2590 - Longest Regular Bracket Sequence

2590.Longest Regular Bracket Sequence

Time Limit: 1s Memory Limit: 256MB

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 Format(From the terminal/stdin)

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

Output Format(To the terminal/stdout)

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".

Sample Input 1

Copy

)((())))(()())
              \n

Sample Output 1

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6 2
 · \n

Sample Input 2

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))(
   \n

Sample Output 2

Copy

0 1
 · \n

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