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
from collections import defaultdict as di
range = xrange
input = raw_input

n = int(input())

A = [int(x) for x in input().split()]

count = di(int)
for x in A:
    count[x]+=1

single = [x for x in count if count[x]==1]
extra = [x for x in count if count[x]>=3]


L = []
#R = []
Lscore = 0
Rscore = 0
for x in single:
    if Lscore < Rscore:
        Lscore += 1
        L.append(x)
    else:
        Rscore += 1
        #R.append(x)

for x in extra:
    if Lscore<Rscore:
        Lscore += 1
        L.append(x)
        
#       for _ in range(count[x]-1):
#            R.append(x)
    elif Lscore>Rscore:
        
        Rscore += 1
#       R.append(x)
            
        for _ in range(count[x]-1):
            L.append(x)
if Lscore!=Rscore:
    print 'NO'
else:
    print 'YES'


    Lcount = di(int)
    for l in L:
        Lcount[l]+=1

    out = []
    for x in A:
        if Lcount[x]>0:
            out.append('A')
            Lcount[x]-=1
        else:
            out.append('B')
    print ''.join(out)