#include #include #include using namespace std; constexpr int Z = 998244353; using pii = pair; using vp = vector; using vi = vector; int bexp(int a, int n) { if (n == 0) { return 1; } if (n % 2 == 1) { return 1ll * a * bexp(a, n - 1) % Z; } int t = bexp(a, n / 2); return 1ll * t * t % Z; } int inv(int a) { return bexp(a, Z - 2); } void dfs0(vp e[], int u, int p, vi dp[]) { dp[u].resize(e[u].size()); dp[u][0] = 1; int pu = 1; for (int i = 1; i < (int)e[u].size(); i++) { auto [ord, v] = e[u][i]; if (v != p) { dfs0(e, v, u, dp); dp[u][i] = 1ll * (dp[v][(int)e[v].size()-1] - dp[v][ord] + Z) * inv(bexp(v + 1, ord)) % Z; dp[u][i] = (dp[u][i] + 1ll * dp[v][ord] * bexp(v + 1, (int)e[v].size() - ord)) % Z; } pu = 1ll * pu * (u + 1) % Z; dp[u][i] = (1ll * pu * dp[u][i] + dp[u][i-1]) % Z; } } void dfs1(vp e[], int u, int p, vi dp[], int ans[]) { for (int i = 1; i < (int)e[u].size(); i++) { auto [ord, v] = e[u][i]; if (v == p) { continue; } int dp1v = 1ll * (dp[u][(int)e[u].size()-1] - dp[u][i]) * inv(bexp(u + 1, i)) % Z; dp1v = (dp1v + 1ll * dp[u][i-1] * bexp(u + 1, (int)e[u].size() - i)) % Z; dp1v = 1ll * dp1v * bexp(v + 1, ord) % Z; for (int j = ord; j < (int)e[v].size(); j++) { dp[v][j] = (dp[v][j] + dp1v) % Z; } ans[v] = dp[v].back(); dfs1(e, v, u, dp, ans); } } int main() { int n; cin >> n; vp e[n]; pii e2[n-1]; fill(e2, e2 + n - 1, pii(-1, -1)); for (int i = 0; i < n; i++) { int d; cin >> d; e[i].resize(d + 1); for (int j = 1; j <= d; j++) { cin >> e[i][j].first; e[i][j].first--; pii &t = e2[e[i][j].first]; (t.first == -1 ? t.first : t.second) = i; } } pii ord[n-1]; for (int i = 0; i < n; i++) { for (int j = 1; j < (int)e[i].size(); j++) { int id = e[i][j].first; (e2[id].first == i ? ord[id].first : ord[id].second) = j; } } for (int i = 0; i < n; i++) { for (int j = 1; j < (int)e[i].size(); j++) { int id = e[i][j].first; e[i][j] = e2[id].first == i ? pii(ord[id].second, e2[id].second) : pii(ord[id].first, e2[id].first); } } vi dp[n]; dfs0(e, 0, -1, dp); int ans[n]; ans[0] = dp[0].back(); dfs1(e, 0, -1, dp, ans); for (int i = 0; i < n; i++) { cout << (ans[i] - 1 + Z) % Z << endl; } return 0; }