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 collections
def main():

    N, A, B, C = map(int, input().split())

    ans = ""
    s = []
    for _ in range(N):
        s.append(input())

    d = dict()
    d['A'] = A
    d['B'] = B
    d['C'] = C
    ans = ""
    for i in range(N):
        if d[s[i][0]] == 0 and d[s[i][1]] == 0:
            break
        elif d[s[i][0]] == 0:
            d[s[i][0]] += 1
            d[s[i][1]] -= 1
            ans += s[i][0]
        elif d[s[i][1]] == 0:
            d[s[i][1]] += 1
            d[s[i][0]] -= 1
            ans += s[i][1]
        else:
            if d[s[i][0]] == 1 and d[s[i][1]] == 1 and d['A'] + d['B'] + d['C'] == 2:
                if i < N-1 and s[i] != s[i+1] and s[i][0] in s[i+1]:
                    d[s[i][0]] += 1
                    d[s[i][1]] -= 1
                    ans += s[i][0]
                else:
                    d[s[i][1]] += 1
                    d[s[i][0]] -= 1
                    ans += s[i][1]
            elif d[s[i][0]] < d[s[i][1]]:
                d[s[i][0]] += 1
                d[s[i][1]] -= 1
                ans += s[i][0]
            else:
                d[s[i][1]] += 1
                d[s[i][0]] -= 1
                ans += s[i][1]

    if len(ans) == N:
        print("Yes")
        for c in ans:
            print(c)
    else:
        print("No")

if __name__ == '__main__':
    main()