CHW$5\mathrm{.}1.$ So many options: Flying from O'Hare to LAX with at most one layover

Connections between airports can be modelled by a graph. The nodes represent airports, and the edges represent nonstop flight routes between the airports. Two nodes are connected by a edge if there is a nonstop flight between the two airports; for simplicity, we assume that if there is a nonstop flight from one airport to another, there is a returning nonstop flight so that the graph is undirected.

The matrix nonstop$\_$flights represents a network of $100$ U$.$S$.$ airports as described above. We ask you to determine the number of distinct routes to fly from O'Hare Airport $($ORD$)$ to Los Angeles International Airport $($LAX$)$ with at most one layover $($that is$,$ either nonstop or with exactly one layover$).$

Compute a $100100-$matrix A such that the entry in the $i-$th row and the $j-$th column of $A$ is the number of walks from node $j$ to node $i$ of length at most $2.$ Store this matrix as atmost$\_1\_$layover.

Assuming that ORD is airport # $63($the ${64}^{th}$ row$/$column of the adjacency matrix when one$-$indexing$)$ and LAX is airport # $84($the ${85}^{th}$ row$/$column of the adjacency matrix when one$-$indexing$).$ Compute the number of distict routes to fly from ORD to LAX with at most one layover. Save this as num$\_$options.

The setup code gives the following variables:

$\backslash$table$[[$Name$,$Type,Description$],[$nonstop$\_$flights,$\backslash$table$[[$numpy$],[$array$]],\backslash$table$[[$Network of nonstop flight connections, $100100$