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.util.*;
import java.lang.Math;
import java.io.* ;

public class Account {
	
	class Pair {
        int key ;
        int val ;
        
        Pair(int key ,int val) {
            this.key = key ;
            this.val = val ;
        }
        
        int getKey() {
        	return this.key ;
        }
        
        int getVal() {
        	return this.val ;
        }
    }
	
	public static void main (String[] args) {
		
//		Scanner sc= new Scanner(System.in) ;
		FastReader sc= new FastReader() ;
//		StringBuilder res= new StringBuilder() ;
		int t= 1 ;  
		t= sc.nextInt() ;
		while(t-- > 0) {
			long n= sc.nextLong() ;
			int rt= (int) Math.sqrt(n) ;
			int x= -1 ;
			boolean flg= false ;
			int m= rt - ((rt*rt == n) ? 1 : 0) ;
			for(int i=2 ;i<=m ;i++) {
				if(x == -1  &&  n%i == 0) {
					x= i ;
				}else if(n%(x*i) == 0) {
					long num= (n) / (x*i) ;
					if(num != x  &&  num != i) {
						flg= true ;
						System.out.println("YES");
						System.out.println(x+" "+i+" "+num);
					}
					break ;
				}
			}if(flg == false) {
				System.out.println("NO");
			}
		}
	}
	
	


	public static int gcd(int a, int b)
	{
	    if (b == 0)
	        return a;
	    return gcd(b, a % b);
	     
	}

	
	public 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;
        }
 
        int [] readintarray(int n) {
            int res [] = new int [n];
            for(int i = 0; i<n; i++)res[i] = nextInt();
            return res;
        }
        long [] readlongarray(int n) {
            long res [] = new long [n];
            for(int i = 0; i<n; i++)res[i] = nextLong();
            return res;
        }
    }	
	
}