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Ivo has an N×N table. The table has the integers 1 through N2inscribed 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, []) 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:

Image: dsadss

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


InputThe 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.

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

Input:
[c]4 1
6 3 4
Output:
3

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