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:
# coding: utf-8
import sys
sysread = sys.stdin.readline
sys.setrecursionlimit(10**7)
def run():
    pri = []
    N, A, B, C = map(int, sysread().split())
    vals = {'A':A, 'B':B, 'C':C}
    S = [sysread() for _ in range(N)]

    pri = []
    for idx, s in enumerate(S):
        if vals[s[0]] == vals[s[1]] and vals[s[0]] == 1 and idx !=len(S)-1:
            if s[0] in S[idx+1]:
                vals[s[0]] += 1
                vals[s[1]] -= 1
                pri.append(s[0])
            else:
                vals[s[0]] -= 1
                vals[s[1]] += 1
                pri.append(s[1])
        else:
            if vals[s[0]] <= vals[s[1]]:
                vals[s[0]] += 1
                vals[s[1]] -= 1
                pri.append(s[0])
            else:
                vals[s[0]] -= 1
                vals[s[1]] += 1
                pri.append(s[1])

        if not check_vals(vals):
            print('No')
            return None
    print('Yes')
    for st in pri:
        print(st)

def check_vals(vals):
    for v in vals.values():
        if v < 0:
            return False
    return True

if __name__ == "__main__":
    run()