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
// package com.company;



import java.io.IOException;
import java.util.*;

public class Main {
   static  ArrayList<Integer> tree[];
   static int p[];
    public static void main(String[] args) throws IOException {
        Scanner input = new Scanner(System.in);
        int n=input.nextInt();
        tree=new ArrayList[n+1];
        for (int i = 0; i <=n ; i++) {
            tree[i]=new ArrayList<>();
        }
        for (int i = 2; i <=n ; i++) {
            tree[input.nextInt()].add(i);
        }
        p=new int[n+1];
        for (int i = 1; i <=n ; i++) {
            p[i]=input.nextInt();
        }
        dfs(1,1,p[0]);
        if (pos){
            System.out.println(-1);
        }else {
            System.out.println(res);
        }


    }

    static long res=0;
    private static long dfs(int root, int h,int max) {


        long sum=0;
        if (h%2==0) {
            if (tree[root].size()>0) sum=Integer.MAX_VALUE;
            for (int child : tree[root]) {
                long temp=dfs(child, h + 1,max);
                sum=Math.min(sum,temp);

            }
            res-=tree[root].size()*sum;
            res+=sum;
        }else {
            if (max>p[root]){
                pos=true;
            }
            int tot=0;
            for (int child : tree[root]) {
               long temp= dfs(child, h + 1,Math.max(max,p[root]));
               if (temp>=p[root]){
                   res-=p[root];
               }
            }
            res+=p[root];


            sum=p[root];

        }
        return sum;
    }
    static boolean pos=false;
}