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())
ls = list(map(int, input().split()))

if ls == sorted(ls):
    print(0)
elif ls == sorted(ls, reverse=True):
    if n == 2:
        print(1)
    else:
        print(-1)
else:
    counter = 0
    b = False
    for i in range(1, n):
        if i == n-1 and ls[-1] > ls[0]:
            counter = -1
            break

        if ls[i] < ls[i-1] and not b:
            counter += 1
            b = True

        elif not b and ls[i] < ls[i-1]:
            counter = -1
            break

        elif b:
            if ls[i] >= ls[i-1]:
                counter += 1
            else:
                counter = -1
                break

    print(counter)