Central Element#523
This is an interactive problem.
There is a permutation of numbers from to , which is unknown to you, P = \langle P_1, P_2, \dots, P_n \rangle. You can ask questions of the following type: given three distinct positions , , and , which of P_i, P_j, and P_k is central? An element is central if it is neither minimal nor maximal among the three.
For example, if the permutation is \langle 2, 1, 4, 3 \rangle and you ask about positions , , and , you receive , because is the central element of the set \{P_1, P_2, P_3\} = \{2, 1, 4\}. Note that you do not get information about which of the positions , , or it is located at.
Your task is to find the permutation . In fact, for each permutation there is a set of permutations that cannot be distinguished from using the allowed questions. You must find any permutation from this set.
The first line of the standard input contains , the size of the permutation (3 \leq n \leq 200).
Each of the next lines of the standard input contains the response to your query: the number that is central among the elements at the given positions.
First, your program must read from the standard input one line with the integer , the size of the permutation.
Then, your program should write to the standard output a line with three positions for a query, and wait for a line in the standard input with the response. Continue asking queries and reading responses in this way, until you can determine up to .
When you know the answer, output a line with the word OK and the permutation .
When asking a query, each line of the standard output should contain three different integers from to , separated by spaces. You can ask at most queries.
When you state the answer, the line of the standard output should contain the word OK and the numbers P_1, P_2, \dots, P_n, all space-separated. After printing this line, your program must exit.
You must flush the standard output after printing each line.
Example 1