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:
from heapq import heappush, heappop

N, A, B, C = [int(x) for x in input().split()]
S = [input() for i in range(N)]


sToIndex = {
    "AB": (0, 1),
    "AC": (0, 2),
    "BC": (1, 2),
}
heap = [(0, -min(A, B, C), (A, B, C))]
parent = {}
while heap:
    original = heappop(heap)
    negT, negMin, state = original

    if negT == -N:

        print("Yes")
        ans = []
        last = original
        while last in parent:
            nextLast = parent[last]
            diffIndex = None
            for i in range(3):
                if nextLast[2][i] + 1 == last[2][i]:
                    diffIndex = i
                    break
            ans.append("ABC"[diffIndex])
            last = nextLast
        print("\n".join(reversed(ans)))
        exit()

    index1, index2 = sToIndex[S[-negT]]

    nbr1 = list(state)
    nbr1[index1] += 1
    nbr1[index2] -= 1
    min1 = min(nbr1)
    if min1 >= 0:
        node = (negT - 1, -min1, tuple(nbr1))
        if node not in parent:
            heappush(heap, node)
            parent[node] = original

    nbr2 = list(state)
    nbr2[index1] -= 1
    nbr2[index2] += 1
    min2 = min(nbr2)
    if min2 >= 0:
        node = (negT - 1, -min2, tuple(nbr2))
        if node not in parent:
            heappush(heap, node)
            parent[node] = original

print("No")