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 C {

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