Description

Little W defines a kind of “good partition”:

For a positive integer $n$, if there exist $n$ integers $(a_1,a_2,\cdots,a_n)$ such that $\sum\limits_{i=1}^n a_i=\prod\limits_{i=1}^n a_i=n$, then $n$ is called “good”, and $(a_1,a_2,\cdots,a_n)$ is a “good partition” of $n$.

Now, Little W gives you some $n$. He wants you to determine whether each $n$ is “good”. If it is good, output any “good partition” of $n$.

Input Format

The first line contains an integer $T$, indicating the number of test cases.

The next $T$ lines each contain an integer $n$, representing one query from Little W.

Output Format

For each test case, output several lines.

If $n$ is not “good”, output only one line NO.

Otherwise, output YES in the first line. Then output one integer $a$ in the next line, meaning how many different values appear in your “good partition”. In the next $a$ lines, output two integers $x,y$, meaning there are $x$ occurrences of $y$.

3
1
2
5

YES
1
1 1
NO
YES
3
1 5
2 1
2 -1

Hint

Sample Explanation

When $n=1$, $(1)$ is a “good partition” of $1$.

When $n=2$, $2$ has no “good partition”.

When $n=5$, $5+1+1+(-1)+(-1)=5\times1\times1\times(-1)\times(-1)=5$, so $(5,1,1,-1,-1)$ is a “good partition” of $5$.

Constraints

This problem is not bundled for judging.
$\text{Subtask\;1(10\;pts)}$: $n=1,T=1000$;
$\text{Subtask\;2(30\;pts)}$: $n\le 10^4,T=100$;
$\text{Subtask\;3(60\;pts)}$: $T=1000$.
For all testdata, $1\le n\le10^9$.

Notes

This problem uses $\text{SPJ}$.

A test point gets full score if and only if, for all $T$ test cases in that test point:

• The answer in the first line is the same.
• If the answer in the first line is YES, it must also satisfy $1\le a\le 20$, $1\le x\le n$, $\sum y\times x=\prod y^x=\sum x=n$.

To make it easier to write the $\text{SPJ}$, it is allowed that some $y$ are the same. Also, please make sure there is one and only one newline at the end of the output file.

For the $\text{SPJ}$ source code, please see the Cloud Clipboard.

Translated by ChatGPT 5