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:


# if i is 0, it doesn't add anything - ignore
# if i is 1, it always adds 1 - choose?
# if i is = 2, it can add 1 to each or 0 to each - ignore
# if i is >2, it can add 1 or 0 - split

n = int(input())
line = input()
list = [int(s)-1 for s in line.split()]
count = [0 for i in range(0, 100)]
for x in list:
  count[x] = count[x] + 1
one = []
two = []
greater = []
first_greater = -1
for i in range(0, 100):
  c = count[i]
  if (c == 1):
    one.append(i)
  elif (c == 2):
    two.append(i)
  elif (c > 2):
    greater.append(i)
    if (first_greater == -1):
      first_greater = i
if len(one) % 2 == 0:
  print("YES")
  num = len(one)/2
  c = 0
  for i in list:
    if (count[i] == 1):
      if (c < num):
        print("A", end="")
        c = c+1
      else:
        print("B", end="")
    else:
      print("A", end="")
elif len(greater) != 0:
  print("YES")
  num = len(one)//2
  c = 0
  for i in list:
    if (count[i] == 1):
      if (c < num):
        print("A", end="")
        c = c+1
      else:
        print("B", end="")
    elif (count[i] > 2):
      if (i == first_greater):
        print("A", end="")
        first_greater = -1
      else:
        print("B", end="")
    else:
      print("B", end="")
else:
  print("NO")