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.IOException;
import java.util.ArrayList;
import java.util.Scanner;

public class ProblemD {
	static void dfs(int node,int size,ArrayList<ArrayList<Integer>> graph){
		if(sum[node]==-1){
			if(graph.get(node).size()==0){
				sum[node]=sum[parentList[node]];
				arr[node]=0;
			}else{
				int min = Integer.MAX_VALUE;
				for(int child:graph.get(node)){
					min=Math.min(sum[child],min);
					if(min<sum[parentList[node]]){
						System.out.println("-1");
						System.exit(0);
					}
				}
				sum[node]=min;
				arr[node]=min-sum[parentList[node]];
			}
		}else{
			arr[node]=sum[node]-sum[parentList[node]];
		}
		ans+=arr[node];
		for(int child:graph.get(node)){
			dfs(child,size,graph);
		}
	}
	static long ans;
	static int[] sum;
	static int[] arr;
	static int[] parentList;
	public static void main(String[] args) throws IOException {
		Scanner scan = new Scanner(System.in);
		ArrayList<ArrayList<Integer>> graph= new ArrayList<ArrayList<Integer>>();
		int n = scan.nextInt();
		sum = new int[n+1];
		arr = new int[n+1];
		parentList = new int[n+1];
		for(int i=0;i<=n;i++) {
			graph.add(new ArrayList<Integer>());
		}
		for(int i=2;i<=n;i++){
			int parent = scan.nextInt();
			parentList[i]=parent;
			graph.get(parent).add(i);
		}
		for(int i=1;i<=n;i++){
			sum[i]=scan.nextInt();
		}
		ans = 0L;
		dfs(1,n,graph);
		System.out.println(ans);
		scan.close();
	}
}
