A16363. 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.