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 mut visitor = DfsVisitor::new(&s, a, b, c);
    let result = visitor.visit();
    if result.len() < n {
        println!("No");
    } else {
        println!("Yes");
        for chosen in result {
            println!("{}", chosen);
        }
    }
}

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, selectable: &String, choose: i64) -> Self {
        match &selectable[..] {
            "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) -> Self {
        Self::new(self.a + choose, self.b - choose, self.c)
    }

    fn choice_ac(&mut self, choose: i64) -> Self {
        Self::new(self.a + choose, self.b, self.c - choose)
    }

    fn choice_bc(&mut self, choose: i64) -> Self {
        Self::new(self.a, self.b + choose, self.c - choose)
    }
}

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

    fn visit(&mut self) -> &Vec<char> {
        if self.depth < self.s.len() {
            let selectable = &self.s[self.depth];
            let (choice01, choice10) = (
                self.variable.choice(selectable, 1),
                self.variable.choice(selectable, -1),
            );
            if choice01.alive() {
                self.selected.push(selectable.chars().nth(0).unwrap());
                self.depth += 1;
                self.visit()
            } else if choice10.alive() {
                self.selected.push(selectable.chars().nth(1).unwrap());
                self.depth += 1;
                self.visit()
            } else {
                &self.selected
            }
        } else {
            &self.selected
        }
    }
}