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())
s = list(map(int, input().split()))
# n = 12
# s = [1, 2, 3, 4, 5, 5, 6, 6, 6, 7, 9, 11]


str = [0 for i in range(n)]
count_ = [s.count(i) for i in s]
#print(count_)
    
One_occur_index = [i for i in range(n) if s.count(s[i]) == 1]
Two_occur_index = [i for i in range(n) if s.count(s[i]) == 2 ]    
many_occur_index = [i for i in range(n) if s.count(s[i]) >= 3]

if len(One_occur_index)%2 and len(many_occur_index) == 0:
    print('NO')
else:

    for i in Two_occur_index:
        str[i] = 0
    
    for i in One_occur_index[0:len(One_occur_index)//2]:
            str[i] = 1

    if len(One_occur_index)%2:       
        str[many_occur_index[0]] = 1  
    
    output = ['A' if str[i] else 'B' for i in range(n)]
    # print(s)
    print('YES')
    print(''.join(output))