Ways to color a 3xN Board

Problem Setter: raghav_aggiwal
Problem Tester: glowing_glare

Given a 3Xn board, find the number of ways to color it using at most 4 colors such that no two adjacent boxes have same color. Diagonal neighbors are not treated as adjacent boxes.
Output the ways%1000000007 as the answer grows quickly.

1<= n < 100000

Example:
Input: n = 1
Output: 36

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 doubt? Checkout Sample Codes for more details.
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