CF1129E.Legendary Tree

This is an interactive problem.

A legendary tree rests deep in the forest. Legend has it that individuals who realize this tree would eternally become a Legendary Grandmaster.

To help you determine the tree, Mikaela the Goddess has revealed to you that the tree contains $n$ vertices, enumerated from $1$ through $n$. She also allows you to ask her some questions as follows. For each question, you should tell Mikaela some two disjoint non-empty sets of vertices $S$ and $T$, along with any vertex $v$ that you like. Then, Mikaela will count and give you the number of pairs of vertices $(s, t)$ where $s \in S$ and $t \in T$ such that the simple path from $s$ to $t$ contains $v$.

Mikaela the Goddess is busy and will be available to answer at most $11\,111$ questions.

This is your only chance. Your task is to determine the tree and report its edges.

这是一个交互式问题。

一棵传说中的树深藏于森林之中。传说，凡能识得此树者，将永为“传奇大师”。

为助你确定这棵树，女神米凯拉向你揭示：该树包含 $n$ 个顶点，编号为 $1$ 至 $n$。她还允许你向她提出若干问题，形式如下：对每个问题，你需向米凯拉指定两个互不相交的非空顶点集合 $S$ 和 $T$，以及任一顶点 $v$；随后，米凯拉将统计并告诉你满足以下条件的顶点对 $(s, t)$ 的数量：其中 $s \in S$、$t \in T$，且从 $s$ 到 $t$ 的简单路径经过顶点 $v$。

女神米凯拉事务繁忙，最多只愿回答 $11\,111$ 个问题。

这是你唯一的机会。你的任务是确定该树的结构，并报告其所有边。

The first line contains an integer $n$ ($2 \leq n \leq 500$) — the number of vertices in the tree.

第一行包含一个整数 $n$（$2 \leq n \leq 500$）——树中顶点的数量。

When program has realized the tree and is ready to report the edges, print "ANSWER" in a separate line. Make sure that all letters are capitalized.

Then, print $n-1$ lines, each containing two space-separated integers, denoting the vertices that are the endpoints of a certain edge. Each edge should be reported exactly once. Your program should then immediately terminate.

当程序已构建好树并准备报告边时，请在单独一行中输出 “ANSWER”。请确保所有字母均为大写。

然后，输出 $n-1$ 行，每行包含两个以空格分隔的整数，表示某条边的两个端点顶点。每条边必须且仅能报告一次。此后，您的程序应立即终止。

In the sample, the tree is as follows.

$n = 5$ is given to the program. The program then asks Mikaela a question where $S = {1, 2, 3}$, $T = {4, 5}$, and $v = 2$, to which she replies with $5$ (the pairs $(s, t)$ are $(1, 4)$, $(1, 5)$, $(2, 4)$, $(2, 5)$, and $(3, 5)$).

在样例中，树的结构如下所示。

程序输入 $n = 5$。随后，程序向米凯拉提出一个问题：其中 $S = \{1, 2, 3\}$，$T = \{4, 5\}$，且 $v = 2$；她回答 $5$（满足条件的点对 $(s, t)$ 为 $(1, 4)$、$(1, 5)$、$(2, 4)$、$(2, 5)$ 和 $(3, 5)$）。