An equilateral triangle with side length 33 is divided into 33^2 smaller unit equilateral triangles each with side 1, forming a triangular lattice.

We color each segment of length 1 either Red, Blue or Green, subject to the condition that each small unit equilateral triangle has 3 sides with

either 3 different colors or all the same color. If there are N distinct ways to color this triangle, what is the value of log(base)9 N??