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.*;

public class Main { 
    
    public static void main(String[] args) throws java.lang.Exception { 
        Reader pm =new Reader(); 
        //Scanner pm = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int a = pm.nextInt();
        int b = pm.nextInt();
        int c = pm.nextInt();
        int d = pm.nextInt();
        int ta = a;
        
        if(a == 0 && (c-b) == d+1){
            int loop = 0;
            StringBuffer sb = new StringBuffer();
            for(int i=0;i<2*b;i++){
                if(loop%2 == 0)
                    sb.append("2 ");
                else
                    sb.append("1 ");
                loop++;
            }
            sb.append("2 ");
            loop = 0;
            for(int i=0;i<2*d;i++){
                if(loop%2 == 0)
                    sb.append("3 ");
                else
                    sb.append("2 ");
                loop++;
            }
            System.out.println("YES");
            System.out.println(sb);
        }
        else{
        ArrayList<Integer> al = new ArrayList<>();
        if(a == 0 && b == 0 && c == 0 && d == 1){
            System.out.println("YES\n3");
        }
        else if(a == 0 && b == 0 && d == 0 && c == 1){
            System.out.println("YES\n2");
        }
        else if(a == 0 && d == 0 && c == 0 && b == 1){
            System.out.println("YES\n1");
        }
        else if(d == 0 && b == 0 && c == 0 && a == 1){
            System.out.println("YES\n0");
        }
        else if(a == 0 && b == 0){
            StringBuffer pl = new StringBuffer();
            if(c>d && c==d+1){
                int ct = 0;
                pl.append("2 ");
                while(true){
                    if(ct%2 == 0){
                        pl.append("3 ");
                        d--;
                    }
                    else    
                        pl.append("2 ");
                    ct++;
                    if(d == 0)
                        break;
                }
                pl.append("2");
                System.out.println("YES");
                System.out.println(pl);
            }
            else if(d>c && d==c+1){
                int ct = 0;
                pl.append("3 ");
                while(true){
                    if(ct%2 == 0){
                        pl.append("2 ");
                        c--;
                    }
                    else    
                        pl.append("3 ");
                    ct++;
                    if(c == 0)
                        break;
                }
                pl.append("3");
                System.out.println("YES");
                System.out.println(pl);
            }
            
            else if(c == d){
                int loop = 0;
                StringBuffer op = new StringBuffer();
                for(int i=0;i<c*2;i++){
                    if(loop%2 == 0)
                        op.append("2 ");
                    else
                        op.append("3 ");
                    loop++;
                }
                System.out.println("YES");
                System.out.println(op);
            }
            else{
                System.out.println("NO");
            }
        }
        else if(c == 0 && d == 0){
            StringBuffer pl2 = new StringBuffer();
            if(a>b && a==b+1){
                int ct2 = 0;
                pl2.append("0 ");
                while(true){
                    if(ct2%2 == 0){
                        pl2.append("1 ");
                        b--;
                    }
                    else    
                        pl2.append("0 ");
                    ct2++;
                    if(b == 0)
                        break;
                }
                pl2.append("0");
                System.out.println("YES");
                System.out.println(pl2);
            }
            else if(b>a && b==a+1){
                int ct2 = 0;
                pl2.append("1 ");
                while(true){
                    if(ct2%2 == 0){
                        pl2.append("0 ");
                        a--;
                    }
                    else    
                        pl2.append("1 ");
                    ct2++;
                    if(a == 0)
                        break;
                }
                pl2.append("1");
                System.out.println("YES");
                System.out.println(pl2);
            }
            else if(a == b){
                int loop = 0;
                StringBuffer op = new StringBuffer();
                for(int i=0;i<a*2;i++){
                    if(loop%2 == 0)
                        op.append("0 ");
                    else
                        op.append("1 ");
                    loop++;
                }
                System.out.println("YES");
                System.out.println(op);
            }
            else{
                System.out.println("NO");
            }
        }
        else if(a == 0 && d == 0){
            StringBuffer pl2 = new StringBuffer();
            if(b>c && b==c+1){
                int ct2 = 0;
                pl2.append("1 ");
                while(true){
                    if(ct2%2 == 0){
                        pl2.append("2 ");
                        c--;
                    }
                    else    
                        pl2.append("1 ");
                    ct2++;
                    if(c == 0)
                        break;
                }
                pl2.append("1 ");
                System.out.println("YES");
                System.out.println(pl2);
            }
            else if(c>b && c==b+1){
                int ct2 = 0;
                pl2.append("2 ");
                while(true){
                    if(ct2%2 == 0){
                        pl2.append("1 ");
                        b--;
                    }
                    else    
                        pl2.append("2 ");
                    ct2++;
                    if(b == 0)
                        break;
                }
                pl2.append("2 ");
                System.out.println("YES");
                System.out.println(pl2);
            }
            else if(c == b){
                int loop = 0;
                StringBuffer op = new StringBuffer();
                for(int i=0;i<c*2;i++){
                    if(loop%2 == 0)
                        op.append("1 ");
                    else
                        op.append("2 ");
                    loop++;
                }
                System.out.println("YES");
                System.out.println(op);
            }
            else{
                System.out.println("NO");
            }
        }
        else{
            if(b < a){
                System.out.println("NO");
            }
            else if(c < d){
                System.out.println("NO");
            }
            else{
                StringBuffer sb = new StringBuffer();
                int cnt = 0;
                int onelastTime = 0;
                while(true){
                    if(cnt % 2 == 0 && a > 0){
                        sb.append("0 ");
                        a--;
                    }
                    else if(cnt % 2 == 1 && b > 0){
                        sb.append("1 ");
                        b--;
                    }
                    cnt++;
                    if(onelastTime == 1)
                        break;
                    if(a <= 0)
                        onelastTime = 1;
                }
                int atMax = c-d;
                /*if(b > atMax && (b-atMax) > 1){
                    System.out.println("NO");
                }*/
                //else{
                    int leftC;
                    if(b > atMax)
                        leftC = atMax;
                    else
                        leftC = b;
                    int temp = leftC;
                    //System.out.println(leftC+" "+b);
                    if(leftC > 0 && b > 0){
                        cnt = 0;
                        onelastTime = 0;
                        while(true){
                            if(cnt % 2 ==  0 && leftC > 0){
                                sb.append("2 ");
                                leftC--;
                            }
                            else if(cnt % 2 == 1 && b > 0){
                                sb.append("1 ");
                                b--;
                            }
                            cnt++;
                            if(onelastTime == 1)
                                break;
                            if(leftC == 0)
                                onelastTime = 1;
                            if(b == 0)
                                onelastTime = 1;
                        }
                        c = c-temp;    
                    }
                    /*System.out.println(c);
                    System.out.println(sb);*/
                    
                    if(c > d+1){
                        System.out.println("NO");
                    }
                    else{
                        cnt = 0;
                        onelastTime = 0;
                        while(true){
                            if(cnt % 2 ==  0 && c > 0){
                                sb.append("2 ");
                                c--;
                            }
                            else if(cnt % 2 == 1 && d > 0){
                                sb.append("3 ");
                                d--;
                            }
                            cnt++;
                            //System.out.println(c+" "+d+" "+onelastTime);
                            if(onelastTime == 1)
                                break;
                            if(c == 0 && d == 1)
                                onelastTime = 1;
                            if(c == 0 && d != 1)
                                break;
                            if(d <= 0)
                                onelastTime = 1;
                        }
                        /*System.out.println(sb);
                        System.out.println(c+" "+d);*/
                        if(d > 0){
                            System.out.println("NO");
                        }
                        else {
                            if(c == 1)
                                sb.append("2");
                            if(c > 1){
                                System.out.println("NO");
                            }
                            else if(b == 0){
                                System.out.println("YES");
                                System.out.println(sb);
                            }
                            else{
                                //System.out.println("NOpe");
                                if(b > 1){
                                    System.out.println("NO");
                                }
                                else{
                                    if(ta == 0)
                                        System.out.println("NO");
                                    else{
                                        StringBuffer sb2 = new StringBuffer();
                                        sb2.append("1 ");
                                        sb2.append(sb);
                                        System.out.println("YES");
                                        System.out.println(sb2);
                                    }
                                }
                            }
                        }
                    }
                //}
            }
        }
        }
        
    }
    
    static class Reader { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
}