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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.StringTokenizer;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class P1265D {

    static boolean multipleIndependent = false;

    final int n = 4;
    int[] remaining;
    int k;
    int[] s;

    void run() {
        remaining = in.nextIntArray(n);
        int sum = IntStream.of(remaining).sum();
        s = new int[sum];
        int pivot = 0;
        while (remaining[pivot] == 0) {
            pivot++;
        }
        s[k] = pivot;
        remaining[pivot]--;
        traverse();
        debug();
        if (k + 1 != sum) {
            flip();
            traverse();
        }
        debug();
        if (k + 1 != sum) {
            out.println("NO");
        } else {
            out.println("YES");
            out.println(
                    IntStream.of(s).mapToObj(String::valueOf)
                            .collect(Collectors.joining(" "))
            );
        }
    }

    void debug() {
        if (1 == 1) {
            return;
        }
        out.println(k);
        out.println(
                IntStream.of(s).mapToObj(String::valueOf)
                        .collect(Collectors.joining(" "))
        );
    }

    void flip() {
        int n = k + 1;
        for (int i = 0; i < n / 2; i++) {
            int tmp = s[i];
            s[i] = s[n - i - 1];
            s[n - i - 1] = tmp;
        }
    }

    void traverse() {
        while (canGoRight()) {
            goRight();
            while (!canGoRight() && canGoleft()) {
                goLeft();
            }
        }
    }

    boolean canGoRight() {
        return s[k] + 1 < n && remaining[s[k] + 1] > 0;
    }

    void goRight() {
        int right = s[k] + 1;
        remaining[right]--;
        s[++k] = right;
    }

    boolean canGoleft() {
        return s[k] - 1 >= 0 && remaining[s[k] - 1] > 0;
    }

    void goLeft() {
        int left = s[k] - 1;
        remaining[left]--;
        s[++k] = left;
    }

    /* -----: Template :----- */
    static InputReader in = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    public static void main(String[] args) {
        int q = multipleIndependent ? in.nextInt() : 1;
        while (q-- > 0) {
            new P1265D().run();
        }
        out.flush();
    }

    static class InputReader {

        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            int bufferSize = 32 * 1024;
            reader = new BufferedReader(new InputStreamReader(stream), bufferSize);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public <T> T[] nextIntArrayWithFunction(int n, Function<Integer, T> function, Class<T> c) {
            T[] arr = (T[]) Array.newInstance(c, n);
            for (int i = 0; i < n; i++) {
                arr[i] = function.apply(nextInt());
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        public <T> T[] nextLongArrayWithFunction(int n, Function<Long, T> function, Class<T> c) {
            T[] arr = (T[]) Array.newInstance(c, n);
            for (int i = 0; i < n; i++) {
                arr[i] = function.apply(nextLong());
            }
            return arr;
        }

        public int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = nextIntArray(m);
            }
            return map;
        }

        public long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = nextLongArray(m);
            }
            return map;
        }

        public char[][] nextCharMap(int n) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++) {
                map[i] = next().toCharArray();
            }
            return map;
        }
    }

//    static int numLength(long n) {
//        int l = 0;
//        while (n > 0) {
//            n /= 10;
//            l++;
//        }
//        return l;
//    }
//
//    static <R> long binarySearch(long lowerBound, long upperBound,
//            R value, Function<Long, R> generatorFunction, Comparator<R> comparator) {
//        if (lowerBound <= upperBound) {
//            long mid = (lowerBound + upperBound) / 2;
//            int compare = comparator.compare(generatorFunction.apply(mid), value);
//            if (compare == 0) {
//                return mid;
//            } else if (compare < 0) {
//                return binarySearch(mid + 1, upperBound, value, generatorFunction, comparator);
//            } else {
//                return binarySearch(lowerBound, mid - 1, value, generatorFunction, comparator);
//            }
//        } else {
//            return -1;
//        }
//    }
//
//    static <T> Integer[] sortSimultaneously(T[] key, Comparator<T> comparator,
//            Object[]... moreArrays) {
//        int n = key.length;
//        for (Object[] array : moreArrays) {
//            if (array.length != n) {
//                throw new RuntimeException("Arrays must have equals lengths");
//            }
//        }
//        Integer[] indices = new Integer[n];
//        for (int i = 0; i < n; i++) {
//            indices[i] = i;
//        }
//        Comparator<Integer> delegatingComparator = (a, b) -> {
//            return comparator.compare(key[a], key[b]);
//        };
//        Arrays.sort(indices, delegatingComparator);
//        reorder(indices, key);
//        for (Object[] array : moreArrays) {
//            reorder(indices, array);
//        }
//        return indices;
//    }
//
//    static void reorder(Integer[] indices, Object[] arr) {
//        if (indices.length != arr.length) {
//            throw new RuntimeException("Arrays must have equals lengths");
//        }
//        int n = arr.length;
//        Object[] copy = new Object[n];
//        for (int i = 0; i < n; i++) {
//            copy[i] = arr[indices[i]];
//        }
//        System.arraycopy(copy, 0, arr, 0, n);
//    }
//    static int prodMod(int a, int b, int mod) {
//        return (int) (((long) a) * b % mod);
//    }
//
//    static long prodMod(long a, long b, long mod) {
//        long res = 0;
//        a %= mod;
//        b %= mod;
//        while (b > 0) {
//            if ((b & 1) > 0) {
//                res = (res + a) % mod;
//            }
//            a = (a << 1) % mod;
//            b >>= 1;
//        }
//        return res;
//    }
//
//    static long sumMod(int[] b, long mod) {
//        long res = 0;
//        for (int i = 0; i < b.length; i++) {
//            res = (res + b[i] % mod) % mod;
//        }
//        return res;
//    }
//
//    static long sumMod(long[] a, long mod) {
//        long res = 0;
//        for (int i = 0; i < a.length; i++) {
//            res = (res + a[i] % mod) % mod;
//        }
//        return res;
//    }
//
//    static long sumProdMod(int[] a, long b, long mod) {
//        long res = sumMod(a, mod);
//        return prodMod(res, b, mod);
//    }
//
//    static long sumProdMod(long[] a, long b, long mod) {
//        long res = sumMod(a, mod);
//        return prodMod(res, b, mod);
//    }
//
//    static long sumProdMod(int[] a, int[] b, long mod) {
//        if (a.length != b.length) {
//            throw new RuntimeException("Arrays must have equals lengths");
//        }
//        long res = 0;
//        for (int i = 0; i < a.length; i++) {
//            res = (res + prodMod(a[i], b[i], mod)) % mod;
//        }
//        return res;
//    }
//
//    static long sumProdMod(long[] a, long[] b, long mod) {
//        if (a.length != b.length) {
//            throw new RuntimeException("Arrays must have equals lengths");
//        }
//        long res = 0;
//        for (int i = 0; i < a.length; i++) {
//            res = (res + prodMod(a[i], b[i], mod)) % mod;
//        }
//        return res;
//    }
//
//    static int[] toPrimitive(Integer[] arr) {
//        int[] res = new int[arr.length];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = arr[i];
//        }
//        return res;
//    }
//
//    static int[][] toPrimitive(Integer[][] arr) {
//        int[][] res = new int[arr.length][];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = toPrimitive(arr[i]);
//        }
//        return res;
//    }
//
//    static long[] toPrimitive(Long[] arr) {
//        long[] res = new long[arr.length];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = arr[i];
//        }
//        return res;
//    }
//
//    static long[][] toPrimitive(Long[][] arr) {
//        long[][] res = new long[arr.length][];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = toPrimitive(arr[i]);
//        }
//        return res;
//    }
//
//    static Integer[] toWrapper(int[] arr) {
//        Integer[] res = new Integer[arr.length];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = arr[i];
//        }
//        return res;
//    }
//
//    static Integer[][] toWrapper(int[][] arr) {
//        Integer[][] res = new Integer[arr.length][];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = toWrapper(arr[i]);
//        }
//        return res;
//    }
//
//    static Long[] toWrapper(long[] arr) {
//        Long[] res = new Long[arr.length];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = arr[i];
//        }
//        return res;
//    }
//
//    static Long[][] toWrapper(long[][] arr) {
//        Long[][] res = new Long[arr.length][];
//        for (int i = 0; i < arr.length; i++) {
//            res[i] = toWrapper(arr[i]);
//        }
//        return res;
//    }
}