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 math


def main():
    N, A, B, C = map(int, input().split())
    s = [input() for _ in range(N)] + ['']

    # dp_abc = [None for _ in range(N+1)]
    # dp_history = [[] for _ in range(N+1)]
    #
    # dp_abc[0] = (A, B, C)

    history = []

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

    for i in range(N):
        x, y = s[i][0], s[i][1]
        if cnt[x] > cnt[y]:
            cnt[x] -= 1
            cnt[y] += 1
            history.append(y)
        elif cnt[x] < cnt[y]:
            cnt[x] += 1
            cnt[y] -= 1
            history.append(x)
        else:
            if x in s[i + 1]:
                cnt[x] += 1
                cnt[y] -= 1
                history.append(x)
            else:
                cnt[x] -= 1
                cnt[y] += 1
                history.append(y)

        if cnt[x] < 0 or cnt[y] < 0:
            print('No')
            return

    print('Yes')
    for c in history:
        print(c)


if __name__ == '__main__':
    main()