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 *
from sys import *


def arr_inp():
    return [int(x) for x in stdin.readline().split()]


def flip(x):
    if x == 'A':
        return 'B'
    else:
        return 'A'


n, a = int(input()), arr_inp()
c = Counter(a)
ones, l, c_sort = list(c.values()).count(1), len(c), OrderedDict(reversed(c.most_common()))

if ones % 2 == 0:
    flag = 'A'
    print('YES')
    for i in a:
        if c[i] > 1:
            print('A', end='')
        else:
            print(flag, end='')
            flag = flip(flag)
else:
    if l > ones and max(c.values()) > 2:
        flag, flag2 = 'A', 0
        for i, j in c_sort.items():
            if c_sort[i] == 1:
                c_sort[i] = flag
                flag = flip(flag)
            elif c_sort[i] == 2:
                c_sort[i] = flag
            elif c_sort[i] >= 3:
                if flag2:
                    c_sort[i] = flag
                else:
                    flag2, c_sort[i] = 1, [flag, flip(flag)]
                    flag = flip(flag)
        # print(c_sort)

        flag=0
        print('YES')
        for i in a:
            if c_sort[i] in ['A', 'B']:
                print(c_sort[i], end='')
            elif flag:
                print(c_sort[i][1], end='')
            else:
                flag = 1
                print(c_sort[i][0], end='')

    else:
        print('NO')