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(raw_input())
P = map(int, raw_input().split())
sums = map(int, raw_input().split())
children = {}

for i, x in enumerate(P):
    if (x - 1) in children:
        children[x - 1].append(i + 1)
    else:
        children[x - 1] = [i + 1]


root = 0
a = [0] * n
a[root] = sums[root]
to_check = [root]
while len(to_check) > 0:
    root = to_check[0]
    del to_check[0]
    if root not in children:
        continue
    for unknown in children[root]:
        if unknown not in children:
            a[unknown] = 0
            sums[unknown] = sums[root]
            continue
        min_sum_in_children = min(sums[c] for c in children[unknown])
        if min_sum_in_children < sums[root]:
            print -1
            exit()
        else:
            a[unknown] = min_sum_in_children - sums[root]
            sums[unknown] = min_sum_in_children
        for c in children[unknown]:
            a[c] = sums[c] - min_sum_in_children
            to_check.append(c)
print sum(a)
