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
def read(type = 1):
    if type:
        file = open("input.dat", "r")
        n = int(file.readline())
        line = list(map(int, file.readline().split()))
        line1 = list(map(int, file.readline().split()))
        file.close()
    else:
        n = int(input().strip())
        line = list(map(int, input().strip().split()))
        line1 = list(map(int, input().strip().split()))
    return n, line, line1


def solve():
    mins = [v[0]]
    kids = [-1 for i in range(n)]
    sol = v[0]
    for i in range(1,n):
        if v[i] != -1 and v[i] < mins[p[i-1]-1]:
            return -1
        mins.append(max(mins[p[i-1]-1], v[i]))
        if mins[i] < kids[p[i-1]-1] or kids[p[i-1]-1] == -1:
            kids[p[i-1]-1] = mins[i]
    for i in range(1,n):
        if kids[i] > mins[i]:
            mins[i] = kids[i]
        sol += mins[i] - mins[p[i-1]-1]
    return sol


n, p, v = read(0)
sol = solve()
print(sol)