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.text.*;
import java.lang.*;
import java.math.*;
 
public class Myclass{
    //static ArrayList[] a=new ArrayList[30];
    static Vector<Integer> f(int a[]) {
    	  int ans[] = new  int [a[0] + a[1] +a[2] +a[3]];
          int idx = 0;
          boolean chk = true;
          while(a[3] > 0) {
          	ans[idx] = 3;
          	idx++;
          	a[3] -- ;

          	if(a[2] > 0 && a[3] > 0)
          	{
          		ans[idx] = 2;
          		idx ++;
              	a[2] --;
          	}
          	else if(a[3] > 1)
          		break;
          }
          while(a[2] > 0 ) {
          	ans[idx] = 2;
          	idx++;           	
          	a[2] -- ;
          	if(a[1] > 0 && a[2]>0)
          	{
          		ans[idx] = 1;
          		idx++;
              	a[1] --;
          	}
          	else if(a[2] > 1 )
          		break;
          }
          while(a[1] > 0 ) {
          	ans[idx] = 1;
          	idx++;
          	a[1] -- ;
          	if(a[0] > 0)
          	{
          		ans[idx] = 0;
              	a[0] --;
              	idx ++;
          	}
          	else if(a[1] >= 1 )
          		break;
          }
          Vector<Integer> v = new Vector<>();
          if(ans[0] > 0 && a[ans[0] - 1] >0) {
        	  v.add(ans[0] - 1);
          }
          for(int i = 0 ; i < idx ; i++) {
        	  v.add(ans[i]);
          }
		return v;
          
    }
    static boolean chk(Vector<Integer>v , int t) {
    	if(v.size() != t) return false;
    	for(int i = 1 ; i < v.size(); i++) {
    		if(Math.abs(v.get(i) - v.get(i -1 ))!= 1) return false;
    	}
    	return true;
    }
     public void solve () throws FileNotFoundException  {
    	InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int []a = new int[4];
        for(int i = 0 ; i < 4; i++)
        	a[i] = in.nextInt();
        int b[] = a.clone();
        Vector<Integer> v = f(b);
        int tot = a[0] + a[1] + a[2] + a[3];
        if(chk(v,tot)) {
        	pw.println("YES");
        	for(int i = 0 ; i < v.size() ; i++)
        		pw.print(v.get(i)+" ");
        }
        else {
        	b[0] = a[3] ; b[1] = a[2] ; b[2] = a[1]; b[3] = a[0];
        	v = f(b);
        	int tmp []= {3,2,1,0};
        	 if(chk(v,tot)) {
             	pw.println("YES");
             	for(int i = 0 ; i < v.size() ; i++) {
             		pw.print(tmp[v.get(i)] +" ");
             	}
             	
             }
        	 else
        		 pw.println("NO");
        }
        pw.flush();
        pw.close();
    }
    public static void main(String[] args) throws Exception {
        
        
        new Thread(null,new Runnable() {
            public void run() {
                    try {
						new Myclass().solve();
					} catch (FileNotFoundException e) {
						// TODO Auto-generated catch block
						e.printStackTrace();
					}
            }
        },"1",1<<26).start();
        
        
    }
   
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(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;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        public void extended(int a,int b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                int temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
       
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static long GCD(long n,long m)
        {
            if(m==0)
                return n;
            else
                return GCD(m,n%m);
        }
        public static long LCM (long a,long b) {
            return ((a*b)/(GCD(a,b)));
        }
        
        static class pair implements Comparable<pair>
        {
           Long x, y;
            
            pair(long seg,long minValue)
            {
                this.x=seg;
                this.y=minValue;
            }

            public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
                return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            
            public int hashCode()
            {
                return new Double(x).hashCode()*31 + new Long(y).hashCode();
            }
        }
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
       
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        static class Segment{ 
        	long seg[][]; 
        	long a[];
        	long lazy[];
            Segment (int n){
        		seg=new long[4*n][2];
        		lazy=new long[4*n];
        	}
            public void build(int node,int start,int end) {
            	if(start==end) {
            		seg[node][0]=0L;
            		seg[node][1] = 0L;
            		return ;
            	}
            	int mid=(start+end)/2;
            	build(2*node+1,start,mid);
            	build(2*node+2,mid+1,end);
            }
            /*public void update(int node,int start,int end,int id,int val) {
            	if(start==end) {
            		seg[node][]=a[start]=val;
            		return;
            	}
            	int mid=(start+end)/2;
            	if(id>=start && id<=mid) {
            		update(2*node+1,start,mid,id,val);
            	}
            	else
            		update(2*node+2,mid+1,end,id,val);
            	seg[node]=seg[2*node+1]+seg[2*node+2];
            }
            public long query(int node,int start,int end,int l,int r) {
            	if(l>end || r<start)
            		return 0;
            	if(start>=l && end<=r)
            		return seg[node];
            	
            	int  mid=(start+end)/2;
            	return query(2*node+1,start,mid,l,r) + query(2*node+2,mid+1,end,l,r);
            }*/
            public void updateRange(int node,int start,int end,int l,int r,int val) {
        
            	if(lazy[node]!=0) {
            		seg[node][0]+=lazy[node];
            		seg[node][1]+=lazy[node];

            		if(start!=end) {
            			lazy[2*node+1]+=lazy[node];
            			lazy[2*node+2]+=lazy[node];
            		}
            		lazy[node]=0;
            	}
            	if(l>end || r<start)
            		return ;
            	if(start>=l && end<=r) {
            		seg[node][0]+=val;
            		seg[node][1]+=val;
            		if(start!=end) {
            			lazy[2*node+1]+=val;
            			lazy[2*node+2]+=val;
            		}
            		lazy[node]=0;
            		return ;
            	}
            	int mid=(start+end)/2;
            	updateRange(2*node+1,start,mid,l,r,val);
            	updateRange(2*node+2,mid+1,end,l,r,val);
            	seg[node][0]=Math.min(seg[2*node+1][0] , seg[2*node+2][0]);
            	seg[node][1]=Math.max(seg[2*node+1][1] , seg[2*node+2][1]);

            }
            public pair queryRange(int node,int start,int end,int l,int r) {
            	if(l>end || r<start)
            		return new pair(Long.MAX_VALUE,Long.MIN_VALUE);
            	if(lazy[node]!=0) {
            		seg[node][0]+=lazy[node];
            		seg[node][1]+=lazy[node];
            		if(start!=end) {
            			lazy[2*node+1]+=lazy[node];
            			lazy[2*node+2]+=lazy[node];
            		}
            		lazy[node]=0;
            	}
            	if(start>=l && end<=r)
            		return new pair(seg[node][0],seg[node][1]);
            	
            	int  mid=(start+end)/2;
            	pair p1 = queryRange(2*node+1,start,mid,l,r);
            	pair p2 = queryRange(2*node+2,mid+1,end,l,r);
            	return new pair(Math.min(p1.x, p2.x) , Math.max(p1.y, p2.y));
            }
            
        }

        
         
}