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.BufferedReader;
import java.io.InputStreamReader;
import java.util.List;
import java.util.Scanner;
import java.util.Vector;

public class Main {
	
	public static void main(String[] args) {

		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		
		int n = in.nextInt();
		
		List<Integer>[] tree = new List[n];
		long[] s = new long[n];
		long[] a = new long[n];
		int[] p = new int[n];
		
		for(int i = 0; i < n; i++) {
			tree[i] = new Vector<>();
		}
		
		p[0] = 0;
		
		for(int i = 1; i < n; i++) {
			
			int parent = in.nextInt() - 1;
			
			tree[parent].add(i);
			p[i] = parent;
			
		}
		
		for(int i = 0; i < n; i++) {
			s[i] = in.nextInt();
			a[i] = -1;
		}
		
		BFS(0, tree, s, a, p, 1);
		
		long soma = 0;
		for(int i = 0; i < n; i++) {
			
			if(a[i] < 0) {
				System.out.println(-1);
				return;
			}
			
			soma += a[i];
		}
		
		System.out.println(soma);
	}
	
	public static void BFS(int v, List<Integer>[] tree, long[] s, long[] a, int[] p, int depth) {
		
		if(depth == 1) {
			a[v] = s[v];
		}
		else if(depth % 2 == 0 && tree[v].isEmpty() == false) {
			
			int parent = p[v];
			a[v] = Integer.MAX_VALUE;
	
			for(Integer child: tree[v]) {
				a[v] = Math.min(a[v], s[child] - s[parent]);
			}
			s[v] = s[parent] + a[v];
		}
		else if(depth % 2 == 0 && tree[v].isEmpty() == true) {
			
			int parent = p[v];
			a[v] = 0;
			s[v] = s[parent] + 0;
		}
		else {
			int parent = p[v];
			a[v] = s[v] - s[parent];
		}
		
		
		for(Integer child: tree[v]) {
			
			BFS(child, tree, s, a, p, depth + 1);
			
		}
		
	}
	
} 
