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())
    li_str = input().split(" ")
    minval = int(li_str[0])
    min_idx = -1
    for i in range(n):
        if int(li_str[i]) >= minval:
            minval = int(li_str[i])
        else:
            if min_idx == -1:
                min_idx = i
                minval = int(li_str[i])
            else:
                print("-1")
                return 0
    if min_idx == -1:
        print("0")
    else:
        if n == 2:
            if int(li_str[0]) > int(li_str[1]):
                print("1")
            else:
                print("0")
            return 0
        if int(li_str[0]) < int(li_str[n-1]):
            print("-1")
        else:
            print(str(n-min_idx))
        
main()
