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:
n = int(raw_input())
arr = raw_input().split()
dic = dict()

for num in arr:
	if num in dic:
		dic[num] += 1
	else:
		dic[num] = 1

one_count = []
three_count = []

for key in dic:
	if dic[key] == 1:
		one_count.append(key)
	elif dic[key] >= 3:
		three_count.append(key)

set_map = {}

one_len = len(one_count)
if one_len%2 == 0:
	print "YES"
	for num in arr:
		set_map[num] = 'A'
	for i in range(len(one_count)):
		set_map[one_count[i]] = 'A' if i%2==0 else 'B'
	out = ""
	for num in arr:
		out += set_map[num]
	print out

else:
	if len(three_count) == 0:
		print "NO"
	else:
		print "YES"
		for num in arr:
			set_map[num] = 'A'
		for i in range(len(one_count)):
			set_map[one_count[i]] = 'A' if i%2==0 else 'B'
		three_split = three_count[0]
		out = ""
		three_split_included = False
		for num in arr:
			if num==three_split:
				if three_split_included:
					out+="A"
				else:
					out+="B"
					three_split_included = True
			else:
				out+=set_map[num]
		print out