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/python3
import sys
input = lambda: sys.stdin.readline().strip()
N, A, B, C = [int(x) for x in input().split()]
s = [input() for _ in range(N)]
abc = {'A': A, 'B': B, 'C': C}
can = True
moves = []
for i in range(N):
    moves.append(next(j for j in (0, 1) if abc[s[i][j]] < abc[s[i][j ^ 1]] or abc[s[i][j]] == abc[s[i][j ^ 1]] and (i + 1 == N or s[i + 1] == s[i] or s[i][j ^ 1] not in s[i + 1])))
    abc[s[i][moves[-1]]] += 1
    abc[s[i][moves[-1] ^ 1]] -= 1
    can &= all(x >= 0 for x in abc.values())
if can:
    print('Yes')
    print(*(s[i][moves[i]] for i in range(N)), sep='\n')
else:
    print('No')