Problem Statement

You are given a permutation $P$ of the integers $1$ to $N$. The $i$-th term of the permutation $P$ is denoted by $P_i$.

You may repeat the following operation any number of times, possibly $0$ times.

• Choose integers $i$,$j$ $\left( 1 \le i < j \le N\right)$ satisfying $|P_i - P_j| \le 1$, and swap the values of $P_i$ and $P_j$.

Determine whether $P$ can be made into a monotonically increasing sequence, and if it is possible, find the minimum number of operations.

Here, $P$ is said to be a monotonically increasing sequence if $P_i < P_{i+1}$ holds for all $i \left( 1 \le i < N\right)$.

Input

$N$
$P_1\ P_2\ ...\ P_N$

• All input values are integers.
• $2 \le N \le 3000$
• $1 \le P_i \le N$
• Every integer $i \left(1 \le i \le N\right)$ appears exactly $1$ time in $P$.

Output

If the sequence cannot be made monotonically increasing no matter how many operations are performed, print $-1$.

Otherwise, print the minimum number of operations required to make it monotonically increasing.

Print a newline at the end.

Sample

3
3 2 1

3

5
1 2 3 4 5

0

10
1 3 7 2 10 9 8 4 5 6

17