P16013 [ICPC 2021 NAC] AND Permutation

You are given a sequence of $n$ distinct nonnegative integers $a_1, a_2, \dots, a_n$. For the given sequence, it is guaranteed that for all nonnegative numbers $x$, if there is some $i$ such that $a_i\ \&\ x = x$, then there is a $j$ such that $a_j = x$. Here, $\&$ refers to the bitwise **AND** operator. Find a permutation $b_1, b_2, \dots, b_n$ of $a_1, a_2, \dots, a_n$ such that $b_i\ \&\ a_i = 0$ for all $i$. If there are multiple solutions, find any such permutation. It is guaranteed that a solution always exists.

The first line of input contains an integer $n$ ($1 \le n < 2^{18}$), which is the number of integers in the permutation. Each of the next $n$ lines contains an integer $a_i$ ($0 \le a_i < 2^{60}$), which is the input sequence, in order of $i$. All of the $a_i$'s are guaranteed to be distinct. For all nonnegative numbers $x$, if there is some $i$ such that $a_i\ \&\ x = x$, then there is a $j$ such that $a_j = x$.

Output $n$ lines, each containing a single integer, which are the $b_i$'s, in order of $i$.