CF1430C.Numbers on Whiteboard

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:

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

数字 $1, 2, 3, \dots, n$（即从 $1$ 到 $n$ 的每个整数各出现一次）被写在一块黑板上。每次操作中，你可以擦去黑板上的任意两个数 $a$ 和 $b$，并写下 $\frac{a + b}{2}$ 向上取整后的整数。

你需要恰好执行 $n - 1$ 次上述操作，使得最终留在黑板上的那个数尽可能小。

例如，当 $n = 4$ 时，以下操作过程是最优的：

1. 选择 $a = 4$ 和 $b = 2$，得到新数 $3$，此时黑板上的数为 $[1, 3, 3]$；
2. 选择 $a = 3$ 和 $b = 3$，得到新数 $3$，此时黑板上的数为 $[1, 3]$；
3. 选择 $a = 1$ 和 $b = 3$，得到新数 $2$，此时黑板上的数为 $[2]$。

显然，经过 $n - 1$ 次操作后，黑板上将仅剩一个数。你的目标是使该数最小化。

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 $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 1000$）—— 测试用例的数量。

每个测试用例仅有一行，包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$）—— 最初写在黑板上的整数个数。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

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.

对于每个测试用例，在第一行输出经过 $n - 1$ 次操作后，留在黑板上的最小可能的数。接下来的 $n - 1$ 行中，每行应包含两个整数 —— 即每次操作中所选并擦除的数 $a$ 和 $b$。