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 JAVA):

Solution:

import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader;
import java.util.*;  
import java.io.*;
  
public class Linkedlist
{ 
	static PrintWriter pw;
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
 
    public static int gcd(int a,int b)
    {
        return b==0?a:gcd(b,a%b);
    }
 
    public static boolean isPrime(long n)
    {
        if(n==2)return true;
        int i=2;
        while(i*i<=n)
        {
            if(n%i==0) return false;
            i++;
        }
        return true;
    }
    
    public static long[] remove(long n)
    {
        long res[]=new long[1000000000];
        long rese=0;
        int i=0;
        while(n>0)
        {
            long dig=n%10;
            n=n/10;
            if(dig>0)
            {
                rese=dig;
                	res[i++]=rese;
            }
        }
        return res;
    }

    public static void main(String[] args) 
    {
    	
        FastReader ob=new FastReader();
        pw = new PrintWriter(System.out);
        int t=ob.nextInt();
        while(t-->0) {
        	int n=ob.nextInt(),a=0,b=0,c=0;
        	for(int i=2;i<Math.sqrt(n);i++)
        	{
        		if(n%i==0)
        		{
        			if(a==0)
        			{
        				a=i;n/=i;
        			}
        			else
        			{
        				b=i;
        				n/=i;
        				if(a<b && b<n)
        				{
        					c=1;
        					break;
        				}
        			}
        		}
        	}
        	if(c==1)
        		{
        			pw.println("YES");
        			pw.println(a+" "+b+" "+n);
        		}
        	else
        		pw.println("NO");
        }
        pw.flush();
    }
}