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: Accepted)

#include<bits/stdc++.h>
using namespace std;

vector<int>G[1010];
int g[5050],h[5050],f[1010],x,n,a[1010];

void U(int &x,int y){
	x=min(x,y);
}

void dfs(int x){
	for (auto y:G[x]) dfs(y);
	memset(g,33,sizeof g); g[0]=0;
	int b,c;
	for (auto y:G[x]){
		memset(h,33,sizeof h);
		b=f[y], c=a[y];
		for (int i=0;i<=5001;++i)
			U(h[min(i+b,5001)],g[i]+c),
			U(h[min(i+c,5001)],g[i]+b);
		memcpy(g,h,sizeof g);
	}
	for (int i=0;i<=5001;++i){
		if (i<=a[x]) U(f[x],g[i]);
		if (g[i]<=a[x]) U(f[x],i);
	}
	if (f[x]>1e8) exit(0*puts("IMPOSSIBLE"));
}

int main(){
	cin>>n;
	for (int i=2;i<=n;++i) cin>>x, G[x].push_back(i);
	for (int i=1;i<=n;++i) cin>>a[i];
	memset(f,33,sizeof f);
	dfs(1);
	puts("POSSIBLE");
}