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.io.*;
public class ProductofThreeNumbers
{
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int T=Integer.parseInt(br.readLine());
        while(T-->0)
        {
            int n=Integer.parseInt(br.readLine());
            Set<Integer> st=new HashSet<>();
            for(int i=2;i*i<=n;i++)
            {
                if(n%i==0 && st.add(i))
                {
                    n/=i;
                    break;
                }
            }
            for(int i=2;i*i<=n;i++)
            {
                if(n%i==0 && st.add(i))
                {
                    n/=i;
                    break;
                }
            }
            if(st.size()<2 || st.contains(n) || n==1)
            {
                System.out.println("NO");
            }
            else
            {
                System.out.println("YES");
                st.add(n);
                for(int i:st)
                System.out.print(i+" ");
                
                System.out.println();
            }
        }
    }
}