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 OCaml (4.10.0) (judge verdict: Accepted)

let rec solve a b c acc ss =
  if a < 0 || b < 0 || c < 0 then raise Not_found;
  match ss with
  | [] -> acc
  | "AB" :: rest ->
      begin try solve (a + 1) (b - 1) c ('A' :: acc) rest with
      | Not_found -> solve (a - 1) (b + 1) c ('B' :: acc) rest
      end
  | "AC" :: rest ->
      begin try solve (a + 1) b (c - 1) ('A' :: acc) rest with
      | Not_found -> solve (a - 1) b (c + 1) ('C' :: acc) rest
      end
  | "BC" :: rest ->
      begin try solve a (b + 1) (c - 1) ('B' :: acc) rest with
      | Not_found -> solve a (b - 1) (c + 1) ('C' :: acc) rest
      end

let () = Scanf.scanf "%d %d %d %d\n" @@ fun n a b c ->
  let ss = List.init n @@ fun _ -> Scanf.scanf "%s\n" Fun.id in
  try
    let ans = solve a b c [] ss in
    print_endline "Yes";
    List.iter (Printf.printf "%c\n") (List.rev ans)
  with Not_found -> print_endline "No"