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:
import math
def function(num):
	var = int(math.sqrt(num)) + 1
	for i in range(2,var+1):
		if (num%i == 0) and (num//i != i):
			return list((i,num//i))
			
	


t  = int(input())
for _ in range(t):
	count = 0
	n = int(input())
	num = int(math.sqrt(n)) + 1
	for i in range(2,num):
		if n%i == 0:
			func = function(n//i)
			if func == None:pass
			else:
				if len(set([i,func[0],func[1]])) == 3:
					count = 1
					print('YES')
					print('{} {} {}'.format(i,func[0],func[1]))
					break
				else:pass		 
	if count == 0:
		print("NO")