Longest Regular Bracket Sequence


给出一个括号序列,求出最长合法子串和它的数量。 合法的定义:这个序列中左右括号匹配


This 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.



The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed $ 10^{6} $ .


Print 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".


输入样例 #1


输出样例 #1

6 2

输入样例 #2


输出样例 #2

0 1