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.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.IOException;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;


@SuppressWarnings("unchecked")
public class C {

	// 21:15-(21:26)-22:01
	public static void main(String[] args) throws IOException {
		try (PrintStream out = new PrintStream(new BufferedOutputStream(System.out))) {
			Scanner sc = new Scanner(new BufferedInputStream(System.in));

			int n = sc.nextInt();

			int[] a = new int[n];
			int[] s = new int[n];

			List[] g = new List[n];
			for (int i = 0; i < g.length; i++) g[i] = new ArrayList();
			for (int i = 1; i < n; i++) g[sc.nextInt() - 1].add(i);
			for (int i = 0; i < s.length; i++) s[i] = sc.nextInt();

			doit(0, g, 0, s, a);

			long sum = 0;
			for (int val : a) {
				sum += val;
				if (val < 0) {
					out.println(-1);
					return;
				}
			}

			out.println(sum);
		}
	}

	private static void doit(int v, List[] g, int x, int[] s, int[] a) {
		List<Integer> children = g[v];
		if (s[v] == -1) {
			if (!children.isEmpty()) {
				int min = Integer.MAX_VALUE;
				for (Integer child : children) min = Math.min(min, s[child]);
				a[v] = min - x;
			}
		} else {
			a[v] = s[v] - x;
		}

		for (Integer child : children) {
			doit(child, g, x + a[v], s, a);
		}
	}

}
