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:
from sys import setrecursionlimit
setrecursionlimit(10 ** 6)

*I, = open(0).read().split()
N, A, B, C = map(int, I[:4])
S = I[4:]

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

ans = [""] * N
def dfs(i):
    if i == N:
        print("Yes")
        print("\n".join(ans))
        quit()

    for L, R in (S[i], reversed(S[i])):
        if Cnt[R] > 0:
            Cnt[L] += 1
            Cnt[R] -= 1

            ans[i] = L
            dfs(i + 1)

            Cnt[L] -= 1
            Cnt[R] += 1


dfs(0)
print("No")