Currency arbitrage cycle

You are given an n x n matrix `rates` where `rates[i][j]` is the exchange rate from currency i to currency j (rates[i][i] = 1). An arbitrage opportunity exists if you can start with one unit of some currency, perform a sequence of conversions, and end up with strictly more than one unit of the same currency. Return true if any arbitrage cycle exists, false otherwise. Assume 2 <= n <= 60 and all rates are positive.