You have a standard, $30-$year mortgage with fixed monthly payments. Making only the required monthly payment, you will pay $$150,000$ in principal and $$123,610\mathrm{.}07$ in interest over the life of the mortgage. During the early years, most of the payment will go toward interest, and during the later years, most of the payment will go toward principal. In fact, the $N^{th}$ payment is the first payment where over $50\%$ of the payment is applied to principal instead of interest.

What is $N?$

Enter only the integer, without punctuation. For example, if your answer is "the $112$th payment", enter $"112".$