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 PYTHON3):

Solution:
from sys import stdin
from collections import deque
mod = 10**9 + 7
# def rl():
#     return [int(w) for w in stdin.readline().split()]
from bisect import bisect_right
from bisect import bisect_left
from collections import defaultdict
from math import sqrt,factorial,gcd,log2,inf,ceil
# map(int,input().split())
# # l = list(map(int,input().split()))
# from itertools import permutations

# a = int(input())
# b = int(input())
# c = int(input())
# d = int(input())
# e = int(input())
# f = int(input())
# ans = 0
#
# for i in range(d+1):
#     c = e*(min(i,a)) + f*(min(d-i,c,b))
#     ans = max(c,ans)
#     print(c,i,a)
#
# print(ans)
# ans1 = 0
# ans2 = 0
# def bfs(n):
#     global ans1
#     boo1[n] = True
#     queue = [n]
#
#     while queue:
#
#         z = queue.pop(0)
#         if len(hash[z]) == 0:
#             ans1+=1
#         for i in hash[z]:
#
#             if not boo1[i]:
#                 queue.append(i)
#                 boo1[i] = True
#
# def bfs1(n):
#     global ans2
#     boo2[n] = True
#     queue = [n]
#
#     while queue:
#
#         z = queue.pop(0)
#         if len(hash1[z]) == 0:
#             ans2+=1
#         for i in hash1[z]:
#
#             if not boo2[i]:
#                 queue.append(i)
#                 boo2[i] = True
#
#
#
#
#
#
#
#
#
# hash = defaultdict(list)
# hash1 = defaultdict(list)
# n,m = map(int,input().split())
#
# for i in range(m):
#     a,b = map(int,input().split())
#     hash[a].append(b)
#     hash1[b].append(a)
#
#
#
# boo1 = defaultdict(bool)
# boo2 = defaultdict(bool)
#
# for i in range(1,n+1):
#     if boo1[i] == False:
#         bfs(i)
#     if boo2[i] == False:
#         bfs1(i)
#
#
# print(max(ans1,ans2))
#
#
#
#

a,b,c,d = map(int,input().split())
n = a+b+c+d
g = [a,b,c,d]
g.sort()
if g[0] == 0 and g[1] == 0 and g[2] == 0 and g[3]!=1:
    print('NO')
    exit()
if n == 1:
    print('YES')
    print(*[0*a+1*b+2*c+3*d])
    exit()
ans = []
if a == 0 and b == 0 and abs(c-d) == 1:
    if c>=d:
        for i in range(n):
            if i%2 == 0:
                ans.append(2)
            else:
                ans.append(3)
    else:
        for i in range(n):
            if i%2 == 0:
                ans.append(3)
            else:
                ans.append(2)
    print('YES')
    print(*ans)
    exit()

if c == 0 and d == 0 and abs(a-b) == 1:
    if a>=b:
        for i in range(n):
            if i%2 == 0:
                ans.append(0)
            else:
                ans.append(1)
    else:
        for i in range(n):
            if i%2 == 0:
                ans.append(1)
            else:
                ans.append(0)
    print('YES')
    print(*ans)
    exit()




if a>=0:

    if a == b:
        ans = []
        for i in range(2*a):
            if i%2 == 0:
                ans.append(0)
            else:
                ans.append(1)
        b-=a
        cnt = 0

        while True:
            if c == 0 or d == 0:
                break
            if cnt%2 == 0:
                ans.append(2)
                c-=1
            else:
                ans.append(3)
                d-=1

            cnt+=1

        if ans[-1] == 3 :
            if c == 1:
             c-=1
             ans.append(2)
        if ans[-1] == 2 :
            if d == 1:
             ans.append(3)
             d-=1

        if ans[-1] == 1 and c!=0:
            c-=1
            ans.append(2)

        if c == 0 and d == 0:
            print('YES')
            print(*ans)

        else:
            print('NO')


    elif b>a:

        ans = [1]
        b-=1
        for i in range(2*a):
            if i%2 == 0:
                ans.append(0)
            else:
                ans.append(1)


        b-=a
        cnt = 0

        while True:
            if b == 0 or c == 0:
                break
            if cnt%2 == 0:
                    ans.append(2)
                    c-=1
            if cnt%2!=0:
                    ans.append(1)
                    b-=1
            cnt+=1

        if ans[-1] == 1 and c == 0 and b == 0:
            if d!=0 :
                print('NO')
                exit()
            print('YES')
            print(*ans)

        elif ans[-1] == 1 and b == 0:
            cnt = 0

            while True:
             if c == 0 or d == 0:
                break
             if cnt%2 == 0:
                ans.append(2)
                c-=1
             else:
                ans.append(3)
                d-=1
             cnt+=1

            if c == 0 and d == 0 :
                 print('YES')
                 print(*ans)
            elif c == 1 and d == 0 :
                 print('YES')
                 print(*([2] + ans))
            elif  c == 2 and d == 0 :
                print('YES')
                print(*([2] + ans + [2]))


            elif c == 0 and d == 1 :
                print('YES')
                print(*(ans + [3]))
            else:
                print('NO')

        elif ans[-1] == 2 and b == 1 and d!=0:
            print('NO')

        elif ans[-1] == 2 and b == 1 and d == 0:
            print('YES')
            print(*(ans + [1]))

        elif ans[-1] == 2 and b == 0:
            cnt = 0

            while True:
                if c == 0 or d == 0:
                    break
                if cnt%2 != 0:
                    ans.append(2)
                    c-=1
                else:
                    ans.append(3)
                    d-=1
                cnt+=1

            if c == 0 and d == 0:
                    print('YES')
                    print(*ans)
            elif c == 1 and d == 0:
                    print('YES')
                    print(*([2] + ans))

            elif c == 0 and d == 1:
                print('YES')
                print(*(ans + [3]))
            elif  c == 2 and d == 0:
                print('YES')
                print(*([2] + ans + [2]))
            else:
                print('NO')
        else:
            print('NO')
    else:

        if b == 1 and a == 2 and c == 0 and d == 0:
            print('YES')
            print(*[0,1,0])
        else:
            print('NO')