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 s3 {       

         static class Graph 
                {
                    int V;      
                    LinkedList<Integer> adjList[];
                         Graph(int x)
                           {
                                V=x;
                                adjList = new LinkedList[V];
                                 for(int i=0;i<x;i++)
                                   adjList[i] = new LinkedList();
                            }
                  }
          static void addEdge(Graph g,int s,int d)
                        {
                               g.adjList[s].add(d);
                               g.adjList[d].add(s);
                         }
          static void BFS(Graph g,int parent[] ,int sum[])
                          {
                                int level[] = new int[g.V+1];
                                int arr[] = new int[g.V+1];
                                    arr[1]=sum[1];
                                boolean visited[] = new boolean[g.V+1];
                               LinkedList<Integer> queue = new LinkedList<Integer>();

                                  queue.add(1);        visited[1]=true; level[1]=1;     
                               int flag=1;                      
                                 while(queue.size()>0)
                                      {
                                     
                                           int s = queue.poll(); 
                                              if(level[s]%2==0)
                                                          {                             
                                                               int min=Integer.MAX_VALUE;
                                                              for(Integer p:g.adjList[s])
                                                                if(min>sum[p]&&p!=parent[s])
                                                                    min=sum[p];
                                                             if(min!=Integer.MAX_VALUE)
                                                                {
                                                                   arr[s]=min-sum[parent[s]]; 
                                                                     if(arr[s]<0)
                                                                        flag=0;
                                                              
                                                                   sum[s]=min;
                                                                 for(Integer p:g.adjList[s])
                                                                     if(p!=parent[s])
                                                                    arr[p]=sum[p]-min;
                                                                 }
                                                              else
                                                                 arr[s]=0;
                                                           }
                                         for(Integer p: g.adjList[s])
                                            if(visited[p]==false)
                                               {   
                                                       queue.add(p);
                                                       visited[p]=true;
                                                        level[p]=level[s]+1;
                                                }
                                        }
                                if(flag==0)
                                    System.out.println("-1");
                                else
                                   {
                                         long ans=0;
                                        for(int i=1;i<arr.length;i++)
                                             ans=ans+arr[i];
                                           System.out.println(ans);
                                     }  
                          }   
      public static void main(String args[]) 
              { 
                    Scanner sc = new Scanner(System.in);
                    PrintWriter out = new PrintWriter(System.out);
                         int n = sc.nextInt();
                         Graph g = new Graph(n+1);
                      int parent[] = new int[n+1];
                      int sum[] = new int[n+1];
                       for(int i=2;i<=n;i++)
                          {
                                    parent[i]=sc.nextInt();
                                    addEdge(g,i,parent[i]);
                           } 
                       for(int i=1;i<=n;i++)
                             sum[i]=sc.nextInt();                       
                          BFS(g,parent,sum);
               }
}