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

int dist[501][501];
int n;

int merge(int a, int b) {
    int maxx = 0;
    for (int i  = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            maxx = max(maxx, min(dist[i][j], min(dist[i][a] + dist[b][j], dist[i][b] + dist[a][j])));
        }
    }
    return maxx;
}

void solve() {
    cin >> n;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            char c; cin >> c;
            if (c == '1') dist[i][j] = 1;
            else dist[i][j] = 1e9;
            if (i == j) dist[i][j] = 0;
        }
    }
    for (int k = 1; k <= n; k++) {
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }
    int MAX = 0;
    int u, v;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            if (dist[i][j] > MAX) {
                MAX = dist[i][j];
                u = i;
                v = j;
            }
        }
    }
    int ans = merge(1, 1);
    for (int i = 1; i <= n; i++) {
        for (int j = i+1; j <= n; j++) {
            if (min(dist[u][i]+dist[j][v], dist[u][j] + dist[i][v]) >= ans) continue;
            ans = min(ans, merge(i, j));
        }
    }
    cout << ans << '\n';
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int t; cin >> t;
    while (t--) {
        solve();
    }
}