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 = list(map(int, input().split()))
s = [input() for _ in range(N)]

DP = [[0] * 3 for _ in range(N + 1)]
DP[0] = [A, B, C]

L = [""] * N
R = {}
R[0] = "A"
R[1] = "B"
R[2] = "C"
A = []
B = []
for i in range(N):
  t = s[i]
  if t == "AB":
    x = 0
    y = 1
  if t == "BC":
    x = 1
    y = 2
  if t == "AC":
    x = 0
    y = 2
  if DP[i][y] != 0:
    DP[i + 1] = DP[i]
    DP[i + 1][x] += 1
    DP[i + 1][y] -= 1
    L[i] = R[x]
    if x == 0:
      A.append([i, y])
    else:
      B.append([i, y])
  elif DP[i][x] != 0:
    DP[i + 1] = DP[i]
    DP[i + 1][x] -= 1
    DP[i + 1][y] += 1
    L[i] = R[y]
  else:
    if x == 0:
      if len(B) == 0:
        print("No")
        exit()
      z = 1
      k, n = B.pop()
    if x == 1:
      if len(A) == 0:
        print("No")
        exit()
      z = 0
      k, n = A.pop()
    DP[i + 1] = DP[i]
    DP[i + 1][z] -= 2
    DP[i + 1][n] += 2
    if n == x:
      x, y = y, x
    DP[i + 1][x] += 1
    DP[i + 1][y] -= 1
    if DP[i + 1][z] < 0:
      print("No")
      exit()
    L[i] = R[x]
    L[k] = R[y]

print("Yes")
for i in L:
  print(i)