Numbers on Whiteboard

题意翻译

$T$ 次询问，对于每一次询问： 给定 $n$ 个数，为 $1,2,3,...,n$，每次可以选择两个数 $a,b$ 并删除，然后把 $\left\lceil\frac{a+b}{2}\right\rceil$ 加入到这些数中。最小化最后剩下的一个数，输出这个数并且输出构造方案。 $2\leq n\leq 2\cdot10^5,\sum n \leq 2\cdot10^5$

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

1
4

输出样例 #1

2
2 4
3 3
3 1