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 MyClass {
    
    public static void main(String args[]) {
      FastReader sc = new FastReader();     //For Fast IO
      //func f = new func();                  //Call func for swap , permute, upper bound and for sort.
      int t = sc.nextInt();
      while(t-->0){
          long n = sc.nextLong();
          TreeSet<Long> ts = new TreeSet<>();
          long num=n;
          long curr=1;
          for(int i=2;i*i<=num;i++){
              if(n%i==0){
                  while(n%i==0){
                      curr *= i;
                      n /= i;
                      if(!ts.contains(curr)){
                          ts.add(curr);
                          curr=1;
                      }
                      if(ts.size()==2){
                          break;
                      }
                  }
                  if(ts.size()==2){
                      break;
                  }
              }
          }
          if(n>1){
              ts.add(n);
          }
          if(ts.size()==3){
              System.out.println("YES");
              for(Long n1 : ts){System.out.print(n1+" ");}
              System.out.println();
          }
          else{
              System.out.println("NO");
          }
          
      }
      
      
      
      
    }
}
class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 
 
		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 
 
		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 
 
		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 
 
		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 
 
		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 
 
		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	}
class func{
    static ArrayList<String> al = new ArrayList<>();
        public static void sort(long[] arr) {
            int n = arr.length, mid, h, s, l, i, j, k;
            long[] res = new long[n];
            for (s = 1; s < n; s <<= 1) {
                for (l = 0; l < n - 1; l += (s << 1)) {
                    h = Math.min(l + (s << 1) - 1, n - 1);
                    mid = Math.min(l + s - 1, n - 1);
                    i = l;
                    j = mid + 1;
                    k = l;
                    while (i <= mid && j <= h) res[k++] = (arr[i] <= arr[j] ? arr[i++] : arr[j++]);
                    while (i <= mid) res[k++] = arr[i++];
                    while (j <= h) res[k++] = arr[j++];
                    for (k = l; k <= h; k++) arr[k] = res[k];
                }
            }
        }
        public static void permute(char a[] , int i , int n){
            if(i==n-1){
                String s = new String(a);
                al.add(s);                      // al stores all permutations of string. 
                return;
            }
            for(int j=i;j<n;j++){
                swap(a,i,j);
                permute(a,i+1,n);
                swap(a,i,j);
            }
        }
        public static void swap(char a[],int i, int j){
            char temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }
        public static void swap(int a[],int i, int j){
            int temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }
		//-It returns index of first element which is strictly greater than searched value.
		public static int upperBound(long[] array, int length, long value) {
            int low = 0;
            int high = length;
            while (low < high) {
                final int mid = (low + high) / 2;
                if (value >= array[mid]) {
                    low = mid + 1;
                } else {
                    high = mid;
                }
        }
        return low;
    }
	/*If searched element doesn't exist function returns index of first element which is bigger than searched value.<br>
 * -If searched element is bigger than any array element function returns first index after last element.<br>
 * -If searched element is lower than any array element function returns index of first element.<br>
 * -If there are many values equals searched value function returns first occurrence.<br>*/
	public static int lowerBound(long[] array, int length, long value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value <= array[mid]) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }
        
 
}