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:
from collections import Counter

n = int(input())
numbers = [i for i in input().split()]

dict = Counter(numbers)
count = 0

for key, value in dict.items():
    if value == 1:
        count += 1

if not count:
    print('YES')
    print('B' * n)
else:
    if count % 2 == 0:
        print('YES')
        uniqe = [key for key, value in dict.items() if value == 1]
        len_uq_A = len(uniqe) // 2
        res_string = ''
        for i in numbers:
            if i in uniqe and len_uq_A > 0:
                res_string += 'A'
                len_uq_A -= 1
            else:
                res_string += 'B'
        print(res_string)
    else:
        ok = False
        super_num = None
        for key, value in dict.items():
            if value >= 3:
                ok = True
                super_num = key
                break
        if ok:
            print('YES')
            uniqe = [key for key, value in dict.items() if value == 1]
            len_uq_A = len(uniqe) // 2 + 1
            res_string = ''
            for i in numbers:
                if i in uniqe and len_uq_A > 0:
                    res_string += 'A'
                    len_uq_A -= 1
                    if i == super_num:
                        del uniqe[-1]
                else:
                    res_string += 'B'
            index = numbers.index(super_num)
            res_string = res_string.replace('A', 'B', 1)
            res_string = res_string[:index] + 'A' + res_string[index + 1:]
            print(res_string)
        else:
            print('NO')