/*
Things to notice:
1. do not calculate useless values
2. do not use similar names
 
Things to check:
1. submit the correct file
2. time (it is log^2 or log)
3. memory
4. prove your naive thoughts 
5. long long
6. corner case like n=0,1,inf or n=m
7. check if there is a mistake in the ds or other tools you use
8. fileio in some oi-contest

9. module on time 
10. the number of a same divisor in a math problem
11. multi-information and queries for dp and ds problems
*/
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define pii pair<long long,long long>
#define mp make_pair
#define pb push_back
const int mod=998244353;
const int inf=0x3f3f3f3f;
const int INF=1e18;
int fpow(int x,int b)
{
	if(x==0) return 0;
	if(b==0) return 1;
	int res=1;
	while(b>0)
	{
		if(b&1)	res=1LL*res*x%mod;
		x=1LL*x*x%mod;
		b>>=1;
	}
	return res;
}
int fac[300005],ifac[300005];
int C(int x,int y)
{
	if(y>x) return 0;
	if(x==y||y==0) return 1;
	return 1LL*fac[x]*ifac[x-y]%mod*ifac[y]%mod;
}
void init(int x)
{
	fac[0]=fac[1]=1;
	for(int i=2;i<=x;i++) fac[i]=1LL*fac[i-1]*i%mod;
	ifac[x]=fpow(fac[x],mod-2);  // x should be less than mod!!!
	for(int i=x-1;i>=0;i--) ifac[i]=1LL*ifac[i+1]*(i+1)%mod;
}
int dp[100005][105],f[100005][105];
int n;
vector <int> g[100005];
int dep[100005],siz[100005];
int sum1[105],sum2[105];
const int D=100;
void dfs0(int u)
{
	siz[u]=1;
	if(!g[u].size())
	{
		for(int i=1;i<=dep[u]+1;i++) dp[u][i-1]=ifac[i];
		return;
	}
	g[u].insert(g[u].begin(),-1);
	
	for(int i=1;i<g[u].size();i++) dep[g[u][i]]=dep[u]+1,dfs0(g[u][i]),siz[u]+=siz[g[u][i]];
	for(int i=0;i<=g[u].size();i++) memset(f[i],0,sizeof(f[i]));
	f[0][0]=1;
	for(int i=1;i<g[u].size();i++) 
	{
		int v=g[u][i];
		for(int j=0;j<=dep[u]+1;j++) if(f[i-1][j]) for(int k=0;k<=dep[v]&&j+k<=dep[u]+1;k++) 
			f[i][j+k]=(f[i][j+k]+f[i-1][j]*dp[v][k])%mod;
	}
	for(int s=0;s<=dep[u]+1;s++) if(f[g[u].size()-1][s])
	{
		int x=f[g[u].size()-1][s];
		for(int c=0;s-1+c<=dep[u];c++) if(s-1+c>=0) dp[u][s-1+c]=(dp[u][s-1+c]+x*ifac[c])%mod;
	}
//	for(int j=0;j<=D;j++) cout<<dp[u][j]<<" ";
//	cout<<"\n";
}
void solve()
{
	init(100005);
	
	cin>>n;
	for(int i=2;i<=n;i++)
	{
		int x;
		cin>>x;
		g[x].pb(i);
	}
	
	dep[1]=0;
	dfs0(1);
	int ans=dp[1][0];
	cout<<ans*fac[n]%mod<<"\n";
}
signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	int _=1;
//	cin>>_;
	while(_--) solve();
	return 0;
}