Virus Removal

There are $N$ regions arranged in a circle, numbered from $1$ to $N$. Regions $i$ and $i+1$ are adjacent ($1 \leq i < N$), and regions $N$ and $1$ are adjacent. Initially, every region is infected with a virus.

At noon each day, choose exactly three distinct regions and remove the virus from them. You may choose regions that are already uninfected.

At midnight each day, the virus spreads simultaneously to adjacent regions. A region is infected immediately after midnight if it or at least one of its neighbors was infected immediately before midnight. Newly infected regions do not spread the virus again during the same midnight step.

Find any way to remove the virus from all regions within $N$ days. You do not need to minimize the number of days.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, output the following.

First, print the number of days $X$ ($1 \leq X \leq N$).

On the $d$-th of the next $X$ lines, print three distinct region numbers $$ (), separated by spaces. These are the regions to clean at noon on day .

• $1 \leq T \leq 1\,000$.
• $3 \leq N \leq 5\,000$.
• The sum of $N$ over all test cases in one input file is at most .