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#include <iostream>
#include <string>
#include <queue>
#include <vector>
#include <algorithm>
using namespace std;

const int ALOT = 10000;
const int MAXN = 400;


int conn[MAXN][MAXN];

void do_test_case() {
  int n;
  cin >> n;
  string data[n];
  for(int i = 0; i < n; i++)
    cin >> data[i];
    
  for(int i = 0; i < n; i++)
    for(int j = 0; j < n; j++)
      conn[i][j] = data[i][j] == '1' ? 1 : ALOT;
  for(int i = 0; i < n; i++)
    conn[i][i] = 0;
      
  for(int i = 0; i < n; i++) {
    queue< int > q;
    for(int j = 0; j < n; j++)
	if(conn[i][j] == 1)
	    q.push(j);
    for(; !q.empty(); q.pop()) {
      int akt = q.front();
      int b = conn[i][akt]+1;
      for(int k = 0; k < n; k++) {
        if(data[akt][k] == '1' && conn[i][k] == ALOT) {
          conn[i][k] = b;
          q.push(k);
        }
      }
    }
  }

    //-------------------------
/*
  int result = ALOT;  
  for(int i = 0; i < n; i++)
    for(int j = i+1; j < n; j++) {
      int max_dist = 0;
      
      for(int p1 = 0; p1 < n; p1++)
       for(int p2 = p1+1; p2 < n; p2++) {
         int akt = min(min(conn[p1][p2], conn[p1][i] + conn[p2][j]), conn[p2][i] + conn[p1][j]);
         if(akt > max_dist)
           max_dist = akt;
       }
      if(max_dist < result)
	result = max_dist; 
    }
*/    

  //-------------------------
  
 
  vector< pair<int,int> > vec;
  vec.reserve(MAXN*MAXN / 2);
  for(int i = 0; i < n; i++)
    for(int j = i+1; j < n; j++)
      vec.push_back( pair<int,int>(i,j) );
      
  sort(vec.begin(), vec.end(), 
  		[=](auto p1, auto p2)  // lambda expression
		{
			return conn[p1.first][p1.second] > conn[p2.first][p2.second];
		});
    
  vector < pair< pair<int,int>, int> > teleporty;
  teleporty.reserve(MAXN*MAXN / 2);
  for(int i = 0; i < n; i++)
    for(int j = i+1; j < n; j++)
       teleporty.push_back( pair< pair<int,int>, int>( pair<int,int>(i,j), 0 ) );

  for(int far_pair_idx = 0; far_pair_idx < vec.size(); far_pair_idx++) {
    int far_city1 = vec[far_pair_idx].first;
    int far_city2 = vec[far_pair_idx].second;
    int b = conn[far_city1][far_city2];

    for(int i = 0; i < teleporty.size(); i++) {
      int tele_city1 = teleporty[i].first.first;
      int tele_city2 = teleporty[i].first.second;
      int dist = min( conn[tele_city1][far_city1]+conn[tele_city2][far_city2],
                      conn[tele_city1][far_city2]+conn[tele_city2][far_city1] );
      teleporty[i].second = max( teleporty[i].second, dist );
      if(teleporty[i].second >= b) {
          teleporty[i] = teleporty.back();
          teleporty.pop_back();
          i--;
      }
      if(teleporty.empty()) {
        cout << b << endl;
        return;
      }
    }
    
  }
   
  cout << "Should not happen!" << endl;
}



int main() {
  int t;
  cin >> t;
  for(int it = 0; it < t; it++)
    do_test_case();
  return 0;
}