Sum of Three Primes

In number theory, the 3-primes problem is the following conjecture.

"Every odd number greater than 5 can be written as a sum of three primes. The same prime may be added more than once."

For example, $7 = 2 + 2 + 3$, $11 = 2 + 2 + 7$, and $25 = 3 + 3 + 19$.

Read an odd number $K$ greater than 5 and write $K$ as a sum of three primes.

Several triples can work, so the output is fixed to one of them. Sort each triple in ascending order as $(a, b, c)$ and choose the lexicographically smallest one: the smallest $a$, and among those the smallest $b$.

The first line contains the number of test cases $T$.

Each of the next $T$ lines contains one integer $K$. $K$ is odd and $7 \le K < 1000$.

Print one line for each test case.

If $K$ can be written as a sum of three primes, print the lexicographically smallest triple in ascending order, separated by single spaces. Otherwise print 0.