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())
column = [a, b, c]
dict_convert = {"A": 0, "B": 1, "C": 2}
reverse_convert = {0: "A", 1: "B", 2: "C"}
s = list()
for _ in range(n):
  pair = tuple(dict_convert[val] for val in tuple(input()))
  s.append(pair)
choices = list()
def generate_play():
  for i in range(n):
    if column[s[i][0]] == 0 and column[s[i][1]] == 0:
      return "No"
    elif column[s[i][0]] == 1 and column[s[i][1]] == 1 and i<n-1:
      other_index = next(x for x in range(3) if x not in (s[i][0], s[i][1]))
      if s[i+1] == (other_index, s[i][0]) or s[i+1] == (s[i][0], other_index):
        choice = s[i][0]
        column[s[i][1]] -= 1
        column[s[i][0]] += 1
      else:
        choice = s[i][1]
        column[s[i][1]] += 1
        column[s[i][0]] -= 1
      choices.append(choice)
    else:
      if column[s[i][0]] >= column[s[i][1]]:
        choice = s[i][1]
        column[s[i][1]] += 1
        column[s[i][0]] -= 1
      else:
        choice = s[i][0]
        column[s[i][1]] -= 1
        column[s[i][0]] += 1
      choices.append(choice)
  return "Yes"
ans = generate_play()
print(ans)
if ans == "Yes":
  [print(reverse_convert[val]) for val in choices]