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 collections import defaultdict, deque


def read_nums():
    return [int(x) for x in input().split()]


def main():
    n, = read_nums()
    graph = defaultdict(list)

    index = 2
    for parent in read_nums():
        graph[parent].append(index)
        index += 1

    index = 1
    vertex_values = {}
    for s in read_nums():
        vertex_values[index] = s
        index += 1

    output = {}
    if vertex_values[1] == -1:
        output[1] = 0
    else:
        output[1] = vertex_values[1]

    d = deque()
    for ch in graph[1]:
        d.appendleft((ch, output[1]))  # vertex, parent_sum

    while len(d) > 0:
        vertex, parent_sum = d.pop()
        s = vertex_values[vertex]

        if s == -1:
            if len(graph[vertex]) == 0:
                output[vertex] = 0
            else:
                children_values = [vertex_values[ch] for ch in graph[vertex]]
                if any(map(lambda x: x < parent_sum, children_values)):
                    print(-1)
                    exit(0)
                else:
                    output[vertex] = min(children_values) - parent_sum
        else:
            if s < parent_sum:
                print(-1)
                exit(0)
            else:
                output[vertex] = s - parent_sum

        children = graph[vertex]
        for ch in children:
            d.appendleft((ch, parent_sum + output[vertex]))

    print(sum(output.values()))


if __name__ == '__main__':
    main()
