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)

N, A, B, C = gets.split.map(&:to_i)
Commands = N.times.map{gets.chomp}

def bfs(state, hist)
  a, b, c = state
  if (a < 0) or (b < 0) or (c < 0)
    return
  end

  level = hist.size
  if level == N
    puts 'Yes'
    hist.each{|s| puts(s)}
    exit(0)
  end

  command = Commands[level]
  case command
  when 'AB'
    hist.push 'A'
    bfs([a+1, b-1, c], hist)
    hist.pop
    hist.push 'B'
    bfs([a-1, b+1, c], hist)
    hist.pop
  when 'BC'
    hist.push 'B'
    bfs([a, b+1, c-1], hist)
    hist.pop
    hist.push 'C'
    bfs([a, b-1, c+1], hist)
    hist.pop
  when 'AC'
    hist.push 'A'
    bfs([a+1, b, c-1], hist)
    hist.pop
    hist.push 'C'
    bfs([a-1, b, c+1], hist)
    hist.pop
  end
end

bfs([A, B, C], [])
puts 'No'