#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
// typedef __int128 ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define FR first
#define SE second
#define MP make_pair
#define PB push_back
#define vc vector
#define db double
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bin(x) (1ll<<(x))
#define fo(i,l,r) for(int i=(l),I=(r);i<=I;i++)
#define fd(i,r,l) for(int i=(r),I=(l);i>=I;i--)
#define mem(x,val) memset(x,val,sizeof x)
#define Swap(a,b,n) for(int I=0;I<=n;I++) swap(a[I],b[I])
#define PC __builtin_popcountll
#ifdef DEBUG
	#define debug(A,args...) fprintf(stderr,A,##args)
#else
	#define debug(A,args...) printf("")
#endif
#define deb debug("line %d\n",__LINE__)
namespace mine
{
	ll qread()
	{
		ll ans=0,f=1;char c=getchar();
		while(c<'0' or c>'9') {if(c=='-')f=-1;c=getchar();}
		while('0'<=c and c<='9') ans=ans*10+c-'0',c=getchar();
		return ans*f;
	}
	void write(ll num){if(num<0) putchar('-'),num=-num;if(num>=10) write(num/10);putchar('0'+num%10);}
	void write1(ll num){write(num);putchar(' ');}
	void write2(ll num){write(num);putchar('\n');}
	template<typename T>inline bool chmax(T&a,const T&b){return a<b?a=b,1:0;}
	template<typename T>inline bool chmin(T&a,const T&b){return a>b?a=b,1:0;}
	ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
	bool IN(ll x,ll l,ll r){return l<=x and x<=r;}
	void GG(){puts("-1");exit(0);}
	
	const db eps=1e-8;
	const int INF=0x3f3f3f3f;
	const int MOD=1e9+7;
	int mm(const int x){return x>=MOD?x-MOD:x;}
	template<typename T> void add(T &x,const int &y){x=(x+y>=MOD?x+y-MOD:x+y);}
	ll qpower(ll x,ll e,int mod=MOD){ll ans=1;while(e){if(e&1)ans=ans*x%mod;x=x*x%mod;e>>=1;}return ans;}
	ll invm(ll x){return qpower(x,MOD-2);}
	const int MM=1e6+10;
	ll fac[MM],facinv[MM],Inv[MM];ll Comb(int n,int m){return n<0 or n<m?0:fac[n]*facinv[m]%MOD*facinv[n-m]%MOD;}
	void PRE()
	{
		fac[0]=1;fo(i,1,MM-1) fac[i]=fac[i-1]*i%MOD;
		facinv[MM-1]=invm(fac[MM-1]);fd(i,MM-1,1) facinv[i-1]=facinv[i]*i%MOD;
		Inv[1]=1;fo(i,2,MM-1) Inv[i]=(MOD-MOD/i)*Inv[MOD%i]%MOD;
	}
	const int N=1e6+10;
	//------------------FIXED------------------
	vc<int> son[N];int mxlen[N],mx2[N],mxson[N];
	int real[2][N+N],cur=0;
	int *dp[N],*cc[N];
	void pre(int x)
	{
		for(auto y:son[x]) {pre(y);if(chmax(mxlen[x],mxlen[y]+1)) mxson[x]=y;}
		for(auto y:son[x]) if(mxson[x]!=y) chmax(mx2[x],mxlen[y]+1);
	}
	void solve(int x)
	{
		dp[x][0]=1,cc[x][0]=2;vc<int> f(mx2[x]+1),g(mx2[x]+1);
		if(mxson[x])
		{
			int y=mxson[x];
			dp[y]=dp[x]+1,cc[y]=cc[x]+1;solve(y);
			fo(i,0,mx2[x]-1) f[i+1]=dp[y][i],g[i+1]=(cc[y][i]+MOD-dp[y][i])*invm(dp[y][i])%MOD;
		}
		for(auto y:son[x]) if(y!=mxson[x])
		{
			dp[y]=real[0]+cur,cc[y]=real[1]+cur,cur+=mxlen[y]+1;
			solve(y);
			fo(i,0,mxlen[y])
				cc[x][i+1]=(ll)cc[x][i+1]*cc[y][i]%MOD,f[i+1]=(ll)f[i+1]*dp[y][i]%MOD,
				add(g[i+1],(cc[y][i]+MOD-dp[y][i])*invm(dp[y][i])%MOD );
		}
		fo(i,1,mx2[x]) dp[x][i]=mm(cc[x][i]+MOD-(ll)f[i]*g[i]%MOD);
	}
	void main()
	{
		int n=qread();fo(i,1,n) son[qread()].PB(i);pre(0);
		dp[0]=real[0]+cur,cc[0]=real[1]+cur,cur+=mxlen[0]+1;
		solve(0);
		int ans=0;fo(i,0,mxlen[0]) add(ans, mm(1+MOD-dp[0][i]*invm(cc[0][i])%MOD) );
		write(qpower(2,n+1)*ans%MOD);
	}
};//变量重名！
signed main()
{
	#ifdef DEBUG
	//freopen("a.in","r",stdin);
	freopen("z.txt","r",stdin);
	//freopen("a.out","w",stdout);
	#endif
	srand(time(0));
	mine::PRE();
	mine::main();
	debug("\n------------------------------------------\nTime: %.2lf s",1.0*clock()/CLOCKS_PER_SEC);
}

Measured memory_bytes: 102912