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 $$k \leq 31$$.