// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 1_000_000_007;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

    pub trait Modulo {
        fn modulo() -> u32;
    }

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

    pub struct ModularInteger<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModularInteger<T> {
        fn clone(&self) -> Self {
            ModularInteger::new_unchecked(self.0)
        }
    }

    impl<T> Copy for ModularInteger<T> {}

    impl<T: Modulo> Add for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn add(self, rhs: Self) -> Self::Output {
            let mut d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModularInteger::new_unchecked(d)
        }
    }

    impl<T: Modulo> AddAssign for ModularInteger<T> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<T: Modulo> Sub for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn sub(self, rhs: Self) -> Self::Output {
            let mut d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModularInteger::new_unchecked(d)
        }
    }

    impl<T: Modulo> SubAssign for ModularInteger<T> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<T: Modulo> Mul for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn mul(self, rhs: Self) -> Self::Output {
            let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
            ModularInteger::new_unchecked(v as u32)
        }
    }

    impl<T: Modulo> MulAssign for ModularInteger<T> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<T: Modulo> Neg for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn neg(self) -> Self::Output {
            if self.0 == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(T::modulo() - self.0)
            }
        }
    }

    impl<T> std::fmt::Display for ModularInteger<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl<T: Modulo> std::str::FromStr for ModularInteger<T> {
        type Err = std::num::ParseIntError;
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            let val = s.parse::<u32>()?;
            Ok(ModularInteger::new(val))
        }
    }

    impl<T: Modulo> From<usize> for ModularInteger<T> {
        fn from(val: usize) -> ModularInteger<T> {
            ModularInteger::new_unchecked((val % T::modulo() as usize) as u32)
        }
    }

    impl<T: Modulo> From<i64> for ModularInteger<T> {
        fn from(val: i64) -> ModularInteger<T> {
            let m = T::modulo() as i64;
            ModularInteger::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModularInteger<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModularInteger(d, PhantomData)
        }
        pub fn zero() -> Self {
            ModularInteger::new_unchecked(0)
        }
        pub fn one() -> Self {
            ModularInteger::new_unchecked(1)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModularInteger<T> {
        pub fn new(d: u32) -> Self {
            ModularInteger::new_unchecked(d % T::modulo())
        }
        pub fn pow(&self, mut n: u64) -> Self {
            let mut t = Self::one();
            let mut s = *self;
            while n > 0 {
                if n & 1 == 1 {
                    t *= s;
                }
                s *= s;
                n >>= 1;
            }
            t
        }
        pub fn inv(&self) -> Self {
            assert!(self.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }

    #[allow(dead_code)]
    pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 {
        let mut t = 1 % m;
        let mut s = r % m;
        while n > 0 {
            if n & 1 == 1 {
                t = t * s % m;
            }
            s = s * s % m;
            n >>= 1;
        }
        t
    }
}
// ---------- end ModInt ----------

use proconio::*;
use std::collections::*;

use modint::*;
type ModInt = ModularInteger<Mod>;

fn run() {
    input! {
        n: usize,
        p: [usize; n],
    }
    let mut child = vec![vec![]; n + 1];
    for (i, p) in p.into_iter().enumerate() {
        child[p].push(i + 1);
    }
    let mut dp: Vec<Option<VecDeque<ModInt>>> = vec![None; n + 1];
    let inv2 = ModInt::new(2).inv();
    for (i, child) in child.iter().enumerate().rev() {
        let mut deq = vec![VecDeque::new(); 2];
        for &u in child.iter() {
            deq.push(dp[u].take().unwrap());
        }
        deq.sort_by_key(|d| d.len());
        let mut res = deq.pop().unwrap();
        for i in 0..deq.last().unwrap().len() {
            let mut dp = (ModInt::zero(), ModInt::zero(), ModInt::zero());
            dp.1 = *res.get(i).unwrap();
            dp.0 = ModInt::one() - dp.1;
            for deq in deq.iter().rev() {
                if let Some(&v) = deq.get(i) {
                    dp.2 += dp.1 * v;
                    dp.1 = dp.1 * (ModInt::one() - v) + dp.0 * v;
                    dp.0 *= ModInt::one() - v;
                } else {
                    break;
                }
            }
            *res.get_mut(i).unwrap() = dp.1;
        }
        res.push_front(inv2);
        dp[i] = Some(res);
    }
    let ans = ModInt::new(2).pow((n + 1) as u64) * dp[0].take().unwrap().into_iter().fold(ModInt::zero(), |s, a| s + a);
    println!("{}", ans);
}

fn main() {
    run();
}


Measured memory_bytes: 31588