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.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		int n=s.nextInt();
		
		int[] parent=new int[n+1];
		
		for(int i=2;i<n+1;i++)
		{
			parent[i]=s.nextInt();
		}
		
		long[] sum=new long[n+1];
		
		for(int i=1;i<n+1;i++)
		{
			sum[i]=s.nextLong();
		}
		
		ArrayList<Integer>[] arr=new ArrayList[n+1];
		
		for(int i=0;i<n+1;i++)
		{
			ArrayList<Integer> list=new ArrayList<>();
			arr[i]=list;
		}
		
		for(int i=2;i<n+1;i++)
		{
			arr[i].add(parent[i]);
			arr[parent[i]].add(i);
		}
		
		long[] val=new long[n+1];
		val[1]=sum[1];
		int[] visited=new int[n+1];
		
		dfs(arr,visited,val,1,1,parent,sum);
		
		int p=0;
		
		long ans=0;
		
		for(int i=1;i<n+1;i++)
		{
			ans=ans+val[i];
			
			if(val[i]<0)
				p=1;
		}
		
		if(p==0)
		{
			System.out.println(ans);
		}
		else
		{
			System.out.println(-1);
			
		}
		
	}
	
	public static void dfs(ArrayList<Integer>[] arr,int[] visited,long[] val,int curr,int level,int[] parent,long[] sum)
	{
		visited[curr]=1;
		
		if(level%2==0)
		{
			sum[curr]=Integer.MAX_VALUE;
			
			for(int i=0;i<arr[curr].size();i++)
			{
				int now=arr[curr].get(i);
				
				if(visited[now]==0)
				sum[curr]=Math.min(sum[now],sum[curr]);
			}
		}
		
		int p=0;
		
		for(int i=0;i<arr[curr].size();i++)
		{
			int now=arr[curr].get(i);
			
			if(visited[now]==0)
			{
				dfs(arr,visited,val,now,level+1,parent,sum);
				p=1;
			}
		}
		
		if(level%2==0)
		{
			if(p==1)
			{
				val[curr]=sum[curr]-sum[parent[curr]];
			}
			else
			{
				val[curr]=0;
			}
		}
		else
		{
			val[curr]=sum[curr]-sum[parent[curr]];
		}
	}
	
}