CF5C.Longest Regular Bracket Sequence

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.

这又是一道关于合法括号序列的问题。

我们需要提醒您：若能在括号序列中插入「+」和「1」使其成为一个正确的数学表达式，则该括号序列被称为合法括号序列。例如，序列 «(())()»、«()» 和 «(()(()))» 是合法的，而 «)(»、«(()» 和 «(()))(» 则不是。

给定一个仅由 «(» 和 «)» 字符组成的字符串。您需要找出其中最长的合法括号子串，并同时求出这样的子串的个数。

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

输入文件的第一行包含一个非空字符串，该字符串仅由字符 ( 和 ) 组成。其长度不超过 $10^6$。

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".

输出最长的合法括号序列子串的长度，以及该长度的合法括号序列子串的个数。如果没有这样的子串，则仅输出一行 "0 1"。