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, deque

n=int(input())
p=list(map(int, input().split(' ')))
s=list(map(int, input().split(' ')))

a=[-1 for _ in range(n)]
c=defaultdict(list)
for i,e in enumerate(p):
    c[e].append(i+2)

p=[1]+p
q=[1]
flag=0
while q:
    elem=q.pop(0)
    q+=c[elem]
    if elem==1:
        a[elem-1]=s[elem-1]
    else:
        if s[elem-1]==-1:
            min_val=0 if not c[elem] else min([s[x-1] for x in c[elem]])
            a[elem-1]=0 if not c[elem] else min_val-s[p[elem-1]-1]
            #s[elem-1]=s[p[elem-1]-1]
            s[elem-1]=min_val
        else:
            if s[elem-1]<s[p[p[elem-1]-1]-1]:
                print('-1')
                q=deque([])
                flag=-1
                break
            a[elem-1]=s[elem-1]-s[p[elem-1]-1]
    # print(elem, a[elem-1], s[elem-1])

# print(c)
# print(a)
if flag==0:
    print(sum(a))
