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#include <iostream>
#include <cstring>

using namespace std;

const int MAX_N = 400;
int graph[MAX_N + 1][MAX_N + 1];
int dist[MAX_N + 1][MAX_N + 1];   

int main() {
    int t;
    cin >> t;
    
    for (int test = 0; test < t; test++) {
        int n;
        cin >> n;
        

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                char c;
                cin >> c;
                graph[i][j] = (c == '1' ? 1 : (i == j ? 0 : 1000));
            }
        }
        

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                dist[i][j] = graph[i][j];
            }
        }
        
        for (int k = 1; k <= n; k++) {
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= n; j++) {
                    if (dist[i][k] + dist[k][j] < dist[i][j]) {
                        dist[i][j] = dist[i][k] + dist[k][j];
                    }
                }
            }
        }
        

        int max_dist = 0;
        for (int i = 1; i <= n; i++) {
            for (int j = i + 1; j <= n; j++) {
                if (dist[i][j] != 1000) {
                    max_dist = max(max_dist, dist[i][j]);
                }
            }
        }
        
        int min_bak = max_dist;
        for (int t1 = 1; t1 <= n; t1++) {
            for (int t2 = t1 + 1; t2 <= n; t2++) {
                int local_max = 0;
                for (int i = 1; i <= n; i++) {
                    for (int j = i + 1; j <= n; j++) {
                        int shortest_path = dist[i][j];
                        shortest_path = min(shortest_path, dist[i][t1] + dist[t2][j]);
                        shortest_path = min(shortest_path, dist[i][t2] + dist[t1][j]);
                        local_max = max(local_max, shortest_path);
                    }
                }
                min_bak = min(min_bak, local_max);
            }
        }
        
        cout << min_bak << endl;
    }
    
    return 0;
}