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 PYTHON):

Solution:
t=input()
import math 
from collections import Counter 
# A function to print all prime factors of  
# a given number n 
def f(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 i in range(t):
    n=input()
    l=f(n)
    c=Counter(l)
    if len(c)==0:
        print "NO"
    elif len(c)==1:
        for key in c:
            if c[key]>=6:
                print "YES"
                print key,key**2,key**(c[key]-3)
                break
            else:
                print "NO"
                break
    elif len(c)==2:
        x=0
        lis=[]
        for key in c:
            x+=c[key]
            lis.append(key)
            
        if x>=4:
            print "YES"
            print lis[0],lis[1],n/(lis[0]*lis[1])
        else:
            print "NO"
    else:
        j=0
        s=''
        x=1
        for key in c:
            if j<=1:
                s=s+str(key)+' '
                x=x*key
                j+=1
        t=n/x
        print "YES"
        print str(t)+' '+s