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:
N, A, B, C = map(int, input().split())
inputs = tuple(tuple(input()) for _ in range(N))

dic = {
    "A": A,
    "B": B,
    "C": C
}

ans = [0] * N
depth = 0
while depth < N:
    key1, key2 = inputs[depth]
    if dic[key1] < dic[key2]:
        dic[key1] += 1
        dic[key2] -= 1
        ans[depth] = key1
    elif dic[key1] > dic[key2]:
        dic[key2] += 1
        dic[key1] -= 1
        ans[depth] = key2
    else:
        if not dic[key1]:
            break
        elif dic[key1] == 1 and depth + 1 < N:
            next_key1, next_key2 = inputs[depth + 1]
            common_key, *_ = {key1, key2} & {next_key1, next_key2}
            else_key, *_ = {key1, key2} - {common_key}
            dic[common_key] += 1
            dic[else_key] -= 1
            ans[depth] = common_key
        else:
            dic[key1] += 1
            dic[key2] -= 1
            ans[depth] = key1
    depth += 1
else:
    print("Yes")
    print(*ans, sep="\n")
    quit()
print("No")