CF1886A Sum of Three

Monocarp has an integer $ n $ . He wants to represent his number as a sum of three distinct positive integers $ x $ , $ y $ , and $ z $ . Additionally, Monocarp wants none of the numbers $ x $ , $ y $ , and $ z $ to be divisible by $ 3 $ . Your task is to help Monocarp to find any valid triplet of distinct positive integers $ x $ , $ y $ , and $ z $ , or report that such a triplet does not exist.

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of testcases. The only line of each testcase contains a single integer $ n $ ( $ 1 \le n \le 10^{9} $ ).

For each testcase, if there is no valid triplet $ x $ , $ y $ , and $ z $ , print NO on the first line. Otherwise, print YES on the first line. On the second line, print any valid triplet of distinct positive integers $ x $ , $ y $ , and $ z $ such that $ x + y + z = n $ , and none of the printed numbers are divisible by $ 3 $ . If there are multiple valid triplets, you can print any of them.

In the first testcase, one of the valid triplets is $ x = 4 $ , $ y = 5 $ , $ z = 1 $ . None of these numbers are divisible by three, and $ 4 + 5 + 1 = 10 $ . In the second testcase, there is no valid triplet. In the third testcase, one of the valid triplets is $ x = 2 $ , $ y = 8 $ , $ z = 5 $ . None of these numbers are divisible by three, and $ 2 + 8 + 5 = 15 $ . In the fourth testcase, there is no valid triplet.