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: Runtime Error)

#include<iostream>
#include<cstring>
#include<cstdio>
#include<vector>
using namespace std;
#define in read()
#define fur(i,a,b) for(int i=a;i<=b;i++)
#define fdr(i,a,b) for(int i=a;i>=b;i--)
#define int long long
#define xx 1100
const int inf=123456789;
inline int read()
{
    int x=0,f=1;char ch=getchar();
    for(;!isalnum(ch);ch=getchar()) if(ch=='-') f=-1;
    for(;isalnum(ch);ch=getchar()) x=x*10+ch-'0';
    return x*f;
}
int sum[xx],w[xx],f[xx];
vector<int>e[xx];
inline void dfs(int g)
{
	fur(i,0,(int)e[g].size()-1) dfs(e[g][i]);
	memset(f,inf,sizeof(f));f[0]=0;
	fur(i,0,(int)e[g].size()-1)
	{
		int k=e[g][i];
		fdr(j,w[g],0)
		{
			int tmp=inf;
			if(j>=sum[k]) tmp=min(tmp,f[j-sum[k]]+w[k]);
			if(j>=w[k]) tmp=min(tmp,f[j-w[k]]+sum[k]);
			f[j]=tmp;
		}
	}
	fdr(i,w[g],0) sum[g]=min(sum[g],f[i]);
}
signed main()
{
	memset(sum,inf,sizeof(sum));
    int n=in;
    fur(i,2,n)
    {
        int x=in;
        e[x].push_back(i);
    }
    fur(i,1,n) w[i]=in;
    dfs(1);
    if(sum[1]<inf) printf("POSSIBLE\n");
    else printf("IMPOSSIBLE\n");
    return 0;
}