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 decimal
decimal.getcontext().prec = 100
def sum1(pre,l,r):
    l=max(l,0)
    if(l==0):
        return pre[r]
    return pre[r] - pre[l - 1]

n=int(raw_input())
p=map(int,raw_input().split())
a = map(int,raw_input().split()) 
p=[0,0]+p
a=[0]+a
b={}

for i in range(1,n+1):
    if a[p[i]]<0:
        if(b.get(p[i])):
            b[p[i]].append(a[i])
        else:
            b[p[i]]=[a[i]]   

for i in range(1,n+1):
    if b.get(i):
        a[i]=min(b[i])
# print a
final_a=[0]
for i in range(1,n+1):
    if a[i]>=0:
        if a[i]<a[p[i]]:
            print -1
            exit()
        final_a.append(a[i]-a[p[i]])
    else:
        final_a.append(0)
# print final_a
print sum(final_a)