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
n = list(map(int, input().split()))[0]
a = list(map(int, input().split()))

flag = 0
for i in range(1,n):
	if a[i] < a[i-1]:
		flag = i

ans = True
for i in range (flag+1,n-1):
	if a[i+1] < a[i] :
		ans = False

for i in range (flag-1) :
	if a[i+1] < a[i] :
		ans = False

if flag != 0 and a[n-1] > a[0] :
	ans = False

if not ans:
	print("-1")
else:
	print((n-flag)%n)