Problem: An integer sequence is called beautiful if the difference between any two consecutive numbers is equal to 1. More formally, a sequence s_1, s_2, …, s_{n} is beautiful if |s_i - s_{i+1}| = 1 for all 1 ≤ i ≤ n - 1.

Trans has a numbers 0, b numbers 1, c numbers 2 and d numbers 3. He wants to construct a beautiful sequence using all of these a + b + c + d numbers.

However, it turns out to be a non-trivial task, and Trans was not able to do it. Could you please help Trans?

Input

The only input line contains four non-negative integers a, b, c and d (0 < a+b+c+d ≤ 10^5).

Output

If it is impossible to construct a beautiful sequence satisfying the above constraints, print "NO" (without quotes) in one line.

Otherwise, print "YES" (without quotes) in the first line. Then in the second line print a + b + c + d integers, separated by spaces — a beautiful sequence. There should be a numbers equal to 0, b numbers equal to 1, c numbers equal to 2 and d numbers equal to 3.

If there are multiple answers, you can print any of them.

Examples

Input


2 2 2 1


Output


YES
0 1 0 1 2 3 2


Input


1 2 3 4


Output


NO


Input


2 2 2 3


Output


NO

Note

In the first test, it is easy to see, that the sequence is beautiful because the difference between any two consecutive numbers is equal to 1. Also, there are exactly two numbers, equal to 0, 1, 2 and exactly one number, equal to 3.

It can be proved, that it is impossible to construct beautiful sequences in the second and third tests.

Solution (in JAVA):

Solution:

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

/**
 * @author Mubtasim Shahriar
 */

public class BetSeq {


	public static void main(String[] args) {

		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader sc = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Solver solver = new Solver();
//		int t = sc.nextInt();
		int t = 1;
		while(t--!=0) {
			solver.solve(sc, out);
		}		
		out.close();

	}

	static class Solver {
		public void solve(InputReader sc, PrintWriter out) {
			Dll dl = new Dll();
			int a = sc.nextInt();
			int b = sc.nextInt();
			int c = sc.nextInt();
			int d = sc.nextInt();
//			while(a>0 && b>0) {
//				dl.addLast(0);
//				a--;
//				dl.addLast(1);
//				b--;
//			}
//			if(a>0 && dl.size==0) {
//				dl.addLast(0);
//				a--;
//			}
//			if(b>0 && dl.size==0) {
//				dl.addLast(1);
//				b--;
//			}
//			if(c>0 && dl.size==0) {
//				dl.addLast(2);
//				c--;
//			}
//			if(d>0 && dl.size==0) {
//				dl.addLast(3);
//				d--;
//			}
//			if(a>0 && dl.tail.data==1) {
//				dl.addLast(0);
//				a--;
//			}
////			out.println(dl);
//			if(dl.tail!=null && dl.tail.data==1) {
//				while(c>0 && b>0 && c>d) {
//					dl.addLast(2);
//					c--;
//					dl.addLast(1);
//					b--;
//				}
//			}
////			if(dl.tail!=null && dl.tail.data==1 && c>0) {
////				dl.addLast(2);
////				c--;
////			}
//			if(dl.size>0 && dl.tail.data==1 && c>0) {
//				dl.addLast(2);
//				c--;
//			}
//			if(dl.size>0 && dl.head.data==1 && c>0) {
//				dl.addFirst(2);
//				c--;
//			}
////			out.println(dl);
//			if(dl.tail!=null && dl.tail.data==2) {
//				while(c>0 && d>0) {
//					dl.addLast(3);
//					d--;
//					dl.addLast(2);
//					c--;
//				}
//			}
//			if(dl.size>0 && dl.tail.data==2 && d>0) {
//				dl.addLast(3);
//				d--;
//			}
//			if(dl.size>0 && dl.head.data==2 && d>0) {
//				dl.addFirst(3);
//				d--;
//			}
////			out.println(dl);
//			if(c>0 && dl.tail!=null && dl.tail.data==3) {
//				dl.addLast(2);
//				c--;
//			}
//			if(d>0 && dl.tail!=null && dl.tail.data==2) {
//				dl.addLast(3);
//				d--;
//			}
//			if(b>0 && dl.head.data==0) {
//				dl.addFirst(1);
//				b--;
//			}
//			if(a>0 || b>0 || c>0 || d>0) {
//				out.println("NO");
//				return;
//			}
//			out.println("YES");
//			out.println(dl);
			if(a>0 && dl.size==0) {
				dl.addLast(0);
				a--;
			}
			if(b>0 && dl.size==0) {
				dl.addLast(1);
				b--;
			}
			if(c>0 && dl.size==0) {
				dl.addLast(2);
				c--;
			}
			if(d>0 && dl.size==0) {
				dl.addLast(3);
				d--;
			}
//			out.println(dl);
			if(dl.tail.data==0) {
				while(b>0 && a>0) {
					dl.addLast(1);
					b--;
					dl.addLast(0);
					a--;
				}
			}
//			out.println(dl);
			if(dl.size>0 && dl.tail.data==0 && b>0) {
				dl.addLast(1);
				b--;
			}
//			out.println(dl);
			if(dl.tail.data==1) {
				while(c>0 && b>0 && c>d) {
					dl.addLast(2);
					c--;
					dl.addLast(1);
					b--;
				}
			}
			if(b>0 && dl.head.data==0) {
				dl.addFirst(1);
				b--;
			}
//			out.println(dl);
			if(dl.size>0 && dl.tail.data==1 && c>0) {
				dl.addLast(2);
				c--;
			}
			if(dl.tail.data==2) {
				while(d>0 && c>0) {
					dl.addLast(3);
					d--;
					dl.addLast(2);
					c--;
				}
			}
//			out.println(dl);
//			out.println(a + " " + b + " " + c + " " + d);
			if(dl.size>0 && dl.tail.data==2 && d>0) {
				dl.addLast(3);
				d--;
			}
			if(c>0 && dl.head.data==1 && c>0) {
				dl.addFirst(2);
				c--;
			}
			if(a>0 && dl.tail.data==1 && a>0) {
				dl.addLast(0);
				a--;
			}
			if(b>0 && dl.tail.data==2 && b>0) {
				dl.addLast(1);
				b--;
			}
			if(c>0 && dl.tail.data==3 && c>0) {
				dl.addLast(2);
				c--;
			}
			if(d>0 && dl.tail.data==2  && d>0) {
				dl.addLast(3);
				d--;
			}
			if(d>0 && dl.head.data==2 && d>0) {
				dl.addFirst(3);
				d--;
			}
			if(a==0 && b==0 && c==0 && d==0) {
				out.println("YES");
				out.println(dl);
			} else {
				out.println("NO");
			}
		}
	}
	static class Dll {
		Node head;
		Node tail;
		int size;
		
		Dll() {
			this.size=0;
		}
		
		int size() {
			return this.size();
		}
		
		boolean isEmpty() {
			return this.size==0;
		}
		
		void addFirst(int data) {
			Node tmp = new Node(data, head, null);
			if(head != null ) {head.prev = tmp;}
	        head = tmp;
	        if(tail == null) { tail = tmp;}
	        size++;
		}
		
		void addLast(int data) {
	        Node tmp = new Node(data, null, tail);
	        if(tail != null) {tail.next = tmp;}
	        tail = tmp;
	        if(head == null) { head = tmp;}
	        size++;
	    }
		
		public int removeFirst() {
	        if (size == 0) throw new NoSuchElementException();
	        Node tmp = head;
	        head = head.next;
	        head.prev = null;
	        size--;
	        return tmp.data;
	    }
		
		public int removeLast() {
	        if (size == 0) throw new NoSuchElementException();
	        Node tmp = tail;
	        tail = tail.prev;
	        tail.next = null;
	        size--;
	        return tmp.data;
	    }
		
		public String toString() {
			Node tmp = head;
			StringBuilder sb = new StringBuilder();
			while(tmp != null) {
				sb.append(tmp.data);
				sb.append(" ");
				tmp = tmp.next;
			}
			return sb.toString();
		}
	}
	
	static class Node {
		int data;
		Node prev, next;
		
		Node(int data, Node next, Node prev) {
			this.data=data;
			this.next=next;
			this.prev=prev;
		}
	}

	static class InputReader { 
		private boolean finished = false;

		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1) {
				throw new InputMismatchException();
			}
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}

		public int peek() {
			if (numChars == -1) {
				return -1;
			}
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					return -1;
				}
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar];
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				if (Character.isValidCodePoint(c)) {
					res.appendCodePoint(c);
				}
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null) {
				return filter.isSpaceChar(c);
			}
			return isWhitespace(c);
		}

		public static boolean isWhitespace(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuilder buf = new StringBuilder();
			int c = read();
			while (c != '\n' && c != -1) {
				if (c != '\r') {
					buf.appendCodePoint(c);
				}
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0) {
				s = readLine0();
			}
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines) {
				return readLine();
			} else {
				return readLine0();
			}
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(nextString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char nextCharacter() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			return (char) c;
		}

		public double nextDouble() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c == 'e' || c == 'E') {
					return res * Math.pow(10, nextInt());
				}
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c == 'e' || c == 'E') {
						return res * Math.pow(10, nextInt());
					}
					if (c < '0' || c > '9') {
						throw new InputMismatchException();
					}
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}

		public boolean isExhausted() {
			int value;
			while (isSpaceChar(value = peek()) && value != -1) {
				read();
			}
			return value == -1;
		}

		public String next() {
			return nextString();
		}

		public SpaceCharFilter getFilter() {
			return filter;
		}

		public void setFilter(SpaceCharFilter filter) {
			this.filter = filter;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
		public int[] nextIntArray(int n){
			int[] array=new int[n];
			for(int i=0;i<n;++i)array[i]=nextInt();
			return array;
		}
		public int[] nextSortedIntArray(int n){
			int array[]=nextIntArray(n);
			Arrays.sort(array);
			return array;
		}
		public int[] nextSumIntArray(int n){
			int[] array=new int[n];
			array[0]=nextInt();
			for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
			return array;
		}
		public long[] nextLongArray(int n){
			long[] array=new long[n];
			for(int i=0;i<n;++i)array[i]=nextLong();
			return array;
		}
		public long[] nextSumLongArray(int n){
			long[] array=new long[n];
			array[0]=nextInt();
			for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
			return array;
		}
		public long[] nextSortedLongArray(int n){
			long array[]=nextLongArray(n);
			Arrays.sort(array);
			return array;
		}
	}


}