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:
n, a, b, c = list(map(int, input().split()))
s = [list(input()) for _ in range(n)]
s.append(["A", "B"])
d = {"A": a, "B": b, "C": c}
ans = []

def calc(add, sub):
    d[add] += 1
    d[sub] -= 1
    ans.append(add)

for i, [j, k] in enumerate(s):
    if i == n:
        print('Yes')
        print('\n'.join(ans))
        break
    if d[j] == 0 and d[k] == 0:
        print("No")
        break
    elif j == "A" and k == "B":
        
        if d[j] < d[k]:
            calc(j, k)
        elif d[j] > d[k]:
            calc(k, j)
        else:
            if s[i + 1][0] == "A":
                calc(j, k)
            else:
                calc(k, j)
    elif j == "A" and k == "C":

        if d[j] < d[k]:
            calc(j, k)
        elif d[j] > d[k]:
            calc(k, j)
        else:
            if s[i + 1][0] == "A":
                calc(j, k)
            else:
                calc(k, j)
    elif j == "B" and k == "C":

        if d[j] < d[k]:
            calc(j, k)
        elif d[j] > d[k]:
            calc(k, j)
        else:
            if s[i + 1][0] == "A" and s[i + 1][1] == "C":
                calc(k, j)
            else:
                calc(j, k)