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#include <bits/stdc++.h>
using namespace std;
#define fwd(i, a, n) for (int i = (a); i < (n); i++)
#define rep(i, n)    fwd(i, 0, n)
#define all(X)       X.begin(), X.end()
#define sz(X)        int(size(X))
#define pb           push_back
#define eb           emplace_back
#define st           first
#define nd           second
using pii = pair<int, int>;
using vi = vector<int>;
using ll = long long;
using ld = long double;
#ifdef LOC
auto SS = signal(6, [](int) {
	*(int *)0 = 0;
});
#	define DTP(x, y)                                      \
		auto operator<<(auto &o, auto a)->decltype(y, o) { \
			o << "(";                                      \
			x;                                             \
			return o << ")";                               \
		}
DTP(o << a.st << ", " << a.nd, a.nd);
DTP(for (auto i : a) o << i << ", ", all(a));
void dump(auto... x) {
	((cerr << x << ", "), ...) << '\n';
}
#	define deb(x...) cerr << setw(4) << __LINE__ << ":[" #x "]: ", dump(x)
#else
#	define deb(...) 0
#endif

void sol() {
	int n;
	cin >> n;
	vector<vi> dist(n, vi(n));
	rep(i, n) {
		string s;
		cin >> s;
		rep(j, n) {
			if (i == j)
				dist[i][j] = 0;
			else if (s[j] == '1')
				dist[i][j] = 1;
			else
				dist[i][j] = n;
		}
	}
	rep(k, n) rep(i, n) rep(j, n) dist[i][j] =
		min(dist[i][j], dist[i][k] + dist[k][j]);
	vector<vi> diam(n, vi(n));
	vi depth_to_diam(n);
	rep(s, n) rep(v, n) {
		fill(all(depth_to_diam), 0);
		rep(u, n) {
			int s_dist = dist[s][u], v_dist = dist[v][u];
			int threshold = max(0, s_dist - v_dist);
			depth_to_diam[threshold] = max(depth_to_diam[threshold], s_dist);
		}
		rep(i, n - 1) depth_to_diam[i + 1] =
			max(depth_to_diam[i + 1], depth_to_diam[i]);
		for (int i = n - 2; i >= 0; i--)
			depth_to_diam[i] = max(depth_to_diam[i], depth_to_diam[i + 1] - 1);
		int v_dist = dist[s][v];
		rep(u, n) {
			int u_dist = dist[s][u];
			if (u_dist <= v_dist)
				diam[v][u] = max(diam[v][u], depth_to_diam[u_dist]);
		}
	}
	int min_diam = n;
	rep(i, n) rep(j, n) min_diam = min(min_diam, max(diam[i][j], diam[j][i]));
	cout << min_diam << '\n';
}

int32_t main() {
	cin.tie(0)->sync_with_stdio(0);
	cout << fixed << setprecision(10);
	int t;
	cin >> t;
	rep(i, t) sol();
#ifdef LOCF
	cout.flush();
	cerr << "- - - - - - - - -\n";
	(void)!system(
		"grep VmPeak /proc/$PPID/status | sed s/....kB/\' MB\'/1 >&2"); // 4x.kB
																		// ....kB
#endif
}