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// Witold Milewski
// PA 2025
#include <bits/stdc++.h>
using namespace std;
#define FOR(i, a, b) for(int i=a; i<=b; ++i)
#define FORB(i, b, a) for(int i=b; i>=a; --i)
#define sz(A) (int)(A.size())
#define eb emplace_back
#define pb push_back
#define pi pair<int, int>
#define f first
#define s second
#define rs resize
#define V vector

const int maxn=401, inf=500;
int n;
int A[maxn][maxn], D[maxn][maxn];
int dp[maxn][maxn][maxn];
int zlicz_bliskie[maxn];

bool check(int X) {
  FOR(i, 1, n) zlicz_bliskie[i]=0;
  FOR(a, 1, n) FOR(b, 1, n) FOR(c, 0, X) dp[a][b][c]=0;
  FOR(i, 1, n) FOR(j, 1, n) {
    if(i==j) continue;
    if(D[i][j]<=X) {
      ++zlicz_bliskie[i];
      continue;
    }
    FOR(v, 1, n) {
      int d = D[v][j];
      if(d<=X) ++dp[i][v][d];
    }
  }
  FOR(i, 1, n) FOR(v, 1, n) FOR(d, 1, X) dp[i][v][d]+=dp[i][v][d-1];

  FOR(la, 1, n) FOR(lb, la+1, n) {
    int a = la;
    int b = lb;
    bool ok=1;
    FOR(i, 1, n) {
      if(D[a][i]<D[b][i]) swap(a, b);
      int d = X-D[b][i];
      int ile_par_dalekich=0;
      if(d>=0) ile_par_dalekich = dp[i][a][d];
      int ile_par_bliskich = zlicz_bliskie[i];
      if(ile_par_bliskich+ile_par_dalekich!=n-1) {
        ok=0;
        break;
      }
    }
    if(ok) return 1;
  }
  return 0;
}

void solve() {
  cin >> n;
  FOR(i, 1, n) FOR(j, 1, n) D[i][j]=inf;
  FOR(i, 1, n) {
    string s;
    cin >> s;
    FOR(j, 1, n) {
      int x = s[j-1]-'0';
      if(x==0) D[i][j]=inf;
      else D[i][j]=1;
    }
  }

  FOR(i, 1, n) D[i][i]=0;
  FOR(a, 1, n) FOR(b, 1, n) FOR(c, 1, n) if(D[b][a]<inf && D[a][c]<inf) D[b][c]=min(D[b][c], D[b][a]+D[a][c]);

  int lo=1, hi=n;
  while(lo<hi) {
    int mid = (lo+hi)/2;
    if(check(mid)) hi=mid;
    else lo=mid+1;
  }
  cout << lo << '\n';
}

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