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
sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))
def resolve():
    N, A, B, C = lr()
    ABC = [A, B, C]
    ans = []
    def ope(u, v):
        ABC[u] += 1
        ABC[v] -= 1
        ans.append(chr(ord('A')+u))
    q = []
    for i in range(N):
        s = sr()
        if s == 'AB':
            x, y = 0, 1
        elif s == 'AC':
            x, y = 0, 2
        else:
            x, y = 1, 2
        q.append([x, y])
    for i in range(N):
        x, y = q[i]
        if ABC[x] == 0 and ABC[y] == 0:
            print('No')
            return
        if ABC[x] == 0:
            ope(x, y)
            continue
        if ABC[y] == 0:
            ope(y, x)
            continue
        if i < N-1:
            nx, ny = q[i+1]
            if x == nx or x == ny:
                ope(x, y)
                continue
        ope(y, x)
    print('Yes')
    print(*ans, sep='\n')
resolve()