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. \textbf{N} professors discussed the curriculum and decided that there would be exactly N2 labs, the first professor would hold labs with numbers \textbf{1}, \textbf{N+1}, \textbf{2N+1}, …, \textbf{N^2−N+1}, the second one --- labs with numbers \textbf{2}, \textbf{N+2}, \textbf{2N+2}, …, \textbf{N^2−N+2}, etc. \textbf{N}-th professor would hold labs with numbers \textbf{N}, \textbf{2N}, \textbf{3N}, …, \textbf{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 \textbf{K} of these students were admitted to the exam. Find the minimal \textbf{N} which makes that possible. \InputFile An integer \textbf{K} (\textbf{1} ≤ \textbf{K} ≤ \textbf{2·10^9}). \OutputFile Output the minimal possible \textbf{N} which satisfies the problem statement. If there is no \textbf{N} for which exactly \textbf{K} students would be admitted to the exam, output \textbf{0}.