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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

import static java.lang.Math.abs;
import static java.lang.Math.copySign;
import static java.lang.Math.max;
import static sun.nio.ch.IOStatus.check;

public class D {

    public static void main(String[] args) {

        MyScanner in = new MyScanner();
        int n = in.nextInt();

        int[] p = new int[n];
        int[] s = new int[n];
     //   int[] a = new int[n];

        List<Integer>[] tree = new List[n];
        for (int i = 0; i < n; ++i) {
            tree[i] = new ArrayList<>();
        }

        for (int i = 0; i < n - 1; ++i) {
            p[i + 1] = in.nextInt() - 1;
            tree[p[i + 1]].add(i + 1);
        }

        for (int i = 0; i < n; ++i) {
            s[i] = in.nextInt();
        }

        Queue<Integer> queue = new ArrayDeque<>();
        queue.add(0);

        long result = 0;

        while(!queue.isEmpty()){
            int index = queue.poll();
            if(index == 0){
                result += s[index];
            }else if(s[index] == -1){

                int childMin = Integer.MAX_VALUE;

                for(Integer c:tree[index]){
                    childMin = Math.min(childMin, s[c]);
                }

                if(childMin < s[p[index]]){
                    System.out.println(-1);
                    return;
                }

                if(childMin == Integer.MAX_VALUE){
                    childMin = s[p[index]];
                }

                s[index] = childMin;
              //  System.out.println(index+" "+s[index]);
                result += s[index] - s[p[index]];

            }else{
                if(s[index] < s[p[index]]){
                    System.out.println("-1");
                    return;
                }else{
                    result += s[index] - s[p[index]];
                }
            }
            for(Integer c:tree[index]){
                queue.add(c);
            }
        }

        System.out.println(result);
    }


    // -----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    // --------------------------------------------------------


}
