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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

/**
 * #
 *
 * @author pttrung
 */
public class B_Round_604_Div1 {
    public static long MOD = 1000000007;


    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int[] data = new int[4];
        int total = 0;
        for (int i = 0; i < data.length; i++) {
            data[i] = in.nextInt();
            total += data[i];
        }
        boolean ok = true;
        int[] count = new int[4];
        int cur = 0;
        int last = 1;
        ArrayList<Integer> list = new ArrayList<>();
        while (cur < total) {
            if (last > 0 && count[last - 1] < data[last - 1]) {
                count[last - 1]++;
                last = last - 1;
                list.add(last);
                cur++;
            } else if (last + 1 < data.length && count[last + 1] < data[last + 1]) {
                count[last + 1]++;
                last = last + 1;
                list.add(last);
                cur++;
            } else {
                ok = false;
                break;
            }
        }
        //System.out.println(list + " " + ok + " " + cur);
        if (ok) {
            out.println("YES");
            for (int i : list) {
                out.print(i + " ");
            }
        } else {
            list.clear();
            cur = 0;
            last = 0;
            Arrays.fill(count, 0);
            ok = true;
            while (cur < total) {
                if (last > 0 && count[last - 1] < data[last - 1]) {
                    count[last - 1]++;
                    last = last - 1;
                    list.add(last);
                    cur++;
                } else if (last + 1 < data.length && count[last + 1] < data[last + 1]) {
                    count[last + 1]++;
                    last = last + 1;
                    list.add(last);
                    cur++;
                } else {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                out.println("YES");
                for (int i : list) {
                    out.print(i + " ");
                }
            } else {
                list.clear();
                cur = 0;
                last = 3;
                Arrays.fill(count, 0);
                ok = true;
                while (cur < total) {
                    if (last + 1 < data.length && count[last + 1] < data[last + 1]) {
                        count[last + 1]++;
                        last = last + 1;
                        list.add(last);
                        cur++;
                    } else if (last > 0 && count[last - 1] < data[last - 1]) {
                        count[last - 1]++;
                        last = last - 1;
                        list.add(last);
                        cur++;
                    } else {
                        ok = false;
                        break;
                    }
                }
                if (ok) {
                    out.println("YES");
                    for (int i : list) {
                        out.print(i + " ");
                    }
                } else {
                    list.clear();
                    cur = 0;
                    last = 2;
                    Arrays.fill(count, 0);
                    ok = true;
                    while (cur < total) {
                        if (last + 1 < data.length && count[last + 1] < data[last + 1]) {
                            count[last + 1]++;
                            last = last + 1;
                            list.add(last);
                            cur++;
                        } else if (last > 0 && count[last - 1] < data[last - 1]) {
                            count[last - 1]++;
                            last = last - 1;
                            list.add(last);
                            cur++;
                        } else {
                            ok = false;
                            break;
                        }
                    }
                }
                if (ok) {
                    out.println("YES");
                    for (int i : list) {
                        out.print(i + " ");
                    }
                } else {
                    out.println("NO");
                }
            }
        }

        out.close();
    }


    static class P {
        int index;
        long val;

        P(int index, long val) {
            this.index = index;
            this.val = val;
        }

    }

    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }

        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * (val * a);

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}