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:
import sys
from array import array  # noqa: F401
from collections import Counter


def readline() -> str: return sys.stdin.buffer.readline().decode('utf-8')


n = int(readline())
a = list(map(int, readline().split()))
cnt = Counter(a)
ans = ['A']*n
nice_a, nice_b = 0, 0
dic = dict()

for i, x in enumerate(a):
    if cnt[x] == 1:
        if nice_a == nice_b:
            nice_a += 1
            ans[i] = 'A'
        else:
            nice_b += 1
            ans[i] = 'B'
    elif cnt[x] > 2:
        if x not in dic:
            dic[x] = []
        dic[x].append(i)

for i, x in enumerate(a):
    if cnt[x] == 2:
        cnt[x] = -2
    elif cnt[x] == -2:
        ans[i] = 'B'

for i, key in zip(range(len(dic.keys())-1, -1, -1), dic.keys()):
    if i == 0 and nice_a == nice_b:
        break
    if nice_a == nice_b:
        for j in dic[key][1:]:
            ans[j] = 'B'
        nice_a += 1
    else:
        ans[dic[key][0]] = 'B'
        nice_b += 1

if nice_a != nice_b:
    print('NO')
else:
    print('YES')
    print(*ans, sep='')