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:
#####################################   
import atexit, io, sys, collections, math, heapq,fractions
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   

##################################### 

n = int(raw_input())
ais = map(int, raw_input().split())#3 5 7 1
cc = collections.Counter(ais)
def check(ais,cc):
	aa = 0
	bb = 0
	for k in cc:
		if cc[k] == 1: aa += 1
		if cc[k] > 2: bb += 1
	return aa %2 == 0 or bb >= 1

def build(ais, cc):
	
	r = []
	for k in cc:
		if cc[k] == 1:
			r.append(k)
	
	if len(r) == 0:
		return 'A' * len(ais)
	key = -1
	if len(r) % 2:
		for k in cc:
			if cc[k] > 2:
				key = k
				r.append(key)
				break

	color = {}
	for i in range(len(r)//2):
		color[r[i]] = 'A'
	for i in range(len(r)//2, len(r)):
		if r[i] == key:
			color[r[i]] = 'A'
		else:
			color[r[i]] = 'B'

	rr = [(color[ai] if ai in color else 'A') for ai in ais]
	if key != -1:
		for i in range(len(ais)):
			if ais[i] == key:
				rr[i] = 'B'
				break
	return ''.join(rr)
	
	

if check(ais,cc):
	print 'YES'
	print build(ais, cc)
else:
	print 'NO'