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#include<bits/stdc++.h>
#define fi first
#define se second
using namespace std;

typedef pair<int, int> par;
typedef pair<int, par> tri;
vector<tri> v;
int tab[409][409];
string s;

void solve()
{
	int n, a, b, wyn = 0;
	tri t;
	cin>>n;
	for(int i=1; i<=n; i++) {
		cin>>s;
		for(int j=0; j<n; j++) {
			if(s[j] == '1') tab[i][j+1] = 1;
			else if(i == j + 1) tab[i][j+1] = 0;
			else tab[i][j+1] = 1001;
		}
	}
	for(int k=1; k<=n; k++) {
		for(int i=1; i<=n; i++) {
			for(int j=1; j<=n; j++) {
				if(tab[i][j] > tab[i][k] + tab[k][j]) tab[i][j] = tab[i][k] + tab[k][j];
			}
		}
	}
	v.clear();
	for(int i=1; i<n; i++) {
		for(int j=i+1; j<=n; j++) {
			if(tab[i][j] > wyn) wyn = tab[i][j];
			v.push_back(tri(tab[i][j], par(i, j)));
		}
	}
	
	sort(v.begin(), v.end());
	
	for(int i=1; i<n; i++) {
		for(int j=i+1; j<=n; j++) {
			a = 0;
			for(int k=v.size()-1; k>=0; k--) {
				t = v[k];
				if(t.fi <= a) break;
				if(i == t.se.fi && j == t.se.se) continue;
				b = t.fi;
				if(b > tab[t.se.fi][i] + tab[j][t.se.se]) b = tab[t.se.fi][i] + tab[j][t.se.se];
				if(b > tab[t.se.fi][j] + tab[i][t.se.se]) b = tab[t.se.fi][j] + tab[i][t.se.se];
				if(b >= wyn) {
					a = wyn;
					break;
				}
				if(b > a) a = b;
			}
			if(a < wyn) wyn = a;
		}
	}
	
	cout<<wyn<<'\n';
	return;
}

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