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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Class1 {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        StringBuffer rs = new StringBuffer();
        while (t-- > 0) {
            int n=Integer.parseInt(br.readLine());
            ArrayList<Integer> ar=new ArrayList<>();
            for(int i=2;i<=(int)Math.sqrt(n);i++){
                if(n%i==0){
                    ar.add(i);
                    ar.add(n/i);
                }
            }
            int fl=0;
            for(int i:ar){
                for(int j:ar){
                    for(int k:ar){
                        if(i==j||i==k||j==k){
                            continue;
                        }
                        if(i*j*k==n){
                            rs.append("YES\n");
                            rs.append(i+" "+j+" "+k+"\n");
                            fl=1;
                            break;
                        }
                    }
                    if (fl==1){
                        break;
                    }
                }
                if(fl==1){
                    break;
                }
            }
            if(fl==0){
                rs.append("NO\n");
            }
        }
        System.out.println(rs);
    }
}