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#include<bits/stdc++.h>
#define st first
#define nd second
#define all(x) x.begin(), x.end()
#define BOOST cin.tie(NULL); ios_base::sync_with_stdio(false);
 
// #define int ll
typedef long long ll;

using namespace std;
template <typename T> struct tag:reference_wrapper <T>{ using reference_wrapper <T>::reference_wrapper; };
template <typename T1, typename T2> static inline tag <ostream> operator<<(tag <ostream> os, pair<T1, T2> const& p){ return os.get()<<"{"<<p.first<<", "<<p.second<<"}", os;}
template <typename Other> static inline tag <ostream> operator<<(tag <ostream> os, Other const& o){ os.get()<<o; return os; }
template <typename T> static inline tag <ostream> operator <<(tag <ostream> os, vector <T> const& v){ os.get()<<"["; for (int i=0; i<v.size(); i++) if (i!=v.size()-1) os.get()<<v[i]<<", "; else os.get()<<v[i]; return os.get()<<"]", os; }
template <typename T> static inline tag <ostream> operator <<(tag <ostream> os, set <T> const& s){ vector <T> v; for (auto i: s) v.push_back(i); os.get()<<"["; for (int i=0; i<v.size(); i++) if (i!=v.size()-1) os.get()<<v[i]<<", "; else os.get()<<v[i]; return os.get()<<"]", os; }

int infi = 1000;
int dist[500][500];
pair<int,int> closest[500][500];
int acc[500][500];
int tmp_acc[500][500];
vector<pair<int,int>> good_edges;

void floyd_warshall(int n){
    for(int k = 0; k < n; k++){
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(dist[i][j] > dist[i][k] + dist[k][j]){
                    dist[i][j] = dist[i][k] + dist[k][j];
                }
            }
        }
    }
}

void calc_closest(int n){
    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
            closest[i][j] = {dist[i][j], j};
        }
        sort(closest[i], closest[i] + n);
    }
}

void find_good_edges(int idx, int tank, int n){
    vector<int> ltrip;
    for(int i = 0; i < n; i++){
        if(dist[idx][i] > tank){
            ltrip.push_back(i);
        }
    }

    int dlim = infi;
    int tts,tte;
    for(int te = 0; te < n; te++){
        dlim = infi;
        for(int i : ltrip){
            dlim = min(dlim, tank - dist[te][i]);
        }
        for(int i = 0; i < n; i++){
            if(closest[idx][i].first <= dlim){
                tts = closest[idx][i].second;
                tte = te;
                if(tts > tte) swap(tts,tte);
                tmp_acc[tts][tte] = 1;
            } else {
                break;
            }
        }
    }
    for(int ts = 0; ts < n; ts++){
        for(int te = ts; te < n; te++){
            acc[ts][te] += tmp_acc[ts][te];
            tmp_acc[ts][te] = 0;
        }
    }

}

bool check(int tank, int n){
    for(int i = 0; i < n; i++){
        for(int j = i; j < n; j++){
            acc[i][j] = 0;
            tmp_acc[i][j] = 0;
        }
    }

    for(int i = 0; i < n; i++){
        find_good_edges(i, tank, n);
    }

    for(int i = 0; i < n; i++){
        for(int j = i; j < n; j++){
            assert(acc[i][j] <= n);
            if(acc[i][j] == n){
                return true;
            }
        }
    }
    return false;
}

void solve(){
    int n; cin >> n;

    good_edges.resize(n * n);

    string s;
    for(int i = 0; i < n; i++){
        cin >> s;
        for(int j = 0; j < n; j++){
            if(s[j] == '0'){
                dist[i][j] = infi;
            } else {
                dist[i][j] = 1;
            }
        }
        dist[i][i] = 0;
    }
    floyd_warshall(n);
    calc_closest(n);

    int p = -1, k = n, sr;
    while(p + 1 < k){
        sr = (p + k)/2;
        if(check(sr, n)){
            k = sr;
        } else {
            p = sr;
        }
    }
    cout << k << "\n";
}


int32_t main(){
    BOOST;
    
    int q; cin >> q;
    while(q--){
        solve();
    }

    return 0;
}