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.*;
import java.io.*;
public class code{
    public static int n;
    public static int[] p;
    public static int[] s;
    public static int[] a;
    public static boolean ok = false;
    public static ArrayList<Integer>[] fils;
    public static void dfs1(int som,int somme){
        a[som] = s[som];
        if(s[som]<somme&&s[som]!=-1) ok = true;
        if(a[som]!=-1) a[som]-=somme;
        int k = a[som];
        if(k==-1) k=0;
        for(int x:fils[som]){
            dfs1(x,somme+k);
        }
    }
    public static int dfs2(int som){
        int min = -1;
        if(fils[som].size()==0) {
            if(a[som]==-1) a[som] = 0;
            return a[som];
        }
        for(int x:fils[som]){
            if(min==-1) min = dfs2(x);
            else min = Math.min(min,dfs2(x));
        }
        if(a[som]==-1){
            a[som] = min;
            for(int x:fils[som]){
                a[x] -= min;
            }
        }
        return a[som];
    }
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(br.readLine());
        p = new int[n];
        fils = new ArrayList[n];
        for(int i=0;i<n;i++) fils[i] = new ArrayList<Integer>();
        p[0] = -1;
        StringTokenizer st = new StringTokenizer(br.readLine());
        for(int i=1;i<n;i++){
            p[i] = Integer.parseInt(st.nextToken())-1;
            fils[p[i]].add(i);
        }
        s = new int[n];
        st = new StringTokenizer(br.readLine());
        for(int i=0;i<n;i++){
            s[i] = Integer.parseInt(st.nextToken());
        }
        a = new int[n];
        dfs1(0,0);
        //for(int i=0;i<n;i++){
        //    System.out.print(" "+a[i]);
        //}
        //System.out.println("");
        long k = (long)dfs2(0);
        k = 0;
        for(int i=0;i<n;i++){
            //System.out.print(" "+a[i]);
            k += (long)a[i];
        }
        if(ok) k=-1;
        System.out.println(k);
    }
}