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:
#!/usr/bin/env python
# -*- coding: utf-8 -*-


def main():
  N, A, B, C = map(int, input().split())
  values = [A, B, C]
  moves = [input().strip() for _ in range(N)] + ['AB']
  cmds = []

  for move, next_move in zip(moves[:-1], moves[1:]):
    if move == 'AB':
      i, j, lc, rc = 0, 1, 'A', 'B'
    elif move == 'AC':
      i, j, lc, rc = 0, 2, 'A', 'C'
    elif move == 'BC':
      i, j, lc, rc = 1, 2, 'B', 'C'

    if next_move == 'AB':
      ni, nj = 0, 1
    elif next_move == 'AC':
      ni, nj = 0, 2
    elif next_move == 'BC':
      ni, nj = 1, 2

    if values[i] == 0 and values[j] == 0:
      cmds = None
      break
    elif values[i] < values[j]:
      cmds.append(lc)
      values[i] += 1
      values[j] -= 1
    elif values[i] > values[j]:
      cmds.append(rc)
      values[i] -= 1
      values[j] += 1
    elif ni == i or nj == i:
      cmds.append(lc)
      values[i] += 1
      values[j] -= 1
    elif ni == j or nj == j:
      cmds.append(rc)
      values[i] -= 1
      values[j] += 1
    else:
      cmds.append(lc)
      values[i] += 1
      values[j] -= 1

  if cmds is not None:
    print('Yes')
    for c in cmds:
      print(c)
  else:
    print('No')


if __name__ == '__main__':
  main()