C. Longest Regular Bracket Sequencetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis is yet another problem dealing with regular bracket sequences.We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not. You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.InputThe first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.OutputPrint the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".ExamplesInput)((())))(()())Output6 2Input))(Output0 1
Input)((())))(()())
Output6 2
['constructive algorithms', 'data structures', 'dp', 'greedy', 'sortings', 'strings', '*1900']