#include <bits/stdc++.h>
#define int long long
#define mp make_pair
#define pb push_back
#define ld long double
#define pii pair<int,int>
#define sz(x) (int)x.size()
#define piii pair<pii,pii>
#define precise cout<<fixed<<setprecision(10)
#define st first
#define nd second
#define ins insert
#define vi vector<int>
#define BOOST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
using namespace std;
const int MAX=6000;
vi P[MAX];
int c[MAX];
/*
void add(int x){
	for (int i=MAX-1;i>=0;i--)
		if (dp[i] && i+x<=MAX-1)dp[i+x]=true;
}
*/
int dfs(int u){
	bitset<MAX>dp;
	dp[0]=1;
	int sum=0;
	for (auto it:P[u]){
		int ile=dfs(it);
		sum+=ile+c[it];
		dp=(dp<<c[it])|(dp<<ile);
		//add(ile);
		//add(c[it]);
	}
	int largest=c[u];
	while (largest && !dp[largest])largest--;
	if(!dp[largest])cout<<"IMPOSSIBLE",exit(0);
	return sum-largest;
}
int32_t main()
{
  BOOST;
  int n;
  cin>>n;
  for (int i=2;i<=n;i++){
  	int a;
  	cin>>a;
  	P[a].pb(i);
  }
  for (int i=1;i<=n;i++)cin>>c[i];
  dfs(1);
  cout<<"POSSIBLE";
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 <bits/stdc++.h>
#define int long long
#define mp make_pair
#define pb push_back
#define ld long double
#define pii pair<int,int>
#define sz(x) (int)x.size()
#define piii pair<pii,pii>
#define precise cout<<fixed<<setprecision(10)
#define st first
#define nd second
#define ins insert
#define vi vector<int>
#define BOOST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
using namespace std;
const int MAX=6000;
vi P[MAX];
int c[MAX];
/*
void add(int x){
	for (int i=MAX-1;i>=0;i--)
		if (dp[i] && i+x<=MAX-1)dp[i+x]=true;
}
*/
int dfs(int u){
	bitset<MAX>dp;
	dp[0]=1;
	int sum=0;
	for (auto it:P[u]){
		int ile=dfs(it);
		sum+=ile+c[it];
		dp=(dp<<c[it])|(dp<<ile);
		//add(ile);
		//add(c[it]);
	}
	int largest=c[u];
	while (largest && !dp[largest])largest--;
	if(!dp[largest])cout<<"IMPOSSIBLE",exit(0);
	return sum-largest;
}
int32_t main()
{
  BOOST;
  int n;
  cin>>n;
  for (int i=2;i<=n;i++){
  	int a;
  	cin>>a;
  	P[a].pb(i);
  }
  for (int i=1;i<=n;i++)cin>>c[i];
  dfs(1);
  cout<<"POSSIBLE";
  return 0;
}

```