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~

Subtask 1 [30%]

~N \le 200~

Subtask 2 [40%]

~N \le 10^5~

Subtask 3 [30%]

No additional constraints.

Input Specification

The first line will contain a single integer, ~N~.

Output Specification

Output the number of polygons mod ~10^9~.

Sample Input 1

3

Sample Output 1

8

Sample Input 2

4

Sample Output 2

40