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.io.*;

public class Practice {
  BufferedReader br;
  PrintWriter out;
  StringTokenizer st;
  boolean eof;
  private static final long MOD = 1000L * 1000L * 1000L + 7;
  private static final int[] dx = {0, -1, 0, 1};
  private static final int[] dy = {1, 0, -1, 0};
  private static final String yes = "Yes";
  private static final String no = "No";

  void solve() {
    int T = 1;
//    int T = nextInt();
    for (int i = 0; i < T; i++) {
      helper();
    }
  }

  void helper() {
    int zero = nextInt();
    int one = nextInt();
    int two = nextInt();
    int three = nextInt();
    int m1 = Math.min(zero, one);
    zero -= m1;
    one -= m1;
    if (zero > 1) {
      outln(no.toUpperCase());
      return;
    }
    if (zero != 0 && two + three > 0) {
      outln(no.toUpperCase());
      return;
    } else if (zero != 0 && two + three == 0) {
      List<Integer> res = find(zero + m1, one + m1, 0, 1);
      outln(yes.toUpperCase());
      for (int v : res) {
        out(v + " ");
      }
      outln("");
      return;
    }
    int m2 = Math.min(two, three);
    two -= m2;
    three -= m2;
    if (three > 1) {
      outln(no.toUpperCase());
      return;
    }
    if (three != 0 && zero + one + m1 > 0) {
      outln(no.toUpperCase());
      return;
    } else if (three != 0 && zero + one + m1 == 0) {
      List<Integer> res = find(two + m2, three + m2, 2, 3);
      outln(yes.toUpperCase());
      for (int v : res) {
        out(v + " ");
      }
      outln("");
      return;
    }
    int df = Math.abs(one - two);
    if (df > 1) {
      outln(no.toUpperCase());
      return;
    }

    List<Integer> first = find(m1, m1, 0, 1);
    List<Integer> second = find(one, two, 1, 2);
    List<Integer> third = find(m2, m2, 2, 3);
    List<List<Integer>> all = new ArrayList<>();
    all.add(first);
    all.add(second);
    all.add(third);
    for (int mask = 0; mask < (1 << 3); mask++) {
      List<Integer> cand = new ArrayList<>();
      for (int i = 0; i < 3; i++) {
        List<Integer> ls = new ArrayList<>(all.get(i));
        if ((mask & (1 << i)) != 0) {
          Collections.reverse(ls);
        }
        cand.addAll(ls);
      }
      boolean valid = true;
      for (int i = 0; i < cand.size() - 1; i++) {
        int d = Math.abs(cand.get(i + 1) - cand.get(i));
        if (d != 1) {
          valid = false;
        }
      }
      if (valid) {
        outln(yes.toUpperCase());
        for (int v : cand) {
          out(v + " ");
        }
        outln("");
        return;
      }
    }
    outln(no.toUpperCase());
  }

  List<Integer> find(int c1, int c2, int v1, int v2) {
    List<Integer> res = new ArrayList<>();
    if (c1 == c2) {
      for (int i = 0; i < c1; i++) {
        res.add(v1);
        res.add(v2);
      }
    } else if (c1 > c2) {
      res.add(v1);
      for (int i = 0; i < c2; i++) {
        res.add(v2);
        res.add(v1);
      }
    } else {
      res.add(v2);
      for (int i = 0; i < c1; i++) {
        res.add(v1);
        res.add(v2);
      }
    }
    return res;
  }

  void shuffle(long[] a) {
    int n = a.length;
    for(int i = 0; i < n; i++) {
      int r = i + (int) (Math.random() * (n - i));
      long tmp = a[i];
      a[i] = a[r];
      a[r] = tmp;
    }
  }
  long gcd(long a, long b) {
    while(a != 0 && b != 0) {
      long c = b;
      b = a % b;
      a = c;
    }
    return a + b;
  }
  private void outln(Object o) {
      out.println(o);
  }
  private void out(Object o) {
      out.print(o);
  }
  private void formatPrint(double val) {
      outln(String.format("%.9f%n", val));
  }
  public Practice() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);
    solve();
    out.close();
  }
  public static void main(String[] args) {
    new Practice();
  }

  public long[] nextLongArr(int n) {
    long[] res = new long[n];
    for(int i = 0; i < n; i++)
      res[i] = nextLong();
    return res;
  }
  public int[] nextIntArr(int n) {
    int[] res = new int[n];
    for(int i = 0; i < n; i++)
      res[i] = nextInt();
    return res;
  }
  public String nextToken() {
    while (st == null || !st.hasMoreTokens()) {
      try {
        st = new StringTokenizer(br.readLine());
      } catch (Exception e) {
        eof = true;
        return null;
      }
    }
    return st.nextToken();
  }
  public String nextString() {
    try {
      return br.readLine();
    } catch (IOException e) {
      eof = true;
      return null;
    }
  }
  public int nextInt() {
    return Integer.parseInt(nextToken());
  }
  public long nextLong() {
    return Long.parseLong(nextToken());
  }
  public double nextDouble() {
    return Double.parseDouble(nextToken());
  }
}