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#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define pb push_back
#define st first
#define nd second
const int MAXN = 407;
int dl[MAXN][MAXN];
bool krawedzie[MAXN][MAXN];
int jakie[MAXN][MAXN];
bool odw[MAXN];

void bfs(int v, int n) {
    int w = v;
    queue<pair<int, int>> q;
    q.push({v, 0});
    while (!q.empty()) {
        pair<int, int> p = q.front();
        q.pop();
        v = p.st;
        if (odw[v]) {
            continue;
        }
        odw[v] = true;
        dl[w][v] = p.nd;
        for (int i = 1; i <= n; i++) {
            if (odw[i]) {
                continue;
            }
            if (krawedzie[v][i]) {
                q.push({i, p.nd + 1});
            }
        }
    }
}

bool spr(int d, int n) {
    for (int a = 1; a <= n; a++) {
        for (int p2 = 1; p2 <= n; p2++) {
            jakie[a][p2] = 1e9;
            for (int b = 1; b <= n; b++) {
                if (dl[a][b] > d) {
                    jakie[a][p2] = min(jakie[a][p2], max(0, d + 1 - dl[b][p2]));
                }
            }
        }
    }
    for (int p1 = 1; p1 <= n; p1++) {
        for (int p2 = p1 + 1; p2 <= n; p2++) {
            bool czy = true;
            for (int a = 1; a <= n; a++) {
                if (dl[a][p1] <= dl[a][p2]) {
                    if (dl[a][p1] >= jakie[a][p2]) {
                        czy = false;
                        break;
                    }
                }
                else {
                    if (dl[a][p2] >= jakie[a][p1]) {
                        czy = false;
                        break;
                    }
                }
            }
            if (czy) {
                return true;
            }
        }
    }
    return false;
}

void solve() {
    int n;
    cin >> n;
    rep(i, n) {
        string s;
        cin >> s;
        rep(j, n) {
            if (s[j] == '1') {
                krawedzie[i + 1][j + 1] = true;
            }
            else {
                krawedzie[i + 1][j + 1] = false;
            }
        }
    }
    for (int w = 1; w <= n; w++) {
        bfs(w, n);
        rep(i, n + 1) {
            odw[i] = false;
        }
    }
    int poc = 0;
    int kon = n + 1;
    int odp = n + 1;
    while (poc < kon) {
        int sr = (poc + kon)/2;
        if (spr(sr, n)) {
            odp = sr;
            kon = sr;
        }
        else {
            poc = sr + 1;
        }
    }
    cout << odp << '\n';
}

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