Analyze the following recurrence relation by completing the tasks below

$T(n)=\{\begin{array}{cc}1,& n=1\\ 7T(\frac{n}{2})+n^2,& n>1\end{array}$

$(1)$ Draw the recursion tree for the recurrence. In your sketch, include:

The number of levels of the tree

The cost of each node, detailing at least the top three levels from top to bottom

$<mn>1</mn><mn>5</mn><mi>p</mi>$

$(2)$ Find the total cost with asymptotic $O-$notation.