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=int(raw_input())
N=[int(x) for x in raw_input().split()]

A=[]
B=[]

A.append(N[0])
a=True

for i in xrange(1,n):
	if N[i]>=N[i-1]:
		if a:
			A.append(N[i])
		else:
			B.append(N[i])
	else:
		if a:
			a=False
			B.append(N[i])
		else:
			print -1
			import sys
			sys.exit()

if len(B)==0 or (A[0]>=B[-1]):
	print len(B)
else:
	print -1