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

using vi = vector<int>;
using vvi = vector<vi>;
using pi = pair<int, int>;
#define all(x) x.begin(), x.end()
#define INF 1000000

int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        int n;
        cin >> n;
        vvi dist(n, vi(n, 0));
        for (int i = 0; i < n; i++)
        {
            string s;
            cin >> s;
            for (int j = 0; j < n; j++)
            {
                if (i == j)
                    continue;
                dist[i][j] = s[j] == '1' ? 1 : INF;
            }
        }
        for (int k = 0; k < n; k++)
        {
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
                }
            }
        }
        vector<pi> pair_nodes;
        pair_nodes.reserve(n * (n - 1) / 2);
        for (int i = 0; i < n; i++)
        {
            for (int j = i + 1; j < n; j++)
            {
                pair_nodes.push_back({i, j});
            }
        }
        sort(all(pair_nodes), [&](pi a, pi b)
             { return dist[a.first][a.second] > dist[b.first][b.second]; });

        int min_diam = INF;
        for (auto [v, u] : pair_nodes)
        {
            int diam = 0;
            for (auto [a, b] : pair_nodes)
            {
                if (dist[a][b] <= diam)
                    break;
                int new_dist = min({dist[a][b],
                                    dist[a][v] + dist[u][b],
                                    dist[a][u] + dist[v][b]});
                diam = max(diam, new_dist);
                if (diam >= min_diam)
                    break;
            }
            min_diam = min(min_diam, diam);
        }

        cout << min_diam << '\n';
    }
}