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#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) int((x).size())
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

#ifdef LOCAL
auto operator<<(auto& o, auto x) -> decltype(x.first, o);
auto operator<<(auto& o, auto x) -> decltype(x.end(), o) {
  o << "{";
  for (int i = 0; auto y : x) o << ", " + !i++ * 2 << y;
  return o << "}"; }
auto operator<<(auto& o, auto x) -> decltype(x.first, o) {
  return o << "(" << x.first << ", " << x.second << ")"; }
void __print(auto... x) { ((cerr << x << " "), ...) << endl; }
#define debug(x...) __print("[" #x "]:", x)
#else
#define debug(...) 2137
#endif

const int nax = 405;
int d[nax][nax];
bitset<nax> bt[nax][nax];

void solve() {
  int n;
  cin >> n;
  for(int i = 0; i < n; i++) {
    string s;
    cin >> s;
    assert(s.length() == n);
    for(int j = 0; j < n; j++) {
      if(i == j) d[i][j] = 0;
      else if(s[j] == '1') d[i][j] = 1;
      else d[i][j] = 1e9;
    }
  }
  for(int k = 0; k < n; k++) {
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
      }
    }
  }

  for(int i = 0; i < n; i++) {
    for(int dist = 0; dist < n; dist++) {
      bt[i][dist].reset();
    }
    for(int b = 0; b < n; b++) {
      bt[i][d[i][b]][b] = 1;
    }
    for(int dist = 1; dist < n; dist++) {
      bt[i][dist] |= bt[i][dist - 1];
    }
  }

  int l = 0, r = n - 1;
  while(l < r) {
    int m = (l + r) >> 1;
    bool f = 0;
    for(int a = 0; a < n; a++) {
      bitset<nax> res;
      res.set();
      for(int i = 0; i < n; i++) {
        for(int j = i + 1; j < n; j++) {
          if(d[i][j] > m) {
            bitset<nax> b;
            if(m >= d[a][i]) b |= bt[j][m - d[a][i]];
            if(m >= d[a][j]) b |= bt[i][m - d[a][j]];
            res &= b;
          }
        }
      }
      if(res.count()) {
        f = 1;
        break;
      }
    }
    if(f) r = m;
    else l = m + 1;
  }
  cout << l << endl;
}

int main() {
  cin.tie(0)->sync_with_stdio(0);

  int t;
  cin >> t;
  while(t--) solve();
}