Problem: Vasya has a multiset s consisting of n integer numbers. Vasya calls some number x nice if it appears in the multiset exactly once. For example, multiset \{1, 1, 2, 3, 3, 3, 4\} contains nice numbers 2 and 4.

Vasya wants to split multiset s into two multisets a and b (one of which may be empty) in such a way that the quantity of nice numbers in multiset a would be the same as the quantity of nice numbers in multiset b (the quantity of numbers to appear exactly once in multiset a and the quantity of numbers to appear exactly once in multiset b).

Input

The first line contains a single integer n~(2 ≤ n ≤ 100).

The second line contains n integers s_1, s_2, ... s_n~(1 ≤ s_i ≤ 100) — the multiset s.

Output

If there exists no split of s to satisfy the given requirements, then print "NO" in the first line.

Otherwise print "YES" in the first line.

The second line should contain a string, consisting of n characters. i-th character should be equal to 'A' if the i-th element of multiset s goes to multiset a and 'B' if if the i-th element of multiset s goes to multiset b. Elements are numbered from 1 to n in the order they are given in the input.

If there exist multiple solutions, then print any of them.

Examples

Input

4
3 5 7 1


Output

YES
BABA


Input

3
3 5 1


Output

NO

Solution (in PYTHON):

Solution:
#coding:utf-8
n = int(raw_input())
line = raw_input().split()
data = {}
for i in line:
	if i in data:
		data[i] += 1
	else:
		data[i] = 1
# print(data)
good = 0 #1
bad = 0 #2
other = 0 # > 2

for i in line:
	if data[i] == 1:
		good += 1
	elif data[i] == 2:
		bad += 1
	else:
		other += 1

# print(good,bad,other)
out = []
flag = "YES"
h = 1
if good % 2 == 0: #1平均分，其他给B
	for i in range(n):
		num = line[i]
		if data[num] == 1:
			if h == 1:
				out.append("B")
				h *= -1 
			else:
				out.append("A")
				h *= -1
		else:
			out.append("B")
else:
	tmp = 0
	if other > 0:
		for i in line:
			if data[i] == 1:
				if h == 1:
					out.append("B")
					h *= -1 
				else:
					out.append("A")
					h *= -1 
			elif data[i] == 2:
				out.append("B")
			else:
				if tmp == 0:
					out.append("A")
					tmp +=1
				else:
					out.append("B")
	else:
		flag = "NO"

print(flag)
# print(out)
if flag == "YES":
	print("".join(out))