逆向 ㄷㄷㄷㅈ - Problema

#18703. 逆向 ㄷㄷㄷㅈ

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AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

UCPC 出题组在制作 D 题：ㄷㄷㄷㅈ 的数据时，发现构造节点较多的 DUDUDUNGA-树非常困难。给定 $N$，请编写一个程序，输出一个拥有 $N$ 个节点的 DUDUDUNGA-树。

输入格式

第一行给定树的节点数 $N$。($6 \le N \le 300\,000$)

输出格式

输出 $N-1$ 行，每行包含两个由空格分隔的整数，表示一条边的两个端点。节点编号必须是 $1$ 到 $N$ 之间的整数。

样例

样例输入 1

样例输出 1

说明

DUDUDUNGA-树的定义请参考 D 题：ㄷㄷㄷㅈ。对于输入的 $N$，总是存在一个拥有 $N$ 个节点的 DUDUDUNGA-树。

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