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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

import qualified Data.Map as M
import Data.List

data ABC = AB | BC | AC deriving Read

main = do
  li <- getLine
  let [n,a,b,c] = map read $ words li
  co <- getContents
  let ss = map read $ lines co
  let ans = compute n a b c ss
  putStrLn ans

compute :: Int -> Int -> Int -> Int -> [ABC] -> String
compute n a b c ss =
  case M.lookupMin $ foldl step (M.singleton (a,b,c) "") ss of
    Nothing -> "No"
    Just (_,ts) -> "Yes\n" ++ intersperse '\n' (reverse ts)

step m abc = M.fromList [ e1 | e0 <- M.assocs m, e1@((a,b,c),_) <- f abc e0, a >= 0, b >= 0, c >= 0]

-- Lensを使えばこのクローンはきれいにできそうだが。
f AB ((a,b,c),st) = [((succ a, pred b, c),'A':st) | a <= b] ++ [((pred a, succ b, c),'B':st) | a >= b]
f AC ((a,b,c),st) = [((succ a, b, pred c),'A':st) | a <= c] ++ [((pred a, b, succ c),'C':st) | a >= c]
f BC ((a,b,c),st) = [((a, succ b, pred c),'B':st) | b <= c] ++ [((a, pred b, succ c),'C':st) | b >= c]