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:
def is_unique(a):
    global multi
    return True if multi.count(a) == 1 else False

def is_semiunique(a):
    global multi
    return True if multi.count(a) > 2 else False

n = int(input())
multi = list(map(int, input().split()))
uniques = []
semi_uniques = []

for i in range(n):
    if is_unique(multi[i]):
        uniques.append(i)
    elif is_semiunique(multi[i]):
        semi_uniques.append(i)

multi_ = ['B'] * len(multi)

x = len(uniques)
        
if x % 2 == 0:
    for i in uniques[:x//2]:
        multi_[i] = 'A'
    print('YES')    
    print(''.join(multi_))

else:
    if not semi_uniques:
        print('NO')
    else:
        for i in uniques[:x//2]:
            multi_[i] = 'A'
        multi_[semi_uniques[0]] = 'A'
        print('YES')
        print(''.join(multi_))