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 

# A function to print all prime factors of 
# a given number n 
def primeFactors(n,l): 
	
	# Print the number of two's that divide n 
	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 
			
	# Condition if n is a prime 
	# number greater than 2 
	if n > 2: 
		l.append(n)
	return l
for _ in range(int(input())):
    n=int(input())
    ar=[]
    l=primeFactors(n,ar)
    s=[]
    s=set(s)
    temp=1
    for i in l:
        temp*=i
        if temp not in s and len(s)<2:
            s.add(temp)
            temp=1
    if temp!=1:
        s.add(temp)
    if len(s)>2:
        print("YES")
        s=list(s)
        for i in s:
            print(i,end=" ")
    else:
        print("NO",end=" ")
    print()