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 sqrt
t = int(input())
for _ in range(t):
	n = int(input())
	i = 2
	fact = []
	while n%i == 0:
		n = n//i
		fact.append(i)
	for i in range(3, int(sqrt(n))+1, 2):
		while n%i == 0:
			n = n//i
			fact.append(i)
	if n != 1:
		fact.append(n)

	if len(fact) < 3:
		print('NO')
		continue
	ans = 1
	i = 0
	fact.sort()
	if len(fact) == 3:
		if len(set(fact)) < 3:
			print('NO')
			continue
	if 4 <= len(fact) <= 5:
		if len(set(fact)) < 2:
			print('NO')
			continue
	if len(set(fact)) == 1:
		a = fact[0]*fact[1]
		b = 1
		i = 2
		while i < len(fact) - 1:
			b *= fact[i]
			i += 1
		c = fact[-1]
		print('YES')
		print(a, b, c)
	else:
		a = fact[0]
		b = 1
		i = 1
		while i < len(fact) - 1:
			b *= fact[i]
			i += 1
		c = fact[-1]
		print('YES')
		print(a, b, c)