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.*;
import java.util.*;
public class A1098
{
    static int n,arr[],val[];
    static boolean vis[];
    static HashMap<Integer,ArrayList<Integer>> map;
    static boolean dfs(int ind,int p)
    {
        if(arr[ind]==-1)
        {
            if(map.get(ind).size()==0)
            {
                arr[ind]=p;
            }
            else
            {
                int min=Integer.MAX_VALUE;
                for(int i:map.get(ind))
                {
                    min=Math.min(min,arr[i]);
                }
                if(min<p)
                    return false;
                arr[ind]=min;
                val[ind]=arr[ind]-p;
            }
        }
        else
        {
            val[ind]=arr[ind]-p;
            if(val[ind]<0)
                return false;
        }
        for(int i:map.get(ind))
        {
            if(!dfs(i,arr[ind]))
                return false;
        }
        return true;
    }
    public static void main(String args[])throws IOException
    {
        Scanner sc=new Scanner(System.in);
        n=sc.nextInt();
        arr=new int[n+1];
        vis=new boolean[n+1];
        val=new int[n+1];
        map=new HashMap<>();
        for(int i=1;i<=n;i++)
        {
            map.put(i,new ArrayList<>());
        }
        for(int i=2;i<=n;i++)
        {
            int x=sc.nextInt();
            map.get(x).add(i);
        }
        for(int i=1;i<=n;i++)
        {
            arr[i]=sc.nextInt();
        }
        if(dfs(1,0))
        {
            long sum=0;
            for(int i=1;i<=n;i++)
            {
                sum+=val[i];
            }
            System.out.println(sum);
        }
        else
            System.out.println(-1);
    }
}