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:
# A Better (than Naive) Solution to find all divisiors 
import math 

# method to print the divisors 
def printDivisors(n) : 
    fact = []
	
    # Note that this loop runs till square root 
    i = 1
    while i <= math.sqrt(n): 
    	
    	if (n % i == 0) : 
    		
    		# If divisors are equal, print only one 
    		if (n / i == i) : 
    			fact.append(i) 
    		else : 
    			# Otherwise print both 
    			fact.append(i) 
    			fact.append(n//i) 
    
    	i = i + 1
    fact.sort()
    return fact[1:]



for _ in range(int(input())):
    n=int(input())
    
    f1=printDivisors(n)
    a=f1[0]
    if len(f1)==1 or len(f1)==2:
        print("NO")
        continue
    
    f2 = printDivisors(n//a)
    try:
        f2.remove(a)
    except:
        pass
        
    b = f2[0]
   
    
    c= n//(a*b)
    
    if (a>1 and b>1 and c>1  and a!=b and b!=c and a!=c):
        print("YES")
        print(a,b,c)
    else:
        print("NO")