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

using namespace std;

const int INF = 1e9;

void floydWarshall(vector<vector<int>>& graf) {
    int V = graf.size();

    for (int k = 0; k < V; k++) {
        for (int i = 0; i < V; i++) {
            for (int j = 0; j < V; j++) {
                if (graf[i][k] != INF && graf[k][j] != INF)
                    graf[i][j] = min(graf[i][j], graf[i][k] + graf[k][j]);
            }
        }
    }
}

int fd(const vector<vector<int>>& dist) {
    int srednica = 0;
    int n = dist.size();
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            if (i != j)
                srednica = max(srednica, dist[i][j]);
    return srednica;
}

int fot(const vector<vector<int>>& dist, int n) {
    int best = fd(dist);

    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            if (dist[i][j] > 1) {
                int nowa_srednica = 0;
                for (int a = 0; a < n; a++) {
                    for (int b = 0; b < n; b++) {
                        int new_dist = min(dist[a][b], min(dist[a][i] + 1 + dist[j][b], dist[a][j] + 1 + dist[i][b]));
                        nowa_srednica = max(nowa_srednica, new_dist);
                    }
                }

                best = min(best, nowa_srednica);
            }
        }
    }
    return best;
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int Q, n;
    cin >> Q;
    while (Q--) {
        cin >> n;
        vector<vector<int>> dist(n, vector<int>(n, INF));
        for (int i = 0; i < n; i++) {
            string ciag;
            cin >> ciag;
            for (int j = 0; j < n; j++) {
                if (ciag[j] == '1')
                    dist[i][j] = 1;
                if (i == j)
                    dist[i][j] = 0;
            }
        }
        floydWarshall(dist);
        cout << fot(dist, n) << endl;
    }
}