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 main():
    n=int(input())
    numbers=map(int,raw_input().split(" "))
    #print numbers
    i_stop=None
    isBreak=False
    for i in range(1,n):
        i_stop=i
        if numbers[i]<numbers[i-1]:
            isBreak=True
            break
    if not isBreak:
        print 0
    else:
        checkBreak=False
        if i_stop+1!=n:  #the last element
            #i_stop -> n  should be non decreasing
            #checkBreak=False
            for i in range(i_stop+1,n):
                if numbers[i]<numbers[i-1]:
                    checkBreak=True
                    break
        if numbers[0] < numbers[-1] or checkBreak:
            print -1
        else:
            print n-i_stop



        




main()