Mitya has a rooted tree with n vertices indexed from 1 to n, where the root has index 1. Each vertex v initially had an integer number a_v ≥ 0 written on it. For every vertex v Mitya has computed s_v: the sum of all values written on the vertices on the path from vertex v to the root, as well as h_v — the depth of vertex v, which denotes the number of vertices on the path from vertex v to the root. Clearly, s_1=a_1 and h_1=1.

Then Mitya erased all numbers a_v, and by accident he also erased all values s_v for vertices with even depth (vertices with even h_v). Your task is to restore the values a_v for every vertex, or determine that Mitya made a mistake. In case there are multiple ways to restore the values, you're required to find one which minimizes the total sum of values a_v for all vertices in the tree.

Input

The first line contains one integer n — the number of vertices in the tree (2 ≤ n ≤ 10^5). The following line contains integers p_2, p_3, ... p_n, where p_i stands for the parent of vertex with index i in the tree (1 ≤ p_i < i). The last line contains integer values s_1, s_2, ..., s_n (-1 ≤ s_v ≤ 10^9), where erased values are replaced by -1.

Output

Output one integer — the minimum total sum of all values a_v in the original tree, or -1 if such tree does not exist.

Examples

Input


5
1 1 1 1
1 -1 -1 -1 -1


Output


1


Input


5
1 2 3 1
1 -1 2 -1 -1


Output


2


Input


3
1 2
2 -1 1


Output


-1
import java.util.*;
import java.io.*;

public class D{
   public static void main(String[] args) throws IOException{
      BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
      int n = Integer.parseInt(f.readLine());
      Node[] nodes = new Node[n+1];
      for(int i = 1; i <= n; i++){
         nodes[i] = new Node();
      }
      StringTokenizer st = new StringTokenizer(f.readLine());
      for(int i = 2; i <= n; i++){
         int k = Integer.parseInt(st.nextToken());
         nodes[k].children.add(nodes[i]);
      }
      st = new StringTokenizer(f.readLine());
      for(int i = 1; i <= n; i++){
         int k = Integer.parseInt(st.nextToken());
         nodes[i].sum = k;
      }
      
      dfs(nodes[1], nodes[1].sum);
      System.out.println(totalSum(nodes[1], 0));
   }
   
   public static void dfs(Node n, int sum){
      if(n.sum >= 0){
         for(Node c: n.children){
            dfs(c, n.sum);
         }
      }else{
         int minSum = Integer.MAX_VALUE;
         for(Node c: n.children){
            minSum = Math.min(minSum, c.sum);
         }
         if(minSum == Integer.MAX_VALUE) minSum = sum;
         if(minSum < sum){
            System.out.println(-1);
            System.exit(0);
         }
         n.sum = minSum;
         for(Node c: n.children){
            dfs(c, n.sum);
         }
      }
   }
   
   public static long totalSum(Node n, long prevSum){
      long newSum = n.sum-prevSum;
      for(Node c: n.children){
         newSum += totalSum(c, n.sum);
      }
      return newSum;
   }
      
}

class Node{
   public int sum;
   public LinkedList<Node> children;
   
   public Node(){
      sum = 0;
      children = new LinkedList<Node>();
   }
}
   