C. Product of Three Numbers
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given one integer number $n$. Find three distinct integers $a, b, c$ such that $2 \le a, b, c$ and $a \cdot b \cdot c = n$ or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer $t$ independent test cases.

Input

The first line of the input contains one integer $t$ ($1 \le t \le 100$) — the number of test cases.

The next $n$ lines describe test cases. The $i$-th test case is given on a new line as one integer $n$ ($2 \le n \le 10^9$).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent $n$ as $a \cdot b \cdot c$ for some distinct integers $a, b, c$ such that $2 \le a, b, c$.

Otherwise, print "YES" and any possible such representation.

Example
Input
5
64
32
97
2
12345

Output
YES
2 4 8
NO
NO
NO
YES
3 5 823