You are given an integer $N$. To solve the problem, you must find the minimum number of elements that must be removed from the set $S = \lbrace 1, 2, ..., N \rbrace$ such that the bitwise XOR of the remaining elements is $0$.

Input format

• The first line contains an integer $t (1 \leq t \leq 10^5)$ representing the number of test cases.
• The first and only line of each test case contains an integer $N (1 \leq N \leq 10^9)$ representing the number presented to you.

Output format

For each test case, print a single line.

The first integer $k$ represents the minimum number of elements and you must remove from $S$. Then, $k$ space-separated integers $a_1, a_2, ..., a_k$ follows representing the elements that you have to remove from $S$.

If there are multiple possible solutions, output the lexicographically largest one. A solution $a_1, a_2, ..., a_k$ is lexicographically larger than solution $b_1, b_2, ..., b_k$, if $a_i > b_i$ where $i$ is the smallest index where $a_i \neq b_i$. 

It can be proved that in an optimal solution $k \leq 31$.