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())
p=[int(x) for x in input().split()]
a=[0 for i in range(101)]
type1=[]
type2=[]
resa=[]
for i in p:
  a[i]+=1
for i in range(len(a)):
  if a[i]:
    if a[i]==1:
      type1.append(i)
    if a[i]>=3:
      type2.append(i)
if len(type1)%2==0:
  print ("YES")
  resa=type1[:len(type1)//2]
  for i in range(len(p)):
    if p[i] in resa:
      print ('A', end='')
    else:
      print ('B', end='')
  print()
else:
  if len(type2)>=1:
    print ("YES")
    resa=type1[:len(type1)//2]
    resb=[type2[0]]
    f=1
    for i in p:
      if i in resa:
        print ('A', end='')
      elif i in resb and f:
        f=0
        print ('A', end='')
      else:
        print ('B', end='')
  else:
    print ('NO')