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

#define rep(i, b, e) for(int i = (b); i <= (e); i++)
#define per(i, b, e) for(int i = (e); i >= (b); i--)
#define FOR(i, b, e) rep(i, b, (e) - 1)
#define SZ(x) int(x.size())
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define st first
#define nd second
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;

auto &operator<<(auto &o, pair<auto, auto> p) {
    return o << "(" << p.st << ", " << p.nd << ")"; }
auto operator<<(auto &o, auto x)->decltype(end(x), o) {
    o << "{"; int i=0; for(auto e: x) o << ", " + 2*!i++ << e;
    return o << "}"; }
#ifdef LOCAL
#define deb(x...) cerr << "[" #x "]: ", [](auto...$) { \
    ((cerr << $ << "; "),...) << endl; }(x)
#else
#define deb(...)
#endif

const int N = 400, INF = 1e9;
int g[N][N], dist[N][N], good[N][N], farthest[N];
int n;

bool check(int d) {
    FOR(i, 0, n) FOR(j, i + 1, n) good[i][j] = 1;
    FOR(i, 0, n) {
        vi needs;
        FOR(j, 0, n) if(dist[i][j] > d) needs.pb(j);
        FOR(j, 0, n) {
            int maxi = 0;
            for(int &k: needs) if(maxi < dist[j][k]) maxi = dist[j][k];
            farthest[j] = maxi;
        }
        FOR(j, 0, n) FOR(k, j + 1, n) {
            int d1 = dist[i][j] + farthest[k];
            int d2 = dist[i][k] + farthest[j];
            good[j][k] &= d1 <= d || d2 <= d;
        }
    }
    FOR(i, 0, n) FOR(j, i + 1, n) if(good[i][j]) return 1;
    return 0;
}

void solve() {
    cin >> n;
    FOR(i, 0, n) {
        string s;
        cin >> s;
        FOR(j, 0, n) g[i][j] = s[j] - '0';
    }
    FOR(i, 0, n) FOR(j, 0, n) dist[i][j] = (i == j ? 0 : (g[i][j] ? 1 : INF));
    FOR(k, 0, n) FOR(i, 0, n) FOR(j, 0, n) {
        dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
    }
    int l = -1, r = n;
    while(l + 1 < r) {
        int mid = (l + r) / 2;
        (check(mid) ? r : l) = mid;
    }
    cout << r << '\n';
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    int tt = 1;
    cin >> tt;
    FOR(te, 0, tt) solve();
    return 0;
}