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 = map(int, input())
values = list(map(int, input().split()))
freq = {}

for v in values:
    if v not in freq:
        freq[v] = 0
    freq[v] += 1

single_ids = []

for v in freq:
    if freq[v] == 1:
        single_ids.append(v)

key_greater_than_2 = False
key = None

for v in freq:
    if freq[v] > 2:
        key_greater_than_2 = True
        key = v
        break

if (len(single_ids) == len(values) and len(single_ids) % 2 == 1) or (
        len(single_ids) % 2 == 1 and not key_greater_than_2):
    print('NO')
else:
    print('YES')
    mapping = {}
    unique_count = 1

    for v in freq:
        if freq[v] == 1:
            mapping[v] = 'A' if unique_count <= (len(single_ids) / 2) else 'B'
            unique_count += 1
        else:
            mapping[v] = 'A'

    answers = []
    filled = False

    for v in values:
        if v == key and len(single_ids) % 2 == 1:
            if not filled:
                answers.append('A')
                filled = True
            else:
                answers.append('B')
        else:
            answers.append(mapping[v])

    print(''.join(answers))