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 pony(arr):
    cont = 0
    bandera = False
    a=len(arr)
    for i in range(0, a - 1):
        if arr[i] <= arr[i + 1] and bandera == False:
            continue
        elif arr[i] <= arr[i + 1] and bandera == True:
            cont = cont + 1
        elif arr[i] > arr[i + 1]:
            bandera = True
            cont = cont + 1
            if cont>=2:
                return -1
    if arr[0]<arr[-1] and bandera == True:
        return -1

    return cont


n = int(input())
arr1 = list(map(int, input().strip().split()))
print(pony(arr1))