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())
p = list(map(int, input().split()))

c = {}
for i in range(0, n-1):
    if p[i] in c:
        c[p[i]].append(i+2)
    else:
        c[p[i]] = [i+2]
x = dict(zip(range(2, n+1), p))

s = [0]+list(map(int, input().split()))
a = [0]+[s[1]] + [0]*(n-1)

stack = [1]
succ = True
while stack:
    p = stack.pop()

    if p in c:
        if s[p] != -1:
            if p != 1:
                a[p] = s[p] - s[x[p]]
        else:
            mn = 99999999999999
            for m in c[p]:
                if s[m]-s[x[p]] < mn:
                    mn = s[m]-s[x[p]]
            if not succ:
                break
            if mn < 0:
                succ = False
                break
            else:
                a[p] = mn
                s[p] = s[x[p]] + mn
        for child in c[p]:
            stack.append(child)
    else:
        if s[p] != -1:
            a[p] = s[p] - s[x[p]]
        else:
            a[p] = 0
            s[p] = s[x[p]]

if succ:
    print(sum(a))
else:
    print('-1')
