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/*
 * Opis: Główny nagłówek
 */
#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,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
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

const int inf = 1e9 + 5;

void solve() {
	int n;
	cin >> n;
	vector<string> arr(n);
	for (auto& s : arr) {
		cin >> s;
	}

	vector<vector<int>> shortest(n);
	REP(i, n) {
		shortest[i].resize(n, inf);
		shortest[i][i] = 0;
	}
	REP(i, n) {
		REP(j, n) {
			if (arr[i][j] == '1') {
				shortest[i][j] = 1;
			}
		}
	}

	REP(k, n) {
		REP(i, n) {
			REP(j, n) {
				shortest[i][j] = min(shortest[i][j], shortest[i][k] + shortest[k][j]);
			}
		}
	}

	int start = 0;
	REP(i, n) {
		REP(j, n) {
			start = max(start, shortest[i][j]);
		}
	}
	int res = start;
	vector<array<int, 3>> cands;
	REP(i, n) {
		REP(j, i) {
			cands.push_back({j, i, shortest[i][j]});
		}
	}
	sort(cands.begin(), cands.end(), [&] (array<int, 3> a, array<int, 3> b) {
			return a[2] > b[2];
	});
	for (auto [a, b, old_cost] : cands) {
		if (old_cost < start - res) {
			break;
		}
		int new_res = 0;
		for (auto [x, y, cost] : cands) {
			if (cost <= new_res) {
				break;
			}
			int curr = min(shortest[x][a] + shortest[b][y],
						   shortest[x][b] + shortest[a][y]);
			curr = min(curr, cost);
			new_res = max(new_res, curr);
			if (new_res >= res) {
				break;
			}
		}
		res = min(res, new_res);
	}
	cout << res << "\n";
}



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