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.util.Comparator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class D {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();

        Node[] nodes = new Node[n];
        nodes[0] = new Node();

        for (int i = 1; i < n; i++) {
            Node node = new Node();
            int parent = scan.nextInt() - 1;
            nodes[parent].addChild(node);
            node.parent = nodes[parent];
            nodes[i] = node;
        }

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

        Queue<Node> queue = new LinkedList<>(nodes[0].children);
        long result = nodes[0].a;

        while (!queue.isEmpty()) {
            Node node = queue.poll();
            int min = node.min();
            if (min == -1) {
                node.a = 0;
                continue;
            }
            if (min < node.parent.s) {
                System.out.println("-1");
                return;
            }

            node.a = min - node.parent.s;
            node.s = min;
            result += node.a;
            for (Node child : node.children) {
                child.a = child.s - node.s;
                queue.addAll(child.children);
                result  += child.a;
            }
        }
        System.out.println(result);

    }

    static class Node {
        int a;
        int s;
        Node parent;
        LinkedList<Node> children = new LinkedList<>();

        void addChild(Node child) {
            children.add(child);
        }

        int min() {
            return children.stream()
                    .mapToInt(n -> n.s)
                    .min()
                    .orElse(-1);
        }
    }
}
