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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<cstdio>
#include<math.h>
#include<string>
#include<algorithm>
#include<functional>
#include<vector>
#include<set>
#include<map>
#define INF 999999
#define EPS 1.0e-6

using namespace std;

typedef long long ll;
typedef pair<int, int> P;
typedef pair<int, P> PP;

int n;
int p[1050];
int x[1050];

//つねにfirst<secondとなるようにしておく
P tree[1050];
int v[1050];

int main()
{
	cin >> n;
	for (int i = 2; i <= n; i++) {
		cin >> p[i];
	}
	for (int i = 1; i <= n; i++) {
		cin >> x[i];
	}

	int ope = 0;
	for (int i = n; i > 0; i--) {
		int white = tree[i].first;
		int black = tree[i].second;
		int pwh = tree[p[i]].first;
		int pbl = tree[p[i]].second;

		if (x[i] >= black) {
			if (pbl + x[i] <= x[p[i]]||pwh + x[i] > x[p[i]]) {
				tree[p[i]].first += white;
				tree[p[i]].second += x[i];
			}
			else{
				tree[p[i]].first += x[i];
				tree[p[i]].second += white;
			}
			v[i] = x[i] - black;
		}
		else if (x[i] >= white) {
			if (pbl + black <= x[p[i]]||pwh + black > x[p[i]]) {
				tree[p[i]].first += x[i];
				tree[p[i]].second += black;
			}
			else {
				tree[p[i]].first += black;
				tree[p[i]].second += x[i];
			}
			v[i] = x[i] - white;
		}
		else {
			ope++; break;
		}
		if (tree[p[i]].first > tree[i].second)swap(tree[p[i]].first, tree[p[i]].second);
	}

	/*
	for (int i = 1; i <= n; i++) {
		cout << i<<":";
		cout << v[i] << endl;
	}
	*/
	
	
	if (ope == 0)cout << "POSSIBLE" << endl;
	else cout << "IMPOSSIBLE" << endl;
	
	return 0;
}