PEG Judge - COCI08 Regional

COCI 2008/2009, Croatian Regional

Task TABLICA

Ivo has an N×N table. The table has the integers 1 through N² inscribed in row-major order. The following operations can be done on the table:

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

The first line contains two integers N (2 ≤ N ≤ 10 000) and K (1 ≤ K ≤ 1000), the table dimension and the number of moves.
Each of the following K lines contains three integers X (1 ≤ X ≤ N2), R and C (1 ≤ R, C ≤ N), the description of one move Ivo wants to make. Ivo does the moves in the order in which they are given.