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

public class Main {
    static boolean bad = false;
    public static long dfs(List<Integer>[] tree, int[] vals, int cur, int pass) {
        int curVal = vals[cur];
        long sums = curVal - pass;
        for(int evenChild : tree[cur]) {
            int minimum = Integer.MAX_VALUE;
            for (int oddChild: tree[evenChild]) {
                minimum = Math.min(minimum, vals[oddChild]);
            }
            if (minimum == Integer.MAX_VALUE) {
                minimum = curVal;
            }
            if (minimum < curVal) {
                bad = true;
                return Long.MIN_VALUE;
            }
            sums += minimum - curVal;
            for (int oddChild: tree[evenChild]) {
                sums += dfs(tree, vals, oddChild, minimum);
            }
        }
        return sums;
    }

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Integer>[] tree = new List[n];
        for (int i = 0; i < n; i++) {
            tree[i] = new ArrayList<>();
        }
        for (int i = 1; i < n; i++) {
            int a = sc.nextInt() - 1;
            tree[a].add(i);
        }
        int[] vals = new int[n];
        for (int i = 0; i < n; i++) {
            vals[i] = sc.nextInt();
        }
        long x = dfs(tree, vals, 0, 0);
        System.out.println(bad ? -1 : x);
    }
}

								 	 			 		   	  				  		