D. Guess the Permutationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis is an interactive problem.Jury initially had a sequence a of length n, such that a_i = i.The jury chose three integers i, j, k, such that 1 \leq i < j < k \leq n, j - i > 1. After that, Jury reversed subsegments [i, j - 1] and [j, k] of the sequence a.Reversing a subsegment [l, r] of the sequence a means reversing the order of elements a_l, a_{l+1}, \ldots, a_r in the sequence, i. e. a_l is swapped with a_r, a_{l+1} is swapped with a_{r-1}, etc.You are given the number n and you should find i, j, k after asking some questions.In one question you can choose two integers l and r (1 \leq l \leq r \leq n) and ask the number of inversions on the subsegment [l, r] of the sequence a. You will be given the number of pairs (i, j) such that l \leq i < j \leq r, and a_i > a_j.Find the chosen numbers i, j, k after at most 40 questions.The numbers i, j, and k are fixed before the start of your program and do not depend on your queries.InputEach test consists of multiple test cases. The first line contains a single integer t (1 \leq t \leq 100) — the number of test cases. Description of the test cases follows.The single line of each test case contains a single integer n (4 \leq n \leq 10^9). After reading it you should start an interaction process by asking questions for that test case. After giving an answer you should:  Terminate your program if that is the last test case.  Proceed to the next test case otherwise. InteractionTo ask number of inversions on a subsegment [l, r], print "? l r", where (1 \leq l \leq r \leq n). You can ask at most 40 questions in each test case. As a result you should read a single integer x.  If x = -1, your program made an invalid question or you exceeded the number of questions for that test case. Your program should terminate immediately (otherwise it can get any verdict instead of "Wrong Answer").  Otherwise x is equal to the number of inversions on the subsegment [l, r] of the sequence a. To give the answer, print "! i j k", where i, j, k are the numbers you found. You should continue solving the next test cases or terminate the program after that.After printing a question or an answer do not forget to print the end of line and flush the output. Otherwise, you will get an "Idleness limit exceeded" verdict. To do this, use: fflush(stdout) or cout.flush() in C++; System.out.flush() in Java; flush(output) in Pascal; stdout.flush() in Python; See the documentation for other languages.HacksTo make a hack, use the following format:The first line contains a single integer t (1 \leq t \leq 100) — the number of test cases.Each of the next t lines contains four integers n, i, j, k (4 \leq n \leq 10^9, 1 \leq i < j < k \leq n, j - i > 1).ExampleInput
2 
5 

4 

3 

3 

5 

2 

2 

1 Output


? 1 5

? 2 5

? 3 5

! 1 3 5

? 1 5

? 2 5

? 3 5

! 2 4 5NoteIn the first test case, i = 1, j = 3, k = 5, so the sequence a is [2, 1, 5, 4, 3].In the second test case, i = 2, j = 4, k = 5, so the sequence a is [1, 3, 2, 5, 4].
2 
5 

4 

3 

3 

5 

2 

2 

1 
  ? 1 5  ? 2 5  ? 3 5  ! 1 3 5  ? 1 5  ? 2 5  ? 3 5  ! 2 4 5
['binary search', 'combinatorics', 'interactive', 'math', '*2000']