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

#define rep(i, b, e) for (int i = (b); i <= (e); i++)
#define per(i, b, e) for (int i = (e); i >= (b); i--)
#define FOR(i, b, e) rep(i, b, (e)-1)
#define SZ(x) int(x.size())
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define st first
#define nd second
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;

auto& operator<<(auto& o, pair<auto, auto> p) {
  return o << "(" << p.st << ", " << p.nd << ")";
}
auto operator<<(auto& o, auto x) -> decltype(end(x), o) {
  o << "{";
  int i = 0;
  for (auto e : x)
    o << ", " + 2 * !i++ << e;
  return o << "}";
}
#ifdef LOCAL
#define deb(x...)                       \
  cerr << "[" #x "]: ", [](auto... $) { \
    ((cerr << $ << "; "), ...) << endl; \
  }(x)
#else
#define deb(...)
#endif

bool check(int k, int n, const vector<vector<bitset<400>>>& ktore_blisko,
           const vector<vector<int>>& dist) {
  vector<bitset<400>> dobre(400, 0);

  for (auto& b : dobre) {
    b = ~b;
  }
  int ile = n;

  for (int u = 0; u < n; u++) {
    for (int v = 0; v < n; v++) {
      if (dist[u][v] <= k)
        continue;
      for (int i = 0; i < n; i++) {
        if (dobre[i] == 0) {
          continue;
        }

        bitset<400> ktore_dobre;

        if (dist[i][u] <= k) {
          ktore_dobre |= ktore_blisko[v][k - dist[i][u]];
        }
        if (dist[i][v] <= k) {
          ktore_dobre |= ktore_blisko[u][k - dist[i][v]];
        }

        dobre[i] &= ktore_dobre;
        if (dobre[i] == 0) {
          ile--;
          if (ile == 0) {
            return false;
          }
        }
      }
    }
  }

  // if (ile > 0) {
  //   for (int i = 0; i < n; i++) {
  //     for (int j = 0; j < n; j++) {
  //       if (dobre[i][j]) {
  //         deb(i, j, dist[i][j]);
  //       }
  //     }
  //   }
  // }

  return ile > 0;
}

void solve() {
  int n;
  cin >> n;
  const int INF = 500;
  vector<vi> dist(n, vi(n, INF));
  vector<vi> G(n);

  for (int i = 0; i < n; i++) {
    string s;
    cin >> s;
    dist[i][i] = 0;
    for (int j = 0; j < n; j++) {
      if (s[j] == '1') {
        G[i].push_back(j);
        dist[i][j] = 1;
      }
    }
  }

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

  vector<vector<bitset<400>>> ktore_blisko(n, vector<bitset<400>>(n, 0));

  int maks_dist = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      ktore_blisko[i][dist[i][j]][j] = 1;

      maks_dist = max(maks_dist, dist[i][j]);
    }

    for (int d = 1; d < n; d++) {
      ktore_blisko[i][d] |= ktore_blisko[i][d - 1];
    }
  }

  int lo = 0;
  int hi = maks_dist;

  while (lo < hi) {
    int mid = (lo + hi) / 2;

    if (check(mid, n, ktore_blisko, dist)) {
      hi = mid;
    } else {
      lo = mid + 1;
    }
  }
  cout << lo << "\n";
}

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