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)

pub fn read1<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
    let s = read1::<String>();
    s.split(delimiter).map(|e| e.parse().ok().unwrap()).collect::<Vec<T>>()
}

fn depth(pi: usize, p: &Vec<usize>) -> usize {
    if pi == 1 {
        return 1;
    }
    depth(p[pi-2], p) + 1
}

const INF: usize = 1000000;

fn main() {
    let n = read1::<usize>();
    if n == 1 {
        let _p = read1::<String>();
        let _x = read1::<String>();
        println!("POSSIBLE");
        return;
    }
    let p = readn::<usize>(" ");
    let x = readn::<usize>(" ");

    let mut c = vec![Vec::new(); n];
    for i in 0..n-1 {
        c[p[i]-1].push(i+1);
    }

    let mut d = Vec::with_capacity(n);
    d.push((0, 0));
    for i in 0..n-1 {
        d.push((depth(p[i], &p), i+1));
    }
    d.sort_by(|a, b| (b.0).cmp(&(a.0)));
    
    let mut dp = vec![INF; n];
    for i in 0..n {
        let v = d[i].1;
        if c[v].len() == 0 {
            dp[v] = 0;
        } else {
            let c_num = c[v].len();
            let mut x_max = 0;
            let mut x_min = 0;
            let mut x_delta = Vec::new();
            for j in 0..c_num {
                if dp[c[v][j]] < x[c[v][j]] {
                    x_min += dp[c[v][j]];
                    x_max += x[c[v][j]];
                    x_delta.push(x[c[v][j]] - dp[c[v][j]]);
                } else {
                    x_min += x[c[v][j]];
                    x_max += dp[c[v][j]];
                    x_delta.push(dp[c[v][j]] - x[c[v][j]]);
                }
            }
            if x_min > x[v] {
                println!("IMPOSSIBLE");
                return;
            }
            let rest = x[v] - x_min;
            let mut dp2 = vec![vec![x_max; rest+1]; c_num+1];

            for y in 0..c_num {
                for x in 0..rest {
                    dp2[y+1][x+1] = std::cmp::min(dp2[y][x+1], dp2[y+1][x]);
                    if x_delta[y] <= x + 1 {
                        dp2[y+1][x+1] = std::cmp::min(dp2[y+1][x+1], dp2[y][x+1-x_delta[y]] - x_delta[y]);
                    }
                }
            }
            dp[v] = dp2[c_num][rest];
        }
    }

    println!("POSSIBLE");
}