#include<bits/stdc++.h>

#define ll long long
#define pi pair<int,int>
#define vi vector<int>
#define cpy(x,y,s) memcpy(x,y,sizeof(x[0])*(s))
#define mset(x,v,s) memset(x,v,sizeof(x[0])*(s))
#define all(x) begin(x),end(x)
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ary array
#define eb emplace_back
#define IL inline

using namespace std;

#define mod 998244353
#define N 500005

IL int pls(int x,int y){return (x+y>=mod?x+y-mod:x+y);}
IL int sub(int x,int y){return (x-y<0?x-y+mod:x-y);}
IL void Add(int &x,int y){x=pls(x,y);}
IL void Dec(int &x,int y){x=sub(x,y);}
IL int mul(int x,int y){return x*1ll*y%mod;}
IL int qp(int x,int y=mod-2){int ans=1;while(y){if(y&1)ans=mul(ans,x);x=mul(x,x);y>>=1;}return ans;}

int fac[N],ifac[N],inv[N];
IL int C(int x,int y){return mul(fac[x],mul(ifac[y],ifac[x-y]));}
IL void init(){
    fac[0]=ifac[0]=inv[0]=inv[1]=1;
    for(int i=1;i<N;i++)fac[i]=mul(fac[i-1],i);
    ifac[N-1]=qp(fac[N-1]);
    for(int i=N-2;i>=1;i--)ifac[i]=mul(ifac[i+1],i+1);
    for(int i=2;i<N;i++)inv[i]=mul((mod-mod/i),inv[mod%i]);
}

int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0' || ch>'9')f=(ch=='-'?-1:f),ch=getchar();
    while(ch>='0' && ch<='9')x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
    return x*f;
}
void write(int x){
    if(x<0)x=-x,putchar('-');
    if(x/10)write(x/10);
    putchar(x%10+'0');
}

int f[N][41],g[41],dep[N],siz[N];
vi e[N];

void dfs(int x){
    f[x][0]=1;siz[x]=0;
    for(auto v:e[x]){
        dep[v]=dep[x]+1;dfs(v);
        for(int i=0;i<=dep[x];i++){
            for(int j=0;j<=dep[x];j++){
                if(i+j>dep[x])break;
                //cerr<<x<<' '<<(mul(f[x][i],f[v][j]),C(i+j+siz[x]+siz[v],i+siz[x]))<<' '<<i<<' '<<j<<' '<<f[x][i]<<"**"<<endl;
                Add(g[i+j],mul(mul(f[x][i],f[v][j]),C(i+j+siz[x]+siz[v],i+siz[x])));
            }
        }
        for(int j=0;j<=dep[x];j++)f[x][j]=g[j],g[j]=0;
        siz[x]+=siz[v];
    }
    //cerr<<f[x][0]<<' '<<f[x][1]<<' '<<f[x][2]<<endl;
    for(int i=0;i<=dep[x];i++){
        for(int j=0;j<=dep[x];j++){
            if(i+j>dep[x])break;
            Add(g[i+j],mul(f[x][i],C(i+siz[x]+j,i+siz[x])));
        }
    }
    for(int j=1;j<=dep[x];j++)f[x][j-1]=g[j],g[j]=0;
    //cerr<<x<<' '<<f[x][0]<<' '<<f[x][1]<<' '<<f[x][2]<<endl;
    siz[x]++;g[0]=0;
}

int main(){
    #ifdef EAST_CLOUD
    freopen("a.in","r",stdin);
    //freopen("a.out","w",stdout);
    #endif

    int n=read();init();
    for(int i=2,p=0;i<=n;i++)p=read(),e[p].pb(i);
    dep[1]=1;dfs(1);
    write(f[1][0]);
    return 0;
}