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.math.BigInteger;
import java.util.*;

public class A {
    static MyScanner sc;
    static PrintWriter pw;

    public static void main(String[] args) throws Throwable {
        sc = new MyScanner();
        pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        int[] p = new int[n];
        ArrayList<Integer>[] adj = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adj[i] = new ArrayList<>();
        for (int i = 1; i < n; i++) {
            p[i] = sc.nextInt() - 1;
            adj[p[i]].add(i);
        }
        int[] s = new int[n];
        for (int i = 0; i < n; i++)
            s[i] = sc.nextInt();
        boolean ok = true;
        long ans = s[0];
        for (int i = 1; i < n; i++) {
            if (s[i] == -1) {
                int mnDif = Integer.MAX_VALUE;
                for (int v : adj[i])
                    mnDif = Math.min(mnDif, s[v] - s[p[i]]);
                if (mnDif < 0) {
                    ok = false;
                    break;
                }
                if (mnDif == Integer.MAX_VALUE)
                    mnDif = 0;
                s[i] = s[p[i]] + mnDif;
                ans += mnDif;
            } else
                ans += s[i] - s[p[i]];
        }

        if (ok)
            pw.println(ans);
        else
            pw.println(-1);

        pw.flush();
        pw.close();
    }

    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;
        }
    }
}