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:
n, av, bv, cv = list(map(int, input().split()))
s = []
for i in range(n):
    s.append(input())

v = {'A':av, 'B':bv, 'C':cv}

selection = []
for i in range(n):
    if v[s[i][0]] == 0:
        selection.append(s[i][0])
        v[s[i][0]] += 1
        v[s[i][1]] -= 1
    elif v[s[i][1]] == 0:
        selection.append(s[i][1])
        v[s[i][0]] -= 1
        v[s[i][1]] += 1
    elif v[s[i][0]] == 1 and v[s[i][1]] == 1:
        if i == n-1:
            selection.append(s[i][0])
            v[s[i][0]] += 1
            v[s[i][1]] -= 1       
        else:
            if s[i+1][0] == s[i][0] or s[i+1][1] == s[i][0]:
                selection.append(s[i][0])
                v[s[i][0]] += 1
                v[s[i][1]] -= 1 
            else:
                selection.append(s[i][1])
                v[s[i][0]] -= 1
                v[s[i][1]] += 1
    else:
        if v[s[i][0]] > v[s[i][1]]:
            selection.append(s[i][1])
            v[s[i][0]] -= 1
            v[s[i][1]] += 1
        else:
            selection.append(s[i][0])
            v[s[i][0]] += 1
            v[s[i][1]] -= 1
    
    if v['A'] < 0 or v['B'] < 0 or v['C'] < 0:
        print('No')
        break
else:
    print('Yes')
    for i in range(n):
        print(selection[i])