#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#define SIZE 5005
#define INF 1000000000

using namespace std;

vector <int> vec[SIZE];
int X[SIZE];
int dp[SIZE];
int nap[SIZE];

bool dfs(int v=0,int p=-1)
{
	for(int i=0;i<vec[v].size();i++)
	{
		int to=vec[v][i];
		if(!dfs(to,v)) return false;
	}
	for(int i=0;i<SIZE;i++) nap[i]=0;
	for(int i=0;i<vec[v].size();i++)
	{
		int to=vec[v][i];
		for(int j=SIZE-1;j>=0;j--)
		{
			int mn=INF;
			if(j>=X[to]) mn=min(mn,nap[j-X[to]]+dp[to]);
			if(j>=dp[to]) mn=min(mn,nap[j-dp[to]]+X[to]);
			nap[j]=mn;
		}
	}
	if(nap[X[v]]==INF) return false;
	dp[v]=nap[X[v]];
	return true;
}
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=0;i<n-1;i++)
	{
		int p;
		scanf("%d",&p);p--;
		vec[p].push_back(i+1);
	}
	for(int i=0;i<n;i++) scanf("%d",&X[i]);
	if(!dfs()) puts("IMPOSSIBLE");
	else puts("POSSIBLE");
	return 0;
}

### Prompt

Create a solution in CPP for 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 <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#define SIZE 5005
#define INF 1000000000

using namespace std;

vector <int> vec[SIZE];
int X[SIZE];
int dp[SIZE];
int nap[SIZE];

bool dfs(int v=0,int p=-1)
{
	for(int i=0;i<vec[v].size();i++)
	{
		int to=vec[v][i];
		if(!dfs(to,v)) return false;
	}
	for(int i=0;i<SIZE;i++) nap[i]=0;
	for(int i=0;i<vec[v].size();i++)
	{
		int to=vec[v][i];
		for(int j=SIZE-1;j>=0;j--)
		{
			int mn=INF;
			if(j>=X[to]) mn=min(mn,nap[j-X[to]]+dp[to]);
			if(j>=dp[to]) mn=min(mn,nap[j-dp[to]]+X[to]);
			nap[j]=mn;
		}
	}
	if(nap[X[v]]==INF) return false;
	dp[v]=nap[X[v]];
	return true;
}
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=0;i<n-1;i++)
	{
		int p;
		scanf("%d",&p);p--;
		vec[p].push_back(i+1);
	}
	for(int i=0;i<n;i++) scanf("%d",&X[i]);
	if(!dfs()) puts("IMPOSSIBLE");
	else puts("POSSIBLE");
	return 0;
}

```