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
from sys import exit

n = int(input())
inp = input().split()
nums = [int(x) for x in inp]
if nums[-1] > nums[0]:
	if nums == sorted(nums):
		print(0)
	else:
		print(-1)
	exit()
c = 0
t = 1
for i in range(1,n):
	if nums[i-1] > nums[i]:
		t -= 1
	if t == 0:
		c += 1
	elif t == -1:
		print(-1)
		exit()
print(c)
