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#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define rep(a, b) for(int a = 0; a < (b); ++a)
#define st first
#define nd second
#define pb push_back
#define all(a) a.begin(), a.end()
const int LIM=407, INF=1e9+7;
int T[LIM][LIM], odl[LIM][LIM], zle[LIM], lok[LIM][LIM], glo[LIM][LIM], n;
void BFS(int x) {
	odl[x][x]=0;
	queue<int>q;
	q.push(x);
	while(!q.empty()) {
		int p=q.front(); q.pop();
		rep(i, n) if(odl[x][i]==INF && T[p][i]) {
			odl[x][i]=odl[x][p]+1;
			q.push(i);
		}
	}
}
bool check(int k) {
	rep(i, n) rep(j, n) glo[i][j]=1;
	rep(a, n) {
		rep(i, n) rep(j, n) lok[i][j]=1;
		rep(i, n) zle[i]=n;
		rep(b, n) if(odl[a][b]>k) {
			rep(y, n) zle[y]=min(zle[y], k-odl[b][y]);
		}
		rep(x, n) rep(y, n) if(odl[a][x]>zle[y]) lok[x][y]=0;
		rep(x, n) rep(y, n) if(!lok[x][y] && !lok[y][x]) glo[x][y]=0;
	}
	rep(x, n) rep(y, n) if(glo[x][y]) return true;
	return false;
}
void solve() {
	cin >> n;
	rep(i, n) rep(j, n) {
		T[i][j]=0;
		odl[i][j]=INF;
	}
	rep(i, n) rep(j, n) {
		char c;
		cin >> c;
		if(c=='1') T[i][j]=1;
	}
	rep(i, n) BFS(i);
	int po=1, ko=n-1;
	while(po<ko) {
		int sr=(po+ko)/2;
		if(check(sr)) ko=sr; else po=sr+1;
	}
	cout << po << '\n';
}
int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);
	int _=1;
	cin >> _;
	while(_--) solve();
}