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: Wrong Answer)

use io::*;

fn main() {
    let input = read_string();
    let mut sc = Scanner::new(&input);
    let n: usize = sc.next();
    if n == 1 {
        println!("POSSIBLE");
        return;
    }
    let mut nodes: Vec<Vec<usize>> = vec![Vec::new();n];
    for i in 1..n {
        let p: usize = sc.next();
        nodes[p-1].push(i);
    }
    let xs = sc.next_vec::<usize>(n);
    let mut q: Vec<[usize;3]> = vec![[xs[0],usize::max_value(),0]];
    loop {
        if q.is_empty() {
            break;
        }
        let s = q.pop().unwrap();
        let mut a = s[0];
        let mut b = s[1];
        let i = s[2];
        for v in nodes[i].clone() {
            if xs[v] > b {
                println!("IMPOSSIBLE");
                return;
            } else if xs[v] <= a {
                a -= xs[v];
                q.push([xs[v],b,v]);
            } else {
                b -= xs[v];
                q.push([a,xs[v],v]);
            }
        }
    }
    println!("POSSIBLE");
}

pub mod io {
    use std;
    use std::str::FromStr;

    pub struct Scanner<'a> {
        iter: std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new(s: &'a str) -> Scanner<'a> {
            Scanner {
                iter: s.split_whitespace(),
            }
        }

        pub fn next<T: FromStr>(&mut self) -> T {
            let s = self.iter.next().unwrap();
            if let Ok(v) = s.parse::<T>() {
                v
            } else {
                panic!("Parse error")
            }
        }

        pub fn next_vec_len<T: FromStr>(&mut self) -> Vec<T> {
            let n: usize = self.next();
            self.next_vec(n)
        }

        pub fn next_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.next()).collect()
        }

        pub fn next_mat<T: FromStr>(&mut self, w: usize, h: usize) -> Vec<Vec<T>> {
            (0..h).map(|_| self.next_vec(w)).collect()
        }

        pub fn next_vec_char(&mut self) -> Vec<char> {
            self.next::<String>().chars().collect()
        }

        pub fn next_mat_char(&mut self, n: usize) -> Vec<Vec<char>> {
            (0..n).map(|_| self.next_vec_char()).collect()
        }
    }

    pub fn read_string() -> String {
        use std::io::Read;

        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    }

    pub fn read_line() -> String {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned()
    }
}