Ceil Divisions

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The first and only line of each test case contains the single integer $$$n$$$ ($$$3 \le n \le 2 \cdot 10^5$$$) — the length of array $$$a$$$.

It's guaranteed that the sum of $$$n$$$ over test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, print the sequence of operations that will make $$$a$$$ as $$$n - 1$$$ ones and $$$1$$$ two in the following format: firstly, print one integer $$$m$$$ ($$$m \le n + 5$$$) — the number of operations; next print $$$m$$$ pairs of integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le n$$$; $$$x \neq y$$$) ($$$x$$$ may be greater or less than $$$y$$$) — the indices of the corresponding operation.

It can be proven that for the given constraints it's always possible to find a correct sequence of operations.

Sample Input:

2
3
4

Sample Output:

2
3 2
3 2
3
3 4
4 2
4 2

Note:

In the first test case, you have array $$$a = [1, 2, 3]$$$. For example, you can do the following:

1. choose $$$3$$$, $$$2$$$: $$$a_3 = \left\lceil \frac{a_3}{a_2} \right\rceil = 2$$$ and array $$$a = [1, 2, 2]$$$;
2. choose $$$3$$$, $$$2$$$: $$$a_3 = \left\lceil \frac{2}{2} \right\rceil = 1$$$ and array $$$a = [1, 2, 1]$$$.

You've got array with $$$2$$$ ones and $$$1$$$ two in $$$2$$$ steps.

In the second test case, $$$a = [1, 2, 3, 4]$$$. For example, you can do the following:

1. choose $$$3$$$, $$$4$$$: $$$a_3 = \left\lceil \frac{3}{4} \right\rceil = 1$$$ and array $$$a = [1, 2, 1, 4]$$$;
2. choose $$$4$$$, $$$2$$$: $$$a_4 = \left\lceil \frac{4}{2} \right\rceil = 2$$$ and array $$$a = [1, 2, 1, 2]$$$;
3. choose $$$4$$$, $$$2$$$: $$$a_4 = \left\lceil \frac{2}{2} \right\rceil = 1$$$ and array $$$a = [1, 2, 1, 1]$$$.