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.HashMap;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		long res = 0;
		int[] p = new int[n];
		p[0] = 1;
		HashMap<Integer, ArrayList<Integer>> tree = new HashMap<Integer, ArrayList<Integer>>();
		for (int i = 2; i <= n; i++) {
			int pi = in.nextInt();
			p[i - 1] = pi;
			if (!tree.containsKey(pi)) {
				tree.put(pi, new ArrayList<Integer>());
				tree.get(pi).add(i);
			} else {
				tree.get(pi).add(i);
			}
		}
		int[] s = new int[n];
		for (int i = 0; i < n; i++) {
			s[i] = in.nextInt();
		}
		for (int i = 1; i <= n; i++) {
			if (s[i - 1] == -1) {
				if (tree.containsKey(i)) {

					int min = Integer.MAX_VALUE;
					for (int j = 0; j < tree.get(i).size(); j++) {
						min = Math.min(min, s[tree.get(i).get(j) - 1]);
					}
					if (min < s[p[i - 1] - 1]) {
						System.out.println("-1");
						return;
					}
					res += min - s[p[i - 1] - 1];
					for (int j = 0; j < tree.get(i).size(); j++) {

						res += s[tree.get(i).get(j) - 1] - min;
					}

				}
			}
		}

		System.out.println(res + s[0]);

	}
}