Answer To: 1. Write an M file spline.m such that spline(m(k),m(k+1),p(k), q(k),x0(k), x0(k+1) , x )...
Abr Writing answered on Apr 09 2021
math4446/dspline.m
function Skp = dspline(mk,mkp1,pk,qk,xk,xkp1,x)
hk = xkp1-xk;
Skp = -mk./(2.*hk).*(x-xkp1).^2 + ...
mkp1./(2.*hk).*(x-xk).^2 - pk + qk;
end
math4446/gesolve.m
function x = gesolve(a,b,c,f)
d(1) = a(1);
z(1) = f(1);
n = length(f);
for i=2:n
d(i) = a(i) - b(i-1)*c(i-1)/d(i-1);
z(i) = f(i) - b(i-1)*z(i-1)/d(i-1);
end
%
%solve Ux =z or Backward substitution step
%
x(n) = z(n)/d(n);
for i=n-1:-1:1
x(i) = (z(i) - c(i)*x(i+1))/d(i);
end
x = x';
end
math4446/headbot.m
headb=[
-1,0
-0.95,-0.31225
-0.9,-0.43589
-0.85,-0.52678
-0.8,-0.6
-0.75,-0.66144
-0.7,-0.71414
-0.65,-0.75993
-0.6,-0.8
-0.55,-0.83516
-0.5,-0.86603
-0.45,-0.89303
-0.4,-0.91652
-0.35,-0.93675
-0.3,-0.95394
-0.25,-0.96825
-0.2,-0.9798
-0.15,-0.98869
-0.1,-0.99499
-0.05,-0.99875
0,-1
0.05,-0.99875
0.1,-0.99499
0.15,-0.98869
0.2,-0.9798
0.25,-0.96825
0.3,-0.95394
0.35,-0.93675
0.4,-0.91652
0.45,-0.89303
0.5,-0.86603
0.55,-0.83516
0.6,-0.8
0.65,-0.75993
0.7,-0.71414
0.75,-0.66144
0.8,-0.6
0.85,-0.52678
0.9,-0.43589
0.95,-0.31225
1,0 ];
math4446/headtop.m
headt=[
-1,0
-0.95,0.31225
-0.9,0.43589
-0.85,0.52678
-0.8,0.6
-0.75,0.66144
-0.7,0.71414
-0.65,0.75993
-0.6,0.8
-0.55,0.83516
-0.5,0.86603
-0.45,0.89303
-0.4,0.91652
-0.35,0.93675
-0.3,0.95394
-0.25,0.96825
-0.2,0.9798
-0.15,0.98869
-0.1,0.99499
-0.05,0.99875
0,1
0.05,0.99875
0.1,0.99499
0.15,0.98869
0.2,0.9798
0.25,0.96825
0.3,0.95394
0.35,0.93675
0.4,0.91652
0.45,0.89303
0.5,0.86603
0.55,0.83516
0.6,0.8
0.65,0.75993
0.7,0.71414
0.75,0.66144
0.8,0.6
0.85,0.52678
0.9,0.43589
0.95,0.31225
1,0];
math4446/leyebot.m
leyeb=[
-0.7,0.5
-0.69,0.46878
-0.68,0.45641
-0.67,0.44732
-0.66,0.44
-0.65,0.43386
-0.64,0.42859
-0.63,0.42401
-0.62,0.42
-0.61,0.41648
-0.6,0.4134
-0.59,0.4107
-0.58,0.40835
-0.57,0.40633
-0.56,0.40461
-0.55,0.40318
-0.54,0.40202
-0.53,0.40113
-0.52,0.4005
-0.51,0.40013
-0.5,0.4
-0.49,0.40013
-0.48,0.4005
-0.47,0.40113
-0.46,0.40202
-0.45,0.40318
-0.44,0.40461
-0.43,0.40633
-0.42,0.40835
-0.41,0.4107
-0.4,0.4134
-0.39,0.41648
-0.38,0.42
-0.37,0.42401
-0.36,0.42859
-0.35,0.43386
-0.34,0.44
-0.33,0.44732
-0.32,0.45641
-0.31,0.46878
-0.3,0.5];
math4446/leyetop.m
leyet=[
-0.7,0.5
-0.69,0.53122
-0.68,0.54359
-0.67,0.55268
-0.66,0.56
-0.65,0.56614
-0.64,0.57141
-0.63,0.57599
-0.62,0.58
-0.61,0.58352
-0.6,0.5866
-0.59,0.5893
-0.58,0.59165
-0.57,0.59367
-0.56,0.59539
-0.55,0.59682
-0.54,0.59798
-0.53,0.59887
-0.52,0.5995
-0.51,0.59987
-0.5,0.6
-0.49,0.59987
-0.48,0.5995
-0.47,0.59887
-0.46,0.59798
-0.45,0.59682
-0.44,0.59539
-0.43,0.59367
-0.42,0.59165
-0.41,0.5893
-0.4,0.5866
-0.39,0.58352
-0.38,0.58
-0.37,0.57599
-0.36,0.57141
-0.35,0.56614
-0.34,0.56
-0.33,0.55268
-0.32,0.54359
-0.31,0.53122
-0.3,0.5 ];
math4446/mouth.m
mouthd=[
-0.5,-0.2
-0.475,-0.27806
-0.45,-0.30897
-0.425,-0.3317
-0.4,-0.35
-0.375,-0.36536
-0.35,-0.37854
-0.325,-0.38998
-0.3,-0.4
-0.275,-0.40879
-0.25,-0.41651
-0.225,-0.42326
-0.2,-0.42913
-0.175,-0.43419
-0.15,-0.43848
-0.125,-0.44206
-0.1,-0.44495
-0.075,-0.44717
-0.05,-0.44875
-0.025,-0.44969
0,-0.45
0.025,-0.44969
0.05,-0.44875
0.075,-0.44717
0.1,-0.44495
0.125,-0.44206
0.15,-0.43848
0.175,-0.43419
0.2,-0.42913
0.225,-0.42326
0.25,-0.41651
0.275,-0.40879
0.3,-0.4
0.325,-0.38998
0.35,-0.37854
0.375,-0.36536
0.4,-0.35
0.425,-0.3317
0.45,-0.30897
0.475,-0.27806
0.5,-0.2];
math4446/nose.m
nosed=[
-0.2,0.44
-0.19,0.3776
-0.18,0.3184
-0.17,0.2624
-0.16,0.2096
-0.15,0.16
-0.14,0.1136
-0.13,0.0704
-0.12,0.0304
-0.11,-0.0064
-0.1,-0.04
-0.09,-0.0704
-0.08,-0.0976
-0.07,-0.1216
-0.06,-0.1424
-0.05,-0.16
-0.04,-0.1744
-0.03,-0.1856
-0.02,-0.1936
-0.01,-0.1984
0,-0.2
0.01,-0.1984
0.02,-0.1936
0.03,-0.1856
0.04,-0.1744
0.05,-0.16
0.06,-0.1424
0.07,-0.1216
0.08,-0.0976
0.09,-0.0704
0.1,-0.04
0.11,-0.0064
0.12,0.0304
0.13,0.0704
0.14,0.1136
0.15,0.16
0.16,0.2096
0.17,0.2624
0.18,0.3184
0.19,0.3776
0.2,0.44];
math4446/project2.docx
Matt 4446 Project 2
Clearing the workspace
clear;
close;
clc;
Seleting the format for results
format long e
Problem I
Testing the program
% Defining the given parameters
A = [
5 2 0 0
4 13 -4 0
0 7 15 6
0 0 12 -16
];
f = [
1
2
3
4
];
Getting the solution using MATLAB command
x = A\f
Now getting the solution using the Gaussian elimination and forward algorithm defined under gesolve
n = length(f);
a = zeros(n, 1);
b = zeros(n-1, 1);
c = zeros(n-1, 1);
for i=1:n
a(i) = A(i, i);
if i ~= n
b(i) = A(i+1, i);
c(i) = A(i, i+1);
end
end
x = gesolve(a, b, c, f)
From the results above, we can see that the results are exactly the same from the algorithm to the results from MATLAB command.
Problem II
Testing the program
% Defining the given variables
x = [ -2,-1,0,1,2];
y = [ 2,1,0,1,2];
m =[ 0 , -6/7 , 24/7, -6/7, 0];
p = [ 2,8/7, -4/7, 8/7];
q =[ 8/7, -4/7 , 8/7, 2 ];
figure;
spline_nat(x, y)
Running the MATLAB smile program to plot the natural spline approximation of the smiling face.
figure;
smile
Problem III
Testing the code for a cubic function
x0 = [-1 2 5 8];
n = length(x0);
func = @(x) x.^3;
funcprime = @(x) 3*(x.^2);
y0 = func(x0);
fp = funcprime(x0);
fp0 = fp(1);
fp1 = fp(n);
spline_clam(x0,y0,fp0,fp1,func,funcprime)
From the plot above, as expected we can see that the error is almost equal to zero.
Now testing the code for
i = 0:10;
x0 = i*0.2;
n = length(x0);
func = @(x) x.*exp(x);
funcprime = @(x) exp(x) + x.*exp(x);
y0 = func(x0);
fp = funcprime(x0);
fp0 = fp(1);
fp1 = fp(n);
spline_clam(x0,y0,fp0,fp1,func,funcprime)
Yes, the average error tends to be about zero, which is very small, but the round-off error is not exactly equal to 0. This is still quite a good approximation, although it is not as reliable as in the cubic function.
Appendix
function x = gesolve(a,b,c,f)
d(1) = a(1);
z(1) = f(1);
n = length(f);
for i=2:n
d(i) = a(i) - b(i-1)*c(i-1)/d(i-1);
z(i) = f(i) - b(i-1)*z(i-1)/d(i-1);
end
%
%solve Ux =z or Backward substitution step
%
x(n) = z(n)/d(n);
for i=n-1:-1:1
x(i) = (z(i) - c(i)*x(i+1))/d(i);
end
x = x';
end
function Sk = spline(mk,mkp1,pk,qk,xk,xkp1,x)
hk = xkp1 - xk;
Sk = - mk./(6.*hk).*(x - xkp1).^3 + ...
mkp1./(6.*hk).*(x - xk).^3 + ...
pk.*(xkp1 - x) + ...
qk.*(x - xk);
end
function spline_nat(x0,y0)
n = length(x0);
x0=reshape(x0,1,n);
y0=reshape(y0,1,n);
h = x0(2:n) - x0(1:(n-1));
d = (y0(2:n) - y0(1:(n-1)))./h;
a = 2*(h(1:(n-2)) + h(2:(n-1)));
b = h(2:(n-2));
u = 6*(d(2:n-1) - d(1:n-2));
m = gesolve(a,b,b,u);
m = [0 m' 0];
p = y0(1:(n-1))./h - m(1:(n-1)).*h/6;
q = y0(2:n)./h - m(2:n).*h/6;
hold on
plot(x0, y0, '*');
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),1000);
Sk = spline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
plot(x,Sk,'linewidth',1.5);
end
xlabel('x');
ylabel('f(x)');
title('Natural spline for f(x)');
end
function Skp = dspline(mk,mkp1,pk,qk,xk,xkp1,x)
hk = xkp1-xk;
Skp = -mk./(2.*hk).*(x-xkp1).^2 + ...
mkp1./(2.*hk).*(x-xk).^2 - pk + qk;
end
function spline_clam(x0,y0,fp0,fp1,func,funcprime)
n = length(x0);
x0=reshape(x0,1,n);
y0=reshape(y0,1,n);
h = x0(2:n) - x0(1:(n-1));
d = (y0(2:n) - y0(1:(n-1)))./h;
a = 2*(h(1:(n-2)) + h(2:(n-1)));
a(1) = 3*h(1)/2 + 2*h(2);
a(n-2) = 3/2*h(n-1) + 2*h(n-2);
b = h(2:(n-2));
f=6*(d(2:n-1) - d(1:n-2));
f(1) = f(1) - 3*(d(1) - fp0);
f(n-2) = f(n-2) - 3*(fp1 - d(end));
m = gesolve(a,b,b,f);
m0 = 3*(d(1) - fp0)/h(1) - m(1)/2;
mn = 3*(fp1 - d(end))/h(end) - m(end)/2;
m =[m0 m' mn];
p = y0(1:(n-1))./h - m(1:(n-1)).*h/6;
q = y0(2:n)./h - m(2:n).*h/6;
figure(1);
clf
hold on
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),100);
Sk = spline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
F = func(x);
plot(x,Sk,'linewidth',1.5)
plot(x,F,'linewidth',1.5)
end
xlabel('x')
ylabel('f(x)')
title('Clamped cubic spline and f(x)')
pause
figure(2);
clf
clear F
hold on
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),100);
Skp = dspline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
F = funcprime(x);
plot(x,Skp,'linewidth',1.5)
plot(x,F,'linewidth',1.5)
end
xlabel('x')
ylabel('g(x)')
title('Derivative of clamped cubic spline, g(x)')
pause;
figure(3);
clf;
clear F;
hold on;
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),100);
Sk = spline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
F = func(x);
e = Sk - F;
plot(x,e,'linewidth',1.5)
end
xlabel('x')
ylabel('f(x)')
title('Error of the clamped cubic spline for f(x)')
end
math4446/project2.mlx
[Content_Types].xml
_rels/.rels
mathml/eqn1.mml
mathml/eqn2.mml
matlab/_rels/document.xml.rels
matlab/document.xml
Matt 4446 Project 2 Clearing the workspace clear;
close;
clc; Seleting the format for results format long e Problem I Testing the program % Defining the given parameters
A = [
5 2 0 0
4 13 -4 0
0 7 15 6
0 0 12 -16
];
f = [
1
2
3
4
]; Getting the solution using MATLAB command A\backslash f x = A\f Now getting the solution using the Gaussian elimination and forward algorithm defined under gesolve n = length(f);
a = zeros(n, 1);
b = zeros(n-1, 1);
c = zeros(n-1, 1);
for i=1:n
a(i) = A(i, i);
if i ~= n
b(i) = A(i+1, i);
c(i) = A(i, i+1);
end
end
x = gesolve(a, b, c, f) From the results above, we can see that the results are exactly the same from the algorithm to the results from MATLAB command. Problem II Testing the program % Defining the given variables
x = [ -2,-1,0,1,2];
y = [ 2,1,0,1,2];
m =[ 0 , -6/7 , 24/7, -6/7, 0];
p = [ 2,8/7, -4/7, 8/7];
q =[ 8/7, -4/7 , 8/7, 2 ];
figure;
spline_nat(x, y) Running the MATLAB smile program to plot the natural spline approximation of the smiling face. figure;
smile Problem III Testing the code for a cubic function x0 = [-1 2 5 8];
n = length(x0);
func = @(x) x.^3;
funcprime = @(x) 3*(x.^2);
y0 = func(x0);
fp = funcprime(x0);
fp0 = fp(1);
fp1 = fp(n);
spline_clam(x0,y0,fp0,fp1,func,funcprime) From the plot above, as expected we can see that the error is almost equal to zero. Now testing the code for f\left(x\right)=x\times \mathrm{exp}\left(x\right) i = 0:10;
x0 = i*0.2;
n = length(x0);
func = @(x) x.*exp(x);
funcprime = @(x) exp(x) + x.*exp(x);
y0 = func(x0);
fp = funcprime(x0);
fp0 = fp(1);
fp1 = fp(n);
spline_clam(x0,y0,fp0,fp1,func,funcprime) Yes, the average error tends to be about zero, which is very small, but the round-off error is not exactly equal to 0. This is still quite a good approximation, although it is not as reliable as in the cubic function. Appendix function x = gesolve(a,b,c,f)
d(1) = a(1);
z(1) = f(1);
n = length(f);
for i=2:n
d(i) = a(i) - b(i-1)*c(i-1)/d(i-1);
z(i) = f(i) - b(i-1)*z(i-1)/d(i-1);
end
%
%solve Ux =z or Backward substitution step
%
x(n) = z(n)/d(n);
for i=n-1:-1:1
x(i) = (z(i) - c(i)*x(i+1))/d(i);
end
x = x';
end
function Sk = spline(mk,mkp1,pk,qk,xk,xkp1,x)
hk = xkp1 - xk;
Sk = - mk./(6.*hk).*(x - xkp1).^3 + ...
mkp1./(6.*hk).*(x - xk).^3 + ...
pk.*(xkp1 - x) + ...
qk.*(x - xk);
end
function spline_nat(x0,y0)
n = length(x0);
x0=reshape(x0,1,n);
y0=reshape(y0,1,n);
h = x0(2:n) - x0(1:(n-1));
d = (y0(2:n) - y0(1:(n-1)))./h;
a = 2*(h(1:(n-2)) + h(2:(n-1)));
b = h(2:(n-2));
u = 6*(d(2:n-1) - d(1:n-2));
m = gesolve(a,b,b,u);
m = [0 m' 0];
p = y0(1:(n-1))./h - m(1:(n-1)).*h/6;
q = y0(2:n)./h - m(2:n).*h/6;
hold on
plot(x0, y0, '*');
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),1000);
Sk = spline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
plot(x,Sk,'linewidth',1.5);
end
xlabel('x');
ylabel('f(x)');
title('Natural spline for f(x)');
end
function Skp = dspline(mk,mkp1,pk,qk,xk,xkp1,x)
hk = xkp1-xk;
Skp = -mk./(2.*hk).*(x-xkp1).^2 + ...
mkp1./(2.*hk).*(x-xk).^2 - pk + qk;
end
function spline_clam(x0,y0,fp0,fp1,func,funcprime)
n = length(x0);
x0=reshape(x0,1,n);
y0=reshape(y0,1,n);
h = x0(2:n) - x0(1:(n-1));
d = (y0(2:n) - y0(1:(n-1)))./h;
a = 2*(h(1:(n-2)) + h(2:(n-1)));
a(1) = 3*h(1)/2 + 2*h(2);
a(n-2) = 3/2*h(n-1) + 2*h(n-2);
b = h(2:(n-2));
f=6*(d(2:n-1) - d(1:n-2));
f(1) = f(1) - 3*(d(1) - fp0);
f(n-2) = f(n-2) - 3*(fp1 - d(end));
m = gesolve(a,b,b,f);
m0 = 3*(d(1) - fp0)/h(1) - m(1)/2;
mn = 3*(fp1 - d(end))/h(end) - m(end)/2;
m =[m0 m' mn];
p = y0(1:(n-1))./h - m(1:(n-1)).*h/6;
q = y0(2:n)./h - m(2:n).*h/6;
figure(1);
clf
hold on
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),100);
Sk = spline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
F = func(x);
plot(x,Sk,'linewidth',1.5)
plot(x,F,'linewidth',1.5)
end
xlabel('x')
ylabel('f(x)')
title('Clamped cubic spline and f(x)')
pause
figure(2);
clf
clear F
hold on
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),100);
Skp = dspline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
F = funcprime(x);
plot(x,Skp,'linewidth',1.5)
plot(x,F,'linewidth',1.5)
end
xlabel('x')
ylabel('g(x)')
title('Derivative of clamped cubic spline, g(x)')
pause;
figure(3);
clf;
clear F;
hold on;
for i = 1:(n-1)
x=linspace(x0(i),x0(i+1),100);
Sk = spline(m(i),m(i+1),p(i),q(i),x0(i),x0(i+1),x);
F = func(x);
e = Sk - F;
plot(x,e,'linewidth',1.5)
end
xlabel('x')
ylabel('f(x)')
title('Error of the clamped cubic spline for f(x)')
end
matlab/output.xml
manual document ready 0.4 matrix x 4×1 4 1 double 1.338393927287255e-01
1.654015181781862e-01
1.713943268078306e-01
-1.214542548941270e-01
double double [[{"value":"{\"value\":\"1.338393927287255e-01\"}"},{"value":"{\"value\":\"1.654015181781862e-01\"}"},{"value":"{\"value\":\"1.713943268078306e-01\"}"},{"value":"{\"value\":\"-1.214542548941270e-01\"}"}]] 19 matrix x 4×1 4 1 double 1.338393927287255e-01
1.654015181781862e-01
1.713943268078306e-01
-1.214542548941270e-01
double double [[{"value":"{\"value\":\"1.338393927287255e-01\"}"},{"value":"{\"value\":\"1.654015181781862e-01\"}"},{"value":"{\"value\":\"1.713943268078306e-01\"}"},{"value":"{\"value\":\"-1.214542548941270e-01\"}"}]] 32 figure cba6917a-d32d-4f77-852e-b33351d568dd data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA0gAAAJ2CAYAAABl4KKyAAAgAElEQVR4AezBD1zVhaH//5cfRORY1hFRPMUwHk0K2trilEFOsjFzpc4ymJpS1FILWypb/+xeYvda7RalRXbJzPJUOtBaLDQbE/8UpDusmw3t1GLQseOfE51vlkfwKOf3+/j7fu6P67XCf8if9/NphEVEREREROQwAxERERERETnMQERERERERA4zEBERERERkcMMRERERERE5DADEREREREROcxAREREREREDjMQERERERGRwwxERERERETkMAMRERERERE5zEBEREREREQOMxAREREREZHDDEREREREROQwAxERERERETnMQERERERERA4zEBERERERkcMMRERERERE5DADEREREREROcxAREREREREDjMQERERERGRwwxERERERETkMAMRERERERE5zEBEREREREQOMxARkf+2adMmxo4dy9ixY7nxxhtpbW3laP7lX/6FsWPHMnbsWJqbmzkZGhsb6ayqqqoYO3YsY8eO5cknn6SzqKqqYuzYsYwdO5Ynn3wSS1VVFWPHjmXs2LE8+eSTdCZ79+5l1qxZnH322fTq1Yv+/ftz/fXXczrs3buXWbNmcfbZZ9OrVy/69+/P9ddfT1sZGRn06tWLJUuWcDwCgQB9+vThjDPOoL6+HhGRzs5ARET+m8/no6KigoqKCl555RXmz5/P0bz77rtUVFRQUVHBwYMHORH19fVMmDCBvLw8OqsdO3ZQUVFBRUUFH3zwAZ3Fjh07qKiooKKigg8++ADLjh07qKiooKKigg8++IDOZMaMGTz99NN8+eWXmL766iuam5s5HWbMmMHTTz/Nl19+iemrr76iubkZi8vlYuPGjQwcOJDc3FyOh91u51e/+hX79u3j17/+NSIinZ2BiIh8o/nz51NfX8+pUltbywUXXMDrr7+O9AyrVq3C8sgjj/Daa68xb948TodVq1ZheeSRR3jttdeYN28eptbWVh544AFMubm5GIbB8brpppswVVRUsGnTJkREOjMDERH5Ri0tLfz617/mVNm9ezehUAg5uaZNm0Y4HCYcDrN48WI6i4MHDxIKhTBFRkZyzz33MGHCBK644go62sGDBwmFQpgiIyO55557mDBhAldccQWmpUuX8umnn2LKycnhRAwfPpykpCRMv/vd7xAR6cwMRETkW1VUVFBeXs6xqKqq4u677+bGG2/kxhtv5LbbbmP58uUcOHAAy6ZNm1i3bh2WHTt24HK5qKysxPSPf/wDl8uFy+Vi8+bNtHXw4EFcLhcul4s//OEPtLV582ZcLhcul4vPPvuMd955h5tuuokZM2ZQU1ODpaqqirvvvpsbb7yRG2+8kdtuu43ly5dz4MABToYDBw6wfPlybrvtNiZPnsy0adOYN28emzZt4kgfffQRLpcLl8uF1+vl66+/ZtGiRUybNo2bbrqJV199lWNRX1+Py+XC5XJRU1ODpb6+HpfLhcvlorGxEdPy5cvJzc1l2rRpPPbYYzQ1NXE0n332Gb///e+ZNm0a06ZN4/HHH8fr9dJeGzZswOVy0ZbL5cLlcrFz507a2rRpE7Nnz+bGG2/kpptuYtGiRfj9fo60efNmXC4XLpeLzz77jHfeeYebbrqJGTNmUFNTwzfZsGEDLpeLtlwuFy6Xi507d2J69tlnMSUmJnLRRRdh+a//+i9cLhculwuXy0VzczNtuVwuXC4XLpeLrVu3YsnKysJUWVlJfX09IiKdlYGIiBxVVFQUlrvuuovm5ma+S2trKxMmTOCqq67i0Ucf5ZVXXuGVV17hueeeY8qUKVx00UXs3LkT06JFiygqKsLy/vvvk5OTw+9//3tMGzZsICcnh5ycHFwuF201NzeTk5NDTk4Os2bNoi2Xy0VOTg45OTksXLiQUaNGsWzZMp599lmee+45WltbmTBhAldddRWPPvoor7zyCq+88grPPfccU6ZM4aKLLmLnzp2ciMbGRpKSkpgyZQrPPfccK1as4KWXXuKhhx5i5MiRTJ48mbYqKyvJyckhJyeHVatWcfHFF5OXl8dLL73EsmXLmDhxIj/96U/5+uuvaY933nmHnJwccnJyeP7557G888475OTkkJOTw5/+9CeGDx/OlClTeOGFF3jppZf47W9/S3JyMvX19bT1hz/8gaSkJO69915eeuklXnrpJfLz8/n+97/P0qVLaY+FCxdyyy23YAmFQuTk5JCTk0NdXR2mnTt3csUVVzBy5EgWLlzIK6+8wrJly8jLy+O8885j6dKltOVyucjJySEnJ4eFCxcyatQoli1bxrPPPstzzz3HN1m4cCG33HILllAoRE5ODjk5OdTV1VFfX8+WLVswXXnllbQ1ePBg7rrrLnJycsjJyeHBBx/E8vDDD5OTk0NOTg6/+c1vGDx4MJbhw4djKSsrQ0SkszIQEZGjysrKYujQoZgaGhqYP38+3+XRRx/l9ddfxzRw4EAmTZrExIkTOeusszB9/PHHPPjgg3SUxx9/nFAohGXq1Kk8+uijvP7665gGDhzIpEmTmDhxImeddRamjz/+mAcffJATcfPNN9PQ0IApKyuLe+65h1tuuQW73Y5pxYoVLFq0iKO59957qa+vZ+TIkVx55ZVY1q1bx2233cbJcu+991JbW8u4ceO47rrriIiIwLRnzx4KCwuxvPPOO0yaNIl9+/Zh+vnPf87EiROJioqipaWFW265hTfffJPv0rt3b6KiomgrKiqKqKgoIiIiCAaDZGRkUF1djSkiIoLLL7+cuLg4TPv27eOWW27hxRdf5Ggef/xxQqEQlqlTp/JNevfuTVRUFG1FRUURFRVFREQEmzZtwpKZmUlbQ4YM4bnnnsPy2GOP8V//9V98+OGHFBYWYnnxxRcZPHgwltGjR2OpqqpCRKSzMhARkaPq27cvTz31FJaHH36Ybdu28W327t3LD37wA6Kiovjb3/7G8uXLWblyJa+99hoWr9eLafny5VRUVGC59tprCYfD/PnPf+ZkOXToEMuWLaOlpYU1a9YwatQo9u7dyw9+8AOioqL429/+xvLly1m5ciWvvfYaFq/Xy/FqbW1l/fr1mEaMGEFpaSmPPPIIS5YsYe3atVx99dXccsstXHjhhRxNS0sLa9asYcOGDVRVVbF27VoiIiIwrVixgo8++oiTobm5mU2bNlFeXs6rr77Kk08+ieWtt97Ccvfdd2N54YUXWL16NStXruSdd94hIiIC0wMPPMB3KS0tZe/evViioqJobm6mubmZUaNG8eijj/Lxxx9jGjp0KJ988gk1NTXs3LmToqIiLHfeeSdNTU0c6dChQyxbtoyWlhbWrFnDqFGj+CalpaXs3bsXS1RUFM3NzTQ3NzNq1CjWrVuHJTY2liNdf/31/OpXv8J06NAhbr75ZqZMmUJLSwumu+66izFjxtBWnz59OPPMMzFt3LgREZHOykBERL7R2LFj+cUvfoHp0KFDzJgxg28zf/58tm7dSjAYJD4+HtPBgwf5/PPPsXg8HjrKyJEjmTZtGn369GHMmDGY5s+fz9atWwkGg8THx2M6ePAgn3/+ORaPx8PxMgyDyMhITG+//TZXXHEFDz/8MJs2bSI1NZU333yTJUuWMGrUKI7m5z//OWPGjMEyevRoxo8fj+Wtt97iZBg9ejRpaWlYfvnLX2LZt28fpkAgQHV1NaZ+/fpx0003YUlNTWX06NGYamtr8fv9nIhly5ZhKSkpISEhAcvcuXMZOXIkpq+++opVq1ZxpJEjRzJt2jT69OnDmDFjOBGBQADLZZddxtEsXLiQ73//+5jef/993nvvPUwpKSk88sgjHM2IESMw7d+/n+bmZkREOiMDERH5Vk8//TRnnnkmprfffhuXy8W3OXDgAGVlZeTm5jJ8+HD69u1LdnY2lubmZjrKsGHDOJoDBw5QVlZGbm4uw4cPp2/fvmRnZ2Npbm7mRMyaNQtLdXU1999/PyNHjsRms5Gdnc0777zDN0lNTeVIw4cPx/Lee+9xMgwePJi2zjzzTCwHDhzAtHnzZiytra1MnjyZyZMnM3nyZCZPnkxdXR2Wv/71rxyvAwcOUF9fjykiIoLMzEyOlJmZiaWmpoYjDRs2jJNl3759WPr27cvR2Gw2SktLiYiIwBIVFcWKFSvo27cvR9O7d28s9fX1iIh0RgYiIvKtzjnnHB588EEsv/nNbwgEAhxNTU0NCQkJTJo0iRdeeIEtW7YQHx/PlClTsMTGxnKiWltbaY9BgwZxpJqaGhISEpg0aRIvvPACW7ZsIT4+nilTpmCJjY3lRDz++OP867/+KwMHDqStlpYWysrKGDFiBA8//DBHc9ZZZ3GkgQMHYjl48CAnQ+/evfkura2tWPbv38+KFStYsWIFK1asYMWKFXz66adY9u3bx/E6cOAAlt69e2MYBkdyOBxYDh48yJEGDRrEybJ7924sffr04Zucc845xMTE0F69e/fG0tTUhIhIZ2QgIiLfae7cuVx88cWY9uzZQ21tLUdqbW1l0qRJ7Nq1C9NDDz3Erl27+Oc//8kzzzyDJTY2lmMVCoVoa/v27bRHYmIibbW2tjJp0iR27dqF6aGHHmLXrl3885//5JlnnsESGxvLiSosLGT37t2sW7eO+++/nyuvvJLIyEgsBQUFHDx4kCPV1dVxpA8++ADL4MGD6ShnnXUWlu9///ts3LiRjRs3snHjRjZu3MjGjRvZuHEjGzdu5Morr+R42Ww2IiIiMLW0tBAIBDhSbW0tliFDhnCkxMRETpbvfe97WA4cOMA3ue2229izZw+WlpYWpkyZwoEDBziaAwcOYPnxj3+MiEhnZCAiIu3ywgsv8G22bt3Kp59+iumyyy7jvvvuY/DgwZjef/99jpVhGFiCwSBtffjhhxyPrVu38umnn2K67LLLuO+++xg8eDCm999/n5PB6/Xy8ssvM2vWLJ588klGjRrF/PnzqaqqYvfu3fTr1w9TKBRi9+7dHOnNN9/k66+/pq1169Zhufzyy+kow4cPJzIyElNDQwPJycn85Cc/4Sc/+Qk/+clPeO211/j00085ePAgMTExHC/DMLjiiiuwLFiwgLYCgQCvv/46lmuvvZZT6ayzzsJSX1/P0SxZsoTXX38dk8PhwOFwYPrggw+49957OZodO3ZgioiI4IwzzkBEpDMyEBGRdvnRj37E7bffzjc544wzsLz33nvU1tZi8nq93H333Vg++ugjLIZhYHnvvfd44403eOONNzDZ7XYsr7/+OpWVlRw8eJDVq1dz9913czzOOOMMLO+99x61tbWYvF4vd999N5aPPvqI4xUIBJg6dSpPP/009957L2+++SaWjz76iAMHDmDq168fQ4YM4Ui7du3i2muv5Z133mHr1q1MmzaNDz74ANPAgQMZO3YsHaV3797cdNNNmEKhEJMmTcLr9dLa2srDDz/ME088wdSpU8nJyeFEzZo1C8vvfvc75s2bx1tvvUV5eTmjRo3C5/NhSk9PJyMjg1MpOTkZyz/+8Q+O9I9//IM5c+ZgWbx4MYsXL8byxBNPUFVVxZE+/PBDTBdddBEiIp2VgYiItNv8+fOJi4vjaM4//3wuu+wyTKFQiOHDh3P22Wdz3nnn8e6779KvXz9Mu3fvxpKenk5ERAQmn8/HuHHjmDJlCqbRo0cTFxeH6auvvuJnP/sZkZGRXHvttcTExBAdHc2xOv/887nsssswhUIhhg8fztlnn815553Hu+++S79+/TDt3r2b4/XDH/6Qe+65B1NLSws///nPsdls2Gw2Lr/8ckKhEKb/+I//wDAMjnTWWWexceNGRowYwcUXX8xLL72Epbi4mD59+tCR/v3f/x2Hw4GpsrKS733ve0RERHD//fdjWbJkCYZhcCKysrLIy8vD8tBDD3H11Vfzi1/8gvfffx/TueeeS2lpKadaWloalo8++oi2WltbufHGG/nqq68w3XzzzVxzzTVcc801TJ06FcvUqVMJBAJYGhsbaWlpwTR8+HBERDorAxERaTe73c7jjz/ON/njH//IiBEjMB06dIgvv/ySYcOGsX79eq677jpMLS0tbNiwAVP//v155JFHiIiIwHLw4EFMNpuN8vJykpKSaGvixIls2LCB3r17czz++Mc/MmLECEyHDh3iyy+/ZNiwYaxfv57rrrsOU0tLCxs2bOB4PfLII5SUlPC9730P0/79+9m/fz+moUOHsmzZMu644w6OZurUqRQVFREVFYXF4XCwatUqfvnLX9LRBg8ejNvt5rrrriMiIoK2UlJSWL9+PaNHj+ZkKC4uZtmyZVx44YW0FRkZyc0338zf/vY3zjnnHE61q666ijPPPBPTu+++S1v/9m//xpYtWzDFxcXx+OOPY1mwYAGDBg3C5PP5mDFjBpZ3330Xy7XXXouISGdlICIi/+2Xv/wl4XCYcDjM4sWLOZrJkycTDocJh8OEw2HOOOMMLEOGDGHTpk18/PHHrF27Fo/Hw7Zt28jIyMDlchEOhwmHw2RkZGD5zW9+g9/vZ82aNVRXV/P1119jufTSS/nwww+pq6tjzZo1fPnll6xcuZLY2Fj27t1LOBzG7/fTVnFxMeFwmHA4zK233sqRhgwZwqZNm/j4449Zu3YtHo+Hbdu2kZGRgcvlIhwOEw6HycjIwDJt2jTC4TDhcJjFixfTHtOnT6exsZEdO3awdu1a1q5di8/n45///CfTpk3j28ydO5evv/6aP//5z2zZsoXPPvuM66+/niNNmzaNcDhMOBxm8eLFWKZNm0Y4HCYcDrN48WIs06ZNIxwOEw6HWbx4MW316dOHcDhMOBymubmZtoYMGcKrr75Kc3Mz69evZ82aNezYsYO///3vZGRk0F59+vQhHA4TDodpbm7maKZNm8a2bdvw+XysWbOGt99+m2AwyNKlS4mNjaWt4uJiwuEw4XCYW2+9lWPRp08fwuEw4XCY5uZm2jIMg8mTJ2NavXo1bRUUFBAOhwmHw+zcuRO73Y4lJiaG3bt3Ew6HCYfDlJaWYnnzzTcxDRw4kLFjxyIi0lkZSIcKhUJs2LCB1atXs27dOoLBIMeqV/46RKRzO//88xk9ejTDhg2jPex2O2PGjCEtLQ3DMDhScnIyY8aMoX///pws559/PqNHj2bYsGGcSueccw6jR49m9OjRDBkyhPbq3bs3mZmZXHrppXQWvXv3JiMjgzFjxnDOOedwKg0ZMoQxY8ZwxRVX0Lt3bzpaXl4epn379lFVVcWJaG1t5c0338R06623YhgGInLq9Mpfhxw/A+kwK1euZPjw4UyfPp05c+Zw++23c+mll7J48WJEREQ6kx/+8IeMGzcO0/PPP8+JWL16Nbt27aJfv37MmTMHEZHOzEA6RGVlJfPmzWPo0KG8/PLLbN26lVdffZUf//jHPPbYY7zyyit8k1GL/sb6TwIcTcMXzeSu2I6IiMjJ9sgjjxAREcEf/vAHdu/ezfF64oknMP32t79l8ODBiMjJNWrR31j/SYCjafiimdwV25H2M5AOsWjRInr37s3zzz+P0+kkKiqKlJQUnn32Wc4880yee+45vsnSScnkrtjO+k8CtNXwRTO5K7ZRMPo8RES6sjFjxvDaa6/x2muvMX36dKRzSE5O5sknn2Ty5Ml88MEHHI+mpibOPfdcfvWrX3HfffchIiff0knJ5K7YzvpPArTV8EUzuSu2UTD6PKT9DKRDREREMGLECM4++2zastlspKam8tlnn/FNhg7oS9Xtl5C7YjvrPwlgaviimdwV21g6KZmhA/oiItKVJSYmMmHCBCZMmMAPf/hDpPO44447ePHFF8nMzOR4xMTE8OKLL7J48WL69OmDiJx8Qwf0per2S8hdsZ31nwQwNXzRTO6KbSydlMzQAX2R9jOQDlFWVkZJSQlHam1t5e9//zv9+vXj2wwd0Jeq2y8hd8V2TLkrtrF0UjJDB/RFRERERHq2oQP6UnX7JeSu2I4pd8U2lk5KZuiAvsixMZDT6sUXX+Tzzz8nKyuLI/XKX0ev/HX0yl9Hr/x1nDe/moYvmpn1f17lY8/HnDe/ml756+iVv45e+evolb8OEREREekZeuWvo1f+Onrlr6NX/jrGL17Imb03YVr/yf/hvPnV9MpfR6/8dfTKX0ev/HXIdzOQ02bTpk089thjnHPOOeTl5XGkcNFVhIuuIlx0FeGiqzhwz/d5zFjNnV++yrrP5jCxajrD3ridYW/czrA3bufJoXWIiIiISM8QLrqKcNFVhIuu4ot/u4Brzl/BNeev4JrzVzB0QF+q7vgx4aKrCBddRbjoKsJFVyHfzUBOi8rKSu644w7OOussnn/+efr378+3afiimdEr/dyYcJDPeg/E9OjwGEpWv4vH48Hj8XDnnXciIiIiIj1LIOijzF1AW1W3X0Luiu2s/ySAHBsD6XAlJSXk5eURGxvLypUrGTp0KN+m4YtmcldsY+mkZOJmLcAUGRtPyO9lV/Ec1n8SQERERER6ptqGcur9bkx2m4PV/5jE0AF9qbr9EnJXbGf9JwGk/QykQ91///08/vjj/OhHP2LlypU4HA6+y4t/3cnSSckMHdAX070xMwj5vZgu8b7FmtdXIyIiIiI9T21jOZXbSzDZbQ6ynIVYhg7oS9Xtl1C49p9I+xlIh/n1r3/NqlWr+NnPfsayZcsYMGAA7VFw9XkMHdAXy5a+FxKTnY/l1urfEqyrRkRERER6jkDQR5m7AJPd5iA1YRyJsU7aGjqgL1V3XIK0n4F0iGeeeYa1a9dy7bXXUlxcTFRUFCciJjuf6JQ0TJGx8TSVFiEiIiIiPUMg6KPMXYAlMdZJZvJM5MQZyCn3xRdfsGjRIkzNzc3MnTuXuXPnMnfuXObOncvcuXOZO3cuhw4doj2GvXE7pvjCVUSnpBHye9lfV0NTaREiIiIi0v3VNpRT73djstscZDkLsYSLrkKOn4Gcclu2bOHAgQOY/vKXv1BRUUFFRQUVFRVUVFRQUVFBRUUFra2tHKuY7HwsTaVFBOuqEREREZHuq7axnMrtJZjsNgdZzkLk5DGQU27MmDF4PB48Hg8ejwePx4PH48Hj8eDxePB4PHg8HiIjIzlWtpR04vIWYNlRcAOhPV5EREREpPsJBH1UbivBZLc5SE0YR2KsEzl5DKTL6z8qm+iUNCxNpUWIiIiISPcSCPoocxcQCPow2fs5yEyeiZxcBtItxOUtIDI2HtPe9aU0lRYhIiIiIt1HbUM59X43ptSE8WQ5C5GTz0C6hchB8Qye9QSWvVWlBOuqEREREZGur97vpnJ7CZbUhHHYbQ7k5DOQbsOWkk5Mdj6mkN/L7uI5iIiIiEjXFgj6qNxegiXzwhkkxjqRU8NAupWY7HyiU9IwhfxevAUTEREREZGuKRD0UeYuoN7vxmS3OchMnomcOgbS7cTlLcCyv66GptIiRERERKTrqW0op97vxmS3OZiesRg5tQyk24kcFM+5hSux7K0qJVhXjYiIiIh0HYGgj8rtJVgyk2dgtzmQU8tAuiVbSjrRKWlExsYT8ntpKi1CRERERLqGQNDHsxtuw5KaMJ7UhPHIqWcg3VZ84Sp6DzoX0/66GrwFExERERGRzq9yWwmBoA+T3eYgy1mIdAwD6dbi8hZg2V9Xw96qUkRERESk86ptLKe2sRyT3eZgesZipOMYSLcWOSiecwtXYmkqLSJYV42IiIiIdD6BoI8ydwGW1IRx2G0OpOMYSLdnS0knOiUNU8jvZXfxHERERESkcwkEfTy74TYsqQnjyUyeiXQsA+kR4gtXEZ2Shink9+ItmIiIiIiIdB71fjeBoA+T3eYgy1mIdDwD6TFisvOx7K+rIVhXjYiIiIicfrWN5ZS5CzDZbQ6ynIXI6WEgPYYtJZ2Y7HwsOwpuIFhXjYiIiIicPoGgj8ptJVhSE8aRGOtETg8D6VFisvOJTknD0lRahIiIiIicHoGgjzJ3AYGgD7vNQWKsk8zkmcjpYyA9TnzhKiJj44mMjWd/XQ1NpUWIiIiISMerbSin3u/GkuUsRE4vA+mRBs96gpDfi6mptIhgXTUiIiIi0nFqG8up3F6CyW5zkOUsxG5zIKeXgfRItpR0YrLzMUXGxrOj4AZCe7yIiIiIyKkXCPqo3FaCJTVhHImxTuT0M5AeKyY7n/5XZhPyezHteno2IiIiInJqBYI+ytwFBII+THabg8zkmUjnYCA9Wkx2Ppb9dTU0lRYhIiIiIqdObUM59X43JrvNwfSMxUjnYSA9WuSgeM4tXImlqbSIYF01IiIiInLy1fvdVG4vwZLlLMRucyCdh4H0eLaUdGKy87HsLp6DiIiIiJxcgaCPMncBltSE8STGOpHOxUDk/xWTnU90ShqmkN+Lt2AiIiIiInLyVG4rIRD0YbLbHGQ5C5HOx0Dk/4rLW0BkbDym/XU1BOuqEREREZETV9tYTm1jOSa7zUGWsxDpnAxE/q/IQfHEZOdj2VFwA8G6akRERETk+AWCPsrcBVhSE8aRGOtEOicDkTb6j8omOiUNy+7iOYiIiIjI8QkEfTy74TYsqQnjyUyeiXReBiJHiC9cRXRKGqaQ38uu4tmIiIiIyLGrbSgnEPRhstscZDkLkc7NQOQoYrLzsexdX0qwrhoRERERab/axnIqt5dgstscZDkLkc7PQOQobCnpxOUtwLKj4AZCe7yIiIiIyHcLBH2UuQuwpCaMIzHWiXR+BiLfoP+obKJT0rDseno2IiIiIvLtAkEfZe4CLImxTjKTZyJdg4HIt4jLW4Blf10NTaVFiIiIiMg3q20oJ7DPh8luc5DlLES6DgORbxE5KJ7zFm3G0lRaRLCuGhERERH53+r9biq3lxAI+jBlOQux2xxI12Eg8h0iB8UTk52PZXfxHERERETkfwoEfZS5C7CkJownMdaJdC0GIu0Qk51PdEoappDfi7dgIiIiIiLy/ytzFxAI+jDZbQ6ynIVI12Mgx626uoF8whgAACAASURBVBqv18uxOnToEBs2bGD16tVs2LCBQ4cO0RXE5S3Asr+uhr1VpYiIiIgI1DaWU+93Y7LbHEzPWIx0TQZyXDZv3kxubi6bN2/mWLz99tuMHDmS6dOnM2fOHKZPn87IkSN5++236ewiB8VzbuFKLLuenk2wrhoRERGRniwQ9FHmLsCSmjAOu82BdE0Gcsy2bNlCXl4ex8rr9ZKXl4dhGDz33HP8/e9/x+VyYRgGt99+Ow0NDXR2tpR0olPSsOwunoOIiIhITxUI+ihzF2BJTRhPZvJMpOsykHYLhUIsWrSIm2++mZaWFo7V66+/TnNzM/fccw8/+clPiIyM5LLLLmPevHkcOHCAsrIyuoL4wlVExsZjCvm97CqejYiIiEhPVNtQTr3fjcluc5DlLES6NgNpt1mzZrFw4UIyMjJ44IEHOFafffYZpgEDBtDWhRdeiOnzzz+nqxg86wkse9eXEqyrRkRERKQnqW0sp3J7CSa7zUGWsxDp+gyk3S644AKWLFnCM888Q0xMDMfqiiuuwPTXv/6Vtt566y1MF198MV2FLSWduLwFWHYU3EBojxcRERGRniAQ9FG5rQRLasI4EmOdSNdnIO02Z84cRowYwfEaO3YsEyZMYNGiRdx1112sWrWK3/72tzz22GNcffXVTJo0ia6k/6hsolPSsOx6ejYiIiIi3V0g6KPMXUAg6MOUmjCezOSZSPdgIB3q6quvJj4+njfffJP777+f8vJy4uLimDhxIoZh0F5JSUkkJSWRlJREUlISSUlJPPXUU3S0uLwFWPbX1dBUWoSIiIhId1bbUE69343JbnOQmTwD6T4MpMMsX76c22+/nYSEBNauXYvH42Ht2rVccMEFTJ8+nZdeeon28ng8eDwePB4PHo8Hj8fDnXfeSUeLHBTPuYUrsTSVFhGsq0ZERESkOwoEfVRuL8GSmTwDu82BdB8G0iFaW1spKioiLi6O4uJihg4dimno0KEsWrSI8847j8cee4xDhw7R1dhS0olOScOyu3gOIiIiIt1NIOjj2Q23YUlNGE9qwnikezGQDvHpp5/y1VdfcemllxIdHU1bERERXHLJJezfv5/NmzfTFcUXriI6JQ1TyO9lV/FsRERERLqTym0lBII+THabgyxnIdL9GEiH6N+/P6ZQKMTRHDp0CFN0dDRdVUx2Ppa960sJ1lUjIiIi0h3UNpZT21iOyW5zkOUsRLonA+kQAwYMICEhgcrKSnbu3Elbe/fupbq6mpiYGC6++GK6KltKOjHZ+Vh2FNxAaI8XERERka4sEPRR5i7AkpowjsRYJ9I9GchJ53a7SUpKIjc3l7bmzZvHwYMHmTJlCqtWraK6upo33niDKVOmsGfPHu6//34Mw6Ari8nOJzolDcuup2cjIiIi0lUFgj7K3AVYEmOdZCbPRLovA+kwGRkZLFmyhIiICO6//35yc3PJz89n3759LFy4kLFjx9IdxOUtwLK/roam0iJEREREuqLahnLq/W5MdpuDLGch0r0ZyHHJzMzE4/Fwww03cCSn04nH42Hp0qUcacSIEVRWVrJ27VqWLl3K2rVrqaqqYsyYMXQXkYPiObdwJZGx8ZiaSosI1lUjIiIi0pUEgj4qt5dgyUyegd3mQLo3Azkthg4dSnp6OkOHDqU7sqWk03vQuViaSosQERER6SoCQR/PbrgNS2rCeFITxiPdn4HIKRJfuIrolDRMB/fswFswEREREZGuoLahnEDQh93mwG5zkOUsRHoGA5FTKCY7n8jYeEJ+L/vragjt8SIiIiLSmdU2llPb+CcsWc5CpOcwEDmFbCnp9B+VjeWfdwwntMeLiIiISGcUCPqo3FZCIOjDlJowjsRYJ9JzGIicYjHZ+USnpBEZG4+pqbQIERERkc4mEPRR5i4gEPRhSox1kpk8E+lZDEQ6QFzeAkJ+L6a960tpKi1CREREpDOpbSin3u/GZLc5yHIWIj2PgUgHiBwUz7mFK7E0lRYRrKtGREREpDMIBH1Ubi/Bkpk8A7vNgfQ8BiIdxJaSTnRKGpbdxXMQEREROd0CQR9l7gIsqQnjSU0Yj/RMBiIdKL5wFZGx8ZhCfi+7imcjIiIicjrVNpRT73djstscZDkLkZ7LQKSDDZ71BJa960sJ1lUjIiIicjrU+91Ubi/BZLc5yHIWIj2bgUgHs6WkE5Odj2V38RxEREREOlog6KPMXYAlNWEcibFOpGczEDkNYrLziU5JwxTye/EWTERERESkI5W5CwgEfZjsNgeZyTMRMRA5TeLyFmA5uGcHwbpqRERERDpCbWM59X43psRYJ9MzFiNiMhA5TSIHxROXtwBTyO9lR8ENBOuqERERETmVAkEfZe4CLIkDU7HbHIiYDEROo/6jsolOScOyv64GERERkVMlEPRR5i7AkhjrJDN5JiIWA5HTLL5wFZa9VaU0lRYhIiIicirUNpRT73djstscZDkLEWnLQKQTOLdwJZGx8YT8XppKiwjWVSMiIiJyMgWCPiq3l2DJchZitzkQactApBOwpaQTnZKGpam0CBEREZGTJRD08eyG27CkJownMdaJyJEMRDqJuFkLiIyNx7S/roZdxbMRERERORlqG8oJBH2Y7DYHWc5CRI7GQKQTGTzrCSx715cSrKtGRERE5ETU+91Ubi/BZLc5yHIWIvJNDEQ6EVtKOjHZ+Vh2F89BRERE5HgFgj4qt5dgSU0YR2KsE5FvYiDSycRk5xOdkoYp5PfiLZiIiIiIyPGo3FZCvd+NyW5zkJk8E5FvYyDSCcXlLcCyv66GYF01IiIiIseitrGc2sZyTHabgyxnISLfxUCkE4ocFE9Mdj6WHQU3ENrjRURERKQ9AkEfZe4CTImxTlITxpEY60TkuxiIdFIx2flEp6Rh2fX0bERERETao8xdgN3mwJKZPBOR9jAQ6cTi8hZg2V9XQ1NpESIiIiLfpraxnMA+H4GgD7vNQZazEJH2MhDpxCIHxXNu4UosTaVFBOuqERERETmaQNBHmbuAQNCHKTN5BnabA5H2MhDp5Gwp6USnpGFpKi1CRERE5EiBoI8ydwF2mwNTasJ4UhPGI3IsDES6gPjCVVj219XQVFqEiIiISFu1DeUE9vkIBH3YbQ4yk2cgcqwMRLqIcwtXYmkqLSJYV42IiIiIKRD0Ubm9hEDQhynLWYjd5kDkWBmIdBG2lHSiU9Kw7C6eg4iIiEgg6KNyWwmW1ITxJMY6ETkeBiJdSHzhKiJj4zGF/F52Fc9GREREerbahnJqG8sx2W0OspyFiBwvA5EuZvCsJ7DsXV9KsK4aERER6Znq/W4qt5dgyXIWInIiDES6GFtKOv2vzMayu3gOIiIi0vMEgj7K3AVYUhPGkxjrROREGIh0QXGzFhCdkoYp5PfSVFqEiIiI9Cy1DeUEgj5MdpuDLGchIifKQKSLisnOx9JUWkSwrhoRERHpGer9biq3l2C3ObDbHGQ5CxE5GQzkuFVXV+P1ejkeH3/8MW+99RaVlZX4/X7k2NlS0onJzseyu3gOIiIi0v0Fgj7K3AWYAkEfibFOEmOdiJwMBnJcNm/eTG5uLps3b+ZYfP755+Tm5jJ27FjuvPNO8vLyyMjIYOHChcixi8nOp/+V2ZhCfi+7imcjIiIi3VvlthICQR8mu81BlrMQkZPFQI7Zli1byMvL41gdOnSI3NxctmzZwrx589i6dStr1qzh0ksvZdGiRaxatQo5dv1HZWPZu76UYF01IiIi0j3V+93UNpZjstscZDkLETmZDKTdQqEQixYt4uabb6alpYVjtXz5cj766CPuuececnJyiIqKIjExkSeeeILevXvz8ssvI8fOlpJOTHY+lt3FcxAREZHuJxD0UeYuwJKaMI7EWCciJ5OBtNusWbNYuHAhGRkZPPDAAxyrN954g5iYGKZOnUpbAwYM4Pnnn+eee+5Bjk9Mdj7RKWmYQn4v3oKJiIiISPdSua2EQNCHyW5zkJk8E5GTzUDa7YILLmDJkiU888wzxMTEcCxaW1vZunUrl19+OYZhcOjQId5++22qq6s5dOgQw4cPZ/jw4cjxi8nOJzI2HtP+uhqCddWIiIhI91DbWE5tYzkmu81BlrMQkVPBQNptzpw5jBgxguPh9Xo5dOgQ/fv3Z/ny5aSmpnLrrbeSm5vL8OHDee211zgWSUlJJCUlkZSURFJSEklJSTz11FP0ZLaUdPqPysayo+AGREREpOsLBH1UbivBkpowjsRYJyKngoF0CK/Xi6mqqopHHnmE6dOn85//+Z/Mnz+ffv36ce+997J69Wray+Px4PF48Hg8eDwePB4Pd955Jz1dTHY+0SlpWLwFExEREZGurXJbCYGgD5Pd5iAzeSYip4qBdIhwOIxp165dPPnkk9xxxx2MGjWKG264gRUrVtC7d28ee+wx5MTFZOdjObhnB8G6akRERKRrqm0sp97vxmS3OchyFiJyKhlIh4iKisLkcDjIyMigrSFDhvDTn/6Uzz77jM8//xw5MbaUdOLyFmAK+b3sKLgBERER6XoCQR+V20oIBH2YUhPGkRjrRORUMpAO8eMf/xjTsGHDOJp+/fphamhoQE5c/1HZRKekYfEWTERERES6lsptJQSCPkx2m4PM5JmInGoG0iEiIyNxOBy8++67tLa2cqR9+/Zhuvjii5GTIy5vAZb9dTUE66oRERGRrqHe76a2sRyT3eYgy1mISEcwkA4zYcIEmpubKSsroy2fz8df/vIXUlNTiYyMRE6OyEHxxGTnY9lRcAMiIiLS+QWCPsrcBVhSE8aRGOtEpCMYyEnndrtJSkoiNzeXtnJzcznnnHP43e9+R3FxMW+//TZvvPEGU6dOxXTfffchJ1dMdj7RKWlYvAUTERERkc6tclsJgaAPk93mIDN5JiIdxUA6TP/+/SktLSUjI4OnnnqKW2+9lfz8fEyLFy/mBz/4AXLyxWTnExkbj2l/XQ3BumpERESkc6ptLKe2sRyT3eYgy1mISEcykOOSmZmJx+Phhhtu4EhOpxOPx8PSpUs50sCBA1m0aBG1tbUsXbqUNWvWsG7dOtLT05FTw5aSTv9R2Vh2FNyAiIiIdD6BoI/axj9hSU0YR2KsE5GOZCCnxRlnnEF6ejqJiYnIqReTnU90ShqWXcWzERERkc6lclsJ9X43JrvNQWbyTEQ6moFIDxGTnY9l7/pSgnXViIiISOdQ73dT21iOyW5zkOUsROR0MBDpIWwp6cRk52PZXTwHEREROf0CQR9l7gIsqQnjSIx1InI6GIj0IDHZ+USnpGEK+b3sKp6NiIiInF61DeUEgj5MdpuDzOSZiJwuBiI9TEx2Ppa960sJ1lUjIiIip0e9301t458w2W0OspyFiJxOBiI9jC0lnZjsfCy7i+cgIiIiHS8Q9FG5vYRA0IcpMdZJYqwTkdPJQKQHisnOJzolDVPI72VX8WxERESkY9U2lFPvd2Oy2xxkOQsROd0MRHqomOx8LPvragjWVSMiIiIdo97vpnJ7CZYsZyEinYGBSA9lS0knJjufyNh4Qn4vu4vnICIiIqdeIOijcnsJltSE8STGOhHpDAxEerCY7HwsIb+XptIiRERE5NSqbSin3u/GZLc5yHIWItJZGIj0cINnPYGlqbSIYF01IiIicmoEgj4qt5dgyXIWItKZGIj0cLaUdKJT0rA0lRYhIiIiJ18g6KPMXYDd5sCUmjCexFgnIp2JgYgQX7gKy/66GppKixAREZGTq97vpt7vJhD0kRjrJDN5BiKdjYGIHBaXtwBLU2kRoT1eRERE5OQIBH2UuQuwpCaMw25zINLZGIjIYf1HZROdkoZl19OzERERkZOjzF2AJTHWSWrCeEQ6IwMR+W9xeQuw7K+rYW9VKSIiInJiahvLqfe7MdltDrKchYh0VgYi8t8iB8UTl7cAS1NpEaE9XkREROT4BII+ytwFWFITxmG3ORDprAxE5H/oPyqb6JQ0TCG/l11Pz0ZERESOT+W2Eix2m4PM5JmIdGYGIvK/xGTnY9lfV0OwrhoRERE5NrWN5dQ2lmOy2xxkOQsR6ewMROR/saWkE5Odj2V38RxERESk/QJBH5XbSjDZbQ5SE8aRGOtEpLMzEJGjisnOJzolDVPI72VX8WxERESkfWobygkEfVgyk2ci0hUYiMg3isnOx7K/roZgXTUiIiLy7QJBH5XbS7BkOQsR6SoMROQb2VLS6X9lNqaQ30tTaREiIiLyzQJBH2XuAiypCeNJjHUi0lUYiMi3ipu1gOiUNEz762poKi1CREREjq7e76be78ZktznIchYi0pUYiMh3isnOx9JUWkSwrhoRERH5nwJBH2XuAiyZyTMQ6WoMROQ72VLSiU5Jw9JUWoSIiIj8T2XuAiyJsU5SE8Yj0tUYiEi7xOUtwLK/roZgXTUiIiLy/6ltLKfe78ZktznIchYi0hUZiEi7RA6KJyY7H8uOghsQERERCAR9VG4rwZKaMA67zYFIV2QgIu0Wk51PdEoall3FsxEREenpKreVEAj6MNltDjKTZyLSVRmIyDGJyc7Hsnd9KcG6akRERHqqer+b2sZyTHabgyxnISJdmYGIHBNbSjr9r8zGsrt4DiIiIj1RIOijcnsJlsRYJ4mxTkS6MgMROWZxsxYQGRuPKeT3sreqFBERkZ6mtqGcer8bk93mIMtZiEhXZyAix2XwrCew7Hp6NsG6akRERHqKQNBH5fYS7DYHdpuDzOQZiHQHBiJyXGwp6USnpGGKjI1nb1UpIiIiPUWZuwBTIOjD3s9BasJ4RLoDAxE5bnF5CzCF/F72ri8lWFeNiIhId1fbWE69343JbnOQ5SxEpLswkONWXV2N1+vlRPj9fiorK/niiy+QridyUDxxeQuIjI0nMjaeHQU3ICIi0p0Fgj4qt5VgSU0Yh93mQKS7MJDjsnnzZnJzc9m8eTMn4q677iIvL48PP/wQ6Zr6j8qm96BzCfm9mHYVz0ZERKS7qtxWQiDow2S3OchMnolId2Igx2zLli3k5eVxokpKSqitrUW6vri8BVj2ri8lWFeNiIhIdxMI+qhtLMdktznIchYi0t0YSLuFQiEWLVrEzTffTEtLCydi+/btLFy4ELvdjnR9kYPiiU5Jw9JUWoSIiEh3Egj6KHMXYEmMdZIY60SkuzGQdps1axYLFy4kIyODBx54gOPV0tLCnDlzuOSSS7jmmmuQ7iG+cBWmyNh49tfVsLeqFBERke6i3u+m3u/GZLc5yEyegUh3ZCDtdsEFF7BkyRKeeeYZYmJiOF6///3v+fzzzykqKkK6l7i8BYT8Xky7np5NaI8XERGRri4Q9FHmLsCSmTwDu82BSHdkIO02Z84cRowYwYmoqqri5ZdfpqCggMGDByPdS/9R2USnpGFpKi1CRESkq6ttKMeSGOskNWE8It2VgXSYL774gnnz5jFmzBjGjRvHiUhKSiIpKYmkpCSSkpJISkriqaeeQk6/mOx8LHvXlxKsq0ZERKSrqve7qdxegsluc5B54QxEujMD6TD33XcfERERFBYWcqI8Hg8ejwePx4PH48Hj8XDnnXcip58tJZ3+V2Zj2V08BxERka4oEPRRuf3/YQ9+gKOuD/z/P/2QuOxitwkhlW43sKa9W01G+beeCVgxNAe21Uw9Qup0nLYZexBFLmKu7VX7k5FDpzc1PXJQDLaWqf9/SajTnFrppAQVk6jLwaEJ9yltunS3ex5JSH57uiHkj7/vfvt9f49akAD5t5vX47ETIzc7QG52AJFUZiET4tlnn2Xfvn08/PDDZGRkIKlt7t1bceYXYvTUVSMiIpJsOruCdHYFSch0eVgTeBCRVGchE2Lfvn0kfOMb38Dv9+P3+/H7/Tz99NMklJeX4/f76evrQ1LDx2/8MgmDXWF66qoZPB5GREQkWfTGo9QHN2EU561DZDqwkAmxbNky1qxZw5o1a1izZg1r1qxhzZo1fPrTnybhhhtuYM2aNVx66aVIanAXleHML8R494f3ICIikizqg5swcrMDLJlfgsh0YCET4qtf/Spbtmxhy5YtbNmyhS1btrBlyxYKCgpIKC8vZ8uWLbhcLiR1ZJVVYfS3txJvb0FERGSq6+wK0tkVJCHT5aH4qnWITBcWMuaCwSB+v5/y8nJkenPlL8V9YxnGf23fiIiIyFTWG4/SdGQnxpL5t5CbHUBkurAQkXE19+6tpGfnkDDYFaanrhoREZGpqrMrSGdXkIRMl4fivApEphMLuSDFxcXYtk1paSkfFggEsG2bXbt2cS4PPPAAtm2zdOlSJHVllVVh9NRVM3g8jIiIyFTTG49SH9yEUZy3DpHpxkJExp27qAxnfiHGuz+8BxERkammPrgJIzc7wJL5JYhMNxYiMiHmrt+K0d/eSry9BRERkamisytIZ1eQhEyXh+Kr1iEyHVmIyIRI/0QO7hvLMP5r+0ZERESmgt54lKYjOzFyswPkZgcQmY4sRGTCzL17K+nZOSQMdoXpqatGRERksnV2BensCpKQ6fKwJvAgItOVhYhMqKyyKoyeumoGj4cRERGZLL3xKPXBTRjFeesQmc4sRGRCuYvKcOYXYvTUVSMiIjJZmjp2YuRmB1gyvwSR6cxCRCZcVlkVRn97K/H2FkRERCZaZ1eQA8caSch0eSi+ah0i052FiEw4V/5S3DeWkTDYFaanrhoREZGJ1BuP0nRkJ0ZudoDc7AAi052FiEyKuXdvxehvbyXWXIeIiMhE6ewK0tkVJCHT5aE4bx0iAhYiMmm8DzZg9NRVIyIiMhF641Hqg5swivPWkenyICJgISKTxpW/FGd+IQmDXWHe3X4PIiIi462pYydGpsvDkvkliMgfWYjIpMoqq8KI7asj3t6CiIjIeOmNRzlwrBFjTeBBROR/WIjIpHLlL8WZX4jRU1eNiIjIeKkPbsJYMr+E3OwAIvI/LERk0s1dvxWjv72VeHsLIiIiY+3AsUZ634+SkOnyUJy3DhH5UxYiMunSP5FDVlkVxn9t34iIiMhY6o1HaerYSW88SkJudoBMlwcR+VMWIjIlZJVV4cwvJGGwK0xPXTUiIiJjpbMrSG88SkKmy8OawIOIyJ+zEJEp4+M3fhmjp66aweNhRERELlZvPEp9cBMJmS4PxXnrEJEzsxCRKcNdVIYzvxCjp64aERGRi3Ug1IiROcvDkvkliMiZWYjIlJJVVoUR21dHvL0FERGRC9XZFaTpyE4SMl0eiq9ah4icnYWITCmu/KW4byzD6KmrRkRE5EI1HdmJkZsdIDc7gIicnYWITDlz796K0d/eSqy5DhERkfN14FgjnV1BEnKzAxTnrUNEPpqFiExJWWVVGO/+8B5ERETOR288SlPHTozcOUvIdHkQkY9mISJTUlZZFenZORg9ddWIiIiM1oFQI73xKAmZLg/FeRWIyLlZiMiUlVVWhdFTV83g8TAiIiLn0huP0nRkJ8aawIOIyOhYiMiU5S4qw5lfiNHf3oqIiMi5NHXsxMjNDpCbHUBERsdCRKa0rLIqjHd/eA/x9hZERETOprMryIFjjSRkujwUX7UOERk9CxGZ0lz5S3HfWIbRU1eNiIjI2TQd2YmRmx0gNzuAiIyehYhMeXPv3orR395KvL0FERGRDztwrJHOriAJmS4PxXnrEJHzYyEiSSGrrArjv7ZvRERE5HS98ShNHTsxlsy/hUyXBxE5PxYikhSyyqpIz84hYbArTE9dNSIiIkZnV5DeeJSETJeH4rwKROT8WYhI0sgqq8Loqatm8HgYERGR3niU+uAmjOK8dYjIhbEQkaThLirDmV+I0VNXjYiISFPHToxMl4cl80sQkQtjISJJJausioT07Bxi++qIt7cgIiLTV288yoFjjRhrAg8iIhfOQkSSiit/Kc78Qga7wiT01FUjIiLTV31wEwmZLg+52QFyswOIyIWzEJGkM3f9Voz+9lbi7S2IiMj009kVpLMriFF81TpE5OJYiEjSSf9EDu4byzB66qoREZHppTcepenITozc7AC52QFE5OJYyAVraWkhHA5zvgYHB3nllVd46aWX2Lt3L/F4HJHzNffurRj97a3EmusQEZHpo7MrSGdXkIRMl4fivHWIyMWzkAvyxhtvUF5ezhtvvMH5aGho4LrrrmPt2rVs3LiRO++8k2uvvZYf/ehHiJyvueu3kpCenUNPXTUiIjI99MajNHXsxCjOW0emy4OIXDwLOW9vvvkm69ev53w1NTVx//334/P5ePrppzl8+DA/+9nPWLRoEY888gjPPPMMIufDXVRGenYOCYNdYXrqqhERkdTX2RWkNx4lITc7wJL5JYjI2LCQURscHGTHjh18/etfZ2BggPO1Y8cO0tLS+MlPfkIgEMDhcJCfn89jjz3Gxz72MX784x8jcr6yyqoY7AqT0FNXzeDxMCIikrp641Hqg5swlsy/BREZOxYyanfffTc1NTUsX76c7373u5yvGTNmcP3115ORkcHpXC4XS5Ys4Q9/+AMi58tdVIYzvxCjp64aERFJXU0dO8l0ech0ech0eVgyvwQRGTsWMmpXXnkljz/+OI8++ihZWVmcr/r6enbu3MmHjYyM8M477zBr1ixELkRWWRVGbF8d8fYWREQk9fTGoxw41khvPEpvPMqawIOIyNiykFHbuHEj119/PWPtpz/9Kd3d3axZs4bR8vv9+P1+/H4/fr8fv9/Ptm3bkOnJlb8UZ34hRqy5DhERST31wU0YudkBcrMDiMjYspBJ9dprr/HII4/wqU99ivXr1zNatm1j2za2bWPbNrZts2HDBmT6mrt+K0ZsXx3x9hZERCR1dHYF6ewKkpDp8lB81TpEZOxZyKRpamrirrvu4uMf/zg/+clPcLvdiFyo9E/kkFVWhRFrrkNERFLHgWP/ipGbHSA3O4CIjD0LmRQ7d+5k/fr1ZGdn09DQgM/nQ+RiZZVVkZ6dQ0JsCkxXcAAAIABJREFUXx2Dx8OIiEjyO3CskQPHGknIdHkozluHiIwPC5lw9913Hz/4wQ9YuHAhDQ0NeDweRMaKu6gMI7KpFBERSW698SgHjv0rRm52gEyXBxEZHxYyof7u7/6O3bt389d//dc88cQTzJ49G5GxlFVWRXp2DgmDXWFizXWIiEjy6uwK0tkVJCHT5WFN4EFEZPxYyIR59NFH2bNnD1/84hfZvn07DocDkfGQVVaF8e4P70FERJJTbzxKU8dOjDWBBxGR8WUhYy4YDOL3+ykvL8c4ceIEO3bsIOHkyZPce++93Hvvvdx7773ce++93Hvvvdx7770MDw8jcrHcRWWkZ+dg9NRVIyIiyaf3/Si98SgJmS4PudkBRGR8WciEePPNNzl16hQJv/rVr3jxxRd58cUXefHFF3nxxRd58cUXefHFFxkZGUFkLGSVVWH01FUzeDyMiIgkj954lMde/VuM4rx1iMj4s5ALUlxcjG3blJaW8mGBQADbttm1axfGTTfdhG3b2LaNbdvYto1t29i2jW3b2LaNbdukp6cjMhbcRWW4byzD6KmrRkREkkdTx06MTJeHJfNLEJHxZyEiKctdVIYR21fH4PEwIiIy9fXGoxw41oixJvAgIjIxLEQkZbnyl+LML8Tob29FRESmvqaOnRhL5peQmx1ARCaGhYiktKyyKtKzc0h494f3EG9vQUREpq7eeJQDxxoxlsy/BRGZOBYiktJc+UtJ+4QXo6euGhERmbrqg5swcrMD5GYHEJGJYyEiKW/u+q0YQ8cjxNtbEBGRqaezK0hnV5CETJeH4qvWISITy0JEUl76J3Jw31hGwmBXmJ66akREZOo5cOxfMXKzA+RmBxCRiWUhItPC3Lu3YgwdjxBvb0FERKaOzq4gB441kpDp8lCctw4RmXgWIjJtZJVVkTDYFaanrhoREZkaeuNRmo7sxMjNDpDp8iAiE89CRKaNrLIqjP72VmLNdYiIyOTr7ArS2RUkITc7wJrAg4jI5LAQkWklq6wKo6euGhERmXwHjv0rRqbLg4hMHgsRmVayyqowBrvCxJrrEBGRyXPgWCOdXUESMl0e1gQeREQmj4WITDtz12/FePeH9yAiIpOjNx6lqWMnRnHeOkRkclmIyLTjLiojPTsHI9Zch4iITLzOriC98SgJmS4PS+aXICKTy0JEpqWssiqMd394DyIiMrF641Hqg5swivPWISKTz0JEpiV3URnp2TkYPXXViIjIxOnsCmJkujwsmV+CiEw+CxGZtrLKqjB66qoZPB5GRETGX288Sn1wE0Zx3jpEZGqwEJFpy11UhjO/EKOnrhoRERl/TR07MTJdHpbML0FEpgYLEZnWPn7jlzFi++oYPB5GRETGT288yoFjjRhrAg8iIlOHhYhMa+6iMpz5hRg9ddWIiMj4aerYiZHp8pCbHUBEpg4LEZn2ssqqMGL76hg8HkZERMZebzzKgWONGGsCDyIiU4uFiEx7rvylOPMLMXrqqhERkbHX1LETIzc7QG52ABGZWixERP6XrLIqjNi+OgaPhxERkbHTG49y4FgjRvFV6xCRqcdCROR/ceUvxZlfiNFTV42IiIydpo6dZLo8JORmB8jNDiAiU4+FiMj/kVVWhRHbV8fg8TAiInLxeuNRDhxrpDceJaH4qnWIyNRkISLyf7jyl+LML8ToqatGREQuXn1wE0ZudoDc7AAiMjVZiIicJqusCqO/vZV4ewsiInLheuNRet+PYhRftQ4RmbosRERO48pfijO/kITBrjCx5jpEROTC1Qc30RuPkpCbHSA3O4CITF0WKWZ4eJhoNEp7eztbtmzh9ttv56mnnuLo0aOcOHECETm3rLIqjP72VuLtLYiIyPnrjUfp7ApiFF+1DhGZ2ixSxMGDBykuLiYvL4+ioiL+5m/+hieffJK33nqLf/zHf+Tmm2+msLCQhQsXct9999HX14eInJkrfynO/EISBrvCxJrrEBGR81cf3ISRmx0gNzuAiExtFknul7/8JYsXL+a2224jHA7zsY99jCuuuIIlS5bw0EMP8eyzz/K9732P/Px8PvWpT3Hq1Cl2797Nddddx1e+8hVisRgi8ueyyqpIz84hIbavjnh7CyIiMnq98SidXUESMl0eiq9ah4hMfRZJqr+/n1tuuYUNGzYwa9Ysvve97/HWW28RDAZ5+eWXeeaZZygtLWXx4sXceuut/OxnP2Pv3r10dHTQ3NzMDTfcwIEDB7j22mvZvn07IvKnXPlLSfuEFyPWXIeIiIxefXATRuYsD7nZAURk6rNIUgsXLiQWi7Fnzx5ee+01br31VtxuN6Ph8Xj40Y9+xJEjR6isrGTbtm3cddddiMifmrt+K0ZsXx3x9hZEROTceuNROruCGGsCDyIiycEiST366KO88sor+Hw+LpRlWdx1113Yts11112HiPyp9E/k4MwvxIg11yEiIudWH9yEsWR+CZkuDyKSHCyS1IoVKxhLX/va1xCRP5dVVoUR21dHvL0FERE5u954lM6uIAmZLg9L5t+CiCQPixQxMDDAaG3fvh0RGR1X/lKc+YUYseY6RETk7OqDmzByswPkZgcQkeRhkSJ+/etfU1BQwHvvvcfZ9Pf3U1xczI4dO5gKWlpaCIfDiEx1c9dvxYjtqyPe3sIlVXsREZH/cUnVXnrjUXrfj5KQ6fKwZP4tiEhysUghvb29LFmyhN27d/NhP//5z1m4cCHhcJjMzEwm2xtvvEF5eTlvvPEGIlNd+idyyCqrwog11yEiIn+uPriJ3niUhMxZHnKzA4hIcrFIEVdffTUPPfQQCffddx/r1q3DuOOOO/jWt75FwoYNG3j99deZTG+++Sbr169HJJlUvns1RmxfHX918ghG6MRJyp87gojIdFK049/Y99tejI87TtDZFSTh/xuYzf7wSkQk+VikkNLSUt566y3mzJnDvn37WLBgAXl5eezfv5+srCxaW1u5++67mSyDg4Ps2LGDr3/96wwMDCCSTLbcfgPPX/ZZjL95/1USQidOUv5cB5tWXoGIyHSy67Y8yp87wr7f9pLwhc88h2HNyGfz529BRJKPRYpxu928/vrr3HDDDZw8eZLh4WEKCgpoaWlh9uzZTKa7776bmpoali9fzne/+11Ekolv9kw2fLOShPTsHG597zWOvLaX8uc62HVbHr7ZMxERmU58s2fSfOdiyp87wvOHO5j38d9iVK34Kr7ZMxGR5GORYmKxGCtXruTVV1/FaGtrY9myZZw4cYLJdOWVV/L444/z6KOPkpWVhUiyceUvxZlfyGBXmIR//9kT7LotD9/smYiITEe+2TNpvnMx9cEHMHKzA+RmBxCR5GSRQh599FGuvfZajh07Rl5eHu+88w62bXP99dfT3d1NYWEh27dvZ7Js3LiR66+/nrHg9/vx+/34/X78fj9+v59t27YhMtYuqdrLJVV7uaRqL5dU7aW0ewUJ1mWXUHjpr7j9h7u4pGovl1Tt5ZKqvVxStRcRkVR2SdVeLqnayyVVe7mkai+L/p99XHHoMoyHmv+KS6r2cknVXi6p2sslVXsRkeRhkSLefvtttm7dSsK3vvUtnn/+edLT00l4/PHHqa6uJmHbtm189rOfJdnZto1t29i2jW3b2LbNhg0bEBlrH1Sv4IPqFXxQvYIPqlfw//7jHRycn8/HV6bzsWVp7Lm5kw+qV/BB9Qo+qF7BB9UrEBFJZR9Ur+CD6hV8UL2CD6pX8IOB/ybt1QVcuu1v+MNrK/np7aV8UL2CD6pX8EH1Cj6oXoGIJA+LFOJ2u3n99de54447+LCbb76ZQ4cO8elPf5qenh5E5PyFTpyk/LkOllTcz4zLLiFhINzAYHcbIiLTUV80RigYIeGSvsu44wvfoPy5I+z7bS8ikpwsUkR+fj5vvfUWc+bM4WycTicvvfQSGzZsQETOT+jEScqf62DXbXl85i9u5Nl3l2H8ct+P2ffbXkREppPQiZP8890/xwhlXsaNK/+C5jsXU/7cEfb9thcRST4WSaqzs5PTWZbFaN1555182P79+xGRs/vpW//Jrtvy8M2eScKz/7UMo/DSX/GTV4KIiEwnW39uQ2c3xitXXE6Cb/ZMmu9czIN7foeIJB+LJPX5z3+e8vJy3nvvPS5Gc3MzgUCAHTt2ICJnt2nVFfhmz8R4vc9PWlYBxs5l7YiITCfLf/cuhi/g5VjmZRi+2TNpvmsxIpJ8LJLUL37xC/793/+dJUuW8IUvfIFjx44xWn19fezYsYPFixdTUVHBDTfcwDPPPIOInB+nvxJjILybkXgEEZHpoC8a41BjBwkZHjdFFYWISGqwSFK5ubn827/9Gxs2bOC3v/0tK1euxO/3U1xczLp163j77bf5zW9+Q2dnJ7/5zW944YUXuPXWWykoKOC6666jpqaGWbNm8eKLL/KDH/wAETk/H1SvIH1OAWlZBSSMxCP02zWIiEwHzbWtGBkeN76Alw+qVyAiyc8iyd199910dHTw93//97jdbsLhMPv27aO0tJQvfvGLfP7zn+eLX/wiVVVVdHR00NvbyxVXXEFTUxOvvfYan/nMZxCRC+f0V2IMhBsYiUcQEUllfdEYhxo7MIoqChGR1GGRAmbMmMHf/u3f8tZbb/H666/zs5/9jM997nNceeWV/MVf/AXXXHMNmzdvZs+ePbzzzju8/PLL5OTkMJmKi4uxbZvS0lJEkln6nALSsgow+u0aRERSWXNtK4Yv4MUX8CIiqcMiSd1000187Wtf43QDAwPMmTOH/Px8duzYwc9//nNeeOEF6uvr+fKXv4zP5yM9PR0RGVuOeauxXF4SBsINjMQjiIikor5ojEONHRhFFYWISGqxSFK/+93vCIfDGG+//TbXXHMNAwMDiMjEcuSUkp5VgNFv1yAikoqaa1sxMjxufAEvIpJaLJLUjBkzOHHiBCIyNaTNuQ5jINyAiEiq6YvGONTYgXHr5lWISOqxSFLz5s2jv7+f/Px8li1bRkVFBQkrVqxg2bJlLFu2jGXLlrFs2TKWLVvGsmXLWLZsGcuWLeOzn/0sIjK2HDmlpGUVYPTbWxERSSWhYAQjw+PGF/AiIqnHIkm9/PLLeDwehoaG6O7upru7m4Tu7m66u7vp7u6mu7ub7u5uuru76e7upru7m+7ubnp6ehCRseeYtxqj365BRCRV9EVjPP/AHoyiikJEJDVZJLHm5mbeeecdDh8+zNNPP03CW2+9xeHDhzl8+DCHDx/m8OHDHD58mMOHD3P48GEOHz7MwYMHEZGx58gpxXJ5MfrtrYiIpIJQMIKR4XGzsCQPEUlNFkkuPT0dh8OBw+Fg7ty5OBwOHA4HDocDh8OBw+HA4XDgcDhwOBw4HA4cDgciMj6c/kqMfrsGEZFk1xeN0VzbilFUUYiIpC6LFHH11Vfzyiuv4HA4EJHJ48gpxXJ5MQbCDYiIJLNQMEJfNEZChsfNwpI8RCR1WYiIjDGnvxLj/YPfREQkWfVFYxxsbCfD4yahqKIQEUltFiIiY8yRU4rl8mIMhBsQEUlGoWCEUDBCXzRGhsfNwpI8RCS1WYiIjANHzmqMfrsGEZFk0xeNcbCxHWNhSR4ikvosRETGgdN/D6cb7G5DRCSZ9EVjhIIREjI8booqChGR1GchIjJOHDmlJIzEI/TbNYiIJJPm2lYMX8CLiEwPFiIi42TWou9jDPW0MdjdhohIMggFI4SCERIyPG6KKgoRkenBQkRkHDn9lRj9dg0iIsmgubYVwxfwkuFxIyLTg4WIyDhy5JRiDPW0MdjdhojIVBYKRggFIyRkeNwsKslHRKYPCxGRcWS5vDhySrFcXhJOhXcjIjKVNde2YvgCXnwBLyIyfViIiIyzS3NWMxKPkDAQbmCwuw0RkamoLxojFIxgLCrJR0SmFwsRkXGWPqeAtKwCjFPh3YiITEXPP7AHwxfw4gt4EZHpxUJEZAI4/ZUYA+EGRuIRRESmkr5ojFAwglFUUYiITD8WIiITIH1OAWlZBRj9dg0iIlNJc20rhi/gxRfwIiLTj4WIyARx+isxBsINjMQjiIhMBX3RGIcaOzCKKgoRkenJQkRkgqTPKSAtqwCj365BRGQqONjYjpHhceMLeBGR6clCRGQCOeatxhgINyAiMtn6ojH21bZh3Lp5FSIyfVmIiEwgR04plsuL0W9vRURkMoWCEYwMjxtfwIuITF8WIiITbNbC72MMhHcjIjJZ+qIxmmtbMYoqChGR6c1CRGSCpc8pwHJ5SRiJRxgINyAiMhlCwQh90RgJGR43C0vyEJHpzUJEZBI4/ZUkWC4v/XYNIiITrS8a42BjO0ZRRSEiIhYiIpPAkVNKwkg8wkg8wkC4ARGRidQXjREKRkjI8LhZWJKHiIiFiMgkcforMQZ+vxsRkYnUXNtKQobHjS/gRUQkwUJEZJI4/fdgDPW0MdjdhojIRAgFI4SCEYyiikJERBIsREQmkSOnFKPfrkFEZCI017Zi+AJeMjxuREQSLEREJpHTX4kx1NPGYHcbIiLjqS8aIxSMkOFxk+Fxs6gkHxERw0JEZBJZLi+OnFKMU+HdiIiMp+cf2ENCXzSGL+DFF/AiImJYiIhMsktzVmMMhBsYiUcQERkvoWAEY1FJPiIip7OQ8zIyMkJLSwsvvfQSLS0tjIyMcL6Gh4d55ZVXeOmll3jllVcYHh5GZDpLn1NAWlYBRr9dg4jIeHj+gT0YvoAXX8CLiMjpLGTU3n77bYqLiykvL2fjxo2Ul5dTXFzMkSNHGK39+/dzww03sHbtWjZu3MjatWu54YYb2L9/PyLTmdNfiTEQbmAkHkFEZCz1RWMcauzAKKooRETkwyxkVGKxGOvWrePkyZM89thjHD58mG3btnHy5EnWrl3Le++9x7mEw2HWr1+PZVn8+Mc/5p133uHJJ5/EsizuvPNOQqEQItNV+pwC0rIKMPrtGkRExtLBxnaMDI8bX8CLiMiHWcioPPXUU/T09PDAAw+wfPlyHA4HK1euZPPmzRw/fpwnn3ySc/n5z3/OyZMn+fa3v81nP/tZ0tPT+au/+ivuv/9+Tp06RX19PSLTmWPeaoyBcAMiImOlLxpjX20bxq2bVyEiciYWMip79uxh5syZrFy5ktMVFxczc+ZMXn75Zc7lD3/4AwmzZ8/mdFdddRUJ3d3diExnjpxSLJcXYyDcgIjIWAgFIxgZHje+gBcRkTOxkHMaGRnh6NGjXHPNNViWxYctXryYo0ePMjIywkdZtmwZCW+99Ran++Uvf0nCggULEJnunP5KjPcPfhMRkYvVF43RXNuKUVRRiIjI2VjIOcXjcYaHh5k9ezZn4na7GR4eZmBggI9y880386UvfYkdO3ZQWVnJ7t27+eY3v8kjjzzCqlWruO222xCZ7hw5pVguL8ZAuAERkYsRCkboi8ZIyPC4WViSh4jI2VjIOfX29pJw6aWXciYzZswgIRQKcS6rVq0iJyeHl19+mfvuu4/Gxkbmzp3L6tWrsSyL0fL7/fj9fvx+P36/H7/fz7Zt2xBJBU5/JUa/XYOIyIXqi8Y42NiOsbAkDxGRj2Ih5zRz5kxGw7IsPsqzzz7LnXfeyfz589mzZw+2bbNnzx6uvPJK1q5dy1NPPcVo2baNbdvYto1t29i2zYYNGxBJBY6cUk432N2GiMiF6IvGCAUjJGR43BRVFCIi8lEs5Jwuu+wyEk6dOsWZDA0NkTBv3jzOZmRkhOrqaubOncv27dvx+Xwk+Hw+duzYwRVXXMEjjzzC8PAwIgKOnFISRuIR+u0aREQuRHNtK4Yv4EVE5Fws5JycTidpaWmcOHGCMzlx4gRpaWk4nU7O5ve//z3//d//zbXXXovT6eR0M2bMYPHixfT39/PGG28gIjBr0fcxhnraGOxuQ0TkfISCEULBCAkZHjdFFYWIiJyLhYzKggULOHToECMjI5xuZGSEgwcPsmDBAj6K2+0mYXBwkDMZHh4mwel0IiJ/5MgpxTgV3o2IyPlorm3F8AW8ZHjciIici4WMyqpVqzh16hT19fWcrr6+nqGhIVatWsVHmT17NvPnz6epqYn//M//5HSxWIyWlhaysrJYsGABIvJHTn8lxkC4gcHuNkRERqMvGiMUjGAsKslHRGQ0LGRUbrvtNubPn8/DDz/ME088QUtLC0888QRbtmxh/vz53HbbbRjBYBC/3095eTmnu//++xkaGuIrX/kKu3fvpqWlhRdeeIGvfOUrHD9+nPvuuw/LshCRP7JcXtKyCjBOhXcjIjIazbWtGL6AF1/Ai4jIaFjIqDgcDn7605+Sn5/PQw89RHl5OQ899BBXX301Tz75JA6Hg3NZvnw5jz/+ODNmzOC+++6jvLycqqoq3n//fWpqarj55psRkT/l9FdiDIQbGIlHEBH5KH3RGIcaOzCKKgoRERktCxm1T37ykzzzzDPs37+fXbt28eqrr/LMM89w+eWXc7pAIIBt2+zatYsPu/7662lqamLPnj3s2rWLPXv20NzczE033YSI/Ln0OQWkZRVgDIQbEBH5KM21rRi+gBdfwIuIyGhZyHnLzs5m6dKlXH755Vwon8/H0qVL8fl8iMhHc8xbjdFv1yAicjZ90RiHGjswiioKERE5HxYiIlOcI6cUy+XF6Le3IiJyJqFgBCPD48YX8CIicj4sRESSgNNfidFv1yAi8mF90RjNta0Y5T9eg4jI+bIQEUkCjpxSLJcXYyDcgIjI6ULBCH3RGAkZHjcZHjciIufLQkQkSTj9lRj9dg0iIkZfNMbvgmGMoopCREQuhIWISJJw5JRijMQjDIQbEBFJ6IvGONTYQUKGx83CkjxERC6EhYhIEnHklGIM/H43IiIJzbWtGL6AFxGRC2UhIpJEZi36PsZQTxuD3W2IyPQWCkYIBSMkZHjcFFUUIiJyoSxERJKMI6cU41R4NyIyvTXXtmL4Al4yPG5ERC6UhYhIknH6K7FcXhIGwg0MdrchItNTXzRGKBjBWFSSj4jIxbAQEUkylsuL5fRinArvRkSmp+cf2IOxsCQPX8CLiMjFsBARSUJOfyWWy0vCQLiBkXgEEZle+qIxQsEIxqKSfERELpaFiEgSSp9TgOX0YvTbNYjI9NJc24rhC3jxBbyIiFwsCxGRJOWYtxpjINyAiEwffdEYhxo7MIoqChERGQsWIiJJypFTiuXyYvTbWxGR6SEUjGBkeNz4Al5ERMaChYhIEnP6KzH67RpEJPX1RWM8/8AeMjxuEooqChERGSsWIiJJzJFTiuXykmC5vAyEGxCR1BYKRkjoi8bI8LhZWJKHiMhYsRARSXJOfyUJI/EI/XYNIpK6+qIxDja2YywsyUNEZCxZiIgkOUdOKcZIPMJAuAERSU190RihYISEDI+boopCRETGkoWISApw+isxBn6/GxFJTc21rRi+gBcRkbFmISKSApz+ezCGetoY7G5DRFJLKBghFIyQkOFxU1RRiIjIWLMQEUkRTn8lxqnwbkQktTTXtmL4Al4yPG5ERMaahYhIinDklGIMhBsY7G5DRFJDXzRGKBghIcPjZlFJPiIi48FCRCRFWC4vaVkFGEM9bYhIamiubcXI8LjxBbyIiIwHCxGRFOL0V2L02zWMxCOISHLri8Y41NiBUVRRiIjIeLEQEUkh6XMKSMsqwOi3axCR5NZc24rhC3jxBbyIiIwXCxGRFOOYtxpjINzASDyCiCSnvmiMQ40dGEUVhYiIjCcLEZEU48gpJS2rAGMg3ICIJKdQMIKR4XHjC3gRERlPFiIiKcgxbzVGv12DiCSfvmiMg43tGEUVhYiIjDcLEZEU5MgpxXJ5MQbCDYhIcgkFI4SCERIyPG4WluQhIjLeLEREUpTTX4nx/sFvIiLJoy8a42BjO0ZRRSEiIhPBQkQkRTlySrFcXoyBcAMikhz6ojFCwQgJGR43C0vyEBGZCBYiIinMkbMaY+D3uxGR5NBc24rhC3gREZkoFiIiKczpvwdjqKeNwe42RGRqCwUjhIIREjI8bm7dvAoRkYliISKS4pz+Sox+uwYRmdqaa1sxfAEvIiITyUJEJMU5/fdgDPW0MdjdhohMTaFghFAwQkKGx82iknxERCaShZyXkZERWlpaeOmll2hpaWFkZIQLcfToUX75y1/S1NREV1cXIjK+HDmlGKfCuxGRqam5thXDF/DiC3gREZlIFjJqb7/9NsXFxZSXl7Nx40bKy8spLi7myJEjjFZ3dzfl5eXcfPPNbNiwgfXr17N8+XJqamoQkfFzac5qjIFwA4PdbYjI1NIXjREKRjAWleQjIjLRLGRUYrEY69at4+TJkzz22GMcPnyYbdu2cfLkSdauXct7773HuQwPD1NeXs6bb77J/fffz+HDh/nFL37Btddey44dO9i9ezciMj7S5xTgyCnFOBXejYhMLc21rRi+gBdfwIuIyESzkFF56qmn6Onp4YEHHmD58uU4HA5WrlzJ5s2bOX78OE8++STn8uyzz/LrX/+ab3/723z1q1/F4XCQm5vLP//zP5OWlsbTTz+NiIyfS3NWYwyEGxiJRxCRqaEvGuNQYwfGrZtXISIyGSxkVPbs2cPMmTNZuXIlpysuLmbmzJm8/PLLnMsLL7xAVlYWt99+O6ebPXs2P/nJT/j2t7+NiIyf9DkFpGUVYPTbNYjI1NBc24rhC3jJ8LgREZkMFnJOIyMjHD16lGuuuQbLsviwxYsXc/ToUUZGRjibkZERDh8+TEFBAZZlMTw8zP79+2lpaWF4eJjrrruO6667DhEZX455q7FcXhIGe9oQkcnXF41xqLEDo6iiEBGRyWIh5xSPxxkeHmb27NmcidvtZnh4mIGBAc4mHA4zPDyM2+3m2WefZcmSJdxxxx2Ul5dz3XXX8fzzz3M+/H4/fr8fv9+P3+/H7/ezbds2ROSjOXJKMUbiEfrtrYjI5AoFIxgZHje+gBcRkcmNKUiFAAAgAElEQVRiIefU29tLwqWXXsqZzJgxg4RQKMTZhMNhEpqbm/ne977H2rVrqa2t5aGHHmLWrFn8wz/8Ay+99BKjZds2tm1j2za2bWPbNhs2bEBEzs3pr8Tot2sQkcnTF43RXNuKUVRRiIjIZLKQc5o5cyajYVkWZ/PBBx+Q8O677/Iv//Iv3HXXXRQVFVFaWspzzz1HWloajzzyCCIy/hw5pVguL8ZAuAERmRyhYIS+aIyEDI+bhSV5iIhMJgs5p8suu4yEU6dOcSZDQ0MkzJs3j7NxOBwkeDweli9fzuk++clP8rnPfY4//OEPdHd3IyLjz+mvxHj/4DcRkYnXF41xsLEdo6iiEBGRyWYh5+R0OklLS+PEiROcyYkTJ0hLS8PpdHI2ixYtIuEv//IvOZNZs2aREAqFEJHx58gpxXJ5MQbCDYjIxAoFI4SCERIyPG4WluQhIjLZLGRUFixYwKFDhxgZGeF0IyMjHDx4kAULFvBR0tPT8Xg8tLW1MTIywoe9//77JCxYsAARmRiOnNUY/XYNIjKxDja2Y/gCXkREpgILGZVVq1Zx6tQp6uvrOV19fT1DQ0OsWrWKc/nSl77EyZMnqa+v53TRaJRf/epXLFmyhPT0dERkYjj992CMxCMMdrchIhOjLxqjLxojIcPj5tbNqxARmQosZFRuu+025s+fz8MPP8wTTzxBS0sLTzzxBFu2bGH+/PncdtttGMFgEL/fT3l5OacrLy/nU5/6FJs3b2b79u3s37+fF154gdtvv52E73znO4jIxHL6KzH67RpEZGI8/8Ae+qIxEnwBLyIiU4WFjIrD4eCnP/0p+fn5PPTQQ5SXl/PQQw9x9dVX8+STT+JwODgXt9tNXV0dy5cvZ9u2bdxxxx1UVVWR8KMf/Yirr74aEZlYTv89GEM9bQx2tyEi4ysUjBAKRkjI8LgpqihERGSqsJBR++QnP8kzzzzD/v372bVrF6+++irPPPMMl19+OacLBALYts2uXbv4sDlz5rBjxw4OHDjArl27+MUvfsHevXtZunQpIjI5HDmlGP12DSIyvpprWzF8AS8ZHjciIlOFhZy37Oxsli5dyuWXX86Fuuyyy1i6dCm5ubmIyORy+isxhnraGOxuQ0TGR180RigYISHD42ZRST4iIlOJhYjINGe5vDhySjFOhXcjIuPj+Qf2YGR43PgCXkREphILERHh0pzVGAPhBkbiEURkbPVFY4SCEYyiikJERKYaCxERIX1OAWlZBRj9dg0iMrYONraT4XGT4At48QW8iIhMNRYiIvK/Of2VGAPhBkbiEURkbPRFY+yrbaMvGiPD46aoohARkanIQkRE/rf0OQWkZRVg9Ns1iMjYaK5tJcPjJiHD48YX8CIiMhVZiIjI/+WYtxpjsKeNkXgEEbk4fdEYhxo76IvGyPC4uXXzKkREpioLERH5vxw5paRlFZAwEo/Qb9cgIhfnYGM7p8vwuBERmaosRETkTzjmrcYYCDcgIheuLxpjX20bxq2bVyEiMpVZiIjIn3DklGK5vBj99lZE5MKEghGMDI8bX8CLiMhUZiEiIn/G6a/EcnlJ6LdrEJHz1xeN0VzbilFUUYiIyFRnISIif8aRU8rpBsINiMj5CQUj9EVjJGR43CwsyUNEZKqzEBGRM3L6KzHeP/hNRGT0+qIxmmtbMYoqChERSQYWIiJyRo6cUiyXF2Mg3ICIjE4oGKEvGiMhw+NmYUkeIiLJwEJERM7K6a/EeP/gNxGRc+uLxjjY2I4v4CWhqKIQEZFkYSEiImflyCnFcnkxBsINiMhHCwUjhIIRQsEIGR43C0vyEBFJFhYiIvKRHDmrMQZ+vxsRObu+aIzfBcMYvoAXEZFkYiEiIh/J6b8HY6injcHuNkTkzELBCIcaO0jwBbzcunkVIiLJxEJERM7J6a/EOBXejYic2e+CYTI8bhJ8AS8iIsnGQkREzsnpvwdjINzAYHcbIvKnQsEIhxo76IvGyPC4KaooREQk2ViIiMioOHJKMfrtGkTkTzXXtmL4Al5ERJKRhYiIjMqsRd/HGOppY7C7DRH5o1AwQigYISHD46aoohARkWRkISIio+bIKcXot2sQkT9qrm0lw+MmwRfwkuFxIyKSjCxERGTUZi36PsZQTxuD3W2ITHehYIRQMEJfNEaGx01RRSEiIsnKQkREzosjpxSj365BZLprrm3F8AW8ZHjciIgkKwsRETkvsxZ9H2Oop43B7jZEpqtQMEIoGCEhw+NmUUk+IiLJzEJERM6bI6cUo9+uQWS6aq5txfAFvPgCXkREkpmFiIicN6e/EmOop43B7jZEpptQMEIoGCEhw+NmUUk+IiLJzkJERM6b5fLiyCnF6LdrEJlummtbMXwBL76AFxGRZGchIiIXxOmvxBjqaWOwuw2R6SIUjBAKRkjI8LhZVJKPiEgqsBARkQtiubw4ckpJyyogod+uQWS6aK5tJSHD48YX8OILeBERSQUWIiJywZz+SoZ62kgY6mljsLsNkVQXCkYIBSMYi0ryERFJFRYiInLBLJcXR04pRr9dg0iqa65txfAFvPgCXkREUoWFiIhcFKe/EmOop43B7jZEUlUoGCEUjJCQ4XGzqCQfEZFUYiEiIhfFcnlx5JRinArvRiRVNde2YvgCXnwBLyIiqcRCzsvIyAgtLS289NJLtLS0MDIywsXo6uqiqamJEydOICLJy+mvxBgINzDY3YZIqgkFI4SCERIyPG4WleQjIpJqLGTU3n77bYqLiykvL2fjxo2Ul5dTXFzMkSNHuFCVlZWsX7+e//iP/0BEkpfl8uLIKcXot2sQSTXNta0YvoAXX8CLiEiqsZBRicVirFu3jpMnT/LYY49x+PBhtm3bxsmTJ1m7di3vvfce52vnzp0cOHAAEUkNTn8lxlBPG4PdbYikilAwQigYISHD42ZRST4iIqnIQkblqaeeoqenhwceeIDly5fjcDhYuXIlmzdv5vjx4zz55JOcjyNHjlBTU0NmZiYikhoslxdHTilGv12DSKporm3F8AW8+AJeRERSkYWMyp49e5g5cyYrV67kdMXFxcycOZOXX36Z0RoYGGDjxo0sXryYL3zhC4hI6nD6KzGGetoY7G5DJNmFghFCwQgJGR43i0ryERFJVRZyTiMjIxw9epRrrrkGy7L4sMWLF3P06FFGRkYYjX/6p3+iu7ub6upqRCS1WC4vjpxSjH67BpFk11zbiuELePEFvIiIpCoLOad4PM7w8DCzZ8/mTNxuN8PDwwwMDHAuzc3NPP3002zatInLL78cEUk9Tn8lxlBPG4PdbYgkq1AwQigYISHD46aoohARkVRmIefU29tLwqWXXsqZzJgxg4RQKMRHOXHiBPfffz833XQTt9xyCxfD7/fj9/vx+/34/X78fj/btm1DRCaf5fLiyCnF6LdrEElWzbWtGL6AlwyPGxGRVGYh5zRz5kxGw7IsPsp3vvMdZsyYwYMPPsjFsm0b27axbRvbtrFtmw0bNiAiU8OsRd/HGOppY7C7DZFkEwpGCAUjJGR43BRVFCIikuos5Jwuu+wyEk6dOsWZDA0NkTBv3jzO5tlnn2Xfvn08/PDDZGRkICKpz5FTinEqvBuRZHOwsR3DF/CS4XEjIpLqLOScnE4naWlpnDhxgjM5ceIEaWlpOJ1Ozmbfvn0kfOMb38Dv9+P3+/9/9uAHuArCXvv89x4CSQBPzws4tmnUvF47jwspcGiqAe1LeTchd9spI3M9o64d18ztIC1eLe6wTm2H+4qh013YVoYMoFUZAcF3iKXDVJbscAutbQhuXLJoYZ5h797MJM074wuYOcqBcJLj7rndM1JLkX/yL7/PB0m8+uqrFDU3NyOJgYEBQgjXh3HpFZQM9raRP9JJCNeKnq4+urcfpChVlWTOwpmEEMJIkCCck2nTptHd3U2hUOB0hUKB/fv3M23aNM7m7rvvJpPJkMlkyGQyZDIZMpkMf/u3f0vRf/gP/4FMJsOYMWMIIVw/KvUEJce7lxDCtWCgP8vudXspqamrJlWVJIQQRoIE4Zw0NTVx6tQptm7dyum2bt3K0NAQTU1NnM3DDz9MS0sLLS0ttLS00NLSQktLC/X19RQ1NzfT0tLC2LFjCSFcPyr1fRJjqykq5PoY7G0jhKtdT1cfPV19FNXUVTN/WRMhhDBSJAjn5IEHHuDWW2/lxz/+MRs2bKCjo4MNGzbQ0tLCrbfeygMPPEBJV1cXkmhubiaEEMpv/ntKTngVIVzNBvqz7N/+B4pSVUlSVUlCCGEkSRDOSXl5Oa+88gpTpkxh+fLlNDc3s3z5cr785S+zceNGysvLCSGEM6nU90mMraaokOtjsLeNEK5WPV199HT1UTJ/WRMhhDCSJAjn7Atf+AKbN2/md7/7HevXr+e3v/0tmzdv5qabbuJ0dXV12Gb9+vV8mqVLl2KbWbNmEUK4flXqCUqO719CCFejgf4su9ftpWTOwpmEEMJIkyCctxtvvJFZs2Zx0003EUII56L85vtIjK2mJH+kkxCuNj1dfQz0Z0lVJampq2b6vMmEEMJIkyCEEMJlUaknKPmg40FCuJoM9GfZtrSdooH+LOl5UwghhJEoQQghhMui/Ob7SIytpuSEnyOEq0VPVx8lqaok0+dNJoQQRqIEIYQQLptKPUHJYO/rFHJ9hHClDfRn2ba0nZL5y5oIIYSRKkEIIYTLpvzm+yibWE9RIdfHCa8ihCtt97q9lKSqktTUVRNCCCNVghBCCJdVpZ6gZLC3jUKujxCulIH+LN3bD1KUqkoyf1kTIYQwkiUIIYRwWY2eVE/ZxHpKTngVIVwp+7f/gZJUVZKaumpCCGEkSxBCCOGyq9QTlAz2tpE/0kkIl9tAf5Y96zopmbNwJiGEMNIlCCGEcNmNnlRP2cR6Sk54FSFcbtuWtlMyfd5kauqqCSGEkS5BCCGEK2J8egUlQ0c7yR/pJITLpaerj56uPopq6qpJz5tCCCEESBBCCOGKSIytpvzm+yg54VWEcLnsXreXklRVkpq6akIIIUCCEEIIV8y49AoSY6spGjrayWBvGyF81rq3H6Snq4+iVFWSOQtnEkII4U8ShBBCuKLKb/57Sk54FSF8lgb6s+xet5eS6fMmk6pKEkII4U8ShBBCuKIq9X0SY6spKuT6OOHnCOGz0tPVR1GqKkmqKsmchTMJIYTwsQQhhBCuuEo9QckJryKEz8JAf5ZtS9sZ6M8y0J9lzsKZhBBC+HMJQgghXHHlN99H2cR6So7vX0IIl9rudXspSVUlmT5vMiGEEP5cghBCCFeFSj1ByWBvG/kjnYRwqQz0Z+nefpCS+cuaCCGE8JcShBBCuCqMnlRP2cR6Sk71vk4Il8q2pe2U1NRVU1NXTQghhL+UIIQQwlVjfHoFJYO9beSPdBLCxerp6qOnq4+imrpq5iycSQghhDNLEEII4aqRGFtN+c33UXLCqwjhYgz0Z9m//Q+UpKqS1NRVE0II4cwShBBCuKqMS6+gZOhoJ4O9bYRwoQb6s3RvP0hRqirJnIUzCSGE8NclCCGEcNUZl15ByfH9SwjhQgz0Z9m2tJ2S6fMmk6pKEkII4a9LEEII4apTfvN9JMZWU3LCzxHC+dq//Q8M9GcpSlUlmbNwJiGEEM4uQQghhKvSuOkrKDnhVRRyfYRwrgb6s+xZ10nJ/GVNhBBC+HQJQgghXJVGT6qnbGI9JR/uX0II52rb0nZKauqqqamrJoQQwqdLEEII4ao1Pr2CkqGjneSPdBLCp+np6qOnq4+iVFWSOQtnEkII4dwkCCGEcNVKjK2m/Ob7KDnevYQQzmagP8vudXspqamrpqaumhBCCOcmQQghhKvauPQKSgq5PgZ72wjhr+np6qOnq4+iVFWS+cuaCCGEcO4ShBBCuOqNS6+g5Pj+JRRyfYTwSQP9WbYtbadkzsKZhBBCOD8JQgghXPXKb76Pson1lJzwKkL4pN3r9lKSqkoyfd5kQgghnJ8EIYQQrgmVeoKixNhqBnvbyB/pJISSnq4+urcfpGT+siZCCCGcvwQhhBCuCaMn1VN+830Ucn0UnfAqQiga6M+ye91eSqbPm0xNXTUhhBDOX4IQQgjXjHHpFZQMHe1ksLeNEHq6+ujp6qMoVZVk/rImQgghXJgEIYQQrinj0isoOb5/CYVcH2HkGujPsm1pO6mqJEVzFs4khBDChUsQQgjhmlJ+832UTayn5IRXEUau3ev2UjTQnyVVlWT6vMmEEEK4cAlCCCFccyr1BCWDvW3kj3QSRp6erj66tx+kKFWVZP6yJkIIIVycBOG8FAoFOjo62LFjBx0dHRQKBc5XPp/nN7/5DTt27ODXv/41uVyOEEI4H6Mn1VN+832UHO9eQhhZBvqz7N/+B0pq6qqpqasmhBDCxUkQztk777xDQ0MDzc3NLF68mObmZhoaGjh06BDnqq2tjbvuuosFCxawePFivvvd7/LVr36Vn//854QQwvkYl15BYmw1RYVcHyf8HGHk2L/9D3RvP0hRqirJ/GVNhBBCuHgJwjnJZrM8+uijnDx5khdeeIEDBw6wevVqTp48yYIFC/jwww/5NLt27eKHP/whNTU1vPrqqxw4cIBf/OIXpNNpVq5cyebNmwkhhPMxbvoKSk54FfkjnYTr30B/lj3rOimZv6yJEEIIl0aCcE42bdrE0aNHWbp0KbNnz6a8vJy5c+eybNky3nvvPTZu3MinWbNmDWVlZbz88svU1dVRXl7OlClTeOGFF7jhhht48cUXCSGE8zF6Uj1lE+spOeFVhOvftqXtlNTUVVNTV00IIYRLI0E4J+3t7VRUVDB37lxO19DQQEVFBTt37uTTjBo1invuuYdUKsXpxo4dy1e+8hX++Mc/EkII52t8egWJsdUUFU70MdjbRrh+dW8/SE9XH0WpqiTzlzURQgjh0kkQPlWhUODw4cNMnTqVRCLBJ82YMYPDhw9TKBQ4m61bt/L888/zSYVCgXfffZdx48YRQgjnKzG2mko9QVEh18fx/Uso5PoI15+B/izblrZTMmfhTFJVSUIIIVw6CcKnyuVyDA8PM2HCBM4kmUwyPDzM4OAgF+KVV17hyJEjZDIZzpUkJCEJSUhi9erVhBBGpvKb76NsYj0lH+5fQrj+bFvaTklNXTXT500mhBDCpZUgfKr333+fojFjxnAmo0aNoqinp4fz9eabb7Jy5Uq++MUvsmjRIs6VbWxjG9vY5h//8R8JIYxc49MrKBk62kn+SCfh+tG9/SA9XX0UpaqSzFk4kxBCCJdegvCpKioqOBeJRILzsWvXLr73ve/xuc99jpdffplkMkkIIVyoxNhqKvUEJR90PEi4fmxb2k5RqirJ9HmTqamrJoQQwqWXIHyq8ePHU3Tq1CnOZGhoiKJbbrmFc/X888+zaNEibrzxRtra2qipqSGEEC5Wpb5P2cR6SrK/f5Bw7du2tJ3TzVk4kxBCCJ+NBOFTVVZWUlZWxrFjxziTY8eOUVZWRmVlJefi6aef5qc//SnTp0+nra2NqqoqQgjhUqnUE5QMHe0kf6STcO3q3n6Q7u0HKUpVJZm/rIkQQgifnQThnEybNo3u7m4KhQKnKxQK7N+/n2nTpnEuHn/8cV5//XUaGxvZsGEDEyZMIIQQLqXRk+qp1BOUfNDxIOHaNNCfZfe6vZRMnzeZmrpqQgghfHYShHPS1NTEqVOn2Lp1K6fbunUrQ0NDNDU18WnWrl1Le3s73/zmN2ltbaW8vJwQQvgsVOr7lE2sp+T4/iWEa8+2pe0M9GcpSlUlmbNwJiGEED5bCcI5eeCBB7j11lv58Y9/zIYNG+jo6GDDhg20tLRw66238sADD1DS1dWFJJqbmyk5duwYa9asoejkyZM8+eSTPPnkkzz55JM8+eSTPPnkkzz55JMMDw8TQgiXwvj0CkoGe9vIH+kkXDu6tx+kp6uPVFWSVFWS+cuaCCGE8NlLEM5JeXk5r7zyClOmTGH58uU0NzezfPlyvvzlL7Nx40bKy8s5m7feeotTp05R9M///M+88cYbvPHGG7zxxhu88cYbvPHGG7zxxhsUCgVCCOFSSIytZlx6BWUT6yn6oONBCrk+wtVvoD/LtqXtpKqSDPRnmT5vMjV11YQQQvjsJQjn7Atf+AKbN2/md7/7HevXr+e3v/0tmzdv5qabbuJ0dXV12Gb9+vWU/N3f/R22sY1tbGMb29jGNrYZPXo0IYRwqZTffB+n+3D/EsLVb9vSdooG+rPU1FUzZ+FMQgghXB4Jwnm78cYbmTVrFjfddBMhhHC1G59eQcnQ0U5O+DnC1at7+0F6uvooSlUlmb+siRBCCJdPghBCCNe1xNhqbpi1hZITXkX+SCfh6jPQn2Xb0nZK5iycSaoqSQghhMsnQQghhOve6En1lE2sp+R49xLC1WWgP8v672ylZPq8yUyfN5kQQgiXV4IQQggjQvLuLZRNrKeokOvj+P4lhKvH/u1/YKA/S1GqKsn8ZU2EEEK4/BKEEEIYMSr1BCWDvW3kj3QSrryerj66tx+kKFWVZP6yJkIIIVwZCUIIIYwYoyfVU6knKPmg40HyRzoJV85Af5ZtS9sZ6M9SNH3eZGrqqgkhhHBlJAghhDCiVOr7lE2sp+SEVxGujIH+LNuWtjPQn6Vo+rzJzFk4kxBCCFdOghBCCCNO8u4tJMZWUzR0tJPj+5cQLr/92/9AT1cfRamqJHMWziSEEMKVlSCEEMKING76CkoGe9vIH+kkXD7d2w+yZ10nRamqJPOXNZGqShJCCOHKShBCCGFEGj2pnnHpFZR80PEg+SOdhM/eQH+WbUvbKZk+bzI1ddWEEEK48hKEEEIYscpvvo+yifWUHO9eQvhsDfRnWf+drZR8fWE9cxbOJIQQwtUhQQghhBEtefcWyibWkxhbTSHXR/b3DxI+GwP9WbYtbWegP0tRqirJnIUzCSGEcPVIEEIIYcQbn15BIddH0dDRTk74OcKlt3/7H+jp6qMoVZWk+cUMIYQQri4JQgghjHiJsdXcMGsLJSe8ivyRTsKl0739IHvWdVKUqkoyf1kTqaokIYQQri4JQgghhP/P6En13DBrCyUfdDxI/kgn4eIN9GfZtrSdkunzJlNTV00IIYSrT4IQQgjh/zd6Uj3lN99HyfHuJeSPdBIu3EB/lvXf2UrJ1xfWM2fhTEIIIVydEoQQQginGZdeQfnN95EYW00h18fx7iWECzPQn2X9d7Yy0J+laPq8ycxZOJMQQghXrwQhhBDCJ4xLr2D0xHqKCrk+sr9/kHB+BvqzbFvazkB/lqJUVZL5y5oIIYRwdUsQQgghnEGlniAxtpqioaOdZH//IOHc7d/+B3q6+ihKVSVpfjFDCCGEq1+CEEII4QwSY6tJztpCydDRTo7vX0L4dLvX7WXPuk6KUlVJml/MkKpKEkII4eqXIIQQQvgrEmOruWHWFkoGe9s44ecIf93udXvZs66TolRVkvnLmkhVJQkhhHBtSBBCCCGcxehJ9dwwawslJ7yKwd42wl/avW4ve9Z1UpSqSjJ/WRM1ddWEEEK4diQIIYQQPsXoSfXcMGsLJcf3L2Gwt43wsd3r9rJnXSdFqaok0+dNpqaumhBCCNeWBCGEEMI5GD2pnhtmbaEoMbaa4/uXMNjbRoDd6/ayZ10nRamqJNPnTWbOwpmEEEK49iQIIYQQztHoSfXcMGsLhVwfRcf3L2Gwt42RbPe6vexZ10mqKklNXTVzFs5kzsKZhBBCuDYlCCGEEM7D6En13DBrCyXH9y/hhJ9jJNq9bi/d2w9SUlNXzfR5kwkhhHDtShBCCCGcp9GT6rlh1hYSY6spOuFVnPBzjBQD/Vm6tx9kz7pOBvqzpKqSTJ83mTkLZxJCCOHaliCEEEK4AKMn1TNu+gpKBntfJ/v7B7neDfRn2b1uL9uWtlOUqkoyZ+FM5iycSQghhGtfghBCCOECjZ5Uzw2ztlBUyPUxdLSTgV1fo5Dr43o00J9l/Xe20r39IEU1ddXMX9bE9HmTCSGEcH1IEEIIIVyE0ZPqSTW8SUkh10e240HyRzq5nvR09fGzb7zEQH+WVFWSVFWS+cuaqKmrJoQQwvUjQQghhHCREmOrSTW8SdnEeooKuT4+6HiQE36Oa91Af5bd6/ay/jtbKUlVJVm84x9IVSUJIYRwfUkQQgghXAKJsdUk795C2cR6Sk54FdnfP8i1aqA/y+51e9mzrpNUVZKi6fMm0/xihhBCCNenBCGEEMIllLx7C5V6gpLCiT4Gdn2N/JFOriXd2w/ys2+8RPf2g5R8fWE985c1EUII4fqVIIQQQrjEKvV9bpi1haJCro9Cro8POh4k+/sHudoN9GfZvW4v25a2U5KqSjJn4UzmLJxJCCGE61uCEEII4TMwelI9qYY3KZtYT8nQ0U4Gdn2NE36Oq81Af5bd6/bys2+8RPf2g5SkqpI0v5hh+rzJhBBCuP4lCJdVoVCgo6ODHTt20NHRQaFQIFx+q1evJlyc1atXEy7e6tWruZ4lxlaTvHsLlXqCkkKujxNexcCur5E/0snF+pv/8ddcrIH+LOu/s5U96zpJVSUZ6M+Sqkry9YX1LN7xD6SqklzPVq9eTbh4q1evJlyc1atXEy7O6tWrCRcnQbhs3nnnHRoaGmhubmbx4sU0NzfT0NDAoUOHCJdXa2sr4eK0trYSLl5raysjQaW+T6rhTcom1lNSyPXxQceDDOz6GvkjnVwJA/1Z1n9nK+u/s5WB/iwlqaokzS9mmLNwJiNBa2sr4eK1trYSLk5rayvh4rS2thIuToJwWWSzWR599FFOnjzJCy+8wIEDB1i9ejUnT55kwYIFfPjhh4QQwvUsMbaa5N1bqNQTnK6Q6+N49xIGdn2Nwd42Ps2cNf8ne/7lfc6k59hJml87xNkM9Gfp3n6Q9d/Zys++8RI9XX0M9GcpSgNMbG0AACAASURBVFUlmT5vMot3/AOpqiQhhBBGngThsti0aRNHjx5l6dKlzJ49m/LycubOncuyZct477332LhxIyGEMBJU6vukGt7khllbKCnk+ijk+jjhVQzs+hon/Bz5I52cyfoHJtP82iH2/Mv7nK7n2EmaXzvIP83995zJQH+W3ev28rNvvMS2pe30dPVRkqpK8vWF9Sze8Q/MWTiTEEIII1eCcFm0t7dTUVHB3LlzOV1DQwMVFRXs3LmTEEIYKRJjqxk9qZ5Uw5tU6glKCrk+Crk+TngVH3Q8yMCur3HCzzHY20b+SCdFNRMq2P3dGTS/dog9//I+RT3HTtL82kHWPzCZmgkVFA30Z+nefpBtS9v5p+k/42ffeIk96zo5XaoqyfR5k2l+McOchTMJIYQQEoTPXKFQ4PDhw0ydOpVEIsEnzZgxg8OHD1MoFAghhJEkMbaaSn2fVMObVOoJEmOrOV0h18cJr+L4/iV80PEg2d8/SPb3DzLhUDM7/uNvObT3f+ahj97mPy3535h3sJf9z/2G9d/Zys++8RI/+8ZLbFvaTvf2g5wuVZUkVZXk6wvraX4xw/xlTaSqkoQQQghFCcJnLpfLMTw8zIQJEziTZDLJ8PAwg4ODnIs777wTSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIYkiSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIYkiSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJFElCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlI4r9J/7dMn7eWuxa9x6J1Zbz4v4/idP/l/b+haOhoJ0NHOxk62slN//V57k/+Z/77j97m1rd7GPjd/0P39oN0v/seA/1ZPun4Rx/wr8PmF/+6iXX/8r+w8GePcNecryIJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhiSJJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUkUSUISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUkUSUISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUnceeedhIuTIHzm3n//fYrGjBnDmYwaNYqinp4ezsXGjRuxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNrbZsuMw/1Pr/82Eef/KDbO2MC69gptvv4uyifUkxlZzusTYaj4pdfIUqaokNXXVpKqSTJ83meYXM6z8v5ay4Z11vHloN7axjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNhs3biRcnAThM1dRUcG5SCQShBBC+NjoSfWU33wfybu3kLx7C8lZW7hh1hb+663P8p+z91N+89+z+W++wtcX1vPKjL/l3/0Pd9L8YobmFzM0v5hh8Y5/YP6yJmrqqgkhhBDORYLwmRs/fjxFp06d4kyGhoYouuWWWwghhPDXJcZW88fEdBb+fjL/3Tf+E5X6Pq/+zVeYs3Ame1bOZVXub+j5d+NIVSUJIYQQLkSC8JmrrKykrKyMY8eOcSbHjh2jrKyMyspKQgghnN0r/8d/Yf0Dk6mZUMHpaiZUsPu7M3im/V8JIYQQLlSCcFlMmzaN7u5uCoUCpysUCuzfv59p06YRQgjh0/1T07+nZkIFZ1IzoYLd35tBCCGEcKEShMuiqamJU6dOsXXrVk63detWhoaGaGpqIoQQQgghhHBlJQiXxQMPPMCtt97Kj3/8YzZs2EBHRwcbNmygpaWFW2+9lQceeIAQQgjn76P/9T8SQgghXCoJwmVRXl7OK6+8wpQpU1i+fDnNzc0sX76cL3/5y2zcuJHy8nJCCCGEEEIIV1aCcNl84QtfYPPmzfzud79j/fr1/Pa3v2Xz5s3cdNNNhBBCCCGEEK68BOGyu/HGG5k1axY33XQTIYQQQgghhKtHghBCCCGEEEII/yZBCCGEEEIIIYR/kyCEEEIIIYQQwr9JEEIIIYQQQgjh3yQI16R8Ps9vfvMbduzYwa9//WtyuRzhzDo6Oujt7eV8DA8Pk8vlyOVy5HI5crkcuVyOXC7H4OAg4cw6Ojro7e0lfKxQKNDR0cGOHTvo6OigUChwPoaHh8nlcuRyOXK5HLlcjlwuRy6XY3BwkJGsUCjQ0dHBjh076OjooFAoEP5coVCgo6ODHTt20NHRQaFQ4HwMDw+Ty+XI5XLkcjlyuRy5XI5cLsfg4CDhz3V0dNDb20s4u46ODnp7ezkfw8PD5HI5crkcuVyOXC5HLpcjl8sxODhIgHw+z29+8xt27NjBr3/9a3K5HOHCJAjXnLa2Nu666y4WLFjA4sWL+e53v8tXv/pVfv7znxP+3L59+2hubmbfvn2cj2eeeYZ0Ok06nSadTpNOp0mn06TTaX7wgx8Q/tK+fftobm5m3759hD955513aGhooLm5mcWLF9Pc3ExDQwOHDh3iXD3zzDOk02nS6TTpdJp0Ok06nSadTvODH/yAkeqdd96hoaGB5uZmFi9eTHNzMw0NDRw6dIjwJ++88w4NDQ00NzezePFimpubaWho4NChQ5yrZ555hnQ6TTqdJp1Ok06nSafTpNNpfvCDHxA+tm/fPpqbm9m3bx/hr9u3bx/Nzc3s27eP8/HMM8+QTqdJp9Ok02nS6TTpdJp0Os0PfvADRrq2tjbuuusuFixYwOLFi/nud7/LV7/6VX7+858Tzl+CcE3ZtWsXP/zhD6mpqeHVV1/lwIED/OIXvyCdTrNy5Uo2b95M+JO33nqLRYsWcSF6e3sZM2YMmUyGTCZDJpMhk8mQyWS46667CH/urbfeYtGiRYSPZbNZHn30UU6ePMkLL7zAgQMHWL16NSdPnmTBggV8+OGHnIve3l7GjBlDJpMhk8mQyWTIZDJkMhnuuusuRqJsNsujjz7KyZMneeGFFzhw4ACrV6/m5MmTLFiwgA8//JCRLpvN8uijj3Ly5EleeOEFDhw4wOrVqzl58iQLFizgww8/5Fz09vYyZswYMpkMmUyGTCZDJpMhk8lw1113Ef7krbfeYtGiRYSze+utt1i0aBEXore3lzFjxpDJZMhkMmQyGTKZDJlMhrvuuouRbNeuXfzwhz+kpqaGV199lQMHDvCLX/yCdDrNypUr2bx5M+H8JAjXlDVr1lBWVsbLL79MXV0d5eXlTJkyhRdeeIEbbriBF198kZEun8+zZs0aHnnkEQYHB7kQXV1d1NfX09LSQktLCy0tLbS0tNDS0sL9999P+JN8Ps+aNWt45JFHGBwcJHxs06ZNHD16lKVLlzJ79mzKy8uZO3cuy5Yt47333mPjxo2ci66uLurr62lpaaGlpYWWlhZaWlpoaWnh/vvvZyTatGkTR48eZenSpcyePZvy8nLmzp3LsmXLeO+999i4cSMj3aZNmzh69ChLly5l9uzZlJeXM3fuXJYtW8Z7773Hxo0bORddXV3U19fT0tJCS0sLLS0ttLS00NLSwv33389Il8/nWbNmDY888giDg4OEM8vn86xZs4ZHHnmEwcFBLkRXVxf19fW0tLTQ0tJCS0sLLS0ttLS0cP/99zOSrVmzhrKyMl5++WXq6uooLy9nypQpvPDCC9xwww28+OKLhPOTIFxTRo0axT333EMqleJ0Y8eO5Stf+Qp//OMfGekee+wxVq1axezZs/nRj37E+ert7eXUqVPcfvvthLN77LHHWLVqFbNnz+ZHP/oR4WPt7e1UVFQwd+5cTtfQ0EBFRQU7d+7k0/T29nLq1Cluv/12wsfa29upqKhg7ty5nK6hoYGKigp27tzJSNfe3k5FRQVz587ldA0NDVRUVLBz504+TW9vL6dOneL2228nnNljjz3GqlWrmD17Nj/60Y8IZ/bYY4+xatUqZs+ezY9+9CPOV29vL6dOneL2228n/KVRo0Zxzz33kEqlON3YsWP5yle+wh//+EfC+UkQrilbt27l+eef55MKhQLvvvsu48aNY6S74447eOmll1i7di0TJ07kfB06dIiidDpNV1cXmzZt4vXXX+fQoUOEP3fHHXfw0ksvsXbtWiZOnEj4k0KhwOHDh5k6dSqJRIJPmjFjBocPH6ZQKHA2hw4doiidTtPV1cWmTZt4/fXXOXToECNVoVDg8OHDTJ06lUQiwSfNmDGDw4cPUygUGKkKhQKHDx9m6tSpJBIJPmnGjBkcPnyYQqHA2Rw6dIiidDpNV1cXmzZt4vXXX+fQoUOEP7njjjt46aWXWLt2LRMnTiSc2R133MFLL73E2rVrmThxIufr0KFDFKXTabq6uti0aROvv/46hw4dIsDWrVt5/vnn+aRCocC7777LuHHjCOcnQbguvPLKKxw5coRMJsNIt3jxYu655x4u1IEDByhavnw5Dz30EM8++yxPP/009957L0899RTDw8OEP1m8eDH33HMP4c/lcjmGh4eZMGECZ5JMJhkeHmZwcJCzOXDgAEXLly/noYce4tlnn+Xpp5/m3nvv5amnnmJ4eJiRJpfLMTw8zIQJEziTZDLJ8PAwg4ODjFS5XI7h4WEmTJjAmSSTSYaHhxkcHORsDhw4QNHy5ct56KGHePbZZ3n66ae59957eeqppxgeHmakW7x4Mffccw/h7BYvXsw999zDhTpw4ABFy5cv56GHHuLZZ5/l6aef5t577+Wpp55ieHiY8JdeeeUVjhw5QiaTIZyfBOGa9+abb7Jy5Uq++MUvsmjRIsLF6enpoWjy5Mn86le/4t133+W1115j6tSp/PKXv+QnP/kJIZzN+++/T9GYMWM4k1GjRlHU09PD2fT09FA0efJkfvWrX/Huu+/y2muvMXXqVH75y1/yk5/8hJHm/fffp2jMmDGcyahRoyjq6elhpHr//fcpGjNmDGcyatQoinp6ejibnp4eiiZPnsyvfvUr3n33XV577TWmTp3KL3/5S37yk58QwuXQ09ND0eTJk/nVr37Fu+++y2uvvcbUqVP55S9/yU9+8hPCn3vzzTdZuXIlX/ziF1m0aBHh/CQIV5VCoUA+nyefz5PP58nn8+Tzef6aXbt28b3vfY/Pfe5zvPzyyySTSa53hUKBfD5PPp8nn8+Tz+fJ5/NcKg8//DArV65k7dq1fOlLX2L06NGk02nWr1/PxIkT2bx5M9lslutdoVAgn8+Tz+fJ5/Pk83ny+TzhY4VCgXw+Tz6fJ5/Pk8/nyefzVFRUcC4SiQRn8/DDD7Ny5UrWrl3Ll770JUaPHk06nWb9+vVMnDiRzZs3k81mGUkqKio4F4lEgpGqoqKCc5FIJDibhx9+mJUrV7J27Vq+9KUvMXr0aNLpNOvXr2fixIls3ryZbDZLCJ+1hx9+mJUrV7J27Vq+9KUvMXr0aNLpNOvXr2fixIls3ryZbDZL+JNdu3bxve99j8997nO8/PLLJJNJwvlJEK4qO3fupLa2ltraWmpra6mtraW2tpYzef7551m0aBE33ngjbW1t1NTUMBLs3LmT2tpaamtrqa2tpba2ltraWi6VO++8k29961t80vjx47n77rsZGhri7bff5nq3c+dOamtrqa2tpba2ltraWmprawkf27lzJ7W1tdTW1lJbW0ttbS21tbWMHz+eolOnTnEmQ0NDFN1yyy2czZ133sm3vvUtPmn8+PHcfffdDA0N8fbbbzOSjB8/nqJTp05xJkNDQxTdcsstjFTjx4+n6NSpU5zJ0NAQRbfccgtnc+edd/Ktb32LTxo/fjx33303Q0NDvP3224TwWbvzzjv51re+xSeNHz+eu+++m6GhId5++20CPP/88yxatIgbb7yRtrY2ampqCOcvQbiqfP7zn6exsZHGxkYaGxtpbGyksbGRT3r66af56U9/yvTp02lra6OqqoqR4vOf/zyNjY00NjbS2NhIY2MjjY2NXA7l5eUUffTRR1zvPv/5z9PY2EhjYyONjY00NjbS2NhI+NjnP/95GhsbaWxspLGxkcbGRhobG6msrKSsrIxjx45xJseOHaOsrIzKykouVHl5OUUfffQRI0llZSVlZWUcO3aMMzl27BhlZWVUVlYyUlVWVlJWVsaxY8c4k2PHjlFWVkZlZSUXqry8nKKPPvqIEK6k8vJyij766CNGuqeffpqf/vSnTJ8+nba2NqqqqggXJkG4qsyYMYPW1lZaW1tpbW2ltbWV1tZWTvf444/z+uuv09jYyIYNG5gwYQIjyYwZM2htbaW1tZXW1lZaW1tpbW3lUsjn83z729/m8ccf50yOHTtG0W233cb1bsaMGbS2ttLa2kprayutra20trYSPjZjxgxaW1tpbW2ltbWV1tZWWltbKZo2bRrd3d0UCgVOVygU2L9/P9OmTeNs8vk83/72t3n88cc5k2PHjlF02223MdJMmzaN7u5uCoUCpysUCuzfv59p06Yx0k2bNo3u7m4KhQKnKxQK7N+/n2nTpnE2+Xyeb3/72zz++OOcybFjxyi67bbbCOGzlM/n+fa3v83jjz/OmRw7doyi2267jZHs8ccf5/XXX6exsZENGzYwYcIEwoVLEK4pa9eupb29nW9+85u0trZSXl5OuHRGjx5Nf38/u3btoqenh9MdPnyYPXv2MGXKFGpqagjhbJqamjh16hRbt27ldFu3bmVoaIimpibOZvTo0fT397Nr1y56eno43eHDh9mzZw9TpkyhpqaGkaapqYlTp06xdev/2x78hLZZNwAc//LMNorgRUPoQVKKNYWSW/GQc2gH4kHoIbcQPIgVBJ+h1BaxYtOC6EE7NsYOD00glxZK1McqbHSEksPsjoI/dtkurXjYRYRSl/KyiLx9h75z9f1D6Pfz2eCkjY0N7t+/z8zMDGfdzMwMR0dHbGxscNLGxgb3799nZmaGf2doaIj9/X2uXbvGnTt3OOn27dvcuHGDyclJRkdHkf6bhoaG2N/f59q1a9y5c4eTbt++zY0bN5icnGR0dJSz6vLly3z77be8/PLLXLx4kUwmg/6eCA2Me/fucenSJR44PDwkjmPiOCaOY+I4Jo5j4jim1+uhR9vb26NQKFCr1ThpYWGBXq9HtVpla2uLbrfL5uYm1WqV4eFhVldXkR6lUqmQz+dZWVmh0WjQ7XZpNBosLy+Tz+epVCr8bm9vj0KhQK1W46SFhQV6vR7VapWtrS263S6bm5tUq1WGh4dZXV3lLKpUKuTzeVZWVmg0GnS7XRqNBsvLy+TzeSqVCmddpVIhn8+zsrJCo9Gg2+3SaDRYXl4mn89TqVT43d7eHoVCgVqtxkkLCwv0ej2q1SpbW1t0u102NzepVqsMDw+zurqK9J+0t7dHoVCgVqtx0sLCAr1ej2q1ytbWFt1ul83NTarVKsPDw6yurnJW3bt3j0uXLvHA4eEhcRwTxzFxHBPHMXEcE8cxvV4P/XURGhg3b97k6OiIB65fv06apqRpSpqmpGlKmqakacrx8TE6vXK5zNraGlEUMT8/T61WY3FxkWw2S7PZpFAoID1KJpNhfX2dyclJ6vU6tVqNer1OsVik2WySyWR4lHK5zNraGlEUMT8/T61WY3FxkWw2S7PZpFAocBZlMhnW19eZnJykXq9Tq9Wo1+sUi0WazSaZTIazLpPJsL6+zuTkJPV6nVqtRr1ep1gs0mw2yWQyPEq5XGZtbY0oipifn6dWq7G4uEg2m6XZbFIoFJD+F8rlMmtra0RRxPz8PLVajcXFRbLZLM1mk0KhwFl18+ZNjo6OeOD69eukaUqapqRpSpqmpGlKmqYcHx+jvy5CA+P8+fOEEAghEEIghEAIgRACIQRCCIQQGBoaQr8pl8uEEJidneVhU1NThBBIkoSHTU9Ps7Ozw/b2NkmS0Ol0aLfbFItF9MfK5TIhBGZnZ9FvRkZGaLVa7O7ukiQJnU6HVqtFLpfjpKmpKUIIJEnCw6anp9nZ2WF7e5skSeh0OrTbbYrFImfZyMgIrVaL3d1dkiSh0+nQarXI5XLoNyMjI7RaLXZ3d0mShE6nQ6vVIpfLcdLU1BQhBJIk4WHT09Ps7Oywvb1NkiR0Oh3a7TbFYhH9q3K5TAiB2dlZ9OfK5TIhBGZnZ3nY1NQUIQSSJOFh09PT7OzssL29TZIkdDod2u02xWKRs+z8+fOEEAghEEIghEAIgRACIQRCCIQQGBoaQn9dhKQ/NTY2RqlUIpfLIZ1WNpulVCqRy+U4rbGxMUqlErlcDv1TNpulVCqRy+XQH8tms5RKJXK5HKc1NjZGqVQil8sh/T+NjY1RKpXI5XJI/y0RkiRJkqS+CEmSJElSX4QkSZIkqS9CkiRJktQXIUmSJEnqi5AkSZIk9UVIkiRJkvoiJEmSJEl9EZIkSZKkvghJkiRJUl+EJEmSJKkvQpIkSZLUFyFJkiRJ6ouQJEmSJPVFSJIkSZL6IiRJkiRJfRGSJA2Q/f192u027XabP/L111/Tbrc5ODhAkqTHFSFJ0gB59tlnuXLlCu+++y5Xr17lpM3NTd5++22uXr3Kc889hyRJjytCkqQBkslk+Oyzzzh37hyff/45d+/e5YG7d+/y0Ucf8dRTT3Hx4kWGhoaQJOlxRUiSNGDGx8e5cOECR0dHvPfeexwfH/PWW29xeHjIBx98wOjoKJIknUaEJEkD6LXXXuOll17i1q1bzM7O8sMPP/DKK6/w6quvIknSaUVIkjSgPv74Y5555hm+//57nn/+eZaWlpAk6e+IkCRpQD399NM8+eSTPPDrr79yfHyMJEl/R4QkSQPq/fff56effmJ8fJwff/yRpaUlJEn6OyIkSRpA7Xabb775homJCb744gsmJiZI05SvvvoKSZJOK0KSpAFzcHDAhx9+yBNPPMGnn35KFEV88sknnDt3jqWlJQ4ODpAk6TQiJEkaMBcuXOCXX37hzTff5IUXXuCB8fFx5ubm+Pnnn3nnnXeQJOk0IiRJGiBXrlzh1q1bTExMMDc3x0lzc3O8+OKLfPfdd1y+fBlJkh5XhCRJA+T1118nhEC73eZhURTx5ZdfEkLgjTfeQJKkxxUhSZIkSeqLkCRJkiT1RUiSJEmS+iIkSZIkSX0RkiRJkqS+CEmSJElSX4QkSZIkqS9CkiRJktQXIUmSB3vNJAAAAAlJREFUJEnq+wcvW5z2M8ibrwAAAABJRU5ErkJggg== 560 420 18 19 18 39 40 figure 4c3cdf34-276d-426f-8981-d3251db459f3...