Value of strings


I have a set of strings $ s_1,. . . , s_n$ from small letters of total length S =$ \sum\limits_{i = 1}^n |s_i|$ . Each line is associated with the value $ a_1,. . . , a_n$ . The $ value$ of a string $ t$ from small letters is called $ \sum\limits_{i = 1}^n cnt (s_i, t) ยท ai$ , where $ cnt (s_i, t)$ is the number of occurrences of the string si in the string $ t$ (occurrences can overlap). Using the number l, find the maximum possible cost of a string $ t$ of length $ l$ . Asymptotics: $ O (S^3\log l).$