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()]
res = ['A']*n
cnt = [0]*101
for i in a:
    cnt[i] += 1
good_num = cnt.count(1)
bad_above_2 = False
for i in range(101):
    if cnt[i] > 2:
        bad_above_2 = True
        break
        
if good_num%2 == 0 or bad_above_2 > 0:
    print('YES')
    to_b = False

    for i in range(n):
        if cnt[a[i]] == 1:
            if to_b:
                res[i] = 'B'
            to_b = not to_b
            
    if good_num%2 != 0:
        for i in range(n):
            if cnt[a[i]] > 2:
                res[i] = 'B'
                break
    print(''.join(res))
else:
    print('NO')