# Longest Regular Bracket Sequence

## 题目描述

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.

## 输入输出格式

### 输入格式

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

### 输出格式

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".

## 输入输出样例

### 输入样例 #1

``````)((())))(()())
``````

### 输出样例 #1

``````6 2
``````

### 输入样例 #2

``````))(
``````

### 输出样例 #2

``````0 1
``````