// gcc -O3 -o sync sync.c
#include<stdint.h>
#include<stdio.h>
#include<stdlib.h>
#include<stdarg.h>
#include<math.h>
#include<string.h>
#include<time.h>

int w[9000000], a, l, i, j, k, t, mor[10][1000000];
char ch[1000000];

int eq(int *g, int *d, int l){
 for(; l--; ) if(g[l] != d[l]) return 0;
 return 1;
}//*/

void out(char* ch){
 printf("%s\n", ch);
 exit(0);
}

void main(int ac, char **av){
 FILE *in = fopen(av[1], "r");
 if(ac < 2) out("Usage: ./sync morphism_file");
 for(fgets(ch, 200000, in), a = 0; strcmp(ch, "\n"); fgets(ch, 200000, in), a++){
  if(!a) l = strlen(ch)-1; else if(l != strlen(ch)-1) out("the morphism is not uniform");
  for(j = l; j--; ) mor[a][j] = ch[j]-'0';
 }
 printf("%d-uniform %d-ary morphism\n", l, a);
 for(i = 0; i < a; i++){
  for(t = 0; t < l; t++) w[t] = mor[i][t];
  for(j = 0; j < a; j++){
   for(t = 0; t < l; t++) w[l+t] = mor[j][t];
   for(k = 0; k < a; k++) for(t = 1; t < l; t++) if(eq(w+t, mor[k], l)) out("the morphism is not synchronizing");
  }
 }
 out("the morphism is synchronizing");
}