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
readline = sys.stdin.readline
read = sys.stdin.read
sys.setrecursionlimit(10**6)

#n = int(input())
n,*a = [int(i) for i in readline().split()]
s = read().split()

dx = {"AB":0,"BC":1,"AC":2}
ans = ["Yes"]

def dfs(i):
    if i==n:
        print(*ans,sep="\n")
        exit()
    x = dx[s[i]]
    y = (x+1)%3
    for j in [x,y]:
        if a[j]:
            ans.append("ABC"[x+y-j])
            a[j] -= 1
            a[x+y-j] += 1
            dfs(i+1)
            ans.pop()    
            a[j] += 1
            a[x+y-j] -= 1

dfs(0)
print("No")