SILK-ROAD 2022 Problem 4

In a language $,$ an alphabet with $25$ letters is used $;$ words are exactly all sequences of $($ not necessarily different $)$ letters of length $17.$ Two ends of a paper strip are glued so that the strip forms a ring $;$ the strip bears a sequence of $5^{18}$ letters $.$ Say that a word is singular if one can cut a piece bearing exactly that word from the strip $,$ but one cannot cut out two such non-overlapping pieces $.$ It is known that one can cut out $5^{16}$ non-overlapping pieces each containing the same word $.$ Determine the largest possible number of singular words $.$ (Bogdanov I.)