// what is matter? never mind. 
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2") 
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
#define int long long
#define ull unsigned long long
using namespace std;
inline int read()
{
    char c=getchar();int x=0;bool f=0;
    for(;!isdigit(c);c=getchar())f^=!(c^45);
    for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
    if(f)x=-x;return x;
}

#define mod 998244353
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,int b){return a.x==b;}
	friend bool operator !=(modint a,int b){return a.x!=b;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define maxn 100005
#define inf 0x3f3f3f3f
#define poly vector<modint>

int n,fa[maxn],dep[maxn];
vi e[maxn];
poly operator *(poly a,poly b){
	if(!a.size()||!b.size())return {};
	if(1){
		poly c(a.size()+b.size()-1,0);
		for(int i=0;i<a.size();++i)for(int j=0;j<b.size();++j)c[i+j]+=a[i]*b[j];
		return c; 
	}
}
poly f[maxn];

poly gen(int n){
	poly f(n+1);
	For(i,0,n) f[i]=ifac[i];
	return f;
}
poly divx(poly f){
	int n=f.size();
	For(i,0,n-2) f[i]=f[i+1]; f.pop_back(); return f;
}

signed main()
{
	n=read(); initC(n+5);
	For(i,2,n)fa[i]=read(),e[fa[i]].pb(i);
	For(i,1,n)dep[i]=dep[fa[i]]+1,f[i]={1};
	Rep(i,n,1){
		f[i]=f[i]*gen(dep[i]);
		if(f[i].size()>dep[i]+1) f[i].resize(dep[i]+1);
		f[i]=divx(f[i]);
		
		f[fa[i]]=f[fa[i]]*f[i];
		if(f[fa[i]].size()>dep[fa[i]]+1) f[fa[i]].resize(dep[fa[i]]+1);
	}
	modint res=f[1][0]*fac[n];
	cout<<res.x;
	return 0;
}
/*
1 1 1 2 6 19 61 200 670 
1 0 0 1 4 13 42
*/