Bipartite Graph

In this problem, you have to construct a bipartite graph with the following properties:

1. The number of vertices in the first part is $d$.
2. The number of vertices in the second part is $d - 2$.
3. The number of edges is at most $3d$.
4. For every bipartite graph obtained by removing two vertices from the first part, there is a perfect matching.

A bipartite graph has its vertices divided into two parts so that each edge connects a vertex from the first part with a vertex from the second part. A perfect matching is a set of edges such that every vertex of the graph is an endpoint of exactly one edge in the set.

The first line contains an integer $T$, the number of test cases ($1 \le T \le 100$). Each of the next $T$ lines contains an integer $d$, the number of vertices in the corresponding test case ($3 \le d \le 100$).

For each test case, print an integer $m$, the number of edges, on its own line. Then print $m$ lines, each describing one edge as a pair of integers $u$ and $v$: the numbers of the vertices in the first and second part connected by that edge ($0 \le u < d$, $0 \le v < d - 2$).

The graph must not contain multiple edges.

You do not need to minimize the number of edges.