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>.
s = input()
n = len(s)
c = [-1]*n
d = [-1]*n
stack = []
for i in range(0,n):
    if(s[i]=='('):
        stack.append(i)
    elif(s[i]==')'):
        if(len(stack)==0):
            c[i] = -1 
            d[i] = -1
        else:
            d[i] = stack.pop()
            c[i] = d[i]
            if(d[i]>1):
                if(s[d[i]-1]==')' and c[d[i]-1]>-1):
                    c[i] = c[d[i] - 1]
cnt = 0
maxlen = 0
for i in range(0,n):
    if(c[i]>-1):
        if((i-c[i]+1)>maxlen):
            maxlen = i-c[i]+1
            cnt = 1
        elif((i-c[i]+1)==maxlen):
            cnt+=1
if(maxlen==0):
    cnt=1
print(maxlen,cnt)