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:
import sys
n = int(sys.stdin.readline())
inarr = map(int, sys.stdin.readline().split())
histDict = dict()
# histogram

for i in inarr:
  if i in histDict:
    histDict[i] += 1
  else:
    histDict[i] = 1

# check number of uniques

numUniques = histDict.values().count(1)
numTwices = histDict.values().count(2)
numThreePluses = len(histDict) - numUniques - numTwices

# if num uniques is odd and no three pluses: print no, exit

if((numUniques % 2 == 1) and numThreePluses == 0):
  print('NO')
  exit()



# if num uniques is even: split the uniques

if(numUniques % 2 == 0):
  outStr = ''
  print('YES')
  numUniquesMoved = 0
  for i in inarr:
    if (histDict[i] == 1) and numUniquesMoved < numUniques/2:
      outStr += 'B'
      numUniquesMoved += 1
    else:
      outStr += 'A'
  print(outStr)
  exit()

# if num uniques is odd and there is a three plus: split them and one threeplus 
if((numUniques % 2 == 1) and numThreePluses > 0):
  outStr = ''
  print('YES')
  numUniquesMoved = 0
  numThreePlusesMoved = 0
  for i in inarr:
    if (histDict[i] == 1) and numUniquesMoved < (numUniques - 1)/2:
      outStr += 'B'
      numUniquesMoved += 1
    elif (histDict[i] > 2 and numThreePlusesMoved == 0):
      outStr += 'B'
      numThreePlusesMoved += 1
    else:
      outStr += 'A'
  print(outStr)
  exit()