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
def is_sorted(n, list):
    if n == 1 or n == 0:
        return 0
   
    i = 1
    while i < n:
        if list[i - 1] > list[i]:
            return i
        i += 1
    return 0

n = input()
string_numbers = raw_input()

list_numbers = string_numbers.split()
list_numbers = map(int, list_numbers)

result = is_sorted(n, list_numbers)
if result != 0:
    if is_sorted(n, list_numbers[result:] + list_numbers[:result]) == 0:
        print(n - result)
    else: 
        print(-1)
else:
    print(0)

 		  	 			 		 			  	 		  		  	