CF1051C Vasya and Multisets

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 first line contains a single integer $ n~(2 \le n \le 100) $ . The second line contains $ n $ integers $ s_1, s_2, \dots s_n~(1 \le s_i \le 100) $ — the multiset $ s $ .

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.