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#include <bits/stdc++.h>
using namespace std;
#define fwd(i, a, n) for (int i = (a); i < (n); i++)
#define rep(i, n) fwd(i, 0, n)
#define all(X) X.begin(), X.end()
#define sz(X) int(size(X))
#define pb push_back
#define eb emplace_back
#define st first
#define nd second
using pii = pair<int, int>; using vi = vector<int>;
using ll = long long; using ld = long double;
#ifdef LOC
auto SS = signal(6, [](int) { *(int *)0 = 0; });
#define DTP(x, y) auto operator << (auto &o, auto a) -> decltype(y, o) { o << "("; x; return o << ")"; }
DTP(o << a.st << ", " << a.nd, a.nd);
DTP(for (auto i : a) o << i << ", ", all(a));
void dump(auto... x) { (( cerr << x << ", " ), ...) <<
'\n'; }
#define deb(x...) cerr << setw(4) << __LINE__ << ":[" #x "]: ", dump(x)
#else
#define deb(...) 0
#endif

const int INF = 1e4;
const int N = 512;

void solve(){
    short n; cin >> n;
    vector<vector<short>> dist(n, vector<short>(n, INF));
    rep(i, n){
        string str; cin >> str;
        rep(j, n){
            if(str[j] == '1')dist[i][j] = 1;
        }
        dist[i][i] = 0;
    }
    rep(k, n) rep(i, n) rep(j, n){
        dist[i][j] = min<short>(dist[i][j], dist[i][k] + dist[k][j]);
    }
    deb(dist);
    vector<vector<short>> d(n, vector<short>(n+1, -INF));
    vector<vector<short>> v(n, vector<short>(n+1));
    rep(i, n){
        vector<pair<short, short>> t(n);
        rep(j, n){
            t[j] = {dist[i][j], j};
        }
        sort(all(t));
        rep(j, n){
            d[i][j+1] = t[j].st;
            v[i][j+1] = t[j].nd;
        }
    }
    deb(d);
    deb(v);
    vector<bitset<N>> ok(n);
    vector<short> l(n, n);
    auto check = [&](short D){
        deb("check", D);
        rep(i, n)ok[i].set();
        rep(a, n){
            vector<bitset<N>> ok2(n);
            rep(i, n)l[i] = n;
            fwd(b, a+1, n){
                if(dist[a][b] <= D)continue;
                short j = n;
                rep(i, n){
                    while(d[a][j] + d[b][i+1] > D)j--;
                    int ind = v[b][i+1];
                    l[ind] = min<short>(l[ind], j);
                }
                deb(b);
                deb(l);
            }
            deb(a, l);
            rep(i, n){
                for(int j = 0; j < l[i]; j++){
                    ok2[i][v[a][j + 1]] = true;
                    ok2[v[a][j + 1]][i] = true;
                }
            }
            rep(i, n)ok[i] &= ok2[i];
            deb(ok);
        }
        rep(i, n)rep(j, n)if(ok[i][j])return true;
        return false;
    };
    int x = 1;
    int y = 1;
    rep(i, n)rep(j, n)y = max<short>(y, dist[i][j]);
    while(x < y){
        int m = (x + y) / 2;
        if(check(m)){
            y = m;
        }else{
            x = m + 1;
        }
    }
    cout << x << "\n";
}

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