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 C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<algorithm>
#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<map>
#include<cstdio>
#include<iomanip>
#include<cmath>
using namespace std;

string ans;
bool dfs(int A, int B, int C, int index, vector<string> &S, string s) {
    if (A < 0 || B < 0 || C < 0) {
        return false;
    }
    
    if (index == S.size()) {
        ans = s;
        return true;
    }
    
    bool result = false;
    if (S[index] == "AB") {
        result = dfs(A-1, B+1, C, index + 1, S, s + "B") || dfs(A+1, B-1, C, index + 1, S, s + "A");
    } else if (S[index] == "AC") {
        result = dfs(A-1, B, C+1, index + 1, S, s + "C") || dfs(A+1, B, C-1, index + 1, S, s + "A");
    } else if (S[index] == "BC") {
        result = dfs(A, B-1, C+1, index + 1, S, s + "C") || dfs(A, B+1, C-1, index + 1, S, s + "B");
    }
    return result;
}

int main() {
    int N, A, B, C;
    cin >> N >> A >> B >> C;
    vector<string> S(N);
    for (int i = 0; i < N; i++) {
        cin >> S[i];
    }
    
    bool result = dfs(A, B, C, 0, S, "");
    if (result == false) {
        cout << "No";
    } else {
        cout << "Yes" << endl;
        for (int i = 0; i < ans.size(); i++) {
            cout << ans[i] << endl;
        }
    }

    return 0;
}