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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.util.StringTokenizer;
import java.io.Closeable;
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.Flushable;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	static class TaskAdapter implements Runnable {
		@Override
		public void run() {
			InputStream inputStream = System.in;
			OutputStream outputStream = System.out;
			Input in = new Input(inputStream);
			Output out = new Output(outputStream);
			ACaptainFlintAndCrewRecruitment solver = new ACaptainFlintAndCrewRecruitment();
			int testCount = Integer.parseInt(in.next());
			for(int i = 1; i<=testCount; i++)
				solver.solve(i, in, out);
			out.close();
		}
	}

	public static void main(String[] args) throws Exception {
		Thread thread = new Thread(null, new TaskAdapter(), "", 1<<29);
		thread.start();
		thread.join();
	}
	static class ACaptainFlintAndCrewRecruitment {
		public ACaptainFlintAndCrewRecruitment() {
		}

		public void solve(int kase, Input in, Output pw) {
			int n = in.nextInt(), sum = 6+10+14;
			if(n<=sum) {
				pw.println("NO");
			}else {
				pw.println("YES");
				if(n==36) {
					pw.println(6, 10, 15, 5);
					return;
				}else if(n==40) {
					pw.println(6, 10, 15, 9);
					return;
				}else if(n==44) {
					pw.println(6, 10, 15, 13);
					return;
				}
				pw.println(6, 10, 14, n-sum);
			}
		}

	}

	static class Input {
		BufferedReader br;
		StringTokenizer st;

		public Input(InputStream is) {
			this(is, 1<<20);
		}

		public Input(InputStream is, int bs) {
			br = new BufferedReader(new InputStreamReader(is), bs);
			st = null;
		}

		public boolean hasNext() {
			try {
				while(st==null||!st.hasMoreTokens()) {
					String s = br.readLine();
					if(s==null) {
						return false;
					}
					st = new StringTokenizer(s);
				}
				return true;
			}catch(Exception e) {
				return false;
			}
		}

		public String next() {
			if(!hasNext()) {
				throw new InputMismatchException();
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

	}

	static class Output implements Closeable, Flushable {
		public StringBuilder sb;
		public OutputStream os;
		public int BUFFER_SIZE;
		public boolean autoFlush;
		public String LineSeparator;

		public Output(OutputStream os) {
			this(os, 1<<16);
		}

		public Output(OutputStream os, int bs) {
			BUFFER_SIZE = bs;
			sb = new StringBuilder(BUFFER_SIZE);
			this.os = new BufferedOutputStream(os, 1<<17);
			autoFlush = false;
			LineSeparator = System.lineSeparator();
		}

		public void print(String s) {
			sb.append(s);
			if(autoFlush) {
				flush();
			}else if(sb.length()>BUFFER_SIZE >> 1) {
				flushToBuffer();
			}
		}

		public void println(Object... o) {
			for(int i = 0; i<o.length; i++) {
				if(i!=0) {
					print(" ");
				}
				print(String.valueOf(o[i]));
			}
			println();
		}

		public void println(String s) {
			sb.append(s);
			println();
			if(autoFlush) {
				flush();
			}else if(sb.length()>BUFFER_SIZE >> 1) {
				flushToBuffer();
			}
		}

		public void println() {
			sb.append(LineSeparator);
		}

		private void flushToBuffer() {
			try {
				os.write(sb.toString().getBytes());
			}catch(IOException e) {
				e.printStackTrace();
			}
			sb = new StringBuilder(BUFFER_SIZE);
		}

		public void flush() {
			try {
				flushToBuffer();
				os.flush();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			flush();
			try {
				os.close();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

	}
}

