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.util.*;
import java.lang.*;
import java.io.*;

public class D {
	private static FastReader fr;
    private static OutputStream out;
    
	private static class FastReader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public FastReader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public FastReader(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[1024];
            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(); 
        } 
        
        public int[] nextIntArray(int n) throws IOException {
        	int arr[] = new int[n];
        	for(int i=0;i<n;i++){
        		arr[i] = nextInt();
        	}
        	return arr;
        }
    } 
 
	private static void print(Object str) {
        try {
            out.write(str.toString().getBytes());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
	
	private static void println(Object str) {
        try {
            out.write((str.toString() + "\n").getBytes());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
	
	private static void printArray(int arr[]){
		for(int val: arr){
			print(val + " ");
		}
	}
	
	public static void main(String args[]) throws IOException{
		run();
	}
	
	private static void run() throws IOException{
		fr = new FastReader();
		out = new BufferedOutputStream(System.out);
		solve();
		out.flush();
		out.close();
	}
	
	private static void solve() throws IOException{
		int a = fr.nextInt();
		int b = fr.nextInt();
		int c = fr.nextInt();
		int d = fr.nextInt();
		
		if(a > b + 1 || d > c + 1) {
			println("NO");
			return;
		}
		
		int n = a + b + c + d;
		int ans[] = new int[n]; 
		int i = 1;
		
		if(b > a && (b - a) > (c - d) && b > 0) {
			ans[0] = 1;
			b--;
		}else if(a > 0){
			ans[0] = 0;
			a--;
		}else if(c >= d) {
			ans[0] = 2;
			c--;
		}else {
			ans[0] = 3;
			d--;
		}
		
		while(a != 0 && b != 0) {
			int prev = ans[i-1];
			if(prev == 0) {
				ans[i] = 1;
				b--;
			}else {
				ans[i] = 0;
				a--;
			}
			i++;
		}
		
		while(a != 0) {
			ans[i] = 0;
			a--;
			i++;
		}
		
		while(b != 0 && c != 0) {
			int prev = ans[i-1];
			if(prev == 1) {
				ans[i] = 2;
				c--;
			}else {
				ans[i] = 1;
				b--;
			}
			i++;
		}
		
		while(b != 0) {
			ans[i] = 1;
			b--;
			i++;
		}
		
		while(c != 0 && d != 0) {
			int prev = ans[i-1];
			if(prev == 2) {
				ans[i] = 3;
				d--;
			}else {
				ans[i] = 2;
				c--;
			}
			i++;
		}
		
		while(c != 0) {
			ans[i] = 2;
			c--;
			i++;
		}
		
		while(d != 0) {
			ans[i] = 3;
			d--;
			i++;
		}
		
		boolean bool = false;
		for(int j=1;j<n;j++) {
			int diff = Math.abs(ans[j] - ans[j-1]);
			if(diff != 1) {
				bool = true;
				break;
			}
		}
		
		if(bool) {
			println("NO");
		}else {
			println("YES");
			for(i=0;i<n;i++) {
				print(ans[i] + " ");
			}
			println("");
		}
	}
	
	private static int factorial(int n){
		int fac = 1;
		for(int i=2;i<=n;i++){
			fac *= i;
		}
		
		return fac;
	}
	
	private boolean isPrime(int n){
		if(n == 0 || n == 1){
			return false;
		}else if(n%2 == 0){
			return false;
		}else{
			int x = (int)(Math.sqrt(n)) + 1;
			for(int i=3;i<=x;i+=2){
				if(n % i == 0){
					return false;
				}
			}
			return true;
		}
	}
	
	private long pow(int base,int exp){
		if(exp == 0){
			return 1;
		}else if(exp == 1){
			return base;
		}else{
			long a = pow(base,exp/2);
			if(exp%2 == 0){
				return a * a;
			}else{
				return a * a * base;
			}
		}
		
	}

	private static int gcd(int a,int b){
		if(a == 0){
			return b;
		}
		
		return gcd(b%a,a);
	}
	
	private static int lcm(int a,int b){
		return (a * b)/gcd(a,b);
	}
	
	private static ArrayList<Integer> SieveOfEratosthenes(int n){
		boolean b[] = new boolean[n+1];
		b[0] = true;
		b[1] = true;
		for(int i=2;i<=5;i++){
			int j = 2;
			while(i * j <= n && !b[i]){
				b[i * j] = true;
				j++;
			}
		}
		
		ArrayList<Integer> arr = new ArrayList<>();
		for(int i=2;i<n+1;i++){
			if(!b[i]){
				arr.add(i);
			}
		}
		
		return arr;
	}

}