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 = [int(x) for x in input().split()]
m = {}
for aa in a:
    if aa in m:
        m[aa] += 1
    else:
        m[aa] = 1

count = 0
trick = False
for k in m:
    if m[k] == 1:
        count += 1
    elif m[k] > 2:
        trick = True

if count % 2 == 1:
    if trick:
        count += 1
    else:
        print('NO')
        exit()
else:
    trick = False

print('YES')
count = count / 2
r = []
for aa in a:
    if m[aa] == 1:
        if count > 0:
            r.append('A')
            count -= 1
        else:
            r.append('B')
    elif m[aa] == 2:
        r.append('A')
    elif trick:
        r.append('B')
        trick = False
    else:
        r.append('A')

print(''.join(r))