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.util.Scanner;

public class Problem4 {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] p = new int[n+1];
		int[] s = new int[n+1];
		for (int i=2; i<=n; i++) {
			p[i] = sc.nextInt();
		}
		for (int i=1; i<=n; i++) {
			s[i] = sc.nextInt();
			if (s[i] == -1) {
				s[i] = 1000000001;
			}
		}
		for (int i=2; i<=n; i++) {
			s[p[i]] = Math.min(s[i], s[p[i]]);
		}
		long sum = 0;
		for (int i=2; i<=n; i++) {
			int temp = s[i]-s[p[i]];
			if (temp < 0) {
				System.out.println(-1);
				sc.close();
				return;
			}
			if (s[i] <= 1000000000) {
				sum += temp;
			}
		}
		System.out.println(s[1] + sum);
		sc.close();
	}

}
