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 PYTHON):

Solution:
import math
def de(m):
	ret = []
	n = m 
	for i in range(2,int(math.sqrt(n))+1):
		while n%i == 0:
			ret.append(i)
			n/= i
	if n!= 1:
		ret.append(n)
	return ret



def solve(n):
	lst = de(n)
	args = list(set(lst))
	if len(args) >= 3:
		print "YES"
		print args[0],args[1],n/args[0]/args[1]
	elif len(args) == 2:
		if len(lst)<=3:
			print "NO"
		else:
			print "YES"
			print args[0],args[1],n/args[0]/args[1]
	elif len(args) == 1:
		if len(lst) >= 6:
			print "YES"
			print args[0],args[0]*args[0],n/args[0]/args[0]/args[0]
		else:
			print 'NO'



t = input()
for _ in range(t):
	solve(input())