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 PYTHON3):

Solution:


n = int(input())

qtt = {}  # element quantity
dst = {}  # distribution pattern
tab = []  # elements themselves
out = ['']*n  # full distribution set

monos = [] # x1
dulis = [] # x2
polis = [] # x3+

inp = input().split(' ')
for i in range(n):
  s = inp[i]
  tab.append(s)
  if s in qtt:
    qtt[s] += 1
  else:
    qtt[s] = 1
    dst[s] = 'A'

for i in qtt:
  if qtt[i]==1:
    monos.append(i)
  elif qtt[i]==2:
    dulis.append(i)
  else:
    polis.append(i)

if len(monos)%2!=0 and len(polis)<1:
  print('NO')
else:
  #
  if len(monos)%2==0:
    prcd = 0  # proceeded element
    for i in monos:
      if prcd<len(monos)/2:
        dst[i] = 'B'
      else:
        break
      prcd += 1
    charity = False
  else:
    prcd = 0  # proceeded element
    for i in monos:
      if prcd<(len(monos)-1)/2:
        dst[i] = 'B'
      else:
        break
      prcd += 1
    for i in polis:
      charity = i
      break
  
  # AND NOW THE DISTRIBUTION FOR ALL COMPUTER GODS' SAKE!!!!!!

  for i in range(len(tab)):
    if tab[i]==charity:
      out[i] = 'B'
      charity = False
    else:
      out[i]=dst[tab[i]]

  print('YES')
  for i in out:
    print(i, end='')