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:
# -*- coding: utf-8 -*-
"""
Created on Wed Jan 22 19:40:08 2020

@author: DELL
"""
  
import math 
  
# A function to print all prime factors of  
# a given number n 
def primeFactors(n): 
    li=[]
    # Print the number of two's that divide n 
    while n % 2 == 0: 
        li.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: 
            li.append(i)
            n = n / i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        li.append(int(n))
    return li
t=int(input())
for i in range(t):
    n=int(input())
    p = primeFactors(n)
    k=set(p)
    w=list(k)
    if len(w)==1:
        if p.count(w[0])>5:
            print("YES")
            a=p[0]
            b=p[1]*p[2]
            c=1
            for i in range(3,len(p)):
                c=c*p[i]
            print(str(a)+" "+str(b)+" "+str(c))
        else:
            print("NO")
    elif len(w)==2:
        if len(p)<=3:
            print("NO")
        else:
            if len(p)==5:
                print("YES")
                a=p[0]
                b=p[1]*p[2]*p[3]
                c=p[4]
                print(str(a)+" "+str(b)+" "+str(c))
            else:
                print("YES")
                a=p[0]
                b=p[1]*p[2]
                c=1
                for i in range(3,len(p)):
                    c=c*p[i]
                print(str(a)+" "+str(b)+" "+str(c))
    elif len(w)==0:
        print("NO")
    else:
        if len(p)==3:
             print("YES")
             a=p[0]
             b=p[1]
             c=p[2]
             print(str(a)+" "+str(b)+" "+str(c))
        else:
            print("YES")
            a=p[0]
            b=p[1]*p[2]
            c=1
            for i in range(3,len(p)):
                c=c*p[i]
            print(str(a)+" "+str(b)+" "+str(c))