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>
#pragma GCC optimize("O3")
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
const long long MAXN = 1000005;
const long long SQRTN = 1003;
const long long LOGN = 22;
const double PI = acos(-1);
const long long INF = 1e16;
const long long MOD = 1000000007;
const long long FMOD = 998244353;
const double eps = 1e-9;
mt19937 RNG(chrono::steady_clock::now().time_since_epoch().count());
template <typename T>
T gcd(T a, T b) {
  return (b ? __gcd(a, b) : a);
}
template <typename T>
T lcm(T a, T b) {
  return (a * (b / gcd(a, b)));
}
long long add(long long a, long long b, long long c = MOD) {
  long long res = a + b;
  return (res >= c ? res - c : res);
}
long long mod_neg(long long a, long long b, long long c = MOD) {
  long long res;
  if (abs(a - b) < c)
    res = a - b;
  else
    res = (a - b) % c;
  return (res < 0 ? res + c : res);
}
long long mul(long long a, long long b, long long c = MOD) {
  long long res = (long long)a * b;
  return (res >= c ? res % c : res);
}
long long mulmod(long long a, long long b, long long m = MOD) {
  long long q = (long long)(((long double)a * (long double)b) / (long double)m);
  long long r = a * b - q * m;
  if (r > m) r %= m;
  if (r < 0) r += m;
  return r;
}
template <typename T>
T expo(T e, T n) {
  T x = 1, p = e;
  while (n) {
    if (n & 1) x = x * p;
    p = p * p;
    n >>= 1;
  }
  return x;
}
template <typename T>
T power(T e, T n, T m = MOD) {
  T x = 1, p = e;
  while (n) {
    if (n & 1) x = mul(x, p, m);
    p = mul(p, p, m);
    n >>= 1;
  }
  return x;
}
template <typename T>
T extended_euclid(T a, T b, T& x, T& y) {
  T xx = 0, yy = 1;
  y = 0;
  x = 1;
  while (b) {
    T q = a / b, t = b;
    b = a % b;
    a = t;
    t = xx;
    xx = x - q * xx;
    x = t;
    t = yy;
    yy = y - q * yy;
    y = t;
  }
  return a;
}
template <typename T>
T mod_inverse(T a, T n = MOD) {
  T x, y, z = 0;
  T d = extended_euclid(a, n, x, y);
  return (d > 1 ? -1 : mod_neg(x, z, n));
}
void solvethetestcase();
signed main() {
  cout << fixed << setprecision(10);
  long long t = 1;
  for (long long testcase = 1; testcase < t + 1; testcase++) {
    solvethetestcase();
  }
}
long long a, b, c, d;
bool check(long long a, long long b, long long c, long long d) {
  if (d > c + 1) return false;
  if (d == c + 1) {
    if (a or b) return false;
  }
  if (c > b + d + 1) return false;
  if (c == b + d + 1) {
    if (a) return false;
  }
  swap(a, d);
  swap(b, c);
  if (d > c + 1) return false;
  if (d == c + 1) {
    if (a or b) return false;
  }
  if (c > b + d + 1) return false;
  if (c == b + d + 1) {
    if (a) return false;
  }
  return true;
}
bool gg(long long a, long long b, long long c, long long d, long long star) {
  vector<long long> v;
  long long left = a + b + c + d;
  for (long long i = 0; i < left; i++) {
    v.push_back(star);
    if (star == 0) {
      if (a == 0) return false;
      a--;
      star = 1;
    } else if (star == 3) {
      if (d == 0) return false;
      d--;
      star = 2;
    } else if (star == 1) {
      if (b == 0) return false;
      b--;
      if (a != 0) {
        star = 0;
      } else {
        star = 2;
      }
    } else {
      if (c == 0) return false;
      c--;
      if (d != 0) {
        star = 3;
      } else {
        star = 1;
      }
    }
  }
  printf("YES\n");
  for (auto x : v) {
    printf("%lld ", x);
  }
  printf("\n");
  return true;
}
void solvethetestcase() {
  scanf("%lld%lld", &a, &b);
  scanf("%lld%lld", &c, &d);
  if (!check(a, b, c, d)) {
    printf("NO\n");
    return;
  }
  for (long long i = 0; i < 4; i++) {
    if (gg(a, b, c, d, i)) {
      return;
    }
  }
  printf("NO\n");
}