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#include <bits/stdc++.h>

#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

template<class T> void chkmn(T &x, T y) { if (y < x) x = y; }
template<class T> void chkmx(T &x, T y) { if (y > x) x = y; }

using namespace std;

const int maxn = 410;

int n, a[maxn][maxn];
string str;

void work() {
  cin >> n;
  rep (i, 1, n) {
    cin >> str;
    rep (j, 1, n) a[i][j] = str[j - 1] - '0';
  }
  rep (i, 1, n) rep (j, 1, n) if (i != j && !a[i][j]) a[i][j] = 1e9;
  rep (k, 1, n) rep (i, 1, n) rep (j, 1, n) chkmn(a[i][j], a[i][k] + a[k][j]);
  vector<pii> vec;
  rep (i, 1, n) rep (j, i + 1, n) vec.emplace_back(i, j);
  sort(ALL(vec), [&](pii x, pii y) { return a[x.fi][x.se] > a[y.fi][y.se]; });
  int ans = 1e9;
  rep (u, 1, n) rep (v, u + 1, n) {
    int mx = 0, cur;
    for (auto [x, y] : vec) {
      if (a[x][y] <= mx) break;
      if ((cur = min(a[x][u] + a[v][y], a[x][v] + a[u][y])) >= a[x][y]) { chkmx(mx, a[x][y]); break; }
      chkmx(mx, cur);
    }
    chkmn(ans, mx);
  }
  cout << ans << '\n';
}

int main() {
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  int t; cin >> t;
  while (t--) work();
}