Educational Codeforces Round 61 (Rated for Div. 2) C. Painting the Fence（dp）

You have a long fence which consists of nn sections. Unfortunately, it is not painted, so you decided to hire qq painters to paint it. ii-th painter will paint all sections xx such that li≤x≤rili≤x≤ri.

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

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

Input

The first line contains two integers nn and qq (3≤n,q≤50003≤n,q≤5000) — the number of sections and the number of painters availible for hire, respectively.

Then qq lines follow, each describing one of the painters: ii-th line contains two integers lili and riri (1≤li≤ri≤n1≤li≤ri≤n).

Output

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

Examples

input

Copy

7 5
1 4
4 5
5 6
6 7
3 5

output

Copy

7

input

Copy

4 3
1 1
2 2
3 4

output

Copy

2

input

Copy

4 4
1 1
2 2
2 3
3 4

output

Copy

3

题意：给出n,m。n指木板长度（1-n），m指m个工人。

接下来给m个区间，表示工人的粉刷范围，求m-2个工人最多粉刷多长的木板。

来自一个大佬博客：http://www.bubuko.com/infodetail-2977901.html

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