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:
from collections import Counter
n=int(raw_input())
A=map(int,raw_input().split())
count=Counter(A)
new={}
new[1]=[]
for key in count.keys():
	if count[key] in new.keys():
		new[count[key]].append(key)
	else:
		new[count[key]]=[key]
# print new
s=''
if len(new[1])%2==0:
	print 'YES'
	flag=True
	for i in A:
		if i in new[1]:
			if flag:
				s+='A'
				flag=False
			else:
				s+='B'
				flag=True
		else:
			s+='B'
	print s
else:
	if (len(new.keys())==1) or (2 in new.keys() and len(new.keys())==2):
		print 'NO'
	else:
		print 'YES'
		for i in new.keys():
			if i!=1 and i!=2:
				element=new[i][0]
				break
		count=0
		limit=(len(new[1])/2)+1
		flag=True
		for i in A:
			if i in new[1]:
				if count<limit:
					s+='A'
				else:
					s+='B'
				count+=1
			elif i==element:
				if flag:
					s+='B'
					flag=False
				else:
					s+='A'
			else:
				s+='B'

		print s