You are given a positive integer \textbf{x}. Find the smallest positive integer \textbf{n} for which there exists \textbf{k} such that \textbf{C}(\textbf{n}, \textbf{k}) = \textbf{x}. \InputFile The first line contains the positive integer\textbf{ x} ≤ \textbf{10^100}. \OutputFile Print the required integer \textbf{n} without leading zeros.