For the first two problems, assume that the input size is n$=1000$ and each algorithm runs $10$ seconds. Given this, what is the runtime of the following two algorithms for an input size of one million? You will want to make use of the fact that the original input size is squared.

$(3\mathrm{.}1)$ An algorithm with a bound of Theta$($lgn$).(5$ points for both result and explanation of how you arrived at the result$)$

$(3\mathrm{.}2)$ An algorithm with a bound of Theta$($nlgn$).(5$ points for both result and explanation of how you arrived at the result$)$