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.
For at most 30% of marks, .
For at most 70% of marks, .
The first line will contain a single integer, .
Output the number of polygons mod .