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Ural SU contest. Petrozavodsk training camp. Summer 2008

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D. Admission to Exam

Time limit: 2.0 second
Memory limit: 64 MB
At the end of the previous semester the students of the Department of Mathematics and Mechanics of the Yekaterinozavodsk State University had to take an exam in network technologies. N professors discussed the curriculum and decided that there would be exactly N2 labs, the first professor would hold labs with numbers 1, N + 1, 2N + 1, …, N2N + 1, the second one — labs with numbers 2, N + 2, 2N + 2, …, N2N + 2, etc. N-th professor would hold labs with numbers N, 2N, 3N, …, N2. The professors remembered that during the last years lazy students didn't attend labs and as a result got bad marks at the exam. So they decided that a student would be admitted to the exam only if he would attend at least one lab of each professor.
N roommates didn't know the number of labs and professors in this semester. These students had different diligence: the first student attended all labs, the second one — only labs which numbers were a multiple of two, the third one — only labs which numbers were a multiple of three, etc… At the end of the semester it turned out that only K of these students were admitted to the exam. Find the minimal N which makes that possible.


An integer K (1 ≤ K ≤ 2·109).


Output the minimal possible N which satisfies the problem statement. If there is no N for which exactly K students would be admitted to the exam, output 0.


Problem Author: Igor Chevdar
Problem Source: Ural SU Contest. Petrozavodsk Summer Session, August 2008
To submit the solution for this problem go to the Problem set: 1673. Admission to Exam