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 CF {
    static ArrayList<Integer>[] arr;
    static int n;
    static int[] p;
    static int[] s;
    static int[] a;
    static long ans;
    static boolean bad = false;

    public static void main(String[] args) throws IOException {
        BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(file.readLine());
        StringTokenizer st = new StringTokenizer(file.readLine());
        arr = new ArrayList[n];
        p = new int[n];
        for (int i=0; i<n; i++){
            arr[i] = new ArrayList<>();
        }
        for (int i=0; i<n-1; i++){
            int curr = Integer.parseInt(st.nextToken())-1;
            p[i+1] = curr;
            arr[curr].add(i+1);
            arr[i+1].add(curr);
        }
        st = new StringTokenizer(file.readLine());
        s = new int[n];
        for (int i=0; i<n; i++){
            s[i] = Integer.parseInt(st.nextToken());
        }
        a = new int[n];
        a[0] = s[0];
        ans = s[0];
        dfs(0, -1);
        if (bad){
            System.out.println(-1);
        }else{
            System.out.println(ans);
        }
    }
    public static void dfs(int curr, int parent){
        if (s[curr] == -1){
            int min = Integer.MAX_VALUE;
            for (int i : arr[curr]){
                if (i != parent){
                    if (s[i] < s[parent]){
                        bad = true;
                        return;
                    }
                    min = Math.min(s[i] - s[parent], min);
                }
            }
            if (min == Integer.MAX_VALUE){
                s[curr] = s[parent];
            }else{
                a[curr] = min;
                s[curr] = s[parent]+min;
                ans += min;
            }
        }else if (parent != -1){
            ans += s[curr]-s[parent];
        }
        for (int i : arr[curr]){
            if (i != parent){
                dfs(i, curr);
            }
        }
    }
}