import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = cast(uint)(x_ % M); } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; int N; int[] C; int[][] G; int[][] E; int[] par; Mint[] dp, DP; void dfs(int u, int p) { par[u] = p; if (~p) { foreach (c; 0 .. C[u]) if (E[u][c] == p) { E[u] = E[u][c .. $] ~ E[u][0 .. c]; break; } } debug { writeln(u, " ", p, " ", E[u]); } foreach (c; 1 .. C[u]) if (~E[u][c]) { dfs(E[u][c], u); } auto ws = new Mint[C[u] + 1]; ws[0] = 1; foreach (c; 1 .. C[u] + 1) ws[c] = ws[c - 1] * Mint(u + 1); dp[u] = 0; foreach (c; 1 .. C[u]) { dp[u] += ws[c] * ((~E[u][c]) ? dp[E[u][c]] : Mint(1)); } } void DFS(int u, int p) { auto ws = new Mint[C[u] + 1]; ws[0] = 1; foreach (c; 1 .. C[u] + 1) ws[c] = ws[c - 1] * Mint(u + 1); auto pre = new Mint[C[u] + 1]; auto suf = new Mint[C[u] + 1]; foreach (c; 0 .. C[u]) pre[c + 1] = pre[c] + ws[c] * ((~E[u][c]) ? (c ? dp[E[u][c]] : DP[u]) : Mint(1)); foreach_reverse (c; 0 .. C[u]) suf[c] = ((~E[u][c]) ? (c ? dp[E[u][c]] : DP[u]) : Mint(1)) + ws[1] * suf[c + 1]; foreach (c; 1 .. C[u]) if (~E[u][c]) { DP[E[u][c]] = ws[1] * suf[c + 1] + ws[C[u] - c] * pre[c]; } foreach (c; 1 .. C[u]) if (~E[u][c]) { DFS(E[u][c], u); } } void main() { try { for (; ; ) { N = readInt; C = new int[N]; G = new int[][N]; foreach (u; 0 .. N) { C[u] = readInt + 1; G[u] = new int[C[u]]; foreach (c; 1 .. C[u]) { G[u][c] = readInt - 1; } G[u][0] = -1; } auto uss = new int[][N - 1]; foreach (u; 0 .. N) foreach (c; 1 .. C[u]) { uss[G[u][c]] ~= u; } E = new int[][N]; foreach (u; 0 .. N) { E[u] = new int[C[u]]; E[u][0] = -1; foreach (c; 1 .. C[u]) { const i = G[u][c]; E[u][c] = uss[i][0] ^ uss[i][1] ^ u; } } par.length = N; dp.length = N; DP.length = N; const rt = 0; dfs(rt, -1); DFS(rt, -1); debug { writeln("rt = ", rt); writeln("dp = ", dp); writeln("DP = ", DP); } foreach (u; 0 .. N) { int c0 = -1; foreach (c; 0 .. C[u]) if (!~E[u][c]) c0 = c; const Mint w = Mint(u + 1); Mint ans; void add(int c) { ans += (c ? dp[E[u][c]] : DP[u]); ans *= w; } foreach_reverse (c; 0 .. c0) add(c); foreach_reverse (c; c0 + 1 .. C[u]) add(c); writeln(ans); } } } catch (EOFException e) { } }