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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int t = Integer.parseInt(sc.next());
        
        for(int i = 0; i < t; i++){
            int n = Integer.parseInt(sc.next());
            List<Long> list = primeFactorization(n);
            if(list.size() < 3){
                System.out.println("NO");
            }else{
                long a = list.get(0);
                long b = list.get(list.size()-1);
                long c = 1;
                for(int j = 1; j < list.size()-1; j++){
                    c *= list.get(j);
                }
                if(a == b || b == c || c == a){
                    if(list.size() < 6){
                        System.out.println("NO");
                    }else{
                        b = list.get(1) * list.get(2);
                        c = 1;
                        for(int j = 3; j < list.size(); j++){
                            c *= list.get(j);
                        }
                        System.out.println("YES");
                        System.out.println(a + " " + b + " " + c);
                    }
                }else{
                    System.out.println("YES");
                    System.out.println(a + " " + b + " " + c);
                }
            }
        }
    }
    
    static List<Long> primeFactorization(long n){
        
        List<Long> list = new ArrayList<>();
        while(n%2 == 0){
            n /= 2;
            list.add(2L);
        }
        double sqrt = Math.sqrt(n);
        for(long l = 3; l <= sqrt; l += 2){
            while(n%l == 0){
                n /= l;
                list.add(l);
            }
        }
        if(n > 1) list.add(n);
        return list;
    }
}