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 Test {

    static boolean vis[];
    static int n, mums[], s[], a[];
    static ArrayList<Integer> g[];

    static final int cnst = 0;

    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        n = in.nextInt(); mums = new int[n]; s = new int[n]; a = new int[n];
        g = new ArrayList[n]; vis = new boolean[n];
        for(int i = 0; i<n; i++) g[i] = new ArrayList<>();

        for(int i = 1; i<n; i++){
            int v = in.nextInt()-1;
            g[v].add(i); g[i].add(v);
            mums[i] = v;
        }
        for(int i = 0; i<n; i++){
            s[i] = in.nextInt();
        }

        a[0] = s[0];
        dfs(0);

        long ans = 0;
        for(int x:a) ans+= x;
        System.out.println(ans);

    }

    static void dfs(int now){
        if(vis[now]) return;
        vis[now] = true;
        if(s[now]==-1){
            a[now] = 10000000;
            for(int x:g[now])
                if(!vis[x])
                    a[now] = Math.min(a[now], s[x]-s[mums[now]]);
            if(a[now]<0) impossible();
            if(a[now]==10000000) a[now] = 0;
            s[now] = a[now]+s[mums[now]];
            for(int x:g[now]){
                if(!vis[x])
                    a[x] = s[x]-s[now];
            }
        }
        for(int x:g[now])
            dfs(x);
    }

    static void impossible(){
        System.out.println(-1);
        System.exit(0);
    }

}