Problem $1(5$ marks$)$ We have an array of size $n.$ Program A reads locations $1,4,9$dots, i$.$c$.,$ all squares up to $n.$ Program B reads locations $1,2,4,$dots, i$.$e$.,$ all powers of $2$ up to $n.$ A spends time $\sqrt[\phantom{2}]{i}$ at each location $i$ it visits and B spends time i when it reads location $i.$ Let $f_A(n)$ and $f_B(n)$ be the number of locations read by A and B respectively and let $g_A(n)$ and $g_B(n)$ be the time spent by A and B respectively. $(1)(1$ marks$)$ Is $f_A(n)$ in or $(f_B(n))?(2)(4$ marks$)$ Is $g_A(n)$ in or $(g_B(n))?$ Show your working.