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
import collections
import sys


def read_arr():
    return map(int, input().split())


n = int(input())
parent = read_arr()
s = list(read_arr())

adjl = [[] for _ in range(n)]

for i, p in enumerate(parent):
    adjl[p - 1].append(i + 1)


Q = collections.deque()
Q.append((0, 0))
min_sum = 0

while Q:
    root, curr_sum = Q.pop()

    if s[root] != -1:
        av = s[root] - curr_sum
    else:
        if len(adjl[root]) > 0:
            min_s = min(map(lambda c: s[c], adjl[root]))
            av = min_s - curr_sum
        else:
            av = 0
        if av < 0:
            print(-1)
            sys.exit()

    min_sum += av

    for child in adjl[root]:
        Q.append((child, curr_sum + av))



print(min_sum)