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 Main
{
	 public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0) {
        	 int n = sc.nextInt();
             int[] arr = new int[3];
             int index=0, divisor=2;
             while(n%divisor==0 && index<2) {
             	arr[index++]=divisor;
             	n/=divisor;
             	divisor*=divisor;
             }
             for (int i = 3; i <= Math.sqrt(n) && index<2; i+= 2) {
             	divisor=i;
             	while(n%divisor==0 && index<2) {
                 	arr[index++]=divisor;
                 	n/=divisor;
                 	divisor*=divisor;
                 }
             }
             if(n==1 || n==0 || n==arr[0] || n==arr[1] || arr[0]==0 || arr[1]==0)
             	System.out.println("NO");
             else {
             	System.out.println("YES");
             	System.out.println(arr[0]+" "+arr[1]+" "+n);
             }
        }
       
    }
}