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.ArrayList;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {
    static ArrayList<Integer> tree [] ;
    static int s [];
    static int p [];
    public static void main (String [] args)throws Exception{
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
        int n  = Integer.parseInt(input.readLine());
        tree = new ArrayList[n];
        tree[0]=new ArrayList<>();
        s= new int [n];
        p = new int [n];
        StringTokenizer st = new StringTokenizer(input.readLine());
        p[0]=-1;
        for (int i =1 ; i <n; i++){
            tree[i]=new ArrayList<>();
            p[i] = Integer.parseInt(st.nextToken())-1;
            tree[p[i]].add(i);
        }

        st = new StringTokenizer(input.readLine());
        for (int i = 0 ; i<n ;i++){
            s[i]= Integer.parseInt(st.nextToken());
        }

        System.out.println(dfs());

    }
    static long dfs (){
        Stack<Integer> stack = new Stack();
        int max = 0 ;
        stack.push(0);
        long total = s[0];
        while(!stack.isEmpty()){
            int temp = stack.pop();
            if (s[temp] != -1 && p[temp] !=-1){
                if ( s[p[temp]]>s[temp])
                    return -1;
                total+=s[temp]-s[p[temp]];
            }
            int min =Integer.MAX_VALUE;
            for (int child :tree[temp]){
                stack.push(child);
                min = Math.min(min, s[child]);
            }
            if (min!= Integer.MAX_VALUE && s[temp]==-1){
                if(min < s[p[temp]])
                    return -1;
                s[temp]=min;
                total+=min-s[p[temp]];
            }

        }

        return total;
    }


}
