Content-Type: multipart/mixed; boundary="-------------0409210533372" This is a multi-part message in MIME format. ---------------0409210533372 Content-Type: text/plain; name="04-294.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-294.keywords" planar vector fields,uniqueness of limit cycles ---------------0409210533372 Content-Type: application/x-tex; name="carletti.tex" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="carletti.tex" %&LaTeX \documentclass{amsart} \usepackage{amsmath,amsfonts} \usepackage{amscd,amsthm} \usepackage[dvips]{epsfig} % COSTRUZIONI % \newcommand{\R}{\mathop{\mathbb{R}}} \newcommand{\Q}{\mathop{\mathbb{Q}}} \newcommand{\Z}{\mathop{\mathbb{Z}}} \newcommand{\N}{\mathop{\mathbb{N}}} \newcommand{\C}{\mathop{\mathbb{C}}} \newcommand{\D}{\mathop{\mathbb{D}}} \newcommand{\Lip}[1]{\mathop{\mathit{Lip}\left( #1 \right)}} % ENVIRONMENTS ET AL. % \theoremstyle{plain} %% This is the default \newtheorem{theorem}{Theorem}[section] \newtheorem{corollary}[theorem]{Corollary} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{definition}[theorem]{Definition} \newtheorem{remark}[theorem]{Remark} \newtheorem{notation}[theorem]{Notation} \renewcommand{\thenotation}{} \numberwithin{equation}{section} \begin{document} \title{Uniqueness of limit cycles for a class of planar vector fields.} \author{Timoteo Carletti} \date{\today} \address[Timoteo Carletti]{Scuola Normale Superiore, piazza dei Cavalieri 7, 56126 Pisa, Italy} \email[Timoteo Carletti]{t.carletti@sns.it} \keywords{planar vector fields,uniqueness of limit cycles} \begin{abstract} In this paper we give sufficient conditions to ensure uniqueness of limit cycles for a class of planar vector fields. We also exhibit a class of examples with exactly one limit cycle. \end{abstract} \maketitle \section{Introduction} \label{sec:intro} In this paper we consider the problem of determine the number of limit cycles, i.e. isolated closed trajectories, for planar vector fields. This is a classical problem, included as part of the XVI Hilbert's problem. The literature is huge and still growing, for a review see~\cite{Sansone} and the more recent~\cite{Zhang,Ye}. An important subproblem is to study systems with a unique limit cycle, in fact in this case the dynamics of the cycle can ''dominate'' the global dynamics of the whole system. Let us consider planar vector fields of the form: % \begin{equation} \label{eq:vf} \begin{cases} \dot x &= \beta(x)\left[ \phi(y)-F(x,y)\right] \\ \dot y &= -\alpha(y)g(x) \, , \end{cases} \end{equation} % under the regularity assumptions (to ensure the existence and uniqueness of the Cauchy initial problem) there exists: $-\infty \leq a<0 0$ and let us consider the energy level $\mathcal{H}_{\lambda}= \{ (x,y)\in \R^2: \Phi(y)+G(x)~=~\lambda \}$, the knowledge of the flow through $\mathcal{H}_{\lambda}$ can give informations about the existence of limit cycles. Because \begin{equation*} <\nabla \mathcal{H}_{\lambda}, X(x,y)>\Big \rvert_{\mathcal{H}_{\lambda}}=-F(x,y)g(x) \, , \end{equation*} where $X(x,y)= (\phi(y)-F(x,y),-g(x))$, no limit cycles can be completely contained in a region where $gF$ doesn't change sign. We will see in a while that the set of zeros of $F$ will play a fundamental role in our construction. For Li\'enard systems the set of zeros of $F$ is given by vertical lines $x=x_k$ s.t. $F(x_k)=0$. In a recent paper~\cite{SabatiniVillari} authors, using ideas taken from Li\'enard systems~\cite{CarlettiVillari}, proved a uniqueness result for systems~\eqref{eq:vecfiel} assuming that $F(x,y)$ vanishes only at three vertical lines $x=x_-<0$, $x=0$ and $x=x_+>0$. We generalize this condition by assuming that zeros of $F(x,y)$ lie on (quite) general curves. More precisely let us assume there exist $\psi_j:\R \rightarrow \R$, $j\in \{1,2\}$, such that~\footnote{We remark that our main result still holds, even if one assume there exist $\alpha_j<0<\beta_j$, $j\in \{1,2\}$, and the functions $\psi_j$ to be defined in $[\alpha_j,\beta_j]$ and verify hypothesis B) on their new domain of definition.}: %% $-\infty \leq \alpha_j<0<\beta_j \leq +\infty$ and functions %% $\psi_j:[\alpha,\beta]\rightarrow \R$, $j\in \{1,2\}$, such that: \begin{enumerate} \item[B0)] $F(0,y)=0$ for all real $y$; \item[B1)] $y\mapsto\psi_1(y)$, is {\em positive} for all $y\in \R $, increasing for negative $y$, decreasing for positive $y$, $\psi_1(0) < b$; \item[B2)] $y\mapsto\psi_2(y)$, is {\em negative} for all $y\in \R$, decreasing for negative $y$, increasing for positive $y$, $\psi_2(0) > a$; \item[B3)] for all $y\in \R$, $j\in \{ 1,2 \}$, we have: %% \item[B1)] $y\mapsto\psi_1(y)$, is {\em positive} for all $y\in [\alpha_1,\beta_1]$, %% increasing for negative $y$, decreasing for positive $y$, $\psi_1(0) < b$; %% \item[B2)] $y\mapsto\psi_2(y)$, is {\em negative} for all $y\in [\alpha_2,\beta_2]$, %% decreasing for negative $y$, increasing for positive $y$, $\psi_2(0) > a$; %% \item[B3)] for all $y\in [\alpha_j,\beta_j]$, $j\in \{ 1,2 \}$, we have: % \begin{equation*} F(\psi_j(y),y)\equiv 0 \, , \end{equation*} % these curves will be called ''non--trivial zeros'' of $F(x,y)$ (in opposition with the trivial zeros given by $x=0$). \end{enumerate} Let us divide the strip $(a,b)\times \R $ into four distinct domains: %% Let us divide the (possible unbounded) rectangles $(a,b)\times [\alpha_j,\beta_j]$ %% into four distinct domains: \begin{itemize} \item $D_1^{>}:=\{ (x,y) \in (a,b)\times \R : x > \psi_1(y) \}$; \item $D_1^{<}:=\{ (x,y) \in (a,b)\times \R : 0}:=\{ (x,y) \in (a,b)\times \R : \psi_2(y) < x < 0 \}$; \item $D_2^{<}:=\{ (x,y) \in (a,b)\times \R : x < \psi_2(y) \}$. %% \item $D_1^{>}:=\{ (x,y) \in (a,b)\times [\alpha_1,\beta_1]: x > \psi_1(y) \}$; %% \item $D_1^{<}:=\{ (x,y) \in (a,b)\times [\alpha_1,\beta_1]: 0}:=\{ (x,y) \in (a,b)\times [\alpha_2,\beta_2]: \psi_2(y) < x < 0 \}$; %% \item $D_2^{<}:=\{ (x,y) \in (a,b)\times [\alpha_2,\beta_2]: x < \psi_2(y) \}$. \end{itemize} The following assumptions generalize ''standard sign ones'': \begin{enumerate} \item[C1)] $y\phi(y)>0$ for all $y\neq 0$ and $xg(x) >0$ for all $x\in (a,b)\setminus \{ 0 \}$; \item[C2)] $g(x)F(x,y)<0$ for all $(x,y)\in D_1^< \cup D_2^>$. \end{enumerate} We remark that hypothesis C2) can be weakened into: \begin{enumerate} \item[C2')] $g(x)F(x,y)\leq 0$ for all $(x,y)\in D_1^< \cup D_2^>$ except at some $(x_0,y_0)$ where strictly inequality holds. \end{enumerate} With these hypotheses we ensures that $(0,0)$ is the only singular point of system~\eqref{eq:vecfiel} and trajectories wind clockwise around it. We are now able to state our main result % \begin{theorem} \label{thm:main} Let us consider system~\eqref{eq:vecfiel} and let us assume Hypotheses A), B) and C) to hold. Then there is at most one limit cycles which intersect both curves $x=\psi_1(y)$ and $x=\psi_2(y)$ contained in $(a,b)\times \R$, provided: \begin{enumerate} \item[D1)] the function $y\mapsto F(x,y)/\phi(y)$ is strictly increasing for $(x,y) \in D_1^{<}$ and $y\neq 0$; \item[D2)] the function $y\mapsto F(x,y)/\phi(y)$ is strictly decreasing for $(x,y) \in D_2^{>}$ and $y\neq 0$; \item[E)] the function $x\mapsto F(x,y)$ is positive in $D_1^{>}$, negative in $D_2^{<}$ and increasing in $D_1^{>} \cup D_2^{<}$; \item[F)] let $A_j(y)=\left[\phi(y)\partial_x F(x,y)-g(x)\partial_y F(x,y)\right]\Big \rvert_{x=\psi_j(y)}$, then $A_j(y)y>0$ for $y\neq 0$, $j\in \{1,2\}$. \end{enumerate} \end{theorem} % Hypotheses D) and E) naturally generalize hypotheses used in the Li\'enard case~\cite{CarlettiVillari} or in the more general situation studied in~\cite{SabatiniVillari}. Also hypothesis F) is very natural: each closed trajectory intersects the non--trivial zeros of $F(x,y)$ at most once in any quadrant. We remark that this condition is trivially verified if the functions $\psi_j$ are indentically constant, namely in the case considered in~\cite{SabatiniVillari}. The proof of this result will be given in the next section. In the last section (\S~\ref{sec:example}) we will provide a family of systems with exactly one limit cycle. \section{Proof of Theorem~\ref{thm:main}} \label{sec:proof} The aim of this section is to prove our main result Theorem~\ref{thm:main}. The proof is based on the following remark, % \begin{remark} \label{rem:integral} Along any closed curve $\gamma:[0,T]\rightarrow (a,b)\times \R$ one has: % \begin{equation*} \int_0^T \frac{d}{dt}H\Big \rvert_{\text{flow}}\circ \gamma(s) \, ds = H\circ \gamma (T)- H\circ \gamma (0) =0 \, , \end{equation*} % moreover if $\gamma$ is an integral curve of system~\eqref{eq:vecfiel} we can evaluate the integrand function to obtain: % \begin{equation} \label{eq:intzero} I_{\gamma}:=\int_0^T g(x_{\gamma}(s)) F(x_{\gamma}(s),y_{\gamma}(s)) \, ds = 0 \, , \end{equation} % where $\gamma(s)=(x_{\gamma}(s),y_{\gamma}(s))$. \end{remark} % The uniqueness result will be proved by showing that the existence of two limit cycles, $\gamma_1$ contained~\footnote{By this we mean $\gamma_1$ is properly contained in the compact set whose boundary is $\gamma_2$.} in $\gamma_2$, both intersecting $x=\psi_1(y)$ and $x=\psi_2(y)$, will imply: $I_{\gamma_1}< I_{\gamma_2}$, which contradicts~\eqref{eq:intzero}. From now on we will assume the existence of two limit cycles, $\gamma_1$ contained in $\gamma_2$, which intersect both non--trivial zeros of $F$. Let us now consider the set of zeros of the equation: $\phi(y)-F(x,y)=0$ inside $D_1^< \cup D_2^>$; we claim that this set is the graph of some function $x\mapsto \zeta(x)$. Moreover this function vanishes for $x\in \{\psi_2(0),0,\psi_1(0) \}$, it is positive for $x\in (\psi_2(0),0)$ and negative for $x\in (0,\psi_1(0))$. The first statement follows from hypotheses D). In fact, let assume the claim to be false, then there exist $(\bar x,y_k)\in D_2^>$, such that: % \begin{equation*} y_1 < y_2 \quad \text{and} \quad \phi(y_k)-F(\bar x,y_k)=0 \quad k\in\{1,2\} \, . \end{equation*} % Then using the decreasing property (hypothesis D)) we obtain a contradiction: % \begin{equation*} 0=\left[F(\bar x,y_1)-\phi(y_1)\right]/\phi(y_1)> \left[F(\bar x,y_2)-\phi(y_2)\right]/\phi(y_2)=0\, . \end{equation*} % We can do the same construction for $D_1^<$, and the statement is proved. The sign properties of $\zeta$ can be proved as follows. Let $\psi_2(0)0$. The case $0=\left[\phi(y)\partial_x F(x,y) -g(x)\partial_y F(x,y)\right]\Big\rvert_{\mathcal{F}_0} =A_j(y)\quad j\in \{1,2 \} \, . \end{equation*} % For instance, because the angle between the vector field and $\{ (x,y): x=\psi_1(y) \}\cap \{ y >0 \}$ is in absolute value smaller than $\pi/2$, a trajectory starting at $(0,\bar{y})$, for some $\bar{y}>0$, which will intersect $\{ (x,y): x=\psi_1(y) \}\cap \{ y >0 \}$, could not meet anew $\{ (x,y): x=\psi_1(y) \}\cap \{ y >0 \}$. From hypotheses D) and the sign of $F$ on $D_2^< \cup D_1^>$, it follows easily that for all $(x,y)\in D_2^< \cup D_1^>$ one has: $\left(y-\zeta(x)\right)\left(\phi(y)-F(x,y)\right)>0$. Hence a cycle intersects $\left(D_2^< \cup D_1^>\right)\cap \{ y>0 \}$ in a region where $\phi(y)-F(x,y)>0$, whereas the intersection with $\left(D_2^< \cup D_1^>\right)\cap \{ y<0 \}$ holds where $\phi(y)-F(x,y)<0$. This remark allows us to divide the path of integration needed to evaluate $I_{\gamma_j}$, $j\in \{1,2\}$, in two parts: an ''horizontal'' one where $\dot x >0$ and a vertical one, where $\dot x$ vanishes. Let us define (see Figure~\ref{fig:figura1}), for $j\in \{1,2\}$, $A_j$ (respectively $B_j$) the intersection point of $\gamma_j$ with $x=\psi_1(y)$ for $y>0$ (respectively $y<0$), and $C_j$ (respectively $D_j$) the intersection point of $\gamma_j$ with $x=\psi_2(y)$ for $y<0$ (respectively $y>0$). Let also introduce, $A_*$ being the intersection point of $\gamma_1$ and the line $x=x_{A_2}$ contained in the first quadrant, and $A_{**}$ being the intersection point of $\gamma_2$ and the line $y=y_{A_1}$ contained in the first quadrant. Similarly we introduce points: $B_*$, $B_{**}$, $C_*$, $C_{**}$ and $D_*$, $D_{**}$ (see Figure~\ref{fig:figura1}). \begin{center} \begin{figure}[ht] \makebox{ \epsfig{file=figura1.eps,height=12cm,width=12cm,angle=-90}} \caption{The non--trivial zeros of $F$ (thick), the limit cycles $\gamma_1$ and $\gamma_2$ (thin) intersecting both non--trivial zeros of $F$ and their subdivision into arcs.} \label{fig:figura1} \end{figure} \end{center} According to this subdivision of the arcs of limit cycles, we evaluate $I_{\gamma_j}$ as follows: % \begin{eqnarray} \label{eq:sudiv} I_{\gamma_1}=\int_{ {D_*A_*}}+\int_{{A_*A_1}}+ \int_{ {A_1B_1}}+ \int_{ {B_1B_*}}+ \int_{ {A_*C_*}}+ \int_{ {C_*C_1}}+ \int_{ {C_1D_1}}+ \int_{ {D_1D_*}} \\ I_{\gamma_2}=\int_{ {D_2A_2}}+\int_{ {A_2A_{**}}} +\int_{ {A_{**}B_{**}}}+\int_{ {B_{**}B_2}} +\int_{ {B_2C_2}}+\int_{ {C_{2}C_{**}}} +\int_{ {C_{**}D_{**}}}+\int_{ {D_{**}D_2}} \notag\, . \end{eqnarray} % Let now show that $I_{\gamma_1}y_1(x)$ for all $x\in (x_{D_*},x_{A_*})$, using hypotheses D) and the sign assumptions C) we get: % \begin{equation*} \frac{g(x)F(x,y_1(x))}{\phi(y_1(x))-F(x,y_1(x))} < \frac{g(x)F(x,y_2(x))}{\phi(y_2(x))-F(x,y_2(x))} \, , \end{equation*} % hence: % \begin{eqnarray} \label{eq:d1a1} \int_{x_{D_{1}}}^{x_{A_{1}}} \frac{g(x) F(x,y_1(x))}{\phi(y_1(x))-F(x,y_1(x))} \, dx & < \int_{x_{D_{1}}}^{x_{D_{*}}} \frac{g(x) F(x,y_1(x))}{\phi(y_1(x))-F(x,y_1(x))} \, dx+\int_{x_{A_*}}^{x_{A_1}} \frac{g(x) F(x,y_1(x))}{\phi(y_1(x))-F(x,y_1(x))} \, dx \notag \\ &+\int_{x_{D_2}}^{x_{A_2}} \frac{g(x) F(x,y_2(x))}{\phi(y_2(x))-F(x,y_2(x))} \, dx \leq \int_{x_{D_2}}^{x_{A_2}} \frac{g(x) F(x,y_2(x))}{\phi(y_2(x))-F(x,y_2(x))} \, dx \, , \end{eqnarray} % the last step follows because the integrand function is negative by hypothesis C2) and from the previous discussion on the sign of $\phi(y)-F(x,y)$. In a very similar way we can prove that: % \begin{equation} \label{eq:b1c1} \int_{x_{B_{1}}}^{x_{C_{1}}} \frac{g(x) F(x,y_1(x))}{\phi(y_1(x))-F(x,y_1(x))} \, dx < \int_{x_{B_2}}^{x_{C_2}} \frac{g(x) F(x,y_2(x))}{\phi(y_2(x))-F(x,y_2(x))} \, dx \, . \end{equation} % \subsection{Integration along ''vertical arcs''.} \label{ssec:intvert} Along vertical arcs $\dot y$ never vanishes, hence we can perform the integration w.r.t. the $y$ variable and getting for example: % \begin{equation*} \int_{ {A_jB_j}}g(x)F(x,y)\, dt= \int_{y_{B_j}}^{y_{A_j}} F(x_j(y),y)\, dy \, , \end{equation*} % where $x_j(y)$, $j\in \{1,2 \}$, is the parametrization of $\gamma_j$ as graph over $y$ for $y\in(y_{B_j},y_{A_j})$. Because $x_2(y)>x_1(y)$ for all $y\in (y_{A_{**}},y_{B_{**}})$, from hypotheses E) and the definition of $A_{**}$ and $B_{**}$, we get: % \begin{equation*} \int_{y_{B_{1}}}^{y_{A_{1}}} F(x_1(y),y)\, dy < \int_{y_{B_{**}}}^{y_{A_{**}}} F(x_2(y),y)\, dy \, . \end{equation*} % Again from the sign assumption on $F$ in $D_1^{>}$, we get: % \begin{equation*} \int_{y_{A_{**}}}^{y_{A_{2}}} F(x_2(y),y)\, dy >0 \quad\text{and}\quad \int_{y_{B_{2}}}^{y_{B_{**}}} F(x_2(y),y)\, dy >0 \, , \end{equation*} % hence we obtain: % \begin{equation} \label{eq:a2b2} \int_{y_{B_1}}^{y_{A_1}} F(x_1(y),y)\, dy <\int_{y_{B_2}}^{y_{A_2}} F(x_2(y),y)\, dy \, . \end{equation} % Analogously we can prove that: % \begin{equation} \label{eq:c2d2} \int_{y_{C_1}}^{y_{D_1}} F(x_1(y),y)\, dy <\int_{y_{C_2}}^{y_{D_2}} F(x_2(y),y)\, dy \, . \end{equation} % \subsection{Conclusion of the proof.} \label{ssec:concpro} We are now able to complete our proof. In fact from~\eqref{eq:d1a1} and~\eqref{eq:b1c1} of \S~\ref{ssec:intoriz}, from~\eqref{eq:a2b2} and~\eqref{eq:c2d2} of \S~\ref{ssec:intvert} and the subdivision~\eqref{eq:sudiv} we get: % \begin{equation*} I_{\gamma_1}$ and it is tangent to $x=\psi_j(y)$ at $y=0$, for $j\in \{ 1,2\}$, thus any limit cycle must intersect both curves $x=\psi_j(y)$, $j\in \{ 1,2\}$.} from (1) and (2) plus some easy calculations that we omit. \begin{thebibliography}{XXX} \bibitem[CV2003]{CarlettiVillari} T. Carletti and G. Villari: {\it A note on existence and uniqueness of limit cycles for Li\'enard systems}, preprint, Univ. Firenze (2003), {\bf 16}. \bibitem[SV2004]{SabatiniVillari} M. Sabatini and G. Villari: {\it About limit cycle's uniqueness for a class of generalized Li\'enard systems}, preprint, Univ. Trento (2004), {\bf 672}. \bibitem[CS1964]{Sansone} R. Conti e G. Sansone: {\it Non--linear differential equations}, Pergamon Press, (1964). \bibitem[Ye1986]{Ye} Ye Yanquia et al.: {\it Theory of limit cycles}, Trans. Math. Monog., Vol. 66, Americ. Math. Soc., Providence, Rhode Island, (1986). \bibitem[Zh1992]{Zhang} Zhang Zhi-fen et al.: {\it Qualitative Theory of differential equations}, Trans. Math. Monog., Vol. 101, Americ. Math. Soc., Providence, Rhode Island, (1992). \end{thebibliography} \end{document} ---------------0409210533372 Content-Type: application/postscript; name="figura1.eps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="figura1.eps" %!PS-Adobe-3.0 EPSF-2.0 %%Title: Maple plot %%Creator: Maple %%Pages: 1 %%BoundingBox: 72 72 540 719 %%DocumentNeededResources: font Helvetica %%EndComments 20 dict begin gsave /drawborder true def /m {moveto} def /l {lineto} def /C {setrgbcolor} def /Y /setcmykcolor where { %%ifelse Use built-in operator /setcmykcolor get }{ %%ifelse Emulate setcmykcolor with setrgbcolor { %%def 1 sub 3 { %%repeat 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor } bind } ifelse def /G {setgray} def /S {stroke} def /NP {newpath} def %%%%This draws a filled polygon and avoids bugs/features %%%% of some postscript interpreters %%%%GHOSTSCRIPT: has a bug in reversepath - removing %%%%the call to reversepath is a sufficient work around /P {gsave fill grestore reversepath stroke} def %%%%This function is needed for drawing text. 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2457 3333 l S NP 2906 3460 m 2688 3411 l S NP 3167 3495 m 2906 3460 l S NP 3460 3507 m 3167 3495 l S NP 3767 3495 m 3460 3507 l S NP 4049 3464 m 3767 3495 l S NP 4372 3408 m 4049 3464 l S NP 4682 3335 m 4372 3408 l S NP 4982 3247 m 4682 3335 l S NP 5252 3152 m 4982 3247 l S NP 5489 3053 m 5252 3152 l S NP 5710 2942 m 5489 3053 l S NP 5889 2828 m 5710 2942 l S NP 6019 2715 m 5889 2828 l S NP 6090 2615 m 6019 2715 l S NP 6119 2500 m 6090 2615 l S NP 3461 4413 m 3461 4500 l S NP 3461 4332 m 3461 4413 l S NP 3461 4247 m 3461 4332 l S NP 3461 4168 m 3461 4247 l S NP 3461 4079 m 3461 4168 l S NP 3461 4002 m 3461 4079 l S NP 3461 3918 m 3461 4002 l S NP 3461 3833 m 3461 3918 l S NP 3461 3750 m 3461 3833 l S NP 3461 3664 m 3461 3750 l S NP 3461 3582 m 3461 3664 l S NP 3461 3498 m 3461 3582 l S NP 3461 3417 m 3461 3498 l S NP 3461 3331 m 3461 3417 l S NP 3461 3253 m 3461 3331 l S NP 3461 3167 m 3461 3253 l S NP 3461 3086 m 3461 3167 l S NP 3461 2996 m 3461 3086 l S NP 3461 2915 m 3461 2996 l S NP 3461 2831 m 3461 2915 l S NP 3461 2745 m 3461 2831 l S NP 3461 2662 m 3461 2745 l S NP 3461 2586 m 3461 2662 l S NP 3461 2498 m 3461 2586 l S NP 3461 2413 m 3461 2498 l S NP 3461 2334 m 3461 2413 l S NP 3461 2248 m 3461 2334 l S NP 3461 2166 m 3461 2248 l S NP 3461 2080 m 3461 2166 l S NP 3461 2001 m 3461 2080 l S NP 3461 1912 m 3461 2001 l S NP 3461 1836 m 3461 1912 l S NP 3461 1746 m 3461 1836 l S NP 3461 1670 m 3461 1746 l S NP 3461 1587 m 3461 1670 l S NP 3461 1500 m 3461 1587 l S NP 3461 1414 m 3461 1500 l S NP 3461 1337 m 3461 1414 l S NP 3461 1250 m 3461 1337 l S NP 3461 1165 m 3461 1250 l S NP 3461 1081 m 3461 1165 l S NP 3461 998 m 3461 1081 l S NP 3461 919 m 3461 998 l S NP 3461 834 m 3461 919 l S NP 3461 748 m 3461 834 l S NP 3461 663 m 3461 748 l S NP 3461 587 m 3461 663 l S NP 3461 500 m 3461 587 l S thick setlinewidth NP 2907 4414 m 2907 4500 l S NP 2907 4243 m 2907 4414 l S NP 2907 4096 m 2907 4243 l S NP 2907 3968 m 2907 4096 l S NP 2907 3831 m 2907 3968 l S NP 2907 3705 m 2907 3831 l S NP 2907 3567 m 2907 3705 l S NP 2905 3438 m 2907 3567 l S NP 2896 3294 m 2905 3438 l S NP 2887 3229 m 2896 3294 l S NP 2872 3164 m 2887 3229 l S NP 2848 3097 m 2872 3164 l S NP 2812 3030 m 2848 3097 l S NP 2788 2996 m 2812 3030 l S NP 2761 2961 m 2788 2996 l S NP 2731 2927 m 2761 2961 l S NP 2697 2893 m 2731 2927 l S NP 2661 2860 m 2697 2893 l S NP 2623 2827 m 2661 2860 l S NP 2584 2793 m 2623 2827 l S NP 2545 2760 m 2584 2793 l S NP 2509 2730 m 2545 2760 l S NP 2475 2699 m 2509 2730 l S NP 2444 2668 m 2475 2699 l S NP 2415 2637 m 2444 2668 l S NP 2369 2567 m 2415 2637 l S NP 2353 2496 m 2369 2567 l S NP 2371 2428 m 2353 2496 l S NP 2416 2360 m 2371 2428 l S NP 2445 2329 m 2416 2360 l S NP 2478 2298 m 2445 2329 l S NP 2513 2266 m 2478 2298 l S NP 2550 2235 m 2513 2266 l S NP 2591 2200 m 2550 2235 l S NP 2631 2166 m 2591 2200 l S NP 2669 2132 m 2631 2166 l S NP 2706 2097 m 2669 2132 l S NP 2737 2065 m 2706 2097 l S NP 2766 2032 m 2737 2065 l S NP 2792 1999 m 2766 2032 l S NP 2814 1966 m 2792 1999 l S NP 2850 1897 m 2814 1966 l S NP 2874 1828 m 2850 1897 l S NP 2888 1765 m 2874 1828 l S NP 2897 1702 m 2888 1765 l S NP 2905 1560 m 2897 1702 l S NP 2907 1438 m 2905 1560 l S NP 2907 1294 m 2907 1438 l S NP 2907 1172 m 2907 1294 l S NP 2907 1039 m 2907 1172 l S NP 2907 900 m 2907 1039 l S NP 2907 749 m 2907 900 l S NP 2907 589 m 2907 749 l S NP 2907 500 m 2907 589 l S thin setlinewidth NP 6110 2500 m 6230 2500 l S NP 5998 2500 m 6110 2500 l S NP 5881 2500 m 5998 2500 l S NP 5771 2500 m 5881 2500 l S NP 5648 2500 m 5771 2500 l S NP 5541 2500 m 5648 2500 l S NP 5425 2500 m 5541 2500 l S NP 5307 2500 m 5425 2500 l S NP 5193 2500 m 5307 2500 l S NP 5073 2500 m 5193 2500 l S NP 4959 2500 m 5073 2500 l S NP 4843 2500 m 4959 2500 l S NP 4731 2500 m 4843 2500 l S NP 4613 2500 m 4731 2500 l S NP 4505 2500 m 4613 2500 l S NP 4385 2500 m 4505 2500 l S NP 4273 2500 m 4385 2500 l S NP 4148 2500 m 4273 2500 l S NP 4036 2500 m 4148 2500 l S NP 3920 2500 m 4036 2500 l S NP 3801 2500 m 3920 2500 l S NP 3687 2500 m 3801 2500 l S NP 3580 2500 m 3687 2500 l S NP 3458 2500 m 3580 2500 l S NP 3341 2500 m 3458 2500 l S NP 3232 2500 m 3341 2500 l S NP 3113 2500 m 3232 2500 l S NP 2999 2500 m 3113 2500 l S NP 2880 2500 m 2999 2500 l S NP 2771 2500 m 2880 2500 l S NP 2648 2500 m 2771 2500 l S NP 2542 2500 m 2648 2500 l S NP 2417 2500 m 2542 2500 l S NP 2312 2500 m 2417 2500 l S NP 2197 2500 m 2312 2500 l S NP 2077 2500 m 2197 2500 l S NP 1957 2500 m 2077 2500 l S NP 1851 2500 m 1957 2500 l S NP 1731 2500 m 1851 2500 l S NP 1614 2500 m 1731 2500 l S NP 1496 2500 m 1614 2500 l S NP 1383 2500 m 1496 2500 l S NP 1273 2500 m 1383 2500 l S NP 1155 2500 m 1273 2500 l S NP 1036 2500 m 1155 2500 l S NP 918 2500 m 1036 2500 l S NP 813 2500 m 918 2500 l S NP 692 2500 m 813 2500 l S thick setlinewidth NP 3738 4414 m 3738 4500 l S NP 3738 4243 m 3738 4414 l S NP 3738 4096 m 3738 4243 l S NP 3739 3968 m 3738 4096 l S NP 3742 3831 m 3739 3968 l S NP 3750 3705 m 3742 3831 l S NP 3769 3567 m 3750 3705 l S NP 3809 3438 m 3769 3567 l S NP 3844 3366 m 3809 3438 l S NP 3892 3294 m 3844 3366 l S NP 3948 3229 m 3892 3294 l S NP 4017 3164 m 3948 3229 l S NP 4101 3097 m 4017 3164 l S NP 4198 3030 m 4101 3097 l S NP 4251 2996 m 4198 3030 l S NP 4306 2961 m 4251 2996 l S NP 4363 2927 m 4306 2961 l S NP 4421 2893 m 4363 2927 l S NP 4531 2827 m 4421 2893 l S NP 4634 2760 m 4531 2827 l S NP 4716 2699 m 4634 2760 l S NP 4782 2637 m 4716 2699 l S NP 4830 2567 m 4782 2637 l S NP 4846 2496 m 4830 2567 l S NP 4828 2428 m 4846 2496 l S NP 4781 2360 m 4828 2428 l S NP 4713 2298 m 4781 2360 l S NP 4627 2235 m 4713 2298 l S NP 4575 2200 m 4627 2235 l S NP 4520 2166 m 4575 2200 l S NP 4464 2132 m 4520 2166 l S NP 4406 2097 m 4464 2132 l S NP 4297 2032 m 4406 2097 l S NP 4193 1966 m 4297 2032 l S NP 4094 1897 m 4193 1966 l S NP 4009 1828 m 4094 1897 l S NP 3943 1765 m 4009 1828 l S NP 3890 1702 m 3943 1765 l S NP 3843 1631 m 3890 1702 l S NP 3808 1560 m 3843 1631 l S NP 3771 1438 m 3808 1560 l S NP 3750 1294 m 3771 1438 l S NP 3742 1172 m 3750 1294 l S NP 3739 1039 m 3742 1172 l S NP 3738 900 m 3739 1039 l S NP 3738 749 m 3738 900 l S NP 3738 589 m 3738 749 l S NP 3738 500 m 3738 589 l S thin setlinewidth medium setlinewidth (x) dup 0 stringbbox 2600 exch sub exch 2 idiv 6400 exch sub exch m show (y) dup 0 stringbbox 4600 exch sub exch 2 idiv 3400 exch sub exch m show %(g1 \(t\)) dup 0 stringbbox 3600 exch sub exch 2 idiv 4600 exch sub exch m show %(g2 \(t\)) dup 0 stringbbox 2840 exch sub exch 2 idiv 5500 exch sub exch m show (A) dup 0 stringbbox 3650 exch sub exch 2 idiv 3900 exch sub exch m show (2) dup 0 stringbbox 3600 exch sub exch 2 idiv 3980 exch sub exch m show (A) dup 0 stringbbox 3100 exch sub exch 2 idiv 4400 exch sub exch m show (1) dup 0 stringbbox 3050 exch sub exch 2 idiv 4480 exch sub exch m show (A) dup 0 stringbbox 3150 exch sub exch 2 idiv 3900 exch sub exch m show (*) dup 0 stringbbox 3100 exch sub exch 2 idiv 3980 exch sub exch m show (A) dup 0 stringbbox 3150 exch sub exch 2 idiv 5800 exch sub exch m show (**) dup 0 stringbbox 3050 exch sub exch 2 idiv 5880 exch sub exch m show (B) dup 0 stringbbox 1440 exch sub exch 2 idiv 3880 exch sub exch m show (2) dup 0 stringbbox 1390 exch sub exch 2 idiv 3960 exch sub exch m show (B) dup 0 stringbbox 2000 exch sub exch 2 idiv 4400 exch sub exch m show (1) dup 0 stringbbox 1950 exch sub exch 2 idiv 4480 exch sub exch m show (B) dup 0 stringbbox 1950 exch sub exch 2 idiv 3900 exch sub exch m show (*) dup 0 stringbbox 1900 exch sub exch 2 idiv 3980 exch sub exch m show (B) dup 0 stringbbox 2050 exch sub exch 2 idiv 5800 exch sub exch m show (**) dup 0 stringbbox 1950 exch sub exch 2 idiv 5880 exch sub exch m show (D) dup 0 stringbbox 3650 exch sub exch 2 idiv 2780 exch sub exch m show (2) dup 0 stringbbox 3600 exch sub exch 2 idiv 2860 exch sub exch m show (D) dup 0 stringbbox 3120 exch sub exch 2 idiv 2650 exch sub exch m show (1) dup 0 stringbbox 3070 exch sub exch 2 idiv 2720 exch sub exch m show (D) dup 0 stringbbox 3150 exch sub exch 2 idiv 3000 exch sub exch m show (*) dup 0 stringbbox 3100 exch sub exch 2 idiv 3080 exch sub exch m show (D) dup 0 stringbbox 3100 exch sub exch 2 idiv 1800 exch sub exch m show (**) dup 0 stringbbox 3030 exch sub exch 2 idiv 1880 exch sub exch m show (C) dup 0 stringbbox 1500 exch sub exch 2 idiv 2780 exch sub exch m show (2) dup 0 stringbbox 1450 exch sub exch 2 idiv 2860 exch sub exch m show (C) dup 0 stringbbox 2000 exch sub exch 2 idiv 2650 exch sub exch m show (1) dup 0 stringbbox 1950 exch sub exch 2 idiv 2730 exch sub exch m show (C) dup 0 stringbbox 1950 exch sub exch 2 idiv 3000 exch sub exch m show (*) dup 0 stringbbox 1900 exch sub exch 2 idiv 3080 exch sub exch m show (C) dup 0 stringbbox 2050 exch sub exch 2 idiv 1820 exch sub exch m show (**) dup 0 stringbbox 1950 exch sub exch 2 idiv 1900 exch sub exch m show %thick setlinewidth %A2B2 NP 3790 3500 m 3790 3400 l S NP 3790 3300 m 3790 3200 l S NP 3790 3100 m 3790 3000 l S NP 3790 2900 m 3790 2800 l S NP 3790 2700 m 3790 2600 l S NP 3790 2500 m 3790 2400 l S NP 3790 2300 m 3790 2200 l S NP 3790 2100 m 3790 2000 l S NP 3790 1900 m 3790 1800 l S NP 3790 1700 m 3790 1600 l S NP 3790 1500 m 3790 1490 l S %D2C2 NP 2906 3470 m 2906 3370 l S NP 2906 3270 m 2906 3170 l S NP 2906 3070 m 2906 2970 l S NP 2906 2870 m 2906 2770 l S NP 2906 2670 m 2906 2570 l S NP 2906 2470 m 2906 2370 l S NP 2906 2270 m 2906 2170 l S NP 2906 2070 m 2906 1970 l S NP 2906 1870 m 2906 1770 l S NP 2906 1670 m 2906 1530 l S %D1C1 NP 2750 2950 m 2750 2850 l S NP 2750 2750 m 2750 2650 l S NP 2750 2550 m 2750 2450 l S NP 2750 2350 m 2750 2250 l S NP 2750 2150 m 2750 2050 l S %A1A** NP 3460 2940 m 3560 2940 l S NP 3660 2940 m 3760 2940 l S NP 3860 2940 m 3960 2940 l S NP 4060 2940 m 4160 2940 l S NP 4260 2940 m 4360 2940 l S NP 4460 2940 m 4560 2940 l S NP 4660 2940 m 4760 2940 l S NP 4860 2940 m 4960 2940 l S NP 5060 2940 m 5160 2940 l S NP 5260 2940 m 5360 2940 l S NP 5460 2940 m 5560 2940 l S NP 5660 2940 m 5720 2940 l S %B1B** NP 3460 2060 m 3560 2060 l S NP 3660 2060 m 3760 2060 l S NP 3860 2060 m 3960 2060 l S NP 4060 2060 m 4160 2060 l S NP 4260 2060 m 4360 2060 l S NP 4460 2060 m 4560 2060 l S NP 4660 2060 m 4760 2060 l S NP 4860 2060 m 4960 2060 l S NP 5060 2060 m 5160 2060 l S NP 5260 2060 m 5360 2060 l S NP 5460 2060 m 5560 2060 l S NP 5660 2060 m 5720 2060 l S %D1D** NP 1880 2950 m 1980 2950 l S NP 2080 2950 m 2180 2950 l S NP 2280 2950 m 2380 2950 l S NP 2480 2950 m 2580 2950 l S NP 2680 2950 m 2780 2950 l S NP 2880 2950 m 2980 2950 l S NP 3080 2950 m 3180 2950 l S NP 3280 2950 m 3380 2950 l S %C1C** NP 1880 2050 m 1980 2050 l S NP 2080 2050 m 2180 2050 l S NP 2280 2050 m 2380 2050 l S NP 2480 2050 m 2580 2050 l S NP 2680 2050 m 2780 2050 l S NP 2880 2050 m 2980 2050 l S NP 3080 2050 m 3180 2050 l S NP 3280 2050 m 3380 2050 l S %A1B1 NP 4334 2950 m 4334 2850 l S NP 4334 2750 m 4334 2650 l S NP 4334 2550 m 4334 2450 l S NP 4334 2350 m 4334 2250 l S NP 4334 2150 m 4334 2050 l S boundarythick setlinewidth showpage grestore end %%EOF ---------------0409210533372 Content-Type: application/postscript; name="figura2.eps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="figura2.eps" %!PS-Adobe-3.0 EPSF-2.0 %%Title: Maple plot %%Creator: Maple %%Pages: 1 %%BoundingBox: 72 72 540 719 %%DocumentNeededResources: font Helvetica %%EndComments 20 dict begin gsave /drawborder true def /m {moveto} def /l {lineto} def /C {setrgbcolor} def /Y /setcmykcolor where { %%ifelse Use built-in operator /setcmykcolor get }{ %%ifelse Emulate setcmykcolor with setrgbcolor { %%def 1 sub 3 { %%repeat 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor } bind } ifelse def /G {setgray} def /S {stroke} def /NP {newpath} def %%%%This draws a filled polygon and avoids bugs/features %%%% of some postscript interpreters %%%%GHOSTSCRIPT: has a bug in reversepath - removing %%%%the call to reversepath is a sufficient work around /P {gsave fill grestore reversepath stroke} def %%%%This function is needed for drawing text. It takes two arguments: a %%%%string and a rotation. It outputs width and height. /stringbbox { gsave NP 0 0 m % Set origin for easy calculations. dup rotate exch % Set orientation, and put string on top. false charpath flattenpath 0 exch sub rotate % Undo rotation. pathbbox 4 2 roll pop pop % Get dimens. of our string. 1.1 mul cvi exch 1.1 mul cvi exch % Pad some. grestore} def /thin 3 def /medium 7 def /thick 16 def /boundarythick 20 def % thichess of bounding box %%IncludeResource: font Helvetica 540.000000 72.000000 translate 90 rotate /defaultTitleFont {/Helvetica findfont 219 scalefont setfont} def /defaultFont {/Helvetica findfont 133 scalefont setfont} def 0.0936 0.0936 scale 1 setlinejoin 1 setlinecap 0.0 setgray /inch {72 mul} def /fheight 0.35 inch neg def 0 G medium setlinewidth [] 0 setdash defaultFont thick setlinewidth NP 4352 4169 m 4327 4262 l S NP 4382 4061 m 4352 4169 l S NP 4413 3953 m 4382 4061 l S NP 4446 3845 m 4413 3953 l S NP 4478 3738 m 4446 3845 l S NP 4541 3529 m 4478 3738 l S NP 4599 3320 m 4541 3529 l S NP 4646 3127 m 4599 3320 l S NP 4683 2934 m 4646 3127 l S NP 4711 2712 m 4683 2934 l S NP 4720 2490 m 4711 2712 l S NP 4710 2276 m 4720 2490 l S NP 4683 2062 m 4710 2276 l S NP 4644 1864 m 4683 2062 l S NP 4596 1666 m 4644 1864 l S NP 4566 1558 m 4596 1666 l S NP 4535 1450 m 4566 1558 l S NP 4503 1342 m 4535 1450 l S NP 4470 1234 m 4503 1342 l S NP 4408 1027 m 4470 1234 l S NP 4349 821 m 4408 1027 l S NP 4327 737 m 4349 821 l S NP 2463 4169 m 2472 4262 l S NP 2449 4061 m 2463 4169 l S NP 2434 3953 m 2449 4061 l S NP 2417 3845 m 2434 3953 l S NP 2397 3738 m 2417 3845 l S NP 2377 3633 m 2397 3738 l S NP 2356 3529 m 2377 3633 l S NP 2334 3424 m 2356 3529 l S NP 2311 3320 m 2334 3424 l S NP 2291 3223 m 2311 3320 l S NP 2271 3127 m 2291 3223 l S NP 2254 3030 m 2271 3127 l S NP 2238 2934 m 2254 3030 l S NP 2211 2712 m 2238 2934 l S NP 2202 2490 m 2211 2712 l S NP 2212 2276 m 2202 2490 l S NP 2238 2062 m 2212 2276 l S NP 2255 1963 m 2238 2062 l S NP 2273 1864 m 2255 1963 l S NP 2293 1765 m 2273 1864 l S NP 2314 1666 m 2293 1765 l S NP 2337 1558 m 2314 1666 l S NP 2360 1450 m 2337 1558 l S NP 2382 1342 m 2360 1450 l S NP 2402 1234 m 2382 1342 l S NP 2420 1131 m 2402 1234 l S NP 2437 1027 m 2420 1131 l S NP 2451 924 m 2437 1027 l S NP 2464 821 m 2451 924 l S NP 2472 737 m 2464 821 l S NP 3461 4169 m 3461 4262 l S NP 3461 3738 m 3461 4169 l S NP 3461 3320 m 3461 3738 l S NP 3461 2934 m 3461 3320 l S NP 3461 2490 m 3461 2934 l S NP 3461 2062 m 3461 2490 l S NP 3461 1666 m 3461 2062 l S NP 3461 1234 m 3461 1666 l S NP 3461 821 m 3461 1234 l S NP 3461 737 m 3461 821 l S thin setlinewidth NP 2333 3195 m 2364 3251 l S NP 2303 3137 m 2333 3195 l S NP 2275 3077 m 2303 3137 l S NP 2248 3017 m 2275 3077 l S NP 2223 2955 m 2248 3017 l S NP 2200 2892 m 2223 2955 l S NP 2178 2828 m 2200 2892 l S NP 2158 2762 m 2178 2828 l S NP 2141 2696 m 2158 2762 l S NP 2125 2630 m 2141 2696 l S NP 2111 2562 m 2125 2630 l S NP 2099 2494 m 2111 2562 l S NP 2090 2425 m 2099 2494 l S NP 2082 2357 m 2090 2425 l S NP 2077 2287 m 2082 2357 l S NP 2074 2218 m 2077 2287 l S NP 2074 2149 m 2074 2218 l S NP 2076 2079 m 2074 2149 l S NP 2082 2010 m 2076 2079 l S NP 2091 1942 m 2082 2010 l S NP 2104 1874 m 2091 1942 l S NP 2121 1807 m 2104 1874 l S NP 2143 1741 m 2121 1807 l S NP 2169 1677 m 2143 1741 l S NP 2202 1614 m 2169 1677 l S NP 2240 1553 m 2202 1614 l S NP 2284 1494 m 2240 1553 l S NP 2335 1437 m 2284 1494 l S NP 2392 1384 m 2335 1437 l S NP 2454 1334 m 2392 1384 l S NP 2522 1287 m 2454 1334 l S NP 2595 1243 m 2522 1287 l S NP 2671 1204 m 2595 1243 l S NP 2750 1168 m 2671 1204 l S NP 2831 1137 m 2750 1168 l S NP 2913 1109 m 2831 1137 l S NP 2995 1086 m 2913 1109 l S NP 3077 1067 m 2995 1086 l S NP 3157 1052 m 3077 1067 l S NP 3237 1041 m 3157 1052 l S NP 3314 1033 m 3237 1041 l S NP 3389 1030 m 3314 1033 l S NP 3462 1030 m 3389 1030 l S NP 3533 1033 m 3462 1030 l S NP 3601 1040 m 3533 1033 l S NP 3667 1051 m 3601 1040 l S NP 3731 1064 m 3667 1051 l S NP 3792 1081 m 3731 1064 l S NP 3852 1100 m 3792 1081 l S NP 3909 1123 m 3852 1100 l S NP 3964 1148 m 3909 1123 l S NP 4018 1176 m 3964 1148 l S NP 4069 1206 m 4018 1176 l S NP 4119 1239 m 4069 1206 l S NP 4168 1274 m 4119 1239 l S NP 4214 1312 m 4168 1274 l S NP 4259 1352 m 4214 1312 l S NP 4303 1394 m 4259 1352 l S NP 4345 1438 m 4303 1394 l S NP 4386 1484 m 4345 1438 l S NP 4425 1533 m 4386 1484 l S NP 4463 1583 m 4425 1533 l S NP 4499 1635 m 4463 1583 l S NP 4534 1688 m 4499 1635 l S NP 4568 1744 m 4534 1688 l S NP 4599 1801 m 4568 1744 l S NP 4630 1859 m 4599 1801 l S NP 4658 1919 m 4630 1859 l S NP 4685 1980 m 4658 1919 l S NP 4711 2043 m 4685 1980 l S NP 4734 2106 m 4711 2043 l S NP 4756 2171 m 4734 2106 l S NP 4776 2237 m 4756 2171 l S NP 4794 2303 m 4776 2237 l S NP 4811 2371 m 4794 2303 l S NP 4825 2439 m 4811 2371 l S NP 4838 2508 m 4825 2439 l S NP 4849 2577 m 4838 2508 l S NP 4857 2647 m 4849 2577 l S NP 4864 2717 m 4857 2647 l S NP 4869 2788 m 4864 2717 l S NP 4872 2858 m 4869 2788 l S NP 4872 2929 m 4872 2858 l S NP 4870 2999 m 4872 2929 l S NP 4865 3069 m 4870 2999 l S NP 4857 3139 m 4865 3069 l S NP 4845 3208 m 4857 3139 l S NP 4830 3277 m 4845 3208 l S NP 4811 3344 m 4830 3277 l S NP 4787 3411 m 4811 3344 l S NP 4758 3475 m 4787 3411 l S NP 4724 3539 m 4758 3475 l S NP 4683 3600 m 4724 3539 l S NP 4636 3658 m 4683 3600 l S NP 4582 3715 m 4636 3658 l S NP 4523 3768 m 4582 3715 l S NP 4456 3817 m 4523 3768 l S NP 4385 3864 m 4456 3817 l S NP 4308 3906 m 4385 3864 l S NP 4227 3944 m 4308 3906 l S NP 4144 3978 m 4227 3944 l S NP 4057 4008 m 4144 3978 l S NP 3970 4034 m 4057 4008 l S NP 3882 4055 m 3970 4034 l S NP 3795 4071 m 3882 4055 l S NP 3709 4084 m 3795 4071 l S NP 3624 4092 m 3709 4084 l S NP 3542 4096 m 3624 4092 l S NP 3462 4096 m 3542 4096 l S NP 3384 4092 m 3462 4096 l S NP 3308 4085 m 3384 4092 l S NP 3236 4073 m 3308 4085 l S NP 3165 4059 m 3236 4073 l S NP 3097 4040 m 3165 4059 l S NP 3032 4019 m 3097 4040 l S NP 2968 3994 m 3032 4019 l S NP 2907 3967 m 2968 3994 l S NP 2847 3936 m 2907 3967 l S NP 2789 3902 m 2847 3936 l S NP 2733 3866 m 2789 3902 l S NP 2677 3827 m 2733 3866 l S NP 2623 3785 m 2677 3827 l S NP 2570 3740 m 2623 3785 l S NP 2517 3693 m 2570 3740 l S NP 2465 3643 m 2517 3693 l S NP 2413 3591 m 2465 3643 l S NP 2361 3536 m 2413 3591 l S NP 2308 3478 m 2361 3536 l S NP 2255 3418 m 2308 3478 l S NP 2200 3355 m 2255 3418 l S NP 2144 3289 m 2200 3355 l S NP 2084 3220 m 2144 3289 l S NP 2021 3148 m 2084 3220 l S NP 1952 3073 m 2021 3148 l S NP 1874 2993 m 1952 3073 l S NP 1784 2910 m 1874 2993 l S NP 1674 2820 m 1784 2910 l S NP 1530 2724 m 1674 2820 l S NP 1321 2617 m 1530 2724 l S NP 944 2491 m 1321 2617 l S NP 4804 2446 m 4792 2379 l S NP 4813 2514 m 4804 2446 l S NP 4820 2582 m 4813 2514 l S NP 4825 2650 m 4820 2582 l S NP 4826 2718 m 4825 2650 l S NP 4825 2787 m 4826 2718 l S NP 4821 2855 m 4825 2787 l S NP 4814 2922 m 4821 2855 l S NP 4803 2989 m 4814 2922 l S NP 4789 3056 m 4803 2989 l S NP 4770 3121 m 4789 3056 l S NP 4747 3186 m 4770 3121 l S NP 4719 3249 m 4747 3186 l S NP 4686 3310 m 4719 3249 l S NP 4648 3369 m 4686 3310 l S NP 4604 3426 m 4648 3369 l S NP 4555 3481 m 4604 3426 l S NP 4500 3533 m 4555 3481 l S NP 4440 3582 m 4500 3533 l S NP 4376 3628 m 4440 3582 l S NP 4307 3670 m 4376 3628 l S NP 4235 3709 m 4307 3670 l S NP 4160 3744 m 4235 3709 l S NP 4083 3775 m 4160 3744 l S NP 4005 3802 m 4083 3775 l S NP 3927 3825 m 4005 3802 l S NP 3849 3845 m 3927 3825 l S NP 3772 3860 m 3849 3845 l S NP 3696 3872 m 3772 3860 l S NP 3621 3880 m 3696 3872 l S NP 3549 3884 m 3621 3880 l S NP 3478 3885 m 3549 3884 l S NP 3411 3883 m 3478 3885 l S NP 3345 3877 m 3411 3883 l S NP 3282 3868 m 3345 3877 l S NP 3221 3856 m 3282 3868 l S NP 3162 3841 m 3221 3856 l S NP 3106 3823 m 3162 3841 l S NP 3052 3803 m 3106 3823 l S NP 3000 3780 m 3052 3803 l S NP 2951 3754 m 3000 3780 l S NP 2903 3726 m 2951 3754 l S NP 2857 3696 m 2903 3726 l S NP 2813 3664 m 2857 3696 l S NP 2771 3629 m 2813 3664 l S NP 2731 3593 m 2771 3629 l S NP 2692 3554 m 2731 3593 l S NP 2656 3514 m 2692 3554 l S NP 2621 3472 m 2656 3514 l S NP 2588 3428 m 2621 3472 l S NP 2556 3383 m 2588 3428 l S NP 2527 3336 m 2556 3383 l S NP 2499 3288 m 2527 3336 l S NP 2474 3239 m 2499 3288 l S NP 2450 3188 m 2474 3239 l S NP 2429 3137 m 2450 3188 l S NP 2410 3084 m 2429 3137 l S NP 2394 3031 m 2410 3084 l S NP 2380 2977 m 2394 3031 l S NP 2369 2922 m 2380 2977 l S NP 2361 2867 m 2369 2922 l S NP 2356 2812 m 2361 2867 l S NP 2354 2757 m 2356 2812 l S NP 2355 2701 m 2354 2757 l S NP 2360 2646 m 2355 2701 l S NP 2368 2592 m 2360 2646 l S NP 2380 2538 m 2368 2592 l S NP 2395 2484 m 2380 2538 l S NP 2414 2432 m 2395 2484 l S NP 2437 2381 m 2414 2432 l S NP 2463 2331 m 2437 2381 l S NP 2493 2282 m 2463 2331 l S NP 2526 2236 m 2493 2282 l S NP 2561 2191 m 2526 2236 l S NP 2600 2148 m 2561 2191 l S NP 2641 2107 m 2600 2148 l S NP 2684 2068 m 2641 2107 l S NP 2729 2031 m 2684 2068 l S NP 2775 1997 m 2729 2031 l S NP 2823 1965 m 2775 1997 l S NP 2871 1935 m 2823 1965 l S NP 2920 1908 m 2871 1935 l S NP 2968 1884 m 2920 1908 l S NP 3017 1862 m 2968 1884 l S NP 3065 1842 m 3017 1862 l S NP 3112 1824 m 3065 1842 l S NP 3158 1809 m 3112 1824 l S NP 3204 1796 m 3158 1809 l S NP 3248 1786 m 3204 1796 l S NP 3291 1777 m 3248 1786 l S NP 3332 1771 m 3291 1777 l S NP 3372 1766 m 3332 1771 l S NP 3411 1764 m 3372 1766 l S NP 3448 1763 m 3411 1764 l S NP 3483 1764 m 3448 1763 l S NP 3517 1767 m 3483 1764 l S NP 3549 1771 m 3517 1767 l S NP 3580 1777 m 3549 1771 l S NP 3609 1785 m 3580 1777 l S NP 3636 1794 m 3609 1785 l S NP 3662 1804 m 3636 1794 l S NP 3686 1815 m 3662 1804 l S NP 3709 1827 m 3686 1815 l S NP 3730 1841 m 3709 1827 l S NP 3750 1855 m 3730 1841 l S NP 3768 1871 m 3750 1855 l S NP 3785 1887 m 3768 1871 l S NP 3800 1904 m 3785 1887 l S NP 3814 1921 m 3800 1904 l S NP 3827 1940 m 3814 1921 l S NP 3838 1959 m 3827 1940 l S NP 3847 1978 m 3838 1959 l S NP 3856 1998 m 3847 1978 l S NP 3863 2018 m 3856 1998 l S NP 3868 2038 m 3863 2018 l S NP 3873 2059 m 3868 2038 l S NP 3876 2079 m 3873 2059 l S NP 3878 2100 m 3876 2079 l S NP 3878 2121 m 3878 2100 l S NP 3878 2142 m 3878 2121 l S NP 3877 2163 m 3878 2142 l S NP 3874 2183 m 3877 2163 l S NP 3871 2204 m 3874 2183 l S NP 3866 2224 m 3871 2204 l S NP 3861 2244 m 3866 2224 l S NP 3855 2264 m 3861 2244 l S NP 3848 2283 m 3855 2264 l S NP 3841 2302 m 3848 2283 l S NP 3832 2321 m 3841 2302 l S NP 3823 2339 m 3832 2321 l S NP 3814 2356 m 3823 2339 l S NP 3804 2374 m 3814 2356 l S NP 3794 2390 m 3804 2374 l S NP 3783 2406 m 3794 2390 l S NP 3772 2422 m 3783 2406 l S NP 3760 2437 m 3772 2422 l S NP 3749 2451 m 3760 2437 l S NP 3737 2465 m 3749 2451 l S NP 3725 2478 m 3737 2465 l S NP 3713 2491 m 3725 2478 l S NP 4581 1776 m 4549 1720 l S NP 4612 1834 m 4581 1776 l S NP 4641 1893 m 4612 1834 l S NP 4668 1953 m 4641 1893 l S NP 4693 2015 m 4668 1953 l S NP 4717 2077 m 4693 2015 l S NP 4739 2141 m 4717 2077 l S NP 4759 2206 m 4739 2141 l S NP 4777 2272 m 4759 2206 l S NP 4793 2339 m 4777 2272 l S NP 4807 2406 m 4793 2339 l S NP 4819 2474 m 4807 2406 l S NP 4829 2542 m 4819 2474 l S NP 4836 2611 m 4829 2542 l S NP 4842 2680 m 4836 2611 l S NP 4844 2749 m 4842 2680 l S NP 4845 2818 m 4844 2749 l S NP 4842 2887 m 4845 2818 l S NP 4837 2956 m 4842 2887 l S NP 4829 3024 m 4837 2956 l S NP 4816 3092 m 4829 3024 l S NP 4800 3159 m 4816 3092 l S NP 4780 3225 m 4800 3159 l S NP 4755 3290 m 4780 3225 l S NP 4725 3353 m 4755 3290 l S NP 4690 3415 m 4725 3353 l S NP 4649 3474 m 4690 3415 l S NP 4602 3531 m 4649 3474 l S NP 4549 3585 m 4602 3531 l S NP 4491 3637 m 4549 3585 l S NP 4427 3685 m 4491 3637 l S NP 4359 3730 m 4427 3685 l S NP 4286 3771 m 4359 3730 l S NP 4210 3809 m 4286 3771 l S NP 4131 3842 m 4210 3809 l S NP 4050 3872 m 4131 3842 l S NP 3968 3897 m 4050 3872 l S NP 3887 3918 m 3968 3897 l S NP 3805 3936 m 3887 3918 l S NP 3725 3949 m 3805 3936 l S NP 3646 3958 m 3725 3949 l S NP 3569 3963 m 3646 3958 l S NP 3495 3965 m 3569 3963 l S NP 3422 3963 m 3495 3965 l S NP 3352 3958 m 3422 3963 l S NP 3285 3949 m 3352 3958 l S NP 3219 3937 m 3285 3949 l S NP 3157 3922 m 3219 3937 l S NP 3096 3903 m 3157 3922 l S NP 3038 3882 m 3096 3903 l S NP 2982 3858 m 3038 3882 l S NP 2928 3832 m 2982 3858 l S NP 2876 3802 m 2928 3832 l S NP 2826 3771 m 2876 3802 l S NP 2778 3737 m 2826 3771 l S NP 2731 3700 m 2778 3737 l S NP 2686 3661 m 2731 3700 l S NP 2642 3620 m 2686 3661 l S NP 2600 3577 m 2642 3620 l S NP 2559 3532 m 2600 3577 l S NP 2520 3485 m 2559 3532 l S NP 2482 3436 m 2520 3485 l S NP 2445 3385 m 2482 3436 l S NP 2410 3333 m 2445 3385 l S NP 2376 3279 m 2410 3333 l S NP 2343 3223 m 2376 3279 l S NP 2312 3165 m 2343 3223 l S NP 2283 3106 m 2312 3165 l S NP 2255 3046 m 2283 3106 l S NP 2228 2984 m 2255 3046 l S NP 2203 2921 m 2228 2984 l S NP 2180 2857 m 2203 2921 l S NP 2159 2792 m 2180 2857 l S NP 2139 2726 m 2159 2792 l S NP 2121 2659 m 2139 2726 l S NP 2105 2591 m 2121 2659 l S NP 2091 2523 m 2105 2591 l S NP 2078 2454 m 2091 2523 l S NP 2067 2384 m 2078 2454 l S NP 2059 2314 m 2067 2384 l S NP 2052 2243 m 2059 2314 l S NP 2047 2173 m 2052 2243 l S NP 2045 2102 m 2047 2173 l S NP 2044 2031 m 2045 2102 l S NP 2047 1960 m 2044 2031 l S NP 2052 1890 m 2047 1960 l S NP 2060 1820 m 2052 1890 l S NP 2073 1750 m 2060 1820 l S NP 2089 1682 m 2073 1750 l S NP 2111 1614 m 2089 1682 l S NP 2137 1548 m 2111 1614 l S NP 2170 1484 m 2137 1548 l S NP 2210 1421 m 2170 1484 l S NP 2256 1361 m 2210 1421 l S NP 2309 1303 m 2256 1361 l S NP 2369 1249 m 2309 1303 l S NP 2435 1197 m 2369 1249 l S NP 2508 1150 m 2435 1197 l S NP 2585 1106 m 2508 1150 l S NP 2667 1066 m 2585 1106 l S NP 2752 1031 m 2667 1066 l S NP 2839 1000 m 2752 1031 l S NP 2926 973 m 2839 1000 l S NP 3014 951 m 2926 973 l S NP 3102 933 m 3014 951 l S NP 3188 919 m 3102 933 l S NP 3272 910 m 3188 919 l S NP 3355 904 m 3272 910 l S NP 3435 903 m 3355 904 l S NP 3513 906 m 3435 903 l S NP 3588 912 m 3513 906 l S NP 3661 922 m 3588 912 l S NP 3732 935 m 3661 922 l S NP 3800 952 m 3732 935 l S NP 3866 973 m 3800 952 l S NP 3931 996 m 3866 973 l S NP 3993 1023 m 3931 996 l S NP 4054 1052 m 3993 1023 l S NP 4114 1085 m 4054 1052 l S NP 4172 1121 m 4114 1085 l S NP 4228 1159 m 4172 1121 l S NP 4284 1200 m 4228 1159 l S NP 4339 1244 m 4284 1200 l S NP 4394 1291 m 4339 1244 l S NP 4447 1340 m 4394 1291 l S NP 4501 1392 m 4447 1340 l S NP 4555 1447 m 4501 1392 l S NP 4609 1504 m 4555 1447 l S NP 4663 1564 m 4609 1504 l S NP 4719 1627 m 4663 1564 l S NP 4776 1693 m 4719 1627 l S NP 4836 1762 m 4776 1693 l S NP 4900 1833 m 4836 1762 l S NP 4970 1909 m 4900 1833 l S NP 5047 1988 m 4970 1909 l S NP 5138 2072 m 5047 1988 l S NP 5248 2161 m 5138 2072 l S NP 5392 2258 m 5248 2161 l S NP 5601 2365 m 5392 2258 l S NP 5978 2491 m 5601 2365 l S NP 4647 1907 m 4619 1848 l S thick setlinewidth %qui1 NP 4674 1968 m 4647 1907 l S NP 4699 2030 m 4674 1968 l S NP 4722 2093 m 4699 2030 l S NP 4744 2157 m 4722 2093 l S NP 4763 2222 m 4744 2157 l S NP 4780 2288 m 4763 2222 l S NP 4796 2355 m 4780 2288 l S NP 4810 2422 m 4796 2355 l S NP 4821 2490 m 4810 2422 l S NP 4830 2558 m 4821 2490 l S NP 4837 2627 m 4830 2558 l S NP 4842 2696 m 4837 2627 l S NP 4844 2765 m 4842 2696 l S NP 4844 2835 m 4844 2765 l S NP 4841 2904 m 4844 2835 l S NP 4834 2972 m 4841 2904 l S NP 4825 3040 m 4834 2972 l S NP 4812 3108 m 4825 3040 l S NP 4795 3175 m 4812 3108 l S NP 4773 3240 m 4795 3175 l S NP 4747 3305 m 4773 3240 l S NP 4715 3367 m 4747 3305 l S NP 4678 3428 m 4715 3367 l S NP 4636 3487 m 4678 3428 l S NP 4587 3543 m 4636 3487 l S NP 4533 3597 m 4587 3543 l S NP 4473 3647 m 4533 3597 l S NP 4408 3695 m 4473 3647 l S NP 4339 3739 m 4408 3695 l S NP 4265 3779 m 4339 3739 l S NP 4188 3815 m 4265 3779 l S NP 4109 3848 m 4188 3815 l S NP 4028 3876 m 4109 3848 l S NP 3946 3900 m 4028 3876 l S NP 3864 3920 m 3946 3900 l S NP 3783 3936 m 3864 3920 l S NP 3704 3949 m 3783 3936 l S %qui1 NP 3626 3957 m 3704 3949 l S NP 3549 3961 m 3626 3957 l S NP 3475 3962 m 3549 3961 l S NP 3404 3959 m 3475 3962 l S NP 3334 3953 m 3404 3959 l S NP 3268 3943 m 3334 3953 l S NP 3203 3930 m 3268 3943 l S NP 3141 3914 m 3203 3930 l S NP 3082 3895 m 3141 3914 l S NP 3024 3873 m 3082 3895 l S NP 2969 3849 m 3024 3873 l S NP 2916 3822 m 2969 3849 l S NP 2864 3792 m 2916 3822 l S NP 2815 3759 m 2864 3792 l S %qui NP 2767 3725 m 2815 3759 l S NP 2721 3688 m 2767 3725 l S NP 2676 3648 m 2721 3688 l S NP 2633 3607 m 2676 3648 l S NP 2592 3564 m 2633 3607 l S NP 2551 3518 m 2592 3564 l S NP 2513 3471 m 2551 3518 l S NP 2475 3421 m 2513 3471 l S NP 2439 3370 m 2475 3421 l S NP 2405 3318 m 2439 3370 l S NP 2371 3263 m 2405 3318 l S NP 2340 3207 m 2371 3263 l S NP 2310 3149 m 2340 3207 l S NP 2281 3090 m 2310 3149 l S NP 2254 3030 m 2281 3090 l S %qui2 NP 2228 2968 m 2254 3030 l S NP 2205 2906 m 2228 2968 l S NP 2183 2842 m 2205 2906 l S NP 2163 2777 m 2183 2842 l S NP 2144 2711 m 2163 2777 l S NP 2128 2644 m 2144 2711 l S NP 2114 2577 m 2128 2644 l S NP 2102 2509 m 2114 2577 l S NP 2092 2441 m 2102 2509 l S NP 2084 2372 m 2092 2441 l S NP 2078 2303 m 2084 2372 l S NP 2075 2233 m 2078 2303 l S NP 2074 2164 m 2075 2233 l S NP 2076 2095 m 2074 2164 l S NP 2081 2026 m 2076 2095 l S NP 2090 1957 m 2081 2026 l S NP 2102 1889 m 2090 1957 l S NP 2118 1822 m 2102 1889 l S NP 2138 1756 m 2118 1822 l S NP 2164 1691 m 2138 1756 l S NP 2195 1628 m 2164 1691 l S NP 2233 1566 m 2195 1628 l S NP 2276 1507 m 2233 1566 l S NP 2325 1450 m 2276 1507 l S NP 2381 1396 m 2325 1450 l S NP 2442 1345 m 2381 1396 l S NP 2509 1298 m 2442 1345 l S NP 2580 1254 m 2509 1298 l S NP 2656 1213 m 2580 1254 l S NP 2734 1177 m 2656 1213 l S NP 2815 1145 m 2734 1177 l S NP 2897 1116 m 2815 1145 l S NP 2979 1092 m 2897 1116 l S NP 3061 1072 m 2979 1092 l S NP 3141 1056 m 3061 1072 l S NP 3221 1044 m 3141 1056 l S NP 3299 1036 m 3221 1044 l S NP 3374 1032 m 3299 1036 l S NP 3448 1031 m 3374 1032 l S NP 3519 1034 m 3448 1031 l S NP 3587 1040 m 3519 1034 l S NP 3654 1050 m 3587 1040 l S NP 3718 1063 m 3654 1050 l S NP 3780 1079 m 3718 1063 l S NP 3839 1098 m 3780 1079 l S %qui3 NP 3897 1120 m 3839 1098 l S NP 3952 1144 m 3897 1120 l S NP 4006 1171 m 3952 1144 l S NP 4058 1201 m 4006 1171 l S NP 4108 1234 m 4058 1201 l S NP 4157 1268 m 4108 1234 l S NP 4204 1306 m 4157 1268 l S NP 4249 1345 m 4204 1306 l S NP 4293 1386 m 4249 1345 l S NP 4335 1430 m 4293 1386 l S NP 4376 1476 m 4335 1430 l S NP 4415 1524 m 4376 1476 l S NP 4453 1573 m 4415 1524 l S NP 4490 1625 m 4453 1573 l S NP 4525 1678 m 4490 1625 l S NP 4558 1733 m 4525 1678 l S NP 4590 1789 m 4558 1733 l S NP 4620 1847 m 4590 1789 l S NP 4649 1907 m 4620 1847 l S NP 4676 1967 m 4649 1907 l S NP 4701 2029 m 4676 1967 l S NP 4724 2092 m 4701 2029 l S NP 4746 2157 m 4724 2092 l S NP 4766 2222 m 4746 2157 l S NP 4784 2288 m 4766 2222 l S NP 4800 2355 m 4784 2288 l S NP 4814 2423 m 4800 2355 l S NP 4825 2491 m 4814 2423 l S 0.368627 G medium setlinewidth %qui6 inizio frecce NP 5862 4056 m 5928 4055 l S %qui5 NP 6095 4136 m 5862 4056 l S %qui4 NP 5608 4045 m 5674 4050 l S NP 5819 4147 m 5608 4045 l S NP 5367 4030 m 5428 4046 l S NP 5530 4162 m 5367 4030 l S NP 5146 4016 m 5194 4044 l S NP 5221 4177 m 5146 4016 l S NP 4939 4013 m 4963 4052 l S NP 4898 4179 m 4939 4013 l S NP 4722 4024 m 4721 4066 l S NP 4585 4168 m 4722 4024 l S NP 4486 4039 m 4466 4079 l S NP 4291 4153 m 4486 4039 l S NP 4238 4053 m 4205 4090 l S NP 4009 4139 m 4238 4053 l S NP 3984 4068 m 3940 4100 l S NP 3733 4124 m 3984 4068 l S NP 3725 4086 m 3672 4111 l S NP 3462 4106 m 3725 4086 l S NP 3460 4107 m 3398 4123 l S NP 3197 4085 m 3460 4107 l S NP 3185 4130 m 3119 4135 l S NP 2942 4062 m 3185 4130 l S NP 2904 4147 m 2838 4142 l S NP 2693 4045 m 2904 4147 l S NP 2629 4154 m 2565 4144 l S NP 2438 4038 m 2629 4154 l S NP 2363 4155 m 2299 4145 l S NP 2174 4037 m 2363 4155 l S NP 2103 4152 m 2038 4143 l S NP 1904 4040 m 2103 4152 l S NP 1845 4146 m 1779 4141 l S NP 1632 4046 m 1845 4146 l S NP 1587 4140 m 1521 4139 l S NP 1360 4053 m 1587 4140 l S NP 1327 4133 m 1261 4136 l S NP 1090 4059 m 1327 4133 l S NP 1066 4128 m 1001 4133 l S NP 821 4065 m 1066 4128 l S NP 5862 3888 m 5928 3887 l S NP 6095 3968 m 5862 3888 l S NP 5609 3877 m 5674 3882 l S NP 5818 3979 m 5609 3877 l S NP 5367 3862 m 5428 3878 l S NP 5530 3994 m 5367 3862 l S NP 5144 3848 m 5193 3876 l S NP 5223 4008 m 5144 3848 l S NP 4935 3845 m 4961 3883 l S NP 4902 4011 m 4935 3845 l S NP 4718 3855 m 4719 3897 l S NP 4589 4001 m 4718 3855 l S NP 4482 3869 m 4465 3909 l S NP 4295 3987 m 4482 3869 l S NP 4235 3883 m 4205 3920 l S NP 4012 3973 m 4235 3883 l S NP 3982 3898 m 3940 3931 l S NP 3735 3958 m 3982 3898 l S NP 3725 3917 m 3672 3942 l S NP 3462 3939 m 3725 3917 l S NP 3459 3941 m 3398 3956 l S NP 3198 3915 m 3459 3941 l S NP 3181 3966 m 3115 3968 l S NP 2946 3890 m 3181 3966 l S NP 2898 3983 m 2833 3975 l S NP 2699 3873 m 2898 3983 l S NP 2622 3990 m 2559 3977 l S NP 2445 3866 m 2622 3990 l S NP 2357 3990 m 2294 3977 l S NP 2180 3866 m 2357 3990 l S NP 2099 3986 m 2035 3976 l S NP 1908 3870 m 2099 3986 l S NP 1843 3980 m 1777 3974 l S NP 1634 3876 m 1843 3980 l S NP 1586 3973 m 1519 3971 l S NP 1361 3883 m 1586 3973 l S NP 1327 3966 m 1261 3968 l S NP 1090 3890 m 1327 3966 l S NP 1066 3960 m 1000 3966 l S NP 821 3896 m 1066 3960 l S NP 5862 3720 m 5928 3719 l S NP 6095 3800 m 5862 3720 l S NP 5609 3709 m 5674 3714 l S NP 5818 3811 m 5609 3709 l S NP 5366 3694 m 5428 3710 l S NP 5531 3826 m 5366 3694 l S NP 5142 3680 m 5192 3708 l S NP 5225 3840 m 5142 3680 l S NP 4932 3676 m 4959 3715 l S NP 4905 3844 m 4932 3676 l S NP 4714 3685 m 4717 3727 l S NP 4593 3835 m 4714 3685 l S NP 4479 3698 m 4464 3739 l S NP 4298 3821 m 4479 3698 l S NP 4233 3712 m 4204 3750 l S NP 4014 3808 m 4233 3712 l S NP 3981 3727 m 3941 3761 l S NP 3736 3792 m 3981 3727 l S NP 3724 3747 m 3673 3773 l S NP 3463 3773 m 3724 3747 l S NP 3459 3775 m 3397 3789 l S NP 3198 3745 m 3459 3775 l S NP 3177 3803 m 3111 3803 l S NP 2950 3716 m 3177 3803 l S NP 2890 3821 m 2826 3809 l S NP 2707 3699 m 2890 3821 l S NP 2614 3827 m 2553 3811 l S NP 2453 3693 m 2614 3827 l S NP 2351 3826 m 2289 3810 l S NP 2186 3694 m 2351 3826 l S NP 2095 3821 m 2031 3809 l S NP 1912 3699 m 2095 3821 l S NP 1840 3814 m 1775 3807 l S NP 1637 3706 m 1840 3814 l S NP 1584 3806 m 1518 3804 l S NP 1363 3714 m 1584 3806 l S NP 1326 3799 m 1260 3801 l S NP 1091 3721 m 1326 3799 l S NP 1066 3793 m 1000 3798 l S NP 821 3727 m 1066 3793 l S NP 5862 3552 m 5928 3551 l S NP 6095 3632 m 5862 3552 l S NP 5609 3540 m 5674 3546 l S NP 5818 3643 m 5609 3540 l S NP 5366 3526 m 5428 3542 l S NP 5531 3658 m 5366 3526 l S NP 5141 3512 m 5190 3540 l S NP 5226 3671 m 5141 3512 l S NP 4928 3508 m 4957 3546 l S NP 4909 3676 m 4928 3508 l S NP 4709 3516 m 4715 3557 l S NP 4598 3668 m 4709 3516 l S NP 4475 3528 m 4463 3569 l S NP 4302 3656 m 4475 3528 l S NP 4229 3541 m 4203 3580 l S NP 4018 3642 m 4229 3541 l S NP 3979 3556 m 3941 3591 l S NP 3738 3627 m 3979 3556 l S NP 3724 3577 m 3673 3604 l S NP 3463 3606 m 3724 3577 l S NP 3458 3609 m 3395 3622 l S NP 3199 3575 m 3458 3609 l S NP 3170 3642 m 3104 3637 l S NP 2957 3542 m 3170 3642 l S NP 2879 3659 m 2818 3643 l S NP 2718 3525 m 2879 3659 l S NP 2604 3663 m 2545 3643 l S NP 2463 3521 m 2604 3663 l S NP 2343 3661 m 2283 3643 l S NP 2194 3522 m 2343 3661 l S NP 2089 3656 m 2027 3642 l S NP 1918 3528 m 2089 3656 l S NP 1837 3648 m 1772 3639 l S NP 1640 3536 m 1837 3648 l S NP 1582 3640 m 1516 3636 l S NP 1365 3544 m 1582 3640 l S NP 1325 3632 m 1259 3633 l S NP 1092 3552 m 1325 3632 l S NP 1065 3625 m 999 3630 l S NP 822 3559 m 1065 3625 l S NP 5862 3383 m 5929 3382 l S NP 6095 3464 m 5862 3383 l S NP 5609 3372 m 5675 3378 l S NP 5818 3475 m 5609 3372 l S NP 5366 3358 m 5427 3373 l S NP 5531 3489 m 5366 3358 l S NP 5139 3345 m 5189 3372 l S NP 5228 3503 m 5139 3345 l S NP 4924 3340 m 4955 3377 l S NP 4913 3508 m 4924 3340 l S NP 4705 3346 m 4713 3388 l S NP 4602 3501 m 4705 3346 l S NP 4470 3358 m 4461 3399 l S NP 4307 3490 m 4470 3358 l S NP 4226 3370 m 4203 3410 l S NP 4021 3477 m 4226 3370 l S NP 3976 3385 m 3940 3420 l S NP 3741 3463 m 3976 3385 l S NP 3723 3407 m 3674 3435 l S NP 3464 3440 m 3723 3407 l S NP 3457 3444 m 3393 3456 l S NP 3200 3403 m 3457 3444 l S NP 3159 3482 m 3095 3472 l S NP 2968 3366 m 3159 3482 l S NP 2864 3497 m 2807 3476 l S NP 2733 3351 m 2864 3497 l S NP 2591 3500 m 2536 3476 l S NP 2477 3348 m 2591 3500 l S NP 2333 3497 m 2276 3476 l S NP 2204 3350 m 2333 3497 l S NP 2083 3491 m 2022 3475 l S NP 1924 3356 m 2083 3491 l S NP 1833 3483 m 1769 3472 l S NP 1644 3365 m 1833 3483 l S NP 1580 3473 m 1515 3469 l S NP 1367 3374 m 1580 3473 l S NP 1324 3465 m 1258 3465 l S NP 1093 3383 m 1324 3465 l S NP 1065 3458 m 999 3462 l S NP 822 3390 m 1065 3458 l S NP 5862 3215 m 5929 3214 l S NP 6095 3296 m 5862 3215 l S NP 5609 3204 m 5674 3210 l S NP 5818 3307 m 5609 3204 l S NP 5365 3190 m 5427 3206 l S NP 5532 3321 m 5365 3190 l S NP 5137 3177 m 5188 3204 l S NP 5230 3334 m 5137 3177 l S NP 4920 3172 m 4953 3208 l S NP 4917 3340 m 4920 3172 l S NP 4699 3177 m 4711 3218 l S NP 4608 3335 m 4699 3177 l S NP 4465 3187 m 4459 3229 l S NP 4312 3324 m 4465 3187 l S NP 4221 3199 m 4201 3239 l S NP 4026 3313 m 4221 3199 l S NP 3973 3213 m 3940 3250 l S NP 3744 3299 m 3973 3213 l S NP 3722 3236 m 3674 3265 l S NP 3465 3275 m 3722 3236 l S NP 3455 3281 m 3390 3290 l S NP 3202 3230 m 3455 3281 l S NP 3143 3323 m 3082 3307 l S NP 2984 3188 m 3143 3323 l S NP 2844 3335 m 2793 3308 l S NP 2753 3177 m 2844 3335 l S NP 2575 3336 m 2525 3308 l S NP 2492 3176 m 2575 3336 l S NP 2321 3333 m 2268 3308 l S NP 2216 3179 m 2321 3333 l S NP 2075 3326 m 2016 3307 l S NP 1932 3185 m 2075 3326 l S NP 1829 3317 m 1765 3305 l S NP 1648 3194 m 1829 3317 l S NP 1578 3307 m 1512 3302 l S NP 1369 3204 m 1578 3307 l S NP 1323 3298 m 1257 3298 l S NP 1094 3213 m 1323 3298 l S NP 1064 3291 m 998 3295 l S NP 823 3221 m 1064 3291 l S NP 5862 3047 m 5929 3046 l S NP 6095 3128 m 5862 3047 l S NP 5609 3036 m 5674 3042 l S NP 5818 3139 m 5609 3036 l S NP 5364 3023 m 5426 3038 l S NP 5533 3153 m 5364 3023 l S NP 5134 3010 m 5186 3036 l S NP 5233 3166 m 5134 3010 l S NP 4916 3004 m 4950 3040 l S NP 4921 3172 m 4916 3004 l S NP 4693 3008 m 4708 3049 l S NP 4613 3168 m 4693 3008 l S NP 4459 3017 m 4457 3059 l S NP 4318 3159 m 4459 3017 l S NP 4215 3027 m 4199 3068 l S NP 4031 3148 m 4215 3027 l S NP 3968 3040 m 3939 3078 l S NP 3749 3135 m 3968 3040 l S NP 3721 3064 m 3675 3095 l S NP 3466 3111 m 3721 3064 l S NP 3450 3121 m 3384 3126 l S NP 3207 3054 m 3450 3121 l S NP 3117 3164 m 3064 3140 l S NP 3010 3011 m 3117 3164 l S NP 2821 3170 m 2779 3138 l S NP 2776 3005 m 2821 3170 l S NP 2557 3170 m 2514 3138 l S NP 2510 3005 m 2557 3170 l S NP 2308 3168 m 2259 3139 l S NP 2229 3008 m 2308 3168 l S NP 2066 3162 m 2010 3140 l S NP 1941 3014 m 2066 3162 l S NP 1823 3152 m 1761 3138 l S NP 1654 3023 m 1823 3152 l S NP 1575 3142 m 1510 3134 l S NP 1372 3034 m 1575 3142 l S NP 1321 3132 m 1255 3131 l S NP 1096 3044 m 1321 3132 l S NP 1063 3124 m 997 3127 l S NP 824 3052 m 1063 3124 l S NP 5862 2879 m 5928 2878 l S NP 6095 2960 m 5862 2879 l S NP 5608 2869 m 5674 2874 l S NP 5819 2971 m 5608 2869 l S NP 5363 2855 m 5425 2870 l S NP 5534 2984 m 5363 2855 l S NP 5131 2842 m 5184 2868 l S NP 5236 2997 m 5131 2842 l S NP 4910 2836 m 4947 2871 l S NP 4927 3004 m 4910 2836 l S NP 4687 2838 m 4704 2879 l S NP 4620 3001 m 4687 2838 l S NP 4452 2846 m 4454 2888 l S NP 4325 2993 m 4452 2846 l S NP 4208 2855 m 4197 2897 l S NP 4039 2984 m 4208 2855 l S NP 3961 2866 m 3938 2906 l S NP 3756 2973 m 3961 2866 l S NP 3717 2890 m 3675 2922 l S NP 3470 2949 m 3717 2890 l S NP 3438 2967 m 3372 2964 l S NP 3219 2872 m 3438 2967 l S NP 3083 3003 m 3042 2970 l S NP 3044 2837 m 3083 3003 l S NP 2797 3004 m 2764 2967 l S NP 2800 2836 m 2797 3004 l S NP 2539 3004 m 2503 2968 l S NP 2529 2836 m 2539 3004 l S NP 2294 3002 m 2251 2970 l S NP 2243 2837 m 2294 3002 l S NP 2057 2997 m 2003 2972 l S NP 1950 2843 m 2057 2997 l S NP 1818 2987 m 1757 2970 l S NP 1659 2852 m 1818 2987 l S NP 1572 2976 m 1507 2967 l S NP 1375 2864 m 1572 2976 l S NP 1320 2965 m 1254 2963 l S NP 1097 2874 m 1320 2965 l S NP 1063 2957 m 996 2959 l S NP 825 2883 m 1063 2957 l S NP 5862 2712 m 5928 2710 l S NP 6095 2792 m 5862 2712 l S NP 5607 2701 m 5673 2706 l S NP 5820 2802 m 5607 2701 l S NP 5361 2688 m 5424 2702 l S NP 5536 2815 m 5361 2688 l S NP 5127 2676 m 5181 2700 l S NP 5240 2828 m 5127 2676 l S NP 4903 2668 m 4943 2702 l S NP 4934 2835 m 4903 2668 l S NP 4678 2669 m 4700 2709 l S NP 4629 2834 m 4678 2669 l S NP 4443 2675 m 4450 2717 l S NP 4334 2828 m 4443 2675 l S NP 4199 2683 m 4194 2724 l S NP 4048 2821 m 4199 2683 l S NP 3951 2691 m 3935 2732 l S NP 3766 2812 m 3951 2691 l S NP 3710 2712 m 3675 2748 l S NP 3477 2791 m 3710 2712 l S NP 3399 2823 m 3341 2803 l S NP 3258 2681 m 3399 2823 l S NP 3045 2835 m 3020 2796 l S NP 3082 2668 m 3045 2835 l S NP 2773 2834 m 2752 2794 l S NP 2824 2669 m 2773 2834 l S NP 2521 2835 m 2493 2797 l S NP 2546 2668 m 2521 2835 l S NP 2280 2835 m 2242 2801 l S NP 2257 2668 m 2280 2835 l S NP 2046 2831 m 1997 2803 l S NP 1961 2672 m 2046 2831 l S NP 1812 2822 m 1752 2803 l S NP 1665 2682 m 1812 2822 l S NP 1569 2810 m 1505 2800 l S NP 1378 2693 m 1569 2810 l S NP 1318 2799 m 1252 2796 l S NP 1099 2705 m 1318 2799 l S NP 1062 2789 m 996 2792 l S NP 825 2714 m 1062 2789 l S NP 5861 2544 m 5928 2543 l S NP 6095 2623 m 5861 2544 l S NP 5606 2534 m 5672 2538 l S NP 5821 2633 m 5606 2534 l S NP 5359 2522 m 5422 2534 l S NP 5538 2645 m 5359 2522 l S NP 5122 2509 m 5178 2532 l S NP 5245 2658 m 5122 2509 l S NP 4895 2501 m 4938 2533 l S NP 4942 2666 m 4895 2501 l S NP 4668 2500 m 4695 2539 l S NP 4639 2667 m 4668 2500 l S NP 4432 2504 m 4445 2546 l S NP 4345 2663 m 4432 2504 l S NP 4187 2510 m 4189 2552 l S NP 4060 2657 m 4187 2510 l S NP 3936 2515 m 3929 2557 l S NP 3781 2652 m 3936 2515 l S NP 3690 2526 m 3671 2566 l S NP 3497 2641 m 3690 2526 l S NP 3305 2666 m 3282 2627 l S NP 3352 2501 m 3305 2666 l S NP 3012 2661 m 3004 2619 l S NP 3115 2506 m 3012 2661 l S NP 2753 2662 m 2741 2621 l S NP 2844 2505 m 2753 2662 l S NP 2504 2666 m 2485 2625 l S NP 2563 2502 m 2504 2666 l S NP 2267 2668 m 2234 2631 l S NP 2270 2500 m 2267 2668 l S NP 2037 2665 m 1990 2635 l S NP 1970 2502 m 2037 2665 l S NP 1806 2656 m 1748 2635 l S NP 1671 2511 m 1806 2656 l S NP 1566 2644 m 1502 2632 l S NP 1381 2523 m 1566 2644 l S NP 1317 2632 m 1251 2628 l S NP 1100 2535 m 1317 2632 l S NP 1061 2622 m 995 2624 l S NP 826 2545 m 1061 2622 l S NP 5861 2377 m 5927 2375 l S NP 6096 2454 m 5861 2377 l S NP 5605 2367 m 5671 2371 l S NP 5822 2464 m 5605 2367 l S NP 5356 2355 m 5420 2367 l S NP 5541 2476 m 5356 2355 l S NP 5117 2343 m 5174 2364 l S NP 5250 2488 m 5117 2343 l S NP 4886 2334 m 4932 2364 l S NP 4951 2497 m 4886 2334 l S NP 4657 2331 m 4688 2368 l S NP 4650 2499 m 4657 2331 l S NP 4419 2334 m 4438 2374 l S NP 4358 2497 m 4419 2334 l S NP 4171 2337 m 4181 2379 l S NP 4076 2494 m 4171 2337 l S NP 3913 2339 m 3920 2381 l S NP 3804 2492 m 3913 2339 l S NP 3627 2334 m 3645 2375 l S NP 3560 2497 m 3627 2334 l S NP 3235 2475 m 3252 2435 l S NP 3422 2356 m 3235 2475 l S NP 2988 2485 m 2994 2443 l S NP 3139 2346 m 2988 2485 l S NP 2737 2490 m 2734 2448 l S NP 2861 2341 m 2737 2490 l S NP 2491 2495 m 2478 2454 l S NP 2576 2336 m 2491 2495 l S NP 2255 2499 m 2228 2461 l S NP 2282 2332 m 2255 2499 l S NP 2028 2498 m 1985 2466 l S NP 1979 2333 m 2028 2498 l S NP 1800 2490 m 1744 2467 l S NP 1677 2341 m 1800 2490 l S NP 1563 2477 m 1500 2465 l S NP 1384 2354 m 1563 2477 l S NP 1316 2465 m 1250 2460 l S NP 1101 2366 m 1316 2465 l S NP 1061 2455 m 994 2456 l S NP 827 2376 m 1061 2455 l S NP 5860 2209 m 5926 2207 l S NP 6097 2285 m 5860 2209 l S NP 5604 2200 m 5670 2203 l S NP 5823 2295 m 5604 2200 l S NP 5353 2189 m 5417 2199 l S NP 5544 2306 m 5353 2189 l S NP 5111 2177 m 5170 2196 l S NP 5256 2318 m 5111 2177 l S NP 4877 2168 m 4926 2196 l S NP 4960 2327 m 4877 2168 l S NP 4643 2164 m 4681 2198 l S NP 4664 2331 m 4643 2164 l S NP 4403 2164 m 4430 2202 l S NP 4374 2331 m 4403 2164 l S NP 4151 2165 m 4172 2205 l S NP 4096 2330 m 4151 2165 l S NP 3881 2165 m 3904 2204 l S NP 3836 2330 m 3881 2165 l S NP 3530 2174 m 3586 2196 l S NP 3657 2321 m 3530 2174 l S NP 3213 2289 m 3247 2252 l S NP 3444 2206 m 3213 2289 l S NP 2972 2308 m 2988 2268 l S NP 3155 2186 m 2972 2308 l S NP 2724 2317 m 2729 2275 l S NP 2873 2178 m 2724 2317 l S NP 2480 2324 m 2473 2282 l S NP 2587 2171 m 2480 2324 l S NP 2245 2330 m 2222 2290 l S NP 2292 2165 m 2245 2330 l S NP 2020 2331 m 1980 2297 l S NP 1988 2164 m 2020 2331 l S NP 1795 2323 m 1741 2299 l S NP 1682 2172 m 1795 2323 l S NP 1561 2310 m 1498 2297 l S NP 1386 2184 m 1561 2310 l S NP 1315 2298 m 1249 2293 l S NP 1102 2197 m 1315 2298 l S NP 1060 2287 m 994 2289 l S NP 827 2208 m 1060 2287 l S NP 5859 2042 m 5926 2040 l S NP 6097 2116 m 5859 2042 l S NP 5602 2034 m 5668 2036 l S NP 5825 2125 m 5602 2034 l S NP 5350 2023 m 5415 2032 l S NP 5547 2136 m 5350 2023 l S NP 5105 2012 m 5166 2029 l S NP 5262 2147 m 5105 2012 l S NP 4866 2002 m 4919 2027 l S NP 4971 2157 m 4866 2002 l S NP 4629 1997 m 4672 2029 l S NP 4678 2162 m 4629 1997 l S NP 4385 1995 m 4420 2031 l S NP 4392 2163 m 4385 1995 l S NP 4128 1995 m 4159 2032 l S NP 4119 2163 m 4128 1995 l S NP 3843 1996 m 3883 2030 l S NP 3874 2163 m 3843 1996 l S NP 3486 2030 m 3552 2034 l S NP 3701 2129 m 3486 2030 l S NP 3205 2110 m 3246 2077 l S NP 3452 2049 m 3205 2110 l S NP 2962 2133 m 2985 2094 l S NP 3165 2025 m 2962 2133 l S NP 2714 2144 m 2725 2103 l S NP 2883 2014 m 2714 2144 l S NP 2471 2153 m 2469 2111 l S NP 2596 2005 m 2471 2153 l S NP 2236 2161 m 2218 2120 l S NP 2301 1998 m 2236 2161 l S NP 2013 2163 m 1976 2128 l S NP 1994 1996 m 2013 2163 l S NP 1791 2156 m 1738 2131 l S NP 1686 2002 m 1791 2156 l S NP 1559 2143 m 1497 2129 l S NP 1388 2015 m 1559 2143 l S NP 1314 2130 m 1248 2125 l S NP 1103 2028 m 1314 2130 l S NP 1060 2120 m 994 2121 l S NP 827 2039 m 1060 2120 l S NP 5859 1875 m 5925 1872 l S NP 6098 1947 m 5859 1875 l S NP 5601 1867 m 5667 1868 l S NP 5826 1955 m 5601 1867 l S NP 5347 1857 m 5412 1865 l S NP 5550 1965 m 5347 1857 l S NP 5099 1847 m 5161 1861 l S NP 5268 1976 m 5099 1847 l S NP 4856 1837 m 4913 1859 l S NP 4981 1986 m 4856 1837 l S NP 4615 1831 m 4663 1860 l S NP 4692 1992 m 4615 1831 l S NP 4367 1828 m 4409 1861 l S NP 4410 1994 m 4367 1828 l S NP 4103 1828 m 4145 1861 l S NP 4144 1994 m 4103 1828 l S NP 3808 1834 m 3860 1859 l S NP 3909 1989 m 3808 1834 l S NP 3473 1877 m 3539 1872 l S NP 3714 1946 m 3473 1877 l S NP 3202 1935 m 3247 1905 l S NP 3455 1887 m 3202 1935 l S NP 2955 1959 m 2983 1921 l S NP 3172 1863 m 2955 1959 l S NP 2707 1972 m 2723 1931 l S NP 2890 1850 m 2707 1972 l S NP 2463 1982 m 2466 1941 l S NP 2604 1840 m 2463 1982 l S NP 2229 1991 m 2214 1950 l S NP 2308 1831 m 2229 1991 l S NP 2007 1995 m 1972 1959 l S NP 2001 1827 m 2007 1995 l S NP 1788 1989 m 1736 1963 l S NP 1689 1833 m 1788 1989 l S NP 1558 1976 m 1496 1961 l S NP 1390 1846 m 1558 1976 l S NP 1313 1963 m 1248 1957 l S NP 1104 1860 m 1313 1963 l S NP 1060 1952 m 993 1953 l S NP 828 1871 m 1060 1952 l S NP 5858 1708 m 5924 1704 l S NP 6099 1778 m 5858 1708 l S NP 5599 1701 m 5665 1701 l S NP 5828 1786 m 5599 1701 l S NP 5344 1692 m 5409 1697 l S NP 5553 1795 m 5344 1692 l S NP 5093 1682 m 5157 1694 l S NP 5274 1805 m 5093 1682 l S NP 4847 1672 m 4906 1692 l S NP 4990 1814 m 4847 1672 l S NP 4601 1666 m 4654 1691 l S NP 4706 1820 m 4601 1666 l S NP 4348 1663 m 4397 1691 l S NP 4429 1823 m 4348 1663 l S NP 4079 1664 m 4130 1691 l S NP 4168 1822 m 4079 1664 l S NP 3781 1675 m 3842 1692 l S NP 3936 1811 m 3781 1675 l S NP 3468 1717 m 3532 1708 l S NP 3719 1769 m 3468 1717 l S NP 3200 1763 m 3248 1734 l S NP 3457 1723 m 3200 1763 l S NP 2950 1786 m 2982 1750 l S NP 3177 1700 m 2950 1786 l S NP 2701 1800 m 2721 1760 l S NP 2896 1686 m 2701 1800 l S NP 2457 1812 m 2463 1770 l S NP 2610 1675 m 2457 1812 l S NP 2222 1822 m 2211 1781 l S NP 2315 1664 m 2222 1822 l S NP 2001 1827 m 1969 1790 l S NP 2006 1659 m 2001 1827 l S NP 1784 1822 m 1733 1795 l S NP 1693 1664 m 1784 1822 l S NP 1556 1809 m 1494 1794 l S NP 1391 1678 m 1556 1809 l S NP 1313 1795 m 1247 1789 l S NP 1104 1691 m 1313 1795 l S NP 1059 1784 m 993 1785 l S NP 828 1702 m 1059 1784 l S NP 5857 1541 m 5923 1537 l S NP 6100 1609 m 5857 1541 l S NP 5598 1534 m 5664 1534 l S NP 5829 1616 m 5598 1534 l S NP 5341 1526 m 5407 1530 l S NP 5556 1624 m 5341 1526 l S NP 5088 1517 m 5153 1527 l S NP 5279 1634 m 5088 1517 l S NP 4839 1508 m 4900 1524 l S NP 4998 1642 m 4839 1508 l S NP 4589 1502 m 4646 1523 l S NP 4718 1648 m 4589 1502 l S NP 4332 1499 m 4386 1523 l S NP 4445 1651 m 4332 1499 l S NP 4059 1502 m 4116 1523 l S NP 4188 1649 m 4059 1502 l S NP 3764 1516 m 3828 1527 l S NP 3953 1634 m 3764 1516 l S NP 3465 1554 m 3529 1543 l S NP 3722 1596 m 3465 1554 l S NP 3199 1592 m 3248 1564 l S NP 3458 1558 m 3199 1592 l S NP 2946 1614 m 2982 1579 l S NP 3181 1536 m 2946 1614 l S NP 2696 1629 m 2720 1589 l S NP 2901 1522 m 2696 1629 l S NP 2451 1641 m 2461 1600 l S NP 2616 1509 m 2451 1641 l S NP 2216 1652 m 2208 1611 l S NP 2321 1498 m 2216 1652 l S NP 1995 1659 m 1966 1621 l S NP 2012 1491 m 1995 1659 l S NP 1781 1655 m 1731 1627 l S NP 1696 1496 m 1781 1655 l S NP 1555 1642 m 1493 1626 l S NP 1393 1509 m 1555 1642 l S NP 1312 1628 m 1247 1621 l S NP 1105 1523 m 1312 1628 l S NP 1059 1616 m 993 1617 l S NP 828 1534 m 1059 1616 l S NP 5856 1374 m 5922 1369 l S NP 6101 1440 m 5856 1374 l S NP 5596 1368 m 5662 1366 l S NP 5831 1446 m 5596 1368 l S NP 5339 1360 m 5405 1363 l S NP 5558 1454 m 5339 1360 l S NP 5084 1352 m 5149 1360 l S NP 5283 1462 m 5084 1352 l S NP 4831 1344 m 4894 1357 l S NP 5006 1470 m 4831 1344 l S NP 4578 1338 m 4638 1356 l S NP 4729 1476 m 4578 1338 l S NP 4318 1336 m 4376 1356 l S NP 4459 1478 m 4318 1336 l S NP 4044 1340 m 4105 1356 l S NP 4203 1474 m 4044 1340 l S NP 3753 1357 m 3818 1362 l S NP 3964 1458 m 3753 1357 l S NP 3464 1390 m 3527 1377 l S NP 3723 1424 m 3464 1390 l S NP 3198 1422 m 3249 1395 l S NP 3459 1392 m 3198 1422 l S NP 2944 1443 m 2981 1408 l S NP 3184 1371 m 2944 1443 l S NP 2692 1457 m 2719 1419 l S NP 2905 1357 m 2692 1457 l S NP 2446 1470 m 2459 1429 l S NP 2621 1344 m 2446 1470 l S NP 2210 1483 m 2206 1441 l S NP 2327 1332 m 2210 1483 l S NP 1990 1491 m 1963 1452 l S NP 2017 1324 m 1990 1491 l S NP 1777 1488 m 1729 1459 l S NP 1700 1327 m 1777 1488 l S NP 1553 1474 m 1492 1458 l S NP 1394 1340 m 1553 1474 l S NP 1311 1460 m 1246 1453 l S NP 1106 1354 m 1311 1460 l S NP 1059 1448 m 993 1449 l S NP 828 1366 m 1059 1448 l S NP 5856 1208 m 5921 1202 l S NP 6101 1271 m 5856 1208 l S NP 5595 1201 m 5661 1199 l S NP 5832 1277 m 5595 1201 l S NP 5336 1194 m 5403 1196 l S NP 5561 1284 m 5336 1194 l S NP 5080 1187 m 5145 1193 l S NP 5287 1292 m 5080 1187 l S NP 4825 1179 m 4889 1190 l S NP 5012 1299 m 4825 1179 l S NP 4569 1174 m 4631 1189 l S NP 4738 1304 m 4569 1174 l S NP 4306 1173 m 4368 1189 l S NP 4470 1305 m 4306 1173 l S NP 4032 1178 m 4096 1190 l S NP 4215 1300 m 4032 1178 l S NP 3745 1195 m 3812 1196 l S NP 3972 1283 m 3745 1195 l S NP 3463 1224 m 3525 1210 l S NP 3724 1254 m 3463 1224 l S NP 3198 1252 m 3249 1226 l S NP 3459 1226 m 3198 1252 l S NP 2941 1272 m 2981 1238 l S NP 3186 1206 m 2941 1272 l S NP 2689 1286 m 2718 1249 l S NP 2908 1192 m 2689 1286 l S NP 2442 1300 m 2458 1259 l S NP 2625 1178 m 2442 1300 l S NP 2205 1313 m 2203 1271 l S NP 2332 1165 m 2205 1313 l S NP 1984 1322 m 1959 1283 l S NP 2024 1156 m 1984 1322 l S NP 1772 1320 m 1726 1290 l S NP 1705 1158 m 1772 1320 l S NP 1550 1307 m 1490 1290 l S NP 1397 1171 m 1550 1307 l S NP 1310 1293 m 1245 1286 l S NP 1107 1185 m 1310 1293 l S NP 1058 1281 m 992 1281 l S NP 829 1197 m 1058 1281 l S NP 5855 1040 m 5920 1034 l S NP 6102 1101 m 5855 1040 l S NP 5594 1035 m 5660 1032 l S NP 5833 1107 m 5594 1035 l S NP 5334 1028 m 5401 1029 l S NP 5563 1114 m 5334 1028 l S NP 5077 1021 m 5143 1026 l S NP 5290 1121 m 5077 1021 l S NP 4820 1015 m 4885 1024 l S NP 5017 1127 m 4820 1015 l S NP 4562 1010 m 4625 1022 l S NP 4745 1132 m 4562 1010 l S NP 4298 1010 m 4361 1022 l S NP 4479 1132 m 4298 1010 l S NP 4023 1016 m 4088 1024 l S NP 4224 1126 m 4023 1016 l S NP 3741 1033 m 3807 1031 l S NP 3976 1109 m 3741 1033 l S NP 3463 1058 m 3524 1043 l S NP 3724 1084 m 3463 1058 l S NP 3197 1083 m 3250 1057 l S NP 3460 1059 m 3197 1083 l S NP 2940 1101 m 2982 1068 l S NP 3187 1041 m 2940 1101 l S NP 2686 1116 m 2717 1078 l S NP 2911 1026 m 2686 1116 l S NP 2438 1129 m 2456 1089 l S NP 2629 1013 m 2438 1129 l S NP 2199 1143 m 2201 1101 l S NP 2338 999 m 2199 1143 l S NP 1977 1153 m 1956 1113 l S NP 2030 989 m 1977 1153 l S NP 1767 1153 m 1722 1122 l S NP 1710 989 m 1767 1153 l S NP 1548 1141 m 1488 1122 l S NP 1399 1001 m 1548 1141 l S NP 1309 1126 m 1244 1118 l S NP 1108 1016 m 1309 1126 l S NP 1058 1113 m 992 1113 l S NP 829 1029 m 1058 1113 l S NP 5854 873 m 5920 867 l S NP 6102 932 m 5854 873 l S NP 5593 868 m 5659 864 l S NP 5834 938 m 5593 868 l S NP 5333 862 m 5399 861 l S NP 5564 944 m 5333 862 l S NP 5074 856 m 5140 859 l S NP 5293 950 m 5074 856 l S NP 4816 850 m 4881 857 l S NP 5021 956 m 4816 850 l S NP 4556 846 m 4621 855 l S NP 4751 960 m 4556 846 l S NP 4291 846 m 4355 855 l S NP 4486 960 m 4291 846 l S NP 4017 853 m 4083 858 l S NP 4230 953 m 4017 853 l S NP 3737 869 m 3803 864 l S NP 3980 937 m 3737 869 l S NP 3462 891 m 3524 876 l S NP 3725 914 m 3462 891 l S NP 3197 913 m 3250 888 l S NP 3460 892 m 3197 913 l S NP 2938 931 m 2982 899 l S NP 3189 875 m 2938 931 l S NP 2684 945 m 2717 908 l S NP 2913 861 m 2684 945 l S NP 2434 958 m 2455 918 l S NP 2633 848 m 2434 958 l S NP 2193 972 m 2199 930 l S NP 2344 834 m 2193 972 l S NP 1970 984 m 1952 944 l S NP 2037 822 m 1970 984 l S NP 1761 986 m 1718 953 l S NP 1716 820 m 1761 986 l S NP 1544 974 m 1486 954 l S NP 1403 832 m 1544 974 l S NP 1308 959 m 1243 950 l S NP 1109 847 m 1308 959 l S NP 1057 946 m 991 945 l S NP 830 860 m 1057 946 l S 0 G medium setlinewidth NP 3461 743 m 3461 4256 l S thin setlinewidth NP 3439 854 m 3461 854 l S NP 3439 980 m 3461 980 l S NP 3439 1106 m 3461 1106 l S NP 3417 1232 m 3461 1232 l S NP 3439 1358 m 3461 1358 l S NP 3439 1484 m 3461 1484 l S NP 3439 1610 m 3461 1610 l S NP 3439 1736 m 3461 1736 l S NP 3417 1861 m 3461 1861 l S NP 3439 1987 m 3461 1987 l S NP 3439 2113 m 3461 2113 l S NP 3439 2239 m 3461 2239 l S NP 3439 2365 m 3461 2365 l S NP 3417 2491 m 3461 2491 l S NP 3439 2617 m 3461 2617 l S NP 3439 2743 m 3461 2743 l S NP 3439 2868 m 3461 2868 l S NP 3439 2994 m 3461 2994 l S NP 3417 3120 m 3461 3120 l S NP 3439 3246 m 3461 3246 l S NP 3439 3372 m 3461 3372 l S NP 3439 3498 m 3461 3498 l S NP 3439 3624 m 3461 3624 l S NP 3417 3750 m 3461 3750 l S NP 3439 3875 m 3461 3875 l S NP 3439 4001 m 3461 4001 l S NP 3439 4127 m 3461 4127 l S NP 3439 4253 m 3461 4253 l S medium setlinewidth NP 692 2491 m 6230 2491 l S thin setlinewidth NP 692 2474 m 692 2491 l S NP 944 2458 m 944 2491 l S NP 1195 2474 m 1195 2491 l S NP 1447 2474 m 1447 2491 l S NP 1699 2474 m 1699 2491 l S NP 1951 2474 m 1951 2491 l S NP 2202 2458 m 2202 2491 l S NP 2454 2474 m 2454 2491 l S NP 2706 2474 m 2706 2491 l S NP 2958 2474 m 2958 2491 l S NP 3209 2474 m 3209 2491 l S NP 3713 2474 m 3713 2491 l S NP 3964 2474 m 3964 2491 l S NP 4216 2474 m 4216 2491 l S NP 4468 2474 m 4468 2491 l S NP 4720 2458 m 4720 2491 l S NP 4971 2474 m 4971 2491 l S NP 5223 2474 m 5223 2491 l S NP 5475 2474 m 5475 2491 l S NP 5727 2474 m 5727 2491 l S NP 5978 2458 m 5978 2491 l S NP 6230 2474 m 6230 2491 l S medium setlinewidth (\2611) dup 0 stringbbox 2 idiv 1232 exch sub exch 3398 exch sub exch m show (\2610.5) dup 0 stringbbox 2 idiv 1861 exch sub exch 3398 exch sub exch m show (0) dup 0 stringbbox 2491 exch sub exch 3398 exch sub exch m show (0.5) dup 0 stringbbox 2 idiv 3120 exch sub exch 3398 exch sub exch m show (1) dup 0 stringbbox 2 idiv 3750 exch sub exch 3398 exch sub exch m show (y) dup 0 stringbbox 2 idiv 4298 exch sub exch 3408 exch sub exch m show (\2612) dup 0 stringbbox 2444 exch sub exch 2 idiv 944 exch sub exch m show (\2611) dup 0 stringbbox 2444 exch sub exch 2 idiv 2202 exch sub exch m show (1) dup 0 stringbbox 2444 exch sub exch 2 idiv 4720 exch sub exch m show (2) dup 0 stringbbox 2444 exch sub exch 2 idiv 5978 exch sub exch m show (x) dup 0 stringbbox 2644 exch sub exch 2 idiv 6200 exch sub exch m show boundarythick setlinewidth % The following draws a box around the plot, % if the variable drawborder is true % drawborder { % /bd boundarythick 2 idiv def % [] 0 setdash % NP bd bd m bd 5000 bd sub l % 6923 bd sub 5000 bd sub l % 6923 bd sub bd l % bd bd l S % } if % end of if to draw the border showpage grestore end %%EOF ---------------0409210533372--