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
# -*- coding: utf-8 -*-
# @Time    : 2019/1/6 1:37
# @Author  : LunaFire
# @Email   : gilgemesh2012@gmail.com
# @File    : D. Sum in the tree.py

from collections import deque


def main():
    n = int(input())
    p = list(map(int, input().split()))
    s = list(map(int, input().split()))

    s.insert(0, 0)
    a = [0] * len(s)
    a[1] = s[1]

    child_dict, parent_dict = {}, {}
    for i in range(len(p)):
        if p[i] not in child_dict:
            child_dict[p[i]] = []
        child_dict[p[i]].append(i + 2)
        parent_dict[i + 2] = p[i]

    q = deque()
    q.append(1)
    while q:
        node = q.popleft()
        if s[node] == -1:
            if node not in child_dict or not child_dict[node]:
                s[node] = s[parent_dict[node]]
            else:
                s[node] = s[child_dict[node][0]]
                for x in child_dict[node]:
                    s[node] = min(s[node], s[x])
        if node in child_dict:
            for x in child_dict[node]:
                q.append(x)

    for i in range(2, n + 1):
        a[i] = s[i] - s[parent_dict[i]]
        if a[i] < 0:
            print(-1)
            return
    print(sum(a))


if __name__ == '__main__':
    main()
