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())
parent=list(map(int,input().split()))
s=list(map(int,input().split()))
t=[0 for i in range(n)]
d={i:[] for i in range(n)}
for i in range(n-1):
    x=parent[i]
    d[x-1].append(i+2)
k=[]
for i in range(n):
    if(s[i]==(-1)):
        k.append(i+1)
for y in k:
    z=s[parent[(y-2)]-1]
    b=d[y-1]
    v=1000000000
    for i in b:
        if(s[i-1]<z):
            print(-1)
            exit(0)
        else:
            v=min(v,s[i-1])
    if(v==1000000000):
        s[y-1]=s[parent[y-2]-1]
    else:
        s[y-1]=v
summ=0
for i in range(n-1):
    j=parent[i]
    summ+=(s[i+1]-s[j-1])
print(summ+s[0])
    

