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#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int, int> pii;

#define FOR(x, b, e) for(int x = (b); x <= (e); ++(x))
#define FORD(x, b, e) for(int x = (b); x >= (e); --(x))
#define REP(x, n) for(int x = 0; x < (n); ++x)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(x) ((int)(x).size())
#define FOREACH(a, b) for (auto&a : (b))
#define PB push_back
#define PF push_front
#define ST first
#define ND second
#define DBG(vari) cerr<<#vari<<" = "<<(vari)<<endl

template <typename T>
std::ostream& operator<<(std::ostream &output, const vector<T> &vec)
{
    output << "[";
    FOREACH(x, vec) output << x << ", ";
    output << "]";
    return output;
}

template <typename T, typename U>
std::ostream& operator<<(std::ostream &output, const pair<T,U> &p)
{
    output << "(";
    output << p.ST << ", " << p.ND;
    output << ")";
    return output;
}


int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);

  const int MAX = 1000;

  int t; cin >> t;
  while (t--) {
    int n; cin >> n;

    vector<vector<int>> dist(n);
    REP(i, n) dist[i].resize(n); 


    REP(i, n) REP(j, n) dist[i][j] = MAX;

    REP(i, n) {
      string s; cin >> s;
      REP(j, n) {
        if (s[j] == '1')
          dist[i][j] = 1;
      }
    }
    
    REP(i, n) dist[i][i] = 0;

    REP(k, n)
      REP(i, n)
        REP(j, n)
          if (dist[i][j] > dist[i][k] + dist[k][j])
            dist[i][j] = dist[i][k] + dist[k][j];

    int w = MAX;

    vector<pii> uv;
    REP(i, n) FOR(j, i+1, n-1) uv.emplace_back(i, j);

    sort(ALL(uv), [&](pii x, pii y) {
      return dist[x.ST][x.ND] > dist[y.ST][y.ND];
    }); 

    REP(a, n) FOR(b, a+1, n-1) {
      int wyn=0;

      REP(i, SIZE(uv)) {
        int u, v; tie(u, v) = uv[i];

        int z = min(dist[u][v], min(dist[a][u]+dist[b][v], dist[a][v]+dist[b][u])); 
        wyn = max(wyn, z);

        if (z == dist[u][v])
          break;
      }

      w = min(w, wyn);
    }

    cout << w << endl;

  }
}