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.*;
public class Main {
    public static class Graph {
        int n;
        TreeSet<Integer>[] adj;
        long[] val;
        public Graph(int n) {
            this.n = n;
            adj = new TreeSet[n];
            for (int i = 0; i < n; i++) {
                adj[i] = new TreeSet<>();
            }
            val = new long[n];
        }
        public void addEdge(int i, int j) {
            adj[i].add(j);
        }
        public void set(int i, long x) {
            val[i] = x;
        }
        public String toString() {
            String out = "";
            for (int i = 0; i < n; i++) {
                out += i + ": ";
                for (int v : adj[i]) {
                    out += v + " ";
                }
                out += "\n";
            }
            return out;
        }
    }
    public static Graph graph;
    public static long sum = 0;
    public static boolean flag = true;
    public static void dfs(int i, long x, int depth) {
        if (depth == 0) {
            long value = graph.val[i];
            if (value < x) {
                flag = false;
                return;
            }
            sum += (value - x);
            for (int v : graph.adj[i]) {
                dfs(v, value, 1);
            }
        } else {
            if (graph.adj[i].isEmpty()) {
                return;
            }
            long min = Long.MAX_VALUE;
            for (int v : graph.adj[i]) {
                min = Math.min(min, graph.val[v]);
            }
            if (min < x) {
                flag = false;
                return;
            }
            sum += (min - x);
            for (int v : graph.adj[i]) {
                dfs(v, min, 0);
            }
        }
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        graph = new Graph(n);
        for (int i = 0; i < n - 1; i++) {
            int p = in.nextInt();
            graph.addEdge(p - 1, i + 1);
        }
        for (int i = 0; i < n; i++) {
            graph.set(i, in.nextLong());
        }
        dfs(0, 0, 0);
        System.out.println(flag ? sum : -1);
    }
}