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 C1294 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int T = in.nextInt();
        main: for (int t=0; t<T; t++) {
            long N = in.nextLong();
            for (long a=2; a*a*a<N; a++) {
                if (N%a == 0) {
                    for (long b=a+1; b*b<N/a; b++) {
                        if (N%(a*b) == 0) {
                            System.out.println("YES");
                            System.out.println(a + " " + b + " " + N/(a*b));
                            continue main;
                        }
                    }
                }
            }
            System.out.println("NO");
        }
    }

}