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
for _ in range(int(input())):
	n=(int(input()))
	f=0
	s=0
	k=0
	if(n<24):
		f=1
	else:
	    for i in range(2,int(math.sqrt(n))+1):
		    if(n%i==0):
			    f=0
			    k=i
			    break
	    if(k==int(math.sqrt(n))):
		    f=1
	#print(f)
	if(n>=24 and f==0):
		f=1
		for i in range(2,int(math.sqrt(n))+1):
			if(n%i==0):
				x=n//i
				a=i
				#print(x,i)
				for j in range(2,int(math.sqrt(x))+1):
					b=j
					c=x//j
					if(x%j==0):
						if(a!=b and b!=c and c!=a):
							f=0
							#print(a,b,c)
							break
				if(f==0):
					break
			#print(f)
	if(f==0):
		print('YES')
		print(a,b,c)
	else:
		print('NO')