Ways to color a 3xN Board

Given a 3 x A board, find the number of ways to color it using at most 4 colors such that no 2 adjacent boxes have same color.

Diagonal neighbors are not treated as adjacent boxes.

Return the ways modulo 10⁹ + 7 as the answer grows quickly.

Input Format:

The first and the only argument contains an integer, A.

Output Format:

Return an integer representing the number of ways to color the board.

Constraints:

1 <= A < 100000

Examples:

Input 1:
    A = 1

Output 1:
    36

Input 2:
    A = 2

Output 2:
    588

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.