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
amount = int(input())
preds = [int(s) for s in input().split()]
s = [int(s) for s in input().split()]
min_ = 10e18
childs = [[] for i in range(len(s))]
a = [0] * len(s)
a[0] = s[0]
for i in range(len(preds)):
    childs[preds[i] - 1].append(i + 1)
for i in range(len(childs)):
    if s[i] == -1:
        if len(childs[i]) > 0:
            min_ = 10e18
            for child in childs[i]:
                if s[child] < min_:
                    min_ = s[child]
            a[i] = min_ - s[preds[i - 1] - 1]
            if a[i] < 0:
                print(-1)
                sys.exit(0)
        #print(a[i])
        #print(i)
            for child in childs[i]:
                a[child] = s[child] - min_
                #print(child - 1)
#print(a)
print(sum(a))
#print(childs[0:2])   
#if min_ < s[0]:
  #  print(-1)
#else:
  #  print(min_)