> //
> //                    ACM ICPC 2003-2004
> //               Northeastern European Region
> //               Northern Subregional Contest
> //
> //     Problem C. Crankshaft
> //     Authors: Nikolay Durov, Dmitry Shtukenberg
> //     Solution: Dmitry Shtukenberg
> //
> 
> #include <stdio.h>
> #include <process.h>
> #include <math.h>
> 
> int N;
> int V;
> int X[2000];
> int Y[2000];
> 
> double XR = 0;
> double YR = 0;
> double Mass = 0;
> 
> void readXY( FILE* f ) {
>   fscanf( f, "%d", &V );
>   for( int i = 0; i < V; i++ )
>     fscanf( f, "%d %d", X+i, Y+i );
>   X[V] = X[0];
>   X[V+1] = X[1];
>   Y[V] = Y[0];
>   Y[V+1] = Y[1];
> }
> 
> int crosses( int* _X, int* _Y, int from, int to, double _x, double _y ) {
>   if( (_X[from] < _x) != (_X[to] > _x) ) return 0;
>   double t = (_X[to]-_x)/(-_X[from]+_X[to]);
>   double yc = _Y[from]*t + _Y[to]*(1-t);
>   return yc < _y;
> }
> 
> int checkinside( int from, int to ) {
> // 1. The edge should not cross other edges
>   for( int i = 0; i < V; i++ ) {
>     double d = (X[i+1]-X[i])*(Y[to]-Y[from]) - (X[to]-X[from])*(Y[i+1]-Y[i]);
>     if( fabs(d) < 1e-10 ) return 0;
>     double t1 = ((X[from]-X[i])*(Y[to]-Y[from])-(X[to]-X[from])*(Y[from]-Y[i]))/d;
>     double t2 = -((X[i]-X[from])*(Y[i+1]-Y[i])-(X[i+1]-X[i])*(Y[i]-Y[from]))/d;
> 
>     if( t1 > 1e-10 && t1 < 1-1e-10 &&
> 	t2 > -1e-10 && t2 < 1+1e-10 ) return 0;
>     if( t1 > -1e-10 && t1 < 1+1e-10 &&
> 	t2 > 1e-10 && t2 < 1-1e-10 ) return 0;
>   }
> 
> // 2. The edge should lie inside polygon
>   double goldcut = (-1+sqrt(5))/2;
>   double xm = X[to]*goldcut + X[from]*(1-goldcut);
>   double ym = Y[to]*goldcut + Y[from]*(1-goldcut);
>   int cnt = 0;
>   {
>     for( int i = 0; i < V; i++ ) {
>       if( X[from] != X[to] ) cnt += crosses( X, Y, i, i+1, xm, ym );
>       else cnt += crosses( Y, X, i, i+1, ym, xm );
>     }
>   }
>   return cnt % 2;
> }
> 
> double dist( int from, int to ) {
>   return sqrt((X[from]-X[to])*(X[from]-X[to]) + (Y[from]-Y[to])*(Y[from]-Y[to]));
> }
> 
> int processtriangle() {
>   for( int i = 0; i < V; i++ )
>     if( V == 3 || checkinside( i, i+2 ) ) {
>       double a = dist(i,i+1);
>       double b = dist(i+1,i+2);
>       double c = dist(i,i+2);
>       double p = (a+b+c)/2;
>       double trmass = sqrt(p*(p-a)*(p-b)*(p-c));
>       Mass += trmass;
>       XR += (X[i]+X[i+1]+X[i+2])*trmass/3;
>       YR += (Y[i]+Y[i+1]+Y[i+2])*trmass/3;
> 
>       if( V == 3 ) return 0;
> 
>       for( int j = i+1; j < V+2; j++ ) {
>         X[j] = X[j+1];
>         Y[j] = Y[j+1];
>       }
>       V--;
>       return 1;
>     }
>   printf( "Error!\n" );
>   exit(1);
>   return 0;
> }
> 
> void computecm() {
>   while( processtriangle() );
> }
> 
> int main() {
>   FILE* f = fopen( "cranksft.in", "rt" );
>   fscanf( f, "%d", &N );
>   for( int i = 0; i < N; i++ ) {
>     readXY( f );
>     computecm();
>   }
>   fclose( f );
> 
>   f = fopen( "cranksft.out", "wt" );
>   if( !Mass ) exit(1);
>   fprintf( f, "%lf %lf\n", XR/Mass, YR/Mass );
>   fclose( f );
> 
>   return 0;
> }