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 defaultdict

n = int(input().rstrip())

s = list(map(int, input().rstrip().split(' ')))

items = defaultdict(int)

for element in s:
    items[element] += 1

noice = 0
potentialNoice = 0

for val in items.values():
    if val == 1:
        noice += 1
    elif val > 2:
        potentialNoice += 1

if noice % 2 == 0:
    print('YES')
    
    noiceA = 0

    for element in s:
        if noiceA < noice // 2:
            if items[element] == 1:
                print('A', end='')
                noiceA += 1
                continue
        print('B', end='')

elif potentialNoice:
    print('YES')

    noiceA = 0
    potentialNoiceA = 0
    for element in s:
        if noiceA < noice // 2:
            if items[element] == 1:
                print('A', end='')
                noiceA += 1
                continue
        if not potentialNoiceA:
            if items[element] > 2:
                print('A', end='')
                potentialNoiceA += 1
                continue
        print('B', end='')
        
else:
    print('NO')