$)$ Where indicated below, complete the function, lagrange$(),$ which takes two input vectors of data points x and y$,$ of any length n $($either both column or row vectors$),$ along with input scalar, a$,$ and computes output, p$,$ which is $,$ the Lagrange interolating polynomial, $,$ evaluated at a:

$($In the formula, $,,$ and refer to elements in vectors x and y$.)$

Use one outer for$-$loop with one inner for$-$loop with an if$-$statement $($or two successive inner for$-$loops without an if statement$).$ You may need to initialize a running sum before the outer loop, and initialize a running product just before the inner loop.