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.*;
import java.util.*;
 
public class A {	
	
	public static void main(String[] args) throws IOException{	
		
		//0-1 Knapsack Problem
		
		FastScanner fs = new FastScanner();
		int test = fs.nextInt();
		while(test-->0) {
			int n = fs.nextInt();
			ArrayList<Integer> f = new ArrayList<Integer>();
			for(int i=2 ; i<=Math.sqrt(n) ; i++) {
				if(n%i==0) {
					f.add(i);
					n/=i;
					break;
				}
			}
			if(f.size()==0) {
				System.out.println("NO");
				continue;
			}else {
				for(int i=f.get(0) + 1 ; i*i<=n ; i++) {
					if(n%i==0) {
						f.add(i);
						n/=i;
						break;
					}
				}
				if(f.size()==1 || f.get(0)==f.get(1) || n==1 || n==f.get(0) || n==f.get(1)) {
					System.out.println("NO");
				}else {
					System.out.println("YES");
					System.out.println(f.get(0) + " " + f.get(1) + " "+ n);
				}
			}
		}
	}
	
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		String[] readStringArray(int n) {
			String[] a=new String[n];
			for (int i=0; i<n; i++) a[i]=next();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	static class Pair implements Comparable<Pair> {
	       
        int x;
        int y;
    
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    
        @Override
        public int hashCode() {
            return this.x ^ this.y;
        }
    
        @Override
        public boolean equals(Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            Pair other = (Pair) obj;
            if (x != other.x)
                return false;
            if (y != other.y)
                return false;
            return true;
        }
        @Override
        public int compareTo(Pair o) {
			if(x!=o.x)return x-o.x;
            return y-o.y;
        }
	}
}