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Do note that this website only supports submissions in C++.

### Problem Description

You have *N* points on a plot of land. You are allowed to select *up to* 4 points and fence up the area contained within the selected points. However, you are greedy and want to maximize the largest area you can have. Find out what is this maximum area!

### Input

First line of input contains an integer, *N*.

Following *N* lines will have 2 **floating point values** each, the *X* and *Y* co-ordinates of each point respectively.

Please use double type floating point (or higher precision) to input the co-ordinates.

### Output

The maximum possible area contained within *up to* 4 of the *N* points. Print your answer to 3 decimal places.

### Limits

For all testcases, -10^{5} ≤ *X*, *Y* ≤ 10^{5}.

Subtask 1 (30%): 4 ≤ *N* ≤ 50.

Subtask 2 (20%): 4 ≤ *N* ≤ 1000. In addition, the points are randomly distributed in an uniform manner.

Subtask 3 (50%): 4 ≤ *N* ≤ 2000.

Subtask 4 (0%): Sample Testcases.

### Sample Testcase

#### Input

5 0 0 1 0 1 1 0 1 0.5 0.5

#### Output

1.000

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 30 | 4 | 0.5s | 128MB | Minimum |

2 | 20 | 6 | 0.5s | 128MB | Minimum |

3 | 50 | 11 | 0.5s | 128MB | Minimum |

4 | 0 | 1 | 0.5s | 128MB | Minimum |

### Judge Compile Command

g++-7 ans.cpp -o land -Wall -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512