Create a Python$($or Pseudo Python$)$ function that solves how many non$-$negative integer solutions there are in a linear equation in the form: x$1+$ x$2+$ x$3+$ x$4+...+$ x$=$ S Where each xi variable may have some restriction on its value. The less than or equal to constraintsvare stored in a list lower constraints $(0$ is stored if there is no constraint$).$ The upper bound

constraints are stored in the list upper constraints as PAIRS: $($i$,$ k$)$ indicating that xi $$ k$,$ andvlen$($upper constraints$)3.[$Hint: Be careful of double constraints $($eg$.3$x$28)].$ Write a program that determines the number of non$-$negative integer solutions. Your program should

accept as input the variables LENGTH $=$ l and VALUE $=$ S $($these should be defined constants at the top

of your code$).$

Your code should do the following:

$$ Check the number of upper bound constraints, then appropriately compute the PIE for that number

of constraints $($hint: you should have conditionals where you then have the formula for the $2-$set

and $3-$set PIE$)$

$$ If one of your computations of setting aside bars yields a negative number of stars to place, you

should ensure your code computes this to be $0.$

$$ The lower constraints should be applied first and continue throughout your code.

$$ Your code must be WELL COMMENTED $$ your algorithmic structure should be very clear. If

needed, it is recommended you also include a paragraph describing your code in your assignment $$

essentially a README

$$ Your code must be less than $60$ lines.