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
n = int(input())
pa={}
li = [0]+[0]+list(map(int,input().split()))
for i in range(2,n+1) :
    pa[i]=li[i]
#print(pa)
d=pa.copy()
l2 = [0] + list(map(int,input().split()))
l1=l2[:]
for i in range(2,n+1) :
    if  l2[i]!=-1 and l2[pa[i]]== -1 :
        if l1[pa[i]]== -1 :
            l1[pa[i]]=l2[i] 
        else :
            l1[pa[i]]=min(l1[pa[i]],l2[i])
#print(l1)
su=l1[1]
for i in range(2,n+1) :
    if l1[i]!= -1 :
        t=l1[i]-l1[pa[i]]
        if t<0 :
            print("-1")
            exit()
        su+=t
print(su)
    