101665: [AtCoder]ABC166 F - Three Variables Game

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