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
t = int(input())
for i in range(t):
	n = int(input())
	a=0
	b=0
	c=0
	j=2

	while(j<=math.sqrt(n)):
		if(n%j==0):
			if(a==0):
				a=j
				n=int(n/j)
				j+=1
			else:
				b=j
				c=int(n/j)
				break
		else:
			j+=1
	if(a!=0 and b!=0 and c!=0) and(a!=b and b!=c and a!=c) and (a>=2 and b>=2 and c>=2):
		print("YES")
		print(a,b,c)
	else:
		print("NO")