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 whatever //do not write package name here */

import java.util.*;

public class GFG {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t-- > 0){
		    long num = sc.nextLong();
		    long n = num;
		    int count = 0;
		    long[] arr = new long[3];
		    for(long i = 2;i * i <= num;i++){
		        if(n % i == 0){
		            n /= i;
		            arr[count] = i;
		            count++;
		        }
		        
		        if(count == 2){
		            arr[count] = n;
		            break;
		        }
		    }
		    if(count < 2 || arr[0] == arr[2] || arr[1] == arr[2]){
		        System.out.println("NO");
		    }else{
		        System.out.println("YES");
		        System.out.println(arr[0] + " " + arr[1] + " " + arr[2]);
		    }
		}
	}
}