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.lang.*;
public class Cf1294C {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t,n,i,j,k,p,q,r;
		t=sc.nextInt();
		while(t>0) {
			p=0;
			q=0;
			r=0;
			n=sc.nextInt();
			for(i=2;i<(int)Math.sqrt(n);i++) {
				if(n%i==0) {
					p=i;
					break;
				}
			}
			for(j=i+1;j<(int)Math.sqrt(n);j++) {
				if((n/p)%j==0) {
					q=j;
					break;
				}
			}
			
			if(p!=0 && q!=0 && n/(p*q)!=p && n/(p*q)!=q && n/(p*q)!=1) {
				System.out.println("YES");
				System.out.println(p+" "+q+" "+n/(p*q));
			}
			else
				System.out.println("NO");
			t--;
		}
		sc.close();
	}

}