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 
/******************************************************************************

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import java.util.*;

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