Find an arrangement of the following functions f1, f2, , f10 so that f1=O(f2), f2 = O(f3), , f(9)=O(f10). Also indicate which functions grow at the same asymptotic rate.

lg(n!), ln(n), n, 2⁽²ⁿ⁾, 2⁽ⁿ⁺¹⁾, nlg(n), lg(n), n², 1, lg²(n)