Part $2.$ An Euler Brick is an a $$ b $$ c cuboid where the dimensions a$,$ b$,$ c are positive integers,

as are the diagonals of each face. The first, $(44,117,240),$ was discovered in $1719$ by Paul Halcke.

$($a$)$ Write a function IsItEuler$($triple$1,$triple$2)$ which accepts as input two tuples repre$-$ senting distinct Pythagorean triples and returns True if together they describe two faces of an Euler Brick, and False otherwise. For example the inputs $(44,117,125),(117,240,267)$ should return True, as should $(117,240,267),(117,44,125),$ etc..

$($b$)$ Write a function Bricks$($n$)$ to return a list of Euler bricks $($a$,$ b$,$ c$)$ where $0<$ a $<$ b $<$ c $<$ n$.$ Hint: Use your functions Pyth and IsItEuler.

$($c$)$ How many Euler bricks are there with all dimensions $<1000?$ How many of them are primitive? Write your answer as a comment, explaining what a $$primitive$$ Euler brick is$.$