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
# bayan
from collections import deque
import pdb
from math import *


def rI():
    return [int(i) for i in input().split()]


n = rI()[0]
p = [0, 0] + rI()
s = [0] + rI()

# pdb.set_trace()
dat = [[] for i in range(n + 1)]
vis = [False for i in range(n + 1)]
a = [-1 for i in range(n + 1)]
a[1] = s[1]
a[0] = 0
for i in range(2, n + 1):
    dat[p[i]].append(i)

que = deque()
que.append(1)

for i in range(1, n + 1):
    if(len(dat[i]) == 0):
        a[i] = 0


while (len(que) != 0):
    c = que.popleft()  # current vertex
    vis[c] = True
    for i in dat[c]:
        if(vis[i] is False):
            que.append(i)

    if(s[c] != -1):
        continue
    if(a[c] == -1):
        # pdb.set_trace()
        mn = 999999999999
        for i in dat[c]:
            if(vis[i] is False):
                mn = min(s[i], mn)
        a[c] = mn - s[p[c]]
        if(a[c] < 0):
            print(-1)
            exit()
        s[c] = s[p[c]] + a[c]

# for i in range(1,n+1):
#     s[i] =
# print(a)
for i in range(2, n + 1):
    if(s[i] == -1):
        a[i] = 0
    else:
        a[i] = s[i] - s[p[i]]
# print(a)
print(sum(a))
# print(dat)
# print(a)
# print(s)
