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 *  

n = int(input())
p = [0, 0] + list(map(int, input().split()))
s = [0] + list(map(int, input().split()))
g = defaultdict(list)
for i in range(2, len(p)):
    g[p[i]].append(i)
sum = s[1]
a = [0] + [0 for i in range(n)]

q = deque()
q.append(1)

while len(q) > 0:
    cur = q.popleft()
    for ch in g[cur]:
        q.append(ch)
    if cur == 1:
        continue
    elif s[cur] == -1:
        if len(g[cur]) > 0:
            a[cur] = min([s[val] for val in g[cur]]) - s[p[cur]]
            s[cur] = s[p[cur]] + a[cur]
            sum += a[cur]
            if a[cur] < 0:
                print(-1)
                exit(0)
    else:
        a[cur] = s[cur] - s[p[cur]]
        sum += a[cur]
print(sum)