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())
s = [int(i) for i in input().split(" ")]
from collections import Counter

def find_goods(s):
    c = Counter(s)
    good = set()
    for n in c:
        if c[n] == 1:
            good.add(n)
    return good, c

goods, counter = find_goods(s)
def has_cris(counter):
    for n in counter:
        if counter[n] > 2:
            return n
    return -1

if len(goods) % 2 == 1:
    chris = has_cris(counter)
    if chris == -1:
        print("NO")
    else:
        print("YES")
        chet = True
        res = []
        for n in s:
            if n in goods:
                if chet:
                    res.append('A')
                else:
                    res.append('B')
                chet = not chet
            else:
                if n == chris:
                    res.append('B')
                    chris = -1.1
                else:
                    res.append('A')
        print("".join(res))

else:
    print("YES")
    chet = True
    res = []
    for n in s:
        if n in goods:
            if chet:
                res.append('A')
            else:
                res.append('B')
            chet = not chet
        else:
            res.append('B')
    print("".join(res))