
#include <bitset>
#include <cstdio>
#include <cstdlib>

using namespace std;
const int Max_N(1050);

int N, Head[Max_N], Total, To[Max_N], Next[Max_N], X[Max_N], Y[Max_N];

inline void Add_Edge(const int &s, const int &t)
{
	++Total, To[Total] = t, Next[Total] = Head[s], Head[s] = Total;
}

inline void GG()
{
	puts("IMPOSSIBLE"), exit(0);
}

bitset<5050> F;
void dfs(const int &u)
{
	for (int i = Head[u];i;i = Next[i])
		dfs(To[i]);
	F.reset(), F.set(0);
	int Sum(0);
	for (int i = Head[u], v;i;i = Next[i])
		v = To[i], F = ((F << X[v]) | (F << Y[v])), Sum += X[v] + Y[v];
	for (int i = X[u];i >= 0;--i)
		if (F[i])
		{
			Y[u] = Sum - i;
			goto loop;
		}
	GG();
	loop :
	;
}

int main()
{
	scanf("%d", &N);
	for (int i = 2, fa;i <= N;++i)
		scanf("%d", &fa), Add_Edge(fa, i);
	for (int i = 1;i <= N;++i)
		scanf("%d", X + i);
	dfs(1);
	puts("POSSIBLE");
	return 0;
}
### Prompt

Please create a solution in CPP 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 <bitset>
#include <cstdio>
#include <cstdlib>

using namespace std;
const int Max_N(1050);

int N, Head[Max_N], Total, To[Max_N], Next[Max_N], X[Max_N], Y[Max_N];

inline void Add_Edge(const int &s, const int &t)
{
	++Total, To[Total] = t, Next[Total] = Head[s], Head[s] = Total;
}

inline void GG()
{
	puts("IMPOSSIBLE"), exit(0);
}

bitset<5050> F;
void dfs(const int &u)
{
	for (int i = Head[u];i;i = Next[i])
		dfs(To[i]);
	F.reset(), F.set(0);
	int Sum(0);
	for (int i = Head[u], v;i;i = Next[i])
		v = To[i], F = ((F << X[v]) | (F << Y[v])), Sum += X[v] + Y[v];
	for (int i = X[u];i >= 0;--i)
		if (F[i])
		{
			Y[u] = Sum - i;
			goto loop;
		}
	GG();
	loop :
	;
}

int main()
{
	scanf("%d", &N);
	for (int i = 2, fa;i <= N;++i)
		scanf("%d", &fa), Add_Edge(fa, i);
	for (int i = 1;i <= N;++i)
		scanf("%d", X + i);
	dfs(1);
	puts("POSSIBLE");
	return 0;
}
```