AND Permutation

You are given a sequence of $n$ distinct nonnegative integers $a\_1, a\_2, \ldots, a\_n$.

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 $b\_1, b\_2, \ldots, b\_n$ of $a\_1, a\_2, \ldots, a\_n$ 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 $i$.