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.*;
public class A_1098 {
	public static void main(String[]args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[]parent=new int[n];
		HashMap<Integer,HashSet<Integer>>children=new HashMap<Integer,HashSet<Integer>>();
		children.put(0,new HashSet<Integer>());
		for(int i=1;i<n;i++){
			children.put(i,new HashSet<Integer>());
			int p=sc.nextInt()-1;
			parent[i]=p;
			children.get(p).add(i);
		}
		int[]h=new int[n];
		h[0]=1;
		for(int i=1;i<n;i++)
			h[i]=h[parent[i]]+1;
		int[]s=new int[n];
		boolean possible=true;
		for(int i=0;i<n;i++){
			s[i]=sc.nextInt();
			if((s[i]==-1)!=(h[i]%2==0))
				possible=false;
		}
		sc.close();
		long sum=s[0];
		if(possible){
			for(int i=0;i<n;i++)
				if(s[i]==-1){
					int min=Integer.MAX_VALUE;
					for(int c:children.get(i))
						min=Math.min(min,s[c]);
					if(children.get(i).isEmpty())
						min=s[parent[i]];
					if(min<s[parent[i]])
						possible=false;
					s[i]=min;
				}
			for(int i=1;i<n;i++)
				sum+=s[i]-s[parent[i]];
		}
		System.out.println(possible?sum:-1);
	}
}