#include <stdio.h>

#define  MAXN  16

int		a[MAXN][MAXN], pm[MAXN], us[MAXN];
int		n, n1, sw;
long int	icnt, count, t1, t2;

main(argc, argv)
int		argc;
char	*argv[];
{
	char	buf[256];
	int		i, j;

	t1 = time(NULL);

	if (argc > 1)
		usage();

	icnt = 0;
	count = 0;
	while (fgets(buf, 256, stdin) != NULL)
	{
		icnt ++;
		i = 0;
		while (buf[i] != ':')
			i ++;
		while (buf[i] != '0' && buf[i] != '1')
			i ++;
		n = 2;
		while (buf[i] == '0' || buf[i] == '1')
		{
			n ++;
			for (j = 2; j < n; j ++, i ++)
			{
				a[j][n] = (buf[i] == '1') ? 1 : 0;
				a[n][j] = - a[j][n];
			}
			while (buf[i] == ' ')
				i ++;
		}
		n += 2;
		if (count == 0)
			fprintf(stderr, "n = %d\n", n);
		n1 = n - 1;
		subr1(1);
	}

	t2 = time(NULL);
	fprintf(stderr, "in  count: %ld\n", icnt);
	fprintf(stderr, "out count: %ld\n", count);
	fprintf(stderr, "time: %ld sec\n", t2 - t1);
}

usage()
{
	fputs("usage: soku3 <infile >outfile\n", stderr);
	fputs("input(n=4) is\n", stderr);
	fputs(" 1: 0\n", stderr);
	fputs(" 2: 1\n", stderr);
	fputs("^z\n", stderr);
	exit(0);
}

subr1(i)
int	i;
{
	int	k;

	if (i == n-2)
	{
		check();
	}
	else
	{
		i++;
		a[i][n1] = 0;
		a[n1][i] = 0;
		subr1(i);
		if (i>=3)
		{
			for (k=2; k<=i-1; k++)
				if (a[k][i]==1 && a[k][n1]==0)
					return;
		}
/* all 1 tate
	if (i == n-2) {
		for (k = 2; k < i; k++)
			if (a[k][n1] == 0)
				break;
		if (k >= i)
			return;
	}
*/
		a[i][n1] = 1;
		a[n1][i] = -1;
		subr1(i);
	}
}

check()
{
	int	k, l, m;

	if (n1>=4)
	{
		for (k=3; k<=n-2; k++)
			if (a[k][n1] != 1)
			{
				m = 0;
				for (l=k-1; l>=2; l--)
				{
					if (a[l][k]==0 || a[l][n1]==0)
						continue;
					if (m>0 && a[l][m]==0)
						return;
					if (m==0)
						m = l;
				}
			}
	}
	for (k = 2; k < n; k++)
		us[k] = 0;
	sw = 1;
	unique(2);
	if (sw) display();
}

unique(i)
int	i;
{
	int	k, m;

	if (i >= n)
		pmchk();
	else
		for (k = 2; k < n; k++)
		{
			if (us[k])
				goto aa;
			for (m = 2; m < n; m++)
				if (us[m] == 0 && a[k][m] < 0)
					goto aa;
			pm[i] = k;
			us[k] = 1;
			unique(i+1);
			if (sw == 0)
				return;
			us[k] = 0;
aa:	;
		}
}

pmchk()
{
	int	k, l, kk, ll;

	for (k = 3; k <= n-1; k++)
	{
		kk = pm[k];
		for (l = 2; l <= k-1; l++)
		{
			ll = pm[l];
			if (a[ll][kk] > a[l][k])
				return;
			if (a[ll][kk] < a[l][k])
			{
				sw = 0;
				return;
			}
		}
	}
}

display()
{
	int	k, l;

	count++;
	printf("%8ld: " ,count);
	for (k=3; k<=n-1; k++)
	{
		printf(" ");
		for (l=2; l<=k-1; l++)
			printf("%1d", a[l][k]);
	}
	printf("\n");
}