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:
for _ in range(int(input())):
	n=int(input())
	t=pow(n,0.5)+3
	l=[]
	co=0
	i=2
	while i<t:
		if n%i==0:
			n=n//i
			l.append(i)
		else:
			i+=1
	# print(l)
	if n!=1:
		l.append(n)
	flag="YES"
	t=len(l)
	if t>=3:
		a=l[-1]
		l.pop(-1)
		b=l[-1]
		l.pop(-1)
		if a==b:
			b=b*l[-1]
			l.pop(-1)
		c=1
		for i in l:
			c=c*i
	if t>=3:
		if c>1 and a>1 and b>1 and b!=c and a!=b and a!=c:
			print("YES")
			print(a,b,c)
		else:
			print("NO")
	else:
		print("NO")