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())
vet = input().split()


vet[0] = int(vet[0])
menor = vet[0]
ind_menor = 0
possible = True

for i in range(1, n):
    vet[i] = int(vet[i])
    if vet[i] < menor or (vet[i] == menor and vet[i - 1] != vet[i]):
        menor = vet[i]
        ind_menor = i

ordened_vet = vet[ind_menor:] + vet[:ind_menor]

for i in range(1, n):
    if ordened_vet[i] < ordened_vet[i - 1]:
        possible = False
        break

if possible and ind_menor == 0:
    print('0')
elif possible and menor == ordened_vet[0] and ordened_vet[0] == ordened_vet[-1]:
    print('0')
elif possible:
    print(n - ind_menor)
else:
    print('-1')
