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.io.*;
import java.util.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(in.readLine());
        for(int rc=0; rc<t; rc++) {
            int n = Integer.parseInt(in.readLine());
            int a = -1, b = -1, c = -1;
            int cur = 2;
            int div = 1;
            while(cur <= Math.sqrt(n)) {
                if(n%cur==0) {
                    div *= cur;
                    n /= cur;
                    if(a == -1) {
                        a = div;
                        div = 1;
                    } else if(b == -1 && div != a) {
                        b = div;
                        c = n;
                        break;
                    }
                } else cur++;
            }
            if(a != -1 && b != -1 && c != -1 && c != b && c != a) {
                System.out.println("YES\n"+a+" "+b+" "+c);
            } else {
                System.out.println("NO");
            }
        }
    }
}