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.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Scanner;

public class D {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		tree = new HashSet[n + 1];

		long[] sv = new long[n + 1];
		long[] av = new long[n + 1];

		for (int i = 0; i <= n; i++)
			tree[i] = new HashSet<>();

		for (int i = 2; i <= n; i++)
			tree[sc.nextInt()].add(i);

		for (int i = 1; i <= n; i++)
			sv[i] = sc.nextLong();

		if (dfs(1, sv, av, 0)) {
			long ans = 0;
			for (int i = 1; i <= n; i++)
				ans += av[i];
			System.out.println(ans);
		} else {
			System.out.println(-1);
		}
	}

	public static HashSet<Integer>[] tree;

	private static boolean dfs(int n, long[] sv, long[] av, long path) {
		if (sv[n] == -1) {
			if (tree[n].size() != 0) {
				long min = Long.MAX_VALUE;
				for (int c : tree[n])
					min = Math.min(min, sv[c]);
				if (min < path)
					return false;
				av[n] = min - path;
			}
			sv[n] = path + av[n];
		} else {
			av[n] = sv[n] - path;
			if (av[n] < 0)
				return false;
		}
		for (int child : tree[n])
			if (dfs(child, sv, av, sv[n]) == false)
				return false;
		return true;
	}

}
