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


def read():
    return [int(v) for v in input().split()]


def main():
    n = read()[0]
    a = read()
    c = Counter(a)
    d = [[], []]
    k = 0
    for i, v in enumerate(a):
        if c[v] == 1:
            d[k].append(i)
            k = 1 - k

    if len(d[0]) != len(d[1]):
        m = c.most_common(1)[0]
        if m[1] > 2:
            l = a.index(m[0])
            d[k].append(a.index(m[0]))
            for i in range(m[1] - 1):
                l = a.index(m[0], l + 1)
                d[1-k].append(l)
        else:
            print('NO')
            return
    print('YES')
    for i in range(n):
        if i in d[0] or not i in d[1]:
            c = 'A'
        else:
            c = 'B'
        print(c, end='')


if __name__ == '__main__':
    main()