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 <iostream>
#include <cstdio>
#include <queue>
#include <cstring>

using namespace std;
const int MAX = 1e5 + 111;
int n, a, b, c;
struct node {
    int a, b, c, k;
    string ans;
};
string e[MAX];

string bfs(int k, int a, int b, int c){
    queue<node> q;
    q.push({a, b, c, k, ""});

    while (!q.empty()){
        node t = q.front(); q.pop();
        if (t.k > n) {
            return t.ans;
        }
        if (e[t.k]=="AB"){
            if (t.a-1>=0){
                q.push({t.a-1, t.b+1, t.c, t.k+1, t.ans+'B'});
            }
            if (t.b-1>=0){
                q.push({t.a+1, t.b-1, t.c, t.k+1, t.ans+'A'});
            }
        }
        else if (e[t.k]=="AC"){
            if (t.a-1>=0){
                q.push({t.a-1, t.b, t.c+1, t.k+1, t.ans+'C'});
            }
            if (t.c-1>=0){
                q.push({t.a+1, t.b, t.c-1, t.k+1, t.ans+'A'});
            }
        }
        else if (e[t.k]=="BC"){
            if (t.b-1>=0){
                q.push({t.a, t.b-1, t.c+1, t.k+1, t.ans+'C'});
            }
            if (t.c-1>=0){
                q.push({t.a, t.b+1, t.c-1, t.k+1, t.ans+'B'});
            }
        }
    }

    return "No";
}

int main(){
    scanf("%d%d%d%d", &n, &a, &b, &c);
    for (int i = 1; i <= n; i++) cin >> e[i];
    a = min(a, 2), b = min(b, 2), c = min(c, 2);
    string ans = bfs(1, a, b, c);
    if (ans == "No") cout << ans << endl;
    else {
        cout << "Yes\n";
        for (int i = 0; i<ans.size(); i++) cout << ans[i] << endl;
    }
}