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 main
{ 


   
   public static void main(String[] args){
  Scanner sc=new Scanner(System.in);
  int n=sc.nextInt();
  int parent[]=new int[n+1];
  int min[]=new int[n+1];
  Arrays.fill(min,Integer.MAX_VALUE);
  for(int i=2;i<=n;i++) {
	  parent[i]=sc.nextInt();
  }
  int sum[]=new int[n+1];
  for(int i=1;i<=n;i++) {
	  sum[i]=sc.nextInt();
	  min[parent[i]]=Math.min(min[parent[i]],sum[i]);
  }
  long ans=sum[1];
  for(int i=2;i<=n;i++) {
	  if(sum[i]==-1) {
		  if(min[i]!=Integer.MAX_VALUE) {
			  sum[i]=min[i];
			  if(sum[i]<sum[parent[i]]) {
				  ans=-1;
				  break;
			  }
			  else {
				  ans+=(sum[i]-sum[parent[i]]);
			  }
		  }
	  }
	  else {
		  if(sum[i]<sum[parent[i]]) {
			  ans=-1;
			  break;
		  }
		  else {
			  ans+=(sum[i]-sum[parent[i]]);
		  }
	  }
  }
  System.out.println(ans);
	}
   }