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Time Limit: 1 second
Memory Limit: 256 MB
Overview
This is an INTERACTIVE PROBLEM. There are N kinds of minerals. For each kind there are exactly 2 slices, for a total of 2N slices numbered 1..2N. The judge fixes a hidden pairing: for each kind, the two slices of that kind form one pair. Your task is to determine all N pairs.
You have access to a device. You may insert or extract slices from the device one at a time. After each operation, you learn how many DISTINCT kinds of minerals are currently present among the slices inside the device.
Goal
Determine all N pairs while MINIMIZING the number of queries you use. You may use at most 1,000,000 queries. Any correct solution using β€ 1,000,000 queries is accepted; fewer queries are considered better.
Interaction Protocol (standard input/output)
1) At the start, the judge outputs a single integer:
N
β’ 1 β€ N β€ 43,000.
2) You may then repeatedly perform queries. To toggle the presence of slice x in the device:
β’ Output a line: ? x
where 1 β€ x β€ 2N
β’ Flush stdout.
β’ Read a single integer r from stdin.
r is the number of DISTINCT kinds currently present among all slices inside the device after this toggle:
β If x was not in the device, it is now inserted.
β If x was already in the device, it is extracted.
β r counts how many mineral kinds appear at least once among the slices currently in the device.
3) When you have determined a pair (a, b), output exactly one line:
β’ Output: ! a b
where 1 β€ a β€ 2N and 1 β€ b β€ 2N.
Over the entire run you must output exactly N such lines, and together they must use each index 1..2N exactly once.
4) Order is flexible:
β’ You may interleave β? xβ queries and β! a bβ answers in any order.
β’ The judge terminates the interaction immediately after reading the N-th valid β! a bβ line. Do not send any further output after that point.
Important Rules and Constraints
β’ Only print lines of the form β? xβ and β! a bβ.
β’ Indices in queries and answers must satisfy their ranges.
β’ Exactly N answer lines must be printed and together cover each index 1..2N exactly once.
β’ A βqueryβ is defined as one printed line β? xβ. You may perform at most 1,000,000 queries.
β’ Flush stdout after every line you print (interactive).
β’ If you violate the protocol (bad format, invalid index, wrong pairings, too many queries, wrong number of answers), the judge will return a Wrong Answer verdict with a message.
Device Behavior (for clarity)
β’ The device maintains a set S of slices currently inside.
β’ Query β? xβ toggles membership of x in S:
β If x β S, insert x.
β Else (x β S), remove x.
β’ The judge replies with r = number of DISTINCT mineral kinds represented by S. If S is empty, r = 0.
Scoring / Ratio (informative)
β’ Let Q be your total number of β? xβ queries.
β’ The judge also knows an optimal_queries value for the instance.
β’ Your ratio is (1,000,000 β Q) / (1,000,000 β optimal_queries).
β’ The judge reports this ratio and scores only on Accepted submissions.
Sample Communication
Judge β program:
4
Program β judge:
? 1
Judge β program:
1
Program β judge:
? 2
Judge β program:
2
Program β judge:
? 5
Judge β program:
2
Program β judge:
? 2
Judge β program:
1
Program β judge:
! 3 4
Program β judge:
! 5 1
Program β judge:
! 8 7
Program β judge:
! 2 6
(Here, the program used 4 queries total.)
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