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 ProductOfThreeNumbers{
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        for(int i=0;i<t;i++){
            long n=sc.nextLong();
            long arr[]=new long[3];
            int c=0;
            for(int j=2;j<=Math.sqrt(n);j++){
                if(n%j==0){
                    arr[c++]=j;n/=j;
                }
                if(c==2){arr[c++]=n;break;}
            }
            if(c==3&&arr[0]!=arr[2]&&arr[1]!=arr[2])System.out.println("Yes\n"+arr[0]+" "+arr[1]+" "+arr[2]);
            else System.out.println("NO");
        }
    }
}