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 atexit, io, sys, collections, math, heapq, fractions
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   
####################################




def f(n):
	u = 2
	on = n
	r = []
	limit = int(on **0.5)
	while(u <= limit):
		if n % u == 0:
			c = 0
			while(n % u == 0):
				n /= u
				c+=1
			r.append((u,c))
		u+= 1
	if n > 1:
		r.append((n,1))
	r.sort(key = lambda x:-x[1])
	if len(r) >= 3:
		print 'YES'
		print ' '.join(map(str,[r[0][0], r[1][0], on / (r[0][0] * r[1][0])]))
		return 
	if len(r) == 2:
		if r[0][1] >= 3:
			e = r[0][0]
			print 'YES'
			print ' '.join(map(str,[e, e ** 2, on / (e ** 3)])) 
			return 
		if r[1][1] >= 3:
			e = r[1][0]
			print 'YES'
			print ' '.join(map(str,[e, e ** 2, on / (e ** 3)]))
			return 
		a = r[0][0]
		b = r[1][0]
		if on / (a*b) not in [a,b,1]:
			print 'YES'
			print ' '.join(map(str,[a, b, on / (a * b)]))
			return 
		print 'NO'
		return 
		
	if len(r) == 1:
		if r[0][1] >= 6:
			e = r[0][0]
			print 'YES'
			print ' '.join(map(str,[e, e** 2, on / (e ** 3)])) 
			return 
		print 'NO'
		return 
	

for i in range(int(raw_input())):
	n = int(raw_input())
	f(n)