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 Main {
    public static void main(String[] args)  {
        __SolutionBase begin = new __SolutionBase();
        begin.Solve();
    }
}

class __SolutionBase {

    public void Solve() {
        init();
        Solution();
        out.close();
    }

    private List<Integer>[] graph;
    private int[] sum;
    private int[] a;
    private void Solution(){
        int n = readInt();
        graph = new List[n];
        for (int i = 0;i < n;i++) graph[i] = new ArrayList<>();

        for (int i = 1;i < n;i++){
            int input = readInt() - 1;
            graph[input].add(i);
        }

        sum = new int[n];
        a = new int[n];
        for (int i = 0; i < n;i++)
            sum[i] = readInt();

        a[0] = sum[0];
        dfs(0,0,1);
        long sum = 0;
        for (int i = 0;i < n;i++)
            sum += a[i];
        out.println(sum);
    }


    private void dfs(int from,int parent,int depth){
        if (depth % 2 == 0){
            int min = Integer.MAX_VALUE;
            for (int elem:graph[from]){
                if (sum[elem] < sum[parent]){
                    out.println(-1);
                    out.close();
                    System.exit(0);
                }
                min = Math.min(min,sum[elem] - sum[parent]);
            }
            a[from] = min == Integer.MAX_VALUE? 0 : min;
            for (int elem:graph[from])
                a[elem] = sum[elem] - sum[parent] - a[from];
        }
        for (int elem:graph[from])
            dfs(elem,from,depth + 1);
    }

    /**
     * readLong, readDouble and other are similar
     *
     * @return int type from input
     */
    private int readInt() {
        return Integer.parseInt(readString());
    }

    private long readLong() {
        return Long.parseLong(readString());
    }
    /**
     * Tokens are separated by space or endExclusive of line
     *
     * @return non-empty string token from input (or null if there is no any token)
     */
    private String readString() {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) return null;
            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken();
    }

    /**
     * @return whole line from input
     */
    private String readLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer tok = new StringTokenizer(" ");

    /**
     * For local testing I use pair 'input.txt'/'output.txt' in the project root
     */
    private void init() {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (FileNotFoundException e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }
}