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
//package suminthetree;

import java.util.*;
import java.io.*;

public class suminthetree {
	public static void main(String[] args) throws IOException {
		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(fin.readLine());
		ArrayList<ArrayList<Integer>> c = new ArrayList<ArrayList<Integer>>();
		for(int i = 0; i < n; i++) {
			c.add(new ArrayList<Integer>());
		}
		StringTokenizer st = new StringTokenizer(fin.readLine());
		for(int i = 1; i < n; i++) {
			int next = Integer.parseInt(st.nextToken()) - 1;
			c.get(next).add(i);
		}
		int[] nums = new int[n];
		st = new StringTokenizer(fin.readLine());
		for(int i = 0; i < n; i++) {
			nums[i] = Integer.parseInt(st.nextToken());
		}
		boolean isValid = true;
		long ans = 0;
		Queue<Integer> q = new ArrayDeque<Integer>();
		Queue<Integer> s = new ArrayDeque<Integer>();
		q.add(0);
		s.add(0);
		while(q.size() != 0) {
			int cur = q.poll();
			int prevSum = s.poll();
			int curSum = nums[cur];
			if(curSum == -1 && c.get(cur).size() != 0) {
				curSum = Integer.MAX_VALUE;
				for(int i = 0; i < c.get(cur).size(); i++) {
					curSum = Math.min(curSum, nums[c.get(cur).get(i)]);
				}
			}
			else if(curSum == -1){
				curSum = prevSum;
			}
			if(curSum < prevSum) {
				isValid = false;
				break;
			}
			ans += (long) (curSum - prevSum);
			for(int i = 0; i < c.get(cur).size(); i++) {
				q.add(c.get(cur).get(i));
				s.add(curSum);
			}
			//System.out.println(cur + " " + curSum);
		}
		if(isValid) {
			System.out.println(ans);
		}
		else {
			System.out.println("-1");
		}
	}
}
