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문제

JOI Store sells N items, numbered from 0 through N − 1. The price of the item i (0 ≤ i ≤ N − 1) is Pi. The prices of any two items are different.

Anna comes to JOI Store for shopping. Among the items whose indices are between L and R, inclusive, Anna wants to buy the cheapest one. Since Anna does not know the price of each item, she will communicate with Bruno, a clerk of JOI Store, to decide which item to buy. Bruno knows the price of every item, but he does not know the values of L and R.

Anna and Bruno will use a telecommunication device to send characters. Every character they will send is 0 or 1. Anna can send at most 18 characters to Bruno, and Bruno can send at most 10 000 characters to Anna. Bruno wants to send as few characters as possible.

The values of N, L, and R will be given to Anna, and the value of N and the price of each item will be given to Bruno. Write program which implements Anna’s strategy and Bruno’s strategy so that Anna can decide which item to buy.

구현

You need to submit two files.

The first file is Anna.cpp. It should implement Anna’s strategy. It should implement the following function. The program should include Anna.h using the preprocessing directive #include.

  • void InitA(int N, int L, int R)
    For each test case, this function is called exactly once in the beginning.
    • The parameter N is the number of items N.
    • The parameters L and R mean Anna wants to buy the cheapest item among the items whose indices are between L and R, inclusive.
  • void ReceiveA(bool x)
    This function is called every time when Bruno sends a character to Anna.
    • The parameter x denotes the character sent by Bruno to Anna. Here true denotes the character 1, and false denotes the character 0.
  • int Answer()
    This function is called exactly once when all of the calls are finished. This function should return the index of the item Anna will buy.
    • The return value should be an integer between L and R, inclusive. If this condition is not satisfied, your program is judged as Wrong Answer [1]. If the return value is different from the item Anna will buy, your program is judged as Wrong Answer [2].

In this file, your program can call the following function.

  • void SendA(bool y)
    Anna can send a character to Bruno by this function.
    • The parameter y denotes the character sent by Anna to Bruno. Here true denotes the character 1, and false denotes the character 0.

The second file is Bruno.cpp. It should implement Bruno’s strategy. It should implement the following function. The program should include Bruno.h using the preprocessing directive #include.

  • void InitB(int N, std::vector P)
    For each test case, this function is called exactly once in the beginning.
    • The parameter N is the number of items N.
    • The parameter P is an array of length N. It means P[i] is the price Pi of the item i (0 ≤ i ≤ N − 1).
  • void ReceiveB(bool y)
    This function is called every time when Anna sends a character to Bruno.
    • The parameter y denotes the character sent by Anna to Bruno. Here true denotes the character 1, and false denotes the character 0

In this file, your program can call the following function.

  • void SendB(bool x)
    Bruno can send a character to Anna by this function.
    • The parameter x denotes the character sent by Bruno to Anna. Here true denotes the character 1, and false denotes the character 0

You can assume the program will be executed as follows. For each test case, two queues are prepared: QY for characters sent by Anna and QX for characters sent by Bruno. In the beginning, the functions InitA and InitB are called and characters sent by these functions are pushed to the corresponding queues. Then we will repeat the following processes.

  • If either QX or QY is non-empty, we pop a character from it, and call the corresponding function ReceiveA or ReceiveB. If both QX and QY are non-empty, it is not determined which of ReceiveA or ReceiveB will be called.
  • Whenever SendA is called during executions of ReceiveA, the sent character is pushed to QY.
  • Whenever SendB is called during executions of ReceiveB, the sent character is pushed to QX.
  • If both of the queues are empty, Answer is called, and the program will be terminated.

Anna should not send more than 18 characters to Bruno. If it exceeds, your program is judged as Wrong Answer [3]. Bruno should not send more than 10 000 characters to Anna. If it exceeds, your program is judged as Wrong Answer [4].

입력

The sample grader reads the following data from the standard input.

N L R
P0 P1 · · · PN−1

출력

When the program terminates successfully, the sample grader writes the following information to the standard output (quotes for clarity).

  • If the answer is correct, it writes the total number Y of characters sent from Anna to Bruno and the total number X of characters sent from Bruno to Anna as “Accepted: Y X”.
  • If your program is judged as Wrong Answer, it writes its type as “Wrong Answer [1]”.
  • If your program is judged as several types of Wrong Answer, the sample grader reports only one of them.

제한

  • 1 ≤ N ≤ 1 000 000.
  • 0 ≤ L ≤ R ≤ N − 1.
  • 1 ≤ Pi ≤ N (0 ≤ i ≤ N − 1).
  • Pi ≠ Pj (0 ≤ i < j ≤ N − 1).

서브태스크 1 (1점)

N ≤ 1 000.

서브태스크 2 (9점)

N ≤ 10 000.

서브태스크 3 (90점)

No additional constraints.

  • Let T be the maximum of the number of characters sent from Bruno to Anna for every test case of this Subtask.
  • Your score of this Subtask is calculated as follows.
    • If 5 000 < T ≤ 10 000, your score is ⌊25 × (10000 − T) / 5000⌋points.
    • If 1 000 < T ≤ 5 000, your score is 25 + ⌊40 × (5000 − T) / 4000⌋ points.
      If 300 < T ≤ 1 000, your score is 65 + ⌊25 × (1000 − T) / 700⌋ points.
      If T ≤ 300, your score is 90 points.

Here ⌊x⌋ is the largest integer not exceeding x.

예제

Here is a sample input for the sample grader and corresponding function calls.

Sample Input 1 Sample Function Calls
Call Call Return
4 0 2
3 1 4 2
InitA(4, 0, 2)    
  SendA(true)  
  SendA(false)  
InitB(4, {3, 1, 4, 2})    
ReceiveB(true)    
  SendB(true)  
ReceiveA(true)    
ReceiveB(false)    
Answer()   1

제출할 수 있는 언어

C++17, C++14, C++20, C++14 (Clang), C++17 (Clang), C++20 (Clang)

채점 및 기타 정보

  • 예제는 채점하지 않는다.