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())
s=[input() for _ in range(n)]
abc=[a,b,c]
d={'A':0,'B':1,'C':2}
dr={0:'A',1:'B',2:'C'}
ans=[]
for i,x in enumerate(s):
  x=[d[y] for y in list(x)]
  if abc[x[0]]==abc[x[1]]==1 and i<n-1:
    nx=[d[y] for y in list(s[i+1])]
    for j,y in enumerate(x):
      if y in nx:
        abc[y]+=1
        abc[x[(j+1)%2]]-=1
        ans.append(dr[y])
        break
  elif abc[x[0]]>abc[x[1]]:
    abc[x[1]]+=1
    abc[x[0]]-=1
    ans.append(dr[x[1]])
  else:
    abc[x[0]]+=1
    abc[x[1]]-=1
    ans.append(dr[x[0]])
  for y in abc:
    if y<0:
      print('No')
      exit()
  
print('Yes')
print(*ans,sep='\n')