TABLICA

문제

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: 

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:

[이미지 1]

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

입력

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. 

출력

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