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.Scanner;

public class ProductOfThreeNumbers{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t-- > 0){
            long n = sc.nextLong();
            long a = 1, b = 1, c = 1;
            for(long i = 2; i * i <= n; i++){
                if(n % i == 0){
                    if(a == 1){
                        a = i;
                        n /= i;
                    }else if((n/i) != i && b == 1 && i != a){
                        b = i;
                        break;
                    }
                }
            }
            c = n/b;
            if(a != b && b != c && c != 1 && a != 1 && b != 1){
                System.out.println("YES");
                System.out.println(a + " " + b + " " + c);
            }else{
                System.out.println("NO");
            }
        }
    }
}