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 one_shift(n,x):
    c = x.copy()
    c.sort()
    if c ==x:
        return 0

    set =0
    for i in range(n):
        if x[i+1] < x[i] and not set:
            set = 1
            if (x[i+1:] + x[:i+1])== c:
                return n-i-1
            else:
                return -1
        if x[i+1] < x[i] and set:
            return -1
    return n - i -1


n = int(input())
x = list(map(int, input().split()))
print(one_shift(n,x))