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 PYTHON):

Solution:
#!/usr/bin/python

R = lambda: map(int, raw_input().split())

S = 128
n = input()
a = [[] for _ in range(S)]
for i, x in enumerate(map(int, raw_input().split())):
  a[x] += i,
c, d = 0, 0
for x in range(S):
  if 1 == len(a[x]):
    c += 1
  if len(a[x]) > 2:
    d += 1
v = ['A'] * n
if c % 2:
  if d:
    print 'YES'
    d = 1
    f = 0
    for x in range(S):
      if 1 == len(a[x]):
        v[a[x][0]] = 'AB' [f]
        f = 1 - f
      elif d and len(a[x]) > 2:
        v[a[x][0]] = 'AB' [f]
        f = 1 - f
        for i in a[x][1:]:
          v[i] = 'AB' [f]
        d = 0
    print ''.join(v)
  else:
    print 'NO'
else:
  print 'YES'
  f = 0
  for x in range(S):
    if 1 == len(a[x]):
      v[a[x][0]] = 'AB' [f]
      f = 1 - f
  print ''.join(v)