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 math
from collections import deque


def get_min_sum(n, parents, sums):
    values = [None] * n
    values[0] = sums[0]
    edges = [[] for _ in range(n)]
    for i in range(n-1):
        edges[parents[i] - 1].append(i+1)
    heights = [None] * n
    heights[0] = 1
    queue = deque([0])
    total = values[0]
    while len(queue):
        cur = queue.pop()
        h = heights[cur]
        for child in edges[cur]:
            heights[child] = h + 1
            queue.appendleft(child)
        # Нечетные, есть sums
        if h % 2:
            if values[cur] is None:
                if sums[cur] < sums[parents[cur-1]-1]:
                    # print('Wrong sum', cur)
                    return -1
                values[cur] = sums[cur] - sums[parents[cur-1]-1]
                total += values[cur]
        # Четные, нет sums
        else:
            parent_value = values[parents[cur-1]-1]
            min_child_sum = math.inf
            for child in edges[cur]:
                min_child_sum = min(min_child_sum, sums[child])
            if min_child_sum != math.inf:
                values[cur] = min_child_sum - sums[parents[cur-1]-1]
                if values[cur] < 0:
                    # print('Wrong current values', cur, values[cur])
                    return -1
                total += values[cur]
            else:
                values[cur] = 0
            sums[cur] = sums[parents[cur-1]-1] + values[cur]
    # print(sums)
    # print(values)
    return total



if __name__ == '__main__':
    n = int(input())
    parents = list(map(int, input().split()))
    s = list(map(int, input().split()))
    print(get_min_sum(n, parents, s))
