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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.LinkedList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Hung Vu
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DSumInTheTree solver = new DSumInTheTree();
        solver.solve(1, in, out);
        out.close();
    }

    static class DSumInTheTree {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            LinkedList<Integer>[] list = new LinkedList[n];
            long[] a = new long[n];
            long[] p = new long[n];
            for (int i = 0; i < n; i++)
                list[i] = new LinkedList<>();

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

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

            long res = a[0];

            LinkedList<Integer> queue = new LinkedList<Integer>();
            queue.add(0);
            while (queue.size() != 0) {
                int v = queue.poll();
//            out.println(v);
//            out.println(res);
                if (a[v] == -1) {
                    if (list[v].size() != 0) {
                        long minVal = Long.MAX_VALUE;
                        for (int i : list[v]) {
                            minVal = Math.min(minVal, a[i]);
                        }

                        if (minVal < p[v]) {
                            out.println(-1);
                            return;
                        } else {
                            a[v] = minVal;
                            res += a[v] - p[v];
                        }

                        for (int i : list[v]) {
                            p[i] = a[v];
                            res += a[i] - minVal;
                            queue.add(i);
                        }
                    }
                } else {
                    for (int i : list[v]) {
                        p[i] = a[v];
                        queue.add(i);
                    }
                }
            }
//        for (int i = 0; i < n; i++) {
//            out.println(p[i]);
//        }
            out.println(res);
        }

    }
}

