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 = [int(x) for x in input().split()]
score = {}
score["A"] = a
score["B"] = b
score["C"] = c     
S = [input().rstrip() for _ in range(n)]
ans = []

for i in range(n - 1):
    s = S[i]
    next_s = S[i + 1]
    s1 = s[0]
    s2 = s[1]
    if score[s1] == 0 and score[s2] == 0:
        print("No")
        sys.exit()
    elif score[s1] == 0:
        ans.append(s1)
        score[s1] += 1
        score[s2] -= 1
    elif score[s2] == 0:
        ans.append(s2)
        score[s1] -= 1
        score[s2] += 1
    else:
        if next_s == s:
            ans.append(s1)
            score[s1] += 1
            score[s2] -= 1
        elif s1 in next_s:
            ans.append(s1)
            score[s1] += 1
            score[s2] -= 1
        else:
            ans.append(s2)
            score[s2] += 1
            score[s1] -= 1
s = S[-1]
s1 = s[0]
s2 = s[1]

if score[s1] == 0 and score[s2] == 0:
        print("No")
        sys.exit()
elif score[s1] == 0:
    ans.append(s1)
    score[s1] += 1
    score[s2] -= 1
elif score[s2] == 0:
    ans.append(s2)
    score[s1] -= 1
    score[s2] += 1
else:
    ans.append(s1)
print("Yes")
for i in ans:
    print(i)