Admission to Exam
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, …, N^2−N+1, the second one — labs with numbers 2, N+2, 2N+2, …, N^2−N+2, etc. N-th professor would hold labs with numbers N, 2N, 3N, …, N^2. 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.
Input
An integer K (1 ≤ K ≤ 2·10^9).
Output
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.