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.ArrayList;
import java.util.BitSet;
import java.util.Scanner;


public class CF1294C {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int tc = sc.nextInt();
		BitSet sieve = new BitSet();
		for(int i=2; i<=1000000; i++) sieve.set(i);
		for(int i=2; i<=1000000; i++)
			if(sieve.get(i))
				for(int j=i+i; j<=1000000; j+=i) sieve.set(j, false);
		ArrayList<Integer> primes = new ArrayList<>();
		for(int i=2; i<=1000000; i++) if(sieve.get(i)) primes.add(i);
		while(tc-->0){
			int n = sc.nextInt();
			int sqrt = (int) Math.sqrt(n)+1;
			ArrayList<Integer> ans = new ArrayList<>();
			for(int i=0; ans.size()<3 && i<primes.size() && primes.get(i)<sqrt; i++){
				int prime = primes.get(i);
				if(n%prime==0){
					n/=prime;
					ans.add(prime);
					if(ans.size()==2 && !ans.contains(n) && n>1) ans.add(n);
					if(ans.size()<3 && n%(prime*prime)==0){
						n/=prime*prime;
						ans.add(prime*prime);
						if(ans.size()==2 && !ans.contains(n) && n>1) ans.add(n);
					}
				}
			}
			System.out.println(ans.size()!=3 ? "NO" : "YES\n"+ans.get(0)+" "+ans.get(1)+" "+ans.get(2));
		}
	}
}