(20 points) Sort the following 25 functions from asymptotically smallest to asymptotically largest, indicating ties if there are any. You do not need to turn in proofs (in fact, please don't turn in proofs) 2.1 lg'(n/8) glg lg n (lg" n)*n cos(n) 2 Agn g n 2 n3/(2 lg n) nlglg n 12+11g lg nj (lg n)lgn n 154 nl/lg lg n n1/125 To simplify notation put all the functions in a single column, where f(n) being above g(n) in the column means f(n) = o(g(n)). If f(n) = (g(n), then write f(n) and g(n) separated by a comma on the same line. For example, the functions n2, n, )nshould be written Hint: When considering two functions f(n) and g(n) it is sometimes useful to consider the functions log f(n) and logg(n), since log f(n) = o(logg(n)) implies f(n) = o(g(n)) (but be careful, the implication does not work in the other direction, and in particular log f(n)-O(log g(n)) does NOT imply f(n) - O(g(n)))