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 prbl7 {
	static boolean[] visited;
	static LinkedList<Integer>[] tab;
	static Queue<Integer> q;
	static int ct=0;
	static long[] val;
	static long[] s;
	static int n;
	static long[] si;
	public static void DFS(int a) {
		q.add(a);
		visited[a-1]=true;
		while (!q.isEmpty()) {
			long ans=Long.MAX_VALUE;				
			int n=q.peek();
			q.remove();
			for (int i : tab[n-1]) {
			
					if (s[n-1]!=-1) {
					    //si[n-1]=s[n-1];
						si[i-1]=s[n-1];
						
					}
					else {
						//System.out.println(s[i-1]-si[n-1]+" cou");
						ans=Math.min(s[i-1]-si[n-1], ans);
						si[i-1]=s[i-1];
						
					}
					q.add(i);
					visited[i-1]=true;
					
				
				//s[n-1]=s[i-1]+val[n-1];
			}
			
			if (s[n-1]==-1) {
				
				if (ans!=Long.MAX_VALUE)
					val[n-1]=ans;			
				si[n-1]=si[n-1]+val[n-1];
				for (int i : tab[n-1]) {
					val[i-1]=s[i-1]-si[n-1];
				}
			}
		
			
			ct++;
			
		}
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		n=sc.nextInt();
		visited=new boolean[n];
		tab=new LinkedList[n];
		for (int i=0; i<n; i++) {
			tab[i]=new LinkedList<Integer>();
		}
		q=new LinkedList<Integer>();
		si=new long[n];
		ct=0;
		val=new long[n];
		s=new long[n];
		for (int i=0; i<n-1; i++) {
			int a=sc.nextInt();
			tab[a-1].add(i+2);
		}
		for (int i=0; i<n; i++) {
			s[i]=sc.nextInt();
		}
		DFS(1);
		val[0]=s[0];
		long ans=0;
		boolean found=true;
		for (long i :val) {
			//System.out.println(i);
			if (i<0) {
				System.out.println(-1);
				found=false;
			    break;
			}
			
			ans+=i;
			
		}
		if (found)
			System.out.println(ans);

	}

}
