Description:
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.
Input Format:
The first line contains an integer $$$n$$$ ($$$2 \leq n \leq 500$$$) — the number of vertices in the tree.
Output Format:
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.
Note:
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 $$$(3, 5)$$$).