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 deque


def solve(p, s):
    children = {}
    parents = {}
    for i, e in enumerate(p):
        if e not in children:
            children[e] = []
        children[e].append(i+2)
        parents[i+2] = e

    sums = {}
    for i, e in enumerate(s):
        sums[i+1] = e if e != -1 else None

    queue = deque([1])

    while len(queue) > 0:
        to_visit = queue.popleft()
        if to_visit in children:
            for child in children[to_visit]:
                queue.append(child)

        if sums[to_visit] is None:
            parent = sums[parents[to_visit]]
            if to_visit in children:
                min_child = min(map(lambda x: sums[x], children[to_visit]))
                if min_child - parent < 0:
                    return -1
                sums[to_visit] = min_child
            else:
                sums[to_visit] = parent

    result = 0

    for key in sums:
        if key in parents:
            result += sums[key] - sums[parents[key]]
        else:
            result += sums[key]

    return result






if __name__ == "__main__":
    n = int(input())
    p = map(int, input().split())
    s = map(int, input().split())
    print(solve(p, s))