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:
# -*- coding: utf-8 -*-
n, a, b, c = map(int, input().split())

value_dict = {'A': a, 'B': b, 'C': c}
result_list = []
input_list = []
flag = True

for i in range(n):
    input_list.append(input())

for next, input in enumerate(input_list, 1):
    if value_dict[input[0]] < value_dict[input[1]]:
        value_dict[input[0]] += 1
        value_dict[input[1]] -= 1
        result_list.append(input[0])
    elif value_dict[input[1]] < value_dict[input[0]]:
        value_dict[input[1]] += 1
        value_dict[input[0]] -= 1
        result_list.append(input[1])
    else:
        if value_dict[input[0]] == 0:
            flag = False
            break
        elif next == len(input_list):
            result_list.append(input[0])
        elif input[0] in input_list[next]:
            value_dict[input[0]] += 1
            value_dict[input[1]] -= 1
            result_list.append(input[0])
        else:
            value_dict[input[1]] += 1
            value_dict[input[0]] -= 1
            result_list.append(input[1])

if flag:
    print('Yes')
    for result in result_list:
        print(result)

else:
    print('No')