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:
Arr=list(map(int,input().split()))
L=[]
for i in range(Arr[0]):
    S=input()
    if S=="AB":
        L.append([1,2])
    elif S=="BC":
        L.append([2,3])
    else:
        L.append([1,3])
D={}
D[1]="A"
D[2]="B"
D[3]="C"

if Arr[L[0][0]]+Arr[L[0][1]]==0:
    print("No")
else:
    ANS=["Yes"]
    for i in range(len(L)):
        if Arr[L[i][0]]==Arr[L[i][1]] and Arr[L[i][0]]==1:
            if i!=len(L)-1 and L[i]!=L[i+1]:
                if L[i][0] in L[i+1]:
                    ANS.append(D[L[i][0]])
                    Arr[L[i][0]]+=1
                    Arr[L[i][1]]-=1
                else:
                    ANS.append(D[L[i][1]])
                    Arr[L[i][1]]+=1
                    Arr[L[i][0]]-=1
            else:
                ANS.append(D[L[i][0]])
                Arr[L[i][0]]+=1
                Arr[L[i][1]]-=1
        elif Arr[L[i][0]]+Arr[L[i][1]]==0:
            print("No")
            exit()
        else:
            if Arr[L[i][0]]>=Arr[L[i][1]]:
                ANS.append(D[L[i][1]])
                Arr[L[i][1]]+=1
                Arr[L[i][0]]-=1
            else:
                ANS.append(D[L[i][0]])
                Arr[L[i][0]]+=1
                Arr[L[i][1]]-=1
    for j in range(len(ANS)):
        print(ANS[j])