Inspired by the 15-puzzle, Cuber QQ invents a new puzzle game, named confusing puzzle, as it always makes players confused.

The puzzle is a parallelogram, which contains vertices. We'll consider the parallelogram rows numbered from bottom to top through , and the columns numbered from left to right through . Then we'll denote the position of vertices in row and column as and its initial id is .

The following figure shows the initial parallelogram:



Each time, the player can operate the parallelogram in the following two ways:

• , select an \textbf{upright} equilateral triangle (positions of vertices on it is and ) and rotate it clockwise.
• , select a diamond (positions of vertices on it is and ) and rotate it clockwise.

Cuber QQ will give you a scrambled puzzle, and ask you to restore it within operations.

输入描述:

First line contains two integers  ().

The following  lines, each line contains  integres, denotes the vertices id in the scrambled puzzle.

输出描述:

In the first line, you should output an integer , which is the number of operations.

The following  lines, each line contains three integers .

, the operation is selecting an upright equilateral triangle (positions of vertices on it is  and ) and rotate it clockwise.
, the operation is selectng a diamond (positions of vertices on it is  and ) and rotate it clockwise.

It is guaranteed that the scrambled puzzle has at least one solution.

If there are multiple answers, print any.

2 3
4 1 2
5 6 3

2
1 1 1
2 1 2