There are many countries on a map. Each of them has a unique ID, which is a positive integer. All of them want to expand their territories. A country can expand its territory if its neighboring land (up, down, left, and right) has not been occupied by any other countries. The expansion speeds are the same for all countries. (We may consider that all countries simultaneously perform one expansion move at a time.) If two or more countries want to occupy the same land, the country with the smaller ID can occupy the land. The expansion stops if no changes of the map can be made.
The input file begins with an integer T (1 < T < 1000), indicating the number of test cases. Each test case begins with three integers N, M, and K (0 < N < 300, 0 < M < 300, K
For each test case, output the final area (number of lands) of each county, ordered by the country’s ID (from small to large). Print a blank after each case.