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=input()
s=map(int, raw_input().split())
cnt=dict()
for value in s:
	cnt[value]=cnt.get(value, 0)+1
special=0
one=0
for v, c in cnt.items():
	if c>=3:
		special=v
	elif c==1:
		one+=1
result=[None]*n
if one%2==1:
	if not special:
		print "NO"
		exit()
	for i in xrange(n):
		if s[i]==special:
			result[i]='B'
			break
for i in xrange(n):
	if cnt[s[i]]==1:
		one-=1
		if one%2==0:
			result[i]='A'
		else:
			result[i]='B'
	elif not result[i]:
		result[i]='A'
print "YES"
print "".join(result)