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.*;

public class CodeforcesContest {

    private static void sport(int n) {
        int r=n;
        Set<Integer> used = new HashSet<>();
        int a = div(n, used);
        if (a < 0) {
            System.out.println("NO");
            return;
        }
        n/=a;
        used.add(a);
        int b = div(n, used);
        if (b < 0) {
            System.out.println("NO");
            return;
        }
        used.add(b);
        int c = r % (a * b) == 0 ? r / (a * b) : -1;
        if (c < 2 || c == a || c == b) {
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
        System.out.println(a + " " + b + " " + c);
    }

    private static int div(int n, Set<Integer> set) {
        int k = (int) Math.sqrt(n);
        for (int i = 2; i <= k; i++) {
            if (n % i == 0 && !set.contains(i)) {
                return i;
            }
        }
        return -1;
    }

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