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, copy, math, heapq, bisect
from itertools import accumulate
from collections import deque, defaultdict, Counter
sys.setrecursionlimit(500000)


N,A,B,C = map(int,input().split())
ABC = [A,B,C]
S = []
SS = ('A','B','C')
d = [0,0,0]
flag = True
for i in range(N):
    s = input()
    if s=="AB":
        S.append(2)
        d[0] += 1
        d[1] += 1
    elif s=="BC":
        S.append(0)
        d[1] += 1
        d[2] += 1
    else:
        S.append(1)
        d[2] += 1
        d[0] += 1
ans = []
for i in range(N):
    x,y = (S[i]+1)%3,(S[i]+2)%3
    if ABC[x]<ABC[y]:
        ans.append(SS[x])
        ABC[y] -= 1
        ABC[x] += 1
    elif ABC[x]>ABC[y]:
        ans.append(SS[y])
        ABC[y] += 1
        ABC[x] -= 1
    else:
        if i < N-1:
            if S[i+1]==y:
                ans.append(SS[x])
                ABC[y] -= 1
                ABC[x] += 1
            else:
                ans.append(SS[y])
                ABC[y] += 1
                ABC[x] -= 1
        else:
            ans.append(SS[y])
            ABC[y] += 1
            ABC[x] -= 1




    if ABC[0]<0 or ABC[1]<0 or ABC[2]<0:
        flag = False
        break


if flag:
    print('Yes')
    print(*ans,sep='\n')
else:
    print('No')