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 ti in range(t):
	n = int(input())

	try:
		a = 0
		b = 0 
		c = 0
		for i in range(2,int(sqrt(n))+1):
			if n % i == 0:
				a = i
				break

		# a is 1st factor

		for i in range(2,int(sqrt(n/a))+1):
			if int(n/a) % i == 0 and i != a:
				b = i
				c = int(n/(a*b))
				if c == b:
					raise Exception
				break

		if a == 0 or b == 0 or c == 0:
			raise Exception
		else:
			print("YES")
			print(a,b,c)		
	except:
		print("NO")