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<cstdio>
#include<cstdlib>
using namespace std;
const int maxn=1010;
const int maxv=5010;
const int INF=1e9;
void chkmin(int &x,int y){
	x=x<y?x:y;
}
void chkmax(int &x,int y){
	x=x>y?x:y;
}
int f[maxn];
int beg[maxn],nex[maxn<<1],tto[maxn<<1],e;
void putin(int s,int t){
	tto[++e]=t;
	nex[e]=beg[s];
	beg[s]=e;
}
int a[maxn],dp[maxn];
int b[maxv],c[maxv];
void dfs(int u){
	for(int i=beg[u];i;i=nex[i])
		dfs(tto[i]);
	for(int i=1;i<=a[u];i++)
		b[i]=INF;
	b[0]=0;
	for(int i=beg[u];i;i=nex[i]){
		for(int j=a[u];j>=0;j--){
			c[j]=INF;
			if(j>=dp[tto[i]])
				chkmin(c[j],b[j-dp[tto[i]]]+a[tto[i]]);
			if(j>=a[tto[i]])
				chkmin(c[j],b[j-a[tto[i]]]+dp[tto[i]]);
		}
		for(int j=0;j<=a[u];j++)
			b[j]=c[j];
	}
	dp[u]=INF;
	for(int i=0;i<=a[u];i++)
		chkmin(dp[u],b[i]);
	if(dp[u]==INF){
		printf("IMPOSSIBLE\n");
		exit(0);
	}
}
int main(){
//	freopen("E.in","r",stdin);
//	freopen("E.out","w",stdout);
	int n;
	scanf("%d",&n);
	for(int i=2;i<=n;i++){
		scanf("%d",&f[i]);
		putin(f[i],i);
	}
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]);
	dfs(1);
	printf("POSSIBLE\n");
	return 0;
}