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:

//package codeforce;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Iterator;

public class product {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while (t-- > 0) {
			HashSet<Integer> set = new HashSet<Integer>();
			int n = Integer.parseInt(br.readLine());
			for (int i = 2; i * i <= n; i++) {
				if (n % i == 0 && !set.contains(i)) {
					n /= i;
					set.add(i);
					break;
				}
			}
			for (int i = 2; i * i <= n; i++) {
				if (n % i == 0 && !set.contains(i)) {
					n /= i;
					set.add(i);
					break;
				}
			}
			if (set.size() != 2 || set.contains(n) || n == 1) {
				System.out.println("No");
			} else {
				System.out.println("Yes");
				set.add(n);
				Iterator<Integer> itr = set.iterator();
				while (itr.hasNext()) {
					System.out.print(itr.next() + " ");
				}
				System.out.println();
			}

		}
	}

}