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 C++11 (GCC 4.8.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <string>
#include <functional>
#include <utility>
#include <queue>
#include <vector>
#include <string>
#include <stack>
#define rep(i,n) for(ll i=0;i<n;i++)
using namespace std;
typedef long long int ll;
const ll  MOD = 1000000007;
typedef pair<ll,ll> P;
const ll INF = 100100100100100100;


ll N;
ll p[2000];
ll X[2000];
P node_sum[2000];
queue<ll> next;
bool appear[2000];


P saiki(ll index){
  if(appear[index]){
    return node_sum[index];
  }
  P child_sum = make_pair(0,0);
  rep(i,N-1){
    if(p[i+1] == index){
      P tmp = saiki(i+1);
      child_sum.first += min(tmp.first , tmp.second);
      child_sum.second += max(tmp.first , tmp.second);
    }
  }
  if(child_sum.second <= X[index]){
    child_sum.second = X[index];
  }
  else if(child_sum.first <= X[index]){
    child_sum.first = X[index];
  }
  else{
    child_sum.first = INF;
    child_sum.second = INF;
  }
  return child_sum;
}

int main(){
  cin >> N;
  rep(i,N-1){
    cin >> p[i+1];
    p[i+1]--;
  }
  rep(i,N){
    cin >> X[i];
    node_sum[i] = make_pair(0,X[i]);
    appear[i] = true;
  }
  rep(i,N-1){
    node_sum[p[i+1]] = make_pair(0,0);
    appear[p[i+1]] = false;
  }
  P ans = saiki(0);
  if(ans.first == INF){
    cout << "IMPOSSIBLE" << endl;
  }
  else{
    cout << "POSSIBLE" << endl;
  }
}