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#include <bits/stdc++.h>


#define ll long long
#define ve vector
#define fi first
#define se second
#define ld long double
#define all(x) x.begin(), x.end()

using namespace std;

typedef pair<int, int> pii;

const int MAXN = 401;

int g[MAXN][MAXN];
int d[MAXN][MAXN];

void bfs(int s, int n){
    queue<int> q;
    q.push(s);
    d[s][s] = 0;
    while(!q.empty()){
        int v = q.front();
        q.pop();
        for(int to = 0; to < n; to++)
            if(g[v][to] && d[s][to] == 0 && to != s){
                d[s][to] = d[s][v] + 1;
                q.push(to);
            }
    }
}

struct path{
    int a, b, d;
};

void solve(){
    int n;
    cin >> n;
    for(int i = 0; i < n; i++)
        for(int j = 0; j < n; j++){
            char x;
            cin >> x;
            g[i][j] = x - '0';
            d[i][j] = 0;
        }
    for(int i = 0; i < n; i++)
        bfs(i, n);
    ve<path> v;
    for(int i = 0; i < n; i++)
        for(int j = 0; j < i; j++)
            v.push_back({i, j, d[i][j]});
    int res = n;
    sort(all(v), [](auto a, auto b){
        return a.d > b.d;
    });
    for(auto [a, b, cd] : v){
        int cans = 0;
        for(auto [a1, b1, d1] : v){
            if(d1 <= cans || cans >= res) break;
            cans = max(cans, min({d[a1][b] + d[b1][a], d[a1][a] + d[b1][b], d1}));
        }
        res = min(res, cans);
    }
    cout << res << "\n";
    
}


signed main(){
    ios_base::sync_with_stdio(0); cin.tie(0);
    int T= 1;
    cin >> T;
    while(T--)
        solve();
}