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 random
from collections import deque
import sys
sys.setrecursionlimit(10**7)

def input():
    return sys.stdin.readline().strip()

# スペース区切りの入力を読み込んで数値リストにして返します。
def get_nums_l():
    return [ int(s) for s in input().split(" ")]

def log(*args):
    print("DEBUG:", *args, file=sys.stderr)

n,a,b,c = get_nums_l()
d = {
    "A": a,
    "B": b,
    "C": c
}
S = []
for _ in range(n):
    S.append(input())

def dfs(i, x, history):

    if d[S[i][1-x]] == 0:
        return False

    d[S[i][x]] += 1
    d[S[i][1-x]] -= 1

    history.append(S[i][x])

    if i == n-1:
        return True

    nex = random.randint(0, 1)

    ok = dfs(i+1, nex, history)
    if ok:
        return ok

    ok = dfs(i+1, 1-nex, history)

    if ok:
        return ok

    # バックトラック
    history.pop()
    d[S[i][x]] -= 1
    d[S[i][1-x]] += 1

    return False

history = deque()
ok = dfs(0, 0, history) or dfs(0, 1, history)

print("Yes" if ok else "No")
if ok:
    for s in history:
        print(s)