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;
import java.util.Stack;

public class Main {

    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);

        int t = s.nextInt();
        while (t-- > 0) {
            int n = s.nextInt();
            int i = 2;
            int a = -1;
            int b = -1;
            while (i * i <= n) {
                if (n % i == 0) {
                    a = i;
                    b = getB(n / i, a);
                    if (b != -1)
                        break;
                }
                i++;
            }
            if (a != -1 && b != -1)
                System.out.println("YES\n" + a + " " + b + " " + (n / (a * b)));
            else
                System.out.println("NO");
        }

    }

    private static int getB(int n, int a) {
        int i = 2;
        while (i * i < n) {
            if (i == a) {
                i++;
                continue;
            }
            if (n % i == 0 && (n / i) != a) return i;
            i++;
        }
        return -1;
    }
    
}