Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 1
4 3 2

Sample Output 1

POSSIBLE

For example, the following allocation satisfies the condition:

Set the color of Vertex 1 to white and its weight to 2.

Set the color of Vertex 2 to black and its weight to 3.

Set the color of Vertex 3 to white and its weight to 2.

There are also other possible allocations.

Sample Input 2

3
1 2
1 2 3

Sample Output 2

IMPOSSIBLE

If the same color is allocated to Vertex 2 and Vertex 3, Vertex 2 cannot be allocated a non-negative weight.

If different colors are allocated to Vertex 2 and 3, no matter which color is allocated to Vertex 1, it cannot be allocated a non-negative weight.

Thus, there exists no allocation of colors and weights that satisfies the condition.

Sample Input 3

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3

Sample Output 3

POSSIBLE

Sample Input 4

1

0

Sample Output 4

POSSIBLE

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main
import "fmt"
var tree [][]int
var x []int64
func main() {
  var n,p int
  fmt.Scan(&n)
  if n == 1 { fmt.Println("POSSIBLE");return }
  tree = make([][]int,n)
  x = make([]int64,n)
  for i:=1;i<n;i++ {
    fmt.Scan(&p)
    tree[p-1] = append(tree[p-1],i)
  }
  for i:=0;i<n;i++ { fmt.Scan(&x[i]) }
  if dfs(0) < 0 {
    fmt.Println("IMPOSSIBLE")
  } else {
    fmt.Println("POSSIBLE")
  }
}
func dfs(v int) int64 {
  if len(tree[v]) == 0 { return 0 }
  s := int64(0)
  dp := make([]bool,x[v]+1)
  dp[0] = true
  zero := true
  for _,e := range tree[v] {
    y := dfs(e)
    if y < 0 { return -1 }
    z := x[e]
    if y > z { y,z = z,y }
    if y > 0 { zero = false }
    s += y+z
    for i:=x[v];i>y-1;i-- {
      if dp[i-y] { dp[i] = true;continue }
      if i > z-1 && dp[i-z] { dp[i] = true }
    }
  }
  dp[0] = zero
  for i:=x[v];i>-1;i-- {
    if dp[i] { return s-int64(i) }
  }
  return -1
}