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:
def miller_rabin_primalitytest(n,a):
	z=n-1
	d=z
	while(d%2==0):
		d=d//2
	if(pow(a,d,n)!=1):
		x=d
		while(x<n):
			r=pow(a,x,n)
			if(r==n-1):
				return "Probable Prime"
			else:
				x=2*x
		return "Composite"
	else:
		return "Probable Prime"


def isprimeoptimized(n):
	if(n%2==0 and n>2):
		return False
	elif(n==2):
		return True
	elif(n==1):
		return False
	else:
		if(n<2047):
			L=[2]		

		else:
			L=[2,3,5,7]
		
		i=0
		while(i<len(L)):
			if(miller_rabin_primalitytest(n,L[i])=="Probable Prime"):	#WORKS FOR ALL NUMBERS LESS THAN 2^64.
				i+=1
			else:
				return False
		return True




t=int(input())
for i in range(0,t):
	n=int(input())
	if(isprimeoptimized(n)):
		print("NO")
	elif(n<24):
		print("NO")
	
	else:
		L=[]
		for i in range(2,int(n**0.5)+1):
			if(n%i==0):
				L.append(i)
				n=n//i
				break
		for i in range(2,int(n**0.5)+1):
			if(n%i==0 and L[0]!=i and L[0]!=n//i and i*i!=n):
				L.append(i)
				L.append(n//i)
				break
		if(len(L)==3):
			print("YES")
			print(*L)
		else:
			print("NO")