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.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class A {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scan = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        int[] p = new int[n]; for(int i=0; i<n-1; i++) p[i+1] = Integer.parseInt(st.nextToken())-1;
        p[0] = -1;
        st = new StringTokenizer(bf.readLine());
        int[] s = new int[n]; for(int i=0; i<n; i++) s[i] = Integer.parseInt(st.nextToken());
        int[] a = new int[n];
        a[0] = s[0];

        ArrayList<ArrayList<Integer>> children = new ArrayList<ArrayList<Integer>>();
        for(int i=0; i<n; i++) children.add(new ArrayList<Integer>());
        for(int i=1; i<n; i++) children.get(p[i]).add(i);
        long ans = 0;
        ans += a[0];
        for(int i=0; i<n; i++) {
          long cur_ans = 0;
          if(s[i] == -1) {
            if(children.get(i).size() == 0) cur_ans = 0;
            else {
              int min = Integer.MAX_VALUE;
              for(int j : children.get(i)) if(s[j] < min) min = s[j];
              //out.println(min);
              min -= s[p[i]];
              if(min < 0) {
                out.println("-1");
                out.close();
                System.exit(0);
              }
              else {
                cur_ans += min;
                for(int j : children.get(i)) cur_ans += s[j] - min - s[p[i]];

              }
            }
          }
          ans += cur_ans;
        }
        out.println(ans);
        // int n = Integer.parseInt(st.nextToken());
        // int n = scan.nextInt();

        out.close(); System.exit(0);
    }
}
