#include "my.h"
#include <string.h>

#define LEN 20

int gen[10];
double p0, q0, n ;

main()
{
	int  s1, nsites, *pos , i , j, k, *nall, count, nsam  ;
	int a, b, count1, count2, countq ;
	int gc[3][3], s2 ;
	char ***gam ;
	double dmin, dmax, dprime, d, rsq;
	double mled(), lnli(double) ;

scanf( " %d", &nsam);
scanf(" %d", &nsites );
printf(" nsam: %d  nsites: %d\n", nsam, nsites);
pos = (int *)malloc( (nsites+1)*sizeof( int ) ) ;
nall  = (int *)malloc( (nsites+1)*sizeof( int ) ) ;
gam = (char ***)malloc( 2*nsam*sizeof( char **) ) ;
for(i=0; i< 2*nsam; i++) {
	 gam[i] = (char **)malloc( (nsites+1)*sizeof( char *) ) ;
	 for( j=0; j<=nsites; j++) gam[i][j] = (char *) malloc( LEN*sizeof(char) ) ;
	}

for( i=1; i<= nsites; i++) scanf(" %d",pos+i );
for( i=1; i<= nsites; i++) printf(" %d", pos[i] ) ;
printf("\n");
for( j=0; j< 2*nsam; j++)
  for( i=0; i <= nsites; i++) scanf(" %s",gam[j][i] ) ;

for( s1 = 1; s1 <= nsites; s1++) {
	i=0;
	while( (i < 2*nsam) && ( gam[i][s1][0] == '?')  ) {  i++;  }
	if( i == 2*nsam ) nall[s1]  = 0 ;
	else{
	  for( j= i+1; j< 2*nsam; j++) if(  strcmp( gam[i][s1], gam[j][s1]  ) == 0   ) { gam[j][s1][0] = 1 ;  }
	  gam[i][s1][0] = 1 ;
	  j = i+1 ;
	  while( ( j < 2*nsam) && (( gam[j][s1][0] == '?' ) || (gam[j][s1][0] == 1 ) )  ) { j++ ;  }
	  if( j == 2*nsam ) nall[s1] = 1 ;
	  else {
	    for( k=j+1; k< 2*nsam; k++){
		if( strcmp( gam[j][s1],  gam[k][s1]) == 0 ){  gam[k][s1][0] = 2 ; }
		}
	    gam[j][s1][0] = 2 ;
	    count1 = count2 = countq = 0 ;
	    for( i=0; i< 2*nsam; i++){
	      a = gam[i][s1][0] ;
	      if( a == 1 ) count1++;
	      else if( a == 2 ) count2++;
	      else if( a == '?' ) countq++;
	      }
	    if( count1+count2 + countq == 2*nsam ) nall[s1] =2  ;
	    else nall[s1] = 3 ; 
	    }
	  }
        printf("  %d ",nall[s1]);
	}
/*
	for( i=0; i< 2*nsam; i++) {
	 printf("\n");
	 for( j=1; j<=nsites; j++) printf(" %d",gam[i][j][0] );
	 }
*/
	printf("\n");

	for( s1=1; s1 < nsites; s1++){
	  if( nall[s1] == 2 ) 
	  for( s2 = s1+1; s2 <= nsites; s2++){
	    if( nall[s2] == 2 ) {
		for( i=0; i<3; i++)
	  		for( j=0; j<3; j++) gc[i][j] = 0 ;
		for( i=0; i<nsam; i++){
		  if( (gam[2*i][s1][0] == 1 )&&( gam[2*i+1][s1][0] == 1 ) ) a = 0; 
		  else if( (gam[2*i][s1][0] == 1 )&&( gam[2*i+1][s1][0] == 2 ) ) a = 1; 
		  else if( (gam[2*i][s1][0] == 2 )&&( gam[2*i+1][s1][0] == 1 ) ) a = 1; 
		  else if( (gam[2*i][s1][0] == 2 )&&( gam[2*i+1][s1][0] == 2 ) ) a = 2; 
		  else a = -1 ;
		  if( (gam[2*i][s2][0] == 1 )&&( gam[2*i+1][s2][0] == 1 ) ) b = 0; 
		  else if( (gam[2*i][s2][0] == 1 )&&( gam[2*i+1][s2][0] == 2 ) ) b = 1; 
		  else if( (gam[2*i][s2][0] == 2 )&&( gam[2*i+1][s2][0] == 1 ) ) b = 1; 
		  else if( (gam[2*i][s2][0] == 2 )&&( gam[2*i+1][s2][0] == 2 ) ) b = 2; 
		  else b = -1 ;
		 if( ( a >= 0 ) && ( b >= 0 ) ) gc[a][b]++ ;
		 }
		printf("%d %d %d    %d %d %d %d %d %d %d %d %d  ",pos[s1],pos[s2],pos[s2]-pos[s1],
	 gc[0][0],gc[0][1],gc[0][2],gc[1][0],
	gc[1][1],gc[1][2],gc[2][0],gc[2][1],gc[2][2] ) ;

	gen[1] = gc[0][0]; gen[2] = gc[0][1]; gen[3] = gc[0][2];  gen[4] = gc[1][0]; gen[5] = gc[1][1];
	gen[6] = gc[1][2]; gen[7] = gc[2][0]; gen[8] = gc[2][1]; gen[9] = gc[2][2] ;

	n = gen[1] + gen[2] + gen[3] + gen[4] + gen[5] + gen[6] + gen[7] + gen[8] + gen[9] ;
	p0 = ( gen[1] + gen[2] + gen[3] + 0.5*(gen[4] + gen[5] + gen[6]) ) / n ;
	q0 = ( gen[1] + gen[4] + gen[7] + 0.5*(gen[2] + gen[5] + gen[8]) ) / n ;
		dmin = MAX( -p0*q0, -(1.0-p0)*(1.0-q0) )   ; 
		dmax = MIN( (1.0-p0)*q0, p0*(1.0-q0) )   ; 
	d = mled(  );
	dprime = (d < 0) ? -d/dmin : d/dmax ;
	rsq =  (d*d)/(p0*(1.0-p0)*q0*(1.0-q0)) ;
	printf(" %lf %lf %lf %lf %lf\n",p0,q0,d, dprime, rsq   );    


		}
	     }}



}

	double
mled( )

{

	double d,  ep,  dmin, dmax ;


	double p00 ;
	double lnli(double);
	double best;

	if( gen[5] == 0 ){
		p00 = (2*gen[1] + gen[2] + gen[4])/(2.0*n) ;
		return( p00 - p0*q0 ) ;
		}
	else{                               /* need to determine whether, mininum is at extreme*/
		dmin = MAX( -p0*q0, -(1.0-p0)*(1.0-q0) )   ; 
		dmax = MIN( (1.0-p0)*q0, p0*(1.0-q0) )   ; 
		ep = (dmax - dmin)/1000.0 ;
	best = dmin ;	
	for( d = dmin; d<= dmax; d += ep ){
	    if( lnli( d) < lnli( best ) ) best = d ;
/*  printf(" %lf %lf\n",d,lnli(d) ) ;
*/

	    }
	if( lnli(dmax ) < lnli(best)  ) best = dmax ;
	return( best ) ;

	}
}


                        

	double	
lnli( double  d)
{
	int i;
	double p00, p01, p10, p11, xi[10] ;
	double sum ;

	p00 = p0*q0 + d ;
	p01 = p0*(1.0-q0) -d ;
	p10 = (1.0-p0)*q0 -d ;
	p11 = (1.0-p0)*(1.0-q0) + d ;
	xi[1] = p00*p00;
	xi[2] = 2.0*p00*p01 ;
	xi[3] = p01*p01 ;
	xi[4] = 2.0*p00*p10 ;
	xi[5] = 2.0*p00*p11 + 2.0*p01*p10 ;
	xi[6] = 2.0*p01*p11 ;
	xi[7] = p10*p10 ;
	xi[8] = 2.0*p10*p11 ;
	xi[9] = p11*p11 ;

	sum = 0.0 ;
	for( i=1;i<=9; i++){
	  if( (gen[i] > 0) && (xi[i]>0) ) sum += gen[i]*log( xi[i] ) ;
	  else if(  (gen[i] >0) && (xi[i] <= 0) ) sum += -999999. ;
	  } 
	return( (-1.0)*sum ) ;

}