/* This program outputs the definition of a matrix whose determinant is 
 * the number of domino tilings of the input region (up to a factor of
 * some power of i).  The matrix should be fed to Mathematica.  This 
 * input format allows for computing the number of matchings of any 
 * bipartite planar graph.
 *
 * The region should be given as a pattern of V's, A's, <'s, >'s, and X's.
 * All characters after a percent are ignored.  Currently, the input must 
 * fit in a rectangle with 500 rows and 200 columns.
 * 
 * You can compile the program with the Unix command 
 *
 * cc vaxmathematica.c -o vaxmathematica
 *
 * There is supposedly a way to run Mathematica in command-line mode;
 * if so, Unix users might be able to pipe the output of vaxmathematica
 * to a Mathematica kernel. Otherwise, you'll have to settle for a
 * two-stage process: use vaxmathematica to create Mathematica code
 * and then copy and paste that code into a Mathematica window.
 *
 * Greg Kuperberg, Jim Propp, and David Wilson
 */ 

#include <stdio.h>

#define WIDTH 202
#define LENGTH 502
#define FREE -1

char pict[LENGTH][WIDTH];
int p[LENGTH][WIDTH];
char gap[LENGTH][WIDTH];

int main()
{
  int i,j,k;
  int rows,columns;
  
  for (i=0; i<LENGTH;i++) for(j=0;j<WIDTH;j++) pict[i][j] = ' ';
  
  for (i=1; i<LENGTH-1 && gets(&(pict[i][1])) != NULL; ++i);
  
  for (i=0;i<LENGTH;i++) {
    int pflag = 0;
    for(j=0;j<WIDTH;j++) {
      if(pict[i][j] == 0) pflag = 1;
      if(pict[i][j] == '%') pflag = 1;
      if(pflag) pict[i][j] = ' ';
    }
  }
  
  rows = columns = 0;
  for(i=0;i<LENGTH;i++) {
    int gaps=1;
    for(j=0;j<WIDTH;j++) {
      if (pict[i][j] == ' ') gaps *= -1;
      gap[i][j] = gaps;
      if((i+j)&1)
	p[i][j] = (pict[i][j] == ' '?FREE:columns++);
      else
	p[i][j] = (pict[i][j] == ' '?FREE:rows++);
    }
  }
  
  /* printf("with(linalg,det):\nx := -1:\n"); */
  /* printf("a := array([\n"); */
  printf("x=-1; Abs[Det[{");
  
  for(i=1;i<LENGTH-1;i++) for(j= i&1;j<WIDTH-1;j+=2)
    if(p[i][j] != FREE) {
      printf("{");
      for(k=0;k<columns;k++) {
	char *entries = "x01";
	int entry=0;
	if (k == p[i+1][j] && pict[i][j] != 'V' && pict[i+1][j] != 'A')
	  entry = gap[i][j];
	if (k == p[i-1][j] && pict[i][j] != 'A' && pict[i-1][j] != 'V')
	  entry = gap[i-1][j];
	if (k == p[i][j+1] && pict[i][j] != '>' && pict[i][j+1] != '<')
	  entry = 1;
	if (k == p[i][j-1] && pict[i][j] != '<' && pict[i][j-1] != '>')
	  entry = -1;
	putchar(entries[entry+1]);
	if(k<columns-1) putchar(',');
      }
      if(p[i][j] < rows-1) printf("},\n");
    }
  printf("}}]]\n");
}