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
input()
xs = [int(x) for x in input().split()]

def solve(xs):
    divide = 0
    cnt = 0
    for i in range(1, len(xs)):
        if xs[i] < xs[i-1]:
            cnt += 1
            if cnt == 2:
                return -1
            divide = i
    if divide != 0 and xs[0] < xs[len(xs) - 1]:
        return -1
    if divide == 0:
        return 0
    return len(xs) - divide

print (solve(xs))
