101665: [AtCoder]ABC166 F - Three Variables Game

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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

Input

题意翻译

你开始有三个变量$A$,$B$,$C$,它们各自有一个值. 你需要依次进行$n$次操作,对于每次操作,有一个参数$s$,这个参数只可能是"AB","AC","BC"中的一个. 当s="AB"时,你可以选择以下方案中的一种: 1. $A=A+1,B=B-1$ 2. $A=A-1,B=B+1$ 当s="AC"时,你可以选择以下方案中的一种: 1. $A=A+1,C=C-1$ 2. $A=A-1,C=C+1$ 当s="BC"时,你可以选择以下方案中的一种: 1. $B=B+1,C=C-1$ 2. $B=B-1,C=C+1$ 若存在一种选择操作的方案使每次操作结束之后$A$,$B$,$C$均为自然数,输出"Yes",并依次输出每次操作中变大的变量名.否则输出"No".

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