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

void relax(vector<vector<int>>& fw) {
    for (int k = 0; k < fw.size(); ++k)
        for (int i = 0; i < fw.size(); ++i)
            for (int j = 0; j < fw.size(); ++j)
                if (fw[i][j] > fw[i][k] + fw[k][j])
                    fw[i][j] = fw[i][k] + fw[k][j];
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        vector<vector<int>> matrix(n, vector<int>(n, 0));
        for (int i = 0; i < n; ++i) {
            string s;
            cin >> s;
            for (int j = 0; j < n; ++j)
                if (i != j) {
                    if (s[j] == '1') {
                        matrix[i][j] = 1;
                    } else {
                        matrix[i][j] = 1000000000;
                    }
                }
        }

        relax(matrix);

        vector<pair<int, int>> most_expensive;

        for (int i = 0; i < n; ++i)
            for (int j = i + 1; j < n; ++j)
                most_expensive.emplace_back(i, j);
        most_expensive.emplace_back(0, 0);
        
        sort(most_expensive.begin(), most_expensive.end(), [&matrix](pair<int, int> x, pair<int, int> y) {
            return matrix[y.first][y.second] < matrix[x.first][x.second];
        });

        int worst = matrix[most_expensive[0].first][most_expensive[0].second];
        int best = worst;

        for (auto [x, y] : most_expensive) {
            if (matrix[x][y] < worst - best)
                break;
            int sol_here = 0;
            for (auto [i, j] : most_expensive) {
                if (matrix[i][j] <= sol_here) { 
                    if (best > sol_here)
                        best = sol_here;
                    break;
                }
                int new_distance = min({matrix[i][j], matrix[i][x] + matrix[y][j], matrix[i][y] + matrix[x][j]});
                if (new_distance >= best)
                    break;
                if (new_distance > sol_here)
                    sol_here = new_distance;
            }
        }
        cout << best << endl;
    }
}