Detect Currency Arbitrage with a Cycle Fee

You are given n currencies and an n × n matrix of positive floating-point exchange rates: rates[i][j] is the amount of currency j received for one unit of currency i. A transaction sequence starts with one currency and eventually returns to that same currency. After the complete closed sequence, a fee equal to 0.01% of the starting amount is charged; equivalently, the final amount is multiplied by 0.9999. Determine whether an arbitrage opportunity exists: whether there is a closed exchange sequence whose amount after the fee is strictly greater than the starting amount. Input n rates[0][0] rates[0][1] ... rates[0][n-1] ... rates[n-1][0] ... rates[n-1][n-1] All exchange rates are positive. Output Print: True if arbitrage exists; otherwise print: False Example Input 2 1 0.5 2.0 1 Output False This formulation follows the literal wording that the fee is charged once after the entire closed sequence. If a cycle has a product greater than 1, it may be repeated enough times to overcome that fixed fee. Example Input 2 1 0.5 2.0 1 Output False