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:
# -*- coding: utf-8 -*-
N,A,B,C = map(int, input().split())
list_choice = [input() for i in range(N)]
list_choice.append('')

def operation(A,B,C,S,nextS):
  if S=='AB':
    if max(A,B)==0:
      return ('No','',0,0,0)
    elif (A<B) or (A==1 and B==1 and nextS=='AC'):
      return ('Yes','A',A+1,B-1,C)
    else:
      return ('Yes','B',A-1,B+1,C)
  elif S=='AC':
    if max(A,C)==0:
      return ('No','',0,0,0)
    elif (A<C) or (A==1 and C==1 and nextS=='AB'):
      return ('Yes','A',A+1,B,C-1)
    else:
      return ('Yes','C',A-1,B,C+1)
  else: # S=='BC'
    if max(B,C)==0:
      return ('No','',0,0,0)
    elif (B<C) or (B==1 and C==1 and nextS=='AB'):
      return ('Yes','B',A,B+1,C-1)
    else:
      return ('Yes','C',A,B-1,C+1)
  
def func(A,B,C,list_choice):
  list_add = []
  for i in range(N):
    answer,add,A,B,C = operation(A,B,C,list_choice[i],list_choice[i+1])
    if answer=='No':
      return ('No', [])
    else:
      list_add.append(add)
  return ('Yes',list_add)
  
answer, list_add = func(A,B,C,list_choice)
print(answer)
if answer == 'Yes':
  for add in list_add:
    print(add)