You are given points on the plane, such that no three points lie on the same line.

We say that line segments and *cross* if they share a point **different** from the points , , and .

Let be the set of all line segments between pairs of the given points. Find the number of segments in that don't cross with any other segment in .

#### Input Specification

The first line contains an integer , the number of points.

The following lines contain integers and , the coordinates of the points.

#### Output Specification

Output the requested number of segments.

#### Constraints

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

1 | 20 | |

2 | 30 | |

3 | 60 | No additional constraints. |

#### Sample Input 1

```
4
1 1
-1 1
-1 -1
1 -1
```

#### Sample Output 1

`4`

#### Sample Input 2

```
4
-1 -1
1 -1
0 1
0 0
```

#### Sample Output 2

`6`

## Comments