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 Rust (1.42.0) (judge verdict: Accepted)

//! Framework <https://github.com/vain0x/procon>

#![allow(non_snake_case)]
#![allow(unused_imports)]

use std::collections::*;

pub struct Scan(Box<dyn Iterator<Item = &'static str>>); // '

impl Scan {
    fn new() -> Self {
        let mut buf = String::new();
        let read_line = move || {
            std::io::stdin().read_line(&mut buf).unwrap();
            Box::leak(buf.split_off(0).into_boxed_str()).split_whitespace()
        };
        Scan(Box::new(std::iter::repeat_with(read_line).flatten()))
    }

    pub fn word<T: std::str::FromStr>(&mut self) -> T {
        self.0.next().unwrap().parse().ok().unwrap()
    }

    pub fn list<T: std::str::FromStr>(&mut self, len: usize) -> Vec<T> {
        std::iter::repeat_with(|| self.word()).take(len).collect()
    }
}

#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
enum Var {
    A,
    B,
    C,
}

impl Var {
    fn as_str(self) -> &'static str {
        match self {
            Var::A => "A",
            Var::B => "B",
            Var::C => "C",
        }
    }
}

#[derive(Clone, Copy)]
enum Command {
    AB,
    AC,
    BC,
}

impl Command {
    fn parse(s: &str) -> Command {
        match s {
            "AB" => Command::AB,
            "AC" => Command::AC,
            "BC" => Command::BC,
            _ => panic!(),
        }
    }

    fn vars(self) -> (Var, Var, Var) {
        match self {
            Command::AB => (Var::A, Var::B, Var::C),
            Command::AC => (Var::A, Var::C, Var::B),
            Command::BC => (Var::B, Var::C, Var::A),
        }
    }
}

#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)]
struct State {
    A: usize,
    B: usize,
    C: usize,
}

impl State {
    fn get(self, v: Var) -> usize {
        match v {
            Var::A => self.A,
            Var::B => self.B,
            Var::C => self.C,
        }
    }

    fn get_mut(&mut self, v: Var) -> &mut usize {
        match v {
            Var::A => &mut self.A,
            Var::B => &mut self.B,
            Var::C => &mut self.C,
        }
    }
}

fn solve(mut state: State, commands: &[Command]) -> Option<Vec<Var>> {
    let N = commands.len();

    state.A = state.A.min(2);
    state.B = state.B.min(2);
    state.C = state.C.min(2);
    #[cfg(debug_assertions)]
    eprintln!("\x1B[33m{}\x1B[0m = {:?}", "state", state);

    // dp[i][s] = back
    // commands[..i] を処理した後、
    // 各変数の値が s の状態に遷移できるとき dp[i][s] が存在し、
    // i = 0 なら back = None
    // i > 0 なら直前のコマンドで増加させた変数を up、遷移元の状態を s' として、
    // back = Some((up, s'))

    let mut dp = vec![HashMap::new(); N + 1];
    dp[0].insert(state, None);

    for i in 0..N {
        let command = commands[i];
        let (u, v, w) = command.vars();

        for un in 0..7 {
            for vn in 0..7 {
                if un == 0 && vn == 0 {
                    continue;
                }

                let mut state = State::default();
                *state.get_mut(u) = un;
                *state.get_mut(v) = vn;

                for wn in 0..7 {
                    *state.get_mut(w) = wn;

                    if !dp[i].contains_key(&state) {
                        continue;
                    }

                    for &(up, down) in &[(u, v), (v, u)] {
                        if state.get(down) == 0 {
                            continue;
                        }

                        let mut next = state;
                        *next.get_mut(up) += 1;
                        *next.get_mut(down) -= 1;

                        dp[i + 1].insert(next, Some((up, state)));
                    }
                }
            }
        }
    }

    let mut vars = vec![Var::A; N];
    let mut i = N;
    let mut back = *dp[N].values().next()?;

    while i >= 1 {
        i -= 1;

        let (up, prev) = back.unwrap();
        vars[i] = up;
        state = prev;
        back = dp[i].get(&state).cloned().unwrap();
    }

    Some(vars)
}

fn main() {
    let mut scan = Scan::new();

    let N = scan.word::<usize>();
    let A = scan.word::<usize>();
    let B = scan.word::<usize>();
    let C = scan.word::<usize>();
    let s = scan.list::<String>(N);

    let state = State { A, B, C };
    let commands = s
        .into_iter()
        .map(|s| Command::parse(&s))
        .collect::<Vec<_>>();

    match solve(state, &commands) {
        Some(vars) => {
            println!("Yes");
            for i in 0..N {
                println!("{}", vars[i].as_str());
            }
        }
        None => {
            println!("No");
        }
    }
}