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.Scanner;
import java.math.BigInteger;
public class Main {
    private static Scanner sc = new Scanner(System.in);
    public static void main(String[] args) {
        int N = sc.nextInt();
        int[] fathers = new int[N + 1];
        int[] sums = new int[N + 1];
        int[] sums2 = new int[N + 1];
        for (int i = 2; i <= N; i++) {
            fathers[i] = sc.nextInt();
        }
        for (int i = 1; i <= N; i++) {
            sums[i] = sc.nextInt();
            sums2[i] = sums[i];
            if (sums[i] < 0) {
                sums[i] = Integer.MAX_VALUE;
            }
        }
        for (int i = N; i > 1; i--) {
            if (sums[fathers[i]] > sums[i]) {
                sums[fathers[i]] = sums[i];
            }
        }
        long total = 0;
        for (int i = 1; i <= N; i++) {
            if (sums2[i] >= 0 && sums2[i] != sums[i]) {
                System.out.print("-1");
                return;
            }
            if (sums[i] < Integer.MAX_VALUE) total += (sums[i] - sums[fathers[i]]);
        }
        System.out.print("" + total);
    }
}