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 4\,000~
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 proven that this is the minimal distance required.