AtCoder Study

Seogang Village is a straight village with a total of $2N-1$ buildings in a row, numbered from 1 to $2N-1$ from left to right. $M$ of Gunsu live in this village, along with Seunghyeong. All of the Gunsu are in different buildings, and Seunghyeong is in building $N$, where K512 is located. The Gunsu and Seunghyeong hold an AtCoder study every Monday. Five minutes before the study starts, not a single Gunsu has arrived! Angry, Seunghyeong plans to use a secret special movement method to bring back the Gunsu scattered around the village to K512.

Seunghyeong can use the following three movement methods.

1. He can move to a neighboring building in 1 second. That is, he can move from building $i$ to building $i+1$ or building $i-1$. If he is in building 1 or building $2N-1$, he can only move to building 2 or building $2N-2$, respectively.
2. He can skip exactly $N$ buildings in 1 second. That is, for $i > N$, he can move from building $i$ to building $i-N$, and for $i < N$, he can move from building $i$ to building $i+N$.
3. He can instantly move to any building he has visited before, without spending any time. However, buildings skipped while using method 2 do not count as visited.

When Seunghyeong reaches a building with a Gunsu, he picks up the Gunsu right away, so collecting them takes no extra time. Let us calculate the minimum time needed to bring back all the Gunsu.

The first line contains the integers $N$ and $M$. ($2 \le N \le 10^6$; $1 \le M \le 2N-2$)

The second line contains the positions $a_1$ through $a_M$ of the Gunsu, separated by spaces, where $a_i$ is the position of the $i$-th Gunsu. All positions are distinct, and $a_i = N$ never happens. ($1 \le a_i \le 2N-1$)

Print the minimum time Seunghyeong needs to bring back all the Gunsu.