ABC 219

void solve() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    ll N = 4;
    vvint A(N, vint(N));
    rep(i, N) rep(j, N) cin >> A[i][j];

    vint di = {0, 1, 0, -1};
    vint dj = {1, 0, -1, 0};

    int ans = 0;
    rep(state, 1ll << N * N) {
        vvint grid(N, vint(N));

        dsu uf(N * N + 1);
        rep(i, N * N) {
            if (state >> i & 1) {
                int r = i / N;
                int c = i % N;
                grid[r][c] = 1;
            }
        }

        int ok = 1;
        rep(r, N) rep(c, N) {
            if (A[r][c] && !grid[r][c]) ok = 0;
        }
        if (!ok) continue;

        rep(r, N) rep(c, N) {
            rep(d, 4) {
                ll nr = r + di[d], nc = c + dj[d];
                if (clamp(nr, 0ll, N - 1) != nr || clamp(nc, 0ll, N - 1) != nc) continue;
                if (grid[nr][nc] == grid[r][c]) {
                    int L = nr * N + nc, R = r * N + c;
                    uf.merge(L, R);
                }
            }
            if (grid[r][c] == 0 && (r == 0 || r == N - 1 || c == 0 || c == N - 1)) {
                uf.merge(r * N + c, N * N);
            }
        }

        // 堀に囲まれた壁に連結していない領域がないかチェック
        rep(r, N) rep(c, N) {
            if (grid[r][c] == 0 && !uf.same(r * N + c, N * N)) ok = 0;
        }
        if (!ok) continue;

        // 堀で囲まれた領域が一つだけであることをチェック
        set<int> ch;
        rep(i, N) rep(j, N) {
            if (grid[i][j]) ch.insert(uf.leader(i * N + j));
        }
        if (ch.size() != 1) continue;
        ans++;
    }
    cout << ans << endl;
}