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
import sys

n = int(raw_input())
numbers = [int(x) for x in raw_input().split()]
divider_found = False
swaps = 0
for i in range(0, n - 1):
	if numbers[i] > numbers[i + 1]:
		if divider_found:
			swaps = -1
			break
		else:
			divider_found = True;
	if divider_found:
		swaps += 1
if swaps > 0 and numbers[n - 1] > numbers[0]:
	swaps = -1
print swaps



