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())
numbers = list(map(int, input().split(' ')))

odd = 0
count = [0] * 101
three = 0
assign = ['A'] * (n + 1)

for number in numbers:
  count[number] += 1

  if count[number] == 1:
    odd += 1
  elif count[number] == 2:
    odd -= 1
  elif count[number] == 3 and not three:
    three = number

assignToB = False
index = 1

if odd % 2 == 0:
  for number in numbers:
    if count[number] == 1:
      if assignToB:
        assign[index] = 'B'

      assignToB = not assignToB

    index += 1
else:
  if three:
    assign[numbers.index(three) + 1] = 'B'

    for number in numbers:
      if count[number] == 1:
        if assignToB:
          assign[index] = 'B'

        assignToB = not assignToB

      index += 1

if odd & 1 and not three:
  print('NO')
else:
  print('YES')
  print(''.join(assign[1:]))