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Points:
7

Time limit:
0.6s

Memory limit:
32M

Problem types

Allowed languages

Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, ~~CommonLisp~~, D, Dart, F#, Forth, Fortran, Go, ~~Groovy~~, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, ~~Nim~~, ~~ObjC~~, OCaml, ~~Octave~~, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Consider a convex polygon with vertices, with the additional property that no three diagonals intersect in a single point. Find the number of intersections between pairs of diagonals in such a polygon.

The figure below shows one such polygon with 6 vertices.

**Note:** a polygon is convex if all of its interior angles are less than 180 degrees.

#### Input Specification

The first and only line of input contains a single integer .

#### Output Specification

Output the number of intersections on a single line.

#### Sample Input 1

`3`

#### Sample Output 1

`0`

#### Sample Input 2

`4`

#### Sample Output 2

`1`

#### Sample Input 3

`6`

#### Sample Output 3

`15`

## Comments