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