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 Scala (2.13.1) (judge verdict: Accepted)

import java.util.Scanner

object Main extends App {
  val ABC = Array("A", "B", "C")
  def printABC(n: Int): Unit = {
    println(ABC(n))
  }

  val sc = new Scanner(System.in)
  val n = sc.nextInt()
  val (a, b, c) = (sc.nextInt(), sc.nextInt(), sc.nextInt())
  val ss = (1 to n).map { _ =>
    val s = sc.next()
    S.find(s)
  }

  var state = State(Array(a, b, c), Nil)
  ss.zipWithIndex.foreach { case (s, idx) =>
    val Array(i, j) = s.target
    if(state(i) + state(j) <= 0) {
      println("No")
      sys.exit(0)
    }
    state = if(state(i) == 0) state.add(i, j)
    else if(state(j) == 0) state.add(j, i)
    else {
      ss.lift(idx + 1).fold { state.add(i, j) } { nextS =>
        if(nextS.target.contains(i)) state.add(i, j) else state.add(j, i)
      }
    }
  }
  println("Yes")
  state.result.reverse.foreach(printABC)

}

case class State(ary: Array[Int], result: List[Int]) {
  def add(incr: Int, decr: Int): State = {
    val nextAry = ary.clone()
    nextAry(incr) += 1
    nextAry(decr) -= 1
    State(nextAry, incr :: result)
  }

  def apply(n: Int): Int = ary(n)
}

sealed abstract class S {
  lazy val name: String = getClass.getSimpleName.init

  def target: Array[Int]

  def dup(s: S): Int = (target.toSet & s.target.toSet).head
}

object S {
  case object AB extends S {
    override val target: Array[Int] = Array(0, 1)
  }

  case object AC extends S {
    override val target: Array[Int] = Array(0, 2)
  }

  case object BC extends S {
    override val target: Array[Int] = Array(1, 2)
  }

  val values: Seq[S] = AB :: AC :: BC :: Nil
  def find(name: String): S = values.find(_.name == name).get
}