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(sys.stdin.readline())

ok = True 
inc = True
last, res, i   = 0,0,0
first = 0

for num in sys.stdin.readline().split():
	num = int(num)
	if first == 0:
		first = num

	if last > num:
		if inc:
			inc = False
			res = n - i
		else :
			ok = False
	last = num	
	i = i + 1

if last > first:
	if inc:
		pass
	else:
		ok = False
	
if ok:
	print(res)
else:
	print(-1)