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: Runtime Error)

#![allow(unused_imports, unused_variables, dead_code)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

trait InputValue {
    fn parse(s: &str) -> Self;
}

fn read<T: InputValue>() -> T {
    let mut buf = String::new();
    let _ = stdin().read_line(&mut buf);
    T::parse(&buf.trim())
}

fn readnc<T: InputValue>() -> Vec<T> {
    let mut vec = vec![];
    let line: String = read();
    for token in line.split_whitespace() {
        vec.push(T::parse(token));
    }
    vec
}

fn readn<T: InputValue>(n: usize) -> Vec<T> {
    let mut vec = vec![];
    for _ in 0..n {
        vec.push(read());
    }
    vec
}

macro_rules! parse_single_value {
    ($($t:ty),*) => {
        $(
            impl InputValue for $t {
                fn parse(s: &str) -> $t { s.parse().unwrap() }
            }
        )*
	}
}
parse_single_value!(i32, i64, f32, f64, usize, String);

macro_rules! parse_tuple {
	($($t:ident),*) => {
		impl<$($t),*> InputValue for ($($t),*) where $($t: InputValue),* {
			fn parse(s: &str) -> ($($t),*) {
				let mut tokens = s.split_whitespace();
				let t = ($($t::parse(tokens.next().unwrap())),*);
				t
			}
		}
	}
}
parse_tuple!(A, B);
parse_tuple!(A, B, C);

// ===

trait Monoid {
    fn mul(&self, Self) -> Self;

    fn one() -> Self;
}

struct SegmentTree<T> {
    n: usize,
    data: Vec<T>
}

impl<T: Monoid + Clone> SegmentTree<T> {
    fn new(n: usize, initial: T) -> Self {
        let vs = (n-1).next_power_of_two() << 1;
        SegmentTree { n: n, data: vec![initial; vs] }
    }

    fn new_with(v: &Vec<T>) -> Self {
        let vs = max(4, (v.len()-1).next_power_of_two() << 1);
        let n = v.len();
        let mut data: Vec<T> = vec![T::one(); vs];

        let bottom = vs/2-1;
        for i in 0..n {
            data[bottom+i] = v[i].clone();
        }
        for i in (0..bottom).rev() {
            data[i] = data[i*2+1].mul(data[i*2+2].clone());
        }
        SegmentTree { n: v.len(), data: data }
    }

    fn change(&mut self, idx: usize, new_value: T) {
        let mut pos = self.data.len() / 2 - 1 + idx;
        self.data[pos] = new_value;
        while pos >= 1 {
            let to = (pos - 1) / 2;
            self.data[to] = self.data[to*2+1].mul(self.data[to*2+2].clone());
            pos = to;
        }
    }

    fn range(&self, l: usize, r: usize) -> T {
        self.range2(l, r, 0, 0, self.data.len() / 2)
    }

    fn range2(&self, l: usize, r: usize, idx: usize, segl: usize, segr: usize) -> T {
        if r <= segl || segr <= l {
            return T::one()
        }
        if l <= segl && segr <= r {
            return self.data[idx].clone()
        }
        let med = (segl + segr) / 2;
        self.range2(l, r, idx*2+1, segl, med).mul(self.range2(l, r, idx*2+2, med, segr))
    }
}


// ===

#[derive(Clone, Debug, Copy)]
struct I64(i64);

impl Monoid for I64 {
    fn mul(&self, other: Self) -> Self {
        if self.0 < other.0 { I64(other.0) } else { I64(self.0) }
    }

    fn one() -> Self { I64(0) }
}

// ===

fn solve0(xy: &Vec<(i64, i64)>) -> i64 {
    // fix rmin and bmax

    let n = xy.len();
    if n == 1 {
        return 0
    }

    let mut rmin = xy[0].0;
    let mut rmax = xy[0].0;
    let mut bmin = xy[0].1;
    let mut bmax = xy[0].1;

    let mut bi = 0;
    for i in 0..n {
        if bmax <= xy[i].1 {
            bmax = xy[i].1;
            bi = i;
        }
    }
    rmin = min(rmin, xy[bi].0);
    rmax = max(rmax, xy[bi].0);

    for i in 0..n {
        if i == 0 || i == bi {
            continue
        }
        bmin = min(bmin, xy[i].1);
        rmax = max(rmax, xy[i].0);
    }

    (rmax - rmin) * (bmax - bmin)
}

fn solve1(xy: &Vec<(i64, i64)>) -> i64 {
    // fix rmin and rmax
    let n = xy.len();
    if n == 1 {
        return 0
    }

    let mut rmin = xy[0].0;
    let mut rmax = xy[0].0;
    let mut bmin = xy[0].1;
    let mut bmax = xy[0].1;

    let mut bi = 0;
    for i in 1..n {
        if rmax <= xy[i].1 {
            rmax = xy[i].1;
            bi = i;
        }
    }
    bmin = min(bmin, xy[bi].0);
    bmax = max(bmax, xy[bi].0);

    if n == 2 {
        return (rmax - rmin) * (bmax - bmin)
    }

    let mut pairs = vec![];
    for i in 0..n {
        if i != 0 && i != bi {
            pairs.push(xy[i]);
        }
    }

    let pn = pairs.len();
    let mut r = SegmentTree::new(n+10, I64::one());
    for i in 0..pn {
        r.change(i, I64(pairs[i].1));
    }

    let mut best_blue = (0, 1e11 as i64);
    for i in 0..pn {
        let bmin = min(bmin, pairs[i].0);
        let bmax = max(bmax, r.range(0, i).0);

        if best_blue.1 - best_blue.0 >= bmax - bmin {
            best_blue = (bmin, bmax);
        }
    }

    (rmax - rmin) * (best_blue.1 - best_blue.0)
}

fn main() {
    let n: usize = read();
    let mut xy: Vec<(i64, i64)> = readn(n);

    for i in 0..n {
        if xy[i].1 < xy[i].0 {
            xy[i] = (xy[i].1, xy[i].0);
        }
    }
    xy.sort();

    // println!("{:?}", xy);
    println!("{}", min(solve0(&xy), solve1(&xy)));
}