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 itertools

n = int(input())
s = list(map(int,input().split()))

if s==[s[0]]*n:
    print('YES')
    print('A'*n)
    exit()

three = 0
check = 0
for k,v in itertools.groupby(sorted(s)):
    vv = len(list(v))
    if vv==1:
        check += 1
    elif vv>=3:
        three += 1
if check%2==1 and three==0:
    print('NO')
    exit()

res = ''
flag = {}
index = 1
for k,v in itertools.groupby(sorted(s)):
    if len(list(v))==1:
        if index*2<=check:
            flag[k] = -1
        else:
            flag[k] = 1
        index += 1
for k,v in itertools.groupby(sorted(s)):
    if len(list(v))>=3:
        if check%2==1:
            flag[k] = -1
            check += 1
        else:
            flag[k] = 2

for num in s:
    for k,v in itertools.groupby(sorted(s)):
        if k==num and (len(list(v)) not in (0,2)):
            if flag[k]==-1:
                flag[k] = -2
                res += 'A'
            elif flag[k]==1:
                flag[k] = 2
                res += 'B'
            elif flag[k]==-2:
                res += 'B'
            else:
                res += 'A'
            break
    else:
        res += 'A'

print('YES')
print(res)