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Problems

# Racing Gems

You are playing a racing game. Your character starts at the x axis (y = 0) and proceeds up the race track, which has a boundary at the line x = 0 and another at x = w. You may start the race at any horizontal position you want, as long as it is within the track boundary. The finish line is at y = h, and the game ends when you reach that line. You proceed at a fixed vertical velocity v, but you can control your horizontal velocity to be any value between -v / r and v / r, and change it at any time.

There are n gems at speci fic points on the race track. Your job is to collect as many gems as possible. How many gems can you collect?

#### Input

The first line contains four space-separated integers n, r, w and h (1n`105`, 1r10, 1w, h`109`). Each of the following n lines contains two space-separated integers `xi` and `yi`, denoting the coordinate of the i-th gem (0`xi`w, 0 < `yi`h). There will be at most one gem per location.

The input does not include a value for v.

#### Output

Print the maximum number of gems that can be collected during the race.

Time limit 1 second
Memory limit 128 MiB
Input example #1
```5 1 10 10
8 8
5 1
4 6
4 7
7 9
```
Output example #1
```3
```
Input example #2
```5 1 100 100
27 75
79 77
40 93
62 41
52 45
```
Output example #2
```3
```
Source 2015 ACM North America - Pacific Northwest, Division 1, Problem G