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ACM-ICPC亚洲区预选赛(北京赛区)游戏对抗邀请赛​正在报名中

Language:
Fiber Communications
 Time Limit: 1000MS Memory Limit: 30000K Total Submissions: 4521 Accepted: 1358

Description

Farmer John wants to connect his N (1 <= N <= 1,000) barns (numbered 1..N) with a new fiber-optic network. However, the barns are located in a circle around the edge of a large pond, so he can only connect pairs of adjacent barns. The circular configuration means that barn N is adjacent to barn 1.

FJ doesn't need to connect all the barns, though, since only certain pairs of cows wish to communicate with each other. He wants to construct as few
connections as possible while still enabling all of these pairs to communicate through the network. Given the list of barns that wish to communicate with each other, determine the minimum number of lines that must be laid. To communicate from barn 1 to barn 3, lines must be laid from barn 1 to barn 2 and also from barn 2 to barn 3(or just from barn 3 to 1,if n=3).

Input

* Line 1: Two integers, N and P (the number of communication pairs, 1 <= P <= 10,000)

* Lines 2..P+1: two integers describing a pair of barns between which communication is desired. No pair is duplicated in the list.

Output

One line with a single integer which is the minimum number of direct connections FJ needs to make.

Sample Input

```5 2
1 3
4 5
```

Sample Output

`3`

Hint

[Which connect barn pairs 1-2, 2-3, and 4-5.]

Source

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