## Mock CCO '18 Contest 1 Problem 5 - A Counting Problem

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Points: 25 (partial)
Time limit: 0.25s
Memory limit: 16M

Problem type

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