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: Wrong Answer)

use proconio::input;

fn main() {
    input! {
        n: usize,
        a: i64,
        b: i64,
        c: i64,
        s: [String; n],
    }
    let result = dfs(&s, 0, Vec::new(), Variable::new(a, b, c));
    if result.len() < n {
        println!("No");
    } else {
        println!("Yes");
        for chosen in result {
            println!("{}", chosen);
        }
    }
}

#[derive(Clone)]
struct Variable {
    a: i64,
    b: i64,
    c: i64,
}
impl Variable {
    fn new(a: i64, b: i64, c: i64) -> Self {
        Self { a, b, c }
    }

    fn valid(choose: i64) -> i64 {
        if choose < 0 {
            -1
        } else {
            1
        }
    }

    fn alive(&self) -> bool {
        !(self.a < 0 || self.b < 0 || self.c < 0)
    }

    fn choice(&mut self, abc: &String, choose: i64) -> bool {
        match &abc[..] {
            "AB" => self.choice_ab(Variable::valid(choose)),
            "AC" => self.choice_ac(Variable::valid(choose)),
            "BC" => self.choice_bc(Variable::valid(choose)),
            _ => panic!(),
        }
    }

    fn choice_ab(&mut self, choose: i64) -> bool {
        self.a += choose;
        self.b -= choose;
        self.alive()
    }

    fn choice_ac(&mut self, choose: i64) -> bool {
        self.a += choose;
        self.c -= choose;
        self.alive()
    }

    fn choice_bc(&mut self, choose: i64) -> bool {
        self.b += choose;
        self.c -= choose;
        self.alive()
    }
}

// struct DfsVisitor {
//     s: Vec<String>,
//     depth: usize,
//     selected: Vec<String>,
//     variable: Variable,
// }
// impl DfsVisitor {
//     fn new(s: Vec<String>, a: i64, b: i64, c: i64) -> Self {
//         Self {
//             s,
//             depth: 0,
//             selected: Vec::new(),
//             variable: Variable::new(a, b, c),
//         }
//     }
// }

fn dfs(s: &Vec<String>, depth: usize, mut selected: Vec<char>, mut abc: Variable) -> Vec<char> {
    if depth < s.len() {
        if abc.choice(&s[depth], 1) {
            selected.push(s[depth].chars().nth(0).unwrap());
            dfs(s, depth + 1, selected, abc)
        } else {
            abc.choice(&s[depth], -1);
            if abc.choice(&s[depth], -1) {
                selected.push(s[depth].chars().nth(1).unwrap());
                dfs(s, depth + 1, selected, abc)
            } else {
                selected
            }
        }
    } else {
        selected
    }
}