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/env python

n,a,count,label=input(),[],0,0
a=[int(i) for i in raw_input().split()]
for i in range(n):
    if (i>0) and (a[i]<a[i-1]):
        label=i
        count+=1
if count==0:
    print 0
elif count>1:
    print -1
elif a[n-1]<=a[0]:
    print (n-label)
else:
    print -1






