You are given two boxes: one box filled with mason jars of different sizes, and another box filled with corresponding screw top lids. You can test whether a given jar and lid are a match, from which1 you learn whether the jar is too large, too small, or an exact match for the lid. The differences insize between pairs of jars or lids are too small to see by eye, so you cannot compare the sizes oftwo jars or two lids directly. You are to match each jar to each lid, with the assumption that notwo jars or two lids are of the same size, and that every jar in one box has a corresponding lid inthe other box. Give a randomized O(nlogn) expected time algorithm for this problem.

Write a function balancechemical to balance chemical reactions by solving a linear set of equations. the inputs arguments are: reagents: symbols of reagents in string row array products: symbols of products in string row array elements: elements in the reaction in string row array elcmpreag: elemental composition of reactants in two dimensional numeric array elcmpprdcts: elemental composition of prducts in two dimensional numeric array hint: the first part of the problem is setting up the set of linear equations that should be solve. the second part of the problem is to find the integers from the solution. one way to do this is to mulitiply the rational basis for the nullspace by increasing larger integers until both the left-and right-side integers exist. for example, for the reaction that involves reacting with to produce and : reagents=["ch4", "o2"]; products =["co2", "h2o"]; elements =["c","h", "o"] elcmpreag=[1,4,0;