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 sys
n = int(input())
parents = list(map(int, input().split()))
dict1 = {}
for i,j in enumerate(parents):
	if j in dict1:
		dict1[j].append(i+2)
	else:
		dict1[j] = [i+2]
s = list(map(int, input().split()))
dict2 = {}
dict3 = {}
dict2[1] = s[0]
dict3[1] = s[0]
for i,j in enumerate(s):
	if j != -1:
		dict2[i+1] = j
for i in range(2,n+1):
	if i not in dict2:
		p = parents[i-2]
		s = dict2[p]
		a = 0
		if i in dict1:
			a = 10**10
			for j in dict1[i]:
				if dict2[j] < s:
					print(-1)
					sys.exit()
				elif dict2[j] - s < a:
					a = dict2[j] - s 
		dict2[i] = a+s
		dict3[i] = a
	else:
		p = parents[i-2]
		s = dict2[p]
		if dict2[i] < s:
			print(-1)
			sys.exit()
		else:
			dict3[i] = dict2[i]-s
ans = 0
for i in dict3:
	ans += dict3[i]
print(ans)
			