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=input()
    a=map(int,raw_input().split())
    f=1
    for i in range(n-1):
        if a[i]>a[i+1]:
            f=0
            break
    if f:
        print '0'
    else:
        f=0
        j=0
        for i in range(n-1):
            if a[i]>a[i+1]:
                f+=1
                j=i+1
        if f==1:
            if a[0]>=a[n-1]:
                print n-j
            else:
                print "-1"
        else:
            print "-1"
