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
#!/usr/bin/python
# -*- coding: utf-8 -*-
######################################################################### # File Name: b.py # Author: nkuflk
# mail: nkuflk@gmail.com
# Created Time: 2014-08-07 17:37:11
#########################################################################

import sys

n = input()
array = [int(i) for i in raw_input().split()]

flag = True
temp = True
count = 0
for i in range(1,n):
    if temp==False:
        break
    if flag:
        if array[i]>=array[i-1]:
            continue
        else:
            count = i
            flag = False
    else:
        if array[i]>=array[i-1]:
            continue
        else:
            temp = False

if flag:
    print 0
    sys.exit(0)

if temp==False:
    print -1
else:
    if array[n-1]<=array[0]:
        print n-count
    else:
        print -1
