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.*;
import java.util.*;

public class Codeforces1098A {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());

		st = new StringTokenizer(br.readLine());
		int[] p = new int[n];
		for (int i = 1; i < n; i++) {
			p[i] = Integer.parseInt(st.nextToken())-1;
		}
		
		st = new StringTokenizer(br.readLine());
		int[] s = new int[n];
		for (int i = 0; i < n; i++) {
			s[i] = Integer.parseInt(st.nextToken());
		}
		
		//keep track of all descendants
		int[] numdes = new int[n];
		for (int i = 0; i < n; i++) {
			numdes[p[i]]++;
		}
		
		int[] mindes = new int[n];
		for (int i = 0; i < n; i++) {
			mindes[i] = 1000000007;
		}
		for (int i = 0; i < n; i++) {
			mindes[p[i]] = Math.min(mindes[p[i]], s[i]);
		}
		
		for (int i = 0; i < n; i++) {
			if (s[i] == -1) {
				if (numdes[i] == 0) {
					s[i] = s[p[i]];
				}
				else {
					s[i] = mindes[i];
				}
			}
		}
		
		long sum = s[0];
		for (int i = 1; i < n; i++) {
			if ((sum >= 0) && (s[i] - s[p[i]] >= 0))
				sum += (long) (s[i] - s[p[i]]);
			else
				sum = -1;
		}
		System.out.println(sum);
		
	}

}
