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()))
z = ['A'] * len(a)
d = {}
for i in a:
    if i in d.keys():
        d[i] += 1
    else:
        d[i] = 1
ka , kb = 0, 0
for i, x in enumerate(a):
    if d[x] == 1:
        if ka > kb :
            z[i] = 'B'
            kb += 1
        else:
            z[i] = 'A'
            ka += 1
if ka > kb :
    for i , x in enumerate(a):
        if d[x] > 2 :
            z[i] = 'B'
            kb += 1
            break
if ka == kb :
    print('YES')
    print(''.join(z))
else:
    print('NO')