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

n = int(input())
lis1 = list(map(int,input().split()))
lis2 = list(map(int,input().split()))
lism = []
root = lis2[0]
c = root

class tree:
    def __init__(self,root):
        self.root = root
    
        
for i in range(n-1):
    if lis2[i+1] == -1:
        lism.append([lis1[i],lis2[i+1],-1])
    else:
        lism.append([lis1[i],lis2[i+1],0])
lisc = lism.copy()
lism.sort()
for i in range(n-1):
    
    if lism[i][1] != -1:
        temp = 0
        if lisc[lism[i][0]-2][2] != -1:
            if lisc[lism[i][0]-2][0] == 1:
                c+= lism[i][1] - lisc[lism[i][0]-2][2] - root
            else:
                c+= lism[i][1] - lisc[lism[i][0]-2][2] - lisc[lisc[lism[i][0]-2][0]-2][1]
            continue
        if lisc[lism[i][0]-2][0] == 1:
            temp = lism[i][1] - root
            lisc[lism[i][0]-2][2] = temp
            c += temp
        else:
            temp =lism[i][1] - lisc[lisc[lism[i][0]-2][0]-2][1]
            lisc[lism[i][0]-2][2] = temp
            c += temp
        if temp < 0:
            print(-1)
            quit()
print(c)
