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 main():
    N, A, B, C = [int(i) for i in input().split()]

    if A == B == C == 0:
        print("No")
        return

    S = [input() for _ in range(N)]
    d = {"A": A, "B": B, "C": C}
    order = []

    for i, s in enumerate(S):
        s1, s2 = s

        if d[s1] == d[s2] == 0:
            print("No")
            return
        elif d[s1] == 0:
            d[s1] += 1
            d[s2] -= 1
            order.append(s1)
        elif d[s2] == 0:
            d[s2] += 1
            d[s1] -= 1
            order.append(s2)
        elif d[s1] == d[s2] == 1:
            try:
                if s1 in S[i + 1]:
                    d[s1] += 1
                    d[s2] -= 1
                    order.append(s1)
                else:
                    d[s2] += 1
                    d[s1] -= 1
                    order.append(s2)
            except:
                order.append(s1)
        else:
            if d[s1] > d[s2]:
                d[s1] -= 1
                d[s2] += 1
                order.append(s2)
            else:
                d[s2] -= 1
                d[s1] += 1
                order.append(s1)
    
    print("Yes")
    for o in order:
        print(o)


main()