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()))

non_good_numbers = []
raw_numbers = []
for i in s:
    count = s.count(i)
    if count == 1:
        raw_numbers.append(i)
    elif count > 2:
        non_good_numbers.append(i)
if (len(raw_numbers) % 2) == 1 and (len(non_good_numbers) == 0):
    print('NO')
else:
    if (len(raw_numbers) % 2) == 1:
        use_non_good_number = non_good_numbers[0]
    else:
        use_non_good_number = None
    is_non_good_used = False
    res = []
    number_flag = 'A'
    for i in s:
        if i == use_non_good_number:
            if not is_non_good_used:
                res.append('B')
                is_non_good_used = True
            else:
                res.append('A')
        else:
            if i in raw_numbers:
                res.append(number_flag)
                number_flag = 'B' if number_flag == 'A' else 'A'
            else:
                res.append('A')

    print('YES')
    print(''.join(res))