Recall that a partition of a positive integer n means a way of writing n as the sum of some positive integers, where the order of the parts does not matter. For example, there are five partitions of 4:
4 = 3+1 = 2+2 = 1+1+1+1.
How many partitions of 12 are there that have at least four parts, such that the largest, second-largest, third-largest, and fourth-largest parts are respectively greater than or equal to 4,3,2,1?