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 Hemose {
    static int n;
    static ArrayList<Integer>[]g;
    static long[]nums;
    static boolean[]vis;
    static long sum;
    static void dfs(int u ,long p){
        vis[u]=true;
        long t=nums[u]-p;
        if (nums[u]==-1){
            t=g[u].isEmpty()?0:1000000000000l;
            for (int v:g[u]){
                t=Math.min(t,nums[v]-p);
            }
        }
        if (sum>=0&&t>=0){
            sum+=t;
        }
        else sum=-1;
        for (int v:g[u]){
            if (!vis[v]){
                dfs(v,p+t);
            }
        }
    }
    public  static  void  main(String[]args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        g=new ArrayList[n];
        for (int i=0;i<n;i++){
            g[i]=new ArrayList<>();
        }
        for (int i =1;i<n;i++){
            g[sc.nextInt()-1].add(i);
        }
//        System.out.println(Arrays.toString(g));

        vis= new boolean[n];
        nums= new long[n];
        for (int i=0;i<n;i++)
            nums[i]=sc.nextLong();
        sum=0;
       dfs(0,0);
       pw.println(sum);
       pw.flush();
    }
    static class Scanner
    {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

        public String next() throws IOException
        {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {return br.readLine();}

        public double nextDouble() throws IOException
        {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if(x.charAt(0) == '-')
            {
                neg = true;
                start++;
            }
            for(int i = start; i < x.length(); i++)
                if(x.charAt(i) == '.')
                {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                }
                else
                {
                    sb.append(x.charAt(i));
                    if(dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg?-1:1);
        }

        public boolean ready() throws IOException {return br.ready();}


    }
}