// need
#include <iostream>
#include <algorithm>

// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <complex>
//#include <deque>
#include <valarray>
#include <unordered_map>
#include <array>

// stream
//#include <istream>
//#include <sstream>
//#include <ostream>
#include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
//#include <chrono>
#include <random>
#include <numeric>

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w=0; w<n; ++w){MACRO_VEC_ROW_Scan(w, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& r:c)for(auto& w:r)std::cin>>w;

// output
#define OUT(dist) std::cout<<(dist);
#define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist);
#define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist);
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(dist) {std::cerr << #dist << "\t:" << (dist) << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t:";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}

// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(w, a, n) for(int w=(a);w<(n);++w)
#define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w)
#define REP(w, n) for(int w=0;w<int(n);++w)
#define RREP(w, n) for(int w=int(n)-1;w>=0;--w)
#define FORLL(w, a, n) for(ll w=ll(a);w<ll(n);++w)
#define RFORLL(w, a, n) for(ll w=ll(n)-1;w>=ll(a);--w)
#define REPLL(w, n) for(ll w=0;w<ll(n);++w)
#define RREPLL(w, n) for(ll w=ll(n)-1;w>=0;--w)
#define IN(a, x, b) (a<=x && x<b)
template<class T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
#define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;}
//void CHECKTIME(std::function<void()> f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start)).count(); std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n"; }

// test
template<class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
	return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}

// type/const
#define int ll
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                          // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-10;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

template<class T, size_t N> void FILL(T(&a)[N], const T& val) { for (auto& x : a) x = val; }
template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T& val) { for (auto& b : a) FILL(b, val); }
template<class T> void FILL(std::vector<T>& a, const T& val) { for (auto& x : a) x = val; }
template<class ARY, class T> void FILL(std::vector<std::vector<ARY>>& a, const T& val) { for (auto& b : a) FILL(b, val); }

// ------------>8------------------------------------->8------------

ll powMod(ll n, ll p, ll mod) {
	ll res = 1;
	while (p) {
		if (p & 1) (res *= n) %= mod;
		(n *= n) %= mod;
		p >>= 1;
	}
	return res;
}

using S = std::array<int, 3>;
std::deque<S> dp[200005];
// dp[v][t][x] := 頂点vにt秒後x個玉がある場合の数

void push(S& l, const S r) {
	l = S{ l[0] * r[0] % MOD,
		  (l[0] * r[1] + l[1] * r[0]) % MOD,
		  (l[0] * r[2] + l[1] * (r[1] + r[2]) + l[2] * (r[0] + r[1] + r[2])) % MOD };
}

namespace TRUEANS {
	int calc(std::vector<std::vector<int>> g) {
		int n = g.size();
		int res = 0;
		REP(i, 1 << n) {
			std::vector<int> dp(n);
			REP(j, n) dp[j] = !!(i & 1 << j);

			bool f = false;
			std::function<void(int, int)> dfs = [&](int v, int par) {
				if (v != 0 && dp[v]) {
					f = true;
					dp[par] += dp[v];
					dp[v] = 0;
				}
				for (auto& to : g[v]) if (to != par) {
					dfs(to, v);
				}
				dp[v] = dp[v] == 1;
			};
			while (true) {
				f = false;
				res += dp[0];
				dp[0] = 0;
				dfs(0, -1);
				if (f) continue;
				break;
			}
		}
		return res % MOD;
	}
}

signed main() {
	INIT;

	VAR(int, n);
	VEC(int, p, n);

	//std::mt19937 mt(0);
	//while (true) {
	//	std::vector<int> p(n);
	//	REP(i, n) {
	//		std::uniform_int_distribution<> rand(/* min */0, /* max */i);
	//		p[i] = rand(mt);
	//	}
	//	dp[0].resize(0);

		std::vector<std::vector<int>> g(n + 1);
		REP(i, n) {
			g[p[i]].emplace_back(i + 1);
			g[i + 1].emplace_back(p[i]);
		}

		//int trueans = TRUEANS::calc(g);

		std::vector<int> depth(n + 1, 0);
		{
			std::function<void(int, int)> dfs = [&](int v, int par) {
				for (auto& to : g[v]) if (to != par) {
					depth[to] = depth[v] + 1;
					dfs(to, v);
				}
			};
			dfs(0, -1);
		}
		std::vector<int> cnt(n + 1, 0);
		REP(i, n + 1) ++cnt[depth[i]];

		std::function<void(int, int)> dfs = [&](int v, int par) {
			dp[v].push_back(S{ 1, 1, 0 });
			int ma = 0, mai = -1;
			REP(ti, g[v].size()) if (g[v][ti] != par) {
				dfs(g[v][ti], v);

				if (ma < dp[g[v][ti]].size()) {
					ma = dp[g[v][ti]].size();
					mai = ti;
				}
			}
			if (mai == -1) return;
			dp[g[v][mai]].push_front(dp[v].front()); dp[v].pop_front();
			std::swap(dp[v], dp[g[v][mai]]);

			ma = 0;
			REP(ti, g[v].size()) if (ti != mai && g[v][ti] != par) {
				CHMAX(ma, (int)dp[g[v][ti]].size());
				auto it = dp[v].begin();
				++it;
				while (!dp[g[v][ti]].empty()) {
					push(*it, dp[g[v][ti]].front()); dp[g[v][ti]].pop_front();
					++it;
				}
			}
			auto it = dp[v].begin();
			REP(_, ma + 1) {
				(*it)[0] += (*it)[2];
				(*it)[2] = 0;
				++it;
			}
		};

		dfs(0, -1);

		//SHOWVECTOR2(dp[0]);

		int ans = 0;
		int pos = 0;
		for (auto& x : dp[0]) {
			(ans += powMod(2, n + 1 - cnt[pos], MOD) * x[1]) %= MOD;
			++pos;
		}
		OUT(ans)ENDL;
/*
		if (trueans != ans) {
			SHOW(n);
			SHOWVECTOR(p);
			SHOW(trueans);
			SHOW(ans);
			VAR(int, x);
		}
	}*/

	return 0;
}

Measured memory_bytes: 186368