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#pragma GCC optimize("Ofast", "unroll-loops")
//#pragma GCC target("sse", "sse2", "sse3", "ssse3", "sse4")

#include <bits/stdc++.h>

#define all(a) a.begin(),a.end()
#define len(a) (int)(a.size())
#define mp make_pair
#define pb push_back
#define fir first
#define sec second
#define fi first
#define se second

using namespace std;

typedef pair<int, int> pii;
typedef long long ll;
typedef long double ld;

template<typename T>
bool umin(T &a, T b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

template<typename T>
bool umax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

#ifdef KIVI
#define DEBUG for (bool _FLAG = true; _FLAG; _FLAG = false)
#define LOG(...) print(#__VA_ARGS__" ::", __VA_ARGS__) << endl

template<class ...Ts>
auto &print(Ts ...ts) { return ((cerr << ts << " "), ...); }

#else
#define DEBUG while (false)
#define LOG(...)
#endif

mt19937 rng(4242);

const int max_n = -1, inf = 1000111222;

void solve() {
    int n;
    cin >> n;
    vector<string> grid(n);
    for (int i = 0; i < n; i++) {
//        grid[i] = string(n, '0');
        cin >> grid[i];
//        for(int j = 0; j < n; j++) {
//            if(j < i) grid[i][j] = grid[j][i];
//            else grid[i][j] = ('0' + rng() % 2);
//        }
    }
    vector<vector<int>> dist(n, vector<int>(n, inf));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if(i == j) dist[i][j] = 0;
            else if(grid[i][j] == '1') dist[i][j] = 1;
        }
    }
    for (int k = 0; k < n; k++) {
        for (int i = 0; i < n; i++) {
            if(dist[i][k] == inf) continue;
            for (int j = 0; j < n; j++) {
                if(dist[k][j] == inf) continue;
                umin(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }
    int origDiam = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if(dist[i][j] < inf)
                umax(origDiam, dist[i][j]);
        }
    }
    int best = origDiam;
    vector<pair<int, pair<int, int> > > cand;
    for (int x = 0; x < n; x++) {
        for (int y = x + 1; y < n; y++) {
            cand.pb({dist[x][y], {x, y}});
        }
    }
    sort(all(cand)); reverse(all(cand));
    for(auto &tp : cand) {
        int x, y;
        tie(x, y) = tp.se;
        int curMax = 0;
        bool abortCandidate = false;
        for (int u = 0; u < n; u++) {
            for (int v = 0; v < n; v++) {
                int option1 = dist[u][v];
                int option2 = dist[u][x] + dist[y][v];
                int option3 = dist[u][y] + dist[x][v];
                int eff = min({option1, option2, option3});
                umax(curMax, eff);
                if(curMax >= best) {
                    abortCandidate = true;
                    break;
                }
            }
            if(abortCandidate) break;
        }
        if(!abortCandidate) {
            umin(best, curMax);
            if(best <= 1) break;
        }
    }
    cout << best << "\n";
}

int main() {
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);

    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int t = 1;

    cin >> t;

    while (t--) solve();

}

/*
KoRoVa!
*/