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.*;

public class geek {


    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);
        int t = s.nextInt();
        while (t-- > 0) {
            int n = s.nextInt();

                int a = 0;
                int b = 0;
                int c = 0;
                boolean flag = true;
                boolean flag1 = true;
                boolean flag2 = true;
                StringBuffer sb = new StringBuffer();
                for (int i = 2; i <= Math.sqrt(n); i++) {
                    if (n % i == 0) {
                        a = i;
                        flag = false;
                        break;
                    }
                }
                if (flag) {
                    System.out.println("NO");
                } else {

                    int k = n / a;
                    for (int i = a + 1; i <= Math.sqrt(k); i++) {
                        if (k % i == 0) {
                            b = i;
                            break;
                        }
                    }if(b<2){
                        System.out.println("NO");
                    }else {
                        int p = k / b;
                        if (p != a && p != b && a != b) {
                            System.out.println("YES\n" + "" + a + " " + b + " " + p);
                        } else {
                            System.out.println("NO");
                        }
                    }
                }


        }
    }
}