#include<bits/stdc++.h>
using namespace std;

#define pb push_back
const int N=5e3+100,MOD=998244353;
inline void mod(int &x){ if(x>=MOD) x-=MOD; }
inline int qm(int x,int y=MOD-2){ int res=1; for(;y;y>>=1,x=1ll*x*x%MOD) if(y&1) res=1ll*res*x%MOD; return res; }
#define gc getchar()
#define rd read()
inline int read(){
	int x=0,f=0; char c=gc;
	for(;c<'0'||c>'9';c=gc) f|=(c=='-');
	for(;c>='0'&&c<='9';c=gc) x=(x<<1)+(x<<3)+(c^48);
	return f?-x:x;
}

int jc[N],fjc[N];
void init(int n){
	jc[0]=1; for(int i=1;i<=n;++i) jc[i]=1ll*jc[i-1]*i%MOD;
	fjc[n]=qm(jc[n]); for(int i=n-1;~i;--i) fjc[i]=1ll*fjc[i+1]*(i+1)%MOD;
}
inline int C(int n,int m){ return n<0||m<0||m>n?0:1ll*jc[n]*fjc[m]%MOD*fjc[n-m]%MOD; }

int n,mul[N],siz[N],fmul[N],f[N][N];
vector<int> G[N];

void dfs0(int u){ siz[u]=mul[u]=1; for(int v:G[u]) dfs0(v),siz[u]+=siz[v],mul[u]=1ll*mul[u]*mul[v]%MOD; mul[u]=1ll*mul[u]*siz[u]%MOD; }
void dfs1(int u){
	for(int v:G[u]){
		for(int i=1,sum=0,p,q;i<=n;++i){
			p=1ll*sum*jc[siz[u]-siz[v]-1]%MOD;
			q=1ll*fmul[u]*siz[u]%MOD*mul[v]%MOD;
			f[v][i]=1ll*p*q%MOD;
			mod(sum+=1ll*f[u][i]*C(n-i-siz[v],siz[u]-siz[v]-1)%MOD);
		}
		dfs1(v);
	}
}

int main(){

	init(n=rd); for(int i=2;i<=n;++i) G[rd].pb(i);
	
	dfs0(1);
	for(int i=1;i<=n;++i) fmul[i]=qm(mul[i]);
	f[1][1]=1;
	dfs1(1);
	
	for(int i=1,p,q;i<=n;++i){
		p=1ll*f[i][i]*C(n-i,siz[i]-1)%MOD;
		q=1ll*jc[siz[i]]*fmul[i]%MOD;
		printf("%d ", 1ll*p*q%MOD);
	}

	return 0;
}

answer.code:24:27: error: ‘int fmul [5100]’ redeclared as different kind of entity
   24 | int n,mul[N],siz[N],fmul[N],f[N][N];
      |                           ^
In file included from /usr/include/c++/13/cmath:47,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:114,
                 from answer.code:1:
/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h:30:20: note: previous declaration ‘float fmul(double, double)’
   30 | __MATHCALL_NARROW (__MATHCALL_NAME (mul), __MATHCALL_REDIR_NAME (mul), 2);
      |                    ^~~~~~~~~~~~~~~
answer.code: In function ‘void dfs1(int)’:
answer.code:32:37: warning: pointer to a function used in arithmetic [-Wpointer-arith]
   32 |                         q=1ll*fmul[u]*siz[u]%MOD*mul[v]%MOD;
      |                                     ^
answer.code:32:30: error: invalid operands of types ‘long long int’ and ‘float(double, double) throw ()’ {aka ‘float(double, double)’} to binary ‘operator*’
   32 |                         q=1ll*fmul[u]*siz[u]%MOD*mul[v]%MOD;
      |                           ~~~^~~~~~~~
      |                           |         |
      |                           |         float(double, double) throw () {aka float(double, double)}
      |                           long long int
answer.code: In function ‘int main()’:
answer.code:45:37: warning: pointer to a function used in arithmetic [-Wpointer-arith]
   45 |         for(int i=1;i<=n;++i) fmul[i]=qm(mul[i]);
      |                                     ^
answer.code:45:38: error: assignment of read-only location ‘*(fmul + ((sizetype)i))’
   45 |         for(int i=1;i<=n;++i) fmul[i]=qm(mul[i]);
      |                               ~~~~~~~^~~~~~~~~~~
answer.code:51:40: warning: pointer to a function used in arithmetic [-Wpointer-arith]
   51 |                 q=1ll*jc[siz[i]]*fmul[i]%MOD;
      |                                        ^
answer.code:51:33: error: invalid operands of types ‘long long int’ and ‘float(double, double) throw ()’ {aka ‘float(double, double)’} to binary ‘operator*’
   51 |                 q=1ll*jc[siz[i]]*fmul[i]%MOD;
      |                   ~~~~~~~~~~~~~~^~~~~~~~
      |                      |                 |
      |                      long long int     float(double, double) throw () {aka float(double, double)}
answer.code:52:26: warning: format ‘%d’ expects argument of type ‘int’, but argument 2 has type ‘long long int’ [-Wformat=]
   52 |                 printf("%d ", 1ll*p*q%MOD);
      |                         ~^    ~~~~~~~~~~~
      |                          |           |
      |                          int         long long int
      |                         %lld