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.*;

public class Main {


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] parents = new int[n];
        int[] s = new int[n];
        int[] a = new int[n];
        int[] depth = new int[n];
        boolean possible = true;
        long answer = 0;

        List<Set<Integer>> children = new ArrayList<>();
        for (int i = 0; i < n; i++) children.add(new HashSet<>());
        depth[0] = 1;

        for (int i = 1; i < n; i++) {
            parents[i] = sc.nextInt()-1;
            children.get(parents[i]).add(i);
            depth[i] = depth[parents[i]] + 1;
        }
        for (int i = 0; i < n; i++) {
            s[i] = sc.nextInt();
        }
        for (int i = 1; i < n; i++) {
            if (children.get(i).isEmpty() && s[i] == -1) {
                s[i] = s[parents[i]];
                continue;
            }
            if (s[i] != -1) continue;

            int min = Integer.MAX_VALUE;
            for (Integer child : children.get(i)) {
                min = Math.min(min, s[child]);
            }
            if (min < s[parents[i]]) {
                possible = false;
                break;
            }
            s[i] = min;
        }
        for (int i = 0; i < n; i++) {
            if (i == 0) a[i] = s[i];
//            else if (children.get(i).isEmpty()) a[i] = 0;
            else a[i] = s[i] - s[parents[i]];
            answer += a[i];
        }
        System.out.println(possible ? answer : -1);
    }
}
