405725: GYM102055 L Ultra Weak Goldbach's Conjecture

In number theory, Goldbach's conjecture states that every even integer greater than $$$2$$$ is the sum of two prime numbers. A weaker version of this conjecture states that every odd number greater than $$$5$$$ is the sum of three prime numbers.

Here is an ultra weak version of Goldbach's conjecture: every integer greater than $$$11$$$ is the sum of $$$\textbf{six}$$$ prime numbers. Can you help to verify or disprove this conjecture?

The first line of the input gives the number of test cases, $$$T$$$ ($$$1 \le T \le 200$$$). $$$T$$$ test cases follow.

Each test case contains one integer $$$N$$$ ($$$1 \le N \le 10^{12}$$$).

For each test case, output "Case x:" first, where x is the test case number (starting from $$$1$$$). If the solution exist, output six prime numbers separated by spaces; otherwise output "IMPOSSIBLE" (quotes for clarity) when the solution does not exist. When the solution exists, any valid solution is acceptable.

5
6
13
200
570
680

Case 1: IMPOSSIBLE
Case 2: 2 2 2 2 2 3
Case 3: 43 29 31 29 31 37
Case 4: 97 101 103 107 101 61
Case 5: 137 137 107 113 89 97