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
a = int(input())
b = list(map(int, input().split(" ")))

x = 0
y = 0

for i in range(len(b) - 1):
	if b[i] > b[i+1]:
		x = i
		y = y + 1
if b[a-1] > b[0]:
	x = a - 1
	y = y + 1

if y == 0:
	print(0)
elif y > 1:
	print(-1)
else:
	print(a - x - 1)