Willson the Canada Goose is like any other Canada Goose - he likes to engage in target practice.

There are unsuspecting targets that Willson can practice on. The target is located at .

Unlike other geese who choose a circular area for target practice, Willson is unique and decides to choose an equilateral triangle with side length as his area, with the additional constraint that one side of the triangle must be parallel to the line .

Could you tell Willson the maximum number of targets that could be in such an area?

**Note:** A target on the perimeter of the triangle is counted.

#### Constraints

For all subtasks:

All coordinates satisfy .

Subtask | Points | Additional Constraints |
---|---|---|

1 | 5 | |

2 | 15 | |

3 | 20 | |

4 | 30 | |

5 | 30 | No additional constraints |

**Note 1:** There can be multiple targets at the same coordinate.

**Note 2:** Python users are recommended to submit in PyPy.

#### Input Specification

The first line of input will contain two integers, and .

lines of input follow. The line will contain two integers, and .

#### Output Specification

Output a single integer, the maximum number of targets that can be in an area as described above.

#### Sample Input

```
5 3
1 1
2 0
2 4
3 2
3 3
```

#### Sample Output

`3`

## Comments