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#include <bits/stdc++.h>
using namespace std;
#define REP(i,a,b) for (int i = (a); i <= (b); ++i)
#define REPD(i,a,b) for (int i = (a); i >= (b); --i)
#define FORI(i,n) REP(i,1,n)
#define FOR(i,n) REP(i,0,int(n)-1)
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define vi vector<int>
#define ll long long
#define SZ(x) int((x).size())
#define DBG(v) cerr << #v << " = " << (v) << endl;
#define FOREACH(i,t) for (typeof(t.begin()) i=t.begin(); i!=t.end(); i++)
#define fi first
#define se second

const int inf = 1000100100;
const int N = 404;

struct dst {
	int d,i,j;
	dst(int d_, int i_, int j_) : d(d_), i(i_), j(j_) {}
	dst() : d(0), i(0), j(0) {}
	bool operator< (dst x) const {
		if (d != x.d) return d > x.d;
		if (i != x.i) return i < x.i;
		return j < x.j;
	}
};

int n;
int d[N][N];
char s[N][N];
dst t[N*N];

void test() {
	scanf("%d", &n);
	FOR(i,n) {
		scanf(" %s", s[i]);
		FOR(j,n) {
			d[i][j] = inf;
			if (s[i][j] == '1') d[i][j] = 1;
		}
		d[i][i] = 0;
	}
	FOR(k,n) {
		FOR(i,n) FOR(j,n) if (d[i][j] > d[i][k] + d[k][j]) d[i][j] = d[i][k] + d[k][j];
	}
	int nn = 0;
	FOR(i,n) FOR(j,i) t[nn++] = dst(d[i][j],i,j);
	sort(t,t+nn);
	int res = t[0].d;
	FOR(a,n) FOR(b,a) {
		int worst_d = 0;
		FOR(k,nn) {
			if (t[k].d <= worst_d) break;
			int cur_d = t[k].d;
			cur_d = min(cur_d, d[t[k].i][a] + d[b][t[k].j]);
			cur_d = min(cur_d, d[t[k].i][b] + d[a][t[k].j]);
			worst_d = max(worst_d, cur_d);
		}
		res = min(res, worst_d);
	}
	printf("%d\n", res);
}

int main() {
	int tt;
	scanf("%d", &tt);
	FOR(i,tt) test();
	return 0;
}