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 
def primeFactors(n): 
	
	# Print the number of two's that divide n 
	l=[]
	while n % 2 == 0: 
		l.append(2) 
		n = n / 2
		
	# n must be odd at this point 
	# so a skip of 2 ( i = i + 2) can be used 
	for i in range(3,int(math.sqrt(n))+1,2): 
		
		# while i divides n , print i ad divide n 
		while n % i== 0: 
			l.append(i) 
			n = n / i 

	if n > 2: 
		l.append(n)
	return l	
		

t=int(input())
while t:
    n=int(input())
    l=[]
    l=primeFactors(n)
    n1=len(l)
    a,b,c=0,0,0
    a=l[0]
    x=list(set(l))
    n2=len(x)
    if n1>=5:
        if l[0]!=l[1]:
            b=l[1]
            r=2
        else:
            b=l[1]*l[2]
            r=3
        c=1
        for i in range(r,n1):
            c=c*l[i]
    if n1==3 and n2==3:
        b=l[1]
        c=l[2]
    if n1==4:
        if l[0]!=l[1]:
            b=l[1]
            c=l[2]*l[3]
        else:    
            b=l[1]*l[2]
            c=l[3]
    a=int(a)
    b=int(b)
    c=int(c)
    if a!=b and b!=c and c!=a:
        print("YES")
        print(a,b,c)
    else:
        print("NO")
    t-=1