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)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn push(ncandidate: &mut Vec<i32>, a: i32, b: i32) {
    if 5000 < a {
        return;
    }
    ncandidate[a as usize] = std::cmp::min(ncandidate[a as usize], b);
}

fn main() {
    let n: usize = read();
    let mut ps = vec![0 as usize; n];
    let mut childs = vec![vec![]; n];
    let mut xs = vec![0 as i32; n];
    for i in 1..n {
        ps[i] = read();
        ps[i] -= 1;
        childs[ps[i]].push(i);
    }
    for i in 0..n {
        xs[i] = read();
    }
    let mut min_value = vec![1 << 30; n];
    for i in (0..n).rev() {
        if childs[i].len() == 0 {
            min_value[i] = 0;
            continue;
        }
        let mut candidate = vec![1 << 30; 5001];
        candidate[0] = 0;
        for &c in childs[i].iter() {
            let mut ncandidate = vec![1 << 30; 5001];
            for w in 0..5001 {
                if candidate[w as usize] == 1 << 30 {
                    continue;
                }
                push(
                    &mut ncandidate,
                    w + xs[c],
                    candidate[w as usize] + min_value[c],
                );
                push(
                    &mut ncandidate,
                    w + min_value[c],
                    candidate[w as usize] + xs[c],
                );
                push(
                    &mut ncandidate,
                    candidate[w as usize] + xs[c],
                    w + min_value[c],
                );
                push(
                    &mut ncandidate,
                    candidate[w as usize] + min_value[c],
                    w + xs[c],
                );
            }
            candidate = ncandidate;
        }
        for w in 0..5001 {
            if candidate[w] == 1 << 30 {
                continue;
            }
            if w as i32 <= xs[i] {
                min_value[i] = std::cmp::min(min_value[i], candidate[w]);
            }
            if candidate[w] <= xs[i] {
                min_value[i] = std::cmp::min(min_value[i], w as i32);
            }
        }
    }
    if min_value[0] != 1 << 30 {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE");
    }
}