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 10<sup class="upper-index">6</sup>.
count=open=m=0
for i in input():
    if i == '(':
            count+=(open==0)    
            open+=1
            if open > m:
                  m = open   
    else:
        if open > 0:
            open-=1         
print(['%d %d'%(m*2,count),'0 1'][open != 0])            
  
		  	 				   				 				 					  	