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
tree = {1:[]}
n = int(input())
p = list(map(int, input().split()))
s = list(map(int, input().split()))
a = [0]*n
a[0] = s[0]

for i,e in enumerate(p):
    if e in tree:
        tree[e].append(i+2)
    else:
        tree[e] = [i+2]
flag = 0
stack = [1]
while len(stack)!=0:
    root = stack.pop()
    rs = s[root-1]
    if root not in tree:
        continue
    for i in tree[root]:
        stack.append(i)
        if (s[i-1]==-1) and (i not in tree):
            s[i-1]=rs
        elif (s[i-1]==-1):
            minn = int(1e9+1)
            for j in tree[i]:
                if s[j-1]<minn:
                    minn = s[j-1]
            s[i-1] = minn
            if s[i-1]<rs:
                flag = 1
                stack.clear()
                break
        elif s[i-1]<rs: 
            flag = 1
            stack.clear()
            break
        a[i-1] = s[i-1]-rs
# print(a)
if flag==0:
    print(sum(a))
else:
    print(-1)
