A12394 | Painting the Fence

You have a long fence which consists of $n$ sections. Unfortunately, it is not painted, so you decided to hire $q$ painters to paint it. $i$ -th painter will paint all sections $x$ such that $l_i \le x \le r_i$ .

Unfortunately, you are on a tight budget, so you may hire only $q - 2$ painters. Obviously, only painters you hire will do their work.

You want to maximize the number of painted sections if you choose $q - 2$ painters optimally. A section is considered painted if at least one painter paints it.

The first line contains two integers $n$ and $q$ ( $3 \le n, q \le 5000$ ) — the number of sections and the number of painters availible for hire, respectively.

Then $q$ lines follow, each describing one of the painters: $i$ -th line contains two integers $l_i$ and $r_i$ ( $1 \le l_i \le r_i \le n$ ).

Print one integer — maximum number of painted sections if you hire $q - 2$ painters.