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.*;
public class S{

   static  ArrayList<Integer> al=new ArrayList<>();
    public static ArrayList<Integer> primeFactors(int n)
    {
        // Print the number of 2s that divide n
        while (n%2==0)
        {
            al.add(2);
            //System.out.print(2 + " ");
            n /= 2;
        }

        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            // While i divides n, print i and divide n
            while (n%i == 0)
            {
                //System.out.print(i + " ");
                al.add(i);
                n /= i;
            }
        }

        // This condition is to handle the case when
        // n is a prime number greater than 2
        if (n > 2)
            al.add(n);
            //System.out.print(n);
        return al;
    }
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        for(int i=0;i<t;i++) {
            int n = sc.nextInt();
            ArrayList<Integer> list = primeFactors(n);
            Set<Integer> s = new HashSet<>(list);
            //System.out.println(list);
            //System.out.println(s);
            int l = list.size();
            if (l < 3) {
                System.out.println("NO");
            } else if (l == 3) {
                if (s.size() == l) {
                    System.out.println("YES");
                    //System.out.println(list);
                    for(int j=0;j<list.size();j++)
                    {
                        System.out.print(list.get(j)+" ");
                    }
                    System.out.println("");
                } else {
                    System.out.println("NO");
                }
            } else {
                ArrayList<Integer> ll=new ArrayList<>();
                int str=0;
                ll.add(list.get(0));
                if(list.get(1)!=list.get(0))
                {
                    ll.add(list.get(1));
                     str=n/(ll.get(0)*ll.get(1));
                }
                else
                {
                    ll.add(list.get(1)*list.get(2));
                     str=n/(ll.get(0)*ll.get(1));
                }
//                ll.add(list.get(1)*list.get(2));
//                int str=n/(ll.get(0)*ll.get(1));
                if(str!=ll.get(0) && str!=ll.get(1) && str>2)
                {
                    System.out.println("YES");
                    ll.add(str);
                    for(int j=0;j<ll.size();j++)
                    {
                        System.out.print(ll.get(j)+" ");
                    }
                    System.out.println("");
                }
                else
                {
                    System.out.println("NO");
                }
            }
            list.clear();
            s.clear();
        }
    }


}