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:
X = [0, 0, 0]
N, X[0], X[1], X[2] = map(int, input().split())
Q = []
for _ in range(N):
    s = input()
    if s == 'AB':
        Q.append([0, 1])
    elif s == 'AC':
        Q.append([0, 2])
    else:
        Q.append([1, 2])
ans = True
ret = ''
for i in range(N):
    a = Q[i][0]
    b = Q[i][1]
    if X[a] == X[b] == 0:
        ans = False
        break
    elif X[a] < X[b]:
        ret += chr(ord(str(a)) + 17)
        X[a] += 1
        X[b] -= 1
    elif X[a] > X[b] or i == N - 1:
        ret += chr(ord(str(b)) + 17)
        X[a] -= 1
        X[b] += 1
    else:
        s = Q[i + 1][0]
        t = Q[i + 1][1]
        if a == s or a == t:
            ret += chr(ord(str(a)) + 17)
            X[a] += 1
            X[b] -= 1
        else:
            ret += chr(ord(str(b)) + 17)
            X[a] -= 1
            X[b] += 1
    if X[a] < 0 or X[b] < 0:
        ans = False
        break
if ans:
    print('Yes')
    print('\n'.join(ret))
else:
    print('No')