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