Find the number of ways to partition the numbers 1, 2, . . . , 12 into four sets of three numbers, so that the sum of the number
s in each set is divisible by 3. (The order of the sets does not matter, and the order of the elements within each set does not matter. For example, the partition {1, 5, 12}, {2, 9, 10}, {3, 4, 8}, {6, 7, 11} is the same as the partition {8, 3, 4}, {9, 10, 2}, {7, 11, 6}, {12, 5, 1}.)
