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, a, b, c = map(int, input().split())
variables = [a, b, c]
alph = ["A", "B", "C"]
s = [[] for _ in range(n)]
for i in range(n):
	u, v = map(lambda x: alph.index(x) , list(input()))
	s[i] = [u, v]
# print(s)

can_do = True
ans = []
for i in range(n):
	u, v = s[i][0], s[i][1]
	if variables[u] + variables[v] == 0:
		can_do = False
	elif variables[v] == 0:
			variables[u] -= 1
			variables[v] += 1
			ans.append(alph[v])
	elif variables[u] == 0:
			variables[v] -= 1
			variables[u] += 1
			ans.append(alph[u])
	else:
		# both are > 0
		if i == n-1:
			# do whatever you want
			variables[u] -= 1
			variables[v] += 1
			ans.append(alph[v])
		else:
			# need to think about next step
			if variables[u] > 0 and variables[v] > 0:
				next_u, next_v = s[i+1][0], s[i+1][1]
				if variables[next_u] + variables[next_v] >= 2:
					# can subsctact and whatever
					if variables[u] < variables[v]:
						u, v = v, u
					variables[u] -= 1
					variables[v] += 1
					ans.append(alph[v])
				else:
					# need to sponsor
					common = list( {u, v}.intersection({next_u, next_v}) )[0]
					# print("common", common)
					not_common = u + v - common
					variables[common] += 1
					variables[not_common] -= 1
					ans.append(alph[common])

if can_do:
	print("Yes")
	for item in ans:
		print(item)
else:
	print("No")