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:
# Python program to print prime factors 
import math 


# a given number n 
def prime(n): 
	
	a= []# Print the number of two's that divide n 
	while n % 2 == 0: 
		a.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: 
			a.append(int(i))
			n = n / i 
			
	# Condition if n is a prime 
	# number greater than 2 
	if n > 2: 
		a.append(int(n))
	return a
# Driver Program to test above function 
t= int(input())
while(t>0):
    n = int(input())
    a = prime(n)
    l = len(a)
    if l<3:
        print('NO')
    elif l==3 and len(set(a))==3:
        print('YES')
        for i in a:
            print(i,end=' ')
        print()
    else:
        i = 0
        k = 1
        temp = []
        temp.append(a[i])
        i+=1
        if a[i]!=a[i-1]:
            temp.append(a[i])
            i+=1
        else:
            temp.append(a[i]*a[i+1])
            i+=2
        for j in range(i,l):
            k*=a[j] 
        if k!=1 and k not in temp:
            temp.append(k)
        s=  set(temp)
        if len(s)==3 and temp[0]*temp[1]*temp[2]==n:
            print('YES')
            for i in s:
                print(i,end=' ')
            print()
        else:
            print('NO')
    t-=1