Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ 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 ≤ t ≤ 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 ≤ n ≤ 10^9).

Output

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

Solution (in PYTHON3):

Solution:
#    Unmesh Kumar
#    IITR CSE '22
from math import *

for _ in range(int(input())):
	n=int(input())
	pos=False
	for a in range(2,int(pow(n,1/3))+1):
		if n%a==0:
			z=n//a
			for b in range(a+1,int(sqrt(z))+1):
				if z%b==0 and b*b!=z:
					pos=True
					print('YES')
					print(a,b,z//b)
					break
		if pos:
			break
	if not pos:
		print('NO')