Despite his bad reputation, Captain Flint is a friendly person (at least, friendly to animals). Now Captain Flint is searching worthy sailors to join his new crew (solely for peaceful purposes). A sailor is considered as worthy if he can solve Flint's task.

Recently, out of blue Captain Flint has been interested in math and even defined a new class of integers. Let's define a positive integer x as nearly prime if it can be represented as p ⋅ q, where 1 < p < q and p and q are prime numbers. For example, integers 6 and 10 are nearly primes (since 2 ⋅ 3 = 6 and 2 ⋅ 5 = 10), but integers 1, 3, 4, 16, 17 or 44 are not.

Captain Flint guessed an integer n and asked you: can you represent it as the sum of 4 different positive integers where at least 3 of them should be nearly prime.

Uncle Bogdan easily solved the task and joined the crew. Can you do the same?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

Next t lines contain test cases — one per line. The first and only line of each test case contains the single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number Flint guessed.

Output

For each test case print: 

  * YES and 4 different positive integers such that at least 3 of them are nearly prime and their sum is equal to n (if there are multiple answers print any of them); 
  * NO if there is no way to represent n as the sum of 4 different positive integers where at least 3 of them are nearly prime. 

You can print each character of YES or NO in any case.

Example

Input


7
7
23
31
36
44
100
258


Output


NO
NO
YES
14 10 6 1
YES
5 6 10 15
YES
6 7 10 21
YES
2 10 33 55
YES
10 21 221 6

Note

In the first and second test cases, it can be proven that there are no four different positive integers such that at least three of them are nearly prime.

In the third test case, n=31=2 ⋅ 7 + 2 ⋅ 5 + 2 ⋅ 3 + 1: integers 14, 10, 6 are nearly prime.

In the fourth test case, n=36=5 + 2 ⋅ 3 + 2 ⋅ 5 + 3 ⋅ 5: integers 6, 10, 15 are nearly prime.

In the fifth test case, n=44=2 ⋅ 3 + 7 + 2 ⋅ 5 + 3 ⋅ 7: integers 6, 10, 21 are nearly prime.

In the sixth test case, n=100=2 + 2 ⋅ 5 + 3 ⋅ 11 + 5 ⋅ 11: integers 10, 33, 55 are nearly prime.

In the seventh test case, n=258=2 ⋅ 5 + 3 ⋅ 7 + 13 ⋅ 17 + 2 ⋅ 3: integers 10, 21, 221, 6 are nearly prime.
import java.io.*;
import java.util.*;
import java.math.*;
import java.util.stream.*;

/**
 * Author :     AV
 * At   :       @Home
 * Date :       20.8.19
 * ver. :       0.1
 * link :       
 * file :       cf/      
 */

public class I_AM_AV{
// class I_AM_AV{
    static private I_AM_AV_Template sc=new I_AM_AV_Template();
    static private StringBuilder sb=new StringBuilder();

    public static void code(int n){
        if(n<=30){
            sb.append("NO\n");
            return ;
        }
        int rem = n - 30;
        sb.append("YES\n");
        switch (rem) {
            case 6:
                // n = 36
                sb.append("15 10 6 5");
                break;
            case 10:
                // n = 40
                sb.append("1 10 14 15");
                break;
            case 14:
                // n = 44
                sb.append("6 10 15 13");
                break;
            default:
                sb.append("6 10 14 "+rem);
                break;
        }
        sb.append("\n");
    }

    public static void main(String[] args) {
        int T=1;
        T=sc.nextInt();
        while(T-->0){
            int n=sc.nextInt();
            code(n);
        }
        System.out.print(sb);
    }
}

class I_AM_AV_Template{
    static private BufferedReader br;
    static private StringTokenizer st; 
    static public final int MOD=1000000007; //10^9+7

    I_AM_AV_Template(){
        br=new BufferedReader(new InputStreamReader(System.in));
    }  
    I_AM_AV_Template(String input)throws FileNotFoundException{
        System.setOut(new PrintStream(input));
    }
    I_AM_AV_Template(String input, String output)throws FileNotFoundException{
        System.setIn(new FileInputStream(input));
        System.setOut(new PrintStream(output));
    }
    /**
     * Use StringBuilder for output
     */
    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; 
    }
    public int[] input(int n){
        int[] a=new int[n];
        for(int i=0;i<n;i++)
            a[i]=this.nextInt();
        return a;
    }
    public int sum(int[] a, int start, int end){
        return Arrays.stream(a, start, end).sum();
    }
    public <E>void display(E[] a, int start, int end){
        for (;start<end; start++) {
            System.out.print(a[start]+" ");
        }
        System.out.println();
    }
    public void displayMatrix(int[][] a){
        for(int[] x: a)
            System.out.println(Arrays.toString(x));
    }

    public int max(int[] arr){ return Arrays.stream(arr).max().getAsInt(); }
    public int min(int[] arr){ return Arrays.stream(arr).min().getAsInt(); }

    public <E> E max(E[] a, int n){
        E max=a[0];
        return max;
    }
    public boolean isPrime(int number){
        if(number <= 2)
            return number == 2;
        else
            return  (number % 2) != 0
                    &&
                IntStream.rangeClosed(3, (int) Math.sqrt(number))
                    .filter(n -> n % 2 != 0)
                    .noneMatch(n -> (number % n == 0));
        }
}


