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
def core():
	n = int(input())
	p = [None, None] + [int(x) for x in input().split()]
	s = [None] + [int(x) for x in input().split()]
	
	ip = [[] for _ in range(n+1)]
	for i in range(2, n+1):
		ip[p[i]].append(i)
	
	a = [None, s[1]]
	for i in range(2, n+1):
		if s[i] == -1:
			if ip[i]:
				s[i] = min(s[j] for j in ip[i])
			else:
				s[i] = s[p[i]]
		a.append(s[i] - s[p[i]])
		if a[-1] < 0:
			return -1
	
	#print(n, p, s, a, ip)
	return sum(a[1:])

print(core())