Extra credit: 6. [20 points] Consider the generic algorithm SolveP given below, which solves a problem P by finding the output (solution) O that corresponds to an input I. ALGORITHM SolveP(input I, output\& O) / I Input: I (of size n ) for problem P / Output: O, the solution to problem P if size (I) ==1 Compute solution o to basic problem directly else partition I into 5 inputs I1,I2,,I5, of size n/3 each for j 1 to 5 do SolveP (Ij, Oj) Combine O1,O2,,O5 to get solution o for P with input I Assume that the algorithm performs g(n) operations for partitioning and combining and no basic operations for an instance of size 1. Write and solve the recurrence equation T(n) for the number of basic operations needed to solve P when the input size is n and g(n)=n