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#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define deb(...)
#define DBP(...)
using namespace std;
using   ll         = long long;
using   vi         = vector<int>;
using   pii        = pair<int, int>;
#define pb           push_back
#define mp           make_pair
#define x            first
#define y            second
#define rep(i, b, e) for (int i = (b); i < (e); i++)
#define each(a, x)   for (auto& a : (x))
#define all(x)       (x).begin(), (x).end()
#define sz(x)        int((x).size())

void run();

int main() {
	cin.sync_with_stdio(0); cin.tie(0);
	cout << fixed << setprecision(12);
	run();
	cout << flush; _Exit(0);
}

constexpr int MX = 405;
constexpr int INF = 1e8;

int n, lim;
int dist[MX][MX];
bitset<MX> masks[MX];

void updateMasks() {
	rep(i, 0, n) {
		masks[i].reset();
		rep(j, 0, n) if (dist[i][j] > lim) masks[i].set(j);
	}
}

void check(int t1, int t2) {
	int tel[MX];
	rep(i, 0, n) tel[i] = min(dist[t1][i], dist[t2][i]);

	int cnt[MX];
	fill(cnt, cnt+n+1, 0);
	rep(i, 0, n) cnt[tel[i]]++;
	rep(i, 1, n+1) cnt[i] += cnt[i-1];

	int ord[MX];
	rep(i, 0, n) ord[--cnt[tel[i]]] = i;

	while (true) {
		bitset<MX> bad;
		int pos = n-1;
		rep(i, 0, n) {
			int v = ord[i];
			while (pos >= 0 && tel[v]+tel[ord[pos]] > lim) {
				bad.set(ord[pos--]);
			}
			if ((masks[v] & bad).any()) {
				return;
			}
		}
		lim--;
		updateMasks();
	}
}

void solve() {
	string s;
	cin >> n;

	rep(i, 0, n) {
		cin >> s;
		rep(j, 0, n) {
			if (i != j) {
				dist[i][j] = (s[j] == '1' ? 1 : INF);
			} else {
				dist[i][j] = 0;
			}
		}
	}

	rep(k, 0, n) rep(i, 0, n) rep(j, 0, n) {
		dist[i][j] = min(dist[i][j], dist[i][k]+dist[k][j]);
	}

	lim = n;
	updateMasks();
	rep(t1, 0, n) rep(t2, t1+1, n) check(t1, t2);
	cout << lim+1 << '\n';
}

void run() {
	int t; cin >> t;
	while (t--) solve();
}