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
import queue

q = queue.Queue()
sys.setrecursionlimit(10**7)
INF = 10**10
MOD = 10**9 + 7
S = []
history = []
N, A, B ,C = map(int,input().split())
d = {}
d['A'] = A
d['B'] = B
d['C'] = C

for n in range(N):
    s = input()
    S.append(s)

def select(L,R,x):
    diff = 1
    if L!=x:
        diff *= -1
    d[L] += diff
    d[R] -= diff
    history.append(x)

for n in range(N):
    L, R = S[n]
    if d[L] >= 2:
        select(L,R,R)
    elif d[L] == 0:
        if d[R] == 0:
            print ('No')
            exit()
        else:
            select(L,R,L)
    elif d[L] == 1:
        if d[R] >= 2:
            select(L,R,L)
        elif d[R] == 0:
            select(L,R,R)
        elif d[R] == 1:
            if n!=N-1:
                if L in S[n+1]:
                    select(L,R,L)
                else:
                    select(L,R,R)
            else:
                select(L,R,L) # どちらでもOK
print ('Yes')
for h in history:
    print (h)