You are in charge of a large scientific project studying an unusual function. To carry it out, you hired (10^{10^{100}}) students and numbered them with natural numbers from (1) to (10^{10^{100}}). The students form a hierarchy: Student (1) is the main one. For any (i \geq 2), the direct supervisor of student (i) is student (\left\lfloor \frac{i}{2} \right\rfloor). The direct subordinates of student (i) are students (2i) and (2i+1) (if these numbers do not exceed (10^{10^{100}})). Subordination is transitive: if (a) is subordinate to (b), and (b) is subordinate to (c), then (a) is subordinate to (c). There are (n) days left until the project is completed. Each day consists of two stages: Hiring. Each working student (i) hires all the non-working students who are directly subordinate to him: If student (2i) is not working and (2i \leq 10^{10^{100}}), he starts working. If student (2i + 1) is not working and (2i + 1 \leq 10^{10^{100}}), he starts working. Newly hired students cannot hire anyone on the same day. If student (2i) is not working and (2i \leq 10^{10^{100}}), he starts working. If student (2i + 1) is not working and (2i + 1 \leq 10^{10^{100}}), he starts working. Firing. You may choose any set of working students and directly fire each of them. If student (i) is directly fired, then all of his subordinates are automatically fired as well. Such firings are called indirect . Student (1) cannot be fired. Additional restriction: Each student may be fired (directly or indirectly) at most once. If a previously fired student is hired again, it is forbidden to perform a firing that would cause this student to be fired again. Below (showing only the first (15) students) are examples of how to choose students for direct firing on each day so that after (2) days exactly (5) students remain. The number at the top corresponds to the s