrated in fig. \ref{fig:multimodalPath}, where a graph-based structure prohibits walking through walls and considers the human movement speed. +An example is illustrated in fig. \ref{fig:multimodalPath}, where the state dynamics prohibit walking through walls and consider the human movement speed. % \begin{figure}[t] \centering @@ -35,23 +35,24 @@ An example is illustrated in fig. \ref{fig:multimodalPath}, where a graph-based \label{fig:multimodalPath} \end{figure} % -Due to uncertain measurements the posterior distribution of the particle filter is captured within a room. +Due to uncertain measurements, the posterior distribution of the particle filter is captured within a room. Between time $t-1$ and $t$, the resampling step abandons all particles on the corridor and drawing new particles outside the room is not possible due to the restricted transition. At this point, standard filtering methods are not able to recover. A simple solution would be drawing a handful new particles randomly in the building. -However, it is obvious that this leads to a higher uncertainty and possible a highly multimodal posterior distribution. -Additionally, very uncertain absolute measurements, like attenuated Wi-Fi signals, can cause unpredictable jumps to such a newly drawn position, which would otherwise be not possible. -Especially, methods using relative measurements like pedestrian dead reckoning approaches are losing their importance. +However, it is obvious that this leads to a higher uncertainty and possibly a multimodal posterior distribution. +Additionally, very uncertain absolute measurements, like attenuated Wi-Fi signals, can cause unpredictable jumps to such a newly drawn position, which would otherwise not be possible. +Especially, methods using relative measurements like pedestrian dead reckoning are losing their importance. As mentioned before, sample degeneracy and impoverishment are a pair of contradictions that can be described as a trade-off between the need of diversity and the need of focus \cite{Li2014}. -We tackle this problem in context of indoor localisation by deploying an interacting multiple model particle filter (IMMPF) for jump Markov non-linear systems \cite{Driessen2005}. -This enables a merging between posterior probability distributions approximated by particle filters, refereed as modes within this context. -We combine two similar particle filters using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between the modes and a Wi-Fi quality factor. -One with a very restrictive transition scheme, providing very accurate results. -The other with more flexible and simple dynamics, resulting in a higher sample diversity. -Both are then successfully combined, to satisfy the need of diversity and the need of focus. -The main benefit of this approach is that it can be easily adapted to other existing localization approaches based on particle filters. +We tackle this problem in the context of indoor localisation by deploying an interacting multiple model particle filter (IMMPF) for jump Markov non-linear systems \cite{Driessen2005}. +This enables merging of posterior probability distributions, approximated by particle filters. +Within this context a particle filter is also refereed to as a mode of the IMMPF. +We combine two modes using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between them and a Wi-Fi quality factor. +One mode with a very restrictive transition scheme, providing very accurate localisation results. +The other with more flexible, robust and simple transition, resulting in a higher sample diversity. +The modes are then successfully combined, to satisfy \textit{both}, the need of diversity and the need of focus. +This approaches main benefit is, that it can be easily adapted to other existing methods based on particle filters. diff --git a/tex/chapters/method.tex b/tex/chapters/method.tex index b6280ad..8431eb5 100644 --- a/tex/chapters/method.tex +++ b/tex/chapters/method.tex @@ -1,22 +1,17 @@ \section{IMMPF and Mixing} \label{sec:immpf} -In the previous section we have introduced a standard particle filter, an evaluation step and two different transition models. -Using this, we are able to implement two different localisation schemes. -One providing a high diversity with a robust, but uncertain position estimation. -The other keeps the localisation error low by using a very realistic propagation model, while being prone to sample impoverishment \cite{Ebner-15}. -In the following, we will combine those filters using the Interacting Multiple Model Particle Filter (IMMPF) and a non-trivial Markov switching process. - %Einführen des IMMPF Consider a jump Markov non-linear system that is represented by different particle filters as state space description, where the characteristics change in time according to a Markov chain. The posterior distribution is then described by % \begin{equation} - p(\mStateVec_{t}, m_t \mid \mObsVec_{1:t}) = P(m_k \mid \mObsVec_{1:t}) p(\mStateVec_{t} \mid m_t, \mObsVec_{1:t}) + p(\mStateVec_{t}, m_t \mid \mObsVec_{1:t}) = P(m_t \mid \mObsVec_{1:t}) p(\mStateVec_{t} \mid m_t, \mObsVec_{1:t}) \label{equ:immpfPosterior} \end{equation} % -where $m_t\in M\subset \mathbb{N}$ is the modal state of the system \cite{Driessen2005}. +where $m_t\in M\subset \mathbb{N}$ is the modal state of the system and thus describes the current mode (particle filter) \cite{Driessen2005}. +The notation $P(\cdot)$ provides a discrete probability distribution. Given \eqref{equ:immpfPosterior} and \eqref{equ:bayesInt}, the mode conditioned filtering stage can be written as % \begin{equation} @@ -31,7 +26,7 @@ Given \eqref{equ:immpfPosterior} and \eqref{equ:bayesInt}, the mode conditioned \label{equ:immpfFiltering} \end{equation} % -and the posterior mode probabilities are calculated by +and the posterior mode probabilities, providing how likely it is that a considered mode represents the system's state, are calculated by % \begin{equation} p(m_t \mid \mObsVec_{1:t}) \propto p(\mStateVec_{t} \mid m_t, \mObsVec_{1:t-1}) P(m_t \mid \mObsVec_{1:t-1}) @@ -40,7 +35,7 @@ and the posterior mode probabilities are calculated by \end{equation} % It should be noted that \eqref{equ:immpfFiltering} and \eqref{equ:immpModeProb} are not normalized and thus such a step is required. -To provide a solution for $P(m_t \mid \mObsVec_{1:t-1})$, the recursion for $m_t$ in \eqref{equ:immpfPosterior} is now derived by the mixing stage \cite{Driessen2005}. +To provide a solution for the probability distribution $P(m_t \mid \mObsVec_{1:t-1})$, the recursion for $m_t$ in \eqref{equ:immpfPosterior} is now derived by the so called mixing stage \cite{Driessen2005}. Here, we compute % \begin{equation} @@ -68,14 +63,26 @@ and \end{equation} % where \eqref{equ:immpModeMixing} is a weighted sum of distributions and the weights are provided through \eqref{equ:immpModeMixing2}. -The transition probability $P(m_{t+1} = k \mid m_t = l)$ is given by the Markov transition matrix $[\Pi_t]_{kl}$. -Sampling from \eqref{equ:immpModeMixing} is done by first drawing a modal state $m_t$ from $P(m_t \mid m_{t+1}, \mObsVec_{1:t})$ and then drawing a state $\mStateVec_{t}$ from $p(\mStateVec_{t} \mid m_t, \mObsVec_{1:t})$ in dependence to that $m_t$. +To find a solution for $P(m_t \mid \mObsVec_{1:t})$, an estimate of the posterior probability $p(m_t \mid \mObsVec_{1:t})$ in \eqref{equ:immpModeProb} can be calculated according to + % + \begin{equation} + P(m_t \mid \mObsVec_{1:t}) = \frac{\omega_t^{m_t} P(m_t \mid \mObsVec_{1:t-1})}{\sum_{m=1}^M \omega_t^{m_t} P(m_t \mid \mObsVec_{1:t-1})} + \enspace . + \label{equ:immpMode2} + \end{equation} + % +Here, $\omega_t^{m_t}$ is the unnormalized weight given by the state evaluation of the respective mode $m_t$. +The initial mode probabilities $P(m_1 \mid \mObsVec_{1})$ have to be defined beforehand. +The transition probability $P(m_{t+1} = k \mid m_t = l)$ in \eqref{equ:immpModeMixing3} is given by the Markov transition matrix $[\Pi_t]_{kl}$. +The matrix $\Pi_t$ is a real square matrix, with each row summing to 1. +It provides the probability of moving from $m_t$ to $m_{t+1}$ in one time step. +Sampling from \eqref{equ:immpModeMixing} is done by first drawing a modal state $m_t$ from $P(m_t \mid m_{t+1}, \mObsVec_{1:t})$ and then drawing a state $\mStateVec_{t}$ from $p(\mStateVec_{t} \mid m_t, \mObsVec_{1:t})$ in regard to that $m_t$. In context of particle filtering, this means that \eqref{equ:immpModeMixing} enables us to pick particles from all available modes in regard to the discrete distribution $P(m_t \mid m_{t+1}, \mObsVec_{1:t})$. Further, the number of particles in each mode can be selected independently of the actual mode probabilities. Algorithm \ref{alg:immpf} shows the complete IMMPF procedure in detail. As prior knowledge, $M$ initial probabilities $P(m_1 \mid \mObsVec_{1})$ and initial distributions $p(\mStateVec_{1} \mid m_1, \mObsVec_{1})$ providing a particle set $\{W^i_{1}, \vec{X}^i_{1} \}_{i=1}^N$ are available. -The mixing step requires that the independent running filtering process are all finished. +The mixing step requires that the independently running filtering processes are all finished. \begin{algorithm}[t] \caption{IMMPF Algorithm} @@ -106,31 +113,32 @@ The mixing step requires that the independent running filtering process are all %grundidee warum die matrix so gewählt wird. -With the above, we are finally able to combine the two filters described in section \ref{sec:rse}. -The basic idea of our approach is to utilize the restrictive filter as the dominant one, providing the state estimation for the localisation. -Due to its robustness and good diversity the other, more permissive one, is then used as support for possible sample impoverishment. -If we recognize that the dominant filter gets stuck or loses track, particles from the supporting filter will be picked with a higher probability while mixing the new particle set for the dominant filter. +With the above, we are finally able to combine the two filters described in section \ref{sec:rse} and realize the considerations made in section \ref{sec:divergence}. +Within the IMMPF we utilize the restrictive graph-based filter as the \textit{dominant} one, providing the state estimation for the localisation. +Due to its robustness and good diversity the simple, more permissive filter, is then used as \textit{support} for possible sample impoverishment. -%kld -This is achieved by measuring the Kullback-Leibler divergence $D_{\text{KL}}(P \|Q)$ between both filtering posterior distributions $p(\mStateVec_{t} \mid m_t, \mObsVec_{1:t})$. -The Kullback-Leibler divergence is a non-symmetric non-negative difference between two probability distributions $Q$ and $P$. -It is also stated as the amount of information lost when $Q$ is used to approximate $P$ \cite{Sun2013}. -We set $D_{\text{KL}} = D_{\text{KL}}(P \|Q)$, while $P$ is the dominant and $Q$ the supporting filter. -Since the supporting filter is more robust and ignores all environmental restrictions, we are able to make a statement whether state estimation is stuck due to sample impoverishment or not by looking at the positive exponential distribution +As a reminder, both filters (modes) are running in parallel for the entire estimation life cycle. +If we recognize that the dominant filter diverges from the supporting filter and thus got stuck or lost track, particles from the supporting filter will be picked with a higher probability while mixing the new particle set for the dominant filter. +As seen before, the Markov transition matrix $\Pi_t$ provides the probability $P(m_{t+1} \mid m_t)$ for transitioning between modes. +%In our approach those modes are the dominant graph-based filter and the supporting simple filter. +The dominant filter's probability to draw particles from its own posterior is given by the positive exponential distribution % \begin{equation} f(D_{\text{KL}}, \lambda) = e^{-\lambda D_{\text{KL}}} + \enspace . \label{equ:KLD} \end{equation} % -If $D_{\text{KL}}$ increases to a certain point, \eqref{equ:KLD} provides a probability that allows for mixing the particle sets. +Therefore, drawing particles from the support is given by $1 - f(D_{\text{KL}}, \lambda)$. +If the Kullback-Leibler divergence $D_{\text{KL}}$ increases to a certain point, \eqref{equ:KLD} provides a probability that allows for mixing the particle sets. $\lambda$ depends highly on the respective filter models and is therefore chosen heuristically. In most cases $\lambda$ tends to be somewhere between $0.01$ and $0.10$. -However, it is obvious that \eqref{equ:KLD} only works reliable if the measurement noises are within reasonable limits, because the support filter depends solely on them. -Especially Wi-Fi serves as the main source for estimation and thus attenuated or bad Wi-Fi readings are causing $D_{\text{KL}}$ to grow, even if the dominant filter provides a good position estimation. +However, \eqref{equ:KLD} only works reliable if the measurement noise is within reasonable limits, because the support filter using the simple transition depends solely on them. +Especially \docWIFI{} serves as the main source for estimation and thus attenuated or bad \docWIFI{} readings are causing bad estimation results for the supporting filter. +This further leads to a growing $D_{\text{KL}}$, even if the dominant filter provides a good position estimation. In such scenarios a lower diversity and higher focus of the particle set, as given by the dominant filter, is required. -We achieves this by introducing a Wi-Fi quality factor, allowing the support filter to pick particles from the dominant filter and prevent the later from doing it vice versa. +We achieves this by introducing a \docWIFI{} quality factor, allowing the support filter to pick particles from the dominant filter and prevent the later from doing it vice versa. The quality factor is defined by % \begin{equation} @@ -150,13 +158,13 @@ The quality factor is defined by \label{eq:wifiQuality} \end{equation} % -where $\bar\mRssi_\text{wifi}$ is the average of all signal-strength measurements received from the observation $\mObsVec_t$. An upper and lower bound is given by $l_\text{max}$ and $l_\text{min}$. - +where $\bar\mRssi_\text{wifi}$ is the average of all signal strength measurements received from the observation $\mObsVec_t^{\mRssiVec_\text{wifi}}$. An upper and lower bound is given by $l_\text{max}$ and $l_\text{min}$. +%matrix To incorporate all this within the IMMPF, we utilize a non-trivial Markov switching process. This is done by updating the Markov transition matrix $\Pi_t$ at every time step $t$. -As reminder, $\Pi_t$ highly influences the mixing process in \eqref{equ:immpModeMixing2}. -Considering the above presented measures, $\Pi_t$ is two-dimensional and given by +As reminder, $\Pi_t$ highly influences the mixing process in \eqref{equ:immpModeMixing2} and is responsible for providing the probability of moving from $m_t$ to $m_{t+1}$ in one time step. +Considering the measures \eqref{equ:KLD} and \eqref{eq:wifiQuality} presented above, the $2$x$2$ matrix $\Pi_t$ is given by % \begin{equation} \Pi_t = @@ -169,6 +177,12 @@ Considering the above presented measures, $\Pi_t$ is two-dimensional and given b \end{equation} % This matrix is the centrepiece of our approach. -It is responsible for controlling and satisfying the need of diversity and the need of focus for the whole localization approach. +It is responsible for controlling and satisfying the need of diversity and the need of focus for the whole localisation approach. +How $\Pi_t$ works is straightforward. +If the dominant graph-based filter suffers from sample impoverishment (get stuck or lose track), the probability in $[\Pi_t]_{12} = (1 - f(D_{\text{KL}}))$ increases with diverging support filter. +Consequently, the number of particles, the dominant filter draws from the supporting filter, also increases by $[\Pi_t]_{12} \cdot 100\%$. +Similar behaviour applies to the \docWIFI{} quality factor $q(\mObsVec_t^{\mRssiVec_\text{wifi}})$. +If the quality is low, the supporting filter regains focus by obtaining particles from the dominant's posterior. Therefore, recovering from sample impoverishment or degeneracy depends to a large extent on $\Pi_t$. + diff --git a/tex/chapters/relatedwork.tex b/tex/chapters/relatedwork.tex index 3771dec..930ae36 100644 --- a/tex/chapters/relatedwork.tex +++ b/tex/chapters/relatedwork.tex @@ -4,43 +4,47 @@ %klassisch resampling A common way to handle degeneracy and impoverishment is to apply suitable resampling methods. -The four most popular and well established approaches found in literature are multinomial, stratified, systematic and residual resampling. +The four most popular and well established approaches found in literature are multinomial-, stratified-, systematic- and residual resampling. They are also referred to as traditional methods, since a single distribution is used for resampling and the number of times a particle is re-drawn is always proportional to is weight \cite{Li2015b}. %advanced resampling -A more advanced method, with an adaptive particle size instead of a fixed one, is KLD-resampling. -It determines the number of particles to resample so that the Kullback-Leibler divergence between the distribution before resampling and after resampling does not exceed a pre-specified error bound \cite{Sun2013}. +A more advanced method, with an adaptive number of particles instead of a fixed one, is KLD-resampling. +It determines the number of particles to resample so that the Kullback-Leibler divergence between the distribution before resampling and after resampling does not exceed a pre-specified value \cite{Sun2013}. The key idea is to choose a small number of samples if the distribution is focused on a small part of the state space and a large number of particles if the distribution is much more spread out and requires a higher diversity of samples. +The problem of sample degeneracy and impoverishment is therefore encountered by adapting the number of particles depend upon the systems current uncertainty. In \cite{Li2015b} an overview of different resampling approaches are given. %allgemien auf andere methoden überleiten -As seen, resampling methods are able to reduce impoverishment to a certain degree by themselves. -However, in practice sample impoverishment is also a problem of environmental restrictions and system dynamics. +As seen in the example of KLD-resampling, some resampling methods are able to reduce impoverishment to a certain degree by themselves. +However, in practice, sample impoverishment is also a problem of environmental restrictions and system dynamics. Here, classical resampling schemes fail, since they are not able to propagate new particles into the state space. More promising and intelligent solutions are given by techniques of Particle Distribution Optimization (PDO). These variations of techniques are acting in different ways to optimize the spatial distribution of particles and are particularly effective in alleviating sample degeneracy and impoverishment \cite{Li2014}. For example in \cite{Xiaoqin2008} a Particle Swarm Optimization is used as importance distribution for visual tracking. Particles are iteratively updated according to their own experience and the experience of the swarm (or neighboring particles). -This allows for a multi-layer importance sampling and incorporation of the current measurement into the importance distribution, dealing with the sample impoverishment. +This allows for a multi-layer importance sampling and incorporation of the current measurements into the importance distribution, dealing with the sample impoverishment. Other PDO methods are presented in \cite{Li2014}. %hinführen zu IMM -In context of this work, our aim is to present a general solution that can be easily adapted to common localisation systems. +In context of this work, our aim is to present a general solution that can easily be adapted to common localisation systems. A promising approach for an easy to deploy PDO are Interacting Multiple Models (IMM) \cite{Bar-Shalom1988}. -IMM are able to mix appropriate dynamical systems based on a Bayesian probability metric and Gaussian noise. -Therefore, a set of modes like Kalman Filters are running in parallel. +IMMs are able to mix appropriate systems based on a Bayesian probability metric and Gaussian noise. +Therefore, a set of modes, like Kalman filters, are running in parallel. The mixing between modes is done by using a Markov Chain process, providing a probability for every mode and a transition matrix for switching between them. The most proper mode is then chosen for the current state estimation, what allows -the right choice to the right time. -For example \cite{Zhang2013} uses IMM to switch between a line-of-sight and a non-line-of-sight filtering procedure for indoor localisation. -Thereby, they are able to provide a robust and stable position estimation in both environments. +the right choice for every instant in time. +For example, \cite{Zhang2013} deploys an IMM for a time difference of arrival (TDOA) based localisation using an ultrasonic system. +Here, line-of-sight (LOS) and non-line-of-sight (NLOS) measurement noises are considered through switching between two extended Kalman filters, one for each condition. +Thereby, they are able to provide a robust and stable position estimation with high accuracy in both LOS and NLOS noise scenarios. -An extension to particle filters and therefore to non-linear and non-Gaussian system was presented by \cite{Boers2003}. +An extension to particle filters, and therefore to non-linear and non-Gaussian system, was presented by \cite{Boers2003}. The so called Interacting Multiple Model Particle Filter (IMMPF) was then further developed by \cite{Driessen2005}, adding a direct sampling approach. -This allows a merging between different particle filters by providing a possibility for each filter to additional sample particles from all available particle sets and not just from its own. -It is obvious that the possibility to draw from other particle sets is based on the mode probability and the transition matrix provided by the Markov Chain process and therefore does not violate the Markov property. +This allows a merging between different particle filters by providing a possibility for each filter to sample additional particles from all available particle sets and not just from its own. +It is obvious that the possibility to draw from other particle sets is based on the mode's probability and the transition matrix provided by the Markov Chain process and therefore does not violate the Markov property. Now, the key idea of this work is to satisfy the trade-off between diversity and focus by using appropriate modes within the IMMPF. +Warum? Weil die meinsten loca systeme auf particle filtern basieren und deswegen bietet es sich an. es erlaubt bereits vorhandene methoden die auf die jeweils einzeln auf die probleme eingehen zu kombinieren und so ein hybrid zu schaffen. + %Therefore, two different dynamical models are utilized and a novel approach for a non-trivial Markov switching Process based on Kullback-Leibler divergence and a Wi-Fi quality factor are presented. diff --git a/tex/chapters/system.tex b/tex/chapters/system.tex index b0b4750..1356e8f 100644 --- a/tex/chapters/system.tex +++ b/tex/chapters/system.tex @@ -3,7 +3,7 @@ In this section, we present two common localisation schemes based on particle filtering using two different transition models for propagating new states and an identical evaluation step for udpating the weights. -As mentioned before, we consider indoor localisation as a time-sequential, non-linear and non-Gaussian state estimation problem. +%As mentioned before, we consider indoor localisation as a time-sequential, non-linear and non-Gaussian state estimation problem. Recursive filters, like the aforementioned particle filter, use all observations $\mObsVec_{t}$ until the current time $t$ for computing an estimation of the hidden state $\mStateVec_{t}$. In a Bayesian setting, this can be formalized as the computation of the posterior distribution: % @@ -19,11 +19,8 @@ In a Bayesian setting, this can be formalized as the computation of the posterio \end{equation} % Here, the previous observation $\mObsVec_{t-1}$ is included into the state transition \cite{Ebner-15}. -For approximating $p(\mStateVec_{t} \mid \mObsVec_{1:t})$ with a particle filter, a sample set of $N$ independet random variables, $\vec{X}^i_{t} \sim p(\mStateVec_t \mid \mObsVec_{1:t})$ for $i = 1,...,N$, is used. -Due to importance sampling, a weight $W^i_t$ is assigned to each sample $\vec{X}^i_{t}$. -A particle set of the filter is then given by $\{W^i_{1:t}, \vec{X}^i_{1:t} \}_{i=1}^N$. The transition is used as proposal distribution, also known as CONDENSATION algorithm \cite{Isard98:CCD}. -This algorithm also performs a traditional resampling step. +%This algorithm also performs a traditional resampling step. For indoor localisation we define the hidden state $\mStateVec$ as follows: \begin{equation} @@ -32,16 +29,18 @@ For indoor localisation we define the hidden state $\mStateVec$ as follows: \end{equation} % where $x, y, z$ represent the position in 3D space, $\mStateHeading$ the user's heading and $\mStatePressure$ the relative atmospheric pressure prediction in hectopascal (hPa). -A particle is therefore a weighted representation of one possible system state $\mStateVec$. All relevant sensor measurements are incorporated into the observation $\mObsVec$ given by +All relevant sensor measurements are incorporated into the observation $\mObsVec$ given by % \begin{equation} \mObsVec = (\mObsHeading, \mObsSteps, \mRssiVec_\text{wifi}, \mObsPressure) \enspace, \end{equation} % Here, $\mObsHeading$ and $\mObsSteps$ describe the relative angular change and the number of steps detected for the pedestrian. -Further, $\mRssiVec_\text{wifi}$ and $\mRssiVec_\text{ib}$ contain the measurements of all nearby \docAP{}s (\docAPshort{}). +Further, $\mRssiVec_\text{wifi}$ contains the measurements of all nearby \docAP{}s (\docAPshort{}). Finally, $\mObsPressure$ is the relative barometric pressure with respect to a fixed reference. +%\subsection{Evaluation} + We assume a statistical independence of all sensors. The probability density of the state evaluation is then given by the following components: % \begin{equation} @@ -54,127 +53,156 @@ We assume a statistical independence of all sensors. The probability density of \label{eq:evalBayes} \end{equation} % -The current pressure value is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$ and absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}. +%The current pressure value is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$ and absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}. -\subsection{Evaluation} - -%Barometer -First, the smartphone’s barometer is used to infer the likeliness of the current $z$-location. -Due to noisy sensors, we calculate the average $\overline{\mObsPressure}$ of several sensor readings and the sensor's uncertainty $\sigma_\text{baro}$. -This average serves as relative base for all future measurements and is carried out while the pedestrian chooses his destination \cite{Fetzer2016OMC}. - -The evaluation step for time $t$ is given by - % - \begin{equation} - p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2) \enspace. - \label{eq:baroEval} - \end{equation} - % +The smartphone's barometer is used to infer the likeliness of the current $z$-location in $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$ and thus enables to walk stairs or to drive elevators. Here, every predicted relative pressure $\mState_t^{\mStatePressure}$ is compared with the observed one $\mObs_t^{\mObsPressure}$ using a normal distribution. -The state's relative pressure prediction $\mStatePressure$ is estimated within each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ by tracking every height-change ($z$-axis): +The state's relative pressure prediction $\mStatePressure$ is estimated within each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ by tracking the pressure between every height-change on the $z$-axis. + +Absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}. +We are using the wall attenuation factor model based on Friis transmission equation to predict an \docAP{}'s (\docAPshort{}) signal strength at an arbitrary position $\fPos{\mStateVec_t} = (x, y,z)^T$. +This predicted signal strength is then matched against the current observation $\mObs_t^{\mRssiVec_\text{wifi}}$ received from this particular \docAPshort{}, providing a likelihood of the pedestrian being at $\fPos{\mStateVec_t}$. +The positions of detected \docAPshort{}'s are known beforehand. +The main advantage of this approach is that no time-consuming initial calibration phase and updates in case of infrastructural changes are needed. + +%Barometer +%Due to noisy sensors, we calculate the average $\overline{\mObsPressure}$ of several sensor readings and the sensor's uncertainty $\sigma_\text{baro}$. +%This average serves as relative base for all future measurements and is carried out while the pedestrian chooses his destination \cite{Fetzer2016OMC}. + +%The evaluation step for time $t$ is given by + % +% \begin{equation} +% p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2) \enspace. +% \label{eq:baroEval} +% \end{equation} + % +%Here, every predicted relative pressure $\mState_t^{\mStatePressure}$ is compared with the observed one $\mObs_t^{\mObsPressure}$ using a normal distribution. +%The state's relative pressure prediction $\mStatePressure$ is estimated within each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ by tracking every height-change ($z$-axis): % - \begin{equation} - \mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot b - ,\enskip - \Delta z = \mState_{t-1}^{z} - \mState_{t}^z - ,\enskip - b \in \R - \enspace , - \label{eq:baroTransition} - \end{equation} +% \begin{equation} +% \mState_{t}^{\mStatePressure} = \mState_{t-1}^{\mStatePressure} + \Delta z \cdot b +% ,\enskip +% \Delta z = \mState_{t-1}^{z} - \mState_{t}^z +% ,\enskip +% b \in \R +% \enspace , +% \label{eq:baroTransition} +% \end{equation} % -Here, $b$ denotes the common pressure change in $\frac{\text{hPa}}{\text{m}}$. +%Here, $b$ denotes the common pressure change in $\frac{\text{hPa}}{\text{m}}$. %WI-FI -Signal strength models are a well-established and popular method for estimating a pedestrian's position in indoor environments. -We are using the wall attenuation factor model based on Friis transmission equation to predict an \docAP{}’s (\docAPshort{}) signal strength at an arbitrary position $\mStateVec_t$ \cite{Ebner-15}. -Here, the positions of detected \docAP{}s (\docAPshort{}) are known beforehand. -The main advantage of this approach is that no time-consuming initial calibration phase and updates in case of infrastructural changes are needed. -Using the 3D distance $d$ and the number of floors $\Delta f$ between the transmitter and the state-in-question, it can be described by +%Signal strength models are a well-established and popular method for estimating a pedestrian's position in indoor environments. +%We are using the wall attenuation factor model based on Friis transmission equation to predict an \docAP{}’s (\docAPshort{}) signal strength at an arbitrary position $\mStateVec_t$ \cite{Ebner-15}. +%Here, the positions of detected \docAP{}s (\docAPshort{}) are known beforehand. +%The main advantage of this approach is that no time-consuming initial calibration phase and updates in case of infrastructural changes are needed. +%Using the 3D distance $d$ and the number of floors $\Delta f$ between the transmitter and the state-in-question, it can be described by % - \begin{equation} - P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF \enspace , - \label{eq:waf} - \end{equation} +% \begin{equation} +% P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} %\mWAF \enspace , +% \label{eq:waf} +% \end{equation} % -where $\mTXP$ contains the AP’s signal strength at $\mMdlDist_0$ and $\mPLE$ models the signal’s depletion with growing distance. -The attenuation per floor is described by $\mWAF$. -To reduce the system's setup time, we use the same values for all \docAP{}s at the cost of accuracy. +%where $\mTXP$ contains the AP’s signal strength at $\mMdlDist_0$ and $\mPLE$ models the signal’s depletion with growing distance. +%The attenuation per floor is described by $\mWAF$. +%To reduce the system's setup time, we use the same values for all \docAP{}s at the cost of accuracy. -By assuming statistical independence, the overall probability can be determined using +%By assuming statistical independence, the overall probability can be determined using % - \begin{equation} - \mProb(\mObsVec_t \mid \mStateVec_t)_\text{wifi} = - \prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2) \enspace . - \label{eq:wifiTotal} - \end{equation} -The uncertainty of the measurements is given by $\Delta{f_{i}}$. More details on this approach and possible extensions can be found in \cite{Ebner-15} and \cite{Ebner-17}. +% \begin{equation} +% \mProb(\mObsVec_t \mid \mStateVec_t)_\text{wifi} = +% \prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2) \enspace . +% \label{eq:wifiTotal} +% \end{equation} +%The uncertainty of the measurements is given by $\Delta{f_{i}}$. More details on this approach and possible extensions can be found in \cite{Ebner-15} and \cite{Ebner-17}. -\subsection{Transition} +%\subsection{Graph-based Transition} + +%Keine Überschriften. Transition über liste trennen As mentioned before, we are searching for a solution to satisfy both, sample diversity and focus. -In the following, two very different transition models, each providing one of this abilities, are presented. +Therefore, we utilize two very different transition models, each providing one of these abilities. +\begin{itemize} + \item The \textit{graph-based transition} samples only new states that are allowed by a gridded graph, which is generated from the building's floorplan. Thus walking through walls, ceilings or obstacles is prohibited. Additionally, the human movement is considered by randomly walking along adjacent edges into a given direction until a to-be-walked distance is reached. To provide a direction and distance, turns and steps are detected using the smartphone's IMU. All this promises a very focused propagation for new states and draws only valid movements. +% + \item \textit{The simple transition} is a continuous model, that draws new states depending on a random direction and distance provided by a multivariate normal distribution. That means, no environmental knowledge and no statement about the pedestrian's (real) movement are considered. +\end{itemize} +For further explanations and details of the localisation filter please refer to \cite{Ebner-15}. -The first transition model is based upon random walks on a graph $G=(V,E)$ with vertices $\mVertexA \in V$ and undirected edges $\mEdgeAB \in E$, which is generated from the buildings floorplan \cite{Ebner-16}. -Starting at the vertex of the position $\fPos{\mStateVec_{t-1}} = (x, y,z)^T$ a new particle is sampled by walking along adjacent nodes into a given walking-direction $\gHead$ until a distance $\gDist$ is reached \cite{Ebner-15}. -During the random walk, each edge has its own probability $p(\mEdgeAB)$ which depends on the edge’s direction $\angle \mEdgeAB$ and the pedestrian’s current heading $\gHead$. -The to-be-walked edge is thus drawn according to their resemblance: - % - \begin{equation} - p(\mEdgeAB)_\text{head} = p(\mEdgeAB \mid \gHead) = \mathcal{N} (\angle \mEdgeAB \mid \gHead, \sigma_\text{head}^2) - \enspace . - \label{eq:transHeading} - \end{equation} - % -While the distribution \refeq{eq:transHeading} does not integrate to $1.0$ due to circularity of angular data, in our case, the normal distribution can be assumed as sufficient for small enough $\sigma^2$. +Given the above, we are now able to implement two different localisation schemes, one for each transition model presented. +The graph-based transition keeps the localisation error low by using a very realistic propagation model, while being prone to sample impoverishment. +On the other hand, the simple transition provides a high diversity with a robust, but uncertain position estimation. +Both are evaluating a state $\mStateVec_{t}$ using \eqref{eq:evalBayes}. -To provide $\gHead$ and $\gDist$, steps and turns are detected using the smartphone's IMU, implemented as described in \cite{Ebner-15}. -The number of steps detected since the last transition is used to estimate the to-be-walked distance $\gDist$ by assuming a fixed step-size with some deviation: - % - \begin{equation} - \gDist = \mObs_{t-1}^{\mObsSteps} \cdot \mStepSize + \mathcal{N}(0, \sigma_{\gDist}^2) - \enspace . - \end{equation} - % -Turn-Detection supplies the magnitude of the detected heading change by integrating over the gyroscope's change since the last transition. -Together with some deviation and the state's previous heading, the magnitude is used to estimate the current state's heading: - % - \begin{equation} - \gHead = \mState_{t}^{\mStateHeading} = \mState_{t-1}^{\mStateHeading} + \mObs_{t-1}^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\ - \end{equation} - % -All this promises a very focused propagation for new particles and draws only valid movements, as ambient conditions (walls, doors, stairs, etc.) are considered. -Additionally, the graph-based approach offers plenty of scope for further extension as can be seen in \cite{Ebner2016OPN}. +% +%In the following, two very different transition models, each providing one of this abilities, are presented. -The second transition model is very simple and thus often used in scenarios with little or rough information provided by sensors. -Especially in cases without any regular statements about the pedestrian's movement. -This continuous model just moves into a random direction, ignoring the graph and thus any floorplan knowledge: +%The first transition model is based upon random walks on a gridded graph $G=(V,E)$ with vertices $\mVertexA \in V$ and undirected edges $\mEdgeAB \in E$, which is generated from the buildings floorplan \cite{Ebner-16}. +%Starting at the vertex of the position $\fPos{\mStateVec_{t-1}} = (x, y,z)^T$ a new particle is sampled by walking along adjacent nodes into a given walking-direction $\gHead$ until a distance $\gDist$ is reached \cite{Ebner-15}. +%During the random walk, each edge has its own probability $p(\mEdgeAB)$ which depends on the edge’s direction $\angle \mEdgeAB$ and the pedestrian’s current heading $\gHead$. +%The to-be-walked edge is thus drawn according to their resemblance: % - \begin{equation} - \begin{split} - \mProb(\mStateVec_{t} \mid \mStateVec_{t-1}) &= - \mathcal{N}\left( - \fPos{\mStateVec_{t}} - \mid{} - \fPos{\mStateVec_{t-1}}, - \mat{\Sigma}_{\text{move}} - \right),\\ - \mat{\Sigma}_{\text{move}} &= - \begin{pmatrix} - \sigma_{\text{move}} & 0 & 0\\ - 0 & \sigma_{\text{move}} & 0\\ - 0 & 0 & \sigma_{\text{floor}}\\ - \end{pmatrix} - \end{split} - \label{eq:simpleTrans} - \end{equation} +% \begin{equation} +% p(\mEdgeAB)_\text{head} = p(\mEdgeAB \mid \gHead) = \mathcal{N} (\angle \mEdgeAB \mid \gHead, \sigma_\text{head}^2) +% \enspace . +% \label{eq:transHeading} +% \end{equation} % -The only restriction made, is that newly drawn particles need to be somewhere in between the graphs boundaries and therefore have a valid vertex for $\fPos{\mStateVec_{t}}$. -If the particle does not satisfy this condition, the position of nearest available vertex is chosen instead. -This ensures that a particle resides always on a valid vertex $\mVertexA$, what will be of importance for the upcoming IMMPF. +%While the distribution \refeq{eq:transHeading} does not integrate to $1.0$ due to circularity of angular data, in our case, the normal distribution can be assumed as sufficient for small enough $\sigma^2$. + +%To provide $\gHead$ and $\gDist$, steps and turns are detected using the smartphone's IMU, implemented as described in \cite{Ebner-15}. +%The number of steps detected since the last transition is used to estimate the to-be-walked distance $\gDist$ by assuming a fixed step-size with some deviation: + % +% \begin{equation} +% \gDist = \mObs_{t-1}^{\mObsSteps} \cdot \mStepSize + \mathcal{N}(0, \sigma_{\gDist}^2) +% \enspace . +% \end{equation} + % +%Turn-Detection supplies the magnitude of the detected heading change by integrating over the gyroscope's change since the last transition. +%Together with some deviation and the state's previous heading, the magnitude is used to estimate the current state's heading: + % +% \begin{equation} +% \gHead = \mState_{t}^{\mStateHeading} = \mState_{t-1}^{\mStateHeading} + \mObs_{t-1}^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\ +% \end{equation} + % +%All this promises a very focused propagation for new particles and draws only valid movements, as ambient conditions (walls, doors, stairs, etc.) are considered. +%Additionally, the graph-based approach offers plenty of scope for further extension as can be seen in \cite{Ebner-16}. + +%\subsection{Simple Transition} + +%The second transition model is very simple and thus often used in scenarios with little or rough information provided by sensors. +%Especially in cases without any regular statements about the pedestrian's movement. +%This continuous model just moves into a random direction, ignoring the graph and thus any floorplan %knowledge: +% % +% \begin{equation} +% \begin{split} +% \mProb(\mStateVec_{t} \mid \mStateVec_{t-1}) &= +% \mathcal{N}\left( +% \fPos{\mStateVec_{t}} +% \mid{} +% \fPos{\mStateVec_{t-1}}, +% \mat{\Sigma}_{\text{move}} +% \right),\\ +% \mat{\Sigma}_{\text{move}} &= +% \begin{pmatrix} +% \sigma_{\text{move}} & 0 & 0\\ +% 0 & \sigma_{\text{move}} & 0\\ +% 0 & 0 & \sigma_{\text{floor}}\\ +% \end{pmatrix} +% \end{split} +% \label{eq:simpleTrans} +% \end{equation} + % +%The only restriction made, is that newly drawn particles need to be somewhere in between the graphs boundaries and therefore have a valid vertex for $\fPos{\mStateVec_{t}}$. +%If the particle does not satisfy this condition, the position of nearest available vertex is chosen instead. +%This ensures that a particle resides always on a valid vertex $\mVertexA$, what will be of importance for the upcoming IMMPF. + +%For further explanations of the filtering process for indoor localisation please refer to \cite{Ebner-15}. + + diff --git a/tex/egbib.bib b/tex/egbib.bib index 525c52c..84f1d78 100644 --- a/tex/egbib.bib +++ b/tex/egbib.bib @@ -1721,8 +1721,10 @@ doi={10.1109/PLANS.2008.4570051},} booktitle={Indoor Positioning and Indoor Navigation (IPIN), Int. Conf. on}, title={{Multi Sensor 3D Indoor Localisation}}, year={2015}, + publisher = {IEEE}, + address = {Banff, Canada}, IGNOREmonth={October}, - pages={1-10}, + pages={}, } @inproceedings{Ebner-16, @@ -2746,7 +2748,7 @@ keywords = {Artificial intelligence,Impoverishment,Machine learning,Markov Chain mendeley-groups = {IPIN 2017}, number = {8}, pages = {3944--3954}, -title = {{Fight sample degeneracy and impoverishment in particle filters: A review of intelligent approaches}}, +title = {{Fight Sample Degeneracy and Impoverishment in Particle Filters: A Review of Intelligent Approaches}}, volume = {41}, year = {2014} } @@ -2761,7 +2763,7 @@ journal = {Radar, Sonar and Navigation, IEE Proceedings -}, mendeley-groups = {IPIN 2017}, number = {5}, pages = {323--326}, -title = {{Efficient particle filter for jump Markov nonlinear systems}}, +title = {{Efficient Particle Filter for Jump Markov Nonlinear Systems}}, volume = {152}, year = {2005} } @@ -2772,10 +2774,9 @@ author = {Li, Tiancheng and Boli{\'{c}}, Miodrag and Djuri{\'{c}}, Petar M.}, doi = {10.1109/MSP.2014.2330626}, issn = {10535888}, journal = {IEEE Signal Processing Magazine}, -month = {may}, number = {3}, pages = {70--86}, -title = {{Resampling Methods for Particle Filtering: Classification, implementation, and strategies}}, +title = {{Resampling Methods for Particle Filtering: Classification, Implementation, and Strategies}}, volume = {32}, year = {2015} } @@ -2789,10 +2790,9 @@ isbn = {1350-911X}, issn = {0013-5194}, journal = {Electronics Letters}, mendeley-groups = {IPIN 2017}, -month = {jun}, number = {12}, pages = {740--742}, -title = {{Adapting sample size in particle filters through KLD-resampling}}, +title = {{Adapting Sample Size in Particle Filters through KLD-resampling}}, volume = {49}, year = {2013} } @@ -2807,10 +2807,9 @@ isbn = {1063-6919}, issn = {1063-6919}, keywords = {Bayes methods,Bayesian inference view,Bayesian methods,Inference algorithms,Monte Carlo methods,Motion measurement,Nonhomogeneous media,Particle filters,Particle swarm optimization,Particle tracking,Video sequences,image sampling,image sequences,importance sampling,motion estimation,multilayer importance sampling,particle filtering (numerical methods),particle swarm optimisation,sequential particle swarm optimization,temporal continuity information,unscented particle filter,video sequence,video signal processing,visual tracking}, mendeley-groups = {IPIN 2017}, -month = {jun}, pages = {1--8}, publisher = {IEEE}, -title = {{Sequential particle swarm optimization for visual tracking}}, +title = {{Sequential Particle Swarm Optimization for Visual Tracking}}, year = {2008} } @@ -2824,10 +2823,9 @@ isbn = {9781467315906}, issn = {00189456}, keywords = {Indoor localization,Kalman filter,M-estimator,interacting multiple model (IMM),time difference of arrival (TDOA),ultrasound}, mendeley-groups = {IPIN 2017}, -month = {aug}, number = {8}, pages = {2205--2214}, -title = {{TDOA-Based localization using interacting multiple model estimator and ultrasonic transmitter/receiver}}, +title = {{TDOA-Based Localization using Interacting Multiple Model Estimator and Ultrasonic Transmitter/Receiver}}, volume = {62}, year = {2013} } @@ -2843,7 +2841,7 @@ journal = {IEEE Transactions on Automatic Control}, mendeley-groups = {IPIN 2017}, number = {8}, pages = {780--783}, -title = {{Interacting multiple model algorithm for systems with Markovian switching coefficients.}}, +title = {{Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients.}}, volume = {33}, year = {1988} } @@ -2858,7 +2856,7 @@ journal = {October}, mendeley-groups = {IPIN 2017}, number = {5}, pages = {344--349}, -title = {{Interacting multiple model particle filter}}, +title = {{Interacting Multiple Model Particle Filter}}, volume = {150}, year = {2003} } @@ -2869,23 +2867,10 @@ year = {2003} booktitle = {Indoor Positioning and Indoor Navigation (IPIN), Int. Conf. on}, editor = {}, year = {2016}, - month = {October}, publisher = {IEEE}, pages = {}, address = {Madrid, Spain}, issn = {} } -@inproceedings{Ebner2016OPN, - author = {F. Ebner and T. Fetzer and M. Grzegorzek and F. Deinzer}, - title = {{On Prior Navigation Knowledge in Multi Sensor Indoor Localisation}}, - booktitle = {International Conference on Information Fusion (FUSION 2016)}, - editor = {}, - year = {2016}, - month = {July}, - publisher = {IEEE}, - address = {Heidelberg, Germany}, - pages = {}, - isbn = {} -} diff --git a/tex/gfx/eval/paths.eps b/tex/gfx/eval/paths.eps index 2e1578e..e647c6a 100755 --- a/tex/gfx/eval/paths.eps +++ b/tex/gfx/eval/paths.eps @@ -1,10557 +1,4546 @@ -%!PS-Adobe-2.0 EPSF-2.0 -%%Title: /mnt/vm/paper/OTHER2017/for_toni/out//paths.tex -%%Creator: gnuplot 5.0 patchlevel 5 -%%CreationDate: Fri May 5 08:33:17 2017 -%%DocumentFonts: -%%BoundingBox: 50 50 293 177 +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: cairo 1.14.8 (http://cairographics.org) +%%CreationDate: Sun May 7 13:41:25 2017 +%%Pages: 1 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%BoundingBox: 2 1 241 125 %%EndComments %%BeginProlog -/gnudict 256 dict def -gnudict begin -% -% The following true/false flags may be 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0 360 arc closepath} bind def -/C9 {BL [] 0 setdash 2 copy moveto - 2 copy vpt 270 450 arc closepath fill - vpt 0 360 arc closepath} bind def -/C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill - 2 copy moveto - 2 copy vpt 90 180 arc closepath fill - vpt 0 360 arc closepath} bind def -/C11 {BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 180 arc closepath fill - 2 copy moveto - 2 copy vpt 270 360 arc closepath fill - vpt 0 360 arc closepath} bind def -/C12 {BL [] 0 setdash 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath} bind def -/C13 {BL [] 0 setdash 2 copy moveto - 2 copy vpt 0 90 arc closepath fill - 2 copy moveto - 2 copy vpt 180 360 arc closepath fill - vpt 0 360 arc closepath} bind def -/C14 {BL [] 0 setdash 2 copy moveto - 2 copy vpt 90 360 arc closepath fill - vpt 0 360 arc} bind def -/C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill - vpt 0 360 arc closepath} bind def -/Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto - neg 0 rlineto closepath} bind def -/Square {dup Rec} bind def -/Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def -/S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def -/S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def -/S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def -/S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def -/S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def -/S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill - exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def -/S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def -/S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill - 2 copy vpt Square fill Bsquare} bind def -/S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def -/S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def -/S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill - Bsquare} bind def -/S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill - Bsquare} bind def -/S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def -/S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy vpt Square fill Bsquare} bind def -/S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill - 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def -/S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def -/D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def -/D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def -/D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def -/D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def -/D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def -/D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def -/D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def -/D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def -/D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def -/D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def -/D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def -/D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def -/D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def -/D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def -/D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def -/D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def -/DiaE {stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V closepath stroke} def -/BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V closepath stroke} def -/TriUE {stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V closepath stroke} def -/TriDE {stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V closepath stroke} def -/PentE {stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - closepath stroke grestore} def -/CircE {stroke [] 0 setdash - hpt 0 360 arc stroke} def -/Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def -/DiaW {stroke [] 0 setdash vpt add M - hpt neg vpt neg V hpt vpt neg V - hpt vpt V hpt neg vpt V Opaque stroke} def -/BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M - 0 vpt2 neg V hpt2 0 V 0 vpt2 V - hpt2 neg 0 V Opaque stroke} def -/TriUW {stroke [] 0 setdash vpt 1.12 mul add M - hpt neg vpt -1.62 mul V - hpt 2 mul 0 V - hpt neg vpt 1.62 mul V Opaque stroke} def -/TriDW {stroke [] 0 setdash vpt 1.12 mul sub M - hpt neg vpt 1.62 mul V - hpt 2 mul 0 V - hpt neg vpt -1.62 mul V Opaque stroke} def -/PentW {stroke [] 0 setdash gsave - translate 0 hpt M 4 {72 rotate 0 hpt L} repeat - Opaque stroke grestore} def -/CircW {stroke [] 0 setdash - hpt 0 360 arc Opaque stroke} def -/BoxFill {gsave Rec 1 setgray fill grestore} def -/Density { - /Fillden exch def - currentrgbcolor - /ColB exch def /ColG exch def /ColR exch def - /ColR ColR Fillden mul Fillden sub 1 add def - /ColG ColG Fillden mul Fillden sub 1 add def - /ColB ColB Fillden mul Fillden sub 1 add def - ColR ColG ColB setrgbcolor} def -/BoxColFill {gsave Rec PolyFill} def -/PolyFill {gsave Density fill grestore grestore} def -/h {rlineto rlineto rlineto gsave closepath fill grestore} bind def -% -% PostScript Level 1 Pattern Fill routine for rectangles -% Usage: x y w h s a XX PatternFill -% x,y = lower left corner of box to be filled -% w,h = width and height of box -% a = angle in degrees between lines and x-axis -% XX = 0/1 for no/yes cross-hatch -% -/PatternFill {gsave /PFa [ 9 2 roll ] def - PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add 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-LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 736 801 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 868 778 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 1000 754 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1132 731 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1264 707 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1396 684 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1527 660 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1659 637 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2075 671 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 625 930 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 757 906 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 889 883 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1020 859 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.55 0.55 C gsave 1152 836 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1284 812 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1416 789 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1548 765 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1680 742 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1811 718 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1943 694 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 493 953 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2207 647 N 132 -23 V 75 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2339 624 N 130 -24 V 76 41 V -131 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2469 600 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2601 577 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2733 553 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2865 530 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2997 506 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3128 483 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3260 459 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3392 436 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2657 513 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1340 748 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1472 724 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1603 701 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1735 677 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1867 654 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1999 630 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2131 607 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2262 583 N 131 -23 V 76 40 V -130 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2393 560 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2525 536 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.91 0.90 C gsave 2373 455 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2789 489 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2921 466 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 3052 442 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 3184 419 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 3316 395 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 3448 372 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 3580 348 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3711 325 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3843 301 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 361 977 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1431 514 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.91 0.90 C gsave 2146 332 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2277 309 N 131 -24 V 76 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.85 C gsave 2408 285 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 2540 262 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 2672 238 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 2804 215 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2935 191 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.75 C gsave 3067 168 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 3199 144 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3331 121 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3463 97 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2014 356 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 1563 491 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 1694 467 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1826 444 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 1958 420 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2090 397 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.91 0.90 C gsave 2222 373 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2353 350 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.85 C gsave 2484 326 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 2616 303 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 2748 279 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 2728 174 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1279 433 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 1410 409 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 1542 386 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1674 362 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 1806 339 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 1938 315 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.91 0.90 C gsave 2069 292 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2201 268 N 132 -23 V 75 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.85 C gsave 2333 245 N 131 -24 V 76 41 V -132 23 V -75 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 2464 221 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 2596 198 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2880 256 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.72 0.72 C gsave 2859 151 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.75 C gsave 2991 127 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 3123 104 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3255 80 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3387 57 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1355 474 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 1487 450 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 1618 427 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1750 403 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 1882 380 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 924 713 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3088 273 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.75 C gsave 3219 249 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 3351 226 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3483 202 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3615 179 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 133 854 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 265 831 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 397 807 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 529 784 N 131 -24 V 76 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 660 760 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 792 737 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2956 296 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1056 690 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1188 666 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1319 643 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1451 619 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1583 596 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 1715 572 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 1847 549 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1978 525 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2110 502 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2242 478 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1507 555 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3012 232 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.75 C gsave 3143 209 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 3275 185 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3407 162 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3539 138 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 57 814 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 189 790 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 321 767 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 452 743 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 584 720 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3524 412 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 1639 532 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 1771 508 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1902 485 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2034 461 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2166 437 N 132 -23 V 75 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.91 0.90 C gsave 2298 414 N 131 -24 V 76 41 V -132 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2429 390 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.85 C gsave 2560 367 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 2692 343 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 2824 320 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 818 1221 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2586 851 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 2718 828 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 2850 804 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2982 781 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 3114 757 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3641 663 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.63 0.62 C gsave 3773 639 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.63 0.62 C gsave 3904 616 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.65 0.65 C gsave 4036 592 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.65 0.65 C gsave 4168 569 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.65 0.65 C gsave 4300 545 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 2454 875 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 950 1198 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.90 0.89 C gsave 1082 1174 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 1213 1151 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.67 0.66 C gsave 1345 1127 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1477 1103 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.76 C gsave 1609 1080 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.73 0.73 C gsave 1741 1056 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 1873 1033 N 131 -24 V 76 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 2004 1009 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2136 986 N 132 -24 V 75 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1006 1133 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2248 857 N 130 -23 V 76 41 V -130 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 2378 834 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.86 C gsave 2510 810 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.86 C gsave 2642 787 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.86 C gsave 2774 763 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.90 0.89 C gsave 2906 740 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 3037 716 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 3565 622 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 3696 599 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 742 1180 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 874 1157 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2268 962 N 131 -23 V 76 41 V -132 23 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 1137 1110 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1269 1086 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1401 1063 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.76 C gsave 1533 1039 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.73 0.73 C gsave 1665 1016 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 1796 992 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1928 969 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2060 945 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2192 922 N 132 -24 V 75 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2324 898 N 130 -23 V 77 40 V -132 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.66 0.66 C gsave 3134 862 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.76 C gsave 1685 1121 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1817 1097 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 1949 1074 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 2080 1050 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2212 1027 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.86 C gsave 2343 1003 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2475 980 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2607 956 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2738 933 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2870 909 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 3002 886 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.70 0.69 C gsave 1553 1144 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 3266 838 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3398 815 N 131 -24 V 76 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3529 791 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3661 768 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3793 744 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3925 721 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4057 697 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4188 674 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4320 650 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4452 627 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3717 704 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2399 939 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 2531 915 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2662 892 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2794 868 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 2926 845 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 3058 821 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 3190 798 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3321 774 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3453 751 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3585 727 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2116 881 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3849 680 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3980 657 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4112 633 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4244 610 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4376 586 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 894 1262 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 1026 1238 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 1158 1215 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.78 0.78 C gsave 1290 1191 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.70 0.69 C gsave 1421 1168 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 909 988 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 3073 547 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3205 524 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3336 500 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3468 477 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3600 453 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3732 429 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3864 406 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3995 382 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 514 1058 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 645 1035 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 777 1011 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2941 571 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1041 964 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1173 941 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.55 0.55 C gsave 1304 917 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1436 894 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1568 870 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1700 846 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1832 823 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1964 799 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2095 776 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2227 752 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1492 829 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3656 389 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3788 365 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3919 342 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 437 1017 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 569 994 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 701 970 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 833 947 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 965 923 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1097 900 N 131 -24 V 76 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.55 0.55 C gsave 1228 876 N 132 -23 V 76 41 V -132 23 V -76 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132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.63 0.62 C gsave 3773 1083 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.63 0.62 C gsave 3904 1059 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.65 0.65 C gsave 4036 1036 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.65 0.65 C gsave 4168 1012 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.65 0.65 C gsave 4300 988 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 818 1663 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 950 1640 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.86 C gsave 1082 1616 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 1213 1593 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1345 1569 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1477 1546 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.76 C gsave 1609 1522 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1741 1499 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 1873 1475 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2850 1247 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2136 1428 N 132 -24 V 75 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.86 C gsave 2268 1404 N 131 -22 V 76 40 V -132 23 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2399 1382 N 132 -24 V 76 40 V -132 24 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2531 1358 N 131 -23 V 76 41 V -131 22 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.93 C gsave 2662 1335 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2794 1311 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.74 C gsave 2926 1288 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.87 C gsave 3058 1264 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 3190 1241 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3321 1217 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3453 1194 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3585 1170 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3717 1147 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1006 1575 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.92 0.92 C gsave 1457 1441 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.87 C gsave 1588 1417 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 1720 1394 N 132 -23 V 76 40 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1852 1371 N 132 -23 V 76 39 V -132 24 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 1984 1348 N 132 -24 V 76 41 V -132 22 V -76 -39 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2116 1324 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2248 1301 N 130 -24 V 76 41 V -130 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2378 1277 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2510 1253 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.90 0.90 C gsave 2642 1230 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2774 1206 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 3696 1042 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 742 1622 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 874 1599 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3849 1123 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 1137 1552 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1269 1528 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 1401 1505 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.76 C gsave 1533 1481 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.73 0.73 C gsave 1665 1458 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 1796 1434 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1928 1411 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2060 1387 N 132 -22 V 76 39 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2192 1365 N 132 -24 V 75 41 V -131 22 V -76 -39 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2324 1341 N 130 -23 V 77 40 V -132 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 2454 1318 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2586 1294 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 2718 1271 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4396 1134 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4188 1117 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4320 1093 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4452 1070 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2946 1392 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3078 1369 N 132 -23 V 76 40 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3210 1346 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3342 1322 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.78 0.78 C gsave 3474 1299 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3605 1275 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3737 1252 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3869 1228 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4001 1205 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4133 1181 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4265 1158 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4057 1141 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4528 1111 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3022 1433 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3154 1409 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3286 1386 N 132 -23 V 76 40 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3418 1363 N 132 -23 V 76 40 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3550 1340 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3682 1316 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3813 1293 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3945 1269 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4077 1245 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4209 1222 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4341 1198 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4472 1175 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2212 1469 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3980 1100 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4112 1076 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4244 1053 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 4376 1029 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 894 1704 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 1026 1680 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 1158 1657 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.69 0.69 C gsave 1290 1633 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.70 0.69 C gsave 1421 1610 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.70 0.69 C gsave 1553 1586 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1685 1563 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1817 1539 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 1949 1516 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 2080 1492 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3463 540 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.86 C gsave 2343 1445 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2475 1422 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2607 1398 N 131 -22 V 77 39 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2738 1376 N 132 -24 V 76 40 V -131 23 V -77 -39 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2870 1352 N 132 -23 V 76 40 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3002 1329 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.67 0.67 C gsave 3134 1305 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 3266 1282 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3398 1258 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3529 1235 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3661 1211 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3793 1188 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 3925 1164 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 529 1227 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.91 0.90 C gsave 2298 857 N 131 -23 V 76 40 V -132 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2429 834 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.85 C gsave 2560 810 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 2692 787 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 2824 763 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 2956 739 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.74 C gsave 3088 716 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.74 C gsave 3219 692 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 3351 669 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3483 645 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3615 622 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 133 1298 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 265 1274 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 397 1251 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2166 881 N 132 -24 V 75 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 660 1204 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 3164 757 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 3296 733 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 3427 710 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3559 686 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3691 663 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 209 1338 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 341 1315 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 473 1291 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 605 1268 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 736 1244 N 132 -23 V 76 40 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 3240 797 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3372 774 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.74 C gsave 3143 652 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3331 564 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1431 957 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 1563 934 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 1694 910 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1826 887 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 1958 863 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2090 840 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.91 0.90 C gsave 2222 816 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 2353 793 N 131 -24 V 76 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.85 C gsave 2484 769 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 2616 746 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 2748 722 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 2880 699 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.72 0.72 C gsave 3012 675 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 1193 1488 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.94 0.93 C gsave 3275 628 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3407 605 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3539 581 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 57 1257 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 189 1233 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 321 1210 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 452 1186 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 584 1163 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1507 998 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.64 0.64 C gsave 1639 975 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 1771 951 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1902 928 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2034 904 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1776 1330 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 645 1477 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 777 1453 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 909 1430 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1041 1406 N 132 -22 V 76 39 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.78 0.78 C gsave 3544 960 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 590 1541 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 722 1517 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 853 1494 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 985 1470 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 1117 1447 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.90 0.90 C gsave 1249 1423 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.92 0.92 C gsave 1381 1400 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.87 C gsave 1512 1377 N 132 -23 V 76 40 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1644 1354 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3635 727 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 1908 1307 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.79 C gsave 2040 1283 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2171 1260 N 132 -24 V 75 41 V -130 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2303 1236 N 131 -23 V 76 40 V -132 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.83 C gsave 2434 1213 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.90 0.90 C gsave 2566 1189 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.85 C gsave 2698 1166 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3620 1001 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.95 0.94 C gsave 666 1582 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 798 1558 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 929 1535 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 1061 1511 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 1325 1464 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 3468 920 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3503 750 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3767 703 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 285 1379 N 132 -23 V 76 39 V -132 24 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 417 1356 N 132 -24 V 76 41 V -132 22 V -76 -39 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 549 1332 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 681 1309 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 813 1285 N 131 -24 V 76 41 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 3316 838 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 3448 815 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.80 C gsave 3580 791 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3711 768 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3843 744 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 361 1419 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 493 1395 N 132 -22 V 76 39 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 757 1349 N 132 -23 V 76 40 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 625 1373 N 132 -24 V 76 40 V -132 23 V -76 -39 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 514 1500 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 965 1366 N 132 -23 V 76 41 V -132 22 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 833 1389 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 701 1412 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 569 1436 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.81 C gsave 437 1460 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 1.00 1.00 C gsave 3919 785 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3788 808 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3656 832 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3524 855 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 3392 879 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 889 1326 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -1.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -0.50 0.50 0.50 C 1208 1625 N -72 39 V --72 -39 V -Z stroke -1.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -0.50 0.50 0.50 C 1178 1630 N -33 -6 V --33 6 V -Z stroke -1.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -0.50 0.50 0.50 C 1030 1657 N -112 -20 V --112 20 V -Z stroke -1.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -0.50 0.50 0.50 C 1119 1704 N -23 13 V --23 -13 V -Z stroke -1.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -0.50 0.50 0.50 C 1030 1657 N -72 38 V --72 -38 V -Z stroke -1.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -0.50 0.50 0.50 C 1001 1641 N -10 5 V --10 -5 V -Z stroke -1.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -0.50 0.50 0.50 C 873 1664 N -72 1237 L -801 427 V -Z stroke -1.000 UL -LTb -LCb 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132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 285 1755 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 417 1731 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 549 1708 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1609 1899 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.74 C gsave 2926 1664 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.80 0.80 C gsave 2794 1687 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.86 C gsave 2662 1711 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2531 1734 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2399 1758 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.86 C gsave 2268 1781 N 131 -23 V 76 40 V -132 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2136 1805 N 132 -24 V 75 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 2004 1828 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 1873 1852 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1741 1875 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.87 C gsave 3058 1640 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 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1646 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 2454 1693 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 1949 1892 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 3266 1657 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.74 C gsave 3134 1681 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.65 0.65 C gsave 3002 1704 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2870 1728 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.86 C gsave 2738 1751 N 132 -23 V 76 41 V -131 23 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2607 1775 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2475 1798 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.86 C gsave 2343 1822 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.84 C gsave 2212 1845 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 2080 1869 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 1249 1800 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1817 1916 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.82 C gsave 1685 1939 N 132 -23 V 76 41 V 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0.85 0.84 C gsave 1644 2106 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.87 C gsave 1512 2130 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.92 0.92 C gsave 1381 2153 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.83 0.83 C gsave 1249 2177 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 1117 2200 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 985 2224 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 853 2247 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 722 2271 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 590 2294 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 1041 2159 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 909 2183 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 777 2206 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.81 0.81 C gsave 2303 1989 N 131 -24 V 76 41 V -132 23 V -75 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.83 C gsave 2434 1965 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.90 0.90 C gsave 2566 1942 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.85 C gsave 2698 1918 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.87 C gsave 2830 1894 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.87 C gsave 2961 1871 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 666 2335 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 798 2311 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 929 2288 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.76 0.76 C gsave 1061 2264 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1193 2241 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash 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-0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 473 2044 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 341 2067 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 209 2091 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 660 1956 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 529 1979 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 397 2003 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 285 2131 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 133 2050 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 584 1915 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 452 1939 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 321 1962 N 131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 189 1986 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.85 0.84 C gsave 3266 2034 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.92 C gsave 57 2009 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 645 2230 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 417 2108 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 549 2084 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 681 2061 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.74 0.73 C gsave 813 2037 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 361 2172 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 493 2149 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 625 2125 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.93 C gsave 757 2102 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 889 2078 N 131 -24 V 77 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 437 2213 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 569 2189 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.82 0.82 C gsave 701 2166 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.93 0.93 C gsave 833 2142 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.88 0.88 C gsave 965 2119 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 514 2254 N 131 -24 V 77 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2399 2134 N 132 -23 V 76 40 V 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0.89 0.89 C gsave 2531 2111 N 131 -24 V 76 41 V -131 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.71 0.71 C gsave 1158 2410 N 132 -23 V 76 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.84 0.83 C gsave 2268 2158 N 131 -24 V 76 41 V -132 24 V -75 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 2136 2181 N 132 -23 V 75 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.76 C gsave 2004 2205 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.78 C gsave 1873 2228 N 131 -23 V 76 41 V -131 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.77 C gsave 1741 2252 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.75 0.75 C gsave 1609 2275 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill 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131 -23 V 77 40 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.77 0.76 C gsave 2080 2246 N 132 -24 V 76 41 V -131 23 V -77 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.79 0.79 C gsave 2212 2222 N 131 -23 V 76 40 V -131 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.87 0.86 C gsave 2343 2199 N 132 -24 V 76 41 V -132 23 V -76 -40 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2475 2175 N 132 -24 V 76 41 V -132 24 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.89 0.89 C gsave 2607 2151 N 131 -23 V 77 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.86 0.86 C gsave 2738 2128 N 132 -24 V 76 41 V -131 24 V -77 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor -[] 0 setdash -1.00 0.50 0.49 C gsave 2870 2104 N 132 -23 V 76 41 V -132 23 V -76 -41 V 1 PolyFill -0.000 UL -LTb -LCb setrgbcolor 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