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
from sys import stdin ,stdout
from os import path
rd = lambda:stdin.readline().strip()
wr = stdout.write
if(path.exists('input.txt')):
    stdin = open("input.txt","r")
import time ,math
#------------------------------------=
x = int(rd())
mylist = list(map(int,rd().split()))
left = mid = right = 0 
while mid+1 < x and mylist[mid+1] >= mylist[mid]:
	mid+=1

right = mid
if right+1 < x :
	right = mid+1
while right+1 < x and mylist[right+1] >= mylist[right]:
	right+=1
if right < x-1 or (mylist[-1] > mylist[0] and mid!= x-1) :
	print(-1)
else:
	print(right-mid)