In △ABC, A1 and A2 are two points on side BC. B1 and B2 are two points on side CA. C1 and C2 are two points on side AB.
A, A1, A2, B, B1, B2, C, C1, and C2 are nine distinct points. The six line segments AA1, AA2, BB1, BB2, CC1, and CC2 divide △ABC into n non-overlapping regions. What is the smallest possible value of n?