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:
import sys


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


def solve():
    def distribute(fm, to):
        count[fm] -= 1
        count[to] += 1
        ans.append(to)

    n, a, b, c = map(int, input().split())
    queries = [input() for _ in range(n)]

    count = {'A': a, 'B': b, 'C': c}
    ans = ['Yes']

    for i in range(n):
        x, y = queries[i]
        if count[x] == count[y] == 0:
            return 'No'
        elif count[x] == count[y] == 1:
            if i == n - 1:
                distribute(x, y)
            else:
                if x in queries[i + 1]:
                    distribute(y, x)
                else:
                    distribute(x, y)
        elif count[y] > count[x]:
            distribute(y, x)
        else:
            distribute(x, y)
    return '\n'.join(ans)


print(solve())