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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class productOfThree {
    static BufferedReader b = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter p = new PrintWriter(System.out);

    public static void main(String arg[]) throws IOException {
        int t = Integer.parseInt(b.readLine());
        while(t > 0){
            t--;
            int prod = Integer.parseInt(b.readLine());
            int k = prod;
            int a = 0;
            int b = 0;
            int c = 0;
            for(int x = 2; x < Math.sqrt(k); x++){
                if(k % x == 0){
                    if(a == 0){
                        a = x;
                    } else {
                        b = x;
                        break;
                    }
                    k /= x;
                }
            }
            if(a == 0 || b == 0){
                p.println("NO");
            } else {
                c = prod / a / b;
                if(c == a || c == b || c == 1){
                    p.println("NO");
                } else {
                    p.println("YES");
                    p.println(a + " " + b + " " + c);
                }
            }
        }
        p.close();
    }
}