#P5C. Longest Regular Bracket Sequence

    ID: 1863 Type: RemoteJudge 2000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>constructive algorithmsdata structuresdpgreedysortingsstrings*1900

Longest Regular Bracket Sequence

No submission language available for this problem.

Description

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 106.

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".

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".

Samples

)((())))(()())

6 2

))(

0 1