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
# your code goes here
n = int(input())
a = [int(x) for x in input().split()]
ok = True
idx = 0
for i in range(1, n):
	if a[i] < a[i - 1]:
		ok = False
		idx = i
		break

if not ok:
	ok = True
	for i in range(idx, n-1):
		if a[i] > a[i+1]:
			ok = False
			break
	if not ok or a[-1] > a[0]:
		print(-1)
	else:
		print(n - idx )
else:
	print(0)