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(raw_input())

    a=map(int,raw_input().strip().split())

    i=0

    while i<n-1 and a[i]<=a[i+1]:i+=1
    if i==n-1:print 0
    elif a[0]<a[-1] :print -1
    else:
        i+=1
        res=n-i
        while i<n-1 and a[i]<=a[i+1]:i+=1
        if i!=n-1:print -1
        else:print res


main()
    
