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
N = input()
par = [0] + list(map(int,raw_input().split()))
s = map(int,raw_input().split())
a = [-1]*N
a[0] = s[0]
for i in range(N): par[i] -= 1
chd = [[] for _ in range(N)]
for i in range(1,N):
    chd[par[i]].append(i)
q = deque()
for ch in chd[0]: q.append(ch)
while q:
    cur = q.popleft()
    for ch in chd[cur]: q.append(ch)
    if s[cur] != -1:
        a[cur] = s[cur] - s[par[cur]]
        continue
    mi = 10**20
    for ch in chd[cur]: mi = min(s[ch],mi)
    if mi == 10**20: a[cur] = 0
    else: 
        a[cur] = mi - s[par[cur]]
        s[cur] = mi
        if a[cur] < 0:
            print -1
            exit()
print sum(a)
