Today, you need to solve a problem on a Puzzled Grid game. "In a grid of $$n \times n$$ size, where each cell has a positive integer, two players compete in several rounds.
Each round starts by both players putting a rock in a random location of the grid. Then, the two players must connect the two rocks with a line that passes through the grid cells (e.g: from a grid cell the line can can expand either horizontally or vertically and never out the grid). Since there may be a lot of ways to connect the two stones, we are only interested in those lines that minimizes the highest cell in their path (e.g: the cell with the highest number should be as small as possible).
You need to find and print this minimized maximum. Can you do it?
First line contains two integers $$n$$ and $$Q$$, where $$n$$ is the grid size and $$Q$$ is the number of rounds of the game. Next $$n$$ lines contain each $$n$$ integer denoting the grid cell numbers. Then, next $$Q$$ lines contain each $$4$$ integers $$x1, y1, x2, y2$$ denoting the first and second stone locations -- the indexes are 0 based and the origin is the top leftmost cell.
Print $$Q$$ lines, each denoting the answer for each round.
Left grid shows the optimal solution for the first round, and the right one is for the second round.