#ifndef LOCAL
#define NDEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
namespace iefnah {
template <int MOD_> struct modnum {
static constexpr int MOD = MOD_;
static_assert(MOD_ > 0, "MOD must be positive");
private:
using ll = long long;
int v;
static int minv(int a, int m) {
a %= m;
assert(a);
return a == 1 ? 1 : int(m - ll(minv(m, a)) * ll(m) / a);
}
public:
modnum() : v(0) {}
modnum(ll v_) : v(int(v_ % MOD)) { if (v < 0) v += MOD; }
explicit operator int() const { return v; }
friend std::ostream& operator << (std::ostream& out, const modnum& n) { return out << int(n); }
friend std::istream& operator >> (std::istream& in, modnum& n) { ll v_; in >> v_; n = modnum(v_); return in; }
friend bool operator == (const modnum& a, const modnum& b) { return a.v == b.v; }
friend bool operator != (const modnum& a, const modnum& b) { return a.v != b.v; }
modnum inv() const {
modnum res;
res.v = minv(v, MOD);
return res;
}
friend modnum inv(const modnum& m) { return m.inv(); }
modnum neg() const {
modnum res;
res.v = v ? MOD-v : 0;
return res;
}
friend modnum neg(const modnum& m) { return m.neg(); }
modnum operator- () const {
return neg();
}
modnum operator+ () const {
return modnum(*this);
}
modnum& operator ++ () {
v ++;
if (v == MOD) v = 0;
return *this;
}
modnum& operator -- () {
if (v == 0) v = MOD;
v --;
return *this;
}
modnum& operator += (const modnum& o) {
v += o.v;
if (v >= MOD) v -= MOD;
return *this;
}
modnum& operator -= (const modnum& o) {
v -= o.v;
if (v < 0) v += MOD;
return *this;
}
modnum& operator *= (const modnum& o) {
v = int(ll(v) * ll(o.v) % MOD);
return *this;
}
modnum& operator /= (const modnum& o) {
return *this *= o.inv();
}
friend modnum operator ++ (modnum& a, int) { modnum r = a; ++a; return r; }
friend modnum operator -- (modnum& a, int) { modnum r = a; --a; return r; }
friend modnum operator + (const modnum& a, const modnum& b) { return modnum(a) += b; }
friend modnum operator - (const modnum& a, const modnum& b) { return modnum(a) -= b; }
friend modnum operator * (const modnum& a, const modnum& b) { return modnum(a) *= b; }
friend modnum operator / (const modnum& a, const modnum& b) { return modnum(a) /= b; }
};
template <typename T> T pow(T a, long long b) {
assert(b >= 0);
T r = 1; while (b) { if (b & 1) r *= a; b >>= 1; a *= a; } return r;
}
using num = modnum<int(1e9)+7>;
class RestrictedLeaves {
public:
int count(vector<int> parent) {
int N = int(parent.size());
vector<vector<int>> adj(N);
for (int i = 1; i < N; i++) {
assert(parent[i] < i);
adj[parent[i]].push_back(i);
}
vector<array<num, 8>> dp(N); // left/right/self
for (int cur = N-1; cur >= 0; cur--) {
dp[cur].fill(0);
if (adj[cur].empty()) {
dp[cur][0] = dp[cur][7] = 1;
continue;
}
sort(adj[cur].begin(), adj[cur].end());
for (int m = 0; m < 8; m++) {
bool isFirst = true;
array<num, 2> tmp = {1, 0};
for (int nxt : adj[cur]) {
array<num, 2> ntmp = {};
for (int t = 0; t < 8; t++) {
if ((m & 4) && (t & 4)) continue;
if (isFirst && (m & 1) != (t & 1)) continue;
for (int a = 0; a < 2; a++) {
if (a && (t & 1)) continue;
ntmp[bool(t & 2)] += tmp[a] * dp[nxt][t];
}
}
tmp = std::move(ntmp);
isFirst = false;
}
dp[cur][m] = tmp[bool(m & 2)];
}
}
num ans = 0;
for (int m = 0; m < 8; m++) {
if (bool(m & 1) && bool(m & 2)) continue;
ans += dp[0][m];
}
return int(ans);
}
};
} // namespace iefnah
using iefnah::RestrictedLeaves;