Problem A
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 $a_i\mathrm{\&}x=x$, then there is a $j$ such that $a_j=x$. Here, $\mathrm{\&}$ 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 $b_i\mathrm{\&}{a}_i=0$ for all $i$. If there are multiple solutions, find any such permutation. It is guaranteed that a solution always exists.

Input

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 $a_i\mathrm{\&}x=x$, then there is a $j$ such that $a_j=x$.

Output

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

6
0
1
4
5
2
6

4
6
0
2
5
1