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 3N lattice points with x-coordinates between 0 and 2 and y-coordinates between 0 and N-1. 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 3N points to form a polygon such that the polygon is simple and any two adjacent points in the polygon are neighbors.

Constraints

1 \le N \le 10^9

For at most 30% of marks, N \le 200.

For at most 70% of marks, N \le 10^5.

Input Specification

The first line will contain a single integer, N.

Output Specification

Output the number of polygons mod 10^9.

Sample Input

3

Sample Output

8

Sample Input

4

Sample Output

40

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