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.*;
import java.io.*;
public class Solution {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	public static void main(String args[]) throws IOException {
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0) {
		    boolean flag = true;
			int n = Integer.parseInt(br.readLine());
			first : for(int i = 2; (i * i) <= n; i++) {
			    if(n % i == 0) {
			        for(int j = 2; (j * j) <= i; j++) {
			            if(i % j == 0) {
			                if(allDistinct(n / i, j, i / j)) {
			                    bw.write("YES\n");
			                    flag = false;
			                    bw.write((n / i) + " " + j + " " + (i / j) + "\n");
			                    break first;
			                }
			            }
			        }
			        for(int j = 2; (j * j) <= (n / i); j++) {
			            if((n / i) % j == 0) {
			                if(allDistinct(i, j, (n / i) / j)) {
			                    bw.write("YES\n");
			                    flag = false;
			                    bw.write((i) + " " + j + " " + ((n / i) / j) + "\n");
			                    break first;
			                }
			            }
			        }
			    }
			}
			if(flag) {
			    bw.write("NO\n");
			}
		}
		bw.flush();
	}
	public static boolean allDistinct(int a, int b, int c) {
	    if(a == b || a == c || b == c) {
	        return false;
	    }
	    return true;
	}
}