A13593 · Captain Flint and Crew Recruitment

题目描述

Despite his bad reputation, Captain Flint is a friendly person (at least, friendly to animals). Now Captain Flint is searching worthy sailors to join his new crew (solely for peaceful purposes). A sailor is considered as worthy if he can solve Flint's task. Recently, out of blue Captain Flint has been interested in math and even defined a new class of integers. Let's define a positive integer $x$ as nearly prime if it can be represented as $p \cdot q$ , where $1 < p < q$ and $p$ and $q$ are prime numbers. For example, integers $6$ and $10$ are nearly primes (since $2 \cdot 3 = 6$ and $2 \cdot 5 = 10$ ), but integers $1$ , $3$ , $4$ , $16$ , $17$ or $44$ are not. Captain Flint guessed an integer $n$ and asked you: can you represent it as the sum of $4$ different positive integers where at least $3$ of them should be nearly prime. Uncle Bogdan easily solved the task and joined the crew. Can you do the same?

The first line contains a single integer $t$ ( $1 \le t \le 1000$ ) — the number of test cases. Next $t$ lines contain test cases — one per line. The first and only line of each test case contains the single integer $n$ $(1 \le n \le 2 \cdot 10^5)$ — the number Flint guessed.

For each test case print: - YES and $4$ different positive integers such that at least $3$ of them are nearly prime and their sum is equal to $n$ (if there are multiple answers print any of them); - NO if there is no way to represent $n$ as the sum of $4$ different positive integers where at least $3$ of them are nearly prime. You can print each character of YES or NO in any case.

输入 #1

输出 #1

NO
NO
YES
14 10 6 1
YES
5 6 10 15
YES
6 7 10 21
YES
2 10 33 55
YES
10 21 221 6