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.*;
import java.math.*;
/*
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
StringTokenizer st = new StringTokenizer(br.readLine());
Integer.parseInt(st.nextToken());
Long.parseLong(st.nextToken());
Scanner sc = new Scanner(System.in);


*/

public class Waw{
    
    static HashMap<Integer,Node> luckup = new HashMap<Integer,Node>();
    public static Node getNode(int id){
        return luckup.get(id);
    }
    
    public static class Node{
        LinkedList<Integer> suns = new LinkedList<Integer>();
        long s;
        long origin;
        long moin;
        int id;
        int p;
        int h;
        public Node(int id,int p,int h){
            this.id = id;
            moin = 0;
            s = -1;
            this.p = p;
            this.h = h;
            origin = -1;
        }
    }
    
    public static void addEdges(int first,int second){
        Node node = getNode(first);
        node.suns.add(second);
    }
    
    public static class Turn implements Comparable<Turn>{
        int h;
        int id;
        public Turn(int id,int h){
            this.id = id;
            this.h = h;
        }
        
        @Override
        public int compareTo(Turn t){
            if(h-t.h!=0) return t.h-h;
            else return t.id - id;
        }
    }
    
    public static void main(String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        luckup.put(1,new Node(1,0,1));
        int p;
        st = new StringTokenizer(br.readLine());
        for(int i=2;i<=n;i++){
            p = Integer.parseInt(st.nextToken());
            luckup.put(i,new Node(i,p,getNode(p).h+1));
            getNode(p).suns.add(i);
            
        }
        st = new StringTokenizer(br.readLine());
        long s;
        TreeSet<Turn> nextToVisit = new TreeSet<Turn>();
        for(int i=1;i<=n;i++){
            s = Long.parseLong(st.nextToken());
            getNode(i).s = s;
            if(s!=-1){
                getNode(i).origin = s;
                nextToVisit.add(new Turn(i,getNode(i).h));
            }
        }
        Turn t;
        Node node;
        int eror = 0;
        while(!nextToVisit.isEmpty()){
            t = nextToVisit.pollFirst();
            if(t.id==1) break;
            node = getNode(t.id);
            
            if(node.s<getNode(node.p).origin) {
                eror = -1;
                break;
            }
            if(getNode(node.p).s==-1 || node.s<getNode(node.p).s) {
                getNode(node.p).s = node.s;
                nextToVisit.add(new Turn(node.p,getNode(node.p).h));
                
            }
        }
        if(eror==-1) System.out.println("-1");
        else{
            
            LinkedList<Integer> next = new LinkedList<Integer>();
            long res = 0;
            next.add(1);
        
            while(!next.isEmpty()){
                node = getNode(next.poll());
                if(node.s!=-1) 
                    res += node.s - node.moin;
                for(int id:node.suns){
                    if(node.s!=-1) 
                        getNode(id).moin = node.s;
                    next.add(id);
                }
            }
            
            System.out.println(res);
            
            
            
            
        }
        
    }
    

    
    
}