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:
from math import *

t = int(input())

def check(x):
	count = 0
	flag = 0
	for i in range(2,floor(sqrt(x))+1):
		if x%i == 0:
			flag = 1
			break
	if flag!=0:		
		for j in range(2,floor(sqrt(x/i))+1):	
			if j!=i and (x/i)%j == 0:
				count = 1
				break
		if count != 0:		
			if x/(i*j)!=i and x/(i*j)!=1 and x/(i*j)!= j:
				return "YES\n"+str(i)+" "+str(j)+" "+str(int(x/(i*j)))
	return "NO"	 		

for _ in range(t):
	x = int(input())
	print(check(x))