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 Python (3.4.3) (judge verdict: Accepted)

import sys
input = sys.stdin.readline
import numpy as np
sys.setrecursionlimit(10**6)

N = int(input())
graph = [[] for _ in range(N+1)] # parent to child
for i,p in enumerate(input().split(),2):
    graph[int(p)].append(i)
X = [None] + [int(x) for x in input().split()]

def dfs(v):
    # None または 白、黒の2つ組を返す
    child = []
    for w in graph[v]:
        c = dfs(w)
        if c is None:
            return None
        child.append(c)
    S = sum(a+b for a,b in child)
    x = X[v]
    dp = np.zeros(x+1, dtype=np.bool) # 2択の繰り返しで作れる和
    dp[0] = 1
    for a,b in child:
        prev = dp
        dp = np.zeros_like(prev)
        if a <= x:
            dp[a:] = prev[:x+1-a]
        if b <= x:
            dp[b:] |= prev[:x+1-b]
    nz = np.nonzero(dp)[0]
    if len(nz) == 0:
        return None
    return x, S - nz[-1]

answer = 'POSSIBLE' if dfs(1) is not None else 'IMPOSSIBLE'
print(answer)