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
from collections import defaultdict

n = int(raw_input())
p = map(int, raw_input().split())
s = map(int, raw_input().split())
# n = 4
# p = [1,2,2,3]
# s = [3,-1,8,5]
children = defaultdict(list)
heights = [1]
v = {1:s[0]}

for count,i in enumerate(p):
    children[i].append(count+2)
    heights.append(1 + heights[i-1])

#List of (heights, indices)
order = sorted(zip(heights, [i for i in range(1,n+1)]))
#print "The order of vertices is ", order

for i in order[1:]:

    #print "order", i
    if i[0]%2 == 0:
        if len(children[i[1]]) == 0:
            v[i[1]] = 0

        else:
            v[i[1]] = min([s[j-1] for j in children[i[1]]]) - s[p[i[1]-2]-1]
            #print(s[p[i[1]-2]-1])
            s[i[1]-1] = v[i[1]] + s[p[i[1]-2]-1]
    else:
        v[i[1]] = s[i[1]-1] - s[p[i[1]-2]-1]
    #print(s, i[1])
    #print(v[i[1]], s[i[1]-1])

out = [v[i] for i in range(1,n+1)]
#print(out)

fail = False
for i in out:
    if i < 0:
        fail = True
if fail:
    print -1
else:
    print sum(out)







