Numbers on Whiteboard

2000ms

262144K

Description:

Numbers $$$1, 2, 3, \dots n$$$ (each integer from $$$1$$$ to $$$n$$$ once) are written on a board. In one operation you can erase any two numbers $$$a$$$ and $$$b$$$ from the board and write one integer $$$\frac{a + b}{2}$$$ rounded up instead.

You should perform the given operation $$$n - 1$$$ times and make the resulting number that will be left on the board as small as possible.

For example, if $$$n = 4$$$, the following course of action is optimal:

choose $$$a = 4$$$ and $$$b = 2$$$, so the new number is $$$3$$$, and the whiteboard contains $$$[1, 3, 3]$$$;
choose $$$a = 3$$$ and $$$b = 3$$$, so the new number is $$$3$$$, and the whiteboard contains $$$[1, 3]$$$;
choose $$$a = 1$$$ and $$$b = 3$$$, so the new number is $$$2$$$, and the whiteboard contains $$$[2]$$$.

It's easy to see that after $$$n - 1$$$ operations, there will be left only one number. Your goal is to minimize it.

Input:

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

The only line of each test case contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of integers written on the board initially.

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

Output:

For each test case, in the first line, print the minimum possible number left on the board after $$$n - 1$$$ operations. Each of the next $$$n - 1$$$ lines should contain two integers — numbers $$$a$$$ and $$$b$$$ chosen and erased in each operation.

Sample Input:

1
4

Sample Output:

Informação

Provedor Codeforces

Código CF1430C