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
def R(): return map(int, input().split())
def I(): return int(input())
def S(): return str(input())

def L(): return list(R())

from collections import Counter 

import math
import sys

from itertools import permutations


import bisect

mod=10**9+7

#print(bisect.bisect_right([1,2,3],2))
#print(bisect.bisect_left([1,2,3],2))

n=I()

a=L()

for i in range(n-1):
    if a[i]>a[i+1]: break

if i==n-2 and a[n-2]<=a[n-1]:
    print('0')
    exit()

for j in range(i+1,n-1):
    if a[j]>a[j+1]:
        print('-1')
        exit()

print([n-1-i,'-1'][a[0]<a[n-1]])



    

    

    

