#ifndef __clang__
#pragma GCC optimize "-O3"
#pragma GCC target "tune=native"
#endif
#ifdef ONLINE_JUDGE
#define NDEBUG 1
#endif
#include <stdio.h>
#include <bits/stdc++.h>

#define FOR(i, n)     for(lli i = 0; i < (lli)(n); ++i)
#define FORU(i, j, k) for(lli i = (j); i <= (lli)(k); ++i)
#define FORD(i, j, k) for(lli i = (j); i >= (lli)(k); --i)

#define SQ(x) ((x)*(x))

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back

using namespace std;

template<typename... As>
struct tpl : public std::tuple<As...> {
  using std::tuple<As...>::tuple;
  tpl(){}
  tpl(std::tuple<As...> const& b) { std::tuple<As...>::operator=(b); }

  template<typename T = tuple<As...> >
  typename tuple_element<0, T>::type const&
  x() const { return get<0>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<0, T>::type&
  x() { return get<0>(*this); }

  template<typename T = tuple<As...> >
  typename tuple_element<1, T>::type const&
  y() const { return get<1>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<1, T>::type&
  y() { return get<1>(*this); }

  template<typename T = tuple<As...> >
  typename tuple_element<2, T>::type const&
  z() const { return get<2>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<2, T>::type&
  z() { return get<2>(*this); }

  template<typename T = tuple<As...> >
  typename tuple_element<3, T>::type const&
  w() const { return get<3>(*this); }
  template<typename T = tuple<As...> >
  typename tuple_element<3, T>::type&
  w() { return get<3>(*this); }
};

using lli   = long long int;
using llu   = long long unsigned;

using pii   = tpl<lli, lli>;
using piii  = tpl<lli, lli, lli>;
using piiii = tpl<lli, lli, lli, lli>;
using vi    = vector<lli>;
using vii   = vector<pii>;
using viii  = vector<piii>;
using vvi   = vector<vi>;
using vvii  = vector<vii>;
using vviii = vector<viii>;

template<class T>
using min_queue = priority_queue<T, vector<T>, greater<T> >;
template<class T>
using max_queue = priority_queue<T>;

template<size_t... I>
struct my_index_sequence {
  using type = my_index_sequence;
  static constexpr array<size_t, sizeof...(I)> value = { {I...} };
};

namespace my_index_sequence_detail {
  template<typename I, typename J> struct concat;
  template<size_t... I, size_t... J>
  struct concat<my_index_sequence<I...>, my_index_sequence<J...> > :
    my_index_sequence<I..., (sizeof...(I)+J)...> { };
  template<size_t N> struct make_index_sequence :
    concat<typename make_index_sequence<N/2>::type, typename make_index_sequence<N-N/2>::type>::type { };
  template <> struct make_index_sequence<0> : my_index_sequence<>{};
  template <> struct make_index_sequence<1> : my_index_sequence<0>{};
}

template<class... A>
using my_index_sequence_for = typename my_index_sequence_detail::make_index_sequence<sizeof...(A)>::type;

template<class T, size_t... I>
void print_tuple(ostream& s, T const& a, my_index_sequence<I...>){
  using swallow = int[];
  (void)swallow{0, (void(s << (I == 0? "" : ", ") << get<I>(a)), 0)...};
}

template<class T>
ostream& print_collection(ostream& s, T const& a);
template<class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a);
template<class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a);
template<class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a);

template<class T, size_t I>
ostream& operator<<(ostream& s, array<T, I> const& a) { return print_collection(s, a); }
template<class T>
ostream& operator<<(ostream& s, vector<T> const& a) { return print_collection(s, a); }
template<class T, class U>
ostream& operator<<(ostream& s, multimap<T, U> const& a) { return print_collection(s, a); }
template<class T>
ostream& operator<<(ostream& s, multiset<T> const& a) { return print_collection(s, a); }
template<class T, class U>
ostream& operator<<(ostream& s, map<T, U> const& a) { return print_collection(s, a); }
template<class T>
ostream& operator<<(ostream& s, set<T> const& a) { return print_collection(s, a); }

template<class T>
ostream& print_collection(ostream& s, T const& a){
  s << '[';
  for(auto it = begin(a); it != end(a); ++it){
    s << *it;
    if(it != prev(end(a))) s << " ";
  }
  return s << ']';
}

template<class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a){
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}

template<class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a){
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}

template<class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a){
  return s << "(" << get<0>(a) << ", " << get<1>(a) << ")";
}

//------------------------------------------------------------------------------

// --- BEGIN SNIPPET MODULAR ---

const lli MOD = 1e9+7;

inline lli fexp(lli a, lli b, lli m=MOD) {
  lli r = 1;
  while(b){
    if(b&1) r = (r*a)%m;
    a = (a*a)%m;
    b /= 2;
  }
  return r;
}

inline lli invmod(lli a, lli m=MOD) {
  return fexp(a, m-2, m);
}

pii egcd(lli a, lli b) {
  if(a%b==0) {
    return mt(0,1);
  }else{
    pii p = egcd(b,a%b);
    int u=p.x(), v=p.y();
    return mt(v, u-(a/b)*v);
  }
}

// solve x*a = b [mod m]
int solveInv(lli a, lli b, lli m) {
  if(b==0) return 0;
  pii p = egcd(a,m);
  lli g=__gcd(m,a);
  return (((b/g)*p.x())%m+m)%m;
}

// --- END SNIPPET MODULAR ---


const lli N = 3e5;
lli parent[N];

int main(){
  ios::sync_with_stdio(0); cin.tie(0);
  lli n; cin>>n;
  vvi G(n+1);
  parent[0] = -1;
  FORU(i,1,n) {
    lli p; cin>>p;
    G[p].pb(i);
    parent[i]=p;
  }

  map<lli,lli> M;

  function<void(int, vii& R, lli)> dfs = [&](int i, vii& R, lli d) {
    M[d]++;
    vvii V;
    int ix=-1;
    for(int j : G[i]) {
      V.emplace_back();
      dfs(j,V.back(),d+1);
      if(ix == -1 || V.back().size() > V[ix].size()) {
        ix = V.size()-1;
      }
    }
    if(ix == -1) {
      R.clear();
    }else{
      R = move(V[ix]);
      FOR(k,R.size()) {
        bool ok = 0;
        lli cnt_all = 1;
        lli cnt_0 = 1;
        FOR(j,V.size()) if(j != ix && k < (lli)V[j].size()) {
          ok=1;
          (cnt_all *= (V[j][V[j].size()-1-k].x()+V[j][V[j].size()-1-k].y())) %= MOD;
          (cnt_0 *= V[j][V[j].size()-1-k].y()) %= MOD;
        }
        { (cnt_all *= (R[R.size()-1-k].x()+R[R.size()-1-k].y())) %= MOD;
          (cnt_0 *= R[R.size()-1-k].y()) %= MOD;
        }
        if(!ok) break;
        lli v1=0;
        FOR(j,V.size()) if(j!=ix && k < (lli)V[j].size()) (v1 += cnt_0 * invmod(V[j][V[j].size()-1-k].y()) %MOD * V[j][V[j].size()-1-k].x() %MOD) %= MOD;
        (v1 += cnt_0 * invmod(R[R.size()-1-k].y()) %MOD * R[R.size()-1-k].x() %MOD) %= MOD;
        lli v0 = (cnt_all-v1+MOD)%MOD;
        R[R.size()-1-k] = mt(v1,v0);
      }
    }
    R.pb(mt(1,1));
  };

  vii R;
  dfs(0,R,0);

  lli ans = 0;
  FOR(i,R.size()) (ans += R[R.size()-1-i].x()*fexp(2,(n+1)-M[i])%MOD) %= MOD;
  cout << ans << endl;
  return 0;
}


Measured memory_bytes: 80500