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:
from sys import stdin, setrecursionlimit

setrecursionlimit(10 ** 9)


def input():
    return stdin.readline().strip()


N, A, B, C = map(int, input().split())
strings = [input() for _ in range(N)]


def dfs(index, hp):
    if index == N:
        return ''

    s1, s2 = strings[index]
    if hp[s1] > 0:
        hp2 = hp.copy()
        hp2[s1] -= 1
        hp2[s2] += 1
        ret = dfs(index + 1, hp2)
        if ret != False:
            return  s2 + ret
    if hp[s2] > 0:
        hp2 = hp.copy()
        hp2[s2] -= 1
        hp2[s1] += 1
        ret = dfs(index + 1, hp2)
        if ret != False:
            return s1 + ret

    return False


d = {'A': A, 'B': B, 'C': C}
ans = dfs(0, d)
if ans == False:
    print('No')
else:
    print('Yes')
    for c in ans:
        print(c)