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.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class Solution{
    public static void main(String[] args){
        try{
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

            int t=Integer.parseInt(br.readLine());
            for(int i=0;i<t;i++){
                int n=Integer.parseInt(br.readLine());
                int u=0,v=0;
                for(int j=2;j<Math.sqrt(n);j++){
                    if(n%j==0){
                        u=j;
                        n=n/j;
                        break;
                    }
                }
                if(u!=0){
                    for(int j=2;j<Math.sqrt(n);j++){
                        if(n%j==0 && j!=u && n/j != u){
                            v=j;
                            n=n/j;
                            break;
                        }
                    }
                }
                if(v!=0){
                    System.out.println("YES");
                    System.out.println(u+" "+v+" "+n);
                }else{
                    System.out.println("NO");
                }
            }

        }catch(Exception e){
            System.out.println("kkkk");
        }
    }
    static int lcm(int a,int b){
        return (a*b)/hcf(a,b);
    }
    static int hcf(int a,int b){
        if(a==0){
            return b;
        }
        if(b==0){
            return a;
        }
        if(a>b)
        return hcf(a%b,b);

        return hcf(a,b%a);
    }

    static class pair{
        int a,b;
        public pair(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
}