/*  This Code is Submitted by wywcgs for Problem 1260 on 2006-05-17 at 20:04:56 */ 
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int EN = 32;

int eo[EN], n, ek = 3;
char ele[EN], table[EN][EN], x, y, z;

void checkGroup();

int main()
{
	int i, t;

	for(t = 0; scanf("%d\n", &n) != EOF && n != 0; t++) {
		memset(eo, -1, sizeof(eo));
		n = strlen(gets(ele));
		for(i = 0; i < n; i++) eo[ele[i]-'a'] = i;
		for(i = 0; i < n; i++) gets(table[i]);
		checkGroup();
		printf("S = {");
		for(i = 0; i < n; i++) printf("%c%c", ele[i], i == n-1 ? '}' : ',');
		printf("\n #|%s\n", ele); printf(" -+");
		for(i = 0; i < n; i++) putchar('-'); putchar('\n');
		for(i = 0; i < n; i++) printf(" %c|%s\n", ele[i], table[i]); putchar('\n');
		switch(ek) {
		case 0: printf("NOT A SEMIGROUP: %c#%c = %c  WHICH IS NOT AN ELEMENT OF THE SET\n", x, y, z); break;
		case 1: printf("NOT A SEMIGROUP: (%c#%c)#%c IS NOT EQUAL TO %c#(%c#%c)\n", x, y, z, x, y, z); break;
		case 2: printf("SEMIGROUP BUT NOT COMMUTATIVE  (%c#%c IS NOT EQUAL TO %c#%c)\n", x, y, y, x); break;
		default: printf("COMMUTATIVE SEMIGROUP\n");
		}
		printf("------------------------------\n\n");
	}
	
	return 0;
}


void checkGroup()
{
	int i, j, k; ek = 3;
	for(i = 0; i < n; i++)
		for(j = 0; j < n; j++)
			if(eo[table[i][j]-'a'] == -1) { ek = 0; x = ele[i]; y = ele[j]; z = table[i][j]; return; }
	for(i = 0; i < n; i++)
		for(j = 0; j < n; j++)
			for(k = 0; k < n; k++) 
				if(table[eo[table[i][j]-'a']][k] != table[i][eo[table[j][k]-'a']])
					{ ek = 1; x = ele[i]; y = ele[j]; z = ele[k]; return; }
	for(i = 0; i < n; i++)
		for(j = i; j < n; j++)
			if(table[i][j] != table[j][i]) { ek = 2; x = ele[i]; y = ele[j]; return; }
}