Painting the Fence
Description
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.
Input
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 $r_i$ ($1 \le l_i \le r_i \le n$).
Output
Print one integer — maximum number of painted sections if you hire $q - 2$ painters.
Samples
7 5
1 4
4 5
5 6
6 7
3 5
7
4 3
1 1
2 2
3 4
2
4 4
1 1
2 2
2 3
3 4
3