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C. Product of Three Numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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