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

void solve(){
    int n;
    cin >> n;
    vector<vector<int>> adj(n,vector<int>(n));
    for (int i = 0; i<n; i++){
        char c;
        for (int j = 0; j<n; j++){
            cin >> c;
            adj[i][j]=c-'0';
        }
    }
    vector<vector<int>> odl(n,vector<int>(n));
    vector<vector<bitset<400>>> bs(n,vector<bitset<400>>(n));
    vector<int> vis(n);
    int iter=0;
    int mn=1;
    for (int i = 0; i<n; i++){
        queue<int> q;
        q.push(i);
        vis[i]=++iter;
        while(q.size()){
            int v = q.front();
            q.pop();
            bs[i][odl[i][v]][v]=1;
            for (int j = 0; j<n; j++){
                if (adj[v][j] && vis[j]!=iter){
                    vis[j]=iter;
                    q.push(j);
                    odl[i][j]=odl[i][v]+1;
                    mn=max(mn,odl[i][j]);
                }
            }
        }
        for (int j = n-2; j>=0; j--)bs[i][j]|=bs[i][j+1];
    }
    for (int A = 0; A<n; A++){
        for (int B = A+1; B<n; B++){
            vector<bitset<400>> tmp(n);
            for (int i = 0; i<n; i++)tmp[i]=bs[A][i]&bs[B][i];
            int mx=0;
            for (int C = 0; C<n && mx<mn; C++){
                int d=min(odl[A][C],odl[B][C]);
                int l=mx,p=mn,md;
                while(l<p){
                    md=(l+p+1)/2;
                    if ((bs[C][md]&tmp[max(md-d,0)]).none())p=md-1;
                    else l=md;
                }
                mx=max(mx,l);
            }
            mn=min(mn,mx);
        }
    }
    cout << mn << '\n';
}

int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int t;
    cin >> t;
    while(t--)solve();
}