After creating problem Q, we thought it would be entertaining to put you into problemsetters’ shoes for a moment. In this task you will find out a way to create test data for problem Q.
You are given integers R, C, and A such that A divides RC.
Your task is to take a R × C rectangle and divide it into polygons. Each of the polygons must consist of exactly A unit squares. All polygons must be distinct, except for two polygons that must be identical.
Note: We call two polygons identical iff one of them can be obtained from the other by a combination of translations and rotations. Note that it is not allowed to use axis symmetry – i.e., if a polygon is just a mirror image of another one, they are considered distinct for the purpose of this problem.
The input contains a single line with the three integers R, C, and A.
After you divide the rectangle into N = RC∕A polygons, number them from 1 to N (in any order you wish).
Output R rows with C integers in each of them. The c-th integer in the r-th row must be the number of the polygon that contains the cell (r,c).
Any valid output will be accepted.
5 6 5
1 1 2 2 2 3
1 4 4 2 2 3
1 1 4 3 3 3
6 6 4 4 5 5
6 6 6 5 5 5