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.util.*;

public class qwe{
    int n;
    int x;
    int s[];
    long res;
    ArrayList<Integer> g[];
    void dfs(int v, int p, int d){
        if(d % 2 == 0){
            int mn = (int)1e9;
            s[v] = s[p];
            for(int to: g[v]){
                mn = Math.min(mn, s[to]);
            }
            if(mn != (int)1e9 && mn > s[v]){
                s[v] = mn;
            }
        }
        if(s[v] < s[p]){
            System.out.print("-1\n");
            System.exit(0);
        }
        res += s[v] - s[p];
        for(int to: g[v]){
            if(to == p){
                continue;
            }
            dfs(to, v, d + 1);
        }
    }
    void solve(Scanner in, PrintWriter out) {
        n = in.nextInt();
        s = new int[n + 1];
        g = new ArrayList[n + 1];
        for(int i = 1; i <= n; i ++){
            g[i] = new ArrayList<>();
        }
        for(int i = 2; i <= n; i ++){
            x = in.nextInt();
            g[x].add(i);
        }
        for(int i = 1; i <= n; i ++){
            s[i] = in.nextInt();
        }
        dfs(1, 0, 1);
        out.print(res + "\n");
        return;
    }
    void run(){
        try(
                Scanner cin = new Scanner(System.in);
                PrintWriter cout = new PrintWriter(System.out)){

                solve(cin, cout);
        }
    }
    public static void main(String args[]) {
        new qwe().run();
    }
}