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:
import sys
K = list(map(int,input().split()))
N = K[0]
S = sum(K[1:4])

if S == 0:
  print("No")
  sys.exit()

s = input()
out = [0 for _ in range(N)]

for ct in range(N):
  #print(K)
  if ct < N-1:
    s_next = input()
    
  if s == "AB":
    i = 1
    j = 2
  elif s == "BC":
    i = 2
    j = 3
  else:
    i = 1
    j = 3
  
  if K[i] + K[j] == 0:
      print("No")
      sys.exit()
  elif K[i] > K[j]:
    K[i] -= 1
    K[j] += 1
    log = j
  elif K[i] < K[j]:
    K[i] += 1
    K[j] -= 1
    log = i
  elif K[i] == K[j]:
    if ct == N-1:
      K[i] += 1
      K[j] -= 1
      log = i
      out[ct] = i
      break
      
    if s_next == "AB":
      i_n = 1
      j_n = 2
    elif s_next == "BC":
      i_n = 2
      j_n = 3
    else:
      i_n = 1
      j_n = 3
      
    if i_n == i or j_n == i:
      K[i] += 1
      K[j] -= 1
      log = i
    else:
      K[j] += 1
      K[i] -= 1  
      log = j
  #print(log)
  out[ct] = log
  if ct < N-1:
    s = s_next

print("Yes")
for o in out:
  print(chr(64+o))