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:
def printf(strs):
  print(strs, end='')

def get_data(ls):
  power = 0
  data = {}
  more_than_two = False
  for i in ls:
    if(i not in data):
      data[i] = 1
      power += 1
    else:
      if(data[i]<2):
        power -= 1
      data[i] += 1
      if(data[i]>2):
        more_than_two = True

  return {'power':power, 'data':data, 'more_than_two':more_than_two}

n = int(input())
lst = list(map(int, input().split()))

prev_group = 'A'
prev_inc = 'A'

power = get_data(lst)['power']
data = get_data(lst)['data']

if(power%2 == 1 and not get_data(lst)['more_than_two']):
  print('NO')
else:
  print('YES')
  for i in range(n):
    if(data[lst[i]] == 1):
      if(prev_inc == 'A'):
        prev_inc = 'B'
      else:
        prev_inc = 'A'
      printf(prev_inc)
    elif(data[lst[i]] > 2 and power%2==1):
      prev_group = prev_inc
      if(prev_inc == 'A'):
        prev_inc = 'B'
      else:
        prev_inc = 'A'
      printf(prev_inc)
      power += 1
      continue
    else:
      printf(prev_group)