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>.
l=input()
lx=list(l)
l1=[]
leng=[]    #看硬币
ans=0
count=1
if "()"not in l:
    print("0 1")
else:
    for i in range(len(l)):
        if l[i]=="(":
            l1.append(i)
        else:
            if l1!=[]:
                lx[i]=1
                lx[l1[-1]]=1
                l1.pop()
    lx.append(0)
    for j in range(1,len(lx)):
        if lx[j-1]!=1 and lx[j]==1:
            n=1
        elif lx[j-1]==lx[j]==1:
            n+=1
        elif lx[j-1]==1 and lx[j]!=1:
            leng.append(n)
    ans=max(leng)
    count=leng.count(ans)
    print(str(ans)+" "+str(count))

