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();
		for(int j=0;j<t;j++)
		{
		    int n=sc.nextInt();
		    int a=0,b=0,c=0,d=0,x=0,flag=0;
		    for(int i=2;i<=Math.sqrt(n);i++){
		    if(n%i==0){
		    a=i;
		    b=n/i;
		    break;
		    }
		    }
		    x=(int)Math.max(a,b);
		    for(int i=(int)Math.min(a,b)+1;i<Math.sqrt(x);i++){
		        if(x%i==0){
		    c=i;
		    d=x/i;
		    break;
		    }
		}
		if(flag==1 || a==0 || b==0 || c==0 || d==0)
		System.out.println("NO");
		else{
		   System.out.println("YES");
		System.out.println(a+" "+c+" "+d);
		}
		}
	}
}