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#include <bits/stdc++.h>
using namespace std;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t; cin >> t;
    while (t--) {
        int n; cin >> n;
        string s;
        vector<vector<int>> d(n, vector<int>(n, n + 1));
        for (int i = 0; i < n; i++) {
            cin >> s;
            for (int j = 0 ; j < n; j++) {
                if (s[j] == '1') d[i][j] = 1;
            }
            d[i][i] = 0;
        }
        // floyd
        for (int k = 0; k < n; k++) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
                }
            }
        }
        if (n > 150) {
            int answer = 0;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    answer = max(answer, d[i][j]);
                }
            }
            auto check = [&](int x) {
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        bool ok = true;
                        for (int z = 0; z < n; z++) {
                            if (min(d[i][z], d[j][z]) > x) {
                                ok = false;
                                break;
                            }
                        }
                        if (ok) return true;
                    }
                }
                return false;
            };
            int lo = 0, hi = n - 1;
            while (lo < hi) {
                int mid = (lo + hi) >> 1;
                if (check(mid)) hi = mid;
                else lo = mid + 1;
            }
            answer = min(answer, 2 * lo);
            cout << answer << "\n";
        } else {
            int answer = n + 1;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    int max_dist = 0;
                    for (int x = 0; x < n; x++) {
                        for (int y = 0; y < n; y++) {
                            int dist = min(d[x][y], min(d[x][i] + d[j][y], d[x][j] + d[i][y]));
                            max_dist = max(max_dist, dist);
                        }
                    }
                    answer = min(answer, max_dist);
                }
            }
            cout << answer << "\n";
        }
    }
}