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.*;
import java.math.*;

 
public class S{
   static class Pair implements Comparable<Pair>{
   int a;
   int b;
   public Pair(int x,int y){a=x;b=y;}
   public Pair(){}
   public int compareTo(Pair p1){
       if(a == p1.a)
       return b - p1.b;
       return a - p1.a;
   }
 }
static class TrieNode{
  TrieNode[]child;
  int w;
  boolean term;
  TrieNode(){
    child = new TrieNode[26];  
  }
}
  public static int gcd(int a,int b)
  {
    if(a<b)
      return gcd(b,a);
    if(b==0)
      return a;
    return gcd(b,a%b);
    
  }
  //static long ans = 0;
  static long mod =(long)( 1e9 + 7);
   
    public static void main(String[] args) throws Exception {
       new Thread(null, null, "Anshum Gupta", 99999999) {
            public void run() {
                try {
                    solve();
                } catch(Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
static void insert(TrieNode head,String str){
    int n = str.length();
    TrieNode cur = head;
    for(int i=0;i<n;i++){
       int ch = str.charAt(i)-'A';
       if(cur.child[ch] == null)
       cur.child[ch]=new TrieNode();
       cur = cur.child[ch];
    }
    
    cur.term = true;
    
}
static boolean isRoot(TrieNode cur){
    if(cur==root)return true;
    return false;
}
static int f(TrieNode head){
    int ans = 0;
    for(int i=0;i<26;i++){
        if(head.child[i]!=null){
            ans += f(head.child[i]);
        }
    }
    if(head.term)ans++;
    if(ans >=2 && !isRoot(head))
    ans-=2;
    return ans;
}
static boolean done(int[]arr){
    for(int i=1;i<arr.length;i++){
        if(arr[i-1] > arr[i] )
        return  false;
    }
    return true;
}
static TrieNode root;
 public static void solve() throws Exception {
   // solve the problem here
   MyScanner s = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out), true);
        int t = s.nextInt();
        int tc = 0;
        while(tc++<t){
            int n = s.nextInt();
            int a=0,b=0,c=0;
            for(int i = 2;i*i <= n;i++){
                if(n%i == 0){
                    a = i;
                    break;
                }
            }
            if(a==0)
            {
                out.println("NO");
                continue;
            }
            for(int i=a+1;i*i<=n;i++){
                if(n%(i*a) == 0 ){
                    b = i;
                    break;
                }
            }
            if(b==0)
            {
                out.println("NO");
                continue;
            }
            c = n/(a*b);
            if(a == 0 || b==0 || c==0 || a==b || b==c || c==a)
            out.println("NO");
            else {
                out.println("YES");
                out.println(a+" "+b+" "+c);
            }
            
        }
        out.flush();
}
 
     
 
 
 
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
 
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            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;
        }
    }
    //--------------------------------------------------------
}