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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.lang.*;
import java.io.*;
import java.util.*;

public class Main {
  public static void main(String arg[]) throws IOException { new Main().bw.close(); }

  BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
  BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

  StringTokenizer st = null;
  String nxttok() { 
    try { while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine()); }
    catch(Exception e) { return "";}
    return st.nextToken();
  }

  int nxtint() { return  Integer.parseInt(nxttok()); }
  long nxtlong() { return Long.parseLong(nxttok()); }

  int maxm = 5050;
  int n;
  ArrayList<Integer> gr[];
  int a[];
  int dp[][];

  Main() throws IOException {
    n = nxtint();
    gr = new ArrayList[n];
    gr[0] = new ArrayList<Integer>();
    for (int i = 0; ++i < n; ) {
      int u = nxtint() - 1;
      //System.err.println(u);
      gr[u].add(i);
      gr[i] = new ArrayList<Integer>();
    }
    a = new int[n];
    for (int i = -1; ++i < n; ) a[i] = nxtint();
    dp = new int[n][2];

    for (int u = n; u-- > 0; ) {
      int min0[][] = new int[maxm][2];
      int min1[][] = new int[maxm][2];

      for (int i = 0; ++i < maxm; ) 
          min0[i][1] = min1[i][1] = maxm;

      int s = 0;
      for (int v : gr[u]) {
        for (int i = -1; ++i < maxm; ) min0[i][s] = min1[i][s] = maxm;
        for (int i = 0; i <= 1; ++i) {
          int t[] = new int[2];
          t[i] = a[v];
          t[i ^ 1] = dp[v][i];
          
          for (int f = maxm; f-- > 0; ) {
            if (f + t[0] < maxm)
              min0[f + t[0]][s] = Math.min(min0[f + t[0]][s], min0[f][s ^ 1] + t[1]);
            if (f + t[1] < maxm)
              min1[f + t[1]][s] = Math.min(min1[f + t[1]][s], min1[f][s ^ 1]  + t[0]);
          }
        }
        s ^= 1;
      }
      
      s ^= 1;
      dp[u][0] = dp[u][1] = maxm;
      for (int i = 0; i <= a[u]; ++i) {
        dp[u][0] = Math.min(dp[u][0], min0[i][s]);
        dp[u][1] = Math.min(dp[u][1], min1[i][s]);
      }
      if (dp[u][0] == maxm && dp[u][1] == maxm) {
        bw.write("IMPOSSIBLE");
        return;
      }
    }
    bw.write("POSSIBLE");
  }
}