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
n=int(input())
for i in range(n):
	t=int(input())
	if t<24:
		print("NO")
		continue
	else:
		a,b=0,0
		for j in range(2,int(sqrt(t))+1):
			if t%j==0:
				a=j
				t//=j
				break
		for j in range(2,int(sqrt(t))+1):
			if t%j==0 and j!=a:
				b=j
				t//=j
				break
		if a==0 or b==0 or t==b or t==a or t<2:		
			print("NO")
		else:
			print("YES")
			print(a,b,t)