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 debug import debug
import sys

t_ = int(input())
while t_:
	t_-=1
	n = int(input())
	if n<24:
		print("NO")
	else:
		i = 2
		a = b = c = 0
		while i*i<n:
			if n%i == 0:
				a = i
				n = n//i
				break
			i+=1
		if a == 0:
			print("NO")
		else:
			i = 3
			while i*i<n:
				if n%i == 0 and i != a:
					b = i
					c = n//i
					break
				i+=1
			if b<2 or c<2 or b == c:
				print("NO")
			else:
				print("YES")
				print(a,b,c)