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 nt in range(int(input())):
	n = int(input())
	if n<24:
		print ("NO")
		continue
	p = []
	curr = 2
	while curr*curr<n:
		if n%curr==0:
			n=n//curr
			p.append(curr)
		if len(p)==2:
			break
		curr+=1
	if len(p)<=1:
		print ("NO")
		continue
	if n not in p:
		print ("YES")
		print (p[0],p[1],n)
	else:
		print ("NO")