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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T1, typename T2>
inline ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << "(" << p.first << "," << p.second << ")";
}
template <typename T>
inline ostream& operator<<(ostream& os, const vector<T>& v) {
  bool first = true;
  os << "{";
  for (unsigned int i = 0; i < v.size(); i++) {
    if (!first) os << ",";
    os << v[i];
    first = false;
  }
  return os << "}";
}
template <typename T>
inline ostream& operator<<(ostream& os, const set<T>& v) {
  bool first = true;
  os << "{";
  for (typename set<T>::const_iterator ii = v.begin(); ii != v.end(); ++ii) {
    if (!first) os << ",";
    os << *ii;
    first = false;
  }
  return os << "}";
}
template <typename T>
inline ostream& operator<<(ostream& os, const multiset<T>& v) {
  bool first = true;
  os << "{";
  for (typename multiset<T>::const_iterator ii = v.begin(); ii != v.end();
       ++ii) {
    if (!first) os << ",";
    os << *ii;
    first = false;
  }
  return os << "}";
}
template <typename T1, typename T2>
inline ostream& operator<<(ostream& os, const map<T1, T2>& v) {
  bool first = true;
  os << "{";
  for (typename map<T1, T2>::const_iterator ii = v.begin(); ii != v.end();
       ++ii) {
    if (!first) os << ",";
    os << *ii;
    first = false;
  }
  return os << "}";
}
template <typename T>
bool isPrime(T n) {
  T i, lmt = sqrt(n);
  for (i = 2; i <= lmt; i++)
    if (n % i == 0) return false;
  return true;
}
template <typename T>
T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <typename T>
T BigMod(T b, T p, T m) {
  if (p == 0)
    return 1 % m;
  else if (p & 1)
    return ((b % m) * (BigMod(b, p - 1, m) % m)) % m;
  else {
    T s = BigMod(b, p / 2, m);
    return ((s % m) * (s % m)) % m;
  }
}
template <typename T>
T power(T b, T p) {
  if (p == 0)
    return 1;
  else if (p & 1)
    return b * power(b, p - 1);
  else {
    T ret = power(b, p / 2);
    return ret * ret;
  }
}
template <typename T>
T ModInv(T b, T m) {
  if (isPrime(b))
    return BigMod(b, m - 2, m) % m;
  else if (gcd(b, m) == 1)
    return BigMod(b, m - 1, m) % m;
}
template <typename T>
T egcd(T a, T b, T& x, T& y) {
  T d;
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  } else {
    T x1, y1;
    d = egcd(b % a, a, x1, y1);
    x = y1 - (b / a) * x1;
    y = x1;
  }
  return d;
}
int toint(string s) {
  int i, j, l;
  int num;
  l = s.size();
  for (i = l - 1, j = 0, num = 0; i >= 0; i--, j++) {
    num += (s[i] - 48) * power(10, j);
  }
  return num;
}
const double pi = acos(-1);
const int inf = (1 << 30);
const long long INF = (1LL << 62) - 1;
const int mod = (int)1e9 + 7;
const long long MOD = (long long)1e9 + 7;
const double EPS = 1e-9;
const int dx8[] = {-1, 0, +1, -1, +1, -1, 0, +1};
const int dy8[] = {+1, +1, +1, 0, 0, -1, -1, -1};
const int dx4[] = {0, -1, +1, 0};
const int dy4[] = {+1, 0, 0, -1};
const int dx2[] = {+1, 0};
const int dy2[] = {0, +1};
const int dxkn[] = {1, -1, 1, -1, 2, -2, -2, 2};
const int dykn[] = {2, 2, -2, -2, 1, 1, -1, -1};
string str1 = "", str2 = "", first = "";
string solve(char p, char q, int val_p, int val_q) {
  string str = "";
  int i;
  if (val_p == val_q) {
    for (i = 0; i < val_p; i++) {
      str += p;
      str += q;
    }
  } else if (val_p == val_q + 1) {
    for (i = 0; i < val_q; i++) {
      str += p;
      str += q;
    }
    str += p;
  } else if (val_p + 1 == val_q) {
    for (i = 0; i < val_p; i++) {
      str += p;
      str += q;
    }
    string tmp = str;
    str = q;
    str += tmp;
  } else
    str = "";
  return str;
}
int main() {
  int a, b, c, d, i;
  cin >> a >> b >> c >> d;
  if (a + b + c + d == 1) {
    cout << "YES"
         << "\n";
    if (a)
      cout << "0"
           << "\n";
    if (b)
      cout << "1"
           << "\n";
    if (c)
      cout << "2"
           << "\n";
    if (d)
      cout << "3"
           << "\n";
    return 0;
  }
  if (!a && !b && c && d) str1 = solve('2', '3', c, d);
  if (!a && b && c && !d) str1 = solve('1', '2', b, c);
  if (a && b && !c && !d) str1 = solve('0', '1', a, b);
  if (str1 != "") {
    cout << "YES"
         << "\n";
    for (i = 0; i < str1.size(); i++) {
      cout << str1[i] << " ";
    }
    cout << "\n";
    return 0;
  }
  if (a > b || d > c) {
    cout << "NO"
         << "\n";
  } else {
    for (i = 0; i < a; i++) {
      str1 += "01";
    }
    b -= a;
    for (i = 0; i < d; i++) {
      str2 += "23";
    }
    c -= d;
    if (b == c) {
      for (i = 0; i < b; i++) {
        str1 += "21";
      }
    } else if (b + 1 == c) {
      for (i = 0; i < b; i++) {
        str1 += "21";
      }
      str2 += "2";
    } else if (c + 1 == b) {
      for (i = 0; i < c; i++) {
        str1 += "21";
      }
      first += "1";
    } else {
      cout << "NO"
           << "\n";
      return 0;
    }
    cout << "YES"
         << "\n";
    if (first != "") cout << first << " ";
    str1 += str2;
    for (i = 0; i < str1.size(); i++) {
      cout << str1[i] << " ";
    }
    cout << "\n";
  }
  return 0;
}