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
from sys import stdin
from itertools import repeat
def main():
    n = int(stdin.readline())
    p = [0, 0] + map(int, stdin.readline().split(), repeat(10, n - 1))
    s = [0] + map(int, stdin.readline().split(), repeat(10, n))
    t = [1001001001] * (n + 1)
    for i in xrange(n, 1, -1):
        x = p[i]
        if s[i] == -1:
            if t[i] == 1001001001:
                continue
            else:
                s[i] = t[i]
        if s[x] == -1:
            if t[x] > s[i]:
                t[x] = s[i]
        elif s[x] > s[i]:
            print -1
            return
    print sum(s[i] - s[p[i]] for i in xrange(1, n + 1) if s[i] != -1)
main()
