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#include<bits/stdc++.h>
using namespace std;
using LL=long long;
#define FOR(i,l,r)for(int i=(l);i<=(r);++i)
#define REP(i,n)FOR(i,0,(n)-1)
#define ssize(x)int(x.size())
#ifdef DEBUG
auto operator<<(auto&o,auto x)->decltype(x.end(),o);
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<", "<<get<3>(t)<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

constexpr int N = 400;
using B = bitset<N>;

void solve() {
	mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());

	int n;
	cin >> n;
	debug(n);

	vector<pair<int, int>> edges;
	REP(i, n) {
		string s;
		cin >> s;
		REP(j, n) {
			if (s[j] == '1')
				edges.emplace_back(i, j);
		}
	}
	debug(edges);

	{
		vector perm(n, 0);
		iota(perm.begin(), perm.end(), 0);
		shuffle(perm.begin(), perm.end(), rng);
		for (auto& [a, b] : edges) {
			a = perm[a];
			b = perm[b];
		}
	}
	debug(edges);

	vector graph(n, vector (n, n));
	for (auto [i, j] : edges) {
		graph[i][j] = 1;
	}
	REP(i, n)
		graph[i][i] = 0;
	debug(graph);

	auto dist = graph;
	REP(k, n) {
		REP(i, n) {
			REP(j, n) {
				dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
			}
		}
	}
	REP(i, n) {
		REP(j, n) {
			assert(dist[i][j] < n);
		}
	}
	debug(dist);

	// from_me[x][d] - vertices at most d away from x
	vector from_me(n, vector<B>(n));
	REP(x, n) {
		REP(b, n) {
			FOR(d, dist[x][b], n - 1) {
				from_me[x][d][b] = 1;
			}
		}
	}

	auto okay = [&](const int ss) -> bool {
		vector<int> ids(n);
		iota(ids.begin(), ids.end(), 0);
		shuffle(ids.begin(), ids.end(), rng);
		for (const int a : ids) {
			B valid_b;
			valid_b.set();
			B filter;
			REP(x, n) {
				REP(y, x + 1) {
					if (dist[x][y] <= ss)
						continue;
					filter.reset();
					if (dist[a][x] <= ss) {
						filter |= from_me[y][ss - dist[a][x]];
					}
					if (dist[a][y] <= ss) {
						filter |= from_me[x][ss - dist[a][y]];
					}
					valid_b &= filter;
				}
				if (valid_b.none())
					break;
			}
			debug(ss, a, valid_b);
			if (valid_b.any())
				return true;
		}
		return false;
	};
	int bb = 0, ee = n;
	while (ee - bb > 1) {
		const int ss = (bb + ee) / 2;
		if (okay(ss)) {
			ee = ss;
		}
		else {
			bb = ss;
		}
	}
	cout << ee << '\n';
}

int main() {
	cin.tie(0)->sync_with_stdio(0);

	int t;
	cin >> t;
	REP(tt, t) {
		solve();
	}
}