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// Szybszy brut + heura
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double db;
typedef pair<int,int> pii;

const int N = 405;
const int INF = 1e9;
bool g[N][N];
int dist[N][N];
int Prev[N];
mt19937 rnd(458865456);

int ran(const int &a, const int &b){
    return rnd()%(b-a+1)+a;
}

void bfs(int v, int n){
    const int V = v;
    for(int i=0; i<n; ++i)
        dist[V][i] = INF;
    queue<int> q;
    q.push(v);
    dist[V][v] = 0;

    while(!q.empty()){
        v = q.front();
        q.pop();
        for(int u=0; u<n; ++u) if(g[v][u] && dist[V][u]==INF){
            dist[V][u] = dist[V][v] + 1;
            Prev[u] = v;
            q.push(u);
        }
    }
}

void solve(){
    int n;
    cin >> n;
    for(int i=0; i<n; ++i){
        for(int j=0; j<n; ++j){
            char c;
            cin >> c;
            g[i][j] = c-'0';
        }
    }
    for(int v=0; v<n; ++v)
        bfs(v,n);
    int min_dist = INF;
    if(n <= 120){
        for(int t1=0; t1<n; ++t1){
            for(int t2=t1+1; t2<n; ++t2){
                int max_dist = 0;
                for(int v=0; v<n; ++v){
                    for(int u=v+1; u<n; ++u){
                        max_dist = max(max_dist, min({dist[u][v], dist[u][t1]+dist[t2][v], dist[u][t2]+dist[t1][v]}));
                    }
                }
                min_dist = min(min_dist, max_dist);
            }
        }
        cout << min_dist << "\n";
        return;
    }

    for(int t1=0; t1<n; ++t1){
        bfs(t1, n);
        int diameter_u = 0;
        int len = 0;
        for(int u=0; u<n; ++u){
            if(dist[t1][u] > len){
                len = dist[t1][u];
                diameter_u = u;
            }
        }
        int cnt = 15;
        for(int i=0; i<len*0.2; ++i)
            diameter_u = Prev[diameter_u];

        while(cnt-->0 && diameter_u!=t1){
            diameter_u = Prev[diameter_u];
        
            int t2 = diameter_u;
            int max_dist = 0;
            for(int v=0; v<n; ++v){
                for(int u=v+1; u<n; ++u){
                    max_dist = max(max_dist, min({dist[u][v], dist[t1][u]+dist[t2][v], dist[t2][u]+dist[t1][v]}));
                }
            }
            min_dist = min(min_dist, max_dist);
        }
    }
    cout << min_dist << "\n";
}

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