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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.HashSet;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Actual solution is at the top
 *
 * @author harshit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        cf604d solver = new cf604d();
       // int testCount = Integer.parseInt(in.next());
        //for (int i = 1; i <= testCount; i++)
            solver.solve(0, in, out);
        out.close();
    }

    static class cf604d {
        

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int[] arr2=in.readIntArray(4);
            int[] arr=new int[4];
            
            int[][] seq={{0,1,2,3},{3,2,1,0},{1,0,2,3},{0,2,1,3},};
            int sum=0;
            for(int a:arr2)sum+=a;
            int[] ans=new int[sum];
            for(int[] s:seq){
                System.arraycopy(arr2,0,arr,0,4);
                //out.println(Arrays.toString(arr));
                        Arrays.fill(ans,-1);
                        int flag=0;
                         
                outer:
                for(int i:s){
                int ptr=0;
                   
                while(ptr<sum&&ans[ptr]!=-1){ptr++;}
                while(arr[i]>0){
                    if(ptr>=sum){flag=1;break outer;}
                    ans[ptr]=i;
                    arr[i]--;
                    
                    if((ptr-1>=0&&ans[ptr-1]!=-1&&Math.abs(ans[ptr-1]-ans[ptr])!=1)||(ptr+1<sum&&ans[ptr+1]!=-1&&Math.abs(ans[ptr+1]-ans[ptr])!=1))
                        {flag=2;break outer;}
                    ptr+=2;
                }
            
                }
                //out.println(flag+" "+Arrays.toString(ans));
                if(flag==0){
            out.println("YES");
            for(int a:ans)out.print(a+" ");
                out.println("");
            return;}
            }

            out.println("NO");



            
           
    }
}

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

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

        public int[] readIntArray(int tokens) {
            int[] ret = new int[tokens];
            for (int i = 0; i < tokens; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        public int read() {
            if (this.numChars == -1) {
                throw new InputMismatchException();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
                ;
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public String next() {
            int c;
            while (isSpaceChar(c = this.read())) {
                ;
            }

            StringBuilder result = new StringBuilder();
            result.appendCodePoint(c);

            while (!isSpaceChar(c = this.read())) {
                result.appendCodePoint(c);
            }

            return result.toString();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

        public void println(int i) {
            writer.println(i);
        }
        public void println(String i) {
            writer.println(i);
        }

        public void print(String i) {
            writer.print(i);
        }        
    }

    static class Utils {
        public static long mod_exp(long b, long e, long mod) {
            long res = 1;
            while (e > 0) {
                if ((e & 1) == 1)
                    res = (res * b) % mod;
                b = (b * b) % mod;
                e >>= 1;
            }
            return res % mod;
        }

    }

    static class AUtils {
        public static void reverse(int[] arr) {
            for (int i = 0, j = arr.length - 1; i < j; i++, j--) {
                int t = arr[i];
                arr[i] = arr[j];
                arr[j] = t;
            }
        }

        public static void sort(int[] arr) {
            shuffle(arr);
            Arrays.sort(arr);
        }

        public static void shuffle(int[] arr) {
            for (int i = 1; i < arr.length; i++) {
                int j = (int) (Math.random() * (i + 1));
                if (i != j) {
                    int t = arr[i];
                    arr[i] = arr[j];
                    arr[j] = t;
                }
            }
        }

    }
}