COCI '08 Regional #4 Tablica

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Points: 15
Time limit: 1.0s
Memory limit: 32M

Problem type

Ivo has an N\times N table. The table has the integers 1 through N^2 inscribed in row-major order. The following operations can be done on the table:

  1. Rotate a row – all cells in a single row are rotated right, so that the number in the last column moves to the first.
  2. Rotate a column – all cells in a single column are rotated down, so that the number in the last row moves to the first.

Ivo occasionally feels the urge to move a number X to cell (R, C) and proceeds as follows:

  • While X is not in column C, rotate the row it is in.
  • While X is not in row R, rotate the column it is in.

Here is an example of how to move number 6 to cell (3, 4), start from the initial configuration:

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
1 2 3 4
8 5 6 7
9 10 11 12
13 14 15 16
1 2 3 4
7 8 5 6
9 10 11 12
13 14 15 16
1 2 3 16
7 8 5 4
9 10 11 6
13 14 15 12

Ivo wants to move K numbers one after another. Write a program that calculates the number of rotations needed.

Input Specification

The first line contains two integers N (2 \le N \le 10\,000) and K (1 \le K \le 1000), the table dimension and the number of moves.

Each of the following K lines contains three integers X (1 \le X \le N^2), R and C (1 \le R, C \le N), the description of one move Ivo wants to make. Ivo does the moves in the order in which they are given.

Output Specification

Output K lines; for each move, output the number of rotations needed.

Sample Input 1

4 1
6 3 4

Sample Output 1

3

Sample Input 2

4 2
6 3 4
6 2 2

Sample Output 2

3
5

Sample Input 3

5 3
1 2 2
2 2 2
12 5 5

Sample Output 3

2
5
3

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