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
//package com.company;

import java.io.*;
import java.util.*;


public class Main {
    public static class Task {
        boolean bad = false;
        public long dfs(List<Integer>[] tree, int[] vals, int cur, int pass) {
            int curVal = vals[cur];
            long sums = curVal - pass;
            for(int evenChild : tree[cur]) {
                int minimum = Integer.MAX_VALUE;
                for (int oddChild: tree[evenChild]) {
                    minimum = Math.min(minimum, vals[oddChild]);
                }
                if (minimum == Integer.MAX_VALUE) {
                    minimum = curVal;
                }
                if (minimum < curVal) {
                    bad = true;
                    return Long.MIN_VALUE;
                }
                sums += minimum - curVal;
                for (int oddChild: tree[evenChild]) {
                    sums += dfs(tree, vals, oddChild, minimum);
                }
            }
            return sums;
        }

        public void solve(Scanner sc, PrintWriter pw) throws IOException {
            int n = sc.nextInt();
            List<Integer>[] tree = new List[n];
            for (int i = 0; i < n; i++) {
                tree[i] = new ArrayList<>();
            }
            for (int i = 1; i < n; i++) {
                int a = sc.nextInt() - 1;
                tree[a].add(i);
            }
            int[] vals = new int[n];
            for (int i = 0; i < n; i++) {
                vals[i] = sc.nextInt();
            }
            long x = dfs(tree, vals, 0, 0);
            pw.println(bad ? -1 : x);
        }

    }

    private static long TIME_START, TIME_END;
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
//        Scanner sc = new Scanner(new FileInputStream("B-large.in"));
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
//        PrintWriter pw = new PrintWriter(new FileOutputStream("Test.out"));
//        PrintWriter pw = new PrintWriter(new FileOutputStream("Test.in"));
        Runtime runtime = Runtime.getRuntime();
        long usedMemoryBefore = runtime.totalMemory() - runtime.freeMemory();
        TIME_START = System.currentTimeMillis();
        Task t = new Task();
        t.solve(sc, pw);
        TIME_END = System.currentTimeMillis();
        long usedMemoryAfter = runtime.totalMemory() - runtime.freeMemory();
        pw.close();
        System.out.println("Memory increased:" + (usedMemoryAfter-usedMemoryBefore) / 1000000 );
        System.out.println("Time used: " + (TIME_END - TIME_START) + ".");
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

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

        public Scanner(FileReader s) throws FileNotFoundException {br = new BufferedReader(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 { return Double.parseDouble(next()); }

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