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
import sys
range = xrange
input = raw_input

n = int(input())
P = [0] + [int(x)-1 for x in input().split()]
S = [int(x) for x in input().split()]

big = 10**18

X = [big]*n
for i in range(n):
    if S[i]>=0:
        X[P[i]] = min(X[P[i]],S[i])

X = [x if x!=big else -1 for x in X]

S = [S[i] if S[i]>=0 else X[i] for i in range(n)]

for i in range(n):
    if S[i]<0:
        S[i] = S[P[i]]

A = [S[i]-S[P[i]] for i in range(n)]
A[0] = S[0]

if any(a<0 for a in A):
    print -1
else:
    print sum(A)
