#include<iostream>
#include<cstdio>
#include<cstring>
const int N=1002;

inline void apn(int &a,int b){
	if(a>b)a=b;
}

inline char get_c(){
	static char buf[20000],*h,*t;
	if(h==t){
		t=(h=buf)+fread(buf,1,20000,stdin);
	}
	return h==t?EOF:*h++;
}

inline int nxi(){
	int x=0;
	char c;
	while((c=get_c())>'9'||c<'0');
	while(x=x*10+c-48,(c=get_c())>='0'&&c<='9');
	return x;
}

int main(){
	static int fa[N],hx[N],dp[N][5002];
	int n=nxi();
	for(int i=2;i<=n;++i) fa[i]=nxi();
	for(int i=1;i<=n;++i) hx[i]=nxi();

	for(int x=n;x;--x){
		int y=fa[x];
		for(int i=hx[y];i>=0;--i){
			int p=dp[y][i];
			dp[y][i]=1e5;
			if(hx[x]<=i){
				dp[y][i]=(hx[x]?dp[y][i-hx[x]]:p)+dp[x][hx[x]];
			}
			if(dp[x][hx[x]]<=i){
				apn(dp[y][i],(dp[x][hx[x]]?dp[y][i-dp[x][hx[x]]]:p)+hx[x]);
			}
		}
	}
	puts(dp[1][hx[1]]>=1e5?"IMPOSSIBLE":"POSSIBLE");
	return 0;
}
### Prompt

Generate a cpp solution to the following problem:

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`.

Examples

Input

3
1 1
4 3 2


Output

POSSIBLE


Input

3
1 2
1 2 3


Output

IMPOSSIBLE


Input

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3


Output

POSSIBLE


Input

1

0


Output

POSSIBLE

### Response

```cpp
#include<iostream>
#include<cstdio>
#include<cstring>
const int N=1002;

inline void apn(int &a,int b){
	if(a>b)a=b;
}

inline char get_c(){
	static char buf[20000],*h,*t;
	if(h==t){
		t=(h=buf)+fread(buf,1,20000,stdin);
	}
	return h==t?EOF:*h++;
}

inline int nxi(){
	int x=0;
	char c;
	while((c=get_c())>'9'||c<'0');
	while(x=x*10+c-48,(c=get_c())>='0'&&c<='9');
	return x;
}

int main(){
	static int fa[N],hx[N],dp[N][5002];
	int n=nxi();
	for(int i=2;i<=n;++i) fa[i]=nxi();
	for(int i=1;i<=n;++i) hx[i]=nxi();

	for(int x=n;x;--x){
		int y=fa[x];
		for(int i=hx[y];i>=0;--i){
			int p=dp[y][i];
			dp[y][i]=1e5;
			if(hx[x]<=i){
				dp[y][i]=(hx[x]?dp[y][i-hx[x]]:p)+dp[x][hx[x]];
			}
			if(dp[x][hx[x]]<=i){
				apn(dp[y][i],(dp[x][hx[x]]?dp[y][i-dp[x][hx[x]]]:p)+hx[x]);
			}
		}
	}
	puts(dp[1][hx[1]]>=1e5?"IMPOSSIBLE":"POSSIBLE");
	return 0;
}
```