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#include<bits/stdc++.h>
#define FOR(i,a,b) for(int i=a;i<(int)b;++i)
#define FORD(i,a,b) for(int i=a;i>=(int)b;--i)
#define PB push_back
#define EB emplace_back
#define FI first
#define SE second
#define umap unordered_map
#define uset unordered_set
#define vi vector<int>
#define vvi vector<vi>
#define vll vector<ll>
#define vvll vector<vll>
#define vpii vector<pii>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define ALL(X) (X).begin(),(X).end()
//#ifndef DEBUG
//#define endl (char)10
//#endif
using namespace std;
using ll = long long;
using ld = long double;
template<class T, class U>
ostream& operator<< (ostream& os, const pair<T, U>& p){
    os << p.FI << " " << p.SE;
    return os;
}
template <class T>
istream& operator>> (istream& is, vector<T>& vec){
    FOR(i,0,vec.size()) is >> vec[i];
    return is;
}
template <class T>
ostream& operator<< (ostream& os, vector<T>& vec){
    for(auto& t : vec) os << t << " ";
    return os;
}

template<class T, class U>
istream& operator>> (istream& is, pair<T, U>& p){
    is >> p.FI >> p.SE;
    return is;
}

void st() {
	int n;
	cin >> n;
	vector<string> S(n);
	cin >> S;
	vvi d(n, vi(n, INT_MAX));
	FOR(i,0,n){
		d[i][i] = 0;
		queue<int> Q;
		Q.push(i);
		while(!Q.empty()) {
			int v = Q.front();
			Q.pop();
			FOR(j,0,n) if (S[v][j] == '1' && d[i][j] == INT_MAX) {
				d[i][j] = d[i][v] + 1;
				Q.push(j);
			}
		}
	}
	vpii P;
	FOR(i,0,n) FOR(j,i+1,n) P.EB(i, j);
	sort(ALL(P), [&d](const pii& a, const pii& b) { return d[a.FI][a.SE] > d[b.FI][b.SE]; });
	
	int ans = d[P[0].FI][P[0].SE];
	for(const auto& [a, b] : P){
		int cans = 0;
		for(auto& [u, v] : P) {
			if (d[u][v] <= cans) break;
			cans = max(cans, min({d[u][v], d[u][a] + d[v][b], d[u][b] + d[v][a]}));
			if(cans >= ans) break;
		}
		if (cans < ans) ans = cans;
	}
	cout << ans << endl;
}

int main () {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int t;
    cin >> t;
    while(t--) {
		st();
    }
}