# Problem N

Bitwise Independent Divisors

Given an integer $n$, find the largest subset of its divisors such that for any two distinct elements $x$, $y$ in the subset, $x \& y = 0$, where $\& $ represents the bitwise AND operation.

## Input

The first line of the input contains a single integer $t$ ($1 \le t \le 10^4$) —the number of test cases. The description of the test cases follows.

Each test case consists of a single line with an integer $n$ ($1 \le n \le 10^9$), as described above.

## Output

The first line of output for each test case should contain a single integer $k$ —the maximum size of such a subset of divisors of $n$.

The second line of output for each test case should contain $k$ distinct divisors of $n$ —one subset of size $k$ satisfying the necessary constraints.

If there are multiple solutions, print any.

Sample Input 1 | Sample Output 1 |
---|---|

6 1 10 11 36 54 35360 |
1 1 2 2 5 1 11 3 1 12 18 2 6 9 6 2 65 136 260 544 1040 |