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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 N = 404;
const int INF = 1e6;
int n;
int d[N][N];
int mx[N][N];
int lew[N], pra[N];

void solve() {
  cin >> n;
  rep(i, 0, n) rep(j, 0, n) {
    d[i][j] = i != j ? INF : 0;
    mx[i][j] = 0;
  }
  rep(i, 0, n) {
    string g;
    cin >> g;
    rep(j, 0, n) if (g[j] == '1') d[i][j] = 1;
  }
  rep(i, 0, n) rep(j, 0, n) rep(k, 0, n) d[j][k] = min(d[j][k], d[j][i] + d[i][k]);
  rep(b, 0, n) rep(r, 0, n) {
    rep(i, 0, n) lew[i] = pra[i] = 0;
    rep(i, 0, n) {
      int p = max(0, d[r][i] - d[b][i]);
      lew[p] = max(lew[p], d[r][i]);
      if (p) pra[p - 1] = max(pra[p - 1], d[b][i]);
    }
    rep(i, 1, n) lew[i] = max(lew[i], lew[i - 1]);
    for (int i = n - 2; i >= 0; i--) pra[i] = max(pra[i], pra[i + 1]);
    rep(a, 0, n) {
      if (d[r][a] <= d[r][b]) {
        mx[a][b] = max(mx[a][b], max(lew[d[r][a]], pra[d[r][a]] + d[r][a]));
        mx[b][a] = max(mx[b][a], max(lew[d[r][a]], pra[d[r][a]] + d[r][a]));
      }
    }
  }
  int odp = INF;
  rep(i, 0, n) rep(j, 0, n) odp = min(odp, mx[i][j]);
  cout << odp << '\n';
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  int t;
  cin >> t;
  while (t--) solve();
}