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
# input = sys.stdin.readline
n, a, b, c = map(int,input().split())
S = [input() for i in range(n)]
A = [a,b,c]

D = {"A":0, "B":1, "C":2}
E = ["A","B","C"]
ANS = []
ng = 0

for i in range(n):
    x = D[S[i][0]]
    y = D[S[i][1]]

    if A[x] > A[y]:
        A[x] -= 1
        A[y] += 1
        ANS.append(E[y])
    elif A[y] > A[x]:
        A[y] -= 1
        A[x] += 1
        ANS.append(E[x])
    else:
        if A[x] == 0 and A[y] == 0:
            ng = 1
            break
        elif A[x] == 1 and A[y] == 1 and i != n-1:
            xx = D[S[i+1][0]]
            yy = D[S[i+1][1]]
            if S[i] != S[i+1] and (xx == x or yy == x):
                A[x] += 1
                A[y] -= 1
                ANS.append(E[x])
            else:
                A[y] += 1
                A[x] -= 1
                ANS.append(E[y])
        else:
            A[y] += 1
            A[x] -= 1
            ANS.append(E[y])

if ng == 1:
    print("No")
else:
    print("Yes")
    for i in range(len(ANS)):
        print(ANS[i])