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
n=int(input())
l=list(map(int,input().split()))
if n==2:
    if l[1]>=l[0]:
        print(0)
    else:
        print(1)
else:
    if l[n-1]>l[0]:
        print(-1)
    else:
        x=0
        h=-1
        for q in range(n-2,-1,-1):
            if l[q+1]<l[q]:
                x+=1
                h=n-q-1
        if x>1:
            print(-1)
        else:
            if x==0:
                print(0)
            else:
                print(h)
