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:
def f_three_variables_game():
    N, A, B, C = list(map(int, input().split()))
    Selections = [input() for i in range(N)]

    count = {'A': A, 'B': B, 'C': C}
    ans = []
    for turn, string in enumerate(Selections):
        s0, s1 = string

        variable_up, variable_down = None, None
        # 変数の両方が 0。ゲーム続行不可能。
        if count[s0] == count[s1] == 0:
            return 'No'
        # 変数の片方が 0。そちらを増やすほかない。
        elif count[s0] == 0:
            variable_up, variable_down = s0, s1
        elif count[s1] == 0:
            variable_up, variable_down = s1, s0
        # 不適切な方法を取るとゲーム続行が不可能なので、さらに次の操作を先読みする。
        # (ただし、現時点が最後の操作なら、好きにしていい)
        elif turn + 1 == N:
            variable_up, variable_down = s0, s1
        # 次の操作に関わっている変数を増やす
        elif s0 in Selections[turn + 1]:
            variable_up, variable_down = s0, s1
        else:
            variable_up, variable_down = s1, s0

        count[variable_up] += 1
        count[variable_down] -= 1
        ans.append(variable_up)

    return ' '.join(['Yes'] + ans)

print(f_three_variables_game())