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.Map;
import java.util.Map.Entry;
import java.util.Scanner;
import java.util.TreeMap;



public class Main {

	public static class Node{
		Node parent;
		ArrayList<Node> children = new ArrayList<>();
		int index;
		long a;
		long s;
	}

	public static void dfs(int depth, Node curr, Map<Integer, ArrayList<Node>> map){
		if(!map.containsKey(depth)){
			map.put(depth, new ArrayList<Node>());
		}
		
		map.get(depth).add(curr);
		
		for(int i = 0; i < curr.children.size();i++){
			dfs(depth + 1, curr.children.get(i), map);
		}
	}
	
	public static void main(String[] args){
		
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		
		Node[] nodes = new Node[n + 1];
		
		for(int i = 1; i <= n; i++){
			nodes[i] = new Node();
		}
		for(int i = 2; i <= n; i++){
			int parent = sc.nextInt();
			nodes[i].parent = nodes[parent];
			nodes[i].index = i;
			nodes[parent].children.add(nodes[i]);
		}

		for(int i = 1; i <= n; i++){
			nodes[i].s = sc.nextLong();
		}
		Map<Integer, ArrayList<Node>> levels = new TreeMap<Integer, ArrayList<Node>>();
		dfs(1, nodes[1], levels);
		
		long sum = nodes[1].s;
		nodes[1].a = nodes[1].s;
		for(Entry<Integer, ArrayList<Node>> entry : levels.entrySet()){
			if(entry.getKey() % 2 == 0){
				for(Node node : entry.getValue()){
					if(node.children.size() == 0){
						continue;
					}
					long min = Long.MAX_VALUE;
					for(Node child : node.children){
						min = Math.min(min, child.s);
					}
					node.a = min - node.parent.s;
					
					if(node.a < 0){
						System.out.println(-1);
						return;
					}
					sum += node.a;
					
					for(Node child : node.children){
						child.a = child.s - node.a - node.parent.s;
						sum += child.a;
					}
				}
			}
		}
		System.out.println(sum);
	}
}
