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.*;
import java.util.*;
import java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;
 
public class Solution implements Runnable 
{
	static class InputReader 
	{
		private InputStream stream;private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        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 String nextLine(){String str = "";try{str = br.readLine();}catch (IOException e){e.printStackTrace();}return str;}
		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 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 String readString(){int c = read();while (isSpaceChar(c))c = read();StringBuilder res = new StringBuilder();do{res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();}
		public boolean isSpaceChar(int c){if (filter != null)return filter.isSpaceChar(c);return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;}
		public String next(){return readString();}
        public interface SpaceCharFilter{public boolean isSpaceChar(int ch);}
	}
		
	public static void main(String args[]) throws Exception{new Thread(null, new Solution(),"Main",1<<27).start();}

	public static long gcd(long a, long b) { 	if (a == 0) return b; return gcd(b % a, a);} 
  
	public static long findGCD(long arr[], int n) { 	long result = arr[0]; for (int i = 1; i < n; i++) result = gcd(arr[i], result);return result; }	 
	
	static void sortbycolomn(long arr[][], int col)
    { 
        Arrays.sort(arr, new Comparator<long[]>() { 
        @Override              
        public int compare(final long[] entry1,final long[] entry2) { 
            if (entry1[col] > entry2[col])return 1; 
            else return -1; 
        } 
        });   
    } 
	
	public void run()
    {
        InputReader in = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
		
		int a=in.nextInt();
		int b=in.nextInt();
		int c=in.nextInt();
		int d=in.nextInt();
		
		if(b==a-1){
		    if(c!=0 || d!=0)
		        w.println("NO");
		    else{
		        w.println("YES");
		        int[] arr=new int[a+b];
		        for(int i=0;i<a+b;i+=2)
		            arr[i]=0;
		        for(int i=1;i<b+a;i+=2)
		            arr[i]=1;
		        for(int i=0;i<a+b;i++)
		            w.print(arr[i]+" ");
		            w.println();
		    }
		}
		else if(b<a-1)
		    w.println("NO");
		else if(d==c+1){
		    if(a!=0 || b!=0)
		        w.println("NO");
		    else{
		        w.println("YES");
		        int[] arr=new int[c+d];
		        for(int i=0;i<c+d;i+=2)
		            arr[i]=3;
		        for(int i=1;i<d+c;i+=2)
		            arr[i]=2;
		        for(int i=0;i<c+d;i++)
		            w.print(arr[i]+" ");
		            w.println();
		    }
		}
		else if(d>c+1)
		    w.println("NO");
		else{
		    int restab=b-a;
		    int restcd=c-d;
		    if(restcd==restab){
		        w.println("YES");
		        int[] arr=new int[a+b+c+d];
		        Arrays.fill(arr,-1);
		        int temp=a;
		        for(int i=0;temp>0;i+=2,temp--)
		            arr[i]=0;
		        temp=b;
		        for(int i=1;temp>0;i+=2,temp--)
		            arr[i]=1;
		        temp=c;
		        for(int i=a*2;temp>0;i+=2,temp--)
		            arr[i]=2;
		        for(int i=0;i<(a+b+c+d);i++){
		            if(arr[i]==-1)
		                w.print("3 ");
		            else
		                w.print(arr[i]+" ");
		        }
		        w.println();
		    }
		    else if(restab!=0 && restcd==restab-1){
		        w.println("YES");
		        int[] arr=new int[a+b+c+d];
		        Arrays.fill(arr,-1);
		        int temp=b;
		        for(int i=0;temp>0;i+=2,temp--)
		            arr[i]=1;
		        temp=a;
		        for(int i=1;temp>0;i+=2,temp--)
		            arr[i]=0;
		        temp=c;
		        for(int i=(a*2+1);temp>0;i+=2,temp--)
		            arr[i]=2;
		        for(int i=0;i<(a+b+c+d);i++){
		            if(arr[i]==-1)
		                w.print("3 ");
		            else
		                w.print(arr[i]+" ");
		        }
		        w.println();
		    }
		    else if(restcd==restab+1){
		        w.println("YES");
		        int[] arr=new int[a+b+c+d-1];
		        Arrays.fill(arr,-1);
		        int temp=a;
		        for(int i=0;temp>0;i+=2,temp--)
		            arr[i]=0;
		        temp=b;
		        for(int i=1;temp>0;i+=2,temp--)
		            arr[i]=1;
		        temp=c-1;
		        for(int i=a*2;temp>0;i+=2,temp--)
		            arr[i]=2;
		        for(int i=0;i<(a+b+c+d-1);i++){
		            if(arr[i]==-1)
		                w.print("3 ");
		            else
		                w.print(arr[i]+" ");
		        }
		        w.println("2 ");
		    }
		    else
		        w.println("NO");
		}
		            
		      	    
		
		
	    w.flush();
        w.close();
    }
}