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.PrintStream;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.Stack;

public class SumInTheTree {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintStream out = System.out;
        solve(in, out);
    }

    static void solve(Scanner in, PrintStream out) {
        int n = in.nextInt();
        Node[] nodes = new Node[n];
        nodes[0] = new Node(0, null);
        for (int i = 1; i < n; i++) {
            nodes[i] = new Node(i, nodes[in.nextInt() - 1]);
            nodes[i].parent.children.add(nodes[i]);
        }
        for (int i = 0; i < n; i++) {
            nodes[i].s = in.nextLong();
        }
        Stack<Node> stack = new Stack<>();
        long sum = 0;
        stack.push(nodes[0]);
        while (!stack.isEmpty()) {
            Node node = stack.pop();
            if (node.s == -1) {
                if (node.children.isEmpty()) {
                    node.a = 0;
                    node.s = node.parent.s;
                } else {
                    long minSOfChildren = Long.MAX_VALUE;
                    for (Node child : node.children) {
                        minSOfChildren = Math.min(minSOfChildren, child.s);
                    }
                    node.a = minSOfChildren - node.parent.s;
                    node.s = minSOfChildren;
                }
            } else if (node.parent == null) {
                node.a = node.s;
            } else {
                node.a = node.s - node.parent.s;
            }
            if (node.a < 0) {
                out.println("-1");
                return;
            }
            sum += node.a;
            //out.println("for node " + (node.ix + 1) + ", a = " + node.a);
            for (Node child : node.children) {
                stack.push(child);
            }
        }
        out.println(sum);
    }

    static class Node {
        final int ix;
        final Node parent;
        final List<Node> children = new ArrayList<>();
        long a = -1;
        long s = -1;

        Node(int ix, Node parent) {
            this.ix = ix;
            this.parent = parent;
        }
    }
}
