Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Zoo

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Zoo in the Grid Kingdom is represented by an infinite grid. The Zoo has *n* observation binoculars located at the *OX* axis. For each *i* between 1 and *n*, inclusive, there exists a single binocular located at the point with coordinates (*i*, 0). There are *m* flamingos in the Zoo, located at points with positive coordinates. The flamingos are currently sleeping and you can assume that they don't move.

In order to get a good view over the flamingos, each of the binoculars can be independently rotated to face any angle (not necessarily integer). Then, the binocular can be used to observe all flamingos that is located at the straight line passing through the binocular at the angle it is set. In other words, you can assign each binocular a direction corresponding to any straight line passing through the binocular, and the binocular will be able to see all flamingos located on that line.

Today, some kids from the prestigious Codeforces kindergarten went on a Field Study to the Zoo. Their teacher would like to set each binocular an angle to maximize the number of flamingos that can be seen by the binocular. The teacher is very interested in the sum of these values over all binoculars. Please help him find this sum.

Input

The first line contains two space-separated integers *n* and *m* (1 ≤ *n* ≤ 10^{6}, 1 ≤ *m* ≤ 250), denoting the number of binoculars and the number of flamingos, respectively.

Then *m* lines follow, the *i*-th line will contain two space-separated integers *x*_{i} and *y*_{i} (1 ≤ *x*_{i}, *y*_{i} ≤ 10^{9}), which means that the *i*-th flamingo is located at point (*x*_{i}, *y*_{i}).

All flamingos will be located at distinct points.

Output

Print a single integer denoting the maximum total number of flamingos that can be seen by all the binoculars.

Examples

Input

5 5

2 1

4 1

3 2

4 3

4 4

Output

11

Note

This picture shows the answer to the example test case.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/25/2018 08:40:20 (d1).

Desktop version, switch to mobile version.

User lists

Name |
---|