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 Graphs;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;

public class SumInTheTree {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        int a[]=new int[n+1];
        ArrayList<Integer> children[]=new ArrayList[n+1];
        String line[]=br.readLine().split(" ");
        int parent[]=new int[n+1];
        for(int i=1;i<=n;i++){
            children[i]=new ArrayList<>();
        }
        for(int i=2;i<=n;i++){
            int p=Integer.parseInt(line[i-2]);
            parent[i]=p;
            children[p].add(i);
        }
        int sum[]=new int[n+1];
        line=br.readLine().split(" ");
        for(int i=1;i<=n;i++){
            sum[i]=Integer.parseInt(line[i-1]);
        }
        a[1]=sum[1];
        Queue<Integer> queue=new LinkedList<>();
        queue.add(1);
        while(!queue.isEmpty()){
            int curr=queue.remove();
            ArrayList<Integer> child=children[curr];
            if(sum[curr]==-1){
                if(child.size()==0){
                    a[curr]=0;
                    sum[curr]=sum[parent[curr]];
                }
                else{
                    int min=sum[child.get(0)];
                    for(int i=0;i<child.size();i++){
                        int temp=child.get(i);
                        queue.add(temp);
                        min=Math.min(min,sum[temp]);
                    }
                    if(min<sum[parent[curr]]){
                        System.out.println(-1);
                        return;
                    }
                    a[curr]=min-sum[parent[curr]];
                    sum[curr]=sum[parent[curr]]+a[curr];
                }
            }
            else{
                for(int i=0;i<child.size();i++){
                    int temp=child.get(i);
                    queue.add(temp);
                }
                a[curr]=sum[curr]-sum[parent[curr]];
            }
        }
        long ans=0;
        for(int i=1;i<=n;i++){
//            System.out.println(a[i]);
            ans+=a[i];
        }
        System.out.println(ans);
    }
}
