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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
// dbg {{{
#[allow(dead_code)]
mod dbg {
    use std::fmt::{Debug, Formatter};

    #[derive(Clone)]
    pub struct Tabular<'a, T: Debug>(pub &'a [Vec<T>]);

    impl<'a, T: Debug> Debug for Tabular<'a, T> {
        fn fmt(&self, f: &mut Formatter) -> std::fmt::Result {
            for i in 0..self.0.len() {
                writeln!(f, "{:2} | {:?}", i, &self.0[i])?;
            }
            Ok(())
        }
    }
}
// }}}

fn main() {
    input!(
        n: usize,
        p: [proconio::marker::Usize1; n - 1],
        a: [usize; n]
    );
    let mut g = vec![vec![]; n];
    for (i, x) in p.iter().enumerate().map(|(i, &x)| (i + 1, x)) {
        g[x].push(i);
    }
    let mut dp = vec![0; n];
    fn dfs(x: usize, dp: &mut [usize], g: &[Vec<usize>], a: &[usize]) {
        for &y in &g[x] {
            dfs(y, dp, g, a);
        }
        let mut table = vec![false; a[x] + 1];
        table[0] = true;
        for (w0, w1) in g[x].iter().copied().map(|y| (a[y], dp[y])) {
            for i in (0..=a[x]).rev() {
                for w in [w0, w1].iter() {
                    if i + w <= a[x] {
                        table[i + w] |= table[i];
                    }
                }
                if w0 != 0 && w1 != 0 {
                    table[i] = false;
                }
            }
        }
        if let Some(z) = (0..=a[x]).rfind(|&w| table[w]) {
            dp[x] = g[x].iter().map(|&y| a[y] + dp[y]).sum::<usize>() - z;
        } else {
            println!("IMPOSSIBLE");
            std::process::exit(0);
        }
    }
    dfs(0, &mut dp, &g, &a);
    println!("POSSIBLE");
}