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())

def factor(n):
	factors = []
	div = int(sqrt(n))
	i = 2
	count = 1
	aux_n = n
	while n > 1 and i <= div:
		while n%i == 0:
			factors.append(i)
			n = n//i
			count *= i
		i += 1
	if n > 1:
		factors.append(aux_n//count)
	return factors


for _ in range(t):
	n = int(input())
	primes = factor(n)
	ans = []
	i = 0
	while i < len(primes):
		count = primes[i]
		if count not in ans:
			ans.append(count)
			i += 1
		else:
			i += 1
			while i < len(primes) and count in ans:
				count *= primes[i]
				i += 1
			ans.append(count)

	if len(ans) > 2:
		last = 1
		for i in range(2, len(ans)): last *= ans[i]
		ans = [ans[0], ans[1], last]
		if len(set(ans)) == 3:
			print("YES")
			print(ans[0], ans[1], last)
		else:
			print("NO")
	else:
		print("NO")