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 = input()
r = map(int,raw_input().split())
f = 0
c = 0
for i in xrange(1,n,1):
	if r[i]<r[i-1]:
		f+=1
		c = i
	if f>=2:
		print -1
		exit(0)
#print f,r[:c],r[c:]
if f==0:
	print 0
	exit()
if r[-1]<=r[0]:
	print n-c
else:
	print -1