#include <bits/stdc++.h>
using namespace std;
typedef signed long long ll;

#define _P(...) (void)printf(__VA_ARGS__)
#define FOR(x,to) for(x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define FORR2(x,y,arr) for(auto& [x,y]:arr)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
template<class T> bool chmax(T &a, const T &b) { if(a<b){a=b;return 1;}return 0;}
template<class T> bool chmin(T &a, const T &b) { if(a>b){a=b;return 1;}return 0;}
//-------------------------------------------------------

int N;
int P[5050];
vector<int> E[5050];
map<pair<int,int>,ll> dp[5050];
const ll mo=998244353;
void dfs(int cur) {
	map<pair<int,int>,ll> F;
	F[{0,1}]=1;
	FORR(e,E[cur]) {
		dfs(e);
		map<pair<int,int>,ll> T;
		FORR2(a,b,F) {
			FORR2(a2,b2,dp[e]) {
				(T[{max(a.first,a2.first),a.second+a2.second}]+=b*b2)%=mo;
			}
		}
		swap(F,T);
	}
	FORR2(a,b,F) {
		int i;
		FOR(i,a.second+1) (dp[cur][{a.first+i,a.second-i}]+=b)%=mo;
	}
	
}

void solve() {
	int i,j,k,l,r,x,y; string s;
	
	cin>>N;
	for(i=1;i<N;i++) {
		cin>>P[i];
		P[i]--;
		E[P[i]].push_back(i);
	}
	dfs(0);
	ll ret=0;
	FORR2(a,b,dp[0]) ret+=b;
	cout<<ret%mo<<endl;
}


int main(int argc,char** argv){
	string s;int i;
	if(argc==1) ios::sync_with_stdio(false), cin.tie(0);
	FOR(i,argc-1) s+=argv[i+1],s+='\n'; FOR(i,s.size()) ungetc(s[s.size()-1-i],stdin);
	cout.tie(0); solve(); return 0;
}