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
sys.setrecursionlimit(10 ** 7)

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

ans = []


def game(i, a, b, c, prev):
    if i == N:
        ans.append(prev)
        return True
    x, y = command[i]
    if x == "A" and y == "B":
        if b:
            bl = game(i + 1, a + 1, b - 1, c, x)
            if bl:
                ans.append(prev)
                return True
        if a:
            bl = game(i + 1, a - 1, b + 1, c, y)
            if bl:
                ans.append(prev)
                return True
    elif x == "A" and y == "C":
        if c:
            bl = game(i + 1, a + 1, b, c - 1, x)
            if bl:
                ans.append(prev)
                return True
        if a:
            bl = game(i + 1, a - 1, b, c + 1, y)
            if bl:
                ans.append(prev)
                return True
    else:
        if c:
            bl = game(i + 1, a, b + 1, c - 1, x)
            if bl:
                ans.append(prev)
                return True
        if b:
            bl = game(i + 1, a, b - 1, c + 1, y)
            if bl:
                ans.append(prev)
                return True

    return False


bl = game(0, A, B, C, "?")
if not bl:
    print("No")
else:
    print("Yes")
    ans.pop()
    for x in ans[::-1]:
        print(x)