It is well known that Mark likes creating mathematical tasks very much. Recently he has invented the following one: for given \textbf{S} find all positive integers \textbf{А} and \textbf{В}, that \textbf{А} ≤ \textbf{В} and \textbf{А + (А + 1) + (А + 2) + … + (В - 1) + В = S}. \InputFile Input contains one integer \textbf{S} (\textbf{1} ≤ \textbf{S} ≤ \textbf{10^12}). \OutputFile First line at output should contain one integer \textbf{K} -- number of pairs that have been found. Each of following \textbf{K} lines should contain \textbf{2} integers, first not greater than second -- corresponding pair. Pairs should be printed sorted ascending by first number.