Gomoku - Beat the First Player's Strategy

This is an interactive problem based on the game of Gomoku played on a 19×19 grid. Two players alternate placing marks on the board. The first player uses black marks and plays first, always starting at the center. The winning condition is to have five consecutive marks in a row in one of the three directions: horizontal, vertical, or diagonal.

The first player's strategy is as follows:

• For the first move, she places her mark in the center cell.
• For subsequent moves, she evaluates all possible sequences of 5 consecutive cells that could eventually form a winning line.
• If a sequence contains both players' marks or is empty, it is disregarded.
• For each sequence that contains exactly k marks for a player (with 1 ≤ k ≤ 5) and no opponent marks, the following points are added to the evaluation score:
• For the first player: add \(50^{2k-1}\).
• For the second player: subtract \(50^{2k}\) (if any are present in the sequence).
• Finally, a random integer uniformly chosen between 0 and \(50^2 - 1\) is added to the score.

In case of ties (extremely rare due to the random addition), the move with the smallest x-coordinate is selected and if still tied, the one with the smallest y-coordinate.

Your task is to write a program that plays as the second player and beats the above strategy in 100 games (with different seeds). Although the interactive protocol is not fully standardized in this description, your solution should implement an interactive approach that would allow you to output moves and eventually force a win for the second player.

Note: In our testing environment, this interactive problem is simulated by providing dummy input. Your solution is expected to compile and run without errors, though the provided sample solutions here are stubs that do not implement the full interactive logic.

inputFormat

This is an interactive problem. In a real contest, your program would interact with a judge. For the purpose of testing, the input will be provided as dummy data (possibly empty). Your program should be prepared to handle interactive input and output as described in the problem statement.

outputFormat

Output the chosen move for the second player in response to the game state. In our simulated environment, the output can be empty or a dummy response as long as it compiles and runs. In a real interactive contest, you must flush your output after each move.

sample