Sum of Three (Codeforces 1886A)
Tags: Math, brute force

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.

Input: 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 $$$n$$$ ($$$1 \le n \le 10^{9}$$$).

Output: 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.

Note: 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.

Sample Inputs:
4
10
4
15
9

Sample Outputs:
YES
4 5 1
NO
YES
2 8 5
NO

Solution (Python):
for n in [*open(0)][1:]:
    i = int(n)
    k = 4 >> (i % 3 > 0)
    print(('NO', f'YES 1 {k} {i - k - 1}')[6 < i != 9])

Solution (Python):
for n in [*open(0)][1:]:
    i = int(n)
    k = 4 >> (i % 3 > 0)
    print(('NO', f'YES 1 {k} {i - k - 1}')[6 < i != 9])

Solution (Python):
for n in [*open(0)][1:]:
    i = int(n)
    k = 4 >> (i % 3 > 0)
    print(('NO', f'YES 1 {k} {i - k - 1}')[6 < i != 9])