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#include <bits/stdc++.h>
using namespace std;

#define int long long
#define ii pair<int,int>
#define iii tuple<int,int,int>
#define fi first
#define se second
#define endl '\n'

#define pub push_back
#define pob pop_back
#define puf push_front
#define pof pop_front
#define lb lower_bound
#define ub upper_bound

#define rep(x,start,end) for(int x=(start)-((start)>(end));x!=(end)-((start)>(end));((start)<(end)?x++:x--))
#define all(x) (x).begin(),(x).end()
#define sz(x) (int)(x).size()

mt19937 rng(chrono::system_clock::now().time_since_epoch().count());

int n;
string s[405];
int apsp[405][405];

bitset<405> has[405][405];

signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin.exceptions(ios::badbit | ios::failbit);
	
	int TC;
	cin>>TC;
	while (TC--){
		cin>>n;
		rep(x,0,n) cin>>s[x];
		
		rep(x,0,n) rep(y,0,n) apsp[x][y]=1e9;
		rep(x,0,n) apsp[x][x]=1;
		rep(x,0,n) rep(y,0,n) if (s[x][y]=='1') apsp[x][y]=1;
		
		rep(k,0,n) rep(i,0,n) rep(j,0,n) apsp[i][j]=min(apsp[i][j],apsp[i][k]+apsp[k][j]);
		
		rep(x,0,n) rep(y,0,n) has[x][y].reset();
		rep(x,0,n) rep(y,0,n) has[x][apsp[x][y]][y]=1;
		rep(x,0,n) rep(y,1,n) has[x][y]|=has[x][y-1];
		
		bitset<405> one;
		rep(x,0,n) one[x]=1;
		
		int ans=n-2;
		rep(a,0,n) rep(b,a+1,n){
			while (ans){
				bool ok=true;
				rep(x,0,n){
					bitset<405> bm=has[x][ans];
					if (apsp[x][a]<=ans) bm|=has[b][ans-apsp[x][a]];
					if (apsp[x][b]<=ans) bm|=has[a][ans-apsp[x][b]];
					
					if (bm!=one){
						ok=false;
						break;
					}
				}
				
				if (ok) ans--;
				else break;
			}
		}
		
		cout<<ans+1<<endl;
	}
}