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())
s=list(map(int,input().split()))
c=[0]*101
for i in range(n):
  c[s[i]]+=1
cnt=0
cc=0
for i in range(n):
  if c[s[i]]==1:
    cnt+=1
  elif c[s[i]]>=3:
    cc+=1
if cnt%2==1 and cc==0:
  print("NO")
else:
  ans=[""]*n
  al=["A","B"]
  if cnt%2==0 and cc==0:
    d=0
    for i in range(n):
      if c[s[i]]==1:
        ans[i]=al[d]
        d=1-d
      else:
        ans[i]="A"
  elif cnt%2==1 and cc>=1:
    d=0
    e=-1
    for i in range(n):
      if c[s[i]]>=3:
        e=s[i]
        break
    flag=1
    for i in range(n):
      if c[s[i]]==1:
        ans[i]=al[d]
        d=1-d
      else:
        if flag and s[i]==e:
          ans[i]="B"
          flag=0
        else:
          ans[i]="A"
  else:
    d=0
    for i in range(n):
      if c[s[i]]==1:
        ans[i]=al[d]
        d=1-d
      else:
        ans[i]="A"
  print("YES")
  print("".join(ans))