AT_arc226_c [ARC226C] Square Corner Packing

There is a grid with $ H $ rows and $ W $ columns. Let $ (i,j) $ denote the cell at the $ i $ -th row from the top and the $ j $ -th column from the left. Initially, all cells are white. You may perform the following operation any number of times. - Choose integers $ r,c,s $ satisfying all of the following conditions, and paint the cells $ (r,c),(r+s,c),(r,c+s),(r+s,c+s) $ black. - $ 1\le r

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case is given in the following format: > $ H $ $ W $

For each test case, let $ K $ be the maximum possible number of operations, and let $ r_i,c_i,s_i $ be the integers chosen in the $ i $ -th operation; output them in the following format: > $ K $ $ r_1 $ $ c_1 $ $ s_1 $ $ r_2 $ $ c_2 $ $ s_2 $ $ \vdots $ $ r_K $ $ c_K $ $ s_K $ If there are multiple sequences of operations that achieve the maximum, any of them will be accepted.

### Sample Explanation 1 For the first test case, performing the six output operations paints the following cells black. The digit $ i $ represents a cell painted black by the $ i $ -th operation, and `.` represents a cell that is never painted. ``` 135135 66.... 664242 135135 ..4242 ``` There are other outputs that will be accepted. ### Constraints - $ 1\le T\le 500 $ - $ 2\le H,W\le 500 $ - The sum of $ HW $ over all test cases is at most $ 250000 $ . - All input values are integers.