Problem:
Score : 700 points

Problem Statement

We have a tree with N vertices. Vertex 1 is the root of the tree, and the parent of Vertex i (2 \leq i \leq N) is Vertex P_i.

To each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight.

Snuke has a favorite integer sequence, X_1, X_2, ..., X_N, so he wants to allocate colors and weights so that the following condition is satisfied for all v.

The total weight of the vertices with the same color as v among the vertices contained in the subtree whose root is v, is X_v.

Here, the subtree whose root is v is the tree consisting of Vertex v and all of its descendants.

Determine whether it is possible to allocate colors and weights in this way.

Constraints

1 \leq N \leq 1 000

1 \leq P_i \leq i - 1

0 \leq X_i \leq 5 000

Inputs

Input is given from Standard Input in the following format:

N
P_2 P_3 ... P_N
X_1 X_2 ... X_N

Outputs

If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3
1 1
4 3 2

Sample Output 1

POSSIBLE

For example, the following allocation satisfies the condition:

Set the color of Vertex 1 to white and its weight to 2.

Set the color of Vertex 2 to black and its weight to 3.

Set the color of Vertex 3 to white and its weight to 2.

There are also other possible allocations.

Sample Input 2

3
1 2
1 2 3

Sample Output 2

IMPOSSIBLE

If the same color is allocated to Vertex 2 and Vertex 3, Vertex 2 cannot be allocated a non-negative weight.

If different colors are allocated to Vertex 2 and 3, no matter which color is allocated to Vertex 1, it cannot be allocated a non-negative weight.

Thus, there exists no allocation of colors and weights that satisfies the condition.

Sample Input 3

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3

Sample Output 3

POSSIBLE

Sample Input 4

1

0

Sample Output 4

POSSIBLE

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet};

mod util {
    use std::io::stdin;
    use std::str::FromStr;
    use std::fmt::Debug;

    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn get<T: FromStr>() -> T
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    }

    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }
}

fn cost(i: usize, p: &Vec<usize>, x: &Vec<usize>) -> Option<(usize, usize)> {
    let childs: Vec<_> = (0..p.len())
        .filter(|&k| p[k] == i + 1)
        .map(|x| x + 1)
        .collect();
    if childs.is_empty() {
        return Some((x[i], 0));
    }

    let costs: Vec<_> = childs.iter().map(|&c| cost(c, p, x)).collect();
    if costs.iter().any(|c| c.is_none()) {
        None
    } else {
        let costs: Vec<_> = costs.iter().map(|o| o.unwrap()).collect();
        let total = costs.iter().map(|t| t.0 + t.1).sum::<usize>();

        let mut memo: HashSet<usize> = HashSet::new();
        memo.insert(0);
        for &(a, b) in &costs {
            let mut next = HashSet::new();
            for c in &memo {
                if c + a <= x[i] {
                    next.insert(c + a);
                }

                if c + b <= x[i] {
                    next.insert(c + b);
                }
            }
            memo = next;
        }

        memo.iter().max().map(|c| (x[i], total - c))
    }

}

fn main() {
    let n: usize = util::get();
    let p: Vec<usize> = util::gets();
    let x: Vec<usize> = util::gets();

    if cost(0, &p, &x).is_some() {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE");
    }
}