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
q=int(input())


for j in range(q):
	n=int(input())
	d=[]
	flag=0

	
	for i in range(2,int(math.sqrt(n))+1):
		if n%i==0:			
			if len(d)==2:	
				break

			else:
				d.append(i)
				n=int(n/i)


	if len(d)==1 or len(d)==0:
		flag=1

	elif len(d)==2:
		if n>1:
			if n!=d[0] and n!=d[1]:
				print("YES")
				print(d[0],end=" ")
				print(d[1],end=" ")
				print(n)
			else:
				flag=1
				# print("NO")
		else:
			flag=1

	if flag==1:
		print("NO")