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.ArrayList;
import java.util.Scanner;

/*
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/**
 *
 * @author Andy Phan
 */
public class p1098a {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        ArrayList<Integer>[] children = new ArrayList[n];
        int[] par = new int[n];
        for(int i = 0 ; i < n; i++) children[i] = new ArrayList<>();
        for(int i = 1; i < n; i++) {
            par[i] = in.nextInt()-1;
            children[par[i]].add(i);
        }
        par[0] = -1;
        long[] val = new long[n];
        for(int i = 0; i < n; i++) val[i] = in.nextInt();
        long tot = 0;
        for(int i = 0; i < n; i++) {
            if(val[i] == -1) {
                val[i] = Integer.MAX_VALUE;
                for(int a : children[i]) val[i] = Math.min(val[i], val[a]);
                if(val[i] == Integer.MAX_VALUE) val[i] = val[par[i]];
            }
            if(children[i].isEmpty()) tot += val[i];
            else tot -= (children[i].size()-1)*val[i];
        }
        for(int i = 0; i < n; i++) {
            if(par[i] == -1) continue;
            if(val[i] < val[par[i]]) {
                System.out.println(-1);
                return;
            }
        }
        System.out.println(tot);
    }
}
