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())
ara = list(map(int, input().strip().split()))
ara2 = ara
ara = sorted(ara)
if ara2 == ara:
    print('0')

else:
    pos = 0
    count = 0
    for i in range(n):
        if i != n - 1 and ara2[i] > ara2[i + 1]:
            count += 1
            pos = i
        elif i == n-1 and ara2[i] > ara2[0]:
            count += 1
            pos = i
    if count > 1:
        print(-1)
    else:
        print(n - 1 - pos)
