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
from functools import reduce
	
t = int(input())
for _ in range(t):
	n = int(input())
	m = n
	sqrt_n = int(math.sqrt(n))
	res = []
	for i in range(2, sqrt_n):
		if n == 1:
			break
		while n > 1 and n % i == 0:
			res.append(i)
			n //= i
	if n > 1:
		res.append(n)
	if len(res) < 3:
		print('NO')
	elif len(res) == 3:
		if len(set(res)) < 3:
			print('NO')
		else:
			print('YES')
			print(res[0], res[1], res[2])
	elif len(res) == 4:
		if len(set(res)) == 1:
			print('NO')
		else:
			print('YES')
			print(res[0], res[1] * res[2], res[3])
	elif len(res) == 5:
		if len(set(res)) == 1:
			print('NO')
		else:
			print('YES')
			print(res[0], res[1] * res[2] * res[3], res[4])
	else:
		print('YES')
		print(res[0], res[1] * res[2], reduce(lambda x, y: x * y, res[3:]))