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
sys.setrecursionlimit(1000000)

def F(S,curr,D,res):
    if D["A"]<0 or D["B"]<0 or D["C"]<0:
        return False
    if len(S)==curr:
        print("Yes")
        for c in res:
            print(c)
        #print("".join(res))
        return True
    s=S[curr]
    
    a=False
    b=False
    if D[s[0]]>=1:
        D[s[0]]-=1
        D[s[1]]+=1
        res.append(s[1])
        a=F(S,curr+1,D,res)
        res.pop(-1)
        D[s[0]]+=1
        D[s[1]]-=1
    if a:
        return a

    if D[s[1]]>=1:
            D[s[1]]-=1
            D[s[0]]+=1
            res.append(s[0])
            b=F(S,curr+1,D,res)
            res.pop()
            D[s[1]]+=1
            D[s[0]]-=1
    return a or b


N,A,B,C=map(int,input().strip().split())
D={"A":A,"B":B,"C":C}
S=[]
res=[]
for i in range(N):
    S.append(input())
if not (F(S,0,D,res)):
    print("No")