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:
n = int(input())
a = list(map(int, input().split()))

from collections import Counter
counter = Counter(a)

unique = set()
option = None

for k in counter:
    if counter[k] == 1:
        unique.add(k)
    elif counter[k] != 2:
        option = k

if len(unique) % 2 == 0:
    option = None

choices = "AB"
choice = 0
result = ""
used_option = False

if option or (len(unique) % 2) == 0:
    for value in a:
        if value == option:
            result += choices[1 - used_option]
            used_option = True
        elif value in unique:
            result = result + choices[choice]
            choice = (choice + 1) % 2
        else:
            result = result + "B"

    print("YES")
    print(result)
else:
    print("NO")