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#include <iostream>
#include <algorithm>
#include <vector>
#include <string>

int main() {
    int t;
    std::cin >> t;

    int n;
    for (int test = 0; test < t; ++test) {
        std::cin >> n;
        std::vector<bool> adj(n*n, false);
        std::string line;
        for (int i = 0; i < n; ++i) {
            std::cin >> line;
            for (int j = 0; j < n; ++j) {
                if (line[j] == '1') {
                    adj[i*n + j] = true;
                }
            }
        }

        std::vector<int> dist(n*n, n);
        for (int i = 0; i < n; ++i) {
            dist[i*n + i] = 0;
            for (int j = 0; j < n; ++j) {
                if (adj[i*n + j]) {
                    dist[i*n + j] = 1;
                    dist[j*n + i] = 1;
                }
            }
        }

        for (int k = 0; k < n; ++k) {
            for (int i = 0; i < n; ++i) {
                for (int j = i + 1; j < n; ++j) {
                    int d = dist[i*n + k] + dist[k*n + j];
                    if (dist[i*n + j] > d) {
                        dist[i*n + j] = d;
                        dist[j*n + i] = d;
                    }
                }
            }
        }

        int bestDia = n + 1;
        for (int p = 0; p < n; ++p) {
            for (int q = p + 1; q < n; ++q) {
                int dia = 0;
                for (int i = 0; i < n; ++i) {
                    for (int j = i + 1; j < n; ++j) {
                        int d = std::min({dist[i*n + j],
                                          dist[q*n + i] + dist[p*n + j],
                                          dist[q*n + j] + dist[p*n + i]});
                        if (d > dia) {
                            dia = d;
                        }
                    }
                }
                if (dia < bestDia) {
                    bestDia = dia;
                }
            }
        }
        std::cout << bestDia << std::endl;
    }

    return 0;
}