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:
input()
s = []
d = {}
unic = 0
more_2 = 0
for a in input().split():
    a = int(a)
    s.append(a)
    if a in d:
        d[a] += 1
        if d[a] == 2:
            unic -= 1
        else:
            more_2 += 1
    else:
        d[a] = 1
        unic += 1

if unic % 2 == 1 and more_2 == 0:
    print('NO')
else:
    print('YES')
    splt = unic % 2 == 1
    a_left = unic // 2
    for a in s:
        if d[a] == 1:
            if a_left > 0:
                print('A', end='')
                a_left -= 1
            else:
                print('B', end='')
        elif splt and d[a] > 2:
            print('A', end='')
            splt = False
        else:
            print('B', end='')
    print()