One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
#n,m = map(int, input().strip().split(' '))
n=int(input())
lst = list(map(int, input().strip().split(' ')))
f=0
for j in range(1,n):
    if lst[j]>=lst[j-1]:
        if j==n-1:
            f=1
        continue
    else:
        break
if f==1:
    print(0)
else:
    k=[]
    p=[]
    for i in range(j,n):
        k.append(lst[i])
        p.append(lst[i])
    for i in range(j):
        k.append(lst[i])
        p.append(lst[i])
        
    p.sort()
    if k==p:
        print(n-j)
    else:
        print('-1')