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#include <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

void doit() {
  int n; scanf(" %d", &n);

  char ss[402][402];
  for (int i=0; i<n; ++i) {
    scanf(" %s", ss[i]);
  }

  vector<int> si(n);
  for (int i=0; i<n; ++i) si[i] = i;
  random_shuffle(si.begin(), si.end());
  
  char s[402][402];
  for (int i=0; i<n; ++i) for (int j=0; j<n; ++j) s[i][j] = ss[si[i]][si[j]];

  int t[402][402];
  for (int i=0; i<n; ++i) for (int j=0; j<n; ++j) {
    if (i==j) t[i][j] = 0;
    else if (s[i][j] == '1') t[i][j] = 1;
    else t[i][j] = 800;
  }

  for (int k=0; k<n; ++k) for (int i=0; i<n; ++i) for (int j=0; j<n; ++j) t[i][j] = min(t[i][j], t[i][k] + t[k][j]);

  int best = 800;
  for (int i=0; i<n; ++i) for (int j=0; j<n; ++j) {
    int curr = 0;
    for (int k=0; k<n; ++k) {
      if (curr >= best) break;
      for (int l=0; l<n; ++l) {
        curr = max(curr, min(min(t[i][k] + t[j][l], t[j][k] + t[i][l]), t[k][l]));
      }
    }
    best = min(best, curr);
  }
  printf("%d\n", best);
}

int main() {
  int t; scanf(" %d", &t);
  while (t--) doit();
}