#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define mkp make_pair
#define pb push_back
typedef pair <int, int> pii;

inline int read() {
	int x = 0, f = 0;
	char c = getchar();
	while (!isdigit(c)) {if (c == '-') f = 1; c = getchar();}
	while (isdigit(c)) x = (x << 1) + (x << 3) + (c & 15), c = getchar();
	return f? -x : x;
}

const int MAXN = 5000;
const int Mod = 998244353;
vector <int> G[MAXN + 10];
int f[MAXN + 10], siz[MAXN + 10];
int dp[MAXN + 10][MAXN + 10], g[MAXN + 10];
int fac[MAXN + 10], ifac[MAXN + 10];

inline int fastpow(int x, int p) {
	int ans = 1;
	while (p) {
		if (p & 1) ans = 1ll * ans * x % Mod;
		x = 1ll * x * x % Mod;
		p >>= 1;
	}
	return ans;
}

inline int C(int n, int m) {
	if (n < m || n < 0 || m < 0) return 0;
	return 1ll * fac[n] * ifac[m] % Mod * ifac[n - m] % Mod;
}
void dfs(int x) {
	g[x] = 1;
	for (auto v : G[x]) {
		dfs(v);
		siz[x] += siz[v];
		g[x] = 1ll * g[x] * g[v] % Mod * C(siz[x], siz[v]) % Mod;
	}
	++siz[x];
}

int n;
void DP(int x) {
	int prod = 1;
	for (auto v : G[x])
		prod = 1ll * prod * g[v] % Mod;
	for (auto v : G[x]) {
		int val = 1ll * prod * fastpow(g[v], Mod - 2) % Mod;
		int sum = 0;
		for (int j = 1; j <= n - siz[v] + 1; ++j) {
			dp[v][j] = (dp[v][j - 1] + 1ll * dp[x][j - 1] * C(n - siz[v] - (j - 1), siz[x] - siz[v] - 1)) % Mod;
		}
		for (int j = 1; j <= n - siz[v] + 1; ++j)
			dp[v][j] = 1ll * dp[v][j] * val % Mod;
		DP(v);
	}
}

signed main() {
//	freopen ("std.in", "r", stdin);
//	freopen ("std.out", "w", stdout);
	n = read();
	for (int i = 2; i <= n; ++i) {
		f[i] = read();
		G[f[i]].pb(i);
	}
	fac[0] = 1;
	for (int i = 1; i <= n; ++i)
		fac[i] = 1ll * fac[i - 1] * i % Mod;
	ifac[n] = fastpow(fac[n], Mod - 2);
	for (int i = n - 1; i >= 0; --i)
		ifac[i] = 1ll * ifac[i + 1] * (i + 1) % Mod;
	dp[1][1] = 1;
	dfs(1);
	DP(1);
	//cerr << C(4, 2) << endl;
	for (int i = 1; i <= n; ++i)
		printf("%lld ", 1ll * dp[i][i] * C(n - i, siz[i] - 1) % Mod * g[i] % Mod);
	return 0;
}