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
dict_in={"AB":[0,1],"AC":[0,2],"BC":[1,2]}
dict_out={0:"A",1:"B",2:"C"}
n,a,b,c=map(int,input().split())
var=[a,b,c]
s=[dict_in[input()] for i in range(n)]
ans=[]
for i in range(n):
  if var[s[i][0]]>var[s[i][1]]:
    var[s[i][0]]-=1
    var[s[i][1]]+=1
    ans.append(dict_out[s[i][1]])
  elif var[s[i][0]]<var[s[i][1]]:
    var[s[i][0]]+=1
    var[s[i][1]]-=1
    ans.append(dict_out[s[i][0]])
  else:
    if var[s[i][0]]==0 and var[s[i][1]]==0:
      print("No")
      sys.exit()
    inc=s[i][1]
    for j in range(i+1,n):
      if not(s[i][0] in s[j]):
        inc=s[i][1]
        break
      elif not(s[i][1] in s[j]):
        inc=s[i][0]
        var[s[i][0]]+=1
        var[s[i][1]]-=1
        break
    if inc==s[i][1]:
      var[s[i][0]]-=1
      var[s[i][1]]+=1
    ans.append(dict_out[inc])
print("Yes")
for i in range(len(ans)):
  print(ans[i])