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
input = sys.stdin.readline
n, a, b, c = map(int, input().split())
S = [input().rstrip().replace("AC", "CA") for _ in range(n)]
D = ["AB", "BC", "CA"]
X = [a+b, b+c, c+a]
L = []
for i, s in enumerate(S):
  k = D.index(s)
  if X[k] == 0:
    print("No")
    exit()
  if X[(k+1)%3] == 1 and X[(k+2)%3] == 1 and i < n-1:
    l = D.index(S[i+1])
    if l == (k+1)%3:
      X[(k+1)%3] += 1
      X[(k+2)%3] -= 1
      L.append(s[1])
    else:
      X[(k+2)%3] += 1
      X[(k+1)%3] -= 1
      L.append(s[0])
  else:
    if X[(k+1)%3] < X[(k+2)%3]:
      X[(k+1)%3] += 1
      X[(k+2)%3] -= 1
      L.append(s[1])
    else:
      X[(k+2)%3] += 1
      X[(k+1)%3] -= 1
      L.append(s[0])
print("Yes")
print(*L, sep="\n")