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;

/**
 * Created by abhay.kumar on 26/01/20.
 * 1294 C
 */
public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] query = new int[n];
        for (int i = 0; i < n; i++) {
            query[i] = sc.nextInt();
        }
        productOfThree(query);
    }

    private static void productOfThree(int[] query) {
        for (int val : query) {
            int a = 0;
            for (int i = 2; i * i <= val; i++) {
                if (val % i == 0) {
                    a = i;
                    val = val / a;
                    break;
                }
            }
            if (a < 2) {
                System.out.println("NO");
                continue;
            }

            boolean found = false;
            for (int i = 2; i * i <= val; i++) {
                if (val % i == 0 && i != a && val / i != i) {
                    System.out.println("YES");
                    System.out.println(a + " " + i + " " + val / i);
                    found = true;
                    break;
                }
            }
            if (!found) {
                System.out.println("NO");
            }
        }
    }
}