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 SumInTheTree {
	public static void main (String [] args) throws IOException{
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(in.readLine());
		Node tree [] = new Node[n];
		tree[0] = new Node();
		
		StringTokenizer st = new StringTokenizer(in.readLine());
		for (int i = 1; i < n; i++) {
			tree[i] = new Node(tree[Integer.parseInt(st.nextToken()) - 1]);
			tree[i].parent.child.add(tree[i]);
		}
		
		st = new StringTokenizer(in.readLine());
		for (int i = 0; i < n; i++)
			tree[i].sum = Integer.parseInt(st.nextToken());
		
		long ans = tree[0].sum;
		for (int i = 1; i < n; i++) {
			if (tree[i].sum == -1) {
				tree[i].sum = tree[i].min();
			}
			if (tree[i].sum  < tree[i].parent.sum) {System.out.println(-1); return;}
			ans += tree[i].sum - tree[i].parent.sum;
		}
		
		System.out.println(ans);
	}
	static class Node {
		Node parent;
		int sum;
		ArrayList<Node> child = new ArrayList<Node>();
		public Node () {}
		public Node (Node parent) {this.parent = parent;}
		
		public int min () {
			if (child.size() == 0)
				return parent.sum;
			
			int m = Integer.MAX_VALUE;
			for (Node n: child) 
				m = Math.min(m, n.sum);
			return m;
		}
	}
}
