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 = map(int, input().split())
s=[input() for i in range(n)]
ans=[]
from collections import defaultdict
d = defaultdict(int)
d["A"]=a
d["B"]=b
d["C"]=c
def add(c1,c2):
    global d
    ans.append(c1)
    d[c1]+=1
    d[c2]-=1

for i in range(n):
    que = s[i]
    nxt="NONE"
    if i!=n-1:
        nxt = s[i+1]

    q1,q2=que

    if d[q1]==d[q2]==0:
        print("No")
        exit()
    if d[q1]==d[q2]==1:
        if q1 in nxt:
            add(q1,q2)
        else:
            add(q2,q1)
    elif d[q1]>=d[q2]:
        add(q2,q1)
    else:
        add(q1,q2)

print("Yes")
for a in ans:
    print(a)