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Points:
25 (partial)

Time limit:
0.18s

Memory limit:
16M

Problem type

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 the lattice points with x-coordinates between 0 and 2 and y-coordinates between 0 and . Define two points to be neighbors if their x-coordinates differ by at most 1 and their y-coordinates differ by at most 1. Compute the number of ways to connect all points to form a polygon such that the polygon is simple and any two adjacent points in the polygon are neighbors.

#### Constraints

For at most 30% of marks, .

For at most 70% of marks, .

#### Input Specification

The first line will contain a single integer, .

#### Output Specification

Output the number of polygons mod .

#### Sample Input

`3`

#### Sample Output

`8`

#### Sample Input

`4`

#### Sample Output

`40`

## Comments