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())
arr = list(map(int, input().split()))
go = False
go2 = False

if arr[-1] <= arr[0]:
    reset = 1
    prev = arr[0]
    sr_idx = None 
    for i in range(1,n):
        if arr[i] < prev:
            if reset < 2:
                reset+= 1
                sr_idx = i
            else:
                print(-1)
                go2 = True
                break
        prev = arr[i]      
else:
    go = True
    if n == 2:
        print(0)
    else:
        print(-1)

if not go and not go2:
    if sr_idx == None:
        print(0)
    elif reset == 2:
        print(n-sr_idx)