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


parents = [0]*(10**5+10)
children = [[] for x in range(10**5+10)]
values = [0]*(10**5+10)

n = int(input())
i = 1
for p in [int(x) for x in input().split()]:
    p -= 1
    children[p].append(i)
    parents[i] = p
    i += 1

sums = [int(x) for x in input().split()]



i = 0
to_check = [[0,0]]

while i != len(to_check):
    [index,parent_sum] = to_check[i]
    if sums[index] == -1:
        if children[index]:
            min_value = sums[children[index][0]]
            for c in children[index]:
                min_value = min(min_value, sums[c])
            my_value = min_value-parent_sum
            if my_value < 0:
                print(-1)
                exit()
            values[index] = my_value
            sums[index] = min_value
        else:
            values[index] = 0
            sums[index] = parent_sum
    else:
        values[index] = sums[index] - parent_sum
    for c in children[index]:
        to_check.append([c,sums[index]])
    i += 1
print(sum(values))
# print(values)