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

using ll=long long;

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using P=pair<int,int>;
using vi=vc<int>;
using uint=unsigned int;
const uint mod=998244353;
struct mint{
	uint v;
	mint(ll vv=0){s(vv%mod+mod);}
	mint& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	mint operator-()const{return mint()-*this;}
	mint& operator+=(const mint&r){return s(v+r.v);}
	mint&operator-=(const mint&r){return s(v+mod-r.v);}
	mint&operator*=(const mint&r){v=(unsigned ll)v*r.v%mod;return *this;}
	mint&operator/=(const mint&r){return *this*=r.inv();}
	mint operator+(const mint&r)const{return mint(*this)+=r;}
	mint operator-(const mint&r)const{return mint(*this)-=r;}
	mint operator*(const mint&r)const{return mint(*this)*=r;}
	mint operator/(const mint&r)const{return mint(*this)/=r;}
	mint pow(ll n)const{
		if(n<0)return inv().pow(-n);
		mint res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	mint inv()const{return pow(mod-2);}
};


void solve(){
	int n;
	cin>>n;
	vc<vc<int>> vec(n);
	for(int i=1;i<n;i++){
		int p;
		cin>>p;
		vec[p-1].pb(i);
	}
	vc<mint> finv(n+1),fac(n+1);
	finv[0]=fac[0]=1;
	for(int i=1;i<=n;i++){
		fac[i]=fac[i-1]*i;
		finv[i]=finv[i-1]/i;
	}
	vc<vc<mint>> dp(n);
	auto dfs=[&](int v,int d,auto self)->void{
		dp[v].pb(1);
		for(int i=0;i<vec[v].size();i++){
			int to=vec[v][i];
			self(to,d+1,self);
			vc<mint> nxt(d+2);
			for(int j=0;j<dp[v].size();j++){
				for(int k=0;k<dp[to].size();k++){
					if(j+k<=d+1){
						nxt[j+k]+=dp[v][j]*dp[to][k];
					}
				}
			}
			dp[v]=nxt;
		}
		vc<mint> nxt(d+1);
		for(int i=0;i<=d+1;i++){
			for(int j=0;j<dp[v].size();j++){
				if(i+j>=1&&i+j<=d+1){
					nxt[i+j-1]+=dp[v][j]*finv[i];
				}
			}
		}
		dp[v]=nxt;
	};
	dfs(0,0,dfs);
	cout<<(dp[0][0]*fac[n]).v<<endl;
}
int main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	int T=1;
	while(T--) solve();
}