You are an expert competitive programmer. You will be given a problem statement and some example inputs. You need to code a python input generator that will create tricky inputs, incorporating a random number generator (no fixed seed) so that multiple test cases can be generated with the same code. 
NOTE:
1. Your generator does not receive any external input. Keep in mind that you do not need to fully solve the problem, just figure out which inputs would be harder. 
2. The generated test input must adhere to problem requirements while using the hardest parameters allowed by the constraints (randomness should create different hard solutions, not some easy and some hard, i.e., if there is an input that defines the number of... it should likely be quite high so as to not be easy, not necessarily the max, but high), to weed out and stress-test brute force solutions. 3. Please reason step by step, and put your final answer within ```python and ```. If you'd like, you may provide multiple types of tricky input generators, each in its ``python ...``` block.

Below is the Problem Statement:
{problem}