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#ifdef DEBUG
#define _GLIBCXX_DEBUG
#endif
//#pragma GCC optimize("O3")
#include<bits/stdc++.h>
using namespace std;

#ifdef DEBUG
#include "lib/debug.h"
#else
#define debug(...) 228
#endif

#define pb push_back

typedef long long ll;
typedef long double ld;
const int maxN = 405;
int n;
void solve() {
    cin >> n;
    const int INF = 1e8;
    vector<vector<int>> dist(n, vector<int>(n, INF));
    for (int i = 0; i < n; i++) {
        dist[i][i] = 0;
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            char c;
            cin >> c;
            if (c == '1') dist[i][j] = 1;
        }
    }
    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]);
            }
        }
    }
//    debug(dist);
    vector<vector<int>> f(n, vector<int>(n));
    vector<int> cnt(n);
    vector<int> id(2 * n);
    for (int p = 0; p < n; p++) {
        for (int x = 0; x < n; x++) {
            fill(cnt.begin(), cnt.end(), 0);
            for (int y = 0; y < n; y++) {
                if (dist[p][x] >= dist[p][y]) {
                    cnt[dist[p][y]] += 1;
                }
                cnt[max(dist[p][y] - dist[x][y], 0)] += 1;
            }
            //bucket sort to flex
            for (int val = 0; val < n - 1; val++) cnt[val + 1] += cnt[val];
            int tot_size = cnt[n - 1];
            for (int y = 0; y < n; y++) {
                if (dist[p][x] >= dist[p][y]) {
                    id[--cnt[dist[p][y]]] = y;
                }
            }
            for (int y = 0; y < n; y++) {
                int d = max(dist[p][y] - dist[x][y], 0);
                id[--cnt[d]] = y + n;
            }
//            debug(p, x, id, tot_size);
            int mx = -INF;
            for (int i = tot_size - 1; i >= 0; i--) {
                if (id[i] >= n) {
                    mx = max(mx, dist[x][id[i] - n]);
                }
                else {
                    f[x][id[i]] = max(f[x][id[i]], dist[p][id[i]] + mx);
                }
            }
            mx = -INF;
            for (int i = 0; i < tot_size; i++) {
                if (id[i] >= n) {
                    mx = max(mx, dist[p][id[i] - n]);
                }
                else {
                    f[x][id[i]] = max(f[x][id[i]], mx);
                }
            }
        }
    }
    int best = INF;
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            best = min(best, max(f[j][i], f[i][j]));
        }
    }
    cout << best << '\n';
}
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#ifdef DEBUG
    freopen("input.txt", "r", stdin);
#endif
    int tst;
    cin >> tst;
    while (tst--) solve();
    return 0;
}