Problem:
Score : 600 points

Problem Statement

There is a game that involves three variables, denoted A, B, and C.

As the game progresses, there will be N events where you are asked to make a choice.
Each of these choices is represented by a string s_i. If s_i is AB, you must add 1 to A or B then subtract 1 from the other; if s_i is AC, you must add 1 to A or C then subtract 1 from the other; if s_i is BC, you must add 1 to B or C then subtract 1 from the other.

After each choice, none of A, B, and C should be negative.

Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices.

Constraints

1 \leq N \leq 10^5

0 \leq A,B,C \leq 10^9

N, A, B, C are integers.

s_i is AB, AC, or BC.

Input

Input is given from Standard Input in the following format:

N A B C
s_1
s_2
:
s_N

Output

If it is possible to make N choices under the condition, print Yes; otherwise, print No.

Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (A, B, or C) to which you add 1 in the i-th choice.

Sample Input 1

2 1 3 0
AB
AC

Sample Output 1

Yes
A
C

You can successfully make two choices, as follows:

In the first choice, add 1 to A and subtract 1 from B. A becomes 2, and B becomes 2.

In the second choice, add 1 to C and subtract 1 from A. C becomes 1, and A becomes 1.

Sample Input 2

3 1 0 0
AB
BC
AB

Sample Output 2

No

Sample Input 3

1 0 9 0
AC

Sample Output 3

No

Sample Input 4

8 6 9 1
AC
BC
AB
BC
AC
BC
AB
AB

Sample Output 4

Yes
C
B
B
C
C
B
A
A

Solution in Ruby (2.7.1) (judge verdict: Accepted)

# https://scrapbox.io/rustacean/ABC166-F_Three_Variables_Game

def dfs(i, a, b, c)
  
  return if a < 0 || b < 0 || c < 0
  
  if i == N
    puts "Yes"
    puts $ans
    exit
  end
  
  if S[i] == "AB"
    $ans[i] = 'A'
    dfs(i+1, a+1, b-1, c  )
    $ans[i] = 'B'
    dfs(i+1, a-1, b+1, c  )
  elsif S[i] == "AC"
    $ans[i] = 'A'
    dfs(i+1, a+1, b  , c-1)
    $ans[i] = 'C'
    dfs(i+1, a-1, b  , c+1)
  else
    $ans[i] = 'B'
    dfs(i+1, a  , b+1, c-1)
    $ans[i] = 'C'
    dfs(i+1, a  , b-1, c+1)
  end
end

N, a, b, c = gets.to_s.split.map{|e|e.to_i}
S = Array.new(N){ gets.to_s.chomp }

$ans = Array.new(N)
dfs(0, a, b, c)

puts "No"

# def solve1(a,b,c)
  
#   N.times do |i|
    
#     s = gets.to_s.chomp
    
#     if s == "AB"
#       a > b ? ( a-=1; b+=1) : (a+=1; b-=1)
#     elsif s == "AC"
#       a > c ? ( a-=1; c+=1) : (a+=1; c-=1)
#     else
#       b > c ? ( b-=1; c+=1) : (b+=1; c-=1)
#     end
    
#     return "No" if a < 0 || b < 0 || c < 0
#   end
  
#   "Yes"
# end

# def solve2(a, b, c)
  
#   N.times do |i|
#   s = gets.to_s.chomp
#     if (s == "AB" && (a == 0 && b == 0)) || (s == "AC" && (a == 0 && c == 0)) || (s == "BC" && (b == 0 && c == 0))
#       return "No"
#     else
#       return "Yes"
#     end
#   end
# end

# N, a, b, c = gets.to_s.split.map{|e|e.to_i}
# if 0 == a + b + c
#   puts "No"
# elsif 1 == a + b + c
#   puts solve1(a, b, c)
# else # 1 < a + b + c
#   puts solve2(a, b, c)
# end