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 
import java.util.*;

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

        int T = in.nextInt();
        while (T-->0) {
            int n = in.nextInt();

            int a=0, b=0;
            for (int i=2; (i*i)<n; i++) {
                if (n%i==0) {
                    n /= i;
                    if(a==0) {
                        a = i;
                    } else {
                        b = i;
                        break;
                    }
                }
            }

            if(a != 0 && b != 0 && n > b) {
                System.out.println("YES");
                System.out.println(a + " " + b + " " + n);
            } else {
                System.out.println("NO");
            }
        }
    }
}
