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Riemann-Hilbert problem, Toda lattice, solitons
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\begin{document}


\title[Long-Time Asymptotics of the Toda Lattice]{Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited}

\author[H. Kr\"uger]{Helge Kr\"uger}
\address{Department of Mathematics\\ Rice University\\ Houston\\ TX 77005\\ USA}
\email{\href{mailto:helge.krueger@rice.edu}{helge.krueger@rice.edu}}
\urladdr{\href{http://math.rice.edu/~hk7/}{http://math.rice.edu/\~{}hk7/}}

\author[G. Teschl]{Gerald Teschl}
\address{Faculty of Mathematics\\
Nordbergstrasse 15\\ 1090 Wien\\ Austria\\ and International Erwin Schr\"odinger
Institute for Mathematical Physics, Boltzmanngasse 9\\ 1090 Wien\\ Austria}
\email{\href{mailto:Gerald.Teschl@univie.ac.at}{Gerald.Teschl@univie.ac.at}}
\urladdr{\href{http://www.mat.univie.ac.at/~gerald/}{http://www.mat.univie.ac.at/\~{}gerald/}}

\thanks{Research supported by the Austrian Science Fund (FWF) under Grant No.\ Y330.}
\thanks{\today}


\keywords{Riemann--Hilbert problem, Toda lattice, solitons}
\subjclass[2000]{Primary 37K40, 37K45; Secondary 35Q15, 37K10}

\begin{abstract}
The purpose of this article is to give a streamlined and self-contained
treatment of the long-time asymptotics of the
Toda lattice for decaying initial data in the soliton and in the similarity region
via the method of nonlinear steepest descent.
\end{abstract}


\maketitle



\section{Introduction}




In this paper we want to compute the long time asymptotics for
the doubly infinite Toda lattice which reads in Flaschka's
variables (see e.g.\ \cite{tjac}, \cite{taet}, or \cite{ta})
\be \label{tl}
\aligned
\dot b(n,t) &= 2(a(n,t)^2 -a(n-1,t)^2),\\
\dot a(n,t) &= a(n,t) (b(n+1,t) -b(n,t)),
\endaligned
\ee
$(n,t) \in \Z \times \R$. Here the dot denotes differentiation with
respect to time. We will consider solutions $(a,b)$ satisfying
\be \label{decay}
\sum_n (1+|n|)^{l+2} (|a(n,t) - \frac{1}{2}| + |b(n,t)|) < \infty
\ee
for some $l\in\N$ for one (and hence for all, see \cite{tjac}) $t\in\R$. It is
well-known that the corresponding initial value problem has unique global solutions 
which can be computed via the inverse scattering transform \cite{tjac}.

The Toda lattice is one of the most prominent soliton equations. The classical result
going back to Zabusky and Kruskal \cite{zakr} states that a "short range" perturbation
of the constant solution of a soliton equation eventually splits into a number
of stable solitons and a decaying background radiation component.
In particular, the solitons constitute the stable part of the solutions arising from
arbitrary short range initial conditions.
\begin{figure}
\includegraphics[width=8cm]{TodaRHP1}
\caption{Numerically computed solution of the Toda lattice, with initial
condition the constant solution perturbed at one point in the middle.} \label{fig1}
\end{figure}
This is illustrated in Figure~\ref{fig1} which shows the numerically computed
solution $a(n,t)$ corresponding to the initial condition $a(n,0)=\frac{1}{2}$, $b(n,0)=
\delta_{0,n}$ at some large time $t=150$. You can see the soliton region $|\frac{n}{t}|>1$
with one single soliton on the very left and the similarity region $|\frac{n}{t}|<1$ where
there are some small oscillations which decay like $t^{-1/2}$. The goal is to
mathematically justify this picture and to derive an asymptotic formula for the solution
in  the similarity region.

This was first done by Novokshenov and Habibullin \cite{nh} and was later made
rigorous by Kamvissis \cite{km} under the the additional assumption that no solitons
are present and that the underlying Jacobi operator is resonant at the band edges of
the spectrum (i.e., the reflection coefficient has absolute value strictly less than one, which
is generically not the case). The case of solitons was recently investigated by us in \cite{krt}.

We also want to mention that one could also replace the constant background solution
by a periodic one. However, this case exhibits a much different behaviour as was pointed
out by Kamvissis and one of us in \cite{kt} (see also \cite{emtist}, \cite{emtsr}, \cite{kt2}, \cite{kt3},
and \cite{krt2} for a rigorous mathematical treatment).

The main purpose of the present paper is to revisit this classical problem using the
method of nonlinear steepest descent by Deift and Zhou \cite{dz} and 
give a complete and expository introduction. We are trying to present a streamlined and
simplified approach with complete proofs. In particular, we have added two appendices
which show how to solve the localized Riemann--Hilbert problem on a  small cross via
parabolic cylinder functions and how to rewrite Riemann--Hilbert problems as singular
integral equations. Only some basic knowledge on Riemann--Hilbert problems, which
can be found for example in the beautiful lecture notes by Deift \cite{deiftbook}, is required.

As one of our main simplifications in contradistinction to \cite{km} we will work with the vector
Riemann--Hilbert problem which arises naturally from the inverse scattering theory, thus avoiding the detour
over the associated matrix Riemann--Hilbert problem. This also avoids the singularities appearing
in the matrix Riemann--Hilbert problem in case the reflection coefficient is $-1$ at the
band edges. In particular, this will remove the corresponding assumption $|R(z)|<1$
imposed in \cite{km}.

To state the main results, we begin by recalling that the sequences $a(n,t)$, $b(n,t)$, $n\in\Z$,
for fixed $t\in\R$, are uniquely determined by its scattering data, that is, by its right reflection
coefficient $R_+(z,t)$, $|z|=1$, and its eigenvalues $\lam_j\in(-\infty,-1)\cup(1,\infty)$, $j=1,\dots, N$,
together with the corresponding right norming constants $\gam_{+,j}(t)>0$, $j=1,\dots, N$.
It is well-known that under the assumption (\ref{decay}) the reflection coefficients are $C^{l+1}(\T)$.
Rather than in the complex plane, we will work on the unit disc using the usual
Joukowski transformation
\be\label{defzlam}
\lam = \frac{1}{2} \left(z + \frac{1}{z}\right),\quad z= \lam - \sqrt{\lam^2 -1}, \qquad
\lam\in\C, \: |z|\leq 1.
\ee
In these new coordinates the eigenvalues $\lam_j\in(-\infty,-1)\cup(1,\infty)$ will be denoted by
$\zeta_j\in(-1,0)\cup(0,1)$. The continuous spectrum $[-1,1]$ is mapped to the unit circle
$\T$. Moreover, the phase of the associated Riemann--Hilbert problem is given by
\begin{equation} \label{eq:Phi}
\Phi(z)=z-z^{-1}+2 \frac{n}{t} \log(z)
\end{equation}
and the stationary phase points, $\Phi'(z)=0$, are denoted by
\be
z_0=  -\frac{n}{t} - \sqrt{(\frac{n}{t})^2 -1}, \quad z_0^{-1}= -\frac{n}{t} + \sqrt{(\frac{n}{t})^2 -1},
\qquad \lam_0=-\frac{n}{t}.
\ee
Here the branch of the square root is chosen such that $\im(\sqrt{z})\ge 0$.
For $\frac{n}{t}<-1$ we have $z_0\in(0,1)$, for $-1\le \frac{n}{t} \le1$
we have $z_0\in\T$ (and hence $z_0^{-1}=\ol{z_0}$), and for $\frac{n}{t}>1$
we have $z_0\in(-1,0)$. For $|\frac{n}{t}|>1$ we will also need the value
$\zeta_0\in(-1,0)\cup(0,1)$ defined via $\re(\Phi(\zeta_0))=0$, that is,
\be
\frac{n}{t} = -\frac{\zeta_0 - \zeta_0^{-1}}{2\log(|\zeta_0|)}.
\ee
We will set $\zeta_0=-1$ if $|\frac{n}{t}|\le 1$ for notational convenience.
A simple analysis shows that for $\frac{n}{t}<-1$ we have $0<\zeta_0 < z_0 <1$ and
for $\frac{n}{t}>1$ we have $-1<z_0 < \zeta_0 <0$.

Furthermore, recall that the transmission coefficient $T(z)$, $|z|\le 1$, is time independent
and can be reconstructed using the Poisson--Jensen formula. In particular, we define
the partial transmission coefficient with respect to $z_0$ by
\begin{align}\nn
T(z,z_0) &=\\ \label{def:Tzz0}
& \begin{cases}
\prod\limits_{\zeta_k\in(\zeta_0,0)} |\zeta_k| \frac{z-\zeta_k^{-1}}{z-\zeta_k}, & z_0 \in (-1,0), \\
\left(\prod\limits_{\zeta_k\in(-1,0)} |\zeta_k| \frac{z-\zeta_k^{-1}}{z-\zeta_k} \right)
\exp\left(\frac{1}{2\pi\I}\int\limits_{\ol{z_0}}^{z_0}\log(|T(s)|) \frac{s+z}{s-z} \frac{ds}{s}\right), & |z_0| = 1, \\
\left(\prod\limits_{\zeta_k\in(-1,0)\cup(\zeta_0,1)}\!\!\! |\zeta_k| \frac{z-\zeta_k^{-1}}{z-\zeta_k} \right)
\exp\left(\frac{1}{2\pi\I}\int\limits_{\T}\log(|T(s)|) \frac{s+z}{s-z} \frac{ds}{s}\right), & z_0 \in (0,1).
\end{cases}
\end{align}
Here the integral is to be taken along the arc $\Sigma(z_0) = \{z \in\T | \re(z)<\re(z_0)\}$ oriented
counterclockwise.
Observe that $T(z,z_0)=T(z)$ once $z_0\in(0,1)$ and $(0,\zeta_0)$ contains no eigenvalues. Moreover,
$T(z,z_0)$ can be computed in terms of the scattering data since $|T(z)|^2= 1- |R_+(z,t)|^2$.

Moreover, we set
\begin{align}\nn
T_0(z_0) &= T(0,z_0)\\
&= \begin{cases}
\prod\limits_{\zeta_k\in(\zeta_0,0)} |\zeta_k|^{-1}, & z_0 \in (-1,0),\\
\left(\prod\limits_{\zeta_k\in(-1,0)} |\zeta_k|^{-1} \right)
\exp\left(\frac{1}{2\pi\I}\int\limits_{\ol{z_0}}^{z_0}\log(|T(s)|) \frac{ds}{s}\right), & |z_0| = 1, \\
\left(\prod\limits_{\zeta_k\in(-1,0)\cup(\zeta_0,1)} |\zeta_k|^{-1} \right)
\exp\left(\frac{1}{2\pi \I}\int\limits_{\T}\log(|T(s)|) \frac{ds}{s}\right), & z_0 \in (0,1),
\end{cases}
\end{align}
and
\begin{align} \nn
T_1(z_0) &= \frac{\partial}{\partial z} \log T(z,z_0) \Big|_{z=0}\\
&= \begin{cases}
\sum\limits_{\zeta_k\in(\zeta_0,0)} (\zeta_k^{-1} -\zeta_k), & z_0 \in (-1,0),\\
\sum\limits_{\zeta_k\in(-1,0)} (\zeta_k^{-1} -\zeta_k) +
\frac{1}{\pi\I}\int\limits_{\ol{z_0}}^{z_0}\log(|T(s)|) \frac{ds}{s^2}, & |z_0| = 1, \\
\sum\limits_{\zeta_k\in(-1,0)\cup(\zeta_0,1)} (\zeta_k^{-1} -\zeta_k) +
\frac{1}{\pi \I}\int\limits_{\T}\log(|T(s)|) \frac{ds}{s^2}, & z_0 \in (0,1).
\end{cases}
\end{align}
In other words, $T(z,z_0)=T_0(z_0) ( 1 + T_1(z_0) z + O(z^2))$.

\begin{theorem}[Soliton region]\label{thm:asym}
Assume (\ref{decay}) and abbreviate by $c_k= -\frac{\zeta_k - \zeta_k^{-1}}{2\log(|\zeta_k|)}$
the velocity of the $k$'th soliton determined by $\re(\Phi(\zeta_k))=0$.
Then the asymptotics in the soliton region, $|n/t| \geq 1 + C/t \log(t)^2$ for some
$C>0$, are as follows.

Let $\eps > 0$ sufficiently small such that the intervals
$[c_k-\eps,c_k+\eps]$, $1\le k \le N$, are disjoint and lie inside $(-1,0)\cup(0,1)$. 

If $|\frac{n}{t} - c_k|<\eps$ for some $k$, one has
\begin{align}\nn
\prod_{j=n}^\infty (2 a(j,t)) &= T_0(z_0) \left(
\sqrt{\frac{1-\zeta_k^2 + \gam_k(n,t)}{1-\zeta_k^2 + \gam_k(n,t) \zeta_k^2}} + O(t^{-l}) \right),\\
\sum_{j=n+1}^\infty b(j,t) &= \frac{1}{2} T_1(z_0) -
\frac{\gam_k(n,t)  \zeta_k (\zeta_k^2-1)}{2((\gam_k(n,t) -1) \zeta_k^2+1)} + O(t^{-l}),
\end{align}
for any $l \geq 1$, where
\be
\gam_k(n,t) = \gam_k T(\zeta_k,c_k)^{-2} \E^{t (\zeta_k - \zeta_k^{-1})} \zeta_k^{2n}.
\ee

If $|\frac{n}{t} -c_k| \geq \eps$, for all $k$, one has
\begin{align}\nn
\prod_{j=n}^\infty (2 a(j,t)) &= T_0(z_0) \left(1 + O(t^{-l}) \right),\\
\sum_{j=n+1}^\infty b(j,t) &= \frac{1}{2} T_1(z_0) + O(t^{-l}),
\end{align}
for any $l \geq 1$.
\end{theorem}

In the remaining region, we will show

\begin{theorem}[Similarity region]\label{thm:asym2}
Assume (\ref{decay}) with $l\ge 3$, then, away from the soliton region, $|n/t| \leq 1 - C$ for some
$C>0$. Then the asymptotics are given by
\begin{align}\nn
\prod_{j=n}^\infty (2 a(j,t)) = & T_0(z_0) \Bigg(1 + \left(\frac{\nu}{- 2\sin(\theta_0) t}\right)^{1/2}
\cos\big(t \Phi_0 + \nu\log(t) - \delta\big)\\
& + O(t^{-\alpha}) \Bigg),\\ \nn
\sum_{j=n+1}^\infty b(j,t) = &  \frac{1}{2} T_1(z_0) + \left(\frac{\nu}{-2\sin(\theta_0) t}\right)^{1/2}
\cos\big(t \Phi_0 + \nu\log(t) - \delta  +  \theta_0\big)\\
& +O(t^{-\alpha}),
\end{align}
for any $\alpha<1$. Here 
\begin{align}\nn
\theta_0 &= \arg(z_0),\\\nn
\Phi_0 &= 2 (\sin(\theta_0) - \theta_0\cos(\theta_0)), \\\label{eq:defvar}
\delta &= \pi/4 - 3 \nu \log |2\sin(\theta_0)| + 2 \arg(\ti{T}(z_0,z_0)) -  \arg(R(z_0))+\arg(\Gamma(\I\nu)), \\ \nn
\ti{T}(z,z_0) &= \prod\limits_{\zeta_k\in(-1,0)} |\zeta_k| \frac{z-\zeta_k^{-1}}{z-\zeta_k} \cdot
\exp\left(\frac{1}{2\pi\I}\int\limits_{\ol{z_0}}^{z_0}\log\Big(\frac{|T(s)|}{|T(z_0)|}\Big) \frac{s+z}{s-z} \frac{ds}{s}\right).
\end{align}
\end{theorem}

We will not address the asymptotics in the missing region around $|n| \approx t$.
In the case $|R(z)|<1$ the solution can be given in terms of Painlev\'e II transcendents \cite{km}.
In the general case an outline using the $g$-function method was given in \cite{dvz}
(for the case of the Korteweg--de Vires equation). The method can also be used to obtain
further terms in the asymptotic expansion \cite{dz2}.

Finally, note that one can obtain the asymptotics for $n \geq 0$ from the
ones for $n\leq 0$ by virtue of a simple reflection. Similarly for $t\geq 0$
versus $t\le 0$.

\begin{lemma}
Suppose $a(n,t)$, $b(n,t)$ satisfy the Toda equation (\ref{tl}), then so do
$$
\ti{a}(n,t) =a(-n-1,t),\quad \ti{b}(n,t) = - b(-n,t)
$$
respectively
$$
\ti{a}(n,t) =a(n,-t),\quad \ti{b}(n,t) = - b(n,-t).
$$
\end{lemma}




\section{The Inverse scattering transform and the Riemann--Hilbert problem}
\label{sec:istrhp}



In this section we want to derive the Riemann--Hilbert problem from scattering theory.
The special case without eigenvalues was first given in Kamvissis \cite{km}. How eigenvalues
can be added was first shown in Deift, Kamvissis, Kriecherbauer, and Zhou \cite{dkkz}.
We essentially follow \cite{krt} in this section.

For the necessary results from scattering theory respectively the inverse
scattering transform for the Toda lattice we refer to \cite{tist}, \cite{tivp}, \cite{tjac}.

Associated with $a(t), b(t)$ is a self-adjoint Jacobi operator
\begin{equation} \label{defjac}
H(t) = a(t) S^+  + a^-(t) S^-  + b(t)
\end{equation}
in $\lz$, where $S^\pm f(n) = f^\pm(n)= f(n\pm1)$ are the usual shift operators and
$\lz$ denotes the Hilbert space of square summable (complex-valued) sequences
over $\Z$. By our assumption (\ref{decay}) the spectrum of $H$ consists of an absolutely
continuous part $[-1,1]$ plus a finite number of eigenvalues $\lam_k\in\R\backslash[-1,1]$,
$1\le k \le N$. In addition, there exist two Jost functions $\psi_\pm(z,n,t)$
which solve the recurrence equation
\be
H(t) \psi_\pm(z,n,t) = \frac{z+z^{-1}}{2} \psi_\pm(z,n,t), \qquad |z|\le 1,
\ee
and asymptotically look like the free solutions
\be
\lim_{n \to \pm \infty} z^{\mp  n} \psi_{\pm}(z,n,t) =1.
\ee
Both $\psi_\pm(z,n,t)$ are analytic for $0<|z|<1$ with smooth boundary values
for $|z|=1$.
The asymptotics of the two projections of the Jost function are
\be\label{eq:psiasym}
\psi_\pm(z,n,t) =  \frac{z^{\pm n}}{A_\pm(n,t)} \Big(1 + 2 B_\pm(n,t) z + O(z^2) \Big),
\ee
as $z \to 0$, where
\be \label{defAB}
\aligned
A_+(n,t) &= \prod_{j=n}^{\infty} 2 a(j,t), \quad
B_+(n,t)= -\sum_{j=n+1}^\infty b(j,t), \\
A_-(n,t) &= \!\!\prod_{j=- \infty}^{n-1}\! 2 a(j,t), \quad
B_-(n,t) = -\sum_{j=-\infty}^{n-1} b(j,t).
\endaligned
\ee

One has the scattering relations
\be \label{relscat}
T(z) \psi_\mp(z,n,t) =  \ol{\psi_\pm(z,n,t)} +
R_\pm(z,t) \psi_\pm(z,n,t),  \qquad |z|=1,
\ee
where $T(z)$, $R_\pm(z,t)$ are the transmission respectively reflection coefficients.
The transmission and reflection coefficients have the following well-known properties:

\begin{lemma}
The transmission coefficient $T(z)$ has a meromorphic extension to the
interior of the unit circle with simple poles at the images of the eigenvalues $\zeta_j$.
The residues of $T(z)$ are given by
\be\label{eq:resT}
\res_{\zeta_k} T(z) = - \zeta_k \frac{\gam_{+,k}(t)}{\mu_k(t)} = - \zeta_k \gam_{-,k}(t) \mu_k(t),
\ee
where
\be
\gam_{\pm,k}(t)^{-1} = \sum_{n\in\Z} |\psi_\pm(\zeta_k,n,t)|^2
\ee
and $\psi_- (\zeta_k,n,t) = \mu_k(t) \psi_+(\zeta_k,n,t)$.

Moreover,
\be \label{reltrpm} 
T(z) \ol{R_+(z,t)} + \ol{T(z)} R_-(z,t)=0, \qquad |T(z)|^2 + |R_\pm(z,t)|^2=1.
\ee
\end{lemma}

In particular one reflection coefficient, say $R(z,t)=R_+(z,t)$, and one set of
norming constants, say $\gam_k(t)= \gam_{+,k}(t)$, suffices. Moreover,
the time dependence is given by:

\begin{lemma}
The time evolutions of the quantities $R_+(z,t)$, $\gam_{+,k}(t)$ are given by
\begin{align}
R(z,t) &= R(z) \E^{t (z - z^{-1})}\\
\gam_k(t) &= \gam_k \E^{t (\zeta_k - \zeta_k^{-1})},
\end{align}
where $R(z)=R(z,0)$ and $\gam_k=\gam_k(0)$.
\end{lemma}

We will define a Riemann--Hilbert problem as follows:
\be\label{defm}
m(z,n,t)= \left\{\begin{array}{c@{\quad}l}
\begin{pmatrix} T(z) \psi_-(z,n,t) z^n  & \psi_+(z,n,t) z^{-n} \end{pmatrix},
& |z|<1,\\
\begin{pmatrix} \psi_+(z^{-1},n,t) z^n & T(z^{-1}) \psi_-(z^{-1},n,t) z^{-n} \end{pmatrix}, 
& |z|>1.
\end{array}\right.
\ee

We are interested in the jump condition of $m(z,n,t)$ on the unit circle $\T$ (oriented
counterclockwise).
To formulate our jump condition we use the following convention:
When representing functions on $\T$, the lower subscript denotes
the non-tangential limit from different sides,
\be
m_\pm(z) = \lim_{ \zeta\to z,\; |\zeta|^{\pm 1}<1} m(\zeta), \qquad |z|=1.
\ee
Using the notation above implicitly assumes that these limits exist in the sense that
$m(z)$ extends to a continuous function on the boundary.


\begin{theorem}[Vector Riemann--Hilbert problem]\label{thm:vecrhp}
Let $\mathcal{S}_+(H(0))=\{ R(z),\; |z|=1; \: (\zeta_k, \gam_k), \: 1\le k \le N \}$
the left scattering data of the operator $H(0)$. Then $m(z)=m(z,n,t)$ defined in (\ref{defm})
is meromorphic away from the unit circle with simple poles at $\zeta_k$, $\zeta_k^{-1}$ and satisfies:
\begin{enumerate}
\item The jump condition
\be \label{eq:jumpcond}
m_+(z)=m_-(z) v(z), \qquad
v(z)=\begin{pmatrix}
1-|R(z)|^2 & - \ol{R(z)} \E^{-t\Phi(z)} \\ 
R(z) \E^{t\Phi(z)} & 1
\end{pmatrix},
\ee
for $z \in\T$,
\item
the pole conditions
\be\label{eq:polecond}
\aligned
\res_{\zeta_k} m(z) &= \lim_{z\to\zeta_k} m(z)
\begin{pmatrix} 0 & 0\\ - \zeta_k \gam_k \E^{t\Phi(\zeta_k)}  & 0 \end{pmatrix},\\
\res_{\zeta_k^{-1}} m(z) &= \lim_{z\to\zeta_k^{-1}} m(z)
\begin{pmatrix} 0 & \zeta_k^{-1} \gam_k \E^{t\Phi(\zeta_k)} \\ 0 & 0 \end{pmatrix},
\endaligned
\ee
\item
the symmetry condition
\be \label{eq:symcond}
m(z^{-1}) = m(z) \sigI 
\ee
\item
and the normalization
\be\label{eq:normcond}
m(0) = (m_1\quad m_2),\quad m_1 \cdot m_2 = 1\quad m_1 > 0.
\ee
\end{enumerate}
Here the phase is given by
\begin{equation}
\Phi(z)=z-z^{-1}+2 \frac{n}{t} \log \, z.
\end{equation}
\end{theorem}

\begin{proof}
The jump condition (\ref{eq:jumpcond}) is a simple calculation using the scattering relations
(\ref{relscat}) plus (\ref{reltrpm}). The pole conditions follow since $T(z)$ is meromorphic in $|z| <1$
with simple poles at $\zeta_k$ and residues given by (\ref{eq:resT}).
The symmetry condition holds by construction and the normalization (\ref{eq:normcond})
is immediate from the following lemma.
\end{proof}

Observe that the pole condition at $\zeta_k$ is sufficient since the one at $\zeta_k^{-1}$ follows
by symmetry. Moreover, it can be shown that the solution of the above Riemann--Hilbert problem
is unique \cite{krt}. However, we will not need this fact here and it will follow as a byproduct of
our analysis at least for sufficiently large $t$.

Moreover, we have the following asymptotic behaviour near $z=0$:

\begin{lemma}
The function $m(z,n,t)$ defined in (\ref{defm}) satisfies
\be\label{eq:AB}
m(z,n,t) = \begin{pmatrix}
A(n,t) (1 - 2 B(n-1,t) z) &
\frac{1}{A(n,t)}(1 + 2 B(n,t) z )
\end{pmatrix} + O(z^2).
\ee
Here $A(n,t)= A_+(n,t)$ and $B(n,t)= B_+(n,t)$ are defined in (\ref{defAB}).
\end{lemma}

\begin{proof}
This follows from (\ref{eq:psiasym}) and $T(z)= A_+ A_- ( 1 - 2(B_+ - b +B_-)z+ O(z^2))$.
\end{proof}

For our further analysis it will be convenient to rewrite the pole condition as a jump
condition and hence turn our meromorphic Riemann--Hilbert problem into a holomorphic Riemann--Hilbert problem following \cite{dkkz}.
Choose $\eps$ so small that the discs $|z-\zeta_k|<\eps$ are inside the unit circle and
do not intersect. Then redefine $m$ in a neighborhood of $\zeta_k$ respectively $\zeta_k^{-1}$ according to
\be\label{eq:redefm}
m(z) = \begin{cases} m(z) \begin{pmatrix} 1 & 0 \\
\frac{\zeta_k \gamma_k \E^{t\Phi(\zeta_k)} }{z-\zeta_k} & 1 \end{pmatrix},  &
|z-\zeta_k|< \eps,\\
m(z) \begin{pmatrix} 1 & -\frac{z \gamma_k \E^{t\Phi(\zeta_k)} }{z-\zeta_k^{-1}} \\
0 & 1 \end{pmatrix},  &
|z^{-1}-\zeta_k|< \eps,\\
m(z), & \text{else}.\end{cases}
\ee
and for $|z|>1$ by symmetry (\ref{eq:symcond}). Then a straightforward calculation using
$\res_\zeta m = \lim_{z\to\zeta} (z-\zeta)m(z)$ shows

\begin{lemma}
Suppose $m(z)$ is redefined as in (\ref{eq:redefm}). Then $m(z)$ is holomorphic away from
the unit circle and satisfies (\ref{eq:jumpcond}), (\ref{eq:symcond}), (\ref{eq:normcond})
and the pole condition is replaced by the jump condition
\be \label{eq:jumpcond2}
\aligned
m_+(z) &= m_-(z) \begin{pmatrix} 1 & 0 \\
\frac{\zeta_k \gamma_k \E^{t\Phi(\zeta_k)}}{z-\zeta_k} & 1 \end{pmatrix},\quad |z-\zeta_k|=\eps,\\
m_+(z) &= m_-(z) \begin{pmatrix} 1 & -\frac{z \gamma_k \E^{t\Phi(\zeta_k)}}{z-\zeta_k^{-1}} \\
0 & 1 \end{pmatrix},\quad |z^{-1}-\zeta_k|=\eps,
\endaligned
\ee
where the small circle around $\zeta_k$ is oriented counterclockwise.
\end{lemma}

Finally, we note that the case of just one eigenvalue and zero reflection coefficient can be
solved explicitly.

\begin{lemma}[One soliton solution]\label{lem:singlesoliton}
Suppose there is only one eigenvalue and a vanishing reflection coefficient, that is,
$\mathcal{S}_+(H(t))=\{ R(z)\equiv 0,\; |z|=1; \: (\zeta, \gam) \}$.
Then the solution of the Riemann--Hilbert problem (\ref{eq:jumpcond})--(\ref{eq:normcond})
is given by
\begin{align}\label{eq:oss}
m_0(z) &= \begin{pmatrix} f(z) & f(1/z) \end{pmatrix} \\
\nn f(z) &= \frac{1}{\sqrt{1 - \zeta^2 + \gamma} \sqrt{1 - \zeta^2 + \zeta^2 \gamma}}
\left(\gamma \zeta^2 \frac{z-\zeta^{-1}}{z - \zeta} + 1 - \zeta^2\right).
\end{align}
In particular,
\be
A_+ = \sqrt{\frac{1-\zeta^2 + \gamma}{1 - \zeta^2 + \gamma \zeta^2}}, \qquad
B_+= \frac{\gam  \zeta (\zeta ^2-1)}{2 ((\gam -1) \zeta ^2+1)}.
\ee
\end{lemma}






\section{Conjugation and deformation}
\label{sec:conjdef}



This section demonstrates how to conjugate our Riemann--Hilbert problem and
deform the jump contours, such that the jumps will be exponentially decreasing
away from the stationary phase points. In order to do this we will assume that $R(z)$
has an analytic extension to a strip around the unit circle throughout this and the
following section. This is for example the case if the decay in (\ref{decay}) is exponentially.
We will eventually show how to remove this assumption in Section~\ref{sec:analapprox}.

For easy reference we note the following result which can be checked by a straightforward
calculation.

\begin{lemma}[Conjugation]\label{lem:conjug}
Assume that $\wti{\Sigma}\subseteq\Sigma$. Let $D$ be a matrix of the form
\be
D(z) = \begin{pmatrix} d(z)^{-1} & 0 \\ 0 & d(z) \end{pmatrix},
\ee
where $d: \C\backslash\wti{\Sigma}\to\C$ is a sectionally analytic function. Set
\be
\ti{m}(z) = m(z) D(z),
\ee
then the jump matrix transforms according to
\be
\ti{v}(z) = D_-(z)^{-1} v(z) D_+(z).
\ee
If $d$ satisfies $d(z^{-1}) = d(z)^{-1}$ and $d(0) > 0$. Then the transformation $\ti{m}(z) = m(z) D(z)$
respects our symmetry, that is, $\ti{m}(z)$ satisfies (\ref{eq:symcond}) if and only if $m(z)$ does.
\end{lemma}

In particular, we obtain
\be
\ti{v} = \begin{pmatrix} v_{11} & v_{12} d^{2} \\ v_{21} d^{-2}  & v_{22} \end{pmatrix},
\qquad z\in\Sigma\backslash\wti{\Sigma},
\ee
respectively
\be
\ti{v} = \begin{pmatrix} \frac{d_-}{d_+} v_{11} & v_{12} d_+ d_- \\
v_{21} d_+^{-1} d_-^{-1}  & \frac{d_+}{d_-} v_{22} \end{pmatrix},
\qquad z\in\Sigma\cap\wti{\Sigma}.
\ee

In order to remove the poles there are two cases to distinguish. If
$\lam_k >\frac{1}{2}(\zeta_0+\zeta_0^{-1})$ the jump is exponentially decaying and there is nothing
to do. 

Otherwise we use conjugation to turn the jumps into exponentially decaying
ones, again following Deift, Kamvissis, Kriecherbauer, and Zhou \cite{dkkz} (see also \cite{krt}).
It turns out that we will have to handle the poles at $\zeta_k$ and $\zeta_k^{-1}$
in one step in order to preserve symmetry and in order to not add additional poles
elsewhere.

\begin{lemma}\label{lem:twopolesinc}
Assume that the Riemann--Hilbert problem for $m$ has jump conditions near $\zeta$ and
$\zeta^{-1}$ given by
\be
\aligned
m_+(z)&=m_-(z)\begin{pmatrix}1&0\\ \frac{\gam \zeta}{z-\zeta}&1\end{pmatrix}, && |z-\zeta|=\eps, \\
m_+(z)&=m_-(z)\begin{pmatrix}1&-\frac{\gam z}{z-\zeta^{-1}}\\0&1\end{pmatrix}, && |z^{-1}- \zeta|=\eps.
\endaligned
\ee
Then this Riemann--Hilbert problem is equivalent to a Riemann--Hilbert problem for $\ti{m}$ which has jump conditions near $\zeta$ and
$\zeta^{-1}$ given by
\begin{align*}
\ti{m}_+(z)&= \ti{m}_-(z)\begin{pmatrix}1& \frac{(\zeta z-1)^2}{\zeta (z-\zeta) \gam}\\ 0 &1\end{pmatrix},
&& |z-\zeta|=\eps, \\
\ti{m}_+(z)&= \ti{m}_-(z)\begin{pmatrix}1& 0 \\ -\frac{(z-\zeta)^2}{\zeta z (\zeta z-1) \gam}&1\end{pmatrix},
&& |z^{-1}- \zeta|=\eps,
\end{align*}
and all remaining data conjugated (as in Lemma~\ref{lem:conjug}) by
\be
D(z) = \begin{pmatrix} \frac{z - \zeta}{\zeta z-1} & 0 \\ 0 & \frac{\zeta z-1}{z-\zeta} \end{pmatrix}.
\ee
\end{lemma}

\begin{proof}
To turn $\gam$ into $\gam^{-1}$, introduce $D$ by
$$
D(z) = \begin{cases}
\begin{pmatrix} 1 & \frac{1}{\gam} \frac{z-\zeta}{\zeta}\\ - \gam \frac{\zeta}{z-\zeta} & 0 \end{pmatrix}
\begin{pmatrix} \frac{z - \zeta}{\zeta z-1} & 0 \\ 0 & \frac{\zeta z-1}{z-\zeta} \end{pmatrix}, &  |z-\zeta|<\eps, \\
\begin{pmatrix} 0 & \gam \frac{z \zeta}{z \zeta -1} \\ -\frac{1}{\gam} \frac{z \zeta -1}{z \zeta} & 1 \end{pmatrix} 
\begin{pmatrix} \frac{z - \zeta}{\zeta z-1} & 0 \\ 0 & \frac{\zeta z-1}{z-\zeta} \end{pmatrix}, & |z^{-1}-\zeta|<\eps, \\ 
\begin{pmatrix} \frac{z - \zeta}{\zeta z-1} & 0 \\ 0 & \frac{\zeta z-1}{z-\zeta} \end{pmatrix}, & \text{else},
\end{cases}
$$
and note that $D(z)$ is analytic away from the two circles. Now set $\ti{m}(z) = m(z) D(z)$.
\end{proof}

The jumps along $\T$ are of oscillatory type and our aim is to apply a contour deformation which will
move them into regions where the oscillatory terms will decay exponentially. Since the
jump matrix $v$ contains both $\exp(t \Phi)$ and $\exp(-t \Phi)$ we need to separate them
in order to be able to move them to different regions of the complex plane. For this
we will need the following factorizations of the jump condition (\ref{eq:jumpcond}).
First of all
\be
v(z)= b_-(z)^{-1} b_+(z),
\ee
where 
$$
b_-(z)= \begin{pmatrix}
1 & \ol{R(z)}  \E^{-t\Phi(z)} \\ 0 &1
\end{pmatrix}, \qquad
b_+(z)= \begin{pmatrix}
1 & 0 \\ R(z) \E^{t\Phi(z)} & 1
\end{pmatrix}.
$$
This will be the proper factorization for $z>z_0$. Here $z>z_0$ has to be understood as $\lam(z)>\lam_0$
(or equivalently $\re(z)>\re(z_0)$). Similarly, we have
\be\label{facB}
v(z)= B_-(z)^{-1} \begin{pmatrix} 1-|R(z)|^2 & 0 \\ 0 & \frac{1}{1-|R(z)|^2}\end{pmatrix} B_+(z),
\ee
where 
$$
B_-(z) =\begin{pmatrix}
1 & 0 \\ - \frac{R(z)  \E^{t\Phi(z)}}{1-|R(z)|^2} &1
\end{pmatrix}, \qquad
B_+(z)= \begin{pmatrix}
1 & -\frac{\ol{R(z)}  \E^{-t\Phi(z)}}{1-|R(z)|^2} \\ 0 & 1
\end{pmatrix}.
$$
This will be the right factorization for $z<z_0$. 

To get rid of the diagonal part we need to solve the corresponding scalar Riemann--Hilbert problem.
Moreover, for $z_0\in(-1,0)$ we have $\re(\Phi(z))>0$ for $z\in(\zeta_0,0)$ and $\re(\Phi(z))<0$
for $z\in(-1,\zeta_0)\cup(0,1)$, for $z_0\in\T$ we have $\re(\Phi(z))>0$ for $z\in(-1,0)$ and
$\re(\Phi(z))<0$ for $z\in(0,1)$, and for $z_0\in(0,1)$ we have $\re(\Phi(z))>0$ for
$z\in(-1,0)\cup(\zeta_0,1)$ and $\re(\Phi(z))<0$ for $z\in(0,\zeta_0)$ (compare Figure~\ref{fig:signRePhi}
and note that by $\re(\Phi(z^{-1}))= -\re(\Phi(z))$ the curves $\re(\Phi(z))=0$ are symmetric
with respect to $z\mapsto z^{-1}$).

Together with the Blaschke factors needed to conjugate the jumps near the eigenvalues,
this is just the partial transmission coefficient $T(z,z_0)$ introduced in (\ref{def:Tzz0}). In fact, it
satisfies the following scalar meromorphic Riemann--Hilbert problem:

\begin{lemma}
The partial transmission coefficient $T(z,z_0)$ is meromorphic in $\C\backslash\Sigma(z_0)$,
where $\Sigma(z_0)$ is the arc given by $\Sigma(z_0) = \{z \in\T | \re(z)<\re(z_0)\}$, with
simple poles at $\zeta_j$ and simple zeros at $\zeta_j^{-1}$ for all $j$ with
$\frac{1}{2}(\zeta_j+\zeta_j^{-1})<\lam_0$, and satisfies the jump condition
$$
T_+(z,z_0) = T_-(z,z_0) (1 - |R(z)|^2), \qquad z\in\Sigma(z_0).
$$
Moreover,
\begin{enumerate}
\item
$T(z^{-1},z_0) = T(z,z_0)^{-1}$, $z\in\C\backslash\Sigma(z_0)$, and $T(0,z_0)>0$,
\item
$\ol{T(z,z_0)}=T(\ol{z},z_0)$ and in particular $T(z,z_0)$ is real-valued for $z\in\R$,
\item
$T(z) / T(z,z_0) =O(1)$ for $z$ in the interior of $\Sigma(z_0)$.
\end{enumerate}
\end{lemma}

\begin{proof}
That $\zeta_j$ are simple poles and $\zeta_j^{-1}$ are simple zeros is obvious from the Blaschke
factors and that $T(z,z_0)$ has the given jump follows from Plemelj's formulas.
(i)--(iii) are straightforward to check.
\end{proof}
Observe that for $\zeta_0 < \zeta_N$ if $\zeta_N\in(0,1)$ respectively $\zeta_0 < 1$ else we have
$T(z)=T(z,z_0)$.

Moreover, note that (i) and (ii) imply
\be\label{absparT}
|T(z,z_0)|^2 = T(\ol{z},z_0) T(z,z_0)  = T(z^{-1},z_0) T(z,z_0) = 1, \qquad z\in\T\backslash\Sigma(z_0).
\ee

Now we are ready to perform our conjugation step. Introduce
$$
D(z) = \begin{cases}
\begin{pmatrix} 1 & \frac{z-\zeta_k}{\zeta_k \gam_k \E^{t\Phi(\zeta_k)}}\\
- \frac{\zeta_k \gam_k \E^{t\Phi(\zeta_k)}}{z-\zeta_k} & 0 \end{pmatrix}
D_0(z), &  |z-\zeta_k|<\eps, \: \lam_k < \frac{1}{2}(\zeta_0+\zeta_0^{-1}),\\
\begin{pmatrix} 0 & \frac{z \zeta_k \gam_k \E^{t\Phi(\zeta_k)}}{z \zeta_k -1} \\
-\frac{z \zeta_k -1}{z \zeta_k \gam_k \E^{t\Phi(\zeta_k)}} & 1 \end{pmatrix}
D_0(z), & |z^{-1}-\zeta_k|<\eps, \: \lam_k < \frac{1}{2}(\zeta_0+\zeta_0^{-1}),\\ 
D_0(z), & \text{else},
\end{cases}
$$
where 
$$
D_0(z) = \begin{pmatrix} T(z,z_0)^{-1} & 0 \\ 0 & T(z,z_0) \end{pmatrix}.
$$
Note that we have
$$
D(z^{-1})= \sigI D(z) \sigI.
$$
Now we conjugate our problem using $D(z)$ and observe that, since $T(z,z_0)$ has
the same behaviour as $T(z)$ for $z=\pm 1 >z_0$, the new vector
\be\label{eq:tim}
\ti{m}(z)=m(z) D(z)
\ee
is again continuous near $z=\pm 1$ (even if $T(z)$ vanishes there).

Then using Lemma~\ref{lem:conjug} and Lemma~\ref{lem:twopolesinc} the jump
corresponding $\lam_k <\frac{1}{2}(\zeta_0+\zeta_0^{-1})$ (if any) is given by
\be
\aligned
\ti{v}(z) &= \begin{pmatrix}1& \frac{z-\zeta_k}{\zeta_k
\gam_k T(z,z_0)^{-2} \E^{t\Phi(\zeta_k)} }\\ 0 &1\end{pmatrix},
\qquad |z-\zeta_k|=\eps, \\
\ti{v}(z) &= \begin{pmatrix}1& 0 \\ -\frac{\zeta_k z -1}{\zeta_k z \gam_k T(z,z_0)^2
\E^{t\Phi(\zeta_k)}}&1\end{pmatrix},
\qquad |z^{-1}- \zeta_k|=\eps,
\endaligned
\ee
and corresponding $\lam_k > \frac{1}{2}(\zeta_0+\zeta_0^{-1})$ (if any) by
\be
\aligned
\ti{v}(z) &= \begin{pmatrix} 1 & 0 \\ \frac{\zeta_k \gam_k T(z,z_0)^{-2} \E^{t\Phi(\zeta_k)}}{z-\zeta_k}
 & 1 \end{pmatrix},
\qquad |z-\zeta_k|=\eps, \\
\ti{v}(z) &= \begin{pmatrix} 1 & -\frac{z \gam_k T(z,z_0)^2 \E^{t\Phi(\zeta_k)}}{z-\zeta_k^{-1}} \\
0 & 1 \end{pmatrix},
\qquad |z^{-1}-\zeta_k|=\eps.
\endaligned
\ee
In particular, all jumps corresponding to poles, except for possibly one if
$\zeta_k=\zeta_0$, are exponentially decreasing. In this case we will keep the
pole condition which now reads
\be
\aligned
\res_{\zeta_k} \ti{m}(z) &= \lim_{z\to\zeta_k} \ti{m}(z)
\begin{pmatrix} 0 & 0\\ - \zeta_k \gam_k T(\zeta_k,z_0)^{-2} \E^{t\Phi(\zeta_k)}  & 0 \end{pmatrix},\\
\res_{\zeta_k^{-1}} \ti{m}(z) &= \lim_{z\to\zeta_k^{-1}} \ti{m}(z)
\begin{pmatrix} 0 & \zeta_k^{-1} \gam_k T(\zeta_k,z_0)^{-2} \E^{t\Phi(\zeta_k)} \\ 0 & 0 \end{pmatrix}.
\endaligned
\ee
Furthermore, the jump along
$\T$ is given by
\be
\ti{v}(z) = \begin{cases}
\ti{b}_-(z)^{-1} \ti{b}_+(z), \qquad \lam(z)> \lam_0,\\
\ti{B}_-(z)^{-1} \ti{B}_+(z), \qquad \lam(z)< \lam_0,\\
\end{cases}
\ee
where
\be\label{eq:deftib}
\ti{b}_-(z) = \begin{pmatrix} 1 & \frac{R(z^{-1}) \E^{-t\Phi(z)}}{T(z^{-1},z_0)^2} \\ 0 & 1 \end{pmatrix}, \quad
\ti{b}_+(z) = \begin{pmatrix} 1 & 0 \\ \frac{R(z) \E^{t\Phi(z)}}{T(z,z_0)^2}& 1 \end{pmatrix},
\ee
and
\begin{align}\nn
\ti{B}_-(z) &= \begin{pmatrix} 1 & 0 \\ - \frac{T_-(z,z_0)^{-2}}{1-R(z)R(z^{-1})} R(z) \E^{t\Phi(z)} & 1 \end{pmatrix}, \\
\ti{B}_+(z) &= \begin{pmatrix} 1 & - \frac{T_+(z,z_0)^2}{1-R(z)R(z^{-1})} R(z^{-1}) \E^{-t\Phi(z)} \\ 0 & 1 \end{pmatrix}.
\end{align}
Here we have used $T_\pm(z^{-1},z_0)=T_\pm(\ol{z},z_0)=\ol{T_\pm(z,z_0)}$ and
$R(z^{-1})=R(\ol{z})=\ol{R(z)}$ for $z\in\T$ to show that there exists an analytic continuation
into a neighborhood of the unit circle. Moreover, using
$$
T_\pm(z,z_0)=T_\mp(z^{-1},z_0)^{-1}, \qquad z\in\Sigma(z_0).
$$
we can write
\be \label{eq:relB}
\frac{T_-(z,z_0)^{-2}}{1-R(z)R(z^{-1})} = \frac{\ol{T_-(z,z_0)}}{T_-(z,z_0)}, \quad
\frac{T_+(z,z_0)^2}{1-R(z)R(z^{-1})} = \frac{T_+(z,z_0)}{\ol{T_+(z,z_0)}}
\ee
for $z\in\T$, which shows that the matrix entries are in fact bounded.

Now we deform the jump along $\T$ to move the oscillatory terms
into regions where they are decaying. There are three cases to distinguish (see
Figure~\ref{fig:signRePhi}):
\begin{figure}
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\caption{Sign of $\re(\Phi(z))$ for different values of $z_0$}\label{fig:signRePhi}
\end{figure}


{\bf Case 1: $z_0\in(-1,0)$.}
In this case we will set $\Sigma_\pm=\{ z |\, |z|=(1-\eps)^{\pm 1}\}$ for some small
$\eps\in(0,1)$ such that $\Sigma_\pm$ lies in the region with $\pm \re(\Phi(z))< 0$
and such that we do not intersect any other contours.
Then we can split our jump by redefining $\ti{m}(z)$ according to
\be
\hat{m}(z) = \begin{cases}
\ti{m}(z) \ti{b}_+(z)^{-1}, & (1-\eps)<|z|<1,\\
\ti{m}(z) \ti{b}_-(z)^{-1}, & 1<|z|<(1-\eps)^{-1},\\
\ti{m}(z), & \text{else}.
\end{cases}
\ee
It is straightforward to check that the jump along $\T$ disappears and the
jump along $\Sigma_\pm$ is given by
\be\label{eq:jumpsolreg}
\hat{v}(z) = \begin{cases}
\ti{b}_+(z), & z\in\Sigma_+, \\
\ti{b}_-(z)^{-1}, & z\in\Sigma_-.
\end{cases}
\ee
All other jumps are unchanged. Note that the resulting Riemann--Hilbert problem still
satisfies our symmetry condition (\ref{eq:symcond}) since we have
$$
\ti{b}_\pm(z^{-1}) = \sigI \ti{b}_\mp(z) \sigI .
$$
By construction the jump along  $\Sigma_\pm$ is exponentially decreasing as $t\to\infty$.

{\bf Case 2: $z_0\in\T\setminus\{\pm1\}$.}
In this case we will set $\Sigma_\pm=\Sigma_\pm^1\cup\Sigma_\pm^2$ as indicated in
Figure~\ref{fig:defcont}. Again note that $\Sigma_\pm^1$ respectively $\Sigma_\mp^2$
lies in the region with $\pm \re(\Phi(z))< 0$.
\begin{figure}
\begin{picture}(6,6)

\put(0,0.7){$\scriptstyle \re(\Phi)<0$}
\put(5.4,0.7){$\scriptstyle \re(\Phi)>0$}
\put(1.6,2.9){$\scriptstyle \re(\Phi)>0$}
\put(3.4,2.9){$\scriptstyle \re(\Phi)<0$}

\put(0.4,4.1){$\scriptstyle \Sigma_-^2$}
\put(4.16,3.5){$\scriptstyle \Sigma_+^1$}
\put(1.1,4){$\scriptstyle \T$}
\put(1.85,3.9){$\scriptstyle \Sigma_+^2$}
\put(5.43,3.3){$\scriptstyle \Sigma_-^1$}


\put(4.65,4.5){$z_0^{-1}$}
\put(4.65,1.4){$z_0$}

\curve(1.38,3., 1.4,2.747, 1.459,2.499, 1.557,2.265, 1.689,2.048,
1.854,1.854, 2.048,1.689, 2.265,1.557, 2.499,1.459, 2.747,1.4,
3.,1.38, 3.253,1.4, 3.501,1.459, 3.739,1.55, 4.029,1.584,
4.428,1.572, 4.852,1.654, 5.15,1.904, 5.302,2.252, 5.39,2.621,
5.42,3., 5.39,3.379, 5.302,3.748, 5.15,4.096, 4.852,4.346,
4.428,4.428, 4.029,4.416, 3.739,4.45, 3.501,4.541, 3.253,4.6,
3.,4.62, 2.747,4.6, 2.499,4.541, 2.265,4.443, 2.048,4.311,
1.854,4.146, 1.689,3.952, 1.557,3.735, 1.459,3.501, 1.4,3.253,
1.38,3.)

\curve(0.531,3., 0.561,2.614, 0.652,2.237, 0.8,1.879, 1.002,1.549,
1.254,1.254, 1.549,1.002, 1.879,0.8, 2.237,0.652, 2.614,0.561,
3.,0.531, 3.386,0.561, 3.763,0.652, 4.116,0.809, 4.343,1.151,
4.4,1.6, 4.413,1.973, 4.477,2.247, 4.572,2.489, 4.633,2.741,
4.653,3., 4.633,3.259, 4.572,3.511, 4.477,3.753, 4.413,4.027,
4.4,4.4, 4.343,4.849, 4.116,5.191, 3.763,5.348, 3.386,5.439,
3.,5.469, 2.614,5.439, 2.237,5.348, 1.879,5.2, 1.549,4.998,
1.254,4.746, 1.002,4.451, 0.8,4.121, 0.652,3.763, 0.561,3.386,
0.531,3.)

\curvedashes{0.05,0.05}
\curve(1.,3., 1.586,1.586, 3.,1., 4.414,1.586, 5.,3., 4.414,4.414,
3.,5., 1.586,4.414, 1.,3.)

\curve(5.441,0.2, 5.317,0.4, 5.186,0.6, 5.046,0.8, 4.897,1.,
4.736,1.2, 4.562,1.4, 4.4,1.6, 4.164,1.8, 3.937,2., 3.693,2.2,
3.449,2.4, 3.231,2.6, 3.072,2.8, 3.,3., 3.072,3.2, 3.231,3.4,
3.449,3.6, 3.693,3.8, 3.937,4., 4.164,4.2, 4.428,4.4, 4.562,4.6,
4.736,4.8, 4.897,5., 5.046,5.2, 5.186,5.4, 5.317,5.6, 5.441,5.8)
\end{picture}
\caption{Deformed contour}\label{fig:defcont}
\end{figure}
Then we can split our jump by redefining $\ti{m}(z)$ according to
\be
\hat{m}(z) = \begin{cases}
\ti{m}(z) \ti{b}_+(z)^{-1}, & z \text { between $\T$ and } \Sigma_+^1,\\
\ti{m}(z) \ti{b}_-(z)^{-1}, & z \text { between $\T$ and } \Sigma_-^1,\\
\ti{m}(z) \ti{B}_+(z)^{-1}, & z \text { between $\T$ and } \Sigma_+^2,\\
\ti{m}(z) \ti{B}_-(z)^{-1}, & z \text { between $\T$ and } \Sigma_-^2,\\
\ti{m}(z), & \text{else}.
\end{cases}
\ee
One checks that the jump along $\T$ disappears and the
jump along $\Sigma_\pm$ is given by
\be
\hat{v}(z) = \begin{cases}
\ti{b}_+(z), & z\in\Sigma_+^1, \\
\ti{b}_-(z)^{-1}, & z\in\Sigma_-^1,\\
\ti{B}_+(z), & z\in\Sigma_+^2,\\
\ti{B}_-(z)^{-1}, & z\in\Sigma_-^2.
\end{cases}
\ee
All other jumps are unchanged. Again the resulting Riemann--Hilbert problem still
satisfies our symmetry condition (\ref{eq:symcond}) and the jump along
$\Sigma_\pm\setminus\{z_0,z_0^{-1}\}$ is exponentially decreasing as $t\to\infty$.

{\bf Case 3: $z_0\in(0,1)$.}
In this case we will set $\Sigma_\pm=\{ z |\, |z|=(1-\eps)^{\pm 1}\}$ for some small
$\eps\in(0,1)$ such that $\Sigma_\pm$ lies in the region with $\mp \re(\Phi(z))< 0$
and such that we do not intersect any other contours.
Then we can split our jump by redefining $\ti{m}(z)$ according to
\be
\hat{m}(z) = \begin{cases}
\ti{m}(z) \ti{B}_+(z)^{-1}, & (1-\eps)<|z|<1,\\
\ti{m}(z) \ti{B}_-(z)^{-1}, & 1<|z|<(1-\eps)^{-1},\\
\ti{m}(z), & \text{else}.
\end{cases}
\ee
One checks that the jump along $\T$ disappears and the
jump along $\Sigma_\pm$ is given by
\be
\hat{v}(z) = \begin{cases} \ti{B}_+(z), & z\in\Sigma_+, \\
\ti{B}_-(z)^{-1}, & z\in\Sigma_-.\end{cases}
\ee
All other jumps are unchanged. Again the resulting Riemann--Hilbert problem still
satisfies our symmetry condition (\ref{eq:symcond}) and the jump along  $\Sigma_\pm$
is exponentially decreasing as $t\to\infty$.

In Case~1 and 3 we can immediately apply Theorem~\ref{thm:remcontour} as follows:
If $|\frac{n}{t} - c_k|>\eps$ for all $k$ we can choose $\gam_0=0$ and $w_0^t\equiv 0$.
Since the error between $w^t$ and $w_0^t$ is exponentially small, this proves the second
part of Theorem~\ref{thm:asym} in the analytic case. The changes necessary for the
general case will be given in Section~\ref{sec:analapprox}.

Otherwise, if $|\frac{n}{t} - c_k|<\eps$ for some $k$, we choose $\gam_0^t=\gam_k(n,t)$ and
$w_0^t \equiv 0$. Again we conclude that the error between $w^t$ and $w_0^t$ is exponentially small,
proving the first part of Theorem~\ref{thm:asym}. The changes necessary for the
general case will also be given in Section~\ref{sec:analapprox}.

In Case~2 the jump will not decay on the two small crosses containing the stationary phase
points $z_0$ and $z_0^{-1}$. Hence we will need to continue the investigation of this problem
in the next section.




\section{Reduction to a Riemann--Hilbert problem on a small cross}
\label{sec:reducecross}



In the previous section we have shown that for $z_0\in\T\backslash\{\pm 1\}$ we can
reduce everything to a Riemann--Hilbert problem for $\hat{m}(z)$ such that the jumps
are of order $O(t^{-1})$ except in a small neighborhoods of the stationary phase
points $z_0$ and $z_0^{-1}$. Denote by $\Sigma^C(z_0^{\pm 1})$ the parts of
$\Sigma_+\cup\Sigma_-$ inside a small neighborhood of $z_0^{\pm 1}$. In this section
we will show that everything can reduced to solving the two problems in the two small
crosses $\Sigma^C(z_0)$ respectively $\Sigma^C(z_0^{-1})$.

It will be slightly more convenient to use the alternate normalization
\be\label{eq:checkm}
\check{m}(z) = \frac{1}{\ti{A}} \hat{m}(z), \qquad A = T_0 \ti{A},
\ee
such that
\be
\check{m}(0) = \begin{pmatrix} 1 & \frac{1}{\ti{A}^2} \end{pmatrix}.
\ee
Without loss of generality we can also assume that $\hat{\Sigma}$ consists of two
straight lines in a sufficiently small neighborhood of $z_0$.

We will need the solution of the corresponding $2\times2$ matrix
\be\label{eq:RHPM}
\aligned
M^C_+(z)&= M^C_-(z) \ti{v}(z), \qquad z\in\Sigma^C,\\
M^C(\infty)&=\id,
\endaligned
\ee
where the jump $\ti{v}$ is the same as for $\ti{m}(z)$ but restricted to a
neighborhood of one of the two crosses $\Sigma^C=(\Sigma_+\cup\Sigma_-)\cap
\{ z | \,|z-z_0|<\eps/2\}$ for some small $\eps>0$.

As a first step we make a change of coordinates
\be\label{eqchoc}
\zeta= \frac{\sqrt{-2\sin(\theta_0)}}{z_0 \I} (z-z_0), \qquad
z= z_0 + \frac{z_0 \I}{\sqrt{-2\sin(\theta_0)}} \zeta
\ee
such that the phase reads $\Phi(z)= \I \Phi_0 + \frac{\I}{2} \zeta^2 +O(\zeta^3)$. 
Here we have set
$$
z_0 = \E^{\I \theta_0}, \qquad \theta_0\in(-\pi,0),
$$
respectively $\cos(\theta_0) = -n/t$, which implies
$$
\Phi_0 = 2(\sin(\theta_0) - \theta_0 \cos(\theta_0)),\qquad
\Phi''(z_0) = 2 \I\E^{-2\I\theta_0} \sin(\theta_0).
$$
The corresponding Riemann--Hilbert problem will be solved in Section~\ref{sec:cross}.
To apply this result we need the behaviour of our jump matrices near $z_0$,
that is, the behaviour of $T(z,z_0)$ near $z\to z_0$.

\begin{lemma}
Let $z_0\in\T$, then
\be
T(z,z_0) = \left(-\ol{z_0}\frac{z-z_0}{z-\ol{z_0}}\right)^{\I\nu} \ti{T}(z,z_0)
\ee
where $\nu = -\frac{1}{\pi} \log(|T(z_0)|)$ and the branch cut of the logarithm used to define $z^{\I\nu}=\E^{\I\nu\log(z)}$
is chosen along the negative real axis. Here
$$
\ti{T}(z,z_0) = \prod\limits_{\zeta_k\in(-1,0)} |\zeta_k| \frac{z-\zeta_k^{-1}}{z-\zeta_k} \cdot
\exp\left(\frac{1}{2\pi\I}\int\limits_{\ol{z_0}}^{z_0}\log\Big(\frac{|T(s)|}{|T(z_0)|}\Big) \frac{s+z}{s-z} \frac{ds}{s}\right),
$$
is H\"older continuous of any exponent less then $1$ at $z=z_0$ and satisfies $\ti{T}(z_0,z_0)\in\T$.
\end{lemma}

\begin{proof}
This follows since
$$
\exp\left(\frac{1}{2\pi\I}\int\limits_{\ol{z_0}}^{z_0}\log\big(|T(z_0)|\big) \frac{s+z}{s-z} \frac{ds}{s}\right) = \left(-\ol{z_0}\frac{z-z_0}{z-\ol{z_0}}\right)^{\I\nu}.
$$
The property $\ti{T}(z_0,z_0)\in\T$ follows after letting $z\to z_0$ in (\ref{absparT}).
\end{proof}

Now if $z(\zeta)$ is defined as in (\ref{eqchoc}) and $0 < \alpha < 1$,
then there is an $L > 0$ such that
$$
|T(z(\zeta), z_0) - \zeta^{\I \nu} \ti{T}(z_0,z_0) \E^{-\frac{3}{2} \I \nu \log(-2\sin(\theta_0))}|
\leq L |\zeta|^{\alpha},
$$
where the branch cut of $\zeta^{\I \nu}$ is tangent to the negative real axis. Clearly
we also have
$$
|R(z(\zeta)) - R(z_0)| \le L  |\zeta|^{\alpha}
$$
and thus the assumptions of Theorem~\ref{thm:solcross} are satisfied with
$$
r = R(z_0) \ti{T}(z_0,z_0)^{-2} \E^{3 \I \nu \log(-2\sin(\theta_0))}
$$
and the solution of (\ref{eq:RHPM}) is given by
\begin{align}
M^C(z) &= \id - \frac{z_0}{(-2\sin(\theta_0) t)^{1/2}}  \frac{M_0}{z - z_0} +
O\left(\frac{1}{t^\alpha}\right), \\ \nn
M_0 &= \begin{pmatrix} 0 & -\beta \\  \ol{\beta} & 0 \end{pmatrix},\\
\beta &=\sqrt{\nu} \E^{\I(\pi/4-\arg(R(z_0)) + \arg(\Gamma(\I\nu)))}
(-2\sin(\theta_0))^{-3\I \nu} \ti{T}(z_0, z_0)^2 \E^{-\I t \Phi_0} t^{-\I\nu},
\end{align}
where  $1/2 < \alpha < 1$, and $\cos(\theta_0)=-\lam_0$.

Now we are ready to show

\begin{theorem}\label{thm:decoupling}
The solution $\check{m}(z)$ is given by
\be
\check{m}(z) = \rI - \frac{1}{(-2\sin(\theta_0) t)^{1/2}} ( m_0(z) + \bar{m}_0(z))
+ O\left(\frac{1}{t^\alpha}\right),
\ee
where
\be
m_0(z) = \begin{pmatrix} \ol{\beta} \frac{z}{z-z_0} & -\beta \frac{z_0}{z-z_0} \end{pmatrix}, \qquad
\bar{m}_0(z) = \ol{m_0(\ol{z})} = m_0(z^{-1})\sigI.
\ee
\end{theorem}

\begin{proof}
Introduce $m(z)$ by
$$
m(z) = \begin{cases}
\check{m}(z) M^C(z)^{-1}, & |z-z_0| \le \eps,\\
\check{m}(z) \ti{M}^C(z)^{-1}, & |z^{-1}-z_0| \le \eps,\\
\check{m}(z), & \text{else},\end{cases}
$$
where
$$
\ti{M}^C(z) = \sigI M^C(z^{-1}) \sigI = \id - \frac{z}{(-2\sin(\theta_0) t)^{1/2}}  \frac{\ol{M_0}}{z - z_0} +
O\left(\frac{1}{t^\alpha}\right).
$$
The Riemann--Hilbert problem for $m$ has jumps given by
$$
v(z) =\begin{cases}
M^C(z)^{-1}, & |z-z_0| = \eps,\\
M^C(z) \hat{v}(z) M^C(z)^{-1}, & z\in \hat{\Sigma}, \frac{\eps}{2} < |z-z_0| < \eps,\\
\id, & z\in \Sigma, |z-z_0|< \frac{\eps}{2},\\
\ti{M}^C(z)^{-1}, & |z^{-1}-z_0| = \eps,\\
\ti{M}^C(z) \hat{v}(z) \ti{M}^C(z)^{-1}, & z\in \hat{\Sigma}, \frac{\eps}{2} < |z^{-1}-z_0| < \eps,\\
\id, & z\in \Sigma, |z^{-1}-z_0|< \frac{\eps}{2},\\
\hat{v}(z), & \text{else}.
\end{cases}
$$
The jumps are $\id+O(t^{-1/2})$ on the loops $|z-z_0|=\eps$, $|z^{-1}-z_0|=\eps$ and
even $\id+O(t^{-\alpha})$ on the rest (in the $L^\infty$ norm, so also in the $L^\infty$ one).
In particular, as in Lemma~\ref{lem:approrhp} we infer
$$
\|\mu - \rI \|_2 = O(t^{-1/2}).
$$
Thus we have with $\Omega_\infty$ as in \eqref{eq:defomegainfty}
\begin{align*}
m(z) = & \rI+ \frac{1}{2\pi\I} \int_{\Sigma} \mu(s) w(s) \Omega_\infty(s,z) \\
= & \rI + \frac{1}{2\pi\I} \int_{|s-z_0|=\eps} \mu(s) (M^C(s)^{-1}-\id) \Omega_\infty(s,z) \\
& + \frac{1}{2\pi\I} \int_{|s^{-1}-z_0|=\eps} \mu(s) (\ti{M}^C(s)^{-1}-\id) \Omega_\infty(s,z)
+ O(t^{-\alpha})\\
= & \rI + \frac{1}{(-2\sin(\theta_0) t)^{1/2}} \rI M_0 \frac{1}{2\pi\I} \int_{|s-z_0|=\eps} \frac{z_0}{s-z_0} \Omega_\infty(s,z)\\
& + \frac{1}{(-2\sin(\theta_0) t)^{1/2}} \rI \ol{M_0} \frac{1}{2\pi\I} \int_{|s^{-1}-z_0|=\eps} \frac{s}{s-\ol{z_0}} \Omega_\infty(s,z) + O(t^{-\alpha})\\
= & \rI - \frac{1}{(-2\sin(\theta_0) t)^{1/2}} ( m_0(z) + \bar{m}_0(z))
+ O\left(\frac{1}{t^\alpha}\right)
\end{align*}
and hence the claim is proven.
\end{proof}

Hence, using (\ref{eq:AB}) and (\ref{eq:checkm}),
\be
\left( \check{m}(z) \right)_2 = \frac{1}{\ti{A}^2} \left( 1 + (T_1+2 B)z + O(z^2) \right)
\ee
and comparing with
\be
\left( \check{m}(z) \right)_2 = \left(1 - \frac{2\re(\beta)}{(-2\sin(\theta_0) t)^{1/2}}\right)
- \left(\frac{2\re(\ol{z_0}\beta)}{(-2\sin(\theta_0) t)^{1/2}}\right)z + O(z^2)
+O\left(\frac{1}{t^\alpha}\right),
\ee
we obtain
\be
\ti{A}^2 = 1 + \frac{2\re(\beta)}{(-2\sin(\theta_0) t)^{1/2}} + O\left(\frac{1}{t^\alpha}\right)
\ee
and
\be
T_1 + 2 B = -\frac{2\re(\ol{z_0}\beta)}{(-2\sin(\theta_0) t)^{1/2}}
+O\left(\frac{1}{t^\alpha}\right).
\ee
In summary we have
\begin{align}
A &= T_0 \left(1 + \frac{\re(\beta)}{(-2\sin(\theta_0) t)^{1/2}} + O\left(\frac{1}{t^\alpha}\right) \right),\\
B &= - \frac{1}{2} T_1 - \frac{\re(\ol{z_0}\beta)}{(-2\sin(\theta_0) t)^{1/2}}
+O\left(\frac{1}{t^\alpha}\right),
\end{align}
which proves Theorem~\ref{thm:asym2} in the analytic case.

\begin{remark}
Note that, in contradistinction to Theorem~\ref{thm:remcontour}, Theorem~\ref{thm:decoupling}
does not require uniform boundedness of the associated integral operators, but only some
knowledge of the solution of the Riemann-Hilbert problem. However, it requires that the
solution is of the form $\id+o(1)$ and hence cannot be used in the soliton region.
\end{remark}



\section{Analytic Approximation}
\label{sec:analapprox}



In this section we want to present the necessary changes in the case where the
reflection coefficient does not have an analytic extension. The idea is to
use an analytic approximation and split the reflection in an analytic part plus
a small rest. The analytic part will be moved to the complex plane while the rest
remains on the unit circle. This needs to be done in such a way that the rest
is of $O(t^{-l})$ and the growth of the analytic part can be controlled by the
decay of the phase.

In the soliton region a straightforward splitting based on the Fourier series
\be
R(z) = \sum_{k=-\infty}^{\infty} \hat{R}(k) z^k.
\ee
will be sufficient. Recall that if $R \in C^l(\T)$, then $\lim_{k\to\pm\infty} k^l \hat{R}(k) = 0$.

\begin{lemma}\label{lem:analapprox}
Suppose $R \in C^{l+1}(\T)$ and let $0 < \eps < 1$, $\beta>0$ be given.
Then we can split the reflection coefficient according to
$R(z)= R_{a,t}(z) + R_{r,t}(z)$ such that $R_{a,t}(z)$ is analytic in $0<|z|<1$ and 
\be
|R_{a,t}(z) \E^{-\beta t} | = O(t^{-l}), \quad 1-\eps \le |z|\le 1, \qquad
|R_{r,t}(z)| = O(t^{-l}), \quad |z|=1.
\ee
\end{lemma}

\begin{proof}
We choose $R_{a,t}(z) = \sum_{k = - K(t)}^\infty \hat{R}(k) z^k$ with $K(t) =
\lfloor \frac{\beta_0}{-\log(1-\eps)} t\rfloor$ for some positive $\beta_0<\beta$. Then, for $1-\eps \le|z|$,
$$
|R_{a,t}(z) \E^{-\beta t} | \le \sum_{k = - K(t)}^\infty |\hat{R}(k)| \E^{-\beta t} (1-\eps)^k \le
\|\hat{R}\|_1 \E^{-\beta t} (1-\eps)^{-K(t)} \le \|\hat{R}\|_1 \E^{-(\beta-\beta_0)t}
$$
Similarly, for $|z|=1$,
$$
|R_{r,t}(z) | \le \sum_{k = - \infty}^{-K(t)-1} |\hat{R}(k)| \le 
const \sum_{k = - \infty}^{-K(t)+1} \frac{1}{k^{l+1}} \le \frac{const}{K(t)^l} \le
\frac{const}{t^l}.
$$
\end{proof}

To apply this lemma in the soliton region $z_0\in(-1,0)$ we choose
\be
\beta= \min_{|z|=1-\eps} \re(\Phi(z))>0.
\ee
and split $R(z) =  R_{a,t}(z) + R_{r,t}(z)$ according to Lemma~\ref{lem:analapprox} to obtain
$$
\ti{b}_\pm(z) = \ti{b}_{a,t,\pm}(z) \ti{b}_{r,t,\pm}(z) = \ti{b}_{r,t,\pm}(z) \ti{b}_{a,t,\pm}(z).
$$
Here $\ti{b}_{a,t,\pm}(z)$, $\ti{b}_{r,t,\pm}(z)$ denote the matrices obtained from $\ti{b}_\pm(z)$
as defined in (\ref{eq:deftib}) by replacing $R(z)$ with $R_{a,t}(z)$, $R_{r,t}(z)$, respectively.
Now we can move the analytic parts into the complex plane as in Section~\ref{sec:conjdef}
while leaving the rest on $\T$. Hence, rather then (\ref{eq:jumpsolreg}), the jump now reads
\be
\hat{v}(z) = \begin{cases}
\ti{b}_{a,t,+}(z), & z\in\Sigma_+, \\
\ti{b}_{a,t,-}(z)^{-1}, & z\in\Sigma_-,\\
\ti{b}_{r,t,-}(z)^{-1} \ti{b}_{r,t,+}(z), & z\in\T.
\end{cases}
\ee
By construction we have $\hat{v}(z)= \id + O(t^{-l})$ on the whole contour and the rest follows as
in Section~\ref{sec:conjdef}.

In the other soliton region $z_0\in(0,1)$ we proceed similarly, with the only difference that the
jump matrices $\ti{B}_\pm(z)$ have at first sight more complicated off diagonal entries. To remedy
this we will rewrite them in terms of left rather then right scattering data. For this purpose
let us use the notation $R_r(z) \equiv R_+(z)$ for the right and $R_l(z) \equiv R_-(z)$ for the
left reflection coefficient. Moreover, let $T_r(z,z_0) \equiv T(z,z_0)$ be the right and
$T_l(z,z_0) \equiv T(z)/T(z,z_0)$ be the left partial transmission coefficient.

With this notation we have
\be
\ti{v}(z) = \begin{cases}
\ti{b}_-(z)^{-1} \ti{b}_+(z), \qquad \lam(z)> \lam_0,\\
\ti{B}_-(z)^{-1} \ti{B}_+(z), \qquad \lam(z)< \lam_0,\\
\end{cases}
\ee
where
$$
\ti{b}_-(z) = \begin{pmatrix} 1 & \frac{R_r(z^{-1}) \E^{-t\Phi(z)}}{T_r(z^{-1},z_0)^2} \\ 0 & 1 \end{pmatrix}, \quad
\ti{b}_+(z) = \begin{pmatrix} 1 & 0 \\ \frac{R_r(z) \E^{t\Phi(z)}}{T_r(z,z_0)^2}& 1 \end{pmatrix},
$$
and
\begin{align*}
\ti{B}_-(z) &= \begin{pmatrix} 1 & 0 \\ - \frac{T_{r,-}(z,z_0)^{-2}}{|T(z)|^2} R_r(z) \E^{t\Phi(z)} & 1 \end{pmatrix}, \\
\ti{B}_+(z) &= \begin{pmatrix} 1 & - \frac{T_{r,+}(z,z_0)^2}{|T(z)|^2} R_r(z^{-1}) \E^{-t\Phi(z)} \\ 0 & 1 \end{pmatrix}.
\end{align*}
Using (\ref{reltrpm}) together with (\ref{eq:relB}) we can further write
\begin{align*}
\ti{B}_-(z) &= \begin{pmatrix} 1 & 0 \\ \frac{R_l(z^{-1}) \E^{-t\Phi(z)}}{T_l(z^{-1},z_0)^2} & 1 \end{pmatrix}, \\
\ti{B}_+(z) &= \begin{pmatrix} 1 & \frac{R_l(z) \E^{t\Phi(z)}}{T_l(z,z_0)^2} \\ 0 & 1 \end{pmatrix}.
\end{align*}
Now we can proceed as before with $\ti{B}_\pm(z)$ as with $\ti{b}_\pm(z)$ by splitting $R_l(z)$ rather than $R_r(z)$.

In the similarity region we need to take the small vicinities of the stationary phase points into account. Since
the phase is quadratic near these points, we cannot use it to dominate the exponential growth of the analytic
part away from the unit circle. Hence we will take the phase as a new variable and use the Fourier transform
with respect to this new variable. Since this change of coordinates is singular near the stationary phase points,
there is a price we have to pay, namely, requiring additional smoothness for $R(z)$. We begin with

\begin{lemma}
Suppose $R(z)\in C^5(\T)$. Then we can split $R(z)$ according to
\be
R(z) = R_0(z) + (z-z_0)(z-\ol{z_0}) H(z), \qquad z \in \Sigma(z_0),
\ee
where $R_0(z)$ is a real polynomial in $z$ such that $H(z)$ vanishes at $z_0, \ol{z_0}$ of order three and
has a Fourier series
\be
H(z) = \sum_{k=-\infty}^\infty \hat{H}_k \E^{k \omega_0 \Phi(z)}, \qquad \omega_0=\frac{\pi}{\pi\cos(\theta_0)+\Phi_0}
\ee
with $k\,\hat{H}_k$ summable. Here $\Phi_0 = \Phi(z_0)/\I$.
\end{lemma}

\begin{proof}
By choosing a polynomial $R_0$ we can match the values of $R$ and its first four derivatives
at $z_0, \ol{z_0}$. Hence $H(z)\in C^4(\T)$ and vanishes together with its first three derivatives at
$z_0, \ol{z_0}$.

When restricted to $\Sigma(z_0)$ the phase $\Phi(z)/\I$ gives a one to one coordinate transform 
$\Sigma(z_0) \to [\I\Phi_0,\I\Phi_0+\I\omega_0]$ and we can hence express $H(z)$ in this new coordinate.
The coordinate transform locally looks like a square root near $z_0$ and $\ol{z_0}$, however, due to our
assumption that $H$ vanishes there, $H$ is still $C^2$ in this new coordinate and the Fourier transform
with respect to this new coordinates exists and has the required properties.
\end{proof}

Moreover, as in Lemma~\ref{lem:analapprox} we obtain:

\begin{lemma}
Let $H(z)$ be as in the previous lemma. Then we can split $H(z)$ according to
$H(z)= H_{a,t}(z) + H_{r,t}(z)$ such that $H_{a,t}(z)$ is analytic in the region $\re(\Phi(z))<0$
and 
\be
|H_{a,t}(z) \E^{\Phi(z) t/2} | = O(1), \: \re(\Phi(z))<0,|z|\le 1, \quad
|H_{r,t}(z)| = O(t^{-1}), \: |z|=1.
\ee
\end{lemma}

\begin{proof}
We choose $H_{a,t}(z) = \sum_{k = - K(t)}^\infty \hat{H}_k \E^{k \omega \Phi(z)}$ with $K(t) =
\lfloor t/(2\omega)\rfloor$. The rest follows as in Lemma~\ref{lem:analapprox}.
\end{proof}

By construction $R_{a,t}(z) = R_0(z) + (z-z_0)(z-\ol{z_0}) H_{a,t}(z)$ will satisfy the required
Lipschitz estimate in a vicinity of the stationary phase points (uniformly in $t$) and all
jumps will be $\id+O(t^{-1})$. Hence we can proceed as in Section~\ref{sec:reducecross}.



\appendix



\section{The solution on a small cross}
\label{sec:cross}



Introduce the cross $\Sigma = \Sigma_1 \cup\dots\cup \Sigma_4$ (see Figure~\ref{fig:contourcross}) by
\begin{align}
\nn \Sigma_1 & = \{u \E^{-\I\pi/4},\,u\in [0,\infty)\} & 
\Sigma_2 & = \{u \E^{\I\pi/4},     \,u\in [0,\infty)\} \\
\Sigma_3 & = \{u \E^{3\I\pi/4},    \,u\in [0,\infty)\} &
\Sigma_4 & = \{u \E^{-3\I\pi/4},   \,u\in [0,\infty)\}.
\end{align}
\begin{figure}
\begin{picture}(7,5.2)

\put(1,5){\line(1,-1){5}}
\put(2,4){\vector(1,-1){0.4}}
\put(4.7,1.3){\vector(1,-1){0.4}}
\put(1,0){\line(1,1){5}}
\put(2,1){\vector(1,1){0.4}}
\put(4.7,3.7){\vector(1,1){0.4}}

\put(6.0,0.1){$\Sigma_1$}
\put(5.3,4.8){$\Sigma_2$}
\put(1.3,4.8){$\Sigma_3$}
\put(1.4,0.1){$\Sigma_4$}

\put(2.8,0.5){$\scriptsize\begin{pmatrix} 1 & - R_1(z) \cdots\\ 0 & 1 \end{pmatrix}$}
\put(4.5,3.1){$\scriptsize\begin{pmatrix} 1 & 0 \\ R_2(z) \cdots & 1 \end{pmatrix}$}
\put(1.9,4.5){$\scriptsize\begin{pmatrix} 1 & - R_3(z) \cdots \\ 0 & 1 \end{pmatrix}$}
\put(0.5,1.8){$\scriptsize\begin{pmatrix} 1 & 0 \\ R_4(z) \cdots  & 1 \end{pmatrix}$}

\end{picture}
\caption{Contours of a cross}
\label{fig:contourcross}
\end{figure}%
Orient $\Sigma$ such that the real part of $z$ increases
in the positive direction. Denote by $\mathbb{D} = \{z,\,|z|<1\}$ the
open unit disc. Throughout this section $z^{\I\nu}$ will denote
the function $\E^{\I \nu \log(z)}$, where the branch cut of the logarithm is chosen along
the negative real axis $(-\infty,0)$.

Introduce the following jump matrices ($v_j$ for $z\in\Sigma_j$)
\begin{align}
\nn v_1 &= \begin{pmatrix} 1 & - R_1(z) z^{2\I\nu} \E^{- t \Phi(z)} \\ 0 & 1 \end{pmatrix}, &
v_2 &= \begin{pmatrix} 1 & 0 \\ R_2(z) z^{-2\I\nu} \E^{t \Phi(z)} & 1 \end{pmatrix},  \\ 
v_3 &= \begin{pmatrix} 1 & - R_3(z) z^{2\I\nu} \E^{- t \Phi(z)} \\ 0 & 1 \end{pmatrix}, & 
v_4 &= \begin{pmatrix} 1 & 0 \\ R_4(z) z^{-2\I\nu} \E^{t \Phi(z)}  & 1 \end{pmatrix}.
\end{align}

Now consider the RHP given by
\begin{align}\label{eq:rhpcross}
m_+(z) &= m_-(z) v_j(z), && z\in\Sigma_j,\quad j=1,2,3,4,\\ \nn
m(z) &\to \id, && z\to \infty.
\end{align}
We have the next theorem, in which we follow the computations of
Sections 3 and 4 in \cite{dz}. The method can be found in earlier literature,
see for example \cite{its}.
One can also find arguments like this in Section 5 in \cite{km} or (3.65) to (3.76)
in \cite{dzp2}.

We will allow some variation, in all parameters as indicated in the next result.

\begin{theorem}\label{thm:solcross}
There is some $\rho_0>0$ such that $v_j(z)=\id$ for $|z|>\rho_0$. Moreover,
suppose that within $|z|\le\rho_0$ the following estimates hold:
\begin{enumerate}
\item
The phase satisfies $\Phi(0)=\I\Phi_0\in\I\R$, $\Phi'(0) = 0$, $\Phi''(0) = \I$ and
\begin{align}\label{estPhi}
\pm \re\big(\Phi(z)-\Phi(0)\big) &\geq \frac{1}{4} |z|^2,\quad
\begin{cases} + & \mbox{for } z\in\Sigma_1\cup\Sigma_3,\\ - &\mbox{else},\end{cases}\\ \label{estPhi2}
|\Phi(z) - \Phi(0) - \frac{\I z^2}{2}| &\leq C |z|^3.
\end{align}
\item 
There is some $r\in\mathbb{D}$ and constants $(\alpha, L) \in (0,1] \times (0,\infty)$
such that $R_j$, $j=1,\dots,4$, satisfy H\"older conditions of the form
\begin{align}\nn
\abs{R_1(z) - \ol{r}} &\leq L |z|^\alpha, &
\abs{R_2(z) - r} &\leq L |z|^\alpha, \\\label{holdcondrj}
\abs{R_3(z) - \frac{\ol{r}}{1-\abs{r}^2}} &\leq L |z|^\alpha, &
\abs{R_4(z) - \frac{r}{1-\abs{r}^2}} &\leq L |z|^\alpha.
\end{align}
\end{enumerate}
Then the solution of the RHP (\ref{eq:rhpcross}) satisfies
\be
m(z) = \id + \frac{1}{z} \frac{\I}{t^{1/2}} \begin{pmatrix} 0 & -\beta \\ \ol{\beta} & 0 \end{pmatrix}
+ O(t^{- \frac{1 + \alpha}{2}}),
\ee
for $|z|>\rho_0$, where
\be
\beta = \sqrt{\nu} \E^{\I(\pi/4-\arg(r)+\arg(\Gamma(\I\nu)))} \E^{-\I t \Phi_0} t^{-\I\nu},
\qquad \nu = - \frac{1}{2\pi} \log(1 - |r|^2).
\ee
Furthermore, if $R_j(z)$ and $\Phi(z)$ depend on some parameter, the error term is uniform
with respect to this parameter as long as $r$ remains within a compact subset of $\mathbb{D}$
and the constants in the above estimates can be chosen independent of the the parameters.
\end{theorem}

Note that the actual value of $\rho_0$ is of no importance. In fact, if we choose $0 < \rho_1 < \rho_0$,
then the solution $\ti{m}$ of the problem with jump $\ti{v}$, where $\ti{v}$ is equal to $v$ for
$|z| < \rho_1$ and $\id$ otherwise, differs from $m$ only by an exponentially
small error. 

This already indicates, that we should be able to replace $R_j(z)$ by their respective values at $z=0$.
To see this we start by rewriting our RHP as a singular integral equation.  We will use the theory
developed in Appendix~\ref{sec:sieq} for the case of $2\times2$ matrix valued functions with
$m_0(z)=\id$ and the usual Cauchy kernel (since we won't require symmetry in this section)
$$
\Omega(s,z) = \id \frac{ds}{s-z}.
$$
Moreover, since our contour is unbounded, we will assume $w\in L^1(\Sigma)\cap L^2(\Sigma)$.
All results from Appendix~\ref{sec:sieq} still hold in this case with some straightforward modifications
if one observes that $\mu-\id \in L^2$. Indeed, as in Theorem~\ref{thm:cauchyop}, in the special case
$b_+(z) = v_j(z)$ and $b_-(z) = \id$ for $z\in\Sigma_j$, we obtain
\be\label{singintcross}
m(z) = \id + \frac{1}{2\pi\I} \int_{\Sigma} \mu (s) w(s) \frac{ds}{s - z}, 
\ee
where $\mu-\id$ is the solution of the singular integral equation
\be
(\id - C_w) (\mu -\id) = C_w \id,
\ee
that is,
\be\label{singinteqcross}
\mu = \id + (\id - C_w)^{-1} C_w \id, \qquad C_w f = \mathcal{C}_- (w f).
\ee
Here $\mathcal{C}$ denotes the usual Cauchy operator and we set $w(z)=w_+(z)$ (since $w_-(z)=0$).

As our first step we will get rid of some constants and rescale the
entire problem by setting
\be\label{scalecross}
\hat{m}(z) = D(t)^{-1} m(z t^{-1/2}) D(t),
\ee
where
\be
D(t) = \begin{pmatrix} d(t)^{-1} & 0 \\ 0 &d(t) \end{pmatrix}, \qquad
d(t) = \E^{\I t \Phi_0 /2} t^{\I\nu/2}, \quad d(t)^{-1} = \ol{d(t)}.
\ee
Then one easily checks that $\hat{m}(z)$ solves the RHP
\begin{align}
\hat{m}_+(z) &= \hat{m}_-(z) \hat{v}_j(z), && z\in\Sigma_j,\quad j=1,2,3,4,\\ \nn
\hat{m}(z) &\to \id, && z\to \infty,\quad z\notin\Sigma,
\end{align}
where $\hat{v}_j(z) = D(t)^{-1} v_j(z t^{-1/2}) D(t)$, $j=1,\dots,4$, explicitly
\begin{align} \nn
\hat{v}_1(z) &= \begin{pmatrix} 1 & -R_1(z t^{-1/2}) z^{2\I\nu} \E^{-t (\Phi(z t^{-1/2}) - \Phi(0))} \\ 0 & 1 \end{pmatrix},\\ \nn
\hat{v}_2(z) &= \begin{pmatrix} 1 & 0 \\ R_2(z t^{-1/2}) z^{-2\I\nu} \E^{t (\Phi(z t^{-1/2}) - \Phi(0))} & 1 \end{pmatrix}, \\ \nn
\hat{v}_3(z) &= \begin{pmatrix} 1 & -R_3(z t^{-1/2}) z^{2\I\nu} \E^{-t (\Phi(z t^{-1/2}) - \Phi(0))}\\ 0 & 1\end{pmatrix},\\
\hat{v}_4(z) &= \begin{pmatrix} 1 & 0 \\ R_2(z t^{-1/2}) z^{-2\I\nu} \E^{t (\Phi(z t^{-1/2}) - \Phi(0))} & 1 \end{pmatrix}.
\end{align}
Our next aim is to show that the solution $\hat{m}(z)$ of the rescaled problem is
close to the solution $\hat{m}^c(z)$ of the RHP 
\begin{align}\label{eq:solrhpcross2}
\hat{m}^c_+(z) &= \hat{m}^c_-(z) \hat{v}^c_j(z), && z\in\Sigma_j,\quad j=1,2,3,4,\\ \nn
\hat{m}^c(z) &\to \id, && z\to \infty,\quad z\notin\Sigma,
\end{align}
associated with the following jump matrices
\begin{align} \nn
\hat{v}_1^c(z) &= \begin{pmatrix} 1 & -\ol{r} z^{2\I\nu} \E^{-\I z^2/2} \\ 0 & 1 \end{pmatrix}, &
\hat{v}_2^c(z) &= \begin{pmatrix} 1 & 0 \\ r z^{-2\I\nu} \E^{\I z^2/2} & 1 \end{pmatrix}, \\
\hat{v}_3^c(z) &= \begin{pmatrix} 1 & -\frac{\ol{r}}{1-\abs{r}^2} z^{2\I\nu} \E^{-\I z^2/2}\\ 0 & 1\end{pmatrix}, &
\hat{v}_4^c(z) &= \begin{pmatrix} 1 & 0 \\\frac{r}{1-\abs{r}^2} z^{-2\I\nu} \E^{\I z^2/2} & 1 \end{pmatrix}.
\end{align}
The difference between these jump matrices can be estimated as follows.

\begin{lemma}\label{lem:esticross}
The matrices $\hat{w}^c$ and $\hat{w}$ are close in the sense that
\be
\hat{w}_j(z) = \hat{w}^c_j(z) + O(t^{-\alpha/2}\E^{-|z|^2/8}),\quad
z \in\Sigma_j,\quad j=1,\dots 4.
\ee
Furthermore, the error term is uniform with respect to parameters as stated in Theorem~\ref{thm:solcross}.
\end{lemma}

\begin{proof}
We only give the proof $z\in\Sigma_1$, the other cases being similar. There is only
one nonzero matrix entry in $\hat{w}_j(z) - \hat{w}^c_j(z)$ given by
$$
W = \begin{cases} - R_1(z t^{-1/2}) z^{2\I\nu} \E^{-t(\Phi(z t^{-1/2}) - \Phi(0))} + \ol{r} z^{2\I\nu} \E^{-\I z^2/2},
& |z| \le \rho_0 t^{1/2},\\ \ol{r} z^{2\I \nu} \E^{-\I z^2/2} & |z| > \rho_0 t^{1/2}. \end{cases}
$$
A straightforward estimate for $|z| \le \rho_0 t^{1/2}$ shows
\begin{align*}
|W| & =  \E^{\nu\pi/4} |R_1(z t^{-1/2}) \E^{-t\hat{\Phi}(z t^{-1/2})} - \ol{r}| \E^{-|z|^2/2}\\
& \le  \E^{\nu\pi/4} |R_1(z t^{-1/2}) - \ol{r} | \E^{\re(-t\hat{\Phi}(z t^{-1/2}))-|z|^2/2} +
\E^{\nu\pi/4} |\E^{-t\hat{\Phi}(z t^{-1/2})}-1| \E^{-|z|^2/2}\\
& \le  \E^{\nu\pi/4} |R_1(z t^{-1/2}) - \ol{r} | \E^{-|z|^2/4} +
\E^{\nu\pi/4}  t |\hat{\Phi}(z t^{-1/2})| \E^{-|z|^2/4},
\end{align*}
where $\hat{\Phi}(z) = \Phi(z) - \Phi(0) - \frac{\I}{2} z^2 = \frac{\Phi'''(0)}{6} z^3 + \dots$.
Here we have used $\frac{\I}{2} z^2= \frac{1}{2}|z|^2$ for $z\in\Sigma_1$ and $\re(-t\hat{\Phi}(z t^{-1/2})) \le |z|^2/4$
by (\ref{estPhi}).
Furthermore, by (\ref{estPhi2}) and (\ref{holdcondrj}),
\begin{align*}
|W| & \le \E^{\nu\pi/4} L t^{-\alpha/2} |z|^\alpha \E^{-|z|^2/4} +
\E^{\nu\pi/4} C t^{-1/2} |z|^3 \E^{-|z|^2/4},
\end{align*}
for $|z| \le \rho_0 t^{1/2}$. For $|z| > \rho_0 t^{1/2}$ we have
$$
|W| \le \E^{\nu\pi/4} \E^{-|z|^2/2} \le \E^{\nu\pi/4} \E^{-\rho_0^2 t/4} \E^{-|z|^2/4}
$$
which finishes the proof.
\end{proof}

The next lemma allows us, to replace $\hat{m}(z)$ by $\hat{m}^c(z)$.

\begin{lemma}\label{lem:approrhp}
Consider the RHP 
\begin{align}
m_+(z) &= m_-(z) v(z), && z\in\Sigma,\\ \nn
m(z) &\to \id, && z\to \infty,\quad z\notin\Sigma.
\end{align}
Assume that $w \in L^2(\Sigma) \cap L^{\infty}(\Sigma)$. Then
\be
\|\mu-\id\|_2 \le \frac{c\|w\|_2}{1-c\|w\|_\infty}
\ee
provided $c\|w\|_\infty<1$, where $c$ is the norm of the Cauchy operator on $L^2(\Sigma)$.
\end{lemma}

\begin{proof}
This follows since $\ti{\mu} = \mu-\id \in L^2(\Sigma)$ satisfies
$(\id - C_w) \ti{\mu} = C_w \id$.
\end{proof}

\begin{lemma}\label{lem:approcross}
The solution $\hat{m}(z)$ has a convergent asymptotic expansion
\be\label{asymhm}
\hat{m}(z) = \id + \frac{1}{z} \hat{M}(t) + O(\frac{1}{z^2})
\ee
for $|z|>\rho_0 t^{1/2}$ with the error term uniformly in $t$. Moreover,
\be
\hat{M}(t) = \hat{M}^c + O(t^{-\alpha/2}).
\ee
\end{lemma}

\begin{proof}
Consider $\hat{m}^d(z)= \hat{m}(z) \hat{m}^c(z)^{-1}$, whose jump matrix is given by
$$
\hat{v}^d(z) = \hat{m}_-^c(z)\hat{v}(z) \hat{v}^c(z)^{-1} \hat{m}_-^c(z)^{-1}=
\id + \hat{m}_-^c(z)\big(\hat{w}(z) - \hat{w}^c(z)\big)\hat{m}_-^c(z)^{-1}. 
$$
By Lemma~\ref{lem:esticross}, we have that $\hat{w} - \hat{w}^c$ is 
decaying of order $t^{-\alpha/2}$ in the norms of $L^1$ and $L^\infty$ and
thus the same is true for $\hat{w}^d = \hat{v}^d - \id$. Hence by the previous lemma
$$
\|\hat{\mu}^d - \id\|_2 = O(t^{-\alpha/2}).
$$
Furthermore, by $\hat{\mu}^d = \hat{m}^d_- = \hat{m}_- (\hat{m}^c_-)^{-1} =
\hat{\mu} (\hat{\mu}^c)^{-1}$ we infer
$$
\|\hat{\mu} - \hat{\mu}^c\|_2 = O(t^{-\alpha/2})
$$
since $ \hat{\mu}^c$ is bounded. Now
$$
\hat{m}(z) = \id - \frac{1}{2\pi\I} \frac{1}{z} \int_\Sigma \hat{\mu}(s) \hat{w}(s) ds +
\frac{1}{2\pi\I} \frac{1}{z} \int_\Sigma s \hat{\mu}(s) \hat{w}(s) \frac{ds}{s - z}
$$
shows (recall that $\hat{w}$ is supported inside $|z|\le\rho_0 t^{1/2}$)
$$
\hat{m}(z) = \id + \frac{1}{z} \hat{M}(t) + O(\frac{\|\hat{\mu}(s)\|_2 \|s \hat{w}(s)\|_2}{z^2}),
$$
where
$$
\hat{M}(t) = -\frac{1}{2\pi\I}  \int_\Sigma \hat{\mu}(s) \hat{w}(s) ds.
$$
Now the rest follows from
$$
\hat{M}(t) = \hat{M}^c - \frac{1}{2\pi\I}  \int_\Sigma (\hat{\mu}(s) \hat{w}(s) -\hat{\mu}^c(s) \hat{w}^c(s)) ds
$$
using $\|\hat{\mu} \hat{w} -\hat{\mu}^c \hat{w}^c\|_1 \le \|\hat{w}-\hat{w}^c\|_1 + \|\hat{\mu}-\id\|_2 \|\hat{w}-\hat{w}^c\|_2 +
\|\hat{\mu}-\hat{\mu}^c\|_2\|\hat{w}^c\|_2$.
\end{proof}

Finally, it remains to solve (\ref{eq:solrhpcross2}) and to show:

\begin{theorem}
The solution of the RHP (\ref{eq:solrhpcross2})
is of the form
\be
\hat{m}^c(z) = \id + \frac{1}{z} \hat{M}^c + O(\frac{1}{z^2}),
\ee
where
\begin{align}
\hat{M}^c &= \I \begin{pmatrix} 0 & -\beta \\ \ol{\beta} & 0 \end{pmatrix},\quad
\beta = \sqrt{\nu} \E^{\I(\pi/4-\arg(r)+\arg(\Gamma(\I\nu)))}.
\end{align}
The error term is uniform with respect to $r$ in compact subsets of $\mathbb{D}$.
Moreover, the solution is bounded (again uniformly with respect to $r$).
\end{theorem}

Given this result, Theorem~\ref{thm:solcross} follows from Lemma~\ref{lem:approcross}
\begin{align}\nn
m(z) &= D(t) \hat{m}(z t^{1/2}) D(t)^{-1} = \id + \frac{1}{t^{1/2} z} D(t) \hat{M}(t) D(t)^{-1}+ O(z^{-2} t^{-1})\\
&= \id + \frac{1}{t^{1/2} z} D(t) \hat{M}^c D(t)^{-1}+ O(t^{-(1+\alpha)/2})
\end{align}
for $|z|>\rho_0$, since $D(t)$ is bounded.

The proof of this result will be given in the remainder of this section.
In order to solve (\ref{eq:solrhpcross2}) we begin with a deformation which moves the jump to $\R$
as follows. Denote the region enclosed by $\mathbb{R}$ and $\Sigma_j$ as $\Omega_j$
(cf.\ Figure~\ref{fig:defcross})
\begin{figure}
\begin{picture}(7,5.2)

\put(1,5){\line(1,-1){5}}
\put(2,4){\vector(1,-1){0.4}}
\put(4.7,1.3){\vector(1,-1){0.4}}
\put(1,0){\line(1,1){5}}
\put(2,1){\vector(1,1){0.4}}
\put(4.7,3.7){\vector(1,1){0.4}}
\put(0.6,2.5){\line(1,0){5.8}}
\put(2,2.5){\vector(1,0){0.4}}
\put(5,2.5){\vector(1,0){0.4}}
%\put(3.5,0){\line(0,1){5}}

\put(6.0,0.1){$\Sigma_1$}
\put(5.3,4.8){$\Sigma_2$}
\put(1.3,4.8){$\Sigma_3$}
\put(1.4,0.1){$\Sigma_4$}
\put(6,2.2){$\R$}

\put(4.8,1.8){$\Omega_1$}
\put(4.8,3){$\Omega_2$}
\put(1.8,3){$\Omega_3$}
\put(1.8,1.8){$\Omega_4$}

\end{picture}
\caption{Deforming back the cross}
\label{fig:defcross}
\end{figure}%
and define
\be\label{eq:mrhpcross3}
\ti{m}^c(z) = \hat{m}^c(z) \begin{cases}
D_0(z) D_j, & z\in\Omega_j,\: j = 1,\dots,4,\\
D_0(z), & \mbox{else}, \end{cases}
\ee
where
$$
D_0(z) = \begin{pmatrix} z^{\I\nu} \E^{-\I z^2/4} & 0 \\ 0 & z^{-\I\nu} \E^{\I z^2/4} \end{pmatrix},
$$
and
\begin{align*}
D_1 &= \begin{pmatrix} 1 & \ol{r}  \\ 0 & 1 \end{pmatrix} &
D_2 &= \begin{pmatrix} 1 & 0 \\ r  & 1 \end{pmatrix} &
D_3 &= \begin{pmatrix} 1 & -\frac{\ol{r}}{1-\abs{r}^2} \\ 0 & 1\end{pmatrix} &
D_4 &= \begin{pmatrix} 1 & 0 \\ -\frac{r}{1-\abs{r}^2} & 1 \end{pmatrix}.
\end{align*}

\begin{lemma}\label{lem:reducetoline}
The function $\ti{m}^c(z)$ defined in (\ref{eq:mrhpcross3}) satisfies the RHP
\begin{align}\label{eq:solrhpcross3}
\ti{m}^c_+ (z) &= \ti{m}^c_-(z) \begin{pmatrix} 1 - \abs{r}^2 & - \ol{r} \\ r & 1 \end{pmatrix},&&
z\in\mathbb{R}\\ \nn
\ti{m}^c(z) &= (\id + \frac{1}{z} \hat{M}^c + \dots) D_0(z),&& z\to\infty,
\: \frac{\pi}{4} < \arg(z) < \frac{3\pi}{4}.
\end{align}
\end{lemma}

\begin{proof}
First, one checks that $\ti{m}^c_+(z) = \ti{m}^c_-(z) D_0(z)^{-1} \hat{v}_1^c(z) D_0(z) D_1 =
\ti{m}^c_-(z)$, $z\in\Sigma_1$ and similarly for $z \in \Sigma_2, \Sigma_3, \Sigma_4$.
To compute the jump along $\R$ observe that, by our choice of branch cut for $z^{\I\nu}$, $D_0(z)$
has a jump along the negative real axis given by
$$
D_{0,\pm}(z) = \begin{pmatrix} \E^{(\log|z| \pm \I \pi) \I \nu} \E^{-\I z^2/4} & 0 \\ 0 & \E^{-(\log|z| \pm \I \pi) \I \nu} \E^{\I z^2/4} \end{pmatrix}, \qquad z<0.
$$
Hence the jump along $\R$ is given by
$$
D_1^{-1} D_2,\quad z>0 \quad\text{and}\quad
D_4^{-1} D_{0,-}^{-1}(z) D_{0,+}(z) D_3,\quad z<0,
$$
and (\ref{eq:solrhpcross3}) follows after recalling $\E^{-2\pi\nu}=1-|r|^2$.
\end{proof}

Now, we can follow (4.17) to (4.51) in \cite{dz} to construct
an approximate solution.

The idea is as follows, since the jump matrix for (\ref{eq:solrhpcross3}), the derivative
$\frac{d}{dz} \ti{m}^c(z)$ has the same jump and hence is given by $n(z) \ti{m}^c(z)$,
where the entire matrix $n(z)$ can be determined from the behaviour $z\to\infty$. Since
this will just serve as a motivation for our ansatz, we will not worry about justifying any
steps.

For $z$ in the sector $\frac{\pi}{4} < \arg(z) < \frac{3\pi}{4}$ (enclosed by $\Sigma_2$ and $\Sigma_3$)
we have $\ti{m}^c(z) =\hat{m}^c(z) D_0(z)$ and hence
\begin{align*}
& \left( \frac{d}{dz} \ti{m}^c(z) + \frac{\I z}{2} \sigma_3 \ti{m}^c(z) \right) \ti{m}^c(z)^{-1}\\
& \qquad = \left( \I(\frac{\nu}{z} - \frac{z}{2}) \hat{m}^c(z) \sig_3 + \frac{d}{dz} \hat{m}^c(z)
+ \I \frac{z}{2} \sig_3 \hat{m}^c(z) \right) \hat{m}^c(z)^{-1}\\
& \qquad = \frac{\I}{2} [\sig_3,  \hat{M}^c] + O(\frac{1}{z}), \qquad
\sigma_3 = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}.
\end{align*}
Since the left hand side has no jump, it is entire and hence by Liouville's theorem a constant
given by the right hand side. In other words,
\be\label{eq:odetimc}
\frac{d}{dz} \ti{m}^c(z) + \frac{\I z}{2} \sigma_3 \ti{m}^c(z) = \beta \ti{m}^c(z),\quad
\beta = \begin{pmatrix} 0 & \beta_{12} \\ \beta_{21} & 0 \end{pmatrix} = \frac{\I}{2} [\sigma_3, \hat{M}^c].
\ee
This differential equation can be solved in terms of parabolic cylinder function which then gives
the solution of (\ref{eq:solrhpcross3}).

\begin{lemma}\label{lem:asymbyparabolic}
The RHP (\ref{eq:solrhpcross3}) has a unique solution, and the term $\hat{M}^c$ is given by
\begin{align}
\hat{M}^c &= \I \begin{pmatrix} 0 & - \beta_{12} \\ \beta_{21} & 0 \end{pmatrix},\quad
&& \beta_{12} = \ol{\beta_{21}} = \sqrt{\nu} \E^{\I(\pi/4-\arg(r)+\arg(\Gamma(\I\nu)))}.
\end{align}
\end{lemma}

\begin{proof}
Uniqueness follows by the standard Liouville argument since the determinant of the jump matrix is equal to $1$.
To find the solution we use the ansatz
$$
\ti{m}^c(z) = \begin{pmatrix} \psi_{11}(z) & \psi_{12}(z) \\ \psi_{21}(z) & \psi_{22}(z) \end{pmatrix},
$$
where the functions $\psi_{jk}(z)$ satisfy
\begin{align*}
\psi_{11}''(z) &=  - \left(\frac{\I}{2} + \frac{1}{4}z^2-\beta_{12}\beta_{21}\right)\psi_{11}(z), &
\psi_{12}(z) &= \frac{1}{\beta_{21}}\left(\frac{d}{dz} - \frac{\I z}{2}\right)\psi_{22}(z),\\
\psi_{21}(z) &= \frac{1}{\beta_{12}}\left(\frac{d}{dz} + \frac{\I z}{2}\right)\psi_{11}(z), &
\psi_{22}''(z) &=  \left(\frac{\I}{2} - \frac{1}{4}z^2+\beta_{12}\beta_{21}\right)\psi_{22}(z).
\end{align*}
That is, $\psi_{11}(\E^{3\pi \I/4}\zeta)$ satisfies the parabolic cylinder equation
$$
D ''(\zeta) + \left(a + \frac{1}{2} - \frac{1}{4} \zeta^2\right) D(\zeta) = 0
$$
with $a= \I\beta_{12}\beta_{21}$ and $\psi_{22}(\E^{\I\pi/4}\zeta)$ satisfies the
parabolic cylinder equation with $a= -\I\beta_{12}\beta_{21}$.

Let $D_a$ be the entire parabolic cylinder function of \S16.5 in \cite{whwa} and set
\begin{align*}
\psi_{11}(z) &= \begin{cases}
\E^{-3\pi\nu/4}D_{\I\nu}(-\E^{\I\pi/4} z), & \im(z)>0,\\
\E^{\pi\nu/4} D_{\I\nu}(\E^{\I\pi/4} z), & \im(z)<0, \end{cases} \\
\psi_{22}(z) &= \begin{cases}
\E^{\pi\nu/4 } D_{-\I\nu}(-\I\E^{\I\pi/4} z), & \im(z)>0,\\
\E^{-3\pi\nu/4} D_{-\I\nu}(\I \E^{\I\pi/4} z), & \im(z)<0.\end{cases}
\end{align*}
Using the asymptotic behavior
$$
D_a(z) = z^a \E^{-z^2/4} \big(1 - \frac{a(a-1)}{2z^2} + O(z^{-4})\big),\quad z\to\infty,\quad \abs{\arg(z)} \leq 3 \pi/4,
$$
shows that the choice $\beta_{12}\beta_{21}=\nu$ ensures the correct asymptotics
\begin{align*}
&\psi_{11}(z) = z^{\I\nu} \E^{-\I z^2 /4} (1 + O(z^{-2})),
&&\psi_{12}(z) = -\I\beta_{12} z^{-\I\nu} \E^{\I z^2 /4} (z^{-1} + O(z^{-3})),\\
&\psi_{21}(z) = \I\beta_{21} z^{\I\nu} \E^{- \I z^2 /4} (z^{-1} + O(z^{-3})),
&&\psi_{22}(z) = z^{-\I\nu} \E^{\I z^2 /4} (1 + O(z^{-2})),
\end{align*}
as $z\to\infty$ inside the half plane $\im(z)\ge 0$. In particular,
$$
\ti{m}^c(z) = \big(\id + \frac{1}{z} \hat{M}^c + O(z^{-2})\big) D_0(z) \quad\mbox{with} \quad
\hat{M}^c = \I \begin{pmatrix} 0 & -\beta_{12} \\ \beta_{21} & 0 \end{pmatrix}. 
$$
It remains to check that we have the correct jump. Since by construction both limits $\ti{m}^c_+(z)$ and
$\ti{m}^c_-(z)$ satisfy the same differential equation (\ref{eq:odetimc}), there is a constant matrix $v$
such that $\ti{m}^c_+(z) = \ti{m}^c_-(z) v$. Moreover, since the coefficient matrix of the linear differential
equation (\ref{eq:odetimc}) has trace $0$, the determinant of $\ti{m}^c_\pm(z)$ is constant and hence
$\det(\ti{m}^c_\pm(z))=1$ by our asymptotics. Moreover, evaluating
$$
v= \ti{m}^c_-(0)^{-1} \ti{m}^c_+(0) = \begin{pmatrix}
\E^{-2\pi\nu} & - \frac{\sqrt{2\pi}\E^{-\I\pi/4} \E^{-\pi\nu/2}}{\sqrt{\nu}\Gamma(\I\nu)} \gamma^{-1}\\
\frac{\sqrt{2\pi}\E^{\I\pi/4} \E^{-\pi\nu/2}}{\sqrt{\nu}\Gamma(-\I\nu)} \gamma & 1
\end{pmatrix}
$$
where $\gamma =\frac{\sqrt{\nu}}{\beta_{12}}=\frac{\beta_{21}}{\sqrt{\nu}}$. Here we have used
$$
D_a(0)= \frac{2^{a/2}\sqrt{\pi}}{\Gamma((1-a)/2)}, \qquad
D_a'(0)= -\frac{2^{(1+a)/2}\sqrt{\pi}}{\Gamma(-a/2)}
$$
plus the duplication formula $\Gamma(z)\Gamma(z+\frac{1}{2})= 2^{1-2z} \sqrt{\pi} \Gamma(2z)$ for
the Gamma function. Hence, if we choose
$$
\gamma= \frac{\sqrt{\nu}\Gamma(-\I\nu)}{\sqrt{2\pi}\E^{\I\pi/4} \E^{-\pi\nu/2}} r,
$$
we have
$$
v= \begin{pmatrix} 1 - |r|^2 & - \ol{r} \\ r & 1 \end{pmatrix}
$$
since $|\gamma|^2=1$. To see this use $|\Gamma(-\I\nu)|^2 = \frac{\Gamma(1-\I\nu)\Gamma(\I\nu)}{-\I\nu}
= \frac{\pi}{\nu \sinh(\pi\nu)}$ which follows from Euler's reflection formula $\Gamma(1-z)\Gamma(z)=\frac{\pi}{\sin(\pi z)}$
for the Gamma function.

In particular,
$$
\beta_{12} = \ol{\beta_{21}}  = \sqrt{\nu} \E^{\I(\pi/4-\arg(r)+\arg(\Gamma(\I\nu)))}
$$
which finishes the proof.
\end{proof}


\begin{remark}
An inspection of the proof shows that $\hat{m}^c$ is given by the solution of a
differential equation depending analytically on $\nu$. Hence, $\hat{m}^c$
depends analytically on $\nu = - \frac{1}{2\pi} \log(1 - |r|^2)$. This
implies local Lipschitz dependence on $r$ as long as $r\in\mathbb{D}$.
\end{remark}




\section{Singular integral equations}
\label{sec:sieq}



In this section we show how to transform a meromorphic vector Riemann--Hilbert problem
with simple poles at $\zeta$, $\zeta^{-1}$,
\begin{align}\nn
& m_+(z) = m_-(z) v(z), \qquad z\in \Sigma,\\ \label{eq:rhp5m}
& \res_{\zeta} m(z) = \lim_{z\to\zeta} m(z)
\begin{pmatrix} 0 & 0\\ - \zeta \gam  & 0 \end{pmatrix},\quad
\res_{\zeta^{-1}} m(z) &= \lim_{z\to\zeta^{-1}} m(z)
\begin{pmatrix} 0 & \zeta^{-1} \gam \\ 0 & 0 \end{pmatrix},\\ \nn
& m(z^{-1}) = m(z) \sigI,\\ \nn
& m(0) = \begin{pmatrix} 1 & m_2\end{pmatrix},
\end{align}
into a singular integral equation.
Since we require the symmetry condition (\ref{eq:symcond}) for our Riemann--Hilbert
problems we need to adapt the usual Cauchy kernel to preserve this symmetry.
Moreover, we keep the single soliton as an inhomogeneous term which will play
the role of the leading asymptotics in our applications.

\begin{hypothesis}\label{hyp:sym}
Let $\Sigma$ consist of a finite number of smooth oriented finite curves in $\C$
which intersect at most finitely many times with all intersections being transversal.
Assume that the contour $\Sigma$ does not contain $0$ and is invariant under
$z\mapsto z^{-1}$. Moreover, suppose the jump matrix $v$
can be factorized according to $v = b_-^{-1} b_+ = (\id-w_-)^{-1}(\id+w_+)$, where
$w_\pm$ are continuous and satisfy
\be
w_\pm(z^{-1}) = \sigI w_\mp(z) \sigI,\quad z\in\Sigma.
\ee
\end{hypothesis}

The classical Cauchy-transform
of a function $f:\Sigma\to \C$ which is square integrable is the
analytic function $C f: \C\backslash\Sigma\to\C$ given by
\be
C f(z) = \frac{1}{2\pi\I} \int_{\Sigma} \frac{f(s)}{s - z} ds,\qquad z\in\C\backslash\Sigma.
\ee
Denote the non-tangential boundary values from both sides (taken possibly
in the $L^2$-sense --- see e.g.\ \cite[eq.\ (7.2)]{deiftbook}) by $C_+ f$ respectively $C_- f$.
Then it is well-known that $C_+$ and $C_-$ are bounded operators $L^2(\Sigma)\to L^2(\Sigma)$, which satisfy $C_+ - C_- = \id$ and $C_+ C_- = 0$ (see e.g. \cite{bc}). Moreover, one has
the Plemelj--Sokhotsky formula (\cite{mu})
$$
C_\pm = \frac{1}{2} (\I H \pm \id),
$$
where
\be
H f(t) = \frac{1}{\pi} \dashint_\Sigma \frac{f(s)}{t-s} ds,\qquad t\in\Sigma,
\ee
is the Hilbert transform and $\dashint$ denotes the principal value integral.

In order to respect the symmetry condition we will restrict our attention to
the set $L^2_{s}(\Sigma)$ of square integrable functions $f:\Sigma\to\C^{2}$ such that
\be\label{eq:sym}
f(z^{-1}) = f(z) \sigI.
\ee
Clearly this will only be possible if we require our jump data to be symmetric as well (i.e.,
Hypothesis~\ref{hyp:sym} holds).

Next we introduce the Cauchy operator
\be
(C f)(z) = \frac{1}{2\pi\I} \int_\Sigma f(s) \Omega_\zeta(s,z)
\ee
acting on vector-valued functions $f:\Sigma\to\C^{2}$.
Here the Cauchy kernel is given by
\be
\Omega_{\zeta}(s,z) =
\begin{pmatrix} \frac{z-\zeta^{-1}}{s-\zeta^{-1}} \frac{1}{s-z} & 0 \\
0 & \frac{z-\zeta}{s-\zeta} \frac{1}{s-z} \end{pmatrix} ds =
\begin{pmatrix} \frac{1}{s-z} - \frac{1}{s-\zeta^{-1}} & 0 \\
0 & \frac{1}{s-z} - \frac{1}{s-\zeta} \end{pmatrix} ds,
\ee
for some fixed $\zeta\notin\Sigma$. In the case $\zeta=\infty$ we set
\be\label{eq:defomegainfty}
\Omega_{\infty}(s,z) =
\begin{pmatrix} \frac{1}{s-z} - \frac{1}{s} & 0 \\
0 & \frac{1}{s-z} \end{pmatrix} ds.
\ee
and one easily checks the symmetry property:
\be\label{eq:symC}
\Omega_\zeta(1/s,1/z) = \sigI \Omega_\zeta(s,z) \sigI.
\ee
The properties of $C$ are summarized in the next lemma.

\begin{lemma}
Assume Hypothesis~\ref{hyp:sym}.
The Cauchy operator $C$ has the properties, that the boundary values
$C_\pm$ are bounded operators $L^2_s(\Sigma) \to L^2_s(\Sigma)$
which satisfy
\be\label{eq:cpcm}
C_+ - C_- = \id
\ee
and
\be\label{eq:Cnorm}
(Cf)(\zeta^{-1}) = (0\quad\ast), \qquad (Cf)(\zeta) = (\ast\quad 0).
\ee
Furthermore, $C$ restricts to $L^2_{s}(\Sigma)$, that is
\be
(C f) (z^{-1}) = (Cf)(z) \sigI,\quad z\in\C\backslash\Sigma
\ee
for $f\in L^2_{s}(\Sigma)$ and if $w_\pm$ satisfy (H.\ref{hyp:sym}) we also have
\be \label{eq:symcpm}
C_\pm(f w_\mp)(1/z) = C_\mp(f w_\pm)(z) \sigI,\quad z\in\Sigma.
\ee
\end{lemma}

\begin{proof}
Everything follows from (\ref{eq:symC}) and the fact that $C$ inherits all properties from
the classical Cauchy operator.
\end{proof}

We have thus obtained a Cauchy transform with the required properties.
Following Section 7 and 8 of \cite{bc}, we can solve our Riemann--Hilbert problem using this
Cauchy operator.

Introduce the operator $C_w: L_s^2(\Sigma)\to L_s^2(\Sigma)$ by
\be
C_w f = C_+(fw_-) + C_-(fw_+),\quad f\in L^2_s(\Sigma)
\ee
and recall from Lemma~\ref{lem:singlesoliton} that the
solution corresponding to $v\equiv \id$ is given by
$$
m_0(z)= \begin{pmatrix} f(z) & f(\frac{1}{z}) \end{pmatrix}, \quad
f(z) = \frac{1}{1 - \zeta^2 + \gamma}
\left(\gamma \zeta^2 \frac{z-\zeta^{-1}}{z - \zeta} + 1 - \zeta^2\right)
$$
Observe that for $\gam=0$ we have $f(z)=1$ and for $\gam=\infty$ we have
$f(z)= \zeta^2\frac{z-\zeta^{-1}}{z - \zeta}$. In particular, $m_0(z)$ is uniformly bounded
away from $\zeta$ for all $\gam\in[0,\infty]$.

Then we have the next result.

\begin{theorem}\label{thm:cauchyop}
Assume Hypothesis~\ref{hyp:sym}.

Suppose $m$ solves the Riemann--Hilbert problem (\ref{eq:rhp5m}). Then
\be\label{eq:mOm}
m(z) = (1-c_0) m_0(z) + \frac{1}{2\pi\I} \int_\Sigma \mu(s) (w_+(s) + w_-(s)) \Omega_\zeta(s,z),
\ee
where
$$
\mu = m_+ b_+^{-1} = m_- b_-^{-1} \quad\mbox{and}\quad
c_0= \left( \frac{1}{2\pi\I} \int_\Sigma \mu(s) (w_+(s) + w_-(s)) \Omega_\zeta(s,0) \right)_{\!1}.
$$
Here $(m)_j$ denotes the $j$'th component of a vector.
Furthermore, $\mu$ solves
\be\label{eq:sing4muc}
(\id - C_w) \mu = (1-c_0) m_0(z).
\ee

Conversely, suppose $\ti{\mu}$ solves 
\be\label{eq:sing4mu}
(\id - C_w) \ti{\mu} = m_0(z),
\ee
and
$$
\ti{c}_0= \left( \frac{1}{2\pi\I} \int_\Sigma \ti{\mu}(s) (w_+(s) + w_-(s)) \Omega_\zeta(s,0) \right)_{\!1} \ne 1,
$$
then $m$ defined via (\ref{eq:mOm}), with $(1-c_0)=(1-\ti{c}_0)^{-1}$ and $\mu=(1-\ti{c}_0)^{-1}\ti{\mu}$,
solves the Riemann--Hilbert problem (\ref{eq:rhp5m}) and $\mu= m_\pm b_\pm^{-1}$.
\end{theorem}

\begin{proof}
First of all note hat by (\ref{eq:symcpm}) $(\id - C_w)$ satisfies the symmetry condition and
hence so do $(\id - C_w)^{-1} m_0$ and $m$.

So if $m$ solves (\ref{eq:rhp5m}) and we set $\mu = m_\pm b_\pm^{-1}$,
then $m$ satisfies an additive jump given by
$$
m_+ - m_- = \mu (w_+ + w_-).
$$
Hence, if we denote the left hand side of (\ref{eq:mOm})
by $\ti{m}$, both functions satisfy the same additive jump. So
$m-\ti{m}$ has no jump and must thus solve (\ref{eq:rhp5m}) with $v\equiv \id$. By
uniqueness (cf.\ \cite{krt}) $m-\ti{m} = \alpha m_0$ for some $\alpha\in\C$ and by looking 
at the first component at $z=0$ we see $\alpha=0$, that is $m=\ti{m}$.

Moreover, if $m$ is given by (\ref{eq:mOm}), then (\ref{eq:cpcm}) implies
\begin{align} \label{eq:singtorhp}
m_\pm &= (1-c_0)m_0 + C_\pm(\mu w_-) + C_\pm(\mu w_+) \\
\nn &= (1-c_0)m_0 + C_w(\mu) \pm \mu w_\pm \\
\nn &= (1-c_0)m_0 - (\id - C_w) \mu + \mu b_\pm.
\end{align}
From this we conclude that $\mu = m_\pm b_\pm^{-1}$ solves (\ref{eq:sing4muc}).

Conversely, if $\ti{\mu}$ solves (\ref{eq:sing4mu}) then (\ref{eq:singtorhp}) implies
$m_\pm= \mu b_\pm$ which shows that $m$ defined via
(\ref{eq:mOm}) solves the Riemann--Hilbert problem (\ref{eq:rhp5m}).
\end{proof}

Note that in the special case $\gamma=0$ we have $m_0(z)= \rI$ and
we can choose $\zeta$ as we please, say $\zeta=\infty$ such that $c_0=\ti{c}_0=0$
in the above theorem.

Hence we have a formula for the solution of our Riemann--Hilbert problem $m(z)$ in terms of
$(\id - C_w)^{-1} m_0$ and this clearly raises the question of bounded
invertibility of $\id - C_w$. This follows from Fredholm theory (cf.\ e.g. \cite{zh}):

\begin{lemma}
Assume Hypothesis~\ref{hyp:sym}.
The operator $\id-C_w$ is Fredholm of index zero,
\be
\ind(\id-C_w) =0.
\ee
\end{lemma}

\begin{proof}
Since one can easily check
\be
(\id-C_w) (\id-C_{-w}) = (\id-C_{-w}) (\id-C_w) = \id- T_w,
\ee
where 
$$
T_w = T_{++} + T_{+-} + T_{-+} + T_{--}, \qquad
T_{\sig_1\sig_2}(f) = C_{\sig_1}[C_{\sig_2}(f w_{-\sig_2})w_{-\sig_1}] ,
$$
it suffices to check that the operators $T_{\sig_1\sig_2}$ are compact (\cite[Thm.~1.4.3]{proe}).
By Mergelyan's theorem we can approximate $w_\pm$ by rational functions and, since
the norm limit of compact operators is compact, we can assume without loss that $w_\pm$ have
an analytic extension to a neighborhood of $\Sigma$.

Indeed, suppose $f_n \in L^2(\Sigma)$ converges weakly to zero. Without loss we can assume
$f_n$ to be continuous. We will show that $\|T_w f_n\|_{L^2} \to 0$.

Using the analyticity of $w$ in a neighborhood of $\Sigma$
and the definition of $C_\pm$, we can slightly deform
the contour $\Sigma$ to some contour 
$\Sigma_\pm$ close to $\Sigma$, on the left, and
have, by Cauchy's theorem,
\begin{align*}
T_{++} f_n(z) =& \frac{1}{2 \pi \I}
\int_{\Sigma_+} (C(f_n w_-)(s) w_-(s)) \Omega_\zeta(s,z).
\end{align*}
Now $(C(f_n w_-) w_-)(z) \to 0$ as $n \to \infty$.
Also
$$
|(C(f_n w_-) w_-)(z)| < const\, \|f_n\|_{L^2} \|w_- \|_{L^\infty}
< const
$$
and thus, by the dominated convergence theorem, $\|T_{++} f_n\|_{L^2} \to 0$ as
desired.

Moreover, considering $\id- \eps C_w = \id- C_{ \eps w}$ for $0 \leq \eps \leq 1$ 
we obtain $\ind(\id-C_w)= \ind(\id) =0$ from homotopy invariance of the index.
\end{proof}

By the Fredholm alternative, it follows that to show the bounded invertibility of $\id-C_w$
we only need to show that $\ker (\id-C_w) =0$. The latter being equivalent to
unique solvability of the corresponding vanishing Riemann--Hilbert problem.

\begin{corollary}
Assume Hypothesis~\ref{hyp:sym}.
A unique solution of the Riemann--Hilbert problem (\ref{eq:rhp5m}) exists if and only if the corresponding
vanishing Riemann--Hilbert problem, where the normalization condition is replaced by
$m(0)= \begin{pmatrix} 0 & m_2\end{pmatrix}$, has at most one solution.
\end{corollary}

We are interested in comparing two Riemann--Hilbert problems associated with
respective jumps $w_0$ and $w$ with $\|w-w_0\|_\infty$ small,
where
\be
\|w\|_\infty= \|w_+\|_{L^\infty(\Sigma)} + \|w_-\|_{L^\infty(\Sigma)}.
\ee
For such a situation we have the following result:

\begin{theorem}\label{thm:remcontour}
Assume that for some data $w_0^t$ the operator
\be
\id-C_{w_0^t}: L^2_s(\Sigma) \to L^2_s(\Sigma)
\ee
has a bounded inverse, where the bound is independent of $t$, and
let $\zeta=\zeta_0$, $\gam^t=\gam_0^t$.

Furthermore, assume $w^t$ satisfies
\be
\|w^t - w_0^t\|_\infty \leq \alpha(t)
\ee
for some function $\alpha(t) \to 0$ as $t\to\infty$. Then
$(\id-C_{w^t})^{-1}: L^2_s(\Sigma)\to L^2_s(\Sigma)$ also exists
for sufficiently large $t$ and the associated solutions of
the Riemann--Hilbert problems (\ref{eq:rhp5m}) only differ by $O(\alpha(t))$.
\end{theorem}

\begin{proof}
By boundedness of the Cauchy transform, one has
$$
\|(C_{w^t} - C_{w_0^t})\| \leq const \|w\|_\infty.
$$
Thus, by the second resolvent identity, we infer that $(\id-C_{w^t})^{-1}$ exists for large $t$ and
$$
\|(\id-C_{w^t})^{-1}-(\id-C_{w_0^t})^{-1}\| = O(\alpha(t)).
$$
From which the claim follows since this implies $\|\mu^t - \mu_0^t\|_{L^2} = O(\alpha(t))$ and thus
$m^t(z) - m_0^t(z) = O(\alpha(t))$ uniformly in $z$ away from $\Sigma$.
\end{proof}



\noindent
{\bf Acknowledgments.}
We thank K.\ Grunert, A.\ Mikikitis-Leitner, and J.\ Michor
for pointing out errors in a previous version of this article.


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1334 1272 m
1334 1266 1331 1260 1327 1255 C
1322 1251 1316 1248 1310 1248 C
1304 1248 1298 1251 1293 1255 C
1289 1260 1286 1266 1286 1272 C
1286 1278 1289 1284 1293 1289 C
1298 1293 1304 1296 1310 1296 C
1316 1296 1322 1293 1327 1289 C
1331 1284 1334 1278 1334 1272 C
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1346 1272 m
1346 1266 1343 1260 1339 1255 C
1334 1251 1328 1248 1322 1248 C
1316 1248 1310 1251 1305 1255 C
1301 1260 1298 1266 1298 1272 C
1298 1278 1301 1284 1305 1289 C
1310 1293 1316 1296 1322 1296 C
1328 1296 1334 1293 1339 1289 C
1343 1284 1346 1278 1346 1272 C
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1357 1273 m
1357 1267 1354 1261 1350 1256 C
1345 1252 1339 1249 1333 1249 C
1327 1249 1321 1252 1316 1256 C
1312 1261 1309 1267 1309 1273 C
1309 1279 1312 1285 1316 1290 C
1321 1294 1327 1297 1333 1297 C
1339 1297 1345 1294 1350 1290 C
1354 1285 1357 1279 1357 1273 C
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1369 1273 m
1369 1267 1366 1261 1362 1256 C
1357 1252 1351 1249 1345 1249 C
1339 1249 1333 1252 1328 1256 C
1324 1261 1321 1267 1321 1273 C
1321 1279 1324 1285 1328 1290 C
1333 1294 1339 1297 1345 1297 C
1351 1297 1357 1294 1362 1290 C
1366 1285 1369 1279 1369 1273 C
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1380 1274 m
1380 1268 1377 1262 1373 1257 C
1368 1253 1362 1250 1356 1250 C
1350 1250 1344 1253 1339 1257 C
1335 1262 1332 1268 1332 1274 C
1332 1280 1335 1286 1339 1291 C
1344 1295 1350 1298 1356 1298 C
1362 1298 1368 1295 1373 1291 C
1377 1286 1380 1280 1380 1274 C
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1392 1275 m
1392 1269 1389 1263 1385 1258 C
1380 1254 1374 1251 1368 1251 C
1362 1251 1356 1254 1351 1258 C
1347 1263 1344 1269 1344 1275 C
1344 1281 1347 1287 1351 1292 C
1356 1296 1362 1299 1368 1299 C
1374 1299 1380 1296 1385 1292 C
1389 1287 1392 1281 1392 1275 C
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1403 1277 m
1403 1271 1400 1265 1396 1260 C
1391 1256 1385 1253 1379 1253 C
1373 1253 1367 1256 1362 1260 C
1358 1265 1355 1271 1355 1277 C
1355 1283 1358 1289 1362 1294 C
1367 1298 1373 1301 1379 1301 C
1385 1301 1391 1298 1396 1294 C
1400 1289 1403 1283 1403 1277 C
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1415 1281 m
1415 1275 1412 1269 1408 1264 C
1403 1260 1397 1257 1391 1257 C
1385 1257 1379 1260 1374 1264 C
1370 1269 1367 1275 1367 1281 C
1367 1287 1370 1293 1374 1298 C
1379 1302 1385 1305 1391 1305 C
1397 1305 1403 1302 1408 1298 C
1412 1293 1415 1287 1415 1281 C
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1426 1285 m
1426 1279 1423 1273 1419 1268 C
1414 1264 1408 1261 1402 1261 C
1396 1261 1390 1264 1385 1268 C
1381 1273 1378 1279 1378 1285 C
1378 1291 1381 1297 1385 1302 C
1390 1306 1396 1309 1402 1309 C
1408 1309 1414 1306 1419 1302 C
1423 1297 1426 1291 1426 1285 C
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1438 1290 m
1438 1284 1435 1278 1431 1273 C
1426 1269 1420 1266 1414 1266 C
1408 1266 1402 1269 1397 1273 C
1393 1278 1390 1284 1390 1290 C
1390 1296 1393 1302 1397 1307 C
1402 1311 1408 1314 1414 1314 C
1420 1314 1426 1311 1431 1307 C
1435 1302 1438 1296 1438 1290 C
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1449 1297 m
1449 1291 1446 1285 1442 1280 C
1437 1276 1431 1273 1425 1273 C
1419 1273 1413 1276 1408 1280 C
1404 1285 1401 1291 1401 1297 C
1401 1303 1404 1309 1408 1314 C
1413 1318 1419 1321 1425 1321 C
1431 1321 1437 1318 1442 1314 C
1446 1309 1449 1303 1449 1297 C
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1461 1304 m
1461 1298 1458 1292 1454 1287 C
1449 1283 1443 1280 1437 1280 C
1431 1280 1425 1283 1420 1287 C
1416 1292 1413 1298 1413 1304 C
1413 1310 1416 1316 1420 1321 C
1425 1325 1431 1328 1437 1328 C
1443 1328 1449 1325 1454 1321 C
1458 1316 1461 1310 1461 1304 C
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1473 1312 m
1473 1306 1470 1300 1466 1295 C
1461 1291 1455 1288 1449 1288 C
1443 1288 1437 1291 1432 1295 C
1428 1300 1425 1306 1425 1312 C
1425 1318 1428 1324 1432 1329 C
1437 1333 1443 1336 1449 1336 C
1455 1336 1461 1333 1466 1329 C
1470 1324 1473 1318 1473 1312 C
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1484 1321 m
1484 1315 1481 1309 1477 1304 C
1472 1300 1466 1297 1460 1297 C
1454 1297 1448 1300 1443 1304 C
1439 1309 1436 1315 1436 1321 C
1436 1327 1439 1333 1443 1338 C
1448 1342 1454 1345 1460 1345 C
1466 1345 1472 1342 1477 1338 C
1481 1333 1484 1327 1484 1321 C
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1496 1330 m
1496 1324 1493 1318 1489 1313 C
1484 1309 1478 1306 1472 1306 C
1466 1306 1460 1309 1455 1313 C
1451 1318 1448 1324 1448 1330 C
1448 1336 1451 1342 1455 1347 C
1460 1351 1466 1354 1472 1354 C
1478 1354 1484 1351 1489 1347 C
1493 1342 1496 1336 1496 1330 C
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1507 1337 m
1507 1331 1504 1325 1500 1320 C
1495 1316 1489 1313 1483 1313 C
1477 1313 1471 1316 1466 1320 C
1462 1325 1459 1331 1459 1337 C
1459 1343 1462 1349 1466 1354 C
1471 1358 1477 1361 1483 1361 C
1489 1361 1495 1358 1500 1354 C
1504 1349 1507 1343 1507 1337 C
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1519 1342 m
1519 1336 1516 1330 1512 1325 C
1507 1321 1501 1318 1495 1318 C
1489 1318 1483 1321 1478 1325 C
1474 1330 1471 1336 1471 1342 C
1471 1348 1474 1354 1478 1359 C
1483 1363 1489 1366 1495 1366 C
1501 1366 1507 1363 1512 1359 C
1516 1354 1519 1348 1519 1342 C
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1530 1340 m
1530 1334 1527 1328 1523 1323 C
1518 1319 1512 1316 1506 1316 C
1500 1316 1494 1319 1489 1323 C
1485 1328 1482 1334 1482 1340 C
1482 1346 1485 1352 1489 1357 C
1494 1361 1500 1364 1506 1364 C
1512 1364 1518 1361 1523 1357 C
1527 1352 1530 1346 1530 1340 C
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1542 1324 m
1542 1318 1539 1312 1535 1307 C
1530 1303 1524 1300 1518 1300 C
1512 1300 1506 1303 1501 1307 C
1497 1312 1494 1318 1494 1324 C
1494 1330 1497 1336 1501 1341 C
1506 1345 1512 1348 1518 1348 C
1524 1348 1530 1345 1535 1341 C
1539 1336 1542 1330 1542 1324 C
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1553 1286 m
1553 1280 1550 1274 1546 1269 C
1541 1265 1535 1262 1529 1262 C
1523 1262 1517 1265 1512 1269 C
1508 1274 1505 1280 1505 1286 C
1505 1292 1508 1298 1512 1303 C
1517 1307 1523 1310 1529 1310 C
1535 1310 1541 1307 1546 1303 C
1550 1298 1553 1292 1553 1286 C
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1565 1230 m
1565 1224 1562 1218 1558 1213 C
1553 1209 1547 1206 1541 1206 C
1535 1206 1529 1209 1524 1213 C
1520 1218 1517 1224 1517 1230 C
1517 1236 1520 1242 1524 1247 C
1529 1251 1535 1254 1541 1254 C
1547 1254 1553 1251 1558 1247 C
1562 1242 1565 1236 1565 1230 C
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1576 1200 m
1576 1194 1573 1188 1569 1183 C
1564 1179 1558 1176 1552 1176 C
1546 1176 1540 1179 1535 1183 C
1531 1188 1528 1194 1528 1200 C
1528 1206 1531 1212 1535 1217 C
1540 1221 1546 1224 1552 1224 C
1558 1224 1564 1221 1569 1217 C
1573 1212 1576 1206 1576 1200 C
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1588 1233 m
1588 1227 1585 1221 1581 1216 C
1576 1212 1570 1209 1564 1209 C
1558 1209 1552 1212 1547 1216 C
1543 1221 1540 1227 1540 1233 C
1540 1239 1543 1245 1547 1250 C
1552 1254 1558 1257 1564 1257 C
1570 1257 1576 1254 1581 1250 C
1585 1245 1588 1239 1588 1233 C
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1600 1295 m
1600 1289 1597 1283 1593 1278 C
1588 1274 1582 1271 1576 1271 C
1570 1271 1564 1274 1559 1278 C
1555 1283 1552 1289 1552 1295 C
1552 1301 1555 1307 1559 1312 C
1564 1316 1570 1319 1576 1319 C
1582 1319 1588 1316 1593 1312 C
1597 1307 1600 1301 1600 1295 C
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1611 1337 m
1611 1331 1608 1325 1604 1320 C
1599 1316 1593 1313 1587 1313 C
1581 1313 1575 1316 1570 1320 C
1566 1325 1563 1331 1563 1337 C
1563 1343 1566 1349 1570 1354 C
1575 1358 1581 1361 1587 1361 C
1593 1361 1599 1358 1604 1354 C
1608 1349 1611 1343 1611 1337 C
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1623 1342 m
1623 1336 1620 1330 1616 1325 C
1611 1321 1605 1318 1599 1318 C
1593 1318 1587 1321 1582 1325 C
1578 1330 1575 1336 1575 1342 C
1575 1348 1578 1354 1582 1359 C
1587 1363 1593 1366 1599 1366 C
1605 1366 1611 1363 1616 1359 C
1620 1354 1623 1348 1623 1342 C
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1634 1304 m
1634 1298 1631 1292 1627 1287 C
1622 1283 1616 1280 1610 1280 C
1604 1280 1598 1283 1593 1287 C
1589 1292 1586 1298 1586 1304 C
1586 1310 1589 1316 1593 1321 C
1598 1325 1604 1328 1610 1328 C
1616 1328 1622 1325 1627 1321 C
1631 1316 1634 1310 1634 1304 C
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1646 1234 m
1646 1228 1643 1222 1639 1217 C
1634 1213 1628 1210 1622 1210 C
1616 1210 1610 1213 1605 1217 C
1601 1222 1598 1228 1598 1234 C
1598 1240 1601 1246 1605 1251 C
1610 1255 1616 1258 1622 1258 C
1628 1258 1634 1255 1639 1251 C
1643 1246 1646 1240 1646 1234 C
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1657 1199 m
1657 1193 1654 1187 1650 1182 C
1645 1178 1639 1175 1633 1175 C
1627 1175 1621 1178 1616 1182 C
1612 1187 1609 1193 1609 1199 C
1609 1205 1612 1211 1616 1216 C
1621 1220 1627 1223 1633 1223 C
1639 1223 1645 1220 1650 1216 C
1654 1211 1657 1205 1657 1199 C
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1669 1250 m
1669 1244 1666 1238 1662 1233 C
1657 1229 1651 1226 1645 1226 C
1639 1226 1633 1229 1628 1233 C
1624 1238 1621 1244 1621 1250 C
1621 1256 1624 1262 1628 1267 C
1633 1271 1639 1274 1645 1274 C
1651 1274 1657 1271 1662 1267 C
1666 1262 1669 1256 1669 1250 C
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1680 1321 m
1680 1315 1677 1309 1673 1304 C
1668 1300 1662 1297 1656 1297 C
1650 1297 1644 1300 1639 1304 C
1635 1309 1632 1315 1632 1321 C
1632 1327 1635 1333 1639 1338 C
1644 1342 1650 1345 1656 1345 C
1662 1345 1668 1342 1673 1338 C
1677 1333 1680 1327 1680 1321 C
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1692 1345 m
1692 1339 1689 1333 1685 1328 C
1680 1324 1674 1321 1668 1321 C
1662 1321 1656 1324 1651 1328 C
1647 1333 1644 1339 1644 1345 C
1644 1351 1647 1357 1651 1362 C
1656 1366 1662 1369 1668 1369 C
1674 1369 1680 1366 1685 1362 C
1689 1357 1692 1351 1692 1345 C
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1704 1304 m
1704 1298 1701 1292 1697 1287 C
1692 1283 1686 1280 1680 1280 C
1674 1280 1668 1283 1663 1287 C
1659 1292 1656 1298 1656 1304 C
1656 1310 1659 1316 1663 1321 C
1668 1325 1674 1328 1680 1328 C
1686 1328 1692 1325 1697 1321 C
1701 1316 1704 1310 1704 1304 C
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1715 1223 m
1715 1217 1712 1211 1708 1206 C
1703 1202 1697 1199 1691 1199 C
1685 1199 1679 1202 1674 1206 C
1670 1211 1667 1217 1667 1223 C
1667 1229 1670 1235 1674 1240 C
1679 1244 1685 1247 1691 1247 C
1697 1247 1703 1244 1708 1240 C
1712 1235 1715 1229 1715 1223 C
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1727 1205 m
1727 1199 1724 1193 1720 1188 C
1715 1184 1709 1181 1703 1181 C
1697 1181 1691 1184 1686 1188 C
1682 1193 1679 1199 1679 1205 C
1679 1211 1682 1217 1686 1222 C
1691 1226 1697 1229 1703 1229 C
1709 1229 1715 1226 1720 1222 C
1724 1217 1727 1211 1727 1205 C
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1738 1280 m
1738 1274 1735 1268 1731 1263 C
1726 1259 1720 1256 1714 1256 C
1708 1256 1702 1259 1697 1263 C
1693 1268 1690 1274 1690 1280 C
1690 1286 1693 1292 1697 1297 C
1702 1301 1708 1304 1714 1304 C
1720 1304 1726 1301 1731 1297 C
1735 1292 1738 1286 1738 1280 C
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1750 1342 m
1750 1336 1747 1330 1743 1325 C
1738 1321 1732 1318 1726 1318 C
1720 1318 1714 1321 1709 1325 C
1705 1330 1702 1336 1702 1342 C
1702 1348 1705 1354 1709 1359 C
1714 1363 1720 1366 1726 1366 C
1732 1366 1738 1363 1743 1359 C
1747 1354 1750 1348 1750 1342 C
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1761 1323 m
1761 1317 1758 1311 1754 1306 C
1749 1302 1743 1299 1737 1299 C
1731 1299 1725 1302 1720 1306 C
1716 1311 1713 1317 1713 1323 C
1713 1329 1716 1335 1720 1340 C
1725 1344 1731 1347 1737 1347 C
1743 1347 1749 1344 1754 1340 C
1758 1335 1761 1329 1761 1323 C
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1773 1238 m
1773 1232 1770 1226 1766 1221 C
1761 1217 1755 1214 1749 1214 C
1743 1214 1737 1217 1732 1221 C
1728 1226 1725 1232 1725 1238 C
1725 1244 1728 1250 1732 1255 C
1737 1259 1743 1262 1749 1262 C
1755 1262 1761 1259 1766 1255 C
1770 1250 1773 1244 1773 1238 C
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1784 1202 m
1784 1196 1781 1190 1777 1185 C
1772 1181 1766 1178 1760 1178 C
1754 1178 1748 1181 1743 1185 C
1739 1190 1736 1196 1736 1202 C
1736 1208 1739 1214 1743 1219 C
1748 1223 1754 1226 1760 1226 C
1766 1226 1772 1223 1777 1219 C
1781 1214 1784 1208 1784 1202 C
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1796 1278 m
1796 1272 1793 1266 1789 1261 C
1784 1257 1778 1254 1772 1254 C
1766 1254 1760 1257 1755 1261 C
1751 1266 1748 1272 1748 1278 C
1748 1284 1751 1290 1755 1295 C
1760 1299 1766 1302 1772 1302 C
1778 1302 1784 1299 1789 1295 C
1793 1290 1796 1284 1796 1278 C
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1807 1343 m
1807 1337 1804 1331 1800 1326 C
1795 1322 1789 1319 1783 1319 C
1777 1319 1771 1322 1766 1326 C
1762 1331 1759 1337 1759 1343 C
1759 1349 1762 1355 1766 1360 C
1771 1364 1777 1367 1783 1367 C
1789 1367 1795 1364 1800 1360 C
1804 1355 1807 1349 1807 1343 C
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1819 1311 m
1819 1305 1816 1299 1812 1294 C
1807 1290 1801 1287 1795 1287 C
1789 1287 1783 1290 1778 1294 C
1774 1299 1771 1305 1771 1311 C
1771 1317 1774 1323 1778 1328 C
1783 1332 1789 1335 1795 1335 C
1801 1335 1807 1332 1812 1328 C
1816 1323 1819 1317 1819 1311 C
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1831 1218 m
1831 1212 1828 1206 1824 1201 C
1819 1197 1813 1194 1807 1194 C
1801 1194 1795 1197 1790 1201 C
1786 1206 1783 1212 1783 1218 C
1783 1224 1786 1230 1790 1235 C
1795 1239 1801 1242 1807 1242 C
1813 1242 1819 1239 1824 1235 C
1828 1230 1831 1224 1831 1218 C
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1842 1218 m
1842 1212 1839 1206 1835 1201 C
1830 1197 1824 1194 1818 1194 C
1812 1194 1806 1197 1801 1201 C
1797 1206 1794 1212 1794 1218 C
1794 1224 1797 1230 1801 1235 C
1806 1239 1812 1242 1818 1242 C
1824 1242 1830 1239 1835 1235 C
1839 1230 1842 1224 1842 1218 C
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1854 1313 m
1854 1307 1851 1301 1847 1296 C
1842 1292 1836 1289 1830 1289 C
1824 1289 1818 1292 1813 1296 C
1809 1301 1806 1307 1806 1313 C
1806 1319 1809 1325 1813 1330 C
1818 1334 1824 1337 1830 1337 C
1836 1337 1842 1334 1847 1330 C
1851 1325 1854 1319 1854 1313 C
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1865 1340 m
1865 1334 1862 1328 1858 1323 C
1853 1319 1847 1316 1841 1316 C
1835 1316 1829 1319 1824 1323 C
1820 1328 1817 1334 1817 1340 C
1817 1346 1820 1352 1824 1357 C
1829 1361 1835 1364 1841 1364 C
1847 1364 1853 1361 1858 1357 C
1862 1352 1865 1346 1865 1340 C
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1877 1258 m
1877 1252 1874 1246 1870 1241 C
1865 1237 1859 1234 1853 1234 C
1847 1234 1841 1237 1836 1241 C
1832 1246 1829 1252 1829 1258 C
1829 1264 1832 1270 1836 1275 C
1841 1279 1847 1282 1853 1282 C
1859 1282 1865 1279 1870 1275 C
1874 1270 1877 1264 1877 1258 C
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1888 1200 m
1888 1194 1885 1188 1881 1183 C
1876 1179 1870 1176 1864 1176 C
1858 1176 1852 1179 1847 1183 C
1843 1188 1840 1194 1840 1200 C
1840 1206 1843 1212 1847 1217 C
1852 1221 1858 1224 1864 1224 C
1870 1224 1876 1221 1881 1217 C
1885 1212 1888 1206 1888 1200 C
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1900 1283 m
1900 1277 1897 1271 1893 1266 C
1888 1262 1882 1259 1876 1259 C
1870 1259 1864 1262 1859 1266 C
1855 1271 1852 1277 1852 1283 C
1852 1289 1855 1295 1859 1300 C
1864 1304 1870 1307 1876 1307 C
1882 1307 1888 1304 1893 1300 C
1897 1295 1900 1289 1900 1283 C
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1911 1345 m
1911 1339 1908 1333 1904 1328 C
1899 1324 1893 1321 1887 1321 C
1881 1321 1875 1324 1870 1328 C
1866 1333 1863 1339 1863 1345 C
1863 1351 1866 1357 1870 1362 C
1875 1366 1881 1369 1887 1369 C
1893 1369 1899 1366 1904 1362 C
1908 1357 1911 1351 1911 1345 C
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1923 1278 m
1923 1272 1920 1266 1916 1261 C
1911 1257 1905 1254 1899 1254 C
1893 1254 1887 1257 1882 1261 C
1878 1266 1875 1272 1875 1278 C
1875 1284 1878 1290 1882 1295 C
1887 1299 1893 1302 1899 1302 C
1905 1302 1911 1299 1916 1295 C
1920 1290 1923 1284 1923 1278 C
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1934 1199 m
1934 1193 1931 1187 1927 1182 C
1922 1178 1916 1175 1910 1175 C
1904 1175 1898 1178 1893 1182 C
1889 1187 1886 1193 1886 1199 C
1886 1205 1889 1211 1893 1216 C
1898 1220 1904 1223 1910 1223 C
1916 1223 1922 1220 1927 1216 C
1931 1211 1934 1205 1934 1199 C
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1946 1272 m
1946 1266 1943 1260 1939 1255 C
1934 1251 1928 1248 1922 1248 C
1916 1248 1910 1251 1905 1255 C
1901 1260 1898 1266 1898 1272 C
1898 1278 1901 1284 1905 1289 C
1910 1293 1916 1296 1922 1296 C
1928 1296 1934 1293 1939 1289 C
1943 1284 1946 1278 1946 1272 C
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1958 1345 m
1958 1339 1955 1333 1951 1328 C
1946 1324 1940 1321 1934 1321 C
1928 1321 1922 1324 1917 1328 C
1913 1333 1910 1339 1910 1345 C
1910 1351 1913 1357 1917 1362 C
1922 1366 1928 1369 1934 1369 C
1940 1369 1946 1366 1951 1362 C
1955 1357 1958 1351 1958 1345 C
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1969 1277 m
1969 1271 1966 1265 1962 1260 C
1957 1256 1951 1253 1945 1253 C
1939 1253 1933 1256 1928 1260 C
1924 1265 1921 1271 1921 1277 C
1921 1283 1924 1289 1928 1294 C
1933 1298 1939 1301 1945 1301 C
1951 1301 1957 1298 1962 1294 C
1966 1289 1969 1283 1969 1277 C
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1981 1200 m
1981 1194 1978 1188 1974 1183 C
1969 1179 1963 1176 1957 1176 C
1951 1176 1945 1179 1940 1183 C
1936 1188 1933 1194 1933 1200 C
1933 1206 1936 1212 1940 1217 C
1945 1221 1951 1224 1957 1224 C
1963 1224 1969 1221 1974 1217 C
1978 1212 1981 1206 1981 1200 C
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1992 1284 m
1992 1278 1989 1272 1985 1267 C
1980 1263 1974 1260 1968 1260 C
1962 1260 1956 1263 1951 1267 C
1947 1272 1944 1278 1944 1284 C
1944 1290 1947 1296 1951 1301 C
1956 1305 1962 1308 1968 1308 C
1974 1308 1980 1305 1985 1301 C
1989 1296 1992 1290 1992 1284 C
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2004 1343 m
2004 1337 2001 1331 1997 1326 C
1992 1322 1986 1319 1980 1319 C
1974 1319 1968 1322 1963 1326 C
1959 1331 1956 1337 1956 1343 C
1956 1349 1959 1355 1963 1360 C
1968 1364 1974 1367 1980 1367 C
1986 1367 1992 1364 1997 1360 C
2001 1355 2004 1349 2004 1343 C
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2015 1254 m
2015 1248 2012 1242 2008 1237 C
2003 1233 1997 1230 1991 1230 C
1985 1230 1979 1233 1974 1237 C
1970 1242 1967 1248 1967 1254 C
1967 1260 1970 1266 1974 1271 C
1979 1275 1985 1278 1991 1278 C
1997 1278 2003 1275 2008 1271 C
2012 1266 2015 1260 2015 1254 C
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2027 1207 m
2027 1201 2024 1195 2020 1190 C
2015 1186 2009 1183 2003 1183 C
1997 1183 1991 1186 1986 1190 C
1982 1195 1979 1201 1979 1207 C
1979 1213 1982 1219 1986 1224 C
1991 1228 1997 1231 2003 1231 C
2009 1231 2015 1228 2020 1224 C
2024 1219 2027 1213 2027 1207 C
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2038 1313 m
2038 1307 2035 1301 2031 1296 C
2026 1292 2020 1289 2014 1289 C
2008 1289 2002 1292 1997 1296 C
1993 1301 1990 1307 1990 1313 C
1990 1319 1993 1325 1997 1330 C
2002 1334 2008 1337 2014 1337 C
2020 1337 2026 1334 2031 1330 C
2035 1325 2038 1319 2038 1313 C
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2050 1328 m
2050 1322 2047 1316 2043 1311 C
2038 1307 2032 1304 2026 1304 C
2020 1304 2014 1307 2009 1311 C
2005 1316 2002 1322 2002 1328 C
2002 1334 2005 1340 2009 1345 C
2014 1349 2020 1352 2026 1352 C
2032 1352 2038 1349 2043 1345 C
2047 1340 2050 1334 2050 1328 C
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2062 1217 m
2062 1211 2059 1205 2055 1200 C
2050 1196 2044 1193 2038 1193 C
2032 1193 2026 1196 2021 1200 C
2017 1205 2014 1211 2014 1217 C
2014 1223 2017 1229 2021 1234 C
2026 1238 2032 1241 2038 1241 C
2044 1241 2050 1238 2055 1234 C
2059 1229 2062 1223 2062 1217 C
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F
2073 1242 m
2073 1236 2070 1230 2066 1225 C
2061 1221 2055 1218 2049 1218 C
2043 1218 2037 1221 2032 1225 C
2028 1230 2025 1236 2025 1242 C
2025 1248 2028 1254 2032 1259 C
2037 1263 2043 1266 2049 1266 C
2055 1266 2061 1263 2066 1259 C
2070 1254 2073 1248 2073 1242 C
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F
2085 1342 m
2085 1336 2082 1330 2078 1325 C
2073 1321 2067 1318 2061 1318 C
2055 1318 2049 1321 2044 1325 C
2040 1330 2037 1336 2037 1342 C
2037 1348 2040 1354 2044 1359 C
2049 1363 2055 1366 2061 1366 C
2067 1366 2073 1363 2078 1359 C
2082 1354 2085 1348 2085 1342 C
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F
2096 1278 m
2096 1272 2093 1266 2089 1261 C
2084 1257 2078 1254 2072 1254 C
2066 1254 2060 1257 2055 1261 C
2051 1266 2048 1272 2048 1278 C
2048 1284 2051 1290 2055 1295 C
2060 1299 2066 1302 2072 1302 C
2078 1302 2084 1299 2089 1295 C
2093 1290 2096 1284 2096 1278 C
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F
2108 1202 m
2108 1196 2105 1190 2101 1185 C
2096 1181 2090 1178 2084 1178 C
2078 1178 2072 1181 2067 1185 C
2063 1190 2060 1196 2060 1202 C
2060 1208 2063 1214 2067 1219 C
2072 1223 2078 1226 2084 1226 C
2090 1226 2096 1223 2101 1219 C
2105 1214 2108 1208 2108 1202 C
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F
2119 1307 m
2119 1301 2116 1295 2112 1290 C
2107 1286 2101 1283 2095 1283 C
2089 1283 2083 1286 2078 1290 C
2074 1295 2071 1301 2071 1307 C
2071 1313 2074 1319 2078 1324 C
2083 1328 2089 1331 2095 1331 C
2101 1331 2107 1328 2112 1324 C
2116 1319 2119 1313 2119 1307 C
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F
2131 1326 m
2131 1320 2128 1314 2124 1309 C
2119 1305 2113 1302 2107 1302 C
2101 1302 2095 1305 2090 1309 C
2086 1314 2083 1320 2083 1326 C
2083 1332 2086 1338 2090 1343 C
2095 1347 2101 1350 2107 1350 C
2113 1350 2119 1347 2124 1343 C
2128 1338 2131 1332 2131 1326 C
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F
2142 1211 m
2142 1205 2139 1199 2135 1194 C
2130 1190 2124 1187 2118 1187 C
2112 1187 2106 1190 2101 1194 C
2097 1199 2094 1205 2094 1211 C
2094 1217 2097 1223 2101 1228 C
2106 1232 2112 1235 2118 1235 C
2124 1235 2130 1232 2135 1228 C
2139 1223 2142 1217 2142 1211 C
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F
2154 1259 m
2154 1253 2151 1247 2147 1242 C
2142 1238 2136 1235 2130 1235 C
2124 1235 2118 1238 2113 1242 C
2109 1247 2106 1253 2106 1259 C
2106 1265 2109 1271 2113 1276 C
2118 1280 2124 1283 2130 1283 C
2136 1283 2142 1280 2147 1276 C
2151 1271 2154 1265 2154 1259 C
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F
2165 1343 m
2165 1337 2162 1331 2158 1326 C
2153 1322 2147 1319 2141 1319 C
2135 1319 2129 1322 2124 1326 C
2120 1331 2117 1337 2117 1343 C
2117 1349 2120 1355 2124 1360 C
2129 1364 2135 1367 2141 1367 C
2147 1367 2153 1364 2158 1360 C
2162 1355 2165 1349 2165 1343 C
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F
2177 1243 m
2177 1237 2174 1231 2170 1226 C
2165 1222 2159 1219 2153 1219 C
2147 1219 2141 1222 2136 1226 C
2132 1231 2129 1237 2129 1243 C
2129 1249 2132 1255 2136 1260 C
2141 1264 2147 1267 2153 1267 C
2159 1267 2165 1264 2170 1260 C
2174 1255 2177 1249 2177 1243 C
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F
2189 1224 m
2189 1218 2186 1212 2182 1207 C
2177 1203 2171 1200 2165 1200 C
2159 1200 2153 1203 2148 1207 C
2144 1212 2141 1218 2141 1224 C
2141 1230 2144 1236 2148 1241 C
2153 1245 2159 1248 2165 1248 C
2171 1248 2177 1245 2182 1241 C
2186 1236 2189 1230 2189 1224 C
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F
2200 1339 m
2200 1333 2197 1327 2193 1322 C
2188 1318 2182 1315 2176 1315 C
2170 1315 2164 1318 2159 1322 C
2155 1327 2152 1333 2152 1339 C
2152 1345 2155 1351 2159 1356 C
2164 1360 2170 1363 2176 1363 C
2182 1363 2188 1360 2193 1356 C
2197 1351 2200 1345 2200 1339 C
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F
2212 1274 m
2212 1268 2209 1262 2205 1257 C
2200 1253 2194 1250 2188 1250 C
2182 1250 2176 1253 2171 1257 C
2167 1262 2164 1268 2164 1274 C
2164 1280 2167 1286 2171 1291 C
2176 1295 2182 1298 2188 1298 C
2194 1298 2200 1295 2205 1291 C
2209 1286 2212 1280 2212 1274 C
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F
2223 1207 m
2223 1201 2220 1195 2216 1190 C
2211 1186 2205 1183 2199 1183 C
2193 1183 2187 1186 2182 1190 C
2178 1195 2175 1201 2175 1207 C
2175 1213 2178 1219 2182 1224 C
2187 1228 2193 1231 2199 1231 C
2205 1231 2211 1228 2216 1224 C
2220 1219 2223 1213 2223 1207 C
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F
2235 1326 m
2235 1320 2232 1314 2228 1309 C
2223 1305 2217 1302 2211 1302 C
2205 1302 2199 1305 2194 1309 C
2190 1314 2187 1320 2187 1326 C
2187 1332 2190 1338 2194 1343 C
2199 1347 2205 1350 2211 1350 C
2217 1350 2223 1347 2228 1343 C
2232 1338 2235 1332 2235 1326 C
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F
2246 1294 m
2246 1288 2243 1282 2239 1277 C
2234 1273 2228 1270 2222 1270 C
2216 1270 2210 1273 2205 1277 C
2201 1282 2198 1288 2198 1294 C
2198 1300 2201 1306 2205 1311 C
2210 1315 2216 1318 2222 1318 C
2228 1318 2234 1315 2239 1311 C
2243 1306 2246 1300 2246 1294 C
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F
2258 1202 m
2258 1196 2255 1190 2251 1185 C
2246 1181 2240 1178 2234 1178 C
2228 1178 2222 1181 2217 1185 C
2213 1190 2210 1196 2210 1202 C
2210 1208 2213 1214 2217 1219 C
2222 1223 2228 1226 2234 1226 C
2240 1226 2246 1223 2251 1219 C
2255 1214 2258 1208 2258 1202 C
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F
2269 1316 m
2269 1310 2266 1304 2262 1299 C
2257 1295 2251 1292 2245 1292 C
2239 1292 2233 1295 2228 1299 C
2224 1304 2221 1310 2221 1316 C
2221 1322 2224 1328 2228 1333 C
2233 1337 2239 1340 2245 1340 C
2251 1340 2257 1337 2262 1333 C
2266 1328 2269 1322 2269 1316 C
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F
2281 1304 m
2281 1298 2278 1292 2274 1287 C
2269 1283 2263 1280 2257 1280 C
2251 1280 2245 1283 2240 1287 C
2236 1292 2233 1298 2233 1304 C
2233 1310 2236 1316 2240 1321 C
2245 1325 2251 1328 2257 1328 C
2263 1328 2269 1325 2274 1321 C
2278 1316 2281 1310 2281 1304 C
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F
2293 1201 m
2293 1195 2290 1189 2286 1184 C
2281 1180 2275 1177 2269 1177 C
2263 1177 2257 1180 2252 1184 C
2248 1189 2245 1195 2245 1201 C
2245 1207 2248 1213 2252 1218 C
2257 1222 2263 1225 2269 1225 C
2275 1225 2281 1222 2286 1218 C
2290 1213 2293 1207 2293 1201 C
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F
2304 1313 m
2304 1307 2301 1301 2297 1296 C
2292 1292 2286 1289 2280 1289 C
2274 1289 2268 1292 2263 1296 C
2259 1301 2256 1307 2256 1313 C
2256 1319 2259 1325 2263 1330 C
2268 1334 2274 1337 2280 1337 C
2286 1337 2292 1334 2297 1330 C
2301 1325 2304 1319 2304 1313 C
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F
2316 1305 m
2316 1299 2313 1293 2309 1288 C
2304 1284 2298 1281 2292 1281 C
2286 1281 2280 1284 2275 1288 C
2271 1293 2268 1299 2268 1305 C
2268 1311 2271 1317 2275 1322 C
2280 1326 2286 1329 2292 1329 C
2298 1329 2304 1326 2309 1322 C
2313 1317 2316 1311 2316 1305 C
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F
2327 1202 m
2327 1196 2324 1190 2320 1185 C
2315 1181 2309 1178 2303 1178 C
2297 1178 2291 1181 2286 1185 C
2282 1190 2279 1196 2279 1202 C
2279 1208 2282 1214 2286 1219 C
2291 1223 2297 1226 2303 1226 C
2309 1226 2315 1223 2320 1219 C
2324 1214 2327 1208 2327 1202 C
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F
2339 1317 m
2339 1311 2336 1305 2332 1300 C
2327 1296 2321 1293 2315 1293 C
2309 1293 2303 1296 2298 1300 C
2294 1305 2291 1311 2291 1317 C
2291 1323 2294 1329 2298 1334 C
2303 1338 2309 1341 2315 1341 C
2321 1341 2327 1338 2332 1334 C
2336 1329 2339 1323 2339 1317 C
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F
2350 1297 m
2350 1291 2347 1285 2343 1280 C
2338 1276 2332 1273 2326 1273 C
2320 1273 2314 1276 2309 1280 C
2305 1285 2302 1291 2302 1297 C
2302 1303 2305 1309 2309 1314 C
2314 1318 2320 1321 2326 1321 C
2332 1321 2338 1318 2343 1314 C
2347 1309 2350 1303 2350 1297 C
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F
2362 1204 m
2362 1198 2359 1192 2355 1187 C
2350 1183 2344 1180 2338 1180 C
2332 1180 2326 1183 2321 1187 C
2317 1192 2314 1198 2314 1204 C
2314 1210 2317 1216 2321 1221 C
2326 1225 2332 1228 2338 1228 C
2344 1228 2350 1225 2355 1221 C
2359 1216 2362 1210 2362 1204 C
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F
2373 1327 m
2373 1321 2370 1315 2366 1310 C
2361 1306 2355 1303 2349 1303 C
2343 1303 2337 1306 2332 1310 C
2328 1315 2325 1321 2325 1327 C
2325 1333 2328 1339 2332 1344 C
2337 1348 2343 1351 2349 1351 C
2355 1351 2361 1348 2366 1344 C
2370 1339 2373 1333 2373 1327 C
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F
2385 1279 m
2385 1273 2382 1267 2378 1262 C
2373 1258 2367 1255 2361 1255 C
2355 1255 2349 1258 2344 1262 C
2340 1267 2337 1273 2337 1279 C
2337 1285 2340 1291 2344 1296 C
2349 1300 2355 1303 2361 1303 C
2367 1303 2373 1300 2378 1296 C
2382 1291 2385 1285 2385 1279 C
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F
2396 1213 m
2396 1207 2393 1201 2389 1196 C
2384 1192 2378 1189 2372 1189 C
2366 1189 2360 1192 2355 1196 C
2351 1201 2348 1207 2348 1213 C
2348 1219 2351 1225 2355 1230 C
2360 1234 2366 1237 2372 1237 C
2378 1237 2384 1234 2389 1230 C
2393 1225 2396 1219 2396 1213 C
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F
2408 1338 m
2408 1332 2405 1326 2401 1321 C
2396 1317 2390 1314 2384 1314 C
2378 1314 2372 1317 2367 1321 C
2363 1326 2360 1332 2360 1338 C
2360 1344 2363 1350 2367 1355 C
2372 1359 2378 1362 2384 1362 C
2390 1362 2396 1359 2401 1355 C
2405 1350 2408 1344 2408 1338 C
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F
2420 1252 m
2420 1246 2417 1240 2413 1235 C
2408 1231 2402 1228 2396 1228 C
2390 1228 2384 1231 2379 1235 C
2375 1240 2372 1246 2372 1252 C
2372 1258 2375 1264 2379 1269 C
2384 1273 2390 1276 2396 1276 C
2402 1276 2408 1273 2413 1269 C
2417 1264 2420 1258 2420 1252 C
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F
2431 1236 m
2431 1230 2428 1224 2424 1219 C
2419 1215 2413 1212 2407 1212 C
2401 1212 2395 1215 2390 1219 C
2386 1224 2383 1230 2383 1236 C
2383 1242 2386 1248 2390 1253 C
2395 1257 2401 1260 2407 1260 C
2413 1260 2419 1257 2424 1253 C
2428 1248 2431 1242 2431 1236 C
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F
2443 1342 m
2443 1336 2440 1330 2436 1325 C
2431 1321 2425 1318 2419 1318 C
2413 1318 2407 1321 2402 1325 C
2398 1330 2395 1336 2395 1342 C
2395 1348 2398 1354 2402 1359 C
2407 1363 2413 1366 2419 1366 C
2425 1366 2431 1363 2436 1359 C
2440 1354 2443 1348 2443 1342 C
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F
2454 1220 m
2454 1214 2451 1208 2447 1203 C
2442 1199 2436 1196 2430 1196 C
2424 1196 2418 1199 2413 1203 C
2409 1208 2406 1214 2406 1220 C
2406 1226 2409 1232 2413 1237 C
2418 1241 2424 1244 2430 1244 C
2436 1244 2442 1241 2447 1237 C
2451 1232 2454 1226 2454 1220 C
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F
2466 1274 m
2466 1268 2463 1262 2459 1257 C
2454 1253 2448 1250 2442 1250 C
2436 1250 2430 1253 2425 1257 C
2421 1262 2418 1268 2418 1274 C
2418 1280 2421 1286 2425 1291 C
2430 1295 2436 1298 2442 1298 C
2448 1298 2454 1295 2459 1291 C
2463 1286 2466 1280 2466 1274 C
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F
2477 1324 m
2477 1318 2474 1312 2470 1307 C
2465 1303 2459 1300 2453 1300 C
2447 1300 2441 1303 2436 1307 C
2432 1312 2429 1318 2429 1324 C
2429 1330 2432 1336 2436 1341 C
2441 1345 2447 1348 2453 1348 C
2459 1348 2465 1345 2470 1341 C
2474 1336 2477 1330 2477 1324 C
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F
2489 1202 m
2489 1196 2486 1190 2482 1185 C
2477 1181 2471 1178 2465 1178 C
2459 1178 2453 1181 2448 1185 C
2444 1190 2441 1196 2441 1202 C
2441 1208 2444 1214 2448 1219 C
2453 1223 2459 1226 2465 1226 C
2471 1226 2477 1223 2482 1219 C
2486 1214 2489 1208 2489 1202 C
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F
2500 1319 m
2500 1313 2497 1307 2493 1302 C
2488 1298 2482 1295 2476 1295 C
2470 1295 2464 1298 2459 1302 C
2455 1307 2452 1313 2452 1319 C
2452 1325 2455 1331 2459 1336 C
2464 1340 2470 1343 2476 1343 C
2482 1343 2488 1340 2493 1336 C
2497 1331 2500 1325 2500 1319 C
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F
2512 1279 m
2512 1273 2509 1267 2505 1262 C
2500 1258 2494 1255 2488 1255 C
2482 1255 2476 1258 2471 1262 C
2467 1267 2464 1273 2464 1279 C
2464 1285 2467 1291 2471 1296 C
2476 1300 2482 1303 2488 1303 C
2494 1303 2500 1300 2505 1296 C
2509 1291 2512 1285 2512 1279 C
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F
2523 1220 m
2523 1214 2520 1208 2516 1203 C
2511 1199 2505 1196 2499 1196 C
2493 1196 2487 1199 2482 1203 C
2478 1208 2475 1214 2475 1220 C
2475 1226 2478 1232 2482 1237 C
2487 1241 2493 1244 2499 1244 C
2505 1244 2511 1241 2516 1237 C
2520 1232 2523 1226 2523 1220 C
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F
2535 1342 m
2535 1336 2532 1330 2528 1325 C
2523 1321 2517 1318 2511 1318 C
2505 1318 2499 1321 2494 1325 C
2490 1330 2487 1336 2487 1342 C
2487 1348 2490 1354 2494 1359 C
2499 1363 2505 1366 2511 1366 C
2517 1366 2523 1363 2528 1359 C
2532 1354 2535 1348 2535 1342 C
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F
2547 1223 m
2547 1217 2544 1211 2540 1206 C
2535 1202 2529 1199 2523 1199 C
2517 1199 2511 1202 2506 1206 C
2502 1211 2499 1217 2499 1223 C
2499 1229 2502 1235 2506 1240 C
2511 1244 2517 1247 2523 1247 C
2529 1247 2535 1244 2540 1240 C
2544 1235 2547 1229 2547 1223 C
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F
2558 1279 m
2558 1273 2555 1267 2551 1262 C
2546 1258 2540 1255 2534 1255 C
2528 1255 2522 1258 2517 1262 C
2513 1267 2510 1273 2510 1279 C
2510 1285 2513 1291 2517 1296 C
2522 1300 2528 1303 2534 1303 C
2540 1303 2546 1300 2551 1296 C
2555 1291 2558 1285 2558 1279 C
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F
2570 1315 m
2570 1309 2567 1303 2563 1298 C
2558 1294 2552 1291 2546 1291 C
2540 1291 2534 1294 2529 1298 C
2525 1303 2522 1309 2522 1315 C
2522 1321 2525 1327 2529 1332 C
2534 1336 2540 1339 2546 1339 C
2552 1339 2558 1336 2563 1332 C
2567 1327 2570 1321 2570 1315 C
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F
2581 1204 m
2581 1198 2578 1192 2574 1187 C
2569 1183 2563 1180 2557 1180 C
2551 1180 2545 1183 2540 1187 C
2536 1192 2533 1198 2533 1204 C
2533 1210 2536 1216 2540 1221 C
2545 1225 2551 1228 2557 1228 C
2563 1228 2569 1225 2574 1221 C
2578 1216 2581 1210 2581 1204 C
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F
2593 1335 m
2593 1329 2590 1323 2586 1318 C
2581 1314 2575 1311 2569 1311 C
2563 1311 2557 1314 2552 1318 C
2548 1323 2545 1329 2545 1335 C
2545 1341 2548 1347 2552 1352 C
2557 1356 2563 1359 2569 1359 C
2575 1359 2581 1356 2586 1352 C
2590 1347 2593 1341 2593 1335 C
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F
2604 1243 m
2604 1237 2601 1231 2597 1226 C
2592 1222 2586 1219 2580 1219 C
2574 1219 2568 1222 2563 1226 C
2559 1231 2556 1237 2556 1243 C
2556 1249 2559 1255 2563 1260 C
2568 1264 2574 1267 2580 1267 C
2586 1267 2592 1264 2597 1260 C
2601 1255 2604 1249 2604 1243 C
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F
2616 1259 m
2616 1253 2613 1247 2609 1242 C
2604 1238 2598 1235 2592 1235 C
2586 1235 2580 1238 2575 1242 C
2571 1247 2568 1253 2568 1259 C
2568 1265 2571 1271 2575 1276 C
2580 1280 2586 1283 2592 1283 C
2598 1283 2604 1280 2609 1276 C
2613 1271 2616 1265 2616 1259 C
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F
2627 1325 m
2627 1319 2624 1313 2620 1308 C
2615 1304 2609 1301 2603 1301 C
2597 1301 2591 1304 2586 1308 C
2582 1313 2579 1319 2579 1325 C
2579 1331 2582 1337 2586 1342 C
2591 1346 2597 1349 2603 1349 C
2609 1349 2615 1346 2620 1342 C
2624 1337 2627 1331 2627 1325 C
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F
2639 1203 m
2639 1197 2636 1191 2632 1186 C
2627 1182 2621 1179 2615 1179 C
2609 1179 2603 1182 2598 1186 C
2594 1191 2591 1197 2591 1203 C
2591 1209 2594 1215 2598 1220 C
2603 1224 2609 1227 2615 1227 C
2621 1227 2627 1224 2632 1220 C
2636 1215 2639 1209 2639 1203 C
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F
2651 1333 m
2651 1327 2648 1321 2644 1316 C
2639 1312 2633 1309 2627 1309 C
2621 1309 2615 1312 2610 1316 C
2606 1321 2603 1327 2603 1333 C
2603 1339 2606 1345 2610 1350 C
2615 1354 2621 1357 2627 1357 C
2633 1357 2639 1354 2644 1350 C
2648 1345 2651 1339 2651 1333 C
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F
2662 1243 m
2662 1237 2659 1231 2655 1226 C
2650 1222 2644 1219 2638 1219 C
2632 1219 2626 1222 2621 1226 C
2617 1231 2614 1237 2614 1243 C
2614 1249 2617 1255 2621 1260 C
2626 1264 2632 1267 2638 1267 C
2644 1267 2650 1264 2655 1260 C
2659 1255 2662 1249 2662 1243 C
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F
2674 1264 m
2674 1258 2671 1252 2667 1247 C
2662 1243 2656 1240 2650 1240 C
2644 1240 2638 1243 2633 1247 C
2629 1252 2626 1258 2626 1264 C
2626 1270 2629 1276 2633 1281 C
2638 1285 2644 1288 2650 1288 C
2656 1288 2662 1285 2667 1281 C
2671 1276 2674 1270 2674 1264 C
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F
2685 1318 m
2685 1312 2682 1306 2678 1301 C
2673 1297 2667 1294 2661 1294 C
2655 1294 2649 1297 2644 1301 C
2640 1306 2637 1312 2637 1318 C
2637 1324 2640 1330 2644 1335 C
2649 1339 2655 1342 2661 1342 C
2667 1342 2673 1339 2678 1335 C
2682 1330 2685 1324 2685 1318 C
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F
2697 1206 m
2697 1200 2694 1194 2690 1189 C
2685 1185 2679 1182 2673 1182 C
2667 1182 2661 1185 2656 1189 C
2652 1194 2649 1200 2649 1206 C
2649 1212 2652 1218 2656 1223 C
2661 1227 2667 1230 2673 1230 C
2679 1230 2685 1227 2690 1223 C
2694 1218 2697 1212 2697 1206 C
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F
2708 1340 m
2708 1334 2705 1328 2701 1323 C
2696 1319 2690 1316 2684 1316 C
2678 1316 2672 1319 2667 1323 C
2663 1328 2660 1334 2660 1340 C
2660 1346 2663 1352 2667 1357 C
2672 1361 2678 1364 2684 1364 C
2690 1364 2696 1361 2701 1357 C
2705 1352 2708 1346 2708 1340 C
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F
2720 1223 m
2720 1217 2717 1211 2713 1206 C
2708 1202 2702 1199 2696 1199 C
2690 1199 2684 1202 2679 1206 C
2675 1211 2672 1217 2672 1223 C
2672 1229 2675 1235 2679 1240 C
2684 1244 2690 1247 2696 1247 C
2702 1247 2708 1244 2713 1240 C
2717 1235 2720 1229 2720 1223 C
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F
2731 1293 m
2731 1287 2728 1281 2724 1276 C
2719 1272 2713 1269 2707 1269 C
2701 1269 2695 1272 2690 1276 C
2686 1281 2683 1287 2683 1293 C
2683 1299 2686 1305 2690 1310 C
2695 1314 2701 1317 2707 1317 C
2713 1317 2719 1314 2724 1310 C
2728 1305 2731 1299 2731 1293 C
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F
2743 1288 m
2743 1282 2740 1276 2736 1271 C
2731 1267 2725 1264 2719 1264 C
2713 1264 2707 1267 2702 1271 C
2698 1276 2695 1282 2695 1288 C
2695 1294 2698 1300 2702 1305 C
2707 1309 2713 1312 2719 1312 C
2725 1312 2731 1309 2736 1305 C
2740 1300 2743 1294 2743 1288 C
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F
2754 1228 m
2754 1222 2751 1216 2747 1211 C
2742 1207 2736 1204 2730 1204 C
2724 1204 2718 1207 2713 1211 C
2709 1216 2706 1222 2706 1228 C
2706 1234 2709 1240 2713 1245 C
2718 1249 2724 1252 2730 1252 C
2736 1252 2742 1249 2747 1245 C
2751 1240 2754 1234 2754 1228 C
closepath
F
2766 1336 m
2766 1330 2763 1324 2759 1319 C
2754 1315 2748 1312 2742 1312 C
2736 1312 2730 1315 2725 1319 C
2721 1324 2718 1330 2718 1336 C
2718 1342 2721 1348 2725 1353 C
2730 1357 2736 1360 2742 1360 C
2748 1360 2754 1357 2759 1353 C
2763 1348 2766 1342 2766 1336 C
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F
2778 1203 m
2778 1197 2775 1191 2771 1186 C
2766 1182 2760 1179 2754 1179 C
2748 1179 2742 1182 2737 1186 C
2733 1191 2730 1197 2730 1203 C
2730 1209 2733 1215 2737 1220 C
2742 1224 2748 1227 2754 1227 C
2760 1227 2766 1224 2771 1220 C
2775 1215 2778 1209 2778 1203 C
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F
2789 1332 m
2789 1326 2786 1320 2782 1315 C
2777 1311 2771 1308 2765 1308 C
2759 1308 2753 1311 2748 1315 C
2744 1320 2741 1326 2741 1332 C
2741 1338 2744 1344 2748 1349 C
2753 1353 2759 1356 2765 1356 C
2771 1356 2777 1353 2782 1349 C
2786 1344 2789 1338 2789 1332 C
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F
2801 1233 m
2801 1227 2798 1221 2794 1216 C
2789 1212 2783 1209 2777 1209 C
2771 1209 2765 1212 2760 1216 C
2756 1221 2753 1227 2753 1233 C
2753 1239 2756 1245 2760 1250 C
2765 1254 2771 1257 2777 1257 C
2783 1257 2789 1254 2794 1250 C
2798 1245 2801 1239 2801 1233 C
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F
2812 1287 m
2812 1281 2809 1275 2805 1270 C
2800 1266 2794 1263 2788 1263 C
2782 1263 2776 1266 2771 1270 C
2767 1275 2764 1281 2764 1287 C
2764 1293 2767 1299 2771 1304 C
2776 1308 2782 1311 2788 1311 C
2794 1311 2800 1308 2805 1304 C
2809 1299 2812 1293 2812 1287 C
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F
2824 1288 m
2824 1282 2821 1276 2817 1271 C
2812 1267 2806 1264 2800 1264 C
2794 1264 2788 1267 2783 1271 C
2779 1276 2776 1282 2776 1288 C
2776 1294 2779 1300 2783 1305 C
2788 1309 2794 1312 2800 1312 C
2806 1312 2812 1309 2817 1305 C
2821 1300 2824 1294 2824 1288 C
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F
2835 1234 m
2835 1228 2832 1222 2828 1217 C
2823 1213 2817 1210 2811 1210 C
2805 1210 2799 1213 2794 1217 C
2790 1222 2787 1228 2787 1234 C
2787 1240 2790 1246 2794 1251 C
2799 1255 2805 1258 2811 1258 C
2817 1258 2823 1255 2828 1251 C
2832 1246 2835 1240 2835 1234 C
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F
2847 1330 m
2847 1324 2844 1318 2840 1313 C
2835 1309 2829 1306 2823 1306 C
2817 1306 2811 1309 2806 1313 C
2802 1318 2799 1324 2799 1330 C
2799 1336 2802 1342 2806 1347 C
2811 1351 2817 1354 2823 1354 C
2829 1354 2835 1351 2840 1347 C
2844 1342 2847 1336 2847 1330 C
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F
2858 1205 m
2858 1199 2855 1193 2851 1188 C
2846 1184 2840 1181 2834 1181 C
2828 1181 2822 1184 2817 1188 C
2813 1193 2810 1199 2810 1205 C
2810 1211 2813 1217 2817 1222 C
2822 1226 2828 1229 2834 1229 C
2840 1229 2846 1226 2851 1222 C
2855 1217 2858 1211 2858 1205 C
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F
2870 1341 m
2870 1335 2867 1329 2863 1324 C
2858 1320 2852 1317 2846 1317 C
2840 1317 2834 1320 2829 1324 C
2825 1329 2822 1335 2822 1341 C
2822 1347 2825 1353 2829 1358 C
2834 1362 2840 1365 2846 1365 C
2852 1365 2858 1362 2863 1358 C
2867 1353 2870 1347 2870 1341 C
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F
2882 1211 m
2882 1205 2879 1199 2875 1194 C
2870 1190 2864 1187 2858 1187 C
2852 1187 2846 1190 2841 1194 C
2837 1199 2834 1205 2834 1211 C
2834 1217 2837 1223 2841 1228 C
2846 1232 2852 1235 2858 1235 C
2864 1235 2870 1232 2875 1228 C
2879 1223 2882 1217 2882 1211 C
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F
2893 1321 m
2893 1315 2890 1309 2886 1304 C
2881 1300 2875 1297 2869 1297 C
2863 1297 2857 1300 2852 1304 C
2848 1309 2845 1315 2845 1321 C
2845 1327 2848 1333 2852 1338 C
2857 1342 2863 1345 2869 1345 C
2875 1345 2881 1342 2886 1338 C
2890 1333 2893 1327 2893 1321 C
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F
2905 1243 m
2905 1237 2902 1231 2898 1226 C
2893 1222 2887 1219 2881 1219 C
2875 1219 2869 1222 2864 1226 C
2860 1231 2857 1237 2857 1243 C
2857 1249 2860 1255 2864 1260 C
2869 1264 2875 1267 2881 1267 C
2887 1267 2893 1264 2898 1260 C
2902 1255 2905 1249 2905 1243 C
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F
2916 1284 m
2916 1278 2913 1272 2909 1267 C
2904 1263 2898 1260 2892 1260 C
2886 1260 2880 1263 2875 1267 C
2871 1272 2868 1278 2868 1284 C
2868 1290 2871 1296 2875 1301 C
2880 1305 2886 1308 2892 1308 C
2898 1308 2904 1305 2909 1301 C
2913 1296 2916 1290 2916 1284 C
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F
2928 1282 m
2928 1276 2925 1270 2921 1265 C
2916 1261 2910 1258 2904 1258 C
2898 1258 2892 1261 2887 1265 C
2883 1270 2880 1276 2880 1282 C
2880 1288 2883 1294 2887 1299 C
2892 1303 2898 1306 2904 1306 C
2910 1306 2916 1303 2921 1299 C
2925 1294 2928 1288 2928 1282 C
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F
2939 1246 m
2939 1240 2936 1234 2932 1229 C
2927 1225 2921 1222 2915 1222 C
2909 1222 2903 1225 2898 1229 C
2894 1234 2891 1240 2891 1246 C
2891 1252 2894 1258 2898 1263 C
2903 1267 2909 1270 2915 1270 C
2921 1270 2927 1267 2932 1263 C
2936 1258 2939 1252 2939 1246 C
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F
2951 1315 m
2951 1309 2948 1303 2944 1298 C
2939 1294 2933 1291 2927 1291 C
2921 1291 2915 1294 2910 1298 C
2906 1303 2903 1309 2903 1315 C
2903 1321 2906 1327 2910 1332 C
2915 1336 2921 1339 2927 1339 C
2933 1339 2939 1336 2944 1332 C
2948 1327 2951 1321 2951 1315 C
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F
2962 1218 m
2962 1212 2959 1206 2955 1201 C
2950 1197 2944 1194 2938 1194 C
2932 1194 2926 1197 2921 1201 C
2917 1206 2914 1212 2914 1218 C
2914 1224 2917 1230 2921 1235 C
2926 1239 2932 1242 2938 1242 C
2944 1242 2950 1239 2955 1235 C
2959 1230 2962 1224 2962 1218 C
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F
2974 1335 m
2974 1329 2971 1323 2967 1318 C
2962 1314 2956 1311 2950 1311 C
2944 1311 2938 1314 2933 1318 C
2929 1323 2926 1329 2926 1335 C
2926 1341 2929 1347 2933 1352 C
2938 1356 2944 1359 2950 1359 C
2956 1359 2962 1356 2967 1352 C
2971 1347 2974 1341 2974 1335 C
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F
2985 1205 m
2985 1199 2982 1193 2978 1188 C
2973 1184 2967 1181 2961 1181 C
2955 1181 2949 1184 2944 1188 C
2940 1193 2937 1199 2937 1205 C
2937 1211 2940 1217 2944 1222 C
2949 1226 2955 1229 2961 1229 C
2967 1229 2973 1226 2978 1222 C
2982 1217 2985 1211 2985 1205 C
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F
2997 1341 m
2997 1335 2994 1329 2990 1324 C
2985 1320 2979 1317 2973 1317 C
2967 1317 2961 1320 2956 1324 C
2952 1329 2949 1335 2949 1341 C
2949 1347 2952 1353 2956 1358 C
2961 1362 2967 1365 2973 1365 C
2979 1365 2985 1362 2990 1358 C
2994 1353 2997 1347 2997 1341 C
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F
3009 1204 m
3009 1198 3006 1192 3002 1187 C
2997 1183 2991 1180 2985 1180 C
2979 1180 2973 1183 2968 1187 C
2964 1192 2961 1198 2961 1204 C
2961 1210 2964 1216 2968 1221 C
2973 1225 2979 1228 2985 1228 C
2991 1228 2997 1225 3002 1221 C
3006 1216 3009 1210 3009 1204 C
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F
3020 1337 m
3020 1331 3017 1325 3013 1320 C
3008 1316 3002 1313 2996 1313 C
2990 1313 2984 1316 2979 1320 C
2975 1325 2972 1331 2972 1337 C
2972 1343 2975 1349 2979 1354 C
2984 1358 2990 1361 2996 1361 C
3002 1361 3008 1358 3013 1354 C
3017 1349 3020 1343 3020 1337 C
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F
3032 1212 m
3032 1206 3029 1200 3025 1195 C
3020 1191 3014 1188 3008 1188 C
3002 1188 2996 1191 2991 1195 C
2987 1200 2984 1206 2984 1212 C
2984 1218 2987 1224 2991 1229 C
2996 1233 3002 1236 3008 1236 C
3014 1236 3020 1233 3025 1229 C
3029 1224 3032 1218 3032 1212 C
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F
3043 1327 m
3043 1321 3040 1315 3036 1310 C
3031 1306 3025 1303 3019 1303 C
3013 1303 3007 1306 3002 1310 C
2998 1315 2995 1321 2995 1327 C
2995 1333 2998 1339 3002 1344 C
3007 1348 3013 1351 3019 1351 C
3025 1351 3031 1348 3036 1344 C
3040 1339 3043 1333 3043 1327 C
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F
3055 1225 m
3055 1219 3052 1213 3048 1208 C
3043 1204 3037 1201 3031 1201 C
3025 1201 3019 1204 3014 1208 C
3010 1213 3007 1219 3007 1225 C
3007 1231 3010 1237 3014 1242 C
3019 1246 3025 1249 3031 1249 C
3037 1249 3043 1246 3048 1242 C
3052 1237 3055 1231 3055 1225 C
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F
3066 1314 m
3066 1308 3063 1302 3059 1297 C
3054 1293 3048 1290 3042 1290 C
3036 1290 3030 1293 3025 1297 C
3021 1302 3018 1308 3018 1314 C
3018 1320 3021 1326 3025 1331 C
3030 1335 3036 1338 3042 1338 C
3048 1338 3054 1335 3059 1331 C
3063 1326 3066 1320 3066 1314 C
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F
3078 1238 m
3078 1232 3075 1226 3071 1221 C
3066 1217 3060 1214 3054 1214 C
3048 1214 3042 1217 3037 1221 C
3033 1226 3030 1232 3030 1238 C
3030 1244 3033 1250 3037 1255 C
3042 1259 3048 1262 3054 1262 C
3060 1262 3066 1259 3071 1255 C
3075 1250 3078 1244 3078 1238 C
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F
3089 1302 m
3089 1296 3086 1290 3082 1285 C
3077 1281 3071 1278 3065 1278 C
3059 1278 3053 1281 3048 1285 C
3044 1290 3041 1296 3041 1302 C
3041 1308 3044 1314 3048 1319 C
3053 1323 3059 1326 3065 1326 C
3071 1326 3077 1323 3082 1319 C
3086 1314 3089 1308 3089 1302 C
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F
3101 1250 m
3101 1244 3098 1238 3094 1233 C
3089 1229 3083 1226 3077 1226 C
3071 1226 3065 1229 3060 1233 C
3056 1238 3053 1244 3053 1250 C
3053 1256 3056 1262 3060 1267 C
3065 1271 3071 1274 3077 1274 C
3083 1274 3089 1271 3094 1267 C
3098 1262 3101 1256 3101 1250 C
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F
3112 1292 m
3112 1286 3109 1280 3105 1275 C
3100 1271 3094 1268 3088 1268 C
3082 1268 3076 1271 3071 1275 C
3067 1280 3064 1286 3064 1292 C
3064 1298 3067 1304 3071 1309 C
3076 1313 3082 1316 3088 1316 C
3094 1316 3100 1313 3105 1309 C
3109 1304 3112 1298 3112 1292 C
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F
3124 1259 m
3124 1253 3121 1247 3117 1242 C
3112 1238 3106 1235 3100 1235 C
3094 1235 3088 1238 3083 1242 C
3079 1247 3076 1253 3076 1259 C
3076 1265 3079 1271 3083 1276 C
3088 1280 3094 1283 3100 1283 C
3106 1283 3112 1280 3117 1276 C
3121 1271 3124 1265 3124 1259 C
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F
3136 1285 m
3136 1279 3133 1273 3129 1268 C
3124 1264 3118 1261 3112 1261 C
3106 1261 3100 1264 3095 1268 C
3091 1273 3088 1279 3088 1285 C
3088 1291 3091 1297 3095 1302 C
3100 1306 3106 1309 3112 1309 C
3118 1309 3124 1306 3129 1302 C
3133 1297 3136 1291 3136 1285 C
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F
3147 1264 m
3147 1258 3144 1252 3140 1247 C
3135 1243 3129 1240 3123 1240 C
3117 1240 3111 1243 3106 1247 C
3102 1252 3099 1258 3099 1264 C
3099 1270 3102 1276 3106 1281 C
3111 1285 3117 1288 3123 1288 C
3129 1288 3135 1285 3140 1281 C
3144 1276 3147 1270 3147 1264 C
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F
3159 1281 m
3159 1275 3156 1269 3152 1264 C
3147 1260 3141 1257 3135 1257 C
3129 1257 3123 1260 3118 1264 C
3114 1269 3111 1275 3111 1281 C
3111 1287 3114 1293 3118 1298 C
3123 1302 3129 1305 3135 1305 C
3141 1305 3147 1302 3152 1298 C
3156 1293 3159 1287 3159 1281 C
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F
3170 1265 m
3170 1259 3167 1253 3163 1248 C
3158 1244 3152 1241 3146 1241 C
3140 1241 3134 1244 3129 1248 C
3125 1253 3122 1259 3122 1265 C
3122 1271 3125 1277 3129 1282 C
3134 1286 3140 1289 3146 1289 C
3152 1289 3158 1286 3163 1282 C
3167 1277 3170 1271 3170 1265 C
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F
3182 1282 m
3182 1276 3179 1270 3175 1265 C
3170 1261 3164 1258 3158 1258 C
3152 1258 3146 1261 3141 1265 C
3137 1270 3134 1276 3134 1282 C
3134 1288 3137 1294 3141 1299 C
3146 1303 3152 1306 3158 1306 C
3164 1306 3170 1303 3175 1299 C
3179 1294 3182 1288 3182 1282 C
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F
3193 1263 m
3193 1257 3190 1251 3186 1246 C
3181 1242 3175 1239 3169 1239 C
3163 1239 3157 1242 3152 1246 C
3148 1251 3145 1257 3145 1263 C
3145 1269 3148 1275 3152 1280 C
3157 1284 3163 1287 3169 1287 C
3175 1287 3181 1284 3186 1280 C
3190 1275 3193 1269 3193 1263 C
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F
3205 1286 m
3205 1280 3202 1274 3198 1269 C
3193 1265 3187 1262 3181 1262 C
3175 1262 3169 1265 3164 1269 C
3160 1274 3157 1280 3157 1286 C
3157 1292 3160 1298 3164 1303 C
3169 1307 3175 1310 3181 1310 C
3187 1310 3193 1307 3198 1303 C
3202 1298 3205 1292 3205 1286 C
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F
3216 1258 m
3216 1252 3213 1246 3209 1241 C
3204 1237 3198 1234 3192 1234 C
3186 1234 3180 1237 3175 1241 C
3171 1246 3168 1252 3168 1258 C
3168 1264 3171 1270 3175 1275 C
3180 1279 3186 1282 3192 1282 C
3198 1282 3204 1279 3209 1275 C
3213 1270 3216 1264 3216 1258 C
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F
3228 1293 m
3228 1287 3225 1281 3221 1276 C
3216 1272 3210 1269 3204 1269 C
3198 1269 3192 1272 3187 1276 C
3183 1281 3180 1287 3180 1293 C
3180 1299 3183 1305 3187 1310 C
3192 1314 3198 1317 3204 1317 C
3210 1317 3216 1314 3221 1310 C
3225 1305 3228 1299 3228 1293 C
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F
3240 1249 m
3240 1243 3237 1237 3233 1232 C
3228 1228 3222 1225 3216 1225 C
3210 1225 3204 1228 3199 1232 C
3195 1237 3192 1243 3192 1249 C
3192 1255 3195 1261 3199 1266 C
3204 1270 3210 1273 3216 1273 C
3222 1273 3228 1270 3233 1266 C
3237 1261 3240 1255 3240 1249 C
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F
3251 1303 m
3251 1297 3248 1291 3244 1286 C
3239 1282 3233 1279 3227 1279 C
3221 1279 3215 1282 3210 1286 C
3206 1291 3203 1297 3203 1303 C
3203 1309 3206 1315 3210 1320 C
3215 1324 3221 1327 3227 1327 C
3233 1327 3239 1324 3244 1320 C
3248 1315 3251 1309 3251 1303 C
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F
3263 1237 m
3263 1231 3260 1225 3256 1220 C
3251 1216 3245 1213 3239 1213 C
3233 1213 3227 1216 3222 1220 C
3218 1225 3215 1231 3215 1237 C
3215 1243 3218 1249 3222 1254 C
3227 1258 3233 1261 3239 1261 C
3245 1261 3251 1258 3256 1254 C
3260 1249 3263 1243 3263 1237 C
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F
3274 1316 m
3274 1310 3271 1304 3267 1299 C
3262 1295 3256 1292 3250 1292 C
3244 1292 3238 1295 3233 1299 C
3229 1304 3226 1310 3226 1316 C
3226 1322 3229 1328 3233 1333 C
3238 1337 3244 1340 3250 1340 C
3256 1340 3262 1337 3267 1333 C
3271 1328 3274 1322 3274 1316 C
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F
3286 1223 m
3286 1217 3283 1211 3279 1206 C
3274 1202 3268 1199 3262 1199 C
3256 1199 3250 1202 3245 1206 C
3241 1211 3238 1217 3238 1223 C
3238 1229 3241 1235 3245 1240 C
3250 1244 3256 1247 3262 1247 C
3268 1247 3274 1244 3279 1240 C
3283 1235 3286 1229 3286 1223 C
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F
3297 1328 m
3297 1322 3294 1316 3290 1311 C
3285 1307 3279 1304 3273 1304 C
3267 1304 3261 1307 3256 1311 C
3252 1316 3249 1322 3249 1328 C
3249 1334 3252 1340 3256 1345 C
3261 1349 3267 1352 3273 1352 C
3279 1352 3285 1349 3290 1345 C
3294 1340 3297 1334 3297 1328 C
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F
3309 1211 m
3309 1205 3306 1199 3302 1194 C
3297 1190 3291 1187 3285 1187 C
3279 1187 3273 1190 3268 1194 C
3264 1199 3261 1205 3261 1211 C
3261 1217 3264 1223 3268 1228 C
3273 1232 3279 1235 3285 1235 C
3291 1235 3297 1232 3302 1228 C
3306 1223 3309 1217 3309 1211 C
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F
3320 1338 m
3320 1332 3317 1326 3313 1321 C
3308 1317 3302 1314 3296 1314 C
3290 1314 3284 1317 3279 1321 C
3275 1326 3272 1332 3272 1338 C
3272 1344 3275 1350 3279 1355 C
3284 1359 3290 1362 3296 1362 C
3302 1362 3308 1359 3313 1355 C
3317 1350 3320 1344 3320 1338 C
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F
3332 1204 m
3332 1198 3329 1192 3325 1187 C
3320 1183 3314 1180 3308 1180 C
3302 1180 3296 1183 3291 1187 C
3287 1192 3284 1198 3284 1204 C
3284 1210 3287 1216 3291 1221 C
3296 1225 3302 1228 3308 1228 C
3314 1228 3320 1225 3325 1221 C
3329 1216 3332 1210 3332 1204 C
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F
3343 1341 m
3343 1335 3340 1329 3336 1324 C
3331 1320 3325 1317 3319 1317 C
3313 1317 3307 1320 3302 1324 C
3298 1329 3295 1335 3295 1341 C
3295 1347 3298 1353 3302 1358 C
3307 1362 3313 1365 3319 1365 C
3325 1365 3331 1362 3336 1358 C
3340 1353 3343 1347 3343 1341 C
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F
3355 1206 m
3355 1200 3352 1194 3348 1189 C
3343 1185 3337 1182 3331 1182 C
3325 1182 3319 1185 3314 1189 C
3310 1194 3307 1200 3307 1206 C
3307 1212 3310 1218 3314 1223 C
3319 1227 3325 1230 3331 1230 C
3337 1230 3343 1227 3348 1223 C
3352 1218 3355 1212 3355 1206 C
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F
3367 1333 m
3367 1327 3364 1321 3360 1316 C
3355 1312 3349 1309 3343 1309 C
3337 1309 3331 1312 3326 1316 C
3322 1321 3319 1327 3319 1333 C
3319 1339 3322 1345 3326 1350 C
3331 1354 3337 1357 3343 1357 C
3349 1357 3355 1354 3360 1350 C
3364 1345 3367 1339 3367 1333 C
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F
3378 1222 m
3378 1216 3375 1210 3371 1205 C
3366 1201 3360 1198 3354 1198 C
3348 1198 3342 1201 3337 1205 C
3333 1210 3330 1216 3330 1222 C
3330 1228 3333 1234 3337 1239 C
3342 1243 3348 1246 3354 1246 C
3360 1246 3366 1243 3371 1239 C
3375 1234 3378 1228 3378 1222 C
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F
3390 1311 m
3390 1305 3387 1299 3383 1294 C
3378 1290 3372 1287 3366 1287 C
3360 1287 3354 1290 3349 1294 C
3345 1299 3342 1305 3342 1311 C
3342 1317 3345 1323 3349 1328 C
3354 1332 3360 1335 3366 1335 C
3372 1335 3378 1332 3383 1328 C
3387 1323 3390 1317 3390 1311 C
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F
3401 1251 m
3401 1245 3398 1239 3394 1234 C
3389 1230 3383 1227 3377 1227 C
3371 1227 3365 1230 3360 1234 C
3356 1239 3353 1245 3353 1251 C
3353 1257 3356 1263 3360 1268 C
3365 1272 3371 1275 3377 1275 C
3383 1275 3389 1272 3394 1268 C
3398 1263 3401 1257 3401 1251 C
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F
3413 1276 m
3413 1270 3410 1264 3406 1259 C
3401 1255 3395 1252 3389 1252 C
3383 1252 3377 1255 3372 1259 C
3368 1264 3365 1270 3365 1276 C
3365 1282 3368 1288 3372 1293 C
3377 1297 3383 1300 3389 1300 C
3395 1300 3401 1297 3406 1293 C
3410 1288 3413 1282 3413 1276 C
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F
3424 1290 m
3424 1284 3421 1278 3417 1273 C
3412 1269 3406 1266 3400 1266 C
3394 1266 3388 1269 3383 1273 C
3379 1278 3376 1284 3376 1290 C
3376 1296 3379 1302 3383 1307 C
3388 1311 3394 1314 3400 1314 C
3406 1314 3412 1311 3417 1307 C
3421 1302 3424 1296 3424 1290 C
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F
3436 1237 m
3436 1231 3433 1225 3429 1220 C
3424 1216 3418 1213 3412 1213 C
3406 1213 3400 1216 3395 1220 C
3391 1225 3388 1231 3388 1237 C
3388 1243 3391 1249 3395 1254 C
3400 1258 3406 1261 3412 1261 C
3418 1261 3424 1258 3429 1254 C
3433 1249 3436 1243 3436 1237 C
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F
3447 1325 m
3447 1319 3444 1313 3440 1308 C
3435 1304 3429 1301 3423 1301 C
3417 1301 3411 1304 3406 1308 C
3402 1313 3399 1319 3399 1325 C
3399 1331 3402 1337 3406 1342 C
3411 1346 3417 1349 3423 1349 C
3429 1349 3435 1346 3440 1342 C
3444 1337 3447 1331 3447 1325 C
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F
3459 1208 m
3459 1202 3456 1196 3452 1191 C
3447 1187 3441 1184 3435 1184 C
3429 1184 3423 1187 3418 1191 C
3414 1196 3411 1202 3411 1208 C
3411 1214 3414 1220 3418 1225 C
3423 1229 3429 1232 3435 1232 C
3441 1232 3447 1229 3452 1225 C
3456 1220 3459 1214 3459 1208 C
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F
3470 1341 m
3470 1335 3467 1329 3463 1324 C
3458 1320 3452 1317 3446 1317 C
3440 1317 3434 1320 3429 1324 C
3425 1329 3422 1335 3422 1341 C
3422 1347 3425 1353 3429 1358 C
3434 1362 3440 1365 3446 1365 C
3452 1365 3458 1362 3463 1358 C
3467 1353 3470 1347 3470 1341 C
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F
3482 1207 m
3482 1201 3479 1195 3475 1190 C
3470 1186 3464 1183 3458 1183 C
3452 1183 3446 1186 3441 1190 C
3437 1195 3434 1201 3434 1207 C
3434 1213 3437 1219 3441 1224 C
3446 1228 3452 1231 3458 1231 C
3464 1231 3470 1228 3475 1224 C
3479 1219 3482 1213 3482 1207 C
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F
3494 1326 m
3494 1320 3491 1314 3487 1309 C
3482 1305 3476 1302 3470 1302 C
3464 1302 3458 1305 3453 1309 C
3449 1314 3446 1320 3446 1326 C
3446 1332 3449 1338 3453 1343 C
3458 1347 3464 1350 3470 1350 C
3476 1350 3482 1347 3487 1343 C
3491 1338 3494 1332 3494 1326 C
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F
3505 1240 m
3505 1234 3502 1228 3498 1223 C
3493 1219 3487 1216 3481 1216 C
3475 1216 3469 1219 3464 1223 C
3460 1228 3457 1234 3457 1240 C
3457 1246 3460 1252 3464 1257 C
3469 1261 3475 1264 3481 1264 C
3487 1264 3493 1261 3498 1257 C
3502 1252 3505 1246 3505 1240 C
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F
3517 1280 m
3517 1274 3514 1268 3510 1263 C
3505 1259 3499 1256 3493 1256 C
3487 1256 3481 1259 3476 1263 C
3472 1268 3469 1274 3469 1280 C
3469 1286 3472 1292 3476 1297 C
3481 1301 3487 1304 3493 1304 C
3499 1304 3505 1301 3510 1297 C
3514 1292 3517 1286 3517 1280 C
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F
3528 1295 m
3528 1289 3525 1283 3521 1278 C
3516 1274 3510 1271 3504 1271 C
3498 1271 3492 1274 3487 1278 C
3483 1283 3480 1289 3480 1295 C
3480 1301 3483 1307 3487 1312 C
3492 1316 3498 1319 3504 1319 C
3510 1319 3516 1316 3521 1312 C
3525 1307 3528 1301 3528 1295 C
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F
3540 1226 m
3540 1220 3537 1214 3533 1209 C
3528 1205 3522 1202 3516 1202 C
3510 1202 3504 1205 3499 1209 C
3495 1214 3492 1220 3492 1226 C
3492 1232 3495 1238 3499 1243 C
3504 1247 3510 1250 3516 1250 C
3522 1250 3528 1247 3533 1243 C
3537 1238 3540 1232 3540 1226 C
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F
3551 1336 m
3551 1330 3548 1324 3544 1319 C
3539 1315 3533 1312 3527 1312 C
3521 1312 3515 1315 3510 1319 C
3506 1324 3503 1330 3503 1336 C
3503 1342 3506 1348 3510 1353 C
3515 1357 3521 1360 3527 1360 C
3533 1360 3539 1357 3544 1353 C
3548 1348 3551 1342 3551 1336 C
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F
3563 1203 m
3563 1197 3560 1191 3556 1186 C
3551 1182 3545 1179 3539 1179 C
3533 1179 3527 1182 3522 1186 C
3518 1191 3515 1197 3515 1203 C
3515 1209 3518 1215 3522 1220 C
3527 1224 3533 1227 3539 1227 C
3545 1227 3551 1224 3556 1220 C
3560 1215 3563 1209 3563 1203 C
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F
3574 1332 m
3574 1326 3571 1320 3567 1315 C
3562 1311 3556 1308 3550 1308 C
3544 1308 3538 1311 3533 1315 C
3529 1320 3526 1326 3526 1332 C
3526 1338 3529 1344 3533 1349 C
3538 1353 3544 1356 3550 1356 C
3556 1356 3562 1353 3567 1349 C
3571 1344 3574 1338 3574 1332 C
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F
3586 1236 m
3586 1230 3583 1224 3579 1219 C
3574 1215 3568 1212 3562 1212 C
3556 1212 3550 1215 3545 1219 C
3541 1224 3538 1230 3538 1236 C
3538 1242 3541 1248 3545 1253 C
3550 1257 3556 1260 3562 1260 C
3568 1260 3574 1257 3579 1253 C
3583 1248 3586 1242 3586 1236 C
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F
3598 1279 m
3598 1273 3595 1267 3591 1262 C
3586 1258 3580 1255 3574 1255 C
3568 1255 3562 1258 3557 1262 C
3553 1267 3550 1273 3550 1279 C
3550 1285 3553 1291 3557 1296 C
3562 1300 3568 1303 3574 1303 C
3580 1303 3586 1300 3591 1296 C
3595 1291 3598 1285 3598 1279 C
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F
3609 1302 m
3609 1296 3606 1290 3602 1285 C
3597 1281 3591 1278 3585 1278 C
3579 1278 3573 1281 3568 1285 C
3564 1290 3561 1296 3561 1302 C
3561 1308 3564 1314 3568 1319 C
3573 1323 3579 1326 3585 1326 C
3591 1326 3597 1323 3602 1319 C
3606 1314 3609 1308 3609 1302 C
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F
3621 1216 m
3621 1210 3618 1204 3614 1199 C
3609 1195 3603 1192 3597 1192 C
3591 1192 3585 1195 3580 1199 C
3576 1204 3573 1210 3573 1216 C
3573 1222 3576 1228 3580 1233 C
3585 1237 3591 1240 3597 1240 C
3603 1240 3609 1237 3614 1233 C
3618 1228 3621 1222 3621 1216 C
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F
3632 1341 m
3632 1335 3629 1329 3625 1324 C
3620 1320 3614 1317 3608 1317 C
3602 1317 3596 1320 3591 1324 C
3587 1329 3584 1335 3584 1341 C
3584 1347 3587 1353 3591 1358 C
3596 1362 3602 1365 3608 1365 C
3614 1365 3620 1362 3625 1358 C
3629 1353 3632 1347 3632 1341 C
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F
3644 1210 m
3644 1204 3641 1198 3637 1193 C
3632 1189 3626 1186 3620 1186 C
3614 1186 3608 1189 3603 1193 C
3599 1198 3596 1204 3596 1210 C
3596 1216 3599 1222 3603 1227 C
3608 1231 3614 1234 3620 1234 C
3626 1234 3632 1231 3637 1227 C
3641 1222 3644 1216 3644 1210 C
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F
3655 1309 m
3655 1303 3652 1297 3648 1292 C
3643 1288 3637 1285 3631 1285 C
3625 1285 3619 1288 3614 1292 C
3610 1297 3607 1303 3607 1309 C
3607 1315 3610 1321 3614 1326 C
3619 1330 3625 1333 3631 1333 C
3637 1333 3643 1330 3648 1326 C
3652 1321 3655 1315 3655 1309 C
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F
3667 1276 m
3667 1270 3664 1264 3660 1259 C
3655 1255 3649 1252 3643 1252 C
3637 1252 3631 1255 3626 1259 C
3622 1264 3619 1270 3619 1276 C
3619 1282 3622 1288 3626 1293 C
3631 1297 3637 1300 3643 1300 C
3649 1300 3655 1297 3660 1293 C
3664 1288 3667 1282 3667 1276 C
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F
3678 1233 m
3678 1227 3675 1221 3671 1216 C
3666 1212 3660 1209 3654 1209 C
3648 1209 3642 1212 3637 1216 C
3633 1221 3630 1227 3630 1233 C
3630 1239 3633 1245 3637 1250 C
3642 1254 3648 1257 3654 1257 C
3660 1257 3666 1254 3671 1250 C
3675 1245 3678 1239 3678 1233 C
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F
3690 1338 m
3690 1332 3687 1326 3683 1321 C
3678 1317 3672 1314 3666 1314 C
3660 1314 3654 1317 3649 1321 C
3645 1326 3642 1332 3642 1338 C
3642 1344 3645 1350 3649 1355 C
3654 1359 3660 1362 3666 1362 C
3672 1362 3678 1359 3683 1355 C
3687 1350 3690 1344 3690 1338 C
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F
3701 1205 m
3701 1199 3698 1193 3694 1188 C
3689 1184 3683 1181 3677 1181 C
3671 1181 3665 1184 3660 1188 C
3656 1193 3653 1199 3653 1205 C
3653 1211 3656 1217 3660 1222 C
3665 1226 3671 1229 3677 1229 C
3683 1229 3689 1226 3694 1222 C
3698 1217 3701 1211 3701 1205 C
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F
3713 1316 m
3713 1310 3710 1304 3706 1299 C
3701 1295 3695 1292 3689 1292 C
3683 1292 3677 1295 3672 1299 C
3668 1304 3665 1310 3665 1316 C
3665 1322 3668 1328 3672 1333 C
3677 1337 3683 1340 3689 1340 C
3695 1340 3701 1337 3706 1333 C
3710 1328 3713 1322 3713 1316 C
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F
3725 1272 m
3725 1266 3722 1260 3718 1255 C
3713 1251 3707 1248 3701 1248 C
3695 1248 3689 1251 3684 1255 C
3680 1260 3677 1266 3677 1272 C
3677 1278 3680 1284 3684 1289 C
3689 1293 3695 1296 3701 1296 C
3707 1296 3713 1293 3718 1289 C
3722 1284 3725 1278 3725 1272 C
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F
3736 1232 m
3736 1226 3733 1220 3729 1215 C
3724 1211 3718 1208 3712 1208 C
3706 1208 3700 1211 3695 1215 C
3691 1220 3688 1226 3688 1232 C
3688 1238 3691 1244 3695 1249 C
3700 1253 3706 1256 3712 1256 C
3718 1256 3724 1253 3729 1249 C
3733 1244 3736 1238 3736 1232 C
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F
3748 1339 m
3748 1333 3745 1327 3741 1322 C
3736 1318 3730 1315 3724 1315 C
3718 1315 3712 1318 3707 1322 C
3703 1327 3700 1333 3700 1339 C
3700 1345 3703 1351 3707 1356 C
3712 1360 3718 1363 3724 1363 C
3730 1363 3736 1360 3741 1356 C
3745 1351 3748 1345 3748 1339 C
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F
3759 1209 m
3759 1203 3756 1197 3752 1192 C
3747 1188 3741 1185 3735 1185 C
3729 1185 3723 1188 3718 1192 C
3714 1197 3711 1203 3711 1209 C
3711 1215 3714 1221 3718 1226 C
3723 1230 3729 1233 3735 1233 C
3741 1233 3747 1230 3752 1226 C
3756 1221 3759 1215 3759 1209 C
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F
3771 1303 m
3771 1297 3768 1291 3764 1286 C
3759 1282 3753 1279 3747 1279 C
3741 1279 3735 1282 3730 1286 C
3726 1291 3723 1297 3723 1303 C
3723 1309 3726 1315 3730 1320 C
3735 1324 3741 1327 3747 1327 C
3753 1327 3759 1324 3764 1320 C
3768 1315 3771 1309 3771 1303 C
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F
3782 1292 m
3782 1286 3779 1280 3775 1275 C
3770 1271 3764 1268 3758 1268 C
3752 1268 3746 1271 3741 1275 C
3737 1280 3734 1286 3734 1292 C
3734 1298 3737 1304 3741 1309 C
3746 1313 3752 1316 3758 1316 C
3764 1316 3770 1313 3775 1309 C
3779 1304 3782 1298 3782 1292 C
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F
3794 1214 m
3794 1208 3791 1202 3787 1197 C
3782 1193 3776 1190 3770 1190 C
3764 1190 3758 1193 3753 1197 C
3749 1202 3746 1208 3746 1214 C
3746 1220 3749 1226 3753 1231 C
3758 1235 3764 1238 3770 1238 C
3776 1238 3782 1235 3787 1231 C
3791 1226 3794 1220 3794 1214 C
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F
3805 1341 m
3805 1335 3802 1329 3798 1324 C
3793 1320 3787 1317 3781 1317 C
3775 1317 3769 1320 3764 1324 C
3760 1329 3757 1335 3757 1341 C
3757 1347 3760 1353 3764 1358 C
3769 1362 3775 1365 3781 1365 C
3787 1365 3793 1362 3798 1358 C
3802 1353 3805 1347 3805 1341 C
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F
3817 1232 m
3817 1226 3814 1220 3810 1215 C
3805 1211 3799 1208 3793 1208 C
3787 1208 3781 1211 3776 1215 C
3772 1220 3769 1226 3769 1232 C
3769 1238 3772 1244 3776 1249 C
3781 1253 3787 1256 3793 1256 C
3799 1256 3805 1253 3810 1249 C
3814 1244 3817 1238 3817 1232 C
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F
3829 1264 m
3829 1258 3826 1252 3822 1247 C
3817 1243 3811 1240 3805 1240 C
3799 1240 3793 1243 3788 1247 C
3784 1252 3781 1258 3781 1264 C
3781 1270 3784 1276 3788 1281 C
3793 1285 3799 1288 3805 1288 C
3811 1288 3817 1285 3822 1281 C
3826 1276 3829 1270 3829 1264 C
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F
3840 1329 m
3840 1323 3837 1317 3833 1312 C
3828 1308 3822 1305 3816 1305 C
3810 1305 3804 1308 3799 1312 C
3795 1317 3792 1323 3792 1329 C
3792 1335 3795 1341 3799 1346 C
3804 1350 3810 1353 3816 1353 C
3822 1353 3828 1350 3833 1346 C
3837 1341 3840 1335 3840 1329 C
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F
3852 1203 m
3852 1197 3849 1191 3845 1186 C
3840 1182 3834 1179 3828 1179 C
3822 1179 3816 1182 3811 1186 C
3807 1191 3804 1197 3804 1203 C
3804 1209 3807 1215 3811 1220 C
3816 1224 3822 1227 3828 1227 C
3834 1227 3840 1224 3845 1220 C
3849 1215 3852 1209 3852 1203 C
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F
3863 1313 m
3863 1307 3860 1301 3856 1296 C
3851 1292 3845 1289 3839 1289 C
3833 1289 3827 1292 3822 1296 C
3818 1301 3815 1307 3815 1313 C
3815 1319 3818 1325 3822 1330 C
3827 1334 3833 1337 3839 1337 C
3845 1337 3851 1334 3856 1330 C
3860 1325 3863 1319 3863 1313 C
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F
3875 1290 m
3875 1284 3872 1278 3868 1273 C
3863 1269 3857 1266 3851 1266 C
3845 1266 3839 1269 3834 1273 C
3830 1278 3827 1284 3827 1290 C
3827 1296 3830 1302 3834 1307 C
3839 1311 3845 1314 3851 1314 C
3857 1314 3863 1311 3868 1307 C
3872 1302 3875 1296 3875 1290 C
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F
3886 1211 m
3886 1205 3883 1199 3879 1194 C
3874 1190 3868 1187 3862 1187 C
3856 1187 3850 1190 3845 1194 C
3841 1199 3838 1205 3838 1211 C
3838 1217 3841 1223 3845 1228 C
3850 1232 3856 1235 3862 1235 C
3868 1235 3874 1232 3879 1228 C
3883 1223 3886 1217 3886 1211 C
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F
3898 1338 m
3898 1332 3895 1326 3891 1321 C
3886 1317 3880 1314 3874 1314 C
3868 1314 3862 1317 3857 1321 C
3853 1326 3850 1332 3850 1338 C
3850 1344 3853 1350 3857 1355 C
3862 1359 3868 1362 3874 1362 C
3880 1362 3886 1359 3891 1355 C
3895 1350 3898 1344 3898 1338 C
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F
3909 1251 m
3909 1245 3906 1239 3902 1234 C
3897 1230 3891 1227 3885 1227 C
3879 1227 3873 1230 3868 1234 C
3864 1239 3861 1245 3861 1251 C
3861 1257 3864 1263 3868 1268 C
3873 1272 3879 1275 3885 1275 C
3891 1275 3897 1272 3902 1268 C
3906 1263 3909 1257 3909 1251 C
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F
3921 1236 m
3921 1230 3918 1224 3914 1219 C
3909 1215 3903 1212 3897 1212 C
3891 1212 3885 1215 3880 1219 C
3876 1224 3873 1230 3873 1236 C
3873 1242 3876 1248 3880 1253 C
3885 1257 3891 1260 3897 1260 C
3903 1260 3909 1257 3914 1253 C
3918 1248 3921 1242 3921 1236 C
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F
3932 1342 m
3932 1336 3929 1330 3925 1325 C
3920 1321 3914 1318 3908 1318 C
3902 1318 3896 1321 3891 1325 C
3887 1330 3884 1336 3884 1342 C
3884 1348 3887 1354 3891 1359 C
3896 1363 3902 1366 3908 1366 C
3914 1366 3920 1363 3925 1359 C
3929 1354 3932 1348 3932 1342 C
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F
3944 1225 m
3944 1219 3941 1213 3937 1208 C
3932 1204 3926 1201 3920 1201 C
3914 1201 3908 1204 3903 1208 C
3899 1213 3896 1219 3896 1225 C
3896 1231 3899 1237 3903 1242 C
3908 1246 3914 1249 3920 1249 C
3926 1249 3932 1246 3937 1242 C
3941 1237 3944 1231 3944 1225 C
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F
3956 1262 m
3956 1256 3953 1250 3949 1245 C
3944 1241 3938 1238 3932 1238 C
3926 1238 3920 1241 3915 1245 C
3911 1250 3908 1256 3908 1262 C
3908 1268 3911 1274 3915 1279 C
3920 1283 3926 1286 3932 1286 C
3938 1286 3944 1283 3949 1279 C
3953 1274 3956 1268 3956 1262 C
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F
3967 1336 m
3967 1330 3964 1324 3960 1319 C
3955 1315 3949 1312 3943 1312 C
3937 1312 3931 1315 3926 1319 C
3922 1324 3919 1330 3919 1336 C
3919 1342 3922 1348 3926 1353 C
3931 1357 3937 1360 3943 1360 C
3949 1360 3955 1357 3960 1353 C
3964 1348 3967 1342 3967 1336 C
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F
3979 1211 m
3979 1205 3976 1199 3972 1194 C
3967 1190 3961 1187 3955 1187 C
3949 1187 3943 1190 3938 1194 C
3934 1199 3931 1205 3931 1211 C
3931 1217 3934 1223 3938 1228 C
3943 1232 3949 1235 3955 1235 C
3961 1235 3967 1232 3972 1228 C
3976 1223 3979 1217 3979 1211 C
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F
3990 1279 m
3990 1273 3987 1267 3983 1262 C
3978 1258 3972 1255 3966 1255 C
3960 1255 3954 1258 3949 1262 C
3945 1267 3942 1273 3942 1279 C
3942 1285 3945 1291 3949 1296 C
3954 1300 3960 1303 3966 1303 C
3972 1303 3978 1300 3983 1296 C
3987 1291 3990 1285 3990 1279 C
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F
4002 1329 m
4002 1323 3999 1317 3995 1312 C
3990 1308 3984 1305 3978 1305 C
3972 1305 3966 1308 3961 1312 C
3957 1317 3954 1323 3954 1329 C
3954 1335 3957 1341 3961 1346 C
3966 1350 3972 1353 3978 1353 C
3984 1353 3990 1350 3995 1346 C
3999 1341 4002 1335 4002 1329 C
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F
4013 1206 m
4013 1200 4010 1194 4006 1189 C
4001 1185 3995 1182 3989 1182 C
3983 1182 3977 1185 3972 1189 C
3968 1194 3965 1200 3965 1206 C
3965 1212 3968 1218 3972 1223 C
3977 1227 3983 1230 3989 1230 C
3995 1230 4001 1227 4006 1223 C
4010 1218 4013 1212 4013 1206 C
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F
4025 1287 m
4025 1281 4022 1275 4018 1270 C
4013 1266 4007 1263 4001 1263 C
3995 1263 3989 1266 3984 1270 C
3980 1275 3977 1281 3977 1287 C
3977 1293 3980 1299 3984 1304 C
3989 1308 3995 1311 4001 1311 C
4007 1311 4013 1308 4018 1304 C
4022 1299 4025 1293 4025 1287 C
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F
4036 1326 m
4036 1320 4033 1314 4029 1309 C
4024 1305 4018 1302 4012 1302 C
4006 1302 4000 1305 3995 1309 C
3991 1314 3988 1320 3988 1326 C
3988 1332 3991 1338 3995 1343 C
4000 1347 4006 1350 4012 1350 C
4018 1350 4024 1347 4029 1343 C
4033 1338 4036 1332 4036 1326 C
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F
4048 1205 m
4048 1199 4045 1193 4041 1188 C
4036 1184 4030 1181 4024 1181 C
4018 1181 4012 1184 4007 1188 C
4003 1193 4000 1199 4000 1205 C
4000 1211 4003 1217 4007 1222 C
4012 1226 4018 1229 4024 1229 C
4030 1229 4036 1226 4041 1222 C
4045 1217 4048 1211 4048 1205 C
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F
4059 1286 m
4059 1280 4056 1274 4052 1269 C
4047 1265 4041 1262 4035 1262 C
4029 1262 4023 1265 4018 1269 C
4014 1274 4011 1280 4011 1286 C
4011 1292 4014 1298 4018 1303 C
4023 1307 4029 1310 4035 1310 C
4041 1310 4047 1307 4052 1303 C
4056 1298 4059 1292 4059 1286 C
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F
4071 1329 m
4071 1323 4068 1317 4064 1312 C
4059 1308 4053 1305 4047 1305 C
4041 1305 4035 1308 4030 1312 C
4026 1317 4023 1323 4023 1329 C
4023 1335 4026 1341 4030 1346 C
4035 1350 4041 1353 4047 1353 C
4053 1353 4059 1350 4064 1346 C
4068 1341 4071 1335 4071 1329 C
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F
4083 1209 m
4083 1203 4080 1197 4076 1192 C
4071 1188 4065 1185 4059 1185 C
4053 1185 4047 1188 4042 1192 C
4038 1197 4035 1203 4035 1209 C
4035 1215 4038 1221 4042 1226 C
4047 1230 4053 1233 4059 1233 C
4065 1233 4071 1230 4076 1226 C
4080 1221 4083 1215 4083 1209 C
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F
4094 1274 m
4094 1268 4091 1262 4087 1257 C
4082 1253 4076 1250 4070 1250 C
4064 1250 4058 1253 4053 1257 C
4049 1262 4046 1268 4046 1274 C
4046 1280 4049 1286 4053 1291 C
4058 1295 4064 1298 4070 1298 C
4076 1298 4082 1295 4087 1291 C
4091 1286 4094 1280 4094 1274 C
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F
4106 1337 m
4106 1331 4103 1325 4099 1320 C
4094 1316 4088 1313 4082 1313 C
4076 1313 4070 1316 4065 1320 C
4061 1325 4058 1331 4058 1337 C
4058 1343 4061 1349 4065 1354 C
4070 1358 4076 1361 4082 1361 C
4088 1361 4094 1358 4099 1354 C
4103 1349 4106 1343 4106 1337 C
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F
4117 1219 m
4117 1213 4114 1207 4110 1202 C
4105 1198 4099 1195 4093 1195 C
4087 1195 4081 1198 4076 1202 C
4072 1207 4069 1213 4069 1219 C
4069 1225 4072 1231 4076 1236 C
4081 1240 4087 1243 4093 1243 C
4099 1243 4105 1240 4110 1236 C
4114 1231 4117 1225 4117 1219 C
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F
4129 1253 m
4129 1247 4126 1241 4122 1236 C
4117 1232 4111 1229 4105 1229 C
4099 1229 4093 1232 4088 1236 C
4084 1241 4081 1247 4081 1253 C
4081 1259 4084 1265 4088 1270 C
4093 1274 4099 1277 4105 1277 C
4111 1277 4117 1274 4122 1270 C
4126 1265 4129 1259 4129 1253 C
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F
4140 1343 m
4140 1337 4137 1331 4133 1326 C
4128 1322 4122 1319 4116 1319 C
4110 1319 4104 1322 4099 1326 C
4095 1331 4092 1337 4092 1343 C
4092 1349 4095 1355 4099 1360 C
4104 1364 4110 1367 4116 1367 C
4122 1367 4128 1364 4133 1360 C
4137 1355 4140 1349 4140 1343 C
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F
4152 1243 m
4152 1237 4149 1231 4145 1226 C
4140 1222 4134 1219 4128 1219 C
4122 1219 4116 1222 4111 1226 C
4107 1231 4104 1237 4104 1243 C
4104 1249 4107 1255 4111 1260 C
4116 1264 4122 1267 4128 1267 C
4134 1267 4140 1264 4145 1260 C
4149 1255 4152 1249 4152 1243 C
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F
4163 1225 m
4163 1219 4160 1213 4156 1208 C
4151 1204 4145 1201 4139 1201 C
4133 1201 4127 1204 4122 1208 C
4118 1213 4115 1219 4115 1225 C
4115 1231 4118 1237 4122 1242 C
4127 1246 4133 1249 4139 1249 C
4145 1249 4151 1246 4156 1242 C
4160 1237 4163 1231 4163 1225 C
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F
4175 1338 m
4175 1332 4172 1326 4168 1321 C
4163 1317 4157 1314 4151 1314 C
4145 1314 4139 1317 4134 1321 C
4130 1326 4127 1332 4127 1338 C
4127 1344 4130 1350 4134 1355 C
4139 1359 4145 1362 4151 1362 C
4157 1362 4163 1359 4168 1355 C
4172 1350 4175 1344 4175 1338 C
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F
4187 1281 m
4187 1275 4184 1269 4180 1264 C
4175 1260 4169 1257 4163 1257 C
4157 1257 4151 1260 4146 1264 C
4142 1269 4139 1275 4139 1281 C
4139 1287 4142 1293 4146 1298 C
4151 1302 4157 1305 4163 1305 C
4169 1305 4175 1302 4180 1298 C
4184 1293 4187 1287 4187 1281 C
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F
4198 1202 m
4198 1196 4195 1190 4191 1185 C
4186 1181 4180 1178 4174 1178 C
4168 1178 4162 1181 4157 1185 C
4153 1190 4150 1196 4150 1202 C
4150 1208 4153 1214 4157 1219 C
4162 1223 4168 1226 4174 1226 C
4180 1226 4186 1223 4191 1219 C
4195 1214 4198 1208 4198 1202 C
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F
4210 1310 m
4210 1304 4207 1298 4203 1293 C
4198 1289 4192 1286 4186 1286 C
4180 1286 4174 1289 4169 1293 C
4165 1298 4162 1304 4162 1310 C
4162 1316 4165 1322 4169 1327 C
4174 1331 4180 1334 4186 1334 C
4192 1334 4198 1331 4203 1327 C
4207 1322 4210 1316 4210 1310 C
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F
4221 1324 m
4221 1318 4218 1312 4214 1307 C
4209 1303 4203 1300 4197 1300 C
4191 1300 4185 1303 4180 1307 C
4176 1312 4173 1318 4173 1324 C
4173 1330 4176 1336 4180 1341 C
4185 1345 4191 1348 4197 1348 C
4203 1348 4209 1345 4214 1341 C
4218 1336 4221 1330 4221 1324 C
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F
4233 1211 m
4233 1205 4230 1199 4226 1194 C
4221 1190 4215 1187 4209 1187 C
4203 1187 4197 1190 4192 1194 C
4188 1199 4185 1205 4185 1211 C
4185 1217 4188 1223 4192 1228 C
4197 1232 4203 1235 4209 1235 C
4215 1235 4221 1232 4226 1228 C
4230 1223 4233 1217 4233 1211 C
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F
4244 1255 m
4244 1249 4241 1243 4237 1238 C
4232 1234 4226 1231 4220 1231 C
4214 1231 4208 1234 4203 1238 C
4199 1243 4196 1249 4196 1255 C
4196 1261 4199 1267 4203 1272 C
4208 1276 4214 1279 4220 1279 C
4226 1279 4232 1276 4237 1272 C
4241 1267 4244 1261 4244 1255 C
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F
4256 1344 m
4256 1338 4253 1332 4249 1327 C
4244 1323 4238 1320 4232 1320 C
4226 1320 4220 1323 4215 1327 C
4211 1332 4208 1338 4208 1344 C
4208 1350 4211 1356 4215 1361 C
4220 1365 4226 1368 4232 1368 C
4238 1368 4244 1365 4249 1361 C
4253 1356 4256 1350 4256 1344 C
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F
4267 1264 m
4267 1258 4264 1252 4260 1247 C
4255 1243 4249 1240 4243 1240 C
4237 1240 4231 1243 4226 1247 C
4222 1252 4219 1258 4219 1264 C
4219 1270 4222 1276 4226 1281 C
4231 1285 4237 1288 4243 1288 C
4249 1288 4255 1285 4260 1281 C
4264 1276 4267 1270 4267 1264 C
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F
4279 1205 m
4279 1199 4276 1193 4272 1188 C
4267 1184 4261 1181 4255 1181 C
4249 1181 4243 1184 4238 1188 C
4234 1193 4231 1199 4231 1205 C
4231 1211 4234 1217 4238 1222 C
4243 1226 4249 1229 4255 1229 C
4261 1229 4267 1226 4272 1222 C
4276 1217 4279 1211 4279 1205 C
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F
4290 1310 m
4290 1304 4287 1298 4283 1293 C
4278 1289 4272 1286 4266 1286 C
4260 1286 4254 1289 4249 1293 C
4245 1298 4242 1304 4242 1310 C
4242 1316 4245 1322 4249 1327 C
4254 1331 4260 1334 4266 1334 C
4272 1334 4278 1331 4283 1327 C
4287 1322 4290 1316 4290 1310 C
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F
4302 1330 m
4302 1324 4299 1318 4295 1313 C
4290 1309 4284 1306 4278 1306 C
4272 1306 4266 1309 4261 1313 C
4257 1318 4254 1324 4254 1330 C
4254 1336 4257 1342 4261 1347 C
4266 1351 4272 1354 4278 1354 C
4284 1354 4290 1351 4295 1347 C
4299 1342 4302 1336 4302 1330 C
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F
4314 1221 m
4314 1215 4311 1209 4307 1204 C
4302 1200 4296 1197 4290 1197 C
4284 1197 4278 1200 4273 1204 C
4269 1209 4266 1215 4266 1221 C
4266 1227 4269 1233 4273 1238 C
4278 1242 4284 1245 4290 1245 C
4296 1245 4302 1242 4307 1238 C
4311 1233 4314 1227 4314 1221 C
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F
4325 1232 m
4325 1226 4322 1220 4318 1215 C
4313 1211 4307 1208 4301 1208 C
4295 1208 4289 1211 4284 1215 C
4280 1220 4277 1226 4277 1232 C
4277 1238 4280 1244 4284 1249 C
4289 1253 4295 1256 4301 1256 C
4307 1256 4313 1253 4318 1249 C
4322 1244 4325 1238 4325 1232 C
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F
4337 1335 m
4337 1329 4334 1323 4330 1318 C
4325 1314 4319 1311 4313 1311 C
4307 1311 4301 1314 4296 1318 C
4292 1323 4289 1329 4289 1335 C
4289 1341 4292 1347 4296 1352 C
4301 1356 4307 1359 4313 1359 C
4319 1359 4325 1356 4330 1352 C
4334 1347 4337 1341 4337 1335 C
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F
4348 1306 m
4348 1300 4345 1294 4341 1289 C
4336 1285 4330 1282 4324 1282 C
4318 1282 4312 1285 4307 1289 C
4303 1294 4300 1300 4300 1306 C
4300 1312 4303 1318 4307 1323 C
4312 1327 4318 1330 4324 1330 C
4330 1330 4336 1327 4341 1323 C
4345 1318 4348 1312 4348 1306 C
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F
4360 1205 m
4360 1199 4357 1193 4353 1188 C
4348 1184 4342 1181 4336 1181 C
4330 1181 4324 1184 4319 1188 C
4315 1193 4312 1199 4312 1205 C
4312 1211 4315 1217 4319 1222 C
4324 1226 4330 1229 4336 1229 C
4342 1229 4348 1226 4353 1222 C
4357 1217 4360 1211 4360 1205 C
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F
4371 1253 m
4371 1247 4368 1241 4364 1236 C
4359 1232 4353 1229 4347 1229 C
4341 1229 4335 1232 4330 1236 C
4326 1241 4323 1247 4323 1253 C
4323 1259 4326 1265 4330 1270 C
4335 1274 4341 1277 4347 1277 C
4353 1277 4359 1274 4364 1270 C
4368 1265 4371 1259 4371 1253 C
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F
4383 1342 m
4383 1336 4380 1330 4376 1325 C
4371 1321 4365 1318 4359 1318 C
4353 1318 4347 1321 4342 1325 C
4338 1330 4335 1336 4335 1342 C
4335 1348 4338 1354 4342 1359 C
4347 1363 4353 1366 4359 1366 C
4365 1366 4371 1363 4376 1359 C
4380 1354 4383 1348 4383 1342 C
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F
4394 1296 m
4394 1290 4391 1284 4387 1279 C
4382 1275 4376 1272 4370 1272 C
4364 1272 4358 1275 4353 1279 C
4349 1284 4346 1290 4346 1296 C
4346 1302 4349 1308 4353 1313 C
4358 1317 4364 1320 4370 1320 C
4376 1320 4382 1317 4387 1313 C
4391 1308 4394 1302 4394 1296 C
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F
4406 1203 m
4406 1197 4403 1191 4399 1186 C
4394 1182 4388 1179 4382 1179 C
4376 1179 4370 1182 4365 1186 C
4361 1191 4358 1197 4358 1203 C
4358 1209 4361 1215 4365 1220 C
4370 1224 4376 1227 4382 1227 C
4388 1227 4394 1224 4399 1220 C
4403 1215 4406 1209 4406 1203 C
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F
4418 1254 m
4418 1248 4415 1242 4411 1237 C
4406 1233 4400 1230 4394 1230 C
4388 1230 4382 1233 4377 1237 C
4373 1242 4370 1248 4370 1254 C
4370 1260 4373 1266 4377 1271 C
4382 1275 4388 1278 4394 1278 C
4400 1278 4406 1275 4411 1271 C
4415 1266 4418 1260 4418 1254 C
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F
4429 1341 m
4429 1335 4426 1329 4422 1324 C
4417 1320 4411 1317 4405 1317 C
4399 1317 4393 1320 4388 1324 C
4384 1329 4381 1335 4381 1341 C
4381 1347 4384 1353 4388 1358 C
4393 1362 4399 1365 4405 1365 C
4411 1365 4417 1362 4422 1358 C
4426 1353 4429 1347 4429 1341 C
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F
4441 1306 m
4441 1300 4438 1294 4434 1289 C
4429 1285 4423 1282 4417 1282 C
4411 1282 4405 1285 4400 1289 C
4396 1294 4393 1300 4393 1306 C
4393 1312 4396 1318 4400 1323 C
4405 1327 4411 1330 4417 1330 C
4423 1330 4429 1327 4434 1323 C
4438 1318 4441 1312 4441 1306 C
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F
4452 1210 m
4452 1204 4449 1198 4445 1193 C
4440 1189 4434 1186 4428 1186 C
4422 1186 4416 1189 4411 1193 C
4407 1198 4404 1204 4404 1210 C
4404 1216 4407 1222 4411 1227 C
4416 1231 4422 1234 4428 1234 C
4434 1234 4440 1231 4445 1227 C
4449 1222 4452 1216 4452 1210 C
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F
4464 1234 m
4464 1228 4461 1222 4457 1217 C
4452 1213 4446 1210 4440 1210 C
4434 1210 4428 1213 4423 1217 C
4419 1222 4416 1228 4416 1234 C
4416 1240 4419 1246 4423 1251 C
4428 1255 4434 1258 4440 1258 C
4446 1258 4452 1255 4457 1251 C
4461 1246 4464 1240 4464 1234 C
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F
4475 1328 m
4475 1322 4472 1316 4468 1311 C
4463 1307 4457 1304 4451 1304 C
4445 1304 4439 1307 4434 1311 C
4430 1316 4427 1322 4427 1328 C
4427 1334 4430 1340 4434 1345 C
4439 1349 4445 1352 4451 1352 C
4457 1352 4463 1349 4468 1345 C
4472 1340 4475 1334 4475 1328 C
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F
4487 1330 m
4487 1324 4484 1318 4480 1313 C
4475 1309 4469 1306 4463 1306 C
4457 1306 4451 1309 4446 1313 C
4442 1318 4439 1324 4439 1330 C
4439 1336 4442 1342 4446 1347 C
4451 1351 4457 1354 4463 1354 C
4469 1354 4475 1351 4480 1347 C
4484 1342 4487 1336 4487 1330 C
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F
4498 1239 m
4498 1233 4495 1227 4491 1222 C
4486 1218 4480 1215 4474 1215 C
4468 1215 4462 1218 4457 1222 C
4453 1227 4450 1233 4450 1239 C
4450 1245 4453 1251 4457 1256 C
4462 1260 4468 1263 4474 1263 C
4480 1263 4486 1260 4491 1256 C
4495 1251 4498 1245 4498 1239 C
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F
4510 1204 m
4510 1198 4507 1192 4503 1187 C
4498 1183 4492 1180 4486 1180 C
4480 1180 4474 1183 4469 1187 C
4465 1192 4462 1198 4462 1204 C
4462 1210 4465 1216 4469 1221 C
4474 1225 4480 1228 4486 1228 C
4492 1228 4498 1225 4503 1221 C
4507 1216 4510 1210 4510 1204 C
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F
4521 1288 m
4521 1282 4518 1276 4514 1271 C
4509 1267 4503 1264 4497 1264 C
4491 1264 4485 1267 4480 1271 C
4476 1276 4473 1282 4473 1288 C
4473 1294 4476 1300 4480 1305 C
4485 1309 4491 1312 4497 1312 C
4503 1312 4509 1309 4514 1305 C
4518 1300 4521 1294 4521 1288 C
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F
4533 1345 m
4533 1339 4530 1333 4526 1328 C
4521 1324 4515 1321 4509 1321 C
4503 1321 4497 1324 4492 1328 C
4488 1333 4485 1339 4485 1345 C
4485 1351 4488 1357 4492 1362 C
4497 1366 4503 1369 4509 1369 C
4515 1369 4521 1366 4526 1362 C
4530 1357 4533 1351 4533 1345 C
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F
4545 1302 m
4545 1296 4542 1290 4538 1285 C
4533 1281 4527 1278 4521 1278 C
4515 1278 4509 1281 4504 1285 C
4500 1290 4497 1296 4497 1302 C
4497 1308 4500 1314 4504 1319 C
4509 1323 4515 1326 4521 1326 C
4527 1326 4533 1323 4538 1319 C
4542 1314 4545 1308 4545 1302 C
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F
4556 1214 m
4556 1208 4553 1202 4549 1197 C
4544 1193 4538 1190 4532 1190 C
4526 1190 4520 1193 4515 1197 C
4511 1202 4508 1208 4508 1214 C
4508 1220 4511 1226 4515 1231 C
4520 1235 4526 1238 4532 1238 C
4538 1238 4544 1235 4549 1231 C
4553 1226 4556 1220 4556 1214 C
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F
4568 1218 m
4568 1212 4565 1206 4561 1201 C
4556 1197 4550 1194 4544 1194 C
4538 1194 4532 1197 4527 1201 C
4523 1206 4520 1212 4520 1218 C
4520 1224 4523 1230 4527 1235 C
4532 1239 4538 1242 4544 1242 C
4550 1242 4556 1239 4561 1235 C
4565 1230 4568 1224 4568 1218 C
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F
4579 1304 m
4579 1298 4576 1292 4572 1287 C
4567 1283 4561 1280 4555 1280 C
4549 1280 4543 1283 4538 1287 C
4534 1292 4531 1298 4531 1304 C
4531 1310 4534 1316 4538 1321 C
4543 1325 4549 1328 4555 1328 C
4561 1328 4567 1325 4572 1321 C
4576 1316 4579 1310 4579 1304 C
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F
4591 1345 m
4591 1339 4588 1333 4584 1328 C
4579 1324 4573 1321 4567 1321 C
4561 1321 4555 1324 4550 1328 C
4546 1333 4543 1339 4543 1345 C
4543 1351 4546 1357 4550 1362 C
4555 1366 4561 1369 4567 1369 C
4573 1369 4579 1366 4584 1362 C
4588 1357 4591 1351 4591 1345 C
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F
4602 1304 m
4602 1298 4599 1292 4595 1287 C
4590 1283 4584 1280 4578 1280 C
4572 1280 4566 1283 4561 1287 C
4557 1292 4554 1298 4554 1304 C
4554 1310 4557 1316 4561 1321 C
4566 1325 4572 1328 4578 1328 C
4584 1328 4590 1325 4595 1321 C
4599 1316 4602 1310 4602 1304 C
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F
4614 1221 m
4614 1215 4611 1209 4607 1204 C
4602 1200 4596 1197 4590 1197 C
4584 1197 4578 1200 4573 1204 C
4569 1209 4566 1215 4566 1221 C
4566 1227 4569 1233 4573 1238 C
4578 1242 4584 1245 4590 1245 C
4596 1245 4602 1242 4607 1238 C
4611 1233 4614 1227 4614 1221 C
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F
4625 1207 m
4625 1201 4622 1195 4618 1190 C
4613 1186 4607 1183 4601 1183 C
4595 1183 4589 1186 4584 1190 C
4580 1195 4577 1201 4577 1207 C
4577 1213 4580 1219 4584 1224 C
4589 1228 4595 1231 4601 1231 C
4607 1231 4613 1228 4618 1224 C
4622 1219 4625 1213 4625 1207 C
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F
4637 1281 m
4637 1275 4634 1269 4630 1264 C
4625 1260 4619 1257 4613 1257 C
4607 1257 4601 1260 4596 1264 C
4592 1269 4589 1275 4589 1281 C
4589 1287 4592 1293 4596 1298 C
4601 1302 4607 1305 4613 1305 C
4619 1305 4625 1302 4630 1298 C
4634 1293 4637 1287 4637 1281 C
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F
4648 1339 m
4648 1333 4645 1327 4641 1322 C
4636 1318 4630 1315 4624 1315 C
4618 1315 4612 1318 4607 1322 C
4603 1327 4600 1333 4600 1339 C
4600 1345 4603 1351 4607 1356 C
4612 1360 4618 1363 4624 1363 C
4630 1363 4636 1360 4641 1356 C
4645 1351 4648 1345 4648 1339 C
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F
4660 1335 m
4660 1329 4657 1323 4653 1318 C
4648 1314 4642 1311 4636 1311 C
4630 1311 4624 1314 4619 1318 C
4615 1323 4612 1329 4612 1335 C
4612 1341 4615 1347 4619 1352 C
4624 1356 4630 1359 4636 1359 C
4642 1359 4648 1356 4653 1352 C
4657 1347 4660 1341 4660 1335 C
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F
4672 1274 m
4672 1268 4669 1262 4665 1257 C
4660 1253 4654 1250 4648 1250 C
4642 1250 4636 1253 4631 1257 C
4627 1262 4624 1268 4624 1274 C
4624 1280 4627 1286 4631 1291 C
4636 1295 4642 1298 4648 1298 C
4654 1298 4660 1295 4665 1291 C
4669 1286 4672 1280 4672 1274 C
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F
4683 1207 m
4683 1201 4680 1195 4676 1190 C
4671 1186 4665 1183 4659 1183 C
4653 1183 4647 1186 4642 1190 C
4638 1195 4635 1201 4635 1207 C
4635 1213 4638 1219 4642 1224 C
4647 1228 4653 1231 4659 1231 C
4665 1231 4671 1228 4676 1224 C
4680 1219 4683 1213 4683 1207 C
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F
4695 1215 m
4695 1209 4692 1203 4688 1198 C
4683 1194 4677 1191 4671 1191 C
4665 1191 4659 1194 4654 1198 C
4650 1203 4647 1209 4647 1215 C
4647 1221 4650 1227 4654 1232 C
4659 1236 4665 1239 4671 1239 C
4677 1239 4683 1236 4688 1232 C
4692 1227 4695 1221 4695 1215 C
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F
4706 1283 m
4706 1277 4703 1271 4699 1266 C
4694 1262 4688 1259 4682 1259 C
4676 1259 4670 1262 4665 1266 C
4661 1271 4658 1277 4658 1283 C
4658 1289 4661 1295 4665 1300 C
4670 1304 4676 1307 4682 1307 C
4688 1307 4694 1304 4699 1300 C
4703 1295 4706 1289 4706 1283 C
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F
4718 1334 m
4718 1328 4715 1322 4711 1317 C
4706 1313 4700 1310 4694 1310 C
4688 1310 4682 1313 4677 1317 C
4673 1322 4670 1328 4670 1334 C
4670 1340 4673 1346 4677 1351 C
4682 1355 4688 1358 4694 1358 C
4700 1358 4706 1355 4711 1351 C
4715 1346 4718 1340 4718 1334 C
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F
4729 1343 m
4729 1337 4726 1331 4722 1326 C
4717 1322 4711 1319 4705 1319 C
4699 1319 4693 1322 4688 1326 C
4684 1331 4681 1337 4681 1343 C
4681 1349 4684 1355 4688 1360 C
4693 1364 4699 1367 4705 1367 C
4711 1367 4717 1364 4722 1360 C
4726 1355 4729 1349 4729 1343 C
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F
4741 1312 m
4741 1306 4738 1300 4734 1295 C
4729 1291 4723 1288 4717 1288 C
4711 1288 4705 1291 4700 1295 C
4696 1300 4693 1306 4693 1312 C
4693 1318 4696 1324 4700 1329 C
4705 1333 4711 1336 4717 1336 C
4723 1336 4729 1333 4734 1329 C
4738 1324 4741 1318 4741 1312 C
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F
4752 1254 m
4752 1248 4749 1242 4745 1237 C
4740 1233 4734 1230 4728 1230 C
4722 1230 4716 1233 4711 1237 C
4707 1242 4704 1248 4704 1254 C
4704 1260 4707 1266 4711 1271 C
4716 1275 4722 1278 4728 1278 C
4734 1278 4740 1275 4745 1271 C
4749 1266 4752 1260 4752 1254 C
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F
4764 1205 m
4764 1199 4761 1193 4757 1188 C
4752 1184 4746 1181 4740 1181 C
4734 1181 4728 1184 4723 1188 C
4719 1193 4716 1199 4716 1205 C
4716 1211 4719 1217 4723 1222 C
4728 1226 4734 1229 4740 1229 C
4746 1229 4752 1226 4757 1222 C
4761 1217 4764 1211 4764 1205 C
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F
4776 1214 m
4776 1208 4773 1202 4769 1197 C
4764 1193 4758 1190 4752 1190 C
4746 1190 4740 1193 4735 1197 C
4731 1202 4728 1208 4728 1214 C
4728 1220 4731 1226 4735 1231 C
4740 1235 4746 1238 4752 1238 C
4758 1238 4764 1235 4769 1231 C
4773 1226 4776 1220 4776 1214 C
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F
4787 1267 m
4787 1261 4784 1255 4780 1250 C
4775 1246 4769 1243 4763 1243 C
4757 1243 4751 1246 4746 1250 C
4742 1255 4739 1261 4739 1267 C
4739 1273 4742 1279 4746 1284 C
4751 1288 4757 1291 4763 1291 C
4769 1291 4775 1288 4780 1284 C
4784 1279 4787 1273 4787 1267 C
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F
4799 1313 m
4799 1307 4796 1301 4792 1296 C
4787 1292 4781 1289 4775 1289 C
4769 1289 4763 1292 4758 1296 C
4754 1301 4751 1307 4751 1313 C
4751 1319 4754 1325 4758 1330 C
4763 1334 4769 1337 4775 1337 C
4781 1337 4787 1334 4792 1330 C
4796 1325 4799 1319 4799 1313 C
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F
4810 1336 m
4810 1330 4807 1324 4803 1319 C
4798 1315 4792 1312 4786 1312 C
4780 1312 4774 1315 4769 1319 C
4765 1324 4762 1330 4762 1336 C
4762 1342 4765 1348 4769 1353 C
4774 1357 4780 1360 4786 1360 C
4792 1360 4798 1357 4803 1353 C
4807 1348 4810 1342 4810 1336 C
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F
4822 1342 m
4822 1336 4819 1330 4815 1325 C
4810 1321 4804 1318 4798 1318 C
4792 1318 4786 1321 4781 1325 C
4777 1330 4774 1336 4774 1342 C
4774 1348 4777 1354 4781 1359 C
4786 1363 4792 1366 4798 1366 C
4804 1366 4810 1363 4815 1359 C
4819 1354 4822 1348 4822 1342 C
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F
4833 1339 m
4833 1333 4830 1327 4826 1322 C
4821 1318 4815 1315 4809 1315 C
4803 1315 4797 1318 4792 1322 C
4788 1327 4785 1333 4785 1339 C
4785 1345 4788 1351 4792 1356 C
4797 1360 4803 1363 4809 1363 C
4815 1363 4821 1360 4826 1356 C
4830 1351 4833 1345 4833 1339 C
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F
4845 1332 m
4845 1326 4842 1320 4838 1315 C
4833 1311 4827 1308 4821 1308 C
4815 1308 4809 1311 4804 1315 C
4800 1320 4797 1326 4797 1332 C
4797 1338 4800 1344 4804 1349 C
4809 1353 4815 1356 4821 1356 C
4827 1356 4833 1353 4838 1349 C
4842 1344 4845 1338 4845 1332 C
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F
4856 1324 m
4856 1318 4853 1312 4849 1307 C
4844 1303 4838 1300 4832 1300 C
4826 1300 4820 1303 4815 1307 C
4811 1312 4808 1318 4808 1324 C
4808 1330 4811 1336 4815 1341 C
4820 1345 4826 1348 4832 1348 C
4838 1348 4844 1345 4849 1341 C
4853 1336 4856 1330 4856 1324 C
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F
4868 1315 m
4868 1309 4865 1303 4861 1298 C
4856 1294 4850 1291 4844 1291 C
4838 1291 4832 1294 4827 1298 C
4823 1303 4820 1309 4820 1315 C
4820 1321 4823 1327 4827 1332 C
4832 1336 4838 1339 4844 1339 C
4850 1339 4856 1336 4861 1332 C
4865 1327 4868 1321 4868 1315 C
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F
4879 1307 m
4879 1301 4876 1295 4872 1290 C
4867 1286 4861 1283 4855 1283 C
4849 1283 4843 1286 4838 1290 C
4834 1295 4831 1301 4831 1307 C
4831 1313 4834 1319 4838 1324 C
4843 1328 4849 1331 4855 1331 C
4861 1331 4867 1328 4872 1324 C
4876 1319 4879 1313 4879 1307 C
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F
4891 1299 m
4891 1293 4888 1287 4884 1282 C
4879 1278 4873 1275 4867 1275 C
4861 1275 4855 1278 4850 1282 C
4846 1287 4843 1293 4843 1299 C
4843 1305 4846 1311 4850 1316 C
4855 1320 4861 1323 4867 1323 C
4873 1323 4879 1320 4884 1316 C
4888 1311 4891 1305 4891 1299 C
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F
4903 1292 m
4903 1286 4900 1280 4896 1275 C
4891 1271 4885 1268 4879 1268 C
4873 1268 4867 1271 4862 1275 C
4858 1280 4855 1286 4855 1292 C
4855 1298 4858 1304 4862 1309 C
4867 1313 4873 1316 4879 1316 C
4885 1316 4891 1313 4896 1309 C
4900 1304 4903 1298 4903 1292 C
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F
4914 1287 m
4914 1281 4911 1275 4907 1270 C
4902 1266 4896 1263 4890 1263 C
4884 1263 4878 1266 4873 1270 C
4869 1275 4866 1281 4866 1287 C
4866 1293 4869 1299 4873 1304 C
4878 1308 4884 1311 4890 1311 C
4896 1311 4902 1308 4907 1304 C
4911 1299 4914 1293 4914 1287 C
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F
4926 1282 m
4926 1276 4923 1270 4919 1265 C
4914 1261 4908 1258 4902 1258 C
4896 1258 4890 1261 4885 1265 C
4881 1270 4878 1276 4878 1282 C
4878 1288 4881 1294 4885 1299 C
4890 1303 4896 1306 4902 1306 C
4908 1306 4914 1303 4919 1299 C
4923 1294 4926 1288 4926 1282 C
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F
4937 1279 m
4937 1273 4934 1267 4930 1262 C
4925 1258 4919 1255 4913 1255 C
4907 1255 4901 1258 4896 1262 C
4892 1267 4889 1273 4889 1279 C
4889 1285 4892 1291 4896 1296 C
4901 1300 4907 1303 4913 1303 C
4919 1303 4925 1300 4930 1296 C
4934 1291 4937 1285 4937 1279 C
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F
4949 1276 m
4949 1270 4946 1264 4942 1259 C
4937 1255 4931 1252 4925 1252 C
4919 1252 4913 1255 4908 1259 C
4904 1264 4901 1270 4901 1276 C
4901 1282 4904 1288 4908 1293 C
4913 1297 4919 1300 4925 1300 C
4931 1300 4937 1297 4942 1293 C
4946 1288 4949 1282 4949 1276 C
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F
4960 1274 m
4960 1268 4957 1262 4953 1257 C
4948 1253 4942 1250 4936 1250 C
4930 1250 4924 1253 4919 1257 C
4915 1262 4912 1268 4912 1274 C
4912 1280 4915 1286 4919 1291 C
4924 1295 4930 1298 4936 1298 C
4942 1298 4948 1295 4953 1291 C
4957 1286 4960 1280 4960 1274 C
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F
4972 1273 m
4972 1267 4969 1261 4965 1256 C
4960 1252 4954 1249 4948 1249 C
4942 1249 4936 1252 4931 1256 C
4927 1261 4924 1267 4924 1273 C
4924 1279 4927 1285 4931 1290 C
4936 1294 4942 1297 4948 1297 C
4954 1297 4960 1294 4965 1290 C
4969 1285 4972 1279 4972 1273 C
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F
4983 1273 m
4983 1267 4980 1261 4976 1256 C
4971 1252 4965 1249 4959 1249 C
4953 1249 4947 1252 4942 1256 C
4938 1261 4935 1267 4935 1273 C
4935 1279 4938 1285 4942 1290 C
4947 1294 4953 1297 4959 1297 C
4965 1297 4971 1294 4976 1290 C
4980 1285 4983 1279 4983 1273 C
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F
4995 1272 m
4995 1266 4992 1260 4988 1255 C
4983 1251 4977 1248 4971 1248 C
4965 1248 4959 1251 4954 1255 C
4950 1260 4947 1266 4947 1272 C
4947 1278 4950 1284 4954 1289 C
4959 1293 4965 1296 4971 1296 C
4977 1296 4983 1293 4988 1289 C
4992 1284 4995 1278 4995 1272 C
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F
5006 1272 m
5006 1266 5003 1260 4999 1255 C
4994 1251 4988 1248 4982 1248 C
4976 1248 4970 1251 4965 1255 C
4961 1260 4958 1266 4958 1272 C
4958 1278 4961 1284 4965 1289 C
4970 1293 4976 1296 4982 1296 C
4988 1296 4994 1293 4999 1289 C
5003 1284 5006 1278 5006 1272 C
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F
5018 1272 m
5018 1266 5015 1260 5011 1255 C
5006 1251 5000 1248 4994 1248 C
4988 1248 4982 1251 4977 1255 C
4973 1260 4970 1266 4970 1272 C
4970 1278 4973 1284 4977 1289 C
4982 1293 4988 1296 4994 1296 C
5000 1296 5006 1293 5011 1289 C
5015 1284 5018 1278 5018 1272 C
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F
5030 1272 m
5030 1266 5027 1260 5023 1255 C
5018 1251 5012 1248 5006 1248 C
5000 1248 4994 1251 4989 1255 C
4985 1260 4982 1266 4982 1272 C
4982 1278 4985 1284 4989 1289 C
4994 1293 5000 1296 5006 1296 C
5012 1296 5018 1293 5023 1289 C
5027 1284 5030 1278 5030 1272 C
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F
5041 1272 m
5041 1266 5038 1260 5034 1255 C
5029 1251 5023 1248 5017 1248 C
5011 1248 5005 1251 5000 1255 C
4996 1260 4993 1266 4993 1272 C
4993 1278 4996 1284 5000 1289 C
5005 1293 5011 1296 5017 1296 C
5023 1296 5029 1293 5034 1289 C
5038 1284 5041 1278 5041 1272 C
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F
5053 1272 m
5053 1266 5050 1260 5046 1255 C
5041 1251 5035 1248 5029 1248 C
5023 1248 5017 1251 5012 1255 C
5008 1260 5005 1266 5005 1272 C
5005 1278 5008 1284 5012 1289 C
5017 1293 5023 1296 5029 1296 C
5035 1296 5041 1293 5046 1289 C
5050 1284 5053 1278 5053 1272 C
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F
5064 1272 m
5064 1266 5061 1260 5057 1255 C
5052 1251 5046 1248 5040 1248 C
5034 1248 5028 1251 5023 1255 C
5019 1260 5016 1266 5016 1272 C
5016 1278 5019 1284 5023 1289 C
5028 1293 5034 1296 5040 1296 C
5046 1296 5052 1293 5057 1289 C
5061 1284 5064 1278 5064 1272 C
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F
5076 1272 m
5076 1266 5073 1260 5069 1255 C
5064 1251 5058 1248 5052 1248 C
5046 1248 5040 1251 5035 1255 C
5031 1260 5028 1266 5028 1272 C
5028 1278 5031 1284 5035 1289 C
5040 1293 5046 1296 5052 1296 C
5058 1296 5064 1293 5069 1289 C
5073 1284 5076 1278 5076 1272 C
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F
5087 1272 m
5087 1266 5084 1260 5080 1255 C
5075 1251 5069 1248 5063 1248 C
5057 1248 5051 1251 5046 1255 C
5042 1260 5039 1266 5039 1272 C
5039 1278 5042 1284 5046 1289 C
5051 1293 5057 1296 5063 1296 C
5069 1296 5075 1293 5080 1289 C
5084 1284 5087 1278 5087 1272 C
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F
5099 1272 m
5099 1266 5096 1260 5092 1255 C
5087 1251 5081 1248 5075 1248 C
5069 1248 5063 1251 5058 1255 C
5054 1260 5051 1266 5051 1272 C
5051 1278 5054 1284 5058 1289 C
5063 1293 5069 1296 5075 1296 C
5081 1296 5087 1293 5092 1289 C
5096 1284 5099 1278 5099 1272 C
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F
5110 1272 m
5110 1266 5107 1260 5103 1255 C
5098 1251 5092 1248 5086 1248 C
5080 1248 5074 1251 5069 1255 C
5065 1260 5062 1266 5062 1272 C
5062 1278 5065 1284 5069 1289 C
5074 1293 5080 1296 5086 1296 C
5092 1296 5098 1293 5103 1289 C
5107 1284 5110 1278 5110 1272 C
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F
5122 1272 m
5122 1266 5119 1260 5115 1255 C
5110 1251 5104 1248 5098 1248 C
5092 1248 5086 1251 5081 1255 C
5077 1260 5074 1266 5074 1272 C
5074 1278 5077 1284 5081 1289 C
5086 1293 5092 1296 5098 1296 C
5104 1296 5110 1293 5115 1289 C
5119 1284 5122 1278 5122 1272 C
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F
5134 1272 m
5134 1266 5131 1260 5127 1255 C
5122 1251 5116 1248 5110 1248 C
5104 1248 5098 1251 5093 1255 C
5089 1260 5086 1266 5086 1272 C
5086 1278 5089 1284 5093 1289 C
5098 1293 5104 1296 5110 1296 C
5116 1296 5122 1293 5127 1289 C
5131 1284 5134 1278 5134 1272 C
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F
5145 1272 m
5145 1266 5142 1260 5138 1255 C
5133 1251 5127 1248 5121 1248 C
5115 1248 5109 1251 5104 1255 C
5100 1260 5097 1266 5097 1272 C
5097 1278 5100 1284 5104 1289 C
5109 1293 5115 1296 5121 1296 C
5127 1296 5133 1293 5138 1289 C
5142 1284 5145 1278 5145 1272 C
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F
5157 1272 m
5157 1266 5154 1260 5150 1255 C
5145 1251 5139 1248 5133 1248 C
5127 1248 5121 1251 5116 1255 C
5112 1260 5109 1266 5109 1272 C
5109 1278 5112 1284 5116 1289 C
5121 1293 5127 1296 5133 1296 C
5139 1296 5145 1293 5150 1289 C
5154 1284 5157 1278 5157 1272 C
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F
5168 1272 m
5168 1266 5165 1260 5161 1255 C
5156 1251 5150 1248 5144 1248 C
5138 1248 5132 1251 5127 1255 C
5123 1260 5120 1266 5120 1272 C
5120 1278 5123 1284 5127 1289 C
5132 1293 5138 1296 5144 1296 C
5150 1296 5156 1293 5161 1289 C
5165 1284 5168 1278 5168 1272 C
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F
5180 1272 m
5180 1266 5177 1260 5173 1255 C
5168 1251 5162 1248 5156 1248 C
5150 1248 5144 1251 5139 1255 C
5135 1260 5132 1266 5132 1272 C
5132 1278 5135 1284 5139 1289 C
5144 1293 5150 1296 5156 1296 C
5162 1296 5168 1293 5173 1289 C
5177 1284 5180 1278 5180 1272 C
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F
5191 1272 m
5191 1266 5188 1260 5184 1255 C
5179 1251 5173 1248 5167 1248 C
5161 1248 5155 1251 5150 1255 C
5146 1260 5143 1266 5143 1272 C
5143 1278 5146 1284 5150 1289 C
5155 1293 5161 1296 5167 1296 C
5173 1296 5179 1293 5184 1289 C
5188 1284 5191 1278 5191 1272 C
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F
5203 1272 m
5203 1266 5200 1260 5196 1255 C
5191 1251 5185 1248 5179 1248 C
5173 1248 5167 1251 5162 1255 C
5158 1260 5155 1266 5155 1272 C
5155 1278 5158 1284 5162 1289 C
5167 1293 5173 1296 5179 1296 C
5185 1296 5191 1293 5196 1289 C
5200 1284 5203 1278 5203 1272 C
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F
5214 1272 m
5214 1266 5211 1260 5207 1255 C
5202 1251 5196 1248 5190 1248 C
5184 1248 5178 1251 5173 1255 C
5169 1260 5166 1266 5166 1272 C
5166 1278 5169 1284 5173 1289 C
5178 1293 5184 1296 5190 1296 C
5196 1296 5202 1293 5207 1289 C
5211 1284 5214 1278 5214 1272 C
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F
5226 1272 m
5226 1266 5223 1260 5219 1255 C
5214 1251 5208 1248 5202 1248 C
5196 1248 5190 1251 5185 1255 C
5181 1260 5178 1266 5178 1272 C
5178 1278 5181 1284 5185 1289 C
5190 1293 5196 1296 5202 1296 C
5208 1296 5214 1293 5219 1289 C
5223 1284 5226 1278 5226 1272 C
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F
5237 1272 m
5237 1266 5234 1260 5230 1255 C
5225 1251 5219 1248 5213 1248 C
5207 1248 5201 1251 5196 1255 C
5192 1260 5189 1266 5189 1272 C
5189 1278 5192 1284 5196 1289 C
5201 1293 5207 1296 5213 1296 C
5219 1296 5225 1293 5230 1289 C
5234 1284 5237 1278 5237 1272 C
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F
5249 1272 m
5249 1266 5246 1260 5242 1255 C
5237 1251 5231 1248 5225 1248 C
5219 1248 5213 1251 5208 1255 C
5204 1260 5201 1266 5201 1272 C
5201 1278 5204 1284 5208 1289 C
5213 1293 5219 1296 5225 1296 C
5231 1296 5237 1293 5242 1289 C
5246 1284 5249 1278 5249 1272 C
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F
5261 1272 m
5261 1266 5258 1260 5254 1255 C
5249 1251 5243 1248 5237 1248 C
5231 1248 5225 1251 5220 1255 C
5216 1260 5213 1266 5213 1272 C
5213 1278 5216 1284 5220 1289 C
5225 1293 5231 1296 5237 1296 C
5243 1296 5249 1293 5254 1289 C
5258 1284 5261 1278 5261 1272 C
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F
5272 1272 m
5272 1266 5269 1260 5265 1255 C
5260 1251 5254 1248 5248 1248 C
5242 1248 5236 1251 5231 1255 C
5227 1260 5224 1266 5224 1272 C
5224 1278 5227 1284 5231 1289 C
5236 1293 5242 1296 5248 1296 C
5254 1296 5260 1293 5265 1289 C
5269 1284 5272 1278 5272 1272 C
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F
5284 1272 m
5284 1266 5281 1260 5277 1255 C
5272 1251 5266 1248 5260 1248 C
5254 1248 5248 1251 5243 1255 C
5239 1260 5236 1266 5236 1272 C
5236 1278 5239 1284 5243 1289 C
5248 1293 5254 1296 5260 1296 C
5266 1296 5272 1293 5277 1289 C
5281 1284 5284 1278 5284 1272 C
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F
5295 1272 m
5295 1266 5292 1260 5288 1255 C
5283 1251 5277 1248 5271 1248 C
5265 1248 5259 1251 5254 1255 C
5250 1260 5247 1266 5247 1272 C
5247 1278 5250 1284 5254 1289 C
5259 1293 5265 1296 5271 1296 C
5277 1296 5283 1293 5288 1289 C
5292 1284 5295 1278 5295 1272 C
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F
5307 1272 m
5307 1266 5304 1260 5300 1255 C
5295 1251 5289 1248 5283 1248 C
5277 1248 5271 1251 5266 1255 C
5262 1260 5259 1266 5259 1272 C
5259 1278 5262 1284 5266 1289 C
5271 1293 5277 1296 5283 1296 C
5289 1296 5295 1293 5300 1289 C
5304 1284 5307 1278 5307 1272 C
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F
5318 1272 m
5318 1266 5315 1260 5311 1255 C
5306 1251 5300 1248 5294 1248 C
5288 1248 5282 1251 5277 1255 C
5273 1260 5270 1266 5270 1272 C
5270 1278 5273 1284 5277 1289 C
5282 1293 5288 1296 5294 1296 C
5300 1296 5306 1293 5311 1289 C
5315 1284 5318 1278 5318 1272 C
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F
5330 1272 m
5330 1266 5327 1260 5323 1255 C
5318 1251 5312 1248 5306 1248 C
5300 1248 5294 1251 5289 1255 C
5285 1260 5282 1266 5282 1272 C
5282 1278 5285 1284 5289 1289 C
5294 1293 5300 1296 5306 1296 C
5312 1296 5318 1293 5323 1289 C
5327 1284 5330 1278 5330 1272 C
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F
5341 1272 m
5341 1266 5338 1260 5334 1255 C
5329 1251 5323 1248 5317 1248 C
5311 1248 5305 1251 5300 1255 C
5296 1260 5293 1266 5293 1272 C
5293 1278 5296 1284 5300 1289 C
5305 1293 5311 1296 5317 1296 C
5323 1296 5329 1293 5334 1289 C
5338 1284 5341 1278 5341 1272 C
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F
5353 1272 m
5353 1266 5350 1260 5346 1255 C
5341 1251 5335 1248 5329 1248 C
5323 1248 5317 1251 5312 1255 C
5308 1260 5305 1266 5305 1272 C
5305 1278 5308 1284 5312 1289 C
5317 1293 5323 1296 5329 1296 C
5335 1296 5341 1293 5346 1289 C
5350 1284 5353 1278 5353 1272 C
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F
5365 1272 m
5365 1266 5362 1260 5358 1255 C
5353 1251 5347 1248 5341 1248 C
5335 1248 5329 1251 5324 1255 C
5320 1260 5317 1266 5317 1272 C
5317 1278 5320 1284 5324 1289 C
5329 1293 5335 1296 5341 1296 C
5347 1296 5353 1293 5358 1289 C
5362 1284 5365 1278 5365 1272 C
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F
5376 1272 m
5376 1266 5373 1260 5369 1255 C
5364 1251 5358 1248 5352 1248 C
5346 1248 5340 1251 5335 1255 C
5331 1260 5328 1266 5328 1272 C
5328 1278 5331 1284 5335 1289 C
5340 1293 5346 1296 5352 1296 C
5358 1296 5364 1293 5369 1289 C
5373 1284 5376 1278 5376 1272 C
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F
5388 1272 m
5388 1266 5385 1260 5381 1255 C
5376 1251 5370 1248 5364 1248 C
5358 1248 5352 1251 5347 1255 C
5343 1260 5340 1266 5340 1272 C
5340 1278 5343 1284 5347 1289 C
5352 1293 5358 1296 5364 1296 C
5370 1296 5376 1293 5381 1289 C
5385 1284 5388 1278 5388 1272 C
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F
5399 1272 m
5399 1266 5396 1260 5392 1255 C
5387 1251 5381 1248 5375 1248 C
5369 1248 5363 1251 5358 1255 C
5354 1260 5351 1266 5351 1272 C
5351 1278 5354 1284 5358 1289 C
5363 1293 5369 1296 5375 1296 C
5381 1296 5387 1293 5392 1289 C
5396 1284 5399 1278 5399 1272 C
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F
5411 1272 m
5411 1266 5408 1260 5404 1255 C
5399 1251 5393 1248 5387 1248 C
5381 1248 5375 1251 5370 1255 C
5366 1260 5363 1266 5363 1272 C
5363 1278 5366 1284 5370 1289 C
5375 1293 5381 1296 5387 1296 C
5393 1296 5399 1293 5404 1289 C
5408 1284 5411 1278 5411 1272 C
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F
5422 1272 m
5422 1266 5419 1260 5415 1255 C
5410 1251 5404 1248 5398 1248 C
5392 1248 5386 1251 5381 1255 C
5377 1260 5374 1266 5374 1272 C
5374 1278 5377 1284 5381 1289 C
5386 1293 5392 1296 5398 1296 C
5404 1296 5410 1293 5415 1289 C
5419 1284 5422 1278 5422 1272 C
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F
5434 1272 m
5434 1266 5431 1260 5427 1255 C
5422 1251 5416 1248 5410 1248 C
5404 1248 5398 1251 5393 1255 C
5389 1260 5386 1266 5386 1272 C
5386 1278 5389 1284 5393 1289 C
5398 1293 5404 1296 5410 1296 C
5416 1296 5422 1293 5427 1289 C
5431 1284 5434 1278 5434 1272 C
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F
5445 1272 m
5445 1266 5442 1260 5438 1255 C
5433 1251 5427 1248 5421 1248 C
5415 1248 5409 1251 5404 1255 C
5400 1260 5397 1266 5397 1272 C
5397 1278 5400 1284 5404 1289 C
5409 1293 5415 1296 5421 1296 C
5427 1296 5433 1293 5438 1289 C
5442 1284 5445 1278 5445 1272 C
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F
5457 1272 m
5457 1266 5454 1260 5450 1255 C
5445 1251 5439 1248 5433 1248 C
5427 1248 5421 1251 5416 1255 C
5412 1260 5409 1266 5409 1272 C
5409 1278 5412 1284 5416 1289 C
5421 1293 5427 1296 5433 1296 C
5439 1296 5445 1293 5450 1289 C
5454 1284 5457 1278 5457 1272 C
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F
5468 1272 m
5468 1266 5465 1260 5461 1255 C
5456 1251 5450 1248 5444 1248 C
5438 1248 5432 1251 5427 1255 C
5423 1260 5420 1266 5420 1272 C
5420 1278 5423 1284 5427 1289 C
5432 1293 5438 1296 5444 1296 C
5450 1296 5456 1293 5461 1289 C
5465 1284 5468 1278 5468 1272 C
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F
5480 1272 m
5480 1266 5477 1260 5473 1255 C
5468 1251 5462 1248 5456 1248 C
5450 1248 5444 1251 5439 1255 C
5435 1260 5432 1266 5432 1272 C
5432 1278 5435 1284 5439 1289 C
5444 1293 5450 1296 5456 1296 C
5462 1296 5468 1293 5473 1289 C
5477 1284 5480 1278 5480 1272 C
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F
P
16 w
0 g
[ ] 0 setdash
2 setlinecap
0 setlinejoin
10 setmiterlimit
%Trailer
%EOF
---------------0804291559766--
