Canonicalized Input Description:

An integer m (1 ≤ m ≤ 16), representing some quantity or size.
An integer n (1 ≤ n ≤ 16), representing some quantity or size.
A list of m lists, each containing n real numbers representing probabilities, given up to three decimal places.

### Example Input:

```
2 3
0.900 0.500 0.100
0.500 0.500 0.500
```

### Function Signature:
Write a function f(m, n, probabilities) that takes in the input.
```python
def f(m: int, n: int, probabilities: List[List[float]]):
    '''
    m: an integer
    n: an integer
    probabilities: a list of lists of real numbers
    '''
```