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

using ll = long long;
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define rep2(i, l, r) for(ll i = l; i < r; ++i)

using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;

#define all(A) A.begin(), A.end()
#define elif else if
using pii = pair<ll, ll>;

bool chmin(auto &a, auto b) {return a > b ? a = b, 1 : 0;}
bool chmax(auto &a, auto b) {return a < b ? a = b, 1 : 0;}

struct IOSetup {
  IOSetup() {
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
} iosetup;

template<class T>
void print(vector<T> a) {
  for(auto x : a) cout << x << ' ';
  cout << endl;
}

void print(auto x) {cout << x << endl;}

template<class Head, class...Tail>
void print(Head &&head, Tail &&...tail) {
  cout << head << ' ';
  pritn(forward<Tail>(tail)...);
}

const ll mod=998244353;

ll powll(ll x,ll k){
  ll v=1;
  while(k){
    if(k&1)v=(v*x)%mod;
    x=(x*x)%mod;k>>=1;
  }
  return v;
}

int len=2e5;
vll fac,finv;

void precalc(){
  fac.assign(len,1),finv.assign(len,1);
  rep2(i,2,len)fac[i]=fac[i-1]*i%mod;
  finv[len-1]=powll(fac[len-1],mod-2);
  for(int i=len-2;i>=0;i--)finv[i]=finv[i+1]*(i+1)%mod;
}

ll binom(ll n,ll k){
  if(n<0||k<0||k>n)return 0;
  return fac[n]*finv[k]%mod*finv[n-k]%mod;
}

vector<vector<int>> G;
int N;
vector<vector<ll>> DP;
vector<ll> C,D;



void predfs(int n){
  C[n]=1;
  for(int v:G[n]){
    D[v]=D[n]+1;
    predfs(v);
    C[n]+=C[v];
  }
}

void dfs(int n){
  DP[n].assign(D[n]+1,0);
  vector<ll> g(D[n]+2,0);
  g[0]=1;
  ll sum=0;
  for(int v:G[n]){
    dfs(v);
    vector<ll> NDP(D[n]+2,0);
    for(int k=0;k<=D[n]+1;k++){
      for(int l=0;l<=k;l++){
        if(k-l>=int(DP[v].size()))continue;
        ll res=g[l]*DP[v][k-l]%mod*binom(sum+C[v]+k,sum+l)%mod;
        NDP[k]+=res;
        NDP[k]%=mod;
      }
    }
    sum+=C[v];
    swap(g,NDP);
  }
  vector<ll> NDP(D[n]+2,0);
  for(ll k=0;k<=D[n]+1;k++){
    for(ll l=0;l+k<=D[n]+1;l++){
      NDP[k+l]+=g[k]*binom(sum+k+l,l);
      NDP[k+l]%=mod;
    }
  }
  for(int i=0;i<=D[n];i++)DP[n][i]=NDP[i+1];
  // cout<<n<<" "<<DP[n][0]<<endl;
}

int main(){

  cin>>N;
  G.resize(N);
  precalc();
  for(int i=1;i<N;i++){
    int p;
    cin>>p;
    G[p-1].push_back(i);
  }
  C.assign(N,0);
  D.assign(N,0);
  DP.resize(N);
  predfs(0);
  // for(int i=0;i<N;i++)cout<<D[i]<<endl;
  dfs(0);
  cout<<DP[0][0]<<endl;

}