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.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

 public class Solution {
 
 static boolean[] vis;
 static long ans;
 static int[] a;
 static int[] sum;
 static ArrayList<Integer> adj[];
 static int[] p;
    public static void main(String[] args) {
//         /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
        FastReader s=new FastReader();
       int n=s.nextInt();
      int i;
       adj=new ArrayList[n+1];
      vis=new boolean[n+1];
       p=new int[n+1];
      for(i=1;i<=n;i++){
        adj[i]=new ArrayList();
      }
      for(i=2;i<=n;i++){
        int p=s.nextInt();
        adj[p].add(i);
       }
     
       sum = new int[n+1];
       a=new int[n+1];
    for( i=1;i<=n;i++){sum[i] = s.nextInt();
    a[i]=Integer.MAX_VALUE;}
    
      
      dfs(1,0);
        System.out.println(ans);
    }
    static void dfs(int v,int prev){
         
            if(sum[v]==-1){
              Iterator<Integer> it1=adj[v].iterator();
              while(it1.hasNext()){
                int i1=it1.next();
                //System.out.println(i1+" "+prev);
                a[v]=Math.min(a[v],sum[i1]-prev);
              }
              if(adj[v].size()==0){
                a[v]=0;
              }
              if(a[v]<0){
               
                ans=-1;
                // System.out.println(ans+" 777");
                return;
              }
              sum[v]=a[v]+prev;
            }
            else{
              a[v]=sum[v]-prev;
              if(a[v]<0){
                ans=-1;
                //System.out.println(ans+" 222");
                return;
              }
            }
            if(ans!=-1){
            ans+=a[v];}
            //System.out.println(ans);
            vis[v]=true;
            Iterator<Integer> it=adj[v].iterator();
            while(it.hasNext()){
              int i=it.next();
              if(!vis[i]){
                dfs(i,sum[v]);
              }
            }
          }
}
// //     static int valid(String a){
// //         String[] arr=a.split("\\.");
// //         int i;
// //        // System.out.println(a+" "+arr.length);
// //         for(i=0;i<4;i++){
// //          // System.out.println(i+" ");
// //             int num=Integer.parseInt(arr[i]);
// //             if(arr[i].length()>3 || num>255){
// //                 return 0;
// //             }
// //             if(arr[i].length()>1 && arr[i].charAt(0)=='0'){
    //           return 0;
    //         }
    //         // if(num!=0 && arr[i].charAt(0)=='0'){
    //         //     return 0;
    //         // }
    //     }
    //     return 1;
    // }
//}
// class Comp implements Comparator<Pair>{
//     public int compare(Pair p1,Pair p2){
//       return (p1.c-p2.c);
//     }
// }
// class Pair{
//   int c,q;
//   public Pair(int q,int c){
//     this.q=q;
//     this.c=c;
//   }
// }

  //  static void dfs(int v){
  //     vis[v]=true;
  //     list.add(v);
  //     Iterator<Integer> it=adj[v].iterator();
  //     while(it.hasNext()){
  //       int i=it.next();
  //       if(!vis[i]){
  //        dfs(i);
  //       }
     
  //  }}}
     class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 


