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>.
x = input()
ex=[-1]*len(x);m=0;ex[0]=-50
f=[0]*len(x);ans1=-1;ans2=flag=1;s=[]
for index,i in enumerate(x):
    if i=='(':
        s.append(index)     
    else:
        if len(s) > 0 :
            p = s.pop()
            ex[index] = p
            if  p > 0  and   ex[p-1] > -1 :
                ex[index] = ex[p-1]  
            f[index-ex[index]]+=1
            ans1 = max(ans1,index-ex[index])                  
print(ans1+1,f[ans1])            







