Problem: 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.

Examples

Input

2 1 3 0
AB
AC


Output

Yes
A
C


Input

3 1 0 0
AB
BC
AB


Output

No


Input

1 0 9 0
AC


Output

No


Input

8 6 9 1
AC
BC
AB
BC
AC
BC
AB
AB


Output

Yes
C
B
B
C
C
B
A
A

Solution (in PYTHON3):

Solution:
import sys
readline = sys.stdin.readline


def solve(writer):
    N, A, B, C = map(int, input().split())

    variables = {
        'A': A,
        'B': B,
        'C': C
    }

    queries = (list(readline().strip()) for _ in range(N))

    next_q = next(queries)

    for i in range(N):

        let_1, let_2 = next_q
        next_q = next(queries) if i != N - 1 else ()

        if variables[let_1] == variables[let_2] == 0:
            return False

        if variables[let_1] == variables[let_2] == 1 and let_2 in next_q \
                or variables[let_1] > variables[let_2]:
            let_1, let_2 = let_2, let_1

        variables[let_1] += 1
        variables[let_2] -= 1

        writer.append(let_1)

    return True


def main():
    writer = ['Yes']
    ok = solve(writer)
    if ok:
        for w in writer:
            print(w)
    else:
        print('No')


if __name__ == "__main__":
    main()