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.math.*;
import java.text.*;
import java.util.*;

public class Solution{
    BufferedReader br;
    PrintWriter out;
    static String input[];
    static int id = 0;
    public String next() throws Exception{
        if(input == null || input.length == id){
            input = br.readLine().split(" ");
            id=0;
        }
        return input[id++];
    }
    public String ns() throws Exception{
        return next();
    }
    public int ni() throws Exception{
        return Integer.parseInt(next());
    }
    public long nl() throws Exception{
        return Long.parseLong(next());
    }
    public double nd() throws Exception{
        return Double.parseDouble(next());
    }
    public int[] na(int n) throws Exception{
        int[] arr = new int[n];
        for(int i=0;i<n;i++){
            arr[i] = ni();
        }
        return arr;
    }

    public void run() throws Exception{
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int T=1;
        for(int t=1;t<=T;t++){
            solve();
        }
        out.flush();
    }

    public static void main(String[] args) throws Exception{new Solution().run();}
    
    public void solve() throws Exception{
        int[] spf = SPF(100000);
        ArrayList<Integer> primes = getPrimes(spf);
        int x = primes.size();
        int T = ni();
        for(int t=0;t<T;t++){
            int n = ni();
            int sqrt = (int)Math.sqrt(n);
            int a=1;
            int i=0;
            while(i<x && primes.get(i) <= sqrt){
                if(n%primes.get(i) == 0){
                    a = primes.get(i);
                    break;
                }
                i++;
            }
            if(a == 1){
                out.println("NO");
                continue;
            }
            n = n/a;
            i = a + 1;
            int b = 1;
            while(i <= sqrt){
                if(n%i== 0){
                    b = i;
                    if(n/b == a || b*b == n){
                        b=1;
                    }
                    break;
                }
                i++;
            }
            if(b==1){
                out.println("NO");
                continue;
            }
            out.println("YES");
            out.println(a+" "+b+" "+n/b);
        }
    }

    ArrayList<Integer> getPrimes(int[] spf){
        int n = spf.length;
        ArrayList<Integer> res = new ArrayList<Integer>();
        res.add(2);
        for(int i=3; i<n; i+=2){
            if(spf[i]==i) res.add(i);
        }
        return res;
    }

    public int[] SPF(int n){
        int[] arr = new int[n+1];
        for(int i=2;i<=n;i+=2){
            arr[i] = 2;
            arr[i-1] = i-1;
        }
        for(int i=3;i*i <= n; i++){
            if(arr[i]==i){
                for(int j=i*i; j<=n; j+=i){
                    if(arr[j] == j){
                        arr[j]=i;
                    }
                }
            }
        }
        return arr;
    }
}