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, a, b, c) : (usize, usize, usize, usize),
        s : [String; n]
    };
    let mut dp = vec![[[[(3, 0); 7]; 7]; 7]; n+1];
    dp[0][a.min(6)][b.min(6)][c.min(6)].0 = 0;
    for i in 0..n {
        for ia in 0..=6 {
            for ib in 0..=6 {
                for ic in 0..=6 {
                    if dp[i][ia][ib][ic].0 == 3 { continue; }
                    if s[i] == "AB" {
                        if ib > 0 { dp[i+1][6.min(ia+1)][ib-1][ic] = (0, (ia*7+ib)*7+ic); }
                        if ia > 0 { dp[i+1][ia-1][6.min(ib+1)][ic] = (1, (ia*7+ib)*7+ic); }
                    }
                    if s[i] == "AC" {
                        if ic > 0 { dp[i+1][6.min(ia+1)][ib][ic-1] = (0, (ia*7+ib)*7+ic); }
                        if ia > 0 { dp[i+1][ia-1][ib][6.min(ic+1)] = (2, (ia*7+ib)*7+ic); }
                    }
                    if s[i] == "BC" {
                        if ic > 0 { dp[i+1][ia][6.min(ib+1)][ic-1] = (1, (ia*7+ib)*7+ic); }
                        if ib > 0 { dp[i+1][ia][ib-1][6.min(ic+1)] = (2, (ia*7+ib)*7+ic); }
                    }
                }
            }
        }
    }
    for ia in 0..=6 {
        for ib in 0..=6 {
            for ic in 0..=6 {
                if dp[n][ia][ib][ic].0 != 3 {
                    let mut res = vec![0; n];
                    let mut sa = ia;
                    let mut sb = ib;
                    let mut sc = ic;
                    for i in (0..n).rev() {
                        res[i] = dp[i+1][sa][sb][sc].0;
                        let idx = dp[i+1][sa][sb][sc].1;
                        sa = idx/7/7;
                        sb = idx/7%7;
                        sc = idx%7;
                    }
                    println!("YES");
                    for t in res { println!("{}", ["A", "B", "C"][t]); }
                    return;
                }
            }
        }
    }
    println!("NO");
}