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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int a = 0, b = 0, c = 0;
			for (int i = 2; i <= 1000 && i < n; i++) {
				if (n % i == 0) {
					int sum = n / i;
					for (int j = i + 1; j < 30000 && j < sum; j++) {
						if (sum % j == 0 && sum / j != i && sum / j != j) {
							a = j;
							b = sum / j;
							c = i;
							break;
						}
					}
				}
				if (a != 0)
					break;
			}
			if (a != 0) {
				System.out.println("YES");
				System.out.println(a + " " + c + " " + b);
 
			} else
				System.out.println("NO");
		}
	}
}