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

if __name__ == '__main__':
    n = int(input())
    sarr = list(map(int, input().split()))

    dct = Counter(sarr)

    if dct.most_common(1)[0][1] == 1:
        if n % 2:
            print('NO')
        else:
            print('YES')
            print(''.join(['A' if i % 2 else 'B' for i in range(n)]))
        exit(0)

    occ = list(filter(lambda o: o[1] == 1, dct.most_common()))

    if not occ:
        print('YES')
        print(''.join(['A' for i in range(n)]))
        exit(0)

    hn = None
    ndct = {}

    if len(occ) % 2:
        cmn = dct.most_common(1)[0]
        if cmn[1] < 3:
            print('NO')
            exit(0)
        hn = cmn[0]

    for i, o in enumerate(occ):
        if i % 2:
            ndct[o[0]] = 'B'

    rez = [None for _ in range(n)]

    for i, s in enumerate(sarr):
        if s in ndct:
            rez[i] = 'B'
        else:
            rez[i] = 'A'

    if hn:
        rez[sarr.index(hn)] = 'B'

    print('YES')
    print(''.join(rez))