#include<bits/stdc++.h>
using namespace std;
using ll=long long;
const ll mod=998244353;
const int N=5010;
int n,sz[N];
ll C[N][N],dp[N][N],pre[N][N],fac[N],f[N],prod[N];
vector<int> v[N];
bool vis[N];
ll qui(ll a,ll b, ll c){
ll ret=1;
while(b){
if(b&1) ret=ret*a%c;
a=a*a%c;
b>>=1;
}
return ret;
}
ll inv(ll a){
return qui(a,mod-2,mod);
}
void init()
{
fac[0]=1;
for(int i=1;i<N;++i) fac[i]=fac[i-1]*i%mod;
C[0][0]=1;
for(int i=1;i<N;++i)
{
for(int j=0;j<N;++j)
{
if(!j) C[i][0]=1;
if(j>i) break;
C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
}
}
}
void initDfs(int u,int fa){
sz[u]=1;
for(auto j:v[u]){
if(j==fa) continue;
initDfs(j,u);
sz[u]+=sz[j];
}
}
void initDfs2(int u,int fa){
ll tmp=1;
f[u]=1;
for(auto j:v[u]){
if(j==fa) continue;
tmp=tmp*fac[sz[j]]%mod;
}
f[u]=f[u]*fac[sz[u]-1]%mod*inv(tmp)%mod;
for(auto j:v[u]){
if(j==fa) continue;
initDfs2(j,u);
f[u]=f[u]*f[j]%mod;
}
}
void initDfs3(int u,int fa){
prod[u]=sz[u];
for(auto j:v[u]){
if(j==fa) continue;
initDfs3(j,u);
}
for(auto j:v[u]){
if(j==fa) continue;
prod[u]=prod[u]*prod[j]%mod;
}
}
void dfs(int fa,int lll){
vis[fa]=true;
ll t1=1;
for(auto u:v[fa]){
if(u==lll) continue;
t1=t1*f[u]%mod;
t1=t1*inv(fac[sz[u]])%mod;
}
for(auto u:v[fa]){
if(vis[u]) continue;
ll t2=fac[sz[fa]-sz[u]-1];
vector<ll> pre(n+1);
for(int i=1;i<=n;++i){
if(n-i-sz[u]>=0&&sz[fa]-sz[u]-1>=0)
pre[i]=dp[fa][i]*C[n-i-sz[u]][sz[fa]-sz[u]-1]%mod;
}
for(int i=1;i<=n;++i){
pre[i]=pre[i-1]+pre[i];
pre[i]%=mod;
}
for(int i=1;i<=n;++i){
dp[u][i]=pre[i-1]*t1%mod*t2%mod*inv(f[u])%mod*fac[sz[u]]%mod
}
dfs(u,fa);
}
}
void solve(){
cin >> n;
for(int i=2;i<=n;++i){
int x;
cin >> x;
v[x].push_back(i);
}
init();
initDfs(1,0);
initDfs2(1,0);
initDfs3(1,0);
dp[1][1]=1;
dfs(1,0);
for(int i=1;i<=n;++i){
ll ans=dp[i][i]*f[i]%mod*C[n-i][sz[i]-1]%mod;
cout<<ans<<" ";
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}