There is a line of $N$ boxes on a table, indexed from $1$ to $N$. Each box is assigned a number $a_i$ between $1$ and $M$ such that every number from $1$ to $M$ appears at least once. In order to open a box with $a_i=m$, you must have already opened a box with $a_i=m-1$. You do not need to open anything before opening a box with $a_i=1$.

In addition, to get from index $i$ to index $j$, you need to travel a distance of $|j-i|$. You are initially at index $0$, and all the boxes are closed. What is the minimum distance you need to travel in order to open a box with $a_i=M$?

Constraints

For all subtasks:

• $1\le a_i\le M\le N$
• There is always at least one box with $a_i=m$ for all $1\le m\le M$.

Points Awarded	$N$
5 points	$1\le N\le 4000$
10 points	$1\le N\le 5\times {10}^5$

Input Specification

The first line contains two integers $N$ and $M$.

The second line contains $N$ integers $a_i$.

Output Specification

Output the minimum distance required. Please note that this number may not fit inside a 32-bit integer.

Sample Input

4 3
3 1 2 2

Sample Output

5

Explanation for Sample Output

Starting from index $0$, we go to index $2$, then to index $3$ and then back to index $1$. The total distance travelled is $|2-0|+|3-2|+|1-3|=5$. It can be shown that this is the minimal distance required.