#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> Pr;
#define fi first
#define se second
#define mkp make_pair
#define pb emplace_back
// #define mid ((l+r)>>1)
#define popcnt __builtin_popcountll
const ll mod = 998244353;
inline ll read(){
	ll x=0, f=1; char ch=getchar();
	while(ch<'0' || ch>'9') { if(ch=='-') f=-1; ch=getchar(); }
	while(ch>='0' && ch<='9') x=x*10+ch-'0', ch=getchar();
	return x*f;
}
inline ll lg2(ll x){ return 63^__builtin_clzll(x); }
inline ll qpow(ll a,ll b){
	ll ans=1, base=a;
	while(b){
		if(b&1) ans=ans*base%mod;
		base=base*base%mod; b>>=1;
	}
	return ans;
}
int f[5005][5005], n, fa[5005], C[5005][5005], dp[5005], fac[5005], inv[5005];
int idp[5005], sz[5005], d[5005][5005];
vector<int>E[5005];

void addmod(int &x){ if(x >= mod) x-=mod; }
void init(){
	C[0][0]=fac[0]=1;
	for(int i=1;i<=5000;i++){
		C[i][0]=1; fac[i]=fac[i-1]*i%mod; inv[i]=qpow(fac[i], mod-2);
		for(int j=1;j<=i;j++){
			addmod(C[i][j]=C[i-1][j]+C[i-1][j-1]);
		}
	}
}
void procedure(){
	n=read();
	for(int i=2;i<=n;i++) fa[i]=read(), E[fa[i]].pb(i);
	for(int i=n;i>=1;i--){
		sz[i]++;
		sz[fa[i]]+=sz[i];
	}
	for(int i=n;i>=1;i--){
		dp[i]=qpow(sz[i], mod-2); idp[i]=sz[i];
		for(auto j: E[i]) dp[i]=1ull*dp[i]*dp[j]%mod, idp[i]=1ull*idp[i]*idp[j]%mod;
	}

	f[1][1] = 1;
	for(int i=1;i<=n;i++){
		for(int x=1;x<=n;x++){
			addmod(d[x][i] += d[x][i-1]);
			addmod(f[x][i] += d[x][i]);
			if(!f[x][i] || !E[x].size()) continue;
			for(auto y: E[x]){
				int coef = 1ull*dp[x]*idp[y]%mod*fac[sz[x]-sz[y]-1]%mod*sz[x]%mod*C[n-i-sz[y]][sz[x]-sz[y]-1]%mod*f[x][i]%mod;
				addmod(d[y][i+1] += coef);
			}
		}
	}

	for(int i=1;i<=n;i++) printf("%lld ", 1ll*f[i][i]*C[n-i][sz[i]-1]%mod*dp[i]%mod*fac[sz[i]]%mod);
}
int main(){
	#ifdef LOCAL
		assert(freopen("input.txt","r",stdin));
		assert(freopen("output.txt","w",stdout));
	#endif
	ll T=1;
	init();
	while(T--) procedure();
	return 0;
}