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)

use proconio::*;

#[fastout]
fn run() {
    input! {
        n: usize,
        mut cnt: [usize; 3],
        s: [String; n],
    }
    let s: Vec<usize> = s
        .into_iter()
        .map(|s| {
            if s == "AB" {
                0
            } else if s == "BC" {
                1
            } else {
                2
            }
        })
        .collect();
    let w = 2usize;
    let encode = |c: &[usize]| -> usize {
        c.iter().fold(0, |c, a| c * (w + 1) + std::cmp::min(w, *a))
    };
    let decode = |mut c: usize| -> [usize; 3] {
        let mut id = [0; 3];
        for id in id.iter_mut().rev() {
            *id = c % (w + 1);
            c /= w + 1;
        }
        id
    };
    let mut dp = vec![vec![false; (w + 1).pow(3)]; n + 1];
    let mut prev = vec![vec![((w + 1).pow(3), 3); (w + 1).pow(3)]; n + 1];
    for c in cnt.iter_mut() {
        *c = std::cmp::min(*c, w);
    }
    dp[0][encode(&cnt)] = true;
    for i in 0..n {
        let x = s[i];
        let y = (x + 1) % 3;
        for j in 0..(w + 1).pow(3) {
            if !dp[i][j] {
                continue;
            }
            let mut c = decode(j);
            for &(x, y) in [(x, y), (y, x)].iter() {
                if c[x] > 0 {
                    c[x] -= 1;
                    c[y] += 1;
                    let id = encode(&c);
                    dp[i + 1][id] = true;
                    prev[i + 1][id] = (j, y);
                    c[x] += 1;
                    c[y] -= 1;
                }
            }
        }
    }
    if dp[n].iter().all(|p| !*p) {
        println!("No");
        return;
    }
    let mut ans = vec![];
    let mut pos = 0;
    for i in 0.. {
        if dp[n][i] {
            pos = i;
            break;
        }
    }
    for k in (1..=n).rev() {
        ans.push(prev[k][pos].1);
        pos = prev[k][pos].0;
    }
    ans.reverse();
    let c: Vec<_> = "ABC".chars().collect();
    println!("Yes");
    for a in ans {
        println!("{}", c[a]);
    }
}

fn main() {
    run();
}