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:
num = int(input())
multiset = [int(x) for x in input().split(' ')]
non_multiset = set(multiset)
help_dict = dict()

good = True
add = False
add_num = 0
count = 0
for x in non_multiset:
    if multiset.count(x) == 1:
        if good:
            help_dict[x] = 'A'
        else:
            help_dict[x] = 'B'
        good = not good
        count += 1
    if multiset.count(x) >= 3:
        add = True
        add_num = x

if count % 2 == 1:
    if add:
        first = True
        print('YES')
        res = ''
        for x in multiset:
            if multiset.count(x) == 1:
                res += help_dict[x]
            elif x == add_num and first:
                res += 'B'
                first = False
            else:
                res += 'A'
        print(res)
    else:
        print('NO')
        
else:
    print('YES')
    res = ''
    for x in multiset:
        if multiset.count(x) == 1:
            res += help_dict[x]
        else:
            res += 'A'
    print(res)