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.io.*;
import java.util.*;

public class ProductofThreeNumbers {

	public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
		int t = in.nextInt();
		while(t-->0) {
			int n = in.nextInt();
			int a,b,c;
			a=b=c=-1;
			for(int i=2;i*i<n;i++) {
				if(n%i==0) {
					a = i;
					break;
				}
			}
			if(a==-1) out.println("NO");
			else {
				n /= a;
				for(int i=a+1;i*i<n;i++) {
					if(n%i==0&&n/i!=i) {
						b = i;
						break;
					}
				}
				if(b==-1) out.println("NO");
				else {
					n /= b;
					c = n;
					if(c<2||c==a) out.println("NO");
					else {
						out.println("YES");
						out.println(a+" "+b+" "+c);
					}
				}
			}
		}out.close();
	}
}