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++ (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<vector>
#include<algorithm>
using namespace std;
int dp[2][5555];
vector<int>ko[1111];
int mok[1111];
int dfs(int node)
{
	vector<int>v;
	for (int i = 0; i < ko[node].size(); i++)v.push_back(dfs(ko[node][i]));
	int cur = 0;
	for (int i = 0; i <= mok[node]; i++)dp[0][i] = 0, dp[1][i] = 1000000000;
	for (int i = 0; i < ko[node].size(); i++)
	{
		int z = v[i], y = mok[ko[node][i]];
		for (int j = 0; j <= mok[node]; j++)
		{
			if (j + y <= mok[node])dp[1 - cur][j + y] = min(dp[1 - cur][j + y], dp[cur][j] + z);
			if (j + z <= mok[node])dp[1 - cur][j + z] = min(dp[1 - cur][j + z], dp[cur][j] + y);
		}
		for (int j = 0; j <= mok[node]; j++)dp[cur][j] = 1000000000;
		cur = 1 - cur;
	}
	return dp[cur][mok[node]];
}
int main()
{
	int num;
	scanf("%d", &num);
	for (int i = 1; i < num; i++)
	{
		int z;
		scanf("%d", &z);
		z--;
		ko[z].push_back(i);
	}
	for (int i = 0; i < num; i++)scanf("%d", &mok[i]);
	if (dfs(0) >= 1000000000)printf("IMPOSSIBLE\n");
	else printf("POSSIBLE\n");
}