#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;

const int MAX_N = 1005;

int f[1005][5005], fa[MAX_N], X[MAX_N];
int g[5005];

inline void chmin(int &x, int y) {
  if (x > y) x = y;
}

int main() {
  int N;
  scanf("%d", &N);
  for (int i = 2; i <= N; ++i)
    scanf("%d", &fa[i]);
  for (int i = 1; i <= N; ++i)
    scanf("%d", &X[i]);
  
  memset(f, 0x3f, sizeof f);
  for (int i = 1; i <= N; ++i) f[i][0] = 0;
  
  for (int i = N; i; --i) {
    int mn = 0x3f3f3f3f;
    for (int j = 0; j <= X[i]; ++j)
      mn = min(mn, f[i][j]);
    if (mn == 0x3f3f3f3f) {
      puts("IMPOSSIBLE");
      return 0;
    }
    
    if (fa[i]) {
      memset(g, 0x3f, sizeof g);
      for (int j = 0; j <= X[fa[i]]; ++j) {
	chmin(g[j + X[i]], f[fa[i]][j] + mn);
	chmin(g[j + mn], f[fa[i]][j] + X[i]);
      }
      memcpy(f[fa[i]], g, sizeof g);
    }
  }

  puts("POSSIBLE");
  
  return 0;
}

### Prompt

In CPP, your task is to solve 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 <algorithm>
#include <cstring>
using namespace std;

const int MAX_N = 1005;

int f[1005][5005], fa[MAX_N], X[MAX_N];
int g[5005];

inline void chmin(int &x, int y) {
  if (x > y) x = y;
}

int main() {
  int N;
  scanf("%d", &N);
  for (int i = 2; i <= N; ++i)
    scanf("%d", &fa[i]);
  for (int i = 1; i <= N; ++i)
    scanf("%d", &X[i]);
  
  memset(f, 0x3f, sizeof f);
  for (int i = 1; i <= N; ++i) f[i][0] = 0;
  
  for (int i = N; i; --i) {
    int mn = 0x3f3f3f3f;
    for (int j = 0; j <= X[i]; ++j)
      mn = min(mn, f[i][j]);
    if (mn == 0x3f3f3f3f) {
      puts("IMPOSSIBLE");
      return 0;
    }
    
    if (fa[i]) {
      memset(g, 0x3f, sizeof g);
      for (int j = 0; j <= X[fa[i]]; ++j) {
	chmin(g[j + X[i]], f[fa[i]][j] + mn);
	chmin(g[j + mn], f[fa[i]][j] + X[i]);
      }
      memcpy(f[fa[i]], g, sizeof g);
    }
  }

  puts("POSSIBLE");
  
  return 0;
}

```