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
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, A, B, C = mapint()
costs = {'A': A, 'B': B, 'C': C}
old_a, old_b = list(input())

if costs[old_a]==0 and costs[old_b]==0:
    print('No')
    exit()

commands = []
for _ in range(N-1):
    nx_a, nx_b = list(input())
    if costs[old_a]==0 and costs[old_b]==0:
        print('No')
        exit()
    elif costs[old_a]==0:
        costs[old_a] += 1
        costs[old_b] -= 1
        commands.append(old_a)
        
    elif costs[old_b]==0:
        costs[old_b] += 1
        costs[old_a] -= 1
        commands.append(old_b)

    else:
        if old_a==nx_a or old_a==nx_b:
            commands.append(old_a)
            costs[old_a] += 1
            costs[old_b] -= 1
        else:
            commands.append(old_b)
            costs[old_b] += 1
            costs[old_a] -= 1
    old_a, old_b = nx_a, nx_b

if costs[old_a]==0 and costs[old_b]==0:
    print('No')
    exit()
elif costs[old_a]==0:
    costs[old_a] += 1
    costs[old_b] -= 1
    commands.append(old_a)
    
else:
    costs[old_b] += 1
    costs[old_a] -= 1
    commands.append(old_b)

print('Yes')
print('\n'.join(commands))