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 f(a, n):
    i = 1
    while i < n and a[i] >= a[i-1]:
        i += 1
    if i == n:
        return 0
    else:
        st1, en1 = i, n-1
        st2, en2 = 0, i-1
        for j in range(st1, en1):
            if a[j] <= a[j+1]:
                continue
            else:
                return -1
        for j in range(st2,en2):
            if a[j] <= a[j+1]:
                continue
            else:
                return -1
        if a[0] >= a[-1]:
            return n-i
        else:
            return -1

n = int(input())
a = list(map(int, input().split()))
print(f(a, n))