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
'''
Created on Sep 12, 2015

@author: sshadmin
'''
n=input()
a=map(int,raw_input().strip().split())
if len(a)==1 :
    print 0
elif len(a)==2:
    if a[0] > a[1]:
        print 1
    else:
        print 0
else:
    i=1
    while i < len(a) and a[i] >= a[i-1]:
        i+=1
    if i==len(a):
        print 0
    else:
        if a[i::]==sorted(a[i::]) and a[-1]<= a[0]:
            print len(a)-i
        else:
            print -1
    
    