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**6)
result = []
def calc(a, b, c, i):
    if a < 0 or b < 0 or c < 0:
        return False
    if i >= N:
        return True
    command = s[i]
    if command == "AB":
        if calc(a+1, b-1, c, i+1):
            result.append("A")
            return True
        if calc(a-1, b+1, c, i+1):
            result.append("B")
            return True
        return False
    elif command == "AC":
        if calc(a+1, b, c-1, i+1):
            result.append("A")
            return True
        if calc(a-1, b, c+1, i+1):
            result.append("C")
            return True
        return False
    elif command == "BC":
        if calc(a, b-1, c+1, i+1):
            result.append("C")
            return True
        if calc(a, b+1, c-1, i+1):
            result.append("B")
            return True
        return False
def main():
    global N, s
    N, A, B, C = map(int, input().split())
    s = [input() for _ in range(N)]
    if calc(A, B, C, 0):
        print("Yes")
        for c in result[::-1]:
            print(c)
    else:
        print("No")
main()