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 = input() 
lst = map(int, raw_input().split()) 

def find_break(lst): 
    pos = -1 
    pre = 0
    for cur in range(1, len(lst)): 
        if lst[cur] < lst[pre]: 
            pos  = cur 
            break 
        pre = cur
    return pos 

pos_1 = find_break(lst)
if pos_1 == -1: 
    print 0
else: 
    lst = lst[pos_1:] + lst[:pos_1] 
    pos_2 = find_break(lst)

    if pos_2 != -1: 
        print -1
    else: 
        print n - pos_1
