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())
l = list(map(int, input().split()))

d = {}

for i in l:
  try:
    d[i] += 1
  except KeyError:
    d[i] = 1


nice = 0
gt2elem = -1



for i in d.keys():
    if d[i]==1:
      nice += 1
    elif d[i] > 2:
      gt2elem = i

#print(gt2elem)
if nice%2 == 0 or gt2elem != -1:
  x = 0
  ans = []
  for i in l:
    if d[i] == 1:
      ans.append('AB'[x])
      x = 1 - x
    elif nice%2 == 1 and i == gt2elem:
      ans.append('B')
      gt2elem = -1
    else:
      ans.append('A')
  print('YES')
  print(''.join(ans))
else:
  print('NO')