Encoded Strings II

题号：NC230858
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 512 M，其他语言1024 M
64bit IO Format: %lld

题目描述

Tommy has just invented an interesting string encoding algorithm, which is described below.

For every string $S$ , we may define a character-mapping function $F_S$ , which maps every character occurring in $S$ to a lowercase letter, as below

$F_S(c) = \operatorname{chr}(G(c, S))$
where $\operatorname{chr}(i)$ is the $(i+1)$ -th lowercase Latin letter, and $G(c, S)$ is the number of different characters after the last occurrence of $c$ in $S$ .

To encode a string $S$ by Tommy's algorithm, replace every character $c$ in $S$ by $F_S(c)$ simultaneously.

For example, the encoded string of "abc" is "cba", and the encoded string of "cac" is "aba".

You are given a string of length $n$ and then encode all the $2^n-1$ nonempty subsequences. Your task is to find the encoded string that has the greatest lexicographical order among all the encoded strings.

输入描述:

The first line contains an integer  .

The second line contains a string of length , which consists of only the first  lowercase letters, 'a' to 't'.

输出描述:

Output the encoded string that has the greatest lexicographical order among all the encoded strings.

示例1

输入

复制

4
aacc

输出

复制

bbaa

示例2

输入

复制

4
acac

输出

复制

bba