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.PrintWriter;
import java.util.Scanner;

public class ProductOfThreeNumbers {

	public static Scanner sc = new Scanner(System.in);
	public static PrintWriter out = new PrintWriter(System.out, true);
	public static int n;

	public static void Input() {
		
		n = sc.nextInt();
		
	}	
	
	public static int smallestDivisor(int x, int min)
	{
		int ans=0;
		for (int i=min; i*i<=x; i++)
		{
			if (x % i == 0)
			{
				ans=i;
				break;
			}			
		}
		return ans;
	}
	
	public static void Solve() {
	
		int a=smallestDivisor(n, 2); 
		if (a>=n || a==0) {System.out.println("NO"); return;}
		
		int b=0;
		int min=2;
		while (true)
		{
			b=smallestDivisor(n/a, min); 
			if (b>=n/a || b==0) {System.out.println("NO"); return;}
			if (b>0 && b!=a) {break;}
			min=b+1;
		}	
	
		int c = n/a/b;
		if (c==a || c==b) {System.out.println("NO"); return;}

		System.out.println("YES");
		System.out.println(a +  " " + b + " " + c);
	
	}
	
	public static void main(String[] args) {
			int t = sc.nextInt();
			while (t-- > 0) {Input(); Solve();}
	}
	
}