\documentstyle[preprint,aps]{revtex}
\def\btt#1{{\tt$\backslash$#1}}
\begin{document}
\draft
\preprint{}
\title{Spinodal Decomposition in Binary Gases}
\author{S. Bastea and J.L. Lebowitz}
\address{Department of Physics and Mathematics, Rutgers University,
Piscataway, New Jersey, 08855-0849}
\maketitle
\begin{abstract}
We carried out three-dimensional simulations, with about
$1.4\times10^6$ particles, of phase segregation in a low density
binary fluid mixture, described mesoscopically by energy and momentum
conserving Boltzmann-Vlasov equations. Using a combination of Direct
Simulation Monte Carlo(DSMC) for the short range collisions and a
version of Particle-In-Cell(PIC) evolution for the smooth long range
interaction, we found dynamical scaling after the ratio of the
interface thickness(whose shape is described approximately by a
hyperbolic tangent profile) to the domain size is less than
$\sim0.1$. The scaling length $R(t)$ grows at late times like
$t^\alpha$, with $\alpha=1$ for critical quenches and
$\alpha=\frac{1}{3}$ for off-critical ones. We also measured the
variation of temperature, total particle density and hydrodynamic
velocity during the segregation process.
\end{abstract}
\pacs{PACS numbers:  64.75.+g, 68.10.-m, 47.70.Nd}

\widetext
%\section{Introduction}
The process of phase segregation through which a system evolves towards
equilibrium following a temperature quench from a homogeneous phase
into a two phase region of its phase diagram has been of continuing interest
during the last decades \cite{gunton1},
but many problems still remain to be solved. 
This is particularly so for fluids,when particle,
momentum and energy densities are conserved locally; these are
currently the focus of both numerical studies 
\cite{ma1,valls1,frank1,wu1,bastea1,toxvaerd2} and  
micro-gravity experiments \cite{beysans1,perrot1}. 

In this paper we present computer simulations of spinodal
decomposition in a three-dimensional mixture of two kinds of particles that
we label 1 and 2 using a novel microscopic dynamics and computational
scheme. The particles interact with each
other through short range interactions modeled here by hard spheres having
the same mass $m$ and diameter $d$. Particles of different kinds
interact also through a long range repulsive Kac potential,
$V(r)=\gamma^{3}U(\gamma r)$. The equilibrium properties of such
a system are well understood, there is even a rigorous proof of a phase
transition at low temperatures to an immiscible state \cite{lieb},
which in the limit
$\gamma\rightarrow0$ \cite{lebowitz1}, is described by mean
field theory. 
When the density $n$
is low enough, $nd^3\ll1$, and the potential sufficiently long ranged,
$n\gamma^{-3}\gg1$, the free energy of the system is well approximated
by $F= 
k_BT\int[n_1(\vec r)\ln n_1(\vec r)+n_2(\vec r)\ln n_2(\vec r)]d\vec
r + \int V(|\vec r_1-\vec r_2|)n_1(\vec r_1)n_2(\vec
r_2)d\vec r_1 d\vec r_2$ and the $\gamma\rightarrow0$ critical
temperature, which should be an upper bound for $T_c^\gamma$ at
$\gamma>0$, is given by
$k_BT_c^0=\frac{1}{2}n\int U(r)d\vec r$. In this regime the 
dynamical evolution of the system should be well described by two 
coupled Boltzmann - Vlasov equations:
\begin{equation}
\frac{\partial f_i}{\partial t}+\vec v \cdot \frac{\partial
f_i}{\partial \vec r}+\frac{\vec F_i}{m}\cdot\frac{\partial
f_i}{\partial \vec v}=J[f_i,f_1 + f_2],\;\;\;\;\;i=1,2
\end{equation}
where $f_i(\vec r,\vec v,t)$ are the one-particle distribution functions, 
$\vec F_i(\vec r,t)=-\nabla\int V(|\vec r-\vec r\prime|)n_j(\vec
r\prime)d\vec r\prime$, $n_j(\vec r\prime)=\int f_j(\vec r\prime, \vec v,
t)d\vec v$ with $i,j=1,2$,$i\neq j$, and $J[f,g]$ is
the Boltzmann collision operator for hard core interactions \cite{chapman1}.
Kinetic equations of this type have been proposed in \cite{sobrino}, 
and if the system is quenched inside
the coexistence region they will describe gas-gas segregation
\cite{schouten} into two phases, one rich in particles
of type 1 and the other rich in particles of type 2. 
(Examples of gas mixtures that have a miscibility gap are
helium-hydrogen, helium-nitrogen, neon-xenon etc. \cite{schouten}.)
We believe that the model contains the essential features of phase 
separation in general binary fluid mixtures.

To simulate our system we modeled the Boltzmann collisional part using
a stochastic
algorithm due to Bird \cite{bird1}, known as Direct Simulation Monte
Carlo (DSMC), while for the Vlasov part we used the particle-to-grid-weighting
method, well known in plasma physics \cite{langdon1}.
In the DSMC method the physical space is divided into cells containing
typically tens of particles. The main ingredients of this procedure
are the alternation of free flow over a time interval $\Delta t$ 
and representative collisions among pairs of particles 
sharing the same cell. In the
particle-to-grid-weighting algorithm the particle densities are computed
on a spatial grid through some weighting depending on the particle
position, then the Vlasov forces are calculated on the same
grid. Finally, the forces at the position of each particle are
interpolated from the forces on the grid.
The coupling of these methods, which have been extensively 
used individually, made possible our simulations of phase segregation 
with $1.4\times 10^6$ particles, with only modest computational
resources: a typical run took about 32 CPU hours on a 233 MHz Alpha
Station.  It appears that this method can be extended to the study of
the effects of phase segregation on inhomogeneous hydrodynamical flows
of practical importance \cite{shell}.
 
Since one of our main interests was the late time hydrodynamical
regime, a delicate balance had to be struck between the size of the
system, the range of the potential, the temperature and the particle
density, making sure that each of the methods is used within its
range of validity and that their combination remains computer
manageable. On the one hand the potential must be reasonably long
ranged so that the Vlasov description is physically appropriate and 
numerically sound, and on the other hand it must have a range much smaller
than the size of the system. This restriction made necessary the use
of two spatial grids: a somewhat coarse one for the collisions and
a finer grid for the long range potential. It also imposed the use of
quadratic spline interpolation for the calculation of grid
quantities and a ten-point difference scheme for the calculation of the
forces \cite{langdon1}. 

Our results were obtained
using a system with 1382400 particles in a cube with
periodic boundary conditions. We also studied smaller
systems to identify unavoidable finite-size effects. The interaction 
potential used
was gaussian, $U(x) = \alpha \pi^{-\frac{3}{2}}e^{-x^2}$, $\alpha >
0$, but there is no reason to believe that different
repulsive potentials would qualitatively change the results.
All quenches were performed at a total particle density $nd^3\simeq0.01$
and an initial temperature $T_0$, $T_0/T_c^0=0.5$. 
The initial conditions for each run were random positions for all particles
and velocities distributed according to a maxwellian of constant
temperature.( In the DSMC evolution, as in the Boltzmann-Vlasov
equations, the hard cores only enter in determining the collision
cross sections.) 
The total energy of the system was very well conserved by the
dynamics. This meant that the kinetic energy and hence the temperature
increased as the system segregated, but at
late times it changed very slowly on the time scale of our
simulations. We indicate the final temperature T in the figures. The 
effective number of particles in the range of the potential was about 100-500.

In the following we compare results of our simulations
with available theoretical and experimental work 
and check various assumptions made in the former, 
e.g. the neglect of density and temperature variations.
We are also currently investigating both
formal and rigorous Chapman-Enskog and Hilbert expansion methods for
derivation of macroscopic evolution equations for this model \cite{bastea3}.
The units used for lengths and times are the mean-free path, 
$\lambda=(2^{\frac{1}{2}}\pi nd^2)^{-1}$, and mean-free time, 
$\tau=\lambda/c$, where $c=(2k_BT_0/m)^{\frac{1}{2}}$ and
$T_0=\frac{1}{2}T^0_c$ is the initial temperature.

%\section{Critical Quenches}

We first present results for critical
quenches (equal volume fractions of the two species). Three different
potential ranges were used, and for each one of them 10-12
quenches were performed. 
The domain size was probed using the pair correlation function, 
$C(\vec r,t) = {\mathcal{V}}^{-1}<\sum_{\vec x}\phi(\vec x,t)\phi(\vec
x+\vec r,t)>$, 
where $\phi=(n_1-n_2)/(n_1+n_2)$ is the local order parameter, 
$n_1$ and $n_2$ are the local particle densities, $\mathcal{V}$ is
the volume and the average is over the different runs.
We determined $C(\vec r,t)$ by an inverse Fourier transform of the
structure function $S(\vec k,t)=|\tilde{\phi}(\vec k,t)|^2$; the order
parameter
$\phi(\vec r,t)$ and its Fourier transform $\tilde{\phi}(\vec k,t)$ were
computed on a $64\times64\times64$ cubic grid. The first zero of the 
spherically averaged correlation function, $C(r, t)$, was used as a
measure of the typical domain size, $R(t)$. The data are averages of 
the independent runs.

Assuming the existence of a single characteristic length scale,
the dynamical scaling prediction \cite{gunton1} for the
late time spherically averaged correlation function is
$C(r,t)\simeq C(r/R(t))$. 
In Fig.\ \ref{corelation} the correlation function for 
potential range $\gamma^{-1}=0.4$ is plotted starting at
$t=160$, showing that the system is well within the scaling regime.

Simple dimensional analysis of the hydrodynamical evolution equations
in the limit of large domain sizes, appropriate for late times
, yields a linear growth law for the
domain sizes \cite{siggia1}, $R(t)\propto(\sigma/\eta)t$, when
$R$ is below $R_h=\eta^2/\rho\sigma$ and a $t^\frac{2}{3}$ law,
$R(t)\propto(\sigma/\rho)^\frac{1}{3}t^\frac{2}{3}$, for $R$
above $R_h$ \cite{furukawa2,bastea2}; $\sigma$ is the surface tension
coefficient, $\eta$ is the shear viscosity and $\rho$ is the density. 
We measured $\sigma$ directly using Laplace's law and
$\eta$ by studying the decay of a sinusoidal velocity profile.
The time evolution of $R(t)$ in our simulations is at late times (see
Fig. 2) $R(t)=a+b(\sigma/\eta)t$, with 
$b\simeq0.13\pm0.2$($\sigma=260$ and
$\eta=3250$ for $\gamma^{-1}=0.4$, $T/T_c^0=0.6$). This numerical factor
is similar to the one
observed in experiments \cite{beysans1} and recent large scale
molecular dynamics simulations \cite{toxvaerd2}. 
Whether or not a crossover to a $t^\frac{2}{3}$ growth occurs at
later times/larger domain sizes cannot be decided by our present results.
We estimated that we would need a system with at least 4 times
as many particles as the present one to be able to observe the
growth of domains with sizes bigger than $R_h$.

The linear regime starts around the time when
dynamical scaling begins to hold,
i.e. at a domain size of about 12-15 times $\gamma^{-1}$, the range of
the potential. 
This is in agreement with Siggia \cite{siggia1} who argued that the
linear regime is due to surface tension driven flows, so the
interfaces should be well defined, i.e. their width should be small
compared to the domain size. This width is usually taken to be of
order $\xi$, the correlation
length of order parameter fluctuations in the bulk phases. One expects
$\xi$ to be roughly equal to $\gamma^{-1}$, far away from the critical 
temperature, as we are\cite{rowlinson}. 

We also looked directly at the wall profiles separating different phases and 
found that they are approximately described by solitonic
solutions \cite{giacomin}. These are particle densities $n_i(z)$
depending on a single spatial coordinate, such that 
$f_i(z, \vec v)=n_i(z)exp(-mv^2/2k_BT)$ are stationary solutions of
Eq.(1) and $n_1(\pm\infty)=n_2(\mp\infty)$ are the mean-field equilibrium
densities at temperature $T$.
The order parameter profiles which satisfy the equation and the ones 
observed in the simulations(see Fig.\ \ref{wallp}) have both
approximately the hyperbolic 
tangent form \cite{rowlinson}, $tanh(z/2\xi)$, with $z$ the 
coordinate perpendicular to
the domain wall and $\xi$ a parameter which characterizes the
interface thickness. We found that this 
thickness is about $50$ percents bigger than $\gamma^{-1}$. The
total density is about $20$ percents smaller(for $\gamma^{-1}=0.4$,
$T/T_c^0=0.6$) at the interface
than in the bulk, in very good agreement with the solitonic solution
(see Fig.\ \ref{wallp}). The solitonic profiles were calculated at an 
effective temperature $T_{eff}$ for
which the asymptotic values of the order parameter matched the ones
observed in the simulations.  These asymptotically matched mean-field
profiles are steeper(in units of $\gamma^{-1}$) than the ones
observed, with better agreement as $\gamma$ is decreased. We believe
that this discrepancy is due to the fact that
$T/T_c^\gamma>T_{eff}/T_c^0$, as the equilibrium curve for $\gamma>0$ is
flatter around $T_c$ than the mean-field curve.


The need for a clear separation between boundary width and domain size
may explain why in earlier molecular dynamics 
simulations \cite{ma1}, a smaller 
exponent is found: in those computations the maximum domain size
observed is only 6-8 times the range of the potential, so the true
hydrodynamic regime was probably never reached.
In simulations using the lattice Boltzmann method
the interaction range is 
of the order of one lattice spacing and the 
hydrodynamic exponent is observed when the domain size is
about 10 lattice units \cite{frank1}, in agreement with our analysis.

At early times the growth is consistent with a $t^{\frac{1}{3}}$ behavior,
for all potential ranges\cite{siggia1,akcasu}. 
This exponent is not associated with
a scaling regime and it may not be universal, but it is not inconsistent
with the experimental results \cite{beysans1,perrot1}.
In fact, we were able to collapse the three curves onto
each other through scaling of the lengths and times Fig.\
\ref{cscaling} \cite{bastea1}.

%\section{Off-critical Quenches}

Off-critical quenches were performed for a single range of the
potential and three volume fractions. To our knowledge no
published results of such simulations exist, although they
are mentioned in \cite{toxvaerd2}. Therefore, we
compare our results to recent experimental work \cite{perrot1}
and analyze them using the known coarsening mechanisms
\cite{siggia1,vadim1}. In Fig.\ \ref{offc} we present the domain growth
for $\gamma^{-1}=0.4$ and volume fractions 0.16, 0.22 and 0.28. We plot
$R^3(t).vs.t$, and the late times regime is clearly
consistent with a $\frac{1}{3}$ exponent. In this regime the 
system satisfies dynamical scaling very well.
The presence of a late times $t^\frac{1}{3}$ growth at volume fractions
less or equal than about $0.3$ was observed recently in 
micro-gravity experiments
\cite{perrot1} and reasonably explained theoretically using a droplet
coalescence mechanism \cite{siggia1,vadim1}. This
regime was also analyzed by Siggia who predicted a prefactor
proportional to $v^\frac{1}{3}$($v$ being the volume fraction of the
minority species). In our simulations the prefactors are in reasonable
agreement with the above prediction. Furthermore, we can clearly see
the motion and coalescence of the droplets in movies of the dynamics.


%\section{Hydrodynamical Averages}
In writing down evolution equations for the order parameter and
velocity fields in a symmetric binary system with momentum and energy
conservation it is generally assumed that the density and temperature
variations are small\cite{hohenberg1}.
We were able to check these
quantities directly by dividing the system into 
'hydrodynamical' cells, each containing about 100 particles, and computing
the order parameter, density, temperature($k_BT\equiv\frac{1}{3}m(\langle\vec
v^2\rangle-\langle\vec v\rangle^2)$, averages over the cell) and fluid
velocity in each cell. While the statistical fluctuations of these
quantities are not  vanishingly small, as they should be for true
hydrodynamic variables,  they are small enough for such a description
to be at least reasonable.
As already mentioned the total density is smaller at the boundary
between domains. Away from the domain boundaries the values of
the density and order parameter were close to their equilibrium
values. The temperature appeared to be uniform, with normal
equilibrium fluctuations everywhere in the system. 
This shows that the time scales over which heat
transport takes place are much smaller than the time scales
over which there is significant phase separation. 

If, as argued, the linear growth regime is due to surface tension
driven flows, one would expect bigger hydrodynamic velocities close to
the interfaces than in the bulk. 
We looked therefore at the distribution of hydrodynamic velocities as a
function of the order parameter for critical quenches.
As the system segregates, bigger hydrodynamic velocities
are typically observed close to the domain walls, identified by small
values of the order parameter. While this may be due in part to the
density being smaller at the boundary between domains,
it is also consistent with
the idea that at late times the flows are generated mainly by the
curvature of well formed interfaces. We are planning to study this issue
more carefully using bigger systems.

A natural refinement of our model would be the use of the Enskog
correction for the collisions \cite{chapman1}(which would require
numerically replacing the DSMC part with its recently proposed
extension \cite{frank2}, the Consistent Boltzmann Algorithm(CBA)) and
of long range attractive forces between like particles.

We believe that we have introduced a new model which is closer
to reality than lattice gases usually simulated, but still tractable
numerically by the new techniques that we have introduced. These
techniques are of independent interest and have enabled us to compute
temperature changes, density variations and profiles not done
before. Furthermore, we can compare our results to some exact ones. In
fact, we think that this model is a paradigm for the rigorous
derivation of hydrodynamic equations. 

We would like to thank Frank Alexander for useful discussions. This
research was supported in part by AFOSR Grant 0159 and 
NSF Grant 92-13424.

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\begin{figure}
\caption{Scaled two-point correlation function for critical quench with
$\gamma^{-1}=0.4$. Final temperature $T=0.6T^0_c$.}
\label{corelation}
\end{figure}

\begin{figure}
\caption{Scaled domain growth at critical quench; the $\gamma^{-1}=0.3$
and $\gamma^{-1}=0.5$ curves have been collapsed onto the
$\gamma^{-1}=0.4$ curve. A straight line fit($\alpha=1$) is drawn for
late times and a $\propto t^{\frac{1}{3}}$ fit($\alpha=\frac{1}{3}$) is drawn
for early times.}
\label{cscaling}
\end{figure}

\begin{figure}
\caption{Domain growth for off-critical quenches with $\gamma^{-1}=0.4$;
straight line fits are drawn.}
\label{offc}
\end{figure}


\begin{figure}
\caption{Total density $n(*)$ and order parameter $\phi(+)$
variations at the interface between the two phases;
$\gamma^{-1}=0.4$ and $T/T^0_c=0.6$. The full lines are the solitonic
solution(see text).}
\label{wallp}
\end{figure}


\end{document}


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0 18 C 6 12 C 12 12 C 18 6 C 24 6 C 12 6 C 6 12 C 0 12 C -6 12 C -18 6 C -24 0 C -18 -6 6151 3831 L -12 -18 C -6 -30 C 0 -18 C
6 -30 C 12 -18 C 18 -6 C 12 0 C 18 6 C 12 18 C 6 30 C 0 18 C -6 30 C -12 18 C -18 6 C -12 0 C
66 0 5887 3636 L -36 -48 C 18 0 C 12 -6 C 6 -6 C 6 -18 C 0 -12 C -6 -18 C -12 -12 C -18 -6 C -18 0 C -18 6 C -6 6 C -6 12 C
-18 -6 6031 3636 L -12 -18 C -6 -30 C 0 -18 C 6 -30 C 12 -18 C 18 -6 C 12 0 C 18 6 C 12 18 C 6 30 C 0 18 C -6 30 C -12 18 C -18 6 C
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-18 6 C -12 0 C
/M2 {MB 0 7 moveto 0 -14 rlineto -7 0 moveto                                    
14 0 rlineto stroke ME} bind def                                                
/MFAC      5.999 def    
2625 6094 M2 2754 5643 M2 2862 5406 M2 2966 5191 M2 3067 4931 M2 3174 4617 M2 3274 4306 M2 3375 3989 M2 3478 3649 M2 3580 3339 M2
3682 3017 M2 3782 2767 M2 3883 2505 M2 3987 2270 M2 4088 2088 M2 4188 1943 M2 4289 1832 M2 4390 1741 M2 4492 1693 M2 4594 1670 M2
4695 1670 M2 4796 1682 M2 4897 1716 M2 4998 1756 M2 5099 1802 M2 5200 1849 M2 5303 1897 M2 5404 1940 M2 5505 1979 M2 5605 2012 M2
5706 2040 M2 5808 2058 M2 5909 2073 M2 6011 2080 M2 6112 2084 M2 6213 2080 M2 6314 2073 M2 6415 2068 M2 6516 2054 M2 6617 2041 M2
6718 2028 M2 6819 2011 M2 6920 1999 M2 7022 1982 M2 7124 1969 M2 7225 1956 M2 7325 1942 M2 7426 1935 M2
0 -84 5643 4970 L 84 0 5601 4928 L
/M4 {MB 0 0 7 CC ME} bind def                                                   
2625 6132 M4 2749 5687 M4 2853 5458 M4 2952 5253 M4 3050 5008 M4 3152 4709 M4 3248 4411 M4 3346 4106 M4 3444 3776 M4 3543 3473 M4
3640 3154 M4 3736 2902 M4 3833 2635 M4 3933 2389 M4 4030 2194 M4 4127 2032 M4 4223 1904 M4 4321 1791 M4 4418 1724 M4 4516 1680 M4
4613 1663 M4 4710 1658 M4 4807 1681 M4 4905 1712 M4 5001 1752 M4 5099 1798 M4 5197 1849 M4 5294 1897 M4 5391 1943 M4 5488 1983 M4
5584 2022 M4 5682 2049 M4 5779 2073 M4 5877 2088 M4 5974 2097 M4 6071 2100 M4 6168 2094 M4 6265 2090 M4 6362 2076 M4 6460 2059 M4
6556 2043 M4 6653 2021 M4 6751 2004 M4 6848 1982 M4 6946 1965 M4 7043 1947 M4 7140 1930 M4 7236 1922 M4
-18 -6 5637 4775 L -12 -12 C -6 -18 C 0 -12 C 6 -18 C 12 -12 C 18 -6 C 12 0 C 18 6 C 12 12 C 6 18 C 0 12 C -6 18 C -12 12 C -18 6 C
-12 0 C
/M3 {MB 0 6 moveto 0 -6 lineto -5 3 moveto 5 -3 lineto                          
5 3 moveto -5 -3 lineto stroke ME} bind def                                     
2625 6176 M3 2745 5736 M3 2846 5516 M3 2942 5319 M3 3036 5083 M3 3135 4794 M3 3228 4505 M3 3323 4208 M3 3418 3886 M3 3513 3586 M3
3608 3270 M3 3701 3018 M3 3795 2747 M3 3891 2494 M3 3986 2289 M3 4079 2116 M3 4172 1974 M3 4267 1845 M3 4361 1762 M3 4456 1703 M3
4550 1671 M3 4644 1653 M3 4738 1665 M3 4832 1688 M3 4926 1721 M3 5020 1764 M3 5115 1814 M3 5209 1863 M3 5303 1913 M3 5397 1957 M3
5490 2002 M3 5585 2034 M3 5679 2066 M3 5773 2087 M3 5868 2100 M3 5961 2107 M3 6056 2103 M3 6149 2100 M3 6243 2088 M3 6337 2070 M3
6431 2053 M3 6525 2027 M3 6619 2008 M3 6714 1983 M3 6808 1963 M3 6902 1943 M3 6996 1923 M3 7090 1915 M3
0 -72 5643 4574 L 60 -36 5613 4556 L -60 -36 5673 4556 L
/M6 {MB -6 -6 moveto 0 12 rlineto 12 0 rlineto                                  
0 -12 rlineto closepath stroke ME} bind def                                     
2625 6198 M6 2741 5763 M6 2838 5549 M6 2931 5362 M6 3022 5137 M6 3117 4861 M6 3207 4584 M6 3298 4297 M6 3389 3984 M6 3481 3691 M6
3572 3380 M6 3662 3129 M6 3753 2858 M6 3846 2601 M6 3937 2390 M6 4026 2207 M6 4117 2055 M6 4207 1913 M6 4299 1816 M6 4390 1743 M6
4481 1698 M6 4571 1667 M6 4661 1667 M6 4752 1682 M6 4843 1705 M6 4934 1743 M6 5025 1790 M6 5116 1837 M6 5206 1888 M6 5297 1931 M6
5387 1980 M6 5478 2016 M6 5569 2051 M6 5660 2077 M6 5751 2093 M6 5841 2105 M6 5932 2104 M6 6022 2102 M6 6113 2094 M6 6204 2075 M6
6294 2059 M6 6385 2032 M6 6475 2013 M6 6567 1986 M6 6658 1964 M6 6748 1943 M6 6839 1922 M6 6929 1913 M6
0 -72 5607 4379 L 72 0 C 0 72 C -72 0 C
/M5 {MB -5 -5 moveto 10 10 rlineto -5 5 moveto                                  
10 -10 rlineto stroke ME} bind def                                              
2625 6232 M5 2737 5801 M5 2831 5592 M5 2921 5411 M5 3009 5192 M5 3101 4925 M5 3188 4656 M5 3276 4375 M5 3365 4070 M5 3454 3783 M5
3542 3475 M5 3629 3227 M5 3717 2955 M5 3807 2696 M5 3895 2481 M5 3982 2291 M5 4069 2132 M5 4157 1979 M5 4245 1872 M5 4334 1788 M5
4422 1732 M5 4509 1689 M5 4597 1680 M5 4685 1685 M5 4772 1700 M5 4860 1732 M5 4949 1773 M5 5037 1817 M5 5124 1866 M5 5212 1908 M5
5299 1957 M5 5387 1994 M5 5475 2032 M5 5563 2060 M5 5651 2079 M5 5739 2095 M5 5827 2097 M5 5914 2096 M5 6002 2092 M5 6090 2075 M5
6177 2060 M5 6265 2033 M5 6353 2015 M5 6441 1989 M5 6530 1967 M5 6617 1945 M5 6705 1924 M5 6792 1915 M5
60 -60 5613 4178 L -60 -60 5673 4178 L
/M7 {MB 0 8 moveto -7 -4 lineto 7 -4 lineto closepath                           
stroke ME} bind def                                                             
2734 5821 M7 2825 5618 M7 2912 5443 M7 2997 5233 M7 3087 4975 M7 3171 4714 M7 3256 4443 M7 3342 4145 M7 3429 3864 M7 3514 3562 M7
3598 3316 M7 3683 3045 M7 3771 2786 M7 3856 2568 M7 3940 2374 M7 4025 2208 M7 4110 2047 M7 4196 1932 M7 4281 1838 M7 4367 1772 M7
4452 1719 M7 4536 1700 M7 4622 1697 M7 4707 1702 M7 4792 1728 M7 4878 1763 M7 4963 1802 M7 5048 1848 M7 5133 1888 M7 5217 1936 M7
5303 1973 M7 5388 2013 M7 5473 2042 M7 5559 2063 M7 5644 2082 M7 5729 2086 M7 5814 2088 M7 5899 2087 M7 5984 2072 M7 6069 2059 M7
6154 2035 M7 6239 2017 M7 6325 1993 M7 6410 1972 M7 6495 1949 M7 6580 1930 M7 6664 1920 M7
-42 -72 5643 4001 L 84 0 C -42 72 C
/M12 {MB 0 9 moveto -2 3 lineto -8 3 lineto -3 -1 lineto                        
-5 -7 lineto 0 -3 lineto 5 -7 lineto 3 -1 lineto 8 3                            
lineto 2 3 lineto closepath stroke ME} bind def                                 
2730 5846 M12 2819 5647 M12 2903 5478 M12 2986 5274 M12 3073 5022 M12 3154 4769 M12 3237 4505 M12 3321 4214 M12 3404 3939 M12
3487 3642 M12 3568 3400 M12 3651 3131 M12 3736 2873 M12 3818 2652 M12 3900 2455 M12 3982 2285 M12 4065 2117 M12 4148 1995 M12
4231 1892 M12 4313 1817 M12 4396 1754 M12 4478 1725 M12 4561 1714 M12 4643 1709 M12 4726 1728 M12 4809 1755 M12 4892 1789 M12
4974 1831 M12 5056 1866 M12 5138 1912 M12 5221 1948 M12 5304 1988 M12 5386 2018 M12 5469 2040 M12 5552 2061 M12 5634 2069 M12
5716 2072 M12 5799 2075 M12 5881 2064 M12 5963 2053 M12 6046 2032 M12 6129 2017 M12 6212 1995 M12 6294 1976 M12 6377 1954 M12
6459 1937 M12 6541 1927 M12
-12 -36 5643 3813 L -36 0 C 30 -24 C -12 -36 C 30 24 C 30 -24 C -12 36 C 30 24 C -36 0 C -12 36 C
/M14 {MB -2 6 moveto -2 2 lineto -6 2 lineto -6 -2 lineto                       
-2 -2 lineto -2 -6 lineto 2 -6 lineto 2 -2 lineto                               
6 -2 lineto 6 2 lineto 2 2 lineto 2 6 lineto closepath                          
stroke ME} bind def                                                             
2727 5870 M14 2813 5675 M14 2895 5511 M14 2976 5314 M14 3060 5070 M14 3139 4824 M14 3220 4566 M14 3301 4282 M14 3382 4013 M14
3462 3720 M14 3542 3481 M14 3622 3213 M14 3704 2956 M14 3784 2734 M14 3864 2534 M14 3944 2361 M14 4024 2186 M14 4105 2058 M14
4185 1947 M14 4265 1863 M14 4346 1791 M14 4425 1753 M14 4506 1732 M14 4586 1718 M14 4666 1728 M14 4747 1748 M14 4827 1774 M14
4907 1811 M14 4987 1842 M14 5067 1885 M14 5147 1920 M14 5228 1958 M14 5308 1989 M14 5388 2013 M14 5468 2036 M14 5549 2047 M14
5628 2053 M14 5708 2059 M14 5789 2052 M14 5869 2044 M14 5949 2028 M14 6029 2015 M14 6110 1997 M14 6190 1980 M14 6270 1960 M14
6350 1946 M14 6430 1937 M14
0 -24 5631 3600 L -24 0 C 0 -24 C 24 0 C 0 -24 C 24 0 C 0 24 C 24 0 C 0 24 C -24 0 C 0 24 C -24 0 C
PGPLOT restore showpage
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%%%%%%% Here begins the file fig2.ps %%%%%%%%%
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%%Title: PGPLOT PostScript plot
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%%CreationDate:  2-Dec-1996 12:35
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%%BeginProlog
/L {moveto rlineto currentpoint stroke moveto} bind def
/C {rlineto currentpoint stroke moveto} bind def
/D {moveto 0 0 rlineto currentpoint stroke moveto} bind def
/SLW {5 mul setlinewidth} bind def
/SCF /pop load def
/BP {newpath moveto} bind def
/LP /rlineto load def
/EP {rlineto closepath eofill} bind def
/MB {gsave translate MFAC dup scale 1 setlinewidth 2 setlinecap 0 setlinejoin newpath} bind def
/ME /grestore load def
/CC {0 360 arc stroke} bind def
/FC {0 360 arc fill} bind def
%%EndProlog
 
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/M3 {MB 0 6 moveto 0 -6 lineto -5 3 moveto 5 -3 lineto                          
5 3 moveto -5 -3 lineto stroke ME} bind def                                     
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/M4 {MB 0 0 7 CC ME} bind def                                                   
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/M5 {MB -5 -5 moveto 10 10 rlineto -5 5 moveto                                  
10 -10 rlineto stroke ME} bind def                                              
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PGPLOT restore showpage
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%%%%%%%%%% Here begins the file fig3.ps%%%%%%%%%%%%%%%%%%
%!PS-Adobe-3.0 EPSF-3.0
%%For: sbastea
%%Title: PGPLOT PostScript plot
%%Creator: PGPLOT
%%CreationDate:  2-Dec-1996 12:11
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%%LanguageLevel: 1
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%%BeginProlog
/L {moveto rlineto currentpoint stroke moveto} bind def
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/D {moveto 0 0 rlineto currentpoint stroke moveto} bind def
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/ME /grestore load def
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/FC {0 360 arc fill} bind def
%%EndProlog
 
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/M3 {MB 0 6 moveto 0 -6 lineto -5 3 moveto 5 -3 lineto                          
5 3 moveto -5 -3 lineto stroke ME} bind def                                     
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/M4 {MB 0 0 7 CC ME} bind def                                                   
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48 30 C 47 30 C 47 30 C 47 30 C 48 31 C 47 30 C 47 30 C 47 30 C 48 30 C 47 31 C 47 30 C 47 30 C 48 30 C 47 30 C 47 31 C 47 30 C
48 30 C 47 30 C 47 30 C 47 31 C 48 30 C 47 30 C 47 30 C 47 30 C 48 31 C 47 30 C 47 30 C 47 30 C 48 30 C 47 31 C 47 30 C 47 30 C
48 30 C 47 30 C 47 31 C 47 30 C 47 30 C 48 30 C 47 30 C 47 30 C 47 31 C 48 30 C 47 30 C 47 30 C 47 30 C 48 31 C 47 30 C 47 30 C
47 30 C 48 30 C 47 31 C 47 30 C 47 30 C 48 30 C 47 30 C 47 31 C 47 30 C 48 30 C 47 30 C 47 30 C 47 31 C 48 30 C 47 30 C 47 30 C
47 30 C 48 31 C 47 30 C 47 30 C 47 30 C 48 30 C 47 31 C 47 30 C 47 30 C 48 30 C 47 30 C 47 31 C 47 30 C 48 30 C 47 30 C 47 30 C
47 31 C 48 30 C 47 30 C 47 30 C 47 30 C 48 30 C 47 31 C
0.000 setgray
/M5 {MB -5 -5 moveto 10 10 rlineto -5 5 moveto                                  
10 -10 rlineto stroke ME} bind def                                              
2640 1597 M5 2655 1627 M5 2670 1653 M5 2685 1680 M5 2700 1702 M5 2715 1720 M5 2730 1747 M5 2745 1765 M5 2760 1787 M5 2775 1800 M5
2790 1816 M5 2805 1840 M5 2820 1860 M5 2835 1875 M5 2850 1887 M5 2865 1903 M5 2880 1920 M5 2895 1935 M5 2910 1958 M5 2925 1976 M5
2940 1999 M5 2955 2016 M5 2970 2031 M5 2985 2045 M5 3000 2064 M5 3015 2077 M5 3030 2090 M5 3045 2099 M5 3060 2113 M5 3075 2127 M5
3090 2143 M5 3105 2152 M5 3120 2160 M5 3135 2173 M5 3150 2185 M5 3165 2197 M5 3180 2208 M5 3195 2222 M5 3210 2237 M5 3225 2248 M5
3240 2259 M5 3255 2266 M5 3270 2278 M5 3285 2289 M5 3300 2296 M5 3315 2306 M5 3330 2316 M5 3345 2325 M5 3360 2332 M5 3375 2332 M5
3390 2343 M5 3405 2355 M5 3420 2366 M5 3435 2373 M5 3450 2383 M5 3465 2392 M5 3480 2401 M5 3495 2413 M5 3510 2425 M5 3525 2432 M5
3540 2443 M5 3555 2453 M5 3570 2463 M5 3585 2471 M5 3600 2482 M5 3615 2489 M5 3630 2498 M5 3645 2505 M5 3660 2515 M5 3675 2523 M5
3690 2531 M5 3705 2541 M5 3720 2551 M5 3735 2562 M5 3750 2569 M5 3765 2577 M5 3780 2586 M5 3795 2601 M5 3810 2610 M5 3825 2618 M5
3840 2621 M5 3855 2630 M5 3870 2641 M5 3885 2651 M5 3900 2660 M5 3915 2670 M5 3930 2676 M5 3945 2686 M5 3960 2693 M5 3975 2704 M5
3990 2710 M5 4005 2716 M5 4020 2725 M5 4035 2733 M5 4050 2746 M5 4065 2757 M5 4080 2766 M5 4095 2779 M5 4110 2786 M5 4125 2795 M5
4140 2804 M5 4155 2813 M5 4170 2824 M5 4185 2830 M5 4200 2839 M5 4215 2845 M5 4230 2853 M5 4245 2862 M5 4260 2871 M5 4275 2877 M5
4290 2885 M5 4305 2892 M5 4320 2901 M5 4335 2907 M5 4350 2913 M5 4365 2917 M5 4380 2922 M5 4395 2930 M5 4410 2937 M5 4425 2943 M5
4440 2949 M5 4455 2960 M5 4470 2969 M5 4485 2973 M5 4500 2981 M5 4515 2988 M5 4530 2998 M5 4545 3006 M5 4560 3015 M5 4575 3026 M5
4590 3035 M5 4605 3046 M5 4620 3056 M5 4635 3067 M5 4650 3078 M5 4665 3088 M5 4680 3095 M5 4695 3105 M5 4710 3115 M5 4725 3123 M5
4740 3131 M5 4755 3142 M5 4770 3152 M5 4785 3164 M5 4800 3172 M5 4815 3180 M5 4830 3188 M5 4845 3198 M5 4860 3209 M5 4875 3215 M5
4890 3224 M5 4905 3232 M5 4920 3238 M5 4935 3247 M5 4950 3257 M5 4965 3266 M5 4980 3275 M5 4995 3281 M5 5010 3289 M5 5025 3298 M5
5040 3302 M5 5055 3307 M5 5070 3315 M5 5085 3322 M5 5100 3330 M5 5115 3340 M5 5130 3348 M5 5145 3355 M5 5160 3363 M5 5175 3376 M5
5190 3386 M5 5205 3396 M5 5220 3404 M5 5235 3411 M5 5250 3415 M5 5264 3422 M5 5279 3431 M5 5294 3438 M5 5309 3446 M5 5324 3456 M5
5339 3468 M5 5354 3475 M5 5369 3483 M5 5384 3491 M5 5399 3501 M5 5414 3508 M5 5429 3519 M5 5444 3529 M5 5459 3539 M5 5474 3546 M5
5489 3556 M5 5504 3562 M5 5519 3574 M5 5534 3585 M5 5549 3595 M5 5564 3603 M5 5579 3613 M5 5594 3625 M5 5609 3634 M5 5624 3647 M5
5639 3657 M5 5654 3665 M5 5669 3677 M5 5684 3691 M5 5699 3705 M5 5714 3713 M5 5729 3724 M5 5744 3732 M5 5759 3744 M5 5774 3752 M5
5789 3759 M5 5804 3763 M5 5819 3769 M5 5834 3781 M5 5849 3794 M5 5864 3803 M5 5879 3811 M5 5894 3819 M5 5909 3828 M5 5924 3835 M5
5939 3843 M5 5954 3852 M5 5969 3864 M5 5984 3874 M5 5999 3882 M5 6014 3891 M5 6029 3898 M5 6044 3906 M5 6059 3916 M5 6074 3926 M5
6089 3939 M5 6104 3948 M5 6119 3954 M5 6134 3966 M5 6149 3978 M5 6164 3993 M5 6179 4001 M5 6194 4010 M5 6209 4017 M5 6224 4026 M5
6239 4029 M5 6254 4038 M5 6269 4046 M5 6284 4057 M5 6299 4066 M5 6314 4078 M5 6329 4087 M5 6344 4095 M5 6359 4104 M5 6374 4110 M5
6389 4113 M5 6404 4122 M5 6419 4131 M5 6434 4137 M5 6449 4146 M5 6464 4152 M5 6479 4157 M5 6494 4165 M5 6509 4171 M5 6524 4178 M5
60 -60 3251 4763 L -60 -60 3311 4763 L
0.000 setgray 46 27 2887 2056 L 46 26 C 47 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C 46 27 C 46 27 C
46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C 46 27 C 46 27 C 46 26 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C 46 27 C
46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 26 C 46 27 C 46 27 C 47 27 C 46 27 C
46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 26 C
46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C
46 27 C 46 27 C 46 27 C 46 26 C 46 27 C 46 27 C 46 27 C 46 27 C 47 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C
47 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C 46 27 C
0.000 setgray
PGPLOT restore showpage
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%%%%%%%%%%%%% Here begins the file fig4.ps %%%%%%%%%%%%%%%%%%%%%%%%%%
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%%Title: PGPLOT PostScript plot
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%%BeginProlog
/L {moveto rlineto currentpoint stroke moveto} bind def
/C {rlineto currentpoint stroke moveto} bind def
/D {moveto 0 0 rlineto currentpoint stroke moveto} bind def
/SLW {5 mul setlinewidth} bind def
/SCF /pop load def
/BP {newpath moveto} bind def
/LP /rlineto load def
/EP {rlineto closepath eofill} bind def
/MB {gsave translate MFAC dup scale 1 setlinewidth 2 setlinecap 0 setlinejoin newpath} bind def
/ME /grestore load def
/CC {0 360 arc stroke} bind def
/FC {0 360 arc fill} bind def
%%EndProlog
 
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0.072 0.072 scale
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-18 -6 2242 4818 L -12 -18 C -6 -30 C 0 -18 C 6 -30 C 12 -18 C 18 -6 C 12 0 C 18 6 C 12 18 C 6 30 C 0 18 C -6 30 C -12 18 C -18 6 C
-12 0 C -6 -6 2338 4704 L 6 -6 C 6 6 C -6 6 C -60 0 2458 4818 L -6 -54 C 6 6 C 18 6 C 18 0 C 18 -6 C 12 -12 C 6 -18 C 0 -12 C
-6 -18 C -12 -12 C -18 -6 C -18 0 C -18 6 C -6 6 C -6 12 C 12 6 2404 5857 L 18 18 C 0 -126 C
14 14 5142 1113 L 14 7 C 8 0 C 14 -7 C 7 -7 C 7 -22 C 0 -29 C -7 -36 C -7 -21 5257 1134 L -8 -15 C -43 -65 C -14 -28 C -7 -22 C
0 -101 5300 1134 L 7 22 5300 1091 L 14 14 C 15 7 C 21 0 C
201 -57 2006 3766 L 7 -21 2056 3730 L 15 -15 C 21 -7 C 22 0 C 14 7 C 15 15 C 7 21 C 0 15 C -7 21 C -15 15 C -21 7 C -22 0 C -14 -7 C
-15 -15 C -7 -21 C 0 -15 C 7 -7 2150 3853 L -7 -8 C -8 8 C 8 7 C 14 0 C 14 -7 C 8 -8 C 101 0 2056 4025 L -22 22 2085 4025 L -7 14 C
0 22 C 7 14 C 22 8 C 72 0 C
0 -151 4951 541 L 93 0 4951 541 L 57 0 4951 469 L 7 -7 5073 541 L 8 7 C -8 7 C -7 -7 C 0 -101 5080 491 L 0 -115 5217 491 L -7 -22 C
-7 -7 C -15 -7 C -21 0 C -15 7 C -14 15 5217 469 L -15 7 C -21 0 C -15 -7 C -14 -15 C -7 -21 C 0 -15 C 7 -21 C 14 -15 C 15 -7 C
21 0 C 15 7 C 14 15 C -7 -7 5282 404 L 7 -7 C 7 7 C -7 7 C -72 -101 5527 541 L 108 0 C 0 -151 5527 541 L
/M2 {MB 0 7 moveto 0 -14 rlineto -7 0 moveto                                    
14 0 rlineto stroke ME} bind def                                                
/MFAC      5.999 def    
2666 2009 M2 2753 2011 M2 2841 2011 M2 2928 2008 M2 3016 2012 M2 3103 2011 M2 3191 2011 M2 3278 2008 M2 3366 2013 M2 3453 2016 M2
3541 2016 M2 3628 2020 M2 3716 2025 M2 3803 2027 M2 3891 2036 M2 3978 2039 M2 4066 2059 M2 4153 2078 M2 4240 2099 M2 4328 2140 M2
4415 2174 M2 4503 2229 M2 4590 2294 M2 4678 2386 M2 4765 2501 M2 4853 2648 M2 4940 2823 M2 5028 3032 M2 5115 3276 M2 5203 3540 M2
5291 3812 M2 5378 4085 M2 5466 4324 M2 5553 4541 M2 5641 4720 M2 5728 4862 M2 5816 4982 M2 5903 5074 M2 5991 5144 M2 6078 5196 M2
6165 5241 M2 6253 5264 M2 6341 5288 M2 6428 5309 M2 6515 5320 M2 6603 5329 M2 6690 5339 M2 6778 5343 M2 6865 5352 M2 6953 5351 M2
7040 5363 M2 7128 5362 M2 7215 5368 M2 7303 5366 M2 7390 5367 M2 7478 5368 M2 7565 5371 M2 7653 5369 M2 7740 5370 M2 7828 5376 M2
/M3 {MB 0 6 moveto 0 -6 lineto -5 3 moveto 5 -3 lineto                          
5 3 moveto -5 -3 lineto stroke ME} bind def                                     
2666 5810 M3 2753 5807 M3 2841 5807 M3 2928 5809 M3 3016 5813 M3 3103 5815 M3 3191 5812 M3 3278 5813 M3 3366 5808 M3 3453 5809 M3
3541 5807 M3 3628 5795 M3 3716 5803 M3 3803 5796 M3 3891 5790 M3 3978 5781 M3 4066 5774 M3 4153 5766 M3 4240 5742 M3 4328 5723 M3
4415 5703 M3 4503 5666 M3 4590 5638 M3 4678 5598 M3 4765 5555 M3 4853 5514 M3 4940 5471 M3 5028 5434 M3 5115 5399 M3 5203 5391 M3
5291 5388 M3 5378 5399 M3 5466 5431 M3 5553 5466 M3 5641 5505 M3 5728 5546 M3 5816 5598 M3 5903 5635 M3 5991 5666 M3 6078 5695 M3
6165 5722 M3 6253 5744 M3 6341 5750 M3 6428 5770 M3 6515 5778 M3 6603 5784 M3 6690 5790 M3 6778 5794 M3 6865 5802 M3 6953 5803 M3
7040 5806 M3 7128 5810 M3 7215 5809 M3 7303 5815 M3 7390 5813 M3 7478 5809 M3 7565 5813 M3 7653 5818 M3 7740 5813 M3 7828 5819 M3
781 0 2625 2013 L 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C
2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 1 C
2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 1 C
2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 1 C 2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C
2 0 C 1 1 C 2 0 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 0 C 1 1 C 2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 0 C 2 1 C 2 0 C 1 1 C
2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C
2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 1 C 2 0 C 2 1 C 2 0 C 1 1 C 2 0 C 2 1 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 1 C 2 0 C 2 1 C 2 0 C 1 1 C
2 1 C 2 0 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 0 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C 2 1 C
2 0 C 1 1 C 2 1 C 2 1 C 2 1 C 1 0 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C
2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C
2 1 C 1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 1 C 1 2 C 2 1 C 2 1 C 2 1 C 1 2 C 2 1 C 2 1 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C
2 1 C 2 2 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 2 C 2 1 C 2 2 C 1 1 C 2 2 C 2 1 C 2 2 C 1 1 C 2 2 C 2 1 C 2 2 C 1 2 C 2 1 C 2 2 C
2 2 C 1 1 C 2 2 C 2 2 C 2 1 C 1 2 C 2 2 C 2 1 C 2 2 C 1 2 C 2 2 C 2 2 C 2 1 C 1 2 C 2 2 C 2 2 C 2 2 C 1 2 C 2 2 C 2 2 C 2 1 C 1 2 C
2 2 C 2 2 C 2 2 C 1 2 C 2 3 C 2 2 C 2 2 C 1 2 C 2 2 C 2 2 C 2 2 C 1 2 C 2 2 C 2 3 C 2 2 C 1 2 C 2 2 C 2 3 C 2 2 C 1 2 C 2 3 C 2 2 C
2 2 C 1 3 C 2 2 C 2 3 C 2 2 C 1 2 C 2 3 C 2 2 C 2 3 C 1 3 C 2 2 C 2 3 C 2 2 C 1 3 C 2 3 C 2 2 C 2 3 C 1 3 C 2 3 C 2 2 C 2 3 C 1 3 C
2 3 C 2 3 C 2 2 C 1 3 C 2 3 C 2 3 C 2 3 C 1 3 C 2 3 C 2 3 C 2 3 C 1 3 C 2 4 C 2 3 C 2 3 C 1 3 C 2 3 C 2 4 C 2 3 C 1 3 C 2 3 C 2 4 C
2 3 C 1 4 C 2 3 C 2 3 C 2 4 C 1 3 C 2 4 C 2 4 C 2 3 C 1 4 C 2 3 C 2 4 C 2 4 C 1 4 C 2 3 C 2 4 C 2 4 C 1 4 C 2 4 C 2 4 C 2 3 C 1 4 C
2 4 C 2 4 C 2 5 C 1 4 C 2 4 C 2 4 C 2 4 C 1 4 C 2 4 C 2 5 C 2 4 C 1 4 C 2 5 C 2 4 C 2 5 C 1 4 C 2 4 C 2 5 C 2 5 C 1 4 C 2 5 C 2 4 C
2 5 C 1 5 C 2 4 C 2 5 C 2 5 C 1 5 C 2 5 C 2 5 C 2 5 C 1 5 C 2 5 C 2 5 C 2 5 C 1 5 C 2 5 C 2 5 C 2 5 C 1 6 C 2 5 C 2 5 C 2 6 C 1 5 C
2 5 C 2 6 C 2 5 C 1 6 C 2 5 C 2 6 C 2 6 C 1 5 C 2 6 C 2 6 C 2 6 C 1 5 C 2 6 C 2 6 C 2 6 C 1 6 C 2 6 C 2 6 C 2 6 C 1 6 C 2 6 C 2 6 C
2 6 C 1 7 C 2 6 C 2 6 C 2 7 C 1 6 C 2 6 C 2 7 C 2 6 C 1 7 C 2 6 C 2 7 C 2 6 C 1 7 C 2 7 C 2 6 C 2 7 C 1 7 C 2 7 C 2 7 C 2 6 C 1 7 C
2 7 C 2 7 C 2 7 C 1 7 C 2 7 C 2 8 C 2 7 C 1 7 C 2 7 C 2 7 C 2 8 C 1 7 C 2 7 C 2 7 C 2 8 C 1 7 C 2 8 C 2 7 C 2 8 C 1 7 C 2 8 C 2 7 C
2 8 C 1 8 C 2 7 C 2 8 C 2 8 C 1 8 C 2 7 C 2 8 C 2 8 C 1 8 C 2 8 C 2 8 C 2 8 C 1 8 C 2 8 C 2 8 C 2 8 C 1 8 C 2 8 C 2 8 C 2 8 C 1 8 C
2 8 C 2 9 C 2 8 C 1 8 C 2 8 C 2 9 C 2 8 C 1 8 C 2 8 C 2 9 C 2 8 C 1 9 C 2 8 C 2 8 C 2 9 C 1 8 C 2 9 C 2 8 C 2 9 C 1 8 C 2 9 C 2 8 C
2 9 C 1 8 C 2 9 C 2 8 C 2 9 C 1 8 C 2 9 C 2 9 C 2 8 C 1 9 C 2 9 C 2 8 C 2 9 C 1 8 C 2 9 C 2 9 C 2 8 C 1 9 C 2 9 C 2 8 C 2 9 C 1 9 C
2 8 C 2 9 C 2 9 C 1 8 C 2 9 C 2 9 C 2 8 C 1 9 C 2 8 C 2 9 C 2 9 C 1 8 C 2 9 C 2 9 C 2 8 C 1 9 C 2 8 C 2 9 C 2 9 C 1 8 C 2 9 C 2 8 C
2 9 C 1 8 C 2 9 C 2 8 C 2 9 C 1 8 C 2 9 C 2 8 C 2 9 C 1 8 C 2 8 C 2 9 C 2 8 C 1 9 C 2 8 C 2 8 C 2 8 C 1 9 C 2 8 C 2 8 C 2 8 C 1 9 C
2 8 C 2 8 C 2 8 C 1 8 C 2 8 C 2 8 C 2 8 C 1 9 C 2 8 C 2 7 C 2 8 C 1 8 C 2 8 C 2 8 C 2 8 C 1 8 C 2 8 C 2 7 C 2 8 C 1 8 C 2 8 C 2 7 C
2 8 C 1 7 C 2 8 C 2 8 C 2 7 C 1 8 C 2 7 C 2 7 C 2 8 C 1 7 C 2 8 C 2 7 C 2 7 C 1 7 C 2 8 C 2 7 C 2 7 C 1 7 C 2 7 C 2 7 C 2 7 C 1 7 C
2 7 C 2 7 C 2 7 C 1 7 C 2 7 C 2 6 C 2 7 C 1 7 C 2 7 C 2 6 C 2 7 C 1 6 C 2 7 C 2 7 C 2 6 C 1 6 C 2 7 C 2 6 C 2 7 C 1 6 C 2 6 C 2 6 C
2 7 C 1 6 C 2 6 C 2 6 C 2 6 C 1 6 C 2 6 C 2 6 C 2 6 C 1 6 C 2 6 C 2 6 C 2 5 C 1 6 C 2 6 C 2 5 C 2 6 C 1 6 C 2 5 C 2 6 C 2 5 C 1 6 C
2 5 C 2 6 C 2 5 C 1 5 C 2 6 C 2 5 C 2 5 C 1 5 C 2 5 C 2 6 C 2 5 C 1 5 C 2 5 C 2 5 C 2 5 C 1 5 C 2 5 C 2 4 C 2 5 C 1 5 C 2 5 C 2 4 C
1 5 C 2 5 C 2 4 C 2 5 C 1 5 C 2 4 C 2 5 C 2 4 C 1 5 C 2 4 C 2 4 C 2 5 C 1 4 C 2 4 C 2 4 C 2 5 C 1 4 C 2 4 C 2 4 C 2 4 C 1 4 C 2 4 C
2 4 C 2 4 C 1 4 C 2 4 C 2 4 C 2 4 C 1 4 C 2 4 C 2 3 C 2 4 C 1 4 C 2 4 C 2 3 C 2 4 C 1 3 C 2 4 C 2 4 C 2 3 C 1 4 C 2 3 C 2 3 C 2 4 C
1 3 C 2 4 C 2 3 C 2 3 C 1 4 C 2 3 C 2 3 C 2 3 C 1 3 C 2 4 C 2 3 C 2 3 C 1 3 C 2 3 C 2 3 C 2 3 C 1 3 C 2 3 C 2 3 C 2 3 C 1 3 C 2 3 C
2 2 C 2 3 C 1 3 C 2 3 C 2 3 C 2 2 C 1 3 C 2 3 C 2 2 C 2 3 C 1 3 C 2 2 C 2 3 C 2 2 C 1 3 C 2 2 C 2 3 C 2 2 C 1 3 C 2 2 C 2 3 C 2 2 C
1 3 C 2 2 C 2 2 C 2 3 C 1 2 C 2 2 C 2 2 C 2 3 C 1 2 C 2 2 C 2 2 C 2 2 C 1 3 C 2 2 C 2 2 C 2 2 C 1 2 C 2 2 C 2 2 C 2 2 C 1 2 C 2 2 C
2 2 C 2 2 C 1 2 C 2 2 C 2 2 C 2 2 C 1 2 C 2 2 C 2 2 C 2 1 C 1 2 C 2 2 C 2 2 C 2 2 C 1 1 C 2 2 C 2 2 C 2 2 C 1 1 C 2 2 C 2 2 C 2 1 C
1 2 C 2 2 C 2 1 C 2 2 C 1 1 C 2 2 C 2 2 C 2 1 C 1 2 C 2 1 C 2 2 C 2 1 C 1 2 C 2 1 C 2 2 C 2 1 C 1 1 C 2 2 C 2 1 C 2 2 C 1 1 C 2 1 C
2 2 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 1 C 1 2 C 2 1 C 2 1 C 2 1 C
1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C
2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C 2 1 C 2 1 C 1 0 C 2 1 C 2 1 C 2 1 C
1 1 C 2 0 C 2 1 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 0 C 2 1 C 2 1 C 2 1 C 1 0 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C
2 0 C 2 1 C 1 0 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 1 C 2 0 C 2 1 C 2 0 C 1 1 C 2 0 C 2 1 C 2 0 C
1 1 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 0 C 1 1 C 2 0 C 2 1 C 2 0 C 1 1 C 2 0 C
2 1 C 2 0 C 1 1 C 2 0 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 0 C 1 1 C 2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 0 C 2 1 C 2 0 C
1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C
2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 1 C
1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C
2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C
2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C
2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 969 0 C
781 0 2625 5814 L 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 -1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 -1 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 -1 C
2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 -1 C
2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C
2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 -1 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 0 C
2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 -1 C 2 0 C 2 0 C 1 0 C 2 0 C
2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C
2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 -1 C 2 0 C
1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 -1 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 -1 C
2 0 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 -1 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 -1 C 2 0 C 2 -1 C 1 0 C 2 0 C
2 -1 C 2 0 C 1 -1 C 2 0 C 2 0 C 2 -1 C 1 0 C 2 -1 C 2 0 C 2 -1 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 0 C 1 -1 C 2 0 C
2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 0 C 1 -1 C 2 0 C
2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 0 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 -1 C 1 0 C 2 -1 C
2 -1 C 2 0 C 1 -1 C 2 0 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 0 C 1 -1 C 2 -1 C 2 0 C 2 -1 C 1 -1 C 2 -1 C 2 0 C 2 -1 C 1 -1 C 2 0 C
2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 0 C 2 -1 C 2 -1 C 1 -1 C
2 -1 C 2 0 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 0 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C
1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 0 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C
2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C
2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -1 C
2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -1 C 2 -2 C
1 -1 C 2 -1 C 2 -2 C 2 -1 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -2 C 2 -1 C
2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -2 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C
2 -2 C 2 -1 C 1 -1 C 2 -2 C 2 -1 C 2 -2 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -2 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C
2 -2 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -2 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -2 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -2 C 2 -1 C
1 -2 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -2 C 2 -1 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C
2 -2 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -1 C 2 -2 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C
2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -2 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -2 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C
2 -1 C 2 -1 C 2 -2 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 -1 C 2 -1 C 2 0 C 2 -1 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C
1 -1 C 2 -1 C 2 -1 C 2 0 C 1 -1 C 2 -1 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 -1 C
2 0 C 1 -1 C 2 0 C 2 -1 C 2 -1 C 1 0 C 2 -1 C 2 0 C 2 -1 C 1 0 C 2 -1 C 2 0 C 2 -1 C 1 0 C 2 -1 C 2 0 C 2 0 C 1 -1 C 2 0 C 2 0 C
2 -1 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 -1 C 2 0 C 2 0 C 1 0 C 2 0 C 2 -1 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C
1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 0 C 2 0 C 2 0 C 2 0 C 1 1 C 2 0 C 2 0 C 2 0 C 1 0 C 2 1 C 2 0 C 2 0 C 1 0 C 2 1 C
2 0 C 2 0 C 1 1 C 2 0 C 2 1 C 2 0 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 0 C 2 1 C 1 0 C 2 1 C 2 1 C 2 0 C
1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 0 C 2 1 C
2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 1 C
1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 1 C 1 2 C 2 1 C 2 1 C 2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 2 C 2 1 C
2 1 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 2 C 2 1 C 1 1 C 2 2 C 2 1 C 2 2 C 1 1 C 2 1 C 2 2 C 2 1 C 1 1 C 2 2 C 2 1 C 2 2 C
1 1 C 2 1 C 2 2 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 2 C 2 1 C 2 1 C 1 2 C 2 1 C 2 2 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 2 C
2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 2 C 2 1 C 2 2 C 1 1 C 2 1 C 2 2 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 2 C 2 1 C 2 2 C 1 1 C
2 1 C 2 2 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 2 C 2 1 C 2 1 C 1 2 C 2 1 C 2 2 C 2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 2 C 2 1 C 2 1 C
2 2 C 1 1 C 2 2 C 2 1 C 2 1 C 1 2 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 2 C 2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 1 C
2 2 C 2 1 C 2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 1 C 2 1 C 2 2 C 2 1 C 1 1 C 2 1 C 2 1 C 2 2 C 1 1 C 2 1 C 2 1 C
2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 2 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C
2 1 C 2 2 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 1 C 2 1 C 2 1 C
2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 1 C 2 1 C 2 1 C 1 0 C
2 1 C 2 1 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 1 C 2 0 C
2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 0 C 2 1 C 2 1 C 2 0 C 1 1 C 2 1 C 2 0 C 2 1 C 1 1 C 2 0 C 2 1 C 2 1 C 1 0 C 2 1 C 2 1 C 2 0 C 1 1 C
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