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 = int(input())
 
lst = list(map(int, input().split()))
 
ans = 0
 
for i in range(1, n):
    if lst[i] < lst[i-1]:
        ans = i
        break
 
for i in range(ans+1, n):
    if lst[i] < lst[i-1]:
        ans = -1
        break
 
if ans == 0:
    print(0)
elif ans != -1 and lst[-1] <= lst[0]:
    print(n-ans)
else:
    print(-1)