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::cmp;
use std::collections::BTreeSet;

const INF: usize = 1e16 as usize;

fn main() {
    let sc = std::io::stdin();
    let mut sc = Scanner { reader: sc.lock() };
    let n: usize = sc.read();
    let p: Vec<usize> = sc.read_vec(n - 1);
    let x: Vec<usize> = sc.read_vec(n);

    let mut graph = vec![vec![]; n];
    for i in 1..n {
        let parent = p[i - 1] - 1;
        graph[i].push(parent);
        graph[parent].push(i);
    }

    if dfs(0, 0, &graph, &x) < INF {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE");
    }
}

fn dfs(v: usize, p: usize, tree: &Vec<Vec<usize>>, x: &Vec<usize>) -> usize {
    if tree[v].len() == 1 && v != 0 {
        return 0;
    }

    let mut set: BTreeSet<(usize, usize)> = BTreeSet::new();
    set.insert((0, 0));
    for &next in tree[v].iter() {
        if next != p {
            let mut next_set = BTreeSet::new();
            let black = x[next];
            let white = dfs(next, v, tree, x);
            for &(b, w) in set.iter() {
                next_set.insert((b + black, w + white));
                next_set.insert((w + black, b + white));
            }
            set = next_set;
        }
    }

    let min1 = set
        .iter()
        .filter(|&&(_, y)| y <= x[v])
        .map(|&(x, _)| x)
        .min()
        .unwrap_or(INF);
    let min2 = set
        .iter()
        .filter(|&&(y, _)| y <= x[v])
        .map(|&(_, y)| y)
        .min()
        .unwrap_or(INF);
    cmp::min(min1, min2)
}

pub struct Scanner<R> {
    reader: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn read_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}