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.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;

public class Main {
	private static long gcd(long a, long b) {
		return (a == 0 ? b : gcd(b % a, a));
	}

	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);

		int t = cin.nextInt();
		while (t-- != 0) {
			int n = cin.nextInt();
			int a = 0,b = 0,c = 0;
			int flag = 0;
			for(int i = 2;i * i <= n;i++) {
				if(n % i == 0) {
					for(int j = 2;j * j <= n / i;j++) {
						if((n / i) % j == 0 && ((n / i) / j) >= 2 && (i) != (n / i / j) && i != j && j != (n / i / j)) {
							a = i;
							b = j;
							c = n / i / j;
							flag = 1;
							break;
						}
					}
				}
				if(flag == 1)break;
			}
			if(flag == 1)System.out.println("YES" + "\n" + a + " " + b + " " + c);
			else System.out.println("NO");
	}
	}
}