//copied
#include <bits/stdc++.h>
int n, Li[1005], Mv[5005], Sum;
std::vector<int> g[1005];
std::bitset<5005> v;

int main() {
	scanf("%d", &n);
	for (int i = 2, u; i <= n; ++i)
		scanf("%d", &u), g[u].push_back(i);
	for (int i = 1; i <= n; ++i)
		scanf("%d", &Li[i]);
	for (int i, x = n; x >= 1; --x) {
		v = 1, Sum = 0;
		for (int y : g[x])
			v = (v << Li[y]) | (v << Mv[y]), Sum += Li[y] + Mv[y];
		for (i = Li[x]; i >= 0 && !v[i]; --i)
			;
		std::string mystring = v.to_string<char, std::string::traits_type,
				std::string::allocator_type>();

//		std::cout << x << ' ' << i << ": " << mystring << ' '<<Li[x] << ' ' << Mv[x]
//				<< '\n';
		if (i == -1)
			return puts("IMPOSSIBLE"), 0;
		Mv[x] = Sum - i;
	}
	return puts("POSSIBLE"), 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
//copied
#include <bits/stdc++.h>
int n, Li[1005], Mv[5005], Sum;
std::vector<int> g[1005];
std::bitset<5005> v;

int main() {
	scanf("%d", &n);
	for (int i = 2, u; i <= n; ++i)
		scanf("%d", &u), g[u].push_back(i);
	for (int i = 1; i <= n; ++i)
		scanf("%d", &Li[i]);
	for (int i, x = n; x >= 1; --x) {
		v = 1, Sum = 0;
		for (int y : g[x])
			v = (v << Li[y]) | (v << Mv[y]), Sum += Li[y] + Mv[y];
		for (i = Li[x]; i >= 0 && !v[i]; --i)
			;
		std::string mystring = v.to_string<char, std::string::traits_type,
				std::string::allocator_type>();

//		std::cout << x << ' ' << i << ": " << mystring << ' '<<Li[x] << ' ' << Mv[x]
//				<< '\n';
		if (i == -1)
			return puts("IMPOSSIBLE"), 0;
		Mv[x] = Sum - i;
	}
	return puts("POSSIBLE"), 0;
}

```