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

start = 0
for i in range(1, n):
	if (a[i-1] > a[i]):
		start = i
		break

yes = 1
idx = start+1
if (idx == n): idx = 0
pre = a[start]

for i in range(1, n):
	if (pre > a[idx]):
		yes = 0
		break
	pre = a[idx]
	idx+=1
	if (idx == n): idx = 0

if (yes == 0): print "-1"
elif (start == 0): print start
else: print n-start