P7186 [CRCI2008-2009] TABLICA

Xiao Q has an $N \times N$ table. If $N = 4$, then he fills $1$ into the cell in row $1$, column $1$, $2$ into row $1$, column $2$, $\cdots$, $5$ into row $2$, column $1$, $\cdots$, $15$ into row $4$, column $3$, and $16$ into row $4$, column $4$. Now, Xiao Q performs the following operations on the table: 1. Shift a row: shift all cells in a row to the right, so that the number in the last column moves to the first column. 2. Shift a column: shift all cells in a column downward, so that the number in the last row moves to the first row. Xiao Q wants to move a number $X$ to the cell $(R, C)$, so he performs the following steps: - When $X$ is not in column $C$, shift the row that contains $X$. - When $X$ is not in row $R$, shift the column that contains $X$. Below is an example of how to move the number $6$ to the cell $(3, 4)$.  Xiao Q wants to move $K$ numbers. What is the minimum number of operations needed?

The first line contains two positive integers $N$ and $K$, representing the table size and the number of moves. In the next $K$ lines, each line contains: - Three integers $X, R, C$, as described above.

Output $K$ lines in total. For each query: - Output the minimum number of moves needed.

#### Constraints For $100\%$ of the testdata: $2 \le N \le 10^4$, $1 \le K \le 10^3$, $1 \le X \le N^2$, $1 \le R, C \le N$. #### Notes - The full score for this problem is $100$ points. - This problem is translated from [COCI2008-2009](https://hsin.hr/coci/archive/2008_2009/) [CRCI2008-2009](https://hsin.hr/coci/archive/2008_2009/regional_tasks.pdf) TABLICA, translator @[tearing](https://www.luogu.com.cn/user/219791)。 Translated by ChatGPT 5