#include <bits/stdc++.h>
#define pb emplace_back
#define fst first
#define scd second
#define mkp make_pair
#define uint unsigned
#define mems(a, x) memset((a), (x), sizeof(a))

using namespace std;
typedef long long ll;
typedef double db;
typedef unsigned long long ull;
typedef long double ldb;
typedef pair<ll, ll> pii;

const int maxn = 5050;
const ll mod = 998244353;

inline ll qpow(ll b, ll p) {
	ll res = 1;
	while (p) {
		if (p & 1) {
			res = res * b % mod;
		}
		b = b * b % mod;
		p >>= 1;
	}
	return res;
}

ll n, fac[maxn], ifac[maxn], inv[maxn], a[maxn], fa[maxn];
vector<int> G[maxn];

inline ll C(ll n, ll m) {
	if (n < m || n < 0 || m < 0) {
		return 0;
	} else {
		return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
	}
}

ll sz[maxn], g[maxn], h[maxn];

void dfs(int u) {
	sz[u] = 1;
	g[u] = h[u] = 1;
	for (int v : G[u]) {
		dfs(v);
		sz[u] += sz[v];
		g[u] = g[u] * g[v] % mod;
		h[u] = h[u] * h[v] % mod;
	}
	g[u] = g[u] * inv[sz[u]] % mod;
	h[u] = h[u] * sz[u] % mod;
}

ll K, U;

int dfs2(int u) {
	if (u == U) {
		return 0;
	}
	int s = 1;
	for (int v : G[u]) {
		int t = dfs2(v);
		s += t;
	}
	K = K * inv[s] % mod;
	return s;
}

void solve() {
	scanf("%lld", &n);
	for (int i = 2, p; i <= n; ++i) {
		scanf("%d", &p);
		G[p].pb(i);
		fa[i] = p;
	}
	fac[0] = 1;
	for (int i = 1; i <= n; ++i) {
		fac[i] = fac[i - 1] * i % mod;
	}
	ifac[n] = qpow(fac[n], mod - 2);
	for (int i = n - 1; ~i; --i) {
		ifac[i] = ifac[i + 1] * (i + 1) % mod;
	}
	inv[1] = 1;
	for (int i = 2; i <= n; ++i) {
		inv[i] = (mod - mod / i) * inv[mod % i] % mod;
	}
	dfs(1);
	for (int i = 1; i <= n; ++i) {
		K = 1;
		U = i;
		dfs2(1);
		a[i] = fac[n - sz[i]] * K % mod;
	}
	for (int i = 1; i <= n; ++i) {
		ll ans = 0, o = 1, k = 1;
		for (int j = i; j; j = fa[j], o = mod - o) {
			if (j != i) {
				k = k * sz[j] % mod * inv[sz[j] - sz[i]] % mod;
			}
			ll t = k * g[j] % mod * h[i] % mod * fac[sz[j] - sz[i]] % mod;
			ans = (ans + o * C(n - sz[j] - i + sz[j], sz[j] - 1) % mod * a[j] % mod * C(sz[j] - 1, sz[i] - 1) % mod * t) % mod;
		}
		printf("%lld%c", ans * g[i] % mod * fac[sz[i]] % mod, " \n"[i == n]);
	}
}

int main() {
	int T = 1;
	// scanf("%d", &T);
	while (T--) {
		solve();
	}
	return 0;
}