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 python3

N, A, B, C = (int(_) for _ in input().split())
status = [A, B, C]
name = ['A', 'B', 'C']
sel_num = {'AB': (0, 1),
           'BC': (1, 2),
           'AC': (2, 0)}

S = []
for n in range(N):
    S.append(sel_num[input()])

if A + B + C > 2:
    difficult = False
else:
    difficult = True

ret = []
try:
    for i in range(len(S)):
        a1, a2 = S[i]
        if status[a2] < status[a1]:
            a1, a2 = a2, a1
        if (difficult and
            (status[a1] == 1) and
            (status[a2] == 1) and
            (i + 1 < len(S)) and
            S[i] != S[i + 1]):
            b1, b2 = S[i + 1]
            if a2 == b1:
                a1, a2 = a2, a1
        ret.append(name[a1])
        status[a1] += 1
        status[a2] -= 1
        assert status[a2] >= 0
except:
    print('No')
    exit(0)

print('Yes')
for r in ret:
    print(r)