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.IOException;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.nio.file.Paths;
import java.util.ArrayList;
import java.util.Scanner;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author HavroninaTE
 */
public class SumInATree {

    static ArrayList<Integer> g[];
    static long sums[];
    static int av[];
    static boolean error = false;

    public static void main(String[] args) throws IOException {
      //  Scanner sc = new Scanner(Paths.get("D:\\Литература\\JAVA\\projects\\CodeForces\\src\\SumInATree\\input4.txt"), "UTF-8");
         Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        g = new ArrayList[n];
        sums = new long[n];
        av = new int[n];
        for (int i = 0; i < n; i++) {
            g[i] = new ArrayList();
        }
        for (int u, i = 1; i < n; i++) {
            u = sc.nextInt() - 1;
            g[u].add(i);
            g[i].add(u);
        }
        for (int i = 0; i < n; i++) {
            sums[i] = sc.nextInt();
        }
        av[0] = (int)sums[0];
        dfs(0, -1, 1);
        BigInteger result = new BigInteger("0");
        error=false;
        for(int i=0;i<n;i++)
        {
            if(av[i]<0)
                error=true;
            result=result.add(new BigInteger(new Integer(av[i]).toString()));
        }
        if(error)
            System.out.println("-1");
        else
            System.out.println(result);

    }

    static private void dfs(int v, int p, int depth) {
        if (depth % 2 == 1) //неизвестные частичные суммы
        {
            for (int u : g[v]) {
                if (u != p) {
                if(g[u].size()==1 && v!=-1)
                    av[u]=0;
                else
                    av[u]=Integer.MAX_VALUE;
                   for(int u1: g[u])
                   {
                       if(u1!=v)
                       {
                           av[u]=(int) Math.min(av[u], sums[u1]-sums[v]);
                       }
                   }
                   sums[u]=sums[v]+av[u];
                   dfs(u,v,depth+1);
                }
            }
        }
        else
        {
            for (int u : g[v]) {
                if (u != p) {
                   av[u]=(int) (sums[u]-sums[v]);
                   dfs(u,v,depth+1);
                }
            }
        }
    }

}
