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();
		for (int i = 0; i < t; i++) {
			int n = sc.nextInt();
			int cnt = 0;
			int[] res = new int[3];
			for (int j = 2; j * j <= n; j++) {
				if(cnt == 2) break;
				if(n % j == 0) {
					res[cnt] = j;
					cnt++;
					n /= j;
				}
			}
			if(cnt < 2 || n <= res[1]) System.out.println("NO");
			else {
				res[2] = n;
				System.out.println("YES");
				for (int j = 0; j < res.length; j++) {
					System.out.print(res[j]+" ");
				}
			}
		}
		sc.close();
	}
}