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#F1477. Longest Regular Bracket Sequence

    ID: 1483 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 6 上传者: 标签>构造数据结构动态规划贪心排序字符串算法思想编程与模拟提高难度共享题库Codeforces英文题面题目来源题面语言

Longest Regular Bracket Sequence

题目描述

C. Longest Regular Bracket Sequence
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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

Output

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".

Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 985 题。保留原作者与原赛事署名。