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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