Valid Molecule Placement in Grid

You are given an n by m grid. Your task is to count the number of valid ways to place exactly k molecules 'A' into the grid such that no two 'A' molecules share the same row or column.

This is equivalent to selecting k rows from n available rows and k columns from m available columns, then arranging the k molecules in these positions in a one-to-one manner. Mathematically, the answer can be expressed as:

$$ \binom{n}{k} \times \binom{m}{k} \times k! $$

If k is greater than either n or m, then it is impossible to place the molecules and the answer is 0.

inputFormat

The input consists of a single line containing three space-separated integers: n m k, where n and m are the dimensions of the grid and k is the number of molecules to place.

outputFormat

Output a single integer which is the number of valid configurations.

2 2 2

2