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
if __name__ == '__main__':
    n = int(raw_input(""))
    a = map(int, raw_input("").split())

    shi = False
    shii = -1
    k = 0
    m = a[0]
    while k < n-1:
        if a[k]>a[k+1]:
            if not shi:
                shi = True
                shii = k+1
            else:
                print "-1"
                exit(0)
        k += 1
        
    if not shi:
        print 0
        exit(0)
    if a[-1] <= m:
        print n-shii
    else:
        print -1
