Write down the closed form (no "..." going to infinity allowed) of the generating function where the coefficient of x^n is the number of partitions of n are there such that the following conditions are satisfied:

i. Only parts 2, 6, 7 and 9 appears, and

ii. there is an odd number of 2s, and

iii. there are at least three 6s, and

iv. there are at most three 7s, and

v. there are either zero, one, or three 9s.