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(10000000)
input = sys.stdin.readline
N, A, B, C = map(int, input().split())
S = [input().strip("\n").replace("A", "0").replace("B", "1").replace("C", "2") for _ in range(N)]
Ans = [None] * N

def search(i, num):
    if i == N:
        if min(num) >= 0: return True
        else: return False
    if min(num) < 0: return False
    L = [num[0], num[1], num[2]]
    f = S[i][0]
    s = S[i][1]
    L[int(f)] += 1
    L[int(s)] -= 1
    if search(i+1, L):
        Ans[i] = f
        return True
    L[int(f)] -= 2
    L[int(s)] += 2
    if search(i+1, L):
        Ans[i] = s
        return True
    return False

def solve():
    if search(0, [A, B, C]):
        print("Yes")
        for i, a in enumerate(Ans):
            if a == "0": print("A")
            elif a == "1": print("B")
            else: print("C")
    else: print("No")
    #print(Ans)

    return 0

if __name__ == "__main__":
    solve()