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 ProductOfThreeNumbers {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt();
			int k=n;
			int ans=0;
			int count=0;
			outer:
			for(int i=2;i<Math.sqrt(n)+1;i++) {
				n=k;
				if(n%i==0 && i!=n) {
					ans=i;
					n=n/i;
					for(int j=2;j<Math.sqrt(n)+1;j++) {
						//System.out.println(i+" "+j+" "+n+" "+(n/j));
						if(j!=i && n%j==0 && (n/j)!=j && (n/j)!=i) {
							count++;
							System.out.println("YES");
							System.out.println(ans+" "+j+" "+(n/j));
							break outer;
						}
					}
				}
			}
			if(count==0) {
				System.out.println("NO");
			}
		}
	}

}