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 solve():
    num_nodes = int(input())
    parents = [0] + [int(x)-1 for x in input().split()]
    S = [int(x) for x in input().split()]

    children = [[] for _ in parents]
    for child, parent in enumerate(parents):
        children[parent].append(child)

    for node in range(num_nodes):
        if S[node] == -1:
            S[node] = min((S[child] for child in children[node]), default=S[parents[node]])

    A = [None for _ in range(num_nodes)]
    A[0] = S[0]
    for node in range(1, num_nodes):
        A[node] = S[node] - S[parents[node]]
        if A[node] < 0:
            print('-1')
            return False

    print(sum(A))

solve()
    
