A14900 | Minimal String Xoration

You are given an integer $n$ and a string $s$ consisting of $2^n$ lowercase letters of the English alphabet. The characters of the string $s$ are $s_0s_1s_2\cdots s_{2^n-1}$ .

A string $t$ of length $2^n$ (whose characters are denoted by $t_0t_1t_2\cdots t_{2^n-1}$ ) is a xoration of $s$ if there exists an integer $j$ ( $0\le j \leq 2^n-1$ ) such that, for each $0 \leq i \leq 2^n-1$ , $t_i = s_{i \oplus j}$ (where $\oplus$ denotes the operation [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR)).

Find the lexicographically minimal xoration of $s$ .

A string $a$ is lexicographically smaller than a string $b$ if and only if one of the following holds:

- $a$ is a prefix of $b$ , but $a \ne b$ ;
- in the first position where $a$ and $b$ differ, the string $a$ has a letter that appears earlier in the alphabet than the corresponding letter in $b$ .

The first line contains a single integer $n$ ( $1 \le n \le 18$ ).

The second line contains a string $s$ consisting of $2^n$ lowercase letters of the English alphabet.

Print a single line containing the lexicographically minimal xoration of $s$ .